tt(abstractness_v11_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_closure2 B A))  =>  ((v11_closure2 B A) =>  (B = (g1_closure2 A (u3_msualg_1 A B) (u1_closure2 A B))) ) ) ) ).
tt(abstractness_v12_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((v12_pcs_0 A) =>  (A = (g2_pcs_0 (u1_struct_0 A) (u1_orders_2 A) (u1_pcs_0 A))) ) ) ) ).
tt(abstractness_v15_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v15_algstr_0 A) =>  (A = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ).
tt(abstractness_v1_algstr_3,ax, (! [A:$i] :  ((l1_algstr_3 A) =>  ((v1_algstr_3 A) =>  (A = (g1_algstr_3 (u1_struct_0 A) (u2_struct_0 A) (u3_struct_0 A) (u1_algstr_3 A))) ) ) ) ).
tt(abstractness_v1_analmetr,ax, (! [A:$i] :  ((l1_analmetr A) =>  ((v1_analmetr A) =>  (A = (g1_analmetr (u1_struct_0 A) (u1_analoaf A) (u1_analmetr A))) ) ) ) ).
tt(abstractness_v1_analoaf,ax, (! [A:$i] :  ((l1_analoaf A) =>  ((v1_analoaf A) =>  (A = (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) ) ) ) ).
tt(abstractness_v1_bcialg_4,ax, (! [A:$i] :  ((l1_bcialg_4 A) =>  ((v1_bcialg_4 A) =>  (A = (g1_bcialg_4 (u1_struct_0 A) (u1_bcialg_4 A) (u1_bcialg_1 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v1_bhsp_1,ax, (! [A:$i] :  ((l1_bhsp_1 A) =>  ((v1_bhsp_1 A) =>  (A = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ).
tt(abstractness_v1_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) =>  ((v1_cat_1 A) =>  (A = (g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A))) ) ) ) ).
tt(abstractness_v1_cfuncdom,ax, (! [A:$i] :  ((l1_cfuncdom A) =>  ((v1_cfuncdom A) =>  (A = (g1_cfuncdom (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_clvect_1 A) (u3_struct_0 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v1_cgames_1,ax, (! [A:$i] :  ((l1_cgames_1 A) =>  ((v1_cgames_1 A) =>  (A = (g1_cgames_1 (u1_cgames_1 A) (u2_cgames_1 A))) ) ) ) ).
tt(abstractness_v1_clopban2,ax, (! [A:$i] :  ((l1_clopban2 A) =>  ((v1_clopban2 A) =>  (A = (g1_clopban2 (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_clvect_1 A) (u3_struct_0 A) (u2_struct_0 A) (u1_normsp_0 A))) ) ) ) ).
tt(abstractness_v1_clvect_1,ax, (! [A:$i] :  ((l1_clvect_1 A) =>  ((v1_clvect_1 A) =>  (A = (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) ) ) ) ).
tt(abstractness_v1_collsp,ax, (! [A:$i] :  ((l1_collsp A) =>  ((v1_collsp A) =>  (A = (g1_collsp (u1_struct_0 A) (u1_collsp A))) ) ) ) ).
tt(abstractness_v1_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((v1_compos_1 A) =>  (A = (g1_compos_1 (u1_compos_1 A))) ) ) ) ).
tt(abstractness_v1_csspace,ax, (! [A:$i] :  ((l1_csspace A) =>  ((v1_csspace A) =>  (A = (g1_csspace (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A) (u1_csspace A))) ) ) ) ).
tt(abstractness_v1_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) =>  ((v1_e_siec A) =>  (A = (g1_e_siec (u1_struct_0 A) (u1_e_siec A) (u2_e_siec A))) ) ) ) ).
tt(abstractness_v1_extpro_1,ax, (! [A:$i,B:$i] :  ((l1_extpro_1 B A) =>  ((v1_extpro_1 B A) =>  (B = (g1_extpro_1 A (u1_struct_0 B) (u2_struct_0 B) (u1_compos_1 B) (u1_memstr_0 A B) (u2_memstr_0 A B) (u1_extpro_1 A B))) ) ) ) ).
tt(abstractness_v1_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((v1_fomodel1 A) =>  (A = (g1_fomodel1 (u1_struct_0 A) (u2_struct_0 A) (u3_struct_0 A) (u1_fomodel1 A))) ) ) ) ).
tt(abstractness_v1_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) & (l1_fsm_3 C A B)) )  =>  ((v1_fsm_3 C A B) =>  (C = (g1_fsm_3 A B (u1_struct_0 C) (u1_rewrite3 B C) (u1_fsm_3 A B C))) ) ) ) ).
tt(abstractness_v1_funcsdom,ax, (! [A:$i] :  ((l1_funcsdom A) =>  ((v1_funcsdom A) =>  (A = (g1_funcsdom (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u3_struct_0 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v1_geomtrap,ax, (! [A:$i] :  ((l1_geomtrap A) =>  ((v1_geomtrap A) =>  (A = (g1_geomtrap (u1_struct_0 A) (u1_midsp_1 A) (u1_analoaf A))) ) ) ) ).
tt(abstractness_v1_graph_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ((v1_graph_1 A) =>  (A = (g1_graph_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A))) ) ) ) ).
tt(abstractness_v1_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((v1_grcat_1 A) =>  (A = (g1_grcat_1 (u1_grcat_1 A) (u2_grcat_1 A) (u3_grcat_1 A))) ) ) ) ).
tt(abstractness_v1_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v1_incsp_1 A) =>  (A = (g1_incsp_1 (u1_incsp_1 A) (u2_incsp_1 A) (u3_incsp_1 A))) ) ) ) ).
tt(abstractness_v1_lang1,ax, (! [A:$i] :  ((l1_lang1 A) =>  ((v1_lang1 A) =>  (A = (g1_lang1 (u1_struct_0 A) (u1_lang1 A))) ) ) ) ).
tt(abstractness_v1_lattices,ax, (! [A:$i] :  ((l1_lattices A) =>  ((v1_lattices A) =>  (A = (g1_lattices (u1_struct_0 A) (u1_lattices A))) ) ) ) ).
tt(abstractness_v1_lopban_2,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  ((v1_lopban_2 A) =>  (A = (g1_lopban_2 (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u3_struct_0 A) (u2_struct_0 A) (u1_normsp_0 A))) ) ) ) ).
tt(abstractness_v1_memstr_0,ax, (! [A:$i,B:$i] :  ((l1_memstr_0 B A) =>  ((v1_memstr_0 B A) =>  (B = (g1_memstr_0 A (u1_struct_0 B) (u2_struct_0 B) (u1_memstr_0 A B) (u2_memstr_0 A B))) ) ) ) ).
tt(abstractness_v1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v1_metric_1 A) =>  (A = (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A))) ) ) ) ).
tt(abstractness_v1_midsp_1,ax, (! [A:$i] :  ((l1_midsp_1 A) =>  ((v1_midsp_1 A) =>  (A = (g1_midsp_1 (u1_struct_0 A) (u1_midsp_1 A))) ) ) ) ).
tt(abstractness_v1_midsp_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (l1_midsp_3 B A))  =>  ((v1_midsp_3 B A) =>  (B = (g1_midsp_3 A (u1_struct_0 B) (u1_midsp_1 B) (u1_midsp_3 A B))) ) ) ) ).
tt(abstractness_v1_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (l1_modelc_3 B A))  =>  ((v1_modelc_3 B A) =>  (B = (g1_modelc_3 A (u1_modelc_3 A B) (u2_modelc_3 A B) (u3_modelc_3 A B))) ) ) ) ).
tt(abstractness_v1_msualg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_msualg_1 A) =>  (A = (g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A))) ) ) ) ).
tt(abstractness_v1_normsp_1,ax, (! [A:$i] :  ((l1_normsp_1 A) =>  ((v1_normsp_1 A) =>  (A = (g1_normsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_normsp_0 A))) ) ) ) ).
tt(abstractness_v1_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 A) =>  (A = (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) ) ) ) ).
tt(abstractness_v1_parsp_1,ax, (! [A:$i] :  ((l1_parsp_1 A) =>  ((v1_parsp_1 A) =>  (A = (g1_parsp_1 (u1_struct_0 A) (u1_parsp_1 A))) ) ) ) ).
tt(abstractness_v1_petri,ax, (! [A:$i] :  ((l1_petri A) =>  ((v1_petri A) =>  (A = (g1_petri (u1_struct_0 A) (u4_struct_0 A) (u1_petri A) (u2_petri A))) ) ) ) ).
tt(abstractness_v1_polyalg1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_polyalg1 B A))  =>  ((v1_polyalg1 B A) =>  (B = (g1_polyalg1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_algstr_0 B) (u2_struct_0 B) (u3_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ).
tt(abstractness_v1_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_pre_topc A) =>  (A = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) ) ) ) ).
tt(abstractness_v1_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  ((v1_qmax_1 A) =>  (A = (g1_qmax_1 (u1_qmax_1 A) (u2_qmax_1 A) (u3_qmax_1 A))) ) ) ) ).
tt(abstractness_v1_rewrite3,ax, (! [A:$i,B:$i] :  ((l1_rewrite3 B A) =>  ((v1_rewrite3 B A) =>  (B = (g1_rewrite3 A (u1_struct_0 B) (u1_rewrite3 A B))) ) ) ) ).
tt(abstractness_v1_rlvect_1,ax, (! [A:$i] :  ((l1_rlvect_1 A) =>  ((v1_rlvect_1 A) =>  (A = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ).
tt(abstractness_v1_sgraph1,ax, (! [A:$i] :  ((l1_sgraph1 A) =>  ((v1_sgraph1 A) =>  (A = (g1_sgraph1 (u1_struct_0 A) (u1_sgraph1 A))) ) ) ) ).
tt(abstractness_v1_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) =>  ((v1_stacks_1 A) =>  (A = (g1_stacks_1 (u1_struct_0 A) (u4_struct_0 A) (u1_stacks_1 A) (u2_stacks_1 A) (u3_stacks_1 A) (u4_stacks_1 A))) ) ) ) ).
tt(abstractness_v1_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_struct_0 A) =>  (A = (g1_struct_0 (u1_struct_0 A))) ) ) ) ).
tt(abstractness_v1_symsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (l1_symsp_1 B A))  =>  ((v1_symsp_1 B A) =>  (B = (g1_symsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B) (u1_orders_2 B))) ) ) ) ).
tt(abstractness_v1_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  ((v1_turing_1 A) =>  (A = (g1_turing_1 (u1_turing_1 A) (u2_turing_1 A) (u3_turing_1 A) (u4_turing_1 A) (u5_turing_1 A))) ) ) ) ).
tt(abstractness_v1_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ((v1_unialg_1 A) =>  (A = (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) ) ) ) ).
tt(abstractness_v1_waybel_9,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ((v1_waybel_9 A) =>  (A = (g1_waybel_9 (u1_struct_0 A) (u1_orders_2 A) (u1_pre_topc A))) ) ) ) ).
tt(abstractness_v1_zmodul01,ax, (! [A:$i] :  ((l1_zmodul01 A) =>  ((v1_zmodul01 A) =>  (A = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ) ).
tt(abstractness_v22_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ((v22_algstr_0 A) =>  (A = (g4_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (u3_struct_0 A))) ) ) ) ).
tt(abstractness_v29_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((v29_algstr_0 A) =>  (A = (g5_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (u2_struct_0 A) (u3_struct_0 A))) ) ) ) ).
tt(abstractness_v2_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  ((v2_armstrng A) =>  (A = (g1_armstrng (u1_armstrng A) (u2_armstrng A) (u3_armstrng A))) ) ) ) ).
tt(abstractness_v2_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ((v2_bcialg_1 A) =>  (A = (g2_bcialg_1 (u1_struct_0 A) (u1_bcialg_1 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v2_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) =>  ((v2_cat_4 A) =>  (A = (g1_cat_4 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (u1_cat_4 A) (u2_cat_4 A) (u3_cat_4 A) (u4_cat_4 A))) ) ) ) ).
tt(abstractness_v2_conlat_1,ax, (! [A:$i] :  ((l1_conlat_1 A) =>  ((v2_conlat_1 A) =>  (A = (g1_conlat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_conlat_1 A))) ) ) ) ).
tt(abstractness_v2_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (l2_fsm_1 C A B))  =>  ((v2_fsm_1 C A B) =>  (C = (g2_fsm_1 A B (u1_struct_0 C) (u1_fsm_1 B C) (u3_fsm_1 A B C) (u2_fsm_1 B C))) ) ) ) ).
tt(abstractness_v2_group_9,ax, (! [A:$i,B:$i] :  ((l1_group_9 B A) =>  ((v2_group_9 B A) =>  (B = (g1_group_9 A (u1_struct_0 B) (u2_algstr_0 B) (u1_group_9 A B))) ) ) ) ).
tt(abstractness_v2_lang1,ax, (! [A:$i] :  ((l2_lang1 A) =>  ((v2_lang1 A) =>  (A = (g2_lang1 (u1_struct_0 A) (u2_lang1 A) (u1_lang1 A))) ) ) ) ).
tt(abstractness_v2_lattices,ax, (! [A:$i] :  ((l2_lattices A) =>  ((v2_lattices A) =>  (A = (g2_lattices (u1_struct_0 A) (u2_lattices A))) ) ) ) ).
tt(abstractness_v2_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ((v2_mod_2 B A) =>  (B = (g1_mod_2 A (u1_mod_2 A B) (u2_mod_2 A B) (u3_mod_2 A B))) ) ) ) ).
tt(abstractness_v2_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v2_pcs_0 A) =>  (A = (g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A))) ) ) ) ).
tt(abstractness_v2_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((v2_ringcat1 A) =>  (A = (g1_ringcat1 (u1_ringcat1 A) (u2_ringcat1 A) (u3_ringcat1 A))) ) ) ) ).
tt(abstractness_v2_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ((v2_robbins1 A) =>  (A = (g2_robbins1 (u1_struct_0 A) (u2_lattices A) (u1_robbins1 A))) ) ) ) ).
tt(abstractness_v2_vectsp_2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_vectsp_2 B A))  =>  ((v2_vectsp_2 B A) =>  (B = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B))) ) ) ) ).
tt(abstractness_v36_algstr_0,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ((v36_algstr_0 A) =>  (A = (g6_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_algstr_0 A) (u3_struct_0 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v3_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  ((v3_abcmiz_0 A) =>  (A = (g1_abcmiz_0 (u1_abcmiz_0 A) (u2_abcmiz_0 A))) ) ) ) ).
tt(abstractness_v3_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (l3_fsm_1 C A B))  =>  ((v3_fsm_1 C A B) =>  (C = (g3_fsm_1 A B (u1_struct_0 C) (u1_fsm_1 B C) (u4_fsm_1 A B C) (u2_fsm_1 B C))) ) ) ) ).
tt(abstractness_v3_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) & (l2_fsm_3 C A B)) )  =>  ((v3_fsm_3 C A B) =>  (C = (g2_fsm_3 A B (u1_struct_0 C) (u1_rewrite3 B C) (u1_fsm_3 A B C) (u2_fsm_3 A B C))) ) ) ) ).
tt(abstractness_v3_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ((v3_lattices A) =>  (A = (g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A))) ) ) ) ).
tt(abstractness_v3_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  & (l3_msualg_1 B A))  =>  ((v3_msualg_1 B A) =>  (B = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ).
tt(abstractness_v3_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ((v3_osalg_1 A) =>  (A = (g3_osalg_1 (u1_struct_0 A) (u1_orders_2 A) (u4_struct_0 A) (u1_osalg_1 A) (u1_msualg_1 A) (u2_msualg_1 A))) ) ) ) ).
tt(abstractness_v3_qmax_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ((v3_qmax_1 A) =>  (A = (g2_qmax_1 (u1_struct_0 A) (u1_orders_2 A) (u1_robbins1 A))) ) ) ) ).
tt(abstractness_v3_vectsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) & (l2_vectsp_2 C A B)) )  =>  ((v3_vectsp_2 C A B) =>  (C = (g2_vectsp_2 A B (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C) (u1_vectsp_1 B C) (u1_vectsp_2 B C))) ) ) ) ).
tt(abstractness_v4_conlat_1,ax, (! [A:$i,B:$i] :  ( ((l5_struct_0 A) & (l2_conlat_1 B A))  =>  ((v4_conlat_1 B A) =>  (B = (g2_conlat_1 A (u2_conlat_1 A B) (u3_conlat_1 A B))) ) ) ) ).
tt(abstractness_v4_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ((v4_robbins1 A) =>  (A = (g4_robbins1 (u1_struct_0 A) (u2_lattices A) (u1_lattices A) (u1_robbins1 A))) ) ) ) ).
tt(abstractness_v4_vectmetr,ax, (! [A:$i] :  ((l1_vectmetr A) =>  ((v4_vectmetr A) =>  (A = (g1_vectmetr (u1_struct_0 A) (u1_metric_1 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ).
tt(abstractness_v5_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) =>  ((v5_cat_4 A) =>  (A = (g2_cat_4 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (u5_cat_4 A) (u6_cat_4 A) (u7_cat_4 A) (u8_cat_4 A))) ) ) ) ).
tt(abstractness_v5_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_closure1 B A))  =>  ((v5_closure1 B A) =>  (B = (g1_closure1 A (u3_msualg_1 A B) (u1_closure1 A B))) ) ) ) ).
tt(abstractness_v5_combgras,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) & (l1_combgras C A B)) )  =>  ((v5_combgras C A B) =>  (C = (g1_combgras A B (u1_combgras A B C) (u2_combgras A B C))) ) ) ) ).
tt(abstractness_v5_rltopsp1,ax, (! [A:$i] :  ((l1_rltopsp1 A) =>  ((v5_rltopsp1 A) =>  (A = (g1_rltopsp1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_pre_topc A))) ) ) ) ).
tt(abstractness_v6_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ((v6_altcat_1 A) =>  (A = (g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A))) ) ) ) ).
tt(abstractness_v6_fsm_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (l2_fsm_2 C A B))  =>  ((v6_fsm_2 C A B) =>  (C = (g2_fsm_2 A B (u1_struct_0 C) (u1_fsm_1 B C) (u4_fsm_1 A B C) (u2_fsm_1 B C) (u1_fsm_2 B C))) ) ) ) ).
tt(abstractness_v6_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ((v6_robbins3 A) =>  (A = (g3_robbins3 (u1_struct_0 A) (u2_lattices A) (u1_lattices A) (u1_orders_2 A))) ) ) ) ).
tt(abstractness_v6_waybel_0,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_waybel_0 B A))  =>  ((v6_waybel_0 B A) =>  (B = (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) (u1_waybel_0 A B))) ) ) ) ).
tt(abstractness_v7_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  ((v7_abcmiz_0 A) =>  (A = (g2_abcmiz_0 (u1_struct_0 A) (u1_abcmiz_0 A) (u1_orders_2 A) (u2_abcmiz_0 A) (u3_abcmiz_0 A))) ) ) ) ).
tt(abstractness_v7_clvect_1,ax, (! [A:$i] :  ((l2_clvect_1 A) =>  ((v7_clvect_1 A) =>  (A = (g2_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A) (u1_normsp_0 A))) ) ) ) ).
tt(abstractness_v7_modelc_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (l2_modelc_3 B A))  =>  ((v7_modelc_3 B A) =>  (B = (g2_modelc_3 A (u1_struct_0 B) (u4_modelc_3 A B) (u5_modelc_3 A B) (u6_modelc_3 A B))) ) ) ) ).
tt(abstractness_v7_vectsp_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_vectsp_1 B A))  =>  ((v7_vectsp_1 B A) =>  (B = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ).
tt(abstractness_v8_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((v8_algstr_0 A) =>  (A = (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))) ) ) ) ).
tt(abstractness_v9_functor0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) & (l2_functor0 C A B)) )  =>  ((v9_functor0 C A B) =>  (C = (g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C))) ) ) ) ).
tt(abstractness_v9_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  ((v9_modelc_1 A) =>  (A = (g2_modelc_1 (u1_struct_0 A) (u3_modelc_1 A) (u1_lattices A) (u1_robbins1 A) (u4_modelc_1 A) (u5_modelc_1 A) (u6_modelc_1 A))) ) ) ) ).
tt(abstractness_v9_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  ((v9_modelc_2 A) =>  (A = (g1_modelc_2 (u1_struct_0 A) (u1_modelc_2 A) (u1_lattices A) (u2_lattices A) (u1_robbins1 A) (u2_modelc_2 A) (u3_modelc_2 A) (u4_modelc_2 A))) ) ) ) ).
tt(antisymmetry_r1_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_exchsort A B C) =>  (~ (r1_exchsort A C B)) ) ) ) ).
tt(antisymmetry_r1_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k5_numbers)) & (m1_subset_1 C (k4_finseq_2 A k5_numbers))) )  =>  ((r1_polynom3 A B C) =>  (~ (r1_polynom3 A C B)) ) ) ) ).
tt(antisymmetry_r1_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) )  =>  ((r1_pre_poly A B C) =>  (~ (r1_pre_poly A C B)) ) ) ) ).
tt(antisymmetry_r2_hidden,ax, (! [A:$i,B:$i] :  ((r2_hidden A B) =>  (~ (r2_hidden B A)) ) ) ).
tt(antisymmetry_r2_xboole_0,ax, (! [A:$i,B:$i] :  ((r2_xboole_0 A B) =>  (~ (r2_xboole_0 B A)) ) ) ).
tt(antisymmetry_r3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((r3_pboole A B C) =>  (~ (r3_pboole A C B)) ) ) ) ).
tt(cc10_abcmiz_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v13_abcmiz_1 B A)) ) ) ) ) ) ) ) ).
tt(cc10_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) ) ).
tt(cc10_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((v14_algstr_0 A) =>  ((v12_algstr_0 A) & (v13_algstr_0 A)) ) ) ) ).
tt(cc10_card_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_zfmisc_1 A))  => (v3_card_1 A 1)) ) ).
tt(cc10_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 B)) => (v4_relat_1 C A)) ) ) ) ).
tt(cc10_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) &  ((v5_cgames_1 A) &  (~ (v7_cgames_1 A)) ) )  =>  ((v2_cgames_1 A) & (v9_cgames_1 A)) ) ) ).
tt(cc10_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure2 B A) =>  ((v15_closure2 B A) => (v16_closure2 B A)) ) ) ) ) ).
tt(cc10_cohsp_1,ax, (! [A:$i] :  ((v3_cohsp_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v5_cohsp_1 B)) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v8_cohsp_1 B)) ) ) ) ) ) ) ) ).
tt(cc10_compact1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v7_compact1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v6_compact1 C A B)) ) ) ) ) ) ) ).
tt(cc10_comput_1,ax, (! [A:$i] :  ((v7_comput_1 A) =>  ((v1_relat_1 A) & (v1_funct_1 A)) ) ) ).
tt(cc10_dilworth,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) => (v6_dilworth B A)) ) ) ) ).
tt(cc10_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  ((v3_euclid_7 B) => (v1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A)))) ) ) ) ) ).
tt(cc10_exchsort,ax, (! [A:$i,B:$i] :  ( ((v3_membered B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_funct_2 A B)) => (v3_valued_0 C)) ) ) ) ).
tt(cc10_finseq_1,ax, (! [A:$i] :  ((v3_finseq_1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_finseq_1 B)) ) ) ) ).
tt(cc10_fomodel0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_finseq_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_pre_poly B)) ) ) ) ) ) ).
tt(cc10_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v4_fomodel1 B A) =>  (~ (v7_fomodel1 B A)) ) ) ) ) ) ).
tt(cc10_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v15_fomodel1 B A) => (v3_fomodel2 B A k6_numbers)) ) ) ) ) ).
tt(cc10_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [E:$i] :  ((v8_fomodel4 E A B (k6_subset_1 C D)) => (v8_fomodel4 E A B (k2_xboole_0 C D))) ) ) ) ).
tt(cc10_funct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_funct_1 C B)) )  =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) ) ) ) ) ) ).
tt(cc10_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) => (v4_glib_000 B)) ) ) ) ).
tt(cc10_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k3_glib_002 A)))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) => (v4_glib_002 C A)) ) ) ) ).
tt(cc10_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_tops_1 B A))  => (v6_tops_1 B A)) ) ) ) ) ).
tt(cc10_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v19_lattices B A) => (v21_lattices B A)) ) ) ) ) ).
tt(cc10_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v2_lfuzzy_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v9_waybel_1 A) & (v2_lfuzzy_0 A)) ) ) ) ) ).
tt(cc10_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k4_numbers)) => (v5_membered A)) ) ).
tt(cc10_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v1_orders_4 A))  =>  ((v2_pre_topc A) & (v1_metrizts A)) ) ) ) ).
tt(cc10_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (v13_monoid_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (v16_monoid_0 A)) ) ) ) ) ).
tt(cc10_ordinal1,ax, (! [A:$i] :  ((v6_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v6_ordinal1 B)) ) ) ) ).
tt(cc10_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_pcs_0 A) &  ((v6_pcs_0 A) & (v13_pcs_0 A)) ) ) )  => (v15_pcs_0 A)) ) ) ).
tt(cc10_pre_poly,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k15_pre_poly A))) =>  (! [C:$i] :  ((m1_subset_1 C B) => (v4_relat_1 C A)) ) ) ) ).
tt(cc10_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_rewrite1 A))  =>  ((v1_relat_1 A) & (v4_rewrite1 A)) ) ) ).
tt(cc10_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  ((v4_scmyciel A) & (v11_scmyciel A)) ) ) ).
tt(cc10_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v1_matroid0 A) & (v3_simplex0 A))  => (v3_matroid0 A)) ) ) ).
tt(cc10_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v7_struct_0 A))  => (v13_struct_0 A 1)) ) ) ).
tt(cc10_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tsep_1 B A) => (v1_borsuk_1 B A)) ) ) ) ) ).
tt(cc10_tex_2,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_tex_2 B A)) ) ) ) ) ) ) ).
tt(cc10_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) &  (~ (v2_tex_3 B A)) )  =>  (~ (v1_tex_3 B A)) ) ) ) ) ) ).
tt(cc10_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_topalg_6 A)) =>  ((v5_topalg_6 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc10_topgen_4,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v4_card_3 A)) ) ).
tt(cc10_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_trees_3 B A) => (v3_trees_3 B)) ) ) ) ).
tt(cc10_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v6_pre_topc B)) ) ) ) ) ) ).
tt(cc10_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tex_2 B A) & (v2_tsp_2 B A))  =>  (~ (v1_borsuk_1 B A)) ) ) ) ) ) ).
tt(cc10_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_valued_0 B)) ) ) ) ).
tt(cc10_valued_2,ax, (! [A:$i] :  ((v2_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_valued_2 B)) ) ) ) ).
tt(cc10_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v1_lattice3 A) & (v24_waybel_0 A)) )  =>  ((v3_orders_2 A) &  ((v1_lattice3 A) & (v2_yellow_0 A)) ) ) ) ) ).
tt(cc10_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v11_waybel_1 A))  =>  ( (~ (v2_struct_0 A))  & (v9_waybel_1 A)) ) ) ) ).
tt(cc10_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (v2_waybel18 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (v1_waybel25 A)) ) ) ) ) ) ).
tt(cc10_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (v3_waybel_3 A)) ) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (v3_waybel30 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(cc10_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) & (v1_xxreal_2 A))  =>  ((v3_membered A) & (v3_xxreal_2 A)) ) ) ).
tt(cc10_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v8_yellow_0 B A) => (v6_yellow_0 B A)) ) ) ) ) ).
tt(cc10_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v3_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v3_yellow21 B)) ) ) ) ) ) ) ) ).
tt(cc11_abcmiz_1,ax, (! [A:$i] :  ( ((v12_abcmiz_1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v13_abcmiz_1 B A)) ) ) ) ) ) ) ) ).
tt(cc11_algstr_0,ax, (! [A:$i] :  ( ((v12_algstr_0 A) & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v9_algstr_0 B A)) ) ) ) ).
tt(cc11_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_card_3 A)) => (v5_funct_1 B A)) ) ) ) ).
tt(cc11_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) & (v8_cgames_1 A))  =>  ((v2_cgames_1 A) &  ( (~ (v5_cgames_1 A))  &  (~ (v6_cgames_1 A)) ) ) ) ) ).
tt(cc11_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure2 B A) =>  ((v13_closure2 B A) => (v17_closure2 B A)) ) ) ) ) ).
tt(cc11_cohsp_1,ax, (! [A:$i] :  ((v2_finsub_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v7_cohsp_1 B) & (v8_cohsp_1 B)) ) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v9_cohsp_1 B)) ) ) ) ) ) ) ) ).
tt(cc11_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v7_comput_1 A))  =>  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) ) ).
tt(cc11_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_dilworth B A) => (v1_dilworth B A)) ) ) ) ) ).
tt(cc11_euclid_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_real_ns1 A)))) =>  ((v3_euclid_7 B) => (v1_rlvect_3 B (k7_real_ns1 A))) ) ) ) ) ).
tt(cc11_exchsort,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  (! [C:$i] :  ((m1_exchsort C B) => (v5_relat_1 C A)) ) ) ) ).
tt(cc11_finseq_1,ax, (! [A:$i] :  ((v3_finseq_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v3_finseq_1 B)) ) ) ) ).
tt(cc11_fomodel0,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k9_funct_2 A (k3_finseq_2 B))) => (v1_pre_poly C)) ) ) ).
tt(cc11_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v4_fomodel1 B A) =>  (~ (v6_fomodel1 B A)) ) ) ) ) ) ).
tt(cc11_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v3_fomodel2 C A B) => (v4_fomodel2 C A)) ) ) ) ) ).
tt(cc11_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [E:$i] :  ((v8_fomodel4 E A B (k3_xboole_0 C D)) => (v8_fomodel4 E A B C)) ) ) ) ).
tt(cc11_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v5_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) => (v5_glib_000 B)) ) ) ) ).
tt(cc11_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v3_glib_002 A)) ) ) ) ) ) )  &  ((v11_glib_000 B A) & (m1_subset_1 B (k6_glib_000 A))) )  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) => (v3_glib_002 C)) ) ) ) ).
tt(cc11_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) =>  ((v4_pre_topc B A) & (v4_tops_1 B A)) ) ) ) ) ) ).
tt(cc11_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) => (v6_membered A)) ) ).
tt(cc11_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_monoid_0 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc11_pcs_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v16_pcs_0 A))  =>  ((v1_relat_1 A) &  ((v1_yellow_1 A) & (v7_pcs_0 A)) ) ) ) ).
tt(cc11_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k15_pre_poly A))))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) ).
tt(cc11_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_rewrite1 A) & (v4_rewrite1 A)) )  =>  ((v1_relat_1 A) & (v8_rewrite1 A)) ) ) ).
tt(cc11_robbins3,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v8_robbins1 A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) ) ) ) ) ).
tt(cc11_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  ((v4_scmyciel A) & (v12_scmyciel A)) ) ) ).
tt(cc11_simplex0,ax, (! [A:$i] :  ( ((v2_simplex0 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) => (v1_finset_1 B)) ) ) ) ) ).
tt(cc11_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v13_struct_0 A 1) =>  ( (~ (v2_struct_0 A))  & (v7_struct_0 A)) ) ) ) ).
tt(cc11_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_borsuk_1 B A) => (v1_tsep_1 B A)) ) ) ) ) ).
tt(cc11_tex_2,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v1_tex_2 B A)) )  =>  ( (~ (v2_struct_0 B))  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(cc11_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_tsep_1 B A))  =>  ( (~ (v2_struct_0 B))  &  (~ (v3_tex_3 B A)) ) ) ) ) ) ) ).
tt(cc11_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_topalg_6 A)) =>  ((v6_topalg_6 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc11_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v5_topgen_4 B A) & (v6_topgen_4 B A)) ) ) ) ) ) ).
tt(cc11_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_trees_3 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C B) => (v5_relat_1 C A)) ) ) ) ).
tt(cc11_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v6_pre_topc A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v1_tex_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v6_pre_topc B)) ) ) ) ) ) ) ).
tt(cc11_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_valued_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_valued_0 B)) ) ) ) ).
tt(cc11_valued_2,ax, (! [A:$i] :  ((v3_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v3_valued_2 B)) ) ) ) ).
tt(cc11_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v3_lattice3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (v25_waybel_0 A)) ) ) ) ) ) ).
tt(cc11_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) & (v2_xxreal_2 A))  =>  ((v3_membered A) & (v4_xxreal_2 A)) ) ) ).
tt(cc11_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (v5_yellow_0 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_lattice3 B) &  ((v4_yellow_0 B A) & (v5_yellow_0 B A)) ) ) ) ) ) ) ) ).
tt(cc12_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))) =>  ( ((v1_xboole_0 B) & (v1_funct_1 B))  =>  ((v1_funct_1 B) & (v15_abcmiz_1 B A)) ) ) ) ) ) ).
tt(cc12_algstr_0,ax, (! [A:$i] :  ( ((v13_algstr_0 A) & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v10_algstr_0 B A)) ) ) ) ).
tt(cc12_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k8_card_3 B)) => (v4_relat_1 C A)) ) ) ) ).
tt(cc12_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) &  ( (~ (v5_cgames_1 A))  &  (~ (v6_cgames_1 A)) ) )  =>  ((v2_cgames_1 A) & (v8_cgames_1 A)) ) ) ).
tt(cc12_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v4_cohsp_1 A) & (v9_cohsp_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v10_cohsp_1 A)) ) ) ) ).
tt(cc12_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k9_comput_1) => (v7_comput_1 A)) ) ).
tt(cc12_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_card_1 B 1) => (v7_dilworth B A)) ) ) ) ) ).
tt(cc12_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_2 A C)) => (v5_relat_1 D B)) ) ) ) ).
tt(cc12_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) &  ((v5_valued_0 A) & (v1_finseq_1 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) ) ) ) ) ).
tt(cc12_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_xcmplx_0 A 1)) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(cc12_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ( ((v5_fomodel1 B A) & (v8_fomodel1 B A))  =>  ((v5_fomodel1 B A) & (v6_fomodel1 B A)) ) ) ) ) ) ).
tt(cc12_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v3_fomodel2 D A (k1_nat_1 B (k4_nat_1 k6_numbers C))) => (v3_fomodel2 D A (k2_xcmplx_0 B C))) ) ) ) ) ).
tt(cc12_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) & (m1_subset_1 D (k1_zfmisc_1 C))) )  =>  (! [E:$i] :  ((v8_fomodel4 E A B D) => (v8_fomodel4 E A B C)) ) ) ) ).
tt(cc12_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A)))) )  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k21_glib_000 A B)))) ) )  =>  (! [D:$i] :  ((m2_glib_000 D A B C) => (v2_glib_000 D)) ) ) ) ).
tt(cc12_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v4_tops_1 B A))  => (v5_tops_1 B A)) ) ) ) ) ).
tt(cc12_membered,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xcmplx_0 B)) ) ) ) ).
tt(cc12_monoid_0,ax, (! [A:$i] :  ( ((v1_monoid_0 A) & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v1_monoid_0 B)) ) ) ) ).
tt(cc12_pcs_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v17_pcs_0 A))  =>  ((v1_relat_1 A) & (v16_pcs_0 A)) ) ) ).
tt(cc12_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k18_pre_poly A B)) => (v4_valued_0 C)) ) ) ) ).
tt(cc12_rewrite1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v6_rewrite1 A)) ) ) ).
tt(cc12_robbins3,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v6_oposet_1 A) &  ((v7_oposet_1 A) & (v10_oposet_1 A)) ) ) ) ) ) ) ).
tt(cc12_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v12_scmyciel A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))) =>  ((v9_scmyciel B A) =>  ((v1_finset_1 B) & (v9_scmyciel B A)) ) ) ) ) ) ).
tt(cc12_simplex0,ax, (! [A:$i] :  ( ((v3_matroid0 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) => (v5_finset_1 B)) ) ) ) ) ).
tt(cc12_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ( (~ (v2_struct_0 A))  => (v14_struct_0 A)) ) ) ).
tt(cc12_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_tdlat_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v4_tdlat_3 A)) ) ) ) ) ).
tt(cc12_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v7_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc12_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v3_tex_3 B A))  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_tsep_1 B A)) ) ) ) ) ) ) ).
tt(cc12_topgen_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v7_topgen_4 A))  =>  ((v2_pre_topc A) & (v6_pre_topc A)) ) ) ) ).
tt(cc12_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C A B))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (v3_trees_2 C)) ) ) ) ) ) ) ).
tt(cc12_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v6_pre_topc A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v6_pre_topc B))  =>  ( (~ (v2_struct_0 B))  & (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc12_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v3_valued_0 B)) ) ) ) ).
tt(cc12_valued_2,ax, (! [A:$i] :  ((v4_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v4_valued_2 B)) ) ) ) ).
tt(cc12_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v25_waybel_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v1_yellow_0 A)) ) ) ) ) ).
tt(cc12_xxreal_2,ax, (! [A:$i] :  ( ((v5_membered A) & (v5_xxreal_2 A))  =>  ((v5_membered A) & (v1_finset_1 A)) ) ) ).
tt(cc12_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (v6_yellow_0 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v1_lattice3 B) &  ((v4_yellow_0 B A) & (v6_yellow_0 B A)) ) ) ) ) ) ) ) ).
tt(cc13_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v16_algstr_0 B A) & (v17_algstr_0 B A))  => (v18_algstr_0 B A)) ) ) ) ) ).
tt(cc13_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 B)) => (v1_partfun1 C A)) ) ) ) ).
tt(cc13_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k9_comput_1) =>  ((v2_margrel1 A) & (v3_margrel1 A k5_numbers)) ) ) ).
tt(cc13_fomodel0,ax, (! [A:$i] :  ((v3_finseq_1 A) => (v5_finset_1 A)) ) ).
tt(cc13_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v12_fomodel1 B A) => (v3_fomodel0 B (k15_fomodel1 A))) ) ) ) ).
tt(cc13_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v5_fomodel2 B A) =>  (~ (v15_fomodel1 B A)) ) ) ) ) ) ).
tt(cc13_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((v12_fomodel4 B 1 A) => (v12_fomodel4 B k6_numbers A)) ) ) ) ) ).
tt(cc13_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k1_zfmisc_1 (k21_glib_000 A (k6_domain_1 (k6_glib_000 A) B))))) )  =>  (! [D:$i] :  ((m2_glib_000 D A (k6_domain_1 (k6_glib_000 A) B) C) => (v4_glib_000 D)) ) ) ) ).
tt(cc13_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_isomichi B A) =>  ( (~ (v4_isomichi B A))  &  (~ (v5_isomichi B A)) ) ) ) ) ) ) ).
tt(cc13_membered,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xxreal_0 B)) ) ) ) ).
tt(cc13_monoid_0,ax, (! [A:$i] :  ( ((v2_monoid_0 A) & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v2_monoid_0 B)) ) ) ) ).
tt(cc13_pcs_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v17_pcs_0 A))  =>  ((v1_relat_1 A) &  ((v5_waybel_3 A) &  ((v1_pcs_0 A) &  ((v9_pcs_0 A) & (v11_pcs_0 A)) ) ) ) ) ) ).
tt(cc13_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_finseq_1 C (k4_finseq_2 B A)) => (v1_pre_poly C)) ) ) ) ).
tt(cc13_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v3_rewrite1 A) & (v9_rewrite1 A)) )  =>  ((v1_relat_1 A) & (v7_rewrite1 A)) ) ) ).
tt(cc13_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v10_robbins3 A) & (v11_robbins3 A)) ) ) ) ) ) ).
tt(cc13_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) &  ((v6_scmyciel A) & (v12_scmyciel A)) )  =>  ((v1_finset_1 A) & (v4_scmyciel A)) ) ) ).
tt(cc13_simplex0,ax, (! [A:$i] :  ( ( (~ (v5_simplex0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_pre_topc B A)) ) ) ) ) ).
tt(cc13_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ((v11_struct_0 A) => (v14_struct_0 A)) ) ) ).
tt(cc13_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_tdlat_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_tdlat_3 A)) ) ) ) ) ).
tt(cc13_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v1_tex_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) ) ) ) ) ) ) ).
tt(cc13_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tex_3 B A) =>  (~ (v3_tex_3 B A)) ) ) ) ) ) ).
tt(cc13_topgen_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v7_pre_topc A))  =>  ((v2_pre_topc A) & (v7_topgen_4 A)) ) ) ) ).
tt(cc13_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v4_trees_3 A) &  ((v5_trees_3 A) & (v6_trees_3 A)) ) ) ) ) ) ).
tt(cc13_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v5_relat_1 B k3_numbers)) ) ) ) ).
tt(cc13_valued_2,ax, (! [A:$i] :  ((v5_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v5_valued_2 B)) ) ) ) ).
tt(cc13_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (v24_waybel_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v3_lattice3 A)) ) ) ) ) ) ) ).
tt(cc13_xxreal_2,ax, (! [A:$i] :  ( ((v6_membered A) & (v4_xxreal_2 A))  =>  ((v6_membered A) &  ((v1_finset_1 A) & (v4_xxreal_2 A)) ) ) ) ).
tt(cc14_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v18_algstr_0 B A) =>  ((v16_algstr_0 B A) & (v17_algstr_0 B A)) ) ) ) ) ) ).
tt(cc14_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 B)) => (v1_partfun1 C A)) ) ) ) ).
tt(cc14_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_comput_1 k5_numbers)) =>  ((v7_comput_1 A) => (v3_margrel1 A k5_numbers)) ) ) ).
tt(cc14_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_fomodel0 (k3_finseq_2 A) (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)))) =>  ( (~ (v1_xboole_0 B))  =>  (~ (v3_relat_1 B)) ) ) ) ) ) ).
tt(cc14_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v3_fomodel0 B (k15_fomodel1 A)) => (v12_fomodel1 B A)) ) ) ) ).
tt(cc14_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k33_fomodel2 A)) => (v4_fomodel2 B A)) ) ) ) ).
tt(cc14_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((v12_fomodel4 B 2 A) => (v12_fomodel4 B 1 A)) ) ) ) ) ).
tt(cc14_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_domain_1 (k6_glib_000 A) B) k1_xboole_0) =>  ((v2_glib_000 C) & (v4_glib_000 C)) ) ) ) ) ).
tt(cc14_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_isomichi B A) =>  ( (~ (v3_isomichi B A))  &  (~ (v5_isomichi B A)) ) ) ) ) ) ) ).
tt(cc14_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xreal_0 B)) ) ) ) ).
tt(cc14_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v1_group_1 B)) ) ) ) ).
tt(cc14_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v21_pcs_0 B A)) ) ) ) ) ).
tt(cc14_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v10_rewrite1 A))  =>  ((v1_relat_1 A) &  ((v3_rewrite1 A) & (v7_rewrite1 A)) ) ) ) ).
tt(cc14_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v10_robbins3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ).
tt(cc14_simplex0,ax, (! [A:$i,B:$i] :  ( ((v3_pencil_1 B) & (m1_simplex0 B A))  =>  (! [C:$i] :  ((m2_simplex0 C A B) => (v3_pencil_1 C)) ) ) ) ).
tt(cc14_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ( ((v2_struct_0 A) & (v14_struct_0 A))  => (v11_struct_0 A)) ) ) ).
tt(cc14_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_tsep_1 B A))  =>  ( (~ (v2_struct_0 B))  & (v4_tdlat_3 B)) ) ) ) ) ) ).
tt(cc14_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tdlat_3 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(cc14_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v3_tex_3 B A) =>  (~ (v2_tex_3 B A)) ) ) ) ) ) ).
tt(cc14_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B (u1_struct_0 A)) & (v4_prob_1 B (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B (u1_struct_0 A)) &  ((v4_prob_1 B (u1_struct_0 A)) & (v3_topgen_4 B (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(cc14_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_trees_3 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_trees_3 A)) ) ) ) ).
tt(cc14_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v5_relat_1 B k4_numbers)) ) ) ) ).
tt(cc14_valued_2,ax, (! [A:$i] :  ((v6_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v6_valued_2 B)) ) ) ) ).
tt(cc14_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (v25_waybel_0 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (v2_lattice3 A)) ) ) ) ) ) ).
tt(cc14_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v5_xxreal_2 A))  =>  ((v2_membered A) & (v3_membered A)) ) ) ).
tt(cc15_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ((v19_algstr_0 A) & (v20_algstr_0 A))  => (v21_algstr_0 A)) ) ) ).
tt(cc15_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v7_comput_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v2_comput_1 A)) ) ) ) ) ).
tt(cc15_fomodel0,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_finseq_2 A)) => (v1_xboole_0 B)) ) ) ) ).
tt(cc15_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc15_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k35_fomodel2 A B)) =>  (~ (v5_fomodel2 C A)) ) ) ) ) ).
tt(cc15_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [D:$i] :  ((v3_fomodel4 D A B C) => (v2_fomodel4 D A)) ) ) ) ).
tt(cc15_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A)))) )  =>  (! [C:$i] :  ((m2_glib_000 C A B k1_xboole_0) => (v7_glib_000 C)) ) ) ) ).
tt(cc15_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_isomichi B A) =>  ( (~ (v3_isomichi B A))  &  (~ (v4_isomichi B A)) ) ) ) ) ) ) ).
tt(cc15_membered,ax, (! [A:$i] :  ((v4_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_rat_1 B)) ) ) ) ).
tt(cc15_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v3_group_1 B)) ) ) ) ).
tt(cc15_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v3_rewrite1 A) & (v7_rewrite1 A)) )  =>  ((v1_relat_1 A) & (v10_rewrite1 A)) ) ) ).
tt(cc15_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  (! [B:$i] :  ((m3_robbins3 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc15_simplex0,ax, (! [A:$i,B:$i] :  ( ((v2_simplex0 B) & (m1_simplex0 B A))  =>  (! [C:$i] :  ((m2_simplex0 C A B) => (v2_simplex0 C)) ) ) ) ).
tt(cc15_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ( ( (~ (v11_struct_0 A))  & (v14_struct_0 A))  =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc15_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v5_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v5_tdlat_3 B)) ) ) ) ) ) ).
tt(cc15_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tdlat_3 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(cc15_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_3 B A) => (v3_tex_3 B A)) ) ) ) ) ).
tt(cc15_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_topgen_4 B A) => (v8_topgen_4 B A)) ) ) ) ) ).
tt(cc15_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_3 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) => (v4_trees_3 B)) ) ) ) ).
tt(cc15_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v4_valued_0 B)) ) ) ) ).
tt(cc15_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_valued_0 B)) ) ) ) ).
tt(cc15_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (v25_waybel_0 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_yellow_0 A)) ) ) ) ) ) ) ).
tt(cc15_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v1_xboole_0 A))  =>  ((v2_membered A) & (v6_xxreal_2 A)) ) ) ).
tt(cc16_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v21_algstr_0 A) =>  ((v19_algstr_0 A) & (v20_algstr_0 A)) ) ) ) ).
tt(cc16_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_margrel1 A) & (v8_comput_1 A 1)) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) ) ) ) ) ).
tt(cc16_fomodel0,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  (~ (v1_xboole_0 B)) ) )  =>  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  & (v5_relat_1 B A)) ) ) ) ) ) ).
tt(cc16_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ( ( (~ (v6_struct_0 A))  & (v11_fomodel1 A))  =>  ( (~ (v6_struct_0 A))  &  ( (~ (v8_struct_0 A))  & (v11_fomodel1 A)) ) ) ) ) ).
tt(cc16_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k36_fomodel2 A B)) => (v5_fomodel2 C A)) ) ) ) ).
tt(cc16_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((v12_fomodel4 B k6_numbers A) =>  ( (~ (v1_xboole_0 B))  & (v12_fomodel4 B k6_numbers A)) ) ) ) ) ) ).
tt(cc16_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (k7_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) B) => (v9_glib_000 C A)) ) ) ) ).
tt(cc16_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_isomichi B A) => (v3_isomichi B A)) ) ) ) ) ).
tt(cc16_membered,ax, (! [A:$i] :  ((v5_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_int_1 B)) ) ) ) ).
tt(cc16_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v5_group_1 B)) ) ) ) ).
tt(cc16_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v7_lattices B)) ) ) ) ).
tt(cc16_simplex0,ax, (! [A:$i,B:$i] :  ( ((v4_matroid0 B) & (m1_simplex0 B A))  =>  (! [C:$i] :  ((m2_simplex0 C A B) => (v4_matroid0 C)) ) ) ) ).
tt(cc16_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ((v11_struct_0 A) => (v15_struct_0 A)) ) ) ).
tt(cc16_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_pre_topc B))  =>  (~ (v1_tdlat_3 B)) ) ) ) ) ) ).
tt(cc16_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v3_tex_3 B A))  =>  (~ (v4_tex_3 B A)) ) ) ) ) ) ).
tt(cc16_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_topgen_4 B A) => (v8_topgen_4 B A)) ) ) ) ) ).
tt(cc16_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_trees_3 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) => (v5_trees_3 B)) ) ) ) ).
tt(cc16_valued_0,ax, (! [A:$i,B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v1_valued_0 C)) ) ) ) ).
tt(cc16_valued_2,ax, (! [A:$i] :  ((v2_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v2_valued_0 B)) ) ) ) ).
tt(cc16_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v1_xxreal_2 A))  =>  ((v2_membered A) &  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc17_algstr_0,ax, (! [A:$i] :  ( ((v19_algstr_0 A) & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v16_algstr_0 B A)) ) ) ) ).
tt(cc17_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_margrel1 A) & (v8_comput_1 A 2)) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) ) ) ) ) ).
tt(cc17_fomodel0,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_setfam_1 B)) ) ) ) ).
tt(cc17_fomodel1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  ((v14_fomodel1 C A B) => (v13_fomodel1 C B)) ) ) ) ) ).
tt(cc17_fomodel2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  ( (~ (v3_fomodel2 C B A))  =>  (~ (v3_fomodel2 C B A)) ) ) ) ) ) ).
tt(cc17_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v13_fomodel4 B A) => (v1_finset_1 B)) ) ) ) ).
tt(cc17_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_glib_000 B A (k6_glib_000 A) k1_xboole_0) => (v9_glib_000 B A)) ) ) ) ).
tt(cc17_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_isomichi B A) => (v3_isomichi B A)) ) ) ) ) ).
tt(cc17_membered,ax, (! [A:$i] :  ((v6_membered A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v7_ordinal1 B)) ) ) ) ).
tt(cc17_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v13_monoid_0 B)) ) ) ) ).
tt(cc17_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v5_lattices B)) ) ) ) ).
tt(cc17_simplex0,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_finset_1 A) & (v1_int_1 A)) ) ) ).
tt(cc17_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ( (~ (v7_struct_0 A))  =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc17_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_pre_topc B))  =>  (~ (v2_tdlat_3 B)) ) ) ) ) ) ).
tt(cc17_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_3 B A) =>  (~ (v1_tex_3 B A)) ) ) ) ) ) ).
tt(cc17_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) => (v6_trees_3 B)) ) ) ) ).
tt(cc17_valued_0,ax, (! [A:$i,B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v2_valued_0 C)) ) ) ) ).
tt(cc17_valued_2,ax, (! [A:$i] :  ((v3_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v3_valued_0 B)) ) ) ) ).
tt(cc17_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v2_xxreal_2 A))  =>  ((v2_membered A) &  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc18_algstr_0,ax, (! [A:$i] :  ( ((v20_algstr_0 A) & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v17_algstr_0 B A)) ) ) ) ).
tt(cc18_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_margrel1 A) & (v8_comput_1 A 3)) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) ) ) ) ) ).
tt(cc18_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_funct_1 (k28_fomodel1 A) B)) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc18_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k16_fomodel2 A B)) => (v4_relat_1 C (k37_fomodel1 A))) ) ) ) ).
tt(cc18_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v13_fomodel4 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v13_fomodel4 C A)) ) ) ) ).
tt(cc18_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski B))) => (v9_glib_000 C A)) ) ) ) ).
tt(cc18_membered,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v6_membered A)) ) ).
tt(cc18_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v16_monoid_0 B)) ) ) ) ).
tt(cc18_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v6_lattices B)) ) ) ) ).
tt(cc18_simplex0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m3_simplex0 B A (k2_xxreal_3 1)) => (v1_xboole_0 B)) ) ) ) ).
tt(cc18_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tdlat_3 B) => (v3_tdlat_3 B)) ) ) ) ) ).
tt(cc18_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_3 B A) =>  (~ (v4_tex_3 B A)) ) ) ) ) ) ).
tt(cc18_valued_0,ax, (! [A:$i,B:$i] :  ((v3_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v3_valued_0 C)) ) ) ) ).
tt(cc18_valued_2,ax, (! [A:$i] :  ((v4_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v5_relat_1 B k3_numbers)) ) ) ) ).
tt(cc19_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v23_algstr_0 B A) & (v24_algstr_0 B A))  => (v25_algstr_0 B A)) ) ) ) ) ).
tt(cc19_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k29_fomodel1 A)) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc19_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k16_fomodel2 A B)) =>  ((v4_relat_1 C (k37_fomodel1 A)) =>  ((v4_relat_1 C (k37_fomodel1 A)) & (v1_partfun1 C (k37_fomodel1 A))) ) ) ) ) ) ).
tt(cc19_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v1_fomodel4 B A) => (v11_fomodel4 B A)) ) ) ) ).
tt(cc19_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) B)) => (v9_glib_000 C A)) ) ) ) ).
tt(cc19_membered,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_membered B)) ) ) ) ).
tt(cc19_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v17_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_monoid_0 B A) => (v17_monoid_0 B)) ) ) ) ).
tt(cc19_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v4_lattices B)) ) ) ) ).
tt(cc19_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v3_tdlat_3 B))  =>  (~ (v1_tdlat_3 B)) ) ) ) ) ) ).
tt(cc19_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) & (v3_tex_3 B A))  => (v4_tex_3 B A)) ) ) ) ) ).
tt(cc19_valued_0,ax, (! [A:$i,B:$i] :  ((v4_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v5_relat_1 C k3_numbers)) ) ) ) ).
tt(cc19_valued_2,ax, (! [A:$i] :  ((v5_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v5_relat_1 B k4_numbers)) ) ) ) ).
tt(cc1_abcmiz_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) & (v3_lattice3 A)) ) ) ) ).
tt(cc1_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  (~ (v1_xtuple_0 C)) ) ) ) ) ).
tt(cc1_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  ((v1_abcmiz_1 B) =>  ((v1_abcmiz_1 B) & (v1_abcmiz_a B)) ) ) ) ) ) ).
tt(cc1_abian,ax, (! [A:$i] :  ((v2_setfam_1 A) => (v1_zfmisc_1 A)) ) ).
tt(cc1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) ) ) ) ).
tt(cc1_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v7_ordinal1 A) & (v6_membered A)) ) ) ).
tt(cc1_afvect0,ax, (! [A:$i] :  ((l1_analoaf A) =>  ( ( (~ (v2_struct_0 A))  & (v2_tdgroup A))  =>  ( (~ (v2_struct_0 A))  & (v1_afvect0 A)) ) ) ) ).
tt(cc1_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m2_algspec1 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc1_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v2_algstr_0 B A) & (v3_algstr_0 B A))  => (v4_algstr_0 B A)) ) ) ) ) ).
tt(cc1_algstr_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_algstr_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v6_algstr_0 A) &  ((v2_algstr_1 A) & (v3_algstr_1 A)) ) ) ) ) ) ) ).
tt(cc1_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v8_altcat_1 A) & (v9_altcat_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v10_altcat_1 A)) ) ) ) ).
tt(cc1_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v12_altcat_1 A))  =>  ( (~ (v2_struct_0 A))  & (v1_altcat_2 A)) ) ) ) ).
tt(cc1_ami_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 A) &  (~ (v1_setfam_1 A)) ) ) ) ) ).
tt(cc1_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) => (v4_compos_0 B (u1_compos_1 (k4_amistd_1 A)))) ) ) ) ).
tt(cc1_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (v1_amistd_2 C A B)) ) ) ) ).
tt(cc1_amistd_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v1_amistd_5 C A B) => (v3_amistd_2 C A B)) ) ) ) ) ).
tt(cc1_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_extpro_1 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (v2_ami_wstd B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (v1_ami_wstd B A)) ) ) ) ) ) ) ) ).
tt(cc1_analmetr,ax, (! [A:$i] :  ((l1_analmetr A) =>  ( ( (~ (v2_struct_0 A))  & (v3_analmetr A))  =>  ( (~ (v2_struct_0 A))  & (v2_analmetr A)) ) ) ) ).
tt(cc1_anproj_2,ax, (! [A:$i] :  ((l1_rlvect_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (v1_anproj_2 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) & (v8_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_aofa_000,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc1_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C k5_numbers)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k4_finseq_2 C B)))) =>  ( ((v1_funct_1 D) & (v1_funct_2 D A (k4_finseq_2 C B)))  =>  ((v1_funct_1 D) &  ((v1_funct_2 D A (k4_finseq_2 C B)) & (v1_pre_poly D)) ) ) ) ) ) ) ).
tt(cc1_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_arrow A)) => (v1_relat_1 B)) ) ) ) ).
tt(cc1_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((v3_ordinal1 A) =>  ((v3_ordinal1 A) & (v7_ordinal1 A)) ) ) ) ).
tt(cc1_asympt_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v3_asympt_0 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v4_asympt_0 A)) ) ) ) ) ).
tt(cc1_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v20_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v13_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc1_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m2_bcialg_1 B A))  =>  (! [C:$i] :  ((m4_bcialg_2 C A B) =>  ((v1_partfun1 C (u1_struct_0 A)) &  ((v3_relat_2 C) & (v8_relat_2 C)) ) ) ) ) ) ).
tt(cc1_bcialg_5,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (v11_bcialg_3 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (v1_bcialg_3 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_binom,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) & (v2_rlvect_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v5_algstr_0 A)) ) ) ) ).
tt(cc1_binop_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 k1_xboole_0) k1_xboole_0))) =>  ( ((v1_funct_1 A) & (v1_funct_2 A (k2_zfmisc_1 k1_xboole_0 k1_xboole_0) k1_xboole_0))  =>  ((v1_funct_1 A) &  ((v1_xboole_0 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_xboole_0 k1_xboole_0) k1_xboole_0) &  ((v1_binop_1 A k1_xboole_0) & (v2_binop_1 A k1_xboole_0)) ) ) ) ) ) ) ).
tt(cc1_binop_2,ax, (! [A:$i] :  ((m1_subset_1 A k3_numbers) => (v1_rat_1 A)) ) ).
tt(cc1_bintree1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_2 A)) ) ) ) ).
tt(cc1_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) ) ) ) ).
tt(cc1_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_borsuk_2 A) & (l1_pre_topc A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) => (v5_pre_topc D k5_topmetr A)) ) ) ) ).
tt(cc1_borsuk_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) & (v1_compts_1 A)) ) ) ) ).
tt(cc1_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ( (~ (v1_zfmisc_1 A))  & (v1_topreal2 A)) ) ) ) ).
tt(cc1_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A k3_numbers) => (v1_xreal_0 A)) ) ).
tt(cc1_borsuk_6,ax, (! [A:$i] :  ( ((v3_topmetr A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_xreal_0 B)) ) ) ) ).
tt(cc1_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_c0sp1 B A) =>  ((v1_ideal_1 B A) & (v1_c0sp1 B A)) ) ) ) ) ) ).
tt(cc1_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_cantor_1 B A))  =>  ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (v2_cantor_1 B A)) ) ) ) ) ) ) ).
tt(cc1_card_1,ax, (! [A:$i] :  ((v1_card_1 A) => (v3_ordinal1 A)) ) ).
tt(cc1_card_2,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v4_ordinal1 A) & (v1_card_1 A)) ) ) ).
tt(cc1_card_3,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) ) ) ) ).
tt(cc1_card_5,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc1_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ( ((v1_card_fil B A) & (v3_card_fil B A))  =>  (~ (v2_card_fil B A)) ) ) ) ) ) ).
tt(cc1_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v1_finset_1 A))  & (v1_card_1 A)) )  =>  ((v3_ordinal1 A) & (v4_ordinal1 A)) ) ) ).
tt(cc1_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) &  (~ (v11_struct_0 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v3_cat_1 A) & (v5_cat_1 A)) ) ) ) ) ) ).
tt(cc1_cat_5,ax, (! [A:$i] :  ((l1_cat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (v3_cat_5 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (v1_cat_5 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_catalan2,ax, (! [A:$i,B:$i] :  ((m1_catalan2 B A) =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v5_ordinal1 C) &  ((v5_relat_1 C A) & (v1_finset_1 C)) ) ) ) ) ) ).
tt(cc1_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v4_msualg_1 B A) =>  (~ (v1_catalg_1 B A)) ) ) ) ) ) ).
tt(cc1_cayley,ax, (! [A:$i] :  ((v3_matrix_2 A) => (v4_funct_1 A)) ) ).
tt(cc1_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers))) =>  ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v1_cfdiff_1 A k6_numbers)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc1_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_cgames_1 A)) => (v2_cgames_1 B)) ) ) ) ).
tt(cc1_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) => (v2_finset_1 B)) ) ) ) ).
tt(cc1_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_chord A)) ) ) ) ) ) ) ).
tt(cc1_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (v3_circcmb3 B A)) )  =>  ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (v2_circcmb3 B A)) ) ) ) ) ) ) ).
tt(cc1_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v3_circcomb A))  =>  ( (~ (v2_struct_0 A))  & (v5_circcomb A)) ) ) ) ).
tt(cc1_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) =>  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) ) ) ) ).
tt(cc1_circuit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  & (v1_finset_1 D)) ) ) ) ) ) ) ).
tt(cc1_classes2,ax, (! [A:$i] :  ((v2_classes1 A) => (v1_classes1 A)) ) ).
tt(cc1_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_clopban1 A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc1_clopban2,ax, (! [A:$i] :  ((l1_clopban2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) & (v5_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_clopban1 A) &  ((v2_cfuncdom A) &  ((v2_clopban2 A) &  ((v3_clopban2 A) & (v4_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v1_clopban3 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v9_clvect_1 B A)) ) ) ) ) ) ) ).
tt(cc1_closure1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ((v4_closure1 C A B) => (v2_closure1 C A B)) ) ) ) ) ).
tt(cc1_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v2_closure2 C A B) => (v1_closure2 C A B)) ) ) ) ) ).
tt(cc1_cohsp_1,ax, (! [A:$i] :  ((v1_cohsp_1 A) =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc1_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_coh_sp A)) =>  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) ) ) ) ).
tt(cc1_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_compact1 B A)) ) ) ) ) ).
tt(cc1_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) => (v1_xcmplx_0 A)) ) ).
tt(cc1_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_compl_sp B A)) ) ) ) ) ).
tt(cc1_compos_0,ax, (! [A:$i] :  ((v1_compos_0 A) => (v1_relat_1 A)) ) ).
tt(cc1_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_zfmisc_1 B) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v4_compos_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_compts_1 B A)) ) ) ) ) ).
tt(cc1_comput_1,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_rfunct_3 C A B) =>  ( (~ (v1_xboole_0 C))  =>  ( (~ (v1_xboole_0 C))  & (v4_funct_1 C)) ) ) ) ) ).
tt(cc1_comseq_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v2_comseq_2 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v1_comseq_2 A)) ) ) ) ) ).
tt(cc1_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v1_series_1 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc1_conlat_1,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v11_struct_0 A) & (l5_struct_0 A)) )  =>  (! [B:$i] :  ((l2_conlat_1 B A) => (v5_conlat_1 B A)) ) ) ) ).
tt(cc1_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) => (v2_connsp_1 B A)) ) ) ) ) ).
tt(cc1_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v1_convex4 B A)) ) ) ) ) ).
tt(cc1_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) => (v1_margrel1 B)) ) ) ) ).
tt(cc1_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_zfmisc_1 B) => (v1_dilworth B A)) ) ) ) ) ).
tt(cc1_dtconstr,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_trees_3 B A))  =>  (! [C:$i] :  ((m1_finseq_1 C B) => (v6_trees_3 C)) ) ) ) ).
tt(cc1_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_dynkin B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v1_matrprob A) =>  ( (~ (v1_xboole_0 A))  & (v4_partfun3 A)) ) ) ) ).
tt(cc1_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_euclid_7,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_euclid_7 A)) ) ).
tt(cc1_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) => (v5_relat_1 B k1_numbers)) ) ) ) ).
tt(cc1_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_euclid A)) => (v3_card_1 B A)) ) ) ) ).
tt(cc1_exchsort,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) ) ) ) ).
tt(cc1_facirc_1,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc1_facirc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v11_struct_0 A) =>  ((v1_circcomb A) &  ((v2_circcomb A) & (v3_circcomb A)) ) ) ) ) ).
tt(cc1_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v3_funct_1 A))  =>  ((v1_funct_1 A) & (v1_fcont_1 A)) ) ) ) ).
tt(cc1_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_xboole_0 A) => (v2_rcomp_1 A)) ) ) ).
tt(cc1_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v1_fdiff_1 A k6_numbers)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc1_fib_num2,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_setfam_1 B)) ) ) ) ).
tt(cc1_filter_0,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v3_filter_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (v3_filter_0 A)) ) ) ) ) ) ).
tt(cc1_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 A))  =>  ((v1_relat_1 A) & (v1_finseq_1 A)) ) ) ).
tt(cc1_finseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_finseq_2 B A)) => (v3_card_1 C B)) ) ) ) ).
tt(cc1_finseq_4,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_eqrel_1 B A) => (v1_finset_1 B)) ) ) ) ).
tt(cc1_finset_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_finset_1 A)) ) ).
tt(cc1_finsub_1,ax, (! [A:$i] :  ((v4_finsub_1 A) =>  ((v1_finsub_1 A) & (v3_finsub_1 A)) ) ) ).
tt(cc1_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v4_fin_topo B A)) ) ) ) ) ).
tt(cc1_fomodel0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v2_setfam_1 A)) ) ).
tt(cc1_fomodel1,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_int_1 A))  =>  ((v7_ordinal1 A) & (v1_int_1 A)) ) ) ).
tt(cc1_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v8_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (! [D:$i] :  ((m1_fomodel2 D A B C) => (v5_relat_1 D B)) ) ) ) ).
tt(cc1_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k8_eqrel_1 A B)) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc1_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_fomodel4 A))) => (v2_fomodel4 B A)) ) ) ) ).
tt(cc1_frechet,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 C A) & (v1_yellow_8 C A B))  =>  ( (~ (v1_xboole_0 C))  &  ((v1_tops_2 C A) & (v1_yellow_8 C A B)) ) ) ) ) ) ) ).
tt(cc1_funcop_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) ) ) ) ) ).
tt(cc1_funct_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_funct_1 A)) ) ).
tt(cc1_funct_2,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_partfun1 C A) => (v1_funct_2 C A B)) ) ) ) ).
tt(cc1_funct_7,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) ) ) ) ).
tt(cc1_funct_8,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v2_funct_8 A)) ) ) ).
tt(cc1_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) ) ) )  =>  (! [F:$i] :  ((m1_functor0 F A B C D E) => (v1_funcop_1 F)) ) ) ) ).
tt(cc1_functor2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v8_functor0 C A B) & (v12_functor0 C A B)) ) ) ) ) ).
tt(cc1_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))) =>  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) & (v1_funct_2 B A k1_numbers)) )  =>  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (v3_valued_0 B)) ) ) ) ) ) ) ) ).
tt(cc1_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))) =>  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) & (v1_funct_2 B A k1_numbers)) )  =>  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) & (v1_funct_2 B A k1_numbers)) ) ) ) ) ) ) ).
tt(cc1_fvaluat1,ax, (! [A:$i] :  ((v1_fvaluat1 A) => (v1_xxreal_0 A)) ) ).
tt(cc1_fvsum_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (v4_rlvect_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v1_algstr_1 A)) ) ) ) ).
tt(cc1_gcd_1,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v3_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v6_vectsp_1 A)) ) ) ) ).
tt(cc1_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v5_glib_000 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v6_glib_000 A)) ) ) ) ) ) ) ).
tt(cc1_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_glib_001 B A) => (v4_glib_001 B A)) ) ) ) ) ).
tt(cc1_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) ) ) ) ).
tt(cc1_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) ) ).
tt(cc1_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m2_glib_000 C A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k21_glib_000 A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)))) => (v1_glib_002 C)) ) ) ) ).
tt(cc1_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) ) ) ) ).
tt(cc1_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ((v1_xboole_0 B) => (v7_graph_1 B A)) ) ) ) ) ).
tt(cc1_graph_2,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v2_finseq_1 C)) ) ) ) ).
tt(cc1_gr_cy_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v1_gr_cy_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v5_group_1 A)) ) ) ) ) ) ).
tt(cc1_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_gr_cy_1 A))) => (v7_ordinal1 B)) ) ) ) ).
tt(cc1_grfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_funct_1 C B)) )  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_funct_1 C A)) ) ) ) ) ) ).
tt(cc1_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_grnilp_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (v1_grnilp_1 B)) ) ) ) ).
tt(cc1_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v2_group_1 A) => (v1_group_1 A)) ) ) ).
tt(cc1_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (v3_group_1 B)) ) ) ) ).
tt(cc1_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_group_6 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) & (v1_group_6 C A B)) ) ) ) ) ) ) ) ).
tt(cc1_group_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_group_7 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) ) ) ) ).
tt(cc1_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_10 B A) & (l3_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v1_groupp_1 C A B)) ) ) ) ).
tt(cc1_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v1_hahnban1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v2_hahnban1 C A B)) ) ) ) ) ) ) ).
tt(cc1_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v2_hahnban B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v1_hahnban B A)) ) ) ) ) ) ) ).
tt(cc1_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_finseq_1 B (k1_zfmisc_1 A)) =>  ( ( (~ (v1_xboole_0 B))  & (v1_hallmar1 B A))  =>  ( (~ (v1_xboole_0 B))  & (v2_relat_1 B)) ) ) ) ) ) ).
tt(cc1_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v1_hermitan B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v2_hahnban1 B k1_complfld A)) ) ) ) ) ) ) ).
tt(cc1_hilbert1,ax, (! [A:$i] :  ((v5_hilbert1 A) =>  ( (~ (v1_xboole_0 A))  &  ((v1_hilbert1 A) &  ((v2_hilbert1 A) &  ((v3_hilbert1 A) & (v4_hilbert1 A)) ) ) ) ) ) ).
tt(cc1_hilbert3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ((m1_subset_1 B k1_hilbert1) &  ((m1_subset_1 C k1_hilbert1) & (m1_subset_1 D k1_hilbert1)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k3_hilbert3 A (k3_hilbert1 B (k3_hilbert1 C D)))) => (v1_funcop_1 E)) ) ) ) ).
tt(cc1_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k14_idea_1) => (v1_finseq_1 A)) ) ).
tt(cc1_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v2_ideal_1 B A))  =>  ( (~ (v1_xboole_0 B))  & (v3_ideal_1 B A)) ) ) ) ) ) ).
tt(cc1_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v15_incsp_1 A) =>  ((v5_incsp_1 A) &  ((v6_incsp_1 A) &  ((v7_incsp_1 A) &  ((v8_incsp_1 A) &  ((v9_incsp_1 A) &  ((v10_incsp_1 A) &  ((v11_incsp_1 A) &  ((v12_incsp_1 A) &  ((v13_incsp_1 A) & (v14_incsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc1_instalg1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_msualg_1 A C (k11_msafree A B))) => (v6_trees_3 D)) ) ) ) ).
tt(cc1_int_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) => (v1_int_1 A)) ) ).
tt(cc1_int_3,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v1_vectsp_2 A) & (v1_int_3 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v1_vectsp_2 A) & (v3_gcd_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_measure5 A) => (v1_rcomp_1 A)) ) ) ).
tt(cc1_intpro_1,ax, (! [A:$i] :  ((v7_intpro_1 A) =>  ( (~ (v1_xboole_0 A))  &  ((v1_intpro_1 A) &  ((v2_intpro_1 A) &  ((v3_intpro_1 A) &  ((v4_intpro_1 A) &  ((v5_intpro_1 A) & (v6_intpro_1 A)) ) ) ) ) ) ) ) ).
tt(cc1_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v1_isomichi B A)) ) ) ) ) ).
tt(cc1_jordan12,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v3_topreal1 A) => (v1_goboard5 A)) ) ) ).
tt(cc1_jordan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v1_convex1 B (k15_euclid A)) => (v2_connsp_1 B (k15_euclid A))) ) ) ) ) ).
tt(cc1_jordan1h,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) & (v5_goboard1 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v2_relat_1 A) &  ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) & (v5_goboard1 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_jordan21 A) =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc1_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_jordan23 A)) ) ) ) ) ).
tt(cc1_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))) & (v1_jordan24 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))) & (v5_pre_topc B (k3_pcomps_1 A) (k3_pcomps_1 A))) ) ) ) ) ) ) ).
tt(cc1_jordan2b,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (v5_relat_1 B k1_numbers)) ) ) ) ).
tt(cc1_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v2_compts_1 B (k15_euclid A)) => (v9_rltopsp1 B (k15_euclid A))) ) ) ) ) ).
tt(cc1_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_finset_1 A) => (v1_rcomp_1 A)) ) ) ).
tt(cc1_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (~ (v1_zfmisc_1 B)) ) ) ) ) ).
tt(cc1_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (v2_sppol_1 A)) )  => (v1_jordan21 A)) ) ) ).
tt(cc1_knaster,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v4_lattice3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v15_lattices A)) ) ) ) ) ).
tt(cc1_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A)))) =>  ( ((v1_funct_1 B) & (v1_funct_2 B k5_numbers (k9_setfam_1 A)))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) & (v1_funct_2 B k5_numbers (k9_setfam_1 A))) ) ) ) ) ) ).
tt(cc1_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v1_lattice2 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (v3_filter_0 A)) ) ) ) ) ) ).
tt(cc1_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lattice3 A) =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc1_lattice6,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v4_lattice3 A)) ) ) ) ) ).
tt(cc1_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  & (v10_lattices A))  =>  ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_lattices A) &  ((v7_lattices A) &  ((v8_lattices A) & (v9_lattices A)) ) ) ) ) ) ) ) ) ).
tt(cc1_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) &  ((v13_glib_000 A) & (v2_lexbfs A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v3_lexbfs A)) ) ) ) ) ) ).
tt(cc1_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_lfuzzy_0 A) =>  ( (~ (v2_struct_0 A))  & (v1_lfuzzy_0 A)) ) ) ) ).
tt(cc1_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))) =>  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) & (v1_funct_2 B A k1_numbers)) )  =>  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (v3_valued_0 B)) ) ) ) ) ) ) ) ).
tt(cc1_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_lopban_1 A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc1_lopban_2,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (v5_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_lopban_1 A) &  ((v2_lopban_2 A) &  ((v3_lopban_2 A) & (v4_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v1_lopban_3 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v3_normsp_1 B A)) ) ) ) ) ) ) ).
tt(cc1_lpspace2,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v1_lpspace2 A))  =>  ((v2_xxreal_0 A) & (v1_xreal_0 A)) ) ) ).
tt(cc1_margrel1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v2_card_3 A)) ) ).
tt(cc1_matrix13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_prvect_1 A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc1_matrix_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_1 C B) =>  ((v2_matrix_1 C B) &  ((v1_matrix_2 C A B) & (v2_matrix_2 C A B)) ) ) ) ) ) ) ).
tt(cc1_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))) =>  ((v2_matrixj1 B A) => (v1_matrixj1 B A)) ) ) ) ) ).
tt(cc1_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))) =>  ((v1_matrixj2 B A) => (v2_matrixj1 B (u1_struct_0 A))) ) ) ) ) ).
tt(cc1_matrlin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B (k3_finseq_2 A)) =>  ((v1_matrix_1 B) =>  ((v1_matrix_1 B) & (v1_pre_poly B)) ) ) ) ) ) ).
tt(cc1_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_pre_topc B A)) ) ) ) ) ).
tt(cc1_matrprob,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) & (v4_matrprob A))  =>  ((v1_matrix_1 A) &  ((v2_matrprob A) & (v3_matrprob A)) ) ) ) ) ).
tt(cc1_matrtop3,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_matrtop3 C B)) ) )  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_matrtop3 C A)) ) ) ) ) ) ) ).
tt(cc1_mcart_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) => (v2_xtuple_0 D)) ) ) ) ).
tt(cc1_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v1_finsub_1 B) & (v1_prob_1 B A))  => (v2_finsub_1 B)) ) ) ) ).
tt(cc1_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_measure5 A) => (v6_xxreal_2 A)) ) ) ).
tt(cc1_measure6,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v6_ordinal1 B) &  ( (~ (v1_xboole_0 B))  & (v1_setfam_1 B)) )  => (v3_finset_1 B)) ) ) ) ).
tt(cc1_membered,ax, (! [A:$i] :  ((v6_membered A) => (v5_membered A)) ) ).
tt(cc1_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc1_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))) =>  ( ((v1_funct_1 B) & (v6_supinf_2 B))  =>  ((v1_funct_1 B) & (v3_mesfunc5 B)) ) ) ) ) ) ).
tt(cc1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) & (v9_metric_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (v11_metric_1 A)) ) ) ) ) ) ) ) ).
tt(cc1_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_metric_2 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) & (v3_pcomps_1 A)) ) ) ) ).
tt(cc1_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v1_mfold_1 B A) => (v3_pre_topc B (k15_euclid A))) ) ) ) ) ).
tt(cc1_midsp_2,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v2_midsp_2 A))  =>  ( (~ (v2_struct_0 A))  & (v12_vectsp_1 A)) ) ) ) ).
tt(cc1_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v2_mod_4 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v13_vectsp_1 C A B) & (v1_mod_4 C A B)) ) ) ) ) ) ) ) ) ).
tt(cc1_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) => (v1_finset_1 A)) ) ).
tt(cc1_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_modcat_1 B (k3_modcat_1 A B))) => (v2_mod_2 C B)) ) ) ) ).
tt(cc1_moebius1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_int_2 A) =>  (~ (v1_moebius1 A)) ) ) ) ).
tt(cc1_monoid_0,ax, (! [A:$i] :  ( ((v1_monoid_0 A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(cc1_msafree1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v3_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_prob_2 B)) ) ) ) ) ) ) ).
tt(cc1_msafree2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v11_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v2_msafree2 A)) ) ) ) ).
tt(cc1_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc1_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_msaterm A B)) => (v1_finset_1 C)) ) ) ) ).
tt(cc1_msscyc_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v11_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v2_msscyc_1 A)) ) ) ) ).
tt(cc1_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v3_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) ) ) ) ) ).
tt(cc1_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k10_xtuple_0 (u3_msualg_1 A B))) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc1_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m1_msualg_4 D A B C) => (v2_funcop_1 D)) ) ) ) ).
tt(cc1_msualg_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v2_msualg_4 C A B) => (v1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ) ).
tt(cc1_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v4_msualg_1 B A) => (v1_msualg_6 B A)) ) ) ) ) ).
tt(cc1_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v1_msualg_7 B A) => (v4_lattice3 B)) ) ) ) ) ).
tt(cc1_msualg_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_subset_1 C (u4_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_msualg_1 A C B)) => (v1_finseq_1 D)) ) ) ) ).
tt(cc1_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v8_struct_0 A) => (v1_mycielsk A)) ) ) ).
tt(cc1_nagata_1,ax, (! [A:$i] :  ( (~ (v4_card_3 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc1_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v3_ordinal1 A) & (v7_ordinal1 A)) ) ) ).
tt(cc1_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 A) & (v1_int_2 A)) ) ) ) ).
tt(cc1_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xreal_0 B)) ) ) ) ).
tt(cc1_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) => (v3_card_1 B (k3_finseq_1 A))) ) ) ) ).
tt(cc1_neckla_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k4_classes1 A)) => (v1_finset_1 B)) ) ) ) ).
tt(cc1_neckla_3,ax, (! [A:$i,B:$i] :  ( ((v1_zfmisc_1 A) & (v1_zfmisc_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v1_zfmisc_1 C)) ) ) ) ).
tt(cc1_necklace,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_zfmisc_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) ) ) ) ).
tt(cc1_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) & (v3_funct_1 B))  =>  ((v1_funct_1 B) & (v1_nfcont_3 B A)) ) ) ) ) ) ).
tt(cc1_nfcont_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))) =>  ( ((v1_funct_1 B) & (v3_funct_1 B))  =>  ((v1_funct_1 B) & (v1_nfcont_4 B A)) ) ) ) ) ) ).
tt(cc1_openlatt,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (v1_lattice2 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (v3_filter_0 A)) ) ) ) ) ) ).
tt(cc1_oposet_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_oposet_1 A))  =>  ( (~ (v2_struct_0 A))  & (v3_oposet_1 A)) ) ) ) ).
tt(cc1_orders_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) &  ((v2_wellord1 A) &  ((v1_orders_1 A) &  ((v2_orders_1 A) & (v3_orders_1 A)) ) ) ) ) ) ).
tt(cc1_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_orders_2 A) => (v2_orders_2 A)) ) ) ).
tt(cc1_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v1_orders_3 A)) ) ) ).
tt(cc1_orders_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ).
tt(cc1_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_ordinal1 A) & (v2_ordinal1 A)) ) ) ).
tt(cc1_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) ) )  =>  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) ) ) ) ) ) ) ).
tt(cc1_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A)))) =>  ( ((v1_funct_1 B) & (v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)))  =>  ((v5_ordinal1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (v1_ordinal2 B)) ) ) ) ) ) ) ) ).
tt(cc1_ordinal5,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 A) & (v1_ordinal2 A)) ) ) ).
tt(cc1_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_ordinal6 A)) ) ).
tt(cc1_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ((v4_osalg_1 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ).
tt(cc1_osalg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  ((v12_osalg_1 C A) =>  ((v12_osalg_1 C A) & (v13_osalg_1 C A)) ) ) ) ) ) ).
tt(cc1_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) ) )  =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) B C) =>  ((v1_osalg_4 D A B C) => (v11_osalg_1 D A)) ) ) ) ) ).
tt(cc1_partfun1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v1_partfun1 C A)) ) ) ) ).
tt(cc1_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_partfun3 A))  =>  ((v1_relat_1 A) &  ((v2_relat_1 A) & (v4_partfun3 A)) ) ) ) ).
tt(cc1_partit_2,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) &  ((v2_relat_2 A) &  ((v5_relat_2 A) & (v8_relat_2 A)) ) ) ) ) ).
tt(cc1_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc1_pcs_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v2_orders_2 A)) ) ) ).
tt(cc1_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v2_fdiff_1 A))  =>  ((v1_funct_1 A) &  ((v1_partfun1 A k1_numbers) & (v2_fdiff_1 A)) ) ) ) ) ).
tt(cc1_pdiff_6,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 C B A) & (v2_pdiff_6 C B A)) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 C B A) &  ((v2_pdiff_6 C B A) & (v3_pdiff_6 C A B)) ) ) ) ) ) ) ) ) ).
tt(cc1_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v11_pencil_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) ) ) ) ).
tt(cc1_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v2_finseq_1 A)) ) ) ) ) ).
tt(cc1_polynom1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_struct_0 A) &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_polynom4,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (v1_algstr_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v1_vectsp_2 A) & (v1_algstr_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_polynom8,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v1_vectsp_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_poset_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_poset_1 A) => (v1_yellow_0 A)) ) ) ).
tt(cc1_pralg_2,ax, (! [A:$i] :  ( ((v4_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v2_card_3 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v4_relat_1 B (k9_card_3 A))) ) ) ) ).
tt(cc1_pre_circ,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_trees_3 A)) => (v1_finset_1 B)) ) ) ) ).
tt(cc1_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_finseq_2 A)) => (v1_finseq_1 B)) ) ) ).
tt(cc1_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v2_pre_topc B)) ) ) ) ).
tt(cc1_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) & (v4_prob_1 B A)) )  =>  ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (v4_prob_1 B A)) ) ) ) ) ) ) ).
tt(cc1_projdes1,ax, (! [A:$i] :  ((l1_collsp A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  (~ (v7_anproj_2 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v5_anproj_2 A) &  (~ (v7_anproj_2 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) => (v1_finseq_1 B)) ) ) ) ).
tt(cc1_prvect_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [C:$i] :  ((m1_prvect_2 C A B) => (v1_finseq_1 C)) ) ) ) ).
tt(cc1_pscomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_compts_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_pscomp_1 A)) ) ) ) ) ).
tt(cc1_pua2mss1,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  (! [B:$i] :  ((m1_finseq_1 B A) => (v2_relat_1 B)) ) ) ) ).
tt(cc1_pythtrip,ax, (! [A:$i] :  ((v1_pythtrip A) => (v7_ordinal1 A)) ) ).
tt(cc1_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v1_relat_1 A) &  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc1_quantal1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v6_quantal1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v4_quantal1 A) & (v5_quantal1 A)) ) ) ) ) ).
tt(cc1_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k15_quatern2)) => (v1_quaterni A)) ) ).
tt(cc1_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_quaterni) => (v1_quaterni A)) ) ).
tt(cc1_quofield,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (v5_vectsp_1 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (v1_vectsp_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (v1_xreal_0 A)) ) ).
tt(cc1_ratfunc1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v1_vectsp_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v30_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) ).
tt(cc1_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_rcomp_1 A) => (v2_rcomp_1 A)) ) ) ).
tt(cc1_rcomp_3,ax, (! [A:$i] :  ((m1_topmetr A k8_metric_1) => (v3_topmetr A)) ) ).
tt(cc1_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (v1_xreal_0 A)) ) ).
tt(cc1_realset2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (v5_vectsp_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v6_struct_0 A))  & (v1_realset2 A)) ) ) ) ).
tt(cc1_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_relat_1 A)) ) ).
tt(cc1_relat_2,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) &  ((v1_relat_2 A) &  ((v2_relat_2 A) &  ((v3_relat_2 A) &  ((v4_relat_2 A) &  ((v5_relat_2 A) &  ((v6_relat_2 A) &  ((v7_relat_2 A) & (v8_relat_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_relset_1,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v1_relat_1 C)) ) ) ).
tt(cc1_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_rewrite1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_rewrite2,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_rewrite2 A)) ) ) ) ).
tt(cc1_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_funct_1 A) & (v3_valued_0 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_comseq_2 A)) ) ) ) ) ).
tt(cc1_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v7_valued_0 A))  =>  ((v1_funct_1 A) & (v1_rfunct_2 A)) ) ) ) ).
tt(cc1_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered B))  =>  (! [C:$i] :  ((m1_subset_1 C (k3_rfunct_3 A B)) => (v3_valued_0 C)) ) ) ) ).
tt(cc1_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_ring_1 B A) =>  ((v1_subset_1 B (u1_struct_0 A)) & (v1_ring_1 B A)) ) ) ) ) ) ).
tt(cc1_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_ringcat1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v1_group_6 C A B) & (v13_vectsp_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(cc1_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v1_rlaffin1 B A)) ) ) ) ) ).
tt(cc1_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) =>  ((v1_finset_1 B) & (v1_rlaffin1 B A)) ) ) ) ) ) ).
tt(cc1_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_rltopsp1 B A)) ) ) ) ) ).
tt(cc1_rlvect_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v9_rlvect_1 A))  =>  ( (~ (v2_struct_0 A))  & (v4_rlvect_1 A)) ) ) ) ).
tt(cc1_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (v1_rlvect_5 B)) ) ) ) ).
tt(cc1_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (v7_robbins1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v14_lattices A)) ) ) ) ).
tt(cc1_robbins2,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_robbins2 A))  =>  ( (~ (v2_struct_0 A))  & (v4_lattices A)) ) ) ) ).
tt(cc1_robbins3,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  & (v10_lattices A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_robbins3 A) &  ((v2_robbins3 A) & (v3_robbins3 A)) ) ) ) ) ) ).
tt(cc1_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) & (v3_robbins3 A)) ) ) ) ).
tt(cc1_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v3_card_1 B 1) =>  ((v1_finset_1 B) & (v3_card_1 B 1)) ) ) ) ) ) ).
tt(cc1_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (v1_rusub_4 B)) ) ) ) ).
tt(cc1_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (v1_valued_0 A)) ) ).
tt(cc1_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v6_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(cc1_scmfsa7b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v6_amistd_1 A 3 k1_scmfsa_2) & (v1_scmfsa7b A)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa6b A)) ) ) ) ) ) ) ) ) ).
tt(cc1_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v6_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc1_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scmpds_4 A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmpds_4 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_scmyciel,ax, (! [A:$i] :  ((v1_scmyciel A) => (v1_finset_1 A)) ) ).
tt(cc1_seq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_comseq_2 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) &  ((v1_seq_2 A) & (v2_seq_2 A)) ) ) ) ) ) ).
tt(cc1_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v3_funct_1 A) & (v1_funct_2 A k5_numbers k1_numbers)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc1_seqm_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v3_funct_1 A))  =>  ((v1_funct_1 A) &  ((v7_valued_0 A) & (v8_valued_0 A)) ) ) ) ) ).
tt(cc1_series_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_series_1 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v1_series_1 A)) ) ) ) ) ).
tt(cc1_setfam_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_sheffer1,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v17_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) & (v4_sheffer1 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_sheffer2,ax, (! [A:$i] :  ((l1_sheffer1 A) =>  ( ( (~ (v2_struct_0 A))  & (v7_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v1_sheffer2 A)) ) ) ) ).
tt(cc1_simplex0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_classes1 A)) ) ).
tt(cc1_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v4_simplex0 B))  & (m1_simplex0 B (u1_struct_0 A))) )  =>  (! [C:$i] :  ((m1_simplex1 C A B) =>  (~ (v4_simplex0 C)) ) ) ) ) ).
tt(cc1_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v6_tbsp_1 B A)) ) ) ) ) ).
tt(cc1_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (~ (v1_zfmisc_1 A))  & (v1_sppol_1 A))  =>  (~ (v2_sppol_1 A)) ) ) ) ).
tt(cc1_sppol_2,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) =>  ( (~ (v1_zfmisc_1 A))  &  ((v2_funct_1 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) & (v3_topreal1 A)) ) ) ) ) ) ) ).
tt(cc1_sprect_1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_sprect_1 A) =>  (~ (v3_funct_1 A)) ) ) ) ).
tt(cc1_sprect_3,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) & (v1_sprect_1 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (v1_sprect_2 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k8_stacks_1 A))) => (v1_finseq_1 B)) ) ) ) ).
tt(cc1_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v7_ordinal1 B)) ) ) ) ).
tt(cc1_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_struct_0 A) => (v7_struct_0 A)) ) ) ).
tt(cc1_subset_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_xboole_0 B)) ) ) ) ).
tt(cc1_substlat,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_substlat A B)) => (v1_finset_1 C)) ) ) ).
tt(cc1_supinf_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k7_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (v3_supinf_2 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v1_supinf_2 C A B) & (v2_supinf_2 C A B)) ) ) ) ) ) ) ) ).
tt(cc1_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v2_tbsp_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v3_tbsp_1 B A)) ) ) ) ) ) ) ).
tt(cc1_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_tdlat_3 A) => (v2_pre_topc A)) ) ) ).
tt(cc1_termord,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A)))) =>  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (v2_bagorder B A)) ) ) )  =>  ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_wellord1 B) & (v2_bagorder B A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_tex_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v13_struct_0 A 1) & (v2_pre_topc A))  =>  ((v13_struct_0 A 1) &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (v2_tdlat_3 A)) ) ) ) ) ) ).
tt(cc1_tex_2,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_subset_1 B A) => (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) & (v1_tex_3 B A))  =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc1_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_4 B A) => (v2_tdlat_3 B)) ) ) ) ) ).
tt(cc1_toler_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 A))  =>  ((v1_relat_1 A) &  ((v1_relat_2 A) &  ((v2_relat_2 A) &  ((v3_relat_2 A) &  ((v4_relat_2 A) &  ((v5_relat_2 A) &  ((v6_relat_2 A) &  ((v7_relat_2 A) & (v8_relat_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc1_topalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((m1_borsuk_2 D (k15_euclid A) B C) & (m1_borsuk_2 E (k15_euclid A) B C)) ) ) )  =>  (! [F:$i] :  ((m1_borsuk_6 F (k15_euclid A) B C D E) => (v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) (k15_euclid A))) ) ) ) ).
tt(cc1_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_pre_topc B (k15_euclid A)) =>  ( ( (~ (v2_struct_0 B))  & (v1_topalg_2 B A))  =>  ( (~ (v2_struct_0 B))  & (v1_borsuk_2 B)) ) ) ) ) ) ).
tt(cc1_topalg_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_struct_0 A) => (v1_connsp_1 A)) ) ) ).
tt(cc1_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v3_funct_1 C) & (v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(cc1_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v1_topdim_1 B A)) ) ) ) ) ).
tt(cc1_topdim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_finset_1 B) => (v1_topdim_2 B A)) ) ) ) ).
tt(cc1_topgen_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v8_struct_0 A) => (v1_orders_4 A)) ) ) ).
tt(cc1_topgen_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_struct_0 A) => (v1_topgen_2 A)) ) ) ).
tt(cc1_topgen_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_struct_0 A) => (v5_waybel23 A)) ) ) ).
tt(cc1_topgen_5,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v1_topgen_5 A))  =>  ((v2_pre_topc A) & (v9_pre_topc A)) ) ) ) ).
tt(cc1_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_connsp_2 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc1_topmetr,ax, (! [A:$i] :  ( ((v3_topmetr A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v3_topmetr B)) ) ) ) ).
tt(cc1_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v5_topreal1 A) =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc1_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ( (~ (v1_xboole_0 A))  & (v2_compts_1 A (k15_euclid 2))) ) ) ) ).
tt(cc1_topreal5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ((v1_topreal2 A) &  ( (~ (v1_sppol_1 A))  &  (~ (v2_sppol_1 A)) ) ) ) ) ) ).
tt(cc1_topreal6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_connsp_1 B A)) ) ) ) ) ).
tt(cc1_topreala,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v2_monoid_0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v2_monoid_0 B)) ) ) ) ).
tt(cc1_toprealb,ax, (! [A:$i] :  ((m1_pre_topc A (k15_euclid 2)) =>  ((v1_toprealb A) =>  ( (~ (v2_struct_0 A))  &  ((v1_compts_1 A) & (v1_borsuk_2 A)) ) ) ) ) ).
tt(cc1_toprealc,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_toprealc A) => (v1_toprealc A)) ) ) ).
tt(cc1_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_pre_topc B A)) ) ) ) ) ).
tt(cc1_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m4_trees_1 B A) => (v1_finset_1 B)) ) ) ) ).
tt(cc1_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) =>  ((v2_trees_2 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc1_trees_3,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_trees_3 A) &  ((v2_trees_3 A) & (v3_trees_3 A)) ) ) ) ).
tt(cc1_trees_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_finseq_1 C B) => (v6_trees_3 C)) ) ) ) ).
tt(cc1_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_2 A)) ) ) ) ).
tt(cc1_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  & (v7_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v6_pre_topc A)) ) ) ) ).
tt(cc1_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v2_tsp_2 B A))  =>  ( (~ (v2_struct_0 B))  & (v6_pre_topc B)) ) ) ) ) ) ).
tt(cc1_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) => (v2_unialg_2 B)) ) ) ) ).
tt(cc1_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  ((v1_relat_1 A) & (v5_relat_1 A k4_numbers)) ) ) ).
tt(cc1_valued_2,ax, (! [A:$i] :  ((v6_valued_2 A) => (v5_valued_2 A)) ) ).
tt(cc1_vectsp10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v13_vectsp_1 C B A)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v2_hahnban1 C A B)) ) ) ) ) ) ) ).
tt(cc1_vectsp_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v5_vectsp_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (v2_vectsp_1 A)) ) ) ) ) ).
tt(cc1_vectsp_2,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v6_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v4_vectsp_1 A)) ) ) ) ).
tt(cc1_vectsp_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_xboole_0 C) => (v1_vectsp_7 C A B)) ) ) ) ) ).
tt(cc1_vectsp_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (v1_matrlin C A)) ) ) ) ).
tt(cc1_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v1_waybel_0 B A) & (v2_waybel_0 B A)) ) ) ) ) ) ).
tt(cc1_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v6_waybel_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v11_quantal1 B) & (v5_orders_3 B A A)) ) ) ) ) ) ) ) ).
tt(cc1_waybel11,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v1_finset_1 B)) ) ) ) ).
tt(cc1_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v12_waybel_0 B A) & (v1_waybel_6 B A))  => (v2_waybel_0 B A)) ) ) ) ) ).
tt(cc1_waybel13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v23_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (v18_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(cc1_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel15 B A) => (v6_waybel_6 B A)) ) ) ) ) ).
tt(cc1_waybel17,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v22_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(cc1_waybel18,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_waybel18 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) ) ) ) ).
tt(cc1_waybel19,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v3_orders_2 A)) )  =>  ((v13_struct_0 A 1) &  ((v2_pre_topc A) &  ((v3_orders_2 A) & (v1_waybel19 A)) ) ) ) ) ) ).
tt(cc1_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v4_waybel_1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v17_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(cc1_waybel21,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v19_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(cc1_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k8_waybel_0 A)))) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc1_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel23 B A) => (v1_waybel23 B A)) ) ) ) ) ).
tt(cc1_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v3_funct_1 C) & (v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(cc1_waybel25,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v4_waybel11 A)) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ) ) ) ) ).
tt(cc1_waybel26,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) => (v1_relat_1 C)) ) ) ) ).
tt(cc1_waybel27,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_waybel27 A) &  ((v2_waybel27 A) & (v3_waybel27 A)) ) ) ) ) ) ).
tt(cc1_waybel29,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_waybel11 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_lattice3 A)) ) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v2_waybel18 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_lattice3 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc1_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v16_waybel_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ).
tt(cc1_waybel30,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v7_struct_0 B)) ) ) ) ).
tt(cc1_waybel31,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_8 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ) ) ) ).
tt(cc1_waybel32,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v3_orders_2 A)) )  =>  ((v13_struct_0 A 1) &  ((v2_pre_topc A) &  ((v3_orders_2 A) & (v1_waybel32 A)) ) ) ) ) ) ).
tt(cc1_waybel33,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_waybel33 A))  =>  ( (~ (v2_struct_0 A))  & (v2_pre_topc A)) ) ) ) ).
tt(cc1_waybel34,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v18_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_waybel34 C A B)) ) ) ) ) ) ) ).
tt(cc1_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v1_waybel35 B A) =>  ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (v4_waybel_4 B A)) ) ) ) ) ) ) ).
tt(cc1_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel_0 B A) & (v2_waybel_0 B A)) ) ) ) ) ).
tt(cc1_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v5_waybel_4 B A) =>  ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) & (v4_waybel_4 B A)) ) ) ) ) ) ) ) ).
tt(cc1_waybel_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A C (k7_funcop_1 A B)) => (v2_relat_1 D)) ) ) ) ).
tt(cc1_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_orders_2 B A) =>  ((v6_orders_2 B A) &  ((v1_waybel_0 B A) & (v2_waybel_0 B A)) ) ) ) ) ) ) ).
tt(cc1_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (v3_waybel_7 B A)) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 A)) &  ((v2_waybel_0 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ) ) ).
tt(cc1_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v2_waybel_8 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) ) ) ) ).
tt(cc1_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v8_pre_topc B)) ) ) ) ) ) ).
tt(cc1_wellord1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_wellord1 A))  =>  ((v1_relat_1 A) &  ((v1_relat_2 A) &  ((v4_relat_2 A) &  ((v6_relat_2 A) &  ((v8_relat_2 A) & (v1_wellord1 A)) ) ) ) ) ) ) ).
tt(cc1_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) => (v7_ordinal1 A)) ) ).
tt(cc1_xcmplx_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (v1_xcmplx_0 A)) ) ).
tt(cc1_xreal_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (v1_xreal_0 A)) ) ).
tt(cc1_xreal_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (v1_xxreal_0 A)) ) ).
tt(cc1_xtuple_0,ax, (! [A:$i] :  ((v2_xtuple_0 A) => (v1_xtuple_0 A)) ) ).
tt(cc1_xxreal_0,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (v1_xxreal_0 A)) ) ).
tt(cc1_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  ( (~ (v3_xxreal_0 A))  &  (~ (v1_xreal_0 A)) ) )  =>  ((v1_xxreal_0 A) & (v2_xxreal_0 A)) ) ) ).
tt(cc1_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v3_lattice3 A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ).
tt(cc1_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v1_waybel_6 B A)) ) ) ) ) ).
tt(cc1_yellow11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (v2_waybel_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (v1_yellow11 A)) ) ) ) ) ) ) ).
tt(cc1_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_cantor_1 B A))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_tops_2 B A) & (v1_cantor_1 B A)) ) ) ) ) ) ) ).
tt(cc1_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v4_pre_topc B A)) ) ) ) ) ).
tt(cc1_yellow14,ax, (! [A:$i] :  ( ((v1_monoid_0 A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) => (v1_yellow14 B A)) ) ) ) ).
tt(cc1_yellow15,ax, (! [A:$i] :  ((m1_finseq_1 A k6_margrel1) => (v1_margrel1 A)) ) ).
tt(cc1_yellow16,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_yellow16 A))  =>  ((v1_relat_1 A) &  ((v1_yellow_1 A) & (v5_waybel_3 A)) ) ) ) ).
tt(cc1_yellow18,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v8_altcat_1 A) &  ((v11_altcat_1 A) & (v12_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v2_yellow18 A)) ) ) ) ) ) ) ).
tt(cc1_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_yellow19 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc1_yellow_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_yellow_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) ) ) ) ).
tt(cc1_yellow21,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v3_yellow21 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v2_yellow21 A)) ) ) ) ) ) ) ).
tt(cc1_yellow_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v24_waybel_0 A) & (v25_waybel_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v3_lattice3 A)) ) ) ) ) ) ) ).
tt(cc1_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v1_yellow_3 A)) ) ) ).
tt(cc1_yellow_6,ax, (! [A:$i,B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((m3_yellow_6 C A B) => (v1_yellow_1 C)) ) ) ) ).
tt(cc1_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_waybel_5 A))  =>  ( (~ (v2_struct_0 A))  & (v3_lattice3 A)) ) ) ) ).
tt(cc1_yellow_8,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_yellow_8 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc1_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc1_zfmisc_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_zfmisc_1 A)) ) ).
tt(cc20_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v25_algstr_0 B A) =>  ((v23_algstr_0 B A) & (v24_algstr_0 B A)) ) ) ) ) ) ).
tt(cc20_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v14_fomodel1 B k6_numbers A) => (v3_card_1 B 1)) ) ) ) ) ).
tt(cc20_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel1 B)) =>  ((v7_fomodel2 D C B) => (v7_fomodel2 D A B)) ) ) ) ) ).
tt(cc20_membered,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_membered B)) ) ) ) ).
tt(cc20_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v1_monoid_0 B)) ) ) ) ) ) ).
tt(cc20_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v8_lattices B)) ) ) ) ).
tt(cc20_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tdlat_3 B) => (v3_tdlat_3 B)) ) ) ) ) ).
tt(cc20_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v3_tex_3 B A) &  (~ (v4_tex_3 B A)) )  =>  (~ (v1_borsuk_1 B A)) ) ) ) ) ) ).
tt(cc20_valued_0,ax, (! [A:$i,B:$i] :  ((v5_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v5_relat_1 C k4_numbers)) ) ) ) ).
tt(cc20_valued_2,ax, (! [A:$i] :  ((v6_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v4_valued_0 B)) ) ) ) ).
tt(cc21_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ((v26_algstr_0 A) & (v27_algstr_0 A))  => (v28_algstr_0 A)) ) ) ).
tt(cc21_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k32_fomodel1 A)) => (v15_fomodel1 B A)) ) ) ) ).
tt(cc21_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel1 C)) =>  ( (~ (v7_fomodel2 D (k13_fomodel0 B A) C))  =>  (~ (v7_fomodel2 D (k3_xboole_0 A B) C)) ) ) ) ) ) ).
tt(cc21_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v3_membered B)) ) ) ) ).
tt(cc21_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v1_monoid_0 B)) ) ) ) ) ) ).
tt(cc21_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_lattices A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v9_lattices B)) ) ) ) ).
tt(cc21_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v3_tdlat_3 B))  =>  (~ (v2_tdlat_3 B)) ) ) ) ) ) ).
tt(cc21_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) &  (~ (v4_tex_3 B A)) )  =>  (~ (v3_tex_3 B A)) ) ) ) ) ) ).
tt(cc21_valued_0,ax, (! [A:$i,B:$i] :  ((v6_membered B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v4_valued_0 C)) ) ) ) ).
tt(cc21_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v7_valued_2 B)) ) ) ) ) ) ) ).
tt(cc22_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ((v28_algstr_0 A) =>  ((v26_algstr_0 A) & (v27_algstr_0 A)) ) ) ) ).
tt(cc22_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k35_fomodel1 A)) => (v13_fomodel1 B A)) ) ) ) ).
tt(cc22_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel1 C)) =>  ( ( (~ (v7_fomodel2 D A C))  &  (~ (v7_fomodel2 D B C)) )  =>  ( (~ (v7_fomodel2 D A C))  &  (~ (v7_fomodel2 D (k2_xboole_0 B A) C)) ) ) ) ) ) ) ).
tt(cc22_membered,ax, (! [A:$i] :  ((v4_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v4_membered B)) ) ) ) ).
tt(cc22_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v2_monoid_0 B)) ) ) ) ) ) ).
tt(cc22_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_robbins3 A) & (l4_robbins1 A)) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v9_robbins3 B)) ) ) ) ).
tt(cc22_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v1_tdlat_3 B) & (v2_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(cc22_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  &  (~ (v3_tex_3 B A)) ) ) ) ) ) ) ).
tt(cc22_valued_0,ax, (! [A:$i] :  ( ((v1_zfmisc_1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) &  ((v5_valued_0 A) & (v6_valued_0 A)) ) ) ) ) ) ).
tt(cc22_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v12_valued_2 A))  =>  ((v1_relat_1 A) & (v11_valued_2 A)) ) ) ).
tt(cc23_algstr_0,ax, (! [A:$i] :  ( ((v26_algstr_0 A) & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v23_algstr_0 B A)) ) ) ) ).
tt(cc23_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ( ( (~ (v7_fomodel1 B A))  & (v10_fomodel1 B A))  =>  ((v8_fomodel1 B A) & (v10_fomodel1 B A)) ) ) ) ) ) ).
tt(cc23_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v6_fomodel2 B A) => (v9_fomodel2 B A)) ) ) ) ).
tt(cc23_membered,ax, (! [A:$i] :  ((v5_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v5_membered B)) ) ) ) ).
tt(cc23_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v2_monoid_0 B)) ) ) ) ) ) ).
tt(cc23_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (v10_robbins3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v3_orders_2 A)) ) ) ) ).
tt(cc23_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  & (v2_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc23_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_2 B A) =>  (~ (v1_tex_3 B A)) ) ) ) ) ) ).
tt(cc23_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v5_valued_0 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v7_valued_0 A)) ) ) ) ) ).
tt(cc23_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v11_valued_2 A))  =>  ((v1_relat_1 A) & (v10_valued_2 A)) ) ) ).
tt(cc24_algstr_0,ax, (! [A:$i] :  ( ((v27_algstr_0 A) & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v24_algstr_0 B A)) ) ) ) ).
tt(cc24_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ( ( (~ (v4_fomodel1 B A))  & (v8_fomodel1 B A))  =>  ((v6_fomodel1 B A) & (v8_fomodel1 B A)) ) ) ) ) ) ).
tt(cc24_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k43_fomodel2 A)) =>  ((v4_fomodel2 B A) & (v5_fomodel2 B A)) ) ) ) ) ).
tt(cc24_membered,ax, (! [A:$i] :  ((v6_membered A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v6_membered B)) ) ) ) ).
tt(cc24_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v4_vectsp_1 B)) ) ) ) ) ) ).
tt(cc24_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) & (v10_robbins3 A)) )  =>  ( (~ (v2_struct_0 A))  & (v4_orders_2 A)) ) ) ) ).
tt(cc24_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  & (v1_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v2_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc24_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_3 B A) =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc24_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v6_valued_0 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v8_valued_0 A)) ) ) ) ) ).
tt(cc24_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v10_valued_2 A))  =>  ((v1_relat_1 A) & (v9_valued_2 A)) ) ) ).
tt(cc25_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ( ((v30_algstr_0 A) & (v31_algstr_0 A))  => (v32_algstr_0 A)) ) ) ).
tt(cc25_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k16_fomodel1 A)) => (v4_fomodel1 B A)) ) ) ) ).
tt(cc25_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k43_fomodel2 A)) => (v4_fomodel2 B A)) ) ) ) ).
tt(cc25_membered,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v6_membered A)) ) ).
tt(cc25_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v5_group_1 B)) ) ) ) ) ) ).
tt(cc25_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (v10_robbins3 A)) )  =>  ( (~ (v2_struct_0 A))  & (v5_orders_2 A)) ) ) ) ).
tt(cc25_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v7_struct_0 B) & (v2_pre_topc B)) )  =>  ( (~ (v2_struct_0 B))  &  ((v1_tdlat_3 B) & (v2_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc25_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  &  (~ (v4_tex_3 B A)) ) ) ) ) ) ) ).
tt(cc25_valued_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m1_valued_0 C B) => (v5_relat_1 C A)) ) ) ) ).
tt(cc25_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v9_valued_2 A))  =>  ((v1_relat_1 A) & (v8_valued_2 A)) ) ) ).
tt(cc26_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((v32_algstr_0 A) =>  ((v30_algstr_0 A) & (v31_algstr_0 A)) ) ) ) ).
tt(cc26_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v14_fomodel1 D (k2_xcmplx_0 B (k3_xcmplx_0 k6_numbers C)) A) => (v14_fomodel1 D (k2_xcmplx_0 B C) A)) ) ) ) ) ).
tt(cc26_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k43_fomodel2 A)) => (v5_fomodel2 B A)) ) ) ) ).
tt(cc26_membered,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v7_membered A)) ) ).
tt(cc26_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v5_group_1 B)) ) ) ) ) ) ).
tt(cc26_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v8_robbins3 B)) ) ) ) ).
tt(cc26_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tex_2 B A))  =>  ((v1_borsuk_1 B A) & (v1_tsep_1 B A)) ) ) ) ) ) ).
tt(cc26_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_2 B A) =>  (~ (v2_tex_3 B A)) ) ) ) ) ) ).
tt(cc26_valued_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v3_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  (! [C:$i] :  ((m1_valued_0 C B) => (v3_funct_1 C)) ) ) ) ).
tt(cc26_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v9_valued_2 A))  =>  ((v1_relat_1 A) & (v7_valued_2 A)) ) ) ).
tt(cc27_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ( ( (~ (v5_fomodel1 B A))  & (v9_fomodel1 B A))  =>  ((v4_fomodel1 B A) & (v9_fomodel1 B A)) ) ) ) ) ) ).
tt(cc27_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) &  ((v16_fomodel1 C B) & (l1_fomodel1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D C A)) )  =>  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D B A)) ) ) ) ) ) ).
tt(cc27_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v3_group_1 B)) ) ) ) ) ) ).
tt(cc27_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_robbins3 B A) => (v10_robbins1 B)) ) ) ) ).
tt(cc27_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tsep_1 B A))  => (v1_tex_2 B A)) ) ) ) ) ).
tt(cc27_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tex_3 B A) =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc27_valued_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_setfam_1 A))  &  ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  (! [C:$i] :  ((m1_valued_0 C B) => (v2_relat_1 C)) ) ) ) ).
tt(cc27_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 A))  =>  ((v1_relat_1 A) & (v12_valued_2 A)) ) ) ).
tt(cc28_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v13_fomodel1 B A) => (v5_relat_1 B (k5_fomodel1 A))) ) ) ) ) ).
tt(cc28_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k16_fomodel2 B A)) & (v10_fomodel2 D A B C)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 D)) => (v10_fomodel2 E A B C)) ) ) ) ).
tt(cc28_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v3_group_1 B)) ) ) ) ) ) ).
tt(cc28_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_borsuk_1 B A))  => (v1_tex_2 B A)) ) ) ) ) ).
tt(cc28_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v3_tex_3 B A))  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_borsuk_1 B A)) ) ) ) ) ) ) ).
tt(cc28_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k2_numbers))  =>  ((v1_relat_1 A) & (v1_valued_0 A)) ) ) ).
tt(cc28_valued_2,ax, (! [A:$i,B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v7_valued_2 C)) ) ) ) ) ) ).
tt(cc29_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v15_fomodel1 B A) => (v5_relat_1 B (k17_fomodel1 A))) ) ) ) ) ).
tt(cc29_robbins3,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (v8_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) ) ) ) ).
tt(cc29_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v2_tdlat_3 B))  =>  ( (~ (v2_struct_0 B))  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(cc29_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_borsuk_1 B A))  =>  ( (~ (v2_struct_0 B))  &  (~ (v3_tex_3 B A)) ) ) ) ) ) ) ).
tt(cc29_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k7_numbers))  =>  ((v1_relat_1 A) & (v2_valued_0 A)) ) ) ).
tt(cc29_valued_2,ax, (! [A:$i,B:$i] :  ((v2_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v8_valued_2 C)) ) ) ) ) ) ).
tt(cc2_abcmiz_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) & (v1_abcmiz_0 A)) ) ) ) ).
tt(cc2_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_finseq_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) => (v6_trees_3 C)) ) ) ) ).
tt(cc2_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) => (v1_xtuple_0 A)) ) ).
tt(cc2_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  ( (~ (v1_xboole_0 A))  & (v1_int_1 A)) ) ) ).
tt(cc2_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_card_1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) ) ) ) ) ).
tt(cc2_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  ((v1_relat_1 A) & (v4_partfun3 A)) ) ) ).
tt(cc2_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m2_algspec1 B A) =>  (~ (v11_struct_0 B)) ) ) ) ) ).
tt(cc2_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_algstr_0 B A) =>  ((v2_algstr_0 B A) & (v3_algstr_0 B A)) ) ) ) ) ) ).
tt(cc2_algstr_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v6_algstr_0 A) &  ((v2_algstr_1 A) & (v3_algstr_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v4_algstr_1 A)) ) ) ) ).
tt(cc2_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v10_altcat_1 A) & (v12_altcat_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v8_altcat_1 A) & (v9_altcat_1 A)) ) ) ) ) ).
tt(cc2_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  & (v2_altcat_2 B A))  => (v2_altcat_1 B)) ) ) ) ) ).
tt(cc2_amistd_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) =>  (~ (v2_extpro_1 C A B)) ) ) ) ) ) ).
tt(cc2_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v4_compos_0 C (u1_compos_1 B))) ) ) ) ) ).
tt(cc2_amistd_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (v1_amistd_5 C A B)) ) ) ) ).
tt(cc2_ami_wstd,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v3_ami_wstd C A B) =>  (~ (v2_extpro_1 C A B)) ) ) ) ) ) ).
tt(cc2_aofa_000,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg A B))) => (v3_trees_2 C)) ) ) ) ).
tt(cc2_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (v1_finset_1 B)) ) ) ) ).
tt(cc2_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k3_arrow A)) => (v1_relat_1 B)) ) ) ) ).
tt(cc2_asympt_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v4_asympt_0 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (v5_asympt_0 A)) ) ) ) ) ) ).
tt(cc2_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v13_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v20_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc2_bcialg_5,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (v11_bcialg_3 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (v10_bcialg_3 A)) ) ) ) ) ) ) ) ) ).
tt(cc2_binom,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) & (v2_rlvect_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v6_algstr_0 A)) ) ) ) ).
tt(cc2_bintree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) &  ((v2_dtconstr A) &  ((v3_bintree1 A) & (l1_lang1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_dtconstr A)) => (v2_bintree1 B)) ) ) ) ).
tt(cc2_borsuk_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_borsuk_2 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_connsp_1 A)) ) ) ) ) ).
tt(cc2_borsuk_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v1_rat_1 A)) )  =>  ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A)) ) ) ).
tt(cc2_borsuk_6,ax, (! [A:$i] :  ( ((v3_topmetr A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v3_topmetr B)) ) ) ) ).
tt(cc2_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_ideal_1 B A) & (v1_c0sp1 B A))  => (v2_c0sp1 B A)) ) ) ) ) ).
tt(cc2_card_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_card_1 A)) ) ).
tt(cc2_card_3,ax, (! [A:$i,B:$i] :  ((v1_setfam_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C A B))  =>  ((v2_relat_1 C) &  ((v1_funct_1 C) & (v1_funct_2 C A B)) ) ) ) ) ) ) ).
tt(cc2_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v4_card_fil A)) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  ((v2_card_1 A) & (v1_card_5 A)) ) ) ) ) ).
tt(cc2_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  ((v3_ordinal1 A) &  (~ (v1_finset_1 A)) ) ) ) ).
tt(cc2_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (v15_struct_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_cat_1 A) & (v6_cat_1 A)) ) ) ) ) ) ).
tt(cc2_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) => (v3_cat_5 B)) ) ) ) ).
tt(cc2_catalg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (v2_catalg_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (v1_instalg1 A)) ) ) ) ) ).
tt(cc2_cgames_1,ax, (! [A:$i] :  ((l1_cgames_1 A) =>  ((v2_cgames_1 A) => (v1_cgames_1 A)) ) ) ).
tt(cc2_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_chord A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v6_chord A)) ) ) ) ) ) ) ).
tt(cc2_circcmb3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v4_circcmb3 A) =>  ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v1_msualg_1 A) &  ((v1_circcomb A) & (v2_circcomb A)) ) ) ) ) ) ) ) ).
tt(cc2_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_circcomb A))  =>  ( (~ (v2_struct_0 A))  & (v2_msafree2 A)) ) ) ) ).
tt(cc2_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) => (v3_trees_2 D)) ) ) ) ).
tt(cc2_circuit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) => (v3_trees_2 D)) ) ) ) ).
tt(cc2_classes2,ax, (! [A:$i] :  ((v1_classes2 A) =>  ((v1_ordinal1 A) & (v2_classes1 A)) ) ) ).
tt(cc2_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc2_clopban2,ax, (! [A:$i] :  ((l1_clopban2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_clopban1 A) &  ((v2_cfuncdom A) &  ((v2_clopban2 A) &  ((v3_clopban2 A) & (v4_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) & (v5_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc2_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v2_clopban3 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v1_clopban3 B A)) ) ) ) ) ) ) ).
tt(cc2_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure1 B A) =>  ((v7_closure1 B A) => (v6_closure1 B A)) ) ) ) ) ).
tt(cc2_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v4_closure2 C A B) => (v3_closure2 C A B)) ) ) ) ) ).
tt(cc2_cohsp_1,ax, (! [A:$i] :  ((v2_cohsp_1 A) =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc2_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v6_waybel_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_compact1 A)) ) ) ) ) ).
tt(cc2_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_compl_sp B A)) ) ) ) ) ).
tt(cc2_compos_0,ax, (! [A:$i] :  ((v5_compos_0 A) =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc2_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_xboole_0 B) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v2_compos_1 B A)) ) ) ) ) ) ) ) ) ).
tt(cc2_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_compts_1 B A) => (v4_pre_topc B A)) ) ) ) ) ).
tt(cc2_comput_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v2_margrel1 A)) ) ) ).
tt(cc2_comseq_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  (~ (v1_comseq_2 A)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  (~ (v2_comseq_2 A)) ) ) ) ) ) ).
tt(cc2_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_series_1 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v1_series_1 A)) ) ) ) ) ).
tt(cc2_conlat_1,ax, (! [A:$i] :  ( ((v1_conlat_1 A) & (l5_struct_0 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) => (v6_conlat_1 B A)) ) ) ) ).
tt(cc2_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc2_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k2_finseq_1 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_finseq_1 A)) & (v1_descip_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_finseq_1 A)) &  ((v3_funct_2 B A (k2_finseq_1 A)) & (v1_descip_1 B A)) ) ) ) ) ) ) ) ).
tt(cc2_dilworth,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_dilworth B A) => (v6_orders_2 B A)) ) ) ) ) ).
tt(cc2_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) & (v3_matrprob A))  =>  ( (~ (v3_relat_1 A))  & (v1_matrix_1 A)) ) ) ) ).
tt(cc2_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) => (v1_setfam_1 B)) ) ) ).
tt(cc2_euclid_7,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v2_euclid_7 A)) ) ).
tt(cc2_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) => (v3_card_1 B A)) ) ) ) ).
tt(cc2_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (v1_finseq_1 B)) ) ) ) ).
tt(cc2_facirc_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v7_ordinal1 A) &  (~ (v1_xtuple_0 A)) ) ) ) ).
tt(cc2_facirc_2,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (~ (v1_xtuple_0 A)) ) ) ).
tt(cc2_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v1_xboole_0 A))  =>  ((v1_funct_1 A) & (v1_fcont_1 A)) ) ) ) ).
tt(cc2_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_xboole_0 A) => (v3_rcomp_1 A)) ) ) ).
tt(cc2_filter_0,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v3_filter_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (v3_filter_0 A)) ) ) ) ) ) ).
tt(cc2_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) ) ).
tt(cc2_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_2 B A) => (v4_funct_1 B)) ) ) ).
tt(cc2_finset_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_finset_1 B)) ) ) ) ).
tt(cc2_finsub_1,ax, (! [A:$i] :  ( ((v1_finsub_1 A) & (v3_finsub_1 A))  => (v4_finsub_1 A)) ) ).
tt(cc2_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_fintopo6 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v3_orders_2 B)) ) ) ) ) ) ).
tt(cc2_fomodel0,ax, (! [A:$i] :  ((v2_setfam_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_setfam_1 B)) ) ) ) ).
tt(cc2_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v9_fomodel1 B A) => (v10_fomodel1 B A)) ) ) ) ) ).
tt(cc2_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v4_fomodel1 B A) => (v9_fomodel1 B A)) ) ) ) ) ).
tt(cc2_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k37_fomodel1 A)) => (v9_fomodel1 B A)) ) ) ) ).
tt(cc2_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel4 A)) => (v1_fomodel4 B A)) ) ) ) ).
tt(cc2_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_frechet A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_frechet A)) ) ) ) ) ).
tt(cc2_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funcop_1 A)) ) ) ) ).
tt(cc2_funct_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) ) ) ) ).
tt(cc2_funct_2,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_2 C A B) => (v1_partfun1 C A)) ) ) ) ) ).
tt(cc2_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_funct_7 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funcop_1 A) & (v1_finseq_1 A)) ) ) ) ) ).
tt(cc2_funct_8,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) &  ((v2_funct_8 C) & (v3_funct_8 C A B)) )  =>  ((v1_funct_1 C) & (v4_funct_8 C A B)) ) ) ) ) ) ).
tt(cc2_functor0,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v12_altcat_1 A))  =>  ( (~ (v2_struct_0 A))  & (v1_altcat_2 A)) ) ) ) ).
tt(cc2_functor2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v15_functor0 C A B) =>  ((v10_functor0 C A B) & (v13_functor0 C A B)) ) ) ) ) ) ).
tt(cc2_fvaluat1,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_fvaluat1 A)) ) ).
tt(cc2_gcd_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v1_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v5_vectsp_1 A)) ) ) ) ).
tt(cc2_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v7_glib_000 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v5_glib_000 A)) ) ) ) ) ) ) ) ).
tt(cc2_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) => (v5_glib_001 B A)) ) ) ) ) ).
tt(cc2_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v4_glib_000 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) ) ) ) ).
tt(cc2_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m2_glib_000 C A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))) => (v1_glib_002 C)) ) ) ) ).
tt(cc2_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ( ((v2_funct_1 B) & (v1_xboole_0 B))  =>  ((v2_funct_1 B) & (v9_graph_1 B A)) ) ) ) ) ) ).
tt(cc2_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ((v1_xboole_0 B) => (v2_funct_1 B)) ) ) ) ) ).
tt(cc2_grfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_funct_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v5_funct_1 C A)) ) ) ) ).
tt(cc2_grnilp_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v5_group_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v1_grnilp_1 A)) ) ) ) ) ) ).
tt(cc2_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (v5_group_1 B)) ) ) ) ).
tt(cc2_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k12_pralg_1 (k1_tarski 1) (k9_finseq_1 A)))) => (v1_finseq_1 B)) ) ) ) ).
tt(cc2_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_10 B A) & (l3_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) => (v2_group_10 C A)) ) ) ) ).
tt(cc2_hahnban1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (v4_hahnban1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (v3_hahnban1 C A B)) ) ) ) ) ) ) ).
tt(cc2_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v3_hahnban B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v4_hahnban B A)) ) ) ) ) ) ) ).
tt(cc2_hallmar1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_finseq_1 B (k1_zfmisc_1 A)))  & (m1_subset_1 C k5_numbers)) )  =>  (! [D:$i] :  ((m3_hallmar1 D A B C) =>  (~ (v1_xboole_0 D)) ) ) ) ) ).
tt(cc2_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) => (v5_glib_001 B A)) ) ) ) ) ).
tt(cc2_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v3_hermitan B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v4_hermitan B A)) ) ) ) ) ) ) ).
tt(cc2_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v1_hilbert3 A) => (v2_hilbert3 A)) ) ) ).
tt(cc2_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v3_ideal_1 B A))  =>  ( (~ (v1_xboole_0 B))  & (v2_ideal_1 B A)) ) ) ) ) ) ).
tt(cc2_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( (~ (v2_struct_0 A))  => (v1_instalg1 A)) ) ) ).
tt(cc2_int_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_int_1 A)) ) ).
tt(cc2_int_3,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_rlvect_1 A) & (v4_vectsp_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v1_int_3 A)) ) ) ) ).
tt(cc2_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ( (~ (v2_relat_1 A))  &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) ) ) ) ).
tt(cc2_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ( (~ (v1_xboole_0 A))  & (v2_measure5 A))  => (v5_xxreal_2 A)) ) ) ).
tt(cc2_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ((v1_isomichi B A) & (v2_isomichi B A)) ) ) ) ) ) ).
tt(cc2_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ((v1_topreal2 A) & (v1_jordan21 A)) ) ) ) ).
tt(cc2_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_jordan23 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_jordan23 A)) ) ) ) ) ).
tt(cc2_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))) &  ((v2_funct_2 B (u1_struct_0 (k3_pcomps_1 A))) & (v1_jordan24 B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))) & (v3_tops_2 B (k3_pcomps_1 A) (k3_pcomps_1 A))) ) ) ) ) ) ) ).
tt(cc2_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v1_xboole_0 B) => (v9_rltopsp1 B (k15_euclid A))) ) ) ) ) ).
tt(cc2_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (v3_filter_0 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v1_lattice2 A)) ) ) ) ) ).
tt(cc2_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_lattice3 A) =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc2_lattice6,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v1_lattice6 A)) ) ) ) ) ).
tt(cc2_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_lattices A) &  ((v7_lattices A) &  ((v8_lattices A) & (v9_lattices A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v10_lattices A)) ) ) ) ).
tt(cc2_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v3_lexbfs A)) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v13_glib_000 A)) ) ) ) ) ) ).
tt(cc2_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v1_lfuzzy_0 A)) ) ) ).
tt(cc2_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(cc2_lopban_2,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_lopban_1 A) &  ((v2_lopban_2 A) &  ((v3_lopban_2 A) & (v4_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (v5_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc2_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v2_lopban_3 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (v1_lopban_3 B A)) ) ) ) ) ) ) ).
tt(cc2_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) => (v1_xboolean A)) ) ).
tt(cc2_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_matroid0 A) => (v3_matroid0 A)) ) ) ).
tt(cc2_matrprob,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) &  ((v2_matrprob A) & (v3_matrprob A)) )  =>  ((v1_matrix_1 A) & (v4_matrprob A)) ) ) ) ).
tt(cc2_matrtop3,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) &  ((v1_matrtop3 C A) & (v1_matrtop3 C B)) ) ) )  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_matrtop3 C (k3_xboole_0 A B))) ) ) ) ) ) ).
tt(cc2_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) => (v3_xtuple_0 E)) ) ) ) ).
tt(cc2_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v2_finsub_1 B) & (v1_prob_1 B A))  => (v1_finsub_1 B)) ) ) ) ).
tt(cc2_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_measure5 A) => (v6_xxreal_2 A)) ) ) ).
tt(cc2_membered,ax, (! [A:$i] :  ((v5_membered A) => (v4_membered A)) ) ).
tt(cc2_memstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  & (l1_memstr_0 B A))  =>  (! [C:$i] :  ( ((v1_xboole_0 C) &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) )  =>  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v4_memstr_0 C A B)) ) ) ) ) ) ) ) ).
tt(cc2_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))) =>  ( ((v1_funct_1 B) & (v2_mesfunc5 B))  =>  ((v1_funct_1 B) & (v4_mesfunc5 B)) ) ) ) ) ) ).
tt(cc2_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v3_pcomps_1 A))  =>  ((v2_pre_topc A) & (v12_pre_topc A)) ) ) ) ).
tt(cc2_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v2_mfold_1 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v1_frechet B)) ) ) ) ) ) ) ).
tt(cc2_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v13_vectsp_1 C A B) & (v1_mod_4 C A B)) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v2_mod_4 C A B)) ) ) ) ) ) ) ).
tt(cc2_monoid_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_monoid_0 A) => (v1_monoid_0 A)) ) ) ).
tt(cc2_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( ((v4_msualg_1 B A) & (v4_msafree2 B A))  =>  ((v4_msualg_1 B A) & (v3_msafree2 B A)) ) ) ) ) ) ).
tt(cc2_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  ((v1_finset_1 C) & (v3_trees_2 C)) ) ) ) ) ).
tt(cc2_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_struct_0 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_graph_1 B A) => (v1_xboole_0 B)) ) ) ) ).
tt(cc2_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((m3_pboole C A B) => (v2_finset_1 C)) ) ) ) ).
tt(cc2_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k10_xtuple_0 (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A B)))) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc2_msualg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( ((v2_msualg_4 C A B) & (v3_msualg_6 C A B))  =>  ((v2_msualg_4 C A B) & (v2_msualg_6 C A B)) ) ) ) ) ) ).
tt(cc2_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v2_msualg_7 B A) => (v4_lattice3 B)) ) ) ) ) ).
tt(cc2_msualg_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_pralg_2 D B A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (k10_pralg_2 B A D) C)) =>  ((v1_relat_1 E) & (v1_funct_1 E)) ) ) ) ) ).
tt(cc2_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v8_struct_0 A) => (v2_mycielsk A)) ) ) ).
tt(cc2_nat_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v3_xxreal_0 A)) ) ) ).
tt(cc2_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xreal_0 B)) ) ) ) ).
tt(cc2_neckla_2,ax, (! [A:$i] :  ((m1_subset_1 A k13_classes2) => (v1_finset_1 A)) ) ).
tt(cc2_neckla_3,ax, (! [A:$i] :  ((v1_zfmisc_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_zfmisc_1 B) &  ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v7_relat_2 B) & (v8_relat_2 B)) ) ) ) ) ) ) ) ).
tt(cc2_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))) =>  ( ((v1_xboole_0 B) & (v1_funct_1 B))  =>  ((v1_funct_1 B) & (v1_nfcont_3 B A)) ) ) ) ) ) ).
tt(cc2_nfcont_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))) =>  ( ((v1_xboole_0 B) & (v1_funct_1 B))  =>  ((v1_funct_1 B) & (v1_nfcont_4 B A)) ) ) ) ) ) ).
tt(cc2_openlatt,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v3_filter_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v14_lattices A)) ) ) ) ) ).
tt(cc2_oposet_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v6_oposet_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ) ).
tt(cc2_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v6_orders_2 B A)) ) ) ) ) ).
tt(cc2_orders_4,ax, (! [A:$i] :  ((m1_orders_4 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ).
tt(cc2_ordinal1,ax, (! [A:$i] :  ( ((v1_ordinal1 A) & (v2_ordinal1 A))  => (v3_ordinal1 A)) ) ).
tt(cc2_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v3_ordinal1 B)) ) ) ) ).
tt(cc2_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v2_ordinal2 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v2_ordinal5 A)) ) ) ) ) ) ).
tt(cc2_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v3_ordinal1 B)) ) ) ) ).
tt(cc2_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (v6_osalg_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (v5_osalg_1 A)) ) ) ) ) ).
tt(cc2_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_osalg_4 A)) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc2_partfun1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (~ (v1_partfun1 C A)) ) ) ) ) ).
tt(cc2_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_partfun3 A))  =>  ((v1_relat_1 A) &  ((v2_relat_1 A) & (v3_partfun3 A)) ) ) ) ).
tt(cc2_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v3_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ( (~ (v2_relat_1 B))  &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc2_pdiff_6,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 C (k4_real_ns1 A) (k4_real_ns1 B)) & (v1_lopban_1 C (k4_real_ns1 A) (k4_real_ns1 B))) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 C (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v1_lopban_1 C (k4_real_ns1 A) (k4_real_ns1 B)) & (v2_lopban_1 C (k4_real_ns1 A) (k4_real_ns1 B))) ) ) ) ) ) ) ) ) ).
tt(cc2_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v14_pencil_1 A))  =>  ((v1_relat_1 A) & (v4_waybel_3 A)) ) ) ).
tt(cc2_polynom1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) ) ).
tt(cc2_polynom7,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (v3_polynom7 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 C (k15_pre_poly A) B)) ) ) ) ) ) ) ).
tt(cc2_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v2_poset_1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(cc2_pralg_2,ax, (! [A:$i] :  ( ((v4_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v2_card_3 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_partfun1 B (k9_card_3 A))) ) ) ) ).
tt(cc2_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k5_finsub_1 A))))  =>  (! [C:$i] :  ((m1_subset_1 C B) => (v1_finset_1 C)) ) ) ) ).
tt(cc2_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v4_pre_topc B A)) ) ) ) ) ).
tt(cc2_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) => (v10_valued_0 C)) ) ) ) ).
tt(cc2_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_prvect_1 B A) => (v1_finseq_1 B)) ) ) ) ).
tt(cc2_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) ) ) ).
tt(cc2_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_pscomp_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v5_measure6 B (u1_struct_0 A)) &  ((v6_measure6 B (u1_struct_0 A)) & (v1_comseq_2 B)) ) ) ) ) ) ) ) ) ).
tt(cc2_pua2mss1,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ((v4_unialg_1 A) =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc2_pythtrip,ax, (! [A:$i] :  ((m1_pythtrip A) => (v1_finset_1 A)) ) ).
tt(cc2_quantal1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_quantal1 A) & (v5_quantal1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v6_quantal1 A)) ) ) ) ).
tt(cc2_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) => (v1_quaterni A)) ) ).
tt(cc2_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_quofield C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v1_group_6 C A B) & (v13_vectsp_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(cc2_rat_1,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_rat_1 A)) ) ).
tt(cc2_ratfunc1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v1_vectsp_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v31_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) ).
tt(cc2_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_rcomp_1 B A) => (v3_rcomp_1 B)) ) ) ) ).
tt(cc2_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((v2_connsp_1 A k2_topalg_2) => (v6_xxreal_2 A)) ) ) ).
tt(cc2_realset2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (v1_realset2 A)) ) ) ) ) )  =>  ( (~ (v6_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (v4_vectsp_1 A)) ) ) ) ) ) ) ).
tt(cc2_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_relat_1 B)) ) ) ) ).
tt(cc2_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v3_relat_2 A) & (v8_relat_2 A)) )  =>  ((v1_relat_1 A) & (v1_relat_2 A)) ) ) ).
tt(cc2_relset_1,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v4_relat_1 C A) & (v5_relat_1 C B)) ) ) ) ).
tt(cc2_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_rewrite1 A))  =>  ((v1_relat_1 A) &  ((v2_relat_2 A) & (v1_rewrite1 A)) ) ) ) ).
tt(cc2_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_1 B (k8_afinsq_1 A)) => (v1_rewrite2 B)) ) ) ).
tt(cc2_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v8_valued_0 A))  =>  ((v1_funct_1 A) & (v1_rfunct_2 A)) ) ) ) ).
tt(cc2_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_subset_1 B (u1_struct_0 A)) & (v1_ring_1 B A))  => (v2_ring_1 B A)) ) ) ) ) ).
tt(cc2_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v1_group_6 C A B) & (v13_vectsp_1 C A B)) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_ringcat1 C A B)) ) ) ) ) ) ) ).
tt(cc2_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) => (v1_rlaffin1 B A)) ) ) ) ) ).
tt(cc2_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v2_rusub_4 B (k15_euclid A)) => (v4_pre_topc B (k15_euclid A))) ) ) ) ) ).
tt(cc2_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_rltopsp1 B A) => (v2_rltopsp1 B A)) ) ) ) ) ).
tt(cc2_rlvect_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (v4_rlvect_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v9_rlvect_1 A)) ) ) ) ).
tt(cc2_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (v6_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v7_robbins1 A)) ) ) ) ).
tt(cc2_robbins2,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_robbins2 A))  =>  ( (~ (v2_struct_0 A))  & (v5_lattices A)) ) ) ) ).
tt(cc2_robbins3,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v9_lattices A) &  ((v1_robbins3 A) &  ((v2_robbins3 A) & (v3_robbins3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v10_lattices A)) ) ) ) ).
tt(cc2_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) ) ) ) ) ) ).
tt(cc2_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa6b A)) ) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v6_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(cc2_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc2_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v3_scmyciel B A) => (v5_finset_1 B)) ) ) ) ).
tt(cc2_seq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) &  ((v1_seq_2 A) & (v2_seq_2 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_comseq_2 A)) ) ) ) ) ).
tt(cc2_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v7_valued_0 A) & (v1_seq_2 A)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc2_seqm_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v7_valued_0 A) & (v8_valued_0 A)) )  =>  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) ) ).
tt(cc2_setfam_1,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc2_sheffer1,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) & (v4_sheffer1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v17_lattices A)) ) ) ) ) ).
tt(cc2_simplex0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc2_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  ((v4_simplex0 B) => (v1_simplex1 B A)) ) ) ) ) ).
tt(cc2_simplex2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ((v1_simplex2 C A) & (m1_simplex0 C B)) )  =>  (! [D:$i] :  ((m2_simplex0 D B C) => (v1_simplex2 D A)) ) ) ) ).
tt(cc2_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (~ (v1_zfmisc_1 A))  & (v2_sppol_1 A))  =>  (~ (v1_sppol_1 A)) ) ) ) ).
tt(cc2_sppol_2,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ( (~ (v1_zfmisc_1 A))  &  ((v2_funct_1 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) & (v3_topreal1 A)) ) ) )  => (v4_topreal1 A)) ) ) ).
tt(cc2_sprect_1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ( (~ (v1_xboole_0 A))  & (v1_sprect_1 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) & (v2_goboard5 A)) ) ) ) ) ) ) ) ).
tt(cc2_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ( (~ (v7_struct_0 A))  =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc2_subset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (~ (v1_subset_1 B A))  =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc2_substlat,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_substlat A B)) => (v4_funct_1 C)) ) ) ).
tt(cc2_supinf_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k7_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v1_supinf_2 C A B) & (v2_supinf_2 C A B)) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (v3_supinf_2 C A B)) ) ) ) ) ) ) ).
tt(cc2_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v6_tbsp_1 B A)) ) ) ) ) ).
tt(cc2_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_tdlat_3 A) => (v2_pre_topc A)) ) ) ).
tt(cc2_tex_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (v2_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v2_pre_topc A)) ) ) ) ) ).
tt(cc2_tex_2,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (~ (v1_xboole_0 B))  =>  (~ (v1_subset_1 B A)) ) ) ) ) ) ).
tt(cc2_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tex_2 B A) & (v1_tex_3 B A))  =>  (~ (v1_borsuk_1 B A)) ) ) ) ) ) ).
tt(cc2_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_tdlat_3 B))  =>  (~ (v4_tex_4 B A)) ) ) ) ) ) ).
tt(cc2_topalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m1_borsuk_2 E B C D) & (m1_borsuk_2 F B C D)) ) ) ) )  =>  (! [G:$i] :  ((m1_borsuk_6 G B C D E F) => (v5_pre_topc G (k2_borsuk_1 k5_topmetr k5_topmetr) B)) ) ) ) ).
tt(cc2_topalg_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v2_pre_topc A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_borsuk_2 A)) ) ) ) ) ).
tt(cc2_topalg_6,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v2_mfold_1 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ( (~ (v8_struct_0 B))  & (v2_pre_topc B)) ) ) ) ) ) ) ).
tt(cc2_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_xboole_0 B) => (v2_topdim_1 B A)) ) ) ) ) ).
tt(cc2_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_card_3 B) => (v1_topdim_1 B A)) ) ) ) ) ).
tt(cc2_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_topgen_1 B A) =>  ((v4_pre_topc B A) & (v2_topgen_1 B A)) ) ) ) ) ) ).
tt(cc2_topgen_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (~ (v1_topgen_2 A))  =>  (~ (v8_struct_0 A)) ) ) ) ).
tt(cc2_topgen_4,ax, (! [A:$i] :  ( (~ (v4_card_3 A))  =>  (~ (v1_finset_1 A)) ) ) ).
tt(cc2_topgrp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v3_tops_2 C A B)) )  =>  ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_funct_2 C (u1_struct_0 B)) & (v5_pre_topc C A B)) ) ) ) ) ) ) ) ) ).
tt(cc2_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (~ (v1_sppol_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc2_topreala,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (v2_tdlat_3 A)) ) ) ) ) ).
tt(cc2_toprealc,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_toprealc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v1_toprealc B)) ) ) ) ).
tt(cc2_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_tops_1 B A)) ) ) ) ) ).
tt(cc2_trees_3,ax, (! [A:$i] :  ((v2_trees_3 A) => (v1_trees_3 A)) ) ).
tt(cc2_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_2 A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) ) ) ) ).
tt(cc2_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v6_pre_topc A)) ) ) ) ) ).
tt(cc2_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v6_pre_topc B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v2_tsp_2 B A)) ) ) ) ) ) ) ).
tt(cc2_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  =>  ((v1_relat_1 A) & (v5_relat_1 A k3_numbers)) ) ) ).
tt(cc2_valued_2,ax, (! [A:$i] :  ((v5_valued_2 A) => (v4_valued_2 A)) ) ).
tt(cc2_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v3_vectmetr B A)) )  =>  ((v1_funct_1 B) &  ((v2_funct_1 B) & (v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(cc2_vectsp10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v1_hahnban1 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (v2_hahnban1 C A B)) ) ) ) ) ) ) ).
tt(cc2_vectsp_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (v2_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v5_vectsp_1 A)) ) ) ) ).
tt(cc2_vectsp_2,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v3_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v4_vectsp_1 A)) ) ) ) ).
tt(cc2_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v7_yellow_0 B A) => (v3_waybel_0 B A)) ) ) ) ) ).
tt(cc2_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v7_yellow_0 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ) ).
tt(cc2_waybel11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v12_waybel_0 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ).
tt(cc2_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) => (v1_waybel_6 B A)) ) ) ) ) ).
tt(cc2_waybel17,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(cc2_waybel19,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v1_waybel19 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ) ) ) ).
tt(cc2_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_waybel_1 C B A)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v18_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(cc2_waybel21,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_yellow_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel21 C A B) => (v19_waybel_0 C A B)) ) ) ) ).
tt(cc2_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel23 B A) => (v2_waybel23 B A)) ) ) ) ) ).
tt(cc2_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) => (v2_waybel18 B)) ) ) ) ) ).
tt(cc2_waybel26,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_pre_topc (k2_borsuk_1 A B))) => (v1_relat_1 C)) ) ) ) ).
tt(cc2_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_monoid_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v1_monoid_0 B)) ) ) ) ) ) ).
tt(cc2_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v24_waybel_0 B)) ) ) ) ).
tt(cc2_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v2_waybel_1 A) & (v10_waybel_1 A)) ) ) ) ) ) ).
tt(cc2_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v3_orders_2 A)) )  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) & (v4_waybel11 A)) ) ) ) ) ).
tt(cc2_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(cc2_waybel33,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v7_struct_0 A) &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v1_waybel33 A)) ) ) ) ) ) ) ) ) ).
tt(cc2_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v6_waybel34 B A) =>  ((v6_yellow_0 B A) & (v7_waybel34 B A)) ) ) ) ) ) ).
tt(cc2_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (v4_waybel_4 B A)) )  => (v1_waybel35 B A)) ) ) ) ) ).
tt(cc2_waybel_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v16_waybel_0 A) & (v24_waybel_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (v16_waybel_0 A)) ) ) ) ) ) ) ) ).
tt(cc2_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) & (v4_waybel_4 B A)) ) )  => (v5_waybel_4 B A)) ) ) ) ) ).
tt(cc2_waybel_5,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) )  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v1_waybel_5 A)) ) ) ) ) ) ) ).
tt(cc2_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v2_waybel_8 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (v1_waybel_8 A)) ) ) ) ) ) ).
tt(cc2_wellord1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_2 A) &  ((v4_relat_2 A) &  ((v6_relat_2 A) &  ((v8_relat_2 A) & (v1_wellord1 A)) ) ) ) )  =>  ((v1_relat_1 A) & (v2_wellord1 A)) ) ) ).
tt(cc2_xcmplx_0,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_xcmplx_0 A)) ) ).
tt(cc2_xreal_0,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_xreal_0 A)) ) ).
tt(cc2_xtuple_0,ax, (! [A:$i] :  ((v3_xtuple_0 A) => (v2_xtuple_0 A)) ) ).
tt(cc2_xxreal_0,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_xxreal_0 A)) ) ).
tt(cc2_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) )  =>  ((v2_membered A) &  ( (~ (v1_xboole_0 A))  &  ((v1_xxreal_2 A) & (v2_xxreal_2 A)) ) ) ) ) ).
tt(cc2_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  ( (~ (v2_xxreal_0 A))  &  (~ (v1_xreal_0 A)) ) )  =>  ((v1_xxreal_0 A) & (v3_xxreal_0 A)) ) ) ).
tt(cc2_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v3_lattice3 A)) ) ) ) ) ) ) ).
tt(cc2_yellow11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v2_yellow11 B A))  => (v1_waybel_0 B A)) ) ) ) ) ).
tt(cc2_yellow12,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 C A) & (v1_yellow_8 C A B))  =>  ( (~ (v1_xboole_0 C))  &  ((v1_tops_2 C A) & (v1_yellow_8 C A B)) ) ) ) ) ) ) ).
tt(cc2_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_pre_topc A) & (v7_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) ) ) ) ) ).
tt(cc2_yellow14,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v23_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(cc2_yellow18,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v4_yellow18 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (v3_yellow18 A)) ) ) ) ) ) ) ) ) ).
tt(cc2_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((v4_orders_2 B) & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ((m1_yellow_6 C A B) =>  ((v2_yellow_6 C A B) =>  ((v4_orders_2 C) & (v2_yellow_6 C A B)) ) ) ) ) ) ).
tt(cc2_yellow21,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v2_yellow21 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v4_yellow18 A) & (v1_yellow21 A)) ) ) ) ) ) ) ) ).
tt(cc2_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v1_yellow_3 A))  =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc2_yellow_6,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) => (v4_waybel_3 C)) ) ) ) ).
tt(cc2_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_yellow_8 B A) => (v1_zfmisc_1 B)) ) ) ) ) ).
tt(cc2_yellow_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v3_orders_2 B)) ) ) ) ).
tt(cc2_zfmisc_1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ).
tt(cc30_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  =>  (! [B:$i] :  ((l1_fomodel1 B) =>  ((v16_fomodel1 B A) =>  (~ (v6_struct_0 B)) ) ) ) ) ) ).
tt(cc30_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v2_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc30_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tex_2 B A) & (v1_tex_3 B A))  =>  (~ (v1_tsep_1 B A)) ) ) ) ) ) ).
tt(cc30_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k1_numbers))  =>  ((v1_relat_1 A) & (v3_valued_0 A)) ) ) ).
tt(cc30_valued_2,ax, (! [A:$i,B:$i] :  ((v3_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v9_valued_2 C)) ) ) ) ) ) ).
tt(cc31_fomodel1,ax, (! [A:$i] :  ( ((v11_fomodel1 A) & (l1_fomodel1 A))  =>  (! [B:$i] :  ((l1_fomodel1 B) =>  ((v16_fomodel1 B A) => (v11_fomodel1 B)) ) ) ) ) ).
tt(cc31_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v16_monoid_0 B)) ) ) ) ) ) ).
tt(cc31_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_tdlat_3 B))  =>  ( (~ (v2_struct_0 B))  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(cc31_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (v1_tex_3 B A))  =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc31_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k5_numbers))  =>  ((v1_relat_1 A) & (v4_valued_0 A)) ) ) ).
tt(cc31_valued_2,ax, (! [A:$i,B:$i] :  ((v4_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v10_valued_2 C)) ) ) ) ) ) ).
tt(cc32_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_monoid_0 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v16_monoid_0 B)) ) ) ) ) ) ).
tt(cc32_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc32_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (v1_tex_2 B A))  =>  (~ (v1_tex_3 B A)) ) ) ) ) ) ).
tt(cc32_valued_2,ax, (! [A:$i,B:$i] :  ((v5_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v11_valued_2 C)) ) ) ) ) ) ).
tt(cc33_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) &  ((v17_monoid_0 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m3_monoid_0 B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v17_monoid_0 B)) ) ) ) ) ) ).
tt(cc33_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_tex_2 B A))  =>  ( (~ (v2_struct_0 B))  &  ( (~ (v1_borsuk_1 B A))  &  ( (~ (v1_tsep_1 B A))  & (v1_tex_2 B A)) ) ) ) ) ) ) ) ).
tt(cc33_valued_2,ax, (! [A:$i,B:$i] :  ((v6_valued_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 C) =>  ((v1_funct_1 C) & (v12_valued_2 C)) ) ) ) ) ) ).
tt(cc34_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_monoid_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (v13_monoid_0 B)) )  =>  ( (~ (v2_struct_0 B))  &  ((v1_group_1 B) &  ((v2_group_1 B) & (v16_monoid_0 B)) ) ) ) ) ) ) ) ).
tt(cc34_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v1_tdlat_3 B))  =>  ( (~ (v2_struct_0 B))  &  ((v7_struct_0 B) &  ((v1_tdlat_3 B) & (v1_tex_2 B A)) ) ) ) ) ) ) ) ).
tt(cc35_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v4_tex_2 B A))  =>  ( (~ (v2_struct_0 B))  & (v1_tdlat_3 B)) ) ) ) ) ) ).
tt(cc36_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v1_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v4_tex_2 B A)) ) ) ) ) ) ) ).
tt(cc37_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_2 B A) =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc38_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_2 B A) =>  (~ (v4_tex_2 B A)) ) ) ) ) ) ).
tt(cc39_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tex_2 B A))  => (v4_tex_2 B A)) ) ) ) ) ).
tt(cc3_abcmiz_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v2_abcmiz_0 A)) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_yellow_0 A) & (v1_abcmiz_0 A)) ) ) ) ) ) ) ) ).
tt(cc3_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_abcmiz_1) => (v2_funct_1 A)) ) ).
tt(cc3_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((v2_abcmiz_a B A) => (v5_abcmiz_1 B A (k28_abcmiz_1 A))) ) ) ) ) ).
tt(cc3_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_card_1 B A)) ) ) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_finset_1 B) & (v3_card_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(cc3_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ( ((v5_algstr_0 A) & (v6_algstr_0 A))  => (v7_algstr_0 A)) ) ) ).
tt(cc3_algstr_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_algstr_1 A))  =>  ( (~ (v2_struct_0 A))  & (v2_algstr_1 A)) ) ) ) ).
tt(cc3_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ((v13_struct_0 A 1) => (v13_altcat_1 A)) ) ) ).
tt(cc3_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  & (v2_altcat_1 B))  =>  ( (~ (v2_struct_0 B))  & (v11_altcat_1 B)) ) ) ) ) ) ).
tt(cc3_amistd_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) =>  (~ (v4_amistd_1 C A B)) ) ) ) ) ) ).
tt(cc3_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) => (v4_compos_0 C (u1_compos_1 B))) ) ) ) ) ).
tt(cc3_ami_wstd,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) =>  (~ (v3_ami_wstd C A B)) ) ) ) ) ) ).
tt(cc3_aofa_000,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  (! [C:$i] :  ((m1_finseq_1 C (u1_struct_0 (k7_freealg A B))) => (v6_trees_3 C)) ) ) ) ).
tt(cc3_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v6_armstrng B A) =>  ((v8_relat_2 B) &  ((v3_armstrng B A) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) ) ) ) ) ) ).
tt(cc3_asympt_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (v5_asympt_0 A)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v4_asympt_0 A)) ) ) ) ) ).
tt(cc3_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v20_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v17_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc3_binom,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v6_algstr_0 A)) ) ) ) ).
tt(cc3_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_c0sp1 B A) => (v2_c0sp1 B A)) ) ) ) ) ).
tt(cc3_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_card_1 A)) ) ).
tt(cc3_card_3,ax, (! [A:$i] :  ((v3_card_3 A) =>  ((v4_funct_1 A) & (v2_card_3 A)) ) ) ).
tt(cc3_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v5_card_fil A)) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v2_card_1 A)) ) ) ) ).
tt(cc3_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) ) ) ) ).
tt(cc3_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_catalg_1 B A) => (v2_catalg_1 B)) ) ) ).
tt(cc3_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_finseq_1 A)) =>  ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc3_chord,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v6_chord A)) ) ) ) )  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) => (v6_chord C)) ) ) ) ).
tt(cc3_circcmb3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_circcmb3 A))  =>  ( (~ (v2_struct_0 A))  & (v5_circcomb A)) ) ) ) ).
tt(cc3_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v6_circcomb B A) =>  ((v4_msualg_1 B A) & (v4_msafree2 B A)) ) ) ) ) ) ).
tt(cc3_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m3_msaterm C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C))) =>  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) ) ) ) ).
tt(cc3_classes2,ax, (! [A:$i] :  ( ((v1_ordinal1 A) & (v2_classes1 A))  => (v1_classes2 A)) ) ).
tt(cc3_clopban3,ax, (! [A:$i] :  ((l1_clopban2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) & (v5_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v2_cfuncdom A) & (v5_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc3_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure1 B A) =>  ((v9_closure1 B A) => (v8_closure1 B A)) ) ) ) ) ).
tt(cc3_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v4_closure2 C A B) => (v5_closure2 C A B)) ) ) ) ) ).
tt(cc3_cohsp_1,ax, (! [A:$i] :  ((v1_classes1 A) => (v2_finsub_1 A)) ) ).
tt(cc3_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v9_pre_topc A) & (v5_compact1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v9_pre_topc A) & (v6_waybel_3 A)) ) ) ) ) ) ).
tt(cc3_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v2_compos_1 B A)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v4_compos_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(cc3_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v8_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) & (v1_compts_1 A)) ) ) ) ).
tt(cc3_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 k5_numbers) k5_numbers))) =>  ((v1_funct_1 A) =>  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v4_valued_0 A)) ) ) ) ) ).
tt(cc3_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v1_comseq_3 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc3_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) => (v4_pre_topc B A)) ) ) ) ) ).
tt(cc3_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_zfmisc_1 B) => (v2_dilworth B A)) ) ) ) ) ).
tt(cc3_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) & (v4_matrprob A))  =>  ( (~ (v3_relat_1 A))  & (v1_matrix_1 A)) ) ) ) ).
tt(cc3_euclid_7,ax, (! [A:$i] :  ((v3_euclid_7 A) =>  ((v1_euclid_7 A) & (v2_euclid_7 A)) ) ) ).
tt(cc3_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (v3_valued_0 B)) ) ) ) ).
tt(cc3_exchsort,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_exchsort A k1_xboole_0)) ) ) ) ).
tt(cc3_facirc_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (~ (v1_facirc_1 A)) ) ) ).
tt(cc3_facirc_2,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_facirc_1 A)) ) ) ) ).
tt(cc3_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v1_xboole_0 A))  =>  ((v1_funct_1 A) & (v2_fcont_1 A)) ) ) ) ).
tt(cc3_filter_0,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v17_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (v3_filter_0 A)) ) ) ) ) ) ).
tt(cc3_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_1 B A) => (v5_relat_1 B A)) ) ) ).
tt(cc3_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_2 B A) => (v3_finseq_1 B)) ) ) ).
tt(cc3_finset_1,ax, (! [A:$i,B:$i] :  ((v1_finset_1 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C A B))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(cc3_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) => (v1_finset_1 B)) ) ) ).
tt(cc3_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_fintopo6 B A)) ) ) ) ) ).
tt(cc3_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k4_finseq_2 1 A))) => (v3_fomodel0 B A)) ) ) ) ).
tt(cc3_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v7_fomodel1 B A) => (v5_fomodel1 B A)) ) ) ) ) ).
tt(cc3_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) ) ) ) ) ) ).
tt(cc3_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k37_fomodel1 A)) => (v10_fomodel1 B A)) ) ) ) ).
tt(cc3_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [C:$i] :  ((v7_fomodel4 C A B) => (v3_fomodel4 C A B k1_xboole_0)) ) ) ) ).
tt(cc3_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_frechet A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v4_frechet A)) ) ) ) ) ).
tt(cc3_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) ) ) ) ).
tt(cc3_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_funct_1 B)) ) ) ) ).
tt(cc3_funct_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_2 C A B) => (v1_partfun1 C A)) ) ) ) ) ).
tt(cc3_funct_7,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_funct_7 A)) ) ) ) ) ).
tt(cc3_funct_8,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v4_funct_8 C A B))  =>  ((v1_funct_1 C) &  ((v2_funct_8 C) & (v3_funct_8 C A B)) ) ) ) ) ) ) ).
tt(cc3_functor0,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ( (~ (v2_struct_0 B))  & (l1_struct_0 B)) )  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v10_functor0 C A B) => (v6_functor0 C A B)) ) ) ) ) ).
tt(cc3_functor2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ( ((v10_functor0 C A B) & (v13_functor0 C A B))  => (v15_functor0 C A B)) ) ) ) ) ).
tt(cc3_fvaluat1,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v1_fvaluat1 A))  => (v1_int_1 A)) ) ).
tt(cc3_gcd_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v2_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v5_vectsp_1 A)) ) ) ) ).
tt(cc3_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v5_glib_000 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v7_glib_000 A)) ) ) ) ) ) ) ).
tt(cc3_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) => (v6_glib_001 B A)) ) ) ) ) ).
tt(cc3_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_002 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v7_glib_000 A)) ) ) ) ) ) ) ).
tt(cc3_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ((v1_xboole_0 B) => (v7_graph_1 B A)) ) ) ) ) ).
tt(cc3_grnilp_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v1_gr_cy_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (v1_grnilp_1 A)) ) ) ) ) ) ).
tt(cc3_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (v8_struct_0 B)) ) ) ) ).
tt(cc3_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)))) => (v1_finseq_1 B)) ) ) ) ).
tt(cc3_groupp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l3_algstr_0 B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (v3_groupp_1 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_10 B A) & (v2_groupp_1 B A)) ) ) ) ) ) ) ) ) ).
tt(cc3_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v5_hahnban1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v7_hahnban1 B k1_complfld A)) ) ) ) ) ) ) ).
tt(cc3_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v5_hahnban B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v4_hahnban B A)) ) ) ) ) ) ) ).
tt(cc3_hallmar1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m4_hallmar1 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc3_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( ( (~ (v3_glib_001 B A))  & (v5_glib_001 B A))  =>  ( (~ (v1_glib_001 B A))  & (v5_glib_001 B A)) ) ) ) ) ) ).
tt(cc3_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear B k1_complfld A A) & (v3_hermitan B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v2_bilinear B k1_complfld A A)) ) ) ) ) ) ) ).
tt(cc3_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (v1_finseq_1 A)) ) ).
tt(cc3_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v11_struct_0 A) => (v1_instalg1 A)) ) ) ).
tt(cc3_int_1,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_xreal_0 A)) ) ).
tt(cc3_int_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 A) & (v1_int_2 A)) ) ) ) ).
tt(cc3_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_int_6 B A) => (v5_relat_1 B k4_numbers)) ) ) ) ).
tt(cc3_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_integra1 A)) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(cc3_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) => (v1_finseq_1 A)) ) ).
tt(cc3_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_isomichi B A) & (v2_isomichi B A))  => (v4_tops_1 B A)) ) ) ) ) ).
tt(cc3_jordan23,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_jordan23 A)) ) ) ) ) ).
tt(cc3_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (~ (v9_rltopsp1 B (k15_euclid A)))  =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc3_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v13_lattices A)) ) ) ) ) ).
tt(cc3_lattice6,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v2_lattice6 A)) ) ) ) ) ).
tt(cc3_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_lattices A) & (v14_lattices A)) )  =>  ( (~ (v2_struct_0 A))  & (v15_lattices A)) ) ) ) ).
tt(cc3_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_lexbfs B A) =>  ((v4_lexbfs B A) =>  ((v13_glib_000 B) & (v2_lexbfs B)) ) ) ) ) ) ).
tt(cc3_lfuzzy_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_xreal_0 B)) ) ) ) ).
tt(cc3_lopban_3,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (v5_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) & (v5_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc3_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1))) =>  ( ((v1_funct_1 B) & (v1_funct_2 B A k6_margrel1))  =>  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (v1_margrel1 B)) ) ) ) ) ) ).
tt(cc3_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_struct_0 A) => (v4_matroid0 A)) ) ) ).
tt(cc3_matrprob,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) & (v6_matrprob A))  =>  ((v1_matrix_1 A) &  ((v2_matrprob A) & (v5_matrprob A)) ) ) ) ) ).
tt(cc3_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (v1_pre_poly C)) ) ) ) ) ) ) ).
tt(cc3_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v2_finsub_1 B) & (v1_prob_1 B A))  => (v3_finsub_1 B)) ) ) ) ).
tt(cc3_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_measure5 A) => (v6_xxreal_2 A)) ) ) ).
tt(cc3_membered,ax, (! [A:$i] :  ((v4_membered A) => (v3_membered A)) ) ).
tt(cc3_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v5_topgen_4 B A)) ) ) ) ) ).
tt(cc3_mfold_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_mfold_1 A k1_xboole_0)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) ) ) ) ) ).
tt(cc3_monoid_0,ax, (! [A:$i] :  ( ((v2_monoid_0 A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_finseq_1 B)) ) ) ) ).
tt(cc3_msafree2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) ) ) ) ) ).
tt(cc3_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) => (v3_trees_9 C)) ) ) ) ).
tt(cc3_msscyc_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v11_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v3_msscyc_1 A)) ) ) ) ).
tt(cc3_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v2_mssubfam C A B) => (v1_mssubfam C A B)) ) ) ) ) ).
tt(cc3_msualg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( ((v2_msualg_4 C A B) & (v2_msualg_6 C A B))  =>  ((v2_msualg_4 C A B) & (v3_msualg_6 C A B)) ) ) ) ) ) ).
tt(cc3_mycielsk,ax, (! [A:$i] :  ((m1_mycielsk A k6_numbers) => (v2_struct_0 A)) ) ).
tt(cc3_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v7_ordinal1 A) &  (~ (v3_xxreal_0 A)) ) ) ) ).
tt(cc3_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A k6_nat_lat) =>  ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A)) ) ) ).
tt(cc3_neckla_3,ax, (! [A:$i] :  ( ((v3_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) =>  ((v4_yellow_0 B A) & (v3_necklace B)) ) ) ) ) ) ).
tt(cc3_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))) =>  ( ((v1_xboole_0 B) & (v1_funct_1 B))  =>  ((v1_funct_1 B) & (v2_nfcont_3 B A)) ) ) ) ) ) ).
tt(cc3_nfcont_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))) =>  ( ((v1_xboole_0 B) & (v1_funct_1 B))  =>  ((v1_funct_1 B) & (v2_nfcont_4 B A)) ) ) ) ) ) ).
tt(cc3_oposet_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v6_oposet_1 A)) ) ) ) ).
tt(cc3_orders_4,ax, (! [A:$i] :  ((m1_orders_4 A) =>  ( (~ (v2_struct_0 A))  =>  ( (~ (v2_struct_0 A))  & (v16_waybel_0 A)) ) ) ) ).
tt(cc3_ordinal1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v3_ordinal1 A)) ) ).
tt(cc3_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v1_ordinal5 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v3_ordinal5 A)) ) ) ) ) ) ).
tt(cc3_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v2_ordinal6 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) ) ) ) ).
tt(cc3_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (v7_osalg_1 B A)) ) ) ) ).
tt(cc3_osalg_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v1_orders_3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v2_osalg_4 A)) ) ) ) ) ) ) ).
tt(cc3_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v3_relat_2 A) & (v8_relat_2 A)) )  =>  ((v1_relat_1 A) & (v1_relat_2 A)) ) ) ).
tt(cc3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) => (v1_funcop_1 D)) ) ) ) ).
tt(cc3_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v4_pcs_0 A) => (v3_pcs_0 A)) ) ) ).
tt(cc3_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v15_pencil_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v4_waybel_3 A) & (v11_pencil_1 A)) ) ) ) ) ).
tt(cc3_polynom7,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (v4_polynom7 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (v3_polynom7 C A B)) ) ) ) ) ) ) ).
tt(cc3_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_1 B (k3_finseq_2 A)) => (v1_pre_poly B)) ) ) ).
tt(cc3_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v11_pre_topc A) =>  ((v7_pre_topc A) & (v9_pre_topc A)) ) ) ) ).
tt(cc3_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pua2mss1 B A) =>  ((v2_relat_1 B) & (v2_funct_1 B)) ) ) ) ).
tt(cc3_quantal1,ax, (! [A:$i] :  ((l2_quantal1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) & (v8_quantal1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v9_quantal1 A) & (v10_quantal1 A)) ) ) ) ) ) ) ).
tt(cc3_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v1_group_6 C A B) & (v13_vectsp_1 C A B)) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_quofield C A B)) ) ) ) ) ) ) ).
tt(cc3_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (v1_ratfunc1 B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (v2_ratfunc1 B A)) ) ) ) ) ) ) ) ).
tt(cc3_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((v6_xxreal_2 A) => (v2_connsp_1 A k2_topalg_2)) ) ) ).
tt(cc3_relat_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v3_relat_1 A)) ) ) ).
tt(cc3_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_2 A) & (v8_relat_2 A)) )  =>  ((v1_relat_1 A) & (v5_relat_2 A)) ) ) ).
tt(cc3_relset_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (v1_xboole_0 C)) ) ) ) ).
tt(cc3_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_2 A) & (v1_rewrite1 A)) )  =>  ((v1_relat_1 A) & (v3_rewrite1 A)) ) ) ).
tt(cc3_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  (~ (v1_rfunct_2 A)) )  =>  ((v1_funct_1 A) &  ( (~ (v7_valued_0 A))  &  (~ (v8_valued_0 A)) ) ) ) ) ) ).
tt(cc3_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_ring_1 B A) =>  ((v1_subset_1 B (u1_struct_0 A)) & (v3_ring_1 B A)) ) ) ) ) ) ).
tt(cc3_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_xboole_0 B) => (v2_rlaffin1 B A)) ) ) ) ) ).
tt(cc3_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v9_rltopsp1 B A)) ) ) ) ) ).
tt(cc3_rlvect_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (v2_rlvect_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v12_algstr_0 A)) ) ) ) ).
tt(cc3_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (v9_robbins1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (v6_robbins1 A)) ) ) ) ) ) ) ).
tt(cc3_robbins2,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_robbins2 A))  =>  ( (~ (v2_struct_0 A))  & (v5_robbins1 A)) ) ) ) ).
tt(cc3_robbins3,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v6_oposet_1 A) & (v10_oposet_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v1_oposet_1 A) & (v6_oposet_1 A)) ) ) ) ) ).
tt(cc3_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) ) ) ) ) ) ).
tt(cc3_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_3 A) => (v1_roughs_1 A)) ) ) ).
tt(cc3_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) ) ) ) ).
tt(cc3_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scm_halt A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc3_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v3_scmyciel B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v3_scmyciel C A)) ) ) ) ).
tt(cc3_seq_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v3_funct_1 A) & (v1_funct_2 A k5_numbers k1_numbers)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc3_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v8_valued_0 A) & (v2_seq_2 A)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc3_seqm_3,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (v4_valued_0 A)) ) ).
tt(cc3_setfam_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  =>  (~ (v2_setfam_1 A)) ) ) ).
tt(cc3_sheffer1,ax, (! [A:$i] :  ((l1_sheffer1 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) & (v12_sheffer1 A)) ) ) ) ) ) ).
tt(cc3_simplex0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  =>  (~ (v1_setfam_1 A)) ) ) ).
tt(cc3_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  ((v4_simplex0 B) => (v2_simplex1 B A)) ) ) ) ) ).
tt(cc3_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 (k15_euclid A))) =>  ((v2_simplex2 B A) => (v1_simplex2 B (k14_euclid A))) ) ) ) ) ).
tt(cc3_sppol_2,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc3_struct_0,ax, (! [A:$i] :  ((l4_struct_0 A) =>  ( (~ (v6_struct_0 A))  =>  (~ (v7_struct_0 A)) ) ) ) ).
tt(cc3_subset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_xboole_0 B) => (v1_subset_1 B A)) ) ) ) ) ).
tt(cc3_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v6_tbsp_1 B A)) ) ) ) ) ).
tt(cc3_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_tdlat_3 A) => (v3_tdlat_3 A)) ) ) ).
tt(cc3_tex_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v1_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  & (v2_pre_topc A)) ) ) ) ) ).
tt(cc3_tex_2,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_subset_1 B A)) )  =>  ( (~ (v1_xboole_0 B))  & (v1_zfmisc_1 B)) ) ) ) ) ) ).
tt(cc3_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) & (v1_tex_2 B A))  =>  (~ (v1_tex_3 B A)) ) ) ) ) ) ).
tt(cc3_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (v2_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  & (v4_tex_4 B A)) ) ) ) ) ) ).
tt(cc3_topalg_2,ax, (! [A:$i] :  ((m1_pre_topc A k2_topalg_2) =>  ( ( (~ (v2_struct_0 A))  & (v2_topalg_2 A))  =>  ( (~ (v2_struct_0 A))  & (v1_borsuk_2 A)) ) ) ) ).
tt(cc3_topalg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) => (v5_pre_topc C k5_topmetr A)) ) ) ) ).
tt(cc3_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_topalg_6 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (v1_topalg_6 A)) ) ) ) ) ) ).
tt(cc3_topdim_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) & (v3_topdim_1 A)) ) ) ) ).
tt(cc3_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v2_topgen_1 B A))  => (v5_topgen_1 B A)) ) ) ) ) ).
tt(cc3_topgen_4,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_zfmisc_1 A)) ) ) ).
tt(cc3_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v2_struct_0 B))  & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v3_tops_2 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_t_0topsp C A B)) ) ) ) ) ) ) ).
tt(cc3_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (~ (v2_sppol_1 A))  =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc3_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(cc3_toprealc,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v2_toprealc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v2_toprealc B)) ) ) ) ).
tt(cc3_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v3_tops_1 B A)) ) ) ) ) ).
tt(cc3_trees_3,ax, (! [A:$i] :  ((v1_trees_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_trees_3 B)) ) ) ) ).
tt(cc3_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v2_trees_9 A)) ) ) ) ) ).
tt(cc3_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v6_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v1_tdlat_3 A)) ) ) ) ) ) ).
tt(cc3_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tsp_2 B A) => (v1_tex_3 B A)) ) ) ) ) ).
tt(cc3_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  =>  ((v1_relat_1 A) & (v3_valued_0 A)) ) ) ).
tt(cc3_valued_2,ax, (! [A:$i] :  ((v4_valued_2 A) => (v3_valued_2 A)) ) ).
tt(cc3_vectsp10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) =>  ( ((v1_funct_1 C) &  ((v1_zfmisc_1 C) & (v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A))) )  =>  ((v1_funct_1 C) &  ((v3_funct_1 C) & (v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(cc3_vectsp_1,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_vectsp_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (v6_vectsp_1 A)) ) ) ) ) ).
tt(cc3_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v8_yellow_0 B A) => (v4_waybel_0 B A)) ) ) ) ) ).
tt(cc3_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v8_yellow_0 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ) ).
tt(cc3_waybel11,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v13_waybel_0 B A)) ) ) ) ).
tt(cc3_waybel17,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v22_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(cc3_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_yellow_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v1_yellow_0 B)) ) ) ) ).
tt(cc3_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v7_waybel_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v6_waybel_1 B A)) ) ) ) ) ) ) ).
tt(cc3_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel23 B A) => (v2_waybel_0 B A)) ) ) ) ) ).
tt(cc3_waybel25,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) & (v5_pre_topc C (k1_waybel25 A) (k1_waybel25 B))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) & (v5_orders_3 C (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ) ) ).
tt(cc3_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(cc3_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) & (v1_waybel_2 A)) ) ) ) ) ).
tt(cc3_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v7_struct_0 A) &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_lattice3 A)) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v2_waybel19 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc3_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v24_waybel_0 B)) ) ) ) ).
tt(cc3_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v25_waybel_0 B)) ) ) ) ).
tt(cc3_waybel_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v13_struct_0 A 1) & (v3_orders_2 A))  =>  ((v13_struct_0 A 1) &  ((v3_orders_2 A) & (v2_waybel_3 A)) ) ) ) ) ).
tt(cc3_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_waybel_4 B A) & (v2_waybel_4 B A))  => (v8_relat_2 B)) ) ) ) ) ).
tt(cc3_waybel_5,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v1_waybel_5 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) ) ) ) ) ).
tt(cc3_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_waybel_8 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v2_waybel_8 A)) ) ) ) ) ) ) ) ).
tt(cc3_xcmplx_0,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (v1_xcmplx_0 A)) ) ).
tt(cc3_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xcmplx_0 A)) ) ).
tt(cc3_xxreal_0,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) ) ) ) ) ).
tt(cc3_xxreal_2,ax, (! [A:$i] :  ( ((v6_membered A) &  (~ (v1_xboole_0 A)) )  =>  ((v6_membered A) &  ( (~ (v1_xboole_0 A))  & (v1_xxreal_2 A)) ) ) ) ).
tt(cc3_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v3_lattice3 A))  =>  ( (~ (v2_struct_0 A))  & (v3_yellow_0 A)) ) ) ) ).
tt(cc3_yellow11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v2_yellow11 B A))  => (v2_waybel_0 B A)) ) ) ) ) ).
tt(cc3_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v8_struct_0 A) & (v2_pre_topc A))  =>  ((v2_pre_topc A) & (v1_compts_1 A)) ) ) ) ).
tt(cc3_yellow14,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v3_yellow_0 A)) ) ) ).
tt(cc3_yellow18,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (v3_yellow18 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (v4_yellow18 A)) ) ) ) ) ) ) ).
tt(cc3_yellow21,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_wellord1 A))  =>  ((v1_relat_1 A) &  ((v1_wellord1 A) &  ((v1_relat_2 A) &  ((v4_relat_2 A) &  ((v6_relat_2 A) & (v8_relat_2 A)) ) ) ) ) ) ) ).
tt(cc3_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v3_orders_2 A))  =>  (~ (v1_yellow_3 A)) ) ) ) ).
tt(cc3_yellow_6,ax, (! [A:$i,B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((m3_yellow_6 C A B) => (v4_waybel_3 C)) ) ) ) ).
tt(cc3_yellow_9,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v4_orders_2 B)) ) ) ) ).
tt(cc40_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v4_tex_2 B A))  => (v1_tex_2 B A)) ) ) ) ) ).
tt(cc41_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v4_tex_2 B A))  =>  ( (~ (v2_struct_0 B))  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(cc42_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v4_tex_2 B A)) ) ) ) ) ) ) ).
tt(cc43_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v7_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v4_tex_2 B A)) ) ) ) ) ) ).
tt(cc44_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v4_tex_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) ) ) ) ) ) ) ).
tt(cc45_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v4_tex_2 B A))  =>  ( (~ (v2_struct_0 B))  & (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc46_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  (~ (v1_tex_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v4_tex_2 B A)) ) ) ) ) ) ) ).
tt(cc47_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v2_tdlat_3 A))  &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v4_tex_2 B A))  =>  ( (~ (v2_struct_0 B))  &  (~ (v7_struct_0 B)) ) ) ) ) ) ) ).
tt(cc48_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v2_tdlat_3 A))  &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  & (v7_struct_0 B))  =>  ( (~ (v2_struct_0 B))  &  (~ (v4_tex_2 B A)) ) ) ) ) ) ) ).
tt(cc4_abcmiz_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v1_abcmiz_0 A)) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_abcmiz_0 A)) ) ) ) ) ) ) ).
tt(cc4_abcmiz_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ((v1_instalg1 A) & (v1_abcmiz_1 A))  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (v1_instalg1 A)) ) ) ) ) ).
tt(cc4_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v4_abcmiz_a B A) => (v2_abcmiz_1 B A)) ) ) ) ) ).
tt(cc4_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_valued_0 A)) ) ) ) ) ) ) ).
tt(cc4_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v7_algstr_0 A) =>  ((v5_algstr_0 A) & (v6_algstr_0 A)) ) ) ) ).
tt(cc4_algstr_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) & (v4_algstr_1 A)) ) ) ) ) ).
tt(cc4_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ((v13_altcat_1 A) => (v2_altcat_1 A)) ) ) ).
tt(cc4_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  & (v12_altcat_1 B)) ) ) ) ) ) ).
tt(cc4_amistd_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v5_amistd_1 C A B)) ) ) ) ) ) )  =>  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v6_amistd_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(cc4_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) => (v3_amistd_2 C A B)) ) ) ) ) ).
tt(cc4_ami_wstd,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_xboole_0 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v5_ami_wstd C A B)) ) ) ) ) ) ) ) ) ).
tt(cc4_aofa_000,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) & (v6_aofa_000 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ( (~ (v10_aofa_000 A))  & (v11_aofa_000 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc4_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v8_relat_2 B) &  ((v3_armstrng B A) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) )  => (v6_armstrng B A)) ) ) ) ).
tt(cc4_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v13_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v16_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc4_card_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) => (v1_finset_1 A)) ) ).
tt(cc4_card_3,ax, (! [A:$i] :  ((v5_card_3 A) =>  ( (~ (v1_finset_1 A))  & (v4_card_3 A)) ) ) ).
tt(cc4_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v6_card_fil A)) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  ((v1_card_5 A) & (v5_card_fil A)) ) ) ) ) ).
tt(cc4_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_catalg_1 B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc4_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k10_cgames_1 A)) => (v2_cgames_1 B)) ) ) ) ).
tt(cc4_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc4_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( ((v4_msafree2 B A) & (v5_circcmb3 B A))  =>  ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) & (v4_msafree2 B A)) ) ) ) ) ) ) ).
tt(cc4_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m3_msaterm C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C))) => (v3_trees_2 D)) ) ) ) ).
tt(cc4_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure1 B A) =>  ((v9_closure1 B A) => (v10_closure1 B A)) ) ) ) ) ).
tt(cc4_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v5_closure2 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ) ).
tt(cc4_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) &  ((v1_coh_sp A) & (v3_cohsp_1 A)) ) ) ) ) ).
tt(cc4_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_compact1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v4_compact1 A)) ) ) ) ) ).
tt(cc4_compts_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v2_compts_1 B A)) ) ) ) ) ).
tt(cc4_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 k5_numbers) k5_numbers))) =>  ( ((v1_funct_1 A) & (v3_margrel1 A k5_numbers))  =>  ((v1_funct_1 A) & (v2_comput_1 A)) ) ) ) ).
tt(cc4_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v2_comseq_3 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (v1_comseq_3 A)) ) ) ) ) ).
tt(cc4_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v2_connsp_1 B A)) ) ) ) ) ).
tt(cc4_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v8_struct_0 A) => (v3_dilworth A)) ) ) ).
tt(cc4_euclid_7,ax, (! [A:$i] :  ( ((v1_euclid_7 A) & (v2_euclid_7 A))  => (v3_euclid_7 A)) ) ).
tt(cc4_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (v3_card_1 B A)) ) ) ) ).
tt(cc4_facirc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  (~ (v1_facirc_1 A)) )  => (v1_xboole_0 A)) ) ).
tt(cc4_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v3_funct_1 A))  =>  ((v1_funct_1 A) & (v2_fcont_1 A)) ) ) ) ).
tt(cc4_filter_0,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v3_filter_0 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v11_lattices A)) ) ) ) ) ).
tt(cc4_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 A))  =>  ((v1_relat_1 A) & (v1_finseq_1 A)) ) ) ).
tt(cc4_finset_1,ax, (! [A:$i] :  ((v1_zfmisc_1 A) => (v1_finset_1 A)) ) ).
tt(cc4_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v5_relat_1 C B))  =>  ((v1_relat_1 C) & (v5_relat_1 C A)) ) ) ) ) ).
tt(cc4_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v6_fomodel1 B A) => (v8_fomodel1 B A)) ) ) ) ) ).
tt(cc4_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v9_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (! [D:$i] :  ((m1_fomodel2 D A B C) =>  (~ (v1_xboole_0 D)) ) ) ) ) ).
tt(cc4_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v7_fomodel1 C A))  &  ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) )  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ((m1_fomodel2 E A B C) =>  ((v2_fomodel3 E A B C D) => (v1_fomodel3 E (k9_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) D)) ) ) ) ) ).
tt(cc4_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [C:$i] :  ((v3_fomodel4 C A B k1_xboole_0) => (v7_fomodel4 C A B)) ) ) ) ).
tt(cc4_funct_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) ) ).
tt(cc4_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_funct_2 B A A) => (v1_partfun1 B A)) ) ) ) ).
tt(cc4_funct_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_7 B A) =>  ((v2_relat_1 B) & (v1_funct_7 B)) ) ) ) ) ).
tt(cc4_funct_8,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) &  ((v2_funct_8 C) & (v5_funct_8 C A B)) )  =>  ((v1_funct_1 C) & (v6_funct_8 C A B)) ) ) ) ) ) ).
tt(cc4_functor0,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ( (~ (v2_struct_0 B))  & (l1_struct_0 B)) )  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v11_functor0 C A B) => (v6_functor0 C A B)) ) ) ) ) ).
tt(cc4_functor2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v16_functor0 C A B) =>  ((v11_functor0 C A B) & (v14_functor0 C A B)) ) ) ) ) ) ).
tt(cc4_gcd_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc4_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v6_glib_000 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v8_glib_000 A)) ) ) ) ) ) ) ).
tt(cc4_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v6_glib_001 B A) => (v5_glib_001 B A)) ) ) ) ) ).
tt(cc4_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_002 A) & (v2_glib_002 A)) ) ) ) ) ) ) ) ).
tt(cc4_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ( ((v1_glib_003 B) & (v4_glib_003 B A))  =>  ((v1_glib_003 B) &  ((v4_glib_003 B A) & (v7_glib_003 B)) ) ) ) ) ) ) ).
tt(cc4_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k12_pralg_1 (k2_tarski 1 2) (k10_finseq_1 A B)))) => (v1_finseq_1 C)) ) ) ) ).
tt(cc4_groupp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l3_algstr_0 B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_10 B A) & (v2_groupp_1 B A)) ) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (v3_groupp_1 B A)) ) ) ) ) ) ) ) ).
tt(cc4_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v5_hahnban B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v7_hahnban B A)) ) ) ) ) ) ) ).
tt(cc4_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) & (v3_hermitan B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v1_bilinear B k1_complfld A A)) ) ) ) ) ) ) ).
tt(cc4_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ((v2_struct_0 A) & (v1_instalg1 A))  => (v11_struct_0 A)) ) ) ).
tt(cc4_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_integra1 A)) =>  ((v1_finseq_1 B) & (v3_valued_0 B)) ) ) ) ) ).
tt(cc4_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_isomichi B A) => (v1_decomp_1 B A)) ) ) ) ) ).
tt(cc4_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_jordan23 A)) ) ) ) ) ).
tt(cc4_jordan,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) => (v1_subset_1 B (u1_struct_0 (k15_euclid A)))) ) ) ) ) ).
tt(cc4_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v14_lattices A)) ) ) ) ) ).
tt(cc4_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  & (v15_lattices A))  =>  ( (~ (v2_struct_0 A))  &  ((v13_lattices A) & (v14_lattices A)) ) ) ) ) ).
tt(cc4_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lfuzzy_0 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ).
tt(cc4_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_tdlat_3 A) =>  ((v1_tdlat_3 A) &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (v2_matroid0 A)) ) ) ) ) ) ).
tt(cc4_matrprob,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) =>  ( ((v1_matrix_1 A) &  ((v2_matrprob A) & (v5_matrprob A)) )  =>  ((v1_matrix_1 A) & (v6_matrprob A)) ) ) ) ).
tt(cc4_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_matrtop3 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) &  ((v3_tops_2 B (k15_euclid A) (k15_euclid A)) & (v2_matrtop3 B A)) ) ) ) ) ) ) ) ) ) ).
tt(cc4_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v1_prob_1 B A) & (v4_prob_1 B A))  => (v3_measure1 B A)) ) ) ) ).
tt(cc4_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_measure5 A) => (v6_xxreal_2 A)) ) ) ).
tt(cc4_membered,ax, (! [A:$i] :  ((v3_membered A) => (v2_membered A)) ) ).
tt(cc4_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v6_topgen_4 B A)) ) ) ) ) ).
tt(cc4_mfold_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_mfold_1 A k1_xboole_0)) ) ) ) ) ).
tt(cc4_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (v3_group_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v13_monoid_0 A)) ) ) ) ).
tt(cc4_msafree2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) ) ) ) ) ) ).
tt(cc4_msafree3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) ) ) ) ).
tt(cc4_msscyc_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ( ( (~ (v2_struct_0 A))  &  (~ (v3_msscyc_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  (~ (v11_struct_0 A)) ) ) ) ) ).
tt(cc4_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v4_mssubfam C A B) => (v3_mssubfam C A B)) ) ) ) ) ).
tt(cc4_msualg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v2_msualg_4 C A B) => (v2_relat_1 C)) ) ) ) ) ).
tt(cc4_mycielsk,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (~ (v2_struct_0 B)) ) ) ) ) ).
tt(cc4_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A)) ) ) ).
tt(cc4_neckla_3,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) =>  ((v4_yellow_0 B A) & (v1_necklace B)) ) ) ) ) ) ).
tt(cc4_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) & (v3_funct_1 B))  =>  ((v1_funct_1 B) & (v2_nfcont_3 B A)) ) ) ) ) ) ).
tt(cc4_nfcont_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))) =>  ( ((v1_funct_1 B) & (v3_funct_1 B))  =>  ((v1_funct_1 B) & (v2_nfcont_4 B A)) ) ) ) ) ) ).
tt(cc4_orders_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( ( (~ (v2_struct_0 B))  & (v4_yellow_0 B A))  =>  ( (~ (v2_struct_0 B))  & (v16_waybel_0 B)) ) ) ) ) ) ).
tt(cc4_ordinal1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v5_ordinal1 A)) ) ).
tt(cc4_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal5 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) ) ) ).
tt(cc4_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v2_ordinal6 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) &  ((v2_ordinal2 A) & (v3_ordinal2 A)) ) ) ) ) ) ) ).
tt(cc4_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (v6_osalg_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (v8_osalg_1 A)) ) ) ) ) ) ) ).
tt(cc4_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_osalg_4 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_osalg_4 A)) => (v1_waybel_0 B A)) ) ) ) ).
tt(cc4_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc4_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v2_struct_0 A) =>  ((v4_pcs_0 A) &  ((v5_pcs_0 A) & (v6_pcs_0 A)) ) ) ) ) ).
tt(cc4_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v11_pencil_1 A) & (v15_pencil_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v11_pencil_1 A) & (v12_pencil_1 A)) ) ) ) ) ).
tt(cc4_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) ) ) ) ).
tt(cc4_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v7_pre_topc A) & (v9_pre_topc A))  => (v11_pre_topc A)) ) ) ).
tt(cc4_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_pua2mss1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc4_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v4_quofield C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_quofield C A B) & (v3_quofield C A B)) ) ) ) ) ) ) ) ).
tt(cc4_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  (~ (v2_ratfunc1 B A)) ) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  (~ (v1_ratfunc1 B A)) ) ) ) ) ) ) ) ) ).
tt(cc4_relat_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v2_relat_1 A)) ) ) ).
tt(cc4_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_2 A))  =>  ((v1_relat_1 A) &  ((v2_relat_2 A) & (v4_relat_2 A)) ) ) ) ).
tt(cc4_relset_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) => (v1_xboole_0 C)) ) ) ) ).
tt(cc4_rewrite1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) &  ((v2_rewrite1 A) & (v3_rewrite1 A)) ) ) ) ).
tt(cc4_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v7_valued_0 A) & (v8_valued_0 A)) )  =>  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) ) ).
tt(cc4_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_subset_1 B (u1_struct_0 A)) & (v3_ring_1 B A))  => (v4_ring_1 B A)) ) ) ) ) ).
tt(cc4_rltopsp1,ax, (! [A:$i] :  ((l1_rltopsp1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) & (v7_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) & (v7_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc4_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (v5_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (v6_robbins1 A)) ) ) ) ) ) ).
tt(cc4_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (v2_robbins4 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (v1_robbins4 A)) ) ) ) ) ) ) ) ).
tt(cc4_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v1_roughs_1 A))  =>  (~ (v1_orders_3 A)) ) ) ) ).
tt(cc4_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scm_halt A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc4_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v3_scmyciel A 1)) ) ) ) ).
tt(cc4_seq_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v1_comseq_2 A)) ) ) ) ) ).
tt(cc4_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers))) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v1_seqm_3 A) & (v1_comseq_2 A)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (v2_comseq_2 A)) ) ) ) ) ).
tt(cc4_seqm_3,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (v3_valued_0 A)) ) ).
tt(cc4_setfam_1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (~ (v2_setfam_1 A)) ) ) ).
tt(cc4_sheffer1,ax, (! [A:$i] :  ((l2_lattices A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v4_lattices A) & (v5_lattices A)) ) ) ) ) ).
tt(cc4_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (~ (v5_simplex0 A))  =>  (~ (v3_pencil_1 A)) ) ) ) ).
tt(cc4_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) )  =>  (! [C:$i] :  ((m2_simplex0 C (u1_struct_0 A) B) => (v1_simplex1 C A)) ) ) ) ).
tt(cc4_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 (k15_euclid A))) =>  ((v2_simplex0 B) => (v2_simplex2 B A)) ) ) ) ) ).
tt(cc4_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) =>  (~ (v1_xboole_0 A)) ) ) ) ).
tt(cc4_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_struct_0 A) =>  ((v2_struct_0 A) & (v8_struct_0 A)) ) ) ) ).
tt(cc4_subset_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~ (v1_subset_1 B A)) ) ) ) ) ).
tt(cc4_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_tdlat_3 A) => (v3_tdlat_3 A)) ) ) ).
tt(cc4_tex_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v2_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  & (v2_pre_topc A)) ) ) ) ) ).
tt(cc4_tex_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ( (~ (v1_xboole_0 B))  & (v1_zfmisc_1 B))  =>  ( (~ (v1_xboole_0 B))  & (v1_subset_1 B A)) ) ) ) ) ) ).
tt(cc4_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tex_3 B A) => (v1_tex_3 B A)) ) ) ) ) ).
tt(cc4_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) &  (~ (v4_tex_4 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v2_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc4_topalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  =>  (! [F:$i] :  ((m1_borsuk_6 F A B C D E) => (v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) A)) ) ) ) ).
tt(cc4_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (v1_topalg_6 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_topalg_6 A)) ) ) ) ) ).
tt(cc4_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_topdim_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v1_topdim_1 B A)) ) ) ) ).
tt(cc4_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v5_topgen_1 B A)) ) ) ) ) ).
tt(cc4_topgen_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_waybel23 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v7_topgen_1 A)) ) ) ) ) ).
tt(cc4_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_topgrp_1 B A) => (v3_tops_2 B A A)) ) ) ) ).
tt(cc4_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v2_topreal4 A (k15_euclid 2)) =>  ((v3_pre_topc A (k15_euclid 2)) & (v2_connsp_1 A (k15_euclid 2))) ) ) ) ).
tt(cc4_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_xboole_0 C) & (v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(cc4_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) => (v2_tops_1 B A)) ) ) ) ) ).
tt(cc4_trees_3,ax, (! [A:$i] :  ((v2_trees_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_trees_3 B)) ) ) ) ).
tt(cc4_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v2_trees_9 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) ) ) ) ).
tt(cc4_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (v2_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v6_pre_topc A)) ) ) ) ) ) ).
tt(cc4_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tex_3 B A))  =>  (~ (v2_tsp_2 B A)) ) ) ) ) ) ).
tt(cc4_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  =>  ((v1_relat_1 A) & (v3_valued_0 A)) ) ) ).
tt(cc4_valued_2,ax, (! [A:$i] :  ((v3_valued_2 A) => (v1_valued_2 A)) ) ).
tt(cc4_vectsp10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l6_algstr_0 A)) )  &  ( (~ (v7_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_hahnban1 C A B) &  (~ (v2_vectsp10 C A B)) ) ) )  =>  ((v1_funct_1 C) &  ( (~ (v3_funct_1 C))  & (v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(cc4_vectsp_1,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (v6_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v1_group_1 A)) ) ) ) ).
tt(cc4_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (v8_waybel_0 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (v10_waybel_0 B A)) ) ) ) ) ) ) ).
tt(cc4_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v2_waybel11 B A) & (v3_waybel11 B A)) ) ) ) ) ) ).
tt(cc4_waybel17,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v22_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(cc4_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v3_waybel_3 B)) ) ) ) ).
tt(cc4_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v8_waybel_1 B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (v6_waybel_1 B A)) ) ) ) ) ) ) ).
tt(cc4_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel23 B A) => (v1_waybel_0 B A)) ) ) ) ) ).
tt(cc4_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_waybel25 A)))) =>  ((v3_pre_topc B (k1_waybel25 A)) => (v13_waybel_0 B (k1_waybel25 A))) ) ) ) ) ).
tt(cc4_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v2_waybel_2 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (v1_waybel_2 A)) ) ) ) ) ) ).
tt(cc4_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (v3_waybel_3 A)) ) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_lattice3 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc4_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) => (v3_waybel11 B A)) ) ) ) ) ).
tt(cc4_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v2_lattice3 B)) ) ) ) ).
tt(cc4_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( ((v4_yellow_0 B A) & (v7_waybel34 B A))  =>  ( (~ (v2_struct_0 B))  &  ((v1_yellow_0 B) & (v4_yellow_0 B A)) ) ) ) ) ) ) ).
tt(cc4_waybel_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v3_waybel_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (v2_waybel_3 A)) ) ) ) ) ) ).
tt(cc4_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v2_waybel_2 A)) ) ) ) ) ) ) ) ) ).
tt(cc4_waybel_5,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v1_waybel_5 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v9_waybel_1 A)) ) ) ) ) ) ) ) ).
tt(cc4_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v7_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_waybel_8 A)) ) ) ) ) ) ) ) ).
tt(cc4_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xxreal_0 A)) ) ).
tt(cc4_xxreal_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) ) )  =>  ((v1_xxreal_0 A) & (v2_xxreal_0 A)) ) ) ).
tt(cc4_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v5_xxreal_2 A))  =>  ((v2_membered A) &  ((v3_xxreal_2 A) & (v4_xxreal_2 A)) ) ) ) ).
tt(cc4_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_yellow_0 A) =>  ((v1_yellow_0 A) & (v2_yellow_0 A)) ) ) ) ).
tt(cc4_yellow11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v2_lattice3 A)) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (v1_yellow_0 A)) ) ) ) ) ) ) ).
tt(cc4_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) )  =>  ((v2_pre_topc A) &  ((v7_pre_topc A) &  ((v8_pre_topc A) &  ((v9_pre_topc A) & (v10_pre_topc A)) ) ) ) ) ) ) ).
tt(cc4_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((v13_waybel_0 B A) & (v1_waybel11 B A)) ) ) ) ) ) ).
tt(cc4_yellow18,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v1_relat_1 D) & (v1_funct_1 D)) ) ) ) ) ).
tt(cc4_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v3_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v3_yellow18 B)) ) ) ) ) ) ) ) ).
tt(cc4_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (v1_yellow_6 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (v3_yellow_6 B A)) ) ) ) ) ) ) ) ).
tt(cc4_yellow_8,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v4_yellow_8 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v6_pre_topc A)) ) ) ) ) ).
tt(cc4_yellow_9,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v5_orders_2 B)) ) ) ) ).
tt(cc5_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((v6_abcmiz_1 B A) =>  ( (~ (v7_abcmiz_1 B A))  & (v8_abcmiz_1 B A)) ) ) ) ) ) ).
tt(cc5_abcmiz_a,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (v3_abcmiz_a A)) )  =>  ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (v12_abcmiz_1 A)) ) ) ) ) ).
tt(cc5_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v4_valued_0 A)) ) ) ) ) ) ) ).
tt(cc5_algstr_0,ax, (! [A:$i] :  ( ((v5_algstr_0 A) & (l1_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_algstr_0 B A)) ) ) ) ).
tt(cc5_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v21_algstr_0 A) &  ((v5_algstr_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v23_algstr_0 B A)) ) ) ) ).
tt(cc5_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v3_amistd_2 C A B)) ) ) ) ) ).
tt(cc5_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k1_zfmisc_1 B))) )  =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  ((v13_aofa_000 D A B) & (v14_aofa_000 D A B)) ) ) ) ) ).
tt(cc5_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v3_armstrng B A) & (v4_armstrng B A))  => (v7_armstrng B A)) ) ) ) ).
tt(cc5_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v19_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v16_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc5_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 A)) ) ).
tt(cc5_card_3,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v4_card_3 A))  => (v5_card_3 A)) ) ).
tt(cc5_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v6_card_fil A)) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v4_card_fil A)) ) ) ) ).
tt(cc5_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) & (v7_cgames_1 A))  =>  ((v2_cgames_1 A) &  ((v5_cgames_1 A) & (v6_cgames_1 A)) ) ) ) ).
tt(cc5_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (v5_circcmb3 B A)) )  =>  ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (v3_circcmb3 B A)) ) ) ) ) ) ) ).
tt(cc5_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure1 B A) =>  ((v7_closure1 B A) => (v11_closure1 B A)) ) ) ) ) ).
tt(cc5_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v2_closure2 C A B) => (v6_closure2 C A B)) ) ) ) ) ).
tt(cc5_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_cohsp_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v6_cohsp_1 A)) ) ) ) ).
tt(cc5_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v4_compact1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_compact1 A)) ) ) ) ) ).
tt(cc5_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_struct_0 A) => (v8_pre_topc A)) ) ) ).
tt(cc5_comput_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v3_comput_1 A)) ) ) ).
tt(cc5_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_dilworth B A) =>  ((v1_finset_1 B) & (v1_dilworth B A)) ) ) ) ) ) ).
tt(cc5_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v5_euclid_7 B A) =>  ((v3_euclid_7 B) & (v4_euclid_7 B A)) ) ) ) ) ) ).
tt(cc5_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_exchsort A) & (v2_exchsort A k1_xboole_0)) ) )  =>  ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) ) ) ) ) ).
tt(cc5_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v2_fcont_1 A))  =>  ((v1_funct_1 A) & (v1_fcont_1 A)) ) ) ) ).
tt(cc5_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) ) ) ).
tt(cc5_finset_1,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_zfmisc_1 A)) ) ) ).
tt(cc5_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_finseq_2 A)) => (v5_relat_1 B A)) ) ) ).
tt(cc5_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v4_fomodel1 B A) => (v8_fomodel1 B A)) ) ) ) ) ).
tt(cc5_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k9_funct_2 A C)))) =>  ( ((v1_funct_1 D) & (v1_funct_2 D B (k9_funct_2 A C)))  =>  ((v1_funct_1 D) &  ((v1_funct_2 D B (k9_funct_2 A C)) & (v1_funcop_1 D)) ) ) ) ) ) ) ).
tt(cc5_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v7_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ((m1_fomodel2 E A B C) =>  ((v2_fomodel3 E A B C D) => (v1_fomodel3 E (k9_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) (k3_fomodel2 k6_margrel1))) ) ) ) ) ).
tt(cc5_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) & (v1_xboole_0 C)) )  =>  (! [D:$i] :  ((v3_fomodel4 D A B C) => (v7_fomodel4 D A B)) ) ) ) ).
tt(cc5_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  (~ (v3_funct_1 A)) ) )  =>  ( (~ (v1_zfmisc_1 A))  &  ((v1_relat_1 A) & (v1_funct_1 A)) ) ) ) ).
tt(cc5_funct_2,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v3_funct_2 C A B))  =>  ((v1_funct_1 C) &  ((v2_funct_1 C) & (v2_funct_2 C B)) ) ) ) ) ) ).
tt(cc5_funct_8,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v6_funct_8 C A B))  =>  ((v1_funct_1 C) &  ((v2_funct_8 C) & (v5_funct_8 C A B)) ) ) ) ) ) ) ).
tt(cc5_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v15_functor0 C A B) => (v6_functor0 C A B)) ) ) ) ) ).
tt(cc5_functor2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ( ((v11_functor0 C A B) & (v14_functor0 C A B))  => (v16_functor0 C A B)) ) ) ) ) ).
tt(cc5_gcd_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v3_gcd_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(cc5_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v8_glib_000 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v6_glib_000 A)) ) ) ) ) ) ) ) ).
tt(cc5_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_002 A) & (v2_glib_002 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) ) ) ) ).
tt(cc5_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ( ((v1_glib_003 B) & (v4_glib_003 B A))  =>  ((v1_glib_003 B) &  ((v4_glib_003 B A) & (v8_glib_003 B)) ) ) ) ) ) ) ).
tt(cc5_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)))) => (v1_finseq_1 C)) ) ) ) ).
tt(cc5_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_groupp_1 B A) & (l3_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) => (v2_groupp_1 C A)) ) ) ) ).
tt(cc5_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v6_hahnban B A)) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v5_hahnban B A)) ) ) ) ) ) ) ).
tt(cc5_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v4_bilinear B k1_complfld A A) & (v3_hermitan B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v2_hermitan B A A)) ) ) ) ) ) ) ).
tt(cc5_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ( (~ (v11_struct_0 A))  & (v1_instalg1 A))  =>  (~ (v2_struct_0 A)) ) ) ) ).
tt(cc5_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_decomp_1 B A) => (v2_isomichi B A)) ) ) ) ) ).
tt(cc5_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v8_pre_topc B)) ) ) ) ) ) ).
tt(cc5_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v15_lattices A)) ) ) ) ) ).
tt(cc5_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  & (v17_lattices A))  =>  ( (~ (v2_struct_0 A))  &  ((v11_lattices A) &  ((v15_lattices A) & (v16_lattices A)) ) ) ) ) ) ).
tt(cc5_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_lfuzzy_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (v1_lfuzzy_0 A)) ) ) ) ) ).
tt(cc5_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (v2_matrtop3 B A)) ) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_tops_2 B (k15_euclid A) (k15_euclid A))) ) ) ) ) ) ) ).
tt(cc5_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v1_prob_1 B A) & (v3_measure1 B A))  => (v4_prob_1 B A)) ) ) ) ).
tt(cc5_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_xboole_0 A) => (v1_measure5 A)) ) ) ).
tt(cc5_membered,ax, (! [A:$i] :  ((v3_membered A) => (v1_membered A)) ) ).
tt(cc5_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (v1_metrizts A)) )  =>  ((v2_pre_topc A) &  ((v5_waybel23 A) & (v3_pcomps_1 A)) ) ) ) ) ).
tt(cc5_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v3_mfold_1 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v8_pre_topc B) &  ((v5_waybel23 B) & (v2_mfold_1 B A)) ) ) ) ) ) ) ) ) ).
tt(cc5_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (v13_monoid_0 A)) )  =>  ( (~ (v2_struct_0 A))  & (v2_group_1 A)) ) ) ) ).
tt(cc5_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_msualg_6 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msualg_2 C A B) => (v1_msualg_6 C A)) ) ) ) ).
tt(cc5_msscyc_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v3_msscyc_1 A))  =>  ( (~ (v2_struct_0 A))  & (v2_msscyc_1 A)) ) ) ) ).
tt(cc5_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v4_mssubfam C A B) => (v5_mssubfam C A B)) ) ) ) ) ).
tt(cc5_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) => (v8_struct_0 B)) ) ) ) ).
tt(cc5_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v1_orders_2 A)) )  =>  ( (~ (v2_struct_0 A))  & (v1_neckla_2 A)) ) ) ) ).
tt(cc5_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))) =>  ( ((v1_funct_1 B) & (v2_nfcont_3 B A))  =>  ((v1_funct_1 B) & (v1_nfcont_3 B A)) ) ) ) ) ) ).
tt(cc5_nfcont_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))) =>  ( ((v1_funct_1 B) & (v2_nfcont_4 B A))  =>  ((v1_funct_1 B) & (v1_nfcont_4 B A)) ) ) ) ) ) ).
tt(cc5_orders_4,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) => (v8_struct_0 B)) ) ) ) ).
tt(cc5_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v3_ordinal1 B)) ) ) ) ).
tt(cc5_ordinal5,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 A) &  ((v2_ordinal2 A) & (v1_ordinal5 A)) ) ) ) ).
tt(cc5_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) &  ((v2_ordinal2 A) & (v3_ordinal2 A)) ) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v2_ordinal6 A)) ) ) ) ) ) ).
tt(cc5_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v6_osalg_1 A) & (v8_osalg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) & (v10_osalg_1 A)) ) ) ) ) ) ) ) ).
tt(cc5_osalg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ((m1_osalg_4 C A B) =>  ( ((v2_msualg_4 C A B) & (v3_osalg_4 C A B))  =>  ((v2_msualg_4 C A B) & (v3_msualg_4 C A B)) ) ) ) ) ) ).
tt(cc5_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc5_pcs_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 A))  =>  ((v1_relat_1 A) &  ((v9_pcs_0 A) &  ((v10_pcs_0 A) & (v11_pcs_0 A)) ) ) ) ) ).
tt(cc5_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v11_pencil_1 A) & (v15_pencil_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v11_pencil_1 A) & (v14_pencil_1 A)) ) ) ) ) ).
tt(cc5_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) ) ) ) ).
tt(cc5_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v12_pre_topc A) =>  ((v7_pre_topc A) & (v10_pre_topc A)) ) ) ) ).
tt(cc5_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_quofield C A B) & (v3_quofield C A B)) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v4_quofield C A B)) ) ) ) ) ) ) ).
tt(cc5_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((v6_ratfunc1 B A) => (v5_ratfunc1 B A)) ) ) ) ) ).
tt(cc5_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v4_relat_1 C A)) ) ) ) ).
tt(cc5_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v7_relat_2 A))  =>  ((v1_relat_1 A) &  ((v1_relat_2 A) & (v6_relat_2 A)) ) ) ) ).
tt(cc5_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_rewrite1 A))  =>  ((v1_relat_1 A) & (v2_rewrite1 A)) ) ) ).
tt(cc5_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))) =>  ( ((v1_funct_1 A) & (v3_funct_1 A))  =>  ((v1_funct_1 A) &  ((v7_valued_0 A) & (v8_valued_0 A)) ) ) ) ) ).
tt(cc5_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (v4_ring_1 B A)) ) ) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (v2_ring_1 B A)) ) ) ) ) ) ) ) ) ).
tt(cc5_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (v10_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v6_lattices A)) ) ) ) ).
tt(cc5_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (v1_robbins4 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (v2_robbins4 A)) ) ) ) ) ) ) ) ).
tt(cc5_roughs_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_prob_2 A)) ) ) ) ).
tt(cc5_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa6b A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc5_scmyciel,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v3_scmyciel A 1)) )  => (v4_scmyciel A)) ) ).
tt(cc5_sheffer1,ax, (! [A:$i] :  ((l1_lattices A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v6_lattices A) & (v7_lattices A)) ) ) ) ) ).
tt(cc5_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (~ (v4_simplex0 A))  =>  (~ (v3_pencil_1 A)) ) ) ) ).
tt(cc5_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) )  =>  (! [C:$i] :  ((m2_simplex0 C (u1_struct_0 A) B) => (v2_simplex1 C A)) ) ) ) ).
tt(cc5_simplex2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v2_simplex2 B A) & (m1_simplex0 B (u1_struct_0 (k15_euclid A)))) )  =>  (! [C:$i] :  ((m1_simplex1 C (k15_euclid A) B) => (v2_simplex2 C A)) ) ) ) ).
tt(cc5_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) =>  (~ (v1_zfmisc_1 A)) ) ) ) ).
tt(cc5_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ( (~ (v8_struct_0 A))  =>  ( (~ (v2_struct_0 A))  &  (~ (v8_struct_0 A)) ) ) ) ) ).
tt(cc5_subset_1,ax, (! [A:$i] :  ((v1_zfmisc_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_zfmisc_1 B)) ) ) ) ).
tt(cc5_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_borsuk_1 B A) &  ((v1_tsep_1 B A) & (v1_tdlat_3 B)) ) ) ) ) ) ).
tt(cc5_tex_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v3_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  &  (~ (v2_tdlat_3 A)) ) ) ) ) ) ) ).
tt(cc5_tex_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_subset_1 B A)) )  =>  ( (~ (v1_xboole_0 B))  &  (~ (v1_zfmisc_1 B)) ) ) ) ) ) ) ).
tt(cc5_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tex_3 B A))  =>  (~ (v2_tex_3 B A)) ) ) ) ) ) ).
tt(cc5_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_tdlat_3 B) &  (~ (v4_tex_4 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_tsep_1 B A)) ) ) ) ) ) ) ).
tt(cc5_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v2_pre_topc A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_topalg_6 A)) ) ) ) ) ).
tt(cc5_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v6_topgen_1 B A))  =>  (~ (v2_topgen_1 B A)) ) ) ) ) ) ).
tt(cc5_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) & (v4_prob_1 B A)) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (v3_topgen_4 B A)) ) ) ) ) ) ) ).
tt(cc5_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) & (v1_topgrp_1 A)) ) ) ) ).
tt(cc5_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v3_pre_topc A (k15_euclid 2)) & (v2_connsp_1 A (k15_euclid 2)))  => (v2_topreal4 A (k15_euclid 2))) ) ) ).
tt(cc5_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v2_tops_1 B A))  => (v3_tops_1 B A)) ) ) ) ) ).
tt(cc5_trees_3,ax, (! [A:$i] :  ((v3_trees_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v3_trees_3 B)) ) ) ) ).
tt(cc5_trees_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k5_trees_3 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C B) => (v1_finset_1 C)) ) ) ) ).
tt(cc5_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (v2_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v2_pre_topc A)) ) ) ) ) ).
tt(cc5_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (v2_tsp_2 B A))  =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc5_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  =>  ((v1_relat_1 A) & (v2_valued_0 A)) ) ) ).
tt(cc5_valued_2,ax, (! [A:$i] :  ((v3_valued_2 A) => (v2_valued_2 A)) ) ).
tt(cc5_vectsp_1,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v4_vectsp_1 A))  =>  ( (~ (v2_struct_0 A))  & (v1_group_1 A)) ) ) ) ).
tt(cc5_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (v9_waybel_0 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (v11_waybel_0 B A)) ) ) ) ) ) ) ).
tt(cc5_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v1_waybel11 B A)) ) ) ) ).
tt(cc5_waybel19,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v2_waybel19 A)) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v7_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v1_compts_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(cc5_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v9_waybel_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ) ) ) ) ).
tt(cc5_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_waybel23 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc5_waybel25,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B))) =>  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) & (v7_waybel_0 C)) )  =>  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (v1_yellow14 C (k3_waybel24 A (k1_waybel25 B)))) ) ) ) ) ) ) ) ).
tt(cc5_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (v1_waybel_2 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v2_waybel_2 A)) ) ) ) ) ).
tt(cc5_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (v2_waybel_2 A)) ) ) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) ) ) ) ) ) ).
tt(cc5_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ( ((v4_yellow_0 B A) &  ((v6_yellow_0 B A) & (v7_waybel34 B A)) )  =>  ((v4_yellow_0 B A) & (v6_waybel34 B A)) ) ) ) ) ) ).
tt(cc5_waybel35,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ((v1_zfmisc_1 C) => (v3_waybel35 C A B)) ) ) ) ) ).
tt(cc5_waybel_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v24_waybel_0 A) & (v2_waybel_3 A)) ) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) ) ) ) ).
tt(cc5_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v8_waybel_4 B A) => (v9_waybel_4 B A)) ) ) ) ) ).
tt(cc5_xxreal_0,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) ) ) ) ) ).
tt(cc5_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  ((v3_xxreal_2 A) & (v4_xxreal_2 A)) )  =>  ((v2_membered A) & (v5_xxreal_2 A)) ) ) ).
tt(cc5_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v1_yellow_0 A) & (v2_yellow_0 A))  => (v3_yellow_0 A)) ) ) ).
tt(cc5_yellow11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) )  =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v3_lattice3 A)) ) ) ) ) ) ) ) ).
tt(cc5_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v12_pre_topc A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v9_pre_topc A)) ) ) ) ) ).
tt(cc5_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v13_waybel_0 B A) & (v1_waybel11 B A))  => (v3_pre_topc B A)) ) ) ) ) ).
tt(cc5_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v2_yellow18 B)) ) ) ) ) ) ) ) ).
tt(cc5_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) => (v1_relat_1 B)) ) ) ) ).
tt(cc5_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) => (v3_lattice3 B)) ) ) ) ).
tt(cc6_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((v7_abcmiz_1 B A) =>  ( (~ (v6_abcmiz_1 B A))  & (v8_abcmiz_1 B A)) ) ) ) ) ) ).
tt(cc6_abcmiz_a,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (v3_abcmiz_a A)) )  =>  ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (v3_abcmiz_1 A)) ) ) ) ) ).
tt(cc6_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_afinsq_1 A)) ) ) ) ).
tt(cc6_algstr_0,ax, (! [A:$i] :  ( ((v6_algstr_0 A) & (l1_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_algstr_0 B A)) ) ) ) ).
tt(cc6_algstr_1,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v7_algstr_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v32_algstr_0 A) & (v6_algstr_1 A)) ) ) ) ) ).
tt(cc6_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v4_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (v3_amistd_2 C A B)) ) ) ) ).
tt(cc6_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v8_relat_2 B) & (v7_armstrng B A))  =>  ((v3_armstrng B A) & (v4_armstrng B A)) ) ) ) ) ).
tt(cc6_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v15_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v16_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc6_card_1,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v1_finset_1 A))  => (v7_ordinal1 A)) ) ).
tt(cc6_card_3,ax, (! [A:$i] :  ((v1_finset_1 A) => (v4_card_3 A)) ) ).
tt(cc6_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v1_card_5 A)) ) ) ) ).
tt(cc6_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) &  ((v5_cgames_1 A) & (v6_cgames_1 A)) )  =>  ((v2_cgames_1 A) & (v7_cgames_1 A)) ) ) ).
tt(cc6_circcmb3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  & (m1_circcmb3 B A))  =>  (! [C:$i] :  ((m2_circcmb3 C A B) =>  ((v4_msualg_1 C B) & (v4_circcomb C B)) ) ) ) ) ).
tt(cc6_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v6_closure2 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ) ).
tt(cc6_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_cohsp_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_cohsp_1 A)) ) ) ) ).
tt(cc6_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_compact1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_compact1 A)) ) ) ) ) ).
tt(cc6_compts_1,ax, (! [A:$i] :  ( ((v8_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v8_pre_topc B)) ) ) ) ).
tt(cc6_comput_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_comput_1 A)) => (v2_margrel1 B)) ) ) ).
tt(cc6_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v8_struct_0 A) => (v4_dilworth A)) ) ) ).
tt(cc6_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ( ((v3_euclid_7 B) & (v4_euclid_7 B A))  => (v5_euclid_7 B A)) ) ) ) ) ).
tt(cc6_exchsort,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_xboole_0 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  ((v1_xboole_0 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_exchsort B) & (v5_exchsort B A)) ) ) ) ) ) ) ) ) ).
tt(cc6_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) ) ) ) ).
tt(cc6_finset_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v5_finset_1 A)) ) ).
tt(cc6_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A (k1_tarski k1_xboole_0)))  =>  ((v1_relat_1 A) & (v3_relat_1 A)) ) ) ).
tt(cc6_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v8_fomodel1 B A) => (v9_fomodel1 B A)) ) ) ) ) ).
tt(cc6_fomodel2,ax, (! [A:$i] :  ((v3_finseq_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) ) ) ) ) ).
tt(cc6_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) => (v1_pre_poly B)) ) ) ) ).
tt(cc6_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v1_fomodel4 B A) => (v11_fomodel4 B A)) ) ) ) ).
tt(cc6_funct_1,ax, (! [A:$i] :  ( ((v1_zfmisc_1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) ) ).
tt(cc6_funct_2,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (v2_funct_2 C B)) )  =>  ((v1_funct_1 C) & (v3_funct_2 C A B)) ) ) ) ) ).
tt(cc6_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v16_functor0 C A B) => (v6_functor0 C A B)) ) ) ) ) ).
tt(cc6_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v4_glib_000 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) ) ) ) ).
tt(cc6_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v8_glib_001 B A) =>  ((v1_glib_001 B A) &  ( (~ (v3_glib_001 B A))  & (v5_glib_001 B A)) ) ) ) ) ) ) ).
tt(cc6_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  (! [C:$i] :  ((m2_glib_000 C A (k6_domain_1 (k6_glib_000 A) B) k1_xboole_0) => (v3_glib_002 C)) ) ) ) ).
tt(cc6_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( (~ (v2_struct_0 C))  & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k12_pralg_1 (k1_enumset1 1 2 3) (k11_finseq_1 A B C)))) => (v1_finseq_1 D)) ) ) ) ).
tt(cc6_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((l3_algstr_0 B) =>  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (v2_group_10 B A)) ) ) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (v3_groupp_1 B A)) ) ) ) ) ) ) ) ).
tt(cc6_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v4_hahnban B A) & (v7_hahnban B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (v5_hahnban B A)) ) ) ) ) ) ) ).
tt(cc6_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)))) =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_hermitan B A A) & (v3_hermitan B A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v4_bilinear B k1_complfld A A)) ) ) ) ) ) ) ).
tt(cc6_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) => (v1_instalg1 B)) ) ) ) ).
tt(cc6_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v5_tops_1 B A) & (v6_tops_1 B A)) ) ) ) ) ) ).
tt(cc6_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (v11_lattices A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v1_lattice2 A)) ) ) ) ) ).
tt(cc6_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v11_lattices A) &  ((v15_lattices A) & (v16_lattices A)) ) )  =>  ( (~ (v2_struct_0 A))  & (v17_lattices A)) ) ) ) ).
tt(cc6_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v1_lfuzzy_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (v1_lfuzzy_0 A)) ) ) ) ) ) ).
tt(cc6_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v3_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((v1_finset_1 B) & (v3_pre_topc B A)) ) ) ) ) ) ).
tt(cc6_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) & (v4_prob_1 B A)) )  =>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) & (v4_prob_1 B A)) ) ) ) ) ) ).
tt(cc6_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) => (v1_membered A)) ) ).
tt(cc6_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (v1_metrizts A)) )  =>  ((v2_pre_topc A) &  ((v7_topgen_1 A) & (v3_pcomps_1 A)) ) ) ) ) ).
tt(cc6_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v8_pre_topc B) &  ((v5_waybel23 B) & (v2_mfold_1 B A)) ) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v3_mfold_1 B A)) ) ) ) ) ) ) ).
tt(cc6_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v13_monoid_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v11_monoid_0 A) & (v12_monoid_0 A)) ) ) ) ) ).
tt(cc6_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v5_mssubfam C A B) => (v2_relat_1 C)) ) ) ) ) ).
tt(cc6_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v1_neckla_3 A)) ) ) ).
tt(cc6_oposet_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ( ( (~ (v2_struct_0 A))  & (v6_oposet_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v5_orders_2 A)) ) ) ) ) ) ).
tt(cc6_ordinal1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_ordinal1 A)) ) ).
tt(cc6_ordinal5,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v4_ordinal5 A))  =>  ( (~ (v1_xboole_0 A))  &  ((v3_ordinal1 A) & (v4_ordinal1 A)) ) ) ) ).
tt(cc6_ordinal6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (v3_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k2_ordinal1 A)))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C B (k2_ordinal1 A)))  =>  ((v1_funct_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_2 C B (k2_ordinal1 A)) & (v1_ordinal2 C)) ) ) ) ) ) ) ) ).
tt(cc6_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (v9_osalg_1 B A)) ) ) ) ).
tt(cc6_osalg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_osalg_4 C A B) =>  ( ((v2_msualg_4 C A B) & (v3_msualg_4 C A B))  =>  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (v3_osalg_4 C A B)) ) ) ) ) ) ) ).
tt(cc6_pcs_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_pcs_0 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) ) ) ) ).
tt(cc6_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) ) ) ) ) ).
tt(cc6_pre_poly,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (v1_card_3 A)) ) ).
tt(cc6_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v7_pre_topc A) & (v10_pre_topc A))  => (v12_pre_topc A)) ) ) ).
tt(cc6_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (v5_relat_1 C A)) ) ) ) ).
tt(cc6_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v8_rewrite1 A))  =>  ((v1_relat_1 A) & (v7_rewrite1 A)) ) ) ).
tt(cc6_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (v8_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v6_robbins1 A) & (v8_robbins1 A)) ) ) ) ) ) ).
tt(cc6_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v12_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) & (v9_robbins3 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (v1_robbins4 A)) ) ) ) ) ) ) ) ).
tt(cc6_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_roughs_1 A) => (v3_roughs_1 A)) ) ) ).
tt(cc6_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scm_halt A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) ) ) ) ).
tt(cc6_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  ((v4_scmyciel A) & (v6_scmyciel A)) ) ) ).
tt(cc6_sheffer1,ax, (! [A:$i] :  ((l3_lattices A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v8_lattices A) &  ((v9_lattices A) & (v17_lattices A)) ) ) ) ) ) ).
tt(cc6_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v3_pencil_1 A))  & (v4_simplex0 A))  =>  (~ (v5_simplex0 A)) ) ) ) ).
tt(cc6_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v4_pre_topc B (k15_euclid A)) & (v9_rltopsp1 B (k15_euclid A)))  => (v2_compts_1 B (k15_euclid A))) ) ) ) ) ).
tt(cc6_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) =>  ((v2_compts_1 A (k15_euclid 2)) & (v1_topreal4 A)) ) ) ) ).
tt(cc6_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v7_struct_0 A) => (v8_struct_0 A)) ) ) ).
tt(cc6_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) => (v2_tdlat_3 B)) ) ) ) ).
tt(cc6_tex_2,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  ( (~ (v1_xboole_0 B))  &  (~ (v1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(cc6_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v1_tex_2 B A))  => (v2_tex_3 B A)) ) ) ) ) ).
tt(cc6_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (v2_tdlat_3 B)) )  =>  ( (~ (v2_struct_0 B))  & (v4_tex_4 B A)) ) ) ) ) ) ).
tt(cc6_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  ((v3_funct_1 C) => (v3_topalg_6 C A B)) ) ) ) ) ).
tt(cc6_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v2_topgen_1 B A))  =>  (~ (v6_topgen_1 B A)) ) ) ) ) ) ).
tt(cc6_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_topgen_4 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc6_topgrp_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v2_group_1 A) &  ((v3_group_1 A) & (v5_group_1 A)) ) ) ) ) ) ).
tt(cc6_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_xboole_0 A) => (v1_sppol_1 A)) ) ) ).
tt(cc6_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_tops_1 B A))  => (v1_xboole_0 B)) ) ) ) ) ).
tt(cc6_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(cc6_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_trees_9 A)) => (v1_finset_1 B)) ) ) ) ).
tt(cc6_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (v6_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v2_tdlat_3 A)) ) ) ) ) ) ).
tt(cc6_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (v1_tex_2 B A))  =>  (~ (v2_tsp_2 B A)) ) ) ) ) ) ).
tt(cc6_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  =>  ((v1_relat_1 A) & (v1_valued_0 A)) ) ) ).
tt(cc6_valued_2,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v6_valued_2 A)) ) ).
tt(cc6_vectsp_1,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (v6_vectsp_1 A)) )  =>  ( (~ (v2_struct_0 A))  & (v3_vectsp_1 A)) ) ) ) ).
tt(cc6_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (v3_orders_2 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (v16_waybel_0 A)) ) ) ) ) ).
tt(cc6_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) => (v3_waybel11 B A)) ) ) ) ) ).
tt(cc6_waybel19,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (v2_waybel19 A)) ) ) ) ) ) ) )  =>  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (v3_waybel_3 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(cc6_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v9_waybel_1 A))  =>  ( (~ (v2_struct_0 A))  & (v2_waybel_1 A)) ) ) ) ).
tt(cc6_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_waybel23 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(cc6_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) &  ((v2_pre_topc A) & (v6_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (v1_waybel25 A)) ) ) ) ) ) ).
tt(cc6_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v9_waybel_1 A) & (v3_lattice3 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) & (v2_waybel_2 A)) ) ) ) ) ) ) ) ).
tt(cc6_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_waybel30 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_waybel30 A)) ) ) ) ) ).
tt(cc6_waybel34,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v18_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v4_waybel34 C A B)) ) ) ) ) ) ) ).
tt(cc6_waybel_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (v16_waybel_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (v2_waybel_3 A)) ) ) ) ) ) ) ) ).
tt(cc6_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((v5_waybel_4 B A) &  ((v6_waybel_4 B A) & (v9_waybel_4 B A)) )  =>  ((v5_waybel_4 B A) &  ((v6_waybel_4 B A) & (v8_waybel_4 B A)) ) ) ) ) ) ) ).
tt(cc6_xxreal_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) ) )  =>  ((v1_xxreal_0 A) & (v3_xxreal_0 A)) ) ) ).
tt(cc6_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) & (v1_finset_1 A))  =>  ((v3_membered A) & (v5_xxreal_2 A)) ) ) ).
tt(cc6_yellow_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) =>  ((v3_orders_2 B) & (v4_yellow_0 B A)) ) ) ) ) ) ).
tt(cc6_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v11_pre_topc A))  =>  ((v2_pre_topc A) & (v8_pre_topc A)) ) ) ) ).
tt(cc6_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  & (v2_altcat_1 B))  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v9_altcat_1 B)) ) ) ) ) ) ) ).
tt(cc6_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v8_yellow_6 B A) =>  ((v4_yellow_6 B A) &  ((v5_yellow_6 B A) &  ((v6_yellow_6 B A) & (v7_yellow_6 B A)) ) ) ) ) ) ) ) ).
tt(cc6_yellow_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(cc7_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ( ( (~ (v6_abcmiz_1 B A))  & (v8_abcmiz_1 B A))  =>  ((v7_abcmiz_1 B A) & (v8_abcmiz_1 B A)) ) ) ) ) ) ).
tt(cc7_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) ) ).
tt(cc7_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v9_algstr_0 B A) & (v10_algstr_0 B A))  => (v11_algstr_0 B A)) ) ) ) ) ).
tt(cc7_algstr_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) ) ) ) ) ) ) ).
tt(cc7_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v3_armstrng B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc7_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v20_bcialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (v16_bcialg_1 A)) ) ) ) ) ) ) ) ).
tt(cc7_card_1,ax, (! [A:$i] :  ((v3_card_1 A k1_xboole_0) => (v1_xboole_0 A)) ) ).
tt(cc7_card_3,ax, (! [A:$i] :  ((v4_card_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v4_card_3 B)) ) ) ) ).
tt(cc7_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) & (v10_cgames_1 A))  =>  ((v2_cgames_1 A) &  ((v6_cgames_1 A) &  (~ (v7_cgames_1 A)) ) ) ) ) ).
tt(cc7_circcmb3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((v8_struct_0 B) & (m1_circcmb3 B A)) )  =>  (! [C:$i] :  ((m2_circcmb3 C A B) => (v3_circcmb3 C B)) ) ) ) ).
tt(cc7_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (v10_closure2 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (v8_closure2 C A B)) ) ) ) ) ) ) ).
tt(cc7_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_cohsp_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_cohsp_1 A)) ) ) ) ).
tt(cc7_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (v5_compact1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (v3_compact1 A)) ) ) ) ) ) ).
tt(cc7_comput_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_comput_1 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C B) => (v2_margrel1 C)) ) ) ) ).
tt(cc7_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_dilworth B A) =>  ((v1_finset_1 B) & (v2_dilworth B A)) ) ) ) ) ) ).
tt(cc7_euclid_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v5_euclid_7 B A) =>  ( (~ (v1_xboole_0 B))  & (v5_euclid_7 B A)) ) ) ) ) ) ).
tt(cc7_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v2_finseq_1 A)) ) ) ) ) ).
tt(cc7_finset_1,ax, (! [A:$i] :  ((v5_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_finset_1 B)) ) ) ) ).
tt(cc7_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_relat_1 A))  =>  ((v1_relat_1 A) & (v5_relat_1 A (k1_tarski k1_xboole_0))) ) ) ).
tt(cc7_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v6_fomodel1 B A) => (v5_fomodel1 B A)) ) ) ) ) ).
tt(cc7_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  (! [D:$i] :  ((v2_fomodel2 D A B C) => (v1_funct_1 D)) ) ) ) ).
tt(cc7_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel4 A)) => (v11_fomodel4 B A)) ) ) ) ).
tt(cc7_funct_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v4_funct_1 A)) ) ).
tt(cc7_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((v1_relat_2 B) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funct_2 B A A)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (v3_funct_2 B A A)) ) ) ) ) ) ).
tt(cc7_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v4_glib_000 A) & (v6_glib_000 A)) ) ) ) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) ) ) ) ).
tt(cc7_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) => (v2_glib_002 B)) ) ) ) ).
tt(cc7_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( (~ (v2_struct_0 C))  & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_group_7 (k1_enumset1 1 2 3) (k11_finseq_1 A B C)))) => (v1_finseq_1 D)) ) ) ) ).
tt(cc7_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) => (v3_pre_topc B A)) ) ) ) ) ).
tt(cc7_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v11_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v12_lattices A)) ) ) ) ) ).
tt(cc7_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v2_lfuzzy_0 A))  =>  ( (~ (v2_struct_0 A))  & (v3_yellow_0 A)) ) ) ) ).
tt(cc7_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_matroid0 B A) =>  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) ) ) ) ).
tt(cc7_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) & (v3_measure1 B A)) )  =>  ( (~ (v1_xboole_0 B))  & (v1_finsub_1 B)) ) ) ) ) ).
tt(cc7_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) => (v2_membered A)) ) ).
tt(cc7_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) &  ((v7_topgen_1 A) & (v3_pcomps_1 A)) )  =>  ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (v1_metrizts A)) ) ) ) ) ).
tt(cc7_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v3_mfold_1 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (v4_mfold_1 B)) ) ) ) ) ) ) ).
tt(cc7_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v11_monoid_0 A) & (v12_monoid_0 A)) )  =>  ( (~ (v2_struct_0 A))  & (v13_monoid_0 A)) ) ) ) ).
tt(cc7_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v2_mssubfam C A B) => (v6_mssubfam C A B)) ) ) ) ) ).
tt(cc7_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v16_waybel_0 A))  =>  ( (~ (v2_struct_0 A))  & (v1_neckla_3 A)) ) ) ) ).
tt(cc7_ordinal1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v7_ordinal1 A)) ) ).
tt(cc7_ordinal5,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v5_ordinal5 A))  =>  ( (~ (v1_xboole_0 A))  & (v3_ordinal1 A)) ) ) ).
tt(cc7_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C A B))  =>  ((v1_funct_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_2 C A B) & (v1_ordinal2 C)) ) ) ) ) ) ) ) ).
tt(cc7_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_orders_3 A) &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (v12_osalg_1 B A)) ) ) ) ).
tt(cc7_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((v14_pcs_0 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v4_pcs_0 A) &  ((v6_pcs_0 A) & (v13_pcs_0 A)) ) ) ) ) ) ) ).
tt(cc7_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pre_poly A)) ) ) ) ).
tt(cc7_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v7_pre_topc A) => (v6_pre_topc A)) ) ) ).
tt(cc7_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((v1_xboole_0 B) &  ((v1_relat_1 B) & (v4_relat_1 B A)) ) ) ) ) ) ).
tt(cc7_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v7_rewrite1 A))  =>  ((v1_relat_1 A) &  ((v8_rewrite1 A) & (v9_rewrite1 A)) ) ) ) ).
tt(cc7_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v6_robbins1 A) & (v10_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (v10_robbins1 A)) ) ) ) ) ) ).
tt(cc7_robbins4,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v1_robbins4 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) &  ((v9_robbins3 A) & (v1_robbins4 A)) ) ) ) ) ) ) ) ) ).
tt(cc7_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_3 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~ (v4_roughs_1 B A)) ) ) ) ) ).
tt(cc7_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v1_scmfsa7b A) & (v1_scm_halt A)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scm_halt A)) ) ) ) ) ) ) ) ) ).
tt(cc7_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v3_pencil_1 A))  & (v1_matroid0 A))  =>  (~ (v5_simplex0 A)) ) ) ) ).
tt(cc7_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ( (~ (v8_struct_0 A))  =>  (~ (v7_struct_0 A)) ) ) ) ).
tt(cc7_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v1_tdlat_3 A))  =>  ((v2_pre_topc A) & (v3_tdlat_3 A)) ) ) ) ).
tt(cc7_tex_2,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_subset_1 B (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 B))  & (v1_zfmisc_1 B)) ) ) ) ) ) ).
tt(cc7_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_tex_3 B A))  => (v1_tex_2 B A)) ) ) ) ) ).
tt(cc7_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) &  (~ (v4_tex_4 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v2_tdlat_3 B)) ) ) ) ) ) ) ).
tt(cc7_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topalg_6 A) & (l1_pre_topc A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) => (v3_topalg_6 C A B)) ) ) ) ).
tt(cc7_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) => (v6_topgen_1 B A)) ) ) ) ) ).
tt(cc7_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_prob_1 B (u1_struct_0 A)) &  ((v1_topgen_4 B A) & (v3_topgen_4 B (u1_struct_0 A))) )  =>  ((v2_topgen_4 B A) & (v4_topgen_4 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(cc7_topgrp_1,ax, (! [A:$i] :  ((l1_topgrp_1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (v4_topgrp_1 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (v1_topgrp_1 A)) ) ) ) ) ) ) ).
tt(cc7_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_xboole_0 A) => (v2_sppol_1 A)) ) ) ).
tt(cc7_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_trees_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_finset_1 B)) ) ) ) ).
tt(cc7_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (v3_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) ) ) ) ) ).
tt(cc7_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tex_2 B A) & (v2_tsp_2 B A))  =>  (~ (v1_tsep_1 B A)) ) ) ) ) ) ).
tt(cc7_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  ((v1_relat_1 A) & (v5_relat_1 A k3_numbers)) ) ) ).
tt(cc7_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) => (v4_funct_1 A)) ) ).
tt(cc7_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v17_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v19_waybel_0 C A B) & (v21_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(cc7_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v9_waybel_1 A))  =>  ( (~ (v2_struct_0 A))  & (v2_yellow_0 A)) ) ) ) ).
tt(cc7_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_waybel23 B A) => (v2_waybel23 B A)) ) ) ) ).
tt(cc7_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) =>  ((v4_waybel11 B) & (v1_waybel25 B)) ) ) ) ) ) ).
tt(cc7_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v3_lattice3 A) & (v2_waybel_2 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v9_waybel_1 A)) ) ) ) ) ) ) ).
tt(cc7_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v2_waybel30 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_waybel30 A)) ) ) ) ) ).
tt(cc7_waybel34,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v4_waybel34 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v20_waybel_0 C A B) & (v5_waybel34 C A B)) ) ) ) ) ) ) ) ).
tt(cc7_waybel_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (v1_compts_1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v9_pre_topc A) &  ((v10_pre_topc A) & (v6_waybel_3 A)) ) ) ) ) ) ) ).
tt(cc7_xxreal_0,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 A))  =>  ((v1_xxreal_0 A) &  ( (~ (v2_xxreal_0 A))  &  (~ (v3_xxreal_0 A)) ) ) ) ) ).
tt(cc7_xxreal_2,ax, (! [A:$i] :  ( ((v5_membered A) &  ( (~ (v1_xboole_0 A))  & (v4_xxreal_2 A)) )  =>  ((v5_membered A) &  ( (~ (v1_xboole_0 A))  & (v2_xxreal_2 A)) ) ) ) ).
tt(cc7_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) =>  ((v4_orders_2 B) & (v4_yellow_0 B A)) ) ) ) ) ) ).
tt(cc7_yellow13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_yellow13 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(cc7_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v1_yellow21 B)) ) ) ) ) ) ) ) ).
tt(cc7_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ( ((v4_yellow_6 B A) &  ((v5_yellow_6 B A) &  ((v6_yellow_6 B A) & (v7_yellow_6 B A)) ) )  => (v8_yellow_6 B A)) ) ) ) ) ).
tt(cc7_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (l1_pre_topc B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (~ (v2_struct_0 C)) ) ) ) ) ).
tt(cc8_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ( ( (~ (v7_abcmiz_1 B A))  & (v8_abcmiz_1 B A))  =>  ((v6_abcmiz_1 B A) & (v8_abcmiz_1 B A)) ) ) ) ) ) ).
tt(cc8_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) ) ) ) ).
tt(cc8_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_algstr_0 B A) =>  ((v9_algstr_0 B A) & (v10_algstr_0 B A)) ) ) ) ) ) ).
tt(cc8_algstr_1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v7_struct_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (v4_vectsp_1 A)) ) ) ) ) ).
tt(cc8_card_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v3_card_1 A k1_xboole_0)) ) ).
tt(cc8_card_3,ax, (! [A:$i] :  ((v2_card_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_card_3 B)) ) ) ) ).
tt(cc8_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) &  ((v6_cgames_1 A) &  (~ (v7_cgames_1 A)) ) )  =>  ((v2_cgames_1 A) & (v10_cgames_1 A)) ) ) ).
tt(cc8_circcmb3,ax, (! [A:$i] :  ( (~ (v1_facirc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~ (v1_facirc_1 B)) ) ) ) ) ).
tt(cc8_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure2 B A) =>  ((v13_closure2 B A) => (v12_closure2 B A)) ) ) ) ) ).
tt(cc8_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v9_cohsp_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_cohsp_1 A) & (v8_cohsp_1 A)) ) ) ) ) ).
tt(cc8_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_compts_1 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_compact1 A)) ) ) ) ) ).
tt(cc8_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_comput_1 k5_numbers)) =>  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) ).
tt(cc8_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_dilworth A) & (v4_dilworth A))  => (v8_struct_0 A)) ) ) ).
tt(cc8_euclid_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_real_ns1 A))) => (v3_valued_0 B)) ) ) ) ).
tt(cc8_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_exchsort A)) ) )  =>  (! [B:$i] :  ((m1_exchsort B A) => (v3_valued_0 B)) ) ) ) ).
tt(cc8_finseq_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v3_finseq_1 A)) ) ).
tt(cc8_finset_1,ax, (! [A:$i] :  ((v5_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v5_finset_1 B)) ) ) ) ).
tt(cc8_fomodel0,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v3_xxreal_0 A)) )  =>  ((v7_ordinal1 A) & (v1_int_1 A)) ) ) ).
tt(cc8_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v5_fomodel1 B A) => (v10_fomodel1 B A)) ) ) ) ) ).
tt(cc8_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k16_fomodel2 A B)) => (v1_fomodel2 C A B)) ) ) ) ).
tt(cc8_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) & (v7_ordinal1 C)) )  =>  (! [E:$i] :  ((v4_fomodel4 E C A B D) => (v1_fomodel4 E A)) ) ) ) ).
tt(cc8_funct_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(cc8_funct_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((v1_funct_1 C) & (v1_funct_2 C A B))  =>  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  & (v1_funct_2 C A B)) ) ) ) ) ) ) ).
tt(cc8_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) => (v2_glib_000 B)) ) ) ) ).
tt(cc8_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ((v4_glib_002 B A) => (v1_glib_002 B)) ) ) ) ) ).
tt(cc8_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) => (v4_pre_topc B A)) ) ) ) ) ).
tt(cc8_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) =>  ((v18_lattices B A) & (v19_lattices B A)) ) ) ) ) ) ).
tt(cc8_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v2_lfuzzy_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_lattice3 A) & (v2_lfuzzy_0 A)) ) ) ) ) ).
tt(cc8_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (v3_membered A)) ) ).
tt(cc8_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v5_waybel23 A))  =>  ((v2_pre_topc A) & (v1_metrizts A)) ) ) ) ).
tt(cc8_mfold_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v5_waybel23 A) & (v1_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v3_mfold_1 A k1_xboole_0)) ) ) ) ) ).
tt(cc8_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  & (v16_monoid_0 A))  =>  ( (~ (v2_struct_0 A))  &  ((v14_monoid_0 A) & (v15_monoid_0 A)) ) ) ) ) ).
tt(cc8_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v6_mssubfam C A B) => (v2_relat_1 C)) ) ) ) ) ).
tt(cc8_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v1_neckla_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (v16_waybel_0 A)) ) ) ) ) ) ).
tt(cc8_ordinal1,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) => (v7_ordinal1 A)) ) ).
tt(cc8_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_xboole_0 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v6_ordinal5 A)) ) ) ) ) ) ).
tt(cc8_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k7_osalg_1 A)) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc8_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v4_pcs_0 A) &  ((v6_pcs_0 A) & (v13_pcs_0 A)) ) ) )  => (v14_pcs_0 A)) ) ) ).
tt(cc8_pre_poly,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pre_poly B)) ) ) ) ) ) ) ) ).
tt(cc8_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_pre_topc A) => (v7_pre_topc A)) ) ) ).
tt(cc8_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  ((v1_xboole_0 B) &  ((v1_relat_1 B) & (v5_relat_1 B A)) ) ) ) ) ) ).
tt(cc8_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v6_rewrite1 A))  =>  ((v1_relat_1 A) & (v7_rewrite1 A)) ) ) ).
tt(cc8_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v5_robbins1 A) & (v10_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (v17_lattices A)) ) ) ) ) ).
tt(cc8_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  ((v4_scmyciel A) & (v8_scmyciel A)) ) ) ).
tt(cc8_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_simplex0 A) =>  ((v1_matroid0 A) & (v2_simplex0 A)) ) ) ) ).
tt(cc8_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_struct_0 A) => (v13_struct_0 A k1_xboole_0)) ) ) ).
tt(cc8_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v2_tdlat_3 A))  =>  ((v2_pre_topc A) & (v3_tdlat_3 A)) ) ) ) ).
tt(cc8_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v1_zfmisc_1 B))  =>  ( (~ (v1_xboole_0 B))  & (v1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(cc8_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (v1_tex_3 B A))  => (v2_tex_3 B A)) ) ) ) ) ).
tt(cc8_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_tdlat_3 B) &  (~ (v4_tex_4 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  (~ (v1_borsuk_1 B A)) ) ) ) ) ) ) ).
tt(cc8_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_topalg_6 A)) =>  ( ((v5_topalg_6 B A) & (v6_topalg_6 B A))  => (v7_topalg_6 B A)) ) ) ) ) ).
tt(cc8_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) & (v4_pre_topc B A)) ) ) ) ) ).
tt(cc8_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_prob_1 B (u1_struct_0 A)) &  ((v2_topgen_4 B A) & (v4_topgen_4 B (u1_struct_0 A))) )  =>  ((v1_topgen_4 B A) & (v3_topgen_4 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(cc8_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) => (v2_connsp_1 A (k15_euclid 2))) ) ) ).
tt(cc8_trees_3,ax, (! [A:$i] :  ((v3_trees_3 A) => (v4_funct_1 A)) ) ).
tt(cc8_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (v3_tdlat_3 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v6_pre_topc A)) ) ) ) ) ) ).
tt(cc8_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) & (v2_tsp_2 B A))  =>  (~ (v1_tex_2 B A)) ) ) ) ) ) ).
tt(cc8_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  ((v1_relat_1 A) & (v3_valued_0 A)) ) ) ).
tt(cc8_valued_2,ax, (! [A:$i] :  ((v2_valued_2 A) => (v4_funct_1 A)) ) ).
tt(cc8_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v18_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v20_waybel_0 C A B) & (v22_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(cc8_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  & (v11_waybel_1 A))  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) &  ((v2_waybel_1 A) & (v10_waybel_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(cc8_waybel23,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_waybel23 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc8_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((l1_waybel_0 B (k1_waybel25 A)) =>  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (v10_waybel_0 B (k1_waybel25 A))) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v10_waybel_0 B (k1_waybel25 A)) & (v3_yellow_6 B (k1_waybel25 A))) ) ) ) ) ) ) ) ) ).
tt(cc8_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ( (~ (v2_struct_0 A))  & (v2_tdlat_3 A))  =>  ( (~ (v2_struct_0 A))  &  ((v1_waybel30 A) & (v3_waybel30 A)) ) ) ) ) ).
tt(cc8_xxreal_0,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  ( (~ (v2_xxreal_0 A))  &  (~ (v3_xxreal_0 A)) ) )  =>  ((v1_xboole_0 A) & (v1_xxreal_0 A)) ) ) ).
tt(cc8_xxreal_2,ax, (! [A:$i] :  ( ((v5_membered A) &  ( (~ (v1_xboole_0 A))  & (v3_xxreal_2 A)) )  =>  ((v5_membered A) &  ( (~ (v1_xboole_0 A))  & (v1_xxreal_2 A)) ) ) ) ).
tt(cc8_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) =>  ((v5_orders_2 B) & (v4_yellow_0 B A)) ) ) ) ) ) ).
tt(cc8_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m2_yellow13 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(cc8_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (v3_altcat_2 B A)) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v2_yellow21 B)) ) ) ) ) ) ) ) ).
tt(cc8_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (l1_pre_topc B))  =>  (! [C:$i] :  ((m3_yellow_9 C B A) =>  (~ (v2_struct_0 C)) ) ) ) ) ).
tt(cc9_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) => (v1_xtuple_0 B)) ) ) ) ).
tt(cc9_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) ) ) ) ).
tt(cc9_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ( ((v12_algstr_0 A) & (v13_algstr_0 A))  => (v14_algstr_0 A)) ) ) ).
tt(cc9_algstr_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v13_struct_0 A 1) =>  ((v13_struct_0 A 1) &  ((v2_group_1 A) &  ((v3_group_1 A) & (v5_group_1 A)) ) ) ) ) ) ).
tt(cc9_card_1,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  ( (~ (v1_xboole_0 A))  & (v1_zfmisc_1 A)) ) ) ).
tt(cc9_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 A)) => (v5_funct_1 B A)) ) ) ) ).
tt(cc9_cgames_1,ax, (! [A:$i] :  ( ((v2_cgames_1 A) & (v9_cgames_1 A))  =>  ((v2_cgames_1 A) &  ((v5_cgames_1 A) &  (~ (v7_cgames_1 A)) ) ) ) ) ).
tt(cc9_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure2 B A) =>  ((v15_closure2 B A) => (v14_closure2 B A)) ) ) ) ) ).
tt(cc9_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v10_cohsp_1 A)) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v4_cohsp_1 A) & (v9_cohsp_1 A)) ) ) ) ) ).
tt(cc9_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v1_tdlat_3 A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (v5_compact1 A)) ) ) ) ) ).
tt(cc9_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k9_comput_1) => (v2_margrel1 A)) ) ).
tt(cc9_dilworth,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) =>  ((v1_xboole_0 B) => (v5_dilworth B A)) ) ) ) ) ).
tt(cc9_euclid_7,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k10_funcsdom A))) => (v3_valued_0 B)) ) ) ).
tt(cc9_exchsort,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_funct_2 A B)) => (v5_ordinal1 C)) ) ) ) ).
tt(cc9_finseq_1,ax, (! [A:$i] :  ((v3_finseq_1 A) => (v4_funct_1 A)) ) ).
tt(cc9_finset_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v2_finset_1 A)) ) ) ).
tt(cc9_fomodel0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_xcmplx_0 A k1_xboole_0)) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(cc9_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v8_fomodel1 B A) =>  (~ (v7_fomodel1 B A)) ) ) ) ) ) ).
tt(cc9_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v3_fomodel2 B A k6_numbers) => (v15_fomodel1 B A)) ) ) ) ) ).
tt(cc9_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [E:$i] :  ((v8_fomodel4 E A B (k6_subset_1 C D)) => (v8_fomodel4 E A B C)) ) ) ) ).
tt(cc9_funct_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v4_funct_1 B)) ) ) ) ).
tt(cc9_funct_2,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_funct_2 C A B) => (v4_funct_1 C)) ) ) ).
tt(cc9_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) => (v3_glib_000 B)) ) ) ) ).
tt(cc9_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  (! [C:$i] :  ((m2_glib_000 C A (k1_glib_002 A B) (k21_glib_000 A (k1_glib_002 A B))) => (v4_glib_002 C A)) ) ) ) ).
tt(cc9_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) =>  ((v3_pre_topc B A) & (v4_tops_1 B A)) ) ) ) ) ) ).
tt(cc9_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v18_lattices B A) => (v20_lattices B A)) ) ) ) ) ).
tt(cc9_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (v16_waybel_0 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (v2_waybel_1 A)) ) ) ) ) ) ) ) ).
tt(cc9_membered,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k3_numbers)) => (v4_membered A)) ) ).
tt(cc9_metrizts,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) &  ((v9_pre_topc A) & (v1_metrizts A)) )  =>  ((v2_pre_topc A) & (v10_pre_topc A)) ) ) ) ).
tt(cc9_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v14_monoid_0 A) & (v15_monoid_0 A)) )  =>  ( (~ (v2_struct_0 A))  & (v16_monoid_0 A)) ) ) ) ).
tt(cc9_ordinal1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v6_ordinal1 A)) ) ).
tt(cc9_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v6_ordinal5 A)) ) ) )  =>  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v1_ordinal5 A)) ) ) ) ) ) ).
tt(cc9_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((v15_pcs_0 A) =>  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_pcs_0 A) &  ((v6_pcs_0 A) & (v13_pcs_0 A)) ) ) ) ) ) ) ).
tt(cc9_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k15_pre_poly A))) => (v4_funct_1 B)) ) ) ).
tt(cc9_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_struct_0 A) => (v6_pre_topc A)) ) ) ).
tt(cc9_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v8_rewrite1 A))  =>  ((v1_relat_1 A) & (v5_rewrite1 A)) ) ) ).
tt(cc9_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (v8_robbins1 A)) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v5_robbins1 A) & (v8_robbins1 A)) ) ) ) ) ) ).
tt(cc9_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))) =>  ((v1_zfmisc_1 B) => (v9_scmyciel B A)) ) ) ) ) ).
tt(cc9_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_simplex0 A) =>  ((v4_matroid0 A) & (v3_simplex0 A)) ) ) ) ).
tt(cc9_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v13_struct_0 A k1_xboole_0) => (v2_struct_0 A)) ) ) ).
tt(cc9_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( (~ (v2_struct_0 B))  =>  ( (~ (v2_struct_0 B))  & (v3_tdlat_3 B)) ) ) ) ) ) ).
tt(cc9_tex_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_subset_1 B (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 B))  &  (~ (v1_zfmisc_1 B)) ) ) ) ) ) ) ).
tt(cc9_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tex_3 B A) &  (~ (v2_tex_3 B A)) )  =>  (~ (v1_tsep_1 B A)) ) ) ) ) ) ).
tt(cc9_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_topalg_6 A)) =>  ((v7_topalg_6 B A) =>  ((v5_topalg_6 B A) & (v6_topalg_6 B A)) ) ) ) ) ) ).
tt(cc9_topgen_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v2_pre_topc A) & (v1_orders_4 A))  =>  ((v2_pre_topc A) & (v7_topgen_1 A)) ) ) ) ).
tt(cc9_topgen_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_xboole_0 B) =>  ((v1_tops_2 B A) & (v2_tops_2 B A)) ) ) ) ) ) ).
tt(cc9_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v3_trees_2 B)) ) ) ) ).
tt(cc9_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  (~ (v1_tdlat_3 A)) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  (~ (v3_tdlat_3 A)) ) ) ) ) ) ).
tt(cc9_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_borsuk_1 B A) & (v1_tex_2 B A))  =>  (~ (v2_tsp_2 B A)) ) ) ) ) ) ).
tt(cc9_valued_0,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_relat_1 A) & (v4_valued_0 A)) ) ) ).
tt(cc9_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_valued_2 B)) ) ) ) ).
tt(cc9_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v23_waybel_0 C A B)) )  =>  ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 C A B)) ) ) ) ) ) ) ) ).
tt(cc9_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) &  ((v2_waybel_1 A) & (v10_waybel_1 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  & (v11_waybel_1 A)) ) ) ) ).
tt(cc9_waybel25,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))))) =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) & (v5_pre_topc C (k1_waybel25 A) (k1_waybel25 B))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) & (v22_waybel_0 C (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ) ) ).
tt(cc9_waybel30,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v3_orders_2 A)) )  =>  ((v13_struct_0 A 1) & (v2_waybel30 A)) ) ) ) ).
tt(cc9_xxreal_2,ax, (! [A:$i] :  ((v6_membered A) =>  ((v6_membered A) & (v3_xxreal_2 A)) ) ) ).
tt(cc9_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v7_yellow_0 B A) => (v5_yellow_0 B A)) ) ) ) ) ).
tt(cc9_yellow13,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v3_orders_2 A)) )  =>  ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (v2_yellow13 A)) ) ) ) ) ).
tt(cc9_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) &  ((v4_yellow21 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v2_altcat_2 B A) & (v3_altcat_2 B A)) ) )  =>  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (v4_yellow21 B)) ) ) ) ) ) ) ) ).
tt(commutativity_k10_arytm_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_arytm_3) & (m1_subset_1 B k5_arytm_3))  =>  ((k10_arytm_3 A B) = (k10_arytm_3 B A)) ) ) ).
tt(commutativity_k10_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k10_bvfunc_1 A B C) = (k10_bvfunc_1 A C B)) ) ) ).
tt(commutativity_k10_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((k10_group_2 A B C) = (k10_group_2 A C B)) ) ) ).
tt(commutativity_k10_margrel1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k10_margrel1 A B) = (k10_margrel1 B A)) ) ) ).
tt(commutativity_k10_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((k10_polynom1 A B C D) = (k10_polynom1 A B D C)) ) ) ).
tt(commutativity_k10_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k10_xboolean A B) = (k10_xboolean B A)) ) ) ).
tt(commutativity_k11_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k11_binop_2 A B) = (k11_binop_2 B A)) ) ) ).
tt(commutativity_k11_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k11_openlatt A B C) = (k11_openlatt A C B)) ) ) ).
tt(commutativity_k11_pnproc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m2_pnproc_1 B A) &  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B)))) )  =>  ((k11_pnproc_1 A B C D) = (k11_pnproc_1 A B D C)) ) ) ).
tt(commutativity_k11_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((k11_pre_poly A B C) = (k11_pre_poly A C B)) ) ) ).
tt(commutativity_k11_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  =>  ((k11_rvsum_2 A B) = (k11_rvsum_2 B A)) ) ) ).
tt(commutativity_k11_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k11_toprealc A B C) = (k11_toprealc A C B)) ) ) ).
tt(commutativity_k12_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 C (k4_finseq_2 A k6_margrel1))) )  =>  ((k12_descip_1 A B C) = (k12_descip_1 A C B)) ) ) ).
tt(commutativity_k12_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k12_ideal_1 A B C) = (k12_ideal_1 A C B)) ) ) ).
tt(commutativity_k12_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k12_lattice3 A B C) = (k12_lattice3 A C B)) ) ) ).
tt(commutativity_k12_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  =>  ((k12_member_1 A B) = (k12_member_1 B A)) ) ) ).
tt(commutativity_k12_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k12_openlatt A B C) = (k12_openlatt A C B)) ) ) ).
tt(commutativity_k12_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  =>  ((k12_rvsum_2 A B C) = (k12_rvsum_2 A C B)) ) ) ).
tt(commutativity_k13_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k13_ideal_1 A B C) = (k13_ideal_1 A C B)) ) ) ).
tt(commutativity_k13_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k13_lattice3 A B C) = (k13_lattice3 A C B)) ) ) ).
tt(commutativity_k13_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  ((k13_member_1 A B) = (k13_member_1 B A)) ) ) ).
tt(commutativity_k13_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k13_polynom3 A B C) = (k13_polynom3 A C B)) ) ) ).
tt(commutativity_k14_margrel1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k14_margrel1 A B) = (k14_margrel1 B A)) ) ) ).
tt(commutativity_k14_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k14_rvsum_1 A B) = (k14_rvsum_1 B A)) ) ) ).
tt(commutativity_k15_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k15_binop_2 A B) = (k15_binop_2 B A)) ) ) ).
tt(commutativity_k15_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k15_csspace A B C) = (k15_csspace A C B)) ) ) ).
tt(commutativity_k15_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k15_ideal_1 A B C) = (k15_ideal_1 A C B)) ) ) ).
tt(commutativity_k15_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k15_mmlquery A B C) = (k15_mmlquery A C B)) ) ) ).
tt(commutativity_k15_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  =>  ((k15_rvsum_1 A B C) = (k15_rvsum_1 A C B)) ) ) ).
tt(commutativity_k15_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k14_seq_4 A))) )  =>  ((k15_seq_4 A B C) = (k15_seq_4 A C B)) ) ) ).
tt(commutativity_k16_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) )  =>  ((k16_aofa_i00 A B C) = (k16_aofa_i00 A C B)) ) ) ).
tt(commutativity_k16_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k16_csspace A B C) = (k16_csspace A C B)) ) ) ).
tt(commutativity_k16_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k16_margrel1 A B C) = (k16_margrel1 A C B)) ) ) ).
tt(commutativity_k16_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k16_mmlquery A B C) = (k16_mmlquery A C B)) ) ) ).
tt(commutativity_k17_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k17_binop_2 A B) = (k17_binop_2 B A)) ) ) ).
tt(commutativity_k17_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((m1_group_9 C A B) & (m1_group_9 D A B)) )  =>  ((k17_group_9 A B C D) = (k17_group_9 A B D C)) ) ) ).
tt(commutativity_k18_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((k18_valued_1 A B) = (k18_valued_1 B A)) ) ) ).
tt(commutativity_k19_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k19_bvfunc_1 A B) = (k19_bvfunc_1 B A)) ) ) ).
tt(commutativity_k19_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k19_mmlquery A B C) = (k19_mmlquery A C B)) ) ) ).
tt(commutativity_k19_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k19_valued_1 A B C D E) = (k19_valued_1 A B C E D)) ) ) ).
tt(commutativity_k1_arytm_0,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k1_arytm_0 A B) = (k1_arytm_0 B A)) ) ) ).
tt(commutativity_k1_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((k1_asympt_0 A B) = (k1_asympt_0 B A)) ) ) ).
tt(commutativity_k1_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k1_binarith A B) = (k1_binarith B A)) ) ) ).
tt(commutativity_k1_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k1_bvfunc26 A B) = (k1_bvfunc26 B A)) ) ) ).
tt(commutativity_k1_card_2,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  =>  ((k1_card_2 A B) = (k1_card_2 B A)) ) ) ).
tt(commutativity_k1_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((k1_euclid_9 A B C) = (k1_euclid_9 A C B)) ) ) ).
tt(commutativity_k1_extreal1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_extreal1 A B) = (k1_extreal1 B A)) ) ) ).
tt(commutativity_k1_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_extreal2 A B) = (k1_extreal2 B A)) ) ) ).
tt(commutativity_k1_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k1_finsub_1 A B C) = (k1_finsub_1 A C B)) ) ) ).
tt(commutativity_k1_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k1_fuzzy_1 A B C) = (k1_fuzzy_1 A C B)) ) ) ).
tt(commutativity_k1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k1_geomtrap A B C) = (k1_geomtrap A C B)) ) ) ).
tt(commutativity_k1_grnilp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((k1_grnilp_1 A B C) = (k1_grnilp_1 A C B)) ) ) ).
tt(commutativity_k1_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((k1_groeb_3 A B C D) = (k1_groeb_3 A B D C)) ) ) ).
tt(commutativity_k1_hausdorf,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  =>  ((k1_hausdorf A B C) = (k1_hausdorf A C B)) ) ) ).
tt(commutativity_k1_helly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((k1_helly A B) = (k1_helly B A)) ) ) ).
tt(commutativity_k1_jct_misc,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((k1_jct_misc A B) = (k1_jct_misc B A)) ) ) ).
tt(commutativity_k1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k1_lfuzzy_1 A B C) = (k1_lfuzzy_1 A C B)) ) ) ).
tt(commutativity_k1_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k1_measure1 A B C D) = (k1_measure1 A B D C)) ) ) ).
tt(commutativity_k1_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  =>  ((k1_nat_1 A B) = (k1_nat_1 B A)) ) ) ).
tt(commutativity_k1_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k1_normform A B C D) = (k1_normform A B D C)) ) ) ).
tt(commutativity_k1_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  =>  ((k1_polyform A B) = (k1_polyform B A)) ) ) ).
tt(commutativity_k1_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k1_rltopsp1 A B C) = (k1_rltopsp1 A C B)) ) ) ).
tt(commutativity_k1_series_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_membered A) & (v7_membered A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  ((k1_series_1 A B C) = (k1_series_1 A C B)) ) ) ).
tt(commutativity_k1_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k1_setlim_2 A B C) = (k1_setlim_2 A C B)) ) ) ).
tt(commutativity_k1_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k1_square_1 A B) = (k1_square_1 B A)) ) ) ).
tt(commutativity_k1_topreal6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k1_topreal6 A B C) = (k1_topreal6 A C B)) ) ) ).
tt(commutativity_k1_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ((k1_tsep_1 A B C) = (k1_tsep_1 A C B)) ) ) ).
tt(commutativity_k1_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((k1_valued_1 A B) = (k1_valued_1 B A)) ) ) ).
tt(commutativity_k1_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k1_xxreal_3 A B) = (k1_xxreal_3 B A)) ) ) ).
tt(commutativity_k1_yellow20,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((k1_yellow20 A B) = (k1_yellow20 B A)) ) ) ).
tt(commutativity_k20_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k20_binop_2 A B) = (k20_binop_2 B A)) ) ) ).
tt(commutativity_k20_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k20_bvfunc_1 A B) = (k20_bvfunc_1 B A)) ) ) ).
tt(commutativity_k20_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k20_mmlquery A B C) = (k20_mmlquery A C B)) ) ) ).
tt(commutativity_k20_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k20_valued_1 A B C D E) = (k20_valued_1 A B C E D)) ) ) ).
tt(commutativity_k21_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k21_bvfunc_1 A B) = (k21_bvfunc_1 B A)) ) ) ).
tt(commutativity_k22_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k22_binop_2 A B) = (k22_binop_2 B A)) ) ) ).
tt(commutativity_k22_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k22_rvsum_1 A B) = (k22_rvsum_1 B A)) ) ) ).
tt(commutativity_k22_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v5_membered B) &  ((v5_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k22_valued_1 A B C D E) = (k22_valued_1 A B C E D)) ) ) ).
tt(commutativity_k23_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k23_binop_2 A B) = (k23_binop_2 B A)) ) ) ).
tt(commutativity_k23_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k23_rvsum_1 A B) = (k23_rvsum_1 B A)) ) ) ).
tt(commutativity_k24_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k24_binop_2 A B) = (k24_binop_2 B A)) ) ) ).
tt(commutativity_k26_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k26_quaterni A B) = (k26_quaterni B A)) ) ) ).
tt(commutativity_k2_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_aff_1 A B C) = (k2_aff_1 A C B)) ) ) ).
tt(commutativity_k2_arytm_0,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k2_arytm_0 A B) = (k2_arytm_0 B A)) ) ) ).
tt(commutativity_k2_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k2_arytm_3 A B) = (k2_arytm_3 B A)) ) ) ).
tt(commutativity_k2_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_bhsp_1 A B C) = (k2_bhsp_1 A C B)) ) ) ).
tt(commutativity_k2_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k2_binarith A B) = (k2_binarith B A)) ) ) ).
tt(commutativity_k2_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) & (v1_xreal_0 B))  =>  ((k2_borsuk_7 A B) = (k2_borsuk_7 B A)) ) ) ).
tt(commutativity_k2_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k2_bvfunc_1 A B C) = (k2_bvfunc_1 A C B)) ) ) ).
tt(commutativity_k2_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k2_bvfunc26 A B) = (k2_bvfunc26 B A)) ) ) ).
tt(commutativity_k2_card_2,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  =>  ((k2_card_2 A B) = (k2_card_2 B A)) ) ) ).
tt(commutativity_k2_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k2_eqrel_1 A B C) = (k2_eqrel_1 A C B)) ) ) ).
tt(commutativity_k2_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k2_euclid_4 A B C) = (k2_euclid_4 A C B)) ) ) ).
tt(commutativity_k2_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k2_extreal2 A B) = (k2_extreal2 B A)) ) ) ).
tt(commutativity_k2_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_fuzzy_1 A B C) = (k2_fuzzy_1 A C B)) ) ) ).
tt(commutativity_k2_fuzzy_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_fuzzy_2 A B C) = (k2_fuzzy_2 A C B)) ) ) ).
tt(commutativity_k2_gate_1,ax, (! [A:$i,B:$i] :  ((k2_gate_1 A B) = (k2_gate_1 B A)) ) ).
tt(commutativity_k2_groeb_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((k2_groeb_2 A B C) = (k2_groeb_2 A C B)) ) ) ).
tt(commutativity_k2_int_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k2_int_2 A B) = (k2_int_2 B A)) ) ) ).
tt(commutativity_k2_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_lfuzzy_0 A B C) = (k2_lfuzzy_0 A C B)) ) ) ).
tt(commutativity_k2_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_lfuzzy_1 A B C) = (k2_lfuzzy_1 A C B)) ) ) ).
tt(commutativity_k2_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k2_lopclset A B C) = (k2_lopclset A C B)) ) ) ).
tt(commutativity_k2_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k2_measure1 A B C D) = (k2_measure1 A B D C)) ) ) ).
tt(commutativity_k2_morph_01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k2_morph_01 A B C) = (k2_morph_01 A C B)) ) ) ).
tt(commutativity_k2_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k2_nat_1 A B) = (k2_nat_1 B A)) ) ) ).
tt(commutativity_k2_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k2_normform A B C D) = (k2_normform A B D C)) ) ) ).
tt(commutativity_k2_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k2_openlatt A B C) = (k2_openlatt A C B)) ) ) ).
tt(commutativity_k2_partit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_eqrel_1 B A) & (m1_eqrel_1 C A)) )  =>  ((k2_partit1 A B C) = (k2_partit1 A C B)) ) ) ).
tt(commutativity_k2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k2_pboole A B C) = (k2_pboole A C B)) ) ) ).
tt(commutativity_k2_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((k2_pcs_0 A B C D E F) = (k2_pcs_0 A B C D F E)) ) ) ).
tt(commutativity_k2_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((k2_pnproc_1 A B C) = (k2_pnproc_1 A C B)) ) ) ).
tt(commutativity_k2_pzfmisc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k2_pzfmisc1 A B C) = (k2_pzfmisc1 A C B)) ) ) ).
tt(commutativity_k2_setfam_1,ax, (! [A:$i,B:$i] :  ((k2_setfam_1 A B) = (k2_setfam_1 B A)) ) ).
tt(commutativity_k2_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k2_setlim_2 A B C) = (k2_setlim_2 A C B)) ) ) ).
tt(commutativity_k2_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k2_square_1 A B) = (k2_square_1 B A)) ) ) ).
tt(commutativity_k2_substlat,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_substlat A B)) & (m1_subset_1 D (k1_substlat A B)))  =>  ((k2_substlat A B C D) = (k2_substlat A B D C)) ) ) ).
tt(commutativity_k2_tarski,ax, (! [A:$i,B:$i] :  ((k2_tarski A B) = (k2_tarski B A)) ) ).
tt(commutativity_k2_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k2_topgen_4 A B C) = (k2_topgen_4 A C B)) ) ) ).
tt(commutativity_k2_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k2_valued_1 A B C D E) = (k2_valued_1 A B C E D)) ) ) ).
tt(commutativity_k2_vectsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_vectsp_4 D A B)) ) )  =>  ((k2_vectsp_5 A B C D) = (k2_vectsp_5 A B D C)) ) ) ).
tt(commutativity_k2_xboole_0,ax, (! [A:$i,B:$i] :  ((k2_xboole_0 A B) = (k2_xboole_0 B A)) ) ).
tt(commutativity_k2_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k2_xcmplx_0 A B) = (k2_xcmplx_0 B A)) ) ) ).
tt(commutativity_k2_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k2_yellow_4 A B C) = (k2_yellow_4 A C B)) ) ) ).
tt(commutativity_k33_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k33_aofa_i00 A B C D E F) = (k33_aofa_i00 A B C D F E)) ) ) ).
tt(commutativity_k34_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k34_aofa_i00 A B C D E F) = (k34_aofa_i00 A B C D F E)) ) ) ).
tt(commutativity_k34_gate_1,ax, (! [A:$i,B:$i] :  ((k34_gate_1 A B) = (k34_gate_1 B A)) ) ).
tt(commutativity_k3_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((k3_armstrng A B C) = (k3_armstrng A C B)) ) ) ).
tt(commutativity_k3_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k3_arytm_3 A B) = (k3_arytm_3 B A)) ) ) ).
tt(commutativity_k3_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k3_binop_2 A B) = (k3_binop_2 B A)) ) ) ).
tt(commutativity_k3_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_boolealg A B C) = (k3_boolealg A C B)) ) ) ).
tt(commutativity_k3_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k3_bvfunc_1 A B) = (k3_bvfunc_1 B A)) ) ) ).
tt(commutativity_k3_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k3_bvfunc26 A B C) = (k3_bvfunc26 A C B)) ) ) ).
tt(commutativity_k3_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k3_closure3 A B C D) = (k3_closure3 A B D C)) ) ) ).
tt(commutativity_k3_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  =>  ((k3_complsp2 A B C) = (k3_complsp2 A C B)) ) ) ).
tt(commutativity_k3_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k3_eqrel_1 A B C) = (k3_eqrel_1 A C B)) ) ) ).
tt(commutativity_k3_finance1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k3_finance1 A B) = (k3_finance1 B A)) ) ) ).
tt(commutativity_k3_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k3_finsub_1 A B C) = (k3_finsub_1 A C B)) ) ) ).
tt(commutativity_k3_fuzzy_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k3_fuzzy_2 A B C) = (k3_fuzzy_2 A C B)) ) ) ).
tt(commutativity_k3_gate_1,ax, (! [A:$i,B:$i] :  ((k3_gate_1 A B) = (k3_gate_1 B A)) ) ).
tt(commutativity_k3_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k3_group_2 A B C) = (k3_group_2 A C B)) ) ) ).
tt(commutativity_k3_hausdorf,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  ((k3_hausdorf A B C) = (k3_hausdorf A C B)) ) ) ).
tt(commutativity_k3_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((k3_idea_1 A B C) = (k3_idea_1 A C B)) ) ) ).
tt(commutativity_k3_int_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k3_int_2 A B) = (k3_int_2 B A)) ) ) ).
tt(commutativity_k3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_lattices A B C) = (k3_lattices A C B)) ) ) ).
tt(commutativity_k3_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_lfuzzy_0 A B C) = (k3_lfuzzy_0 A C B)) ) ) ).
tt(commutativity_k3_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k3_lopclset A B C) = (k3_lopclset A C B)) ) ) ).
tt(commutativity_k3_member_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k3_member_1 A B) = (k3_member_1 B A)) ) ) ).
tt(commutativity_k3_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) ) ) )  =>  ((k3_mesfunc1 A B C) = (k3_mesfunc1 A C B)) ) ) ).
tt(commutativity_k3_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_midsp_1 A B C) = (k3_midsp_1 A C B)) ) ) ).
tt(commutativity_k3_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((k3_nagata_1 A B C) = (k3_nagata_1 A C B)) ) ) ).
tt(commutativity_k3_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  =>  ((k3_nat_1 A B) = (k3_nat_1 B A)) ) ) ).
tt(commutativity_k3_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k3_openlatt A B C) = (k3_openlatt A C B)) ) ) ).
tt(commutativity_k3_partit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_eqrel_1 B A) & (m1_eqrel_1 C A)) )  =>  ((k3_partit1 A B C) = (k3_partit1 A C B)) ) ) ).
tt(commutativity_k3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k3_pboole A B C) = (k3_pboole A C B)) ) ) ).
tt(commutativity_k3_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  =>  ((k3_random_1 A B C D) = (k3_random_1 A B D C)) ) ) ).
tt(commutativity_k3_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k3_real_1 A B) = (k3_real_1 B A)) ) ) ).
tt(commutativity_k3_rlvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_rlvect_1 A) & (l1_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_rlvect_1 A B C) = (k3_rlvect_1 A C B)) ) ) ).
tt(commutativity_k3_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  =>  ((k3_rvsum_2 A B) = (k3_rvsum_2 B A)) ) ) ).
tt(commutativity_k3_setfam_1,ax, (! [A:$i,B:$i] :  ((k3_setfam_1 A B) = (k3_setfam_1 B A)) ) ).
tt(commutativity_k3_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k3_setwiseo A B C) = (k3_setwiseo A C B)) ) ) ).
tt(commutativity_k3_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k3_supinf_2 A B) = (k3_supinf_2 B A)) ) ) ).
tt(commutativity_k3_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k3_topgen_4 A B C) = (k3_topgen_4 A C B)) ) ) ).
tt(commutativity_k3_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k3_valued_1 A B C D E) = (k3_valued_1 A B C E D)) ) ) ).
tt(commutativity_k3_vfunct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((k3_vfunct_2 A B C D) = (k3_vfunct_2 A B D C)) ) ) ).
tt(commutativity_k3_xboole_0,ax, (! [A:$i,B:$i] :  ((k3_xboole_0 A B) = (k3_xboole_0 B A)) ) ).
tt(commutativity_k3_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k3_xcmplx_0 A B) = (k3_xcmplx_0 B A)) ) ) ).
tt(commutativity_k3_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k3_xxreal_0 A B) = (k3_xxreal_0 B A)) ) ) ).
tt(commutativity_k3_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_yellow_5 A B C) = (k3_yellow_5 A C B)) ) ) ).
tt(commutativity_k3_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k3_zf_refle A B C) = (k3_zf_refle A C B)) ) ) ).
tt(commutativity_k4_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_bhsp_1 A B C) = (k4_bhsp_1 A C B)) ) ) ).
tt(commutativity_k4_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k4_bvfunc_1 A B) = (k4_bvfunc_1 B A)) ) ) ).
tt(commutativity_k4_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k4_bvfunc26 A B C) = (k4_bvfunc26 A C B)) ) ) ).
tt(commutativity_k4_catalan2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k4_catalan2 A B) = (k4_catalan2 B A)) ) ) ).
tt(commutativity_k4_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k4_closure3 A B C D) = (k4_closure3 A B D C)) ) ) ).
tt(commutativity_k4_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k4_eqrel_1 A B C) = (k4_eqrel_1 A C B)) ) ) ).
tt(commutativity_k4_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k4_euclid_4 A B C) = (k4_euclid_4 A C B)) ) ) ).
tt(commutativity_k4_gate_1,ax, (! [A:$i,B:$i] :  ((k4_gate_1 A B) = (k4_gate_1 B A)) ) ).
tt(commutativity_k4_jordan1k,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ) )  =>  ((k4_jordan1k A B C) = (k4_jordan1k A C B)) ) ) ).
tt(commutativity_k4_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_lattices A B C) = (k4_lattices A C B)) ) ) ).
tt(commutativity_k4_matrix13,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k4_matrix13 A B) = (k4_matrix13 B A)) ) ) ).
tt(commutativity_k4_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v8_metric_1 A) & (l1_metric_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_metric_1 A B C) = (k4_metric_1 A C B)) ) ) ).
tt(commutativity_k4_msualg_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  &  ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B)) ) ) )  =>  ((k4_msualg_5 A B C D) = (k4_msualg_5 A B D C)) ) ) ).
tt(commutativity_k4_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k4_nat_1 A B) = (k4_nat_1 B A)) ) ) ).
tt(commutativity_k4_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  =>  ((k4_quofield A B C) = (k4_quofield A C B)) ) ) ).
tt(commutativity_k4_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k4_real_1 A B) = (k4_real_1 B A)) ) ) ).
tt(commutativity_k4_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_robbins3 A B C) = (k4_robbins3 A C B)) ) ) ).
tt(commutativity_k4_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k4_rvsum_1 A B) = (k4_rvsum_1 B A)) ) ) ).
tt(commutativity_k4_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  =>  ((k4_rvsum_2 A B C) = (k4_rvsum_2 A C B)) ) ) ).
tt(commutativity_k4_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k4_setlim_2 A B C) = (k4_setlim_2 A C B)) ) ) ).
tt(commutativity_k4_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k4_subset_1 A B C) = (k4_subset_1 A C B)) ) ) ).
tt(commutativity_k4_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k4_xboolean A B) = (k4_xboolean B A)) ) ) ).
tt(commutativity_k4_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k4_xxreal_0 A B) = (k4_xxreal_0 B A)) ) ) ).
tt(commutativity_k4_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k4_xxreal_3 A B) = (k4_xxreal_3 B A)) ) ) ).
tt(commutativity_k4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k4_yellow_4 A B C) = (k4_yellow_4 A C B)) ) ) ).
tt(commutativity_k5_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_arytm_2) & (m1_subset_1 B k1_arytm_2))  =>  ((k5_arytm_2 A B) = (k5_arytm_2 B A)) ) ) ).
tt(commutativity_k5_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k5_asympt_0 A B) = (k5_asympt_0 B A)) ) ) ).
tt(commutativity_k5_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k5_binop_2 A B) = (k5_binop_2 B A)) ) ) ).
tt(commutativity_k5_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k5_bvfunc_1 A B C) = (k5_bvfunc_1 A C B)) ) ) ).
tt(commutativity_k5_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k5_bvfunc26 A B C) = (k5_bvfunc26 A C B)) ) ) ).
tt(commutativity_k5_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k5_classes2 A B C) = (k5_classes2 A C B)) ) ) ).
tt(commutativity_k5_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  =>  ((k5_convex4 A B C) = (k5_convex4 A C B)) ) ) ).
tt(commutativity_k5_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k5_eqrel_1 A B C) = (k5_eqrel_1 A C B)) ) ) ).
tt(commutativity_k5_gate_1,ax, (! [A:$i,B:$i] :  ((k5_gate_1 A B) = (k5_gate_1 B A)) ) ).
tt(commutativity_k5_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k5_lang1 A B C D) = (k5_lang1 A B D C)) ) ) ).
tt(commutativity_k5_matrixc1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  =>  ((k5_matrixc1 A B) = (k5_matrixc1 B A)) ) ) ).
tt(commutativity_k5_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) ) ) )  =>  ((k5_mesfunc1 A B C) = (k5_mesfunc1 A C B)) ) ) ).
tt(commutativity_k5_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k5_nat_d A B) = (k5_nat_d B A)) ) ) ).
tt(commutativity_k5_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k5_pboole A B C) = (k5_pboole A C B)) ) ) ).
tt(commutativity_k5_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((k5_polynom1 A B C D) = (k5_polynom1 A B D C)) ) ) ).
tt(commutativity_k5_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k5_prob_1 A B C D) = (k5_prob_1 A B D C)) ) ) ).
tt(commutativity_k5_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  =>  ((k5_quofield A B C) = (k5_quofield A C B)) ) ) ).
tt(commutativity_k5_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  =>  ((k5_rfunct_3 A B C D) = (k5_rfunct_3 A B D C)) ) ) ).
tt(commutativity_k5_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_robbins1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k5_robbins1 A B C) = (k5_robbins1 A C B)) ) ) ).
tt(commutativity_k5_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k5_robbins3 A B C) = (k5_robbins3 A C B)) ) ) ).
tt(commutativity_k5_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  =>  ((k5_rvsum_1 A B C) = (k5_rvsum_1 A C B)) ) ) ).
tt(commutativity_k5_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ((k5_scmfsa_m A B) = (k5_scmfsa_m B A)) ) ) ).
tt(commutativity_k5_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  =>  ((k5_setwiseo A B C) = (k5_setwiseo A C B)) ) ) ).
tt(commutativity_k5_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k5_subset_1 A B C) = (k5_subset_1 A C B)) ) ) ).
tt(commutativity_k5_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  ((k5_supinf_2 A B) = (k5_supinf_2 B A)) ) ) ).
tt(commutativity_k5_xboole_0,ax, (! [A:$i,B:$i] :  ((k5_xboole_0 A B) = (k5_xboole_0 B A)) ) ).
tt(commutativity_k5_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k5_xboolean A B) = (k5_xboolean B A)) ) ) ).
tt(commutativity_k6_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_arytm_2) & (m1_subset_1 B k1_arytm_2))  =>  ((k6_arytm_2 A B) = (k6_arytm_2 B A)) ) ) ).
tt(commutativity_k6_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k6_bhsp_1 A B C) = (k6_bhsp_1 A C B)) ) ) ).
tt(commutativity_k6_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k6_bilinear A B C D E) = (k6_bilinear A B C E D)) ) ) ).
tt(commutativity_k6_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k6_bvfunc_1 A B C) = (k6_bvfunc_1 A C B)) ) ) ).
tt(commutativity_k6_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k6_bvfunc26 A B C) = (k6_bvfunc26 A C B)) ) ) ).
tt(commutativity_k6_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k6_fuzzy_1 A B C) = (k6_fuzzy_1 A C B)) ) ) ).
tt(commutativity_k6_gate_1,ax, (! [A:$i,B:$i] :  ((k6_gate_1 A B) = (k6_gate_1 B A)) ) ).
tt(commutativity_k6_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k6_nat_1 A B) = (k6_nat_1 B A)) ) ) ).
tt(commutativity_k6_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k6_nat_d A B) = (k6_nat_d B A)) ) ) ).
tt(commutativity_k6_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k6_prob_1 A B C D) = (k6_prob_1 A B D C)) ) ) ).
tt(commutativity_k6_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  =>  ((k6_random_1 A B C D) = (k6_random_1 A B D C)) ) ) ).
tt(commutativity_k6_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (l2_robbins1 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k6_robbins1 A B C) = (k6_robbins1 A C B)) ) ) ).
tt(commutativity_k6_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((k6_vfunct_1 A B C D) = (k6_vfunct_1 A B D C)) ) ) ).
tt(commutativity_k6_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_zmodul01 B A) & (m1_zmodul01 C A)) )  =>  ((k6_zmodul01 A B C) = (k6_zmodul01 A C B)) ) ) ).
tt(commutativity_k7_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  =>  ((k7_arytm_2 A B) = (k7_arytm_2 B A)) ) ) ).
tt(commutativity_k7_chain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B C))) & (m1_subset_1 E (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ) )  =>  ((k7_chain_1 A B C D E) = (k7_chain_1 A B C E D)) ) ) ).
tt(commutativity_k7_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k7_classes2 A B C) = (k7_classes2 A C B)) ) ) ).
tt(commutativity_k7_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k7_domain_1 A B C) = (k7_domain_1 A C B)) ) ) ).
tt(commutativity_k7_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k7_euclid A B C) = (k7_euclid A C B)) ) ) ).
tt(commutativity_k7_gate_1,ax, (! [A:$i,B:$i] :  ((k7_gate_1 A B) = (k7_gate_1 B A)) ) ).
tt(commutativity_k7_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k7_nat_1 A B) = (k7_nat_1 B A)) ) ) ).
tt(commutativity_k7_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k7_quaterni A B) = (k7_quaterni B A)) ) ) ).
tt(commutativity_k7_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k7_real_1 A B) = (k7_real_1 B A)) ) ) ).
tt(commutativity_k7_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  =>  ((k7_rfunct_3 A B C D) = (k7_rfunct_3 A B D C)) ) ) ).
tt(commutativity_k7_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  =>  ((k7_rlvect_2 A B C) = (k7_rlvect_2 A C B)) ) ) ).
tt(commutativity_k7_rusub_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k7_rusub_4 A B C) = (k7_rusub_4 A C B)) ) ) ).
tt(commutativity_k7_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k7_xboolean A B) = (k7_xboolean B A)) ) ) ).
tt(commutativity_k7_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_zmodul01 B A) & (m1_zmodul01 C A)) )  =>  ((k7_zmodul01 A B C) = (k7_zmodul01 A C B)) ) ) ).
tt(commutativity_k8_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  =>  ((k8_arytm_2 A B) = (k8_arytm_2 B A)) ) ) ).
tt(commutativity_k8_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k8_bvfunc_1 A B) = (k8_bvfunc_1 B A)) ) ) ).
tt(commutativity_k8_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  =>  ((k8_complex1 A B) = (k8_complex1 B A)) ) ) ).
tt(commutativity_k8_group_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ).
tt(commutativity_k8_matrixc1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  =>  ((k8_matrixc1 A B C) = (k8_matrixc1 A C B)) ) ) ).
tt(commutativity_k8_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  =>  ((k8_member_1 A B) = (k8_member_1 B A)) ) ) ).
tt(commutativity_k8_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k8_ordinal3 A B) = (k8_ordinal3 B A)) ) ) ).
tt(commutativity_k8_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k8_polynom3 A B C) = (k8_polynom3 A C B)) ) ) ).
tt(commutativity_k8_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k8_real_1 A B) = (k8_real_1 B A)) ) ) ).
tt(commutativity_k8_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k8_subset_1 A B C) = (k8_subset_1 A C B)) ) ) ).
tt(commutativity_k8_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k8_xboolean A B) = (k8_xboolean B A)) ) ) ).
tt(commutativity_k9_arytm_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_arytm_3) & (m1_subset_1 B k5_arytm_3))  =>  ((k9_arytm_3 A B) = (k9_arytm_3 B A)) ) ) ).
tt(commutativity_k9_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k9_binop_2 A B) = (k9_binop_2 B A)) ) ) ).
tt(commutativity_k9_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  =>  ((k9_complex1 A B) = (k9_complex1 B A)) ) ) ).
tt(commutativity_k9_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  =>  ((k9_member_1 A B) = (k9_member_1 B A)) ) ) ).
tt(commutativity_k9_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k9_ordinal3 A B) = (k9_ordinal3 B A)) ) ) ).
tt(commutativity_k9_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  =>  ((k9_seq_4 A B) = (k9_seq_4 B A)) ) ) ).
tt(commutativity_k9_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k9_subset_1 A B C) = (k9_subset_1 A C B)) ) ) ).
tt(commutativity_k9_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k9_xboolean A B) = (k9_xboolean B A)) ) ) ).
tt(connectedness_r1_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  =>  ((r1_arytm_2 A B) | (r1_arytm_2 B A)) ) ) ).
tt(connectedness_r1_ordinal1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  =>  ((r1_ordinal1 A B) | (r1_ordinal1 B A)) ) ) ).
tt(connectedness_r1_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((r1_xxreal_0 A B) | (r1_xxreal_0 B A)) ) ) ).
tt(connectedness_r3_arytm_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_arytm_3) & (m1_subset_1 B k5_arytm_3))  =>  ((r3_arytm_3 A B) | (r3_arytm_3 B A)) ) ) ).
tt(d10_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  =>  ((v9_abcmiz_0 A) <=>  ((v1_funct_1 (u3_abcmiz_0 A)) &  ((v1_funct_2 (u3_abcmiz_0 A) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 (k3_yellow_1 (u1_abcmiz_0 A))))) &  ((v20_waybel_0 (u3_abcmiz_0 A) A (k7_lattice3 (k3_yellow_1 (u1_abcmiz_0 A)))) & (m1_subset_1 (u3_abcmiz_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 (k3_yellow_1 (u1_abcmiz_0 A)))))))) ) ) ) ) ) ).
tt(d10_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v10_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((r2_hidden C B) &  ((r2_hidden F B) &  ((r1_aff_1 A C D G) &  ((r1_aff_1 A C E H) &  ((r2_analoaf A D E G H) &  ((r2_analoaf A D F G I) &  ((r2_analoaf A E F H I) & (r2_aff_1 A D E B)) ) ) ) ) ) ) )  =>  ((r2_hidden D B) |  ( (C = F)  |  ( (D = E)  | (r2_hidden I B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_afinsq_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_tarski k5_numbers A) =>  ((r1_xxreal_0 C (k3_finseq_1 B)) |  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  & (v1_finset_1 D)) ) ) ) )  =>  ( (D = (k11_afinsq_1 A B C))  <=>  ( ((k3_finseq_1 B) = (k1_funct_1 D k6_numbers))  &  ( ((k1_afinsq_1 D) = C)  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 D E) = (k1_funct_1 B E)) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~ (r1_xxreal_0 E (k3_finseq_1 B)))  &  ( (~ (r1_xxreal_0 C E))  &  (~  ((k1_funct_1 D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k8_afinsq_1 A)) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ( (C = (k8_afinsq_2 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) (k8_afinsq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) (k8_afinsq_1 A))))) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ((k5_binop_1 (k8_afinsq_1 A) D E F) = (k15_afinsq_1 A E F)) ) ) ) )  &  (C = (k6_afinsq_2 (k8_afinsq_1 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k10_afproj A) = (k2_xboole_0 (k2_zfmisc_1 (k1_afproj A) (k1_tarski 1)) (k2_zfmisc_1 (k8_afproj A) (k1_tarski 2)))) ) ) ).
tt(d10_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  ((r4_afvect0 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (r3_afvect0 A B C)) ) ) ) ) ) ) ).
tt(d10_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) =>  ((k4_alg_1 A B) = (g1_unialg_1 (k8_eqrel_1 (u1_struct_0 A) B) (k3_alg_1 A B))) ) ) ) ) ).
tt(d10_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v7_algstr_1 A) <=>  ((v6_algstr_1 A) &  ((v32_algstr_0 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d10_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_algstr_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d10_altcat_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((v4_funct_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 B A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (k2_zfmisc_1 B A)) &  ((v1_funcop_1 C) & (v7_altcat_1 C)) ) ) ) )  =>  (C = (k6_altcat_1 A B)) ) ) ) ) ) ) ).
tt(d10_altcat_3,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_altcat_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A C B)) &  ((r2_hidden D (k1_altcat_1 A C B)) & (v1_zfmisc_1 (k1_altcat_1 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(d10_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k9_ami_3 A B) = (k3_xtuple_0 8 (k9_finseq_1 A) (k9_finseq_1 B))) ) ) ) ) ).
tt(d10_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  ((v6_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ((v1_partfun1 D (u1_struct_0 B)) & (v5_memstr_0 D A B k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ((r1_tarski C E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B E D F)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((v5_ami_wstd C A B) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_ami_wstd A B E D) => (r2_hidden E (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r5_analmetr A B C D) <=> (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(d10_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v3_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (B = D) )  &  ( (~  (C = D) )  & (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_unialg_1 A))  =>  ((v3_aofa_000 A) <=>  ((r2_hidden 1 (k4_finseq_1 (u1_unialg_1 A))) &  ( (~ (v1_xboole_0 (k1_funct_1 (u1_unialg_1 A) 1)))  &  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 A) 1)) &  ((v2_margrel1 (k1_funct_1 (u1_unialg_1 A) 1)) &  ((v3_margrel1 (k1_funct_1 (u1_unialg_1 A) 1) (u1_struct_0 A)) &  ((v8_comput_1 (k1_funct_1 (u1_unialg_1 A) 1) k6_numbers) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 A) 1) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d10_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  ( (D = (k9_aofa_i00 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k4_numbers D E) = (k3_xcmplx_0 (k3_funct_2 A k4_numbers B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_armstrng,ax, (! [A:$i] :  ((k7_armstrng A) = (a_1_1_armstrng A)) ) ).
tt(d10_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( ( (B = k1_xboole_0)  =>  ((k8_arytm_3 A B) = k1_xboole_0) )  &  ( ( ((k4_arytm_3 B A) = 1)  =>  ((k8_arytm_3 A B) = (k4_arytm_3 A B)) )  &  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  ((k4_arytm_3 B A) = 1) )  &  (~  ((k8_arytm_3 A B) = (k4_tarski (k4_arytm_3 A B) (k4_arytm_3 B A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k7_asympt_0 A) = (a_1_1_asympt_0 A)) ) ) ).
tt(d10_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_partfun1 C (k15_pre_poly (k1_nat_1 A 1))) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k1_nat_1 A 1)) (k15_pre_poly (k1_nat_1 A 1)))))) ) ) )  =>  (! [D:$i] :  ( ((v1_partfun1 D (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1)))) &  ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))) (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))))))) ) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E (k15_pre_poly B)) &  ((v1_relat_2 E) &  ((v4_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (k15_pre_poly B))))) ) ) )  =>  ( (E = (k8_bagorder A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F B) &  ((v1_funct_1 F) &  ((v1_partfun1 F B) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G B) &  ((v1_funct_1 G) &  ((v1_partfun1 G B) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r2_hidden (k4_tarski F G) E) <=>  ( ( (~  ((k1_bagorder B k6_numbers (k1_nat_1 A 1) F) = (k1_bagorder B k6_numbers (k1_nat_1 A 1) G)) )  & (r2_hidden (k4_tarski (k1_bagorder B k6_numbers (k1_nat_1 A 1) F) (k1_bagorder B k6_numbers (k1_nat_1 A 1) G)) C))  |  ( ((k1_bagorder B k6_numbers (k1_nat_1 A 1) F) = (k1_bagorder B k6_numbers (k1_nat_1 A 1) G))  & (r2_hidden (k4_tarski (k1_bagorder B (k1_nat_1 A 1) B F) (k1_bagorder B (k1_nat_1 A 1) B G)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  ((m1_bcialg_1 B A) <=>  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((u1_bcialg_1 B) = (k1_realset1 (u1_bcialg_1 A) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d10_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((m2_bcialg_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_hidden (k4_tarski (k1_bcialg_1 A E C) (k1_bcialg_1 A E D)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_bcialg_3 B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden E B))  => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D (k1_bcialg_1 A D C))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_bcialg_4 A B) = (a_2_0_bcialg_4 A B)) ) ) ) ) ).
tt(d10_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m5_bcialg_2 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A C))) &  ((v2_bcialg_6 D A (k9_bcialg_2 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A C)))))) ) )  =>  ( (D = (k6_bcialg_6 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A C)) D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( (F = (k9_bilinear A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) F G H) = (k6_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r5_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A B (k3_binop_1 A C D E) F) = (k3_binop_1 A C (k3_binop_1 A B D F) (k3_binop_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k34_binop_2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_binop_1 A B C) = (k10_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d10_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k10_bor_cant A B C) = (k1_prob_1 A (k9_bor_cant A C))) ) ) ) ) ) ) ).
tt(d10_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((m1_borsuk_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m2_connsp_2 D A C) =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc E A) &  ((r1_tarski C E) &  ((r1_tarski E D) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden F B) =>  ((r1_xboole_0 F E) | (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  ( (A = k8_borsuk_6)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) &  ( (B = (k4_borsuk_1 k5_topmetr k5_topmetr C D))  & (r1_xxreal_0 D (k9_real_1 (k8_real_1 2 C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(d10_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k8_toprealb (k1_nat_1 A 1))) (u1_struct_0 (k8_toprealb A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_toprealb (k1_nat_1 A 1))) (u1_struct_0 (k8_toprealb A)))))) )  =>  ( (C = (k16_borsuk_7 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1))) =>  ( (E = (k30_valued_1 D))  =>  ((k1_funct_1 C D) = (k15_borsuk_7 A (k5_algstr_0 (k15_euclid A) (k3_funct_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) B D) (k3_funct_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (B = (k11_bvfunc_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k7_margrel1) ) ) ) ) ) ) ) ).
tt(d10_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((k7_bvfunc_2 A B C D) = (k17_bvfunc_1 A B (k5_bvfunc_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(d10_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_c0sp1 B A) <=>  ((v1_ideal_1 B A) &  ((v1_c0sp1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r5_calcul_1 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) &  ((r1_tarski (k2_relset_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) D)) C) &  ( ((k2_calcul_1 A D) = B)  & (r4_calcul_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_card_3,ax, (! [A:$i] :  ((v2_card_3 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((k9_xtuple_0 B) = (k9_xtuple_0 C)) ) ) ) ) ) ) ) ).
tt(d10_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((k4_card_fil A) = (a_1_1_card_fil A)) ) ) ).
tt(d10_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v4_card_lar A) <=> (r4_card_lar A (a_1_0_card_lar A))) ) ) ).
tt(d10_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v6_cat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_cat_1 C A B B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_cat_1 E A B D) =>  ((k1_cat_1 A C E) = E) ) ) )  &  ( (~  ((k2_cat_1 A D B) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_cat_1 E A D B) =>  ((k1_cat_1 A E C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((k14_cat_2 A B) = (k9_funct_3 (u4_struct_0 A) (u4_struct_0 B))) ) ) ) ) ).
tt(d10_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A D) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  ((k9_cat_3 A B C D E F) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A D B) =>  (! [F:$i] :  ((m1_cat_1 F A D C) =>  (~  ( (~  ((k2_cat_1 A D B) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D C) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_cat_1 G A D (k2_cat_4 A B C)) =>  ( (G = (k9_cat_4 A B C D E F))  <=>  ( ((k5_cat_1 A D (k2_cat_4 A B C) B G (k7_cat_4 A B C)) = E)  &  ((k5_cat_1 A D (k2_cat_4 A B C) C G (k8_cat_4 A B C)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_cat_5 A B) = (k8_relset_1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(d10_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k7_catalg_1 A B C) = (k4_tarski 2 (k11_finseq_1 A B C))) ) ) ) ).
tt(d10_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_cc0sp1 A) = (g1_clopban2 (k2_cc0sp1 A) (k2_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k1_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k1_cc0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k4_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k3_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k6_cc0sp1 A))) ) ) ).
tt(d10_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k9_cc0sp2 A) = (g2_clvect_1 (k6_cc0sp2 A) (k10_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k1_c0sp1 (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k9_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k8_cc0sp2 A))) ) ) ).
tt(d10_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  ((v5_cfdiff_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers B) A) & (v2_comseq_2 B))  => (r2_hidden (k3_comseq_2 B) A)) ) ) ) ) ) ).
tt(d10_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_cgames_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v2_cgames_1 (k1_funct_1 A B))) ) ) ) ) ).
tt(d10_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A B A)) =>  ( (C = (k8_chain_1 A B))  <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ( (C = (k3_chain_1 A D E))  &  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 E F)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 D F) (k1_seq_1 E F)) (k2_chain_1 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_chord B A) <=>  (? [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  &  (? [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  &  ( (~ (r1_xxreal_0 D (k1_nat_1 C 2)))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( (~  ((k1_funct_1 B C) = (k1_funct_1 B D)) )  &  ( (? [E:$i] : (r1_glib_000 A (k1_funct_1 B C) (k1_funct_1 B D) E))  &  (! [E:$i] :  (~  ((r2_hidden E (k14_glib_001 A B)) & (r1_glib_000 A (k1_funct_1 B C) (k1_funct_1 B D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  (! [C:$i] :  ( ((v4_msafree2 C B) & (l3_msualg_1 C B))  =>  ((m2_circcmb3 C A B) <=>  ((v4_circcomb C B) &  ((v3_funct_1 (u3_msualg_1 B C)) &  ((k3_funct_1 (u3_msualg_1 B C)) = A) ) ) ) ) ) ) ) ) ) ).
tt(d10_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v4_circcomb B A) <=>  (! [C:$i] :  ((r2_hidden C (u4_struct_0 A)) =>  (C = (k4_tarski (k1_xtuple_0 C) (k1_funct_1 (u4_msualg_1 A B) C))) ) ) ) ) ) ) ) ).
tt(d10_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r2_circtrm1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_funct_1 C)) )  &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_funct_1 D)) )  & (r1_circtrm1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d10_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((k12_clopban1 A B C) = (a_3_0_clopban1 A B C)) ) ) ) ) ) ) ).
tt(d10_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  ((v3_clopban2 A) <=>  ((k1_normsp_0 A (k5_struct_0 A)) = 1) ) ) ) ).
tt(d10_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ((v7_closure2 C A B) <=>  (! [D:$i] :  ((m1_closure2 D A B (k6_closure2 A B)) => (r2_pboole A D (k7_closure2 A B C D))) ) ) ) ) ) ) ) ).
tt(d10_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k4_clvect_1 A) = (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) ) ) ).
tt(d10_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_clvect_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k1_normsp_1 A B D)) C)) ) ) ) ) ) ) ) ) ) ).
tt(d10_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v5_cohsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_xtuple_0 A))) =>  ( ((v1_cohsp_1 B) & (r2_hidden (k3_tarski B) (k9_xtuple_0 A)))  =>  ((k1_funct_1 A (k3_tarski B)) = (k3_tarski (k7_relat_1 A B))) ) ) ) ) ) ) ).
tt(d10_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  ( ((k7_coh_sp A B) = (k6_coh_sp A C))  =>  ((k9_coh_sp A B C) = (k4_tarski (k4_tarski (k6_coh_sp A B) (k7_coh_sp A C)) (k3_relat_1 (k2_xtuple_0 B) (k2_xtuple_0 C)))) ) ) ) ) ) ) ).
tt(d10_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((k4_combgras A B C D) = (k7_relat_1 (u1_combgras A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d10_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k13_complex1 A B) = (k2_xcmplx_0 (k10_real_1 (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))) (k7_real_1 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B)))) (k3_xcmplx_0 (k10_real_1 (k9_real_1 (k8_real_1 (k3_complex1 B) (k4_complex1 A)) (k8_real_1 (k3_complex1 A) (k4_complex1 B))) (k7_real_1 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B)))) k7_complex1))) ) ) ) ) ).
tt(d10_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) k1_numbers)))) )  =>  ( (D = (k2_compl_sp A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) =>  (! [F:$i] :  ((m1_subset_1 F (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ( (E = (k4_tarski G I))  &  (F = (k4_tarski H J)) )  =>  ( ( (G = H)  =>  ((k1_metric_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) D E F) = (k2_metric_1 A I J)) )  &  ( (~  (G = H) )  =>  ((k1_metric_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) D E F) = (k7_real_1 (k2_metric_1 A I B) (k2_metric_1 A B J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((k2_compos_1 A) = (k6_compos_0 (u1_compos_1 A))) ) ) ).
tt(d10_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (! [E:$i] :  ((m2_rfunct_3 E (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  ( (E = (k6_comput_1 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k2_comput_1 k5_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_comput_1 k5_numbers))))) )  &  ( (E = (k8_nat_1 (k2_comput_1 k5_numbers) F (k7_partfun1 k5_numbers D C)))  &  ( ( ((r2_hidden C (k4_finseq_1 D)) & (r2_hidden (k2_finseq_3 C D) (k1_relset_1 (k3_finseq_2 k5_numbers) A)))  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = (k16_funcop_1 (k3_funct_7 k5_numbers D C k6_numbers) (k1_recdef_1 A (k2_finseq_3 C D)))) )  &  ( ( (~  ((r2_hidden C (k4_finseq_1 D)) & (r2_hidden (k2_finseq_3 C D) (k1_relset_1 (k3_finseq_2 k5_numbers) A))) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = k1_xboole_0) )  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ( ((r2_hidden C (k4_finseq_1 D)) &  ((r2_hidden (k3_funct_7 k5_numbers D C G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F G))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers D C G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers D C G)))) (k1_relset_1 (k3_finseq_2 k5_numbers) B))) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 G 1)) = (k1_funct_4 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k16_funcop_1 (k3_funct_7 k5_numbers D C (k2_nat_1 G 1)) (k1_recdef_1 B (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers D C G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers D C G)))))))) )  &  ( (~  ((r2_hidden C (k4_finseq_1 D)) &  ((r2_hidden (k3_funct_7 k5_numbers D C G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F G))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers D C G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers D C G)))) (k1_relset_1 (k3_finseq_2 k5_numbers) B))) ) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 G 1)) = (k8_nat_1 (k2_comput_1 k5_numbers) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  ((v7_conlat_1 B A) <=>  ( ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (u2_conlat_1 A B)) = (u3_conlat_1 A B))  &  ((k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (u3_conlat_1 A B)) = (u2_conlat_1 A B)) ) ) ) ) ) ) ).
tt(d10_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ((k8_convex4 A B) = (k7_convex4 A (k10_complex1 k6_complex1) B)) ) ) ) ) ).
tt(d10_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k13_cqc_sim1 A B) = (k25_qc_lang1 A (k12_cqc_sim1 A B))) ) ) ) ) ).
tt(d10_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_cqc_the1 B A) <=> (r2_hidden B (k4_cqc_the1 A))) ) ) ) ) ).
tt(d10_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k9_csspace4 A B) = (g2_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace4 A B))) ) ) ) ) ).
tt(d10_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ((v1_xboole_0 B) |  ((k10_csspace A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(d10_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_decomp_1 A B) = (k4_subset_1 (u1_struct_0 A) (k1_decomp_1 A B) (k2_decomp_1 A B))) ) ) ) ) ).
tt(d10_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v4_dickson A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((r1_dickson A B C) & (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(d10_diff_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k10_diff_1 A B C D) = (k10_real_1 (k9_real_1 (k9_diff_1 A B C) (k9_diff_1 A C D)) (k6_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(d10_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  =>  ( (B = (k6_dilworth A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (r3_waybel_4 A (k2_struct_0 A) C)) ) ) ) )  &  ((v2_struct_0 A) =>  ( (B = (k6_dilworth A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d10_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  =>  ((m1_dist_1 B A) <=>  ( ((k3_finseq_1 B) = (k5_card_1 A))  &  (? [C:$i] :  ((m2_finseq_1 C A) &  ((k4_dist_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(d10_dtconstr,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k4_dtconstr k5_dtconstr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_dtconstr k5_dtconstr))))) )  =>  ( (A = k14_dtconstr)  <=>  ( ((k8_nat_1 (k4_dtconstr k5_dtconstr) A k6_numbers) = (k2_trees_4 k5_numbers k6_numbers))  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k8_nat_1 (k4_dtconstr k5_dtconstr) A (k1_nat_1 B 1)) = (k13_dtconstr (k8_nat_1 (k4_dtconstr k5_dtconstr) A B))) ) ) ) ) ) ) ).
tt(d10_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [C:$i] :  ((m2_subset_1 C (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ((r1_ec_pf_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) &  ( (~  (D = (k4_struct_0 (k9_int_3 A))) )  &  ( ((k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) = (k8_group_1 (k9_int_3 A) D (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) C)))  &  ( ((k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) = (k8_group_1 (k9_int_3 A) D (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) C)))  &  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) = (k8_group_1 (k9_int_3 A) D (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ens_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) A)))) )  =>  ( (B = (k9_ens_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  ((k3_funct_2 (k2_ens_1 A) A B C) = (k4_ens_1 A C)) ) ) ) ) ) ) ) ).
tt(d10_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k7_entropy1 A) = (k6_entropy1 (k2_entropy1 k1_numbers A))) ) ) ).
tt(d10_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k8_e_siec A) = (k4_xboole_0 (u1_struct_0 A) (k7_e_siec A))) ) ) ).
tt(d10_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r1_euclid_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B D) (k1_rlvect_1 (k15_euclid A) C E)) = (k4_struct_0 (k15_euclid A)))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  ( (C = (k4_euclid_7 A B))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_funct_1 B 1) = (k1_funct_1 C 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_funct_1 C (k1_nat_1 D 1)) = (k7_euclid A (k7_partfun1 (k1_euclid A) C D) (k7_partfun1 (k1_euclid A) B (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k18_euclid A) = (k1_seq_1 A 2)) ) ) ).
tt(d10_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v1_euclidlp B A) <=>  (? [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) &  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ((r3_euclidlp A (k8_euclid A D C) (k8_euclid A E C)) &  (B = (k4_euclidlp A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_exchsort,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  ((v5_exchsort B A) <=>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r2_hidden C (k9_xtuple_0 B)) &  ((r2_hidden D (k9_xtuple_0 B)) & (r2_hidden C D)) )  => (r1_orders_2 A (k7_partfun1 (u1_struct_0 A) B C) (k7_partfun1 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d10_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((v4_extpro_1 D A B C) <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski C E) & (r1_tarski C F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 B)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 A B)) & (v1_partfun1 G (u1_struct_0 B))) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 B)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 A B)) & (v1_partfun1 H (u1_struct_0 B))) ) ) )  =>  ( ((r1_tarski D G) & (r1_tarski D H))  =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((k5_relat_1 (k5_extpro_1 A B E G I) (k9_xtuple_0 D)) = (k5_relat_1 (k5_extpro_1 A B F H I) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((k6_facirc_1 A B C) = (k7_circcomb 2 k6_margrel1 C (k10_finseq_1 A B))) ) ) ) ) ).
tt(d10_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k10_ff_siec A) = (k2_xboole_0 (k1_net_1 A) (k4_relat_1 (k2_net_1 A)))) ) ) ).
tt(d10_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_filter_0 A B C) = (k4_lattices A (k4_filter_0 A B C) (k4_filter_0 A C B))) ) ) ) ) ) ) ).
tt(d10_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_lattices A C D) B) <=>  ((r2_hidden C B) | (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (G = (k10_finance1 A B C D E F))  <=>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((k1_seq_1 G H) = (k11_binop_2 (k1_seq_1 (k8_finance1 A B C (k3_funct_2 k5_numbers C E H)) D) (k1_seq_1 F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k11_finseq_1 A B C) = (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B)) (k9_finseq_1 C))) ) ) ) ).
tt(d10_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (E = (k8_finseq_8 A B C D))  <=>  ( ( (~  (E = k6_numbers) )  =>  ((r1_xxreal_0 D E) &  ((r1_tarski C (k2_rfinseq A (k7_nat_d E 1) B)) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 D F) & (r1_tarski C (k2_rfinseq A (k7_nat_d F 1) B)))  =>  ((r1_xxreal_0 F k6_numbers) | (r1_xxreal_0 E F)) ) ) ) ) ) )  &  (~  ( (E = k6_numbers)  & (r2_finseq_8 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fintopo2 A B) = (a_2_1_fintopo2 A B)) ) ) ) ) ).
tt(d10_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_fintopo3 A B C) = (k7_fintopo3 A (k1_fin_topo A C) B)) ) ) ) ) ) ) ).
tt(d10_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k10_fin_topo A B) = (a_2_3_fin_topo A B)) ) ) ) ) ).
tt(d10_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_fomodel0 A) = (k5_fomodel0 A (k1_fomodel0 A))) ) ) ).
tt(d10_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k10_fomodel1 A) = (k6_subset_1 (k1_fomodel1 A) (k1_tarski (k8_fomodel1 A)))) ) ) ).
tt(d10_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k35_fomodel1 A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) B)))) )  =>  ( (D = (k10_fomodel2 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  ((k3_funct_2 (k35_fomodel1 A) B D E) = (k9_fomodel2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  (! [E:$i] :  ((m2_fomodel2 E A B C) =>  ( ( (~ (v7_fomodel1 C A))  =>  ((v2_fomodel3 E A B C D) <=> (v1_fomodel3 E (k9_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) D)) )  &  ((v7_fomodel1 C A) =>  ((v2_fomodel3 E A B C D) <=> (v1_fomodel3 E (k9_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) (k3_fomodel2 k6_margrel1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((v6_fomodel4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_fomodel4 A))) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (~  ((r1_tarski C D) &  ((r2_hidden E B) &  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (~  ((r2_hidden F B) & (r1_tarski (k1_funct_1 E C) (k1_funct_1 F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v2_margrel1 D) &  ((v3_margrel1 D (k4_dtconstr (k3_freealg A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))))) ) ) )  =>  ( (D = (k5_freealg A B C))  <=>  ( ((k1_relset_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) D) = (k4_finseq_2 (k7_partfun1 k5_numbers A C) (k4_dtconstr (k3_freealg A B))))  &  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k3_freealg A B))) (k4_dtconstr (k3_freealg A B))) =>  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) D)) =>  ((k1_funct_1 D E) = (k8_trees_4 (u1_struct_0 (k3_freealg A B)) (k4_freealg A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r5_fsm_1 A B C D E) <=>  (! [F:$i] :  ((m2_finseq_1 F A) =>  ((k4_fsm_1 A B C D F) = (k4_fsm_1 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k10_ftacell1 A B C D E) = (k24_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d10_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C))))) )  =>  (D = (k17_funcop_1 A B C)) ) ) ) ) ) ).
tt(d10_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_funct_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A)))  =>  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) ) ) ) ).
tt(d10_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( (E = (k7_funct_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((r2_hidden F E) <=>  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) &  ((r2_hidden G D) &  (F = (k7_relset_1 A B C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k10_funct_6 A) = (k3_funct_5 (k2_funct_5 A))) ) ) ).
tt(d10_funct_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m2_funct_7 B A) <=>  ( ((k2_nat_1 (k3_finseq_1 B) 1) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r2_hidden (k1_funct_1 B C) (k1_funct_2 (k1_funct_1 A C) (k1_funct_1 A (k2_nat_1 C 1))))) ) ) ) ) ) ) ) ) ).
tt(d10_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v6_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) D D) = (k4_tarski (k3_functor0 A B C D) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(d10_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( (C = (k5_fvaluat1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k7_numbers B D) = (k4_xxreal_3 (k3_funct_2 (u1_struct_0 A) k7_numbers C D) (k1_fvaluat1 (k2_relset_1 k7_numbers B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k10_gate_5 A B C D E F) = (k10_gate_1 (k7_gate_5 A B C D E) (k2_gate_1 A F) k1_xboole_0)) ) ) ) ) ) ) ).
tt(d10_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ((v2_gcd_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d10_geomtrap,ax, (! [A:$i] :  ((l1_geomtrap A) =>  ((k8_geomtrap A) = (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) ) ) ).
tt(d10_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k10_gfacirc1 A B C) = (k8_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d10_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_glib_000 A) <=>  ((r2_hidden k1_glib_000 (k1_relset_1 k5_numbers A)) &  ((r2_hidden k2_glib_000 (k1_relset_1 k5_numbers A)) &  ((r2_hidden k3_glib_000 (k1_relset_1 k5_numbers A)) &  ((r2_hidden k4_glib_000 (k1_relset_1 k5_numbers A)) &  ( (~ (v1_xboole_0 (k6_glib_000 A)))  &  ( ((v1_funct_1 (k8_glib_000 A)) &  ((v1_funct_2 (k8_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k8_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) )  &  ((v1_funct_1 (k9_glib_000 A)) &  ((v1_funct_2 (k9_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k9_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k7_glib_001 A B C) = (k4_graph_2 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B C)) )  &  ( (~  ((k4_glib_001 A B) = (k3_glib_001 A C)) )  =>  ((k7_glib_001 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(d10_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v5_glib_002 B A) <=>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) => (r2_hidden (k4_glib_002 A) (k4_glib_002 C))) ) ) ) ) ) ) ).
tt(d10_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) & (m1_glib_000 B A))  =>  ((v4_glib_003 B A) <=>  ((k5_glib_003 B) = (k5_relat_1 (k5_glib_003 A) (k25_glib_000 A B))) ) ) ) ) ) ).
tt(d10_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_glib_005 C A B) =>  ( ( ((k2_glib_005 A B C) = k1_xboole_0)  =>  ((k3_glib_005 A B C) = C) )  &  ( (~  ( (~  ((k2_glib_005 A B C) = k1_xboole_0) )  &  ( (~ (r2_hidden (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k2_glib_005 A B C))) (k1_relset_1 (k6_glib_000 A) C)))  &  (~  ((k3_glib_005 A B C) = (k1_funct_4 C (k16_funcop_1 (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k2_glib_005 A B C))) (k10_subset_1 (k2_glib_005 A B C))))) ) ) ) )  &  (~  ( (~  ((k2_glib_005 A B C) = k1_xboole_0) )  &  ( (~  ( (~  ((k2_glib_005 A B C) = k1_xboole_0) )  &  (~ (r2_hidden (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k2_glib_005 A B C))) (k1_relset_1 (k6_glib_000 A) C))) ) )  &  (~  ((k3_glib_005 A B C) = (k1_funct_4 C (k16_funcop_1 (k1_funct_1 (k11_glib_000 A) (k10_subset_1 (k2_glib_005 A B C))) (k10_subset_1 (k2_glib_005 A B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v5_graph_1 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (~  ((r1_subset_1 (u1_struct_0 B) (u1_struct_0 C)) & (r1_graph_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(d10_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  ( (~  (B = k1_xboole_0) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k7_graph_2 A B))  <=>  ((r1_graph_2 A C B) &  ((k1_funct_1 C 1) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B 1))) ) ) ) ) ) ) ) ) ) ).
tt(d10_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u4_struct_0 A) (k9_graph_3 A)) =>  ((r1_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C)) =>  ((r1_xboole_0 (k1_graph_3 A (k10_xtuple_0 B)) (k1_graph_3 A (k10_xtuple_0 C))) |  (! [D:$i] :  ((m2_finseq_2 D (u4_struct_0 A) (k9_graph_3 A)) =>  ( (D = (k11_graph_3 A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (E = (k10_subset_1 (k9_subset_1 (u1_struct_0 A) (k1_graph_3 A (k10_xtuple_0 B)) (k1_graph_3 A (k10_xtuple_0 C)))))  &  (D = (k8_finseq_1 (u4_struct_0 A) (k10_graph_3 A E B) (k10_graph_3 A E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  ((k6_graph_5 A B) = (a_2_3_graph_5 A B)) ) ) ) ) ).
tt(d10_graphsp,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k15_graphsp A B C))  <=>  ( (~  ( (~  (A = k1_xboole_0) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (E = D)  &  ((r2_hidden E A) &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F A) => (r1_xxreal_0 (k7_partfun1 k1_numbers B (k2_nat_1 (k4_nat_1 2 C) E)) (k7_partfun1 k1_numbers B (k2_nat_1 (k4_nat_1 2 C) F)))) ) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r2_hidden F A) &  ((k7_partfun1 k1_numbers B (k2_nat_1 (k4_nat_1 2 C) E)) = (k7_partfun1 k1_numbers B (k2_nat_1 (k4_nat_1 2 C) F))) )  => (r1_xxreal_0 E F)) ) ) ) ) ) ) ) ) ) )  &  ( (A = k1_xboole_0)  =>  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((k8_grcat_1 A) = (u2_grcat_1 A)) ) ) ).
tt(d10_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r6_groeb_2 A B C D E) <=>  (? [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) & (r4_groeb_2 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ( (E = (k10_group_10 A B C D))  <=>  ((u1_struct_0 E) = (a_4_0_group_10 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_group_1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k5_group_1 A C B) = (k1_group_1 A))  =>  (C = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(d10_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( (D = (k9_group_2 A B C))  <=>  ((u1_struct_0 D) = (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k8_group_2 A B) (k8_group_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d10_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_group_3 A B) = (a_2_1_group_3 A B)) ) ) ) ) ).
tt(d10_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A))))) )  =>  ( (B = (k9_group_4 A))  <=>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ((k1_binop_1 B C D) = (k8_group_4 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( (B = (k10_group_5 A))  <=>  ((u1_struct_0 B) = (a_1_0_group_5 A)) ) ) ) ) ) ).
tt(d10_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D B))  =>  ( (D = (k10_group_6 A B C))  <=>  ((u1_struct_0 D) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d10_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((v4_group_9 C A B) <=>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D B))  =>  ( (D = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)))  => (v1_group_3 D B)) ) ) ) ) ) ) ) ) ).
tt(d10_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  ((k10_heyting1 A B) = (k1_zfmisc_1 B)) ) ) ) ).
tt(d10_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  ((v6_hilbert1 A) <=>  ((r2_hidden k2_hilbert1 A) &  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ((r2_hidden (k3_hilbert1 B (k3_hilbert1 C B)) A) &  ((r2_hidden (k3_hilbert1 (k3_hilbert1 B (k3_hilbert1 C D)) (k3_hilbert1 (k3_hilbert1 B C) (k3_hilbert1 B D))) A) &  ((r2_hidden (k3_hilbert1 (k4_hilbert1 B C) B) A) &  ((r2_hidden (k3_hilbert1 (k4_hilbert1 B C) C) A) &  ((r2_hidden (k3_hilbert1 B (k3_hilbert1 C (k4_hilbert1 B C))) A) &  ( ((r2_hidden B A) & (r2_hidden (k3_hilbert1 B C) A))  => (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k3_hilbert2 A) = (k1_funct_1 k2_hilbert2 A)) ) ) ).
tt(d10_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k8_hurwitz A B) = (k3_normsp_1 k1_complfld (k3_polynom5 k1_complfld A (k2_polynom4 k1_complfld (k7_hurwitz A) B)) (k3_polynom5 k1_complfld (k7_hurwitz A) (k2_polynom4 k1_complfld A B)))) ) ) ) ) ).
tt(d10_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_idea_1 A B) & (v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k10_idea_1 A B))  <=>  ( ((k9_idea_1 A B C) = 1)  & (r1_idea_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d10_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((m3_ideal_1 C A B) <=>  (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 k5_numbers C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_subset_1 F (u1_struct_0 A) B) =>  (~  ((k7_partfun1 (u1_struct_0 A) C D) = (k6_algstr_0 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v7_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E))  =>  ( (B = C)  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (? [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ( (~ (v11_struct_0 G))  &  ((v2_cat_1 G) &  ((v3_cat_1 G) &  ((v4_cat_1 G) &  ((v5_cat_1 G) &  ((v6_cat_1 G) & (l1_cat_1 G)) ) ) ) ) ) )  &  (G = (g1_cat_1 A B C D E)) ) )  =>  (! [G:$i] :  ((m3_index_1 G A B C D) =>  ((m5_index_1 G A B C D E F) <=>  ( (! [H:$i] :  ((m1_subset_1 H A) => (r1_funct_2 (u4_struct_0 (k2_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) (k3_funct_2 A B F H))) (u4_struct_0 (k2_index_1 B (k3_relat_1 D (k1_xtuple_0 G)) (k3_funct_2 A B F H))) (u4_struct_0 (k2_index_1 A (k1_xtuple_0 G) H)) (u4_struct_0 (k2_index_1 A (k1_xtuple_0 G) H)) (k7_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) (k3_relat_1 D (k1_xtuple_0 G)) (k8_index_1 A B C D G) (k3_funct_2 A B F H)) (k10_cat_1 (k2_index_1 A (k1_xtuple_0 G) H)))) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  ( ((k3_funct_2 B A C I) = (k3_funct_2 B A D H))  =>  ((k1_funct_1 (k8_index_1 A B C D G) (k1_funct_1 E (k4_tarski I H))) = (k1_partfun1 (u4_struct_0 (k2_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) H)) (u4_struct_0 (k2_index_1 B (k3_relat_1 D (k1_xtuple_0 G)) H)) (u4_struct_0 (k2_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) I)) (u4_struct_0 (k2_index_1 B (k3_relat_1 D (k1_xtuple_0 G)) I)) (k7_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) (k3_relat_1 D (k1_xtuple_0 G)) (k8_index_1 A B C D G) H) (k7_index_1 B (k3_relat_1 C (k1_xtuple_0 G)) (k3_relat_1 D (k1_xtuple_0 G)) (k8_index_1 A B C D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ( (~  (B = k6_numbers) )  =>  ((k6_int_1 A B) = (k6_xcmplx_0 A (k3_xcmplx_0 (k5_int_1 A B) B))) )  &  ( (B = k6_numbers)  =>  ((k6_int_1 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(d10_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A))))) )  =>  ( (B = (k7_int_3 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k7_card_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k7_card_1 A)) =>  ((k5_binop_1 (k7_card_1 A) B C D) = (k4_nat_d (k24_binop_2 C D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ((k8_integr15 A B C D) = (k80_valued_2 B B (k1_euclid A) (k1_euclid A) C D)) ) ) ) ) ) ) ) ).
tt(d10_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_integra1 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_integra1 A) k1_numbers)))) )  =>  ( (C = (k8_integra1 A B))  <=>  (! [D:$i] :  ((m1_integra1 D A) =>  ((k1_seq_1 C D) = (k6_integra1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ((k10_interva1 A B) = (k9_interva1 A (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A)) B)) ) ) ) ) ).
tt(d10_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((k3_intpro_1 A B) = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 k5_numbers 1) A) B)) ) ) ) ) ).
tt(d10_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r2_isocat_1 A B) <=>  (? [C:$i] :  ((m2_cat_1 C A B) &  (? [D:$i] :  ((m2_cat_1 D B A) &  ((r3_nattra_1 A A (k9_cat_1 A B A C D) (k10_cat_1 A)) & (r3_nattra_1 B B (k9_cat_1 B A B D C) (k10_cat_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(d10_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  (! [E:$i] :  ((m2_cat_1 E A (k8_cat_2 B C)) =>  (! [F:$i] :  ((m2_nattra_1 F A (k8_cat_2 B C) D E) =>  ((k12_isocat_2 A B C D E F) = (k4_isocat_1 A (k8_cat_2 B C) C D E F (k15_cat_2 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k10_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d10_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B C) <=>  (~  ( (~  ((r2_hidden B (k8_jordan6 A)) &  ((r2_hidden C (k9_jordan6 A)) &  (~  (C = (k18_pscomp_1 A)) ) ) ) )  &  ( (~  ((r2_hidden B (k8_jordan6 A)) &  ((r2_hidden C (k8_jordan6 A)) & (r1_jordan5c (k8_jordan6 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B C)) ) )  &  (~  ((r2_hidden B (k9_jordan6 A)) &  ((r2_hidden C (k9_jordan6 A)) &  ( (~  (C = (k18_pscomp_1 A)) )  & (r1_jordan5c (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k9_knaster A B) = (k5_knaster A B (k5_lattices A) (k2_card_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(d10_kolmog01,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( (E = (k8_kolmog01 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 A)))  & (r2_hidden F (k4_kolmog01 A B C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v2_lang1 B) & (l2_lang1 B))  =>  ( (B = (k9_lang1 A))  <=>  ( ((u1_struct_0 B) = (k1_ordinal1 A))  &  ( ((u2_lang1 B) = A)  &  ((u1_lang1 B) = (k2_xboole_0 (a_1_3_lang1 A) (k1_tarski (k4_tarski A k1_xboole_0)))) ) ) ) ) ) ) ) ).
tt(d10_laplace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k12_laplace A B C) = (k4_matrix_3 A (k10_laplace (u1_struct_0 A) C) B)) ) ) ) ) ) ) ).
tt(d10_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_lattice4 C A) =>  ( (C = (k3_lattice4 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ((m2_lattice4 D A) =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k5_lattice5 A) (k5_lattice5 A)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_lattice5 A) (k5_lattice5 A)) (u1_struct_0 B))))) )  =>  ( (E = (k6_lattice5 A B C D))  <=>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k1_binop_1 E F G) = (k3_lattice5 A B C F G)) ) ) ) )  &  ( ((k1_binop_1 E (k1_tarski A) (k1_tarski A)) = (k3_yellow_0 B))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) (k1_tarski (k1_tarski A))) = (k3_yellow_0 B))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski (k1_tarski A))) (k1_tarski (k1_tarski (k1_tarski A)))) = (k3_yellow_0 B))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) (k1_tarski (k1_tarski (k1_tarski A)))) = (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski (k1_tarski A))) (k1_tarski (k1_tarski A))) = (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))  &  ( ((k1_binop_1 E (k1_tarski A) (k1_tarski (k1_tarski A))) = (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) (k1_tarski A)) = (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))  &  ( ((k1_binop_1 E (k1_tarski A) (k1_tarski (k1_tarski (k1_tarski A)))) = (k13_lattice3 B (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski (k1_tarski A))) (k1_tarski A)) = (k13_lattice3 B (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k1_binop_1 E F (k1_tarski A)) = (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E (k1_tarski A) F) = (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E F (k1_tarski (k1_tarski A))) = (k13_lattice3 B (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) F) = (k13_lattice3 B (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E F (k1_tarski (k1_tarski (k1_tarski A)))) = (k13_lattice3 B (k3_lattice5 A B C F (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ((k1_binop_1 E (k1_tarski (k1_tarski (k1_tarski A))) F) = (k13_lattice3 B (k3_lattice5 A B C F (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_lattice6 B A) <=> (r1_lattice6 A B (k5_lattices A))) ) ) ) ) ).
tt(d10_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) (u1_struct_0 B)) &  ((v1_lattice5 E D B) &  ((v2_lattice5 E D B) &  ((v3_lattice5 E D B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) (u1_struct_0 B))))) ) ) ) )  =>  ((r2_lattice8 A B C D E) <=>  (? [F:$i] :  ((m1_lattice5 F A B C) &  ( (D = (k7_lattice8 A B C))  &  (E = (k8_lattice8 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v10_lattices A) <=>  ((v4_lattices A) &  ((v5_lattices A) &  ((v8_lattices A) &  ((v6_lattices A) &  ((v7_lattices A) & (v9_lattices A)) ) ) ) ) ) ) ) ).
tt(d10_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((r1_xxreal_0 (k39_glib_000 B) C) =>  ( (D = (k6_lexbfs A B C))  <=>  (D = (k10_subset_1 (k6_glib_000 A))) ) )  &  ( (~ (r1_xxreal_0 (k39_glib_000 B) C))  =>  ( (D = (k6_lexbfs A B C))  <=>  ( (~ (r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))))  &  ((k5_lexbfs A B (k1_nat_1 C 1)) = (k1_funct_4 (k5_lexbfs A B C) (k16_funcop_1 D (k7_nat_d (k39_glib_000 B) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((k5_lfuzzy_1 A B) = (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) (a_2_0_lfuzzy_1 A B))) ) ) ) ) ).
tt(d10_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 B) & (r1_tarski (k2_relset_1 k1_numbers B) (k1_relset_1 k1_numbers A)))  => (v1_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) ) ) ) ) ) ) ).
tt(d10_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k11_lopban_1 A B) = (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) ) ) ) ) ).
tt(d10_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  ((v3_lopban_2 A) <=>  ((k1_normsp_0 A (k5_struct_0 A)) = 1) ) ) ) ).
tt(d10_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k6_lopban_3 A B C) = (k1_normsp_1 A (k5_lopban_3 A B) C)) ) ) ) ) ) ) ).
tt(d10_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k9_lopban_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = (k1_lopban_3 A (k1_lopban_4 A C))) ) ) ) ) ) ) ) ).
tt(d10_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r1_lpspace1 A B C D E) <=>  (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( ((k3_funct_2 B k7_numbers C F) = k6_numbers)  & (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers D (k3_subset_1 A F)) (k2_partfun1 A k1_numbers E (k3_subset_1 A F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k1_numbers (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D))))) )  =>  ( (E = (k9_lpspace2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 (k1_lpspace2 A B C D)) (k6_lpspace2 A B C D)) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_hidden H G) =>  ((k2_binop_1 k1_numbers (k6_lpspace2 A B C D) (k6_lpspace2 A B C D) E F G) = (k5_lpspace2 A B C (k26_valued_1 A k1_numbers H F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r1_xxreal_0 k6_numbers E) &  ((r1_xxreal_0 E 1) &  ((r2_hidden C B) & (r2_hidden D B)) ) )  => (r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D (k9_real_1 1 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((v5_matrix16 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  & (r3_matrix16 A B C)) ) ) ) ) ) ) ) ).
tt(d10_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k11_matrix_1 A B) = (k5_finseq_2 (k4_finseq_2 B (u1_struct_0 A)) B (k5_finseq_2 (u1_struct_0 A) B (k4_struct_0 A)))) ) ) ) ) ).
tt(d10_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (l3_algstr_0 B))  =>  ( (B = (k13_matrix_2 A))  <=>  ( ((u1_struct_0 B) = (k12_matrix_2 A))  &  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  ((k1_binop_1 (u2_algstr_0 B) C D) = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( (D = (k13_matrix_3 A B C))  <=>  ( ((k3_finseq_1 D) = A)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 D E) = (k3_matrix_1 (u1_struct_0 B) C E E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( (B = (k11_matrixc1 A))  <=>  ( ((k3_finseq_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 A))) =>  ((k9_matrix_5 B C) = (k17_rvsum_1 (k9_matrix_1 k2_numbers A C))) ) ) ) ) ) ) ) ) ) ).
tt(d10_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_matrixj1 D (u1_struct_0 A)) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( (D = (k25_matrixj1 A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k2_matrixj1 (u1_struct_0 A) D E) = (k3_matrix_3 A (k2_matrixj1 (u1_struct_0 A) B E) (k2_matrixj1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k10_matrixr1 A))  <=>  ( ((k1_matrix_1 B) = (k3_finseq_1 A))  &  ( ((k3_finseq_1 B) = 1)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k3_matrix_1 k1_numbers B 1 C) = (k1_seq_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_matroid0 A B C) <=>  ((v3_pre_topc B A) &  ((r1_tarski B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) &  ((r1_tarski D C) & (r1_tarski B D)) )  =>  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ( (F = (k6_mcart_1 A B C D E))  <=>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (E = (k6_xtuple_0 G H I J))  =>  (F = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_measure6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v2_seq_2 B) <=> (v3_xxreal_2 (k7_relset_1 A k1_numbers B A))) ) ) ) ).
tt(d10_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k9_setfam_1 k1_numbers) k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 k1_numbers) k7_numbers)))) )  =>  ( (A = k10_measure7)  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((k12_supinf_2 A B) = (k7_supinf_2 (k8_measure7 B))) ) ) ) ) ) ).
tt(d10_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ((m4_measure8 D A B C) =>  (! [E:$i] :  ((m3_measure8 E A (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) C)) B) =>  ( (E = (k8_measure8 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_measure8 A B E F) = (k1_measure8 A B (k3_measure8 A B C D (k1_recdef_1 (k4_funct_2 k5_numbers k5_numbers k5_numbers k7_measure8) F)) (k1_recdef_1 (k5_funct_2 k5_numbers k5_numbers k5_numbers k7_measure8) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k13_member_1 A B) = (a_2_5_member_1 A B)) ) ) ) ) ).
tt(d10_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_memstr_0 A B C) = (k16_funcop_1 (k4_struct_0 B) C)) ) ) ) ) ) ) ).
tt(d10_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( (C = (k10_mesfun7c A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k1_funct_1 C D) = (k3_comseq_2 (k9_mesfun7c A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k10_mesfunc1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k12_supinf_2 C D) = (k3_extreal1 (k12_supinf_2 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v9_mesfunc5 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ((v7_ordinal1 D) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k8_nat_1 k7_numbers A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_metric_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ( (B = (k5_metric_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k1_metric_1 A A B C C) = k6_numbers)  &  ( (~  (C = D) )  =>  ((k1_metric_1 A A B C D) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k7_metric_2 A) = (a_1_3_metric_2 A)) ) ) ).
tt(d10_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers)))) )  =>  ( (C = (k10_metric_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [I:$i] :  ((m1_subset_1 I (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ( ( (H = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D F))  &  (I = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) E G)) )  =>  ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C H I) = (k7_square_1 (k7_real_1 (k5_square_1 (k4_metric_1 A D E)) (k5_square_1 (k4_metric_1 B F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_midsp_1 A B C) = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(d10_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((k7_midsp_2 A B C) = C) ) ) ) ) ) ) ).
tt(d10_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  ((k9_midsp_3 A B C D E) = (k9_midsp_2 B C D (k4_midsp_3 A B D (k7_midsp_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k10_mmlquery A B C D) = (a_4_5_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d10_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_mod_2 B A) & (l1_mod_2 B A))  =>  (! [C:$i] :  ( ((v3_mod_2 C A) & (l1_mod_2 C A))  =>  ( ((k2_mod_2 A B) = (k3_mod_2 A C))  =>  (! [D:$i] :  ( ((v2_mod_2 D A) &  ((v3_mod_2 D A) & (l1_mod_2 D A)) )  =>  ( (D = (k8_mod_2 A B C))  <=>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E A) &  ((v9_vectsp_1 E A) &  ((v10_vectsp_1 E A) &  ((v11_vectsp_1 E A) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E A)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v8_vectsp_1 F A) &  ((v9_vectsp_1 F A) &  ((v10_vectsp_1 F A) &  ((v11_vectsp_1 F A) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l1_vectsp_1 F A)) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v13_algstr_0 G) &  ((v8_vectsp_1 G A) &  ((v9_vectsp_1 G A) &  ((v10_vectsp_1 G A) &  ((v11_vectsp_1 G A) &  ((v2_rlvect_1 G) &  ((v3_rlvect_1 G) &  ((v4_rlvect_1 G) & (l1_vectsp_1 G A)) ) ) ) ) ) ) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 F) (u1_struct_0 G)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 F) (u1_struct_0 G))))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  ( ( ((g1_mod_2 A (u1_mod_2 A B) (u2_mod_2 A B) (u3_mod_2 A B)) = (g1_mod_2 A F G H))  &  ((g1_mod_2 A (u1_mod_2 A C) (u2_mod_2 A C) (u3_mod_2 A C)) = (g1_mod_2 A E F I)) )  =>  (D = (g1_mod_2 A E G (k1_partfun1 (u1_struct_0 E) (u1_struct_0 F) (u1_struct_0 F) (u1_struct_0 G) I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_mod_4 C A B) <=>  ((v1_ringcat1 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d10_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ((k12_modal_1 A B) = (k7_trees_2 (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 2) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) (k12_finseq_1 k5_numbers k6_numbers) A) (k12_finseq_1 k5_numbers 1) B)) ) ) ) ) ).
tt(d10_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k10_modelc_1 A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 3) A)) ) ) ).
tt(d10_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((v1_modelc_2 A) <=> (m1_subset_1 A k9_modelc_2)) ) ) ).
tt(d10_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_group_1 A) <=> (v1_setwiseo (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d10_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( ( (~ (v11_struct_0 A))  =>  ((v3_msafree2 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_msualg_1 C)) )  =>  ( (C = A)  =>  (! [D:$i] :  ((l3_msualg_1 D C) =>  (~  ( (D = B)  &  (! [E:$i] :  ((m1_msafree E C D) =>  (~ (v2_finset_1 E)) ) ) ) ) ) ) ) ) ) ) )  &  ((v11_struct_0 A) =>  ((v3_msafree2 B A) <=> (v2_finset_1 (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(d10_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_msafree A B C) = (a_3_0_msafree A B C)) ) ) ) ) ) ) ).
tt(d10_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) (k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) D))) =>  ( (F = (k9_msaterm A B C D E))  <=>  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finset_1 G) & (v3_trees_2 G)) ) )  &  ((r1_msaterm A B C D E G) &  (F = (k1_funct_1 G k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k8_msualg_1 A) = (u1_unialg_1 A)) ) ) ).
tt(d10_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( (D = (k5_msualg_2 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (k9_funct_2 (u1_struct_0 A) (k9_setfam_1 (k3_card_3 (u3_msualg_1 A B))))) &  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A B)) &  (! [F:$i] :  ((m3_pboole F (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( (F = E)  =>  ((v3_msualg_2 F A B) &  ((r2_pboole (u1_struct_0 A) (k2_msualg_2 A B) F) & (r2_pboole (u1_struct_0 A) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r4_msualg_3 A B C D) <=>  ((r2_msualg_3 A B C D) & (r3_msualg_3 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 A)) 1)) =>  ( (B = (k7_mycielsk A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( (B = (k1_funct_1 C A))  &  ( ((k9_xtuple_0 C) = k5_numbers)  &  ( ((k1_funct_1 C k6_numbers) = (k5_mycielsk 2))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_mycielsk E (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 D)) 1)) =>  ( (E = (k1_funct_1 C D))  =>  ((k1_funct_1 C (k2_xcmplx_0 D 1)) = (k6_mycielsk (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 D)) 1) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_nagata_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) <=>  ((v2_metric_1 B A) &  ((v4_metric_1 B A) & (v5_metric_1 B A)) ) ) ) ) ) ).
tt(d10_nat_lat,ax, (k10_nat_lat = (g3_lattices k6_nat_lat k9_nat_lat k8_nat_lat)) ).
tt(d10_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ((v1_nattra_1 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (v9_cat_1 (k4_nattra_1 A B C D E F) B (k8_cat_1 A B C F) (k8_cat_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) B)) &  ((v3_normsp_1 D A) &  ((k6_normsp_1 A D) = C) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k2_numbers (u1_struct_0 A) D B)) &  ((k7_partfun1 k2_numbers B C) = (k3_comseq_2 (k8_funct_2 k5_numbers k2_numbers (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ((r6_nfcont_1 A B C) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C E) (k7_partfun1 k1_numbers C F))) (k8_real_1 D (k1_normsp_0 A (k5_algstr_0 A E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  ((k9_normform A B) = (a_2_0_normform A B)) ) ) ) ).
tt(d10_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A))))) )  =>  ( (B = (k14_openlatt A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k9_openlatt A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_openlatt A)) =>  ((k5_binop_1 (k9_openlatt A) B C D) = (k12_openlatt A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_orders_2 A) <=>  ((v8_relat_2 (u1_orders_2 A)) & (m1_subset_1 (u1_orders_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(d10_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) )  =>  ( (D = (k10_oppcat_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) D E) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k6_oppcat_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r5_orders_1 A B) <=>  (! [C:$i] :  (~  ((r1_tarski C B) &  ((v3_orders_1 (k2_wellord1 A C)) &  (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  ((r2_hidden E C) => (r2_hidden (k4_tarski D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_orders_2 A B C) = (k9_subset_1 (u1_struct_0 A) (k2_orders_2 A (k6_domain_1 (u1_struct_0 A) C)) B)) ) ) ) ) ) ) ).
tt(d10_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k3_ordinal1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C A) &  (? [D:$i] :  ((v3_ordinal1 D) &  ( (C = D)  & (v4_ordinal1 D)) ) ) ) ) ) ) ) ) ).
tt(d10_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  ( (? [B:$i] :  ((v3_ordinal1 B) & (r1_ordinal2 B A)) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k8_ordinal2 A))  <=> (r1_ordinal2 B A)) ) ) ) ) ) ).
tt(d10_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ( ((r2_hidden 1 B) & (r2_hidden k6_numbers A))  =>  ( (C = (k5_ordinal5 A B))  <=>  ((r1_ordinal1 (k12_ordinal2 B C) A) &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r1_ordinal1 (k12_ordinal2 B D) A) => (r1_ordinal1 D C)) ) ) ) ) )  &  ( (~  ((r2_hidden 1 B) & (r2_hidden k6_numbers A)) )  =>  ( (C = (k5_ordinal5 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d10_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v8_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d10_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B))) =>  ( (C = (k7_osafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) => (r2_funct_2 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) D) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) D) (k5_msualg_4 A (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) C D) (k6_osafree A B D))) ) ) ) ) ) ) ) ) ).
tt(d10_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r4_osalg_1 A B C D) <=>  ((r1_osalg_1 A B C) &  ((r2_osalg_1 A D (k1_msualg_1 A C)) &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((r1_osalg_1 A B E) & (r2_osalg_1 A D (k1_msualg_1 A E)))  => (r3_orders_2 A (k2_msualg_1 A C) (k2_msualg_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( (E = (k8_osalg_2 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ((m2_osalg_2 G A B) &  ((r2_hidden G (k5_osalg_2 A B C)) &  (F = (k1_funct_1 G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_eqrel_1 (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k5_osalg_4 A B C (k3_osalg_4 A D))))) =>  ( (E = (k6_osalg_4 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ((r2_hidden G (k1_funct_1 (u3_msualg_1 A B) D)) &  (F = (k6_eqrel_1 (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k5_osalg_4 A B C (k3_osalg_4 A D)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k8_parsp_1 A) = (k7_parsp_1 A)) ) ) ).
tt(d10_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A B C) <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ).
tt(d10_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v5_pcs_0 A) <=> (r2_relat_2 (u1_pcs_0 A) (u1_struct_0 A))) ) ) ).
tt(d10_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  ((k9_pdiff_1 A B C D E) = (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 B) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k7_pdiff_1 A C E) D) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C A) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  ((k7_pdiff_4 A B C D) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k9_real_1 (k11_pdiff_1 3 2 C D) (k11_pdiff_1 3 3 B D))) (k9_euclid 3 k3_euclid_8 (k9_real_1 (k11_pdiff_1 3 3 A D) (k11_pdiff_1 3 1 C D)))) (k9_euclid 3 k4_euclid_8 (k9_real_1 (k11_pdiff_1 3 1 B D) (k11_pdiff_1 3 2 A D))))) ) ) ) ) ) ) ) ) ).
tt(d10_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r1_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k1_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G D) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B) D)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J D)) (k1_seq_1 I (k9_real_1 J D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((r5_pdiff_9 A B C D) <=>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_finseq_1 E k5_numbers))  =>  ( ((r1_xxreal_0 (k3_finseq_1 E) C) & (r1_tarski (k1_rvsum_1 E) (k2_finseq_1 A)))  => (r4_pdiff_9 A D E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v9_pencil_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ( (B = (k1_funct_1 D 1))  &  ( (C = (k1_funct_1 D (k3_finseq_1 D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 D) E) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (F = (k1_funct_1 D E))  &  (G = (k1_funct_1 D (k1_nat_1 E 1))) )  => (r1_pencil_1 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_petri_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri_2 A)) ) ) )  =>  ((k8_petri_2 A) = (a_1_0_petri_2 A)) ) ) ).
tt(d10_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_petri B A) <=> (m1_subset_1 (k7_petri A B) (k1_zfmisc_1 (k6_petri A B)))) ) ) ) ) ).
tt(d10_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k8_pnproc_1 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_funcop_1 E) & (v1_finseq_1 E)) ) )  &  ( (D = (k4_funct_7 (k9_funct_2 A k5_numbers) E))  &  ( ((k3_finseq_1 E) = (k3_finseq_1 C))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 C)) =>  ((k1_funct_1 E F) = (k7_pnproc_1 A (k7_partfun1 B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k13_polyform A) = (k11_polyform A 1)) ) ) ).
tt(d10_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v36_algstr_0 C) & (l6_algstr_0 C)) )  =>  ( (C = (k11_polynom1 A B))  <=>  ( (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 F (k15_pre_poly A) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 G (k15_pre_poly A) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( ( (D = F)  &  (E = G) )  =>  ((k1_algstr_0 C D E) = (k4_polynom1 A B F G)) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 F (k15_pre_poly A) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 G (k15_pre_poly A) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( ( (D = F)  &  (E = G) )  =>  ((k6_algstr_0 C D E) = (k9_polynom1 A B F G)) ) ) ) ) ) ) ) ) )  &  ( ((k4_struct_0 C) = (k7_polynom1 A B))  &  ((k5_struct_0 C) = (k8_polynom1 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v36_algstr_0 B) & (l6_algstr_0 B)) )  =>  ( (B = (k14_polynom3 A))  <=>  ( (! [C:$i] :  ((r2_hidden C (u1_struct_0 B)) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_algstr_0 B C D) = (k2_normsp_1 A E F)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 B C D) = (k11_polynom3 A E F)) ) ) ) ) ) ) ) ) )  &  ( ((k4_struct_0 B) = (k9_polynom3 A))  &  ((k5_struct_0 B) = (k10_polynom3 A)) ) ) ) ) ) ) ) ) ) ).
tt(d10_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k7_polynom5 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) C D) = (k3_vectsp_1 A (k3_funct_2 k5_numbers (u1_struct_0 A) B D) (k3_funct_2 k5_numbers (u1_struct_0 A) B (k7_nat_d (k1_algseq_1 A B) 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d10_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l5_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( (E = (k6_polynom7 A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((k3_polynom1 A B E F) = (k6_algstr_0 B (k3_polynom1 A B C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r8_polyred A B C D E F) <=> (r3_polyred A B C D E F (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (D = (k8_poset_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v6_orders_2 F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ( (F = (k7_poset_1 A B C E))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E) = (k1_yellow_0 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 B))) ) )  =>  ( (D = (k10_pralg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_funct_1 D E) = (k4_card_3 (k9_pralg_2 A B E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r2_pre_poly A B C) <=>  ((r1_pre_poly A B C) | (r6_pboole A B C)) ) ) ) ) ) ) ) ).
tt(d10_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r2_hidden B D) &  ((r2_hidden C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_prob_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k10_prob_1 A) = (k4_xxreal_1 k2_xxreal_0 A)) ) ) ).
tt(d10_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_prob_3 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v2_prob_1 C) & (r1_tarski (k2_relset_1 (k9_setfam_1 A) C) B))  => (r2_hidden (k3_prob_1 A C) B)) ) ) ) ) ) ) ).
tt(d10_prvect_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_prvect_2 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k9_pscomp_1 A) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) A) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A))) ) ) ).
tt(d10_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) =>  ((m3_pua2mss1 B A) <=>  (! [C:$i] :  ((m1_pua2mss1 C (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A))) => (r2_pua2mss1 (u1_struct_0 A) C B)) ) ) ) ) ) ) ).
tt(d10_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((v1_qc_lang1 B A) <=>  ((m1_subset_1 B (k1_zfmisc_1 (k13_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))))) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  => (r2_hidden (k7_finseq_1 (k12_finseq_1 (k8_qc_lang1 A C) D) E) B)) ) ) ) ) )  &  ((r2_hidden (k9_finseq_1 (k4_tarski k6_numbers k6_numbers)) B) &  ( (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  ((r2_hidden C B) => (r2_hidden (k7_finseq_1 (k9_finseq_1 (k4_tarski 1 k6_numbers)) C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 (k4_tarski 2 k6_numbers)) C) D) B)) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  ((r2_hidden D B) => (r2_hidden (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 (k4_tarski 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) C)) D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v1_qc_lang2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k3_qc_lang2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  ((r3_qmax_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k3_qmax_1 A)) => (r1_xxreal_0 (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A B) D) (k7_qmax_1 A B)) (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A C) D) (k7_qmax_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(d10_quatern2,ax, (! [A:$i] :  ( ((v36_algstr_0 A) & (l6_algstr_0 A))  =>  ( (A = k16_quatern2)  <=>  ( ((u1_struct_0 A) = k1_quaterni)  &  ( ((u1_algstr_0 A) = k10_quatern2)  &  ( ((u2_algstr_0 A) = k12_quatern2)  &  ( ((k5_struct_0 A) = k2_quatern2)  &  ((k4_struct_0 A) = k1_quatern2) ) ) ) ) ) ) ) ).
tt(d10_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ( (C = (k10_quaterni A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  ( (A = (k6_quaterni D E F G))  &  ( (B = (k6_quaterni H I J K))  &  (C = (k6_quaterni (k9_real_1 (k9_real_1 (k9_real_1 (k8_real_1 D H) (k8_real_1 E I)) (k8_real_1 F J)) (k8_real_1 G K)) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 D I) (k8_real_1 E H)) (k8_real_1 F K)) (k8_real_1 G J)) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 D J) (k8_real_1 H F)) (k8_real_1 I G)) (k8_real_1 K E)) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 D K) (k8_real_1 G H)) (k8_real_1 E J)) (k8_real_1 F I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (C = (k13_quofield A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  ((r2_hidden E B) &  ((k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) = (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k4_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( ( (~ (r1_xxreal_0 A 2))  =>  ((k11_radix_1 A) = 1) )  &  ( ( (~ (r1_xxreal_0 (k4_xcmplx_0 2) A))  =>  ((k11_radix_1 A) = (k4_xcmplx_0 1)) )  &  ( ((r1_xxreal_0 A 2) & (r1_xxreal_0 (k4_xcmplx_0 2) A))  =>  ((k11_radix_1 A) = k6_numbers) ) ) ) ) ) ).
tt(d10_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k4_radix_3 B)))  =>  ((k12_radix_3 A B C D) = (k3_xcmplx_0 (k13_newton (k1_radix_1 B) (k7_nat_d A 1)) (k11_radix_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d10_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ( ( (~ (r1_xxreal_0 A B))  =>  ((k9_radix_6 A B C) = k6_numbers) )  &  ( ( (A = B)  =>  ((k9_radix_6 A B C) = 1) )  &  ((r1_xxreal_0 A B) =>  ( (A = B)  |  ((k9_radix_6 A B C) = (k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 C)) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((v5_ratfunc1 B A) <=>  (~ (r2_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B))) ) ) ) ) ) ).
tt(d10_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( (B = (k4_relat_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C A) &  (C = D) ) ) ) ) ) ) ) ) ).
tt(d10_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_relat_2 A) <=> (r2_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d10_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r8_rewrite1 A B C) <=>  (? [D:$i] :  ( ((r2_hidden (k4_tarski D B) A) |  (B = D) )  &  ((r2_hidden (k4_tarski D C) A) |  (C = D) ) ) ) ) ) ) ) ) ).
tt(d10_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (C = (k18_rfunct_3 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k1_seq_1 C D) = (k1_rfunct_3 (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_ringcat1 D B C) =>  (! [E:$i] :  ((m1_ringcat1 E A B) =>  ( ((r1_ringcat1 A B) & (r1_ringcat1 B C))  =>  ((k7_ringcat1 A B C D E) = (k6_ringcat1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k3_rltopsp1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k1_algstr_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v13_algstr_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k4_algstr_0 A B))  <=>  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d10_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( (D = (k7_rlvect_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers D E) = (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B E) (k3_funct_2 (u1_struct_0 A) k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ( (E = (k7_rmod_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) = (k6_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ((v8_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_lattices A (k3_robbins1 A B) B)) ) ) ) ) ).
tt(d10_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_robbins3 A))  =>  ((v10_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) <=>  ((k1_lattices A B C) = C) ) ) ) ) ) ) ) ) ).
tt(d10_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k7_roughs_1 A B C))  <=>  ( ((k1_relset_1 k5_numbers D) = (k1_relset_1 k5_numbers B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 D E) = (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k1_roughs_1 (u1_struct_0 A) B E)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k9_rsspace4 A B) = (g1_normsp_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace4 A B))) ) ) ) ) ).
tt(d10_rsspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  ((v1_xboole_0 B) |  ((k10_rsspace A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(d10_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (B = (k16_rvsum_1 A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k2_numbers) &  ( (C = A)  &  (B = (k1_finsop_1 k2_numbers C k27_binop_2)) ) ) ) ) ) ) ) ) ).
tt(d10_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( (A = (k4_tarski k6_numbers k6_numbers))  =>  ((k13_scm_comp A B) = (k5_afinsq_1 (k3_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))))) )  &  ( ( (A = (k4_tarski k6_numbers 1))  =>  ((k13_scm_comp A B) = (k5_afinsq_1 (k4_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))))) )  &  ( ( (A = (k4_tarski k6_numbers 2))  =>  ((k13_scm_comp A B) = (k5_afinsq_1 (k5_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))))) )  &  ( ( (A = (k4_tarski k6_numbers 3))  =>  ((k13_scm_comp A B) = (k5_afinsq_1 (k6_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))))) )  &  ( (A = (k4_tarski k6_numbers 4))  =>  ((k13_scm_comp A B) = (k6_afinsq_1 (k6_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))) (k2_ami_3 (k10_ami_3 B) (k10_ami_3 (k2_nat_1 B 1))))) ) ) ) ) ) ) ) ) ) ).
tt(d10_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k8_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  (? [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  &  ( (A = D)  &  ( (B = E)  &  (C = (k4_ami_3 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k9_scmpds_2 A B C) = (k3_xtuple_0 6 k1_xboole_0 (k11_finseq_1 A B C))) ) ) ) ) ) ) ).
tt(d10_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ((v4_scmpds_4 A) <=>  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 2)  |  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14) )  &  (~ (r1_xxreal_0 (k2_compos_0 (u1_compos_1 k1_scmpds_2) A) 6)) ) ) ) ) ) ).
tt(d10_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k8_scmpds_6 A B C) = (k1_scmpds_4 (k4_scmpds_4 (k8_scmpds_2 A B 2) (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 1))) C)) ) ) ) ) ) ) ).
tt(d10_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((m2_subset_1 F k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 F k1_xboole_0 (k7_finseq_4 B C D E))) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k11_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 2)) ) ) ) ) ) ) ) ) ) ).
tt(d10_scmyciel,ax, (! [A:$i] :  ((k5_scmyciel A) = (a_1_3_scmyciel A)) ) ).
tt(d10_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k13_seq_4 A) = (k4_finseqop k2_numbers k1_numbers A k8_seq_4)) ) ) ).
tt(d10_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k10_seqfunc A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k1_seq_1 (k1_seqfunc A k1_numbers B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v3_funct_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d10_setfam_1,ax, (! [A:$i] :  ((v2_setfam_1 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~ (r2_hidden B A)) ) ) ) ) ).
tt(d10_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_sgraph1 A B C D) = (a_4_0_sgraph1 A B C D)) ) ) ) ) ) ) ) ).
tt(d10_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  ((v6_simplex0 B A) <=>  ((k2_struct_0 B) = A) ) ) ) ) ).
tt(d10_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (D = (k9_sin_cos A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E A) =>  ((k8_nat_1 k2_numbers D E) = (k3_xcmplx_0 (k3_xcmplx_0 (k8_nat_1 k2_numbers (k6_sin_cos A) E) (k1_newton B E)) (k1_newton C (k7_nat_d A E)))) )  &  ( (~ (r1_xxreal_0 E A))  =>  ((k8_nat_1 k2_numbers D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  ((v4_stacks_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k6_stacks_1 A (k7_stacks_1 A B C))) ) ) ) ) ) ) ) ).
tt(d10_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v7_struct_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) ) ) ) ).
tt(d10_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (! [D:$i] :  ( (D = (k16_sublemma A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ( (F = E)  &  ((r2_hidden F (k24_qc_lang1 A B)) &  (F = (k1_funct_1 (k2_substut1 A C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_substut1 A)))  =>  ((k11_substut1 A B) = (a_2_2_substut1 A B)) ) ) ) ) ).
tt(d10_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((m1_supinf_2 B A) <=>  (A = (k2_relset_1 k7_numbers B)) ) ) ) ) ) ).
tt(d10_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A))))) )  =>  ( (B = (k10_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ((k5_binop_1 (k9_tdlat_1 A) B C D) = (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(d10_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k8_tmap_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (u1_struct_0 B))  =>  (C = (k6_tmap_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v6_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((k3_topalg_6 A B) = (k1_funct_1 B (k1_xxreal_2 (k9_xtuple_0 B)))) ) ) ) ) ).
tt(d10_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k4_topgen_4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=> (r1_topgen_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k4_topreal1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C B) <=>  ( ((k17_euclid C) = (k17_euclid A))  & (r1_xxreal_0 (k18_euclid A) (k18_euclid C))) ) ) ) ) ) ) ) ) ).
tt(d10_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ( ((v1_pre_topc B) & (m1_pre_topc B (k8_toprealb 2)))  =>  ( (B = (k11_toprealb A))  <=>  ((u1_struct_0 B) = (k6_subset_1 (u1_struct_0 (k8_toprealb 2)) (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) A))) ) ) ) ) ) ).
tt(d10_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v6_transgeo B A) <=> (r3_transgeo A B)) ) ) ) ) ).
tt(d10_trees_1,ax, (! [A:$i] :  ((v2_trees_1 A) <=>  ( (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~  (B = C) )  & (r3_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ( (C = (k5_trees_2 A B))  <=>  ( ((k9_xtuple_0 C) = (k4_trees_1 (k9_xtuple_0 A) B))  &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((r2_hidden D (k4_trees_1 (k9_xtuple_0 A) B)) =>  ((k1_funct_1 C D) = (k1_funct_1 A (k8_finseq_1 k5_numbers B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v5_trees_3 A) <=> (v2_trees_3 (k10_xtuple_0 A))) ) ) ).
tt(d10_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k11_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k1_binarith B C))) ) ) ) ) ) ) ) ).
tt(d10_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k6_unialg_2 A) = (a_1_0_unialg_2 A)) ) ) ).
tt(d10_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k14_polynom3 A))) =>  ( (D = (k9_uproots A B C))  <=>  ( ((k3_finseq_1 D) = C)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k50_valued_1 A B) = (k18_valued_1 A (k35_valued_1 B))) ) ) ) ) ).
tt(d10_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k4_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ) ) ) ).
tt(d10_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k11_algstr_0 A B))  <=>  ((k8_group_1 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d10_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_vectsp_2 C A B))  =>  ((v5_vectsp_2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k4_vectsp_1 A C D (k5_vectsp_2 B C E F)) = (k5_vectsp_2 B C E (k4_vectsp_1 A C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ((k7_vectsp_6 A B C) = (k6_vectsp_6 A B (k4_algstr_0 A (k5_struct_0 A)) C)) ) ) ) ) ) ) ).
tt(d10_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ( (D = (k3_waybel11 A B C))  <=>  ( ((u1_struct_0 D) = B)  &  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 A) B (u1_struct_0 A) (u1_waybel_0 A D) C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ((r1_orders_2 D E F) <=> (r1_orders_2 A (k2_waybel_0 A D E) (k2_waybel_0 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_waybel_1 C A B) =>  ((v3_waybel_1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ( (C = (k1_waybel_1 A B D E))  &  ((v5_orders_3 D A B) &  ((v5_orders_3 E B A) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 B F (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D G)) <=> (r1_orders_2 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A))))) )  =>  ( (C = (k3_waybel23 A B))  <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D B) &  ((v12_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((k1_funct_1 C D) = (k1_yellow_0 A D)) ) ) ) ) ) ) ) ) ) ).
tt(d10_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v3_altcat_2 B (k4_waybel34 A)) & (m1_altcat_2 B (k4_waybel34 A))) ) ) )  =>  ( (B = (k8_waybel34 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel34 A))) => (m1_subset_1 C (u1_struct_0 B))) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel34 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel34 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  (F = D) )  =>  ( ((k1_altcat_1 (k4_waybel34 A) C D) = k1_xboole_0)  |  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 (k4_waybel34 A) C D)) =>  ((r2_hidden G (k1_altcat_1 B E F)) <=> (v22_waybel_0 (k5_yellow21 (k4_waybel34 A) C D G) (k3_yellow21 (k4_waybel34 A) C) (k3_yellow21 (k4_waybel34 A) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ( (D = (k5_waybel35 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (E = (k1_yellow_0 A (k4_waybel35 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(d10_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((k5_waybel_4 A B C) = (a_3_0_waybel_4 A B C)) ) ) ) ) ) ) ).
tt(d10_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((k10_weierstr A B C) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) C))) ) ) ) ) ) ) ).
tt(d10_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ( (A = B)  <=>  ((r1_tarski A B) & (r1_tarski B A)) ) ) ) ).
tt(d10_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A B) = (k3_xboolean (k5_xboolean A B))) ) ) ) ) ).
tt(d10_xtuple_0,ax, (! [A:$i] :  ((k7_xtuple_0 A) = (k1_xtuple_0 (k1_xtuple_0 (k1_xtuple_0 A)))) ) ).
tt(d10_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((r1_xxreal_0 B A) =>  ((k4_xxreal_0 A B) = A) )  &  ( (~ (r1_xxreal_0 B A))  =>  ((k4_xxreal_0 A B) = B) ) ) ) ) ) ) ).
tt(d10_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v4_xxreal_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) & (m1_xxreal_2 B A)) ) ) ) ) ).
tt(d10_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_yellow_0 A B) =>  ( (C = (k2_yellow_0 A B))  <=>  ((r1_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) => (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v3_yellow18 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_altcat_1 A B) = (k6_partfun1 (k3_yellow18 A B))) ) ) ) ) ) ).
tt(d10_yellow21,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xboole_0 B)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) &  ((v2_yellow21 B) & (l2_altcat_1 B)) ) ) ) ) )  =>  ( (B = (k6_yellow21 A))  <=>  ( (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=>  ((v1_orders_2 C) &  ((v3_lattice3 C) & (r2_hidden (u1_struct_0 C) A)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D))) &  ((v5_orders_3 E (k3_yellow21 B C) (k3_yellow21 B D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D)))))) ) )  =>  ((r2_hidden E (k1_altcat_1 B C D)) <=> (v22_waybel_0 E (k3_yellow21 B C) (k3_yellow21 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d10_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v6_waybel_0 D A) & (m1_yellow_6 D A B))  =>  ( (D = (k5_yellow_6 A B C))  <=>  ( ((v4_yellow_0 D B) & (m1_yellow_0 D B))  &  ((u1_struct_0 D) = (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(d10_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v5_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (a_3_1_zf_fund1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d10_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_zf_lang A) <=>  (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  (A = (k4_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d10_zfmisc_1,ax, (! [A:$i] :  ((v1_zfmisc_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  (B = C) ) ) ) ) ) ).
tt(d10_zf_model,ax, (k10_zf_model = (k8_zf_lang (k2_zf_lang k6_numbers) (k13_zf_lang (k2_zf_lang 1) (k8_zf_lang (k2_zf_lang 2) (k12_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang 1)) (k8_zf_lang (k2_zf_lang 3) (k11_zf_lang (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang 2)) (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang k6_numbers))))))))) ).
tt(d10_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ( (B = (k3_zmodul01 A))  <=>  ((u1_struct_0 B) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ).
tt(d11_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l2_abcmiz_0 A)) ) ) )  =>  ((v9_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_abcmiz_0 A (k13_lattice3 A B C)) = (k3_finsub_1 (k1_zfmisc_1 (u1_abcmiz_0 A)) (k2_abcmiz_0 A B) (k2_abcmiz_0 A C))) ) ) ) ) ) ) ) ).
tt(d11_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v2_abcmiz_1 B A) <=>  ( (~  (B = k9_abcmiz_1) )  &  (~  (B = k10_abcmiz_1) ) ) ) ) ) ) ) ).
tt(d11_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((v2_abcmiz_a B A) <=>  ((v5_abcmiz_1 B A (k28_abcmiz_1 A)) &  ((v2_abcmiz_1 (k10_abcmiz_a A B) A) & (m1_subset_1 (k10_abcmiz_a A B) (u4_struct_0 A))) ) ) ) ) ) ) ).
tt(d11_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v11_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r5_aff_1 A B C) &  ((r5_aff_1 A B D) &  ((r2_hidden E B) &  ((r2_hidden H B) &  ((r2_hidden F C) &  ((r2_hidden I C) &  ((r2_hidden G D) &  ((r2_hidden J D) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_analoaf A E F H I) & (r2_analoaf A E G H J)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  | (r2_analoaf A F G I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_afinsq_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((v7_ordinal1 (k1_funct_1 B k6_numbers)) & (r2_hidden (k1_funct_1 B k6_numbers) (k1_afinsq_1 B)))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( (C = (k12_afinsq_1 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k1_funct_1 B k6_numbers))  =>  ( ((k3_finseq_1 C) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E D))  =>  ((k1_funct_1 C E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_afproj A) (k10_afproj A)))) =>  ( (B = (k11_afproj A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  (~  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 E A) &  ( (D = (k4_tarski E 1))  &  ( ((r2_hidden C (u1_struct_0 A)) & (r2_hidden C E))  |  (C = (k5_afproj A E)) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 E A) &  ((v1_aff_4 F A) &  ( (C = (k5_afproj A E))  &  ( (D = (k4_tarski (k6_afproj A F) 2))  & (r1_aff_4 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k4_alg_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_alg_1 A B)))))) )  =>  ( (C = (k5_alg_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k4_alg_1 A B)) C D) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_algstr_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d11_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v32_algstr_0 A) &  ((v6_algstr_1 A) & (l5_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k11_algstr_0 A B))  <=>  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d11_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v2_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k8_algstr_4 A B) = (k1_realset1 (u2_algstr_0 A) B)) ) ) ) ) ).
tt(d11_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((m1_altcat_2 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) & (r2_altcat_2 (k3_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (u2_altcat_1 B) (u2_altcat_1 A))) ) ) ) ) ) ) ).
tt(d11_altcat_3,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v8_altcat_3 B A) <=>  ((v6_altcat_3 B A) & (v7_altcat_3 B A)) ) ) ) ) ) ).
tt(d11_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k10_ami_3 A) = (k4_tarski 1 A)) ) ) ).
tt(d11_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  ((v7_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ((v1_partfun1 D (u1_struct_0 B)) & (v5_memstr_0 D A B k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ((r1_tarski C E) => (r1_extpro_1 A B E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k6_ami_wstd A B C))  <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v6_membered E)) )  &  ( (E = (a_3_0_ami_wstd A B C))  &  (D = (k1_ami_wstd A B (k1_xxreal_2 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k4_analmetr A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) <=> (r5_analmetr A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ((v4_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_collsp A B C D) &  ((r1_collsp A E F D) &  ((r1_collsp A B E G) &  ((r1_collsp A C F G) &  ((r1_collsp A B F H) &  ((r1_collsp A C E H) &  ((r1_collsp A G D H) &  ( (~ (r1_collsp A B C F))  &  ( (~ (r1_collsp A B C E))  &  ( (~ (r1_collsp A B E F))  &  (~ (r1_collsp A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_unialg_1 A))  =>  ((v4_aofa_000 A) <=>  ((r2_hidden 2 (k4_finseq_1 (u1_unialg_1 A))) &  ( (~ (v1_xboole_0 (k1_funct_1 (u1_unialg_1 A) 2)))  &  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 A) 2)) &  ((v2_margrel1 (k1_funct_1 (u1_unialg_1 A) 2)) &  ((v3_margrel1 (k1_funct_1 (u1_unialg_1 A) 2) (u1_struct_0 A)) &  ((v8_comput_1 (k1_funct_1 (u1_unialg_1 A) 2) 2) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 A) 2) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d11_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  ( (D = (k15_aofa_i00 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k4_numbers D E) = (k6_xcmplx_0 (k3_funct_2 A k4_numbers B E) (k3_funct_2 A k4_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v3_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r2_hidden (k6_armstrng A C C) B)) ) ) ) ) ) ).
tt(d11_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ((k9_arytm_3 A B) = (k8_arytm_3 (k8_ordinal3 (k9_ordinal3 (k6_arytm_3 A) (k7_arytm_3 B)) (k9_ordinal3 (k6_arytm_3 B) (k7_arytm_3 A))) (k9_ordinal3 (k7_arytm_3 A) (k7_arytm_3 B)))) ) ) ) ) ).
tt(d11_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k8_asympt_0 A) = (k3_xboole_0 (k6_asympt_0 A) (k7_asympt_0 A))) ) ) ).
tt(d11_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( (B = (k9_bagorder A))  <=>  ( ((u1_struct_0 B) = (k15_pre_poly A))  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) (u1_orders_2 B)) <=> (r3_pre_poly A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) <=>  ((k1_bcialg_1 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d11_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((m3_bcialg_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_hidden (k4_tarski (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((v10_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d11_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v4_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) C) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(d11_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  ((k7_bcialg_6 A B C D) = (k3_tarski (a_4_0_bcialg_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d11_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v1_bilinear D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (v13_vectsp_1 (k7_bilinear A B C D E) C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r6_binop_1 A B C) <=>  ((r4_binop_1 A B C) & (r5_binop_1 A B C)) ) ) ) ) ) ) ).
tt(d11_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k35_binop_2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_binop_1 A B C) = (k11_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d11_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (E = (k11_bor_cant A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers E F) = (k4_series_1 (k8_prob_1 A B (k1_valued_0 (k9_setfam_1 A) D F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_borsuk_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v4_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(d11_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ((r3_borsuk_2 A B C D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A))))) )  =>  ((m1_borsuk_6 F A B C D E) <=>  ((v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) A) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 F G k6_numbers) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) D G))  &  ( ((k1_binop_1 F G 1) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) E G))  &  ( ((k1_binop_1 F k6_numbers G) = B)  &  ((k1_binop_1 F 1 G) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) =>  (! [C:$i] :  (! [D:$i] :  ((m1_borsuk_2 D (k8_toprealb 2) A B) =>  ((r2_hidden C (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k1_tarski A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr))))) )  =>  ( (E = (k17_borsuk_7 A B C D))  <=>  ( ((k1_funct_1 E k6_numbers) = C)  &  ((r2_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 2)) D (k1_partfun1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) E k12_toprealb)) &  ((v5_pre_topc E k17_borsuk_1 k3_topmetr) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr))))) )  =>  ( ((v5_pre_topc F k17_borsuk_1 k3_topmetr) &  ((r2_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 2)) D (k1_partfun1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) F k12_toprealb)) &  ((k1_funct_1 F k6_numbers) = C) ) )  => (r2_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (B = (k12_bvfunc_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k8_margrel1) ) ) ) ) ) ) ) ).
tt(d11_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_c0sp1 B A) =>  ((v1_xboole_0 B) |  ((k5_c0sp1 A B) = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B))) ) ) ) ) ) ) ).
tt(d11_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r6_calcul_1 A B C D E) <=>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden F B) => (r1_valuat_1 A C F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_card_3,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((k9_card_3 A) = (k1_setfam_1 (a_1_0_card_3 A))) ) ) ).
tt(d11_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((k5_card_fil A) = (k1_card_fil A (k4_card_fil A))) ) ) ).
tt(d11_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v5_card_lar A) <=> (r4_card_lar A (a_1_1_card_lar A))) ) ) ).
tt(d11_cat_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_cat_1 A B) = (g1_cat_1 (k1_tarski A) (k1_tarski B) (k18_funcop_1 B A) (k18_funcop_1 B A) (k17_funcop_1 B B B))) ) ) ).
tt(d11_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((k15_cat_2 A B) = (k10_funct_3 (u4_struct_0 A) (u4_struct_0 B))) ) ) ) ) ).
tt(d11_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_cat_4 A B) = (k8_cat_4 A (k1_cat_4 A) B)) ) ) ) ) ).
tt(d11_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v1_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  =>  ( (C = (k11_cat_5 A B))  <=>  ( ((u1_struct_0 C) = (k9_cat_5 A B))  &  ( (! [D:$i] :  ((m2_subset_1 D (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ( ((k3_graph_1 A E) = (k4_graph_1 A F))  &  (D = (k1_cat_1 A F E)) )  => (m1_subset_1 (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A D E) F) (u4_struct_0 C))) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (? [E:$i] :  ((m2_subset_1 E (u4_struct_0 A) (k9_cat_5 A B)) &  (? [F:$i] :  ((m2_subset_1 F (u4_struct_0 A) (k9_cat_5 A B)) &  (? [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) &  ( (D = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A E F) G))  &  ( ((k3_graph_1 A F) = (k4_graph_1 A G))  &  (E = (k1_cat_1 A G F)) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m2_subset_1 F (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [G:$i] :  ((m2_subset_1 G (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [H:$i] :  ((m2_subset_1 H (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 A)) =>  ( ( (D = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A F G) I))  &  (E = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A G H) J)) )  =>  ((k1_cat_1 C D E) = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A F H) (k1_cat_1 A I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B))))))) )  =>  ( (D = (k11_catalg_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_catalg_1 (u1_struct_0 A)))) =>  ((k3_funct_2 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B))) D E) = (k4_tarski k6_numbers (k3_relat_1 (k2_xtuple_0 E) (k7_cat_1 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  ((v6_cfdiff_1 A) <=> (v5_cfdiff_1 (k3_subset_1 k2_numbers A))) ) ) ).
tt(d11_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v3_cgames_1 A)) ) ) )  =>  ((v4_cgames_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  ( (~ (r1_xxreal_0 B 1))  => (r2_hidden (k1_funct_1 A (k6_xcmplx_0 B 1)) (k8_cgames_1 (k1_funct_1 A B)))) ) ) ) ) ) ).
tt(d11_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A B C)) =>  ((k9_chain_1 A B C D) = (a_4_0_chain_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d11_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v6_chord A) <=>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v8_glib_001 B A) =>  ((r1_xxreal_0 (k15_glib_001 A B) 3) | (v5_chord B A)) ) ) ) ) ) ) ).
tt(d11_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v6_circcmb3 A) <=>  (~ (v1_facirc_1 (k2_msafree2 A))) ) ) ) ).
tt(d11_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v5_circcomb A) <=>  (? [B:$i] :  ((l3_msualg_1 B A) & (v4_circcomb B A)) ) ) ) ) ).
tt(d11_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_circtrm1 A B C) <=> (r1_tarski (k7_relat_1 C (k2_msafree2 A)) (k2_msafree2 B))) ) ) ) ) ) ) ).
tt(d11_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k8_clopban1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_clopban1 A B) k1_numbers)))) )  =>  ( (C = (k13_clopban1 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k8_clopban1 A B)) =>  ((k1_seq_1 C D) = (k4_seq_4 (k12_clopban1 A B (k11_clopban1 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d11_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  ((v4_clopban2 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_clvect_1 A (k6_algstr_0 A C D) B) = (k6_algstr_0 A C (k1_clvect_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d11_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ((v8_closure2 C A B) <=>  (! [D:$i] :  ((m1_closure2 D A B (k6_closure2 A B)) =>  (! [E:$i] :  ((m1_closure2 E A B (k6_closure2 A B)) =>  ((r2_pboole A D E) => (r2_pboole A (k7_closure2 A B C D) (k7_closure2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((k5_clvect_1 A B C) = (a_3_1_clvect_1 A B C)) ) ) ) ) ) ) ).
tt(d11_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  ((v4_clvect_2 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 B A) => (v1_clvect_2 B A)) ) ) ) ) ) ).
tt(d11_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v6_cohsp_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r1_tarski B C)) )  => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ).
tt(d11_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k5_coh_sp A) (k3_coh_sp A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k3_coh_sp A))))) )  =>  ( (B = (k10_coh_sp A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  ((k3_funct_2 (k5_coh_sp A) (k3_coh_sp A) B C) = (k6_coh_sp A C)) ) ) ) ) ) ) ).
tt(d11_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 B))) =>  ((k5_combgras A B C D) = (k8_relat_1 (u1_combgras A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d11_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k14_complex1 A) = (k6_xcmplx_0 (k3_complex1 A) (k3_xcmplx_0 (k4_complex1 A) k7_complex1))) ) ) ).
tt(d11_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((k3_compl_sp A B C) = (g1_metric_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_compl_sp A B C))) ) ) ) ) ) ).
tt(d11_compos_0,ax, (! [A:$i] :  ((v5_compos_0 A) =>  ((k6_compos_0 A) = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ) ) ).
tt(d11_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_compos_1 A)) & (v1_funct_1 B)) )  =>  ((v2_compos_1 B A) <=>  (~ (r2_hidden (k2_compos_1 A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(d11_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  ( (D = (k7_comput_1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers))))) )  &  ( (D = (k3_card_3 E))  &  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  ((k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) E F) = (k6_comput_1 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  ((v8_conlat_1 B A) <=>  ((u2_conlat_1 A B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(d11_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((k9_convex4 A B C) = (k5_convex4 A B (k8_convex4 A C))) ) ) ) ) ) ) ).
tt(d11_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k14_cqc_sim1 A B) = (k10_cqc_sim1 A B (k13_cqc_sim1 A B) (k11_cqc_sim1 (k3_qc_lang1 A)))) ) ) ) ) ).
tt(d11_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_csspace))) =>  ( (A = k11_csspace)  <=>  ( (~ (v1_xboole_0 A))  &  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_csspace) & (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace B)) (k55_valued_1 k5_numbers k2_numbers (k2_csspace B))))) ) ) ) ) ) ) ).
tt(d11_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k6_decomp_1 A) = (a_1_0_decomp_1 A)) ) ) ).
tt(d11_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( ((k9_xtuple_0 A) = k5_numbers)  & (r2_hidden B (k10_xtuple_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k7_dickson A B))  <=>  ( ((k1_funct_1 A C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k1_funct_1 A D) = B)  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_diff_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ((k11_diff_1 A B C D E) = (k10_real_1 (k9_real_1 (k10_diff_1 A B C D) (k10_diff_1 A C D E)) (k6_xcmplx_0 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) =>  ((v5_dilworth B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ((v1_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(d11_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_dist_1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 (k4_dist_1 A B))) =>  ((k1_funct_1 (k4_dist_1 A B) C) = (k12_binop_2 1 (k5_card_1 A))) ) ) ) ) ) ) ) ) ).
tt(d11_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((r2_hidden B (k4_dtconstr A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_lang1 A)) =>  ( (C = (k15_dtconstr A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_dtconstr A) (k3_finseq_2 (k1_lang1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr A) (k3_finseq_2 (k1_lang1 A)))))) )  &  ( (C = (k1_funct_1 D B))  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k1_lang1 A)) =>  ((k1_funct_1 D (k2_trees_4 (u1_struct_0 A) E)) = (k3_pre_poly (u1_struct_0 A) E)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_trees_4 F (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  ((r1_lang1 A E (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) F)) =>  ((k1_funct_1 D (k8_trees_4 (u1_struct_0 A) E F)) = (k5_pre_poly (k1_lang1 A) (k4_finseqop (k4_dtconstr A) (k3_finseq_2 (k1_lang1 A)) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k7_ec_pf_1 A) = (a_1_0_ec_pf_1 A)) ) ) ).
tt(d11_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) (k2_ens_1 A)) (k2_ens_1 A)))))  =>  ( (B = (k10_ens_1 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ((r2_hidden (k1_domain_1 (k2_ens_1 A) (k2_ens_1 A) C D) (k9_xtuple_0 B)) <=>  ((k3_ens_1 A C) = (k4_ens_1 A D)) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ( ((k3_ens_1 A C) = (k4_ens_1 A D))  =>  ((k1_funct_1 B (k1_domain_1 (k2_ens_1 A) (k2_ens_1 A) C D)) = (k6_ens_1 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k8_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k6_entropy1 (k8_matrix_1 k1_numbers A C))) ) ) ) ) ) ) ) ) ) ).
tt(d11_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k9_e_siec A) = (k4_xboole_0 (k2_xboole_0 (k2_relat_1 (u1_e_siec A)) (u2_e_siec A)) (k3_struct_0 A))) ) ) ).
tt(d11_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_euclid_3 A (k5_algstr_0 (k15_euclid A) C B) (k5_algstr_0 (k15_euclid A) D B)) & (r2_hidden E (k9_euclid_3 A B C D)))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (F = (k10_euclid_3 A B C D E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( ((k7_real_1 (k7_real_1 F G) H) = 1)  &  (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B F) (k1_rlvect_1 (k15_euclid A) C G)) (k1_rlvect_1 (k15_euclid A) D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((k5_euclid_7 A B) = (k1_funct_1 (k4_euclid_7 A B) (k3_finseq_1 B))) )  &  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) =>  ((k5_euclid_7 A B) = (k5_euclid A)) ) ) ) ) ) ) ).
tt(d11_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k20_euclid A) = (k5_finseq_2 k1_numbers A 1)) ) ) ).
tt(d11_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k5_euclidlp A) = (a_1_1_euclidlp A)) ) ) ).
tt(d11_exchsort,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  ((k6_exchsort A B) = (a_2_0_exchsort A B)) ) ) ) ) ).
tt(d11_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((v5_extpro_1 D A B C) <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  ((r1_tarski D E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ((r1_tarski C F) => (r1_extpro_1 A B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ((k7_facirc_1 A B C D) = (k7_circcomb 3 k6_margrel1 D (k11_finseq_1 A B C))) ) ) ) ) ) ).
tt(d11_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k11_ff_siec A) = (u1_struct_0 A)) ) ) ).
tt(d11_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k8_filter_0 A B))  <=>  ((r1_tarski (k1_relat_1 C) (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E) C) <=> (r2_hidden (k7_filter_0 A D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k8_filter_2 A B C) = (a_3_0_filter_2 A B C)) ) ) ) ) ) ) ).
tt(d11_finance1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers E)))) )  =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((k11_finance1 A B C D E F G) = (k1_seq_1 (k3_series_1 (k10_finance1 C D E G F B)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k13_finseq_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m2_finseq_1 C A)) ) ) ) ) ).
tt(d11_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k9_finseq_8 A B C) = (k5_finseq_8 A B C)) ) ) ) ) ) ) ).
tt(d11_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k10_fintopo2 A B) = (a_2_2_fintopo2 A B)) ) ) ) ) ).
tt(d11_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_fin_topo A B) = (k7_subset_1 (u1_struct_0 A) B (k10_fin_topo A B))) ) ) ) ) ).
tt(d11_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_fomodel0 A) = (k1_funct_4 (k16_funcop_1 k1_xboole_0 k1_xboole_0) (k5_fomodel0 (k3_finseq_2 A) (k11_monoid_0 A)))) ) ) ).
tt(d11_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k11_fomodel1 A) = (k4_finseq_2 1 (k2_fomodel1 A))) ) ) ).
tt(d11_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  ((k11_fomodel2 A B C) = (k1_funct_4 C (k16_funcop_1 (k18_fomodel1 A) (k2_fomodel2 B)))) ) ) ) ) ) ) ).
tt(d11_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 A) (k10_eqrel_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (C = (k14_fomodel3 A B))  <=>  (B = (k6_domain_1 A C)) ) ) ) ) ) ) ) ).
tt(d11_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k4_partfun1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))) =>  ( (C = (k6_freealg A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k5_freealg A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r6_fsm_1 A B C D E F) <=>  (! [G:$i] :  ((m2_finseq_1 G A) =>  ((r1_xxreal_0 (k3_finseq_1 G) F) =>  ((k4_fsm_1 A B C D G) = (k4_fsm_1 A B C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k11_ftacell1 A B C D E) = (k33_gfacirc1 (k24_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d11_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (A = B)  <=>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d11_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E B) & (v1_funct_1 E)) )  =>  ((r1_tarski (k2_relset_1 C D) (k9_xtuple_0 E)) =>  ((k8_funct_2 A B C D E) = (k3_relat_1 D E)) ) ) ) ) ) ) ) ) ) ).
tt(d11_funct_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k9_funct_7 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))))))) )  &  ( (C = (k1_funct_1 D B))  &  ((r2_relset_1 (k1_relat_1 A) (k1_relat_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) D k6_numbers) (k6_partfun1 (k1_relat_1 A))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) D (k1_nat_1 E 1)) = (k3_relat_1 A (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v8_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ((k1_funct_1 (u1_altcat_1 B) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((k6_fvaluat1 A B) = (a_2_1_fvaluat1 A B)) ) ) ) ) ).
tt(d11_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k11_gate_5 A B C D E F) = (k35_gate_1 (k7_gate_5 A B C D E) (k2_gate_1 A F) (k8_gate_5 A B C D E) (k2_gate_1 B F) k1_xboole_0)) ) ) ) ) ) ) ).
tt(d11_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v3_gcd_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_gcd_1 A D B) &  ((r1_gcd_1 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_gcd_1 A E B) & (r1_gcd_1 A E C))  => (r1_gcd_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_geomtrap A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_geomtrap A B C) = (k5_binop_1 (u1_struct_0 A) (u1_midsp_1 A) B C)) ) ) ) ) ) ) ).
tt(d11_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k11_gfacirc1 A B C) = (k10_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d11_glib_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((k12_glib_000 A B C D) = (k7_finseq_4 A B C D)) ) ) ) ) ) ) ) ).
tt(d11_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((v1_abian C) |  ((v1_abian D) |  ((k8_glib_001 A B C D) = (k2_graph_2 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B C D)) ) ) )  &  ( (~  ( (~ (v1_abian C))  &  ( (~ (v1_abian D))  &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) ) )  =>  ((k8_glib_001 A B C D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v5_glib_002 B A) <=>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  (~ (r1_xxreal_0 (k5_glib_002 C) (k5_glib_002 A))) ) ) ) ) ) ) ) ).
tt(d11_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_004 C A) =>  ( (C = (k10_glib_004 A B))  <=>  ( ((k9_glib_004 A C k6_numbers) = (k8_glib_004 A B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k9_glib_004 A C (k1_nat_1 D 1)) = (k7_glib_004 A (k9_glib_004 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_graph_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ((v6_graph_1 A) <=>  ((v1_finset_1 (u1_struct_0 A)) & (v1_finset_1 (u4_struct_0 A))) ) ) ) ).
tt(d11_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k8_graph_2 A B C))  <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k4_numbers))) )  &  ( (E = (k10_xtuple_0 (k2_graph_2 k4_numbers A B C)))  &  ((k2_nat_1 D 1) = (k2_nat_1 (k4_finseq_4 (k2_graph_2 k4_numbers A B C) (k2_xxreal_2 E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~  ((k7_graph_3 A B C) = k6_numbers) )  =>  ((k12_graph_3 A B C) = (a_3_1_graph_3 A B C)) ) ) ) ) ) ) ).
tt(d11_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((k7_graph_5 A) = (a_1_0_graph_5 A)) ) ) ).
tt(d11_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_funct_2 B (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  ( (B = (k16_graphsp A))  <=>  ( ((k9_xtuple_0 B) = (k3_finseq_2 k1_numbers))  &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k6_graphsp B C) = (k2_graphsp (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1) (k15_graphsp (k7_graphsp C A) C A) C (k1_real_1 1))) ) ) ) ) ) ) ) ) ).
tt(d11_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((k9_grcat_1 A) = (u3_grcat_1 A)) ) ) ).
tt(d11_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k11_group_10 A B C D) = (k10_group_10 A B C (k6_domain_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d11_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v4_group_1 B A) =>  ( (C = (k6_group_1 A B))  <=>  (C = k6_numbers) ) )  &  ( (~ (v4_group_1 B A))  =>  ( (C = (k6_group_1 A B))  <=>  ( ((k5_group_1 A C B) = (k1_group_1 A))  &  ( (~  (C = k6_numbers) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k5_group_1 A D B) = (k1_group_1 A))  =>  ( (D = k6_numbers)  | (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_group_2 A B C) = (k2_group_2 A C (k8_group_2 A B))) ) ) ) ) ) ) ).
tt(d11_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r5_group_3 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (k6_group_3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A))))) )  =>  ( (B = (k10_group_4 A))  <=>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ((k1_binop_1 B C D) = (k10_group_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((r1_group_6 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d11_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( (C = (k6_group_9 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v2_group_9 D A) & (m1_group_9 D A B)) ) ) ) ) ) ) ) ).
tt(d11_hahnban1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ((v3_hahnban1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 B) k1_numbers C (k1_algstr_0 B D E)) (k7_real_1 (k3_funct_2 (u1_struct_0 B) k1_numbers C D) (k3_funct_2 (u1_struct_0 B) k1_numbers C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((k6_hermitan A B C) = (k3_hermitan A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k16_bilinear k1_complfld A B (k3_hermitan A B C)))) ) ) ) ) ) ) ).
tt(d11_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)))))) )  =>  ( (C = (k11_heyting1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ((k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) C D) = (k6_subset_1 B D)) ) ) ) ) ) ) ) ) ).
tt(d11_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ( (B = (k5_hilbert1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_hilbert1)) =>  ( ((v6_hilbert1 D) & (r1_tarski A D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( (D = (k11_idea_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( ( (E = 1)  =>  ((k1_recdef_1 D E) = (k9_idea_1 A (k1_recdef_1 B 1) (k1_recdef_1 C 1))) )  &  ( ( (E = 2)  =>  ((k1_recdef_1 D E) = (k4_idea_1 A (k1_recdef_1 B 2) (k1_recdef_1 C 2))) )  &  ( ( (E = 3)  =>  ((k1_recdef_1 D E) = (k4_idea_1 A (k1_recdef_1 B 3) (k1_recdef_1 C 3))) )  &  ( ( (E = 4)  =>  ((k1_recdef_1 D E) = (k9_idea_1 A (k1_recdef_1 B 4) (k1_recdef_1 C 4))) )  &  (~  ( (~  (E = 1) )  &  ( (~  (E = 2) )  &  ( (~  (E = 3) )  &  ( (~  (E = 4) )  &  (~  ((k1_recdef_1 D E) = (k1_recdef_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_ideal_1 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((r1_ideal_1 A B C D) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ( ((k1_funct_1 C E) = (k6_algstr_0 A (k6_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) D E)) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) D E))) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) D E))))  & (r2_hidden (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v8_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) & (r2_incsp_1 A C B)) ) ) ) ) ) ) ).
tt(d11_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ((m2_cat_1 D A C) =>  ( (D = (k9_index_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) D E) = (k4_tarski (k4_tarski (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) (k3_graph_1 A E)) (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) (k4_graph_1 A E))) (k7_index_1 (u4_struct_0 A) (k3_relat_1 (u1_graph_1 A) (k1_xtuple_0 B)) (k3_relat_1 (u2_graph_1 A) (k1_xtuple_0 B)) (k8_index_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k7_card_1 A) (k7_card_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A))))) )  =>  ( (B = (k8_int_3 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k7_card_1 A)) =>  ((k1_funct_1 B C) = (k6_int_1 (k21_binop_2 A C) A)) ) ) ) ) ) ) ) ) ).
tt(d11_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (k1_euclid A)))))  =>  ((k9_integr15 A B C D) = (k43_valued_2 C (k1_euclid A) D B)) ) ) ) ) ) ) ) ).
tt(d11_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_integra1 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_integra1 A) k1_numbers)))) )  =>  ( (C = (k9_integra1 A B))  <=>  (! [D:$i] :  ((m1_integra1 D A) =>  ((k1_seq_1 C D) = (k7_integra1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((k4_intpro_1 A B) = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 k5_numbers 2) A) B)) ) ) ) ) ).
tt(d11_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r2_isocat_1 A B) =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((m1_isocat_1 C A B) <=>  (? [D:$i] :  ((m2_cat_1 D B A) &  ((r3_nattra_1 A A (k9_cat_1 A B A C D) (k10_cat_1 A)) & (r3_nattra_1 B B (k9_cat_1 B A B D C) (k10_cat_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 A C F G))  =>  (! [H:$i] :  ((m1_nattra_1 H A B D E) =>  (! [I:$i] :  ((m1_nattra_1 I A C F G) =>  ((k13_isocat_2 A B C D E F G H I) = (k14_funct_3 (u1_struct_0 A) (u4_struct_0 B) (u4_struct_0 C) H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k11_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k23_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d11_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k10_jordan6 A) = (k1_jordan5c (k9_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) ) ) ).
tt(d11_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k10_knaster A B) = (k6_knaster A B (k6_lattices A) (k2_card_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(d11_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_lattice4 A B) = (a_2_0_lattice4 A B)) ) ) ) ) ).
tt(d11_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((v1_card_1 D) =>  ( (D = (k7_lattice5 A B C))  <=> (r2_tarski D (a_3_0_lattice5 A B C))) ) ) ) ) ) ) ) ) ).
tt(d11_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_lattice6 B A) <=> (r1_lattice6 A (k6_lattices A) B)) ) ) ) ) ).
tt(d11_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((m1_lattice8 D A B C) <=>  ( ((k9_xtuple_0 D) = k5_numbers)  &  ( ((k1_funct_1 D k6_numbers) = (k4_tarski A C))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ( (~ (v1_xboole_0 F))  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 F F) (u1_struct_0 B)) &  ((v1_lattice5 G F B) &  ((v2_lattice5 G F B) &  ((v3_lattice5 G F B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 F F) (u1_struct_0 B))))) ) ) ) )  &  (? [H:$i] :  ( (~ (v1_xboole_0 H))  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 H H) (u1_struct_0 B)) &  ((v1_lattice5 I H B) &  ((v2_lattice5 I H B) &  ((v3_lattice5 I H B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 H H) (u1_struct_0 B))))) ) ) ) )  &  ((r2_lattice8 F B G H I) &  ( ((k1_funct_1 D E) = (k4_tarski F G))  &  ((k1_funct_1 D (k2_nat_1 E 1)) = (k4_tarski H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v11_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_lattices A B (k1_lattices A C D)) = (k1_lattices A (k2_lattices A B C) (k2_lattices A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d11_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k9_lexbfs A) = (k4_tarski k1_xboole_0 (k7_funcop_1 (k6_glib_000 A) k1_xboole_0))) ) ) ).
tt(d11_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v8_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 B) & (r1_tarski (k2_relset_1 k1_numbers B) (k1_relset_1 k1_numbers A)))  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) ) ) ) ) ) ) ).
tt(d11_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~  (C = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((m9_lmod_7 D A B C) <=> (m1_subset_1 D C)) ) ) ) ) ) ) ) ) ) ).
tt(d11_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k10_lopban_1 A B)) =>  ((k13_lopban_1 A B C) = C) ) ) ) ) ) ) ).
tt(d11_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  ((v4_lopban_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_rlvect_1 A (k6_algstr_0 A C D) B) = (k6_algstr_0 A C (k1_rlvect_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d11_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_lopban_4 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k9_lopban_4 A) B)) ) ) ) ) ).
tt(d11_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k11_lpspace1 A B C) = (a_3_1_lpspace1 A B C)) ) ) ) ) ) ) ).
tt(d11_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_rlvect_1 E) & (l1_rlvect_1 E))  =>  ( (E = (k10_lpspace2 A B C D))  <=>  ( ((u1_struct_0 E) = (k6_lpspace2 A B C D))  &  ( ((u1_algstr_0 E) = (k7_lpspace2 A B C D))  &  ( ((k4_struct_0 E) = (k8_lpspace2 A B C D))  &  ((u1_rlvect_1 E) = (k9_lpspace2 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1)))) )  =>  ( (B = (k11_ltlaxio1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C k2_hilbert1)) = k6_numbers)  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C (k1_hilbert2 D))) = 1)  <=> (r2_hidden (k1_hilbert2 D) (k3_funct_2 k5_numbers (k1_zfmisc_1 k10_ltlaxio1) A C))) ) )  &  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (! [E:$i] :  ((m1_subset_1 E k1_hilbert1) =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C (k3_hilbert1 D E))) = (k6_xboolean (k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C D)) (k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C E))))  &  ( (~  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C (k4_hilbert1 D E))) = 1)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C F) E)) = 1)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 1 G) =>  ((r1_xxreal_0 F G) |  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C G) D)) = 1) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C F) E)) = 1)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 1 G) =>  ((r1_xxreal_0 F G) |  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C G) D)) = 1) ) ) ) ) ) ) ) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 B (k1_domain_1 k5_numbers k1_hilbert1 C (k4_hilbert1 D E))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_margrel1,ax, (k6_margrel1 = (k2_tarski k6_numbers 1)) ).
tt(d11_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_matrix16 B A) <=>  (? [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) (k3_finseq_1 B) (k3_finseq_1 B)) & (r3_matrix16 A C B)) ) ) ) ) ) ) ).
tt(d11_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ( (C = (k12_matrix_1 A B))  <=>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski D D) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 A) C D D) = (k5_struct_0 A)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ( (D = E)  |  ((k3_matrix_1 (u1_struct_0 A) C D E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ((v4_matrix_2 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden C (k9_xtuple_0 B)) &  ((r2_hidden D (k9_xtuple_0 B)) &  ( (~  (C = D) )  &  ( ((k1_funct_1 B C) = D)  &  ( ((k1_funct_1 B D) = C)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 B)) =>  ( (E = C)  |  ( (E = D)  |  ((k1_funct_1 B E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k12_matrixc1 A) = (k17_rvsum_1 (k10_matrixc1 A))) ) ) ).
tt(d11_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_matrixj1 D (u1_struct_0 A)) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( (D = (k26_matrixj1 A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k2_matrixj1 (u1_struct_0 A) D E) = (k4_matrix_3 A (k2_matrixj1 (u1_struct_0 A) B E) (k2_matrixj1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k11_matrixr1 A B) = (k9_matrix_1 k1_numbers (k6_matrixr1 A (k9_matrixr1 B)) 1)) ) ) ) ) ).
tt(d11_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_matroid0 A B) = (k3_tarski (a_2_1_matroid0 A B))) ) ) ) ) ).
tt(d11_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F D) =>  ( (F = (k7_mcart_1 A B C D E))  <=>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (E = (k6_xtuple_0 G H I J))  =>  (F = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_measure6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_seq_2 B) <=> (v4_xxreal_2 (k7_relset_1 A k1_numbers B A))) ) ) ) ).
tt(d11_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ((m2_measure7 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))))) )  =>  ( ((k11_funcop_1 k5_numbers k5_numbers k5_numbers C) = (k2_zfmisc_1 k5_numbers k5_numbers))  =>  (! [D:$i] :  ((m1_measure7 D (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) A))) =>  ( (D = (k11_measure7 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k2_measure7 (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) A)) D E) = (k2_measure7 (k8_nat_1 (k9_setfam_1 k1_numbers) A (k1_recdef_1 (k4_funct_2 k5_numbers k5_numbers k5_numbers C) E)) (k4_measure7 A B (k1_recdef_1 (k4_funct_2 k5_numbers k5_numbers k5_numbers C) E)) (k1_recdef_1 (k5_funct_2 k5_numbers k5_numbers k5_numbers C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_measure8 C A B) <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  ((r2_hidden (k3_tarski (k2_relset_1 B D)) B) =>  ((k19_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)) = (k1_mesfunc9 C (k3_tarski (k2_relset_1 B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d11_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k14_member_1 A B) = (k12_member_1 A (k6_member_1 B))) ) ) ) ) ).
tt(d11_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((v5_memstr_0 D A B C) <=>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) &  ((k5_memstr_0 A B D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k11_mesfun7c A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C D)) = (k1_relset_1 A (k4_mesfunc5 A k2_numbers B D)))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k1_numbers C D))) =>  ((k1_seq_1 (k4_mesfunc5 A k1_numbers C D) E) = (k1_seq_1 (k7_comseq_3 (k9_mesfun7c A B E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_mesfunc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ( (C = (k11_mesfunc1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) &  (~ (r1_xxreal_0 B (k12_supinf_2 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d11_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 A) <=>  (~  ( (~ (v7_mesfunc5 A))  &  ( (~ (v8_mesfunc5 A))  &  (~ (v9_mesfunc5 A)) ) ) ) ) ) ) ).
tt(d11_metric_1,ax, (! [A:$i] :  ((k6_metric_1 A) = (g1_metric_1 A (k5_metric_1 A))) ) ).
tt(d11_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k8_metric_2 A) = (a_1_4_metric_2 A)) ) ) ).
tt(d11_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  ((m2_midsp_3 B A) <=> (v2_midsp_3 B A)) ) ) ) ) ).
tt(d11_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k11_mmlquery A B C D) = (a_4_6_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d11_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_mod_2 E A C D) =>  (! [F:$i] :  ((m1_mod_2 F A B C) =>  ((k9_mod_2 A B C D E F) = (k8_mod_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_mod_4 C A B) <=>  ((v2_mod_4 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d11_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_modcat_1 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) B)))) )  =>  ( (C = (k8_modcat_1 A B))  <=>  (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  ((k3_funct_2 (k4_modcat_1 A B) B C D) = (k5_modcat_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k11_modelc_1 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 4) A) B)) ) ) ) ) ).
tt(d11_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_2 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (A = (k2_modelc_2 B)) ) ) ) ) ) ).
tt(d11_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  ((v3_modelc_3 B A) <=>  ((u2_modelc_3 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d11_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v5_group_1 A) <=> (v1_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d11_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v4_msafree2 B A) <=> (v2_finset_1 (u3_msualg_1 A B))) ) ) ) ) ).
tt(d11_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  ( (C = (k8_msafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k7_msafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k9_msualg_1 A) = (g3_msualg_1 (k6_msualg_1 A) (k7_msualg_1 A) (k8_msualg_1 A))) ) ) ).
tt(d11_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( (C = (k6_msualg_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_funct_2 (u1_struct_0 A) (k9_setfam_1 (k3_card_3 (u3_msualg_1 A B))))) &  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) &  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( (E = D)  => (v3_msualg_2 E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((r5_msualg_3 A B C) <=>  (? [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (r4_msualg_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d11_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v3_msualg_6 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ( (D = (k6_msualg_6 A B C))  <=>  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ( ((v3_msualg_6 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r2_pboole (u1_struct_0 A) C E) => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  ((k11_nat_lat A) = A) ) ) ).
tt(d11_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r3_nattra_1 A B C D) <=>  ((r2_nattra_1 A B C D) &  (? [E:$i] :  ((m2_nattra_1 E A B C D) & (v1_nattra_1 E A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r7_ncfcont1 A B C D) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) => (r1_ncfcont1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k10_normform A B C) = (k8_subset_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A) (a_3_0_normform A B C))) ) ) ) ) ) ).
tt(d11_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((k15_openlatt A) = (g3_lattices (k9_openlatt A) (k13_openlatt A) (k14_openlatt A))) ) ) ).
tt(d11_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_oposet_1 A) <=>  ((v2_oposet_1 A) & (v4_orders_2 A)) ) ) ) ).
tt(d11_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)))))) )  =>  ( (D = (k11_oppcat_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) D E) = (k5_oppcat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r6_orders_1 A B) <=>  ((r2_hidden B (k1_relat_1 A)) &  (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 A)) &  ( (~  (C = B) )  & (r2_hidden (k4_tarski B C) A)) ) ) ) ) ) ) ) ) ).
tt(d11_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~  (B = k1_xboole_0) )  =>  ((m1_orders_2 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) &  (C = (k3_orders_2 A B D)) ) ) ) ) )  &  ( (B = k1_xboole_0)  =>  ((m1_orders_2 C A B) <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d11_ordinal1,ax, (! [A:$i] :  ( (A = k4_ordinal1)  <=>  ((r2_hidden k1_xboole_0 A) &  ((v4_ordinal1 A) &  ((v3_ordinal1 A) &  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden k1_xboole_0 B) & (v4_ordinal1 B))  => (r1_tarski A B)) ) ) ) ) ) ) ) ).
tt(d11_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((v6_ordinal5 A) <=>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) => (v5_ordinal5 (k1_funct_1 A B))) ) )  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B C) & (r2_hidden C (k9_xtuple_0 A)))  => (r2_hidden (k5_ordinal5 (k1_funct_1 A C) k4_ordinal1) (k5_ordinal5 (k1_funct_1 A B) k4_ordinal1))) ) ) ) ) ) ) ) ) ).
tt(d11_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  ((k7_ordinal6 A) = (k2_ordinal6 (a_1_1_ordinal6 A))) ) ) ).
tt(d11_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v10_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  ((v9_o_ring_1 (k7_partfun1 (u1_struct_0 A) B 1) A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v9_o_ring_1 D A) &  ((k7_partfun1 (u1_struct_0 A) B (k1_nat_1 C 1)) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k8_osafree A B) = (g3_msualg_1 A (k5_osafree A B) (k7_osafree A B))) ) ) ) ) ).
tt(d11_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r5_osalg_1 A B C D) <=>  ((r3_osalg_1 A B C D) & (r4_osalg_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ( (D = (k9_osalg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k1_setfam_1 (k8_osalg_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (u1_struct_0 A)) & (v11_osalg_1 D A)) ) ) )  =>  ( (D = (k7_osalg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k6_osalg_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k9_parsp_1 A) = (g1_parsp_1 (k5_parsp_1 A) (k8_parsp_1 A))) ) ) ).
tt(d11_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r7_pboole A B C) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D B) => (r1_pboole A D C)) ) ) ) ) ) ) ) ) ).
tt(d11_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v6_pcs_0 A) <=> (r3_relat_2 (u1_pcs_0 A) (u1_struct_0 A))) ) ) ).
tt(d11_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r3_pdiff_1 A B C D) <=> (r1_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B D) C) (k1_seq_1 (k1_pdiff_1 B A) D))) ) ) ) ) ) ) ) ) ).
tt(d11_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r2_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G E) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B) E)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J E)) (k1_seq_1 I (k9_real_1 J E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v10_pencil_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_pencil_1 C A) &  ((v2_pencil_1 C A) &  (! [D:$i] :  ((m2_finseq_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (C = (k1_funct_1 D 1))  &  ((r2_hidden B (k1_funct_1 D (k3_finseq_1 D))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E (k10_xtuple_0 D)) =>  ((v1_pencil_1 E A) & (v2_pencil_1 E A)) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 D) E) | (r1_ordinal1 2 (k1_card_1 (k3_xboole_0 (k1_funct_1 D E) (k1_funct_1 D (k1_nat_1 E 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_petri_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri_2 A)) ) ) )  =>  ((v3_petri_2 A) <=>  ((r1_tarski (k9_xtuple_0 (u2_petri_2 A)) (k6_subset_1 (u4_struct_0 A) (k8_petri_2 A))) &  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (~  ((r2_hidden B (k9_xtuple_0 (u2_petri_2 A))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_petri_2 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_petri A (k6_domain_1 (u4_struct_0 A) B)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_petri A (k6_domain_1 (u4_struct_0 A) B)))) =>  (~  ((v1_funct_1 (k1_funct_1 (u2_petri_2 A) B)) &  ((v1_funct_2 (k1_funct_1 (u2_petri_2 A) B) (k2_petri_2 C D) (k2_petri_2 C E)) & (m1_subset_1 (k1_funct_1 (u2_petri_2 A) B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_petri_2 C D) (k2_petri_2 C E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k14_polyform A) = (k11_polyform A 2)) ) ) ).
tt(d11_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (D = (k8_polynom5 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D E) = (k6_algstr_0 A B (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r9_polyred A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (r8_polyred A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k9_poset_1 A B) = (k6_struct_0 A B (k3_yellow_0 B))) ) ) ) ) ).
tt(d11_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) )  =>  ( ( (~  (A = k1_xboole_0) )  =>  ( (D = (k11_pralg_2 A B C))  <=>  (! [E:$i] :  (~  ((r2_hidden E A) &  (! [F:$i] :  ((l3_msualg_1 F B) =>  (~  ( (F = (k1_funct_1 C E))  &  ((k1_funct_1 D E) = (u4_msualg_1 B F)) ) ) ) ) ) ) ) ) )  &  ( (A = k1_xboole_0)  =>  ( (D = (k11_pralg_2 A B C))  <=>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A B C) <=>  (! [D:$i] : (r1_xxreal_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ).
tt(d11_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v9_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  ((r2_hidden B (k3_subset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r2_hidden B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_prob_1,ax, (k11_prob_1 = a_0_0_prob_1) ).
tt(d11_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ( ((v2_prob_3 C A) &  ((v3_prob_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( (C = (k10_prob_3 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ((r1_tarski B D) &  ((v2_prob_3 D A) &  ((v3_prob_3 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid (k3_finseq_1 A))) =>  ( (C = (k12_prvect_2 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 A)) =>  ((k1_seq_1 C D) = (k1_seq_1 (u1_normsp_0 (k11_prvect_2 A D)) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k10_pscomp_1 A) = (k19_euclid (k6_pscomp_1 A) (k9_pscomp_1 A))) ) ) ).
tt(d11_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m2_pua2mss1 B (u1_struct_0 A)) =>  ((m4_pua2mss1 B A) <=> (m3_pua2mss1 (k3_pua2mss1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(d11_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (B = (k9_qc_lang1 A))  <=>  ((v1_qc_lang1 B A) &  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_qc_lang1 C A) => (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(d11_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k2_qc_lang2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  ((r4_qmax_1 A B C) <=>  ((r3_qmax_1 A B C) & (r3_qmax_1 A C B)) ) ) ) ) ) ) ) ).
tt(d11_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 A B) = (k27_quaterni A (k31_quaterni B))) ) ) ) ) ).
tt(d11_quaterni,ax, (k11_quaterni = (k6_quaterni k6_numbers k6_numbers 1 k6_numbers)) ).
tt(d11_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (~  (B = (k11_quofield A)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (C = (k14_quofield A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  ((r2_hidden E B) &  ((k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) = (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k12_radix_1 A B) = (k6_xcmplx_0 A (k3_xcmplx_0 (k11_radix_1 A) (k1_radix_1 B)))) ) ) ) ) ).
tt(d11_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k4_radix_3 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k4_numbers))  =>  ( (D = (k13_radix_3 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k4_numbers D E) = (k12_radix_3 E B A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( (D = (k10_radix_6 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E C A D) = (k9_radix_6 E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((v6_ratfunc1 B A) <=>  ((v5_ratfunc1 B A) & (v3_ratfunc1 (k5_ratfunc1 A B) A)) ) ) ) ) ) ).
tt(d11_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k5_relat_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D B) & (r2_hidden (k4_tarski D E) A)) ) ) ) ) ) ) ) ) ) ).
tt(d11_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_relat_2 A) <=> (r3_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d11_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r9_rewrite1 A B) <=>  (? [C:$i] : (r4_rewrite1 A B C)) ) ) ) ) ).
tt(d11_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (C = (k19_rfunct_3 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k1_seq_1 C D) = (k2_rfunct_3 (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  ((v8_rltopsp1 A) <=>  (? [B:$i] :  ((m1_yellow13 B A (k4_struct_0 A)) & (v1_rltopsp1 B A)) ) ) ) ) ).
tt(d11_rlvect_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A B C) = (k1_algstr_0 A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(d11_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( (D = (k8_rlvect_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers D E) = (k8_real_1 B (k3_funct_2 (u1_struct_0 A) k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ((k8_rmod_4 A B C) = (k7_rmod_4 A B (k4_algstr_0 A (k1_group_1 A)) C)) ) ) ) ) ) ) ).
tt(d11_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ( ((v4_robbins1 B) & (l4_robbins1 B))  =>  ( (B = (k8_robbins1 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((u2_lattices B) = (u2_lattices A))  &  ( ((u1_robbins1 B) = (u1_robbins1 A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_binop_1 (u1_lattices B) C D) = (k4_robbins1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_roughs_1 A B C) <=> (r1_tarski (k3_roughs_1 A B) (k3_roughs_1 A C))) ) ) ) ) ) ) ).
tt(d11_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_rsspace))) =>  ( (A = k11_rsspace)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_rsspace) & (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace B) (k2_rsspace B)))) ) ) ) ) ) ).
tt(d11_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k17_rvsum_1 A) = (k1_finsop_1 k2_numbers A k27_binop_2)) ) ) ).
tt(d11_scm_comp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))))))) )  =>  ( (A = k14_scm_comp)  <=>  ( (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))))) )  &  ( (C = (k3_funct_2 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) A (k3_scm_comp B)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)) C D) = (k5_afinsq_1 (k2_ami_3 (k10_ami_3 D) (k4_scm_comp B)))) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_scm_comp)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k1_scm_comp)) =>  (~  ( (E = (k1_bintree1 (u1_struct_0 k1_scm_comp) C))  &  ( (F = (k1_bintree1 (u1_struct_0 k1_scm_comp) D))  &  ((r1_lang1 k1_scm_comp B (k4_pre_poly (u1_struct_0 k1_scm_comp) E F)) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))))) )  =>  (~  ( (G = (k3_funct_2 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) A (k2_scm_comp B C D)))  &  ( (H = (k3_funct_2 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) A C))  &  ( (I = (k3_funct_2 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) A D))  &  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)) G J) = (k1_ordinal4 (k15_afinsq_1 (u1_compos_1 k1_ami_3) (k3_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)) H J) (k3_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)) I (k2_nat_1 J 1))) (k13_scm_comp B J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k9_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  (? [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  &  ( (A = D)  &  ( (B = E)  &  (C = (k5_ami_3 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k10_scmpds_2 A B C) = (k3_xtuple_0 7 k1_xboole_0 (k11_finseq_1 A B C))) ) ) ) ) ) ) ).
tt(d11_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k9_scmpds_6 A B C) = (k2_scmpds_4 (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 1)) C)) ) ) ) ) ) ) ).
tt(d11_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((m2_subset_1 F k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 F k1_xboole_0 (k7_finseq_4 B C D E))) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k12_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 3)) ) ) ) ) ) ) ) ) ) ).
tt(d11_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k6_scmyciel A) = (k6_subset_1 (k5_scmyciel (k3_tarski A)) (k1_scmyciel A))) ) ) ).
tt(d11_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k14_seq_4 A) = (k4_finseq_2 A k2_numbers)) ) ) ).
tt(d11_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) <=>  ((r1_seqfunc A k1_numbers B C) &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ( (C = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k18_complex1 (k9_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers B H) E) (k1_seq_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_setfam_1 B A) <=> (r1_tarski A (k3_tarski B))) ) ) ).
tt(d11_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  ((r4_sgraph1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) & (r2_hidden C (k5_sgraph1 A B D D))) ) ) ) ) ) ) ).
tt(d11_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_sheffer1 A) B C)) ) ) ) ) ) ) ).
tt(d11_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k5_simplex0 A B) = (g1_pre_topc A (k2_simplex0 A B))) ) ) ) ).
tt(d11_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (D = (k10_sin_cos A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E A) =>  ((k8_nat_1 k2_numbers D E) = (k9_complex1 (k8_nat_1 k2_numbers (k3_sin_cos B) E) (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos C)) (k7_nat_d A E)))) )  &  ( (~ (r1_xxreal_0 E A))  =>  ((k8_nat_1 k2_numbers D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  ((v5_stacks_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k5_stacks_1 A (k7_stacks_1 A B C))) ) ) ) ) ) ) ) ).
tt(d11_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v8_struct_0 A) <=> (v1_finset_1 (u1_struct_0 A))) ) ) ).
tt(d11_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_substut1 A)))  =>  ((k12_substut1 A B C) = (k7_subset_1 k1_numbers k5_numbers (k4_subset_1 (k1_qc_lang1 A) (k10_substut1 A B) (k11_substut1 A C)))) ) ) ) ) ) ) ).
tt(d11_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) )  =>  (! [B:$i] :  ((m1_supinf_2 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (C = (k15_supinf_2 A B))  <=>  ( ((k12_supinf_2 C k6_numbers) = (k12_supinf_2 B k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k7_numbers) =>  ( (E = (k12_supinf_2 C D))  =>  ((k12_supinf_2 C (k2_nat_1 D 1)) = (k3_supinf_2 E (k12_supinf_2 B (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A))))) )  =>  ( (B = (k11_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ((k5_binop_1 (k9_tdlat_1 A) B C D) = (k9_subset_1 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(d11_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_tex_4 A B) = (k3_tarski (a_2_6_tex_4 A B))) ) ) ) ) ).
tt(d11_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B)))))) )  =>  ( (C = (k9_tmap_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (u1_struct_0 B))  => (r1_funct_2 (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B)) (u1_struct_0 A) (u1_struct_0 (k6_tmap_1 A D)) C (k7_tmap_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d11_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((r1_topalg_6 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_borsuk_2 F A D E) &  (? [G:$i] :  ((m1_borsuk_2 G A D E) &  ( (F = (k3_relat_1 (k1_borsuk_6 k6_numbers 1 (k2_xxreal_2 (k9_xtuple_0 B)) (k1_xxreal_2 (k9_xtuple_0 B))) B))  &  ( (G = (k3_relat_1 (k1_borsuk_6 k6_numbers 1 (k2_xxreal_2 (k9_xtuple_0 C)) (k1_xxreal_2 (k9_xtuple_0 C))) C))  & (r3_borsuk_2 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_topgen_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_xboole_0 C))  &  ((r1_tarski C B) & (v2_topgen_1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(d11_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_prob_1 B (u1_struct_0 A)) &  ((v1_topgen_4 B A) &  ((v3_topgen_4 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ( (B = (k5_topgen_4 A))  <=>  (! [C:$i] :  ( ((v1_prob_1 C (u1_struct_0 A)) &  ((v1_topgen_4 C A) &  ((v3_topgen_4 C (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(d11_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k5_topreal1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C B) <=>  ((r1_xxreal_0 (k17_euclid A) (k17_euclid C)) &  ((k18_euclid C) = (k18_euclid A)) ) ) ) ) ) ) ) ) ) ).
tt(d11_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)))))) )  =>  ( (A = k12_toprealb)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_funct_1 A B) = (k19_euclid (k21_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) (k18_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)))) ) ) ) ) ) ).
tt(d11_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v7_transgeo B A) <=>  ((v6_transgeo B A) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_partfun1 (u1_struct_0 A))) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (C = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((v2_trees_1 B) =>  ((m4_trees_1 B A) <=> (r1_tarski B A)) ) ) ) ) ).
tt(d11_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((r2_hidden B (k9_xtuple_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  ( (D = (k7_trees_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k5_trees_1 (k9_xtuple_0 A) B (k9_xtuple_0 C)))  &  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (~  ((r2_hidden E (k5_trees_1 (k9_xtuple_0 A) B (k9_xtuple_0 C))) &  ( (~  ( (~ (r1_tarski B E))  &  ((k1_funct_1 D E) = (k1_funct_1 A E)) ) )  &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (~  ((r2_hidden F (k9_xtuple_0 C)) &  ((r2_relset_1 k5_numbers k5_numbers E (k8_finseq_1 k5_numbers B F)) &  ((k1_funct_1 D E) = (k1_funct_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v6_trees_3 A) <=> (v3_trees_3 (k10_xtuple_0 A))) ) ) ).
tt(d11_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  ((k9_trees_9 A) = (a_1_2_trees_9 A)) ) ) ).
tt(d11_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (C = (k1_tsp_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k4_tex_4 A D))) ) ) ) ) ) ) ) ) ).
tt(d11_turing_1,ax, (k13_turing_1 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k12_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) k6_numbers) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 2 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 3 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 4 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 1 (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 4 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 5 k6_numbers k6_numbers)))) ).
tt(d11_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k12_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k1_binarith (k9_margrel1 B) C))) ) ) ) ) ) ) ) ).
tt(d11_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v2_unialg_2 A) <=>  (? [B:$i] :  ((m5_margrel1 B (u1_struct_0 A) (k1_unialg_2 A)) &  ((k19_margrel1 B) = k6_numbers) ) ) ) ) ) ).
tt(d11_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (C = (k10_uproots A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k14_polynom3 A)))) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ( ((k3_finseq_1 D) = (k5_card_1 (k13_pre_poly B)))  &  ( (E = (k1_uproots (k13_pre_poly B)))  &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_funct_1 D F) = (k9_uproots A (k7_partfun1 (u1_struct_0 A) E F) (k1_recdef_1 B (k7_partfun1 (u1_struct_0 A) E F)))) ) ) )  &  (C = (k3_group_4 (k14_polynom3 A) (k5_pre_poly (u1_struct_0 (k14_polynom3 A)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ( (B = (k54_valued_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k17_complex1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d11_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k5_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ) ) ) ) ).
tt(d11_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B)) )  =>  ( (D = (k9_vectsp10 A B C))  <=>  ((u1_struct_0 D) = (k8_vectsp10 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d11_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_vectsp_1 A B C) = (k8_group_1 A B (k11_algstr_0 A C))) ) ) ) ) ) ) ).
tt(d11_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((k8_vectsp_6 A B C D) = (k5_vectsp_6 A B C (k7_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ).
tt(d11_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((r1_waybel_0 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B D E) => (r2_hidden (k2_waybel_0 A B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v6_waybel_0 C A) & (l1_waybel_0 C A))  =>  ( (C = (k4_waybel11 A B))  <=>  ( ((u1_struct_0 C) = (k6_domain_1 (u1_struct_0 A) B))  &  ( ((u1_orders_2 C) = (k6_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B B)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) B) (u1_waybel_0 A C) (k6_partfun1 (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ).
tt(d11_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_waybel_1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  & (v3_waybel_1 (k1_waybel_1 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(d11_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ( (C = (k4_waybel23 A B))  <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D B) &  ((v12_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = E)  &  ((k1_funct_1 C D) = (k3_waybel_0 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v3_altcat_2 B (k5_waybel34 A)) & (m1_altcat_2 B (k5_waybel34 A))) ) ) )  =>  ( (B = (k9_waybel34 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel34 A))) => (m1_subset_1 C (u1_struct_0 B))) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel34 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_waybel34 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  (F = D) )  =>  ( ((k1_altcat_1 (k5_waybel34 A) C D) = k1_xboole_0)  |  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 (k5_waybel34 A) C D)) =>  ((r2_hidden G (k1_altcat_1 B E F)) <=> (v22_waybel_0 (k2_waybel34 (k3_yellow21 (k5_waybel34 A) D) (k3_yellow21 (k5_waybel34 A) C) (k5_yellow21 (k5_waybel34 A) C D G)) (k3_yellow21 (k5_waybel34 A) D) (k3_yellow21 (k5_waybel34 A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d11_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((k6_waybel_4 A B C) = (a_3_1_waybel_4 A B C)) ) ) ) ) ) ) ).
tt(d11_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k10_xboolean A B) = (k3_xboolean (k7_xboolean A B))) ) ) ) ) ).
tt(d11_xtuple_0,ax, (! [A:$i] :  ((k8_xtuple_0 A) = (k2_xtuple_0 (k1_xtuple_0 (k1_xtuple_0 A)))) ) ).
tt(d11_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (r1_xxreal_0 A B))  =>  ((k5_xxreal_0 A B C D) = C) )  &  ((r1_xxreal_0 A B) =>  ((k5_xxreal_0 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(d11_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v5_xxreal_2 A) <=>  ((v3_xxreal_2 A) & (v4_xxreal_2 A)) ) ) ) ).
tt(d11_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k3_yellow_0 A) = (k1_yellow_0 A k1_xboole_0)) ) ) ).
tt(d11_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v2_altcat_2 B (k6_yellow21 A)) &  ((v3_altcat_2 B (k6_yellow21 A)) & (m1_altcat_2 B (k6_yellow21 A))) ) ) ) )  =>  ( (B = (k7_yellow21 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_yellow21 A))) =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v3_waybel_3 (k4_yellow21 (k6_yellow21 A) C))) ) ) ) ) ) ) ) ).
tt(d11_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( (B = (k6_yellow_6 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v6_waybel_0 D A) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) ) )  &  ( (D = C)  & (r2_hidden (u1_struct_0 D) (k1_yellow_6 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(d11_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v6_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (a_3_2_zf_fund1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d11_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_zf_lang A) <=>  (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  (A = (k5_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d11_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((k11_zf_model A) = (k11_zf_lang (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang A (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers)))))) (k8_zf_lang (k2_zf_lang 1) (k13_zf_lang (k2_zf_lang 2) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang (k5_zf_lang (k2_zf_lang 4) (k2_zf_lang 2)) (k13_zf_lang (k2_zf_lang 3) (k7_zf_lang (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang 1)) A)))))))) ) ) ).
tt(d11_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((k4_zmodul01 A) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ).
tt(d12_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k3_abcmiz_0 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (D = E)  & (r2_hidden B (k2_abcmiz_0 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) ) )  =>  ((v3_abcmiz_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  ( ((k2_msualg_1 A B) = k6_abcmiz_1)  &  ( ((k1_msualg_1 A B) = k1_xboole_0)  &  ( ((k2_msualg_1 A C) = k7_abcmiz_1)  &  ((k1_msualg_1 A C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v12_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r5_aff_1 A B C) &  ((r2_hidden E B) &  ((r2_hidden H B) &  ((r2_hidden F C) &  ((r2_hidden I C) &  ((r2_hidden G D) &  ((r2_hidden J D) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A E G H J) & (r2_analoaf A F G I J)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ((r1_aff_1 A E F G) |  ( (G = J)  | (r5_aff_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_afinsq_1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((r1_xxreal_0 C B) | (r2_hidden B (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ).
tt(d12_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_afproj A) (k8_afproj A)))) =>  ( (B = (k12_afproj A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ( (C = (k5_afproj A E))  &  ( (D = (k6_afproj A F))  &  ((v1_aff_1 E A) &  ((v1_aff_4 F A) & (r1_aff_4 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  (! [D:$i] :  ((m1_alg_1 D A) =>  ( (D = (k6_alg_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski E F) D) <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_algstr_4 C A))  =>  ( (C = (k9_algstr_4 A B))  <=>  ((r1_tarski B (u1_struct_0 C)) &  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_algstr_4 D A))  =>  ((r1_tarski B (u1_struct_0 D)) => (m1_algstr_4 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  ((v9_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A B D) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( (E = G)  &  ( (F = H)  &  (~  ((k5_altcat_1 A B C D E F) = (k3_relat_1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v6_altcat_1 C) & (m1_altcat_2 C A))  =>  ( (C = (k6_altcat_2 A B))  <=>  ( ((u1_struct_0 C) = (k6_domain_1 (u1_struct_0 A) B))  &  ( ((u1_altcat_1 C) = (k17_funcop_1 B B (k1_altcat_1 A B B)))  &  ((u2_altcat_1 C) = (k16_funcop_1 (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B B B) (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B B B))) ) ) ) ) ) ) ) ) ) ).
tt(d12_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v9_altcat_3 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((v8_altcat_3 E A) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A B E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E C)) =>  (D = (k5_altcat_1 A B E C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_analmetr B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (C = D) )  &  (B = (k4_analmetr A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ((v5_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A C D K) &  ((r1_collsp A F G K) &  ((r1_collsp A D E I) &  ((r1_collsp A G H I) &  ((r1_collsp A C E J) &  ((r1_collsp A F H J) &  ((r1_collsp A B C F) &  ((r1_collsp A B D G) & (r1_collsp A B E H)) ) ) ) ) ) ) )  =>  ( (B = F)  |  ( (C = F)  |  ( (B = G)  |  ( (D = G)  |  ( (B = H)  |  ( (E = H)  |  ((r1_collsp A B C D) |  ((r1_collsp A B C E) |  ((r1_collsp A B D E) | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_unialg_1 A))  =>  ((v5_aofa_000 A) <=>  ((r2_hidden 3 (k4_finseq_1 (u1_unialg_1 A))) &  ( (~ (v1_xboole_0 (k1_funct_1 (u1_unialg_1 A) 3)))  &  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 A) 3)) &  ((v2_margrel1 (k1_funct_1 (u1_unialg_1 A) 3)) &  ((v3_margrel1 (k1_funct_1 (u1_unialg_1 A) 3) (u1_struct_0 A)) &  ((v8_comput_1 (k1_funct_1 (u1_unialg_1 A) 3) 3) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 A) 3) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d12_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v4_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) & (r3_armstrng A (k6_armstrng A C D) (k6_armstrng A E F)))  => (r2_hidden (k6_armstrng A E F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ((k10_arytm_3 A B) = (k8_arytm_3 (k9_ordinal3 (k6_arytm_3 A) (k6_arytm_3 B)) (k9_ordinal3 (k7_arytm_3 A) (k7_arytm_3 B)))) ) ) ) ) ).
tt(d12_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((k9_asympt_0 A B) = (a_2_0_asympt_0 A B)) ) ) ) ).
tt(d12_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k4_bcialg_1 A) = (a_1_0_bcialg_1 A)) ) ) ).
tt(d12_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((m4_bcialg_2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden (k1_bcialg_1 A D E) B) & (r2_hidden (k1_bcialg_1 A E D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((v11_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A C B)) = B) ) ) ) ) ) ) ) ).
tt(d12_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ((v5_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bcialg_4 A B B) = B) ) ) ) ) ) ).
tt(d12_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k7_bcialg_6 A B C D) (k7_bcialg_6 A B C D)) (k7_bcialg_6 A B C D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_bcialg_6 A B C D) (k7_bcialg_6 A B C D)) (k7_bcialg_6 A B C D))))) )  =>  ( (E = (k8_bcialg_6 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F (u1_struct_0 A) (k7_bcialg_6 A B C D)) =>  (! [G:$i] :  ((m2_subset_1 G (u1_struct_0 A) (k7_bcialg_6 A B C D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ( (F = H)  &  (G = I) )  =>  ((k5_binop_1 (k7_bcialg_6 A B C D) E F G) = (k1_bcialg_1 A H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v2_bilinear D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (v13_vectsp_1 (k8_bilinear A B C D E) B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r7_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 B (k3_binop_1 A C D E)) = (k1_binop_1 C (k1_funct_1 B D) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_borsuk_1 B A) =>  ((v2_borsuk_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_compts_1 C A)) ) ) ) ) ) ) ) ).
tt(d12_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r1_borsuk_7 A B C D E) <=>  ((m1_subset_1 C (u1_struct_0 (k7_toprealb A B E))) &  ((m1_subset_1 D (u1_struct_0 (k7_toprealb A B E))) & (r2_hidden B (k1_rltopsp1 (k15_euclid A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k3_funct_2 A k6_margrel1 B D) = k8_margrel1)  =>  ((k3_funct_2 A k6_margrel1 C D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v5_c0sp1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k1_rlvect_1 A C B) = (k4_struct_0 A))  &  ( (~  (B = k6_numbers) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_calcul_1 A B C) <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r6_calcul_1 A B D E F) => (r1_valuat_1 A D C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_card_3,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k10_card_3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_card_3 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k5_card_3 C A)) ) ) ) ) ) ) ) ) ).
tt(d12_card_fil,ax, (r3_card_fil <=>  (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((k2_card_1 A) = (k3_card_2 2 A)) ) ) ) ).
tt(d12_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_cat_1 C A B B) =>  ( (C = (k4_cat_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_cat_1 E A B D) =>  ((k1_cat_1 A C E) = E) ) ) )  &  ( (~  ((k2_cat_1 A D B) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_cat_1 E A D B) =>  ((k1_cat_1 A E C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k11_cat_4 A B) = (k9_cat_4 A (k1_cat_4 A) B B (k6_cat_4 A B) (k4_cat_1 A B))) ) ) ) ) ).
tt(d12_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v1_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  =>  ( (C = (k12_cat_5 A B))  <=>  ( ((u1_struct_0 C) = (k10_cat_5 A B))  &  ( (! [D:$i] :  ((m2_subset_1 D (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ( ((k3_graph_1 A F) = (k4_graph_1 A D))  &  ((k1_cat_1 A D F) = E) )  => (m1_subset_1 (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A D E) F) (u4_struct_0 C))) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (? [E:$i] :  ((m2_subset_1 E (u4_struct_0 A) (k10_cat_5 A B)) &  (? [F:$i] :  ((m2_subset_1 F (u4_struct_0 A) (k10_cat_5 A B)) &  (? [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) &  ( (D = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A E F) G))  &  ( ((k3_graph_1 A G) = (k4_graph_1 A E))  &  ((k1_cat_1 A E G) = F) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m2_subset_1 F (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [G:$i] :  ((m2_subset_1 G (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [H:$i] :  ((m2_subset_1 H (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 A)) =>  ( ( (D = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A F G) I))  &  (E = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A G H) J)) )  =>  ((k1_cat_1 C D E) = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A F H) (k1_cat_1 A I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B))))))) )  =>  ( (D = (k12_catalg_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k3_catalg_1 (u1_struct_0 A)))) =>  ((k3_funct_2 (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B))) D E) = (k4_tarski (k1_xtuple_0 E) (k3_relat_1 (k2_xtuple_0 E) (k7_cat_1 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((r2_cfdiff_1 A B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( (C = (k3_cfdiff_1 A B))  <=>  ( ((k1_relset_1 k2_numbers C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_hidden D B) =>  ((k7_partfun1 k2_numbers C D) = (k2_cfdiff_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( (B = (k10_cgames_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_1 D) &  ((v3_cgames_1 D) & (v4_cgames_1 D)) ) ) ) )  &  ( ((k1_funct_1 D 1) = C)  &  ((k1_funct_1 D (k3_finseq_1 D)) = A) ) ) ) ) ) ) ) ) ) ).
tt(d12_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B (k2_nat_1 C 1)))) =>  ((k10_chain_1 A B C D) = (a_4_1_chain_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d12_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k6_glib_000 A)) =>  ((m3_chord B A) <=>  ((v2_funct_1 B) &  ((k10_xtuple_0 B) = (k6_glib_000 A)) ) ) ) ) ) ) ).
tt(d12_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ((r4_circtrm1 A B C D E F) <=>  ((v2_funct_1 C) &  ((v2_funct_1 D) &  ((r3_pua2mss1 A B C D) &  ( ((u3_msualg_1 A E) = (k3_relat_1 C (u3_msualg_1 B F)))  &  ((u4_msualg_1 A E) = (k3_relat_1 D (u4_msualg_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k14_clopban1 A B) = (g2_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k13_clopban1 A B))) ) ) ) ) ).
tt(d12_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A B B) =>  (! [D:$i] :  ((m3_pboole D A B) =>  ( (D = (k5_closure1 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden F A) =>  ((r2_hidden E (k1_funct_1 D F)) <=>  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  ( (G = (k1_funct_1 C F))  &  ((r2_hidden E (k9_xtuple_0 G)) &  ((k1_funct_1 G E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ((v9_closure2 C A B) <=>  (! [D:$i] :  ((m1_closure2 D A B (k6_closure2 A B)) => (r6_pboole A (k7_closure2 A B C D) (k7_closure2 A B C (k7_closure2 A B C D)))) ) ) ) ) ) ) ) ).
tt(d12_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_clvect_1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k5_clvect_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d12_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v7_cohsp_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ((r2_cohsp_1 (k9_xtuple_0 A) B C) =>  ((k1_funct_1 A (k3_xboole_0 B C)) = (k3_xboole_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ).
tt(d12_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k5_coh_sp A) (k3_coh_sp A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k3_coh_sp A))))) )  =>  ( (B = (k11_coh_sp A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  ((k3_funct_2 (k5_coh_sp A) (k3_coh_sp A) B C) = (k7_coh_sp A C)) ) ) ) ) ) ) ).
tt(d12_combgras,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  ((k6_combgras A B) = (a_2_2_combgras A B)) ) ) ) ).
tt(d12_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k16_complex1 A) = (k7_square_1 (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))))) ) ) ).
tt(d12_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) &  ((v2_compos_0 A) &  ((v3_compos_0 A) & (v5_compos_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v6_compos_0 B A) <=>  (~  (B = (k6_compos_0 A)) ) ) ) ) ) ) ).
tt(d12_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ((r1_compos_1 A B C) <=>  ((r2_hidden C (k9_xtuple_0 B)) &  ((k1_funct_1 B C) = (k2_compos_1 A)) ) ) ) ) ) ) ) ).
tt(d12_comput_1,ax, (! [A:$i] :  ((v4_comput_1 A) <=>  (! [B:$i] :  ((m2_rfunct_3 B (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  (! [C:$i] :  ( ((v3_comput_1 C) & (m2_finseq_1 C (k2_comput_1 k5_numbers)))  =>  ( ((r2_hidden B A) &  ( ((k19_margrel1 B) = (k3_finseq_1 C))  & (r1_tarski (k10_xtuple_0 C) A)) )  => (r2_hidden (k3_relat_1 (k6_funct_6 C) B) A)) ) ) ) ) ) ) ).
tt(d12_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  ((v9_conlat_1 B A) <=>  ((u3_conlat_1 A B) = (u4_struct_0 A)) ) ) ) ) ) ).
tt(d12_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ( (B = (k10_convex4 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m1_convex4 C A)) ) ) ) ) ) ).
tt(d12_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))))) =>  ((r1_cqc_sim1 A B C) <=>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) B (k13_cqc_sim1 A B) (k1_setwiseo (k3_qc_lang1 A)) (k11_cqc_sim1 (k3_qc_lang1 A))) C) &  ( (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k6_cqc_lang A D) E F G) C) => (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D E F G) C)) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_qc_lang1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [H:$i] :  ((m2_funct_2 H (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k7_cqc_lang A D E) F G H) C) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D F G H) C) & (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) E (k30_qc_lang1 A F (k7_cqc_sim1 A D)) G H) C)) ) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_qc_lang1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [H:$i] :  ((m2_funct_2 H (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k11_cqc_lang A E D) F G H) C) => (r2_hidden (k6_xtuple_0 D (k28_qc_lang1 A F) (k2_xboole_0 G (k6_domain_1 (k3_qc_lang1 A) E)) (k1_funct_4 H (k16_funcop_1 E (k2_qc_lang3 A F)))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_csspace A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A B C) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) k2_numbers (u1_csspace A) B C)) ) ) ) ) ) ) ).
tt(d12_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k7_decomp_1 A) = (a_1_1_decomp_1 A)) ) ) ).
tt(d12_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (~ (r1_xxreal_0 E D))  &  ((k8_nat_1 (u1_struct_0 A) B E) = C) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (E = (k8_dickson A B C D))  <=>  ( ((k8_nat_1 (u1_struct_0 A) B E) = C)  &  ( (~ (r1_xxreal_0 E D))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((k8_nat_1 (u1_struct_0 A) B F) = C)  =>  ((r1_xxreal_0 F D) | (r1_xxreal_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) =>  ((v6_dilworth B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(d12_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A)) =>  ( (B = (k10_dist_1 A))  <=>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden C B) <=> (v1_dist_1 C A)) ) ) ) ) ) ) ) ).
tt(d12_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((r2_hidden B (k4_dtconstr A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k16_dtconstr A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A)))))) )  &  ( (C = (k1_funct_1 D B))  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k1_lang1 A)) =>  ((k1_funct_1 D (k2_trees_4 (u1_struct_0 A) E)) = (k3_pre_poly (u1_struct_0 A) E)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_trees_4 F (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ( (G = (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) F))  & (r1_lang1 A E G))  =>  (! [H:$i] :  ((m2_finseq_1 H (k3_finseq_2 (u1_struct_0 A))) =>  ( (H = (k4_finseqop (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A)) F D))  =>  ((k1_funct_1 D (k8_trees_4 (u1_struct_0 A) E F)) = (k1_pre_poly (u1_struct_0 A) (k3_pre_poly (u1_struct_0 A) E) (k5_pre_poly (u1_struct_0 A) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ((k8_ec_pf_1 A B C) = (k9_subset_1 (k2_zfmisc_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C)) (k7_ec_pf_1 A) (k1_eqrel_1 (k6_ec_pf_1 A B C)))) ) ) ) ) ) ) ).
tt(d12_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k10_e_siec A) = (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d12_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_euclid_3 A (k5_algstr_0 (k15_euclid A) C B) (k5_algstr_0 (k15_euclid A) D B)) & (r2_hidden E (k9_euclid_3 A B C D)))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (F = (k11_euclid_3 A B C D E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( ((k7_real_1 (k7_real_1 G F) H) = 1)  &  (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B G) (k1_rlvect_1 (k15_euclid A) C F)) (k1_rlvect_1 (k15_euclid A) D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  ( (C = (k7_euclid_7 A B))  <=>  ( ((k3_finseq_1 C) = A)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k1_funct_1 C D) = (k9_euclid A (k6_euclid_7 A D) (k23_rvsum_1 B (k6_euclid_7 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k22_euclid A) = (k21_euclid A)) ) ) ).
tt(d12_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r7_euclidlp A B C) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) &  ((r1_tarski B (k4_euclidlp A D E F)) & (r1_tarski C (k4_euclidlp A D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  ((k6_exchsort A B) = (a_2_1_exchsort A B)) ) ) ) ) ).
tt(d12_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  =>  ((m1_extpro_1 D A B C) <=>  ((v4_extpro_1 D A B C) & (v5_extpro_1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d12_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((k8_facirc_1 A B C D) = (k2_circcomb (k5_circcomb D (k10_finseq_1 A B)) (k5_circcomb D (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) D) C)))) ) ) ) ) ) ).
tt(d12_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k12_ff_siec A) = (u4_struct_0 A)) ) ) ).
tt(d12_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_filter_0 A B C D) <=> (r2_hidden (k7_filter_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d12_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) =>  ((k9_filter_2 A B C) = (a_3_2_filter_2 A B C)) ) ) ) ) ) ) ) ).
tt(d12_finance1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers E)))) )  =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((k12_finance1 A B C D E F G) = (k1_seq_1 (k3_series_1 (k10_nat_1 k1_numbers (k10_finance1 C D E G F B) 1)) (k10_binop_2 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_finseq_1 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski (k9_xtuple_0 A) (k2_finseq_1 B))) ) ) ) ) ).
tt(d12_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r5_finseq_8 A B C) <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) k6_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 B)) &  ((k8_finseq_8 A B C 1) = (k7_nat_d (k2_nat_1 (k3_finseq_1 B) 1) (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(d12_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_fintopo2 A B) = (a_2_3_fintopo2 A B)) ) ) ) ) ).
tt(d12_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k12_fin_topo A B) = (a_2_4_fin_topo A B)) ) ) ) ) ).
tt(d12_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k10_eqrel_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k10_eqrel_1 A) A)))) )  =>  ( (B = (k15_fomodel3 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) (k10_eqrel_1 A)) =>  ((k3_funct_2 (k10_eqrel_1 A) A B C) = (k14_fomodel3 A C)) ) ) ) ) ) ) ) ).
tt(d12_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  (! [D:$i] :  ((v8_fomodel4 D A B C) <=>  (~  ( (~ (v7_fomodel4 (k1_tarski (k4_tarski C D)) A B))  &  (! [E:$i] :  (~  ((r1_tarski (k1_xtuple_0 E) C) &  ( ((k2_xtuple_0 E) = D)  & (v7_fomodel4 (k1_tarski E) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  ((k7_freealg A B) = (g1_unialg_1 (k4_dtconstr (k3_freealg A B)) (k6_freealg A B))) ) ) ) ) ).
tt(d12_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_partfun1 E (u1_struct_0 C)) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) )  =>  ( (E = (k6_fsm_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 C) (u1_struct_0 C) F G) E) <=> (r6_fsm_1 A B C F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k12_ftacell1 A B C D E) = (k36_gfacirc1 (k24_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d12_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_funct_1 A) =>  ((v1_xboole_0 A) |  (! [B:$i] :  ( (B = (k3_funct_1 A))  <=>  (? [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) &  (B = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d12_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((m1_funct_2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(d12_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A)))  =>  ((k10_funct_7 A B C) = (k2_funct_7 (k2_funct_7 A B (k1_funct_1 A C)) C (k1_funct_1 A B))) )  &  ( (~  ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A))) )  =>  ((k10_funct_7 A B C) = A) ) ) ) ) ) ) ).
tt(d12_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v10_functor0 C A B) <=> (v1_functor0 (u1_functor0 A B C) (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d12_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v36_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  ( (C = (k7_fvaluat1 A B))  <=>  ( ((u1_struct_0 C) = (k6_fvaluat1 A B))  &  ( ((u1_algstr_0 C) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u1_algstr_0 A) (k2_zfmisc_1 (k6_fvaluat1 A B) (k6_fvaluat1 A B))))  &  ( ((u2_algstr_0 C) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 A) (k2_zfmisc_1 (k6_fvaluat1 A B) (k6_fvaluat1 A B))))  &  ( ((u2_struct_0 C) = (k4_struct_0 A))  &  ((u3_struct_0 C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) ) )  =>  ((k12_gate_1 A B C) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~  ((k12_gate_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d12_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k12_gate_5 A B C D E F) = (k37_gate_1 (k7_gate_5 A B C D E) (k2_gate_1 A F) (k8_gate_5 A B C D E) (k2_gate_1 B F) (k9_gate_5 A B C D E) (k2_gate_1 C F) k1_xboole_0)) ) ) ) ) ) ) ).
tt(d12_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v3_gcd_1 A) & (l4_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (E = (k5_gcd_1 A B C D))  <=>  ((r2_hidden E B) &  ((r2_gcd_1 A E C) &  ((r2_gcd_1 A E D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_gcd_1 A F C) & (r2_gcd_1 A F D))  => (r2_gcd_1 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_geomtrap A))  =>  ((v2_geomtrap A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((k9_geomtrap A B C) = (k9_geomtrap A C B))  &  ( ((k9_geomtrap A B B) = B)  &  ( ((k9_geomtrap A (k9_geomtrap A B C) (k9_geomtrap A D E)) = (k9_geomtrap A (k9_geomtrap A B D) (k9_geomtrap A C E)))  &  ( (? [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) &  ((k9_geomtrap A L B) = C) ) )  &  ( ( ((k9_geomtrap A B C) = (k9_geomtrap A B D))  =>  (C = D) )  &  ( ((r2_analoaf A B C D E) => (r2_analoaf A B C (k9_geomtrap A B D) (k9_geomtrap A C E)))  &  ( (~  ((r2_analoaf A B C D E) &  ( (~ (r2_analoaf A B C (k9_geomtrap A B E) (k9_geomtrap A C D)))  &  (~ (r2_analoaf A B C (k9_geomtrap A C D) (k9_geomtrap A B E))) ) ) )  &  ( ( ((r2_analoaf A B C D E) &  ( ((k9_geomtrap A B F) = J)  &  ( ((k9_geomtrap A C G) = J)  &  ( ((k9_geomtrap A D H) = J)  &  ((k9_geomtrap A E I) = J) ) ) ) )  => (r2_analoaf A F G H I))  &  ( ( ((r2_analoaf A J K B F) &  ((r2_analoaf A J K C G) &  ((r2_analoaf A J K D H) &  ((r2_analoaf A J K E I) & (r2_analoaf A B C D E)) ) ) )  =>  ( (J = K)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C C D) =>  ( (B = C)  &  (C = D) ) )  &  ( ( ((r2_analoaf A B C F G) & (r2_analoaf A B C H I))  =>  ( (B = C)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C D E) =>  ((r2_analoaf A D E B C) & (r2_analoaf A C B E D)) )  &  ( (~  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( (~ (r2_analoaf A B C D L))  &  (~ (r2_analoaf A B C L D)) ) ) ) )  &  (~  ((r2_analoaf A B C D J) &  ((r2_analoaf A B C D K) &  ( (~  (B = C) )  &  (~  (J = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k12_gfacirc1 A B C) = (k9_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d12_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((k13_glib_000 A B C) = (k1_funct_4 A (k16_funcop_1 B C))) ) ) ) ) ) ).
tt(d12_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((v1_abian C) |  ((v1_abian D) |  ((k9_glib_001 A B C D) = (k7_glib_001 A (k8_glib_001 A B 1 C) (k8_glib_001 A B D (k3_finseq_1 B)))) ) ) )  &  ( (~  ( (~ (v1_abian C))  &  ( (~ (v1_abian D))  &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) )  =>  ((k9_glib_001 A B C D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k11_glib_004 A B) = (k40_glib_000 (k10_glib_004 A B))) ) ) ) ) ).
tt(d12_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m2_glib_005 D A B) =>  ( (D = (k5_glib_005 A B C))  <=>  ( ((k4_glib_005 A B D k6_numbers) = (k16_funcop_1 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 (k6_glib_000 A) (k2_xboole_0 (k6_domain_1 k5_numbers 1) (k7_glib_000 A)) (k4_glib_005 A B D (k1_nat_1 E 1)) (k3_glib_005 A B (k4_glib_005 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_graph_1 A B C D) <=>  ( ( ((k1_funct_1 (u1_graph_1 A) D) = B)  &  ((k1_funct_1 (u2_graph_1 A) D) = C) )  |  ( ((k1_funct_1 (u1_graph_1 A) D) = C)  &  ((k1_funct_1 (u2_graph_1 A) D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r3_graph_2 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B D) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 E C)) )  => (r1_xxreal_0 (k1_funct_1 A D) (k1_funct_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v1_abian (k7_graph_3 A D C))) )  =>  ( ((k7_graph_3 A B C) = k6_numbers)  |  ((k13_graph_3 A B C) = (a_3_2_graph_3 A B C)) ) ) ) ) ) ) ) ).
tt(d12_graph_5,ax, (k8_graph_5 = a_0_0_graph_5) ).
tt(d12_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k17_graphsp A B C) = (k7_real_1 (k7_partfun1 k1_numbers A (k7_real_1 (k4_nat_1 2 B) (k7_partfun1 k1_numbers A (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1)))) (k7_partfun1 k1_numbers A (k7_real_1 (k7_real_1 (k4_nat_1 2 B) (k8_real_1 B (k7_partfun1 k1_numbers A (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1)))) C)))) ) ) ) ) ) ) ).
tt(d12_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((r1_group_10 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (D = (k1_funct_1 (k1_group_10 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v5_group_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(d12_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k12_group_2 A B C) = (k2_group_2 A (k8_group_2 A B) C)) ) ) ) ) ) ) ).
tt(d12_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_group_3 A))) =>  ( (C = (k9_group_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  &  ( (D = E)  & (r5_group_3 A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k11_group_4 A) = (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) ) ) ).
tt(d12_group_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v5_group_9 A) <=>  ( (~ (v7_struct_0 A))  &  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (~  ( (~  (B = (k7_group_2 A)) )  &  (~  (B = (k6_group_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(d12_hahnban1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ((v4_hahnban1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) k1_numbers C (k1_algstr_0 B D E)) = (k7_real_1 (k3_funct_2 (u1_struct_0 B) k1_numbers C D) (k3_funct_2 (u1_struct_0 B) k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear D k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_bilinear D k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v4_bilinear D k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_hermitan D (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ( (D = (k7_hermitan A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (E = (k3_vectsp_4 k1_complfld A G (k13_bilinear k1_complfld A B C)))  &  (F = (k3_vectsp_4 k1_complfld B H (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) )  =>  ((k2_binop_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) (u1_struct_0 k1_complfld) D E F) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) C G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_hilbert1,ax, (k6_hilbert1 = (k5_hilbert1 (k1_subset_1 k1_hilbert1))) ).
tt(d12_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( (D = (k12_idea_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( ( (E = 1)  =>  ((k1_recdef_1 D E) = (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k9_idea_1 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 2)) (k1_binari_3 A (k1_recdef_1 B 4))))) (k1_recdef_1 C 6)))))) )  &  ( ( (E = 2)  =>  ((k1_recdef_1 D E) = (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 2)) (k1_binari_3 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k9_idea_1 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 2)) (k1_binari_3 A (k1_recdef_1 B 4))))) (k1_recdef_1 C 6))))))) )  &  ( ( (E = 3)  =>  ((k1_recdef_1 D E) = (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 3)) (k1_binari_3 A (k9_idea_1 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 2)) (k1_binari_3 A (k1_recdef_1 B 4))))) (k1_recdef_1 C 6)))))) )  &  ( ( (E = 4)  =>  ((k1_recdef_1 D E) = (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 4)) (k1_binari_3 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k9_idea_1 A (k4_idea_1 A (k9_idea_1 A (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 1)) (k1_binari_3 A (k1_recdef_1 B 3)))) (k1_recdef_1 C 5)) (k6_binarith A (k3_idea_1 A (k1_binari_3 A (k1_recdef_1 B 2)) (k1_binari_3 A (k1_recdef_1 B 4))))) (k1_recdef_1 C 6))))))) )  &  (~  ( (~  (E = 1) )  &  ( (~  (E = 2) )  &  ( (~  (E = 3) )  &  ( (~  (E = 4) )  &  (~  ((k1_recdef_1 D E) = (k1_recdef_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_ideal_1 A B C D) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ( ((k1_funct_1 C E) = (k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E)) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E))))  & (r2_hidden (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v8_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A C I))  &  ( (~ (r1_incsp_1 A D I))  &  ( (~ (r1_incsp_1 A B J))  &  ( (~ (r1_incsp_1 A E J))  &  ( (~ (r1_incsp_1 A B K))  &  ( (~ (r1_incsp_1 A D K))  &  ( (~ (r1_incsp_1 A C L))  &  ( (~ (r1_incsp_1 A E L))  &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F B E) I) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F C D) J) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G C E) K) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G B D) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H B C) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H D E) N) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) F G) O) & (r1_incsp_1 A H O)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v9_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) & (r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ( ((v1_cat_1 C) & (m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B))  =>  ( (C = (k10_index_1 A B))  <=>  (! [D:$i] :  ((m4_index_1 D (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (C = (k4_cat_5 A D (k9_index_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d12_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k9_int_3 A) = (g6_algstr_0 (k7_card_1 A) (k3_gr_cy_1 A) (k7_int_3 A) (k1_funct_7 1 (k7_card_1 A)) (k1_funct_7 k6_numbers (k7_card_1 A)))) ) ) ).
tt(d12_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (B = (k7_integr10 A))  <=>  ( ((k1_relset_1 k1_numbers B) = (k3_limfunc1 k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k1_relset_1 k1_numbers B)) =>  ((k1_seq_1 B C) = (k3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers A (k6_integr10 C)) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(d12_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ((v1_integr15 C A B) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) => (v1_comseq_2 (k1_partfun1 B (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 D A)))) ) ) ) ) ) ) ) ) ) ).
tt(d12_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_integra1 B A) <=> (v3_xxreal_2 (k1_rvsum_1 (k8_integra1 A B)))) ) ) ) ) ).
tt(d12_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((k5_intpro_1 A B) = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 k5_numbers 3) A) B)) ) ) ) ) ).
tt(d12_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u4_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A))))) )  =>  ( (B = (k7_isocat_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u4_struct_0 A) B C) = (k4_cat_1 A C)) ) ) ) ) ) ) ) ).
tt(d12_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 A C F G))  =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  (! [I:$i] :  ((m2_nattra_1 I A C F G) =>  ((k14_isocat_2 A B C D E F G H I) = (k13_isocat_2 A B C D E F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k12_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d12_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k11_jordan6 A) = (k1_jordan5c (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) ) ) ).
tt(d12_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_lattice3 A) <=>  (! [B:$i] :  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k5_lattice4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = (k7_lattices A C)) ) ) ) ) ) ) ) ).
tt(d12_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( (C = (k8_lattice5 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v5_ordinal1 D)) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = A)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k5_lattice5 (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k3_tarski (k2_relset_1 (k10_xtuple_0 D) (k5_relat_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v12_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattices A B D) =>  ((k1_lattices A B (k2_lattices A C D)) = (k2_lattices A (k1_lattices A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( ( ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)) = (k6_glib_000 A))  =>  ( (C = (k10_lexbfs A B))  <=>  (C = (k10_subset_1 (k6_glib_000 A))) ) )  &  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)) = (k6_glib_000 A)) )  =>  ( (C = (k10_lexbfs A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 k5_numbers)))) )  &  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k15_pre_poly k5_numbers)))) )  &  (? [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  &  ( (D = (k10_xtuple_0 F))  &  ( (F = (k5_relset_1 (k6_glib_000 A) (k5_finsub_1 k5_numbers) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) (k6_subset_1 (k6_glib_000 A) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)))))  &  ( (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers)))  =>  ((r2_hidden G D) => (r2_hidden (k2_uproots k5_numbers G 1) E)) ) )  &  ( (! [G:$i] :  (~  ((r2_hidden G E) &  (! [H:$i] :  ( ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 k5_numbers)))  =>  (~  ((r2_hidden H D) &  (G = (k2_uproots k5_numbers H 1)) ) ) ) ) ) ) )  &  (C = (k10_subset_1 (k8_relat_1 F (k1_tarski (k13_pre_poly (k4_lexbfs k5_numbers (k4_bagorder k5_numbers) E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v3_limfunc1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = (k4_limfunc1 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 C) & (r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers A)))  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( (D = (k7_lmod_7 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (E = (k3_vectsp_4 A B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((k14_lopban_1 A B C) = (a_3_0_lopban_1 A B C)) ) ) ) ) ) ) ).
tt(d12_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k12_lpspace1 A B C) = (g1_rlvect_1 (k11_lpspace1 A B C) (k1_funct_7 (k4_struct_0 (k10_lpspace1 A B C)) (k11_lpspace1 A B C)) (k1_ideal_1 (k10_lpspace1 A B C) (k11_lpspace1 A B C)) (k1_lpspace1 (k10_lpspace1 A B C) (k11_lpspace1 A B C)))) ) ) ) ) ) ) ).
tt(d12_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k10_lpspace2 A B C D)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_lpspace2 A B C D)) k1_numbers)))) )  =>  ( (E = (k11_lpspace2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k10_lpspace2 A B C D))) =>  (? [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden G F) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers G))))  &  ((k1_seq_1 E F) = (k4_power H (k10_real_1 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r1_ltlaxio1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 A) (k1_domain_1 k5_numbers k1_hilbert1 C B)) = 1) ) ) ) ) ) ) ) ).
tt(d12_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_matrix16 B A) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) (k3_finseq_1 B) (k3_finseq_1 B)) =>  ( (C = (k3_matrix16 A B))  <=> (r3_matrix16 A C B)) ) ) ) ) ) ) ) ).
tt(d12_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( (D = (k13_matrix_1 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_algstr_0 A (k3_matrix_1 (u1_struct_0 A) C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ((v5_matrix_2 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k13_matrix_2 A))) &  ( ((k4_nat_d (k3_finseq_1 C) 2) = k6_numbers)  &  ( (B = (k3_group_4 (k13_matrix_2 A) C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 A)) =>  (~  ( ((k1_funct_1 C D) = E)  & (v4_matrix_2 E (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k2_numbers)))  =>  ( (D = (k13_matrixc1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) =>  ((k3_matrix_1 k2_numbers D E F) = (k5_binop_2 (k5_binop_2 (k9_matrix_5 A E) (k3_matrix_1 k2_numbers C E F)) (k15_complex1 (k9_matrix_5 B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k12_matrixr1 A B) = (k8_matrix_1 k1_numbers (k6_matrixr1 (k10_matrixr1 B) A) 1)) ) ) ) ) ).
tt(d12_mcart_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k11_mcart_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k1_xtuple_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d12_measure6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v5_measure6 B A) <=> (v2_xxreal_2 (k7_relset_1 A k1_numbers B A))) ) ) ) ).
tt(d12_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v2_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C k7_numbers) &  ((v10_valued_0 E) &  ((v6_supinf_2 E) &  ((v4_measure1 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  ((r1_measure8 A B C D E) <=>  (! [F:$i] :  ((r2_hidden F B) =>  ((k1_mesfunc9 E F) = (k1_mesfunc9 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k15_member_1 A B) = (k13_member_1 A (k7_member_1 B))) ) ) ) ) ).
tt(d12_membered,ax, (! [A:$i] :  ((v6_membered A) =>  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(d12_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((v5_memstr_0 D A B C) <=>  ((k5_memstr_0 A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d12_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k12_mesfun7c A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C D)) = (k1_relset_1 A (k4_mesfunc5 A k2_numbers B D)))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k1_numbers C D))) =>  ((k1_seq_1 (k4_mesfunc5 A k1_numbers C D) E) = (k1_seq_1 (k8_comseq_3 (k9_mesfun7c A B E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_mesfunc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ( (C = (k12_mesfunc1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) & (r1_xxreal_0 (k12_supinf_2 A D) B)) ) ) ) ) ) ) ) ) ).
tt(d12_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 A) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (B = (k2_mesfunc5 A))  <=>  (~  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (B = C)  &  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k3_extreal1 (k4_supinf_2 (k8_nat_1 k7_numbers A F) B)))) ) ) ) ) ) ) ) )  & (v7_mesfunc5 A)) ) ) ) )  &  ( (~  ( (B = k1_supinf_1)  & (v8_mesfunc5 A)) )  &  (~  ( (B = k2_supinf_1)  & (v9_mesfunc5 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_metric_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k7_metric_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_metric_1 k1_numbers k1_numbers A B C) = (k18_complex1 (k9_real_1 B C))) ) ) ) ) ) ) ) ).
tt(d12_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k9_metric_2 A) = (a_1_5_metric_2 A)) ) ) ).
tt(d12_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((k10_midsp_1 A) = (a_1_1_midsp_1 A)) ) ) ).
tt(d12_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  (! [B:$i] :  ((l1_midsp_2 B A) =>  ((v4_midsp_2 B A) <=>  ((v2_midsp_2 (u1_midsp_2 A B)) &  ((v3_rlvect_1 (u1_midsp_2 A B)) &  ((v4_rlvect_1 (u1_midsp_2 A B)) &  ((v13_algstr_0 (u1_midsp_2 A B)) &  ((v2_rlvect_1 (u1_midsp_2 A B)) &  ((v1_midsp_2 (u2_midsp_2 A B) A (u1_midsp_2 A B)) & (r1_midsp_2 (u1_struct_0 A) (u1_midsp_2 A B) (u2_midsp_2 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (u1_midsp_2 B C))) =>  ( (E = (k10_midsp_3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (E = (k9_midsp_3 A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k12_mmlquery A B C D) = (a_4_7_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d12_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) =>  ( ( (A = k6_numbers)  =>  ((k10_mod_2 A) = k6_numbers) )  &  ( ( (A = 1)  =>  ((k10_mod_2 A) = 2) )  &  ( (A = 2)  =>  ((k10_mod_2 A) = 1) ) ) ) ) ) ).
tt(d12_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_mod_4 C A B) <=>  ((v3_mod_4 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d12_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_modcat_1 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) B)))) )  =>  ( (C = (k9_modcat_1 A B))  <=>  (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  ((k3_funct_2 (k4_modcat_1 A B) B C D) = (k6_modcat_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (A = k12_modelc_1)  <=>  ( (! [B:$i] :  ((r2_hidden B A) => (m2_finseq_1 B k5_numbers)) )  &  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k6_modelc_1 B) A)) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k7_modelc_1 B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k8_modelc_1 B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k9_modelc_1 B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k10_modelc_1 B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k11_modelc_1 B C) A)) ) ) ) )  &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (! [C:$i] :  ((r2_hidden C B) => (m2_finseq_1 C k5_numbers)) )  &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_hidden (k6_modelc_1 C) B)) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k7_modelc_1 C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k8_modelc_1 C D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k9_modelc_1 C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k10_modelc_1 C) B)) ) )  &  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k11_modelc_1 C D) B)) ) ) ) ) ) ) ) ) ) )  => (r1_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (A = (k3_modelc_2 B)) ) ) ) ) ) ).
tt(d12_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v3_group_1 A) <=> (v2_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d12_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) & (l3_msualg_1 B A))  =>  ( (B = (k7_msafree2 A))  <=> (r8_pboole (u1_struct_0 A) (u3_msualg_1 A B) (k7_funcop_1 (u1_struct_0 A) (k1_tarski k1_xboole_0)))) ) ) ) ) ).
tt(d12_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)) C))))) )  =>  ( (D = (k9_msafree A B C))  <=>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k4_dtconstr (k5_msafree A B))) =>  ((r1_lang1 (k5_msafree A B) (k6_msafree A B C) (k1_dtconstr (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) E)) =>  ((k1_funct_1 D E) = (k8_trees_4 (u1_struct_0 (k5_msafree A B)) (k6_msafree A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_msualg_1,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( (C = (k10_msualg_1 A B))  <=> (m1_subset_1 C (k10_xtuple_0 (u3_msualg_1 A B)))) ) ) ) ) ) ).
tt(d12_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ( ((v3_msualg_1 E A) &  ((v4_msualg_1 E A) & (m1_msualg_2 E A C)) )  =>  ( (E = (k6_msualg_3 A B C D))  <=> (r8_pboole (u1_struct_0 A) (u3_msualg_1 A E) (k9_pboole (u1_struct_0 A) (u3_msualg_1 A B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B))))) )  =>  ( (E = (k11_msualg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  ((r2_hidden (k6_msualg_4 A B C D F) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B)) =>  ((k1_funct_1 E (k6_msualg_4 A B C D F)) = (k1_funct_1 (k1_partfun1 (k3_msualg_1 A B C) (k4_msualg_1 A B C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B) (k5_msualg_1 A B C) (k7_msualg_4 A B C D)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v4_msualg_6 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ( (D = (k7_msualg_6 A B C))  <=>  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ( ((v4_msualg_6 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r2_pboole (u1_struct_0 A) C E) => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_nat_lat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ((m2_nat_lat B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u2_lattices B) = (k1_realset1 (u2_lattices A) (u1_struct_0 B)))  &  ((u1_lattices B) = (k1_realset1 (u1_lattices A) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d12_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ((v1_nattra_1 E A B C D) =>  (! [F:$i] :  ((m1_nattra_1 F A B D C) =>  ( (F = (k8_nattra_1 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k4_nattra_1 A B D C F G) = (k6_cat_1 B (k8_cat_1 A B C G) (k8_cat_1 A B D G) (k4_nattra_1 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r8_ncfcont1 A B C D) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) => (r2_ncfcont1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_normform,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_lattices B) & (l3_lattices B))  =>  ( (B = (k12_normform A))  <=>  ( ((u1_struct_0 B) = (k8_normform A))  &  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ( ((k1_binop_1 (u2_lattices B) C D) = (k9_normform A (k5_setwiseo (k7_normform A) C D)))  &  ((k1_binop_1 (u1_lattices B) C D) = (k9_normform A (k10_normform A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ((v1_pre_topc B) & (l1_pre_topc B))  =>  ( (B = (k17_openlatt A))  <=>  ( ((u1_struct_0 B) = (k7_openlatt A))  &  ((u1_pre_topc B) = (a_1_1_openlatt A)) ) ) ) ) ) ) ).
tt(d12_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_oposet_1 A) <=>  ((v3_orders_2 A) & (v4_orders_2 A)) ) ) ) ).
tt(d12_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k12_oppcat_1 A) = (k11_oppcat_1 A A (k10_cat_1 A))) ) ) ).
tt(d12_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r7_orders_1 A B) <=>  ((r2_hidden B (k1_relat_1 A)) &  (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 A)) &  ( (~  (C = B) )  & (r2_hidden (k4_tarski C B) A)) ) ) ) ) ) ) ) ) ).
tt(d12_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v6_orders_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_orders_2 C A B) <=>  ( (~  (C = k1_xboole_0) )  &  ((r2_wellord1 (u1_orders_2 A) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  ((k1_funct_1 B (k1_orders_2 A (k3_orders_2 A C D))) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ordinal1,ax, (! [A:$i] :  ((v7_ordinal1 A) <=> (r2_hidden A k4_ordinal1)) ) ).
tt(d12_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  ((v2_ordinal2 A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B C) & (r2_hidden C (k9_xtuple_0 A)))  => (r2_hidden (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(d12_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( (B = (k8_ordinal6 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 (k1_funct_1 A k6_numbers)))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k3_tarski (a_2_0_ordinal6 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d12_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v10_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d12_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k10_osafree A B C))  <=>  ((r2_hidden C (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) E)) => (r3_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v9_osalg_1 B A) <=>  ((v7_osalg_1 B A) &  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (~  ((r2_osalg_1 A C (k1_msualg_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~ (r3_osalg_1 A B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) )  =>  ( (D = (k10_osalg_2 A B C))  <=>  ((m2_osalg_2 C A D) &  (! [E:$i] :  ( ((v12_osalg_1 E A) & (m1_msualg_2 E A B))  =>  ((m2_osalg_2 C A E) =>  ((v12_osalg_1 D A) & (m1_msualg_2 D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((k8_osalg_4 A B C D E) = (k6_eqrel_1 (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k5_osalg_4 A B C (k3_osalg_4 A D)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_parsp_1 A))  =>  ((v2_parsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r1_parsp_1 A B C C B) &  ((r1_parsp_1 A B C D D) &  ( (~  ((r1_parsp_1 A B C F G) &  ((r1_parsp_1 A B C H I) &  ( (~ (r1_parsp_1 A F G H I))  &  (~  (B = C) ) ) ) ) )  &  ( ((r1_parsp_1 A B C B D) => (r1_parsp_1 A C B C D))  &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ((r1_parsp_1 A B C D J) & (r1_parsp_1 A B D C J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v3_relat_1 B) <=>  (! [C:$i] :  ((r2_hidden C A) => (v1_xboole_0 (k1_funct_1 B C))) ) ) ) ) ) ).
tt(d12_pcs_0,ax, (k5_pcs_0 = (g1_pcs_0 k1_xboole_0 (k1_partit_2 k1_xboole_0 k1_xboole_0))) ).
tt(d12_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k10_pdiff_1 A B C D) = (k1_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B D) C) (k1_seq_1 (k1_pdiff_1 B A) D))) ) ) ) ) ) ) ) ) ).
tt(d12_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k3_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G F) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B) F)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J F)) (k1_seq_1 I (k9_real_1 J F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_petri,ax, (! [A:$i] :  ((l1_petri A) =>  ((k11_petri A) = (g1_petri (u1_struct_0 A) (u4_struct_0 A) (k3_relset_1 (u4_struct_0 A) (u1_struct_0 A) (u2_petri A)) (k3_relset_1 (u1_struct_0 A) (u4_struct_0 A) (u1_petri A)))) ) ) ).
tt(d12_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k10_pnproc_1 A B C D) = (a_4_0_pnproc_1 A B C D)) ) ) ) ) ) ) ) ).
tt(d12_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k11_polyform A B)))  =>  ((k15_polyform A B C) = (k1_funct_1 (k10_polyform A B) C)) ) ) ) ) ) ) ) ).
tt(d12_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k9_polynom5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k2_polynom4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r10_polyred A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((r2_hidden F E) & (r9_polyred A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A))))) )  =>  ( (B = (k10_poset_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_poset_1 A A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (C = D)  =>  ((k3_funct_2 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A) B C) = (k3_poset_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ((k12_pralg_2 A B C D) = (k1_funct_1 (k10_funct_6 (k11_pralg_2 A B C)) D)) ) ) ) ) ) ) ) ).
tt(d12_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) ) )  =>  ((m1_prelamb B A) <=>  ((v1_finset_1 (k9_xtuple_0 B)) &  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) => (v2_prelamb C A B)) ) ) ) ) ) ) ) ).
tt(d12_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k14_pre_poly A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) ) ) ) ) ).
tt(d12_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v10_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((r1_xboole_0 B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_prob_1,ax, (k12_prob_1 = (k9_prob_1 k1_numbers k11_prob_1)) ).
tt(d12_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_card_3 (k4_prvect_2 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k4_prvect_2 A)) k1_numbers)))) )  =>  ( (B = (k13_prvect_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k4_prvect_2 A))) =>  ((k1_seq_1 B C) = (k12_euclid (k12_prvect_2 A C))) ) ) ) ) ) ) ) ).
tt(d12_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k11_pscomp_1 A) = (k19_euclid (k6_pscomp_1 A) (k7_pscomp_1 A))) ) ) ).
tt(d12_pua2mss1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ((l1_msualg_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) <=>  ( ((k9_xtuple_0 C) = (u1_struct_0 A))  &  ( ((k9_xtuple_0 D) = (u4_struct_0 A))  &  ((r1_tarski (k10_xtuple_0 C) (u1_struct_0 B)) &  ((r1_tarski (k10_xtuple_0 D) (u4_struct_0 B)) &  ( ((k3_relat_1 (u2_msualg_1 A) C) = (k3_relat_1 D (u2_msualg_1 B)))  &  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r2_hidden E (u4_struct_0 A)) &  (F = (k1_funct_1 (u1_msualg_1 A) E)) )  =>  ((k3_relat_1 F C) = (k1_funct_1 (u1_msualg_1 B) (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_qc_lang1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_qc_lang1 A)) =>  ( ((k7_qc_lang1 A B) = (k3_finseq_1 C))  =>  ((k10_qc_lang1 A B C) = (k7_finseq_1 (k12_finseq_1 (k6_qc_lang1 A) B) C)) ) ) ) ) ) ) ) ).
tt(d12_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k4_qc_lang2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B (k5_qmax_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k5_qmax_1 A) (k5_qmax_1 A))))) ) )  =>  ( (B = (k9_qmax_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_qmax_1 A)) =>  ((r2_hidden (k1_domain_1 (k5_qmax_1 A) (k5_qmax_1 A) C D) B) <=> (r4_qmax_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v14_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattices A C D) => (r1_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d12_quaterni,ax, (k12_quaterni = (k6_quaterni k6_numbers k6_numbers k6_numbers 1)) ).
tt(d12_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A))))) )  =>  ( (B = (k15_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) B C D) = (k8_quofield A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d12_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_radix_1 A B C) <=>  (~ (r1_xxreal_0 (k1_newton (k1_radix_1 C) A) B)) ) ) ) ) ) ) ) ).
tt(d12_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k4_radix_3 B)))  =>  ((k14_radix_3 A B C) = (k1_gr_cy_1 (k13_radix_3 A B C))) ) ) ) ) ) ) ).
tt(d12_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ((r2_radix_6 A B C D) <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 E A))  =>  ((k4_radix_1 E C (k2_xcmplx_0 B 2) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((k6_ratfunc1 A B) = (k3_ratfunc1 A (k3_polynom5 A (k4_ratfunc1 A B) (k3_vectsp_1 A (k5_struct_0 A) (k2_ratfunc1 A (k5_ratfunc1 A B)))) (k3_polynom5 A (k5_ratfunc1 A B) (k3_vectsp_1 A (k5_struct_0 A) (k2_ratfunc1 A (k5_ratfunc1 A B)))))) ) ) ) ) ).
tt(d12_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k6_relat_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden E A) & (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ).
tt(d12_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_relat_2 A) <=> (r4_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d12_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((r9_rewrite1 A B) &  (! [C:$i] :  (! [D:$i] :  ( ((r4_rewrite1 A B C) & (r4_rewrite1 A B D))  =>  (C = D) ) ) ) )  =>  (! [C:$i] :  ( (C = (k2_rewrite1 A B))  <=> (r4_rewrite1 A B C)) ) ) ) ) ) ).
tt(d12_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_rfunct_3 A B) <=>  ((r1_tarski B (k1_relset_1 k1_numbers A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 C 1))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden D B) &  ((r2_hidden E B) & (r2_hidden (k7_real_1 (k8_real_1 C D) (k8_real_1 (k9_real_1 1 C) E)) B)) )  => (r1_xxreal_0 (k1_seq_1 A (k7_real_1 (k8_real_1 C D) (k8_real_1 (k9_real_1 1 C) E))) (k7_real_1 (k8_real_1 C (k1_seq_1 A D)) (k8_real_1 (k9_real_1 1 C) (k1_seq_1 A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_ringcat1,ax, (! [A:$i] :  ((v5_ringcat1 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ((v2_ringcat1 B) &  ((v3_ringcat1 B) & (l1_ringcat1 B)) ) ) ) ) ) ).
tt(d12_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v9_rltopsp1 B A) <=>  (! [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 E D))  => (r1_tarski B (k1_convex1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k4_rlvect_1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ( (C = (k8_nat_1 (u1_struct_0 A) D (k3_finseq_1 B)))  &  ( ((k8_nat_1 (u1_struct_0 A) D k6_numbers) = (k4_struct_0 A))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (F = (k1_funct_1 B (k2_nat_1 E 1)))  =>  ((r1_xxreal_0 (k3_finseq_1 B) E) |  ((k8_nat_1 (u1_struct_0 A) D (k2_nat_1 E 1)) = (k1_algstr_0 A (k8_nat_1 (u1_struct_0 A) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((k9_rlvect_2 A B) = (k8_rlvect_2 A (k1_real_1 1) B)) ) ) ) ) ).
tt(d12_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((k9_rmod_4 A B C D) = (k6_rmod_4 A B C (k8_rmod_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(d12_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_robbins1 A)) )  =>  ((v6_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C))) (k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)))) = C) ) ) ) ) ) ) ) ).
tt(d12_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_roughs_1 A B C) <=> (r1_tarski (k4_roughs_1 A B) (k4_roughs_1 A C))) ) ) ) ) ) ) ).
tt(d12_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k11_rsspace k11_rsspace) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k11_rsspace k11_rsspace) k1_numbers)))) )  =>  ( (A = k12_rsspace)  <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B k11_rsspace) & (r2_hidden C k11_rsspace))  =>  ((k1_binop_1 A B C) = (k4_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace B) (k2_rsspace C)))) ) ) ) ) ) ) ).
tt(d12_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k18_rvsum_1 A) = (k1_finsop_1 k1_numbers A k33_binop_2)) ) ) ).
tt(d12_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k15_scm_comp A B) = (k1_funct_1 (k3_funct_2 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))) k14_scm_comp A) B)) ) ) ) ) ).
tt(d12_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k10_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  (? [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  &  ( (A = D)  &  ( (B = E)  &  (C = (k6_ami_3 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k11_scmpds_2 A B C) = (k3_xtuple_0 8 k1_xboole_0 (k11_finseq_1 A B C))) ) ) ) ) ) ) ).
tt(d12_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k10_scmpds_6 A B C) = (k1_scmpds_4 (k4_scmpds_4 (k9_scmpds_2 A B 2) (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 1))) C)) ) ) ) ) ) ) ).
tt(d12_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((m2_subset_1 F k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 F k1_xboole_0 (k7_finseq_4 B C D E))) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k13_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 4)) ) ) ) ) ) ) ) ) ) ).
tt(d12_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((k7_scmyciel A B) = (k3_xboole_0 A (k1_zfmisc_1 B))) ) ) ) ).
tt(d12_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k16_seq_4 A) = (k5_finseq_2 k2_numbers A k5_complex1)) ) ) ).
tt(d12_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r3_seqfunc A B C) <=>  ((r1_seqfunc A k1_numbers B C) &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ( (C = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) &  (? [H:$i] :  ((m1_subset_1 H A) &  ((r1_xxreal_0 F G) &  ((r2_hidden H C) & (r1_xxreal_0 E (k18_complex1 (k9_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers B G) H) (k1_seq_1 D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_setfam_1 B A) <=>  (~ (r2_hidden A B)) ) ) ) ) ).
tt(d12_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_sheffer1 A))  =>  ((v9_sheffer1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_sheffer1 A B B) = (k3_robbins1 A B)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B C) = (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C C))) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattices A B C) = (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B C))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B C) = (k1_lattices A (k3_robbins1 A B) (k3_robbins1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((v4_matroid0 A) =>  ((v3_pencil_1 A) |  ( (B = (k6_simplex0 A))  <=>  ( (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc C A) => (r1_xxreal_0 (k5_card_1 C) (k1_xxreal_3 B 1))) ) )  &  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc C A) &  ((k1_card_1 C) = (k1_xxreal_3 B 1)) ) ) ) ) ) ) )  &  ( ((v3_pencil_1 A) =>  ( (B = (k6_simplex0 A))  <=>  (B = (k2_xxreal_3 1)) ) )  &  (~  ( (~  ( (~ (v3_pencil_1 A))  & (v4_matroid0 A)) )  &  ( (~ (v3_pencil_1 A))  &  (~  ( (B = (k6_simplex0 A))  <=>  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  ((v6_stacks_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r1_stacks_1 A (k7_stacks_1 A B C))) ) ) ) ) ) ) ) ).
tt(d12_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_struct_0 B A) <=>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(d12_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_substut1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k13_substut1 A B C) = (o_3_0_substut1 A B C)) ) ) ) ) ) ) ).
tt(d12_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k12_tdlat_1 A) = (g3_lattices (k9_tdlat_1 A) (k10_tdlat_1 A) (k11_tdlat_1 A))) ) ) ).
tt(d12_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r1_tarski B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ) ).
tt(d12_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  =>  ( (G = (k10_tmap_1 A B C D E F))  <=>  ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) C G) E) & (r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) D G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ( ((m2_subset_1 (k2_xboole_0 B C) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((k4_topalg_6 A B C) = (k2_xboole_0 B C)) )  &  ( (~ (m2_subset_1 (k2_xboole_0 B C) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((k4_topalg_6 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d12_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k4_topgen_1 A))  <=>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v1_tops_1 C A) &  (B = (k1_card_1 C)) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 C A) => (r1_ordinal1 B (k1_card_1 C))) ) ) ) ) ) ) ) ) ).
tt(d12_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k6_topreal1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C B) <=>  ( ((k17_euclid C) = (k17_euclid A))  & (r1_xxreal_0 (k18_euclid C) (k18_euclid A))) ) ) ) ) ) ) ) ) ).
tt(d12_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_topalg_2)) =>  ((k13_toprealb A) = (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k2_rcomp_1 A (k3_real_1 A 1)))) ) ) ).
tt(d12_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v8_transgeo B A) <=> (r2_transgeo (u1_struct_0 A) B (u1_analoaf A))) ) ) ) ) ).
tt(d12_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k6_trees_1 A))  <=>  ( (? [C:$i] :  ((m2_finseq_1 C k5_numbers) &  ((r2_hidden C A) &  ((k3_finseq_1 C) = B) ) ) )  &  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 (k3_finseq_1 C) B)) ) ) ) ) ) ) ) ) ).
tt(d12_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((k8_trees_2 A B) = (k5_card_1 (k1_trees_2 A B))) ) ) ) ) ).
tt(d12_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((k8_trees_3 A B C) = (k3_relat_1 C (k6_trees_3 A B))) ) ) ) ) ) ) ).
tt(d12_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  (! [B:$i] :  ((k12_trees_9 A B) = (a_2_1_trees_9 A B)) ) ) ) ).
tt(d12_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (C = (k1_tsp_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (u1_struct_0 B))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) D (k3_tex_4 A E)) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_turing_1 A B C D) <=>  ( ((k1_funct_1 B C) = k6_numbers)  &  ( ((k1_funct_1 B D) = k6_numbers)  &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 D E))  &  (~  ((k1_funct_1 B E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k13_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k1_binarith (k9_margrel1 B) (k9_margrel1 C)))) ) ) ) ) ) ) ) ).
tt(d12_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( ((k6_unialg_2 A) = k1_xboole_0)  &  (B = k1_xboole_0) ) )  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  ( (C = (k7_unialg_2 A B))  <=>  ((r1_tarski B (u1_struct_0 C)) &  (! [D:$i] :  ((m1_unialg_2 D A) =>  ((r1_tarski B (u1_struct_0 D)) => (m1_unialg_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_valued_0 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v7_ordinal1 (k1_funct_1 A B))) ) ) ) ) ).
tt(d12_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k61_valued_1 A B))  <=>  ( ((k9_xtuple_0 C) = (a_2_0_valued_1 A B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C (k2_nat_1 D B)) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k6_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ).
tt(d12_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((r1_tarski (u1_struct_0 C) (k8_vectsp10 A B D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k6_vectsp10 A B C)) (u1_struct_0 A)) &  ((v13_vectsp_1 E (k6_vectsp10 A B C) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B C)) (u1_struct_0 A))))) ) )  =>  ( (E = (k10_vectsp10 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_vectsp10 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (F = (k3_vectsp_4 A B G C))  =>  ((k3_funct_2 (u1_struct_0 (k6_vectsp10 A B C)) (u1_struct_0 A) E F) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k4_vectsp_1 A B C D) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_vectsp_1 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(d12_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((r2_waybel_0 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((r1_orders_2 B D E) & (r2_hidden (k2_waybel_0 A B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((k5_waybel11 A) = (u1_pre_topc (k13_yellow_6 A (k2_waybel11 A)))) ) ) ).
tt(d12_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v5_waybel_1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v3_waybel_1 (k1_waybel_1 A B D C) A B)) ) ) ) ) ) ) ) ) ).
tt(d12_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))))))) )  =>  ( (C = (k5_waybel23 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))) C D) = (k9_subset_1 (u1_struct_0 A) (k1_waybel_3 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d12_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v2_altcat_2 B (k8_waybel34 A)) &  ((v3_altcat_2 B (k8_waybel34 A)) & (m1_altcat_2 B (k8_waybel34 A))) ) ) ) )  =>  ( (B = (k10_waybel34 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_waybel34 A))) =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v3_waybel_3 (k4_yellow21 (k8_waybel34 A) C))) ) ) ) ) ) ) ) ).
tt(d12_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) &  ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ( (C = (k7_waybel_4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) C D) = (k5_waybel_4 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d12_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k11_xboolean A B) = (k4_xboolean A (k3_xboolean B))) ) ) ) ) ).
tt(d12_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k9_xtuple_0 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] : (r2_hidden (k4_tarski C D) A)) ) ) ) ) ) ).
tt(d12_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v6_xxreal_2 A) <=>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_tarski (k1_xxreal_1 B C) A)) ) ) ) ) ) ) ) ).
tt(d12_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k4_yellow_0 A) = (k2_yellow_0 A k1_xboole_0)) ) ) ).
tt(d12_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) &  ((v4_yellow18 B) & (l2_altcat_1 B)) ) ) ) ) )  =>  ( (B = (k4_yellow18 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((r2_hidden D (k3_yellow18 B C)) <=>  ((r2_hidden D (k3_card_3 (k2_card_3 (u1_altcat_1 A)))) &  (C = (k16_mcart_1 D)) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ((r2_hidden E (k1_funct_2 (k3_yellow18 B C) (k3_yellow18 B D))) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A F G)) &  ( (F = C)  &  ( (G = D)  &  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A I F) = k1_xboole_0) )  =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 A I F)) =>  ((k1_funct_1 E (k4_tarski J (k4_tarski I F))) = (k4_tarski (k5_altcat_1 A I F G J H) (k4_tarski I G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v2_altcat_2 B (k7_yellow21 A)) &  ((v3_altcat_2 B (k7_yellow21 A)) & (m1_altcat_2 B (k7_yellow21 A))) ) ) ) )  =>  ( (B = (k8_yellow21 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_yellow21 A))) =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v2_waybel_8 (k4_yellow21 (k7_yellow21 A) C))) ) ) ) ) ) ) ) ).
tt(d12_yellow_6,ax, (! [A:$i] :  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m3_yellow_6 C A B) <=>  (! [D:$i] :  ((r2_hidden D (k10_xtuple_0 C)) =>  ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v7_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (a_3_3_zf_fund1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d12_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_zf_lang A) <=>  (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (A = (k6_zf_lang B)) ) ) ) ) ) ).
tt(d12_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_zf_model A) <=>  ((v1_ordinal1 A) &  ((r2_zf_model A k7_zf_model) &  ((r2_zf_model A k8_zf_model) &  ((r2_zf_model A k9_zf_model) &  ((r2_zf_model A k10_zf_model) &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) => (r2_zf_model A (k11_zf_model B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d12_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((k5_zmodul01 A B C) = (a_3_1_zmodul01 A B C)) ) ) ) ) ) ) ).
tt(d13_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k4_abcmiz_0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_abcmiz_0 A)) =>  ((r2_hidden E B) => (r2_hidden D (k3_abcmiz_0 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k12_abcmiz_1 A) = k6_abcmiz_1) ) ) ).
tt(d13_abcmiz_a,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v4_abcmiz_a B A) <=>  ((k1_msualg_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d13_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v13_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r5_aff_1 A B C) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_analoaf A D H E G) & (r2_analoaf A E I F H)) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  | (r2_analoaf A D I F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k13_afproj A) = (g1_incsp_1 (k9_afproj A) (k10_afproj A) (k11_afproj A))) ) ) ).
tt(d13_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_alg_1 A (k6_alg_1 A B C))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_alg_1 A (k6_alg_1 A B C))) (u1_struct_0 B))))) )  =>  ( (D = (k7_alg_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k6_alg_1 A B C) E)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v9_algstr_0 B A) & (v3_algstr_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k4_algstr_0 A B))  <=>  ((k1_algstr_0 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d13_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers))))))) )  =>  ( (B = (k10_algstr_4 A))  <=>  ( ((k3_funct_2 k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers))) B k6_numbers) = k1_xboole_0)  &  ( ((k3_funct_2 k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers))) B 1) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 2 C) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( ((k3_finseq_1 D) = (k6_xcmplx_0 C 1))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k6_xcmplx_0 C 1)))  =>  ((k1_funct_1 D E) = (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 B (k6_xcmplx_0 C E)))) ) ) )  &  ((k1_funct_1 B C) = (k3_card_3 (k2_card_3 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  ((v10_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D) = (k5_relat_1 (k6_altcat_1 (k1_funct_2 B C) (k1_funct_2 C D)) (k2_zfmisc_1 (k1_altcat_1 A C D) (k1_altcat_1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(d13_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ((v2_altcat_2 B A) <=>  ((u1_altcat_1 B) = (k1_realset1 (u1_altcat_1 A) (u1_struct_0 B))) ) ) ) ) ) ).
tt(d13_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r6_analmetr A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (~  (E = F) )  &  ( (D = (k4_analmetr A E F))  & (r4_analmetr A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ((v6_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) &  ((r1_collsp A B C E) &  ((r1_collsp A B F G) &  ((r1_collsp A B F H) &  ((r1_collsp A C G K) &  ((r1_collsp A F D K) &  ((r1_collsp A C H J) &  ((r1_collsp A E F J) &  ((r1_collsp A D H I) & (r1_collsp A E G I)) ) ) ) ) ) ) ) )  =>  ( (B = D)  |  ( (B = E)  |  ( (D = E)  |  ( (C = D)  |  ( (C = E)  |  ( (B = G)  |  ( (B = H)  |  ( (G = H)  |  ( (F = G)  |  ( (F = H)  |  ((r1_collsp A B C F) | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_unialg_1 A))  =>  ((v6_aofa_000 A) <=>  ((r2_hidden 4 (k4_finseq_1 (u1_unialg_1 A))) &  ( (~ (v1_xboole_0 (k1_funct_1 (u1_unialg_1 A) 4)))  &  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 A) 4)) &  ((v2_margrel1 (k1_funct_1 (u1_unialg_1 A) 4)) &  ((v3_margrel1 (k1_funct_1 (u1_unialg_1 A) 4) (u1_struct_0 A)) &  ((v8_comput_1 (k1_funct_1 (u1_unialg_1 A) 4) 2) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 A) 4) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d13_aofa_i00,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k17_aofa_i00 A B C))  <=>  ( (? [E:$i] :  ( (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  ((r2_hidden G (k9_xtuple_0 B)) & (r2_hidden F (k10_xtuple_0 G))) ) ) ) )  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 D)) <=>  ((r2_hidden F (k1_funct_2 A E)) &  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  ( (F = G)  & (r2_hidden (k3_relat_1 C G) (k9_xtuple_0 B))) ) ) ) ) ) ) )  &  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k1_funct_1 B (k3_relat_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v5_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) & (r2_hidden (k6_armstrng A E F) B))  => (r2_hidden (k6_armstrng A (k4_subset_1 A C E) (k4_subset_1 A D F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ((r3_arytm_3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k5_arytm_3) &  (B = (k9_arytm_3 A C)) ) ) ) ) ) ) ) ).
tt(d13_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((k10_asympt_0 A B) = (a_2_1_asympt_0 A B)) ) ) ) ).
tt(d13_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k11_bagorder A B))  <=>  ((r2_hidden C B) & (r2_waybel_4 B C (u1_orders_2 A))) ) ) ) ) ) ) ) ) ).
tt(d13_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( (B = (k3_bcialg_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m2_bcialg_1 D A) & (m4_bcialg_2 C A D)) ) ) ) ) ) ) ) ).
tt(d13_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ((v6_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_4 A B C) = (k1_bcialg_4 A C B)) ) ) ) ) ) ) ) ).
tt(d13_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  ((k9_bcialg_6 A B C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d13_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v3_bilinear D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (v1_hahnban1 (k7_bilinear A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_borsuk_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (A = k17_borsuk_1)  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 k8_metric_1)))) =>  ( (B = (k1_rcomp_1 k6_numbers 1))  =>  (A = (k1_pre_topc (k3_pcomps_1 k8_metric_1) B)) ) ) ) ) ) ) ).
tt(d13_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r2_borsuk_7 A B C D E F) <=>  ((r1_borsuk_7 A B C D E) &  ((r2_hidden C (k9_xtuple_0 F)) &  ((r2_hidden D (k9_xtuple_0 F)) &  ((k1_funct_1 F C) = (k1_funct_1 F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k8_margrel1) ) )  =>  ((k13_bvfunc_1 A B) = (k12_bvfunc_1 A)) )  &  ( (~  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k8_margrel1) ) ) )  =>  ((k13_bvfunc_1 A B) = (k11_bvfunc_1 A)) ) ) ) ) ) ) ).
tt(d13_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_c0sp1 A) = (a_1_0_c0sp1 A)) ) ) ).
tt(d13_card_3,ax, (! [A:$i] :  ((v3_card_3 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  (A = (k4_card_3 B)) ) ) ) ) ).
tt(d13_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v4_card_fil A) <=>  ((v1_card_5 A) & (v2_card_1 A)) ) ) ) ).
tt(d13_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  ((k5_cat_1 A B C D E F) = (k1_cat_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) )  =>  ((m1_cat_3 D A B C) <=> (r2_funct_2 C (u1_struct_0 A) (k2_cat_3 A C D) (k8_funcop_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ).
tt(d13_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_cat_4 A B) = (k7_cat_4 A B (k1_cat_4 A))) ) ) ) ) ).
tt(d13_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_cat_1 C (k11_cat_5 A (k3_graph_1 A B)) (k11_cat_5 A (k4_graph_1 A B))) =>  ( (C = (k19_cat_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k11_cat_5 A (k3_graph_1 A B)))) =>  ((k3_funct_2 (u4_struct_0 (k11_cat_5 A (k3_graph_1 A B))) (u4_struct_0 (k11_cat_5 A (k4_graph_1 A B))) C D) = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A (k1_cat_1 A (k14_cat_5 A (k3_graph_1 A B) D) B) (k1_cat_1 A (k15_cat_5 A (k3_graph_1 A B) D) B)) (k13_cat_5 A (k3_graph_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d13_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B (k3_catalg_1 (u1_struct_0 A))) & (l3_msualg_1 B (k3_catalg_1 (u1_struct_0 A))))  =>  ( (B = (k13_catalg_1 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) B) (k9_catalg_1 (u1_struct_0 A) C D)) = (k2_cat_1 A C D)) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k8_catalg_1 (u1_struct_0 A) C) B) k1_xboole_0) = (k4_cat_1 A C)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  ( ( ((k3_graph_1 A F) = C)  &  ( ((k4_graph_1 A F) = D)  &  ( ((k3_graph_1 A G) = D)  &  ((k4_graph_1 A G) = E) ) ) )  =>  ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) C D E) B) (k2_finseq_4 (u4_struct_0 A) G F)) = (k1_cat_1 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((k11_cgames_1 A) = (k6_subset_1 (k10_cgames_1 A) (k1_tarski A))) ) ) ).
tt(d13_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) =>  ((v7_chord B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  (! [D:$i] :  ((m2_glib_000 D A (k4_chord A B C) (k21_glib_000 A (k4_chord A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 D)) =>  ( (E = (k1_funct_1 B C))  => (v3_chord E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v3_msualg_1 E (k5_circcomb C D)) &  ((v4_msualg_1 E (k5_circcomb C D)) & (l3_msualg_1 E (k5_circcomb C D))) )  =>  ( (E = (k7_circcomb A B C D))  <=>  ((r8_pboole (u1_struct_0 (k5_circcomb C D)) (u3_msualg_1 (k5_circcomb C D) E) (k7_funcop_1 (u1_struct_0 (k5_circcomb C D)) B)) &  ((k1_funct_1 (u4_msualg_1 (k5_circcomb C D) E) (k4_tarski D C)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ((r5_circtrm1 A B C D E F) <=>  ((r4_circtrm1 A B C D E F) & (r4_circtrm1 B A (k2_funct_1 C) (k2_funct_1 D) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_clopban1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_csspace3 B A) => (v9_clvect_1 B A)) ) ) ) ) ) ).
tt(d13_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) &  ((v3_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) ) )  =>  (! [D:$i] :  ( ((v9_closure1 D A) & (l1_closure1 D A))  =>  ( (D = (k6_closure1 A B C))  <=>  (? [E:$i] :  ((m3_pboole E (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) B)) &  ((r6_pboole (u1_struct_0 A) E (k5_closure1 (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) C)) &  (D = (g1_closure1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ((v10_closure2 C A B) <=>  (! [D:$i] :  ((m1_closure2 D A B (k6_closure2 A B)) =>  (! [E:$i] :  ((m1_closure2 E A B (k6_closure2 A B)) =>  ((k1_funct_1 C (k2_pboole A D E)) = (k2_pboole A (k7_closure2 A B C D) (k7_closure2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_clvect_1 A))  =>  ((v8_clvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k1_normsp_0 A (k1_clvect_1 A B D)) = (k8_real_1 (k17_complex1 D) (k1_normsp_0 A B)))  & (r1_xxreal_0 (k1_normsp_0 A (k1_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(d13_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v8_cohsp_1 A) <=>  ((v3_cohsp_1 (k9_xtuple_0 A)) & (v5_cohsp_1 A)) ) ) ) ).
tt(d13_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k5_coh_sp A)) (k5_coh_sp A)))))  =>  ( (B = (k12_coh_sp A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_coh_sp A)) =>  ((r2_hidden (k4_tarski C D) (k1_relset_1 (k2_zfmisc_1 (k5_coh_sp A) (k5_coh_sp A)) B)) <=>  ((k6_coh_sp A C) = (k7_coh_sp A D)) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_coh_sp A)) =>  ( ((k6_coh_sp A C) = (k7_coh_sp A D))  =>  ((k1_funct_1 B (k4_tarski C D)) = (k9_coh_sp A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((v1_finset_1 C) =>  ( ((k5_card_1 C) = (k5_real_1 A 1))  =>  ((k7_combgras A B C) = (k6_combgras B C)) ) ) ) ) ) ) ) ) ) ).
tt(d13_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_compos_1 A B C) <=>  ((k3_compos_1 A B C) = (k2_compos_1 A)) ) ) ) ) ) ) ) ).
tt(d13_comput_1,ax, (! [A:$i] :  ((v5_comput_1 A) <=>  (! [B:$i] :  ((m2_rfunct_3 B (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_comput_1 B C D E) &  ((r2_hidden C A) & (r2_hidden D A)) )  => (r2_hidden B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) &  ((v8_conlat_1 B A) & (l2_conlat_1 B A)) ) ) )  =>  ( (B = (k5_conlat_1 A))  <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) &  ( (B = (g2_conlat_1 A C D))  &  ( (C = (k1_funct_1 (k2_conlat_1 A) k1_xboole_0))  &  (D = (k1_funct_1 (k1_conlat_1 A) (k1_funct_1 (k2_conlat_1 A) k1_xboole_0))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k10_convex4 A)) =>  ((k11_convex4 A B) = B) ) ) ) ) ).
tt(d13_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))))) =>  ( (C = (k15_cqc_sim1 A B))  <=>  ((r1_cqc_sim1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))))) =>  ((r1_cqc_sim1 A B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_csspace A))  =>  ((v2_csspace A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k12_csspace A B B) = k6_numbers)  =>  (B = (k4_struct_0 A)) )  &  ( ( (B = (k4_struct_0 A))  =>  ((k12_csspace A B B) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k3_complex1 (k12_csspace A B B))) &  ( (k6_numbers = (k4_complex1 (k12_csspace A B B)))  &  ( ((k12_csspace A B C) = (k15_complex1 (k12_csspace A C B)))  &  ( ((k12_csspace A (k1_algstr_0 A B C) D) = (k2_xcmplx_0 (k12_csspace A B D) (k12_csspace A C D)))  &  ((k12_csspace A (k1_clvect_1 A B E) C) = (k3_xcmplx_0 E (k12_csspace A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k8_decomp_1 A) = (a_1_2_decomp_1 A)) ) ) ).
tt(d13_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_dickson A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( (C = (k9_dickson A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (r1_dickson A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_dilworth B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (? [D:$i] :  ( ((v5_dilworth D (k5_yellow_0 A C)) & (m1_eqrel_1 D (u1_struct_0 (k5_yellow_0 A C))))  &  ((r1_xxreal_0 (k5_card_1 D) (k2_dilworth A)) &  (? [E:$i] :  ((r2_hidden E D) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) C B) E) &  (! [F:$i] :  ((r2_hidden F D) =>  ( (F = E)  |  ((k8_subset_1 (u1_struct_0 A) B F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k11_dist_1 A) = (k4_dist_1 A (k1_uproots A))) ) ) ).
tt(d13_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((r2_hidden B (k4_dtconstr A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k17_dtconstr A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A)))))) )  &  ( (C = (k1_funct_1 D B))  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k1_lang1 A)) =>  ((k1_funct_1 D (k2_trees_4 (u1_struct_0 A) E)) = (k3_pre_poly (u1_struct_0 A) E)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_trees_4 F (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ( (G = (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) F))  & (r1_lang1 A E G))  =>  (! [H:$i] :  ((m2_finseq_1 H (k3_finseq_2 (u1_struct_0 A))) =>  ( (H = (k4_finseqop (k4_dtconstr A) (k3_finseq_2 (u1_struct_0 A)) F D))  =>  ((k1_funct_1 D (k8_trees_4 (u1_struct_0 A) E F)) = (k1_pre_poly (u1_struct_0 A) (k5_pre_poly (u1_struct_0 A) H) (k3_pre_poly (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k11_ens_1 A) = (g1_cat_1 A (k2_ens_1 A) (k8_ens_1 A) (k9_ens_1 A) (k10_ens_1 A))) ) ) ).
tt(d13_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k11_e_siec A) = (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d13_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_euclid_3 A (k5_algstr_0 (k15_euclid A) C B) (k5_algstr_0 (k15_euclid A) D B)) & (r2_hidden E (k9_euclid_3 A B C D)))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (F = (k12_euclid_3 A B C D E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( ((k7_real_1 (k7_real_1 G H) F) = 1)  &  (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B G) (k1_rlvect_1 (k15_euclid A) C H)) (k1_rlvect_1 (k15_euclid A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k8_euclid_7 A) = (a_1_0_euclid_7 A)) ) ) ).
tt(d13_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((k7_exchsort A B C D) = (k1_funct_4 (k15_funct_3 (k10_funct_7 (k6_partfun1 (k9_xtuple_0 B)) C D) (k10_funct_7 (k6_partfun1 (k9_xtuple_0 B)) C D)) (k6_partfun1 (k2_xboole_0 (k2_zfmisc_1 (k1_tarski C) (k6_subset_1 (k1_ordinal1 D) C)) (k2_zfmisc_1 (k6_subset_1 (k1_ordinal1 D) C) (k1_tarski D)))))) ) ) ) ) ) ) ).
tt(d13_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  =>  ((m1_extpro_1 D A B C) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_finset_1 E)) ) ) )  =>  ( (E = (k7_extpro_1 A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ((r1_tarski C F) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 B)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 A B)) & (v1_partfun1 G (u1_struct_0 B))) ) ) )  =>  ((r1_tarski D G) =>  (E = (k5_relat_1 (k6_extpro_1 A B F G) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((k9_facirc_1 A B C D) = (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) D) C) D)) ) ) ) ) ) ).
tt(d13_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k13_ff_siec A) = (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) ) ) ).
tt(d13_finseq_1,ax, (! [A:$i] :  ( (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski A (k2_finseq_1 B))) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( (B = (k14_finseq_1 A))  <=>  ( ((k10_xtuple_0 B) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( (E = (k1_funct_1 B C))  &  ( (F = (k1_funct_1 B D))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k12_fintopo2 A B) = (k7_subset_1 (u1_struct_0 A) B (k11_fintopo2 A B))) ) ) ) ) ).
tt(d13_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_fin_topo A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_fin_topo A B)) => (r2_hidden B (k1_fin_topo A C))) ) ) ) ) ) ) ) ).
tt(d13_fomodel0,ax, (k4_numbers = (k2_xboole_0 k5_numbers (k6_subset_1 (k2_zfmisc_1 (k1_tarski k1_xboole_0) k5_numbers) (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))))) ).
tt(d13_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ( ((v15_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k13_fomodel2 A B C D) = (k1_funct_1 (k12_fomodel2 A B C (k11_fomodel2 A B C) (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) D)) (k3_relat_1 (k34_fomodel1 A D) (k10_fomodel2 A B C)))) ) ) ) ) ) ) ) ) ).
tt(d13_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k8_eqrel_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k8_eqrel_1 A B))))) )  =>  ( (C = (k17_fomodel3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A (k8_eqrel_1 A B) C D) = (k9_eqrel_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  (! [D:$i] :  ((v8_fomodel4 D A B C) <=>  (? [E:$i] :  ((r1_tarski (k1_xtuple_0 E) C) &  ( ((k2_xtuple_0 E) = D)  & (v7_fomodel4 (k1_tarski E) A B)) ) ) ) ) ) ) ) ) ) ).
tt(d13_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  ((k8_freealg A B) = (a_2_0_freealg A B)) ) ) ) ) ).
tt(d13_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_fsm_1 A B C D) = (k8_eqrel_1 (u1_struct_0 C) (k6_fsm_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d13_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k13_ftacell1 A B C D E) = (k2_circcomb (k37_gfacirc1 A B C) (k25_gfacirc1 (k36_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d13_funct_1,ax, (! [A:$i] :  ((v4_funct_1 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(d13_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k10_funct_2 A B C D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ).
tt(d13_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((k11_funct_7 A B) = (k2_funct_7 (k7_funcop_1 k5_numbers B) k6_numbers A)) ) ) ).
tt(d13_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v11_functor0 C A B) <=> (v2_functor0 (u1_functor0 A B C) (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d13_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k8_fvaluat1 A B) = (a_2_2_fvaluat1 A B)) ) ) ) ) ) ).
tt(d13_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  (~  ((k13_gate_1 A B C) = (k1_gate_1 k1_xboole_0)) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) ) )  =>  ((k13_gate_1 A B C) = k1_xboole_0) ) ) ) ) ) ).
tt(d13_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k13_gate_5 A B C D E F) = (k38_gate_1 (k7_gate_5 A B C D E) (k2_gate_1 A F) (k8_gate_5 A B C D E) (k2_gate_1 B F) (k9_gate_5 A B C D E) (k2_gate_1 C F) k1_xboole_0)) ) ) ) ) ) ) ).
tt(d13_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v3_gcd_1 A) & (l4_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r5_gcd_1 A B C D) <=>  ((k5_gcd_1 A B C D) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d13_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v3_geomtrap A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_analoaf A B C C D) =>  ( (B = C)  &  (C = D) ) )  &  ( ( ((r2_analoaf A B C F G) & (r2_analoaf A B C H I))  =>  ( (B = C)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C D E) =>  ((r2_analoaf A D E B C) & (r2_analoaf A C B E D)) )  &  ( (~  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( (~ (r2_analoaf A B C D L))  &  (~ (r2_analoaf A B C L D)) ) ) ) )  &  (~  ((r2_analoaf A B C D J) &  ((r2_analoaf A B C D K) &  ( (~  (B = C) )  &  (~  (J = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k13_gfacirc1 A B C) = (k2_circcomb (k10_gfacirc1 A B C) (k7_gfacirc1 A B C))) ) ) ) ).
tt(d13_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ( ( ((k1_funct_1 (k10_glib_000 A) D) = B)  &  ((k1_funct_1 (k11_glib_000 A) D) = C) )  |  ( ((k1_funct_1 (k10_glib_000 A) D) = C)  &  ((k1_funct_1 (k11_glib_000 A) D) = B) ) ) ) ) ) ) ) ) ) ).
tt(d13_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((k10_glib_001 A B C) = (k7_glib_001 A B (k2_glib_001 A (k4_glib_001 A B) (k29_glib_000 A (k4_glib_001 A B) C) C))) ) ) ) ) ) ).
tt(d13_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (C = (k12_glib_004 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r3_glib_000 A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k6_subset_1 (k6_glib_000 A) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B)) D) &  (! [E:$i] :  ((r3_glib_000 A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k6_subset_1 (k6_glib_000 A) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B)) E) => (r1_xxreal_0 (k1_seq_1 (k5_glib_003 A) D) (k1_seq_1 (k5_glib_003 A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k6_glib_005 A B C) = (k40_glib_000 (k5_glib_005 A B C))) ) ) ) ) ) ) ).
tt(d13_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r4_graph_2 A B) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C B) & (r1_xxreal_0 D (k3_finseq_1 A))) )  =>  ((r1_xxreal_0 D B) | (r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  (~  ( (~  ((k10_xtuple_0 B) = (u4_struct_0 A)) )  &  ( (~ (v1_xboole_0 B))  &  (~  (! [C:$i] :  ((m2_finseq_2 C (u4_struct_0 A) (k9_graph_3 A)) =>  ( (C = (k14_graph_3 A B))  <=>  (? [D:$i] :  ((m2_finseq_2 D (u4_struct_0 A) (k9_graph_3 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (E = (k10_subset_1 (a_2_0_graph_3 A B)))  &  ( (D = (k10_subset_1 (k13_graph_3 A E (k6_subset_1 (u4_struct_0 A) (k10_xtuple_0 B)))))  &  (C = (k11_graph_3 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r5_graph_5 A B) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B (u4_struct_0 A) k8_graph_5) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k8_graph_5)))) ) ) ) ) ) ) ).
tt(d13_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((r1_graphsp A B C) <=>  ( (~  ( (~  ((k1_seq_1 C (k2_nat_1 A B)) = (k1_real_1 1)) )  & (r1_xxreal_0 (k7_partfun1 k1_numbers C (k2_nat_1 (k4_nat_1 2 A) B)) (k17_graphsp C A B))) )  &  ((r1_xxreal_0 k6_numbers (k7_partfun1 k1_numbers C (k7_real_1 (k7_real_1 (k4_nat_1 2 A) (k8_real_1 A (k7_partfun1 k1_numbers C (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1)))) B))) &  (~  ((k1_seq_1 C B) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((v2_grcat_1 A) <=> (v13_vectsp_1 (k9_grcat_1 A) (k7_grcat_1 A) (k8_grcat_1 A))) ) ) ).
tt(d13_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  ( ( (~ (v1_xboole_0 B))  =>  ((k12_group_10 A B C) = (a_3_0_group_10 A B C)) )  &  ((v1_xboole_0 B) =>  ((k12_group_10 A B C) = (k1_subset_1 B)) ) ) ) ) ) ) ) ).
tt(d13_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((l3_algstr_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_group_1 C A B) <=>  ((k1_funct_1 C (k1_group_1 A)) = (k1_group_1 B)) ) ) ) ) ) ) ) ).
tt(d13_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_group_2 A B C) = (k4_group_2 A C (k8_group_2 A B))) ) ) ) ) ) ) ).
tt(d13_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v1_group_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_group_3 A B C) = (g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B))) ) ) ) ) ) ) ) ).
tt(d13_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((v6_group_9 B A) <=>  ( (~ (v7_struct_0 B))  &  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (~  ( (~  (C = (k5_group_9 A B)) )  &  (~  (C = (k4_group_9 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v5_hahnban1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_vectsp_1 k1_complfld A (k1_hahnban1 D k6_numbers) C)) = (k8_real_1 D (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ).
tt(d13_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( (B = (k13_idea_1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_recdef_1 B C) = (k15_funcop_1 k5_numbers C 2 (k1_recdef_1 A 3) (k15_funcop_1 k5_numbers C 3 (k1_recdef_1 A 2) (k1_recdef_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(d13_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m3_ideal_1 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r3_ideal_1 A B C D) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ( ((k1_funct_1 C E) = (k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E)) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E))))  & (r2_hidden (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v9_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  (! [S:$i] :  ((m1_subset_1 S (u2_incsp_1 A)) =>  (! [T:$i] :  ((m1_subset_1 T (u2_incsp_1 A)) =>  (~  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B F E) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B H G) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H F K) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H I D) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F J D) Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) K E G) R) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C I G) S) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C J E) T) &  ((r1_zfmisc_1 L M N) &  ( (~  (B = D) )  &  ( (~  (B = F) )  &  ( (~  (B = H) )  &  ( (~  (B = C) )  &  ( (~  (B = E) )  &  ( (~  (B = G) )  &  ( (~  (D = C) )  &  ( (~  (F = E) )  &  ( (~  (H = G) )  &  (! [U:$i] :  ((m1_subset_1 U (u2_incsp_1 A)) =>  (~ (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) I J K) U)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v10_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  ( ((r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E) & (r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) F))  =>  ((v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ((v2_integr15 C A B) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) => (v3_integra1 (k1_partfun1 B (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 D A)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d13_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v2_integra1 B A) <=> (v4_xxreal_2 (k1_rvsum_1 (k9_integra1 A B)))) ) ) ) ) ).
tt(d13_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 A))) (k8_mcart_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))) => (m2_interva1 B A)) ) ) ) ).
tt(d13_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  ((k6_intpro_1 A) = (k7_finseq_1 (k12_finseq_1 k5_numbers 6) A)) ) ) ).
tt(d13_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k13_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k25_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d13_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_finseq_2 A) (k3_finseq_2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 B))))) )  =>  ( (D = (k12_lang1 A B C))  <=>  (! [E:$i] :  ((m2_finseq_2 E A (k3_finseq_2 A)) =>  ((k3_funct_2 (k3_finseq_2 A) (k3_finseq_2 B) D E) = (k11_lang1 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v5_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k10_lattice3 A B C))  <=>  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) &  ((v1_funct_1 D) & (v5_ordinal1 D)) ) )  =>  ((m1_lattice5 D A B C) <=>  ((v1_card_1 (k9_xtuple_0 D)) &  ((v2_funct_1 D) &  ((k2_relset_1 (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B)) D) = (a_3_0_lattice5 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v8_lattice6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  (C = (k15_lattice3 A D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v13_lattices A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_lattices A B C) = B)  &  ((k2_lattices A C B) = B) ) ) ) ) ) ) ) ) ).
tt(d13_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k11_lexbfs A B C D) = (k4_tarski (k1_funct_4 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B) (k16_funcop_1 C (k7_nat_d (k15_glib_000 A) D))) (k1_lexbfs (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) (k4_rfunct_3 (k6_glib_000 A) (k1_zfmisc_1 k5_numbers) (k2_finsub_1 (k1_zfmisc_1 (k6_glib_000 A)) (k2_chord A (k6_domain_1 (k6_glib_000 A) C)) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B))) (k6_domain_1 k5_numbers (k7_nat_d (k15_glib_000 A) D)))))) ) ) ) ) ) ) ) ) ).
tt(d13_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_limfunc1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = (k5_limfunc1 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 C) & (r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers A)))  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k8_lmod_7 A B C D) = (k3_vectsp_4 A B D C)) ) ) ) ) ) ) ) ) ).
tt(d13_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k10_lopban_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k10_lopban_1 A B) k1_numbers)))) )  =>  ( (C = (k15_lopban_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k10_lopban_1 A B)) =>  ((k1_seq_1 C D) = (k4_seq_4 (k14_lopban_1 A B (k13_lopban_1 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d13_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k13_lpspace1 A B C D) = (a_4_0_lpspace1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d13_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k12_lpspace2 A B C D) = (g1_normsp_1 (u1_struct_0 (k10_lpspace2 A B C D)) (u2_struct_0 (k10_lpspace2 A B C D)) (u1_algstr_0 (k10_lpspace2 A B C D)) (u1_rlvect_1 (k10_lpspace2 A B C D)) (k11_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d13_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r2_ltlaxio1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r2_hidden C B) => (r1_ltlaxio1 A C)) ) ) ) ) ) ) ) ).
tt(d13_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) B B) =>  ( (E = (k14_matrix_1 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 A) E F G) = (k1_algstr_0 A (k3_matrix_1 (u1_struct_0 A) C F G) (k3_matrix_1 (u1_struct_0 A) D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_matrix_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 B)) =>  ( ((v5_matrix_2 D (k11_matrix_2 (k12_matrix_2 B))) =>  ((k14_matrix_2 A B C D) = C) )  &  ( (~ (v5_matrix_2 D (k11_matrix_2 (k12_matrix_2 B))))  =>  ((k14_matrix_2 A B C D) = (k4_algstr_0 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v4_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_matroid0 B A) <=> (r1_matroid0 A B (k2_struct_0 A))) ) ) ) ) ).
tt(d13_mcart_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k12_mcart_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k2_xtuple_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d13_measure6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v6_measure6 B A) <=> (v1_xxreal_2 (k7_relset_1 A k1_numbers B A))) ) ) ) ).
tt(d13_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k16_member_1 A B) = (k8_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d13_membered,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ( (A = B)  <=>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden C A) <=> (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d13_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k8_memstr_0 A B C) = (k1_funct_4 C (k7_memstr_0 A B k6_numbers))) ) ) ) ) ) ) ).
tt(d13_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_mesfun7c A B C) <=>  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden F (k1_funct_1 D E)) & (r2_hidden G (k1_funct_1 D E))) )  =>  ((k1_funct_1 C F) = (k1_funct_1 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_mesfunc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ( (C = (k13_mesfunc1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) &  (~ (r1_xxreal_0 (k12_supinf_2 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d13_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (D = (k3_mesfunc5 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_nat_1 k7_numbers D E) = (k12_supinf_2 (k1_seqfunc A k7_numbers B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_metric_1,ax, (k8_metric_1 = (g1_metric_1 k1_numbers k7_metric_1)) ).
tt(d13_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A)) k1_numbers)))) )  =>  ( (B = (k10_metric_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  =>  ((k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) B C D) = (k4_metric_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers)))) )  =>  ( (D = (k13_metric_3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 C)) =>  (! [K:$i] :  ((m1_subset_1 K (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ( ( (K = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) E G I))  &  (L = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) F H J)) )  =>  ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) D K L) = (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k4_metric_1 A E F)) (k5_square_1 (k4_metric_1 B G H))) (k5_square_1 (k4_metric_1 C I J))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k10_midsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k10_midsp_1 A)) =>  ( (D = (k11_midsp_1 A B C))  <=>  (! [E:$i] :  ((m1_midsp_1 E A) =>  (! [F:$i] :  ((m1_midsp_1 F A) =>  ( ( (B = E)  &  (C = F) )  =>  (D = (k7_midsp_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((l1_midsp_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k9_midsp_2 A B C D) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (u1_midsp_2 A B)) (u2_midsp_2 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(d13_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k13_mmlquery A B C D) = (a_4_8_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d13_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  ( ( (A = k6_numbers)  =>  ((k11_mod_2 A B) = B) )  &  ( ( (B = k6_numbers)  =>  ((k11_mod_2 A B) = A) )  &  ( ( ( (A = 1)  &  (B = 1) )  =>  ((k11_mod_2 A B) = 2) )  &  ( ( ( (A = 1)  &  (B = 2) )  =>  ((k11_mod_2 A B) = k6_numbers) )  &  ( ( ( (A = 2)  &  (B = 1) )  =>  ((k11_mod_2 A B) = k6_numbers) )  &  ( ( (A = 2)  &  (B = 2) )  =>  ((k11_mod_2 A B) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v8_mod_4 C A B) <=>  ((v4_mod_4 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d13_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((v1_modelc_1 A) <=> (m1_subset_1 A k12_modelc_1)) ) ) ).
tt(d13_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k4_modelc_2 B C)) ) ) ) ) ) ) ) ).
tt(d13_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k7_modelc_3 A) = k1_xboole_0) ) ) ).
tt(d13_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v10_monoid_0 A) <=> (v3_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d13_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v5_msafree2 A) <=>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v3_msafree2 B A) & (l3_msualg_1 B A)) )  => (v4_msafree2 B A)) ) ) ) ) ).
tt(d13_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B))) =>  ( (C = (k10_msafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) => (r6_pboole (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) D) (k1_msualg_3 (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)) C D) (k9_msafree A B D))) ) ) ) ) ) ) ) ) ).
tt(d13_msualg_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k11_msualg_1 A B) = (u4_msualg_1 A B)) ) ) ) ) ).
tt(d13_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( (E = (k8_msualg_2 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ((m3_pboole G (u1_struct_0 A) (u3_msualg_1 A B)) &  ((r2_hidden G (k5_msualg_2 A B C)) &  (F = (k1_funct_1 G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ((m2_pboole D (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A B C))) =>  ( (D = (k12_msualg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) => (r2_funct_2 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A B C))) E) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A B C)) E) (k5_msualg_4 A (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A B C)) D E) (k11_msualg_4 A E B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v3_msualg_6 D A B) &  ((v4_msualg_6 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ( (D = (k8_msualg_6 A B C))  <=>  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ( ((v3_msualg_6 E A B) &  ((v4_msualg_6 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((r2_pboole (u1_struct_0 A) C E) => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ( ((r2_nattra_1 A B C D) & (v1_nattra_1 E A B C D))  =>  ((k9_nattra_1 A B C D E) = (k8_nattra_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r9_ncfcont1 A B C D) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) => (r3_ncfcont1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k10_net_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r1_tarski D (k2_net_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k2_net_1 A)) &  ((r2_hidden E B) &  (D = (k5_net_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k13_oppcat_1 A) = (k10_oppcat_1 A A (k10_cat_1 A))) ) ) ).
tt(d13_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r8_orders_1 A B) <=>  ((r2_hidden B (k1_relat_1 A)) &  (! [C:$i] :  ((r2_hidden C (k1_relat_1 A)) =>  ( (C = B)  | (r2_hidden (k4_tarski C B) A)) ) ) ) ) ) ) ) ).
tt(d13_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (C = (k4_orders_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (m2_orders_2 D A B)) ) ) ) ) ) ) ) ).
tt(d13_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  ((v3_ordinal2 A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((v4_ordinal1 B) &  (C = (k1_funct_1 A B)) ) )  =>  ( (B = k1_xboole_0)  | (r1_ordinal2 C (k5_relat_1 A B))) ) ) ) ) ) ) ) ) ).
tt(d13_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v12_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ( (~ (v9_o_ring_1 (k7_partfun1 (u1_struct_0 A) B C) A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ( ((k7_partfun1 (u1_struct_0 A) B C) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B E)))  |  ((k7_partfun1 (u1_struct_0 A) B C) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B E))) )  &  ( (~  (D = k6_numbers) )  &  ( (~ (r1_xxreal_0 C D))  &  ( (~  (E = k6_numbers) )  &  (~ (r1_xxreal_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_trees_4 C (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( (D = (k11_osafree A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (~  ( (F = (k1_funct_1 C E))  &  ((k1_funct_1 D E) = (k10_osafree A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  ((v10_osalg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (v9_osalg_1 B A)) ) ) ) ) ).
tt(d13_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (m1_msualg_2 D A B))  =>  (! [E:$i] :  ( ((v3_msualg_1 E A) &  ((v12_osalg_1 E A) & (m1_msualg_2 E A B)) )  =>  ( (E = (k11_osalg_2 A B C D))  <=>  (! [F:$i] :  ((m2_osalg_2 F A B) =>  ((r8_pboole (u1_struct_0 A) F (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D))) =>  (E = (k10_osalg_2 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k3_relat_1 (k1_msualg_1 A B) (k7_osalg_4 A C D)))) =>  ( (F = (k9_osalg_4 A B C D E))  <=>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden G (k4_finseq_1 (k1_msualg_1 A B))) &  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A C) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G))) =>  (~  ( (H = (k1_funct_1 E G))  &  ((k1_funct_1 F G) = (k8_osalg_4 A C D (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v2_relat_1 B) <=>  (! [C:$i] :  (~  ((r2_hidden C A) & (v1_xboole_0 (k1_funct_1 B C))) ) ) ) ) ) ) ).
tt(d13_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r4_pdiff_1 A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 A))) &  ( (D = F)  &  ( (E = G)  & (r2_pdiff_1 B A C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r4_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k4_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G D) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B) D)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J D)) (k1_seq_1 I (k9_real_1 J D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k12_petri A B) = B) ) ) ) ) ).
tt(d13_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k11_pnproc_1 A B C D) = (a_4_1_pnproc_1 A B C D)) ) ) ) ) ) ) ) ).
tt(d13_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A (k6_xcmplx_0 B 1))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_polyform A B)) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 B (k7_polyform A)))  =>  ((k16_polyform A B C D) = (k1_binop_1 (k9_polyform A B) C D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 (k11_polynom1 A C)) (u1_struct_0 (k11_polynom1 A C))))) =>  ( (E = (k3_polyred A B C D))  <=>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden (k4_tarski F G) E) <=> (r5_polyred A B C F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_pralg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k12_pralg_1 A B))  <=>  (! [D:$i] :  (~  ((r2_hidden D A) &  (! [E:$i] :  ((l1_struct_0 E) =>  (~  ( (E = (k1_funct_1 B D))  &  ((k1_funct_1 C D) = (u1_struct_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m2_pboole D (u4_struct_0 B) (k3_relat_1 (u1_msualg_1 B) (k6_finseq_2 (u1_struct_0 B) (k10_pralg_2 A B C))) (k3_relat_1 (u2_msualg_1 B) (k10_pralg_2 A B C))) =>  ( ( (~  (A = k1_xboole_0) )  =>  ( (D = (k13_pralg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  ((k1_funct_1 D E) = (k14_funcop_1 (k1_msualg_1 B E) k1_xboole_0 (k10_funct_6 (k12_pralg_2 A B C E)) (k1_pralg_2 (k2_pralg_2 (k12_pralg_2 A B C E))))) ) ) ) )  &  ( (A = k1_xboole_0)  =>  (D = (k13_pralg_2 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d13_pre_poly,ax, (! [A:$i] :  ((k16_pre_poly A) = (k8_funcop_1 k5_numbers A k6_numbers)) ) ).
tt(d13_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_normsp_1 B) & (l1_normsp_1 B)) )  =>  ( (B = (k14_prvect_2 A))  <=>  ( ((g1_rlvect_1 (u1_struct_0 B) (u2_struct_0 B) (u1_algstr_0 B) (u1_rlvect_1 B)) = (k10_prvect_2 A))  & (r1_funct_2 (u1_struct_0 B) k1_numbers (k4_card_3 (k4_prvect_2 A)) k1_numbers (u1_normsp_0 B) (k13_prvect_2 A))) ) ) ) ) ) ).
tt(d13_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k12_pscomp_1 A) = (k19_euclid (k8_pscomp_1 A) (k7_pscomp_1 A))) ) ) ).
tt(d13_pua2mss1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ((l1_msualg_1 B) =>  ((r4_pua2mss1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ((r3_pua2mss1 B A C D) &  ( ((k10_xtuple_0 C) = (u1_struct_0 A))  &  ((k10_xtuple_0 D) = (u4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k11_qc_lang1 A B) = B) ) ) ) ) ).
tt(d13_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang2 B A) <=>  (? [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k5_qc_lang2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))))) =>  ( (B = (k10_qmax_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k5_qmax_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k5_qmax_1 A))) =>  ((r2_hidden (k1_domain_1 (k1_zfmisc_1 (k5_qmax_1 A)) (k1_zfmisc_1 (k5_qmax_1 A)) C D) B) <=>  ((r2_hidden C (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) &  ((r2_hidden D (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) &  (! [E:$i] :  ((m1_subset_1 E (k5_qmax_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_qmax_1 A)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r3_qmax_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v15_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k15_lattice3 A C)) (k15_lattice3 A (a_3_4_quantal1 A B C)))) ) ) ) ) ) ) ).
tt(d13_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ( ((r2_hidden A k2_numbers) =>  ( (B = (k13_quaterni A))  <=>  (? [C:$i] :  ((v1_xcmplx_0 C) &  ( (A = C)  &  (B = (k3_complex1 C)) ) ) ) ) )  &  ( (~ (r2_hidden A k2_numbers))  =>  ( (B = (k13_quaterni A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 4 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 4 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_seq_1 C k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(d13_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A))))) )  =>  ( (B = (k16_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) B C D) = (k9_quofield A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d13_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 A)))  =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k3_radix_1 A)))  =>  ( ((r2_hidden B (k2_finseq_1 C)) & (r1_xxreal_0 2 A))  =>  ((k13_radix_1 A B C D E) = (k2_xcmplx_0 (k12_radix_1 (k2_xcmplx_0 (k4_radix_1 B A C D) (k4_radix_1 B A C E)) A) (k11_radix_1 (k2_xcmplx_0 (k4_radix_1 (k7_nat_d B 1) A C D) (k4_radix_1 (k7_nat_d B 1) A C E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  =>  ((k7_ratfunc1 A) = (k3_ratfunc1 A (k9_polynom3 A) (k10_polynom3 A))) ) ) ).
tt(d13_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k7_relat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((r2_hidden (k4_tarski E D) A) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ).
tt(d13_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v5_relat_2 A) <=> (r5_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d13_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_finset_1 (k1_relset_1 A (k2_partfun1 A k1_numbers B C))) =>  (! [D:$i] :  ( ((v8_valued_0 D) & (m2_finseq_1 D k1_numbers))  =>  ( (D = (k20_rfunct_3 A B C))  <=> (r2_classes1 (k2_partfun1 A k1_numbers B C) D)) ) ) ) ) ) ) ) ) ).
tt(d13_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v5_ringcat1 C))  =>  ((m4_ringcat1 C A B) <=>  (! [D:$i] :  ((m3_ringcat1 D C) => (m1_ringcat1 D A B)) ) ) ) ) ) ) ) ) ).
tt(d13_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k4_rltopsp1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k1_rlvect_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d13_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v9_rlvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B (k4_struct_0 A)) = B)  &  ((k1_algstr_0 A (k4_struct_0 A) B) = B) ) ) ) ) ) ) ).
tt(d13_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k10_rlvect_2 A B C) = (k7_rlvect_2 A B (k9_rlvect_2 A C))) ) ) ) ) ) ) ).
tt(d13_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rmod_4 C A B) <=>  (! [D:$i] :  ((m2_rmod_4 D A B C) =>  ( ((k5_rmod_4 A B D) = (k4_struct_0 B))  =>  ((k2_rmod_4 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v9_robbins1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((k1_lattices A B B) = B) ) ) ) ) ) ).
tt(d13_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_roughs_1 A B C) <=>  ((r1_roughs_1 A B C) & (r2_roughs_1 A B C)) ) ) ) ) ) ) ) ).
tt(d13_rsspace,ax, (k13_rsspace = (g1_bhsp_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace) k12_rsspace)) ).
tt(d13_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (B = (k19_rvsum_1 A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k2_numbers) &  ( (C = A)  &  (B = (k1_finsop_1 k2_numbers C k29_binop_2)) ) ) ) ) ) ) ) ) ).
tt(d13_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k16_scm_comp A))  <=>  ((k10_ami_3 B) = A) ) ) ) ) ) ).
tt(d13_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k11_scmfsa_2 A) = (k7_ami_3 A)) ) ) ).
tt(d13_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k12_scmpds_2 A B C D) = (k3_xtuple_0 9 k1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d13_scmpds_i,ax, (k14_scmpds_i = k6_numbers) ).
tt(d13_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((v5_scmyciel A) <=>  (A = (k5_scmyciel (k3_tarski A))) ) ) ) ).
tt(d13_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k22_seq_4 A) = (k7_square_1 (k18_rvsum_1 (k12_rvsum_1 (k13_seq_4 A))))) ) ) ).
tt(d13_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (D = (k11_seqfunc A B C))  <=>  ( ((k1_relset_1 A D) = C)  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  ((k1_seq_1 D E) = (k2_seq_2 (k10_seqfunc A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_sgraph1 B k5_numbers) =>  ( (B = (k7_sgraph1 A))  <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_sgraph1 (k2_finseq_1 A)))))  &  ( (C = (a_1_2_sgraph1 A))  &  (B = (g1_sgraph1 (k2_finseq_1 A) C)) ) ) ) ) ) ) ) ) ).
tt(d13_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  ((v10_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A B B)) = B) ) ) ) ) ) ).
tt(d13_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C A)) )  =>  ((m2_simplex0 C A B) <=>  ((r1_tarski (k2_struct_0 C) (k2_struct_0 B)) & (r1_tarski (u1_pre_topc C) (u1_pre_topc B))) ) ) ) ) ) ) ).
tt(d13_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (D = (k12_sin_cos A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E C) =>  ((k8_nat_1 k2_numbers D E) = (k9_complex1 (k8_nat_1 k2_numbers (k3_sin_cos A) E) (k11_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos B)) C) (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos B)) (k7_nat_d C E))))) )  &  ( (~ (r1_xxreal_0 E C))  =>  ((k8_nat_1 k2_numbers D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( (C = (k9_stacks_1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))))) )  &  ( (C = (k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) D B))  &  ( (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r1_stacks_1 A E) =>  ((k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) D E) = k1_xboole_0) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) D (k7_stacks_1 A E F)) = (k7_finseq_1 (k12_finseq_1 (u1_struct_0 A) F) (k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) =>  ((v11_struct_0 A) <=> (v1_xboole_0 (u4_struct_0 A))) ) ) ).
tt(d13_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_substut1 A)))  =>  ( (? [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) &  (D = (k7_substut1 A B (k15_qc_lang1 A B C) E)) ) )  =>  ( ((r2_hidden B (k10_xtuple_0 D)) =>  ((k14_substut1 A B C D) = (k2_xboole_0 D (k6_domain_1 (k2_zfmisc_1 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k1_domain_1 (k3_qc_lang1 A) (k3_qc_lang1 A) B (k2_qc_lang3 A (k13_substut1 A D C)))))) )  &  ( (~ (r2_hidden B (k10_xtuple_0 D)))  =>  ((k14_substut1 A B C D) = (k2_xboole_0 D (k6_domain_1 (k2_zfmisc_1 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k1_domain_1 (k3_qc_lang1 A) (k3_qc_lang1 A) B B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_topalg_6 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_topalg_6 A)) =>  ( (C = (k5_topalg_6 A B))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_funct_1 B 1) = (k1_funct_1 C 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_funct_1 C (k1_nat_1 D 1)) = (k4_topalg_6 A (k7_partfun1 (k1_topalg_6 A) C D) (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v7_topgen_1 A) <=> (r1_ordinal1 (k4_topgen_1 A) k4_ordinal1)) ) ) ).
tt(d13_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k7_topreal1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C B) <=>  ((r1_xxreal_0 (k17_euclid C) (k17_euclid A)) &  ((k18_euclid C) = (k18_euclid A)) ) ) ) ) ) ) ) ) ) ).
tt(d13_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) )  =>  ( (A = k14_toprealb)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_toprealb k9_toprealb))) =>  (? [C:$i] :  ((v1_xreal_0 C) &  (? [D:$i] :  ((v1_xreal_0 D) &  ( (B = (k19_euclid C D))  &  ( ((r1_xxreal_0 k6_numbers D) =>  ((k3_funct_2 (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) A B) = (k10_real_1 (k6_sin_cos6 C) (k8_real_1 2 k32_sin_cos))) )  &  ((r1_xxreal_0 D k6_numbers) =>  ((k3_funct_2 (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) A B) = (k9_real_1 1 (k10_real_1 (k6_sin_cos6 C) (k8_real_1 2 k32_sin_cos)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k7_trees_1 A))  <=>  (? [C:$i] :  ((m4_trees_1 C A) &  ( (B = (k5_card_1 C))  &  (! [D:$i] :  ((m4_trees_1 D A) => (r1_xxreal_0 (k5_card_1 D) (k5_card_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(d13_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((k9_trees_3 A B C) = (k3_relat_1 C (k7_trees_3 A B))) ) ) ) ) ) ) ).
tt(d13_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B A) => (v1_finset_1 B)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k12_trees_9 A B) (k3_finseq_2 (k9_trees_9 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k12_trees_9 A B) (k3_finseq_2 (k9_trees_9 A)))))) )  =>  ( (C = (k13_trees_9 A B))  <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  ((r2_hidden D (k12_trees_9 A B)) =>  (! [E:$i] :  ((m2_finseq_1 E (k9_trees_9 A)) =>  ( (E = (k1_funct_1 C D))  =>  (D = (k4_trees_4 (k1_funct_1 D k1_xboole_0) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_turing_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m2_funct_2 C k4_numbers (u1_turing_1 B) (k9_funct_2 k4_numbers (u1_turing_1 B))) =>  ((r2_turing_1 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 A) D) | (r1_turing_1 B C (k3_real_1 (k1_gr_cy_1 (k4_turing_1 D A)) (k8_real_1 2 (k9_real_1 D 1))) (k3_real_1 (k1_gr_cy_1 (k4_turing_1 (k2_nat_1 D 1) A)) (k4_nat_1 2 D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k14_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k2_binarith B C)) ) ) ) ) ) ) ) ).
tt(d13_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_unialg_2 C A) =>  (! [D:$i] :  ( ((v1_unialg_1 D) & (m1_unialg_2 D A))  =>  ( (D = (k8_unialg_2 A B C))  <=>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (E = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C)))  =>  (D = (k7_unialg_2 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k7_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ) ).
tt(d13_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ((k11_vectsp10 A B C) = (k10_vectsp10 A B (k9_vectsp10 A B C) C)) ) ) ) ) ) ) ).
tt(d13_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k5_vectsp_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = (k4_algstr_0 A C)) ) ) ) ) ) ) ) ).
tt(d13_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v10_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_waybel_0 A B (a_3_0_waybel_0 A B C))) ) ) ) ) ) ) ).
tt(d13_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) <=>  ((v11_quantal1 B) & (v5_orders_3 B A A)) ) ) ) ) ) ).
tt(d13_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v2_altcat_2 B (k9_waybel34 A)) &  ((v3_altcat_2 B (k9_waybel34 A)) & (m1_altcat_2 B (k9_waybel34 A))) ) ) ) )  =>  ( (B = (k11_waybel34 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_waybel34 A))) =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v3_waybel_3 (k4_yellow21 (k9_waybel34 A) C))) ) ) ) ) ) ) ) ).
tt(d13_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( (B = (k8_waybel_4 A))  <=>  (! [C:$i] :  ( (~  ((r2_hidden C (u1_struct_0 B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  (~  ( (C = D)  &  ((v5_orders_3 D A (k2_yellow_1 (k7_waybel_0 A))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_tarski (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) D E) (k5_waybel_0 A E))) ) ) ) ) ) ) ) )  &  ( ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  &  ( (C = D)  &  ((v5_orders_3 D A (k2_yellow_1 (k7_waybel_0 A))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_tarski (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) D E) (k5_waybel_0 A E))) ) ) ) ) )  => (r2_hidden C (u1_struct_0 B)))  &  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) (u1_orders_2 B)) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  &  ( (D = F)  &  ( (E = G)  &  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) & (r1_yellow_2 (u1_struct_0 A) (k2_yellow_1 (k7_waybel_0 A)) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k10_xtuple_0 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] : (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ).
tt(d13_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((m1_yellow_0 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) & (r1_tarski (u1_orders_2 B) (u1_orders_2 A))) ) ) ) ) ) ).
tt(d13_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v6_waybel_0 D A) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) ) )  =>  ( (D = (k8_yellow_6 A B C))  <=>  ( ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (k3_yellow_3 B (k5_yellow_1 (u1_struct_0 B) C)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r2_hidden E (u1_struct_0 B)) & (r2_hidden F (u1_struct_0 (k5_yellow_1 (u1_struct_0 B) C))))  =>  ((k1_binop_1 (u1_waybel_0 A D) E F) = (k1_funct_1 (u1_waybel_0 A (k7_yellow_6 (u1_struct_0 B) A C E)) (k1_funct_1 F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v8_zf_fund1 B A) <=>  ((v1_zf_fund1 B A) &  ((v2_zf_fund1 B A) &  ((v3_zf_fund1 B A) &  ((v4_zf_fund1 B A) &  ((v5_zf_fund1 B A) &  ((v6_zf_fund1 B A) & (v7_zf_fund1 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d13_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_zf_lang A) <=>  (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k7_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d13_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_zmodul01 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k5_zmodul01 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d14_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  ((v10_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  (~ (v1_xboole_0 (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A B) (k3_abcmiz_0 A (k1_abcmiz_0 A B))))) ) ) ) ) ) ).
tt(d14_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k13_abcmiz_1 A) = k7_abcmiz_1) ) ) ).
tt(d14_abcmiz_a,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v5_abcmiz_a B A) <=>  ((k3_finseq_1 (k1_msualg_1 A B)) = 1) ) ) ) ) ) ).
tt(d14_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v14_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r5_aff_1 A B C) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_analoaf A D H E G) &  ((r2_analoaf A E I F H) & (r2_analoaf A D I F G)) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (G = H)  | (r2_hidden I C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k16_afinsq_1 A B C D) = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 A) (k5_afinsq_1 B)) (k5_afinsq_1 C)) (k5_afinsq_1 D))) ) ) ) ) ).
tt(d14_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k14_afproj A) = (g1_incsp_1 (k7_afproj A) (k8_afproj A) (k12_afproj A))) ) ) ).
tt(d14_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A B C) = (k1_algstr_0 A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(d14_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k11_algstr_4 A B) = (k1_funct_1 (k10_algstr_4 A) B)) ) ) ) ).
tt(d14_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_altcat_1 B) &  ((v10_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  ( (B = (k7_altcat_1 A))  <=>  ( ((u1_struct_0 B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_altcat_1 B C D) = (k1_funct_2 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( (~ (v2_struct_0 B))  =>  ((v3_altcat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  => (r2_hidden (k8_altcat_1 A D) (k1_altcat_1 B C C))) ) ) ) ) ) )  &  ((v2_struct_0 B) => (v3_altcat_2 B A)) ) ) ) ) ) ).
tt(d14_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ( ( (? [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 (k7_ami_2 B (k4_scm_inst A) (k1_funct_1 B (k5_scm_inst A))) (k4_card_1 (k5_ami_2 B)))) )  &  ( ( (? [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 (k7_ami_2 B (k4_scm_inst A) (k2_xcmplx_0 (k1_funct_1 B (k4_scm_inst A)) (k1_funct_1 B (k5_scm_inst A)))) (k4_card_1 (k5_ami_2 B)))) )  &  ( ( (? [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 (k7_ami_2 B (k4_scm_inst A) (k6_xcmplx_0 (k1_funct_1 B (k4_scm_inst A)) (k1_funct_1 B (k5_scm_inst A)))) (k4_card_1 (k5_ami_2 B)))) )  &  ( ( (? [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 (k7_ami_2 B (k4_scm_inst A) (k3_xcmplx_0 (k1_funct_1 B (k4_scm_inst A)) (k1_funct_1 B (k5_scm_inst A)))) (k4_card_1 (k5_ami_2 B)))) )  &  ( ( (? [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 5 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 (k7_ami_2 (k7_ami_2 B (k4_scm_inst A) (k5_int_1 (k1_funct_1 B (k4_scm_inst A)) (k1_funct_1 B (k5_scm_inst A)))) (k5_scm_inst A) (k6_int_1 (k1_funct_1 B (k4_scm_inst A)) (k1_funct_1 B (k5_scm_inst A)))) (k4_card_1 (k5_ami_2 B)))) )  &  ( ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (A = (k3_xtuple_0 6 (k9_finseq_1 C) k1_xboole_0)) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 B (k6_scm_inst A))) )  &  ( ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 7 (k9_finseq_1 C) (k12_finseq_1 k2_ami_2 D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 B (k15_funcop_1 k4_ordinal1 (k1_funct_1 B (k8_scm_inst A)) k6_numbers (k7_scm_inst A) (k4_card_1 (k5_ami_2 B))))) )  &  ( ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (A = (k3_xtuple_0 8 (k9_finseq_1 C) (k12_finseq_1 k2_ami_2 D))) ) ) ) )  =>  ((k8_ami_2 A B) = (k6_ami_2 B (k5_xxreal_0 (k1_funct_1 B (k8_scm_inst A)) k6_numbers (k7_scm_inst A) (k4_card_1 (k5_ami_2 B))))) )  &  ( ( (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 5 k1_xboole_0 (k10_finseq_1 C D))) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (A = (k3_xtuple_0 6 (k9_finseq_1 C) k1_xboole_0)) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 7 (k9_finseq_1 C) (k12_finseq_1 k2_ami_2 D))) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (~  (A = (k3_xtuple_0 8 (k9_finseq_1 C) (k12_finseq_1 k2_ami_2 D))) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_ami_2 A B) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_ami_wstd A B C D) = (k1_ami_wstd A B (k7_nat_d (k3_ami_wstd A B C) D))) ) ) ) ) ) ) ) ) ).
tt(d14_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r7_analmetr A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~  (D = E) )  &  ( (B = (k4_analmetr A D E))  & (r6_analmetr A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ((v7_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_collsp A B C F) & (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_unialg_1 A))  =>  ((v7_aofa_000 A) <=>  ( (~ (v1_xboole_0 (k1_funct_1 (u1_unialg_1 A) 2)))  &  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 A) 2)) &  ((v2_margrel1 (k1_funct_1 (u1_unialg_1 A) 2)) &  ((v3_margrel1 (k1_funct_1 (u1_unialg_1 A) 2) (u1_struct_0 A)) &  ((v8_comput_1 (k1_funct_1 (u1_unialg_1 A) 2) 2) &  ((v1_aofa_000 (k1_funct_1 (u1_unialg_1 A) 2)) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 A) 2) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d14_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 C k4_numbers))) =>  (! [E:$i] :  ((m1_aofa_000 E A (k9_funct_2 C k4_numbers) D) =>  ((r1_aofa_i00 A B C D E) <=>  ((r2_hidden B (k18_aofa_000 A)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 C k4_numbers) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 C k4_numbers) C)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k9_funct_2 C k4_numbers) k4_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 C k4_numbers) k4_numbers)))) )  &  (! [H:$i] :  ((m2_funct_2 H C k4_numbers (k9_funct_2 C k4_numbers)) =>  ((k2_binop_1 (k9_funct_2 C k4_numbers) (u1_struct_0 A) (k9_funct_2 C k4_numbers) E H B) = (k15_funct_7 C k4_numbers H (k3_funct_2 (k9_funct_2 C k4_numbers) C F H) (k3_funct_2 (k9_funct_2 C k4_numbers) k4_numbers G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v6_armstrng B A) <=>  ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) ) ) ) ) ) ).
tt(d14_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((k11_asympt_0 A B) = (a_2_2_asympt_0 A B)) ) ) ) ).
tt(d14_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))))))) )  =>  ( (B = (k12_bagorder A))  <=>  ( ((k1_relset_1 k5_numbers B) = k5_numbers)  &  ( ((k8_nat_1 (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))) B k6_numbers) = (a_1_0_bagorder A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_nat_1 (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))) B (k1_nat_1 C 1)) = (a_3_0_bagorder A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d14_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A C B) = (k4_struct_0 A))  =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(d14_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k4_bcialg_2 A) = (a_1_0_bcialg_2 A)) ) ) ).
tt(d14_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ((v7_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_4 A (k1_bcialg_1 A B C) C) = (k1_bcialg_4 A B C)) ) ) ) ) ) ) ) ).
tt(d14_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  ((k10_bcialg_6 A B C D) = (g2_bcialg_1 (k7_bcialg_6 A B C D) (k8_bcialg_6 A B C D) (k9_bcialg_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d14_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v4_bilinear D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (v1_hahnban1 (k8_bilinear A B C D E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_borsuk_1,ax, (k18_borsuk_1 = k6_numbers) ).
tt(d14_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k7_toprealb A C D)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb A C D)) (u1_struct_0 (k15_euclid B)))))) )  =>  ((v2_borsuk_7 E A B C D) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) & (r2_borsuk_7 A C F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k7_margrel1) ) )  =>  ((k14_bvfunc_1 A B) = (k11_bvfunc_1 A)) )  &  ( (~  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A k6_margrel1 B C) = k7_margrel1) ) ) )  =>  ((k14_bvfunc_1 A B) = (k12_bvfunc_1 A)) ) ) ) ) ) ) ).
tt(d14_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_c0sp1 A) = (g1_funcsdom (k6_c0sp1 A) (k2_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k1_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k5_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k4_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k3_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)))) ) ) ).
tt(d14_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r9_calcul_1 A B C D E) <=> (r6_calcul_1 A (k2_relset_1 (k3_cqc_lang A) B) C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_card_3,ax, (! [A:$i] :  ((v4_card_3 A) <=> (r1_ordinal1 (k1_card_1 A) k4_ordinal1)) ) ).
tt(d14_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v5_card_fil A) <=>  (! [B:$i] :  ((v1_card_1 B) =>  ((r2_hidden B A) => (r2_hidden (k3_card_2 2 B) A)) ) ) ) ) ) ).
tt(d14_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v7_cat_1 D A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F A E B) =>  (! [G:$i] :  ((m1_cat_1 G A E B) =>  ( ((k5_cat_1 A E B C F D) = (k5_cat_1 A E B C G D))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) )  =>  ((r1_cat_3 A B C D) <=>  ((m1_cat_3 D A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_3 F A E C) =>  (~  ((r2_funct_2 C (u1_struct_0 A) (k3_cat_3 A C D) (k3_cat_3 A C F)) &  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (~  ((r2_hidden G (k2_cat_1 A E B)) &  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ((r2_hidden H (k2_cat_1 A E B)) =>  ( (! [I:$i] :  ((r2_hidden I C) =>  ((k1_cat_1 A H (k7_partfun1 (u4_struct_0 A) D I)) = (k7_partfun1 (u4_struct_0 A) F I)) ) )  <=>  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_cat_4 A B) = (k9_cat_4 A B (k1_cat_4 A) B (k4_cat_1 A B) (k6_cat_4 A B))) ) ) ) ) ).
tt(d14_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_cat_1 C (k12_cat_5 A (k4_graph_1 A B)) (k12_cat_5 A (k3_graph_1 A B))) =>  ( (C = (k20_cat_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k12_cat_5 A (k4_graph_1 A B)))) =>  ((k3_funct_2 (u4_struct_0 (k12_cat_5 A (k4_graph_1 A B))) (u4_struct_0 (k12_cat_5 A (k3_graph_1 A B))) C D) = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A (k1_cat_1 A B (k17_cat_5 A (k4_graph_1 A B) D)) (k1_cat_1 A B (k18_cat_5 A (k4_graph_1 A B) D))) (k16_cat_5 A (k4_graph_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d14_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( (B = (k13_cgames_1 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( ((k9_xtuple_0 C) = (k10_cgames_1 A))  &  ( (B = (k1_funct_1 C A))  &  (! [D:$i] :  ((v2_cgames_1 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (g1_cgames_1 (a_2_1_cgames_1 C D) (a_2_2_cgames_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B C))) =>  ((m3_chain_1 D A B C) <=>  (~  ( (~  ( (C = k6_numbers)  & (v1_abian (k5_card_1 D))) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (C = (k2_nat_1 E 1))  &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k4_chain_1 A B (k2_nat_1 E 1)))) &  ( (F = D)  &  ((k10_chain_1 A B E F) = (k5_chain_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v6_circcomb B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (u3_msualg_1 A B) C) = k6_margrel1) ) ) ) ) ) ) ) ).
tt(d14_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ((r6_circtrm1 A B C D) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  (? [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  & (r5_circtrm1 A B E F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v9_closure1 B A) & (l1_closure1 B A))  =>  (! [C:$i] :  ( ((v1_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v2_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v3_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ( (C = (k7_closure1 A B))  <=>  (! [D:$i] :  ((m1_pboole D (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B))) =>  (! [E:$i] :  ( ((v2_relat_1 E) & (m3_pboole E (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B))))  =>  ( (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 A)) &  ((v1_funct_1 F) & (v1_partfun1 F (u1_struct_0 A))) ) )  =>  ((r1_pboole (u1_struct_0 A) F E) <=>  ((r1_pboole (u1_struct_0 A) F (u1_closure1 A B)) & (r2_pboole (u1_struct_0 A) D F)) ) ) )  => (r6_pboole (u1_struct_0 A) (k2_closure1 (u1_struct_0 A) (u3_msualg_1 A B) C D) (k4_mssubfam (u1_struct_0 A) (u3_msualg_1 A B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k6_clvect_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_clvect_1 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v9_cohsp_1 A) <=>  ((v2_finsub_1 (k9_xtuple_0 A)) &  ((v8_cohsp_1 A) & (v7_cohsp_1 A)) ) ) ) ) ).
tt(d14_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) &  ((v3_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [D:$i] :  ( ((v5_combgras D (k1_combgras A B) (k1_combgras A B)) & (l1_combgras D (k1_combgras A B) (k1_combgras A B)))  =>  ( (D = (k8_combgras A B C))  <=>  ( (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k1_combgras A B))) =>  ((k2_combgras (k1_combgras A B) (k1_combgras A B) D E) = (k7_relat_1 C E)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k1_combgras A B))) =>  ((k3_combgras (k1_combgras A B) (k1_combgras A B) D E) = (k7_relat_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v3_compos_1 B A) <=>  ((k1_funct_1 B (k62_valued_1 B)) = (k2_compos_1 A)) ) ) ) ) ) ).
tt(d14_comput_1,ax, (! [A:$i] :  ((v6_comput_1 A) <=>  ((r2_hidden (k3_comput_1 k6_numbers k6_numbers) A) &  ((r2_hidden (k4_comput_1 1 1) A) &  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B))  => (r2_hidden (k5_comput_1 B C) A)) ) ) ) )  &  ((v4_comput_1 A) & (v5_comput_1 A)) ) ) ) ) ) ).
tt(d14_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) &  ((v9_conlat_1 B A) & (l2_conlat_1 B A)) ) ) )  =>  ( (B = (k6_conlat_1 A))  <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) &  ( (B = (g2_conlat_1 A C D))  &  ( (C = (k1_funct_1 (k2_conlat_1 A) (k1_funct_1 (k1_conlat_1 A) k1_xboole_0)))  &  (D = (k1_funct_1 (k1_conlat_1 A) k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ((k12_convex4 A B) = B) ) ) ) ) ).
tt(d14_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_cqc_sim1 A B C) <=>  ((k14_cqc_sim1 A B) = (k14_cqc_sim1 A C)) ) ) ) ) ) ) ) ).
tt(d14_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) <=>  ((k12_csspace A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d14_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_decomp_1 A) = (a_1_3_decomp_1 A)) ) ) ).
tt(d14_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ( (B = (k25_descip_1 A))  <=>  ( ((k10_descip_1 64 B 1) = (k10_descip_1 64 A 58))  &  ( ((k10_descip_1 64 B 2) = (k10_descip_1 64 A 50))  &  ( ((k10_descip_1 64 B 3) = (k10_descip_1 64 A 42))  &  ( ((k10_descip_1 64 B 4) = (k10_descip_1 64 A 34))  &  ( ((k10_descip_1 64 B 5) = (k10_descip_1 64 A 26))  &  ( ((k10_descip_1 64 B 6) = (k10_descip_1 64 A 18))  &  ( ((k10_descip_1 64 B 7) = (k10_descip_1 64 A 10))  &  ( ((k10_descip_1 64 B 8) = (k10_descip_1 64 A 2))  &  ( ((k10_descip_1 64 B 9) = (k10_descip_1 64 A 60))  &  ( ((k10_descip_1 64 B 10) = (k10_descip_1 64 A 52))  &  ( ((k10_descip_1 64 B 11) = (k10_descip_1 64 A 44))  &  ( ((k10_descip_1 64 B 12) = (k10_descip_1 64 A 36))  &  ( ((k10_descip_1 64 B 13) = (k10_descip_1 64 A 28))  &  ( ((k10_descip_1 64 B 14) = (k10_descip_1 64 A 20))  &  ( ((k10_descip_1 64 B 15) = (k10_descip_1 64 A 12))  &  ( ((k10_descip_1 64 B 16) = (k10_descip_1 64 A 4))  &  ( ((k10_descip_1 64 B 17) = (k10_descip_1 64 A 62))  &  ( ((k10_descip_1 64 B 18) = (k10_descip_1 64 A 54))  &  ( ((k10_descip_1 64 B 19) = (k10_descip_1 64 A 46))  &  ( ((k10_descip_1 64 B 20) = (k10_descip_1 64 A 38))  &  ( ((k10_descip_1 64 B 21) = (k10_descip_1 64 A 30))  &  ( ((k10_descip_1 64 B 22) = (k10_descip_1 64 A 22))  &  ( ((k10_descip_1 64 B 23) = (k10_descip_1 64 A 14))  &  ( ((k10_descip_1 64 B 24) = (k10_descip_1 64 A 6))  &  ( ((k10_descip_1 64 B 25) = (k10_descip_1 64 A 64))  &  ( ((k10_descip_1 64 B 26) = (k10_descip_1 64 A 56))  &  ( ((k10_descip_1 64 B 27) = (k10_descip_1 64 A 48))  &  ( ((k10_descip_1 64 B 28) = (k10_descip_1 64 A 40))  &  ( ((k10_descip_1 64 B 29) = (k10_descip_1 64 A 32))  &  ( ((k10_descip_1 64 B 30) = (k10_descip_1 64 A 24))  &  ( ((k10_descip_1 64 B 31) = (k10_descip_1 64 A 16))  &  ( ((k10_descip_1 64 B 32) = (k10_descip_1 64 A 8))  &  ( ((k10_descip_1 64 B 33) = (k10_descip_1 64 A 57))  &  ( ((k10_descip_1 64 B 34) = (k10_descip_1 64 A 49))  &  ( ((k10_descip_1 64 B 35) = (k10_descip_1 64 A 41))  &  ( ((k10_descip_1 64 B 36) = (k10_descip_1 64 A 33))  &  ( ((k10_descip_1 64 B 37) = (k10_descip_1 64 A 25))  &  ( ((k10_descip_1 64 B 38) = (k10_descip_1 64 A 17))  &  ( ((k10_descip_1 64 B 39) = (k10_descip_1 64 A 9))  &  ( ((k10_descip_1 64 B 40) = (k10_descip_1 64 A 1))  &  ( ((k10_descip_1 64 B 41) = (k10_descip_1 64 A 59))  &  ( ((k10_descip_1 64 B 42) = (k10_descip_1 64 A 51))  &  ( ((k10_descip_1 64 B 43) = (k10_descip_1 64 A 43))  &  ( ((k10_descip_1 64 B 44) = (k10_descip_1 64 A 35))  &  ( ((k10_descip_1 64 B 45) = (k10_descip_1 64 A 27))  &  ( ((k10_descip_1 64 B 46) = (k10_descip_1 64 A 19))  &  ( ((k10_descip_1 64 B 47) = (k10_descip_1 64 A 11))  &  ( ((k10_descip_1 64 B 48) = (k10_descip_1 64 A 3))  &  ( ((k10_descip_1 64 B 49) = (k10_descip_1 64 A 61))  &  ( ((k10_descip_1 64 B 50) = (k10_descip_1 64 A 53))  &  ( ((k10_descip_1 64 B 51) = (k10_descip_1 64 A 45))  &  ( ((k10_descip_1 64 B 52) = (k10_descip_1 64 A 37))  &  ( ((k10_descip_1 64 B 53) = (k10_descip_1 64 A 29))  &  ( ((k10_descip_1 64 B 54) = (k10_descip_1 64 A 21))  &  ( ((k10_descip_1 64 B 55) = (k10_descip_1 64 A 13))  &  ( ((k10_descip_1 64 B 56) = (k10_descip_1 64 A 5))  &  ( ((k10_descip_1 64 B 57) = (k10_descip_1 64 A 63))  &  ( ((k10_descip_1 64 B 58) = (k10_descip_1 64 A 55))  &  ( ((k10_descip_1 64 B 59) = (k10_descip_1 64 A 47))  &  ( ((k10_descip_1 64 B 60) = (k10_descip_1 64 A 39))  &  ( ((k10_descip_1 64 B 61) = (k10_descip_1 64 A 31))  &  ( ((k10_descip_1 64 B 62) = (k10_descip_1 64 A 23))  &  ( ((k10_descip_1 64 B 63) = (k10_descip_1 64 A 15))  &  ((k10_descip_1 64 B 64) = (k10_descip_1 64 A 7)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_dickson,ax, (k10_dickson = a_0_0_dickson) ).
tt(d14_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k18_dtconstr A B) = (a_2_0_dtconstr A B)) ) ) ) ) ).
tt(d14_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k12_ens_1 A B) = B) ) ) ) ) ).
tt(d14_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k12_e_siec A) = (u1_struct_0 A)) ) ) ).
tt(d14_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) ) )  =>  ((m2_exchsort C A B) <=>  ( ((k1_funct_1 C (k1_exchsort C)) = B)  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((v1_relat_1 (k1_funct_1 C D)) &  ((v5_relat_1 (k1_funct_1 C D) (u1_struct_0 A)) &  ((v1_funct_1 (k1_funct_1 C D)) & (v1_exchsort (k1_funct_1 C D))) ) ) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D (k9_xtuple_0 C)) &  ((r2_hidden (k1_ordinal1 D) (k9_xtuple_0 C)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 A)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden (k4_tarski F G) (k6_exchsort A E)) &  ( ((k1_funct_1 C D) = E)  &  ((k1_funct_1 C (k1_ordinal1 D)) = (k10_funct_7 E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_extpro_1 A B C D E) <=>  (! [F:$i] :  (~  ((r2_hidden F (k9_xtuple_0 E)) &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 B)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 A B)) & (v1_finset_1 G)) ) ) )  =>  (~  ( (F = G)  &  ((m1_extpro_1 (k1_funct_4 D G) A B C) & (r1_tarski (k1_funct_1 E G) (k7_extpro_1 A B C (k1_funct_4 D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((k10_facirc_1 A B C D) = (k3_circcomb (k5_circcomb D (k10_finseq_1 A B)) (k5_circcomb D (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) D) C)) (k6_facirc_1 A B D) (k6_facirc_1 (k4_tarski (k10_finseq_1 A B) D) C D))) ) ) ) ) ) ).
tt(d14_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k14_ff_siec A) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) ) ) ).
tt(d14_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m2_nat_lat C A) =>  ( (C = (k10_filter_2 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ( (D = (k1_realset1 (u2_lattices A) B))  &  ( (E = (k1_realset1 (u1_lattices A) B))  &  (C = (g3_lattices B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((k15_finseq_1 A) = (k3_relat_1 (k14_finseq_1 (k9_xtuple_0 A)) A)) ) ) ).
tt(d14_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k13_fintopo2 A B) = (k9_subset_1 (u1_struct_0 A) B (k8_fintopo2 A B))) ) ) ) ) ).
tt(d14_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_fin_topo B A) <=>  (B = (k8_fin_topo A B)) ) ) ) ) ) ).
tt(d14_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k11_fomodel0 A B) = (k3_xboole_0 A B)) ) ) ).
tt(d14_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v4_fomodel1 B A) <=> (r2_hidden B (k2_fomodel1 A))) ) ) ) ) ).
tt(d14_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k15_fomodel2 A B) = (a_2_0_fomodel2 A B)) ) ) ) ) ).
tt(d14_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k18_fomodel3 A B C) = (k4_relset_1 (k4_finseq_2 B (k8_eqrel_1 A C)) (k4_finseq_2 B A) (k4_finseq_2 B A) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B)) (k8_fomodel3 (k8_eqrel_1 A C) A (k3_relset_1 A (k8_eqrel_1 A C) (k17_fomodel3 A C)) B) (k17_fomodel3 (k4_finseq_2 B A) (k13_fomodel3 A C B)))) ) ) ) ) ) ) ).
tt(d14_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_freealg A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_freealg A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_freealg A B) C)))) )  =>  ((r2_hidden D (k6_dtconstr (k3_freealg A B))) =>  ((k10_freealg A B C D E) = (k1_funct_1 E (k2_trees_4 (u1_struct_0 (k3_freealg A B)) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_eqrel_1 D (u1_struct_0 C)) =>  ((v4_fsm_1 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((r5_fsm_1 A B C E F) <=>  (? [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 (u1_struct_0 C)) D) &  ((r2_hidden E G) & (r2_hidden F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k14_ftacell1 A B C D E) = (k3_circcomb (k37_gfacirc1 A B C) (k25_gfacirc1 (k36_gfacirc1 A B C) E D) (k38_gfacirc1 A B C) (k26_gfacirc1 (k36_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d14_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v5_funct_1 B A) <=>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) => (r2_hidden (k1_funct_1 B C) (k1_funct_1 A C))) ) ) ) ) ) ) ).
tt(d14_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k13_funct_7 A B C) = (k1_funct_4 (k7_funcop_1 k5_numbers C) (k4_funct_4 k6_numbers 1 A B))) ) ) ) ).
tt(d14_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((l1_altcat_1 B) =>  (! [C:$i] :  ((l2_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k4_functor0 A B C D E) = (k1_binop_1 (u2_functor0 A B C) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v3_fvaluat1 A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B)))))  =>  ((k9_fvaluat1 A B C) = (k13_ideal_1 A (k8_relset_1 (u1_struct_0 A) k7_numbers B (k6_domain_1 k7_numbers (k7_supinf_2 (k7_relset_1 (u1_struct_0 A) k7_numbers B C)))) C)) ) ) ) ) ) ) ) ).
tt(d14_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~  ((k14_gate_1 A B C D) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) ) )  =>  ((k14_gate_1 A B C D) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d14_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k14_gate_5 A B C D E) = (k10_gate_1 C D (k11_gate_1 A B E))) ) ) ) ) ) ).
tt(d14_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v3_gcd_1 A) & (l4_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_gcd_1 A B C) <=>  (? [D:$i] :  ((m2_gcd_1 D A) &  ((k5_gcd_1 A D B C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d14_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v4_geomtrap A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ( (~  ((r2_analoaf A B C D E) &  ((r2_analoaf A B C D G) &  ( (~  (B = C) )  &  (~  (E = G) ) ) ) ) )  &  ( ( ((r2_analoaf A F G B C) & (r2_analoaf A F G D E))  =>  ( (F = G)  | (r2_analoaf A B C D E)) )  &  ( ((r2_analoaf A B C D E) => (r2_analoaf A D E B C))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) & (r2_analoaf A B C D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k14_gfacirc1 A B C) = (k3_circcomb (k10_gfacirc1 A B C) (k7_gfacirc1 A B C) (k11_gfacirc1 A B C) (k8_gfacirc1 A B C))) ) ) ) ).
tt(d14_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_glib_000 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ( ((k1_funct_1 (k10_glib_000 A) D) = B)  &  ((k1_funct_1 (k11_glib_000 A) D) = C) ) ) ) ) ) ) ) ) ).
tt(d14_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_glib_001 C A) =>  ( (C = (k11_glib_001 A B))  <=>  ( ((k2_nat_1 (k3_finseq_1 B) 1) = (k4_nat_1 2 (k3_finseq_1 C)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k1_funct_1 C D) = (k1_funct_1 B (k6_xcmplx_0 (k4_nat_1 2 D) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((v8_glib_003 A) <=> (r1_tarski (k10_xtuple_0 (k5_glib_003 A)) k8_graph_5)) ) ) ).
tt(d14_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  ((k13_glib_004 A) = (k4_tarski (k6_domain_1 (k6_glib_000 A) (k10_subset_1 (k6_glib_000 A))) k1_xboole_0)) ) ) ).
tt(d14_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ( ((v5_glib_001 E A) &  ((v6_glib_001 E A) & (m3_glib_001 E A)) )  =>  ( ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k6_glib_005 A B C))) =>  ( (E = (k7_glib_005 A B C D))  <=>  ((r1_glib_001 A C D E) &  ((r5_glib_005 A B E) &  (! [F:$i] :  ( ((v7_ordinal1 F) & (v1_abian F))  =>  ((r2_hidden F (k1_relset_1 k5_numbers E)) =>  ((k1_funct_1 E F) = (k1_funct_1 (k6_glib_005 A B C) (k1_funct_1 E (k1_nat_1 F 1)))) ) ) ) ) ) ) )  &  ( (~ (r2_hidden D (k1_relset_1 (k6_glib_000 A) (k6_glib_005 A B C))))  =>  ( (E = (k7_glib_005 A B C D))  <=> (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) E (k1_glib_001 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_graph_1 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (r2_hidden (k1_funct_1 B C) (u4_struct_0 A))) ) )  &  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 B) 1))  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r2_hidden (k1_funct_1 C D) (u1_struct_0 A))) ) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (E = (k1_funct_1 C D))  &  ( (F = (k1_funct_1 C (k2_nat_1 D 1)))  & (r2_graph_1 A E F (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  =>  ((v1_graph_3 B A) <=>  ((k10_xtuple_0 B) = (u4_struct_0 A)) ) ) ) ) ) ).
tt(d14_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r6_graph_5 A B) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B (u4_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k1_numbers)))) ) ) ) ) ) ) ).
tt(d14_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ( (C = (k18_graphsp A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ( ((r1_xxreal_0 D (k4_nat_1 2 B)) =>  ((r1_xxreal_0 D B) |  ( ((r1_graphsp B (k7_nat_d D B) A) =>  ((k1_seq_1 C D) = (k7_partfun1 k1_numbers A (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1))) )  &  ( (~ (r1_graphsp B (k7_nat_d D B) A))  =>  ((k1_seq_1 C D) = (k1_seq_1 A D)) ) ) ) )  &  ( ((r1_xxreal_0 D (k4_nat_1 3 B)) =>  ((r1_xxreal_0 D (k4_nat_1 2 B)) |  ( ((r1_graphsp B (k7_nat_d D (k4_nat_1 2 B)) A) =>  ((k1_seq_1 C D) = (k17_graphsp A B (k7_nat_d D (k4_nat_1 2 B)))) )  &  ( (~ (r1_graphsp B (k7_nat_d D (k4_nat_1 2 B)) A))  =>  ((k1_seq_1 C D) = (k1_seq_1 A D)) ) ) ) )  &  ( (~  ( (~ (r1_xxreal_0 D B))  & (r1_xxreal_0 D (k4_nat_1 3 B))) )  =>  ((k1_seq_1 C D) = (k1_seq_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v2_grcat_1 C) & (l1_grcat_1 C))  =>  ((m1_grcat_1 C A B) <=>  ( ((k7_grcat_1 C) = A)  &  ((k8_grcat_1 C) = B) ) ) ) ) ) ) ) ) ).
tt(d14_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_group_10 A B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (E = (k1_funct_1 (k1_group_10 A B C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k14_group_2 A B C) = (k5_group_2 A C (k8_group_2 A B))) ) ) ) ) ) ) ).
tt(d14_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( (C = (k10_group_3 A B))  <=>  ((u1_struct_0 C) = (a_2_3_group_3 A B)) ) ) ) ) ) ) ) ).
tt(d14_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( (D = (k7_group_9 A B C))  <=>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E B) & (m1_group_2 E B)) )  =>  ( (E = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)))  =>  (D = (k15_group_2 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v6_hahnban1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_vectsp_1 k1_complfld A D C)) = (k8_real_1 (k17_complex1 D) (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ).
tt(d14_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k8_hermitan A B) = (k7_hermitan A A B)) ) ) ) ) ).
tt(d14_idea_1,ax, (k14_idea_1 = (k3_finseq_2 k5_numbers)) ).
tt(d14_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v2_ideal_1 C A) &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (C = (k7_ideal_1 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D A) &  ((v2_ideal_1 D A) &  ((v3_ideal_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v10_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  (! [S:$i] :  ((m1_subset_1 S (u2_incsp_1 A)) =>  (! [T:$i] :  ((m1_subset_1 T (u2_incsp_1 A)) =>  ( ((r2_zfmisc_1 B C D E) &  ((r2_zfmisc_1 B F G H) &  ((r1_incsp_1 A B N) &  ((r1_incsp_1 A B Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D H I) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E F J) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C G K) R) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C H J) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E G I) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D F K) S) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F G H) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D E) Q) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) I J) T)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (N = Q)  | (r1_incsp_1 A K T)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v11_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ( (~  (D = E) )  &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) B) & (r5_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) C)) ) ) ) ) )  => (r3_incsp_1 A B C)) ) ) ) ) ) ) ) ).
tt(d14_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (D = (k10_integr15 A B C))  <=>  ( ((k4_finseq_1 D) = (k2_finseq_1 A))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_seq_1 D E) = (k12_integra1 B (k1_partfun1 B (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k10_integra1 A B) = (k5_seq_4 (k1_rvsum_1 (k8_integra1 A B)))) ) ) ) ) ).
tt(d14_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v8_intpro_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C B)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B (k3_intpro_1 C D)) (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 B D))) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) B) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) C) A) &  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C (k4_intpro_1 B C))) A) &  ((r2_hidden (k3_intpro_1 B (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 C (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B D) (k3_intpro_1 (k3_intpro_1 C D) (k3_intpro_1 (k5_intpro_1 B C) D))) A) &  ((r2_hidden (k3_intpro_1 k2_intpro_1 B) A) &  ( ((r2_hidden B A) & (r2_hidden (k3_intpro_1 B C) A))  => (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k14_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d14_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v5_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k11_lattice3 A B C))  <=>  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k9_lattice5 A B C D E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v9_lattice6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  (C = (k16_lattice3 A D)) ) ) ) ) ) ) ) ) ) ).
tt(d14_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v14_lattices A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_lattices A B C) = B)  &  ((k1_lattices A C B) = B) ) ) ) ) ) ) ) ) ).
tt(d14_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  ( ((r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)))) =>  ((k12_lexbfs A B) = B) )  &  ( (~ (r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)))))  =>  ((k12_lexbfs A B) = (k11_lexbfs A B (k10_lexbfs A B) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B))))) ) ) ) ) ) ) ).
tt(d14_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k16_lopban_1 A B) = (g1_normsp_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k15_lopban_1 A B))) ) ) ) ) ).
tt(d14_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k14_lpspace1 A B C) = (a_3_2_lpspace1 A B C)) ) ) ) ) ) ) ).
tt(d14_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r3_ltlaxio1 A B) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((r2_ltlaxio1 C A) => (r1_ltlaxio1 C B)) ) ) ) ) ) ) ) ).
tt(d14_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((v2_matrix_1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  ( ((k3_matrix_1 (u1_struct_0 A) B C D) = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_matrix_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k15_matrix_2 A) = A) ) ) ).
tt(d14_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_matroid0 A B C) <=>  ((k4_matroid0 A (k4_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) = (k4_matroid0 A C)) ) ) ) ) ) ) ) ).
tt(d14_mcart_1,ax, (! [A:$i] :  ((k13_mcart_1 A) = (k1_xtuple_0 (k1_xtuple_0 A))) ) ).
tt(d14_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k17_member_1 A B) = (k9_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d14_membered,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( (A = B)  <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) <=> (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d14_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k9_memstr_0 A B C D) = (k1_funct_4 C (k7_memstr_0 A B (k2_nat_1 (k5_memstr_0 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(d14_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  ((r2_mesfun7c A B C D E) <=>  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_seq_1 C G) = (k1_seq_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_mesfunc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ( (C = (k14_mesfunc1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) & (r1_xxreal_0 B (k12_supinf_2 A D))) ) ) ) ) ) ) ) ) ).
tt(d14_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (~  ((k1_relset_1 A D) = k1_xboole_0) )  =>  ((k5_mesfunc5 A B C D) = (k1_mesfunc3 A B C D)) )  &  ( ((k1_relset_1 A D) = k1_xboole_0)  =>  ((k5_mesfunc5 A B C D) = k1_supinf_2) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  =>  ( (D = (k9_metric_1 A B C))  <=>  (D = (a_3_0_metric_1 A B C)) ) )  &  ((v2_struct_0 A) =>  ( (D = (k9_metric_1 A B C))  <=> (v1_xboole_0 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A)) (k10_midsp_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A)) (k10_midsp_1 A))))) )  =>  ( (B = (k12_midsp_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k10_midsp_1 A)) =>  ((k5_binop_1 (k10_midsp_1 A) B C D) = (k11_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d14_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((l1_midsp_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (u1_midsp_2 A B))) =>  ((k10_midsp_2 A B C D) = (k2_midsp_2 (u1_struct_0 A) (u1_midsp_2 A B) (u2_midsp_2 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(d14_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k14_mmlquery A B C D) = (a_4_9_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d14_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  ( ( (B = k6_numbers)  =>  ((k12_mod_2 A B) = k6_numbers) )  &  ( ( (A = k6_numbers)  =>  ((k12_mod_2 A B) = k6_numbers) )  &  ( ( (B = 1)  =>  ((k12_mod_2 A B) = A) )  &  ( ( (A = 1)  =>  ((k12_mod_2 A B) = B) )  &  ( ( (A = 2)  &  (B = 2) )  =>  ((k12_mod_2 A B) = 1) ) ) ) ) ) ) ) ) ) ).
tt(d14_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v9_mod_4 B A) <=> (v1_ringcat1 B A A)) ) ) ) ) ).
tt(d14_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) =>  ((k16_modal_1 A) = (k8_funcop_1 k3_modal_1 (k2_trees_1 k6_numbers) A)) ) ) ).
tt(d14_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) (k4_modcat_1 A B)) (k4_modcat_1 A B)))))  =>  ( (C = (k10_modcat_1 A B))  <=>  ( (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  (! [E:$i] :  ((m4_modcat_1 E A (k4_modcat_1 A B)) =>  ((r2_hidden (k4_tarski D E) (k1_relset_1 (k2_zfmisc_1 (k4_modcat_1 A B) (k4_modcat_1 A B)) C)) <=>  ((k5_modcat_1 A B D) = (k6_modcat_1 A B E)) ) ) ) ) )  &  (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  (! [E:$i] :  ((m4_modcat_1 E A (k4_modcat_1 A B)) =>  ((r2_hidden (k4_tarski D E) (k1_relset_1 (k2_zfmisc_1 (k4_modcat_1 A B) (k4_modcat_1 A B)) C)) =>  ((k1_binop_1 C D E) = (k8_mod_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (A = (k6_modelc_1 B)) ) ) ) ) ) ).
tt(d14_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k5_modelc_2 B C)) ) ) ) ) ) ) ) ).
tt(d14_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k8_modelc_3 A) = (k1_tarski A)) ) ) ).
tt(d14_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v11_monoid_0 A) <=> (v3_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d14_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (E = (k8_msafree2 A B C D))  <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  &  (? [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_finset_1 G) & (v1_trees_1 G)) )  &  ( (F = D)  &  ( (G = (k9_xtuple_0 F))  &  (E = (k6_trees_1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k11_msafree A B) = (g3_msualg_1 A (k8_msafree A B) (k10_msafree A B))) ) ) ) ) ).
tt(d14_msualg_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k12_msualg_1 A B) = (g1_unialg_1 (k10_msualg_1 A B) (k11_msualg_1 A B))) ) ) ) ) ).
tt(d14_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( (D = (k9_msualg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k1_setfam_1 (k8_msualg_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((k13_msualg_4 A B C) = (g3_msualg_1 A (k4_msualg_4 A B C) (k12_msualg_4 A B C))) ) ) ) ) ) ) ).
tt(d14_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((k9_msualg_6 A B C) = (k3_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) C)) ) ) ) ) ) ) ).
tt(d14_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r3_nattra_1 A B C D) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ((m3_nattra_1 E A B C D) <=> (v1_nattra_1 E A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((r10_ncfcont1 A B C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r4_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k2_numbers B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d14_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k11_net_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r1_tarski D (k2_net_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k2_net_1 A)) &  ((r2_hidden E B) &  (D = (k6_net_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r9_orders_1 A B) <=>  ((r2_hidden B (k1_relat_1 A)) &  (! [C:$i] :  ((r2_hidden C (k1_relat_1 A)) =>  ( (C = B)  | (r2_hidden (k4_tarski B C) A)) ) ) ) ) ) ) ) ).
tt(d14_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (C = (k10_ordinal2 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_ordinal2 D)) ) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = A)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k1_ordinal1 (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k4_ordinal2 (k5_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v13_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v12_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d14_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r1_lang1 (k2_osafree A B) (k9_osafree A B (k2_osalg_1 A C (k11_osafree A B D))) (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) D)) =>  ((k12_osafree A B C D) = (k8_trees_4 (u1_struct_0 (k2_osafree A B)) (k9_osafree A B (k2_osalg_1 A C (k11_osafree A B D))) D)) ) ) ) ) ) ) ) ) ) ).
tt(d14_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_osalg_1 A C (k1_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( (D = (k2_osalg_1 A B C))  <=> (r3_osalg_1 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(d14_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( (C = (k12_osalg_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v3_msualg_1 D A) &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(d14_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B))))) )  =>  ( (E = (k10_osalg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A C) (k2_msualg_1 A B))) =>  ((k1_funct_1 E F) = (k8_osalg_4 A C D (k2_msualg_1 A B) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m1_pboole C A B) <=>  (! [D:$i] :  ((r2_hidden D A) => (m1_subset_1 (k1_funct_1 C D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ).
tt(d14_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r4_pdiff_1 A B C D E) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid B)) =>  ( (F = (k12_pdiff_1 A B C D E))  <=>  (? [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k4_real_ns1 A))) &  ( (D = G)  &  ( (E = H)  &  (F = (k1_funct_1 (k9_pdiff_1 A B C G H) (k12_finseq_1 k5_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r5_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k5_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G E) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B) E)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J E)) (k1_seq_1 I (k9_real_1 J E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_petri A B) = B) ) ) ) ) ).
tt(d14_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ( (C = (k12_pnproc_1 A B))  <=>  ( ((k9_xtuple_0 C) = (a_2_0_pnproc_1 A B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C (k2_nat_1 B D)) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k17_polyform A B) = (k7_bspace (k8_polyform A B))) ) ) ) ) ).
tt(d14_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r11_polyred A B C D) <=> (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d14_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  ((k14_pralg_2 A B C) = (g3_msualg_1 B (k10_pralg_2 A B C) (k13_pralg_2 A B C))) ) ) ) ) ) ).
tt(d14_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( (B = (k17_pre_poly A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) <=> (r2_pre_poly A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d14_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k13_pscomp_1 A) = (k19_euclid (k8_pscomp_1 A) (k9_pscomp_1 A))) ) ) ).
tt(d14_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m3_pua2mss1 B A) =>  (! [C:$i] :  ( ((v1_msualg_1 C) & (l1_msualg_1 C))  =>  ( (C = (k11_pua2mss1 A B))  <=>  ( ((u1_struct_0 C) = B)  &  ( ((u4_struct_0 C) = (a_2_2_pua2mss1 A B))  &  (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [E:$i] :  ((m2_finseq_2 E B (k3_finseq_2 B)) =>  ( (~ (r2_subset_1 (k4_card_3 E) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A D))))  =>  ( ((k1_funct_1 (u1_msualg_1 C) (k4_tarski D E)) = E)  & (r1_tarski (k7_relset_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k2_pua2mss1 A D) (k4_card_3 E)) (k1_funct_1 (u2_msualg_1 C) (k4_tarski D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k12_qc_lang1 A) = (k9_finseq_1 (k4_tarski k6_numbers k6_numbers))) ) ) ).
tt(d14_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k10_qc_lang2 A B) = (k18_qc_lang1 A (k19_qc_lang1 A (k18_qc_lang1 A B)))) ) ) ) ) ).
tt(d14_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)))))) )  =>  ( (B = (k11_qmax_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  ((k1_funct_1 B (k6_eqrel_1 (k5_qmax_1 A) (k5_qmax_1 A) (k9_qmax_1 A) C)) = (k6_eqrel_1 (k5_qmax_1 A) (k5_qmax_1 A) (k9_qmax_1 A) (k8_qmax_1 A C))) ) ) ) ) ) ) ) ).
tt(d14_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ( ((r2_hidden A k2_numbers) =>  ( (B = (k14_quaterni A))  <=>  (? [C:$i] :  ((v1_xcmplx_0 C) &  ( (A = C)  &  (B = (k4_complex1 C)) ) ) ) ) )  &  ( (~ (r2_hidden A k2_numbers))  =>  ( (B = (k14_quaterni A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 4 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 4 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_seq_1 C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d14_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k7_quofield A) (k7_quofield A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A))))) )  =>  ( (B = (k17_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k3_funct_2 (k7_quofield A) (k7_quofield A) B C) = (k13_quofield A C)) ) ) ) ) ) ) ) ).
tt(d14_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E (k3_radix_1 B)))  =>  ( (E = (k14_radix_1 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k4_radix_1 F B A E) = (k13_radix_1 B F A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  =>  ((k8_ratfunc1 A) = (k3_ratfunc1 A (k10_polynom3 A) (k10_polynom3 A))) ) ) ).
tt(d14_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k8_relat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((r2_hidden (k4_tarski D E) A) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ).
tt(d14_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_relat_2 A) <=> (r6_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d14_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_rewrite1 A) <=>  (! [B:$i] :  ((r2_hidden B (k1_relat_1 A)) => (r9_rewrite1 A B)) ) ) ) ) ).
tt(d14_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((k21_rfunct_3 A B C) = (k18_rvsum_1 (k20_rfunct_3 A B C))) ) ) ) ) ) ).
tt(d14_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k11_rlvect_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m1_rlvect_2 C A)) ) ) ) ) ) ).
tt(d14_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ( (D = (k10_rmod_4 A B C))  <=>  ((u1_struct_0 D) = (a_3_1_rmod_4 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d14_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_robbins1 A B C) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C))) ) ) ) ) ) ) ).
tt(d14_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k20_rvsum_1 A) = (k1_finsop_1 k2_numbers A k29_binop_2)) ) ) ).
tt(d14_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k17_scm_comp A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_dtconstr k1_scm_comp) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k1_scm_comp) k5_numbers)))) )  &  ( (B = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers C A))  &  ( (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers C (k3_scm_comp D)) = (k16_scm_comp D)) ) )  &  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k1_scm_comp)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k1_scm_comp)) =>  ( ( (G = (k1_bintree1 (u1_struct_0 k1_scm_comp) E))  &  ( (H = (k1_bintree1 (u1_struct_0 k1_scm_comp) F))  & (r1_lang1 k1_scm_comp D (k4_pre_poly (u1_struct_0 k1_scm_comp) G H))) )  =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( (I = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers C E))  &  (J = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers C F)) )  =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers C (k2_scm_comp D E F)) = (k7_nat_1 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k12_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  ( (B = D)  &  (C = (k8_ami_3 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k13_scmpds_2 A B C D) = (k3_xtuple_0 10 k1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d14_scmpds_i,ax, (k15_scmpds_i = 1) ).
tt(d14_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  ( ( (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (? [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) &  (B = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A (k4_scmring1 A C (k2_scmringi A B) (k5_scmring1 A C (k3_scmringi A B))) (k1_ordinal1 (k2_scmring1 A C)))) )  &  ( ( (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (? [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) &  (B = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A (k4_scmring1 A C (k2_scmringi A B) (k1_algstr_0 A (k5_scmring1 A C (k2_scmringi A B)) (k5_scmring1 A C (k3_scmringi A B)))) (k1_ordinal1 (k2_scmring1 A C)))) )  &  ( ( (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (? [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) &  (B = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A (k4_scmring1 A C (k2_scmringi A B) (k5_algstr_0 A (k5_scmring1 A C (k2_scmringi A B)) (k5_scmring1 A C (k3_scmringi A B)))) (k1_ordinal1 (k2_scmring1 A C)))) )  &  ( ( (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (? [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) &  (B = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A (k4_scmring1 A C (k2_scmringi A B) (k6_algstr_0 A (k5_scmring1 A C (k2_scmringi A B)) (k5_scmring1 A C (k3_scmringi A B)))) (k1_ordinal1 (k2_scmring1 A C)))) )  &  ( ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (B = (k3_xtuple_0 6 (k12_finseq_1 k5_numbers D) k1_xboole_0)) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A C (k4_scmringi A B))) )  &  ( ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) &  (B = (k3_xtuple_0 7 (k12_finseq_1 k5_numbers D) (k12_finseq_1 k2_ami_2 E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A C (k14_funcop_1 (k5_scmring1 A C (k6_scmringi A B)) (k4_struct_0 A) (k5_scmringi A B) (k1_ordinal1 (k2_scmring1 A C))))) )  &  ( ( (? [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (B = (k3_xtuple_0 5 k1_xboole_0 (k6_scmring1 A D E))) ) ) ) )  =>  ((k7_scmring1 A B C) = (k3_scmring1 A (k4_scmring1 A C (k8_scmringi A B) (k9_scmringi A B)) (k1_ordinal1 (k2_scmring1 A C)))) )  &  ( ( (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  (~  (B = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  (~  (B = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  (~  (B = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  (~  (B = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 D E))) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  (B = (k3_xtuple_0 6 (k12_finseq_1 k5_numbers D) k1_xboole_0)) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  (~  (B = (k3_xtuple_0 7 (k12_finseq_1 k5_numbers D) (k12_finseq_1 k2_ami_2 E))) ) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (B = (k3_xtuple_0 5 k1_xboole_0 (k6_scmring1 A D E))) ) ) ) ) ) ) ) ) ) ) )  =>  ((k7_scmring1 A B C) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ((v1_seq_4 B A) <=>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_finseq_2 E k2_numbers (k14_seq_4 A)) =>  ( (~ (r1_xxreal_0 D (k22_seq_4 E)))  => (r2_hidden (k15_seq_4 A C E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_sgraph1,ax, (k8_sgraph1 = (k7_sgraph1 3)) ).
tt(d14_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  ((v11_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A C C))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ) ).
tt(d14_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  ((v7_simplex0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r2_hidden D (u1_pre_topc B)) => (v3_pre_topc D C)) ) ) ) ) ) ) ) ) ).
tt(d14_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k13_sin_cos)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_funct_1 A B) = (k11_comseq_3 (k3_sin_cos B))) ) ) ) ) ) ).
tt(d14_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_stacks_1 A B C) <=>  ((k9_stacks_1 A B) = (k9_stacks_1 A C)) ) ) ) ) ) ) ) ).
tt(d14_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k6_struct_0 A B C) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) C)) ) ) ) ) ) ) ).
tt(d14_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (! [D:$i] :  ((r1_substut1 A B C D) <=>  ( ((v5_qc_lang1 B A) =>  (D = (k14_substut1 A (k21_qc_lang1 A B) (k22_qc_lang1 A B) (k7_substut1 A (k21_qc_lang1 A B) B C))) )  &  ( (~ (v5_qc_lang1 B A))  =>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_topalg_6 A)) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((k6_topalg_6 A B) = (k1_funct_1 (k5_topalg_6 A B) (k3_finseq_1 B))) )  &  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) =>  ((k6_topalg_6 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d14_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))))))) )  =>  ( (A = k15_toprealb)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_toprealb k10_toprealb))) =>  (? [C:$i] :  ((v1_xreal_0 C) &  (? [D:$i] :  ((v1_xreal_0 D) &  ( (B = (k19_euclid C D))  &  ( ((r1_xxreal_0 k6_numbers D) =>  ((k3_funct_2 (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))) A B) = (k7_real_1 1 (k10_real_1 (k6_sin_cos6 C) (k8_real_1 2 k32_sin_cos)))) )  &  ((r1_xxreal_0 D k6_numbers) =>  ((k3_funct_2 (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))) A B) = (k9_real_1 1 (k10_real_1 (k6_sin_cos6 C) (k8_real_1 2 k32_sin_cos)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_trees_1,ax, (k8_trees_1 = a_0_0_trees_1) ).
tt(d14_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((m4_trees_3 B A) <=>  (! [C:$i] :  ((m1_trees_1 C B) =>  (~  ( (~ (r2_hidden C A))  &  (! [D:$i] :  ((m3_trees_3 D A) =>  (~ (r2_xboole_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v6_pre_topc B) <=>  ((v2_struct_0 B) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ( (~  (C = D) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc E A) &  ((r2_hidden C E) &  (~ (r2_hidden D E)) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc E A) &  ( (~ (r2_hidden C E))  & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_turing_1,ax, (! [A:$i] :  ( ((v1_turing_1 A) & (l1_turing_1 A))  =>  ( (A = k14_turing_1)  <=>  ( ((u1_turing_1 A) = (k7_domain_1 k5_numbers k6_numbers 1))  &  ( ((u2_turing_1 A) = (k3_turing_1 5))  &  ((r1_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) k13_turing_1) &  ( ((u4_turing_1 A) = k6_numbers)  &  ((u5_turing_1 A) = 5) ) ) ) ) ) ) ) ).
tt(d14_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k15_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k2_binarith (k9_margrel1 B) C)) ) ) ) ) ) ) ) ).
tt(d14_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( (B = (k9_unialg_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_unialg_1 C) & (m1_unialg_2 C A)) ) ) ) ) ) ) ).
tt(d14_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k8_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k3_numbers)))) ) ) ) ) ) ).
tt(d14_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  ((v8_vectsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k4_vectsp_1 A B C (k1_algstr_0 B D E)) = (k1_algstr_0 B (k4_vectsp_1 A B C D) (k4_vectsp_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d14_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v11_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_waybel_0 A B (a_3_1_waybel_0 A B C))) ) ) ) ) ) ) ).
tt(d14_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v7_waybel_1 B A) <=>  ((v6_waybel_1 B A) & (r1_yellow_2 (u1_struct_0 A) A (k3_struct_0 A) B)) ) ) ) ) ) ).
tt(d14_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_waybel34 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_waybel_3 D A) => (v1_waybel_3 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d14_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A)))))) )  =>  ( (B = (k9_waybel_4 A))  <=>  (! [C:$i] :  ( ((v5_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((k1_funct_1 B C) = (k7_waybel_4 A C)) ) ) ) ) ) ) ) ).
tt(d14_xtuple_0,ax, (! [A:$i] :  ((k11_xtuple_0 A) = (k9_xtuple_0 (k9_xtuple_0 A))) ) ).
tt(d14_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_yellow_0 B A) <=>  ((u1_orders_2 B) = (k1_toler_1 (u1_orders_2 A) (u1_struct_0 B))) ) ) ) ) ) ).
tt(d14_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_yellow_6 A B) = (k7_lattice3 (k2_yellow_1 (a_2_0_yellow_6 A B)))) ) ) ) ) ).
tt(d14_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_zf_lang A) <=>  (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k8_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d14_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ( ((v1_zmodul01 D) & (m1_zmodul01 D A))  =>  ( (D = (k6_zmodul01 A B C))  <=>  ((u1_struct_0 D) = (a_3_2_zmodul01 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d15_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r1_abcmiz_0 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D (k3_abcmiz_0 A C)) & (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d15_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k14_abcmiz_1 A) = k8_abcmiz_1) ) ) ).
tt(d15_abcmiz_a,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v6_abcmiz_a B A) <=>  ((k3_finseq_1 (k1_msualg_1 A B)) = 2) ) ) ) ) ) ).
tt(d15_algstr_4,ax, (! [A:$i] :  ((k12_algstr_4 A) = (k3_card_3 (k2_card_3 (k2_partfun1 k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers))) (k10_algstr_4 A) k6_nat_lat)))) ) ).
tt(d15_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  ((v11_altcat_1 A) <=> (v3_altcat_1 (u2_altcat_1 A) (u1_struct_0 A) (u1_altcat_1 A))) ) ) ).
tt(d15_ami_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k3_scm_inst (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k3_scm_inst (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))))) )  =>  ( (A = k9_ami_2)  <=>  (! [B:$i] :  ((m1_subset_1 B k3_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ((k1_funct_1 (k3_funct_2 k3_scm_inst (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) A B) C) = (k8_ami_2 B C)) ) ) ) ) ) ) ) ).
tt(d15_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r8_analmetr A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (D = E) )  &  ( (~  (F = G) )  &  ( (B = (k4_analmetr A D E))  &  ( (C = (k4_analmetr A F G))  & (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ((v8_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r1_collsp A B D G) &  ((r1_collsp A C E H) & (r1_collsp A F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) & (l1_unialg_1 A))  =>  ((v8_aofa_000 A) <=>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v2_margrel1 B) &  ((v3_margrel1 B (u1_struct_0 A)) &  ((v8_comput_1 B 2) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) )  &  ( (B = (k1_funct_1 (u1_unialg_1 A) 2))  & (r1_aofa_000 B (k1_funct_1 (k2_pua2mss1 A (k1_funct_7 1 (k4_finseq_1 (u1_unialg_1 A)))) k1_xboole_0))) ) ) ) ) ) ).
tt(d15_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ((m1_aofa_000 D A (k9_funct_2 B k4_numbers) C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 B k4_numbers) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 B k4_numbers) k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) k4_numbers)))) )  =>  ((r2_aofa_i00 A B C D E F) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((r2_hidden G (k18_aofa_000 A)) &  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) D H G) = (k15_funct_7 B k4_numbers H (k3_funct_2 (k9_funct_2 B k4_numbers) B E H) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v7_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r1_tarski D C) => (r2_hidden (k6_armstrng A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d15_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k12_asympt_0 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k1_seq_1 A (k4_nat_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d15_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k13_bagorder A) = (k3_tarski (k10_xtuple_0 (k12_bagorder A)))) ) ) ).
tt(d15_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k5_bcialg_1 A) = (a_1_1_bcialg_1 A)) ) ) ).
tt(d15_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k5_bcialg_2 A) = (a_1_1_bcialg_2 A)) ) ) ).
tt(d15_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v8_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A C B)) = B) ) ) ) ) ) ) ) ).
tt(d15_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k7_bcialg_6 A B C D)) =>  (! [F:$i] :  ((m2_subset_1 F (u1_struct_0 A) (k7_bcialg_6 A B C D)) =>  ((k11_bcialg_6 A B C D E F) = (k5_binop_1 (k7_bcialg_6 A B C D) (k8_bcialg_6 A B C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((k10_bilinear A B C D) = (a_4_0_bilinear A B C D)) ) ) ) ) ) ) ) ) ).
tt(d15_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers)))) )  =>  ( (A = k39_binop_2)  <=>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ((k1_binop_1 A B C) = (k15_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d15_borsuk_1,ax, (k19_borsuk_1 = 1) ).
tt(d15_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_bvfunc_1 A B C) <=>  (! [D:$i] :  ((r2_hidden D C) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E D) & (r2_hidden F D))  =>  ((k1_funct_1 B E) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r2_hidden B (k6_c0sp1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( (C = (k8_c0sp1 A B))  <=>  ( (C = B)  & (v1_comseq_2 (k2_partfun1 A k1_numbers C A))) ) ) ) ) ) ) ) ).
tt(d15_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r10_calcul_1 A B C) <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r9_calcul_1 A B D E F) => (r1_valuat_1 A D C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v6_card_fil A) <=>  ((v1_card_5 A) & (v5_card_fil A)) ) ) ) ).
tt(d15_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v8_cat_1 D A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A C E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F A C E) =>  (! [G:$i] :  ((m1_cat_1 G A C E) =>  ( ((k5_cat_1 A B C E D F) = (k5_cat_1 A B C E D G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r2_cat_3 A B C D) <=>  ( ((k3_graph_1 A C) = B)  &  ( ((k3_graph_1 A D) = B)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (~  ((r2_hidden F (k2_cat_1 A E (k4_graph_1 A C))) &  ((r2_hidden G (k2_cat_1 A E (k4_graph_1 A D))) &  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  (~  ((r2_hidden H (k2_cat_1 A E B)) &  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 A)) =>  ((r2_hidden I (k2_cat_1 A E B)) =>  ( ( ((k1_cat_1 A I C) = F)  &  ((k1_cat_1 A I D) = G) )  <=>  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k14_cat_4 A B C) = (k9_cat_4 A C B (k2_cat_4 A B C) (k8_cat_4 A B C) (k7_cat_4 A B C))) ) ) ) ) ) ) ).
tt(d15_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v5_cgames_1 A) <=>  (? [B:$i] :  ((r2_hidden A B) &  (! [C:$i] :  ((v2_cgames_1 C) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((v2_cgames_1 D) =>  (~  ((r2_hidden D (k7_cgames_1 C)) &  (! [E:$i] :  ((v2_cgames_1 E) =>  (~  ((r2_hidden E (k6_cgames_1 D)) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m3_chain_1 D A B (k2_nat_1 C 1)) =>  ((k10_chain_1 A B C D) = (k5_chain_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(d15_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A C))))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r7_circtrm1 A B C D E F) <=>  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ((r4_circtrm1 (k1_circtrm1 A C D) E G H (k6_circtrm1 A C D B) F) & (r3_circtrm1 (k1_circtrm1 A C D) E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v10_cohsp_1 A) <=>  ((v9_cohsp_1 A) & (v4_cohsp_1 A)) ) ) ) ).
tt(d15_coh_sp,ax, (! [A:$i] :  ((k13_coh_sp A) = (g1_cat_1 (k3_coh_sp A) (k5_coh_sp A) (k10_coh_sp A) (k11_coh_sp A) (k12_coh_sp A))) ) ).
tt(d15_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v4_compos_1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k1_funct_1 B C) = (k2_compos_1 A))  & (r2_hidden C (k9_xtuple_0 B)))  =>  (C = (k62_valued_1 B)) ) ) ) ) ) ) ) ) ).
tt(d15_comput_1,ax, (k9_comput_1 = (k1_setfam_1 a_0_0_comput_1)) ).
tt(d15_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((m1_conlat_1 B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) ) ) ) ) ) ) ) ).
tt(d15_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k10_convex4 A) (k10_convex4 A)) (k10_convex4 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_convex4 A) (k10_convex4 A)) (k10_convex4 A))))) )  =>  ( (B = (k13_convex4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k10_convex4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k10_convex4 A)) =>  ((k5_binop_1 (k10_convex4 A) B C D) = (k5_convex4 A (k11_convex4 A C) (k11_convex4 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d15_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_csspace A B) = (k7_square_1 (k17_complex1 (k12_csspace A B B)))) ) ) ) ) ).
tt(d15_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k10_decomp_1 A) = (a_1_4_decomp_1 A)) ) ) ).
tt(d15_descip_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) )  =>  ( (A = k26_descip_1)  <=>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k3_funct_2 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) A B) = (k25_descip_1 B)) ) ) ) ) ) ).
tt(d15_dickson,ax, (k11_dickson = (g1_orders_2 k5_numbers k10_dickson)) ).
tt(d15_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k19_dtconstr A B) = (a_2_1_dtconstr A B)) ) ) ) ) ).
tt(d15_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ((k13_ens_1 A B) = B) ) ) ) ) ).
tt(d15_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k13_e_siec A) = (k2_relat_1 (k2_xboole_0 (u1_e_siec A) (u2_e_siec A)))) ) ) ).
tt(d15_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  (! [C:$i] :  ((m2_exchsort C A B) =>  ((v6_exchsort C A B) <=> (v5_exchsort (k4_exchsort C) A)) ) ) ) ) ) ) ).
tt(d15_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k8_extpro_1 A B C D))  <=>  ( ((k3_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k2_compos_1 B))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k3_extpro_1 A B C (k5_extpro_1 A B C D F)) = (k2_compos_1 B))  => (r1_xxreal_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k12_facirc_1 A B C) = (k9_facirc_1 A B C k1_facirc_1)) ) ) ) ).
tt(d15_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k15_ff_siec A) = (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A)))) ) ) ).
tt(d15_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k16_finseq_1 A B) = (k5_relat_1 B (k2_finseq_1 A))) ) ) ) ) ).
tt(d15_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k14_fintopo2 A B) = (k9_subset_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 A) B) (k8_fintopo2 A B))) ) ) ) ) ).
tt(d15_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fin_topo B A) <=>  (B = (k9_fin_topo A B)) ) ) ) ) ) ).
tt(d15_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k12_fomodel0 A B) = (k3_xboole_0 A B)) ) ) ).
tt(d15_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k16_fomodel2 A B) (k32_fomodel1 A)) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k16_fomodel2 A B) (k32_fomodel1 A)) k6_margrel1)))) )  =>  ( (C = (k17_fomodel2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k32_fomodel1 A)) =>  ((k2_binop_1 (k16_fomodel2 A B) (k32_fomodel1 A) k6_margrel1 C D E) = (k14_fomodel2 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ((m2_fomodel2 E A B C) =>  ( ( (~ (v7_fomodel1 C A))  =>  ((k20_fomodel3 A B C D E) = (k4_relset_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) (k8_eqrel_1 B D)) (k8_eqrel_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C)))) (k8_eqrel_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C)))) (k8_eqrel_1 B D) (k19_fomodel3 B (k1_int_2 (k19_fomodel1 A C)) D) (k12_fomodel3 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) B (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) D E))) )  &  ((v7_fomodel1 C A) =>  ((k20_fomodel3 A B C D E) = (k4_relset_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) (k8_eqrel_1 B D)) (k8_eqrel_1 k6_margrel1 (k3_fomodel2 k6_margrel1)) (k10_eqrel_1 k6_margrel1) k6_margrel1 (k4_relset_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) (k8_eqrel_1 B D)) (k8_eqrel_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C)))) (k8_eqrel_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C)))) (k8_eqrel_1 k6_margrel1 (k3_fomodel2 k6_margrel1)) (k19_fomodel3 B (k1_int_2 (k19_fomodel1 A C)) D) (k12_fomodel3 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) k6_margrel1 (k13_fomodel3 B D (k1_int_2 (k19_fomodel1 A C))) (k3_fomodel2 k6_margrel1) E)) (k15_fomodel3 k6_margrel1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((k5_fomodel4 A B C) = (a_3_0_fomodel4 A B C)) ) ) ) ) ) ).
tt(d15_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_freealg A B))) =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  & (r1_lang1 (k3_freealg A B) C D)) )  =>  ((k11_freealg A B C) = C) ) ) ) ) ) ) ).
tt(d15_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ((m1_eqrel_1 D (u1_struct_0 C)) =>  ( (D = (k8_fsm_1 A B C))  <=> (v4_fsm_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(d15_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k15_ftacell1 A B C D E) = (k33_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d15_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)) = k1_xboole_0) )  &  (~  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((k6_functor0 A B C D E F) = (k1_funct_1 (k5_functor0 A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A (k4_vectsp_2 A)) =>  ((m2_fvaluat1 C A B) <=>  ((u1_struct_0 C) = B) ) ) ) ) ) ) ) ).
tt(d15_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) & (v1_xboole_0 D)) ) ) )  =>  ((k15_gate_1 A B C D) = (k1_gate_1 k1_xboole_0)) )  &  (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  (~  ((k15_gate_1 A B C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k15_gate_5 A B C D E) = (k3_gate_1 (k2_gate_1 C D) (k2_gate_1 (k3_gate_1 C D) (k11_gate_1 A B E)))) ) ) ) ) ) ).
tt(d15_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v3_gcd_1 A) & (l5_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r8_gcd_1 A B C D) <=>  ( ((k5_gcd_1 A B C D) = (k5_struct_0 A))  &  ((r2_hidden D B) &  (~  (D = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r3_glib_000 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ( ((r2_hidden (k1_funct_1 (k10_glib_000 A) D) B) & (r2_hidden (k1_funct_1 (k11_glib_000 A) D) C))  |  ((r2_hidden (k1_funct_1 (k10_glib_000 A) D) C) & (r2_hidden (k1_funct_1 (k11_glib_000 A) D) B)) ) ) ) ) ) ) ) ) ).
tt(d15_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m2_glib_001 C A) =>  ( (C = (k12_glib_001 A B))  <=>  ( ((k3_finseq_1 B) = (k2_nat_1 (k4_nat_1 2 (k3_finseq_1 C)) 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k1_funct_1 C D) = (k1_funct_1 B (k4_nat_1 2 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))) =>  ( ( ((k12_glib_004 A B) = k1_xboole_0)  =>  ((k14_glib_004 A B) = B) )  &  ( ((r2_hidden (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k12_glib_004 A B))) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B)) =>  ( ((k12_glib_004 A B) = k1_xboole_0)  |  ((k14_glib_004 A B) = (k4_tarski (k2_xboole_0 (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k1_funct_1 (k11_glib_000 A) (k10_subset_1 (k12_glib_004 A B))))) (k2_xboole_0 (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k10_subset_1 (k12_glib_004 A B)))))) ) )  &  (~  ( (~  ((k12_glib_004 A B) = k1_xboole_0) )  &  ( (~  ( (~  ((k12_glib_004 A B) = k1_xboole_0) )  & (r2_hidden (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k12_glib_004 A B))) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B))) )  &  (~  ((k14_glib_004 A B) = (k4_tarski (k2_xboole_0 (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k12_glib_004 A B))))) (k2_xboole_0 (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k10_subset_1 (k12_glib_004 A B)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r5_glib_005 A B C) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( (D = (k8_glib_005 A B C))  <=>  ( ((k1_relset_1 k5_numbers D) = (k1_relset_1 k5_numbers (k12_glib_001 A C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ( ((r2_glib_000 A (k1_funct_1 C (k6_xcmplx_0 (k4_nat_1 2 E) 1)) (k1_funct_1 C (k2_nat_1 (k4_nat_1 2 E) 1)) (k1_funct_1 C (k4_nat_1 2 E))) =>  ((k1_funct_1 D E) = (k6_xcmplx_0 (k1_funct_1 (k5_glib_003 A) (k1_funct_1 C (k4_nat_1 2 E))) (k1_funct_1 B (k1_funct_1 C (k4_nat_1 2 E))))) )  &  ( (~ (r2_glib_000 A (k1_funct_1 C (k6_xcmplx_0 (k4_nat_1 2 E) 1)) (k1_funct_1 C (k2_nat_1 (k4_nat_1 2 E) 1)) (k1_funct_1 C (k4_nat_1 2 E))))  =>  ((k1_funct_1 D E) = (k1_funct_1 B (k1_funct_1 C (k4_nat_1 2 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  ((v7_graph_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) |  ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 B (k2_nat_1 C 1))) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(d15_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r6_graph_5 A C) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k9_graph_5 A B C))  <=>  ( ((k4_finseq_1 B) = (k4_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_seq_1 D E) = (k1_funct_1 C (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_funct_2 B (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  ( (B = (k19_graphsp A))  <=>  ( ((k9_xtuple_0 B) = (k3_finseq_2 k1_numbers))  &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k6_graphsp B C) = (k18_graphsp C A)) ) ) ) ) ) ) ) ) ).
tt(d15_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  ((k11_grcat_1 A) = (g1_grcat_1 A A (k3_struct_0 A))) ) ) ).
tt(d15_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k13_group_10 A B C D) = (a_4_1_group_10 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d15_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k15_group_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (D = (k13_group_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k11_group_3 A B) = (k10_group_3 A (k8_group_2 A B))) ) ) ) ) ).
tt(d15_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k7_group_9 A B C) (k7_group_9 A B C)) (k7_group_9 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_group_9 A B C) (k7_group_9 A B C)) (k7_group_9 A B C))))) )  =>  ( (D = (k8_group_9 A B C))  <=>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E B) & (m1_group_2 E B)) )  =>  ( (E = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)))  =>  (D = (k4_group_6 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k15_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k11_idea_1 A (k13_idea_1 (k12_idea_1 A D B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d15_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (C = (k8_ideal_1 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D A) &  ((v2_ideal_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v12_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  ((r2_incsp_1 A B C) &  ((r2_incsp_1 A B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~  ( (~  (B = E) )  &  ((r2_incsp_1 A E C) & (r2_incsp_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((k13_index_1 A B C) = (k4_tarski (k7_cat_1 A B C) (k12_mcart_1 C))) ) ) ) ) ) ) ).
tt(d15_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v3_integr15 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) => (v1_comseq_2 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers B (k1_pdiff_1 C A)))) ) ) ) ) ) ) ) ).
tt(d15_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k11_integra1 A B) = (k4_seq_4 (k1_rvsum_1 (k9_integra1 A B)))) ) ) ) ) ).
tt(d15_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  ((k14_interva1 A B) = (k1_xtuple_0 B)) ) ) ) ) ).
tt(d15_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_intpro_1)) =>  ( (B = (k7_intpro_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_intpro_1)) =>  ( ((v8_intpro_1 D) & (r1_tarski A D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k15_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k20_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d15_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_lattices B) &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  ( (B = (k14_lattice3 A))  <=>  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k3_lattice3 B)) ) ) ) ) ) ) ).
tt(d15_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((k10_lattice5 A B C) = C) ) ) ) ) ) ) ).
tt(d15_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((k5_lattice6 A) = (a_1_0_lattice6 A)) ) ) ).
tt(d15_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v15_lattices A) <=>  ((v13_lattices A) & (v14_lattices A)) ) ) ) ).
tt(d15_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k7_lmod_7 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (k7_lmod_7 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k7_lmod_7 A B C)) =>  ( (F = (k10_lmod_7 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (D = (k8_lmod_7 A B C G))  &  (E = (k8_lmod_7 A B C H)) )  =>  (F = (k8_lmod_7 A B C (k3_rlvect_1 B G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_lopban_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_rsspace3 B A) => (v3_normsp_1 B A)) ) ) ) ) ) ).
tt(d15_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k14_lpspace1 A B C) (k14_lpspace1 A B C)) (k14_lpspace1 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_lpspace1 A B C) (k14_lpspace1 A B C)) (k14_lpspace1 A B C))))) )  =>  ( (D = (k15_lpspace1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k9_lpspace1 A B C)) (k14_lpspace1 A B C)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k9_lpspace1 A B C)) (k14_lpspace1 A B C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden G E) & (r2_hidden H F))  =>  ((k5_binop_1 (k14_lpspace1 A B C) D E F) = (k13_lpspace1 A B C (k3_valued_1 A k1_numbers k1_numbers G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_hilbert1 k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_hilbert1 k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  ( (B = (k12_ltlaxio1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k3_funct_2 k1_hilbert1 k6_margrel1 B k2_hilbert1) = k6_numbers)  &  ( ((k3_funct_2 k1_hilbert1 k6_margrel1 B (k1_hilbert2 E)) = (k3_funct_2 k1_hilbert1 k6_margrel1 A (k1_hilbert2 E)))  &  ( ((k3_funct_2 k1_hilbert1 k6_margrel1 B (k3_hilbert1 C D)) = (k6_xboolean (k3_funct_2 k1_hilbert1 k6_margrel1 B C) (k3_funct_2 k1_hilbert1 k6_margrel1 B D)))  &  ((k3_funct_2 k1_hilbert1 k6_margrel1 B (k4_hilbert1 C D)) = (k3_funct_2 k1_hilbert1 k6_margrel1 A (k4_hilbert1 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_margrel1,ax, (! [A:$i] :  ( ( (~ (r2_hidden k7_margrel1 A))  =>  ((k11_margrel1 A) = k8_margrel1) )  &  ((r2_hidden k7_margrel1 A) =>  ((k11_margrel1 A) = k7_margrel1) ) ) ) ).
tt(d15_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_matroid0 A B) = (a_2_2_matroid0 A B)) ) ) ) ) ).
tt(d15_mcart_1,ax, (! [A:$i] :  ((k14_mcart_1 A) = (k2_xtuple_0 (k1_xtuple_0 A))) ) ).
tt(d15_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k18_member_1 A B) = (k10_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d15_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v3_membered B) =>  ( (A = B)  <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) <=> (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d15_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k10_memstr_0 A B C D) = (k1_funct_4 C (k7_memstr_0 A B (k7_nat_d (k5_memstr_0 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(d15_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k2_numbers) =>  ((r3_mesfun7c A B C D E) <=>  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_funct_1 C G) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_mesfunc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ( (C = (k10_relat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) &  ((k12_supinf_2 A D) = B) ) ) ) ) ) ) ) ) ) ).
tt(d15_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 D) =>  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  ( (E = (k1_relset_1 A D))  & (r1_mesfunc1 A B D E)) ) ) )  |  (! [E:$i] :  ((m1_subset_1 E k7_numbers) =>  ( (E = (k6_mesfunc5 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers F H)) &  ((k1_relset_1 A (k4_mesfunc5 A k7_numbers F H)) = (k1_relset_1 A D)) ) ) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers F H))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r1_xxreal_0 H I) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  ((r2_hidden J (k1_relset_1 A D)) => (r1_xxreal_0 (k12_supinf_2 (k4_mesfunc5 A k7_numbers F H) J) (k12_supinf_2 (k4_mesfunc5 A k7_numbers F I) J))) ) ) ) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H (k1_relset_1 A D)) =>  ((v10_mesfunc5 (k3_mesfunc5 A F H)) &  ((k2_mesfunc5 (k3_mesfunc5 A F H)) = (k12_supinf_2 D H)) ) ) ) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k8_nat_1 k7_numbers G H) = (k5_mesfunc5 A B C (k4_mesfunc5 A k7_numbers F H))) ) )  &  ((v10_mesfunc5 G) &  (E = (k2_mesfunc5 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  =>  ( (D = (k10_metric_1 A B C))  <=>  (D = (a_3_1_metric_1 A B C)) ) )  &  ((v2_struct_0 A) =>  ( (D = (k10_metric_1 A B C))  <=> (v1_xboole_0 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k10_midsp_1 A) (k10_midsp_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A))))) )  =>  ( (B = (k13_midsp_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  ((k11_midsp_1 A C (k3_funct_2 (k10_midsp_1 A) (k10_midsp_1 A) B C)) = (k6_midsp_1 A)) ) ) ) ) ) ) ) ).
tt(d15_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  ((k11_midsp_2 A B) = (k4_struct_0 (u1_midsp_2 A B))) ) ) ) ) ).
tt(d15_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (C = (k18_mmlquery A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k2_mmlquery A C D) = (k3_tarski (a_3_2_mmlquery A B D))) ) ) ) ) ) ) ) ) ).
tt(d15_mod_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2))))) )  =>  ( (A = k13_mod_2)  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_enumset1 k6_numbers 1 2)) =>  ((k5_binop_1 (k1_enumset1 k6_numbers 1 2) A B C) = (k11_mod_2 B C)) ) ) ) ) ) ) ) ).
tt(d15_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v10_mod_4 B A) <=> (v2_mod_4 B A A)) ) ) ) ) ).
tt(d15_modal_1,ax, (k17_modal_1 = (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 k6_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers))) ).
tt(d15_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((k11_modcat_1 A B) = (g1_cat_1 (k3_modcat_1 A B) (k4_modcat_1 B (k3_modcat_1 A B)) (k8_modcat_1 B (k3_modcat_1 A B)) (k9_modcat_1 B (k3_modcat_1 A B)) (k10_modcat_1 B (k3_modcat_1 A B)))) ) ) ) ) ).
tt(d15_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_1 A) <=>  (? [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  &  (A = (k7_modelc_1 B)) ) ) ) ) ) ).
tt(d15_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (A = (k6_modelc_2 B)) ) ) ) ) ) ).
tt(d15_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k9_modelc_3 A) = (g1_modelc_3 A (k7_modelc_3 A) (k7_modelc_3 A) (k7_modelc_3 A))) ) ) ).
tt(d15_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v12_monoid_0 A) <=> (v4_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d15_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_funct_1 (k8_msafree A B) C))) =>  ( (D = (k12_msafree A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F (k1_funct_1 B C)) &  (E = (k1_trees_4 (k4_tarski F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((v3_msualg_2 C A B) =>  ((k10_msualg_2 A B C) = (g3_msualg_1 A C (k4_msualg_2 A B C))) ) ) ) ) ) ) ) ).
tt(d15_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (k4_msualg_4 A B C) D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (k4_msualg_4 A B C) D))))) )  =>  ( (E = (k14_msualg_4 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((k1_funct_1 E F) = (k6_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k2_msualg_4 A B C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_6 D A B) &  ((v4_msualg_6 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ( (D = (k10_msualg_6 A B C))  <=>  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_6 E A B) &  ((v4_msualg_6 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((r2_pboole (u1_struct_0 A) C E) => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((m4_nattra_1 C A B) <=>  (! [D:$i] :  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_nattra_1 G A B E F) =>  (~  ( (D = (k4_tarski (k4_tarski E F) G))  & (r2_nattra_1 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((r11_ncfcont1 A B C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r5_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k1_numbers B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d15_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((k12_net_1 A B) = (k3_tarski (k10_net_1 A B))) ) ) ) ).
tt(d15_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (C = (k11_ordinal2 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_ordinal2 D)) ) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 A))  &  ( ((k1_funct_1 D k1_xboole_0) = k1_xboole_0)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 A)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k10_ordinal2 (k1_funct_1 D E) B)) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 A)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k3_tarski (k4_ordinal2 (k5_relat_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ( (B = (k11_ordinal6 A))  <=>  ( ((k9_xtuple_0 B) = (k2_ordinal1 A))  &  ( ((k1_funct_1 B k6_numbers) = (k6_ordinal6 A k4_ordinal1))  &  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden (k1_ordinal1 C) (k2_ordinal1 A)) =>  ((k1_funct_1 B (k1_ordinal1 C)) = (k3_ordinal6 (k1_funct_1 B C))) ) ) )  &  (! [C:$i] :  ( ((v3_ordinal1 C) &  ((v4_ordinal1 C) &  (~ (v1_xboole_0 C)) ) )  =>  ((r2_hidden C (k2_ordinal1 A)) =>  ((k1_funct_1 B C) = (k7_ordinal6 (k5_relat_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  & (r1_lang1 (k2_osafree A B) C D)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( (D = (k13_osafree A B C))  <=>  ((k4_tarski D (u1_struct_0 A)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k3_osalg_1 A B) = (k7_funcop_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(d15_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B))))) )  =>  ( (C = (k14_osalg_2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  (! [F:$i] :  ( ((v3_msualg_1 F A) &  ((v12_osalg_1 F A) & (m1_msualg_2 F A B)) )  =>  (! [G:$i] :  ( ((v3_msualg_1 G A) &  ((v12_osalg_1 G A) & (m1_msualg_2 G A B)) )  =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k13_osalg_2 A B) C D E) = (k11_osalg_2 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((m2_pboole D A B C) <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((v1_funct_1 (k1_funct_1 D E)) &  ((v1_funct_2 (k1_funct_1 D E) (k1_funct_1 B E) (k1_funct_1 C E)) & (m1_subset_1 (k1_funct_1 D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ((r5_pdiff_1 A B C D E F) <=> (r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k7_pdiff_1 A C F) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) E (k4_pdiff_1 D B))) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r6_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k6_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G F) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B) F)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J F)) (k1_seq_1 I (k9_real_1 J F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  ((k13_pnproc_1 A B) = (k6_domain_1 (k3_finseq_2 B) (k2_pre_poly B))) ) ) ) ).
tt(d15_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k18_polyform A B) = (k1_zfmisc_1 (k8_polyform A B))) ) ) ) ) ).
tt(d15_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 A k5_numbers))) =>  ( (C = (k18_pre_poly A B))  <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v4_valued_0 D)) ) ) )  =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((r2_hidden E A) => (r1_xxreal_0 (k1_funct_1 D E) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k14_pscomp_1 A) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)) A)) ) ) ).
tt(d15_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  (! [D:$i] :  ((m2_pua2mss1 D (u4_struct_0 B)) =>  ((r6_pua2mss1 A B C D) <=>  ((m4_pua2mss1 (u3_msualg_1 B C) A) &  ( ((k9_xtuple_0 D) = (k4_finseq_1 (u1_unialg_1 A)))  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 (u1_unialg_1 A))) => (m2_pua2mss1 (k5_relat_1 (u4_msualg_1 B C) (k1_funct_1 D E)) (k2_pua2mss1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k13_qc_lang1 A B) = (k7_finseq_1 (k9_finseq_1 (k4_tarski 1 k6_numbers)) (k11_qc_lang1 A B))) ) ) ) ) ).
tt(d15_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k11_qc_lang2 A B) = (k18_qc_lang1 A (k20_qc_lang1 A (k18_qc_lang1 A B)))) ) ) ) ) ).
tt(d15_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_quantal1 A B C) = (k15_lattice3 A (a_3_6_quantal1 A B C))) ) ) ) ) ) ) ).
tt(d15_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ( ((r2_hidden A k2_numbers) =>  ( (B = (k15_quaterni A))  <=>  (B = k6_numbers) ) )  &  ( (~ (r2_hidden A k2_numbers))  =>  ( (B = (k15_quaterni A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 4 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 4 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_seq_1 C 2)) ) ) ) ) ) ) ) ) ) ).
tt(d15_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k7_quofield A) (k7_quofield A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A))))) )  =>  ( (B = (k18_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k3_funct_2 (k7_quofield A) (k7_quofield A) B C) = (k14_quofield A C)) ) ) ) ) ) ) ) ).
tt(d15_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  ((k9_ratfunc1 A B C) = (k3_ratfunc1 A (k2_normsp_1 A (k11_polynom3 A (k4_ratfunc1 A B) (k5_ratfunc1 A C)) (k11_polynom3 A (k5_ratfunc1 A B) (k4_ratfunc1 A C))) (k11_polynom3 A (k5_ratfunc1 A B) (k5_ratfunc1 A C)))) ) ) ) ) ) ) ).
tt(d15_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_relat_1 A) <=> (r1_tarski (k10_xtuple_0 A) (k1_tarski k1_xboole_0))) ) ) ).
tt(d15_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_relat_2 A) <=> (r7_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d15_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_rewrite1 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  (~  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_hidden (k4_tarski (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 1))) A)) ) ) ) ) ) ) ) ).
tt(d15_ringcat1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_ringcat1 A B) <=>  (? [C:$i] :  (? [D:$i] :  (? [E:$i] :  (? [F:$i] :  (? [G:$i] :  (? [H:$i] :  ( (A = (k3_xtuple_0 (k6_xtuple_0 C D E F) G H))  &  (? [I:$i] :  ( ( (~ (v2_struct_0 I))  &  ((v13_algstr_0 I) &  ((v36_algstr_0 I) &  ((v2_rlvect_1 I) &  ((v3_rlvect_1 I) &  ((v4_rlvect_1 I) &  ((v3_group_1 I) &  ((v4_vectsp_1 I) &  ((v5_vectsp_1 I) & (l6_algstr_0 I)) ) ) ) ) ) ) ) )  &  ( (B = I)  &  ( (C = (u1_struct_0 I))  &  ( (D = (u1_algstr_0 I))  &  ( (E = (k5_vectsp_1 I))  &  ( (F = (k4_struct_0 I))  &  ( (G = (u2_algstr_0 I))  &  (H = (k5_struct_0 I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k11_rlvect_2 A)) =>  ((k12_rlvect_2 A B) = B) ) ) ) ) ).
tt(d15_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_robbins1 A B C) = (k9_robbins1 A (k1_lattices A B C) (k9_robbins1 A B C))) ) ) ) ) ) ) ).
tt(d15_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k21_rvsum_1 A) = (k1_finsop_1 k1_numbers A k35_binop_2)) ) ) ).
tt(d15_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  ((k10_scmfsa_1 A) = (k1_funct_1 A k5_numbers)) ) ) ).
tt(d15_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k13_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  ( (B = D)  &  (C = (k9_ami_3 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k14_scmpds_2 A B C D) = (k3_xtuple_0 11 k1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d15_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_scmringi A) (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_scmringi A) (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))))))) )  =>  ( (B = (k8_scmring1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_scmringi A)) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  ((k1_funct_1 (k3_funct_2 (k1_scmringi A) (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) B C) D) = (k7_scmring1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d15_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k8_scmyciel A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v4_scmyciel C) &  ((v5_scmyciel C) & (m1_subset_1 C (k1_zfmisc_1 A))) ) )  &  ((k2_scmyciel C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v4_scmyciel C) &  ((v5_scmyciel C) & (m1_subset_1 C (k1_zfmisc_1 A))) ) )  => (r1_xxreal_0 (k2_scmyciel C) B)) ) ) ) ) ) ) ) ).
tt(d15_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ((v2_seq_4 B A) <=>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_finseq_2 E k2_numbers (k14_seq_4 A)) =>  (~  ( (~ (r1_xxreal_0 D (k22_seq_4 E)))  & (r2_hidden (k15_seq_4 A C E) B)) ) ) ) ) ) ) )  => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d15_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  ((v12_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A C D))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C C) B) (k5_sheffer1 A (k5_sheffer1 A D D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d15_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k14_sin_cos A) = (k1_funct_1 k13_sin_cos A)) ) ) ).
tt(d15_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v7_stacks_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_stacks_1 A B C) =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d15_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k15_substut1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) &  (? [F:$i] :  ( (C = (k4_tarski (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) D E) F))  & (r1_substut1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (B = (k18_supinf_2 A))  <=>  (! [C:$i] :  ((m1_supinf_2 C (k17_supinf_2 A)) =>  ((r2_funct_2 k5_numbers k7_numbers C A) => (r2_funct_2 k5_numbers k7_numbers B (k15_supinf_2 (k17_supinf_2 A) C))) ) ) ) ) ) ) ) ).
tt(d15_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_tex_4 A B) = (k8_subset_1 (u1_struct_0 A) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) (k1_setfam_1 (a_2_9_tex_4 A B)))) ) ) ) ) ).
tt(d15_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v4_trees_3 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (B = (k11_trees_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (~  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 A) D))  &  ((r2_hidden E (k1_funct_1 A (k2_nat_1 D 1))) &  (C = (k7_finseq_1 (k12_finseq_1 k5_numbers D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r3_turing_1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [D:$i] :  ((m2_funct_2 D k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  ( ((r2_hidden F (k9_xtuple_0 B)) &  ( (C = (k4_domain_1 (u2_turing_1 A) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (u4_turing_1 A) E D))  & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers E) F) A D)) )  =>  ((v2_turing_1 C A) &  (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) &  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ( ((k2_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k11_turing_1 A C)) = G)  &  ( (H = (k1_funct_1 B F))  & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers G) (k12_finseq_1 k5_numbers H)) A (k3_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k11_turing_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k16_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k2_binarith (k9_margrel1 B) (k9_margrel1 C))) ) ) ) ) ) ) ) ).
tt(d15_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A))))) )  =>  ( (B = (k10_unialg_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k9_unialg_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_unialg_2 A)) =>  (! [E:$i] :  ( ((v1_unialg_1 E) & (m1_unialg_2 E A))  =>  (! [F:$i] :  ( ((v1_unialg_1 F) & (m1_unialg_2 F A))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k9_unialg_2 A) B C D) = (k8_unialg_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(d15_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k9_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k3_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k3_numbers)))) ) ) ) ) ) ) ).
tt(d15_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  ((v9_vectsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k4_vectsp_1 A B (k1_algstr_0 A C D) E) = (k1_algstr_0 B (k4_vectsp_1 A B C E) (k4_vectsp_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k3_waybel_0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_orders_2 A D E) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v8_waybel_1 B A) <=>  ((v6_waybel_1 B A) & (r1_yellow_2 (u1_struct_0 A) A B (k3_struct_0 A))) ) ) ) ) ) ).
tt(d15_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_waybel34 C A B) <=>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  => (r4_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d15_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))))))) )  =>  ( (B = (k10_waybel_4 A))  <=>  (! [C:$i] :  (~  ((r2_hidden C (u1_struct_0 (k8_waybel_4 A))) &  (! [D:$i] :  ( ((v5_waybel_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (~  ( (D = (k1_funct_1 B C))  &  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  &  ( (G = E)  &  ( (H = F)  &  ( (I = C)  & (r2_hidden G (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_xtuple_0,ax, (! [A:$i] :  ((k12_xtuple_0 A) = (k10_xtuple_0 (k9_xtuple_0 A))) ) ).
tt(d15_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_orders_2 C) &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) )  =>  ( (C = (k5_yellow_0 A B))  <=>  ((u1_struct_0 C) = B) ) ) ) ) ) ) ) ).
tt(d15_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k10_yellow_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_connsp_2 E A D) => (r1_waybel_0 A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d15_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_zf_lang A) <=>  ((v2_zf_lang A) | (v3_zf_lang A)) ) ) ) ).
tt(d15_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ( ((v1_zmodul01 D) & (m1_zmodul01 D A))  =>  ( (D = (k7_zmodul01 A B C))  <=>  ((u1_struct_0 D) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(d16_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r2_abcmiz_0 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_tarski C (k2_abcmiz_0 A D)) & (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d16_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k15_abcmiz_1 A) = k10_abcmiz_1) ) ) ).
tt(d16_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((k13_abcmiz_a A) = A) ) ) ).
tt(d16_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((v13_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v10_algstr_0 B A)) ) ) ) ) ).
tt(d16_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k12_algstr_4 A) (k12_algstr_4 A)) (k12_algstr_4 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k12_algstr_4 A) (k12_algstr_4 A)) (k12_algstr_4 A))))) )  =>  ( ( (~ (v1_xboole_0 A))  =>  ( (B = (k13_algstr_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k12_algstr_4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k12_algstr_4 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ( (E = (k2_xtuple_0 C))  &  (F = (k2_xtuple_0 D)) )  =>  ((k5_binop_1 (k12_algstr_4 A) B C D) = (k4_tarski (k4_tarski (k4_tarski (k1_xtuple_0 C) (k1_xtuple_0 D)) (k2_xtuple_0 C)) (k2_xcmplx_0 E F))) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_xboole_0 A) =>  ( (B = (k13_algstr_4 A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(d16_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  ((v12_altcat_1 A) <=>  ((v5_altcat_1 (u2_altcat_1 A) (u1_struct_0 A) (u1_altcat_1 A)) & (v4_altcat_1 (u2_altcat_1 A) (u1_struct_0 A) (u1_altcat_1 A))) ) ) ) ).
tt(d16_ami_2,ax, (! [A:$i] :  ((v1_ami_2 A) <=> (r2_hidden A k2_ami_2)) ) ).
tt(d16_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) & (l1_unialg_1 A)) )  =>  ((k12_aofa_000 A) = (k1_funct_1 (k2_pua2mss1 A (k1_funct_7 1 (k4_finseq_1 (u1_unialg_1 A)))) k1_xboole_0)) ) ) ).
tt(d16_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ((m1_aofa_000 D A (k9_funct_2 B k4_numbers) C) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r1_aofa_i00 A E B C D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 B k4_numbers) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) B)))) )  =>  ((m2_aofa_i00 E A B C D) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 B k4_numbers) k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) k4_numbers)))) )  & (r2_aofa_i00 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k8_armstrng A B) = (k1_armstrng B (k7_armstrng A))) ) ) ) ).
tt(d16_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_asympt_0 A B) <=>  ((v6_asympt_0 A) & (r2_hidden (k12_asympt_0 A B) (k6_asympt_0 A))) ) ) ) ) ) ).
tt(d16_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k14_bagorder A) = (g1_orders_2 (k5_finsub_1 (u1_struct_0 A)) (k13_bagorder A))) ) ) ).
tt(d16_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v11_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) & (r1_bcialg_1 A C B)) ) ) ) ) ) ) ).
tt(d16_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k6_bcialg_2 A) = (a_1_2_bcialg_2 A)) ) ) ).
tt(d16_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((k11_bilinear A B C D) = (a_4_1_bilinear A B C D)) ) ) ) ) ) ) ) ) ).
tt(d16_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A C B D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d16_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_borsuk_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k16_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k15_bvfunc_1 A E C)) =>  ((k3_funct_2 A k6_margrel1 B F) = k8_margrel1) ) ) )  =>  ((k3_funct_2 A k6_margrel1 D E) = k8_margrel1) )  &  ( (? [F:$i] :  ((m1_subset_1 F A) &  ((r2_hidden F (k15_bvfunc_1 A E C)) &  (~  ((k3_funct_2 A k6_margrel1 B F) = k8_margrel1) ) ) ) )  =>  ((k3_funct_2 A k6_margrel1 D E) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k9_c0sp1 A B) = (a_2_0_c0sp1 A B)) ) ) ) ) ).
tt(d16_calcul_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r1_calcul_1 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ) ).
tt(d16_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k12_card_3 A B))  <=>  ( ((k9_xtuple_0 C) = (k4_card_3 A))  &  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k1_funct_1 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) <=>  (? [B:$i] :  ((m1_card_fil B A) &  ((r1_card_fil A A B) &  ( (~ (v2_card_fil B A))  & (v3_card_fil B A)) ) ) ) ) ) ) ).
tt(d16_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 D A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) )  =>  ((m2_cat_3 D A B C) <=> (r2_funct_2 C (u1_struct_0 A) (k3_cat_3 A C D) (k8_funcop_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ).
tt(d16_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k15_cat_4 A B) = (k9_cat_4 A B B B (k4_cat_1 A B) (k4_cat_1 A B))) ) ) ) ) ).
tt(d16_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v6_cgames_1 A) <=> (v5_cgames_1 (k13_cgames_1 A))) ) ) ).
tt(d16_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_algstr_0 D) &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) ) ) )  =>  ( (D = (k15_chain_1 A B C))  <=>  ( ((u1_struct_0 D) = (k1_chain_1 (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A B C)))  &  ( ((k4_struct_0 D) = (k11_chain_1 A B C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k4_chain_1 A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k4_chain_1 A B C))) =>  ( ( (E = G)  &  (F = H) )  =>  ((k3_rlvect_1 D E F) = (k7_chain_1 A B C G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A C))))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r8_circtrm1 A B C D E F) <=> (r6_circtrm1 E (k1_circtrm1 A C D) F (k6_circtrm1 A C D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k7_clvect_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k5_cohsp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((v1_finset_1 D) &  (? [E:$i] :  ( (C = (k4_tarski D E))  &  ((r2_hidden D (k9_xtuple_0 A)) & (r2_hidden E (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k14_coh_sp A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ).
tt(d16_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((k4_compos_1 A) = (k3_afinsq_1 (k2_compos_1 A))) ) ) ).
tt(d16_comput_1,ax, (! [A:$i] :  ((v7_comput_1 A) <=> (r2_hidden A k9_comput_1)) ) ).
tt(d16_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) )  =>  ((r2_conlat_1 A B C) <=> (r1_tarski (u2_conlat_1 A B) (u2_conlat_1 A C))) ) ) ) ) ) ) ).
tt(d16_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k2_numbers (k10_convex4 A)) (k10_convex4 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k10_convex4 A)) (k10_convex4 A))))) )  =>  ( (B = (k14_convex4 A))  <=>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k10_convex4 A)) =>  ((k1_funct_1 B (k4_tarski C D)) = (k7_convex4 A C (k11_convex4 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d16_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k14_csspace A B C) = (k13_csspace A (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(d16_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k11_decomp_1 A) = (a_1_5_decomp_1 A)) ) ) ).
tt(d16_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ( (B = (k27_descip_1 A))  <=>  ( ((k10_descip_1 64 B 1) = (k10_descip_1 64 A 40))  &  ( ((k10_descip_1 64 B 2) = (k10_descip_1 64 A 8))  &  ( ((k10_descip_1 64 B 3) = (k10_descip_1 64 A 48))  &  ( ((k10_descip_1 64 B 4) = (k10_descip_1 64 A 16))  &  ( ((k10_descip_1 64 B 5) = (k10_descip_1 64 A 56))  &  ( ((k10_descip_1 64 B 6) = (k10_descip_1 64 A 24))  &  ( ((k10_descip_1 64 B 7) = (k10_descip_1 64 A 64))  &  ( ((k10_descip_1 64 B 8) = (k10_descip_1 64 A 32))  &  ( ((k10_descip_1 64 B 9) = (k10_descip_1 64 A 39))  &  ( ((k10_descip_1 64 B 10) = (k10_descip_1 64 A 7))  &  ( ((k10_descip_1 64 B 11) = (k10_descip_1 64 A 47))  &  ( ((k10_descip_1 64 B 12) = (k10_descip_1 64 A 15))  &  ( ((k10_descip_1 64 B 13) = (k10_descip_1 64 A 55))  &  ( ((k10_descip_1 64 B 14) = (k10_descip_1 64 A 23))  &  ( ((k10_descip_1 64 B 15) = (k10_descip_1 64 A 63))  &  ( ((k10_descip_1 64 B 16) = (k10_descip_1 64 A 31))  &  ( ((k10_descip_1 64 B 17) = (k10_descip_1 64 A 38))  &  ( ((k10_descip_1 64 B 18) = (k10_descip_1 64 A 6))  &  ( ((k10_descip_1 64 B 19) = (k10_descip_1 64 A 46))  &  ( ((k10_descip_1 64 B 20) = (k10_descip_1 64 A 14))  &  ( ((k10_descip_1 64 B 21) = (k10_descip_1 64 A 54))  &  ( ((k10_descip_1 64 B 22) = (k10_descip_1 64 A 22))  &  ( ((k10_descip_1 64 B 23) = (k10_descip_1 64 A 62))  &  ( ((k10_descip_1 64 B 24) = (k10_descip_1 64 A 30))  &  ( ((k10_descip_1 64 B 25) = (k10_descip_1 64 A 37))  &  ( ((k10_descip_1 64 B 26) = (k10_descip_1 64 A 5))  &  ( ((k10_descip_1 64 B 27) = (k10_descip_1 64 A 45))  &  ( ((k10_descip_1 64 B 28) = (k10_descip_1 64 A 13))  &  ( ((k10_descip_1 64 B 29) = (k10_descip_1 64 A 53))  &  ( ((k10_descip_1 64 B 30) = (k10_descip_1 64 A 21))  &  ( ((k10_descip_1 64 B 31) = (k10_descip_1 64 A 61))  &  ( ((k10_descip_1 64 B 32) = (k10_descip_1 64 A 29))  &  ( ((k10_descip_1 64 B 33) = (k10_descip_1 64 A 36))  &  ( ((k10_descip_1 64 B 34) = (k10_descip_1 64 A 4))  &  ( ((k10_descip_1 64 B 35) = (k10_descip_1 64 A 44))  &  ( ((k10_descip_1 64 B 36) = (k10_descip_1 64 A 12))  &  ( ((k10_descip_1 64 B 37) = (k10_descip_1 64 A 52))  &  ( ((k10_descip_1 64 B 38) = (k10_descip_1 64 A 20))  &  ( ((k10_descip_1 64 B 39) = (k10_descip_1 64 A 60))  &  ( ((k10_descip_1 64 B 40) = (k10_descip_1 64 A 28))  &  ( ((k10_descip_1 64 B 41) = (k10_descip_1 64 A 35))  &  ( ((k10_descip_1 64 B 42) = (k10_descip_1 64 A 3))  &  ( ((k10_descip_1 64 B 43) = (k10_descip_1 64 A 43))  &  ( ((k10_descip_1 64 B 44) = (k10_descip_1 64 A 11))  &  ( ((k10_descip_1 64 B 45) = (k10_descip_1 64 A 51))  &  ( ((k10_descip_1 64 B 46) = (k10_descip_1 64 A 19))  &  ( ((k10_descip_1 64 B 47) = (k10_descip_1 64 A 59))  &  ( ((k10_descip_1 64 B 48) = (k10_descip_1 64 A 27))  &  ( ((k10_descip_1 64 B 49) = (k10_descip_1 64 A 34))  &  ( ((k10_descip_1 64 B 50) = (k10_descip_1 64 A 2))  &  ( ((k10_descip_1 64 B 51) = (k10_descip_1 64 A 42))  &  ( ((k10_descip_1 64 B 52) = (k10_descip_1 64 A 10))  &  ( ((k10_descip_1 64 B 53) = (k10_descip_1 64 A 50))  &  ( ((k10_descip_1 64 B 54) = (k10_descip_1 64 A 18))  &  ( ((k10_descip_1 64 B 55) = (k10_descip_1 64 A 58))  &  ( ((k10_descip_1 64 B 56) = (k10_descip_1 64 A 26))  &  ( ((k10_descip_1 64 B 57) = (k10_descip_1 64 A 33))  &  ( ((k10_descip_1 64 B 58) = (k10_descip_1 64 A 1))  &  ( ((k10_descip_1 64 B 59) = (k10_descip_1 64 A 41))  &  ( ((k10_descip_1 64 B 60) = (k10_descip_1 64 A 9))  &  ( ((k10_descip_1 64 B 61) = (k10_descip_1 64 A 49))  &  ( ((k10_descip_1 64 B 62) = (k10_descip_1 64 A 17))  &  ( ((k10_descip_1 64 B 63) = (k10_descip_1 64 A 57))  &  ((k10_descip_1 64 B 64) = (k10_descip_1 64 A 25)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k20_dtconstr A B) = (a_2_2_dtconstr A B)) ) ) ) ) ).
tt(d16_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ((k14_ens_1 A B) = B) ) ) ) ) ).
tt(d16_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k14_e_siec A) = (k2_xboole_0 (k2_xboole_0 (k2_relat_1 (u1_e_siec A)) (u2_e_siec A)) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d16_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k13_facirc_1 A B C) = (k10_facirc_1 A B C k1_facirc_1)) ) ) ) ).
tt(d16_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k16_ff_siec A) = (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A)))) ) ) ).
tt(d16_finseq_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (B = (k18_finseq_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C (k1_relat_1 A)) &  ((r2_hidden D (k1_relat_1 A)) &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ((r1_xxreal_0 1 (k3_finseq_1 E)) &  ( ((k1_funct_1 E 1) = C)  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = D)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) | (r2_hidden (k4_tarski (k1_funct_1 E F) (k1_funct_1 E (k1_nat_1 F 1))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fintopo2 B A) <=>  (B = (k10_fintopo2 A B)) ) ) ) ) ) ).
tt(d16_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_fin_topo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ( (~  (C = k1_xboole_0) )  &  ( (~  (D = k1_xboole_0) )  &  ((r1_xboole_0 C D) & (r1_xboole_0 (k9_fin_topo A C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k13_fomodel0 A B) = B) ) ) ).
tt(d16_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v6_fomodel1 B A) <=> (r2_hidden B (k3_fomodel1 A))) ) ) ) ) ).
tt(d16_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  (! [E:$i] :  ((m2_subset_1 E (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ( ( (? [F:$i] :  ((m1_subset_1 F B) &  (? [G:$i] :  ( ((v4_fomodel1 G A) & (m1_subset_1 G (k1_fomodel1 A)))  &  ( ((k1_funct_1 E 1) = G)  &  ((k1_binop_1 D (k5_fomodel2 C G F) (k1_rfinseq 1 E)) = k8_margrel1) ) ) ) ) )  =>  ((k18_fomodel2 A B C D E) = k8_margrel1) )  &  ( (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ( ((v4_fomodel1 G A) & (m1_subset_1 G (k1_fomodel1 A)))  =>  (~  ( ((k1_funct_1 E 1) = G)  &  ((k1_binop_1 D (k5_fomodel2 C G F) (k1_rfinseq 1 E)) = k8_margrel1) ) ) ) ) ) )  =>  ((k18_fomodel2 A B C D E) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v10_fomodel4 C A B) <=>  (! [D:$i] :  ((v8_fomodel4 D A B C) => (r1_tarski (k1_tarski D) C)) ) ) ) ) ) ) ) ).
tt(d16_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v2_margrel1 D) &  ((v3_margrel1 D (k4_dtconstr (k3_freealg A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))))) ) ) )  =>  ( (D = (k13_freealg A B C))  <=>  ( ((k1_relset_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) D) = (k4_finseq_2 (k7_partfun1 k5_numbers A C) (k4_dtconstr (k3_freealg A B))))  &  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k3_freealg A B))) (k4_dtconstr (k3_freealg A B))) =>  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) D)) =>  ((k1_funct_1 D E) = (k8_trees_4 (u1_struct_0 (k3_freealg A B)) (k4_freealg A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k16_ftacell1 A B C D E) = (k36_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d16_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D)) = k1_xboole_0) )  &  (~  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((k8_functor0 A B C D E F) = (k1_funct_1 (k7_functor0 A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) ) )  =>  ((k16_gate_1 A B C D) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~  ((k16_gate_1 A B C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k16_gate_5 A B C D E F G) = (k10_gate_1 E F (k15_gate_5 A B C D G))) ) ) ) ) ) ) ) ).
tt(d16_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r7_gcd_1 A C D) &  ((r7_gcd_1 A E F) &  ( (D = (k4_gcd_1 A B D))  &  (F = (k4_gcd_1 A B F)) ) ) )  =>  ( ( (C = (k4_struct_0 A))  =>  ((k6_gcd_1 A B C D E F) = E) )  &  ( ( (E = (k4_struct_0 A))  =>  ((k6_gcd_1 A B C D E F) = C) )  &  ( ( ((k5_gcd_1 A B D F) = (k5_struct_0 A))  =>  ((k6_gcd_1 A B C D E F) = (k3_rlvect_1 A (k8_group_1 A C F) (k8_group_1 A D E))) )  &  ( ( ((k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) = (k4_struct_0 A))  =>  ((k6_gcd_1 A B C D E F) = (k4_struct_0 A)) )  &  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  ( (~  ((k5_gcd_1 A B D F) = (k5_struct_0 A)) )  &  ( (~  ((k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) = (k4_struct_0 A)) )  &  (~  ((k6_gcd_1 A B C D E F) = (k1_gcd_1 A (k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) (k5_gcd_1 A B (k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) (k5_gcd_1 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r4_glib_000 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k10_glib_000 A) D) B) & (r2_hidden (k1_funct_1 (k11_glib_000 A) D) C)) ) ) ) ) ) ) ) ).
tt(d16_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k13_glib_001 A B) = (k2_relset_1 (k6_glib_000 A) (k11_glib_001 A B))) ) ) ) ) ).
tt(d16_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r5_glib_005 A B C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (~ (v3_glib_001 C A))  =>  ( (D = (k9_glib_005 A B C))  <=>  ((r2_hidden D (k2_relset_1 k5_numbers (k8_glib_005 A B C))) &  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden E (k2_relset_1 k5_numbers (k8_glib_005 A B C))) => (r1_xxreal_0 D E)) ) ) ) ) )  &  ((v3_glib_001 C A) =>  ( (D = (k9_glib_005 A B C))  <=>  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  ((v2_funct_1 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k10_graph_5 A B C) = (k18_rvsum_1 (k9_graph_5 A B C))) ) ) ) ) ) ) ).
tt(d16_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_graphsp A B C D) <=>  ( ((k4_finseq_1 A) = (k4_finseq_1 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 A)) &  ((r1_xxreal_0 C E) & (r1_xxreal_0 E D)) )  =>  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_grcat_1,ax, (! [A:$i] :  ( ((v2_grcat_1 A) & (l1_grcat_1 A))  =>  (! [B:$i] :  ( ((v2_grcat_1 B) & (l1_grcat_1 B))  =>  ( ((k7_grcat_1 A) = (k8_grcat_1 B))  =>  (! [C:$i] :  ( ((v1_grcat_1 C) &  ((v2_grcat_1 C) & (l1_grcat_1 C)) )  =>  ( (C = (k13_grcat_1 A B))  <=>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l2_algstr_0 E)) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l2_algstr_0 F)) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( ( ((g1_grcat_1 (u1_grcat_1 A) (u2_grcat_1 A) (u3_grcat_1 A)) = (g1_grcat_1 E F G))  &  ((g1_grcat_1 (u1_grcat_1 B) (u2_grcat_1 B) (u3_grcat_1 B)) = (g1_grcat_1 D E H)) )  =>  (C = (g1_grcat_1 D F (k1_partfun1 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 F) H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  ((k14_group_10 A B C) = (a_3_1_group_10 A B C)) ) ) ) ) ) ) ).
tt(d16_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k16_group_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (D = (k14_group_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 (k7_group_9 A B C) (k7_group_9 A B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 (k7_group_9 A B C) (k7_group_9 A B C)))))) )  =>  ( ( (~ (v1_xboole_0 A))  =>  ( (D = (k9_group_9 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 D E) = (a_4_0_group_9 A B C E)) ) ) ) )  &  ((v1_xboole_0 A) =>  ( (D = (k9_group_9 A B C))  <=>  (D = (k2_zfmisc_1 k1_xboole_0 (k1_tarski (k6_partfun1 (k7_group_9 A B C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k16_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k12_idea_1 A (k11_idea_1 A (k13_idea_1 D) B) B)) ) ) ) ) ) ) ) ) ) ).
tt(d16_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (C = (k9_ideal_1 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D A) &  ((v3_ideal_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v13_incsp_1 A) <=>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m5_index_1 E (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) (u1_cat_1 C) (k7_isocat_1 C)) =>  ((m3_cat_2 (k4_cat_5 A B D) C) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  ( (F = (k14_index_1 A B C D E))  <=>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ((r1_funct_2 (u4_struct_0 A) (u4_struct_0 C) (u4_struct_0 A) (u4_struct_0 B) G D) =>  (F = (k13_index_1 A (k10_index_1 C E) (k9_cat_1 A C (k10_index_1 C E) G (k9_index_1 C E (k10_index_1 C E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_integr15 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) => (r1_integra5 B (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 D A)))) ) ) ) ) ) ) ) ) ) ).
tt(d16_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v3_integra1 B A) <=>  ((v1_integra1 B A) &  ((v2_integra1 B A) &  ((k10_integra1 A B) = (k11_integra1 A B)) ) ) ) ) ) ) ) ).
tt(d16_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  ((k15_interva1 A B) = (k2_xtuple_0 B)) ) ) ) ) ).
tt(d16_intpro_1,ax, (k8_intpro_1 = (k7_intpro_1 (k1_subset_1 k1_intpro_1))) ).
tt(d16_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k16_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k21_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d16_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r3_lattice3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r1_lattices A B D)) ) ) ) ) ) ) ) ) ).
tt(d16_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  (! [F:$i] :  ( (F = (k11_lattice5 A B C D E))  <=>  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v5_ordinal1 G)) )  &  ( (F = (k1_ordinal2 G))  &  ( ((k9_xtuple_0 G) = (k1_ordinal1 E))  &  ( ((k1_funct_1 G k1_xboole_0) = C)  &  ( (! [H:$i] :  ((v3_ordinal1 H) =>  ((r2_hidden (k1_ordinal1 H) (k1_ordinal1 E)) =>  ((k1_funct_1 G (k1_ordinal1 H)) = (k6_lattice5 (k8_lattice5 A H) B (k10_lattice5 (k8_lattice5 A H) B (k1_funct_1 G H)) (k9_lattice5 A B C D H))) ) ) )  &  (! [H:$i] :  ((v3_ordinal1 H) =>  ( ((r2_hidden H (k1_ordinal1 E)) & (v4_ordinal1 H))  =>  ( (H = k1_xboole_0)  |  ((k1_funct_1 G H) = (k3_tarski (k2_relset_1 (k10_xtuple_0 G) (k5_relat_1 G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((k6_lattice6 A) = (a_1_1_lattice6 A)) ) ) ).
tt(d16_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v13_lattices A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k5_lattices A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_lattices A B C) = B)  &  ((k2_lattices A C B) = B) ) ) ) ) ) ) ) ) ) ).
tt(d16_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_lexbfs B A) =>  (! [C:$i] :  ((m1_lexbfs C A) =>  ( (C = (k15_lexbfs A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 (k6_glib_000 A) k5_numbers (k5_lexbfs A C D) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A B D)))) ) ) ) ) ) ) ) ) ).
tt(d16_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k9_lpspace1 A B C)) (k14_lpspace1 A B C)) =>  ( (D = (k16_lpspace1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_relset_1 A k1_numbers E (k8_lpspace1 A k6_numbers)) &  ((r2_hidden E (k9_lpspace1 A B C)) &  (D = (k13_lpspace1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v1_ltlaxio1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_hilbert1 k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  ((k3_funct_2 k1_hilbert1 k6_margrel1 (k12_ltlaxio1 B) A) = 1) ) ) ) ) ) ).
tt(d16_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k16_matrix_1 A) = (k3_card_3 (k3_funct_6 A))) ) ) ).
tt(d16_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_matroid0 B A) <=>  ( (~ (v3_pre_topc B A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (v3_pre_topc (k7_subset_1 (u1_struct_0 A) B (k1_tarski C)) A)) ) ) ) ) ) ) ) ) ).
tt(d16_mcart_1,ax, (! [A:$i] :  ((k15_mcart_1 A) = (k1_xtuple_0 (k2_xtuple_0 A))) ) ).
tt(d16_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k19_member_1 A B) = (k11_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d16_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v2_memstr_0 B A) & (l1_memstr_0 B A))  =>  ((k11_memstr_0 A B) = (a_2_0_memstr_0 A B)) ) ) ) ) ).
tt(d16_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc1 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k9_subset_1 A D (k15_mesfunc1 A C (k1_measure6 E))) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((k7_mesfunc5 A B C D) = (k4_supinf_2 (k6_mesfunc5 A B C (k1_mesfunc2 A D)) (k6_mesfunc5 A B C (k2_mesfunc2 A D)))) ) ) ) ) ) ) ) ) ).
tt(d16_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  =>  ( (D = (k11_metric_1 A B C))  <=>  (D = (a_3_2_metric_1 A B C)) ) )  &  ((v2_struct_0 A) =>  ( (D = (k11_metric_1 A B C))  <=> (v1_xboole_0 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_metric_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers)))) )  =>  ( (A = k16_metric_3)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [G:$i] :  ((m1_subset_1 G (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ( ( (F = (k1_domain_1 k1_numbers k1_numbers B D))  &  (G = (k1_domain_1 k1_numbers k1_numbers C E)) )  =>  ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) A F G) = (k7_real_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 B C) (k1_metric_1 k1_numbers k1_numbers k7_metric_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((k14_midsp_1 A) = (k6_midsp_1 A)) ) ) ).
tt(d16_mod_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2))))) )  =>  ( (A = k14_mod_2)  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_enumset1 k6_numbers 1 2)) =>  ((k5_binop_1 (k1_enumset1 k6_numbers 1 2) A B C) = (k12_mod_2 B C)) ) ) ) ) ) ) ) ).
tt(d16_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k7_mod_4 A B C) = C) ) ) ) ) ) ) ).
tt(d16_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((v1_modal_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k3_modal_1) &  (A = (k16_modal_1 B)) ) ) ) ) ) ).
tt(d16_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_1 A) <=>  (? [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k8_modelc_1 B C)) ) ) ) ) ) ) ) ).
tt(d16_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k7_modelc_2 B C)) ) ) ) ) ) ) ) ).
tt(d16_modelc_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ( ((v1_modelc_3 A B) & (l1_modelc_3 A B))  =>  ((k10_modelc_3 A B) = A) )  &  ( (~  ((v1_modelc_3 A B) & (l1_modelc_3 A B)) )  =>  ((k10_modelc_3 A B) = (g1_modelc_3 B (k7_modelc_3 B) (k7_modelc_3 B) (k7_modelc_3 B))) ) ) ) ) ) ).
tt(d16_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v13_monoid_0 A) <=> (v5_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d16_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_msafree C A (k11_msafree A B)) =>  ( (C = (k13_msafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k12_msafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d16_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D A B) =>  (! [E:$i] :  ( ((v3_msualg_1 E A) & (m1_msualg_2 E A B))  =>  ( (E = (k11_msualg_2 A B C D))  <=>  ((r8_pboole (u1_struct_0 A) (u3_msualg_1 A E) (k3_pboole (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D))) &  (! [F:$i] :  ((m3_pboole F (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) F (u3_msualg_1 A E)) =>  ((v3_msualg_2 F A B) & (r8_pboole (u4_struct_0 A) (u4_msualg_1 A E) (k4_msualg_2 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C))) =>  ( (D = (k15_msualg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) E) (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (k4_msualg_4 A B C) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C)) D E) (k14_msualg_4 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m4_nattra_1 C A B) =>  ( (C = (k10_nattra_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m2_cat_1 E A B) &  (? [F:$i] :  ((m2_cat_1 F A B) &  (? [G:$i] :  ((m2_nattra_1 G A B E F) &  ( (D = (k4_tarski (k4_tarski E F) G))  & (r2_nattra_1 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((r12_ncfcont1 A B C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r6_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k2_numbers B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d16_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((k13_net_1 A B) = (k3_tarski (k11_net_1 A B))) ) ) ) ).
tt(d16_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v8_oposet_1 A) <=>  ((v2_necklace A) & (v4_orders_2 A)) ) ) ) ).
tt(d16_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (C = (k12_ordinal2 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_ordinal2 D)) ) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = 1)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k11_ordinal2 A (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k8_ordinal2 (k5_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k12_ordinal6 A B) = (k1_funct_1 (k1_funct_1 (k11_ordinal6 (k1_classes1 (k2_xboole_0 (k2_xboole_0 A B) k4_ordinal1))) A) B)) ) ) ) ) ).
tt(d16_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) =>  ((r2_hidden C (k6_dtconstr (k2_osafree A B))) =>  ((k14_osafree A B C) = (k2_trees_4 (u1_struct_0 (k2_osafree A B)) C)) ) ) ) ) ) ) ) ).
tt(d16_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v11_osalg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) => (r1_tarski (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d16_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B))))) )  =>  ( (C = (k15_osalg_2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  (! [F:$i] :  ( ((v3_msualg_1 F A) &  ((v12_osalg_1 F A) & (m1_msualg_2 F A B)) )  =>  (! [G:$i] :  ( ((v3_msualg_1 G A) &  ((v12_osalg_1 G A) & (m1_msualg_2 G A B)) )  =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k13_osalg_2 A B) C D E) = (k11_msualg_2 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k6_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ((k13_pdiff_1 A B C D E F) = (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k7_pdiff_1 A C F) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) E (k4_pdiff_1 D B))) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r7_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k7_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G D) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B) D)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J D)) (k1_seq_1 I (k9_real_1 J D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pencil_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v13_pencil_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (v1_zfmisc_1 B)) ) ) ) ) ).
tt(d16_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_petri A))) =>  ((k15_petri A B) = B) ) ) ) ) ).
tt(d16_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A (k6_xcmplx_0 B 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 k2_bspace)) =>  ( (E = (k19_polyform A B C D))  <=>  ( ((v1_xboole_0 (k8_polyform A (k6_xcmplx_0 B 1))) =>  (E = (k2_pre_poly k1_xboole_0)) )  &  ( (~ (v1_xboole_0 (k8_polyform A (k6_xcmplx_0 B 1))))  =>  ( ((k3_finseq_1 E) = (k11_polyform A B))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k11_polyform A B)))  =>  ((k1_funct_1 E F) = (k8_group_1 k2_bspace (k3_bspace D (k15_polyform A B F)) (k16_polyform A B C (k15_polyform A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pralg_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_pralg_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k1_funct_1 A B) = D)  &  ((k1_funct_1 A C) = E) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ( (~ (v1_xboole_0 H))  =>  (! [I:$i] :  ( (~ (v1_xboole_0 I))  =>  ( ( ((k9_xtuple_0 D) = (k4_finseq_2 F H))  &  ((k9_xtuple_0 E) = (k4_finseq_2 G I)) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ( (~ (v1_xboole_0 J))  &  ((v2_margrel1 J) &  ((v3_margrel1 J H) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 H) H)))) ) ) )  =>  (! [K:$i] :  ( ((v1_funct_1 K) &  ( (~ (v1_xboole_0 K))  &  ((v2_margrel1 K) &  ((v3_margrel1 K I) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 I) I)))) ) ) )  =>  ( ( (D = J)  &  (E = K) )  =>  ((k19_margrel1 J) = (k19_margrel1 K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k15_pre_poly A)) =>  ( (C = (k20_pre_poly A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A)))) )  &  ( (C = (k7_pre_poly (k15_pre_poly A) D (k17_pre_poly A)))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E D) <=> (r3_pre_poly A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k15_pscomp_1 A) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)) A)) ) ) ).
tt(d16_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  ((r7_pua2mss1 A B) <=>  (? [C:$i] :  ((l3_msualg_1 C B) &  (? [D:$i] :  ((m2_pua2mss1 D (u4_struct_0 B)) & (r6_pua2mss1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d16_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k14_qc_lang1 A B C) = (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 (k4_tarski 2 k6_numbers)) (k11_qc_lang1 A B)) (k11_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(d16_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k12_qc_lang2 A B) = (k19_qc_lang1 A (k18_qc_lang1 A B))) ) ) ) ) ).
tt(d16_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_quantal1 A B C) = (k15_lattice3 A (a_3_7_quantal1 A B C))) ) ) ) ) ) ) ).
tt(d16_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ( ((r2_hidden A k2_numbers) =>  ( (B = (k16_quaterni A))  <=>  (B = k6_numbers) ) )  &  ( (~ (r2_hidden A k2_numbers))  =>  ( (B = (k16_quaterni A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 4 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 4 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_seq_1 C 3)) ) ) ) ) ) ) ) ) ) ).
tt(d16_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k19_quofield A) = (g6_algstr_0 (k7_quofield A) (k15_quofield A) (k16_quofield A) (k12_quofield A) (k11_quofield A))) ) ) ).
tt(d16_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  ((k10_ratfunc1 A B C) = (k3_ratfunc1 A (k11_polynom3 A (k4_ratfunc1 A B) (k4_ratfunc1 A C)) (k11_polynom3 A (k5_ratfunc1 A B) (k5_ratfunc1 A C)))) ) ) ) ) ) ) ).
tt(d16_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k9_relat_1 A B) = (k7_relat_1 A (k1_tarski B))) ) ) ) ).
tt(d16_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_relat_2 A) <=> (r8_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d16_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_rewrite1 A) <=>  (! [B:$i] :  (~  ((r1_tarski B (k1_relat_1 A)) &  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  (~  ((r2_hidden D B) &  ( (~  (C = D) )  & (r2_hidden (k4_tarski C D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( (B = (k9_ringcat1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((r2_hidden D A) & (r2_ringcat1 D C)) ) ) ) ) ) ) ) ).
tt(d16_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((k13_rlvect_2 A B) = B) ) ) ) ) ).
tt(d16_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k11_robbins1 A B) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) B))) ) ) ) ) ).
tt(d16_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k22_rvsum_1 A B) = (k18_rvsum_1 (k14_rvsum_1 A B))) ) ) ) ) ).
tt(d16_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  ( ((r1_xxreal_0 (k4_xtuple_0 A) 8) =>  ( (C = (k11_scmfsa_1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k3_scm_inst) &  (? [E:$i] :  ((m1_subset_1 E (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) &  ( (A = D)  &  ( (E = (k11_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1) B k1_ami_2))  &  (C = (k1_funct_4 B (k8_ami_2 D E))) ) ) ) ) ) ) ) )  &  ( ( ((k4_xtuple_0 A) = 9)  =>  ( (C = (k11_scmfsa_1 A B))  <=>  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (E = (k1_int_2 (k1_funct_1 B (k4_scmfsa_i A))))  &  ( (D = (k7_partfun1 k4_numbers (k9_scmfsa_1 B (k5_scmfsa_i A)) E))  &  (C = (k6_scmfsa_1 (k7_scmfsa_1 B (k3_scmfsa_i A) D) (k4_card_1 (k10_scmfsa_1 B)))) ) ) ) ) ) ) ) )  &  ( ( ((k4_xtuple_0 A) = 10)  =>  ( (C = (k11_scmfsa_1 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (E = (k1_int_2 (k1_funct_1 B (k4_scmfsa_i A))))  &  ( (D = (k2_funct_7 (k9_scmfsa_1 B (k5_scmfsa_i A)) E (k1_funct_1 B (k3_scmfsa_i A))))  &  (C = (k6_scmfsa_1 (k8_scmfsa_1 B (k5_scmfsa_i A) D) (k4_card_1 (k10_scmfsa_1 B)))) ) ) ) ) ) ) ) )  &  ( ( ((k4_xtuple_0 A) = 11)  =>  ( (C = (k11_scmfsa_1 A B))  <=>  (C = (k6_scmfsa_1 (k7_scmfsa_1 B (k7_scmfsa_i A) (k3_finseq_1 (k9_scmfsa_1 B (k8_scmfsa_i A)))) (k4_card_1 (k10_scmfsa_1 B)))) ) )  &  ( ( ((k4_xtuple_0 A) = 12)  =>  ( (C = (k11_scmfsa_1 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (E = (k1_int_2 (k1_funct_1 B (k7_scmfsa_i A))))  &  ( (D = (k5_finseq_2 k5_numbers E k6_numbers))  &  (C = (k6_scmfsa_1 (k8_scmfsa_1 B (k8_scmfsa_i A) D) (k4_card_1 (k10_scmfsa_1 B)))) ) ) ) ) ) ) ) )  &  ( ( ((k4_xtuple_0 A) = 13)  =>  ( (C = (k11_scmfsa_1 A B))  <=>  (? [D:$i] :  ((v1_int_1 D) &  ( (D = 1)  &  (C = (k6_scmfsa_1 (k7_scmfsa_1 B (k6_scmfsa_i A) D) (k4_card_1 (k10_scmfsa_1 B)))) ) ) ) ) )  &  (~  ( (~ (r1_xxreal_0 (k4_xtuple_0 A) 8))  &  ( (~  ((k4_xtuple_0 A) = 9) )  &  ( (~  ((k4_xtuple_0 A) = 10) )  &  ( (~  ((k4_xtuple_0 A) = 11) )  &  ( (~  ((k4_xtuple_0 A) = 12) )  &  ( (~  ((k4_xtuple_0 A) = 13) )  &  (~  ( (C = (k11_scmfsa_1 A B))  <=>  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k14_scmfsa_2 A B C) = (k3_xtuple_0 9 k1_xboole_0 (k11_finseq_1 A C B))) ) ) ) ) ) ) ).
tt(d16_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k15_scmpds_2 A B C D) = (k3_xtuple_0 12 k1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d16_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_eqrel_1 B (k3_tarski A)) =>  ((v7_scmyciel B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ((v4_scmyciel (k7_scmyciel A C)) &  ((v5_scmyciel (k7_scmyciel A C)) & (m1_subset_1 (k7_scmyciel A C) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ).
tt(d16_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k23_seq_4 A B C) = (a_3_0_seq_4 A B C)) ) ) ) ) ) ) ).
tt(d16_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_sheffer1 A B) = (k5_sheffer1 A B B)) ) ) ) ) ).
tt(d16_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v1_pre_topc D) &  ((v7_simplex0 D A B) & (m2_simplex0 D A B)) )  =>  ( (D = (k7_simplex0 A B C))  <=>  ((k2_struct_0 D) = C) ) ) ) ) ) ) ) ) ).
tt(d16_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k16_sin_cos)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 A B) = (k4_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 B k7_complex1))))) ) ) ) ) ) ).
tt(d16_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A)))) =>  ( (B = (k10_stacks_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u4_struct_0 A) (u4_struct_0 A) C D) B) <=> (r2_stacks_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d16_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k7_struct_0 A) = (k1_card_1 (u1_struct_0 A))) ) ) ).
tt(d16_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((v1_substut1 B A) <=>  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k13_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) (k1_substut1 A)))) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_substut1 A)) => (r2_hidden (k4_tarski (k7_finseq_1 (k12_finseq_1 (k8_qc_lang1 A C) D) E) F) B)) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) => (r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))) (k1_substut1 A) (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) C) B)) )  &  ( (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) (k1_substut1 A) C D) B) => (r2_hidden (k4_tarski (k7_finseq_1 (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) C) D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) =>  ( ((r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) (k1_substut1 A) C E) B) & (r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) (k1_substut1 A) D E) B))  => (r2_hidden (k4_tarski (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) C) D) E) B)) ) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) =>  ((r2_hidden (k4_tarski D (k1_funct_1 (k15_substut1 A) (k4_tarski (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) C)) D) E))) B) => (r2_hidden (k4_tarski (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) C)) D) E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_supinf_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_supinf_2 A) <=> (v5_supinf_2 (k10_xtuple_0 A))) ) ) ).
tt(d16_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_4 B A) <=>  ((v2_tdlat_3 B) &  (! [C:$i] :  ((m1_pre_topc C A) =>  ( ((v2_tdlat_3 C) & (r1_tarski (u1_struct_0 B) (u1_struct_0 C)))  =>  ((u1_struct_0 B) = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(d16_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k12_trees_3 A) = (k11_trees_3 (k9_finseq_1 A))) ) ) ).
tt(d16_turing_1,ax, (k15_turing_1 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k12_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) k6_numbers) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 2 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 3 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 1 (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 4 k6_numbers k6_numbers)))) ).
tt(d16_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k17_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k10_margrel1 (k10_margrel1 B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d16_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A))))) )  =>  ( (B = (k11_unialg_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k9_unialg_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_unialg_2 A)) =>  (! [E:$i] :  ( ((v1_unialg_1 E) & (m1_unialg_2 E A))  =>  (! [F:$i] :  ( ((v1_unialg_1 F) & (m1_unialg_2 F A))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k9_unialg_2 A) B C D) = (k5_unialg_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(d16_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k10_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ) ) ).
tt(d16_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  ((v10_vectsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k4_vectsp_1 A B (k6_algstr_0 A C D) E) = (k4_vectsp_1 A B C (k4_vectsp_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k4_waybel_0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_orders_2 A E D) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k2_waybel_1 A B C) = (k6_relset_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k1_yellow_2 A B C)) C)) ) ) ) ) ) ) ).
tt(d16_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_waybel34 C A B) <=> (r4_waybel_0 A B C (k1_struct_0 A))) ) ) ) ) ) ) ).
tt(d16_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ( (C = (k11_waybel_4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A D (k1_yellow_0 A B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) C D) = (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A D) B)) )  &  ( (~ (r3_orders_2 A D (k1_yellow_0 A B)))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) C D) = (k5_waybel_0 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d16_xtuple_0,ax, (! [A:$i] :  ((k13_xtuple_0 A) = (k9_xtuple_0 (k11_xtuple_0 A))) ) ).
tt(d16_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v5_yellow_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (u1_struct_0 B)) &  ((r2_hidden D (u1_struct_0 B)) & (r2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D))) )  => (r2_hidden (k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(d16_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((v3_yellow_6 B A) <=>  (~  ((k10_yellow_6 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d16_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k10_zf_lang A B) = (k6_zf_lang (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)))) ) ) ) ) ).
tt(d16_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k8_zmodul01 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_zmodul01 C) & (m1_zmodul01 C A)) ) ) ) ) ) ) ).
tt(d17_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l2_abcmiz_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((k5_abcmiz_0 A B C) = (k1_yellow_0 A (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A C) (k5_waybel_0 A B)))) ) ) ) ) ) ) ).
tt(d17_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k16_abcmiz_1 A) = k9_abcmiz_1) ) ) ).
tt(d17_abcmiz_a,ax, (k15_abcmiz_a = (k40_abcmiz_1 k27_abcmiz_1 (k1_subset_1 (k38_abcmiz_1 k27_abcmiz_1)) (k12_abcmiz_a k27_abcmiz_1 (k14_abcmiz_a k8_abcmiz_a)))) ).
tt(d17_algstr_4,ax, (! [A:$i] :  ((k14_algstr_4 A) = (g3_algstr_0 (k12_algstr_4 A) (k13_algstr_4 A))) ) ).
tt(d17_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_altcat_1 A B B)) =>  ( (C = (k8_altcat_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B D)) =>  ((k5_altcat_1 A B B D C E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v4_aofa_000 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_aofa_000 A B C) = (k1_funct_1 (k2_pua2mss1 A (k1_funct_7 2 (k4_finseq_1 (u1_unialg_1 A)))) (k2_finseq_4 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(d17_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ((m1_aofa_000 D A (k9_funct_2 B k4_numbers) C) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r1_aofa_i00 A E B C D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 B k4_numbers) k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) k4_numbers)))) )  =>  ((m3_aofa_i00 E A B C D) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 B k4_numbers) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) B)))) )  & (r2_aofa_i00 A B C D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  (! [D:$i] :  ((r4_armstrng A B C D) <=> (r2_hidden (k4_tarski C D) (k8_armstrng A B))) ) ) ) ) ) ).
tt(d17_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v7_asympt_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 2 B) => (r2_asympt_0 A B)) ) ) ) ) ) ).
tt(d17_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((v1_wellfnd1 A) & (r1_tarski B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k15_bagorder A B))  <=>  ((r2_hidden C B) & (r4_waybel_4 B C (u1_orders_2 A))) ) ) ) ) ) ) ) ) ).
tt(d17_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  ((k7_bcialg_1 A B) = (a_2_0_bcialg_1 A B)) ) ) ) ) ).
tt(d17_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))))) )  =>  ( (C = (k7_bcialg_2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k8_eqrel_1 (u1_struct_0 A) B)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)) (k8_eqrel_1 (u1_struct_0 A) B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (D = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B F))  &  (E = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B G)) )  =>  ((k5_binop_1 (k8_eqrel_1 (u1_struct_0 A) B) C D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k1_bcialg_1 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ((k12_bilinear A B C) = (a_3_0_bilinear A B C)) ) ) ) ) ) ) ).
tt(d17_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r2_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A C D B) = D) ) ) ) ) ) ) ) ) ) ).
tt(d17_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers)))) )  =>  ( (A = k41_binop_2)  <=>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ((k1_binop_1 A B C) = (k17_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d17_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((r1_borsuk_1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (v3_borsuk_1 C A B)) ) ) ) ) ) ) ).
tt(d17_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k17_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ( (? [F:$i] :  ((m1_subset_1 F A) &  ((r2_hidden F (k15_bvfunc_1 A E C)) &  ((k3_funct_2 A k6_margrel1 B F) = k8_margrel1) ) ) )  =>  ((k3_funct_2 A k6_margrel1 D E) = k8_margrel1) )  &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ((r2_hidden F (k15_bvfunc_1 A E C)) &  ((k3_funct_2 A k6_margrel1 B F) = k8_margrel1) ) ) ) )  =>  ((k3_funct_2 A k6_margrel1 D E) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k6_c0sp1 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_c0sp1 A) k1_numbers)))) )  =>  ( (B = (k10_c0sp1 A))  <=>  (! [C:$i] :  ((r2_hidden C (k6_c0sp1 A)) =>  ((k1_seq_1 B C) = (k4_seq_4 (k9_c0sp1 A (k8_c0sp1 A C)))) ) ) ) ) ) ) ) ).
tt(d17_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_funct_1 C B) & (v1_partfun1 C A)) ) ) )  =>  ((k13_card_3 A B C) = C) ) ) ) ) ) ).
tt(d17_card_fil,ax, (! [A:$i] :  ( ((v1_card_1 A) &  (~ (v2_card_1 A)) )  =>  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k6_card_fil A))  <=>  (A = (k2_card_1 B)) ) ) ) ) ) ).
tt(d17_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 D A B C) =>  (! [E:$i] :  ((m1_cat_1 E A C B) =>  ( (E = (k6_cat_1 A B C D))  <=>  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) )  =>  ((r3_cat_3 A B C D) <=>  ((m2_cat_3 D A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_cat_3 F A E C) =>  (~  ((r2_funct_2 C (u1_struct_0 A) (k2_cat_3 A C D) (k2_cat_3 A C F)) &  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (~  ((r2_hidden G (k2_cat_1 A B E)) &  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ((r2_hidden H (k2_cat_1 A B E)) =>  ( (! [I:$i] :  ((r2_hidden I C) =>  ((k1_cat_1 A (k7_partfun1 (u4_struct_0 A) D I) H) = (k7_partfun1 (u4_struct_0 A) F I)) ) )  <=>  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k16_cat_4 A B C D) = (k9_cat_4 A B (k2_cat_4 A C D) (k2_cat_4 A (k2_cat_4 A B C) D) (k5_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B C) B (k7_cat_4 A (k2_cat_4 A B C) D) (k7_cat_4 A B C)) (k9_cat_4 A C D (k2_cat_4 A (k2_cat_4 A B C) D) (k5_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B C) C (k7_cat_4 A (k2_cat_4 A B C) D) (k8_cat_4 A B C)) (k8_cat_4 A (k2_cat_4 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(d17_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r7_circtrm1 A C B D E F) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v2_funct_1 G)) )  =>  ((m2_circtrm1 G A B C D E F) <=>  ((r3_circtrm1 (k1_circtrm1 A B D) E G) &  (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  & (r4_circtrm1 (k1_circtrm1 A B D) E G H (k6_circtrm1 A B D C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k7_cohsp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  (? [E:$i] :  ( (C = (k4_tarski D E))  &  ((r2_hidden D (k9_xtuple_0 A)) &  ((r2_hidden E (k1_funct_1 A D)) &  (! [F:$i] :  ( ((r2_hidden F (k9_xtuple_0 A)) &  ((r1_tarski F D) & (r2_hidden E (k1_funct_1 A F))) )  =>  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_coh_sp,ax, (! [A:$i] :  ((k15_coh_sp A) = (k3_tarski (a_1_3_coh_sp A))) ) ).
tt(d17_comput_1,ax, (k10_comput_1 = (k2_xboole_0 (k2_tarski (k3_comput_1 k6_numbers k6_numbers) (k4_comput_1 1 1)) a_0_1_comput_1)) ).
tt(d17_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k7_conlat_1 A) = (a_1_0_conlat_1 A)) ) ) ).
tt(d17_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((k15_convex4 A) = (g1_clvect_1 (k10_convex4 A) (k12_convex4 A (k2_convex4 A)) (k13_convex4 A) (k14_convex4 A))) ) ) ).
tt(d17_csspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k11_csspace k11_csspace) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k11_csspace k11_csspace) k2_numbers)))) )  =>  ( (A = k17_csspace)  <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B k11_csspace) & (r2_hidden C k11_csspace))  =>  ((k1_binop_1 A B C) = (k11_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace B) (k2_comseq_2 k5_numbers (k2_csspace C))))) ) ) ) ) ) ) ).
tt(d17_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k12_decomp_1 A) = (a_1_6_decomp_1 A)) ) ) ).
tt(d17_descip_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) )  =>  ( (A = k28_descip_1)  <=>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k3_funct_2 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) A B) = (k27_descip_1 B)) ) ) ) ) ) ).
tt(d17_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k11_ens_1 A))) =>  ((k15_ens_1 A B) = B) ) ) ) ) ).
tt(d17_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k15_e_siec A) = (k2_xboole_0 (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u2_e_siec A)))))) ) ) ).
tt(d17_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k14_facirc_1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k3_facirc_1 (k10_finseq_1 A B)) (k5_circcomb k3_facirc_1 (k10_finseq_1 B C))) (k5_circcomb k3_facirc_1 (k10_finseq_1 C A)))) ) ) ) ).
tt(d17_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k17_ff_siec A) = (k2_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k4_relat_1 (u4_struct_0 A)))) ) ) ).
tt(d17_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (A = B)  <=>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d17_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_fintopo2 B A) <=>  (B = (k9_fintopo2 A B)) ) ) ) ) ) ).
tt(d17_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k14_fomodel0 A B) = (k6_subset_1 A B)) ) ) ).
tt(d17_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v7_fomodel1 B A) <=> (r2_hidden B (k4_fomodel1 A))) ) ) ) ) ).
tt(d17_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_rfunct_3 C (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  ( (D = (k19_fomodel2 A B C))  <=>  ( (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) D)) <=>  (? [G:$i] :  ( ((v4_fomodel1 G A) & (m1_subset_1 G (k1_fomodel1 A)))  &  (? [H:$i] :  ((m2_subset_1 H (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) E H) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) C)) &  (F = (k7_finseq_1 (k12_finseq_1 (k1_fomodel1 A) G) H)) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) D)) =>  ((k1_binop_1 D E F) = (k18_fomodel2 A B E C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k22_fomodel3 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k37_fomodel1 A))  &  (! [F:$i] :  ((m2_subset_1 F (k15_fomodel1 A) (k37_fomodel1 A)) =>  ((k1_funct_1 E F) = (k20_fomodel3 A B F C (k4_fomodel2 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) =>  (! [C:$i] :  ((m2_finseq_1 C (k4_partfun1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))) =>  ( (C = (k14_freealg A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k13_freealg A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k17_ftacell1 A B C D E) = (k21_gfacirc1 (k36_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d17_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B C C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 B C C)) =>  (! [E:$i] :  ( ((v9_functor0 E A B) & (l2_functor0 E A B))  =>  ( (E = (k9_functor0 A B C D))  <=>  ((r8_pboole (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_functor0 A B E) (k7_funcop_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k4_tarski C C))) &  ((u2_functor0 A B E) = (a_4_0_functor0 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  (~  ((k17_gate_1 A B C D) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) & (v1_xboole_0 D)) ) ) )  =>  ((k17_gate_1 A B C D) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d17_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k17_gate_5 A B C D E F G) = (k9_gate_1 (k2_gate_1 E F) (k2_gate_1 (k3_gate_1 E F) (k2_gate_1 C D)) (k8_gate_1 (k3_gate_1 E F) (k3_gate_1 C D) (k11_gate_1 A B G)))) ) ) ) ) ) ) ) ).
tt(d17_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r7_gcd_1 A C D) &  ((r7_gcd_1 A E F) &  ( (D = (k4_gcd_1 A B D))  &  (F = (k4_gcd_1 A B F)) ) ) )  =>  ( ( (C = (k4_struct_0 A))  =>  ((k7_gcd_1 A B C D E F) = F) )  &  ( ( (E = (k4_struct_0 A))  =>  ((k7_gcd_1 A B C D E F) = D) )  &  ( ( ((k5_gcd_1 A B D F) = (k5_struct_0 A))  =>  ((k7_gcd_1 A B C D E F) = (k8_group_1 A D F)) )  &  ( ( ((k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) = (k4_struct_0 A))  =>  ((k7_gcd_1 A B C D E F) = (k5_struct_0 A)) )  &  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  ( (~  ((k5_gcd_1 A B D F) = (k5_struct_0 A)) )  &  ( (~  ((k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) = (k4_struct_0 A)) )  &  (~  ((k7_gcd_1 A B C D E F) = (k1_gcd_1 A (k8_group_1 A D (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k5_gcd_1 A B (k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) (k5_gcd_1 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k17_gfacirc1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k3_gfacirc1 (k10_finseq_1 A B)) (k5_circcomb k3_twoscomp (k10_finseq_1 B C))) (k5_circcomb k2_twoscomp (k10_finseq_1 C A)))) ) ) ) ).
tt(d17_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v2_glib_000 A) <=>  ((v1_finset_1 (k6_glib_000 A)) & (v1_finset_1 (k7_glib_000 A))) ) ) ) ).
tt(d17_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k14_glib_001 A B) = (k2_relset_1 (k7_glib_000 A) (k12_glib_001 A B))) ) ) ) ) ).
tt(d17_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_004 B A) =>  ( (B = (k16_glib_004 A))  <=>  ( ((k15_glib_004 A B k6_numbers) = (k13_glib_004 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k15_glib_004 A B (k1_nat_1 C 1)) = (k14_glib_004 A (k15_glib_004 A B C))) ) ) ) ) ) ) ) ) ).
tt(d17_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ((r5_glib_005 A B C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k7_glib_000 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (k7_glib_000 A)) & (v4_valued_0 D)) ) ) )  =>  ( (D = (k10_glib_005 A B C))  <=>  ( (! [E:$i] :  ((r2_hidden E (k7_glib_000 A)) =>  ((r2_hidden E (k14_glib_001 A C)) |  ((k1_funct_1 D E) = (k1_funct_1 B E)) ) ) )  &  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) E))  =>  ( ((r2_glib_000 A (k1_funct_1 C E) (k1_funct_1 C (k1_nat_1 E 2)) (k1_funct_1 C (k1_nat_1 E 1))) =>  ((k1_funct_1 D (k1_funct_1 C (k1_nat_1 E 1))) = (k2_xcmplx_0 (k1_funct_1 B (k1_funct_1 C (k1_nat_1 E 1))) (k9_glib_005 A B C))) )  &  ( (~ (r2_glib_000 A (k1_funct_1 C E) (k1_funct_1 C (k1_nat_1 E 2)) (k1_funct_1 C (k1_nat_1 E 1))))  =>  ((k1_funct_1 D (k1_funct_1 C (k1_nat_1 E 1))) = (k6_xcmplx_0 (k1_funct_1 B (k1_funct_1 C (k1_nat_1 E 1))) (k9_glib_005 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r7_graph_5 A B C D E) <=>  ((r1_graph_5 A D B C) &  (! [F:$i] :  ( ((v7_graph_1 F A) & (m2_graph_1 F A))  =>  ((r1_graph_5 A F B C) => (r1_xxreal_0 (k10_graph_5 A D E) (k10_graph_5 A F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_graphsp,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r3_graphsp A B C D) <=>  ( ((k1_seq_1 A (k3_finseq_1 A)) = C)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 A) E) |  ((k1_seq_1 A (k9_real_1 (k3_finseq_1 A) E)) = (k1_seq_1 B (k2_nat_1 D (k7_partfun1 k5_numbers A (k7_real_1 (k9_real_1 (k3_finseq_1 A) E) 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((v2_group_10 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  ((k7_struct_0 B) = (k1_newton A C)) ) ) ) ) ) ) ) ).
tt(d17_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k17_group_2 A B) = (k1_card_1 (k15_group_2 A B))) ) ) ) ) ).
tt(d17_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  ((k10_group_9 A B C) = (g1_group_9 A (k7_group_9 A B C) (k8_group_9 A B C) (k9_group_9 A B C))) ) ) ) ) ) ).
tt(d17_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (l1_rlvect_1 B))  =>  ( (B = (k10_hahnban1 A))  <=>  ( ((g2_algstr_0 (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B)) = (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A)))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_binop_1 (u1_rlvect_1 B) C D) = (k4_vectsp_1 k1_complfld A (k1_hahnban1 C k6_numbers) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_matrix_1 D k5_numbers B 6) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( (E = (k17_idea_1 A B C D))  <=>  ( ((k3_finseq_1 E) = A)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k15_idea_1 C (k8_matrix_1 k5_numbers D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  ((v14_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  ( ((r1_incsp_1 A B C) & (r3_incsp_1 A C D))  => (r2_incsp_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d17_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  ( (F = (k15_index_1 A B C D E))  <=>  (! [G:$i] :  ((m4_index_1 G (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [H:$i] :  ((m2_cat_1 H G D) =>  ( ( (G = C)  & (r1_funct_2 (u4_struct_0 G) (u4_struct_0 D) (u4_struct_0 C) (u4_struct_0 D) H E))  =>  (F = (k13_index_1 A D (k9_cat_1 A G D (k9_index_1 A B G) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (D = (k11_integr15 A B C))  <=>  ( ((k4_finseq_1 D) = (k2_finseq_1 A))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_seq_1 D E) = (k2_integra5 B (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k12_integra1 A B) = (k10_integra1 A B)) ) ) ) ) ).
tt(d17_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((r2_interva1 A B C) <=>  ( ((k14_interva1 A B) = (k14_interva1 A C))  &  ((k15_interva1 A B) = (k15_interva1 A C)) ) ) ) ) ) ) ) ) ).
tt(d17_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r4_lattice3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r1_lattices A D B)) ) ) ) ) ) ) ) ) ).
tt(d17_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((k13_lattice5 A B C) = (k8_lattice5 A (k7_lattice5 A B C))) ) ) ) ) ) ) ).
tt(d17_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v14_lattices A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k6_lattices A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_lattices A B C) = B)  &  ((k1_lattices A C B) = B) ) ) ) ) ) ) ) ) ) ).
tt(d17_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_lexbfs B A) =>  ( (B = (k16_lexbfs A))  <=>  ( ((k13_lexbfs A B k6_numbers) = (k9_lexbfs A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k13_lexbfs A B (k1_nat_1 C 1)) = (k12_lexbfs A (k13_lexbfs A B C))) ) ) ) ) ) ) ) ) ).
tt(d17_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k7_lmod_7 A B C) (k7_lmod_7 A B C)) (k7_lmod_7 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_lmod_7 A B C) (k7_lmod_7 A B C)) (k7_lmod_7 A B C))))) )  =>  ( (D = (k12_lmod_7 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k7_lmod_7 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k7_lmod_7 A B C)) =>  ((k5_binop_1 (k7_lmod_7 A B C) D E F) = (k10_lmod_7 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers (k14_lpspace1 A B C)) (k14_lpspace1 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k14_lpspace1 A B C)) (k14_lpspace1 A B C))))) )  =>  ( (D = (k17_lpspace1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k9_lpspace1 A B C)) (k14_lpspace1 A B C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_hidden G F) =>  ((k2_binop_1 k1_numbers (k14_lpspace1 A B C) (k14_lpspace1 A B C) D E F) = (k13_lpspace1 A B C (k26_valued_1 A k1_numbers G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_ltlaxio1,ax, (! [A:$i] :  ((v2_ltlaxio1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ( ((v1_ltlaxio1 B) => (r2_hidden B A))  &  ((r2_hidden (k3_hilbert1 (k1_ltlaxio1 (k2_ltlaxio1 B)) (k2_ltlaxio1 (k1_ltlaxio1 B))) A) &  ((r2_hidden (k3_hilbert1 (k2_ltlaxio1 (k1_ltlaxio1 B)) (k1_ltlaxio1 (k2_ltlaxio1 B))) A) &  ((r2_hidden (k3_hilbert1 (k2_ltlaxio1 (k3_hilbert1 B C)) (k3_hilbert1 (k2_ltlaxio1 B) (k2_ltlaxio1 C))) A) &  ((r2_hidden (k3_hilbert1 (k6_ltlaxio1 B) (k4_ltlaxio1 B (k2_ltlaxio1 (k6_ltlaxio1 B)))) A) &  ((r2_hidden (k3_hilbert1 (k4_hilbert1 B C) (k5_ltlaxio1 (k2_ltlaxio1 C) (k2_ltlaxio1 (k4_ltlaxio1 B (k4_hilbert1 B C))))) A) &  ((r2_hidden (k3_hilbert1 (k5_ltlaxio1 (k2_ltlaxio1 C) (k2_ltlaxio1 (k4_ltlaxio1 B (k4_hilbert1 B C)))) (k4_hilbert1 B C)) A) & (r2_hidden (k3_hilbert1 (k4_hilbert1 B C) (k2_ltlaxio1 (k7_ltlaxio1 C))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_mcart_1,ax, (! [A:$i] :  ((k16_mcart_1 A) = (k2_xtuple_0 (k2_xtuple_0 A))) ) ).
tt(d17_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k20_member_1 A B) = (k10_member_1 A (k1_tarski B))) ) ) ) ) ).
tt(d17_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 A B) (k11_memstr_0 A B)))))  =>  ((v6_memstr_0 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((v4_memstr_0 D A B) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) & (v5_funct_1 E (k2_memstr_0 A B))) ) )  =>  ( (E = (k1_funct_1 C D))  => (v4_memstr_0 E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc5 A B C D) <=>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( (E = (k1_relset_1 A D))  & (r1_mesfunc1 A B D E)) ) )  &  ( (~ (r1_xxreal_0 k1_supinf_1 (k6_mesfunc5 A B C (k1_mesfunc2 A D))))  &  (~ (r1_xxreal_0 k1_supinf_1 (k6_mesfunc5 A B C (k2_mesfunc2 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_metric_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((v10_metric_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~  (C = D) )  & (r1_xxreal_0 (k1_metric_1 A A B C D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((k15_midsp_1 A) = (g2_algstr_0 (k10_midsp_1 A) (k12_midsp_1 A) (k14_midsp_1 A))) ) ) ).
tt(d17_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E B) &  ((v9_vectsp_1 E B) &  ((v10_vectsp_1 E B) &  ((v11_vectsp_1 E B) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E B)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ((m1_mod_4 F A B C D E) <=>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) F (k3_rlvect_1 D G H)) = (k3_rlvect_1 E (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) F G) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) F H))) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) F (k4_vectsp_1 A D G H)) = (k4_vectsp_1 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C G) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((v2_modal_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k6_modal_1) &  (A = (k10_modal_1 B)) ) ) ) ) ) ).
tt(d17_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_1 A) <=>  (? [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  &  (A = (k9_modelc_1 B)) ) ) ) ) ) ).
tt(d17_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_modelc_2 A) <=>  (? [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k8_modelc_2 B C)) ) ) ) ) ) ) ) ).
tt(d17_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k11_modelc_3 A) = (g1_modelc_3 A (k7_modelc_3 A) (k7_modelc_3 A) (k8_modelc_3 A))) ) ) ).
tt(d17_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v14_monoid_0 A) <=> (v6_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d17_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k12_msafree A B C) (k1_funct_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k12_msafree A B C) (k1_funct_1 B C))))) )  =>  ( (D = (k14_msafree A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_msafree A B))) =>  ((r2_hidden (k2_trees_4 (u1_struct_0 (k5_msafree A B)) E) (k12_msafree A B C)) =>  ((k1_funct_1 D (k2_trees_4 (u1_struct_0 (k5_msafree A B)) E)) = (k1_xtuple_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) & (m1_msualg_2 D A B))  =>  ( (D = (k12_msualg_2 A B C))  <=>  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A D)) &  (! [E:$i] :  ((m1_msualg_2 E A B) =>  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A E)) => (m1_msualg_2 D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v3_relat_2 F) &  ((v8_relat_2 F) &  ((v1_partfun1 F (k1_funct_1 (u3_msualg_1 A B) E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) E))))) ) )  =>  ( (F = (k16_msualg_4 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((r2_hidden (k4_tarski G H) F) <=>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) G) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  ( (C = (k11_nattra_1 A B))  <=>  ( ((u1_struct_0 C) = (k4_cat_2 A B))  &  ( ((u4_struct_0 C) = (k10_nattra_1 A B))  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  ( ((k3_graph_1 C D) = (k1_xtuple_0 (k1_xtuple_0 D)))  &  ((k4_graph_1 C D) = (k2_xtuple_0 (k1_xtuple_0 D))) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  ( ((k3_graph_1 C E) = (k4_graph_1 C D))  => (r2_hidden (k10_cat_2 C C E D) (k9_xtuple_0 (u1_cat_1 C)))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (~  ((r2_hidden (k10_cat_2 C C E D) (k9_xtuple_0 (u1_cat_1 C))) &  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_cat_1 G A B) =>  (! [H:$i] :  ((m2_cat_1 H A B) =>  (! [I:$i] :  ((m2_nattra_1 I A B F G) =>  (! [J:$i] :  ((m2_nattra_1 J A B G H) =>  (~  ( (D = (k4_tarski (k4_tarski F G) I))  &  ( (E = (k4_tarski (k4_tarski G H) J))  &  ((k1_funct_1 (u1_cat_1 C) (k10_cat_2 C C E D)) = (k4_tarski (k4_tarski F H) (k7_nattra_1 A B F G H I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( (E = D)  =>  ((k4_cat_1 C D) = (k4_tarski (k4_tarski E E) (k6_nattra_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r13_ncfcont1 A B C D) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden F C) & (r2_hidden G C))  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D F) (k7_partfun1 (u1_struct_0 B) D G))) (k8_real_1 E (k1_normsp_0 A (k5_algstr_0 A F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v9_oposet_1 B A) <=>  ((v1_partit_2 B) & (v5_waybel_0 B A A)) ) ) ) ) ) ).
tt(d17_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_ordinal2 A B) <=>  (? [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  &  ( ((k9_xtuple_0 C) = B)  &  ((r1_tarski (k10_xtuple_0 C) A) &  ((v2_ordinal2 C) &  (A = (k4_ordinal2 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_ordinal6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k13_ordinal6 A B) = (k1_funct_1 (k1_funct_1 (k11_ordinal6 (k1_classes1 (k2_xboole_0 B k4_ordinal1))) A) B)) ) ) ) ) ).
tt(d17_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) &  ((v3_osalg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) ) )  =>  ( (C = (k15_osafree A B))  <=>  (! [D:$i] :  ( ((v2_msualg_4 D A (k8_osafree A B)) &  ((v3_msualg_4 D A (k8_osafree A B)) &  ((v3_osalg_4 D A (k8_osafree A B)) & (m1_osalg_4 D A (k8_osafree A B))) ) )  => (r2_pboole (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(d17_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v12_osalg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) => (r1_tarski (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d17_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((k16_osalg_2 A B) = (g3_lattices (k13_osalg_2 A B) (k14_osalg_2 A B) (k15_osalg_2 A B))) ) ) ) ) ).
tt(d17_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k7_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k1_funct_2 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r6_pdiff_1 A B C D E F) <=> (r1_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A C F) (k1_partfun1 (k1_euclid A) (k1_euclid B) (k1_euclid B) k1_numbers E (k1_pdiff_1 D B))) (k1_seq_1 (k1_pdiff_1 C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r8_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k8_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G E) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B) E)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J E)) (k1_seq_1 I (k9_real_1 J E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pencil_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v14_pencil_1 A) <=>  (! [B:$i] :  ((l1_struct_0 B) =>  (~  ((r2_hidden B (k10_xtuple_0 A)) & (v7_struct_0 B)) ) ) ) ) ) ) ).
tt(d17_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) =>  ( (D = (k20_polyform A B C))  <=>  ( ((v1_xboole_0 (k8_polyform A (k6_xcmplx_0 B 1))) =>  (D = (k4_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) )  &  ( (~ (v1_xboole_0 (k8_polyform A (k6_xcmplx_0 B 1))))  =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((r2_hidden E D) <=>  ((k4_rlvect_1 k2_bspace (k19_polyform A B E C)) = (k5_struct_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pralg_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k15_pralg_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C D) = (k1_funct_1 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k4_finseq_2 2 (k15_pre_poly A))) =>  ( (C = (k21_pre_poly A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 (k20_pre_poly A B)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( ((r2_hidden D (k4_finseq_1 C)) & (r6_pboole A E (k7_partfun1 (k15_pre_poly A) (k20_pre_poly A B) D)))  =>  ((k9_pre_poly (k15_pre_poly A) k5_numbers (k4_finseq_2 2 (k15_pre_poly A)) C D) = (k10_finseq_1 E (k12_pre_poly A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k16_pscomp_1 A) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)) A)) ) ) ).
tt(d17_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k15_qc_lang1 A B C) = (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 (k4_tarski 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) B)) (k11_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(d17_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k13_qc_lang2 A B) = (k12_qc_lang2 A (k19_qc_lang1 A B))) ) ) ) ) ).
tt(d17_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v17_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_quantal1 A (k1_quantal1 A C B) B) = C)  &  ((k1_quantal1 A (k2_quantal1 A C B) B) = C) ) ) ) ) ) ) ) ) ).
tt(d17_quaterni,ax, (k21_quaterni = k6_numbers) ).
tt(d17_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k20_quofield A B C) = (k8_group_1 A B (k11_algstr_0 A C))) ) ) ) ) ) ) ).
tt(d17_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  ( ( (~ (v4_ratfunc1 B A))  =>  ( (C = (k11_ratfunc1 A B))  <=>  (? [D:$i] :  ((m1_ratfunc1 D A) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 E A) &  ( (~ (v1_ratfunc1 E A))  & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ( (B = (k3_ratfunc1 A (k13_polynom3 A E (k4_ratfunc1 A D)) (k13_polynom3 A E (k5_ratfunc1 A D))))  &  ((v5_ratfunc1 D A) &  ( (C = (k6_ratfunc1 A D))  &  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k14_polynom3 A))) &  ( (E = (k3_group_4 (k14_polynom3 A) F))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 F)) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) H) &  ((k1_funct_1 F G) = (k3_hurwitz A H 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((v4_ratfunc1 B A) =>  ( (C = (k11_ratfunc1 A B))  <=>  (C = (k7_ratfunc1 A)) ) ) ) ) ) ) ) ) ) ).
tt(d17_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k10_relat_1 A B) = (k8_relat_1 A (k1_tarski B))) ) ) ) ).
tt(d17_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r10_rewrite1 A B) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden (k4_tarski C D) A) &  ((r2_hidden (k4_tarski C E) B) &  (! [F:$i] :  (~  ((r1_rewrite1 B D F) & (r1_rewrite1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v5_ringcat1 B))  =>  ( (B = (k10_ringcat1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m2_ringcat1 D A) &  (? [E:$i] :  ((m2_ringcat1 E A) &  ((r1_ringcat1 D E) & (m1_ringcat1 C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k11_rlvect_2 A) (k11_rlvect_2 A)) (k11_rlvect_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k11_rlvect_2 A) (k11_rlvect_2 A)) (k11_rlvect_2 A))))) )  =>  ( (B = (k14_rlvect_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k11_rlvect_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k11_rlvect_2 A)) =>  ((k5_binop_1 (k11_rlvect_2 A) B C D) = (k7_rlvect_2 A (k12_rlvect_2 A C) (k12_rlvect_2 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d17_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_robbins1 A B) = (k1_lattices A B B)) ) ) ) ) ).
tt(d17_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((r1_rvsum_1 A B) <=>  ((k23_rvsum_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(d17_scmfsa_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_scmfsa_i (k1_funct_2 (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_scmfsa_i (k1_funct_2 (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))))))) )  =>  ( (A = k12_scmfsa_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_scmfsa_i) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  ((k1_funct_1 (k3_funct_2 k2_scmfsa_i (k1_funct_2 (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) A B) C) = (k11_scmfsa_1 B C)) ) ) ) ) ) ) ) ).
tt(d17_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k15_scmfsa_2 A B C) = (k3_xtuple_0 10 k1_xboole_0 (k11_finseq_1 A C B))) ) ) ) ) ) ) ).
tt(d17_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k16_scmpds_2 A B C D) = (k3_xtuple_0 13 k1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d17_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k24_seq_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) =>  ( (E = (a_3_1_seq_4 A B C))  =>  (D = (k5_seq_4 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k8_simplex0 A B C) = (k5_simplex0 (u1_struct_0 B) (k3_simplex0 (u1_struct_0 B) (u1_pre_topc B) (k1_xxreal_3 C 1)))) ) ) ) ) ) ).
tt(d17_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k17_sin_cos A) = (k1_seq_1 k16_sin_cos A)) ) ) ).
tt(d17_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ( (C = (k11_stacks_1 A B))  <=>  ((r2_hidden B C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r2_hidden E C) =>  ((r2_hidden (k7_stacks_1 A E D) C) &  ( (~ (r1_stacks_1 A E))  => (r2_hidden (k5_stacks_1 A E) C)) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) =>  ( ((r2_hidden B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ((r2_hidden F D) =>  ((r2_hidden (k7_stacks_1 A F E) D) &  ( (~ (r1_stacks_1 A F))  => (r2_hidden (k5_stacks_1 A F) D)) ) ) ) ) ) ) )  => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d17_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) =>  ((k8_struct_0 A) = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_tarski (k4_struct_0 A)))) ) ) ).
tt(d17_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (B = (k16_substut1 A))  <=>  ((v1_substut1 B A) &  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_substut1 C A) => (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(d17_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k19_supinf_2 A) = (k8_supinf_2 (k17_supinf_2 (k18_supinf_2 A)))) ) ) ).
tt(d17_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  =>  ( (C = (k5_tex_4 A B))  <=>  ((u1_struct_0 C) = (k2_tex_4 A B)) ) ) ) ) ) ) ) ).
tt(d17_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((k13_trees_3 A B) = (k11_trees_3 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d17_turing_1,ax, (! [A:$i] :  ( ((v1_turing_1 A) & (l1_turing_1 A))  =>  ( (A = k16_turing_1)  <=>  ( ((u1_turing_1 A) = (k7_domain_1 k5_numbers k6_numbers 1))  &  ( ((u2_turing_1 A) = (k3_turing_1 4))  &  ((r1_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) k15_turing_1) &  ( ((u4_turing_1 A) = k6_numbers)  &  ((u5_turing_1 A) = 4) ) ) ) ) ) ) ) ).
tt(d17_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k18_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d17_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  ((k12_unialg_2 A) = (g3_lattices (k9_unialg_2 A) (k10_unialg_2 A) (k11_unialg_2 A))) ) ) ).
tt(d17_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  ((m1_valued_0 B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  (B = (k3_relat_1 C A)) ) ) ) ) ) ) ) ).
tt(d17_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((k62_valued_1 A) = (k1_xxreal_2 (k1_relset_1 k5_numbers A))) ) ) ).
tt(d17_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k11_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ) ) ) ).
tt(d17_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  ((v11_vectsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_vectsp_1 A B (k5_struct_0 A) C) = C) ) ) ) ) ) ) ) ).
tt(d17_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_waybel_0 A B) = (k3_waybel_0 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(d17_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k3_waybel_1 A B C) = (k3_struct_0 (k1_yellow_2 A B C))) ) ) ) ) ) ) ).
tt(d17_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_waybel34 C A B) <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_yellow_0 A)) = (k3_yellow_0 B)) ) ) ) ) ) ) ) ).
tt(d17_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v6_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k1_yellow_0 A (k5_waybel_4 A C B))) ) ) ) ) ) ) ) ).
tt(d17_xtuple_0,ax, (! [A:$i] :  ((k14_xtuple_0 A) = (k10_xtuple_0 (k11_xtuple_0 A))) ) ).
tt(d17_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v6_yellow_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (u1_struct_0 B)) &  ((r2_hidden D (u1_struct_0 B)) & (r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D))) )  => (r2_hidden (k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(d17_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v3_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k11_yellow_6 A B))  <=> (r2_hidden C (k10_yellow_6 A B))) ) ) ) ) ) ) ).
tt(d17_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k11_zf_lang A B) = (k6_zf_lang (k7_zf_lang A (k6_zf_lang B)))) ) ) ) ) ).
tt(d17_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_zmodul01 A B C) <=>  ( ((g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A)) = (k6_zmodul01 A B C))  &  ((k7_zmodul01 A B C) = (k3_zmodul01 A)) ) ) ) ) ) ) ) ) ).
tt(d18_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l2_abcmiz_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((k6_abcmiz_0 A B C) = (k1_yellow_0 A (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_abcmiz_0 A C) (k5_waybel_0 A B)))) ) ) ) ) ) ) ).
tt(d18_abcmiz_1,ax, (k17_abcmiz_1 = (k2_zfmisc_1 (k1_tarski k6_abcmiz_1) (k2_zfmisc_1 k4_abcmiz_1 k5_numbers))) ).
tt(d18_abcmiz_a,ax, (! [A:$i] :  ((m2_finseq_1 A k2_abcmiz_1) =>  (! [B:$i] :  ((m1_trees_4 B (k3_card_3 (u3_msualg_1 k27_abcmiz_1 (k1_msafree3 k27_abcmiz_1 (k28_abcmiz_1 k27_abcmiz_1)))) (k34_abcmiz_1 k27_abcmiz_1)) =>  ( (B = (k16_abcmiz_a A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_funct_1 B C) = (k35_abcmiz_1 (k7_partfun1 k2_abcmiz_1 A C) k27_abcmiz_1)) ) ) ) ) ) ) ) ) ) ).
tt(d18_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k5_binop_1 (u1_struct_0 A) (u2_algstr_0 A) B C)) ) ) ) ) ) ) ).
tt(d18_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  ( ( (~ (v1_xboole_0 A))  =>  ((k15_algstr_4 A B) = (k2_xtuple_0 B)) )  &  ((v1_xboole_0 A) =>  ((k15_algstr_4 A B) = k6_numbers) ) ) ) ) ) ).
tt(d18_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ((v13_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d18_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v5_aofa_000 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k14_aofa_000 A B C D) = (k1_funct_1 (k2_pua2mss1 A (k1_funct_7 3 (k4_finseq_1 (u1_unialg_1 A)))) (k3_finseq_4 (u1_struct_0 A) B C D))) ) ) ) ) ) ) ) ) ).
tt(d18_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) )  =>  ( (C = (k22_aofa_i00 A B))  <=>  (! [D:$i] :  ((m2_funct_2 D A k4_numbers (k9_funct_2 A k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 A k4_numbers) k4_numbers C D) = (k21_aofa_i00 A k4_numbers D B)) ) ) ) ) ) ) ) ) ) ).
tt(d18_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v8_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((r3_armstrng A (k6_armstrng A D E) (k6_armstrng A C C)) & (r2_hidden (k6_armstrng A D E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_asympt_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_funct_2 B A k1_numbers) =>  (! [C:$i] :  ((m1_funct_2 C A k1_numbers) =>  ((k13_asympt_0 A B C) = (a_3_0_asympt_0 A B C)) ) ) ) ) ) ) ).
tt(d18_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_bcialg_1 B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A C D) B) & (r2_hidden D B))  => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  ((k8_bcialg_2 A B) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A))) ) ) ) ) ).
tt(d18_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B)) )  =>  ( (E = (k13_bilinear A B C D))  <=>  ((u1_struct_0 E) = (k10_bilinear A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r4_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A B D (k3_binop_1 A C E F)) = (k3_binop_1 A C (k3_binop_1 A B D E) (k3_binop_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((r2_borsuk_1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A k17_borsuk_1)) (u1_struct_0 A)) &  ((v5_pre_topc C (k2_borsuk_1 A k17_borsuk_1) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A k17_borsuk_1)) (u1_struct_0 A))))) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 A k17_borsuk_1)) (u1_struct_0 A) C (k4_borsuk_1 A k17_borsuk_1 D k18_borsuk_1)) = D)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 (k2_borsuk_1 A k17_borsuk_1)) (u1_struct_0 A) C (k4_borsuk_1 A k17_borsuk_1 D k19_borsuk_1)) (u1_struct_0 B)) &  ((r2_hidden D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k17_borsuk_1)) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 A k17_borsuk_1)) (u1_struct_0 A) C (k4_borsuk_1 A k17_borsuk_1 D E)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((k18_bvfunc_1 A B) = (k6_subset_1 (k2_tarski (a_2_0_bvfunc_1 A B) (a_2_1_bvfunc_1 A B)) (k1_tarski k1_xboole_0))) ) ) ) ) ).
tt(d18_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k11_c0sp1 A) = (g1_lopban_2 (k6_c0sp1 A) (k2_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k1_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k5_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k4_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k3_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) (k10_c0sp1 A))) ) ) ).
tt(d18_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k6_card_fil A) A) (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k6_card_fil A) A) (k9_setfam_1 A))))) )  =>  ((r4_card_fil A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C (k6_card_fil A)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (~  (D = E) )  => (v1_xboole_0 (k9_subset_1 A (k2_binop_1 (k6_card_fil A) A (k9_setfam_1 A) B C D) (k2_binop_1 (k6_card_fil A) A (k9_setfam_1 A) B C E)))) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k6_card_fil A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_card_fil A)) =>  ( (~  (D = E) )  => (v1_xboole_0 (k9_subset_1 A (k2_binop_1 (k6_card_fil A) A (k9_setfam_1 A) B D C) (k2_binop_1 (k6_card_fil A) A (k9_setfam_1 A) B E C)))) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k6_card_fil A)) => (r1_ordinal1 (k1_card_1 (k6_subset_1 A (k3_tarski (a_3_2_card_fil A B C)))) (k6_card_fil A))) )  &  (! [C:$i] :  ((m1_subset_1 C A) => (r1_ordinal1 (k1_card_1 (k6_subset_1 A (k3_tarski (a_3_3_card_fil A B C)))) (k6_card_fil A))) ) ) ) ) ) ) ) ) ) ).
tt(d18_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_cat_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_cat_1 D A C B) &  (! [E:$i] :  ((m1_cat_1 E A C B) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r4_cat_3 A B C D) <=>  ( ((k4_graph_1 A C) = B)  &  ( ((k4_graph_1 A D) = B)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (~  ((r2_hidden F (k2_cat_1 A (k3_graph_1 A C) E)) &  ((r2_hidden G (k2_cat_1 A (k3_graph_1 A D) E)) &  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  (~  ((r2_hidden H (k2_cat_1 A B E)) &  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 A)) =>  ((r2_hidden I (k2_cat_1 A B E)) =>  ( ( ((k1_cat_1 A C I) = F)  &  ((k1_cat_1 A D I) = G) )  <=>  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k17_cat_4 A B C D) = (k9_cat_4 A (k2_cat_4 A B C) D (k2_cat_4 A B (k2_cat_4 A C D)) (k9_cat_4 A B C (k2_cat_4 A B (k2_cat_4 A C D)) (k7_cat_4 A B (k2_cat_4 A C D)) (k5_cat_1 A (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A C D) C (k8_cat_4 A B (k2_cat_4 A C D)) (k7_cat_4 A C D))) (k5_cat_1 A (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A C D) D (k8_cat_4 A B (k2_cat_4 A C D)) (k8_cat_4 A C D)))) ) ) ) ) ) ) ) ) ).
tt(d18_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( (C = (k9_cohsp_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v9_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  (D = (k8_cohsp_1 A B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_coh_sp,ax, (! [A:$i] :  ((k16_coh_sp A) = (a_1_4_coh_sp A)) ) ).
tt(d18_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_comput_1 k5_numbers))) =>  ((k11_comput_1 A) = (k2_xboole_0 A (a_1_3_comput_1 A))) ) ) ).
tt(d18_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A))))) )  =>  ( (B = (k9_conlat_1 A))  <=>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_conlat_1 D A) &  ( (~ (v5_conlat_1 D A))  &  ((v7_conlat_1 D A) & (l2_conlat_1 D A)) ) )  =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u4_struct_0 A))) &  ( ((k1_binop_1 B C D) = (g2_conlat_1 A E F))  &  ( (E = (k9_subset_1 (u1_struct_0 A) (u2_conlat_1 A C) (u2_conlat_1 A D)))  &  (F = (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k4_subset_1 (u4_struct_0 A) (u3_conlat_1 A C) (u3_conlat_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_csspace,ax, (k18_csspace = (g1_csspace k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace) k17_csspace)) ).
tt(d18_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k13_decomp_1 A) = (a_1_7_decomp_1 A)) ) ) ).
tt(d18_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k16_ens_1 A) = (a_1_3_ens_1 A)) ) ) ).
tt(d18_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k16_e_siec A) = (k2_xboole_0 (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A)))))) ) ) ).
tt(d18_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k15_facirc_1 A B C) = (k2_circcomb (k14_facirc_1 A B C) (k5_circcomb k4_facirc_1 (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1))))) ) ) ) ).
tt(d18_finseq_1,ax, (! [A:$i] :  ((v3_finseq_1 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(d18_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k15_fomodel0 A B) = A) ) ) ).
tt(d18_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v8_fomodel1 B A) <=> (r2_hidden B (k5_fomodel1 A))) ) ) ) ) ).
tt(d18_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ( ( (? [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) &  (? [G:$i] :  ((m2_subset_1 G (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) D F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) C)) &  ( ((k1_binop_1 C D F) = k7_margrel1)  &  ( ((k1_binop_1 C D G) = k7_margrel1)  &  (E = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k1_fomodel1 A) (k1_fomodel2 A)) F) G)) ) ) ) ) ) ) )  =>  ((k20_fomodel2 A B C D E) = k8_margrel1) )  &  ( (! [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (~  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) D F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) C)) &  ( ((k1_binop_1 C D F) = k7_margrel1)  &  ( ((k1_binop_1 C D G) = k7_margrel1)  &  (E = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k1_fomodel1 A) (k1_fomodel2 A)) F) G)) ) ) ) ) ) ) ) )  =>  ((k20_fomodel2 A B C D E) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k22_fomodel3 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k37_fomodel1 A))  &  (! [F:$i] :  ( ((v9_fomodel1 F A) & (m1_subset_1 F (k1_fomodel1 A)))  =>  ((k1_funct_1 E F) = (k20_fomodel3 A B F C (k4_fomodel2 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r1_fomodel4 A B C) <=> (r2_hidden (k2_xtuple_0 C) (k1_xtuple_0 C))) ) ) ) ) ) ).
tt(d18_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) =>  ((k15_freealg A B) = (g1_unialg_1 (k4_dtconstr (k3_freealg A B)) (k14_freealg A B))) ) ) ) ) ).
tt(d18_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ((v2_fsm_1 D A B) & (l2_fsm_1 D A B))  =>  ( (D = (k11_fsm_1 A B C))  <=>  ( ((u1_struct_0 D) = (k8_fsm_1 A B C))  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r2_hidden G E) =>  ((r2_hidden (k2_binop_1 (u1_struct_0 C) A (u1_struct_0 C) (u1_fsm_1 A C) G F) (k1_binop_1 (u1_fsm_1 A D) E F)) &  ((k2_binop_1 (u1_struct_0 C) A B (u3_fsm_1 A B C) G F) = (k1_binop_1 (u3_fsm_1 A B D) E F)) ) ) ) ) ) ) ) )  & (r2_hidden (u2_fsm_1 A C) (u2_fsm_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k18_ftacell1 A B C D E) = (k24_gfacirc1 (k36_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d18_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  ((v8_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ((k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~  ((k18_gate_1 A B C D E) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) ) )  =>  ((k18_gate_1 A B C D E) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d18_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ( (C = (k4_struct_0 A))  |  (E = (k4_struct_0 A)) )  =>  ((k8_gcd_1 A B C D E F) = (k4_struct_0 A)) )  &  ( ( ( (D = (k5_struct_0 A))  &  (F = (k5_struct_0 A)) )  =>  ((k8_gcd_1 A B C D E F) = (k8_group_1 A C E)) )  &  ( ( (D = (k5_struct_0 A))  =>  ( (F = (k4_struct_0 A))  |  ((k8_gcd_1 A B C D E F) = (k1_gcd_1 A (k8_group_1 A C E) (k5_gcd_1 A B C F))) ) )  &  ( ( (F = (k5_struct_0 A))  =>  ( (D = (k4_struct_0 A))  |  ((k8_gcd_1 A B C D E F) = (k1_gcd_1 A (k8_group_1 A C E) (k5_gcd_1 A B E D))) ) )  &  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  ( (~  ( (D = (k5_struct_0 A))  &  (F = (k5_struct_0 A)) ) )  &  ( (~  ( (~  (F = (k4_struct_0 A)) )  &  (D = (k5_struct_0 A)) ) )  &  ( (~  ( (~  (D = (k4_struct_0 A)) )  &  (F = (k5_struct_0 A)) ) )  &  (~  ((k8_gcd_1 A B C D E F) = (k8_group_1 A (k1_gcd_1 A C (k5_gcd_1 A B C F)) (k1_gcd_1 A E (k5_gcd_1 A B E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k18_gfacirc1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k3_gfacirc1 (k10_finseq_1 A B)) (k5_circcomb k3_twoscomp (k10_finseq_1 B C))) (k5_circcomb k2_twoscomp (k10_finseq_1 C A)) (k3_circcomb (k5_circcomb k3_gfacirc1 (k10_finseq_1 A B)) (k5_circcomb k3_twoscomp (k10_finseq_1 B C)) (k6_facirc_1 A B k3_gfacirc1) (k6_facirc_1 B C k3_twoscomp)) (k6_facirc_1 C A k2_twoscomp))) ) ) ) ).
tt(d18_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v3_glib_000 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (k7_glib_000 A)) &  ((k1_funct_1 (k10_glib_000 A) B) = (k1_funct_1 (k11_glib_000 A) B)) ) ) ) ) ) ) ).
tt(d18_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k15_glib_001 A B) = (k3_finseq_1 (k12_glib_001 A B))) ) ) ) ) ).
tt(d18_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k8_glib_003 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k12_glib_001 A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k1_funct_1 C D) = (k1_funct_1 (k5_glib_003 A) (k1_funct_1 (k12_glib_001 A B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  ((k17_glib_004 A) = (k40_glib_000 (k16_glib_004 A))) ) ) ).
tt(d18_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ( ((r2_hidden C (k1_relset_1 (k6_glib_000 A) (k6_glib_005 A B D))) =>  ((k11_glib_005 A B C D) = (k10_glib_005 A B (k7_glib_005 A B D C))) )  &  ( (~ (r2_hidden C (k1_relset_1 (k6_glib_000 A) (k6_glib_005 A B D))))  =>  ((k11_glib_005 A B C D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ((m3_graph_1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((r1_tarski (u4_struct_0 B) (u4_struct_0 A)) &  (! [C:$i] :  ((r2_hidden C (u4_struct_0 B)) =>  ( ((k1_funct_1 (u1_graph_1 B) C) = (k1_funct_1 (u1_graph_1 A) C))  &  ( ((k1_funct_1 (u2_graph_1 B) C) = (k1_funct_1 (u2_graph_1 A) C))  &  ((r2_hidden (k1_funct_1 (u1_graph_1 A) C) (u1_struct_0 B)) & (r2_hidden (k1_funct_1 (u2_graph_1 A) C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r8_graph_5 A B C D E F) <=>  ((r2_graph_5 A B C D E) &  (! [G:$i] :  ( ((v7_graph_1 G A) & (m2_graph_1 G A))  =>  ((r2_graph_5 A B C G E) => (r1_xxreal_0 (k10_graph_5 A D F) (k10_graph_5 A G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_graphsp,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r4_graphsp A B C D) <=>  ( ((k1_seq_1 A 1) = 1)  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 1))  &  ((r3_graphsp A B C D) & (v2_funct_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_grcat_1,ax, (! [A:$i] :  ((v4_grcat_1 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) ) ) ) ) ) ).
tt(d18_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  ((r3_group_10 A B C) <=>  ((v2_group_10 C A) &  (~ (r1_nat_d A (k18_group_2 B C))) ) ) ) ) ) ) ) ) ).
tt(d18_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v1_finset_1 (k15_group_2 A B)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k18_group_2 A B))  <=>  (? [D:$i] :  ((v1_finset_1 D) &  ( (D = (k15_group_2 A B))  &  (C = (k5_card_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((v7_group_9 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k3_group_9 A B E) F)) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k3_group_9 A C E) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) )  =>  ( (C = (k11_hahnban1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k3_complex1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d18_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_matrix_1 D k5_numbers B 6) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( (E = (k18_idea_1 A B C D))  <=>  ( ((k3_finseq_1 E) = A)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k16_idea_1 C (k8_matrix_1 k5_numbers D (k2_nat_1 (k7_nat_d A F) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_ideal_1 A B C) = (a_3_1_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(d18_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m5_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  ((k16_index_1 A B C D) = (k14_index_1 A (k10_index_1 A C) B (k9_index_1 A C (k10_index_1 A C)) D)) ) ) ) ) ) ) ) ) ).
tt(d18_integr15,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid C)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid C)) =>  ( (E = (k12_integr15 A B C D))  <=>  ( ((k4_finseq_1 E) = (k2_finseq_1 C))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k2_finseq_1 C)) =>  ((k1_seq_1 E F) = (k4_integra5 A B (k1_partfun1 k1_numbers (k1_euclid C) (k1_euclid C) k1_numbers D (k1_pdiff_1 F C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_integra1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_integra1 A B) <=>  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)) & (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(d18_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k16_interva1 A B C) = (k4_tarski (k4_subset_1 (u1_struct_0 A) (k14_interva1 A B) (k14_interva1 A C)) (k4_subset_1 (u1_struct_0 A) (k15_interva1 A B) (k15_interva1 A C)))) ) ) ) ) ) ) ).
tt(d18_intpro_1,ax, (k10_intpro_1 = (k3_intpro_1 k2_intpro_1 k2_intpro_1)) ).
tt(d18_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v4_lattice3 A) <=>  (! [B:$i] :  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r4_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_lattice3 A D B) => (r1_lattices A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d18_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  ((k14_lattice5 A B C D) = (k12_lattice5 A B C D (k7_lattice5 A B C))) ) ) ) ) ) ) ) ) ).
tt(d18_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattices A B C) <=>  ( ((k1_lattices A B C) = (k6_lattices A))  &  ( ((k1_lattices A C B) = (k6_lattices A))  &  ( ((k2_lattices A B C) = (k5_lattices A))  &  ((k2_lattices A C B) = (k5_lattices A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) k5_numbers))))  =>  ((v5_lexbfs B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ((r2_hidden C (k1_relset_1 (k6_glib_000 A) B)) &  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) B)) &  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) B)) &  ( (~ (r1_xxreal_0 (k1_recdef_1 B D) (k1_recdef_1 B C)))  &  ( (~ (r1_xxreal_0 (k1_recdef_1 B E) (k1_recdef_1 B D)))  &  ((r1_chord A C E) &  ( (~ (r1_chord A D E))  &  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 A)) =>  (~  ((r2_hidden F (k1_relset_1 (k6_glib_000 A) B)) &  ( (~ (r1_xxreal_0 (k1_recdef_1 B F) (k1_recdef_1 B E)))  &  ((r1_chord A D F) &  ( (~ (r1_chord A C F))  &  (! [G:$i] :  ((m1_subset_1 G (k6_glib_000 A)) =>  (~  ( (~  (G = F) )  &  ((r1_chord A G D) &  ( (~ (r1_chord A G C))  & (r1_xxreal_0 (k1_recdef_1 B F) (k1_recdef_1 B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k13_lmod_7 A B C) = (g2_algstr_0 (k7_lmod_7 A B C) (k12_lmod_7 A B C) (k8_lmod_7 A B C (k4_struct_0 B)))) ) ) ) ) ) ) ).
tt(d18_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v1_rlvect_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) & (l1_rlvect_1 D)) ) ) ) ) ) ) ) ) )  =>  ( (D = (k18_lpspace1 A B C))  <=>  ( ((u1_struct_0 D) = (k14_lpspace1 A B C))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D)) (u1_struct_0 D) (k2_zfmisc_1 (k14_lpspace1 A B C) (k14_lpspace1 A B C)) (k14_lpspace1 A B C) (u1_algstr_0 D) (k15_lpspace1 A B C)) &  ( ((k4_struct_0 D) = (k16_lpspace1 A B C))  & (r1_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 D)) (u1_struct_0 D) (k2_zfmisc_1 k1_numbers (k14_lpspace1 A B C)) (k14_lpspace1 A B C) (u1_rlvect_1 D) (k17_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  ( (A = k13_ltlaxio1)  <=>  ((v2_ltlaxio1 A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((v2_ltlaxio1 B) => (r1_tarski A B)) ) ) ) ) ) ) ).
tt(d18_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k21_member_1 A B) = (k11_member_1 A (k1_tarski B))) ) ) ) ) ).
tt(d18_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 A B)) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 A B)) k5_numbers)))) )  =>  ((v7_memstr_0 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  ( ((k6_memstr_0 A B D) = (k6_memstr_0 A B E))  =>  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((k8_mesfunc5 A B C D E) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v11_metric_1 A) <=> (v10_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ).
tt(d18_metric_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers)))) )  =>  ( (A = k18_metric_3)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [G:$i] :  ((m1_subset_1 G (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ( ( (F = (k1_domain_1 k1_numbers k1_numbers B D))  &  (G = (k1_domain_1 k1_numbers k1_numbers C E)) )  =>  ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) A F G) = (k7_square_1 (k7_real_1 (k5_square_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 B C)) (k5_square_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_mod_2,ax, (k16_mod_2 = 1) ).
tt(d18_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((v3_modal_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k6_modal_1) &  (A = (k11_modal_1 B)) ) ) ) ) ) ).
tt(d18_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_1 A) <=>  (? [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  &  (A = (k10_modelc_1 B)) ) ) ) ) ) ).
tt(d18_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v3_modelc_2 A) =>  ( (B = (k10_modelc_2 A))  <=>  ((k3_modelc_2 B) = A) ) )  &  ( (~ (v3_modelc_2 A))  =>  ( (B = (k10_modelc_2 A))  <=>  ((k6_modelc_2 B) = A) ) ) ) ) ) ) ) ) ).
tt(d18_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  ((k12_modelc_3 A B) = (g1_modelc_3 A (k7_modelc_3 A) (u3_modelc_3 A B) (k7_modelc_3 A))) ) ) ) ) ).
tt(d18_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v15_monoid_0 A) <=> (v7_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d18_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (k13_msafree A B) B) =>  ( (C = (k15_msafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_funct_2 (k1_funct_1 (k13_msafree A B) D) (k1_funct_1 B D) (k12_msafree A B D) (k1_funct_1 B D) (k1_msualg_3 (u1_struct_0 A) (k13_msafree A B) B C D) (k14_msafree A B D))) ) ) ) ) ) ) ) ) ).
tt(d18_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D A B) =>  (! [E:$i] :  ( ((v3_msualg_1 E A) & (m1_msualg_2 E A B))  =>  ( (E = (k13_msualg_2 A B C D))  <=>  (! [F:$i] :  ((m3_pboole F (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) F (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D))) =>  (E = (k12_msualg_2 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ( (E = (k17_msualg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_relset_1 (k1_funct_1 (u3_msualg_1 A B) F) (k1_funct_1 (u3_msualg_1 A B) F) (k2_msualg_4 A B E F) (k16_msualg_4 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v2_nattra_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k4_cat_1 A C)) ) ) ) ) ) ) ) ).
tt(d18_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r14_ncfcont1 A B C D) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden F C) & (r2_hidden G C))  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D F) (k7_partfun1 (u1_struct_0 B) D G))) (k8_real_1 E (k1_normsp_0 A (k5_algstr_0 A F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v10_oposet_1 A) <=> (v9_oposet_1 (u1_robbins1 A) A)) ) ) ).
tt(d18_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k16_osafree A B) = (k16_osalg_4 A (k8_osafree A B) (k15_osafree A B))) ) ) ) ) ).
tt(d18_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k3_osalg_1 A B))) (k3_relat_1 (u2_msualg_1 A) (k3_osalg_1 A B))) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v4_msualg_1 D A) & (l3_msualg_1 D A)) )  =>  ( (D = (k4_osalg_1 A B C))  <=>  ((r8_pboole (u1_struct_0 A) (u3_msualg_1 A D) (k3_osalg_1 A B)) & (r8_pboole (u4_struct_0 A) (u4_msualg_1 A D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d18_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B))))) )  =>  ( (E = (k14_osalg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  ((r2_hidden (k9_osalg_4 A B C D F) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B)) =>  ((k1_funct_1 E (k9_osalg_4 A B C D F)) = (k1_funct_1 (k1_partfun1 (k3_msualg_1 A B C) (k4_msualg_1 A B C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B) (k5_msualg_1 A B C) (k10_osalg_4 A B C D)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m3_pboole C A B) <=> (r2_pboole A C B)) ) ) ) ) ) ).
tt(d18_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((k14_pdiff_1 A B C D E F) = (k1_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A C F) (k1_partfun1 (k1_euclid A) (k1_euclid B) (k1_euclid B) k1_numbers E (k1_pdiff_1 D B))) (k1_seq_1 (k1_pdiff_1 C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r9_pdiff_5 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k9_pdiff_5 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (B = (k11_finseq_1 D E F))  &  (? [G:$i] :  ((m1_rcomp_1 G F) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B))) &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v3_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v2_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 H 1))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_hidden J G) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B) J) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B) F)) = (k7_real_1 (k1_seq_1 H (k9_real_1 J F)) (k1_seq_1 I (k9_real_1 J F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) )  =>  ((v14_pencil_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( (~ (v7_struct_0 B))  & (l1_struct_0 B)) ) ) ) ) ) ).
tt(d18_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1))))))) )  =>  ( (C = (k21_polyform A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  ((k3_funct_2 (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1))) C D) = (k20_polyform A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d18_pralg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k16_pralg_1 A B C))  <=>  ( ((k9_xtuple_0 D) = A)  &  (! [E:$i] :  ((r2_hidden E A) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( (F = (k1_funct_1 B E))  =>  ((k1_funct_1 D E) = (k1_funct_1 F (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_prelamb A))  =>  ((v10_prelamb A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) B)) )  &  ( (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) D)) C) => (r2_prelamb A B (k2_prelamb A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) D) B) C) => (r2_prelamb A B (k1_prelamb A D C))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_prelamb A B F) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) E)) D) G))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A E F))) B) D) G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_prelamb A B F) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) E)) D) G))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C B) (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A F E))) D) G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) D)) (k12_finseq_1 (u1_struct_0 A) E)) C) F) => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A D E))) C) F)) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_prelamb A B D) & (r2_prelamb A C E))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) B C) (k3_prelamb A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k17_pscomp_1 A) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)) A)) ) ) ).
tt(d18_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) &  (? [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  &  (B = (k10_qc_lang1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k14_qc_lang2 A B) = (k11_qc_lang2 A (k19_qc_lang1 A B))) ) ) ) ) ).
tt(d18_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v18_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_quantal1 A C B) = (k2_quantal1 A C B)) ) ) ) ) ) ) ) ).
tt(d18_quaterni,ax, (k22_quaterni = 1) ).
tt(d18_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield C A B) <=>  ((v13_vectsp_1 C A B) &  ((v1_group_6 C A B) & (v6_group_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(d18_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((k12_ratfunc1 A B) = (k4_xxreal_0 (k2_hurwitz A (k4_ratfunc1 A (k11_ratfunc1 A B))) (k2_hurwitz A (k5_ratfunc1 A (k11_ratfunc1 A B))))) ) ) ) ) ).
tt(d18_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v4_relat_1 B A) <=> (r1_tarski (k9_xtuple_0 B) A)) ) ) ) ).
tt(d18_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r11_rewrite1 A B) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r1_rewrite1 A C D) &  ((r1_rewrite1 B C E) &  (! [F:$i] :  (~  ((r1_rewrite1 B D F) & (r1_rewrite1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ((m2_ringcat1 B A) =>  ((k13_ringcat1 A B) = (k5_ringcat1 B)) ) ) ) ) ).
tt(d18_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A))))) )  =>  ( (B = (k15_rlvect_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k11_rlvect_2 A)) =>  ((k3_funct_2 (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A) B (k1_domain_1 k1_numbers (k11_rlvect_2 A) C D)) = (k8_rlvect_2 A C (k12_rlvect_2 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d18_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_robbins1 A B) = (k1_lattices A (k11_robbins1 A B) B)) ) ) ) ) ).
tt(d18_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ((k16_scmfsa_2 A B) = (k3_xtuple_0 11 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d18_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k17_scmpds_2 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( (D = (k5_memstr_0 2 k1_scmpds_2 A))  &  (C = (k1_int_2 (k2_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v8_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k9_scmyciel A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v7_scmyciel C A) & (m1_eqrel_1 C (k3_tarski A))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v7_scmyciel C A) & (m1_eqrel_1 C (k3_tarski A))) )  => (r1_xxreal_0 B (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(d18_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k25_seq_4 A B C) = (a_3_2_seq_4 A B C)) ) ) ) ) ) ) ).
tt(d18_simplex0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ( ((r1_xxreal_0 (k2_xxreal_3 1) B) & (r1_xxreal_0 B (k6_simplex0 A)))  =>  ((m3_simplex0 C A B) <=>  ((k5_card_1 C) = (k1_xxreal_3 B 1)) ) )  &  ( (~  ((r1_xxreal_0 (k2_xxreal_3 1) B) & (r1_xxreal_0 B (k6_simplex0 A))) )  =>  ((m3_simplex0 C A B) <=> (v1_xboole_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(d18_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k19_sin_cos)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 A B) = (k3_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 B k7_complex1))))) ) ) ) ) ) ).
tt(d18_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A)))) =>  ( (B = (k12_stacks_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u4_struct_0 A) (u4_struct_0 A) C D) B) <=>  (~  ( (~  ( (~ (r1_stacks_1 A C))  &  (D = (k5_stacks_1 A C)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (D = (k7_stacks_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((v7_struct_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(d18_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_qc_lang1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ( ((k7_qc_lang1 A B) = (k3_finseq_1 C))  =>  ((k17_substut1 A B C D) = (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k10_qc_lang1 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d18_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_supinf_2 A) <=> (r2_hidden (k19_supinf_2 A) k1_numbers)) ) ) ).
tt(d18_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  =>  ( (C = (k6_tex_4 A B))  <=>  ((u1_struct_0 C) = (k3_tex_4 A B)) ) ) ) ) ) ) ) ).
tt(d18_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v6_trees_3 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k14_trees_3 A))  <=>  ( ((k1_relset_1 k5_numbers B) = (k1_relset_1 k5_numbers A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  (~  ( (D = (k1_funct_1 A C))  &  ((k1_funct_1 B C) = (k1_funct_1 D k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_turing_1,ax, (k17_turing_1 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k12_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) 1) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 2 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k1_numbers) (k1_domain_1 k5_numbers k5_numbers 3 1) (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 1 (k1_real_1 1))))) ).
tt(d18_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k19_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(d18_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((v3_funct_1 B) <=>  (? [C:$i] :  ((m1_subset_1 C A) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d18_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((k63_valued_1 A) = (k6_subset_1 A (k16_funcop_1 (k62_valued_1 A) (k1_funct_1 A (k62_valued_1 A))))) ) ) ).
tt(d18_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k12_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ) ) ).
tt(d18_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v12_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(d18_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_waybel_0 A B) = (k4_waybel_0 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(d18_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k4_waybel_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k11_lattice3 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d18_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ((v7_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) B C))  &  (C = (k1_yellow_0 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d18_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v7_yellow_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_yellow_0 A C) => (r2_hidden (k2_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d18_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) <=> (r1_tarski B (k2_zfmisc_1 (k6_yellow_6 A) (u1_struct_0 A)))) ) ) ) ).
tt(d18_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k12_zf_lang A B) = (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang B A))) ) ) ) ) ).
tt(d18_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((v8_zmodul01 B A) <=>  (? [C:$i] :  ((m1_zmodul01 C A) & (r1_zmodul01 A C B)) ) ) ) ) ) ) ).
tt(d19_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k7_abcmiz_0 A B C))  <=>  ( ((k3_finseq_1 D) = (k2_nat_1 (k3_finseq_1 C) 1))  &  ( ((k1_funct_1 D 1) = B)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_abcmiz_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  ( (F = (k1_funct_1 C E))  &  (G = (k1_funct_1 D E)) ) )  =>  ((k1_funct_1 D (k2_nat_1 E 1)) = (k5_abcmiz_0 A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_abcmiz_1,ax, (k18_abcmiz_1 = (k2_zfmisc_1 (k1_tarski k7_abcmiz_1) (k2_zfmisc_1 k4_abcmiz_1 k5_numbers))) ).
tt(d19_algstr_0,ax, (k7_algstr_0 = (g3_algstr_0 1 k9_funct_5)) ).
tt(d19_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k11_algstr_4 A B) (u1_struct_0 (k14_algstr_4 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A B) (u1_struct_0 (k14_algstr_4 A)))))) )  =>  ( ( (~ (r1_xxreal_0 B k6_numbers))  =>  ( (C = (k16_algstr_4 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k1_relset_1 (k11_algstr_4 A B) C)) =>  ((k1_funct_1 C D) = (k4_tarski D B)) ) ) ) )  &  ((r1_xxreal_0 B k6_numbers) =>  ( (C = (k16_algstr_4 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d19_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  ((v14_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_zfmisc_1 (k1_altcat_1 A B B))) ) ) ) ) ).
tt(d19_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v5_aofa_000 A) & (l1_unialg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k15_aofa_000 A B C) = (k14_aofa_000 A B C (k12_aofa_000 A))) ) ) ) ) ) ) ).
tt(d19_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 A k4_numbers) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) )  =>  ( (C = (k23_aofa_i00 A B))  <=>  (! [D:$i] :  ((m2_funct_2 D A k4_numbers (k9_funct_2 A k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 A k4_numbers) k4_numbers C D) = (k21_aofa_i00 A k4_numbers D (k3_funct_2 (k9_funct_2 A k4_numbers) A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d19_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v9_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) &  ((r2_hidden (k6_armstrng A E F) B) & (r3_armstrng A (k6_armstrng A C D) (k6_armstrng A E F))) )  =>  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_asympt_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_funct_2 B A k1_numbers) =>  (! [C:$i] :  ((m1_funct_2 C A k1_numbers) =>  ((k14_asympt_0 A B C) = (a_3_1_asympt_0 A B C)) ) ) ) ) ) ) ).
tt(d19_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v12_bcialg_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) => (r2_hidden (k2_bcialg_1 A C) B)) ) ) ) ) ) ) ).
tt(d19_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  ((k9_bcialg_2 A B) = (g2_bcialg_1 (k8_eqrel_1 (u1_struct_0 A) B) (k7_bcialg_2 A B) (k8_bcialg_2 A B))) ) ) ) ) ).
tt(d19_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v7_vectsp_1 E A) & (m1_vectsp_4 E A C)) )  =>  ( (E = (k14_bilinear A B C D))  <=>  ((u1_struct_0 E) = (k11_bilinear A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r5_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A B (k3_binop_1 A C D E) F) = (k3_binop_1 A C (k3_binop_1 A B D F) (k3_binop_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k7_xboolean A B) = (k3_xboolean (k10_xboolean A B))) ) ) ) ) ).
tt(d19_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_cat_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_cat_1 D A B C) &  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  (! [G:$i] :  ((m1_cat_1 G A D E) =>  ((k18_cat_4 A B C D E F G) = (k9_cat_4 A C E (k2_cat_4 A B D) (k5_cat_1 A (k2_cat_4 A B D) B C (k7_cat_4 A B D) F) (k5_cat_1 A (k2_cat_4 A B D) D E (k8_cat_4 A B D) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k10_cohsp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  (? [E:$i] :  ( (C = (k4_tarski D E))  & (r2_hidden (k4_tarski (k1_tarski D) E) (k7_cohsp_1 A))) ) ) ) ) ) ) ) ) ).
tt(d19_coh_sp,ax, (! [A:$i] :  ((k19_coh_sp A) = (k3_tarski (a_1_5_coh_sp A))) ) ).
tt(d19_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_comput_1 k5_numbers))) =>  ((k12_comput_1 A) = (k2_xboole_0 A (a_1_4_comput_1 A))) ) ) ).
tt(d19_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A))))) )  =>  ( (B = (k10_conlat_1 A))  <=>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_conlat_1 D A) &  ( (~ (v5_conlat_1 D A))  &  ((v7_conlat_1 D A) & (l2_conlat_1 D A)) ) )  =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u4_struct_0 A))) &  ( ((k1_binop_1 B C D) = (g2_conlat_1 A E F))  &  ( (E = (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k4_subset_1 (u1_struct_0 A) (u2_conlat_1 A C) (u2_conlat_1 A D)))))  &  (F = (k9_subset_1 (u4_struct_0 A) (u3_conlat_1 A C) (u3_conlat_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ((k17_convex4 A B) = (u1_struct_0 B)) ) ) ) ) ).
tt(d19_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k14_decomp_1 A) = (a_1_8_decomp_1 A)) ) ) ).
tt(d19_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C)))))) )  =>  ( (D = (k17_ens_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r2_hidden E (k2_cat_1 A B (k3_graph_1 A C))) =>  ((k1_funct_1 D E) = (k1_cat_1 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k17_e_siec A) = (k2_xboole_0 (k4_xboole_0 (k2_xboole_0 (u1_e_siec A) (u2_e_siec A)) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A)))))) ) ) ).
tt(d19_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k16_facirc_1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k3_facirc_1 (k10_finseq_1 A B)) (k5_circcomb k3_facirc_1 (k10_finseq_1 B C))) (k5_circcomb k3_facirc_1 (k10_finseq_1 C A)) (k3_circcomb (k5_circcomb k3_facirc_1 (k10_finseq_1 A B)) (k5_circcomb k3_facirc_1 (k10_finseq_1 B C)) (k6_facirc_1 A B k3_facirc_1) (k6_facirc_1 B C k3_facirc_1)) (k6_facirc_1 C A k3_facirc_1))) ) ) ) ).
tt(d19_fomodel0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k16_fomodel0)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_funct_1 A B) = (k2_xcmplx_0 B 1)) ) ) ) ) ) ).
tt(d19_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v9_fomodel1 B A) <=> (r2_hidden B (k9_fomodel1 A))) ) ) ) ) ).
tt(d19_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_rfunct_3 C (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  ( (D = (k21_fomodel2 A B C))  <=>  ( (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) D)) <=>  (? [G:$i] :  ((m2_subset_1 G (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) &  (? [H:$i] :  ((m2_subset_1 H (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ( (F = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k1_fomodel1 A) (k1_fomodel2 A)) G) H))  &  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E G) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) C)) & (r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E H) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) C))) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [F:$i] :  ((m2_subset_1 F (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) E F) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) D)) =>  ((k1_binop_1 D E F) = (k20_fomodel2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ((m2_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  (! [D:$i] :  ( ((v15_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k26_fomodel3 A B C D) = (k7_finseq_1 (k31_fomodel2 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) D)) (k1_funct_1 (k21_fomodel1 A) (k3_relat_1 (k34_fomodel1 A D) (k10_fomodel2 A (k35_fomodel1 A) (k37_fomodel2 A (k35_fomodel1 A) (k7_fomodel3 A k1_xboole_0) B C)))))) ) ) ) ) ) ) ) ) ).
tt(d19_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r2_fomodel4 A B C) <=>  (? [D:$i] :  ((r2_hidden D A) &  ((r1_tarski (k1_xtuple_0 D) (k1_xtuple_0 C)) &  ((k2_xtuple_0 C) = (k2_xtuple_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(d19_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) =>  ((k16_freealg A B) = (a_2_1_freealg A B)) ) ) ) ) ).
tt(d19_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  ((r7_fsm_1 A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  &  ((v3_funct_2 E (u1_struct_0 C) (u1_struct_0 D)) &  ( ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) E (u2_fsm_1 A C)) = (u2_fsm_1 A D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) E (k2_binop_1 (u1_struct_0 C) A (u1_struct_0 C) (u1_fsm_1 A C) F G)) = (k2_binop_1 (u1_struct_0 D) A (u1_struct_0 D) (u1_fsm_1 A D) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) E F) G))  &  ((k2_binop_1 (u1_struct_0 C) A B (u3_fsm_1 A B C) F G) = (k2_binop_1 (u1_struct_0 D) A B (u3_fsm_1 A B D) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k19_ftacell1 A B C D E) = (k2_circcomb (k49_gfacirc1 A B C) (k49_gfacirc1 (k48_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d19_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  ((v8_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ((k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) & (v1_xboole_0 E)) ) ) ) )  =>  ((k19_gate_1 A B C D E) = (k1_gate_1 k1_xboole_0)) )  &  (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  (~  ((k19_gate_1 A B C D E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r7_gcd_1 A C D) &  ((r7_gcd_1 A E F) &  ( (D = (k4_gcd_1 A B D))  &  (F = (k4_gcd_1 A B F)) ) ) )  =>  ( ( ( (C = (k4_struct_0 A))  |  (E = (k4_struct_0 A)) )  =>  ((k9_gcd_1 A B C D E F) = (k5_struct_0 A)) )  &  ( ( ( (D = (k5_struct_0 A))  &  (F = (k5_struct_0 A)) )  =>  ((k9_gcd_1 A B C D E F) = (k5_struct_0 A)) )  &  ( ( (D = (k5_struct_0 A))  =>  ( (F = (k4_struct_0 A))  |  ((k9_gcd_1 A B C D E F) = (k1_gcd_1 A F (k5_gcd_1 A B C F))) ) )  &  ( ( (F = (k5_struct_0 A))  =>  ( (D = (k4_struct_0 A))  |  ((k9_gcd_1 A B C D E F) = (k1_gcd_1 A D (k5_gcd_1 A B E D))) ) )  &  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  ( (~  ( (D = (k5_struct_0 A))  &  (F = (k5_struct_0 A)) ) )  &  ( (~  ( (~  (F = (k4_struct_0 A)) )  &  (D = (k5_struct_0 A)) ) )  &  ( (~  ( (~  (D = (k4_struct_0 A)) )  &  (F = (k5_struct_0 A)) ) )  &  (~  ((k9_gcd_1 A B C D E F) = (k8_group_1 A (k1_gcd_1 A D (k5_gcd_1 A B E D)) (k1_gcd_1 A F (k5_gcd_1 A B C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k19_gfacirc1 A B C) = (k2_circcomb (k17_gfacirc1 A B C) (k5_circcomb k25_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))))) ) ) ) ).
tt(d19_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v4_glib_000 A) <=>  ((k1_card_1 (k6_glib_000 A)) = 1) ) ) ) ).
tt(d19_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r2_hidden C (k13_glib_001 A B)) =>  ( (D = (k16_glib_001 A B C))  <=>  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B D) = C)  &  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  ( ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = C) )  => (r1_xxreal_0 D E)) ) ) ) ) ) )  &  ( (~ (r2_hidden C (k13_glib_001 A B)))  =>  ( (D = (k16_glib_001 A B C))  <=>  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k10_glib_003 A B) = (k18_rvsum_1 (k9_glib_003 A B))) ) ) ) ) ).
tt(d19_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_glib_000 B A) &  ((v3_glib_002 B) &  ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m1_glib_000 B A)) ) ) )  =>  ((v1_glib_004 B A) <=>  (! [C:$i] :  ( ((v9_glib_000 C A) &  ((v3_glib_002 C) &  ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m1_glib_000 C A)) ) ) )  => (r1_xxreal_0 (k4_glib_004 B) (k4_glib_004 C))) ) ) ) ) ) ) ).
tt(d19_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k6_graph_1 A))  <=>  (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (u1_struct_0 A))  &  (B = (k5_card_1 C)) ) ) ) ) ) ) ) ) ).
tt(d19_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r9_graph_5 A B C D E) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F C) &  ( (~  (F = D) )  &  (! [G:$i] :  ( ((v7_graph_1 G A) & (m2_graph_1 G A))  =>  (~  ((r8_graph_5 A D F G C E) & (r1_xxreal_0 (k10_graph_5 A G E) (k10_graph_5 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r5_graphsp A B C) <=>  ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 B) 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 B D)) = (k1_funct_1 C D))  &  ((k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D)) = (k1_funct_1 C (k1_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v4_grcat_1 C))  =>  ((m4_grcat_1 C A B) <=>  (! [D:$i] :  ((m3_grcat_1 D C) =>  ((v1_grcat_1 D) & (m1_grcat_1 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(d19_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k15_group_10 A B) = (a_2_1_group_10 A B)) ) ) ) ) ).
tt(d19_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  ((r2_group_9 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  & (v3_funct_2 D (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ).
tt(d19_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) )  =>  ( (C = (k12_hahnban1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k4_complex1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d19_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k19_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k11_idea_1 B D A)) ) ) ) ) ) ) ) ) ) ).
tt(d19_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_ideal_1 A B C) = (a_3_2_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(d19_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ( (D = (k1_incsp_1 A B C))  <=> (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d19_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_integra1 B C) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 B)) =>  ( (E = (k13_integra1 A B C D))  <=>  ((r2_hidden E (k4_finseq_1 C)) &  ((k1_seq_1 B D) = (k1_seq_1 C E)) ) ) )  &  ( (~ (r2_hidden D (k4_finseq_1 B)))  =>  ( (E = (k13_integra1 A B C D))  <=>  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k17_interva1 A B C) = (k4_tarski (k9_subset_1 (u1_struct_0 A) (k14_interva1 A B) (k14_interva1 A C)) (k9_subset_1 (u1_struct_0 A) (k15_interva1 A B) (k15_interva1 A C)))) ) ) ) ) ) ) ).
tt(d19_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v9_intpro_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C B)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B (k3_intpro_1 C D)) (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 B D))) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) B) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) C) A) &  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C (k4_intpro_1 B C))) A) &  ((r2_hidden (k3_intpro_1 B (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 C (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B D) (k3_intpro_1 (k3_intpro_1 C D) (k3_intpro_1 (k5_intpro_1 B C) D))) A) &  ((r2_hidden (k3_intpro_1 k2_intpro_1 B) A) &  ((r2_hidden (k5_intpro_1 B (k3_intpro_1 B k2_intpro_1)) A) &  ( ((r2_hidden B A) & (r2_hidden (k3_intpro_1 B C) A))  => (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v5_lattice3 A) <=>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r4_lattice3 A C B) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r4_lattice3 A F B) => (r1_lattices A C F)) ) )  &  ((r4_lattice3 A E (a_3_0_lattice3 A B D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r4_lattice3 A F (a_3_0_lattice3 A B D)) => (r1_lattices A E F)) ) ) ) ) )  => (r1_lattices A (k2_lattices A D C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) (u1_struct_0 B)) &  ((v1_lattice5 E D B) &  ((v2_lattice5 E D B) &  ((v3_lattice5 E D B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) (u1_struct_0 B))))) ) ) ) )  =>  ((r2_lattice5 A B C D E) <=>  (? [F:$i] :  ((m1_lattice5 F A B C) &  ( (D = (k13_lattice5 A B C))  & (r1_funct_2 (k2_zfmisc_1 D D) (u1_struct_0 B) (k2_zfmisc_1 (k13_lattice5 A B C) (k13_lattice5 A B C)) (u1_struct_0 B) E (k15_lattice5 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v16_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_lattices A C B)) ) ) ) ) ) ) ).
tt(d19_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k18_lexbfs A) = (k4_tarski k1_xboole_0 (k8_funcop_1 k5_numbers (k6_glib_000 A) k6_numbers))) ) ) ).
tt(d19_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k14_lmod_7 A B C D) = (k8_lmod_7 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d19_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k18_lpspace1 A B C)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k18_lpspace1 A B C)) k1_numbers)))) )  =>  ( (D = (k19_lpspace1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k18_lpspace1 A B C))) =>  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden F E) &  ((k3_funct_2 (u1_struct_0 (k18_lpspace1 A B C)) k1_numbers D E) = (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r4_ltlaxio1 A B) <=>  (B = (k2_ltlaxio1 A)) ) ) ) ) ) ).
tt(d19_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (C = (k15_margrel1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A k6_margrel1 C D) = (k9_margrel1 (k3_funct_2 A k6_margrel1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d19_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k22_member_1 A B) = (k12_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d19_mod_2,ax, (k17_mod_2 = k6_numbers) ).
tt(d19_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((v4_modal_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k6_modal_1) &  (? [C:$i] :  ((m1_subset_1 C k6_modal_1) &  (A = (k12_modal_1 B C)) ) ) ) ) ) ) ) ).
tt(d19_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_1 A) <=>  (? [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_modelc_1 B C)) ) ) ) ) ) ) ) ).
tt(d19_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v4_modelc_2 A) =>  ( (B = (k11_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k4_modelc_2 B C) = A) ) ) ) )  &  ( ((v5_modelc_2 A) =>  ( (B = (k11_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k5_modelc_2 B C) = A) ) ) ) )  &  ( ((v7_modelc_2 A) =>  ( (B = (k11_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k7_modelc_2 B C) = A) ) ) ) )  &  (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~  ( (B = (k11_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k8_modelc_2 B C) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r5_modelc_3 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  ( ((v1_modelc_3 D A) & (l1_modelc_3 D A))  =>  (! [E:$i] :  ( ((v1_modelc_3 E A) & (l1_modelc_3 E A))  =>  (~  ( (D = (k1_funct_1 B C))  &  ( (E = (k1_funct_1 B (k1_nat_1 C 1)))  & (r4_modelc_3 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v16_monoid_0 A) <=> (v8_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d19_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (k13_msafree A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_msafree A B))) =>  ((r2_hidden E (k6_dtconstr (k5_msafree A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_card_3 C)) =>  ( (F = (k16_msafree A B C D E))  <=>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( (G = (k1_funct_1 D (k2_xtuple_0 E)))  =>  (F = (k1_funct_1 G (k2_trees_4 (u1_struct_0 (k5_msafree A B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( (C = (k14_msualg_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v3_msualg_1 D A) & (m1_msualg_2 D A B)) ) ) ) ) ) ) ) ) ).
tt(d19_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_msualg_3 A B C D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E))))) )  =>  ( (F = (k18_msualg_4 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((k1_funct_1 F (k6_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) E) (k16_msualg_4 A B C D E) G)) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_cat_1 B) &  ((v2_nattra_1 B) & (m3_cat_2 B A)) )  =>  ( (B = (k12_nattra_1 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((u4_struct_0 B) = (a_1_0_nattra_1 A)) ) ) ) ) ) ) ).
tt(d19_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r15_ncfcont1 A B C D) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden F C) & (r2_hidden G C))  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D F) (k7_partfun1 (u1_struct_0 B) D G))) (k8_real_1 E (k1_normsp_0 A (k5_algstr_0 A F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r1_oposet_1 A B) <=>  ((v9_oposet_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) & (r2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ) ).
tt(d19_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) =>  ((k17_osafree A B C) = (a_3_1_osafree A B C)) ) ) ) ) ) ) ).
tt(d19_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  (! [D:$i] :  ((m2_pboole D (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A B C))) =>  ( (D = (k15_osalg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) => (r2_funct_2 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A B C))) E) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A B C)) E) (k5_msualg_4 A (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A B C)) D E) (k14_osalg_4 A E B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_pboole,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k8_pboole A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k3_relat_1 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((r7_pdiff_1 A B C D E) <=>  ((r1_tarski E (k1_relset_1 (u1_struct_0 (k4_real_ns1 A)) D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ((r2_hidden F E) => (r2_pdiff_1 B A C (k2_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k22_polyform A B) = (k1_ranknull k2_bspace (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1)) (k21_polyform A B))) ) ) ) ) ).
tt(d19_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_prelamb A B C) <=>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) C) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(d19_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k18_pscomp_1 A) = (k19_euclid (k6_pscomp_1 A) (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k14_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k14_pscomp_1 A))))) ) ) ).
tt(d19_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) &  (B = (k13_qc_lang1 A C)) ) ) ) ) ) ) ) ).
tt(d19_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B C) <=>  (~  ( (~  (C = (k13_qc_lang1 A B)) )  &  ( (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( (~  (C = (k14_qc_lang1 A B D)) )  &  (~  (C = (k14_qc_lang1 A D B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (~  (C = (k15_qc_lang1 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  =>  ((v20_quantal1 A) <=> (v18_quantal1 (u1_quantal1 A) A)) ) ) ).
tt(d19_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ( (C = (k23_quaterni A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (B = (k6_quaterni D E F G))  &  (C = (k6_quaterni (k7_real_1 A D) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_quofield C A B) <=>  ((v1_quofield C A B) &  ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(d19_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_ratfunc1 A B C) = (k3_vectsp_1 A (k2_polynom4 A (k4_ratfunc1 A B) C) (k2_polynom4 A (k5_ratfunc1 A B) C))) ) ) ) ) ) ) ).
tt(d19_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v5_relat_1 B A) <=> (r1_tarski (k10_xtuple_0 B) A)) ) ) ) ).
tt(d19_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r3_rewrite1 A B) &  ((r3_rewrite1 A C) & (r2_rewrite1 A B C)) )  =>  (B = C) ) ) ) ) ) ) ).
tt(d19_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k16_rlvect_2 A) = (g1_rlvect_1 (k11_rlvect_2 A) (k13_rlvect_2 A (k4_rlvect_2 A)) (k14_rlvect_2 A) (k15_rlvect_2 A))) ) ) ).
tt(d19_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k14_robbins1 A B) = (k1_lattices A (k11_robbins1 A B) (k12_robbins1 A B))) ) ) ) ) ).
tt(d19_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ((k17_scmfsa_2 A B) = (k3_xtuple_0 12 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d19_scmpds_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  ((k4_scmpds_1 A B) = (k2_nat_1 (k1_int_2 (k1_funct_1 A B)) 2)) ) ) ) ) ).
tt(d19_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))) =>  ((v9_scmyciel B A) <=>  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (C = D) )  &  ((r2_hidden C B) &  ((r2_hidden D B) & (r2_hidden (k2_tarski C D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k26_seq_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) =>  ( (E = (a_3_3_seq_4 A B C))  =>  (D = (k5_seq_4 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_simplex0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((v1_int_1 B) & (r1_xxreal_0 B (k6_simplex0 A)))  =>  (! [C:$i] :  ((m3_simplex0 C A B) =>  (! [D:$i] :  ((m3_simplex0 D A (k4_xxreal_0 (k3_xxreal_3 B 1) (k2_xxreal_3 1))) =>  ((m4_simplex0 D A B C) <=> (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ).
tt(d19_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k20_sin_cos A) = (k1_seq_1 k19_sin_cos A)) ) ) ).
tt(d19_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( (C = (k13_stacks_1 A B))  <=>  ((r1_stacks_1 A C) &  (? [D:$i] :  ( ((v5_relat_1 D (u4_struct_0 A)) & (m1_rewrite1 D (k12_stacks_1 A)))  &  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = C)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 D) E) |  ( (~ (r1_stacks_1 A (k7_partfun1 (u4_struct_0 A) D E)))  &  ((k7_partfun1 (u4_struct_0 A) D (k1_nat_1 E 1)) = (k5_stacks_1 A (k7_partfun1 (u4_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_struct_0,ax, (! [A:$i] :  (! [B:$i] :  ((l1_struct_0 B) =>  ((v13_struct_0 B A) <=> (v3_card_1 (u1_struct_0 B) A)) ) ) ) ).
tt(d19_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v2_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) &  (B = (k1_domain_1 (k3_cqc_lang A) (k1_substut1 A) (k5_cqc_lang A) C)) ) ) ) ) ) ) ) ).
tt(d19_turing_1,ax, (! [A:$i] :  ( ((v1_turing_1 A) & (l1_turing_1 A))  =>  ( (A = k18_turing_1)  <=>  ( ((u1_turing_1 A) = (k7_domain_1 k5_numbers k6_numbers 1))  &  ( ((u2_turing_1 A) = (k3_turing_1 4))  &  ((r1_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) k17_turing_1) &  ( ((u4_turing_1 A) = k6_numbers)  &  ((u5_turing_1 A) = 4) ) ) ) ) ) ) ) ).
tt(d19_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k20_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C)) (k9_margrel1 D))) ) ) ) ) ) ) ) ) ) ).
tt(d19_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v10_valued_0 A) <=>  ((k1_funct_1 A k1_xboole_0) = k6_numbers) ) ) ) ).
tt(d19_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  =>  ((k64_valued_1 A) = (k2_xxreal_2 (k1_relset_1 k5_numbers A))) ) ) ).
tt(d19_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k13_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ) ) ) ).
tt(d19_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((v12_vectsp_1 A) <=>  (~  ((k1_algstr_0 A (k5_struct_0 A) (k5_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(d19_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r1_orders_2 A D C))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(d19_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v9_waybel_1 A) <=>  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_waybel_1 (k4_waybel_1 A B) A A)) ) ) ) ) ) ).
tt(d19_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v7_waybel34 B A) <=> (r2_hidden (k3_yellow_0 A) (u1_struct_0 B))) ) ) ) ) ).
tt(d19_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k12_waybel_4 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v5_waybel_4 C A) &  ((v6_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(d19_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v8_yellow_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_yellow_0 A C) => (r2_hidden (k1_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d19_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ( (B = (k12_yellow_6 A))  <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C (k6_yellow_6 A)) & (r2_hidden D (k10_yellow_6 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d19_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k13_zf_lang A B) = (k6_zf_lang (k8_zf_lang A (k6_zf_lang B)))) ) ) ) ) ).
tt(d19_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((v8_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((m3_zmodul01 C A B) <=> (r1_zmodul01 A C B)) ) ) ) ) ) ) ) ).
tt(d1_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_abcmiz_1 A))  <=>  ((r1_tarski A B) &  ( (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) => (r1_tarski C B)) ) )  &  (! [C:$i] :  ( ((r1_tarski A C) &  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) => (r1_tarski D C)) ) ) )  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(d1_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v1_abcmiz_a A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v2_abcmiz_1 B A) =>  ((r2_hidden B k20_abcmiz_1) &  ( ((k1_xtuple_0 B) = (k2_msualg_1 A B))  &  ((k1_card_1 (k1_xtuple_0 (k2_xtuple_0 B))) = (k3_finseq_1 (k1_msualg_1 A B))) ) ) ) ) ) ) ) ) ).
tt(d1_abian,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) <=> (r1_int_1 2 A)) ) ) ).
tt(d1_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) =>  ((k16_complex1 A) = A) )  &  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k16_complex1 A) = (k4_xcmplx_0 A)) ) ) ) ) ).
tt(d1_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_aff_1 A B C D) <=> (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(d1_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_analoaf A D H E G) & (r2_analoaf A E I F H)) ) ) ) ) ) ) ) )  => (r2_analoaf A D I F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden E C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden E D) &  ((r2_hidden J D) &  ((r2_hidden K D) &  ((r1_aff_1 A H F L) &  ((r1_aff_1 A I G L) &  ((r1_aff_1 A H J M) &  ((r1_aff_1 A I K M) & (r2_analoaf A F J G K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (C = B)  |  ( (C = D)  |  ( (B = D)  |  ( (E = F)  |  ( (E = H)  |  ( (E = J)  |  ( (L = M)  |  ((r1_aff_1 A H F J) |  ((r1_aff_1 A I G K) |  ( (F = G)  | (r2_analoaf A F J L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_aff_4 A B C) = (a_3_0_aff_4 A B C)) ) ) ) ) ) ) ).
tt(d1_afinsq_1,ax, (! [A:$i] :  ((k3_afinsq_1 A) = (k16_funcop_1 k6_numbers A)) ) ).
tt(d1_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ( (B = (k1_afinsq_2 A))  <=>  ( ((k1_afinsq_1 B) = (k1_afinsq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 B C) = (k1_funct_1 A (k21_binop_2 (k1_afinsq_1 A) (k23_binop_2 C 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k1_afproj A) = (a_1_0_afproj A)) ) ) ).
tt(d1_afvect01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_afvect01 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C C B)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_analoaf A B C B B) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A D E F G))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_analoaf A B D D C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_analoaf A F B F C) & (r2_analoaf A F D F E))  =>  ( (B = C)  |  ( (D = E)  | (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = D) )  & (r2_analoaf A B C C D)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (E = F) )  &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B E E C) & (r2_analoaf A B F F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C C G) &  ((r2_analoaf A C D E F) &  ((r2_analoaf A C E E D) & (r2_analoaf A C F F D)) ) )  => (r2_analoaf A B D D G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ((r2_analoaf A B C C E) &  ((r2_analoaf A B D D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (F = G) )  &  ((r2_analoaf A C D F G) &  ((r2_analoaf A C F F D) & (r2_analoaf A C G G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C E F) &  ((r2_analoaf A B D G H) &  ((r2_analoaf A B E E C) &  ((r2_analoaf A B G G D) &  ((r2_analoaf A B F F C) &  ((r2_analoaf A B H H D) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ((r2_analoaf A C D I J) &  ((r2_analoaf A C I I D) & (r2_analoaf A C J J D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_afvect0 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) =>  (B = C) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A D E F G))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r2_analoaf A B C D E)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C E F) & (r2_analoaf A B D E G))  => (r2_analoaf A C D F G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_analoaf A B D D C)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) <=>  ((r1_unialg_2 A B) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 (u1_unialg_1 A))) =>  (! [E:$i] :  ((m5_margrel1 E (u1_struct_0 A) (k1_unialg_2 A)) =>  (! [F:$i] :  ((m5_margrel1 F (u1_struct_0 B) (k1_unialg_2 B)) =>  ( ( (E = (k1_funct_1 (u1_unialg_1 A) D))  &  (F = (k1_funct_1 (u1_unialg_1 B) D)) )  =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  ((r2_hidden G (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) E)) =>  ((k1_funct_1 C (k1_funct_1 E G)) = (k1_funct_1 F (k4_finseqop (u1_struct_0 A) (u1_struct_0 B) G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_algseq_1 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((k1_funct_1 B D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k1_algspec1 A B) = (k1_funct_4 (k6_partfun1 A) (k5_relat_1 B A))) ) ) ) ).
tt(d1_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) B C)) ) ) ) ) ) ) ).
tt(d1_algstr_1,ax, (! [A:$i] :  ((k1_algstr_1 A) = A) ) ).
tt(d1_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v3_algstr_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k1_algstr_2 A B))  <=>  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d1_algstr_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_3 A B C D) = (k2_multop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_3 A) B C D)) ) ) ) ) ) ) ) ) ).
tt(d1_ali2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v1_ali2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k4_metric_1 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E)) (k8_real_1 C (k4_metric_1 A D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_altcat_1,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_altcat_1 A B C) = (k1_binop_1 (u1_altcat_1 A) B C)) ) ) ) ) ) ) ).
tt(d1_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) =>  ((r1_altcat_3 A B C D E) <=>  ((k5_altcat_1 A C B C E D) = (k8_altcat_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (m1_altcat_2 B A)) ) )  =>  ( (B = (k1_altcat_4 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C D)) =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  & (v4_altcat_3 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ami_2,ax, (k1_ami_2 = (k2_xboole_0 (k1_tarski k5_numbers) k2_scm_inst)) ).
tt(d1_ami_3,ax, (k1_ami_3 = (g1_extpro_1 2 k1_ami_2 (k1_funct_7 k5_numbers k1_ami_2) k3_scm_inst k3_ami_2 k4_ami_2 k9_ami_2)) ).
tt(d1_ami_4,ax, (k1_ami_4 = (k1_funct_4 (k16_funcop_1 k6_numbers (k2_ami_3 (k10_ami_3 2) (k10_ami_3 1))) (k1_funct_4 (k16_funcop_1 1 (k6_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k1_funct_4 (k16_funcop_1 2 (k2_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 2))) (k1_funct_4 (k16_funcop_1 3 (k9_ami_3 k6_numbers (k10_ami_3 1))) (k16_funcop_1 4 (k2_compos_1 k1_ami_3))))))) ).
tt(d1_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_extpro_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_compos_0 (u1_compos_1 B))) =>  ((v1_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_compos_1 B)) =>  ( ( ((k2_compos_0 (u1_compos_1 B) F) = C)  & (r2_hidden E (k8_struct_0 B)))  =>  ((k1_funct_1 (k2_extpro_1 A B F D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v1_amistd_2 C A B) <=>  ((k2_amistd_1 A B C) = (k10_xtuple_0 (k5_xtuple_0 C))) ) ) ) ) ) ) ) ).
tt(d1_amistd_3,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k5_numbers)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D k5_numbers) &  ((v5_ordinal1 D) & (v1_funct_1 D)) ) )  =>  ( (D = (k1_amistd_3 A B C))  <=>  ( ((k9_xtuple_0 D) = (k1_card_1 C))  &  (! [E:$i] :  ((r2_hidden E (k1_card_1 C)) =>  ((k1_funct_1 D E) = (k1_funct_1 (k3_wellord1 (k1_wellord2 (k2_wellord2 (k1_wellord2 C))) (k1_wellord2 C)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v1_amistd_5 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  => (r8_pboole (u1_struct_0 B) (k2_extpro_1 A B (k5_compos_0 (u1_compos_1 B) C (k2_xcmplx_0 D E)) (k9_memstr_0 A B F E)) (k9_memstr_0 A B (k2_extpro_1 A B (k5_compos_0 (u1_compos_1 B) C D) F) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_ami_wstd A B C D) <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_finseq_1 E k5_numbers))  &  ( ((k7_partfun1 k5_numbers E 1) = C)  &  ( ((k7_partfun1 k5_numbers E (k3_finseq_1 E)) = D)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) | (r2_hidden (k7_partfun1 k5_numbers E (k2_nat_1 F 1)) (k3_amistd_1 A B (k7_partfun1 k5_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analoaf A B C D E) <=>  (~  ( (~  (B = C) )  &  ( (~  (D = E) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 G k6_numbers))  &  ((k1_rlvect_1 A (k5_algstr_0 A C B) F) = (k1_rlvect_1 A (k5_algstr_0 A E D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_analort A B C D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k2_geomtrap A B C D)) (k1_rlvect_1 A C (k1_real_1 (k3_geomtrap A B C D))))) ) ) ) ) ) ) ) ) ).
tt(d1_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_anproj_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( ((k1_rlvect_1 A B D) = (k1_rlvect_1 A C E))  &  ( (~  (D = k6_numbers) )  &  (~  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_anproj_2 A B C D) <=>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  (~ (v9_struct_0 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  =>  (! [B:$i] :  ((r1_aofa_000 A B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k10_finseq_1 C D) (k9_xtuple_0 A)) | (r2_hidden (k10_finseq_1 D C) (k9_xtuple_0 A)))  =>  ((r2_hidden (k10_finseq_1 B C) (k9_xtuple_0 A)) &  ( ((k1_funct_1 A (k10_finseq_1 B C)) = C)  &  ((r2_hidden (k10_finseq_1 C B) (k9_xtuple_0 A)) &  ((k1_funct_1 A (k10_finseq_1 C B)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k1_aofa_i00 A B C) = (a_3_0_aofa_i00 A B C)) ) ) ) ) ).
tt(d1_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (C = (k1_armstrng A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (r2_waybel_4 A D B)) ) ) ) ) ) ) ) ).
tt(d1_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (B = (k2_arrow A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k4_tarski D E) C) | (r2_hidden (k4_tarski E D) C)) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski E F) C))  => (r2_hidden (k4_tarski D F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2))  =>  ( (C = (k1_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = D)  &  ( (B = E)  &  (C = (k7_arytm_2 D E)) ) ) ) ) ) ) ) )  &  ( ( ((r2_hidden A k2_arytm_2) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ( (C = (k1_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = D)  &  ( (B = (k4_tarski k6_numbers E))  &  (C = (k2_arytm_1 D E)) ) ) ) ) ) ) ) )  &  ( ( ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ( (C = (k1_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = (k4_tarski k6_numbers D))  &  ( (B = E)  &  (C = (k2_arytm_1 E D)) ) ) ) ) ) ) ) )  &  (~  ( (~  ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2)) )  &  ( (~  ((r2_hidden A k2_arytm_2) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) )  &  ( (~  ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) )  &  (~  ( (C = (k1_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = (k4_tarski k6_numbers D))  &  ( (B = (k4_tarski k6_numbers E))  &  (C = (k4_tarski k6_numbers (k7_arytm_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 B A) =>  ( (C = (k1_arytm_1 A B))  <=>  ((k7_arytm_2 C B) = A) ) )  &  ( (~ (r1_arytm_2 B A))  =>  ( (C = (k1_arytm_1 A B))  <=>  (C = k11_arytm_3) ) ) ) ) ) ) ) ) ) ).
tt(d1_arytm_2,ax, (k1_arytm_2 = (k6_subset_1 a_0_0_arytm_2 (k1_tarski k5_arytm_3))) ).
tt(d1_arytm_3,ax, (k1_arytm_3 = 1) ).
tt(d1_asympt_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_asympt_0 A) <=>  ( (~ (r1_xxreal_0 A k6_numbers))  &  (~  (A = 1) ) ) ) ) ) ).
tt(d1_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k1_asympt_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k4_power A (k7_real_1 (k8_real_1 B E) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) =>  ( (B = (k1_autalg_1 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_hidden C B) <=> (r4_alg_1 A A C)) ) ) ) ) ) ) ) ).
tt(d1_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) =>  ( (B = (k1_autgroup A))  <=>  ( (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_group_6 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_group_6 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r2_hidden C B) <=>  ((v2_funct_1 C) & (v2_funct_2 C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d1_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (k7_nat_d C B)) &  ((v1_funct_1 E) & (v1_partfun1 E (k7_nat_d C B))) ) )  =>  ( (E = (k1_bagorder A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k7_nat_d C B)) =>  ((k1_funct_1 E F) = (k1_funct_1 D (k1_nat_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bcialg_1,ax, (! [A:$i] :  ((l1_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_bcialg_1 A) B C)) ) ) ) ) ) ) ).
tt(d1_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (E = (k1_bcialg_2 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ( (E = (k3_funct_2 k5_numbers (u1_struct_0 A) F D))  &  ( ((k3_funct_2 k5_numbers (u1_struct_0 A) F k6_numbers) = B)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( (~ (r1_xxreal_0 D G))  =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) F (k2_nat_1 G 1)) = (k1_bcialg_1 A (k3_funct_2 k5_numbers (u1_struct_0 A) F G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v1_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(d1_bcialg_4,ax, (! [A:$i] :  ((l1_bcialg_4 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_4 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_bcialg_4 A) B C)) ) ) ) ) ) ) ).
tt(d1_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_bcialg_5 A B C D E) = (k1_bcialg_2 A (k1_bcialg_2 A B (k1_bcialg_1 A B C) (k2_nat_1 D 1)) (k1_bcialg_1 A C B) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  =>  ( (B = (k2_bcialg_6 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C k6_numbers) = (k4_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C (k23_binop_2 D 1)) = (k1_bcialg_1 A C (k2_bcialg_1 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bciideal A B) = (a_2_0_bciideal A B)) ) ) ) ) ).
tt(d1_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bhsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bhsp_1 A B C) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_bhsp_1 A) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(d1_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k4_bhsp_1 A (k1_normsp_1 A B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k4_bhsp_1 A (k1_normsp_1 A B E) (k1_normsp_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k1_bhsp_4 A B))  <=>  ( ((k1_normsp_1 A C k6_numbers) = (k1_normsp_1 A B k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C (k2_nat_1 D 1)) = (k1_algstr_0 A (k1_normsp_1 A C D) (k1_normsp_1 A B (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k1_bhsp_6 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ((v2_funct_1 D) &  ( ((k2_relset_1 (u1_struct_0 A) D) = B)  &  (C = (k1_finsop_1 (u1_struct_0 A) D (u1_algstr_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((l1_vectsp_1 B A) =>  (! [C:$i] :  ((l1_vectsp_1 C A) =>  ((k1_bilinear A B C) = (k8_funcop_1 (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (k4_struct_0 A))) ) ) ) ) ) ) ).
tt(d1_binari_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( (B = (k1_binari_2 A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 B C) = (k15_funcop_1 k6_margrel1 C 1 k8_margrel1 k7_margrel1)) ) ) ) ) ) ) ) ) ).
tt(d1_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( (C = (k1_binari_3 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 C D) = (k15_funcop_1 k6_margrel1 (k4_nat_d (k3_nat_d B (k5_series_1 2 (k7_nat_d D 1))) 2) k6_numbers k7_margrel1 k8_margrel1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k1_binari_4 A B))  <=>  ((r1_xxreal_0 B (k5_series_1 2 C)) &  ((r1_xxreal_0 A C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 B (k5_series_1 2 D)) & (r1_xxreal_0 A D))  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_binarith,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( (C = (k3_binarith A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 C D) = (k9_margrel1 (k7_partfun1 k6_margrel1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k1_binom A B C))  <=>  ( ((k1_relset_1 k5_numbers D) = (k1_relset_1 k5_numbers B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 D)))  =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B E) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_binop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k1_binop_1 A B C) = (k1_funct_1 A (k4_tarski B C))) ) ) ) ) ).
tt(d1_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k25_binop_2)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_funct_1 A B) = (k1_binop_2 B)) ) ) ) ) ) ).
tt(d1_bintree1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((k1_bintree1 A B) = (k1_funct_1 B k1_xboole_0)) ) ) ) ) ).
tt(d1_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_trees_2 A B) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_trees_2 A B) k5_numbers)))) )  =>  ( (C = (k1_bintree2 A B))  <=>  (! [D:$i] :  ((m1_bintree2 D A) =>  ((r2_hidden D (k2_trees_2 A B)) =>  (! [E:$i] :  ((m2_finseq_2 E k6_margrel1 (k4_finseq_2 B k6_margrel1)) =>  ( (E = (k4_finseq_5 k6_margrel1 D))  =>  ((k1_funct_1 C D) = (k2_nat_1 (k6_binarith B E) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_birkhoff,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) B (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)) (u3_msualg_1 A C)) =>  ( (E = (k1_birkhoff A B C D))  <=>  ((r1_msualg_3 A (k11_msafree A B) C E) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)) (u3_msualg_1 A C) (k13_msafree A B) E) (k3_msualg_3 (u1_struct_0 A) (k13_msafree A B) B (u3_msualg_1 A C) (k15_msafree A B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_boolealg A B C) = (k4_lattices A B (k7_lattices A C))) ) ) ) ) ) ) ).
tt(d1_boolmark,ax, (! [A:$i] :  ((l1_petri A) =>  ((k1_boolmark A) = (k9_funct_2 (u1_struct_0 A) k6_margrel1)) ) ) ).
tt(d1_bor_cant,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k2_bor_cant A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 B C) = (k4_series_1 (k4_sin_cos (k4_xcmplx_0 (k1_funct_1 A C))))) ) ) ) ) ) ) ) ).
tt(d1_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_connsp_2 E B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_connsp_2 F A D) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_borsuk_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_2 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  &  ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_borsuk_4,ax, (! [A:$i] :  ( ((v1_pre_topc A) & (m1_pre_topc A k5_topmetr))  =>  ( (A = k1_borsuk_4)  <=>  ((u1_struct_0 A) = (k2_rcomp_1 k6_numbers 1)) ) ) ) ).
tt(d1_borsuk_5,ax, (k1_borsuk_5 = (k6_subset_1 k1_numbers k3_numbers)) ).
tt(d1_borsuk_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_borsuk_6 A B C D) = (k1_partfun1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr C D)) (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1)) (k3_treal_1 C D (k1_treal_1 C D) (k2_treal_1 C D)))) ) ) ) ) ) ) ) ) ).
tt(d1_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k1_borsuk_7 A B C D E F) = (k1_funct_4 (k4_funct_4 A B D E) (k16_funcop_1 C F))) ) ) ) ) ) ) ).
tt(d1_brouwer,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((k1_brouwer A B) = (a_2_0_brouwer A B)) ) ) ) ) ).
tt(d1_bspace,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k1_bspace A) = (k6_finseq_1 (k2_struct_0 A))) ) ) ).
tt(d1_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((r1_xxreal_0 A B) <=>  ((k6_xboolean A B) = k8_margrel1) ) ) ) ) ) ).
tt(d1_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( (C = (k2_bvfunc_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ( ((k9_xtuple_0 E) = B)  &  ( ((k10_xtuple_0 E) = F)  &  ( (! [G:$i] :  ((r2_hidden G B) => (r2_hidden (k1_funct_1 E G) G)) )  &  ( (D = (k8_setfam_1 A F))  &  (~  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_c0sp1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ) ).
tt(d1_c0sp2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_c0sp2 A B) = (k7_funcop_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(d1_calcul_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ( (C = (k1_calcul_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k3_finseq_1 B) = (k2_nat_1 D 1))  => (r2_relset_1 k5_numbers A C (k2_partfun1 k5_numbers A B (k2_finseq_1 D)))) ) ) ) )  &  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) =>  ( (C = (k1_calcul_1 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d1_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_calcul_2 A B) = (a_2_0_calcul_2 A B)) ) ) ) ) ).
tt(d1_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k1_cantor_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((r1_tarski E B) &  (D = (k5_setfam_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_card_1,ax, (! [A:$i] :  ((v1_card_1 A) <=>  (? [B:$i] :  ((v3_ordinal1 B) &  ( (A = B)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_wellord2 C B) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ).
tt(d1_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k1_card_2 A B) = (k1_card_1 (k10_ordinal2 A B))) ) ) ) ) ).
tt(d1_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_card_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_card_1 (k1_funct_1 A B))) ) ) ) ) ).
tt(d1_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k1_card_5 A))  <=>  ((r2_ordinal2 A B) &  (! [C:$i] :  ((v1_card_1 C) =>  ((r2_ordinal2 A C) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ) ).
tt(d1_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((m1_card_fil B A) <=>  ( (~ (r2_hidden k1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k9_subset_1 A C D) B))  &  ( ((r2_hidden C B) & (r1_tarski C D))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cardfin2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_cardfin2 A) = (k1_int_1 (k9_binop_2 A (k18_binop_2 1 2)))) ) ) ).
tt(d1_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 A (k2_tarski C D)))) =>  ( (E = (k1_card_fin A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (k2_tarski C D)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (k2_tarski C D))))) )  &  ( (G = F)  &  ((k5_card_1 (k8_relset_1 A (k2_tarski C D) G (k1_tarski C))) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((r1_card_lar A B) <=>  ((r1_tarski B A) &  ((k3_ordinal2 B) = A) ) ) ) ) ) ).
tt(d1_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_hidden (k4_tarski C B) (k9_xtuple_0 (u1_cat_1 A))) =>  ((k1_cat_1 A B C) = (k1_binop_1 (u1_cat_1 A) C B)) ) ) ) ) ) ) ) ).
tt(d1_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_cat_2 A B C) = (k8_funcop_1 (u4_struct_0 B) (u4_struct_0 A) (k4_cat_1 B C))) ) ) ) ) ) ) ).
tt(d1_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (D = (k2_cat_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k3_graph_1 A (k7_partfun1 (u4_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_cat_1 A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_cat_1 D A B C) &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v1_cat_5 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (? [C:$i] :  (B = (k4_tarski (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k3_graph_1 A B) (k4_graph_1 A B)) C)) ) ) ) ) ) ) ).
tt(d1_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_catalan1 A) = (k10_real_1 (k6_newton (k7_nat_d A 1) (k7_nat_d (k4_nat_1 2 A) 2)) A)) ) ) ).
tt(d1_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_catalan2 A) <=>  ((r1_tarski (k2_relset_1 k5_numbers A) (k7_domain_1 k5_numbers k6_numbers 1)) &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 (k24_binop_2 2 (k7_afinsq_2 (k5_relat_1 A B))) B)) ) ) ) ) ) ) ).
tt(d1_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) )  =>  ( (D = (k1_catalg_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k5_relat_1 C (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cayley,ax, (! [A:$i] :  ((k1_cayley A) = (a_1_0_cayley A)) ) ).
tt(d1_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v2_cfuncdom B) & (l1_cfuncdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((m1_cc0sp1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((u1_clvect_1 B) = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers (u1_struct_0 B))))  &  ( ((k5_struct_0 B) = (k5_struct_0 A))  &  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cc0sp2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ((v1_cc0sp2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k2_numbers)) =>  ((v5_cfdiff_1 C) => (v4_pre_topc (k8_relset_1 (u1_struct_0 A) k2_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(d1_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r1_cfcont_1 A B) <=>  ((r2_hidden B (k1_relset_1 k2_numbers A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers C) (k1_relset_1 k2_numbers A)) &  ((v2_comseq_2 C) &  ((k3_comseq_2 C) = B) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C A)) &  ((k7_partfun1 k2_numbers A B) = (k3_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cfdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_cfdiff_1 B A) <=>  ((v2_comseq_2 B) &  ((k3_comseq_2 B) = A) ) ) ) ) ) ) ).
tt(d1_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) )  =>  ( (B = (k1_cfuncdom A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers B C D) (k3_funcsdom k2_numbers A k27_binop_2 C D))) ) ) ) ) ) ) ) ) ).
tt(d1_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( (D = (k1_cfunct_1 A B C))  <=>  ( ((k1_relset_1 A D) = (k9_subset_1 A (k1_relset_1 A B) (k7_subset_1 A (k1_relset_1 A C) (k8_relset_1 A k2_numbers C (k1_tarski k6_numbers)))))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  ((k7_partfun1 k2_numbers D E) = (k9_complex1 (k7_partfun1 k2_numbers B E) (k12_complex1 (k7_partfun1 k2_numbers C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cgames_1,ax, (k1_cgames_1 = (g1_cgames_1 k1_xboole_0 k1_xboole_0)) ).
tt(d1_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_chord A B) = (k10_xtuple_0 (k1_graph_2 A B (k3_finseq_1 A)))) ) ) ) ) ).
tt(d1_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circcmb3 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) & (v1_circuit2 (k5_facirc_1 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(d1_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ((l1_msualg_1 B) =>  ((r1_circcomb A B) <=>  ((r1_partfun1 (u1_msualg_1 A) (u1_msualg_1 B)) & (r1_partfun1 (u2_msualg_1 A) (u2_msualg_1 B))) ) ) ) ) ) ).
tt(d1_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_rltopsp1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 (k18_complex1 D) 1) & (r2_hidden C B))  => (r2_hidden (k1_rlvect_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((k1_circtrm1 A B C) = (g1_msualg_1 (k9_trees_9 C) (k12_trees_9 C (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) (k13_trees_9 C (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) (k6_funct_3 (k9_trees_9 C) (k12_trees_9 C (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))))) ) ) ) ) ) ) ).
tt(d1_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k1_msafree2 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k1_msafree2 A))) ) )  =>  ( (C = (k1_circuit1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_relset_1 (k1_msafree2 A) C)) => (r2_hidden (k1_funct_1 C D) (k1_msualg_2 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (k13_msafree A (u3_msualg_1 A B)) (u3_msualg_1 A (k5_msafree2 A B))) =>  ( (D = (k2_circuit2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E (k2_msafree2 A)) => (r1_funct_2 (k1_funct_1 (k13_msafree A (u3_msualg_1 A B)) E) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) E) (k12_msafree A (u3_msualg_1 A B) E) (k1_tarski (k1_trees_4 (k4_tarski (k1_funct_1 C E) E))) (k1_msualg_3 (u1_struct_0 A) (k13_msafree A (u3_msualg_1 A B)) (u3_msualg_1 A (k5_msafree2 A B)) D E) (k7_funcop_1 (k12_msafree A (u3_msualg_1 A B) E) (k1_trees_4 (k4_tarski (k1_funct_1 C E) E)))))  &  ( ((r2_hidden E (k1_msafree2 A)) => (r1_funct_2 (k1_funct_1 (k13_msafree A (u3_msualg_1 A B)) E) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) E) (k12_msafree A (u3_msualg_1 A B) E) (k1_tarski (k1_trees_4 (k4_tarski (k4_msafree2 A E) (u1_struct_0 A)))) (k1_msualg_3 (u1_struct_0 A) (k13_msafree A (u3_msualg_1 A B)) (u3_msualg_1 A (k5_msafree2 A B)) D E) (k7_funcop_1 (k12_msafree A (u3_msualg_1 A B) E) (k1_trees_4 (k4_tarski (k4_msafree2 A E) (u1_struct_0 A))))))  &  ((r2_hidden E (k7_subset_1 (u1_struct_0 A) (k3_msafree2 A) (k1_msafree2 A))) =>  ((k1_msualg_3 (u1_struct_0 A) (k13_msafree A (u3_msualg_1 A B)) (u3_msualg_1 A (k5_msafree2 A B)) D E) = (k6_partfun1 (k12_msafree A (u3_msualg_1 A B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_classes1,ax, (! [A:$i] :  ((v1_classes1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r1_tarski C B))  => (r2_hidden C A)) ) ) ) ) ).
tt(d1_classes2,ax, (! [A:$i] :  ((v1_classes2 A) <=>  ((v1_ordinal1 A) & (v2_classes1 A)) ) ) ).
tt(d1_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k2_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) )  =>  ( (C = (k2_clopban1 A B))  <=>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_funct_1 (k1_funct_1 C (k4_tarski D E)) F) = (k1_clvect_1 B (k3_funct_2 A (u1_struct_0 B) E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  ((k2_clopban2 A B C) = (k5_binop_1 (k8_clopban1 A A) (k8_csspace (k6_clopban1 A A) (k8_clopban1 A A)) B C)) ) ) ) ) ) ) ).
tt(d1_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clopban3 B A) <=> (v9_clvect_1 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(d1_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k1_clopban4 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C D) = (k1_clvect_1 A (k6_clopban3 A B D) (k13_complex1 k6_complex1 (k3_newton D)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ((v1_closure1 C A B) <=>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) => (r2_pboole A D (k2_closure1 A B C D))) ) ) ) ) ) ) ) ).
tt(d1_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( (C = (k1_closure2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (m3_pboole D A B)) ) ) ) ) ) ) ).
tt(d1_closure3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k1_closure3 A B) = (a_2_0_closure3 A B)) ) ) ) ) ).
tt(d1_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_clvect_1 A B C) = (k1_funct_1 (u1_clvect_1 A) (k4_tarski C B))) ) ) ) ) ) ) ).
tt(d1_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k15_csspace A (k1_normsp_1 A B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) <=> (v1_clvect_2 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(d1_cohsp_1,ax, (! [A:$i] :  ((v1_coh_sp A) <=>  (! [B:$i] :  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k2_xboole_0 C D) A)) ) )  => (r2_hidden (k3_tarski B) A)) ) ) ) ).
tt(d1_coh_sp,ax, (! [A:$i] :  ((v1_coh_sp A) <=>  (! [B:$i] :  ( ((r1_tarski B A) &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k2_xboole_0 C D) A)) ) ) )  => (r2_hidden (k3_tarski B) A)) ) ) ) ).
tt(d1_collsp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_collsp B A) <=> (r1_tarski B (k3_zfmisc_1 A A A))) ) ) ).
tt(d1_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ( ((v1_incsp_1 C) &  ((v5_incsp_1 C) &  ((v7_incsp_1 C) & (l1_incsp_1 C)) ) )  =>  ( (C = (k1_combgras A B))  <=>  ( ((u1_incsp_1 C) = (a_2_0_combgras A B))  &  ( ((u2_incsp_1 C) = (a_2_1_combgras A B))  &  ((u3_incsp_1 C) = (k3_xboole_0 (k1_wellord2 (k9_setfam_1 B)) (k2_zfmisc_1 (u1_incsp_1 C) (u2_incsp_1 C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_commacat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  ( (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (u4_struct_0 C)) & (r2_hidden H (k2_cat_1 C (k8_cat_1 A C D F) (k8_cat_1 B C E G)))) ) ) ) ) )  =>  ((k1_commacat A B C D E) = (a_5_0_commacat A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((r2_hidden A k1_numbers) =>  ( (B = (k1_complex1 A))  <=>  (B = A) ) )  &  ( (~ (r2_hidden A k1_numbers))  =>  ( (B = (k1_complex1 A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 2 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 2 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_funct_1 C k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(d1_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_complex2 A B) = (k3_xcmplx_0 A (k15_complex1 B))) ) ) ) ) ).
tt(d1_complfld,ax, (! [A:$i] :  ( ((v36_algstr_0 A) & (l6_algstr_0 A))  =>  ( (A = k1_complfld)  <=>  ( ((u1_struct_0 A) = k2_numbers)  &  ( ((u1_algstr_0 A) = k27_binop_2)  &  ( ((u2_algstr_0 A) = k29_binop_2)  &  ( ((k5_struct_0 A) = k6_complex1)  &  ((k4_struct_0 A) = k5_complex1) ) ) ) ) ) ) ) ).
tt(d1_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_complsp1 A) = (g1_pre_topc (k14_seq_4 A) (k27_seq_4 A))) ) ) ).
tt(d1_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( (B = (k1_complsp2 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k9_matrix_5 B C) = (k15_complex1 (k9_matrix_5 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((v1_compl_sp B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (v6_tbsp_1 (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(d1_compos_0,ax, (! [A:$i] :  ((v1_compos_0 A) <=>  (? [B:$i] :  ( (~ (v1_xboole_0 B))  & (r1_tarski A (k3_zfmisc_1 k5_numbers (k13_finseq_1 k5_numbers) (k13_finseq_1 B)))) ) ) ) ).
tt(d1_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k1_compos_2 A B C) = (k8_compos_1 A (k11_compos_1 A B) C)) ) ) ) ) ) ) ).
tt(d1_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( (~  (A = k6_numbers) )  =>  ( (B = (k1_comptrig A))  <=>  ( (A = (k2_xcmplx_0 (k8_real_1 (k17_complex1 A) (k21_sin_cos B)) (k3_xcmplx_0 (k8_real_1 (k17_complex1 A) (k18_sin_cos B)) k7_complex1)))  &  ((r1_xxreal_0 k6_numbers B) &  (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) B)) ) ) ) )  &  ( (A = k6_numbers)  =>  ( (B = (k1_comptrig A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d1_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (v1_finset_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_comput_1,ax, (! [A:$i] :  ((v1_comput_1 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_partfun1 B C)) ) ) ) ) ) ) ).
tt(d1_comseq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k1_comseq_3 A))  <=>  ( ((k8_nat_1 k2_numbers B k6_numbers) = k6_complex1)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers B (k2_nat_1 C 1)) = (k3_xcmplx_0 (k8_nat_1 k2_numbers B C) A)) ) ) ) ) ) ) ) ) ).
tt(d1_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v1_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r5_analmetr A B C D) &  ((r5_analmetr A B E F) &  ((r5_analmetr A B G H) &  ((r2_analoaf A C E D F) & (r2_analoaf A C G D H)) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ((r5_analmetr A E F C) |  ((r5_analmetr A C D G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k1_conlat_2 A B) = B) ) ) ) ) ).
tt(d1_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A J K) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((r2_hidden H J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden G J) |  ((r2_hidden I J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden F K) |  ((r2_hidden H K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v1_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B I) &  ((r2_hidden C I) &  ((r2_hidden D I) &  ((r2_hidden E I) &  ((r2_hidden B J) &  ((r2_hidden F J) &  ((r2_hidden G J) &  ((r2_hidden H J) &  ((r10_analmetr A I J) &  ((r2_analoaf A E G D F) & (r2_analoaf A E H C F)) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden G I) |  ((r2_hidden E J) |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  | (r2_analoaf A C G D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  ((r1_xboole_0 (k2_pre_topc A B) C) & (r1_xboole_0 B (k2_pre_topc A C))) ) ) ) ) ) ) ) ).
tt(d1_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_connsp_2 C A B) <=> (r2_hidden B (k1_tops_1 A C))) ) ) ) ) ) ) ).
tt(d1_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_connsp_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) <=>  ((v2_connsp_1 E A) & (r1_tarski B E)) ) ) )  &  ((k5_setfam_1 (u1_struct_0 A) D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_convex1 A B C) = (a_3_0_convex1 A B C)) ) ) ) ) ) ) ).
tt(d1_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k1_convex3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v2_convex1 C A) & (m1_rlvect_2 C A)) ) ) ) ) ) ) ).
tt(d1_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k2_numbers (k9_funct_2 (u1_struct_0 A) k2_numbers)) =>  ((m1_convex4 B A) <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_hidden D C))  =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) )  =>  ( (C = (k1_convfun1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ( ( (D = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) F H))  &  (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) G I)) )  =>  ((k5_binop_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C D E) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u1_algstr_0 A) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) F G)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 B) (u1_algstr_0 B) (k1_domain_1 (u1_struct_0 B) (u1_struct_0 B) H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A)))))  =>  (! [D:$i] :  ((m2_finseq_1 D (k2_qc_lang1 A)) =>  ( (D = (k1_cqc_lang A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ( ((r2_hidden (k1_funct_1 B E) (k9_xtuple_0 C)) =>  ((k1_funct_1 D E) = (k1_funct_1 C (k1_funct_1 B E))) )  &  ( (~ (r2_hidden (k1_funct_1 B E) (k9_xtuple_0 C)))  =>  ((k1_funct_1 D E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v1_cqc_the1 B A) <=>  ((r2_hidden (k5_cqc_lang A) B) &  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C) B) &  ((r2_hidden (k8_cqc_lang A C (k8_cqc_lang A (k6_cqc_lang A C) D)) B) &  ((r2_hidden (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A D E)) (k6_cqc_lang A (k7_cqc_lang A C E)))) B) &  ((r2_hidden (k8_cqc_lang A (k7_cqc_lang A C D) (k7_cqc_lang A D C)) B) &  ( ( ((r2_hidden C B) & (r2_hidden (k8_cqc_lang A C D) B))  => (r2_hidden D B))  &  ((r2_hidden (k8_cqc_lang A (k11_cqc_lang A G C) C) B) &  ( ((r2_hidden (k8_cqc_lang A C D) B) =>  ((r2_hidden G (k24_qc_lang1 A C)) | (r2_hidden (k8_cqc_lang A C (k11_cqc_lang A G D)) B)) )  &  ( ((r2_hidden (k13_cqc_lang A F G) (k3_cqc_lang A)) &  ((r2_hidden (k13_cqc_lang A F H) (k3_cqc_lang A)) & (r2_hidden (k13_cqc_lang A F G) B)) )  =>  ((r2_hidden G (k24_qc_lang1 A F)) | (r2_hidden (k13_cqc_lang A F H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_cqc_the3 A B C) <=> (r3_cqc_the1 A (k6_domain_1 (k3_cqc_lang A) B) C)) ) ) ) ) ) ) ).
tt(d1_csspace3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_csspace))) =>  ( (A = k1_csspace3)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_csspace) & (v2_comseq_3 (k2_csspace B))) ) ) ) ) ) ).
tt(d1_csspace4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_csspace))) =>  ( (A = k1_csspace4)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_csspace) & (v1_comseq_2 (k2_csspace B))) ) ) ) ) ) ).
tt(d1_csspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (A = k1_csspace)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ) ) ) ).
tt(d1_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_decomp_1 B A) <=> (r1_tarski B (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))) ) ) ) ) ).
tt(d1_descip_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k6_descip_1 A) = (k7_finseq_1 (k1_rfinseq 1 A) (k9_finseq_1 (k1_funct_1 A 1)))) ) ) ).
tt(d1_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (C = (k1_diff_1 A B))  <=>  ( ((k1_relset_1 k1_numbers C) = (k2_measure6 (k1_relset_1 k1_numbers A) (k4_xcmplx_0 B)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k2_measure6 (k1_relset_1 k1_numbers A) (k4_xcmplx_0 B))) =>  ((k1_seq_1 C D) = (k1_seq_1 A (k7_real_1 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_diff_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ((k1_diff_2 A B C D E F) = (k10_real_1 (k9_real_1 (k11_diff_1 A B C D E) (k11_diff_1 A C D E F)) (k6_xcmplx_0 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_dilworth B A) <=> (r6_relat_2 (u1_orders_2 A) B)) ) ) ) ) ).
tt(d1_diraf,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( (C = (k1_diraf A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A) (k1_domain_1 A A D E) (k1_domain_1 A A F G)) C) <=>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A) (k1_domain_1 A A D E) (k1_domain_1 A A F G)) B) | (r2_hidden (k1_domain_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A) (k1_domain_1 A A D E) (k1_domain_1 A A G F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_dirort A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_analoaf A B B D F) &  ((r2_analoaf A B D F F) &  ( (~  ((r2_analoaf A B D C E) &  ((r2_analoaf A B D E C) &  ( (~  (B = D) )  &  (~  (C = E) ) ) ) ) )  &  ( (~  ((r2_analoaf A B D C E) &  ((r2_analoaf A B D C F) &  ( (~ (r2_analoaf A B D E F))  &  (~ (r2_analoaf A B D F E)) ) ) ) )  &  ( ((r2_analoaf A B D C E) => (r2_analoaf A D B E C))  &  ( ( ((r2_analoaf A B D C E) & (r2_analoaf A B D E F))  => (r2_analoaf A B D C F))  &  (~  ((r2_analoaf A B C D E) &  ( (~ (r2_analoaf A D E B C))  &  (~ (r2_analoaf A D E C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~  (D = E) )  & (r2_analoaf A D E B C)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~  (D = E) )  & (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((k2_dist_1 A B C) = (k5_card_1 (k1_dist_1 A B C))) ) ) ) ) ) ).
tt(d1_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k5_trees_3 (u1_struct_0 A)))) =>  ( (B = (k4_dtconstr A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_lang1 A)) => (r2_hidden (k2_trees_4 (u1_struct_0 A) C) B)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 A)) B) =>  ((r1_lang1 A C (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) D)) => (r2_hidden (k8_trees_4 (u1_struct_0 A) C D) B)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k5_trees_3 (u1_struct_0 A)))) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_lang1 A)) => (r2_hidden (k2_trees_4 (u1_struct_0 A) D) C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 A)) C) =>  ((r1_lang1 A D (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) E)) => (r2_hidden (k8_trees_4 (u1_struct_0 A) D E) C)) ) ) ) ) )  => (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k2_dynkin A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k9_subset_1 A C (k8_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((m1_ec_pf_1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((k5_struct_0 B) = (k5_struct_0 A))  &  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d1_ec_pf_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_ec_pf_2 B A) <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(d1_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) =>  ( (B = (k1_endalg A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_hidden C B) <=> (r1_alg_1 A A C)) ) ) ) ) ) ) ) ).
tt(d1_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_ens_1 A) = (k3_tarski (a_1_0_ens_1 A))) ) ) ).
tt(d1_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v4_partfun3 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) ) ) ) ).
tt(d1_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (D = (k1_enumset1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (~  ( (~  (E = A) )  &  ( (~  (E = B) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_eqrel_1,ax, (! [A:$i] :  ((k1_eqrel_1 A) = (k2_zfmisc_1 A A)) ) ).
tt(d1_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k1_equation A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k8_relat_1 (k1_funct_1 C E) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) =>  ((v2_e_siec A) <=>  ((r1_tarski (u1_e_siec A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ((r1_tarski (u2_e_siec A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ( ((k3_relat_1 (u1_e_siec A) (u1_e_siec A)) = (u1_e_siec A))  &  ( ((k3_relat_1 (u1_e_siec A) (u2_e_siec A)) = (u1_e_siec A))  &  ( ((k3_relat_1 (u2_e_siec A) (u2_e_siec A)) = (u2_e_siec A))  &  ((k3_relat_1 (u2_e_siec A) (u1_e_siec A)) = (u2_e_siec A)) ) ) ) ) ) ) ) ) ).
tt(d1_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_euclid_3 A) = (k19_euclid (k3_complex1 A) (k4_complex1 A))) ) ) ).
tt(d1_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k1_euclid_4 A B C) = (a_3_0_euclid_4 A B C)) ) ) ) ) ) ) ).
tt(d1_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k1_euclid_5 A) = (k1_seq_1 A 1)) ) ) ).
tt(d1_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k1_euclid_6 A B C) = (k10_real_1 (k7_real_1 (k7_real_1 (k9_real_1 (k8_real_1 (k17_euclid A) (k18_euclid B)) (k8_real_1 (k17_euclid B) (k18_euclid A))) (k9_real_1 (k8_real_1 (k17_euclid B) (k18_euclid C)) (k8_real_1 (k17_euclid C) (k18_euclid B)))) (k9_real_1 (k8_real_1 (k17_euclid C) (k18_euclid A)) (k8_real_1 (k17_euclid A) (k18_euclid C)))) 2)) ) ) ) ) ) ) ).
tt(d1_euclid_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  & (r1_xxreal_0 (k1_seq_1 A (k1_nat_1 B 1)) (k1_seq_1 A B))) ) ) ) ) ) ) ) ).
tt(d1_euclid_8,ax, (k2_euclid_8 = (k1_euclid_8 1 k6_numbers k6_numbers)) ).
tt(d1_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) )  =>  ((k1_euclid_9 A B C) = (o_3_0_euclid_9 A B C)) ) ) ) ) ) ) ).
tt(d1_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_euclid A) = (k4_finseq_2 A k1_numbers)) ) ) ).
tt(d1_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r1_euclidlp A B C) <=>  ( (~  (B = (k5_euclid A)) )  &  ( (~  (C = (k5_euclid A)) )  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (B = (k9_euclid A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v1_euclmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r4_analmetr A B C D E) & (r4_analmetr A C D B E))  => (r4_analmetr A C E B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_euler_1 A) = (k1_card_1 (a_1_0_euler_1 A))) ) ) ).
tt(d1_euler_2,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ( (C = (k2_euler_2 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k1_recdef_1 C D) = (k4_nat_d (k1_recdef_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_exchsort,ax, (! [A:$i] :  ((v1_exchsort A) <=>  (? [B:$i] :  ((v3_ordinal1 B) &  (? [C:$i] :  ((v3_ordinal1 C) &  ((k9_xtuple_0 A) = (k6_subset_1 B C)) ) ) ) ) ) ) ).
tt(d1_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v1_extpro_1 B A) & (l1_extpro_1 B A))  =>  ( (B = (k1_extpro_1 A))  <=>  ( ((u1_struct_0 B) = (k6_domain_1 k5_numbers k6_numbers))  &  ( ((u2_struct_0 B) = k6_numbers)  &  ( ((u1_compos_1 B) = (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)))  &  ( ((u1_memstr_0 A B) = (k16_funcop_1 k6_numbers k6_numbers))  &  ( ((u2_memstr_0 A B) = (k7_funcop_1 A k5_numbers))  &  ((u1_extpro_1 A B) = (k16_funcop_1 (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k6_partfun1 (k4_card_3 (k3_relat_1 (k16_funcop_1 k6_numbers k6_numbers) (k7_funcop_1 A k5_numbers)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) =>  ((k3_extreal1 A) = A) )  &  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k3_extreal1 A) = (k2_supinf_2 A)) ) ) ) ) ).
tt(d1_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v11_struct_0 B) &  ((v1_msualg_1 B) & (l1_msualg_1 B)) )  =>  ( (B = (k1_facirc_2 A))  <=>  ((u1_struct_0 B) = (k1_tarski A)) ) ) ) ) ).
tt(d1_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fcont_1 A B) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers A)) &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = B) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k1_seq_1 A B) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ) ).
tt(d1_fcont_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_fcont_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k1_numbers A)) &  ((r2_hidden E (k1_relset_1 k1_numbers A)) &  ( (~ (r1_xxreal_0 C (k18_complex1 (k9_real_1 D E))))  & (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k1_seq_1 A D) (k1_seq_1 A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_fdiff_1 B A) <=>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = A) ) ) ) ) ) ) ).
tt(d1_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_fdiff_3 A B) <=>  ((r2_hidden B (k1_relset_1 k1_numbers A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k10_prob_1 B) (k1_relset_1 k1_numbers A))) &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = B) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k1_seq_1 A B) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fdiff_9,ax, (k1_fdiff_9 = (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) ).
tt(d1_ff_siec,ax, (! [A:$i] :  (! [B:$i] :  ((r1_xboole_0 A B) =>  ((k1_ff_siec A B) = (g1_petri A B (k1_partit_2 A B) (k1_partit_2 B A))) ) ) ) ).
tt(d1_fib_fusc,ax, (k1_fib_fusc = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 (k9_ami_3 2 (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) (k5_afinsq_1 (k2_ami_3 (k10_ami_3 3) (k10_ami_3 k6_numbers)))) (k5_afinsq_1 (k4_ami_3 (k10_ami_3 1) (k10_ami_3 k6_numbers)))) (k5_afinsq_1 (k8_ami_3 1 (k10_ami_3 1)))) (k5_afinsq_1 (k2_ami_3 (k10_ami_3 4) (k10_ami_3 2)))) (k5_afinsq_1 (k2_ami_3 (k10_ami_3 2) (k10_ami_3 3)))) (k5_afinsq_1 (k3_ami_3 (k10_ami_3 3) (k10_ami_3 4)))) (k5_afinsq_1 (k7_ami_3 3)))) ).
tt(d1_fib_num2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_setfam_1 B) & (v6_membered B)) )  =>  ((k1_fib_num2 A B) = (k15_finseq_1 (k5_relat_1 A B))) ) ) ) ) ).
tt(d1_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k1_fib_num3 A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))))) )  &  ( (B = (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C A)))  &  ( ((k3_funct_2 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C k6_numbers) = (k1_domain_1 k5_numbers k5_numbers 2 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_funct_2 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C (k1_nat_1 D 1)) = (k1_domain_1 k5_numbers k5_numbers (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D)) (k2_nat_1 (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D)) (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fib_num,ax, (k1_fib_num = (k13_complex1 (k2_xcmplx_0 1 (k7_square_1 5)) 2)) ).
tt(d1_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  ((r1_filerec1 A B C D) <=>  ( ((r2_finseq_8 A (k9_finseq_8 A C D) (k1_finseq_8 A D B) 1) | (r1_tarski B (k9_finseq_8 A C D)))  & (r5_finseq_8 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k1_filter_0 A) = (u1_struct_0 A)) ) ) ).
tt(d1_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((m1_filter_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k1_domain_1 A A D E) B) => (r2_hidden (k1_domain_1 A A (k3_funct_2 A A C D) (k3_funct_2 A A C E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_filter_2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  ( (C = (k2_finance1 A B))  <=>  ( ((k3_funct_2 k5_numbers (k9_setfam_1 k1_numbers) C k6_numbers) = (k1_finance1 A (k9_binop_2 B 1)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 k1_numbers) C (k23_binop_2 D 1)) = (k1_finance1 A (k9_binop_2 B (k18_binop_2 1 (k23_binop_2 D 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_finseq_1 A) = (a_1_0_finseq_1 A)) ) ) ).
tt(d1_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_finseq_2 A) = (k6_partfun1 (k2_finseq_1 A))) ) ) ).
tt(d1_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k1_finseq_3 A B) = (k3_relat_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k1_relset_1 k5_numbers A) (k8_relat_1 A B))) A)) ) ) ) ).
tt(d1_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_finseq_4 A B) <=>  ((k8_relat_1 A (k9_relat_1 A B)) = (k1_tarski B)) ) ) ) ) ).
tt(d1_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((k1_finseq_5 A B C) = (k17_finseq_1 A (k4_finseq_4 B C) B)) ) ) ) ) ) ).
tt(d1_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_finseq_6 B A) <=>  ((k7_partfun1 A B 1) = (k7_partfun1 A B (k3_finseq_1 B))) ) ) ) ) ) ).
tt(d1_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k1_finseq_7 A B C D) = (k8_finseq_1 A (k8_finseq_1 A (k17_finseq_1 A (k7_nat_d C 1) B) (k12_finseq_1 A D)) (k2_rfinseq A C B))) )  &  ( (~  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B))) )  =>  ((k1_finseq_7 A B C D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_finseq_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_finseq_8 A B C) = (k16_finseq_1 (k7_nat_d (k1_nat_1 C 1) B) (k1_rfinseq (k7_nat_d B 1) A))) ) ) ) ) ) ) ).
tt(d1_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_finseqop A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k5_binop_1 A C D (k3_funct_2 A A B D)) = (k4_binop_1 A C))  &  ((k5_binop_1 A C (k3_funct_2 A A B D) D) = (k4_binop_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_finset_1,ax, (! [A:$i] :  ((v1_finset_1 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ( ((k10_xtuple_0 B) = A)  & (r2_hidden (k9_xtuple_0 B) k4_ordinal1)) ) ) ) ) ).
tt(d1_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo C A) | (r1_xxreal_0 1 (k3_finseq_1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ( ((v1_setwiseo C A) &  ((k3_finseq_1 B) = k6_numbers) )  =>  ( (D = (k1_finsop_1 A B C))  <=>  (D = (k4_binop_1 A C)) ) )  &  ( (~  ((v1_setwiseo C A) &  ((k3_finseq_1 B) = k6_numbers) ) )  =>  ( (D = (k1_finsop_1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ( ((k8_nat_1 A E 1) = (k1_funct_1 B 1))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~  (k6_numbers = F) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) F))  &  (~  ((k8_nat_1 A E (k2_nat_1 F 1)) = (k1_binop_1 C (k8_nat_1 A E F) (k1_funct_1 B (k2_nat_1 F 1)))) ) ) ) ) ) )  &  (D = (k8_nat_1 A E (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_finsub_1,ax, (! [A:$i] :  ((v1_finsub_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k2_xboole_0 B C) A)) ) ) ) ) ).
tt(d1_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((r2_hidden C (k1_fin_topo A B)) & (r2_hidden C D))  =>  ((k1_fintopo2 A B C D) = k8_margrel1) )  &  ( (~  ((r2_hidden C (k1_fin_topo A B)) & (r2_hidden C D)) )  =>  ((k1_fintopo2 A B C D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_fintopo3 A B) = (a_2_0_fintopo3 A B)) ) ) ) ) ).
tt(d1_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_fintopo4 A B C) <=>  ((r1_xboole_0 (k9_fin_topo A B) C) & (r1_xboole_0 B (k9_fin_topo A C))) ) ) ) ) ) ) ) ).
tt(d1_fintopo5,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_fintopo5 C A B) <=>  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_fin_topo A D)) = (k9_relat_1 (u1_orders_2 B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_fintopo6 A) <=> (v4_fin_topo (k2_struct_0 A) A)) ) ) ).
tt(d1_fin_topo,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_fin_topo A B) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) B)) ) ) ) ) ).
tt(d1_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ( (D = (k6_flang_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((m1_subset_1 F (k3_catalan2 A)) &  (? [G:$i] :  ((m1_subset_1 G (k3_catalan2 A)) &  ((r2_hidden F B) &  ((r2_hidden G C) &  (E = (k1_flang_1 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_flang_2 A B C D) = (k3_tarski (a_4_0_flang_2 A B C D))) ) ) ) ) ) ) ) ).
tt(d1_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_flang_3 A B C) = (k3_tarski (a_3_0_flang_3 A B C))) ) ) ) ) ) ).
tt(d1_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_fomodel0 B A) <=> (v2_funct_1 (k5_relat_1 B A))) ) ) ) ).
tt(d1_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k1_fomodel1 A) = (u1_struct_0 A)) ) ) ).
tt(d1_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k2_fomodel2 A) = (k9_fomodel0 (k7_relset_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A) (k11_monoid_0 A) (k6_partfun1 (k4_finseq_2 1 A))) (k4_finseq_2 2 A))) ) ) ).
tt(d1_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k3_finseq_2 (k1_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) =>  ((k1_fomodel3 A B C) = (k7_finseq_1 (k31_fomodel2 A B) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k1_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)) (k21_fomodel1 A) C))) ) ) ) ) ) ) ).
tt(d1_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k1_fomodel4 A) = (a_1_0_fomodel4 A)) ) ) ).
tt(d1_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_frechet2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) B) & (r2_hidden D (k2_frechet A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_pcomps_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) =>  ( (C = (k1_frechet A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (D = B)  &  (C = (a_2_0_frechet A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_freealg,ax, (! [A:$i] :  ((v1_freealg A) <=> (r1_xboole_0 A k5_numbers)) ) ).
tt(d1_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_fscirc_1 A B C) = (k9_facirc_1 A B C k1_facirc_1)) ) ) ) ).
tt(d1_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_fsm_1 A B C D) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A D C))) ) ) ) ) ) ) ) ) ).
tt(d1_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ((v1_fsm_2 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k1_funct_1 D 1) = (k1_funct_1 E 1))  &  ((r1_xxreal_0 C (k2_nat_1 (k3_finseq_1 D) 1)) & (r1_xxreal_0 C (k2_nat_1 (k3_finseq_1 E) 1))) )  =>  ((k1_funct_1 (k2_fsm_1 A B (u2_fsm_1 A B) D) C) = (k1_funct_1 (k2_fsm_1 A B (u2_fsm_1 A B) E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ( ((v1_rewrite3 D (k9_flang_1 A)) & (l1_rewrite3 D (k9_flang_1 A)))  =>  ( (D = (k1_fsm_3 A B C))  <=>  ( ((u1_struct_0 D) = (k1_zfmisc_1 (u1_struct_0 C)))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C)) (k8_afinsq_1 A)) (k1_zfmisc_1 (u1_struct_0 C)) (k1_domain_1 (k1_zfmisc_1 (u1_struct_0 C)) (k8_afinsq_1 A) E F) G) (u1_rewrite3 (k9_flang_1 A) D)) <=>  ( ((k1_afinsq_1 F) = 1)  &  (G = (k3_rewrite3 A B C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k1_ftacell1 A B C D E) = (k2_circcomb (k13_gfacirc1 A B C) (k13_gfacirc1 (k12_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d1_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_funcop_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ( (! [D:$i] :  (! [E:$i] :  ( ((k1_funct_1 A C) = (k4_tarski D E))  =>  ((k1_funct_1 B C) = (k4_tarski E D)) ) ) )  &  (~  ( (~  ((k1_funct_1 A C) = (k1_funct_1 B C)) )  &  (! [D:$i] :  (! [E:$i] :  (~  ((k1_funct_1 A C) = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) )  =>  ( (B = (k5_funcsdom A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers B C D) (k3_funcsdom k1_numbers A k33_binop_2 C D))) ) ) ) ) ) ) ) ).
tt(d1_funct_1,ax, (! [A:$i] :  ((v1_funct_1 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski B D) A))  =>  (C = D) ) ) ) ) ) ) ).
tt(d1_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ( (~  (B = k1_xboole_0) )  =>  ((v1_funct_2 C A B) <=>  (A = (k1_relset_1 A C)) ) )  &  ( (B = k1_xboole_0)  =>  ((v1_funct_2 C A B) <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d1_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_funct_3 A))  <=>  ( ((k9_xtuple_0 B) = (k1_zfmisc_1 (k9_xtuple_0 A)))  &  (! [C:$i] :  ((r1_tarski C (k9_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k7_relat_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d1_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k1_funct_4 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ( ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k1_funct_1 B D)) )  &  ( (~ (r2_hidden D (k9_xtuple_0 B)))  =>  ((k1_funct_1 C D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_funct_5 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 (k9_xtuple_0 A)))  &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 (k9_xtuple_0 A))) &  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( ((k1_funct_1 B C) = D)  &  ( ((k9_xtuple_0 D) = (k10_xtuple_0 (k3_xboole_0 (k9_xtuple_0 A) (k2_zfmisc_1 (k1_tarski C) (k10_xtuple_0 (k9_xtuple_0 A))))))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k1_binop_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_funct_6 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C A) &  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ) ) ).
tt(d1_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k1_funct_7 A B) = A) ) ) ) ).
tt(d1_funct_8,ax, (! [A:$i] :  ((v1_funct_8 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r2_hidden B A) => (r2_hidden (k4_xcmplx_0 B) A)) ) ) ) ) ).
tt(d1_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_funct_9 B A) <=>  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden C (k9_xtuple_0 B)) => (r2_hidden (k2_xcmplx_0 C A) (k9_xtuple_0 B)))  &  ( ((r2_hidden (k2_xcmplx_0 C A) (k9_xtuple_0 B)) => (r2_hidden C (k9_xtuple_0 B)))  &  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k1_funct_1 B (k2_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (k2_zfmisc_1 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B))))) )  =>  ((v1_functor0 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (r8_binop_1 A A (k2_zfmisc_1 B B) C (k16_funct_3 A A B B D D))) ) ) ) ) ) ) ).
tt(d1_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  ((r1_functor2 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ((m1_functor2 F A B D E) =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  ((r1_functor2 A B D E) =>  (! [H:$i] :  ((m1_functor2 H A C (k1_functor3 A B C D G) (k1_functor3 A B C E G)) =>  ( (H = (k5_functor3 A B C D E F G))  <=>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k1_funct_1 H I) = (k6_functor0 B C G (k3_functor0 A B D I) (k3_functor0 A B E I) (k2_functor2 A B D E F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k1_fuzzy_2 A B C) = (k1_fuzzy_1 A B (k3_fuzzy_1 A C))) ) ) ) ) ) ) ).
tt(d1_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ( (D = (k2_fuzzy_4 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) (k2_zfmisc_1 A B)) =>  ((k1_fuzzy_4 A B D E F) = (k1_fuzzy_4 B A C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_fvaluat1,ax, (! [A:$i] :  ((v1_fvaluat1 A) <=>  ((v1_int_1 A) |  (A = k1_xxreal_0) ) ) ) ).
tt(d1_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_fvsum_1 A B) = (k10_funcop_1 (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) B (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ).
tt(d1_gate_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  =>  ((k1_gate_1 A) = k1_xboole_0) )  &  ((v1_xboole_0 A) =>  ((k1_gate_1 A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(d1_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k1_gate_5 A B C D) = (k2_gate_1 A C)) ) ) ) ) ).
tt(d1_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_gcd_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k6_algstr_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  ((m1_genealg1 B A) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r2_hidden (k1_funct_1 B C) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d1_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_geomtrap A B C D E) <=>  ((r1_analoaf A B C D E) | (r1_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 1 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k1_gfacirc1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ((k1_funct_1 A (k10_binarith k6_margrel1 B)) = (k9_margrel1 B)) ) ) ) ) ) ).
tt(d1_glib_000,ax, (k1_glib_000 = 1) ).
tt(d1_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k6_glib_000 A)) =>  ((m1_glib_001 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  (~ (r1_glib_000 A (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 1)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (? [D:$i] :  ((m3_glib_001 D A) & (r1_glib_001 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d1_glib_003,ax, (k2_glib_003 = 5) ).
tt(d1_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m1_glib_000 B A)) )  =>  (! [C:$i] :  ((r1_glib_004 A B C) <=>  ((v3_glib_002 B) &  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  (? [E:$i] :  ( ((v2_glib_001 E B) &  ((v5_glib_001 E B) & (m3_glib_001 E B)) )  &  ((r1_glib_001 B C D E) &  (! [F:$i] :  ( ((v2_glib_001 F A) &  ((v5_glib_001 F A) & (m3_glib_001 F A)) )  =>  ((r1_glib_001 A C D F) => (r1_xxreal_0 (k10_glib_003 B E) (k10_glib_003 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k1_goboard1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (~  (A = k1_xboole_0) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( (C = (k1_goboard2 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C D E) = (k19_euclid (k1_seq_1 A D) (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_goboard5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 A) B) |  ((k1_goboard5 A B) = (a_2_0_goboard5 A B)) ) )  &  ( ((r1_xxreal_0 (k3_finseq_1 A) B) =>  ((k1_goboard5 A B) = (a_2_1_goboard5 A B)) )  &  (~  ( (~  ((r1_xxreal_0 1 B) &  (~ (r1_xxreal_0 (k3_finseq_1 A) B)) ) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  &  (~  ((k1_goboard5 A B) = (a_2_2_goboard5 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k2_goboard9 A))  <=>  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) B) & (r1_tarski (k1_tops_1 (k15_euclid 2) (k5_goboard5 A 1)) B)) ) ) ) ) ) ).
tt(d1_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_gobrd10 A B) <=>  ( (B = (k2_nat_1 A 1))  |  (A = (k2_nat_1 B 1)) ) ) ) ) ) ) ).
tt(d1_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v1_goedelcp B A) <=>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_henmodel A B C) | (r1_henmodel A B (k6_cqc_lang A C))) ) ) ) ) ) ) ) ).
tt(d1_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( (D = (k1_graph_2 A B C))  <=>  ( ((k2_nat_1 (k3_finseq_1 D) B) = (k1_nat_1 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  =>  ((k1_funct_1 D (k1_nat_1 E 1)) = (k1_funct_1 A (k2_xcmplx_0 B E))) ) ) ) ) ) )  &  ( (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) ) )  =>  ( (D = (k1_graph_2 A B C))  <=>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) =>  ( (D = (k2_graph_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (u4_struct_0 A)) &  ((r2_hidden E C) &  ((k1_funct_1 (u2_graph_1 A) E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r1_graph_4 A B C D) <=>  ( ((k1_funct_1 (u1_graph_1 A) D) = B)  &  ((k1_funct_1 (u2_graph_1 A) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d1_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k1_graph_5 A B) = (k2_tarski (k1_funct_1 (u1_graph_1 A) B) (k1_funct_1 (u2_graph_1 A) B))) ) ) ) ) ).
tt(d1_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k2_graphsp A B C D) = (k1_graphsp (k1_graphsp C A B) B D)) ) ) ) ) ) ) ) ) ).
tt(d1_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_grcat_1 A B) = (k3_tarski (a_2_0_grcat_1 A B))) ) ) ) ) ).
tt(d1_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_gr_cy_3 A) <=>  (? [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  &  ((k2_nat_1 (k4_nat_1 2 B) 1) = A) ) ) ) ) ) ).
tt(d1_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (B = (k2_grnilp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) ) ) ) ) ) ) ) ).
tt(d1_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((k2_groeb_1 A B C D) = (a_4_0_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d1_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (D = (k1_groeb_2 A B C))  <=> (r6_pboole A (k11_pre_poly A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d1_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A))) =>  ((k2_groeb_3 A B C D) = (k1_funct_4 C (k8_funcop_1 (u1_struct_0 B) (k4_xboole_0 (k2_polynom1 (k15_pre_poly A) B C) D) (k4_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(d1_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) )  =>  ((v1_group_10 C A B) <=>  ((r2_funct_2 B B (k1_group_10 A B C (k1_group_1 A)) (k6_partfun1 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_funct_2 B B (k1_group_10 A B C (k6_algstr_0 A D E)) (k1_partfun1 B B B B (k1_group_10 A B C E) (k1_group_10 A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k1_group_11 A B C) = (a_3_0_group_11 A B C)) ) ) ) ) ) ) ).
tt(d1_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_group_7 A B)))) =>  ( (D = (k1_group_12 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_group_7 A B C))) &  (E = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v1_group_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = C)  &  ((k6_algstr_0 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(d1_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_group_2 A B) = (a_2_0_group_2 A B)) ) ) ) ) ).
tt(d1_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (B = (k1_group_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v15_algstr_0 C) & (m1_group_2 C A)) ) ) ) ) ) ) ).
tt(d1_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k2_group_4 A) = A) ) ) ).
tt(d1_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k1_group_5 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_funct_1 D E) = (k2_group_3 A (k7_partfun1 (u1_struct_0 A) B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ((m1_group_6 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) A B) =>  ((k1_group_6 A B C) = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ).
tt(d1_group_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_group_7 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( (~ (v2_struct_0 B))  & (l3_algstr_0 B)) ) ) ) ) ) ).
tt(d1_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((r1_group_9 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ( ((r2_hidden E A) &  (F = (k1_funct_1 C E)) )  => (r1_tarski (k7_relset_1 B B F D) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_groupp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v1_groupp_1 C A B) <=>  (? [D:$i] :  ((v7_ordinal1 D) &  ((k6_group_1 B C) = (k1_newton A D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_grsolv_1 A) <=>  (? [B:$i] :  ((m2_finseq_1 B (k1_group_3 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ( ( (D = (k1_funct_1 B C))  &  (E = (k1_funct_1 B (k2_nat_1 C 1))) )  =>  ( ((v15_algstr_0 E) &  ((v1_group_3 E D) & (m1_group_6 E A D)) )  &  (! [F:$i] :  ( ((v1_group_3 F D) & (m1_group_6 F A D))  =>  ( (F = E)  => (v5_group_1 (k5_group_6 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_hahnban1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_hahnban1 A B) = (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1))) ) ) ) ) ).
tt(d1_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_hahnban B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers B (k3_rlvect_1 A C D)) (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B C) (k3_funct_2 (u1_struct_0 A) k1_numbers B D)))) ) ) ) ) ) ) ) ) ).
tt(d1_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  (! [D:$i] :  ( (D = (k1_hallmar1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F C) &  ((r2_hidden F (k4_finseq_1 B)) & (r2_hidden E (k1_funct_1 B F))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((k1_hausdorf A B C) = (k2_square_1 (k8_weierstr A B C) (k8_weierstr A C B))) ) ) ) ) ) ) ).
tt(d1_heine,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k1_heine A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k4_power B (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k1_helly A B))  <=>  ((r1_tarski C A) &  ((r1_tarski C B) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((r1_tarski D A) & (r1_tarski D B))  => (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_henmodel A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) &  ((r1_tarski (k2_relset_1 (k3_cqc_lang A) D) B) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  ((v1_hermitan B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B (k4_vectsp_1 k1_complfld A D C)) = (k8_group_1 k1_complfld (k2_complfld D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_heyting1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  ((r1_heyting1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) => (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ( (D = (k1_heyting2 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finset_1 F)) )  &  ((r2_hidden F C) & (r2_hidden E (k9_xtuple_0 F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_heyting3,ax, (! [A:$i] :  (! [B:$i] :  ((k1_heyting3 A B) = (k3_lattice3 (k5_substlat A B))) ) ) ).
tt(d1_hilbasis,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly (k1_nat_1 A 1)) (k15_pre_poly (k1_nat_1 A 1))) =>  ( (D = (k1_hilbasis A B C))  <=>  ( ((k5_relat_1 D A) = C)  &  ((k1_recdef_1 D A) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_hilbert1,ax, (! [A:$i] :  ((v1_hilbert1 A) <=> (r2_hidden (k12_finseq_1 k5_numbers k6_numbers) A)) ) ).
tt(d1_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_hilbert2 A) = (k12_finseq_1 k5_numbers (k2_nat_1 3 A))) ) ) ).
tt(d1_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 A B) (k9_funct_2 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B))))) )  =>  ( (E = (k1_hilbert3 A B C D))  <=>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k1_funct_1 E F) = (k1_partfun1 A A A B (k2_funct_2 A C) (k1_partfun1 A B B B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_homothet A B C) <=>  ((v8_transgeo B A) &  ((v1_aff_1 C A) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_aff_1 A D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_polynom3 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k1_hurwitz A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 F A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (F = (k1_funct_1 B E))  &  ((k1_funct_1 D E) = (k1_normsp_1 A F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_idea_1 A) = (k5_finseq_2 k6_margrel1 A k7_margrel1)) ) ) ).
tt(d1_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_ideal_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k1_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  ((k1_incproj A) = (a_1_0_incproj A)) ) ) ).
tt(d1_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ((r1_incsp_1 A B C) <=> (r2_hidden (k1_domain_1 (u1_incsp_1 A) (u2_incsp_1 A) B C) (u3_incsp_1 A))) ) ) ) ) ) ) ).
tt(d1_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_instalg1 A) <=>  ( ((u1_struct_0 A) = k1_xboole_0)  =>  ((u4_struct_0 A) = k1_xboole_0) ) ) ) ) ).
tt(d1_int_1,ax, (! [A:$i] :  ( (A = k4_numbers)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (~  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~  (B = C) )  &  (~  (B = (k1_real_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k2_int_2 A B))  <=>  ((r1_int_1 A C) &  ((r1_int_1 B C) &  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_int_1 A D) & (r1_int_1 B D))  => (r1_int_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers))) =>  ( (B = (k1_int_4 A))  <=>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r2_hidden (k4_tarski C D) B) <=> (r2_int_1 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(d1_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k4_numbers k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers)))) )  =>  ( (B = (k1_int_5 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  ( ((k3_finseq_1 D) = (k3_finseq_1 A))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k3_xcmplx_0 (k1_funct_1 A E) (k1_newton C (k7_nat_d E 1)))) ) ) )  &  ((k3_funct_2 k4_numbers k4_numbers B C) = (k1_gr_cy_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ((k1_funct_1 A B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d1_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  ((v1_int_7 A) <=>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ((r2_hidden B (k1_polynom2 k10_newton A)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((k1_recdef_1 A B) = (k1_newton B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_integr10 A B C) <=>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_xxreal_0 B D) =>  ((r1_xxreal_0 C D) |  ((r1_integra5 (k3_integra5 B D) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 B D)))) ) ) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers D) = (k3_rcomp_1 B C))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k1_relset_1 k1_numbers D)) =>  ((k1_seq_1 D E) = (k4_integra5 B E A)) ) ) )  & (r1_limfunc2 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ((m1_integr15 D A B C) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden F (k1_rvsum_1 (k2_partfun1 A k1_numbers B (k2_integra1 A C E)))) &  ((k1_seq_1 D E) = (k8_real_1 F (k3_integra1 (k2_integra1 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k2_numbers) =>  ((m1_integr16 D A B C) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (~  ((r2_hidden F (k2_relset_1 k2_numbers (k2_partfun1 A k2_numbers B (k2_integra1 A C E)))) &  ((k1_funct_1 D E) = (k5_binop_2 F (k3_integra1 (k2_integra1 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ((m1_integr18 E A B C D) <=>  ( ((k3_finseq_1 E) = (k3_finseq_1 D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 D)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_hidden G (k2_relset_1 (u1_struct_0 A) (k2_partfun1 B (u1_struct_0 A) C (k2_integra1 B D F)))) &  ((k1_funct_1 E F) = (k1_rlvect_1 A G (k3_integra1 (k2_integra1 B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)))))  =>  ((v1_integr19 C A B) <=>  (? [D:$i] :  ((v1_xreal_0 D) &  (! [E:$i] :  (~  ((r2_hidden E (k1_relset_1 B C)) & (r1_xxreal_0 D (k1_normsp_0 A (k7_partfun1 (u1_struct_0 A) C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers)))) )  =>  ( (A = k1_integr1c)  <=>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (C = (k1_xtuple_0 B))  &  (D = (k2_xtuple_0 B)) )  =>  ((k1_funct_1 A (k4_tarski C D)) = (k2_xcmplx_0 C (k3_xcmplx_0 D k7_complex1))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integra2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v1_integra2 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)))  => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A (k2_nat_1 B 1)))) ) ) ) ) ) ).
tt(d1_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ((k1_integra3 A B) = (k1_xxreal_2 (k1_rvsum_1 (k4_integra1 A (k7_rfunct_1 A A) B)))) ) ) ) ) ).
tt(d1_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_integra4 A B C) <=>  ( ((k3_finseq_1 B) = C)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k1_seq_1 B D) = (k7_real_1 (k5_seq_4 A) (k8_real_1 (k10_real_1 (k3_integra1 A) (k3_finseq_1 B)) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra5 A B) <=> (v3_integra1 (k1_integra5 B A) A)) ) ) ) ) ).
tt(d1_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( (C = (k1_integra7 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( (D = E)  &  ((r2_fdiff_1 E A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 E A) (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_integra8 A) = (k8_funcop_1 k1_numbers k1_numbers A)) ) ) ).
tt(d1_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k1_integra9 A B C) = (k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(d1_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_interva1 A B C) = (a_3_0_interva1 A B C)) ) ) ) ) ) ).
tt(d1_intpro_1,ax, (! [A:$i] :  ((v1_intpro_1 A) <=> (r2_hidden (k12_finseq_1 k5_numbers k6_numbers) A)) ) ).
tt(d1_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k1_irrat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k13_complex1 (k6_xcmplx_0 C A) C)) ) ) ) ) ) ) ) ).
tt(d1_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ((m2_cat_1 C A B) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A D))  =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A D E)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_cat_1 D (k11_nattra_1 A B) B) =>  ( (D = (k2_isocat_2 A B C))  <=>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_nattra_1 G A B E F) =>  ((r2_nattra_1 A B E F) =>  ((k1_funct_1 D (k4_tarski (k4_tarski E F) G)) = (k4_nattra_1 A B E F G C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_isomichi,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_isomichi B A) <=>  ((k1_tops_1 A (k2_pre_topc A B)) = (k1_tops_1 A B)) ) ) ) ) ) ).
tt(d1_jct_misc,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = (k1_jct_misc A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) &  ( (D = (a_2_0_jct_misc A B))  &  (C = (k5_seq_4 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jgraph_1,ax, (! [A:$i] :  ((k1_jgraph_1 A) = (g1_graph_1 A (k2_zfmisc_1 A A) (k9_funct_3 A A) (k10_funct_3 A A))) ) ).
tt(d1_jgraph_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)))))) )  =>  ( (A = k1_jgraph_2)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  =>  ( ( ( ((r1_xxreal_0 (k18_euclid B) (k17_euclid B)) & (r1_xxreal_0 (k1_real_1 (k17_euclid B)) (k18_euclid B)))  |  ((r1_xxreal_0 (k17_euclid B) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k1_real_1 (k17_euclid B)))) )  =>  ((k1_funct_1 A B) = (k19_euclid (k10_real_1 1 (k17_euclid B)) (k10_real_1 (k10_real_1 (k18_euclid B) (k17_euclid B)) (k17_euclid B)))) )  &  (~  ( (~  ((r1_xxreal_0 (k18_euclid B) (k17_euclid B)) & (r1_xxreal_0 (k1_real_1 (k17_euclid B)) (k18_euclid B))) )  &  ( (~  ((r1_xxreal_0 (k17_euclid B) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k1_real_1 (k17_euclid B)))) )  &  (~  ((k1_funct_1 A B) = (k19_euclid (k10_real_1 (k10_real_1 (k17_euclid B) (k18_euclid B)) (k18_euclid B)) (k10_real_1 1 (k18_euclid B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jgraph_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (A = k1_jgraph_3)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( (B = (k4_struct_0 (k15_euclid 2)))  =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A B) = B) )  &  ( (~  ( ( ((r1_xxreal_0 (k18_euclid B) (k17_euclid B)) & (r1_xxreal_0 (k1_real_1 (k17_euclid B)) (k18_euclid B)))  |  ((r1_xxreal_0 (k17_euclid B) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k1_real_1 (k17_euclid B)))) )  &  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  &  (~  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A B) = (k19_euclid (k10_real_1 (k17_euclid B) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid B) (k17_euclid B)))))) (k10_real_1 (k18_euclid B) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid B) (k17_euclid B)))))))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 (k18_euclid B) (k17_euclid B)) & (r1_xxreal_0 (k1_real_1 (k17_euclid B)) (k18_euclid B))) )  &  ( (~  ((r1_xxreal_0 (k17_euclid B) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k1_real_1 (k17_euclid B)))) )  &  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  &  (~  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A B) = (k19_euclid (k10_real_1 (k17_euclid B) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid B) (k18_euclid B)))))) (k10_real_1 (k18_euclid B) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid B) (k18_euclid B)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jgraph_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (B = (k1_jgraph_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B C) = (k12_euclid C)) ) ) ) ) ) ) ) ).
tt(d1_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_jgraph_6 A B C D) = (a_4_0_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d1_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k1_jordan10 A) = (a_1_0_jordan10 A)) ) ) ).
tt(d1_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k1_jordan11 A))  <=>  ((r1_jordan1h A B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_jordan1h A C) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ).
tt(d1_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid A))) =>  ((r1_jordan12 A B C) <=>  ((r1_xboole_0 (k3_topreal1 A B) (k10_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) D) | (v1_zfmisc_1 (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k3_topreal1 A B) (k2_topreal1 A C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  &  ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_jordan1h A B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) &  ((v1_sprect_2 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ( (C = (k1_jordan13 A B))  <=>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k3_jordan1h A B) (k3_jordan11 A B)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k7_nat_d (k3_jordan1h A B) 1) (k3_jordan11 A B)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 C)))  =>  ( ( ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) D) A) & (r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) D) A))  => (r2_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D))  &  ( ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) D) A) =>  ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) D) A) | (r3_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D)) )  &  ( (~ (r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) D) A))  => (r1_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_jordan14 A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k3_jordan1h A B) (k3_jordan11 A B))) ) ) ) ) ).
tt(d1_jordan17,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan17 A B C D E) <=>  (~  ( (~  ((r1_jordan6 A B C) &  ((r1_jordan6 A C D) & (r1_jordan6 A D E)) ) )  &  ( (~  ((r1_jordan6 A C D) &  ((r1_jordan6 A D E) & (r1_jordan6 A E B)) ) )  &  ( (~  ((r1_jordan6 A D E) &  ((r1_jordan6 A E B) & (r1_jordan6 A B C)) ) )  &  (~  ((r1_jordan6 A E B) &  ((r1_jordan6 A B C) & (r1_jordan6 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k1_jordan18 A B) = (k19_euclid (k17_euclid A) (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k4_topreal1 A)))))) ) ) ) ) ).
tt(d1_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (B = (k1_jordan19 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 B C) = (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A C)))) ) ) ) ) ) ) ) ).
tt(d1_jordan1a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k1_jordan1a A) = (k2_nat_1 (k3_nat_d (k3_finseq_1 A) 2) 1)) ) ) ).
tt(d1_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r1_tarski (k1_rltopsp1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_jordan1e A B) = (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ).
tt(d1_jordan1h,ax, (k1_jordan1h = a_0_0_jordan1h) ).
tt(d1_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k1_jordan1k A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) &  ( (B = E)  &  ( (C = F)  &  (D = (k7_weierstr (k14_euclid A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 E (k17_euclid F)))  &  ((r1_jordan5c A B C F D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C F G) & (r1_jordan5c A B C G D))  => (r1_xxreal_0 (k17_euclid G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_jordan21 A) <=>  (~ (r1_xboole_0 A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) ) ) ) ).
tt(d1_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_jordan23 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) )  =>  ( ( (B = 1)  &  (C = (k3_finseq_1 A)) )  |  ( ( (B = (k3_finseq_1 A))  &  (C = 1) )  |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_jordan24 A B C D) <=>  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k1_topreal6 A E F) (k1_topreal6 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k1_jordan3 A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k5_numbers)))  &  ( (C = (k6_seq_4 D))  &  (D = (a_2_0_jordan3 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( (~  ((k4_nat_d A (k7_nat_d (k3_finseq_1 B) 1)) = k6_numbers) )  =>  ((k1_jordan4 A B) = (k4_nat_d A (k7_nat_d (k3_finseq_1 B) 1))) )  &  ( ((k4_nat_d A (k7_nat_d (k3_finseq_1 B) 1)) = k6_numbers)  =>  ((k1_jordan4 A B) = (k7_nat_d (k3_finseq_1 B) 1)) ) ) ) ) ) ) ).
tt(d1_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)) & (r1_topreal1 (k15_euclid 2) C D A))  =>  ((r1_xboole_0 A B) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( (E = (k1_jordan5c A B C D))  <=>  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ( ((k1_funct_1 F G) = E)  &  ((r1_xxreal_0 k6_numbers G) & (r1_xxreal_0 G 1)) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers H) &  ( (~ (r1_xxreal_0 G H))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k1_jordan5d A))  <=>  ((r2_hidden (k4_tarski 1 B) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 B) = (k18_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d1_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( (D = (k1_jordan6 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_2_0_jordan6 B C))  =>  (D = (k1_jordan5c A E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( (~  (C = (k18_pscomp_1 A)) )  =>  ((k1_jordan7 A B C) = (a_3_0_jordan7 A B C)) )  &  ( (C = (k18_pscomp_1 A))  =>  ((k1_jordan7 A B C) = (a_2_0_jordan7 A B)) ) ) ) ) ) ) ) ) ).
tt(d1_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( (C = (k1_jordan8 A B))  <=>  ( ((k3_finseq_1 C) = (k1_nat_1 (k2_newton 2 B) 3))  &  ( ((k3_finseq_1 C) = (k1_matrix_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C D E) = (k19_euclid (k7_real_1 (k6_pscomp_1 A) (k4_real_1 (k13_complex1 (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) (k2_newton 2 B)) (k5_real_1 D 2))) (k7_real_1 (k9_pscomp_1 A) (k4_real_1 (k13_complex1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k2_newton 2 B)) (k5_real_1 E 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v2_connsp_1 A (k15_euclid 2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) &  ((v1_sprect_2 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ( (C = (k1_jordan9 A B))  <=>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) &  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k1_matrix_1 (k1_jordan8 A B))))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 D 1) (k1_matrix_1 (k1_jordan8 A B))))  &  ((r2_hidden (k20_pscomp_1 A) (k3_goboard5 (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) &  (~  ((k20_pscomp_1 A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 C)))  =>  ( ( ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) D) A) & (r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) D) A))  => (r1_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D))  &  ( ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) D) A) =>  ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) D) A) | (r3_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D)) )  &  ( (~ (r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) D) A))  => (r2_gobrd13 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (B = (k3_jordan A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers B C) = (k9_real_1 (k17_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) C)) (k17_euclid A))) ) ) ) ) ) ) ) ).
tt(d1_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v6_cohsp_1 C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r1_tarski D E) => (r1_tarski (k3_funct_2 A B C D) (k3_funct_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ( (E = (k1_kolmog01 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ((r2_hidden F E) <=>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((k1_funct_1 D (k8_subset_1 A F G)) = (k3_xcmplx_0 (k3_funct_2 B k1_numbers D F) (k1_funct_1 D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (C = (k3_kurato_0 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( (C = (k1_kurato_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k2_kurato_0 A (k10_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_kurato_1 A B) = (k5_enumset1 B (k2_pre_topc A B) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))))))) ) ) ) ) ).
tt(d1_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_kurato_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_connsp_2 E A D) =>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ( (~ (r1_xxreal_0 G F))  & (r1_xboole_0 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_lang1 A B C) <=> (r2_hidden (k4_tarski B C) (u1_lang1 A))) ) ) ) ) ) ) ).
tt(d1_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) C C) =>  ( ((r2_hidden A (k2_finseq_1 C)) & (r2_hidden B (k2_finseq_1 C)))  =>  ((k2_laplace A B C D E) = (k9_matrix_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_group_3 A) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (B = (k1_latsubgr A))  <=>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((k1_funct_1 B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(d1_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r1_latsum_1 A B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))) & (r2_hidden D (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))))  =>  ((r2_hidden (k4_tarski C D) (u1_orders_2 A)) <=> (r2_hidden (k4_tarski C D) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ).
tt(d1_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_lattice2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k5_binop_1 A B D (k5_binop_1 A C D E)) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_lattices B) & (l3_lattices B))  =>  ( (B = (k1_lattice3 A))  <=>  ( ((u1_struct_0 B) = (k9_setfam_1 A))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((k1_binop_1 (u2_lattices B) C D) = (k4_subset_1 A C D))  &  ((k1_binop_1 (u1_lattices B) C D) = (k9_subset_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m1_lattice4 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_lattices A D E)) = (k3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_lattices A D E)) = (k4_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lattice5,ax, (! [A:$i] :  ((k1_lattice5 A) = (k3_lattice3 (k2_msualg_5 A))) ) ).
tt(d1_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_lattice6 A B) = (a_2_0_lattice6 A B)) ) ) ) ) ).
tt(d1_lattice7,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_lattice7 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_lattice8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lattice8 A) <=>  (? [B:$i] :  ( (~ (v1_xboole_0 B))  &  ( (! [C:$i] :  ((r2_hidden C (u1_struct_0 A)) =>  ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) )  &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E B) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden D (u1_struct_0 A)) &  ((r2_hidden E (u1_struct_0 A)) &  ((r2_hidden (k4_tarski F G) (k5_eqrel_1 B D E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H B))  =>  (~  ( ((k3_finseq_1 H) = C)  & (r1_lattice5 B H F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B C) = (k5_binop_1 (u1_struct_0 A) (u2_lattices A) B C)) ) ) ) ) ) ) ).
tt(d1_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lfuzzy_0 A) <=>  ((r1_tarski (u1_struct_0 A) k1_numbers) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden B (u1_struct_0 A)) & (r2_hidden C (u1_struct_0 A)))  =>  ((r2_hidden (k4_tarski B C) (u1_orders_2 A)) <=> (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r1_lfuzzy_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) => (r1_xxreal_0 (k8_lfuzzy_0 A B C E F) (k8_lfuzzy_0 A B D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_limfunc1 A) = (k3_xxreal_1 k2_xxreal_0 A)) ) ) ).
tt(d1_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 B D))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_limfunc3 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 B E))  &  ((r2_hidden E (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden F (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k10_xtuple_0 D) (k6_subset_1 (k9_xtuple_0 A) (k1_tarski B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_lmod_5 C A B) <=>  (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  ( ((k4_vectsp_6 A B D) = (k4_struct_0 B))  =>  ((k1_vectsp_6 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v7_struct_0 A) <=>  ((k4_struct_0 A) = (k1_group_1 A)) ) ) ) ).
tt(d1_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k9_funct_2 A (u1_struct_0 B)) (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A (u1_struct_0 B)) (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) )  =>  ( (C = (k2_lopban_1 A B))  <=>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) C D E) (k3_funcsdom (u1_struct_0 B) A (u1_algstr_0 B) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  ((k2_lopban_2 A B C) = (k5_binop_1 (k10_lopban_1 A A) (k8_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) B C)) ) ) ) ) ) ) ).
tt(d1_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_lopban_3 B A) <=> (v3_normsp_1 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(d1_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) <=>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(d1_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_lopban_5 A B C) = (a_3_0_lopban_5 A B C)) ) ) ) ) ) ) ).
tt(d1_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((k1_lopclset A) = (a_1_0_lopclset A)) ) ) ).
tt(d1_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_lpspace1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_lpspace2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_lpspace2 A) <=> (r1_xxreal_0 1 A)) ) ) ).
tt(d1_lp_space,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k1_lp_space A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k4_power (k18_complex1 (k1_seq_1 A D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k1_ltlaxio1 A) = (k3_hilbert1 A k2_hilbert1)) ) ) ).
tt(d1_margrel1,ax, (! [A:$i] :  ((v3_finseq_1 A) =>  ((v2_card_3 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(d1_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_mathmorp A B C) = (a_3_0_mathmorp A B C)) ) ) ) ) ) ) ).
tt(d1_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v1_matrix10 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) & (r1_xxreal_0 (k3_matrix_1 k1_numbers A B C) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(d1_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B))))) )  =>  ( (D = (k1_matrix11 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r2_hidden E (k2_finseq_1 (k1_nat_1 A 2))) & (r2_hidden F (k2_finseq_1 (k1_nat_1 A 2))))  =>  ((r1_xxreal_0 F E) |  ( ( (~ (r1_xxreal_0 (k1_funct_1 C F) (k1_funct_1 C E)))  =>  ((k1_funct_1 D (k2_tarski E F)) = (k1_group_1 B)) )  &  ( (~ (r1_xxreal_0 (k1_funct_1 C E) (k1_funct_1 C F)))  =>  ((k1_funct_1 D (k2_tarski E F)) = (k4_algstr_0 B (k1_group_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) A B) =>  ( (G = (k1_matrix12 A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 D))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden H (k4_finseq_1 D)) & (r2_hidden I (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (H = E)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D F I)) )  &  ( ( (H = F)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D E I)) )  &  (~  ( (~  (H = E) )  &  ( (~  (H = F) )  &  (~  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 D k5_numbers)) =>  (! [G:$i] :  ((m1_matrix_1 G A C D) =>  ( (G = (k1_matrix13 A B C D E F))  <=>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden (k4_tarski H I) (k2_matrix_1 G)) =>  ((k3_matrix_1 A G H I) = (k3_matrix_1 A B (k1_funct_1 E H) (k1_funct_1 F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_matrix14 A B) = (k5_finseq_2 (u1_struct_0 A) B (k4_struct_0 A))) ) ) ) ) ).
tt(d1_matrix15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k2_matrix15 A B) = (k10_laplace A B)) ) ) ) ) ).
tt(d1_matrix16,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_matrix16 A B C) <=>  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((k3_matrix_1 A B D E) = (k1_funct_1 C (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 E D) (k3_finseq_1 C)) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_matrix_1 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  (~  ((r2_hidden C (k10_xtuple_0 A)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( (D = C)  &  ((k3_finseq_1 D) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((k1_matrix_2 A B C) = (k2_finseq_2 A (k2_finseq_2 B C))) ) ) ) ) ) ).
tt(d1_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_matrix_3 A B C) = (k5_finseq_2 (k4_finseq_2 C (u1_struct_0 A)) B (k5_finseq_2 (u1_struct_0 A) C (k4_struct_0 A)))) ) ) ) ) ) ) ).
tt(d1_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ((k1_matrix_4 A B C) = (k3_matrix_3 A B (k2_matrix_3 A C))) ) ) ) ) ) ) ).
tt(d1_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k1_matrix_5 A) = A) ) ) ).
tt(d1_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) <=>  ((k4_matrix_3 B C D) = (k4_matrix_3 B D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrix_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden A B) =>  ((k2_matrix_7 A B C D) = C) )  &  ( (~ (r2_hidden A B))  =>  ((k2_matrix_7 A B C D) = D) ) ) ) ) ) ) ).
tt(d1_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_8 C A B) <=>  ((k4_matrix_6 A B C C) = C) ) ) ) ) ) ) ) ).
tt(d1_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k12_matrix_2 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (u1_struct_0 B))))) )  =>  ( (D = (k1_matrix_9 A B C))  <=>  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 A)) =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) D E) = (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B C E) (u2_algstr_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( (B = (k1_matrixc1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 A)) =>  ((k3_matrix_1 k2_numbers B C D) = (k15_complex1 (k3_matrix_1 k2_numbers A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrixj1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k2_finseq_1 (k2_wsierp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k1_matrixj1 A B))  <=>  ((r1_xxreal_0 B (k2_wsierp_1 (k17_finseq_1 k5_numbers C A))) &  ((r2_hidden C (k4_finseq_1 A)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 B (k2_wsierp_1 (k17_finseq_1 k5_numbers D A))) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( (D = (k1_matrixj2 A B C))  <=>  ( ((k3_finseq_1 D) = C)  &  ( ((k1_matrix_1 D) = C)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) =>  ( ( (E = F)  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = B) )  &  ( ( ((k1_nat_1 E 1) = F)  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k1_group_1 A)) )  &  (~  ( (~  (E = F) )  &  ( (~  ((k1_nat_1 E 1) = F) )  &  (~  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k1_matrixr1 A) = A) ) ) ).
tt(d1_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((k3_matrixr2 A B) = (k12_matrix_3 A k2_vectsp_1 (k2_matrixr2 A B))) ) ) ) ) ).
tt(d1_matrlin2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_matrlin2 A B) = (k5_relat_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(d1_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_matrlin B A) <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  & (m1_vectsp_7 C A B)) ) ) ) ) ) ) ).
tt(d1_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k1_matroid0 A) = (u1_pre_topc A)) ) ) ).
tt(d1_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k3_matrprob A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k18_rvsum_1 (k1_matrprob k1_numbers A C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k1_matrtop1 A) = A) ) ) ).
tt(d1_matrtop3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  ((v1_matrtop3 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ( ((k1_funct_1 (k1_funct_1 B C) D) = (k1_funct_1 C D))  | (r2_hidden D A)) ) ) ) ) ) ) ) ) ).
tt(d1_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_mazurulm C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_normsp_0 B (k5_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) = (k1_normsp_0 A (k5_algstr_0 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k1_mboolean A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k1_zfmisc_1 (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d1_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_prob_1 B A) <=>  (! [C:$i] :  ((r2_hidden C B) => (r2_hidden (k6_subset_1 A C) B)) ) ) ) ) ) ).
tt(d1_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((m1_measure2 C A B) <=> (r1_tarski C B)) ) ) ) ) ) ).
tt(d1_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((r1_measure3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ( ((r2_hidden E B) &  ((r1_tarski D E) &  ((k12_supinf_2 C E) = k1_supinf_2) ) )  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_measure4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) k7_numbers)))) )  =>  ((m1_measure4 B A) <=>  ((v6_supinf_2 B) &  ((v10_valued_0 B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r1_tarski C D) =>  ((r1_xxreal_0 (k12_supinf_2 B C) (k12_supinf_2 B D)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_xxreal_0 (k12_supinf_2 B (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) E))) (k19_supinf_2 (k1_partfun1 k5_numbers (k9_setfam_1 A) (k9_setfam_1 A) k7_numbers E B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (k1_measure5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((r2_hidden D C) <=>  ( (~ (r1_xxreal_0 D A))  &  (~ (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_measure6,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_measure6 A) = A) ) ) ).
tt(d1_measure7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (C = (k1_measure7 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden D A) =>  ((k12_supinf_2 C D) = (k12_supinf_2 B D)) )  &  ( (~ (r2_hidden D A))  =>  ((k12_supinf_2 C D) = k1_supinf_2) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  ((k4_member_1 A) = (a_1_0_member_1 A)) ) ) ).
tt(d1_membered,ax, (! [A:$i] :  ((v1_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_xcmplx_0 B)) ) ) ) ).
tt(d1_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v1_memstr_0 B A) & (l1_memstr_0 B A))  =>  ( (B = (k1_memstr_0 A))  <=>  ( ((u1_struct_0 B) = (k6_domain_1 k5_numbers k6_numbers))  &  ( ((u2_struct_0 B) = k6_numbers)  &  ( ((u1_memstr_0 A B) = (k16_funcop_1 k6_numbers k6_numbers))  &  ((u2_memstr_0 A B) = (k8_funcop_1 (k1_zfmisc_1 k1_numbers) A k5_numbers)) ) ) ) ) ) ) ) ) ).
tt(d1_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_menelaus A B C) <=>  (~  ( (~  ((r1_xboole_0 A B) &  ((r1_xboole_0 B C) & (r1_xboole_0 C A)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D A) &  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_mesfun10,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ((v1_mesfun10 B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) => (r1_xxreal_0 (k3_extreal1 (k12_supinf_2 (k4_mesfunc5 A k7_numbers B D) E)) C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfun6c A B C D) <=>  ((r1_mesfunc6 A B (k5_comseq_3 A C) D) & (r1_mesfunc6 A B (k6_comseq_3 A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k1_mesfun7c A B) = B) ) ) ) ) ).
tt(d1_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ( (E = (k1_mesfun9c A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) => (r2_relset_1 A B (k4_mesfunc5 A B E F) (k2_partfun1 A B (k4_mesfunc5 A B C F) D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_mesfunc1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( (A = k1_mesfunc1)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (B = (k1_real_1 C)) ) ) ) ) ) ) ) ) ).
tt(d1_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v3_valued_0 B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  ((r2_hidden C (k1_relset_1 A B)) & (r1_xxreal_0 k1_supinf_1 (k3_extreal1 (k12_supinf_2 B C)))) ) ) ) ) ) ) ) ) ).
tt(d1_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  ((r1_mesfunc3 A B C D E) <=>  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k12_supinf_2 C G) = (k12_supinf_2 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_mesfunc5,ax, (! [A:$i] :  ((v1_mesfunc5 A) <=>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((r2_hidden B A) => (r1_xxreal_0 B k6_numbers)) ) ) ) ) ).
tt(d1_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc6 A B C D) <=> (r1_mesfunc1 A B (k1_mesfunc5 A C) D)) ) ) ) ) ) ) ) ) ).
tt(d1_mesfunc7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers)))) )  =>  ( (A = k1_mesfunc7)  <=>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ((k5_binop_1 k7_numbers A B C) = (k1_extreal1 B C)) ) ) ) ) ) ) ) ).
tt(d1_mesfunc9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (B = (k2_mesfunc9 A))  <=>  ( ((k1_mesfunc9 B k6_numbers) = (k1_mesfunc9 A k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_mesfunc9 B (k1_nat_1 C 1)) = (k3_supinf_2 (k1_mesfunc9 B C) (k1_mesfunc9 A (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(d1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_metric_1 A B C) = (k1_metric_1 (u1_struct_0 A) (u1_struct_0 A) (u1_metric_1 A) B C)) ) ) ) ) ) ) ).
tt(d1_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_metric_2 A B C) <=>  ((k2_metric_1 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d1_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers)))) )  =>  ( (C = (k1_metric_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [I:$i] :  ((m1_subset_1 I (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ( ( (H = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D F))  &  (I = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) E G)) )  =>  ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C H I) = (k7_real_1 (k4_metric_1 A D E) (k4_metric_1 B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_metric_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ( (C = (k1_metric_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_metric_1 A A C D E) = (k10_real_1 (k1_metric_1 A A B D E) (k7_real_1 1 (k1_metric_1 A A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_metrizts A B C D) <=> (r1_borsuk_3 (k1_pre_topc A C) (k1_pre_topc B D))) ) ) ) ) ) ) ) ) ).
tt(d1_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v1_mfold_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  (? [D:$i] :  ((v1_xreal_0 D) &  (B = (k1_topreal9 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (C = (k1_mfold_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k1_seq_1 C D) = (k23_rvsum_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_midsp_1 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_midsp_1 A) B C)) ) ) ) ) ) ) ).
tt(d1_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_midsp_2 A B) = (k1_algstr_0 A B B)) ) ) ) ) ).
tt(d1_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  ((k4_midsp_3 A B C D) = (k1_funct_1 (u1_midsp_3 (k2_nat_1 A 2) B) (k3_midsp_3 A B 1 (k2_nat_1 A 1) (k2_midsp_3 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(d1_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_mmlquery A B C) <=> (r2_hidden (k4_tarski A B) C)) ) ) ) ).
tt(d1_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k1_mod_2 A) = (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))) ) ) ).
tt(d1_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (D = (k1_mod_3 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_mod_3 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((k2_mod_4 A) = (g6_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (k1_mod_4 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A)) (k5_struct_0 A) (k4_struct_0 A))) ) ) ).
tt(d1_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k1_modal_1 A) = k1_xboole_0) ) ) ).
tt(d1_modelc_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) =>  ((k1_modelc_2 A) = A) )  &  ( (~ (v7_ordinal1 A))  =>  ((k1_modelc_2 A) = k6_numbers) ) ) ) ).
tt(d1_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_2 A) =>  ((k2_modelc_3 A) = (k2_tarski (k11_modelc_2 A) (k12_modelc_2 A))) )  &  ( ((v5_modelc_2 A) =>  ((k2_modelc_3 A) = (k1_tarski (k11_modelc_2 A))) )  &  ( ((v6_modelc_2 A) =>  ((k2_modelc_3 A) = k1_xboole_0) )  &  ( ((v7_modelc_2 A) =>  ((k2_modelc_3 A) = (k1_tarski (k11_modelc_2 A))) )  &  ( ((v8_modelc_2 A) =>  ((k2_modelc_3 A) = (k1_tarski (k12_modelc_2 A))) )  &  (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  ( (~ (v8_modelc_2 A))  &  (~  ((k2_modelc_3 A) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_moebius1 A) <=>  (? [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  & (r1_nat_d (k1_newton B 2) A)) ) ) ) ) ).
tt(d1_monoid_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_monoid_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ) ).
tt(d1_monoid_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k1_monoid_1 A B C D) = (k5_funct_6 A (k4_tarski B C) D)) ) ) ) ) ) ).
tt(d1_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_morph_01 A B C) = (a_3_0_morph_01 A B C)) ) ) ) ) ) ) ).
tt(d1_msafree1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_prob_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_card_3 B) (k3_card_3 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 B) (k3_card_3 C))))) )  =>  ( (E = (k1_msafree1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 B F)) =>  ((k1_funct_1 E G) = (k1_funct_1 (k1_msualg_3 A B C D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ( ( (~ (v11_struct_0 A))  =>  ((k1_msafree2 A) = (a_1_0_msafree2 A)) )  &  ((v11_struct_0 A) =>  ((k1_msafree2 A) = k1_xboole_0) ) ) ) ) ).
tt(d1_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) & (l3_msualg_1 C A))  =>  ( (C = (k1_msafree3 A B))  <=>  (? [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))))) &  ( (C = (k12_msualg_2 A (k11_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))) D))  & (r8_pboole (u1_struct_0 A) D (k1_equation (u1_struct_0 A) B (k15_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))))) ) ) ) ) ) ) ) ) ) ).
tt(d1_msafree,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A B) =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A D C) =>  ( (F = (k1_msafree A B C D E))  <=>  (! [G:$i] :  ((r2_hidden G A) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k1_funct_1 B G) (k1_funct_1 C G)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B G) (k1_funct_1 C G))))) )  =>  ( (H = (k1_funct_1 E G))  =>  ((k1_funct_1 F G) = (k2_partfun1 (k1_funct_1 B G) (k1_funct_1 C G) H (k1_funct_1 D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((k1_msaterm A B) = (k4_dtconstr (k5_msafree A B))) ) ) ) ) ).
tt(d1_msinst_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_altcat_1 B) & (l2_altcat_1 B)) )  =>  ( (B = (k1_msinst_1 A))  <=>  ( ((u1_struct_0 B) = (k5_msalimit A))  &  ( (! [C:$i] :  ((m3_msalimit C (k5_msalimit A)) =>  (! [D:$i] :  ((m3_msalimit D (k5_msalimit A)) =>  ((k1_binop_1 (u1_altcat_1 B) C D) = (k6_msalimit C D)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden C (k5_msalimit A)) &  ((r2_hidden D (k5_msalimit A)) & (r2_hidden E (k5_msalimit A))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  ( ((r2_hidden (k4_tarski F G) (k1_binop_1 (u1_altcat_1 B) C D)) & (r2_hidden (k4_tarski H I) (k1_binop_1 (u1_altcat_1 B) D E)))  =>  ((k1_binop_1 (k4_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B) C D E) (k4_tarski H I) (k4_tarski F G)) = (k4_tarski (k3_relat_1 F H) (k3_relat_1 G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_graph_1 B A) <=>  ((m2_finseq_1 B (u4_struct_0 A)) &  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) & (r1_graph_2 A C B)) ) ) ) ) ) ) ) ).
tt(d1_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( (B = (k1_msscyc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  (? [E:$i] :  ( (C = (k4_tarski D E))  &  ((r2_hidden D (u4_struct_0 A)) &  ((r2_hidden E (u1_struct_0 A)) &  (? [F:$i] :  ((v7_ordinal1 F) &  (? [G:$i] :  ((m1_subset_1 G (k13_finseq_1 (u1_struct_0 A))) &  ( ((k1_funct_1 (u1_msualg_1 A) D) = G)  &  ((r2_hidden F (k4_finseq_1 G)) &  ((k1_funct_1 G F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k3_mssubfam A B C))  <=>  (! [E:$i] :  (~  ((r2_hidden E A) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 (k1_funct_1 B E)))) =>  (~  ( (F = (k1_funct_1 C E))  &  ((k1_funct_1 D E) = (k8_setfam_1 (k1_funct_1 B E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k1_msualg_1 A B) = (k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_msualg_1 A) B)) ) ) ) ) ).
tt(d1_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_msualg_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  ( ((k1_funct_1 (u1_msualg_1 A) C) = k1_xboole_0)  &  ((k1_funct_1 (u2_msualg_1 A) C) = B) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A B B) =>  ( (C = (k2_msualg_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k6_partfun1 (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((m1_msualg_4 D A B C) <=>  (! [E:$i] :  ((r2_hidden E A) => (m1_subset_1 (k1_funct_1 D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))))) ) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_5,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (C = (k1_msualg_5 A B))  <=>  ((r1_relset_1 A A B C) &  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_relset_1 A A B D) => (r1_relset_1 A A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v1_msualg_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (~  ( (~  ((k3_msualg_1 A C B) = k1_xboole_0) )  &  ((k4_msualg_1 A C B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v4_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r4_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_lattice3 A D B) => (r1_lattices A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))) =>  ((k1_msualg_8 A B C) = (k16_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) (a_3_0_msualg_8 A B C))) ) ) ) ) ) ) ).
tt(d1_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B (k6_pboole A C D)) =>  (! [F:$i] :  ((m2_pboole F A B C) =>  ( (F = (k1_msualg_9 A B C D E))  <=>  (! [G:$i] :  ((r2_hidden G A) =>  ((k1_funct_1 F G) = (k11_mcart_1 (k1_funct_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_msuhom_1 A B) <=>  ((r1_tarski (u1_struct_0 A) (u1_struct_0 B)) &  ((r1_tarski (u4_struct_0 A) (u4_struct_0 B)) &  ( ((k2_partfun1 (u4_struct_0 B) (k3_finseq_2 (u1_struct_0 B)) (u1_msualg_1 B) (u4_struct_0 A)) = (u1_msualg_1 A))  &  ((k2_partfun1 (u4_struct_0 B) (u1_struct_0 B) (u2_msualg_1 B) (u4_struct_0 A)) = (u2_msualg_1 A)) ) ) ) ) ) ) ) ) ).
tt(d1_multop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k1_multop_1 A B C D) = (k1_funct_1 A (k3_xtuple_0 B C D))) ) ) ) ) ) ).
tt(d1_mycielsk,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_mycielsk A B C) = (a_3_0_mycielsk A B C)) ) ) ) ) ) ).
tt(d1_nagata_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_nagata_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden C D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden E B) & (r2_hidden F B))  =>  ((r1_xboole_0 D E) |  ((r1_xboole_0 D F) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nagata_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) )  =>  ( (A = k1_nagata_2)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers A (k1_domain_1 k5_numbers k5_numbers B C)) = (k9_real_1 (k4_nat_1 (k13_newton 2 B) (k2_nat_1 (k4_nat_1 2 C) 1)) 1)) ) ) ) ) ) ) ) ).
tt(d1_nat_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  ( (B = (k5_nat_1 A))  <=>  ((r2_hidden B A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  =>  ( (B = (k5_nat_1 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ).
tt(d1_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_zfmisc_1 A) <=>  ( (A = k6_numbers)  |  (A = 1) ) ) ) ) ).
tt(d1_nat_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k1_nat_3 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k2_newton (k1_seq_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nat_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ( (C = (k1_nat_4 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_recdef_1 C D) = (k11_nat_3 (k1_recdef_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (B = (k2_nat_5 A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_recdef_1 B C) = (k1_newton C A)) ) ) ) ) ) ) ) ).
tt(d1_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k1_nat_d A B))  <=>  (~  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (A = (k2_xcmplx_0 (k3_xcmplx_0 B C) D))  &  (~ (r1_xxreal_0 B D)) ) ) ) )  &  (~  ( (C = k6_numbers)  &  (B = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nat_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) )  =>  ( (A = k1_nat_lat)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_binop_1 A B C) = (k6_nat_d B C)) ) ) ) ) ) ) ) ).
tt(d1_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_ncfcont1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (a_3_0_ncfcont1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_ncfcont2 A B C D) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ((r2_hidden G A) &  ((r2_hidden H A) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B G H))))  & (r1_xxreal_0 E (k1_normsp_0 C (k5_algstr_0 C (k7_partfun1 (u1_struct_0 C) D G) (k7_partfun1 (u1_struct_0 C) D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ndiff_1,ax, (! [A:$i] :  (! [B:$i] :  ((l2_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v12_struct_0 C A B) <=> (r1_tarski (k2_relset_1 (u1_struct_0 B) C) (k8_struct_0 B))) ) ) ) ) ) ).
tt(d1_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((v1_ndiff_3 B A) <=>  ((v1_partfun1 B k1_numbers) &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v3_normsp_1 (k1_ndiff_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C B) (k37_valued_1 k5_numbers k1_numbers C)) A) &  ((k6_normsp_1 A (k1_ndiff_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C B) (k37_valued_1 k5_numbers k1_numbers C))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d1_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_ndiff_4 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  &  ( (B = D)  & (r1_ndiff_3 (k4_real_ns1 A) D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_neckla_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_neckla_2 A) <=>  (~ (r1_necklace (k4_necklace 4) A)) ) ) ) ).
tt(d1_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r1_necklace A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski D E) (u1_orders_2 A)) <=> (r2_hidden (k4_tarski (k1_funct_1 C D) (k1_funct_1 C E)) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_net_1,ax, (! [A:$i] :  ((l1_petri A) =>  ((k1_net_1 A) = (k2_xboole_0 (u1_petri A) (u2_petri A))) ) ) ).
tt(d1_newton,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_newton A B) = (k19_rvsum_1 (k2_finseq_2 B A))) ) ) ) ) ).
tt(d1_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_nfcont_1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (a_3_0_nfcont_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_nfcont_2 A B C D) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ((r2_hidden G A) &  ((r2_hidden H A) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B G H))))  & (r1_xxreal_0 E (k1_normsp_0 C (k5_algstr_0 C (k7_partfun1 (u1_struct_0 C) D G) (k7_partfun1 (u1_struct_0 C) D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_nfcont_3 A B C) <=>  ((r2_hidden C (k1_relset_1 k1_numbers B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers D) (k1_relset_1 k1_numbers B)) &  ((v2_comseq_2 D) &  ((k2_seq_2 D) = C) ) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B) A) &  ((k7_partfun1 (u1_struct_0 A) B C) = (k6_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_nfcont_4 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  &  ( (B = D)  & (r1_nfcont_3 (k4_real_ns1 A) D C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((r1_normform A B C D) <=>  ((r1_tarski (k2_domain_1 A B C) (k2_domain_1 A B D)) & (r1_tarski (k3_domain_1 A B C) (k3_domain_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_normsp_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_normsp_0 A B) = (k3_funct_2 (u1_struct_0 A) k1_numbers (u1_normsp_0 A) B)) ) ) ) ) ).
tt(d1_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  ((v2_normsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_normsp_0 A (k1_rlvect_1 A B D)) = (k8_real_1 (k18_complex1 D) (k1_normsp_0 A B)))  & (r1_xxreal_0 (k1_normsp_0 A (k1_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( (B = (k1_normsp_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_metric_1 (u1_struct_0 A) (u1_struct_0 A) B C D) = (k1_normsp_0 A (k5_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (C = (k1_ntalgo_1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers E k6_numbers) = (k1_int_2 B))  &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers D (k2_nat_1 F 1)) = (k8_nat_1 k5_numbers E F))  &  ((k8_nat_1 k5_numbers E (k2_nat_1 F 1)) = (k4_nat_d (k8_nat_1 k5_numbers D F) (k8_nat_1 k5_numbers E F))) ) ) )  &  (C = (k8_nat_1 k5_numbers D (k5_nat_1 (a_1_0_ntalgo_1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_numbers,ax, (k1_numbers = (k6_subset_1 (k2_xboole_0 k2_arytm_2 (k2_zfmisc_1 (k1_tarski k1_xboole_0) k2_arytm_2)) (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0)))) ).
tt(d1_numeral1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k1_numeral1 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D k5_numbers) &  ((v1_funct_1 D) &  ((v5_ordinal1 D) & (v1_finset_1 D)) ) ) )  &  ( ((k1_relset_1 k5_numbers D) = (k1_relset_1 k5_numbers A))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k1_recdef_1 D E) = (k24_binop_2 (k1_recdef_1 A E) (k1_newton B E))) ) ) )  &  (C = (k7_afinsq_2 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_openlatt,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k1_openlatt A) = (u1_pre_topc A)) ) ) ).
tt(d1_oposet_1,ax, (k1_oposet_1 = (g2_qmax_1 1 (k6_partfun1 1) k8_funct_5)) ).
tt(d1_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k2_oppcat_1 A) = (g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u2_graph_1 A) (u1_graph_1 A) (k1_oppcat_1 (u4_struct_0 A) (u4_struct_0 A) (u4_struct_0 A) (u1_cat_1 A)))) ) ) ).
tt(d1_orders_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (r2_hidden k1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k3_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski A))))) )  =>  ((m1_orders_1 B A) <=>  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden (k1_funct_1 B C) C)) ) ) ) ) ) ) ) ).
tt(d1_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_3 A) <=> (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (k6_partfun1 (u1_struct_0 A)))) ) ) ).
tt(d1_orders_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((m1_orders_4 A) <=>  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  | (v2_struct_0 A)) ) ) ) ).
tt(d1_ordinal1,ax, (! [A:$i] :  ((k1_ordinal1 A) = (k2_xboole_0 A (k1_tarski A))) ) ).
tt(d1_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((k1_ordinal2 A) = (k1_funct_1 A (k3_tarski (k9_xtuple_0 A)))) ) ) ).
tt(d1_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( (C = (k1_ordinal3 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k10_ordinal2 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) & (v1_funct_1 C)) )  =>  ( (C = (k1_ordinal4 A B))  <=>  ( ((k9_xtuple_0 C) = (k10_ordinal2 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C D) = (k1_funct_1 A D)) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C (k10_ordinal2 (k9_xtuple_0 A) D)) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  ((v1_ordinal5 A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B C) & (r2_hidden C (k9_xtuple_0 A)))  => (r2_hidden (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(d1_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) <=>  (? [B:$i] :  ((v3_ordinal1 B) & (r1_tarski A B)) ) ) ) ).
tt(d1_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_symsp_1 B A)) ) ) ) )  =>  ((v1_ortsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( (~  ( (~  (C = (k4_struct_0 B)) )  &  ( (~  (D = (k4_struct_0 B)) )  &  ( (~  (E = (k4_struct_0 B)) )  &  ( (~  (F = (k4_struct_0 B)) )  &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B I C))  &  ( (~ (r1_orders_2 B I D))  &  ( (~ (r1_orders_2 B I E))  &  (~ (r1_orders_2 B I F)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r1_orders_2 B C D) => (r1_orders_2 B (k4_vectsp_1 A B H C) D))  &  ( ( ((r1_orders_2 B D C) & (r1_orders_2 B E C))  => (r1_orders_2 B (k3_rlvect_1 B D E) C))  &  ( (~  ( (~ (r1_orders_2 B D C))  &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~ (r1_orders_2 B (k5_algstr_0 B G (k4_vectsp_1 A B I D)) C)) ) ) ) )  &  ( ((r1_orders_2 B C (k5_algstr_0 B D E)) & (r1_orders_2 B D (k5_algstr_0 B E C)))  => (r1_orders_2 B E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m1_osafree C A B) <=>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r8_pboole (u1_struct_0 A) D (k2_osalg_2 A C)) => (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k10_osalg_2 A B D)) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(d1_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v1_funcop_1 B)) ) ) )  =>  ((v1_osalg_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) =>  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 (k1_funct_1 B C))) =>  ((r2_hidden E (k9_xtuple_0 (k1_funct_1 B D))) &  ((k1_funct_1 (k1_funct_1 B C) E) = (k1_funct_1 (k1_funct_1 B D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) B C) =>  ((v1_osalg_4 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r3_orders_2 A E F) =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G (k1_funct_1 B E)) & (r2_hidden H (k1_funct_1 C E)))  =>  ((r2_hidden (k4_tarski G H) (k1_msualg_4 (u1_struct_0 A) B C D E)) <=> (r2_hidden (k4_tarski G H) (k1_msualg_4 (u1_struct_0 A) B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v1_translac A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) & (r2_analoaf A B E C D)) )  => (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))))) )  =>  ( (B = (k1_parsp_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k5_binop_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) B C D) = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k3_rlvect_1 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D)) (k3_rlvect_1 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D)) (k3_rlvect_1 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  ((v1_parsp_2 A) <=>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_parsp_1 A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_1 A C D B E) &  ((r1_parsp_1 A B C D E) & (r1_parsp_1 A B D C E)) )  => (r1_parsp_1 A B C B D)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_parsp_1 A B E C F) &  ((r1_parsp_1 A B E D G) &  ((r1_parsp_1 A B C E F) & (r1_parsp_1 A B D E G)) ) )  =>  ((r1_parsp_1 A B E B C) |  ((r1_parsp_1 A B E B D) | (r1_parsp_1 A C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k3_partfun1 A B C) = (k5_relat_1 (k6_relat_1 C A) B)) ) ) ) ) ).
tt(d1_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v3_funct_1 C) <=>  (? [D:$i] :  ((m1_subset_1 D B) &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A C)) =>  ((k1_funct_1 C E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_partfun3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_partfun3 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r2_hidden B (k10_xtuple_0 A)) & (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ).
tt(d1_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((r1_partit1 A B C) <=>  (? [D:$i] :  ((r1_tarski D B) &  ( (~  (D = k1_xboole_0) )  &  (C = (k3_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_partit_2,ax, (! [A:$i] :  (! [B:$i] :  ((k1_partit_2 A B) = k1_xboole_0) ) ) ).
tt(d1_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v1_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_diraf A C F B) &  ((r3_diraf A F D E) & (r2_diraf A C D E B)) )  =>  ((r3_diraf A F C D) | (r1_diraf A D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B C) <=>  (! [D:$i] :  ((r2_hidden D A) => (r2_hidden (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(d1_pcomps_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_pcomps_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden C D) &  ((v3_pre_topc D A) & (v1_finset_1 (a_3_0_pcomps_1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pcomps_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_pcomps_2 A B C) = (k3_tarski (k1_wellord1 B C))) ) ) ) ) ) ).
tt(d1_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k12_pralg_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 C D) = (u1_struct_0 (k10_pralg_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_pdiff_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) k1_numbers)))) )  =>  ( (C = (k1_pdiff_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  ((k1_seq_1 C D) = (k1_seq_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(d1_pdiff_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k1_pdiff_2 A B C D) = (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(d1_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((r1_pdiff_4 A B) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid 3) A)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C B) => (r3_pdiff_1 3 1 (k2_partfun1 (k1_euclid 3) k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d1_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r1_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F C) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B) C)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I C)) (k1_seq_1 H (k9_real_1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pdiff_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid B) (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A))))) )  =>  ((v1_pdiff_6 C A B) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  ((k3_funct_2 (k1_euclid B) (k1_euclid A) C (k7_euclid B D E)) = (k7_euclid A (k3_funct_2 (k1_euclid B) (k1_euclid A) C D) (k3_funct_2 (k1_euclid B) (k1_euclid A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r1_pdiff_7 A B C) <=> (r1_pdiff_1 A 1 (k3_pdiff_1 A B) C)) ) ) ) ) ) ) ).
tt(d1_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((r1_tarski C (k1_relset_1 (k1_euclid A) D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k9_funct_2 (k1_euclid A) (k1_euclid B))))))  =>  ( (E = (k1_pdiff_9 A B C D))  <=>  ( ((k1_relset_1 (k1_euclid A) E) = C)  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) (k1_euclid B)) E F) = (k8_pdiff_1 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_pencil_1 A B C) <=>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_pre_topc A)) =>  (~ (r1_tarski (k2_tarski B C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pencil_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_pencil_2 A B C D) = (k8_finseq_1 A (k17_finseq_1 A (k7_nat_d C 1) B) (k2_rfinseq A D B))) ) ) ) ) ) ) ) ).
tt(d1_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k1_pencil_3 A B C) = (k1_card_1 (a_3_0_pencil_3 A B C))) ) ) ) ) ) ) ).
tt(d1_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_vectsp_5 A B))) =>  ( ((m1_vectsp_4 C A D) =>  ( (E = (k1_pencil_4 A B C D))  <=>  (! [F:$i] :  ( ((v7_vectsp_1 F A) & (m1_vectsp_4 F A B))  =>  ((r2_hidden F E) <=>  ((m1_vectsp_4 C A F) & (m1_vectsp_4 F A D)) ) ) ) ) )  &  ( (~ (m1_vectsp_4 C A D))  =>  ( (E = (k1_pencil_4 A B C D))  <=>  (E = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_pepin A B C) = (k4_nat_d (k1_newton B A) C)) ) ) ) ) ) ) ).
tt(d1_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  ((r1_tarski C B) =>  ((k1_petri_2 A B C D) = (a_4_0_petri_2 A B C D)) ) ) ) ) ) ) ) ).
tt(d1_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r1_pnproc_1 A B C) <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ).
tt(d1_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_polyeq_1 A B C) = (k2_xcmplx_0 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(d1_polyeq_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ((k1_polyeq_2 A B C D E F) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k1_newton F 4)) (k3_xcmplx_0 B (k1_newton F 3))) (k3_xcmplx_0 C (k3_square_1 F))) (k3_xcmplx_0 D F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k1_polyeq_3 A) = (k3_binop_2 (k10_binop_2 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))) (k5_binop_2 (k11_binop_2 2 (k11_binop_2 (k3_complex1 A) (k4_complex1 A))) k7_complex1))) ) ) ).
tt(d1_polyeq_4,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ((k1_polyeq_4 A B C D E F G) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k1_newton G 5)) (k3_xcmplx_0 B (k1_newton G 4))) (k3_xcmplx_0 C (k1_newton G 3))) (k3_xcmplx_0 D (k3_square_1 G))) (k3_xcmplx_0 E G)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polyeq_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_polyeq_5 A B) = (k3_xcmplx_0 (k1_power A (k17_complex1 B)) (k2_xcmplx_0 (k20_sin_cos (k13_complex1 (k1_comptrig B) A)) (k3_xcmplx_0 (k17_sin_cos (k13_complex1 (k1_comptrig B) A)) k7_complex1)))) ) ) ) ) ).
tt(d1_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k9_fvsum_1 A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 B)) =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k6_algstr_0 A C (k7_partfun1 (u1_struct_0 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r1_polynom3 A B C) <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  ( (~ (r1_xxreal_0 (k1_recdef_1 C D) (k1_recdef_1 B D)))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 D E) |  ((k1_recdef_1 B E) = (k1_recdef_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k1_polynom4 A B))  <=>  ( ((k1_normsp_1 A C (k7_nat_d (k1_algseq_1 A B) 1)) = (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~  (D = (k7_nat_d (k1_algseq_1 A B) 1)) )  =>  ((k1_normsp_1 A C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polynom5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k1_polynom5 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k7_partfun1 k1_numbers B C) = (k17_complex1 (k7_partfun1 (u1_struct_0 k1_complfld) A C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_pre_poly (k10_ordinal2 A B)) (k15_pre_poly (k10_ordinal2 A B))) =>  ( (E = (k1_polynom6 A B C D))  <=>  (! [F:$i] :  ((v3_ordinal1 F) =>  ( ((r2_hidden F A) =>  ((k1_funct_1 E F) = (k1_funct_1 C F)) )  &  ((r2_hidden F (k6_subset_1 (k10_ordinal2 A B) A)) =>  ((k1_funct_1 E F) = (k1_funct_1 D (k5_ordinal3 F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((v1_polynom7 C A B) <=>  (~  (C = (k7_polynom1 A B)) ) ) ) ) ) ) ) ).
tt(d1_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_polynom8 A B) = (k5_binom A (k5_struct_0 A) B)) ) ) ) ) ).
tt(d1_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) )  =>  ( (E = (k1_polyred A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r3_pre_poly A B F) =>  ( ((k3_polynom1 A C E F) = (k3_polynom1 A C D (k12_pre_poly A F B)))  &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( (~ (r3_pre_poly A B G))  =>  ((k3_polynom1 A C E G) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_poset_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_poset_1 A) <=>  ((v1_yellow_0 A) &  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 B))  => (r1_yellow_0 A B)) ) ) ) ) ) ) ).
tt(d1_power,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 1 A))  =>  ((k1_power A B) = (k2_prepower A B)) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (v1_abian A))  &  (~  ((k1_power A B) = (k4_xcmplx_0 (k2_prepower A (k4_xcmplx_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k1_pralg_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k1_xtuple_0 (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_pralg_2 A))  <=>  ( (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) <=>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ((r2_hidden D (k9_xtuple_0 A)) &  (C = (k10_funct_6 D)) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k1_funct_1 A (k10_funct_6 C))) ) ) ) ) ) ) ) ) ) ).
tt(d1_pralg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k1_pralg_3 A B C) = (k1_funct_1 (k5_msualg_1 A C B) k1_xboole_0)) ) ) ) ) ) ) ).
tt(d1_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k1_pre_ff A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))))) )  &  ( (B = (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C A)))  &  ( ((k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C k6_numbers) = (k1_domain_1 k5_numbers k5_numbers k6_numbers 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C (k1_nat_1 D 1)) = (k1_domain_1 k5_numbers k5_numbers (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D)) (k2_nat_1 (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D)) (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) C D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_prelamb A B C) = (k5_binop_1 (u1_struct_0 A) (u1_prelamb A) B C)) ) ) ) ) ) ) ).
tt(d1_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_finseq_2 C A (k3_finseq_2 A)) =>  ( (C = (k5_pre_poly A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A))))) )  &  ( (! [E:$i] :  ((m2_finseq_2 E A (k3_finseq_2 A)) =>  (! [F:$i] :  ((m2_finseq_2 F A (k3_finseq_2 A)) =>  ((k5_binop_1 (k3_finseq_2 A) D E F) = (k1_pre_poly A E F)) ) ) ) )  &  (C = (k1_finsop_1 (k3_finseq_2 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k1_prepower A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k1_newton A C)) ) ) ) ) ) ) ) ).
tt(d1_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_pre_topc A) <=>  ((r2_hidden (u1_struct_0 A) (u1_pre_topc A)) &  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (u1_pre_topc A)) => (r2_hidden (k5_setfam_1 (u1_struct_0 A) B) (u1_pre_topc A))) ) )  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B (u1_pre_topc A)) & (r2_hidden C (u1_pre_topc A)))  => (r2_hidden (k9_subset_1 (u1_struct_0 A) B C) (u1_pre_topc A))) ) ) ) ) ) ) ) ) ) ).
tt(d1_prgcor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) |  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k1_prgcor_1 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  (? [E:$i] :  ((m2_finseq_1 E k4_numbers) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  ( ((k3_finseq_1 D) = (k2_xcmplx_0 A 1))  &  ( ((k3_finseq_1 E) = (k2_xcmplx_0 A 1))  &  ( ((k3_finseq_1 F) = (k2_xcmplx_0 A 1))  &  ( ( (~ (r1_xxreal_0 B A))  =>  (C = k6_numbers) )  &  ((r1_xxreal_0 B A) =>  ( ((k1_funct_1 D 1) = B)  &  (? [G:$i] :  ((v1_int_1 G) &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G A) &  ( (! [H:$i] :  ((v1_int_1 H) =>  ((r1_xxreal_0 1 H) =>  ((r1_xxreal_0 G H) |  ( ((k1_funct_1 D (k2_xcmplx_0 H 1)) = (k3_xcmplx_0 (k1_funct_1 D H) 2))  & (r1_xxreal_0 (k1_funct_1 D (k2_xcmplx_0 H 1)) A)) ) ) ) )  &  ( ((k1_funct_1 D (k2_xcmplx_0 G 1)) = (k3_xcmplx_0 (k1_funct_1 D G) 2))  &  ( (~ (r1_xxreal_0 (k1_funct_1 D (k2_xcmplx_0 G 1)) A))  &  ( ((k1_funct_1 F (k2_xcmplx_0 G 1)) = k6_numbers)  &  ( ((k1_funct_1 E (k2_xcmplx_0 G 1)) = A)  &  ( (! [H:$i] :  ((v1_int_1 H) =>  ( ((r1_xxreal_0 1 H) & (r1_xxreal_0 H G))  =>  ( ((r1_xxreal_0 (k1_funct_1 D (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) (k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1)))) =>  ( ((k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) = (k6_xcmplx_0 (k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1))) (k1_funct_1 D (k6_xcmplx_0 (k2_xcmplx_0 G 1) H))))  &  ((k1_funct_1 F (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) = (k2_xcmplx_0 (k3_xcmplx_0 (k1_funct_1 F (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1))) 2) 1)) ) )  &  ( (~ (r1_xxreal_0 (k1_funct_1 D (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) (k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1)))))  =>  ( ((k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) = (k1_funct_1 E (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1))))  &  ((k1_funct_1 F (k6_xcmplx_0 (k2_xcmplx_0 G 1) H)) = (k3_xcmplx_0 (k1_funct_1 F (k6_xcmplx_0 (k2_xcmplx_0 G 1) (k6_xcmplx_0 H 1))) 2)) ) ) ) ) ) )  &  (C = (k1_funct_1 F 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prgcor_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_prgcor_2 A B C) <=>  ((r1_tarski k5_numbers A) &  ( ((k1_funct_1 B k6_numbers) = (k3_finseq_1 C))  &  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) (k3_finseq_1 C)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_prob_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) => (r2_hidden (k3_subset_1 A C) B)) ) ) ) ) ) ) ).
tt(d1_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k2_prob_2 A B C) = (k3_prob_1 A C)) ) ) ) ) ) ).
tt(d1_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k1_prob_3 A B))  <=>  ( ((k1_prob_2 A (k9_setfam_1 A) C k6_numbers) = (k1_prob_2 A (k9_setfam_1 A) B k6_numbers))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_prob_2 A (k9_setfam_1 A) C (k1_nat_1 D 1)) = (k9_subset_1 A (k1_funct_1 C D) (k1_prob_2 A (k9_setfam_1 A) B (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d1_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((k2_prob_4 A B C) = C) ) ) ) ) ) ) ).
tt(d1_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_projdes1 A B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_collsp A B C F) & (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ((r1_projpl_1 A B C D) <=>  ( (~ (r1_incsp_1 A B D))  &  (~ (r1_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A D B))  &  ( (~ (r1_incsp_1 A D C))  &  (~  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 A)))))  =>  ( (E = (k1_projred1 A B C D))  <=>  ((r1_tarski (k1_relset_1 (u1_incsp_1 A) E) (u1_incsp_1 A)) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  ((r2_hidden F (k1_relset_1 (u1_incsp_1 A) E)) <=> (r1_incsp_1 A F B)) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  ( ((r1_incsp_1 A F B) & (r1_incsp_1 A G C))  =>  ( ((k1_funct_1 E F) = G)  <=>  (? [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) &  ((r1_incsp_1 A D H) &  ((r1_incsp_1 A F H) & (r1_incsp_1 A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ((r1_projred2 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r1_incsp_1 A E B) &  ((r1_incsp_1 A E C) & (r1_incsp_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prvect_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A)) (k4_finseq_2 C A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A)) (k4_finseq_2 C A))))) )  =>  ( (D = (k2_prvect_1 A B C))  <=>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 C A)) =>  (! [F:$i] :  ((m2_finseq_2 F A (k4_finseq_2 C A)) =>  ((k5_binop_1 (k4_finseq_2 C A) D E F) = (k1_prvect_1 A C B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((m1_prvect_2 C A B) <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) =>  ((v1_funct_1 (k1_funct_1 C D)) &  ((v1_funct_2 (k1_funct_1 C D) (k2_zfmisc_1 B (k1_funct_1 A D)) (k1_funct_1 A D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (k1_funct_1 A D)) (k1_funct_1 A D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) )  =>  ( (C = (k1_prvect_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k5_binop_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D F) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) E G)) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k1_algstr_0 A D E) (k1_algstr_0 B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_pscomp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k1_pscomp_1 A B) = (k5_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B (u1_struct_0 A)))) ) ) ) ) ).
tt(d1_pua2mss1,ax, (! [A:$i] :  ( ((v4_unialg_1 A) & (l1_unialg_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  ((k2_pua2mss1 A B) = (k1_funct_1 (u1_unialg_1 A) B)) ) ) ) ) ).
tt(d1_pythtrip,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d C A) & (r1_nat_d C B))  =>  (C = 1) ) ) ) ) ) ) ) ) ).
tt(d1_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k1_pzfmisc1 A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k1_tarski (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d1_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) <=>  ( (~ (v1_xboole_0 A))  &  (? [B:$i] :  ((r1_tarski k5_numbers B) &  (A = (k2_zfmisc_1 k5_numbers B)) ) ) ) ) ) ).
tt(d1_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k1_qc_lang2 A) = (k13_qc_lang1 A (k12_qc_lang1 A))) ) ) ).
tt(d1_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k1_qc_lang3 A B C) = (a_3_0_qc_lang3 A B C)) ) ) ) ) ) ) ).
tt(d1_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ( ( ( (B = (k12_qc_lang1 A))  | (v2_qc_lang1 B A))  =>  ((k1_qc_lang4 A B) = (k6_finseq_1 (k9_qc_lang1 A))) )  &  ( ((v3_qc_lang1 B A) =>  ((k1_qc_lang4 A B) = (k12_finseq_1 (k9_qc_lang1 A) (k18_qc_lang1 A B))) )  &  ( ((v4_qc_lang1 B A) =>  ((k1_qc_lang4 A B) = (k2_finseq_4 (k9_qc_lang1 A) (k19_qc_lang1 A B) (k20_qc_lang1 A B))) )  &  (~  ( (~  (B = (k12_qc_lang1 A)) )  &  ( (~ (v2_qc_lang1 B A))  &  ( (~ (v3_qc_lang1 B A))  &  ( (~ (v4_qc_lang1 B A))  &  (~  ((k1_qc_lang4 A B) = (k12_finseq_1 (k9_qc_lang1 A) (k22_qc_lang1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_qmax_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( (C = (k1_qmax_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (m2_prob_1 D A B)) ) ) ) ) ) ) ) ).
tt(d1_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_quantal1 B A) <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_lattices A (k15_lattice3 A C) D) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ( (C = (k5_quatern2 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  ( (A = (k6_quaterni D E F G))  &  ( (B = (k6_quaterni H I J K))  &  (C = (k6_quaterni (k10_real_1 (k7_real_1 (k7_real_1 (k7_real_1 (k8_real_1 H D) (k8_real_1 I E)) (k8_real_1 J F)) (k8_real_1 K G)) (k5_square_1 (k3_quatern2 B))) (k10_real_1 (k7_real_1 (k9_real_1 (k9_real_1 (k8_real_1 H E) (k8_real_1 I D)) (k8_real_1 J G)) (k8_real_1 K F)) (k5_square_1 (k3_quatern2 B))) (k10_real_1 (k9_real_1 (k9_real_1 (k7_real_1 (k8_real_1 H F) (k8_real_1 I G)) (k8_real_1 J D)) (k8_real_1 K E)) (k5_square_1 (k3_quatern2 B))) (k10_real_1 (k9_real_1 (k7_real_1 (k9_real_1 (k8_real_1 H G) (k8_real_1 I F)) (k8_real_1 J E)) (k8_real_1 K D)) (k5_square_1 (k3_quatern2 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k1_quatern3 A) = (k27_quaterni A A)) ) ) ).
tt(d1_quaterni,ax, (k1_quaterni = (k2_xboole_0 (k6_subset_1 (k9_funct_2 4 k1_numbers) a_0_0_quaterni) k2_numbers)) ).
tt(d1_quin_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_quin_1 A B C) = (k6_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C))) ) ) ) ) ) ) ).
tt(d1_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k1_quofield A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E))  &  (~  (E = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_radix_1 A) = (k3_power 2 A)) ) ) ).
tt(d1_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D k5_numbers))  =>  ((k1_radix_2 A B C D) = (k4_nat_1 (k13_newton (k1_radix_1 B) (k7_nat_d A 1)) (k1_recdef_1 D A))) ) ) ) ) ) ) ) ) ).
tt(d1_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_radix_3 A) = (a_1_0_radix_3 A)) ) ) ).
tt(d1_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k4_radix_3 C)))  =>  (! [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E (k4_radix_3 C)))  =>  ( ((r2_hidden A (k2_finseq_1 B)) & (r1_xxreal_0 2 C))  =>  ((k1_radix_4 A B C D E) = (k2_xcmplx_0 (k6_radix_3 (k2_xcmplx_0 (k7_radix_3 A C B D) (k7_radix_3 A C B E)) C) (k5_radix_3 (k2_xcmplx_0 (k7_radix_3 (k7_nat_d A 1) C B D) (k7_radix_3 (k7_nat_d A 1) C B E)) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ( ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 B A) |  ((k1_radix_5 A B C) = (k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 C)) 1)) ) )  &  ( (~  ((r1_xxreal_0 1 A) &  (~ (r1_xxreal_0 B A)) ) )  =>  ((k1_radix_5 A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d1_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ((r2_hidden A (k2_finseq_1 (k2_xcmplx_0 B 2))) =>  ( ((r1_xxreal_0 B A) =>  ((k1_radix_6 A B C D) = (k1_funct_1 D A)) )  &  ( (~ (r1_xxreal_0 B A))  =>  ((k1_radix_6 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ramsey_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_eqrel_1 D (k3_group_10 A B)) =>  ((r1_ramsey_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E D) & (r1_tarski (k3_group_10 C B) E)) ) ) ) ) ) ) ) ) ).
tt(d1_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  ( (B = (k2_random_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_seq_1 B C) = (k1_rpr_1 A C)) ) ) ) ) ) ) ) ).
tt(d1_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) =>  ( ((r1_random_1 A B D C) & (r3_mesfunc6 A B (k2_prob_4 A B C) (k2_mesfun6c 2 A (k7_random_1 A B D))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (E = (k1_random_2 A B C D))  <=>  (? [F:$i] :  ((m1_random_1 F A B) &  (? [G:$i] :  ((m1_random_1 G A B) &  ((r2_funct_2 A k1_numbers G (k8_funcop_1 k1_numbers A (k8_random_1 A B C D))) &  ((r2_funct_2 A k1_numbers F (k4_random_1 A B D G)) &  ((r1_random_1 A B F C) &  ((r3_mesfunc6 A B (k2_prob_4 A B C) (k2_mesfun6c 2 A (k7_random_1 A B F))) &  (E = (k1_mesfunc6 A B (k2_prob_4 A B C) (k2_mesfun6c 2 A (k7_random_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ( (E = (k1_ranknull A B C D))  <=>  ((k2_struct_0 E) = (a_4_0_ranknull A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rat_1,ax, (! [A:$i] :  ( (A = k3_numbers)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  (B = (k7_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ).
tt(d1_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_ratfunc1 B A) <=> (r2_funct_2 k5_numbers (u1_struct_0 A) B (k9_polynom3 A))) ) ) ) ) ).
tt(d1_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_rcomp_1 A B) = (a_2_0_rcomp_1 A B)) ) ) ) ) ).
tt(d1_rcomp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_rcomp_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_connsp_1 C A)) ) ) ) ) ) ) ) ).
tt(d1_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (C = (k1_real_3 A B))  <=>  ( ((k3_funct_2 k5_numbers k5_numbers C k6_numbers) = (k4_nat_d A B))  &  ( ((k3_funct_2 k5_numbers k5_numbers C 1) = (k4_nat_d B (k4_nat_d A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_funct_2 k5_numbers k5_numbers C (k1_nat_1 D 2)) = (k4_nat_d (k1_seq_1 C D) (k3_funct_2 k5_numbers k5_numbers C (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_real_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k1_real_lat)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k5_binop_1 k1_numbers A B C) = (k1_square_1 B C)) ) ) ) ) ) ) ) ).
tt(d1_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A))))) )  =>  ( (B = (k1_real_ns1 A))  <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k5_binop_1 (k1_euclid A) B C D) = (k7_euclid A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_realset1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((m1_realset1 C A B) <=>  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 C C)) => (r2_hidden (k1_funct_1 B D) C)) ) ) ) ) ) ) ) ).
tt(d1_realset2,ax, (k1_realset2 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k13_funcop_1 k6_numbers k6_numbers k6_numbers) (k13_funcop_1 k6_numbers 1 1)) (k13_funcop_1 1 k6_numbers 1)) (k13_funcop_1 1 1 k6_numbers))) ).
tt(d1_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k1_realset3 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) B C D) = (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_rearran1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_rearran1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  (! [C:$i] :  ((v1_finset_1 C) =>  ( (C = (k1_funct_1 A B))  =>  ((k5_card_1 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(d1_recdef_2,ax, (! [A:$i] :  ((v2_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k4_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (A = (k3_xtuple_0 C D E))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d1_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (~  (B = (k4_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(d1_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_relat_2 A B) <=>  (! [C:$i] :  ((r2_hidden C B) => (r2_hidden (k4_tarski C C) A)) ) ) ) ) ) ).
tt(d1_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((r1_relset_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden (k4_tarski E F) C) => (r2_hidden (k4_tarski E F) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_relset_2 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_setfam_1 A))  &  (! [D:$i] :  ((r1_tarski D A) =>  ((k1_funct_1 C D) = (k7_relat_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v3_funct_1 B) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  =>  ((k7_partfun1 A B C) = (k7_partfun1 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ( (A = k1_xboole_0)  |  (B = k1_xboole_0) )  =>  ( (C = (k1_rewrite1 A B))  <=>  (C = (k7_finseq_1 A B)) ) )  &  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ( (C = (k1_rewrite1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ( ((k3_finseq_1 A) = (k2_nat_1 D 1))  &  ( (E = (k5_relat_1 A (k2_finseq_1 D)))  &  (C = (k7_finseq_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((l1_rewrite3 C B) =>  ((v2_rewrite3 C A B) <=>  ( ((v1_relat_1 (u1_rewrite3 B C)) & (v1_funct_1 (u1_rewrite3 B C)))  &  ( (~ (r2_hidden (k2_flang_1 A) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ( ((r2_hidden (k4_tarski D E) (k9_xtuple_0 (u1_rewrite3 B C))) & (r2_hidden (k4_tarski D F) (k9_xtuple_0 (u1_rewrite3 B C))))  =>  ( (E = F)  |  (! [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 A)) =>  ( (~  ((k1_flang_1 A E G) = F) )  &  (~  ((k1_flang_1 A F G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k1_rfinseq2 A))  <=>  ( ( ((k3_finseq_1 A) = k6_numbers)  =>  (B = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((r2_hidden B (k4_finseq_1 A)) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  ( (D = (k1_seq_1 A C))  &  (E = (k1_seq_1 A B)) ) )  => (r1_xxreal_0 D E)) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  ((k1_seq_1 A C) = (k1_seq_1 A B)) )  => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rfinseq,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ( (C = (k1_rfinseq A B))  <=>  ( ((k3_finseq_1 C) = (k9_real_1 (k3_finseq_1 B) A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k1_funct_1 B (k2_xcmplx_0 D A))) ) ) ) ) ) )  &  ( (~ (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ( (C = (k1_rfinseq A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d1_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k1_rfunct_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_subset_1 (k9_xtuple_0 B) (k9_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 B) (k8_relat_1 B (k1_tarski k6_numbers)))))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k3_xcmplx_0 (k1_funct_1 A D) (k5_xcmplx_0 (k1_funct_1 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden B (k1_relset_1 k1_numbers A)) &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_rfunct_3 A) = (k4_xxreal_0 A k6_numbers)) ) ) ).
tt(d1_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r1_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E)) B) &  ( (~  (D = E) )  & (r1_xxreal_0 (k9_binop_2 (k11_binop_2 C (k1_seq_1 A D)) (k11_binop_2 (k10_binop_2 1 C) (k1_seq_1 A E))) (k1_seq_1 A (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_rinfsup1 A) = (k4_seq_4 (k2_relset_1 k1_numbers A))) ) ) ).
tt(d1_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k1_rinfsup2 A) = (k8_supinf_2 (k17_supinf_2 A))) ) ) ).
tt(d1_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_ring_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden (k6_algstr_0 A C D) B) &  ( (~ (r2_hidden C B))  &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_ringcat1 C A B) <=>  ((v13_vectsp_1 C A B) &  ((v1_group_6 C A B) & (v6_group_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(d1_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( (D = (k1_rlaffin1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_seq_1 D E) = (k1_seq_1 B (k5_algstr_0 A E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_rlaffin2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k3_convex1 A B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_xboole_0 E B) & (r2_hidden D (k3_convex1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rlaffin3,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((m1_rlaffin3 B A) <=>  ((k10_xtuple_0 B) = A) ) ) ) ) ) ).
tt(d1_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k3_rlvect_1 A C D) B)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ( ((v1_rlvect_1 D) & (m1_rlsub_1 D A))  =>  ( (D = (k1_rlsub_2 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_rlsub_2 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers E) &  ((r1_xxreal_0 E 1) &  ((r2_hidden C B) & (r2_hidden D B)) ) )  => (r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D (k9_real_1 1 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_rlvect_1 A B C) = (k1_binop_1 (u1_rlvect_1 A) C B)) ) ) ) ) ) ) ).
tt(d1_rlvect_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((r1_struct_0 A B) =>  ((k1_rlvect_2 A B) = B) ) ) ) ) ).
tt(d1_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) <=>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ((k6_rlvect_2 A C) = (k4_struct_0 A))  =>  ((k3_rlvect_2 A C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d1_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) <=>  (? [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_rlvect_3 B A)) ) ) ) ) ).
tt(d1_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( (D = (k1_rlvect_x A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_seq_1 D E) = (k11_binop_2 B (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rmod_2 C A B) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k3_rlvect_1 B D E) C)) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E C) => (r2_hidden (k5_vectsp_2 A B D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  ( (E = (k1_rmod_3 A B C D))  <=>  ((u1_struct_0 E) = (a_4_0_rmod_3 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (D = (k1_rmod_4 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  ( ((k10_xtuple_0 E) = C)  &  ((v2_funct_1 E) &  (D = (k4_rlvect_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v1_robbins2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) D)) (k3_robbins1 A (k1_lattices A B (k3_robbins1 A (k1_lattices A (k3_robbins1 A D) (k3_robbins1 A (k1_lattices A D E)))))))) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v1_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A B (k1_lattices A C D)) = (k1_lattices A C (k1_lattices A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattices A B C) =>  (C = (k1_lattices A B (k2_lattices A (k3_robbins1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(d1_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_roughs_1 A) <=> (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (k6_partfun1 (u1_struct_0 A)))) ) ) ).
tt(d1_rpr_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A B) = (k7_xcmplx_0 (k5_card_1 B) (k5_card_1 A))) ) ) ) ) ).
tt(d1_rsspace3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_rsspace))) =>  ( (A = k1_rsspace3)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_rsspace) & (v2_series_1 (k2_rsspace B))) ) ) ) ) ) ).
tt(d1_rsspace4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k7_rsspace))) =>  ( (A = k1_rsspace4)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k1_rsspace) & (v1_comseq_2 (k2_rsspace B))) ) ) ) ) ) ).
tt(d1_rsspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (A = k1_rsspace)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ) ) ).
tt(d1_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  ((m1_rusub_1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u1_rlvect_1 B) = (k5_relat_1 (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers (u1_struct_0 B))))  &  ((u1_bhsp_1 B) = (k1_realset1 (u1_bhsp_1 A) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(d1_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ( ((v1_bhsp_1 D) & (m1_rusub_1 D A))  =>  ( (D = (k1_rusub_2 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_rusub_2 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( (C = (k1_rusub_3 A B))  <=>  ((u1_struct_0 C) = (a_2_0_rusub_3 A B)) ) ) ) ) ) ) ) ).
tt(d1_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_rusub_4 A) <=>  (? [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_rusub_3 B A)) ) ) ) ) ).
tt(d1_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_rusub_5 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (B = (k6_rusub_4 A C (k6_domain_1 (u1_struct_0 A) D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_rvsum_1,ax, (k34_binop_2 = (k7_finseqop k1_numbers k33_binop_2 (k6_partfun1 k1_numbers) k31_binop_2)) ).
tt(d1_rvsum_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k2_rvsum_2)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_funct_1 A B) = (k3_square_1 B)) ) ) ) ) ) ).
tt(d1_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  ((m1_scm_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 A) C))  =>  ((k1_funct_1 B (k10_ami_3 C)) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d1_scmbsort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k1_scmbsort A) = (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers)) (k6_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 1) A)) (k2_scmfsa8c (k4_scmfsa_2 1) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 1)) (k8_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 3) A)) (k2_scmfsa8c (k4_scmfsa_2 2) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 3)) (k8_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 3) A)) (k14_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 4) A)) (k8_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 5))) (k2_scmfsa8b (k4_scmfsa_2 6) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 4) A) (k15_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 3) A)) (k15_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 4) A)) (k4_compos_1 k1_scmfsa_2)))))))) ) ) ).
tt(d1_scm_comp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lang1 A) &  ((v1_dtconstr A) &  ((v2_dtconstr A) &  ((v3_dtconstr A) &  ((v3_bintree1 A) & (l1_lang1 A)) ) ) ) ) )  =>  ( (A = k1_scm_comp)  <=>  ( ((k6_dtconstr A) = k2_ami_2)  &  ( ((k7_dtconstr A) = (k2_zfmisc_1 1 5))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lang1 A B (k4_pre_poly (u1_struct_0 A) C D)) <=> (r2_hidden B (k2_zfmisc_1 1 5))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmfsa_2,ax, (k1_scmfsa_2 = (g1_extpro_1 3 k1_scmfsa_1 (k1_funct_7 k5_numbers k1_scmfsa_1) k2_scmfsa_i k4_scmfsa_1 k5_scmfsa_1 k12_scmfsa_1)) ).
tt(d1_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_scmfsa6a A B) = (k6_funct_4 A (k2_compos_1 k1_scmfsa_2) (k11_scmfsa_2 B))) ) ) ) ) ).
tt(d1_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((k1_scmfsa6b A B C) = (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_scmfsa_m B))) ) ) ) ) ) ) ).
tt(d1_scmfsa_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ( (~ (r1_xxreal_0 B k6_numbers))  =>  ( (C = (k1_scmfsa_7 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k2_nat_1 D 1) = B)  &  (C = (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k8_funcop_1 (u1_compos_1 k1_scmfsa_2) D (k7_scmfsa_2 A (k4_scmfsa_2 k6_numbers)))) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ) ) )  &  ((r1_xxreal_0 B k6_numbers) =>  ( (C = (k1_scmfsa_7 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k2_xcmplx_0 D B) = 1)  &  (C = (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k8_funcop_1 (u1_compos_1 k1_scmfsa_2) D (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers)))) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmfsa7b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((r1_scmfsa7b A B) <=>  (~  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ( (~  ((k6_scmfsa_2 C B) = A) )  &  ( (~  ((k7_scmfsa_2 C B) = A) )  &  ( (~  ((k8_scmfsa_2 C B) = A) )  &  ( (~  ((k9_scmfsa_2 C B) = A) )  &  ( (~  ((k10_scmfsa_2 C B) = A) )  &  ( (~  ((k10_scmfsa_2 B C) = A) )  &  ( (~  ((k12_scmfsa_2 D B) = A) )  &  ( (~  ((k13_scmfsa_2 D B) = A) )  &  ( (~  ((k14_scmfsa_2 C B E) = A) )  &  ( (~  ((k15_scmfsa_2 B C E) = A) )  &  ( (~  ((k15_scmfsa_2 C B E) = A) )  &  (~  ((k17_scmfsa_2 B E) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmfsa8a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_scmfsa8a A) = (k16_funcop_1 k6_numbers (k11_scmfsa_2 A))) ) ) ).
tt(d1_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_scmfsa8b A B C) = (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a (k4_scmfsa6a (k12_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A) C) (k1_scmfsa8a (k2_nat_1 (k5_card_1 B) 1))) B) (k4_compos_1 k1_scmfsa_2))) ) ) ) ) ) ) ).
tt(d1_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((k1_scmfsa8c A) = (k1_scmfsa6a A k6_numbers)) ) ) ).
tt(d1_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_scmfsa9a A B C D) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) C) = k6_numbers)  =>  ((r5_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) (k1_funct_4 A (k1_scmfsa_9 C D))) & (r6_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) (k1_funct_4 A (k1_scmfsa_9 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_scmfsa_9 A B) = (k1_funct_4 (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers)))) ) ) ) ) ).
tt(d1_scmfsa_i,ax, (k1_scmfsa_i = (k6_subset_1 k4_numbers k5_numbers)) ).
tt(d1_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ((k1_scmfsa_m A) = (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) ) ) ).
tt(d1_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski A C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 C B D)) (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scm_inst,ax, (k2_scm_inst = (k8_mcart_1 k5_numbers k1_numbers (k6_domain_1 k5_numbers 1) k5_numbers)) ).
tt(d1_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) )  =>  ( (E = (k1_scmisort A B C D))  <=>  ((r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E k6_numbers) A) &  (! [F:$i] :  ((v7_ordinal1 F) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E (k1_nat_1 F 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 D (k2_scmfsa_9 C B)) (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F)) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 D (k2_scmfsa_9 C B)) B) (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F))) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmpds_2,ax, (k1_scmpds_2 = (g1_extpro_1 2 k1_ami_2 (k1_funct_7 k5_numbers k1_ami_2) k1_scmpds_i k3_ami_2 k4_ami_2 k6_scmpds_1)) ).
tt(d1_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_scmpds_4 A B) = (k1_funct_4 A (k61_valued_1 B (k5_card_1 A)))) ) ) ) ) ).
tt(d1_scmpds_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_scmpds_6 A) = (k9_compos_1 k1_scmpds_2 (k3_scmpds_2 A))) ) ) ).
tt(d1_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k1_scmpds_7 A B C D) = (k3_scmpds_4 (k3_scmpds_4 (k2_scmpds_4 (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 D) 3)) D) (k11_scmpds_2 A B C)) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 D) 2))))) ) ) ) ) ) ) ) ) ).
tt(d1_scmpds_i,ax, (k1_scmpds_i = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) a_0_0_scmpds_i) a_0_1_scmpds_i) a_0_2_scmpds_i) a_0_3_scmpds_i) a_0_4_scmpds_i)) ).
tt(d1_scmp_gcd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_scmp_gcd A) = (k10_ami_3 A)) ) ) ).
tt(d1_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_extpro_1 B 2) & (l1_extpro_1 B 2))  =>  ( (B = (k1_scmring2 A))  <=>  ( ((u1_struct_0 B) = k1_ami_2)  &  ( ((u2_struct_0 B) = k5_numbers)  &  ( ((u1_compos_1 B) = (k1_scmringi A))  &  ((r1_funct_2 (u1_struct_0 B) 2 k1_ami_2 2 (u1_memstr_0 2 B) k3_ami_2) &  ( ((u2_memstr_0 2 B) = (k1_scmring1 A))  &  ((u1_extpro_1 2 B) = (k8_scmring1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_scmring3 A B) = (k10_ami_3 B)) ) ) ) ) ).
tt(d1_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((k1_scmringi A) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) a_0_0_scmringi) a_0_1_scmringi) a_0_2_scmringi) (a_1_0_scmringi A))) ) ) ).
tt(d1_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (B = (k1_scmyciel A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C A) &  ((k1_card_1 C) = 2) ) ) ) ) ) ) ) ).
tt(d1_scpinvar,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_scpinvar A B) = (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k5_scmpds_2 (k1_scmp_gcd 1) k6_numbers)) (k5_scmpds_2 (k1_scmp_gcd 2) (k4_xcmplx_0 A))) (k5_scmpds_2 (k1_scmp_gcd 3) (k2_nat_1 B 1))) (k1_scmpds_8 k2_scmp_gcd 2 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1))))) ) ) ) ) ).
tt(d1_scpisort,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_scpisort A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 A)))  =>  ((k1_funct_1 A D) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_scpqsort,ax, (k1_scpqsort = (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 2) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 2) k2_scmp_gcd k6_numbers 6))) ).
tt(d1_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_semi_af1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C C B)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C D D)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C B D) => (r2_analoaf A C B C D)) ) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_analoaf A B C B D) &  (~  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B D B E) &  (~  ((r2_analoaf A B F B G) & (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A B E B F) &  ((r2_analoaf A B G B H) &  ((r2_analoaf A C E D F) & (r2_analoaf A C G D H)) ) ) )  =>  ((r2_analoaf A B C B E) |  ((r2_analoaf A B C B G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) )  =>  ((r2_analoaf A B C B D) |  ((r2_analoaf A B C B F) | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A E F E G) &  ((r2_analoaf A B F C E) & (r2_analoaf A C G D F)) ) )  => (r2_analoaf A D E B G)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C B D))  &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) & (r2_analoaf A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_seq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_seq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B (k1_seq_1 A C))) ) ) ) ) ) ) ) ).
tt(d1_seq_4,ax, (! [A:$i] :  ((v3_membered A) =>  ((v4_xxreal_2 A) =>  ((v1_xboole_0 A) |  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (B = (k2_seq_4 A))  <=>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden D A) &  (~ (r1_xxreal_0 D (k10_binop_2 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (D = (k2_seqfunc A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers D E) (k26_valued_1 A k1_numbers (k1_seqfunc A k1_numbers B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A k1_numbers) & (v1_funct_1 A)) ) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_series_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v1_valued_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_partfun1 B k5_numbers) & (v1_valued_0 B)) ) ) )  =>  ( (B = (k2_series_1 A))  <=>  ( ((k1_funct_1 B k6_numbers) = (k1_funct_1 A k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_funct_1 B (k2_nat_1 C 1)) = (k2_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(d1_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k1_series_3 A))  <=>  ( ((k1_seq_1 B k6_numbers) = (k1_seq_1 A k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B (k2_nat_1 C 1)) = (k8_real_1 (k1_seq_1 B C) (k1_seq_1 A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(d1_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~  (A = k1_xboole_0) )  =>  ( (B = (k1_setfam_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (! [D:$i] :  ((r2_hidden D A) => (r2_hidden C D)) ) ) ) ) )  &  ( (A = k1_xboole_0)  =>  ( (B = (k1_setfam_1 A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(d1_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 B A) <=>  ((v3_prob_1 B) | (v2_prob_1 B)) ) ) ) ) ).
tt(d1_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k1_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k9_subset_1 A (k8_nat_1 (k9_setfam_1 A) B E) (k8_nat_1 (k9_setfam_1 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_setwiseo,ax, (! [A:$i] :  ((k1_setwiseo A) = k1_xboole_0) ) ).
tt(d1_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_setwop_2 A B C) = (k2_finsop_1 A (k8_funcop_1 A k5_numbers C) B)) ) ) ) ) ) ) ).
tt(d1_sfmastr2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_sfmastr2 A B) = (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m A) (k2_sf_mastr B))) (k5_scmfsa6a B (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m A) (k2_sf_mastr B))) (k4_scmfsa_2 k6_numbers))))) ) ) ) ) ).
tt(d1_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 F (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k1_sfmastr3 A B C D E F) = (k5_scmfsa_9 (k2_funct_7 (k2_funct_7 F (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 F D) (k1_funct_1 F C)) 1)) B (k1_funct_1 F C)) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers))) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 k2_scmfsa_2)) =>  ( ((r2_hidden (k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) (k3_enumset1 1 2 3 4 5)) =>  ( (B = (k1_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  &  ( (~  ( (~  (A = (k6_scmfsa_2 C D)) )  &  ( (~  (A = (k7_scmfsa_2 C D)) )  &  ( (~  (A = (k8_scmfsa_2 C D)) )  &  ( (~  (A = (k9_scmfsa_2 C D)) )  &  (~  (A = (k10_scmfsa_2 C D)) ) ) ) ) ) )  &  (B = (k5_scmfsa_m C D)) ) ) ) ) ) ) )  &  ( ( ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 7)  |  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 8) )  =>  ( (B = (k1_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ( ( (A = (k12_scmfsa_2 D C))  |  (A = (k13_scmfsa_2 D C)) )  &  (B = (k4_scmfsa_m C)) ) ) ) ) ) ) )  &  ( ( ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 9)  |  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 10) )  =>  ( (B = (k1_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  &  (? [E:$i] :  ((m1_scmfsa_2 E) &  ( ( (A = (k14_scmfsa_2 D C E))  |  (A = (k15_scmfsa_2 D C E)) )  &  (B = (k5_scmfsa_m C D)) ) ) ) ) ) ) ) ) )  &  ( ( ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 11)  |  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 12) )  =>  ( (B = (k1_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ((m1_scmfsa_2 D) &  ( ( (A = (k16_scmfsa_2 C D))  |  (A = (k17_scmfsa_2 C D)) )  &  (B = (k4_scmfsa_m C)) ) ) ) ) ) ) )  &  (~  ( (~ (r2_hidden (k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) (k3_enumset1 1 2 3 4 5)))  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 7) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 8) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 9) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 10) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 11) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 12) )  &  (~  ( (B = (k1_sf_mastr A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sgraph1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_sgraph1 A B) = (a_2_0_sgraph1 A B)) ) ) ) ) ).
tt(d1_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v1_sheffer1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_lattices A B C) = C)  &  ((k2_lattices A C B) = C) ) ) ) ) ) ) ) ) ).
tt(d1_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  ((v1_sheffer2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C B) B)) (k5_sheffer1 A C (k5_sheffer1 A D B))) = C) ) ) ) ) ) ) ) ) ) ).
tt(d1_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_classes1 B) =>  ( (B = (k1_simplex0 A))  <=>  ((r1_tarski A B) &  (! [C:$i] :  ( ((r1_tarski A C) & (v1_classes1 C))  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(d1_simplex1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k1_simplex1 A B C) = C) ) ) ) ) ) ) ).
tt(d1_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v1_compts_1 (k3_pcomps_1 A)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) =>  ( ((v1_tops_2 B (k3_pcomps_1 A)) & (m1_setfam_1 B (u1_struct_0 (k3_pcomps_1 A))))  =>  (! [C:$i] :  ( ((v2_xxreal_0 C) & (m1_subset_1 C k1_numbers))  =>  ((m1_simplex2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) &  ((r2_hidden E B) & (r1_tarski (k9_metric_1 A D C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sincos10,ax, (k1_sincos10 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(d1_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k1_sin_cos2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k10_real_1 (k9_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k24_sin_cos (k7_binop_2 B))) 2)) ) ) ) ) ) ).
tt(d1_sin_cos3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k1_sin_cos3)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers A B) = (k6_binop_2 (k4_binop_2 (k15_sin_cos (k5_binop_2 k7_complex1 B)) (k15_sin_cos (k1_binop_2 (k5_binop_2 k7_complex1 B)))) (k5_binop_2 2 k7_complex1))) ) ) ) ) ) ).
tt(d1_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos4 A) = (k7_xcmplx_0 (k17_sin_cos A) (k20_sin_cos A))) ) ) ).
tt(d1_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos5 A) = (k10_real_1 (k6_sin_cos2 A) (k3_sin_cos2 A))) ) ) ).
tt(d1_sin_cos6,ax, (k1_sin_cos6 = (k2_partfun2 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))) ).
tt(d1_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos7 A) = (k6_power k8_power (k9_binop_2 A (k7_square_1 (k9_binop_2 (k3_square_1 A) 1))))) ) ) ).
tt(d1_sin_cos9,ax, (k1_sin_cos9 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))) ).
tt(d1_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_sppol_1 A B C) <=>  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid A) D E)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D E) C) &  ( (~  (B = D) )  &  (~  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_sppol_2 A B C) <=>  ( (~  (A = B) )  &  (? [D:$i] :  ( ((v4_topreal1 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2))))  &  (? [E:$i] :  ( ((v4_topreal1 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2))))  &  ( (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D 1))  &  ( (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E 1))  &  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D)))  &  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k3_finseq_1 E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E)) = (k2_tarski A B))  &  (C = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k1_sprect_1 A) = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 A) (k12_pscomp_1 A) (k13_pscomp_1 A)) (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k10_pscomp_1 A) (k11_pscomp_1 A)))) ) ) ).
tt(d1_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((r1_xxreal_0 (k6_pscomp_1 (k3_topreal1 2 A)) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C))) &  ((r1_xxreal_0 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C)) (k8_pscomp_1 (k3_topreal1 2 A))) &  ((r1_xxreal_0 (k9_pscomp_1 (k3_topreal1 2 A)) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C))) & (r1_xxreal_0 (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C)) (k7_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_square_1 A) = (k3_xcmplx_0 A A)) ) ) ).
tt(d1_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  =>  ((m1_stacks_1 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  ((r2_hidden (k1_domain_1 B B F G) C) => (r2_hidden (k1_domain_1 B B (k2_binop_1 A B B D E F) (k2_binop_1 A B B D E G)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_stirl2_1 C A B) <=>  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  =>  (A = k6_numbers) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden D (k2_relset_1 B C)) &  ((r2_hidden E (k2_relset_1 B C)) &  ( (~ (r1_xxreal_0 E D))  & (r1_xxreal_0 (k5_nat_1 (k1_stirl2_1 A B C (k1_seq_4 E))) (k5_nat_1 (k1_stirl2_1 A B C (k1_seq_4 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v2_struct_0 A) <=> (v1_xboole_0 (u1_struct_0 A))) ) ) ).
tt(d1_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((k3_sublemma A B C D) = (k4_relset_1 (k3_qc_lang1 A) (k3_qc_lang1 A) (k3_qc_lang1 A) C (k2_substut1 A (k19_substut1 A B)) D)) ) ) ) ) ) ) ) ) ).
tt(d1_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 A))  =>  ((m1_subset_1 B A) <=> (r2_hidden B A)) )  &  ((v1_xboole_0 A) =>  ((m1_subset_1 B A) <=> (v1_xboole_0 B)) ) ) ) ) ).
tt(d1_substlat,ax, (! [A:$i] :  (! [B:$i] :  ((k1_substlat A B) = (a_2_0_substlat A B)) ) ) ).
tt(d1_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k1_substut1 A) = (k4_partfun1 (k3_qc_lang1 A) (k3_qc_lang1 A))) ) ) ).
tt(d1_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k4_substut2 A B C D) = (k39_substut1 A (k2_substut2 A B (k3_substut2 A C D)))) ) ) ) ) ) ) ) ) ).
tt(d1_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( (B = (k3_supinf_1 A))  <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C B) <=> (m1_xxreal_2 C A)) ) ) ) ) ) ) ) ).
tt(d1_supinf_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((k10_supinf_2 A B C D) = (k8_supinf_2 (k2_relset_1 C D))) ) ) ) ) ) ) ) ).
tt(d1_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_symsp_1 B A)) ) ) ) )  =>  ((v2_symsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ( (~  (C = (k4_struct_0 B)) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) => (r1_orders_2 B H C)) ) ) )  &  ( ((r1_orders_2 B C D) => (r1_orders_2 B (k4_vectsp_1 A B G C) D))  &  ( ( ((r1_orders_2 B D C) & (r1_orders_2 B E C))  => (r1_orders_2 B (k3_rlvect_1 B D E) C))  &  ( (~  ( (~ (r1_orders_2 B D C))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~ (r1_orders_2 B (k5_algstr_0 B F (k4_vectsp_1 A B H D)) C)) ) ) ) )  &  ( ((r1_orders_2 B C (k3_rlvect_1 B D E)) & (r1_orders_2 B D (k3_rlvect_1 B E C)))  => (r1_orders_2 B E (k3_rlvect_1 B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k1_sysrel A) = (k3_xboole_0 A (k4_relat_1 (k9_xtuple_0 A)))) ) ) ).
tt(d1_t_0topsp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((r1_t_0topsp A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v3_tops_2 C A B)) ) ) ) ) ) ) ).
tt(d1_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k1_t_1topsp A) = (a_1_0_t_1topsp A)) ) ) ).
tt(d1_tarski,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_tarski A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (C = A) ) ) ) ) ) ).
tt(d1_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  ((m1_taxonom1 B A) <=>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r1_setfam_1 C D))  &  (~ (r1_setfam_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_taxonom2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_taxonom2 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (r8_orders_1 (u1_orders_2 A) B)) ) ) ) ) ).
tt(d1_taylor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (B = (k1_taylor_1 A))  <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_seq_1 B C) = (k4_prepower C A)) ) ) ) ) ) ) ) ).
tt(d1_taylor_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_taylor_2 A B C) = (k6_taylor_1 A B k6_numbers C)) ) ) ) ) ) ) ).
tt(d1_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v1_tbsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_finset_1 C) &  ( ((u1_struct_0 A) = (k5_setfam_1 (u1_struct_0 A) C))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (D = (k9_metric_1 A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_tdgroup A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A C C) = B) ) ) ) ) ) ) ) ).
tt(d1_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k1_tdlat_1 A) = (a_1_0_tdlat_1 A)) ) ) ).
tt(d1_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k1_tdlat_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k1_tops_1 A E))  & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_tdlat_3 A) <=>  ((u1_pre_topc A) = (k9_setfam_1 (u1_struct_0 A))) ) ) ) ).
tt(d1_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((v7_struct_0 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ) ).
tt(d1_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(d1_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tex_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v1_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d1_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) &  ((r2_hidden C D) & (r2_hidden C B)) )  => (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_tietze,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((r1_tietze A B C) <=>  (! [D:$i] :  ((r2_hidden D (k3_xboole_0 C (k9_xtuple_0 A))) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 A D)) B)) ) ) ) ) ) ) ) ).
tt(d1_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ( ((k2_partfun1 C B E (k9_subset_1 A C D)) = (k2_partfun1 D B F (k9_subset_1 A C D)))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_subset_1 A C D) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_subset_1 A C D) B)))) )  =>  ( (G = (k1_tmap_1 A B C D E F))  <=>  ( ((k2_partfun1 (k4_subset_1 A C D) B G C) = E)  &  ((k2_partfun1 (k4_subset_1 A C D) B G D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_toler_1 C A B) <=>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ).
tt(d1_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( (D = (k1_topalg_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=> (m1_borsuk_2 E A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d1_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C))))))) )  =>  ( (E = (k3_topalg_3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_topalg_1 A C))) =>  (? [G:$i] :  ((m1_borsuk_2 G A C C) &  ( (F = (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) G))  &  ((k3_funct_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C))) E F) = (k6_eqrel_1 (k2_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k2_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k4_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) G D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))))))) )  =>  ( (G = (k1_topalg_4 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)))) =>  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 B)) &  ( (H = (k5_group_7 A B I J))  &  ((k3_funct_2 (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))) G H) = (k5_group_7 C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) E I) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 D) F J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2))))) )  =>  ( (B = (k1_topalg_5 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) B C) = (k3_xcmplx_0 A C)) ) ) ) ) ) ) ) ).
tt(d1_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_topalg_6 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v7_struct_0 (k5_topalg_1 A B))) ) ) ) ) ).
tt(d1_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (k9_setfam_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k9_setfam_1 (u1_struct_0 A))))))) )  =>  ( (B = (k1_topdim_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B k6_numbers) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_struct_0 A)))  &  ( (~  ((r2_hidden C (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B (k1_nat_1 D 1))) &  ( (~ (r2_hidden C (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D)))  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_pre_topc A C))) &  (? [F:$i] :  ( ((v3_pre_topc F (k1_pre_topc A C)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))))  &  ((r2_hidden E F) &  (! [G:$i] :  ( ((v3_pre_topc G (k1_pre_topc A C)) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))))  =>  (~  ((r2_hidden E G) &  ((r1_tarski G F) & (r2_hidden (k2_tops_1 (k1_pre_topc A C) G) (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D))) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r2_hidden C (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D)) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_pre_topc A C))) =>  (! [F:$i] :  ( ((v3_pre_topc F (k1_pre_topc A C)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))))  =>  (~  ((r2_hidden E F) &  (! [G:$i] :  ( ((v3_pre_topc G (k1_pre_topc A C)) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))))  =>  (~  ((r2_hidden E G) &  ((r1_tarski G F) & (r2_hidden (k2_tops_1 (k1_pre_topc A C) G) (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D))) ) ) ) ) ) ) ) ) ) ) )  => (r2_hidden C (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) B (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topdim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_topdim_2 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((r1_tarski D B) & (r2_hidden C (k1_card_1 D)))  => (v1_xboole_0 (k6_setfam_1 A D))) ) ) ) ) ) ) ) ) ).
tt(d1_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k1_topgen_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k2_tops_1 A E))  & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_card_1 C) =>  ( (C = (k1_topgen_2 A B))  <=>  ( (? [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (C = (k1_card_1 D)) ) )  &  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (r1_ordinal1 C (k1_card_1 D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_topgen_3 B A) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden C (k3_xboole_0 D E)) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (~  ((r2_hidden F B) &  ((r2_hidden C F) & (r1_tarski F (k3_xboole_0 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topgen_4,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k1_topgen_4 A) = (k1_zfmisc_1 (u1_struct_0 A))) ) ) ).
tt(d1_topgen_5,ax, (k1_topgen_5 = a_0_0_topgen_5) ).
tt(d1_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k1_topgrp_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k6_algstr_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_topmetr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  ((m1_topmetr B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_metric_1 (u1_struct_0 B) (u1_struct_0 B) (u1_metric_1 B) C D) = (k1_binop_1 (u1_metric_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topreal1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_topreal1 A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A D)))))) )  &  ((v3_tops_2 E k5_topmetr (k1_pre_topc A D)) &  ( ((k1_funct_1 E k6_numbers) = B)  &  ((k1_funct_1 E 1) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) k1_topreal1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) k1_topreal1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  & (v3_tops_2 B (k1_pre_topc (k15_euclid 2) k1_topreal1) (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ).
tt(d1_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal4 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) &  ((v4_topreal1 D) &  ( (A = (k3_topreal1 2 D))  &  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D 1))  &  (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k1_topreal6 A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid A))) &  ( (E = B)  &  ( (F = C)  &  (D = (k4_metric_1 (k14_euclid A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ( ((v1_metric_1 C) & (l1_metric_1 C))  =>  ( (C = (k1_topreal7 A B))  <=>  ( ((u1_struct_0 C) = (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) &  ( (D = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) F H))  &  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) G I))  &  ((k1_metric_1 (u1_struct_0 C) (u1_struct_0 C) (u1_metric_1 C) D E) = (k2_square_1 (k1_metric_1 (u1_struct_0 A) (u1_struct_0 A) (u1_metric_1 A) F G) (k1_metric_1 (u1_struct_0 B) (u1_struct_0 B) (u1_metric_1 B) H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_topreal9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_topreal9 A B C) = (a_3_0_topreal9 A B C)) ) ) ) ) ) ) ).
tt(d1_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_topreala A B C D) = (k1_pre_topc (k15_euclid 2) (k2_jgraph_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d1_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_toprealb A B) = (a_2_0_toprealb A B)) ) ) ) ) ).
tt(d1_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_toprns_1 B A) <=> (r1_tarski (k10_xtuple_0 B) (k8_struct_0 (k15_euclid A)))) ) ) ) ) ).
tt(d1_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(d1_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(d1_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  ((k1_tops_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d1_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k2_transgeo A B C) = (k1_transgeo A (k2_funct_2 A C) (k1_transgeo A B C))) ) ) ) ) ) ) ).
tt(d1_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v1_translac A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) & (r2_analoaf A B E C D)) )  => (r1_aff_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_treal_1 A B) = A) ) ) ) ) ) ).
tt(d1_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (A = (k5_relat_1 B (k2_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(d1_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (A = B)  <=>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) <=> (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d1_trees_3,ax, (! [A:$i] :  ( (A = k1_trees_3)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(d1_trees_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ( (A = B)  <=>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d1_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((v1_zfmisc_1 A) <=>  ((k9_xtuple_0 A) = (k2_trees_1 k6_numbers)) ) ) ) ).
tt(d1_trees_a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m4_trees_1 C A) =>  ( (~  (C = k1_xboole_0) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_trees_1 D))  =>  ( (D = (k1_trees_a A B C))  <=>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  ((r2_hidden E D) <=>  (~  ( (~  ((r2_hidden E A) &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (~  ((r2_hidden F C) & (r2_xboole_0 F E)) ) ) ) ) )  &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k5_numbers) =>  (~  ((r2_hidden F C) &  ((r2_hidden G B) &  (E = (k8_finseq_1 k5_numbers F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k1_triang_1 A) = (a_1_0_triang_1 A)) ) ) ).
tt(d1_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_tsep_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(d1_tsep_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tsep_2 A B C) <=>  ((r1_xboole_0 B C) &  ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d1_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((m1_pre_topc B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc D A) &  (C = (k8_subset_1 (u1_struct_0 A) D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_turing_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_turing_1 A) = (a_1_0_turing_1 A)) ) ) ).
tt(d1_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k2_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k10_margrel1 B C)) ) ) ) ) ) ) ) ).
tt(d1_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ((v2_unialg_1 A) <=> (v4_margrel1 (u1_unialg_1 A) (u1_struct_0 A))) ) ) ).
tt(d1_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) <=>  ((k1_unialg_1 A) = (k1_unialg_1 B)) ) ) ) ) ) ).
tt(d1_uniform1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_uniform1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 E (k2_metric_1 A F G)))  & (r1_xxreal_0 D (k2_metric_1 B (k10_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F) (k10_funct_2 (u1_struct_0 A) (u1_struct_0 B) C G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ( (B = (k1_uniroots A))  <=>  ( ((u1_struct_0 B) = (k8_struct_0 A))  &  ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d1_uproots,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k1_uproots A) = (o_1_0_uproots A)) ) ) ).
tt(d1_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (k1_urysohn1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 D (k2_newton 2 A)) &  (C = (k6_real_1 D (k2_newton 2 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((v10_pre_topc A) &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) & (r1_xboole_0 B C)) ) )  =>  ( (B = k1_xboole_0)  |  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((m1_urysohn3 E A B C D) <=>  ((r1_tarski B (k1_funct_1 E k6_numbers)) &  ( (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_funct_1 E 1)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers (k1_urysohn1 D)) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers (k1_urysohn1 D)) =>  ( (~ (r1_xxreal_0 G F))  =>  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E F) A) &  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E G) A) & (r1_tarski (k2_pre_topc A (k4_urysohn1 A (k1_urysohn1 D) E F)) (k4_urysohn1 A (k1_urysohn1 D) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((k1_valuat_1 A B) = (k1_funct_2 (k3_qc_lang1 A) B)) ) ) ) ).
tt(d1_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_valued_0 A) <=> (r1_tarski (k10_xtuple_0 A) k2_numbers)) ) ) ).
tt(d1_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k1_valued_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k2_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_valued_2,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((k1_valued_2 A) = (k3_tarski (a_1_0_valued_2 A))) ) ) ).
tt(d1_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v1_vectmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers D) &  ((r1_xxreal_0 D 1) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( ((k2_metric_1 A B E) = (k8_real_1 D (k2_metric_1 A B C)))  &  ((k2_metric_1 A E C) = (k8_real_1 (k9_real_1 1 D) (k2_metric_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ((v1_vectsp11 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~  (D = (k4_struct_0 B)) )  &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) C D) = (k4_vectsp_1 A B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_1,ax, (k1_vectsp_1 = (g2_algstr_0 k1_numbers k33_binop_2 k6_numbers)) ).
tt(d1_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v1_vectsp_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k6_algstr_0 A B C) = (k4_struct_0 A))  &  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_4 C A B) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k1_algstr_0 B D E) C)) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E C) => (r2_hidden (k4_vectsp_1 A B D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ( (E = (k1_vectsp_5 A B C D))  <=>  ((u1_struct_0 E) = (a_4_0_vectsp_5 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 B) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 A))) =>  ((m1_vectsp_6 C A B) <=>  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r2_hidden E D))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) <=>  (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  ( ((k4_vectsp_6 A B D) = (k4_struct_0 B))  =>  ((k1_vectsp_6 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_8 A B) = (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) ) ) ) ) ).
tt(d1_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_matrlin B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k1_vectsp_9 A B))  <=>  (! [D:$i] :  ((m1_vectsp_7 D A B) =>  (C = (k1_card_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k1_vfunct_1 A B C D))  <=>  ( ((k1_relset_1 A E) = (k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k1_algstr_0 B (k7_partfun1 (u1_struct_0 B) C F) (k7_partfun1 (u1_struct_0 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k1_vfunct_2 A B C D))  <=>  ( ((k1_relset_1 A E) = (k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k1_clvect_1 B (k7_partfun1 (u1_struct_0 B) D F) (k7_partfun1 k2_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ((r1_orders_2 A C E) & (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v4_yellow_0 B (k7_yellow_1 A A)) & (m1_yellow_0 B (k7_yellow_1 A A))) ) )  =>  ( (B = (k2_waybel10 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v7_waybel_1 C A)) ) ) ) ) ) ) ) ).
tt(d1_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel11 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r2_hidden (k1_yellow_0 A C) B) & (r1_xboole_0 C B)) ) ) ) ) ) ) ) ) ).
tt(d1_waybel12,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=> (v3_pre_topc (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(d1_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) )  =>  ((v1_waybel14 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (~  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (k13_yellow_6 A (k2_waybel11 A)))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 C C)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 C C)) (u1_struct_0 C))))) )  =>  (~  ((r1_funct_2 (u1_struct_0 (k2_borsuk_1 C C)) (u1_struct_0 C) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) D B) & (v5_pre_topc D (k2_borsuk_1 C C) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel15 B A) <=>  ((r2_orders_2 A (k3_yellow_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_orders_2 A (k3_yellow_0 A) C) & (r1_orders_2 A C B))  =>  (C = B) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m1_waybel16 C A B) <=>  ((v22_waybel_0 C A B) & (v17_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(d1_waybel17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( (D = (k1_waybel17 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ( (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  (E = (k4_nat_1 2 F)) ) )  =>  ((k3_funct_2 k5_numbers A D E) = B) )  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  (E = (k4_nat_1 2 F)) ) ) )  =>  ((k3_funct_2 k5_numbers A D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  ((v1_waybel19 A) <=>  ((v1_tops_2 (a_1_0_waybel19 A) A) &  ((v2_cantor_1 (a_1_0_waybel19 A) A) & (m1_subset_1 (a_1_0_waybel19 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ).
tt(d1_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_funct_1 C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel20,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k2_waybel20 A B) = B) ) ) ) ) ) ).
tt(d1_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ( ((v2_yellow_0 A) => (v2_yellow_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m1_waybel21 C A B) <=>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((r1_waybel22 A B) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v3_lattice3 C) &  ((v3_waybel_3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C))))) )  =>  (? [E:$i] :  ((m1_waybel16 E A C) &  ( ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 C) E B) = D)  &  (! [F:$i] :  ((m1_waybel16 F A C) =>  ( ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 C) F B) = D)  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 C) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel23 B A) <=> (v5_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(d1_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_waybel24 A B C D E) = (k1_funct_1 (k1_funct_5 D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((r1_waybel18 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_pre_topc D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(d1_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((k1_waybel26 A B) = (k3_waybel24 A (k1_waybel25 B))) ) ) ) ) ).
tt(d1_waybel27,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_waybel27 A) <=>  ( (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k2_funct_5 B)) ) ) ) ) ) ) ) ).
tt(d1_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v1_waybel28 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_orders_2 A C (k2_yellow_6 (u1_struct_0 A) A B C))) ) ) ) ) ) ) ).
tt(d1_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_9 B) &  ((v4_waybel11 B) & (m1_yellow_9 B A)) )  =>  (B = (k1_waybel29 A)) ) ) ) ) ).
tt(d1_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((k1_waybel_2 A B) = (k4_yellow_2 A (u1_waybel_0 A B))) ) ) ) ) ).
tt(d1_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_waybel30 A B) = (a_2_1_waybel30 A B)) ) ) ) ) ).
tt(d1_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k1_waybel31 A) = (k1_setfam_1 (a_1_0_waybel31 A))) ) ) ).
tt(d1_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  ((v1_waybel32 A) <=>  ((v1_tops_2 (a_1_0_waybel32 A) A) &  ((v2_cantor_1 (a_1_0_waybel32 A) A) & (m1_subset_1 (a_1_0_waybel32 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ).
tt(d1_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) )  =>  ((k1_waybel33 A B C) = (k1_yellow_0 A (a_3_0_waybel33 A B C))) ) ) ) ) ) ) ).
tt(d1_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_lattice3 A) & (v17_waybel_0 C A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (D = (k1_waybel34 A B C))  <=> (v3_waybel_1 (k1_waybel_1 A B C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r3_orders_2 A C (k1_yellow_0 A D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E D) & (r3_orders_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k1_waybel_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C D) B) <=> (r1_waybel_3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_xtuple_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (u1_struct_0 A))))) )  =>  ( (C = (k4_waybel_5 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k4_yellow_2 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r1_waybel_3 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden (k12_lattice3 A C D) B) &  ( (~ (r2_hidden C B))  &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_orders_2 B) &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( (B = (k1_waybel_8 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (u1_struct_0 B)) <=> (v1_waybel_3 C A)) ) ) ) ) ) ) ) ).
tt(d1_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) => (r1_orders_2 B (k2_yellow_6 (u1_struct_0 A) B C E) (k2_yellow_6 (u1_struct_0 A) B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( (C = (k1_weddwitt A B))  <=>  ((u1_struct_0 C) = (a_2_0_weddwitt A B)) ) ) ) ) ) ) ) ).
tt(d1_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((k1_weierstr A) = A) ) ) ).
tt(d1_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden (k4_tarski D C) (u1_orders_2 A)))  => (r2_hidden D B)) ) ) ) ) ) ) ) ).
tt(d1_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k1_wellord1 A B) = (k6_subset_1 (k10_relat_1 A B) (k1_tarski B))) ) ) ) ).
tt(d1_wellord2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( (B = (k1_wellord2 A))  <=>  ( ((k1_relat_1 B) = A)  &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D A))  =>  ((r2_hidden (k4_tarski C D) B) <=> (r1_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(d1_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( (~ (r2_hidden A (k4_finseq_1 B)))  =>  ( (C = (k2_finseq_3 A B))  <=>  (C = B) ) )  &  ((r2_hidden A (k4_finseq_1 B)) =>  ( (C = (k2_finseq_3 A B))  <=>  ( ((k2_nat_1 (k3_finseq_1 C) 1) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (~ (r1_xxreal_0 A D))  =>  ((k1_funct_1 C D) = (k1_funct_1 B D)) )  &  ((r1_xxreal_0 A D) =>  ((k1_funct_1 C D) = (k1_funct_1 B (k1_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_xboole_0,ax, (! [A:$i] :  ((v1_xboole_0 A) <=>  (! [B:$i] :  (~ (r2_hidden B A)) ) ) ) ).
tt(d1_xboolean,ax, (k1_xboolean = k6_numbers) ).
tt(d1_xcmplx_0,ax, (k1_xcmplx_0 = (k5_funct_4 k1_numbers k6_numbers 1 k6_numbers 1)) ).
tt(d1_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) <=> (r2_hidden A k1_numbers)) ) ).
tt(d1_xtuple_0,ax, (! [A:$i] :  ((v1_xtuple_0 A) <=>  (? [B:$i] :  (? [C:$i] :  (A = (k4_tarski B C)) ) ) ) ) ).
tt(d1_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) <=> (r2_hidden A k7_numbers)) ) ).
tt(d1_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k1_xxreal_1 A B) = (a_2_0_xxreal_1 A B)) ) ) ) ) ).
tt(d1_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((m1_xxreal_2 B A) <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(d1_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ( ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers))  =>  ((r1_xxreal_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (C = A)  &  ( (D = B)  & (r1_xxreal_0 C D)) ) ) ) ) ) ) )  &  ( (~  ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers)) )  =>  ((r1_xxreal_0 A B) <=>  ( (A = k2_xxreal_0)  |  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(d1_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_orders_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_orders_2 A B B)) ) ) ) ) ).
tt(d1_yellow11,ax, (k1_yellow11 = (k2_yellow_1 (k3_enumset1 k6_numbers (k6_subset_1 3 1) 2 (k6_subset_1 3 2) 3))) ).
tt(d1_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_yellow13 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k1_tops_1 A D)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E C) &  ((r2_hidden B (k1_tops_1 A E)) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r4_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d1_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k6_margrel1) =>  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 A)) =>  ( (D = (k1_yellow15 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_funct_1 D E) = (k14_funcop_1 (k1_funct_1 C E) k8_margrel1 (k1_funct_1 B E) (k6_subset_1 A (k1_funct_1 B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_yellow16 A B C) <=>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v22_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ( ((k5_relat_1 C (u1_struct_0 A)) = (k3_struct_0 A))  &  ((v4_yellow_0 A B) &  ((v4_waybel_0 A B) & (m1_yellow_0 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_yellow19 A B) = (a_2_0_yellow19 A B)) ) ) ) ) ).
tt(d1_yellow_1,ax, (! [A:$i] :  ((k2_yellow_1 A) = (g1_orders_2 A (k1_yellow_1 A))) ) ).
tt(d1_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (r1_partfun1 (k1_funct_1 (u2_altcat_1 A) (k3_xtuple_0 C D E)) (k1_funct_1 (u2_altcat_1 B) (k3_xtuple_0 C D E)))) ) ) ) ) ) ) ) ).
tt(d1_yellow21,ax, (! [A:$i] :  ( ((l1_struct_0 A) =>  ((k1_yellow21 A) = A) )  &  ( (~ (l1_struct_0 A))  =>  ((k1_yellow21 A) = (g1_struct_0 A)) ) ) ) ).
tt(d1_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((r1_yellow_2 A B C D) <=>  (! [E:$i] :  (~  ((r2_hidden E A) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ( (F = (k1_funct_1 C E))  &  ( (G = (k1_funct_1 D E))  & (r1_orders_2 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow_3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k1_yellow_3 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  (? [F:$i] :  (? [G:$i] :  (? [H:$i] :  (? [I:$i] :  ( (D = (k4_tarski F G))  &  ( (E = (k4_tarski H I))  &  ((r2_hidden (k4_tarski F H) A) & (r2_hidden (k4_tarski G I) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A B C) = (k11_lattice3 A B (k7_waybel_1 A C))) ) ) ) ) ) ) ).
tt(d1_yellow_6,ax, (! [A:$i] :  ((k1_yellow_6 A) = (k1_classes1 (k5_classes1 A))) ) ).
tt(d1_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_yellow_8 C A B) <=>  ((r2_hidden B (k8_setfam_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden B D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E C) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_yellow_9,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) =>  ((k1_yellow_9 A B) = (k6_partfun1 (u1_struct_0 B))) ) ) ) ) ) ).
tt(d1_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k1_yoneda_1 A) = (k11_ens_1 (k16_ens_1 A))) ) ) ).
tt(d1_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( (C = (k1_zf_colla A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) & (v1_funct_1 D)) )  &  ( (C = (a_2_0_zf_colla A D))  &  ( ((k9_xtuple_0 D) = B)  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E B) =>  ((k1_funct_1 D E) = (a_3_0_zf_colla A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( ((r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model A)) =>  ((k1_zf_fund2 A B C) = (a_3_0_zf_fund2 A B C)) )  &  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model A)))  =>  ((k1_zf_fund2 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d1_zf_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski B C) =>  ((k1_zf_lang1 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d1_zf_lang,ax, (k1_zf_lang = a_0_0_zf_lang) ).
tt(d1_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_zfmisc_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (r1_tarski C A)) ) ) ) ) ).
tt(d1_zfmodel1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((r1_zf_model B C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang A (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) =>  ((r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model A)) |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ( (D = (k1_zfmodel1 A B C))  <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  (~  ( (~  ((k3_funct_2 k1_zf_lang B E F) = (k3_funct_2 k1_zf_lang B C F)) )  &  ( (~  ((k2_zf_lang k6_numbers) = F) )  &  ( (~  ((k2_zf_lang 3) = F) )  &  (~  ((k2_zf_lang 4) = F) ) ) ) ) ) ) )  =>  ((r1_zf_model B E A) <=>  ((k3_funct_2 B B D (k3_funct_2 k1_zf_lang B E (k2_zf_lang 3))) = (k3_funct_2 k1_zf_lang B E (k2_zf_lang 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (B = (k1_zf_model A))  <=>  (? [C:$i] :  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ((r2_hidden (k4_tarski (k4_zf_lang D E) (k2_tarski D E)) C) & (r2_hidden (k4_tarski (k5_zf_lang D E) (k2_tarski D E)) C)) ) ) ) )  &  ((r2_hidden (k4_tarski A B) C) &  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) =>  ( ((v2_zf_lang D) =>  (E = (k2_tarski (k18_zf_lang D) (k19_zf_lang D))) )  &  ( ((v3_zf_lang D) =>  (E = (k2_tarski (k18_zf_lang D) (k19_zf_lang D))) )  &  ( (~  ((v4_zf_lang D) &  (! [F:$i] :  (~  ( (E = F)  & (r2_hidden (k4_tarski (k20_zf_lang D) F) C)) ) ) ) )  &  ( (~  ((v5_zf_lang D) &  (! [F:$i] :  (! [G:$i] :  (~  ( (E = (k3_tarski (k2_tarski F G)))  &  ((r2_hidden (k4_tarski (k21_zf_lang D) F) C) & (r2_hidden (k4_tarski (k22_zf_lang D) G) C)) ) ) ) ) ) )  &  (~  ((v6_zf_lang D) &  (! [F:$i] :  (~  ( (E = (k6_subset_1 (k3_tarski (k1_tarski F)) (k1_tarski (k23_zf_lang D))))  & (r2_hidden (k4_tarski (k24_zf_lang D) F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d1_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k9_zf_lang)) =>  ((r1_zfrefle1 A B) <=>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r2_hidden C B) => (r2_zf_model A C)) ) ) ) ) ) ) ) ).
tt(d1_zf_refle,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C B))  =>  ((k1_zf_refle A B C) = (k3_card_3 (k6_relat_1 B (k5_relat_1 A (k4_classes1 C))))) ) ) ) ) ) ) ).
tt(d1_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_zmodul01 A B C) = (k1_binop_1 (u1_zmodul01 A) C B)) ) ) ) ) ) ) ).
tt(d20_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((k8_abcmiz_0 A B C) = (k1_funct_1 (k7_abcmiz_0 A B C) (k2_nat_1 (k3_finseq_1 C) 1))) ) ) ) ) ) ) ).
tt(d20_abcmiz_1,ax, (k19_abcmiz_1 = (k2_zfmisc_1 (k1_tarski k8_abcmiz_1) (k2_zfmisc_1 k4_abcmiz_1 k5_numbers))) ).
tt(d20_abcmiz_a,ax, (! [A:$i] :  ((m3_abcmiz_1 A k27_abcmiz_1) =>  ((k18_abcmiz_a A) = (k2_xboole_0 (k9_abcmiz_a k27_abcmiz_1 (k42_abcmiz_1 k27_abcmiz_1 A)) (k3_tarski (a_1_1_abcmiz_a A)))) ) ) ).
tt(d20_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v16_algstr_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k11_algstr_4 A C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k11_algstr_4 A D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A D) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C)) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C)) (u1_struct_0 B))))) )  =>  ( (G = (k17_algstr_4 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C))) =>  (! [I:$i] :  ((m1_subset_1 I (k11_algstr_4 A C)) =>  (! [J:$i] :  ((m1_subset_1 J (k11_algstr_4 A D)) =>  ( ( (I = (k1_xtuple_0 (k1_xtuple_0 H)))  &  (J = (k2_xtuple_0 (k1_xtuple_0 H))) )  =>  ((k3_funct_2 (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C)) (u1_struct_0 B) G H) = (k6_algstr_0 B (k3_funct_2 (k11_algstr_4 A C) (u1_struct_0 B) E I) (k3_funct_2 (k11_algstr_4 A D) (u1_struct_0 B) F J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_altcat_1 B) &  ((v13_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  ( (B = (k9_altcat_1 A))  <=>  ( ((u1_struct_0 B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_altcat_1 B C C) = (k1_tarski (k4_relat_1 C))) ) ) ) ) ) ) ) ) ).
tt(d20_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k16_aofa_000 A B C) = (k1_funct_1 (k2_pua2mss1 A (k1_funct_7 4 (k4_finseq_1 (u1_unialg_1 A)))) (k2_finseq_4 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(d20_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k24_aofa_i00 A B) = (k8_funcop_1 A (k9_funct_2 A k4_numbers) B)) ) ) ) ) ).
tt(d20_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v10_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) &  ((r2_hidden (k6_armstrng A E F) B) & (r1_tarski E D)) )  => (r1_tarski F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_asympt_0,ax, (! [A:$i] :  ((m1_funct_2 A k5_numbers k1_numbers) =>  (! [B:$i] :  ((m1_funct_2 B k5_numbers k1_numbers) =>  ((k15_asympt_0 A B) = (a_2_3_asympt_0 A B)) ) ) ) ) ).
tt(d20_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v13_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A B (k1_bcialg_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d20_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  ((v4_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ( (E = (k15_bilinear A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( (F = (k3_vectsp_4 A B H (k13_bilinear A B C D)))  =>  ((k2_binop_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C) (u1_struct_0 A) E F G) = (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r7_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A A B (k3_binop_1 A C D E)) = (k3_binop_1 A C (k3_funct_2 A A B D) (k3_funct_2 A A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers)))) )  =>  ( (A = k44_binop_2)  <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_binop_1 A B C) = (k20_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d20_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_cat_1 A B C) <=>  (? [D:$i] :  ((m1_cat_1 D A B C) & (v9_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(d20_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v4_cat_4 A) <=>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_cat_3 E A D B) &  ((r2_funct_2 B (u1_struct_0 A) (k2_cat_3 A B E) C) & (r3_cat_3 A D B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( (C = (k12_cohsp_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v10_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  (D = (k11_cohsp_1 A B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_coh_sp,ax, (! [A:$i] :  ((k20_coh_sp A) = (a_1_6_coh_sp A)) ) ).
tt(d20_comput_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (k2_comput_1 k5_numbers))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_comput_1 k5_numbers)))))) )  =>  ( (A = k13_comput_1)  <=>  ( ((k8_nat_1 (k9_setfam_1 (k2_comput_1 k5_numbers)) A k6_numbers) = k10_comput_1)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k8_nat_1 (k9_setfam_1 (k2_comput_1 k5_numbers)) A (k1_nat_1 B 1)) = (k4_subset_1 (k2_comput_1 k5_numbers) (k11_comput_1 (k8_nat_1 (k9_setfam_1 (k2_comput_1 k5_numbers)) A B)) (k12_comput_1 (k8_nat_1 (k9_setfam_1 (k2_comput_1 k5_numbers)) A B)))) ) ) ) ) ) ) ).
tt(d20_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k11_conlat_1 A) = (g3_lattices (k8_conlat_1 A) (k10_conlat_1 A) (k9_conlat_1 A))) ) ) ).
tt(d20_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ((m1_subset_1 E k1_numbers) &  ((r2_hidden C B) & (r2_hidden D B)) )  => (r2_hidden (k1_algstr_0 A (k1_clvect_1 A C (k6_xcmplx_0 k6_complex1 E)) (k1_clvect_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k15_decomp_1 A) = (a_1_9_decomp_1 A)) ) ) ).
tt(d20_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 48 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B (k4_finseq_2 6 k6_margrel1) (k4_finseq_2 8 (k4_finseq_2 6 k6_margrel1))) =>  ( (B = (k31_descip_1 A))  <=>  ( ((k1_funct_1 B 1) = (k2_descip_1 k6_margrel1 6 A))  &  ( ((k1_funct_1 B 2) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 6 A)))  &  ( ((k1_funct_1 B 3) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 12 A)))  &  ( ((k1_funct_1 B 4) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 18 A)))  &  ( ((k1_funct_1 B 5) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 24 A)))  &  ( ((k1_funct_1 B 6) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 30 A)))  &  ( ((k1_funct_1 B 7) = (k2_descip_1 k6_margrel1 6 (k3_descip_1 k6_margrel1 36 A)))  &  ((k1_funct_1 B 8) = (k3_descip_1 k6_margrel1 42 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B))))) )  =>  ( (D = (k18_ens_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r2_hidden E (k2_cat_1 A (k4_graph_1 A C) B)) =>  ((k1_funct_1 D E) = (k1_cat_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) =>  ((k18_e_siec A) = (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))))) ) ) ).
tt(d20_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k17_facirc_1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) k4_facirc_1)) ) ) ) ).
tt(d20_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_fomodel0 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v5_relat_1 F A) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) )  =>  ( ((r2_hidden C B) &  ((r2_hidden E B) &  ((k7_finseq_1 C D) = (k7_finseq_1 E F)) ) )  =>  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  ((v10_fomodel1 B A) <=> (r2_hidden B (k10_fomodel1 A))) ) ) ) ) ).
tt(d20_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))) )  =>  ( (C = (k22_fomodel2 A B))  <=>  ( ((k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) C k6_numbers) = (k17_fomodel2 A B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) C (k2_nat_1 D 1)) = (k1_funct_4 (k7_funct_4 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1 (k19_fomodel2 A B (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) C D)) (k21_fomodel2 A B (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) C D))) (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_pre_poly E)) )  =>  (! [F:$i] :  ( ((v4_fomodel2 F A) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( ( ((k32_fomodel2 A F) = (k1_nat_1 D 1))  =>  ((v5_fomodel2 F A) |  ((k28_fomodel3 A B C D E F) = (k7_finseq_1 (k7_finseq_1 (k31_fomodel2 A (k1_fomodel2 A)) (k1_funct_1 E (k40_fomodel2 A F))) (k1_funct_1 E (k41_fomodel2 A F)))) ) )  &  ( ( ( ((k32_fomodel2 A F) = (k1_nat_1 D 1))  & (v5_fomodel2 F A))  =>  ( ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) F) = B)  |  ((k28_fomodel3 A B C D E F) = (k7_finseq_1 (k31_fomodel2 A (o_4_1_fomodel3 A B C F)) (k1_funct_1 E (k24_fomodel3 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) F) (o_4_1_fomodel3 A B C F) (k40_fomodel2 A F))))) ) )  &  (~  ( (~  ( ((k32_fomodel2 A F) = (k1_nat_1 D 1))  &  (~ (v5_fomodel2 F A)) ) )  &  ( (~  ( ((k32_fomodel2 A F) = (k1_nat_1 D 1))  &  ((v5_fomodel2 F A) &  (~  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) F) = B) ) ) ) )  &  (~  ((k28_fomodel3 A B C D E F) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r3_fomodel4 A B C) <=>  ((v1_xboole_0 (k1_xtuple_0 C)) &  (? [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) D) D)) ) ) ) ) ) ) ) ) ) ).
tt(d20_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_freealg A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k17_freealg A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k17_freealg A B) C)))) )  =>  ((r2_hidden D (k1_lang1 (k3_freealg A B))) =>  ((k18_freealg A B C D E) = (k1_funct_1 E (k2_trees_4 (u1_struct_0 (k3_freealg A B)) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  ((v5_fsm_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  ( (~  (D = E) )  & (r5_fsm_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k20_ftacell1 A B C D E) = (k3_circcomb (k49_gfacirc1 A B C) (k49_gfacirc1 (k48_gfacirc1 A B C) E D) (k50_gfacirc1 A B C) (k50_gfacirc1 (k48_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d20_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v12_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (k4_functor0 A B C D D) (k8_altcat_1 A D)) = (k8_altcat_1 B (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(d20_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) ) )  =>  ((k20_gate_1 A B C D E) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~  ((k20_gate_1 A B C D E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k20_gfacirc1 A B C) = (k3_circcomb (k17_gfacirc1 A B C) (k5_circcomb k25_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) (k18_gfacirc1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp) k25_twoscomp))) ) ) ) ).
tt(d20_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v5_glib_000 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r1_glib_000 A D E B) & (r1_glib_000 A D E C))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d20_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((v1_abian C) |  ( (D = (k17_glib_001 A B C))  <=>  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B D) = (k1_funct_1 B C))  &  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  ( ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = (k1_funct_1 B C)) )  => (r1_xxreal_0 D E)) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_abian C))  & (r1_xxreal_0 C (k3_finseq_1 B))) )  =>  ( (D = (k17_glib_001 A B C))  <=>  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((k11_glib_003 A) = (k9_xtuple_0 (k6_glib_003 A))) ) ) ).
tt(d20_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m3_glib_005 D A) =>  ( (D = (k12_glib_005 A B C))  <=>  ( ((k1_funct_1 D k6_numbers) = (k8_funcop_1 k5_numbers (k7_glib_000 A) k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_1 D (k1_nat_1 E 1)) = (k11_glib_005 A (k1_funct_1 D E) C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k7_graph_1 A))  <=>  (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (u4_struct_0 A))  &  (B = (k5_card_1 C)) ) ) ) ) ) ) ) ) ).
tt(d20_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 B) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) k8_graph_5)))) )  =>  ((r6_graphsp A B C D) <=>  ( ((k3_finseq_1 A) = (k2_nat_1 (k2_nat_1 (k4_nat_1 C C) (k4_nat_1 3 C)) 1))  &  ( ((k2_finseq_1 C) = (u1_struct_0 B))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E C))  =>  ( ((k1_seq_1 A E) = 1)  &  ((k1_seq_1 A (k2_nat_1 (k4_nat_1 2 C) E)) = k6_numbers) ) ) ) )  &  ( ((k1_seq_1 A (k2_nat_1 C 1)) = k6_numbers)  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 2 E) & (r1_xxreal_0 E C))  =>  ((k1_seq_1 A (k2_nat_1 C E)) = (k1_real_1 1)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ( (G = E)  &  (H = F) )  =>  ((k1_seq_1 A (k2_nat_1 (k2_nat_1 (k4_nat_1 2 C) (k4_nat_1 C G)) H)) = (k12_graphsp B E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_group_10 A B) (k15_group_10 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_group_10 A B) (k15_group_10 A B))))) )  =>  ( (E = (k16_group_10 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F (k1_group_3 A) (k15_group_10 A B)) =>  (? [G:$i] :  ((m2_subset_1 G (k1_group_3 A) (k15_group_10 A B)) &  (? [H:$i] :  ( ((v15_algstr_0 H) & (m1_group_2 H A))  &  (? [I:$i] :  ( ((v15_algstr_0 I) & (m1_group_2 I A))  &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (G = (k3_funct_2 (k15_group_10 A B) (k15_group_10 A B) E F))  &  ( (F = H)  &  ( (G = I)  &  ( ((k2_group_1 C D) = J)  & (r1_group_2 A I (k6_group_3 A H J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B C))) &  ((v1_group_6 D B (k10_group_9 A B C)) &  ((v7_group_9 D A B (k10_group_9 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B C)))))) ) ) )  =>  ( (D = (k12_group_9 A B C))  <=>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E B) & (m1_group_2 E B)) )  =>  ( (E = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)))  => (r1_funct_2 (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B C)) (u1_struct_0 B) (u1_struct_0 (k5_group_6 B E)) D (k8_group_6 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) )  =>  ((k13_hahnban1 A B) = B) ) ) ) ) ).
tt(d20_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k20_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k11_idea_1 B D A)) ) ) ) ) ) ) ) ) ) ).
tt(d20_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k13_ideal_1 A B C) = (a_3_3_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(d20_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ( (E = (k2_incsp_1 A B C D))  <=> (r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_integra1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k14_integra1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_seq_1 B C) = (k18_rvsum_1 (k17_finseq_1 k1_numbers C A))) ) ) ) ) ) ) ) ) ) ).
tt(d20_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( (B = (k18_interva1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m2_interva1 C A)) ) ) ) ) ) ).
tt(d20_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_intpro_1)) =>  ( (B = (k11_intpro_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_intpro_1)) =>  ( ((v9_intpro_1 D) & (r1_tarski A D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v6_lattice3 A) <=>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_lattice3 A C B) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r3_lattice3 A F B) => (r1_lattices A F C)) ) )  &  ((r3_lattice3 A E (a_3_1_lattice3 A B D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r3_lattice3 A F (a_3_1_lattice3 A B D)) => (r1_lattices A F E)) ) ) ) ) )  => (r1_lattices A E (k1_lattices A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((m2_lattice5 D A B C) <=>  ( ((k9_xtuple_0 D) = k5_numbers)  &  ( ((k1_funct_1 D k6_numbers) = (k4_tarski A C))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ( (~ (v1_xboole_0 F))  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 F F) (u1_struct_0 B)) &  ((v1_lattice5 G F B) &  ((v2_lattice5 G F B) &  ((v3_lattice5 G F B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 F F) (u1_struct_0 B))))) ) ) ) )  &  (? [H:$i] :  ( (~ (v1_xboole_0 H))  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 H H) (u1_struct_0 B)) &  ((v1_lattice5 I H B) &  ((v2_lattice5 I H B) &  ((v3_lattice5 I H B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 H H) (u1_struct_0 B))))) ) ) ) )  &  ((r2_lattice5 F B G H I) &  ( ((k1_funct_1 D E) = (k4_tarski F G))  &  ((k1_funct_1 D (k2_nat_1 E 1)) = (k4_tarski H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v17_lattices A) <=>  ((v15_lattices A) &  ((v16_lattices A) & (v11_lattices A)) ) ) ) ) ).
tt(d20_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( ( ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)) = (k6_glib_000 A))  =>  ( (C = (k19_lexbfs A B))  <=>  (C = (k10_subset_1 (k6_glib_000 A))) ) )  &  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)) = (k6_glib_000 A)) )  =>  ( (C = (k19_lexbfs A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v6_membered D) & (v1_finset_1 D)) )  &  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  ( (D = (k10_xtuple_0 E))  &  ( (E = (k5_relset_1 (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) (k6_subset_1 (k6_glib_000 A) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)))))  &  (C = (k10_subset_1 (k8_relat_1 E (k1_tarski (k1_xxreal_2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k13_lmod_7 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k13_lmod_7 A B C))) =>  ( (F = (k15_lmod_7 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (E = (k14_lmod_7 A B C G))  =>  (F = (k14_lmod_7 A B C (k4_vectsp_1 A B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k20_lpspace1 A B C) = (g1_normsp_1 (u1_struct_0 (k18_lpspace1 A B C)) (u2_struct_0 (k18_lpspace1 A B C)) (u1_algstr_0 (k18_lpspace1 A B C)) (u1_rlvect_1 (k18_lpspace1 A B C)) (k19_lpspace1 A B C))) ) ) ) ) ) ) ).
tt(d20_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r5_ltlaxio1 A B C) <=>  (B = (k3_hilbert1 A C)) ) ) ) ) ) ) ) ).
tt(d20_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k16_margrel1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k10_margrel1 (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k23_member_1 A B) = (k13_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d20_membered,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_xboole_0 A B) <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden C A) & (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(d20_metric_1,ax, (k12_metric_1 = (k8_funcop_1 k1_numbers (k2_zfmisc_1 2 2) k6_numbers)) ).
tt(d20_metric_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers)))) )  =>  ( (A = k20_metric_3)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ( ( (H = (k4_domain_1 k1_numbers k1_numbers k1_numbers B D F))  &  (I = (k4_domain_1 k1_numbers k1_numbers k1_numbers C E G)) )  =>  ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) A H I) = (k7_real_1 (k7_real_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 B C) (k1_metric_1 k1_numbers k1_numbers k7_metric_1 D E)) (k1_metric_1 k1_numbers k1_numbers k7_metric_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (D = (k23_mmlquery A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((k2_mmlquery A D E) = (k3_tarski (a_4_13_mmlquery A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_mod_2,ax, (k18_mod_2 = (g6_algstr_0 (k1_enumset1 k6_numbers 1 2) k13_mod_2 k14_mod_2 k16_mod_2 k17_mod_2)) ).
tt(d20_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  ((k13_modelc_1 A B) = (k7_modelc_1 (k8_modelc_1 (k7_modelc_1 A) (k7_modelc_1 B)))) ) ) ) ) ).
tt(d20_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v4_modelc_2 A) =>  ( (B = (k12_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k4_modelc_2 C B) = A) ) ) ) )  &  ( ((v5_modelc_2 A) =>  ( (B = (k12_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k5_modelc_2 C B) = A) ) ) ) )  &  ( ((v7_modelc_2 A) =>  ( (B = (k12_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k7_modelc_2 C B) = A) ) ) ) )  &  (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~  ( (B = (k12_modelc_2 A))  <=>  (? [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  &  ((k8_modelc_2 C B) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ((r6_modelc_3 A B C) <=>  ((v3_modelc_3 B A) &  ((v3_modelc_3 C A) &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ((r5_modelc_3 A D) &  ( ((k1_funct_1 D 1) = (k12_modelc_3 A B))  &  ((k1_funct_1 D (k3_finseq_1 D)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v17_monoid_0 A) <=> (v9_monoid_0 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(d20_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_msafree A B))) =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  & (r1_lang1 (k5_msafree A B) C D)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( (D = (k17_msafree A B C))  <=>  ((k4_tarski D (u1_struct_0 A)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B))))) )  =>  ( (C = (k15_msualg_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k14_msualg_2 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k14_msualg_2 A B)) =>  (! [F:$i] :  ( ((v3_msualg_1 F A) & (m1_msualg_2 F A B))  =>  (! [G:$i] :  ( ((v3_msualg_1 G A) & (m1_msualg_2 G A B))  =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k14_msualg_2 A B) C D E) = (k13_msualg_2 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) (u3_msualg_1 A C)) =>  ( (E = (k19_msualg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_funct_2 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) F) (k1_funct_1 (u3_msualg_1 A C) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) (u3_msualg_1 A C) E F) (k18_msualg_4 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r16_ncfcont1 A B C) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C E) (k7_partfun1 k2_numbers C F))) (k8_real_1 D (k1_normsp_0 A (k5_algstr_0 A E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v11_oposet_1 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (u1_robbins1 A)) & (r1_oposet_1 A B)) ) ) ) ) ) ).
tt(d20_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A)))) =>  ((k18_osafree A B C D) = (a_4_0_osafree A B C D)) ) ) ) ) ) ) ) ) ).
tt(d20_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r6_osalg_1 A B C) <=>  ((r1_osalg_1 A B C) &  ((r2_osalg_1 A (k1_msualg_1 A B) (k1_msualg_1 A C)) & (r3_orders_2 A (k2_msualg_1 A B) (k2_msualg_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d20_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  ((k16_osalg_4 A B C) = (g3_msualg_1 A (k7_osalg_4 A B C) (k15_osalg_4 A B C))) ) ) ) ) ) ) ).
tt(d20_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k9_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k7_relat_1 (k1_funct_1 C E) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v7_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k7_pcs_0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 C D) = (u1_pcs_0 (k6_pcs_0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d20_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((r7_pdiff_1 A B C D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)))))))  =>  ( (F = (k15_pdiff_1 A B C D E))  <=>  ( ((k1_relset_1 (u1_struct_0 (k4_real_ns1 A)) F) = E)  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 A))) =>  ((r2_hidden G E) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B))) F G) = (k9_pdiff_1 A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_pencil_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v16_pencil_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C A) &  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  (C = D) )  => (v3_card_1 (k1_funct_1 B D) 1)) ) ) ) ) ) ) ) ) ).
tt(d20_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k23_polyform A B) = (k2_struct_0 (k22_polyform A B))) ) ) ) ) ).
tt(d20_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k19_pscomp_1 A) = (k19_euclid (k6_pscomp_1 A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k14_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k14_pscomp_1 A))))) ) ) ).
tt(d20_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k14_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d20_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ((r1_xxreal_0 1 D) &  ( ((k3_finseq_1 E) = D)  &  ( ((k1_funct_1 E 1) = B)  &  ( ((k1_funct_1 E D) = C)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 D F))  &  (! [G:$i] :  ((m1_subset_1 G (k9_qc_lang1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k9_qc_lang1 A)) =>  (~  ( ((k1_funct_1 E F) = G)  &  ( ((k1_funct_1 E (k2_nat_1 F 1)) = H)  & (r1_qc_lang2 A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  =>  ((v21_quantal1 A) <=> (v17_quantal1 (u1_quantal1 A) A)) ) ) ).
tt(d20_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k24_quaterni A B) = (k23_quaterni A (k8_quaterni B))) ) ) ) ) ).
tt(d20_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_quofield C A B) <=>  ((v1_quofield C A B) & (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(d20_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k10_ringcat1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) A)))) )  =>  ( (B = (k14_ringcat1 A))  <=>  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  ((k3_funct_2 (k10_ringcat1 A) A B C) = (k11_ringcat1 A C)) ) ) ) ) ) ) ) ).
tt(d20_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k15_robbins1 A B) = (k1_lattices A (k11_robbins1 A B) (k1_lattices A (k12_robbins1 A B) B))) ) ) ) ) ).
tt(d20_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_eqrel_1 B (k3_tarski A)) =>  ((v10_scmyciel B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ((v9_scmyciel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_tarski A)))) ) ) ) ) ) ) ) ).
tt(d20_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k27_seq_4 A) = (a_1_0_seq_4 A)) ) ) ).
tt(d20_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_pre_topc D) & (m1_simplex0 D A))  =>  ( (D = (k10_simplex0 A B C))  <=>  ( ((k2_struct_0 D) = (k2_struct_0 B))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  ((v3_pre_topc E D) <=>  (? [F:$i] :  ( ((v6_ordinal1 F) &  ((v1_finset_1 F) &  ((v1_tops_2 F B) & (m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) )  &  (E = (k7_relat_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k22_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k10_real_1 (k8_real_1 (k2_newton (k1_real_1 1) C) (k1_newton A (k2_nat_1 (k4_nat_1 2 C) 1))) (k3_newton (k2_nat_1 (k4_nat_1 2 C) 1)))) ) ) ) ) ) ) ) ).
tt(d20_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_stacks_1 B) & (l1_stacks_1 B))  =>  ( (B = (k14_stacks_1 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((u4_struct_0 B) = (k8_eqrel_1 (u4_struct_0 A) (k10_stacks_1 A)))  &  ( ((u1_stacks_1 B) = (k6_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (u1_stacks_1 A)))  &  ( ((u2_stacks_1 B) = (k3_stacks_1 (u1_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) (u2_stacks_1 A)))  &  ( ((u3_stacks_1 B) = (k2_filter_1 (u4_struct_0 A) (k10_stacks_1 A) (k4_stacks_1 (u4_struct_0 A) (u4_struct_0 A) (u1_stacks_1 A) (u1_stacks_1 A) (u3_stacks_1 A) (k6_partfun1 (u1_stacks_1 A)))))  &  (! [C:$i] :  ((m1_orders_1 C (k8_eqrel_1 (u4_struct_0 A) (k10_stacks_1 A))) =>  ((u4_stacks_1 B) = (k2_funct_7 (k1_partfun1 (k8_eqrel_1 (u4_struct_0 A) (k10_stacks_1 A)) (k3_tarski (k8_eqrel_1 (u4_struct_0 A) (k10_stacks_1 A))) (u4_struct_0 A) (u1_struct_0 A) C (u4_stacks_1 A)) (u1_stacks_1 A) (o_1_1_stacks_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((k20_substut1 A B) = (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k13_qc_lang1 A (k18_substut1 A B)) (k19_substut1 A B))) ) ) ) ) ).
tt(d20_turing_1,ax, (k19_turing_1 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k12_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) k6_numbers) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 2 1) (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 k6_numbers 1))) (k2_turing_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 3 k6_numbers k6_numbers)))) ).
tt(d20_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k21_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(d20_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ((v3_funct_1 A) <=>  (? [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(d20_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v13_vectsp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_algstr_0 A D E)) = (k1_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v13_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r1_orders_2 A C D))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(d20_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_waybel_1 A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k5_waybel_1 A B))  <=> (v3_waybel_1 (k1_waybel_1 A A C (k4_waybel_1 A B)) A A)) ) ) ) ) ) ) ) ).
tt(d20_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v8_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden (k4_tarski C D) B) &  ( (~  (C = D) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden (k4_tarski C E) B) &  ((r2_hidden (k4_tarski E D) B) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d20_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v4_yellow_6 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v1_yellow_6 C A) & (l1_waybel_0 C A)) ) ) )  =>  ((r2_hidden C (k6_yellow_6 A)) => (r2_hidden (k4_tarski C (k4_yellow_6 A C)) B)) ) ) ) ) ) ) ) ).
tt(d20_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_zf_lang A) <=>  (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k10_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d20_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r1_zmodul01 A C D) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( (E = (k9_zmodul01 A B C D))  <=>  ( (B = (k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)))  &  ((r1_struct_0 C (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 D (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_abcmiz_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ( (E = (k1_funct_1 C D))  &  (F = (k1_funct_1 (k7_abcmiz_0 A B C) D)) ) )  => (r1_abcmiz_0 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_abcmiz_1,ax, (k20_abcmiz_1 = (k2_xboole_0 (k2_xboole_0 k17_abcmiz_1 k18_abcmiz_1) k19_abcmiz_1)) ).
tt(d21_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r1_abcmiz_a A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  (B = (k56_abcmiz_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d21_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v17_algstr_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = (k6_algstr_0 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B)))))) )  =>  ( (D = (k18_algstr_4 A B C))  <=>  ((v1_group_6 D (k14_algstr_4 A) (k14_algstr_4 B)) & (r1_algstr_4 D (k3_relat_1 (k2_funct_1 (k16_algstr_4 A 1)) (k1_partfun1 A B (k11_algstr_4 B 1) (u1_struct_0 (k14_algstr_4 B)) C (k16_algstr_4 B 1))))) ) ) ) ) ) ) ) ) ) ).
tt(d21_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k17_aofa_000 A B C D E) = (k13_aofa_000 A B (k16_aofa_000 A C (k13_aofa_000 A D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k25_aofa_i00 A B) = (k7_funcop_1 (k9_funct_2 A k4_numbers) B)) ) ) ) ) ).
tt(d21_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k9_armstrng A B) = (a_2_4_armstrng A B)) ) ) ) ).
tt(d21_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v14_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A B)) = (k2_bcialg_1 A B)) ) ) ) ) ) ).
tt(d21_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear E A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear E A B (k6_vectsp10 A C (k14_bilinear A B C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A))))) ) ) )  =>  ( (E = (k16_bilinear A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ( (F = (k3_vectsp_4 A C H (k14_bilinear A B C D)))  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D))) (u1_struct_0 A) E G F) = (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ((m2_cat_1 C A B) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r2_hidden (k4_tarski E D) (k9_xtuple_0 (u1_cat_1 A))) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A D E)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  =>  ((k19_cat_4 A) = (u5_cat_4 A)) ) ) ).
tt(d21_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B)) &  ((v7_closure2 C (u1_struct_0 A) B) &  ((v8_closure2 C (u1_struct_0 A) B) &  ((v9_closure2 C (u1_struct_0 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v11_closure2 D A) & (l1_closure2 D A))  =>  ( (D = (k10_closure2 A B C))  <=>  ((r6_pboole (u1_struct_0 A) (u3_msualg_1 A D) B) &  ((u1_closure2 A D) = (a_3_0_closure2 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ((k13_cohsp_1 A) = (a_1_0_cohsp_1 A)) ) ) ).
tt(d21_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  ((k21_coh_sp A B) = (k1_xtuple_0 (k1_xtuple_0 B))) ) ) ) ).
tt(d21_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ( (D = (k5_compos_1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 B)) =>  ((k1_funct_1 D E) = (k5_compos_0 (u1_compos_1 A) (k7_partfun1 (u1_compos_1 A) B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_comput_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v2_margrel1 B))  =>  ((v8_comput_1 B A) <=>  ((k18_margrel1 B) = A) ) ) ) ) ).
tt(d21_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_conlat_1 A))) =>  ((k12_conlat_1 A B) = B) ) ) ) ) ).
tt(d21_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k18_convex4 A) = (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) ) ) ).
tt(d21_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k16_decomp_1 A) = (a_1_10_decomp_1 A)) ) ) ).
tt(d21_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)))))) )  =>  ( (C = (k19_ens_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)) C D) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A B (k3_graph_1 A D)) (k2_cat_1 A B (k4_graph_1 A D)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A B (k3_graph_1 A D)) (k2_cat_1 A B (k4_graph_1 A D))) (k17_ens_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d21_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) =>  ((k19_e_siec A) = (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))) ) ) ).
tt(d21_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k18_facirc_1 A B C) = (k3_circcomb (k14_facirc_1 A B C) (k5_circcomb k4_facirc_1 (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1))) (k16_facirc_1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1) k4_facirc_1))) ) ) ) ).
tt(d21_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k17_fomodel0 A B C) = (k6_funct_4 C A B)) ) ) ) ) ).
tt(d21_fomodel1,ax, (! [A:$i] :  ((l4_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A)))) =>  ( ( (B = (u2_struct_0 A))  =>  ((k12_fomodel1 A B) = (k4_xcmplx_0 2)) )  &  ( (~  (B = (u2_struct_0 A)) )  =>  ((k12_fomodel1 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(d21_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_rfunct_3 D (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)) =>  ( (D = (k23_fomodel2 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (B = E)  =>  (D = (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1) (k22_fomodel2 A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_funct_2 E (k33_fomodel2 A) (k33_fomodel2 A) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) =>  (! [F:$i] :  ((m2_funct_2 F (k33_fomodel2 A) (k33_fomodel2 A) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) =>  ( (F = (k31_fomodel3 A B C D E))  <=>  (! [G:$i] :  ( ((v4_fomodel2 G A) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k1_funct_1 F G) = (k29_fomodel3 A B C D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r4_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [E:$i] :  ( ((v13_fomodel1 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [F:$i] :  ( ((v13_fomodel1 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [G:$i] :  ((r2_hidden G A) &  ( ((k1_xtuple_0 C) = (k2_xboole_0 (k1_xtuple_0 G) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) E) F))))  &  ( ((k2_xtuple_0 G) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) D) E))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((v6_fsm_1 D A B C) <=>  (? [E:$i] :  ((m2_finseq_1 E A) & (r1_fsm_1 A C E (u2_fsm_1 A C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k21_ftacell1 A B C D E) = (k45_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d21_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v13_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A E F)) &  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C F))) =>  (~  ( (I = (k1_funct_1 (k4_functor0 A B C D E) G))  &  ( (J = (k1_funct_1 (k4_functor0 A B C E F) H))  &  ((k1_funct_1 (k4_functor0 A B C D F) (k5_altcat_1 A D E F G H)) = (k5_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E) (k3_functor0 A B C F) I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  (~  ((k21_gate_1 A B C D E) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) & (v1_xboole_0 E)) ) ) ) )  =>  ((k21_gate_1 A B C D E) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d21_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k21_gfacirc1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp)) ) ) ) ).
tt(d21_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v6_glib_000 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_glib_000 A D E B) & (r2_glib_000 A D E C))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d21_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r2_hidden C (k13_glib_001 A B)) =>  ( (D = (k18_glib_001 A B C))  <=>  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B D) = C)  &  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = C) )  => (r1_xxreal_0 E D)) ) ) ) ) ) )  &  ( (~ (r2_hidden C (k13_glib_001 A B)))  =>  ( (D = (k18_glib_001 A B C))  <=>  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k7_glib_000 A)) =>  ((k12_glib_003 A B C) = (k13_glib_000 A k3_glib_003 (k1_funct_4 (k6_glib_003 A) (k16_funcop_1 B C)))) )  &  ( (~ (r2_hidden B (k7_glib_000 A)))  =>  ((k12_glib_003 A B C) = A) ) ) ) ) ) ) ).
tt(d21_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k13_glib_005 A B C) = (k40_glib_000 (k12_glib_005 A C B))) ) ) ) ) ) ) ).
tt(d21_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k8_graph_1 A B))  <=>  (? [D:$i] :  ((v1_finset_1 D) &  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (u4_struct_0 A)) &  ((k1_funct_1 (u2_graph_1 A) E) = B) ) ) )  &  (C = (k5_card_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k20_graphsp A) = (k9_graphsp (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A)) A)) ) ) ).
tt(d21_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (k1_funct_2 (k15_group_10 A B) (k15_group_10 A B))) &  ((v1_group_10 D C (k15_group_10 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 (k15_group_10 A B) (k15_group_10 A B)))))) ) )  =>  ( (D = (k17_group_10 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 C) (k1_funct_2 (k15_group_10 A B) (k15_group_10 A B)) D E) = (k16_group_10 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ( (E = (k13_group_9 A B C D))  <=>  ((u1_struct_0 E) = (a_4_1_group_9 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k21_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k11_idea_1 A (k12_idea_1 A D B) B)) ) ) ) ) ) ) ) ) ) ).
tt(d21_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k14_ideal_1 A B C) = (a_3_4_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(d21_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ( (~ (r1_incsp_1 A B C))  =>  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  ( (D = (k3_incsp_1 A B C))  <=>  ((r2_incsp_1 A B D) & (r3_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_intpro_1,ax, (k12_intpro_1 = (k11_intpro_1 (k1_subset_1 k1_intpro_1))) ).
tt(d21_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k15_lattice3 A B))  <=>  ((r4_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_lattice3 A D B) => (r1_lattices A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) &  ((v1_lattice5 B (u1_struct_0 A) A) &  ((v2_lattice5 B (u1_struct_0 A) A) &  ((v3_lattice5 B (u1_struct_0 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) )  =>  ( (B = (k16_lattice5 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (~  (C = D) )  =>  ((k3_lattice5 (u1_struct_0 A) A B C D) = (k13_lattice3 A C D)) )  &  ( (C = D)  =>  ((k3_lattice5 (u1_struct_0 A) A B C D) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k7_lattices A B))  <=> (r2_lattices A C B)) ) ) ) ) ) ) ) ).
tt(d21_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  ((k20_lexbfs A B C) = (k4_tarski (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B) (k3_lexbfs (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) (k2_finsub_1 (k1_zfmisc_1 (k6_glib_000 A)) (k2_chord A (k1_tarski C)) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B))) 1))) ) ) ) ) ) ).
tt(d21_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k13_lmod_7 A B C))) (u1_struct_0 (k13_lmod_7 A B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k13_lmod_7 A B C))) (u1_struct_0 (k13_lmod_7 A B C)))))) )  =>  ( (D = (k16_lmod_7 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k13_lmod_7 A B C))) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 (k13_lmod_7 A B C)) (u1_struct_0 (k13_lmod_7 A B C)) D E F) = (k15_lmod_7 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r6_ltlaxio1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k1_hilbert1) &  (? [E:$i] :  ((m1_subset_1 E k1_hilbert1) &  ( (A = (k3_hilbert1 D E))  &  ( (B = (k3_hilbert1 D (k2_ltlaxio1 D)))  &  (C = (k3_hilbert1 D (k6_ltlaxio1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_margrel1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_margrel1 A) <=> (v2_card_3 (k9_xtuple_0 A))) ) ) ).
tt(d21_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k24_member_1 A B) = (k14_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d21_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v3_membered B) =>  ((r1_xboole_0 A B) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden C A) & (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(d21_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_mmlquery B A) <=> (r1_relset_1 A A B (k4_relat_1 A))) ) ) ) ).
tt(d21_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v3_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  (~ (v6_modelc_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v3_modelc_1 A) =>  ( (B = (k14_modelc_1 A))  <=>  ((k7_modelc_1 B) = A) ) )  &  ( ((v5_modelc_1 A) =>  ( (B = (k14_modelc_1 A))  <=>  ((k9_modelc_1 B) = A) ) )  &  (~  ( (~ (v3_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  (~  ( (B = (k14_modelc_1 A))  <=>  ((k10_modelc_1 B) = A) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_modelc_2 A B) <=>  (~  ( (~  (B = (k3_modelc_2 A)) )  &  ( (~  (B = (k6_modelc_2 A)) )  &  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( (~  (B = (k4_modelc_2 A C)) )  &  ( (~  (B = (k4_modelc_2 C A)) )  &  ( (~  (B = (k5_modelc_2 A C)) )  &  ( (~  (B = (k5_modelc_2 C A)) )  &  ( (~  (B = (k7_modelc_2 A C)) )  &  ( (~  (B = (k7_modelc_2 C A)) )  &  ( (~  (B = (k8_modelc_2 A C)) )  &  (~  (B = (k8_modelc_2 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_modelc_3 A))) =>  ((k13_modelc_3 A B) = B) ) ) ) ) ).
tt(d21_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) <=> (r3_binop_1 (u1_struct_0 A) (k5_struct_0 A) (u2_algstr_0 A))) ) ) ).
tt(d21_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((r2_hidden D (k3_msualg_1 A C B)) =>  ((k18_msafree A B C D) = (k1_funct_1 (k5_msualg_1 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(d21_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B))))) )  =>  ( (C = (k16_msualg_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k14_msualg_2 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k14_msualg_2 A B)) =>  (! [F:$i] :  ( ((v3_msualg_1 F A) & (m1_msualg_2 F A B))  =>  (! [G:$i] :  ( ((v3_msualg_1 G A) & (m1_msualg_2 G A B))  =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k14_msualg_2 A B) C D E) = (k11_msualg_2 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ((r17_ncfcont1 A B C) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C E) (k7_partfun1 k1_numbers C F))) (k8_real_1 D (k1_normsp_0 A (k5_algstr_0 A E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_oposet_1 A B) <=>  ((v9_oposet_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) &  ((r2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) &  ((r4_waybel_1 A (k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) (u1_struct_0 A)) & (r3_waybel_1 A (k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))))))) )  =>  ( (C = (k19_osafree A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_osafree A B))) =>  ((r2_hidden D (k6_dtconstr (k2_osafree A B))) =>  ((k1_funct_1 C (k2_trees_4 (u1_struct_0 (k2_osafree A B)) D)) = (k17_osafree A B D)) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_osafree A B))) =>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r1_lang1 (k2_osafree A B) D (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) E)) =>  ((k1_funct_1 C (k8_trees_4 (u1_struct_0 (k2_osafree A B)) D E)) = (k18_osafree A B D (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  ((v13_osalg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r6_osalg_1 A C D) =>  ((k2_partfun1 (k3_msualg_1 A D B) (k4_msualg_1 A D B) (k5_msualg_1 A D B) (k3_msualg_1 A C B)) = (k5_msualg_1 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (u3_msualg_1 A B) D) (k6_osalg_4 A B C D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k6_osalg_4 A B C D))))) )  =>  ( (E = (k17_osalg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k6_osalg_4 A B C D) E F) = (k8_osalg_4 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r8_pboole A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(d21_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((l1_pcs_0 B) =>  ((k8_pcs_0 A B) = (g1_pcs_0 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k3_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_pcs_0 A) (u1_pcs_0 B)))) ) ) ) ) ).
tt(d21_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (C = (k3_pencil_1 A B))  <=>  (~ (v1_zfmisc_1 (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(d21_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k24_polyform A B) = (k3_ranknull k2_bspace (k17_polyform A (k2_xcmplx_0 B 1)) (k17_polyform A (k6_xcmplx_0 (k2_xcmplx_0 B 1) 1)) (k21_polyform A (k2_xcmplx_0 B 1)))) ) ) ) ) ).
tt(d21_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k20_pscomp_1 A) = (k19_euclid (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k15_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k15_pscomp_1 A))) (k7_pscomp_1 A))) ) ) ).
tt(d21_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v5_qc_lang1 B A) <=>  (? [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k15_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d21_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r3_qc_lang2 A B C) <=>  ((r2_qc_lang2 A B C) &  (~  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d21_quantal1,ax, (! [A:$i] :  ((l3_quantal1 A) =>  ((k3_quantal1 A) = (u1_quantal1 A)) ) ) ).
tt(d21_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ( (C = (k25_quaterni A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (B = (k6_quaterni D E F G))  &  (C = (k6_quaterni (k8_real_1 A D) (k8_real_1 A E) (k8_real_1 A F) (k8_real_1 A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_quofield C A B) <=>  ((v3_quofield C A B) & (v2_quofield C A B)) ) ) ) ) ) ) ) ).
tt(d21_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski B D) A))  => (r7_rewrite1 A C D)) ) ) ) ) ) ) ).
tt(d21_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k10_ringcat1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) A)))) )  =>  ( (B = (k15_ringcat1 A))  <=>  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  ((k3_funct_2 (k10_ringcat1 A) A B C) = (k12_ringcat1 A C)) ) ) ) ) ) ) ) ).
tt(d21_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k16_robbins1 A B) = (k1_lattices A (k11_robbins1 A B) (k1_lattices A (k12_robbins1 A B) (k12_robbins1 A B)))) ) ) ) ) ).
tt(d21_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v5_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  ( (B = (k28_seq_4 A))  <=>  ( ((k1_rvsum_1 B) = (k1_rvsum_1 A))  &  ((k3_finseq_1 B) = (k5_card_1 (k1_rvsum_1 A))) ) ) ) ) ) ) ).
tt(d21_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_simplex0 E A) =>  ( (E = (k11_simplex0 A B C D))  <=>  (? [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  &  ( ((k1_funct_1 F k1_xboole_0) = B)  &  ( ((k1_funct_1 F D) = E)  &  ( ((k9_xtuple_0 F) = k5_numbers)  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((m1_simplex0 H A) =>  ( (H = (k1_funct_1 F G))  =>  ((k1_funct_1 F (k1_nat_1 G 1)) = (k10_simplex0 A H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k23_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k10_real_1 (k8_real_1 (k2_newton (k1_real_1 1) C) (k1_newton A (k4_nat_1 2 C))) (k3_newton (k4_nat_1 2 C)))) ) ) ) ) ) ) ) ).
tt(d21_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_stacks_1 A B C D) <=>  ( ((k9_xtuple_0 C) = (u1_struct_0 A))  &  ( ((k10_xtuple_0 C) = (u1_struct_0 B))  &  ((v2_funct_1 C) &  ( ((k9_xtuple_0 D) = (u4_struct_0 A))  &  ( ((k10_xtuple_0 D) = (u4_struct_0 B))  &  ((v2_funct_1 D) &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ( (F = (k1_funct_1 D E))  =>  ( ((r1_stacks_1 A E) => (r1_stacks_1 B F))  &  ( ((r1_stacks_1 B F) => (r1_stacks_1 A E))  &  ( ( (~ (r1_stacks_1 A E))  =>  ( ((k5_stacks_1 B F) = (k1_funct_1 D (k5_stacks_1 A E)))  &  ((k6_stacks_1 B F) = (k1_funct_1 C (k6_stacks_1 A E))) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( (H = (k1_funct_1 C G))  =>  ((k7_stacks_1 B F H) = (k1_funct_1 D (k7_stacks_1 A E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k21_substut1 A B C) = (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k14_qc_lang1 A (k18_substut1 A B) (k18_substut1 A C)) (k19_substut1 A B))) ) ) ) ) ) ) ) ).
tt(d21_turing_1,ax, (! [A:$i] :  ( ((v1_turing_1 A) & (l1_turing_1 A))  =>  ( (A = k20_turing_1)  <=>  ( ((u1_turing_1 A) = (k7_domain_1 k5_numbers k6_numbers 1))  &  ( ((u2_turing_1 A) = (k3_turing_1 3))  &  ((r1_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) k19_turing_1) &  ( ((u4_turing_1 A) = k6_numbers)  &  ((u5_turing_1 A) = 3) ) ) ) ) ) ) ) ).
tt(d21_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k22_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 B) C) D))) ) ) ) ) ) ) ) ) ) ).
tt(d21_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v14_waybel_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C B) & (r2_lattice3 A B C)) ) ) ) ) ) ) ) ).
tt(d21_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_waybel_1 A B C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_waybel_1 A B) C)) ) ) ) ) ) ) ).
tt(d21_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v9_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden (k4_tarski C D) B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden (k4_tarski C E) B) & (r2_hidden (k4_tarski E D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v5_yellow_6 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m2_yellow_6 D A C) =>  ((r2_hidden D (k6_yellow_6 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C E) B) => (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d21_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) <=>  (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d21_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A))))) )  =>  ( (B = (k10_zmodul01 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k8_zmodul01 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_zmodul01 A)) =>  (! [E:$i] :  ((m1_zmodul01 E A) =>  (! [F:$i] :  ((m1_zmodul01 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k8_zmodul01 A) B C D) = (k6_zmodul01 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((k25_abcmiz_1 A) = (k21_abcmiz_1 (k24_abcmiz_1 A))) ) ) ).
tt(d22_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  ((r2_abcmiz_a A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (r1_tarski (k63_abcmiz_1 A D C) B)) ) ) ) ) ) ) ) ) ).
tt(d22_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  ((k18_aofa_000 A) = (k7_subset_1 (u1_struct_0 A) (k7_subset_1 (u1_struct_0 A) (k7_subset_1 (u1_struct_0 A) (k6_subset_1 (u1_struct_0 A) (k1_tarski (k12_aofa_000 A))) (k2_relset_1 (u1_struct_0 A) (k2_pua2mss1 A (k1_funct_7 3 (k4_finseq_1 (u1_unialg_1 A)))))) (k2_relset_1 (u1_struct_0 A) (k2_pua2mss1 A (k1_funct_7 4 (k4_finseq_1 (u1_unialg_1 A)))))) (a_1_1_aofa_000 A))) ) ) ).
tt(d22_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ((m1_aofa_000 D A (k9_funct_2 B k4_numbers) C) =>  ((v1_aofa_i00 D A B C) <=>  ( (! [E:$i] :  ((m2_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) => (r2_aofa_i00 A B C D E F)) ) ) )  &  ( (! [E:$i] :  ((v1_int_1 E) => (m3_aofa_i00 (k25_aofa_i00 B E) A B C D)) )  &  ( (! [E:$i] :  ((m2_aofa_i00 E A B C D) => (m3_aofa_i00 (k23_aofa_i00 B E) A B C D)) )  &  ( (! [E:$i] :  ((m1_subset_1 E B) => (m2_aofa_i00 (k24_aofa_i00 B E) A B C D)) )  &  ( (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k4_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers B)))) )  &  ((v2_funct_1 (k2_partfun1 k4_numbers B E (k1_card_1 B))) &  (! [F:$i] :  ((m3_aofa_i00 F A B C D) => (m2_aofa_i00 (k1_partfun1 (k9_funct_2 B k4_numbers) k4_numbers k4_numbers B F E) A B C D)) ) ) ) )  &  ( (! [E:$i] :  ((m3_aofa_i00 E A B C D) => (m3_aofa_i00 (k34_valued_1 (k9_funct_2 B k4_numbers) k4_numbers E) A B C D)) )  &  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((m3_aofa_i00 (k22_valued_1 (k9_funct_2 B k4_numbers) k4_numbers k4_numbers E F) A B C D) &  ((m3_aofa_i00 (k16_aofa_i00 (k9_funct_2 B k4_numbers) E F) A B C D) &  ((m3_aofa_i00 (k10_aofa_i00 (k9_funct_2 B k4_numbers) E F) A B C D) &  ((m3_aofa_i00 (k11_aofa_i00 (k9_funct_2 B k4_numbers) E F) A B C D) &  ((m3_aofa_i00 (k12_aofa_i00 (k9_funct_2 B k4_numbers) E F) A B C D) & (m3_aofa_i00 (k13_aofa_i00 (k9_funct_2 B k4_numbers) E F) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((k10_armstrng A B) = (a_2_5_armstrng A B)) ) ) ).
tt(d22_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v15_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) = (k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))))) ) ) ) ) ) ) ) ).
tt(d22_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v2_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v4_bilinear E A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A))))) ) ) ) ) )  =>  ( (E = (k17_bilinear A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  ( ( (F = (k3_vectsp_4 A B H (k13_bilinear A B C D)))  &  (G = (k3_vectsp_4 A C I (k14_bilinear A B C D))) )  =>  ((k2_binop_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D))) (u1_struct_0 A) E F G) = (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers)))) )  =>  ( (A = k46_binop_2)  <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_binop_1 A B C) = (k22_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d22_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (D = (k7_cat_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A E)) = (k4_cat_1 B F))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k20_cat_4 A B C) = (k5_binop_1 (u1_struct_0 A) (u6_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d22_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_closure2 D (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) =>  ( (D = (k11_closure2 A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))) &  ((r6_pboole (u1_struct_0 A) D (k4_mssubfam (u1_struct_0 A) (u3_msualg_1 A B) (k5_closure2 (u1_struct_0 A) (u3_msualg_1 A B) E))) &  (E = (a_3_1_closure2 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  ((k14_cohsp_1 A B) = (k3_card_3 (k2_card_3 (k10_finseq_1 A B)))) ) ) ).
tt(d22_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  ((k22_coh_sp A B) = (k2_xtuple_0 (k1_xtuple_0 B))) ) ) ) ).
tt(d22_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_compos_1 A B C) = (k61_valued_1 (k5_compos_1 A B C) C)) ) ) ) ) ) ) ).
tt(d22_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k14_comput_1 A) = (k3_relat_1 (k6_funct_6 (k10_finseq_1 (k5_comput_1 3 1) (k5_comput_1 3 3))) A)) ) ) ).
tt(d22_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_convex4 A B C) = (a_3_0_convex4 A B C)) ) ) ) ) ) ) ).
tt(d22_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k17_decomp_1 A) = (a_1_11_decomp_1 A)) ) ) ).
tt(d22_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)))))) )  =>  ( (C = (k20_ens_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)) C D) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A D) B) (k2_cat_1 A (k3_graph_1 A D) B))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A (k4_graph_1 A D) B) (k2_cat_1 A (k3_graph_1 A D) B)) (k18_ens_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d22_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k19_facirc_1 A B C) = (k2_circcomb (k8_facirc_1 A B C k1_facirc_1) (k15_facirc_1 A B C))) ) ) ) ).
tt(d22_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  ((k18_fomodel0 A B C D) = (k3_relat_1 D (k2_funct_7 (k6_partfun1 A) B C))) ) ) ) ) ) ).
tt(d22_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))) k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))) k4_numbers)))) )  =>  ( (B = (k14_fomodel1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A)))) =>  ((k3_funct_2 (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))) k4_numbers B C) = (k13_fomodel1 A C)) ) ) ) ) ) ) ) ).
tt(d22_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ((k24_fomodel2 A B C D) = (k1_funct_1 (k1_funct_5 (k23_fomodel2 A C B)) D)) ) ) ) ) ) ) ) ) ).
tt(d22_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_funct_2 D (k33_fomodel2 A) (k33_fomodel2 A) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))))) )  =>  ( (E = (k32_fomodel3 A B C D))  <=>  ( ((k8_nat_1 (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)) E k6_numbers) = D)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)) E (k1_nat_1 F 1)) = (k31_fomodel3 A B C F (k8_nat_1 (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r5_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [E:$i] :  ( ((v13_fomodel1 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ( ((k1_xtuple_0 C) = (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) D) E)))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  ((v7_fsm_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (v6_fsm_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(d22_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k22_ftacell1 A B C D E) = (k48_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d22_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v14_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A E F)) &  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C E))) =>  (~  ( (I = (k1_funct_1 (k4_functor0 A B C D E) G))  &  ( (J = (k1_funct_1 (k4_functor0 A B C E F) H))  &  ((k1_funct_1 (k4_functor0 A B C D F) (k5_altcat_1 A D E F G H)) = (k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C E) (k3_functor0 A B C D) J I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~  ((k22_gate_1 A B C D E F) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) ) )  =>  ((k22_gate_1 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d22_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k22_gfacirc1 A B C) = (k8_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d22_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v7_glib_000 A) <=>  ((v3_glib_000 A) & (v5_glib_000 A)) ) ) ) ).
tt(d22_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((v1_abian C) |  ( (D = (k19_glib_001 A B C))  <=>  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B D) = (k1_funct_1 B C))  &  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = (k1_funct_1 B C)) )  => (r1_xxreal_0 E D)) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_abian C))  & (r1_xxreal_0 C (k3_finseq_1 B))) )  =>  ( (D = (k19_glib_001 A B C))  <=>  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k6_glib_000 A)) =>  ((k13_glib_003 A B C) = (k13_glib_000 A k4_glib_003 (k1_funct_4 (k7_glib_003 A) (k16_funcop_1 B C)))) )  &  ( (~ (r2_hidden B (k6_glib_000 A)))  =>  ((k13_glib_003 A B C) = A) ) ) ) ) ) ) ).
tt(d22_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k9_graph_1 A B))  <=>  (? [D:$i] :  ((v1_finset_1 D) &  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (u4_struct_0 A)) &  ((k1_funct_1 (u1_graph_1 A) E) = B) ) ) )  &  (C = (k5_card_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A C))  =>  ( (E = (k14_group_9 A B C D))  <=>  ((u1_struct_0 E) = (k7_relset_1 (u1_struct_0 B) (u1_struct_0 C) D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( (C = (k15_hahnban1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers C D) = (k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_vectsp_1 k1_complfld A k2_hahnban1 D))) ) ) ) ) ) ) ) ) ) ).
tt(d22_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k14_idea_1 k14_idea_1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) )  =>  ( (C = (k22_idea_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k12_idea_1 A (k11_idea_1 A D B) B)) ) ) ) ) ) ) ) ) ) ).
tt(d22_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r4_ideal_1 A B C) <=>  ((k11_ideal_1 A B C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d22_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A D C)) ) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  ( (D = (k4_incsp_1 A B C))  <=>  ((r3_incsp_1 A B D) & (r3_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v10_intpro_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C B)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B (k3_intpro_1 C D)) (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 B D))) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) B) A) &  ((r2_hidden (k3_intpro_1 (k4_intpro_1 B C) C) A) &  ((r2_hidden (k3_intpro_1 B (k3_intpro_1 C (k4_intpro_1 B C))) A) &  ((r2_hidden (k3_intpro_1 B (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 C (k5_intpro_1 B C)) A) &  ((r2_hidden (k3_intpro_1 (k3_intpro_1 B D) (k3_intpro_1 (k3_intpro_1 C D) (k3_intpro_1 (k5_intpro_1 B C) D))) A) &  ((r2_hidden (k3_intpro_1 k2_intpro_1 B) A) &  ((r2_hidden (k5_intpro_1 B (k3_intpro_1 B k2_intpro_1)) A) &  ((r2_hidden (k3_intpro_1 (k6_intpro_1 (k3_intpro_1 B C)) (k3_intpro_1 (k6_intpro_1 B) (k6_intpro_1 C))) A) &  ((r2_hidden (k3_intpro_1 (k6_intpro_1 B) B) A) &  ((r2_hidden (k3_intpro_1 (k6_intpro_1 B) (k6_intpro_1 (k6_intpro_1 B))) A) &  ( ( ((r2_hidden B A) & (r2_hidden (k3_intpro_1 B C) A))  => (r2_hidden C A))  &  ((r2_hidden B A) => (r2_hidden (k6_intpro_1 B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((k16_lattice3 A B) = (k15_lattice3 A (a_2_1_lattice3 A B))) ) ) ) ).
tt(d22_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v18_lattices B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A C D) & (r2_hidden D B))  => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ).
tt(d22_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  ( (E = (k21_lexbfs A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) &  ( (F = (k4_tarski (k1_funct_4 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B) (k16_funcop_1 C (k7_nat_d (k15_glib_000 A) D))) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B)))  &  (E = (k20_lexbfs A F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k17_lmod_7 A B C) = (g1_vectsp_1 A (u1_struct_0 (k13_lmod_7 A B C)) (u1_algstr_0 (k13_lmod_7 A B C)) (k14_lmod_7 A B C (k4_struct_0 B)) (k16_lmod_7 A B C))) ) ) ) ) ) ) ).
tt(d22_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v3_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (A = (k3_hilbert1 (k1_ltlaxio1 (k2_ltlaxio1 B)) (k2_ltlaxio1 (k1_ltlaxio1 B)))) ) ) ) ) ) ).
tt(d22_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A))))  =>  ((v3_margrel1 B A) <=>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  & (r2_hidden C (k9_xtuple_0 B)))  => (r2_hidden D (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ).
tt(d22_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k25_member_1 A B) = (k15_member_1 (k1_tarski B) A)) ) ) ) ) ).
tt(d22_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_metric_1 A B C D) <=>  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ((k2_metric_1 A B D) = (k7_real_1 (k2_metric_1 A B C) (k2_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_metric_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers)))) )  =>  ( (A = k22_metric_3)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ( ( (H = (k4_domain_1 k1_numbers k1_numbers k1_numbers B D F))  &  (I = (k4_domain_1 k1_numbers k1_numbers k1_numbers C E G)) )  =>  ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) A H I) = (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 B C)) (k5_square_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 D E))) (k5_square_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k24_mmlquery A B) = (k1_card_1 (a_2_0_mmlquery A B))) ) ) ) ).
tt(d22_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_1 A) | (v7_modelc_1 A))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v4_modelc_1 A) =>  ( (B = (k15_modelc_1 A))  <=>  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  ((k8_modelc_1 B C) = A) ) ) ) )  &  ( (~ (v4_modelc_1 A))  =>  ( (B = (k15_modelc_1 A))  <=>  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  ((k11_modelc_1 B C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_modelc_2 A B) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ((r1_xxreal_0 1 C) &  ( ((k3_finseq_1 D) = C)  &  ( ((k1_funct_1 D 1) = A)  &  ( ((k1_funct_1 D C) = B)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 C E))  &  (! [F:$i] :  ( ((v1_modelc_2 F) & (m2_finseq_1 F k5_numbers))  =>  (! [G:$i] :  ( ((v1_modelc_2 G) & (m2_finseq_1 G k5_numbers))  =>  (~  ( ((k1_funct_1 D E) = F)  &  ( ((k1_funct_1 D (k1_nat_1 E 1)) = G)  & (r1_modelc_2 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((k14_modelc_3 A B) = (k2_xboole_0 (k4_subset_1 (k1_modelc_3 A) (u1_modelc_3 A B) (u2_modelc_3 A B)) (k48_modelc_2 (k13_modelc_3 A (u3_modelc_3 A B))))) ) ) ) ) ).
tt(d22_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((l4_algstr_0 B) =>  ((m1_monoid_0 B A) <=>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ).
tt(d22_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k17_msualg_2 A B) = (g3_lattices (k14_msualg_2 A B) (k15_msualg_2 A B) (k16_msualg_2 A B))) ) ) ) ) ).
tt(d22_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r18_ncfcont1 A B C) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C E) (k7_partfun1 k2_numbers C F))) (k8_real_1 D (k1_normsp_0 A (k5_algstr_0 A E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v12_oposet_1 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (u1_robbins1 A)) & (r2_oposet_1 A B)) ) ) ) ) ) ).
tt(d22_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B)))  =>  ( (C = (k20_osafree A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (a_3_2_osafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d22_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v12_osalg_1 D A) & (l3_msualg_1 D A)) )  =>  ( (D = (k6_osalg_1 A B C))  <=>  ((r8_pboole (u1_struct_0 A) (u3_msualg_1 A D) (k3_osalg_1 A B)) &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k5_msualg_1 A E D) = (k8_funcop_1 B (k3_msualg_1 A E D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k16_osalg_4 A B C))) =>  ( (D = (k18_osalg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B C)) E) (k1_funct_1 (u3_msualg_1 A B) E) (k6_osalg_4 A B C E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k16_osalg_4 A B C)) D E) (k17_osalg_4 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((v13_pcs_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_pcs_0 A B D) &  ((r1_orders_2 A C B) & (r1_orders_2 A E D)) )  => (r1_pcs_0 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k4_card_3 (k12_pralg_1 A B))))) =>  ( (C = (k4_pencil_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B)))  &  ( (D = (k4_card_3 E))  &  (? [F:$i] :  ((m1_subset_1 F A) & (m1_subset_1 (k1_funct_1 E F) (u1_pre_topc (k1_pencil_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k25_polyform A B) = (k2_struct_0 (k24_polyform A B))) ) ) ) ) ).
tt(d22_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k21_pscomp_1 A) = (k19_euclid (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k15_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k15_pscomp_1 A))) (k7_pscomp_1 A))) ) ) ).
tt(d22_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k6_qc_lang1 A)) =>  ( (C = (k16_qc_lang1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E (k2_qc_lang1 A)))  &  (? [F:$i] :  ((m2_subset_1 F (k6_qc_lang1 A) (k8_qc_lang1 A D)) &  ( (C = F)  &  (B = (k10_qc_lang1 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( (C = (k15_qc_lang2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) &  ( (E = D)  & (r2_qc_lang2 A E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  =>  ((k4_quantal1 A) = (k1_quantal1 A (k3_quantal1 A) (k3_quantal1 A))) ) ) ).
tt(d22_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k30_quaterni A) = (k26_quaterni (k26_quaterni (k23_quaterni (k17_quaterni A) (k25_quaterni (k1_real_1 (k18_quaterni A)) k1_xcmplx_0)) (k25_quaterni (k1_real_1 (k19_quaterni A)) k11_quaterni)) (k25_quaterni (k1_real_1 (k20_quaterni A)) k12_quaterni))) ) ) ).
tt(d22_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  ((r1_quofield A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v3_quofield C A B)) ) ) ) ) ) ) ).
tt(d22_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  ((r6_rewrite1 A B C) => (r5_rewrite1 A B C)) ) ) ) ) ) ).
tt(d22_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k17_robbins1 A B) = (k5_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k13_robbins1 A B) (k15_robbins1 A B))) B) (k3_robbins1 A (k15_robbins1 A B)))) ) ) ) ) ).
tt(d22_scmpds_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ( ( ((k2_compos_0 k1_scmpds_i A) = 14)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 B (k2_scmpds_1 B (k4_scmpds_i A)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 2)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k5_scmpds_i A) (k6_scmpds_i A)) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 3)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k5_scmpds_i A) (k6_scmpds_i A)) (k5_ami_2 B)) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 1)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k3_scmpds_i A) (k1_funct_1 B (k1_scmpds_1 B (k3_scmpds_i A) k14_scmpds_i))) (k4_scmpds_1 B (k1_scmpds_1 B (k3_scmpds_i A) k15_scmpds_i)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 4)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 B (k14_funcop_1 (k1_funct_1 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A))) k6_numbers (k1_ordinal1 (k5_ami_2 B)) (k2_scmpds_1 B (k9_scmpds_i A))))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 5)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 B (k5_xxreal_0 (k1_funct_1 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A))) k6_numbers (k1_ordinal1 (k5_ami_2 B)) (k2_scmpds_1 B (k9_scmpds_i A))))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 6)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 B (k5_xxreal_0 k6_numbers (k1_funct_1 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A))) (k1_ordinal1 (k5_ami_2 B)) (k2_scmpds_1 B (k9_scmpds_i A))))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 7)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A)) (k9_scmpds_i A)) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 8)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A)) (k2_xcmplx_0 (k1_funct_1 B (k1_scmpds_1 B (k7_scmpds_i A) (k8_scmpds_i A))) (k9_scmpds_i A))) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 9)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A)) (k2_xcmplx_0 (k1_funct_1 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A))) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A))))) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 10)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A)) (k6_xcmplx_0 (k1_funct_1 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A))) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A))))) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 11)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A)) (k3_xcmplx_0 (k1_funct_1 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A))) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A))))) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 13)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A)) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A)))) (k1_ordinal1 (k5_ami_2 B)))) )  &  ( ( ((k2_compos_0 k1_scmpds_i A) = 12)  =>  ((k5_scmpds_1 A B) = (k6_ami_2 (k7_ami_2 (k7_ami_2 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A)) (k5_int_1 (k1_funct_1 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A))) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A))))) (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A)) (k6_int_1 (k1_funct_1 B (k1_scmpds_1 B (k10_scmpds_i A) (k12_scmpds_i A))) (k1_funct_1 B (k1_scmpds_1 B (k11_scmpds_i A) (k13_scmpds_i A))))) (k1_ordinal1 (k5_ami_2 B)))) )  &  (~  ( (~  ((k2_compos_0 k1_scmpds_i A) = 14) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 2) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 3) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 1) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 4) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 5) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 6) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 7) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 8) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 9) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 10) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 11) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 13) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 12) )  &  (~  ((k5_scmpds_1 A B) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k10_scmyciel A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v10_scmyciel C A) & (m1_eqrel_1 C (k3_tarski A))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v10_scmyciel C A) & (m1_eqrel_1 C (k3_tarski A))) )  => (r1_xxreal_0 B (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(d22_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k24_sin_cos)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k4_series_1 (k4_sin_cos B))) ) ) ) ) ) ).
tt(d22_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  ((r4_stacks_1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  & (r3_stacks_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d22_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  ((v3_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) &  ((k19_substut1 A (k22_substut1 A B)) = (k1_funct_1 (k15_substut1 A) (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k15_qc_lang1 A (k23_substut1 A B) (k18_substut1 A (k22_substut1 A B))) C))) ) ) ) ) ) ) ) ).
tt(d22_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  ((k21_turing_1 A B) = (k2_xboole_0 (k2_zfmisc_1 (u2_turing_1 A) (k6_domain_1 (u2_turing_1 B) (u4_turing_1 B))) (k2_zfmisc_1 (k6_domain_1 (u2_turing_1 A) (u5_turing_1 A)) (u2_turing_1 B)))) ) ) ) ) ).
tt(d22_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k23_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C)) D))) ) ) ) ) ) ) ) ) ) ).
tt(d22_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v15_waybel_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C B) & (r1_lattice3 A B C)) ) ) ) ) ) ) ) ).
tt(d22_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_waybel_1 A B) = (k6_waybel_1 A B (k3_yellow_0 A))) ) ) ) ) ).
tt(d22_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((r1_waybel_4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F B) &  ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v6_yellow_6 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C (k6_yellow_6 A)) &  ( (~ (r2_hidden (k4_tarski C D) B))  &  (! [E:$i] :  ((m2_yellow_6 E A C) =>  (~  ((r2_hidden E (k6_yellow_6 A)) &  (! [F:$i] :  ((m2_yellow_6 F A E) =>  (~ (r2_hidden (k4_tarski F D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d22_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) <=>  (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k12_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d22_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A))))) )  =>  ( (B = (k11_zmodul01 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k8_zmodul01 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_zmodul01 A)) =>  (! [E:$i] :  ((m1_zmodul01 E A) =>  (! [F:$i] :  ((m1_zmodul01 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k8_zmodul01 A) B C D) = (k7_zmodul01 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  ((k10_abcmiz_0 A B) = (k3_funct_2 (u1_abcmiz_0 A) (u1_struct_0 A) (u4_abcmiz_0 A) B)) ) ) ) ) ).
tt(d23_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((k26_abcmiz_1 A) = (k22_abcmiz_1 (k24_abcmiz_1 A))) ) ) ).
tt(d23_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ((m3_abcmiz_1 C A) =>  ((r3_abcmiz_a A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((r1_tarski (k63_abcmiz_1 A D (k41_abcmiz_1 A C)) (k41_abcmiz_1 A B)) &  ((k62_abcmiz_1 A D (k42_abcmiz_1 A C)) = (k42_abcmiz_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v19_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v16_algstr_0 B A)) ) ) ) ) ).
tt(d23_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k11_armstrng A B) = (a_2_6_armstrng A B)) ) ) ) ).
tt(d23_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v16_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B D) D) (k1_bcialg_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d23_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v5_bilinear D A B C) <=>  (~  ((k10_bilinear A B C D) = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) )  =>  ( (A = k47_binop_2)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_binop_1 A B C) = (k23_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d23_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k8_cat_1 A B C D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d23_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k21_cat_4 A B C) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u7_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d23_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) &  ((v7_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v8_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v9_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))))) ) ) ) )  =>  ( (C = (k12_closure2 A B))  <=>  (! [D:$i] :  ((m1_closure2 D (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) => (r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) C D) (k11_closure2 A B D))) ) ) ) ) ) ) ) ) ).
tt(d23_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((k15_cohsp_1 A B) = (a_2_0_cohsp_1 A B)) ) ) ) ) ).
tt(d23_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  ((k23_coh_sp A B) = (k4_tarski (k4_tarski B B) (k6_partfun1 (k17_coh_sp A B)))) ) ) ) ).
tt(d23_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  ((k7_compos_1 A B C) = (k1_funct_4 (k63_valued_1 B) (k6_compos_1 A C (k7_nat_d (k5_card_1 B) 1)))) ) ) ) ) ) ) ).
tt(d23_comput_1,ax, (k15_comput_1 = (k7_comput_1 (k5_comput_1 1 1) (k4_comput_1 3 3) 2)) ).
tt(d23_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_convex4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (E = F)  &  ( (~ (r1_xxreal_0 F k1_xboole_0))  &  (~ (r1_xxreal_0 1 F)) ) ) ) ) )  | (r2_hidden (k1_algstr_0 A (k1_clvect_1 A C E) (k1_clvect_1 A D (k6_xcmplx_0 k6_complex1 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k18_decomp_1 A) = (a_1_12_decomp_1 A)) ) ) ).
tt(d23_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C)))))) )  =>  ( (D = (k21_ens_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r2_hidden E (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C))) =>  ((k1_funct_1 D E) = (k1_cat_1 A B (k1_cat_1 A E C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k20_facirc_1 A B C) = (k3_circcomb (k8_facirc_1 A B C k1_facirc_1) (k15_facirc_1 A B C) (k13_facirc_1 A B C) (k18_facirc_1 A B C))) ) ) ) ).
tt(d23_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_finseq_2 A) (k3_finseq_2 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A))))) )  =>  ( (D = (k20_fomodel0 A B C))  <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ((k1_funct_1 D E) = (k19_fomodel0 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((v11_fomodel1 A) <=>  ( (~ (v1_finset_1 (k2_fomodel1 A)))  &  ((k1_funct_1 (u1_fomodel1 A) (k7_fomodel1 A)) = (k4_xcmplx_0 2)) ) ) ) ) ).
tt(d23_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) =>  ( (C = (k25_fomodel2 A B))  <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 A D)) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (B = F)  =>  (C = (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k24_fomodel2 A D F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r6_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v5_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  &  (? [E:$i] :  ( ((v3_card_1 E (k1_int_2 (k19_fomodel1 B D))) & (m2_subset_1 E (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k35_fomodel1 B))))  &  (? [F:$i] :  ( ((v3_card_1 F (k1_int_2 (k19_fomodel1 B D))) & (m2_subset_1 F (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k35_fomodel1 B))))  &  ((v6_fomodel1 D B) &  ( ((k1_xtuple_0 C) = (a_4_0_fomodel4 B D E F))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) (k1_fomodel3 B D E)) (k1_fomodel3 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  ((k12_fsm_1 A B C) = (a_3_0_fsm_1 A B C)) ) ) ) ) ) ) ).
tt(d23_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k23_ftacell1 A B C D E) = (k45_gfacirc1 (k48_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d23_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v10_functor0 C A B) & (l2_functor0 C A B)) )  =>  ((v13_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A E F)) =>  ((k6_functor0 A B C D F (k5_altcat_1 A D E F G H)) = (k5_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E) (k3_functor0 A B C F) (k6_functor0 A B C D E G) (k6_functor0 A B C E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) & (v1_xboole_0 F)) ) ) ) ) )  =>  ((k23_gate_1 A B C D E F) = (k1_gate_1 k1_xboole_0)) )  &  (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  (~  ((k23_gate_1 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k23_gfacirc1 A B C) = (k10_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d23_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m3_glib_001 D A) =>  ((r1_glib_001 A B C D) <=>  ( ((k3_glib_001 A D) = B)  &  ((k4_glib_001 A D) = C) ) ) ) ) ) ) ) ) ).
tt(d23_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((k14_glib_003 A) = (k9_xtuple_0 (k7_glib_003 A))) ) ) ).
tt(d23_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_graph_1 A B) = (k2_nat_1 (k8_graph_1 A B) (k9_graph_1 A B))) ) ) ) ) ).
tt(d23_grcat_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_grcat_1 A B) <=>  (? [C:$i] :  (? [D:$i] :  (? [E:$i] :  (? [F:$i] :  ( (A = (k6_xtuple_0 C D E F))  &  (? [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v8_algstr_0 G) &  ((v13_algstr_0 G) &  ((v3_rlvect_1 G) &  ((v4_rlvect_1 G) & (l2_algstr_0 G)) ) ) ) )  &  ( (B = G)  &  ( (C = (u1_struct_0 G))  &  ( (D = (u1_algstr_0 G))  &  ( (E = (k5_vectsp_1 G))  &  (F = (k4_struct_0 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((k15_group_9 A B C) = (u1_struct_0 C)) ) ) ) ) ) ).
tt(d23_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  ( (C = (k16_hahnban1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) C D) = (k1_hahnban1 (k3_funct_2 (u1_struct_0 A) k1_numbers (k13_hahnban1 A B) D) (k1_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers (k15_hahnban1 A (k13_hahnban1 A B)) D)))) ) ) ) ) ) ) ) ) ) ).
tt(d23_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k16_ideal_1 A B C) = (a_3_5_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(d23_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v3_lattices B) & (l3_lattices B))  =>  ( (B = (k21_interva1 A))  <=>  ( ((u1_struct_0 B) = (k18_interva1 A))  &  (! [C:$i] :  ((m1_subset_1 C (k18_interva1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k18_interva1 A)) =>  (! [E:$i] :  ((m2_interva1 E A) =>  (! [F:$i] :  ((m2_interva1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k1_binop_1 (u2_lattices B) C D) = (k16_interva1 A E F))  &  ((k1_binop_1 (u1_lattices B) C D) = (k17_interva1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_intpro_1)) =>  ( (B = (k13_intpro_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_intpro_1)) =>  ( ((v10_intpro_1 D) & (r1_tarski A D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v19_lattices B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A C D) & (r2_hidden C B))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(d23_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  ( ((r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)))) =>  ((k22_lexbfs A B) = B) )  &  ( (~ (r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)))))  =>  ((k22_lexbfs A B) = (k21_lexbfs A B (k19_lexbfs A B) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B))))) ) ) ) ) ) ) ).
tt(d23_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k18_lmod_7 A B C D) = (k14_lmod_7 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d23_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v4_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (A = (k3_hilbert1 (k2_ltlaxio1 (k1_ltlaxio1 B)) (k1_ltlaxio1 (k2_ltlaxio1 B)))) ) ) ) ) ) ).
tt(d23_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)) =>  ((v4_margrel1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A))))  =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (D = (k1_funct_1 B C)) )  => (v2_margrel1 D)) ) ) ) ) ) ) ) ) ).
tt(d23_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k26_member_1 A B) = (k14_member_1 A (k1_tarski B))) ) ) ) ) ).
tt(d23_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k14_metric_1 A B C) = (a_3_6_metric_1 A B C)) ) ) ) ) ) ) ).
tt(d23_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k25_mmlquery A))  <=>  ( (! [C:$i] : (r1_xxreal_0 (k24_mmlquery A C) B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] : (r1_xxreal_0 (k24_mmlquery A D) C))  => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ).
tt(d23_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_1 A) | (v7_modelc_1 A))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v4_modelc_1 A) =>  ( (B = (k16_modelc_1 A))  <=>  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  ((k8_modelc_1 C B) = A) ) ) ) )  &  ( (~ (v4_modelc_1 A))  =>  ( (B = (k16_modelc_1 A))  <=>  (? [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  &  ((k11_modelc_1 C B) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_modelc_2 A B) <=>  ((r2_modelc_2 A B) &  (~  (A = B) ) ) ) ) ) ) ) ).
tt(d23_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((l3_algstr_0 B) =>  ((m2_monoid_0 B A) <=> (r1_tarski (u2_algstr_0 B) (u2_algstr_0 A))) ) ) ) ) ).
tt(d23_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) C))) =>  ( (D = (k21_osafree A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F (k1_funct_1 B C)) &  (E = (k1_trees_4 (k4_tarski F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  ((k7_osalg_1 A) = (k8_eqrel_1 (u4_struct_0 A) (u1_osalg_1 A))) ) ) ).
tt(d23_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r1_msualg_3 A B C D) & (v1_osalg_3 D A))  =>  ((k19_osalg_4 A B C D) = (k17_msualg_4 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d23_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  ((k5_pencil_1 A B) = (g1_pre_topc (k4_card_3 (k12_pralg_1 A B)) (k4_pencil_1 A B))) ) ) ) ) ).
tt(d23_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k22_pscomp_1 A) = (k19_euclid (k8_pscomp_1 A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k16_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k16_pscomp_1 A))))) ) ) ).
tt(d23_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_qc_lang1 A)) =>  ( (C = (k17_qc_lang1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A D)) &  (? [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F (k2_qc_lang1 A)))  &  ( (C = F)  &  (B = (k10_qc_lang1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_quantal1 A B) = (k1_quantal1 A B (k3_quantal1 A))) ) ) ) ) ).
tt(d23_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k32_quaterni A) = (k7_square_1 (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A))))) ) ) ).
tt(d23_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  ((r2_quofield A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v4_quofield C A B)) ) ) ) ) ) ) ).
tt(d23_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) => (r5_rewrite1 A B C)) ) ) ) ) ) ).
tt(d23_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) (k10_ringcat1 A)) (k10_ringcat1 A)))))  =>  ( (B = (k16_ringcat1 A))  <=>  ( (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  (! [D:$i] :  ((m3_ringcat1 D (k10_ringcat1 A)) =>  ((r2_hidden (k4_tarski C D) (k1_relset_1 (k2_zfmisc_1 (k10_ringcat1 A) (k10_ringcat1 A)) B)) <=>  ((k11_ringcat1 A C) = (k12_ringcat1 A D)) ) ) ) ) )  &  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  (! [D:$i] :  ((m3_ringcat1 D (k10_ringcat1 A)) =>  ((r2_hidden (k4_tarski C D) (k1_relset_1 (k2_zfmisc_1 (k10_ringcat1 A) (k10_ringcat1 A)) B)) =>  ((k1_binop_1 B C D) = (k6_ringcat1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ((v10_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattices A B C) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) (k3_robbins1 A C)))) ) ) ) ) ) ) ) ).
tt(d23_scmpds_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_scmpds_i (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_scmpds_i (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))))) )  =>  ( (A = k6_scmpds_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_scmpds_i) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ((k1_funct_1 (k3_funct_2 k1_scmpds_i (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) A B) C) = (k5_scmpds_1 B C)) ) ) ) ) ) ) ) ).
tt(d23_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k25_sin_cos A) = (k1_seq_1 k24_sin_cos A)) ) ) ).
tt(d23_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  ((v3_substut1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((m1_substut1 C A B) <=>  ((k19_substut1 A (k22_substut1 A B)) = (k1_funct_1 (k15_substut1 A) (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k15_qc_lang1 A (k23_substut1 A B) (k18_substut1 A (k22_substut1 A B))) C))) ) ) ) ) ) ) ) ) ).
tt(d23_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) =>  ((k22_turing_1 A B C) = (k4_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (k1_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (u4_turing_1 B)) (k2_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (k3_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C))) ) ) ) ) ) ) ).
tt(d23_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k24_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C)) (k9_margrel1 D)))) ) ) ) ) ) ) ) ) ) ).
tt(d23_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  ((k7_waybel_0 A) = (a_1_0_waybel_0 A)) ) ) ).
tt(d23_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_waybel_1 A B C) <=>  ( ((k10_lattice3 A B C) = (k4_yellow_0 A))  &  ((k11_lattice3 A B C) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ).
tt(d23_waybel_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_waybel_4 A B C) <=>  ((r2_hidden B A) &  (! [D:$i] :  (~  ((r2_hidden D A) &  ( (~  (D = B) )  & (r2_hidden (k4_tarski B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d23_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v7_yellow_6 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) =>  (! [E:$i] :  ((m3_yellow_6 E (u1_struct_0 C) A) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) => (r2_hidden (k4_tarski (k7_yellow_6 (u1_struct_0 C) A E F) (k2_waybel_0 A C F)) B)) )  => (r2_hidden (k4_tarski (k8_yellow_6 A C E) D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d23_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v11_zf_lang A) <=>  (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k13_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(d23_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k12_zmodul01 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_xxreal_0 k6_numbers C) =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) B C D) = (k1_binop_1 (k3_binom A) C D)) )  &  ( (~ (r1_xxreal_0 k6_numbers C))  =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) B C D) = (k1_binop_1 (k3_binom A) (k4_xcmplx_0 C) (k4_algstr_0 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_abcmiz_1,ax, (! [A:$i] :  ( ((v1_msualg_1 A) &  ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ( (A = k27_abcmiz_1)  <=>  ( ((u4_struct_0 A) = (k2_xboole_0 (k2_tarski k9_abcmiz_1 k10_abcmiz_1) k20_abcmiz_1))  &  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v2_abcmiz_1 B A) =>  ( ((k3_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u2_msualg_1 A) B) = (k1_xtuple_0 B))  &  ((k5_card_1 (k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_msualg_1 A) B)) = (k1_card_1 (k1_xtuple_0 (k2_xtuple_0 B)))) ) ) ) ) ) ) ) ) ).
tt(d24_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((r4_abcmiz_a A B C D) <=>  ((k56_abcmiz_1 A D B) = (k56_abcmiz_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d24_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v20_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v17_algstr_0 B A)) ) ) ) ) ).
tt(d24_aofa_i00,ax, (k26_aofa_i00 = (k2_zfmisc_1 (k9_funct_2 (k9_funct_2 k5_numbers k4_numbers) k5_numbers) (k9_funct_2 (k9_funct_2 k5_numbers k4_numbers) k4_numbers))) ).
tt(d24_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ( ((v6_armstrng C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ( (C = (k12_armstrng A B))  <=>  ((r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B D) & (v6_armstrng D A))  => (r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v17_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(d24_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v6_bilinear D A B C) <=>  (~  ((k11_bilinear A B C D) = (k6_domain_1 (u1_struct_0 C) (k4_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) )  =>  ( (A = k48_binop_2)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_binop_1 A B C) = (k24_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d24_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k10_cat_1 A) = (k6_partfun1 (u4_struct_0 A))) ) ) ).
tt(d24_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k22_cat_4 A B C) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u8_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d24_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((k16_cohsp_1 A B) = (k2_xboole_0 (a_1_1_cohsp_1 A) (a_1_2_cohsp_1 B))) ) ) ) ) ).
tt(d24_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  ( ((k22_coh_sp A B) = (k21_coh_sp A C))  =>  ((k24_coh_sp A B C) = (k4_tarski (k4_tarski (k21_coh_sp A B) (k22_coh_sp A C)) (k3_relat_1 (k2_xtuple_0 B) (k2_xtuple_0 C)))) ) ) ) ) ) ) ).
tt(d24_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) )  =>  ((k10_compos_1 A B) = (k1_ordinal4 B (k4_compos_1 A))) ) ) ) ) ).
tt(d24_comput_1,ax, (k16_comput_1 = (k7_comput_1 (k3_comput_1 1 k6_numbers) (k14_comput_1 k15_comput_1) 2)) ).
tt(d24_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ((v3_convex4 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v2_funct_1 C) &  ( ((k2_relset_1 (u1_struct_0 A) C) = (k1_convex4 A B))  &  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  ( ((k18_rvsum_1 D) = 1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((k1_funct_1 D E) = (k1_funct_1 B (k1_funct_1 C E)))  & (r1_xxreal_0 k1_xboole_0 (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k19_decomp_1 A) = (a_1_13_decomp_1 A)) ) ) ).
tt(d24_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u4_struct_0 (k8_cat_2 A A)) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k8_cat_2 A A)) (k2_ens_1 (k16_ens_1 A)))))) )  =>  ( (B = (k22_ens_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 (k8_cat_2 A A)) (k2_ens_1 (k16_ens_1 A)) B (k10_cat_2 A A C D)) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A C) (k3_graph_1 A D)) (k2_cat_1 A (k3_graph_1 A C) (k4_graph_1 A D)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A (k4_graph_1 A C) (k3_graph_1 A D)) (k2_cat_1 A (k3_graph_1 A C) (k4_graph_1 A D))) (k21_ens_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d24_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((k21_fomodel0 A) = (k3_tarski (a_1_3_fomodel0 A))) ) ) ).
tt(d24_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  ((k19_fomodel1 A B) = (k1_funct_1 (u1_fomodel1 A) B)) ) ) ) ) ).
tt(d24_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v3_fomodel2 C A B) <=> (r2_hidden C (k25_fomodel2 A B))) ) ) ) ) ) ) ).
tt(d24_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k34_fomodel3 A B C) = (k1_funct_4 (k3_fomodel2 (k33_fomodel2 A)) (k33_fomodel3 A B C))) ) ) ) ) ) ) ).
tt(d24_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r7_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v7_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  &  (? [E:$i] :  ( ((v3_card_1 E (k1_int_2 (k19_fomodel1 B D))) & (m2_subset_1 E (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k35_fomodel1 B))))  &  (? [F:$i] :  ( ((v3_card_1 F (k1_int_2 (k19_fomodel1 B D))) & (m2_subset_1 F (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k35_fomodel1 B))))  &  ( ((k1_xtuple_0 C) = (k2_xboole_0 (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k1_fomodel3 B D E)) (a_4_1_fomodel4 B D E F)))  &  ((k2_xtuple_0 C) = (k1_fomodel3 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_fsm_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ((v2_fsm_1 E A B) & (l2_fsm_1 E A B))  =>  ( (E = (k13_fsm_1 A B C D))  <=>  ( ((u1_struct_0 E) = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D)))  &  ( ((u1_fsm_1 A E) = (k1_funct_4 (u1_fsm_1 A C) (u1_fsm_1 A D)))  &  ( ((u3_fsm_1 A B E) = (k1_funct_4 (u3_fsm_1 A B C) (u3_fsm_1 A B D)))  &  ((u2_fsm_1 A E) = (u2_fsm_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k24_ftacell1 A B C D E) = (k48_gfacirc1 (k48_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d24_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v11_functor0 C A B) & (l2_functor0 C A B)) )  =>  ((v14_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A E F)) =>  ((k8_functor0 A B C D F (k5_altcat_1 A D E F G H)) = (k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C E) (k3_functor0 A B C D) (k8_functor0 A B C E F H) (k8_functor0 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) ) )  =>  ((k24_gate_1 A B C D E F) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~  ((k24_gate_1 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k24_gfacirc1 A B C) = (k9_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d24_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k14_glib_000 A) = (k1_card_1 (k6_glib_000 A))) ) ) ).
tt(d24_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_glib_001 B A) <=>  ((k3_glib_001 A B) = (k4_glib_001 A B)) ) ) ) ) ) ).
tt(d24_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ((r4_graph_1 A B) <=> (m3_graph_1 A B)) ) ) ) ) ).
tt(d24_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( (B = (k17_grcat_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((r2_hidden D A) & (r1_grcat_1 D C)) ) ) ) ) ) ) ) ).
tt(d24_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((k16_group_9 A B C D) = (k2_group_2 B (k15_group_9 A B C) (k15_group_9 A B D))) ) ) ) ) ) ) ) ).
tt(d24_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k17_ideal_1 A B) = (a_2_1_ideal_1 A B)) ) ) ) ) ).
tt(d24_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k22_interva1 A) = (k4_tarski k1_xboole_0 k1_xboole_0)) ) ) ).
tt(d24_intpro_1,ax, (k14_intpro_1 = (k13_intpro_1 (k1_subset_1 k1_intpro_1))) ).
tt(d24_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v20_lattices B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k4_lattices A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d24_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v5_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k3_hilbert1 (k2_ltlaxio1 (k3_hilbert1 B C)) (k3_hilbert1 (k2_ltlaxio1 B) (k2_ltlaxio1 C)))) ) ) ) ) ) ) ) ).
tt(d24_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)) =>  ((v5_margrel1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A))))  =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (D = (k1_funct_1 B C)) )  => (v3_margrel1 D A)) ) ) ) ) ) ) ) ) ).
tt(d24_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k27_member_1 A B) = (k15_member_1 A (k1_tarski B))) ) ) ) ) ).
tt(d24_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k15_metric_1 A B C) = (k2_xboole_0 (a_3_6_metric_1 A B C) (k2_tarski B C))) ) ) ) ) ) ) ).
tt(d24_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  (A = k1_xboole_0) )  =>  ((k26_mmlquery A B C) = (a_3_3_mmlquery A B C)) ) ) ) ) ) ) ).
tt(d24_modelc_1,ax, (! [A:$i] :  ( ((r2_hidden A k12_modelc_1) =>  ((k17_modelc_1 A) = A) )  &  ( (~ (r2_hidden A k12_modelc_1))  =>  ((k17_modelc_1 A) = (k6_modelc_1 k6_numbers)) ) ) ) ).
tt(d24_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (B = (k13_modelc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  &  ( (D = C)  & (r2_modelc_2 D A)) ) ) ) ) ) ) ) ) ).
tt(d24_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k16_modelc_3 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden (k1_funct_1 C E) B) =>  ((k1_seq_1 D E) = (k3_finseq_1 (k14_modelc_2 (k1_funct_1 C E)))) )  &  ( (~ (r2_hidden (k1_funct_1 C E) B))  =>  ((k1_seq_1 D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((l4_algstr_0 B) =>  ((m3_monoid_0 B A) <=>  ((r1_tarski (u2_algstr_0 B) (u2_algstr_0 A)) &  (! [C:$i] :  ((l4_algstr_0 C) =>  ( (A = C)  =>  ((k5_struct_0 B) = (k5_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(d24_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B))) =>  ( (C = (k22_osafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k21_osafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d24_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k8_osalg_1 A B) = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (u1_osalg_1 A) B)) ) ) ) ) ).
tt(d24_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_msualg_3 A B C D) & (v1_osalg_3 D A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E))))) )  =>  ( (F = (k20_osalg_4 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((k1_funct_1 F (k8_osalg_4 A B (k19_osalg_4 A B C D) E G)) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d24_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k23_pscomp_1 A) = (k19_euclid (k8_pscomp_1 A) (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k16_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k16_pscomp_1 A))))) ) ) ).
tt(d24_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( (C = (k18_qc_lang1 A B))  <=>  (B = (k13_qc_lang1 A C)) ) ) ) ) ) ) ) ) ).
tt(d24_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k21_quofield A B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ).
tt(d24_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v9_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski B D) A))  => (r5_rewrite1 A C D)) ) ) ) ) ) ) ).
tt(d24_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k17_ringcat1 A) = (g1_cat_1 (k9_ringcat1 A) (k10_ringcat1 (k9_ringcat1 A)) (k14_ringcat1 (k9_ringcat1 A)) (k15_ringcat1 (k9_ringcat1 A)) (k16_ringcat1 (k9_ringcat1 A)))) ) ) ).
tt(d24_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v12_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k11_scmyciel A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v9_scmyciel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_tarski A)))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v9_scmyciel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_tarski A)))) )  => (r1_xxreal_0 (k5_card_1 C) B)) ) ) ) ) ) ) ) ).
tt(d24_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k27_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers B C) = (k13_complex1 (k1_newton A (k2_nat_1 C 1)) (k3_newton (k2_nat_1 C 2)))) ) ) ) ) ) ) ) ).
tt(d24_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) =>  ((k24_substut1 A B C) = (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k15_qc_lang1 A (k23_substut1 A B) (k18_substut1 A (k22_substut1 A B))) C)) ) ) ) ) ) ) ) ).
tt(d24_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) =>  ((k23_turing_1 A B C) = (k4_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) (k1_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C)) (k2_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (k3_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C))) ) ) ) ) ) ) ).
tt(d24_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k25_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k1_binarith (k1_binarith B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d24_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  ((k8_waybel_0 A) = (a_1_1_waybel_0 A)) ) ) ).
tt(d24_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v10_waybel_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r6_waybel_1 A B C)) ) ) ) ) ) ) ).
tt(d24_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_4 A B C) <=> (r2_waybel_4 B C (u1_orders_2 A))) ) ) ) ) ) ).
tt(d24_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  (! [C:$i] :  ( ((v1_pre_topc C) & (l1_pre_topc C))  =>  ( (C = (k13_yellow_6 A B))  <=>  ( ((u1_struct_0 C) = (u1_struct_0 A))  &  ((u1_pre_topc C) = (a_2_1_yellow_6 A B)) ) ) ) ) ) ) ) ) ).
tt(d24_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((k14_zf_lang A B C) = (k8_zf_lang A (k8_zf_lang B C))) ) ) ) ) ) ) ).
tt(d25_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ( (B = (k28_abcmiz_1 A))  <=>  ( ((k1_funct_1 B k6_abcmiz_1) = k1_xboole_0)  &  ( ((k1_funct_1 B k7_abcmiz_1) = k1_xboole_0)  &  ((k1_funct_1 B k8_abcmiz_1) = k2_abcmiz_1) ) ) ) ) ) ) ) ).
tt(d25_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r5_abcmiz_a A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (r4_abcmiz_a A B C D)) ) ) ) ) ) ) ) ) ).
tt(d25_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  ((v11_aofa_000 A) <=> (m1_freealg (k18_aofa_000 A) A)) ) ) ).
tt(d25_aofa_i00,ax, (! [A:$i] :  ((m1_aofa_000 A (k7_freealg k19_aofa_000 k26_aofa_i00) (k9_funct_2 k5_numbers k4_numbers) (k1_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k6_numbers k6_numbers)) =>  ((m4_aofa_i00 A) <=>  (! [B:$i] :  ((m2_funct_2 B k5_numbers k4_numbers (k9_funct_2 k5_numbers k4_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C (k9_funct_2 k5_numbers k4_numbers) k5_numbers (k9_funct_2 (k9_funct_2 k5_numbers k4_numbers) k5_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D (k9_funct_2 k5_numbers k4_numbers) k4_numbers (k9_funct_2 (k9_funct_2 k5_numbers k4_numbers) k4_numbers)) =>  ((k1_binop_1 A B (k1_trees_4 (k4_tarski C D))) = (k15_funct_7 k5_numbers k4_numbers B (k21_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k5_numbers C B) (k21_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k4_numbers D B))) ) ) ) ) ) ) ) ) ) ).
tt(d25_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r5_armstrng A B C) <=>  ((r1_tarski B C) &  (C = (a_2_11_armstrng A B)) ) ) ) ) ) ) ).
tt(d25_bilinear,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_vectsp_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ((v7_bilinear C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 C D E) = (k1_binop_1 C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) <=>  ((v2_funct_1 C) &  ( ((k10_xtuple_0 C) = (u4_struct_0 B))  &  ((k10_xtuple_0 (k7_cat_1 A B C)) = (u1_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(d25_cat_4,ax, (! [A:$i] :  (! [B:$i] :  ((k23_cat_4 A B) = (g2_cat_4 (k1_tarski A) (k1_tarski B) (k18_funcop_1 B A) (k18_funcop_1 B A) (k17_funcop_1 B B B) (k1_algstr_1 A) (k17_funcop_1 A A A) (k17_funcop_1 A A B) (k17_funcop_1 A A B))) ) ) ).
tt(d25_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((k17_cohsp_1 A B) = (k3_tarski (a_2_1_cohsp_1 A B))) ) ) ) ) ).
tt(d25_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k20_coh_sp A) (k16_coh_sp A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k16_coh_sp A))))) )  =>  ( (B = (k25_coh_sp A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  ((k3_funct_2 (k20_coh_sp A) (k16_coh_sp A) B C) = (k21_coh_sp A C)) ) ) ) ) ) ) ).
tt(d25_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k11_compos_1 A B) = (k10_compos_1 A (k9_compos_1 A B))) ) ) ) ) ).
tt(d25_comput_1,ax, (k17_comput_1 = (k7_comput_1 (k3_comput_1 k6_numbers 1) (k3_relat_1 (k6_funct_6 (k10_finseq_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 (k5_comput_1 2 1))) (k4_comput_1 1 1)) (k5_comput_1 2 2))) k16_comput_1) 1)) ).
tt(d25_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k20_convex4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v2_convex4 D A) & (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k20_decomp_1 A) = (a_1_14_decomp_1 A)) ) ) ).
tt(d25_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k23_ens_1 A B C) = (k19_ens_1 B C)) ) ) ) ) ) ) ) ).
tt(d25_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((k21_fomodel0 A) = (k3_tarski (a_1_4_fomodel0 A))) ) ) ).
tt(d25_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k20_fomodel1 A) = (k11_monoid_0 (k15_fomodel1 A))) ) ) ).
tt(d25_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v4_fomodel2 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) & (v3_fomodel2 B A C)) ) ) ) ) ) ) ).
tt(d25_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k37_fomodel3 A B C D) = (k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)) (k32_fomodel3 A B C (k36_fomodel3 A B C)) (k32_fomodel2 A D)) D)) ) ) ) ) ) ) ) ) ).
tt(d25_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r8_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  &  (? [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [F:$i] :  ( ((v13_fomodel1 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ( ((k1_xtuple_0 C) = (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k37_fomodel3 B D F E)))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k31_fomodel2 B D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((m2_functor0 C A B) <=>  ((v8_functor0 C A B) &  ((v12_functor0 C A B) &  ( ((v10_functor0 C A B) & (v13_functor0 C A B))  |  ((v11_functor0 C A B) & (v14_functor0 C A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  (~  ((k25_gate_1 A B C D E F) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) & (v1_xboole_0 F)) ) ) ) ) )  =>  ((k25_gate_1 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d25_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k25_gfacirc1 A B C) = (k2_circcomb (k22_gfacirc1 A B C) (k19_gfacirc1 A B C))) ) ) ) ).
tt(d25_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k16_glib_000 A) = (k1_card_1 (k7_glib_000 A))) ) ) ).
tt(d25_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v2_glib_001 B A) <=>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  =>  ((k1_funct_1 (k10_glib_000 A) (k1_funct_1 B (k2_nat_1 C 1))) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d25_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( (B = (k11_graph_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_graph_1 C) & (m3_graph_1 C A)) ) ) ) ) ) ) ).
tt(d25_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_grcat_1 B))  =>  ( (B = (k18_grcat_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v8_algstr_0 D) & (m2_grcat_1 D A))  &  (? [E:$i] :  ( ((v8_algstr_0 E) & (m2_grcat_1 E A))  &  ((v1_grcat_1 C) & (m1_grcat_1 C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ( (E = (k17_group_9 A B C D))  <=>  ((u1_struct_0 E) = (k9_subset_1 (u1_struct_0 B) (k15_group_9 A B C) (k15_group_9 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v5_ideal_1 B A) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  &  (B = (k7_ideal_1 A C)) ) ) ) ) ) ) ) ).
tt(d25_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k23_interva1 A) = (k4_tarski (k2_struct_0 A) (k2_struct_0 A))) ) ) ).
tt(d25_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v21_lattices B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k3_lattices A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d25_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_lexbfs B A) =>  (! [C:$i] :  ((m1_lexbfs C A) =>  ( (C = (k25_lexbfs A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 (k6_glib_000 A) k5_numbers (k5_lexbfs A C D) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A B D)))) ) ) ) ) ) ) ) ) ).
tt(d25_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v6_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (A = (k3_hilbert1 (k6_ltlaxio1 B) (k4_ltlaxio1 B (k2_ltlaxio1 (k6_ltlaxio1 B))))) ) ) ) ) ) ).
tt(d25_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_margrel1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  & (r2_hidden C (k9_xtuple_0 A))) )  =>  ( (B = (k18_margrel1 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C (k9_xtuple_0 A)) =>  (B = (k3_finseq_1 C)) ) ) ) ) )  &  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~ (r2_hidden C (k9_xtuple_0 A))) ) )  =>  ( (B = (k18_margrel1 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d25_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  (A = k1_xboole_0) )  =>  ((k27_mmlquery A B C D) = (a_4_14_mmlquery A B C D)) ) ) ) ) ) ) ) ) ).
tt(d25_modelc_1,ax, (k18_modelc_1 = a_0_0_modelc_1) ).
tt(d25_modelc_2,ax, (! [A:$i] :  ( ((r2_hidden A k9_modelc_2) =>  ((k14_modelc_2 A) = A) )  &  ( (~ (r2_hidden A k9_modelc_2))  =>  ((k14_modelc_2 A) = (k2_modelc_2 k6_numbers)) ) ) ) ).
tt(d25_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k17_modelc_3 A B C) = (k6_series_1 (k16_modelc_3 A B C) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(d25_monoid_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  (! [B:$i] :  ((l4_algstr_0 B) =>  ((m3_monoid_0 B A) <=>  ((r1_tarski (u2_algstr_0 B) (u2_algstr_0 A)) &  ((k5_struct_0 B) = (k5_struct_0 A)) ) ) ) ) ) ) ).
tt(d25_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osafree A B)) C))) =>  ( (D = (k23_osafree A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F (k1_funct_1 B C)) &  (E = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k16_osalg_4 A (k8_osafree A B) (k15_osafree A B))) (k18_osalg_4 A (k8_osafree A B) (k15_osafree A B)) C) (k1_trees_4 (k4_tarski F C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) (u3_msualg_1 A C)) =>  ( (E = (k21_osalg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_funct_2 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) F) (k1_funct_1 (u3_msualg_1 A C) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) (u3_msualg_1 A C) E F) (k20_osalg_4 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((v5_polyform A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  ((k23_polyform A B) = (k25_polyform A B)) ) ) ) ) ) ).
tt(d25_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k24_pscomp_1 A) = (k19_euclid (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k17_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k17_pscomp_1 A))) (k9_pscomp_1 A))) ) ) ).
tt(d25_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( (C = (k19_qc_lang1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k14_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k19_quofield A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k19_quofield A)))))) )  =>  ( (B = (k22_quofield A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k19_quofield A)) B C) = (k10_quofield A (k21_quofield A C (k5_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(d25_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k12_scmyciel A) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski k1_xboole_0) (a_1_4_scmyciel A)) (k1_scmyciel A)) (a_1_5_scmyciel A)) (a_1_6_scmyciel A))) ) ) ).
tt(d25_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v4_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) &  (? [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  &  (? [F:$i] :  ((m1_subset_1 F (k1_substut1 A)) &  (B = (k17_substut1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d25_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)))) =>  ((k26_turing_1 A B C) = (k24_turing_1 A B (k2_domain_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) C))) ) ) ) ) ) ) ).
tt(d25_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k26_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k1_binarith (k1_binarith (k9_margrel1 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d25_waybel_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r4_waybel_4 A B C) <=>  ((r2_hidden B A) &  (! [D:$i] :  (~  ((r2_hidden D A) &  ( (~  (D = B) )  & (r2_hidden (k4_tarski D B) C)) ) ) ) ) ) ) ) ) ) ).
tt(d25_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ((v8_yellow_6 B A) <=>  ((v4_yellow_6 B A) &  ((v5_yellow_6 B A) &  ((v6_yellow_6 B A) & (v7_yellow_6 B A)) ) ) ) ) ) ) ) ).
tt(d25_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((k15_zf_lang A B C) = (k13_zf_lang A (k13_zf_lang B C))) ) ) ) ) ) ) ).
tt(d26_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  ((v4_abcmiz_1 C A B) <=>  ((k3_card_3 (k2_msafree3 A C)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d26_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r6_abcmiz_a A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v2_funct_1 D) &  ((v15_abcmiz_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  &  ((r1_tarski (k45_abcmiz_1 A C) (k1_relset_1 k2_abcmiz_1 D)) & (r5_abcmiz_a A B (k56_abcmiz_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d26_algstr_0,ax, (k8_algstr_0 = (g4_algstr_0 1 k9_funct_5 k5_funct_5)) ).
tt(d26_aofa_000,ax, (k19_aofa_000 = (k8_finseq_1 k5_numbers (k2_finseq_4 k5_numbers k6_numbers 2) (k2_finseq_4 k5_numbers 3 2))) ).
tt(d26_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k13_armstrng A B) = (a_2_12_armstrng A B)) ) ) ) ).
tt(d26_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = C) ) ) ) ) ) ) ) ).
tt(d26_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ((l1_vectsp_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ((v8_bilinear C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_binop_1 C D D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d26_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v13_cat_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 B (k8_cat_1 A B C D) (k8_cat_1 A B C E)) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F B (k8_cat_1 A B C D) (k8_cat_1 A B C E)) =>  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  (? [G:$i] :  ((m1_cat_1 G A D E) &  (F = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l2_cat_4 A)) ) ) ) ) ) )  =>  ((v6_cat_4 A) <=>  ((v11_cat_1 (u5_cat_4 A) A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u7_cat_4 A) B C)) = B)  &  ( ((k3_graph_1 A (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u8_cat_4 A) B C)) = C)  & (r4_cat_3 A (k5_binop_1 (u1_struct_0 A) (u6_cat_4 A) B C) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u7_cat_4 A) B C) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u8_cat_4 A) B C))) ) ) ) ) ) ) ) ) ) ).
tt(d26_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k20_coh_sp A) (k16_coh_sp A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k16_coh_sp A))))) )  =>  ( (B = (k26_coh_sp A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  ((k3_funct_2 (k20_coh_sp A) (k16_coh_sp A) B C) = (k22_coh_sp A C)) ) ) ) ) ) ) ).
tt(d26_comput_1,ax, (k18_comput_1 = (k7_comput_1 (k3_comput_1 1 1) (k14_comput_1 k16_comput_1) 2)) ).
tt(d26_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k21_convex4 A B) = (k6_setfam_1 (u1_struct_0 A) (k20_convex4 A B))) ) ) ) ) ).
tt(d26_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k7_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d26_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k24_ens_1 A B C) = (k20_ens_1 B C)) ) ) ) ) ) ) ) ).
tt(d26_fomodel0,ax, (! [A:$i] :  ((k22_fomodel0 A) = A) ) ).
tt(d26_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k21_fomodel1 A) = (k8_fomodel0 (k15_fomodel1 A))) ) ) ).
tt(d26_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( (E = (k26_fomodel2 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((v3_fomodel2 D A F) =>  (E = (k1_funct_1 (k24_fomodel2 A B F C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r9_fomodel4 A B C) <=>  (? [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  &  (? [E:$i] :  ( ((v4_fomodel1 E B) & (m1_subset_1 E (k1_fomodel1 B)))  &  (? [F:$i] :  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( ((k1_xtuple_0 C) = (k2_xboole_0 F (k1_tarski (k7_finseq_1 (k31_fomodel2 B D) G))))  &  ( (~ (v7_fomodel2 E (k2_xboole_0 (k2_xboole_0 F (k1_tarski G)) (k1_tarski (k2_xtuple_0 C))) B))  & (r2_hidden (k4_tarski (k2_xboole_0 F (k1_tarski (k1_funct_1 (k20_fomodel0 (k1_fomodel1 B) D E) G))) (k2_xtuple_0 C)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v15_functor0 C A B) <=>  ((v10_functor0 C A B) & (v13_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d26_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~  ((k26_gate_1 A B C D E F G) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) ) )  =>  ((k26_gate_1 A B C D E F G) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d26_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k26_gfacirc1 A B C) = (k3_circcomb (k22_gfacirc1 A B C) (k19_gfacirc1 A B C) (k23_gfacirc1 A B C) (k20_gfacirc1 A B C))) ) ) ) ).
tt(d26_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (C = (k18_glib_000 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k7_glib_000 A)) & (r2_hidden (k1_funct_1 (k11_glib_000 A) D) B)) ) ) ) ) ) ) ) ) ).
tt(d26_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) <=>  ((k15_glib_001 A B) = k6_numbers) ) ) ) ) ) ).
tt(d26_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ((m2_grcat_1 B A) =>  ((k21_grcat_1 A B) = (k11_grcat_1 B)) ) ) ) ) ).
tt(d26_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  ( (D = (k18_group_9 A B C))  <=>  ((r1_tarski C (u1_struct_0 D)) &  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ((r1_tarski C (u1_struct_0 E)) => (m1_group_9 D A E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v6_ideal_1 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v5_ideal_1 B A)) ) ) ) ) ).
tt(d26_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_lexbfs B A) =>  ( (B = (k26_lexbfs A))  <=>  ( ((k23_lexbfs A B k6_numbers) = (k18_lexbfs A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k23_lexbfs A B (k1_nat_1 C 1)) = (k22_lexbfs A (k23_lexbfs A B C))) ) ) ) ) ) ) ) ) ).
tt(d26_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v7_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k3_hilbert1 (k4_hilbert1 B C) (k5_ltlaxio1 (k2_ltlaxio1 C) (k2_ltlaxio1 (k4_ltlaxio1 B (k4_hilbert1 B C)))))) ) ) ) ) ) ) ) ).
tt(d26_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  ((r1_modelc_1 A B C) <=>  (! [D:$i] :  ( ((v1_modelc_1 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((v2_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_funct_1 B D)) )  &  ( ((v3_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 C (k14_modelc_1 D)))) )  &  ( ((v4_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u1_lattices A) (k1_funct_1 C (k15_modelc_1 D)) (k1_funct_1 C (k16_modelc_1 D)))) )  &  ( ((v5_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_funct_1 (u4_modelc_1 A) (k1_funct_1 C (k14_modelc_1 D)))) )  &  ( ((v6_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_funct_1 (u5_modelc_1 A) (k1_funct_1 C (k14_modelc_1 D)))) )  &  ((v7_modelc_1 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u6_modelc_1 A) (k1_funct_1 C (k15_modelc_1 D)) (k1_funct_1 C (k16_modelc_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_modelc_2,ax, (k15_modelc_2 = a_0_0_modelc_2) ).
tt(d26_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k18_modelc_3 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ( ((k10_xtuple_0 D) = (k1_modelc_3 A))  &  ((v2_funct_1 D) &  (C = (k17_modelc_3 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_monoid_0,ax, (k2_monoid_0 = (g3_algstr_0 k1_numbers k33_binop_2)) ).
tt(d26_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_osafree C A (k16_osafree A B)) =>  ( (C = (k24_osafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k23_osafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d26_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  ((v3_osalg_4 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((r6_osalg_1 A D E) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A E B)) =>  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k9_xtuple_0 F)) => (r2_hidden (k4_tarski (k1_funct_1 F H) (k1_funct_1 G H)) (k2_msualg_4 A B C (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A E) H)))) ) )  => (r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A D B) (k4_msualg_1 A D B) (k5_msualg_1 A D B) F) (k3_funct_2 (k3_msualg_1 A E B) (k4_msualg_1 A E B) (k5_msualg_1 A E B) G)) (k2_msualg_4 A B C (k2_msualg_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( (B = (k28_polyform A))  <=>  ( ((k3_finseq_1 B) = (k2_xcmplx_0 (k7_polyform A) 2))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k2_xcmplx_0 (k7_polyform A) 2)))  =>  ((k1_funct_1 B C) = (k1_polyform (k2_polyform (k4_xcmplx_0 1) C) (k11_polyform A (k6_xcmplx_0 C 2)))) ) ) ) ) ) ) ) ) ) ).
tt(d26_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k25_pscomp_1 A) = (k19_euclid (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k17_pscomp_1 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k17_pscomp_1 A))) (k9_pscomp_1 A))) ) ) ).
tt(d26_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( (C = (k20_qc_lang1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k14_qc_lang1 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_quofield A B C) <=>  ((v3_quofield C A B) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  (~  ((v3_quofield E A D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  (~  ((v1_quofield F B D) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 D) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 D) C F) E) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v1_quofield G B D) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 D) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 D) C G) E))  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 D) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r12_rewrite1 A B) <=>  (! [C:$i] :  (! [D:$i] :  ((r2_rewrite1 A C D) <=> (r2_rewrite1 B C D)) ) ) ) ) ) ) ) ).
tt(d26_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  ( (B = (k13_scmyciel A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( (B = C)  &  ( ((k1_funct_1 C k6_numbers) = A)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v4_scmyciel E) =>  ( (E = (k1_funct_1 C D))  =>  ((k1_funct_1 C (k1_nat_1 D 1)) = (k12_scmyciel E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d26_sin_cos,ax, (k29_sin_cos = (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) ).
tt(d26_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v5_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) &  (B = (k20_substut1 A C)) ) ) ) ) ) ) ) ).
tt(d26_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)))) =>  ((k27_turing_1 A B C) = (k25_turing_1 A B (k2_domain_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) C))) ) ) ) ) ) ) ).
tt(d26_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k27_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k1_binarith (k1_binarith (k9_margrel1 B) (k9_margrel1 C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(d26_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_waybel_4 A B C) <=> (r4_waybel_4 B C (u1_orders_2 A))) ) ) ) ) ) ).
tt(d26_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((k16_zf_lang A B C D) = (k8_zf_lang A (k14_zf_lang B C D))) ) ) ) ) ) ) ) ) ).
tt(d27_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r4_abcmiz_0 A B C) <=>  ((r1_orders_2 A B (k10_abcmiz_0 A C)) & (r1_abcmiz_0 A B C)) ) ) ) ) ) ) ) ).
tt(d27_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  ((v5_abcmiz_1 C A B) <=> (r2_hidden (k1_funct_1 C k1_xboole_0) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(d27_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r7_abcmiz_a A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((r4_abcmiz_a A C D E) &  (B = (k56_abcmiz_1 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v23_algstr_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d27_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) )  =>  ((v12_aofa_000 A) <=>  ((k1_unialg_1 A) = k19_aofa_000) ) ) ) ).
tt(d27_armstrng,ax, (! [A:$i] :  ((v11_armstrng A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) &  ((r2_hidden C A) & (r1_tarski B C)) )  =>  (B = C) ) ) ) ) ) ).
tt(d27_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v20_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A (k1_bcialg_1 A B B) C))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B C) C) = (k1_bcialg_1 A B (k1_bcialg_1 A C C))) ) ) ) ) ) ) ) ) ).
tt(d27_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v14_cat_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F A D E) =>  (! [G:$i] :  ((m1_cat_1 G A D E) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C F) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k20_coh_sp A)) (k20_coh_sp A)))))  =>  ( (B = (k27_coh_sp A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k20_coh_sp A)) =>  ((r2_hidden (k4_tarski C D) (k1_relset_1 (k2_zfmisc_1 (k20_coh_sp A) (k20_coh_sp A)) B)) <=>  ((k21_coh_sp A C) = (k22_coh_sp A D)) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k20_coh_sp A)) =>  ( ((k21_coh_sp A C) = (k22_coh_sp A D))  =>  ((k1_funct_1 B (k4_tarski C D)) = (k24_coh_sp A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) & (v1_funct_1 B)) ) )  =>  ((v2_compos_1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k9_xtuple_0 B)) &  ((k1_funct_1 B C) = (k2_compos_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(d27_comput_1,ax, (k19_comput_1 = (k7_comput_1 (k3_comput_1 k6_numbers k6_numbers) (k5_comput_1 2 1) 1)) ).
tt(d27_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k8_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d27_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k25_ens_1 A B) = (k22_ens_1 B)) ) ) ) ) ) ).
tt(d27_fomodel0,ax, (! [A:$i] :  ((k23_fomodel0 A) = (k8_mcart_1 k1_numbers (k7_subset_1 (k1_zfmisc_1 (k10_xtuple_0 A)) (k9_setfam_1 (k10_xtuple_0 A)) (k10_xtuple_0 A)) k5_numbers (k6_domain_1 (k7_subset_1 (k1_zfmisc_1 (k10_xtuple_0 A)) (k9_setfam_1 (k10_xtuple_0 A)) (k10_xtuple_0 A)) (o_1_5_fomodel0 A)))) ) ).
tt(d27_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k22_fomodel1 A) = (k6_fomodel0 (k15_fomodel1 A))) ) ) ).
tt(d27_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k27_fomodel2 A) = (a_1_0_fomodel2 A)) ) ) ).
tt(d27_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r10_fomodel4 A B C) <=>  (? [D:$i] :  (? [E:$i] :  (? [F:$i] :  ( ((v4_fomodel2 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [G:$i] :  ( ((v4_fomodel2 G B) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( ((k1_xtuple_0 D) = (k1_xtuple_0 E))  &  ( ((k1_xtuple_0 E) = (k1_xtuple_0 C))  &  ( ((k2_xtuple_0 D) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) F) F))  &  ( ((k2_xtuple_0 E) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) G) G))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v16_functor0 C A B) <=>  ((v11_functor0 C A B) & (v14_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d27_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) & (v1_xboole_0 G)) ) ) ) ) ) )  =>  ((k27_gate_1 A B C D E F G) = (k1_gate_1 k1_xboole_0)) )  &  (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) &  (~  ((k27_gate_1 A B C D E F G) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (C = (k19_glib_000 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k7_glib_000 A)) & (r2_hidden (k1_funct_1 (k10_glib_000 A) D) B)) ) ) ) ) ) ) ) ) ).
tt(d27_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=> (v2_funct_1 (k12_glib_001 A B))) ) ) ) ) ).
tt(d27_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k18_grcat_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) A)))) )  =>  ( (B = (k22_grcat_1 A))  <=>  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  ((k3_funct_2 (k18_grcat_1 A) A B C) = (k19_grcat_1 A C)) ) ) ) ) ) ) ) ).
tt(d27_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((k19_group_9 A B C D) = (k18_group_9 A B (k4_subset_1 (u1_struct_0 B) (k15_group_9 A B C) (k15_group_9 A B D)))) ) ) ) ) ) ) ) ).
tt(d27_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v7_ideal_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(d27_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) k5_numbers))))  =>  ((v6_lexbfs B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ((r2_hidden C (k1_relset_1 (k6_glib_000 A) B)) &  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) B)) &  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) B)) &  ( (~ (r1_xxreal_0 (k1_recdef_1 B D) (k1_recdef_1 B C)))  &  ( (~ (r1_xxreal_0 (k1_recdef_1 B E) (k1_recdef_1 B D)))  &  ((r1_chord A C E) &  ( (~ (r1_chord A D E))  &  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 A)) =>  (~  ((r2_hidden F (k1_relset_1 (k6_glib_000 A) B)) &  ( (~ (r1_xxreal_0 (k1_recdef_1 B F) (k1_recdef_1 B D)))  &  ((r1_chord A D F) &  (~ (r1_chord A C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v8_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k3_hilbert1 (k5_ltlaxio1 (k2_ltlaxio1 C) (k2_ltlaxio1 (k4_ltlaxio1 B (k4_hilbert1 B C)))) (k4_hilbert1 B C))) ) ) ) ) ) ) ) ).
tt(d27_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k29_mmlquery A B C) = C) ) ) ) ) ) ).
tt(d27_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_modelc_1 A B C D) <=>  (! [E:$i] :  ( ((v1_modelc_1 E) & (m2_finseq_1 E k5_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 E) D) =>  ( ((v2_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_funct_1 B E)) )  &  ( ((v3_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 C (k14_modelc_1 E)))) )  &  ( ((v4_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u1_lattices A) (k1_funct_1 C (k15_modelc_1 E)) (k1_funct_1 C (k16_modelc_1 E)))) )  &  ( ((v5_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_funct_1 (u4_modelc_1 A) (k1_funct_1 C (k14_modelc_1 E)))) )  &  ( ((v6_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_funct_1 (u5_modelc_1 A) (k1_funct_1 C (k14_modelc_1 E)))) )  &  ((v7_modelc_1 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u6_modelc_1 A) (k1_funct_1 C (k15_modelc_1 E)) (k1_funct_1 C (k16_modelc_1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  ((r4_modelc_2 A B C) <=>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((v2_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_funct_1 B D)) )  &  ( ((v3_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 C (k10_modelc_2 D)))) )  &  ( ((v4_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u1_lattices A) (k1_funct_1 C (k11_modelc_2 D)) (k1_funct_1 C (k12_modelc_2 D)))) )  &  ( ((v5_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u2_lattices A) (k1_funct_1 C (k11_modelc_2 D)) (k1_funct_1 C (k12_modelc_2 D)))) )  &  ( ((v6_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_funct_1 (u2_modelc_2 A) (k1_funct_1 C (k10_modelc_2 D)))) )  &  ( ((v7_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u3_modelc_2 A) (k1_funct_1 C (k11_modelc_2 D)) (k1_funct_1 C (k12_modelc_2 D)))) )  &  ((v8_modelc_2 D) =>  ((k1_funct_1 C D) = (k1_binop_1 (u4_modelc_2 A) (k1_funct_1 C (k11_modelc_2 D)) (k1_funct_1 C (k12_modelc_2 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden B (k1_modelc_3 A)) =>  ((k19_modelc_3 A B) = (k2_modelc_3 B)) ) ) ) ) ) ).
tt(d27_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v1_group_1 A) &  ((v17_monoid_0 A) & (m5_monoid_0 A k2_monoid_0 k3_monoid_0)) ) ) )  =>  ( (A = k4_monoid_0)  <=>  ((u1_struct_0 A) = k5_numbers) ) ) ) ).
tt(d27_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k6_osalg_4 A (k8_osafree A B) C (k10_osafree A B D))) =>  ( (E = (k25_osafree A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) F)) =>  ( (D = G)  =>  (E = (k8_osalg_4 A (k8_osafree A B) C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_osalg_4 E A B)) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_msualg_3 A B C D) &  ((v1_osalg_3 D A) & (r2_pboole (u1_struct_0 A) E (k19_osalg_4 A B C D))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B E)) F) (k1_funct_1 (u3_msualg_1 A C) F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B E)) F) (k1_funct_1 (u3_msualg_1 A C) F))))) )  =>  ( (G = (k22_osalg_4 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) F)) =>  ((k1_funct_1 G (k8_osalg_4 A B E F H)) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) F) (k1_funct_1 (u3_msualg_1 A C) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( (B = (k29_polyform A))  <=>  ( ((k3_finseq_1 B) = (k7_polyform A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k7_polyform A)))  =>  ((k1_funct_1 B C) = (k1_polyform (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 C 1)) (k11_polyform A (k6_xcmplx_0 C 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d27_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v5_qc_lang1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (C = (k21_qc_lang1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k15_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_quantal1 A B C) = (k5_quantal1 A (k6_algstr_0 A (k5_quantal1 A B) (k5_quantal1 A C)))) ) ) ) ) ) ) ).
tt(d27_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r13_rewrite1 A B C) <=>  ((r8_rewrite1 A B C) &  (~ (r5_rewrite1 A B C)) ) ) ) ) ) ) ).
tt(d27_sin_cos,ax, (k30_sin_cos = (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) ).
tt(d27_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v6_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) &  ( (B = (k21_substut1 A C D))  &  ((k19_substut1 A C) = (k19_substut1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d27_turing_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A (k2_xboole_0 B C))) =>  ( (? [E:$i] :  (? [F:$i] :  ((m1_subset_1 F B) &  (D = (k4_tarski E F)) ) ) )  =>  ((k28_turing_1 A B C D) = (k3_domain_1 A (k2_xboole_0 B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d27_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k28_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k1_binarith (k1_binarith (k9_margrel1 B) (k9_margrel1 C)) (k9_margrel1 D))) ) ) ) ) ) ) ) ) ) ).
tt(d27_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_waybel_0 A B) = (a_2_2_waybel_0 A B)) ) ) ) ) ).
tt(d27_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((k17_zf_lang A B C D) = (k13_zf_lang A (k15_zf_lang B C D))) ) ) ) ) ) ) ) ) ).
tt(d28_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r5_abcmiz_0 A B C) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_abcmiz_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ( (E = (k1_funct_1 C D))  &  (F = (k1_funct_1 (k7_abcmiz_0 A B C) D)) ) )  => (r4_abcmiz_0 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((m1_abcmiz_1 C A B) <=> (r2_hidden C (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))) B))) ) ) ) ) ) ) ).
tt(d28_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ((v13_aofa_000 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k2_binop_1 B (u1_struct_0 A) B C D (k12_aofa_000 A)) = D) ) ) ) ) ) ) ) ) ) ).
tt(d28_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C A (k1_card_1 A)) &  ((v2_funct_2 C (k1_card_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) )  =>  ((r1_tarski (k2_relset_1 (k1_card_1 A) C) k5_numbers) =>  (! [D:$i] :  ((m1_aofa_000 D (k7_freealg k19_aofa_000 k26_aofa_i00) (k9_funct_2 A k4_numbers) B) =>  ((m6_aofa_i00 D A B C) <=>  (! [E:$i] :  ((m2_funct_2 E A k4_numbers (k9_funct_2 A k4_numbers)) =>  (! [F:$i] :  ((m2_funct_2 F (k9_funct_2 A k4_numbers) A (k9_funct_2 (k9_funct_2 A k4_numbers) A)) =>  (! [G:$i] :  ((m2_funct_2 G (k9_funct_2 A k4_numbers) k4_numbers (k9_funct_2 (k9_funct_2 A k4_numbers) k4_numbers)) =>  ((k1_binop_1 D E (k1_trees_4 (k4_tarski (k17_aofa_i00 k5_numbers (k1_partfun1 (k9_funct_2 A k4_numbers) A A (k1_card_1 A) F C) C) (k17_aofa_i00 k5_numbers G C)))) = (k15_funct_7 A k4_numbers E (k21_aofa_i00 (k9_funct_2 A k4_numbers) A F E) (k21_aofa_i00 (k9_funct_2 A k4_numbers) k4_numbers G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v12_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) & (r2_hidden (k6_armstrng A C E) B))  => (r2_hidden (k6_armstrng A C (k4_subset_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k11_cat_1 A B C D E) = (k2_partfun1 (u4_struct_0 A) (u4_struct_0 B) C (k2_cat_1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B D) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  (~  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_cat_1 G A (k20_cat_4 A B C) D) =>  ( (G = (k29_cat_4 A B C D E F))  <=>  ( ((k5_cat_1 A B (k20_cat_4 A B C) D (k27_cat_4 A B C) G) = E)  &  ((k5_cat_1 A C (k20_cat_4 A B C) D (k28_cat_4 A B C) G) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_comput_1,ax, (k20_comput_1 = (k7_comput_1 (k5_comput_1 1 1) (k14_comput_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 (k5_comput_1 2 2))) k19_comput_1)) 2)) ).
tt(d28_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k6_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d28_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v12_fomodel1 B A) <=> (v3_fomodel0 B (k15_fomodel1 A))) ) ) ) ).
tt(d28_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) =>  ( (C = (k25_fomodel2 A B))  <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 A D)) =>  (C = (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k24_fomodel2 A D B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r11_fomodel4 A B C) <=>  (? [D:$i] :  (? [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [F:$i] :  ( ((v4_fomodel2 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((r2_hidden D A) &  ( ((k1_xtuple_0 D) = (k1_xtuple_0 C))  &  ( ((k2_xtuple_0 D) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) E) F))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_functor0,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  (! [C:$i] :  ( ((v9_functor0 C B A) & (l2_functor0 C B A))  =>  ( (C = (k10_functor0 A B))  <=>  ( ((u1_functor0 B A C) = (k6_partfun1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))  & (r6_pboole (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u2_functor0 B A C) (k2_msualg_3 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_altcat_1 B)))) ) ) ) ) ) ) ) ).
tt(d28_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) ) )  =>  ((k28_gate_1 A B C D E F G) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~  ((k28_gate_1 A B C D E F G) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((k20_glib_000 A B) = (k4_subset_1 (k7_glib_000 A) (k18_glib_000 A B) (k19_glib_000 A B))) ) ) ) ).
tt(d28_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_glib_001 B A) <=>  ((v4_glib_001 B A) &  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 D C) |  ( (C = 1)  &  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k18_grcat_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) A)))) )  =>  ( (B = (k23_grcat_1 A))  <=>  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  ((k3_funct_2 (k18_grcat_1 A) A B C) = (k20_grcat_1 A C)) ) ) ) ) ) ) ) ).
tt(d28_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k6_group_9 A B)) =>  ((v8_group_9 C A B) <=>  ( ((k1_funct_1 C 1) = (k5_group_9 A B))  &  ( ((k1_funct_1 C (k3_finseq_1 C)) = (k4_group_9 A B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 C)) & (r2_hidden (k1_nat_1 D 1) (k4_finseq_1 C)))  =>  (! [E:$i] :  ((m1_group_9 E A B) =>  (! [F:$i] :  ((m1_group_9 F A B) =>  ( ( (E = (k1_funct_1 C D))  &  (F = (k1_funct_1 C (k1_nat_1 D 1))) )  =>  ((v4_group_9 F A E) & (m1_group_9 F A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v8_ideal_1 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v7_ideal_1 B A)) ) ) ) ) ).
tt(d28_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v9_ltlaxio1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k3_hilbert1 (k4_hilbert1 B C) (k2_ltlaxio1 (k7_ltlaxio1 C)))) ) ) ) ) ) ) ) ).
tt(d28_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k30_mmlquery A B) = (k1_mmlquery (u1_struct_0 A) (k29_mmlquery (u1_struct_0 A) (u1_mmlquery A) (u2_mmlquery A)) B)) ) ) ) ) ).
tt(d28_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v1_modelc_1 F) & (m2_finseq_1 F k5_numbers))  =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 F) (k2_nat_1 E 1)))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 C F)) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v2_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 B F)) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v3_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 D (k14_modelc_1 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v4_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_binop_1 (u1_lattices A) (k1_funct_1 D (k15_modelc_1 F)) (k1_funct_1 D (k16_modelc_1 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v5_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 (u4_modelc_1 A) (k1_funct_1 D (k14_modelc_1 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v6_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 (u5_modelc_1 A) (k1_funct_1 D (k14_modelc_1 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v7_modelc_1 F))  =>  ((k19_modelc_1 A B C D E F) = (k1_binop_1 (u6_modelc_1 A) (k1_funct_1 D (k15_modelc_1 F)) (k1_funct_1 D (k16_modelc_1 F)))) )  &  ( ( (~ (r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 F)))  =>  ((k19_modelc_1 A B C D E F) = (k1_funct_1 D F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) (k2_nat_1 E 1)) & (r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 F)))  =>  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v2_modelc_1 F))  |  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v3_modelc_1 F))  |  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v4_modelc_1 F))  |  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v5_modelc_1 F))  |  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v6_modelc_1 F))  |  ( ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  & (v7_modelc_1 F))  |  ((k19_modelc_1 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r5_modelc_2 A B C D) <=>  (! [E:$i] :  ( ((v1_modelc_2 E) & (m2_finseq_1 E k5_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 E) D) =>  ( ((v2_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_funct_1 B E)) )  &  ( ((v3_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 C (k10_modelc_2 E)))) )  &  ( ((v4_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u1_lattices A) (k1_funct_1 C (k11_modelc_2 E)) (k1_funct_1 C (k12_modelc_2 E)))) )  &  ( ((v5_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u2_lattices A) (k1_funct_1 C (k11_modelc_2 E)) (k1_funct_1 C (k12_modelc_2 E)))) )  &  ( ((v6_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_funct_1 (u2_modelc_2 A) (k1_funct_1 C (k10_modelc_2 E)))) )  &  ( ((v7_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u3_modelc_2 A) (k1_funct_1 C (k11_modelc_2 E)) (k1_funct_1 C (k12_modelc_2 E)))) )  &  ((v8_modelc_2 E) =>  ((k1_funct_1 C E) = (k1_binop_1 (u4_modelc_2 A) (k1_funct_1 C (k11_modelc_2 E)) (k1_funct_1 C (k12_modelc_2 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden B (k1_modelc_3 A)) =>  ((k20_modelc_3 A B) = (k3_modelc_3 B)) ) ) ) ) ) ).
tt(d28_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (k22_osafree A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_osafree A B))) =>  ((r2_hidden E (k6_dtconstr (k2_osafree A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_card_3 C)) =>  ( (F = (k26_osafree A B C D E))  <=>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( (G = (k1_funct_1 D (k2_xtuple_0 E)))  =>  (F = (k1_funct_1 G (k2_trees_4 (u1_struct_0 (k2_osafree A B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_osalg_4 E A B)) )  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B E)) (u3_msualg_1 A C)) =>  ( (F = (k23_osalg_4 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) => (r2_funct_2 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B E)) G) (k1_funct_1 (u3_msualg_1 A C) G) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B E)) (u3_msualg_1 A C) F G) (k22_osalg_4 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( (B = (k30_polyform A))  <=>  ( ((k3_finseq_1 B) = (k2_xcmplx_0 (k7_polyform A) 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k2_xcmplx_0 (k7_polyform A) 1)))  =>  ((k1_funct_1 B C) = (k1_polyform (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 C 1)) (k11_polyform A (k6_xcmplx_0 C 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d28_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v5_qc_lang1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( (C = (k22_qc_lang1 A B))  <=>  (? [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (B = (k15_qc_lang1 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d28_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v10_rewrite1 B))  =>  ((m2_rewrite1 B A) <=>  (! [C:$i] :  (! [D:$i] :  ((r2_rewrite1 A C D) <=> (r5_rewrite1 B C D)) ) ) ) ) ) ) ) ).
tt(d28_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (A = k31_sin_cos)  <=>  ( ((k1_seq_1 k29_sin_cos (k6_real_1 A 4)) = 1)  & (r2_hidden A (k2_rcomp_1 k6_numbers 4))) ) ) ) ).
tt(d28_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v7_substut1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) &  (? [D:$i] :  ((m1_substut1 D A C) &  ( (B = (k24_substut1 A C D))  & (v3_substut1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(d28_turing_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A (k2_xboole_0 B C))) =>  ( (? [E:$i] :  (? [F:$i] :  ((m1_subset_1 F C) &  (D = (k4_tarski E F)) ) ) )  =>  ((k29_turing_1 A B C D) = (k3_domain_1 A (k2_xboole_0 B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d28_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k29_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k1_binarith (k1_binarith B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(d28_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k12_waybel_0 A B) = (a_2_3_waybel_0 A B)) ) ) ) ) ).
tt(d28_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_zf_lang A) =>  ((k18_zf_lang A) = (k1_funct_1 A 2)) ) ) ) ).
tt(d29_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r6_abcmiz_0 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) &  ( ((k2_relset_1 (u1_abcmiz_0 A) D) = C)  & (r5_abcmiz_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d29_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  ( ((k3_finseq_1 (k1_msualg_1 A B)) = k6_numbers)  =>  ((k29_abcmiz_1 A B) = (k4_trees_4 (k4_tarski B (u1_struct_0 A)) k1_xboole_0)) ) ) ) ) ) ).
tt(d29_abcmiz_a,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 k4_abcmiz_a))))  =>  ((v7_abcmiz_a A) <=>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) =>  (! [C:$i] :  ((m3_abcmiz_1 C k27_abcmiz_1) =>  ( ((r2_hidden B (k1_relset_1 k2_abcmiz_1 A)) &  (C = (k1_funct_1 A B)) )  =>  ((k48_abcmiz_1 k27_abcmiz_1 C) = (k3_abcmiz_1 B)) ) ) ) ) ) ) ) ) ).
tt(d29_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ((v14_aofa_000 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k2_binop_1 B (u1_struct_0 A) B C D (k13_aofa_000 A E F)) = (k2_binop_1 B (u1_struct_0 A) B C (k2_binop_1 B (u1_struct_0 A) B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  (! [G:$i] :  ((m3_aofa_i00 G A B C D) =>  ( (G = (k35_aofa_i00 A B C D E F))  <=>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G H) = (k5_int_1 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers E H) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v13_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) & (r2_hidden (k6_armstrng A (k4_subset_1 A D E) F) B))  => (r2_hidden (k6_armstrng A (k4_subset_1 A C E) F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k30_cat_4 A B) = (k29_cat_4 A B B B (k4_cat_1 A B) (k4_cat_1 A B))) ) ) ) ) ).
tt(d29_coh_sp,ax, (! [A:$i] :  ((k28_coh_sp A) = (g1_cat_1 (k16_coh_sp A) (k20_coh_sp A) (k25_coh_sp A) (k26_coh_sp A) (k27_coh_sp A))) ) ).
tt(d29_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v8_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k10_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d29_descip_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D (k4_finseq_2 B k6_margrel1) (k4_finseq_2 C (k4_finseq_2 B k6_margrel1))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) &  ((v3_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1))))) ) )  =>  (! [G:$i] :  ((m2_finseq_2 G k6_margrel1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) =>  (! [H:$i] :  ((m2_finseq_2 H k6_margrel1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) =>  ( (H = (k40_descip_1 A B C D E F G))  <=>  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 A k6_margrel1))))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 A k6_margrel1))))) )  &  ( ((k14_descip_1 A k6_margrel1 I k6_numbers) = (k4_descip_1 k6_margrel1 A (k3_funct_2 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) F G)))  &  ( ((k14_descip_1 A k6_margrel1 J k6_numbers) = (k5_descip_1 k6_margrel1 A (k3_funct_2 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) F G)))  &  ( (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers K) & (r1_xxreal_0 K (k6_xcmplx_0 C 1)))  =>  ( ((k14_descip_1 A k6_margrel1 I (k2_nat_1 K 1)) = (k14_descip_1 A k6_margrel1 J K))  &  ((k14_descip_1 A k6_margrel1 J (k2_nat_1 K 1)) = (k12_descip_1 A (k14_descip_1 A k6_margrel1 I K) (k2_binop_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1) (k4_finseq_2 A k6_margrel1) E (k14_descip_1 A k6_margrel1 J K) (k7_partfun1 (k4_finseq_2 B k6_margrel1) D (k2_nat_1 K 1))))) ) ) ) )  &  (H = (k1_funct_1 (k2_funct_2 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) F) (k9_binarith A A k6_margrel1 (k14_descip_1 A k6_margrel1 J C) (k14_descip_1 A k6_margrel1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ((k23_fomodel1 A B C) = (a_3_0_fomodel1 A B C)) ) ) ) ) ) ).
tt(d29_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k28_fomodel2 A B) = (a_2_1_fomodel2 A B)) ) ) ) ) ).
tt(d29_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v11_fomodel4 C B) =>  ((r12_fomodel4 A B C) <=>  (? [D:$i] :  (? [E:$i] :  (? [F:$i] :  ( ((v4_fomodel2 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [G:$i] :  ( ((v4_fomodel2 G B) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  (? [H:$i] :  ( ((v4_fomodel2 H B) & (m2_subset_1 H (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( ((k1_xtuple_0 D) = (k1_xtuple_0 E))  &  ( ((k2_xtuple_0 D) = G)  &  ( ((k2_xtuple_0 E) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) G) H))  &  ( ((k2_xboole_0 (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) F) (k1_xtuple_0 C)) = (k1_xtuple_0 D))  &  ((k2_xtuple_0 C) = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ( ((v9_functor0 B A A) & (l2_functor0 B A A))  =>  ( (B = (k11_functor0 A))  <=>  ((r8_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_functor0 A A B) (k6_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) & (r6_pboole (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u2_functor0 A A B) (k2_msualg_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 A)))) ) ) ) ) ) ).
tt(d29_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) &  (~  ((k29_gate_1 A B C D E F G) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) & (v1_xboole_0 G)) ) ) ) ) ) )  =>  ((k29_gate_1 A B C D E F G) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d29_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k29_gfacirc1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k3_gfacirc1 (k10_finseq_1 B C))) (k5_circcomb k4_twoscomp (k10_finseq_1 C A)))) ) ) ) ).
tt(d29_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((k21_glib_000 A B) = (k9_subset_1 (k7_glib_000 A) (k18_glib_000 A B) (k19_glib_000 A B))) ) ) ) ).
tt(d29_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v6_glib_001 B A) <=>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) (k18_grcat_1 A)) (k18_grcat_1 A)))))  =>  ( (B = (k24_grcat_1 A))  <=>  ( (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  (! [D:$i] :  ((m3_grcat_1 D (k18_grcat_1 A)) =>  ((r2_hidden (k4_tarski C D) (k9_xtuple_0 B)) <=>  ((k19_grcat_1 A C) = (k20_grcat_1 A D)) ) ) ) ) )  &  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  (! [D:$i] :  ((m3_grcat_1 D (k18_grcat_1 A)) =>  ((r2_hidden (k4_tarski C D) (k9_xtuple_0 B)) =>  ((k1_binop_1 B C D) = (k13_grcat_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  ((r4_group_9 A B C D) <=>  (? [E:$i] :  ((r1_tarski E (k4_finseq_1 C)) & (r2_relset_1 k5_numbers (k6_group_9 A B) D (k1_partfun1 k5_numbers k5_numbers k5_numbers (k6_group_9 A B) (k14_finseq_1 E) C))) ) ) ) ) ) ) ) ) ) ).
tt(d29_ltlaxio1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r7_ltlaxio1 A B C) <=>  (~  ( (~ (r2_hidden (k1_funct_1 B A) k13_ltlaxio1))  &  ( (~ (r2_hidden (k1_funct_1 B A) C))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 A D))  &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 A E))  &  ((r5_ltlaxio1 (k7_partfun1 k1_hilbert1 B D) (k7_partfun1 k1_hilbert1 B E) (k7_partfun1 k1_hilbert1 B A)) | (r6_ltlaxio1 (k7_partfun1 k1_hilbert1 B D) (k7_partfun1 k1_hilbert1 B E) (k7_partfun1 k1_hilbert1 B A))) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 A D))  & (r4_ltlaxio1 (k7_partfun1 k1_hilbert1 B D) (k7_partfun1 k1_hilbert1 B A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k31_mmlquery A B) = (k1_mmlquery (u1_struct_0 A) (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k29_mmlquery (u1_struct_0 A) (u1_mmlquery A) (u2_mmlquery A))) B)) ) ) ) ) ).
tt(d29_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_modelc_2 F) & (m2_finseq_1 F k5_numbers))  =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 F) (k1_nat_1 E 1)))  =>  ((k16_modelc_2 A B C D E F) = (k1_funct_1 C F)) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v2_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_funct_1 B F)) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v3_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_funct_1 (u1_robbins1 A) (k1_funct_1 D (k10_modelc_2 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v4_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_binop_1 (u1_lattices A) (k1_funct_1 D (k11_modelc_2 F)) (k1_funct_1 D (k12_modelc_2 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v5_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_binop_1 (u2_lattices A) (k1_funct_1 D (k11_modelc_2 F)) (k1_funct_1 D (k12_modelc_2 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v6_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_funct_1 (u2_modelc_2 A) (k1_funct_1 D (k10_modelc_2 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v7_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_binop_1 (u3_modelc_2 A) (k1_funct_1 D (k11_modelc_2 F)) (k1_funct_1 D (k12_modelc_2 F)))) )  &  ( ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v8_modelc_2 F))  =>  ((k16_modelc_2 A B C D E F) = (k1_binop_1 (u4_modelc_2 A) (k1_funct_1 D (k11_modelc_2 F)) (k1_funct_1 D (k12_modelc_2 F)))) )  &  ( ( (~ (r1_xxreal_0 (k1_nat_1 E 1) (k3_finseq_1 F)))  =>  ((k16_modelc_2 A B C D E F) = (k1_funct_1 D F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) (k1_nat_1 E 1)) & (r1_xxreal_0 (k1_nat_1 E 1) (k3_finseq_1 F)))  =>  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v2_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v3_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v4_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v5_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v6_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v7_modelc_2 F))  |  ( ( ((k3_finseq_1 F) = (k1_nat_1 E 1))  & (v8_modelc_2 F))  |  ((k16_modelc_2 A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((k21_modelc_3 A B) = (k1_int_1 (k18_modelc_3 A (u2_modelc_3 A B)))) ) ) ) ) ).
tt(d29_monoid_0,ax, (k47_binop_2 = (u2_algstr_0 k4_monoid_0)) ).
tt(d29_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((v6_polyform A) <=>  ((k16_rvsum_1 (k29_polyform A)) = (k2_xcmplx_0 1 (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 (k7_polyform A) 1)))) ) ) ) ).
tt(d29_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  ((k23_qc_lang1 A B) = (a_2_1_qc_lang1 A B)) ) ) ) ) ).
tt(d29_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v4_substut1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_qc_lang1 A)) =>  ( (C = (k26_substut1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A D)) &  (? [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F (k2_qc_lang1 A)))  &  (? [G:$i] :  ((m1_subset_1 G (k1_substut1 A)) &  ((r2_relset_1 k5_numbers (k2_qc_lang1 A) C F) &  (B = (k17_substut1 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d29_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)))) =>  ( ( (? [D:$i] :  ((m1_subset_1 D (u2_turing_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_turing_1 A)) &  ( (C = (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 A) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) D (u4_turing_1 B)) E))  &  (~  (D = (u5_turing_1 A)) ) ) ) ) ) )  =>  ((k30_turing_1 A B C) = (k22_turing_1 A B (k3_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) (k1_domain_1 (u2_turing_1 A) (u1_turing_1 A) (k26_turing_1 A B C) (k28_turing_1 (k21_turing_1 A B) (u1_turing_1 A) (u1_turing_1 B) C))))) )  &  ( ( (? [D:$i] :  ((m1_subset_1 D (u2_turing_1 B)) &  (? [E:$i] :  ((m1_subset_1 E (u1_turing_1 B)) &  (C = (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 B) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) D) E)) ) ) ) )  =>  ((k30_turing_1 A B C) = (k23_turing_1 A B (k3_funct_2 (k2_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B)) (k3_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 B) (k1_domain_1 (u2_turing_1 B) (u1_turing_1 B) (k27_turing_1 A B C) (k29_turing_1 (k21_turing_1 A B) (u1_turing_1 A) (u1_turing_1 B) C))))) )  &  ( ( (! [D:$i] :  ((m1_subset_1 D (u2_turing_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_turing_1 A)) =>  (~  ( (C = (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 A) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) D (u4_turing_1 B)) E))  &  (~  (D = (u5_turing_1 A)) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u2_turing_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_turing_1 B)) =>  (~  (C = (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 B) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) D) E)) ) ) ) ) ) )  =>  ((k30_turing_1 A B C) = (k4_domain_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) k1_numbers (k2_domain_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) C) (k3_domain_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) C) (k1_real_1 1))) ) ) ) ) ) ) ) ) ) ).
tt(d29_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k30_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 B) C) D))) ) ) ) ) ) ) ) ) ) ).
tt(d29_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v16_waybel_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) | (r1_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(d29_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_zf_lang A) =>  ((k19_zf_lang A) = (k1_funct_1 A 3)) ) ) ) ).
tt(d2_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_abcmiz_0 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_abcmiz_1,ax, (! [A:$i] :  ( (A = k2_abcmiz_1)  <=>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  &  ( (A = (k3_card_3 B))  &  ( ((k1_funct_1 B k6_numbers) = a_0_0_abcmiz_1)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 B (k1_nat_1 C 1)) = (a_2_0_abcmiz_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d2_abian,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_abian A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (A = (k4_nat_1 2 B)) ) ) ) ) ) ).
tt(d2_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_absvalue A) = 1) )  &  ( ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_absvalue A) = (k1_real_1 1)) )  &  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 k6_numbers A))  =>  ((k1_absvalue A) = k6_numbers) ) ) ) ) ) ).
tt(d2_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k1_aff_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) <=> (r1_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v2_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden D C) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden J C) &  ((r2_analoaf A E I F H) & (r2_analoaf A F J G I)) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = E)  |  ( (D = H)  |  ( (D = F)  |  ( (D = I)  |  ( (D = G)  |  ( (D = J)  | (r2_analoaf A E J G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden E C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden E D) &  ((r2_hidden J D) &  ((r2_hidden K D) &  ((r1_aff_1 A H F L) &  ((r1_aff_1 A I G L) &  ((r1_aff_1 A H J M) &  ((r1_aff_1 A I K M) & (r2_analoaf A F J L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (C = B)  |  ( (C = D)  |  ( (B = D)  |  ( (E = F)  |  ( (E = H)  |  ( (E = J)  |  ( (L = M)  |  ( (J = M)  |  ((r1_aff_1 A H F J) |  ((r1_aff_1 A I G K) | (r2_analoaf A F J G K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ( (~ (r5_aff_1 A C D))  &  (B = (k1_aff_4 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_afinsq_1,ax, (! [A:$i] :  ((k4_afinsq_1 A) = k1_xboole_0) ) ).
tt(d2_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) )  =>  ( (C = (k2_afinsq_2 A B))  <=>  ( ((k1_afinsq_1 C) = (k7_nat_d (k1_afinsq_1 A) B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k1_funct_1 A (k23_binop_2 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k2_afproj A) = (a_1_1_afproj A)) ) ) ).
tt(d2_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_afvect01 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~  (D = E) )  &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D D C) & (r2_analoaf A B E E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_afvect0 A B C) <=>  ((r2_analoaf A B C C B) &  (~  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d2_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r2_alg_1 A B C) <=>  ((r1_alg_1 A B C) & (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(d2_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_algseq_1 A B C) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((k1_funct_1 B D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((m1_algspec1 B A) <=>  ( ((k9_xtuple_0 B) = (k10_xtuple_0 A))  &  ((k3_relat_1 B A) = (k6_partfun1 (k10_xtuple_0 A))) ) ) ) ) ) ) ).
tt(d2_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_algstr_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A (k4_struct_0 A) B) = B) ) ) ) ) ) ).
tt(d2_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v3_algstr_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_algstr_2 A B C) = (k1_algstr_0 A B (k1_algstr_2 A C))) ) ) ) ) ) ) ).
tt(d2_algstr_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k2_algstr_3)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k2_multop_1 k1_numbers k1_numbers k1_numbers k1_numbers A B C D) = (k7_real_1 (k8_real_1 B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_algstr_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_algstr_4 A B) <=>  ((r1_tarski (k9_xtuple_0 B) (k9_xtuple_0 A)) & (r1_partfun1 A B)) ) ) ) ) ) ).
tt(d2_altcat_1,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  ((v2_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ((k1_altcat_1 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_altcat_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  ((r2_altcat_2 A B C D) <=>  ((r1_tarski A B) &  (! [E:$i] :  ((r2_hidden E A) => (r1_tarski (k1_funct_1 C E) (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(d2_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v1_altcat_3 D A B C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) & (r1_altcat_3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (m1_altcat_2 B A)) ) )  =>  ( (B = (k2_altcat_4 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C D)) =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  & (v5_altcat_3 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ami_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 2 k1_ami_3) (k11_memstr_0 2 k1_ami_3)))))  =>  ( (A = k2_ami_4)  <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_finset_1 C)) ) ) )  =>  ((r2_hidden (k4_tarski B C) A) <=>  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (B = (k12_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1) D E))  &  (C = (k11_ami_3 (k10_ami_3 k6_numbers) (k3_int_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_extpro_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_amistd_1 C A B) <=> (v1_amistd_1 (k2_compos_0 (u1_compos_1 B) C) A B)) ) ) ) ) ) ) ).
tt(d2_amistd_3,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  & (v1_finset_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) )  =>  ( (D = (k2_amistd_3 A B C))  <=>  ( ((k1_funct_1 D k1_xboole_0) = (k64_valued_1 C))  &  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 D)) =>  ( ((k1_trees_2 (k9_xtuple_0 D) E) = (a_5_0_amistd_3 A B C D E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_card_1 (k1_amistd_1 A B (k3_trees_2 k5_numbers D E) (k7_partfun1 (u1_compos_1 B) C (k3_trees_2 k5_numbers D E))))) =>  ((k1_funct_1 D (k8_finseq_1 k5_numbers E (k12_finseq_1 k5_numbers F))) = (k1_funct_1 (k1_amistd_3 A B (k1_amistd_1 A B (k3_trees_2 k5_numbers D E) (k7_partfun1 (u1_compos_1 B) C (k3_trees_2 k5_numbers D E)))) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  ((v1_ami_wstd B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_ami_wstd A B C D) & (r1_ami_wstd A B D C))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analmetr A B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (B = (k3_rlvect_1 A (k1_rlvect_1 A D F) (k1_rlvect_1 A E G)))  &  ( (C = (k3_rlvect_1 A (k1_rlvect_1 A D H) (k1_rlvect_1 A E I)))  &  ((k7_real_1 (k8_real_1 F H) (k8_real_1 G I)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) <=> (r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (u1_analoaf A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_analort A B C D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_geomtrap A B C D)) (k1_rlvect_1 A C (k1_real_1 (k2_geomtrap A B C D))))) ) ) ) ) ) ) ) ) ).
tt(d2_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_anproj_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  &  (~  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_anproj_2 A B C D E F G) <=>  ((r2_anproj_1 A B C G) &  ((r2_anproj_1 A B D F) & (r2_anproj_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  =>  ((v1_aofa_000 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k10_finseq_1 B C) (k9_xtuple_0 A)) &  ((r2_hidden (k10_finseq_1 C D) (k9_xtuple_0 A)) &  ((r2_hidden (k10_finseq_1 (k1_funct_1 A (k10_finseq_1 B C)) D) (k9_xtuple_0 A)) & (r2_hidden (k10_finseq_1 B (k1_funct_1 A (k10_finseq_1 C D))) (k9_xtuple_0 A))) ) )  =>  ((k1_funct_1 A (k10_finseq_1 (k1_funct_1 A (k10_finseq_1 B C)) D)) = (k1_funct_1 A (k10_finseq_1 B (k1_funct_1 A (k10_finseq_1 C D))))) ) ) ) ) ) ) ) ).
tt(d2_aofa_i00,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k9_funct_2 A k4_numbers) B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) B) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) => (m1_aofa_i00 E A B C D)) ) ) ) ) ) ) ).
tt(d2_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((r1_armstrng A B) <=>  ((r2_hidden A B) &  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (A = (k3_xboole_0 C D))  &  ( (~  (A = C) )  &  (~  (A = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_arrow A))) =>  ( (B = (k3_arrow A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_arrow A)) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski E D) C))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2))  =>  ( (C = (k2_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = D)  &  ( (B = E)  &  (C = (k8_arytm_2 D E)) ) ) ) ) ) ) ) )  &  ( ( ((r2_hidden A k2_arytm_2) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ( (A = k6_numbers)  |  ( (C = (k2_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = D)  &  ( (B = (k4_tarski k6_numbers E))  &  (C = (k4_tarski k6_numbers (k8_arytm_2 D E))) ) ) ) ) ) ) ) ) )  &  ( ( ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ( (B = k6_numbers)  |  ( (C = (k2_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = (k4_tarski k6_numbers D))  &  ( (B = E)  &  (C = (k4_tarski k6_numbers (k8_arytm_2 E D))) ) ) ) ) ) ) ) ) )  &  ( ( ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ( (C = (k2_arytm_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  (? [E:$i] :  ((m1_subset_1 E k2_arytm_2) &  ( (A = (k4_tarski k6_numbers D))  &  ( (B = (k4_tarski k6_numbers E))  &  (C = (k8_arytm_2 E D)) ) ) ) ) ) ) ) )  &  (~  ( (~  ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2)) )  &  ( (~  ((r2_hidden A k2_arytm_2) &  ((r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  (~  (A = k6_numbers) ) ) ) )  &  ( (~  ((r2_hidden B k2_arytm_2) &  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  (~  (B = k6_numbers) ) ) ) )  &  ( (~  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) )  &  (~  ( (C = (k2_arytm_0 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r1_arytm_2 B A) =>  ((k2_arytm_1 A B) = (k1_arytm_1 A B)) )  &  ( (~ (r1_arytm_2 B A))  =>  ((k2_arytm_1 A B) = (k4_tarski k11_arytm_3 (k1_arytm_1 B A))) ) ) ) ) ) ) ).
tt(d2_arytm_2,ax, (k2_arytm_2 = (k6_subset_1 (k2_xboole_0 k5_arytm_3 k1_arytm_2) a_0_1_arytm_2)) ).
tt(d2_arytm_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_arytm_3 A B) <=>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ( (A = (k11_ordinal2 C D))  &  (B = (k11_ordinal2 C E)) )  =>  (C = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_asympt_0 A) <=>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) ) ) ) ) ).
tt(d2_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (A = k2_asympt_1)  <=>  ( ((k1_seq_1 A k6_numbers) = k6_numbers)  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_seq_1 A B) = (k6_power 2 B)) ) ) ) ) ) ) ) ).
tt(d2_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_autalg_1 A) (k1_autalg_1 A)) (k1_autalg_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_autalg_1 A) (k1_autalg_1 A)) (k1_autalg_1 A))))) )  =>  ( (B = (k2_autalg_1 A))  <=>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) =>  ((k5_binop_1 (k1_autalg_1 A) B C D) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_autgroup A) (k1_autgroup A)) (k1_autgroup A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_autgroup A) (k1_autgroup A)) (k1_autgroup A))))) )  =>  ( (B = (k2_autgroup A))  <=>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A)) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A)) =>  ((k5_binop_1 (k1_autgroup A) B C D) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A B) = (k1_bcialg_1 A (k4_struct_0 A) B)) ) ) ) ) ).
tt(d2_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_2 B A) <=> (r1_bcialg_1 A (k4_struct_0 A) B)) ) ) ) ) ).
tt(d2_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d2_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ((v2_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A B (k1_bcialg_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_xxreal_0 k6_numbers B) =>  ((k3_bcialg_6 A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k2_bcialg_6 A) C (k1_int_2 B))) )  &  ( (~ (r1_xxreal_0 k6_numbers B))  =>  ((k3_bcialg_6 A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k2_bcialg_6 A) (k2_bcialg_1 A C) (k1_int_2 B))) ) ) ) ) ) ) ) ) ).
tt(d2_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bhsp_1 A))  =>  ((v2_bhsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_bhsp_1 A B B) = k6_numbers)  =>  (B = (k4_struct_0 A)) )  &  ( ( (B = (k4_struct_0 A))  =>  ((k1_bhsp_1 A B B) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_bhsp_1 A B B)) &  ( ((k1_bhsp_1 A B C) = (k1_bhsp_1 A C B))  &  ( ((k1_bhsp_1 A (k1_algstr_0 A B C) D) = (k7_real_1 (k1_bhsp_1 A B D) (k1_bhsp_1 A C D)))  &  ((k1_bhsp_1 A (k1_rlvect_1 A B E) C) = (k8_real_1 E (k1_bhsp_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k1_bhsp_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k4_bhsp_1 A (k1_normsp_1 A B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_bhsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k4_bhsp_1 A (k1_normsp_1 A B F) (k1_normsp_1 A C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) <=> (v1_bhsp_2 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(d2_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_bhsp_6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 E))  &  ((r1_tarski E B) &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski E F) &  ((r1_tarski F B) & (r1_xxreal_0 D (k3_bhsp_1 A (k5_algstr_0 A C (k1_bhsp_6 A F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( (F = (k2_bilinear A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) F G H) = (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D G H) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ((k2_binari_2 A B) = (k7_binarith A (k3_binarith A B) (k1_binari_2 A))) ) ) ) ) ).
tt(d2_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ( (~ (r1_xxreal_0 k6_numbers B))  =>  ((k2_binari_4 A B) = (k1_binari_3 A (k1_int_2 (k20_binop_2 (k5_series_1 2 (k1_binari_4 A (k1_int_2 B))) B)))) )  &  ((r1_xxreal_0 k6_numbers B) =>  ((k2_binari_4 A B) = (k1_binari_3 A (k1_int_2 B))) ) ) ) ) ) ) ).
tt(d2_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k6_margrel1))  =>  ( (D = (k4_binarith A B C))  <=>  ( ((k7_partfun1 k6_margrel1 D 1) = k7_margrel1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 A E) |  ((k7_partfun1 k6_margrel1 D (k1_nat_1 E 1)) = (k1_binarith (k1_binarith (k10_margrel1 (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 C E)) (k10_margrel1 (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 D E))) (k10_margrel1 (k7_partfun1 k6_margrel1 C E) (k7_partfun1 k6_margrel1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_binom A B C) = (k1_binop_1 (k4_group_1 A) B C)) ) ) ) ) ) ) ).
tt(d2_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A B C D) = (k3_binop_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(d2_bintree1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((v1_bintree1 A) <=>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( (~ (r2_hidden B (k3_trees_1 A)))  =>  ((k1_trees_2 A B) = (k2_tarski (k7_finseq_1 B (k9_finseq_1 k6_numbers)) (k7_finseq_1 B (k9_finseq_1 1)))) ) ) ) ) ) ) ).
tt(d2_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((v1_bintree2 A) <=>  (A = (k3_finseq_2 (k7_domain_1 k5_numbers k6_numbers 1))) ) ) ) ).
tt(d2_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_boolealg A B C) = (k3_lattices A (k1_boolealg A B C) (k1_boolealg A C B))) ) ) ) ) ) ) ).
tt(d2_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_boolmark A B C) <=> (r1_tarski (k7_relat_1 B (k8_petri A (k6_domain_1 (u4_struct_0 A) C))) (k6_domain_1 k6_margrel1 k8_margrel1))) ) ) ) ) ) ) ).
tt(d2_bor_cant,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (C = (k3_bor_cant A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k5_numbers C D) = (k1_bor_cant k5_numbers D A (k2_nat_1 D B) D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k2_borsuk_1 A B))  <=>  ( ((u1_struct_0 C) = (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))  &  ((u1_pre_topc C) = (a_3_0_borsuk_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(d2_borsuk_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_2 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  ((m1_borsuk_2 D A B C) <=>  ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_borsuk_5 A B) = (k9_subset_1 k1_numbers k3_numbers (k2_rcomp_1 A B))) ) ) ) ) ).
tt(d2_borsuk_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_borsuk_7 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden (k30_valued_1 B) (k9_xtuple_0 A)) &  (C = (k1_funct_1 A B)) ) )  =>  ((k1_funct_1 A (k30_valued_1 B)) = (k30_valued_1 C)) ) ) ) ) ) ) ) ) ).
tt(d2_brouwer,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k2_brouwer A B C) = (k1_pre_topc (k15_euclid A) (k2_topreal9 A B C))) ) ) ) ) ) ) ).
tt(d2_bspace,ax, (k2_bspace = (k9_int_3 2)) ).
tt(d2_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((r1_bvfunc_2 A B C) <=>  ( (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((r2_hidden D B) => (r1_partit1 A D C)) ) )  &  (! [D:$i] :  ( ((r1_tarski D C) &  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r2_hidden E B) => (r1_partit1 A E D)) ) ) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(d2_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k2_c0sp2 A) = (a_1_0_c0sp2 A)) ) ) ).
tt(d2_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((k2_calcul_1 A B) = (k1_funct_1 B (k3_finseq_1 B))) )  &  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) =>  ((k2_calcul_1 A B) = (k5_cqc_lang A)) ) ) ) ) ) ) ).
tt(d2_calcul_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) )  =>  ((k3_calcul_2 A B C) = (k4_relset_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B) k5_numbers A C B)) ) ) ) ) ) ) ).
tt(d2_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_cantor_1 B A) <=> (r1_tarski (u1_pre_topc A) (k1_cantor_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(d2_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k1_card_1 A))  <=> (r2_wellord2 A B)) ) ) ) ).
tt(d2_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k2_card_2 A B) = (k1_card_1 (k2_zfmisc_1 A B))) ) ) ) ) ).
tt(d2_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ( (B = (k1_card_3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k1_card_1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_card_3 C)) )  =>  ( (C = (k2_card_5 A B))  <=>  ( (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) <=>  ((r2_hidden D A) & (v1_card_1 D)) ) )  &  (! [D:$i] :  ((v1_card_1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k3_card_2 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((m2_card_fil B A) <=>  ( (~ (r2_hidden A B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k4_subset_1 A C D) B))  &  ( ((r2_hidden C B) & (r1_tarski D C))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cardfin2,ax, (! [A:$i] :  ((k2_cardfin2 A) = (a_1_0_cardfin2 A)) ) ).
tt(d2_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_tarski (k10_xtuple_0 A)))) =>  ( (D = (k2_card_fin A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (k3_tarski (k10_xtuple_0 A))) &  (! [F:$i] :  ( ((r2_hidden F (k9_xtuple_0 B)) &  ((k1_funct_1 B F) = C) )  => (r2_hidden E (k1_funct_1 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((r2_card_lar A B) <=>  ((r1_tarski B A) &  (! [C:$i] :  ( ((v3_ordinal1 C) &  ((v4_ordinal1 C) &  (~ (v1_finset_1 C)) ) )  =>  ( ((r2_hidden C A) &  ((k3_ordinal2 (k3_xboole_0 B C)) = C) )  => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d2_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( (C = (k2_cat_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (m2_cat_1 D A B)) ) ) ) ) ) ) ) ).
tt(d2_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (D = (k3_cat_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k4_graph_1 A (k7_partfun1 (u4_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v1_cat_4 A) <=>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_cat_3 E A D B) &  ((r2_funct_2 B (u1_struct_0 A) (k3_cat_3 A B E) C) & (r1_cat_3 A D B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (~  ( (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m3_cat_2 A C) & (m3_cat_2 B C)) ) )  &  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 B))) )  &  (~  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  ( (C = (k3_cat_5 A B))  <=>  ( ((u1_struct_0 C) = (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u4_struct_0 C) = (k3_xboole_0 (u4_struct_0 A) (u4_struct_0 B)))  &  ( ((u1_graph_1 C) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) (u4_struct_0 B)))  &  ( ((u2_graph_1 C) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) (u4_struct_0 B)))  &  ((u1_cat_1 C) = (k1_realset1 (u1_cat_1 A) (u4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 (k7_domain_1 k5_numbers k6_numbers 1)))) =>  ( (C = (k2_catalan2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v5_ordinal1 E) &  ((v1_relat_1 E) &  ((v5_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) ) )  &  ( (E = D)  &  ((v1_catalan2 E) &  ( ((k1_relset_1 k5_numbers E) = A)  &  ((k7_afinsq_2 E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cayley,ax, (! [A:$i] :  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_monoid_0 B) & (l3_algstr_0 B)) )  =>  ( (B = (k2_cayley A))  <=>  ( ((u1_struct_0 B) = (k1_cayley A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_algstr_0 B C D) = (k3_relat_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_cc0sp1 B A) <=>  ((v1_ideal_1 B A) &  ((v1_c0sp1 B A) &  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_clvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cc0sp2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_cc0sp2 A B) = (k7_funcop_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(d2_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((r2_cfcont_1 A B) <=>  ((r1_tarski B (k1_relset_1 k2_numbers A)) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r2_hidden C B) => (r1_cfcont_1 (k5_relset_1 k2_numbers k2_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d2_cfdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k1_cfdiff_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers B C) = (k10_real_1 1 (k7_real_1 C A))) ) ) ) ) ) ) ) ).
tt(d2_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) )  =>  ( (B = (k2_cfuncdom A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers B C D) (k3_funcsdom k2_numbers A k29_binop_2 C D))) ) ) ) ) ) ) ) ) ).
tt(d2_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( (C = (k2_cfunct_1 A B))  <=>  ( ((k1_relset_1 A C) = (k7_subset_1 A (k1_relset_1 A B) (k8_relset_1 A k2_numbers B (k1_tarski k6_numbers))))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k7_partfun1 k2_numbers C D) = (k12_complex1 (k7_partfun1 k2_numbers B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (B = (k2_cgames_1 A))  <=>  (? [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) & (v1_funct_1 C)) )  &  ((r2_hidden A (k9_xtuple_0 C)) &  ( ((k1_funct_1 C A) = B)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (a_2_0_cgames_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((v1_xboole_0 A) <=>  (~ (r1_xxreal_0 1 A)) ) ) ) ).
tt(d2_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_chord B A) <=>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A B) C) => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(d2_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  ((v2_circcmb3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) => (v1_circcmb3 C A B)) ) ) ) ) ) ) ).
tt(d2_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_msualg_1 C) & (l1_msualg_1 C)) )  =>  ( (C = (k2_circcomb A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u4_struct_0 C) = (k2_xboole_0 (u4_struct_0 A) (u4_struct_0 B)))  &  ( ((u1_msualg_1 C) = (k1_funct_4 (u1_msualg_1 A) (u1_msualg_1 B)))  &  ((u2_msualg_1 C) = (k1_funct_4 (u2_msualg_1 A) (u2_msualg_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k1_circled1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v3_rltopsp1 D A) & (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) =>  (! [E:$i] :  ((l3_msualg_1 E A) =>  (! [F:$i] :  ( (F = (k2_circtrm1 A B C D E))  <=>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ( (G = D)  =>  (F = (k1_funct_1 (u3_msualg_1 A E) (k7_msaterm A B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  ((v1_msafree2 A) =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_circuit1 A B C D) = (k1_funct_1 (k10_funct_6 C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B))) =>  ( (D = (k3_circuit2 A B C))  <=>  ((r1_msualg_3 A (k5_msafree2 A B) (k5_msafree2 A B) D) & (r2_pboole (u1_struct_0 A) (k2_circuit2 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_classes1,ax, (! [A:$i] :  ((v2_classes1 A) <=>  ((v1_classes1 A) &  ( (! [B:$i] :  ((r2_hidden B A) => (r2_hidden (k9_setfam_1 B) A)) )  &  (! [B:$i] :  (~  ((r1_tarski B A) &  ( (~ (r2_tarski B A))  &  (~ (r2_hidden B A)) ) ) ) ) ) ) ) ) ).
tt(d2_classes2,ax, (k13_classes2 = (k1_classes1 k1_xboole_0)) ).
tt(d2_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k3_clopban1 A B) = (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) ) ) ) ) ).
tt(d2_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  ((k3_clopban2 A B C) = (k1_clopban2 A (k11_clopban1 A A B) (k11_clopban1 A A C))) ) ) ) ) ) ) ).
tt(d2_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_clopban3 A B) = (k7_clvect_1 A (k1_bhsp_4 A B))) ) ) ) ) ).
tt(d2_clopban4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k2_clopban4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k1_normsp_1 B E F) = (k6_algstr_0 B (k1_clvect_1 B (k6_clopban3 B C F) (k8_nat_1 k2_numbers (k5_sin_cos A) F)) (k6_clopban3 B D (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k1_normsp_1 B E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ((v2_closure1 C A B) <=>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  ((r2_pboole A D E) => (r2_pboole A (k2_closure1 A B C D) (k2_closure1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_closure2,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( (~  (A = k1_xboole_0) )  =>  ( (B = (k3_closure2 A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v4_funct_1 C))  &  ( (C = A)  &  ( ((k9_xtuple_0 B) = (k1_setfam_1 (a_1_0_closure2 C)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 B D) = (a_2_0_closure2 C D)) ) ) ) ) ) ) ) )  &  ( (A = k1_xboole_0)  =>  ( (B = (k3_closure2 A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d2_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m3_pboole D A B) =>  ( (D = (k2_closure3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k3_tarski (a_4_0_closure3 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v2_clvect_1 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_clvect_1 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k1_clvect_1 A C B) (k1_clvect_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d2_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k1_clvect_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k15_csspace A (k1_normsp_1 A B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_clvect_3 A B) = (k1_clvect_2 A (k1_bhsp_4 A B))) ) ) ) ) ).
tt(d2_cohsp_1,ax, (! [A:$i] :  ((k1_cohsp_1 A) = (k2_coh_sp A (k6_partfun1 A))) ) ).
tt(d2_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (k3_tarski A)) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) )  =>  ( (B = (k1_coh_sp A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  (? [E:$i] :  ((r2_hidden E A) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C D) <=> (r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C D) (u1_collsp A))) ) ) ) ) ) ) ) ) ).
tt(d2_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((v1_combgras B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~ (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_commacat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  ( (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (u4_struct_0 C)) & (r2_hidden H (k2_cat_1 C (k8_cat_1 A C D F) (k8_cat_1 B C E G)))) ) ) ) ) )  =>  ((k2_commacat A B C D E) = (a_5_1_commacat A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((r2_hidden A k1_numbers) =>  ( (B = (k2_complex1 A))  <=>  (B = k6_numbers) ) )  &  ( (~ (r2_hidden A k1_numbers))  =>  ( (B = (k2_complex1 A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C 2 k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 2 k1_numbers)))) )  &  ( (A = C)  &  (B = (k1_funct_1 C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d2_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_complex2 A B) = (k2_xcmplx_0 (k8_real_1 (k17_complex1 A) (k21_sin_cos (k7_real_1 B (k1_comptrig A)))) (k3_xcmplx_0 (k8_real_1 (k17_complex1 A) (k18_sin_cos (k7_real_1 B (k1_comptrig A)))) k7_complex1))) ) ) ) ) ).
tt(d2_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ((m1_complfld C A B) <=>  ((k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) C B) = A) ) ) ) ) ) ) ) ).
tt(d2_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k6_complsp2 A) = (k12_seq_4 (k9_seq_4 A (k1_complsp2 A)) (k18_binop_2 1 2))) ) ) ).
tt(d2_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k1_compl_sp A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 k1_numbers C D) = (k3_tbsp_1 A (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_compos_0,ax, (! [A:$i] :  ((v1_compos_0 A) =>  ((k1_compos_0 A) = (k11_xtuple_0 A)) ) ) ).
tt(d2_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  ((k2_compos_2 A B C) = (k8_compos_1 A B (k11_compos_1 A C))) ) ) ) ) ) ) ).
tt(d2_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((m1_comptrig C A B) <=>  ((k1_newton C B) = A) ) ) ) ) ) ) ) ).
tt(d2_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v4_pre_topc C A) &  ((r2_hidden B (k3_subset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r2_hidden B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_relat_1 A (k3_finseq_2 k5_numbers)))  =>  ((v2_comput_1 A) <=>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  & (r2_hidden B (k1_relset_1 (k3_finseq_2 k5_numbers) A)))  => (r2_hidden C (k1_relset_1 (k3_finseq_2 k5_numbers) A))) ) ) ) ) ) ) ) ).
tt(d2_comseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( (C = (k2_comseq_2 A B))  <=>  ( ((k1_relset_1 A C) = A)  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A k2_numbers C D) = (k15_complex1 (k3_funct_2 A k2_numbers B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_comseq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_comseq_3 A B) = (k8_nat_1 k2_numbers (k1_comseq_3 A) B)) ) ) ) ) ).
tt(d2_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r4_analmetr A B G B H) &  ((r4_analmetr A C E D F) &  ((r2_analoaf A B C E G) & (r4_analmetr A C G D H)) ) ) ) )  =>  ((r2_analoaf A B G B C) |  ((r2_analoaf A B C B E) | (r4_analmetr A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_conlat_1 A B C) <=> (r2_hidden (k4_tarski B C) (u1_conlat_1 A))) ) ) ) ) ) ) ).
tt(d2_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A)))) =>  ((k2_conlat_2 A B) = (k16_lattice3 (k11_conlat_1 A) B)) ) ) ) ) ).
tt(d2_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [L:$i] :  ((m1_subset_1 L (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 K A) &  ((v1_aff_1 L A) &  ((r2_hidden B K) &  ((r2_hidden B L) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r2_hidden D L) &  ((r2_hidden F L) &  ((r2_hidden H L) &  ((r2_hidden J L) &  ((r2_analoaf A E D I H) &  ((r2_analoaf A D C H G) & (r2_analoaf A C F G J)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden F K) |  ((r2_hidden D K) |  ((r2_hidden H K) |  ((r2_hidden J K) |  ((r2_hidden C L) |  ((r2_hidden E L) |  ((r2_hidden G L) |  ((r2_hidden I L) | (r2_analoaf A E F I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_analmetr I A) &  ((v4_analmetr J A) &  ((r2_hidden B I) &  ((r2_hidden C I) &  ((r2_hidden D I) &  ((r2_hidden E I) &  ((r2_hidden B J) &  ((r2_hidden F J) &  ((r2_hidden G J) &  ((r2_hidden H J) &  ((r2_analoaf A E G D F) & (r2_analoaf A E H C F)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden G I) |  ((r2_hidden E J) |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  | (r2_analoaf A C G D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_connsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ((r1_connsp_1 A B C) &  ( (~  (B = (k1_struct_0 A)) )  &  (~  (C = (k1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_connsp_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_connsp_2 C A B) <=> (r1_tarski B (k1_tops_1 A C))) ) ) ) ) ) ) ).
tt(d2_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_connsp_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) => (v3_connsp_1 D A)) ) )  &  (B = (k5_setfam_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ).
tt(d2_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r1_xxreal_0 E k6_numbers) |  ((r1_xxreal_0 1 E) | (r2_hidden (k1_algstr_0 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D (k9_real_1 1 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k2_numbers (k9_funct_2 (u1_struct_0 A) k2_numbers)) =>  ((k1_convex4 A B) = (a_2_0_convex4 A B)) ) ) ) ) ).
tt(d2_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) )  =>  ( (C = (k2_convfun1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) F G))  =>  ((k2_binop_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C D E) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k3_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k1_domain_1 k1_numbers (u1_struct_0 A) D F)) (k3_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)) (u1_struct_0 B) (u1_rlvect_1 B) (k1_domain_1 k1_numbers (u1_struct_0 B) D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k3_cqc_lang A) = (a_1_0_cqc_lang A)) ) ) ).
tt(d2_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_cqc_lang A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_cqc_lang A))))) )  =>  (! [D:$i] :  ((m2_funct_2 D B (k3_cqc_lang A) (k9_funct_2 B (k3_cqc_lang A))) =>  ( (D = (k2_cqc_sim1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (F = (k3_funct_2 B (k3_cqc_lang A) C E))  =>  ((k3_funct_2 B (k3_cqc_lang A) D E) = (k6_cqc_lang A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( (C = (k1_cqc_the1 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((v1_cqc_the1 E A) & (r1_tarski B E))  => (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r2_cqc_the3 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden D C) => (r3_cqc_the1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_csspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_csspace3 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_csspace3 k1_numbers)))) )  =>  ( (A = k2_csspace3)  <=>  (! [B:$i] :  ((r2_hidden B k1_csspace3) =>  ((k1_seq_1 A B) = (k4_series_1 (k55_valued_1 k5_numbers k2_numbers (k2_csspace B)))) ) ) ) ) ) ).
tt(d2_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_csspace4 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_csspace4 k1_numbers)))) )  =>  ( (A = k2_csspace4)  <=>  (! [B:$i] :  ((r2_hidden B k1_csspace4) =>  ((k1_seq_1 A B) = (k4_seq_4 (k2_relset_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace B))))) ) ) ) ) ) ).
tt(d2_csspace,ax, (! [A:$i] :  ((r2_hidden A k1_csspace) =>  ((k2_csspace A) = A) ) ) ).
tt(d2_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_decomp_1 B A) <=> (r1_tarski B (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ).
tt(d2_descip_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k7_descip_1 A) = (k16_finseq_1 (k3_finseq_1 A) (k7_finseq_1 (k9_finseq_1 (k1_funct_1 A (k3_finseq_1 A))) A))) ) ) ).
tt(d2_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_dickson B A) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_hidden (k4_tarski (k8_nat_1 (u1_struct_0 A) B C) (k8_nat_1 (u1_struct_0 A) B (k2_nat_1 C 1))) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(d2_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (C = (k2_diff_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k3_funct_2 k1_numbers k1_numbers A (k7_real_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(d2_diff_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ((k2_diff_2 A B C D E F G) = (k10_real_1 (k9_real_1 (k1_diff_2 A B C D E F) (k1_diff_2 A C D E F G)) (k6_xcmplx_0 B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_dilworth B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ( (C = D)  |  ( (~ (r1_orders_2 A C D))  &  (~ (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((k2_diraf A) = (g1_analoaf (u1_struct_0 A) (k1_diraf (u1_struct_0 A) (u1_analoaf A)))) ) ) ).
tt(d2_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((k3_dist_1 A B C) = (k12_binop_2 (k2_dist_1 A B C) (k3_finseq_1 B))) ) ) ) ) ) ).
tt(d2_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lang1 A) & (l1_lang1 A)) )  =>  ( (A = k5_dtconstr)  <=>  ( ((u1_struct_0 A) = (k7_domain_1 k5_numbers k6_numbers 1))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_lang1 A B C) <=>  ( (B = 1)  &  ( (C = (k3_pre_poly k5_numbers k6_numbers))  |  (C = (k3_pre_poly k5_numbers 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_prob_2 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 D C))  => (r1_xboole_0 (k8_nat_1 (k9_setfam_1 A) B C) (k8_nat_1 (k9_setfam_1 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  ((k1_ec_pf_2 A) = (a_1_0_ec_pf_2 A)) ) ) ).
tt(d2_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_endalg A) (k1_endalg A)) (k1_endalg A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_endalg A) (k1_endalg A)) (k1_endalg A))))) )  =>  ( (B = (k2_endalg A))  <=>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) =>  ((k5_binop_1 (k1_endalg A) B C D) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k2_ens_1 A) = (a_1_1_ens_1 A)) ) ) ).
tt(d2_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_entropy1 A B) <=>  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ( (C = B)  |  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (E = (k2_enumset1 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (~  ( (~  (F = A) )  &  ( (~  (F = B) )  &  ( (~  (F = C) )  &  (~  (F = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (D = (k5_eqrel_1 A B C))  <=>  ((r1_relset_1 A A (k3_eqrel_1 A B C) D) &  (! [E:$i] :  ( ((v3_relat_2 E) &  ((v8_relat_2 E) &  ((v1_partfun1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_relset_1 A A (k3_eqrel_1 A B C) E) => (r1_relset_1 A A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ( (D = (k2_equation A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ( ((v3_msualg_1 F A) & (m1_msualg_2 F A B))  &  ( (E = F)  & (m1_msualg_2 C A F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) =>  ((v3_e_siec A) <=>  ( ((k3_relat_1 (u1_e_siec A) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ((k3_relat_1 (u2_e_siec A) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0) ) ) ) ) ).
tt(d2_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k2_euclid_3 A) = (k2_xcmplx_0 (k17_euclid A) (k3_xcmplx_0 (k18_euclid A) k7_complex1))) ) ) ).
tt(d2_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v1_euclid_4 B A) <=>  (? [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) &  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  ( (~  (C = D) )  &  (B = (k2_euclid_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k2_euclid_5 A) = (k1_seq_1 A 2)) ) ) ).
tt(d2_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k2_euclid_6 A B C) = (k7_real_1 (k7_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) C B))) (k12_euclid (k5_algstr_0 (k15_euclid 2) A C)))) ) ) ) ) ) ) ).
tt(d2_euclid_7,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ((k2_euclid_7 A B C) = (k1_partfun1 (k4_finseq_1 B) (k4_finseq_1 B) k5_numbers A C B)) ) ) ) ) ) ).
tt(d2_euclid_8,ax, (k3_euclid_8 = (k1_euclid_8 k6_numbers 1 k6_numbers)) ).
tt(d2_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  ((k2_euclid_9 A B) = B) ) ) ) ) ).
tt(d2_euclid,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k2_euclid)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k18_complex1 B)) ) ) ) ) ) ).
tt(d2_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r3_euclidlp A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k7_euclid A (k9_euclid A B D) (k9_euclid A C E)) = (k5_euclid A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v2_euclmetr A) <=> (v2_aff_2 (k3_analmetr A))) ) ) ).
tt(d2_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v2_exchsort B A) <=>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((r2_hidden A (k9_xtuple_0 B)) & (r1_ordinal1 A C)) ) ) ) ) ) ) ) ).
tt(d2_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v2_memstr_0 B A) & (l1_extpro_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k2_extpro_1 A B C D) = (k1_funct_1 (k3_funct_2 (u1_compos_1 B) (k1_funct_2 (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B)))) (u1_extpro_1 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(d2_extreal1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (B = (k4_extreal1 A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (B = (k12_supinf_2 C (k3_finseq_1 A)))  &  ( ((k12_supinf_2 C k6_numbers) = k1_supinf_2)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) D))  =>  ((k12_supinf_2 C (k2_nat_1 D 1)) = (k3_supinf_2 (k12_supinf_2 C D) (k12_supinf_2 A (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_facirc_1,ax, (! [A:$i] :  ((v1_facirc_1 A) <=>  (? [B:$i] :  ((v1_xtuple_0 B) & (r2_hidden B A)) ) ) ) ).
tt(d2_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_fcont_1 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k1_relset_1 k1_numbers A)) => (r1_fcont_1 A B)) ) ) ) ) ) ).
tt(d2_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v2_fdiff_1 A) <=>  ((v1_partfun1 A k1_numbers) &  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v1_fdiff_1 B k6_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers B) (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers B) (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d2_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_fdiff_3 A B) <=>  ((r2_hidden B (k1_relset_1 k1_numbers A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k3_limfunc1 B) (k1_relset_1 k1_numbers A))) &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = B) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k1_seq_1 A B) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fdiff_9,ax, (k2_fdiff_9 = (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos)) ).
tt(d2_ff_siec,ax, (! [A:$i] :  ((k2_ff_siec A) = (k1_ff_siec A k1_xboole_0)) ) ).
tt(d2_fib_fusc,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k2_fib_fusc A))  <=>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (A = C)  &  (B = (k3_pre_ff C)) ) ) ) )  &  (~  ( (~ (m1_subset_1 A k5_numbers))  &  (B = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d2_fib_num2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (A = k2_fib_num2)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k5_numbers A B) = (k1_pre_ff B)) ) ) ) ) ) ).
tt(d2_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (D = (k3_fib_num3 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))))) )  &  ( (D = (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E C)))  &  ( ((k3_funct_2 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E k6_numbers) = (k2_fib_num3 A B))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k3_funct_2 k5_numbers (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E (k1_nat_1 F 1)) = (k2_fib_num3 (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E F)) (k2_nat_1 (k2_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E F)) (k3_domain_1 k5_numbers k5_numbers (k8_nat_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fib_num,ax, (k2_fib_num = (k13_complex1 (k6_xcmplx_0 1 (k7_square_1 5)) 2)) ).
tt(d2_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_filter_0 A B) = (a_2_0_filter_0 A B)) ) ) ) ) ).
tt(d2_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((m2_filter_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden (k1_domain_1 A A D E) B) & (r2_hidden (k1_domain_1 A A F G) B))  => (r2_hidden (k1_domain_1 A A (k5_binop_1 A C D F) (k5_binop_1 A C E G)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_filter_2 A B) = B) ) ) ) ) ).
tt(d2_finance1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((m1_finance1 A) <=>  ( ((k1_seq_1 A k6_numbers) = 1)  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) ) ) ) ).
tt(d2_finseq_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_finseq_1 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  ((k9_xtuple_0 A) = (k2_finseq_1 B)) ) ) ) ) ) ).
tt(d2_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((k2_finseq_2 A B) = (k7_funcop_1 (k2_finseq_1 A) B)) ) ) ) ).
tt(d2_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k2_finseq_3 A B) = (k3_relat_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k1_relset_1 k5_numbers B) (k1_tarski A))) B)) ) ) ) ) ).
tt(d2_finseq_4,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((k1_card_1 (k10_relat_1 A B)) = 1) ) ) ) ) ).
tt(d2_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k2_finseq_5 A B C) = (k8_finseq_1 A (k12_finseq_1 A C) (k2_rfinseq A (k4_finseq_4 B C) B))) ) ) ) ) ) ) ).
tt(d2_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k10_xtuple_0 B)) =>  ((k1_finseq_6 A B C) = (k8_finseq_1 A (k2_finseq_5 A B C) (k2_rfinseq A 1 (k1_finseq_5 A B C)))) )  &  ( (~ (r2_hidden C (k10_xtuple_0 B)))  =>  ((k1_finseq_6 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(d2_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ((k2_finseq_7 A B C D) = (k1_finseq_7 A (k1_finseq_7 A B C (k7_partfun1 A B D)) D (k7_partfun1 A B C))) )  &  ( (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) ) )  =>  ((k2_finseq_7 A B C D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k4_finseq_8 A B C))  <=>  ((r1_xxreal_0 (k3_finseq_1 D) (k3_finseq_1 C)) &  ( (D = (k3_finseq_8 A C 1 (k3_finseq_1 D)))  &  ( (D = (k3_finseq_8 A B (k2_nat_1 (k7_nat_d (k3_finseq_1 B) (k3_finseq_1 D)) 1) (k3_finseq_1 B)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k3_finseq_8 A C 1 E) = (k3_finseq_8 A B (k2_nat_1 (k7_nat_d (k3_finseq_1 B) E) 1) (k3_finseq_1 B))) )  => (r1_xxreal_0 E (k3_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_finseqop B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (r1_finseqop A C B)) ) ) ) ) ) ) ).
tt(d2_finset_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_finset_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (v1_finset_1 B)) ) ) ) ) ).
tt(d2_finsub_1,ax, (! [A:$i] :  ((v2_finsub_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k3_xboole_0 B C) A)) ) ) ) ) ).
tt(d2_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((r2_hidden C (k1_fin_topo A B)) & (r2_hidden C (k3_subset_1 (u1_struct_0 A) D)))  =>  ((k2_fintopo2 A B C D) = k8_margrel1) )  &  ( (~  ((r2_hidden C (k1_fin_topo A B)) & (r2_hidden C (k3_subset_1 (u1_struct_0 A) D))) )  =>  ((k2_fintopo2 A B C D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (C = (k2_fintopo3 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C D))  =>  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C (k2_nat_1 D 1)) = (k9_fin_topo A E)) ) ) ) ) )  &  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(d2_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_fintopo4 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_hidden E (u1_struct_0 A)) &  (F = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) )  => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k10_fintopo3 A k6_numbers E)) (k10_fintopo3 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))))) =>  ( (C = (k2_fintopo5 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (D = (k4_tarski E F))  =>  ((k1_fintopo5 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) C D) = (k2_zfmisc_1 (k1_fintopo5 (k2_finseq_1 A) (k2_finseq_1 A) (k1_fintopo4 A) E) (k1_fintopo5 (k2_finseq_1 B) (k2_finseq_1 B) (k1_fintopo4 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fintopo6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((m1_fintopo6 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r2_hidden C (u1_struct_0 B)) =>  ((k1_fin_topo B C) = (k3_xboole_0 (k9_relat_1 (u1_orders_2 A) C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(d2_fin_topo,ax, (! [A:$i] :  ((k3_fin_topo A) = (k1_tarski (k4_tarski A A))) ) ).
tt(d2_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ( (D = (k7_flang_1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 (k3_catalan2 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k3_catalan2 A)))))) )  &  ( (D = (k5_flang_1 (k3_catalan2 A) E C))  &  ( ((k5_flang_1 (k3_catalan2 A) E k6_numbers) = (k4_flang_1 A (k2_flang_1 A)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k5_flang_1 (k3_catalan2 A) E (k2_xcmplx_0 F 1)) = (k6_flang_1 A (k5_flang_1 (k3_catalan2 A) E F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_2 A B) = (k3_tarski (a_2_0_flang_2 A B))) ) ) ) ).
tt(d2_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_3 A B) = (k3_tarski (a_2_0_flang_3 A B))) ) ) ) ).
tt(d2_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v2_fomodel0 C A B) <=> (v1_fomodel0 B (k2_zfmisc_1 C A))) ) ) ) ) ) ).
tt(d2_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k2_fomodel1 A) = (k8_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (k6_domain_1 k5_numbers k6_numbers))) ) ) ).
tt(d2_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v7_fomodel1 C A) =>  ((m1_fomodel2 D A B C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) k6_margrel1)))) ) ) )  &  ( (~ (v7_fomodel1 C A))  =>  ((m1_fomodel2 D A B C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))))) )  =>  ( (C = (k2_fomodel3 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k3_finseq_2 (k3_finseq_2 (k1_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) =>  ((k3_funct_2 (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) C D) = (k1_fomodel3 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v1_fomodel4 B A) <=> (r2_hidden B (k1_fomodel4 A))) ) ) ) ).
tt(d2_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k2_frechet A B) = (k6_domain_1 (u1_struct_0 A) C)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k2_frechet2 A B))  <=> (r1_frechet A B C)) ) ) ) ) ) ) ) ).
tt(d2_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v1_frechet A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  & (v4_card_3 C)) ) ) ) ) ) ) ).
tt(d2_freealg,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_relat_1 A) <=>  (~ (r2_hidden k6_numbers (k10_xtuple_0 A))) ) ) ) ).
tt(d2_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_fscirc_1 A B C) = (k10_facirc_1 A B C k1_facirc_1)) ) ) ) ).
tt(d2_fscirc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k1_fscirc_2 A B C)) &  ((v4_msafree2 D (k1_fscirc_2 A B C)) &  ((v4_circcomb D (k1_fscirc_2 A B C)) &  ((v6_circcomb D (k1_fscirc_2 A B C)) & (l3_msualg_1 D (k1_fscirc_2 A B C))) ) ) )  =>  ( (D = (k2_fscirc_2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) )  &  ( ((k1_fscirc_2 A B C) = (k1_funct_1 E A))  &  ( (D = (k1_funct_1 F A))  &  ( ((k1_funct_1 E k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 F k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 G k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ( ( (~ (v2_struct_0 I))  & (l1_msualg_1 I))  =>  (! [J:$i] :  ( ((v4_msualg_1 J I) & (l3_msualg_1 J I))  =>  (! [K:$i] :  ( ( (I = (k1_funct_1 E H))  &  ( (J = (k1_funct_1 F H))  &  (K = (k1_funct_1 G H)) ) )  =>  ( ((k1_funct_1 E (k1_nat_1 H 1)) = (k2_circcomb I (k8_fscirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ( ((k1_funct_1 F (k1_nat_1 H 1)) = (k3_circcomb I (k8_fscirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K) J (k9_fscirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ((k1_funct_1 G (k1_nat_1 H 1)) = (k6_fscirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( (E = (k2_fsm_1 A B C D))  <=>  ( ((k1_funct_1 E 1) = C)  &  ( ((k3_finseq_1 E) = (k2_nat_1 (k3_finseq_1 D) 1))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F (k3_finseq_1 D)) &  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ( (G = (k1_funct_1 D F))  &  ( (H = (k1_funct_1 E F))  &  ( (I = (k1_funct_1 E (k1_nat_1 F 1)))  &  ((k1_fsm_1 A B G H) = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_fsm_2 A B C D) <=>  (? [E:$i] :  ((m2_finseq_1 E A) & (r1_fsm_1 A B (k8_finseq_1 A (k12_finseq_1 A D) E) (u2_fsm_1 A B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k2_ftacell1 A B C D E) = (k3_circcomb (k13_gfacirc1 A B C) (k13_gfacirc1 (k12_gfacirc1 A B C) E D) (k14_gfacirc1 A B C) (k14_gfacirc1 (k12_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d2_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_funcop_1 A B) = (k2_zfmisc_1 A (k1_tarski B))) ) ) ).
tt(d2_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) )  =>  ( (B = (k6_funcsdom A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers B C D) (k3_funcsdom k1_numbers A k35_binop_2 C D))) ) ) ) ) ) ) ) ).
tt(d2_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) =>  ( (C = (k1_funct_1 A B))  <=> (r2_hidden (k4_tarski B C) A)) )  &  ( (~ (r2_hidden B (k9_xtuple_0 A)))  =>  ( (C = (k1_funct_1 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d2_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k1_funct_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  ( (D = E)  &  ( ((k9_xtuple_0 E) = A)  & (r1_tarski (k10_xtuple_0 E) B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k3_funct_3 A))  <=>  ( ((k9_xtuple_0 B) = (k1_zfmisc_1 (k10_xtuple_0 A)))  &  (! [C:$i] :  ((r1_tarski C (k10_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k8_relat_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d2_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k2_funct_4 A))  <=>  ( (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) <=>  (? [D:$i] :  (? [E:$i] :  ( (C = (k4_tarski E D))  & (r2_hidden (k4_tarski D E) (k9_xtuple_0 A))) ) ) ) )  &  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k9_xtuple_0 A)) =>  ((k1_binop_1 B D C) = (k1_binop_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k2_funct_5 A))  <=>  ( (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) <=>  (? [D:$i] :  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  (? [F:$i] :  ( (C = (k4_tarski D F))  &  ((r2_hidden D (k9_xtuple_0 A)) &  ( (E = (k1_funct_1 A D))  & (r2_hidden F (k9_xtuple_0 E))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden C (k9_xtuple_0 B)) &  (D = (k1_funct_1 A (k1_xtuple_0 C))) )  =>  ((k1_funct_1 B C) = (k1_funct_1 D (k2_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k2_funct_6 A))  <=>  ( ((k9_xtuple_0 B) = (k8_relat_1 A (k1_funct_6 (k10_xtuple_0 A))))  &  (! [C:$i] :  ((r2_hidden C (k8_relat_1 A (k1_funct_6 (k10_xtuple_0 A)))) =>  ((k1_funct_1 B C) = (k9_xtuple_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_funct_7 A B C) <=>  ((k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) C)) = (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) C))) ) ) ) ) ) ) ).
tt(d2_funct_8,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_funct_8 A) <=> (v1_funct_8 (k9_xtuple_0 A))) ) ) ).
tt(d2_funct_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_9 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) & (v1_funct_9 A B)) ) ) ) ) ).
tt(d2_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (k2_zfmisc_1 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B))))) )  =>  ((v2_functor0 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (r8_binop_1 A A (k2_zfmisc_1 B B) C (k1_functor0 A A (k2_zfmisc_1 B B) (k16_funct_3 A A B B D D)))) ) ) ) ) ) ) ).
tt(d2_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  ((r1_functor2 A B C D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 A)) &  ((v1_funct_1 E) & (v1_partfun1 E (u1_struct_0 A))) ) )  =>  ((m1_functor2 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (m1_subset_1 (k1_funct_1 E F) (k1_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  =>  (! [G:$i] :  ((m1_functor2 G B C D E) =>  ((r1_functor2 B C D E) =>  (! [H:$i] :  ((m1_functor2 H A C (k1_functor3 A B C F D) (k1_functor3 A B C F E)) =>  ( (H = (k6_functor3 A B C D E F G))  <=>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k1_funct_1 H I) = (k2_functor2 B C D E G (k3_functor0 A B F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_fuzzy_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d2_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (D = (k2_fuzzy_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_seq_1 D E) = (k8_real_1 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F A) & (r2_hidden G C))  =>  (! [H:$i] :  ( ((v5_relat_1 H (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 H) &  ((v1_funct_2 H B k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) )  =>  ( (H = (k3_fuzzy_4 A B C D E F G))  <=>  (! [I:$i] :  ((m1_subset_1 I B) =>  ((k1_seq_1 H I) = (k1_square_1 (k1_seq_1 D (k4_tarski F I)) (k1_seq_1 E (k4_tarski I G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_fvaluat1,ax, (! [A:$i] :  ((v2_membered A) =>  ( (? [B:$i] :  ( ((v2_xxreal_0 B) & (v1_fvaluat1 B))  & (r2_hidden B A)) )  =>  (! [B:$i] :  ( ((v2_xxreal_0 B) & (v1_fvaluat1 B))  =>  ( (B = (k1_fvaluat1 A))  <=>  ((r2_hidden B A) &  (! [C:$i] :  ( ((v2_xxreal_0 C) & (v1_fvaluat1 C))  =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k2_fvsum_1 A) = (k7_finseqop (u1_struct_0 A) (u1_algstr_0 A) (k6_partfun1 (u1_struct_0 A)) (k5_vectsp_1 A))) ) ) ).
tt(d2_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_gate_5 A B C D) = (k10_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0)) ) ) ) ) ).
tt(d2_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_gcd_1 B A) <=> (r1_gcd_1 A B (k5_struct_0 A))) ) ) ) ) ).
tt(d2_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_genealg1 A B C D) = (k8_finseq_1 (k3_card_3 A) (k17_finseq_1 (k3_card_3 A) D B) (k2_rfinseq (k3_card_3 A) D C))) ) ) ) ) ) ) ) ) ).
tt(d2_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k1_geomtrap A B C))  <=>  ((k3_rlvect_1 A D D) = (k3_rlvect_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 1 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k2_gfacirc1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ((k1_funct_1 A (k10_binarith k6_margrel1 B)) = B) ) ) ) ) ) ).
tt(d2_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k1_gfacirc2 A B C)) &  ((v4_msafree2 D (k1_gfacirc2 A B C)) &  ((v4_circcomb D (k1_gfacirc2 A B C)) &  ((v6_circcomb D (k1_gfacirc2 A B C)) & (l3_msualg_1 D (k1_gfacirc2 A B C))) ) ) )  =>  ( (D = (k2_gfacirc2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) )  &  ( ((k1_gfacirc2 A B C) = (k1_funct_1 E A))  &  ( (D = (k1_funct_1 F A))  &  ( ((k1_funct_1 E k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 F k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 G k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ( ( (~ (v2_struct_0 I))  & (l1_msualg_1 I))  =>  (! [J:$i] :  ( ((v4_msualg_1 J I) & (l3_msualg_1 J I))  =>  (! [K:$i] :  ( ( (I = (k1_funct_1 E H))  &  ( (J = (k1_funct_1 F H))  &  (K = (k1_funct_1 G H)) ) )  =>  ( ((k1_funct_1 E (k1_nat_1 H 1)) = (k2_circcomb I (k13_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ( ((k1_funct_1 F (k1_nat_1 H 1)) = (k3_circcomb I (k13_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K) J (k14_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ((k1_funct_1 G (k1_nat_1 H 1)) = (k9_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_glib_000,ax, (k2_glib_000 = 2) ).
tt(d2_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k7_glib_000 A)) =>  ((m2_glib_001 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (k6_glib_000 A)) &  ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 B) 1))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  => (r1_glib_000 A (k1_funct_1 C D) (k1_funct_1 C (k2_nat_1 D 1)) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v2_glib_002 A) <=>  (! [B:$i] :  ((m3_glib_001 B A) =>  (~ (v8_glib_001 B A)) ) ) ) ) ) ).
tt(d2_glib_003,ax, (k3_glib_003 = 6) ).
tt(d2_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_glib_001 B A) &  ((v5_glib_001 B A) & (m3_glib_001 B A)) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_glib_004 A B C D) <=>  ((r1_glib_001 A C D B) &  (! [E:$i] :  ( ((v2_glib_001 E A) &  ((v5_glib_001 E A) & (m3_glib_001 E A)) )  =>  ((r1_glib_001 A C D E) => (r1_xxreal_0 (k10_glib_003 A B) (k10_glib_003 A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_005 A B C D) <=>  ((m1_subset_1 C (k6_glib_000 A)) &  ((m1_subset_1 D (k6_glib_000 A)) &  ( (! [E:$i] :  ((r2_hidden E (k7_glib_000 A)) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) & (r1_xxreal_0 (k1_funct_1 B E) (k1_funct_1 (k5_glib_003 A) E))) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ( (~  (E = C) )  &  ( (~  (E = D) )  &  (~  ((k3_uproots (k26_glib_000 A E) (k5_relat_1 B (k26_glib_000 A E))) = (k3_uproots (k27_glib_000 A E) (k5_relat_1 B (k27_glib_000 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k2_goboard1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ((k2_goboard2 A) = (k1_goboard2 (k28_seq_4 (k1_goboard1 A)) (k28_seq_4 (k2_goboard1 A)))) ) ) ).
tt(d2_goboard4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_goboard4 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((r1_xxreal_0 B (k1_seq_1 A D)) & (r1_xxreal_0 (k1_seq_1 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_goboard5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k1_matrix_1 A) B) |  ((k2_goboard5 A B) = (a_2_3_goboard5 A B)) ) )  &  ( ((r1_xxreal_0 (k1_matrix_1 A) B) =>  ((k2_goboard5 A B) = (a_2_4_goboard5 A B)) )  &  (~  ( (~  ((r1_xxreal_0 1 B) &  (~ (r1_xxreal_0 (k1_matrix_1 A) B)) ) )  &  ( (~ (r1_xxreal_0 (k1_matrix_1 A) B))  &  (~  ((k2_goboard5 A B) = (a_2_5_goboard5 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (k3_goboard9 A))  <=>  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) B) & (r1_tarski (k1_tops_1 (k15_euclid 2) (k4_goboard5 A 1)) B)) ) ) ) ) ) ).
tt(d2_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_gobrd10 A B C D) <=>  ( ((r1_gobrd10 A C) &  (B = D) )  |  ( (A = C)  & (r1_gobrd10 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_gobrd13,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (D = (k2_gobrd13 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B E F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  (D = (k3_goboard5 B E F)) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  (D = (k3_goboard5 B E (k7_nat_d F 1))) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  (D = (k3_goboard5 B G H)) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  (D = (k3_goboard5 B (k7_nat_d E 1) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v2_goedelcp B A) <=>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (? [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) & (r1_henmodel A B (k9_cqc_lang A (k6_cqc_lang A (k12_cqc_lang A C D)) (k4_substut2 A D C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_graph_2 A B) = (k7_finseq_1 A (k1_graph_2 B 2 (k3_finseq_1 B)))) ) ) ) ) ).
tt(d2_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) =>  ( (D = (k3_graph_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E (u4_struct_0 A)) &  ((r2_hidden E C) &  ((k1_funct_1 (u1_graph_1 A) E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  ((k2_graph_5 A B) = (a_2_2_graph_5 A B)) ) ) ) ) ).
tt(d2_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_funct_2 A A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_funct_2 A A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_funct_2 A A))))) )  =>  ( (C = (k5_graphsp A B))  <=>  ( ((k8_nat_1 (k1_funct_2 A A) C k6_numbers) = (k11_cqc_sim1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 (k1_funct_2 A A) C (k1_nat_1 D 1)) = (k3_graphsp A (k8_nat_1 (k1_funct_2 A A) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_grcat_1 A B) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) (k1_grcat_1 A B))) ) ) ) ) ).
tt(d2_gr_cy_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  ((k1_gr_cy_1 A) = (k1_finsop_1 k4_numbers A k44_binop_2)) ) ) ).
tt(d2_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_gr_cy_3 A) <=>  ((v7_ordinal1 (k2_nat_1 (k4_nat_1 2 A) 1)) & (v1_int_2 (k2_nat_1 (k4_nat_1 2 A) 1))) ) ) ) ).
tt(d2_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_grnilp_1 A) <=>  (? [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_xcmplx_0 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  =>  ( ( (D = (k1_funct_1 B C))  &  (E = (k1_funct_1 B (k2_xcmplx_0 C 1))) )  =>  ((m1_group_6 E A D) & (m1_group_6 (k5_group_6 D (k1_group_6 A D E)) (k5_group_6 A E) (k10_group_5 (k5_group_6 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k15_pre_poly A))) =>  ((k3_groeb_1 A B) = (a_2_0_groeb_1 A B)) ) ) ) ) ).
tt(d2_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (D = (k2_groeb_2 A B C))  <=>  (! [E:$i] :  ((k1_recdef_1 D E) = (k7_nat_1 (k1_recdef_1 B E) (k1_recdef_1 C E))) ) ) ) ) ) ) ) ) ) ).
tt(d2_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k15_pre_poly A))))  =>  ( (F = (k3_groeb_3 A B C D E))  <=>  ((r1_tarski F (k2_polynom1 (k15_pre_poly A) C D)) &  ( ((k5_card_1 F) = E)  &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  ( ((r2_hidden G F) &  ((r2_hidden H (k2_polynom1 (k15_pre_poly A) C D)) & (r1_termord A B G H)) )  => (r2_hidden H F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 A))) &  ((v1_group_10 B A (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 A)))))) ) )  =>  ( (B = (k2_group_10 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 A)) B C) = (k1_topgrp_1 A C)) ) ) ) ) ) ) ) ).
tt(d2_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k2_group_11 A B C) = (a_3_1_group_11 A B C)) ) ) ) ) ) ) ).
tt(d2_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D (k2_group_7 A B)))  =>  ( (D = (k2_group_12 A B C))  <=>  ((u1_struct_0 D) = (k1_group_12 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v2_group_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = C)  &  ( ((k6_algstr_0 A B C) = C)  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( ((k6_algstr_0 A C D) = B)  &  ((k6_algstr_0 A D C) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_group_2 A B C) = (a_3_0_group_2 A B C)) ) ) ) ) ) ) ).
tt(d2_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_3 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A C) B) C)) ) ) ) ) ) ) ).
tt(d2_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k3_group_4 A B) = (k1_finsop_1 (u1_struct_0 A) B (u2_algstr_0 A))) ) ) ) ) ).
tt(d2_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A B) (k2_group_1 A C)) B) C)) ) ) ) ) ) ) ).
tt(d2_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((v7_struct_0 A) <=>  (? [B:$i] :  ((u1_struct_0 A) = (k1_tarski B)) ) ) ) ) ).
tt(d2_group_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (l3_algstr_0 C))  =>  ( (C = (k2_group_7 A B))  <=>  ( ((u1_struct_0 C) = (k4_card_3 (k12_pralg_1 A B)))  &  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k12_pralg_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k12_pralg_1 A B))) =>  (! [F:$i] :  (~  ((r2_hidden F A) &  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l3_algstr_0 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (~  ( (G = (k1_funct_1 B F))  &  ( (H = (k1_binop_1 (u2_algstr_0 C) D E))  &  ((k1_funct_1 H F) = (k1_binop_1 (u2_algstr_0 G) (k1_funct_1 D F) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ( (E = (k1_group_9 A B C D))  <=>  ((r1_tarski D E) &  ((r1_group_9 A B C E) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ( ((r1_group_9 A B C F) & (r1_tarski D F))  => (r1_tarski E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((v2_group_10 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k1_groupp_1 A B))  <=>  ((k7_struct_0 B) = (k1_newton A C)) ) ) ) ) ) ) ) ) ).
tt(d2_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k1_grsolv_1 A B C D) = (k5_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D))) ) ) ) ) ) ) ) ) ).
tt(d2_hahnban1,ax, (k2_hahnban1 = k7_complex1) ).
tt(d2_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v2_hahnban B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k3_rlvect_1 A C D)) = (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B C) (k3_funct_2 (u1_struct_0 A) k1_numbers B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ((m2_finseq_1 E (k1_zfmisc_1 A)) =>  ( (E = (k2_hallmar1 A B C D))  <=>  ( ((k4_finseq_1 E) = (k4_finseq_1 B))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ( ( (C = F)  =>  ((k1_funct_1 E F) = (k6_subset_1 (k1_funct_1 B F) (k1_tarski D))) )  &  ( (~  (C = F) )  =>  ((k1_funct_1 E F) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ( ((v5_glib_001 D A) & (m3_glib_001 D A))  =>  ( (D = (k2_helly A B C))  <=> (r1_glib_001 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d2_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v1_henmodel B A) <=>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r1_henmodel A B C) & (r1_henmodel A B (k6_cqc_lang A C))) ) ) ) ) ) ) ) ) ).
tt(d2_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  ( (C = (k1_hermitan A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) C D) = (k2_complfld (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_heyting1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_heyting1 A) = A) ) ) ).
tt(d2_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  ((k2_heyting2 A B C) = (a_3_0_heyting2 A B C)) ) ) ) ) ) ).
tt(d2_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B))) =>  ( (C = (k2_heyting3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (~  ( (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  (~  ((r1_xxreal_0 E (k4_nat_1 2 A)) &  ((k1_domain_1 k5_numbers k5_numbers E B) = D) ) ) ) )  &  (~  ((k1_domain_1 k5_numbers k5_numbers (k4_nat_1 2 A) B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k2_hilbasis A B) = (k2_funct_7 (k16_pre_poly A) B 1)) ) ) ) ).
tt(d2_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k1_hilbert1) &  ((v1_funct_1 B) & (v1_partfun1 B k1_hilbert1)) ) )  =>  ( (B = (k2_hilbert3 A))  <=>  ( ((k1_funct_1 B k2_hilbert1) = 1)  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_funct_1 B (k1_hilbert2 C)) = (k1_funct_1 A C)) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ( ((k1_funct_1 B (k4_hilbert1 C D)) = (k2_zfmisc_1 (k1_funct_1 B C) (k1_funct_1 B D)))  &  ((k1_funct_1 B (k3_hilbert1 C D)) = (k1_funct_2 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k2_hurwitz A B) = (k6_xcmplx_0 (k1_algseq_1 A B) 1)) ) ) ) ) ).
tt(d2_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k6_margrel1))  =>  ( (D = (k2_idea_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 D E) = (k2_binarith (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_ideal_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_incproj A)))) =>  ( (B = (k2_incproj A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C (u1_struct_0 A)) &  ((r2_hidden D (k1_incproj A)) &  (? [E:$i] :  ( (D = E)  & (r2_hidden C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_index_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) )  =>  ( (B = (k3_index_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  ( (D = (k1_funct_1 A C))  =>  ((k1_funct_1 B C) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l1_msualg_1 B) =>  ((m1_instalg1 B A) <=> (r3_pua2mss1 B A (k6_partfun1 (u1_struct_0 B)) (k6_partfun1 (u4_struct_0 B)))) ) ) ) ) ).
tt(d2_int_1,ax, (! [A:$i] :  ((v1_int_1 A) <=> (r2_hidden A k4_numbers)) ) ).
tt(d2_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k3_int_2 A B))  <=>  ((r1_int_1 C A) &  ((r1_int_1 C B) &  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_int_1 D A) & (r1_int_1 D B))  => (r1_int_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((r1_int_4 A B) <=>  (? [C:$i] :  ((m2_finseq_1 C k4_numbers) &  ( (B = (k1_rvsum_1 C))  &  ( ((k3_finseq_1 C) = A)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r2_hidden (k1_funct_1 C D) (k6_eqrel_1 k4_numbers k4_numbers (k1_int_4 A) (k7_nat_d D 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_5 A B) <=>  (? [C:$i] :  ((v1_int_1 C) &  ((k6_int_1 (k6_xcmplx_0 (k1_pepin C) A) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d2_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_int_6 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ( (B = C)  | (r1_int_2 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_int_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k1_int_7 A) = (k7_subset_1 k4_ordinal1 (k7_card_1 A) (k6_domain_1 k5_numbers k6_numbers))) ) ) ) ).
tt(d2_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_integr10 A B C) <=>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_xxreal_0 D C) =>  ((r1_xxreal_0 D B) |  ((r1_integra5 (k3_integra5 D C) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 D C)))) ) ) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers D) = (k4_rcomp_1 B C))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k1_relset_1 k1_numbers D)) =>  ((k1_seq_1 D E) = (k4_integra5 E C A)) ) ) )  & (r4_limfunc2 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr15 D A B C) =>  ((k1_integr15 A B C D) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ).
tt(d2_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr16 D A B C) =>  ((k3_integr16 A B C D) = (k17_rvsum_1 D)) ) ) ) ) ) ) ) ) ).
tt(d2_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ((m1_integr18 E A B C D) =>  ((k1_integr18 A B C D E) = (k4_rlvect_1 A E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_integr1c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( (G = (k2_integr1c A B C D E F))  <=>  (? [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  (? [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( (H = (k3_relat_1 (k13_funct_3 C D) (k1_partfun1 (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers k2_numbers k1_numbers k1_integr1c (k5_comseq_3 k2_numbers F))))  &  ( (I = (k3_relat_1 (k13_funct_3 C D) (k1_partfun1 (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers k2_numbers k1_numbers k1_integr1c (k6_comseq_3 k2_numbers F))))  &  (G = (k2_xcmplx_0 (k4_integra5 A B (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 C E)) (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 D E)))) (k3_xcmplx_0 (k4_integra5 A B (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 C E)) (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 D E)))) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v5_valued_0 B) & (m2_finseq_1 B k1_numbers)) )  =>  ((m1_integra1 B A) <=>  ((r1_tarski (k1_rvsum_1 B) A) &  ((k1_seq_1 B (k3_finseq_1 B)) = (k4_seq_4 A)) ) ) ) ) ) ) ).
tt(d2_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k3_integra2 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k6_integra1 A B (k2_integra2 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k2_integra3 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k1_integra3 A (k2_integra2 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k2_integra5 A B) = (k12_integra1 A (k1_integra5 B A))) ) ) ) ) ).
tt(d2_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra7 A B C) <=> (r2_hidden B (k1_integra7 A C))) ) ) ) ) ) ).
tt(d2_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra9 A B C) <=>  ((k1_integra9 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d2_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((m1_interva1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (B = (k1_interva1 A C D)) ) ) ) ) ) ) ) ) ).
tt(d2_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k2_irrat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k3_xcmplx_0 (k6_newton A C) (k3_power C (k4_xcmplx_0 A)))) ) ) ) ) ) ) ) ).
tt(d2_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) =>  ((k1_isocat_1 A B C) = (k2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(d2_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k3_isocat_2 A B C D E) = (k1_funct_1 (k1_funct_5 D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_isomichi,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_isomichi B A) <=>  ((k2_pre_topc A (k1_tops_1 A B)) = (k2_pre_topc A B)) ) ) ) ) ) ).
tt(d2_jgraph_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k2_jgraph_1 A))  <=>  ( ((k3_finseq_1 B) = (k7_nat_d (k3_finseq_1 A) 1))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k1_funct_1 B C) = (k4_tarski (k1_funct_1 A C) (k1_funct_1 A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jgraph_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (E = (k2_jgraph_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E F) = (k19_euclid (k7_real_1 (k4_real_1 A (k17_euclid F)) B) (k7_real_1 (k4_real_1 C (k18_euclid F)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  ((k2_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k9_real_1 1 A)))))) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k9_real_1 1 A))) (k12_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  (~  ((k2_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k7_real_1 1 A)))))) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k7_real_1 1 A))) (k12_euclid B))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) &  (~ (r1_xxreal_0 k6_numbers (k17_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (~ (r1_xxreal_0 k6_numbers (k17_euclid B))) ) )  &  (~  ((k2_jgraph_4 A B) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k2_jgraph_6 A B C D) = (a_4_1_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d2_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k2_jordan10 A) = (a_1_1_jordan10 A)) ) ) ).
tt(d2_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k2_jordan11 A))  <=>  ( (~ (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A (k1_jordan11 A))) B))  &  ((r1_tarski (k3_goboard5 (k1_jordan8 A (k1_jordan11 A)) (k7_nat_d (k3_jordan1h A (k1_jordan11 A)) 1) B) (k1_jordan2c 2 A)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_tarski (k3_goboard5 (k1_jordan8 A (k1_jordan11 A)) (k7_nat_d (k3_jordan1h A (k1_jordan11 A)) 1) C) (k1_jordan2c 2 A)) =>  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A (k1_jordan11 A))) C) | (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid A))) =>  ((r2_jordan12 A B C) <=>  ((r1_jordan12 A B C) & (r1_jordan12 A C B)) ) ) ) ) ) ) ) ).
tt(d2_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k2_jordan18 A B) = (k19_euclid (k17_euclid A) (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_topreal1 A)))))) ) ) ) ) ).
tt(d2_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (B = (k2_jordan19 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 B C) = (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A C)))) ) ) ) ) ) ) ) ).
tt(d2_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_jordan1 A) <=>  ( (~  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = k1_xboole_0) )  &  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  &  ((r1_xboole_0 B C) &  ( ((k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) B) B) = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) C) C))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  ( ( (D = B)  &  (E = C) )  =>  ((v3_connsp_1 D (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) & (v3_connsp_1 E (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_jordan1e A B) = (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ).
tt(d2_jordan1h,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_jordan1h A B) = (k2_nat_1 (k13_newton 2 (k7_nat_d B 1)) 2)) ) ) ) ) ).
tt(d2_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k5_jordan1k A B C) = (k1_jordan1k A (k6_domain_1 (u1_struct_0 (k15_euclid A)) B) C)) ) ) ) ) ) ) ).
tt(d2_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k17_euclid F) E))  &  ((r1_jordan5c A B C F D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C F G) & (r1_jordan5c A B C G D))  => (r1_xxreal_0 E (k17_euclid G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k1_jordan21 A) = (k19_euclid (k10_real_1 (k7_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) 2) (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) 2))))))) ) ) ).
tt(d2_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_jordan23 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  &  ((k1_funct_1 A B) = (k1_funct_1 A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ).
tt(d2_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  ((v1_jordan24 B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_vectmetr C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (r1_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 A)) C B)) ) ) ) ) ) ) ).
tt(d2_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_jordan2c A B C) <=>  ((r3_connsp_1 (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B) C) & (v9_rltopsp1 C (k15_euclid A))) ) ) ) ) ) ) ) ).
tt(d2_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan3 A B C) <=>  ((v4_topreal1 A) &  ( ((k1_funct_1 A 1) = B)  &  ((k1_funct_1 A (k3_finseq_1 A)) = C) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) <=>  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 A D))  &  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 B E) = (k1_funct_1 A (k1_jordan4 (k7_nat_d (k2_nat_1 C E) 1) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)) & (r1_topreal1 (k15_euclid 2) C D A))  =>  ((r1_xboole_0 A B) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( (E = (k2_jordan5c A B C D))  <=>  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ( ((k1_funct_1 F G) = E)  &  ((r1_xxreal_0 k6_numbers G) & (r1_xxreal_0 G 1)) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 H 1) &  ( (~ (r1_xxreal_0 H G))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k2_jordan5d A))  <=>  ((r2_hidden (k4_tarski 1 B) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 B) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d2_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( (D = (k2_jordan6 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_2_1_jordan6 B C))  =>  (D = (k1_jordan5c A E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (B = (k4_jordan A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers B C) = (k9_real_1 (k18_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) C)) (k18_euclid A))) ) ) ) ) ) ) ) ).
tt(d2_knaster,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  =>  ((k1_knaster A B) = (k1_setfam_1 (a_2_0_knaster A B))) ) ) ) ).
tt(d2_kolmog01,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 C))))) )  =>  ((m1_kolmog01 D A B C) <=>  (! [E:$i] :  ((r2_hidden E A) =>  ( (~ (v1_xboole_0 (k13_prob_1 B A C D E)))  &  ((v1_prob_1 (k13_prob_1 B A C D E) B) &  ((v4_prob_1 (k13_prob_1 B A C D E) B) & (m1_subset_1 (k13_prob_1 B A C D E) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (C = (k4_kurato_0 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( (C = (k2_kurato_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k1_kurato_0 A (k10_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_kurato_1 A B) = (k2_xboole_0 (k5_enumset1 B (k2_pre_topc A B) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))))) (k5_enumset1 (k3_subset_1 (u1_struct_0 A) B) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))))))))) ) ) ) ) ).
tt(d2_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k2_kurato_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m2_valued_0 E (k9_setfam_1 (u1_struct_0 A)) B) & (r2_hidden D (k1_kurato_2 A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((k1_lang1 A) = (a_1_0_lang1 A)) ) ) ).
tt(d2_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D B C) =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  (! [G:$i] :  ((m1_matrix_1 G D B C) =>  ( ( ((k3_finseq_1 F) = (k3_finseq_1 E))  =>  ( (G = (k3_laplace A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 G) = (k1_matrix_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden (k4_tarski H I) (k2_matrix_1 E)) =>  ( ( (~  (I = A) )  =>  ((k3_matrix_1 D G H I) = (k3_matrix_1 D E H I)) )  &  ( (I = A)  =>  ((k3_matrix_1 D G H A) = (k1_funct_1 F H)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k3_finseq_1 F) = (k3_finseq_1 E)) )  =>  ( (G = (k3_laplace A B C D E F))  <=>  (G = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_group_3 A))))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( (C = (k2_latsubgr A B))  <=>  ((u1_struct_0 C) = (k6_setfam_1 (u1_struct_0 A) (k7_relset_1 (k1_group_3 A) (k9_setfam_1 (u1_struct_0 A)) (k1_latsubgr A) B))) ) ) ) ) ) ) ) ).
tt(d2_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k1_latsum_1 A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ((u1_orders_2 C) = (k2_xboole_0 (k2_xboole_0 (u1_orders_2 A) (u1_orders_2 B)) (k4_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 A) (u1_orders_2 B)))) ) ) ) ) ) ) ) ) ).
tt(d2_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ((k1_lattice2 A) = (g3_lattices (u1_struct_0 A) (u1_lattices A) (u2_lattices A))) ) ) ).
tt(d2_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k3_lattice3 A) = (g1_orders_2 (u1_struct_0 A) (k2_lattice3 A))) ) ) ).
tt(d2_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ((r1_filter_1 A B) <=>  (? [C:$i] :  ((m1_lattice4 C A B) & (v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d2_lattice5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) => (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_lattice3 A)))) =>  ((k2_lattice6 A B) = (a_2_1_lattice6 A B)) ) ) ) ) ).
tt(d2_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((m1_lattice7 D A B C) <=>  ((r2_hidden B D) &  ((r2_hidden C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) =>  ((r3_orders_2 A B E) & (r3_orders_2 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_lattice8 A B) <=>  (? [C:$i] :  ( (~ (v1_zfmisc_1 C))  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C))) &  ((v19_waybel_0 D A (k1_lattice5 C)) &  ((v20_waybel_0 D A (k1_lattice5 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C)))))) ) ) )  &  ((v2_funct_1 D) &  ((v1_lattice8 (k1_yellow_2 A (k1_lattice5 C) D)) &  ( (? [E:$i] :  ( ((v1_partfun1 E C) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  &  ((r2_hidden E (u1_struct_0 (k1_yellow_2 A (k1_lattice5 C) D))) &  (~  (E = (k6_partfun1 C)) ) ) ) )  & (r1_xxreal_0 (k2_lattice5 C (k1_yellow_2 A (k1_lattice5 C) D)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattices A B C) = (k5_binop_1 (u1_struct_0 A) (u1_lattices A) B C)) ) ) ) ) ) ) ).
tt(d2_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k1_lexbfs A B))  <=>  ( ((k9_xtuple_0 C) = (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 C D) = (k2_xboole_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lfuzzy_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_lfuzzy_0 A) <=>  ((v1_lfuzzy_0 A) &  (? [B:$i] :  ((v1_xreal_0 B) &  (? [C:$i] :  ((v1_xreal_0 C) &  ((r1_xxreal_0 B C) &  ((u1_struct_0 A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_limfunc1 A) = (k2_xxreal_1 A k1_xxreal_0)) ) ) ).
tt(d2_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 B D))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  => (v1_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d2_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_limfunc3 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 B E))  &  ((r2_hidden E (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden F (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k10_xtuple_0 C) (k6_subset_1 (k9_xtuple_0 A) (k1_tarski B)))) )  => (v1_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d2_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (D = (k1_lmod_5 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_lmod_5 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ((k1_lmod_6 A B C) = C) ) ) ) ) ) ) ).
tt(d2_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k1_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) )  =>  ( (C = (k3_lopban_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A (u1_struct_0 B) (k2_funcsdom A (u1_struct_0 B) k1_numbers (k9_funct_2 A (u1_struct_0 B)) C (k1_domain_1 k1_numbers (k9_funct_2 A (u1_struct_0 B)) D E)) F) = (k1_rlvect_1 B (k3_funct_2 A (u1_struct_0 B) E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  ((k3_lopban_2 A B C) = (k1_lopban_2 A (k13_lopban_1 A A B) (k13_lopban_1 A A C))) ) ) ) ) ) ) ).
tt(d2_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_lopban_3 A B) = (k6_normsp_1 A (k1_bhsp_4 A B))) ) ) ) ) ).
tt(d2_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k1_lopban_4 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) C D) = (k1_rlvect_1 A (k6_lopban_3 A B D) (k10_real_1 1 (k3_newton D)))) ) ) ) ) ) ) ) ) ) ).
tt(d2_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k16_lopban_1 A B)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k2_lopban_5 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_normsp_1 B E F) = (k17_lopban_1 A B (k1_normsp_1 (k16_lopban_1 A B) C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A))))) )  =>  ( (B = (k4_lopclset A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  ((k5_binop_1 (k1_lopclset A) B C D) = (k2_lopclset A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_lpspace1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_lpspace1 A B) = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B))) ) ) ) ) ).
tt(d2_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k1_lpspace2 A B C D) = (a_4_0_lpspace2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d2_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k7_rsspace))))  =>  ( (B = (k2_lp_space A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C k1_rsspace) & (v1_series_1 (k1_lp_space (k2_rsspace C) A))) ) ) ) ) ) ) ) ) ).
tt(d2_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k2_ltlaxio1 A) = (k4_hilbert1 k2_hilbert1 A)) ) ) ).
tt(d2_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_mathmorp A B) = (a_2_0_mathmorp A B)) ) ) ) ) ).
tt(d2_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v2_matrix10 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) & (r1_xxreal_0 k6_numbers (k3_matrix_1 k1_numbers A B C))) ) ) ) ) ) ) ) ) ).
tt(d2_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  ((k2_matrix11 A B C) = (k7_setwiseo (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B) (u2_algstr_0 B) (k15_matrix_2 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2)))) (k1_matrix11 A B C))) ) ) ) ) ) ) ).
tt(d2_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) A B) =>  ( (G = (k2_matrix12 A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 D))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden H (k4_finseq_1 D)) & (r2_hidden I (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (H = E)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k8_group_1 C F (k3_matrix_1 (u1_struct_0 C) D E I))) )  &  ( (~  (H = E) )  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ((k6_matrix13 A B C D) = (k1_matrix13 A B (k5_card_1 C) (k5_card_1 D) (k5_matrix13 C) (k5_matrix13 D))) ) ) ) ) ) ) ) ) ).
tt(d2_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_matrix14 A B C) = (k1_finseq_7 (u1_struct_0 A) (k5_finseq_2 (u1_struct_0 A) B (k4_struct_0 A)) C (k5_struct_0 A))) ) ) ) ) ) ) ).
tt(d2_matrix15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k3_matrix15 A B) = (k4_matrix_1 A (k10_laplace A B))) ) ) ) ) ).
tt(d2_matrix16,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((v1_matrix16 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C A) &  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  & (r1_matrix16 A B C)) ) ) ) ) ) ) ).
tt(d2_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ((v2_matrix17 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) &  ( (F = (k6_xcmplx_0 (k2_xcmplx_0 B 1) E))  &  (G = (k6_xcmplx_0 (k2_xcmplx_0 B 1) D)) ) )  =>  ((k3_matrix_1 (u1_struct_0 A) C D E) = (k4_algstr_0 A (k3_matrix_1 (u1_struct_0 A) C F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  ((m1_matrix_1 D A B C) <=>  ( ((k3_finseq_1 D) = B)  &  (! [E:$i] :  ((m2_finseq_1 E A) =>  ((r2_hidden E (k10_xtuple_0 D)) =>  ((k3_finseq_1 E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_matrix_2 A B C D) = (k10_finseq_1 (k10_finseq_1 A B) (k10_finseq_1 C D))) ) ) ) ) ).
tt(d2_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( (C = (k2_matrix_3 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((k3_matrix_1 (u1_struct_0 A) C D E) = (k4_algstr_0 A (k3_matrix_1 (u1_struct_0 A) B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 k1_complfld))))  =>  ((k2_matrix_5 A) = A) ) ) ).
tt(d2_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_6 A B C D) <=>  ( ((k4_matrix_3 B C D) = (k4_matrix_3 B D C))  &  ((k4_matrix_3 B C D) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_1 C B) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r2_hidden E (k2_finseq_1 A)))  =>  ( (D = E)  |  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_8 C A B) <=>  ((k4_matrix_6 A B C C) = (k11_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(d2_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k2_matrix_9 A B C) = (k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k12_matrix_2 A)) (k1_matrix_9 A B C))) ) ) ) ) ) ) ).
tt(d2_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k2_matrixc1 A) = (k1_matrixc1 (k4_matrix_1 k2_numbers A))) ) ) ).
tt(d2_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))) =>  ((v1_matrixj1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((v1_matrix_1 (k1_funct_1 B C)) & (m2_finseq_1 (k1_funct_1 B C) (k3_finseq_2 A))) ) ) ) ) ) ) ) ) ).
tt(d2_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))) =>  ((v1_matrixj2 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((k1_funct_1 B C) = (k2_matrixj2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 k2_vectsp_1))))  =>  ((k2_matrixr1 A) = A) ) ) ).
tt(d2_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_matrixr2 A) = (k2_matrixr1 (k12_matrix_1 k2_vectsp_1 A))) ) ) ).
tt(d2_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ( ((k3_finseq_1 E) = (k3_finseq_1 F))  =>  ((k3_matrlin2 A B C D E F) = (k1_matrlin2 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  ((m1_matrlin C A B) <=>  ((v2_funct_1 C) & (m1_vectsp_7 (k10_xtuple_0 C) A B)) ) ) ) ) ) ) ) ).
tt(d2_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=> (r2_hidden B (k1_matroid0 A))) ) ) ) ) ).
tt(d2_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k4_matrprob A))  <=>  ( ((k3_finseq_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 A))) =>  ((k1_seq_1 B C) = (k18_rvsum_1 (k9_matrix_1 k1_numbers A C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_matrtop1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k2_vectsp_1)) =>  ((k2_matrtop1 A) = A) ) ) ).
tt(d2_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k2_finseq_1 A)) =>  (! [C:$i] :  ( ((v1_matrix_6 C A k2_vectsp_1) & (m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A A))  =>  ( (C = (k1_matrtop3 A B))  <=>  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C B B) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ( ( (D = E)  =>  ( (D = B)  |  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C D D) = (k5_struct_0 k2_vectsp_1)) ) )  &  ( (~  (D = E) )  =>  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C D E) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_mazurulm C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r1_xxreal_0 k6_numbers F) & (r1_xxreal_0 F 1))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_algstr_0 A (k1_rlvect_1 A D (k10_binop_2 1 F)) (k1_rlvect_1 A E F))) = (k1_algstr_0 B (k1_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k10_binop_2 1 F)) (k1_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k2_mboolean A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k3_tarski (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d2_measure1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) )  =>  ((v6_supinf_2 B) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B C))) ) ) ) ) ) ) ).
tt(d2_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_measure2 C A B) =>  ((v1_measure2 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  ( (C = (k4_measure1 A B D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_tarski (k8_nat_1 B D E) (k8_nat_1 B D (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((m1_measure3 D A B C) <=>  (? [E:$i] :  ((r2_hidden E B) &  ((r1_tarski D E) &  ((k12_supinf_2 C E) = k1_supinf_2) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (C = (k1_measure4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ( ((r1_tarski E D) & (r1_tarski F (k6_subset_1 A D)))  => (r1_xxreal_0 (k3_supinf_2 (k12_supinf_2 B E) (k12_supinf_2 B F)) (k12_supinf_2 B (k4_subset_1 A E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_measure5 A) <=>  (? [B:$i] :  ((m1_subset_1 B k7_numbers) &  (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  (A = (k1_measure5 B C)) ) ) ) ) ) ) ) ).
tt(d2_measure6,ax, (! [A:$i] :  ((v1_setfam_1 A) <=>  (~ (r2_hidden k6_numbers A)) ) ) ).
tt(d2_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  ((m1_measure7 B A) <=>  ((r1_tarski A (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) B))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v6_xxreal_2 (k8_nat_1 (k9_setfam_1 k1_numbers) B C)) & (m1_subset_1 (k8_nat_1 (k9_setfam_1 k1_numbers) B C) (k1_zfmisc_1 k1_numbers))) ) ) ) ) ) ) ) ) ).
tt(d2_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((m2_measure8 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k8_nat_1 (k9_setfam_1 A) C D) B)) ) ) ) ) ) ) ) ).
tt(d2_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k5_member_1 A) = (a_1_1_member_1 A)) ) ) ).
tt(d2_membered,ax, (! [A:$i] :  ((v2_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_xxreal_0 B)) ) ) ) ).
tt(d2_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_memstr_0 B A) =>  ((k2_memstr_0 A B) = (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) ) ) ) ) ).
tt(d2_mesfun10,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfun10 A B C) <=>  ((v1_mesfunc8 B A k7_numbers) &  ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)) = (k1_relset_1 A C))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (? [F:$i] :  ((v7_ordinal1 F) &  (? [G:$i] :  ((r1_xxreal_0 E F) &  ((r2_hidden G (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) & (r1_xxreal_0 D (k3_extreal1 (k4_supinf_2 (k12_supinf_2 (k4_mesfunc5 A k7_numbers B F) G) (k12_supinf_2 C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) <=>  ((r3_mesfunc6 A B C (k5_comseq_3 A D)) & (r3_mesfunc6 A B C (k6_comseq_3 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k2_mesfun7c A B) = (k1_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d2_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k2_mesfun9c A B))  <=>  ((r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers C k6_numbers) (k4_mesfunc5 A k1_numbers B k6_numbers)) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers C (k1_nat_1 D 1)) (k3_valued_1 A k1_numbers k1_numbers (k4_mesfunc5 A k1_numbers C D) (k4_mesfunc5 A k1_numbers B (k1_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k3_numbers)) =>  ( (B = (k2_mesfunc1 A))  <=>  (! [C:$i] :  ((v1_rat_1 C) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((v1_int_1 D) &  (C = (k7_xcmplx_0 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k1_mesfunc2 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k1_extreal2 (k12_supinf_2 B D) k1_supinf_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 A D)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 D E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k7_numbers) =>  ( (E = (k1_mesfunc3 A B C D))  <=>  (? [F:$i] :  ( ((v1_prob_2 F) & (m2_finseq_1 F B))  &  (? [G:$i] :  ((m2_finseq_1 G k7_numbers) &  (? [H:$i] :  ((m2_finseq_1 H k7_numbers) &  ((r1_mesfunc3 A B D F G) &  ( ((k12_supinf_2 G 1) = k1_supinf_2)  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r1_xxreal_0 2 I) & (r2_hidden I (k4_finseq_1 G)))  =>  ( (~ (r1_xxreal_0 (k12_supinf_2 G I) k1_supinf_2))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 G I))) ) ) ) )  &  ( ((k4_finseq_1 H) = (k4_finseq_1 F))  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k4_finseq_1 H)) =>  ((k12_supinf_2 H I) = (k1_extreal1 (k12_supinf_2 G I) (k12_supinf_2 (k4_finseqop B k7_numbers F C) I))) ) ) )  &  (E = (k4_extreal1 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc5,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_mesfunc5 A) <=> (v1_mesfunc5 (k10_xtuple_0 A))) ) ) ).
tt(d2_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_mesfunc6 A B C) <=>  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden F (k1_funct_1 D E)) & (r2_hidden G (k1_funct_1 D E))) )  =>  ((k1_seq_1 C F) = (k1_seq_1 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_valued_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (B = (k2_mesfunc7 A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k7_numbers) &  ( (C = A)  &  (B = (k1_finsop_1 k7_numbers C k1_mesfunc7)) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc8,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ((v1_mesfunc8 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_relset_1 A (k4_mesfunc5 A B C D)) = (k1_relset_1 A (k4_mesfunc5 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(d2_mesfunc9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v1_mesfunc9 A) <=> (v10_mesfunc5 (k2_mesfunc9 A))) ) ) ).
tt(d2_metric_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ((v2_metric_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_metric_1 A A B C C) = k6_numbers) ) ) ) ) ) ) ).
tt(d2_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_metric_2 A B) = (a_2_0_metric_2 A B)) ) ) ) ) ).
tt(d2_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_metric_6 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k2_metric_1 A (k2_tbsp_1 A B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_metrizts A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 B A) &  ((m1_setfam_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (v4_card_3 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_mfold_1 A B C) = (k1_pre_topc (k15_euclid A) (k1_topreal9 A B C))) ) ) ) ) ) ) ).
tt(d2_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k2_mfold_2 A B C) = (a_3_0_mfold_2 A B C)) ) ) ) ) ) ) ).
tt(d2_midsp_1,ax, (k2_midsp_1 = (g1_midsp_1 1 k9_funct_5)) ).
tt(d2_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B))))) )  =>  ((v1_midsp_2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k1_midsp_1 A D E) = F)  <=>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C D F) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((m1_midsp_3 B A) <=>  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k2_nat_1 A 1))) ) ) ) ) ) ).
tt(d2_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k2_mmlquery A B C) = (k3_tarski (a_3_0_mmlquery A B C))) ) ) ) ) ) ).
tt(d2_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((v1_mod_2 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k4_vectsp_1 A B E F)) = (k4_vectsp_1 A C E (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_mod_3 C A B) <=>  ((v1_lmod_5 C A B) &  ((k1_mod_3 A B C) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ) ) ) ).
tt(d2_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v2_vectsp_2 C (k2_mod_4 A)) & (l1_vectsp_2 C (k2_mod_4 A)))  =>  ( (C = (k3_mod_4 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k2_mod_4 A))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k2_mod_4 A))) (u1_struct_0 B))))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k2_mod_4 A))) (u1_struct_0 B) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B) D (k1_mod_4 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_vectsp_1 A B))) =>  (C = (g1_vectsp_2 (k2_mod_4 A) (u1_struct_0 B) (u1_algstr_0 B) (k4_struct_0 B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_modal_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((k2_modal_1 A B) = (k3_trees_2 A B (k1_modal_1 (k9_xtuple_0 B)))) ) ) ) ) ).
tt(d2_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((m3_modcat_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) ) ) ) ) ) ) ) ) ).
tt(d2_modelc_1,ax, (! [A:$i] :  ( ((r2_hidden A k5_numbers) =>  ((k2_modelc_1 A) = A) )  &  ( (~ (r2_hidden A k5_numbers))  =>  ((k2_modelc_1 A) = k6_numbers) ) ) ) ).
tt(d2_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_modelc_2 A) = (k12_finseq_1 k5_numbers (k2_nat_1 6 A))) ) ) ).
tt(d2_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_2 A) =>  ((k3_modelc_3 A) = k1_xboole_0) )  &  ( ((v5_modelc_2 A) =>  ((k3_modelc_3 A) = (k1_tarski (k12_modelc_2 A))) )  &  ( ((v6_modelc_2 A) =>  ((k3_modelc_3 A) = k1_xboole_0) )  &  ( ((v7_modelc_2 A) =>  ((k3_modelc_3 A) = (k1_tarski (k12_modelc_2 A))) )  &  ( ((v8_modelc_2 A) =>  ((k3_modelc_3 A) = (k2_tarski (k11_modelc_2 A) (k12_modelc_2 A))) )  &  (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  ( (~ (v8_modelc_2 A))  &  (~  ((k3_modelc_3 A) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_moebius1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ( (A = k1_moebius1)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B A) <=>  (~ (v1_moebius1 B)) ) ) ) ) ) ) ).
tt(d2_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (k9_funct_2 E A) (k9_funct_2 E B)) (k9_funct_2 E C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 E A) (k9_funct_2 E B)) (k9_funct_2 E C))))) )  =>  ( (F = (k8_monoid_1 A B C D E))  <=>  (! [G:$i] :  ((m2_funct_2 G E A (k9_funct_2 E A)) =>  (! [H:$i] :  ((m2_funct_2 H E B (k9_funct_2 E B)) =>  ((k2_binop_1 (k9_funct_2 E A) (k9_funct_2 E B) (k9_funct_2 E C) F G H) = (k3_monoid_1 E A B C D G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (C = (k3_morph_01 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) C D) = (k2_morph_01 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v1_msafree1 B A) <=> (v1_prob_2 (u3_msualg_1 A B))) ) ) ) ) ).
tt(d2_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((k2_msafree2 A) = (k6_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) (u2_msualg_1 A)))) ) ) ).
tt(d2_msafree3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_relat_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  ( (C = (k2_msafree3 A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (a_2_0_msafree3 B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_msafree,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((r2_hidden C A) =>  (! [D:$i] :  ( (D = (k2_msafree A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F (k1_funct_1 B C)) &  (E = (k4_tarski F C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_orders_2 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (u1_orders_2 A)) & (v1_funcop_1 D)) ) ) )  =>  ((m2_msalimit D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_orders_2 A F E) &  ((r1_orders_2 A G F) &  (! [H:$i] :  ((m2_pboole H (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C E)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F))) =>  (! [I:$i] :  ((m2_pboole I (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C G))) =>  (~  ( (H = (k1_binop_1 D F E))  &  ( (I = (k1_binop_1 D G F))  &  ( ((k1_binop_1 D G E) = (k3_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C E)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C G)) H I))  & (r1_msualg_3 B (k5_pralg_2 (u1_struct_0 A) B C E) (k5_pralg_2 (u1_struct_0 A) B C F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k5_msafree A B)) (k7_dtconstr (k5_msafree A B))) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ((m1_msaterm D A B C) <=> (m2_dtconstr D (k5_msafree A B) C)) ) ) ) ) ) ) ) ) ).
tt(d2_msinst_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (C = (k2_msinst_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v3_msualg_1 E A) &  ((v1_msualg_6 E A) & (l3_msualg_1 E A)) )  &  ( (D = E)  &  (! [F:$i] :  ((m1_subset_1 F (k10_xtuple_0 (u3_msualg_1 A E))) => (r1_tarski F B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ((v1_msscyc_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((r1_graph_2 A C B) &  ((k1_funct_1 C 1) = (k1_funct_1 C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d2_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_msscyc_2 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_msscyc_2 A) (u1_struct_0 A))))) )  =>  ( (B = (k2_msscyc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C (k1_msscyc_2 A)) =>  ((k1_funct_1 B C) = (k2_xtuple_0 C)) ) ) ) ) ) ) ) ).
tt(d2_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v1_mssubfam C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r1_pboole A D C) & (r1_pboole A E C))  => (r1_pboole A (k2_pboole A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k2_msualg_1 A B) = (k3_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u2_msualg_1 A) B)) ) ) ) ) ).
tt(d2_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v2_msualg_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_msualg_2 B A)) ) ) ) ) ).
tt(d2_msualg_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_msualg_3 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((k1_funct_1 A B) = C) )  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(d2_msualg_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C A B B) =>  ((v1_msualg_4 C A B) <=>  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B D) (k1_funct_1 B D)))) =>  ( ((r2_hidden D A) &  ((k1_funct_1 C D) = E) )  =>  ((v3_relat_2 E) &  ((v8_relat_2 E) &  ((v1_partfun1 E (k1_funct_1 B D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B D) (k1_funct_1 B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msualg_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_lattices B) &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  ( (B = (k2_msualg_5 A))  <=>  ( ((u1_struct_0 B) = (a_1_0_msualg_5 A))  &  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k1_binop_1 (u1_lattices B) C D) = (k4_eqrel_1 A C D))  &  ((k1_binop_1 (u2_lattices B) C D) = (k5_eqrel_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((m1_msualg_6 C A B) <=> (r1_msualg_3 A B B C)) ) ) ) ) ) ) ).
tt(d2_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v1_msualg_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (r2_hidden (k16_lattice3 A C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d2_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B))))) =>  ((k2_msualg_8 A B C) = (k16_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) (a_3_1_msualg_8 A B C))) ) ) ) ) ) ) ).
tt(d2_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B (k6_pboole A C D)) =>  (! [F:$i] :  ((m2_pboole F A B D) =>  ( (F = (k2_msualg_9 A B C D E))  <=>  (! [G:$i] :  ((r2_hidden G A) =>  ((k1_funct_1 F G) = (k12_mcart_1 (k1_funct_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_msualg_1 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v3_msualg_1 C B) &  ((v4_msualg_1 C B) & (l3_msualg_1 C B)) )  =>  ((r1_msuhom_1 A B) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v4_msualg_1 D A) & (l3_msualg_1 D A)) )  =>  ( (D = (k1_msuhom_1 A B C))  <=>  ( ((u3_msualg_1 A D) = (k5_relat_1 (u3_msualg_1 B C) (u1_struct_0 A)))  &  ((u4_msualg_1 A D) = (k5_relat_1 (u4_msualg_1 B C) (u4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_multop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_multop_1 A B C D E) = (k1_funct_1 A (k6_xtuple_0 B C D E))) ) ) ) ) ) ) ).
tt(d2_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ((v2_nagata_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_nagata_1 (k1_nagata_1 A B C) A)) ) ) ) ) ) ) ).
tt(d2_nagata_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( (D = (k2_nagata_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_seq_1 D E) = (k1_metric_1 A A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_ordinal1 A) = (k1_nat_1 A 1)) ) ) ).
tt(d2_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k4_nat_3 A B C))  <=>  (! [E:$i] :  ((k1_funct_1 D E) = (k11_binop_2 C (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ).
tt(d2_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( (~  (B = k6_numbers) )  =>  ( (C = (k3_nat_5 A B))  <=>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_xboole_0 D)) )  =>  ( (B = D)  =>  (C = (k3_uproots (k3_moebius1 D) (k1_nat_5 k5_numbers (k2_nat_5 A) (k3_moebius1 D)))) ) ) ) ) )  &  ( (B = k6_numbers)  =>  ( (C = (k3_nat_5 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d2_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k2_nat_d A B))  <=>  (~  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (A = (k2_xcmplx_0 (k3_xcmplx_0 B D) C))  &  (~ (r1_xxreal_0 B C)) ) ) ) )  &  (~  ( (C = k6_numbers)  &  (B = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_nat_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) )  =>  ( (A = k2_nat_lat)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_binop_1 A B C) = (k5_nat_d B C)) ) ) ) ) ) ) ) ).
tt(d2_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k2_cat_1 B (k8_cat_1 A B C E) (k8_cat_1 A B D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_ncfcont1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((m2_valued_0 D (u1_struct_0 A) C) &  ((v9_clvect_1 D A) & (r2_hidden (k7_clvect_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r2_ncfcont2 A B C D) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 C) D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (~  ((r2_hidden G A) &  ((r2_hidden H A) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 C (k5_algstr_0 C G H))))  & (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D G) (k7_partfun1 (u1_struct_0 B) D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k1_ndiff_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_rlvect_1 A (k1_normsp_1 A B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 B C))) =>  ((k2_ndiff_2 A B C D E) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k13_lopban_1 A B D) (k13_lopban_1 B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ((v2_ndiff_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers (u1_struct_0 A) B D) = (k1_rlvect_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (D = (k1_ndiff_4 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  &  ( (B = E)  &  (D = (k1_ndiff_3 (k4_real_ns1 A) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_ndiff_5 A B C) = (a_3_0_ndiff_5 A B C)) ) ) ) ) ) ) ).
tt(d2_neckla_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k1_neckla_2 A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ((u1_orders_2 C) = (k2_xboole_0 (u1_orders_2 A) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ).
tt(d2_neckla_3,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  ((v1_neckla_3 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (u1_struct_0 A)) & (r2_hidden C (u1_struct_0 A)))  =>  ( (B = C)  | (r1_rewrite1 (u1_orders_2 A) B C)) ) ) ) ) ) ) ).
tt(d2_necklace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((r3_necklace A B) <=>  ((r2_necklace B A) & (r2_necklace A B)) ) ) ) ) ) ).
tt(d2_net_1,ax, (! [A:$i] :  ((l1_petri A) =>  ((v1_net_1 A) <=>  ((r1_xboole_0 (u1_struct_0 A) (u4_struct_0 A)) & (r1_tarski (k1_net_1 A) (k2_xboole_0 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A)) (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(d2_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_newton A) = (k19_rvsum_1 (k1_finseq_2 A))) ) ) ).
tt(d2_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_nfcont_1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((m2_valued_0 D (u1_struct_0 A) C) &  ((v3_normsp_1 D A) & (r2_hidden (k6_normsp_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r2_nfcont_2 A B C) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden F A) &  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B F G))))  & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C F) (k7_partfun1 k1_numbers C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((v1_nfcont_3 B A) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k1_relset_1 k1_numbers B)) => (r1_nfcont_3 A B C)) ) ) ) ) ) ) ) ).
tt(d2_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( (D = (k1_nfcont_4 A B C))  <=>  ( ((k1_relset_1 B D) = (k1_relset_1 B C))  &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 B D)) =>  ((k7_partfun1 k1_numbers D E) = (k12_euclid (k7_partfun1 (k1_euclid A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((k1_normform A B C D) = (k1_domain_1 A B (k1_finsub_1 A (k2_domain_1 A B C) (k2_domain_1 A B D)) (k1_finsub_1 B (k3_domain_1 A B C) (k3_domain_1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(d2_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k2_normsp_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k2_normsp_2 A) = (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))) ) ) ).
tt(d2_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 k4_numbers k4_numbers k4_numbers)) =>  ( (C = (k2_ntalgo_1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k4_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k4_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers k4_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers k4_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K k5_numbers k4_numbers) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [L:$i] :  ((m2_subset_1 L k1_numbers k5_numbers) &  ( ((k8_nat_1 k4_numbers H k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers I k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers F k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers K k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers J k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers E k6_numbers) = B)  &  ( ((k8_nat_1 k4_numbers G k6_numbers) = k6_numbers)  &  ( (! [M:$i] :  ((m2_subset_1 M k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers F (k2_nat_1 M 1)) = (k5_int_1 (k8_nat_1 k4_numbers D M) (k8_nat_1 k4_numbers E M)))  &  ( ((k8_nat_1 k4_numbers G (k2_nat_1 M 1)) = (k6_int_1 (k8_nat_1 k4_numbers D M) (k8_nat_1 k4_numbers E M)))  &  ( ((k8_nat_1 k4_numbers H (k2_nat_1 M 1)) = (k8_nat_1 k4_numbers K M))  &  ( ((k8_nat_1 k4_numbers I (k2_nat_1 M 1)) = (k8_nat_1 k4_numbers J M))  &  ( ((k8_nat_1 k4_numbers D (k2_nat_1 M 1)) = (k8_nat_1 k4_numbers E M))  &  ( ((k8_nat_1 k4_numbers K (k2_nat_1 M 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers H M) (k3_xcmplx_0 (k8_nat_1 k4_numbers F (k2_nat_1 M 1)) (k8_nat_1 k4_numbers K M))))  &  ( ((k8_nat_1 k4_numbers J (k2_nat_1 M 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers I M) (k3_xcmplx_0 (k8_nat_1 k4_numbers F (k2_nat_1 M 1)) (k8_nat_1 k4_numbers J M))))  &  ((k8_nat_1 k4_numbers E (k2_nat_1 M 1)) = (k8_nat_1 k4_numbers G (k2_nat_1 M 1))) ) ) ) ) ) ) ) ) )  &  ( (L = (k5_nat_1 (a_1_1_ntalgo_1 E)))  &  ( ((r1_xxreal_0 k6_numbers (k8_nat_1 k4_numbers D L)) =>  (C = (k3_xtuple_0 (k8_nat_1 k4_numbers H L) (k8_nat_1 k4_numbers I L) (k8_nat_1 k4_numbers D L))) )  &  ( (~ (r1_xxreal_0 k6_numbers (k8_nat_1 k4_numbers D L)))  =>  (C = (k3_xtuple_0 (k4_xcmplx_0 (k8_nat_1 k4_numbers H L)) (k4_xcmplx_0 (k8_nat_1 k4_numbers I L)) (k4_xcmplx_0 (k8_nat_1 k4_numbers D L)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_numbers,ax, (k2_numbers = (k2_xboole_0 (k6_subset_1 (k9_funct_2 (k2_tarski k1_xboole_0 1) k1_numbers) a_0_0_numbers) k1_numbers)) ).
tt(d2_numeral1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  ( ( (~  (A = k6_numbers) )  =>  ( (C = (k2_numeral1 A B))  <=>  ( ((k1_numeral1 C B) = A)  &  ( (~  ((k1_recdef_1 C (k21_binop_2 (k1_afinsq_1 C) 1)) = k6_numbers) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((r1_xxreal_0 k6_numbers (k1_recdef_1 C D)) &  (~ (r1_xxreal_0 B (k1_recdef_1 C D))) ) ) ) ) ) ) ) )  &  ( (A = k6_numbers)  =>  ( (C = (k2_numeral1 A B))  <=>  (C = (k5_afinsq_1 k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A))))) )  =>  ( (B = (k4_openlatt A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A)) =>  ((k5_binop_1 (k1_openlatt A) B C D) = (k2_openlatt A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_oposet_1,ax, (k2_oposet_1 = (g2_qmax_1 1 (k1_partit_2 1 1) k8_funct_5)) ).
tt(d2_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_oppcat_1 A B) = B) ) ) ) ) ).
tt(d2_orders_1,ax, (! [A:$i] :  ((k1_orders_1 A) = (k7_subset_1 (k1_zfmisc_1 A) (k9_setfam_1 A) (k1_tarski k1_xboole_0))) ) ).
tt(d2_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_orders_2 A) <=> (r1_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d2_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_orders_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (~  (C = k1_xboole_0) )  &  ( (~  (D = k1_xboole_0) )  &  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_xboole_0 C D) &  ((u1_orders_2 A) = (k2_xboole_0 (k2_wellord1 (u1_orders_2 A) C) (k2_wellord1 (u1_orders_2 A) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_orders_4,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_orders_4 A) <=> (v4_card_3 (u1_struct_0 A))) ) ) ).
tt(d2_ordinal1,ax, (! [A:$i] :  ((v1_ordinal1 A) <=>  (! [B:$i] :  ((r2_hidden B A) => (r1_tarski B A)) ) ) ) ).
tt(d2_ordinal2,ax, (! [A:$i] :  ((k2_ordinal2 A) = (k1_setfam_1 (k2_ordinal1 A))) ) ).
tt(d2_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k2_ordinal4 A) = k1_xboole_0) ) ) ).
tt(d2_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  ((v2_ordinal5 A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B C) & (r2_hidden C (k9_xtuple_0 A)))  => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(d2_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B D C))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (F = (k1_ortsp_1 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B G D)) C) =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_osafree C A B) =>  ((v1_osafree C A B) <=>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v12_osalg_1 D A) &  ((v13_osalg_1 D A) & (l3_msualg_1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A D)) =>  (? [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D)) &  ((r1_msualg_3 A B D F) &  ((v1_osalg_3 F A) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_osalg_1 A B C) <=> (r2_hidden (k4_tarski B C) (u1_osalg_1 A))) ) ) ) ) ) ) ).
tt(d2_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m2_osalg_2 C A B) <=>  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (l3_msualg_1 C A))  =>  ((r1_osalg_3 A B C) <=>  (? [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) &  ((r4_msualg_3 A B C D) & (v1_osalg_3 D A)) ) ) ) ) ) ) ) ) ) ).
tt(d2_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((m1_osalg_4 C A B) <=> (v1_osalg_4 C A (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(d2_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k2_parsp_1 A B C) = (k5_binop_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k1_parsp_1 A) B C)) ) ) ) ) ) ) ).
tt(d2_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_parsp_2 A B C D) <=> (r1_parsp_1 A B C B D)) ) ) ) ) ) ) ) ) ).
tt(d2_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((v1_partfun1 B A) <=>  ((k1_relset_1 A B) = A) ) ) ) ) ).
tt(d2_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((r2_partit1 A B C D) <=>  ((r1_partit1 A B D) &  ((r1_partit1 A C D) &  (! [E:$i] :  ( ((r1_tarski E D) &  ((r1_partit1 A B E) & (r1_partit1 A C E)) )  =>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v2_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_diraf A F C D) &  ((r3_diraf A F B E) & (r2_diraf A B C D E)) )  =>  ((r3_diraf A F B C) | (r1_diraf A F B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) <=>  (! [D:$i] :  ((r2_hidden D A) => (r1_tarski (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(d2_pcomps_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k1_pcomps_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k2_pre_topc A E))  & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)))) =>  ( (G = (k3_pcs_0 A B C D E F))  <=>  (! [H:$i] :  (! [I:$i] :  ((r2_hidden (k4_tarski H I) G) <=>  (? [J:$i] :  (? [K:$i] :  (? [L:$i] :  (? [M:$i] :  ( (H = (k4_tarski J K))  &  ( (I = (k4_tarski L M))  &  ((r2_hidden J A) &  ((r2_hidden K C) &  ((r2_hidden L B) &  ((r2_hidden M D) &  ((r2_hidden (k4_tarski J L) E) | (r2_hidden (k4_tarski K M) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k2_pdiff_1 A) = (k3_relat_1 (k1_pdiff_1 1 1) (k3_relat_1 A (k2_funct_1 (k1_pdiff_1 1 1))))) ) ) ).
tt(d2_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((r1_pdiff_2 A B) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid 2) A)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  ((r2_hidden C B) => (r3_pdiff_1 2 1 (k2_partfun1 (k1_euclid 2) k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d2_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r1_pdiff_3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  &  (? [E:$i] :  ((m1_rcomp_1 E C) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B))) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v3_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B) H) (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B) C)) = (k7_real_1 (k1_seq_1 F (k9_real_1 H C)) (k1_seq_1 G (k9_real_1 H C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((r2_pdiff_4 A B) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid 3) A)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C B) => (r3_pdiff_1 3 2 (k2_partfun1 (k1_euclid 3) k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d2_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r2_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pdiff_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid B) (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A))))) )  =>  ((v2_pdiff_6 C A B) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (k1_euclid B) (k1_euclid A) C (k9_euclid B D E)) = (k9_euclid A (k3_funct_2 (k1_euclid B) (k1_euclid A) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k1_pdiff_7 A B C) = (k1_partfun1 (k1_euclid A) (k1_euclid 1) (k1_euclid 1) k1_numbers (k8_pdiff_1 A 1 (k3_pdiff_1 A B) C) (k1_pdiff_1 1 1))) ) ) ) ) ) ) ).
tt(d2_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r1_pdiff_9 A B C) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r2_hidden D B) => (r2_nfcont_4 A (k2_partfun1 (k1_euclid A) k1_numbers C B) D)) ) ) ) ) ) ) ) ) ).
tt(d2_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_pencil_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_pre_topc A)) =>  ((r1_ordinal1 2 (k1_card_1 (k9_subset_1 (u1_struct_0 A) C B))) => (r1_tarski C B)) ) ) ) ) ) ) ) ).
tt(d2_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v11_pencil_1 B) & (v14_pencil_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  ((m1_pencil_2 C A B) <=>  (? [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  &  ( (C = (k4_card_3 D))  &  ((k1_funct_1 D (k3_pencil_1 A D)) = (k2_struct_0 (k1_pencil_1 A B (k3_pencil_1 A D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  ((r1_pencil_3 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_pencil_1 A B))) =>  (~  ((r2_hidden E C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_pencil_1 A B))) =>  (~  ((r2_hidden F D) & (r1_pencil_1 (k5_pencil_1 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k2_pencil_4 A B C D) = (k7_subset_1 (k3_vectsp_5 A B) (k1_pencil_4 A B C D) (k2_tarski (k2_vectsp_4 A C) (k2_vectsp_4 A D)))) ) ) ) ) ) ) ) ) ).
tt(d2_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) =>  ((r1_xxreal_0 B 1) |  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k3_pepin A B))  <=>  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( ((k4_nat_d (k1_newton A C) B) = 1)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k4_nat_d (k1_newton A D) B) = 1)  =>  ((r1_xxreal_0 D k6_numbers) |  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B A))))  =>  ((m1_petri_2 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E D A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  &  ((v1_finset_1 D) &  (C = (k1_petri_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pnproc_1,ax, (! [A:$i] :  ((k1_pnproc_1 A) = (k8_funcop_1 k5_numbers A k6_numbers)) ) ).
tt(d2_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_polyalg1 B A) & (l1_polyalg1 B A)) )  =>  ( (B = (k1_polyalg1 A))  <=>  ( (! [C:$i] :  ((r2_hidden C (u1_struct_0 B)) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_algstr_0 B C D) = (k2_normsp_1 A E F)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 B C D) = (k11_polynom3 A E F)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = E)  =>  ((k4_vectsp_1 A B C D) = (k3_polynom5 A E C)) ) ) ) ) ) ) )  &  ( ((k4_struct_0 B) = (k9_polynom3 A))  &  ((k5_struct_0 B) = (k10_polynom3 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_polyeq_1 A B C D) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C)) ) ) ) ) ) ) ) ) ).
tt(d2_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ((k2_polyeq_2 A B C D E F) = (k3_xcmplx_0 A (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 F B) (k6_xcmplx_0 F C)) (k6_xcmplx_0 F D)) (k6_xcmplx_0 F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_polyeq_3 A) = (k5_binop_2 (k3_square_1 A) A)) ) ) ).
tt(d2_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers)  =>  ( (D = (k2_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (F = (k1_polyeq_5 3 (k3_xcmplx_0 2 E)))  &  (D = (k6_xcmplx_0 F (k13_complex1 C 3))) ) ) ) ) ) ) ) )  &  ( (~  ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers) )  =>  ( (D = (k2_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) 9))  &  ( (F = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (G = (k1_polyeq_5 2 (k2_xcmplx_0 (k1_newton E 3) (k1_newton F 2))))  &  ( (H = (k1_polyeq_5 3 (k2_xcmplx_0 F G)))  &  ( (I = (k10_complex1 (k13_complex1 E H)))  &  (D = (k6_xcmplx_0 (k2_xcmplx_0 H I) (k13_complex1 C 3))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k1_polynom1 A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 B)) =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v4_vectsp_1 C) & (l6_algstr_0 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( (E = (k3_polynom2 A B C D))  <=>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 C)) &  ( ((k3_finseq_1 F) = (k3_finseq_1 (k7_pre_poly A (k1_polynom2 A B) (k1_yellow_1 A))))  &  ( (E = (k3_group_4 C F))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k3_finseq_1 F)))  =>  ((k7_partfun1 (u1_struct_0 C) F G) = (k1_binop_1 (k4_group_1 C) (k7_partfun1 (u1_struct_0 C) (k1_partfun1 k5_numbers A A (u1_struct_0 C) (k7_pre_poly A (k1_polynom2 A B) (k1_yellow_1 A)) D) G) (k7_partfun1 k3_numbers (k2_polynom2 A (k7_pre_poly A (k1_polynom2 A B) (k1_yellow_1 A)) B) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r2_polynom3 A B C) <=>  ((r1_polynom3 A B C) |  (B = C) ) ) ) ) ) ) ) ) ).
tt(d2_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k2_polynom4 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ( (D = (k4_rlvect_1 A E))  &  ( ((k3_finseq_1 E) = (k1_algseq_1 A B))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k6_algstr_0 A (k1_normsp_1 A B (k7_nat_d F 1)) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C (k7_nat_d F 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v3_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k2_polynom5 A B C) = (k1_binop_1 (k4_group_1 (k14_polynom3 A)) B C)) ) ) ) ) ) ) ).
tt(d2_polynom6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 (k11_polynom1 B C))) &  ((v1_polynom1 D (k15_pre_poly A) (k11_polynom1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 (k11_polynom1 B C)))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly (k10_ordinal2 A B)) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly (k10_ordinal2 A B)) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k10_ordinal2 A B)) (u1_struct_0 C))))) ) )  =>  ( (E = (k2_polynom6 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F (k14_pre_poly (k10_ordinal2 A B)) (k15_pre_poly (k10_ordinal2 A B))) =>  (? [G:$i] :  ((m2_subset_1 G (k14_pre_poly A) (k15_pre_poly A)) &  (? [H:$i] :  ((m2_subset_1 H (k14_pre_poly B) (k15_pre_poly B)) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly B) (u1_struct_0 C)) &  ((v1_polynom1 I (k15_pre_poly B) C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 C))))) ) )  &  ( (I = (k3_polynom1 A (k11_polynom1 B C) D G))  &  ((r8_pboole (k10_ordinal2 A B) F (k1_polynom6 A B G H)) &  ((k3_polynom1 (k10_ordinal2 A B) C E F) = (k3_polynom1 B C I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k2_polynom8 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k6_algstr_0 A (k8_nat_1 (u1_struct_0 A) B E) (k8_nat_1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_polyred A B C D E) <=> (r2_hidden (k4_tarski (k2_polynom1 (k15_pre_poly A) C D) (k2_polynom1 (k15_pre_poly A) C E)) (k13_bagorder (g1_orders_2 (k15_pre_poly A) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_poset_1 A B C) = (a_3_0_poset_1 A B C)) ) ) ) ) ) ) ).
tt(d2_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( (C = (k3_power A B))  <=>  (C = (k9_prepower A B)) ) )  &  ( ( (A = k6_numbers)  =>  ((r1_xxreal_0 B k6_numbers) |  ( (C = (k3_power A B))  <=>  (C = k6_numbers) ) ) )  &  ((v1_int_1 B) =>  ( (C = (k3_power A B))  <=>  (? [D:$i] :  ((v1_int_1 D) &  ( (D = B)  &  (C = (k4_prepower A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( (D = (k2_pralg_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k2_xtuple_0 (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k4_card_3 (k2_funct_6 A))) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k4_card_3 (k2_funct_6 A))) & (v1_funcop_1 B)) ) ) )  =>  ( (B = (k2_pralg_2 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C (k4_card_3 (k2_funct_6 A))) =>  ((k1_funct_1 B C) = (k15_pralg_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d2_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 B) (u3_msualg_1 B (k14_pralg_2 A B C)) (u3_msualg_1 B (k5_pralg_2 A B C D))) =>  ( (E = (k2_pralg_3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k1_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k14_pralg_2 A B C)) (u3_msualg_1 B (k5_pralg_2 A B C D)) E F) = (k12_card_3 (k9_pralg_2 A B F C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (A = k6_numbers)  =>  ( (B = (k3_pre_ff A))  <=>  (B = k6_numbers) ) )  &  ( (~  (A = k6_numbers) )  =>  ( (B = (k3_pre_ff A))  <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k3_finseq_2 k5_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k5_numbers))))) )  &  ( ((k2_nat_1 C 1) = A)  &  ( (B = (k7_partfun1 k5_numbers (k2_pre_ff D C) A))  &  ( ((k2_pre_ff D k6_numbers) = (k12_finseq_1 k5_numbers 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((k1_nat_1 E 2) = (k4_nat_1 2 F))  =>  ((k2_pre_ff D (k1_nat_1 E 1)) = (k8_finseq_1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) D E) (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) D E) F)))) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((k1_nat_1 E 2) = (k2_nat_1 (k4_nat_1 2 F) 1))  =>  ((k2_pre_ff D (k1_nat_1 E 1)) = (k8_finseq_1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) D E) (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) D E) F) (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) D E) (k1_nat_1 F 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_prelamb A B C) = (k5_binop_1 (u1_struct_0 A) (u2_prelamb A) B C)) ) ) ) ) ) ) ).
tt(d2_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k7_pre_poly A B C))  <=>  ( ((k2_relset_1 A D) = B)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden F (k4_finseq_1 D)))  =>  ((r1_xxreal_0 F E) |  ( (~  ((k7_partfun1 A D E) = (k7_partfun1 A D F)) )  & (r2_hidden (k4_tarski (k7_partfun1 A D E) (k7_partfun1 A D F)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prepower,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 1 A) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( (~ (r1_xxreal_0 B k6_numbers))  =>  ( (C = (k2_prepower A B))  <=>  ( ((k1_newton C A) = B)  &  (~ (r1_xxreal_0 C k6_numbers)) ) ) )  &  ( (B = k6_numbers)  =>  ( (C = (k2_prepower A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=> (r2_hidden B (u1_pre_topc A))) ) ) ) ) ).
tt(d2_prgcor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k2_prgcor_1 A B))  <=>  (? [D:$i] :  ((v1_int_1 D) &  ( ( (B = k6_numbers)  =>  (C = k6_numbers) )  &  ( (~  (B = k6_numbers) )  =>  ( ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) |  (C = (k1_prgcor_1 A B)) ) )  &  ( (~  ((r1_xxreal_0 k6_numbers A) &  (~ (r1_xxreal_0 B k6_numbers)) ) )  =>  ( ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 k6_numbers B) |  ( (D = (k1_prgcor_1 A (k4_xcmplx_0 B)))  &  ( ( ((k3_xcmplx_0 (k4_xcmplx_0 B) D) = A)  =>  (C = (k4_xcmplx_0 D)) )  &  ( (~  ((k3_xcmplx_0 (k4_xcmplx_0 B) D) = A) )  =>  (C = (k6_xcmplx_0 (k4_xcmplx_0 D) 1)) ) ) ) ) )  &  ( (~  ((r1_xxreal_0 k6_numbers A) &  (~ (r1_xxreal_0 k6_numbers B)) ) )  =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ( (D = (k1_prgcor_1 (k4_xcmplx_0 A) B))  &  ( ( ((k3_xcmplx_0 B D) = (k4_xcmplx_0 A))  =>  (C = (k4_xcmplx_0 D)) )  &  ( (~  ((k3_xcmplx_0 B D) = (k4_xcmplx_0 A)) )  =>  (C = (k6_xcmplx_0 (k4_xcmplx_0 D) 1)) ) ) ) ) ) ) )  &  ( (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  (~ (r1_xxreal_0 B k6_numbers)) ) )  =>  (C = (k1_prgcor_1 (k4_xcmplx_0 A) (k4_xcmplx_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prgcor_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden A B) =>  ((k1_prgcor_2 A B C D E) = C) )  &  ( ( (A = B)  =>  ((k1_prgcor_2 A B C D E) = D) )  &  (~  ( (~ (r2_hidden A B))  &  ( (~  (A = B) )  &  (~  ((k1_prgcor_2 A B C D E) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k2_prob_1 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) C D) = (k3_subset_1 A (k8_nat_1 (k9_setfam_1 A) B D))) ) ) ) ) ) ) ) ) ).
tt(d2_prob_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_prob_2 A) <=>  (! [B:$i] :  (! [C:$i] :  ( (~  (B = C) )  => (r1_xboole_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ).
tt(d2_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k2_prob_3 A B))  <=>  ( ((k1_prob_2 A (k9_setfam_1 A) C k6_numbers) = (k1_prob_2 A (k9_setfam_1 A) B k6_numbers))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_prob_2 A (k9_setfam_1 A) C (k1_nat_1 D 1)) = (k2_xboole_0 (k1_funct_1 C D) (k1_prob_2 A (k9_setfam_1 A) B (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d2_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_projdes1 A B C D E) <=>  ( (~ (r1_collsp A C D E))  &  ( (~ (r1_collsp A B C D))  &  ( (~ (r1_collsp A B D E))  &  (~ (r1_collsp A B E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ((r2_projpl_1 A B C D) <=>  ((r1_incsp_1 A B C) & (r1_incsp_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  ((k1_projred2 A B) = (a_2_0_projred2 A B)) ) ) ) ) ).
tt(d2_prvect_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 C A) (k4_finseq_2 C A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A))))) )  =>  ( (D = (k3_prvect_1 A B C))  <=>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 C A)) =>  ((k3_funct_2 (k4_finseq_2 C A) (k4_finseq_2 C A) D E) = (k4_finseqop A A E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_prvect_2 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (k4_card_3 A)) (k4_card_3 A))))) )  =>  ( (D = (k2_prvect_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 A)) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k4_finseq_1 A)) =>  ((k8_prvect_1 A (k2_binop_1 B (k4_card_3 A) (k4_card_3 A) D E F) G) = (k2_binop_1 B (k1_funct_1 A G) (k1_funct_1 A G) (k1_prvect_2 A B C G) E (k8_prvect_1 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) )  =>  ( (C = (k2_prvect_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k2_binop_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) C D (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) E F)) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k1_rlvect_1 A E D) (k1_rlvect_1 B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_pscomp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k2_pscomp_1 A B) = (k4_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B (u1_struct_0 A)))) ) ) ) ) ).
tt(d2_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((m2_pua2mss1 B A) <=>  ((m1_eqrel_1 (k10_xtuple_0 B) A) & (v2_funct_1 B)) ) ) ) ) ).
tt(d2_pythtrip,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) <=>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (~  ((r1_nat_d C A) & (r1_nat_d C B)) ) ) ) ) ) ) ) ) ).
tt(d2_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k2_pzfmisc1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k2_tarski (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k1_qc_lang1 A) = (k10_xtuple_0 A)) ) ) ).
tt(d2_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k2_qc_lang2 A B C) = (k13_qc_lang1 A (k14_qc_lang1 A B (k13_qc_lang1 A C)))) ) ) ) ) ) ) ).
tt(d2_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  ((k2_qc_lang3 A B) = (k4_tarski 4 B)) ) ) ) ) ).
tt(d2_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k9_qc_lang1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v3_trees_2 C)) ) ) )  =>  ( (C = (k2_qc_lang4 A B))  <=>  ( ((k1_funct_1 C k1_xboole_0) = B)  &  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) =>  ((k2_trees_9 C D) = (k1_qc_lang4 A (k3_trees_2 (k9_qc_lang1 A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  ((k2_qmax_1 A) = (u1_qmax_1 A)) ) ) ).
tt(d2_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v4_quantal1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = B) ) ) ) ) ) ) ) ).
tt(d2_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k7_quatern2 A) = (k6_quatern2 k2_quatern2 A)) ) ) ).
tt(d2_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k3_quatern3 A) = (k27_quaterni (k27_quaterni A A) A)) ) ) ).
tt(d2_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) <=> (r2_hidden A k1_quaterni)) ) ).
tt(d2_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((k2_quofield A B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k1_algstr_0 A (k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)) (k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B))) (k6_algstr_0 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(d2_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_radix_1 A) = (a_1_0_radix_1 A)) ) ) ).
tt(d2_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k5_numbers))  =>  ( (D = (k2_radix_2 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k5_numbers D E) = (k1_radix_2 E B A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_radix_3 A) = (a_1_1_radix_3 A)) ) ) ).
tt(d2_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k4_radix_3 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k4_radix_3 B)))  =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E (k4_radix_3 B)))  =>  ( (E = (k2_radix_4 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k7_radix_3 F B A E) = (k1_radix_4 F A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( (D = (k2_radix_5 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E C A D) = (k1_radix_5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (D = (k2_radix_6 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k2_xcmplx_0 A 2))) =>  ((k4_radix_1 E B (k2_xcmplx_0 A 2) D) = (k1_radix_6 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v2_funct_1 D) & (r1_ordinal1 (k5_card_1 A) (k1_card_1 B)))  =>  ((v1_xboole_0 B) |  ((v1_xboole_0 C) |  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_group_10 B A) (k3_group_10 C A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 B A) (k3_group_10 C A))))) )  =>  ( (E = (k1_ramsey_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k3_group_10 B A)) =>  ((k1_funct_1 E F) = (k7_relat_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((m1_random_1 C A B) <=>  (? [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) &  ( (D = A)  & (r1_mesfunc6 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ((m2_prob_1 E (k2_zfmisc_1 A B) (k1_random_1 (k2_zfmisc_1 A B))) =>  ( (E = (k2_random_2 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  &  ( (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H B))  =>  ((k1_binop_1 F G H) = (k11_binop_2 (k1_seq_1 C (k1_tarski G)) (k1_seq_1 D (k1_tarski H)))) ) ) )  &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 E G) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A C))  =>  ( (E = (k3_ranknull A B C D))  <=>  ((k2_struct_0 E) = (k2_ranknull B C D (k2_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) <=> (r2_hidden A k3_numbers)) ) ).
tt(d2_rcomp_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k2_rcomp_1 A B) = (a_2_1_rcomp_1 A B)) ) ) ) ) ).
tt(d2_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 k1_numbers)) =>  ((m1_rcomp_3 D A B C) <=>  ((r1_tarski (k2_relset_1 (k9_setfam_1 k1_numbers) D) C) &  ( ((k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) D)) = (k1_rcomp_1 A B))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ( (~  ((r1_xxreal_0 E (k3_finseq_1 D)) & (v1_xboole_0 (k7_partfun1 (k9_setfam_1 k1_numbers) D E))) )  &  ( ((r1_xxreal_0 (k1_nat_1 E 1) (k3_finseq_1 D)) =>  ((r1_xxreal_0 (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D E)) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k1_nat_1 E 1)))) &  ((r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D E)) (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k1_nat_1 E 1)))) &  (~ (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D E)) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k1_nat_1 E 1))))) ) ) )  &  ((r1_xxreal_0 (k1_nat_1 E 2) (k3_finseq_1 D)) => (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D E)) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k1_nat_1 E 2))))) ) ) ) ) )  &  ( ((r2_hidden (k1_rcomp_1 A B) C) =>  (D = (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B))) )  &  ( (~ (r2_hidden (k1_rcomp_1 A B) C))  =>  ( (? [E:$i] :  ((v1_xreal_0 E) &  ( (~ (r1_xxreal_0 E A))  &  ((r1_xxreal_0 E B) &  ((k1_funct_1 D 1) = (k3_rcomp_1 A E)) ) ) ) )  &  ( (? [E:$i] :  ((v1_xreal_0 E) &  ((r1_xxreal_0 A E) &  ( (~ (r1_xxreal_0 B E))  &  ((k1_funct_1 D (k3_finseq_1 D)) = (k4_rcomp_1 E B)) ) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~ (r1_xxreal_0 E 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r1_xxreal_0 A F) &  ( (~ (r1_xxreal_0 G F))  &  ((r1_xxreal_0 G B) &  ((k1_funct_1 D E) = (k2_rcomp_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (C = (k2_real_3 A B))  <=>  ( ((k3_funct_2 k5_numbers k5_numbers C k6_numbers) = (k3_nat_d A B))  &  ( ((k3_funct_2 k5_numbers k5_numbers C 1) = (k3_nat_d B (k4_nat_d A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_funct_2 k5_numbers k5_numbers C (k1_nat_1 D 2)) = (k3_nat_d (k1_seq_1 (k1_real_3 A B) D) (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) (k1_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_real_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k2_real_lat)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k5_binop_1 k1_numbers A B C) = (k2_square_1 B C)) ) ) ) ) ) ) ) ).
tt(d2_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A))))) )  =>  ( (B = (k2_real_ns1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k2_binop_1 k1_numbers (k1_euclid A) (k1_euclid A) B C D) = (k9_euclid A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_realset1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k1_realset1 A B) = (k5_relat_1 A (k2_zfmisc_1 B B))) ) ) ) ).
tt(d2_realset2,ax, (k2_realset2 = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k13_funcop_1 k6_numbers k6_numbers k6_numbers) (k13_funcop_1 k6_numbers 1 k6_numbers)) (k13_funcop_1 1 k6_numbers k6_numbers)) (k13_funcop_1 1 1 1))) ).
tt(d2_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (k8_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k8_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k2_realset3 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) B C D) = (k1_binop_1 (k4_realset2 A) C (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_rearran1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_rearran1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k9_real_1 (k3_finseq_1 A) 1)))  => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A (k1_nat_1 B 1)))) ) ) ) ) ) ).
tt(d2_recdef_2,ax, (! [A:$i] :  ((v2_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k5_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (A = (k3_xtuple_0 C D E))  =>  (B = D) ) ) ) ) ) ) ) ) ).
tt(d2_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (A = B)  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) A) <=> (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ).
tt(d2_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_relat_2 A B) <=>  (! [C:$i] :  (~  ((r2_hidden C B) & (r2_hidden (k4_tarski C C) A)) ) ) ) ) ) ) ).
tt(d2_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r2_relset_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden (k4_tarski E F) C) <=> (r2_hidden (k4_tarski E F) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k5_relset_2 A B C D) = (k8_setfam_1 B (k7_relset_1 (k9_setfam_1 A) (k9_setfam_1 B) (k4_relset_2 B A D) (k10_eqrel_1 C)))) ) ) ) ) ) ) ).
tt(d2_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((r1_revrot_1 A B C) <=>  (? [D:$i] :  ((r2_hidden D (k4_finseq_1 B)) &  ( (C = (k7_partfun1 A B D))  &  (! [E:$i] :  (~  ((r2_hidden E (k4_finseq_1 B)) &  ( (~  (E = D) )  &  ((k7_partfun1 A B E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_rewrite1 B A) <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 B)))  => (r2_hidden (k4_tarski (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 1))) A)) ) ) ) ) ) ) ) ) ).
tt(d2_rewrite2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_rewrite2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_rewrite2 C)) )  =>  ( (C = (k1_rewrite2 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k1_ordinal4 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ((l1_rewrite3 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r1_rewrite3 A B C D E) <=> (r2_hidden (k4_tarski (k4_tarski C D) E) (u1_rewrite3 A B))) ) ) ) ) ) ) ).
tt(d2_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k2_rfinseq2 A))  <=>  ( ( ((k3_finseq_1 A) = k6_numbers)  =>  (B = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((r2_hidden B (k4_finseq_1 A)) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  ( (D = (k1_seq_1 A C))  &  (E = (k1_seq_1 A B)) ) )  => (r1_xxreal_0 E D)) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  ((k1_seq_1 A C) = (k1_seq_1 A B)) )  => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k3_rfinseq A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_seq_1 B (k3_finseq_1 B)) = (k1_seq_1 A (k3_finseq_1 A)))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k9_real_1 (k3_finseq_1 B) 1)))  =>  ((k1_seq_1 B C) = (k9_real_1 (k1_seq_1 A C) (k1_seq_1 A (k3_real_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k4_rfunct_1 A))  <=>  ( ((k9_xtuple_0 B) = (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski k6_numbers))))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k5_xcmplx_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden B (k1_relset_1 k1_numbers A)) &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_rfunct_3 A) = (k4_xxreal_0 (k4_xcmplx_0 A) k6_numbers)) ) ) ).
tt(d2_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E)) B) &  (~ (r1_xxreal_0 (k1_seq_1 A (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E))) (k4_xxreal_0 (k1_seq_1 A D) (k1_seq_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k2_rinfsup1 A) = (k5_seq_4 (k2_relset_1 k1_numbers A))) ) ) ).
tt(d2_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k2_rinfsup2 A) = (k7_supinf_2 (k17_supinf_2 A))) ) ) ).
tt(d2_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_ring_1 B A) <=>  ((v1_subset_1 B (u1_struct_0 A)) & (v1_ring_1 B A)) ) ) ) ) ) ).
tt(d2_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((k1_ringcat1 A) = (u1_ringcat1 A)) ) ) ).
tt(d2_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ( (~  (C = k6_numbers) )  =>  ( (D = (k2_rlaffin1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_seq_1 D E) = (k1_seq_1 B (k1_rlvect_1 A E (k2_real_1 C)))) ) ) ) )  &  ( (C = k6_numbers)  =>  ( (D = (k2_rlaffin1 A B C))  <=> (r1_rlvect_2 A D (k4_rlvect_2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k2_rlaffin2 A))  <=>  ( (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_funct_1 B C) = (k1_rlvect_1 A (k2_rlvect_2 A C) (k10_real_1 1 (k5_card_1 C)))) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_finset_1 C))  =>  ((k1_funct_1 B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d2_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_rlaffin3 C A B) =>  (! [D:$i] :  ((k1_rlaffin3 A B C D) = (k4_finseqop (u1_struct_0 A) k1_numbers C (k5_rlaffin1 A B D))) ) ) ) ) ) ) ) ).
tt(d2_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((m1_rlsub_1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ((u1_rlvect_1 B) = (k5_relat_1 (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(d2_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ( ((v1_rlvect_1 D) & (m1_rlsub_1 D A))  =>  ( (D = (k2_rlsub_2 A B C))  <=>  ((u1_struct_0 D) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_rltopsp1 A B C) = (a_3_1_rltopsp1 A B C)) ) ) ) ) ) ) ).
tt(d2_rlvect_1,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v2_rlvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k1_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(d2_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (v4_rlvect_1 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k2_rlvect_2 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ( ((k2_relset_1 (u1_struct_0 A) D) = B)  &  ((v2_funct_1 D) &  (C = (k4_rlvect_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ( (C = (k1_rlvect_3 A B))  <=>  ((u1_struct_0 C) = (a_2_0_rlvect_3 A B)) ) ) ) ) ) ) ) ).
tt(d2_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k1_rlvect_5 A))  <=>  (! [C:$i] :  ((m1_rlvect_3 C A) =>  (B = (k1_card_1 C)) ) ) ) ) ) ) ) ) ).
tt(d2_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_rlvect_x A B) = (a_2_0_rlvect_x A B)) ) ) ) ) ).
tt(d2_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  ((m1_rmod_2 C A B) <=>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 B)) &  ( ((k4_struct_0 C) = (k4_struct_0 B))  &  ( ((u1_algstr_0 C) = (k5_relat_1 (u1_algstr_0 B) (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))  &  ((u1_vectsp_2 A C) = (k5_relat_1 (u1_vectsp_2 A B) (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  ( (E = (k2_rmod_3 A B C D))  <=>  ((u1_struct_0 E) = (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 B) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 A))) =>  ((m1_rmod_4 C A B) <=>  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r2_hidden E D))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v2_robbins2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C)) B) = B) ) ) ) ) ) ) ) ).
tt(d2_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v2_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_lattices A B (k2_lattices A C D)) = (k2_lattices A C (k2_lattices A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ((v2_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B (k2_lattices A (k3_robbins1 A B) (k1_lattices A B C))) = (k1_lattices A B C)) ) ) ) ) ) ) ) ).
tt(d2_rpr_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k2_rpr_1 A B C) = (k10_real_1 (k1_rpr_1 A (k9_subset_1 A C B)) (k1_rpr_1 A B))) ) ) ) ) ) ) ).
tt(d2_rsspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_rsspace3 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_rsspace3 k1_numbers)))) )  =>  ( (A = k2_rsspace3)  <=>  (! [B:$i] :  ((r2_hidden B k1_rsspace3) =>  ((k1_seq_1 A B) = (k4_series_1 (k56_valued_1 k5_numbers k1_numbers (k2_rsspace B)))) ) ) ) ) ) ).
tt(d2_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_rsspace4 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_rsspace4 k1_numbers)))) )  =>  ( (A = k2_rsspace4)  <=>  (! [B:$i] :  ((r2_hidden B k1_rsspace4) =>  ((k1_seq_1 A B) = (k4_seq_4 (k2_relset_1 k1_numbers (k56_valued_1 k5_numbers k1_numbers (k2_rsspace B))))) ) ) ) ) ) ).
tt(d2_rsspace,ax, (! [A:$i] :  ((r2_hidden A k1_rsspace) =>  ((k2_rsspace A) = A) ) ) ).
tt(d2_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( (B = (k1_rusub_1 A))  <=>  ((u1_struct_0 B) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ).
tt(d2_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ( ((v1_bhsp_1 D) & (m1_rusub_1 D A))  =>  ( (D = (k2_rusub_2 A B C))  <=>  ((u1_struct_0 D) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_rusub_3 B A) <=>  ((v1_rlvect_3 B A) &  ((k1_rusub_3 A B) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ) ).
tt(d2_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_rusub_4 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k1_rusub_4 A))  <=>  (! [C:$i] :  ((m1_rusub_3 C A) =>  (B = (k1_card_1 C)) ) ) ) ) ) ) ) ) ).
tt(d2_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_rusub_5 A B C) = (a_3_0_rusub_5 A B C)) ) ) ) ) ) ) ).
tt(d2_rvsum_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k2_rvsum_1)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k3_square_1 B)) ) ) ) ) ) ).
tt(d2_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k3_rvsum_2 A B) = (k3_funcop_1 k27_binop_2 A B)) ) ) ) ) ).
tt(d2_scmbsort,ax, (k2_scmbsort = (k1_scmbsort (k5_scmfsa_2 k6_numbers))) ).
tt(d2_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k4_scm_comp A) = A) ) ) ).
tt(d2_scmfsa_1,ax, (k1_scmfsa_1 = (k2_xboole_0 k1_ami_2 k1_scmfsa_i)) ).
tt(d2_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((k2_scmfsa6a A) = (k1_scmfsa6a A (k5_card_1 A))) ) ) ).
tt(d2_scmfsa_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ( (~ (r1_xxreal_0 B k6_numbers))  =>  ( (C = (k2_scmfsa_7 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k2_nat_1 D 1) = B)  &  (C = (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k8_funcop_1 (u1_compos_1 k1_scmfsa_2) D (k7_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) ) ) ) ) )  &  ((r1_xxreal_0 B k6_numbers) =>  ( (C = (k2_scmfsa_7 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k2_xcmplx_0 D B) = 1)  &  (C = (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k8_funcop_1 (u1_compos_1 k1_scmfsa_2) D (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_scmfsa7b A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) &  ((r2_hidden C (k10_xtuple_0 A)) & (r1_scmfsa7b C B)) ) ) ) ) ) ) ) ).
tt(d2_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a A B C) <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) D)) = (k5_card_1 C))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 D E))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) E)) (k2_afinsq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k2_scmfsa8b A B C) = (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a (k4_scmfsa6a (k13_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A) C) (k1_scmfsa8a (k2_nat_1 (k5_card_1 B) 1))) B) (k4_compos_1 k1_scmfsa_2))) ) ) ) ) ) ) ).
tt(d2_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_scmfsa8c A B) = (k2_scmfsa8b A (k1_scmfsa8c (k1_scmfsa8b A (k1_scmfsa8a 2) (k5_scmfsa6a B (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) (k4_compos_1 k1_scmfsa_2))) ) ) ) ) ).
tt(d2_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r2_scmfsa9a A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) (k2_nat_1 F 1)))) &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) F) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_scmfsa_9 A B) = (k1_funct_4 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers)))) ) ) ) ) ).
tt(d2_scmfsa_i,ax, (k2_scmfsa_i = (k2_xboole_0 (k2_xboole_0 k3_scm_inst a_0_0_scmfsa_i) a_0_1_scmfsa_i)) ).
tt(d2_scmfsa_m,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((v1_scmfsa_m A) <=>  (A = (k4_scmfsa_2 k6_numbers)) ) ) ) ).
tt(d2_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v2_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski A C) => (r1_extpro_1 3 k1_scmfsa_2 C B)) ) ) ) ) ) ) ) ) ).
tt(d2_scm_inst,ax, (k3_scm_inst = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k3_xtuple_0 k1_scm_inst k1_xboole_0 k1_xboole_0)) a_0_0_scm_inst) a_0_1_scm_inst) a_0_2_scm_inst)) ).
tt(d2_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k2_scmisort A) = (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers)) (k6_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 1) A)) (k8_scmfsa_2 (k4_scmfsa_2 1) (k4_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 1) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 2) A) (k8_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 1))) (k6_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 2))) (k7_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 3) A)) (k8_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 4))) (k2_scmfsa_9 (k4_scmfsa_2 2) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 2) A) (k8_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 6))) (k2_scmfsa8b (k4_scmfsa_2 5) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 2))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 4) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 3)) (k8_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 2) A)) (k14_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 3) A)) (k15_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 2) A)) (k15_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 3) A))))))) ) ) ).
tt(d2_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_scmpds_4 A B) = (k1_scmpds_4 (k9_compos_1 k1_scmpds_2 A) B)) ) ) ) ) ).
tt(d2_scmpds_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_scmpds_6 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 C (k10_compos_1 k1_scmpds_2 A)) (k8_memstr_0 2 k1_scmpds_2 B) D)) (k9_xtuple_0 (k10_compos_1 k1_scmpds_2 A)))) ) ) ) ) ) ) ) ) ).
tt(d2_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k2_scmpds_7 A B C D) = (k3_scmpds_4 (k3_scmpds_4 (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 D) 3)) D) (k11_scmpds_2 A B (k4_xcmplx_0 C))) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 D) 2))))) ) ) ) ) ) ) ) ) ).
tt(d2_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_scmpds_8 A B C) = (k3_scmpds_4 (k2_scmpds_4 (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) C) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 1))))) ) ) ) ) ) ) ).
tt(d2_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m2_subset_1 C k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 C k1_xboole_0 (k12_finseq_1 k2_scm_inst B))) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k3_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k2_scm_inst) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 k2_scm_inst C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d2_scmp_gcd,ax, (k2_scmp_gcd = (k1_scmp_gcd k6_numbers)) ).
tt(d2_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E k1_xboole_0 (k2_finseq_4 k2_scm_inst C D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ( (C = (k2_scmringi A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k2_scm_inst) &  ( (D = (k2_xtuple_0 B))  &  (C = (k7_partfun1 k2_scm_inst D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_scmyciel,ax, (! [A:$i] :  ((v1_scmyciel A) <=>  (A = (k1_tarski k1_xboole_0)) ) ) ).
tt(d2_scpinvar,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k3_scpinvar A) = (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k5_scmpds_2 (k1_scmp_gcd 1) k6_numbers)) (k5_scmpds_2 (k1_scmp_gcd 2) 1)) (k5_scmpds_2 (k1_scmp_gcd 3) A)) (k2_scmpds_8 k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1)))))) ) ) ).
tt(d2_scpisort,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_scpisort A B) = (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k10_scmpds_2 k2_scmp_gcd 1 k6_numbers)) (k10_scmpds_2 k2_scmp_gcd 2 (k6_xcmplx_0 A 1))) (k10_scmpds_2 k2_scmp_gcd 3 B)) (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))))) ) ) ) ) ).
tt(d2_scpqsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_scpqsort A B) = (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k5_scmpds_2 k3_scmp_gcd 1)) (k10_scmpds_2 k3_scmp_gcd (k2_nat_1 B A) (k2_nat_1 B 1))) (k10_scmpds_2 k3_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 1) (k2_nat_1 B A))) (k2_scmpds_8 k2_scmp_gcd 1 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k3_scmp_gcd 2 (k2_nat_1 (k2_nat_1 B A) 1)) (k13_scmpds_2 k2_scmp_gcd k3_scmp_gcd 2 (k2_nat_1 B A))) (k3_scmpds_6 k2_scmp_gcd 2 (k1_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k3_scmp_gcd 2 (k2_nat_1 B A)) (k16_scmpds_2 k2_scmp_gcd k3_scmp_gcd 4 (k2_nat_1 (k2_nat_1 B A) 1))) k1_scpqsort) (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 3) (k2_nat_1 (k2_nat_1 B A) 1)) (k16_scmpds_2 k3_scmp_gcd k2_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 1) 4)) (k16_scmpds_2 k3_scmp_gcd k2_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 2) 4)) (k11_scmpds_2 k3_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 1) (k4_xcmplx_0 1))) (k11_scmpds_2 k3_scmp_gcd (k2_nat_1 (k2_nat_1 B A) 2) 1)) (k11_scmpds_2 k2_scmp_gcd 1 2))) (k9_compos_1 k1_scmpds_2 (k11_scmpds_2 k2_scmp_gcd 1 (k4_xcmplx_0 2)))))))) ) ) ) ) ).
tt(d2_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_semi_af1 A B C D) <=> (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(d2_seq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v2_seq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 (k1_seq_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d2_seq_4,ax, (! [A:$i] :  ((v3_membered A) =>  ((v3_xxreal_2 A) =>  ((v1_xboole_0 A) |  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (B = (k3_seq_4 A))  <=>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden D A) &  (~ (r1_xxreal_0 (k9_binop_2 B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k3_seqfunc A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers C D) (k6_rfunct_1 A k1_numbers (k1_seqfunc A k1_numbers B D)))) ) ) ) ) ) ) ) ) ).
tt(d2_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A k1_numbers) & (v1_funct_1 A)) ) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) <=> (v2_comseq_2 (k3_series_1 A))) ) ) ).
tt(d2_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_setfam_1 A B) <=>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r2_hidden D B) & (r1_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(d2_setlim_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_setlim_1 A))  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 B C) = (k1_setfam_1 (a_2_1_setlim_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k2_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k4_subset_1 A (k8_nat_1 (k9_setfam_1 A) B E) (k8_nat_1 (k9_setfam_1 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) <=>  (? [C:$i] :  ((m1_subset_1 C A) & (r3_binop_1 A C B)) ) ) ) ) ) ) ).
tt(d2_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 C A) & (v1_binop_1 C A))  =>  ( ( (~ (v1_setwiseo C A))  &  (~ (r1_xxreal_0 1 (k3_finseq_1 B))) )  |  ((k1_finsop_1 A B C) = (k7_setwiseo k5_numbers A C (k3_finsop_1 B) (k1_setwop_2 A B (k4_binop_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(d2_sfmastr2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sfmastr2 A B) = (k4_scmfsa6a (k6_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m A) (k2_sf_mastr B))) A) (k1_sfmastr2 A B))) ) ) ) ) ).
tt(d2_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 F (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r1_sfmastr3 A B C D E F) <=>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 F D) (k1_funct_1 F C)) 1) G))  =>  ((r5_scmfsa7b E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 A B C D E F) G) (k1_funct_4 A (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers)))))) & (r6_scmfsa7b E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 A B C D E F) G) (k1_funct_4 A (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2)) =>  ( (B = (k2_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k2_scmfsa_2)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k2_scmfsa_2))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ((k3_funct_2 (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k2_scmfsa_2) C D) = (k1_sf_mastr D)) ) )  &  (B = (k3_card_3 (k3_relat_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d2_sgraph1,ax, (! [A:$i] :  ((k2_sgraph1 A) = (a_1_0_sgraph1 A)) ) ).
tt(d2_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v1_sheffer1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k1_sheffer1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_lattices A B C) = C)  &  ((k2_lattices A C B) = C) ) ) ) ) ) ) ) ) ) ).
tt(d2_simplex0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (D = (k3_simplex0 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden E D) <=>  ((r2_hidden E B) & (r1_ordinal1 (k1_card_1 E) (k1_card_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_simplex1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ((k2_simplex1 A B C) = C) ) ) ) ) ) ) ).
tt(d2_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((v1_simplex2 B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D (u1_pre_topc B)) =>  ((v6_tbsp_1 D A) & (r1_xxreal_0 (k3_tbsp_1 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_sincos10,ax, (k2_sincos10 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(d2_sin_cos2,ax, (! [A:$i] :  ((k2_sin_cos2 A) = (k1_seq_1 k1_sin_cos2 A)) ) ).
tt(d2_sin_cos3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k2_sin_cos3)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers A B) = (k6_binop_2 (k3_binop_2 (k15_sin_cos (k5_binop_2 k7_complex1 B)) (k15_sin_cos (k1_binop_2 (k5_binop_2 k7_complex1 B)))) 2)) ) ) ) ) ) ).
tt(d2_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_sin_cos4 A) = (k7_xcmplx_0 (k20_sin_cos A) (k17_sin_cos A))) ) ) ).
tt(d2_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_sin_cos5 A) = (k10_real_1 1 (k6_sin_cos2 A))) ) ) ).
tt(d2_sin_cos6,ax, (! [A:$i] :  ((k2_sin_cos6 A) = (k1_seq_1 k1_sin_cos6 A)) ) ).
tt(d2_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_sin_cos7 A) = (k6_power k8_power (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))))) ) ) ).
tt(d2_sin_cos9,ax, (k2_sin_cos9 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)))) ).
tt(d2_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (A = k2_sin_cos)  <=>  ( ((k8_nat_1 k1_numbers A k6_numbers) = 1)  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A (k2_nat_1 B 1)) = (k8_real_1 (k8_nat_1 k1_numbers A B) (k2_nat_1 B 1))) ) ) ) ) ) ) ).
tt(d2_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_sppol_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((k18_euclid B) = (k18_euclid C)) ) ) ) ) ) ) ) ) ).
tt(d2_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (r1_sppol_2 B C A)) ) ) ) ) ) ) ).
tt(d2_sprect_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_sprect_1 A) <=>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  &  (A = (k1_sprect_1 B)) ) ) ) ) ) ).
tt(d2_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_sprect_2 A B) <=>  ((r1_sprect_2 A B) &  ( ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) = (k6_pscomp_1 (k3_topreal1 2 A)))  &  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) = (k8_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d2_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (B = (k6_square_1 A))  <=>  ((r1_xxreal_0 k6_numbers B) &  ((k3_square_1 B) = A) ) ) ) ) ) ) ) ).
tt(d2_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  =>  ((m1_stacks_1 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A (k8_eqrel_1 B C)) (k8_eqrel_1 B C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A (k8_eqrel_1 B C)) (k8_eqrel_1 B C))))) )  =>  ( (E = (k3_stacks_1 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden F A) &  ((r2_hidden G (k8_eqrel_1 B C)) & (r2_hidden H G)) )  =>  ((k1_binop_1 E F G) = (k6_eqrel_1 B B C (k1_binop_1 D F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_stirl2_1 A B) = (k1_card_1 (a_2_0_stirl2_1 A B))) ) ) ) ) ).
tt(d2_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k1_struct_0 A) = k1_xboole_0) ) ) ).
tt(d2_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m1_valuat_1 E A C) =>  ((r1_sublemma A B C D E) <=> (r1_valuat_1 A C (k2_sublemma A B) E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_subset_1,ax, (! [A:$i] :  ((k1_subset_1 A) = k1_xboole_0) ) ).
tt(d2_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B C) = (a_3_0_substlat A B C)) ) ) ) ) ).
tt(d2_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_substut1 A)) =>  ((k2_substut1 A B) = B) ) ) ) ) ).
tt(d2_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k6_substut2 A) = (k5_relat_1 (k15_substut1 A) (k38_substut1 A))) ) ) ).
tt(d2_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( (B = (k4_supinf_1 A))  <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C B) <=> (m2_xxreal_2 C A)) ) ) ) ) ) ) ) ).
tt(d2_supinf_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((k11_supinf_2 A B C D) = (k7_supinf_2 (k2_relset_1 C D))) ) ) ) ) ) ) ) ).
tt(d2_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B D C))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (F = (k1_symsp_1 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B G D)) C) =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_t_0topsp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_t_0topsp C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc D A) => (v3_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k2_t_1topsp A) = (k11_borsuk_1 A (k12_eqrel_1 (u1_struct_0 A) (k1_t_1topsp A)))) ) ) ).
tt(d2_tarski,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k2_tarski A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ( (D = A)  |  (D = B) ) ) ) ) ) ) ) ).
tt(d2_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  ((m2_taxonom1 B A) <=>  ((m1_taxonom1 B A) &  ((r2_hidden (k1_tarski A) B) & (r2_hidden (k10_eqrel_1 A) B)) ) ) ) ) ) ) ).
tt(d2_taxonom2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_taxonom2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A D B) & (r1_orders_2 A D C)) ) )  &  ( (~ (r1_orders_2 A B C))  &  (~ (r1_orders_2 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (B = (k2_taylor_1 A))  <=>  ( ((k1_relset_1 k1_numbers B) = (k3_limfunc1 k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers (k3_limfunc1 k6_numbers)) =>  ((k1_seq_1 B C) = (k5_power A C)) ) ) ) ) ) ) ) ) ).
tt(d2_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_tbsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k2_metric_1 A (k8_nat_1 (u1_struct_0 A) B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (B = (k1_tdgroup A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski (k4_tarski C D) (k4_tarski E F)) B) <=>  ((k1_algstr_0 A C F) = (k1_algstr_0 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A))))) )  =>  ( (B = (k2_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_1 A)) =>  ((k5_binop_1 (k1_tdlat_1 A) B C D) = (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) (k4_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tdlat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v4_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d2_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_tdlat_3 A) <=>  ((u1_pre_topc A) = (k2_tarski k1_xboole_0 (u1_struct_0 A))) ) ) ) ).
tt(d2_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r1_termord A B C D) <=> (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ) ).
tt(d2_tex_1,ax, (! [A:$i] :  ((k1_tex_1 A) = (k2_tarski k1_xboole_0 A)) ) ).
tt(d2_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) & (m1_pre_topc C A)) )  =>  ( (C = (k1_tex_2 A B))  <=>  ((u1_struct_0 C) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(d2_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tex_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v1_tops_3 C A)) ) ) ) ) ) ) ) ).
tt(d2_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc D A) &  ((r2_hidden C D) & (r2_hidden C B)) )  => (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tmap_1 A B C D) <=>  (! [E:$i] :  ((m1_connsp_2 E B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_connsp_2 F A D) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_toler_1 C A B) =>  ((v1_toler_1 C A B) <=>  (! [D:$i] :  (~  ( (~ (r2_hidden D C))  &  ((r2_hidden D A) &  (! [E:$i] :  (~  ((r2_hidden E C) &  (~ (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_topalg_1 A B) = (k1_topalg_1 A B B)) ) ) ) ) ).
tt(d2_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 B))))) )  =>  ( (E = (k1_topalg_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid A))) =>  ( ( (H = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) C F))  &  (I = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) D F)) )  =>  ((k1_binop_1 E F G) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) H (k9_real_1 1 G)) (k1_rlvect_1 (k15_euclid A) I G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))))))) )  =>  ( (E = (k11_topalg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)))) =>  (? [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D)) &  ( (F = (k6_eqrel_1 (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k4_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) G))  &  ((k3_funct_2 (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))) E F) = (k10_finseq_1 (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) (k9_topalg_4 A B C D G)) (k6_eqrel_1 (k2_topalg_1 B D) (k2_topalg_1 B D) (k4_topalg_1 B D) (k10_topalg_4 A B C D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( (F = (k3_topalg_5 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) F G) = (k1_binop_1 D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_topalg_6 A) <=>  ((v1_topalg_6 A) & (v1_borsuk_2 A)) ) ) ) ).
tt(d2_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_topdim_1 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) & (r2_hidden B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) C))) ) ) ) ) ) ) ).
tt(d2_topdim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((v1_topdim_2 B A) =>  ( (C = (k1_topdim_2 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((r2_hidden (k1_xxreal_3 C 1) (k1_card_1 D)) & (r1_tarski D B))  => (v1_xboole_0 (k6_setfam_1 A D))) ) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((r1_tarski D B) &  ( ((k1_card_1 D) = (k1_xxreal_3 C 1))  &  (~  ((v1_xboole_0 (k6_setfam_1 A D)) &  (~ (v1_xboole_0 D)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_topdim_2 B A))  =>  ( (C = (k1_topdim_2 A B))  <=>  (C = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(d2_topgen_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r1_topgen_1 A B C) <=> (r2_hidden C (k2_pre_topc A (k7_subset_1 (u1_struct_0 A) B (k1_tarski C))))) ) ) ) ) ) ).
tt(d2_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k2_topgen_2 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_ordinal1 (k1_topgen_2 A C) B)) )  &  (! [C:$i] :  ((v1_card_1 C) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_ordinal1 (k1_topgen_2 A D) C)) )  => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ) ).
tt(d2_topgen_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_pre_topc A) &  ((v2_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (A = k2_topgen_3)  <=>  ( ((u1_struct_0 A) = k1_numbers)  &  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) &  ( ((u1_pre_topc A) = (k1_cantor_1 k1_numbers B))  &  (B = a_0_0_topgen_3) ) ) ) ) ) ) ) ).
tt(d2_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_topgen_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d2_topgen_5,ax, (k2_topgen_5 = a_0_1_topgen_5) ).
tt(d2_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k2_topgrp_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k6_algstr_0 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_metric_1 C) & (m1_topmetr C A))  =>  ( (C = (k1_topmetr A B))  <=>  ((u1_struct_0 C) = B) ) ) ) ) ) ) ) ).
tt(d2_topreal1,ax, (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 1) (k19_euclid 1 k6_numbers)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid k6_numbers k6_numbers))))) ).
tt(d2_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ( (~  (B = C) )  &  ((r2_hidden B A) &  ((r2_hidden C A) &  ((r1_topreal4 D B C) &  ((r1_topreal4 E B C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) D E) = (k2_tarski B C))  &  (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_topreal9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k2_topreal9 A B C) = (a_3_1_topreal9 A B C)) ) ) ) ) ) ) ).
tt(d2_topreala,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (A = k2_topreala)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_funct_1 A (k4_tarski B C)) = (k10_finseq_1 B C)) ) ) ) ) ) ) ) ).
tt(d2_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_toprealb A) = A) ) ) ).
tt(d2_toprns_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k1_toprns_1 A B C) = (k1_vfunct_1 k5_numbers (k15_euclid A) B C)) ) ) ) ) ) ) ).
tt(d2_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A B) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(d2_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v4_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(d2_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=>  ((k2_pre_topc A B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(d2_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ((r1_transgeo A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_hidden (k4_tarski (k4_tarski D E) (k4_tarski (k3_funct_2 A A B D) (k3_funct_2 A A B E))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k2_treal_1 A B) = B) ) ) ) ) ) ).
tt(d2_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( (B = (k1_trees_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ( (C = D)  & (r2_xboole_0 D A)) ) ) ) ) ) ) ) ) ).
tt(d2_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((v1_trees_2 A) <=>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m1_trees_1 C A) =>  (~ (r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers B)) A)) ) ) ) ) ) ) ) ).
tt(d2_trees_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_trees_3)) =>  ( (A = k2_trees_3)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) ) ) ) ) ) ).
tt(d2_trees_4,ax, (! [A:$i] :  ((k1_trees_4 A) = (k7_funcop_1 (k2_trees_1 k6_numbers) A)) ) ).
tt(d2_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m4_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ( (~  (B = k1_xboole_0) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  ( (D = (k3_trees_a A B C))  <=>  ( ((k9_xtuple_0 D) = (k1_trees_a (k9_xtuple_0 A) (k9_xtuple_0 C) B))  &  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (~  ((r2_hidden E (k1_trees_a (k9_xtuple_0 A) (k9_xtuple_0 C) B)) &  ( (? [F:$i] :  ((m2_finseq_1 F k5_numbers) &  ((r2_hidden F B) &  (~  ( (~ (r1_tarski F E))  &  ((k1_funct_1 D E) = (k1_funct_1 A E)) ) ) ) ) )  &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k5_numbers) =>  (~  ((r2_hidden F B) &  ((r2_hidden G (k9_xtuple_0 C)) &  ( (E = (k8_finseq_1 k5_numbers F G))  &  ((k1_funct_1 D E) = (k1_funct_1 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_pre_topc D) & (m1_pre_topc D A)) )  =>  ( (D = (k1_tsep_1 A B C))  <=>  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(d2_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r3_tsep_2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (u1_struct_0 B))  &  (E = (u1_struct_0 C)) )  => (r2_tsep_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((m1_pre_topc B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v4_pre_topc C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v4_pre_topc D A) &  (C = (k8_subset_1 (u1_struct_0 A) D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k9_subset_1 (u1_struct_0 A) B (k4_tex_4 A C)) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ).
tt(d2_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_turing_1 A)) =>  ((k5_turing_1 A B C D) = (k1_funct_4 B (k16_funcop_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d2_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k3_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k10_margrel1 (k9_margrel1 B) C)) ) ) ) ) ) ) ) ).
tt(d2_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ((v3_unialg_1 A) <=> (v5_margrel1 (u1_unialg_1 A) (u1_struct_0 A))) ) ) ).
tt(d2_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k1_unialg_2 A) = (k10_xtuple_0 (u1_unialg_1 A))) ) ) ).
tt(d2_uniform1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v2_uniform1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k1_relset_1 k5_numbers A)) &  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k2_uniroots A) = (a_1_0_uniroots A)) ) ) ).
tt(d2_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k2_uproots A B C) = (k1_funct_4 (k16_pre_poly A) (k8_funcop_1 k5_numbers B C))) ) ) ) ) ) ).
tt(d2_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( (A = k2_urysohn1)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) & (r2_hidden B (k1_urysohn1 C))) ) ) ) ) ) ) ) ).
tt(d2_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v10_pre_topc A) &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) & (r1_xboole_0 B C)) ) )  =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A))))))) )  =>  ((m2_urysohn3 D A B C) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((m1_urysohn3 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E) A B C E) &  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E))) =>  ((k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E) F) = (k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D (k2_nat_1 E 1)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  (! [E:$i] :  ((m2_funct_2 E (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( (E = (k3_valuat_1 A B C D))  <=>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 E F) = (k12_margrel1 (a_5_0_valuat_1 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_valued_0 A) <=> (r1_tarski (k10_xtuple_0 A) k7_numbers)) ) ) ).
tt(d2_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k7_valued_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k2_xcmplx_0 B (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k2_vectsp10 A B C) = (a_3_0_vectsp10 A B C)) ) ) ) ) ) ) ).
tt(d2_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ((v1_vectsp11 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((m1_vectsp11 D A B C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (~  (E = (k4_struct_0 B)) )  &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) C E) = (k4_vectsp_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v1_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k11_algstr_0 A B))  <=>  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((m1_vectsp_4 C A B) <=>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 B)) &  ( ((k4_struct_0 C) = (k4_struct_0 B))  &  ( ((u1_algstr_0 C) = (k1_realset1 (u1_algstr_0 B) (u1_struct_0 C)))  &  ((u1_vectsp_1 A C) = (k5_relat_1 (u1_vectsp_1 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ( (E = (k2_vectsp_5 A B C D))  <=>  ((u1_struct_0 E) = (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ((k1_vectsp_6 A B C) = (a_3_0_vectsp_6 A B C)) ) ) ) ) ) ) ).
tt(d2_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (D = (k1_vectsp_7 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_vectsp_7 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d2_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (D = (k2_vectsp_9 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ( ((v7_vectsp_1 F A) & (m1_vectsp_4 F A B))  &  ( (F = E)  &  ((k1_vectsp_9 A F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k2_vfunct_1 A B C D))  <=>  ( ((k1_relset_1 A E) = (k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C F) (k7_partfun1 (u1_struct_0 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k2_vfunct_2 A B C D))  <=>  ( ((k1_relset_1 A E) = (k1_relset_1 A C))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k1_clvect_1 B (k7_partfun1 (u1_struct_0 B) C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ((r1_orders_2 A E C) & (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) & (l1_orders_2 B)) )  =>  ( (B = (k3_waybel10 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) <=>  ((v1_orders_2 C) & (m1_yellow_0 C A)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_orders_2 B C D) <=>  (? [E:$i] :  ((l1_orders_2 E) &  ( (D = E)  & (m1_yellow_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel11 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r1_tarski C B) => (r2_hidden (k1_yellow_0 A C) B)) ) ) ) ) ) ) ) ).
tt(d2_waybel12,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_waybel12 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d2_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k1_waybel15 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (v1_waybel15 C A)) ) ) ) ) ) ) ) ).
tt(d2_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_orders_2 C) &  ((v4_yellow_0 C (k7_yellow_1 A B)) & (m1_yellow_0 C (k7_yellow_1 A B))) )  =>  ( (C = (k2_waybel17 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r2_hidden D (u1_struct_0 C)) <=> (v5_pre_topc D A B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel18,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_waybel18 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k4_card_3 (k12_pralg_1 A B))))) =>  ( (C = (k2_waybel18 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_card_3 (k12_pralg_1 A B)))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  (? [F:$i] :  ((l1_pre_topc F) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 F))) &  ((r2_hidden E A) &  ((v3_pre_topc G F) &  ( (F = (k1_funct_1 B E))  &  (D = (k4_card_3 (k2_funct_7 (k12_pralg_1 A B) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (k1_waybel19 A))  <=>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v1_waybel19 C) & (m1_yellow_9 C A)) )  =>  (B = (u1_pre_topc C)) ) ) ) ) ) ) ) ).
tt(d2_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) => (r1_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ((v1_waybel20 B A) <=>  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ( (~ (v2_struct_0 (k5_yellow_0 (k3_yellow_3 A A) B)))  &  ((v4_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) &  ((v7_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) &  ((v4_waybel_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) & (m1_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A))) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel22,ax, (! [A:$i] :  ((k1_waybel22 A) = (a_1_0_waybel22 A)) ) ).
tt(d2_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel23 B A) <=> (v6_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(d2_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_waybel24 A B C D E) = (k1_funct_1 (k3_funct_5 D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_waybel_9 B) & (l1_waybel_9 B))  =>  ( (B = (k1_waybel25 A))  <=>  ( ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_orders_2 B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (E = (k1_tarski D))  & (r2_hidden C (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_waybel26 A B)) (u1_struct_0 (k1_waybel26 A C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A B)) (u1_struct_0 (k1_waybel26 A C)))))) )  =>  ( (E = (k3_waybel26 A B C D))  <=>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k1_funct_1 E F) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel27,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_waybel27 A) <=>  ( (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ( ((v1_relat_1 B) & (v1_funct_1 B))  & (v1_relat_1 (k9_xtuple_0 B))) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k1_funct_5 B)) ) ) ) ) ) ) ) ).
tt(d2_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ( (D = (k1_waybel28 A B C))  <=>  ( ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (r1_funct_2 (u1_struct_0 D) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A D) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C (u1_waybel_0 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k2_waybel29 A B C) = C) ) ) ) ) ) ) ).
tt(d2_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) )  =>  ( (D = (k2_waybel_2 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k5_finsub_1 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 B) (u1_struct_0 A))))) )  &  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 B)) =>  ( ((k3_funct_2 (k5_finsub_1 B) (u1_struct_0 A) E F) = (k1_yellow_0 A (k7_relset_1 B (u1_struct_0 A) C F)))  &  (D = (g1_waybel_0 A (k5_finsub_1 B) (k1_yellow_1 (k5_finsub_1 B)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_waybel31 A B C) = (k7_subset_1 (u1_struct_0 A) (k2_waybel_3 A C) (k4_waybel_0 A B))) ) ) ) ) ) ) ).
tt(d2_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) & (l1_waybel_9 A)) ) )  =>  ((v2_waybel32 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_waybel_0 A B) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)))  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v10_waybel_0 C A) & (l1_waybel_0 C A)) ) ) )  =>  ( (B = (k1_waybel_2 A C))  =>  (! [D:$i] :  ((m1_connsp_2 D A B) => (r1_waybel_0 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  ((v1_waybel33 A) <=>  ((u1_pre_topc A) = (k4_waybel28 A)) ) ) ) ).
tt(d2_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v3_lattice3 B) & (v18_waybel_0 C B A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (D = (k2_waybel34 A B C))  <=> (v3_waybel_1 (k1_waybel_1 A B D C) A B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel_3 B A) <=> (r1_waybel_3 A B B)) ) ) ) ) ).
tt(d2_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k2_waybel_4 A) = (u1_orders_2 A)) ) ) ).
tt(d2_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_xtuple_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (u1_struct_0 A))))) )  =>  ( (C = (k5_waybel_5 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k5_yellow_2 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (B = (k11_lattice3 A C D))  &  ( (~  (C = B) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v2_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden (k13_lattice3 A C D) B) &  ( (~ (r2_hidden C B))  &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_waybel_8 A B) = (a_2_0_waybel_8 A B)) ) ) ) ) ).
tt(d2_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((k1_waybel_9 A B) = (k5_yellow_2 A (u1_waybel_0 A B))) ) ) ) ) ).
tt(d2_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k7_group_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k7_group_3 A B))))) )  =>  ( (C = (k2_weddwitt A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (k7_group_3 A B) C D) = (k2_group_3 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((k2_weierstr A) = (k4_seq_4 (k1_weierstr A))) ) ) ).
tt(d2_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_wellfnd1 A) <=> (r1_wellord1 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d2_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_wellord1 A) <=>  (! [B:$i] :  (~  ((r1_tarski B (k1_relat_1 A)) &  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  (~  ((r2_hidden C B) & (r1_xboole_0 (k1_wellord1 A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d2_wellord2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_wellord1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k2_wellord2 A))  <=> (r4_wellord1 A (k1_wellord2 B))) ) ) ) ) ) ).
tt(d2_xboole_0,ax, (k1_xboole_0 = o_0_0_xboole_0) ).
tt(d2_xboolean,ax, (k2_xboolean = 1) ).
tt(d2_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) <=> (r2_hidden A k2_numbers)) ) ).
tt(d2_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 A B)) =>  ((k1_xreal_0 A B) = (k6_xcmplx_0 A B)) )  &  ( (~ (r1_xxreal_0 k6_numbers (k6_xcmplx_0 A B)))  =>  ((k1_xreal_0 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(d2_xtuple_0,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k1_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( (A = (k4_tarski C D))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(d2_xxreal_0,ax, (k1_xxreal_0 = k1_numbers) ).
tt(d2_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k2_xxreal_1 A B) = (a_2_1_xxreal_1 A B)) ) ) ) ) ).
tt(d2_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((m2_xxreal_2 B A) <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(d2_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (C = (k1_xxreal_3 A B))  <=>  (? [D:$i] :  ((v1_xcmplx_0 D) &  (? [E:$i] :  ((v1_xcmplx_0 E) &  ( (A = D)  &  ( (B = E)  &  (C = (k2_xcmplx_0 D E)) ) ) ) ) ) ) ) )  &  ( ( ( ( (A = k1_xxreal_0)  &  (~  (B = k2_xxreal_0) ) )  |  ( (B = k1_xxreal_0)  &  (~  (A = k2_xxreal_0) ) ) )  =>  ( (C = (k1_xxreal_3 A B))  <=>  (C = k1_xxreal_0) ) )  &  ( ( ( ( (A = k2_xxreal_0)  &  (~  (B = k1_xxreal_0) ) )  |  ( (B = k2_xxreal_0)  &  (~  (A = k1_xxreal_0) ) ) )  =>  ( (C = (k1_xxreal_3 A B))  <=>  (C = k2_xxreal_0) ) )  &  (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( (~  ( (A = k1_xxreal_0)  &  (~  (B = k2_xxreal_0) ) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (~  (A = k2_xxreal_0) ) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (~  (B = k1_xxreal_0) ) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (~  (A = k1_xxreal_0) ) ) )  &  (~  ( (C = (k1_xxreal_3 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v4_orders_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_orders_2 A B C) & (r1_orders_2 A C D))  => (r1_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow11,ax, (k2_yellow11 = (k2_yellow_1 (k3_enumset1 k6_numbers 1 (k6_subset_1 2 1) (k6_subset_1 3 2) 3))) ).
tt(d2_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_yellow13 C A B) <=>  (! [D:$i] :  ((m1_connsp_2 D A B) =>  (? [E:$i] :  ((m1_connsp_2 E A B) &  ((r2_hidden E C) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k2_yellow15 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 A)) &  ( ((k3_finseq_1 D) = (k5_card_1 B))  &  ( ((k2_relset_1 (k9_setfam_1 A) D) = B)  &  (C = (a_2_0_yellow15 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_yellow16 A B C) <=>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v22_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v22_waybel_0 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ((k3_relat_1 D C) = (k3_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r1_yellow18 A B) <=>  (? [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  (? [D:$i] :  ( ((v15_functor0 D B A) & (m2_functor0 D B A))  &  ((r1_functor3 A A (k1_functor3 A B A C D) (k12_functor0 A)) & (r1_functor3 B B (k1_functor3 B A B D C) (k12_functor0 B))) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_yellow19 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (C = (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A (k4_waybel_9 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow_1,ax, (! [A:$i] :  ((k3_yellow_1 A) = (k3_lattice3 (k1_lattice3 A))) ) ).
tt(d2_yellow20,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k1_yellow20 A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 C D) = (k3_xboole_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow21,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k2_yellow21 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ( ((v1_orders_2 C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  & (r2_hidden (u1_struct_0 (k1_yellow21 C)) A)) ) ) ) ) ) ).
tt(d2_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k1_yellow_2 A B C) = (k5_yellow_0 B (k2_relset_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(d2_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k3_yellow_3 A B))  <=>  ( ((u1_struct_0 C) = (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))  &  ((u1_orders_2 C) = (k2_yellow_3 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 A) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ).
tt(d2_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_yellow_4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_yellow_5 A B C) = (k10_lattice3 A (k1_yellow_5 A B C) (k1_yellow_5 A C B))) ) ) ) ) ) ) ).
tt(d2_yellow_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pralg_1 A)) )  =>  ((v4_waybel_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( (~ (v2_struct_0 B))  & (l1_struct_0 B)) ) ) ) ) ) ).
tt(d2_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_yellow_8 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v4_card_3 B) &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_tops_3 C A)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (C = (k8_setfam_1 (u1_struct_0 A) B))  & (v1_tops_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_yellow_9 A B) = (k6_waybel_9 (k5_yellow_0 A B) A (k1_yellow_9 A (k5_yellow_0 A B)) (k2_waybel_9 (k5_yellow_0 A B)))) ) ) ) ) ).
tt(d2_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_yoneda_1 A B) = (k19_ens_1 A B)) ) ) ) ) ).
tt(d2_zf_colla,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_zf_colla A B C) <=>  ( ((k9_xtuple_0 A) = B)  &  ( ((k10_xtuple_0 A) = C)  &  ((v2_funct_1 A) &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  ( (~  ( (? [F:$i] :  ( (F = E)  & (r2_hidden D F)) )  &  (! [F:$i] :  (~  ( ((k1_funct_1 A E) = F)  & (r2_hidden (k1_funct_1 A D) F)) ) ) ) )  &  (~  ( (? [F:$i] :  ( ((k1_funct_1 A E) = F)  & (r2_hidden (k1_funct_1 A D) F)) )  &  (! [F:$i] :  (~  ( (F = E)  & (r2_hidden D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_zf_fund1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k4_ordinal1 k1_zf_lang) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k4_ordinal1 k1_zf_lang)))) )  =>  ( (A = k2_zf_fund1)  <=>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  ((k3_funct_2 k4_ordinal1 k1_zf_lang A B) = (k2_zf_lang (k5_card_1 B))) ) ) ) ) ) ).
tt(d2_zf_fund2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_zf_fund2 A) <=>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r2_hidden C A) => (r2_hidden (k1_zf_fund2 B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(d2_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((k3_zf_lang1 A) = (k6_subset_1 (k10_xtuple_0 A) (k3_enumset1 k6_numbers 1 2 3 4))) ) ) ).
tt(d2_zf_lang,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_zf_lang A) = (k2_nat_1 5 A)) ) ) ).
tt(d2_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k2_zfmisc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  (? [F:$i] :  ((r2_hidden E A) &  ((r2_hidden F B) &  (D = (k4_tarski E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_zfmodel1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((r1_tarski (k2_zf_model A) (k2_tarski (k2_zf_lang 3) (k2_zf_lang 4))) & (r2_zf_model B (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang A (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ( (C = (k2_zfmodel1 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((r1_zf_model B D A) <=>  ((k3_funct_2 B B C (k3_funct_2 k1_zf_lang B D (k2_zf_lang 3))) = (k3_funct_2 k1_zf_lang B D (k2_zf_lang 4))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d2_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_zf_model A) = (k9_funct_2 k1_zf_lang A)) ) ) ).
tt(d2_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r2_zfrefle1 A B) <=>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( ((k2_zf_model C) = k1_xboole_0)  =>  ((r2_zf_model A C) <=> (r2_zf_model B C)) ) ) ) ) ) ) ) ) ).
tt(d2_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) & (v1_funct_1 B)) ) )  =>  ((v1_zf_refle B A) <=>  ((k9_xtuple_0 B) = (k2_ordinal1 A)) ) ) ) ) ) ).
tt(d2_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  ((v2_zmodul01 A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_zmodul01 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k1_zmodul01 A C B) (k1_zmodul01 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d30_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  ((v14_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_abcmiz_0 A)) =>  (~  ((r4_abcmiz_0 A B D) &  ((r3_orders_2 A (k5_abcmiz_0 A B D) C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_abcmiz_0 A))))  =>  (~  ((r6_abcmiz_0 A (k10_lattice3 A B C) E) &  ((k6_abcmiz_0 A (k10_lattice3 A B C) E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 (k1_msualg_1 A B)) = 1)  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (D = (k1_funct_1 (k1_msualg_1 A B) 1))  & (m1_abcmiz_1 C A D)) ) )  =>  ((k30_abcmiz_1 A B C) = (k4_trees_4 (k4_tarski B (u1_struct_0 A)) (k3_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C))) ) ) ) ) ) ) ) ) ).
tt(d30_abcmiz_a,ax, (! [A:$i] :  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 k4_abcmiz_a))))  =>  ((m2_abcmiz_a B A) <=>  ( ((k1_relset_1 k2_abcmiz_1 B) = (k2_relset_1 k2_abcmiz_1 A))  & (v7_abcmiz_a B)) ) ) ) ) ) ).
tt(d30_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v23_algstr_0 B A) & (v17_algstr_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k9_algstr_0 A B))  <=>  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d30_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ((r2_aofa_000 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_hidden (k2_binop_1 B (u1_struct_0 A) B D E F) C) =>  ((k2_binop_1 B (u1_struct_0 A) B D E (k14_aofa_000 A F G H)) = (k2_binop_1 B (u1_struct_0 A) B D (k2_binop_1 B (u1_struct_0 A) B D E F) G)) )  &  ( (~ (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D E F) C))  =>  ((k2_binop_1 B (u1_struct_0 A) B D E (k14_aofa_000 A F G H)) = (k2_binop_1 B (u1_struct_0 A) B D (k2_binop_1 B (u1_struct_0 A) B D E F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  (! [G:$i] :  ((m3_aofa_i00 G A B C D) =>  ( (G = (k36_aofa_i00 A B C D E F))  <=>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G H) = (k6_int_1 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers E H) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v14_armstrng B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden (k6_armstrng A C D) B) => (r2_hidden (k6_armstrng A (k4_subset_1 A C E) D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B D) =>  (! [G:$i] :  ((m1_cat_1 G A C E) =>  ((k31_cat_4 A B C D E F G) = (k29_cat_4 A B C (k20_cat_4 A D E) (k5_cat_1 A B D (k20_cat_4 A D E) F (k27_cat_4 A D E)) (k5_cat_1 A C E (k20_cat_4 A D E) G (k28_cat_4 A D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v9_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k9_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d30_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A (k4_finseq_2 48 k6_margrel1) (k4_finseq_2 16 (k4_finseq_2 48 k6_margrel1))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) &  ((v3_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [E:$i] :  ((m2_finseq_2 E k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ( (E = (k41_descip_1 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1)) &  ((v3_funct_2 F (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1))))) ) )  &  (? [G:$i] :  ((m2_finseq_2 G k6_margrel1 (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1)) &  ((r1_funct_2 (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 32) k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) F C) &  ( (G = D)  &  (E = (k40_descip_1 32 48 16 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k25_fomodel1 A))  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  ( ((k1_funct_1 B k6_numbers) = (k11_fomodel1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 B (k2_xcmplx_0 C 1)) = (k2_xboole_0 (k3_tarski (a_3_1_fomodel1 A B C)) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(d30_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k29_fomodel2 A B) = (a_2_2_fomodel2 A B)) ) ) ) ) ).
tt(d30_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((l1_altcat_1 B) =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v17_functor0 C A B) <=> (v1_msualg_3 (u2_functor0 A B C))) ) ) ) ) ) ) ).
tt(d30_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  ( (~ (v1_xboole_0 H))  &  (~  ((k30_gate_1 A B C D E F G H) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) ) ) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) ) )  =>  ((k30_gate_1 A B C D E F G H) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k30_gfacirc1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k3_gfacirc1 (k10_finseq_1 B C))) (k5_circcomb k4_twoscomp (k10_finseq_1 C A)) (k3_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k3_gfacirc1 (k10_finseq_1 B C)) (k6_facirc_1 A B k3_twoscomp) (k6_facirc_1 B C k3_gfacirc1)) (k6_facirc_1 C A k4_twoscomp))) ) ) ) ).
tt(d30_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (D = (k22_glib_000 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=> (r3_glib_000 A B C E)) ) ) ) ) ) ) ) ) ).
tt(d30_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k25_grcat_1 A) = (g1_cat_1 (k17_grcat_1 A) (k18_grcat_1 (k17_grcat_1 A)) (k22_grcat_1 (k17_grcat_1 A)) (k23_grcat_1 (k17_grcat_1 A)) (k24_grcat_1 (k17_grcat_1 A)))) ) ) ).
tt(d30_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  ((v9_group_9 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 C)) & (r2_hidden (k1_nat_1 D 1) (k4_finseq_1 C)))  =>  (! [E:$i] :  ((m1_group_9 E A B) =>  (! [F:$i] :  ( ((v4_group_9 F A E) & (m1_group_9 F A E))  =>  (~  ( (E = (k1_funct_1 C D))  &  ( (F = (k1_funct_1 C (k1_nat_1 D 1)))  & (v7_struct_0 (k10_group_9 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r8_ltlaxio1 A B) <=>  (? [C:$i] :  ((m2_finseq_1 C k1_hilbert1) &  ( ((k1_funct_1 C (k3_finseq_1 C)) = B)  &  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r7_ltlaxio1 D C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (B = (k22_modelc_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_modelc_3 D A) & (l1_modelc_3 D A))  &  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(d30_monoid_0,ax, (k6_monoid_0 = (g3_algstr_0 k1_numbers k35_binop_2)) ).
tt(d30_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( (C = (k24_qc_lang1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)))))) )  &  ( (C = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D B))  &  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k12_qc_lang1 A)) = k1_xboole_0)  &  ( ((v2_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (a_2_2_qc_lang1 A E)) )  &  ( ((v3_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k18_qc_lang1 A E))) )  &  ( ((v4_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k4_subset_1 (k3_qc_lang1 A) (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k19_qc_lang1 A E)) (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k20_qc_lang1 A E)))) )  &  ((v5_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k7_subset_1 (k3_qc_lang1 A) (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k22_qc_lang1 A E)) (k1_tarski (k21_qc_lang1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v5_substut1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( (C = (k27_substut1 A B))  <=>  (B = (k20_substut1 A C)) ) ) ) ) ) ) ) ) ).
tt(d30_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) )  =>  ( (C = (k31_turing_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)))) =>  ((k3_funct_2 (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) C D) = (k30_turing_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d30_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k31_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 B) (k9_margrel1 C)) D))) ) ) ) ) ) ) ) ) ) ).
tt(d30_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_waybel_0 A B C D) <=>  ((r2_yellow_0 A D) =>  ((r2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) &  ((k2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k2_yellow_0 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d30_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_zf_lang A) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( (B = (k20_zf_lang A))  <=>  ((k6_zf_lang B) = A) ) ) ) ) ) ) ).
tt(d31_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k11_abcmiz_0 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C D) B) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_abcmiz_0 A)) &  ( (~ (r2_hidden E (k2_abcmiz_0 A D)))  &  ((r4_abcmiz_0 A D E) &  ((k5_abcmiz_0 A D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 (k1_msualg_1 A B)) = 2)  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (E = (k1_funct_1 (k1_msualg_1 A B) 1))  &  ( (F = (k1_funct_1 (k1_msualg_1 A B) 2))  &  ((m1_abcmiz_1 C A E) & (m1_abcmiz_1 D A F)) ) ) ) ) ) )  =>  ((k31_abcmiz_1 A B C D) = (k4_trees_4 (k4_tarski B (u1_struct_0 A)) (k4_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ((r3_aofa_000 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden (k2_binop_1 B (u1_struct_0 A) B D E F) C) =>  ((k2_binop_1 B (u1_struct_0 A) B D E (k16_aofa_000 A F G)) = (k2_binop_1 B (u1_struct_0 A) B D (k2_binop_1 B (u1_struct_0 A) B D (k2_binop_1 B (u1_struct_0 A) B D E F) G) (k16_aofa_000 A F G))) )  &  ( (~ (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D E F) C))  =>  ((k2_binop_1 B (u1_struct_0 A) B D E (k16_aofa_000 A F G)) = (k2_binop_1 B (u1_struct_0 A) B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  (! [G:$i] :  ((m3_aofa_i00 G A B C D) =>  ( (G = (k37_aofa_i00 A B C D E F))  <=>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G H) = (k5_xxreal_0 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers E H) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F H) k6_numbers 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k14_armstrng A B) = (a_2_14_armstrng A B)) ) ) ) ).
tt(d31_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v10_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k11_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d31_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k42_descip_1 A B) = (k41_descip_1 (k39_descip_1 B) k35_descip_1 k26_descip_1 A)) ) ) ) ) ).
tt(d31_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k27_fomodel1 A) = (k3_tarski (k10_xtuple_0 (k25_fomodel1 A)))) ) ) ).
tt(d31_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k32_fomodel2 A B))  <=>  ((v3_fomodel2 B A C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((v3_fomodel2 B A D) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k8_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r1_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d31_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) & (v1_xboole_0 H)) ) ) ) ) ) ) )  =>  ((k31_gate_1 A B C D E F G H) = (k1_gate_1 k1_xboole_0)) )  &  (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) &  ((v1_xboole_0 H) &  (~  ((k31_gate_1 A B C D E F G H) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k31_gfacirc1 A B C) = (k2_circcomb (k29_gfacirc1 A B C) (k5_circcomb k29_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))))) ) ) ) ).
tt(d31_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (D = (k23_glib_000 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=> (r4_glib_000 A B C E)) ) ) ) ) ) ) ) ) ).
tt(d31_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v8_glib_001 B A) <=>  ((v1_glib_001 B A) &  ((v5_glib_001 B A) &  (~ (v3_glib_001 B A)) ) ) ) ) ) ) ) ).
tt(d31_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k26_grcat_1 A) = (a_1_0_grcat_1 A)) ) ) ).
tt(d31_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  ((v10_group_9 C A B) <=>  ((v9_group_9 C A B) &  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ( (~  (D = C) )  &  ((v9_group_9 D A B) & (r4_group_9 A B D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k32_mmlquery A B) = (a_2_1_mmlquery A B)) ) ) ) ) ) ).
tt(d31_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k21_modelc_1 A B C) = (a_3_0_modelc_1 A B C)) ) ) ) ) ) ) ).
tt(d31_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k23_modelc_3 A) = (a_1_0_modelc_3 A)) ) ) ).
tt(d31_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v1_group_1 A) &  ((v17_monoid_0 A) & (m2_monoid_0 A k6_monoid_0)) ) ) )  =>  ( (A = k7_monoid_0)  <=>  ((u1_struct_0 A) = k5_numbers) ) ) ) ).
tt(d31_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)))))) )  =>  ( (C = (k29_osafree A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_osafree A B))) =>  ((r2_hidden D (k6_dtconstr (k2_osafree A B))) =>  ((k1_funct_1 C (k2_trees_4 (u1_struct_0 (k2_osafree A B)) D)) = (k14_osafree A B D)) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_osafree A B))) =>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r1_lang1 (k2_osafree A B) D (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) E)) =>  ((k1_funct_1 C (k8_trees_4 (u1_struct_0 (k2_osafree A B)) D E)) = (k12_osafree A B (k13_osafree A B D) (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((v6_polyform A) <=>  ((k16_rvsum_1 (k28_polyform A)) = k6_numbers) ) ) ) ).
tt(d31_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v6_qc_lang1 B A) <=>  ((k24_qc_lang1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d31_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v6_substut1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( (C = (k28_substut1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) &  ( (B = (k21_substut1 A C D))  &  ((k19_substut1 A C) = (k19_substut1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ( ((v1_turing_1 C) & (l1_turing_1 C))  =>  ( (C = (k32_turing_1 A B))  <=>  ( ((u1_turing_1 C) = (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)))  &  ( ((u2_turing_1 C) = (k21_turing_1 A B))  &  ((r1_funct_2 (k2_zfmisc_1 (u2_turing_1 C) (u1_turing_1 C)) (k3_zfmisc_1 (u2_turing_1 C) (u1_turing_1 C) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 C) (k31_turing_1 A B)) &  ( ((u4_turing_1 C) = (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u4_turing_1 A) (u4_turing_1 B)))  &  ((u5_turing_1 C) = (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) (u5_turing_1 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k32_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 B) (k9_margrel1 C)) (k9_margrel1 D)))) ) ) ) ) ) ) ) ) ) ).
tt(d31_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r4_waybel_0 A B C D) <=>  ((r1_yellow_0 A D) =>  ((r1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) &  ((k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_yellow_0 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d31_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v5_zf_lang A) | (v8_zf_lang A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v5_zf_lang A) =>  ( (B = (k21_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k7_zf_lang B C) = A) ) ) ) )  &  ( (~ (v5_zf_lang A))  =>  ( (B = (k21_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k10_zf_lang B C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) &  ((v14_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_abcmiz_0 A B) = (k2_rewrite1 (k11_abcmiz_0 A) B)) ) ) ) ) ).
tt(d32_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  ((k2_msualg_1 A C) = B) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((m2_abcmiz_1 C A B) <=>  ((k2_msualg_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(d32_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ((m1_aofa_000 D A B C) <=>  ((v13_aofa_000 D A B) &  ((v14_aofa_000 D A B) &  ((r2_aofa_000 A B C D) & (r3_aofa_000 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  (! [G:$i] :  ((m3_aofa_i00 G A B C D) =>  ( (G = (k38_aofa_i00 A B C D E F))  <=>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G H) = (k5_xxreal_0 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers E H) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F H) 1 k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((r6_armstrng A B C) <=>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r1_tarski B D) =>  ( (D = A)  | (r2_hidden D (k14_armstrng A C))) ) ) )  &  (! [D:$i] :  (~  ((r2_xboole_0 D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (~  ((r1_tarski D E) &  ( (~  (E = A) )  &  (~ (r2_hidden E (k14_armstrng A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v11_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k13_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d32_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k43_descip_1 A B) = (k41_descip_1 (k1_descip_1 (k4_finseq_2 48 k6_margrel1) 16 (k39_descip_1 B)) k35_descip_1 k26_descip_1 A)) ) ) ) ) ).
tt(d32_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v13_fomodel1 B A) <=> (r2_hidden B (k27_fomodel1 A))) ) ) ) ) ).
tt(d32_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v5_fomodel2 B A) <=> (v4_fomodel1 (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B) A)) ) ) ) ) ).
tt(d32_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k9_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r2_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d32_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v18_functor0 C A B) <=>  (? [D:$i] :  ((m2_pboole D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 A) (k3_relat_1 (u1_functor0 A B C) (u1_altcat_1 B))) &  ((r6_pboole (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) D (u2_functor0 A B C)) & (v2_msualg_3 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 A) (k3_relat_1 (u1_functor0 A B C) (u1_altcat_1 B)))) ) ) ) ) ) ) ) ) ) ).
tt(d32_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) ) )  =>  ((k32_gate_1 A B C D E F G H) = (k1_gate_1 k1_xboole_0)) )  &  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  ( (~ (v1_xboole_0 H))  &  (~  ((k32_gate_1 A B C D E F G H) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k32_gfacirc1 A B C) = (k3_circcomb (k29_gfacirc1 A B C) (k5_circcomb k29_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))) (k30_gfacirc1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp) k29_twoscomp))) ) ) ) ).
tt(d32_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((m1_glib_000 B A) <=>  ((r1_tarski (k6_glib_000 B) (k6_glib_000 A)) &  ((r1_tarski (k7_glib_000 B) (k7_glib_000 A)) &  (! [C:$i] :  ((r2_hidden C (k7_glib_000 B)) =>  ( ((k1_funct_1 (k10_glib_000 B) C) = (k1_funct_1 (k10_glib_000 A) C))  &  ((k1_funct_1 (k11_glib_000 B) C) = (k1_funct_1 (k11_glib_000 A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 C A B) <=>  ((r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A B) C) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k12_glib_001 A B))) &  ((k12_glib_001 A C) = (k15_finseq_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k27_grcat_1 A) = (k5_grcat_1 (k25_grcat_1 A) (k26_grcat_1 A))) ) ) ).
tt(d32_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (! [E:$i] :  ( ((v8_group_9 E A C) & (m2_finseq_1 E (k6_group_9 A C)))  =>  ((r5_group_9 A B C D E) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( ((k1_nat_1 F 1) = (k3_finseq_1 D))  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_finseq_1 F) (k2_finseq_1 F)) &  ((v3_funct_2 G (k2_finseq_1 F) (k2_finseq_1 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 F) (k2_finseq_1 F))))) ) )  =>  (? [H:$i] :  ((m1_group_9 H A B) &  (? [I:$i] :  ((m1_group_9 I A C) &  (? [J:$i] :  ( ((v4_group_9 J A H) & (m1_group_9 J A H))  &  (? [K:$i] :  ( ((v4_group_9 K A I) & (m1_group_9 K A I))  &  (? [L:$i] :  ((v7_ordinal1 L) &  (? [M:$i] :  ((v7_ordinal1 M) &  ((r1_xxreal_0 1 L) &  ((r1_xxreal_0 L F) &  ( (M = (k1_funct_1 G L))  &  ( (H = (k1_funct_1 D L))  &  ( (I = (k1_funct_1 E M))  &  ( (J = (k1_funct_1 D (k1_nat_1 L 1)))  &  ( (K = (k1_funct_1 E (k1_nat_1 M 1)))  &  (~ (r3_group_9 A (k10_group_9 A H J) (k10_group_9 A I K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k33_mmlquery A B) = (a_2_2_mmlquery A B)) ) ) ) ) ) ).
tt(d32_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((r2_hidden C (k9_funct_2 k12_modelc_1 (u1_struct_0 A))) =>  ((k22_modelc_1 A B C) = C) )  &  ( (~ (r2_hidden C (k9_funct_2 k12_modelc_1 (u1_struct_0 A))))  =>  ((k22_modelc_1 A B C) = (k1_margrel1 (u1_struct_0 A) k12_modelc_1 B)) ) ) ) ) ) ) ) ).
tt(d32_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k18_modelc_2 A B C) = (a_3_0_modelc_2 A B C)) ) ) ) ) ) ) ).
tt(d32_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r7_modelc_3 A B C) <=>  (! [D:$i] :  ( ((r2_hidden D (k22_modelc_3 A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))))  =>  ((v3_modelc_3 (k10_modelc_3 D A) A) |  ((r4_modelc_3 A (k10_modelc_3 D A) (k10_modelc_3 (k1_funct_1 C D) A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 C D) A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((m2_osafree C A B) <=>  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C) = C) ) ) ) ) ) ) ) ).
tt(d32_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((m2_qc_lang1 B A) <=> (r2_wellord1 B (k6_subset_1 (k1_qc_lang1 A) k5_numbers))) ) ) ) ) ).
tt(d32_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v6_substut1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( (C = (k29_substut1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) &  ( (B = (k21_substut1 A D C))  &  ((k19_substut1 A D) = (k19_substut1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d32_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k33_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k2_binarith (k2_binarith B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d32_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k14_valued_2 A B) = (k24_valued_1 A (k7_xcmplx_0 1 B))) ) ) ) ) ).
tt(d32_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d32_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v5_zf_lang A) | (v8_zf_lang A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v5_zf_lang A) =>  ( (B = (k22_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k7_zf_lang C B) = A) ) ) ) )  &  ( (~ (v5_zf_lang A))  =>  ( (B = (k22_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k10_zf_lang C B) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ((k34_abcmiz_1 A) = (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))) (k14_abcmiz_1 A))) ) ) ).
tt(d33_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (! [F:$i] :  ((m1_aofa_000 F A C E) =>  ((r4_aofa_000 A B C D E F) <=>  (? [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m2_finseq_1 G C))  &  ( ((k1_funct_1 G 1) = D)  &  ( (~ (r2_hidden (k1_funct_1 G (k3_finseq_1 G)) E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_xxreal_0 1 H) =>  ((r1_xxreal_0 (k3_finseq_1 G) H) |  ((r2_hidden (k1_funct_1 G H) E) &  ((k1_funct_1 G (k1_nat_1 H 1)) = (k1_binop_1 F (k1_funct_1 G H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v12_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k12_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d33_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  ((v14_fomodel1 C A B) <=> (r2_hidden C (k1_funct_1 (k25_fomodel1 B) A))) ) ) ) ) ) ) ).
tt(d33_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((k38_fomodel2 A B) = (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) B)) ) ) ) ) ).
tt(d33_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k10_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r3_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d33_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((l1_altcat_1 B) =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v19_functor0 C A B) <=>  ((v4_functor0 C A B) & (v17_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d33_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) &  ((v1_xboole_0 H) &  (~  ((k33_gate_1 A B C D E F G H) = (k1_gate_1 k1_xboole_0)) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) & (v1_xboole_0 H)) ) ) ) ) ) ) )  =>  ((k33_gate_1 A B C D E F G H) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k33_gfacirc1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) k29_twoscomp)) ) ) ) ).
tt(d33_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ((v9_glib_000 B A) <=>  ((k24_glib_000 A B) = (k6_glib_000 A)) ) ) ) ) ) ).
tt(d33_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k28_grcat_1 A) = (a_1_1_grcat_1 A)) ) ) ).
tt(d33_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  =>  ( (D = (k20_group_9 A B C))  <=>  ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 D) 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  (! [F:$i] :  ((m1_group_9 F A B) =>  (! [G:$i] :  ( ((v4_group_9 G A F) & (m1_group_9 G A F))  =>  ( ( (F = (k1_funct_1 C E))  &  (G = (k1_funct_1 C (k1_nat_1 E 1))) )  =>  ((k1_funct_1 D E) = (k10_group_9 A F G)) ) ) ) ) ) ) ) ) ) ) )  &  ((r1_xxreal_0 (k3_finseq_1 C) 1) =>  ( (D = (k20_group_9 A B C))  <=>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k34_mmlquery A B) = (a_2_3_mmlquery A B)) ) ) ) ) ) ).
tt(d33_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k23_modelc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k1_zfmisc_1 (k9_funct_2 k12_modelc_1 (u1_struct_0 A)))) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (D = (k21_modelc_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((r2_hidden C (k9_funct_2 k9_modelc_2 (u1_struct_0 A))) =>  ((k19_modelc_2 A B C) = C) )  &  ( (~ (r2_hidden C (k9_funct_2 k9_modelc_2 (u1_struct_0 A))))  =>  ((k19_modelc_2 A B C) = (k1_margrel1 (u1_struct_0 A) k9_modelc_2 B)) ) ) ) ) ) ) ) ).
tt(d33_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r8_modelc_3 A B C) <=>  (! [D:$i] :  ( ((r2_hidden D (k22_modelc_3 A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))))  =>  ((v3_modelc_3 (k10_modelc_3 D A) A) | (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 C D) A)))) ) ) ) ) ) ) ) ) ) ).
tt(d33_monoid_0,ax, (k48_binop_2 = (u2_algstr_0 k7_monoid_0)) ).
tt(d33_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k30_osafree A B) = (k10_xtuple_0 (k29_osafree A B))) ) ) ) ) ).
tt(d33_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ( ( ((r2_hidden B k5_numbers) & (r2_hidden C k5_numbers))  =>  ((r1_qc_lang1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (D = B)  &  ( (E = C)  & (r1_xxreal_0 D E)) ) ) ) ) ) ) )  &  ( (~  ( (~ (r2_hidden B k5_numbers))  &  ( (~ (r2_hidden C k5_numbers))  &  (~  ((r1_qc_lang1 A B C) <=> (r2_hidden (k4_tarski B C) (o_1_1_qc_lang1 A))) ) ) ) )  &  (~  ( (~  ((r2_hidden B k5_numbers) & (r2_hidden C k5_numbers)) )  &  ( (~  ( (~ (r2_hidden B k5_numbers))  &  (~ (r2_hidden C k5_numbers)) ) )  &  (~  ((r1_qc_lang1 A B C) <=> (r2_hidden C k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v7_substut1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (C = (k30_substut1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) &  (? [E:$i] :  ((m1_substut1 E A D) &  ( (B = (k24_substut1 A D E))  &  ( ((k23_substut1 A D) = C)  & (v3_substut1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d33_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k34_twoscomp A B) = (k5_circcomb k15_twoscomp (k10_finseq_1 A B))) ) ) ).
tt(d33_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k15_valued_2 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k30_valued_1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d33_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v18_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r4_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d33_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v6_zf_lang A) | (v11_zf_lang A))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ( ((v6_zf_lang A) =>  ( (B = (k23_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k8_zf_lang B C) = A) ) ) ) )  &  ( (~ (v6_zf_lang A))  =>  ( (B = (k23_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k13_zf_lang B C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  ((k35_abcmiz_1 A B) = (k1_trees_4 (k4_tarski A k8_abcmiz_1))) ) ) ) ) ).
tt(d34_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (! [F:$i] :  ((m1_aofa_000 F A C E) =>  (! [G:$i] :  ((m1_subset_1 G k7_numbers) =>  ( ((r4_aofa_000 A B C D E F) =>  ( (G = (k20_aofa_000 A B C D E F))  <=>  (? [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H C))  &  ( (G = (k6_xcmplx_0 (k3_finseq_1 H) 1))  &  ( ((k1_funct_1 H 1) = D)  &  ( (~ (r2_hidden (k1_funct_1 H (k3_finseq_1 H)) E))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r1_xxreal_0 1 I) =>  ((r1_xxreal_0 (k3_finseq_1 H) I) |  ((r2_hidden (k1_funct_1 H I) E) &  ((k1_funct_1 H (k1_nat_1 I 1)) = (k1_binop_1 F (k1_funct_1 H I) B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (r4_aofa_000 A B C D E F))  =>  ( (G = (k20_aofa_000 A B C D E F))  <=>  (G = k1_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m2_aofa_i00 E A B C D) =>  ((k40_aofa_i00 A B C D E) = (k23_aofa_i00 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v13_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k14_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d34_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v13_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k30_fomodel1 A B) = (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B))) ) ) ) ) ).
tt(d34_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v6_fomodel2 B A) <=>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((r2_hidden C B) <=>  (~ (r2_hidden (k38_fomodel2 A C) B)) ) ) ) ) ) ) ) ).
tt(d34_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k11_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r4_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d34_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((l1_altcat_1 B) =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v20_functor0 C A B) <=>  ((v18_functor0 C A B) & (v5_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d34_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~  ((v1_xboole_0 A) & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) )  &  (~  ((k34_gate_1 A B) = (k1_gate_1 k1_xboole_0)) ) ) ) )  &  ( (~  ( (~  ((v1_xboole_0 A) & (v1_xboole_0 B)) )  &  (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) ) ) )  =>  ((k34_gate_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(d34_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k34_gfacirc1 A B C) = (k8_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d34_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) <=>  ( ((k6_glib_000 A) = (k6_glib_000 B))  &  ( ((k7_glib_000 A) = (k7_glib_000 B))  &  ((r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k10_glib_000 A) (k10_glib_000 B)) & (r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k11_glib_000 A) (k11_glib_000 B))) ) ) ) ) ) ) ) ).
tt(d34_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k29_grcat_1 A) = (k5_grcat_1 (k27_grcat_1 A) (k28_grcat_1 A))) ) ) ).
tt(d34_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ((r6_group_9 A B C D) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_group_1 E) &  ((v3_group_1 E) &  ((v3_group_9 E A) & (l1_group_9 E A)) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_group_1 F) &  ((v3_group_1 F) &  ((v3_group_9 F A) & (l1_group_9 F A)) ) ) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r2_hidden G (k4_finseq_1 B)) &  ( (H = (k1_funct_1 (k2_funct_2 (k4_finseq_1 B) D) G))  &  ( (E = (k1_funct_1 B G))  &  (F = (k1_funct_1 C H)) ) ) )  => (r3_group_9 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k35_mmlquery A B C) = (a_3_4_mmlquery A B C)) ) ) ) ) ) ) ) ).
tt(d34_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k24_modelc_1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  &  ((r1_modelc_1 A B E) &  (D = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k20_modelc_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k1_zfmisc_1 (k9_funct_2 k9_modelc_2 (u1_struct_0 A)))) &  (? [E:$i] :  ((v7_ordinal1 E) &  (D = (k18_modelc_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (k1_modelc_3 A))) =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ( (~ (v3_modelc_3 C A))  =>  ((k24_modelc_3 A B C) = (k1_funct_1 B (u2_modelc_3 A C))) ) ) ) ) ) ) ) ).
tt(d34_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v1_group_1 B) &  ((v3_group_1 B) &  ((v2_monoid_0 B) &  ((v16_monoid_0 B) &  ((v17_monoid_0 B) & (l3_algstr_0 B)) ) ) ) ) ) )  =>  ( (B = (k9_monoid_0 A))  <=>  ( ((u1_struct_0 B) = (k3_finseq_2 A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_algstr_0 B C D) = (k7_finseq_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ((r3_pcs_0 A B) <=>  ((r1_tarski (u1_struct_0 A) (u1_struct_0 B)) &  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 B)) & (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_pcs_0 A) (u1_pcs_0 B))) ) ) ) ) ) ) ).
tt(d34_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ((r2_qc_lang1 A B C) <=>  ((r1_qc_lang1 A B C) &  (~  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d34_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v7_substut1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( (C = (k31_substut1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) &  (? [E:$i] :  ((m1_substut1 E A D) &  ( (B = (k24_substut1 A D E))  &  ( ((k22_substut1 A D) = C)  & (v3_substut1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k35_twoscomp A B) = (k6_facirc_1 A B k15_twoscomp)) ) ) ).
tt(d34_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k20_valued_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k1_relset_1 A C))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k1_funct_1 C (k30_valued_1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v19_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r3_waybel_0 A B C (k7_domain_1 (u1_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d34_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v6_zf_lang A) | (v11_zf_lang A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v6_zf_lang A) =>  ( (B = (k24_zf_lang A))  <=>  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  ((k8_zf_lang C B) = A) ) ) ) )  &  ( (~ (v6_zf_lang A))  =>  ( (B = (k24_zf_lang A))  <=>  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  ((k13_zf_lang C B) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_trees_4 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k1_msualg_1 A B)))  =>  ((k36_abcmiz_1 A B C) = (k4_trees_4 (k4_tarski B (u1_struct_0 A)) C)) ) ) ) ) ) ) ) ).
tt(d35_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)))) =>  ( (E = (k21_aofa_000 A B C D))  <=>  ((r1_tarski (k2_zfmisc_1 B (k18_aofa_000 A)) E) &  ((r1_tarski (k2_zfmisc_1 B (k1_tarski (k12_aofa_000 A))) E) &  ( (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ( ((r2_hidden (k4_tarski F H) E) & (r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D F H) I) E))  => (r2_hidden (k4_tarski F (k13_aofa_000 A H I)) E))  &  ( ( ((r2_hidden (k4_tarski F G) E) &  ((r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D F G) H) E) & (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D F G) C)) )  => (r2_hidden (k4_tarski F (k14_aofa_000 A G H I)) E))  &  ( ( ((r2_hidden (k4_tarski F G) E) & (r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D F G) I) E))  =>  ((r2_hidden (k2_binop_1 B (u1_struct_0 A) B D F G) C) | (r2_hidden (k4_tarski F (k14_aofa_000 A G H I)) E)) )  &  ((r2_hidden (k4_tarski F G) E) =>  ( (! [J:$i] :  ( ( (~ (v1_xboole_0 J))  & (m2_finseq_1 J B))  =>  (~  ( ((k1_funct_1 J 1) = (k2_binop_1 B (u1_struct_0 A) B D F G))  &  ( (~ (r2_hidden (k1_funct_1 J (k3_finseq_1 J)) C))  &  (! [K:$i] :  ((v7_ordinal1 K) =>  ((r1_xxreal_0 1 K) =>  ((r1_xxreal_0 (k3_finseq_1 J) K) |  ((r2_hidden (k1_funct_1 J K) C) &  ((r2_hidden (k4_tarski (k1_funct_1 J K) (k13_aofa_000 A H G)) E) &  ((k1_funct_1 J (k1_nat_1 K 1)) = (k1_binop_1 D (k1_funct_1 J K) (k13_aofa_000 A H G))) ) ) ) ) ) ) ) ) ) ) )  | (r2_hidden (k4_tarski F (k16_aofa_000 A G H)) E)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)))) =>  ( ((r1_tarski (k2_zfmisc_1 B (k18_aofa_000 A)) F) &  ((r1_tarski (k2_zfmisc_1 B (k1_tarski (k12_aofa_000 A))) F) &  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ( ((r2_hidden (k4_tarski G I) F) & (r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D G I) J) F))  => (r2_hidden (k4_tarski G (k13_aofa_000 A I J)) F))  &  ( ( ((r2_hidden (k4_tarski G H) F) &  ((r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D G H) I) F) & (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D G H) C)) )  => (r2_hidden (k4_tarski G (k14_aofa_000 A H I J)) F))  &  ( ( ((r2_hidden (k4_tarski G H) F) & (r2_hidden (k4_tarski (k2_binop_1 B (u1_struct_0 A) B D G H) J) F))  =>  ((r2_hidden (k2_binop_1 B (u1_struct_0 A) B D G H) C) | (r2_hidden (k4_tarski G (k14_aofa_000 A H I J)) F)) )  &  ((r2_hidden (k4_tarski G H) F) =>  ( (! [K:$i] :  ( ( (~ (v1_xboole_0 K))  & (m2_finseq_1 K B))  =>  (~  ( ((k1_funct_1 K 1) = (k2_binop_1 B (u1_struct_0 A) B D G H))  &  ( (~ (r2_hidden (k1_funct_1 K (k3_finseq_1 K)) C))  &  (! [L:$i] :  ((v7_ordinal1 L) =>  ((r1_xxreal_0 1 L) =>  ((r1_xxreal_0 (k3_finseq_1 K) L) |  ((r2_hidden (k1_funct_1 K L) C) &  ((r2_hidden (k4_tarski (k1_funct_1 K L) (k13_aofa_000 A I H)) F) &  ((k1_funct_1 K (k1_nat_1 L 1)) = (k1_binop_1 D (k1_funct_1 K L) (k13_aofa_000 A I H))) ) ) ) ) ) ) ) ) ) ) )  | (r2_hidden (k4_tarski G (k16_aofa_000 A H I)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r1_relset_1 B (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((k41_aofa_i00 A B C D E) = (k24_aofa_i00 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v14_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k15_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d35_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v15_fomodel1 B A) <=>  (? [C:$i] :  ( ((v7_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  (? [D:$i] :  ( ((v3_card_1 D (k1_int_2 (k19_fomodel1 A C))) & (m2_subset_1 D (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A))))  &  (B = (k7_finseq_1 (k4_matrix_2 (k1_fomodel1 A) C) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)) (k21_fomodel1 A) D))) ) ) ) ) ) ) ) ) ) ).
tt(d35_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ( (~ (v15_fomodel1 B A))  =>  ( (C = (k39_fomodel2 A B))  <=>  (? [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ((v5_relat_1 E (k1_fomodel1 A)) &  ( (C = (k4_tarski D E))  &  (B = (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)) D) E)) ) ) ) ) ) ) ) )  &  ((v15_fomodel1 B A) =>  ( (C = (k39_fomodel2 A B))  <=>  (C = (k4_tarski B k1_xboole_0)) ) ) ) ) ) ) ) ) ).
tt(d35_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k12_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r5_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d35_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((l1_altcat_1 B) =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v21_functor0 C A B) <=>  ((v19_functor0 C A B) & (v20_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d35_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k35_gate_1 A B C D E) = (k10_gate_1 C D (k11_gate_1 A B E))) ) ) ) ) ) ).
tt(d35_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k35_gfacirc1 A B C) = (k10_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d35_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r6_glib_000 A B) <=> (m1_glib_000 A B)) ) ) ) ) ).
tt(d35_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) 1))  &  (~  (! [E:$i] :  ( ((v8_group_9 E A B) & (m2_finseq_1 E (k6_group_9 A B)))  =>  ( (E = (k21_group_9 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((m1_group_9 I A B) =>  (! [J:$i] :  ((m1_group_9 J A B) =>  (! [K:$i] :  ((m1_group_9 K A B) =>  ( ( ( (F = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 G 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) H))  &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k6_xcmplx_0 (k3_finseq_1 C) 1)) &  ((r1_xxreal_0 1 H) &  ((r1_xxreal_0 H (k6_xcmplx_0 (k3_finseq_1 D) 1)) &  ( (I = (k1_funct_1 C (k1_nat_1 G 1)))  &  ( (J = (k1_funct_1 C G))  &  (K = (k1_funct_1 D H)) ) ) ) ) ) ) )  =>  ((k1_funct_1 E F) = (k19_group_9 A B I (k17_group_9 A B J K))) )  &  ( ( (F = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 C) 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) 1))  =>  ((k1_funct_1 E F) = (k4_group_9 A B)) )  &  ((k3_finseq_1 E) = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 C) 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_mmlquery,ax, (! [A:$i] :  ( ((v3_mmlquery A) & (l1_mmlquery A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k36_mmlquery A B C) = (a_3_5_mmlquery A B C)) ) ) ) ) ) ) ) ).
tt(d35_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k25_modelc_1 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u4_modelc_1 A) B)) ) ) ) ) ).
tt(d35_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k21_modelc_2 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  &  ((r4_modelc_2 A B E) &  (D = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ( ( ( ( (~ (v7_modelc_2 (k24_modelc_3 B C D)))  & (r8_modelc_2 A (k14_modelc_3 B (k5_modelc_3 B D (k24_modelc_3 B C D)))))  |  ((v7_modelc_2 (k24_modelc_3 B C D)) &  (~ (r7_modelc_2 A (k12_modelc_2 (k24_modelc_3 B C D)))) ) )  =>  ((k25_modelc_3 A B C D) = (k5_modelc_3 B D (k24_modelc_3 B C D))) )  &  (~  ( (~  ( (~ (v7_modelc_2 (k24_modelc_3 B C D)))  & (r8_modelc_2 A (k14_modelc_3 B (k5_modelc_3 B D (k24_modelc_3 B C D))))) )  &  ( (~  ((v7_modelc_2 (k24_modelc_3 B C D)) &  (~ (r7_modelc_2 A (k12_modelc_2 (k24_modelc_3 B C D)))) ) )  &  (~  ((k25_modelc_3 A B C D) = (k6_modelc_3 B D (k24_modelc_3 B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ( (C = (k25_qc_lang1 A B))  <=>  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  ((r2_hidden D B) => (r1_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((k32_substut1 A B) = B) ) ) ) ) ).
tt(d35_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k36_twoscomp A B) = (k4_tarski (k10_finseq_1 A B) k15_twoscomp)) ) ) ).
tt(d35_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k21_valued_2 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k35_valued_1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d35_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v20_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_waybel_0 A B C (k7_domain_1 (u1_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d35_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( (B = (k25_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_zf_lang B C)) ) ) ) ) ) ) ) ) ).
tt(d36_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ( ( (? [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) &  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) )  =>  ((k37_abcmiz_1 A B) = (k5_trees_2 B (k3_pre_poly k5_numbers k6_numbers))) )  &  ( (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (~  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) )  =>  ((k37_abcmiz_1 A B) = (k30_abcmiz_1 A (k32_abcmiz_1 A) B)) ) ) ) ) ) ) ).
tt(d36_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((v30_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  => (v16_algstr_0 B A)) ) ) ) ) ) ).
tt(d36_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v15_aofa_000 B A) <=>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (! [F:$i] :  ((m1_aofa_000 F A C E) => (r2_hidden (k4_tarski D B) (k21_aofa_000 A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d36_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k42_aofa_i00 A B C D E) = (k40_aofa_i00 A B C D (k41_aofa_i00 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d36_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v15_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k16_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d36_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k31_fomodel1 A) = (a_1_0_fomodel1 A)) ) ) ).
tt(d36_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k40_fomodel2 A B) = (k1_xtuple_0 (k39_fomodel2 A B))) ) ) ) ) ).
tt(d36_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k13_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r6_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d36_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  (! [F:$i] :  ( ((v9_functor0 F A C) & (l2_functor0 F A C))  =>  ( (F = (k13_functor0 A B C D E))  <=>  ((r8_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C)) (u1_functor0 A C F) (k1_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C)) (u1_functor0 A B D) (u1_functor0 B C E))) & (r8_pboole (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u2_functor0 A C F) (k8_pboole (u2_functor0 A B D) (k3_relat_1 (u1_functor0 A B D) (u2_functor0 B C E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d36_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k36_gate_1 A B C D E) = (k11_gate_1 C D (k11_gate_1 A B E))) ) ) ) ) ) ).
tt(d36_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k36_gfacirc1 A B C) = (k9_facirc_1 A B C k4_gfacirc1)) ) ) ) ).
tt(d36_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r7_glib_000 A B) <=>  ((r6_glib_000 A B) &  (~ (r5_glib_000 A B)) ) ) ) ) ) ) ).
tt(d36_mmlquery,ax, (! [A:$i] :  ( ((v3_mmlquery A) & (l1_mmlquery A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  =>  ((k37_mmlquery A B C D) = (a_4_15_mmlquery A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d36_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k26_modelc_1 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u5_modelc_1 A) B)) ) ) ) ) ).
tt(d36_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k22_modelc_2 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u2_modelc_2 A) B)) ) ) ) ) ).
tt(d36_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k22_modelc_3 B) (k22_modelc_3 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 B) (k22_modelc_3 B))))) )  =>  ( (D = (k26_modelc_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E (k22_modelc_3 B)) =>  ((k1_funct_1 D E) = (k25_modelc_3 A B C (k10_modelc_3 E B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d36_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k11_monoid_0 A) = (u2_algstr_0 (k9_monoid_0 A))) ) ) ).
tt(d36_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v12_pcs_0 C) & (l2_pcs_0 C))  =>  ( (C = (k17_pcs_0 A B))  <=>  ( ((u1_struct_0 C) = (k3_card_3 (k12_pralg_1 A B)))  &  ( ((u1_orders_2 C) = (k3_card_3 (k4_pcs_0 A B)))  &  ((u1_pcs_0 C) = (k3_card_3 (k7_pcs_0 A B))) ) ) ) ) ) ) ) ) ).
tt(d36_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  ( (B = (k26_qc_lang1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) => (r1_qc_lang1 A B C)) ) ) ) ) ) ) ).
tt(d36_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))) =>  ( ((r2_hidden (k21_qc_lang1 A (k33_substut1 A B)) (k10_xtuple_0 (k7_substut1 A (k21_qc_lang1 A (k33_substut1 A B)) (k33_substut1 A B) (k34_substut1 A B)))) =>  ((k35_substut1 A B) = (k2_qc_lang3 A (k13_substut1 A (k7_substut1 A (k21_qc_lang1 A (k33_substut1 A B)) (k33_substut1 A B) (k34_substut1 A B)) (k22_qc_lang1 A (k33_substut1 A B))))) )  &  ( (~ (r2_hidden (k21_qc_lang1 A (k33_substut1 A B)) (k10_xtuple_0 (k7_substut1 A (k21_qc_lang1 A (k33_substut1 A B)) (k33_substut1 A B) (k34_substut1 A B)))))  =>  ((k35_substut1 A B) = (k21_qc_lang1 A (k33_substut1 A B))) ) ) ) ) ) ) ).
tt(d36_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k37_twoscomp A B) = (k5_circcomb k3_twoscomp (k10_finseq_1 A B))) ) ) ).
tt(d36_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k25_valued_2 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k54_valued_1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d36_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v21_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel_0 D A) =>  ((v1_xboole_0 D) | (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d36_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( (B = (k26_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_zf_lang C B)) ) ) ) ) ) ) ) ) ).
tt(d37_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((v6_abcmiz_1 B A) <=>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (~  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) ) ) ) ) ) ) ).
tt(d37_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((v31_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  => (v17_algstr_0 B A)) ) ) ) ) ) ).
tt(d37_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  ((r5_aofa_000 A B C D E) <=>  (! [F:$i] :  ((m1_subset_1 F B) => (r2_hidden (k4_tarski F D) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d37_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k43_aofa_i00 A B C D E) = (k25_aofa_i00 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d37_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v16_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k17_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d37_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v13_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A))) =>  ( (C = (k33_fomodel1 A B))  <=>  ((v3_card_1 C (k1_int_2 (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)))) &  (B = (k7_finseq_1 (k4_matrix_2 (k15_fomodel1 A) (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)) (k21_fomodel1 A) C))) ) ) ) ) ) ) ) ) ).
tt(d37_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k41_fomodel2 A B) = (k2_xtuple_0 (k39_fomodel2 A B))) ) ) ) ) ).
tt(d37_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k14_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r7_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d37_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_altcat_2 C A))  =>  (! [D:$i] :  ((l2_functor0 D A B) =>  ((k14_functor0 A B C D) = (k13_functor0 C A B (k10_functor0 A C) D)) ) ) ) ) ) ) ) ) ).
tt(d37_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k37_gate_1 A B C D E F G) = (k10_gate_1 E F (k36_gate_1 A B C D G))) ) ) ) ) ) ) ) ).
tt(d37_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k37_gfacirc1 A B C) = (k2_circcomb (k34_gfacirc1 A B C) (k31_gfacirc1 A B C))) ) ) ) ).
tt(d37_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_glib_000 D A) =>  ( ( ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  & (r1_tarski C (k21_glib_000 A B)))  =>  ((m2_glib_000 D A B C) <=>  ( ((k24_glib_000 A D) = B)  &  ((k25_glib_000 A D) = C) ) ) )  &  ( (~  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  & (r1_tarski C (k21_glib_000 A B))) )  =>  ((m2_glib_000 D A B C) <=> (r5_glib_000 D A)) ) ) ) ) ) ) ) ) ).
tt(d37_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k27_modelc_1 A B C) = (k5_binop_1 (u1_struct_0 A) (u6_modelc_1 A) B C)) ) ) ) ) ) ) ).
tt(d37_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k23_modelc_2 A B C) = (k5_binop_1 (u1_struct_0 A) (u3_modelc_2 A) B C)) ) ) ) ) ) ) ).
tt(d37_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_3 A) <=>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((r2_modelc_2 B A) & (v3_modelc_2 B))  => (v2_modelc_2 (k10_modelc_2 B))) ) ) ) ) ) ).
tt(d37_monoid_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_monoid_0 B) & (l3_algstr_0 B)) )  =>  ( (B = (k12_monoid_0 A))  <=>  ( ((u1_struct_0 B) = (k4_partfun1 A A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_algstr_0 B C D) = (k3_relat_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(d37_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  ((k27_qc_lang1 A B) = (a_2_3_qc_lang1 A B)) ) ) ) ) ).
tt(d37_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k36_substut1 A B C) = (k15_qc_lang1 A (k35_substut1 A (k32_substut1 A B)) C)) ) ) ) ) ) ) ).
tt(d37_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k38_twoscomp A B) = (k6_facirc_1 A B k3_twoscomp)) ) ) ).
tt(d37_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k30_valued_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 B))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k7_valued_1 (k1_funct_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d37_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel_0 D A) =>  ((v1_xboole_0 D) | (r4_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d37_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( (B = (k27_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k12_zf_lang B C)) ) ) ) ) ) ) ) ) ).
tt(d38_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((v7_abcmiz_1 B A) <=>  (? [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) &  ((v6_abcmiz_1 C A) &  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) ) ) ) ) ) ) ).
tt(d38_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  ((r6_aofa_000 A B C D E F) <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  ((r2_hidden G F) => (r2_hidden (k4_tarski G D) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d38_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m2_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k44_aofa_i00 A B C D E F) = (k10_subset_1 (a_6_0_aofa_i00 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d38_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k19_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d38_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v15_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ((v3_card_1 C (k1_int_2 (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)))) & (m2_subset_1 C (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A))))  =>  ( (C = (k34_fomodel1 A B))  <=>  (B = (k7_finseq_1 (k4_matrix_2 (k15_fomodel1 A) (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)) (k21_fomodel1 A) C))) ) ) ) ) ) ) ) ).
tt(d38_fomodel2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_fomodel1 B)) =>  ((v7_fomodel2 C A B) <=> (r2_hidden C (k21_fomodel0 (k8_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) A)))) ) ) ) ) ) ).
tt(d38_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k15_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r8_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d38_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ( ((v9_functor0 D B A) & (l2_functor0 D B A))  =>  ( (D = (k15_functor0 A B C))  <=>  ( ((u1_functor0 B A D) = (k2_funct_1 (u1_functor0 A B C)))  &  (? [E:$i] :  ((m2_pboole E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 A) (k3_relat_1 (u1_functor0 A B C) (u1_altcat_1 B))) &  ((r8_pboole (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) E (u2_functor0 A B C)) &  ((u2_functor0 B A D) = (k3_relat_1 (k2_funct_1 (u1_functor0 A B C)) (k4_msualg_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 A) (k3_relat_1 (u1_functor0 A B C) (u1_altcat_1 B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d38_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k38_gate_1 A B C D E F G) = (k11_gate_1 E F (k36_gate_1 A B C D G))) ) ) ) ) ) ) ) ).
tt(d38_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k38_gfacirc1 A B C) = (k3_circcomb (k34_gfacirc1 A B C) (k31_gfacirc1 A B C) (k35_gfacirc1 A B C) (k32_gfacirc1 A B C))) ) ) ) ).
tt(d38_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k26_glib_000 A B) = (k18_glib_000 A (k6_domain_1 (k6_glib_000 A) B))) ) ) ) ) ).
tt(d38_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k28_modelc_1 A B C) = (k3_robbins1 A (k2_lattices A (k3_robbins1 A B) (k3_robbins1 A C)))) ) ) ) ) ) ) ).
tt(d38_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k24_modelc_2 A B C) = (k5_binop_1 (u1_struct_0 A) (u4_modelc_2 A) B C)) ) ) ) ) ) ) ).
tt(d38_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_3 A) <=>  (~  ( (~ (v2_modelc_2 A))  &  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((v2_modelc_2 B) &  (A = (k3_modelc_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(d38_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ((k18_pcs_0 A B) = (k17_pcs_0 (k2_tarski k6_numbers 1) (k6_afinsq_1 A B))) ) ) ) ) ).
tt(d38_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  ((k28_qc_lang1 A B) = (k25_qc_lang1 A (k27_qc_lang1 A B))) ) ) ) ) ).
tt(d38_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( (C = (k37_substut1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k16_substut1 A) (k9_qc_lang1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k16_substut1 A) (k9_qc_lang1 A))))) )  &  ( (C = (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D B))  &  (! [E:$i] :  ((m1_subset_1 E (k16_substut1 A)) =>  ( ((v2_substut1 E A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D E) = (k5_cqc_lang A)) )  &  ( ((v4_substut1 E A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D E) = (k10_qc_lang1 A (k16_qc_lang1 A (k18_substut1 A E)) (k3_substut1 A (k26_substut1 A E) (k19_substut1 A E)))) )  &  ( ((v5_substut1 E A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D E) = (k13_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D (k27_substut1 A E)))) )  &  ( ((v6_substut1 E A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D E) = (k14_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D (k28_substut1 A E)) (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D (k29_substut1 A E)))) )  &  ((v7_substut1 E A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D E) = (k36_substut1 A E (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) D (k31_substut1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d38_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k39_twoscomp A B) = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) ) ) ).
tt(d38_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k36_valued_2 A B C) = (k30_valued_2 A B (k4_xcmplx_0 C))) ) ) ) ) ) ) ).
tt(d38_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (~  ( (~ (v2_struct_0 A))  &  ( (~ (v2_struct_0 B))  &  (~  ((v23_waybel_0 C A B) <=>  ((v2_funct_1 C) &  ((v5_orders_3 C A B) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ( (D = (k2_funct_1 C))  & (v5_orders_3 D B A)) ) ) ) ) ) ) ) ) )  &  ( (~  ( (~ (v2_struct_0 A))  &  (~ (v2_struct_0 B)) ) )  =>  ((v23_waybel_0 C A B) <=>  ((v2_struct_0 A) & (v2_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(d38_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( (B = (k28_zf_lang A))  <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k12_zf_lang C B)) ) ) ) ) ) ) ) ) ).
tt(d39_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((v8_abcmiz_1 B A) <=>  ((v6_abcmiz_1 B A) | (v7_abcmiz_1 B A)) ) ) ) ) ) ).
tt(d39_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((v33_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  => (v23_algstr_0 B A)) ) ) ) ) ) ).
tt(d39_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  ((r7_aofa_000 A B C D E F) <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  ((r2_hidden G F) => (r2_hidden (k2_binop_1 B (u1_struct_0 A) B E G D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d39_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v18_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k18_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d39_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k35_fomodel1 A) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))))) )  =>  ( (B = (k36_fomodel1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  ((k3_funct_2 (k35_fomodel1 A) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) B C) = (k33_fomodel1 A C)) ) ) ) ) ) ) ) ).
tt(d39_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k16_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r9_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d39_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  ((r1_functor0 A B) <=>  (? [C:$i] :  ((m2_functor0 C A B) &  ((v21_functor0 C A B) & (v15_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d39_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((k39_gate_1 A B C D E F G H I) = (k10_gate_1 G H (k38_gate_1 A B C D E F I))) ) ) ) ) ) ) ) ) ) ).
tt(d39_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k27_glib_000 A B) = (k19_glib_000 A (k6_domain_1 (k6_glib_000 A) B))) ) ) ) ) ).
tt(d39_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((m1_modelc_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r2_hidden (k4_tarski (k3_funct_2 k5_numbers A C D) (k3_funct_2 k5_numbers A C (k2_nat_1 D 1))) B)) ) ) ) ) ) ) ) ) ).
tt(d39_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k25_modelc_2 A) = (k9_funct_2 k5_numbers A)) ) ) ).
tt(d39_modelc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l2_modelc_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  ((r9_modelc_3 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  &  ((r2_hidden (k3_funct_2 k5_numbers (u1_struct_0 B) D k6_numbers) (u5_modelc_3 A B)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski (k4_tarski (k1_funct_1 D E) (k1_funct_1 (k27_modelc_2 A C) E)) (k3_funct_2 k5_numbers (u1_struct_0 B) D (k1_nat_1 E 1))) (u4_modelc_3 A B)) &  (! [F:$i] :  ((r2_hidden F (u6_modelc_3 A B)) =>  (~ (v1_finset_1 (a_4_0_modelc_3 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d39_monoid_0,ax, (! [A:$i] :  ((k14_monoid_0 A) = (u2_algstr_0 (k12_monoid_0 A))) ) ).
tt(d39_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v12_pcs_0 C) & (l2_pcs_0 C))  =>  ( (C = (k19_pcs_0 A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (k1_tarski B) (u1_struct_0 A)))  &  ( ((u1_orders_2 C) = (k2_xboole_0 (k2_zfmisc_1 (k1_tarski B) (u1_struct_0 C)) (u1_orders_2 A)))  &  ((u1_pcs_0 C) = (k2_xboole_0 (k2_xboole_0 (k2_zfmisc_1 (k1_tarski B) (u1_struct_0 C)) (k2_zfmisc_1 (u1_struct_0 C) (k1_tarski B))) (u1_pcs_0 A))) ) ) ) ) ) ) ) ) ).
tt(d39_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k38_substut1 A) = (a_1_0_substut1 A)) ) ) ).
tt(d39_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k40_twoscomp A B) = (k2_circcomb (k34_twoscomp A B) (k37_twoscomp A B))) ) ) ).
tt(d39_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k41_valued_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 B))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k24_valued_1 (k1_funct_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d39_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v24_waybel_0 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) => (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d39_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_zf_lang A B) <=>  (~  ( (~  (B = (k6_zf_lang A)) )  &  ( (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( (~  (B = (k7_zf_lang A C)) )  &  (~  (B = (k7_zf_lang C A)) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (~  (B = (k8_zf_lang C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_abcmiz_1,ax, (! [A:$i] :  ((m1_finseq_2 A k2_abcmiz_1) =>  ( (A = k4_abcmiz_1)  <=>  (! [B:$i] :  ((m2_finseq_1 B k2_abcmiz_1) =>  ((r2_hidden B A) <=>  ((v2_funct_1 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_tarski (k1_xtuple_0 (k1_funct_1 B C)) (k2_relset_1 k2_abcmiz_1 (k5_relat_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(d3_abian,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_abian A B) <=>  ((r2_hidden A (k9_xtuple_0 B)) &  (A = (k1_funct_1 B A)) ) ) ) ) ) ).
tt(d3_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (C = D) )  &  (B = (k2_aff_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v3_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden D C) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden I C) &  ((r2_hidden J C) &  ((r2_analoaf A E I F H) &  ((r2_analoaf A F J G I) & (r2_analoaf A E J G H)) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = E)  |  ( (D = H)  |  ( (D = F)  |  ( (D = I)  |  ( (D = G)  |  ( (D = J)  |  ( (F = G)  | (r2_hidden H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v3_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden E C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden J D) &  ((r2_hidden K D) &  ((r1_aff_1 A H F L) &  ((r1_aff_1 A I G L) &  ((r1_aff_1 A H J M) &  ((r1_aff_1 A I K M) &  ((r2_analoaf A F J G K) & (r2_analoaf A F J L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (C = B)  |  ( (C = D)  |  ( (B = D)  |  ( (E = F)  |  ( (E = H)  |  ( (E = J)  |  ( (L = M)  |  ((r1_aff_1 A H F J) |  ((r1_aff_1 A I G K) |  ( (J = K)  | (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k2_aff_4 A B C))  <=>  ((r2_hidden B D) & (r5_aff_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) & (v1_funct_1 C)) )  =>  ( (C = (k1_ordinal4 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_nat_1 (k1_afinsq_1 A) (k1_afinsq_1 B)))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 A)) =>  ((k1_funct_1 C D) = (k1_funct_1 A D)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 B)) =>  ((k1_funct_1 C (k2_nat_1 (k1_afinsq_1 A) D)) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_afinsq_2 A B C) = (k2_afinsq_2 (k5_relat_1 A C) (k7_nat_d B 1))) ) ) ) ) ) ) ).
tt(d3_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k3_afproj A) = (a_1_2_afproj A)) ) ) ).
tt(d3_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_afvect0 A B C D) <=> (r2_analoaf A B C C D)) ) ) ) ) ) ) ) ) ).
tt(d3_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_alg_1 A B C) <=>  ((r1_alg_1 A B C) &  ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(d3_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k1_algseq_1 A B))  <=>  ((r1_algseq_1 A B C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_algseq_1 A B D) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k1_funct_1 (k1_funct_4 (k6_partfun1 (u4_struct_0 A)) C) D) = (k1_funct_1 (k1_funct_4 (k6_partfun1 (u4_struct_0 A)) C) E))  =>  ( ((k3_relat_1 (k1_msualg_1 A D) (k1_funct_4 (k6_partfun1 (u1_struct_0 A)) B)) = (k3_relat_1 (k1_msualg_1 A E) (k1_funct_4 (k6_partfun1 (u1_struct_0 A)) B)))  &  ((k1_funct_1 (k1_funct_4 (k6_partfun1 (u1_struct_0 A)) B) (k2_msualg_1 A D)) = (k1_funct_1 (k1_funct_4 (k6_partfun1 (u1_struct_0 A)) B) (k2_msualg_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_algstr_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B C) = (k1_algstr_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v2_algstr_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) ) ).
tt(d3_algstr_3,ax, (k3_algstr_3 = (g1_algstr_3 k1_numbers k6_numbers 1 k2_algstr_3)) ).
tt(d3_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v1_algstr_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden C (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B D)) & (r2_hidden E (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B F)))  => (r2_hidden (k6_algstr_0 A C E) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k6_algstr_0 A D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_zfmisc_1 A A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k3_zfmisc_1 A A A))) ) )  =>  ( (C = (k2_altcat_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden D A) &  ((r2_hidden E A) & (r2_hidden F A)) )  =>  ((k1_multop_1 C D E F) = (k1_binop_1 B D F)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) )  =>  ( (B = (k2_altcat_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_binop_1 B C D) = (k2_cat_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v2_altcat_3 D A B C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) & (r1_altcat_3 A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (m1_altcat_2 B A)) ) )  =>  ( (B = (k3_altcat_4 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C D)) =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  & (v1_altcat_3 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k2_ami_3 A B) = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d3_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 B)) =>  ((k1_amistd_1 A B C D) = (a_4_0_amistd_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d3_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v3_amistd_2 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ((k2_nat_1 (k5_memstr_0 A B (k2_extpro_1 A B (k5_compos_0 (u1_compos_1 B) C D) F)) E) = (k5_memstr_0 A B (k2_extpro_1 A B (k5_compos_0 (u1_compos_1 B) C (k2_xcmplx_0 D E)) (k9_memstr_0 A B F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_extpro_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = (k2_amistd_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E D) <=>  (~  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ((k1_funct_1 F E) = (k1_funct_1 (k2_extpro_1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  ((v3_amistd_5 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ((v1_finset_1 D) & (v4_extpro_1 D A B C)) ) ) ) )  =>  ( (~ (v1_xboole_0 D))  => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  ((v2_ami_wstd B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v3_funct_2 C k5_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) <=> (r1_ami_wstd A B (k3_funct_2 k5_numbers k5_numbers C D) (k3_funct_2 k5_numbers k5_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r3_analmetr A B C D E F G) <=> (r2_analmetr A (k5_algstr_0 A C B) (k5_algstr_0 A E D) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (B = (k1_analoaf A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F))  &  ( (D = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) G H))  & (r1_analoaf A E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analort A B C D E F G) <=> (r1_analoaf A (k2_analort A B C D) (k2_analort A B C E) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B (k8_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 A) (k8_struct_0 A))))) ) )  =>  ( (B = (k1_anproj_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C (k8_struct_0 A)) &  ((r2_hidden D (k8_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (C = E)  &  ( (D = F)  & (r1_anproj_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r3_anproj_2 A B C D E F G H) <=>  ((r2_anproj_1 A B C F) &  ((r2_anproj_1 A B D G) & (r2_anproj_1 A B E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_armstrng,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (B = (k2_armstrng A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (r1_armstrng C A)) ) ) ) ) ) ) ).
tt(d3_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = (k3_arytm_0 A))  <=>  ((k1_arytm_0 A B) = k6_numbers) ) ) ) ) ) ).
tt(d3_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ( ((r2_hidden A k5_arytm_3) =>  ( (B = (k3_arytm_2 A))  <=>  (? [C:$i] :  ((m1_subset_1 C k5_arytm_3) &  ( (A = C)  &  (B = (a_1_0_arytm_2 C)) ) ) ) ) )  &  ( (~ (r2_hidden A k5_arytm_3))  =>  ( (B = (k3_arytm_2 A))  <=>  (B = A) ) ) ) ) ) ) ) ).
tt(d3_arytm_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_arytm_3 A B) <=>  (? [C:$i] :  ((v3_ordinal1 C) &  (B = (k11_ordinal2 A C)) ) ) ) ) ) ) ) ).
tt(d3_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v3_asympt_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers)) ) ) ) ) ) ).
tt(d3_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k3_asympt_1 A))  <=>  ( ((k1_seq_1 B k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k4_power C A)) ) ) ) ) ) ) ) ) ) ).
tt(d3_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k3_autalg_1 A) = (g3_algstr_0 (k1_autalg_1 A) (k2_autalg_1 A))) ) ) ).
tt(d3_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k3_autgroup A) = (g3_algstr_0 (k1_autgroup A) (k2_autgroup A))) ) ) ).
tt(d3_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bagorder B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k8_nat_1 (u1_struct_0 A) B (k1_nat_1 C 1)) (k8_nat_1 (u1_struct_0 A) B C)) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(d3_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v3_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A D C)) (k1_bcialg_1 A B D)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d3_bcialg_4,ax, (k2_bcialg_4 = (g1_bcialg_4 1 k9_funct_5 k9_funct_5 k5_funct_5)) ).
tt(d3_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v3_bcialg_1 E) &  ((v4_bcialg_1 E) &  ((v5_bcialg_1 E) &  ((v7_bcialg_1 E) & (l2_bcialg_1 E)) ) ) ) )  =>  ((m1_bcialg_5 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ((k1_bcialg_5 E F G A B) = (k1_bcialg_5 E G F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_bcialg_6 A B C) = (k1_binop_1 (k2_bcialg_6 A) C B)) ) ) ) ) ) ) ).
tt(d3_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) <=>  ((k2_bhsp_1 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d3_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k2_bhsp_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k3_bhsp_1 A (k1_normsp_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_bhsp_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k1_normsp_1 A B D)) C)) ) ) ) ) ) ) ) ) ) ).
tt(d3_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k2_bhsp_4 A B) = (k1_bhsp_2 A (k1_bhsp_4 A B))) ) ) ) ) ).
tt(d3_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_bhsp_6 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k2_bhsp_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 E))  &  ((r1_tarski E B) &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski E F) &  ((r1_tarski F B) & (r1_xxreal_0 D (k3_bhsp_1 A (k5_algstr_0 A C (k1_bhsp_6 A F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( (F = (k3_bilinear A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) F G H) = (k6_algstr_0 A E (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_binari_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( ( ((k7_partfun1 k6_margrel1 B A) = k7_margrel1)  =>  ((k3_binari_2 A B) = (k6_binarith A B)) )  &  ( (~  ((k7_partfun1 k6_margrel1 B A) = k7_margrel1) )  =>  ((k3_binari_2 A B) = (k21_binop_2 (k6_binarith A B) (k5_series_1 2 A))) ) ) ) ) ) ) ).
tt(d3_binarith,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k5_numbers))  =>  ( (C = (k5_binarith A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k5_numbers C D) = (k15_funcop_1 k5_numbers (k7_partfun1 k6_margrel1 B D) k7_margrel1 k6_numbers (k5_series_1 2 (k7_nat_d D 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k5_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k3_binom A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) B k6_numbers C) = (k4_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) B (k2_nat_1 D 1) C) = (k1_algstr_0 A C (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_binop_1 A B C (k3_binop_1 A B D E)) = (k3_binop_1 A B (k3_binop_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) )  =>  ( (A = k27_binop_2)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_binop_1 A B C) = (k3_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d3_bintree1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((v2_bintree1 A) <=> (v1_bintree1 (k9_xtuple_0 A))) ) ) ).
tt(d3_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ((k2_bintree2 A B) = (k2_funct_1 (k1_bintree2 A B))) ) ) ) ) ).
tt(d3_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A B C) <=>  ((r3_lattices A B C) & (r3_lattices A C B)) ) ) ) ) ) ) ) ).
tt(d3_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k2_boolmark A B C) = (k1_funct_4 (k1_funct_4 B (k1_margrel1 k6_margrel1 (k8_petri A (k6_domain_1 (u4_struct_0 A) C)) k7_margrel1)) (k1_margrel1 k6_margrel1 (k9_petri A (k6_domain_1 (u4_struct_0 A) C)) k8_margrel1))) ) ) ) ) ) ) ).
tt(d3_bor_cant,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (B = (k4_bor_cant A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k5_numbers B C) = (k2_nat_1 C A)) ) ) ) ) ) ) ) ).
tt(d3_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((k7_borsuk_1 A B C) = (a_3_1_borsuk_1 A B C)) ) ) ) ) ) ) ).
tt(d3_borsuk_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_borsuk_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_borsuk_2 A B C)) ) ) ) ) ) ) ).
tt(d3_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_borsuk_5 A B) = (k9_subset_1 k1_numbers k1_borsuk_5 (k2_rcomp_1 A B))) ) ) ) ) ).
tt(d3_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A C B) =>  ( (E = (k2_borsuk_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) E F) = (k1_funct_1 D (k9_real_1 1 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_borsuk_7,ax, (k8_borsuk_7 = (k4_euclid_5 1 k6_numbers k6_numbers)) ).
tt(d3_brouwer,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ( ( (~ (v3_xxreal_0 E))  & (v1_xreal_0 E))  =>  ( ((m1_subset_1 C (u1_struct_0 (k2_brouwer A B E))) & (m1_subset_1 D (u1_struct_0 (k2_brouwer A B E))))  =>  ( (C = D)  |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( (F = (k3_brouwer A B C D E))  <=>  ((r2_hidden F (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A C D) (k3_topreal9 A B E))) &  (~  (F = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) =>  ((k3_bspace A B) = (k5_struct_0 k2_bspace)) )  &  ( (~ (r2_hidden B A))  =>  ((k3_bspace A B) = (k4_struct_0 k2_bspace)) ) ) ) ) ).
tt(d3_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k3_bvfunc26 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k19_bvfunc_1 (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( ( (~  (B = k1_xboole_0) )  =>  ( (C = (k3_bvfunc_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (r1_bvfunc_2 A B D)) ) ) )  &  ( (B = k1_xboole_0)  =>  ( (C = (k3_bvfunc_2 A B))  <=>  (C = (k10_eqrel_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(d3_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((m1_c0sp1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((k5_struct_0 B) = (k5_struct_0 A))  &  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d3_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k3_c0sp2 A) = (g1_funcsdom (k2_c0sp2 A) (k2_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k1_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k5_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k4_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k3_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)))) ) ) ).
tt(d3_calcul_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_calcul_1 A B) <=> (r2_hidden B (k10_xtuple_0 A))) ) ) ) ).
tt(d3_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ( (C = (k4_calcul_2 A B))  <=>  (C = (k1_funct_1 B 1)) ) )  &  ( (~ (r1_xxreal_0 1 (k3_finseq_1 B)))  =>  ( (C = (k4_calcul_2 A B))  <=>  (C = (k5_cqc_lang A)) ) ) ) ) ) ) ) ) ) ).
tt(d3_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k2_cantor_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((r1_tarski E B) &  ((v1_finset_1 E) &  (D = (k8_setfam_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k2_card_1 A))  <=>  ((r2_hidden (k1_card_1 A) B) &  (! [C:$i] :  ((v1_card_1 C) =>  ((r2_hidden (k1_card_1 A) C) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ).
tt(d3_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k3_card_2 A B) = (k1_card_1 (k1_funct_2 B A))) ) ) ) ) ).
tt(d3_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k2_card_3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 B C) = (k2_zfmisc_1 (k1_funct_1 A C) (k1_tarski C))) ) ) ) ) ) ) ) ) ).
tt(d3_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v1_card_5 A) <=>  ((k1_card_5 A) = A) ) ) ) ).
tt(d3_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_card_fil A B C) <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ((r1_tarski D C) & (r2_hidden (k1_card_1 D) B))  => (r2_hidden (k1_setfam_1 D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d3_cardfin2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k4_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( (A = k3_cardfin2)  <=>  ( ((k8_nat_1 k4_numbers A k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers A 1) = k6_numbers)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k8_nat_1 k4_numbers A (k23_binop_2 B 2)) = (k22_binop_2 (k23_binop_2 B 1) (k20_binop_2 (k8_nat_1 k4_numbers A B) (k8_nat_1 k4_numbers A (k23_binop_2 B 1))))) ) ) ) ) ) ) ) ).
tt(d3_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((r3_card_lar A B) <=>  ((r2_card_lar A B) & (r1_card_lar A B)) ) ) ) ) ).
tt(d3_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u4_struct_0 (k2_oppcat_1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 (k2_oppcat_1 A)))))) )  =>  ( (D = (k4_cat_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  ((k7_partfun1 (u4_struct_0 (k2_oppcat_1 A)) D E) = (k5_oppcat_1 A (k7_partfun1 (u4_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  =>  ((k1_cat_4 A) = (u1_cat_4 A)) ) ) ).
tt(d3_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ( ((v1_cat_1 D) & (m3_cat_2 D B))  =>  ( (D = (k4_cat_5 A B C))  <=>  ( ((u1_struct_0 D) = (k2_relset_1 (u1_struct_0 B) (k7_cat_1 A B C)))  &  ((r1_tarski (k2_relset_1 (u4_struct_0 B) C) (u4_struct_0 D)) &  (! [E:$i] :  ((m3_cat_2 E B) =>  ( ( ((u1_struct_0 E) = (k2_relset_1 (u1_struct_0 B) (k7_cat_1 A B C)))  & (r1_tarski (k2_relset_1 (u4_struct_0 B) C) (u4_struct_0 E)))  => (m3_cat_2 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_msualg_1 B) & (l1_msualg_1 B))  =>  ( (B = (k2_catalg_1 A))  <=>  ( ((u1_struct_0 B) = (k2_zfmisc_1 (k1_tarski k6_numbers) (k4_finseq_2 2 A)))  &  ( ((u4_struct_0 B) = (k2_xboole_0 (k2_zfmisc_1 (k1_tarski 1) (k4_finseq_2 1 A)) (k2_zfmisc_1 (k1_tarski 2) (k4_finseq_2 3 A))))  &  ( (! [C:$i] :  ((r2_hidden C A) =>  ( ((k1_funct_1 (u1_msualg_1 B) (k4_tarski 1 (k9_finseq_1 C))) = k1_xboole_0)  &  ((k1_funct_1 (u2_msualg_1 B) (k4_tarski 1 (k9_finseq_1 C))) = (k4_tarski k6_numbers (k10_finseq_1 C C))) ) ) )  &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C A) &  ((r2_hidden D A) & (r2_hidden E A)) )  =>  ( ((k1_funct_1 (u1_msualg_1 B) (k4_tarski 2 (k11_finseq_1 C D E))) = (k10_finseq_1 (k4_tarski k6_numbers (k10_finseq_1 D E)) (k4_tarski k6_numbers (k10_finseq_1 C D))))  &  ((k1_funct_1 (u2_msualg_1 B) (k4_tarski 2 (k11_finseq_1 C D E))) = (k4_tarski k6_numbers (k10_finseq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cayley,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_cayley A)) (u1_struct_0 (k2_cayley B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_cayley A)) (u1_struct_0 (k2_cayley B)))))) )  =>  ( (D = (k3_cayley A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_cayley A))) =>  ((k3_funct_2 (u1_struct_0 (k2_cayley A)) (u1_struct_0 (k2_cayley B)) D E) = (k3_relat_1 (k2_funct_1 C) (k3_relat_1 E C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_cc0sp1 B A) =>  ((v1_xboole_0 B) |  ((k1_cc0sp1 A B) = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers B))) ) ) ) ) ) ) ).
tt(d3_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k2_cc0sp2 A) = (a_1_0_cc0sp2 A)) ) ) ).
tt(d3_cfcont_1,ax, (! [A:$i] :  ((v1_cfcont_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((r1_tarski (k2_relset_1 k2_numbers B) A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((m2_valued_0 C k2_numbers B) &  ((v2_comseq_2 C) & (r2_hidden (k3_comseq_2 C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v2_cfdiff_1 A) <=>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v1_cfdiff_1 B k6_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v2_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers B) (k8_funct_2 k5_numbers k2_numbers k2_numbers B A))) &  ((k3_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers B) (k8_funct_2 k5_numbers k2_numbers k2_numbers B A))) = k6_numbers) ) ) ) ) ) ) ).
tt(d3_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k2_numbers (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) )  =>  ( (B = (k3_cfuncdom A))  <=>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) B (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) C D)) E) = (k9_complex1 C (k3_funct_2 A k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) <=>  (? [B:$i] :  ((v3_ordinal1 B) & (r2_hidden A (k2_cgames_1 B))) ) ) ) ).
tt(d3_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_finseq_2 B k1_numbers) =>  ( (B = (k1_euclid A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) k1_numbers)))) ) ) ) ) ) ) ) ) ).
tt(d3_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r1_chord A B C) <=>  (? [D:$i] : (r1_glib_000 A B C D)) ) ) ) ) ) ) ) ).
tt(d3_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  ((v3_circcmb3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) => (v1_circuit2 (k5_facirc_1 A B D C) A B)) ) ) ) ) ) ) ) ) ).
tt(d3_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ((r2_circcomb A B C D) <=>  ((r1_circcomb A B) &  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) & (r1_partfun1 (u4_msualg_1 A C) (u4_msualg_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_circled1 A B) = (k6_setfam_1 (u1_struct_0 A) (k1_circled1 A B))) ) ) ) ) ).
tt(d3_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((m3_msaterm C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C))) =>  (! [E:$i] :  ((l3_msualg_1 E A) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( (F = (k3_circtrm1 A B C D E))  <=>  (! [G:$i] :  ((m3_msaterm G A B) =>  ( (G = C)  =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 (k1_circtrm1 A B G))) =>  ( (H = D)  =>  (F = (k1_funct_1 (u4_msualg_1 A E) (k1_xtuple_0 (k1_funct_1 H k1_xboole_0)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_circuit1 A B C D) = (k3_relat_1 (k1_msualg_1 A D) C)) ) ) ) ) ) ) ) ) ).
tt(d3_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  ( (E = (k4_circuit2 A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) &  ( ((k5_card_1 F) = (k4_circuit1 A B C))  &  (E = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B D) C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_classes1 A B) <=>  ((r2_hidden A B) & (v2_classes1 B)) ) ) ) ).
tt(d3_classes2,ax, (k14_classes2 = (k1_classes1 k13_classes2)) ).
tt(d3_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_clvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_clopban1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_clvect_1 A D E)) = (k1_clvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_clopban2 A B C) = (k1_binop_1 (k9_csspace (k6_clopban1 A A) (k8_clopban1 A A)) C B)) ) ) ) ) ) ) ).
tt(d3_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clopban3 B A) <=> (v1_series_1 (k4_normsp_0 A B))) ) ) ) ) ).
tt(d3_clopban4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k3_clopban4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k1_normsp_1 B E F) = (k6_algstr_0 B (k1_clvect_1 B (k6_clopban3 B C F) (k8_nat_1 k2_numbers (k6_sin_cos A) F)) (k6_clopban3 B D (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k1_normsp_1 B E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ((v3_closure1 C A B) <=>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) => (r6_pboole A (k2_closure1 A B C D) (k2_closure1 A B C (k2_closure1 A B C D)))) ) ) ) ) ) ) ) ).
tt(d3_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ( ( (~  (C = k1_xboole_0) )  =>  ((k4_closure2 A B C) = (k3_closure2 C)) )  &  ( (C = k1_xboole_0)  =>  ((k4_closure2 A B C) = (k1_pboole A)) ) ) ) ) ) ) ) ).
tt(d3_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v3_clvect_1 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_clvect_1 A D (k2_xcmplx_0 B C)) = (k1_algstr_0 A (k1_clvect_1 A D B) (k1_clvect_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d3_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k2_clvect_2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k13_csspace A (k1_normsp_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k2_clvect_3 A B C) = (k1_normsp_1 A (k1_bhsp_4 A B) C)) ) ) ) ) ) ) ).
tt(d3_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (B = (k2_cohsp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C A) & (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(d3_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_classes1 C) & (v1_coh_sp C)) )  =>  ( (C = (k2_coh_sp A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E D) & (r2_hidden F D))  => (r2_hidden (k4_tarski E F) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v2_collsp A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) )  => (r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C D) (u1_collsp A))) ) ) ) ) ) ) ) ) ) ).
tt(d3_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((v2_combgras B A) <=>  ((v1_combgras B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((v1_combgras C A) & (r1_tarski B C))  =>  (C = B) ) ) ) ) ) ) ) ) ) ).
tt(d3_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (A = B)  <=>  ( ((k3_complex1 A) = (k3_complex1 B))  &  ((k4_complex1 A) = (k4_complex1 B)) ) ) ) ) ) ) ).
tt(d3_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( (~  ( (~  ((k1_comptrig A) = k6_numbers) )  &  (B = k6_numbers) ) )  =>  ((k3_complex2 A B) = (k1_comptrig (k2_complex2 B (k1_real_1 (k1_comptrig A))))) )  &  (~  ( (~  ((k1_comptrig A) = k6_numbers) )  &  ( (B = k6_numbers)  &  (~  ((k3_complex2 A B) = (k9_real_1 (k8_real_1 2 k32_sin_cos) (k1_comptrig A))) ) ) ) ) ) ) ) ) ) ).
tt(d3_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k7_complsp2 A) = (k12_seq_4 (k10_seq_4 A (k1_complsp2 A)) (k1_binop_2 (k5_binop_2 (k18_binop_2 1 2) k7_complex1)))) ) ) ).
tt(d3_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_compl_sp B A) <=> (r2_hidden B (k2_pcomps_1 A))) ) ) ) ) ).
tt(d3_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 A)) =>  ((k3_compos_0 A B) = (a_2_0_compos_0 A B)) ) ) ) ) ).
tt(d3_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  ((k3_compos_2 A B C) = (k8_compos_1 A (k11_compos_1 A B) (k11_compos_1 A C))) ) ) ) ) ) ) ).
tt(d3_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((r1_xboole_0 B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_comput_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_comput_1 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (r2_hidden C (k10_xtuple_0 A)))  =>  ( (~  ((v1_xboole_0 B) &  ( (~ (v1_xboole_0 C))  &  (~  ((k9_xtuple_0 C) = (k1_tarski k1_xboole_0)) ) ) ) )  &  (~  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (~  ((r1_tarski (k9_xtuple_0 B) (k4_finseq_2 D E)) & (r1_tarski (k9_xtuple_0 C) (k4_finseq_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_comseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_comseq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B (k18_complex1 (k1_funct_1 A C)))) ) ) ) ) ) ) ) ).
tt(d3_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k3_comseq_3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k3_complex1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d3_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v3_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r5_analmetr A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r4_analmetr A E B C D) &  ((r4_analmetr A E C B D) & (r4_analmetr A E D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)))))) )  =>  ( (B = (k1_conlat_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) B C) = (a_2_0_conlat_1 A C)) ) ) ) ) ) ) ) ).
tt(d3_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A)))) =>  ((k3_conlat_2 A B) = (k15_lattice3 (k11_conlat_1 A) B)) ) ) ) ) ).
tt(d3_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v3_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 J A) &  ((v1_aff_1 K A) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((r2_hidden H J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden G J) |  ((r2_hidden I J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden F K) |  ((r2_hidden H K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v3_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r10_analmetr A J K) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((r2_hidden H J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r4_analmetr A B C F G) &  ((r4_analmetr A C D G H) & (r4_analmetr A D E H I)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden C J) |  ((r2_hidden E J) | (r4_analmetr A B E F I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) <=> (v1_connsp_1 (k1_pre_topc A B))) ) ) ) ) ).
tt(d3_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_connsp_2 A B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((m1_connsp_2 C A B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((m1_connsp_2 D A B) &  ((v2_connsp_1 D A) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k2_connsp_3 A B C) = C) ) ) ) ) ) ) ) ).
tt(d3_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((v2_convex1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v2_funct_1 C) &  ( ((k10_xtuple_0 C) = (k3_rlvect_2 A B))  &  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  ( ((k18_rvsum_1 D) = 1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((k1_funct_1 D E) = (k1_funct_1 B (k1_funct_1 C E)))  & (r1_xxreal_0 k6_numbers (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) =>  ((r1_xxreal_0 C k6_numbers) | (r2_hidden (k1_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ( (B = (k2_convex4 A))  <=>  ((k1_convex4 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d3_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  ((k3_convfun1 A B) = (g1_rlvect_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_struct_0 A) (k4_struct_0 B)) (k1_convfun1 A B) (k2_convfun1 A B))) ) ) ) ) ).
tt(d3_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( (D = (k13_cqc_lang A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_qc_lang1 A) (k9_qc_lang1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k9_qc_lang1 A))))) )  &  ( (D = (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E B))  &  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  ( ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E (k5_cqc_lang A)) = (k5_cqc_lang A))  &  ( ((v2_qc_lang1 F A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E F) = (k10_qc_lang1 A (k16_qc_lang1 A F) (k1_cqc_lang A (k17_qc_lang1 A F) (k2_cqc_lang A (k3_qc_lang3 A k6_numbers) C)))) )  &  ( ((v3_qc_lang1 F A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E F) = (k13_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E (k18_qc_lang1 A F)))) )  &  ( ((v4_qc_lang1 F A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E F) = (k14_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E (k19_qc_lang1 A F)) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E (k20_qc_lang1 A F)))) )  &  ((v5_qc_lang1 F A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E F) = (k15_funcop_1 (k9_qc_lang1 A) (k21_qc_lang1 A F) C F (k15_qc_lang1 A (k21_qc_lang1 A F) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) E (k22_qc_lang1 A F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_funct_2 E (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) =>  ( (E = (k3_cqc_sim1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_qc_lang1 A)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [H:$i] :  ((m2_subset_1 H (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [I:$i] :  ((m2_subset_1 I (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ( (H = (k2_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) B F G))  &  (I = (k2_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) C (k30_qc_lang1 A F D) G)) )  =>  ((k2_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) E F G) = (k7_cqc_lang A H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_cqc_the1,ax, (k2_cqc_the1 = a_0_0_cqc_the1) ).
tt(d3_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the3 A B) <=>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden C B) => (v2_cqc_the1 C A)) ) ) ) ) ) ) ) ).
tt(d3_csspace3,ax, (k3_csspace3 = (g2_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3) k2_csspace3)) ).
tt(d3_csspace4,ax, (k3_csspace4 = (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) ).
tt(d3_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_csspace A) = A) ) ) ).
tt(d3_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_decomp_1 B A) <=> (r1_tarski B (k1_tops_1 A (k2_pre_topc A B)))) ) ) ) ) ).
tt(d3_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k8_descip_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k3_finseq_1 B))) =>  ((k1_funct_1 D E) = (k1_funct_1 B (k2_xcmplx_0 (k6_int_1 (k2_xcmplx_0 (k6_xcmplx_0 E 1) C) (k3_finseq_1 B)) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_dickson A) <=>  ((v3_orders_2 A) & (v4_orders_2 A)) ) ) ) ).
tt(d3_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_diff_1 A B) = (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_diff_1 A B) A)) ) ) ) ) ).
tt(d3_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_diraf A B C D) <=> (r2_analoaf A B C C D)) ) ) ) ) ) ) ) ) ).
tt(d3_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_dirort A B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (F = G) )  &  ((r2_analoaf A F G B C) & (r2_analoaf A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( (C = (k4_dist_1 A B))  <=>  ( ((k4_finseq_1 C) = (k2_finseq_1 (k5_card_1 A)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k3_dist_1 A B (k1_funct_1 (k1_uproots A) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((v1_dtconstr A) <=>  (~  ((k1_lang1 A) = k1_xboole_0) ) ) ) ) ).
tt(d3_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_dynkin A B C) = (k7_subset_1 A (k8_nat_1 (k9_setfam_1 A) B C) (k3_tarski (k10_xtuple_0 (k5_relat_1 B C))))) ) ) ) ) ) ) ).
tt(d3_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((v2_ec_pf_1 B A) <=>  ( (~  (B = k6_numbers) )  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) &  ((k2_binom (k9_int_3 A) C 2) = B) ) ) ) ) ) ) ) ) ).
tt(d3_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( (E = (k4_ec_pf_2 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v22_algstr_0 B) & (l4_algstr_0 B))  =>  ( (B = (k3_endalg A))  <=>  ( ((u1_struct_0 B) = (k1_endalg A))  &  ( ((u2_algstr_0 B) = (k2_endalg A))  &  ((k5_struct_0 B) = (k6_partfun1 (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(d3_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ((k3_ens_1 A B) = (k1_xtuple_0 (k1_xtuple_0 B))) ) ) ) ) ).
tt(d3_entropy1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_entropy1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  ( ((k3_matrix_1 k1_numbers B C D) = k6_numbers)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (F = (k3_enumset1 A B C D E))  <=>  (! [G:$i] :  ((r2_hidden G F) <=>  (~  ( (~  (G = A) )  &  ( (~  (G = B) )  &  ( (~  (G = C) )  &  ( (~  (G = D) )  &  (~  (G = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k7_eqrel_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((r2_hidden E A) &  (D = (k6_eqrel_1 A A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((k3_equation A) = (k11_msafree A (k8_funcop_1 (k1_zfmisc_1 k1_numbers) (u1_struct_0 A) k5_numbers))) ) ) ).
tt(d3_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k3_euclid_3 A) = (k1_comptrig (k2_euclid_3 A))) ) ) ).
tt(d3_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k3_euclid_4 A B C) = (a_3_1_euclid_4 A B C)) ) ) ) ) ) ) ).
tt(d3_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k3_euclid_5 A) = (k1_seq_1 A 3)) ) ) ).
tt(d3_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_6 A B C) <=>  (~  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)))  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) C A)))  &  (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_euclid_7,ax, (! [A:$i] :  ((v1_euclid_7 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) )  =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (B = C)  |  ((k23_rvsum_1 B C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(d3_euclid_8,ax, (k4_euclid_8 = (k1_euclid_8 k6_numbers k6_numbers 1)) ).
tt(d3_euclid_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_euclid_9 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C D) = (k2_rcomp_1 (k6_xcmplx_0 (k1_funct_1 A D) B) (k2_xcmplx_0 (k1_funct_1 A D) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k3_euclid A) = (k3_relat_1 A k2_euclid)) ) ) ).
tt(d3_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r4_euclidlp A B C) <=>  ( (~  (B = (k5_euclid A)) )  &  ( (~  (C = (k5_euclid A)) )  & (r1_rvsum_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d3_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v3_euclmetr A) <=> (v4_aff_2 (k3_analmetr A))) ) ) ).
tt(d3_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_exchsort B A) <=>  (A = (k3_ordinal2 (k9_xtuple_0 B))) ) ) ) ) ).
tt(d3_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v2_memstr_0 B A) & (l1_extpro_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k2_extpro_1 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d3_facirc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_facirc_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) & (v1_xtuple_0 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(d3_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v2_fcont_1 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r2_hidden C (k1_relset_1 k1_numbers A)) & (r2_hidden D (k1_relset_1 k1_numbers A)))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 A C) (k1_seq_1 A D))) (k4_real_1 B (k18_complex1 (k6_xcmplx_0 C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v3_fdiff_1 A) <=>  ((v1_partfun1 A k1_numbers) &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_seq_1 A C) = (k8_real_1 B C)) ) ) ) ) ) ) ) ) ).
tt(d3_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r3_fdiff_3 A B) <=>  ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k1_rcomp_1 B (k7_real_1 B C)) (k1_relset_1 k1_numbers A))) ) )  &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers)) ) ) ) )  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers D A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ff_siec,ax, (! [A:$i] :  ((k3_ff_siec A) = (k1_ff_siec k1_xboole_0 A)) ) ).
tt(d3_fib_fusc,ax, (k3_fib_fusc = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 (k8_ami_3 8 (k10_ami_3 1))) (k5_afinsq_1 (k2_ami_3 (k10_ami_3 4) (k10_ami_3 k6_numbers)))) (k5_afinsq_1 (k6_ami_3 (k10_ami_3 1) (k10_ami_3 4)))) (k5_afinsq_1 (k8_ami_3 6 (k10_ami_3 4)))) (k5_afinsq_1 (k3_ami_3 (k10_ami_3 3) (k10_ami_3 2)))) (k5_afinsq_1 (k7_ami_3 k6_numbers))) (k5_afinsq_1 (k3_ami_3 (k10_ami_3 2) (k10_ami_3 3)))) (k5_afinsq_1 (k7_ami_3 k6_numbers))) (k5_afinsq_1 (k2_compos_1 k1_ami_3)))) ).
tt(d3_fib_num2,ax, (k3_fib_num2 = a_0_0_fib_num2) ).
tt(d3_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_0 B A) <=>  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B C) =>  ( (C = (u1_struct_0 A))  |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((m1_filter_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k8_eqrel_1 A B) (k8_eqrel_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B))))) )  =>  ( (D = (k2_filter_1 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k8_eqrel_1 A B)) & (r2_hidden F E))  =>  ((k1_funct_1 D E) = (k6_eqrel_1 A A B (k1_funct_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_lattice2 A))) =>  ((k2_filter_2 A B) = B) ) ) ) ) ).
tt(d3_finance1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k4_finance1 A B C) = (k1_seq_1 (k3_series_1 (k3_finance1 B C)) A)) ) ) ) ) ) ) ).
tt(d3_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k3_finseq_1 A))  <=>  ((k2_finseq_1 B) = (k9_xtuple_0 A)) ) ) ) ) ) ).
tt(d3_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_2 B A) <=>  (! [C:$i] :  ((r2_hidden C B) => (m2_finseq_1 C A)) ) ) ) ) ).
tt(d3_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)))) =>  ( (C = (k3_finseq_3 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ((r2_hidden (k4_tarski D E) C) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_relset_1 k5_numbers D)) => (r2_hidden (k4_tarski (k1_funct_1 D F) (k1_funct_1 E F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  (! [C:$i] :  ( (C = (k1_finseq_4 A B))  <=>  ((r2_hidden C (k9_xtuple_0 A)) &  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ) ).
tt(d3_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k3_finseq_5 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k1_funct_1 A (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(d3_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 B C) =>  ((k2_finseq_6 A B C) = (k16_finseq_1 (k2_nat_1 (k7_nat_d C B) 1) (k1_rfinseq (k7_nat_d B 1) A))) )  &  ( (~ (r1_xxreal_0 B C))  =>  ((k2_finseq_6 A B C) = (k3_finseq_5 (k16_finseq_1 (k2_nat_1 (k7_nat_d B C) 1) (k1_rfinseq (k7_nat_d C 1) A)))) ) ) ) ) ) ) ) ) ).
tt(d3_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k5_finseq_8 A B C) = (k1_finseq_8 A B (k2_rfinseq A (k3_finseq_1 (k4_finseq_8 A B C)) C))) ) ) ) ) ) ) ).
tt(d3_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo B A) &  ((v2_binop_1 B A) & (v1_finseqop B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( (C = (k5_finseqop A B))  <=> (r1_finseqop A C B)) ) ) ) ) ) ) ) ).
tt(d3_finset_1,ax, (! [A:$i] :  ((v3_finset_1 A) <=>  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski B A) &  ((v1_finset_1 B) &  ((k1_setfam_1 B) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d3_finsub_1,ax, (! [A:$i] :  ((v3_finsub_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k6_subset_1 B C) A)) ) ) ) ) ).
tt(d3_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C (k1_fin_topo A B)) =>  ((k3_fintopo2 A B C) = k8_margrel1) )  &  ( (~ (r2_hidden C (k1_fin_topo A B)))  =>  ((k3_fintopo2 A B C) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(d3_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_fintopo3 A B C) = (k1_funct_1 (k2_fintopo3 A B) C)) ) ) ) ) ) ) ).
tt(d3_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A)))) =>  ( (B = (k1_fintopo4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ((k9_relat_1 B C) = (k1_enumset1 C (k7_nat_1 (k7_nat_d C 1) 1) (k3_xxreal_0 (k2_nat_1 C 1) A))) ) ) ) ) ) ) ) ) ).
tt(d3_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_fintopo5 A B) = (g1_orders_2 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_fintopo5 A B))) ) ) ) ) ).
tt(d3_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_orders_2 C) & (m1_fintopo6 C A)) )  =>  ( (C = (k1_fintopo6 A B))  <=>  ((k2_struct_0 C) = B) ) ) ) ) ) ) ) ).
tt(d3_fin_topo,ax, (k4_fin_topo = (g1_orders_2 (k6_domain_1 k5_numbers k6_numbers) (k3_fin_topo k6_numbers))) ).
tt(d3_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k8_flang_1 A B) = (k3_tarski (a_2_0_flang_1 A B))) ) ) ) ).
tt(d3_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_fomodel0 B A) <=> (v2_fomodel0 B (k3_finseq_2 A) (k11_monoid_0 A))) ) ) ) ).
tt(d3_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k3_fomodel1 A) = (k8_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (k7_subset_1 k1_numbers k5_numbers (k6_domain_1 k5_numbers k6_numbers)))) ) ) ).
tt(d3_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((m3_fomodel2 C A B) <=>  (! [D:$i] :  ( ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  => (m2_fomodel2 (k1_funct_1 C D) A B D)) ) ) ) ) ) ) ) ) ).
tt(d3_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ( (~ (v7_fomodel1 B A))  =>  ((k3_fomodel3 A B C) = (k2_partfun1 (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A)))) )  &  ((v7_fomodel1 B A) =>  ((k3_fomodel3 A B C) = (k3_relat_1 (k2_partfun1 (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A))) (k9_fomodel0 C (k32_fomodel1 A)))) ) ) ) ) ) ) ) ).
tt(d3_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v2_fomodel4 B A) <=> (r1_tarski B (k1_fomodel4 A))) ) ) ) ).
tt(d3_frechet2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_frechet2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden C D) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 E F) & (r2_hidden (k8_nat_1 (u1_struct_0 A) B F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_frechet A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden C D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) &  (~ (r2_hidden (k3_funct_2 k5_numbers (u1_struct_0 A) B F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden B (k4_finseq_1 (u1_unialg_1 A))) =>  ((k1_freealg A B) = (k1_funct_1 (u1_unialg_1 A) B)) ) ) ) ) ) ).
tt(d3_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_fscirc_1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C))) (k5_circcomb k3_twoscomp (k10_finseq_1 A C)))) ) ) ) ).
tt(d3_fscirc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k1_fscirc_2 A B C)) (k3_msafree2 (k1_fscirc_2 A B C))) =>  ( (D = (k3_fscirc_2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  ( (D = (k1_funct_1 E A))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 E (k1_nat_1 F 1)) = (k6_fscirc_1 (k1_funct_1 B (k1_nat_1 F 1)) (k1_funct_1 C (k1_nat_1 F 1)) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_fsm_1 A B C D E) <=>  ((k1_funct_1 (k2_fsm_1 A B D C) (k2_nat_1 (k3_finseq_1 C) 1)) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v2_fsm_2 C A B) <=>  (? [D:$i] :  ((m2_finseq_1 D A) & (r1_fsm_1 A B D (u2_fsm_1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(d3_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B))  =>  (! [D:$i] :  ( ((v1_fsm_3 D A (k9_flang_1 A)) & (l1_fsm_3 D A (k9_flang_1 A)))  =>  ( (D = (k2_fsm_3 A B C))  <=>  ( ((g1_rewrite3 (k9_flang_1 A) (u1_struct_0 D) (u1_rewrite3 (k9_flang_1 A) D)) = (k1_fsm_3 A B (g1_rewrite3 B (u1_struct_0 C) (u1_rewrite3 B C))))  &  ((u1_fsm_3 A (k9_flang_1 A) D) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 C)) (k3_rewrite3 A B C (k2_flang_1 A) (u1_fsm_3 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_ftacell1 A B C D E) = (k9_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d3_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k3_funcop_1 A B C) = (k3_relat_1 (k13_funct_3 B C) A)) ) ) ) ) ) ) ).
tt(d3_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k1_numbers (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) )  =>  ( (B = (k7_funcsdom A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  ((k2_binop_1 k1_numbers (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers) B C D) = (k4_funcsdom k1_numbers A k35_binop_2 C D)) ) ) ) ) ) ) ) ) ).
tt(d3_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k10_xtuple_0 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) &  (C = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ).
tt(d3_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  ((v2_funct_2 B A) <=>  ((k2_relset_1 A B) = A) ) ) ) ) ).
tt(d3_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k4_funct_3 A B))  <=>  ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((r2_hidden D B) =>  ( ((r2_hidden D A) =>  ((k1_funct_1 C D) = 1) )  &  ( (~ (r2_hidden D A))  =>  ((k1_funct_1 C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_funct_4 A B))  <=>  ( (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) <=>  (? [E:$i] :  (? [F:$i] :  (? [G:$i] :  (? [H:$i] :  ( (D = (k4_tarski (k4_tarski E G) (k4_tarski F H)))  &  ((r2_hidden (k4_tarski E F) (k9_xtuple_0 A)) & (r2_hidden (k4_tarski G H) (k9_xtuple_0 B))) ) ) ) ) ) ) )  &  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D E) (k9_xtuple_0 A)) & (r2_hidden (k4_tarski F G) (k9_xtuple_0 B)))  =>  ((k1_binop_1 C (k4_tarski D F) (k4_tarski E G)) = (k4_tarski (k1_binop_1 A D E) (k1_binop_1 B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k3_funct_5 A) = (k1_funct_5 (k2_funct_4 A))) ) ) ).
tt(d3_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k3_funct_6 A))  <=>  ( ((k9_xtuple_0 B) = (k8_relat_1 A (k1_funct_6 (k10_xtuple_0 A))))  &  (! [C:$i] :  ((r2_hidden C (k8_relat_1 A (k1_funct_6 (k10_xtuple_0 A)))) =>  ((k1_funct_1 B C) = (k10_xtuple_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d3_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) =>  ((k2_funct_7 A B C) = (k1_funct_4 A (k16_funcop_1 B C))) )  &  ( (~ (r2_hidden B (k9_xtuple_0 A)))  =>  ((k2_funct_7 A B C) = A) ) ) ) ) ) ) ).
tt(d3_funct_8,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v3_funct_8 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden D (k1_relset_1 A C)) & (r2_hidden (k1_real_1 D) (k1_relset_1 A C)))  =>  ((k1_funct_1 C (k1_real_1 D)) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  ( ( (~  (B = k1_xboole_0) )  =>  ((m1_functor0 F A B C D E) <=>  (? [G:$i] :  ( (~ (v1_xboole_0 G))  &  (? [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H G) &  ((v1_funct_1 H) & (v1_partfun1 H G)) ) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I A G) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 A G)))) )  &  ( (C = I)  &  ( (E = H)  & (m2_pboole F A D (k3_relat_1 I H))) ) ) ) ) ) ) ) ) )  &  ( (B = k1_xboole_0)  =>  ((m1_functor0 F A B C D E) <=> (r6_pboole A F (k1_pboole A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m1_functor2 D A B C C) =>  ( (D = (k1_functor2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k8_altcat_1 B (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ((m1_functor2 H A B D E) =>  (! [I:$i] :  ((m1_functor2 I B C F G) =>  ((k7_functor3 A B C D E F G H I) = (k3_functor2 A C (k1_functor3 A B C D F) (k1_functor3 A B C E F) (k1_functor3 A B C E G) (k5_functor3 A B C D E H F) (k6_functor3 A B C F G E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (D = (k1_fuzzy_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_seq_1 D E) = (k1_square_1 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (D = (k3_fuzzy_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_seq_1 D E) = (k9_real_1 (k7_real_1 (k1_seq_1 B E) (k1_seq_1 C E)) (k8_real_1 (k1_seq_1 B E) (k1_seq_1 C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) k1_numbers)))) ) )  =>  ( (F = (k4_fuzzy_4 A B C D E))  <=>  (! [G:$i] :  (! [H:$i] :  ((r2_hidden (k4_tarski G H) (k2_zfmisc_1 A C)) =>  ((k1_fuzzy_4 A C F G H) = (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k3_fvsum_1 A B C) = (k1_finseqop (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) B C)) ) ) ) ) ) ) ).
tt(d3_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_gate_5 A B C D) = (k35_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0 (k2_gate_1 B D) k1_xboole_0)) ) ) ) ) ).
tt(d3_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_gcd_1 A B C) <=>  ((r1_gcd_1 A B C) & (r1_gcd_1 A C B)) ) ) ) ) ) ) ) ).
tt(d3_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k2_genealg1 A B C D E) = (k1_genealg1 A (k1_genealg1 A B C D) (k1_genealg1 A C B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_geomtrap A B C D E F G) <=>  ((r1_analoaf A D E F G) &  ((r3_analmetr A D E (k1_geomtrap A D E) (k1_geomtrap A F G) B C) & (r3_analmetr A F G (k1_geomtrap A D E) (k1_geomtrap A F G) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k3_gfacirc1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k10_margrel1 B (k9_margrel1 C))) ) ) ) ) ) ) ) ).
tt(d3_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k1_gfacirc2 A B C)) (k3_msafree2 (k1_gfacirc2 A B C))) =>  ( (D = (k3_gfacirc2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  ( (D = (k1_funct_1 E A))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 E (k1_nat_1 F 1)) = (k9_gfacirc1 (k1_funct_1 B (k1_nat_1 F 1)) (k1_funct_1 C (k1_nat_1 F 1)) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_glib_000,ax, (k3_glib_000 = 3) ).
tt(d3_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A))) =>  ((m3_glib_001 B A) <=>  ( (~ (v1_abian (k3_finseq_1 B)))  &  ((r2_hidden (k1_funct_1 B 1) (k6_glib_000 A)) &  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  => (r1_glib_000 A (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 2)) (k1_funct_1 B (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ).
tt(d3_glib_003,ax, (k4_glib_003 = 7) ).
tt(d3_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (? [E:$i] :  ( ((v2_glib_001 E A) & (m3_glib_001 E A))  & (r1_glib_001 A B C E)) )  =>  ( (D = (k1_glib_004 A B C))  <=>  (? [E:$i] :  ( ((v2_glib_001 E A) &  ((v5_glib_001 E A) & (m3_glib_001 E A)) )  &  ((r2_glib_004 A E B C) &  (D = (k10_glib_003 A E)) ) ) ) ) )  &  ( (! [E:$i] :  ( ((v2_glib_001 E A) & (m3_glib_001 E A))  =>  (~ (r1_glib_001 A B C E)) ) )  =>  ( (D = (k1_glib_004 A B C))  <=>  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d3_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((k1_glib_005 A B C D) = (k6_xcmplx_0 (k3_uproots (k18_glib_000 A (k1_tarski D)) (k5_relat_1 B (k18_glib_000 A (k1_tarski D)))) (k3_uproots (k19_glib_000 A (k1_tarski D)) (k5_relat_1 B (k19_glib_000 A (k1_tarski D)))))) ) ) ) ) ) ) ).
tt(d3_goboard1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((v3_relat_1 B) <=>  ( (k6_numbers = (k3_finseq_1 B))  |  (k6_numbers = (k1_matrix_1 B)) ) ) ) ) ) ) ).
tt(d3_goboard5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_goboard5 A B C) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_goboard5 A B) (k2_goboard5 A C))) ) ) ) ) ) ) ).
tt(d3_gobrd13,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (D = (k3_gobrd13 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B E F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  (D = (k3_goboard5 B (k7_nat_d E 1) F)) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  (D = (k3_goboard5 B E F)) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  (D = (k3_goboard5 B G (k7_nat_d H 1))) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  (D = (k3_goboard5 B E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( (B = (k1_goedelcp A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  (C = (k12_cqc_lang A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k3_graph_1 A B) = (k3_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) B)) ) ) ) ) ).
tt(d3_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_graph_2 A) <=>  ((k5_card_1 (k10_xtuple_0 A)) = 2) ) ) ) ).
tt(d3_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((k4_graph_3 A B C) = (k4_subset_1 (u4_struct_0 A) (k2_graph_3 A B C) (k3_graph_3 A B C))) ) ) ) ) ) ).
tt(d3_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((k1_graph_4 A B) = (a_2_0_graph_4 A B)) ) ) ) ).
tt(d3_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_graph_5 A B C D) <=>  ( (~  (B = k1_xboole_0) )  &  ( ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 B 1)) = C)  &  ((k1_funct_1 (u2_graph_1 A) (k1_funct_1 B (k3_finseq_1 B))) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k7_graphsp A B) = (a_2_0_graphsp A B)) ) ) ) ) ).
tt(d3_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_grcat_1 A B) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) (k1_grcat_1 A B))) ) ) ) ) ).
tt(d3_gr_cy_1,ax, (k2_gr_cy_1 = (g3_algstr_0 k4_numbers k44_binop_2)) ).
tt(d3_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_gr_cy_3 A) = (k6_xcmplx_0 (k2_newton 2 A) 1)) ) ) ).
tt(d3_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_groeb_1 A B C D) <=> (v9_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(d3_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r1_groeb_2 A B C) <=>  (! [D:$i] :  ( ((k1_recdef_1 B D) = k6_numbers)  |  ((k1_recdef_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(d3_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k4_groeb_3 A B C D E) = (k4_xboole_0 (k2_polynom1 (k15_pre_poly A) C D) (k3_groeb_3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_group_10,ax, (! [A:$i] :  (! [B:$i] :  ((k3_group_10 A B) = (a_2_0_group_10 A B)) ) ) ).
tt(d3_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k3_group_11 A B C) = (a_3_2_group_11 A B C)) ) ) ) ) ) ) ).
tt(d3_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v3_group_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_2 A B C) = (k2_group_2 A (k6_domain_1 (u1_struct_0 A) B) C)) ) ) ) ) ) ) ).
tt(d3_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_group_3 A B C) = (a_3_0_group_3 A B C)) ) ) ) ) ) ) ).
tt(d3_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k4_group_4 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 D E) = (k5_group_1 A (k2_group_4 (k7_partfun1 k4_numbers B E)) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_group_5 A B C D) = (k2_group_5 A (k2_group_5 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d3_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k15_group_2 A B) (k15_group_2 A B)) (k15_group_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k15_group_2 A B) (k15_group_2 A B)) (k15_group_2 A B))))) )  =>  ( (C = (k4_group_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k15_group_2 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k15_group_2 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k15_group_2 A B) C D E) = (k2_group_2 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_group_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v2_group_7 B A) <=>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) & (l3_algstr_0 D)) )  =>  (~  (D = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ( ( ((k3_finseq_1 D) = k6_numbers)  =>  ( (E = (k2_group_9 A B C D))  <=> (r2_funct_2 B B E (k6_partfun1 B))) )  &  ( (~  ((k3_finseq_1 D) = k6_numbers) )  =>  ( (E = (k2_group_9 A B C D))  <=>  (? [F:$i] :  ((m2_finseq_1 F (k1_funct_2 B B)) &  ( (E = (k1_funct_1 F (k3_finseq_1 D)))  &  ( ((k3_finseq_1 F) = (k3_finseq_1 D))  &  ( ((k1_funct_1 F 1) = (k1_funct_1 C (k1_funct_1 D 1)))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ( (~  (G = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) G))  &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H B B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I B B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  (~  ( (H = (k1_funct_1 F G))  &  ( (I = (k1_funct_1 C (k1_funct_1 D (k1_nat_1 G 1))))  &  ((k1_funct_1 F (k1_nat_1 G 1)) = (k1_partfun1 B B B B I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_groupp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((v2_groupp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_group_1 B A (k6_algstr_0 B C D)) = (k6_algstr_0 B (k5_group_1 B A C) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_grsolv_1 A B C D) = (k10_group_6 D B (k1_grsolv_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d3_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (E = (k3_hahnban1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) = (k1_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C F) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v3_hahnban B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k1_rlvect_1 A C D)) = (k8_real_1 D (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ).
tt(d3_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((r1_hallmar1 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D A) &  ( (D = C)  &  ( ((k4_finseq_1 B) = (k4_finseq_1 D))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 B E))) ) )  & (v2_funct_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_hausdorf,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k3_hausdorf A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) &  ( (B = E)  &  ( (C = F)  &  (D = (k1_hausdorf (k14_euclid A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ( (E = (k3_helly A B C D))  <=>  ((k9_subset_1 (k6_glib_000 A) (k9_subset_1 (k6_glib_000 A) (k13_glib_001 A (k2_helly A B C)) (k13_glib_001 A (k2_helly A C D))) (k13_glib_001 A (k2_helly A D B))) = (k1_tarski E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((v2_henmodel B A) <=>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) B (k12_finseq_1 (k3_cqc_lang A) C))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) B (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A C))))) ) ) ) ) ) ) ) ) ).
tt(d3_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((k2_hermitan A B) = (k10_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B)) B)) ) ) ) ) ).
tt(d3_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  ((k3_heyting1 A B) = B) ) ) ) ).
tt(d3_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_heyting2 A B C D) = (k3_xboole_0 (k4_partfun1 A B) (a_4_0_heyting2 A B C D))) ) ) ) ) ) ) ) ).
tt(d3_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B))) =>  ( (C = (k3_heyting3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  &  ((r1_xxreal_0 E (k2_nat_1 (k4_nat_1 2 A) 1)) &  ((k1_domain_1 k5_numbers k5_numbers E B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_group_1 C) & (l5_algstr_0 C)) )  =>  ((k3_hilbasis A B C) = (k15_funct_7 (k15_pre_poly A) (u1_struct_0 C) (k7_polynom1 A C) (k2_hilbasis A B) (k1_group_1 C))) ) ) ) ) ) ).
tt(d3_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k3_hilbert3 A B) = (k1_funct_1 (k2_hilbert3 A) B)) ) ) ) ) ).
tt(d3_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_hurwitz A B C) = (k1_funct_4 (k9_polynom3 A) (k5_funct_4 (u1_struct_0 A) k6_numbers C (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)) (k1_group_1 A)))) ) ) ) ) ) ) ).
tt(d3_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 A B) <=>  (~ (r1_xxreal_0 (k5_series_1 2 A) B)) ) ) ) ) ) ).
tt(d3_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_ideal_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k6_algstr_0 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  ((k3_incproj A) = (g1_incsp_1 (u1_struct_0 A) (k1_incproj A) (k2_incproj A))) ) ) ).
tt(d3_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_index_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) )  =>  ( (B = (k4_index_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  ( (D = (k1_funct_1 A C))  =>  ((k1_funct_1 B C) = (u4_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) =>  (! [F:$i] :  ( ((v3_msualg_1 F A) & (l3_msualg_1 F A))  =>  ( (F = (k1_instalg1 A B C D E))  <=>  ( ((u3_msualg_1 A F) = (k3_relat_1 D (u3_msualg_1 B C)))  &  ((u4_msualg_1 A F) = (k3_relat_1 E (u4_msualg_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) <=>  (? [C:$i] :  ((v1_int_1 C) &  (B = (k3_xcmplx_0 A C)) ) ) ) ) ) ) ) ).
tt(d3_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_2 A B) <=>  ((k3_int_2 A B) = 1) ) ) ) ) ) ).
tt(d3_int_3,ax, (k1_int_3 = (g6_algstr_0 k4_numbers k44_binop_2 k46_binop_2 (k1_funct_7 1 k4_numbers) (k1_funct_7 k6_numbers k4_numbers))) ).
tt(d3_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ((r1_int_5 A B) =>  ( ((k6_int_1 A B) = k6_numbers)  |  ((k2_int_5 A B) = 1) ) )  &  ( ( ((r1_int_5 A B) &  ((k6_int_1 A B) = k6_numbers) )  =>  ((k2_int_5 A B) = k6_numbers) )  &  (~  ( (~  ((r1_int_5 A B) &  (~  ((k6_int_1 A B) = k6_numbers) ) ) )  &  ( (~  ((r1_int_5 A B) &  ((k6_int_1 A B) = k6_numbers) ) )  &  (~  ((k2_int_5 A B) = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k1_int_6 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k6_int_1 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k2_int_7 A) = (k1_realset1 (k7_int_3 A) (k1_int_7 A))) ) ) ).
tt(d3_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_integr10 A B C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k1_integr10 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers E) = (k3_rcomp_1 B C))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_relset_1 k1_numbers E)) =>  ((k1_seq_1 E F) = (k4_integra5 B F A)) ) ) )  &  ((r1_limfunc2 E C) &  (D = (k1_limfunc2 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k3_finseq_2 k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k1_numbers))))) )  =>  ((m2_integr15 D A B C) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (m1_integr15 (k3_funct_2 k5_numbers (k3_finseq_2 k1_numbers) D E) A B (k2_integra2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k3_finseq_2 k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k2_numbers))))) )  =>  ((m2_integr16 D A B C) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (m1_integr16 (k3_funct_2 k5_numbers (k3_finseq_2 k2_numbers) D E) A B (k2_integra2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (u1_struct_0 A)))))) )  =>  ((m2_integr18 E A B C D) <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (m1_integr18 (k8_nat_1 (k3_finseq_2 (u1_struct_0 A)) E F) A B C (k2_integra2 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((v1_integr1c A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 k1_numbers)) &  ((r1_xxreal_0 B C) &  ( ((k1_rcomp_1 B C) = (k1_relset_1 k1_numbers A))  &  ((r1_tarski (k1_rcomp_1 B C) (k1_relset_1 k1_numbers D)) &  ((r1_tarski (k1_rcomp_1 B C) (k1_relset_1 k1_numbers E)) &  ((v3_rcomp_1 F) &  ((r1_tarski (k1_rcomp_1 B C) F) &  ((r2_fdiff_1 D F) &  ((r2_fdiff_1 E F) &  ((v1_fcont_1 (k2_fdiff_1 D F)) &  ((v1_fcont_1 (k2_fdiff_1 E F)) & (r2_relset_1 k1_numbers k2_numbers A (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers D (k25_valued_1 k1_numbers k1_numbers E k7_complex1)) (k1_rcomp_1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( (B = (k1_integra1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m1_integra1 C A)) ) ) ) ) ) ).
tt(d3_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k4_integra2 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_integra1 A B (k2_integra2 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_integra5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k3_integra5 A B) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(d3_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k2_integra9 A B) = (k7_square_1 (k1_integra9 A B B))) ) ) ) ) ).
tt(d3_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k3_interva1 A B C) = (k3_setfam_1 B C)) ) ) ) ) ) ) ).
tt(d3_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k3_irrat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k3_xcmplx_0 (k6_newton C A) (k3_power A (k4_xcmplx_0 C)))) ) ) ) ) ) ) ) ).
tt(d3_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) <=>  ((v2_funct_1 C) &  ((k2_relset_1 (u4_struct_0 B) C) = (u4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(d3_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k4_isocat_2 A B C D E) = (k1_partfun1 (u1_struct_0 B) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) (k7_isocat_1 B) (k3_isocat_2 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ( ((k2_pre_topc A (k1_tops_1 A B)) = (k2_pre_topc A B))  &  ((k1_tops_1 A (k2_pre_topc A B)) = (k1_tops_1 A B)) ) ) ) ) ) ) ).
tt(d3_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_jgraph_1 A B C) <=>  ( ((k1_funct_1 B 1) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 C (k3_finseq_1 C)))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_jgraph_1 A B))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) &  (? [F:$i] :  ( ((v7_graph_1 F (k1_jgraph_1 A)) &  ((v3_graph_2 F (k1_jgraph_1 A)) & (m2_graph_1 F (k1_jgraph_1 A))) )  &  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k1_jgraph_1 A))) &  ( ((k15_finseq_1 D) = F)  &  ( ((k15_finseq_1 E) = C)  &  ( (G = C)  & (r3_graph_4 (k1_jgraph_1 A) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (B = (k3_jgraph_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B C) = (k2_jgraph_4 A C)) ) ) ) ) ) ) ) ).
tt(d3_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_jgraph_6 A B C D) = (a_4_2_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d3_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (C = (k3_jordan11 A B))  <=>  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 A B))) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k2_nat_1 (k4_nat_1 (k13_newton 2 (k7_nat_d B (k1_jordan11 A))) (k7_nat_d (k2_jordan11 A) 2)) 2)))  => (r1_tarski (k3_goboard5 (k1_jordan8 A B) (k7_nat_d (k3_jordan1h A B) 1) D) (k1_jordan2c 2 A))) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A B))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 D E) & (r1_xxreal_0 E (k2_nat_1 (k4_nat_1 (k13_newton 2 (k7_nat_d B (k1_jordan11 A))) (k7_nat_d (k2_jordan11 A) 2)) 2)))  => (r1_tarski (k3_goboard5 (k1_jordan8 A B) (k7_nat_d (k3_jordan1h A B) 1) E) (k1_jordan2c 2 A))) ) ) )  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((r1_jordan18 A B C D E F) <=>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r1_topreal1 (k15_euclid A) C D G) &  ((r1_tarski G B) & (r1_xboole_0 G (k2_tarski E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k3_jordan19 A) = (k1_kurato_2 (k15_euclid 2) (k1_jordan19 A))) ) ) ).
tt(d3_jordan1h,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A B)) C))  & (r1_tarski (k3_goboard5 (k1_jordan8 A B) (k7_nat_d (k3_jordan1h A B) 1) C) (k1_jordan2c 2 A))) ) ) ) ) ) ) ) ).
tt(d3_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r3_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 E (k17_euclid F)))  &  ((r1_jordan5c A B C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C G F) & (r1_jordan5c A B C D G))  => (r1_xxreal_0 (k17_euclid G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k2_jordan21 A) = (k19_euclid (k10_real_1 (k7_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) 2) (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) 2))))))) ) ) ).
tt(d3_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ( (~  ((k3_finseq_1 A) = 2) )  =>  ((v3_jordan23 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  &  ((k1_funct_1 A B) = (k1_funct_1 A (k2_nat_1 B 1))) ) ) ) ) ) ) )  &  ( ((k3_finseq_1 A) = 2)  => (v3_jordan23 A)) ) ) ) ).
tt(d3_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (B = (k1_jordan24 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B C) = (k19_euclid (k3_complex1 (k2_complex2 (k2_xcmplx_0 (k17_euclid C) (k3_xcmplx_0 (k18_euclid C) k1_xcmplx_0)) A)) (k4_complex1 (k2_complex2 (k2_xcmplx_0 (k17_euclid C) (k3_xcmplx_0 (k18_euclid C) k1_xcmplx_0)) A)))) ) ) ) ) ) ) ) ).
tt(d3_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_jordan2c A B C) <=>  ((r3_connsp_1 (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B) C) &  (~ (v9_rltopsp1 C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(d3_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( (~  (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1))) )  =>  ((k2_jordan3 A B) = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1) (k3_finseq_1 A)))) )  &  ( (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1)))  =>  ((k2_jordan3 A B) = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1) (k3_finseq_1 A))) ) ) ) ) ) ) ).
tt(d3_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_jordan4 A B C D) <=>  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 A D))  &  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 B E) = (k1_funct_1 A (k1_jordan4 (k7_nat_d (k2_nat_1 (k3_finseq_1 A) C) E) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan5c A B C D E) <=>  ((r2_hidden D A) &  ((r2_hidden E A) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = B)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 F G) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  ( ((k1_funct_1 F H) = E)  &  ((r1_xxreal_0 k6_numbers H) & (r1_xxreal_0 H 1)) ) ) ) ) ) ) )  => (r1_xxreal_0 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k3_jordan5d A))  <=>  ((r2_hidden (k4_tarski (k3_finseq_1 (k2_goboard2 A)) B) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B) = (k23_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d3_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((k3_jordan6 A B C D) = (a_4_0_jordan6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d3_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((m1_jordan_a B A) <=>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k18_pscomp_1 A))  &  ((v2_funct_1 B) &  ((r1_xxreal_0 8 (k3_finseq_1 B)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) A) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) | (r1_jordan6 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1)))) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) (k2_nat_1 C 1)) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 2)))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1)))) ) ) ) )  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 2))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k7_nat_d (k3_finseq_1 B) 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  &  ((r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k7_nat_d (k3_finseq_1 B) 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 2))) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((r1_gobrd10 C D) | (r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 D 1))))) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) (k2_nat_1 C 1)))  &  (~ (r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_jordan,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (A = k5_jordan)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers A B) = (k9_real_1 (k17_euclid (k1_jordan (k15_euclid 2) (k15_euclid 2) B)) (k17_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) B)))) ) ) ) ) ) ).
tt(d3_knaster,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  =>  ((k2_knaster A B) = (k3_tarski (a_2_1_knaster A B))) ) ) ) ).
tt(d3_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E D B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ((r1_kolmog01 A B C D E) <=>  (! [F:$i] :  ( ((v2_funct_1 F) & (m2_finseq_1 F D))  =>  ( (~  (F = k1_xboole_0) )  =>  ((k21_rvsum_1 (k4_finseqop D k1_numbers F (k1_partfun1 D B B k1_numbers E C))) = (k1_funct_1 C (k1_setfam_1 (k2_relset_1 B (k4_finseqop D B F E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 A) B (k2_nat_1 C 1)) (k3_funct_2 k5_numbers (k9_setfam_1 A) B C))) ) ) ) ) ) ).
tt(d3_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_kurato_1 A B) = (k4_enumset1 (k2_pre_topc A B) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))))))) ) ) ) ) ).
tt(d3_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((k2_lang1 A) = (a_1_1_lang1 A)) ) ) ).
tt(d3_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 B 1))) =>  ((r2_hidden A (k2_finseq_1 (k1_nat_1 B 1))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 B)) =>  ( (D = (k4_laplace A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 B)) =>  ( ( (~ (r1_xxreal_0 A E))  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 C A) (k1_funct_1 C E)))  =>  ((k1_funct_1 D E) = (k1_funct_1 C E)) )  &  ((r1_xxreal_0 (k1_funct_1 C A) (k1_funct_1 C E)) =>  ((k1_funct_1 D E) = (k6_xcmplx_0 (k1_funct_1 C E) 1)) ) ) )  &  ((r1_xxreal_0 A E) =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 C A) (k1_funct_1 C (k1_nat_1 E 1))))  =>  ((k1_funct_1 D E) = (k1_funct_1 C (k1_nat_1 E 1))) )  &  ((r1_xxreal_0 (k1_funct_1 C A) (k1_funct_1 C (k1_nat_1 E 1))) =>  ((k1_funct_1 D E) = (k6_xcmplx_0 (k1_funct_1 C (k1_nat_1 E 1)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k11_group_4 A)) (u1_struct_0 (k11_group_4 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_group_4 A)) (u1_struct_0 (k11_group_4 B)))))) )  =>  ( (D = (k3_latsubgr A B C))  <=>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (F = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 E)))  =>  ((k1_funct_1 D E) = (k5_group_4 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k2_lattice2 A B C D) = (k7_setwiseo A (u1_struct_0 B) (u2_lattices B) C D)) ) ) ) ) ) ) ) ) ).
tt(d3_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattice3 A B) = B) ) ) ) ) ).
tt(d3_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_lattice4 C A B) =>  ((r1_lattice4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_filter_0 A D E)) = (k4_filter_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((v1_relat_1 E) =>  (! [F:$i] :  ((v1_relat_1 F) =>  ((r1_lattice5 A B C D E F) <=>  ( ((k1_funct_1 B 1) = C)  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = D)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 1 G) =>  ((r1_xxreal_0 (k3_finseq_1 B) G) |  ( ( (~ (v1_abian G))  => (r2_hidden (k4_tarski (k1_funct_1 B G) (k1_funct_1 B (k2_nat_1 G 1))) E))  &  ((v1_abian G) => (r2_hidden (k4_tarski (k1_funct_1 B G) (k1_funct_1 B (k2_nat_1 G 1))) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_lattice6 A) <=> (v1_wellfnd1 (k3_lattice3 A))) ) ) ).
tt(d3_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k1_lattice7 A B))  <=>  ( (? [D:$i] :  ((m1_lattice7 D A (k3_yellow_0 A) B) &  (C = (k5_card_1 D)) ) )  &  (! [D:$i] :  ((m1_lattice7 D A (k3_yellow_0 A) B) => (r1_xxreal_0 (k5_card_1 D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d3_lattice8,ax, (! [A:$i] :  ((k1_lattice8 A) = (k2_xboole_0 A (k2_tarski (k1_tarski A) (k1_tarski (k1_tarski A))))) ) ).
tt(d3_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattices A B C) <=>  ((k1_lattices A B C) = C) ) ) ) ) ) ) ) ).
tt(d3_lfuzzy_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v1_orders_2 B) &  ((v1_lfuzzy_0 B) & (l1_orders_2 B)) )  =>  ( (B = (k1_lfuzzy_0 A))  <=>  ((u1_struct_0 B) = A) ) ) ) ) ) ).
tt(d3_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v1_lfuzzy_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k8_lfuzzy_0 A A B C C) = 1) ) ) ) ) ) ) ) ).
tt(d3_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_limfunc1 A) = (k4_xxreal_1 A k1_xxreal_0)) ) ) ).
tt(d3_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r3_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 B D))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d3_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r3_limfunc3 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 B E))  &  ((r2_hidden E (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden F (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k10_xtuple_0 C) (k6_subset_1 (k9_xtuple_0 A) (k1_tarski B)))) )  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d3_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k2_lmod_6 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(d3_lopban_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((k4_lopban_1 A B) = (k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ).
tt(d3_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_lopban_2 A B C) = (k2_binop_1 k1_numbers (k10_lopban_1 A A) (k10_lopban_1 A A) (k9_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) C B)) ) ) ) ) ) ) ).
tt(d3_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_lopban_3 B A) <=> (v1_series_1 (k4_normsp_0 A B))) ) ) ) ) ).
tt(d3_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k2_lopban_4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C A) =>  ((k8_nat_1 k1_numbers B C) = (k10_real_1 (k3_newton A) (k8_real_1 (k3_newton C) (k3_newton (k7_nat_d A C))))) )  &  ( (~ (r1_xxreal_0 C A))  =>  ((k8_nat_1 k1_numbers B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d3_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A))))) )  =>  ( (B = (k5_lopclset A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  ((k5_binop_1 (k1_lopclset A) B C D) = (k3_lopclset A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) )  =>  ( (B = (k3_lpspace1 A))  <=>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers B C D) (k7_rfunct_3 A k1_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(d3_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k2_lpspace2 A B C D) = (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(d3_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_lp_space A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_lp_space A) k1_numbers)))) )  =>  ( (B = (k3_lp_space A))  <=>  (! [C:$i] :  ((r2_hidden C (k2_lp_space A)) =>  ((k1_seq_1 B C) = (k4_power (k4_series_1 (k1_lp_space (k2_rsspace C) A)) (k10_real_1 1 A))) ) ) ) ) ) ) ) ).
tt(d3_ltlaxio1,ax, (k3_ltlaxio1 = (k1_ltlaxio1 k2_hilbert1)) ).
tt(d3_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A B C) = (a_3_1_mathmorp A B C)) ) ) ) ) ) ) ).
tt(d3_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v3_matrix10 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) => (r1_xxreal_0 (k3_matrix_1 k1_numbers A B C) k6_numbers)) ) ) ) ) ) ) ) ).
tt(d3_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D B C) =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  (! [G:$i] :  ((m1_matrix_1 G D B C) =>  ( ( ((k3_finseq_1 F) = (k1_matrix_1 E))  =>  ( (G = (k3_matrix11 A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 G) = (k1_matrix_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden (k4_tarski H I) (k2_matrix_1 E)) =>  ( ( (~  (H = A) )  =>  ((k3_matrix_1 D G H I) = (k3_matrix_1 D E H I)) )  &  ( (H = A)  =>  ((k3_matrix_1 D G A I) = (k1_funct_1 F I)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k3_finseq_1 F) = (k1_matrix_1 E)) )  =>  ( (G = (k3_matrix11 A B C D E F))  <=>  (G = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 C) A B) =>  ( (H = (k3_matrix12 A B C D E F G))  <=>  ( ((k3_finseq_1 H) = (k3_finseq_1 D))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ( ((r2_hidden I (k4_finseq_1 D)) & (r2_hidden J (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (I = E)  =>  ((k3_matrix_1 (u1_struct_0 C) H I J) = (k1_algstr_0 C (k8_group_1 C G (k3_matrix_1 (u1_struct_0 C) D F J)) (k3_matrix_1 (u1_struct_0 C) D E J))) )  &  ( (~  (I = E) )  =>  ((k3_matrix_1 (u1_struct_0 C) H I J) = (k3_matrix_1 (u1_struct_0 C) D I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ((k5_card_1 C) = (k5_card_1 D))  =>  ((k7_matrix13 A B C D) = (k6_matrix13 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_matrix14 A B C) = (k2_finseq_7 (k3_finseq_2 (u1_struct_0 A)) (k12_matrix_1 A B) 1 C)) ) ) ) ) ) ) ).
tt(d3_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ((k4_matrix15 A B C) = (a_3_0_matrix15 A B C)) ) ) ) ) ) ) ).
tt(d3_matrix16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v2_matrix16 B A) <=>  (? [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) & (r1_matrix16 A C B)) ) ) ) ) ) ) ).
tt(d3_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_matrix_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 A) k1_xboole_0))  =>  ( (B = (k1_matrix_1 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((r2_hidden C (k10_xtuple_0 A)) &  ((k3_finseq_1 C) = B) ) ) ) ) )  &  ((r1_xxreal_0 (k3_finseq_1 A) k1_xboole_0) =>  ( (B = (k1_matrix_1 A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d3_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_2 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((r1_xxreal_0 D E) |  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( (D = (k3_matrix_3 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k3_rlvect_1 A (k3_matrix_1 (u1_struct_0 A) B E F) (k3_matrix_1 (u1_struct_0 A) C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((k3_matrix_5 A B) = (k2_matrix_5 (k3_matrix_3 k1_complfld (k1_matrix_5 A) (k1_matrix_5 B)))) ) ) ) ) ).
tt(d3_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) <=>  (? [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) & (r2_matrix_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d3_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v3_matrix_8 C A B) <=>  ((k4_matrix_6 A B C C) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(d3_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( (C = (k8_matrixj1 A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k3_finseq_1 (k2_matrixj1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrixj2 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ((m1_matrixj2 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((k14_matrixj1 (u1_struct_0 A) C D) = (k2_matrixj2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k3_matrixr1 A B) = (k2_matrixr1 (k3_matrix_3 k2_vectsp_1 (k1_matrixr1 A) (k1_matrixr1 B)))) ) ) ) ) ).
tt(d3_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k5_matrixr2 A) = (k8_matrixr1 A A)) ) ) ).
tt(d3_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( (G = (k4_matrlin2 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) G H) = (k4_rlvect_1 C (k5_matrlin A C (k8_matrix_1 (u1_struct_0 A) (k4_matrix_3 A (k2_matrix15 (u1_struct_0 A) (k9_matrlin A B D H)) F) 1) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( (F = (k3_matrlin A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) F G) = (k1_algstr_0 C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_matroid0 A) <=> (v1_classes1 (k1_matroid0 A))) ) ) ).
tt(d3_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k5_matrprob A) = (k18_rvsum_1 (k3_matrprob A))) ) ) ).
tt(d3_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) )  =>  ( ( (~  (A = k6_numbers) )  =>  ( (D = (k3_matrtop1 A B C))  <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E A) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  =>  ((k1_funct_1 D E) = (k8_matrix_1 (u1_struct_0 k2_vectsp_1) (k4_matrix_3 k2_vectsp_1 (k2_matrix15 (u1_struct_0 k2_vectsp_1) (k1_matrtop1 E)) C) 1)) ) ) ) )  &  ( (A = k6_numbers)  =>  ( (D = (k3_matrtop1 A B C))  <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E A) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  =>  ((k1_funct_1 D E) = (k4_struct_0 (k15_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D A))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ( ((v1_matrix_6 E A k2_vectsp_1) & (m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A A))  =>  ( (E = (k2_matrtop3 A B C D))  <=>  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E C C) = (k20_sin_cos B))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E D D) = (k20_sin_cos B))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E C D) = (k17_sin_cos B))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E D C) = (k4_xcmplx_0 (k17_sin_cos B)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 E)) =>  ( ( (F = G)  =>  ( (F = C)  |  ( (F = D)  |  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E F F) = (k5_struct_0 k2_vectsp_1)) ) ) )  &  (~  ( (~  (F = G) )  &  ( (~  ((k4_matrix13 F G) = (k4_matrix13 C D)) )  &  (~  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E F G) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_mazurulm C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_rlvect_1 A (k1_algstr_0 A D E) (k18_binop_2 1 2))) = (k1_rlvect_1 B (k1_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) (k18_binop_2 1 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  =>  ((v2_measure1 C A B) <=>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_xboole_0 D E) =>  ((k12_supinf_2 C (k1_finsub_1 B D E)) = (k3_supinf_2 (k12_supinf_2 C D) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (D = (k2_measure3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F B) &  (? [G:$i] :  ((m1_measure3 G A B C) &  (E = (k2_xboole_0 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_measure4 A B) k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_measure4 A B) k7_numbers)))) )  =>  ( (C = (k3_measure4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D (k1_measure4 A B)) =>  ((k12_supinf_2 C D) = (k12_supinf_2 B D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_measure5 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (? [C:$i] :  ((v1_xreal_0 C) &  (A = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ).
tt(d3_measure6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_setfam_1 B) (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 B) (k9_setfam_1 A))))) )  =>  ( (D = (k3_measure6 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ((k3_funct_2 (k1_zfmisc_1 B) (k9_setfam_1 A) D E) = (k8_relset_1 A B C E)) ) ) ) ) ) ) ) ) ) ).
tt(d3_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 k1_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 k1_numbers)))))) )  =>  ((m2_measure7 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (m1_measure7 (k8_nat_1 (k9_funct_2 k5_numbers (k9_setfam_1 k1_numbers)) B C) (k8_nat_1 (k9_setfam_1 k1_numbers) A C))) ) ) ) ) ) ) ).
tt(d3_measure8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v2_finsub_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m2_measure8 D A C) =>  ((m3_measure8 D A B C) <=> (r1_tarski B (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) D)))) ) ) ) ) ) ) ) ).
tt(d3_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  ((k6_member_1 A) = (a_1_2_member_1 A)) ) ) ).
tt(d3_membered,ax, (! [A:$i] :  ((v3_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_xreal_0 B)) ) ) ) ).
tt(d3_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (E = (k1_mesfun6c A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (F = (k1_mesfunc6 A B C (k5_comseq_3 A D)))  &  ( (G = (k1_mesfunc6 A B C (k6_comseq_3 A D)))  &  (E = (k2_xcmplx_0 F (k3_xcmplx_0 G k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k3_mesfun7c A B) = (k2_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d3_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( (C = (k3_mesfun9c A B))  <=>  ((r2_relset_1 A k2_numbers (k4_mesfunc5 A k2_numbers C k6_numbers) (k4_mesfunc5 A k2_numbers B k6_numbers)) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k2_numbers (k4_mesfunc5 A k2_numbers C (k1_nat_1 D 1)) (k2_valued_1 A k2_numbers k2_numbers (k4_mesfunc5 A k2_numbers C D) (k4_mesfunc5 A k2_numbers B (k1_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ).
tt(d3_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (D = (k3_mesfunc1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k6_subset_1 (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)) (k2_xboole_0 (k3_xboole_0 (k8_relat_1 B (k1_tarski k2_supinf_1)) (k8_relat_1 C (k1_tarski k1_supinf_1))) (k3_xboole_0 (k8_relat_1 B (k1_tarski k1_supinf_1)) (k8_relat_1 C (k1_tarski k2_supinf_1))))))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k12_supinf_2 D E) = (k3_supinf_2 (k12_supinf_2 B E) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k2_mesfunc2 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k1_extreal2 (k2_supinf_2 (k12_supinf_2 B D)) k1_supinf_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mesfunc5,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_mesfunc5 A) <=>  (~ (r2_hidden k2_supinf_1 (k10_xtuple_0 A))) ) ) ) ).
tt(d3_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k1_mesfunc6 A B C D) = (k7_mesfunc5 A B C (k1_mesfunc5 A D))) ) ) ) ) ) ) ) ) ).
tt(d3_mesfunc7,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_mesfunc7 A B) = (k2_mesfunc7 (k5_finseq_2 k7_numbers B A))) ) ) ) ) ).
tt(d3_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k1_mesfunc8 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k2_rinfsup2 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mesfunc9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((k3_mesfunc9 A) = (k2_mesfunc5 (k2_mesfunc9 A))) ) ) ).
tt(d3_metric_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ((v3_metric_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k1_metric_1 A A B C D) = k6_numbers)  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(d3_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_metric_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k1_metric_2 A C)) ) ) ) ) ) ) ) ).
tt(d3_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tbsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski B (k9_metric_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d3_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_metrizts A B C D) <=>  (? [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  &  (? [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski B E) &  ((r1_tarski C F) &  ((r1_xboole_0 E F) &  (D = (k3_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_mfold_1 A) = (k1_mfold_1 A (k4_struct_0 (k15_euclid A)) 1)) ) ) ).
tt(d3_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k3_mfold_2 A B C) = (k1_pre_topc (k15_euclid A) (k2_mfold_2 A B C))) ) ) ) ) ) ) ).
tt(d3_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  ((v2_midsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k1_midsp_1 A B B) = B)  &  ( ((k1_midsp_1 A B C) = (k1_midsp_1 A C B))  &  ( ((k1_midsp_1 A (k1_midsp_1 A B C) (k1_midsp_1 A D E)) = (k1_midsp_1 A (k1_midsp_1 A B D) (k1_midsp_1 A C E)))  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k1_midsp_1 A F B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((r1_midsp_2 A B C) <=>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F A) &  ((k2_binop_1 A A (u1_struct_0 B) C D F) = E) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k2_binop_1 A A (u1_struct_0 B) C D E) = (k2_binop_1 A A (u1_struct_0 B) C D F))  =>  (E = F) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_algstr_0 B (k2_binop_1 A A (u1_struct_0 B) C D E) (k2_binop_1 A A (u1_struct_0 B) C E F)) = (k2_binop_1 A A (u1_struct_0 B) C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  ((v2_midsp_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  ( (! [G:$i] :  ((m1_midsp_3 G A) =>  ((k3_midsp_1 B C (k5_midsp_3 A (u1_struct_0 B) F G)) = (k3_midsp_1 B D (k5_midsp_3 A (u1_struct_0 B) E G))) ) )  =>  ((k3_midsp_1 B C (k4_midsp_3 A B D F)) = (k3_midsp_1 B D (k4_midsp_3 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k3_mmlquery A B C) = (k1_setfam_1 (a_3_0_mmlquery A B C))) ) ) ) ) ) ).
tt(d3_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((l1_mod_2 B A) =>  ((k2_mod_2 A B) = (u1_mod_2 A B)) ) ) ) ) ).
tt(d3_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v2_mod_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) & (v1_mod_3 C A B)) ) ) ) ) ) ) ).
tt(d3_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B))))) )  =>  ((k4_mod_4 A B C) = (k1_mod_4 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(d3_modal_1,ax, (k3_modal_1 = (k8_mcart_1 k5_numbers k1_numbers (k6_domain_1 k5_numbers 3) k5_numbers)) ).
tt(d3_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m3_modcat_1 D A) =>  ((m5_modcat_1 D A B C) <=>  (! [E:$i] :  ((m4_modcat_1 E A D) =>  ((v2_mod_2 E A) & (m1_mod_2 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_modelc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) =>  ((k3_modelc_1 A B C) = (k1_funct_1 A B)) )  &  ( (~ (r2_hidden B (k9_xtuple_0 A)))  =>  ((k3_modelc_1 A B C) = C) ) ) ) ) ) ) ).
tt(d3_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k3_modelc_2 A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers k6_numbers) A)) ) ) ).
tt(d3_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_2 A) =>  ((k4_modelc_3 A) = k1_xboole_0) )  &  ( ((v5_modelc_2 A) =>  ((k4_modelc_3 A) = k1_xboole_0) )  &  ( ((v6_modelc_2 A) =>  ((k4_modelc_3 A) = (k1_tarski (k10_modelc_2 A))) )  &  ( ((v7_modelc_2 A) =>  ((k4_modelc_3 A) = (k1_tarski A)) )  &  ( ((v8_modelc_2 A) =>  ((k4_modelc_3 A) = (k1_tarski A)) )  &  (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  ( (~ (v8_modelc_2 A))  &  (~  ((k4_modelc_3 A) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((v1_moebius1 A) =>  ( (B = (k2_moebius1 A))  <=>  (B = k6_numbers) ) )  &  ( (~ (v1_moebius1 A))  =>  ( (B = (k2_moebius1 A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  &  ( (C = A)  &  (B = (k2_newton (k1_real_1 1) (k5_card_1 (k1_polynom2 k10_newton (k13_nat_3 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v3_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E A) &  ((k5_binop_1 A B E C) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_group_1 A) =>  ((k9_monoid_1 A B) = (g4_algstr_0 (k9_funct_2 B (u1_struct_0 A)) (k8_monoid_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) B) (k5_monoid_1 (u1_struct_0 A) B (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A))))) )  &  ( (~ (v1_group_1 A))  =>  ((k9_monoid_1 A B) = (g3_algstr_0 (k9_funct_2 B (u1_struct_0 A)) (k8_monoid_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) B))) ) ) ) ) ) ).
tt(d3_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (C = (k4_morph_01 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) C D) = (k1_morph_01 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) & (l3_msualg_1 B A))  =>  ( (B = (k2_msafree1 A))  <=>  (! [C:$i] :  ((r2_hidden C (u1_struct_0 A)) =>  ((k1_funct_1 (u3_msualg_1 A B) C) = (k1_tarski C)) ) ) ) ) ) ) ) ).
tt(d3_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((k3_msafree2 A) = (k2_relset_1 (u1_struct_0 A) (u2_msualg_1 A))) ) ) ).
tt(d3_msafree3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_relat_1 C))  =>  ((k3_msafree3 A B C) = (k3_pboole (u1_struct_0 A) B (k2_msafree3 A C))) ) ) ) ) ) ) ).
tt(d3_msafree,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_msafree A B))  <=>  ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k2_msafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_orders_2 A F E) =>  ((k1_msalimit A B C D E F) = (k1_binop_1 D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((k4_msaterm A B C D E) = (k1_trees_4 (k4_tarski E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_msscyc_2 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_msscyc_2 A) (u1_struct_0 A))))) )  =>  ( (B = (k3_msscyc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C (k1_msscyc_2 A)) =>  ((k1_funct_1 B C) = (k1_funct_1 (u2_msualg_1 A) (k1_xtuple_0 C))) ) ) ) ) ) ) ) ).
tt(d3_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v2_mssubfam C A B) <=>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  ((r2_pboole A D C) => (r1_pboole A (k2_mboolean A D) C)) ) ) ) ) ) ) ) ) ).
tt(d3_msualg_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l2_msualg_1 B A) =>  ((v4_msualg_1 B A) <=> (v2_relat_1 (u3_msualg_1 A B))) ) ) ) ) ).
tt(d3_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C))) =>  ( ( (~  ((k1_funct_1 (u3_msualg_1 A B) C) = k1_xboole_0) )  =>  ( (D = (k1_msualg_2 A B C))  <=>  (? [E:$i] :  ( (~ (v1_xboole_0 E))  &  ( (E = (k1_funct_1 (u3_msualg_1 A B) C))  &  (D = (a_4_0_msualg_2 A B C E)) ) ) ) ) )  &  ( ((k1_funct_1 (u3_msualg_1 A B) C) = k1_xboole_0)  =>  ( (D = (k1_msualg_2 A B C))  <=>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((v2_msualg_3 D A B C) <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k10_xtuple_0 (k1_funct_1 D E)) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v2_msualg_4 C A B) <=> (v1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(d3_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C A B B) =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  ( (D = (k3_msualg_5 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_relset_1 (k1_funct_1 B E) (k1_funct_1 B E) (k1_msualg_4 A B B D E) (k1_msualg_5 (k1_funct_1 B E) (k1_msualg_4 A B B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k3_msualg_6 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  (? [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) &  ( ((k2_msualg_1 A E) = D)  &  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r2_hidden F (k4_finseq_1 (k1_msualg_1 A E))) &  ((k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A E) F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v2_msualg_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (r2_hidden (k15_lattice3 A C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d3_msualg_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_msualg_5 (k1_funct_1 B C))))) =>  ( (E = (k3_msualg_8 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v1_msualg_4 G A B) & (m1_msualg_4 G A B B))  &  ( (F = (k1_msualg_4 A B B G C))  & (r2_hidden G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k6_msualg_1 A) = (k6_msualg_1 B))  =>  ((k2_msuhom_1 A B C) = (k16_funcop_1 k6_numbers C)) ) ) ) ) ) ) ) ).
tt(d3_mycielsk,ax, (! [A:$i] :  ( ((v1_mycielsk A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k2_mycielsk A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v6_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v6_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A))) )  => (r1_xxreal_0 B (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(d3_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ((v3_nagata_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_pcomps_1 (k1_nagata_1 A B C) A)) ) ) ) ) ) ) ).
tt(d3_nagata_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( (D = (k3_nagata_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k1_numbers D E) = (k5_seq_4 (k7_relset_1 A k1_numbers (k2_nagata_2 A B E) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_nat_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) )  =>  ( (C = (k9_nat_1 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 C D) = (k1_funct_1 A (k2_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ).
tt(d3_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k5_nat_3 A B C))  <=>  (! [E:$i] :  ( ((r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E)) =>  ((k1_funct_1 D E) = (k1_seq_1 B E)) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E)))  =>  ((k1_funct_1 D E) = (k1_seq_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (B = (k4_nat_5 A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_recdef_1 B C) = (k3_nat_5 A C)) ) ) ) ) ) ) ) ).
tt(d3_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A B) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (B = (k3_xcmplx_0 A C)) ) ) ) ) ) ) ) ).
tt(d3_nat_lat,ax, (k3_nat_lat = (g3_lattices k5_numbers k2_nat_lat k1_nat_lat)) ).
tt(d3_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 B))))) )  =>  ((m1_nattra_1 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (m1_cat_1 (k3_funct_2 (u1_struct_0 A) (u4_struct_0 B) E F) B (k8_cat_1 A B C F) (k8_cat_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_ncfcont1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) & (v9_clvect_1 C A))  => (r2_hidden (k7_clvect_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d3_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_ncfcont2 A B C D) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ((r2_hidden G A) &  ((r2_hidden H A) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B G H))))  & (r1_xxreal_0 E (k1_normsp_0 C (k5_algstr_0 C (k7_partfun1 (u1_struct_0 C) D G) (k7_partfun1 (u1_struct_0 C) D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k2_ndiff_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_rlvect_1 A B (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_ndiff_2 A B C D E) <=>  (? [F:$i] :  ((m1_nfcont_1 F A D) &  ((r1_tarski F (k1_relset_1 (u1_struct_0 A) C)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I (k18_complex1 J)))  &  ( (~  (J = k6_numbers) )  &  ((r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A E J) D) F) & (r1_xxreal_0 H (k1_normsp_0 B (k5_algstr_0 B (k1_rlvect_1 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 A (k1_rlvect_1 A E J) D)) (k7_partfun1 (u1_struct_0 B) C D)) (k2_real_1 J)) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_ndiff_3 A B C) <=>  (? [D:$i] :  ((m1_rcomp_1 D C) &  ((r1_tarski D (k1_relset_1 k1_numbers B)) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_ndiff_3 F A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B G) (k7_partfun1 (u1_struct_0 A) B C)) = (k3_rlvect_1 A (k3_funct_2 k1_numbers (u1_struct_0 A) E (k10_binop_2 G C)) (k7_partfun1 (u1_struct_0 A) F (k10_binop_2 G C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((r2_ndiff_4 A B C) <=>  ((r1_tarski C (k1_relset_1 k1_numbers B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) => (r1_ndiff_4 A (k2_partfun1 k1_numbers (k1_euclid A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)))))) )  =>  ( (C = (k3_ndiff_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  ((k1_funct_1 C D) = (k1_ndiff_5 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_neckla_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k2_neckla_2 A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ((u1_orders_2 C) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (u1_orders_2 A) (u1_orders_2 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(d3_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_neckla_3 A B) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_msualg_5 (u1_struct_0 A) (u1_orders_2 A)) B)) ) ) ) ) ).
tt(d3_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_necklace A) <=> (r3_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d3_net_1,ax, (! [A:$i] :  ((l1_petri A) =>  ((k2_net_1 A) = (k2_xboole_0 (u1_struct_0 A) (u4_struct_0 A))) ) ) ).
tt(d3_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((r1_xxreal_0 A B) =>  ( (C = (k4_newton A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k6_xcmplx_0 B A))  =>  (C = (k10_real_1 (k3_newton B) (k8_real_1 (k3_newton A) (k3_newton D)))) ) ) ) ) )  &  ( (~ (r1_xxreal_0 A B))  =>  ( (C = (k4_newton A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(d3_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_nfcont_1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) & (v3_normsp_1 C A))  => (r2_hidden (k6_normsp_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d3_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v1_nfcont_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E))) (k8_real_1 C (k1_normsp_0 A (k5_algstr_0 A D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((v2_nfcont_3 B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r2_hidden D (k1_relset_1 k1_numbers B)) & (r2_hidden E (k1_relset_1 k1_numbers B)))  => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B E))) (k4_real_1 C (k18_complex1 (k6_xcmplx_0 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ( (D = (k2_nfcont_4 A B C))  <=>  ( ((k1_relset_1 B D) = (k1_relset_1 B C))  &  (! [E:$i] :  ((r2_hidden E (k1_relset_1 B D)) =>  ((k7_partfun1 (k1_euclid A) D E) = (k6_euclid A (k7_partfun1 (k1_euclid A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((k2_normform A B C D) = (k1_domain_1 A B (k3_finsub_1 A (k2_domain_1 A B C) (k2_domain_1 A B D)) (k3_finsub_1 B (k3_domain_1 A B C) (k3_domain_1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(d3_normsp_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (D = (k3_normsp_0 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 C))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k1_normsp_0 B (k7_partfun1 (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k3_normsp_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k3_normsp_2 A) = (k3_pcomps_1 (k2_normsp_2 A))) ) ) ).
tt(d3_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  ( (C = (k3_ntalgo_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ( (D = (k6_int_1 A B))  =>  ( ( ((k3_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D)) = 1)  =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers (k2_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D))))  &  (! [E:$i] :  ((m1_subset_1 E k4_numbers) =>  (~  ( (E = (k2_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D)))  &  (C = (k2_xcmplx_0 B E)) ) ) ) ) ) )  &  ((r1_xxreal_0 k6_numbers (k2_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D))) =>  (C = (k2_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D))) ) ) )  &  ( (~  ((k3_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 B D)) = 1) )  =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_numbers,ax, (k3_numbers = (k6_subset_1 (k2_xboole_0 k5_arytm_3 (k2_zfmisc_1 (k1_tarski k1_xboole_0) k5_arytm_3)) (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0)))) ).
tt(d3_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A))))) )  =>  ( (B = (k5_openlatt A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A)) =>  ((k5_binop_1 (k1_openlatt A) B C D) = (k3_openlatt A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v1_oposet_1 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (u1_robbins1 A)) & (v1_partit_2 B)) ) ) ) ) ) ).
tt(d3_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  ((k4_oppcat_1 A B) = (k3_oppcat_1 (k2_oppcat_1 A) B)) ) ) ) ) ).
tt(d3_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_orders_1 A) <=>  ((v1_relat_2 A) & (v8_relat_2 A)) ) ) ) ).
tt(d3_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v4_orders_2 A) <=> (r8_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d3_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_orders_3 A) <=> (v2_orders_3 (k2_struct_0 A) A)) ) ) ).
tt(d3_orders_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_orders_4 A B C) <=>  ( ((k2_xboole_0 B C) = (u1_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  => (r2_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ordinal1,ax, (! [A:$i] :  ((v2_ordinal1 A) <=>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r2_hidden B C))  &  ( (~  (B = C) )  &  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_ordinal2,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k3_ordinal2 A))  <=>  ((r1_tarski (k2_ordinal1 A) B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_tarski (k2_ordinal1 A) C) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ).
tt(d3_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((k3_ordinal4 A) = 1) ) ) ).
tt(d3_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  ((v1_o_ring_1 (k7_partfun1 (u1_struct_0 A) B 1) A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v1_o_ring_1 D A) &  ((k7_partfun1 (u1_struct_0 A) B (k1_nat_1 C 1)) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B F E))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  ( (~ (r1_orders_2 B H E))  &  (~ (r1_orders_2 B H C)) ) ) )  =>  ( (G = (k2_ortsp_1 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B H E))  &  ( (~ (r1_orders_2 B H C))  &  (~  (G = (k8_group_1 A (k8_group_1 A (k1_ortsp_1 A B E F H) (k1_ortsp_1 A B H E C)) (k1_ortsp_1 A B C H D))) ) ) ) ) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B H E))  &  (~ (r1_orders_2 B H C)) ) ) ) )  =>  ( (G = (k2_ortsp_1 A B C D E F))  <=>  (G = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v2_osafree B A) <=>  (? [C:$i] :  ((m1_osafree C A B) & (v1_osafree C A B)) ) ) ) ) ) ) ).
tt(d3_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  ((v5_osalg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((r1_osalg_1 A B C) &  ( ((k1_msualg_1 A B) = (k1_msualg_1 A C))  &  ((k2_msualg_1 A B) = (k2_msualg_1 A C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d3_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_osalg_2 A B C) = (k3_tarski (a_3_0_osalg_2 A B C))) ) ) ) ) ) ) ).
tt(d3_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (B = (k1_osalg_4 A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  ((r2_hidden C (u1_struct_0 A)) &  ((r2_hidden D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 E) 1))  &  ( ((k1_funct_1 E 1) = C)  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = D)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 2 F) &  ((r1_xxreal_0 F (k3_finseq_1 E)) &  ( (~ (r2_hidden (k4_tarski (k1_funct_1 E F) (k1_funct_1 E (k6_xcmplx_0 F 1))) (u1_orders_2 A)))  &  (~ (r2_hidden (k4_tarski (k1_funct_1 E (k6_xcmplx_0 F 1)) (k1_funct_1 E F)) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))))) )  =>  ( (B = (k3_parsp_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k3_funct_2 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) B C) = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k4_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k4_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k4_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)))) ) ) ) ) ) ) ) ).
tt(d3_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) <=>  ( (~ (r1_parsp_2 A B C D))  &  ((r1_parsp_1 A B C D E) & (r1_parsp_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_partfun1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  ( (D = E)  &  ((r1_tarski (k9_xtuple_0 E) A) & (r1_tarski (k10_xtuple_0 E) B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_partfun3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_partfun3 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k10_xtuple_0 A)) => (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ).
tt(d3_partit1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_partit1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m1_eqrel_1 C A)) ) ) ) ) ).
tt(d3_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_partit_2 B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A B (k3_funct_2 A A B C)) = C) ) ) ) ) ) ) ) ).
tt(d3_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v3_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_diraf A B E C F) &  ((r2_diraf A B E D G) &  ((r1_diraf A B C D) & (r3_diraf A E F G)) ) )  =>  ((r3_diraf A B C E) | (r1_diraf A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pboole,ax, (! [A:$i] :  ((k1_pboole A) = (k7_funcop_1 A k1_xboole_0)) ) ).
tt(d3_pcomps_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_pcomps_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 C A) &  ((m1_setfam_1 C (u1_struct_0 A)) &  ((r1_setfam_1 C B) & (v1_pcomps_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)))) =>  ( (G = (k3_pcs_0 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  (! [K:$i] :  ((m1_subset_1 K D) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D) (k1_domain_1 A C H J) (k1_domain_1 B D I K)) G) <=>  ((r2_hidden (k1_domain_1 A B H I) E) | (r2_hidden (k1_domain_1 C D J K) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pdiff_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((k3_pdiff_1 A B) = (k3_relat_1 B (k2_funct_1 (k1_pdiff_1 1 1)))) ) ) ) ) ).
tt(d3_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((r2_pdiff_2 A B) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid 2) A)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  ((r2_hidden C B) => (r3_pdiff_1 2 2 (k2_partfun1 (k1_euclid 2) k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d3_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r2_pdiff_3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  &  (? [E:$i] :  ((m1_rcomp_1 E D) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B))) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v3_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B) H) (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B) D)) = (k7_real_1 (k1_seq_1 F (k9_real_1 H D)) (k1_seq_1 G (k9_real_1 H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((r3_pdiff_4 A B) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid 3) A)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C B) => (r3_pdiff_1 3 3 (k2_partfun1 (k1_euclid 3) k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d3_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v1_pdiff_7 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) &  ( (C = B)  & (v3_nfcont_1 C (k4_real_ns1 A))) ) ) ) ) ) ) ) ).
tt(d3_pdiff_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) k1_numbers))))  =>  ((r2_pdiff_9 A B C) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  ((r2_hidden D A) => (r1_pdiff_7 B (k2_partfun1 (k1_euclid B) k1_numbers C A) D)) ) ) ) ) ) ) ) ) ).
tt(d3_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_pencil_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r1_pencil_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_pencil_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_pencil_2 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k1_funct_1 D 1))  &  ( (C = (k1_funct_1 D (k3_finseq_1 D)))  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E (k2_relset_1 (k1_zfmisc_1 (u1_struct_0 A)) D)) =>  ((v1_pencil_1 E A) & (v2_pencil_1 E A)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 D) E) | (r1_tarski 2 (k1_card_1 (k3_xboole_0 (k1_funct_1 D E) (k1_funct_1 D (k2_nat_1 E 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (D = (k2_pencil_3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k3_funct_2 A A D E) = F)  <=>  (! [G:$i] :  ((m1_pencil_2 G A B) =>  (! [H:$i] :  ( ( (~ (v13_pencil_1 H))  &  ((v16_pencil_1 H A) & (m3_pboole H A (k12_pralg_1 A B))) )  =>  (! [I:$i] :  ( ( (~ (v13_pencil_1 I))  &  ((v16_pencil_1 I A) & (m3_pboole I A (k12_pralg_1 A B))) )  =>  ( ( (G = (k4_card_3 H))  &  ( ((k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) C G) = (k4_card_3 I))  &  ((k3_pencil_1 A H) = E) ) )  =>  ((k3_pencil_1 A I) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k3_pencil_4 A B C D E) = (k8_subset_1 (k3_vectsp_5 A B) (k2_pencil_4 A B C D) (k2_vectsp_9 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_pepin A) = (k1_nat_1 (k2_newton 2 (k2_newton 2 A)) 1)) ) ) ).
tt(d3_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((k2_petri_2 A B) = (a_2_0_petri_2 A B)) ) ) ) ).
tt(d3_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A B C) <=>  (! [D:$i] :  ((r2_hidden D A) => (r1_xxreal_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(d3_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) =>  (! [C:$i] :  ((l1_polyalg1 C A) =>  ((m1_polyalg1 C A B) <=>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 B)) &  ( ((k5_struct_0 C) = (k5_struct_0 B))  &  ( ((k4_struct_0 C) = (k4_struct_0 B))  &  ( ((u1_algstr_0 C) = (k1_realset1 (u1_algstr_0 B) (u1_struct_0 C)))  &  ( ((u2_algstr_0 C) = (k1_realset1 (u2_algstr_0 B) (u1_struct_0 C)))  &  ((u1_vectsp_1 A C) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_vectsp_1 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k5_polyeq_1 A B C D) = (k3_xcmplx_0 A (k3_xcmplx_0 (k6_xcmplx_0 B C) (k6_xcmplx_0 B D)))) ) ) ) ) ) ) ) ) ).
tt(d3_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k7_polyeq_1 A B C D E) = (k3_binop_2 (k3_binop_2 (k3_binop_2 (k5_binop_2 A (k3_polyeq_3 E)) (k5_binop_2 B (k3_square_1 E))) (k5_binop_2 C E)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers)  =>  ( (D = (k3_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (F = (k1_polyeq_5 3 (k3_xcmplx_0 2 E)))  &  (D = (k8_complex1 (k11_complex1 (k10_complex1 (k13_complex1 F 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 F (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) )  &  ( (~  ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers) )  =>  ( (D = (k3_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) 9))  &  ( (F = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (G = (k1_polyeq_5 2 (k2_xcmplx_0 (k1_newton E 3) (k1_newton F 2))))  &  ( (H = (k1_polyeq_5 3 (k2_xcmplx_0 F G)))  &  ( (I = (k10_complex1 (k13_complex1 E H)))  &  (D = (k8_complex1 (k11_complex1 (k10_complex1 (k13_complex1 (k2_xcmplx_0 H I) 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 H I) (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polyform,ax, (! [A:$i] :  ((l1_polyform A) =>  ((v4_polyform A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 (u1_polyform A))))  =>  ( (~ (v1_xboole_0 (k1_funct_1 (u1_polyform A) B)))  & (v2_funct_1 (k1_funct_1 (u1_polyform A) B))) ) ) ) ) ) ) ).
tt(d3_polynom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l2_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (D = (k2_polynom1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) <=>  (~  ((k3_funct_2 A (u1_struct_0 B) C E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k14_pre_poly A) (k15_pre_poly A)) =>  ((k4_polynom2 A B) = B) ) ) ) ) ).
tt(d3_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k4_finseq_2 A k5_numbers)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k5_numbers) (k4_finseq_2 A k5_numbers))))) ) ) )  =>  ( (B = (k5_polynom3 A))  <=>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r2_hidden (k4_tarski C D) B) <=> (r2_polynom3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k3_polynom5 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) D E) = (k6_algstr_0 A C (k3_funct_2 k5_numbers (u1_struct_0 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((v3_polynom7 C A B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( (~  (E = D) )  =>  ((k3_polynom1 A B C E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 k6_numbers C) =>  ((k3_polynom8 A B C) = (k1_binop_1 (k4_group_1 A) B C)) )  &  ( (~ (r1_xxreal_0 k6_numbers C))  =>  ((k3_polynom8 A B C) = (k11_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k1_int_2 C)))) ) ) ) ) ) ) ) ) ).
tt(d3_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_polyred A B C D E) <=>  ((r1_polyred A B C D E) &  (~  ((k2_polynom1 (k15_pre_poly A) C D) = (k2_polynom1 (k15_pre_poly A) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k2_poset_1 A B) = (k1_poset_1 A B (k3_yellow_0 A))) ) ) ) ) ).
tt(d3_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = (k5_power A B))  <=>  ((k3_power A C) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v2_margrel1 C) &  ((v3_margrel1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v2_margrel1 D) &  ((v3_margrel1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 B) B)))) ) ) )  =>  ( ((k19_margrel1 C) = (k19_margrel1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v2_margrel1 E) &  ((v3_margrel1 E (k2_zfmisc_1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k2_zfmisc_1 A B)) (k2_zfmisc_1 A B))))) ) ) )  =>  ( (E = (k3_pralg_1 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k4_finseq_2 (k19_margrel1 C) (k2_zfmisc_1 A B)))  &  (! [F:$i] :  ((m2_finseq_1 F (k2_zfmisc_1 A B)) =>  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k4_tarski (k1_funct_1 C (k1_pralg_1 A B F)) (k1_funct_1 D (k2_pralg_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_prelamb A B C) = (k5_binop_1 (u1_struct_0 A) (u3_prelamb A) B C)) ) ) ) ) ) ) ).
tt(d3_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_pre_poly A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((v1_relat_1 (k1_funct_1 A B)) &  ((v1_funct_1 (k1_funct_1 A B)) & (v1_finseq_1 (k1_funct_1 A B))) ) ) ) ) ) ) ).
tt(d3_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 k6_numbers B) =>  ((k4_prepower A B) = (k1_newton A (k1_int_2 B))) )  &  ( (~ (r1_xxreal_0 k6_numbers B))  =>  ((k4_prepower A B) = (k5_xcmplx_0 (k1_newton A (k1_int_2 B)))) ) ) ) ) ) ) ).
tt(d3_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=> (v3_pre_topc (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) A)) ) ) ) ) ).
tt(d3_prgcor_2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((v7_ordinal1 (k1_seq_1 B k6_numbers)) =>  ((r1_xxreal_0 (k1_afinsq_1 A) (k1_seq_1 B k6_numbers)) |  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_prgcor_2 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k1_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  &  (? [E:$i] :  ((v1_int_1 E) &  ( ((k1_afinsq_1 D) = (k1_afinsq_1 A))  &  ( ((k1_seq_1 D k6_numbers) = k6_numbers)  &  ( (E = (k1_seq_1 B k6_numbers))  &  ( ( (~  (E = k6_numbers) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  =>  ((k1_seq_1 D (k1_nat_1 F 1)) = (k7_real_1 (k1_seq_1 D F) (k8_real_1 (k1_seq_1 A (k1_nat_1 F 1)) (k1_seq_1 B (k1_nat_1 F 1))))) ) ) ) )  &  (C = (k1_seq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A B) = (k3_subset_1 A (k1_prob_1 A (k2_prob_1 A B)))) ) ) ) ).
tt(d3_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_prob_2 C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  (D = E) )  => (r1_xboole_0 (k1_prob_2 A B C D) (k1_prob_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k3_prob_3 A B))  <=>  ( ((k1_prob_2 A (k9_setfam_1 A) C k6_numbers) = (k1_prob_2 A (k9_setfam_1 A) B k6_numbers))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_prob_2 A (k9_setfam_1 A) C (k1_nat_1 D 1)) = (k7_subset_1 A (k1_prob_2 A (k9_setfam_1 A) B (k1_nat_1 D 1)) (k1_funct_1 (k2_prob_3 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((r1_prob_4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ( ((r2_hidden E B) &  ((r1_tarski D E) &  ((k1_funct_1 C E) = k6_numbers) ) )  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r3_projpl_1 A B C D E) <=>  ((r1_incsp_1 A B C) &  ((r1_incsp_1 A B D) & (r1_incsp_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 A)))))  =>  ((m1_projred2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) &  ( (~ (r1_incsp_1 A C D))  &  ( (~ (r1_incsp_1 A C E))  &  (B = (k1_projred1 A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v13_algstr_0 A)) ) )  =>  ((k4_prvect_1 A B) = (g2_algstr_0 (k4_finseq_2 B (u1_struct_0 A)) (k2_prvect_1 (u1_struct_0 A) (u1_algstr_0 A) B) (k5_finseq_2 (u1_struct_0 A) B (k4_struct_0 A)))) ) ) ) ) ) ).
tt(d3_prvect_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_prvect_2 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  ((k3_prvect_3 A B) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(d3_pscomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 C) => (v4_pre_topc (k8_relset_1 (u1_struct_0 A) k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(d3_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pua2mss1 B A) =>  (! [C:$i] :  ((r2_hidden C A) =>  (! [D:$i] :  ( (D = (k5_pua2mss1 A B C))  <=>  ((r2_hidden D (k9_xtuple_0 B)) & (r2_hidden C (k1_funct_1 B D))) ) ) ) ) ) ) ) ).
tt(d3_pythtrip,ax, (! [A:$i] :  ((v1_pythtrip A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (A = (k1_pepin B)) ) ) ) ) ).
tt(d3_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) <=>  (! [D:$i] :  ( ((r2_hidden D A) &  ((k1_funct_1 C D) = k1_xboole_0) )  =>  ((k1_funct_1 B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d3_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k2_qc_lang1 A) = (k2_xboole_0 (k2_zfmisc_1 (k1_tarski 6) k5_numbers) (k2_zfmisc_1 (k2_tarski 4 5) (k1_qc_lang1 A)))) ) ) ).
tt(d3_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k3_qc_lang2 A B C) = (k13_qc_lang1 A (k14_qc_lang1 A (k13_qc_lang1 A B) (k13_qc_lang1 A C)))) ) ) ) ) ) ) ).
tt(d3_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_qc_lang3 A B) = (k4_tarski 6 B)) ) ) ) ) ).
tt(d3_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m4_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ( (D = (k3_qc_lang4 A B C))  <=>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((r2_hidden E D) <=>  ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  ((k3_qmax_1 A) = (u2_qmax_1 A)) ) ) ).
tt(d3_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v5_quantal1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A C B) = B) ) ) ) ) ) ) ) ).
tt(d3_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k2_quaterni A B C D E F G H) = (k1_funct_4 (k4_funct_4 A B E F) (k4_funct_4 C D G H))) ) ) ) ) ) ) ) ) ).
tt(d3_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((k3_quofield A B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)) (k6_algstr_0 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(d3_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( ((r2_hidden A (k2_finseq_1 C)) =>  ((k4_radix_1 A B C D) = (k1_funct_1 D A)) )  &  ( (A = k6_numbers)  =>  ((k4_radix_1 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k5_numbers))  =>  ((k3_radix_2 A B C) = (k2_wsierp_1 (k2_radix_2 A B C))) ) ) ) ) ) ) ).
tt(d3_radix_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 (k1_radix_1 (k7_nat_d B 1)) A) =>  ((k5_radix_3 A B) = 1) )  &  ( ( (~ (r1_xxreal_0 (k4_xcmplx_0 (k1_radix_1 (k7_nat_d B 1))) A))  =>  ((k5_radix_3 A B) = (k4_xcmplx_0 1)) )  &  ((r1_xxreal_0 (k4_xcmplx_0 (k1_radix_1 (k7_nat_d B 1))) A) =>  ((r1_xxreal_0 (k1_radix_1 (k7_nat_d B 1)) A) |  ((k5_radix_3 A B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(d3_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ( ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 B A) |  ((k3_radix_5 A B C) = (k6_xcmplx_0 (k1_radix_1 C) 1)) ) )  &  ( (~  ((r1_xxreal_0 1 A) &  (~ (r1_xxreal_0 B A)) ) )  =>  ((k3_radix_5 A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d3_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( ((r1_xxreal_0 2 C) & (r2_hidden A (k2_finseq_1 (k2_xcmplx_0 B 2))))  =>  ( ((r1_xxreal_0 B A) =>  ((k3_radix_6 A B C D) = (k1_funct_1 D A)) )  &  ( (~ (r1_xxreal_0 B A))  =>  ((k3_radix_6 A B C D) = (k6_xcmplx_0 (k1_radix_1 C) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((r1_random_1 A B C D) <=> (r3_mesfunc6 A B (k2_prob_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(d3_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((k3_random_2 A B) = (a_2_0_random_2 A B)) ) ) ) ) ).
tt(d3_ranknull,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_ranknull A B) = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) ) ) ) ) ).
tt(d3_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k1_rat_1 A))  <=>  ( (~  (B = k6_numbers) )  &  ( (? [C:$i] :  ((v1_int_1 C) &  (A = (k6_real_1 C B)) ) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (A = (k6_real_1 C D))  =>  ( (D = k6_numbers)  | (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ratfunc1 A B C D) <=>  ((r1_polynom5 A B D) & (r1_polynom5 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_rcomp_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((r1_tarski (k10_xtuple_0 B) A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((m2_valued_0 C k1_numbers B) &  ((v2_comseq_2 C) & (r2_hidden (k2_seq_2 C) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  ((m2_rcomp_3 E A B C D) <=>  ( ((k3_finseq_1 E) = (k2_nat_1 (k3_finseq_1 D) 1))  &  ( ((k1_funct_1 E 1) = A)  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = B)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) (k1_nat_1 F 1)) | (r2_hidden (k1_funct_1 E (k1_nat_1 F 1)) (k2_rcomp_1 (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k1_nat_1 F 1))) (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k3_real_3 A))  <=>  ( ((k3_funct_2 k5_numbers k1_numbers B k6_numbers) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 1)) = (k10_real_1 1 (k4_int_1 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(d3_real_lat,ax, (k3_real_lat = (g3_lattices k1_numbers k2_real_lat k1_real_lat)) ).
tt(d3_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_euclid A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) )  =>  ( (B = (k3_real_ns1 A))  <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k1_seq_1 B C) = (k12_euclid C)) ) ) ) ) ) ) ) ).
tt(d3_rearran1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v3_rearran1 B A) <=>  (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (k3_tarski A))  &  ((k3_finseq_1 B) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(d3_recdef_2,ax, (! [A:$i] :  ((v2_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k2_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (A = (k3_xtuple_0 C D E))  =>  (B = E) ) ) ) ) ) ) ) ) ).
tt(d3_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) A) => (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ).
tt(d3_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r2_hidden (k4_tarski C D) A)) )  => (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ) ).
tt(d3_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) <=>  (? [D:$i] :  ((m1_rewrite1 D A) &  ( ((k1_funct_1 D 1) = B)  &  ((k1_funct_1 D (k3_finseq_1 D)) = C) ) ) ) ) ) ) ) ) ).
tt(d3_rewrite2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_rewrite2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_rewrite2 C)) )  =>  ( (C = (k2_rewrite2 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k1_ordinal4 (k1_funct_1 B D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((l1_rewrite3 C B) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((r2_rewrite3 A B C D E F G) <=>  (? [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 A)) &  (? [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 A)) &  ( (H = G)  &  ((r1_rewrite3 B C D I F) &  (E = (k1_flang_1 A I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k3_rfinseq2 A) = (k1_seq_1 A (k1_rfinseq2 A))) ) ) ).
tt(d3_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden (k3_real_1 B 1) (k4_finseq_1 A)))  => (r1_xxreal_0 (k1_seq_1 A (k3_real_1 B 1)) (k1_seq_1 A B))) ) ) ) ) ) ).
tt(d3_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r2_hidden B (k1_relset_1 k1_numbers A)) & (r2_hidden C (k1_relset_1 k1_numbers A)))  =>  ((r1_xxreal_0 C B) | (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d3_rfunct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_rfunct_3 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(d3_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r3_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E)) B) &  ( (~  ((k1_seq_1 A D) = (k1_seq_1 A E)) )  & (r1_xxreal_0 (k4_xxreal_0 (k1_seq_1 A D) (k1_seq_1 A E)) (k1_seq_1 A (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v4_partfun3 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) ) ) ).
tt(d3_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_rinfsup2 A) <=> (v3_xxreal_2 (k17_supinf_2 A))) ) ) ).
tt(d3_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_ring_1 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v2_ideal_1 C A) &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (~  ((r1_tarski B C) &  ( (~  (C = B) )  & (v1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d3_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((k2_ringcat1 A) = (u2_ringcat1 A)) ) ) ).
tt(d3_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k3_rlaffin1 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ((v2_funct_1 D) &  ( ((k10_xtuple_0 D) = (k3_rlvect_2 A B))  &  (C = (k18_rvsum_1 (k4_finseqop (u1_struct_0 A) k1_numbers D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  ( (D = (k2_rlaffin3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k1_funct_1 (k5_rlaffin1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( (B = (k1_rlsub_1 A))  <=>  ((u1_struct_0 B) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ).
tt(d3_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k3_rlsub_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_rlvect_1 C) & (m1_rlsub_1 C A)) ) ) ) ) ) ) ).
tt(d3_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_rltopsp1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_convex1 C A)) ) ) ) ) ) ) ) ).
tt(d3_rlvect_1,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v3_rlvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k1_numbers (k9_funct_2 (u1_struct_0 A) k1_numbers)) =>  ((m1_rlvect_2 B A) <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_hidden D C))  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_rlvect_3 B A) <=>  ((v1_rlvect_3 B A) &  ((k1_rlvect_3 A B) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ) ).
tt(d3_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( (C = (k2_rlvect_5 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_rlvect_1 E) & (m1_rlsub_1 E A))  &  ( (E = D)  &  ((k1_rlvect_5 E) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k3_rlvect_x A B) = (a_2_1_rlvect_x A B)) ) ) ) ) ).
tt(d3_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ( (C = (k1_rmod_2 A B))  <=>  ((u1_struct_0 C) = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d3_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( (C = (k3_rmod_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  &  (E = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ((k2_rmod_4 A B C) = (a_3_0_rmod_4 A B C)) ) ) ) ) ) ) ).
tt(d3_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u1_robbins1 A) B)) ) ) ) ) ).
tt(d3_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v3_robbins2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C)) (k1_lattices A D C)) = (k1_lattices A C (k1_lattices A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d3_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v3_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B (k2_lattices A B C)) = B) ) ) ) ) ) ) ) ).
tt(d3_robbins4,ax, (k1_robbins4 = (k2_yellow_1 (k4_enumset1 k6_numbers 1 (k6_subset_1 3 1) 2 (k6_subset_1 3 2) 3))) ).
tt(d3_rpr_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_rpr_1 A B C) <=>  ((k1_rpr_1 A (k9_subset_1 A B C)) = (k8_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C))) ) ) ) ) ) ) ) ).
tt(d3_rsspace3,ax, (k3_rsspace3 = (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) ).
tt(d3_rsspace4,ax, (k3_rsspace4 = (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) ).
tt(d3_rsspace,ax, (! [A:$i] :  ((r2_hidden A k1_numbers) =>  ((k3_rsspace A) = A) ) ) ).
tt(d3_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k2_rusub_1 A) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ).
tt(d3_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k3_rusub_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_bhsp_1 C) & (m1_rusub_1 C A)) ) ) ) ) ) ) ).
tt(d3_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (C = (k2_rusub_4 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_bhsp_1 E) & (m1_rusub_1 E A))  &  ( (E = D)  &  ((k1_rusub_4 E) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( (C = (k2_rusub_5 A B))  <=>  ((u1_struct_0 C) = (a_2_1_rusub_5 A B)) ) ) ) ) ) ) ) ).
tt(d3_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_rvsum_1 A) = (k5_funcop_1 k35_binop_2 A (k6_partfun1 k1_numbers))) ) ) ).
tt(d3_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k5_rvsum_2 A) = (k3_relat_1 A k25_binop_2)) ) ) ).
tt(d3_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k5_scm_comp A B) = (k6_trees_4 (k4_tarski k6_numbers k6_numbers) A B)) ) ) ) ) ).
tt(d3_scmfsa_2,ax, (k3_scmfsa_2 = k3_scmfsa_1) ).
tt(d3_scmfsa6c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_scmfsa6c A B) = (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k5_sf_mastr (k11_compos_1 k1_scmfsa_2 (k6_scmfsa_2 A B))) A) (k6_scmfsa_2 A B)) (k6_scmfsa_2 B (k5_sf_mastr (k11_compos_1 k1_scmfsa_2 (k6_scmfsa_2 A B)))))) ) ) ) ) ).
tt(d3_scmfsa_7,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( (C = (k3_scmfsa_7 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D (k8_afinsq_1 (u1_compos_1 k1_scmfsa_2))) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  &  ( ((k1_afinsq_1 D) = (k3_finseq_1 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k1_afinsq_1 D) E))  &  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (F = (k1_funct_1 B (k2_nat_1 E 1)))  &  ((k1_funct_1 D E) = (k1_ordinal4 (k1_ordinal4 (k2_scmfsa_7 (k4_scmfsa_2 1) (k2_nat_1 E 1)) (k2_scmfsa_7 (k4_scmfsa_2 2) F)) (k5_afinsq_1 (k15_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 1) A)))) ) ) ) ) ) ) ) )  &  (C = (k8_afinsq_2 (u1_compos_1 k1_scmfsa_2) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmfsa7b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((r3_scmfsa7b A B) <=>  (~  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ( (~  ((k6_scmfsa_2 B C) = A) )  &  ( (~  ((k7_scmfsa_2 B C) = A) )  &  ( (~  ((k8_scmfsa_2 B C) = A) )  &  ( (~  ((k9_scmfsa_2 B C) = A) )  &  ( (~  ((k10_scmfsa_2 B C) = A) )  &  ( (~  ((k10_scmfsa_2 C B) = A) )  &  ( (~  ((k14_scmfsa_2 B C D) = A) )  &  (~  ((k16_scmfsa_2 B D) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmfsa8b A B C) = (k1_scmfsa8b A C (k2_scmfsa8b A C B))) ) ) ) ) ) ) ).
tt(d3_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r2_scmfsa9a A B C D) =>  ( ( (~ (r1_scmfsa9a A B C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k1_scmfsa9a A B C D))  <=>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (E = F)  &  ( (~  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) F) C) = k6_numbers) )  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) G) C) = k6_numbers) )  => (r1_xxreal_0 F G)) ) )  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B)))) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k3_scmfsa_9 A B) = (k1_funct_4 (k1_scmfsa8b A (k4_compos_1 k1_scmfsa_2) (k2_scmfsa8b A (k4_compos_1 k1_scmfsa_2) (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)))) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers)))) ) ) ) ) ).
tt(d3_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 13)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k3_scmfsa_i A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) &  (? [E:$i] :  ((m1_subset_1 E k2_scm_inst) &  ( ((k11_finseq_1 C D E) = (k2_xtuple_0 A))  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ( (B = (k2_scmfsa_m A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k5_numbers)))  &  ( (B = (k4_scmfsa_2 (k6_seq_4 C)))  &  (C = (a_1_0_scmfsa_m A)) ) ) ) ) ) ) ) ) ).
tt(d3_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v3_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski A C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 C B D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (k7_card_1 9)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k2_finseq_4 k2_scm_inst B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k4_scm_inst A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k2_scm_inst) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 k2_scm_inst C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmisort,ax, (k3_scmisort = (k2_scmisort (k5_scmfsa_2 k6_numbers))) ).
tt(d3_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_scmpds_2 A B) = (k4_tarski 1 (k1_int_2 (k2_xcmplx_0 A B)))) ) ) ) ) ).
tt(d3_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ((k3_scmpds_4 A B) = (k1_scmpds_4 A (k9_compos_1 k1_scmpds_2 B))) ) ) ) ) ).
tt(d3_scmpds_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r2_scmpds_6 A B C) <=> (r1_extpro_1 2 k1_scmpds_2 (k1_funct_4 C (k10_compos_1 k1_scmpds_2 A)) (k8_memstr_0 2 k1_scmpds_2 B))) ) ) ) ) ) ) ).
tt(d3_scmpds_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k3_scmpds_7 A) = (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k10_scmpds_2 k2_scmp_gcd 2 A)) (k10_scmpds_2 k2_scmp_gcd 3 k6_numbers)) (k2_scmpds_7 k2_scmp_gcd 2 1 (k9_compos_1 k1_scmpds_2 (k11_scmpds_2 k2_scmp_gcd 3 1))))) ) ) ).
tt(d3_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k2_scmpds_8 A B C) = (k3_scmpds_4 (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) C) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 1))))) ) ) ) ) ) ) ).
tt(d3_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((v1_int_1 B) &  (? [C:$i] :  ((m2_subset_1 C k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 C k1_xboole_0 (k9_finseq_1 B))) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k4_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k4_numbers) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 k4_numbers C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmp_gcd,ax, (k3_scmp_gcd = (k1_scmp_gcd 1)) ).
tt(d3_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((k1_scmring1 A) = (k6_afinsq_1 k5_numbers (u1_struct_0 A))) ) ) ).
tt(d3_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k3_scmring2 A B C) = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(d3_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E k1_xboole_0 (k2_finseq_4 k2_scm_inst C D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ( (C = (k3_scmringi A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k2_scm_inst) &  ( (D = (k2_xtuple_0 B))  &  (C = (k7_partfun1 k2_scm_inst D 2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_scmyciel,ax, (! [A:$i] :  ((v2_scmyciel A) <=> (v1_xboole_0 (k1_scmyciel A))) ) ).
tt(d3_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k4_scpinvar A B C) = (k3_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k7_scmpds_2 A B 2) (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 2))) C) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 2))))) ) ) ) ) ) ) ).
tt(d3_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) <=>  ( (~ (r1_semi_af1 A B C D))  &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 B (k1_seq_1 A C))) ) ) ) ) ) ) ) ).
tt(d3_seq_4,ax, (k28_binop_2 = (k7_finseqop k2_numbers k27_binop_2 (k6_partfun1 k2_numbers) k25_binop_2)) ).
tt(d3_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k4_seqfunc A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers C D) (k32_valued_1 A k1_numbers (k1_seqfunc A k1_numbers B D)))) ) ) ) ) ) ) ) ) ).
tt(d3_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A k1_numbers) & (v1_funct_1 A)) ) )  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ).
tt(d3_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k4_series_1 A) = (k2_seq_2 (k3_series_1 A))) ) ) ).
tt(d3_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_setfam_1 A B) <=>  (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  (~  ((r2_hidden D A) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ).
tt(d3_setlim_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k3_setlim_1 A))  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 B C) = (k3_tarski (a_2_1_setlim_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d3_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k3_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k7_subset_1 A (k8_nat_1 (k9_setfam_1 A) B E) (k8_nat_1 (k9_setfam_1 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 C B) & (v2_binop_1 C B))  =>  ( ( (D = k1_xboole_0)  &  (~ (v1_setwiseo C B)) )  |  (! [F:$i] :  ((m1_subset_1 F B) =>  ( (F = (k7_setwiseo A B C D E))  <=>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k5_finsub_1 A) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) B)))) )  &  ( (F = (k3_funct_2 (k5_finsub_1 A) B G D))  &  ( (! [H:$i] :  ((m1_subset_1 H B) =>  ((r3_binop_1 B H C) =>  ((k1_funct_1 G k1_xboole_0) = H) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_funct_1 G (k1_tarski H)) = (k3_funct_2 A B E H)) ) )  &  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 A)) =>  ((r1_tarski H D) =>  ( (H = k1_xboole_0)  |  (! [I:$i] :  ((m1_subset_1 I A) =>  ((r2_hidden I (k6_setwiseo A D H)) =>  ((k1_funct_1 G (k2_xboole_0 H (k1_tarski I))) = (k5_binop_1 B C (k3_funct_2 (k5_finsub_1 A) B G H) (k3_funct_2 A B E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((k3_sfmastr2 A B C D) = (k5_scmfsa_9 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m D) (k2_sf_mastr C))) D) (k1_scmfsa_m B)) (k5_scmfsa6a C (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m D) (k2_sf_mastr C))) (k4_scmfsa_2 k6_numbers))) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m D) (k2_sf_mastr C))) A)) ) ) ) ) ) ) ) ) ).
tt(d3_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k2_sfmastr3 A B C D) = (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D))) C) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D))) B)) (k7_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D))) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 A B)) (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D))) (k5_scmfsa6a (k5_scmfsa6a D (k7_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D))) (k4_scmfsa_2 k6_numbers)))))) ) ) ) ) ) ) ) ) ).
tt(d3_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 k3_scmfsa_2)) =>  ( ( ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 9)  |  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 10) )  =>  ( (B = (k3_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  &  (? [E:$i] :  ((m1_scmfsa_2 E) &  ( ( (A = (k14_scmfsa_2 D C E))  |  (A = (k15_scmfsa_2 D C E)) )  &  (B = (k1_tarski E)) ) ) ) ) ) ) ) ) )  &  ( ( ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 11)  |  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 12) )  =>  ( (B = (k3_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  (? [D:$i] :  ((m1_scmfsa_2 D) &  ( ( (A = (k16_scmfsa_2 C D))  |  (A = (k17_scmfsa_2 C D)) )  &  (B = (k1_tarski D)) ) ) ) ) ) ) )  &  (~  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 9) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 10) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 11) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 12) )  &  (~  ( (B = (k3_sf_mastr A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_sgraph1,ax, (! [A:$i] :  ((k3_sgraph1 A) = (a_1_1_sgraph1 A)) ) ).
tt(d3_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v2_sheffer1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_lattices A B C) = C)  &  ((k1_lattices A C B) = C) ) ) ) ) ) ) ) ) ).
tt(d3_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_simplex0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc C A) & (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(d3_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k3_simplex1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) &  ((v3_pre_topc E B) & (r2_hidden D (k3_convex1 A (k1_simplex1 A B E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((v1_simplex2 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( (~ (r1_xboole_0 (u1_pre_topc B) (k9_setfam_1 (k2_struct_0 A))))  =>  ( (C = (k1_simplex2 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D (u1_pre_topc B)) => (r1_xxreal_0 (k3_tbsp_1 A D) C)) ) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E (u1_pre_topc B)) => (r1_xxreal_0 (k3_tbsp_1 A E) D)) ) )  => (r1_xxreal_0 C D)) ) ) ) ) )  &  ((r1_xboole_0 (u1_pre_topc B) (k9_setfam_1 (k2_struct_0 A))) =>  ( (C = (k1_simplex2 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_sincos10,ax, (k3_sincos10 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))) ).
tt(d3_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k4_sin_cos2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k10_real_1 (k7_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k24_sin_cos (k7_binop_2 B))) 2)) ) ) ) ) ) ).
tt(d3_sin_cos3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k3_sin_cos3)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers A B) = (k6_binop_2 (k4_binop_2 (k15_sin_cos B) (k15_sin_cos (k1_binop_2 B))) 2)) ) ) ) ) ) ).
tt(d3_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_sin_cos4 A) = (k7_xcmplx_0 1 (k17_sin_cos A))) ) ) ).
tt(d3_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_sin_cos5 A) = (k10_real_1 1 (k3_sin_cos2 A))) ) ) ).
tt(d3_sin_cos6,ax, (k4_sin_cos6 = (k2_partfun2 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos)))) ).
tt(d3_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_sin_cos7 A) = (k7_binop_2 (k6_power k8_power (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)))))) ) ) ).
tt(d3_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_sin_cos9 A) = (k1_seq_1 k1_sin_cos9 A)) ) ) ).
tt(d3_sin_cos,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_newton A) = (k8_nat_1 k1_numbers k2_sin_cos A)) ) ) ).
tt(d3_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v2_sppol_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((k17_euclid B) = (k17_euclid C)) ) ) ) ) ) ) ) ) ).
tt(d3_sppol_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_sppol_2 A B C D) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))))) ) ) ) ) ) ) ) ) ).
tt(d3_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_jordan1 A) <=>  ( (~  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = k1_xboole_0) )  &  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  &  ((r1_xboole_0 B C) &  ( ((k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) B) B) = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) C) C))  &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) B) & (r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r3_sprect_2 A B) <=>  ((r1_sprect_2 A B) &  ( ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) = (k9_pscomp_1 (k3_topreal1 2 A)))  &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) = (k7_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d3_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((r1_stacks_1 A B) <=> (r2_hidden B (u1_stacks_1 A))) ) ) ) ) ).
tt(d3_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_stirl2_1 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden D (k2_relset_1 B C)) &  ((r2_hidden E (k2_relset_1 B C)) &  ( (~ (r1_xxreal_0 E D))  & (r1_xxreal_0 (k5_nat_1 (k8_relset_1 A B C (k1_seq_4 E))) (k5_nat_1 (k8_relset_1 A B C (k1_seq_4 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k2_struct_0 A) = (u1_struct_0 A)) ) ) ).
tt(d3_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k6_sublemma A B C) = (k21_substut1 A B C)) ) ) ) ) ) ) ) ).
tt(d3_subset_1,ax, (! [A:$i] :  ((k2_subset_1 A) = A) ) ).
tt(d3_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k4_substlat A B C D) = (a_4_0_substlat A B C D)) ) ) ) ) ) ) ).
tt(d3_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_qc_lang1 A)) =>  ( (D = (k3_substut1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ( ((r2_hidden (k1_funct_1 B E) (k9_xtuple_0 C)) =>  ((k1_funct_1 D E) = (k1_funct_1 C (k1_funct_1 B E))) )  &  ( (~ (r2_hidden (k1_funct_1 B E) (k9_xtuple_0 C)))  =>  ((k1_funct_1 D E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_substut2 A B C D) = (k7_sublemma A (k2_substut2 A B (k3_funct_2 (k38_substut1 A) (k1_substut1 A) (k6_substut2 A) (k2_substut2 A (k11_cqc_lang A C B) D))) C)) ) ) ) ) ) ) ) ) ).
tt(d3_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  (! [B:$i] :  ((v2_membered B) =>  ( (B = (k5_supinf_1 A))  <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v2_membered D))  &  ((r2_hidden D A) &  (C = (k1_xxreal_2 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (k5_supinf_2 B C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (k5_supinf_2 B C))))) )  =>  ( (F = (k13_supinf_2 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k12_supinf_2 F G) = (k3_supinf_2 (k12_supinf_2 D G) (k12_supinf_2 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B F E))  &  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  (~  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  ( (~ (r1_orders_2 B H E))  &  (~ (r1_orders_2 B H C)) ) ) )  =>  ( (G = (k2_symsp_1 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B H E))  &  ( (~ (r1_orders_2 B H C))  &  (~  (G = (k8_group_1 A (k8_group_1 A (k1_symsp_1 A B E F H) (k1_symsp_1 A B H E C)) (k1_symsp_1 A B C H D))) ) ) ) ) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B H E))  &  (~ (r1_orders_2 B H C)) ) ) ) )  =>  ( (G = (k2_symsp_1 A B C D E F))  <=>  (G = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (B = (k1_t_0topsp A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc E A) =>  ((r2_hidden C E) <=> (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k3_t_1topsp A) = (k12_borsuk_1 A (k12_eqrel_1 (u1_struct_0 A) (k1_t_1topsp A)))) ) ) ).
tt(d3_tarski,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ).
tt(d3_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (D = (k1_taxonom1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden (k4_tarski E F) D) <=> (r1_xxreal_0 (k1_metric_1 A A B E F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_taxonom2,ax, (! [A:$i] :  ((v3_taxonom2 A) <=>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  (~ (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d3_taylor_1,ax, (k3_taylor_1 = (k2_taylor_1 k8_power)) ).
tt(d3_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_tbsp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k1_tbsp_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k4_metric_1 A (k8_nat_1 (u1_struct_0 A) B F) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k2_tdgroup A) = (g1_analoaf (u1_struct_0 A) (k1_tdgroup A))) ) ) ).
tt(d3_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A))))) )  =>  ( (B = (k3_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_1 A)) =>  ((k5_binop_1 (k1_tdlat_1 A) B C D) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) C D))) (k9_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tdlat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v5_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d3_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (u1_pre_topc A)) => (r2_hidden (k6_subset_1 (u1_struct_0 A) B) (u1_pre_topc A))) ) ) ) ) ) ).
tt(d3_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_termord A B C D) <=>  ((r1_termord A B C D) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tex_1,ax, (! [A:$i] :  ((k2_tex_1 A) = (g1_pre_topc A (k1_tex_1 A))) ) ).
tt(d3_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v3_tex_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v2_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d3_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ( (~ (r1_xboole_0 B C))  &  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tmap_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((l1_struct_0 D) =>  ((r1_tarski (u1_struct_0 D) (u1_struct_0 A)) =>  ((k2_tmap_1 A B C D) = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( (C = (k3_toler_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (m1_toler_1 D A B)) ) ) ) ) ) ) ).
tt(d3_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C)))) =>  ( (D = (k3_topalg_1 A B C))  <=>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  ((r2_hidden (k4_tarski E F) D) <=> (r3_borsuk_2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_topalg_2,ax, (! [A:$i] :  ( ((v3_topmetr A) & (l1_pre_topc A))  =>  ((v2_topalg_2 A) <=> (v6_xxreal_2 (k2_struct_0 A))) ) ) ).
tt(d3_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( (F = (k4_topalg_5 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) F G) = (k1_binop_1 D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  ((v3_topalg_6 C A B) <=>  (? [D:$i] :  ( ((v3_funct_1 D) & (m1_borsuk_2 D A B B))  & (r3_borsuk_2 A B B C D)) ) ) ) ) ) ) ) ) ).
tt(d3_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_topdim_1 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) & (r1_tarski B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) C))) ) ) ) ) ) ) ).
tt(d3_topgen_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k2_topgen_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 A)) =>  ((r2_hidden D C) <=> (r1_topgen_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((m1_topgen_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_tops_2 (k1_funct_1 B C) A) &  ((v1_yellow_8 (k1_funct_1 B C) A C) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(d3_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_topgen_3 A B) <=>  ((r2_hidden B A) &  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 B C))  & (r1_xboole_0 (k2_rcomp_1 C B) A)) ) ) ) ) ) ) ) ).
tt(d3_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_topgen_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d3_topgen_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_pre_topc A) &  ((v2_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (A = k3_topgen_5)  <=>  ( ((u1_struct_0 A) = k2_topgen_5)  &  (? [B:$i] :  ((m1_topgen_2 B A) &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_funct_1 B (k19_euclid C k6_numbers)) = (a_1_0_topgen_5 C)) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  =>  ((k1_funct_1 B (k19_euclid C D)) = (a_2_0_topgen_5 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_metric_1 C) & (m1_topmetr C k8_metric_1)) )  =>  ( (C = (k2_topmetr A B))  <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 k8_metric_1))))  =>  ( (D = (k1_rcomp_1 A B))  =>  (C = (k1_topmetr k8_metric_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k1_nat_1 C 1) (k3_finseq_1 B)))  =>  ((k2_topreal1 A B C) = (k1_rltopsp1 (k15_euclid A) (k7_partfun1 (u1_struct_0 (k15_euclid A)) B C) (k7_partfun1 (u1_struct_0 (k15_euclid A)) B (k1_nat_1 C 1)))) )  &  ( (~  ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k1_nat_1 C 1) (k3_finseq_1 B))) )  =>  ((k2_topreal1 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(d3_topreal4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_topreal4 B A) <=>  ((v3_pre_topc B A) & (v2_connsp_1 B A)) ) ) ) ) ) ).
tt(d3_topreal9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_topreal9 A B C) = (a_3_2_topreal9 A B C)) ) ) ) ) ) ) ).
tt(d3_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k5_toprealb A) = A) ) ) ).
tt(d3_toprealc,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((v1_valued_2 B) =>  ( (B = (k2_toprealc A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((r2_hidden (k30_valued_1 C) B) <=> (r2_hidden C A)) ) ) ) ) ) ) ) ).
tt(d3_toprns_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid B)))))) )  =>  ((k2_toprns_1 A B C) = (k4_vfunct_1 k5_numbers (k15_euclid B) C A)) ) ) ) ) ) ) ).
tt(d3_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=>  ((k2_pre_topc A B) = (k2_struct_0 A)) ) ) ) ) ) ).
tt(d3_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B))))) =>  ( (D = (k1_tops_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ((r2_hidden E D) <=>  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden F C) &  ((k9_subset_1 (u1_struct_0 A) F B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) <=>  ((k1_tops_1 A (k2_pre_topc A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(d3_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ((r2_transgeo A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden (k4_tarski (k4_tarski D E) (k4_tarski F G)) C) <=> (r2_hidden (k4_tarski (k4_tarski (k3_funct_2 A A B D) (k3_funct_2 A A B E)) (k4_tarski (k3_funct_2 A A B F) (k3_funct_2 A A B G))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)))))) )  =>  ( (E = (k3_treal_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  ((k3_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) E F) = (k7_real_1 (k8_real_1 (k9_real_1 1 F) C) (k3_xcmplx_0 F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_trees_1,ax, (! [A:$i] :  ((v1_trees_1 A) <=>  ((r1_tarski A (k3_finseq_2 k5_numbers)) &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r1_tarski (k1_trees_1 B) A)) ) )  &  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers C)) A) & (r1_xxreal_0 D C))  => (r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers D)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((m1_trees_2 B A) <=>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r3_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_trees_3,ax, (! [A:$i] :  ((v1_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(d3_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ( (C = (k3_trees_4 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_trees_1 (k3_finseq_1 B)))  &  ( ((k1_funct_1 C k1_xboole_0) = A)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  =>  ((k1_funct_1 C (k12_finseq_1 k5_numbers D)) = (k1_funct_1 B (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_tsep_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  ((r1_tsep_1 A B) <=> (r1_xboole_0 (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ).
tt(d3_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v6_pre_topc A) <=>  ((v2_struct_0 A) |  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden B D) &  (~ (r2_hidden C D)) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ( (~ (r2_hidden B D))  & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) =>  ((k6_turing_1 A B) = (k3_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) B)) ) ) ) ) ).
tt(d3_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k4_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C))) ) ) ) ) ) ) ) ).
tt(d3_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) =>  ((v4_unialg_1 A) <=>  ( (~  ((u1_unialg_1 A) = k1_xboole_0) )  & (v2_relat_1 (u1_unialg_1 A))) ) ) ) ).
tt(d3_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ((r2_unialg_2 A B C) <=>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((k3_finseq_1 D) = (k19_margrel1 C))  => (r2_hidden (k1_funct_1 C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ( (B = (k3_uniroots A))  <=>  ( ((u1_struct_0 B) = (k2_uniroots A))  &  ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 k1_complfld) (k2_uniroots A))) ) ) ) ) ) ) ).
tt(d3_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = (k3_uproots A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( (C = (k18_rvsum_1 D))  &  (D = (k3_relat_1 (k1_uproots (k13_pre_poly B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_urysohn1,ax, (k3_urysohn1 = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k10_prob_1 k6_numbers) k2_urysohn1) (k3_limfunc1 1))) ).
tt(d3_urysohn3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A k2_urysohn1) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k2_urysohn3 A))  <=>  ( ((r2_hidden A (k1_urysohn1 k6_numbers)) =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  => (r2_hidden A (k1_urysohn1 k6_numbers)))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden A (k1_urysohn1 (k2_nat_1 C 1))) =>  ((r2_hidden A (k1_urysohn1 C)) |  (B = (k2_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  ( (F = (k4_valuat_1 A B C D E))  <=>  ( ((k3_finseq_1 F) = C)  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G C))  =>  ((k1_funct_1 F G) = (k1_funct_1 E (k1_funct_1 D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_valued_0 A) <=> (r1_tarski (k10_xtuple_0 A) k1_numbers)) ) ) ).
tt(d3_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k13_valued_1 A B) = (k7_valued_1 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(d3_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v3_vectmetr B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_metric_1 A C D) = (k2_metric_1 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k2_vectsp10 A B C) (k2_vectsp10 A B C)) (k2_vectsp10 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_vectsp10 A B C) (k2_vectsp10 A B C)) (k2_vectsp10 A B C))))) )  =>  ( (D = (k3_vectsp10 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 B)) (k2_vectsp10 A B C)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (u1_struct_0 B)) (k2_vectsp10 A B C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (E = (k3_vectsp_4 A B G C))  &  (F = (k3_vectsp_4 A B H C)) )  =>  ((k5_binop_1 (k2_vectsp10 A B C) D E F) = (k3_vectsp_4 A B (k3_rlvect_1 B G H) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v1_vectsp11 C A B) & (m1_vectsp11 D A B C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((m2_vectsp11 E A B C D) <=>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) C E) = (k4_vectsp_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v2_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d3_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_vectsp_2 A B C) = (k6_algstr_0 A B (k11_algstr_0 A C))) ) ) ) ) ) ) ).
tt(d3_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ( (C = (k1_vectsp_4 A B))  <=>  ((u1_struct_0 C) = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d3_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( (C = (k3_vectsp_5 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  &  (E = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ( (C = (k2_vectsp_6 A B))  <=>  ((k1_vectsp_6 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d3_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m1_vectsp_7 C A B) <=>  ((v1_vectsp_7 C A B) &  ((k1_vectsp_7 A B C) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ) ) ) ).
tt(d3_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k3_vfunct_1 A B C D))  <=>  ( ((k1_relset_1 A E) = (k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k1_rlvect_1 B (k7_partfun1 (u1_struct_0 B) D F) (k1_seq_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r1_vfunct_2 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k9_subset_1 A D (k1_relset_1 A C))) => (r1_xxreal_0 (k1_normsp_0 B (k7_partfun1 (u1_struct_0 B) C F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v3_waybel_0 B A) <=>  (! [C:$i] :  ( ((v2_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((r2_yellow_0 A C) =>  ( (C = k1_xboole_0)  | (r2_hidden (k2_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(d3_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v4_yellow_0 B (k3_waybel10 A)) & (m1_yellow_0 B (k3_waybel10 A))) ) )  =>  ( (B = (k4_waybel10 A))  <=>  (! [C:$i] :  ( ((v1_orders_2 C) & (m1_yellow_0 C A))  =>  ((m1_subset_1 C (u1_struct_0 B)) <=>  ((v7_yellow_0 C A) & (v4_yellow_0 C A)) ) ) ) ) ) ) ) ) ).
tt(d3_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel11 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r2_hidden (k1_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E C) & (r1_orders_2 A D E))  => (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_waybel12 C A B) <=>  (B = (k4_waybel_0 A (k12_waybel_0 A C))) ) ) ) ) ) ) ) ).
tt(d3_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) <=> (r1_waybel_1 A (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(d3_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ( (D = (k3_waybel17 A B C))  <=>  ( ((u1_struct_0 D) = k5_numbers)  &  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 A) k5_numbers (u1_struct_0 A) (u1_waybel_0 A D) (k1_waybel17 (u1_struct_0 A) B C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ( (E = G)  &  (F = H) )  =>  ((r1_orders_2 D E F) <=> (r1_xxreal_0 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel18,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k3_waybel18 A B))  <=>  ( ((u1_struct_0 C) = (k4_card_3 (k12_pralg_1 A B)))  &  ((v1_tops_2 (k2_waybel18 A B) C) &  ((v2_cantor_1 (k2_waybel18 A B) C) & (m1_subset_1 (k2_waybel18 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ).
tt(d3_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_waybel_9 A)) )  =>  ((v2_waybel19 A) <=>  ((v1_tops_2 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_waybel19 A) (k5_waybel11 A)) A) &  ((v2_cantor_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_waybel19 A) (k5_waybel11 A)) A) & (m1_subset_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_waybel19 A) (k5_waybel11 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ).
tt(d3_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v2_waybel_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k11_lattice3 A B (k10_lattice3 A C D)) = (k10_lattice3 A (k11_lattice3 A B C) (k11_lattice3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (C = (k3_waybel20 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k2_yellow_0 A (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k2_waybel20 A B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A))  =>  ((m2_yellow_6 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ((m2_waybel21 D A B C) <=>  ((r2_relset_1 (u1_struct_0 C) (u1_struct_0 A) (u1_waybel_0 A C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) D (u1_waybel_0 A B))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r1_orders_2 C F G) => (r1_orders_2 B E (k2_yellow_6 (u1_struct_0 C) B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B))))) )  =>  ( (D = (k2_waybel22 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))))) =>  ((k3_funct_2 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B) D E) = (k1_yellow_0 B (a_4_0_waybel22 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel23 B A) <=> (v7_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(d3_waybel24,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_9 B))  =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k3_waybel24 A B))  <=>  ( ((v4_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B)))  &  (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( (D = E)  & (v5_pre_topc E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D C)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 (k6_yellow_1 A B))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v4_orders_2 F) &  ((v6_waybel_0 F B) &  ((v7_waybel_0 F) & (l1_waybel_0 F B)) ) ) )  =>  ( (F = (k2_waybel25 A B C D E))  <=>  ( ((g1_orders_2 (u1_struct_0 F) (u1_orders_2 F)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  &  ((u1_waybel_0 B F) = (k1_funct_1 (k10_funct_6 (u1_waybel_0 C D)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_waybel26 C A)) (u1_struct_0 (k1_waybel26 B A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 C A)) (u1_struct_0 (k1_waybel26 B A)))))) )  =>  ( (E = (k4_waybel26 A B C D))  <=>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 A)) &  ((v5_pre_topc F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) )  =>  ((k1_funct_1 E F) = (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel27,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_waybel27 A) <=>  ( (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k10_funct_6 B)) ) ) ) ) ) ) ) ).
tt(d3_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ( (B = (k3_waybel28 A))  <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r2_hidden C (k6_yellow_6 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  (! [E:$i] :  ((m2_yellow_6 E A C) =>  (D = (k1_waybel11 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k3_waybel24 A (k1_waybel29 (k2_yellow_1 (u1_pre_topc B)))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k3_waybel24 A (k1_waybel29 (k2_yellow_1 (u1_pre_topc B))))))))) )  =>  ( (C = (k3_waybel29 A B))  <=>  (! [D:$i] :  ( ((v3_pre_topc D (k2_borsuk_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  ((k1_funct_1 C D) = (k6_waybel26 D (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A))  =>  (! [D:$i] :  ( ((v6_waybel_0 D A) & (l1_waybel_0 D A))  =>  ( (D = (k3_waybel_2 A B C))  <=>  ( ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (F = (k1_funct_1 (u1_waybel_0 A C) E))  &  ((k1_funct_1 (u1_waybel_0 A D) E) = (k11_lattice3 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  ((v2_waybel30 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_yellow13 C A B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) =>  ((v5_yellow_0 (k5_yellow_0 A D) A) & (v2_compts_1 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ( (D = (k1_waybel32 A B C))  <=>  ( ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (r1_funct_2 (u1_struct_0 D) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel34,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k3_waybel34 A B C) = C) ) ) ) ) ) ) ).
tt(d3_waybel35,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_waybel35 C A B) <=>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~ (r2_hidden (k4_tarski D E) B))  &  ( (~  (D = E) )  &  (~ (r2_hidden (k4_tarski E D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_waybel_3 A B) = (a_2_0_waybel_3 A B)) ) ) ) ) ).
tt(d3_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v1_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_waybel_5 A) <=>  ((v3_lattice3 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ((k5_yellow_2 A (k4_waybel_5 A D)) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (B = (k10_lattice3 A C D))  &  ( (~  (C = B) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v3_waybel_7 B A) <=>  ((v1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r1_tarski B C) &  ( (~  (B = C) )  &  (~  (C = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_waybel_8 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (k2_waybel_8 A B))) ) ) ) ) ) ).
tt(d3_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((r1_waybel_9 A B) <=> (r1_yellow_0 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)))) ) ) ) ) ).
tt(d3_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k3_weddwitt A) = (a_1_0_weddwitt A)) ) ) ).
tt(d3_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((k3_weierstr A) = (k5_seq_4 (k1_weierstr A))) ) ) ).
tt(d3_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_wellfnd1 B A) <=> (r1_wellord1 (u1_orders_2 A) B)) ) ) ) ) ).
tt(d3_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_wellord1 A B) <=>  (! [C:$i] :  (~  ((r1_tarski C B) &  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  (~  ((r2_hidden D C) & (r1_xboole_0 (k1_wellord1 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k2_xboole_0 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D A) | (r2_hidden D B)) ) ) ) ) ) ) ).
tt(d3_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) <=>  ( (A = k1_xboolean)  |  (A = k2_xboolean) ) ) ) ).
tt(d3_xtuple_0,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k2_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( (A = (k4_tarski C D))  =>  (B = D) ) ) ) ) ) ) ) ).
tt(d3_xxreal_0,ax, (k2_xxreal_0 = (k4_tarski k6_numbers k1_numbers)) ).
tt(d3_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k3_xxreal_1 A B) = (a_2_2_xxreal_1 A B)) ) ) ) ) ).
tt(d3_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (B = (k1_xxreal_2 A))  <=>  ((m1_xxreal_2 B A) &  (! [C:$i] :  ((m1_xxreal_2 C A) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(d3_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((v1_xreal_0 A) =>  ( (B = (k2_xxreal_3 A))  <=>  (? [C:$i] :  ((v1_xcmplx_0 C) &  ( (A = C)  &  (B = (k4_xcmplx_0 C)) ) ) ) ) )  &  ( ( (A = k1_xxreal_0)  =>  ( (B = (k2_xxreal_3 A))  <=>  (B = k2_xxreal_0) ) )  &  (~  ( (~ (v1_xreal_0 A))  &  ( (~  (A = k1_xxreal_0) )  &  (~  ( (B = (k2_xxreal_3 A))  <=>  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v5_orders_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_orders_2 A B C) & (r1_orders_2 A C B))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d3_yellow11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_yellow11 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A B D) =>  ((k10_lattice3 A B (k11_lattice3 A C D)) = (k11_lattice3 A (k10_lattice3 A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_yellow13 C A B) =>  ((v1_yellow13 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=> (r2_hidden B (k1_tops_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_yellow15 B A) <=>  (~ (r2_hidden k1_xboole_0 (k2_yellow15 A B))) ) ) ) ) ).
tt(d3_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r3_yellow16 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  & (r1_yellow16 A B C)) ) ) ) ) ) ) ).
tt(d3_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  ((r2_yellow18 A B) <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((u1_altcat_1 B) = (k2_funct_4 (u1_altcat_1 A)))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (F = C)  &  ( (G = D)  &  (H = E) ) )  =>  ((k4_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B) F G H) = (k1_functor0 (k1_binop_1 (u1_altcat_1 A) D C) (k1_binop_1 (u1_altcat_1 A) E D) (k1_binop_1 (u1_altcat_1 A) E C) (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) E D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((k2_yellow19 A B) = (a_2_1_yellow19 A B)) ) ) ) ) ).
tt(d3_yellow_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_yellow_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (l1_orders_2 B)) ) ) ) ) ).
tt(d3_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) =>  (! [C:$i] :  ( ((v6_altcat_1 C) & (l2_altcat_1 C))  =>  ( (C = (k2_yellow20 A B))  <=>  ( ((u1_struct_0 C) = (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u1_altcat_1 C) = (k1_yellow20 (u1_altcat_1 A) (u1_altcat_1 B)))  &  ((u2_altcat_1 C) = (k1_yellow20 (u2_altcat_1 A) (u2_altcat_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v1_yellow21 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((l1_struct_0 C) &  ( (B = C)  &  ((k3_yellow18 A B) = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(d3_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A))))) )  =>  ( (B = (k2_yellow_2 A))  <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k1_funct_1 B C) = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(d3_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_yellow_4 A B C) = (a_3_0_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(d3_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_5 A B C) <=>  (~  ((k11_lattice3 A B C) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ).
tt(d3_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v7_waybel_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A B D) & (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow_8,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_yellow_8 B A) <=>  ( (~ (v1_xboole_0 B))  &  ((v4_pre_topc B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  ((v4_pre_topc D A) &  ( (B = (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) C D))  &  ( (~  (C = B) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_yellow_9 A B) = (k6_waybel_9 (k5_yellow_0 A B) A (k1_yellow_9 A (k5_yellow_0 A B)) (k3_waybel_9 (k5_yellow_0 A B)))) ) ) ) ) ).
tt(d3_zf_colla,ax, (! [A:$i] :  (! [B:$i] :  ((r2_zf_colla A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  & (r1_zf_colla C A B)) ) ) ) ) ).
tt(d3_zf_fund1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k3_zf_fund1 A))  <=>  ((k2_zf_lang B) = A) ) ) ) ) ) ).
tt(d3_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k5_zf_lang1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k4_finseq_1 A))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 A)) =>  ( ( ((k1_funct_1 A E) = B)  =>  ((k1_funct_1 D E) = C) )  &  ( (~  ((k1_funct_1 A E) = B) )  =>  ((k1_funct_1 D E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k4_zf_lang A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers k6_numbers) (k3_zf_lang A)) (k3_zf_lang B))) ) ) ) ) ).
tt(d3_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_zfmisc_1 A B C) = (k2_zfmisc_1 (k2_zfmisc_1 A B) C)) ) ) ) ).
tt(d3_zfmodel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_zfmodel1 A B) <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((r1_tarski (k2_zf_model C) (k2_tarski (k2_zf_lang 3) (k2_zf_lang 4))) &  ((r2_zf_model B (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang C (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) &  (A = (k2_zfmodel1 C B)) ) ) ) ) ) ) ) ) ) ).
tt(d3_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (C = (k4_zf_model A B))  <=>  (? [D:$i] :  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ((r2_hidden (k4_tarski (k4_zf_lang E F) (a_3_0_zf_model B E F)) D) & (r2_hidden (k4_tarski (k5_zf_lang E F) (a_3_1_zf_model B E F)) D)) ) ) ) )  &  ((r2_hidden (k4_tarski A C) D) &  (! [E:$i] :  ( ((v1_zf_lang E) & (m2_finseq_1 E k5_numbers))  =>  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) =>  ( ((v2_zf_lang E) =>  (F = (a_2_0_zf_model B E)) )  &  ( ((v3_zf_lang E) =>  (F = (a_2_1_zf_model B E)) )  &  ( (~  ((v4_zf_lang E) &  (! [G:$i] :  (~  ( (F = (k6_subset_1 (k3_zf_model B) (k3_tarski (k1_tarski G))))  & (r2_hidden (k4_tarski (k20_zf_lang E) G) D)) ) ) ) )  &  ( (~  ((v5_zf_lang E) &  (! [G:$i] :  (! [H:$i] :  (~  ( (F = (k3_xboole_0 (k3_tarski (k1_tarski G)) (k3_tarski (k1_tarski H))))  &  ((r2_hidden (k4_tarski (k21_zf_lang E) G) D) & (r2_hidden (k4_tarski (k22_zf_lang E) H) D)) ) ) ) ) ) )  &  (~  ((v6_zf_lang E) &  (! [G:$i] :  (~  ( (F = (a_3_2_zf_model B E G))  & (r2_hidden (k4_tarski (k24_zf_lang E) G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r3_zfrefle1 A B) <=>  ((r1_tarski A B) &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ((r1_zf_model A D C) <=> (r1_zf_model B (k1_zf_lang1 k1_zf_lang A B D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d3_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  ((v3_zmodul01 A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_zmodul01 A D (k2_xcmplx_0 B C)) = (k1_algstr_0 A (k1_zmodul01 A D B) (k1_zmodul01 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d40_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ((k38_abcmiz_1 A) = (a_1_1_abcmiz_1 A)) ) ) ).
tt(d40_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v19_decomp_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (r2_hidden (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k20_decomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d40_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v13_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k38_fomodel1 A B))  <=>  ((v14_fomodel1 B C A) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((v14_fomodel1 B D A) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d40_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v9_fomodel2 B A) <=>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((r2_hidden C B) | (r2_hidden (k38_fomodel2 A C) B)) ) ) ) ) ) ) ).
tt(d40_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k17_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r10_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d40_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  ((r2_functor0 A B) <=>  (? [C:$i] :  ((m2_functor0 C A B) &  ((v21_functor0 C A B) & (v16_functor0 C A B)) ) ) ) ) ) ) ) ).
tt(d40_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((k40_gate_1 A B C D E F G H I) = (k11_gate_1 G H (k38_gate_1 A B C D E F I))) ) ) ) ) ) ) ) ) ) ).
tt(d40_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k28_glib_000 A B) = (k20_glib_000 A (k6_domain_1 (k6_glib_000 A) B))) ) ) ) ) ).
tt(d40_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k30_modelc_1 A) = (k9_funct_2 A k6_margrel1)) ) ) ).
tt(d40_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((k26_modelc_2 A B) = B) ) ) ) ) ).
tt(d40_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((k27_modelc_3 A B) = (a_2_0_modelc_3 A B)) ) ) ) ) ).
tt(d40_monoid_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v15_algstr_0 B) & (m2_monoid_0 B (k12_monoid_0 A)))  =>  ( (B = (k15_monoid_0 A))  <=>  ((u1_struct_0 B) = (k1_funct_2 A A)) ) ) ) ) ).
tt(d40_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ( ((v12_pcs_0 B) & (l2_pcs_0 B))  =>  ( (B = (k20_pcs_0 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((u1_orders_2 B) = (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))  &  ((u1_pcs_0 B) = (k3_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_pcs_0 A))) ) ) ) ) ) ) ) ).
tt(d40_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  ( (D = (k30_qc_lang1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_qc_lang1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))))) )  &  ( (D = (k3_funct_2 k5_numbers (k1_qc_lang1 A) E C))  &  ( ((k3_funct_2 k5_numbers (k1_qc_lang1 A) E k6_numbers) = B)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_funct_2 k5_numbers (k1_qc_lang1 A) E (k2_nat_1 F 1)) = (k28_qc_lang1 A (k3_funct_2 k5_numbers (k1_qc_lang1 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d40_twoscomp,ax, (! [A:$i] :  (! [B:$i] :  ((k41_twoscomp A B) = (k3_circcomb (k34_twoscomp A B) (k37_twoscomp A B) (k35_twoscomp A B) (k38_twoscomp A B))) ) ) ).
tt(d40_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k47_valued_2 A B C) = (k41_valued_2 A B (k5_xcmplx_0 C))) ) ) ) ) ) ) ).
tt(d40_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v25_waybel_0 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) => (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d40_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_zf_lang A B) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ((r1_xxreal_0 1 C) &  ( ((k3_finseq_1 D) = C)  &  ( ((k1_funct_1 D 1) = A)  &  ( ((k1_funct_1 D C) = B)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 C E))  &  (! [F:$i] :  ( ((v1_zf_lang F) & (m2_finseq_1 F k5_numbers))  =>  (! [G:$i] :  ( ((v1_zf_lang G) & (m2_finseq_1 G k5_numbers))  =>  (~  ( ((k1_funct_1 D E) = F)  &  ( ((k1_funct_1 D (k2_nat_1 E 1)) = G)  & (r1_zf_lang F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d41_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k12_abcmiz_1 A)) =>  ((v9_abcmiz_1 B A) <=>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (~  (B = (k31_abcmiz_1 A (k33_abcmiz_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d41_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k47_aofa_i00 A B C D E F) = (k44_aofa_i00 A B C D (k41_aofa_i00 A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d41_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  (! [B:$i] :  ((l1_fomodel1 B) =>  ((v16_fomodel1 B A) <=>  ((r1_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (u1_fomodel1 B)) &  ( ((k7_fomodel1 A) = (k7_fomodel1 B))  &  ((k8_fomodel1 A) = (k8_fomodel1 B)) ) ) ) ) ) ) ) ).
tt(d41_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k43_fomodel2 A) = (a_1_2_fomodel2 A)) ) ) ).
tt(d41_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k18_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r11_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d41_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k41_gfacirc1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k4_twoscomp (k10_finseq_1 A B)) (k5_circcomb k4_twoscomp (k10_finseq_1 B C))) (k5_circcomb k4_twoscomp (k10_finseq_1 C A)))) ) ) ) ).
tt(d41_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ( ( ((r2_hidden C (k7_glib_000 A)) &  ((k1_funct_1 (k11_glib_000 A) C) = B) )  =>  ((k29_glib_000 A B C) = (k1_funct_1 (k10_glib_000 A) C)) )  &  ( ( ((r2_hidden C (k7_glib_000 A)) &  ((k1_funct_1 (k10_glib_000 A) C) = B) )  =>  ( ((k1_funct_1 (k11_glib_000 A) C) = B)  |  ((k29_glib_000 A B C) = (k1_funct_1 (k11_glib_000 A) C)) ) )  &  (~  ( (~  ((r2_hidden C (k7_glib_000 A)) &  ((k1_funct_1 (k11_glib_000 A) C) = B) ) )  &  ( (~  ((r2_hidden C (k7_glib_000 A)) &  ( ((k1_funct_1 (k10_glib_000 A) C) = B)  &  (~  ((k1_funct_1 (k11_glib_000 A) C) = B) ) ) ) )  &  (~  ((k29_glib_000 A B C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d41_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((r2_hidden B (k30_modelc_1 A)) =>  ((k31_modelc_1 A B) = B) )  &  ( (~ (r2_hidden B (k30_modelc_1 A)))  =>  ((k31_modelc_1 A B) = (k1_margrel1 k6_margrel1 A k7_margrel1)) ) ) ) ) ) ).
tt(d41_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 A)) =>  ((k27_modelc_2 A B) = B) ) ) ) ) ).
tt(d41_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((k28_modelc_3 A B) = (a_2_1_modelc_3 A B)) ) ) ) ) ).
tt(d41_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ((k21_pcs_0 A B) = (g2_pcs_0 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_yellow_3 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 A) (u1_orders_2 B)) (k3_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_pcs_0 A) (u1_pcs_0 B)))) ) ) ) ) ).
tt(d41_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_qc_lang1 A))))  =>  ((k31_qc_lang1 A B) = (o_1_2_qc_lang1 B)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_qc_lang1 A)))) )  =>  ((k31_qc_lang1 A B) = (k26_qc_lang1 A)) ) ) ) ) ) ).
tt(d41_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k51_valued_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k7_valued_1 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d41_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_zf_lang A B) <=>  ((r2_zf_lang A B) &  (~  (A = B) ) ) ) ) ) ) ) ).
tt(d42_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ((k39_abcmiz_1 A) = (a_1_2_abcmiz_1 A)) ) ) ).
tt(d42_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k48_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k42_aofa_i00 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d42_fomodel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fomodel1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_fomodel1 C) & (l1_fomodel1 C)) )  =>  ( (C = (k40_fomodel1 A B))  <=>  ( ((u1_fomodel1 C) = (k1_funct_4 (k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k6_domain_1 (u1_struct_0 B) (u3_struct_0 B)))) (u1_fomodel1 B)))  &  ( ((u2_struct_0 C) = (u2_struct_0 B))  &  ((u3_struct_0 C) = (u3_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(d42_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  (! [D:$i] :  ((v10_fomodel2 D A B C) <=>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((r2_hidden E D) =>  ((k26_fomodel2 B A C E) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d42_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ( (B = (k19_fomodel4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_fomodel4 A)) =>  ((r2_hidden (k1_domain_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A) C D) B) <=> (r12_fomodel4 C A D)) ) ) ) ) ) ) ) ) ) ).
tt(d42_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k42_gfacirc1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k4_twoscomp (k10_finseq_1 A B)) (k5_circcomb k4_twoscomp (k10_finseq_1 B C))) (k5_circcomb k4_twoscomp (k10_finseq_1 C A)) (k3_circcomb (k5_circcomb k4_twoscomp (k10_finseq_1 A B)) (k5_circcomb k4_twoscomp (k10_finseq_1 B C)) (k6_facirc_1 A B k4_twoscomp) (k6_facirc_1 B C k4_twoscomp)) (k6_facirc_1 C A k4_twoscomp))) ) ) ) ).
tt(d42_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k30_glib_000 A B) = (k1_card_1 (k26_glib_000 A B))) ) ) ) ) ).
tt(d42_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k30_modelc_1 A)) =>  ( (C = (k32_modelc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ( ((k3_xboolean (k4_modelc_1 (k1_funct_1 (k31_modelc_1 A B) D))) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 A C) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d42_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k28_modelc_2 A B C) = (k26_modelc_2 A (k10_nat_1 A (k27_modelc_2 A B) C))) ) ) ) ) ) ).
tt(d42_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((k29_modelc_3 A B) = (a_2_2_modelc_3 A B)) ) ) ) ) ).
tt(d42_monoid_0,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) & (m5_monoid_0 B (k12_monoid_0 A) (k15_monoid_0 A))) )  =>  ( (B = (k17_monoid_0 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_monoid_0 A))) =>  ((r2_hidden C (u1_struct_0 B)) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ) ).
tt(d42_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ((k22_pcs_0 A B) = (k21_pcs_0 (k20_pcs_0 A) B)) ) ) ) ) ).
tt(d42_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k57_valued_2 A B C) = (k51_valued_2 A B (k30_valued_1 C))) ) ) ) ) ) ) ).
tt(d42_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (B = (k29_zf_lang A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  &  ( (D = C)  & (r2_zf_lang D A)) ) ) ) ) ) ) ) ) ).
tt(d43_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) <=> (r2_hidden B (k39_abcmiz_1 A))) ) ) ) ).
tt(d43_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v4_funct_1 B) =>  ((k41_fomodel1 A B) = (k40_fomodel1 (k8_funcop_1 k5_numbers (k23_fomodel0 (k2_xboole_0 (k15_fomodel1 A) (k21_fomodel0 B))) k6_numbers) A)) ) ) ) ) ).
tt(d43_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k43_gfacirc1 A B C) = (k2_circcomb (k41_gfacirc1 A B C) (k5_circcomb k29_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))))) ) ) ) ).
tt(d43_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k31_glib_000 A B) = (k1_card_1 (k27_glib_000 A B))) ) ) ) ) ).
tt(d43_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( (B = (k33_modelc_1 A))  <=>  (! [C:$i] :  ((r2_hidden C (k30_modelc_1 A)) =>  ((k1_funct_1 B C) = (k32_modelc_1 A C)) ) ) ) ) ) ) ) ).
tt(d43_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k29_modelc_2 A B C) = (k28_modelc_2 A B C)) ) ) ) ) ) ) ).
tt(d43_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  ((k30_modelc_3 A) = (a_1_1_modelc_3 A)) ) ) ).
tt(d43_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k62_valued_2 A B C))  <=>  ( ((k9_xtuple_0 D) = (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k24_valued_1 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d44_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ( ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A)))  =>  ((k43_abcmiz_1 A B C) = (k4_tarski (k2_xboole_0 (k6_domain_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C) (k41_abcmiz_1 A B)) (k42_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(d44_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v12_fomodel2 B A) <=>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 A C)) =>  (! [E:$i] :  ((v10_fomodel2 E C A D) =>  (! [F:$i] :  ( ((v4_fomodel2 F A) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((r2_hidden (k4_tarski E F) B) =>  ((k26_fomodel2 A C D F) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d44_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  (! [C:$i] :  ((m2_funct_2 C (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ( (C = (k21_fomodel4 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k9_setfam_1 (k1_fomodel4 A))) =>  ((k1_funct_1 C D) = (a_3_1_fomodel4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d44_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k44_gfacirc1 A B C) = (k3_circcomb (k41_gfacirc1 A B C) (k5_circcomb k29_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))) (k42_gfacirc1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp) k29_twoscomp))) ) ) ) ).
tt(d44_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k34_glib_000 A B) = (k1_card_2 (k30_glib_000 A B) (k31_glib_000 A B))) ) ) ) ) ).
tt(d44_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((r2_hidden D A) =>  ( (! [E:$i] :  ((m1_modelc_1 E A B) =>  (~  ( ((k3_funct_2 k5_numbers A E k6_numbers) = D)  &  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A E 1)) = k8_margrel1) ) ) ) )  |  ((k34_modelc_1 A B C D) = k8_margrel1) ) )  &  ( (~  ((r2_hidden D A) &  (? [E:$i] :  ((m1_modelc_1 E A B) &  ( ((k3_funct_2 k5_numbers A E k6_numbers) = D)  &  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A E 1)) = k8_margrel1) ) ) ) ) )  =>  ((k34_modelc_1 A B C D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d44_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k30_modelc_1 (k25_modelc_2 A))) =>  ( (C = (k30_modelc_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k25_modelc_2 A)) =>  ( ((k3_xboolean (k4_modelc_1 (k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) B) D))) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) C) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d44_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  ((k31_modelc_3 A) = (k1_tarski (k11_modelc_3 A))) ) ) ).
tt(d44_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k68_valued_2 A B C) = (k62_valued_2 A B (k35_valued_1 C))) ) ) ) ) ) ) ).
tt(d45_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k9_setfam_1 (k1_funct_1 B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k9_setfam_1 (k1_funct_1 B C)))))) )  =>  ( (D = (k44_abcmiz_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k9_setfam_1 (k1_funct_1 B C)) D E) = (k1_funct_1 (k2_msafree3 A E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d45_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k51_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k43_aofa_i00 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d45_fomodel2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((v13_fomodel2 C A B) <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) =>  ((v10_fomodel2 A D B E) =>  ((k26_fomodel2 B D E C) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d45_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k22_fomodel4 A) = (k21_fomodel4 A (k8_fomodel4 A))) ) ) ).
tt(d45_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k45_gfacirc1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) k29_twoscomp)) ) ) ) ).
tt(d45_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k35_glib_000 A B) = (k2_nat_1 (k32_glib_000 A B) (k33_glib_000 A B))) ) ) ) ) ).
tt(d45_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k30_modelc_1 A)) =>  ( (D = (k35_modelc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ( ((k34_modelc_1 A B (k31_modelc_1 A C) E) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 A D) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d45_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k31_modelc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 B C) = (k30_modelc_2 A C)) ) ) ) ) ) ) ) ).
tt(d45_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((k32_modelc_3 A B) = (a_2_3_modelc_3 A B)) ) ) ) ) ).
tt(d45_pcs_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  ( (C = (k23_pcs_0 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D B) &  ((r2_hidden E B) &  (! [F:$i] :  (~  ((r2_hidden F D) &  (! [G:$i] :  (~  ((r2_hidden G E) & (r2_hidden (k4_tarski F G) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d45_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k72_valued_2 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 D)))  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k1_valued_1 (k1_funct_1 C F) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d46_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((k45_abcmiz_1 A B) = (k1_funct_1 (k2_msafree3 A B) (k14_abcmiz_1 A))) ) ) ) ) ).
tt(d46_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k23_fomodel4 A) = (k21_fomodel4 A (k9_fomodel4 A))) ) ) ).
tt(d46_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k46_gfacirc1 A B C) = (k8_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d46_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k36_glib_000 A B) = (k7_relset_1 (k7_glib_000 A) (k6_glib_000 A) (k10_glib_000 A) (k26_glib_000 A B))) ) ) ) ) ).
tt(d46_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( (C = (k36_modelc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k30_modelc_1 A)) =>  ((k1_funct_1 C D) = (k35_modelc_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d46_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) )  =>  (! [C:$i] :  ( ( ((m1_subset_1 C (k25_modelc_2 A)) &  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 B (k28_modelc_2 A C 1)) = k8_margrel1) )  =>  ((k32_modelc_2 A B C) = k8_margrel1) )  &  ( (~  ((m1_subset_1 C (k25_modelc_2 A)) &  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 B (k28_modelc_2 A C 1)) = k8_margrel1) ) )  =>  ((k32_modelc_2 A B C) = k7_margrel1) ) ) ) ) ) ) ) ).
tt(d46_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  ((k33_modelc_3 A) = (a_1_2_modelc_3 A)) ) ) ).
tt(d46_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  ( (C = (k24_pcs_0 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D B) &  ((r2_hidden E B) &  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F D) & (r2_hidden G E))  => (r2_hidden (k4_tarski F G) (u1_pcs_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d46_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k78_valued_2 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 D)))  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k45_valued_1 (k1_funct_1 C F) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d47_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((k46_abcmiz_1 A B) = (k1_abcmiz_1 (k45_abcmiz_1 A B))) ) ) ) ) ).
tt(d47_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k53_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k33_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d47_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k24_fomodel4 A) = (k21_fomodel4 A (k10_fomodel4 A))) ) ) ).
tt(d47_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k47_gfacirc1 A B C) = (k10_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d47_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k37_glib_000 A B) = (k7_relset_1 (k7_glib_000 A) (k6_glib_000 A) (k11_glib_000 A) (k27_glib_000 A B))) ) ) ) ) ).
tt(d47_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((r2_hidden D A) =>  ( (! [E:$i] :  ((m1_modelc_1 E A B) =>  (~  ( ((k3_funct_2 k5_numbers A E k6_numbers) = D)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A E F)) = k8_margrel1) ) ) ) ) ) )  |  ((k37_modelc_1 A B C D) = k8_margrel1) ) )  &  ( (~  ((r2_hidden D A) &  (? [E:$i] :  ((m1_modelc_1 E A B) &  ( ((k3_funct_2 k5_numbers A E k6_numbers) = D)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A E F)) = k8_margrel1) ) ) ) ) ) ) )  =>  ((k37_modelc_1 A B C D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d47_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k30_modelc_1 (k25_modelc_2 A))) =>  ( (C = (k33_modelc_2 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k25_modelc_2 A)) =>  ( ((k32_modelc_2 A (k31_modelc_1 (k25_modelc_2 A) B) D) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) C) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d47_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  ((k34_modelc_3 A) = (g2_modelc_3 k43_modelc_2 (k23_modelc_3 A) (k30_modelc_3 A) (k31_modelc_3 A) (k33_modelc_3 A))) ) ) ).
tt(d47_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((k25_pcs_0 A B) = (g2_pcs_0 B (k23_pcs_0 A B) (k24_pcs_0 A B))) ) ) ) ).
tt(d47_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k83_valued_2 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 D)))  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k18_valued_1 (k1_funct_1 C F) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d48_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  ((k47_abcmiz_1 A B) = (k2_xboole_0 (k5_setfam_1 (k1_funct_1 (k28_abcmiz_1 A) (k14_abcmiz_1 A)) (k7_relset_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k9_setfam_1 (k1_funct_1 (k28_abcmiz_1 A) (k14_abcmiz_1 A))) (k44_abcmiz_1 A (k28_abcmiz_1 A) (k14_abcmiz_1 A)) (k41_abcmiz_1 A B))) (k45_abcmiz_1 A (k42_abcmiz_1 A B)))) ) ) ) ) ).
tt(d48_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k54_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k34_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d48_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k25_fomodel4 A) = (k21_fomodel4 A (k11_fomodel4 A))) ) ) ).
tt(d48_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k48_gfacirc1 A B C) = (k9_facirc_1 A B C k14_twoscomp)) ) ) ) ).
tt(d48_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k38_glib_000 A B) = (k4_subset_1 (k6_glib_000 A) (k36_glib_000 A B) (k37_glib_000 A B))) ) ) ) ) ).
tt(d48_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k30_modelc_1 A)) =>  ( (D = (k38_modelc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ( ((k37_modelc_1 A B (k31_modelc_1 A C) E) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 A D) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d48_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k34_modelc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 B C) = (k33_modelc_2 A C)) ) ) ) ) ) ) ) ).
tt(d48_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m2_finseq_1 B k5_numbers)) )  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ((r8_modelc_2 A (k14_modelc_3 B D)) =>  ((v3_modelc_3 D B) |  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (E = (k35_modelc_3 A B C D))  <=>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  =>  ( (~ (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) F) D) B) B))  & (r4_modelc_3 B (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) F) D) B) (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) (k1_nat_1 F 1)) D) B))) ) ) )  &  ((v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) E) D) B) B) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 F E) => (r8_modelc_2 A (k14_modelc_3 B (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) F) D) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d48_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((k26_pcs_0 A) = (a_1_0_pcs_0 A)) ) ) ).
tt(d48_valued_2,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( (E = (k89_valued_2 A B C D))  <=>  ( ((k9_xtuple_0 E) = (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 D)))  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k50_valued_1 (k1_funct_1 C F) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d49_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  ((k48_abcmiz_1 A B) = (k1_abcmiz_1 (k47_abcmiz_1 A B))) ) ) ) ) ).
tt(d49_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k55_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k36_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d49_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k26_fomodel4 A) = (k21_fomodel4 A (k12_fomodel4 A))) ) ) ).
tt(d49_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k49_gfacirc1 A B C) = (k2_circcomb (k46_gfacirc1 A B C) (k43_gfacirc1 A B C))) ) ) ) ).
tt(d49_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v10_glib_000 B A) <=>  ((k28_glib_000 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d49_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( (C = (k39_modelc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k30_modelc_1 A)) =>  ((k1_funct_1 C D) = (k38_modelc_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d49_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k30_modelc_1 (k25_modelc_2 A))) =>  ( (D = (k35_modelc_2 A B C))  <=>  (! [E:$i] :  ((r2_hidden E (k25_modelc_2 A)) =>  ( ((k4_xboolean (k4_modelc_1 (k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) B) E)) (k4_modelc_1 (k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) C) E))) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) D) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d49_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m2_finseq_1 B k5_numbers)) )  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ((r8_modelc_2 A (k14_modelc_3 B (k12_modelc_3 B D))) =>  ( ( (~ (v3_modelc_3 (k12_modelc_3 B D) B))  =>  ((k36_modelc_3 A B C D) = (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 B) (k26_modelc_3 A B C) (k35_modelc_3 A B C (k12_modelc_3 B D))) (k12_modelc_3 B D)) B)) )  &  ((v3_modelc_3 (k12_modelc_3 B D) B) =>  ((k36_modelc_3 A B C D) = (k9_modelc_3 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  ((v4_abcmiz_0 A) <=> (v1_xboole_0 (u1_abcmiz_0 A))) ) ) ).
tt(d4_abcmiz_1,ax, (k6_abcmiz_1 = k6_numbers) ).
tt(d4_abian,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r2_abian A B C) <=>  (B = (k3_funct_2 A A C B)) ) ) ) ) ) ) ) ).
tt(d4_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (~  (E = F) )  &  ( (D = (k2_aff_1 A E F))  & (r2_analoaf A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v4_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_hidden E B) &  ((r2_hidden E C) &  ((r2_hidden E D) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r2_hidden G C) &  ((r2_hidden J C) &  ((r2_hidden H D) &  ((r2_hidden K D) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_analoaf A F G I J) & (r2_analoaf A F H I K)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (B = C)  |  ( (B = D)  | (r2_analoaf A G H J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden E D) &  ((r2_hidden J D) &  ((r2_hidden K D) &  ((r1_aff_1 A H F L) &  ((r1_aff_1 A I G L) &  ((r1_aff_1 A H J M) &  ((r1_aff_1 A I K M) &  ((r2_analoaf A F J G K) & (r2_analoaf A F J L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (C = B)  |  ( (C = D)  |  ( (B = D)  |  ( (E = F)  |  ( (E = H)  |  ( (E = J)  |  ( (L = M)  |  ((r1_aff_1 A H F J) |  ((r1_aff_1 A I G K) |  ( (H = I)  |  ( (F = G)  | (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_aff_4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden D C) &  ((v1_aff_1 E A) & (r1_tarski E B)) )  => (r1_tarski (k2_aff_4 A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k5_afinsq_1 A))  <=>  ( ((k9_xtuple_0 B) = 1)  &  ((k1_funct_1 B k6_numbers) = A) ) ) ) ) ) ).
tt(d4_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  ( (B = (k4_afinsq_2 A))  <=>  ( ((k2_relset_1 k5_numbers B) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) D))  &  ( (E = (k1_recdef_1 B C))  &  ( (F = (k1_recdef_1 B D))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k4_afproj A) = (a_1_3_afproj A)) ) ) ).
tt(d4_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k1_afvect0 A B C))  <=> (r2_afvect0 A C B D)) ) ) ) ) ) ) ) ) ).
tt(d4_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r4_alg_1 A B C) <=>  ((r2_alg_1 A B C) & (r3_alg_1 A B C)) ) ) ) ) ) ) ) ).
tt(d4_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k2_algseq_1 A B) = (k7_card_1 (k1_algseq_1 A B))) ) ) ) ) ).
tt(d4_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v1_msualg_1 D) & (l1_msualg_1 D)) ) )  =>  ( (D = (k2_algspec1 A B C))  <=>  ((r3_pua2mss1 A D (k1_algspec1 (u1_struct_0 A) B) (k1_algspec1 (u4_struct_0 A) C)) &  ( ((u1_struct_0 D) = (k10_xtuple_0 (k1_algspec1 (u1_struct_0 A) B)))  &  ((u4_struct_0 D) = (k10_xtuple_0 (k1_algspec1 (u4_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_algstr_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_algstr_0 A C B) = (k1_algstr_0 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v3_algstr_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A A))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k3_zfmisc_1 A A A)) &  ((v1_funct_1 D) & (v1_partfun1 D (k3_zfmisc_1 A A A))) ) )  =>  ( (D = (k3_altcat_1 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden E A) &  ((r2_hidden F A) & (r2_hidden G A)) )  =>  ((k1_multop_1 D E F G) = (k2_zfmisc_1 (k1_binop_1 C F G) (k1_binop_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_pboole B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_altcat_1 (u1_struct_0 A) (k2_altcat_2 A) (k2_altcat_2 A)) (k2_altcat_1 (u1_struct_0 A) (k2_altcat_2 A))) =>  ( (B = (k3_altcat_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k4_altcat_1 (u1_struct_0 A) (k2_altcat_2 A) B C D E) = (k2_partfun1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A)) (u4_struct_0 A) (u1_cat_1 A) (k2_zfmisc_1 (k1_binop_1 (k2_altcat_2 A) D E) (k1_binop_1 (k2_altcat_2 A) C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v1_altcat_3 D A B C) &  ((v2_altcat_3 D A B C) &  (~  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) =>  ( (E = (k1_altcat_3 A B C D))  <=>  ((r1_altcat_3 A C B E D) & (r1_altcat_3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (m1_altcat_2 B A)) ) )  =>  ( (B = (k4_altcat_4 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C D)) =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  & (v2_altcat_3 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ami_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_ami_2 2) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_ami_2 2)))) )  =>  ( (A = k3_ami_2)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_ami_2) =>  ( ( (B = k5_numbers)  =>  ((k3_funct_2 k1_ami_2 2 A B) = k6_numbers) )  &  ((r2_hidden B k2_ami_2) =>  ((k3_funct_2 k1_ami_2 2 A B) = 1) ) ) ) ) ) ) ) ).
tt(d4_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k3_ami_3 A B) = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d4_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((k2_amistd_1 A B C) = (k1_setfam_1 (a_3_0_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(d4_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = (k3_amistd_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E D) <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_memstr_0 A B E)) =>  ((k2_extpro_1 A B C F) = (k2_extpro_1 A B C (k1_amistd_4 A B F E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  ((v4_amistd_5 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v4_extpro_1 D A B C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  ((r1_tarski D E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ((r1_tarski C F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B F E G)) (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k1_ami_wstd A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v3_funct_2 E k5_numbers k5_numbers) &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 F G) <=> (r1_ami_wstd A B (k3_funct_2 k5_numbers k5_numbers E F) (k3_funct_2 k5_numbers k5_numbers E G))) ) ) ) )  &  (D = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (D = (k1_analmetr A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) G H))  &  ( (F = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) I J))  & (r3_analmetr A G H I J B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k2_analoaf A) = (g1_analoaf (u1_struct_0 A) (k1_analoaf A))) ) ) ).
tt(d4_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analort A B C D E F G) <=> (r1_analoaf A (k1_analort A B C D) (k1_analort A B C E) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_anproj_1 A B) = (k6_eqrel_1 (k8_struct_0 A) (k8_struct_0 A) (k1_anproj_1 A) B)) ) ) ) ) ).
tt(d4_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r4_anproj_2 A B C D E F G H) <=>  ( (~ (r2_anproj_1 A B C F))  &  ((r2_anproj_1 A B C D) &  ((r2_anproj_1 A B C E) &  ((r2_anproj_1 A B F G) & (r2_anproj_1 A B F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k2_aofa_000 A B C) = (k1_funct_4 B (k5_relat_1 A C))) ) ) ) ) ) ).
tt(d4_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_armstrng B A) <=> (r2_hidden A B)) ) ) ) ).
tt(d4_arrow,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_arrow A B C) <=> (r2_hidden (k4_tarski B C) A)) ) ) ) ) ).
tt(d4_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( (~  (A = k6_numbers) )  =>  ( (B = (k4_arytm_0 A))  <=>  ((k2_arytm_0 A B) = 1) ) )  &  ( (A = k6_numbers)  =>  ( (B = (k4_arytm_0 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d4_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ( (? [C:$i] :  ((m1_subset_1 C k5_arytm_3) &  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  ((r2_hidden D A) <=>  (~ (r3_arytm_3 C D)) ) ) ) ) )  =>  ( (B = (k4_arytm_2 A))  <=>  (? [C:$i] :  ((m1_subset_1 C k5_arytm_3) &  ( (B = C)  &  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  ((r2_hidden D A) <=>  (~ (r3_arytm_3 C D)) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (~  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  ((r2_hidden D A) <=>  (~ (r3_arytm_3 C D)) ) ) ) ) ) )  =>  ( (B = (k4_arytm_2 A))  <=>  (B = A) ) ) ) ) ) ) ) ).
tt(d4_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C k4_ordinal1) =>  ( (C = (k2_arytm_3 A B))  <=>  ((r2_arytm_3 A C) &  ((r2_arytm_3 B C) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  ( ((r2_arytm_3 A D) & (r2_arytm_3 B D))  => (r2_arytm_3 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v4_asympt_0 A) <=>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(d4_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k4_asympt_1 A) = (k8_funcop_1 k1_numbers k5_numbers A)) ) ) ).
tt(d4_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  ((k4_autalg_1 A B C) = (k4_card_3 (k7_pboole A B C))) ) ) ) ) ) ) ).
tt(d4_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) =>  ( (B = (k4_autgroup A))  <=>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C E) = (k2_group_3 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k3_bagorder A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k5_numbers) &  ( (C = (k2_wsierp_1 D))  &  (D = (k2_polynom2 A (k7_pre_poly A (k1_polynom2 A B) (k1_yellow_1 A)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v4_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) D) (k1_bcialg_1 A (k1_bcialg_1 A B D) C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d4_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_bcialg_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(d4_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = (k4_struct_0 A))  =>  (B = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(d4_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_bcialg_4 A B C) = (a_3_0_bcialg_4 A B C)) ) ) ) ) ) ) ).
tt(d4_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_bcialg_5 A B C D) = (k6_nat_1 (k6_nat_1 A B) (k6_nat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d4_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ( (~  (C = k6_numbers) )  & (r2_hidden (k3_bcialg_6 A C B) (k4_bcialg_1 A))) ) ) ) ) ) ) ) ).
tt(d4_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_bciideal B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden (k1_bcialg_1 A D E) B))  => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_bhsp_1 A B) = (k7_square_1 (k2_bhsp_1 A B B))) ) ) ) ) ).
tt(d4_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k3_bhsp_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 k1_numbers D E) = (k4_bhsp_1 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v3_bhsp_3 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_3 B A) => (v1_bhsp_2 B A)) ) ) ) ) ) ).
tt(d4_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_bhsp_4 A B C) = (k1_normsp_1 A (k1_bhsp_4 A B) C)) ) ) ) ) ) ) ).
tt(d4_bhsp_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((k4_bhsp_5 A B C D) = (k3_relat_1 D C)) ) ) ) ) ) ) ) ) ).
tt(d4_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_hahnban B A) &  ((v3_hahnban B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v2_bhsp_6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k3_funct_2 (u1_struct_0 A) k1_numbers B D)) (k11_binop_2 C (k3_bhsp_1 A D)))) ) ) ) ) ) ) ) ) ) ).
tt(d4_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( (E = (k4_bilinear A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) E F G) = (k4_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((k4_binari_2 A B C) = (k10_margrel1 (k10_margrel1 (k9_margrel1 (k7_partfun1 k6_margrel1 B A)) (k9_margrel1 (k7_partfun1 k6_margrel1 C A))) (k7_partfun1 k6_margrel1 (k4_binarith A B C) A))) ) ) ) ) ) ) ).
tt(d4_binarith,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ((k6_binarith A B) = (k1_finsop_1 k5_numbers (k5_binarith A B) k47_binop_2)) ) ) ) ) ).
tt(d4_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  =>  ( (B = (k4_binom A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C k6_numbers) = (k4_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C (k2_nat_1 D 1)) = (k1_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v3_binop_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_binop_1 A B C C) = C) ) ) ) ) ) ) ).
tt(d4_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) )  =>  ( (A = k28_binop_2)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_binop_1 A B C) = (k4_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d4_bintree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((v3_bintree1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ((r1_lang1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (C = (k4_pre_poly (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_boolealg A B C) <=>  (~  ((k4_lattices A B C) = (k5_lattices A)) ) ) ) ) ) ) ) ) ).
tt(d4_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  ((r2_boolmark A B C) <=>  (~  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  ((m2_finseq_1 D (k1_boolmark A)) =>  (~  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ((r1_boolmark A B (k7_partfun1 (u4_struct_0 A) C 1)) &  ( ((k7_partfun1 (k1_boolmark A) D 1) = (k2_boolmark A B (k7_partfun1 (u4_struct_0 A) C 1)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) E))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (~  ((r1_boolmark A (k7_partfun1 (k1_boolmark A) D E) (k7_partfun1 (u4_struct_0 A) C (k2_nat_1 E 1))) &  ((k7_partfun1 (k1_boolmark A) D (k2_nat_1 E 1)) = (k2_boolmark A (k7_partfun1 (k1_boolmark A) D E) (k7_partfun1 (u4_struct_0 A) C (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bor_cant,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (B = (k5_bor_cant A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k5_numbers B C) = (k1_bor_cant k5_numbers C A k6_numbers 1)) ) ) ) ) ) ) ) ).
tt(d4_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((k8_borsuk_1 A B) = (k2_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 A) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)))) ) ) ) ) ).
tt(d4_borsuk_2,ax, (! [A:$i] :  ( ((v1_borsuk_2 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  ((m1_borsuk_2 D A B C) <=>  ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E k5_topmetr k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) )  =>  ( ( ((k1_funct_1 E k6_numbers) = k6_numbers)  &  ( ((k1_funct_1 E 1) = 1)  & (r1_borsuk_6 A B C)) )  =>  ((k2_borsuk_6 A B C D E) = (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) (u1_struct_0 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_borsuk_7,ax, (k9_borsuk_7 = (k4_euclid_5 (k1_real_1 1) k6_numbers k6_numbers)) ).
tt(d4_brouwer,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_brouwer A B C))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_brouwer A B C)) (u1_struct_0 (k2_brouwer A B C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A B C)) (u1_struct_0 (k2_brouwer A B C)))))) )  =>  ( (~ (r2_abian (u1_struct_0 (k2_brouwer A B C)) D E))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_toprealb A B C))) =>  ( (F = (k4_brouwer A B C D E))  <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid A))) &  ( (G = D)  &  ( (H = (k3_funct_2 (u1_struct_0 (k2_brouwer A B C)) (u1_struct_0 (k2_brouwer A B C)) E D))  &  (F = (k3_brouwer A B H G C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ( (B = (k5_struct_0 k2_bspace))  =>  ((k4_bspace A B C) = C) )  &  ( (B = (k4_struct_0 k2_bspace))  =>  ((k4_bspace A B C) = (k1_subset_1 A)) ) ) ) ) ) ) ) ).
tt(d4_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k5_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k5_xboolean (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k4_bvfunc26 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k20_bvfunc_1 (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_c0sp1 B A) <=>  ((r2_hidden (k5_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k4_c0sp2 A) = (k2_partfun1 (k6_c0sp1 (u1_struct_0 A)) k1_numbers (k10_c0sp1 (u1_struct_0 A)) (k2_c0sp2 A))) ) ) ).
tt(d4_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((r2_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k5_numbers)) & (r1_relset_1 k5_numbers (k3_cqc_lang A) B (k15_finseq_1 (k2_partfun1 k5_numbers (k3_cqc_lang A) C D)))) ) ) ) ) ) ) ) ) ).
tt(d4_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (C = (k5_calcul_2 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) &  ( (C = (k1_funct_1 D (k3_finseq_1 B)))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ( ((k1_funct_1 D 1) = (k4_calcul_2 A B))  |  ((k3_finseq_1 B) = k6_numbers) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) E))  &  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ( (F = (k1_funct_1 B (k2_nat_1 E 1)))  &  ( (G = (k1_funct_1 D E))  &  ((k1_funct_1 D (k2_nat_1 E 1)) = (k8_cqc_lang A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_cantor_1 B A) <=>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  & (r1_tarski C (k2_cantor_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(d4_card_1,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((v2_card_1 A) <=>  (! [B:$i] :  ((v1_card_1 B) =>  (~  (A = (k2_card_1 B)) ) ) ) ) ) ) ).
tt(d4_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k3_card_3 A) = (k3_tarski (k10_xtuple_0 A))) ) ) ).
tt(d4_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r2_card_fil A B C) <=>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ((r1_tarski D C) & (r2_hidden (k1_card_1 D) B))  => (r2_hidden (k3_tarski D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_cardfin2,ax, (! [A:$i] :  (! [B:$i] :  ((k4_cardfin2 A B) = (a_2_0_cardfin2 A B)) ) ) ).
tt(d4_card_fin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finset_1 B)) )  =>  ((v1_finset_1 (k9_xtuple_0 B)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (C = (k3_card_fin A B))  <=>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_finset_1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k5_card_1 (k1_card_fin F A D E)) (k1_card_fin F A D E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k5_card_1 (k1_card_fin F A D E)) (k1_card_fin F A D E))))) )  =>  (~  ( ((k9_xtuple_0 B) = F)  &  ((v2_funct_1 G) &  ( (~  (D = E) )  &  (! [H:$i] :  ( ((v5_ordinal1 H) &  ((v1_relat_1 H) &  ((v5_relat_1 H k5_numbers) &  ((v1_funct_1 H) & (v1_finset_1 H)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers H) = (k1_relset_1 (k5_card_1 (k1_card_fin F A D E)) G))  &  ( (! [I:$i] :  (! [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  =>  ( ((r2_hidden I (k1_relset_1 k5_numbers H)) &  (J = (k1_funct_1 G I)) )  =>  ((k1_recdef_1 H I) = (k1_card_1 (k2_card_fin B J D))) ) ) ) )  &  (C = (k7_afinsq_2 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_card_lar B A) <=>  ((k3_ordinal2 B) = A) ) ) ) ) ) ).
tt(d4_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_cat_1 A B C) = (a_3_0_cat_1 A B C)) ) ) ) ) ) ) ).
tt(d4_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((m3_cat_2 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  => (r1_tarski (k2_cat_1 B C D) (k2_cat_1 A E F))) ) ) ) ) ) ) ) )  &  ((r1_tarski (u1_cat_1 B) (u1_cat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  =>  ((k4_cat_1 B C) = (k4_cat_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 (k2_oppcat_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 (k2_oppcat_1 A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  ( (D = (k5_cat_3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  ((k7_partfun1 (u4_struct_0 A) D E) = (k6_oppcat_1 A (k7_partfun1 (u4_struct_0 (k2_oppcat_1 A)) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_cat_4 A B C) = (k5_binop_1 (u1_struct_0 A) (u2_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d4_cat_5,ax, (! [A:$i] :  ((v2_cat_5 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k4_catalan2 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (? [E:$i] :  ( ((v5_ordinal1 E) &  ((v1_relat_1 E) &  ((v5_relat_1 E k1_numbers) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) ) )  &  ( ((k1_relset_1 k5_numbers E) = (k23_binop_2 D 1))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k23_binop_2 D 1)) =>  ((k1_seq_1 E F) = (k11_binop_2 (k1_seq_1 A F) (k3_funct_2 k5_numbers k1_numbers B (k7_nat_d D F)))) ) ) )  &  ((k7_afinsq_2 E) = (k1_seq_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_catalg_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  ((v2_catalg_1 A) <=>  (? [B:$i] :  ((m1_instalg1 (k2_catalg_1 B) A) &  ((u1_struct_0 A) = (k2_zfmisc_1 (k1_tarski k6_numbers) (k4_finseq_2 2 B))) ) ) ) ) ) ).
tt(d4_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k2_cc0sp1 A) = (a_1_0_cc0sp1 A)) ) ) ).
tt(d4_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k3_cc0sp2 A) = (g1_cfuncdom (k2_cc0sp2 A) (k2_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k1_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k1_cc0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k4_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k3_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)))) ) ) ).
tt(d4_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v3_cfdiff_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k2_numbers) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k7_partfun1 k2_numbers A C) = (k9_complex1 B C)) ) ) ) ) ) ) ) ).
tt(d4_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_cfuncdom A) = (k8_funcop_1 k1_numbers A k6_numbers)) ) ) ).
tt(d4_cgames_1,ax, (k4_cgames_1 = (g1_cgames_1 (k1_tarski k3_cgames_1) k1_xboole_0)) ).
tt(d4_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((k2_chord A B) = (a_2_0_chord A B)) ) ) ) ).
tt(d4_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circcmb3 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  ( (D = (k1_circcmb3 A B C))  <=>  ((v1_circuit2 D A B) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) & (r8_pboole (u1_struct_0 A) D (k5_facirc_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) =>  (! [E:$i] :  ( ((v3_msualg_1 E (k2_circcomb A B)) &  ((v4_msualg_1 E (k2_circcomb A B)) & (l3_msualg_1 E (k2_circcomb A B))) )  =>  ( (E = (k3_circcomb A B C D))  <=>  ( ((u3_msualg_1 (k2_circcomb A B) E) = (k1_funct_4 (u3_msualg_1 A C) (u3_msualg_1 B D)))  &  ((u4_msualg_1 (k2_circcomb A B) E) = (k1_circcomb (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A C))) (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) (u4_struct_0 B) (k3_relat_1 (u1_msualg_1 B) (k6_finseq_2 (u1_struct_0 B) (u3_msualg_1 B D))) (k3_relat_1 (u2_msualg_1 B) (u3_msualg_1 B D)) (u4_msualg_1 A C) (u4_msualg_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((v1_circled1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v2_funct_1 C) &  ( ((k10_xtuple_0 C) = (k3_rlvect_2 A B))  &  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  ( ((k18_rvsum_1 D) = 1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((k1_funct_1 D E) = (k1_funct_1 B (k1_funct_1 C E)))  & (r1_xxreal_0 k6_numbers (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 (k1_circtrm1 A B C))) &  ((v1_funct_1 E) & (v1_partfun1 E (u1_struct_0 (k1_circtrm1 A B C)))) ) )  =>  ( (E = (k4_circtrm1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_circtrm1 A B C))) =>  ((k1_funct_1 E F) = (k2_circtrm1 A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k4_circuit1 A B C))  <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  &  ( (E = (a_3_0_circuit1 A B C))  &  (D = (k1_xxreal_2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ((k5_circuit2 A B C D) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C) (k1_funct_1 (u3_msualg_1 A B) C) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A B) (k6_msafree2 A B) C) (k4_circuit2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d4_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k1_classes1 A))  <=>  ((r1_classes1 A B) &  (! [C:$i] :  ((r1_classes1 A C) => (r1_tarski B C)) ) ) ) ) ) ).
tt(d4_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( (B = (k15_classes2 A))  <=>  ((r1_tarski A B) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ((r1_tarski A C) => (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(d4_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_clopban1 (u1_struct_0 A) B)))) =>  ( (C = (k5_clopban1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_clopban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k8_clopban1 A A) (k8_clopban1 A A)) (k8_clopban1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_clopban1 A A) (k8_clopban1 A A)) (k8_clopban1 A A))))) )  =>  ( (B = (k5_clopban2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  ((k5_binop_1 (k8_clopban1 A A) B C D) = (k3_clopban2 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k2_clopban3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A C (k1_normsp_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_clopban4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k4_clopban4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k1_normsp_1 B E F) = (k6_algstr_0 B (k1_normsp_1 B (k1_clopban4 B C) F) (k1_normsp_1 B (k1_bhsp_4 B (k1_clopban4 B D)) (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k1_normsp_1 B E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ((v4_closure1 C A B) <=>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) => (r6_pboole A (k16_pralg_1 A C (k2_pboole A D E)) (k2_pboole A (k2_closure1 A B C D) (k2_closure1 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(d4_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v1_closure2 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k2_pboole A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v4_clvect_1 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_clvect_1 A D (k3_xcmplx_0 B C)) = (k1_clvect_1 A (k1_clvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k3_clvect_2 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k15_csspace A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_clvect_3 A B C D) = (k5_algstr_0 A (k2_clvect_3 A B C) (k2_clvect_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(d4_cohsp_1,ax, (! [A:$i] :  ((v1_cohsp_1 A) <=>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (? [C:$i] :  ((r1_tarski (k3_tarski B) C) & (r2_hidden C A)) ) ) ) ) ) ).
tt(d4_coh_sp,ax, (! [A:$i] :  ((k3_coh_sp A) = (a_1_0_coh_sp A)) ) ).
tt(d4_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v3_collsp A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C D) (u1_collsp A)) &  ((r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C E) (u1_collsp A)) & (r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C F) (u1_collsp A))) )  =>  ( (B = C)  | (r2_hidden (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D E F) (u1_collsp A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ((v3_combgras C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  ( ((k1_card_1 D) = (k5_real_1 A 1))  &  (C = (a_3_0_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_complex1,ax, (k6_complex1 = 1) ).
tt(d4_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig (k6_xcmplx_0 C B)) (k1_comptrig (k6_xcmplx_0 A B)))) =>  ((k4_complex2 A B C) = (k9_real_1 (k1_comptrig (k6_xcmplx_0 C B)) (k1_comptrig (k6_xcmplx_0 A B)))) )  &  ( (~ (r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig (k6_xcmplx_0 C B)) (k1_comptrig (k6_xcmplx_0 A B)))))  =>  ((k4_complex2 A B C) = (k7_real_1 (k8_real_1 2 k32_sin_cos) (k9_real_1 (k1_comptrig (k6_xcmplx_0 C B)) (k1_comptrig (k6_xcmplx_0 A B))))) ) ) ) ) ) ) ) ) ).
tt(d4_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k8_complsp2 A B) = (k3_binop_2 (k3_binop_2 (k4_binop_2 (k23_rvsum_1 (k6_complsp2 A) (k6_complsp2 B)) (k5_binop_2 k7_complex1 (k23_rvsum_1 (k6_complsp2 A) (k7_complsp2 B)))) (k5_binop_2 k7_complex1 (k23_rvsum_1 (k7_complsp2 A) (k6_complsp2 B)))) (k23_rvsum_1 (k7_complsp2 A) (k7_complsp2 B)))) ) ) ) ) ).
tt(d4_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_compl_sp B A) <=> (v2_compl_sp (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(d4_compos_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((r1_compos_2 A B) <=> (r1_tarski (k63_valued_1 A) B)) ) ) ) ).
tt(d4_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_compts_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 C B) &  ((v1_tops_2 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski D C) &  ((m1_setfam_1 D B) & (v1_finset_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_comput_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_margrel1 C)) )  & (r2_hidden C (k10_xtuple_0 A))) )  =>  ( (B = (k1_comput_1 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_margrel1 C)) )  =>  ((r2_hidden C (k10_xtuple_0 A)) =>  (B = (k19_margrel1 C)) ) ) ) ) )  &  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_margrel1 C)) )  =>  (~ (r2_hidden C (k10_xtuple_0 A))) ) )  =>  ( (B = (k1_comput_1 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d4_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 B (k17_complex1 (k8_nat_1 k2_numbers A C)))) ) ) ) ) ) ) ) ).
tt(d4_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k4_comseq_3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k4_complex1 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d4_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v4_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r4_analmetr A B G B H) &  ((r4_analmetr A C E D F) & (r4_analmetr A C G D H)) ) ) )  =>  ((r2_analoaf A B G B C) |  ((r2_analoaf A B C B E) | (r4_analmetr A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (B = (k2_conlat_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) B C) = (a_2_1_conlat_1 A C)) ) ) ) ) ) ) ) ).
tt(d4_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)))))) )  =>  ( (B = (k4_conlat_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u4_struct_0 A))) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) B C) = (g2_conlat_1 A D E))  &  ( (D = (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k6_domain_1 (u1_struct_0 A) C))))  &  (E = (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 J A) &  ((v1_aff_1 K A) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden G J) &  ((r2_hidden I J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden F K) &  ((r2_hidden H K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden F J) |  ((r2_hidden H J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden G K) |  ((r2_hidden I K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v4_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r10_analmetr A J K) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden G J) &  ((r2_hidden I J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden F K) &  ((r2_hidden H K) &  ((r4_analmetr A B C F G) &  ((r4_analmetr A C D G H) & (r4_analmetr A D E H I)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden C J) |  ((r2_hidden E J) | (r4_analmetr A B E F I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v2_connsp_1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_connsp_2 A B)) ) ) ) ) ).
tt(d4_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k2_convex1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v1_convex1 D A) & (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((m2_convex4 C A B) <=> (r1_tarski (k1_convex4 A C) B)) ) ) ) ) ) ) ).
tt(d4_convfun1,ax, (k4_convfun1 = (g1_rlvect_1 k1_numbers k6_numbers k33_binop_2 k35_binop_2)) ).
tt(d4_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) =>  ( (D = (k4_cqc_sim1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_qc_lang1 A)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (G = (k1_binop_1 B (k28_qc_lang1 A E) (k1_funct_4 F (k16_funcop_1 C (k2_qc_lang3 A E)))))  =>  ((k2_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) D E F) = (k11_cqc_lang A (k2_qc_lang3 A E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = k6_numbers)  =>  ((r1_cqc_the1 A B C D) <=> (r2_hidden (k1_xtuple_0 (k1_funct_1 B C)) D)) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 1)  =>  ((r1_cqc_the1 A B C D) <=>  ((k1_xtuple_0 (k1_funct_1 B C)) = (k5_cqc_lang A)) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 2)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A E) E) E)) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 3)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A E (k8_cqc_lang A (k6_cqc_lang A E) F))) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 4)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A (k8_cqc_lang A E F) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A F G)) (k6_cqc_lang A (k7_cqc_lang A E G))))) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 5)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A (k7_cqc_lang A E F) (k7_cqc_lang A F E))) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 6)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A (k11_cqc_lang A F E) E)) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 7)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  (? [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [H:$i] :  ((m2_subset_1 H (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 C E))  &  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 E F))  &  ( (G = (k1_xtuple_0 (k1_funct_1 B F)))  &  ( (H = (k1_xtuple_0 (k1_funct_1 B C)))  &  ((k1_xtuple_0 (k1_funct_1 B E)) = (k8_cqc_lang A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 8)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 C E))  &  ( ((k1_xtuple_0 (k1_funct_1 B E)) = (k8_cqc_lang A F G))  &  ( (~ (r2_hidden H (k24_qc_lang1 A F)))  &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_cqc_lang A F (k11_cqc_lang A H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k2_xtuple_0 (k1_funct_1 B C)) = 9)  =>  ((r1_cqc_the1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [H:$i] :  ((m1_subset_1 H (k9_qc_lang1 A)) &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 C E))  &  ((r2_hidden (k13_cqc_lang A H F) (k3_cqc_lang A)) &  ((r2_hidden (k13_cqc_lang A H G) (k3_cqc_lang A)) &  ( (~ (r2_hidden F (k24_qc_lang1 A H)))  &  ( ((k13_cqc_lang A H F) = (k1_xtuple_0 (k1_funct_1 B E)))  &  ((k13_cqc_lang A H G) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r4_cqc_the3 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r3_cqc_the1 A B D) <=> (r3_cqc_the1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_csspace3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_csspace3 A B C) = (k1_normsp_0 A (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(d4_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v1_csspace4 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 A (u1_struct_0 B) C E)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_csspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_csspace k1_csspace) k1_csspace) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_csspace k1_csspace) k1_csspace)))) )  =>  ( (A = k4_csspace)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_csspace) =>  (! [C:$i] :  ((m1_subset_1 C k1_csspace) =>  ((k5_binop_1 k1_csspace A B C) = (k1_series_1 k2_numbers (k2_csspace B) (k2_csspace C))) ) ) ) ) ) ) ) ).
tt(d4_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_decomp_1 B A) <=> (r1_tarski B (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))))) ) ) ) ) ).
tt(d4_descip_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  (! [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  (! [D:$i] :  ((m2_finseq_2 D k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  ( (D = (k12_descip_1 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k10_descip_1 A D E) = (k2_binarith (k10_descip_1 A B E) (k10_descip_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_dickson A) =>  ((k1_dickson A) = (k2_eqrel_1 (u1_struct_0 A) (u1_orders_2 A) (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))) ) ) ) ).
tt(d4_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_diff_1 A B) = (k47_valued_1 k1_numbers k1_numbers k1_numbers A (k1_diff_1 A (k4_xcmplx_0 B)))) ) ) ) ) ).
tt(d4_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k1_dilworth A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v1_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r1_xxreal_0 (k5_card_1 C) B)) ) ) ) ) ) ) ) ).
tt(d4_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_diraf A B C D E) <=>  ((r2_analoaf A B C D E) | (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v2_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C E F) &  ((r2_analoaf A H I E F) &  ((r2_analoaf A H I D G) &  ( (~  (H = I) )  &  ( (~  (E = F) )  &  (~ (r2_analoaf A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_dist_1 A B C) <=>  (! [D:$i] :  ((k3_dist_1 A B D) = (k3_dist_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(d4_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((v2_dtconstr A) <=>  (~  ((k2_lang1 A) = k1_xboole_0) ) ) ) ) ).
tt(d4_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k4_dynkin A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 (k9_setfam_1 A) C D) = (k3_dynkin A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((v3_ec_pf_1 B A) <=>  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (~  ((k2_binom (k9_int_3 A) C 2) = B) ) ) ) ) ) ) ) ) ) ).
tt(d4_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( (E = (k5_ec_pf_2 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))))  =>  ( (C = (k4_endalg A B))  <=>  ( (! [D:$i] :  ((m1_autalg_1 D (u1_struct_0 A) (u3_msualg_1 A B) C) => (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  &  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((r2_hidden D C) <=> (r1_msualg_3 A B B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ((k4_ens_1 A B) = (k2_xtuple_0 (k1_xtuple_0 B))) ) ) ) ) ).
tt(d4_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_entropy1 B (k3_finseq_1 A)) & (m1_matrix_1 B k1_numbers (k3_finseq_1 A) (k3_finseq_1 A)))  =>  ( (B = (k1_entropy1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k3_matrix_1 k1_numbers B C C) = (k1_seq_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d4_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (G = (k4_enumset1 A B C D E F))  <=>  (! [H:$i] :  ((r2_hidden H G) <=>  (~  ( (~  (H = A) )  &  ( (~  (H = B) )  &  ( (~  (H = C) )  &  ( (~  (H = D) )  &  ( (~  (H = E) )  &  (~  (H = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((m1_eqrel_1 B A) <=>  ( ((k5_setfam_1 A B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) =>  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D B) &  ( (~  (C = D) )  &  (~ (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((k4_equation A) = (k6_pboole (u1_struct_0 A) (u3_msualg_1 A (k3_equation A)) (u3_msualg_1 A (k3_equation A)))) ) ) ).
tt(d4_e_siec,ax, (! [A:$i] :  ((k2_e_siec A) = (g1_e_siec A (k4_relat_1 A) (k4_relat_1 A))) ) ).
tt(d4_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k4_euclid_3 A B C) = (k4_complex2 (k2_euclid_3 A) (k2_euclid_3 B) (k2_euclid_3 C))) ) ) ) ) ) ) ).
tt(d4_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v2_euclid_4 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) &  ( (~  (C = D) )  &  (B = (k4_euclid_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 A B) = (k4_euclid_5 (k9_real_1 (k8_real_1 (k2_euclid_5 A) (k3_euclid_5 B)) (k8_real_1 (k3_euclid_5 A) (k2_euclid_5 B))) (k9_real_1 (k8_real_1 (k3_euclid_5 A) (k1_euclid_5 B)) (k8_real_1 (k1_euclid_5 A) (k3_euclid_5 B))) (k9_real_1 (k8_real_1 (k1_euclid_5 A) (k2_euclid_5 B)) (k8_real_1 (k2_euclid_5 A) (k1_euclid_5 B))))) ) ) ) ) ).
tt(d4_euclid_7,ax, (! [A:$i] :  ((v2_euclid_7 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ((r2_hidden B A) =>  ((k12_euclid B) = 1) ) ) ) ) ) ).
tt(d4_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k5_euclid_8 A B) = (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 3)) (k11_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 2))) (k10_binop_2 (k11_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 1)) (k11_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 3))) (k10_binop_2 (k11_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 2)) (k11_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 1))))) ) ) ) ) ).
tt(d4_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k4_euclid_9 A B C) = (k4_card_3 (k3_euclid_9 B C))) ) ) ) ) ) ) ).
tt(d4_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_euclid A) = (k5_finseq_2 k1_numbers A k6_numbers)) ) ) ).
tt(d4_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_euclidlp A) = (a_1_0_euclidlp A)) ) ) ).
tt(d4_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v4_euclmetr A) <=> (v1_translac (k3_analmetr A))) ) ) ).
tt(d4_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ( (? [C:$i] :  ((v3_ordinal1 C) & (r2_hidden C (k9_xtuple_0 A))) )  =>  ( (B = (k1_exchsort A))  <=> (v2_exchsort A B)) )  &  ( (! [C:$i] :  ((v3_ordinal1 C) =>  (~ (r2_hidden C (k9_xtuple_0 A))) ) )  =>  ( (B = (k1_exchsort A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d4_facirc_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k1_facirc_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k2_binarith B C)) ) ) ) ) ) ) ) ).
tt(d4_facirc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k3_facirc_2 A B C)) &  ((v4_msafree2 D (k3_facirc_2 A B C)) &  ((v4_circcomb D (k3_facirc_2 A B C)) &  ((v6_circcomb D (k3_facirc_2 A B C)) & (l3_msualg_1 D (k3_facirc_2 A B C))) ) ) )  =>  ( (D = (k4_facirc_2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) )  &  ( ((k3_facirc_2 A B C) = (k1_funct_1 E A))  &  ( (D = (k1_funct_1 F A))  &  ( ((k1_funct_1 E k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 F k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 G k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ( ( (~ (v2_struct_0 I))  & (l1_msualg_1 I))  =>  (! [J:$i] :  ( ((v4_msualg_1 J I) & (l3_msualg_1 J I))  =>  (! [K:$i] :  ( ( (I = (k1_funct_1 E H))  &  ( (J = (k1_funct_1 F H))  &  (K = (k1_funct_1 G H)) ) )  =>  ( ((k1_funct_1 E (k1_nat_1 H 1)) = (k2_circcomb I (k19_facirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ( ((k1_funct_1 F (k1_nat_1 H 1)) = (k3_circcomb I (k19_facirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K) J (k20_facirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ((k1_funct_1 G (k1_nat_1 H 1)) = (k17_facirc_1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (C = (k1_fcont_1 A B))  <=>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_seq_1 C D) = (k2_xcmplx_0 (k3_xcmplx_0 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fdiff_1 A B) <=>  (? [C:$i] :  ((m1_rcomp_1 C B) &  ((r1_tarski C (k1_relset_1 k1_numbers A)) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v3_fdiff_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v2_fdiff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k9_real_1 (k1_seq_1 A F) (k1_seq_1 A B)) = (k7_real_1 (k1_seq_1 D (k9_real_1 F B)) (k1_seq_1 E (k9_real_1 F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_fdiff_3 A B) <=>  ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k1_rcomp_1 (k9_real_1 B C) B) (k1_relset_1 k1_numbers A))) ) )  &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 C E))) ) ) ) )  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers D A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ff_siec,ax, (! [A:$i] :  ((k4_ff_siec A) = (k1_ff_siec k1_xboole_0 (k1_tarski A))) ) ).
tt(d4_fib_num2,ax, (k4_fib_num2 = a_0_1_fib_num2) ).
tt(d4_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (C = (k3_filter_0 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((m2_filter_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B)) (k8_eqrel_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B)) (k8_eqrel_1 A B))))) )  =>  ( (D = (k3_filter_1 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden E (k8_eqrel_1 A B)) &  ((r2_hidden F (k8_eqrel_1 A B)) &  ((r2_hidden G E) & (r2_hidden H F)) ) )  =>  ((k1_binop_1 D E F) = (k6_eqrel_1 A A B (k1_binop_1 C G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_filter_2 A B) = B) ) ) ) ) ).
tt(d4_finance1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k5_finance1 A B C) = (k1_seq_1 (k3_series_1 (k10_nat_1 k1_numbers (k3_finance1 B C) 1)) (k10_binop_2 A 1))) ) ) ) ) ) ) ).
tt(d4_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_finseq_1 B A) <=> (r1_tarski (k10_xtuple_0 B) A)) ) ) ) ).
tt(d4_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((k4_finseq_2 A B) = (a_2_0_finseq_2 A B)) ) ) ) ).
tt(d4_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k8_eqrel_1 A B)) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r1_finseq_3 A B C D) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k6_eqrel_1 A A B (k1_funct_1 D E)) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k4_finseq_4 A B) = (k1_funct_1 (k14_finseq_1 (k8_relat_1 A (k1_tarski B))) 1)) ) ) ) ).
tt(d4_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_finseq_5 A B C D) = (k8_finseq_1 A (k8_finseq_1 A (k17_finseq_1 A D B) (k12_finseq_1 A C)) (k2_rfinseq A D B))) ) ) ) ) ) ) ) ) ).
tt(d4_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k6_finseq_8 A B C) = (k17_finseq_1 A (k7_nat_d (k3_finseq_1 B) (k3_finseq_1 (k4_finseq_8 A B C))) B)) ) ) ) ) ) ) ).
tt(d4_finseqop,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k6_finseqop A B C) = (k3_relat_1 (k15_funct_3 B C) A)) ) ) ) ) ) ) ).
tt(d4_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_finset_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_finset_1 (k1_funct_1 A B))) ) ) ) ) ).
tt(d4_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B C) =>  ((k4_fintopo2 A B C) = k8_margrel1) )  &  ( (~ (r2_hidden B C))  =>  ((k4_fintopo2 A B C) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(d4_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (C = (k4_fintopo3 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C D))  =>  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C (k2_nat_1 D 1)) = (k8_fin_topo A E)) ) ) ) ) )  &  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(d4_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k2_fintopo4 A) = (g1_orders_2 (k2_finseq_1 A) (k1_fintopo4 A))) ) ) ) ).
tt(d4_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))))) =>  ( (C = (k4_fintopo5 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (D = (k4_tarski E F))  =>  ((k1_fintopo5 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) C D) = (k2_xboole_0 (k2_zfmisc_1 (k1_tarski E) (k1_fintopo5 (k2_finseq_1 B) (k2_finseq_1 B) (k1_fintopo4 B) F)) (k2_zfmisc_1 (k1_fintopo5 (k2_finseq_1 A) (k2_finseq_1 A) (k1_fintopo4 A) E) (k1_tarski F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_fintopo6 A B) <=>  ((v4_fin_topo B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_fin_topo C A) & (r1_tarski B C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_orders_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k1_fin_topo A B))) ) ) ) ) ).
tt(d4_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ( (B = (k9_flang_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D A) &  ((r2_hidden D A) &  (C = (k5_afinsq_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_fomodel0,ax, (! [A:$i] :  ((k1_fomodel0 A) = (k9_funct_3 A A)) ) ).
tt(d4_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k4_fomodel1 A) = (k8_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (k6_subset_1 k4_numbers k5_numbers))) ) ) ).
tt(d4_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_fomodel2 C A B) <=>  ((m3_fomodel2 C A B) & (v1_funcop_1 C)) ) ) ) ) ) ) ) ).
tt(d4_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k5_fomodel3 A B))  <=>  ( ((k9_xtuple_0 C) = (k37_fomodel1 A))  &  (! [D:$i] :  ( ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  =>  ((k1_funct_1 C D) = (k4_fomodel3 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((m2_funct_2 C (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ( (C = (k2_fomodel4 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) =>  ((k3_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) C D) = (k3_tarski (k7_relat_1 (k3_tarski B) (k6_domain_1 (k9_setfam_1 (k1_fomodel4 A)) D)))) ) ) ) ) ) ) ) ) ) ).
tt(d4_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_frechet B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_frechet A B C)) ) ) ) ) ) ) ).
tt(d4_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_freealg B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_unialg_2 C A) & (r1_tarski B C))  =>  (C = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d4_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_fscirc_1 A B C) = (k2_circcomb (k3_fscirc_1 A B C) (k5_circcomb k4_facirc_1 (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp))))) ) ) ) ).
tt(d4_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 (k1_fscirc_2 B C D)) (k3_msafree2 (k1_fscirc_2 B C D))) =>  ( (E = (k4_fscirc_2 A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ( (A = (k2_nat_1 F 1))  &  (E = (k1_fscirc_1 (k1_funct_1 C A) (k1_funct_1 D A) (k3_fscirc_2 F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((r2_fsm_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (E = (k1_funct_1 D 1))  &  ((k2_fsm_1 A B E C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ((v3_fsm_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v2_fsm_2 C A B)) ) ) ) ) ) ) ).
tt(d4_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k3_fsm_3 A B C D) = (a_4_0_fsm_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k4_ftacell1 A B C D E) = (k12_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d4_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k4_funcop_1 A B C) = (k3_relat_1 (k13_funct_3 B (k2_funcop_1 (k9_xtuple_0 B) C)) A)) ) ) ) ) ) ).
tt(d4_funcsdom,ax, (! [A:$i] :  ((k8_funcsdom A) = (k8_funcop_1 k5_numbers A k6_numbers)) ) ).
tt(d4_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(d4_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C B) & (v1_funct_1 C)) ) )  =>  ((v3_funct_2 C A B) <=>  ((v2_funct_1 C) & (v2_funct_2 C B)) ) ) ) ) ) ).
tt(d4_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k7_funct_3 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ((k1_binop_1 C D E) = D) ) ) ) ) ) ) ) ) ) ).
tt(d4_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_funct_4 A B C D) = (k1_funct_4 (k16_funcop_1 A C) (k16_funcop_1 B D))) ) ) ) ) ).
tt(d4_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k4_funct_5 A) = (k2_funct_4 (k2_funct_5 A))) ) ) ).
tt(d4_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k4_funct_6 A) = (k1_setfam_1 (k10_xtuple_0 A))) ) ) ).
tt(d4_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k4_funct_7 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v1_funct_1 D) &  ((v1_partfun1 D k5_numbers) & (v1_funcop_1 D)) ) ) )  &  ( (C = (k1_funct_1 D (k3_finseq_1 B)))  &  ( ((k1_funct_1 D k6_numbers) = (k6_partfun1 A))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k2_nat_1 E 1) (k4_finseq_1 B)) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ( (F = (k1_funct_1 D E))  &  (G = (k1_funct_1 B (k2_nat_1 E 1))) )  =>  ((k1_funct_1 D (k2_nat_1 E 1)) = (k3_relat_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  ((m1_functor0 F A B C D E) <=> (m2_pboole F A D (k3_relat_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  ((r1_functor2 A B C D) =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B D F))) =>  ( (G = (k2_functor2 A B C D E F))  <=>  (G = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  ((r1_functor3 A B C D) <=>  ((r2_functor2 A B C D) &  ((r1_functor2 A B D C) &  (? [E:$i] :  ((m2_functor2 E A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (v3_altcat_3 (k2_functor2 A B C D E F) B (k3_functor0 A B C F) (k3_functor0 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (D = (k2_fuzzy_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_seq_1 D E) = (k2_square_1 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k4_fuzzy_2 A B) = (k5_funct_3 k1_xboole_0 (k2_zfmisc_1 A B))) ) ) ) ) ).
tt(d4_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ( (C = (k5_fuzzy_4 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) (k2_zfmisc_1 A B)) =>  ( ( (D = E)  =>  ((k1_fuzzy_4 A B C D E) = 1) )  &  ( (~  (D = E) )  =>  ((k1_fuzzy_4 A B C D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (C = k6_numbers)  =>  ( (D = (k2_fvaluat1 A B C))  <=>  (D = (u1_struct_0 A)) ) )  &  ( (~  (C = k6_numbers) )  =>  ( (D = (k2_fvaluat1 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k1_funct_1 E (k3_finseq_1 E)))  &  ( ((k3_finseq_1 E) = C)  &  ( ((k1_funct_1 E 1) = B)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden F (k4_finseq_1 E)) & (r2_hidden (k3_real_1 F 1) (k4_finseq_1 E)))  =>  ((k1_funct_1 E (k3_real_1 F 1)) = (k14_ideal_1 A B (k7_partfun1 (k1_zfmisc_1 (u1_struct_0 A)) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k5_fvsum_1 A B) = (k4_finseqop (u1_struct_0 A) (u1_struct_0 A) B (k5_vectsp_1 A))) ) ) ) ) ).
tt(d4_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_gate_5 A B C D) = (k36_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0 (k2_gate_1 B D) k1_xboole_0)) ) ) ) ) ).
tt(d4_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_gcd_1 A C B) =>  ( (C = (k4_struct_0 A))  |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k1_gcd_1 A B C))  <=>  ((k8_group_1 A D C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_genealg1 A B C D E F) = (k1_genealg1 A (k2_genealg1 A B C D E) (k2_genealg1 A C B D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (E = (k2_geomtrap A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k4_gfacirc1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k2_binarith B (k9_margrel1 C))) ) ) ) ) ) ) ) ).
tt(d4_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 (k1_gfacirc2 B C D)) (k3_msafree2 (k1_gfacirc2 B C D))) =>  ( (E = (k4_gfacirc2 A B C D))  <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ( (A = (k1_nat_1 F 1))  &  (E = (k12_gfacirc1 (k1_funct_1 C A) (k1_funct_1 D A) (k3_gfacirc2 F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_glib_000,ax, (k4_glib_000 = 4) ).
tt(d4_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k1_glib_001 A B) = (k12_finseq_1 (k6_glib_000 A) B)) ) ) ) ) ).
tt(d4_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r1_glib_002 A B) <=>  ((v3_glib_002 A) &  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (? [D:$i] :  ( ((v2_glib_001 D A) & (m3_glib_001 D A))  & (r1_glib_001 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_glib_003 A) <=>  ((r2_hidden k2_glib_003 (k1_relset_1 k5_numbers A)) &  ((v1_relat_1 (k1_funct_1 A k2_glib_003)) &  ((v4_relat_1 (k1_funct_1 A k2_glib_003) (k7_glib_000 A)) &  ((v1_funct_1 (k1_funct_1 A k2_glib_003)) & (v1_partfun1 (k1_funct_1 A k2_glib_003) (k7_glib_000 A))) ) ) ) ) ) ) ).
tt(d4_glib_004,ax, (k2_glib_004 = (k10_domain_1 k5_numbers k1_glib_000 k2_glib_000 k3_glib_000 k4_glib_000 k2_glib_003)) ).
tt(d4_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_glib_005 A B C D) <=>  ((r1_glib_005 A B C D) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (k7_glib_000 A)) &  ((v1_funct_1 E) &  ((v1_partfun1 E (k7_glib_000 A)) & (v4_valued_0 E)) ) ) )  =>  ((r1_glib_005 A E C D) => (r1_xxreal_0 (k1_glib_005 A E C D) (k1_glib_005 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ((v2_goboard1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (v3_funct_1 (k1_goboard1 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ).
tt(d4_goboard5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_goboard5 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C (k2_nat_1 B 1)))  &  ( (~  ( (~  ( (~ (r1_xxreal_0 B 1))  &  (~ (r1_xxreal_0 (k3_finseq_1 A) C)) ) )  & (r1_xxreal_0 (k3_finseq_1 A) (k2_nat_1 C 1))) )  &  (~ (r1_xboole_0 (k2_topreal1 2 A B) (k2_topreal1 2 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_gobrd13,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (D = (k4_gobrd13 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B E F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  (D = (k3_goboard5 B G H)) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  (D = (k3_goboard5 B G (k7_nat_d H 1))) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  (D = (k3_goboard5 B (k7_nat_d G 1) H)) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  (D = (k3_goboard5 B (k7_nat_d G 1) (k7_nat_d H 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang2 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (C = (k2_goedelcp A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) &  (B = (k5_qc_lang2 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k4_graph_1 A B) = (k3_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) B)) ) ) ) ) ).
tt(d4_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_graph_2 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k1_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k1_funct_1 A (k1_nat_1 B 1))) ) ) ) ) ) ) ) ) ).
tt(d4_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_graph_3 A B) = (k2_graph_3 A B (u4_struct_0 A))) ) ) ) ) ).
tt(d4_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((k2_graph_4 A B) = (a_2_1_graph_4 A B)) ) ) ) ).
tt(d4_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  (! [E:$i] :  ((r2_graph_5 A B C D E) <=>  ((r1_graph_5 A D B C) & (r1_tarski (k7_subset_1 (u1_struct_0 A) (k2_graph_5 A D) (k1_tarski C)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_graphsp,ax, (! [A:$i] :  ((m2_funct_2 A (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) D) B) C) = k1_xboole_0) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k8_graphsp A B C))  <=>  ( ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) D) B) C) = k1_xboole_0)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) E) B) C) = k1_xboole_0)  => (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_grcat_1 A B) = (k1_realset1 (u1_cat_1 A) (k1_grcat_1 A B))) ) ) ) ) ).
tt(d4_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A))))) )  =>  ( (B = (k3_gr_cy_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k7_card_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k7_card_1 A)) =>  ((k5_binop_1 (k7_card_1 A) B C D) = (k4_nat_d (k23_binop_2 C D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r2_groeb_1 A B C D E) <=>  ( ((k7_ideal_1 (k11_polynom1 A C) D) = E)  & (v9_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k3_groeb_2 A B C D E) = (k6_polynom1 A C (k5_polynom7 A C (k1_polyred A (k1_groeb_2 A (k2_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) (k3_termord A B C D)) C D) (k4_termord A B C E)) (k5_polynom7 A C (k1_polyred A (k1_groeb_2 A (k2_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) (k3_termord A B C E)) C E) (k4_termord A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k5_groeb_3 A B C D E) = (k2_groeb_3 A C D (k3_groeb_3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_group_10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (k1_funct_2 A A)) &  ((v1_group_10 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 A A))))) ) )  =>  ((r1_ordinal1 (k5_card_1 B) (k1_card_1 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_group_10 A B) (k3_group_10 A B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 A B) (k3_group_10 A B))))) )  =>  ( (F = (k4_group_10 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k3_group_10 A B)) =>  ((k1_funct_1 F G) = (k7_relset_1 A A (k1_group_10 C A E D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k4_group_11 A B C) = (a_3_3_group_11 A B C)) ) ) ) ) ) ) ).
tt(d4_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v1_group_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k1_group_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = C)  &  ((k6_algstr_0 A B C) = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_group_2 A B C) = (k2_group_2 A C (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(d4_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_group_3 A B C) = (k3_group_3 A B (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(d4_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( (C = (k5_group_4 A B))  <=>  ((r1_tarski B (u1_struct_0 C)) &  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ((r1_tarski B (u1_struct_0 D)) => (m1_group_2 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_5 A B C) = (a_3_0_group_5 A B C)) ) ) ) ) ) ) ).
tt(d4_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((k5_group_6 A B) = (g3_algstr_0 (k15_group_2 A B) (k4_group_6 A B))) ) ) ) ) ).
tt(d4_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 (u1_struct_0 B) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 (u1_struct_0 B) (u1_struct_0 B)))))) )  =>  ((v1_group_9 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D A) =>  ((v1_funct_1 (k1_funct_1 C D)) &  ((v1_funct_2 (k1_funct_1 C D) (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_group_6 (k1_funct_1 C D) B B) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (D = (k4_hahnban1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v4_hahnban B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k1_rlvect_1 A C D)) = (k8_real_1 D (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ((v1_hallmar1 B A) <=>  (! [C:$i] :  ((v1_finset_1 C) =>  ((r1_tarski C (k4_finseq_1 B)) => (r1_xxreal_0 (k5_card_1 C) (k5_card_1 (k1_hallmar1 A B C)))) ) ) ) ) ) ) ) ).
tt(d4_helly,ax, (! [A:$i] :  ((v1_helly A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~  ((r1_tarski B A) &  ( (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) & (r1_xboole_0 C D)) ) ) ) )  &  ((k1_setfam_1 B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d4_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k1_henmodel A) = (k3_qc_lang1 A)) ) ) ).
tt(d4_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  ((v2_hermitan C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v1_hermitan (k7_bilinear k1_complfld A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(d4_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k7_normform A) (u1_struct_0 (k12_normform A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_normform A) (u1_struct_0 (k12_normform A)))))) )  =>  ( (B = (k4_heyting1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((k3_funct_2 (k7_normform A) (u1_struct_0 (k12_normform A)) B C) = (k2_heyting1 A C)) ) ) ) ) ) ) ).
tt(d4_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)))))) )  =>  ( (C = (k4_heyting2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( (E = D)  =>  ((k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) C D) = (k3_substlat A B (k2_heyting2 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B)))) =>  ( (C = (k4_heyting3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (~  ( (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E k5_numbers))  =>  (~  ((r1_xxreal_0 E A) &  (D = (k2_heyting3 E B)) ) ) ) )  &  (~  (D = (k3_heyting3 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_polynom3 A)))))  =>  ((k4_hilbasis A B) = (a_2_0_hilbasis A B)) ) ) ) ) ).
tt(d4_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((m1_hilbert3 B A) <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k1_funct_1 A C) (k1_funct_1 A C)) &  ((v3_funct_2 (k1_funct_1 B C) (k1_funct_1 A C) (k1_funct_1 A C)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (D = (k4_hurwitz A B C))  <=>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 C E))  =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k1_binop_1 (k4_group_1 A) B (k6_xcmplx_0 (k6_xcmplx_0 C E) 1))) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 C E) =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_idea_1 A B C) = (k4_nat_d (k2_xcmplx_0 B C) (k5_series_1 2 A))) ) ) ) ) ) ) ).
tt(d4_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v1_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A C D) &  ((r1_incsp_1 A B E) &  ((r1_incsp_1 A C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ((r4_incsp_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r2_hidden D B) => (r1_incsp_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_index_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_index_1 C A B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  &  (C = (k4_tarski D E)) ) ) ) ) ) ) ) ) ).
tt(d4_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((k2_instalg1 A B C) = (k1_instalg1 B A C (k6_partfun1 (u1_struct_0 B)) (k6_partfun1 (u4_struct_0 B)))) ) ) ) ) ) ) ).
tt(d4_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) <=> (r1_int_1 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(d4_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 A) <=>  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_int_1 B A) &  ( (~  (B = 1) )  &  (~  (B = A) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_int_6 B A) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (E = (k7_xcmplx_0 (k19_rvsum_1 A) (k1_funct_1 A C)))  &  ((r2_int_1 (k3_xcmplx_0 D E) 1 (k1_funct_1 A C)) &  ((k1_funct_1 B C) = (k3_xcmplx_0 D (k7_xcmplx_0 (k19_rvsum_1 A) (k1_funct_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k3_int_7 A) = (g3_algstr_0 (k1_int_7 A) (k2_int_7 A))) ) ) ).
tt(d4_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_integr10 A B C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k2_integr10 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers E) = (k4_rcomp_1 B C))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_relset_1 k1_numbers E)) =>  ((k1_seq_1 E F) = (k4_integra5 F C A)) ) ) )  &  ((r4_limfunc2 E B) &  (D = (k2_limfunc2 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ((m2_integr15 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (E = (k3_integr15 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_seq_1 E F) = (k1_integr15 A B (k2_integra2 A C F) (k2_integr15 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ((m2_integr16 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (E = (k5_integr16 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers E F) = (k3_integr16 A B (k2_integra2 A C F) (k4_integr16 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [E:$i] :  ((m2_integr18 E A B C D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (F = (k3_integr18 A B C D E))  <=>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k1_normsp_1 A F G) = (k1_integr18 A B C (k2_integra2 B D G) (k2_integr18 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k2_numbers B) (k1_relset_1 k2_numbers A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k3_integr1c A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  (? [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  (? [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 k1_numbers)) &  ((r1_xxreal_0 D E) &  ( ((k1_rcomp_1 D E) = (k1_relset_1 k1_numbers B))  &  ((r1_tarski (k1_rcomp_1 D E) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k1_rcomp_1 D E) (k1_relset_1 k1_numbers G)) &  ((v3_rcomp_1 H) &  ((r1_tarski (k1_rcomp_1 D E) H) &  ((r2_fdiff_1 F H) &  ((r2_fdiff_1 G H) &  ((v1_fcont_1 (k2_fdiff_1 F H)) &  ((v1_fcont_1 (k2_fdiff_1 G H)) &  ((r2_relset_1 k1_numbers k2_numbers B (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers F (k25_valued_1 k1_numbers k1_numbers G k7_complex1)) (k1_rcomp_1 D E))) &  (C = (k2_integr1c D E F G H A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (C = 1)  =>  ( (D = (k2_integra1 A B C))  <=>  ( ((k5_seq_4 D) = (k5_seq_4 A))  &  ((k4_seq_4 D) = (k1_seq_1 B C)) ) ) )  &  ( (~  (C = 1) )  =>  ( (D = (k2_integra1 A B C))  <=>  ( ((k5_seq_4 D) = (k1_seq_1 B (k5_real_1 C 1)))  &  ((k4_seq_4 D) = (k1_seq_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_integra5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) =>  ((k4_integra5 A B C) = (k2_integra5 (k3_integra5 A B) C)) )  &  ( (~ (r1_xxreal_0 A B))  =>  ((k4_integra5 A B C) = (k1_real_1 (k2_integra5 (k3_integra5 B A) C))) ) ) ) ) ) ) ) ) ).
tt(d4_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k4_interva1 A B C) = (k2_setfam_1 B C)) ) ) ) ) ) ) ).
tt(d4_irrat_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (A = k4_irrat_1)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k3_power (k2_xcmplx_0 1 (k13_complex1 1 B)) B)) ) ) ) ) ) ).
tt(d4_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r1_isocat_1 A B) <=>  (? [C:$i] :  ((m2_cat_1 C A B) & (v12_cat_1 C A B)) ) ) ) ) ) ) ).
tt(d4_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E A (k11_nattra_1 B C)) =>  ( (E = (k5_isocat_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) E F) = (k4_tarski (k4_tarski (k12_cat_2 A B C D (k3_graph_1 A F)) (k12_cat_2 A B C D (k4_graph_1 A F))) (k4_isocat_2 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_isomichi,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k1_tops_1 A B))) ) ) ) ) ).
tt(d4_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ((v1_jgraph_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xboole_0 (k2_topreal1 A B C) (k2_topreal1 A B D)))  &  ( (~  ( ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal1 A B C) (k2_topreal1 A B D)) = (k1_tarski (k1_funct_1 B C)))  &  ( ((k1_funct_1 B C) = (k1_funct_1 B D))  |  ((k1_funct_1 B C) = (k1_funct_1 B (k2_nat_1 D 1))) ) ) )  &  ( (~  ( ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal1 A B C) (k2_topreal1 A B D)) = (k1_tarski (k1_funct_1 B (k2_nat_1 C 1))))  &  ( ((k1_funct_1 B (k2_nat_1 C 1)) = (k1_funct_1 B D))  |  ((k1_funct_1 B (k2_nat_1 C 1)) = (k1_funct_1 B (k2_nat_1 D 1))) ) ) )  &  (~  ((k2_topreal1 A B C) = (k2_topreal1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 (k18_euclid B) k6_numbers) |  ((k4_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k9_real_1 1 A)) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k9_real_1 1 A)))))) (k12_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 (k18_euclid B) k6_numbers))  &  (~  ((k4_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k7_real_1 1 A)) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k7_real_1 1 A)))))) (k12_euclid B))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) &  (~ (r1_xxreal_0 (k18_euclid B) k6_numbers)) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  (~ (r1_xxreal_0 (k18_euclid B) k6_numbers)) ) )  &  (~  ((k4_jgraph_4 A B) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k4_jgraph_6 A B C D) = (a_4_3_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k4_jordan19 A) = (k1_kurato_2 (k15_euclid 2) (k2_jordan19 A))) ) ) ).
tt(d4_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r4_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k17_euclid F) E))  &  ((r1_jordan5c A B C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C G F) & (r1_jordan5c A B C D G))  => (r1_xxreal_0 E (k17_euclid G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_jordan24,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_jordan24 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc D A) => (v4_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k1_jordan2c A B) = (k3_tarski (a_2_0_jordan2c A B))) ) ) ) ) ).
tt(d4_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( (~  (B = (k1_funct_1 A 1)) )  =>  ((k3_jordan3 A B) = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k1_jordan3 A B)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B))) )  &  ( (B = (k1_funct_1 A 1))  =>  ((k3_jordan3 A B) = (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)) ) ) ) ) ) ) ).
tt(d4_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r3_jordan4 A B C D) <=>  ((r1_jordan4 A B C D) | (r2_jordan4 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k4_jordan5d A))  <=>  ((r2_hidden (k4_tarski (k3_finseq_1 (k2_goboard2 A)) B) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d4_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((k4_jordan6 A B C D) = (a_4_1_jordan6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_jordan_a C A) =>  ( ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 C) B) |  ((k2_jordan_a A B C) = (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k1_nat_1 B 1)))) ) )  &  ( (~  ((r1_xxreal_0 1 B) &  (~ (r1_xxreal_0 (k3_finseq_1 C) B)) ) )  =>  ((k2_jordan_a A B C) = (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))) ) ) ) ) ) ) ) ) ).
tt(d4_jordan,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (A = k6_jordan)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers A B) = (k9_real_1 (k18_euclid (k1_jordan (k15_euclid 2) (k15_euclid 2) B)) (k18_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) B)))) ) ) ) ) ) ).
tt(d4_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( (E = (k3_knaster A B C D))  <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v5_ordinal1 F)) )  &  ( (E = (k1_ordinal2 F))  &  ( ((k9_xtuple_0 F) = (k1_ordinal1 D))  &  ( ((k1_funct_1 F k1_xboole_0) = C)  &  ( (! [G:$i] :  ((v3_ordinal1 G) =>  ((r2_hidden (k1_ordinal1 G) (k1_ordinal1 D)) =>  ((k1_funct_1 F (k1_ordinal1 G)) = (k1_funct_1 B (k1_funct_1 F G))) ) ) )  &  (! [G:$i] :  ((v3_ordinal1 G) =>  ( ((r2_hidden G (k1_ordinal1 D)) & (v4_ordinal1 G))  =>  ( (G = k1_xboole_0)  |  ((k1_funct_1 F G) = (k15_lattice3 A (k2_relset_1 (k10_xtuple_0 F) (k5_relat_1 F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ((m1_kolmog01 E C A B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ((m2_kolmog01 F A B C D E) <=>  (! [G:$i] :  ((r2_hidden G D) => (r2_hidden (k1_funct_1 F G) (k13_prob_1 A C B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 A) B C) (k3_funct_2 k5_numbers (k9_setfam_1 A) B (k2_nat_1 C 1)))) ) ) ) ) ) ).
tt(d4_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_kurato_1 A B) = (k4_enumset1 (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))))))) ) ) ) ) ).
tt(d4_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_lang1 A B C) <=>  (? [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) &  (? [E:$i] :  ((m2_finseq_2 E (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) &  (? [F:$i] :  ((m2_finseq_2 F (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((r2_relset_1 k5_numbers (u1_struct_0 A) B (k1_pre_poly (u1_struct_0 A) (k1_pre_poly (u1_struct_0 A) D (k3_pre_poly (u1_struct_0 A) G)) E)) &  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k1_pre_poly (u1_struct_0 A) (k1_pre_poly (u1_struct_0 A) D F) E)) & (r1_lang1 A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) C C) =>  ((k5_laplace A B C D E) = (k12_matrix_3 (k7_nat_d C 1) D (k2_laplace A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k3_lattice2 A B C D) = (k7_setwiseo A (u1_struct_0 B) (u1_lattices B) C D)) ) ) ) ) ) ) ) ) ).
tt(d4_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_lattice3 A))) =>  ((k5_lattice3 A B) = B) ) ) ) ) ).
tt(d4_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_lattice4 C A B) =>  ((r2_lattice4 A B C) <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k6_lattices A)) = (k6_lattices B)) ) ) ) ) ) ) ) ).
tt(d4_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_yellow_0 B (k1_lattice5 A)) &  ((v6_yellow_0 B (k1_lattice5 A)) & (m1_yellow_0 B (k1_lattice5 A))) )  =>  (~  ( (? [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((r2_hidden C (u1_struct_0 B)) &  (~  (C = (k6_partfun1 A)) ) ) ) )  &  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) &  ((r2_hidden (k4_tarski F G) (k5_eqrel_1 A D E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  =>  (~  ( ((k3_finseq_1 H) = C)  & (r1_lattice5 A H F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (~  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k2_lattice5 A B))  <=>  ( (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) &  ((r2_hidden (k4_tarski F G) (k5_eqrel_1 A D E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  =>  (~  ( ((k3_finseq_1 H) = (k2_nat_1 C 2))  & (r1_lattice5 A H F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (? [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  (? [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  (? [F:$i] :  (? [G:$i] :  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) &  ((r2_hidden (k4_tarski F G) (k5_eqrel_1 A D E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  =>  (~  ( ((k3_finseq_1 H) = (k2_nat_1 C 1))  & (r1_lattice5 A H F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v2_lattice6 A) <=> (v1_wellfnd1 (k7_lattice3 (k3_lattice3 A)))) ) ) ).
tt(d4_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattice7 A B C) <=>  ((r2_orders_2 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_orders_2 A B D) & (r2_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k1_lattice8 A) (k1_lattice8 A)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lattice8 A) (k1_lattice8 A)) (u1_struct_0 B))))) )  =>  ( (E = (k2_lattice8 A B C D))  <=>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k1_binop_1 E F G) = (k3_lattice5 A B C F G)) ) ) ) )  &  ( ((k1_binop_1 E (k1_tarski A) (k1_tarski A)) = (k3_yellow_0 B))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) (k1_tarski (k1_tarski A))) = (k3_yellow_0 B))  &  ( ((k1_binop_1 E (k1_tarski A) (k1_tarski (k1_tarski A))) = (k12_lattice3 B (k13_lattice3 B (k3_lattice5 A B C (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E (k1_tarski (k1_tarski A)) (k1_tarski A)) = (k12_lattice3 B (k13_lattice3 B (k3_lattice5 A B C (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k1_binop_1 E F (k1_tarski A)) = (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E (k1_tarski A) F) = (k13_lattice3 B (k3_lattice5 A B C F (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ( ((k1_binop_1 E F (k1_tarski (k1_tarski A))) = (k13_lattice3 B (k3_lattice5 A B C F (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)))  &  ((k1_binop_1 E (k1_tarski (k1_tarski A)) F) = (k13_lattice3 B (k3_lattice5 A B C F (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v4_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B C) = (k1_lattices A C B)) ) ) ) ) ) ) ) ).
tt(d4_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v4_valued_0 D)) )  =>  ( (D = (k3_lexbfs A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 A))  &  (! [E:$i] :  ( ( ((r2_hidden E B) & (r2_hidden E (k9_xtuple_0 A)))  =>  ((k1_recdef_1 D E) = (k2_nat_1 (k1_recdef_1 A E) C)) )  &  ( (~ (r2_hidden E B))  =>  ((k1_recdef_1 D E) = (k1_recdef_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_lfuzzy_0 A) = (k6_yellow_1 A (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)))) ) ) ).
tt(d4_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v2_lfuzzy_1 B A) <=> (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k2_fuzzy_4 A A B) B)) ) ) ) ) ).
tt(d4_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_limfunc1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C D) & (r1_xxreal_0 (k1_seq_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D B))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_limfunc3 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k1_limfunc3 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k10_xtuple_0 D) (k6_subset_1 (k9_xtuple_0 A) (k1_tarski B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k5_lopban_1 A B) = (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) ) ) ) ) ).
tt(d4_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k10_lopban_1 A A) (k10_lopban_1 A A)) (k10_lopban_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_lopban_1 A A) (k10_lopban_1 A A)) (k10_lopban_1 A A))))) )  =>  ( (B = (k5_lopban_2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  ((k5_binop_1 (k10_lopban_1 A A) B C D) = (k3_lopban_2 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v25_algstr_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( ((k6_algstr_0 A B C) = (k5_struct_0 A))  &  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d4_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k3_lopban_4 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C A) =>  ((k8_nat_1 k1_numbers B C) = (k10_real_1 1 (k8_real_1 (k3_newton C) (k3_newton (k7_nat_d A C))))) )  &  ( (~ (r1_xxreal_0 C A))  =>  ((k8_nat_1 k1_numbers B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d4_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k6_lopclset A) = (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A))) ) ) ).
tt(d4_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k1_numbers (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) )  =>  ( (B = (k4_lpspace1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  ((k2_binop_1 k1_numbers (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers) B C D) = (k12_rfunct_3 A k1_numbers D C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k3_lpspace2 A B C D) = (a_4_1_lpspace2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k4_ltlaxio1 A B) = (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B k2_hilbert1)) k2_hilbert1)) ) ) ) ) ).
tt(d4_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_finseq_1 B) & (v2_card_3 B))  =>  ((m1_margrel1 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C B) =>  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ) ) ).
tt(d4_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_mathmorp A B C) = (k6_rusub_4 A (k3_mathmorp A B C) C)) ) ) ) ) ) ) ).
tt(d4_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v4_matrix10 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) => (r1_xxreal_0 k6_numbers (k3_matrix_1 k1_numbers A B C))) ) ) ) ) ) ) ) ).
tt(d4_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [E:$i] :  ((m1_matrix_1 E C A B) =>  (! [F:$i] :  ((m1_matrix_1 F C A B) =>  ( (F = (k4_matrix11 A B C D E))  <=>  ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 F) = (k1_matrix_1 E))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden (k4_tarski G H) (k2_matrix_1 E)) &  ((k1_funct_1 D G) = I) )  =>  ((k3_matrix_1 C F G H) = (k3_matrix_1 C E I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 (k1_matrix_1 D))) & (r2_hidden F (k2_finseq_1 (k1_matrix_1 D))))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) A B) =>  ( (G = (k4_matrix12 A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 D))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden H (k4_finseq_1 D)) & (r2_hidden I (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (I = E)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H F)) )  &  ( ( (I = F)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H E)) )  &  (~  ( (~  (I = E) )  &  ( (~  (I = F) )  &  (~  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k8_matrix13 A B))  <=>  ( (? [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  &  (? [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  &  ((r1_tarski (k2_zfmisc_1 D E) (k2_matrix_1 B)) &  ( ((k5_card_1 D) = (k5_card_1 E))  &  ( ((k5_card_1 D) = C)  &  (~  ((k12_matrix_3 (k5_card_1 D) A (k7_matrix13 (u1_struct_0 A) B D E)) = (k4_struct_0 A)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski (k2_zfmisc_1 D E) (k2_matrix_1 B)) &  ((k5_card_1 D) = (k5_card_1 E)) )  =>  ( ((k12_matrix_3 (k5_card_1 D) A (k7_matrix13 (u1_struct_0 A) B D E)) = (k4_struct_0 A))  | (r1_xxreal_0 (k5_card_1 D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k5_matrix15 A B C) = (a_3_2_matrix15 A B C)) ) ) ) ) ) ) ).
tt(d4_matrix16,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_matrix16 A B C) <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((k3_matrix_1 A B D E) = (k1_funct_1 C (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 D E) (k3_finseq_1 C)) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix17,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_matrix17 A B C) <=>  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ( ((k2_xcmplx_0 D E) = (k2_xcmplx_0 (k3_finseq_1 C) 1))  |  ((k3_matrix_1 A B D E) = (k1_funct_1 C (k6_int_1 (k6_xcmplx_0 (k2_xcmplx_0 D E) 1) (k3_finseq_1 C)))) ) ) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((k2_xcmplx_0 D E) = (k2_xcmplx_0 (k3_finseq_1 C) 1)) )  =>  ((k3_matrix_1 A B D E) = (k1_funct_1 C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_matrix_1 A)) ) )  =>  ((k2_matrix_1 A) = (k2_zfmisc_1 (k4_finseq_1 A) (k2_finseq_1 (k1_matrix_1 A)))) ) ) ).
tt(d4_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_2 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((r1_xxreal_0 E D) |  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( (D = (k4_matrix_3 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k13_fvsum_1 A (k8_matrix_1 (u1_struct_0 A) B E) (k9_matrix_1 (u1_struct_0 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k4_matrix_5 A) = (k2_matrix_5 (k2_matrix_3 k1_complfld (k1_matrix_5 A)))) ) ) ).
tt(d4_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (D = (k5_matrix_6 A B C))  <=> (r2_matrix_6 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k4_matrix_7 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k7_partfun1 (u1_struct_0 A) C D) = (k2_group_1 A (k7_partfun1 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v4_matrix_8 C A B) <=>  ((v1_matrix_6 C A B) &  ((k5_matrix_6 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(d4_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( (C = (k9_matrixj1 A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k1_matrix_1 (k2_matrixj1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrixj2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ((v2_matrixj2 C A B) <=>  (? [D:$i] :  ((v7_ordinal1 D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C D) E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k4_matrixr1 A) = (k2_matrixr1 (k2_matrix_3 k2_vectsp_1 (k1_matrixr1 A)))) ) ) ).
tt(d4_matrixr2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_matrixr2 A B) = (k2_funct_7 (k5_finseq_2 k1_numbers A k6_numbers) B 1)) ) ) ) ) ).
tt(d4_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( (F = (k4_matrlin A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) F G) = (k4_vectsp_1 A C E (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_matroid0 A) <=>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden B (k1_matroid0 A)) &  ((r2_hidden C (k1_matroid0 A)) &  ( ((k5_card_1 C) = (k2_nat_1 (k5_card_1 B) 1))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k7_subset_1 (u1_struct_0 A) C B)) & (r2_hidden (k2_xboole_0 B (k1_tarski D)) (k1_matroid0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k1_numbers)))  =>  ( (D = (k6_matrprob A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) =>  ((k3_matrix_1 k1_numbers D E F) = (k11_binop_2 (k11_binop_2 (k1_seq_1 A E) (k3_matrix_1 k1_numbers C E F)) (k1_seq_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v2_matrtop3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k12_euclid C) = (k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B C))) ) ) ) ) ) ) ) ).
tt(d4_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k1_mazurulm A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k5_algstr_0 A (k1_rlvect_1 A B 2) D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((m1_measure1 D A B C) <=>  ((k12_supinf_2 C D) = k1_supinf_2) ) ) ) ) ) ) ) ) ).
tt(d4_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k2_measure3 A B C)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (E = (k3_measure3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  ((r2_hidden F B) &  ((r1_tarski F D) & (m1_measure3 (k7_subset_1 A D F) A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_measure5 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  (A = (k3_rcomp_1 B C)) ) ) ) ) ) ) ) ).
tt(d4_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  ((v2_xxreal_2 A) <=>  ((v4_xxreal_2 A) & (r2_hidden (k2_seq_4 A) A)) ) ) ) ).
tt(d4_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_measure7 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (C = (k3_measure7 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k12_supinf_2 C D) = (k2_measure5 (k2_measure7 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d4_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 A)))))) )  =>  ((m4_measure8 D A B C) <=>  (! [E:$i] :  ((v7_ordinal1 E) => (m3_measure8 (k8_nat_1 (k9_funct_2 k5_numbers (k9_setfam_1 A)) D E) A (k8_nat_1 (k9_setfam_1 A) C E) B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k7_member_1 A) = (a_1_3_member_1 A)) ) ) ).
tt(d4_membered,ax, (! [A:$i] :  ((v4_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_rat_1 B)) ) ) ) ).
tt(d4_mesfun6c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( (D = (k2_mesfun6c A B C))  <=>  ( ((k1_relset_1 B D) = (k1_relset_1 B C))  &  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B D)) =>  ((k1_seq_1 D E) = (k3_power (k1_seq_1 C E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k4_mesfun7c A B) = (k3_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d4_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((v1_mesfun9c B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) => (r1_xxreal_0 (k17_complex1 (k1_seq_1 (k4_mesfunc5 A k1_numbers B D) E)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (D = (k4_mesfunc1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k6_subset_1 (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)) (k2_xboole_0 (k3_xboole_0 (k8_relat_1 B (k1_tarski k1_supinf_1)) (k8_relat_1 C (k1_tarski k1_supinf_1))) (k3_xboole_0 (k8_relat_1 B (k1_tarski k2_supinf_1)) (k8_relat_1 C (k1_tarski k2_supinf_1))))))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k12_supinf_2 D E) = (k4_supinf_2 (k12_supinf_2 B E) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc2 A B C) <=>  ((v3_valued_0 C) &  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden F (k1_funct_1 D E)) & (r2_hidden G (k1_funct_1 D E))) )  =>  ((k12_supinf_2 C F) = (k12_supinf_2 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc5,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_mesfunc5 A) <=>  (~ (r2_hidden k1_supinf_1 (k10_xtuple_0 A))) ) ) ) ).
tt(d4_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r3_mesfunc6 A B C D) <=> (r1_mesfunc5 A B C (k1_mesfunc5 A D))) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers))))  =>  ( (D = (k5_mesfunc7 A B C))  <=>  ( ((k1_relset_1 B D) = (k1_relset_1 B C))  &  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B D)) =>  ((k12_supinf_2 D E) = (k4_mesfunc7 (k12_supinf_2 C E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k2_mesfunc8 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k1_rinfsup2 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( (C = (k4_mesfunc9 A B))  <=>  ((r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers C k6_numbers) (k4_mesfunc5 A k7_numbers B k6_numbers)) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers C (k1_nat_1 D 1)) (k3_mesfunc1 A (k4_mesfunc5 A k7_numbers C D) (k4_mesfunc5 A k7_numbers B (k1_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ).
tt(d4_metric_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ((v4_metric_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_metric_1 A A B C D) = (k1_metric_1 A A B D C)) ) ) ) ) ) ) ) ) ).
tt(d4_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k2_metric_2 A) = (a_1_0_metric_2 A)) ) ) ).
tt(d4_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers)))) )  =>  ( (D = (k4_metric_3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 C)) =>  (! [K:$i] :  ((m1_subset_1 K (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ( ( (K = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) E G I))  &  (L = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) F H J)) )  =>  ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) D K L) = (k7_real_1 (k7_real_1 (k4_metric_1 A E F) (k4_metric_1 B G H)) (k4_metric_1 C I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_metric_6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k10_xtuple_0 B) (k9_metric_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d4_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v2_mfold_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_connsp_2 D B C) &  (? [E:$i] :  ( ((v3_pre_topc E (k15_euclid A)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  & (r1_metrizts B (k15_euclid A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_mfold_2 A) = (k8_toprealb (k23_binop_2 A 1))) ) ) ).
tt(d4_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_midsp_1 A B C D E) <=>  ((k3_midsp_1 A B E) = (k3_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_midsp_2 A B C) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (F = (k2_midsp_2 A B C D E))  <=>  ((k2_binop_1 A A (u1_struct_0 B) C D F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  ((r1_midsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  ((k4_midsp_3 A C D (k6_midsp_3 A C E B D)) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k4_mmlquery A B C) = (a_3_1_mmlquery A B C)) ) ) ) ) ) ).
tt(d4_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((l1_mod_2 B A) =>  ((k3_mod_2 A B) = (u2_mod_2 A B)) ) ) ) ) ).
tt(d4_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m1_mod_3 C A B) <=> (v1_mod_3 C A B)) ) ) ) ) ) ) ).
tt(d4_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  (! [C:$i] :  ( ((v7_vectsp_1 C (k2_mod_4 A)) & (l1_vectsp_1 C (k2_mod_4 A)))  =>  ( (C = (k5_mod_4 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 B)) (u1_struct_0 B))))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) D (k1_mod_4 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_vectsp_2 A B))) =>  (C = (g1_vectsp_1 (k2_mod_4 A) (u1_struct_0 B) (u1_algstr_0 B) (k4_struct_0 B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_modal_1,ax, (k4_modal_1 = (k8_mcart_1 k5_numbers k1_numbers (k8_domain_1 k5_numbers k6_numbers 1 2) k5_numbers)) ).
tt(d4_modelc_1,ax, (! [A:$i] :  ( ((v1_xboolean A) =>  ((k4_modelc_1 A) = A) )  &  ( (~ (v1_xboolean A))  =>  ((k4_modelc_1 A) = k7_margrel1) ) ) ) ).
tt(d4_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k4_modelc_2 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 1) A) B)) ) ) ) ) ).
tt(d4_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r2_hidden C (u2_modelc_3 A B)) =>  (! [D:$i] :  ( ((v1_modelc_3 D A) & (l1_modelc_3 D A))  =>  ( (D = (k5_modelc_3 A B C))  <=>  ( ((u1_modelc_3 A D) = (k2_xboole_0 (u1_modelc_3 A B) (k1_tarski C)))  &  ( ((u2_modelc_3 A D) = (k2_xboole_0 (k7_subset_1 (k1_modelc_3 A) (u2_modelc_3 A B) (k1_tarski C)) (k7_subset_1 (k1_modelc_3 C) (k2_modelc_3 C) (u1_modelc_3 A B))))  &  ((u3_modelc_3 A D) = (k2_xboole_0 (u3_modelc_3 A B) (k4_modelc_3 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_moebius1 A) = (a_1_0_moebius1 A)) ) ) ).
tt(d4_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v4_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E A) &  ((k5_binop_1 A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_monoid_1,ax, (! [A:$i] :  ((k13_monoid_1 A) = (k12_monoid_1 k5_monoid_0 A)) ) ).
tt(d4_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v1_msafree2 A) <=>  (~  ((k2_msafree2 A) = k1_xboole_0) ) ) ) ) ).
tt(d4_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ((k4_msafree3 A B C) = (k2_msafree3 A C)) ) ) ) ) ) ) ).
tt(d4_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m1_msafree C A B) <=> (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k12_msualg_2 A B C)) (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(d4_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  ((v1_msalimit D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_binop_1 D E E) = (k2_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 C D)) =>  ((k5_msaterm A B C D E) = (k1_trees_4 (k4_tarski E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msinst_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_altcat_1 C) & (l2_altcat_1 C)) )  =>  ( (C = (k4_msinst_1 A B))  <=>  ( ((u1_struct_0 C) = (k2_msinst_1 A B))  &  ( (! [D:$i] :  ((m1_subset_1 D (k2_msinst_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_msinst_1 A B)) =>  ((k1_binop_1 (u1_altcat_1 C) D E) = (k3_msinst_1 A B D E)) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_funcop_1 G)) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) & (v1_funcop_1 H)) )  =>  ( ((r2_hidden G (k1_binop_1 (u1_altcat_1 C) D E)) & (r2_hidden H (k1_binop_1 (u1_altcat_1 C) E F)))  =>  ((k1_binop_1 (k4_altcat_1 (u1_struct_0 C) (u1_altcat_1 C) (u2_altcat_1 C) D E F) H G) = (k8_pboole G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v3_msscyc_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ( ((v7_graph_1 D A) & (m1_graph_1 D A))  =>  ( ((k1_funct_1 (k7_graph_2 A D) (k2_nat_1 (k3_finseq_1 D) 1)) = B)  =>  ((v1_xboole_0 D) | (r1_xxreal_0 (k3_finseq_1 D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((k4_msscyc_2 A) = (g1_graph_1 (u1_struct_0 A) (k1_msscyc_2 A) (k2_msscyc_2 A) (k3_msscyc_2 A))) ) ) ).
tt(d4_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v3_mssubfam C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r1_pboole A D C) & (r1_pboole A E C))  => (r1_pboole A (k3_pboole A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((k3_msualg_1 A B C) = (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A C))) B)) ) ) ) ) ) ) ).
tt(d4_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( (C = (k2_msualg_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k1_msualg_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ( ((v1_msualg_3 D) & (v2_msualg_3 D A B C))  =>  (! [E:$i] :  ((m2_pboole E A C B) =>  ( (E = (k4_msualg_3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F A) =>  ((k1_funct_1 E F) = (k2_funct_1 (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((v3_msualg_4 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 A D B)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k9_xtuple_0 E)) => (r2_hidden (k4_tarski (k1_funct_1 E G) (k1_funct_1 F G)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) G)))) ) )  => (r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A D B) (k4_msualg_1 A D B) (k5_msualg_1 A D B) E) (k3_funct_2 (k3_msualg_1 A D B) (k4_msualg_1 A D B) (k5_msualg_1 A D B) F)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k2_msualg_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  (! [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  =>  ( (E = (k4_msualg_5 A B C D))  <=>  (? [F:$i] :  ((m1_msualg_4 F A B B) &  ((r8_pboole A F (k2_pboole A C D)) & (r8_pboole A E (k3_msualg_5 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( (F = (k4_msualg_6 A B C D E))  <=>  ( ((k9_xtuple_0 F) = (k1_funct_1 (u3_msualg_1 A D) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) C)))  &  (! [G:$i] :  ((r2_hidden G (k1_funct_1 (u3_msualg_1 A D) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) C))) =>  ((k1_funct_1 F G) = (k1_funct_1 (k5_msualg_1 A B D) (k2_funct_7 E C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_msualg_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  ( (C = (k1_msualg_7 A B))  <=>  ( ((u1_struct_0 C) = (k1_rcomp_1 A B))  &  ( ((u2_lattices C) = (k1_realset1 k2_real_lat (k1_rcomp_1 A B)))  &  ((u1_lattices C) = (k1_realset1 k1_real_lat (k1_rcomp_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v4_nagata_1 B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ((v2_nagata_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) ) )  &  (B = (k2_nagata_1 A C)) ) ) ) ) ) ) ) ).
tt(d4_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k6_nat_3 A B C))  <=>  (! [E:$i] :  ( ((r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E)) =>  ((k1_funct_1 D E) = (k1_seq_1 C E)) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E)))  =>  ((k1_funct_1 D E) = (k1_seq_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_nat_5 A) = (k3_nat_5 1 A)) ) ) ).
tt(d4_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k2_int_2 A B))  <=>  ((r1_nat_d A C) &  ((r1_nat_d B C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_nat_d A D) & (r1_nat_d B D))  => (r1_nat_d C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_nat_lat,ax, (k4_nat_lat = 1) ).
tt(d4_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_nattra_1 D A B C C) =>  ( (D = (k3_nattra_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u4_struct_0 B) D E) = (k4_cat_1 B (k8_cat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers))))  =>  ((r4_ncfcont2 A B C) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden F A) &  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B F G))))  & (r1_xxreal_0 D (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C F) (k7_partfun1 k2_numbers C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_ndiff_1 C A B) <=>  ((v3_normsp_1 C A) &  ((k6_normsp_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(d4_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_ndiff_2 A B C D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (F = (k3_ndiff_2 A B C D E))  <=>  (? [G:$i] :  ((m1_nfcont_1 G A D) &  ((r1_tarski G (k1_relset_1 (u1_struct_0 A) C)) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I (k18_complex1 J)))  &  ( (~  (J = k6_numbers) )  &  ((r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A E J) D) G) & (r1_xxreal_0 H (k1_normsp_0 B (k5_algstr_0 B (k1_rlvect_1 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 A (k1_rlvect_1 A E J) D)) (k7_partfun1 (u1_struct_0 B) C D)) (k2_real_1 J)) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_ndiff_3 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k1_ndiff_3 A B C))  <=>  (? [E:$i] :  ((m1_rcomp_1 E C) &  ((r1_tarski E (k1_relset_1 k1_numbers B)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 F A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_ndiff_3 G A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ( (D = (k3_funct_2 k1_numbers (u1_struct_0 A) F 1))  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B H) (k7_partfun1 (u1_struct_0 A) B C)) = (k3_rlvect_1 A (k3_funct_2 k1_numbers (u1_struct_0 A) F (k10_binop_2 H C)) (k7_partfun1 (u1_struct_0 A) G (k10_binop_2 H C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((r2_ndiff_4 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( (D = (k2_ndiff_4 A B C))  <=>  ( ((k1_relset_1 k1_numbers D) = C)  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = (k1_ndiff_4 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)))))) )  =>  ( (D = (k4_ndiff_5 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A B))) =>  ((k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) D E) = (k2_funct_7 C B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_neckla_2,ax, (! [A:$i] :  ( (A = k3_neckla_2)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (? [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  &  ( (B = C)  & (r2_hidden (u1_struct_0 C) k13_classes2)) ) ) ) ) ) ) ).
tt(d4_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_necklace A) <=> (v5_relat_2 (u1_orders_2 A))) ) ) ).
tt(d4_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_net_1 A B C) <=>  ((r2_hidden (k4_tarski C B) (k1_net_1 A)) & (r2_hidden B (u4_struct_0 A))) ) ) ) ) ) ).
tt(d4_newton,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k7_newton A B C))  <=>  ( ((k3_finseq_1 D) = (k1_nat_1 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden E (k4_finseq_1 D)) &  ( (G = (k5_real_1 E 1))  &  (F = (k6_xcmplx_0 C G)) ) )  =>  ((k1_funct_1 D E) = (k8_real_1 (k8_real_1 (k6_newton G C) (k1_newton A F)) (k1_newton B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 B A) <=> (v2_nfcont_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(d4_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_euclid A)) =>  ((r2_nfcont_4 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) &  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  &  ( (C = D)  &  ( (B = E)  & (r2_nfcont_1 (k4_real_ns1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((k3_normform A B C D) = (k1_domain_1 A B (k2_finsub_1 A (k2_domain_1 A B C) (k2_domain_1 A B D)) (k2_finsub_1 B (k3_domain_1 A B C) (k3_domain_1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(d4_normsp_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k4_normsp_0 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers C D) = (k1_normsp_0 A (k3_funct_2 k5_numbers (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d4_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k4_normsp_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k5_algstr_0 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rltopsp1 B) & (l1_rltopsp1 B)) )  =>  ( (B = (k4_normsp_2 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u1_algstr_0 B) (u1_algstr_0 A)) &  ((r1_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 B) (u1_rlvect_1 A)) &  ((u1_pre_topc B) = (u1_pre_topc (k3_normsp_2 A))) ) ) ) ) ) ) ) ) ) ).
tt(d4_ntalgo_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (k2_zfmisc_1 k4_numbers k4_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  ( (B = (k4_ntalgo_1 A))  <=>  ( ( ((k3_finseq_1 A) = 1)  =>  (B = (k1_xtuple_0 (k1_funct_1 A 1))) )  &  (~  ( (~  ((k3_finseq_1 A) = 1) )  &  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k4_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k4_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k4_numbers) =>  (~  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 A))  &  ( ((k3_finseq_1 E) = (k6_xcmplx_0 (k3_finseq_1 A) 1))  &  ( ((k3_finseq_1 F) = (k6_xcmplx_0 (k3_finseq_1 A) 1))  &  ( ((k1_funct_1 C 1) = 1)  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ((r1_xxreal_0 1 I) &  ((r1_xxreal_0 I (k6_xcmplx_0 (k3_finseq_1 C) 1)) &  (! [J:$i] :  ((m1_subset_1 J k4_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k4_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k4_numbers) =>  (~  ( (K = (k2_xtuple_0 (k1_funct_1 A I)))  &  ( ((k1_funct_1 C (k1_nat_1 I 1)) = (k3_xcmplx_0 (k1_funct_1 C I) K))  &  ( (L = (k1_funct_1 C (k1_nat_1 I 1)))  &  ( (J = (k2_xtuple_0 (k1_funct_1 A (k1_nat_1 I 1))))  &  ( ((k1_funct_1 F I) = (k3_ntalgo_1 L J))  &  ((k1_funct_1 E I) = L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (G = (k2_xtuple_0 (k1_funct_1 A (k3_finseq_1 C))))  &  ( (H = (k3_xcmplx_0 (k1_funct_1 E (k6_xcmplx_0 (k3_finseq_1 C) 1)) G))  &  ( ((k1_funct_1 D 1) = (k1_xtuple_0 (k1_funct_1 A 1)))  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ((r1_xxreal_0 1 I) &  ((r1_xxreal_0 I (k6_xcmplx_0 (k3_finseq_1 C) 1)) &  (! [J:$i] :  ((m1_subset_1 J k4_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k4_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k4_numbers) =>  (~  ( (K = (k1_xtuple_0 (k1_funct_1 A (k1_nat_1 I 1))))  &  ( (L = (k2_xtuple_0 (k1_funct_1 A (k1_nat_1 I 1))))  &  ( (J = (k6_int_1 (k3_xcmplx_0 (k6_xcmplx_0 K (k1_funct_1 D I)) (k1_funct_1 F I)) L))  &  ((k1_funct_1 D (k1_nat_1 I 1)) = (k2_xcmplx_0 (k1_funct_1 D I) (k3_xcmplx_0 J (k1_funct_1 E I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (B = (k6_int_1 (k1_funct_1 D (k3_finseq_1 C)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_numbers,ax, (k4_numbers = (k6_subset_1 (k2_xboole_0 k4_ordinal1 (k2_zfmisc_1 (k1_tarski k1_xboole_0) k4_ordinal1)) (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0)))) ).
tt(d4_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k6_openlatt A) = (g3_lattices (k1_openlatt A) (k4_openlatt A) (k5_openlatt A))) ) ) ).
tt(d4_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v2_oposet_1 A) <=> (v1_relat_2 (u1_orders_2 A))) ) ) ).
tt(d4_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k5_oppcat_1 A B) = B) ) ) ) ) ).
tt(d4_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_orders_1 A) <=>  ((v1_relat_2 A) &  ((v8_relat_2 A) & (v4_relat_2 A)) ) ) ) ) ).
tt(d4_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v5_orders_2 A) <=> (r4_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d4_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) <=>  ((v1_ordinal1 A) & (v2_ordinal1 A)) ) ) ).
tt(d4_ordinal2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_ordinal2 A) <=>  (? [B:$i] :  ((v3_ordinal1 B) & (r1_tarski (k10_xtuple_0 A) B)) ) ) ) ) ).
tt(d4_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( (C = (k4_ordinal3 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k11_ordinal2 (k1_funct_1 B D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (C = (k1_ordinal5 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v5_ordinal1 D) & (v1_ordinal2 D)) ) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = 1)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k12_ordinal2 A (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k8_ordinal2 (k5_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_ordinal6,ax, (! [A:$i] :  ((k1_ordinal6 A) = (k2_wellord2 (k1_wellord2 (k2_ordinal1 A)))) ) ).
tt(d4_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v2_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d4_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))))) =>  ( (C = (k1_osafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B)))) =>  (! [E:$i] :  ((m2_finseq_2 E (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))) =>  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) &  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k4_tarski F (u1_struct_0 A)) = D)  =>  ( ((k3_finseq_1 E) = (k3_finseq_1 (k1_msualg_1 A F)))  &  (! [G:$i] :  ((r2_hidden G (k4_finseq_1 E)) =>  ( ((r2_hidden (k1_funct_1 E G) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ( ((k4_tarski H (u1_struct_0 A)) = (k1_funct_1 E G))  => (r3_orders_2 A (k2_msualg_1 A H) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A F) G))) ) ) )  &  (~  ((r2_hidden (k1_funct_1 E G) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r3_orders_2 A H (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A F) G)) & (r2_hidden (k1_funct_1 E G) (k2_msafree (u1_struct_0 A) B H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  ((v6_osalg_1 A) <=> (r2_relset_1 (u4_struct_0 A) (u4_struct_0 A) (u1_osalg_1 A) (k6_partfun1 (u4_struct_0 A)))) ) ) ).
tt(d4_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) )  =>  ( (C = (k2_osalg_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k3_tarski (a_3_1_osalg_2 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d4_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_osalg_4 A B C) <=> (r2_hidden (k4_tarski B C) (k1_osalg_4 A))) ) ) ) ) ) ) ).
tt(d4_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k4_parsp_1 A B) = (k3_funct_2 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_parsp_1 A) B)) ) ) ) ) ).
tt(d4_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) <=>  (~  ( (~  ( (B = C)  &  (D = E) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_parsp_2 A F G B C) & (r2_parsp_2 A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=>  (! [C:$i] :  ((r2_hidden C (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(d4_partfun3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_partfun3 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k10_xtuple_0 A)) => (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ).
tt(d4_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((k2_partit1 A B C) = (k6_subset_1 (k3_setfam_1 B C) (k1_tarski k1_xboole_0))) ) ) ) ) ) ) ).
tt(d4_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v4_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_diraf A B C E) &  ((r1_diraf A C F D) &  ( (~ (r3_diraf A B C D))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_diraf A B H D) & (r1_diraf A H F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k2_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k2_xboole_0 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (k2_pcomps_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  & (r1_tarski (k9_metric_1 A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)))))) )  =>  ( (C = (k4_pdiff_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 B))) =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C D) = (k12_finseq_1 k1_numbers (k1_seq_1 (k1_pdiff_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  &  (? [E:$i] :  ((m1_rcomp_1 E C) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B))) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v3_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B) H) (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B) C)) = (k7_real_1 (k1_seq_1 F (k9_real_1 H C)) (k1_seq_1 G (k9_real_1 H C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r4_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F C) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B) C)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I C)) (k1_seq_1 H (k9_real_1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid C) (k1_euclid B)))))  =>  ((r1_pdiff_6 A B C D) <=>  ((r1_tarski A (k1_relset_1 (k1_euclid C) D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid C)) =>  ((r2_hidden E A) => (r1_pdiff_1 C B (k2_partfun1 (k1_euclid C) (k1_euclid B) D A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((r2_pdiff_7 A B C D E) <=>  ((r1_tarski E (k1_relset_1 (k1_euclid A) D)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F E) => (r4_pdiff_1 A B C (k2_partfun1 (k1_euclid A) (k1_euclid B) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k9_funct_2 (k1_euclid A) k1_numbers)))))  =>  ( (D = (k2_pdiff_9 A B C))  <=>  ( ((k1_relset_1 (k1_euclid A) D) = B)  &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) D E) = (k1_pdiff_7 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v3_pencil_1 A) <=> (v1_xboole_0 (u1_pre_topc A))) ) ) ).
tt(d4_pencil_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_pencil_2 C A B) <=>  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_t_0topsp C A B) &  ((v3_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) (u1_struct_0 B) (u1_struct_0 A)) & (v1_t_0topsp (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ) ) ) ).
tt(d4_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  =>  ((m1_pencil_2 (k4_card_3 D) A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D))))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D)))))))) )  =>  ( (E = (k3_pencil_3 A B C D))  <=>  ((v1_pencil_2 E (k2_pencil_1 A B (k3_pencil_1 A D)) (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D)))) &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  ( ((m1_subset_1 F (u1_struct_0 (k5_pencil_1 A B))) & (r2_hidden F (k4_card_3 D)))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) & (v1_partfun1 G A)) ) )  =>  ( (G = (k1_funct_1 C F))  =>  ((k1_funct_1 G (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D))) = (k1_funct_1 E (k1_funct_1 F (k3_pencil_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (k2_vectsp_9 A B C)))) =>  ( (D = (k4_pencil_4 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((m1_vectsp_4 F A B) &  (? [G:$i] :  ((m1_vectsp_4 G A B) &  ((m1_vectsp_4 F A G) &  ( ((k1_nat_1 (k1_vectsp_9 A F) 1) = C)  &  ( ((k1_vectsp_9 A G) = (k1_nat_1 C 1))  &  (E = (k3_pencil_4 A B F G C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_petri A B) = (a_2_0_petri A B)) ) ) ) ) ).
tt(d4_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( (D = (k2_pnproc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k2_xcmplx_0 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_polyalg1 C A B) <=>  ((v1_vectsp_4 C A B) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k6_algstr_0 B D E) C)) ) ) ) )  &  ((r2_hidden (k5_struct_0 B) C) & (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k7_polyeq_1 A B C D E) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k1_newton E 3)) (k3_xcmplx_0 B (k3_square_1 E))) (k3_xcmplx_0 C E)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers)  =>  ( (D = (k4_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (F = (k1_polyeq_5 3 (k3_xcmplx_0 2 E)))  &  (D = (k11_complex1 (k11_complex1 (k10_complex1 (k13_complex1 F 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 F (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) )  &  ( (~  ((k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) = k6_numbers) )  =>  ( (D = (k4_polyeq_5 A B C))  <=>  (? [E:$i] :  ((v1_xcmplx_0 E) &  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  ( (E = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) 9))  &  ( (F = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 A)) 54))  &  ( (G = (k1_polyeq_5 2 (k2_xcmplx_0 (k1_newton E 3) (k1_newton F 2))))  &  ( (H = (k1_polyeq_5 3 (k2_xcmplx_0 F G)))  &  ( (I = (k10_complex1 (k13_complex1 E H)))  &  (D = (k11_complex1 (k11_complex1 (k10_complex1 (k13_complex1 (k2_xcmplx_0 H I) 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 H I) (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k7_polyform A) = (k3_finseq_1 (u1_polyform A))) ) ) ).
tt(d4_polynom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l2_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v1_polynom1 C A B) <=> (v1_finset_1 (k2_polynom1 A B C))) ) ) ) ) ) ) ).
tt(d4_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (E = (k5_polynom2 A B C D))  <=>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) &  ( ((k3_finseq_1 F) = (k3_finseq_1 (k7_pre_poly (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) B C) (k17_pre_poly A))))  &  ( (E = (k4_rlvect_1 B F))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k3_finseq_1 F)))  =>  ((k7_partfun1 (u1_struct_0 B) F G) = (k6_algstr_0 B (k7_partfun1 (u1_struct_0 B) (k1_partfun1 k5_numbers (k15_pre_poly A) (k15_pre_poly A) (u1_struct_0 B) (k7_pre_poly (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) B C) (k17_pre_poly A)) C) G) (k3_polynom2 A (k4_polynom2 A (k7_partfun1 (k15_pre_poly A) (k7_pre_poly (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) B C) (k17_pre_poly A)) G)) B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polynom3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (k4_finseq_2 A k5_numbers)) =>  ( (C = (k6_polynom3 A B))  <=>  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k4_finseq_2 A k5_numbers))))  &  ( (C = (k7_pre_poly (k4_finseq_2 A k5_numbers) D (k5_polynom3 A)))  &  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r2_hidden E D) <=>  ((k2_wsierp_1 E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_polynom5 A B C) = (k15_funct_7 k5_numbers (u1_struct_0 A) (k15_funct_7 k5_numbers (u1_struct_0 A) (k9_polynom3 A) k6_numbers B) 1 C)) ) ) ) ) ) ) ).
tt(d4_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((k1_polynom7 A B C D) = (k15_funct_7 (k15_pre_poly A) (u1_struct_0 B) (k7_polynom1 A B) D C)) ) ) ) ) ) ) ) ).
tt(d4_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A 1) =>  ( (D = (k4_polynom8 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ((k3_matrix_1 (u1_struct_0 B) D E 1) = (k1_funct_1 C (k6_xcmplx_0 E 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k2_polyred A B C D) = (k2_polynom1 (k15_pre_poly A) C D)) ) ) ) ) ) ) ) ) ).
tt(d4_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_poset_1 C A B) <=>  ((v5_orders_3 C A B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r4_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (A = k7_power)  <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k4_power (k7_real_1 1 (k10_real_1 1 (k2_nat_1 C 1))) (k2_nat_1 C 1))) ) )  =>  (A = (k2_seq_2 B)) ) ) ) ) ) ) ).
tt(d4_pralg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  (! [C:$i] :  ((m2_finseq_1 C (k4_partfun1 (k3_finseq_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) =>  ( (C = (k4_pralg_1 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 (u1_unialg_1 A)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v2_margrel1 E) &  ((v3_margrel1 E (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v2_margrel1 F) &  ((v3_margrel1 F (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 B)) (u1_struct_0 B))))) ) ) )  =>  ( ( (E = (k1_funct_1 (u1_unialg_1 A) D))  &  (F = (k1_funct_1 (u1_unialg_1 B) D)) )  =>  ((k1_funct_1 C D) = (k3_pralg_1 (u1_struct_0 A) (u1_struct_0 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ((m1_pralg_3 E (k8_eqrel_1 A D) (k6_partfun1 (k8_eqrel_1 A D)) B) =>  ( (E = (k3_pralg_3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F (k8_eqrel_1 A D)) =>  ((k1_funct_1 E F) = (k5_relat_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = k6_numbers)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = k6_numbers)  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k12_finseq_1 (u1_struct_0 A) D) D)) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 1)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 1)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski D (k2_prelamb A E F)))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) D (k12_finseq_1 (u1_struct_0 A) F)) E)) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 2)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 1)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski D (k1_prelamb A F E)))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) F) D) E)) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 3)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 2)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A G H))) D) F) I))  &  ( ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski D H))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) G)) F) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 4)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 2)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E D) (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A H G))) F) I))  &  ( ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski D H))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) G)) F) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 5)  =>  ((v2_prelamb C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 1)  &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m2_finseq_1 H (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A F G))) H) D))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) F)) (k12_finseq_1 (u1_struct_0 A) G)) H) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 6)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 2)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) D E) (k3_prelamb A F G)))  &  ( ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski D F))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)))) = (k4_tarski E G)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 7)  =>  ((v2_prelamb C A B) <=>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 2)  &  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E D) F) H))  &  ( ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))) = (k4_tarski D G))  &  ((k1_xtuple_0 (k1_funct_1 B (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)))) = (k4_tarski (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) G)) F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (~  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = k6_numbers) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 1) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 2) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 3) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 4) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 5) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 6) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 7) )  &  (~  ((v2_prelamb C A B) <=>  (~ $true) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_pre_poly B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_pre_poly C)) )  =>  ( (C = (k8_pre_poly A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  ( ( (E = (k1_funct_1 A D))  &  (F = (k1_funct_1 B D)) )  =>  ((k1_funct_1 C D) = (k7_finseq_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ((k6_prepower A B) = (k2_prepower (k1_rat_1 B) (k4_prepower A (k2_rat_1 B)))) ) ) ) ) ).
tt(d4_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((m1_pre_topc B A) <=>  ((r1_tarski (k2_struct_0 B) (k2_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden C (u1_pre_topc B)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden D (u1_pre_topc A)) &  (C = (k9_subset_1 (u1_struct_0 B) D (k2_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prgcor_2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r2_prgcor_2 A B C D) <=>  ( ((k1_afinsq_1 B) = D)  &  ( ((k1_afinsq_1 A) = D)  &  (? [E:$i] :  ((v1_int_1 E) &  ( ((k1_seq_1 B k6_numbers) = (k1_seq_1 A k6_numbers))  &  ( (E = (k1_seq_1 A k6_numbers))  &  ( (~  (E = k6_numbers) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F E))  =>  ((k1_seq_1 B F) = (k8_real_1 C (k1_seq_1 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prob_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_prob_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(d4_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ((r1_prob_2 A B C D E) <=>  ((k1_seq_1 C (k5_prob_1 A B D E)) = (k8_real_1 (k1_seq_1 C D) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_prob_2 B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  (C = D) )  => (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(d4_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((m1_prob_4 D A B C) <=>  (? [E:$i] :  ((r2_hidden E B) &  ((r1_tarski D E) &  ((k1_funct_1 C E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v1_projpl_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A C D) &  ((r1_incsp_1 A B E) &  ((r1_incsp_1 A C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A))) (k4_finseq_2 B (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A))) (k4_finseq_2 B (u1_struct_0 A)))))) )  =>  ( (C = (k5_prvect_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A))) =>  ((k2_binop_1 (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A)) (k4_finseq_2 B (u1_struct_0 A)) C D E) = (k3_finseqop (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) )  =>  ( (B = (k4_prvect_2 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ((k1_funct_1 B C) = (u1_struct_0 (k3_prvect_2 A C))) ) ) ) ) ) ) ) ) ).
tt(d4_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  ((k4_prvect_3 A B) = (g2_algstr_0 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_prvect_3 A B) (k3_prvect_3 A B))) ) ) ) ) ).
tt(d4_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k6_pua2mss1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  (! [E:$i] :  ((m1_pua2mss1 E (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ((r2_hidden (k7_finseq_1 (k7_finseq_1 F (k12_finseq_1 (u1_struct_0 A) C)) G) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) E)) <=> (r2_hidden (k7_finseq_1 (k7_finseq_1 F (k12_finseq_1 (u1_struct_0 A) D)) G) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ((m1_pythtrip A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k2_nat_1 (k1_pepin B) (k1_pepin C)) = (k1_pepin D))  &  (A = (k8_domain_1 k5_numbers B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k3_qc_lang1 A) = (k2_zfmisc_1 (k1_tarski 4) (k1_qc_lang1 A))) ) ) ).
tt(d4_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k4_qc_lang2 A B C) = (k14_qc_lang1 A (k2_qc_lang2 A B C) (k2_qc_lang2 A C B))) ) ) ) ) ) ) ).
tt(d4_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( (D = (k4_qc_lang3 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_qc_lang1 A) (k1_zfmisc_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k1_zfmisc_1 B))))) )  &  ( (D = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E C))  &  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 B)) =>  ( ( (F = (k12_qc_lang1 A))  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E F) = (k1_subset_1 B)) )  &  ( ((v2_qc_lang1 F A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E F) = (k1_qc_lang3 A (k17_qc_lang1 A F) B)) )  &  ( ( ((v3_qc_lang1 F A) &  (G = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E (k18_qc_lang1 A F))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E F) = G) )  &  ( ( ((v4_qc_lang1 F A) &  ( (G = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E (k19_qc_lang1 A F)))  &  (H = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E (k20_qc_lang1 A F))) ) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E F) = (k4_subset_1 B G H)) )  &  ( ((v5_qc_lang1 F A) &  (G = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E (k22_qc_lang1 A F))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 B) E F) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((m1_qc_lang4 C A B) <=> (r2_qc_lang2 A C B)) ) ) ) ) ) ) ).
tt(d4_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_qmax_1 A)) =>  ((k4_qmax_1 A B C) = (k1_funct_1 (u3_qmax_1 A) (k1_domain_1 (k2_qmax_1 A) (k3_qmax_1 A) B C))) ) ) ) ) ) ) ).
tt(d4_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v6_quantal1 A) <=>  ((v4_quantal1 A) & (v5_quantal1 A)) ) ) ) ).
tt(d4_quaterni,ax, (k4_quaterni = (k3_quaterni k5_numbers k6_numbers 1 2 3 k6_numbers k6_numbers 1 k6_numbers)) ).
tt(d4_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_quofield A))) =>  ( (C = (k6_quofield A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden D C) <=>  ((k6_algstr_0 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B)) = (k6_algstr_0 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) D) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ((k5_radix_1 A B C D) = (k4_radix_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_radix_2 A B C) = (k3_nat_d (k4_nat_d C (k1_newton (k1_radix_1 B) A)) (k13_newton (k1_radix_1 B) (k7_nat_d A 1)))) ) ) ) ) ) ) ).
tt(d4_radix_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_radix_3 A B) = (k6_xcmplx_0 A (k3_xcmplx_0 (k1_radix_1 B) (k5_radix_3 A B)))) ) ) ) ) ).
tt(d4_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( (D = (k4_radix_5 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E C A D) = (k3_radix_5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (D = (k4_radix_6 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k2_xcmplx_0 A 2))) =>  ((k4_radix_1 E B (k2_xcmplx_0 A 2) D) = (k3_radix_6 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) =>  ((r1_random_1 A B D C) =>  ((k8_random_1 A B C D) = (k1_mesfunc6 A B (k2_prob_4 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k6_ranknull A B C D) = (k1_funct_4 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) C D) (k8_funcop_1 (u1_struct_0 A) (k4_ranknull B D) (k4_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(d4_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k2_rat_1 A) = (k8_real_1 (k1_rat_1 A) A)) ) ) ).
tt(d4_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_ratfunc1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r1_ratfunc1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d4_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k10_xtuple_0 B) A) & (v2_comseq_2 B))  => (r2_hidden (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(d4_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( (B = (k4_real_3 A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_seq_1 B C) = (k1_int_1 (k1_seq_1 (k3_real_3 A) C))) ) ) ) ) ) ) ) ).
tt(d4_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) )  =>  ( (B = (k4_real_lat A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers B C D) (k3_funcsdom k1_numbers A k2_real_lat C D))) ) ) ) ) ) ) ) ) ).
tt(d4_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_normsp_1 B) & (l1_normsp_1 B)) )  =>  ( (B = (k4_real_ns1 A))  <=>  ( ((u1_struct_0 B) = (k1_euclid A))  &  ( ((k4_struct_0 B) = (k5_euclid A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A) (u1_algstr_0 B) (k1_real_ns1 A)) &  ((r1_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A) (u1_rlvect_1 B) (k2_real_ns1 A)) & (r1_funct_2 (u1_struct_0 B) k1_numbers (k1_euclid A) k1_numbers (u1_normsp_0 B) (k3_real_ns1 A))) ) ) ) ) ) ) ) ) ).
tt(d4_realset1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((m2_realset1 C A B) <=>  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 B B)) => (r2_hidden (k1_funct_1 C D) B)) ) ) ) ) ) ) ) ).
tt(d4_realset2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ((v1_realset2 A) <=>  ((m3_realset1 (u2_algstr_0 A) (u1_struct_0 A) (k4_struct_0 A)) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ( (B = (k8_struct_0 A))  &  ( (D = (k5_struct_0 A))  &  (C = (k1_realset1 (u2_algstr_0 A) (k8_struct_0 A))) ) )  =>  ( (~ (v2_struct_0 (g2_algstr_0 B C D)))  &  ((v13_algstr_0 (g2_algstr_0 B C D)) &  ((v2_rlvect_1 (g2_algstr_0 B C D)) &  ((v3_rlvect_1 (g2_algstr_0 B C D)) &  ((v4_rlvect_1 (g2_algstr_0 B C D)) & (l2_algstr_0 (g2_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_recdef_2,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k7_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (A = (k6_xtuple_0 C D E F))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden (k4_tarski C D) A) & (r2_hidden (k4_tarski D C) A)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(d4_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) <=> (r1_rewrite1 (k2_xboole_0 A (k2_relat_1 A)) B C)) ) ) ) ) ).
tt(d4_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r1_rewrite2 A B C D) <=> (r2_hidden (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) C D) B)) ) ) ) ) ) ) ) ).
tt(d4_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k8_afinsq_1 A)) (k2_zfmisc_1 (u1_struct_0 C) (k8_afinsq_1 A))))) =>  ( (D = (k1_rewrite3 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((r2_hidden (k4_tarski (k4_tarski E F) (k4_tarski G H)) D) <=> (r2_rewrite3 A B C E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k4_rfinseq2 A) = (k1_seq_1 A (k2_rfinseq2 A))) ) ) ).
tt(d4_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r2_hidden B (k1_relset_1 k1_numbers A)) & (r2_hidden C (k1_relset_1 k1_numbers A)))  =>  ((r1_xxreal_0 C B) | (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A B))) ) ) ) ) ) ) ) ) ).
tt(d4_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) )  =>  ( (B = (k13_rfunct_3 A))  <=>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  ((k5_binop_1 (k3_rfunct_3 A k1_numbers) B C D) = (k5_rfunct_3 A k1_numbers C D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r4_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E)) B) &  ( (~  (D = E) )  & (r1_xxreal_0 (k4_xxreal_0 (k1_seq_1 A D) (k1_seq_1 A E)) (k1_seq_1 A (k9_binop_2 (k11_binop_2 C D) (k11_binop_2 (k10_binop_2 1 C) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k3_rinfsup1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( (D = (a_2_0_rinfsup1 A C))  =>  ((k1_seq_1 B C) = (k5_seq_4 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v2_rinfsup2 A) <=> (v4_xxreal_2 (k17_supinf_2 A))) ) ) ).
tt(d4_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_ring_1 B A) <=>  ((v1_subset_1 B (u1_struct_0 A)) & (v3_ring_1 B A)) ) ) ) ) ) ).
tt(d4_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((k3_ringcat1 A) = (u3_ringcat1 A)) ) ) ).
tt(d4_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) <=>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) & (v1_rlvect_3 (k7_subset_1 (u1_struct_0 A) (k5_rusub_4 A B (k4_algstr_0 A C)) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k2_rlsub_1 A) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ).
tt(d4_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) <=>  ( ((g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)) = (k1_rlsub_2 A B C))  &  ((k2_rlsub_2 A B C) = (k1_rlsub_1 A)) ) ) ) ) ) ) ) ) ).
tt(d4_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_rltopsp1 A B) = (k1_convex1 A B (k1_real_1 1))) ) ) ) ) ).
tt(d4_rlvect_1,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((v4_rlvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) ) ) ) ) ).
tt(d4_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k1_numbers (k9_funct_2 (u1_struct_0 A) k1_numbers)) =>  ((k3_rlvect_2 A B) = (a_2_0_rlvect_2 A B)) ) ) ) ) ).
tt(d4_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ((k2_rmod_2 A B) = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B))) ) ) ) ) ).
tt(d4_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_rmod_3 A B C D) <=>  ( ((g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B)) = (k1_rmod_3 A B C D))  &  ((k2_rmod_3 A B C D) = (k1_rmod_2 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ( (C = (k3_rmod_4 A B))  <=>  ((k2_rmod_4 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d4_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_robbins1 A B C) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) (k3_robbins1 A C)))) ) ) ) ) ) ) ).
tt(d4_robbins3,ax, (k1_robbins3 = (g3_robbins3 1 k9_funct_5 k9_funct_5 (k6_partfun1 1))) ).
tt(d4_robbins4,ax, (! [A:$i] :  ( ((v4_robbins1 A) & (l4_robbins1 A))  =>  ( (A = k2_robbins4)  <=>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (k14_lattice3 k1_robbins4))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 3)) =>  ( (B = C)  =>  ((k1_funct_1 (u1_robbins1 A) B) = (k3_subset_1 3 C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A B) = (a_2_0_roughs_1 A B)) ) ) ) ) ).
tt(d4_rsspace3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rsspace3 A B C) = (k1_normsp_0 A (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(d4_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v1_rsspace4 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 A (u1_struct_0 B) C E)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_rsspace k1_rsspace) k1_rsspace) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_rsspace k1_rsspace) k1_rsspace)))) )  =>  ( (A = k4_rsspace)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_rsspace) =>  (! [C:$i] :  ((m1_subset_1 C k1_rsspace) =>  ((k5_binop_1 k1_rsspace A B C) = (k1_series_1 k1_numbers (k2_rsspace B) (k2_rsspace C))) ) ) ) ) ) ) ) ).
tt(d4_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k3_rusub_1 A B C) = (a_3_0_rusub_1 A B C)) ) ) ) ) ) ) ).
tt(d4_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) <=>  ( ((g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)) = (k1_rusub_2 A B C))  &  ((k2_rusub_2 A B C) = (k1_rusub_1 A)) ) ) ) ) ) ) ) ) ).
tt(d4_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_rusub_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k1_algstr_0 A (k1_rlvect_1 A C (k9_real_1 1 E)) (k1_rlvect_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( (C = (k3_rusub_5 A B))  <=>  ((u1_struct_0 C) = (a_2_2_rusub_5 A B)) ) ) ) ) ) ) ) ).
tt(d4_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k4_rvsum_1 A B) = (k3_funcop_1 k33_binop_2 A B)) ) ) ) ) ).
tt(d4_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k7_rvsum_2 A B) = (k3_funcop_1 k28_binop_2 A B)) ) ) ) ) ).
tt(d4_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k6_scm_comp A B) = (k6_trees_4 (k4_tarski k6_numbers 1) A B)) ) ) ) ) ).
tt(d4_scmfsa_1,ax, (k4_scmfsa_1 = (k1_funct_4 (k8_funcop_1 k5_numbers k1_scmfsa_1 2) k3_ami_2)) ).
tt(d4_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k3_scmfsa6a A B) = (k1_funct_4 (k2_scmfsa6a (k63_valued_1 (k10_compos_1 k1_scmfsa_2 A))) (k6_compos_1 k1_scmfsa_2 B (k5_card_1 A)))) ) ) ) ) ).
tt(d4_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scmfsa6b A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 B 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski A C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 C B D) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 B (k4_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa_7,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ((k4_scmfsa_7 A B) = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k2_scmfsa_7 (k4_scmfsa_2 1) (k3_finseq_1 B)) (k5_afinsq_1 (k17_scmfsa_2 (k4_scmfsa_2 1) A))) (k3_scmfsa_7 A B)) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ) ) ).
tt(d4_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) & (v1_funct_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((r4_scmfsa7b A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) &  ((r2_hidden C (k10_xtuple_0 A)) & (r3_scmfsa7b C B)) ) ) ) ) ) ) ) ).
tt(d4_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a A B C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k2_scmfsa8a A B C))  <=>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) D)) = (k5_card_1 C))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) E)) (k2_afinsq_1 C)))  => (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k4_scmfsa8b A B C D) = (k4_scmfsa6a (k8_scmfsa_2 A B) (k1_scmfsa8b A C D))) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r3_scmfsa9a A B C D) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) C) k6_numbers))  =>  ((r5_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) (k1_funct_4 A (k2_scmfsa_9 C D))) & (r6_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) (k1_funct_4 A (k2_scmfsa_9 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) )  =>  ( (E = (k4_scmfsa_9 A B C D))  <=>  ((r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E k6_numbers) A) &  (! [F:$i] :  ((v7_ordinal1 F) => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E (k1_nat_1 F 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 D (k1_scmfsa_9 C B)) (k1_funct_4 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F) (k7_memstr_0 3 k1_scmfsa_2 k6_numbers)) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 D (k1_scmfsa_9 C B)) B) (k1_funct_4 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F) (k7_memstr_0 3 k1_scmfsa_2 k6_numbers))) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 13)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k4_scmfsa_i A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) &  (? [E:$i] :  ((m1_subset_1 E k2_scm_inst) &  ( ((k11_finseq_1 C D E) = (k2_xtuple_0 A))  &  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k3_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ( (B = (k3_scmfsa_m A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k5_numbers)))  &  ( (B = (k5_scmfsa_2 (k6_seq_4 C)))  &  (C = (a_1_1_scmfsa_m A)) ) ) ) ) ) ) ) ) ).
tt(d4_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_scm_halt A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_scmfsa_m B) D)) (k9_xtuple_0 A))) ) ) ) ) ) ) ) ) ).
tt(d4_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (k7_card_1 9)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k2_finseq_4 k2_scm_inst B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k5_scm_inst A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k2_scm_inst) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 k2_scm_inst C 2)) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k3_scmpds_2 A) = (k3_xtuple_0 14 k1_xboole_0 (k9_finseq_1 A))) ) ) ).
tt(d4_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ((k4_scmpds_4 A B) = (k1_scmpds_4 (k9_compos_1 k1_scmpds_2 A) (k9_compos_1 k1_scmpds_2 B))) ) ) ) ) ).
tt(d4_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k2_scmpds_6 A B C D) = (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_4 (k7_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) C) (k1_scmpds_6 (k2_nat_1 (k5_card_1 D) 1))) D)) ) ) ) ) ) ) ) ) ).
tt(d4_scmpds_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k4_scmpds_7 A B C D E) = (k1_scmpds_4 (k4_scmpds_4 (k10_scmpds_2 (k1_scmp_gcd A) C k6_numbers) (k5_scmpds_2 (k1_scmp_gcd D) E)) (k2_scmpds_7 (k1_scmp_gcd A) B 1 (k4_scmpds_4 (k12_scmpds_2 (k1_scmp_gcd A) (k1_scmp_gcd E) C k6_numbers) (k11_scmpds_2 (k1_scmp_gcd D) k6_numbers 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((m2_subset_1 D k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k2_scmpds_i B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k5_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmp_gcd,ax, (k4_scmp_gcd = (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k5_scmpds_2 k3_scmp_gcd 7)) (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i)) (k3_scmpds_2 2)) (k2_compos_1 k1_scmpds_2)) (k8_scmpds_2 k3_scmp_gcd 3 9)) (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 6 3)) (k15_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 3)) (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 7 3)) (k16_scmpds_2 k3_scmp_gcd k2_scmp_gcd (k2_nat_1 4 k14_scmpds_i) 1)) (k11_scmpds_2 k2_scmp_gcd 1 4)) (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i)) (k3_scmpds_2 (k4_xcmplx_0 7))) (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 6)) (k4_scmpds_2 k3_scmp_gcd))) ).
tt(d4_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  ((k2_scmring1 A B) = (k1_funct_1 B k5_numbers)) ) ) ) ) ).
tt(d4_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k4_scmring2 A B C) = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(d4_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 D (k12_finseq_1 k5_numbers C) k1_xboole_0)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k4_scmringi A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k5_numbers) &  ( (D = (k5_xtuple_0 B))  &  (C = (k7_partfun1 k5_numbers D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v3_scmyciel B A) <=>  (! [C:$i] :  ((r2_hidden C B) => (r1_ordinal1 (k1_card_1 C) (k1_nat_1 A 1))) ) ) ) ) ) ).
tt(d4_scpinvar,ax, (k5_scpinvar = (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))))) ).
tt(d4_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) <=>  (~  ( (~  ( (B = C)  &  (D = E) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_semi_af1 A F G B C) & (r2_semi_af1 A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d4_seq_4,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_seq_4 A) = (k5_funcop_1 k29_binop_2 A (k6_partfun1 k2_numbers))) ) ) ).
tt(d4_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (C = (k5_seqfunc A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers C D) (k56_valued_1 A k1_numbers (k1_seqfunc A k1_numbers B D)))) ) ) ) ) ) ) ) ) ).
tt(d4_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A k1_numbers) & (v1_funct_1 A)) ) )  =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A B))) ) ) ) ) ) ) ) ).
tt(d4_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_series_1 A) <=> (v1_series_1 (k56_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(d4_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k2_setfam_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  (? [F:$i] :  ((r2_hidden E A) &  ((r2_hidden F B) &  (D = (k2_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_kurato_0 A B) = (k1_kurato_0 A (k2_setlim_1 A B))) ) ) ) ).
tt(d4_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k4_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k5_subset_1 A (k8_nat_1 (k9_setfam_1 A) B E) (k8_nat_1 (k9_setfam_1 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_setwiseo,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_finsub_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_finsub_1 A))))) )  =>  ( (B = (k9_setwiseo A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  ((k5_binop_1 (k5_finsub_1 A) B C D) = (k5_setwiseo A C D)) ) ) ) ) ) ) ) ) ).
tt(d4_sfmastr1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((k1_sfmastr1 A B) = (k9_scmfsa_m A (k2_sf_mastr B))) ) ) ) ) ).
tt(d4_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_sfmastr2 A B C D) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_funct_1 B C) E))  =>  ((r5_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 A B D C) E) (k1_funct_4 A (k1_sfmastr2 C D))) & (r6_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 A B D C) E) (k1_funct_4 A (k1_sfmastr2 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ((k3_sfmastr3 A B C D) = (k4_scmfsa6a (k6_scmfsa_2 C A) (k2_sfmastr3 (k9_scmfsa_m 3 (k6_scmfsa_m A B C)) A B (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k9_scmfsa_m 1 (k6_scmfsa_m A B C)) (k9_scmfsa_m 3 (k6_scmfsa_m A B C)) D) (k14_scmfsa_2 (k9_scmfsa_m 2 (k6_scmfsa_m A B C)) C D)) (k5_scmfsa8b (k9_scmfsa_m 2 (k6_scmfsa_m A B C)) (k9_scmfsa_m 1 (k6_scmfsa_m A B C)) (k11_compos_1 k1_scmfsa_2 (k6_scmfsa_2 C (k9_scmfsa_m 3 (k6_scmfsa_m A B C)))) (k4_compos_1 k1_scmfsa_2)))))) ) ) ) ) ) ) ) ) ).
tt(d4_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k3_scmfsa_2)) =>  ( (B = (k4_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k3_scmfsa_2)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k3_scmfsa_2))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ((k3_funct_2 (u1_compos_1 k1_scmfsa_2) (k5_finsub_1 k3_scmfsa_2) C D) = (k3_sf_mastr D)) ) )  &  (B = (k3_card_3 (k3_relat_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d4_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_sgraph1 B) & (l1_sgraph1 B))  =>  ((m1_sgraph1 B A) <=> (m1_subset_1 B (k3_sgraph1 A))) ) ) ) ).
tt(d4_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v2_sheffer1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k2_sheffer1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_lattices A B C) = C)  &  ((k1_lattices A C B) = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k4_simplex0 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (v1_simplex0 C A)) ) ) ) ) ) ) ) ).
tt(d4_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_simplex0 C (u1_struct_0 A)) =>  ((m1_simplex1 C A B) <=>  ((r1_tarski (k3_simplex1 A B) (k3_simplex1 A C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  (~  ((v3_pre_topc D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_pre_topc E B) & (r1_tarski (k3_convex1 A (k1_simplex1 A C D)) (k3_convex1 A (k1_simplex1 A B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v1_simplex2 B A) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_simplex2 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  => (r1_xxreal_0 (k3_tbsp_1 A D) C)) ) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  => (r1_xxreal_0 (k3_tbsp_1 A E) D)) ) )  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_sincos10,ax, (k4_sincos10 = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(d4_sin_cos2,ax, (! [A:$i] :  ((k5_sin_cos2 A) = (k1_seq_1 k4_sin_cos2 A)) ) ).
tt(d4_sin_cos3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  ( (A = k4_sin_cos3)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers A B) = (k6_binop_2 (k3_binop_2 (k15_sin_cos B) (k15_sin_cos (k1_binop_2 B))) 2)) ) ) ) ) ) ).
tt(d4_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_sin_cos4 A) = (k7_xcmplx_0 1 (k20_sin_cos A))) ) ) ).
tt(d4_sin_cos6,ax, (! [A:$i] :  ((k5_sin_cos6 A) = (k1_seq_1 k4_sin_cos6 A)) ) ).
tt(d4_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_sin_cos7 A) = (k11_binop_2 (k18_binop_2 1 2) (k6_power k8_power (k12_binop_2 (k9_binop_2 1 A) (k10_binop_2 1 A))))) ) ) ).
tt(d4_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k4_sin_cos9 A) = (k1_seq_1 k2_sin_cos9 A)) ) ) ).
tt(d4_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k3_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers B C) = (k13_complex1 (k2_comseq_3 A C) (k3_newton C))) ) ) ) ) ) ) ) ).
tt(d4_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v3_sppol_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  ( (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)))) )  &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)))) ) ) ) ) ) ) ) ) ).
tt(d4_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_sprect_2 A) <=> (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k20_pscomp_1 (k3_topreal1 2 A))) 2) (k15_pscomp_1 (k3_topreal1 2 A)))) ) ) ).
tt(d4_stacks_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  & (l1_stacks_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k5_stacks_1 A B) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 A) (u3_stacks_1 A) B)) ) ) ) ) ).
tt(d4_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k3_struct_0 A) = (k6_partfun1 (u1_struct_0 A))) ) ) ).
tt(d4_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k3_subset_1 A B) = (k4_xboole_0 A B)) ) ) ) ).
tt(d4_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v3_lattices C) & (l3_lattices C))  =>  ( (C = (k5_substlat A B))  <=>  ( ((u1_struct_0 C) = (k1_substlat A B))  &  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( ((k1_binop_1 (u2_lattices C) D E) = (k3_substlat A B (k2_substlat A B D E)))  &  ((k1_binop_1 (u1_lattices C) D E) = (k3_substlat A B (k4_substlat A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_qc_lang1 A)) =>  ((k4_substut1 A B) = B) ) ) ) ) ).
tt(d4_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k8_substut2 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(d4_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  (! [B:$i] :  ((v2_membered B) =>  ( (B = (k6_supinf_1 A))  <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v2_membered D))  &  ((r2_hidden D A) &  (C = (k2_xxreal_2 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k6_supinf_2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k6_supinf_2 B))))) )  =>  ( (D = (k14_supinf_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k12_supinf_2 D E) = (k2_supinf_2 (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((k2_t_0topsp A) = (k8_eqrel_1 (u1_struct_0 A) (k1_t_0topsp A))) ) ) ).
tt(d4_tarski,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k3_tarski A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((r2_hidden C D) & (r2_hidden D A)) ) ) ) ) ) ) ).
tt(d4_taxonom1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ((v1_taxonom1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 k6_numbers (k1_metric_1 A A B C D))) ) ) ) ) ) ) ) ).
tt(d4_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((m1_taxonom2 B A) <=> (v3_taxonom2 B)) ) ) ) ).
tt(d4_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (B = (k4_taylor_1 A))  <=>  ( ((k1_relset_1 k1_numbers B) = (k3_limfunc1 k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers (k3_limfunc1 k6_numbers)) =>  ((k1_seq_1 B C) = (k9_prepower C A)) ) ) ) ) ) ) ) ) ).
tt(d4_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_tbsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k2_metric_1 A (k8_nat_1 (u1_struct_0 A) B E) (k8_nat_1 (u1_struct_0 A) B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_tdgroup A B C D E) <=> (r2_hidden (k4_tarski (k4_tarski B C) (k4_tarski D E)) (u1_analoaf (k2_tdgroup A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k4_tdlat_1 A) = (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A))) ) ) ).
tt(d4_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v3_tdlat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v6_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d4_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v3_pre_topc (k2_pre_topc A B) A)) ) ) ) ) ) ).
tt(d4_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r1_termord A B C D) =>  ((k1_termord A B C D) = C) )  &  ( (~ (r1_termord A B C D))  =>  ((k1_termord A B C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tex_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k3_tex_1 A B) = (g1_pre_topc A (k7_subset_1 (k1_zfmisc_1 A) (k9_setfam_1 A) (a_2_0_tex_1 A B)))) ) ) ) ).
tt(d4_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v3_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(d4_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  ( (~ (r1_xboole_0 B C))  &  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_pre_topc D A) =>  ((k2_tmap_1 A B C D) = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D))) ) ) ) ) ) ) ) ) ).
tt(d4_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( (C = (k4_toler_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_toler_1 D A B) & (m1_toler_1 D A B)) ) ) ) ) ) ) ) ).
tt(d4_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_topalg_1 A B) = (k3_topalg_1 A B B)) ) ) ) ) ).
tt(d4_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A))))) )  =>  ( (D = (k3_topalg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  ((k1_binop_1 D E F) = (k7_real_1 (k8_real_1 (k9_real_1 1 F) (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) B E)) (k3_xcmplx_0 F (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)))))) )  =>  ( (B = (k5_topalg_5 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) B C) = (k19_euclid (k21_sin_cos (k8_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) C)) (k18_sin_cos (k8_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) C)))) ) ) ) ) ) ) ) ).
tt(d4_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 A)))))  =>  ((v4_topalg_6 B A) <=>  ( ((v6_xxreal_2 (k1_relset_1 (u1_struct_0 k2_topalg_2) B)) & (m1_subset_1 (k1_relset_1 (u1_struct_0 k2_topalg_2) B) (k1_zfmisc_1 k1_numbers)))  &  (? [C:$i] :  ((m1_pre_topc C k2_topalg_2) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  &  ( (B = D)  &  ( (C = (k1_pre_topc k2_topalg_2 (k1_relset_1 (u1_struct_0 k2_topalg_2) B)))  & (v5_pre_topc D C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v3_topdim_1 A) <=> (v1_topdim_1 (k2_struct_0 A) A)) ) ) ).
tt(d4_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_topgen_1 A B C) <=>  ((r2_hidden C B) &  (~ (r1_topgen_1 A B C)) ) ) ) ) ) ) ) ).
tt(d4_topgen_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_topgen_2 A) <=> (v1_finset_1 (k2_waybel23 A))) ) ) ).
tt(d4_topgen_3,ax, (k3_topgen_3 = (k1_card_1 k1_numbers)) ).
tt(d4_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_topgen_4 B A) <=>  (! [C:$i] :  ( ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_tarski C B) => (r2_hidden (k5_setfam_1 A C) B)) ) ) ) ) ) ) ).
tt(d4_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_topgen_5 A) <=>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C (k3_subset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc D A k5_topmetr) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr))))) ) )  =>  (~  ( ((k1_funct_1 D C) = k6_numbers)  & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr) D B) (k6_domain_1 k1_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((m2_topgrp_1 B A) <=> (v3_tops_2 B A A)) ) ) ) ) ).
tt(d4_topmetr,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_topmetr B A) <=>  (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  (C = (k9_metric_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ((k3_topreal1 A B) = (k3_tarski (a_2_0_topreal1 A B))) ) ) ) ) ).
tt(d4_topreal9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_topreal9 B A) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B (k1_rlvect_1 (k15_euclid A) D C)) = (k1_rlvect_1 (k15_euclid A) (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k6_toprealb A) = A) ) ) ).
tt(d4_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v3_membered C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k15_euclid A)))))) )  =>  ( (E = (k15_toprealc A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k3_funct_2 B (u1_struct_0 (k15_euclid A)) E F) = (k2_finseq_2 A (k3_funct_2 B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_toprns_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k3_toprns_1 A B) = (k5_vfunct_1 k5_numbers (k15_euclid A) B)) ) ) ) ) ).
tt(d4_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=> (v1_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(d4_tops_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ((k2_tops_2 A B C) = (k2_funct_1 C)) ) ) ) ) ) ).
tt(d4_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=>  ((k2_pre_topc A (k1_tops_1 A B)) = (k2_struct_0 A)) ) ) ) ) ) ).
tt(d4_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r3_transgeo A B) <=> (r1_transgeo (u1_struct_0 A) B (u1_analoaf A))) ) ) ) ) ).
tt(d4_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)))))) )  =>  ( (E = (k4_treal_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_topmetr A B))) =>  ((k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) E F) = (k13_complex1 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 B F) C) (k3_xcmplx_0 (k6_xcmplx_0 F A) D)) (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_trees_1 A) = (k2_xboole_0 (a_1_0_trees_1 A) (k1_tarski k1_xboole_0))) ) ) ).
tt(d4_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((m2_trees_2 B A) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (B = (a_2_0_trees_2 A C)) ) ) ) ) ) ) ) ).
tt(d4_trees_3,ax, (! [A:$i] :  ((v2_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) ) ) ) ) ).
tt(d4_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v6_trees_3 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ( (C = (k4_trees_4 A B))  <=>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v6_trees_3 D)) ) )  &  ( (B = D)  &  ((k9_xtuple_0 C) = (k11_trees_3 (k2_funct_6 D))) ) ) )  &  ( ((k1_funct_1 C k1_xboole_0) = A)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  =>  ((k5_trees_2 C (k12_finseq_1 k5_numbers D)) = (k1_funct_1 B (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_pre_topc D) & (m1_pre_topc D A)) )  =>  ( (D = (k2_tsep_1 A B C))  <=>  ((u1_struct_0 D) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_tsp_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_2 B A) <=>  ((v1_tsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tsp_1 C A) & (r1_tarski B C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d4_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ((k7_turing_1 A B) = (k2_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B)) ) ) ) ) ).
tt(d4_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k5_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k10_margrel1 B C))) ) ) ) ) ) ) ) ).
tt(d4_unialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( (B = (k1_unialg_1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 (u1_unialg_1 A)))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v2_margrel1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) )  =>  ( (D = (k1_funct_1 (u1_unialg_1 A) C))  =>  ((k1_funct_1 B C) = (k19_margrel1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_unialg_2 B A) <=>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) => (r2_unialg_2 A B C)) ) ) ) ) ) ) ).
tt(d4_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (B = (k3_unialg_3 A))  <=>  (! [C:$i] :  ((m2_unialg_3 C A (k1_unialg_3 A)) =>  (! [D:$i] :  ((m1_unialg_2 D A) =>  ( (C = D)  =>  ((k3_funct_2 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)) B C) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_uniroots,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_vectsp_1 B) & (l6_algstr_0 B)) )  =>  ((k4_uniroots A B) = (k15_funct_7 k5_numbers (u1_struct_0 B) (k15_funct_7 k5_numbers (u1_struct_0 B) (k9_polynom3 B) k6_numbers (k4_algstr_0 B (k1_group_1 B))) A (k1_group_1 B))) ) ) ) ) ).
tt(d4_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (C = (k4_uproots A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k5_numbers) &  ( (C = (k2_wsierp_1 D))  &  (D = (k3_relat_1 (k1_uproots (k13_pre_poly B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k5_urysohn1 A))  <=>  ( ((k4_finseq_1 B) = (k2_finseq_1 (k1_nat_1 (k2_newton 2 A) 1)))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k10_real_1 (k5_real_1 C 1) (k2_newton 2 A))) ) ) ) ) ) ) ) ) ) ).
tt(d4_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v10_pre_topc A) &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) & (r1_xboole_0 B C)) ) )  =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k3_urysohn1 (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k3_urysohn1 (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (E = (k3_urysohn3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F k3_urysohn1) =>  ( ((r2_hidden F (k10_prob_1 k6_numbers)) =>  ((k1_funct_1 E F) = k1_xboole_0) )  &  ( ((r2_hidden F (k3_limfunc1 1)) =>  ((k1_funct_1 E F) = (u1_struct_0 A)) )  &  ((r2_hidden F k2_urysohn1) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden F (k1_urysohn1 G)) =>  ((k1_funct_1 E F) = (k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k3_margrel1 B)) =>  (! [F:$i] :  ((m2_funct_2 F (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( (F = (k5_valuat_1 A B C D E))  <=>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( ((r2_hidden (k4_valuat_1 A B C D G) E) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 F G) = k8_margrel1) )  &  ( ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 F G) = k8_margrel1)  => (r2_hidden (k4_valuat_1 A B C D G) E))  &  ( ( (~ (r2_hidden (k4_valuat_1 A B C D G) E))  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 F G) = k7_margrel1) )  &  (~  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 F G) = k7_margrel1)  & (r2_hidden (k4_valuat_1 A B C D G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k18_valued_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k3_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( (B = (k1_vectmetr A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v3_vectmetr C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(d4_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k4_vectsp10 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(d4_vectsp11,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (D = (k1_vectsp11 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_monoid_0 (u1_struct_0 A)))) =>  ( (E = B)  =>  (D = (k3_group_4 (k15_monoid_0 (u1_struct_0 A)) (k5_finseq_2 (u1_struct_0 (k15_monoid_0 (u1_struct_0 A))) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v3_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) ) ) ) ) ).
tt(d4_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((k2_vectsp_4 A B) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ).
tt(d4_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) <=>  ( ((g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)) = (k1_vectsp_5 A B C D))  &  ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((m2_vectsp_6 D A B C) <=> (r1_tarski (k1_vectsp_6 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(d4_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B)))))) )  =>  ( (C = (k4_vectsp_8 A B))  <=>  (! [D:$i] :  ((m2_vectsp_8 D A B (k2_vectsp_8 A B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( (D = E)  =>  ((k3_funct_2 (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B)) C D) = (u1_struct_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (E = (k4_vfunct_1 A B C D))  <=>  ( ((k1_relset_1 A E) = (k1_relset_1 A C))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) =>  ((k7_partfun1 (u1_struct_0 B) E F) = (k1_rlvect_1 B (k7_partfun1 (u1_struct_0 B) C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  ((v4_waybel_0 B A) <=>  (! [C:$i] :  ( ((v1_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((r1_yellow_0 A C) =>  ( (C = k1_xboole_0)  | (r2_hidden (k1_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(d4_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A))))))) )  =>  ( (B = (k5_waybel10 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k1_funct_1 B C) = (k1_yellow_2 A A C)) ) ) ) ) ) ) ) ).
tt(d4_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_waybel_9 A)) )  =>  ((v4_waybel11 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((v1_waybel11 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ) ).
tt(d4_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_waybel12 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (C = (k3_yellow_0 A)) )  &  ((k11_lattice3 A B C) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k1_waybel16 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (v1_waybel16 C A)) ) ) ) ) ) ) ) ).
tt(d4_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_waybel17 A B) = (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) (k1_nattra_1 (u1_struct_0 A) (u1_struct_0 A) (k6_partfun1 (u1_struct_0 A)) B))) ) ) ) ) ).
tt(d4_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k6_waybel18 A B C) = (k12_card_3 (k12_pralg_1 A B) C)) ) ) ) ) ) ) ).
tt(d4_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (k2_waybel19 A))  <=>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C A)) )  =>  (B = (u1_pre_topc C)) ) ) ) ) ) ) ) ).
tt(d4_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((r1_waybel_1 A B) <=>  ((r2_yellow_0 A B) & (r2_hidden (k2_yellow_0 A B) B)) ) ) ) ) ).
tt(d4_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k4_waybel20 A B) = (k8_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 (k3_yellow_3 A A)) (k1_waybel20 A A A A B B) (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ).
tt(d4_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_waybel21 C A B) <=>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  ((k2_yellow_6 (u1_struct_0 A) B C (k1_waybel11 A D)) = (k1_waybel11 B (k6_waybel_9 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel23 B A) <=> (v8_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(d4_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_waybel25 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k1_waybel25 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_waybel25 A))))) )  =>  ((r1_yellow_0 (k1_waybel25 A) B) &  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden (k1_yellow_0 (k1_waybel25 A) B) C) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel26,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k5_waybel26 A) = (k2_relat_1 (k3_card_3 (k2_card_3 A)))) ) ) ).
tt(d4_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k2_waybel27 A B))  <=>  ( ((v4_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B)))  &  (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v22_waybel_0 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((k4_waybel28 A) = (u1_pre_topc (k13_yellow_6 A (k3_waybel28 A)))) ) ) ).
tt(d4_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_waybel26 A k9_waybel18)) (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A k9_waybel18)) (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))))))) )  =>  ( (B = (k4_waybel29 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k9_waybel18)) &  ((v5_pre_topc C A k9_waybel18) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k9_waybel18))))) ) )  =>  ((k1_funct_1 B C) = (k8_relset_1 (u1_struct_0 A) (u1_struct_0 k9_waybel18) C (k1_tarski 1))) ) ) ) ) ) ) ) ).
tt(d4_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) )  =>  ( (B = (k4_waybel_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_binop_1 B C D) = (k11_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  ((v3_waybel30 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) => (v5_yellow_0 (k5_yellow_0 A D) A)) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_waybel_0 C A) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ( (C = (k2_waybel32 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ( (C = (k1_waybel32 A B D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_yellow_6 (u1_struct_0 B) A D E) = (k2_yellow_0 A (a_3_1_waybel32 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xboole_0 B)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) &  ((v2_yellow21 B) & (l2_altcat_1 B)) ) ) ) ) )  =>  ( (B = (k4_waybel34 A))  <=>  ( (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=>  ((v1_orders_2 C) &  ((v3_lattice3 C) & (r2_hidden (u1_struct_0 C) A)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D))) &  ((v5_orders_3 E (k3_yellow21 B C) (k3_yellow21 B D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D)))))) ) )  =>  ((r2_hidden E (k1_altcat_1 B C D)) <=> (v17_waybel_0 E (k3_yellow21 B C) (k3_yellow21 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel35,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ((v2_waybel35 C A B) <=>  (! [D:$i] :  ((m1_waybel35 D A B) =>  ((r1_lattice7 A C D) =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_waybel_3 A B) = (a_2_1_waybel_3 A B)) ) ) ) ) ).
tt(d4_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v2_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_orders_2 A F C) &  ((r2_hidden (k4_tarski C D) B) & (r1_orders_2 A D E)) )  => (r2_hidden (k4_tarski F E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k3_waybel_6 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (v2_waybel_6 C A)) ) ) ) ) ) ) ) ).
tt(d4_waybel_7,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_waybel_7 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) & (r2_hidden C D))  =>  (! [E:$i] :  (~  ((r2_hidden E B) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v2_waybel_8 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k2_waybel_8 A B)))  & (v1_waybel_0 (k2_waybel_8 A B) A)) ) )  &  ((v24_waybel_0 A) & (v1_waybel_8 A)) ) ) ) ) ).
tt(d4_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((r2_waybel_9 A B) <=> (r2_yellow_0 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)))) ) ) ) ) ).
tt(d4_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v36_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = (k4_weddwitt A))  <=>  ( ((u1_struct_0 B) = (a_1_1_weddwitt A))  &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ((k5_struct_0 B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d4_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (C = (k4_weierstr A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k4_metric_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d4_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k1_wellfnd1 A))  <=>  (B = (k3_tarski (a_1_0_wellfnd1 A))) ) ) ) ) ) ).
tt(d4_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_wellord1 A) <=>  ((v1_relat_2 A) &  ((v8_relat_2 A) &  ((v4_relat_2 A) &  ((v6_relat_2 A) & (v1_wellord1 A)) ) ) ) ) ) ) ).
tt(d4_wellord2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((v2_funct_1 C) &  ( ((k9_xtuple_0 C) = A)  &  ((k10_xtuple_0 C) = B) ) ) ) ) ) ) ) ).
tt(d4_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k3_xboole_0 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D A) & (r2_hidden D B)) ) ) ) ) ) ) ).
tt(d4_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean A) = (k6_xcmplx_0 1 A)) ) ) ).
tt(d4_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( (C = (k2_xcmplx_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (A = (k5_arytm_0 D E))  &  ( (B = (k5_arytm_0 F G))  &  (C = (k5_arytm_0 (k1_arytm_0 D F) (k1_arytm_0 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xtuple_0 A B C) = (k4_tarski (k4_tarski A B) C)) ) ) ) ).
tt(d4_xxreal_0,ax, (k7_numbers = (k2_xboole_0 k1_numbers (k2_tarski k1_xxreal_0 k2_xxreal_0))) ).
tt(d4_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_1 A B) = (a_2_3_xxreal_1 A B)) ) ) ) ) ).
tt(d4_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (B = (k2_xxreal_2 A))  <=>  ((m2_xxreal_2 B A) &  (! [C:$i] :  ((m2_xxreal_2 C A) => (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(d4_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k3_xxreal_3 A B) = (k1_xxreal_3 A (k2_xxreal_3 B))) ) ) ) ) ).
tt(d4_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_yellow_0 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (r1_lattice3 A (u1_struct_0 A) B)) ) ) ) ) ).
tt(d4_yellow11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k3_yellow11 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) <=>  ((r1_orders_2 A B E) & (r1_orders_2 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m2_yellow13 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_yellow13 B A C)) ) ) ) ) ) ) ).
tt(d4_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r4_yellow16 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  & (r2_yellow16 A B C)) ) ) ) ) ) ) ).
tt(d4_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  ( (B = (k1_yellow18 A))  <=> (r2_yellow18 A B)) ) ) ) ) ).
tt(d4_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ( (D = (k3_yellow19 A B C))  <=>  ( ((u1_struct_0 D) = (a_3_0_yellow19 A B C))  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ((r1_orders_2 D E F) <=> (r1_tarski (k2_xtuple_0 F) (k2_xtuple_0 E))) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ((k2_waybel_0 A D E) = (k1_xtuple_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( (C = (k5_yellow_1 A B))  <=>  ( ((u1_struct_0 C) = (k4_card_3 (k12_pralg_1 A B)))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r2_hidden D (k4_card_3 (k12_pralg_1 A B))) =>  ((r1_orders_2 C D E) <=>  (? [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  &  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  ( (F = D)  &  ( (G = E)  &  (! [H:$i] :  (~  ((r2_hidden H A) &  (! [I:$i] :  ((l1_orders_2 I) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 I)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 I)) =>  (~  ( (I = (k1_funct_1 B H))  &  ( (J = (k1_funct_1 F H))  &  ( (K = (k1_funct_1 G H))  & (r1_orders_2 I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v11_altcat_1 E) &  ((v12_altcat_1 E) & (l2_altcat_1 E)) ) ) )  =>  ((r2_yellow20 A B C D E) <=>  ( ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) )  &  ( ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) )  &  (? [F:$i] :  ( ((v15_functor0 F D E) & (m2_functor0 F D E))  &  ((v21_functor0 F D E) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( (G = H)  =>  ((k3_functor0 D E F G) = (k3_functor0 A B C H)) ) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ( (G = I)  &  (H = J) )  =>  ( ((k1_altcat_1 D G H) = k1_xboole_0)  |  (! [K:$i] :  ((m1_subset_1 K (k1_altcat_1 D G H)) =>  (! [L:$i] :  ((m1_subset_1 L (k1_altcat_1 A I J)) =>  ( (K = L)  =>  ((k6_functor0 D E F G H K) = (k1_funct_1 (k4_functor0 A B C I J) L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v2_yellow21 A) <=>  ((v9_altcat_1 A) &  ((v3_yellow18 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v1_lattice3 D) &  ((v2_lattice3 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v3_orders_2 E) &  ((v4_orders_2 E) &  ((v5_orders_2 E) &  ((v1_lattice3 E) &  ((v2_lattice3 E) & (l1_orders_2 E)) ) ) ) )  =>  ( ( (D = B)  &  (E = C) )  => (r1_tarski (k1_altcat_1 A B C) (k1_orders_3 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ( (B = (k3_yellow_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) B C) = (k5_waybel_0 A C)) ) ) ) ) ) ) ) ).
tt(d4_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_yellow_4 A B C) = (a_3_2_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(d4_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((v1_yellow_6 B A) <=> (v3_funct_1 (u1_waybel_0 A B))) ) ) ) ) ).
tt(d4_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_8 A B C) <=>  ((r2_hidden C B) & (r1_tarski B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ) ).
tt(d4_yellow_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_waybel_9 B) =>  ((m1_yellow_9 B A) <=>  ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) ) ) ) ) ) ).
tt(d4_zf_fund1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)) =>  ((k4_zf_fund1 A) = (k7_relat_1 (k2_funct_1 k2_zf_fund1) A)) ) ) ).
tt(d4_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k5_zf_lang A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 1) (k3_zf_lang A)) (k3_zf_lang B))) ) ) ) ) ).
tt(d4_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_zfmisc_1 A B C D) = (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)) ) ) ) ) ).
tt(d4_zfmodel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r2_zfmodel1 A B) <=>  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  &  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model C)) &  ((r1_zf_model B D (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang C (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) &  (A = (k1_zfmodel1 C B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_zf_model A B C) <=> (r2_hidden B (k5_zf_model C A))) ) ) ) ) ) ) ).
tt(d4_zfrefle1,ax, (! [A:$i] :  ( (A = k1_zfrefle1)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  ((r2_hidden B k9_zf_lang) &  (~  ( (~  (B = k6_zf_model) )  &  ( (~  (B = k7_zf_model) )  &  ( (~  (B = k8_zf_model) )  &  ( (~  (B = k9_zf_model) )  &  ( (~  (B = k10_zf_model) )  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model C)) &  (B = (k11_zf_model C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d4_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  ((v4_zmodul01 A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_zmodul01 A D (k3_xcmplx_0 B C)) = (k1_zmodul01 A (k1_zmodul01 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d50_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  ((v10_abcmiz_1 B A) <=>  ((k47_abcmiz_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d50_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) =>  ((k56_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k35_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d50_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k27_fomodel4 A) = (k21_fomodel4 A (k13_fomodel4 A))) ) ) ).
tt(d50_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k50_gfacirc1 A B C) = (k3_circcomb (k46_gfacirc1 A B C) (k43_gfacirc1 A B C) (k47_gfacirc1 A B C) (k44_gfacirc1 A B C))) ) ) ) ).
tt(d50_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v10_glib_000 B A) <=>  ((k35_glib_000 A B) = k6_numbers) ) ) ) ) ) ).
tt(d50_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k30_modelc_1 A)) =>  ( (D = (k40_modelc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ( ((k4_xboolean (k4_modelc_1 (k1_funct_1 (k31_modelc_1 A B) E)) (k4_modelc_1 (k1_funct_1 (k31_modelc_1 A C) E))) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 A D) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d50_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k36_modelc_2 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden D (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B C D) = (k35_modelc_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(d50_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m2_finseq_1 B k5_numbers)) )  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k23_modelc_3 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 B))))) )  =>  ( (D = (k37_modelc_3 A B C))  <=>  ( ((k3_funct_2 k5_numbers (k23_modelc_3 B) D k6_numbers) = (k11_modelc_3 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k3_funct_2 k5_numbers (k23_modelc_3 B) D (k1_nat_1 E 1)) = (k36_modelc_3 (k29_modelc_2 k43_modelc_2 A E) B C (k10_modelc_3 (k1_funct_1 D E) B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d51_abcmiz_1,ax, (k49_abcmiz_1 = (k7_lattice3 (k2_yellow_1 a_0_2_abcmiz_1))) ).
tt(d51_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k57_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k29_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d51_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k28_fomodel4 A) = (k21_fomodel4 A (k14_fomodel4 A))) ) ) ).
tt(d51_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v11_glib_000 B A) <=>  (? [C:$i] :  ( ((k28_glib_000 A B) = (k1_tarski C))  &  (~ (r1_glib_000 A B B C)) ) ) ) ) ) ) ) ).
tt(d51_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  ( (B = (k41_modelc_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k30_modelc_1 A)) & (r2_hidden D (k30_modelc_1 A)))  =>  ((k1_binop_1 B C D) = (k40_modelc_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(d51_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) )  =>  (! [D:$i] :  ( ((m1_subset_1 D (k25_modelc_2 A)) =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  =>  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 B (k28_modelc_2 A D F)) = k8_margrel1) ) ) )  &  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 C (k28_modelc_2 A D E)) = k8_margrel1) ) ) ) )  |  ((k37_modelc_2 A B C D) = k8_margrel1) ) )  &  ( (~  ((m1_subset_1 D (k25_modelc_2 A)) &  (? [E:$i] :  ((v7_ordinal1 E) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  =>  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 B (k28_modelc_2 A D F)) = k8_margrel1) ) ) )  &  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 C (k28_modelc_2 A D E)) = k8_margrel1) ) ) ) ) )  =>  ((k37_modelc_2 A B C D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d52_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k58_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k31_aofa_i00 A B C D (k42_aofa_i00 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d52_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k29_fomodel4 A) = (k21_fomodel4 A (k15_fomodel4 A))) ) ) ).
tt(d52_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v11_glib_000 B A) <=>  ((k35_glib_000 A B) = 1) ) ) ) ) ) ).
tt(d52_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((r2_hidden E A) =>  ( (! [F:$i] :  ((m1_modelc_1 F A B) =>  (~  ( ((k3_funct_2 k5_numbers A F k6_numbers) = E)  &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( (~ (r1_xxreal_0 G H))  =>  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A F H)) = k8_margrel1) ) ) )  &  ((k3_funct_2 A k6_margrel1 D (k3_funct_2 k5_numbers A F G)) = k8_margrel1) ) ) ) ) ) ) )  |  ((k42_modelc_1 A B C D E) = k8_margrel1) ) )  &  ( (~  ((r2_hidden E A) &  (? [F:$i] :  ((m1_modelc_1 F A B) &  ( ((k3_funct_2 k5_numbers A F k6_numbers) = E)  &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( (~ (r1_xxreal_0 G H))  =>  ((k3_funct_2 A k6_margrel1 C (k3_funct_2 k5_numbers A F H)) = k8_margrel1) ) ) )  &  ((k3_funct_2 A k6_margrel1 D (k3_funct_2 k5_numbers A F G)) = k8_margrel1) ) ) ) ) ) ) ) )  =>  ((k42_modelc_1 A B C D E) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d52_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k30_modelc_1 (k25_modelc_2 A))) =>  ( (D = (k38_modelc_2 A B C))  <=>  (! [E:$i] :  ((r2_hidden E (k25_modelc_2 A)) =>  ( ((k37_modelc_2 A (k31_modelc_1 (k25_modelc_2 A) B) (k31_modelc_1 (k25_modelc_2 A) C) E) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 (k25_modelc_2 A) D) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(d53_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k59_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k36_aofa_i00 A B C D (k42_aofa_i00 A B C D E) (k43_aofa_i00 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d53_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k30_fomodel4 A) = (k21_fomodel4 A (k16_fomodel4 A))) ) ) ).
tt(d53_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k30_modelc_1 A)) =>  ( (E = (k43_modelc_1 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F A) =>  ( ((k42_modelc_1 A B (k31_modelc_1 A C) (k31_modelc_1 A D) F) = k8_margrel1)  <=>  ((k1_funct_1 (k31_modelc_1 A E) F) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d53_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k39_modelc_2 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden D (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B C D) = (k38_modelc_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(d54_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k60_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k35_aofa_i00 A B C D (k42_aofa_i00 A B C D E) (k43_aofa_i00 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d54_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k31_fomodel4 A) = (k21_fomodel4 A (k17_fomodel4 A))) ) ) ).
tt(d54_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ((v13_glib_000 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  ((k1_funct_1 A B) = (k1_funct_1 A (k1_nat_1 B 1))) ) ) ) ) ) ).
tt(d54_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  ( (C = (k44_modelc_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 A)) & (r2_hidden E (k30_modelc_1 A)))  =>  ((k1_binop_1 C D E) = (k43_modelc_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d54_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k40_modelc_2 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden D (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B C D) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k36_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) C) (k1_funct_1 (k31_modelc_2 A) D)))) ) ) ) ) ) ) ) ) ).
tt(d55_abcmiz_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v13_abcmiz_1 B A) <=> (r1_tarski (k8_relat_1 B (k1_tarski k1_xboole_0)) (k2_relset_1 (u1_struct_0 A) (u2_msualg_1 A)))) ) ) ) ) ).
tt(d55_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k32_fomodel4 A) = (k21_fomodel4 A (k18_fomodel4 A))) ) ) ).
tt(d55_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v13_glib_000 A) =>  ( (B = (k39_glib_000 A))  <=>  ( ((k1_funct_1 A B) = (k1_funct_1 A (k2_nat_1 B 1)))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_funct_1 A C) = (k1_funct_1 A (k1_nat_1 C 1)))  => (r1_xxreal_0 B C)) ) ) ) ) )  &  ( (~ (v13_glib_000 A))  =>  ( (B = (k39_glib_000 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d55_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( (D = (k45_modelc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E B) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ( (F = E)  &  ((k1_funct_1 F C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d55_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( (B = (k41_modelc_2 A))  <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden D (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B C D) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k39_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) C) (k1_funct_1 (k31_modelc_2 A) D)))) ) ) ) ) ) ) ) ) ).
tt(d56_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))))))) )  =>  ((m4_abcmiz_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tarski (k7_relset_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) C (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D)) (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D))) ) ) ) ) ) ) ) ) ).
tt(d56_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k33_fomodel4 A) = (k21_fomodel4 A (k19_fomodel4 A))) ) ) ).
tt(d56_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ((k40_glib_000 A) = (k1_funct_1 A (k39_glib_000 A))) ) ) ).
tt(d56_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_zfmisc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_zfmisc_1 B))))) )  =>  ( (C = (k46_modelc_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k45_modelc_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d56_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  ((k42_modelc_2 A B) = (g1_modelc_2 (k30_modelc_1 (k25_modelc_2 A)) B (k36_modelc_2 A) (k40_modelc_2 A) (k31_modelc_2 A) (k34_modelc_2 A) (k39_modelc_2 A) (k41_modelc_2 A))) ) ) ) ) ).
tt(d57_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k34_fomodel4 A) = (k21_fomodel4 A (k20_fomodel4 A))) ) ) ).
tt(d57_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C D) <=>  ((k3_funct_2 (k25_modelc_2 A) k6_margrel1 (k31_modelc_1 (k25_modelc_2 A) D) C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(d58_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((v15_abcmiz_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  (~  ((r2_hidden C (k1_relset_1 k2_abcmiz_1 B)) &  (! [D:$i] :  ((m1_subset_1 D k2_abcmiz_1) =>  (~  ((k1_funct_1 B C) = (k35_abcmiz_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d58_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_subset_1 C (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_subset_1 D (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  =>  ((k35_fomodel4 A B C D) = (a_4_2_fomodel4 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d58_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  ((k48_modelc_1 A B C) = (g2_modelc_1 (k30_modelc_1 A) C (k41_modelc_1 A) (k33_modelc_1 A) (k36_modelc_1 A B) (k39_modelc_1 A B) (k44_modelc_1 A B))) ) ) ) ) ) ) ).
tt(d58_modelc_2,ax, (k43_modelc_2 = (k1_zfmisc_1 k15_modelc_2)) ).
tt(d59_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)) =>  ((k54_abcmiz_1 A B) = (a_2_7_abcmiz_1 A B)) ) ) ) ) ).
tt(d59_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  ((k65_aofa_i00 A B C D E) = (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D C (k36_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d59_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ( (A = k6_numbers)  =>  ((v12_fomodel4 C A B) <=>  ((r2_hidden (k22_fomodel4 B) C) &  ((r2_hidden (k24_fomodel4 B) C) &  ((r2_hidden (k25_fomodel4 B) C) & (r2_hidden (k26_fomodel4 B) C)) ) ) ) )  &  ( ( (A = 1)  =>  ((v12_fomodel4 C A B) <=>  ((r2_hidden (k22_fomodel4 B) C) &  ((r2_hidden (k24_fomodel4 B) C) &  ((r2_hidden (k25_fomodel4 B) C) &  ((r2_hidden (k26_fomodel4 B) C) &  ((r2_hidden (k27_fomodel4 B) C) & (r2_hidden (k28_fomodel4 B) C)) ) ) ) ) ) )  &  ( ( (A = 2)  =>  ((v12_fomodel4 C A B) <=>  ((r2_hidden (k22_fomodel4 B) C) &  ((r2_hidden (k23_fomodel4 B) C) &  ((r2_hidden (k24_fomodel4 B) C) &  ((r2_hidden (k25_fomodel4 B) C) &  ((r2_hidden (k26_fomodel4 B) C) &  ((r2_hidden (k27_fomodel4 B) C) &  ((r2_hidden (k28_fomodel4 B) C) &  ((r2_hidden (k29_fomodel4 B) C) &  ((r2_hidden (k30_fomodel4 B) C) &  ((r2_hidden (k31_fomodel4 B) C) &  ((r2_hidden (k32_fomodel4 B) C) & (r2_hidden (k33_fomodel4 B) C)) ) ) ) ) ) ) ) ) ) ) ) )  &  (~  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  (~  ((v12_fomodel4 C A B) <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d59_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ((r3_modelc_1 A B C D E) <=>  ((k3_funct_2 A k6_margrel1 (k31_modelc_1 A E) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d59_modelc_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( ((r2_hidden B (k25_modelc_2 k43_modelc_2)) & (r2_hidden A (k8_nat_1 k43_modelc_2 (k27_modelc_2 k43_modelc_2 B) k6_numbers)))  =>  ((k44_modelc_2 A B) = k8_margrel1) )  &  ( (~  ((r2_hidden B (k25_modelc_2 k43_modelc_2)) & (r2_hidden A (k8_nat_1 k43_modelc_2 (k27_modelc_2 k43_modelc_2 B) k6_numbers))) )  =>  ((k44_modelc_2 A B) = k7_margrel1) ) ) ) ) ).
tt(d5_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  ((k1_abcmiz_0 A B) = (k1_funct_1 (u2_abcmiz_0 A) B)) ) ) ) ) ).
tt(d5_abcmiz_1,ax, (k7_abcmiz_1 = 1) ).
tt(d5_abcmiz_a,ax, (k4_abcmiz_a = (k39_abcmiz_1 k27_abcmiz_1)) ).
tt(d5_abian,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_abian A) <=>  (? [B:$i] : (r1_abian B A)) ) ) ) ).
tt(d5_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_aff_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (B = (k2_aff_1 A D E))  &  ( (~  (D = E) )  & (r2_aff_1 A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v5_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_hidden E B) &  ((r2_hidden E C) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r2_hidden G C) &  ((r2_hidden J C) &  ((r2_hidden H D) &  ((r2_hidden K D) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_analoaf A F G I J) &  ((r2_analoaf A F H I K) & (r2_analoaf A G H J K)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (B = C)  |  ( (B = D)  |  ((r1_aff_1 A F G H) |  ( (H = K)  | (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v5_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I D) &  ((r2_hidden J D) &  ((r5_aff_1 A B C) &  ((r5_aff_1 A B D) &  ((r1_aff_1 A G E K) &  ((r1_aff_1 A H F K) &  ((r1_aff_1 A G I L) &  ((r1_aff_1 A H J L) & (r2_analoaf A E I F J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (C = D)  |  ((r1_aff_1 A G E I) |  ((r1_aff_1 A H F J) |  ( (K = L)  |  ( (E = F)  | (r2_analoaf A E I K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_4 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B E) &  ((r1_tarski C E) &  ((r1_tarski D E) & (v1_aff_4 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ((k6_afinsq_1 A B) = (k1_ordinal4 (k5_afinsq_1 A) (k5_afinsq_1 B))) ) ) ).
tt(d5_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r1_afinsq_2 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden C A) &  ((r2_hidden D B) & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_afproj A B) = (k6_eqrel_1 (k1_afproj A) (k1_afproj A) (k3_afproj A) B)) ) ) ) ) ).
tt(d5_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (E = (k2_afvect0 A B C D))  <=> (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r5_alg_1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (r4_alg_1 A B C)) ) ) ) ) ) ) ).
tt(d5_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (C = (k3_algseq_1 A B))  <=>  ((r1_xxreal_0 (k1_algseq_1 A C) 1) &  ((k3_funct_2 k5_numbers (u1_struct_0 A) C k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(d5_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  ((m2_algspec1 B A) <=> (m1_instalg1 A B)) ) ) ) ) ).
tt(d5_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v4_algstr_1 A) <=>  ((v5_algstr_0 A) &  ((v6_algstr_0 A) &  ((v2_algstr_1 A) & (v3_algstr_1 A)) ) ) ) ) ) ).
tt(d5_algstr_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_3 A))  =>  ((v2_algstr_3 A) <=>  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_3 A B (k5_struct_0 A) (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_3 A (k5_struct_0 A) B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_3 A B (k4_struct_0 A) C) = C) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_3 A (k4_struct_0 A) B C) = C) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k1_algstr_3 A B C E) = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k1_algstr_3 A B C D) = (k1_algstr_3 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( ((k1_algstr_3 A F B G) = D)  &  ((k1_algstr_3 A F C G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k1_algstr_3 A B F D) = (k1_algstr_3 A C F E)) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( ((k1_algstr_3 A D B F) = (k1_algstr_3 A E B G))  &  ( ((k1_algstr_3 A D C F) = (k1_algstr_3 A E C G))  &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((k4_algstr_4 A B) = (g3_algstr_0 (k8_eqrel_1 (u1_struct_0 A) B) (k3_algstr_4 A B))) ) ) ) ) ).
tt(d5_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  (! [C:$i] :  ((m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)) =>  ((v3_altcat_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( ((r2_hidden H (k1_binop_1 B D E)) &  ((r2_hidden I (k1_binop_1 B E F)) & (r2_hidden J (k1_binop_1 B F G))) )  =>  ((k1_binop_1 (k4_altcat_1 A B C D F G) J (k1_binop_1 (k4_altcat_1 A B C D E F) I H)) = (k1_binop_1 (k4_altcat_1 A B C D E G) (k1_binop_1 (k4_altcat_1 A B C E F G) J I) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k4_altcat_2 A) = (g2_altcat_1 (u1_struct_0 A) (k2_altcat_2 A) (k3_altcat_2 A))) ) ) ).
tt(d5_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v3_altcat_3 D A B C) <=>  ( ((k5_altcat_1 A C B C (k1_altcat_3 A B C D) D) = (k8_altcat_1 A C))  &  ((k5_altcat_1 A B C B D (k1_altcat_3 A B C D)) = (k8_altcat_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) & (m1_altcat_2 B A)) ) )  =>  ( (B = (k5_altcat_4 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_altcat_1 B) (u1_altcat_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C D)) =>  ((r2_hidden E (k1_binop_1 (u1_altcat_1 B) C D)) <=>  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  & (v3_altcat_3 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ami_2,ax, (k4_ami_2 = (k6_afinsq_1 k5_numbers k4_numbers)) ).
tt(d5_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_ami_3 A B) = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d5_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_amistd_1 A B C) = (k3_tarski (a_3_1_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(d5_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = (k4_amistd_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E D) <=>  (~  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_memstr_0 A B E)) =>  ((k2_extpro_1 A B C (k1_amistd_4 A B F E G)) = (k1_amistd_4 A B (k2_extpro_1 A B C F) E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) )  =>  ((v5_amistd_5 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  (~ (v2_compos_1 D B)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v4_extpro_1 E A B D)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 B)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 A B)) & (v1_partfun1 G (u1_struct_0 B))) ) ) )  =>  ( ((r1_tarski E F) & (r1_tarski (k9_memstr_0 A B E C) G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 B)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 B)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ((r1_tarski D H) & (r1_tarski (k6_compos_1 B D C) I))  =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ((k5_compos_0 (u1_compos_1 B) (k3_extpro_1 A B H (k5_extpro_1 A B H F J)) C) = (k3_extpro_1 A B I (k5_extpro_1 A B I G J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k2_ami_wstd A B C))  <=>  ((k1_ami_wstd A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d5_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r4_analmetr A B C D E) <=> (r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (u1_analmetr A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v2_analoaf A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) &  ( ((r2_analoaf A B C C B) =>  (B = C) )  &  ( ( ((r2_analoaf A B C F G) & (r2_analoaf A B C H I))  =>  ( (B = C)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C D E) => (r2_analoaf A C B E D))  &  ( ((r2_analoaf A B C C D) => (r2_analoaf A B C B D))  &  (~  ((r2_analoaf A B C B D) &  ( (~ (r2_analoaf A B C C D))  &  (~ (r2_analoaf A B D D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~ (r2_analoaf A B C D E))  &  (~ (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = D) )  &  ((r2_analoaf A D B B E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (D = (k3_analort A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (E = (k4_tarski G H))  &  ( (F = (k4_tarski I J))  & (r1_analort A B C G H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k3_anproj_1 A))  <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k8_struct_0 A)))) &  ( (C = (k8_eqrel_1 (k8_struct_0 A) (k1_anproj_1 A)))  &  (B = C) ) ) ) ) ) ) ) ).
tt(d5_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r5_anproj_2 A B C D E F G H) <=>  ( (~ (r1_anproj_1 A B D))  &  ( (~ (r1_anproj_1 A B E))  &  ( (~ (r1_anproj_1 A B G))  &  ( (~ (r1_anproj_1 A B H))  &  ( (~ (r1_anproj_1 A C D))  &  ( (~ (r1_anproj_1 A C E))  &  ( (~ (r1_anproj_1 A F G))  &  ( (~ (r1_anproj_1 A F H))  &  ( (~ (r1_anproj_1 A D E))  &  (~ (r1_anproj_1 A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k5_aofa_000 A B) = (a_2_0_aofa_000 A B)) ) ) ) ).
tt(d5_armstrng,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k6_margrel1))  =>  ( (D = (k3_armstrng A B C))  <=>  (! [E:$i] :  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 D E) = (k10_margrel1 (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( (B = k6_numbers)  =>  ((k5_arytm_0 A B) = A) )  &  ( (~  (B = k6_numbers) )  =>  ((k5_arytm_0 A B) = (k5_funct_4 k1_numbers k6_numbers 1 A B)) ) ) ) ) ) ) ).
tt(d5_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ( ((r2_hidden A k5_arytm_3) & (r2_hidden B k5_arytm_3))  =>  ((r1_arytm_2 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k5_arytm_3) &  (? [D:$i] :  ((m1_subset_1 D k5_arytm_3) &  ( (A = C)  &  ( (B = D)  & (r3_arytm_3 C D)) ) ) ) ) ) ) )  &  ( ((r2_hidden A k5_arytm_3) =>  ((r2_hidden B k5_arytm_3) |  ((r1_arytm_2 A B) <=> (r2_hidden A B)) ) )  &  ( ((r2_hidden B k5_arytm_3) =>  ((r2_hidden A k5_arytm_3) |  ((r1_arytm_2 A B) <=>  (~ (r2_hidden B A)) ) ) )  &  (~  ( (~  ((r2_hidden A k5_arytm_3) & (r2_hidden B k5_arytm_3)) )  &  ( (~  ((r2_hidden A k5_arytm_3) &  (~ (r2_hidden B k5_arytm_3)) ) )  &  ( (~  ( (~ (r2_hidden A k5_arytm_3))  & (r2_hidden B k5_arytm_3)) )  &  (~  ((r1_arytm_2 A B) <=> (r1_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C k4_ordinal1) =>  ( (C = (k3_arytm_3 A B))  <=>  ((r2_arytm_3 C A) &  ((r2_arytm_3 C B) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  ( ((r2_arytm_3 D A) & (r2_arytm_3 D B))  => (r2_arytm_3 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_asympt_0 A) <=>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 B C) &  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d5_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k5_asympt_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k9_newton (k2_nat_1 C A))) ) ) ) ) ) ) ) ).
tt(d5_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))))  =>  ( (C = (k5_autalg_1 A B))  <=>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((r2_hidden D C) <=> (r4_msualg_3 A B B D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B (k3_autgroup A)) & (m1_group_2 B (k3_autgroup A))) )  =>  ( (B = (k5_autgroup A))  <=>  ((u1_struct_0 B) = (k4_autgroup A)) ) ) ) ) ) ).
tt(d5_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ((v2_bagorder B A) <=>  ((r7_relat_2 B (k15_pre_poly A)) &  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r2_hidden (k4_tarski (k16_pre_poly A) C) B)) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) => (r2_hidden (k4_tarski (k11_pre_poly A C E) (k11_pre_poly A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v5_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bcialg_1 A B B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(d5_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_bcialg_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A C B)) ) ) ) ) ) ) ).
tt(d5_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v5_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A (k4_struct_0 A) (k1_bcialg_1 A B C))) = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(d5_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_bcialg_5 A B C D) = (k7_nat_1 (k7_nat_1 A B) (k7_nat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d5_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_6 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k4_bcialg_6 A B))  <=>  ((r2_hidden (k3_bcialg_6 A C B) (k4_bcialg_1 A)) &  ( (~  (C = k6_numbers) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden (k3_bcialg_6 A D B) (k4_bcialg_1 A)) =>  ( (D = k6_numbers)  | (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_bciideal B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B) & (r2_hidden D B))  => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_bhsp_1 A B C) = (k3_bhsp_1 A (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(d5_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_bhsp_2 A B C) = (a_3_0_bhsp_2 A B C)) ) ) ) ) ) ) ).
tt(d5_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k4_bhsp_4 A B C D) = (k5_algstr_0 A (k3_bhsp_4 A B C) (k3_bhsp_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(d5_bhsp_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v1_setwiseo C A)) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((r1_tarski D (k9_xtuple_0 E)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (F = (k5_bhsp_5 A B C D E))  <=>  (? [G:$i] :  ((m2_finseq_1 G B) &  ((v2_funct_1 G) &  ( ((k10_xtuple_0 G) = D)  &  (F = (k1_finsop_1 A (k4_bhsp_5 A B E G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_bhsp_6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) &  ((v2_hahnban D A) &  ((v3_hahnban D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v2_bhsp_6 D A) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 F))  &  ((r1_tarski F B) &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski F G) &  ((r1_tarski G B) & (r1_xxreal_0 E (k18_complex1 (k3_funct_2 (u1_struct_0 A) k1_numbers D (k5_algstr_0 A C (k1_bhsp_6 A G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((k4_bilinear A B C D) = (k3_bilinear A B C D (k4_algstr_0 A (k5_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(d5_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((k5_binari_2 A B C) = (k10_margrel1 (k10_margrel1 (k7_partfun1 k6_margrel1 B A) (k7_partfun1 k6_margrel1 C A)) (k9_margrel1 (k7_partfun1 k6_margrel1 (k4_binarith A B C) A)))) ) ) ) ) ) ) ).
tt(d5_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k6_margrel1))  =>  ( (D = (k7_binarith A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 D E) = (k2_binarith (k2_binarith (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 C E)) (k7_partfun1 k6_margrel1 (k4_binarith A B C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k5_binom A B C) = (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) C B)) ) ) ) ) ) ) ).
tt(d5_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A C B D) = D) ) ) ) ) ) ) ) ) ).
tt(d5_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) )  =>  ( (A = k29_binop_2)  <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_binop_1 A B C) = (k5_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d5_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  ( ( (C = k1_xboole_0)  =>  ( (D = (k3_boolmark A B C))  <=> (r2_funct_2 (u1_struct_0 A) k6_margrel1 D B)) )  &  ( (~  (C = k1_xboole_0) )  =>  ( (D = (k3_boolmark A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (k1_boolmark A)) &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  ( (D = (k7_partfun1 (k1_boolmark A) E (k3_finseq_1 E)))  &  ( ((k7_partfun1 (k1_boolmark A) E 1) = (k2_boolmark A B (k7_partfun1 (u4_struct_0 A) C 1)))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) F))  &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (~  ((k7_partfun1 (k1_boolmark A) E (k2_nat_1 F 1)) = (k2_boolmark A (k7_partfun1 (k1_boolmark A) E F) (k7_partfun1 (u4_struct_0 A) C (k2_nat_1 F 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bor_cant,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (C = (k6_bor_cant A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k5_numbers C D) = (k1_bor_cant k5_numbers D (k2_nat_1 A 1) (k2_nat_1 D B) D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((k9_borsuk_1 A B) = (k2_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)))) ) ) ) ) ).
tt(d5_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) =>  ( ((r2_borsuk_2 A B C) & (r2_borsuk_2 A C D))  =>  (! [G:$i] :  ((m1_borsuk_2 G A B D) =>  ( (G = (k1_borsuk_2 A B C D E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r1_xxreal_0 H (k10_real_1 1 2)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) G H) = (k1_funct_1 E (k8_real_1 2 H))) )  &  ((r1_xxreal_0 (k10_real_1 1 2) H) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) G H) = (k1_funct_1 F (k9_real_1 (k8_real_1 2 H) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) )  =>  ( (A = k3_borsuk_6)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ( ((r1_xxreal_0 B (k10_real_1 1 2)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = (k8_real_1 2 B)) )  &  ( (~ (r1_xxreal_0 B (k10_real_1 1 2)))  =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = 1) ) ) ) ) ) ) ) ).
tt(d5_borsuk_7,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_borsuk_7 A B) = (k2_tmap_1 (k15_euclid 2) (k15_euclid 2) (k1_jordan24 B) (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A))) ) ) ) ) ).
tt(d5_brouwer,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k2_brouwer A C B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k2_brouwer A C B)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k7_toprealb A C B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k7_toprealb A C B)))))) )  =>  ( (E = (k5_brouwer A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_brouwer A C B))) =>  ((k3_funct_2 (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k7_toprealb A C B)) E F) = (k4_brouwer A C B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A)) (k1_zfmisc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A)) (k1_zfmisc_1 A))))) )  =>  ( (B = (k5_bspace A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k5_binop_1 (k1_zfmisc_1 A) B C D) = (k5_subset_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(d5_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k6_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k10_xboolean (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ((v2_bvfunc_2 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( ((k9_xtuple_0 C) = B)  &  ( ((k10_xtuple_0 C) = D)  &  ( (! [E:$i] :  ((r2_hidden E B) => (r2_hidden (k1_funct_1 C E) E)) )  &  ((k8_setfam_1 A D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_ideal_1 B A) =>  ((v1_xboole_0 B) |  ((k1_c0sp1 A B) = (k1_realset1 (u1_algstr_0 A) B)) ) ) ) ) ) ) ).
tt(d5_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k5_c0sp2 A) = (g1_lopban_2 (k2_c0sp2 A) (k2_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k1_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k5_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k4_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k3_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) (k4_c0sp2 A))) ) ) ).
tt(d5_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( (C = (k3_calcul_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((r2_hidden E (k1_relset_1 k5_numbers B)) &  ( (F = (k1_funct_1 B E))  & (r2_hidden D (k24_qc_lang1 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (B = (k3_card_1 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_ordinal1 C)) )  &  ( (B = (k1_ordinal2 C))  &  ( ((k9_xtuple_0 C) = (k1_ordinal1 A))  &  ( ((k1_funct_1 C k1_xboole_0) = (k1_card_1 k4_ordinal1))  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden (k1_ordinal1 D) (k1_ordinal1 A)) =>  ((k1_funct_1 C (k1_ordinal1 D)) = (k2_card_1 (k3_tarski (k1_tarski (k1_funct_1 C D))))) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r2_hidden D (k1_ordinal1 A)) & (v4_ordinal1 D))  =>  ( (D = k1_xboole_0)  |  ((k1_funct_1 C D) = (k1_card_1 (k4_ordinal2 (k5_relat_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k4_card_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( (C = D)  &  ( ((k9_xtuple_0 D) = (k9_xtuple_0 A))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 A)) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ((v1_card_fil B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) =>  ((k1_card_1 C) = (k1_card_1 A)) ) ) ) ) ) ) ) ) ).
tt(d5_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v2_card_lar B A) <=>  (! [C:$i] :  ( ((v3_ordinal1 C) &  ((v4_ordinal1 C) &  (~ (v1_finset_1 C)) ) )  =>  ( ((r2_hidden C A) &  ((k3_ordinal2 (k8_subset_1 A B C)) = C) )  => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d5_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((m1_cat_1 D A B C) <=> (r2_hidden D (k2_cat_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ((k5_cat_2 A B) = (k10_cat_1 B)) ) ) ) ) ).
tt(d5_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u4_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  ( (E = (k6_cat_3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F B) =>  ((k7_partfun1 (u4_struct_0 A) E F) = (k1_cat_1 A D (k7_partfun1 (u4_struct_0 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_cat_4 A B C) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u3_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d5_cat_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_cat_5 A) <=>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  ((m1_catalg_1 B A) <=>  ((m1_instalg1 (k2_catalg_1 A) B) &  ((u1_struct_0 B) = (k2_zfmisc_1 (k1_tarski k6_numbers) (k4_finseq_2 2 A))) ) ) ) ) ) ).
tt(d5_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k4_cc0sp2 A) = (k2_partfun1 (k2_cc0sp1 (u1_struct_0 A)) k1_numbers (k6_cc0sp1 (u1_struct_0 A)) (k2_cc0sp2 A))) ) ) ).
tt(d5_cfdiff_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_numbers)) =>  ((m1_cfdiff_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (a_2_0_cfdiff_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d5_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_cfuncdom A) = (k8_funcop_1 k2_numbers A k6_complex1)) ) ) ).
tt(d5_cgames_1,ax, (k5_cgames_1 = (g1_cgames_1 (k1_tarski k3_cgames_1) (k1_tarski k3_cgames_1))) ).
tt(d5_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ((m2_chain_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k1_domain_1 k1_numbers k1_numbers C D))  &  ((r2_hidden C A) &  ((r2_hidden D A) &  ( ( (~ (r1_xxreal_0 D C))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E A) &  ( (~ (r1_xxreal_0 E C))  &  (~ (r1_xxreal_0 D E)) ) ) ) ) ) )  |  ( (~ (r1_xxreal_0 C D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ((r1_xxreal_0 E C) & (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_glib_000 C A) =>  ((m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))) =>  ((m1_chord C A B) <=> (m2_glib_000 C A (k2_chord A B) (k21_glib_000 A (k2_chord A B)))) ) ) ) ) ) ) ).
tt(d5_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circcmb3 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (D = (k2_circcmb3 A B C))  <=>  ((v1_circuit2 (k5_facirc_1 A B C D) A B) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  & (v1_circuit2 (k5_facirc_1 A B C E) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v11_struct_0 D))  &  ((v1_msualg_1 D) & (l1_msualg_1 D)) )  =>  ( (D = (k4_circcomb A B C))  <=>  ( ((u1_struct_0 D) = (k2_xboole_0 (k10_xtuple_0 B) (k1_tarski C)))  &  ( ((u4_struct_0 D) = (k1_tarski (k4_tarski B A)))  &  ( ((k1_funct_1 (u1_msualg_1 D) (k4_tarski B A)) = B)  &  ((k1_funct_1 (u2_msualg_1 D) (k4_tarski B A)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u4_struct_0 (k1_circtrm1 A B C)) (k3_relat_1 (u1_msualg_1 (k1_circtrm1 A B C)) (k6_finseq_2 (u1_struct_0 (k1_circtrm1 A B C)) (k4_circtrm1 A B C D))) (k3_relat_1 (u2_msualg_1 (k1_circtrm1 A B C)) (k4_circtrm1 A B C D))) =>  ( (E = (k5_circtrm1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 (k1_circtrm1 A B C))) =>  ((r2_hidden F (u4_struct_0 (k1_circtrm1 A B C))) =>  ((k1_funct_1 E F) = (k3_circtrm1 A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k5_circuit1 A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A (k11_msafree A (u3_msualg_1 A B))) C)) &  ( (D = F)  &  (E = (k8_msafree2 A (u3_msualg_1 A B) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  ( (D = (k6_circuit2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E (k2_msafree2 A)) =>  ((k1_funct_1 D E) = (k1_funct_1 C E)) )  &  ((r2_hidden E (k3_msafree2 A)) =>  ((k1_funct_1 D E) = (k3_funct_2 (k3_msualg_1 A (k4_msafree2 A E) B) (k4_msualg_1 A (k4_msafree2 A E) B) (k5_msualg_1 A (k4_msafree2 A E) B) (k3_circuit1 A B C (k4_msafree2 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( (C = (k2_classes1 A B))  <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v5_ordinal1 D)) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = (k1_tarski A))  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k2_xboole_0 (k2_xboole_0 (a_3_0_classes1 A D E) (a_3_1_classes1 A D E)) (k8_subset_1 (k1_zfmisc_1 (k1_funct_1 D E)) (k9_setfam_1 (k1_funct_1 D E)) (k1_classes1 A)))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k3_xboole_0 (k3_tarski (k10_xtuple_0 (k5_relat_1 D E))) (k1_classes1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (B = (k16_classes2 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) & (v1_funct_1 C)) )  &  ( (B = (k1_ordinal2 C))  &  ( ((k9_xtuple_0 C) = (k1_ordinal1 A))  &  ( ((k1_funct_1 C k1_xboole_0) = k13_classes2)  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden (k1_ordinal1 D) (k1_ordinal1 A)) =>  ((k1_funct_1 C (k1_ordinal1 D)) = (k1_classes1 (k1_funct_1 C D))) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r2_hidden D (k1_ordinal1 A)) & (v4_ordinal1 D))  =>  ( (D = k1_xboole_0)  |  ((k1_funct_1 C D) = (k15_classes2 (k3_card_3 (k5_relat_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k6_clopban1 A B) = (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) ) ) ) ) ).
tt(d5_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k6_clopban2 A) = (k6_partfun1 (u1_struct_0 A))) ) ) ).
tt(d5_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k3_clopban3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (E = (k5_clopban4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F D) =>  ((k1_normsp_1 A E F) = (k6_algstr_0 A (k1_normsp_1 A (k1_clopban4 A B) F) (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A C)) D) (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A C)) (k7_nat_d D F))))) )  &  ( (~ (r1_xxreal_0 F D))  =>  ((k1_normsp_1 A E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v2_closure2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  ((r1_tarski D C) => (r2_hidden (k2_mboolean A (k5_closure2 A B D)) C)) ) ) ) ) ) ) ) ) ).
tt(d5_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v5_clvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_clvect_1 A B k6_complex1) = B) ) ) ) ) ) ).
tt(d5_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_clvect_2 A B C) = (a_3_0_clvect_2 A B C)) ) ) ) ) ) ) ).
tt(d5_cohsp_1,ax, (! [A:$i] :  ((v2_cohsp_1 A) <=>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (? [C:$i] :  ( (! [D:$i] :  ((r2_hidden D B) => (r1_tarski C D)) )  & (r2_hidden C A)) ) ) ) ) ) ).
tt(d5_coh_sp,ax, (! [A:$i] :  ((k4_coh_sp A) = (k3_tarski (a_1_1_coh_sp A))) ) ).
tt(d5_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_collsp A B C) = (a_3_0_collsp A B C)) ) ) ) ) ) ) ).
tt(d5_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ((v4_combgras C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  ( ((k1_card_1 D) = (k2_nat_1 A 1))  &  (C = (a_3_1_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k8_complex1 A B) = (k2_xcmplx_0 (k7_real_1 (k3_complex1 A) (k3_complex1 B)) (k3_xcmplx_0 (k7_real_1 (k4_complex1 A) (k4_complex1 B)) k7_complex1))) ) ) ) ) ).
tt(d5_compl_sp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((v4_compl_sp B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (v3_pre_topc (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(d5_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  ((v2_compos_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k2_compos_0 A B) = (k2_compos_0 A C))  =>  ((k4_finseq_1 (k5_xtuple_0 B)) = (k4_finseq_1 (k5_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(d5_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_compos_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 A)) =>  ((r2_hidden C (k10_xtuple_0 B)) => (r1_tarski (k10_xtuple_0 (k5_xtuple_0 C)) (k9_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(d5_compts_1,ax, (! [A:$i] :  ((k1_compts_1 A) = (g1_pre_topc A (k2_subset_1 (k9_setfam_1 A)))) ) ).
tt(d5_comput_1,ax, (! [A:$i] :  ((k2_comput_1 A) = (a_1_2_comput_1 A)) ) ).
tt(d5_comseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v1_valued_0 A)) ) ) )  =>  ((v2_comseq_2 A) <=>  (? [B:$i] :  ((m1_subset_1 B k2_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k17_complex1 (k6_xcmplx_0 (k1_funct_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k7_comseq_3 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k3_complex1 (k8_nat_1 k2_numbers A C))) ) ) ) ) ) ) ) ).
tt(d5_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B G B H) &  ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r5_analmetr A B C E) &  ((r5_analmetr A B D F) &  ((r4_analmetr A C G D H) & (r4_analmetr A E G F H)) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ( (C = E)  |  ((r5_analmetr A B G C) | (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k3_conlat_1 A) = (k1_conlat_1 A)) ) ) ).
tt(d5_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)))))) )  =>  ( (B = (k5_conlat_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u4_struct_0 A))) &  ( ((k3_funct_2 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) B C) = (g2_conlat_1 A D E))  &  ( (D = (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k6_domain_1 (u4_struct_0 A) C)))  &  (E = (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k6_domain_1 (u4_struct_0 A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v5_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A J K) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden G J) &  ((r2_hidden I J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden F K) &  ((r2_hidden H K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden F J) |  ((r2_hidden H J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden G K) |  ((r2_hidden I K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r5_analmetr A B C D) &  ((r5_analmetr A B E F) &  ((r5_analmetr A B G H) &  ((r2_analoaf A C E D F) &  ((r2_analoaf A C E B G) & (r2_analoaf A E G F H)) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ((r5_analmetr A E F C) |  ((r5_analmetr A E F G) | (r2_analoaf A C G D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) <=>  ((v2_connsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 C A) & (r1_tarski B C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d5_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_connsp_2 A B C) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (B = D)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_pre_topc A D))) =>  (~  ( (E = C)  & (r1_connsp_2 (k1_pre_topc A D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_connsp_3 A B C) = (k9_subset_1 (u1_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(d5_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_convex1 A B) = (k6_setfam_1 (u1_struct_0 A) (k2_convex1 A B))) ) ) ) ) ).
tt(d5_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k3_convex4 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k1_clvect_1 A (k7_partfun1 (u1_struct_0 A) B E) (k3_funct_2 (u1_struct_0 A) k2_numbers C (k7_partfun1 (u1_struct_0 A) B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) )  =>  ((k5_convfun1 A B) = (a_2_0_convfun1 A B)) ) ) ) ) ).
tt(d5_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m2_funct_2 E (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) =>  ( (E = (k6_cqc_sim1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_qc_lang1 A)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((k2_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) E F G) = (k4_cqc_lang B A C (k5_cqc_sim1 A B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ((r2_cqc_the1 A B C) <=>  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r1_cqc_the1 A C D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r5_cqc_the3 A B C) <=>  ((r1_cqc_the3 A B C) & (r1_cqc_the3 A C B)) ) ) ) ) ) ) ) ).
tt(d5_csspace3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_clvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_csspace3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k4_csspace3 A (k3_funct_2 k5_numbers (u1_struct_0 A) B E) (k3_funct_2 k5_numbers (u1_struct_0 A) B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_clopban1 A B)))) =>  ( (C = (k4_csspace4 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) &  ((v1_csspace4 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_csspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k2_numbers k1_csspace) k1_csspace) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k1_csspace) k1_csspace)))) )  =>  ( (A = k5_csspace)  <=>  (! [B:$i] :  (! [C:$i] :  ( ((v1_xcmplx_0 B) & (r2_hidden C k1_csspace))  =>  ((k1_binop_1 A B C) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace C) (k3_csspace B))) ) ) ) ) ) ) ).
tt(d5_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_decomp_1 B A) <=> (r1_tarski B (k4_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) (k1_tops_1 A (k2_pre_topc A B))))) ) ) ) ) ).
tt(d5_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k2_finseq_1 A))))) )  =>  ((v1_descip_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A (k2_finseq_1 A) B C) = (k16_descip_1 A C)) ) ) ) ) ) ) ) ).
tt(d5_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) (k1_dickson A)) (k8_eqrel_1 (u1_struct_0 A) (k1_dickson A))))) =>  ( (B = (k2_dickson A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (C = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_dickson A) E))  &  ( (D = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_dickson A) F))  & (r1_orders_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k5_diff_1 A B) = (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_diff_1 A (k6_real_1 B 2)) (k1_diff_1 A (k1_real_1 (k6_real_1 B 2))))) ) ) ) ) ).
tt(d5_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_diraf A B C D) <=> (r2_diraf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(d5_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v3_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C E F) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A D G H I) &  ( (~  (H = I) )  &  ( (~  (E = F) )  &  (~ (r2_analoaf A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k5_dist_1 A B) = (a_2_0_dist_1 A B)) ) ) ) ) ).
tt(d5_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((v3_dtconstr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((r2_hidden B (k2_lang1 A)) &  (! [C:$i] :  ((m1_trees_4 C (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (~ (r1_lang1 A B (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((m1_dynkin B A) <=>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((r1_tarski (k10_xtuple_0 C) B) & (v1_prob_2 C))  => (r2_hidden (k1_prob_1 A C) B)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) => (r2_hidden (k3_subset_1 A C) B)) ) )  & (r2_hidden k1_xboole_0 B)) ) ) ) ) ) ) ).
tt(d5_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( ( (B = k6_numbers)  =>  ((k2_ec_pf_1 A B) = k6_numbers) )  &  ( ((v2_ec_pf_1 B A) =>  ((k2_ec_pf_1 A B) = 1) )  &  (~  ( (~  (B = k6_numbers) )  &  ( (~ (v2_ec_pf_1 B A))  &  (~  ((k2_ec_pf_1 A B) = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( (E = (k6_ec_pf_2 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k4_endalg A B) (k4_endalg A B)) (k4_endalg A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_endalg A B) (k4_endalg A B)) (k4_endalg A B))))) )  =>  ( (C = (k5_endalg A B))  <=>  (! [D:$i] :  ((m1_autalg_1 D (u1_struct_0 A) (u3_msualg_1 A B) (k4_endalg A B)) =>  (! [E:$i] :  ((m1_autalg_1 E (u1_struct_0 A) (u3_msualg_1 A B) (k4_endalg A B)) =>  ((k5_binop_1 (k4_endalg A B) C D E) = (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (u3_msualg_1 A B) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k5_ens_1 A B) = (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 B B)) (k1_domain_1 A A B B) (k6_partfun1 B))) ) ) ) ) ).
tt(d5_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ( ((k3_finseq_1 B) = k6_numbers)  =>  ( (C = (k2_entropy1 A B))  <=>  (C = k1_xboole_0) ) )  &  ( (~  ((k3_finseq_1 B) = k6_numbers) )  =>  ( (C = (k2_entropy1 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_finseq_2 A)) &  ( (C = (k1_matrprob A D (k3_finseq_1 B)))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ((k1_matrprob A D 1) = (k1_matrprob A B 1))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 B) E) |  ((k1_matrprob A D (k2_nat_1 E 1)) = (k8_finseq_1 A (k1_matrprob A D E) (k1_matrprob A B (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (H = (k5_enumset1 A B C D E F G))  <=>  (! [I:$i] :  ((r2_hidden I H) <=>  (~  ( (~  (I = A) )  &  ( (~  (I = B) )  &  ( (~  (I = C) )  &  ( (~  (I = D) )  &  ( (~  (I = E) )  &  ( (~  (I = F) )  &  (~  (I = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_eqrel_1,ax, (! [A:$i] :  ((k10_eqrel_1 A) = (k8_eqrel_1 A (k6_partfun1 A))) ) ).
tt(d5_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (k4_equation A) C)) =>  ((r1_equation A B C D) <=>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k3_equation A)) (u3_msualg_1 A B)) =>  ((r1_msualg_3 A (k3_equation A) B E) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k3_equation A)) (u3_msualg_1 A B) E C) (k1_xtuple_0 D)) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k3_equation A)) (u3_msualg_1 A B) E C) (k2_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_e_siec,ax, (! [A:$i] :  ((k3_e_siec A) = (g1_e_siec A k1_xboole_0 k1_xboole_0)) ) ).
tt(d5_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k5_euclid_3 A B C D) = (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) B C) (k1_rltopsp1 (k15_euclid A) C D)) (k1_rltopsp1 (k15_euclid A) D B))) ) ) ) ) ) ) ) ) ).
tt(d5_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k6_euclid_5 A B C) = (k23_rvsum_1 A (k5_euclid_5 B C))) ) ) ) ) ) ) ).
tt(d5_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers (k1_euclid 3)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 3))))) )  =>  ( (D = (k6_euclid_8 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers (k1_euclid 3) D E) = (k1_euclid_8 (k1_seq_1 A E) (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  ((k5_euclid_9 A B) = (a_2_0_euclid_9 A B)) ) ) ) ) ).
tt(d5_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k12_euclid A) = (k7_square_1 (k18_rvsum_1 (k12_rvsum_1 A)))) ) ) ).
tt(d5_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((k2_euclidlp A B C) = (a_3_0_euclidlp A B C)) ) ) ) ) ) ) ).
tt(d5_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v5_euclmetr A) <=> (v7_aff_2 (k3_analmetr A))) ) ) ).
tt(d5_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ( (? [C:$i] :  ((v3_ordinal1 C) & (r2_hidden C (k9_xtuple_0 A))) )  =>  ( (B = (k2_exchsort A))  <=> (v3_exchsort A B)) )  &  ( (! [C:$i] :  ((v3_ordinal1 C) =>  (~ (r2_hidden C (k9_xtuple_0 A))) ) )  =>  ( (B = (k2_exchsort A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d5_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k3_extpro_1 A B C D) = (k7_partfun1 (u1_compos_1 B) C (k5_memstr_0 A B D))) ) ) ) ) ) ) ) ) ).
tt(d5_facirc_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k2_facirc_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k1_binarith B C)) ) ) ) ) ) ) ) ).
tt(d5_facirc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k3_facirc_2 A B C)) (k3_msafree2 (k3_facirc_2 A B C))) =>  ( (D = (k5_facirc_2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  ( (D = (k1_funct_1 E A))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( (G = (k1_funct_1 E F))  =>  ((k1_funct_1 E (k1_nat_1 F 1)) = (k17_facirc_1 (k1_funct_1 B (k1_nat_1 F 1)) (k1_funct_1 C (k1_nat_1 F 1)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fdiff_1 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k1_fdiff_1 A B))  <=>  (? [D:$i] :  ((m1_rcomp_1 D B) &  ((r1_tarski D (k1_relset_1 k1_numbers A)) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v3_fdiff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v2_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 E 1))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k9_real_1 (k1_seq_1 A G) (k1_seq_1 A B)) = (k7_real_1 (k1_seq_1 E (k9_real_1 G B)) (k1_seq_1 F (k9_real_1 G B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_fdiff_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k1_fdiff_3 A B))  <=>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski A))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers B)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 D F))) ) ) ) )  =>  (C = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers E B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ff_siec,ax, (! [A:$i] :  ((k5_ff_siec A) = (k1_ff_siec (k1_tarski A) k1_xboole_0)) ) ).
tt(d5_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k5_fib_num2 A) = (k1_fib_num2 k2_fib_num2 (k3_xboole_0 k3_fib_num2 (k2_finseq_1 A)))) ) ) ).
tt(d5_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v2_filter_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k3_lattices A C D) B) <=>  ((r2_hidden C B) | (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  ( (C = (k4_filter_1 A B))  <=>  (! [D:$i] :  ( ((v1_partfun1 D (u1_struct_0 A)) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (D = (k8_filter_0 A B))  =>  (C = (g3_lattices (k8_eqrel_1 (u1_struct_0 A) D) (k3_filter_1 (u1_struct_0 A) D (u2_lattices A)) (k3_filter_1 (u1_struct_0 A) D (u1_lattices A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A)))) =>  ((k4_filter_2 A B) = B) ) ) ) ) ).
tt(d5_finance1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_finance1 A B C D E) <=>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 B) D) => (m2_subset_1 (a_5_0_finance1 A B D E F) (k1_zfmisc_1 A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_finseq_1,ax, (! [A:$i] :  ((k5_finseq_1 A) = (k1_tarski (k4_tarski 1 A))) ) ).
tt(d5_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k3_finseq_2 A))) ) )  =>  ( (C = (k6_finseq_2 A B))  <=>  (! [D:$i] :  ((m2_finseq_2 D A (k3_finseq_2 A)) =>  ((k1_funct_1 C D) = (k4_card_3 (k3_relat_1 D B))) ) ) ) ) ) ) ) ) ).
tt(d5_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k5_finseq_4 A B))  <=>  (? [D:$i] :  ((v7_ordinal1 D) &  ( (D = (k6_xcmplx_0 (k4_finseq_4 A B) 1))  &  (C = (k5_relat_1 A (k2_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k7_finseq_8 A B C) = (k2_rfinseq A (k3_finseq_1 (k4_finseq_8 A B C)) C)) ) ) ) ) ) ) ).
tt(d5_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  =>  ((v2_finset_1 B) <=>  (! [C:$i] :  ((r2_hidden C A) => (v1_finset_1 (k1_funct_1 B C))) ) ) ) ) ) ).
tt(d5_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((v4_finsub_1 B) =>  ( (B = (k5_finsub_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r1_tarski C A) & (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(d5_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (B = C)  =>  ((k5_fintopo2 A B C) = k8_margrel1) )  &  ( (~  (B = C) )  =>  ((k5_fintopo2 A B C) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(d5_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_fintopo3 A B C) = (k1_funct_1 (k4_fintopo3 A B) C)) ) ) ) ) ) ) ).
tt(d5_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A)))) =>  ( (B = (k3_fintopo4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ( (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 A C))  &  (~  ((k9_relat_1 B C) = (k1_enumset1 C (k7_nat_d C 1) (k2_nat_1 C 1))) ) ) ) )  &  ( ( (C = 1)  =>  ((r1_xxreal_0 A C) |  ((k9_relat_1 B C) = (k1_enumset1 C A (k2_nat_1 C 1))) ) )  &  ( ( (C = A)  =>  ((r1_xxreal_0 C 1) |  ((k9_relat_1 B C) = (k1_enumset1 C (k7_nat_d C 1) 1)) ) )  &  ( ( (C = 1)  &  (C = A) )  =>  ((k9_relat_1 B C) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_fintopo5 A B) = (g1_orders_2 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k4_fintopo5 A B))) ) ) ) ) ).
tt(d5_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_fintopo6 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_fintopo6 A B)))) &  ( (D = C)  & (r1_fintopo6 (k1_fintopo6 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fin_topo A B) = (a_2_0_fin_topo A B)) ) ) ) ) ).
tt(d5_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_fomodel0 B A) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k3_xboole_0 A (k9_xtuple_0 B))) &  ((r2_hidden D (k3_xboole_0 A (k9_xtuple_0 B))) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(d5_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k5_fomodel1 A) = (k8_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) k5_numbers)) ) ) ).
tt(d5_fomodel2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k5_fomodel2 A B C) = (k1_funct_4 A (k16_funcop_1 B (k16_funcop_1 k1_xboole_0 C)))) ) ) ) ) ).
tt(d5_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_fomodel3 A B C D) = (a_4_0_fomodel3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d5_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_fomodel4 A B C) = (k9_funct_7 (k2_fomodel4 A B) C)) ) ) ) ) ) ) ).
tt(d5_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k2_frechet A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=> (r1_frechet A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) =>  ((v2_freealg B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  ((r1_unialg_2 A C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C))))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  &  ((r1_alg_1 A C E) &  ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 C) E B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_fscirc_1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C))) (k5_circcomb k3_twoscomp (k10_finseq_1 A C)) (k3_circcomb (k5_circcomb k3_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C)) (k6_facirc_1 A B k3_twoscomp) (k6_facirc_1 B C k2_twoscomp)) (k6_facirc_1 A C k3_twoscomp))) ) ) ) ).
tt(d5_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (E = (k3_fsm_1 A B C D))  <=> (r1_fsm_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_2 C A))  =>  ((r2_fsm_2 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) &  ((r1_fsm_2 A C D B) & (r2_hidden D (u1_fsm_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k5_ftacell1 A B C D E) = (k9_gfacirc1 (k12_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d5_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k5_funcop_1 A B C) = (k3_relat_1 (k13_funct_3 (k2_funcop_1 (k9_xtuple_0 C) B) C) A)) ) ) ) ) ) ).
tt(d5_funcsdom,ax, (! [A:$i] :  ((k9_funcsdom A) = (k8_funcop_1 k5_numbers A 1)) ) ).
tt(d5_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ((k2_funct_1 A) = (k2_relat_1 A)) ) ) ) ).
tt(d5_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (E = (k4_funct_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A B E F) = (k1_xtuple_0 (k3_funct_2 A (k2_zfmisc_1 B C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k8_funct_3 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ((k1_binop_1 C D E) = E) ) ) ) ) ) ) ) ) ) ).
tt(d5_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k6_funct_4 A B C) = (k1_funct_4 A (k3_relat_1 A (k16_funcop_1 B C)))) ) ) ) ) ).
tt(d5_funct_5,ax, (k6_funct_5 = (k16_funcop_1 k1_xboole_0 k1_xboole_0)) ).
tt(d5_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k5_funct_6 A B C) = (k1_binop_1 (k2_funct_5 A) B C)) ) ) ) ) ).
tt(d5_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funcop_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k5_funct_7 A B))  <=>  ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 A) 1))  &  ( ((k1_funct_1 C 1) = B)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden D (k4_finseq_1 A)) &  (E = (k1_funct_1 A D)) )  =>  ((k1_funct_1 C (k2_nat_1 D 1)) = (k1_funct_1 E (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_funct_8,ax, (! [A:$i] :  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r1_funct_8 A B C D) <=>  ((r1_tarski A (k1_relset_1 B D)) & (v4_funct_8 (k5_relset_1 B C D A) B C)) ) ) ) ) ) ) ) ) ).
tt(d5_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_functor0 A B C D) = (k1_xtuple_0 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) D D))) ) ) ) ) ) ) ) ) ).
tt(d5_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  (! [E:$i] :  ((m2_functor0 E A B) =>  ( ((r1_functor2 A B C D) & (r1_functor2 A B D E))  =>  (! [F:$i] :  ((m1_functor2 F A B C D) =>  (! [G:$i] :  ((m1_functor2 G A B D E) =>  (! [H:$i] :  ((m1_functor2 H A B C E) =>  ( (H = (k3_functor2 A B C D E F G))  <=>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k2_functor2 A B C E H I) = (k5_altcat_1 B (k3_functor0 A B C I) (k3_functor0 A B D I) (k3_functor0 A B E I) (k2_functor2 A B C D F I) (k2_functor2 A B D E G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  ((r1_functor3 A B C D) =>  (! [E:$i] :  ((m2_functor2 E A B C D) =>  ((m1_functor3 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (v3_altcat_3 (k2_functor2 A B C D E F) B (k3_functor0 A B C F) (k3_functor0 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (C = (k3_fuzzy_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_seq_1 C D) = (k9_real_1 1 (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d5_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k5_fuzzy_2 A B) = (k5_funct_3 (k2_zfmisc_1 A B) (k2_zfmisc_1 A B))) ) ) ) ) ).
tt(d5_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 k6_numbers C) =>  ((k3_fvaluat1 A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k1_int_2 C))) )  &  ( (~ (r1_xxreal_0 k6_numbers C))  =>  ((k3_fvaluat1 A B C) = (k11_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k1_int_2 C)))) ) ) ) ) ) ) ) ) ).
tt(d5_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k7_fvsum_1 A B C) = (k1_finseqop (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k2_fvsum_1 A) B C)) ) ) ) ) ) ) ).
tt(d5_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k5_gate_5 A B C D E) = (k2_gate_1 A D)) ) ) ) ) ) ).
tt(d5_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k2_gcd_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=> (r3_gcd_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d5_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k4_genealg1 A B C D E F G) = (k1_genealg1 A (k3_genealg1 A B C D E F) (k3_genealg1 A C B D E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (E = (k3_geomtrap A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_gfacirc1 A B C) = (k2_circcomb (k2_circcomb (k5_circcomb k2_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C))) (k5_circcomb k2_twoscomp (k10_finseq_1 C A)))) ) ) ) ).
tt(d5_glib_000,ax, (k5_glib_000 = (k9_domain_1 k5_numbers k1_glib_000 k2_glib_000 k3_glib_000 k4_glib_000)) ).
tt(d5_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_glib_000 A B C D) =>  ((k2_glib_001 A B C D) = (k11_finseq_1 B D C)) )  &  ( (~ (r1_glib_000 A B C D))  =>  ((k2_glib_001 A B C D) = (k1_glib_001 A (k10_subset_1 (k6_glib_000 A)))) ) ) ) ) ) ) ) ).
tt(d5_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  ( (C = (k1_glib_002 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m3_glib_001 E A) & (r1_glib_001 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v2_glib_003 A) <=>  ((r2_hidden k3_glib_003 (k1_relset_1 k5_numbers A)) &  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ( ((k1_funct_1 A k3_glib_003) = B)  & (r1_tarski (k9_xtuple_0 B) (k7_glib_000 A))) ) ) ) ) ) ) ).
tt(d5_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (B = (k3_glib_004 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_glib_003 D) &  ((v4_glib_003 D A) & (m1_glib_000 D A)) )  &  ( (C = D)  &  ((k1_relset_1 k5_numbers D) = k2_glib_004) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ((v3_goboard1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 A))) => (v3_funct_1 (k2_goboard1 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ).
tt(d5_goboard5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ((v2_goboard5 A) <=> (r1_goboard1 (u1_struct_0 (k15_euclid 2)) A (k2_goboard2 A))) ) ) ).
tt(d5_gobrd13,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (D = (k5_gobrd13 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B E F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  (D = (k3_goboard5 B (k7_nat_d G 1) H)) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  (D = (k3_goboard5 B G H)) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  (D = (k3_goboard5 B (k7_nat_d G 1) (k7_nat_d H 1))) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  (D = (k3_goboard5 B G (k7_nat_d H 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v4_qc_lang2 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (C = (k3_goedelcp A B))  <=>  (? [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (B = (k12_cqc_lang A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( ((r1_partfun1 (u1_graph_1 A) (u1_graph_1 B)) & (r1_partfun1 (u2_graph_1 A) (u2_graph_1 B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_graph_1 C) & (l1_graph_1 C)) )  =>  ( (C = (k5_graph_1 A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u4_struct_0 C) = (k2_xboole_0 (u4_struct_0 A) (u4_struct_0 B)))  &  ( (! [D:$i] :  ((r2_hidden D (u4_struct_0 A)) =>  ( ((k1_funct_1 (u1_graph_1 C) D) = (k1_funct_1 (u1_graph_1 A) D))  &  ((k1_funct_1 (u2_graph_1 C) D) = (k1_funct_1 (u2_graph_1 A) D)) ) ) )  &  (! [D:$i] :  ((r2_hidden D (u4_struct_0 B)) =>  ( ((k1_funct_1 (u1_graph_1 C) D) = (k1_funct_1 (u1_graph_1 B) D))  &  ((k1_funct_1 (u2_graph_1 C) D) = (k1_funct_1 (u2_graph_1 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((k5_graph_2 A B) = (a_2_2_graph_2 A B)) ) ) ) ).
tt(d5_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_graph_3 A B) = (k3_graph_3 A B (u4_struct_0 A))) ) ) ) ) ).
tt(d5_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r3_graph_4 A B C) <=>  ( ((k3_finseq_1 B) = (k2_nat_1 (k3_finseq_1 C) 1))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r1_graph_4 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B (k2_nat_1 D 1)) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_graph_5 A B C) = (a_3_0_graph_5 A B C)) ) ) ) ) ) ) ).
tt(d5_graphsp,ax, (! [A:$i] :  ((m2_funct_2 A (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_funct_2 C (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  ( (C = (k9_graphsp A B))  <=>  ( ((k9_xtuple_0 C) = (k3_finseq_2 k1_numbers))  &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k6_graphsp C D) = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) (k8_graphsp A D B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((k4_gr_cy_1 A) = (g3_algstr_0 (k7_card_1 A) (k3_gr_cy_1 A))) ) ) ).
tt(d5_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( (B = (k4_groeb_1 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) <=> (r3_pre_poly A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k6_groeb_3 A B C D E) = (k2_groeb_3 A C D (k4_groeb_3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_group_10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (k1_funct_2 A A)) &  ((v1_group_10 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 A A))))) ) )  =>  ((r1_ordinal1 (k5_card_1 B) (k1_card_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (k1_funct_2 (k3_group_10 A B) (k3_group_10 A B))) &  ((v1_group_10 E C (k3_group_10 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 (k3_group_10 A B) (k3_group_10 A B)))))) ) )  =>  ( (E = (k5_group_10 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 C) (k1_funct_2 (k3_group_10 A B) (k3_group_10 A B)) E F) = (k4_group_10 A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k2_group_1 A B))  <=>  ( ((k6_algstr_0 A B C) = (k1_group_1 A))  &  ((k6_algstr_0 A C B) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ).
tt(d5_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  ((m1_group_2 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d5_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_group_3 A B C) = (k3_group_3 A (k6_domain_1 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ).
tt(d5_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_group_4 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( ((k5_group_4 A C) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)))  &  (~  ((k5_group_4 A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d5_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k5_group_5 A B C) = (k4_group_5 A (k8_group_2 A B) (k8_group_2 A C))) ) ) ) ) ) ) ).
tt(d5_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_group_6 A B))) =>  ((k6_group_6 A B C) = C) ) ) ) ) ) ) ).
tt(d5_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_group_9 B A))  =>  ((v3_group_9 B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 (u1_struct_0 C) (u1_struct_0 C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 (u1_struct_0 C) (u1_struct_0 C)))))) )  =>  ( ((r1_funct_2 A (k1_funct_2 (u1_struct_0 C) (u1_struct_0 C)) A (k1_funct_2 (u1_struct_0 B) (u1_struct_0 B)) D (u1_group_9 A B)) &  ((g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) = (g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B))) )  => (v1_group_9 D A C)) ) ) ) ) ) ) ) ) ).
tt(d5_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k5_hahnban1 A B C D) = (k3_hahnban1 A B C (k4_hahnban1 A B D))) ) ) ) ) ) ) ) ) ).
tt(d5_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_zfmisc_1 A)) =>  ((m1_hallmar1 D A B C) <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( (E = C)  |  ((k1_funct_1 B E) = (k1_funct_1 D E)) ) ) ) )  & (r1_tarski (k1_funct_1 D C) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [C:$i] :  ((m1_valuat_1 C A (k1_henmodel A)) =>  ((m1_henmodel C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k6_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_margrel1 (k1_henmodel A))) =>  ((r1_margrel1 (k1_henmodel A) (k3_funct_2 (k6_qc_lang1 A) (k3_margrel1 (k1_henmodel A)) C D) E) =>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v5_relat_1 G (k3_qc_lang1 A)) &  ((v3_card_1 G (k7_qc_lang1 A D)) & (m2_finseq_1 G (k2_qc_lang1 A))) )  &  ( (F = G)  & (r1_henmodel A B (k2_henmodel A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  =>  ((v3_hermitan B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C D) = (k2_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B D C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  ( (B = (k5_heyting1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ((k5_binop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) B C D) = (k3_normform (k5_finsub_1 A) (k5_finsub_1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(d5_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) (u1_struct_0 (k5_substlat A B)))))) )  =>  ( (C = (k5_heyting2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_substlat A B))) =>  (! [F:$i] :  ((m2_subset_1 F (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [G:$i] :  ((m2_subset_1 G (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( ( (F = D)  &  (G = E) )  =>  ((k5_binop_1 (u1_struct_0 (k5_substlat A B)) C D E) = (k3_substlat A B (k3_heyting2 A B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A))))) =>  ( (B = (k5_heyting3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k5_numbers))  &  (C = (k4_heyting3 D A)) ) ) ) ) ) ) ) ) ) ).
tt(d5_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (D = (k5_hilbasis A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( (E = B)  =>  ((k8_nat_1 (u1_struct_0 A) D E) = C) )  &  ( (~  (E = B) )  =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_hilbert1,ax, (! [A:$i] :  ((v5_hilbert1 A) <=>  ((r1_tarski A (k13_finseq_1 k5_numbers)) &  ((v1_hilbert1 A) &  ((v2_hilbert1 A) &  ((v3_hilbert1 A) & (v4_hilbert1 A)) ) ) ) ) ) ).
tt(d5_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_hilbert3 B A) =>  (! [C:$i] :  ((m2_pboole C k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A)) =>  ( (C = (k4_hilbert3 A B))  <=>  ( ((k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C k2_hilbert1) = (k6_partfun1 1))  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C (k1_hilbert2 D)) = (k1_funct_1 B D)) ) )  &  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (! [E:$i] :  ((m1_subset_1 E k1_hilbert1) =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_hilbert3 A D) (k3_hilbert3 A D)) &  ((v3_funct_2 F (k3_hilbert3 A D) (k3_hilbert3 A D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 A D) (k3_hilbert3 A D))))) ) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k3_hilbert3 A E) (k3_hilbert3 A E)) &  ((v3_funct_2 G (k3_hilbert3 A E) (k3_hilbert3 A E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 A E) (k3_hilbert3 A E))))) ) )  &  ( (F = (k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C D))  &  ( (G = (k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C E))  &  ( ((k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C (k4_hilbert1 D E)) = (k16_funct_3 (k3_hilbert3 A D) (k3_hilbert3 A E) (k3_hilbert3 A D) (k3_hilbert3 A E) F G))  &  ((k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) C (k3_hilbert1 D E)) = (k1_hilbert3 (k3_hilbert3 A D) (k3_hilbert3 A E) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  (C = (k9_polynom3 A)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (D = (k5_hurwitz A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k8_polynom3 A (k13_polynom3 A D C) E)) &  (~ (r1_xxreal_0 (k2_hurwitz A C) (k2_hurwitz A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 A B) =>  ((k5_idea_1 A B) = (k6_xcmplx_0 (k5_series_1 2 A) B)) ) ) ) ) ) ).
tt(d5_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_ideal_1 A B) = (k1_realset1 (u1_algstr_0 A) B)) ) ) ) ) ).
tt(d5_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v6_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  ((r1_incsp_1 A B D) & (r1_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  ((r5_incsp_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r2_hidden D B) => (r2_incsp_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_index_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_index_1 C A B) =>  ((v2_index_1 C A B) <=> (v1_index_1 (k1_xtuple_0 C))) ) ) ) ) ).
tt(d5_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k3_relat_1 D C))) (u3_msualg_1 A (k1_instalg1 A B (k11_msafree B C) D E))) =>  ( (F = (k3_instalg1 A B C D E))  <=>  ((r1_msualg_3 A (k11_msafree A (k3_relat_1 D C)) (k1_instalg1 A B (k11_msafree B C) D E) F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (k3_relat_1 D C) G)) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k3_relat_1 D C))) (u3_msualg_1 A (k1_instalg1 A B (k11_msafree B C) D E)) F G) (k1_trees_4 (k4_tarski H G))) = (k1_trees_4 (k4_tarski H (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) <=>  (? [D:$i] :  ((v1_int_1 D) &  ((k3_xcmplx_0 C D) = (k6_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ) ).
tt(d5_int_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k1_int_3) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k1_int_3) k5_numbers)))) )  =>  ( (A = k3_int_3)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ((k3_funct_2 (u1_struct_0 k1_int_3) k5_numbers A B) = (k1_funct_1 k2_euclid B)) ) ) ) ) ) ).
tt(d5_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k2_int_6 A B))  <=>  (! [D:$i] :  ((m1_int_6 D B) =>  (C = (k6_int_1 (k16_rvsum_1 (k18_valued_1 A D)) (k19_rvsum_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r3_integr10 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 B C) =>  ((r1_integra5 (k3_integra5 B C) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 B C)))) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers C) = (k2_limfunc1 B))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k1_relset_1 k1_numbers C)) =>  ((k1_seq_1 C D) = (k4_integra5 B D A)) ) ) )  & (v3_limfunc1 C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E (k1_euclid A)) =>  ((m3_integr15 E A B C D) <=>  ( ((k3_finseq_1 E) = (k3_finseq_1 D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 D)) &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden G (k2_relset_1 (k1_euclid A) (k2_partfun1 B (k1_euclid A) C (k2_integra1 B D F)))) &  ((k1_funct_1 E F) = (k9_euclid A G (k3_integra1 (k2_integra1 B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_integr16 B A) <=>  ((v3_integra1 (k5_comseq_3 A B) A) & (v3_integra1 (k6_comseq_3 A B) A)) ) ) ) ) ) ).
tt(d5_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((v1_integr18 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_integra1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [F:$i] :  ((m2_integr18 F A B C E) =>  ( ((v2_comseq_2 (k2_integra3 B E)) &  ((k2_seq_2 (k2_integra3 B E)) = k6_numbers) )  =>  ((v3_normsp_1 (k3_integr18 A B C E F) A) &  ((k6_normsp_1 A (k3_integr18 A B C E F)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  ((r1_integr1c A B) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 k1_numbers)) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 C D) &  ( ((k1_rcomp_1 C D) = (k1_relset_1 k1_numbers B))  &  ((r1_tarski (k1_rcomp_1 C D) (k1_relset_1 k1_numbers E)) &  ((r1_tarski (k1_rcomp_1 C D) (k1_relset_1 k1_numbers F)) &  ((v3_rcomp_1 G) &  ((r1_tarski (k1_rcomp_1 C D) G) &  ((r2_fdiff_1 E G) &  ((r2_fdiff_1 F G) &  ((v1_fcont_1 (k2_fdiff_1 E G)) &  ((v1_fcont_1 (k2_fdiff_1 F G)) & (r2_relset_1 k1_numbers k2_numbers B (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers E (k25_valued_1 k1_numbers k1_numbers F k7_complex1)) (k1_rcomp_1 C D)))) ) ) ) ) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 E G)) (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 F G)))) & (r1_integra5 (k3_integra5 C D) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 E G)) (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k3_integra1 A) = (k9_real_1 (k4_seq_4 A) (k5_seq_4 A))) ) ) ).
tt(d5_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (C = (k5_interva1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (B = (k2_interva1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_irrat_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (A = k5_irrat_1)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 1 (k9_newton B))) ) ) ) ) ) ).
tt(d5_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r1_nattra_1 A B D E) =>  (! [F:$i] :  ((m1_nattra_1 F A B D E) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  ((k2_isocat_1 A B C D E F G) = (k1_partfun1 (u1_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_nattra_1 (k8_cat_2 A B) C D E) =>  (! [F:$i] :  ((m2_nattra_1 F (k8_cat_2 A B) C D E) =>  (! [G:$i] :  ((m2_nattra_1 G A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) =>  ( (G = (k6_isocat_2 A B C D E F))  <=>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C))))) )  =>  ((r1_funct_2 (u1_struct_0 (k8_cat_2 A B)) (u4_struct_0 C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F H) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k4_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E) G I) = (k4_tarski (k9_cat_2 (k11_nattra_1 B C) (k11_nattra_1 B C) (k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) I) (k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C E) I)) (k10_funct_5 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k9_funct_2 (u1_struct_0 B) (u4_struct_0 C)) (k11_funct_5 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_isomichi,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_isomichi A B) = (k1_tops_1 A (k2_tops_1 A B))) ) ) ) ) ).
tt(d5_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (B = (k5_jgraph_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B C) = (k4_jgraph_4 A C)) ) ) ) ) ) ) ) ).
tt(d5_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k5_jgraph_6 A B C) = (a_3_0_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(d5_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r5_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C F D) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C F G) & (r1_jordan5c A B C G D))  =>  ((k17_euclid G) = E) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan5c A B C G F) =>  ( (G = F)  |  ( (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C G H) &  ((r1_jordan5c A B C H F) &  (~ (r1_xxreal_0 (k17_euclid H) E)) ) ) ) )  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C G H) &  ((r1_jordan5c A B C H F) &  (~ (r1_xxreal_0 E (k17_euclid H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k2_jordan2c A B) = (k3_tarski (a_2_1_jordan2c A B))) ) ) ) ) ).
tt(d5_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_jordan3 A B C D) <=>  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers E) &  ((r1_xxreal_0 E 1) &  ( (C = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k9_real_1 1 E)) (k1_rlvect_1 (k15_euclid 2) B E)))  &  ((r1_xxreal_0 k6_numbers F) &  ((r1_xxreal_0 F 1) &  (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k9_real_1 1 F)) (k1_rlvect_1 (k15_euclid 2) B F))) ) ) ) ) )  => (r1_xxreal_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k5_jordan5d A))  <=>  ((r2_hidden (k4_tarski B 1) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1) = (k25_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d5_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((k5_jordan6 A B C D E) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_jordan6 A B C D) (k3_jordan6 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_jordan_a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k3_jordan_a A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) &  ( (D = B)  &  (C = (k3_tbsp_1 (k14_euclid A) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_jordan,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (A = k7_jordan)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers A B) = (k17_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) B))) ) ) ) ) ) ).
tt(d5_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( (E = (k4_knaster A B C D))  <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v5_ordinal1 F)) )  &  ( (E = (k1_ordinal2 F))  &  ( ((k9_xtuple_0 F) = (k1_ordinal1 D))  &  ( ((k1_funct_1 F k1_xboole_0) = C)  &  ( (! [G:$i] :  ((v3_ordinal1 G) =>  ((r2_hidden (k1_ordinal1 G) (k1_ordinal1 D)) =>  ((k1_funct_1 F (k1_ordinal1 G)) = (k1_funct_1 B (k1_funct_1 F G))) ) ) )  &  (! [G:$i] :  ((v3_ordinal1 G) =>  ( ((r2_hidden G (k1_ordinal1 D)) & (v4_ordinal1 G))  =>  ( (G = k1_xboole_0)  |  ((k1_funct_1 F G) = (k16_lattice3 A (k2_relset_1 (k10_xtuple_0 F) (k5_relat_1 F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  (! [E:$i] :  ((m1_kolmog01 E D A B) =>  ((r2_kolmog01 A B C D E) <=>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 D)))  =>  (! [G:$i] :  ((m2_kolmog01 G A B D F E) => (r1_kolmog01 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_kurato_0 B A) <=>  ((k4_kurato_0 A B) = (k3_kurato_0 A B)) ) ) ) ) ).
tt(d5_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_kurato_1 A B) = (k5_enumset1 B (k1_tops_1 A B) (k2_pre_topc A B) (k1_tops_1 A (k2_pre_topc A B)) (k2_pre_topc A (k1_tops_1 A B)) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))) (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))) ) ) ) ) ).
tt(d5_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r3_lang1 A B C) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = C)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (~  ( ((k1_funct_1 D E) = F)  &  ( ((k1_funct_1 D (k2_nat_1 E 1)) = G)  & (r2_lang1 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) C C) =>  ((k6_laplace A B C D E) = (k8_group_1 D (k1_laplace D (k4_group_1 D) (k4_algstr_0 D (k1_group_1 D)) (k2_xcmplx_0 A B)) (k5_laplace A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k7_lattice3 A) = (g1_orders_2 (u1_struct_0 A) (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(d5_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_lattice4 C A B) =>  ((r3_lattice4 A B C) <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k5_lattices A)) = (k5_lattices B)) ) ) ) ) ) ) ) ).
tt(d5_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v1_lattice5 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_lattice5 A B C D E) = (k3_lattice5 A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice6 A B C) <=>  ( (~  (B = C) )  &  ((r3_lattices A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_lattices A C D) &  ((r3_lattices A D B) &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k2_lattice7 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r3_orders_2 A D C)) ) )  & (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d5_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( (C = (k3_lattice8 A B))  <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) & (v1_funct_1 D)) )  &  ( (C = (k1_ordinal2 D))  &  ( ((k9_xtuple_0 D) = (k1_ordinal1 B))  &  ( ((k1_funct_1 D k1_xboole_0) = A)  &  ( (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden (k1_ordinal1 E) (k1_ordinal1 B)) =>  ((k1_funct_1 D (k1_ordinal1 E)) = (k1_lattice8 (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden E (k1_ordinal1 B)) & (v4_ordinal1 E))  =>  ( (E = k1_xboole_0)  |  ((k1_funct_1 D E) = (k3_tarski (k2_relset_1 (k10_xtuple_0 D) (k5_relat_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v5_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A B (k1_lattices A C D)) = (k1_lattices A (k1_lattices A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_lexbfs,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k15_pre_poly A)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (D = (k4_lexbfs A B C))  <=>  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E C) => (r1_termord A B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) =>  ((k5_lfuzzy_0 A B) = B) ) ) ) ) ).
tt(d5_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v2_lfuzzy_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k8_lfuzzy_0 A A B C D) = (k8_lfuzzy_0 A A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_limfunc1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C D) & (r1_xxreal_0 B (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r5_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D B))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  => (v1_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d5_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 A B C) <=> (m1_vectsp_4 B A C)) ) ) ) ) ) ) ).
tt(d5_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_lopban_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_rlvect_1 A D E)) = (k1_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k6_lopban_2 A) = (k6_partfun1 (u1_struct_0 A))) ) ) ).
tt(d5_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k2_lopban_3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A C (k1_normsp_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k4_lopban_4 A B))  <=>  ( ((k8_nat_1 (u1_struct_0 A) C k6_numbers) = (k4_struct_0 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) C (k2_nat_1 D 1)) = (k8_nat_1 (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k7_lopclset A) = (a_1_1_lopclset A)) ) ) ).
tt(d5_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_lpspace1 A) = (k8_funcop_1 k5_numbers A k6_numbers)) ) ) ).
tt(d5_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k4_lpspace2 A B C D) = (g1_rlvect_1 (k3_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k2_lpspace2 A B C D)) (k3_lpspace2 A B C D)) (k1_ideal_1 (k2_lpspace2 A B C D) (k3_lpspace2 A B C D)) (k1_lpspace1 (k2_lpspace2 A B C D) (k3_lpspace2 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(d5_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k5_ltlaxio1 A B) = (k1_ltlaxio1 (k4_ltlaxio1 (k1_ltlaxio1 A) (k1_ltlaxio1 B)))) ) ) ) ) ).
tt(d5_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_finseq_1 B) & (v2_card_3 B))  =>  ((m2_margrel1 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C B) => (r1_tarski (k10_xtuple_0 C) A)) ) ) ) ) ) ) ).
tt(d5_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_mathmorp A B C) = (k3_mathmorp A (k6_rusub_4 A B C) C)) ) ) ) ) ) ) ).
tt(d5_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((r1_matrix10 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden (k4_tarski C D) (k2_matrix_1 A)) & (r1_xxreal_0 (k3_matrix_1 k1_numbers B C D) (k3_matrix_1 k1_numbers A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A)))))) )  =>  ( (B = (k5_matrix11 A))  <=>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((k5_binop_1 (k3_finseq_2 (u1_struct_0 A)) B C D) = (k3_fvsum_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((r2_hidden E (k2_finseq_1 (k1_matrix_1 D))) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) A B) =>  ( (G = (k5_matrix12 A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 D))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden H (k4_finseq_1 D)) & (r2_hidden I (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (I = E)  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k8_group_1 C F (k3_matrix_1 (u1_struct_0 C) D H E))) )  &  ( (~  (I = E) )  =>  ((k3_matrix_1 (u1_struct_0 C) G H I) = (k3_matrix_1 (u1_struct_0 C) D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k6_prvect_1 A B))) =>  ((k10_matrix13 A B C) = C) ) ) ) ) ) ) ).
tt(d5_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k1_matrix_1 B) = k1_xboole_0)  =>  ((k3_finseq_1 B) = k1_xboole_0) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A (k6_prvect_1 A (k1_matrix_1 B))))  =>  ( (C = (k7_matrix15 A B))  <=>  ((u1_struct_0 C) = (k6_matrix15 A B (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 B) (k4_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(d5_matrix16,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((v3_matrix16 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C A) &  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  & (r2_matrix16 A B C)) ) ) ) ) ) ) ).
tt(d5_matrix17,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((v4_matrix17 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C A) &  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  & (r1_matrix17 A B C)) ) ) ) ) ) ) ).
tt(d5_matrix_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (E = (k3_matrix_1 A B C D))  <=>  (? [F:$i] :  ((m2_finseq_1 F A) &  ( (F = (k1_funct_1 B C))  &  (E = (k1_funct_1 F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( (D = (k7_matrix_2 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 D E) = (k2_finseq_3 A (k8_matrix_1 (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( (D = (k6_matrix_3 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 B)) =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k8_group_1 A C (k3_matrix_1 (u1_struct_0 A) B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((k5_matrix_5 A B) = (k2_matrix_5 (k1_matrix_4 k1_complfld (k1_matrix_5 A) (k1_matrix_5 B)))) ) ) ) ) ).
tt(d5_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_6 C A B) <=>  ((k5_matrix_1 A (u1_struct_0 B) C) = C) ) ) ) ) ) ) ) ).
tt(d5_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_8 A B C D) <=>  (? [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) &  ((v1_matrix_6 E A B) &  (C = (k4_matrix_6 A B (k4_matrix_6 A B (k5_matrix_6 A B E) D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k5_matrixc1 A B) = (k1_finseqop k2_numbers k2_numbers k2_numbers k29_binop_2 A B)) ) ) ) ) ).
tt(d5_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  ( (D = (k12_matrixj1 A B C))  <=>  ( ((k3_finseq_1 D) = (k2_wsierp_1 (k10_matrixj1 A C)))  &  ( ((k1_matrix_1 D) = (k2_wsierp_1 (k11_matrixj1 A C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) =>  ( ( (~  ( (~ (r1_xxreal_0 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d (k1_matrixj1 (k10_matrixj1 A C) E) 1) (k11_matrixj1 A C)))))  & (r1_xxreal_0 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k1_matrixj1 (k10_matrixj1 A C) E) (k11_matrixj1 A C))))) )  =>  ((k3_matrix_1 A D E F) = B) )  &  ((r1_xxreal_0 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k1_matrixj1 (k10_matrixj1 A C) E) (k11_matrixj1 A C)))) =>  ((r1_xxreal_0 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d (k1_matrixj1 (k10_matrixj1 A C) E) 1) (k11_matrixj1 A C)))) |  ((k3_matrix_1 A D E F) = (k3_matrix_1 A (k2_matrixj1 A C (k1_matrixj1 (k10_matrixj1 A C) E)) (k7_nat_d E (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d (k1_matrixj1 (k10_matrixj1 A C) E) 1) (k10_matrixj1 A C)))) (k7_nat_d F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d (k1_matrixj1 (k10_matrixj1 A C) E) 1) (k11_matrixj1 A C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrixj2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k9_matrixj2 A B C))  <=>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C D) (k6_grcat_1 B B)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C E) (k6_grcat_1 B B)) => (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k5_matrixr1 A B) = (k2_matrixr1 (k1_matrix_4 k2_vectsp_1 (k1_matrixr1 A) (k1_matrixr1 B)))) ) ) ) ) ).
tt(d5_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_matrixr2 B A) <=>  (? [C:$i] :  ((m1_matrix_1 C k1_numbers A A) &  ( ((k1_matrixr2 A C B) = (k4_matrixr2 A))  &  ((k1_matrixr2 A B C) = (k4_matrixr2 A)) ) ) ) ) ) ) ) ) ).
tt(d5_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((k5_matrlin A B C D) = (k1_finseqop (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_vectsp_1 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(d5_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v1_matrprob A) <=>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) )  &  ((k18_rvsum_1 A) = 1) ) ) ) ) ).
tt(d5_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_matrtop3 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_monoid_0 (u1_struct_0 (k15_euclid A))))) &  ( (B = (k3_group_4 (k15_monoid_0 (u1_struct_0 (k15_euclid A))) C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 F E))  &  ((r1_xxreal_0 F A) &  ((k1_funct_1 C D) = (k3_matrtop1 A A (k2_matrtop3 A G E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (E = (k1_mcart_1 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_measure1 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((r1_tarski C B) => (r2_hidden (k5_setfam_1 A C) B)) ) ) ) ) ) ) ).
tt(d5_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_measure3 A B C) k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A (k2_measure3 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_measure3 A B C) k7_numbers)))) ) ) ) )  =>  ( (D = (k4_measure3 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  (! [F:$i] :  ((m1_measure3 F A B C) =>  ((k12_supinf_2 D (k2_xboole_0 E F)) = (k12_supinf_2 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_measure5 A) <=>  (? [B:$i] :  ((m1_subset_1 B k7_numbers) &  (? [C:$i] :  ((v1_xreal_0 C) &  (A = (k4_rcomp_1 B C)) ) ) ) ) ) ) ) ).
tt(d5_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  ((v1_xxreal_2 A) <=>  ((v3_xxreal_2 A) & (r2_hidden (k3_seq_4 A) A)) ) ) ) ).
tt(d5_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_measure8 D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k7_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (E = (k2_measure8 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_mesfunc9 E F) = (k1_mesfunc9 C (k1_measure8 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k8_member_1 A B) = (a_2_0_member_1 A B)) ) ) ) ) ).
tt(d5_membered,ax, (! [A:$i] :  ((v5_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_int_1 B)) ) ) ) ).
tt(d5_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_memstr_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_memstr_0 A B C) = (k1_funct_1 (k2_memstr_0 A B) C)) ) ) ) ) ) ) ).
tt(d5_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((k3_mesfun6c A B C D E) = (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k5_mesfun7c A B) = (k4_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d5_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r1_mesfun9c A B C) <=>  ((v1_mesfunc8 B A k1_numbers) &  ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers)) = (k1_relset_1 A C))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (? [F:$i] :  ((v7_ordinal1 F) &  (? [G:$i] :  ((m1_subset_1 G A) &  ((r1_xxreal_0 E F) &  ((r2_hidden G (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) & (r1_xxreal_0 D (k17_complex1 (k9_real_1 (k1_seq_1 (k4_mesfunc5 A k1_numbers B F) G) (k1_seq_1 C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (D = (k5_mesfunc1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k12_supinf_2 D E) = (k1_extreal1 (k12_supinf_2 B E) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v3_mesfunc5 B) <=>  (! [C:$i] :  (~ (r1_xxreal_0 (k12_supinf_2 B C) k2_supinf_1)) ) ) ) ) ) ) ).
tt(d5_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((k2_mesfunc6 A B C D E) = (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ( (C = (k3_mesfunc8 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C D)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers C D))) =>  ((k12_supinf_2 (k4_mesfunc5 A k7_numbers C D) E) = (k8_nat_1 k7_numbers (k3_rinfsup2 (k3_mesfunc5 A B E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mesfunc9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ((v2_mesfunc9 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  (C = D) )  =>  (! [E:$i] :  (~  ((r2_hidden E (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers B C)) (k1_relset_1 A (k4_mesfunc5 A k7_numbers B D)))) &  ( ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B C) E) = k1_supinf_1)  &  ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B D) E) = k2_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_metric_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ((v5_metric_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_metric_1 A A B C E) (k7_real_1 (k1_metric_1 A A B C D) (k1_metric_1 A A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(d5_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r4_metric_2 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F C))  =>  ((k2_metric_1 A E F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r2_metric_6 A B C) <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r2_hidden (k2_tbsp_1 A C E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_pre_topc C (k15_euclid A)) =>  ((r2_hidden B (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k3_mfold_2 A B (k4_struct_0 (k15_euclid A))))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k3_mfold_2 A B (k4_struct_0 (k15_euclid A)))))))) )  =>  ( (D = (k5_mfold_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ((r1_struct_0 C E) =>  ((k1_funct_1 D E) = (k1_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) E (k1_rlvect_1 (k15_euclid A) B (k23_rvsum_1 E B))) (k12_binop_2 1 (k10_binop_2 1 (k23_rvsum_1 E B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_midsp_1 A B C) <=> (r1_midsp_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(d5_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  ((r2_midsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  ( ((k1_funct_1 F B) = E)  =>  ((k4_midsp_3 A C D (k6_midsp_3 A C F B (k3_midsp_1 C D E))) = (k3_midsp_1 C D (k4_midsp_3 A C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((l1_mod_2 B A) =>  ((k4_mod_2 A B) = (u3_mod_2 A B)) ) ) ) ) ).
tt(d5_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B))))) )  =>  ((k6_mod_4 A B C) = (k1_mod_4 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(d5_modal_1,ax, (! [A:$i] :  ((m1_trees_3 A (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) =>  ( (A = k6_modal_1)  <=>  ( (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((r2_hidden B A) => (v1_finset_1 B)) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) ) )  =>  ((r2_hidden B A) <=>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  ((r1_xxreal_0 (k5_modal_1 (k9_xtuple_0 B) C) 2) &  ( (~  ( ((k5_modal_1 (k9_xtuple_0 B) C) = k6_numbers)  &  ( (~  ((k3_trees_2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) B C) = (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((k3_trees_2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) B C) = (k1_domain_1 k5_numbers k5_numbers 3 D)) ) ) ) ) ) )  &  ( (~  ( ((k5_modal_1 (k9_xtuple_0 B) C) = 1)  &  ( (~  ((k3_trees_2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) B C) = (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) )  &  (~  ((k3_trees_2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) B C) = (k1_domain_1 k5_numbers k5_numbers 1 1)) ) ) ) )  &  ( ((k5_modal_1 (k9_xtuple_0 B) C) = 2)  =>  ((k3_trees_2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) B C) = (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_modcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  ((r1_modcat_1 A B C) <=>  (? [D:$i] :  (? [E:$i] :  ( (A = (k4_tarski D E))  &  (? [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v7_vectsp_1 F C) &  ((v8_vectsp_1 F C) &  ((v9_vectsp_1 F C) &  ((v10_vectsp_1 F C) &  ((v11_vectsp_1 F C) & (l1_vectsp_1 F C)) ) ) ) ) ) ) ) ) )  &  ( (B = F)  &  ( (D = (g2_algstr_0 (u1_struct_0 F) (u1_algstr_0 F) (u2_struct_0 F)))  &  (E = (u1_vectsp_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k5_modelc_2 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 2) A) B)) ) ) ) ) ).
tt(d5_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r2_hidden C (u2_modelc_3 A B)) =>  (! [D:$i] :  ( ((v1_modelc_3 D A) & (l1_modelc_3 D A))  =>  ( (D = (k6_modelc_3 A B C))  <=>  ( ((u1_modelc_3 A D) = (k2_xboole_0 (u1_modelc_3 A B) (k1_tarski C)))  &  ( ((u2_modelc_3 A D) = (k2_xboole_0 (k7_subset_1 (k1_modelc_3 A) (u2_modelc_3 A B) (k1_tarski C)) (k7_subset_1 (k1_modelc_3 C) (k3_modelc_3 C) (u1_modelc_3 A B))))  &  ((u3_modelc_3 A D) = (u3_modelc_3 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_moebius1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  ( (B = (k4_moebius1 A))  <=>  ( ((k13_pre_poly B) = (k9_subset_1 k5_numbers A k1_moebius1))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k13_pre_poly B)) =>  ((k1_funct_1 B C) = (k2_moebius1 C)) ) ) ) ) ) ) ) ) ).
tt(d5_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v5_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E A) &  (? [F:$i] :  ((m1_subset_1 F A) &  ( ((k5_binop_1 A B C E) = D)  &  ((k5_binop_1 A B F C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k18_monoid_1 A B) = (k16_monoid_1 (k6_domain_1 A B) A)) ) ) ) ) ).
tt(d5_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_msafree2 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_msafree2 A))) ) )  =>  ((m1_msafree2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k2_msafree2 A)) => (r2_hidden (k1_funct_1 C D) (k1_funct_1 (u3_msualg_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d5_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B))) =>  ( (D = (k5_msafree3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (a_4_0_msafree3 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msafree C A B) =>  ((v1_msafree C A B) <=>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A D)) =>  (? [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D)) &  ((r1_msualg_3 A B D F) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  (! [E:$i] :  ((m2_msalimit E A B C) =>  ( (E = (k2_msalimit A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 A G F) =>  ((k1_binop_1 E G F) = (k14_funcop_1 G F (k2_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F))) (k3_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C G)) (k2_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F))) (k1_msalimit A B C D F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k7_msaterm A B C))  <=> (r2_hidden C (k7_msafree A B D))) ) ) ) ) ) ) ) ) ).
tt(d5_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v4_msscyc_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_finset_1 (a_2_0_msscyc_1 A B))) ) ) ) ) ).
tt(d5_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v4_mssubfam C A B) <=>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  ((r2_pboole A D C) => (r1_pboole A (k4_mssubfam A B D) C)) ) ) ) ) ) ) ) ) ).
tt(d5_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((k4_msualg_1 A B C) = (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B)) ) ) ) ) ) ) ).
tt(d5_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r1_msualg_2 A B C D) <=> (r1_tarski (k10_xtuple_0 (k5_relat_1 (k5_msualg_1 A C B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) D)) C))) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) D) C))) ) ) ) ) ) ) ) ) ).
tt(d5_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  (~  ( (~  ((k3_msualg_1 A D B) = k1_xboole_0) )  &  ( (~  ((k3_msualg_1 A D C) = k1_xboole_0) )  &  (~  ((k5_msualg_3 A B C D E F) = (k1_funct_1 (k2_pralg_2 (k3_relat_1 (k1_msualg_1 A D) E)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((k3_msualg_4 A B C D E) = (k6_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k2_msualg_4 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  ( (C = (k5_msualg_5 A B))  <=>  ( (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B)) ) )  &  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  (! [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  =>  ( ((k1_binop_1 (u1_lattices C) D E) = (k3_pboole A D E))  &  ((k1_binop_1 (u2_lattices C) D E) = (k4_msualg_5 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_msualg_6 A B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) &  ( ((k2_msualg_1 A F) = C)  &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ((r2_hidden G (k4_finseq_1 (k1_msualg_1 A F))) &  ( ((k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A F) G) = B)  &  (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ((r2_hidden H (k3_msualg_1 A F D)) &  (E = (k4_msualg_6 A F G D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_mycielsk,ax, (! [A:$i] :  ( ((v2_mycielsk A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k3_mycielsk A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v5_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v5_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A))) )  => (r1_xxreal_0 B (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(d5_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ((v5_nagata_1 B A) <=>  ((v2_nagata_1 B A) &  ((v1_tops_2 (k2_nagata_1 A B) A) &  ((v1_cantor_1 (k2_nagata_1 A B) A) & (m1_subset_1 (k2_nagata_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(d5_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k7_nat_3 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D k2_numbers) &  ( (C = (k20_rvsum_1 D))  &  (D = (k3_relat_1 (k1_uproots (k13_pre_poly B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d5_nat_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ((v1_nat_5 A) <=>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ((r1_int_2 B C) =>  ((k1_recdef_1 A (k24_binop_2 B C)) = (k24_binop_2 (k1_recdef_1 A B) (k1_recdef_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d5_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k3_int_2 A B))  <=>  ((r1_nat_d C A) &  ((r1_nat_d C B) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_nat_d D A) & (r1_nat_d D B))  => (r1_nat_d D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k4_nattra_1 A B C D E F) = (k3_funct_2 (u1_struct_0 A) (u4_struct_0 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k1_relset_1 (u1_struct_0 A) C)) &  ((v9_clvect_1 E A) &  ((k7_clvect_1 A E) = D) ) )  =>  ((v9_clvect_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) B) &  ((k7_partfun1 (u1_struct_0 B) C D) = (k7_clvect_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r5_ncfcont2 A B C) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden F A) &  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B F G))))  & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C F) (k7_partfun1 k1_numbers C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((v2_ndiff_1 C A B) <=>  ((v1_partfun1 C (u1_struct_0 A)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v12_struct_0 D k5_numbers A) &  ((v1_ndiff_1 D A (k4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v3_normsp_1 (k1_ndiff_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) (k37_valued_1 k5_numbers k1_numbers (k4_normsp_0 A D))) B) &  ((k6_normsp_1 B (k1_ndiff_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) (k37_valued_1 k5_numbers k1_numbers (k4_normsp_0 A D)))) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((r2_ndiff_3 A B C) <=>  ((r1_tarski C (k1_relset_1 k1_numbers B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) => (r1_ndiff_3 A (k2_partfun1 k1_numbers (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v1_ndiff_4 B A) <=> (r2_ndiff_4 A B (k1_relset_1 k1_numbers B))) ) ) ) ) ).
tt(d5_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k4_finseq_1 A)) =>  ((k5_ndiff_5 A B) = B) ) ) ) ) ).
tt(d5_neckla_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k3_neckla_2)) =>  ( (A = k4_neckla_2)  <=>  ( (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( ((v3_card_1 (u1_struct_0 B) 1) & (r2_hidden (u1_struct_0 B) k13_classes2))  => (r2_hidden B A)) ) )  &  ( (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( ((r1_xboole_0 (u1_struct_0 B) (u1_struct_0 C)) &  ((r2_hidden B A) & (r2_hidden C A)) )  =>  ((r2_hidden (k1_neckla_2 B C) A) & (r2_hidden (k2_neckla_2 B C) A)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k3_neckla_2)) =>  ( ( (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  ( ((v3_card_1 (u1_struct_0 C) 1) & (r2_hidden (u1_struct_0 C) k13_classes2))  => (r2_hidden C B)) ) )  &  (! [C:$i] :  ( ((v1_orders_2 C) & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_orders_2 D) & (l1_orders_2 D))  =>  ( ((r1_xboole_0 (u1_struct_0 C) (u1_struct_0 D)) &  ((r2_hidden C B) & (r2_hidden D B)) )  =>  ((r2_hidden (k1_neckla_2 C D) B) & (r2_hidden (k2_neckla_2 C D) B)) ) ) ) ) ) )  => (r1_tarski A B)) ) ) ) ) ) ) ) ).
tt(d5_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_necklace A) <=>  (! [B:$i] :  (~  ((r2_hidden B (u1_struct_0 A)) & (r2_hidden (k4_tarski B B) (u1_orders_2 A))) ) ) ) ) ) ).
tt(d5_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_net_1 A B C) <=>  ((r2_hidden (k4_tarski B C) (k1_net_1 A)) & (r2_hidden B (u4_struct_0 A))) ) ) ) ) ) ).
tt(d5_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k8_newton A))  <=>  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (D = (k5_real_1 C 1)) )  =>  ((k1_funct_1 B C) = (k6_newton D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_nfcont_1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k1_relset_1 (u1_struct_0 A) C)) &  ((v3_normsp_1 E A) &  ((k6_normsp_1 A E) = D) ) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) B) &  ((k7_partfun1 (u1_struct_0 B) C D) = (k6_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v1_nfcont_4 B A) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k1_relset_1 k1_numbers B)) => (r1_nfcont_4 A B C)) ) ) ) ) ) ) ) ).
tt(d5_normsp_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_normsp_0 A))  =>  ((v3_normsp_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_normsp_0 A B) = k6_numbers)  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(d5_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k5_normsp_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_rlvect_1 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_numbers,ax, (k7_numbers = (k2_xboole_0 k1_numbers (k2_tarski k1_numbers (k4_tarski k6_numbers k1_numbers)))) ).
tt(d5_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((k7_openlatt A) = (a_1_0_openlatt A)) ) ) ).
tt(d5_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_necklace A) <=> (v2_relat_2 (u1_orders_2 A))) ) ) ).
tt(d5_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k2_oppcat_1 A))) =>  ((k6_oppcat_1 A B) = (k5_oppcat_1 (k2_oppcat_1 A) B)) ) ) ) ) ).
tt(d5_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_orders_1 A) <=>  ((v1_relat_2 A) &  ((v8_relat_2 A) &  ((v4_relat_2 A) & (v6_relat_2 A)) ) ) ) ) ) ).
tt(d5_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) <=> (r2_hidden (k4_tarski B C) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(d5_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ( (F = (k1_funct_1 C D))  &  (G = (k1_funct_1 C E)) )  => (r1_orders_2 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d5_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((k4_ordinal2 A) = (k3_ordinal2 (k10_xtuple_0 A))) ) ) ).
tt(d5_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r1_ordinal1 B A) =>  ( (C = (k5_ordinal3 A B))  <=>  (A = (k10_ordinal2 B C)) ) )  &  ( (~ (r1_ordinal1 B A))  =>  ( (C = (k5_ordinal3 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d5_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal5 A) <=>  ((k12_ordinal2 k4_ordinal1 A) = A) ) ) ) ).
tt(d5_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  ((k1_ordinal6 A) = (k2_wellord2 (k1_wellord2 A))) ) ) ).
tt(d5_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v4_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  ((v1_o_ring_1 (k7_partfun1 (u1_struct_0 A) B 1) A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v1_o_ring_1 D A) &  ((k7_partfun1 (u1_struct_0 A) B (k1_nat_1 C 1)) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((k2_osafree A B) = (g1_lang1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k1_osafree A B))) ) ) ) ) ).
tt(d5_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v3_osalg_1 B) &  ((v4_osalg_1 B) & (l3_osalg_1 B)) ) ) )  =>  ( (B = (k1_osalg_1 A))  <=>  ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ( ((k6_partfun1 (u1_struct_0 A)) = (u1_orders_2 B))  &  ( ((u4_struct_0 A) = (u4_struct_0 B))  &  ( ((k6_partfun1 (u4_struct_0 A)) = (u1_osalg_1 B))  &  ((r1_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u4_struct_0 B) (k3_finseq_2 (u1_struct_0 B)) (u1_msualg_1 A) (u1_msualg_1 B)) & (r1_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u4_struct_0 B) (u1_struct_0 B) (u2_msualg_1 A) (u2_msualg_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(d5_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ( (C = (k3_osalg_2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k1_osalg_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k2_osalg_4 A) = (k8_eqrel_1 (u1_struct_0 A) (k1_osalg_4 A))) ) ) ).
tt(d5_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( (D = (k5_partfun1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ( (F = E)  &  ((v1_partfun1 F A) & (r1_partfun1 C F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k1_partfun3 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k7_square_1 (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d5_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ( (D = (k3_partit1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=> (r2_partit1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v5_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_diraf A B C E) &  ((r1_diraf A B F D) &  ( (~ (r3_diraf A B C D))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_diraf A C H D) & (r1_diraf A F H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k3_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k3_xboole_0 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((k3_pcomps_1 A) = (g1_pre_topc (u1_struct_0 A) (k2_pcomps_1 A))) ) ) ).
tt(d5_pdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k5_pdiff_1 A B))  <=>  ( ((k9_xtuple_0 C) = k1_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 C D) = (k1_finseq_7 k1_numbers B A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r4_pdiff_3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  &  (? [E:$i] :  ((m1_rcomp_1 E D) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B))) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v3_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B) H) (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B) D)) = (k7_real_1 (k1_seq_1 F (k9_real_1 H D)) (k1_seq_1 G (k9_real_1 H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r5_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((r2_pdiff_7 A B C D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ( (F = (k2_pdiff_7 A B C D E))  <=>  ( ((k1_relset_1 (k1_euclid A) F) = E)  &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  ((r2_hidden G E) =>  ((k7_partfun1 (k1_euclid B) F G) = (k12_pdiff_1 A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r3_pdiff_9 A B C D) <=>  ((r1_tarski B (k1_relset_1 (k1_euclid A) D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) => (r3_pdiff_1 A C (k2_partfun1 (k1_euclid A) k1_numbers D B) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_pencil_1 A) <=> (m1_subset_1 (u1_struct_0 A) (u1_pre_topc A))) ) ) ).
tt(d5_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_pencil_1 A B D)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) D)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B D)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) D))))))) )  =>  ( (E = (k4_pencil_3 A B C D))  <=>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  ( ((m1_pencil_2 (k4_card_3 F) A B) &  ((k3_pencil_1 A F) = D) )  => (r1_funct_2 (u1_struct_0 (k2_pencil_1 A B D)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) D))) (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A F))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A F)))) E (k3_pencil_3 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_pencil_4 A B C) = (g1_pre_topc (k2_vectsp_9 A B C) (k4_pencil_4 A B C))) ) ) ) ) ) ) ).
tt(d5_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_petri A B) = (a_2_1_petri A B)) ) ) ) ) ).
tt(d5_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( (D = (k3_pnproc_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k6_xcmplx_0 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_polyalg1 D A) & (m1_polyalg1 D A B)) )  =>  ( (D = (k2_polyalg1 A B C))  <=>  ((r1_tarski C (u1_struct_0 D)) &  (! [E:$i] :  ((m1_polyalg1 E A B) =>  ((r1_tarski C (u1_struct_0 E)) => (r1_tarski (u1_struct_0 D) (u1_struct_0 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ((k9_polyeq_1 A B C D E) = (k3_xcmplx_0 A (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 B C) (k6_xcmplx_0 B D)) (k6_xcmplx_0 B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers)  =>  ( (E = (k5_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (H = (k1_polyeq_5 2 (k6_xcmplx_0 (k1_newton F 2) G)))  &  (E = (k6_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k6_xcmplx_0 F H)))) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers) )  =>  ( (E = (k5_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  (? [J:$i] :  ((v1_xcmplx_0 J) &  (? [K:$i] :  ((v1_xcmplx_0 K) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) 64))  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (I = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (J = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (K = (k10_complex1 (k13_complex1 G (k3_xcmplx_0 I J))))  &  (E = (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 I J) K) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_finset_1 C) =>  ( (C = (k8_polyform A B))  <=>  ( ( (~ (r1_xxreal_0 (k4_xcmplx_0 1) B))  =>  (C = k1_xboole_0) )  &  ( ( (B = (k4_xcmplx_0 1))  =>  (C = (k1_tarski k1_xboole_0)) )  &  ( (~  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 1)))  &  ( (~ (r1_xxreal_0 (k7_polyform A) B))  &  (~  (C = (k10_xtuple_0 (k1_funct_1 (u1_polyform A) (k2_xcmplx_0 B 1)))) ) ) ) )  &  ( ( (B = (k7_polyform A))  =>  (C = (k1_tarski A)) )  &  ( (~ (r1_xxreal_0 B (k7_polyform A)))  =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((k4_polynom1 A B C D) = (k1_vfunct_1 (k15_pre_poly A) B C D)) ) ) ) ) ) ) ) ).
tt(d5_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B))))) )  =>  ( (D = (k6_polynom2 A B C))  <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 E (k15_pre_poly A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ((k1_funct_1 D E) = (k5_polynom2 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (k4_finseq_2 3 k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( (F = (k7_polynom3 A B C D E))  <=>  ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden G (k4_finseq_1 E)) =>  ((k1_funct_1 F G) = (k6_algstr_0 A (k6_algstr_0 A (k1_normsp_1 A B (k7_partfun1 k5_numbers (k9_pre_poly k5_numbers k5_numbers (k4_finseq_2 3 k5_numbers) E G) 1)) (k1_normsp_1 A C (k7_partfun1 k5_numbers (k9_pre_poly k5_numbers k5_numbers (k4_finseq_2 3 k5_numbers) E G) 2))) (k1_normsp_1 A D (k7_partfun1 k5_numbers (k9_pre_poly k5_numbers k5_numbers (k4_finseq_2 3 k5_numbers) E G) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (D = (k5_polynom5 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) &  ( (D = (k4_rlvect_1 (k14_polynom3 A) E))  &  ( ((k3_finseq_1 E) = (k1_algseq_1 A B))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k3_polynom5 A (k2_polynom5 A C (k7_nat_d F 1)) (k3_funct_2 k5_numbers (u1_struct_0 A) B (k7_nat_d F 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (D = (k2_polynom7 A B C))  <=>  (~  ( ((k3_polynom1 A B C D) = (k4_struct_0 B))  &  (~  ( ((k2_polynom1 (k15_pre_poly A) B C) = k1_xboole_0)  &  (D = (k16_pre_poly A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (C = (k5_polynom8 A B))  <=>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  =>  ((k8_nat_1 (u1_struct_0 A) C D) = (k3_matrix_1 (u1_struct_0 A) B (k1_nat_1 D 1) 1)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) =>  ((k8_nat_1 (u1_struct_0 A) C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r3_polyred A B C D E F G) <=>  ( (~  (D = (k7_polynom1 A C)) )  &  ( (~  (E = (k7_polynom1 A C)) )  &  ((r2_hidden G (k2_polynom1 (k15_pre_poly A) C D)) &  (? [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  &  ( ((k11_pre_poly A H (k3_termord A B C E)) = G)  & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) F (k6_polynom1 A C D (k5_polynom7 A C (k1_polyred A H C E) (k3_vectsp_1 C (k3_polynom1 A C D G) (k4_termord A B C E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v2_poset_1 B A A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k3_poset_1 A B))  <=>  ((r2_abian (u1_struct_0 A) C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_abian (u1_struct_0 A) D B) => (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pralg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  ((k5_pralg_1 A B) = (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))) ) ) ) ) ) ).
tt(d5_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m1_pralg_2 C A B) <=>  (! [D:$i] :  ((r2_hidden D A) =>  ((v4_msualg_1 (k1_funct_1 C D) B) & (l3_msualg_1 (k1_funct_1 C D) B)) ) ) ) ) ) ) ) ) ).
tt(d5_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m1_pralg_3 D A C B) =>  (! [E:$i] :  ((m1_pralg_2 E A B) =>  ( (E = (k4_pralg_3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ((r2_hidden F A) &  (! [G:$i] :  ( (~ (v1_xboole_0 G))  =>  (! [H:$i] :  ((m1_pralg_2 H G B) =>  (~  ( (G = (k1_funct_1 C F))  &  ( (H = (k1_funct_1 D F))  &  ((k5_pralg_2 A B E F) = (k14_pralg_2 G B H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k11_pre_poly A B C))  <=>  (! [E:$i] :  ((k1_funct_1 D E) = (k3_binop_2 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ).
tt(d5_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  =>  ( (C = (k1_pre_topc A B))  <=>  ((k2_struct_0 C) = B) ) ) ) ) ) ) ) ).
tt(d5_prgcor_2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r3_prgcor_2 A B C) <=>  ( ((k1_afinsq_1 B) = C)  &  ( ((k1_afinsq_1 A) = C)  &  (? [D:$i] :  ((v1_int_1 D) &  ( ((k1_seq_1 B k6_numbers) = (k1_seq_1 A k6_numbers))  &  ( (D = (k1_seq_1 A k6_numbers))  &  ( (~  (D = k6_numbers) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E D))  =>  ((k1_seq_1 B E) = (k1_real_1 (k1_seq_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_prob_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_prob_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(d5_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  ((r2_prob_2 A B C D E F) <=>  ( ((k1_seq_1 C (k5_prob_1 A B (k5_prob_1 A B D E) F)) = (k8_real_1 (k8_real_1 (k1_seq_1 C D) (k1_seq_1 C E)) (k1_seq_1 C F)))  &  ( ((k1_seq_1 C (k5_prob_1 A B D E)) = (k8_real_1 (k1_seq_1 C D) (k1_seq_1 C E)))  &  ( ((k1_seq_1 C (k5_prob_1 A B D F)) = (k8_real_1 (k1_seq_1 C D) (k1_seq_1 C F)))  &  ((k1_seq_1 C (k5_prob_1 A B E F)) = (k8_real_1 (k1_seq_1 C E) (k1_seq_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k9_setfam_1 A)) =>  ( (C = (k6_prob_3 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k4_prob_3 A C D) = (k3_subset_1 A (k4_prob_3 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (D = (k4_prob_4 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F B) &  (? [G:$i] :  ((m1_prob_4 G A B C) &  (E = (k2_xboole_0 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r4_projpl_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (l1_vectsp_1 C A))  =>  ( (C = (k6_prvect_1 A B))  <=>  ( ((g2_algstr_0 (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C)) = (k4_prvect_1 A B))  &  ((u1_vectsp_1 A C) = (k5_prvect_1 A B)) ) ) ) ) ) ) ) ) ).
tt(d5_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B (k4_prvect_2 A)) =>  ( (B = (k6_prvect_2 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 (k4_prvect_2 A)))  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (k4_prvect_2 A))) => (r1_funct_2 (k2_zfmisc_1 (k1_funct_1 (k4_prvect_2 A) C) (k1_funct_1 (k4_prvect_2 A) C)) (k1_funct_1 (k4_prvect_2 A) C) (k2_zfmisc_1 (u1_struct_0 (k5_prvect_2 A C)) (u1_struct_0 (k5_prvect_2 A C))) (u1_struct_0 (k5_prvect_2 A C)) (k9_prvect_1 (k4_prvect_2 A) B C) (u1_algstr_0 (k5_prvect_2 A C)))) ) ) ) ) ) ) ) ).
tt(d5_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  ((k5_prvect_3 A B) = (g1_rlvect_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k3_prvect_3 A B) (k1_prvect_3 A B) (k2_prvect_3 A B))) ) ) ) ) ).
tt(d5_pscomp_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) k1_numbers)))) )  =>  ( (A = k4_pscomp_1)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_seq_1 A B) = (k17_euclid B)) ) ) ) ) ) ).
tt(d5_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (C = (k7_pua2mss1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden (k4_tarski D E) B) &  (! [F:$i] :  ((m1_pua2mss1 F (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A))) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) & (v1_finseq_1 H)) )  =>  ( ((r2_hidden (k7_finseq_1 (k7_finseq_1 G (k12_finseq_1 (u1_struct_0 A) D)) H) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) F)) & (r2_hidden (k7_finseq_1 (k7_finseq_1 G (k12_finseq_1 (u1_struct_0 A) E)) H) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) F)))  => (r2_hidden (k4_tarski (k1_funct_1 F (k7_finseq_1 (k7_finseq_1 G (k12_finseq_1 (u1_struct_0 A) D)) H)) (k1_funct_1 F (k7_finseq_1 (k7_finseq_1 G (k12_finseq_1 (u1_struct_0 A) E)) H))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ((m1_pythtrip A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C D) &  (A = (k1_enumset1 (k3_xcmplx_0 B (k6_xcmplx_0 (k1_pepin D) (k1_pepin C))) (k4_nat_1 B (k4_nat_1 (k4_nat_1 2 C) D)) (k4_nat_1 B (k2_nat_1 (k1_pepin D) (k1_pepin C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k4_qc_lang1 A) = (k2_zfmisc_1 (k1_tarski 5) (k1_qc_lang1 A))) ) ) ).
tt(d5_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang2 A B C) = (k13_qc_lang1 A (k15_qc_lang1 A B (k13_qc_lang1 A C)))) ) ) ) ) ) ) ).
tt(d5_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A B) = (k4_qc_lang3 A (k5_qc_lang1 A) B)) ) ) ) ) ).
tt(d5_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((m2_qc_lang4 D A B C) <=>  ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(d5_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  ((v7_quantal1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((k6_algstr_0 A B (k15_lattice3 A C)) = (k15_lattice3 A (a_3_0_quantal1 A B C))) ) ) ) ) ) ) ).
tt(d5_quaterni,ax, (k5_quaterni = (k3_quaterni k5_numbers k6_numbers 1 2 3 k6_numbers k6_numbers k6_numbers 1)) ).
tt(d5_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k1_quofield A)))) =>  ( (B = (k7_quofield A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_quofield A))) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  (C = (k6_quofield A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ((k6_radix_1 A B C D) = (k3_xcmplx_0 (k13_newton (k1_radix_1 B) (k7_nat_d A 1)) (k5_radix_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d5_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D k5_numbers))  =>  ( (D = (k5_radix_2 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 B)) =>  ((k1_recdef_1 D E) = (k4_radix_2 E A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k4_radix_3 B)))  =>  ( ((r2_hidden A (k2_finseq_1 C)) =>  ((k7_radix_3 A B C D) = (k1_funct_1 D A)) )  &  ( (A = k6_numbers)  =>  ((k7_radix_3 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ( ( (A = B)  =>  ((k5_radix_5 A B C) = 1) )  &  ( (~  (A = B) )  =>  ((k5_radix_5 A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d5_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( ((r1_xxreal_0 2 C) & (r2_hidden A (k2_finseq_1 (k2_xcmplx_0 B 2))))  =>  ( ((r1_xxreal_0 B A) =>  ((k5_radix_6 A B C D) = (k1_funct_1 D A)) )  &  ( (~ (r1_xxreal_0 B A))  =>  ((k5_radix_6 A B C D) = (k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 C)) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ((m1_vectsp_6 F A C) =>  ( (F = (k8_ranknull A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) F G) = (k2_rlvect_2 A (k5_ranknull A B D (k7_ranknull B C E (k6_domain_1 (u1_struct_0 C) G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_rcomp_1 A) <=> (v2_rcomp_1 (k3_subset_1 k1_numbers A))) ) ) ).
tt(d5_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k5_real_3 A))  <=>  ( ((k3_funct_2 k5_numbers k1_numbers B k6_numbers) = (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers))  &  ( ((k3_funct_2 k5_numbers k1_numbers B 1) = (k7_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) 1) (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers)) 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 2)) = (k7_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 C 2)) (k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 1))) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) )  =>  ( (B = (k5_real_lat A))  <=>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers B C D) (k3_funcsdom k1_numbers A k1_real_lat C D))) ) ) ) ) ) ) ) ) ).
tt(d5_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers)))) )  =>  ( (B = (k6_real_ns1 A))  <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k2_binop_1 (k1_euclid A) (k1_euclid A) k1_numbers B C D) = (k18_rvsum_1 (k14_rvsum_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(d5_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  ((k4_realset2 A) = (u2_algstr_0 A)) ) ) ).
tt(d5_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_rearran1 C) &  ((v2_rearran1 C) &  ((v3_rearran1 C (k1_zfmisc_1 B)) & (m2_finseq_1 C (k1_zfmisc_1 B))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k3_rearran1 A B C D) = (k14_rfunct_3 B (k16_rfunct_3 B (k15_rfunct_3 B C) (k3_rfinseq (k20_rfunct_3 A D A))))) ) ) ) ) ) ) ) ) ).
tt(d5_recdef_2,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k8_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (A = (k6_xtuple_0 C D E F))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(d5_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r5_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden (k4_tarski C D) A) & (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ) ) ) ) ).
tt(d5_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_rewrite1 A B) <=>  (! [C:$i] :  (~ (r2_hidden (k4_tarski B C) A)) ) ) ) ) ) ).
tt(d5_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r2_rewrite2 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) &  (? [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 A)) &  (? [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 A)) &  ( (C = (k1_flang_1 A (k1_flang_1 A E G) F))  &  ( (D = (k1_flang_1 A (k1_flang_1 A E H) F))  & (r1_rewrite2 A B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (? [C:$i] :  (? [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 B)) &  (A = (k4_tarski C D)) ) ) )  =>  ((k2_rewrite3 A B) = (k2_xtuple_0 A)) )  &  ( (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 B)) =>  (~  (A = (k4_tarski C D)) ) ) ) )  =>  ((k2_rewrite3 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d5_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  ( (B = (k5_rfinseq2 A))  <=> (r2_classes1 A B)) ) ) ) ) ).
tt(d5_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_rfunct_2 A) <=>  ((v7_valued_0 A) | (v8_valued_0 A)) ) ) ) ).
tt(d5_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  ((k14_rfunct_3 A B) = (k1_finsop_1 (k3_rfunct_3 A k1_numbers) B (k13_rfunct_3 A))) ) ) ) ) ).
tt(d5_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r5_rfunct_4 A B) <=>  ((r2_hidden B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 D (k18_complex1 (k10_binop_2 E B))))  & (r1_xxreal_0 C (k10_binop_2 (k1_seq_1 A B) (k1_seq_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k4_rinfsup1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( (D = (a_2_0_rinfsup1 A C))  =>  ((k1_seq_1 B C) = (k4_seq_4 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v3_rinfsup2 A) <=>  ((v2_rinfsup2 A) & (v1_rinfsup2 A)) ) ) ) ).
tt(d5_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (C = (k1_ring_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E) C) <=> (r2_hidden (k5_algstr_0 A D E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((v3_ringcat1 A) <=> (v1_ringcat1 (k3_ringcat1 A) (u1_ringcat1 A) (u2_ringcat1 A))) ) ) ).
tt(d5_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_rlaffin1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_rlaffin1 C A)) ) ) ) ) ) ) ) ).
tt(d5_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k3_rlsub_1 A B C) = (a_3_1_rlsub_1 A B C)) ) ) ) ) ) ) ).
tt(d5_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((m1_rlsub_2 C A B) <=> (r1_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(d5_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_rltopsp1 B A) <=>  (B = (k2_rltopsp1 A B)) ) ) ) ) ) ).
tt(d5_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v5_rlvect_1 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_rlvect_1 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k1_rlvect_1 A C B) (k1_rlvect_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(d5_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ( (B = (k4_rlvect_2 A))  <=>  ((k3_rlvect_2 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d5_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k3_rmod_2 A B C D) = (a_4_1_rmod_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d5_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r1_rmod_3 A B D E) =>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) =>  ( (F = (k4_rmod_3 A B C D E))  <=>  ( (C = (k3_rlvect_1 B (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F) (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)))  &  ((r1_struct_0 D (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)) & (r1_struct_0 E (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((m2_rmod_4 D A B C) <=> (r1_tarski (k2_rmod_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(d5_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v5_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A B (k3_robbins1 A C))))) = B) ) ) ) ) ) ) ) ).
tt(d5_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_robbins4 A B C) <=> (r3_lattices A B (k3_robbins1 A C))) ) ) ) ) ) ) ).
tt(d5_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A B) = (a_2_1_roughs_1 A B)) ) ) ) ) ).
tt(d5_rsspace3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_rsspace3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k4_rsspace3 A (k1_normsp_1 A B E) (k1_normsp_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_lopban_1 A B)))) =>  ( (C = (k4_rsspace4 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) &  ((v1_rsspace4 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_rsspace) k1_rsspace) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_rsspace) k1_rsspace)))) )  =>  ( (A = k5_rsspace)  <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B k1_numbers) & (r2_hidden C k1_rsspace))  =>  ((k1_binop_1 A B C) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace C) (k3_rsspace B))) ) ) ) ) ) ) ).
tt(d5_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_rusub_1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k3_rusub_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d5_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((m1_rusub_2 C A B) <=> (r1_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(d5_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((k3_rusub_4 A B) = (u1_struct_0 B)) ) ) ) ) ).
tt(d5_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (k4_rusub_5 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  & (r1_tarski (k4_bhsp_2 A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k6_rvsum_1 A) = (k3_relat_1 A k31_binop_2)) ) ) ).
tt(d5_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k9_rvsum_2 A B) = (k3_relat_1 A (k7_seq_4 B))) ) ) ) ) ).
tt(d5_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k7_scm_comp A B) = (k6_trees_4 (k4_tarski k6_numbers 2) A B)) ) ) ) ) ).
tt(d5_scmfsa_1,ax, (k5_scmfsa_1 = (k7_afinsq_1 k5_numbers k4_numbers (k3_finseq_2 k4_numbers))) ).
tt(d5_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_scmfsa_2)) =>  ((m1_scmfsa_2 A) <=> (r2_hidden A k3_scmfsa_1)) ) ) ).
tt(d5_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_scmfsa6a A B) = (k3_scmfsa6a (k11_compos_1 k1_scmfsa_2 A) B)) ) ) ) ) ).
tt(d5_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) & (v1_funct_1 A)) ) )  =>  ((v1_scmfsa7b A) <=>  (~ (r4_scmfsa7b A (k4_scmfsa_2 k6_numbers))) ) ) ) ).
tt(d5_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_scmfsa8b A B C D) = (k4_scmfsa6a (k8_scmfsa_2 A B) (k2_scmfsa8b A C D))) ) ) ) ) ) ) ) ) ).
tt(d5_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r4_scmfsa9a A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) (k2_nat_1 F 1)))) &  (~ (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) )  =>  ( (E = (k5_scmfsa_9 A B C D))  <=>  ((r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E k6_numbers) A) &  (! [F:$i] :  ((v7_ordinal1 F) => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E (k1_nat_1 F 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 D (k2_scmfsa_9 C B)) (k1_funct_4 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F) (k7_memstr_0 3 k1_scmfsa_2 k6_numbers)) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 D (k2_scmfsa_9 C B)) B) (k1_funct_4 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) E F) (k7_memstr_0 3 k1_scmfsa_2 k6_numbers))) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 13)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_scmfsa_i) =>  ( (B = (k5_scmfsa_i A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) &  (? [E:$i] :  ((m1_subset_1 E k2_scm_inst) &  ( ((k11_finseq_1 C D E) = (k2_xtuple_0 A))  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 k5_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k5_numbers))))) )  =>  ( (B = (k8_scmfsa_m A))  <=>  ( ((k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) B k6_numbers) = (a_1_2_scmfsa_m A))  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k5_numbers)))  =>  ( ((k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) B C) = D)  =>  ((k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) B (k2_nat_1 C 1)) = (k7_subset_1 k5_numbers D (k6_domain_1 k5_numbers (k6_seq_4 D)))) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (v1_finset_1 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) B C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r2_scm_halt A B C) <=> (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_scmfsa_m B))) ) ) ) ) ) ) ).
tt(d5_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C (k7_card_1 9)) &  (A = (k3_xtuple_0 C (k12_finseq_1 k5_numbers B) k1_xboole_0)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k6_scm_inst A))  <=>  (? [C:$i] :  ((m2_finseq_1 C k5_numbers) &  ( (C = (k5_xtuple_0 A))  &  (B = (k7_partfun1 k5_numbers C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d5_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  ((k4_scmpds_2 A) = (k3_xtuple_0 1 k1_xboole_0 (k9_finseq_1 A))) ) ) ).
tt(d5_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((k6_scmpds_4 A B C) = (k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 C (k10_compos_1 k1_scmpds_2 A)) B)) ) ) ) ) ) ) ).
tt(d5_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k3_scmpds_6 A B C D) = (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) C) (k1_scmpds_6 (k2_nat_1 (k5_card_1 D) 1))) D)) ) ) ) ) ) ) ) ) ).
tt(d5_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((m2_subset_1 D k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k2_scmpds_i B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k6_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 2)) ) ) ) ) ) ) ) ) ) ).
tt(d5_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_scmring1 A B C) = (k1_funct_4 B (k16_funcop_1 k5_numbers C))) ) ) ) ) ) ) ).
tt(d5_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k5_scmring2 A B C) = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(d5_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E (k12_finseq_1 k5_numbers C) (k12_finseq_1 k2_scm_inst D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k5_scmringi A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( ((k12_finseq_1 k5_numbers D) = (k5_xtuple_0 B))  &  (C = (k7_partfun1 k5_numbers (k12_finseq_1 k5_numbers D) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (E = (k1_semi_af1 A B C D))  <=> (r3_semi_af1 A D B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k1_numbers)))) )  =>  ( (A = k8_seq_4)  <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k1_numbers A B) = (k17_complex1 B)) ) ) ) ) ) ).
tt(d5_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (D = (k6_seqfunc A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers D E) (k3_valued_1 A k1_numbers k1_numbers (k1_seqfunc A k1_numbers B E) (k1_seqfunc A k1_numbers C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seqm_3 A) <=>  ((v7_valued_0 A) | (v8_valued_0 A)) ) ) ) ).
tt(d5_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_series_1 A B) = (k1_seq_1 (k3_series_1 A) B)) ) ) ) ) ).
tt(d5_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k3_setfam_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  (? [F:$i] :  ((r2_hidden E A) &  ((r2_hidden F B) &  (D = (k3_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k4_kurato_0 A B) = (k3_prob_1 A (k4_setlim_1 A B))) ) ) ) ).
tt(d5_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k5_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k9_subset_1 A C (k8_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k5_finsub_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  ((k10_setwiseo A B C D) = (k7_setwiseo A (k5_finsub_1 B) (k9_setwiseo B) C D)) ) ) ) ) ) ) ) ).
tt(d5_sfmastr1,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_sfmastr1 A B) = (k5_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k9_scmfsa_m 2 (k2_sf_mastr (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))) A) (k8_scmfsa_2 B B)) (k6_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m A B)) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k9_scmfsa_m 1 (k2_sf_mastr (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))) (k9_scmfsa_m 2 (k2_sf_mastr (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))))) (k2_scmfsa8c (k9_scmfsa_m 1 (k2_sf_mastr (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))) (k4_scmfsa6a (k7_scmfsa_2 B (k9_scmfsa_m 1 (k5_scmfsa_m A B))) (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B)))))) (k6_scmfsa_2 A (k9_scmfsa_m 2 (k2_sf_mastr (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B)))))))) ) ) ) ) ).
tt(d5_sfmastr2,ax, (! [A:$i] :  ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  =>  ((k4_sfmastr2 A) = (k2_sfmastr2 A (k5_scmfsa6a (k1_scmfsa_9 A (k11_compos_1 k1_scmfsa_2 (k6_scmfsa_2 A A))) (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) ) ) ).
tt(d5_sfmastr3,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k4_sfmastr3 A B C) = (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m B C)) B A) (k14_scmfsa_2 (k9_scmfsa_m 2 (k5_scmfsa_m B C)) C A)) (k15_scmfsa_2 (k9_scmfsa_m 2 (k5_scmfsa_m B C)) B A)) (k15_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m B C)) C A))) ) ) ) ) ) ) ).
tt(d5_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v3_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A B (k2_lattices A C D)) = (k2_lattices A (k1_lattices A B C) (k1_lattices A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d5_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_simplex0 A) <=> (v1_finset_1 (k4_simplex0 A))) ) ) ).
tt(d5_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) =>  ((k4_simplex1 A B) = (k10_simplex0 (u1_struct_0 A) B (k2_rlaffin2 A))) ) ) ) ) ) ).
tt(d5_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k5_sincos10 A) = (k1_seq_1 k1_sincos10 A)) ) ) ).
tt(d5_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k7_sin_cos2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 A B) = (k10_real_1 (k9_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k24_sin_cos (k7_binop_2 B))) (k7_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k24_sin_cos (k7_binop_2 B))))) ) ) ) ) ) ).
tt(d5_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_sin_cos7 A) = (k11_binop_2 (k18_binop_2 1 2) (k6_power k8_power (k12_binop_2 (k9_binop_2 A 1) (k10_binop_2 A 1))))) ) ) ).
tt(d5_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k4_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k6_real_1 (k1_newton A C) (k3_newton C))) ) ) ) ) ) ) ) ).
tt(d5_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r2_sppol_1 A B C) <=>  ((v3_sppol_1 A) &  ((v4_topreal1 A) &  ((v3_sppol_1 B) &  ((v4_topreal1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))  &  ((v3_sppol_1 (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 2))) &  ((v3_sppol_1 (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k9_real_1 (k3_finseq_1 A) 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k9_real_1 (k3_finseq_1 B) 1)))) &  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) )  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k7_domain_1 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))  &  (C = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_stacks_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  & (l1_stacks_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k6_stacks_1 A B) = (k3_funct_2 (u4_struct_0 A) (u1_struct_0 A) (u4_stacks_1 A) B)) ) ) ) ) ).
tt(d5_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((r1_struct_0 A B) <=> (r2_hidden B (u1_struct_0 A))) ) ) ) ).
tt(d5_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) =>  ((k9_sublemma A B C) = (k24_substut1 A B C)) ) ) ) ) ) ) ) ).
tt(d5_subset_1,ax, (! [A:$i] :  ((k10_subset_1 A) = (o_1_0_subset_1 A)) ) ).
tt(d5_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((k5_substut1 A B C) = (k3_substut1 A (k4_substut1 A B) C)) ) ) ) ) ) ) ).
tt(d5_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A B C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((m1_substut2 D A B C) <=>  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = C)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k9_qc_lang1 A)) =>  (~  ( ((k1_funct_1 D E) = F)  &  ( ((k1_funct_1 D (k2_nat_1 E 1)) = G)  & (r1_qc_lang2 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_supinf_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k7_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_supinf_2 C A B) <=>  (~ (r1_xxreal_0 k1_supinf_1 (k10_supinf_2 k7_numbers A B C))) ) ) ) ) ) ) ).
tt(d5_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k3_t_0topsp A) = (k11_borsuk_1 A (k2_t_0topsp A))) ) ) ).
tt(d5_tarski,ax, (! [A:$i] :  (! [B:$i] :  ((k4_tarski A B) = (k2_tarski (k2_tarski A B) (k1_tarski A))) ) ) ).
tt(d5_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_partit1 A))) =>  ( (C = (k2_taxonom1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ( (~ (v3_xxreal_0 E))  & (v1_xreal_0 E))  &  (? [F:$i] :  ( ((v1_partfun1 F A) &  ((v3_relat_2 F) &  ((v8_relat_2 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((r2_relset_1 A A F (k13_lang1 A (k1_taxonom1 A B E))) &  ((k8_eqrel_1 A F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_taxonom2,ax, (! [A:$i] :  ((v4_taxonom2 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (B = C)  | (r1_xboole_0 B C)) ) ) ) ) ) ).
tt(d5_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  ( (C = (k5_taylor_1 A B))  <=>  ((r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C k6_numbers) (k2_partfun1 k1_numbers k1_numbers A B)) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C (k1_nat_1 D 1)) (k2_fdiff_1 (k1_seqfunc k1_numbers k1_numbers C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d5_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v4_tbsp_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_tbsp_1 B A) => (v2_tbsp_1 B A)) ) ) ) ) ) ).
tt(d5_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v2_tdgroup A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) =>  (B = C) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A D E F G))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r2_analoaf A B C D E)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C E F) & (r2_analoaf A B D E G))  => (r2_analoaf A C D F G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_analoaf A B D D C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C C D) & (r2_analoaf A B E E D))  =>  (C = E) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k5_tdlat_1 A) = (a_1_1_tdlat_1 A)) ) ) ).
tt(d5_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v5_tdlat_3 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  => (v4_tdlat_3 B)) ) ) ) ) ).
tt(d5_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r1_termord A B D C) =>  ((k2_termord A B C D) = C) )  &  ( (~ (r1_termord A B D C))  =>  ((k2_termord A B C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_tdlat_3 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v2_tops_1 B A)) ) ) ) ) ) ).
tt(d5_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_2 B A) <=>  ((v2_tex_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_tex_2 C A) & (r1_tarski B C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d5_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tex_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_tex_4 C A)) ) ) ) ) ) ) ) ).
tt(d5_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  (! [D:$i] :  ((m1_pre_topc D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ((m1_pre_topc D C) =>  ((k3_tmap_1 A B C D E) = (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) E (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (l3_algstr_0 C))  =>  ( (C = (k5_topalg_1 A B))  <=>  ( ((u1_struct_0 C) = (k8_eqrel_1 (k2_topalg_1 A B) (k4_topalg_1 A B)))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_borsuk_2 F A B B) &  (? [G:$i] :  ((m1_borsuk_2 G A B B) &  ( (D = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) F))  &  ( (E = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) G))  &  ((k5_binop_1 (u1_struct_0 C) (u2_algstr_0 C) D E) = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) (k1_borsuk_2 A B B B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topalg_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb)))))) )  =>  ( (A = k7_topalg_5)  <=>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_funct_1 A B) = (k6_eqrel_1 (k2_topalg_1 (k8_toprealb 2) k9_toprealb) (k2_topalg_1 (k8_toprealb 2) k9_toprealb) (k4_topalg_1 (k8_toprealb 2) k9_toprealb) (k6_topalg_5 B))) ) ) ) ) ) ).
tt(d5_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k1_topalg_6 A) = (a_1_0_topalg_6 A)) ) ) ).
tt(d5_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_topdim_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k2_topdim_1 A B))  <=>  ((r2_hidden B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) (k3_real_1 C 1))) &  (~ (r2_hidden B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_topgen_1 B A) <=> (r2_topgen_1 A (k2_struct_0 A) B)) ) ) ) ) ).
tt(d5_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_pre_topc C) & (l1_pre_topc C))  =>  ( (C = (k5_topgen_2 A B))  <=>  ( ((u1_struct_0 C) = A)  &  ((u1_pre_topc C) = (k2_xboole_0 (a_2_0_topgen_2 A B) (a_1_1_topgen_2 A))) ) ) ) ) ) ) ).
tt(d5_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k4_topgen_3 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D A) &  ((k8_nat_1 k1_numbers C D) = (k1_newton B D)) )  |  ( (~ (r2_hidden D A))  &  ((k8_nat_1 k1_numbers C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v4_topgen_4 B A) <=>  (! [C:$i] :  ( ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_tarski C B) => (r2_hidden (k6_setfam_1 A C) B)) ) ) ) ) ) ) ).
tt(d5_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr))))) )  =>  ( (C = (k4_topgen_5 A B))  <=>  ( ((k1_funct_1 C (k19_euclid A k6_numbers)) = k6_numbers)  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_xreal_0 E) &  (~ (v3_xxreal_0 E)) )  =>  ( (~  ( (~  ( (D = A)  &  (E = k6_numbers) ) )  &  ( (~ (r2_hidden (k19_euclid D E) (k1_topreal9 2 (k19_euclid A B) B)))  &  (~  ((k1_funct_1 C (k19_euclid D E)) = 1) ) ) ) )  &  ((r2_hidden (k19_euclid D E) (k1_topreal9 2 (k19_euclid A B) B)) =>  ((k1_funct_1 C (k19_euclid D E)) = (k10_real_1 (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) (k19_euclid A k6_numbers) (k19_euclid D E)))) (k8_real_1 (k8_real_1 2 B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (l3_algstr_0 B))  =>  ( (B = (k5_topgrp_1 A))  <=>  (! [C:$i] :  ( ((r2_hidden C (u1_struct_0 B)) => (m3_topgrp_1 C A))  &  ( ((m3_topgrp_1 C A) => (r2_hidden C (u1_struct_0 B)))  &  (! [D:$i] :  ((m3_topgrp_1 D A) =>  (! [E:$i] :  ((m3_topgrp_1 E A) =>  ((k1_binop_1 (u2_algstr_0 B) D E) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topmetr,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v2_topmetr A) <=> (v1_compts_1 (k3_pcomps_1 A))) ) ) ).
tt(d5_topreal1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_topreal1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k1_nat_1 B 1) (k3_finseq_1 A)) &  ( (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_nat_1 B 1)))) )  &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_nat_1 B 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_topreal9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k4_topreal9 A B C) = (a_3_3_topreal9 A B C)) ) ) ) ) ) ) ).
tt(d5_toprealb,ax, (! [A:$i] :  ((m1_pre_topc A (k15_euclid 2)) =>  ((v1_toprealb A) <=>  ((v1_topreal2 (u1_struct_0 A)) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ).
tt(d5_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) (u1_struct_0 (k15_euclid A)))))) )  =>  ( (B = (k16_toprealc A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k6_toprealc (k15_euclid A) (k15_euclid A) (k15_euclid A) B C D) = (k11_toprealc A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_toprns_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k4_toprns_1 A B C) = (k1_toprns_1 A B (k3_toprns_1 A C))) ) ) ) ) ) ) ).
tt(d5_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) <=> (v2_tops_1 (k2_pre_topc A B) A)) ) ) ) ) ).
tt(d5_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  ((v5_pre_topc C A B) & (v5_pre_topc (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=>  ((k2_pre_topc A (k1_tops_1 A B)) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(d5_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_transgeo A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A F G D E))  =>  ( (F = G)  | (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B B C D)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (B = (k3_trees_1 A))  <=>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) <=>  ((r2_hidden C A) &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D A) & (r2_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((k1_trees_2 A B) = (a_2_1_trees_2 A B)) ) ) ) ) ).
tt(d5_trees_3,ax, (! [A:$i] :  ((v3_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) ) ) ) ).
tt(d5_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((k5_trees_4 A B) = (k4_trees_4 A (k9_finseq_1 B))) ) ) ) ).
tt(d5_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (! [C:$i] :  ( ((v2_funct_1 C) & (m2_finseq_1 C A))  =>  ( (C = (k1_trees_9 A B))  <=>  ( ((k3_finseq_1 C) = (k5_card_1 (k1_trees_2 A B)))  &  ( ((k2_relset_1 A C) = (k1_trees_2 A B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  =>  ((k1_funct_1 C (k2_nat_1 D 1)) = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=> (r1_connsp_1 A (k7_subset_1 (u1_struct_0 A) B C) (k7_subset_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ).
tt(d5_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_2 B A) <=>  ((v1_tsp_1 B A) &  ((k3_tex_4 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(d5_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ((k8_turing_1 A B) = (k1_funct_1 (u3_turing_1 A) (k4_tarski (k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) (k1_funct_1 (k3_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) (k7_turing_1 A B))))) ) ) ) ) ).
tt(d5_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k6_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k10_margrel1 (k9_margrel1 B) C))) ) ) ) ) ) ) ) ).
tt(d5_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ((r2_unialg_2 A B C) =>  ((k2_unialg_2 A B C) = (k2_partfun1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) C (k4_finseq_2 (k19_margrel1 C) B))) ) ) ) ) ) ) ) ).
tt(d5_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_unialg_3 A))))  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  ( (C = (k4_unialg_3 A B))  <=>  ((u1_struct_0 C) = (k6_setfam_1 (u1_struct_0 A) (k7_relset_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)) (k3_unialg_3 A) B))) ) ) ) ) ) ) ) ).
tt(d5_uniroots,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ( (B = (k5_uniroots A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k1_complfld)))) )  &  ( (C = (a_1_3_uniroots A))  & (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) B (k10_uproots k1_complfld (k2_uproots (u1_struct_0 k1_complfld) C 1)))) ) ) ) ) ) ) ) ).
tt(d5_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_uproots B A) <=>  (~  (B = (k9_polynom3 A)) ) ) ) ) ) ) ).
tt(d5_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k6_urysohn1 A B))  <=>  (B = (k6_real_1 C (k2_newton 2 A))) ) ) ) ) ) ) ) ).
tt(d5_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 k7_numbers)) =>  ( (F = (k5_urysohn3 A B C D E))  <=>  (! [G:$i] :  ((r2_hidden G F) <=>  ((r2_hidden G k2_urysohn1) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (H = G)  & (r2_hidden E (k1_funct_1 (k3_urysohn3 A B C D) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k24_valued_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k3_xcmplx_0 B (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectmetr A))  =>  ((v5_vectmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_metric_1 A (k1_rlvect_1 A C B) (k1_rlvect_1 A D B)) = (k8_real_1 (k18_complex1 B) (k2_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (k2_vectsp10 A B C)) (k2_vectsp10 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k2_vectsp10 A B C)) (k2_vectsp10 A B C))))) )  =>  ( (D = (k5_vectsp10 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (u1_struct_0 B)) (k2_vectsp10 A B C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (F = (k3_vectsp_4 A B G C))  =>  ((k2_binop_1 (u1_struct_0 A) (k2_vectsp10 A B C) (k2_vectsp10 A B C) D E F) = (k3_vectsp_4 A B (k4_vectsp_1 A B E G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (D = (k2_vectsp11 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_vectsp11 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp_1,ax, (k2_vectsp_1 = (g6_algstr_0 k1_numbers k33_binop_2 k35_binop_2 1 k6_numbers)) ).
tt(d5_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k3_vectsp_2 A) = (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) ) ) ).
tt(d5_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k3_vectsp_4 A B C D) = (a_4_1_vectsp_4 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((m1_vectsp_5 D A B C) <=> (r1_vectsp_5 A B D C)) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( (E = (k3_vectsp_6 A B C D))  <=>  ( ((k3_finseq_1 E) = (k3_finseq_1 C))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D (k7_partfun1 (u1_struct_0 B) C F)) (k7_partfun1 (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_vectsp_8 A B))))  =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (D = (k5_vectsp_8 A B C))  <=>  ((u1_struct_0 D) = (k6_setfam_1 (u1_struct_0 B) (k7_relset_1 (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B)) (k4_vectsp_8 A B) C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( (D = (k5_vfunct_1 A B C))  <=>  ( ((k1_relset_1 A D) = (k1_relset_1 A C))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  ((k7_partfun1 (u1_struct_0 B) D E) = (k4_algstr_0 B (k7_partfun1 (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ( (F = (k1_funct_1 C D))  &  (G = (k1_funct_1 C E)) )  => (r1_orders_2 B G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k6_waybel10 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k2_yellow_0 A (k8_subset_1 (u1_struct_0 A) (k6_waybel_0 A D) (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  ((v4_waybel11 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=> (v13_waybel_0 B A)) ) ) ) ) ) ).
tt(d5_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel12 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (v2_waybel12 C A)) ) ) ) ) ) ) ) ).
tt(d5_waybel18,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_waybel18 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v5_pre_topc C B A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (~  ((m1_pre_topc B D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc E D A) &  ((k2_partfun1 (u1_struct_0 D) (u1_struct_0 A) E (u1_struct_0 B)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((r2_waybel_1 A B) <=>  ((r1_yellow_0 A B) & (r2_hidden (k1_yellow_0 A B) B)) ) ) ) ) ).
tt(d5_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  (! [C:$i] :  ( ((v1_orders_2 C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) &  ((v3_waybel_3 C) & (l1_orders_2 C)) ) ) ) ) ) ) )  =>  ( (C = (k5_waybel20 A B))  <=>  ( ((u1_struct_0 C) = (k8_eqrel_1 (u1_struct_0 A) (k2_waybel20 A B)))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r3_orders_2 C D E) <=> (r3_orders_2 A (k2_yellow_0 A D) (k2_yellow_0 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel23,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k2_waybel23 A) = (k1_setfam_1 (a_1_0_waybel23 A))) ) ) ).
tt(d5_waybel26,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k6_waybel26 A B))  <=>  ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k9_relat_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 E A B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ((v22_waybel_0 F C D) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k2_waybel27 B C)) (u1_struct_0 (k2_waybel27 A D))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel27 B C)) (u1_struct_0 (k2_waybel27 A D)))))) )  =>  ( (G = (k4_waybel27 A B C D E F))  <=>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 B) (u1_struct_0 C)) &  ((v22_waybel_0 H B C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((k1_funct_1 G H) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 D) E (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) H F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) )  =>  ( (B = (k5_waybel_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_binop_1 B C D) = (k10_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B A) => (v1_xboole_0 B)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v6_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) &  ((v2_yellow21 B) & (l2_altcat_1 B)) ) ) ) ) )  =>  ( (B = (k5_waybel34 A))  <=>  ( (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=>  ((v1_orders_2 C) &  ((v3_lattice3 C) & (r2_hidden (u1_struct_0 C) A)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D))) &  ((v5_orders_3 E (k3_yellow21 B C) (k3_yellow21 B D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow21 B C)) (u1_struct_0 (k3_yellow21 B D)))))) ) )  =>  ((r2_hidden E (k1_altcat_1 B C D)) <=> (v18_waybel_0 E (k3_yellow21 B C) (k3_yellow21 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel35,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ( (D = (k2_waybel35 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((m1_waybel35 E A B) & (r1_tarski C E)) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v2_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (k1_waybel_3 A B))) ) ) ) ) ) ).
tt(d5_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v3_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C E) B) & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E) B))  => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k10_lattice3 A C D) E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A C) B)) &  (C = (k2_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A C) B))) ) ) ) ) ) ) ) ) ).
tt(d5_waybel_7,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_waybel_7 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) & (r2_hidden C D))  => (r2_hidden D B)) ) ) ) ) ) ) ) ).
tt(d5_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v3_waybel_8 A) <=>  ((v2_waybel_8 A) & (v5_yellow_0 (k1_waybel_8 A) A)) ) ) ) ).
tt(d5_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_waybel_0 B A) & (l1_waybel_0 B A))  =>  ( (B = (k2_waybel_9 A))  <=>  ( ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))  &  ((u1_waybel_0 A B) = (k3_struct_0 A)) ) ) ) ) ) ) ).
tt(d5_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v36_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  ( (C = (k5_weddwitt A B))  <=>  ( ((u1_struct_0 C) = (a_2_3_weddwitt A B))  &  ( ((u1_algstr_0 C) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 C)))  &  ( ((u2_algstr_0 C) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 C)))  &  ( ((k4_struct_0 C) = (k4_struct_0 A))  &  ((k5_struct_0 C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (C = (k5_weierstr A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d5_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_wellfnd1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k1_binop_1 C E (k5_relat_1 D (k1_wellord1 (u1_orders_2 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_wellord1 A B) <=>  ((r1_relat_2 A B) &  ((r8_relat_2 A B) &  ((r4_relat_2 A B) &  ((r6_relat_2 A B) & (r1_wellord1 A B)) ) ) ) ) ) ) ) ).
tt(d5_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_xboole_0 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D A) &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ).
tt(d5_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A B) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(d5_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( (C = (k3_xcmplx_0 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (A = (k5_arytm_0 D E))  &  ( (B = (k5_arytm_0 F G))  &  (C = (k5_arytm_0 (k1_arytm_0 (k2_arytm_0 D F) (k3_arytm_0 (k2_arytm_0 E G))) (k1_arytm_0 (k2_arytm_0 D G) (k2_arytm_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ( ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2))  =>  ((r1_xxreal_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = C)  &  ( (B = D)  & (r1_arytm_2 C D)) ) ) ) ) ) ) )  &  ( ( ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)))  =>  ((r1_xxreal_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = (k4_tarski k6_numbers C))  &  ( (B = (k4_tarski k6_numbers D))  & (r1_arytm_2 D C)) ) ) ) ) ) ) )  &  (~  ( (~  ((r2_hidden A k2_arytm_2) & (r2_hidden B k2_arytm_2)) )  &  ( (~  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) & (r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) )  &  (~  ((r1_xxreal_0 A B) <=>  (~  ( (~  ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) )  &  ( (~  (A = k2_xxreal_0) )  &  (~  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v1_xxreal_2 A) <=> (r2_hidden (k2_xxreal_2 A) A)) ) ) ).
tt(d5_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (C = (k4_xxreal_3 A B))  <=>  (? [D:$i] :  ((v1_xcmplx_0 D) &  (? [E:$i] :  ((v1_xcmplx_0 E) &  ( (A = D)  &  ( (B = E)  &  (C = (k3_xcmplx_0 D E)) ) ) ) ) ) ) ) )  &  ( (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( ( ((v2_xxreal_0 A) & (v2_xxreal_0 B))  |  ((v3_xxreal_0 A) & (v3_xxreal_0 B)) )  &  (~  ( (C = (k4_xxreal_3 A B))  <=>  (C = k1_xxreal_0) ) ) ) ) )  &  ( (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( ( ((v2_xxreal_0 A) & (v3_xxreal_0 B))  |  ((v3_xxreal_0 A) & (v2_xxreal_0 B)) )  &  (~  ( (C = (k4_xxreal_3 A B))  <=>  (C = k2_xxreal_0) ) ) ) ) )  &  (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( ((v2_xxreal_0 A) & (v2_xxreal_0 B))  |  ((v3_xxreal_0 A) & (v3_xxreal_0 B)) ) ) )  &  ( (~  ( (~  ((v1_xreal_0 A) & (v1_xreal_0 B)) )  &  ( ((v2_xxreal_0 A) & (v3_xxreal_0 B))  |  ((v3_xxreal_0 A) & (v2_xxreal_0 B)) ) ) )  &  (~  ( (C = (k4_xxreal_3 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_yellow_0 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (r2_lattice3 A (u1_struct_0 A) B)) ) ) ) ) ).
tt(d5_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_waybel_9 A)) )  =>  ((v2_yellow13 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) (u1_struct_0 A))))) )  =>  ((r1_funct_2 (u1_struct_0 (k2_borsuk_1 A A)) (u1_struct_0 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) B (k4_waybel_2 A)) => (v5_pre_topc B (k2_borsuk_1 A A) A)) ) ) ) ) ) ).
tt(d5_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ( ((v9_functor0 C A B) &  ((v16_functor0 C A B) & (m2_functor0 C A B)) )  =>  ( (C = (k2_yellow18 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_functor0 A B C D) = D) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((k8_functor0 A B C D E F) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v1_yellow19 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_waybel_0 A B C) | (r1_waybel_0 A B (k3_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(d5_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_orders_2 B) =>  ((k6_yellow_1 A B) = (k5_yellow_1 A (k7_funcop_1 A B))) ) ) ) ).
tt(d5_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v11_altcat_1 E) &  ((v12_altcat_1 E) & (l2_altcat_1 E)) ) ) )  =>  ((r3_yellow20 A B C D E) <=>  ( ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) )  &  ( ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) )  &  (? [F:$i] :  ( ((v16_functor0 F D E) & (m2_functor0 F D E))  &  ((v21_functor0 F D E) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( (G = H)  =>  ((k3_functor0 D E F G) = (k3_functor0 A B C H)) ) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ( (G = I)  &  (H = J) )  =>  ( ((k1_altcat_1 D G H) = k1_xboole_0)  |  (! [K:$i] :  ((m1_subset_1 K (k1_altcat_1 D G H)) =>  (! [L:$i] :  ((m1_subset_1 L (k1_altcat_1 A I J)) =>  ( (K = L)  =>  ((k8_functor0 D E F G H K) = (k1_funct_1 (k4_functor0 A B C I J) L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k4_yellow_2 A B) = (k1_yellow_0 A (k10_xtuple_0 B))) ) ) ) ) ).
tt(d5_yellow_6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v6_waybel_0 D B) & (l1_waybel_0 D B))  =>  ( (D = (k3_yellow_6 A B C))  <=>  ( ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))  & (r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 B D) (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 D) C))) ) ) ) ) ) ) ) ) ) ).
tt(d5_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_yellow_8 A) <=>  (! [B:$i] :  ( ((v3_yellow_8 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_yellow_8 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_yellow_8 A B D) =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((m2_yellow_9 B A) <=>  ( ((u1_struct_0 A) = (u1_struct_0 B))  & (r1_tarski (u1_pre_topc A) (u1_pre_topc B))) ) ) ) ) ) ).
tt(d5_zf_fund1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (C = (k5_zf_fund1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  &  ( (D = (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 E) (k4_zf_fund1 (k2_zf_model A))))  & (r2_hidden E (k5_zf_model A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d5_zf_lang,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k6_zf_lang A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 2) A)) ) ) ).
tt(d5_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_zfmisc_1 A B C) <=>  ( (~  (A = B) )  &  ( (~  (A = C) )  &  (~  (B = C) ) ) ) ) ) ) ) ).
tt(d5_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_zf_model A B) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  => (r1_zf_model A C B)) ) ) ) ) ) ) ).
tt(d5_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  ((v5_zmodul01 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_zmodul01 A B 1) = B) ) ) ) ) ) ).
tt(d60_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m4_abcmiz_1 C A (k28_abcmiz_1 A)) =>  ( (C = (k55_abcmiz_1 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D k2_abcmiz_1) =>  ( ((r2_hidden D (k1_relset_1 k2_abcmiz_1 B)) =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k35_abcmiz_1 D A)) = (k1_funct_1 B D)) )  &  ( (~ (r2_hidden D (k1_relset_1 k2_abcmiz_1 B)))  =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k35_abcmiz_1 D A)) = (k35_abcmiz_1 D A)) ) ) ) )  &  ( (! [D:$i] :  ( ((v2_abcmiz_1 D A) & (m1_subset_1 D (u4_struct_0 A)))  =>  (! [E:$i] :  ((m1_trees_4 E (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (! [F:$i] :  ((m1_trees_4 F (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  ( ( ((k3_finseq_1 E) = (k3_finseq_1 (k1_msualg_1 A D)))  &  (F = (k11_lang1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) E C)) )  =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k36_abcmiz_1 A D E)) = (k36_abcmiz_1 A D F)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_abcmiz_1 D A (k13_abcmiz_1 A)) =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k30_abcmiz_1 A (k32_abcmiz_1 A) D)) = (k30_abcmiz_1 A (k32_abcmiz_1 A) (k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C D))) ) )  &  (! [D:$i] :  ((m1_abcmiz_1 D A (k13_abcmiz_1 A)) =>  (! [E:$i] :  ((m1_abcmiz_1 E A (k12_abcmiz_1 A)) =>  ((k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k31_abcmiz_1 A (k33_abcmiz_1 A) D E)) = (k31_abcmiz_1 A (k33_abcmiz_1 A) (k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C D) (k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d60_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  ((k66_aofa_i00 A B C D E) = (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D C (k36_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k29_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E 1) (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d60_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k37_fomodel4 A) = (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k13_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A) (k23_fomodel4 A) (k24_fomodel4 A) (k25_fomodel4 A) (k26_fomodel4 A) (k27_fomodel4 A) (k28_fomodel4 A) (k29_fomodel4 A)) (k9_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k30_fomodel4 A) (k31_fomodel4 A) (k32_fomodel4 A) (k33_fomodel4 A)))) ) ) ).
tt(d60_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k18_modelc_1 (u3_modelc_1 (k48_modelc_1 A B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 A B C)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ((v1_modelc_1 F) & (m2_finseq_1 F k5_numbers))  =>  ((r4_modelc_1 A B C D E F) <=> (r3_modelc_1 A B C E (k24_modelc_1 (k48_modelc_1 A B C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d60_modelc_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k30_modelc_1 (k25_modelc_2 k43_modelc_2))) =>  ( (B = (k45_modelc_2 A))  <=>  (! [C:$i] :  ((r2_hidden C (k25_modelc_2 k43_modelc_2)) =>  ((k1_funct_1 (k31_modelc_1 (k25_modelc_2 k43_modelc_2) B) C) = (k44_modelc_2 A C)) ) ) ) ) ) ) ).
tt(d61_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((k56_abcmiz_1 A B C) = (k3_funct_2 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k55_abcmiz_1 A B) C)) ) ) ) ) ) ) ).
tt(d61_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  ((k67_aofa_i00 A B C D E F) = (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D C (k37_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d61_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v10_fomodel4 C A B) <=>  (! [D:$i] :  ((v8_fomodel4 D A B C) => (r2_hidden D C)) ) ) ) ) ) ) ) ).
tt(d61_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_modelc_1 D A B) =>  (! [E:$i] :  ( ( (E = k6_numbers)  =>  ((k49_modelc_1 A B C D E) = C) )  &  ( (~  (E = k6_numbers) )  =>  ((k49_modelc_1 A B C D E) = (k3_funct_2 k5_numbers A D (k2_modelc_1 (k6_xcmplx_0 (k2_modelc_1 E) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d61_modelc_2,ax, (k46_modelc_2 = a_0_1_modelc_2) ).
tt(d62_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) =>  ((k68_aofa_i00 A B C D E F) = (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D C (k38_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d62_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  (! [D:$i] :  ((v8_fomodel4 D A B C) <=>  (? [E:$i] :  (? [F:$i] :  ((v7_ordinal1 F) &  ((r1_tarski E C) & (v4_fomodel4 (k4_tarski E D) F A B k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ).
tt(d62_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k50_modelc_1 A B C) = (a_3_1_modelc_1 A B C)) ) ) ) ) ) ) ).
tt(d62_modelc_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k15_modelc_2 (u1_modelc_2 (k42_modelc_2 k43_modelc_2 k46_modelc_2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 (k42_modelc_2 k43_modelc_2 k46_modelc_2)))))) )  =>  ( (A = k47_modelc_2)  <=>  (! [B:$i] :  ((r2_hidden B k15_modelc_2) =>  ((k1_funct_1 A B) = (k45_modelc_2 B)) ) ) ) ) ) ).
tt(d63_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_trees_4 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  ((k58_abcmiz_1 A B C) = (k11_lang1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C (k55_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(d63_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v12_fomodel4 B k6_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [C:$i] :  ((v10_fomodel4 C A B) =>  ((k38_fomodel4 A B C) = (k22_fomodel3 A (k35_fomodel1 A) (k6_fomodel4 A B C) (k7_fomodel3 A C))) ) ) ) ) ) ) ).
tt(d63_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k51_modelc_1 A B C D) = (a_4_0_modelc_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d63_modelc_2,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r7_modelc_2 A B) <=> (r6_modelc_2 k43_modelc_2 k46_modelc_2 A (k21_modelc_2 (k42_modelc_2 k43_modelc_2 k46_modelc_2) k47_modelc_2 B))) ) ) ) ) ).
tt(d64_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  ((k63_abcmiz_1 A B C) = (a_3_0_abcmiz_1 A B C)) ) ) ) ) ) ) ).
tt(d64_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v13_fomodel4 B A) <=>  ((r1_tarski B (k33_fomodel2 A)) & (v1_finset_1 B)) ) ) ) ) ).
tt(d64_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (E = (k52_modelc_1 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F A) =>  ((k1_funct_1 (k31_modelc_1 A E) F) = (k1_funct_1 (k5_funct_3 D A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d64_modelc_2,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k9_modelc_2)) =>  ((r8_modelc_2 A B) <=>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r2_hidden C B) => (r7_modelc_2 A C)) ) ) ) ) ) ) ) ).
tt(d65_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m3_abcmiz_1 C A) =>  ((k64_abcmiz_1 A B C) = (k40_abcmiz_1 A (k63_abcmiz_1 A B (k41_abcmiz_1 A C)) (k62_abcmiz_1 A B (k42_abcmiz_1 A C)))) ) ) ) ) ) ) ).
tt(d65_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v14_fomodel4 C A B) <=>  (? [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  (? [E:$i] :  ( ((v4_fomodel2 E A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v8_fomodel4 D A B C) & (v8_fomodel4 (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) D) E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d65_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k53_modelc_1 A B C D E) = (k2_lattices (k48_modelc_1 A B C) D (k25_modelc_1 (k48_modelc_1 A B C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d65_modelc_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k9_modelc_2)) =>  ((k48_modelc_2 A) = (a_1_0_modelc_2 A)) ) ) ).
tt(d66_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ( (D = (k65_abcmiz_1 A B C))  <=>  ( ((k1_relset_1 k2_abcmiz_1 D) = (k4_subset_1 k2_abcmiz_1 (k1_relset_1 k2_abcmiz_1 B) (k1_relset_1 k2_abcmiz_1 C)))  &  (! [E:$i] :  ((m1_subset_1 E k2_abcmiz_1) =>  ((r2_hidden E (k1_relset_1 k2_abcmiz_1 D)) =>  ((k1_funct_1 D E) = (k59_abcmiz_1 A C (k59_abcmiz_1 A B (k35_abcmiz_1 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d66_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k72_aofa_i00 A B C D E) = (k65_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d66_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v15_fomodel4 B A) <=>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (~  ((r2_hidden (k30_fomodel2 A (k31_fomodel2 A C) D) B) &  (! [E:$i] :  ( ((v4_fomodel1 E A) & (m1_subset_1 E (k1_fomodel1 A)))  =>  (~  ((r2_hidden (k24_fomodel3 A C E D) B) &  (~ (r2_hidden E (k10_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d66_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((k54_modelc_1 A B C D E) = (k51_modelc_1 A B C (k53_modelc_1 A B C D (k52_modelc_1 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d67_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k73_aofa_i00 A B C D E) = (k66_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d67_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v4_funct_1 C) =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k43_fomodel2 A)) =>  ( (~  ( (~ (v14_fomodel4 (k2_xboole_0 C (k6_domain_1 (k43_fomodel2 A) D)) A B))  &  ( (~  ((k7_subset_1 (k15_fomodel1 A) (k16_fomodel1 A) (k21_fomodel0 (k8_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k2_xboole_0 C (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k40_fomodel2 A D)))))) = k1_xboole_0) )  &  (~  ((k42_fomodel4 A B C D) = (k2_xboole_0 C (k1_tarski (k17_fomodel0 (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) D) (o_3_2_fomodel4 A C D) (k40_fomodel2 A D))))) ) ) ) )  &  ( (~  ( (~ (v14_fomodel4 (k2_xboole_0 C (k6_domain_1 (k43_fomodel2 A) D)) A B))  &  (~  ((k7_subset_1 (k15_fomodel1 A) (k16_fomodel1 A) (k21_fomodel0 (k8_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) (k2_xboole_0 C (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k40_fomodel2 A D)))))) = k1_xboole_0) ) ) )  =>  ((k42_fomodel4 A B C D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d67_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_modelc_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_modelc_1 E A B) =>  ( (E = (k55_modelc_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_funct_2 k5_numbers A E F) = (k3_funct_2 k5_numbers A C (k2_nat_1 F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d68_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k74_aofa_i00 A B C D E F) = (k67_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d68_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((v16_fomodel4 B A) <=>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((v8_fomodel4 C A B D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 E) (k2_xboole_0 E k6_margrel1))) (k16_fomodel2 A E)) =>  ((v10_fomodel2 D E A F) =>  ((k26_fomodel2 A E F C) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d68_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_modelc_1 C A B) =>  (! [D:$i] :  ((m1_modelc_1 D A B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ( (~ (r1_xxreal_0 F E))  =>  ((k56_modelc_1 A B C D E F) = (k3_funct_2 k5_numbers A C E)) )  &  ((r1_xxreal_0 F E) =>  ((k56_modelc_1 A B C D E F) = (k1_funct_1 D (k6_xcmplx_0 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d69_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k75_aofa_i00 A B C D E F) = (k68_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d69_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_funct_2 B (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ((v17_fomodel4 B A) <=>  (! [C:$i] :  ((v12_fomodel2 C A) => (v12_fomodel2 (k1_funct_1 B C) A)) ) ) ) ) ) ) ).
tt(d69_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_modelc_1 C A B) =>  (! [D:$i] :  ((m1_modelc_1 D A B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( (F = (k57_modelc_1 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k3_funct_2 k5_numbers A F G) = (k56_modelc_1 A B C D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  ((v5_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  ((k1_abcmiz_0 A (k1_abcmiz_0 A B)) = B) ) ) ) ) ) ).
tt(d6_abcmiz_1,ax, (k8_abcmiz_1 = 2) ).
tt(d6_abcmiz_a,ax, (k8_abcmiz_a = (k4_tarski k6_abcmiz_1 (k4_tarski k1_xboole_0 k6_numbers))) ).
tt(d6_abian,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v3_abian B A) <=>  ((k3_tarski B) = (k3_tarski (k3_tarski A))) ) ) ) ) ).
tt(d6_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v6_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I D) &  ((r2_hidden J D) &  ((r5_aff_1 A B C) &  ((r5_aff_1 A B D) &  ((r1_aff_1 A G E K) &  ((r1_aff_1 A H F K) &  ((r1_aff_1 A G I L) &  ((r1_aff_1 A H J L) & (r2_analoaf A E I K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (C = D)  |  ((r1_aff_1 A G E I) |  ((r1_aff_1 A H F J) |  ( (K = L)  | (r2_analoaf A E I F J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k3_aff_4 A B C))  <=>  ((r2_hidden B D) &  ((r1_aff_4 A C D) & (v1_aff_4 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k7_afinsq_1 A B C) = (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 A) (k5_afinsq_1 B)) (k5_afinsq_1 C))) ) ) ) ).
tt(d6_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_afinsq_2 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ).
tt(d6_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_afproj A B) = (k6_eqrel_1 (k2_afproj A) (k2_afproj A) (k4_afproj A) B)) ) ) ) ) ).
tt(d6_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (C = (k3_afvect0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) C D E) = (k2_afvect0 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  (! [D:$i] :  ( ((v1_unialg_1 D) & (m1_unialg_2 D B))  =>  ( (D = (k1_alg_1 A B C))  <=>  ((u1_struct_0 D) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_algspec1,ax, (! [A:$i] :  ((m3_algspec1 A) <=>  (? [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  &  ((v1_msualg_6 A B) & (l3_msualg_1 A B)) ) ) ) ) ).
tt(d6_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v5_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_algstr_0 B A)) ) ) ) ) ).
tt(d6_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v5_algstr_1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A B D) = C) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B)))))) )  =>  ( (C = (k5_algstr_4 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B)) C D) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(d6_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  (! [C:$i] :  ((m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)) =>  ((v4_altcat_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((r2_hidden E (k1_binop_1 B D D)) &  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((r2_hidden G (k1_binop_1 B D F)) =>  ((k1_binop_1 (k4_altcat_1 A B C D D F) G E) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_altcat_2,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  ((v1_altcat_2 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (u1_struct_0 A)) &  ((k1_binop_1 (u1_altcat_1 A) B B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d6_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_altcat_3 A B C) <=>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) & (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ((k5_ami_2 A) = (k1_funct_1 A k5_numbers)) ) ) ).
tt(d6_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k5_ami_3 A B) = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d6_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  ((v3_amistd_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_finseq_1 E k5_numbers))  &  ( ((k7_partfun1 k5_numbers E 1) = C)  &  ( ((k7_partfun1 k5_numbers E (k3_finseq_1 E)) = D)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) | (r2_hidden (k7_partfun1 k5_numbers E (k2_nat_1 F 1)) (k3_amistd_1 A B (k7_partfun1 k5_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((k5_amistd_4 A B C) = (k7_subset_1 (u1_struct_0 B) (k4_amistd_4 A B C) (k3_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(d6_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) )  =>  ((v6_amistd_5 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  (~ (v2_compos_1 D B)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v4_extpro_1 E A B D)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 B)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 A B)) & (v1_partfun1 G (u1_struct_0 B))) ) ) )  =>  ( ((r1_tarski E F) & (r1_tarski (k9_memstr_0 A B E C) G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 B)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 B)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ((r1_tarski D H) & (r1_tarski (k6_compos_1 B D C) I))  =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ((k5_relat_1 (k5_extpro_1 A B H F J) (k9_xtuple_0 (k6_memstr_0 A B E))) = (k5_relat_1 (k5_extpro_1 A B I G J) (k9_xtuple_0 (k6_memstr_0 A B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k4_ami_wstd A B C D) = (k1_ami_wstd A B (k2_nat_1 (k3_ami_wstd A B C) D))) ) ) ) ) ) ) ) ) ).
tt(d6_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_analmetr A B C) = (g1_analmetr (u1_struct_0 A) (k1_diraf (u1_struct_0 A) (k1_analoaf A)) (k1_analmetr A B C))) ) ) ) ) ) ) ).
tt(d6_analoaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v3_analoaf A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  ( (~ (r2_analoaf A B C E D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( ((r2_analoaf A B C B F) | (r2_analoaf A B C F B))  &  ((r2_analoaf A D E D F) | (r2_analoaf A D E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (D = (k4_analort A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (E = (k4_tarski G H))  &  ( (F = (k4_tarski I J))  & (r2_analort A B C G H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_collsp B (k3_anproj_1 A)) =>  ( (B = (k4_anproj_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k3_xtuple_0 C D E) B) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (C = (k2_anproj_1 A F))  &  ( (D = (k2_anproj_1 A G))  &  ( (E = (k2_anproj_1 A H))  &  ( (~ (v9_struct_0 F A))  &  ( (~ (v9_struct_0 G A))  &  ( (~ (v9_struct_0 H A))  & (r2_anproj_1 A F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_anproj_2 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_armstrng,ax, (! [A:$i] :  ((k4_armstrng A) = (k8_mcart_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k9_setfam_1 A) (k9_setfam_1 A))) ) ).
tt(d6_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k5_arytm_2 A B) = (a_2_0_arytm_2 A B)) ) ) ) ) ).
tt(d6_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((k4_arytm_3 A B) = (k6_ordinal3 A (k3_arytm_3 A B))) ) ) ) ) ).
tt(d6_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_asympt_0 A) <=>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(d6_asympt_1,ax, (k6_asympt_1 = a_0_0_asympt_1) ).
tt(d6_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k5_autalg_1 A B) (k5_autalg_1 A B)) (k5_autalg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_autalg_1 A B) (k5_autalg_1 A B)) (k5_autalg_1 A B))))) )  =>  ( (C = (k6_autalg_1 A B))  <=>  (! [D:$i] :  ((m1_autalg_1 D (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  (! [E:$i] :  ((m1_autalg_1 E (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  ((k5_binop_1 (k5_autalg_1 A B) C D E) = (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (u3_msualg_1 A B) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  ( (C = (k6_autgroup A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k2_group_3 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( (B = (k4_bagorder A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) <=>  (~  ( (~  (C = D) )  &  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r2_hidden E A) &  ( (~ (r1_xxreal_0 (k1_recdef_1 D E) (k1_recdef_1 C E)))  &  (! [F:$i] :  ((v3_ordinal1 F) =>  ( ((r2_hidden E F) & (r2_hidden F A))  =>  ((k1_recdef_1 C F) = (k1_recdef_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v6_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d6_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_bcialg_2 B A) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  &  ((k1_bcialg_2 A (k4_struct_0 A) B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d6_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  =>  ( (B = (k5_bcialg_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C k6_numbers) = (k4_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C (k2_nat_1 D 1)) = (k1_bcialg_4 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_bcialg_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_bcialg_6 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_bcialg_1 A D E)) = (k1_bcialg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden E B))  => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D (k1_bcialg_1 A D C))) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k5_bhsp_1 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_algstr_0 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k5_bhsp_2 A B C) = (a_3_1_bhsp_2 A B C)) ) ) ) ) ) ) ).
tt(d6_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_bhsp_4 B A) <=> (v1_series_1 (k2_bhsp_2 A B))) ) ) ) ) ).
tt(d6_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((r1_bhsp_6 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 F))  &  ((r1_tarski F B) &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski F G) &  ((r1_tarski G B) & (r1_xxreal_0 E (k18_complex1 (k10_binop_2 D (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 G C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((k5_bilinear A B C D E) = (k2_bilinear A B C D (k4_bilinear A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k6_margrel1))  =>  ( (D = (k6_binari_2 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 D E) = (k2_binarith (k2_binarith (k7_partfun1 k6_margrel1 B E) (k7_partfun1 k6_margrel1 (k2_binari_2 A C) E)) (k7_partfun1 k6_margrel1 (k4_binarith A B (k2_binari_2 A C)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((k8_binarith A B C) = (k1_binarith (k1_binarith (k10_margrel1 (k7_partfun1 k6_margrel1 B A) (k7_partfun1 k6_margrel1 C A)) (k10_margrel1 (k7_partfun1 k6_margrel1 B A) (k7_partfun1 k6_margrel1 (k4_binarith A B C) A))) (k10_margrel1 (k7_partfun1 k6_margrel1 C A) (k7_partfun1 k6_margrel1 (k4_binarith A B C) A)))) ) ) ) ) ) ) ).
tt(d6_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k6_binom A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_binom A) B C)) ) ) ) ) ) ) ).
tt(d6_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r2_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A C D B) = D) ) ) ) ) ) ) ) ) ).
tt(d6_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r1_bor_cant A B C D) <=>  (! [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ( (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k5_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v2_funct_1 F) &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k1_prob_2 A B D (k3_funct_2 k5_numbers k5_numbers F G)) = (k1_prob_2 A B E G)) ) ) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B E C)) F) = (k3_funct_2 B k1_numbers C (k1_prob_2 A B (k1_prob_3 A E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_borsuk_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k10_borsuk_1 A) = (k8_eqrel_1 (u1_struct_0 A) (k6_partfun1 (u1_struct_0 A)))) ) ) ).
tt(d6_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r2_borsuk_2 A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A C B) =>  ( (E = (k2_borsuk_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) E F) = (k1_funct_1 D (k9_real_1 1 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) )  =>  ( (A = k4_borsuk_6)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ( ((r1_xxreal_0 B (k10_real_1 1 2)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = k6_numbers) )  &  ( (~ (r1_xxreal_0 B (k10_real_1 1 2)))  =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = (k9_real_1 (k8_real_1 2 B) 1)) ) ) ) ) ) ) ) ).
tt(d6_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C)))))) )  =>  ( (D = (k11_borsuk_7 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_toprealb A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( (E = F)  =>  ((k3_funct_2 (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C)) D E) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) F C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 k2_bspace) (k1_zfmisc_1 A)) (k1_zfmisc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_bspace) (k1_zfmisc_1 A)) (k1_zfmisc_1 A))))) )  =>  ( (B = (k6_bspace A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k2_binop_1 (u1_struct_0 k2_bspace) (k1_zfmisc_1 A) (k1_zfmisc_1 A) B C D) = (k4_bspace A C D)) ) ) ) ) ) ) ) ) ).
tt(d6_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_c0sp1 B A) =>  ((v1_xboole_0 B) |  ((k2_c0sp1 A B) = (k1_realset1 (u2_algstr_0 A) B)) ) ) ) ) ) ) ).
tt(d6_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k6_c0sp2 A) = (a_1_1_c0sp2 A)) ) ) ).
tt(d6_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (B = (k4_calcul_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=> (m2_finseq_1 C (k3_cqc_lang A))) ) ) ) ) ) ).
tt(d6_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_card_1 A) = A) ) ) ).
tt(d6_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k5_card_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  ((r2_hidden E B) &  (D = (k1_funct_1 E A)) ) ) ) ) ) ) ) ) ) ).
tt(d6_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ((v2_card_fil B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D B) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((v1_card_lar B A) & (r2_hidden C A))  =>  ((k1_card_lar A B C) = (k2_ordinal2 (a_3_1_card_lar A B C))) ) ) ) ) ) ) ) ).
tt(d6_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v2_cat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_hidden (k4_tarski C B) (k9_xtuple_0 (u1_cat_1 A))) <=>  ((k3_graph_1 A C) = (k4_graph_1 A B)) ) ) ) ) ) ) ) ) ).
tt(d6_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ((v1_cat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k2_cat_1 B C D) = (k2_cat_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u4_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  ( (E = (k7_cat_3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F B) =>  ((k7_partfun1 (u4_struct_0 A) E F) = (k1_cat_1 A (k7_partfun1 (u4_struct_0 A) C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_cat_4 A B C) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u4_cat_4 A) B C)) ) ) ) ) ) ) ).
tt(d6_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v3_cat_5 A) <=>  ((v2_cat_5 (u1_struct_0 A)) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( (B = C)  =>  ((k4_cat_1 A B) = (k4_tarski (k4_tarski C C) (k10_cat_1 C))) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (~  ( (C = (k3_graph_1 A B))  &  ( (D = (k4_graph_1 A B))  &  (! [E:$i] :  ((m2_cat_1 E C D) =>  (~  (B = (k4_tarski (k4_tarski C D) E)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_cat_1 E) &  ((v3_cat_1 E) &  ((v4_cat_1 E) &  ((v5_cat_1 E) &  ((v6_cat_1 E) & (l1_cat_1 E)) ) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) & (l1_cat_1 F)) ) ) ) ) ) )  =>  (! [G:$i] :  ((m2_cat_1 G D E) =>  (! [H:$i] :  ((m2_cat_1 H E F) =>  ( ( (B = (k4_tarski (k4_tarski D E) G))  &  (C = (k4_tarski (k4_tarski E F) H)) )  =>  ((k1_cat_1 A B C) = (k4_tarski (k4_tarski D F) (k9_cat_1 D E F G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_catalg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( (B = (k4_catalg_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  ((r2_hidden (k4_tarski D E) (k2_xboole_0 (u1_struct_0 A) (u4_struct_0 A))) & (r2_hidden C (k10_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ).
tt(d6_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_cc0sp1 A) = (g1_cfuncdom (k2_cc0sp1 A) (k2_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k1_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k1_cc0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k4_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) (k3_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)))) ) ) ).
tt(d6_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k5_cc0sp2 A) = (g1_clopban2 (k2_cc0sp2 A) (k2_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k1_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k1_cc0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k4_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k3_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) (k4_cc0sp2 A))) ) ) ).
tt(d6_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_cfdiff_1 A B) <=>  (? [C:$i] :  ((m1_cfdiff_1 C B) &  ((r1_tarski C (k1_relset_1 k2_numbers A)) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_partfun1 D k2_numbers) &  ((v3_cfdiff_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_partfun1 E k2_numbers) &  ((v2_cfdiff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  ((r2_hidden F C) =>  ((k11_complex1 (k7_partfun1 k2_numbers A F) (k7_partfun1 k2_numbers A B)) = (k8_complex1 (k10_funct_2 k2_numbers k2_numbers D (k6_xcmplx_0 F B)) (k10_funct_2 k2_numbers k2_numbers E (k6_xcmplx_0 F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_cfuncdom A) = (g1_clvect_1 (k9_funct_2 A k2_numbers) (k4_cfuncdom A) (k1_cfuncdom A) (k3_cfuncdom A))) ) ) ).
tt(d6_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( (B = (k6_cgames_1 A))  <=>  (? [C:$i] :  ((l1_cgames_1 C) &  ( (A = C)  &  (B = (u1_cgames_1 C)) ) ) ) ) ) ) ) ).
tt(d6_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k3_chain_1 A B C) = (a_3_0_chain_1 A B C)) ) ) ) ) ) ) ).
tt(d6_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v2_chord A) <=>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( (~  (B = C) )  => (r1_chord A B C)) ) ) ) ) ) ) ) ).
tt(d6_circcmb3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v4_circcmb3 A) <=>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D C) & (v1_finseq_1 D)) ) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 C B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C B) B)))) )  &  (A = (k5_circcomb E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v11_struct_0 C))  &  ((v1_msualg_1 C) & (l1_msualg_1 C)) )  =>  ( (C = (k5_circcomb A B))  <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (k10_xtuple_0 B) (k1_tarski (k4_tarski B A))))  &  ( ((u4_struct_0 C) = (k1_tarski (k4_tarski B A)))  &  ( ((k1_funct_1 (u1_msualg_1 C) (k4_tarski B A)) = B)  &  ((k1_funct_1 (u2_msualg_1 C) (k4_tarski B A)) = (k4_tarski B A)) ) ) ) ) ) ) ) ) ) ).
tt(d6_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  ((k6_circtrm1 A B C D) = (g3_msualg_1 (k1_circtrm1 A B C) (k4_circtrm1 A B C D) (k5_circtrm1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d6_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k6_circuit1 A B C))  <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  &  ( (E = (a_3_1_circuit1 A B C))  &  (D = (k1_xxreal_2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circuit2 C A B) <=> (r8_pboole (u1_struct_0 A) C (k6_circuit2 A B C))) ) ) ) ) ) ) ).
tt(d6_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (B = (k4_classes1 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_ordinal1 C)) )  &  ( (B = (k1_ordinal2 C))  &  ( ((k9_xtuple_0 C) = (k1_ordinal1 A))  &  ( ((k1_funct_1 C k1_xboole_0) = k1_xboole_0)  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden (k1_ordinal1 D) (k1_ordinal1 A)) =>  ((k1_funct_1 C (k1_ordinal1 D)) = (k9_setfam_1 (k1_funct_1 C D))) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r2_hidden D (k1_ordinal1 A)) & (v4_ordinal1 D))  =>  ( (D = k1_xboole_0)  |  ((k1_funct_1 C D) = (k3_tarski (k10_xtuple_0 (k5_relat_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v2_clopban1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) (k8_real_1 D (k1_normsp_0 A E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k7_clopban2 A) = (g6_algstr_0 (k8_clopban1 A A) (k8_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k5_clopban2 A) (k6_clopban2 A) (k10_csspace (k6_clopban1 A A) (k8_clopban1 A A)))) ) ) ).
tt(d6_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k4_clopban3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k6_clopban4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = (k1_clopban3 A (k1_clopban4 A C))) ) ) ) ) ) ) ) ).
tt(d6_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v3_closure2 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k3_pboole A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k5_clvect_2 A B C) = (a_3_1_clvect_2 A B C)) ) ) ) ) ) ) ).
tt(d6_cohsp_1,ax, (! [A:$i] :  ((v3_cohsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_cohsp_1 B) => (r2_hidden (k3_tarski B) A)) ) ) ) ) ).
tt(d6_coh_sp,ax, (! [A:$i] :  ((k5_coh_sp A) = (a_1_2_coh_sp A)) ) ).
tt(d6_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v4_collsp A) <=>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d6_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((k2_combgras A B C D) = (k3_funct_2 (u1_incsp_1 A) (u1_incsp_1 B) (u1_combgras A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d6_compact1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v5_compact1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_connsp_2 C A B) & (v2_compts_1 C A)) ) ) ) ) ) ) ).
tt(d6_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k9_complex1 A B) = (k2_xcmplx_0 (k9_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))) (k3_xcmplx_0 (k7_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B)) (k8_real_1 (k3_complex1 B) (k4_complex1 A))) k7_complex1))) ) ) ) ) ).
tt(d6_compl_sp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((v5_compl_sp B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (v4_pre_topc (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(d6_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_comput_1 A B) = (k8_funcop_1 k5_numbers (k4_finseq_2 A k5_numbers) B)) ) ) ) ) ).
tt(d6_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (B = (k3_comseq_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k8_comseq_3 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k4_complex1 (k8_nat_1 k2_numbers A C))) ) ) ) ) ) ) ) ).
tt(d6_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v6_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B G B H) &  ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r5_analmetr A B C E) &  ((r5_analmetr A B D F) &  ((r4_analmetr A C G D H) & (r2_analoaf A C D E F)) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ( (C = E)  |  ((r5_analmetr A B G C) | (r4_analmetr A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k4_conlat_1 A) = (k2_conlat_1 A)) ) ) ).
tt(d6_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k6_conlat_2 A) = (g1_conlat_1 (u1_struct_0 A) (u1_struct_0 A) (k2_lattice3 A))) ) ) ).
tt(d6_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v6_conmetr1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [L:$i] :  ((m1_subset_1 L (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 K A) &  ((v1_aff_1 L A) &  ((r2_hidden B K) &  ((r2_hidden B L) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden H K) &  ((r2_hidden J K) &  ((r2_hidden D L) &  ((r2_hidden F L) &  ((r2_hidden G L) &  ((r2_hidden I L) &  ((r2_analoaf A E D I H) &  ((r2_analoaf A D C H G) & (r2_analoaf A C F G J)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden F K) |  ((r2_hidden D K) |  ((r2_hidden G K) |  ((r2_hidden I K) |  ((r2_hidden C L) |  ((r2_hidden E L) |  ((r2_hidden H L) |  ((r2_hidden J L) | (r2_analoaf A E F I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v6_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_analmetr J A) &  ((v4_analmetr K A) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((r2_hidden H J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden G J) |  ((r2_hidden I J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden F K) |  ((r2_hidden H K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) &  ( (D = C)  & (v3_connsp_1 D (k1_pre_topc A B))) ) ) ) ) ) ) ) ) ) ).
tt(d6_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_connsp_2 B A) <=> (v1_connsp_2 (k1_pre_topc A B))) ) ) ) ) ).
tt(d6_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ((k5_connsp_3 A B C) = C) ) ) ) ) ) ) ).
tt(d6_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k4_convex4 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ((v2_funct_1 D) &  ( ((k2_relset_1 (u1_struct_0 A) D) = (k1_convex4 A B))  &  (C = (k4_rlvect_1 A (k3_convex4 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) )  =>  ((v1_convfun1 B A) <=> (v1_convex1 (k5_convfun1 A B) (k3_convfun1 A k4_convfun1))) ) ) ) ) ).
tt(d6_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k7_cqc_sim1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_cqc_lang A) k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) k5_numbers)))) )  &  ( (C = (k1_recdef_1 D B))  &  ( ((k1_recdef_1 D (k5_cqc_lang A)) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ( ((v5_relat_1 I (k3_qc_lang1 A)) &  ((v3_card_1 I H) & (m2_finseq_1 I (k2_qc_lang1 A))) )  =>  (! [J:$i] :  ((m2_subset_1 J (k6_qc_lang1 A) (k8_qc_lang1 A H)) =>  ( ((k1_recdef_1 D (k4_cqc_lang H A J I)) = k6_numbers)  &  ( ((k1_recdef_1 D (k6_cqc_lang A E)) = (k1_recdef_1 D E))  &  ( ((k1_recdef_1 D (k7_cqc_lang A E F)) = (k2_nat_1 (k1_recdef_1 D E) (k1_recdef_1 D F)))  &  ((k1_recdef_1 D (k11_cqc_lang A G E)) = (k2_nat_1 (k1_recdef_1 D E) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( (~  (B = k1_xboole_0) )  =>  ((k3_cqc_the1 A B) = (k1_xtuple_0 (k1_funct_1 B (k3_finseq_1 B)))) ) ) ) ) ) ).
tt(d6_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r6_cqc_the3 A B C) <=>  ((v6_qc_lang1 B A) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 1 D) &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ( ((k3_finseq_1 E) = D)  &  ( ((k1_funct_1 E 1) = C)  &  ( ((k1_funct_1 E D) = B)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 D F))  &  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ( (H = (k1_funct_1 E F))  &  ((k1_funct_1 E (k2_nat_1 F 1)) = (k11_cqc_lang A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_csspace4 A B) = (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) ) ) ) ) ).
tt(d6_csspace,ax, (! [A:$i] :  ((m1_subset_1 A k1_csspace) =>  ( (A = k6_csspace)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k2_csspace A) B) = k5_complex1) ) ) ) ) ) ).
tt(d6_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_decomp_1 A B) = (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ).
tt(d6_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k3_dickson A) = (k6_subset_1 A (k2_relat_1 A))) ) ) ).
tt(d6_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  ( (C = (k6_diff_1 A B))  <=>  ((r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C k6_numbers) A) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C (k1_nat_1 D 1)) (k3_diff_1 (k1_seqfunc k1_numbers k1_numbers C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d6_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k2_dilworth A))  <=>  ( (? [C:$i] :  ( ((v1_finset_1 C) &  ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((k5_card_1 C) = B) ) )  &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r1_xxreal_0 (k5_card_1 C) B)) ) ) ) ) ) ) ) ).
tt(d6_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_diraf A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ((r2_analoaf A B C D D) &  ( ( ((r2_analoaf A B C D E) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) )  &  ((r2_analoaf A B C B D) => (r2_analoaf A C B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A D B B E) &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v4_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C E F) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A B C D G) &  ( (~  (B = C) )  &  ( (~  (E = F) )  &  (~ (r2_analoaf A D G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k3_finseq_2 A)))) =>  ( (B = (k6_dist_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 A))) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m2_finseq_1 D A) &  (C = (k5_dist_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) &  ((v3_dtconstr A) & (l1_lang1 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k7_dtconstr A)) =>  (! [C:$i] :  ((m1_trees_4 C (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  ((m2_dtconstr C A B) <=> (r1_lang1 A B (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) C))) ) ) ) ) ) ) ).
tt(d6_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_dynkin C A) =>  ( (C = (k5_dynkin A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ((m1_dynkin D A) =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k3_ec_pf_1 A) = (k6_subset_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k6_domain_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k4_struct_0 A) (k4_struct_0 A) (k4_struct_0 A))))) ) ) ).
tt(d6_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)))))) )  =>  ((r1_ec_pf_2 A B C) <=>  ((k3_funct_2 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)) C B) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ).
tt(d6_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v22_algstr_0 C) & (l4_algstr_0 C))  =>  ( (C = (k6_endalg A B))  <=>  ( ((u1_struct_0 C) = (k4_endalg A B))  &  ( ((u2_algstr_0 C) = (k5_endalg A B))  &  ((k5_struct_0 C) = (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(d6_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  ( ((k4_ens_1 A B) = (k3_ens_1 A C))  =>  ((k6_ens_1 A B C) = (k4_tarski (k1_domain_1 A A (k3_ens_1 A B) (k4_ens_1 A C)) (k3_relat_1 (k2_xtuple_0 B) (k2_xtuple_0 C)))) ) ) ) ) ) ) ) ).
tt(d6_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((v4_partfun3 B) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( (C = (k3_entropy1 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ( ( (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers))  =>  ((k1_seq_1 C D) = (k6_power A (k1_seq_1 B D))) )  &  ( ((k1_seq_1 B D) = k6_numbers)  =>  ((k1_seq_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( (I = (k6_enumset1 A B C D E F G H))  <=>  (! [J:$i] :  ((r2_hidden J I) <=>  (~  ( (~  (J = A) )  &  ( (~  (J = B) )  &  ( (~  (J = C) )  &  ( (~  (J = D) )  &  ( (~  (J = E) )  &  ( (~  (J = F) )  &  ( (~  (J = G) )  &  (~  (J = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (D = (k11_eqrel_1 A B C))  <=>  ((r2_hidden B D) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (k4_equation A)) =>  ((r2_equation A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (k4_equation A) D)) =>  ((r2_hidden E (k1_funct_1 C D)) => (r1_equation A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_e_siec,ax, (! [A:$i] :  ((k4_e_siec A) = (g1_e_siec (k1_tarski A) (k4_relat_1 (k1_tarski A)) (k4_relat_1 (k1_tarski A)))) ) ).
tt(d6_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k6_euclid_3 A B C D) = (a_4_0_euclid_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d6_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v4_euclid_7 B A) <=>  (! [C:$i] :  ( ((v3_euclid_7 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))))  =>  ((r1_tarski B C) =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(d6_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((k7_euclid_8 A B C) = (k23_rvsum_1 A (k5_euclid_8 B C))) ) ) ) ) ) ) ).
tt(d6_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers)))) )  =>  ( (B = (k13_euclid A))  <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k2_binop_1 (k1_euclid A) (k1_euclid A) k1_numbers B C D) = (k12_euclid (k8_euclid A C D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((k3_euclidlp A B C) = (k5_seq_4 (k2_euclidlp A B C))) ) ) ) ) ) ) ).
tt(d6_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v6_euclmetr A) <=> (v11_aff_2 (k3_analmetr A))) ) ) ).
tt(d6_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k3_exchsort A) = (k5_ordinal3 (k2_exchsort A) (k1_exchsort A))) ) ) ).
tt(d6_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (u1_compos_1 B)) & (v1_funct_1 D)) )  =>  ((k4_extpro_1 A B C D) = (k2_extpro_1 A B (k3_extpro_1 A B D C) C)) ) ) ) ) ) ) ) ) ).
tt(d6_facirc_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k3_facirc_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k10_margrel1 B C)) ) ) ) ) ) ) ) ).
tt(d6_facirc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 (k3_facirc_2 B C D)) (k3_msafree2 (k3_facirc_2 B C D))) =>  ( (E = (k6_facirc_2 A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ( (A = (k2_nat_1 F 1))  &  (E = (k12_facirc_1 (k1_funct_1 C A) (k1_funct_1 D A) (k5_facirc_2 F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_fdiff_1 A B) <=>  ((r1_tarski B (k1_relset_1 k1_numbers A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) => (r1_fdiff_1 (k2_partfun1 k1_numbers k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d6_fdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r3_fdiff_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_fdiff_3 A B))  <=>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski A))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers B)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 D F) k6_numbers)) ) ) ) )  =>  (C = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers E B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ff_siec,ax, (k6_ff_siec = (k1_ff_siec k1_xboole_0 k1_xboole_0)) ).
tt(d6_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k6_fib_num2 A) = (k1_fib_num2 k2_fib_num2 (k3_xboole_0 k4_fib_num2 (k2_finseq_1 A)))) ) ) ).
tt(d6_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v3_filter_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_lattices A (k2_lattices A B D) C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_lattices A (k2_lattices A B E) C) => (r1_lattices A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_filter_1 A B))) =>  ( (D = (k5_filter_1 A B C))  <=>  (! [E:$i] :  ( ((v1_partfun1 E (u1_struct_0 A)) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (E = (k8_filter_0 A B))  =>  (D = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k5_filter_2 A) = (u1_struct_0 A)) ) ) ).
tt(d6_finance1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  ((k6_finance1 A B C D) = (a_4_0_finance1 A B C D)) ) ) ) ) ) ) ).
tt(d6_finseq_1,ax, (! [A:$i] :  ((k6_finseq_1 A) = k1_xboole_0) ) ).
tt(d6_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k3_finseq_2 (k1_tarski A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (k1_tarski A)))))) )  =>  ( (B = (k7_finseq_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_funct_2 k5_numbers (k3_finseq_2 (k1_tarski A)) B C) = (k2_finseq_2 C A)) ) ) ) ) ) ) ).
tt(d6_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k6_finseq_4 A B))  <=>  ( ((k3_finseq_1 C) = (k6_xcmplx_0 (k3_finseq_1 A) (k4_finseq_4 A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k1_funct_1 A (k1_nat_1 D (k4_finseq_4 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_finseq_8 A B) <=>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k7_nat_d (k2_nat_1 E (k3_finseq_1 B)) 1) (k3_finseq_1 C)) &  ( ((k3_finseq_8 A C D (k7_nat_d (k2_nat_1 D (k3_finseq_1 B)) 1)) = (k3_finseq_8 A C E (k7_nat_d (k2_nat_1 E (k3_finseq_1 B)) 1)))  &  ((k3_finseq_8 A C D (k7_nat_d (k2_nat_1 D (k3_finseq_1 B)) 1)) = B) ) ) )  =>  ((r1_xxreal_0 E D) | (r1_xxreal_0 (k3_finseq_1 B) (k7_nat_d E D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_finset_1,ax, (! [A:$i] :  ((v5_finset_1 A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v1_finset_1 B)) ) ) ) ).
tt(d6_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_fintopo2 A B) = (k3_funct_2 (u1_struct_0 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))) (u1_fintopo2 A) B)) ) ) ) ) ).
tt(d6_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (C = (k6_fintopo3 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C D))  =>  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C (k2_nat_1 D 1)) = (k12_fin_topo A E)) ) ) ) ) )  &  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(d6_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k4_fintopo4 A) = (g1_orders_2 (k2_finseq_1 A) (k3_fintopo4 A))) ) ) ) ).
tt(d6_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_fintopo6 B A) <=>  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_xxreal_0 1 C) &  (D = (k1_funct_1 B C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) C) | (r2_hidden (k1_funct_1 B (k1_nat_1 C 1)) (k1_fin_topo A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_fin_topo A B) = (k9_subset_1 (u1_struct_0 A) B (k5_fin_topo A B))) ) ) ) ) ).
tt(d6_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k3_fomodel0 A B C))  <=>  ( ((k9_xtuple_0 D) = k5_numbers)  &  ( ((k1_funct_1 D k1_xboole_0) = (k1_funct_1 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_1 D (k2_xcmplx_0 E 1)) = (k1_binop_1 B (k1_funct_1 D E) (k1_funct_1 C (k2_xcmplx_0 E 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k6_fomodel1 A) = (k8_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (k6_subset_1 k4_numbers (k6_domain_1 k5_numbers k6_numbers)))) ) ) ).
tt(d6_fomodel2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k6_fomodel2 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C D) = (k3_relat_1 (k1_funct_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k9_fomodel3 A B C) = (k8_fomodel3 A A B C)) ) ) ) ) ) ) ).
tt(d6_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  (! [D:$i] :  ((v3_fomodel4 D A B C) <=> (r1_tarski D (k5_setfam_1 (k1_fomodel4 A) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 A)) (k2_fomodel4 A B)) (k1_tarski C))))) ) ) ) ) ) ) ).
tt(d6_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v3_frechet A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C (k2_pre_topc A B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) B) & (r2_hidden C (k2_frechet A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k6_fscirc_1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) k4_facirc_1)) ) ) ) ).
tt(d6_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  ( (F = (k4_fsm_1 A B C D E))  <=>  ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k4_finseq_1 E)) =>  ((k1_funct_1 F G) = (k1_funct_1 (u3_fsm_1 A B C) (k4_tarski (k1_funct_1 (k2_fsm_1 A C D E) G) (k1_funct_1 E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_2 B A))  =>  ((v5_fsm_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (r2_fsm_2 A C B)) ) ) ) ) ) ) ).
tt(d6_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  (! [D:$i] :  ( ((v3_fsm_3 D A (k9_flang_1 A)) & (l2_fsm_3 D A (k9_flang_1 A)))  =>  ( (D = (k4_fsm_3 A B C))  <=>  ( ((g1_fsm_3 A (k9_flang_1 A) (u1_struct_0 D) (u1_rewrite3 (k9_flang_1 A) D) (u1_fsm_3 A (k9_flang_1 A) D)) = (k2_fsm_3 A B (g1_fsm_3 A B (u1_struct_0 C) (u1_rewrite3 B C) (u1_fsm_3 A B C))))  &  ((u2_fsm_3 A (k9_flang_1 A) D) = (a_4_1_fsm_3 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k6_ftacell1 A B C D E) = (k12_gfacirc1 (k12_gfacirc1 A B C) E D)) ) ) ) ) ) ).
tt(d6_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_funcop_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(d6_funcsdom,ax, (! [A:$i] :  ((k10_funcsdom A) = (g1_rlvect_1 (k9_funct_2 A k1_numbers) (k8_funcsdom A) (k5_funcsdom A) (k7_funcsdom A))) ) ).
tt(d6_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k7_relat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((r2_hidden E (k9_xtuple_0 A)) &  ((r2_hidden E B) &  (D = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( (E = (k5_funct_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A C E F) = (k2_xtuple_0 (k3_funct_2 A (k2_zfmisc_1 B C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k11_funct_3 A))  <=>  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k4_tarski C C)) ) ) ) ) ) ) ) ).
tt(d6_funct_5,ax, (k7_funct_5 = (k17_funcop_1 k1_xboole_0 k1_xboole_0 k1_xboole_0)) ).
tt(d6_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k6_funct_6 A) = (k1_funct_5 (k5_relat_1 (k4_funct_5 A) (k2_zfmisc_1 (k4_funct_6 (k2_funct_6 A)) (k9_xtuple_0 A))))) ) ) ).
tt(d6_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 A) =>  ( (B = (k6_funct_7 A))  <=> (v1_xboole_0 B)) )  &  ( (~ (v1_xboole_0 A))  =>  ( (B = (k6_funct_7 A))  <=>  (B = (k9_xtuple_0 (k1_funct_1 A 1))) ) ) ) ) ) ) ).
tt(d6_funct_8,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v5_funct_8 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden D (k1_relset_1 A C)) & (r2_hidden (k1_real_1 D) (k1_relset_1 A C)))  =>  ((k1_funct_1 C (k1_real_1 D)) = (k4_xcmplx_0 (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v4_functor0 C A B) <=> (v2_funct_1 (u1_functor0 A B C))) ) ) ) ) ) ) ).
tt(d6_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  ((r2_functor2 A B C D) <=>  ((r1_functor2 A B C D) &  (? [E:$i] :  ((m1_functor2 E A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A F G)) =>  ((k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C G) (k3_functor0 A B D G) (k6_functor0 A B C F G H) (k2_functor2 A B C D E G)) = (k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B D F) (k3_functor0 A B D G) (k2_functor2 A B C D E F) (k6_functor0 A B D F G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor3 E A B C D) =>  ((r1_functor3 A B C D) =>  (! [F:$i] :  ((m1_functor3 F A B D C) =>  ( (F = (k8_functor3 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k1_funct_1 F G) = (k1_altcat_3 B (k3_functor0 A B C G) (k3_functor0 A B D G) (k2_functor2 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_fuzzy_1 A) = (k7_rfunct_1 k1_xboole_0 A)) ) ) ).
tt(d6_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_fvaluat1 A B C) = (k1_binop_1 (k4_group_1 A) B C)) ) ) ) ) ) ) ).
tt(d6_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_fvsum_1 A B C) = (k4_finseqop (u1_struct_0 A) (u1_struct_0 A) B (k1_fvsum_1 A C))) ) ) ) ) ) ) ).
tt(d6_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k6_gate_5 A B C D E) = (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)) ) ) ) ) ) ).
tt(d6_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (k3_gcd_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k2_gcd_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((k5_genealg1 A B C D E F G H) = (k1_genealg1 A (k4_genealg1 A B C D E F G) (k4_genealg1 A C B D E F G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k4_geomtrap A B C D E) = (k7_real_1 (k8_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)) (k8_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k6_gfacirc1 A B C) = (k3_circcomb (k2_circcomb (k5_circcomb k2_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C))) (k5_circcomb k2_twoscomp (k10_finseq_1 C A)) (k3_circcomb (k5_circcomb k2_twoscomp (k10_finseq_1 A B)) (k5_circcomb k2_twoscomp (k10_finseq_1 B C)) (k6_facirc_1 A B k2_twoscomp) (k6_facirc_1 B C k2_twoscomp)) (k6_facirc_1 C A k2_twoscomp))) ) ) ) ).
tt(d6_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k5_gfacirc2 A B C)) &  ((v4_msafree2 D (k5_gfacirc2 A B C)) &  ((v4_circcomb D (k5_gfacirc2 A B C)) &  ((v6_circcomb D (k5_gfacirc2 A B C)) & (l3_msualg_1 D (k5_gfacirc2 A B C))) ) ) )  =>  ( (D = (k6_gfacirc2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) )  &  ( ((k5_gfacirc2 A B C) = (k1_funct_1 E A))  &  ( (D = (k1_funct_1 F A))  &  ( ((k1_funct_1 E k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 F k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 G k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ( ( (~ (v2_struct_0 I))  & (l1_msualg_1 I))  =>  (! [J:$i] :  ( ((v4_msualg_1 J I) & (l3_msualg_1 J I))  =>  (! [K:$i] :  ( ( (I = (k1_funct_1 E H))  &  ( (J = (k1_funct_1 F H))  &  (K = (k1_funct_1 G H)) ) )  =>  ( ((k1_funct_1 E (k1_nat_1 H 1)) = (k2_circcomb I (k25_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ( ((k1_funct_1 F (k1_nat_1 H 1)) = (k3_circcomb I (k25_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K) J (k26_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)))  &  ((k1_funct_1 G (k1_nat_1 H 1)) = (k21_gfacirc1 (k1_funct_1 B (k1_nat_1 H 1)) (k1_funct_1 C (k1_nat_1 H 1)) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k6_glib_000 A) = (k1_funct_1 A k1_glib_000)) ) ) ).
tt(d6_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k3_glib_001 A B) = (k1_funct_1 B 1)) ) ) ) ) ).
tt(d6_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  ( (C = (k2_glib_002 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v2_glib_001 E A) & (m3_glib_001 E A))  & (r1_glib_001 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v3_glib_003 A) <=>  ((r2_hidden k4_glib_003 (k1_relset_1 k5_numbers A)) &  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ( ((k1_funct_1 A k4_glib_003) = B)  & (r1_tarski (k9_xtuple_0 B) (k6_glib_000 A))) ) ) ) ) ) ) ).
tt(d6_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  ((k4_glib_004 A) = (k3_uproots (k7_glib_000 A) (k5_glib_003 A))) ) ) ).
tt(d6_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_glib_005 C A B) =>  (! [D:$i] :  ((r3_glib_005 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k10_glib_000 A) D) (k1_relset_1 (k6_glib_000 A) C)) &  ( (~ (r2_hidden (k1_funct_1 (k11_glib_000 A) D) (k1_relset_1 (k6_glib_000 A) C)))  &  (~ (r1_xxreal_0 (k1_funct_1 (k5_glib_003 A) D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ((v4_goboard1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (v5_valued_0 (k2_goboard1 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ).
tt(d6_goboard5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (k4_goboard5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k2_goboard2 A))) &  ((r2_hidden (k4_tarski F G) (k2_matrix_1 (k2_goboard2 A))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D E))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) F G))  &  ( (~  ( (D = F)  &  ( ((k2_nat_1 E 1) = G)  &  (C = (k3_goboard5 (k2_goboard2 A) D E)) ) ) )  &  ( (~  ( ((k2_nat_1 D 1) = F)  &  ( (E = G)  &  (C = (k3_goboard5 (k2_goboard2 A) D (k7_nat_d E 1))) ) ) )  &  ( (~  ( (D = (k2_nat_1 F 1))  &  ( (E = G)  &  (C = (k3_goboard5 (k2_goboard2 A) F G)) ) ) )  &  (~  ( (D = F)  &  ( (E = (k2_nat_1 G 1))  &  (C = (k3_goboard5 (k2_goboard2 A) (k7_nat_d D 1) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_gobrd13,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_gobrd13 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 C)) &  ( ((k7_partfun1 A B D) = (k3_matrix_1 A C E F))  &  ( ((k7_partfun1 A B (k2_nat_1 D 1)) = (k3_matrix_1 A C G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  ((r2_hidden (k4_tarski (k2_nat_1 G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k2_nat_1 G 1) H)) ) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  ((r2_hidden (k4_tarski G (k7_nat_d H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k7_nat_d H 1))) ) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  ((r2_hidden (k4_tarski G (k2_nat_1 H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k2_nat_1 H 1))) ) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  ((r2_hidden (k4_tarski (k7_nat_d G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k7_nat_d G 1) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_cqc_lang A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (D = (k4_goedelcp A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (E = (k3_funct_2 k5_numbers (k3_cqc_lang A) B C))  =>  (D = (k2_goedelcp A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ((r1_graph_1 A B C) <=>  ((r1_partfun1 (u2_graph_1 B) (u2_graph_1 C)) &  ((r1_partfun1 (u1_graph_1 B) (u1_graph_1 C)) &  ((g1_graph_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A)) = (k5_graph_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_graph_2 A B C) <=>  ( ((k3_finseq_1 B) = (k2_nat_1 (k3_finseq_1 C) 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r2_graph_1 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B (k2_nat_1 D 1)) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((k7_graph_3 A B C) = (k2_nat_1 (k5_card_1 (k2_graph_3 A B C)) (k5_card_1 (k3_graph_3 A B C)))) ) ) ) ) ) ).
tt(d6_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_graph_5 A B C D) <=>  ((v1_graph_4 B A) & (r1_graph_5 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d6_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((r2_hidden D (u4_struct_0 A)) & (r1_graph_4 A B C D)) )  =>  (! [D:$i] :  ( (D = (k10_graphsp A B C))  <=>  (? [E:$i] :  ( (D = E)  &  ((r2_hidden E (u4_struct_0 A)) & (r1_graph_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k5_grcat_1 A B) = (g1_cat_1 B (k1_grcat_1 A B) (k2_grcat_1 A B) (k3_grcat_1 A B) (k4_grcat_1 A B))) ) ) ) ) ).
tt(d6_gr_cy_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k5_gr_cy_1 A) = A) ) ) ).
tt(d6_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l5_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r3_groeb_1 A B C D) <=>  ((k4_termord A B C D) = (k5_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)))))  =>  (! [E:$i] :  ((m2_ideal_1 E (k11_polynom1 A B) D) =>  ((r2_groeb_2 A B C D E) <=>  ( ((k4_rlvect_1 (k11_polynom1 A B) E) = C)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 H (k15_pre_poly A) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (~  ((r2_hidden H D) &  ((k7_partfun1 (u1_struct_0 (k11_polynom1 A B)) E F) = (k9_polynom1 A B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C))))) )  =>  ( (D = (k6_group_10 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) C)) =>  (? [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) C)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I C) &  ( (F = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C) D E))  &  ( (H = (k6_algstr_0 A B G))  &  ( (E = (k1_domain_1 (u1_struct_0 A) C G I))  &  (F = (k1_domain_1 (u1_struct_0 A) C H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k3_group_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = (k2_group_1 A C)) ) ) ) ) ) ) ) ).
tt(d6_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r1_group_2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( (D = (k6_group_3 A B C))  <=>  ((u1_struct_0 D) = (k4_group_3 A (k8_group_2 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v2_group_4 B A) <=>  ( (~  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) )  &  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((m1_group_2 B C) =>  ( ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = C)  |  (C = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k6_group_5 A) = (k5_group_5 A (k7_group_2 A) (k7_group_2 A))) ) ) ).
tt(d6_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_group_6 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k6_algstr_0 A D E)) = (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_group_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v2_group_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (v2_group_1 (k1_group_7 A B C))) ) ) ) ) ) ) ).
tt(d6_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C A) =>  ((k3_group_9 A B C) = (k1_funct_1 (u1_group_9 A B) C)) )  &  ( (~ (r2_hidden C A))  =>  ((k3_group_9 A B C) = (k6_partfun1 (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(d6_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (E = (k6_hahnban1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) = (k6_algstr_0 A C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v6_hahnban B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k1_rlvect_1 A C D)) = (k8_real_1 (k18_complex1 D) (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ).
tt(d6_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_zfmisc_1 A)) =>  ((m2_hallmar1 C A B) <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) => (r1_tarski (k1_funct_1 C D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k3_henmodel A) = (k11_cqc_sim1 (k3_qc_lang1 A))) ) ) ).
tt(d6_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  =>  ((v4_hermitan B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d6_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  ((k6_heyting1 A B) = (k8_subset_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A) (a_2_0_heyting1 A B))) ) ) ) ).
tt(d6_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  ((k6_heyting2 A B C) = (k1_zfmisc_1 C)) ) ) ) ) ) ).
tt(d6_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)))))) )  =>  ( (C = (k6_hilbasis A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k11_polynom1 B A))) &  ((v1_algseq_1 D (k11_polynom1 B A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k11_polynom1 B A)))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly B) (u1_struct_0 A)) &  ((v1_polynom1 E (k15_pre_poly B) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 A))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly (k2_nat_1 B 1)) (u1_struct_0 A)) &  ((v1_polynom1 F (k15_pre_poly (k2_nat_1 B 1)) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k2_nat_1 B 1)) (u1_struct_0 A))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (k2_nat_1 B 1)) &  ((v1_funct_1 G) &  ((v1_partfun1 G (k2_nat_1 B 1)) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( ( (F = (k1_funct_1 C D))  &  (E = (k1_normsp_1 (k11_polynom1 B A) D (k1_recdef_1 G B))) )  =>  ((k3_polynom1 (k2_nat_1 B 1) A F G) = (k1_funct_1 E (k5_relat_1 G B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v1_hilbert2 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k4_hilbert1 B C)) ) ) ) ) ) ) ) ).
tt(d6_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_hilbert3 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((k5_hilbert3 A B C) = (k1_msualg_3 k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A) (k4_hilbert3 A B) C)) ) ) ) ) ) ) ).
tt(d6_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k6_hurwitz A B C) = (k3_normsp_1 A B (k13_polynom3 A (k5_hurwitz A B C) C))) ) ) ) ) ) ) ).
tt(d6_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k6_idea_1 A B) = (k4_nat_d (k5_idea_1 A B) (k5_series_1 2 A))) ) ) ) ) ).
tt(d6_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v2_incproj A) <=>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) => (r1_incsp_1 A B C)) ) ) ) ) ) ) ) ).
tt(d6_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((v3_incsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) & (r4_incsp_1 A B C)) ) ) ) ) ) ) ).
tt(d6_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k1_int_1 A))  <=>  ((r1_xxreal_0 B A) &  (~ (r1_xxreal_0 B (k5_real_1 A 1))) ) ) ) ) ) ) ).
tt(d6_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ( (~  (B = (k4_struct_0 k1_int_3)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_int_3)) =>  ( (C = (k4_int_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_int_3)) &  ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 C B) D))  &  ((r1_xxreal_0 (k4_struct_0 k1_int_3) D) &  (~ (r1_xxreal_0 (k2_int_3 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r4_integr10 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C B) =>  ((r1_integra5 (k3_integra5 C B) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 C B)))) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers C) = (k1_limfunc1 B))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k1_relset_1 k1_numbers C)) =>  ((k1_seq_1 C D) = (k4_integra5 D B A)) ) ) )  & (v6_limfunc1 C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ((m3_integr15 E A B C D) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( (F = (k4_integr15 A B C D E))  <=>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r2_hidden G (k2_finseq_1 A)) &  (! [H:$i] :  ((m2_finseq_1 H k1_numbers) =>  (~  ( (H = (k4_finseqop (k1_euclid A) k1_numbers E (k1_pdiff_1 G A)))  &  ((k1_seq_1 F G) = (k18_rvsum_1 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((k6_integr16 A B) = (k3_binop_2 (k12_integra1 A (k5_comseq_3 A B)) (k5_binop_2 (k12_integra1 A (k6_comseq_3 A B)) k7_complex1))) ) ) ) ) ).
tt(d6_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((v1_integr18 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k4_integr18 A B C))  <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_integra1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [F:$i] :  ((m2_integr18 F A B C E) =>  ( ((v2_comseq_2 (k2_integra3 B E)) &  ((k2_seq_2 (k2_integra3 B E)) = k6_numbers) )  =>  ((v3_normsp_1 (k3_integr18 A B C E F) A) &  ((k6_normsp_1 A (k3_integr18 A B C E F)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  ((r2_integr1c A B) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 k1_numbers)) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 C D) &  ( ((k1_rcomp_1 C D) = (k1_relset_1 k1_numbers B))  &  ((r1_tarski (k1_rcomp_1 C D) (k1_relset_1 k1_numbers E)) &  ((r1_tarski (k1_rcomp_1 C D) (k1_relset_1 k1_numbers F)) &  ((v3_rcomp_1 G) &  ((r1_tarski (k1_rcomp_1 C D) G) &  ((r2_fdiff_1 E G) &  ((r2_fdiff_1 F G) &  ((v1_fcont_1 (k2_fdiff_1 E G)) &  ((v1_fcont_1 (k2_fdiff_1 F G)) & (r2_relset_1 k1_numbers k2_numbers B (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers E (k25_valued_1 k1_numbers k1_numbers F k7_complex1)) (k1_rcomp_1 C D)))) ) ) ) ) ) ) ) ) )  =>  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 E G)) (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 F G))) (k3_integra5 C D))) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k2_fdiff_1 E G)) (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k2_fdiff_1 F G))) (k3_integra5 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k4_integra1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_seq_1 D E) = (k8_real_1 (k4_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers B (k2_integra1 A C E)))) (k3_integra1 (k2_integra1 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (C = (k6_interva1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (B = (k2_interva1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_irrat_1,ax, (k7_power = (k4_series_1 k5_irrat_1)) ).
tt(d6_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D B C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  ((r1_nattra_1 B C D E) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m1_nattra_1 G B C D E) =>  ((k3_isocat_1 A B C D E F G) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u4_struct_0 C) (k7_cat_1 A B F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_isomichi B A) <=> (r1_tarski (k1_tops_1 A (k2_pre_topc A B)) (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ).
tt(d6_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 (k17_euclid B) k6_numbers) |  ((k6_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k9_real_1 1 A))))) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k9_real_1 1 A))) (k12_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 (k17_euclid B) k6_numbers))  &  (~  ((k6_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k7_real_1 1 A))))) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid B) (k12_euclid B)) A) (k7_real_1 1 A))) (k12_euclid B))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) &  (~ (r1_xxreal_0 (k17_euclid B) k6_numbers)) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (~ (r1_xxreal_0 (k17_euclid B) k6_numbers)) ) )  &  (~  ((k6_jgraph_4 A B) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k6_jgraph_6 A B C) = (a_3_1_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(d6_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r6_jordan20 A B C D E) <=>  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C D F) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C G F) & (r1_jordan5c A B C D G))  =>  ((k17_euclid G) = E) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan5c A B C F G) =>  ( (G = F)  |  ( (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C H G) &  ((r1_jordan5c A B C F H) &  (~ (r1_xxreal_0 (k17_euclid H) E)) ) ) ) )  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) &  ((r1_jordan5c A B C H G) &  ((r1_jordan5c A B C F H) &  (~ (r1_xxreal_0 E (k17_euclid H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r3_jordan3 A B C D) <=>  ((r2_jordan3 A B C D) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k6_jordan5d A))  <=>  ((r2_hidden (k4_tarski B 1) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d6_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_jordan6 A) = (a_1_2_jordan6 A)) ) ) ).
tt(d6_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k4_jordan_a A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  &  ( (D = (a_2_0_jordan_a A B))  &  (C = (k1_xxreal_2 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_jordan,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) )  =>  ( (A = k8_jordan)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers A B) = (k18_euclid (k2_jordan (k15_euclid 2) (k15_euclid 2) B))) ) ) ) ) ) ).
tt(d6_kolmog01,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((k4_kolmog01 A B C D E) = (k9_prob_1 B (k3_kolmog01 A E B C (k2_kolmog01 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(d6_kurato_1,ax, (k6_kurato_1 = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k1_seq_4 1) (k2_borsuk_5 2 4)) (k2_rcomp_1 4 5)) (k2_rcomp_1 5 k1_xxreal_0))) ).
tt(d6_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lang1 A))  =>  ((k3_lang1 A) = (a_1_2_lang1 A)) ) ) ).
tt(d6_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (D = (k7_laplace A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) =>  ((k3_matrix_1 (u1_struct_0 B) D E F) = (k6_laplace E F A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_lattice3 A B) = B) ) ) ) ) ).
tt(d6_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_lattice4 C A B) =>  ((r4_lattice4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k7_lattices A D)) = (k7_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v2_lattice5 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_lattice5 A B C D D) = (k3_yellow_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattice6 A B) = (k16_lattice3 A (a_2_2_lattice6 A B))) ) ) ) ) ).
tt(d6_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k3_lattice7 A) = (a_1_0_lattice7 A)) ) ) ).
tt(d6_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k4_lattice8 A B C D E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v6_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattices A B C) = (k2_lattices A C B)) ) ) ) ) ) ) ) ).
tt(d6_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ((v2_lexbfs A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_funct_1 A B) = (k1_funct_1 A C))  =>  ((k1_funct_1 A (k1_nat_1 B 1)) = (k1_funct_1 A (k1_nat_1 C 1))) ) ) ) ) ) ) ) ) ).
tt(d6_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k6_lfuzzy_0 A B) = B) ) ) ) ) ).
tt(d6_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v3_lfuzzy_1 B A) <=> (r1_fuzzy_1 (k4_fuzzy_4 A A A B B) B)) ) ) ) ) ).
tt(d6_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v3_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 C) & (r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers A)))  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r6_limfunc2 A B) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D B))  & (r2_hidden D (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  & (r1_tarski (k2_relset_1 k1_numbers C) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(d6_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_lopban_1 (u1_struct_0 A) B)))) =>  ( (C = (k7_lopban_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k7_lopban_2 A) = (g6_algstr_0 (k10_lopban_1 A A) (k8_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k5_lopban_2 A) (k6_lopban_2 A) (k10_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)))) ) ) ).
tt(d6_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k3_lopban_3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A (k1_normsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k5_lopban_4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k6_algstr_0 B (k1_rlvect_1 B (k6_lopban_3 B C F) (k8_nat_1 k1_numbers (k2_lopban_4 A) F)) (k6_lopban_3 B D (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k8_lopclset A))  <=>  ( ((k9_xtuple_0 B) = (u1_struct_0 A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 B C) = (a_2_0_lopclset A C)) ) ) ) ) ) ) ) ) ).
tt(d6_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_lpspace1 A) = (k8_funcop_1 k5_numbers A 1)) ) ) ).
tt(d6_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ((k5_lpspace2 A B C D E) = (a_5_0_lpspace2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k6_ltlaxio1 A) = (k1_ltlaxio1 (k5_ltlaxio1 (k1_ltlaxio1 A) (k4_ltlaxio1 k3_ltlaxio1 (k4_hilbert1 k3_ltlaxio1 (k1_ltlaxio1 A)))))) ) ) ).
tt(d6_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k6_mathmorp A B C) = (a_3_2_mathmorp A B C)) ) ) ) ) ) ) ).
tt(d6_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((r2_matrix10 A B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 A)) => (r1_xxreal_0 (k3_matrix_1 k1_numbers A C D) (k3_matrix_1 k1_numbers B C D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ((r2_hidden E (k2_finseq_1 (k1_matrix_1 D))) & (r2_hidden F (k2_finseq_1 (k1_matrix_1 D))))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 C) A B) =>  ( (H = (k6_matrix12 A B C D E F G))  <=>  ( ((k3_finseq_1 H) = (k3_finseq_1 D))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ( ((r2_hidden I (k4_finseq_1 D)) & (r2_hidden J (k2_finseq_1 (k1_matrix_1 D))))  =>  ( ( (J = E)  =>  ((k3_matrix_1 (u1_struct_0 C) H I J) = (k1_algstr_0 C (k8_group_1 C G (k3_matrix_1 (u1_struct_0 C) D I F)) (k3_matrix_1 (u1_struct_0 C) D I E))) )  &  ( (~  (J = E) )  =>  ((k3_matrix_1 (u1_struct_0 C) H I J) = (k3_matrix_1 (u1_struct_0 C) D I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B C) =>  ((k11_matrix13 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(d6_matrix16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v4_matrix16 B A) <=>  (? [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) & (r2_matrix16 A C B)) ) ) ) ) ) ) ).
tt(d6_matrix17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v5_matrix17 B A) <=>  (? [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) & (r1_matrix17 A C B)) ) ) ) ) ) ) ).
tt(d6_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( (C = (k4_matrix_1 A B))  <=>  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) <=> (r2_hidden (k4_tarski E D) (k2_matrix_1 B))) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski E D) (k2_matrix_1 B)) =>  ((k3_matrix_1 A C D E) = (k3_matrix_1 A B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) C C) =>  ((k9_matrix_2 A B C D E) = (k7_matrix_2 B D (k8_matrix_2 D A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((k6_matrix_5 A B) = (k2_matrix_5 (k4_matrix_3 k1_complfld (k1_matrix_5 A) (k1_matrix_5 B)))) ) ) ) ) ).
tt(d6_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v3_matrix_6 C A B) <=>  ((k5_matrix_1 A (u1_struct_0 B) C) = (k1_matrix_6 A B C)) ) ) ) ) ) ) ) ).
tt(d6_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_8 A B C D) <=>  (? [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) &  ((v1_matrix_6 E A B) &  (C = (k4_matrix_6 A B (k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) E) D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( (C = (k6_matrixc1 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) =>  ((k9_matrix_5 C D) = (k17_rvsum_1 (k5_matrixc1 (k8_matrix_1 k2_numbers A D) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))) =>  ((v2_matrixj1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~ (m1_matrix_1 (k1_funct_1 B C) A D D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k6_matrixr1 A B) = (k2_matrixr1 (k4_matrix_3 k2_vectsp_1 (k1_matrixr1 A) (k1_matrixr1 B)))) ) ) ) ) ).
tt(d6_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_matrixr2 B A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( (C = (k7_matrixr2 A B))  <=>  ( ((k1_matrixr2 A C B) = (k4_matrixr2 A))  &  ((k1_matrixr2 A B C) = (k4_matrixr2 A)) ) ) ) ) ) ) ) ) ) ).
tt(d6_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k6_matrlin A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k7_partfun1 (u1_struct_0 A) C D) = (k4_rlvect_1 A (k9_pre_poly (u1_struct_0 A) k5_numbers (k3_finseq_2 (u1_struct_0 A)) B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v3_matroid0 A) <=> (v5_finset_1 (k1_matroid0 A))) ) ) ).
tt(d6_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v2_matrprob A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) => (r1_xxreal_0 k6_numbers (k3_matrix_1 k1_numbers A B C))) ) ) ) ) ) ) ) ).
tt(d6_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A A) =>  ( (C = (k3_matrtop3 A B))  <=> (r2_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B (k3_matrtop1 A A C))) ) ) ) ) ) ) ).
tt(d6_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (E = (k2_mcart_1 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  =>  ((v4_measure1 C A B) <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  ((k19_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)) = (k12_supinf_2 C (k5_setfam_1 A (k4_measure1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(d6_measure5,ax, (! [A:$i] :  ((v2_membered A) =>  ( ( (~  (A = k1_xboole_0) )  =>  ((k2_measure5 A) = (k4_supinf_2 (k8_supinf_2 A) (k7_supinf_2 A))) )  &  ( (A = k1_xboole_0)  =>  ((k2_measure5 A) = k1_supinf_2) ) ) ) ) ).
tt(d6_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ((v1_measure6 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden B A) => (v3_rcomp_1 B)) ) ) ) ) ) ).
tt(d6_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_measure7 B A) =>  ((k6_measure7 A B) = (k19_supinf_2 (k3_measure7 A B))) ) ) ) ) ).
tt(d6_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v2_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m4_measure8 E A B C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (F = (k4_measure8 A B C D E))  <=>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_mesfunc9 F G) = (k19_supinf_2 (k2_measure8 A B D (k3_measure8 A B C E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k9_member_1 A B) = (a_2_1_member_1 A B)) ) ) ) ) ).
tt(d6_membered,ax, (! [A:$i] :  ((v6_membered A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v7_ordinal1 B)) ) ) ) ).
tt(d6_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_memstr_0 B A))  =>  ((v3_memstr_0 B A) <=>  ((k4_memstr_0 A B (k4_struct_0 B)) = k5_numbers) ) ) ) ) ) ).
tt(d6_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k6_mesfun7c A B) = (k5_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d6_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((v2_mesfun9c B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers))) => (r1_xxreal_0 (k17_complex1 (k1_funct_1 (k4_mesfunc5 A k2_numbers B D) E)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (D = (k6_mesfunc1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 B))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k12_supinf_2 D E) = (k1_extreal1 (k1_measure6 C) (k12_supinf_2 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v4_mesfunc5 B) <=>  (! [C:$i] :  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 B C))) ) ) ) ) ) ) ).
tt(d6_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ( (C = (k4_mesfunc8 A B))  <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C D)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers C D))) =>  ((k12_supinf_2 (k4_mesfunc5 A k7_numbers C D) E) = (k8_nat_1 k7_numbers (k4_rinfsup2 (k3_mesfunc5 A B E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v6_metric_1 A) <=> (v2_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ).
tt(d6_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  ((k3_metric_2 A B C) = (a_3_0_metric_2 A B C)) ) ) ) ) ) ) ).
tt(d6_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k2_metric_6 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k4_metric_1 A (k2_tbsp_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((k4_midsp_1 A B) = (a_2_0_midsp_1 A B)) ) ) ) ) ).
tt(d6_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k3_midsp_2 A B))  <=>  ((k1_midsp_2 A C) = B) ) ) ) ) ) ) ) ).
tt(d6_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  ((r3_midsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  ( ((k1_funct_1 G B) = E)  =>  ((k4_midsp_3 A C D (k6_midsp_3 A C G B (k3_midsp_1 C E F))) = (k3_midsp_1 C (k4_midsp_3 A C D G) (k4_midsp_3 A C D (k6_midsp_3 A C G B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k6_mmlquery A B C D) = (a_4_1_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d6_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_mod_4 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k6_algstr_0 A D E)) = (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( (C = (k2_modcat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((r2_hidden E (a_2_1_modcat_1 A B)) & (r1_modcat_1 E D B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k6_modelc_1 A) = (k12_finseq_1 k5_numbers (k2_nat_1 5 A))) ) ) ).
tt(d6_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k6_modelc_2 A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 3) A)) ) ) ).
tt(d6_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ((l1_modelc_3 C A) =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ((r1_modelc_3 A B C D) <=>  ((r2_hidden D (u2_modelc_3 A B)) &  ( (C = (k5_modelc_3 A B D))  |  ( (~  ( (~ (v5_modelc_2 D))  &  ( (~ (v7_modelc_2 D))  &  (~ (v8_modelc_2 D)) ) ) )  &  (C = (k6_modelc_3 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) & (v1_partfun1 B k10_newton)) ) )  =>  ( (B = (k5_moebius1 A))  <=>  ( ((k13_pre_poly B) = (k1_polynom2 k10_newton (k12_nat_3 A)))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_polynom2 k10_newton (k12_nat_3 A))) =>  ((k1_funct_1 B C) = C) ) ) ) ) ) ) ) ) ) ).
tt(d6_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v6_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k5_binop_1 A B C D) = (k5_binop_1 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v22_algstr_0 B) & (m3_monoid_0 B (k13_monoid_1 A))) )  =>  ( (B = (k19_monoid_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k13_monoid_1 A))) =>  ((r2_hidden C (u1_struct_0 B)) <=> (v1_finset_1 (k8_relat_1 C (k7_subset_1 k1_numbers k5_numbers (k6_domain_1 k5_numbers k6_numbers))))) ) ) ) ) ) ) ).
tt(d6_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v2_msafree2 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  ( (B = A)  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( ((k2_msualg_1 B C) = (k2_msualg_1 B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v2_msafree B A) <=>  (? [C:$i] :  ((m1_msafree C A B) & (v1_msafree C A B)) ) ) ) ) ) ) ).
tt(d6_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  (! [E:$i] :  ( ((v3_msualg_1 E B) & (m1_msualg_2 E B (k14_pralg_2 (u1_struct_0 A) B C)))  =>  ( (E = (k3_msalimit A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (k10_pralg_2 (u1_struct_0 A) B C) F)) =>  ((r2_hidden G (k1_funct_1 (u3_msualg_1 B E) F)) <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r1_orders_2 A I H) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C H)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C I)) (k1_msalimit A B C D H I) F) (k1_funct_1 G H)) = (k1_funct_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ((m2_msaterm C A B) <=> (r2_hidden (k1_funct_1 C k1_xboole_0) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(d6_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v5_mssubfam C A B) <=> (r1_pboole A B C)) ) ) ) ) ) ).
tt(d6_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((k5_msualg_1 A B C) = (k1_funct_1 (u4_msualg_1 A C) B)) ) ) ) ) ) ) ).
tt(d6_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((v3_msualg_2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) => (r1_msualg_2 A B D C)) ) ) ) ) ) ) ) ) ).
tt(d6_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A D C)) =>  ( (G = (k5_msualg_3 A B C D E F))  <=>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k9_xtuple_0 F)) =>  ((k1_funct_1 G H) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) H)) (k1_funct_1 F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 A)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 A))) ) ) )  =>  ( (D = (k4_msualg_4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 D E) = (k8_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) E) (k2_msualg_4 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_lattices C) & (m2_nat_lat C (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B))))  =>  ( (C = (k6_msualg_5 A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D))))) )  =>  ((m2_msualg_6 E A B C D) <=>  (? [F:$i] :  ((m1_rewrite1 F (k3_msualg_6 A)) &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finseq_1 G) & (v1_funcop_1 G)) ) )  &  ( (E = (k4_funct_7 (k1_funct_1 (u3_msualg_1 A B) C) G))  &  ( ((k3_finseq_1 F) = (k2_nat_1 (k3_finseq_1 G) 1))  &  ( (C = (k1_funct_1 F 1))  &  ( (D = (k1_funct_1 F (k3_finseq_1 F)))  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_hidden H (k4_finseq_1 G)) &  ( (I = (k1_funct_1 G H))  &  ( (J = (k1_funct_1 F H))  &  (K = (k1_funct_1 F (k2_nat_1 H 1))) ) ) )  => (r1_msualg_6 A J K B I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k4_mycielsk A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  ((r2_orders_2 A D B) | (r2_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ((v6_nagata_1 B A) <=>  ((v3_nagata_1 B A) &  ((v1_tops_2 (k2_nagata_1 A B) A) &  ((v1_cantor_1 (k2_nagata_1 A B) A) & (m1_subset_1 (k2_nagata_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(d6_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k9_nat_3 A B C))  <=>  ( ((k13_pre_poly D) = (k13_pre_poly B))  &  (! [E:$i] :  ((k1_funct_1 D E) = (k2_newton (k1_seq_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((v2_nat_5 A) <=>  ((k5_nat_5 A) = (k24_binop_2 2 A)) ) ) ) ).
tt(d6_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ( (A = k6_nat_lat)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B A) <=>  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ).
tt(d6_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r1_nattra_1 A B C D) & (r1_nattra_1 A B D E))  =>  (! [F:$i] :  ((m1_nattra_1 F A B C D) =>  (! [G:$i] :  ((m1_nattra_1 G A B D E) =>  (! [H:$i] :  ((m1_nattra_1 H A B C E) =>  ( (H = (k5_nattra_1 A B C D E F G))  <=>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k4_nattra_1 A B C E H I) = (k5_cat_1 B (k8_cat_1 A B C I) (k8_cat_1 A B D I) (k8_cat_1 A B E I) (k4_nattra_1 A B C D F I) (k4_nattra_1 A B D E G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k1_relset_1 (u1_struct_0 A) C)) &  ((v9_clvect_1 E A) &  ((k7_clvect_1 A E) = D) ) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) B) &  ((k7_partfun1 (u1_struct_0 B) C D) = (k6_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers))))  =>  ((r6_ncfcont2 A B C) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden F A) &  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B F G))))  & (r1_xxreal_0 D (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C F) (k7_partfun1 k2_numbers C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ndiff_1 A B C D) <=>  (? [E:$i] :  ((m1_nfcont_1 E A D) &  ((r1_tarski E (k1_relset_1 (u1_struct_0 A) C)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k16_lopban_1 A B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_ndiff_1 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden H E) =>  ((k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C H) (k7_partfun1 (u1_struct_0 B) C D)) = (k3_rlvect_1 B (k17_lopban_1 A B F (k5_algstr_0 A H D)) (k7_partfun1 (u1_struct_0 B) G (k5_algstr_0 A H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((r2_ndiff_3 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( (D = (k2_ndiff_3 A B C))  <=>  ( ((k1_relset_1 k1_numbers D) = C)  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = (k1_ndiff_3 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  ((r3_ndiff_4 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ( (B = D)  &  ( (C = E)  & (r1_pdiff_7 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  ((r1_ndiff_5 A B C D E) <=> (r1_ndiff_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A C))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A C) E) D) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A C))) (k3_ndiff_5 A (k5_ndiff_5 A C)) E))) ) ) ) ) ) ) ) ) ) ).
tt(d6_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( (B = (k1_necklace A))  <=>  ( ((u1_struct_0 B) = A)  &  ((u1_orders_2 B) = (a_1_0_necklace A)) ) ) ) ) ) ) ).
tt(d6_net_1,ax, (! [A:$i] :  ((l1_petri A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (! [C:$i] :  ( (C = (k3_net_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k2_net_1 A)) & (r2_hidden (k4_tarski D B) (k1_net_1 A))) ) ) ) ) ) ) ) ) ).
tt(d6_newton,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ( (A = k10_newton)  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B A) <=> (v1_int_2 B)) ) ) ) ) ) ).
tt(d6_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_nfcont_1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) B)) &  ((v3_normsp_1 D A) &  ((k6_normsp_1 A D) = C) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D B)) &  ((k7_partfun1 k1_numbers B C) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v2_nfcont_4 B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  &  ( (C = B)  & (v2_nfcont_3 C (k4_real_ns1 A))) ) ) ) ) ) ) ) ).
tt(d6_normform,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  ( (B = (k5_normform A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ((k5_binop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) B C D) = (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(d6_normsp_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_normsp_0 A))  =>  ((v4_normsp_0 A) <=>  ((k1_normsp_0 A (k4_struct_0 A)) = k6_numbers) ) ) ) ).
tt(d6_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k8_openlatt A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k9_xtuple_0 B) = (u1_struct_0 A))  &  ((k1_funct_1 B C) = (a_2_0_openlatt A C)) ) ) ) ) ) ) ) ) ).
tt(d6_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_necklace A) <=> (r2_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d6_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((k7_oppcat_1 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d6_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_orders_1 A B) <=>  ((r1_relat_2 A B) & (r8_relat_2 A B)) ) ) ) ) ).
tt(d6_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A B C) <=>  ((r1_orders_2 A B C) &  (~  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d6_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( (C = (k1_orders_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( (D = E)  &  ((r2_hidden E (k1_funct_2 (u1_struct_0 A) (u1_struct_0 B))) & (v5_orders_3 E A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ordinal1,ax, (! [A:$i] :  ((v4_ordinal1 A) <=>  (A = (k3_tarski A)) ) ) ).
tt(d6_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ((k5_ordinal2 A) = (k2_ordinal2 (k10_xtuple_0 A))) ) ) ).
tt(d6_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ( (~  (B = k1_xboole_0) )  =>  ( (C = (k6_ordinal3 A B))  <=>  (? [D:$i] :  ((v3_ordinal1 D) &  ( (A = (k10_ordinal2 (k11_ordinal2 C B) D))  & (r2_hidden D B)) ) ) ) )  &  ( (B = k1_xboole_0)  =>  ( (C = (k6_ordinal3 A B))  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(d6_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v4_ordinal5 B))  =>  ( (B = (k2_ordinal5 A))  <=>  ((r2_hidden A B) &  (! [C:$i] :  ( ((v3_ordinal1 C) & (v4_ordinal5 C))  =>  ((r2_hidden A C) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ) ).
tt(d6_ordinal6,ax, (! [A:$i] :  ((k2_ordinal6 A) = (k3_wellord1 (k1_wellord2 (k1_ordinal6 A)) (k1_wellord2 (k2_ordinal1 A)))) ) ).
tt(d6_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v4_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d6_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k3_osafree A B C) = (k4_tarski C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(d6_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_osalg_1 A B C) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((r2_hidden D (k4_finseq_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (E = (k1_funct_1 B D))  &  (F = (k1_funct_1 C D)) )  => (r3_orders_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_osalg_4 A B) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_osalg_4 A) B)) ) ) ) ) ).
tt(d6_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v5_papdesaf A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B F) &  ((r2_analoaf A B D B G) &  ((r2_analoaf A B E B H) &  ((r2_analoaf A C D F G) & (r2_analoaf A C E F H)) ) ) )  =>  ((r3_diraf A B C D) |  ((r3_diraf A B C E) | (r2_analoaf A D E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_parsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_parsp_1 A B C D E) <=> (r2_hidden (k5_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C D E) (u1_parsp_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k7_partfun1 A B C) = (k1_funct_1 B C)) ) ) ) ) ) ).
tt(d6_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (C = (k4_partit1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) &  ((r2_hidden F B) &  ((r2_hidden D F) & (r2_hidden E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v6_pasch A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) &  ( (~ (r3_diraf A B C D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B F E) & (r1_diraf A C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k4_pboole A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k6_subset_1 (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pcomps_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ( ((k1_metric_1 A A B C D) = k6_numbers)  =>  (C = D) )  &  ( ( (C = D)  =>  ((k1_metric_1 A A B C D) = k6_numbers) )  &  ( ((k1_metric_1 A A B C D) = (k1_metric_1 A A B D C))  & (r1_xxreal_0 (k1_metric_1 A A B C E) (k7_real_1 (k1_metric_1 A A B C D) (k1_metric_1 A A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (C = (k4_pcs_0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 C D) = (u1_orders_2 (k3_waybel_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_pdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( (D = (k7_pdiff_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 1))) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) &  ( (E = (k12_finseq_1 k1_numbers F))  &  ( (G = C)  &  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) D E) = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A B G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r1_pdiff_3 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_pdiff_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k10_finseq_1 D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 G 1))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B) I) (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r6_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r3_pdiff_7 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) &  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  &  ( (D = E)  &  ( (C = F)  & (r1_nfcont_1 (k4_real_ns1 A) (k4_real_ns1 B) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r3_pdiff_9 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( (E = (k3_pdiff_9 A B C D))  <=>  ( ((k1_relset_1 (k1_euclid A) E) = B)  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F B) =>  ((k7_partfun1 k1_numbers E F) = (k11_pdiff_1 A C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v5_pencil_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_pre_topc A)) => (r1_ordinal1 2 (k1_card_1 B))) ) ) ) ) ).
tt(d6_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (k2_vectsp_9 A B C)))) =>  ( (E = (k6_pencil_4 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  (? [G:$i] :  ((m1_vectsp_4 G A B) &  ( ((k1_vectsp_9 A G) = D)  &  (F = (k2_vectsp_9 A G C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k8_petri A B) = (a_2_4_petri A B)) ) ) ) ) ).
tt(d6_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_polyalg1 B A) & (l1_polyalg1 B A)) )  =>  ( (B = (k3_polyalg1 A))  <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_polyalg1 A)))))  &  ( (C = (u1_struct_0 (k14_polynom3 A)))  &  (B = (k2_polyalg1 A (k1_polyalg1 A) C)) ) ) ) ) ) ) ) ) ).
tt(d6_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers)  =>  ( (E = (k6_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (H = (k1_polyeq_5 2 (k6_xcmplx_0 (k1_newton F 2) G)))  &  (E = (k6_xcmplx_0 (k4_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k6_xcmplx_0 F H))))) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers) )  =>  ( (E = (k6_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  (? [J:$i] :  ((v1_xcmplx_0 J) &  (? [K:$i] :  ((v1_xcmplx_0 K) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) 64))  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (I = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (J = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (K = (k10_complex1 (k13_complex1 G (k3_xcmplx_0 I J))))  &  (E = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 I) J) K) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_funct_2 C (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)) (k9_funct_2 (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)))) =>  ( (C = (k9_polyform A B))  <=>  ( ( (~ (r1_xxreal_0 k6_numbers B))  =>  (C = k1_xboole_0) )  &  ( ( (B = k6_numbers)  => (r1_funct_2 (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)) (k2_zfmisc_1 (k1_tarski k1_xboole_0) (k8_polyform A k6_numbers)) (u1_struct_0 k2_bspace) C (k8_funcop_1 (u1_struct_0 k2_bspace) (k2_zfmisc_1 (k1_tarski k1_xboole_0) (k8_polyform A k6_numbers)) (k5_struct_0 k2_bspace))))  &  ( (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k7_polyform A) B))  &  (~  (C = (k1_funct_1 (u2_polyform A) B)) ) ) ) )  &  ( ( (B = (k7_polyform A))  => (r1_funct_2 (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)) (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 (k7_polyform A) 1)) (k1_tarski A)) (u1_struct_0 k2_bspace) C (k8_funcop_1 (u1_struct_0 k2_bspace) (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 (k7_polyform A) 1)) (k1_tarski A)) (k5_struct_0 k2_bspace))))  &  ( (~ (r1_xxreal_0 B (k7_polyform A)))  =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((k6_polynom1 A B C D) = (k4_polynom1 A B C (k5_vfunct_1 (k15_pre_poly A) B D))) ) ) ) ) ) ) ) ).
tt(d6_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_normsp_1 A B C) = (k2_normsp_1 A B (k5_vfunct_1 k5_numbers A C))) ) ) ) ) ) ) ).
tt(d6_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) <=>  ((k2_polynom4 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d6_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ((k3_polynom7 A B C) = (k3_polynom1 A B C (k2_polynom7 A B C))) ) ) ) ) ) ).
tt(d6_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_polynom8 A B C) <=>  ( (~  (C = k6_numbers) )  &  ( ((k2_binom A B C) = (k5_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 C D))  &  ((k2_binom A B D) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r4_polyred A B C D E F) <=>  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  & (r3_polyred A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k4_poset_1 A B) = (a_2_0_poset_1 A B)) ) ) ) ) ).
tt(d6_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) (k2_zfmisc_1 B A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A))))) )  =>  ( (C = (k6_pralg_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((k3_funct_2 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A) C D) = (k1_domain_1 B A (k3_domain_1 A B D) (k2_domain_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_pralg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((k6_pralg_2 A B) = (k3_tarski (k10_xtuple_0 (u3_msualg_1 A B)))) ) ) ) ) ).
tt(d6_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (D = (k12_pre_poly A B C))  <=>  (! [E:$i] :  ((k1_funct_1 D E) = (k7_nat_d (k1_funct_1 B E) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ).
tt(d6_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v5_relat_1 B k3_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k8_prepower A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k6_prepower A (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v4_pre_topc D B) => (v4_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(d6_prgcor_2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k1_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r4_prgcor_2 A B C D) <=>  ( ((k1_afinsq_1 C) = D)  &  ( ((k1_afinsq_1 A) = D)  &  ( ((k1_afinsq_1 B) = D)  &  (? [E:$i] :  ((v1_int_1 E) &  ( ((k1_seq_1 C k6_numbers) = (k1_seq_1 B k6_numbers))  &  ( (E = (k1_seq_1 B k6_numbers))  &  ( (~  (E = k6_numbers) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F E))  =>  ((k1_seq_1 C F) = (k7_real_1 (k1_seq_1 A F) (k1_seq_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v4_prob_1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r1_tarski (k10_xtuple_0 C) B) => (r2_hidden (k3_prob_1 A C) B)) ) ) ) ) ) ) ).
tt(d6_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers))  =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ( (E = (k3_prob_2 A B C D))  <=>  (! [F:$i] :  ((m1_prob_1 F A B) =>  ((k1_seq_1 E F) = (k10_real_1 (k1_seq_1 C (k5_prob_1 A B F D)) (k1_seq_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ( ( (~  (B = k1_xboole_0) )  =>  ((k7_prob_3 A B) = (k3_subset_1 A (k5_prob_3 A (k6_prob_3 A B)))) )  &  ( (B = k1_xboole_0)  =>  ((k7_prob_3 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(d6_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k4_prob_4 A B C)) =>  ((k5_prob_4 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(d6_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((r5_projpl_1 A B C D E) <=>  ( (~ (r4_projpl_1 A B C D))  &  ( (~ (r4_projpl_1 A C D E))  &  ( (~ (r4_projpl_1 A D E B))  &  (~ (r4_projpl_1 A E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((m1_prvect_1 B A) <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 A)) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(d6_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) k1_numbers)))) )  =>  ( (C = (k6_prvect_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid 2)) &  ( (F = (k2_finseq_4 k1_numbers (k1_normsp_0 A D) (k1_normsp_0 B E)))  &  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) k1_numbers C D E) = (k12_euclid F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pscomp_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) k1_numbers)))) )  =>  ( (A = k5_pscomp_1)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_seq_1 A B) = (k18_euclid B)) ) ) ) ) ) ).
tt(d6_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (D = (k8_pua2mss1 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  ( (D = (k1_funct_1 E C))  &  ( ((k1_funct_1 E k6_numbers) = B)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (G = (k1_funct_1 E F))  =>  ((k1_funct_1 E (k2_nat_1 F 1)) = (k7_pua2mss1 A G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_pythtrip,ax, (! [A:$i] :  ((m1_pythtrip A) =>  ((v2_pythtrip A) <=> (r2_hidden k6_numbers A)) ) ) ).
tt(d6_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k5_qc_lang1 A) = (k2_zfmisc_1 (k1_tarski 6) k5_numbers)) ) ) ).
tt(d6_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ((k6_qc_lang2 A B C D) = (k15_qc_lang1 A B (k15_qc_lang1 A C D))) ) ) ) ) ) ) ) ) ).
tt(d6_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k6_qc_lang3 A B) = (k4_qc_lang3 A (k4_qc_lang1 A) B)) ) ) ) ) ).
tt(d6_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  ((k4_qc_lang4 A B C) = (k3_qc_lang4 A B C)) ) ) ) ) ) ) ).
tt(d6_qmax_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r1_qmax_1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_funct_1 B (k1_funct_1 B C)) = C) ) ) ) ) ) ) ).
tt(d6_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  ((v8_quantal1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((k6_algstr_0 A (k15_lattice3 A C) B) = (k15_lattice3 A (a_3_1_quantal1 A B C))) ) ) ) ) ) ) ).
tt(d6_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E k1_quaterni) =>  ( ( ( (C = k6_numbers)  &  (D = k6_numbers) )  =>  ( (E = (k6_quaterni A B C D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (F = A)  &  ( (G = B)  &  (E = (k5_arytm_0 F G)) ) ) ) ) ) ) ) )  &  ( (~  ( (C = k6_numbers)  &  (D = k6_numbers) ) )  =>  ( (E = (k6_quaterni A B C D))  <=>  (E = (k2_quaterni k6_numbers 1 2 3 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (D = (k8_quofield A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden E D) <=>  (? [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  (? [G:$i] :  ((m2_subset_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) G))) = (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_rlvect_1 A (k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) G)) (k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) G) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k4_numbers))  =>  ( (D = (k7_radix_1 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k7_partfun1 k4_numbers D E) = (k6_radix_1 E B A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_radix_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v3_card_1 F E) & (m2_finseq_1 F (k3_radix_1 D)))  =>  ((k6_radix_2 A B C D E F) = (k6_int_1 (k3_xcmplx_0 A (k4_radix_1 C D E F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( ((r2_hidden A (k2_finseq_1 C)) =>  ((k8_radix_3 A B C D) = (k2_xcmplx_0 (k6_radix_3 (k4_radix_1 A B C D) B) (k5_radix_3 (k4_radix_1 (k7_nat_d A 1) B C D) B))) )  &  ( ( (A = (k2_xcmplx_0 C 1))  =>  ((k8_radix_3 A B C D) = (k5_radix_3 (k4_radix_1 (k7_nat_d A 1) B C D) B)) )  &  (~  ( (~ (r2_hidden A (k2_finseq_1 C)))  &  ( (~  (A = (k2_xcmplx_0 C 1)) )  &  (~  ((k8_radix_3 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( (D = (k6_radix_5 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E C A D) = (k5_radix_5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (D = (k6_radix_6 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k2_xcmplx_0 A 2))) =>  ((k4_radix_1 E B (k2_xcmplx_0 A 2) D) = (k5_radix_6 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ((m2_vectsp_6 F A C (k2_ranknull B C E D)) =>  ((v2_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) E D)) =>  ((k9_ranknull A B C D E F) = (k1_funct_4 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) E F) (k8_funcop_1 (u1_struct_0 A) (k4_ranknull B D) (k4_struct_0 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k2_ratfunc1 A B) = (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1))) ) ) ) ) ).
tt(d6_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((m1_rcomp_1 B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (B = (k2_rcomp_1 (k6_xcmplx_0 A C) (k2_xcmplx_0 A C))) ) ) ) ) ) ) ) ) ).
tt(d6_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k6_real_3 A))  <=>  ( ((k3_funct_2 k5_numbers k1_numbers B k6_numbers) = 1)  &  ( ((k3_funct_2 k5_numbers k1_numbers B 1) = (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 2)) = (k7_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 C 2)) (k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 1))) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(d6_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_real_lat A) = (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A))) ) ) ).
tt(d6_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_bhsp_1 B) & (l1_bhsp_1 B)) )  =>  ( (B = (k7_real_ns1 A))  <=>  ( ((u1_struct_0 B) = (k1_euclid A))  &  ( ((k4_struct_0 B) = (k5_euclid A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A) (u1_algstr_0 B) (k1_real_ns1 A)) &  ((r1_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A) (u1_rlvect_1 B) (k2_real_ns1 A)) & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) k1_numbers (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers (u1_bhsp_1 B) (k6_real_ns1 A))) ) ) ) ) ) ) ) ) ).
tt(d6_realset1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((m3_realset1 C A B) <=>  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 (k6_subset_1 A (k1_tarski B)) (k6_subset_1 A (k1_tarski B)))) => (r2_hidden (k1_funct_1 C D) (k6_subset_1 A (k1_tarski B)))) ) ) ) ) ) ) ) ).
tt(d6_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k8_struct_0 A) (k8_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 A) (k8_struct_0 A))))) )  =>  ( (B = (k5_realset2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_binop_1 (k4_realset2 A) C (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) B C)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d6_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_rearran1 C) &  ((v2_rearran1 C) &  ((v3_rearran1 C (k1_zfmisc_1 B)) & (m2_finseq_1 C (k1_zfmisc_1 B))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k4_rearran1 A B C D) = (k14_rfunct_3 B (k16_rfunct_3 B (k15_rfunct_3 B (k2_rearran1 B C)) (k3_rfinseq (k20_rfunct_3 A D A))))) ) ) ) ) ) ) ) ) ).
tt(d6_recdef_2,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k5_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (A = (k6_xtuple_0 C D E F))  =>  (B = E) ) ) ) ) ) ) ) ) ) ).
tt(d6_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k1_relat_1 A) = (k2_xboole_0 (k9_xtuple_0 A) (k10_xtuple_0 A))) ) ) ).
tt(d6_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r6_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  &  ( (~ (r2_hidden (k4_tarski C D) A))  &  (~ (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r4_rewrite1 A B C) <=>  ((r3_rewrite1 A C) & (r1_rewrite1 A B C)) ) ) ) ) ) ).
tt(d6_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  ( (C = (k7_rewrite2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r2_hidden (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) D E) C) <=> (r2_rewrite2 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((r3_rewrite3 A B C D E F G) <=> (r1_rewrite1 (k1_rewrite3 A B C) (k4_tarski D E) (k4_tarski F G))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_integra2 B) & (m2_finseq_1 B k1_numbers))  =>  ( (B = (k6_rfinseq2 A))  <=> (r2_classes1 A B)) ) ) ) ) ).
tt(d6_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) =>  ( (C = (k15_rfunct_3 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k7_rfunct_1 (k1_funct_1 B D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r6_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) => (r5_rfunct_4 (k2_partfun1 k1_numbers k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d6_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k5_rinfsup1 A) = (k2_rinfsup1 (k4_rinfsup1 A))) ) ) ).
tt(d6_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (B = (k3_rinfsup2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k7_numbers)))  &  ( (D = (a_2_0_rinfsup2 A C))  &  ((k12_supinf_2 B C) = (k7_supinf_2 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ( ((v36_algstr_0 C) & (l6_algstr_0 C))  =>  ( (C = (k2_ring_1 A B))  <=>  ( ((u1_struct_0 C) = (k8_eqrel_1 (u1_struct_0 A) (k1_ring_1 A B)))  &  ( ((k5_struct_0 C) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k5_struct_0 A)))  &  ( ((k4_struct_0 C) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k4_struct_0 A)))  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (D = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) F))  &  ( (E = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) G))  &  ((k5_binop_1 (u1_struct_0 C) (u1_algstr_0 C) D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k3_rlvect_1 A F G))) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (D = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) F))  &  ( (E = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) G))  &  ((k5_binop_1 (u1_struct_0 C) (u2_algstr_0 C) D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k6_algstr_0 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k4_ringcat1 A) = (g1_ringcat1 A A (k3_struct_0 A))) ) ) ).
tt(d6_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_rlaffin1 A B) = (k1_setfam_1 (a_2_0_rlaffin1 A B))) ) ) ) ) ).
tt(d6_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_rlsub_1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k3_rlsub_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_rlsub_2 A C D) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( (E = (k4_rlsub_2 A B C D))  <=>  ( (B = (k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)))  &  ((r1_struct_0 C (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 D (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_rltopsp1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 (k18_complex1 C) 1) => (r1_tarski (k1_convex1 A B C) B)) ) ) ) ) ) ) ) ).
tt(d6_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v6_rlvect_1 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_rlvect_1 A D (k2_xcmplx_0 B C)) = (k1_algstr_0 A (k1_rlvect_1 A D B) (k1_rlvect_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(d6_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((m2_rlvect_2 C A B) <=> (r1_tarski (k3_rlvect_2 A C) B)) ) ) ) ) ) ) ).
tt(d6_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m2_rmod_2 D A B C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k3_rmod_2 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B))))) )  =>  ( (C = (k5_rmod_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k3_rmod_3 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_rmod_3 A B)) =>  (! [F:$i] :  ((m1_rmod_2 F A B) =>  (! [G:$i] :  ((m1_rmod_2 G A B) =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k3_rmod_3 A B) C D E) = (k1_rmod_3 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( (E = (k4_rmod_4 A B C D))  <=>  ( ((k3_finseq_1 E) = (k3_finseq_1 C))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k9_xtuple_0 E)) =>  ((k1_funct_1 E F) = (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D (k7_partfun1 (u1_struct_0 B) C F)) (k7_partfun1 (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v6_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) (k3_robbins1 A C))) (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C))) = B) ) ) ) ) ) ) ) ).
tt(d6_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_robbins1 A))  =>  ((v8_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A B)) = B) ) ) ) ) ) ).
tt(d6_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_roughs_1 A B) = (k7_subset_1 (u1_struct_0 A) (k4_roughs_1 A B) (k3_roughs_1 A B))) ) ) ) ) ).
tt(d6_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_rsspace4 A B) = (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) ) ) ) ) ).
tt(d6_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A k1_rsspace) =>  ( (A = k6_rsspace)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 (k2_rsspace A) B) = k6_numbers) ) ) ) ) ) ).
tt(d6_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((r1_rusub_2 A C D) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( (E = (k4_rusub_2 A B C D))  <=>  ( (B = (k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)))  &  ((r1_struct_0 C (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 D (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ((k4_rusub_4 A B) = (u1_struct_0 B)) ) ) ) ) ).
tt(d6_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k5_rusub_5 A) = (g1_pre_topc (u1_struct_0 A) (k4_rusub_5 A))) ) ) ).
tt(d6_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k8_rvsum_1 A B) = (k3_funcop_1 k34_binop_2 A B)) ) ) ) ) ).
tt(d6_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k11_rvsum_2 A B) = (k3_funcop_1 k29_binop_2 A B)) ) ) ) ) ).
tt(d6_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k8_scm_comp A B) = (k6_trees_4 (k4_tarski k6_numbers 3) A B)) ) ) ) ) ).
tt(d6_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_scmfsa_1 A B) = (k1_funct_4 A (k16_funcop_1 k5_numbers B))) ) ) ) ) ).
tt(d6_scmfsa_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_scmfsa_2 A) = (k10_ami_3 A)) ) ) ).
tt(d6_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k5_scmfsa6a A B) = (k3_scmfsa6a A (k11_compos_1 k1_scmfsa_2 B))) ) ) ) ) ).
tt(d6_scmfsa7b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r5_scmfsa7b A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k8_memstr_0 3 k1_scmfsa_2 B) D)) (k2_afinsq_1 A))) ) ) ) ) ) ) ) ) ).
tt(d6_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r4_scmfsa9a A B C D) =>  ( ( (~ (r3_scmfsa9a A B C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k2_scmfsa9a A B C D))  <=>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (E = F)  &  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F) C) k6_numbers) &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) G) C) k6_numbers) => (r1_xxreal_0 F G)) ) )  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B)))) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2)))  =>  ((k9_scmfsa_m A B) = (k4_scmfsa_2 (k6_seq_4 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m B) A)))) ) ) ) ) ).
tt(d6_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (k7_card_1 9)) &  (A = (k3_xtuple_0 D (k12_finseq_1 k5_numbers B) (k12_finseq_1 k2_scm_inst C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (B = (k7_scm_inst A))  <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ( ((k12_finseq_1 k5_numbers C) = (k5_xtuple_0 A))  &  (B = (k7_partfun1 k5_numbers (k12_finseq_1 k5_numbers C) 1)) ) ) ) ) ) ) ) ) ) ).
tt(d6_scmpds_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_scmpds_1 A B C) = (k4_tarski 1 (k1_int_2 (k2_xcmplx_0 (k1_funct_1 A B) C)))) ) ) ) ) ) ) ).
tt(d6_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k5_scmpds_2 A B) = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d6_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scmpds_4 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 A) D) => (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 D B C)) (k2_afinsq_1 (k10_compos_1 k1_scmpds_2 A)))) ) ) ) ) ) ) ) ) ) ).
tt(d6_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k4_scmpds_6 A B C D) = (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_4 (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) C) (k1_scmpds_6 (k2_nat_1 (k5_card_1 D) 1))) D)) ) ) ) ) ) ) ) ) ).
tt(d6_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k7_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d6_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_scmring1 A B C D) = (k1_funct_4 B (k16_funcop_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d6_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k6_scmring2 A B C) = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(d6_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E (k12_finseq_1 k5_numbers C) (k12_finseq_1 k2_scm_inst D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ( (C = (k6_scmringi A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k2_scm_inst) &  ( ((k12_finseq_1 k2_scm_inst D) = (k2_xtuple_0 B))  &  (C = (k7_partfun1 k2_scm_inst (k12_finseq_1 k2_scm_inst D) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v5_finset_1 A))  =>  ((k2_scmyciel A) = (k5_card_1 (k3_tarski A))) ) ) ).
tt(d6_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k2_semi_af1 A B C))  <=>  ((k1_semi_af1 A B D C) = C) ) ) ) ) ) ) ) ) ) ).
tt(d6_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k9_seq_4 A B) = (k1_finseqop k2_numbers k2_numbers k2_numbers k27_binop_2 A B)) ) ) ) ) ).
tt(d6_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k7_seqfunc A B C) = (k6_seqfunc A B (k4_seqfunc A C))) ) ) ) ) ) ) ).
tt(d6_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ).
tt(d6_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_series_1 A B C) = (k9_real_1 (k6_series_1 A B) (k6_series_1 A C))) ) ) ) ) ) ) ).
tt(d6_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_setfam_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  (? [F:$i] :  ((r2_hidden E A) &  ((r2_hidden F B) &  (D = (k6_subset_1 E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k6_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k4_subset_1 A C (k8_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_setwiseo,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k5_finsub_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 A))))) )  =>  ( (B = (k11_setwiseo A))  <=>  (! [C:$i] :  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k1_tarski C)) ) ) ) ) ) ) ).
tt(d6_sfmastr2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_sfmastr2 A B) = (k5_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k1_sfmastr1 1 (k2_sfmastr2 A (k4_scmfsa6a (k7_scmfsa_2 B (k9_scmfsa_m 1 (k5_scmfsa_m A B))) (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B)))))) A) (k8_scmfsa_2 B B)) (k6_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m A B)) (k4_scmfsa_2 k6_numbers))) (k2_sfmastr2 A (k4_scmfsa6a (k7_scmfsa_2 B (k9_scmfsa_m 1 (k5_scmfsa_m A B))) (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B)))))) (k6_scmfsa_2 A (k1_sfmastr1 1 (k2_sfmastr2 A (k4_scmfsa6a (k7_scmfsa_2 B (k9_scmfsa_m 1 (k5_scmfsa_m A B))) (k1_scmfsa6c B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))))))) ) ) ) ) ).
tt(d6_sfmastr3,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k5_sfmastr3 A) = (k4_scmfsa6a (k16_scmfsa_2 (k1_sfmastr1 1 (k4_sfmastr3 A (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k9_scmfsa_m 2 (k1_subset_1 k2_scmfsa_2)))) A) (k2_sfmastr3 (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k4_scmfsa_2 k6_numbers) (k1_sfmastr1 1 (k4_sfmastr3 A (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k9_scmfsa_m 2 (k1_subset_1 k2_scmfsa_2)))) (k3_scmfsa6a (k3_sfmastr3 (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k1_sfmastr1 1 (k4_sfmastr3 A (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k9_scmfsa_m 2 (k1_subset_1 k2_scmfsa_2)))) (k9_scmfsa_m 2 (k1_subset_1 k2_scmfsa_2)) A) (k4_sfmastr3 A (k9_scmfsa_m 1 (k1_subset_1 k2_scmfsa_2)) (k9_scmfsa_m 2 (k1_subset_1 k2_scmfsa_2))))))) ) ) ).
tt(d6_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ( (B = (k5_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)))  &  ( (C = (k4_subset_1 k2_scmfsa_2 (k2_sf_mastr A) (k4_scmfsa_m (k4_scmfsa_2 k6_numbers))))  &  (B = (k2_scmfsa_m C)) ) ) ) ) ) ) ) ) ).
tt(d6_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_sgraph1 A B) <=>  ((r2_hidden (g1_sgraph1 k1_xboole_0 (k1_subset_1 (k2_sgraph1 k1_xboole_0))) B) &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_sgraph1 C))) =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_sgraph1 (k2_xboole_0 C (k1_tarski E))))))  =>  ( ((r2_hidden (g1_sgraph1 C D) B) & (r2_hidden E A))  =>  ((r2_hidden E C) | (r2_hidden (g1_sgraph1 (k2_xboole_0 C (k1_tarski E)) F) B)) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_sgraph1 C))) =>  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden (g1_sgraph1 C D) B) &  ((r2_hidden E C) &  ((r2_hidden F C) &  ( (~  (E = F) )  &  ( (~ (r2_hidden (k2_tarski E F) D))  &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_sgraph1 C))))  =>  (~  ( (G = (k2_xboole_0 D (k1_tarski (k2_tarski E F))))  & (r2_hidden (g1_sgraph1 C G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_sheffer1 A B C) <=>  ( ((k1_lattices A C B) = (k1_sheffer1 A))  &  ( ((k1_lattices A B C) = (k1_sheffer1 A))  &  ( ((k2_lattices A C B) = (k2_sheffer1 A))  &  ((k2_lattices A B C) = (k2_sheffer1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) =>  ((k5_simplex1 A B C) = (k11_simplex0 (u1_struct_0 B) C (k2_rlaffin2 B) A)) ) ) ) ) ) ) ) ).
tt(d6_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 (k15_euclid A))) =>  ((k3_simplex2 A B) = (k1_simplex2 (k14_euclid A) B)) ) ) ) ) ).
tt(d6_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k6_sincos10 A) = (k1_seq_1 k2_sincos10 A)) ) ) ).
tt(d6_sin_cos2,ax, (! [A:$i] :  ((k8_sin_cos2 A) = (k1_seq_1 k7_sin_cos2 A)) ) ).
tt(d6_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_sin_cos7 A) = (k6_power k8_power (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) A))) ) ) ).
tt(d6_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k5_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C A) =>  ((k8_nat_1 k2_numbers B C) = (k10_real_1 (k3_newton A) (k8_real_1 (k3_newton C) (k3_newton (k7_nat_d A C))))) )  &  ( (~ (r1_xxreal_0 C A))  =>  ((k8_nat_1 k2_numbers B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d6_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_stacks_1 A B C) = (k2_binop_1 (u1_struct_0 A) (u4_struct_0 A) (u4_struct_0 A) (u2_stacks_1 A) C B)) ) ) ) ) ) ) ).
tt(d6_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) =>  ((k4_struct_0 A) = (u2_struct_0 A)) ) ) ).
tt(d6_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  ((v7_substut1 B A) =>  ((k10_sublemma A B) = (k31_substut1 A B)) ) ) ) ) ) ).
tt(d6_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_subset_1 B A) <=>  (~  (B = A) ) ) ) ) ) ).
tt(d6_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_substut1 A B C D) = (k6_substut1 A D (a_4_0_substut1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d6_supinf_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k7_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_supinf_2 C A B) <=>  (~ (r1_xxreal_0 (k11_supinf_2 k7_numbers A B C) k2_supinf_1)) ) ) ) ) ) ) ).
tt(d6_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_t_0topsp A) = (k12_borsuk_1 A (k2_t_0topsp A))) ) ) ).
tt(d6_tarski,ax, (! [A:$i] :  (! [B:$i] :  ((r2_tarski A B) <=>  (? [C:$i] :  ( (! [D:$i] :  (~  ((r2_hidden D A) &  (! [E:$i] :  (~  ((r2_hidden E B) & (r2_hidden (k4_tarski D E) C)) ) ) ) ) )  &  ( (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  (~  ((r2_hidden E A) & (r2_hidden (k4_tarski E D) C)) ) ) ) ) )  &  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski F G) C))  =>  ( (D = F)  <=>  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_taxonom1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_taxonom1 A B C D) <=> (r1_xxreal_0 (k2_metric_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(d6_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v5_taxonom2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~ (r2_hidden D C))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D E) &  ((r2_hidden E B) & (r1_xboole_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ((r1_taylor_1 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k5_real_1 B 1)) => (r2_fdiff_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A C) D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v5_tbsp_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k2_metric_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A))))) )  =>  ( (B = (k6_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  ((k5_binop_1 (k5_tdlat_1 A) B C D) = (k4_subset_1 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(d6_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E (k14_pre_poly A) (k15_pre_poly A)) =>  ( (E = (k3_termord A B C D))  <=>  ( ( ((k2_polynom1 (k15_pre_poly A) C D) = k1_xboole_0)  & (r6_pboole A E (k16_pre_poly A)))  |  ((r2_hidden E (k2_polynom1 (k15_pre_poly A) C D)) &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C D)) => (r1_termord A B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v3_tops_1 B A)) ) ) ) ) ) ).
tt(d6_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v3_tex_2 C A)) ) ) ) ) ) ) ) ).
tt(d6_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_tex_4 A B) = (a_2_3_tex_4 A B)) ) ) ) ) ).
tt(d6_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((k4_tmap_1 A B) = (k2_tmap_1 A A (k3_struct_0 A) B)) ) ) ) ) ).
tt(d6_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))))) )  =>  ( (E = (k6_topalg_1 A B C D))  <=>  (! [F:$i] :  ((m1_borsuk_2 F A C C) =>  ((k1_funct_1 E (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) F)) = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) (k1_borsuk_2 A B C B (k1_borsuk_2 A B C C D F) (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((v5_topalg_6 B A) <=> (v1_xxreal_2 (k9_xtuple_0 B))) ) ) ) ) ).
tt(d6_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_topdim_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k3_topdim_1 A B))  <=>  ((r1_tarski B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) (k3_real_1 C 1))) &  ((r1_xxreal_0 (k1_real_1 1) C) &  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_xxreal_0 (k1_real_1 1) D) & (r1_tarski B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) (k3_real_1 D 1))))  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k3_topgen_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (k2_topgen_1 A E))  & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_pre_topc B) &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( (B = (k5_topgen_3 A))  <=>  ( ((u1_struct_0 B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v4_pre_topc C B) <=>  ((v1_finset_1 C) |  (C = A) ) ) ) ) ) ) ) ) ) ).
tt(d6_topgen_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_topgen_4 B A) <=>  (? [C:$i] :  ( ((v4_card_3 C) &  ((v2_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (B = (k5_setfam_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(d6_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr))))) )  =>  ( (D = (k5_topgen_5 A B C))  <=>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_xreal_0 F) &  (~ (v3_xxreal_0 F)) )  =>  ( ( (~ (r2_hidden (k19_euclid E F) (k1_topreal9 2 (k19_euclid A B) C)))  =>  ((k1_funct_1 D (k19_euclid E F)) = 1) )  &  ((r2_hidden (k19_euclid E F) (k1_topreal9 2 (k19_euclid A B) C)) =>  ((k1_funct_1 D (k19_euclid E F)) = (k10_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) (k19_euclid A B) (k19_euclid E F))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_topgrp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m3_topgrp_1 D A) &  ((k1_funct_1 D B) = C) ) ) ) ) ) ) ) ) ) ).
tt(d6_topmetr,ax, (k3_topmetr = (k3_pcomps_1 k8_metric_1)) ).
tt(d6_topreal1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_topreal1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_nat_1 B 2) (k3_finseq_1 A)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A B) (k2_topreal1 2 A (k1_nat_1 B 1))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_nat_1 B 1)))) ) ) ) ) ) ) ).
tt(d6_toprealb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k7_toprealb A B C) = (k1_pre_topc (k15_euclid A) (k3_topreal9 A B C))) ) ) ) ) ) ) ).
tt(d6_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (C = (k17_toprealc A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) C D) = (k7_partfun1 k1_numbers D B)) ) ) ) ) ) ) ) ) ) ).
tt(d6_toprns_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k5_toprns_1 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k12_euclid (k8_nat_1 (u1_struct_0 (k15_euclid A)) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d6_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ((r1_tarski (k1_tops_1 A (k2_pre_topc A B)) B) & (r1_tarski B (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ) ).
tt(d6_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v2_transgeo B A) <=> (r3_transgeo A B)) ) ) ) ) ).
tt(d6_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  ( (C = (k4_trees_1 A B))  <=>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((r2_hidden D C) <=> (r2_hidden (k8_finseq_1 k5_numbers B D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_trees_2 A B) = (a_2_0_trees_2 A B)) ) ) ) ) ).
tt(d6_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((m1_trees_3 B A) <=>  (! [C:$i] :  ((r2_hidden C B) =>  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) ) ) ) ) ) ) ).
tt(d6_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((k6_trees_4 A B C) = (k4_trees_4 A (k10_finseq_1 B C))) ) ) ) ) ) ).
tt(d6_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden B (k9_xtuple_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k2_trees_9 A B))  <=>  (? [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 A)) &  ( (D = B)  &  (C = (k3_relat_1 (k1_trees_9 (k9_xtuple_0 A) D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r3_tsep_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (u1_struct_0 B))  &  (E = (u1_struct_0 C)) )  => (r1_connsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r2_hidden B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) & (r2_hidden C (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(d6_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) &  ((k9_subset_1 (u1_struct_0 A) B (k4_tex_4 A C)) = (k6_domain_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ( ( (~  ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) = (u5_turing_1 A)) )  =>  ((k9_turing_1 A B) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 A B)) (k2_xcmplx_0 (k7_turing_1 A B) (k6_turing_1 A (k8_turing_1 A B))) (k5_turing_1 A (k3_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) (k7_turing_1 A B) (k2_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 A B))))) )  &  ( ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) = (u5_turing_1 A))  =>  ((k9_turing_1 A B) = B) ) ) ) ) ) ) ).
tt(d6_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k7_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k9_margrel1 (k10_margrel1 (k9_margrel1 B) (k9_margrel1 C)))) ) ) ) ) ) ) ) ).
tt(d6_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (k4_partfun1 (k3_finseq_2 B) B)) =>  ( (C = (k3_unialg_2 A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 (u1_unialg_1 A)))  &  (! [D:$i] :  (! [E:$i] :  ((m5_margrel1 E (u1_struct_0 A) (k1_unialg_2 A)) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  (E = (k1_funct_1 (u1_unialg_1 A) D)) )  =>  ((k1_funct_1 C D) = (k2_unialg_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) &  ((v2_unialg_2 B) & (l1_unialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k12_unialg_2 A)) (u1_struct_0 (k12_unialg_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_unialg_2 A)) (u1_struct_0 (k12_unialg_2 B)))))) )  =>  ( (D = (k5_unialg_3 A B C))  <=>  (! [E:$i] :  ( ((v1_unialg_1 E) & (m1_unialg_2 E A))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (F = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 E)))  =>  ((k1_funct_1 D E) = (k7_unialg_2 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (D = (k5_uproots A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k8_nat_1 (u1_struct_0 A) B (k2_xcmplx_0 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  ( (E = (k6_urysohn3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((k5_urysohn3 A B C D F) = k1_xboole_0)  =>  ((k1_seq_1 E F) = k6_numbers) )  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 k7_numbers)))  =>  ( (G = (k5_urysohn3 A B C D F))  =>  ((k1_seq_1 E F) = (k8_supinf_2 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_funct_2 E (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( (E = (k8_valuat_1 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))))) )  &  ((r2_funct_2 (k2_valuat_1 A B) k6_margrel1 E (k6_valuat_1 A B F D)) &  ((r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k6_valuat_1 A B F (k5_cqc_lang A)) (k1_margrel1 k6_margrel1 (k2_valuat_1 A B) k8_margrel1)) &  (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [H:$i] :  ((m2_subset_1 H (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [I:$i] :  ((m2_subset_1 I (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  (! [K:$i] :  ( ((v5_relat_1 K (k3_qc_lang1 A)) &  ((v3_card_1 K J) & (m2_finseq_1 K (k2_qc_lang1 A))) )  =>  (! [L:$i] :  ((m2_subset_1 L (k6_qc_lang1 A) (k8_qc_lang1 A J)) =>  ((r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k6_valuat_1 A B F (k4_cqc_lang J A L K)) (k5_valuat_1 A B J K (k7_valuat_1 A B J C L))) &  ((r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k6_valuat_1 A B F (k6_cqc_lang A G)) (k15_margrel1 (k2_valuat_1 A B) (k6_valuat_1 A B F G))) &  ((r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k6_valuat_1 A B F (k7_cqc_lang A G H)) (k16_margrel1 (k2_valuat_1 A B) (k6_valuat_1 A B F G) (k6_valuat_1 A B F H))) & (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k6_valuat_1 A B F (k11_cqc_lang A I G)) (k3_valuat_1 A B I (k6_valuat_1 A B F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_valued_0 A) <=> (r1_tarski (k10_xtuple_0 A) k5_numbers)) ) ) ).
tt(d6_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k30_valued_1 A) = (k24_valued_1 A (k4_xcmplx_0 1))) ) ) ).
tt(d6_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectmetr A))  =>  ((v6_vectmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_metric_1 A D C) = (k2_metric_1 A (k1_algstr_0 A D B) (k1_algstr_0 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(d6_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v7_vectsp_1 D A) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  ( (D = (k6_vectsp10 A B C))  <=>  ( ((u1_struct_0 D) = (k2_vectsp10 A B C))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D)) (u1_struct_0 D) (k2_zfmisc_1 (k2_vectsp10 A B C) (k2_vectsp10 A B C)) (k2_vectsp10 A B C) (u1_algstr_0 D) (k3_vectsp10 A B C)) &  ( ((k4_struct_0 D) = (k4_vectsp10 A B C))  & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D)) (u1_struct_0 D) (k2_zfmisc_1 (u1_struct_0 A) (k2_vectsp10 A B C)) (k2_vectsp10 A B C) (u1_vectsp_1 A D) (k5_vectsp10 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B (k5_struct_0 A)) = B)  &  ((k6_algstr_0 A (k5_struct_0 A) B) = B) ) ) ) ) ) ) ).
tt(d6_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k4_vectsp_2 A) = (g1_vectsp_2 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) ) ) ).
tt(d6_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m2_vectsp_4 D A B C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k3_vectsp_4 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_vectsp_5 A B D E) =>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) =>  ( (F = (k4_vectsp_5 A B C D E))  <=>  ( (C = (k3_rlvect_1 B (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F) (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)))  &  ((r1_struct_0 D (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)) & (r1_struct_0 E (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ( ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (v13_algstr_0 B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (D = (k4_vectsp_6 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  ((v2_funct_1 E) &  ( ((k10_xtuple_0 E) = (k1_vectsp_6 A B C))  &  (D = (k4_rlvect_1 B (k3_vectsp_6 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v4_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r3_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattice3 A D B) => (r1_lattices A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r1_vfunct_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k9_subset_1 A D (k1_relset_1 A C))) => (r1_xxreal_0 (k1_normsp_0 B (k7_partfun1 (u1_struct_0 B) C F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v7_waybel_0 A) <=> (v1_waybel_0 (k2_struct_0 A) A)) ) ) ).
tt(d6_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v4_yellow_0 B (k2_waybel10 A)) & (m1_yellow_0 B (k2_waybel10 A))) ) )  =>  ( (B = (k7_waybel10 A))  <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v22_waybel_0 C A A)) ) ) ) ) ) ) ) ).
tt(d6_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((k1_waybel11 A B) = (k1_yellow_0 A (a_2_0_waybel11 A B))) ) ) ) ) ).
tt(d6_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_yellow_8 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v4_card_3 B) &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((v3_pre_topc C A) & (v1_tops_1 C A)) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (C = (k8_setfam_1 (u1_struct_0 A) B))  & (v1_tops_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_waybel18,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k7_waybel18 A B C) = (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(d6_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r3_waybel_1 A B C) <=>  ((r2_yellow_0 A C) &  ( (B = (k2_yellow_0 A C))  & (r2_hidden (k2_yellow_0 A C) C)) ) ) ) ) ) ) ) ).
tt(d6_waybel23,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v5_waybel23 A) <=> (r1_ordinal1 (k2_waybel23 A) k4_ordinal1)) ) ) ).
tt(d6_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_waybel_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k11_lattice3 A B (k1_yellow_0 A C)) = (k1_yellow_0 A (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C))) ) ) ) ) ) ) ) ).
tt(d6_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v9_functor0 B (k4_waybel34 A) (k5_waybel34 A)) &  ((v16_functor0 B (k4_waybel34 A) (k5_waybel34 A)) & (m2_functor0 B (k4_waybel34 A) (k5_waybel34 A))) )  =>  ( (B = (k6_waybel34 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel34 A))) =>  ((k3_functor0 (k4_waybel34 A) (k5_waybel34 A) B C) = (k4_yellow21 (k4_waybel34 A) C)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel34 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel34 A))) =>  ( (~  ((k1_altcat_1 (k4_waybel34 A) C D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 (k4_waybel34 A) C D)) =>  ((k8_functor0 (k4_waybel34 A) (k5_waybel34 A) B C D E) = (k1_waybel34 (k3_yellow21 (k4_waybel34 A) C) (k3_yellow21 (k4_waybel34 A) D) (k5_yellow21 (k4_waybel34 A) C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((r1_waybel35 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k4_tarski D E) C) &  ( (~  (D = E) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F B) &  ((r2_hidden (k4_tarski D F) C) &  ((r2_hidden (k4_tarski F E) C) &  (~  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v3_waybel_3 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  & (v1_waybel_0 (k1_waybel_3 A B) A)) ) )  &  ((v24_waybel_0 A) & (v2_waybel_3 A)) ) ) ) ) ).
tt(d6_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v4_waybel_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k3_yellow_0 A) C) B)) ) ) ) ) ) ) ).
tt(d6_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_orders_2 A (k11_lattice3 A C D) B) &  ( (~ (r1_orders_2 A C B))  &  (~ (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) &  ((v1_waybel_7 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  &  (B = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(d6_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_waybel_0 B A) & (l1_waybel_0 B A))  =>  ( (B = (k3_waybel_9 A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ( ((u1_orders_2 B) = (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))  &  ((u1_waybel_0 A B) = (k3_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d6_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v7_vectsp_1 B (k4_weddwitt A)) &  ((v8_vectsp_1 B (k4_weddwitt A)) &  ((v9_vectsp_1 B (k4_weddwitt A)) &  ((v10_vectsp_1 B (k4_weddwitt A)) &  ((v11_vectsp_1 B (k4_weddwitt A)) & (l1_vectsp_1 B (k4_weddwitt A))) ) ) ) ) ) ) ) ) )  =>  ( (B = (k6_weddwitt A))  <=>  ( ((g2_algstr_0 (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B)) = (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A)))  &  ((u1_vectsp_1 (k4_weddwitt A) B) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 (k4_weddwitt A)) (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(d6_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (C = (k6_weierstr A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d6_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_wellfnd1 B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  ((k3_funct_2 k5_numbers (u1_struct_0 A) B (k1_nat_1 C 1)) = (k8_nat_1 (u1_struct_0 A) B C)) )  & (r2_hidden (k4_tarski (k3_funct_2 k5_numbers (u1_struct_0 A) B (k1_nat_1 C 1)) (k8_nat_1 (u1_struct_0 A) B C)) (u1_orders_2 A))) ) ) ) ) ) ) ) ).
tt(d6_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k2_wellord1 A B) = (k3_xboole_0 A (k2_zfmisc_1 B B))) ) ) ) ).
tt(d6_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ((k5_xboole_0 A B) = (k2_xboole_0 (k4_xboole_0 A B) (k4_xboole_0 B A))) ) ) ).
tt(d6_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A B) = (k3_xboolean (k4_xboolean (k3_xboolean A) (k3_xboolean B)))) ) ) ) ) ).
tt(d6_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (B = (k4_xcmplx_0 A))  <=>  ((k2_xcmplx_0 A B) = k6_numbers) ) ) ) ) ) ).
tt(d6_xtuple_0,ax, (! [A:$i] :  ((k4_xtuple_0 A) = (k1_xtuple_0 (k1_xtuple_0 A))) ) ).
tt(d6_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((v2_xxreal_0 A) <=>  (~ (r1_xxreal_0 A k6_numbers)) ) ) ) ).
tt(d6_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v2_xxreal_2 A) <=> (r2_hidden (k1_xxreal_2 A) A)) ) ) ).
tt(d6_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((v1_xreal_0 A) =>  ( (B = (k5_xxreal_3 A))  <=>  (? [C:$i] :  ((v1_xcmplx_0 C) &  ( (A = C)  &  (B = (k5_xcmplx_0 C)) ) ) ) ) )  &  ( (~ (v1_xreal_0 A))  =>  ( (B = (k5_xxreal_3 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d6_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_yellow_0 A) <=>  ((v1_yellow_0 A) & (v2_yellow_0 A)) ) ) ) ).
tt(d6_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((r5_yellow16 A B C) <=>  ((r1_yellow_0 B C) => (r2_hidden (k1_yellow_0 B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(d6_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r3_yellow18 A B) <=> (r1_yellow18 A (k1_yellow18 B))) ) ) ) ) ).
tt(d6_yellow_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_orders_2 C) &  ((v4_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 C (k6_yellow_1 (u1_struct_0 A) B))) )  =>  ( (C = (k7_yellow_1 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r2_hidden D (u1_struct_0 C)) <=>  ((r2_hidden D (k1_funct_2 (u1_struct_0 A) (u1_struct_0 B))) & (v5_orders_3 D A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_yellow21 A B) = B) ) ) ) ) ).
tt(d6_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k5_yellow_2 A B) = (k2_yellow_0 A (k10_xtuple_0 B))) ) ) ) ) ).
tt(d6_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  (! [C:$i] :  ((l1_waybel_0 C A) =>  ((m1_yellow_6 C A B) <=>  ((m1_yellow_0 C B) &  ((u1_waybel_0 A C) = (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ).
tt(d6_yellow_8,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_pre_topc B) & (l1_pre_topc B))  =>  ( (B = (k1_yellow_8 A))  <=>  ( ((u1_struct_0 B) = A)  &  ((k7_setfam_1 (u1_struct_0 B) (u1_pre_topc B)) = (k2_xboole_0 (k1_tarski A) (k5_finsub_1 A))) ) ) ) ) ) ).
tt(d6_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v2_pre_topc C) & (l1_pre_topc C))  =>  ((m3_yellow_9 C A B) <=>  ( ((u1_struct_0 C) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ((v1_tops_2 (k2_xboole_0 (u1_pre_topc A) (u1_pre_topc B)) C) &  ((v2_cantor_1 (k2_xboole_0 (u1_pre_topc A) (u1_pre_topc B)) C) & (m1_subset_1 (k2_xboole_0 (u1_pre_topc A) (u1_pre_topc B)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ).
tt(d6_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  ((v1_yoneda_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F A D E) =>  (! [G:$i] :  ((m1_cat_1 G A D E) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C F) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v1_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C B) => (r2_hidden (a_2_0_zf_fund1 A C) B)) ) ) ) ) ) ) ) ).
tt(d6_zf_lang,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k7_zf_lang A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 3) A) B)) ) ) ) ) ).
tt(d6_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_zfmisc_1 A B C D) <=>  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d6_zf_model,ax, (k6_zf_model = (k14_zf_lang (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k11_zf_lang (k8_zf_lang (k2_zf_lang 2) (k12_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang k6_numbers)) (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang 1)))) (k4_zf_lang (k2_zf_lang k6_numbers) (k2_zf_lang 1))))) ).
tt(d70_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k76_aofa_i00 A B C D E F) = (k67_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d70_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((v18_fomodel4 C A B) <=> (v8_fomodel4 C B (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k34_fomodel4 B)) (k37_fomodel4 B)) A)) ) ) ) ) ) ).
tt(d70_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_zfmisc_1 A) (k1_zfmisc_1 A)) &  ((v6_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A))))) ) )  =>  ( (E = (k58_modelc_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ((k3_funct_2 (k1_zfmisc_1 A) (k1_zfmisc_1 A) E F) = (k54_modelc_1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d71_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k77_aofa_i00 A B C D E F) = (k67_aofa_i00 A B C D (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d71_fomodel4,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))))))) )  =>  ( (E = (k44_fomodel4 A B C D))  <=>  ( ((k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E k6_numbers) = A)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E (k2_xcmplx_0 F 1)) = (k43_fomodel4 B C (k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E F) (k8_nat_1 (k43_fomodel2 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d71_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k59_modelc_1 A B C D E F) = (k28_modelc_1 (k48_modelc_1 A B C) E (k53_modelc_1 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d72_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k78_aofa_i00 A B C D E F) = (k68_aofa_i00 A B C D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d72_fomodel4,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) )  =>  ((k45_fomodel4 A B C D) = (k3_tarski (k10_xtuple_0 (k44_fomodel4 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(d72_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ((k60_modelc_1 A B C D E F) = (k51_modelc_1 A B C (k59_modelc_1 A B C D E (k52_modelc_1 A B C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d73_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k79_aofa_i00 A B C D E F) = (k68_aofa_i00 A B C D (k43_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d73_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k33_fomodel2 B)) =>  ( ( (~ (v8_fomodel4 (k38_fomodel2 B D) B C A))  =>  ((k46_fomodel4 A B C D) = (k2_xboole_0 A (k6_domain_1 (k33_fomodel2 B) D))) )  &  ((v8_fomodel4 (k38_fomodel2 B D) B C A) =>  ((k46_fomodel4 A B C D) = (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k38_fomodel2 B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d73_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 A) (k1_zfmisc_1 A)) &  ((v6_cohsp_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A))))) ) )  =>  ( (F = (k61_modelc_1 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ((k3_funct_2 (k1_zfmisc_1 A) (k1_zfmisc_1 A) F G) = (k60_modelc_1 A B C D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d74_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))))))) )  =>  ( (E = (k48_fomodel4 A B C D))  <=>  ( ((k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E k6_numbers) = A)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E (k2_xcmplx_0 F 1)) = (k47_fomodel4 (k8_nat_1 (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))) E F) B C (k8_nat_1 (k33_fomodel2 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d75_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k81_aofa_i00 A B C D E F) = (k53_aofa_i00 A B C D E (k42_aofa_i00 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d75_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) )  =>  ((k49_fomodel4 A B C D) = (k3_tarski (k10_xtuple_0 (k48_fomodel4 A B C D)))) ) ) ) ) ) ) ) ).
tt(d76_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k82_aofa_i00 A B C D E F) = (k54_aofa_i00 A B C D E (k42_aofa_i00 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d77_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k83_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k36_aofa_i00 A B C D (k42_aofa_i00 A B C D E) (k42_aofa_i00 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d78_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ((k84_aofa_i00 A B C D E F) = (k47_aofa_i00 A B C D E (k35_aofa_i00 A B C D (k42_aofa_i00 A B C D E) (k42_aofa_i00 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  ((v6_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  (~  ((k1_abcmiz_0 A B) = B) ) ) ) ) ) ) ).
tt(d7_abcmiz_1,ax, (k9_abcmiz_1 = k6_numbers) ).
tt(d7_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((m1_abcmiz_a C A B) <=> (r2_hidden C (k3_trees_9 B))) ) ) ) ) ) ) ).
tt(d7_abian,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (C = (k2_abian A B))  <=>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E A))  =>  ((r2_hidden (k4_tarski D E) C) <=>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ((k1_funct_1 (k1_abian A B F) D) = (k1_funct_1 (k1_abian A B G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v7_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((r2_hidden C B) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r1_aff_1 A C D G) &  ((r1_aff_1 A C E H) &  ((r2_analoaf A D E G H) &  ((r2_analoaf A D F G I) & (r2_aff_1 A D E B)) ) ) ) ) ) ) )  =>  ((r2_hidden D B) |  ( (C = F)  |  ( (D = E)  | (r2_analoaf A E F H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I D) &  ((r2_hidden J D) &  ((r5_aff_1 A B D) &  ((r1_aff_1 A G E K) &  ((r1_aff_1 A H F K) &  ((r1_aff_1 A G I L) &  ((r1_aff_1 A H J L) &  ((r2_analoaf A E I F J) & (r2_analoaf A E I K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (C = D)  |  ((r1_aff_1 A G E I) |  ((r1_aff_1 A H F J) |  ( (K = L)  |  ( (E = F)  | (r5_aff_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k8_afinsq_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) ) ) ) ) ).
tt(d7_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((k5_afinsq_2 A B) = (k3_relat_1 (k4_afinsq_2 (k3_xboole_0 B (k1_afinsq_1 A))) A)) ) ) ) ).
tt(d7_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k7_afproj A) = (k8_eqrel_1 (k1_afproj A) (k3_afproj A))) ) ) ).
tt(d7_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (C = (k4_afvect0 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k1_afvect0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m3_algspec1 B) =>  ((m4_algspec1 B A) <=>  (? [C:$i] :  ( ( (~ (v11_struct_0 C))  & (m2_algspec1 C A))  &  ((v1_msualg_6 B C) & (l3_msualg_1 B C)) ) ) ) ) ) ) ) ).
tt(d7_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v6_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_algstr_0 B A)) ) ) ) ) ).
tt(d7_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (v1_funct_1 B)) )  =>  ((k6_algstr_4 A B) = (k1_setfam_1 (a_2_0_algstr_4 A B))) ) ) ) ) ).
tt(d7_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  (! [C:$i] :  ((m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)) =>  ((v5_altcat_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((r2_hidden E (k1_binop_1 B D D)) &  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((r2_hidden G (k1_binop_1 B F D)) =>  ((k1_binop_1 (k4_altcat_1 A B C F D D) E G) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  ((v1_altcat_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k1_altcat_1 A B B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d7_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v4_altcat_3 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A E B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E B)) =>  ( ((k5_altcat_1 A E B C F D) = (k5_altcat_1 A E B C G D))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_ami_2 A B) = (k1_funct_4 A (k16_funcop_1 k5_numbers B))) ) ) ) ) ).
tt(d7_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k6_ami_3 A B) = (k3_xtuple_0 5 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d7_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v1_extpro_1 B A) & (l1_extpro_1 B A))  =>  ( (B = (k4_amistd_1 A))  <=>  ( ((u1_struct_0 B) = (k6_domain_1 k5_numbers k6_numbers))  &  ( ((u2_struct_0 B) = k6_numbers)  &  ( ((u1_compos_1 B) = (k7_domain_1 (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers k6_numbers k6_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers k6_numbers)))  &  ( ((u1_memstr_0 A B) = (k16_funcop_1 k6_numbers k6_numbers))  &  ((r8_pboole A (u2_memstr_0 A B) (k8_funcop_1 (k1_zfmisc_1 k1_numbers) A k5_numbers)) &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 A B)) (k4_card_3 (k2_memstr_0 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 A B)) (k4_card_3 (k2_memstr_0 A B)))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k2_memstr_0 A B))) =>  ((k1_funct_1 C D) = (k1_funct_4 D (k16_funcop_1 k6_numbers (k1_ordinal1 (k1_funct_1 D k6_numbers))))) ) )  &  ((u1_extpro_1 A B) = (k1_funct_4 (k16_funcop_1 (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers k6_numbers) C) (k16_funcop_1 (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers k6_numbers k6_numbers) (k6_partfun1 (k4_card_3 (k2_memstr_0 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k5_ami_wstd A B C) = (k4_ami_wstd A B C 1)) ) ) ) ) ) ) ).
tt(d7_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ((k3_analmetr A) = (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) ) ) ).
tt(d7_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_analort A B C) = (g1_analoaf (u1_struct_0 A) (k3_analort A B C))) ) ) ) ) ) ) ).
tt(d7_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k5_anproj_1 A) = (g1_collsp (k3_anproj_1 A) (k4_anproj_1 A))) ) ) ).
tt(d7_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v2_collsp A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C B) &  ((r1_collsp A B B C) & (r1_collsp A B C C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (D = (k7_aofa_000 A B C))  <=>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 A))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 A)) =>  ( ((r1_tarski (k5_aofa_000 A E) B) =>  ((k1_funct_1 D E) = (k1_funct_1 C E)) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ( (~ (r1_xxreal_0 F G))  => (r2_hidden (k1_funct_1 (k9_funct_7 A G) E) B)) ) )  =>  ((r2_hidden (k1_funct_1 (k9_funct_7 A F) E) B) |  ((k1_funct_1 D E) = (k1_funct_1 (k9_funct_7 A F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_armstrng A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_armstrng A))) =>  ((r2_armstrng A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u3_armstrng A)) =>  (! [E:$i] :  ((m1_subset_1 E (u3_armstrng A)) =>  ( ((k5_relat_1 D B) = (k5_relat_1 E B))  =>  ((k5_relat_1 D C) = (k5_relat_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k6_arytm_2 A B) = (a_2_1_arytm_2 A B)) ) ) ) ) ).
tt(d7_arytm_3,ax, (k5_arytm_3 = (k2_xboole_0 (k6_subset_1 a_0_0_arytm_3 a_0_1_arytm_3) k4_ordinal1)) ).
tt(d7_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (C = (k5_asympt_0 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_square_1 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d7_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( (~  (A = k6_numbers) )  =>  ( (B = (k7_asympt_1 A))  <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 (k9_newton C) A) &  ( (~ (r1_xxreal_0 (k9_newton (k2_nat_1 C 1)) A))  &  (B = (k9_newton C)) ) ) ) ) ) )  &  ( (A = k6_numbers)  =>  ( (B = (k7_asympt_1 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d7_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k7_autalg_1 A B) = (g3_algstr_0 (k5_autalg_1 A B) (k6_autalg_1 A B))) ) ) ) ) ).
tt(d7_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) => (r2_hidden (k4_tarski (k11_pre_poly A C E) (k11_pre_poly A D E)) B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_partfun1 C (k15_pre_poly A)) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( (C = (k5_bagorder A B))  <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden (k4_tarski D E) C) <=>  (~  ((r1_xxreal_0 (k3_bagorder A E) (k3_bagorder A D)) &  (~  ( ((k3_bagorder A D) = (k3_bagorder A E))  & (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v7_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k1_bcialg_1 A B C) = (k4_struct_0 A))  &  ((k1_bcialg_1 A C B) = (k4_struct_0 A)) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d7_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ((v7_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(d7_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k6_bcialg_4 A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k5_bcialg_4 A) B C)) ) ) ) ) ) ) ).
tt(d7_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m3_bciideal B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C (k1_bcialg_1 A D C)) E) B) & (r2_hidden E B))  => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k6_bhsp_2 A B C) = (a_3_2_bhsp_2 A B C)) ) ) ) ) ) ) ).
tt(d7_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k5_bhsp_4 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_rlvect_1 A (k1_normsp_1 A B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((r1_bhsp_6 A B C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (D = (k3_bhsp_6 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 F))  &  ((r1_tarski F B) &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski F G) &  ((r1_tarski G B) & (r1_xxreal_0 E (k18_complex1 (k10_binop_2 D (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 G C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( (F = (k5_bilinear A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) F G H) = (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D G H) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((r1_binarith A B C) <=>  ((k8_binarith A B C) = k7_margrel1) ) ) ) ) ) ) ) ).
tt(d7_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( (E = (k8_binom A B C D))  <=>  ( ((k3_finseq_1 E) = (k2_nat_1 D 1))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ((r2_hidden F (k1_relset_1 k5_numbers E)) &  ( (H = (k6_xcmplx_0 F 1))  &  (G = (k6_xcmplx_0 D H)) ) )  =>  ((k7_partfun1 (u1_struct_0 A) E F) = (k6_algstr_0 A (k5_binom A (k2_binom A B G) (k7_binom H D)) (k2_binom A C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r3_binop_1 A B C) <=>  ((r1_binop_1 A B C) & (r2_binop_1 A B C)) ) ) ) ) ) ) ).
tt(d7_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k31_binop_2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_funct_1 A B) = (k7_binop_2 B)) ) ) ) ) ) ).
tt(d7_bor_cant,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k7_bor_cant A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C D) = (k1_prob_1 A (k1_valued_0 (k9_setfam_1 A) B D))) ) ) ) ) ) ) ) ) ).
tt(d7_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_eqrel_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k11_borsuk_1 A B))  <=>  ( ((u1_struct_0 C) = B)  &  ((u1_pre_topc C) = (a_2_1_borsuk_1 A B)) ) ) ) ) ) ) ) ) ).
tt(d7_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ((r3_borsuk_2 A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A))))) )  &  ((v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) A) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 F G k6_numbers) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) D G))  &  ( ((k1_binop_1 F G 1) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) E G))  &  ( ((k1_binop_1 F k6_numbers G) = B)  &  ((k1_binop_1 F 1 G) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) )  =>  ( (A = k5_borsuk_6)  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ( ((r1_xxreal_0 B (k10_real_1 1 2)) =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = (k8_real_1 (k10_real_1 1 2) B)) )  &  ( ((r1_xxreal_0 B (k10_real_1 3 4)) =>  ((r1_xxreal_0 B (k10_real_1 1 2)) |  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = (k5_real_1 B (k10_real_1 1 4))) ) )  &  ( (~ (r1_xxreal_0 B (k10_real_1 3 4)))  =>  ((k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B) = (k9_real_1 (k8_real_1 2 B) 1)) ) ) ) ) ) ) ) ) ).
tt(d7_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 3))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 3)))))) )  =>  ( (A = k12_borsuk_7)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_funct_1 A B) = (k4_euclid_5 (k21_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) (k18_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) k6_numbers)) ) ) ) ) ) ).
tt(d7_bspace,ax, (! [A:$i] :  ((k7_bspace A) = (g1_vectsp_1 k2_bspace (k1_zfmisc_1 A) (k5_bspace A) (k1_subset_1 A) (k6_bspace A))) ) ).
tt(d7_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ((k5_bvfunc_2 A B C) = (k2_bvfunc_2 A (k7_subset_1 (k1_bvfunc_2 A) C (k4_bvfunc_2 A B)))) ) ) ) ) ) ) ).
tt(d7_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_ideal_1 B A) & (v1_c0sp1 B A))  =>  ((v1_xboole_0 B) |  ((k3_c0sp1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(d7_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k7_c0sp2 A) = (g1_rlvect_1 (k6_c0sp2 A) (k10_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)) (k8_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)) (k9_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)))) ) ) ).
tt(d7_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = k6_numbers)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) &  ((r1_calcul_1 (k1_calcul_1 (k3_cqc_lang A) D) (k2_calcul_1 A D)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = D) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 1)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) &  ((k1_xtuple_0 (k1_funct_1 B C)) = (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k5_cqc_lang A)))) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 2)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_finseq_1 F (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ((r2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E) (k1_calcul_1 (k3_cqc_lang A) F)) &  ( ((k2_calcul_1 A E) = (k2_calcul_1 A F))  &  ( ((k1_xtuple_0 (k1_funct_1 B D)) = E)  &  ((k1_xtuple_0 (k1_funct_1 B C)) = F) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 3)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_finseq_1 F (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_finseq_1 G (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 F) 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 G) 1))  &  ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F)) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) G))) &  ( ((k6_cqc_lang A (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) F))) = (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) G)))  &  ( ((k2_calcul_1 A F) = (k2_calcul_1 A G))  &  ( (F = (k1_xtuple_0 (k1_funct_1 B E)))  &  ( (G = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F)) (k12_finseq_1 (k3_cqc_lang A) (k2_calcul_1 A F))) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 4)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_finseq_1 F (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_finseq_1 G (k3_cqc_lang A)) &  (? [H:$i] :  ((m2_subset_1 H (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 F) 1))  &  ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F) (k1_calcul_1 (k3_cqc_lang A) G)) &  ( ((k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) F)) = (k6_cqc_lang A H))  &  ( ((k6_cqc_lang A (k2_calcul_1 A F)) = (k2_calcul_1 A G))  &  ( (F = (k1_xtuple_0 (k1_funct_1 B E)))  &  ( (G = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F)) (k12_finseq_1 (k3_cqc_lang A) H)) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 5)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m2_finseq_1 F (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_finseq_1 G (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 D E))  &  ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F) (k1_calcul_1 (k3_cqc_lang A) G)) &  ( (F = (k1_xtuple_0 (k1_funct_1 B E)))  &  ( (G = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) F) (k12_finseq_1 (k3_cqc_lang A) (k7_cqc_lang A (k2_calcul_1 A F) (k2_calcul_1 A G)))) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 6)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ( ((k7_cqc_lang A F G) = (k2_calcul_1 A E))  &  ( (E = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) F)) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 7)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ( ((k7_cqc_lang A F G) = (k2_calcul_1 A E))  &  ( (E = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) G)) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ((k2_xtuple_0 (k1_funct_1 B C)) = 8)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ( ((k2_calcul_1 A E) = (k11_cqc_lang A G F))  &  ( (E = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) (k4_substut2 A F G H))) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k2_xtuple_0 (k1_funct_1 B C)) = 9)  =>  ((r3_calcul_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) &  (? [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) &  (? [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) &  (? [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  &  ( ((k2_calcul_1 A E) = (k4_substut2 A F G H))  &  ( (~ (r2_hidden H (k3_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E))))  &  ( (~ (r2_hidden H (k24_qc_lang1 A (k11_cqc_lang A G F))))  &  ( (E = (k1_xtuple_0 (k1_funct_1 B D)))  &  ((k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A G F))) = (k1_xtuple_0 (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_card_1 B A) <=>  ((k1_card_1 B) = A) ) ) ) ).
tt(d7_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  ((k6_card_3 A) = (k1_card_1 (k3_card_3 (k2_card_3 A)))) ) ) ).
tt(d7_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ((v3_card_fil B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) | (r2_hidden (k6_subset_1 A C) B)) ) ) ) ) ) ) ) ).
tt(d7_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v3_card_lar B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((v2_card_lar C A) &  ((v1_card_lar C A) & (v1_xboole_0 (k9_subset_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(d7_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v3_cat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A B))  =>  ( ((k3_graph_1 A (k1_cat_1 A B C)) = (k3_graph_1 A B))  &  ((k4_graph_1 A (k1_cat_1 A B C)) = (k4_graph_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(d7_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((k8_cat_2 A B) = (g1_cat_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)) (k6_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_graph_1 A) (u1_graph_1 B)) (k6_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u2_graph_1 A) (u2_graph_1 B)) (k7_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_cat_1 A) (u1_cat_1 B)))) ) ) ) ) ).
tt(d7_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u4_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  =>  ( (E = (k8_cat_3 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F B) =>  ((k7_partfun1 (u4_struct_0 A) E F) = (k1_cat_1 A (k7_partfun1 (u4_struct_0 A) D F) (k7_partfun1 (u4_struct_0 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_cat_4,ax, (! [A:$i] :  (! [B:$i] :  ((k5_cat_4 A B) = (g1_cat_4 (k1_tarski A) (k1_tarski B) (k18_funcop_1 B A) (k18_funcop_1 B A) (k17_funcop_1 B B B) (k1_algstr_1 A) (k17_funcop_1 A A A) (k17_funcop_1 A A B) (k17_funcop_1 A A B))) ) ) ).
tt(d7_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k7_cat_5 A) = A) ) ) ).
tt(d7_catalg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v3_catalg_1 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( (! [C:$i] :  (~  ((r2_hidden C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ( (C = (k4_tarski D E))  &  ( ((k3_finseq_1 E) = (k3_funct_2 k5_numbers k5_numbers B D))  & (r1_tarski (k2_zfmisc_1 (k1_tarski D) (k4_finseq_2 (k3_funct_2 k5_numbers k5_numbers B D) (k4_catalg_1 A))) (u1_struct_0 A))) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  (~  ((r2_hidden C (u4_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ( (C = (k4_tarski D E))  &  ( ((k3_finseq_1 E) = (k3_funct_2 k5_numbers k5_numbers B D))  & (r1_tarski (k2_zfmisc_1 (k1_tarski D) (k4_finseq_2 (k3_funct_2 k5_numbers k5_numbers B D) (k4_catalg_1 A))) (u4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r2_hidden B (k2_cc0sp1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( (C = (k4_cc0sp1 A B))  <=>  ( (C = B)  & (v1_comseq_2 (k2_partfun1 A k2_numbers C A))) ) ) ) ) ) ) ) ).
tt(d7_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k6_cc0sp2 A) = (a_1_1_cc0sp2 A)) ) ) ).
tt(d7_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_cfdiff_1 A B) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( (C = (k2_cfdiff_1 A B))  <=>  (? [D:$i] :  ((m1_cfdiff_1 D B) &  ((r1_tarski D (k1_relset_1 k2_numbers A)) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_partfun1 E k2_numbers) &  ((v3_cfdiff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_partfun1 F k2_numbers) &  ((v2_cfdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ( (C = (k10_funct_2 k2_numbers k2_numbers E k6_complex1))  &  (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  ((r2_hidden G D) =>  ((k11_complex1 (k7_partfun1 k2_numbers A G) (k7_partfun1 k2_numbers A B)) = (k8_complex1 (k10_funct_2 k2_numbers k2_numbers E (k6_xcmplx_0 G B)) (k10_funct_2 k2_numbers k2_numbers F (k6_xcmplx_0 G B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_cfuncdom A) = (g6_algstr_0 (k9_funct_2 A k2_numbers) (k1_cfuncdom A) (k2_cfuncdom A) (k5_cfuncdom A) (k4_cfuncdom A))) ) ) ).
tt(d7_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( (B = (k7_cgames_1 A))  <=>  (? [C:$i] :  ((l1_cgames_1 C) &  ( (A = C)  &  (B = (u2_cgames_1 C)) ) ) ) ) ) ) ) ).
tt(d7_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C A) =>  ((k4_chain_1 A B C) = (a_3_1_chain_1 A B C)) ) ) ) ) ) ) ) ).
tt(d7_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v3_chord B A) <=>  ( (~  ((k2_chord A (k6_domain_1 (k6_glib_000 A) B)) = k1_xboole_0) )  =>  (! [C:$i] :  ((m1_chord C A (k6_domain_1 (k6_glib_000 A) B)) => (v2_chord C)) ) ) ) ) ) ) ) ).
tt(d7_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v5_circcmb3 B A) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E D) & (v1_finseq_1 E)) ) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 D C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 D C) C)))) )  &  ( (A = (k5_circcomb F E))  &  (B = (k7_circcomb D C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_circcomb A) <=>  ((u2_msualg_1 A) = (k6_partfun1 (u4_struct_0 A))) ) ) ) ).
tt(d7_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  ((m1_dtconstr D (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ( (F = (k7_circtrm1 A B C D E))  <=>  (? [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) &  ( (G = D)  &  (F = (k9_msaterm A B C G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k7_circuit1 A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  &  ( (D = (a_2_0_circuit1 A B))  &  (C = (k1_xxreal_2 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ((k7_circuit2 A B C D) = (k6_circuit2 A B (k1_circuit2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d7_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k5_classes1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  (? [E:$i] :  ((m1_subset_1 E k4_ordinal1) &  ((r2_hidden C (k1_funct_1 D E)) &  ( ((k9_xtuple_0 D) = k4_ordinal1)  &  ( ((k1_funct_1 D k1_xboole_0) = A)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 D (k1_ordinal1 F)) = (k3_tarski (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_clopban1 A B)))) =>  ( (C = (k8_clopban1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_clopban1 D A B) &  ((v2_clopban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_clopban2 A) = (g1_cfuncdom (k8_clopban1 A A) (k5_clopban2 A) (k8_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k9_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k6_clopban2 A) (k10_csspace (k6_clopban1 A A) (k8_clopban1 A A)))) ) ) ).
tt(d7_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k5_clopban3 A B))  <=>  ( ((k1_normsp_1 A C k6_numbers) = (k5_struct_0 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C (k2_nat_1 D 1)) = (k6_algstr_0 A (k1_normsp_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_clopban4 A B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k6_clopban4 A) B)) ) ) ) ) ).
tt(d7_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v4_closure2 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  ((r1_tarski D C) => (r2_hidden (k4_mssubfam A B (k5_closure2 A B D)) C)) ) ) ) ) ) ) ) ) ).
tt(d7_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k3_rlvect_1 A C D) B)) ) ) ) )  &  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_clvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k6_clvect_2 A B C) = (a_3_2_clvect_2 A B C)) ) ) ) ) ) ) ).
tt(d7_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_3 B A) <=> (v1_series_1 (k2_clvect_2 A B))) ) ) ) ) ).
tt(d7_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_cohsp_1 A B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r2_hidden (k3_xboole_0 C D) A) & (r2_hidden (k2_xboole_0 C D) A)) ) ) ) ) ) ) ).
tt(d7_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  ((k6_coh_sp A B) = (k1_xtuple_0 (k1_xtuple_0 B))) ) ) ) ).
tt(d7_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m2_collsp B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (C = D) )  &  (B = (k1_collsp A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ((k3_combgras A B C D) = (k3_funct_2 (u2_incsp_1 A) (u2_incsp_1 B) (u2_combgras A B C) D)) ) ) ) ) ) ) ) ) ).
tt(d7_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_compact1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C))))))) )  &  ( (D = C)  & (v3_tops_2 D A (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C)))) ) ) ) ) ) ) ) ) ) ).
tt(d7_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k10_complex1 A) = (k2_xcmplx_0 (k1_real_1 (k3_complex1 A)) (k3_xcmplx_0 (k1_real_1 (k4_complex1 A)) k7_complex1))) ) ) ).
tt(d7_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((v6_compl_sp B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (v2_compl_sp (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(d7_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  ((v3_compos_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v4_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v4_valued_0 D)) )  =>  ( ((r2_hidden C (k3_compos_0 A B)) &  ((k9_xtuple_0 C) = (k9_xtuple_0 D)) )  =>  (! [E:$i] :  ((r2_hidden (k3_xtuple_0 B C E) A) => (r2_hidden (k3_xtuple_0 B D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  ( (C = (k4_comput_1 A B))  <=>  ( ((k1_relset_1 (k3_finseq_2 k5_numbers) C) = (k4_finseq_2 A k5_numbers))  &  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((k1_recdef_1 C D) = (k2_nat_1 (k7_partfun1 k5_numbers D B) 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k11_comseq_3 A) = (k3_comseq_2 (k10_comseq_3 A))) ) ) ).
tt(d7_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v7_conaffm A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A C D E F) &  ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r5_analmetr A B C E) &  ((r5_analmetr A B D F) &  ((r4_analmetr A C G D H) & (r4_analmetr A E G F H)) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ( (C = E)  |  ((r5_analmetr A B G C) | (r4_analmetr A B G B H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_conlat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_waybel_1 C A B) =>  ((v3_conlat_1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ( (C = (k1_waybel_1 A B D E))  &  ((v5_waybel_0 D A B) &  ((v5_waybel_0 E B A) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ((r1_orders_2 A F (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D F))) & (r1_orders_2 B H (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k7_conlat_2 A) = (g1_conlat_1 (u4_struct_0 A) (u1_struct_0 A) (k3_relset_1 (u1_struct_0 A) (u4_struct_0 A) (u1_conlat_1 A)))) ) ) ).
tt(d7_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v7_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r10_analmetr A J K) &  ((r2_hidden B J) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((r2_hidden H J) &  ((r2_hidden C K) &  ((r2_hidden E K) &  ((r2_hidden G K) &  ((r2_hidden I K) &  ((r2_analoaf A D C H G) &  ((r2_analoaf A C B G F) & (r2_analoaf A B E F I)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden E J) |  ((r2_hidden C J) |  ((r2_hidden G J) |  ((r2_hidden I J) |  ((r2_hidden B K) |  ((r2_hidden D K) |  ((r2_hidden F K) |  ((r2_hidden H K) | (r2_analoaf A D E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_connsp_1 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) <=>  ((v2_connsp_1 E A) & (r2_hidden B E)) ) ) )  &  ((k5_setfam_1 (u1_struct_0 A) D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_connsp_2 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) <=>  ((v3_pre_topc E A) &  ((v4_pre_topc E A) & (r2_hidden B E)) ) ) ) )  &  ((k6_setfam_1 (u1_struct_0 A) D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k6_connsp_3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_pre_topc A B))) =>  ( (E = C)  =>  (D = (k1_connsp_1 (k1_pre_topc A B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((r1_convex4 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers B D) = (k3_funct_2 (u1_struct_0 A) k2_numbers C D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))))) )  =>  ( (B = (k9_cqc_sim1 A))  <=>  ((r8_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) (k8_cqc_sim1 A B (k5_cqc_lang A)) (k8_funcop_1 (k3_cqc_lang A) (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k5_cqc_lang A))) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A C)) => (r8_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) (k8_cqc_sim1 A B (k4_cqc_lang C A E D)) (k6_cqc_sim1 A C E D))) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r8_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) (k8_cqc_sim1 A B (k6_cqc_lang A C)) (k2_cqc_sim1 A (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k8_cqc_sim1 A B C))) &  ((r8_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) (k8_cqc_sim1 A B (k7_cqc_lang A C D)) (k3_cqc_sim1 A (k8_cqc_sim1 A B C) (k8_cqc_sim1 A B D) (k7_cqc_sim1 A C))) & (r8_binop_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k3_cqc_lang A) (k8_cqc_sim1 A B (k11_cqc_lang A E C)) (k4_cqc_sim1 A (k8_cqc_sim1 A B C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k4_cqc_the1 A) = (k1_cqc_the1 A (k1_subset_1 (k3_cqc_lang A)))) ) ) ).
tt(d7_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A B C) <=> (v2_cqc_the1 (k10_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(d7_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k4_csspace4 A B)) =>  ((k6_csspace4 A B C) = C) ) ) ) ) ) ) ).
tt(d7_csspace,ax, (k7_csspace = (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace)) ).
tt(d7_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_decomp_1 A B) = (k9_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k2_pre_topc A B)))) ) ) ) ) ).
tt(d7_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k5_dickson A) = (g1_orders_2 (u1_struct_0 A) (k4_dickson (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(d7_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  ( (C = (k7_diff_1 A B))  <=>  ((r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C k6_numbers) A) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C (k1_nat_1 D 1)) (k4_diff_1 (k1_seqfunc k1_numbers k1_numbers C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d7_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_dilworth A B) = (k4_subset_1 (u1_struct_0 A) B (k3_waybel_0 A B))) ) ) ) ) ).
tt(d7_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v2_diraf A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B F) & (r2_analoaf A D E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v5_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k6_dist_1 A) (k3_finseq_2 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_dist_1 A) (k3_finseq_2 k1_numbers))))) )  =>  ( (B = (k7_dist_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A)) =>  (? [D:$i] :  ((m2_finseq_1 D A) &  ((r2_hidden D C) &  ((k3_funct_2 (k6_dist_1 A) (k3_finseq_2 k1_numbers) B C) = (k4_dist_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_dtconstr,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k11_dtconstr A) = (k1_nat_1 (k1_funct_1 A 1) 1)) ) ) ).
tt(d7_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (D = (k6_dynkin A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden E D) <=> (r2_hidden (k9_subset_1 A E C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  ( (D = (k4_ec_pf_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  ( ( (E = (k4_nat_d 4 A))  &  (F = (k4_nat_d 27 A)) )  =>  (D = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k2_binom (k9_int_3 A) B 3)) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) C 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( ( (~  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) = k6_numbers) )  =>  ((k7_ec_pf_2 A B) = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers (k8_group_1 (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) (k11_algstr_0 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B))) (k8_group_1 (k9_int_3 A) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) (k11_algstr_0 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B))) 1)) )  &  ( ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) B) = k6_numbers)  =>  ((k7_ec_pf_2 A B) = (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers)) ) ) ) ) ) ) ).
tt(d7_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l4_algstr_0 B)) )  =>  ((r1_endalg A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v6_group_1 C A B) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  & (v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d7_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k7_ens_1 A B C) = (a_3_0_ens_1 A B C)) ) ) ) ) ) ) ).
tt(d7_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k4_entropy1 A) = (k14_rvsum_1 A (k3_entropy1 2 A))) ) ) ).
tt(d7_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (J = (k7_enumset1 A B C D E F G H I))  <=>  (! [K:$i] :  ((r2_hidden K J) <=>  (~  ( (~  (K = A) )  &  ( (~  (K = B) )  &  ( (~  (K = C) )  &  ( (~  (K = D) )  &  ( (~  (K = E) )  &  ( (~  (K = F) )  &  ( (~  (K = G) )  &  ( (~  (K = H) )  &  (~  (K = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A)))) =>  ((v1_eqrel_1 B A) <=>  (! [C:$i] :  ((r2_hidden C B) => (m1_eqrel_1 C A)) ) ) ) ) ) ).
tt(d7_e_siec,ax, (! [A:$i] :  ((k5_e_siec A) = (g1_e_siec (k1_tarski A) k1_xboole_0 k1_xboole_0)) ) ).
tt(d7_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k7_euclid_3 A B C D) = (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k6_euclid_3 A B C D) (k5_euclid_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d7_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k8_euclid_8 A B C D) = (k1_euclid_8 (k1_fdiff_1 A D) (k1_fdiff_1 B D) (k1_fdiff_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d7_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k14_euclid A) = (g1_metric_1 (k1_euclid A) (k13_euclid A))) ) ) ).
tt(d7_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r5_euclidlp A B C) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) &  (? [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) &  ( (B = (k2_euclid_4 A D E))  &  ( (C = (k2_euclid_4 A F G))  & (r2_euclidlp A (k8_euclid A E D) (k8_euclid A G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ((v7_euclmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r4_analmetr A B G B H) &  ((r4_analmetr A C E D F) & (r4_analmetr A C G D H)) ) ) )  =>  ((r2_analoaf A B G B C) |  ((r2_analoaf A B C B E) | (r4_analmetr A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  ((k4_exchsort A) = (k1_funct_1 A (k3_tarski (k9_xtuple_0 A)))) ) ) ).
tt(d7_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ( (F = (k5_extpro_1 A B C D E))  <=>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k4_card_3 (k2_memstr_0 A B))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 A B)))))) )  &  ( (F = (k8_nat_1 (k4_card_3 (k2_memstr_0 A B)) G E))  &  ( ((k3_funct_2 k5_numbers (k4_card_3 (k2_memstr_0 A B)) G k6_numbers) = D)  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((k3_funct_2 k5_numbers (k4_card_3 (k2_memstr_0 A B)) G (k1_nat_1 H 1)) = (k4_extpro_1 A B (k8_nat_1 (k4_card_3 (k2_memstr_0 A B)) G H) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_facirc_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k4_facirc_1)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  ((k1_funct_1 A (k11_finseq_1 B C D)) = (k1_binarith (k1_binarith B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_fdiff_1 A B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (C = (k2_fdiff_1 A B))  <=>  ( ((k1_relset_1 k1_numbers C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k1_fdiff_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k7_ff_siec A) = (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d7_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k4_filter_0 A B C))  <=>  ((r3_lattices A (k4_lattices A B D) C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_lattices A (k4_lattices A B E) C) => (r3_lattices A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ((k7_filter_1 A B) = (g3_lattices (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k6_filter_1 (u1_struct_0 A) (u1_struct_0 B) (u2_lattices A) (u2_lattices B)) (k6_filter_1 (u1_struct_0 A) (u1_struct_0 B) (u1_lattices A) (u1_lattices B)))) ) ) ) ) ).
tt(d7_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_filter_2 A B) = (a_2_0_filter_2 A B)) ) ) ) ) ).
tt(d7_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( (E = (k6_finance1 A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F E) =>  ((k7_finance1 A B C D E F) = F) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k7_finseq_1 A B))  <=>  ( ((k4_finseq_1 C) = (k2_finseq_1 (k2_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k1_funct_1 C D) = (k1_funct_1 A D)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k1_funct_1 C (k2_nat_1 (k3_finseq_1 A) D)) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_finseq_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k7_finseq_4 A B C D) = (k7_finseq_1 (k11_finseq_1 A B C) (k9_finseq_1 D))) ) ) ) ) ).
tt(d7_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_finseq_8 A B C D) <=>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k3_finseq_6 A B E (k2_nat_1 (k7_nat_d E 1) (k3_finseq_1 C))) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_fintopo3 A B C) = (k1_funct_1 (k6_fintopo3 A B) C)) ) ) ) ) ) ) ).
tt(d7_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fintopo6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ((v2_fintopo6 E A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) B) &  ( ((k1_funct_1 E 1) = C)  &  ((k1_funct_1 E (k3_finseq_1 E)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_fin_topo A B) = (k9_subset_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 A) B) (k5_fin_topo A B))) ) ) ) ) ).
tt(d7_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 A) (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0))) =>  ((k4_fomodel0 A B C) = (k3_fomodel0 A B C)) ) ) ) ) ) ) ).
tt(d7_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k7_fomodel1 A) = (u2_struct_0 A)) ) ) ).
tt(d7_fomodel2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k7_fomodel2 A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k1_funct_1 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ( ((v1_xboole_0 C) & (v7_ordinal1 C))  =>  ((k10_fomodel3 A B C) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ) ) ) ) ) ) ).
tt(d7_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  (! [E:$i] :  ((v4_fomodel4 E A B C D) <=> (r2_hidden E (k1_funct_1 (k3_fomodel4 B C A) D))) ) ) ) ) ) ) ) ) ).
tt(d7_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v4_frechet A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_frechet C A) & (r1_tarski (k2_relset_1 (u1_struct_0 A) C) B))  => (r1_tarski (k2_frechet A C) B)) ) ) ) ) ) ) ) ) ).
tt(d7_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k4_finseq_1 A) B) (k3_finseq_2 (k2_xboole_0 (k4_finseq_1 A) B))))) =>  ( (C = (k2_freealg A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_xboole_0 (k4_finseq_1 A) B)) =>  (! [E:$i] :  ((m2_finseq_2 E (k2_xboole_0 (k4_finseq_1 A) B) (k3_finseq_2 (k2_xboole_0 (k4_finseq_1 A) B))) =>  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D (k4_finseq_1 A)) &  ((k1_funct_1 A D) = (k3_finseq_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k7_fscirc_1 A B C) = (k3_circcomb (k3_fscirc_1 A B C) (k5_circcomb k4_facirc_1 (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) (k5_fscirc_1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp) k4_facirc_1))) ) ) ) ).
tt(d7_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  ( (F = (k5_fsm_1 A B C D E))  <=>  ( ((k3_finseq_1 F) = (k2_nat_1 (k3_finseq_1 E) 1))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 (k2_nat_1 (k3_finseq_1 E) 1))) =>  ((k1_funct_1 F G) = (k1_funct_1 (u4_fsm_1 A B C) (k1_funct_1 (k2_fsm_1 A C D E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_tarski C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski C D) B)))) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v6_fsm_2 F A B) & (l2_fsm_2 F A B)) )  =>  ( (F = (k1_fsm_2 A B C D E))  <=>  ( ((u1_struct_0 F) = (k2_tarski C D))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 F) A) (u1_struct_0 F) (k2_zfmisc_1 (k2_tarski C D) A) (k1_tarski D) (u1_fsm_1 A F) (k7_funcop_1 (k2_zfmisc_1 (k2_tarski C D) A) D)) &  ((r1_funct_2 (u1_struct_0 F) B (k2_tarski C D) B (u4_fsm_1 A B F) E) &  ( ((u2_fsm_1 A F) = C)  &  ((u1_fsm_2 A F) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k5_fsm_3 A B C D) = (a_4_2_fsm_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d7_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k7_ftacell1 A B C D E) = (k2_circcomb (k25_gfacirc1 A B C) (k37_gfacirc1 (k24_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d7_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k13_funcop_1 A B C) = (k7_funcop_1 (k1_tarski (k4_tarski A B)) C)) ) ) ) ).
tt(d7_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k11_funcsdom A) = (g6_algstr_0 (k9_funct_2 A k1_numbers) (k5_funcsdom A) (k6_funcsdom A) (k9_funcsdom A) (k8_funcsdom A))) ) ) ).
tt(d7_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( (C = (k8_relat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k9_xtuple_0 A)) & (r2_hidden (k1_funct_1 A D) B)) ) ) ) ) ) ) ) ).
tt(d7_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) )  =>  ((r1_funct_2 A B C D E F) <=>  ( (A = C)  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k1_funct_1 E G) = (k1_funct_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k13_funct_3 A B))  <=>  ( ((k9_xtuple_0 C) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k7_funct_6 A))  <=>  ( ((k9_xtuple_0 B) = (k4_card_3 (k2_funct_6 A)))  &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((r2_hidden C (k4_card_3 (k2_funct_6 A))) &  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( ((k1_funct_1 B C) = D)  &  ( ((k9_xtuple_0 D) = (k8_relat_1 A (k1_funct_6 (k10_xtuple_0 A))))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k1_funct_1 D E) = (k1_binop_1 (k2_funct_5 A) E (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 A) =>  ( (B = (k7_funct_7 A))  <=> (v1_xboole_0 B)) )  &  ( (~ (v1_xboole_0 A))  =>  ( (B = (k7_funct_7 A))  <=>  (B = (k10_xtuple_0 (k1_funct_1 A (k3_finseq_1 A)))) ) ) ) ) ) ) ).
tt(d7_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v5_functor0 C A B) <=> (v2_funct_2 (u1_functor0 A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))) ) ) ) ) ) ) ).
tt(d7_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  ((r2_functor2 A B C D) =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  ((m2_functor2 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A F G)) =>  ((k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C G) (k3_functor0 A B D G) (k6_functor0 A B C F G H) (k2_functor2 A B C D E G)) = (k5_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B D F) (k3_functor0 A B D G) (k2_functor2 A B C D E F) (k6_functor0 A B D F G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_fuzzy_1 A) = (k7_rfunct_1 A A)) ) ) ).
tt(d7_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k11_fvsum_1 A B C) = (k1_finseqop (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) B C)) ) ) ) ) ) ) ).
tt(d7_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k7_gate_5 A B C D E) = (k35_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0)) ) ) ) ) ) ).
tt(d7_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_gcd_1 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) & (r4_gcd_1 A D C)) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  (~  ( (~  (C = D) )  & (r3_gcd_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_card_3 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_card_3 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ((k6_genealg1 A B C D E F G H I) = (k1_genealg1 A (k5_genealg1 A B C D E F G H) (k5_genealg1 A C B D E F G H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) =>  ( (D = (k5_geomtrap A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) G H))  &  ( (F = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) I J))  & (r2_geomtrap A B C G H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k7_gfacirc1 A B C) = (k2_circcomb (k5_gfacirc1 A B C) (k5_circcomb k25_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))))) ) ) ) ).
tt(d7_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k5_gfacirc2 A B C)) (k3_msafree2 (k5_gfacirc2 A B C))) =>  ( (D = (k7_gfacirc2 A B C))  <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  &  ( (D = (k1_funct_1 E A))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 E (k1_nat_1 F 1)) = (k21_gfacirc1 (k1_funct_1 B (k1_nat_1 F 1)) (k1_funct_1 C (k1_nat_1 F 1)) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k7_glib_000 A) = (k1_funct_1 A k2_glib_000)) ) ) ).
tt(d7_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k4_glib_001 A B) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ).
tt(d7_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ((v4_glib_002 B A) <=>  ((v1_glib_002 B) &  (! [C:$i] :  ( ((v1_glib_002 C) & (m1_glib_000 C A))  =>  (~ (r7_glib_000 B C)) ) ) ) ) ) ) ) ) ).
tt(d7_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((k5_glib_003 A) = (k1_funct_1 A k2_glib_003)) ) ) ).
tt(d7_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (C = (k6_glib_004 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r4_glib_000 A (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B)) (k6_subset_1 (k6_glib_000 A) (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B))) D) &  (! [E:$i] :  ((r4_glib_000 A (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B)) (k6_subset_1 (k6_glib_000 A) (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B))) E) => (r1_xxreal_0 (k2_xcmplx_0 (k1_seq_1 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_funct_1 (k10_glib_000 A) D)) (k1_seq_1 (k5_glib_003 A) D)) (k2_xcmplx_0 (k1_seq_1 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_funct_1 (k10_glib_000 A) E)) (k1_seq_1 (k5_glib_003 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_glib_005 C A B) =>  (! [D:$i] :  ((r4_glib_005 A B C D) <=>  ((r2_hidden D (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k11_glib_000 A) D) (k1_relset_1 (k6_glib_000 A) C)) &  ( (~ (r2_hidden (k1_funct_1 (k10_glib_000 A) D) (k1_relset_1 (k6_glib_000 A) C)))  &  (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ((v5_goboard1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 A))) => (v5_valued_0 (k1_goboard1 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ).
tt(d7_goboard5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (k5_goboard5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k2_goboard2 A))) &  ((r2_hidden (k4_tarski F G) (k2_matrix_1 (k2_goboard2 A))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D E))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) F G))  &  ( (~  ( (D = F)  &  ( ((k2_nat_1 E 1) = G)  &  (C = (k3_goboard5 (k2_goboard2 A) (k7_nat_d D 1) E)) ) ) )  &  ( (~  ( ((k2_nat_1 D 1) = F)  &  ( (E = G)  &  (C = (k3_goboard5 (k2_goboard2 A) D E)) ) ) )  &  ( (~  ( (D = (k2_nat_1 F 1))  &  ( (E = G)  &  (C = (k3_goboard5 (k2_goboard2 A) F (k7_nat_d G 1))) ) ) )  &  (~  ( (D = F)  &  ( (E = (k2_nat_1 G 1))  &  (C = (k3_goboard5 (k2_goboard2 A) D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_gobrd13,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_gobrd13 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 C)) &  ( ((k7_partfun1 A B D) = (k3_matrix_1 A C E F))  &  ( ((k7_partfun1 A B (k2_nat_1 D 1)) = (k3_matrix_1 A C G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  ((r2_hidden (k4_tarski (k7_nat_d G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k7_nat_d G 1) H)) ) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  ((r2_hidden (k4_tarski G (k2_nat_1 H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k2_nat_1 H 1))) ) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  ((r2_hidden (k4_tarski G (k7_nat_d H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k7_nat_d H 1))) ) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  ((r2_hidden (k4_tarski (k2_nat_1 G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k2_nat_1 G 1) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_cqc_lang A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (D = (k5_goedelcp A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (E = (k3_funct_2 k5_numbers (k3_cqc_lang A) B C))  =>  (D = (k3_goedelcp A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v2_graph_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (u4_struct_0 A)) &  ((r2_hidden C (u4_struct_0 A)) &  ( ((k1_funct_1 (u1_graph_1 A) B) = (k1_funct_1 (u1_graph_1 A) C))  &  ((k1_funct_1 (u2_graph_1 A) B) = (k1_funct_1 (u2_graph_1 A) C)) ) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(d7_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_graph_2 A B) <=>  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( ((k1_card_1 (k5_graph_2 A (k10_xtuple_0 B))) = 2)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 B C)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_graph_1 D) & (l1_graph_1 D)) )  =>  ( (D = (k8_graph_3 A B C))  <=>  ( ((u1_struct_0 D) = (u1_struct_0 A))  &  ( ((u4_struct_0 D) = (k2_xboole_0 (u4_struct_0 A) (k1_tarski (u4_struct_0 A))))  &  ( ((u1_graph_1 D) = (k1_funct_4 (u1_graph_1 A) (k16_funcop_1 (u4_struct_0 A) B)))  &  ((u2_graph_1 D) = (k1_funct_4 (u2_graph_1 A) (k16_funcop_1 (u4_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  ((v1_graph_4 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((r3_graph_4 A C B) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) )  =>  ((r1_xxreal_0 E D) |  ( (D = 1)  &  (E = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r4_graph_5 A B C D E) <=>  ((v1_graph_4 B A) & (r2_graph_5 A C D B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( (? [E:$i] :  ((r2_hidden E (u4_struct_0 A)) & (r1_graph_4 A B C E)) )  =>  ((k11_graphsp A B C D) = (k1_funct_1 D (k10_graphsp A B C))) )  &  ( (! [E:$i] :  (~  ((r2_hidden E (u4_struct_0 A)) & (r1_graph_4 A B C E)) ) )  =>  ((k11_graphsp A B C D) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((k6_grcat_1 A B) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(d7_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_gr_cy_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)) = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(d7_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r4_groeb_1 A B C D) <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden E D) =>  ((r3_groeb_1 A B C E) &  (~ (r7_polyred A B C E (k7_subset_1 (u1_struct_0 (k11_polynom1 A C)) D (k1_groeb_1 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r3_groeb_2 A B C D E F G) <=>  ( ((k4_rlvect_1 (k11_polynom1 A C) F) = D)  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 F)) &  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 I A C) &  ((v3_polynom7 I A C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 J A C) &  ((v1_polynom1 J (k15_pre_poly A) C) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (~  ((r2_hidden J E) &  ( ((k7_partfun1 (u1_struct_0 (k11_polynom1 A C)) F H) = (k9_polynom1 A C I J))  & (r1_termord A B (k3_termord A B C (k9_polynom1 A C I J)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) B) (k2_zfmisc_1 (u1_struct_0 A) B))) &  ((v1_group_10 C A (k2_zfmisc_1 (u1_struct_0 A) B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) B) (k2_zfmisc_1 (u1_struct_0 A) B)))))) ) )  =>  ( (C = (k7_group_10 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) B) (k2_zfmisc_1 (u1_struct_0 A) B)) C D) = (k6_group_10 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  =>  ( (B = (k4_group_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C k6_numbers) = (k1_group_1 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C (k2_nat_1 D 1)) = (k6_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) B C D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( (B = (k6_group_2 A))  <=>  ((u1_struct_0 B) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ) ) ).
tt(d7_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_group_3 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (B = (k2_group_3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ( (? [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  & (v2_group_4 C A)) )  =>  ( (B = (k6_group_4 A))  <=>  ((u1_struct_0 B) = (k1_setfam_1 (a_1_0_group_4 A))) ) )  &  ( (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (~ (v2_group_4 C A)) ) )  =>  ( (B = (k6_group_4 A))  <=>  (B = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ) ) ).
tt(d7_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_group_5 A B C) = (k5_group_4 A (k4_group_5 A B C))) ) ) ) ) ) ) ).
tt(d7_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (C = (k7_group_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_group_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_group_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v3_group_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (v3_group_1 (k1_group_7 A B C))) ) ) ) ) ) ) ).
tt(d7_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  ((m1_group_9 C A B) <=>  ((m1_group_2 C B) &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_group_9 A C D) = (k2_partfun1 (u1_struct_0 B) (u1_struct_0 B) (k3_group_9 A B D) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(d7_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((l1_vectsp_1 B A) =>  ((k7_hahnban1 A B) = (k8_funcop_1 (u1_struct_0 A) (k2_struct_0 B) (k4_struct_0 A))) ) ) ) ) ).
tt(d7_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ( ((k1_funct_1 B C) = k1_xboole_0)  |  (! [D:$i] :  ((m2_hallmar1 D A B) =>  ((m3_hallmar1 D A B C) <=>  ((k1_card_1 (k1_funct_1 D C)) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  =>  ((v5_hermitan B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)))) ) ) ) ) ) ) ).
tt(d7_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k7_heyting1 A B C) = (k8_subset_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A) (a_3_2_heyting1 A B C))) ) ) ) ) ) ).
tt(d7_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)))))) )  =>  ( (D = (k7_heyting2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_substlat A B))) =>  ((k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) D E) = (k6_subset_1 C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))))))) )  =>  ( (C = (k7_hilbasis A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly (k2_nat_1 B 1)) (u1_struct_0 A)) &  ((v1_polynom1 D (k15_pre_poly (k2_nat_1 B 1)) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k2_nat_1 B 1)) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly B) (u1_struct_0 A)) &  ((v1_polynom1 E (k15_pre_poly B) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 A))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 (k11_polynom1 B A))) &  ((v1_algseq_1 F (k11_polynom1 B A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k11_polynom1 B A)))))) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H B) &  ((v1_funct_1 H) &  ((v1_partfun1 H B) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  ( ( (F = (k1_funct_1 C D))  &  (E = (k1_normsp_1 (k11_polynom1 B A) F G)) )  =>  ((k3_polynom1 B A E H) = (k3_polynom1 (k1_nat_1 B 1) A D (k1_hilbasis B G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_hilbert1,ax, (k2_hilbert1 = (k12_finseq_1 k5_numbers k6_numbers)) ).
tt(d7_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v2_hilbert2 A) <=>  (? [B:$i] :  ((m1_subset_1 B k1_hilbert1) &  (? [C:$i] :  ((m1_subset_1 C k1_hilbert1) &  (A = (k3_hilbert1 B C)) ) ) ) ) ) ) ) ).
tt(d7_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v1_hilbert3 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (? [C:$i] :  (! [D:$i] :  ((m1_hilbert3 D B) => (r1_abian C (k5_hilbert3 B D A))) ) ) ) ) ) ) ) ).
tt(d7_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_hurwitz A B C) <=> (r2_funct_2 k5_numbers (u1_struct_0 A) (k6_hurwitz A B C) (k9_polynom3 A))) ) ) ) ) ) ) ).
tt(d7_idea_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (B = k6_numbers)  =>  ((k7_idea_1 A B) = (k5_series_1 2 A)) )  &  ( (~  (B = k6_numbers) )  =>  ((k7_idea_1 A B) = B) ) ) ) ) ) ) ).
tt(d7_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v3_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  ( (~  (E = C) )  &  ((r1_incsp_1 A C B) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((v4_incsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) & (r5_incsp_1 A B C)) ) ) ) ) ) ) ).
tt(d7_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) )  =>  ((m2_index_1 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (m2_cat_1 (k1_funct_1 D E) (k2_index_1 A B E) (k2_index_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k2_int_1 A))  <=>  ((r1_xxreal_0 A B) &  (~ (r1_xxreal_0 (k3_real_1 A 1) B)) ) ) ) ) ) ) ).
tt(d7_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ( (~  (B = (k4_struct_0 k1_int_3)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_int_3)) =>  ( (C = (k5_int_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_int_3)) &  ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 D B) C))  &  ((r1_xxreal_0 (k4_struct_0 k1_int_3) C) &  (~ (r1_xxreal_0 (k2_int_3 B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r3_integr10 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k3_integr10 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers D) = (k2_limfunc1 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k1_relset_1 k1_numbers D)) =>  ((k1_seq_1 D E) = (k4_integra5 B E A)) ) ) )  &  ((v3_limfunc1 D) &  (C = (k4_limfunc1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k3_finseq_2 (k1_euclid A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (k1_euclid A)))))) )  =>  ((m4_integr15 E A B C D) <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (m3_integr15 (k3_funct_2 k5_numbers (k3_finseq_2 (k1_euclid A)) E F) A B C (k2_integra2 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((r1_integr16 A B) <=>  ((r1_integra5 A (k5_comseq_3 k1_numbers B)) & (r1_integra5 A (k6_comseq_3 k1_numbers B))) ) ) ) ) ) ).
tt(d7_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r1_integr18 A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ( (D = (k2_partfun1 k1_numbers (u1_struct_0 A) C B))  & (v1_integr18 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k5_integra1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_seq_1 D E) = (k8_real_1 (k5_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers B (k2_integra1 A C E)))) (k3_integra1 (k2_integra1 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_intpro_1,ax, (! [A:$i] :  ((v7_intpro_1 A) <=>  ((r1_tarski A (k13_finseq_1 k5_numbers)) &  ((v1_intpro_1 A) &  ((v2_intpro_1 A) &  ((v3_intpro_1 A) &  ((v4_intpro_1 A) &  ((v5_intpro_1 A) & (v6_intpro_1 A)) ) ) ) ) ) ) ) ).
tt(d7_irrat_1,ax, (k7_power = (k26_sin_cos 1)) ).
tt(d7_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r2_nattra_1 A B D E) =>  (! [F:$i] :  ((m2_nattra_1 F A B D E) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  ((k4_isocat_1 A B C D E F G) = (k2_isocat_1 A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  ((k9_isocat_2 A B C D) = (k9_cat_1 A (k8_cat_2 B C) B D (k14_cat_2 B C))) ) ) ) ) ) ) ) ) ).
tt(d7_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_isomichi B A) <=> (r2_xboole_0 (k2_pre_topc A (k1_tops_1 A B)) (k1_tops_1 A (k2_pre_topc A B)))) ) ) ) ) ).
tt(d7_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (B = (k7_jgraph_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B C) = (k6_jgraph_4 A C)) ) ) ) ) ) ) ) ).
tt(d7_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k7_jgraph_6 A B C) = (a_3_2_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(d7_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  (~ (r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B))) ) )  |  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) )  =>  ((k4_jordan3 A B C) = (k3_jordan3 (k2_jordan3 A B) C)) )  &  (~  ( (~  ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  (~ (r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B))) ) ) )  &  ( (~  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) )  &  (~  ((k4_jordan3 A B C) = (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 (k2_jordan3 A C) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k7_jordan5d A))  <=>  ((r2_hidden (k4_tarski B (k1_matrix_1 (k2_goboard2 A))) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A))) = (k20_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d7_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_jordan6 A) = (a_1_5_jordan6 A)) ) ) ).
tt(d7_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k5_jordan_a A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  &  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers))) )  &  ( (D = (a_2_1_jordan_a A B))  &  ( (E = (a_2_2_jordan_a A B))  &  (C = (k3_xxreal_0 (k2_xxreal_2 D) (k2_xxreal_2 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_jordan,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  ((m1_subset_1 C (u1_struct_0 (k2_brouwer A B D))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D)))))) )  =>  ( (E = (k9_jordan A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C))))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) &  ( (F = G)  &  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D)) E F) = (k3_brouwer A B C G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_kolmog01,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 B)))) =>  ( (E = (k5_kolmog01 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ((r2_hidden F E) <=>  (? [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 A)))  &  (F = (k4_kolmog01 A B C D (k6_subset_1 A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lang1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_lang1 B) & (l2_lang1 B))  =>  ( (B = (k6_lang1 A))  <=>  ( ((u1_struct_0 B) = (k1_tarski A))  &  ((u1_lang1 B) = (k1_tarski (k4_tarski A k1_xboole_0))) ) ) ) ) ) ).
tt(d7_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A A) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  ( (E = (k8_laplace A B C D))  <=>  ( ((k3_finseq_1 E) = A)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k8_group_1 C (k3_matrix_1 (u1_struct_0 C) D B F) (k6_laplace B F A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lattice3 A))) =>  ((k9_lattice3 A B) = B) ) ) ) ) ).
tt(d7_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  ((k1_lattice4 A B) = (k2_lattice2 (u1_struct_0 A) A B (k3_struct_0 A))) ) ) ) ) ).
tt(d7_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v3_lattice5 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) => (r1_orders_2 B (k3_lattice5 A B C D F) (k13_lattice3 B (k3_lattice5 A B C D E) (k3_lattice5 A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattice6 A B) = (k15_lattice3 A (a_2_3_lattice6 A B))) ) ) ) ) ).
tt(d7_lattice7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k4_lattice7 A) = (a_1_1_lattice7 A)) ) ) ).
tt(d7_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  (! [F:$i] :  ( (F = (k5_lattice8 A B C D E))  <=>  (? [G:$i] :  ( ((v5_ordinal1 G) &  ((v1_relat_1 G) & (v1_funct_1 G)) )  &  ( (F = (k1_ordinal2 G))  &  ( ((k9_xtuple_0 G) = (k1_ordinal1 E))  &  ( ((k1_funct_1 G k1_xboole_0) = C)  &  ( (! [H:$i] :  ((v3_ordinal1 H) =>  ((r2_hidden (k1_ordinal1 H) (k1_ordinal1 E)) =>  ((k1_funct_1 G (k1_ordinal1 H)) = (k2_lattice8 (k3_lattice8 A H) B (k10_lattice5 (k3_lattice8 A H) B (k1_funct_1 G H)) (k4_lattice8 A B C D H))) ) ) )  &  (! [H:$i] :  ((v3_ordinal1 H) =>  ( ((r2_hidden H (k1_ordinal1 E)) & (v4_ordinal1 H))  =>  ( (H = k1_xboole_0)  |  ((k1_funct_1 G H) = (k3_tarski (k2_relset_1 (k10_xtuple_0 G) (k5_relat_1 G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v7_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_lattices A B (k2_lattices A C D)) = (k2_lattices A (k2_lattices A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ((v3_lexbfs A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B C) =>  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(d7_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v3_lfuzzy_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_orders_2 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (k12_lattice3 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (k7_lfuzzy_0 (k2_zfmisc_1 A A) B (k1_domain_1 A A C D)) (k7_lfuzzy_0 (k2_zfmisc_1 A A) B (k1_domain_1 A A D E))) (k7_lfuzzy_0 (k2_zfmisc_1 A A) B (k1_domain_1 A A C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 B) & (r1_tarski (k2_relset_1 k1_numbers B) (k1_relset_1 k1_numbers A)))  => (v1_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) ) ) ) ) ) ) ).
tt(d7_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_limfunc2 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k1_limfunc2 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k8_lopban_1 A B) = (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) ) ) ) ) ).
tt(d7_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_lopban_2 A) = (g1_funcsdom (k10_lopban_1 A A) (k5_lopban_2 A) (k8_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k9_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k6_lopban_2 A) (k10_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)))) ) ) ).
tt(d7_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k4_lopban_3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k6_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k6_lopban_4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k6_algstr_0 B (k1_rlvect_1 B (k6_lopban_3 B C F) (k8_nat_1 k1_numbers (k3_lopban_4 A) F)) (k6_lopban_3 B D (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k10_lopclset A) = (k2_relset_1 (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A))) ) ) ).
tt(d7_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_lpspace1 A) = (g1_rlvect_1 (k3_rfunct_3 A k1_numbers) (k5_lpspace1 A) (k13_rfunct_3 A) (k4_lpspace1 A))) ) ) ).
tt(d7_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k6_lpspace2 A B C D) = (a_4_2_lpspace2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d7_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k7_ltlaxio1 A) = (k1_ltlaxio1 (k6_ltlaxio1 (k1_ltlaxio1 A)))) ) ) ).
tt(d7_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (B = (k3_margrel1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r1_tarski C (k3_finseq_2 A)) &  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_mathmorp A B C D) = (k9_subset_1 (u1_struct_0 A) (k3_mathmorp A B C) (k3_mathmorp A (k3_subset_1 (u1_struct_0 A) B) D))) ) ) ) ) ) ) ) ) ).
tt(d7_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k1_matrix10 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers B C D) = (k18_complex1 (k3_matrix_1 k1_numbers A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrix16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v2_matrix16 B A) =>  (! [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) =>  ( (C = (k1_matrix16 A B))  <=> (r1_matrix16 A C B)) ) ) ) ) ) ) ) ).
tt(d7_matrix17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v5_matrix17 B A) =>  (! [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) =>  ( (C = (k1_matrix17 A B))  <=> (r1_matrix17 A C B)) ) ) ) ) ) ) ) ).
tt(d7_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k6_matrix_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k1_matrix_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k1_matrix_1 B))) =>  ((k1_funct_1 D E) = (k3_matrix_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrix_2,ax, (! [A:$i] :  ((v3_matrix_2 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((r2_hidden C A) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 B) (k2_finseq_1 B)) &  ((v3_funct_2 C (k2_finseq_1 B) (k2_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 B) (k2_finseq_1 B))))) ) ) ) ) ) ) ) ) ).
tt(d7_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( (E = (k10_matrix_3 A B C D))  <=>  ( ((k3_finseq_1 E) = A)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden F (k4_finseq_1 E)) &  (G = (k1_funct_1 D F)) )  =>  ((k1_funct_1 E F) = (k3_matrix_1 (u1_struct_0 B) C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrix_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( (C = (k7_matrix_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ( (D = A)  =>  (C = (k2_matrix_5 (k6_matrix_3 k1_complfld (k1_matrix_5 B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v4_matrix_6 C A B) <=>  ((v1_matrix_6 C A B) &  ((k5_matrix_1 A (u1_struct_0 B) C) = (k5_matrix_6 A B C)) ) ) ) ) ) ) ) ) ).
tt(d7_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B C) = (k4_rlvect_1 B (k13_matrix_3 A B C))) ) ) ) ) ) ) ).
tt(d7_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_matrixc1 A B) = (k7_matrix_5 B A)) ) ) ) ) ).
tt(d7_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k21_matrixj1 A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k12_matrix_3 (k3_finseq_1 (k2_matrixj1 (u1_struct_0 A) B D)) A (k14_matrixj1 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrixr1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( (C = (k7_matrixr1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  ( (D = A)  =>  (C = (k2_matrixr1 (k6_matrix_3 k2_vectsp_1 (k1_matrixr1 B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( (E = (k9_matrlin A B C D))  <=>  ( ((k3_finseq_1 E) = (k3_finseq_1 C))  &  (? [F:$i] :  ((m1_vectsp_6 F A B) &  ( (D = (k4_vectsp_6 A B F))  &  ((r1_tarski (k1_vectsp_6 A B F) (k10_xtuple_0 C)) &  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k3_finseq_1 E)))  =>  ((k7_partfun1 (u1_struct_0 A) E G) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F (k7_partfun1 (u1_struct_0 B) C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_matroid0 A) <=>  ((v3_matroid0 A) &  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc C A) => (r1_xxreal_0 (k5_card_1 C) B)) ) ) ) ) ) ) ) ) ).
tt(d7_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v3_matrprob A) <=>  ((k5_matrprob A) = 1) ) ) ) ).
tt(d7_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  ( (E = (k3_mcart_1 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (D = (k3_xtuple_0 F G H))  =>  (E = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((m2_measure1 D A B C) <=>  ((k12_supinf_2 C D) = k1_supinf_2) ) ) ) ) ) ) ) ) ).
tt(d7_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ((v2_measure6 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden B A) => (v2_rcomp_1 B)) ) ) ) ) ) ).
tt(d7_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ((m2_measure7 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (C = (k7_measure7 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k12_supinf_2 C D) = (k6_measure7 (k8_nat_1 (k9_setfam_1 k1_numbers) A D) (k4_measure7 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d7_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k7_numbers)) =>  ( (E = (k5_measure8 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F k7_numbers) =>  ((r2_hidden F E) <=>  (? [G:$i] :  ((m3_measure8 G A D B) &  (F = (k19_supinf_2 (k2_measure8 A B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k10_member_1 A B) = (k8_member_1 A (k4_member_1 B))) ) ) ) ) ).
tt(d7_membered,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(d7_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k5_memstr_0 A B C) = (k1_funct_1 C (k4_struct_0 B))) ) ) ) ) ) ) ).
tt(d7_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k7_mesfun7c A B) = (k6_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d7_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun9c A B C) <=>  ((v1_mesfunc8 B A k2_numbers) &  ( ((k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers)) = (k1_relset_1 A C))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (? [F:$i] :  ((v7_ordinal1 F) &  (? [G:$i] :  ((m1_subset_1 G A) &  ((r1_xxreal_0 E F) &  ((r2_hidden G (k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers))) & (r1_xxreal_0 D (k17_complex1 (k6_xcmplx_0 (k1_funct_1 (k4_mesfunc5 A k2_numbers B F) G) (k1_funct_1 C G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k7_mesfunc1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k12_supinf_2 C D) = (k2_supinf_2 (k12_supinf_2 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k1_mesfunc5 A B) = B) ) ) ) ) ).
tt(d7_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k5_mesfunc8 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k6_rinfsup2 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v7_metric_1 A) <=> (v3_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ).
tt(d7_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k4_metric_2 A B) = (a_2_1_metric_2 A B)) ) ) ) ) ).
tt(d7_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_metric_1 D) &  ((v7_metric_1 D) &  ((v8_metric_1 D) &  ((v9_metric_1 D) & (l1_metric_1 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) k1_numbers)))) )  =>  ( (E = (k7_metric_3 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 C)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 C)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 D)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 D)) =>  (! [N:$i] :  ((m1_subset_1 N (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) =>  (! [O:$i] :  ((m1_subset_1 O (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) =>  ( ( (N = (k5_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D) F H J L))  &  (O = (k5_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D) G I K M)) )  =>  ((k1_metric_1 (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) E N O) = (k7_real_1 (k7_real_1 (k4_metric_1 A F G) (k4_metric_1 B H I)) (k7_real_1 (k4_metric_1 C J K) (k4_metric_1 D L M)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (D = (k3_metric_6 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k4_metric_1 A (k2_tbsp_1 A B E) (k2_tbsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((m1_midsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  (B = (k4_midsp_1 A C)) ) ) ) ) ) ) ) ).
tt(d7_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  ((r4_midsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((k1_funct_1 E B) = F)  =>  ((k4_midsp_3 A C D (k6_midsp_3 A C E (k2_nat_1 B 1) F)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k7_mmlquery A B C D) = (a_4_2_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d7_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((l1_mod_2 B A) =>  ((v3_mod_2 B A) <=>  ((v13_vectsp_1 (k4_mod_2 A B) (k2_mod_2 A B) (k3_mod_2 A B)) & (v1_mod_2 (k4_mod_2 A B) A (k2_mod_2 A B) (k3_mod_2 A B))) ) ) ) ) ) ).
tt(d7_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_mod_4 C A B) <=>  ((v13_vectsp_1 C A B) &  ((v1_mod_4 C A B) & (v6_group_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(d7_modal_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k9_modal_1 A B C D) = (k7_trees_2 B D C)) ) ) ) ) ) ) ) ) ) ).
tt(d7_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ((m3_modcat_1 C A) =>  ( (C = (k4_modcat_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ( ((v7_vectsp_1 E A) & (m2_modcat_1 E A B))  &  (? [F:$i] :  ( ((v7_vectsp_1 F A) & (m2_modcat_1 F A B))  &  ((v2_mod_2 D A) & (m1_mod_2 D A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k7_modelc_1 A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers k6_numbers) A)) ) ) ).
tt(d7_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k7_modelc_2 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 4) A) B)) ) ) ) ) ).
tt(d7_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ((l1_modelc_3 C A) =>  ((r2_modelc_3 A B C) <=>  (? [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  &  ((r2_hidden D (u2_modelc_3 A B)) &  (C = (k5_modelc_3 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k6_moebius1 A) = (k8_nat_3 k10_newton (k5_moebius1 A))) ) ) ).
tt(d7_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v7_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k5_binop_1 A B D C) = (k5_binop_1 A B E C))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k13_monoid_1 A))) =>  ( (C = (k20_monoid_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k15_monoid_1 A C D) = (k5_card_1 (k1_relset_1 k5_numbers (k6_relset_1 k5_numbers A (k6_domain_1 A D) B)))) ) ) ) ) ) ) ) ) ) ).
tt(d7_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k3_msafree2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( (C = (k4_msafree2 A B))  <=>  ((k2_msualg_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(d7_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))))) =>  ( (C = (k4_msafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B)))) =>  (! [E:$i] :  ((m2_finseq_2 E (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))) =>  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) &  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k4_tarski F (u1_struct_0 A)) = D)  =>  ( ((k3_finseq_1 E) = (k3_finseq_1 (k1_msualg_1 A F)))  &  (! [G:$i] :  ((r2_hidden G (k4_finseq_1 E)) =>  ( ((r2_hidden (k1_funct_1 E G) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ( ((k4_tarski H (u1_struct_0 A)) = (k1_funct_1 E G))  =>  ((k2_msualg_1 A H) = (k1_funct_1 (k1_msualg_1 A F) G)) ) ) ) )  &  ((r2_hidden (k1_funct_1 E G) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) => (r2_hidden (k1_funct_1 E G) (k2_msafree (u1_struct_0 A) B (k1_funct_1 (k1_msualg_1 A F) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((m3_msaterm C A B) <=>  (? [D:$i] :  ((m2_msaterm D A B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ).
tt(d7_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((v6_mssubfam C A B) <=> (r1_pboole A (k1_pboole A) C)) ) ) ) ) ) ).
tt(d7_msualg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v5_msualg_1 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  ((u4_struct_0 A) = (k2_finseq_1 B)) ) ) ) ) ) ).
tt(d7_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r1_msualg_2 A B C D) =>  ((k3_msualg_2 A B C D) = (k5_relat_1 (k5_msualg_1 A C B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) D)) C))) ) ) ) ) ) ) ) ) ) ).
tt(d7_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( (~  ((k3_msualg_1 A E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A E B)) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D (k2_msualg_1 A E)) (k1_funct_1 (k5_msualg_1 A E B) F)) = (k1_funct_1 (k5_msualg_1 A E C) (k5_msualg_3 A B C E D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k3_relat_1 (k1_msualg_1 A B) (k4_msualg_4 A C D)))) =>  ( (F = (k6_msualg_4 A B C D E))  <=>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 (k1_msualg_1 A B))) =>  ((k1_funct_1 F G) = (k6_eqrel_1 (k1_funct_1 (u3_msualg_1 A C) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G)) (k1_funct_1 (u3_msualg_1 A C) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G)) (k2_msualg_4 A C D (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G)) (k1_funct_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v2_msualg_6 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r2_hidden E (k3_msualg_1 A D B)) &  ((r2_hidden F (k3_msualg_1 A D B)) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k4_finseq_1 (k1_msualg_1 A D))) => (r2_hidden (k4_tarski (k1_funct_1 E G) (k1_funct_1 F G)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) G)))) ) ) ) )  => (r2_hidden (k4_tarski (k1_funct_1 (k5_msualg_1 A D B) E) (k1_funct_1 (k5_msualg_1 A D B) F)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k2_msualg_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ((m1_mycielsk B A) <=>  ((u1_struct_0 B) = A) ) ) ) ) ) ).
tt(d7_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( (D = (k3_nagata_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers D E) = (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B E) (k3_funct_2 (u1_struct_0 A) k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (B = 1) )  &  ( (~  (A = k6_numbers) )  &  (~  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k10_nat_3 A B))  <=>  ((r1_nat_d (k1_newton B C) A) &  (~ (r1_nat_d (k1_newton B (k23_binop_2 C 1)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_nat_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( (A = k6_nat_5)  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_recdef_1 A B) = (k1_euler_1 B)) ) ) ) ) ) ).
tt(d7_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r2_nattra_1 A B C D) <=>  ((r1_nattra_1 A B C D) &  (? [E:$i] :  ((m1_nattra_1 E A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_cat_1 H A F G) =>  ((k5_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B C G) (k8_cat_1 A B D G) (k9_cat_3 A F G B C H) (k4_nattra_1 A B C D E G)) = (k5_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B D F) (k8_cat_1 A B D G) (k4_nattra_1 A B C D E F) (k9_cat_3 A F G B D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k1_relset_1 (u1_struct_0 A) C)) &  ((v3_normsp_1 E A) &  ((k6_normsp_1 A E) = D) ) )  =>  ((v9_clvect_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) B) &  ((k7_partfun1 (u1_struct_0 B) C D) = (k7_clvect_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_clvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v1_ncfcont2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E))) (k8_real_1 C (k1_normsp_0 A (k5_algstr_0 A D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ndiff_1 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 A B))) =>  ( (E = (k3_ndiff_1 A B C D))  <=>  (? [F:$i] :  ((m1_nfcont_1 F A D) &  ((r1_tarski F (k1_relset_1 (u1_struct_0 A) C)) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_ndiff_1 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden H F) =>  ((k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C H) (k7_partfun1 (u1_struct_0 B) C D)) = (k3_rlvect_1 B (k17_lopban_1 A B E (k5_algstr_0 A H D)) (k7_partfun1 (u1_struct_0 B) G (k5_algstr_0 A H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((v3_ndiff_3 B A) <=> (r2_ndiff_3 A B (k1_relset_1 k1_numbers B))) ) ) ) ) ).
tt(d7_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_real_ns1 A)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers)))) )  =>  ( (D = (k3_ndiff_4 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) &  ( (B = E)  &  ( (C = F)  & (r1_funct_2 (u1_struct_0 (k4_real_ns1 A)) k1_numbers (k1_euclid A) k1_numbers D (k1_pdiff_7 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  ((k6_ndiff_5 A B C D E) = (k3_ndiff_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A C))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A C) E) D) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A C))) (k3_ndiff_5 A (k5_ndiff_5 A C)) E))) ) ) ) ) ) ) ) ) ) ).
tt(d7_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( (B = (k2_necklace A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((u1_orders_2 B) = (k4_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_orders_2 A) (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))) ) ) ) ) ) ) ).
tt(d7_net_1,ax, (! [A:$i] :  ((l1_petri A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (! [C:$i] :  ( (C = (k4_net_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k2_net_1 A)) & (r2_hidden (k4_tarski B D) (k1_net_1 A))) ) ) ) ) ) ) ) ) ).
tt(d7_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  ( (B = (k11_newton A))  <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C B) <=>  ( (~ (r1_xxreal_0 A C))  & (v1_int_2 C)) ) ) ) ) ) ) ) ) ).
tt(d7_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r3_nfcont_1 A B C D) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) => (r1_nfcont_1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_normform,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B)))))) )  =>  ((k6_normform A B C D) = (k7_setwiseo A (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B)) (k5_normform B) C D)) ) ) ) ) ) ) ) ).
tt(d7_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k6_normsp_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((k9_openlatt A) = (k10_xtuple_0 (k8_openlatt A))) ) ) ).
tt(d7_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_necklace A) <=>  ((v3_relat_2 (u1_orders_2 A)) & (m1_subset_1 (u1_orders_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(d7_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A B) (k3_oppcat_1 A C)) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) (k3_oppcat_1 A B) (k3_oppcat_1 A C)) =>  ((k8_oppcat_1 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d7_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_orders_1 A B) <=>  ((r1_relat_2 A B) &  ((r8_relat_2 A B) & (r4_relat_2 A B)) ) ) ) ) ) ).
tt(d7_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_orders_2 B A) <=> (r7_relat_2 (u1_orders_2 A) B)) ) ) ) ) ).
tt(d7_orders_3,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k2_orders_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((l1_struct_0 D) &  ((r2_hidden D A) &  (C = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(d7_ordinal1,ax, (! [A:$i] :  ((v5_ordinal1 A) <=> (v3_ordinal1 (k9_xtuple_0 A))) ) ).
tt(d7_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k7_ordinal3 A B) = (k5_ordinal3 A (k11_ordinal2 (k6_ordinal3 A B) B))) ) ) ) ) ).
tt(d7_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k3_ordinal5 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  &  ( (B = (k1_ordinal2 C))  &  ( ((k9_xtuple_0 C) = (k1_ordinal1 A))  &  ( ((k1_funct_1 C k1_xboole_0) = (k1_ordinal5 k4_ordinal1 k4_ordinal1))  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden (k1_ordinal1 D) (k1_ordinal1 A)) =>  ((k1_funct_1 C (k1_ordinal1 D)) = (k1_ordinal5 (k1_funct_1 C D) k4_ordinal1)) ) ) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r2_hidden D (k1_ordinal1 A)) & (v4_ordinal1 D))  =>  ( (D = k1_xboole_0)  |  ((k1_funct_1 C D) = (k8_ordinal2 (k5_relat_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((k3_ordinal6 A) = (k2_ordinal6 (a_1_0_ordinal6 A))) ) ) ).
tt(d7_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  ((v5_o_ring_1 (k7_partfun1 (u1_struct_0 A) B 1) A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v5_o_ring_1 D A) &  ((k7_partfun1 (u1_struct_0 A) B (k1_nat_1 C 1)) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_osafree A B C) = (a_3_0_osafree A B C)) ) ) ) ) ) ) ).
tt(d7_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v7_osalg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((r1_osalg_1 A B C) & (r2_osalg_1 A (k1_msualg_1 A B) (k1_msualg_1 A C)))  => (r3_orders_2 A (k2_msualg_1 A B) (k2_msualg_1 A C))) ) ) ) ) ) ) ) ).
tt(d7_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((k5_osalg_2 A B C) = (a_3_2_osalg_2 A B C)) ) ) ) ) ) ) ).
tt(d7_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k2_osalg_4 A)) =>  ((k4_osalg_4 A B C) = (k3_tarski (a_3_0_osalg_4 A B C))) ) ) ) ) ) ) ).
tt(d7_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v6_papdesaf A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A C B B F) &  ((r2_analoaf A D B B G) &  ((r2_analoaf A E B B H) &  ((r2_analoaf A C D G F) & (r2_analoaf A C E H F)) ) ) )  =>  ((r3_diraf A B C D) |  ((r3_diraf A B C E) | (r2_analoaf A D E H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k5_parsp_1 A) = (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) ) ) ).
tt(d7_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r4_pboole A B C) <=>  (! [D:$i] :  (~  ((r2_hidden D A) & (r1_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(d7_pcomps_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) =>  ((k4_pcomps_1 A B) = (g1_metric_1 A B)) ) ) ) ) ).
tt(d7_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_pcs_0 A B C) <=> (r2_hidden (k4_tarski B C) (u1_pcs_0 A))) ) ) ) ) ) ) ).
tt(d7_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) <=>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) &  ( (C = E)  &  ( (D = F)  & (r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r2_pdiff_3 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k3_pdiff_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k10_finseq_1 D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 G 1))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B) I) (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k4_pdiff_4 A B) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k11_pdiff_1 3 1 A B)) (k9_euclid 3 k3_euclid_8 (k11_pdiff_1 3 2 A B))) (k9_euclid 3 k4_euclid_8 (k11_pdiff_1 3 3 A B)))) ) ) ) ) ).
tt(d7_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r7_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F C) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B) C)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I C)) (k1_seq_1 H (k9_real_1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((r4_pdiff_7 A B C D) <=>  ((r1_tarski D (k1_relset_1 (k1_euclid A) C)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E D) => (r3_pdiff_7 A B (k2_partfun1 (k1_euclid A) (k1_euclid B) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 (k1_euclid A) k1_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (k1_euclid A) k1_numbers))))) )  =>  ( (E = (k4_pdiff_9 A B C D))  <=>  ((r2_relset_1 (k1_euclid A) k1_numbers (k1_seqfunc (k1_euclid A) k1_numbers E k6_numbers) D) &  (! [F:$i] :  ((v7_ordinal1 F) => (r2_relset_1 (k1_euclid A) k1_numbers (k1_seqfunc (k1_euclid A) k1_numbers E (k23_binop_2 F 1)) (k3_pdiff_9 A B (k7_partfun1 k5_numbers C (k23_binop_2 F 1)) (k1_seqfunc (k1_euclid A) k1_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v6_pencil_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_pre_topc A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_pre_topc A)) =>  ((r1_ordinal1 2 (k1_card_1 (k3_xboole_0 B C))) =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(d7_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_pencil_4 A B C D) = (g1_pre_topc (k2_vectsp_9 A B C) (k6_pencil_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d7_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k9_petri A B) = (a_2_5_petri A B)) ) ) ) ) ).
tt(d7_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ((m1_pnproc_1 C A) =>  ( ((r2_pnproc_1 A (k4_pnproc_1 A C) B) =>  ((k6_pnproc_1 A B C) = (k2_pnproc_1 A (k3_pnproc_1 A B (k4_pnproc_1 A C)) (k5_pnproc_1 A C))) )  &  ( (~ (r2_pnproc_1 A (k4_pnproc_1 A C) B))  =>  ((k6_pnproc_1 A B C) = B) ) ) ) ) ) ) ) ).
tt(d7_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers)  =>  ( (E = (k7_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (H = (k1_polyeq_5 2 (k6_xcmplx_0 (k1_newton F 2) G)))  &  (E = (k6_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k2_xcmplx_0 F H)))) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers) )  =>  ( (E = (k7_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  (? [J:$i] :  ((v1_xcmplx_0 J) &  (? [K:$i] :  ((v1_xcmplx_0 K) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) 64))  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (I = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (J = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (K = (k10_complex1 (k13_complex1 G (k3_xcmplx_0 I J))))  &  (E = (k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 I) J) K) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k10_polyform A B))  <=>  ( ( (~ (r1_xxreal_0 (k4_xcmplx_0 1) B))  =>  (C = (k2_pre_poly k1_xboole_0)) )  &  ( ( (B = (k4_xcmplx_0 1))  =>  (C = (k3_polyform k1_xboole_0)) )  &  ( (~  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 1)))  &  ( (~ (r1_xxreal_0 (k7_polyform A) B))  &  (~  (C = (k1_funct_1 (u1_polyform A) (k2_xcmplx_0 B 1))) ) ) ) )  &  ( ( (B = (k7_polyform A))  =>  (C = (k9_finseq_1 A)) )  &  ( (~ (r1_xxreal_0 B (k7_polyform A)))  =>  (C = (k2_pre_poly k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((k7_polynom1 A B) = (k8_funcop_1 (u1_struct_0 B) (k15_pre_poly A) (k4_struct_0 B))) ) ) ) ).
tt(d7_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((k9_polynom3 A) = (k8_funcop_1 (u1_struct_0 A) k5_numbers (k4_struct_0 A))) ) ) ).
tt(d7_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_polynom5 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_polynom5 A B C)) ) ) ) ) ) ) ).
tt(d7_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((v4_polynom7 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (~  (D = (k16_pre_poly A)) )  =>  ((k3_polynom1 A B C D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 E B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  ( (E = (k6_polynom8 A B C D))  <=>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 A F))  =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k2_polynom4 B C (k2_binom B D F))) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 A F) =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r5_polyred A B C D E F) <=>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((r2_hidden G F) & (r4_polyred A B C D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_poset_1 A B) (k4_poset_1 A B)))) =>  ( (C = (k5_poset_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D (k4_poset_1 A B)) &  ((r2_hidden E (k4_poset_1 A B)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( (D = F)  &  ( (E = G)  & (r1_yellow_2 (u1_struct_0 A) B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pralg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k1_tarski k1_xboole_0)) (k1_tarski k1_xboole_0)))))  =>  ( (B = (k7_pralg_1 A))  <=>  ( ((k9_xtuple_0 B) = (k1_tarski (k2_finseq_2 A k1_xboole_0)))  &  ((k10_xtuple_0 B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ).
tt(d7_pralg_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  ((k7_pralg_2 A B C) = (k3_tarski (a_3_0_pralg_2 A B C))) ) ) ) ) ) ) ).
tt(d7_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k13_pre_poly A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (~  ((k1_funct_1 A C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(d7_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = (k9_prepower A B))  <=>  (? [D:$i] :  ( ((v5_relat_1 D k3_numbers) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  &  ((v2_comseq_2 (k8_prepower A D)) &  ((k2_seq_2 (k8_prepower A D)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k2_pre_topc A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ((r2_hidden D E) & (r1_xboole_0 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_prgcor_2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k1_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r5_prgcor_2 A B C D) <=>  ( ((k1_afinsq_1 C) = D)  &  ( ((k1_afinsq_1 A) = D)  &  ( ((k1_afinsq_1 B) = D)  &  (? [E:$i] :  ((v1_int_1 E) &  ( ((k1_seq_1 C k6_numbers) = (k1_seq_1 B k6_numbers))  &  ( (E = (k1_seq_1 B k6_numbers))  &  ( (~  (E = k6_numbers) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F E))  =>  ((k1_seq_1 C F) = (k9_real_1 (k1_seq_1 A F) (k1_seq_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((k4_prob_1 A B) = A) ) ) ) ).
tt(d7_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k4_prob_4 A B C)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (E = (k6_prob_4 A B C D))  <=>  (! [F:$i] :  ((r2_hidden F E) <=>  ((r2_hidden F B) &  ((r1_tarski F D) & (m1_prob_4 (k7_subset_1 A D F) A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((m2_prvect_1 B A) <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 A)) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k1_funct_1 A C) (k1_funct_1 A C)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(d7_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) =>  ( (B = (k8_prvect_2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (k4_prvect_2 A))) =>  ((k8_prvect_1 (k4_prvect_2 A) B C) = (u2_struct_0 (k5_prvect_2 A C))) ) ) ) ) ) ) ) ).
tt(d7_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ((k7_prvect_3 A B) = (g1_normsp_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k3_prvect_3 A B) (k1_prvect_3 A B) (k2_prvect_3 A B) (k6_prvect_3 A B))) ) ) ) ) ).
tt(d7_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k6_pscomp_1 A) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) A) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A))) ) ) ).
tt(d7_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k9_pua2mss1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden (k4_tarski C D) (k8_pua2mss1 A (k6_pua2mss1 A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k6_qc_lang1 A) = (a_1_0_qc_lang1 A)) ) ) ).
tt(d7_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ((k7_qc_lang2 A B C D) = (k5_qc_lang2 A B (k5_qc_lang2 A C D))) ) ) ) ) ) ) ) ) ).
tt(d7_qmax_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ((r2_qmax_1 A) <=>  ((r2_orders_1 (u1_orders_2 A) (u1_struct_0 A)) &  ((r1_qmax_1 (u1_struct_0 A) (u1_robbins1 A)) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski B C) (u1_orders_2 A)) => (r2_hidden (k4_tarski (k1_funct_1 (u1_robbins1 A) C) (k1_funct_1 (u1_robbins1 A) B)) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ).
tt(d7_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ( (C = (k7_quaterni A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  ( (A = (k6_quaterni D E F G))  &  ( (B = (k6_quaterni H I J K))  &  (C = (k6_quaterni (k7_real_1 D H) (k7_real_1 E I) (k7_real_1 F J) (k7_real_1 G K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (D = (k9_quofield A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden E D) <=>  (? [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  (? [G:$i] :  ((m2_subset_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) G))) = (k8_group_1 A (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k8_group_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  ((k8_radix_1 A B C) = (k1_gr_cy_1 (k7_radix_1 A B C))) ) ) ) ) ) ) ).
tt(d7_radix_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E (k3_radix_1 B)))  =>  ((r1_xxreal_0 1 D) =>  (! [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F k4_numbers))  =>  ( (F = (k7_radix_2 A B C D E))  <=>  ( ((k1_seq_1 F 1) = (k6_radix_2 A C D B D E))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k5_real_1 D 1)) &  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (~  ( (H = (k1_seq_1 F G))  &  ( (I = (k1_seq_1 F (k1_nat_1 G 1)))  &  (I = (k6_int_1 (k2_xcmplx_0 (k3_xcmplx_0 (k1_radix_1 B) H) (k6_radix_2 A C (k7_nat_d D G) B D E)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( ((r1_xxreal_0 2 B) & (r2_hidden A (k2_finseq_1 (k2_xcmplx_0 C 1))))  =>  ((k9_radix_3 A B C D) = (k8_radix_3 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(d7_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ( ( (A = B)  =>  ((k7_radix_5 A B C) = (k6_xcmplx_0 (k1_radix_1 C) 1)) )  &  ( (~  (A = B) )  =>  ((k7_radix_5 A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d7_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_radix_6 A B C) <=>  ( (~ (r1_xxreal_0 (k1_newton (k1_radix_1 B) A) C))  & (r1_xxreal_0 (k13_newton (k1_radix_1 B) (k7_nat_d A 1)) C)) ) ) ) ) ) ) ) ).
tt(d7_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k10_ranknull A B C D) = (k1_vectsp_9 A (k3_ranknull A B C D))) ) ) ) ) ) ) ) ) ).
tt(d7_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v3_ratfunc1 B A) <=>  ((k2_ratfunc1 A B) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(d7_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k3_rcomp_1 A B) = (a_2_2_rcomp_1 A B)) ) ) ) ) ).
tt(d7_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_real_3 A) = (k52_valued_1 k5_numbers k1_numbers k1_numbers (k5_real_3 A) (k6_real_3 A))) ) ) ).
tt(d7_realset1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m3_realset1 C A B) =>  ((k4_realset1 A B C) = (k1_realset1 C (k6_subset_1 A (k6_domain_1 A B)))) ) ) ) ) ) ) ).
tt(d7_recdef_2,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  (! [B:$i] :  ( (B = (k2_xtuple_0 A))  <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (A = (k6_xtuple_0 C D E F))  =>  (B = F) ) ) ) ) ) ) ) ) ) ).
tt(d7_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (B = (k2_relat_1 A))  <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=> (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ) ) ).
tt(d7_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r7_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r2_hidden (k4_tarski C D) A))  &  (~ (r2_hidden (k4_tarski D C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r5_rewrite1 A B C) <=>  (? [D:$i] :  ((r1_rewrite1 A B D) & (r1_rewrite1 A C D)) ) ) ) ) ) ) ).
tt(d7_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r3_rewrite2 A B C D) <=> (r1_rewrite1 (k7_rewrite2 A B) C D)) ) ) ) ) ) ) ) ).
tt(d7_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r4_rewrite3 A B C D E F) <=> (r3_rewrite3 A B C D E F (k2_flang_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(d7_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_rfunct_3 A k1_numbers)) =>  ( (D = (k16_rfunct_3 A B C))  <=>  ( ((k3_finseq_1 D) = (k6_nat_1 (k3_finseq_1 C) (k3_finseq_1 B)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ( (G = (k1_seq_1 C E))  &  (F = (k1_funct_1 B E)) )  =>  ((k1_funct_1 D E) = (k26_valued_1 A k1_numbers F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r7_rfunct_4 A B) <=>  ((r2_hidden B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_xtuple_0 A)) &  ( (~ (r1_xxreal_0 D (k18_complex1 (k10_binop_2 E B))))  & (r1_xxreal_0 C (k10_binop_2 (k1_seq_1 A E) (k1_seq_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k6_rinfsup1 A) = (k1_rinfsup1 (k3_rinfsup1 A))) ) ) ).
tt(d7_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (B = (k4_rinfsup2 A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k7_numbers)))  &  ( (D = (a_2_0_rinfsup2 A C))  &  ((k12_supinf_2 B C) = (k8_supinf_2 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((r1_ringcat1 A B) <=>  (? [C:$i] :  ( ((v3_ringcat1 C) & (l1_ringcat1 C))  &  ( ((k1_ringcat1 C) = A)  &  ((k2_ringcat1 C) = B) ) ) ) ) ) ) ) ) ).
tt(d7_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) =>  (! [C:$i] :  ((r2_hidden C (k4_rlaffin1 A B)) =>  (! [D:$i] :  ((m2_rlvect_2 D A B) =>  ( (D = (k5_rlaffin1 A B C))  <=>  ( ((k6_rlvect_2 A D) = C)  &  ((k3_rlaffin1 A D) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A))))) )  =>  ( (B = (k5_rlsub_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_rlsub_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_rlsub_2 A)) =>  (! [E:$i] :  ((m1_rlsub_1 E A) =>  (! [F:$i] :  ((m1_rlsub_1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k3_rlsub_2 A) B C D) = (k1_rlsub_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v4_rltopsp1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_rltopsp1 C A)) ) ) ) ) ) ) ) ).
tt(d7_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v7_rlvect_1 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_rlvect_1 A D (k3_xcmplx_0 B C)) = (k1_rlvect_1 A (k1_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (D = (k5_rlvect_2 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 D E) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) B E) (k3_funct_2 (u1_struct_0 A) k1_numbers C (k7_partfun1 (u1_struct_0 A) B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B))))) )  =>  ( (C = (k6_rmod_3 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k3_rmod_3 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_rmod_3 A B)) =>  (! [F:$i] :  ((m1_rmod_2 F A B) =>  (! [G:$i] :  ((m1_rmod_2 G A B) =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k3_rmod_3 A B) C D E) = (k2_rmod_3 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (D = (k5_rmod_4 A B C))  <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  ((v2_funct_1 E) &  ( ((k10_xtuple_0 E) = (k2_rmod_4 A B C))  &  (D = (k4_rlvect_1 B (k4_rmod_4 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  ((v7_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_lattices A B B) = B) ) ) ) ) ) ).
tt(d7_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v9_robbins3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B (k3_robbins1 A B)) = (k1_lattices A C (k3_robbins1 A C))) ) ) ) ) ) ) ) ).
tt(d7_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_roughs_1 B A) <=>  (~  ((k5_roughs_1 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d7_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k4_rsspace4 A B)) =>  ((k6_rsspace4 A B C) = C) ) ) ) ) ) ) ).
tt(d7_rsspace,ax, (k7_rsspace = (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace)) ).
tt(d7_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A))))) )  =>  ( (B = (k5_rusub_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_rusub_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_rusub_2 A)) =>  (! [E:$i] :  ((m1_rusub_1 E A) =>  (! [F:$i] :  ((m1_rusub_1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k3_rusub_2 A) B C D) = (k1_rusub_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_rusub_4 B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r2_hidden (k1_algstr_0 A C D) B) & (r2_hidden (k1_rlvect_1 A C E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k10_rvsum_1 A B) = (k3_relat_1 A (k3_rvsum_1 B))) ) ) ) ) ).
tt(d7_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k9_scm_comp A B) = (k6_trees_4 (k4_tarski k6_numbers 4) A B)) ) ) ) ) ).
tt(d7_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k2_scmfsa_1) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k7_scmfsa_1 A B C) = (k1_funct_4 A (k16_funcop_1 B C))) ) ) ) ) ) ) ).
tt(d7_scmfsa_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_scmfsa_2 A) = (k4_xcmplx_0 (k1_nat_1 A 1))) ) ) ).
tt(d7_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k6_scmfsa6a A B) = (k3_scmfsa6a (k11_compos_1 k1_scmfsa_2 A) (k11_compos_1 k1_scmfsa_2 B))) ) ) ) ) ).
tt(d7_scmfsa7b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r6_scmfsa7b A B C) <=> (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k8_memstr_0 3 k1_scmfsa_2 B))) ) ) ) ) ) ) ).
tt(d7_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) &  (? [D:$i] :  ((m2_subset_1 D k4_ordinal1 (k7_card_1 13)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k7_scmfsa_i A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) &  ( ((k10_finseq_1 C D) = (k2_xtuple_0 A))  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_scmfsa_m,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 3 k1_scmfsa_2) (k11_memstr_0 3 k1_scmfsa_2)))))  =>  ( (A = k10_scmfsa_m)  <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 C)) ) ) )  =>  ((r2_hidden (k4_tarski B C) A) <=>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  (? [E:$i] :  ((m2_finseq_1 E k1_numbers) &  ((r2_classes1 D E) &  ((m2_finseq_1 E k4_numbers) &  ((v8_valued_0 E) &  ( (B = (k16_funcop_1 (k5_scmfsa_2 k6_numbers) D))  &  (C = (k16_funcop_1 (k5_scmfsa_2 k6_numbers) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (k7_card_1 9)) &  (A = (k3_xtuple_0 D (k12_finseq_1 k5_numbers B) (k12_finseq_1 k2_scm_inst C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k8_scm_inst A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  ( ((k12_finseq_1 k2_scm_inst C) = (k2_xtuple_0 A))  &  (B = (k7_partfun1 k2_scm_inst (k12_finseq_1 k2_scm_inst C) 1)) ) ) ) ) ) ) ) ) ) ).
tt(d7_scmpds_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_scmpds_1 A B) = (k1_int_2 (k2_xcmplx_0 (k5_ami_2 A) B))) ) ) ) ) ).
tt(d7_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_scmpds_2 A B) = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(d7_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v2_scmpds_4 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 A) C) => (r1_extpro_1 2 k1_scmpds_2 C B)) ) ) ) ) ) ) ) ).
tt(d7_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_scmpds_6 A B C) = (k2_scmpds_4 (k7_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 1)) C)) ) ) ) ) ) ) ).
tt(d7_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k8_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 2)) ) ) ) ) ) ) ) ) ) ).
tt(d7_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_scmring2 A B C) = (k3_xtuple_0 5 k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(d7_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E k1_xboole_0 (k7_scmringi A C D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ( (C = (k8_scmringi A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k2_xboole_0 k2_scm_inst (u1_struct_0 A))) &  ( (D = (k2_xtuple_0 B))  &  (C = (k7_partfun1 (k2_xboole_0 k2_scm_inst (u1_struct_0 A)) D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k3_scmyciel A) = (k5_card_1 (k1_scmyciel A))) ) ) ).
tt(d7_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_semi_af1 A B C D) = (k1_semi_af1 A B (k2_semi_af1 A C D) D)) ) ) ) ) ) ) ) ) ).
tt(d7_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (B = (k1_seq_2 A))  <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k10_seq_4 A B) = (k1_finseqop k2_numbers k2_numbers k2_numbers k28_binop_2 A B)) ) ) ) ) ).
tt(d7_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (D = (k8_seqfunc A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers D E) (k20_valued_1 A k1_numbers k1_numbers (k1_seqfunc A k1_numbers B E) (k1_seqfunc A k1_numbers C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ) ).
tt(d7_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k7_setfam_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D C) <=> (r2_hidden (k3_subset_1 A D) B)) ) ) ) ) ) ) ) ) ).
tt(d7_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k7_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k7_subset_1 A C (k8_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v4_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(d7_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_simplex0 A) <=> (v2_setfam_1 (u1_pre_topc A))) ) ) ).
tt(d7_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  ((v1_simplex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc C B) => (v1_rlaffin1 (k1_simplex1 A B C) A)) ) ) ) ) ) ) ) ).
tt(d7_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k7_sincos10 A) = (k1_seq_1 k3_sincos10 A)) ) ) ).
tt(d7_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_sin_cos7 A) = (k7_binop_2 (k6_power k8_power (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) A)))) ) ) ).
tt(d7_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k6_sin_cos A))  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C A) =>  ((k8_nat_1 k2_numbers B C) = (k13_complex1 k6_complex1 (k8_real_1 (k3_newton C) (k3_newton (k7_nat_d A C))))) )  &  ( (~ (r1_xxreal_0 C A))  =>  ((k8_nat_1 k2_numbers B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(d7_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_stacks_1 B) & (l1_stacks_1 B)) ) )  =>  ( (B = (k8_stacks_1 A))  <=>  ( ((u1_struct_0 B) = A)  &  ( ((u4_struct_0 B) = (k3_finseq_2 A))  &  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  ( ((r1_stacks_1 B C) => (v1_xboole_0 C))  &  ( ((v1_xboole_0 C) => (r1_stacks_1 B C))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( (D = C)  =>  ( ( (~ (r1_stacks_1 B C))  =>  ( ((k6_stacks_1 B C) = (k1_funct_1 D 1))  &  ((k5_stacks_1 B C) = (k2_finseq_3 1 D)) ) )  &  ( ((r1_stacks_1 B C) =>  ( ((k6_stacks_1 B C) = (o_1_0_stacks_1 B))  &  ((k5_stacks_1 B C) = k1_xboole_0) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k7_stacks_1 B C E) = (k7_finseq_1 (k12_finseq_1 (u1_struct_0 B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_struct_0,ax, (! [A:$i] :  ((l3_struct_0 A) =>  ((k5_struct_0 A) = (u3_struct_0 A)) ) ) ).
tt(d7_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v7_substut1 B A) &  (C = (k39_substut1 A (k10_sublemma A B))) )  =>  ((k11_sublemma A B C) = (k36_substut1 A B C)) ) ) ) ) ) ) ) ).
tt(d7_subset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_zfmisc_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (B = C) ) ) ) ) ) ) ) ).
tt(d7_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  ((k8_substut1 A B) = (a_2_0_substut1 A B)) ) ) ) ) ).
tt(d7_t_0topsp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v6_pre_topc A) <=>  ((v2_struct_0 A) |  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ( ((r2_hidden B D) &  (~ (r2_hidden C D)) )  |  ((r2_hidden C D) &  (~ (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (C = (k3_taxonom1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski D E) C) <=> (r1_taxonom1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v6_taxonom2 B A) <=>  (! [C:$i] :  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C B) &  ((v6_ordinal1 C) &  (! [D:$i] :  (~  ((r2_hidden D B) & (r1_tarski D (k1_setfam_1 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (E = (k6_taylor_1 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_seq_1 E F) = (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A B) F) C) (k1_newton (k6_xcmplx_0 D C) F)) (k3_newton F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tbsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E B))  => (r1_xxreal_0 (k2_metric_1 A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A))))) )  =>  ( (B = (k7_tdlat_1 A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  ((k5_binop_1 (k5_tdlat_1 A) B C D) = (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(d7_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k4_termord A B C D) = (k3_polynom1 A C D (k3_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(d7_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_4 B A) <=>  ((v1_tex_4 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tex_4 C A) & (r1_tarski B C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(d7_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_tmap_1 A B) = (a_2_0_tmap_1 A B)) ) ) ) ) ).
tt(d7_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( (D = (k7_topalg_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k17_borsuk_1)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k17_borsuk_1)) =>  ((k1_binop_1 D E F) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)) B E) (k9_real_1 1 F)) (k1_rlvect_1 (k15_euclid A) (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)) C E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((v6_topalg_6 B A) <=> (v2_xxreal_2 (k9_xtuple_0 B))) ) ) ) ) ).
tt(d7_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k4_topdim_1 A) = (k2_topdim_1 A (k2_struct_0 A))) ) ) ).
tt(d7_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_topgen_1 B A) <=> (r1_tarski B (k2_topgen_1 A B))) ) ) ) ) ).
tt(d7_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k6_topgen_3 A B))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k2_pre_topc C D) = (k14_funcop_1 D k11_arytm_3 D (k2_xboole_0 D (k3_xboole_0 (k1_tarski B) A)))) ) ) ) ) ) ) ) ) ).
tt(d7_topgen_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_topgen_4 B A) <=>  (? [C:$i] :  ( ((v4_card_3 C) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (B = (k6_setfam_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(d7_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l1_topgrp_1 A)) ) )  =>  ((v3_topgrp_1 A) <=> (v5_pre_topc (k3_group_1 A) A A)) ) ) ).
tt(d7_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_topmetr A B) = (k3_pcomps_1 (k2_topmetr A B))) ) ) ) ) ).
tt(d7_topreal1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v3_topreal1 A) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C (k1_nat_1 B 1)))  => (r1_xboole_0 (k2_topreal1 2 A B) (k2_topreal1 2 A C))) ) ) ) ) ) ) ) ).
tt(d7_toprealb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k8_toprealb A) = (k7_toprealb A (k4_struct_0 (k15_euclid A)) 1)) ) ) ).
tt(d7_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v2_toprns_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 C (k12_euclid (k8_nat_1 (u1_struct_0 (k15_euclid A)) B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d7_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) <=>  (B = (k2_pre_topc A (k1_tops_1 A B))) ) ) ) ) ) ).
tt(d7_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v3_transgeo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ).
tt(d7_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) =>  ((v2_trees_2 B A) <=>  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r1_tarski (k1_trees_1 C) B)) ) )  &  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((r2_hidden D B) => (r2_xboole_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_trees_3 B A) =>  ( (B = (k4_trees_3 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(d7_trees_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  ( (D = (k9_trees_4 A B C))  <=>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ((r2_hidden E (k9_xtuple_0 D)) <=>  (~  ( (~ (r2_hidden E (k9_xtuple_0 A)))  &  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 A)) =>  (! [G:$i] :  ((m1_trees_1 G (k9_xtuple_0 B)) =>  (~  ((r2_hidden F (k3_trees_1 (k9_xtuple_0 A))) &  ( ((k1_funct_1 A F) = C)  &  (E = (k8_finseq_1 k5_numbers F G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 A)) =>  ( (~  ((r2_hidden E (k3_trees_1 (k9_xtuple_0 A))) &  ((k1_funct_1 A E) = C) ) )  =>  ((k1_funct_1 D E) = (k1_funct_1 A E)) ) ) )  &  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 A)) =>  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 B)) =>  ( ((r2_hidden E (k3_trees_1 (k9_xtuple_0 A))) &  ((k1_funct_1 A E) = C) )  =>  ((k1_funct_1 D (k8_finseq_1 k5_numbers E F)) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k3_trees_9 A) = (a_1_0_trees_9 A)) ) ) ).
tt(d7_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r4_tsep_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (u1_struct_0 B))  &  (E = (u1_struct_0 C)) )  => (r2_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tsp_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  => (v1_tsp_2 C A)) ) ) ) ) ) ) ) ).
tt(d7_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))))))) )  =>  ( (C = (k10_turing_1 A B))  <=>  ( ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) C k6_numbers) = B)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) C (k1_nat_1 D 1)) = (k9_turing_1 A (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k8_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k1_binarith B C)) ) ) ) ) ) ) ) ).
tt(d7_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_unialg_2 B A) <=>  ((m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (u1_struct_0 B))  =>  ( ((u1_unialg_1 B) = (k3_unialg_2 A C))  & (v1_unialg_2 C A)) ) ) ) ) ) ) ) ) ) ).
tt(d7_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_polynom5 A C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( (~ (r1_xxreal_0 (k1_algseq_1 A C) k6_numbers))  =>  ( (D = (k6_uproots A B C))  <=>  ( ((k2_nat_1 (k1_algseq_1 A D) 1) = (k1_algseq_1 A C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k2_polynom4 A (k5_uproots A C (k1_nat_1 E 1)) B)) ) ) ) ) )  &  ((r1_xxreal_0 (k1_algseq_1 A C) k6_numbers) =>  ( (D = (k6_uproots A B C))  <=> (r2_funct_2 k5_numbers (u1_struct_0 A) D (k9_polynom3 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_urysohn1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v7_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r2_hidden B D) &  ( (~ (r2_hidden C D))  &  ((r2_hidden C E) &  (~ (r2_hidden B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B C D E) <=>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B D C) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_valued_0 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_xcmplx_0 (k1_funct_1 A B))) ) ) ) ) ).
tt(d7_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ( (B = (k35_valued_1 A))  <=>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k5_xcmplx_0 (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ).
tt(d7_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_vectmetr A B) = (k2_metric_1 A (k4_struct_0 A) B)) ) ) ) ) ).
tt(d7_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v5_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_vectsp_2 A B C D) = (k2_binop_1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_vectsp_2 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(d7_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B))))) )  =>  ( (C = (k5_vectsp_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k3_vectsp_5 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_vectsp_5 A B)) =>  (! [F:$i] :  ((m1_vectsp_4 F A B) =>  (! [G:$i] :  ((m1_vectsp_4 G A B) =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k3_vectsp_5 A B) C D E) = (k1_vectsp_5 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((r1_vectsp_6 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A C)))))) )  =>  ( (E = (k6_vectsp_8 A B C D))  <=>  (! [F:$i] :  ( ((v7_vectsp_1 F A) & (m1_vectsp_4 F A B))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (G = (k7_relset_1 (u1_struct_0 B) (u1_struct_0 C) D (u1_struct_0 F)))  =>  ((k1_funct_1 E F) = (k1_vectsp_7 A C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((k1_waybel_0 A B) = (u1_waybel_0 A B)) ) ) ) ) ).
tt(d7_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v4_yellow_0 B (k4_waybel10 A)) & (m1_yellow_0 B (k4_waybel10 A))) ) )  =>  ( (B = (k8_waybel10 A))  <=>  (! [C:$i] :  ( ((v1_orders_2 C) &  ((v4_yellow_0 C A) &  ((v7_yellow_0 C A) & (m1_yellow_0 C A)) ) )  =>  ((m1_subset_1 C (u1_struct_0 B)) <=> (v4_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(d7_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel11 A B C) <=> (r3_orders_2 A C (k1_waybel11 A B))) ) ) ) ) ) ) ).
tt(d7_waybel18,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k8_waybel18 A B C) = C) ) ) ) ) ) ) ).
tt(d7_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r4_waybel_1 A B C) <=>  ((r1_yellow_0 A C) &  ( (B = (k1_yellow_0 A C))  & (r2_hidden (k1_yellow_0 A C) C)) ) ) ) ) ) ) ) ).
tt(d7_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_waybel23 B A) <=>  ((v2_waybel23 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k1_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k1_waybel_3 A C) B))) ) ) ) ) ) ) ) ) ).
tt(d7_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v2_waybel_2 A) <=>  ((v24_waybel_0 A) & (v1_waybel_2 A)) ) ) ) ).
tt(d7_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v9_functor0 B (k5_waybel34 A) (k4_waybel34 A)) &  ((v16_functor0 B (k5_waybel34 A) (k4_waybel34 A)) & (m2_functor0 B (k5_waybel34 A) (k4_waybel34 A))) )  =>  ( (B = (k7_waybel34 A))  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel34 A))) =>  ((k3_functor0 (k5_waybel34 A) (k4_waybel34 A) B C) = (k4_yellow21 (k5_waybel34 A) C)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel34 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_waybel34 A))) =>  ( (~  ((k1_altcat_1 (k5_waybel34 A) C D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 (k5_waybel34 A) C D)) =>  ((k8_functor0 (k5_waybel34 A) (k4_waybel34 A) B C D E) = (k2_waybel34 (k3_yellow21 (k5_waybel34 A) D) (k3_yellow21 (k5_waybel34 A) C) (k5_yellow21 (k5_waybel34 A) C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ((v3_waybel35 C A B) <=> (r1_waybel35 A C B)) ) ) ) ) ) ) ).
tt(d7_waybel_3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_waybel_3 A) <=>  (! [B:$i] :  ((l1_struct_0 B) =>  (~  ((r2_hidden B (k10_xtuple_0 A)) & (v2_struct_0 B)) ) ) ) ) ) ) ).
tt(d7_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k4_waybel_6 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (v5_waybel_6 C A)) ) ) ) ) ) ) ) ).
tt(d7_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v5_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k7_yellow_3 A A C D) B) & (r2_hidden (k7_yellow_3 A A C E) B))  => (r2_hidden (k7_yellow_3 A A C (k11_lattice3 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v6_waybel_0 D A) & (l1_waybel_0 D A))  =>  ( (D = (k4_waybel_9 A B C))  <=>  ( (! [E:$i] :  ((r2_hidden E (u1_struct_0 D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (F = E)  & (r1_orders_2 B C F)) ) ) ) )  &  ((r2_relset_1 (u1_struct_0 D) (u1_struct_0 D) (u1_orders_2 D) (k1_toler_1 (u1_orders_2 B) (u1_struct_0 D))) &  ((u1_waybel_0 A D) = (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A B) (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v7_vectsp_1 C (k4_weddwitt A)) &  ((v8_vectsp_1 C (k4_weddwitt A)) &  ((v9_vectsp_1 C (k4_weddwitt A)) &  ((v10_vectsp_1 C (k4_weddwitt A)) &  ((v11_vectsp_1 C (k4_weddwitt A)) & (l1_vectsp_1 C (k4_weddwitt A))) ) ) ) ) ) ) ) ) )  =>  ( (C = (k7_weddwitt A B))  <=>  ( ((g2_algstr_0 (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C)) = (g2_algstr_0 (u1_struct_0 (k5_weddwitt A B)) (u1_algstr_0 (k5_weddwitt A B)) (u2_struct_0 (k5_weddwitt A B))))  &  ((u1_vectsp_1 (k4_weddwitt A) C) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 (k4_weddwitt A)) (u1_struct_0 (k5_weddwitt A B))))) ) ) ) ) ) ) ) ) ).
tt(d7_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((k7_weierstr A B C) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) C))) ) ) ) ) ) ) ).
tt(d7_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_wellord1 A B C) <=>  ( ((k9_xtuple_0 C) = (k1_relat_1 A))  &  ( ((k10_xtuple_0 C) = (k1_relat_1 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) A) <=>  ((r2_hidden D (k1_relat_1 A)) &  ((r2_hidden E (k1_relat_1 A)) & (r2_hidden (k4_tarski (k1_funct_1 C D) (k1_funct_1 C E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ((r1_xboole_0 A B) <=>  ((k3_xboole_0 A B) = k1_xboole_0) ) ) ) ).
tt(d7_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A B) = (k5_xboolean (k3_xboolean A) B)) ) ) ) ) ).
tt(d7_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( (~  (A = k6_numbers) )  =>  ( (B = (k5_xcmplx_0 A))  <=>  ((k3_xcmplx_0 A B) = 1) ) )  &  ( (A = k6_numbers)  =>  ( (B = (k5_xcmplx_0 A))  <=>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(d7_xtuple_0,ax, (! [A:$i] :  ((k5_xtuple_0 A) = (k2_xtuple_0 (k1_xtuple_0 A))) ) ).
tt(d7_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((v3_xxreal_0 A) <=>  (~ (r1_xxreal_0 k6_numbers A)) ) ) ) ).
tt(d7_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v1_xxreal_2 A))  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (B = (k2_xxreal_2 A))  <=>  ((r2_hidden B A) &  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ).
tt(d7_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_xxreal_3 A B) = (k4_xxreal_3 A (k5_xxreal_3 B))) ) ) ) ) ).
tt(d7_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((r1_yellow_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_lattice3 A B C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) => (r1_orders_2 A C D)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_lattice3 A B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_lattice3 A B E) => (r1_orders_2 A D E)) ) ) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((r6_yellow16 A B C) <=>  ((r2_yellow_0 B C) => (r2_hidden (k2_yellow_0 B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(d7_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v2_yellow18 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tarski (k1_altcat_1 A C D) (k1_funct_2 (k1_funct_1 B C) (k1_funct_1 B D)))) ) ) ) ) ) ) ) ) ).
tt(d7_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((k5_yellow21 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(d7_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  (! [C:$i] :  ((m1_yellow_6 C A B) =>  ((v2_yellow_6 C A B) <=>  ((v4_yellow_0 C B) & (m1_yellow_0 C B)) ) ) ) ) ) ) ) ).
tt(d7_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v2_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_classes2 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d7_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k8_zf_lang A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 4) (k3_zf_lang A)) B)) ) ) ) ) ).
tt(d7_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r3_zfmisc_1 A B C D E) <=>  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (A = E) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d7_zf_model,ax, (k7_zf_model = (k14_zf_lang (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k13_zf_lang (k2_zf_lang 2) (k8_zf_lang (k2_zf_lang 3) (k12_zf_lang (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang 2)) (k10_zf_lang (k4_zf_lang (k2_zf_lang 3) (k2_zf_lang k6_numbers)) (k4_zf_lang (k2_zf_lang 3) (k2_zf_lang 1)))))))) ).
tt(d7_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  =>  ((v6_zmodul01 A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k1_zmodul01 A C B) = (k4_struct_0 A))  &  ( (~  (B = k6_numbers) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_abcmiz_0 A B) = (k1_funct_1 (u3_abcmiz_0 A) B)) ) ) ) ) ).
tt(d8_abcmiz_1,ax, (k10_abcmiz_1 = 1) ).
tt(d8_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((k9_abcmiz_a A B) = (k3_xboole_0 (k9_xtuple_0 (k10_xtuple_0 B)) (a_1_0_abcmiz_a A))) ) ) ) ) ).
tt(d8_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v8_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((r2_hidden C B) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r1_aff_1 A C D G) &  ((r2_analoaf A D E G H) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A D F G I) & (r2_aff_1 A D E B)) ) ) ) ) ) ) )  =>  ((r2_hidden D B) |  ( (C = F)  |  ( (D = E)  | (r1_aff_1 A C E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v8_aff_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I D) &  ((r2_hidden J D) &  ((r5_aff_1 A B C) &  ((r1_aff_1 A G E K) &  ((r1_aff_1 A H F K) &  ((r1_aff_1 A G I L) &  ((r1_aff_1 A H J L) &  ((r2_analoaf A E I F J) & (r2_analoaf A E I K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (C = D)  |  ((r1_aff_1 A G E I) |  ((r1_aff_1 A H F J) |  ( (K = L)  |  ( (I = J)  | (r5_aff_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((v5_relat_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo C A) | (r1_xxreal_0 1 (k1_afinsq_1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ( ((v1_setwiseo C A) &  ((k1_afinsq_1 B) = k6_numbers) )  =>  ( (D = (k6_afinsq_2 A B C))  <=>  (D = (k4_binop_1 A C)) ) )  &  ( (~  ((v1_setwiseo C A) &  ((k1_afinsq_1 B) = k6_numbers) ) )  =>  ( (D = (k6_afinsq_2 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ( ((k3_funct_2 k5_numbers A E k6_numbers) = (k1_funct_1 B k6_numbers))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) (k23_binop_2 F 1)))  =>  ((k3_funct_2 k5_numbers A E (k23_binop_2 F 1)) = (k1_binop_1 C (k8_nat_1 A E F) (k1_funct_1 B (k23_binop_2 F 1)))) ) ) )  &  (D = (k1_funct_1 E (k21_binop_2 (k1_afinsq_1 B) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k8_afproj A) = (k8_eqrel_1 (k2_afproj A) (k4_afproj A))) ) ) ).
tt(d8_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_afvect0 A B) = (g2_algstr_0 (u1_struct_0 A) (k3_afvect0 A B) B)) ) ) ) ) ).
tt(d8_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v2_margrel1 D) &  ((v3_margrel1 D (k8_eqrel_1 (u1_struct_0 A) B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))))) ) ) )  =>  ( (D = (k2_alg_1 A B C))  <=>  ( ((k1_relset_1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) D) = (k4_finseq_2 (k19_margrel1 C) (k8_eqrel_1 (u1_struct_0 A) B)))  &  (! [E:$i] :  ((m2_finseq_1 E (k8_eqrel_1 (u1_struct_0 A) B)) =>  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) D)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  ((r1_finseq_3 (u1_struct_0 A) B E F) =>  ((k1_funct_1 D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k1_funct_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_algstr_1,ax, (k3_algstr_1 = (g5_algstr_0 k1_numbers k35_binop_2 k6_numbers 1)) ).
tt(d8_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (D = (k7_algstr_4 A B C))  <=>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  ((r2_hidden E A) &  ((r2_hidden F A) &  ((k1_funct_1 C E) = (k1_funct_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ((k5_altcat_1 A B C D E F) = (k1_binop_1 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v5_altcat_3 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A C E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C E)) =>  ( ((k5_altcat_1 A B C E D F) = (k5_altcat_1 A B C E D G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k7_ami_2 A B C) = (k1_funct_4 A (k16_funcop_1 B C))) ) ) ) ) ) ) ).
tt(d8_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_ami_3 A) = (k3_xtuple_0 6 (k9_finseq_1 A) k1_xboole_0)) ) ) ).
tt(d8_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k1_funct_1 (k2_extpro_1 A B C D) (k4_struct_0 B)) = (k1_ordinal1 (k5_memstr_0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d8_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v3_ami_wstd C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k1_funct_1 (k2_extpro_1 A B C D) (k4_struct_0 B)) = (k5_ami_wstd A B (k5_memstr_0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d8_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ((v2_analmetr A) <=>  ( ( (~ (v7_struct_0 (g1_analoaf (u1_struct_0 A) (u1_analoaf A))))  &  ((v1_diraf (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) & (l1_analoaf (g1_analoaf (u1_struct_0 A) (u1_analoaf A)))) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B C) =>  (B = C) )  &  ((r4_analmetr A B C D D) &  ( ((r4_analmetr A B C D E) =>  ((r4_analmetr A B C E D) & (r4_analmetr A D E B C)) )  &  ( (~  ((r4_analmetr A B C F G) &  ((r2_analoaf A B C H I) &  ( (~ (r4_analmetr A F G H I))  &  (~  (B = C) ) ) ) ) )  &  ( ((r4_analmetr A B C F G) & (r4_analmetr A B C F I))  => (r4_analmetr A B C G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B E) & (r4_analmetr A B C E D)) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r4_analmetr A B C D E) &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_analort A B C) = (g1_analoaf (u1_struct_0 A) (k4_analort A B C))) ) ) ) ) ) ) ).
tt(d8_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v3_collsp A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) &  ((r1_collsp A B C E) & (r1_collsp A B C F)) )  =>  ( (B = C)  | (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) & (l1_unialg_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k9_aofa_000 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  &  ( (D = (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) E C))  &  ( ((k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) E k6_numbers) = B)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) E (k1_nat_1 F 1)) = (k2_xboole_0 (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) E F) (a_3_0_aofa_000 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  =>  ( (D = (k7_aofa_i00 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k4_numbers D E) = (k2_xcmplx_0 (k3_funct_2 A k4_numbers B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  ((k5_armstrng A) = (a_1_0_armstrng A)) ) ) ).
tt(d8_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ( (B = k11_arytm_3)  =>  ((k7_arytm_2 A B) = A) )  &  ( ( (A = k11_arytm_3)  =>  ((k7_arytm_2 A B) = B) )  &  (~  ( (~  (B = k11_arytm_3) )  &  ( (~  (A = k11_arytm_3) )  &  (~  ((k7_arytm_2 A B) = (k4_arytm_2 (k5_arytm_2 (k3_arytm_2 A) (k3_arytm_2 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  ( ((r2_hidden A k4_ordinal1) =>  ( (B = (k6_arytm_3 A))  <=>  (B = A) ) )  &  ( (~ (r2_hidden A k4_ordinal1))  =>  ( (B = (k6_arytm_3 A))  <=>  (? [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  &  (A = (k4_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(d8_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_asympt_0 A B) <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d8_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k6_bagorder A) = (k5_bagorder A (k17_pre_poly A))) ) ) ).
tt(d8_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v8_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(d8_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_bcialg_2 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  ( (C = (k2_bcialg_2 A B))  <=>  ( ((k1_bcialg_2 A (k4_struct_0 A) B C) = (k4_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k1_bcialg_2 A (k4_struct_0 A) B D) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  | (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k7_bcialg_4 A B) = (k1_finsop_1 (u1_struct_0 A) B (u1_bcialg_4 A))) ) ) ) ) ).
tt(d8_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k5_bcialg_6 A B C) = (a_3_0_bcialg_6 A B C)) ) ) ) ) ) ) ).
tt(d8_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m4_bciideal B A) <=>  ((r2_hidden (k4_struct_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden (k1_bcialg_1 A D E) B))  => (r2_hidden (k1_bcialg_1 A C E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v3_bhsp_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 C E) & (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k1_seq_1 A D) (k1_seq_1 A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_bhsp_5 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ( (C = D)  |  ((k2_bhsp_1 A C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k7_bilinear A B C D E) = (k10_funct_5 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 C) (u1_struct_0 A)) (k11_funct_5 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( (? [C:$i] :  ((m1_subset_1 C A) & (r3_binop_1 A C B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (C = (k4_binop_1 A B))  <=> (r3_binop_1 A C B)) ) ) ) ) ) ) ).
tt(d8_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k8_bor_cant A B C) = (k2_prob_2 A B (k7_bor_cant A C))) ) ) ) ) ) ) ).
tt(d8_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((k12_borsuk_1 A B) = (k13_eqrel_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(d8_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  ( (A = k6_borsuk_6)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) &  ( (B = (k4_borsuk_1 k5_topmetr k5_topmetr C D))  & (r1_xxreal_0 D (k9_real_1 1 (k8_real_1 2 C)))) ) ) ) ) ) ) ) ) ) ).
tt(d8_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 3))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 3)))))) )  =>  ( (B = (k13_borsuk_7 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k17_borsuk_1)) =>  ((k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 3)) B C) = (k4_euclid_5 (k21_sin_cos (k8_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) C)) (k18_sin_cos (k8_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(d8_bspace,ax, (! [A:$i] :  ((k8_bspace A) = (a_1_0_bspace A)) ) ).
tt(d8_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k9_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k5_xboolean (k9_margrel1 (k3_funct_2 A k6_margrel1 B E)) (k3_funct_2 A k6_margrel1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((r3_bvfunc_2 A B C D) <=> (r2_bvfunc_1 A B (k5_bvfunc_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(d8_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_c0sp1 B A) =>  ((v1_xboole_0 B) |  ((k4_c0sp1 A B) = (k5_struct_0 A)) ) ) ) ) ) ) ).
tt(d8_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k8_c0sp2 A) = (k2_partfun1 (k6_c0sp1 (u1_struct_0 A)) k1_numbers (k10_c0sp1 (u1_struct_0 A)) (k6_c0sp2 A))) ) ) ).
tt(d8_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  ((v1_calcul_1 B A) <=>  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (r3_calcul_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(d8_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  ((k7_card_3 A) = (k1_card_1 (k4_card_3 A))) ) ) ).
tt(d8_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k2_card_fil A B C) = (a_3_0_card_fil A B C)) ) ) ) ) ) ) ).
tt(d8_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((r4_card_lar A B) <=>  ((r1_tarski B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((v2_card_lar C A) &  ((v1_card_lar C A) & (v1_xboole_0 (k9_subset_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(d8_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v4_cat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ( ((k3_graph_1 A D) = (k4_graph_1 A C))  &  ((k3_graph_1 A C) = (k4_graph_1 A B)) )  =>  ((k1_cat_1 A (k1_cat_1 A B C) D) = (k1_cat_1 A B (k1_cat_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k12_cat_2 A B C D E) = (k1_funct_1 (k1_funct_5 D) (k4_cat_1 A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v1_cat_3 D A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ((k5_cat_1 A C B C E D) = (k4_cat_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_4 A)) ) ) ) ) ) )  =>  ((v3_cat_4 A) <=>  ((v10_cat_1 (u1_cat_4 A) A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_graph_1 A (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u3_cat_4 A) B C)) = B)  &  ( ((k4_graph_1 A (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u4_cat_4 A) B C)) = C)  & (r2_cat_3 A (k5_binop_1 (u1_struct_0 A) (u2_cat_4 A) B C) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u3_cat_4 A) B C) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u4_struct_0 A) (u4_cat_4 A) B C))) ) ) ) ) ) ) ) ) ) ).
tt(d8_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  ((v4_cat_5 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A)))  =>  (! [D:$i] :  ((m2_cat_1 D B C) => (m1_subset_1 (k4_tarski (k4_tarski B C) D) (u4_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(d8_catalg_1,ax, (! [A:$i] :  ((k5_catalg_1 A) = (k4_tarski 1 (k9_finseq_1 A))) ) ).
tt(d8_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((k5_cc0sp1 A B) = (a_2_0_cc0sp1 A B)) ) ) ) ) ).
tt(d8_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k7_cc0sp2 A) = (g1_clvect_1 (k6_cc0sp2 A) (k10_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k1_c0sp1 (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k9_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)))) ) ) ).
tt(d8_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v4_cfdiff_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r2_hidden B (k1_relset_1 k2_numbers A)) => (r1_cfdiff_1 A B)) ) ) ) ) ) ).
tt(d8_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_cfuncdom A) = (g1_cfuncdom (k9_funct_2 A k2_numbers) (k2_cfuncdom A) (k1_cfuncdom A) (k3_cfuncdom A) (k5_cfuncdom A) (k4_cfuncdom A))) ) ) ).
tt(d8_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((k8_cgames_1 A) = (k2_xboole_0 (k6_cgames_1 A) (k7_cgames_1 A))) ) ) ).
tt(d8_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k5_chain_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d8_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~ (r1_chord A B C))  &  (~  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k6_glib_000 A))) =>  ((m2_chord D A B C) <=>  ( (~ (r2_hidden B D))  &  ( (~ (r2_hidden C D))  &  (! [E:$i] :  ((m2_glib_000 E A (k6_subset_1 (k6_glib_000 A) D) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) D))) =>  (! [F:$i] :  ((m3_glib_001 F E) =>  (~ (r1_glib_001 E B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  ((k3_circcmb3 A) = (k3_tarski (u4_struct_0 A))) ) ) ).
tt(d8_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v2_circcomb A) <=>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  (B = (k4_tarski (k1_funct_1 (u1_msualg_1 A) B) (k2_xtuple_0 B))) ) ) ) ) ) ).
tt(d8_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_msaterm C A B) =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k1_circtrm1 A B C) (k6_circtrm1 A B C D)))) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) B (u3_msualg_1 A D)) =>  ((m1_circtrm1 F A B C D E) <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 B G)) =>  ((r2_hidden (k1_trees_4 (k4_tarski H G)) (k9_trees_9 C)) =>  ((k1_funct_1 (k1_funct_1 F G) H) = (k1_funct_1 E (k1_trees_4 (k4_tarski H G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  ((k8_circuit2 A B C D) = (k1_funct_4 (k1_circuit2 A B D (k2_circuit1 A B C k6_numbers)) (k1_circuit1 A B))) ) ) ) ) ) ) ) ) ).
tt(d8_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k6_classes1 A))  <=>  ((r1_tarski A (k4_classes1 B)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_tarski A (k4_classes1 C)) => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ).
tt(d8_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k9_clopban1 A B) = (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) ) ) ) ) ).
tt(d8_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k9_clopban2 A) = (g1_clopban2 (k8_clopban1 A A) (k5_clopban2 A) (k8_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k9_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k6_clopban2 A) (k10_csspace (k6_clopban1 A A) (k8_clopban1 A A)) (k13_clopban1 A A))) ) ) ).
tt(d8_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k6_clopban3 A B C) = (k1_normsp_1 A (k5_clopban3 A B) C)) ) ) ) ) ) ) ).
tt(d8_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v5_closure2 C A B) <=> (r2_hidden B C)) ) ) ) ) ) ).
tt(d8_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ((m1_clvect_1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ((u1_clvect_1 B) = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(d8_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k15_csspace A (k1_normsp_1 A B E) (k1_normsp_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k6_clvect_3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_clvect_1 A (k1_normsp_1 A B E) (k8_nat_1 k2_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_cohsp_1 A B C) <=> (r1_cohsp_1 A (k2_tarski B C))) ) ) ) ).
tt(d8_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  ((k7_coh_sp A B) = (k2_xtuple_0 (k1_xtuple_0 B))) ) ) ) ).
tt(d8_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  ((v6_combgras C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r1_incsp_1 A D E) <=> (r1_incsp_1 B (k2_combgras A B C D) (k3_combgras A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_compact1 C A B) <=>  ((v6_compact1 C A B) &  ((v1_compts_1 B) & (v1_tops_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_struct_0 A)) B)) ) ) ) ) ) ) ) ) ).
tt(d8_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k11_complex1 A B) = (k2_xcmplx_0 (k9_real_1 (k3_complex1 A) (k3_complex1 B)) (k3_xcmplx_0 (k9_real_1 (k4_complex1 A) (k4_complex1 B)) k7_complex1))) ) ) ) ) ).
tt(d8_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((v7_compl_sp B A) <=>  (! [C:$i] :  ((v7_ordinal1 C) => (v3_compl_sp (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(d8_compos_0,ax, (! [A:$i] :  ((v1_compos_0 A) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v4_compos_0 B A) <=> (v1_xboole_0 (k5_xtuple_0 B))) ) ) ) ) ).
tt(d8_compos_1,ax, (! [A:$i] :  ( ((v1_compos_1 A) & (l1_compos_1 A))  =>  ( (A = k1_compos_1)  <=>  ((u1_compos_1 A) = (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))) ) ) ) ).
tt(d8_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_comput_1 A B) = (k12_card_3 (k5_finseq_2 (k1_zfmisc_1 k1_numbers) A k5_numbers) B)) ) ) ) ) ).
tt(d8_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) <=> (v2_comseq_2 (k10_comseq_3 A))) ) ) ).
tt(d8_conlat_1,ax, (! [A:$i] :  ((l5_struct_0 A) =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  ((v5_conlat_1 B A) <=>  ((v1_xboole_0 (u2_conlat_1 A B)) & (v1_xboole_0 (u3_conlat_1 A B))) ) ) ) ) ) ).
tt(d8_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  (! [C:$i] :  ( ((v4_conlat_1 C (k7_conlat_2 A)) & (l2_conlat_1 C (k7_conlat_2 A)))  =>  ( (C = (k8_conlat_2 A B))  <=>  ( ((u2_conlat_1 (k7_conlat_2 A) C) = (u3_conlat_1 A B))  &  ((u3_conlat_1 (k7_conlat_2 A) C) = (u2_conlat_1 A B)) ) ) ) ) ) ) ) ) ).
tt(d8_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v8_conmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) )  =>  ((r5_analmetr A B C D) |  ((r5_analmetr A B C F) | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ( (D = (k5_convex4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers D E) = (k8_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers B E) (k3_funct_2 (u1_struct_0 A) k2_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((k10_cqc_sim1 A B C D) = (k3_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k8_cqc_sim1 A (k9_cqc_sim1 A) B) (k1_domain_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C D))) ) ) ) ) ) ) ) ) ).
tt(d8_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r3_cqc_the1 A B C) <=> (r2_hidden C (k1_cqc_the1 A B))) ) ) ) ) ) ) ).
tt(d8_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k7_csspace4 A B C) = (a_3_0_csspace4 A B C)) ) ) ) ) ) ) ).
tt(d8_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ((k8_csspace A B) = (k1_realset1 (u1_algstr_0 A) B)) ) ) ) ) ) ).
tt(d8_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_decomp_1 A B) = (k9_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))) ) ) ) ) ).
tt(d8_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k6_dickson A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_dickson A))) &  ((r4_waybel_4 B E (u1_orders_2 (k5_dickson A))) &  (D = (k9_subset_1 (u1_struct_0 A) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_dickson A) E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_diff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  ( (C = (k8_diff_1 A B))  <=>  ((r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C k6_numbers) A) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C (k1_nat_1 D 1)) (k5_diff_1 (k1_seqfunc k1_numbers k1_numbers C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(d8_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_dilworth A B) = (k4_subset_1 (u1_struct_0 A) B (k4_waybel_0 A B))) ) ) ) ) ).
tt(d8_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v6_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  =>  ( (? [C:$i] :  ((m2_finseq_1 C A) &  ((k4_dist_1 A C) = B) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A)) =>  ( (C = (k8_dist_1 A B))  <=>  ((k3_funct_2 (k6_dist_1 A) (k3_finseq_2 k1_numbers) (k7_dist_1 A) C) = B) ) ) ) ) ) ) ) ) ).
tt(d8_dtconstr,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_dtconstr k5_dtconstr) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k5_dtconstr) k5_numbers)))) )  =>  ( (A = k12_dtconstr)  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_dtconstr)) =>  ((r2_hidden B (k6_dtconstr k5_dtconstr)) =>  ((k1_funct_1 A (k2_trees_4 (u1_struct_0 k5_dtconstr) B)) = k6_numbers) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_dtconstr)) =>  (! [C:$i] :  ((m1_trees_4 C (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr)) =>  ((r1_lang1 k5_dtconstr B (k1_dtconstr (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) C)) =>  ((k1_funct_1 A (k8_trees_4 (u1_struct_0 k5_dtconstr) B C)) = (k11_dtconstr (k4_finseqop (k4_dtconstr k5_dtconstr) k5_numbers C A))) ) ) ) ) ) ) ) ) ) ).
tt(d8_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)))))) )  =>  ( (D = (k5_ec_pf_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ((k3_funct_2 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)) D E) = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) 2) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E)) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) 3) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E)) (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) 2))) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) 3))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))))) )  =>  ( (C = (k8_ec_pf_2 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((k3_funct_2 (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) C D) = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) (k4_algstr_0 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(d8_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ((v1_ens_1 B A) <=>  ((k10_xtuple_0 (k2_xtuple_0 B)) = (k4_ens_1 A B)) ) ) ) ) ) ).
tt(d8_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v2_matrprob A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k5_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_matrprob k1_numbers B C) = (k14_rvsum_1 (k8_matrix_1 k1_numbers A C) (k3_entropy1 2 (k8_matrix_1 k1_numbers A C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( (K = (k8_enumset1 A B C D E F G H I J))  <=>  (! [L:$i] :  ((r2_hidden L K) <=>  (~  ( (~  (L = A) )  &  ( (~  (L = B) )  &  ( (~  (L = C) )  &  ( (~  (L = D) )  &  ( (~  (L = E) )  &  ( (~  (L = F) )  &  ( (~  (L = G) )  &  ( (~  (L = H) )  &  ( (~  (L = I) )  &  (~  (L = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_eqrel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C A))  =>  ( (C = (k12_eqrel_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k11_eqrel_1 A D C) = (k1_setfam_1 (a_3_0_eqrel_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d8_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k8_euclid_3 A B C D) = (a_4_1_euclid_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d8_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v6_euclid_7 B A) <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k7_euclid A (k9_euclid A C E) (k9_euclid A D F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_rltopsp1 B) & (l1_rltopsp1 B))  =>  ( (B = (k15_euclid A))  <=>  ( ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (k3_pcomps_1 (k14_euclid A)))  &  ((g1_rlvect_1 (u1_struct_0 B) (u2_struct_0 B) (u1_algstr_0 B) (u1_rlvect_1 B)) = (k10_funcsdom (k2_finseq_1 A))) ) ) ) ) ) ) ).
tt(d8_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r6_euclidlp A B C) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) &  (? [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) &  ( (B = (k2_euclid_4 A D E))  &  ( (C = (k2_euclid_4 A F G))  & (r4_euclidlp A (k8_euclid A E D) (k8_euclid A G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_exchsort A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden B C)) )  => (r2_xboole_0 (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(d8_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) <=>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B C D E)) (k9_xtuple_0 C)) &  ((k3_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k2_compos_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 A B))) =>  ( (E = (k5_facirc_1 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (u3_msualg_1 A B)))))) )  &  ( (E = (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) F D))  &  ( ((k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) F k6_numbers) = C)  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) F (k1_nat_1 G 1)) = (k6_circuit2 A B (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_fdiff_1 A) <=> (r2_fdiff_1 A (k1_relset_1 k1_numbers A))) ) ) ).
tt(d8_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k8_ff_siec A) = (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d8_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k5_filter_0 A B C) = (a_3_0_filter_0 A B C)) ) ) ) ) ) ) ).
tt(d8_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k8_filter_1 A) = (a_1_0_filter_1 A)) ) ) ).
tt(d8_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_filter_2 A B) <=>  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B C) =>  ( (C = (u1_struct_0 A))  | (r1_filter_2 (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ) ).
tt(d8_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( (E = (k8_finance1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_seq_1 E F) = (k1_seq_1 (k7_finance1 A k1_numbers B k12_prob_1 C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k9_finseq_1 A))  <=>  ( ((k9_xtuple_0 B) = (k2_finseq_1 1))  &  ((k1_funct_1 B 1) = A) ) ) ) ) ) ).
tt(d8_finseq_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k8_finseq_4 A B C D E) = (k7_finseq_1 (k11_finseq_1 A B C) (k10_finseq_1 D E))) ) ) ) ) ) ).
tt(d8_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r3_finseq_8 A B C) <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  ((k3_finseq_6 A C 1 (k3_finseq_1 B)) = B) ) ) ) ) ) ) ) ) ) ).
tt(d8_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ((v2_fintopo2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C (k6_fintopo2 A B)) => (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(d8_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (C = (k8_fintopo3 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C D))  =>  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C (k2_nat_1 D 1)) = (k1_fintopo3 A E)) ) ) ) ) )  &  ((k3_funct_2 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)) C k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(d8_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_fintopo6 A B C D E) <=>  ((v2_fintopo6 B A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) B) C) &  ( ((k1_funct_1 B 1) = D)  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = E)  &  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  ( ((v2_fintopo6 F A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) F) C) &  ( ((k1_funct_1 F 1) = D)  &  ((k1_funct_1 F (k3_finseq_1 F)) = E) ) ) )  => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fin_topo A B) = (a_2_1_fin_topo A B)) ) ) ) ) ).
tt(d8_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A)))) )  =>  ( (C = (k5_fomodel0 A B))  <=>  (! [D:$i] :  ((m2_subset_1 D (k3_finseq_2 A) (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0))) =>  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A C D) = (k1_funct_1 (k4_fomodel0 A B D) (k6_xcmplx_0 (k3_finseq_1 D) 1))) ) ) ) ) ) ) ) ) ) ).
tt(d8_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k8_fomodel1 A) = (u3_struct_0 A)) ) ) ).
tt(d8_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_funct_2 (k35_fomodel1 A) B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 (k35_fomodel1 A) B))))) )  =>  ( (E = (k8_fomodel2 A B C D))  <=>  ((r2_relset_1 (k35_fomodel1 A) B (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) E k6_numbers) (k8_funcop_1 B (k35_fomodel1 A) C)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) E (k2_nat_1 F 1)) = (k7_fomodel2 (k3_relat_1 (k22_fomodel1 A) D) (k6_fomodel2 (k36_fomodel1 A) (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ((v1_relat_1 E) =>  ((k11_fomodel3 A B C D E) = (a_5_0_fomodel3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ((k4_fomodel4 A B) = (a_2_0_fomodel4 A B)) ) ) ) ) ).
tt(d8_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_pre_topc A) &  ((v2_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (A = k3_frechet)  <=>  ( ((u1_struct_0 A) = (k2_xboole_0 (k6_subset_1 k1_numbers k5_numbers) (k1_tarski k1_numbers)))  &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k3_topmetr) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A))))) )  &  ( (B = (k1_funct_4 (k6_partfun1 k1_numbers) (k7_funcop_1 k5_numbers k1_numbers)))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) <=> (v4_pre_topc (k8_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A) B C) k3_topmetr)) ) ) ) ) ) ) ) ) ) ).
tt(d8_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((k3_freealg A B) = (g1_lang1 (k2_xboole_0 (k4_finseq_1 A) B) (k2_freealg A B))) ) ) ) ).
tt(d8_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k8_fscirc_1 A B C) = (k2_circcomb (k8_facirc_1 A B C k1_facirc_1) (k4_fscirc_1 A B C))) ) ) ) ).
tt(d8_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_fsm_1 D A B))  =>  ((r3_fsm_1 A B C D) <=>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ((k8_finseq_1 B (k12_finseq_1 B (k3_funct_2 (u1_struct_0 D) B (u4_fsm_1 A B D) (u2_fsm_1 A D))) (k4_fsm_1 A B C (u2_fsm_1 A C) E)) = (k5_fsm_1 A B D (u2_fsm_1 A D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_2 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((r3_fsm_2 A B C D E) <=>  (? [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_subset_1 F k1_numbers k5_numbers))  &  (! [G:$i] :  ((m2_finseq_1 G A) =>  ( ((k1_funct_1 G 1) = D)  =>  ( ((r1_xxreal_0 F (k2_nat_1 (k3_finseq_1 G) 1)) =>  ( (E = (k1_funct_1 (u4_fsm_1 A B C) (k1_funct_1 (k2_fsm_1 A C (u2_fsm_1 A C) G) F)))  & (r2_hidden (k1_funct_1 (k2_fsm_1 A C (u2_fsm_1 A C) G) F) (u1_fsm_2 A C))) )  &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_subset_1 H k1_numbers k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 F H))  &  ((r1_xxreal_0 H (k2_nat_1 (k3_finseq_1 G) 1)) & (r2_hidden (k1_funct_1 (k2_fsm_1 A C (u2_fsm_1 A C) G) H) (u1_fsm_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  ((k6_fsm_3 A B C) = (a_3_0_fsm_3 A B C)) ) ) ) ) ) ) ).
tt(d8_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k8_ftacell1 A B C D E) = (k3_circcomb (k25_gfacirc1 A B C) (k37_gfacirc1 (k24_gfacirc1 A B C) E D) (k26_gfacirc1 A B C) (k38_gfacirc1 (k24_gfacirc1 A B C) E D))) ) ) ) ) ) ).
tt(d8_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (A = B)  =>  ((k14_funcop_1 A B C D) = C) )  &  ( (~  (A = B) )  =>  ((k14_funcop_1 A B C D) = D) ) ) ) ) ) ) ).
tt(d8_funcsdom,ax, (! [A:$i] :  ((k12_funcsdom A) = (g1_funcsdom (k9_funct_2 A k1_numbers) (k6_funcsdom A) (k5_funcsdom A) (k7_funcsdom A) (k9_funcsdom A) (k8_funcsdom A))) ) ).
tt(d8_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_relat_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_xboole_0 (k1_funct_1 A B))) ) ) ) ) ).
tt(d8_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_funct_2 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ).
tt(d8_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k15_funct_3 A B))  <=>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k9_xtuple_0 A)) & (r2_hidden E (k9_xtuple_0 B)))  =>  ((k1_binop_1 C D E) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k8_funct_6 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 A)) =>  ((k1_funct_1 C D) = (k1_funct_2 (k1_funct_1 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d8_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_funct_7 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ( ((k3_finseq_1 B) = (k2_nat_1 (k3_finseq_1 A) 1))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) => (r2_hidden (k1_funct_1 A C) (k1_funct_2 (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 1))))) ) ) ) ) ) ) ) ) ).
tt(d8_funct_8,ax, (! [A:$i] :  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_funct_8 A B C D) <=>  ((r1_tarski A (k1_relset_1 B D)) & (v6_funct_8 (k5_relset_1 B C D A) B C)) ) ) ) ) ) ) ) ) ).
tt(d8_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  ( ((r2_functor2 A B C D) & (r2_functor2 A B D E))  =>  (! [F:$i] :  ((m2_functor2 F A B C D) =>  (! [G:$i] :  ((m2_functor2 G A B D E) =>  (! [H:$i] :  ((m2_functor2 H A B C E) =>  ( (H = (k5_functor2 A B C D E F G))  <=> (r8_pboole (u1_struct_0 A) H (k3_functor2 A B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k6_fuzzy_1 A B C) = (k2_fuzzy_1 A (k1_fuzzy_1 A B (k3_fuzzy_1 A C)) (k1_fuzzy_1 A (k3_fuzzy_1 A B) C))) ) ) ) ) ) ) ).
tt(d8_fvaluat1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ((v3_fvaluat1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) &  ((v2_fvaluat1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) ) )  =>  ((m1_fvaluat1 B A) <=>  ( ((k1_funct_1 B (k4_struct_0 A)) = k1_xxreal_0)  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  => (r2_hidden (k1_funct_1 B C) k4_numbers)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 B (k6_algstr_0 A C D)) = (k1_xxreal_3 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B C)) => (r1_xxreal_0 k6_numbers (k1_funct_1 B (k1_algstr_0 A (k5_struct_0 A) C)))) ) )  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  ((k1_funct_1 B C) = k6_numbers) )  &  (~  ((k1_funct_1 B C) = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A B) = (k1_finsop_1 (u1_struct_0 A) B (u1_algstr_0 A))) ) ) ) ) ).
tt(d8_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k8_gate_5 A B C D E) = (k37_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0 (k2_gate_1 C E) k1_xboole_0)) ) ) ) ) ) ).
tt(d8_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_gcd_1 B A) <=>  ((m1_gcd_1 B A) & (r2_hidden (k5_struct_0 A) B)) ) ) ) ) ) ).
tt(d8_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (B = (k6_geomtrap A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) B C D) = (k1_geomtrap A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k8_gfacirc1 A B C) = (k3_circcomb (k5_gfacirc1 A B C) (k5_circcomb k25_twoscomp (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) (k6_gfacirc1 A B C) (k7_facirc_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp) k25_twoscomp))) ) ) ) ).
tt(d8_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 (k5_gfacirc2 B C D)) (k3_msafree2 (k5_gfacirc2 B C D))) =>  ( (E = (k8_gfacirc2 A B C D))  <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ( (A = (k1_nat_1 F 1))  &  (E = (k24_gfacirc1 (k1_funct_1 C A) (k1_funct_1 D A) (k7_gfacirc2 F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k8_glib_000 A) = (k1_funct_1 A k3_glib_000)) ) ) ).
tt(d8_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((v1_abian C) |  ((k5_glib_001 A B C) = (k1_funct_1 B C)) ) )  &  ( (~  ( (~ (v1_abian C))  & (r1_xxreal_0 C (k3_finseq_1 B))) )  =>  ((k5_glib_001 A B C) = (k3_glib_001 A B)) ) ) ) ) ) ) ) ) ).
tt(d8_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)))))  =>  ( (B = (k3_glib_002 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) &  (C = (k1_glib_002 A D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((k6_glib_003 A) = (k1_funct_1 A k3_glib_003)) ) ) ).
tt(d8_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))) =>  ( ( ((k6_glib_004 A B) = k1_xboole_0)  =>  ((k7_glib_004 A B) = B) )  &  ( (~  ((k6_glib_004 A B) = k1_xboole_0) )  =>  ((k7_glib_004 A B) = (k4_tarski (k1_funct_4 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B) (k16_funcop_1 (k1_funct_1 (k11_glib_000 A) (k10_subset_1 (k6_glib_004 A B))) (k2_xcmplx_0 (k1_seq_1 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_funct_1 (k10_glib_000 A) (k10_subset_1 (k6_glib_004 A B)))) (k1_seq_1 (k5_glib_003 A) (k10_subset_1 (k6_glib_004 A B)))))) (k2_xboole_0 (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k10_subset_1 (k6_glib_004 A B)))))) ) ) ) ) ) ) ).
tt(d8_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r5_glib_005 A B C) <=>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  =>  ( (~  ((r2_glib_000 A (k1_funct_1 C D) (k1_funct_1 C (k1_nat_1 D 2)) (k1_funct_1 C (k1_nat_1 D 1))) & (r1_xxreal_0 (k1_funct_1 (k5_glib_003 A) (k1_funct_1 C (k1_nat_1 D 1))) (k1_funct_1 B (k1_funct_1 C (k1_nat_1 D 1))))) )  &  (~  ( (~ (r2_glib_000 A (k1_funct_1 C D) (k1_funct_1 C (k1_nat_1 D 2)) (k1_funct_1 C (k1_nat_1 D 1))))  & (r1_xxreal_0 (k1_funct_1 B (k1_funct_1 C (k1_nat_1 D 1))) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_goboard1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 A))) =>  ((r1_xxreal_0 (k1_matrix_1 A) 1) |  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( (C = (k3_goboard1 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k1_funct_1 C D) = (k2_finseq_3 B (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_gobrd13,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r3_gobrd13 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 C)) &  ( ((k7_partfun1 A B D) = (k3_matrix_1 A C E F))  &  ( ((k7_partfun1 A B (k2_nat_1 D 1)) = (k3_matrix_1 A C G H))  &  ( (~  ( (E = G)  &  ( ((k2_nat_1 F 1) = H)  &  ((r2_hidden (k4_tarski G (k2_nat_1 H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k2_nat_1 H 1))) ) ) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  ( (F = H)  &  ((r2_hidden (k4_tarski (k2_nat_1 G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k2_nat_1 G 1) H)) ) ) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  ( (F = H)  &  ((r2_hidden (k4_tarski (k7_nat_d G 1) H) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C (k7_nat_d G 1) H)) ) ) ) )  &  (~  ( (E = G)  &  ( (F = (k2_nat_1 H 1))  &  ((r2_hidden (k4_tarski G (k7_nat_d H 1)) (k2_matrix_1 C)) &  ((k7_partfun1 A B (k2_nat_1 D 2)) = (k3_matrix_1 A C G (k7_nat_d H 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((k6_goedelcp A B) = (k3_tarski (a_2_0_goedelcp A B))) ) ) ) ) ).
tt(d8_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v3_graph_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (u4_struct_0 A)) & (r2_hidden C (u4_struct_0 A)))  =>  ( ( (~  ( ((k1_funct_1 (u1_graph_1 A) B) = (k1_funct_1 (u1_graph_1 A) C))  &  ((k1_funct_1 (u2_graph_1 A) B) = (k1_funct_1 (u2_graph_1 A) C)) ) )  &  (~  ( ((k1_funct_1 (u1_graph_1 A) B) = (k1_funct_1 (u2_graph_1 A) C))  &  ((k1_funct_1 (u1_graph_1 A) C) = (k1_funct_1 (u2_graph_1 A) B)) ) ) )  |  (B = C) ) ) ) ) ) ) ) ).
tt(d8_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  ( ( ((k1_card_1 (u1_struct_0 A)) = 1)  |  ( (~  (B = k1_xboole_0) )  &  (~ (r2_graph_2 A B)) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k6_graph_2 A B))  <=> (r1_graph_2 A C B)) ) ) ) ) ) ) ) ).
tt(d8_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_finseq_2 B (u4_struct_0 A)) =>  ( (B = (k9_graph_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v2_funct_1 C) &  ((v1_msscyc_1 C A) & (m2_graph_1 C A)) ) ) ) ) ) ) ) ) ).
tt(d8_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_graph_5 A B C) = (a_3_1_graph_5 A B C)) ) ) ) ) ) ) ).
tt(d8_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k13_graphsp A B) = (a_2_1_graphsp A B)) ) ) ) ) ).
tt(d8_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  ((r4_groeb_2 A B C D E F) <=> (r3_groeb_2 A B C D E F (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_group_2 A C) (k15_group_2 A C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_group_2 A C) (k15_group_2 A C))))) )  =>  ( (E = (k8_group_10 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k15_group_2 A C)) =>  (? [G:$i] :  ((m1_subset_1 G (k15_group_2 A C)) &  (? [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) &  (? [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) &  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ( (G = (k1_funct_1 E F))  &  ( (I = (k4_group_2 A J H))  &  ( (H = F)  &  ( (I = G)  &  (J = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_xxreal_0 k6_numbers B) =>  ((k5_group_1 A B C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C (k1_int_2 B))) )  &  ( (~ (r1_xxreal_0 k6_numbers B))  =>  ((k5_group_1 A B C) = (k2_group_1 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C (k1_int_2 B)))) ) ) ) ) ) ) ) ) ).
tt(d8_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k7_group_2 A) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ).
tt(d8_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_group_3 A B) = (k5_group_3 A (k8_group_2 A (k7_group_2 A)) B)) ) ) ) ) ).
tt(d8_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k7_group_4 A B C) = (k2_group_2 A (k8_group_2 A B) (k8_group_2 A C))) ) ) ) ) ) ) ).
tt(d8_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k8_group_5 A B C) = (k7_group_5 A (k8_group_2 A B) (k8_group_2 A C))) ) ) ) ) ) ) ).
tt(d8_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B)))))) )  =>  ( (C = (k8_group_6 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B)) C D) = (k13_group_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_group_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v4_group_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (v5_group_1 (k1_group_7 A B C))) ) ) ) ) ) ) ).
tt(d8_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  ( (C = (k4_group_9 A B))  <=>  ((u1_struct_0 C) = (k1_tarski (k1_group_1 B))) ) ) ) ) ) ) ).
tt(d8_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v1_hahnban1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_vectsp_1 A B E D)) = (k6_algstr_0 A E (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_hallmar1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ((v2_relat_1 B) =>  (! [C:$i] :  ((m2_hallmar1 C A B) =>  ((m4_hallmar1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k1_card_1 (k1_funct_1 C D)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  ( (D = (k3_hermitan A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) D E F) = (k2_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)))))) )  =>  ( (B = (k8_heyting1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) B C) = (k9_normform A (k6_heyting1 A (k3_heyting1 A C)))) ) ) ) ) ) ) ).
tt(d8_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)))))) )  =>  ( (C = (k8_heyting2 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k4_partfun1 A B)) =>  ((k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) C D) = (k3_substlat A B (k2_setwiseo (k4_partfun1 A B) D))) ) ) ) ) ) ) ) ) ).
tt(d8_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k3_hilbert1 A B) = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 k5_numbers 1) A) B)) ) ) ) ) ).
tt(d8_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v3_hilbert2 A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (A = (k1_hilbert2 B)) ) ) ) ) ) ).
tt(d8_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v2_hilbert3 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m1_hilbert3 C B) =>  (? [D:$i] : (r1_abian D (k5_hilbert3 B C A))) ) ) ) ) ) ) ) ).
tt(d8_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_hurwitz A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ((r1_polynom5 k1_complfld A B) & (r1_xxreal_0 k6_numbers (k3_complex1 B))) ) ) ) ) ) ) ).
tt(d8_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (B = (k5_series_1 2 A))  =>  ((k8_idea_1 A B) = k6_numbers) )  &  ( (~  (B = (k5_series_1 2 A)) )  =>  ((k8_idea_1 A B) = B) ) ) ) ) ) ) ).
tt(d8_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((m1_ideal_1 C A B) <=>  (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 k5_numbers C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m2_subset_1 G (u1_struct_0 A) B) =>  (~  ((k7_partfun1 (u1_struct_0 A) C D) = (k6_algstr_0 A (k6_algstr_0 A E G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_incproj,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v4_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  ((r1_incsp_1 A D I) &  ((r1_incsp_1 A E I) &  ((r1_incsp_1 A F H) &  ((r1_incsp_1 A F I) &  ((r1_incsp_1 A B J) &  ((r1_incsp_1 A D J) &  ((r1_incsp_1 A C K) &  ((r1_incsp_1 A E K) &  ( (~ (r1_incsp_1 A F J))  &  ( (~ (r1_incsp_1 A F K))  &  ( (~  (H = I) )  &  (! [L:$i] :  ((m1_subset_1 L (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A L J) & (r1_incsp_1 A L K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v5_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ( (~  (C = D) )  & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d8_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v2_index_1 E A B) & (m1_index_1 E A B))  =>  ((m3_index_1 E A B C D) <=> (m2_index_1 (k2_xtuple_0 E) B (k3_relat_1 C (k1_xtuple_0 E)) (k3_relat_1 D (k1_xtuple_0 E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_int_1 A) = (k6_xcmplx_0 A (k1_int_1 A))) ) ) ).
tt(d8_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v1_int_3 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers)))) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (D = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (C = (k1_algstr_0 A (k6_algstr_0 A E D) F))  &  (~  ( (~  (F = (k4_struct_0 A)) )  & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k5_numbers B D) (k3_funct_2 (u1_struct_0 A) k5_numbers B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r4_integr10 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k4_integr10 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers D) = (k1_limfunc1 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k1_relset_1 k1_numbers D)) =>  ((k1_seq_1 D E) = (k4_integra5 E B A)) ) ) )  &  ((v6_limfunc1 D) &  (C = (k5_limfunc1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [E:$i] :  ((m4_integr15 E A B C D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( (F = (k6_integr15 A B C D E))  <=>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k1_normsp_1 (k4_real_ns1 A) F G) = (k4_integr15 A B C (k2_integra2 B D G) (k5_integr15 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((k7_integr16 A B) = (k3_binop_2 (k2_integra5 A (k5_comseq_3 k1_numbers B)) (k5_binop_2 (k2_integra5 A (k6_comseq_3 k1_numbers B)) k7_complex1))) ) ) ) ) ).
tt(d8_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k5_integr18 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ( (E = (k2_partfun1 k1_numbers (u1_struct_0 A) C B))  &  (D = (k4_integr18 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_integra1 C A) =>  ((k6_integra1 A B C) = (k18_rvsum_1 (k4_integra1 A B C))) ) ) ) ) ) ) ).
tt(d8_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_interva1 B A) <=>  (? [C:$i] :  (? [D:$i] :  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((r2_hidden E B) <=>  ((r1_tarski C E) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D B C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  ((r2_nattra_1 B C D E) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_nattra_1 G B C D E) =>  ((k5_isocat_1 A B C D E F G) = (k3_isocat_1 A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  ((k10_isocat_2 A B C D) = (k9_cat_1 A (k8_cat_2 B C) C D (k15_cat_2 B C))) ) ) ) ) ) ) ) ) ).
tt(d8_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_isomichi B A) <=>  (~ (r3_xboole_0 (k2_pre_topc A (k1_tops_1 A B)) (k1_tops_1 A (k2_pre_topc A B)))) ) ) ) ) ) ).
tt(d8_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  ((k8_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k9_real_1 1 A)) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k9_real_1 1 A))))))) (k12_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  (~  ((k8_jgraph_4 A B) = (k1_rlvect_1 (k15_euclid 2) (k19_euclid (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k7_real_1 1 A)) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid B) (k12_euclid B)) A) (k7_real_1 1 A))))))) (k12_euclid B))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) &  (~ (r1_xxreal_0 k6_numbers (k18_euclid B))) ) )  &  ( (~  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  (~ (r1_xxreal_0 k6_numbers (k18_euclid B))) ) )  &  (~  ((k8_jgraph_4 A B) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k8_jgraph_6 A B C) = (a_3_3_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(d8_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k8_jordan5d A))  <=>  ((r2_hidden (k4_tarski B (k1_matrix_1 (k2_goboard2 A))) (k2_matrix_1 (k2_goboard2 A))) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A))) = (k21_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(d8_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (B = (k8_jordan6 A))  <=>  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) B) &  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c C (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_jordan,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  ((r2_hidden C (k1_topreal9 A B D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k7_toprealb A B D)) (u1_struct_0 (k7_toprealb A B D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb A B D)) (u1_struct_0 (k7_toprealb A B D)))))) )  =>  ( (E = (k10_jordan A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_toprealb A B D))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) &  ( (F = G)  &  ((k3_funct_2 (u1_struct_0 (k7_toprealb A B D)) (u1_struct_0 (k7_toprealb A B D)) E F) = (k3_brouwer A B G C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_knaster B A) &  ((v3_knaster B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  ( (C = (k7_knaster A B))  <=>  ( ((u1_struct_0 C) = B)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (D = F)  &  ( (E = G)  &  ( ((r3_lattices C D E) => (r3_lattices A F G))  &  ((r3_lattices A F G) => (r3_lattices C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_kolmog01,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  ((k6_kolmog01 A B C D) = (k6_setfam_1 (k9_setfam_1 B) (k5_kolmog01 A B C D))) ) ) ) ) ) ) ) ).
tt(d8_lang1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v2_lang1 C) & (l2_lang1 C))  =>  ( (C = (k7_lang1 A B))  <=>  ( ((u1_struct_0 C) = (k2_tarski A B))  &  ( ((u2_lang1 C) = A)  &  ((u1_lang1 C) = (k1_tarski (k4_tarski A (k9_finseq_1 B)))) ) ) ) ) ) ) ) ).
tt(d8_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A A) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  ( (E = (k9_laplace A B C D))  <=>  ( ((k3_finseq_1 E) = A)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k8_group_1 C (k3_matrix_1 (u1_struct_0 C) D F B) (k6_laplace F B A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(d8_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  ((k2_lattice4 A B) = (k3_lattice2 (u1_struct_0 A) A B (k3_struct_0 A))) ) ) ) ) ).
tt(d8_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k1_lattice5 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k1_lattice5 A)))))) )  =>  ( (D = (k4_lattice5 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ( ((v1_partfun1 F A) &  ((v3_relat_2 F) &  ((v8_relat_2 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( (F = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k1_lattice5 A)) D E))  &  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden (k1_domain_1 A A G H) F) <=> (r3_orders_2 B (k3_lattice5 A B C G H) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_lattice6 B A) <=>  (~  ((k3_lattice6 A B) = B) ) ) ) ) ) ) ).
tt(d8_lattice7,ax, (! [A:$i] :  ((m2_lattice7 A) <=> (r1_cohsp_1 A A)) ) ).
tt(d8_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((k7_lattice8 A B C) = (k3_lattice8 A (k7_lattice5 A B C))) ) ) ) ) ) ) ).
tt(d8_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v8_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A (k2_lattices A B C) C) = C) ) ) ) ) ) ) ) ).
tt(d8_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v4_lfuzzy_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~  ((k8_lfuzzy_0 A A B C D) = k6_numbers) )  &  ( (~  ((k8_lfuzzy_0 A A B D C) = k6_numbers) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v5_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 B) & (r1_tarski (k2_relset_1 k1_numbers B) (k1_relset_1 k1_numbers A)))  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers B A))) ) ) ) ) ) ) ).
tt(d8_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_limfunc2 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_limfunc2 A B))  <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v2_lopban_1 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) (k8_real_1 D (k1_normsp_0 A E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k9_lopban_2 A) = (g1_lopban_2 (k10_lopban_1 A A) (k5_lopban_2 A) (k8_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k9_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k6_lopban_2 A) (k10_rsspace (k8_lopban_1 A A) (k10_lopban_1 A A)) (k15_lopban_1 A A))) ) ) ).
tt(d8_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v25_algstr_0 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k9_algstr_0 A B))  <=>  ( ((k6_algstr_0 A B C) = (k5_struct_0 A))  &  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(d8_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (E = (k7_lopban_4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F A) =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k6_algstr_0 B (k8_nat_1 (u1_struct_0 B) (k1_lopban_4 B C) F) (k8_nat_1 (u1_struct_0 B) (k1_bhsp_4 B (k1_lopban_4 B D)) (k7_nat_d A F)))) )  &  ( (~ (r1_xxreal_0 F A))  =>  ((k8_nat_1 (u1_struct_0 B) E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ((v1_pre_topc B) &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( (B = (k11_lopclset A))  <=>  ( ((u1_struct_0 B) = (k7_lopclset A))  &  ((u1_pre_topc B) = (a_1_2_lopclset A)) ) ) ) ) ) ) ).
tt(d8_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k9_lpspace1 A B C) = (a_3_0_lpspace1 A B C)) ) ) ) ) ) ) ).
tt(d8_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k6_lpspace2 A B C D) (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k6_lpspace2 A B C D) (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D))))) )  =>  ( (E = (k7_lpspace2 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_lpspace2 A B C D)) (k6_lpspace2 A B C D)) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 (k1_lpspace2 A B C D)) (k6_lpspace2 A B C D)) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden H F) & (r2_hidden I G))  =>  ((k5_binop_1 (k6_lpspace2 A B C D) E F G) = (k5_lpspace2 A B C (k3_valued_1 A k1_numbers k1_numbers H I) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k8_ltlaxio1 A B) = (k5_ltlaxio1 B (k4_ltlaxio1 A (k4_hilbert1 A B)))) ) ) ) ) ).
tt(d8_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_mathmorp A B C D) = (k4_subset_1 (u1_struct_0 A) B (k7_mathmorp A B C D))) ) ) ) ) ) ) ) ) ).
tt(d8_matrix16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v4_matrix16 B A) =>  (! [C:$i] :  ((m1_matrix_1 C A (k3_finseq_1 B) (k3_finseq_1 B)) =>  ( (C = (k2_matrix16 A B))  <=> (r2_matrix16 A C B)) ) ) ) ) ) ) ) ).
tt(d8_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( (D = (k7_matrix_1 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_funct_1 D E) = (k3_matrix_1 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (B = (k10_matrix_2 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((r2_hidden C A) &  (B = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(d8_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k12_matrix_2 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (u1_struct_0 B))))) )  =>  ( (D = (k11_matrix_3 A B C))  <=>  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 A)) =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) D E) = (k14_matrix_2 B A (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B C E) (u2_algstr_0 B)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_matrix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k8_matrix_5 A B) = (k2_matrix_5 (k1_matrix_3 k1_complfld A B))) ) ) ) ) ).
tt(d8_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k9_matrixc1 A) = A) ) ) ).
tt(d8_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v2_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( (C = (k23_matrixj1 A B))  <=>  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k14_matrixj1 (u1_struct_0 A) C D) = (k12_matrix_1 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_matrixr1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k8_matrixr1 A B) = (k2_matrixr1 (k1_matrix_3 k2_vectsp_1 A B))) ) ) ) ) ).
tt(d8_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 (u1_struct_0 A))))  =>  ( (G = (k10_matrlin A B C D E F))  <=>  ( ((k3_finseq_1 G) = (k3_finseq_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k9_xtuple_0 E)) =>  ((k9_pre_poly (u1_struct_0 A) k5_numbers (k3_finseq_2 (u1_struct_0 A)) G H) = (k9_matrlin A C F (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k7_partfun1 (u1_struct_0 B) E H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_matroid0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_pre_topc B) & (l1_pre_topc B))  =>  ( (B = (k2_matroid0 A))  <=>  ( ((u1_struct_0 B) = (k3_tarski A))  &  ((k1_matroid0 B) = (a_1_0_matroid0 A)) ) ) ) ) ) ).
tt(d8_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (F = (k4_mcart_1 A B C D E))  <=>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (E = (k6_xtuple_0 G H I J))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k5_measure6 A) = (a_1_0_measure6 A)) ) ) ).
tt(d8_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k7_numbers)) =>  ( (B = (k8_measure7 A))  <=>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_measure7 D A) &  (C = (k6_measure7 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_setfam_1 A) k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) k7_numbers)))) )  =>  ( (D = (k6_measure8 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((k1_mesfunc9 D E) = (k7_supinf_2 (k5_measure8 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k11_member_1 A B) = (k9_member_1 A (k5_member_1 B))) ) ) ) ) ).
tt(d8_membered,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(d8_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_memstr_0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k6_memstr_0 A B C) = (k5_relat_1 C (k8_struct_0 B))) ) ) ) ) ) ) ).
tt(d8_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k8_mesfun7c A B) = (k7_mesfunc8 A (k1_mesfun7c A B))) ) ) ) ) ).
tt(d8_mesfunc1,ax, (k8_mesfunc1 = 1) ).
tt(d8_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_mesfunc5 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k3_extreal1 (k4_supinf_2 (k8_nat_1 k7_numbers A E) (k1_measure6 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k6_mesfunc8 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k5_rinfsup2 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_mesfunc9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ( (E = (k8_mesfunc9 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k4_mesfunc5 A B E F) = (k1_binop_1 C D F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v8_metric_1 A) <=> (v4_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ).
tt(d8_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k5_metric_2 A) = (a_1_1_metric_2 A)) ) ) ).
tt(d8_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((k6_midsp_1 A) = (a_1_0_midsp_1 A)) ) ) ).
tt(d8_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (k15_midsp_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (k15_midsp_1 A)))))) )  =>  ( (B = (k5_midsp_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k15_midsp_1 A)) B C D) = (k8_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  ( (F = (k7_midsp_3 A B C D E))  <=>  (! [G:$i] :  ((m1_midsp_3 G A) =>  ((k5_midsp_3 A (u1_struct_0 B) F G) = (k10_midsp_2 B C D (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 B C)) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k8_mmlquery A B C D) = (a_4_3_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d8_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v3_mod_2 D A) & (l1_mod_2 D A))  =>  ((m1_mod_2 D A B C) <=>  ( ((k2_mod_2 A D) = B)  &  ((k3_mod_2 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_mod_4 C A B) <=>  ((v1_ringcat1 C A B) & (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(d8_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((k10_modal_1 A) = (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 1) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) (k12_finseq_1 k5_numbers k6_numbers) A)) ) ) ).
tt(d8_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ((m4_modcat_1 C A (k4_modcat_1 A B)) =>  ((k5_modcat_1 A B C) = (k2_mod_2 A C)) ) ) ) ) ) ) ).
tt(d8_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k8_modelc_1 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 1) A) B)) ) ) ) ) ).
tt(d8_modelc_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k8_modelc_2 A B) = (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 5) A) B)) ) ) ) ) ).
tt(d8_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ((l1_modelc_3 C A) =>  ((r3_modelc_3 A B C) <=>  (? [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  &  ((r2_hidden D (u2_modelc_3 A B)) &  ( (~  ( (~ (v5_modelc_2 D))  &  ( (~ (v7_modelc_2 D))  &  (~ (v8_modelc_2 D)) ) ) )  &  (C = (k6_modelc_3 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v8_monoid_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ( ((k5_binop_1 A B C D) = (k5_binop_1 A B C E))  |  ((k5_binop_1 A B D C) = (k5_binop_1 A B E C)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B)) (k1_zfmisc_1 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B)) (k1_zfmisc_1 C))))) )  =>  ( (E = (k21_monoid_1 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B))) =>  ((k3_funct_2 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B)) (k1_zfmisc_1 C) E F) = (k7_relset_1 (k2_zfmisc_1 A B) C D (k2_zfmisc_1 (k2_domain_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) F) (k3_domain_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k5_msafree2 A B) = (k11_msafree A (u3_msualg_1 A B))) ) ) ) ) ).
tt(d8_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((k5_msafree A B) = (g1_lang1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k4_msafree A B))) ) ) ) ) ).
tt(d8_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  ((m4_msaterm C A B) <=> (r5_pboole (u1_struct_0 A) C (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(d8_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_struct_0 B) &  ( (~ (v11_struct_0 B))  &  ((v1_msualg_1 B) &  ((v5_msualg_1 B) & (l1_msualg_1 B)) ) ) )  =>  ( (B = (k6_msualg_1 A))  <=>  ( ((u1_struct_0 B) = (k1_tarski k6_numbers))  &  ( ((u4_struct_0 B) = (k4_finseq_1 (k1_unialg_1 A)))  &  ( ((u1_msualg_1 B) = (k1_partfun1 k5_numbers k5_numbers k5_numbers (k3_finseq_2 (k1_tarski k6_numbers)) (k1_unialg_1 A) (k7_finseq_2 k6_numbers)))  &  ((u2_msualg_1 B) = (k1_margrel1 k5_numbers (k4_finseq_1 (k1_unialg_1 A)) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(d8_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m2_pboole D (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) C)) (k3_relat_1 (u2_msualg_1 A) C)) =>  ( (D = (k4_msualg_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k1_funct_1 D E) = (k3_msualg_2 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r2_msualg_3 A B C D) <=>  ((r1_msualg_3 A B C D) & (v2_msualg_3 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d8_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B))))) )  =>  ( (E = (k7_msualg_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A C) (k2_msualg_1 A B))) =>  ((k1_funct_1 E F) = (k3_msualg_4 A C D (k2_msualg_1 A B) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v3_msualg_6 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r1_msualg_6 A D E B F) =>  (! [G:$i] :  (! [H:$i] :  ((r2_hidden (k4_tarski G H) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D)) => (r2_hidden (k4_tarski (k1_funct_1 F G) (k1_funct_1 F H)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  ( (B = (k5_mycielsk A))  <=>  ((u1_orders_2 B) = (k6_subset_1 (k2_zfmisc_1 A A) (k4_relat_1 A))) ) ) ) ) ) ).
tt(d8_nagata_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k9_funct_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (D = (k4_nagata_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A B D E) = (k1_funct_1 (k3_funct_2 A (k9_funct_2 A B) C E) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) & (v1_partfun1 B k10_newton)) ) )  =>  ( (B = (k12_nat_3 A))  <=>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ((k1_funct_1 B C) = (k11_nat_3 A C)) ) ) ) ) ) ) ) ).
tt(d8_nat_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat)))) )  =>  ( (A = k8_nat_lat)  <=>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k6_nat_lat) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k6_nat_lat) =>  ((k5_binop_1 k6_nat_lat A B C) = (k6_nat_d B C)) ) ) ) ) ) ) ) ).
tt(d8_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r2_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ((m2_nattra_1 E A B C D) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_cat_1 H A F G) =>  ((k5_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B C G) (k8_cat_1 A B D G) (k9_cat_3 A F G B C H) (k4_nattra_1 A B C D E G)) = (k5_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B D F) (k8_cat_1 A B D G) (k4_nattra_1 A B C D E F) (k9_cat_3 A F G B D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r4_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) B)) &  ((v9_clvect_1 D A) &  ((k7_clvect_1 A D) = C) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k2_numbers (u1_struct_0 A) D B)) &  ((k7_partfun1 k2_numbers B C) = (k3_comseq_2 (k8_funct_2 k5_numbers k2_numbers (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ndiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r2_ndiff_1 A B C D) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E A) => (r1_ndiff_1 B C (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((r2_ndiff_5 A B C D E) <=>  ((r1_tarski E (k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  ((r2_hidden F E) => (r1_ndiff_5 A B C (k2_partfun1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  =>  ( (B = (k3_necklace A))  <=>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((u1_orders_2 B) = (k7_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k3_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_orders_2 A)) (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(d8_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  =>  (! [C:$i] :  ( (C = (k5_net_1 A B))  <=>  ( ((r2_hidden B (u1_struct_0 A)) =>  (C = (k1_tarski B)) )  &  ((r2_hidden B (u4_struct_0 A)) =>  (C = (k3_net_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(d8_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_int_2 B) & (m2_subset_1 B k1_numbers k5_numbers))  =>  ( (B = (k12_newton A))  <=>  (A = (k5_card_1 (k11_newton B))) ) ) ) ) ) ).
tt(d8_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((r4_nfcont_1 A B C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r2_nfcont_1 A (k2_partfun1 (u1_struct_0 A) k1_numbers B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_normform,ax, (! [A:$i] :  ((k7_normform A) = (a_1_0_normform A)) ) ).
tt(d8_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_openlatt A B) = (a_2_1_openlatt A B)) ) ) ) ) ).
tt(d8_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ( (D = (k9_oppcat_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) D E) = (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) C (k5_oppcat_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_orders_1 A B) <=>  ((r1_relat_2 A B) &  ((r8_relat_2 A B) &  ((r4_relat_2 A B) & (r6_relat_2 A B)) ) ) ) ) ) ) ).
tt(d8_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_orders_2 A B) = (a_2_0_orders_2 A B)) ) ) ) ) ).
tt(d8_ordinal1,ax, (! [A:$i] :  ((v6_ordinal1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r3_xboole_0 B C)) ) ) ) ) ).
tt(d8_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_finset_1 A) & (v1_ordinal2 A)) ) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k4_ordinal5 A))  <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  &  ( (B = (k1_ordinal2 C))  &  ( ((k9_xtuple_0 C) = (k1_ordinal1 (k2_afinsq_1 A)))  &  ( ((k1_funct_1 C k6_numbers) = k6_numbers)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 A)) =>  ((k1_funct_1 C (k1_nat_1 D 1)) = (k10_ordinal2 (k1_funct_1 C D) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  ( (C = (k6_ordinal6 A B))  <=>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((k4_ordinal6 A (k2_ordinal1 A) C D) = (k12_ordinal2 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_o_ring_1 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((v6_o_ring_1 C A) &  (B = (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(d8_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) )  =>  ( (C = (k5_osafree A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 C D) = (k4_osafree A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  ((v8_osalg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (v7_osalg_1 B A)) ) ) ) ) ).
tt(d8_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  ((k6_osalg_2 A B) = (a_2_0_osalg_2 A B)) ) ) ) ) ).
tt(d8_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v2_osalg_4 A) <=>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)) (k2_osalg_4 A)) => (v1_waybel_0 B A)) ) ) ) ) ).
tt(d8_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k6_parsp_1 A) = (k4_zfmisc_1 (k5_parsp_1 A) (k5_parsp_1 A) (k5_parsp_1 A) (k5_parsp_1 A))) ) ) ).
tt(d8_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k6_partit1 A) = (k1_tarski A)) ) ) ).
tt(d8_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r5_pboole A B C) <=>  (! [D:$i] :  ((r2_hidden D A) => (r1_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(d8_pcomps_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v3_pcomps_1 A) <=>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r1_pcomps_1 (u1_struct_0 A) B) &  ((k2_pcomps_1 (k4_pcomps_1 (u1_struct_0 A) B)) = (u1_pre_topc A)) ) ) ) ) ) ) ).
tt(d8_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_euclid A) (k1_euclid B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  ( (E = (k8_pdiff_1 A B C D))  <=>  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 A))) &  ( (C = F)  &  ( (D = G)  &  (E = (k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_3 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k4_pdiff_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k10_finseq_1 D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 G 1))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B) I) (k1_seq_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k5_pdiff_4 A) = (k1_euclid_8 (k10_real_1 (k1_seq_1 A 1) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))) (k5_square_1 (k1_seq_1 A 3))))) (k10_real_1 (k1_seq_1 A 2) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))) (k5_square_1 (k1_seq_1 A 3))))) (k10_real_1 (k1_seq_1 A 3) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))) (k5_square_1 (k1_seq_1 A 3))))))) ) ) ).
tt(d8_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r8_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r4_pdiff_9 A B C D) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k21_binop_2 (k3_finseq_1 C) 1)) => (r3_pdiff_9 A B (k7_partfun1 k5_numbers C (k23_binop_2 E 1)) (k1_seqfunc (k1_euclid A) k1_numbers (k4_pdiff_9 A B C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v7_pencil_1 A) <=>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_pencil_1 A B C)) ) ) ) ) ) ) ) ).
tt(d8_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_petri B A) <=> (m1_subset_1 (k6_petri A B) (k1_zfmisc_1 (k7_petri A B)))) ) ) ) ) ).
tt(d8_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_pnproc_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k7_pnproc_1 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_funct_2 A k5_numbers))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((k1_funct_1 C D) = (k6_pnproc_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(d8_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers)  =>  ( (E = (k8_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (H = (k1_polyeq_5 2 (k6_xcmplx_0 (k1_newton F 2) G)))  &  (E = (k6_xcmplx_0 (k4_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k2_xcmplx_0 F H))))) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  ((k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) = k6_numbers) )  =>  ( (E = (k8_polyeq_5 A B C D))  <=>  (? [F:$i] :  ((v1_xcmplx_0 F) &  (? [G:$i] :  ((v1_xcmplx_0 G) &  (? [H:$i] :  ((v1_xcmplx_0 H) &  (? [I:$i] :  ((v1_xcmplx_0 I) &  (? [J:$i] :  ((v1_xcmplx_0 J) &  (? [K:$i] :  ((v1_xcmplx_0 K) &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 3 (k1_newton D 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 (k3_xcmplx_0 4 C) D)) (k1_newton D 3)) 64))  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 A) (k3_xcmplx_0 (k3_xcmplx_0 64 D) B)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton D 2)) C)) (k3_xcmplx_0 3 (k1_newton D 4))) 1024))  &  ( (I = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (J = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton G 2)) (k6_xcmplx_0 (k1_newton F 2) H) (k3_xcmplx_0 2 F))))  &  ( (K = (k10_complex1 (k13_complex1 G (k3_xcmplx_0 I J))))  &  (E = (k6_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 I J) K) (k13_complex1 D 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k11_polyform A B) = (k5_card_1 (k8_polyform A B))) ) ) ) ) ).
tt(d8_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_vectsp_1 B) & (l5_algstr_0 B)) )  =>  ((k8_polynom1 A B) = (k15_funct_7 (k15_pre_poly A) (u1_struct_0 B) (k7_polynom1 A B) (k16_pre_poly A) (k5_struct_0 B))) ) ) ) ).
tt(d8_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((k10_polynom3 A) = (k15_funct_7 k5_numbers (u1_struct_0 A) (k9_polynom3 A) k6_numbers (k5_struct_0 A))) ) ) ).
tt(d8_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  ((v2_polynom5 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) 1))  => (v1_polynom5 B A)) ) ) ) ) ) ).
tt(d8_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_polynom7 A B C) = (k15_funct_7 (k15_pre_poly A) (u1_struct_0 B) (k7_polynom1 A B) (k16_pre_poly A) C)) ) ) ) ) ) ).
tt(d8_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( (D = (k7_polynom8 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B)) ) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k3_polynom8 A C (k3_xcmplx_0 (k6_xcmplx_0 E 1) (k6_xcmplx_0 F 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r6_polyred A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (r4_polyred A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k6_poset_1 A B) = (g1_orders_2 (k4_poset_1 A B) (k5_poset_1 A B))) ) ) ) ) ).
tt(d8_pralg_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (k4_partfun1 (k3_finseq_2 (k1_tarski k1_xboole_0)) (k1_tarski k1_xboole_0))) =>  ( (B = (k8_pralg_1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (D = (k1_funct_1 A C))  =>  ((k1_funct_1 B C) = (k7_pralg_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_pre_poly A) <=> (v1_finset_1 (k13_pre_poly A))) ) ) ).
tt(d8_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ((m2_prob_1 C A B) <=>  ( (! [D:$i] :  ((m1_prob_1 D A B) => (r1_xxreal_0 k6_numbers (k1_seq_1 C D))) )  &  ( ((k1_seq_1 C A) = 1)  &  ( (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ((r1_xboole_0 D E) =>  ((k1_seq_1 C (k6_prob_1 A B D E)) = (k7_real_1 (k1_seq_1 C D) (k1_seq_1 C E))) ) ) ) ) )  &  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v2_prob_1 D) =>  ((v2_comseq_2 (k8_prob_1 A B D C)) &  ((k2_seq_2 (k8_prob_1 A B D C)) = (k1_seq_1 C (k3_prob_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A (k4_prob_4 A B C)) =>  ( (D = (k7_prob_4 A B C))  <=>  (! [E:$i] :  ((r2_hidden E B) =>  (! [F:$i] :  ((m2_prob_4 F A B C) =>  ((k1_funct_1 D (k2_xboole_0 E F)) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ( (D = (k1_projpl_1 A B C))  <=> (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(d8_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A))))) )  =>  ( (C = (k13_prvect_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 A)) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k4_finseq_1 A)) =>  ((k8_prvect_1 A (k12_prvect_1 (k4_card_3 A) C D E) F) = (k5_binop_1 (k1_funct_1 A F) (k9_prvect_1 A B F) (k8_prvect_1 A D F) (k8_prvect_1 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_2 B (k4_prvect_2 A) k1_numbers) =>  ( (B = (k9_prvect_2 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 (k4_prvect_2 A)))  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (k4_prvect_2 A))) => (r1_funct_2 (k2_zfmisc_1 k1_numbers (k1_funct_1 (k4_prvect_2 A) C)) (k1_funct_1 (k4_prvect_2 A) C) (k2_zfmisc_1 k1_numbers (u1_struct_0 (k5_prvect_2 A C))) (u1_struct_0 (k5_prvect_2 A C)) (k1_prvect_2 (k4_prvect_2 A) k1_numbers B C) (u1_rlvect_1 (k5_prvect_2 A C)))) ) ) ) ) ) ) ) ).
tt(d8_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_pscomp_1 A) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) A) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A))) ) ) ).
tt(d8_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A))))  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r1_pua2mss1 A B C) <=>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) C) & (r1_tarski (k7_relset_1 (k3_finseq_2 A) A B (k4_card_3 D)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_pythtrip,ax, (! [A:$i] :  ((m1_pythtrip A) =>  ((v3_pythtrip A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r2_hidden B A) &  ((r2_hidden C A) & (r1_int_2 B C)) ) ) ) ) ) ) ) ) ).
tt(d8_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (C = (k7_qc_lang1 A B))  <=>  ((k1_xtuple_0 B) = (k2_nat_1 7 C)) ) ) ) ) ) ) ) ).
tt(d8_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ((k8_qc_lang2 A B C D E) = (k15_qc_lang1 A B (k6_qc_lang2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  ((k5_qmax_1 A) = (k2_zfmisc_1 (k2_qmax_1 A) k12_prob_1)) ) ) ).
tt(d8_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( (B = (k8_quaterni A))  <=>  ((k7_quaterni A B) = k6_numbers) ) ) ) ) ) ).
tt(d8_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (B = (k11_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden C B) <=>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(d8_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k9_radix_1 A B C) = (k3_nat_d (k4_nat_d C (k1_newton (k1_radix_1 B) A)) (k13_newton (k1_radix_1 B) (k7_nat_d A 1)))) ) ) ) ) ) ) ).
tt(d8_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E k5_numbers))  =>  ((k8_radix_2 A B C D E) = (k4_nat_d (k1_newton D (k7_partfun1 k5_numbers E C)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 1)) & (m2_finseq_1 D (k4_radix_3 B)))  =>  ( (D = (k10_radix_3 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k2_xcmplx_0 A 1))) =>  ((k7_radix_3 E B (k2_xcmplx_0 A 1) D) = (k9_radix_3 E B A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ( (D = (k8_radix_5 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E C A D) = (k7_radix_5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ((r2_hidden A (k2_finseq_1 (k2_xcmplx_0 B 2))) =>  ( ( (~ (r1_xxreal_0 B A))  =>  ((k7_radix_6 A B C D) = (k1_funct_1 D A)) )  &  ((r1_xxreal_0 B A) =>  ((k7_radix_6 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k11_ranknull A B C D) = (k1_vectsp_9 A (k1_ranknull A B C D))) ) ) ) ) ) ) ) ) ).
tt(d8_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_ratfunc1 B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  (B = (k4_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(d8_rcomp_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_rcomp_1 A B) = (a_2_3_rcomp_1 A B)) ) ) ) ) ).
tt(d8_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k8_real_3 A))  <=>  ( ((k3_funct_2 k5_numbers k1_numbers B k6_numbers) = (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 1)) = (k7_real_1 (k10_real_1 1 (k1_seq_1 B C)) (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(d8_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k3_relat_1 A B))  <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  (? [F:$i] :  ((r2_hidden (k4_tarski D F) A) & (r2_hidden (k4_tarski F E) B)) ) ) ) ) ) ) ) ) ) ).
tt(d8_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r8_relat_2 A B) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k4_tarski C D) A) & (r2_hidden (k4_tarski D E) A)) ) ) )  => (r2_hidden (k4_tarski C E) A)) ) ) ) ) ) ) ) ).
tt(d8_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r6_rewrite1 A B C) <=>  (? [D:$i] :  ((r1_rewrite1 A D B) & (r1_rewrite1 A D C)) ) ) ) ) ) ) ).
tt(d8_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ((k8_rewrite2 A B C) = (a_3_0_rewrite2 A B C)) ) ) ) ) ) ).
tt(d8_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  (! [E:$i] :  ((k3_rewrite3 A B C D E) = (a_5_0_rewrite3 A B C D E)) ) ) ) ) ) ) ) ) ).
tt(d8_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k17_rfunct_3 A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_seq_1 D E) = (k1_funct_1 (k1_funct_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r8_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) => (r7_rfunct_4 (k2_partfun1 k1_numbers k1_numbers A B) C)) ) ) ) ) ) ) ) ).
tt(d8_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k5_rinfsup2 A) = (k2_rinfsup2 (k4_rinfsup2 A))) ) ) ).
tt(d8_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((r1_ringcat1 A B) =>  (! [C:$i] :  ( ((v2_ringcat1 C) &  ((v3_ringcat1 C) & (l1_ringcat1 C)) )  =>  ((m1_ringcat1 C A B) <=>  ( ((k1_ringcat1 C) = A)  &  ((k2_ringcat1 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(d8_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A))))) )  =>  ( (B = (k6_rlsub_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_rlsub_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_rlsub_2 A)) =>  (! [E:$i] :  ((m1_rlsub_1 E A) =>  (! [F:$i] :  ((m1_rlsub_1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k3_rlsub_2 A) B C D) = (k2_rlsub_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  ((v6_rltopsp1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden (k1_algstr_0 A B C) D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ((v3_pre_topc F A) &  ((r2_hidden B E) &  ((r2_hidden C F) & (r1_tarski (k6_rusub_4 A E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v8_rlvect_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_rlvect_1 A B 1) = B) ) ) ) ) ) ).
tt(d8_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k6_rlvect_2 A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  ((v2_funct_1 D) &  ( ((k2_relset_1 (u1_struct_0 A) D) = (k3_rlvect_2 A B))  &  (C = (k4_rlvect_1 A (k5_rlvect_2 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((r1_rmod_4 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) &  ((v7_robbins1 A) & (l2_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k6_lattices A))  <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k5_robbins1 A C (k3_robbins1 A C))) ) ) ) ) ) ) ) ).
tt(d8_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k7_rsspace4 A B C) = (a_3_0_rsspace4 A B C)) ) ) ) ) ) ) ).
tt(d8_rsspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  ((v1_xboole_0 B) |  ((k8_rsspace A B) = (k1_realset1 (u1_algstr_0 A) B)) ) ) ) ) ) ) ).
tt(d8_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A))))) )  =>  ( (B = (k6_rusub_2 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k3_rusub_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_rusub_2 A)) =>  (! [E:$i] :  ((m1_rusub_1 E A) =>  (! [F:$i] :  ((m1_rusub_1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k5_binop_1 (k3_rusub_2 A) B C D) = (k2_rusub_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_rusub_4 A B C) = (a_3_0_rusub_4 A B C)) ) ) ) ) ) ) ).
tt(d8_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k12_rvsum_1 A) = (k3_relat_1 A k2_rvsum_1)) ) ) ).
tt(d8_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( (A = (k4_tarski k6_numbers k6_numbers))  =>  ((k10_scm_comp A B C) = (k2_xcmplx_0 B C)) )  &  ( ( (A = (k4_tarski k6_numbers 1))  =>  ((k10_scm_comp A B C) = (k6_xcmplx_0 B C)) )  &  ( ( (A = (k4_tarski k6_numbers 2))  =>  ((k10_scm_comp A B C) = (k3_xcmplx_0 B C)) )  &  ( ( (A = (k4_tarski k6_numbers 3))  =>  ((k10_scm_comp A B C) = (k5_int_1 B C)) )  &  ( (A = (k4_tarski k6_numbers 4))  =>  ((k10_scm_comp A B C) = (k6_int_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k3_scmfsa_1) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ((k8_scmfsa_1 A B C) = (k1_funct_4 A (k16_funcop_1 B C))) ) ) ) ) ) ) ).
tt(d8_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k6_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  (? [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  &  ( (A = D)  &  ( (B = E)  &  (C = (k2_ami_3 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k3_scmfsa9a A B) = (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k8_scmfsa_2 B B) (k6_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m A B)) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 (k9_scmfsa_m 2 (k5_scmfsa_m A B)) A)) (k2_scmfsa_9 (k9_scmfsa_m 2 (k5_scmfsa_m A B)) (k3_scmfsa6a (k5_scmfsa6a (k1_scmfsa_7 (k9_scmfsa_m 3 (k5_scmfsa_m A B)) 2) (k10_scmfsa_2 (k9_scmfsa_m 2 (k5_scmfsa_m A B)) (k9_scmfsa_m 3 (k5_scmfsa_m A B)))) (k1_scmfsa8b (k9_scmfsa_m 3 (k5_scmfsa_m A B)) (k11_compos_1 k1_scmfsa_2 (k7_scmfsa_2 (k9_scmfsa_m 1 (k5_scmfsa_m A B)) B)) (k11_compos_1 k1_scmfsa_2 (k7_scmfsa_2 B (k9_scmfsa_m 1 (k5_scmfsa_m A B))))))))) ) ) ) ) ).
tt(d8_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) &  (? [D:$i] :  ((m2_subset_1 D k4_ordinal1 (k7_card_1 13)) &  (A = (k3_xtuple_0 D k1_xboole_0 (k10_finseq_1 B C))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_scmfsa_i) =>  ( (B = (k8_scmfsa_i A))  <=>  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) &  ( ((k10_finseq_1 C D) = (k2_xtuple_0 A))  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k7_scmpds_2 A B C) = (k3_xtuple_0 4 k1_xboole_0 (k11_finseq_1 A B C))) ) ) ) ) ) ) ).
tt(d8_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_scmpds_4 A B) <=>  ( (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14)  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (A = (k3_scmpds_2 C))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 B C))) ) ) ) ) )  &  ( (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 4)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (A = (k7_scmpds_2 C D E))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 B E))) ) ) ) ) ) ) ) ) )  &  ( (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 5)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (A = (k8_scmpds_2 C D E))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 B E))) ) ) ) ) ) ) ) ) )  &  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 6)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (A = (k9_scmpds_2 C D E))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k6_scmpds_6 A B C) = (k1_scmpds_4 (k4_scmpds_4 (k7_scmpds_2 A B 2) (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 1))) C)) ) ) ) ) ) ) ).
tt(d8_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 E k1_xboole_0 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k9_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 3)) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k8_scmring2 A B) = (k3_xtuple_0 6 (k12_finseq_1 k5_numbers B) k1_xboole_0)) ) ) ) ) ).
tt(d8_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_subset_1 E k4_ordinal1 (k7_card_1 8)) &  (B = (k3_xtuple_0 E k1_xboole_0 (k7_scmringi A C D))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k9_scmringi A B))  <=>  (? [D:$i] :  ((m2_finseq_1 D (k2_xboole_0 k2_scm_inst (u1_struct_0 A))) &  ( (D = (k2_xtuple_0 B))  &  (C = (k7_partfun1 (k2_xboole_0 k2_scm_inst (u1_struct_0 A)) D 2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_tarski A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_tarski A))) =>  ( (C = (k4_scmyciel A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k3_tarski A)) =>  ((r2_hidden D C) <=> (r2_hidden (k2_tarski B D) (k1_scmyciel A))) ) ) ) ) ) ) ) ) ) ).
tt(d8_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r4_semi_af1 A B C D E F) <=>  ( (~ (r1_semi_af1 A F B D))  &  ((r1_semi_af1 A F B C) &  ((r1_semi_af1 A F D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_seq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_comseq_2 A) <=>  ((v1_seq_2 A) & (v2_seq_2 A)) ) ) ) ).
tt(d8_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k11_seq_4 A) = (k4_finseqop k2_numbers k2_numbers A k25_binop_2)) ) ) ).
tt(d8_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((k9_seqfunc A B C) = (k8_seqfunc A C (k3_seqfunc A B))) ) ) ) ) ) ) ).
tt(d8_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ).
tt(d8_setfam_1,ax, (! [A:$i] :  ((v1_setfam_1 A) <=>  (~ (r2_hidden k1_xboole_0 A)) ) ) ).
tt(d8_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k8_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k7_subset_1 A (k8_nat_1 (k9_setfam_1 A) B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ( (B = (k6_sf_mastr A))  <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k3_scmfsa_2)))  &  ( (C = (k4_sf_mastr A))  &  (B = (k3_scmfsa_m C)) ) ) ) ) ) ) ) ) ).
tt(d8_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (D = (k4_sgraph1 A B C))  <=>  (? [E:$i] :  ((v1_finset_1 E) &  ( (! [F:$i] :  ((r2_hidden F E) <=>  ((r2_hidden F (u1_sgraph1 B)) & (r2_hidden C F)) ) )  &  (D = (k5_card_1 E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v4_sheffer1 A) &  ((v11_lattices A) &  ((v1_sheffer1 A) & (v6_lattices A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = (k3_sheffer1 A B))  <=> (r1_sheffer1 A C B)) ) ) ) ) ) ) ) ).
tt(d8_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  ((v2_simplex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C B) & (v3_pre_topc D B))  =>  ((k9_subset_1 (u1_struct_0 A) (k3_convex1 A (k1_simplex1 A B C)) (k3_convex1 A (k1_simplex1 A B D))) = (k3_convex1 A (k1_simplex1 A B (k9_subset_1 (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k8_sincos10 A) = (k1_seq_1 k4_sincos10 A)) ) ) ).
tt(d8_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k8_sin_cos7 A) = (k6_power k8_power (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k9_binop_2 1 (k3_square_1 A)))) A))) )  &  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k8_sin_cos7 A) = (k6_power k8_power (k12_binop_2 (k10_binop_2 1 (k7_square_1 (k9_binop_2 1 (k3_square_1 A)))) A))) ) ) ) ) ).
tt(d8_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (B = (k7_sin_cos A))  <=>  ( ((k8_nat_1 k2_numbers B k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers B (k2_nat_1 C 1)) = (k8_nat_1 k2_numbers A C)) ) ) ) ) ) ) ) ) ).
tt(d8_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  ((v2_stacks_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u4_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u4_struct_0 A))))) )  =>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) &  ( ((k8_nat_1 (u4_struct_0 A) B C) = D)  &  (~  ( (~ (r1_stacks_1 A D))  &  ((k8_nat_1 (u4_struct_0 A) B (k1_nat_1 C 1)) = (k5_stacks_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_struct_0,ax, (! [A:$i] :  ((l4_struct_0 A) =>  ((v6_struct_0 A) <=>  ((k4_struct_0 A) = (k5_struct_0 A)) ) ) ) ).
tt(d8_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A B C)) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) E (k2_valuat_1 A E)) =>  ((k13_sublemma A B C D E F) = (k4_relset_1 (k3_qc_lang1 A) (k3_qc_lang1 A) (k3_qc_lang1 A) E (k2_substut1 A (k7_substut1 A C (k11_cqc_lang A C (k2_sublemma A B)) D)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( (C = (k9_substut1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)))))) )  &  ( (C = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D B))  &  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( ( (E = (k5_cqc_lang A))  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k1_subset_1 (k3_qc_lang1 A))) )  &  ( ((v2_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k8_substut1 A (k17_qc_lang1 A E))) )  &  ( ( ((v3_qc_lang1 E A) &  (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k18_qc_lang1 A E))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = F) )  &  ( ( ((v4_qc_lang1 E A) &  ( (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k19_qc_lang1 A E)))  &  (G = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k20_qc_lang1 A E))) ) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k4_subset_1 (k3_qc_lang1 A) F G)) )  &  ( ((v5_qc_lang1 E A) &  (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k22_qc_lang1 A E))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k4_subset_1 (k3_qc_lang1 A) F (k6_domain_1 (k3_qc_lang1 A) (k21_qc_lang1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v4_card_3 B) <=>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (~  (B = (k2_relset_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 (u1_struct_0 A)))) =>  ( (B = (k4_taxonom1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ( (~ (v3_xxreal_0 D))  & (v1_xreal_0 D))  &  (? [E:$i] :  ( ((v1_partfun1 E (u1_struct_0 A)) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) E (k13_lang1 (u1_struct_0 A) (k3_taxonom1 A D))) &  ((k8_eqrel_1 (u1_struct_0 A) E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v7_taxonom2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r1_tarski C D) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r1_tarski D E) & (r2_hidden E B))  =>  (E = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tbsp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( (~  (B = k1_xboole_0) )  =>  ( (C = (k3_tbsp_1 A B))  <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E B))  => (r1_xxreal_0 (k2_metric_1 A D E) C)) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k2_metric_1 A E F) D)) ) ) ) )  => (r1_xxreal_0 C D)) ) ) ) ) )  &  ( (B = k1_xboole_0)  =>  ( (C = (k3_tbsp_1 A B))  <=>  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k8_tdlat_1 A) = (g3_lattices (k5_tdlat_1 A) (k6_tdlat_1 A) (k7_tdlat_1 A))) ) ) ).
tt(d8_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k5_termord A B C D) = (k1_polynom7 A C (k4_termord A B C D) (k3_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(d8_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_tex_4 A B) = (k5_setfam_1 (u1_struct_0 A) (k1_tex_4 A B))) ) ) ) ) ).
tt(d8_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_tmap_1 A B) = (g1_pre_topc (u1_struct_0 A) (k5_tmap_1 A B))) ) ) ) ) ).
tt(d8_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (k7_topgen_3 A B))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k1_tops_1 C D) = (k15_funcop_1 (k1_zfmisc_1 (u1_struct_0 C)) D A D (k8_subset_1 (u1_struct_0 C) D B))) ) ) ) ) ) ) ) ) ).
tt(d8_topgen_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v7_topgen_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v4_pre_topc (k2_topgen_1 A B) A)) ) ) ) ) ).
tt(d8_topgrp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_topgrp_1 A))  =>  ((v4_topgrp_1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) (u1_struct_0 A))))) )  =>  ( (B = (u2_algstr_0 A))  => (v5_pre_topc B (k2_borsuk_1 A A) A)) ) ) ) ) ) ).
tt(d8_topmetr,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v3_topmetr A) <=> (v3_membered (u1_struct_0 A))) ) ) ).
tt(d8_topreal1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) <=>  ((v2_funct_1 A) &  ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (v1_topreal1 A)) ) ) ) ) ) ) ).
tt(d8_toprealb,ax, (k9_toprealb = (k19_euclid 1 k6_numbers)) ).
tt(d8_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k12_euclid (k5_algstr_0 (k15_euclid A) (k8_nat_1 (u1_struct_0 (k15_euclid A)) B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) <=>  (B = (k1_tops_1 A (k2_pre_topc A B))) ) ) ) ) ) ).
tt(d8_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) <=> (r1_transgeo (u1_struct_0 A) B (k1_diraf (u1_struct_0 A) (u1_analoaf A)))) ) ) ) ) ).
tt(d8_trees_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_trees_2 A) <=>  ( (~ (v1_xboole_0 (k9_xtuple_0 A)))  & (v1_trees_1 (k9_xtuple_0 A))) ) ) ) ).
tt(d8_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_trees_3 B A) =>  ( (B = (k5_trees_3 A))  <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((v1_finset_1 (k9_xtuple_0 C)) <=> (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d8_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k6_trees_9 A) = (a_1_1_trees_9 A)) ) ) ).
tt(d8_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ((r2_hidden C E) &  (~ (r2_hidden D E)) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ( (~ (r2_hidden C E))  & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ((v2_turing_1 B A) <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) C)) = (u5_turing_1 A)) ) ) ) ) ) ) ) ).
tt(d8_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k9_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k1_binarith (k9_margrel1 B) C)) ) ) ) ) ) ) ) ).
tt(d8_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_unialg_2 B A) =>  ((k4_unialg_2 A B) = (g1_unialg_1 B (k3_unialg_2 A B))) ) ) ) ) ) ).
tt(d8_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (D = (k7_uproots A B C))  <=>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  &  ( (E = (a_3_0_uproots A B C))  &  (D = (k1_xxreal_2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v10_pre_topc A) &  ((v3_pre_topc B A) &  ((v3_pre_topc C A) & (r1_tarski (k2_pre_topc A B) C)) ) )  =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_urysohn1 D A B C) <=>  ( (~  (D = k1_xboole_0) )  &  ((v3_pre_topc D A) &  ((r1_tarski (k2_pre_topc A B) D) & (r1_tarski (k2_pre_topc A D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_valuat_1 A B C D) <=>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) => (r1_valuat_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_valued_0 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_xxreal_0 (k1_funct_1 A B))) ) ) ) ) ).
tt(d8_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k39_valued_1 A) = (k18_valued_1 A A)) ) ) ).
tt(d8_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k2_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ) ) ) ).
tt(d8_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v4_vectmetr B) &  ((v5_vectmetr B) &  ((v6_vectmetr B) & (l1_vectmetr B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = (k4_vectmetr A))  <=>  ( ((u1_struct_0 B) = (k1_euclid A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) k1_numbers (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers (u1_metric_1 B) (k13_euclid A)) &  ( ((k4_struct_0 B) = (k5_euclid A))  &  ( (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k1_binop_1 (u1_algstr_0 B) C D) = (k7_euclid A C D)) ) ) ) )  &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_binop_1 (u1_rlvect_1 B) D C) = (k9_euclid A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_5 D A B (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) =>  ( (~  (C = (k4_struct_0 B)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ( (~ (v3_funct_1 E))  &  ( (~ (v1_zfmisc_1 E))  &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 E B A) &  ((v1_hahnban1 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) )  =>  ( (E = (k7_vectsp10 A B C D))  <=>  ( ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) = (k1_group_1 A))  &  ((k5_relset_1 (u1_struct_0 B) (u1_struct_0 A) E (u1_struct_0 D)) = (k7_hahnban1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v6_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k5_struct_0 A) B) = B) ) ) ) ) ) ).
tt(d8_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((k6_vectsp_2 A B) = (g2_vectsp_2 A B 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1) (k9_funct_3 1 (u1_struct_0 B)))) ) ) ) ) ).
tt(d8_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B))))) )  =>  ( (C = (k6_vectsp_5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (k3_vectsp_5 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_vectsp_5 A B)) =>  (! [F:$i] :  ((m1_vectsp_4 F A B) =>  (! [G:$i] :  ((m1_vectsp_4 G A B) =>  ( ( (D = F)  &  (E = G) )  =>  ((k5_binop_1 (k3_vectsp_5 A B) C D E) = (k2_vectsp_5 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((k5_vectsp_6 A B C D) = (k1_vfunct_1 (u1_struct_0 B) A C D)) ) ) ) ) ) ) ) ) ).
tt(d8_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m3_vectsp_8 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_lattices A D E)) = (k4_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k2_waybel_0 A B C) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_waybel_0 A B) C)) ) ) ) ) ) ) ).
tt(d8_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ( (B = (k2_waybel11 A))  <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v6_waybel_0 C A) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) ) )  =>  ((r2_hidden C (k6_yellow_6 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski C D) B) <=> (r1_waybel11 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_waybel18,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((r1_waybel18 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  &  ((v5_pre_topc C B B) &  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) C C) C) & (r1_t_0topsp (k7_waybel18 B B C) A)) ) ) ) ) ) ) ) ) ).
tt(d8_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r5_waybel_1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v23_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(d8_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_waybel23 B A) <=> (r2_hidden (k3_yellow_0 A) B)) ) ) ) ) ).
tt(d8_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_waybel34 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_waybel_3 A D E) => (r1_waybel_3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_waybel35,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((k3_waybel35 A B C) = (k3_xboole_0 (k8_relat_1 A (k1_tarski C)) B)) ) ) ) ) ).
tt(d8_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( (B = (k3_waybel_4 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v5_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(d8_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_waybel_6 B A) <=> (v5_waybel_6 (k8_lattice3 A B) (k7_lattice3 A))) ) ) ) ) ).
tt(d8_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((l1_waybel_0 D A) =>  (! [E:$i] :  ( ((v6_waybel_0 E B) & (l1_waybel_0 E B))  =>  ( (E = (k6_waybel_9 A B C D))  <=>  ( ((g1_orders_2 (u1_struct_0 E) (u1_orders_2 E)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  &  ((u1_waybel_0 B E) = (k1_partfun1 (u1_struct_0 D) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_waybel_0 A D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((k8_weierstr A B C) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) C))) ) ) ) ) ) ) ).
tt(d8_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r4_wellord1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  & (r3_wellord1 A B C)) ) ) ) ) ) ) ).
tt(d8_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ((r2_xboole_0 A B) <=>  ((r1_tarski A B) &  (~  (A = B) ) ) ) ) ) ).
tt(d8_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k7_xboolean A B) = (k4_xboolean (k6_xboolean A B) (k6_xboolean B A))) ) ) ) ) ).
tt(d8_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 A B) = (k2_xcmplx_0 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(d8_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k6_xtuple_0 A B C D) = (k4_tarski (k3_xtuple_0 A B C) D)) ) ) ) ) ).
tt(d8_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) & (v2_xxreal_2 A))  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (B = (k1_xxreal_2 A))  <=>  ((r2_hidden B A) &  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ).
tt(d8_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((r2_yellow_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice3 A B C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) => (r1_orders_2 A D C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_lattice3 A B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_lattice3 A B E) => (r1_orders_2 A E D)) ) ) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  ((v4_yellow21 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow21 A B)) (u1_struct_0 (k3_yellow21 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow21 A B)) (u1_struct_0 (k3_yellow21 A C)))))) )  =>  ((v23_waybel_0 D (k3_yellow21 A B) (k3_yellow21 A C)) => (r2_hidden D (k1_altcat_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(d8_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((v1_yellow_6 B A) =>  ((v2_struct_0 B) |  ((k4_yellow_6 A B) = (k3_funct_1 (u1_waybel_0 A B))) ) ) ) ) ) ) ).
tt(d8_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v3_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C B) => (r2_hidden (k3_classes2 A C) B)) ) ) ) ) ) ) ) ).
tt(d8_zf_lang,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (A = k9_zf_lang)  <=>  ( (! [B:$i] :  ((r2_hidden B A) => (m2_finseq_1 B k5_numbers)) )  &  ( (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((r2_hidden (k4_zf_lang B C) A) & (r2_hidden (k5_zf_lang B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k6_zf_lang B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k7_zf_lang B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) => (r2_hidden (k8_zf_lang B C) A)) ) ) ) )  &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (! [C:$i] :  ((r2_hidden C B) => (m2_finseq_1 C k5_numbers)) )  &  ( (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((r2_hidden (k4_zf_lang C D) B) & (r2_hidden (k5_zf_lang C D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k6_zf_lang C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k7_zf_lang C D) B)) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((r2_hidden D B) => (r2_hidden (k8_zf_lang C D) B)) ) ) ) ) ) ) ) )  => (r1_tarski A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r4_zfmisc_1 A B C D E F) <=>  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (A = E) )  &  ( (~  (A = F) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  (~  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d8_zf_model,ax, (k8_zf_model = (k8_zf_lang (k2_zf_lang k6_numbers) (k13_zf_lang (k2_zf_lang 1) (k8_zf_lang (k2_zf_lang 2) (k12_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang 1)) (k13_zf_lang (k2_zf_lang 3) (k7_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang 3)) (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang k6_numbers))))))))) ).
tt(d8_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_zmodul01 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k3_rlvect_1 A C D) B)) ) ) ) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_zmodul01 A D C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  ((v8_abcmiz_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (~  ((r2_hidden C (k2_abcmiz_0 A B)) & (r2_hidden (k1_abcmiz_0 A C) (k2_abcmiz_0 A B))) ) ) ) ) ) ) ) ) ).
tt(d9_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  ((v1_abcmiz_1 A) <=>  ( ((u1_struct_0 A) = (k1_enumset1 k6_abcmiz_1 k7_abcmiz_1 k8_abcmiz_1))  &  ((r1_tarski (k2_tarski k9_abcmiz_1 k10_abcmiz_1) (u4_struct_0 A)) &  ( ((k1_funct_1 (u1_msualg_1 A) k9_abcmiz_1) = (k10_finseq_1 k7_abcmiz_1 k6_abcmiz_1))  &  ( ((k1_funct_1 (u1_msualg_1 A) k10_abcmiz_1) = (k9_finseq_1 k7_abcmiz_1))  &  ( ((k1_funct_1 (u2_msualg_1 A) k9_abcmiz_1) = k6_abcmiz_1)  &  ( ((k1_funct_1 (u2_msualg_1 A) k10_abcmiz_1) = k7_abcmiz_1)  &  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (~  ( (~  (B = k9_abcmiz_1) )  &  ( (~  (B = k10_abcmiz_1) )  &  (~ (r2_hidden (k1_funct_1 (u1_msualg_1 A) B) (k3_finseq_2 (k1_tarski k8_abcmiz_1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ((v5_abcmiz_1 B A (k28_abcmiz_1 A)) =>  ((k10_abcmiz_a A B) = (k1_xtuple_0 (k1_funct_1 B k1_xboole_0))) )  &  ( (~ (v5_abcmiz_1 B A (k28_abcmiz_1 A)))  =>  ((k10_abcmiz_a A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d9_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v9_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((r2_hidden C B) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r1_aff_1 A C D G) &  ((r1_aff_1 A C E H) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A D F G I) & (r2_aff_1 A D E B)) ) ) ) ) ) ) )  =>  ((r2_hidden D B) |  ( (C = F)  |  ( (D = E)  | (r2_analoaf A D E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( (C = (k10_afinsq_1 A B))  <=>  ( ((k3_finseq_1 C) = (k1_afinsq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k1_afinsq_1 B)))  =>  ((k1_funct_1 B (k7_nat_d D 1)) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((k7_afinsq_2 A) = (k6_afinsq_2 k2_numbers A k27_binop_2)) ) ) ).
tt(d9_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((k9_afproj A) = (k2_xboole_0 (u1_struct_0 A) (k7_afproj A))) ) ) ).
tt(d9_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_afvect0 A B C) <=>  ((v2_funct_1 C) &  ( ((k10_xtuple_0 C) = (u1_struct_0 B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_algstr_0 A D E)) = (k1_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_algstr_0 A D)) = (k4_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k4_partfun1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))) =>  ( (C = (k3_alg_1 A B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 (u1_unialg_1 A)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  (! [E:$i] :  ((m5_margrel1 E (u1_struct_0 A) (k1_unialg_2 A)) =>  ( ((k1_funct_1 (u1_unialg_1 A) D) = E)  =>  ((k1_funct_1 C D) = (k2_alg_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_algstr_0,ax, (k3_algstr_0 = (g2_algstr_0 1 k9_funct_5 k5_funct_5)) ).
tt(d9_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v6_algstr_1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((l3_algstr_0 B) =>  ((m1_algstr_4 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d9_altcat_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v7_altcat_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( (B = (k4_tarski D C))  &  ((k1_funct_1 A B) = (k3_relat_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_altcat_3,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_altcat_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((r2_hidden D (k1_altcat_1 A B C)) & (v1_zfmisc_1 (k1_altcat_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(d9_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k8_ami_3 A B) = (k3_xtuple_0 7 (k9_finseq_1 A) (k9_finseq_1 B))) ) ) ) ) ).
tt(d9_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((v5_amistd_1 C A B) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r1_tarski (k1_amistd_1 A B D (k7_partfun1 (u1_compos_1 B) C D)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ).
tt(d9_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  ((v4_ami_wstd C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( ((k5_memstr_0 A B D) = (k1_ami_wstd A B k6_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B C D E)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ((v3_analmetr A) <=>  ( ( (~ (v7_struct_0 (g1_analoaf (u1_struct_0 A) (u1_analoaf A))))  &  ((v1_diraf (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) &  ((v2_diraf (g1_analoaf (u1_struct_0 A) (u1_analoaf A))) & (l1_analoaf (g1_analoaf (u1_struct_0 A) (u1_analoaf A)))) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B C) =>  (B = C) )  &  ((r4_analmetr A B C D D) &  ( ((r4_analmetr A B C D E) =>  ((r4_analmetr A B C E D) & (r4_analmetr A D E B C)) )  &  ( (~  ((r4_analmetr A B C F G) &  ((r2_analoaf A B C H I) &  ( (~ (r4_analmetr A F G H I))  &  (~  (B = C) ) ) ) ) )  &  (~  ((r4_analmetr A B C F G) &  ((r4_analmetr A B C H I) &  ( (~ (r2_analoaf A F G H I))  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r4_analmetr A B C D E) &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ((v2_anproj_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_collsp A B C E) &  ((r1_collsp A C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_collsp A B D G) & (r1_collsp A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k10_aofa_000 A) = (k6_subset_1 (u1_struct_0 A) (k3_tarski (a_1_0_aofa_000 A)))) ) ) ).
tt(d9_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k4_armstrng A)) =>  (! [C:$i] :  ((m1_subset_1 C (k4_armstrng A)) =>  ((r3_armstrng A B C) <=>  ((r1_tarski (k1_xtuple_0 B) (k1_xtuple_0 C)) & (r1_tarski (k2_xtuple_0 C) (k2_xtuple_0 B))) ) ) ) ) ) ) ).
tt(d9_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((k8_arytm_2 A B) = (k4_arytm_2 (k6_arytm_2 (k3_arytm_2 A) (k3_arytm_2 B)))) ) ) ) ) ).
tt(d9_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  ( ((r2_hidden A k4_ordinal1) =>  ( (B = (k7_arytm_3 A))  <=>  (B = 1) ) )  &  ( (~ (r2_hidden A k4_ordinal1))  =>  ( (B = (k7_arytm_3 A))  <=>  (? [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  &  (A = (k4_tarski C B)) ) ) ) ) ) ) ) ) ) ).
tt(d9_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k6_asympt_0 A) = (a_1_0_asympt_0 A)) ) ) ).
tt(d9_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k7_bagorder A) = (k5_bagorder A (k4_bagorder A))) ) ) ).
tt(d9_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((m1_bcialg_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k4_tarski C D) B) & (r2_hidden (k4_tarski E F) B))  => (r2_hidden (k4_tarski (k1_bcialg_1 A C E) (k1_bcialg_1 A D F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v3_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(d9_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  ((r1_bcialg_6 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(d9_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m2_bhsp_5 B A) <=>  ((m1_bhsp_5 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k2_bhsp_1 A C C) = 1) ) ) ) ) ) ) ) ) ) ).
tt(d9_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k8_bilinear A B C D E) = (k10_funct_5 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 A)) (k12_funct_5 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r4_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A B D (k3_binop_1 A C E F)) = (k3_binop_1 A C (k3_binop_1 A B D E) (k3_binop_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_binop_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  ( (A = k33_binop_2)  <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_binop_1 A B C) = (k9_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(d9_bor_cant,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (C = (k9_bor_cant A B))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C D) = (k3_prob_1 A (k1_valued_0 (k9_setfam_1 A) B D))) ) ) ) ) ) ) ) ) ).
tt(d9_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  ((k13_borsuk_1 A B C) = (k2_xboole_0 C (a_2_2_borsuk_1 A B))) ) ) ) ) ) ) ).
tt(d9_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  ( (A = k7_borsuk_6)  <=>  (! [B:$i] :  ((r2_hidden B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) &  ( (B = (k4_borsuk_1 k5_topmetr k5_topmetr C D))  &  ((r1_xxreal_0 (k9_real_1 1 (k8_real_1 2 C)) D) & (r1_xxreal_0 (k9_real_1 (k8_real_1 2 C) 1) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  =>  ((k15_borsuk_7 A B) = (k10_toprealc A B (k12_euclid B))) ) ) ) ) ) ).
tt(d9_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_bspace A))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 k2_bspace)) =>  ( (D = (k11_bspace A B C))  <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 D E) = (k3_bspace (k1_funct_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( (D = (k10_bvfunc_1 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k6_margrel1 D E) = (k3_xboolean (k10_xboolean (k3_funct_2 A k6_margrel1 B E) (k3_funct_2 A k6_margrel1 C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((k6_bvfunc_2 A B C D) = (k16_bvfunc_1 A B (k5_bvfunc_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(d9_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) & (l1_funcsdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((m2_c0sp1 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((u1_rlvect_1 B) = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers (u1_struct_0 B))))  &  ( ((k5_struct_0 B) = (k5_struct_0 A))  &  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k9_c0sp2 A) = (g1_normsp_1 (k6_c0sp2 A) (k10_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)) (k8_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)) (k9_rsspace (k10_funcsdom (u1_struct_0 A)) (k6_c0sp2 A)) (k8_c0sp2 A))) ) ) ).
tt(d9_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((r4_calcul_1 A B) <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) &  ((v1_calcul_1 C A) &  (B = (k1_xtuple_0 (k1_funct_1 C (k3_finseq_1 C)))) ) ) ) ) ) ) ) ) ).
tt(d9_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (B = (k8_card_3 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( (C = D)  &  ((r1_tarski (k9_xtuple_0 D) (k9_xtuple_0 A)) &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 D)) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_card_fil A) = (a_1_0_card_fil A)) ) ) ).
tt(d9_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_card_lar A B) = (a_2_0_card_lar A B)) ) ) ) ) ).
tt(d9_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v5_cat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k2_cat_1 A B B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(d9_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k13_cat_2 A B C D E) = (k1_funct_1 (k3_funct_5 D) (k4_cat_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v2_cat_3 D A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_cat_5 A B) = (k8_relset_1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(d9_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ((k6_catalg_1 A B) = (k4_tarski k6_numbers (k10_finseq_1 A B))) ) ) ).
tt(d9_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_cc0sp1 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_cc0sp1 A) k1_numbers)))) )  =>  ( (B = (k6_cc0sp1 A))  <=>  (! [C:$i] :  ((r2_hidden C (k2_cc0sp1 A)) =>  ((k1_seq_1 B C) = (k4_seq_4 (k5_cc0sp1 A (k4_cc0sp1 A C)))) ) ) ) ) ) ) ) ).
tt(d9_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k8_cc0sp2 A) = (k2_partfun1 (k2_cc0sp1 (u1_struct_0 A)) k1_numbers (k6_cc0sp1 (u1_struct_0 A)) (k6_cc0sp2 A))) ) ) ).
tt(d9_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((r2_cfdiff_1 A B) <=>  ((r1_tarski B (k1_relset_1 k2_numbers A)) & (v4_cfdiff_1 (k5_relset_1 k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(d9_cfuncdom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_cfuncdom A))  =>  ((v2_cfuncdom A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((k1_clvect_1 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A (k1_clvect_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (B = (k9_cgames_1 A))  <=>  ((r2_hidden A (k2_cgames_1 B)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C B) & (r2_hidden A (k2_cgames_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(d9_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  ((k6_chain_1 A B) = (k4_chain_1 A B A)) ) ) ) ) ).
tt(d9_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m2_chord D A B C) =>  ((v4_chord D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 D)) =>  (~  ( (~  (E = D) )  & (m2_chord E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v5_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((m1_circcmb3 B A) <=>  (? [C:$i] :  ( ((v4_msafree2 C B) & (l3_msualg_1 C B))  &  ((v3_funct_1 (u3_msualg_1 B C)) &  ( ((k3_funct_1 (u3_msualg_1 B C)) = A)  & (v4_circcomb C B)) ) ) ) ) ) ) ) ) ).
tt(d9_circcomb,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v3_circcomb A) <=>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (C = (k1_funct_1 (u1_msualg_1 A) B))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 (k3_finseq_1 C) k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k3_finseq_1 C) k6_margrel1) k6_margrel1)))) )  =>  (~  (B = (k4_tarski (k1_xtuple_0 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_circtrm1 A B C D) <=>  ((v2_funct_1 C) &  ((v2_funct_1 D) &  ((r3_pua2mss1 A B C D) & (r3_pua2mss1 B A (k2_funct_1 C) (k2_funct_1 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (u3_msualg_1 A B)))))) )  =>  ( (E = (k9_circuit2 A B C D))  <=>  ((r8_pboole (u1_struct_0 A) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) E k6_numbers) (k8_circuit2 A B C D)) &  (! [F:$i] :  ((v7_ordinal1 F) => (r8_pboole (u1_struct_0 A) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) E (k1_nat_1 F 1)) (k7_circuit2 A B (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) E F) (k2_circuit1 A B C (k1_nat_1 F 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_classes1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_classes1 A B) <=>  (! [C:$i] :  ((k1_card_1 (k10_relat_1 A C)) = (k1_card_1 (k10_relat_1 B C))) ) ) ) ) ) ) ).
tt(d9_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k8_clopban1 A B)) =>  ((k11_clopban1 A B C) = C) ) ) ) ) ) ) ).
tt(d9_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  =>  ((v2_clopban2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k6_algstr_0 A B C)) (k8_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ) ).
tt(d9_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ((v6_closure2 C A B) <=> (r2_hidden (k1_pboole A) C)) ) ) ) ) ) ).
tt(d9_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_clvect_1 B) & (m1_clvect_1 B A))  =>  ( (B = (k3_clvect_1 A))  <=>  ((u1_struct_0 B) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ).
tt(d9_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_clvect_2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k15_csspace A (k1_normsp_1 A B F) (k1_normsp_1 A C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_clvect_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v3_clvect_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 C E) & (r1_xxreal_0 B (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers A D) (k8_nat_1 k2_numbers A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_cohsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_xtuple_0 A))) =>  ((r2_hidden (k3_tarski B) (k9_xtuple_0 A)) =>  ((k1_funct_1 A (k3_tarski B)) = (k3_tarski (k7_relat_1 A B))) ) ) ) ) ) ) ).
tt(d9_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_coh_sp A)) =>  ((k8_coh_sp A B) = (k4_tarski (k4_tarski B B) (k6_partfun1 (k3_tarski B)))) ) ) ) ).
tt(d9_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_combgras B A A) =>  ((v7_combgras B A) <=>  ((v3_funct_2 (u2_combgras A A B) (u2_incsp_1 A) (u2_incsp_1 A)) &  ((v3_funct_2 (u1_combgras A A B) (u1_incsp_1 A) (u1_incsp_1 A)) & (v6_combgras B A A)) ) ) ) ) ) ) ).
tt(d9_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_pre_topc B) & (l1_pre_topc B))  =>  ( (B = (k1_compact1 A))  <=>  ( ((u1_struct_0 B) = (k1_ordinal1 (k2_struct_0 A)))  &  ((u1_pre_topc B) = (k2_xboole_0 (u1_pre_topc A) (a_1_0_compact1 A))) ) ) ) ) ) ) ).
tt(d9_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k12_complex1 A) = (k2_xcmplx_0 (k10_real_1 (k3_complex1 A) (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) (k3_xcmplx_0 (k10_real_1 (k1_real_1 (k4_complex1 A)) (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) k7_complex1))) ) ) ).
tt(d9_compl_sp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  ((v4_card_3 B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (v1_finset_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) &  ((v2_compos_0 A) & (v3_compos_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (D = (k5_compos_0 A B C))  <=>  ( ((k2_compos_0 A D) = (k2_compos_0 A B))  &  ( ((k2_xtuple_0 D) = (k2_xtuple_0 B))  &  ((k5_xtuple_0 D) = (k7_valued_1 (k5_xtuple_0 B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_comput_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r1_tarski (k1_relset_1 (k3_finseq_2 k5_numbers) A) (k4_finseq_2 E k5_numbers)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ( ((k2_nat_1 (k19_margrel1 B) 1) = E)  &  ( ((k2_nat_1 E 1) = (k19_margrel1 C))  &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  ( ((k3_finseq_1 F) = E)  =>  ( ((r2_hidden (k3_funct_7 k5_numbers F D k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) => (r2_hidden (k2_finseq_3 D F) (k1_relset_1 (k3_finseq_2 k5_numbers) B)))  &  ( ((r2_hidden (k2_finseq_3 D F) (k1_relset_1 (k3_finseq_2 k5_numbers) B)) => (r2_hidden (k3_funct_7 k5_numbers F D k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) A)))  &  ( ((r2_hidden (k3_funct_7 k5_numbers F D k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) =>  ((k1_recdef_1 A (k3_funct_7 k5_numbers F D k6_numbers)) = (k1_recdef_1 B (k2_finseq_3 D F))) )  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r2_hidden (k3_funct_7 k5_numbers F D (k2_nat_1 G 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) =>  ((r2_hidden (k3_funct_7 k5_numbers F D G) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers F D G) (k12_finseq_1 k5_numbers (k1_recdef_1 A (k3_funct_7 k5_numbers F D G)))) (k1_relset_1 (k3_finseq_2 k5_numbers) C))) )  &  ( ( ((r2_hidden (k3_funct_7 k5_numbers F D G) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers F D G) (k12_finseq_1 k5_numbers (k1_recdef_1 A (k3_funct_7 k5_numbers F D G)))) (k1_relset_1 (k3_finseq_2 k5_numbers) C)))  => (r2_hidden (k3_funct_7 k5_numbers F D (k2_nat_1 G 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) A)))  &  ((r2_hidden (k3_funct_7 k5_numbers F D (k2_nat_1 G 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) =>  ((k1_recdef_1 A (k3_funct_7 k5_numbers F D (k2_nat_1 G 1))) = (k1_recdef_1 C (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers F D G) (k12_finseq_1 k5_numbers (k1_recdef_1 A (k3_funct_7 k5_numbers F D G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_3 A) <=> (v1_series_1 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(d9_conlat_1,ax, (! [A:$i] :  ((l5_struct_0 A) =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  ((v6_conlat_1 B A) <=>  ((v1_xboole_0 (u2_conlat_1 A B)) | (v1_xboole_0 (u3_conlat_1 A B))) ) ) ) ) ) ).
tt(d9_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_lattice4 B (k1_lattice2 (k11_conlat_1 A)) (k11_conlat_1 (k7_conlat_2 A))) =>  ( (B = (k9_conlat_2 A))  <=>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  ((k1_funct_1 B C) = (k8_conlat_2 A C)) ) ) ) ) ) ) ) ).
tt(d9_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ( (D = (k7_convex4 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers D E) = (k3_xcmplx_0 B (k3_funct_2 (u1_struct_0 A) k2_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k12_cqc_sim1 A B) = (a_2_0_cqc_sim1 A B)) ) ) ) ) ).
tt(d9_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_cqc_the1 B A) <=> (r3_cqc_the1 A (k1_subset_1 (k3_cqc_lang A)) B)) ) ) ) ) ).
tt(d9_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_csspace4 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_csspace4 A B) k1_numbers)))) )  =>  ( (C = (k8_csspace4 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k4_csspace4 A B)) =>  ((k1_seq_1 C D) = (k4_seq_4 (k7_csspace4 A B (k6_csspace4 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d9_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ((k9_csspace A B) = (k5_relat_1 (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers B))) ) ) ) ) ) ).
tt(d9_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_decomp_1 A B) = (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))))) ) ) ) ) ).
tt(d9_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r1_dickson A B C) <=>  ((r1_tarski C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_diff_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k9_diff_1 A B C) = (k10_real_1 (k9_real_1 (k1_seq_1 A B) (k1_seq_1 A C)) (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(d9_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  =>  ( (B = (k5_dilworth A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (r5_waybel_4 A (k2_struct_0 A) C)) ) ) ) )  &  ((v2_struct_0 A) =>  ( (B = (k5_dilworth A))  <=>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(d9_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( (C = (k9_dist_1 A B))  <=>  ( ((k4_finseq_1 C) = (k2_finseq_1 (k5_card_1 A)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k11_binop_2 (k3_finseq_1 B) (k1_funct_1 (k4_dist_1 A B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_dtconstr,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr)) =>  ((k13_dtconstr A) = (k4_trees_4 1 (k3_pre_poly (k4_dtconstr k5_dtconstr) A))) ) ) ).
tt(d9_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ((k6_ec_pf_1 A B C) = (a_3_0_ec_pf_1 A B C)) ) ) ) ) ) ) ).
tt(d9_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ens_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) A)))) )  =>  ( (B = (k8_ens_1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  ((k3_funct_2 (k2_ens_1 A) A B C) = (k3_ens_1 A C)) ) ) ) ) ) ) ) ).
tt(d9_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k6_entropy1 A) = (k1_real_1 (k18_rvsum_1 (k4_entropy1 A)))) ) ) ).
tt(d9_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (C = (k13_eqrel_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_hidden D (k3_funct_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d9_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k7_e_siec A) = (k10_xtuple_0 (u1_e_siec A))) ) ) ).
tt(d9_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k9_euclid_3 A B C D) = (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k8_euclid_3 A B C D) (k6_euclid_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(d9_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k17_euclid A) = (k1_seq_1 A 1)) ) ) ).
tt(d9_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k4_euclidlp A B C D) = (a_4_1_euclidlp A B C D)) ) ) ) ) ) ) ) ) ).
tt(d9_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_exchsort B)) )  =>  ((m1_exchsort B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_xtuple_0 A) (k9_xtuple_0 A)) &  ((v3_funct_2 C (k9_xtuple_0 A) (k9_xtuple_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 A) (k9_xtuple_0 A))))) ) )  &  (B = (k3_relat_1 C A)) ) ) ) ) ) ) ) ).
tt(d9_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  ( (E = (k6_extpro_1 A B C D))  <=>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (E = (k5_extpro_1 A B C D F))  &  ((k3_extpro_1 A B C E) = (k2_compos_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((r1_facirc_1 A B C D) <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_1 (k5_facirc_1 A B C E) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((k9_ff_siec A) = (k2_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k4_relat_1 (u1_struct_0 A)))) ) ) ).
tt(d9_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) & (l3_lattices C)) )  =>  ( (C = (k6_filter_0 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ( (D = (k1_realset1 (u2_lattices A) B))  &  ( (E = (k1_realset1 (u1_lattices A) B))  &  (C = (g3_lattices B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ((r1_filter_1 A B) <=> (r4_wellord1 (k8_filter_1 A) (k8_filter_1 B))) ) ) ) ) ).
tt(d9_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (C = (k7_filter_2 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v18_lattices D A) &  ((v21_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_finance1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_prob_1 E C) &  ((v4_prob_1 E C) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  =>  (! [F:$i] :  ( (F = (k6_finance1 B C D E))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers F)))) )  =>  ((k9_finance1 A B C D E F G) = (k1_funct_1 G A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((k10_finseq_1 A B) = (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B))) ) ) ).
tt(d9_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r4_finseq_8 A B C) <=> (r1_tarski (k4_finseq_5 A C) (k4_finseq_5 A B))) ) ) ) ) ) ) ).
tt(d9_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (a_2_0_fintopo2 A B)) ) ) ) ) ).
tt(d9_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k9_fintopo3 A B C) = (k1_funct_1 (k8_fintopo3 A B) C)) ) ) ) ) ) ) ).
tt(d9_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v4_fintopo6 B A) <=>  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( (E = (k1_funct_1 B C))  &  ( (~  (C = D) )  &  ((r2_hidden (k1_funct_1 B D) (k1_fin_topo A E)) &  ( (~  (C = (k1_nat_1 D 1)) )  &  (~  (D = (k1_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fin_topo A B) = (a_2_2_fin_topo A B)) ) ) ) ) ).
tt(d9_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v2_fomodel0 C A B) <=>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden D (k3_xboole_0 C A)) &  ((r2_hidden E (k3_xboole_0 C A)) &  ((r2_hidden F A) &  ((r2_hidden G A) &  ((k1_binop_1 B D F) = (k1_binop_1 B E G)) ) ) ) )  =>  ( (D = E)  &  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((k9_fomodel1 A) = (k6_subset_1 (u1_struct_0 A) (k2_tarski (u2_struct_0 A) (u3_struct_0 A)))) ) ) ).
tt(d9_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (E = (k9_fomodel2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden D (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) G)) =>  (E = (k3_funct_2 (k35_fomodel1 A) B (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B F C) (k2_nat_1 G 1)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_fomodel3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_fomodel3 C A B) <=>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) A) => (r2_hidden (k4_tarski (k1_funct_1 C D) (k1_funct_1 C E)) B)) ) ) ) ) ) ) ) ) ) ).
tt(d9_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_funct_2 B (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ((v5_fomodel4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_fomodel4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_fomodel4 A))) =>  ((r1_tarski C D) => (r1_tarski (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) B C) (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) B D))) ) ) ) ) ) ) ) ) ) ).
tt(d9_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k4_freealg A B C) = C) ) ) ) ) ) ) ).
tt(d9_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_fscirc_1 A B C) = (k3_circcomb (k8_facirc_1 A B C k1_facirc_1) (k4_fscirc_1 A B C) (k2_fscirc_1 A B C) (k7_fscirc_1 A B C))) ) ) ) ).
tt(d9_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  ((r4_fsm_1 A B C D) <=>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ((k4_fsm_1 A B C (u2_fsm_1 A C) E) = (k4_fsm_1 A B D (u2_fsm_1 A D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_fsm_2 C A) &  ((v5_fsm_2 C A) & (l2_fsm_2 C A B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (E = (k2_fsm_2 A B C D))  <=> (r3_fsm_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( ( (? [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) &  ((k1_flang_1 A E C) = B) ) )  =>  ( (D = (k7_fsm_3 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((k1_flang_1 A E C) = B)  =>  (D = E) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (~  ((k1_flang_1 A E C) = B) ) ) )  =>  ( (D = (k7_fsm_3 A B C))  <=>  (D = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k9_ftacell1 A B C D E) = (k21_gfacirc1 A B C)) ) ) ) ) ) ).
tt(d9_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  ((k16_funcop_1 A B) = (k7_funcop_1 (k1_tarski A) B)) ) ) ).
tt(d9_funcsdom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_funcsdom A))  =>  ((v2_funcsdom A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_rlvect_1 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A (k1_rlvect_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) & (v1_xboole_0 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(d9_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (E = (k6_funct_2 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ((r2_hidden F E) <=>  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 B)) &  ((r2_hidden G D) &  (F = (k8_relset_1 A B C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k9_funct_6 A B))  <=>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k1_funct_2 A (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(d9_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_xboole_0 B) => (v1_xboole_0 A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_funct_7 C)) ) )  =>  ((m1_funct_7 C A B) <=>  ( ((k6_funct_7 C) = A)  & (r1_tarski (k7_funct_7 C) B)) ) ) ) ) ) ) ).
tt(d9_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (A = k1_funct_8)  <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers A B) = (k2_absvalue B)) ) ) ) ) ) ).
tt(d9_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v7_functor0 C A B) <=> (r1_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k6_partfun1 (u1_struct_0 B)) (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) (k6_partfun1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(d9_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k4_fvaluat1 A B) = (o_2_0_fvaluat1 A B)) ) ) ) ) ) ).
tt(d9_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k13_fvsum_1 A B C) = (k4_rlvect_1 A (k11_fvsum_1 A B C))) ) ) ) ) ) ) ).
tt(d9_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k9_gate_5 A B C D E) = (k38_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0 (k2_gate_1 C E) k1_xboole_0)) ) ) ) ) ) ).
tt(d9_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k4_gcd_1 A B C))  <=>  ((r2_hidden D B) & (r4_gcd_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_geomtrap A B C) = (g1_geomtrap (u1_struct_0 A) (k6_geomtrap A) (k5_geomtrap A B C))) ) ) ) ) ) ) ).
tt(d9_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_gfacirc1 A B C) = (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp)) ) ) ) ).
tt(d9_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k9_glib_000 A) = (k1_funct_1 A k4_glib_000)) ) ) ).
tt(d9_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k6_glib_001 A B) = (k4_finseq_5 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B)) ) ) ) ) ).
tt(d9_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k4_glib_002 A) = (k1_card_1 (k3_glib_002 A))) ) ) ).
tt(d9_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((k7_glib_003 A) = (k1_funct_1 A k4_glib_003)) ) ) ).
tt(d9_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k8_glib_004 A B) = (k4_tarski (k16_funcop_1 B k6_numbers) k1_xboole_0)) ) ) ) ) ).
tt(d9_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_glib_005 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k7_glib_000 A))) =>  ( (D = (k2_glib_005 A B C))  <=>  (! [E:$i] :  ((r2_hidden E D) <=>  ((r3_glib_005 A B C E) | (r4_glib_005 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_goboard1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ((r1_goboard1 A B C) <=>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) &  ((k7_partfun1 A B D) = (k3_matrix_1 A C E F)) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 D 1) (k4_finseq_1 B)))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 C)) &  ( ((k7_partfun1 A B D) = (k3_matrix_1 A C E F))  &  ((k7_partfun1 A B (k2_nat_1 D 1)) = (k3_matrix_1 A C G H)) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 E G)) (k18_complex1 (k6_xcmplx_0 F H))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v4_graph_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B (u4_struct_0 A)) &  ((k1_funct_1 (u1_graph_1 A) B) = (k1_funct_1 (u2_graph_1 A) B)) ) ) ) ) ) ) ).
tt(d9_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  ((v3_graph_2 B A) <=>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) &  ((r1_graph_2 A C B) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) )  =>  ((r1_xxreal_0 E D) |  ( (D = 1)  &  (E = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u4_struct_0 A) (k9_graph_3 A)) =>  ((r2_hidden B (k1_graph_3 A (k10_xtuple_0 C))) =>  ((k10_graph_3 A B C) = (k10_subset_1 (a_3_0_graph_3 A B C))) ) ) ) ) ) ) ) ).
tt(d9_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((k5_graph_5 A B C D) = (a_4_0_graph_5 A B C D)) ) ) ) ) ) ) ) ).
tt(d9_graphsp,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k14_graphsp A B) = (a_2_2_graphsp A B)) ) ) ) ) ).
tt(d9_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((k7_grcat_1 A) = (u1_grcat_1 A)) ) ) ).
tt(d9_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (k1_funct_2 (k15_group_2 A C) (k15_group_2 A C))) &  ((v1_group_10 D B (k15_group_2 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (k1_funct_2 (k15_group_2 A C) (k15_group_2 A C)))))) ) )  =>  ( (D = (k9_group_10 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (k1_funct_2 (k15_group_2 A C) (k15_group_2 A C)) D E) = (k8_group_10 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_group_1 A B C) = (k1_binop_1 (k4_group_1 A) C B)) ) ) ) ) ) ) ).
tt(d9_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k8_group_2 A B) = (u1_struct_0 B)) ) ) ) ) ).
tt(d9_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_group_3 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (B = (k4_group_3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k8_group_4 A B C) = (k5_group_4 A (k4_subset_1 (u1_struct_0 A) (k8_group_2 A B) (k8_group_2 A C)))) ) ) ) ) ) ) ).
tt(d9_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k9_group_5 A) = (k8_group_5 A (k7_group_2 A) (k7_group_2 A))) ) ) ).
tt(d9_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( (D = (k9_group_6 A B C))  <=>  ((u1_struct_0 D) = (a_3_0_group_6 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_group_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C (k2_group_7 A B)))  =>  ( (C = (k3_group_7 A B))  <=>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) <=>  (? [E:$i] :  ((m1_subset_1 E (k4_card_3 (k12_pralg_1 A B))) &  (? [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 A)))  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G F) &  ((v1_funct_1 G) & (v1_partfun1 G F)) ) )  &  ( (E = (k1_group_1 (k2_group_7 A B)))  &  ( (D = (k1_funct_4 E G))  &  (! [H:$i] :  (~  ((r2_hidden H F) &  (! [I:$i] :  ( ( (~ (v2_struct_0 I))  &  ((v2_group_1 I) & (l3_algstr_0 I)) )  =>  (~  ( (I = (k1_funct_1 B H))  &  ((r2_hidden (k1_funct_1 G H) (u1_struct_0 I)) &  (~  ((k1_funct_1 G H) = (k1_group_1 I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((k5_group_9 A B) = (g1_group_9 A (u1_struct_0 B) (u2_algstr_0 B) (u1_group_9 A B))) ) ) ) ).
tt(d9_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v2_hahnban1 C A B) <=>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_struct_0 B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(d9_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_hermitan A B C) = (k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C))) ) ) ) ) ) ) ).
tt(d9_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) (u1_struct_0 (k12_normform A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) (u1_struct_0 (k12_normform A)))))) )  =>  ( (B = (k9_heyting1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ((k5_binop_1 (u1_struct_0 (k12_normform A)) B C D) = (k9_normform A (k7_heyting1 A (k3_heyting1 A C) (k3_heyting1 A D)))) ) ) ) ) ) ) ) ) ).
tt(d9_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k4_hilbert1 A B) = (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 k5_numbers 2) A) B)) ) ) ) ) ).
tt(d9_hilbert2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_hilbert1) &  ((v1_funct_1 A) & (v1_partfun1 A k1_hilbert1)) ) )  =>  ( (A = k2_hilbert2)  <=>  ( ((k1_funct_1 A k2_hilbert1) = (k2_trees_4 k1_hilbert1 k2_hilbert1))  &  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_funct_1 A (k1_hilbert2 B)) = (k2_trees_4 k1_hilbert1 (k1_hilbert2 B))) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D k1_hilbert1) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) )  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E k1_hilbert1) &  ((v1_funct_1 E) & (v3_trees_2 E)) ) )  &  ( (D = (k1_funct_1 A B))  &  ( (E = (k1_funct_1 A C))  &  ( ((k1_funct_1 A (k4_hilbert1 B C)) = (k6_trees_4 (k4_hilbert1 B C) D E))  &  ((k1_funct_1 A (k3_hilbert1 B C)) = (k6_trees_4 (k3_hilbert1 B C) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ( (B = (k7_hurwitz A))  <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_normsp_1 k1_complfld B C) = (k8_group_1 k1_complfld (k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld)) C) (k2_complfld (k1_normsp_1 k1_complfld A C)))) ) ) ) ) ) ) ) ).
tt(d9_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k9_idea_1 A B C) = (k8_idea_1 A (k4_nat_d (k4_nat_1 (k7_idea_1 A B) (k7_idea_1 A C)) (k2_nat_1 (k5_series_1 2 A) 1)))) ) ) ) ) ) ) ).
tt(d9_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((m2_ideal_1 C A B) <=>  (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 k5_numbers C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_subset_1 F (u1_struct_0 A) B) =>  (~  ((k7_partfun1 (u1_struct_0 A) C D) = (k6_algstr_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_incproj,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  ((v5_incproj A) <=>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v6_incsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(d9_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m3_index_1 E A B C D) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) &  ((v3_cat_5 F) & (l1_cat_1 F)) ) ) ) ) ) ) )  =>  ((m4_index_1 F A B C D E) <=>  ( (! [G:$i] :  ((m1_subset_1 G A) => (m1_subset_1 (k2_index_1 A (k1_xtuple_0 E) G) (u1_struct_0 F))) )  &  (! [G:$i] :  ((m1_subset_1 G B) => (m1_subset_1 (k4_tarski (k4_tarski (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A C G)) (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A D G))) (k7_index_1 B (k3_relat_1 C (k1_xtuple_0 E)) (k3_relat_1 D (k1_xtuple_0 E)) (k8_index_1 A B C D E) G)) (u4_struct_0 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k5_int_1 A B) = (k1_int_1 (k7_xcmplx_0 A B))) ) ) ) ) ).
tt(d9_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_int_3 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers)))) )  =>  ((m1_int_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (D = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (C = (k1_algstr_0 A (k6_algstr_0 A E D) F))  &  (~  ( (~  (F = (k4_struct_0 A)) )  & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k5_numbers B D) (k3_funct_2 (u1_struct_0 A) k5_numbers B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ((k7_integr15 A B C D) = (k74_valued_2 B B (k1_euclid A) (k1_euclid A) C D)) ) ) ) ) ) ) ) ).
tt(d9_integr16,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((k8_integr16 A B C) = (k3_binop_2 (k4_integra5 A B (k5_comseq_3 k1_numbers C)) (k5_binop_2 (k4_integra5 A B (k6_comseq_3 k1_numbers C)) k7_complex1))) ) ) ) ) ) ) ).
tt(d9_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 C D) =>  ((k6_integr18 A B C D) = (k5_integr18 A (k3_integra5 C D) B)) )  &  ( (~ (r1_xxreal_0 C D))  =>  ((k6_integr18 A B C D) = (k4_algstr_0 A (k5_integr18 A (k3_integra5 D C) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_integra1 C A) =>  ((k7_integra1 A B C) = (k18_rvsum_1 (k5_integra1 A B C))) ) ) ) ) ) ) ).
tt(d9_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k9_interva1 A B C) = (k4_setfam_1 B C)) ) ) ) ) ) ) ).
tt(d9_intpro_1,ax, (k2_intpro_1 = (k12_finseq_1 k5_numbers k6_numbers)) ).
tt(d9_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  (! [I:$i] :  ((m2_nattra_1 I B C F G) =>  ((k6_isocat_1 A B C D E F G H I) = (k7_nattra_1 A C (k9_cat_1 A B C D F) (k9_cat_1 A B C E F) (k9_cat_1 A B C E G) (k4_isocat_1 A B C D E H F) (k5_isocat_1 A B C F G E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  (! [E:$i] :  ((m2_cat_1 E A (k8_cat_2 B C)) =>  (! [F:$i] :  ((m2_nattra_1 F A (k8_cat_2 B C) D E) =>  ((k11_isocat_2 A B C D E F) = (k4_isocat_1 A (k8_cat_2 B C) B D E F (k14_cat_2 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (B = (k9_jgraph_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B C) = (k8_jgraph_4 A C)) ) ) ) ) ) ) ) ).
tt(d9_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k9_jgraph_6 A B C) = (a_3_4_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(d9_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (B = (k9_jordan5d A))  <=>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k18_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(d9_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (B = (k9_jordan6 A))  <=>  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) B) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) B) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) B) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) ) ) ) ) ).
tt(d9_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v14_quantal1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  ( (C = (k8_knaster A B))  <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_knaster D A) &  ((v3_knaster D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ( (D = (a_2_2_knaster A B))  &  (C = (k7_knaster A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 C)))  =>  (! [E:$i] :  ((m1_kolmog01 E C A B) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (F = (k7_kolmog01 A B C D E))  <=>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ((r2_hidden G F) <=>  (? [H:$i] :  ( ( (~ (v1_xboole_0 H))  &  ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 C))) )  &  (? [I:$i] :  ((m2_kolmog01 I A B C H E) &  ((r1_tarski H D) &  (G = (k1_setfam_1 (k2_relset_1 B I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lang1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v2_lang1 C) & (l2_lang1 C))  =>  ( (C = (k8_lang1 A B))  <=>  ( ((u1_struct_0 C) = (k2_tarski A B))  &  ( ((u2_lang1 C) = A)  &  ((u1_lang1 C) = (k2_tarski (k4_tarski A (k10_finseq_1 B A)) (k4_tarski A k1_xboole_0))) ) ) ) ) ) ) ) ).
tt(d9_laplace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k11_laplace A B C) = (k4_matrix_3 A B (k4_matrix_1 (u1_struct_0 A) (k10_laplace (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(d9_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattice3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ).
tt(d9_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_lattice4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r2_hidden (k4_lattices A C D) B) & (r2_hidden (k7_lattices A C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lattice5,ax, (! [A:$i] :  ((k5_lattice5 A) = (k2_xboole_0 A (k1_enumset1 (k1_tarski A) (k1_tarski (k1_tarski A)) (k1_tarski (k1_tarski (k1_tarski A)))))) ) ).
tt(d9_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_lattice6 B A) <=>  (~  ((k4_lattice6 A B) = B) ) ) ) ) ) ) ).
tt(d9_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  ((k8_lattice8 A B C D) = (k6_lattice8 A B C D (k7_lattice5 A B C))) ) ) ) ) ) ) ) ) ).
tt(d9_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v9_lattices A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattices A B (k1_lattices A B C)) = B) ) ) ) ) ) ) ) ).
tt(d9_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_lexbfs B A) =>  ((v4_lexbfs B A) <=>  ( ((k5_lexbfs A B k6_numbers) = k1_xboole_0)  &  ((v2_lexbfs B) &  ((v13_glib_000 B) &  ( ((k39_glib_000 B) = (k15_glib_000 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 (k39_glib_000 B) C))  &  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (~  ( (~ (r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))))  &  ((k5_lexbfs A B (k1_nat_1 C 1)) = (k1_funct_4 (k5_lexbfs A B C) (k16_funcop_1 D (k7_nat_d (k39_glib_000 B) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( (D = (k4_lfuzzy_1 A B C))  <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1)))))) )  &  ( (D = (k8_nat_1 (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1)) E C))  &  ( ((k8_nat_1 (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1)) E k6_numbers) = (k5_fuzzy_4 A A))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (? [G:$i] :  ( ((v5_relat_1 G (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  &  ( ((k8_nat_1 (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1)) E F) = G)  &  ((k8_nat_1 (k9_funct_2 (k2_zfmisc_1 A A) (k1_rcomp_1 k6_numbers 1)) E (k1_nat_1 F 1)) = (k4_fuzzy_4 A A A G B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 C) & (r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers A)))  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k8_lopban_1 A B)))) =>  ( (C = (k10_lopban_1 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) &  ((v2_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  =>  ((v2_lopban_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k6_algstr_0 A B C)) (k8_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ) ).
tt(d9_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (C = (k5_lopban_3 A B))  <=>  ( ((k1_normsp_1 A C k6_numbers) = (k5_struct_0 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C (k2_nat_1 D 1)) = (k6_algstr_0 A (k1_normsp_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (E = (k8_lopban_4 A B C D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F D) =>  ((k8_nat_1 (u1_struct_0 A) E F) = (k6_algstr_0 A (k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) F) (k5_algstr_0 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A C)) D) (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A C)) (k7_nat_d D F))))) )  &  ( (~ (r1_xxreal_0 F D))  =>  ((k8_nat_1 (u1_struct_0 A) E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k12_lopclset A) = (k6_lopclset (k11_lopclset A))) ) ) ).
tt(d9_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k10_lpspace1 A B C) = (g1_rlvect_1 (k9_lpspace1 A B C) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k9_lpspace1 A B C)) (k1_ideal_1 (k7_lpspace1 A) (k9_lpspace1 A B C)) (k1_lpspace1 (k7_lpspace1 A) (k9_lpspace1 A B C)))) ) ) ) ) ) ) ).
tt(d9_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k8_lpspace2 A B C D) = (k5_lpspace2 A B C (k8_lpspace1 A k6_numbers) D)) ) ) ) ) ) ) ) ) ).
tt(d9_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k9_ltlaxio1 A B) = (k1_ltlaxio1 (k8_ltlaxio1 (k1_ltlaxio1 A) (k1_ltlaxio1 B)))) ) ) ) ) ).
tt(d9_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k3_margrel1 A)) =>  ( (B = (k4_margrel1 A))  <=>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(d9_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_mathmorp A B C D) = (k7_subset_1 (u1_struct_0 A) B (k7_mathmorp A B C D))) ) ) ) ) ) ) ) ) ).
tt(d9_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r3_matrix16 A B C) <=>  ( ((k3_finseq_1 C) = (k1_matrix_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) & (r1_xxreal_0 D E))  =>  ((k3_matrix_1 (u1_struct_0 A) B D E) = (k1_funct_1 C (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 E D) (k3_finseq_1 C)) 1))) ) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) & (r1_xxreal_0 E D))  =>  ((k3_matrix_1 (u1_struct_0 A) B D E) = (k1_funct_1 (k5_fvsum_1 A C) (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 E D) (k3_finseq_1 C)) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_matrix_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k10_matrix_1 A B) = (k4_finseq_2 B (k4_finseq_2 B (u1_struct_0 A)))) ) ) ) ) ).
tt(d9_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (B = (k12_matrix_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 C (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ) ) ) ) ) ) ) ).
tt(d9_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k12_matrix_3 A B C) = (k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k12_matrix_2 A)) (k11_matrix_3 A B C))) ) ) ) ) ) ) ).
tt(d9_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( (B = (k10_matrixc1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 A))) =>  ((k9_matrix_5 B C) = (k17_rvsum_1 (k8_matrix_1 k2_numbers A C))) ) ) ) ) ) ) ) ) ) ).
tt(d9_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrixj1 D (u1_struct_0 A)) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( (D = (k24_matrixj1 A B C))  <=>  ( ((k4_finseq_1 D) = (k4_finseq_1 B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k2_matrixj1 (u1_struct_0 A) D E) = (k6_matrix_3 A (k2_matrixj1 (u1_struct_0 A) B E) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k9_matrixr1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = 1)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_funct_1 B C) = (k12_finseq_1 k1_numbers (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_pre_topc C) & (l1_pre_topc C))  =>  ( (C = (k3_matroid0 A B))  <=>  ( ((u1_struct_0 C) = (u1_struct_0 B))  &  ((k1_matroid0 C) = (a_2_0_matroid0 A B)) ) ) ) ) ) ) ) ) ).
tt(d9_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v5_matrprob A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k18_rvsum_1 (k1_matrprob k1_numbers A B)) = 1) ) ) ) ) ) ) ).
tt(d9_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ( (F = (k5_mcart_1 A B C D E))  <=>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (E = (k6_xtuple_0 G H I J))  =>  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k6_measure6 A) = (k1_setfam_1 (a_1_1_measure6 A))) ) ) ).
tt(d9_measure8,ax, (k7_measure8 = (k2_funct_1 k1_nagata_2)) ).
tt(d9_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k12_member_1 A B) = (a_2_4_member_1 A B)) ) ) ) ) ).
tt(d9_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((r1_tarski A B) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(d9_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_memstr_0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((v4_memstr_0 C A B) <=> (r1_xboole_0 (k9_xtuple_0 C) (k1_tarski (k4_struct_0 B)))) ) ) ) ) ) ) ).
tt(d9_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (D = (k9_mesfun7c A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_1 D E) = (k1_funct_1 (k4_mesfunc5 A k2_numbers B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (D = (k9_mesfunc1 A B C))  <=>  ( ((k9_xtuple_0 D) = (k6_subset_1 (k9_xtuple_0 B) (k8_relat_1 B (k1_tarski k1_supinf_2))))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_xtuple_0 D)) =>  ((k12_supinf_2 D E) = (k2_extreal1 (k1_measure6 C) (k12_supinf_2 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v8_mesfunc5 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ((v7_ordinal1 D) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 B (k8_nat_1 k7_numbers A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (C = (k7_mesfunc8 A B))  <=>  ( ((k1_relset_1 A C) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((k12_supinf_2 C D) = (k2_mesfunc5 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mesfunc9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ( (E = (k9_mesfunc9 A B C D))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k4_mesfunc5 A B E F) = (k1_binop_1 C F D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v9_metric_1 A) <=> (v5_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ).
tt(d9_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k6_metric_2 A) = (a_1_2_metric_2 A)) ) ) ).
tt(d9_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (! [D:$i] :  ((m1_midsp_1 D A) =>  ( (D = (k7_midsp_1 A B C))  <=>  (? [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ( (B = (k5_midsp_1 A E))  &  ( (C = (k5_midsp_1 A F))  &  ( ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) F))  &  (D = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((r1_midsp_2 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( (D = (k6_midsp_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k2_binop_1 A A (u1_struct_0 B) C E (k5_binop_1 A D E F)) = (k2_binop_1 A A (u1_struct_0 B) C (k5_binop_1 A D E F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  ( (F = (k8_midsp_3 A B C D E))  <=>  (! [G:$i] :  ((m1_midsp_3 G A) =>  ((k5_midsp_3 A (u1_struct_0 (u1_midsp_2 B C)) F G) = (k9_midsp_2 B C D (k5_midsp_3 A (u1_struct_0 B) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k9_mmlquery A B C D) = (a_4_4_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(d9_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((k6_mod_2 A B) = (g1_mod_2 A B B (k3_struct_0 B))) ) ) ) ) ).
tt(d9_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_mod_4 C A B) <=>  ((v2_mod_4 C A B) & (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(d9_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  ((k11_modal_1 A) = (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 1) (k1_domain_1 k5_numbers k5_numbers 1 1)) (k12_finseq_1 k5_numbers k6_numbers) A)) ) ) ).
tt(d9_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ((m4_modcat_1 C A (k4_modcat_1 A B)) =>  ((k6_modcat_1 A B C) = (k3_mod_2 A C)) ) ) ) ) ) ) ).
tt(d9_modelc_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((k9_modelc_1 A) = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 2) A)) ) ) ).
tt(d9_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (A = k9_modelc_2)  <=>  ( (! [B:$i] :  ((r2_hidden B A) => (m2_finseq_1 B k5_numbers)) )  &  ( (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden (k2_modelc_2 B) A)) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k3_modelc_2 B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k4_modelc_2 B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k5_modelc_2 B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) => (r2_hidden (k6_modelc_2 B) A)) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k7_modelc_2 B C) A)) ) ) ) )  &  ( (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k8_modelc_2 B C) A)) ) ) ) )  &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (! [C:$i] :  ((r2_hidden C B) => (m2_finseq_1 C k5_numbers)) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) => (r2_hidden (k2_modelc_2 C) B)) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k3_modelc_2 C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k4_modelc_2 C D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_modelc_2 C D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C B) => (r2_hidden (k6_modelc_2 C) B)) ) )  &  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k7_modelc_2 C D) B)) ) ) ) )  &  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k8_modelc_2 C D) B)) ) ) ) ) ) ) ) ) ) ) )  => (r1_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((l1_modelc_3 B A) =>  (! [C:$i] :  ((l1_modelc_3 C A) =>  ((r4_modelc_3 A B C) <=>  ((r2_modelc_3 A B C) | (r3_modelc_3 A B C)) ) ) ) ) ) ) ) ).
tt(d9_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v9_monoid_0 B A) <=>  ((v1_setwiseo B A) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k5_binop_1 A B C D) = (k4_binop_1 A B))  =>  ( (C = D)  &  (D = (k4_binop_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( ((v1_group_1 A) =>  ((k22_monoid_1 A) = (g4_algstr_0 (k1_zfmisc_1 (u1_struct_0 A)) (k21_monoid_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A)) (k6_domain_1 (u1_struct_0 A) (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A))))) )  &  ( (~ (v1_group_1 A))  =>  ((k22_monoid_1 A) = (g3_algstr_0 (k1_zfmisc_1 (u1_struct_0 A)) (k21_monoid_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A)))) ) ) ) ) ).
tt(d9_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A B)) =>  ( (C = (k6_msafree2 A B))  <=>  ((r1_msualg_3 A (k5_msafree2 A B) B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden F (k7_msafree A (u3_msualg_1 A B) D)) &  ( (F = (k1_trees_4 (k4_tarski E D)))  & (r2_hidden E (k1_funct_1 (u3_msualg_1 A B) D))) )  =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A B) C D) F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k6_msafree A B C) = (k4_tarski C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(d9_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  ((r1_msaterm A B C D E F) <=>  ( ((k9_xtuple_0 F) = (k9_xtuple_0 D))  &  (! [G:$i] :  ((m1_trees_1 G (k9_xtuple_0 F)) =>  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_funct_1 C H)) =>  ( ((k1_funct_1 D G) = (k4_tarski I H))  =>  ((k1_funct_1 F G) = (k3_funct_2 (k1_funct_1 C H) (k1_funct_1 (u3_msualg_1 A B) H) (k1_msualg_3 (u1_struct_0 A) C (u3_msualg_1 A B) E H) I)) ) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_funct_1 (u3_msualg_1 A B) H)) =>  ( ((k1_funct_1 D G) = (k4_tarski I H))  =>  ((k1_funct_1 F G) = I) ) ) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ( ((k1_funct_1 D G) = (k4_tarski H (u1_struct_0 A)))  =>  ((k1_funct_1 F G) = (k1_funct_1 (k5_msualg_1 A H B) (k2_trees_9 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k7_msualg_1 A) = (k16_funcop_1 k6_numbers (u1_struct_0 A))) ) ) ).
tt(d9_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((m1_msualg_2 C A B) <=>  ((m3_pboole (u3_msualg_1 A C) (u1_struct_0 A) (u3_msualg_1 A B)) &  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A C)) =>  ((v3_msualg_2 D A B) & (r8_pboole (u4_struct_0 A) (u4_msualg_1 A C) (k4_msualg_2 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r3_msualg_3 A B C D) <=>  ((r1_msualg_3 A B C D) & (v1_msualg_3 D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v4_msualg_6 C A B) <=>  (! [D:$i] :  ((m1_msualg_6 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k4_tarski F G) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E)) => (r2_hidden (k4_tarski (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D E) F) (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D E) G)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((m1_mycielsk C (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1)) =>  ( (C = (k6_mycielsk A B))  <=>  ((u1_orders_2 C) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (u1_orders_2 B) (a_2_0_mycielsk A B)) (a_2_1_mycielsk A B)) (k2_zfmisc_1 (k1_tarski (k3_xcmplx_0 2 A)) (k6_subset_1 (k3_xcmplx_0 2 A) A))) (k2_zfmisc_1 (k6_subset_1 (k3_xcmplx_0 2 A) A) (k1_tarski (k3_xcmplx_0 2 A))))) ) ) ) ) ) ) ) ).
tt(d9_nagata_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( (D = (k5_nagata_1 A B C))  <=>  (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 D E) = (k3_xxreal_0 B (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) & (v1_partfun1 B k10_newton)) ) )  =>  ( (B = (k13_nat_3 A))  <=>  ( ((k13_pre_poly B) = (k1_polynom2 k10_newton (k12_nat_3 A)))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_polynom2 k10_newton (k12_nat_3 A))) =>  ((k1_funct_1 B C) = (k1_newton C (k11_nat_3 A C))) ) ) ) ) ) ) ) ) ) ).
tt(d9_nat_lat,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat)))) )  =>  ( (A = k9_nat_lat)  <=>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k6_nat_lat) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k6_nat_lat) =>  ((k5_binop_1 k6_nat_lat A B C) = (k5_nat_d B C)) ) ) ) ) ) ) ) ).
tt(d9_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r2_nattra_1 A B C D) & (r2_nattra_1 A B D E))  =>  (! [F:$i] :  ((m2_nattra_1 F A B C D) =>  (! [G:$i] :  ((m2_nattra_1 G A B D E) =>  ((k7_nattra_1 A B C D E F G) = (k5_nattra_1 A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) B)) &  ((v9_clvect_1 D A) &  ((k7_clvect_1 A D) = C) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D B)) &  ((k7_partfun1 k1_numbers B C) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r2_ndiff_1 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k16_lopban_1 A B))))))  =>  ( (E = (k4_ndiff_1 A B C D))  <=>  ( ((k1_relset_1 (u1_struct_0 A) E) = D)  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F D) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) E F) = (k3_ndiff_1 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k4_finseq_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((r2_ndiff_5 A B C D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B))))))  =>  ( (F = (k7_ndiff_5 A B C D E))  <=>  ( ((k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) F) = E)  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_prvect_2 A))) =>  ((r2_hidden G E) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B)) F G) = (k6_ndiff_5 A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_necklace A) = (k2_necklace (k1_necklace A))) ) ) ).
tt(d9_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  =>  (! [C:$i] :  ( (C = (k6_net_1 A B))  <=>  ( ((r2_hidden B (u1_struct_0 A)) =>  (C = (k1_tarski B)) )  &  ((r2_hidden B (u4_struct_0 A)) =>  (C = (k4_net_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(d9_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r5_nfcont_1 A B C D) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden F C) & (r2_hidden G C))  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D F) (k7_partfun1 (u1_struct_0 B) D G))) (k8_real_1 E (k1_normsp_0 A (k5_algstr_0 A F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_normform,ax, (! [A:$i] :  ((k8_normform A) = (a_1_1_normform A)) ) ).
tt(d9_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A))))) )  =>  ( (B = (k13_openlatt A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k9_openlatt A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_openlatt A)) =>  ((k5_binop_1 (k9_openlatt A) B C D) = (k11_openlatt A C D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v2_necklace A) <=> (r5_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(d9_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ((m1_oppcat_1 C A B) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A D))  =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A D E)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_orders_1 A B) <=>  (! [C:$i] :  (~  ((r1_tarski C B) &  ((v3_orders_1 (k2_wellord1 A C)) &  (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  ((r2_hidden E C) => (r2_hidden (k4_tarski E D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_orders_2 A B) = (a_2_1_orders_2 A B)) ) ) ) ) ).
tt(d9_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ( ((v6_altcat_1 B) & (l2_altcat_1 B))  =>  ( (B = (k4_orders_3 A))  <=>  ( ((u1_struct_0 B) = A)  &  (! [C:$i] :  ((m1_orders_3 C A) =>  (! [D:$i] :  ((m1_orders_3 D A) =>  ( ((k1_binop_1 (u1_altcat_1 B) C D) = (k1_orders_3 C D))  &  (! [E:$i] :  ((m1_orders_3 E A) =>  (! [F:$i] :  ((m1_orders_3 F A) =>  (! [G:$i] :  ((m1_orders_3 G A) =>  ((k1_multop_1 (u2_altcat_1 B) E F G) = (k6_altcat_1 (k1_orders_3 E F) (k1_orders_3 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k2_ordinal1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C A) & (v3_ordinal1 C)) ) ) ) ) ) ).
tt(d9_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ( ( (A = k1_xboole_0)  =>  ((r1_ordinal2 A B) <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ((r2_hidden C (k9_xtuple_0 B)) &  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r1_ordinal1 C D) & (r2_hidden D (k9_xtuple_0 B)))  =>  ((k1_funct_1 B D) = k1_xboole_0) ) ) ) ) ) ) ) )  &  ( (~  (A = k1_xboole_0) )  =>  ((r1_ordinal2 A B) <=>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden C A) &  ((r2_hidden A D) &  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r2_hidden E (k9_xtuple_0 B)) &  (! [F:$i] :  ((v3_ordinal1 F) =>  ( ((r1_ordinal1 E F) & (r2_hidden F (k9_xtuple_0 B)))  =>  ((r2_hidden C (k1_funct_1 B F)) & (r2_hidden (k1_funct_1 B F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v5_ordinal5 A) <=>  (? [B:$i] :  ((v3_ordinal1 B) &  (? [C:$i] :  ((v7_ordinal1 C) &  ((r2_hidden k6_numbers C) &  (A = (k11_ordinal2 C (k12_ordinal2 k4_ordinal1 B))) ) ) ) ) ) ) ) ) ).
tt(d9_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v8_o_ring_1 B A) <=>  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ( (~ (v5_o_ring_1 (k7_partfun1 (u1_struct_0 A) B C) A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ((k7_partfun1 (u1_struct_0 A) B C) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B E)))  &  ( (~  (D = k6_numbers) )  &  ( (~ (r1_xxreal_0 C D))  &  ( (~  (E = k6_numbers) )  &  (~ (r1_xxreal_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) C))))) )  =>  ( (D = (k6_osafree A B C))  <=>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r1_lang1 (k2_osafree A B) (k3_osafree A B C) (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) E)) =>  ((k1_funct_1 D E) = (k8_trees_4 (u1_struct_0 (k2_osafree A B)) (k3_osafree A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r3_osalg_1 A B C D) <=>  ((r1_osalg_1 A B C) &  ((r2_osalg_1 A D (k1_msualg_1 A C)) &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((r1_osalg_1 A B E) & (r2_osalg_1 A D (k1_msualg_1 A E)))  => (r2_osalg_1 A (k1_msualg_1 A C) (k1_msualg_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k2_osalg_4 A)) =>  (! [E:$i] :  ( ((v1_partfun1 E (k4_osalg_4 A (u3_msualg_1 A B) D)) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_osalg_4 A (u3_msualg_1 A B) D) (k4_osalg_4 A (u3_msualg_1 A B) D))))) ) )  =>  ( (E = (k5_osalg_4 A B C D))  <=>  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k4_tarski F G) E) <=>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r2_hidden H D) & (r2_hidden (k4_tarski F G) (k2_msualg_4 A B C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (B = (k7_parsp_1 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C (k6_parsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  ( (C = (k5_domain_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) D E F G))  &  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)))) = (k4_struct_0 A))  &  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)))) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k5_pboole A B C) = (k2_pboole A (k4_pboole A B C) (k4_pboole A C B))) ) ) ) ) ) ).
tt(d9_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v4_pcs_0 A) <=> (r1_relat_2 (u1_pcs_0 A) (u1_struct_0 A))) ) ) ).
tt(d9_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 B))) =>  ((r2_pdiff_1 A B C D E) <=> (r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C E) D) (k3_funct_2 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C B) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r4_pdiff_3 A B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k5_pdiff_3 A B))  <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k10_finseq_1 D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 G 1))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B) I) (k1_seq_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((k6_pdiff_4 A B C) = (k7_real_1 (k7_real_1 (k8_real_1 (k11_pdiff_1 3 1 A B) (k1_seq_1 (k5_pdiff_4 C) 1)) (k8_real_1 (k11_pdiff_1 3 2 A B) (k1_seq_1 (k5_pdiff_4 C) 2))) (k8_real_1 (k11_pdiff_1 3 3 A B) (k1_seq_1 (k5_pdiff_4 C) 3)))) ) ) ) ) ) ) ).
tt(d9_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r9_pdiff_5 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B) I) (k1_seq_1 (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((k5_pdiff_9 A B C D) = (k1_seqfunc (k1_euclid A) k1_numbers (k4_pdiff_9 A B C D) (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(d9_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v8_pencil_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_pre_topc A)) & (r2_hidden B C)) ) ) ) ) ) ) ).
tt(d9_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k12_polyform A) = (k11_polyform A k6_numbers)) ) ) ).
tt(d9_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( (E = (k9_polynom1 A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) &  ( ((k3_polynom1 A B E F) = (k4_rlvect_1 B G))  &  ( ((k3_finseq_1 G) = (k3_finseq_1 (k21_pre_poly A F)))  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 G)) &  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I A) &  ((v1_funct_1 I) &  ((v1_partfun1 I A) &  ((v4_valued_0 I) & (v2_pre_poly I)) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J A) &  ((v1_funct_1 J) &  ((v1_partfun1 J A) &  ((v4_valued_0 J) & (v2_pre_poly J)) ) ) ) )  =>  (~  ( ((k9_pre_poly (k15_pre_poly A) k5_numbers (k4_finseq_2 2 (k15_pre_poly A)) (k21_pre_poly A F) H) = (k10_finseq_1 I J))  &  ((k7_partfun1 (u1_struct_0 B) G H) = (k6_algstr_0 B (k3_polynom1 A B C I) (k3_polynom1 A B D J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (D = (k11_polynom3 A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) &  ( ((k3_finseq_1 F) = (k2_nat_1 E 1))  &  ( ((k1_normsp_1 A D E) = (k4_rlvect_1 A F))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden G (k4_finseq_1 F)) =>  ((k1_funct_1 F G) = (k6_algstr_0 A (k1_normsp_1 A B (k7_nat_d G 1)) (k1_normsp_1 A C (k7_nat_d (k2_nat_1 E 1) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k6_polynom5 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=> (r1_polynom5 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l5_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( (E = (k5_polynom7 A B C D))  <=>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((k3_polynom1 A B E F) = (k6_algstr_0 B D (k3_polynom1 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r7_polyred A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (r5_polyred A B C D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_poset_1 A B C D) = (a_4_0_poset_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d9_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_pralg_2 D A B) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ( (~  (A = k1_xboole_0) )  =>  ( (E = (k9_pralg_2 A B C D))  <=>  (! [F:$i] :  (~  ((r2_hidden F A) &  (! [G:$i] :  ((l3_msualg_1 G B) =>  (~  ( (G = (k1_funct_1 D F))  &  ((k1_funct_1 E F) = (k1_funct_1 (u3_msualg_1 B G) C)) ) ) ) ) ) ) ) ) )  &  ( (A = k1_xboole_0)  =>  ( (E = (k9_pralg_2 A B C D))  <=>  (E = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r1_pre_poly A B C) <=>  (? [D:$i] :  ((v3_ordinal1 D) &  ( (~ (r1_xxreal_0 (k1_funct_1 C D) (k1_funct_1 B D)))  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E D) =>  ((k1_funct_1 B E) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ( (C = (k9_prob_1 A B))  <=>  ((r1_tarski B C) &  (! [D:$i] :  ( ((r1_tarski B D) &  ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D A) &  ((v4_prob_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v2_prob_3 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_prob_1 C) & (r1_tarski (k2_relset_1 (k9_setfam_1 A) C) B))  => (r2_hidden (k1_kurato_0 A C) B)) ) ) ) ) ) ) ).
tt(d9_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (D = (k2_projpl_1 A B C))  <=> (r2_projpl_1 A D B C)) ) ) ) ) ) ) ) ) ) ).
tt(d9_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ((k10_prvect_2 A) = (g1_rlvect_1 (k4_card_3 (k4_prvect_2 A)) (k8_prvect_2 A) (k13_prvect_1 (k4_prvect_2 A) (k6_prvect_2 A)) (k2_prvect_2 (k4_prvect_2 A) k1_numbers (k9_prvect_2 A)))) ) ) ).
tt(d9_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k8_pscomp_1 A) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) A) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A))) ) ) ).
tt(d9_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A))))  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_pua2mss1 A B C) <=>  ((r1_pua2mss1 A B C) &  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( (~ (r1_xboole_0 (k4_card_3 D) (k1_relset_1 (k3_finseq_2 A) B)))  => (r1_tarski (k4_card_3 D) (k1_relset_1 (k3_finseq_2 A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k8_qc_lang1 A B) = (a_2_0_qc_lang1 A B)) ) ) ) ) ).
tt(d9_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ((k9_qc_lang2 A B C D E) = (k5_qc_lang2 A B (k7_qc_lang2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  ((k8_qmax_1 A B) = (k1_domain_1 (k2_qmax_1 A) (k1_zfmisc_1 k1_numbers) (k6_qmax_1 A B) (k3_subset_1 k1_numbers (k7_qmax_1 A B)))) ) ) ) ) ).
tt(d9_quantal1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v11_quantal1 A) <=>  ((k3_relat_1 A A) = A) ) ) ) ).
tt(d9_quatern2,ax, (! [A:$i] :  ( ((v8_algstr_0 A) & (l2_algstr_0 A))  =>  ( (A = k15_quatern2)  <=>  ( ((u1_struct_0 A) = k1_quaterni)  &  ( ((u1_algstr_0 A) = k10_quatern2)  &  ((k4_struct_0 A) = k1_quatern2) ) ) ) ) ) ).
tt(d9_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k9_quaterni A B) = (k7_quaterni A (k8_quaterni B))) ) ) ) ) ).
tt(d9_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (B = (k12_quofield A))  <=>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((r2_hidden C B) <=>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ).
tt(d9_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k3_radix_1 A)))  =>  ( (D = (k10_radix_1 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 B)) =>  ((k4_radix_1 E A B D) = (k9_radix_1 E A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E k5_numbers))  =>  ((r1_xxreal_0 1 D) =>  (! [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F k5_numbers))  =>  ( (F = (k9_radix_2 A B C D E))  <=>  ( ((k1_recdef_1 F 1) = (k8_radix_2 D B D C E))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k5_real_1 D 1)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ( (H = (k1_recdef_1 F G))  &  ( (I = (k1_recdef_1 F (k1_nat_1 G 1)))  &  (I = (k4_nat_d (k4_nat_1 (k4_nat_d (k1_newton H (k1_radix_1 A)) B) (k8_radix_2 D B (k7_nat_d D G) C E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k4_radix_3 B)))  =>  ((k11_radix_3 A B C D) = (k7_radix_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(d9_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (D = (k8_radix_6 A B C))  <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k2_xcmplx_0 A 2))) =>  ((k4_radix_1 E B (k2_xcmplx_0 A 2) D) = (k7_radix_6 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((v4_ratfunc1 B A) <=> (r2_funct_2 k5_numbers (u1_struct_0 A) (k4_ratfunc1 A B) (k9_polynom3 A))) ) ) ) ) ).
tt(d9_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_relat_1 A) <=>  (~ (r2_hidden k1_xboole_0 (k10_xtuple_0 A))) ) ) ) ).
tt(d9_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_2 A) <=> (r1_relat_2 A (k1_relat_1 A))) ) ) ).
tt(d9_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r7_rewrite1 A B C) <=>  (? [D:$i] :  ( ((r2_hidden (k4_tarski B D) A) |  (B = D) )  &  ((r2_hidden (k4_tarski C D) A) |  (C = D) ) ) ) ) ) ) ) ) ).
tt(d9_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r4_rewrite2 A B C D) <=>  ((k8_rewrite2 A B D) = (k8_rewrite2 A C D)) ) ) ) ) ) ) ) ) ).
tt(d9_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_rfunct_3 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) => (r2_hidden D (k9_xtuple_0 (k1_funct_1 C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k6_rinfsup2 A) = (k1_rinfsup2 (k3_rinfsup2 A))) ) ) ).
tt(d9_ringcat1,ax, (! [A:$i] :  ( ((v3_ringcat1 A) & (l1_ringcat1 A))  =>  (! [B:$i] :  ( ((v3_ringcat1 B) & (l1_ringcat1 B))  =>  ( ((k1_ringcat1 A) = (k2_ringcat1 B))  =>  (! [C:$i] :  ( ((v2_ringcat1 C) &  ((v3_ringcat1 C) & (l1_ringcat1 C)) )  =>  ( (C = (k6_ringcat1 A B))  <=>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v3_group_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v3_group_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( ( ((g1_ringcat1 (u1_ringcat1 A) (u2_ringcat1 A) (u3_ringcat1 A)) = (g1_ringcat1 E F G))  &  ((g1_ringcat1 (u1_ringcat1 B) (u2_ringcat1 B) (u3_ringcat1 B)) = (g1_ringcat1 D E H)) )  =>  (C = (g1_ringcat1 D F (k1_partfun1 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 F) H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  ((v7_rltopsp1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden (k1_rlvect_1 A C B) D) &  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc F A) &  ((r2_hidden C F) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (~ (r1_xxreal_0 E (k18_complex1 (k9_real_1 G B))))  => (r1_tarski (k1_convex1 A F G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((r1_rlvect_2 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B D) = (k3_funct_2 (u1_struct_0 A) k1_numbers C D)) ) ) ) ) ) ) ) ) ) ).
tt(d9_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ( (E = (k6_rmod_4 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) = (k3_rlvect_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C F) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) &  ((v7_robbins1 A) & (l2_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k7_robbins1 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_robbins1 A B C) = B) ) ) ) ) ) ) ) ).
tt(d9_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( (C = (k6_roughs_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers C D) = (k7_xcmplx_0 (k5_card_1 (k9_subset_1 (u1_struct_0 A) B (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) D))) (k5_card_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) D)))) ) ) ) ) ) ) ) ) ) ).
tt(d9_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_rsspace4 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_rsspace4 A B) k1_numbers)))) )  =>  ( (C = (k8_rsspace4 A B))  <=>  (! [D:$i] :  ((r2_hidden D (k4_rsspace4 A B)) =>  ((k1_seq_1 C D) = (k4_seq_4 (k7_rsspace4 A B (k6_rsspace4 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(d9_rsspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  ((v1_xboole_0 B) |  ((k9_rsspace A B) = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B))) ) ) ) ) ) ) ).
tt(d9_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = (a_3_1_rusub_4 A B C)) ) ) ) ) ) ) ).
tt(d9_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k14_rvsum_1 A B) = (k3_funcop_1 k35_binop_2 A B)) ) ) ) ) ).
tt(d9_scm_comp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k12_scm_comp A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_dtconstr k1_scm_comp) k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k1_scm_comp) k4_numbers)))) )  &  ( (C = (k3_funct_2 (k4_dtconstr k1_scm_comp) k4_numbers D B))  &  ( (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k4_numbers D (k3_scm_comp E)) = (k1_funct_1 A E)) ) )  &  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k1_scm_comp)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k1_scm_comp)) =>  ( ( (H = (k1_bintree1 (u1_struct_0 k1_scm_comp) F))  &  ( (I = (k1_bintree1 (u1_struct_0 k1_scm_comp) G))  & (r1_lang1 k1_scm_comp E (k4_pre_poly (u1_struct_0 k1_scm_comp) H I))) )  =>  (! [J:$i] :  ((m1_subset_1 J k4_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k4_numbers) =>  ( ( (J = (k3_funct_2 (k4_dtconstr k1_scm_comp) k4_numbers D F))  &  (K = (k3_funct_2 (k4_dtconstr k1_scm_comp) k4_numbers D G)) )  =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k4_numbers D (k2_scm_comp E F G)) = (k10_scm_comp E J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (C = (k7_scmfsa_2 A B))  <=>  (? [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  &  (? [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  &  ( (A = D)  &  ( (B = E)  &  (C = (k3_ami_3 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k8_scmpds_2 A B C) = (k3_xtuple_0 5 k1_xboole_0 (k11_finseq_1 A B C))) ) ) ) ) ) ) ).
tt(d9_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v3_scmpds_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmpds_2)) =>  ( ((r2_hidden B (k9_xtuple_0 A)) &  (C = (k1_funct_1 A B)) )  =>  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) C) = 1) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) C) = 3) )  & (r1_scmpds_4 C B)) ) ) ) ) ) ) ) ) ) ).
tt(d9_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k7_scmpds_6 A B C) = (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 1)) C)) ) ) ) ) ) ) ).
tt(d9_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (? [B:$i] :  ((m1_subset_1 B k2_scm_inst) &  (? [C:$i] :  ((m1_subset_1 C k2_scm_inst) &  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((m2_subset_1 F k4_ordinal1 (k7_card_1 15)) &  (A = (k3_xtuple_0 F k1_xboole_0 (k7_finseq_4 B C D E))) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  ( (B = (k10_scmpds_i A))  <=>  (? [C:$i] :  ((m2_finseq_1 C (k2_xboole_0 k2_scm_inst k4_numbers)) &  ( (C = (k2_xtuple_0 A))  &  (B = (k7_partfun1 (k2_xboole_0 k2_scm_inst k4_numbers) C 1)) ) ) ) ) ) ) ) ) ) ).
tt(d9_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k9_scmring2 A B C) = (k3_xtuple_0 7 (k12_finseq_1 k5_numbers B) (k12_finseq_1 (u1_struct_0 (k1_scmring2 A)) C))) ) ) ) ) ) ) ).
tt(d9_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_semi_af1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_semi_af1 A B C D) &  (~  ((r1_semi_af1 A B E F) & (r2_analoaf A C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k12_seq_4 A B) = (k4_finseqop k2_numbers k2_numbers A (k7_seq_4 B))) ) ) ) ) ).
tt(d9_seqfunc,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  (! [D:$i] :  ((r1_seqfunc A B C D) <=>  ( (~  (D = k1_xboole_0) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_tarski D (k1_relset_1 A (k1_seqfunc A B C E)))) ) ) ) ) ) ) ) ) ).
tt(d9_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ).
tt(d9_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~  (B = k1_xboole_0) )  =>  ((k8_setfam_1 A B) = (k6_setfam_1 A B)) )  &  ( (B = k1_xboole_0)  =>  ((k8_setfam_1 A B) = A) ) ) ) ) ) ).
tt(d9_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (D = (k9_setlim_2 A B C))  <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) D E) = (k5_subset_1 A C (k8_nat_1 (k9_setfam_1 A) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ((r3_sgraph1 A B C D E) <=>  ( ((k1_funct_1 E 1) = C)  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = D)  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) | (r2_hidden (k2_tarski (k1_funct_1 E F) (k1_funct_1 E (k2_nat_1 F 1))) (u1_sgraph1 B))) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) |  ((r1_xxreal_0 G F) |  ((r1_xxreal_0 (k3_finseq_1 E) G) |  ( (~  ((k1_funct_1 E F) = (k1_funct_1 E G)) )  &  (~  ((k2_tarski (k1_funct_1 E F) (k1_funct_1 E (k2_nat_1 F 1))) = (k2_tarski (k1_funct_1 E G) (k1_funct_1 E (k2_nat_1 G 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  ((v5_sheffer1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_lattices A B B) = B) ) ) ) ) ) ).
tt(d9_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((l1_pre_topc B) =>  ((m1_simplex0 B A) <=> (r1_tarski (k2_struct_0 B) A)) ) ) ) ).
tt(d9_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (D = (k8_sin_cos A B C))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E A) =>  ((k8_nat_1 k2_numbers D E) = (k3_xcmplx_0 (k3_xcmplx_0 (k8_nat_1 k2_numbers (k5_sin_cos A) E) (k1_newton B E)) (k1_newton C (k7_nat_d A E)))) )  &  ( (~ (r1_xxreal_0 E A))  =>  ((k8_nat_1 k2_numbers D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  ((v3_stacks_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( (~ (r1_stacks_1 A B))  =>  (B = (k7_stacks_1 A (k5_stacks_1 A B) (k6_stacks_1 A B))) ) ) ) ) ) ) ).
tt(d9_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( (C = (k15_sublemma A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) &  ( (E = D)  &  (~ (r2_hidden E (k24_qc_lang1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k10_substut1 A B) = (a_2_1_substut1 A B)) ) ) ) ) ).
tt(d9_supinf_2,ax, (! [A:$i] :  ((v5_supinf_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((r2_hidden B A) => (r1_xxreal_0 k1_supinf_2 B)) ) ) ) ) ).
tt(d9_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k9_tdlat_1 A) = (a_1_2_tdlat_1 A)) ) ) ).
tt(d9_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k6_termord A B C D) = (k6_polynom1 A C D (k5_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(d9_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_4 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C B) &  (B = (k2_tex_4 A C)) ) ) ) ) ) ) ) ) ).
tt(d9_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_tmap_1 A B) = (k6_partfun1 (u1_struct_0 A))) ) ) ) ) ).
tt(d9_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v5_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((k2_topalg_6 A B) = (k1_funct_1 B (k2_xxreal_2 (k9_xtuple_0 B)))) ) ) ) ) ).
tt(d9_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v4_topgen_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_topgen_1 C A)) ) ) ) ) ) ) ) ).
tt(d9_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_topgen_4 A B C) <=>  (! [D:$i] :  ((m1_connsp_2 D A C) =>  (~ (v4_card_3 (k9_subset_1 (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ).
tt(d9_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v5_topreal1 A) <=>  (? [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) &  ((v4_topreal1 B) &  (A = (k3_topreal1 2 B)) ) ) ) ) ) ) ).
tt(d9_toprealb,ax, (k10_toprealb = (k19_euclid (k1_real_1 1) k6_numbers)) ).
tt(d9_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (C = (k6_toprns_1 A B))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k12_euclid (k5_algstr_0 (k15_euclid A) (k8_nat_1 (u1_struct_0 (k15_euclid A)) B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v5_transgeo B A) <=>  ((v4_transgeo B A) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_partfun1 (u1_struct_0 A))) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (C = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  ((r2_hidden B A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_trees_1 D))  =>  ( (D = (k5_trees_1 A B C))  <=>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  ((r2_hidden E D) <=>  (~  ( (~  ((r2_hidden E A) &  (~ (r2_xboole_0 B E)) ) )  &  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (~  ((r2_hidden F C) &  (E = (k8_finseq_1 k5_numbers B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k4_trees_2 A) = (k7_relat_1 A (k3_trees_1 (k9_xtuple_0 A)))) ) ) ).
tt(d9_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_trees_3 A) <=> (v1_trees_3 (k10_xtuple_0 A))) ) ) ).
tt(d9_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((k7_trees_9 A B) = (a_2_0_trees_9 A B)) ) ) ) ).
tt(d9_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc E A) &  ((r2_hidden C E) &  (~ (r2_hidden D E)) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc E A) &  ( (~ (r2_hidden C E))  & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (C = (k1_tsp_2 A B))  <=> (v3_borsuk_1 C A B)) ) ) ) ) ) ) ).
tt(d9_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ((v2_turing_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  ( (C = (k11_turing_1 A B))  <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ( (C = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) D))  &  ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) D)) = (u5_turing_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_twoscomp,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (A = k10_twoscomp)  <=>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k1_funct_1 A (k10_finseq_1 B C)) = (k1_binarith (k9_margrel1 B) (k9_margrel1 C))) ) ) ) ) ) ) ) ).
tt(d9_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_unialg_2 C A) =>  ( (~ (r2_subset_1 (u1_struct_0 B) (u1_struct_0 C)))  =>  (! [D:$i] :  ( ((v1_unialg_1 D) & (m1_unialg_2 D A))  =>  ( (D = (k5_unialg_2 A B C))  <=>  ( ((u1_struct_0 D) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C)))  &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (E = (u1_struct_0 D))  =>  ( ((u1_unialg_1 D) = (k3_unialg_2 A E))  & (v1_unialg_2 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (C = (k8_uproots A B))  <=>  ( ((k13_pre_poly C) = (k6_polynom5 A B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_recdef_1 C D) = (k7_uproots A D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_valued_0 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v1_xreal_0 (k1_funct_1 A B))) ) ) ) ) ).
tt(d9_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k45_valued_1 A B) = (k1_valued_1 A (k30_valued_1 B))) ) ) ) ) ).
tt(d9_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ( (B = (k3_valued_2 A))  <=>  (! [C:$i] :  ((r2_hidden C B) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ) ) ) ) ).
tt(d9_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (l3_algstr_0 B))  =>  ( (B = (k5_vectmetr A))  <=>  ( ((u1_struct_0 B) = (k2_vectmetr (k4_vectmetr A)))  &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden C (k2_vectmetr (k4_vectmetr A))) & (r2_hidden D (k2_vectmetr (k4_vectmetr A))))  =>  ((k1_binop_1 (u2_algstr_0 B) C D) = (k3_relat_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k8_vectsp10 A B C) = (a_3_1_vectsp10 A B C)) ) ) ) ) ) ) ).
tt(d9_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v33_algstr_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  ((v4_vectsp_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((k5_vectsp_2 A B C (k1_algstr_0 B E F)) = (k1_algstr_0 B (k5_vectsp_2 A B C E) (k5_vectsp_2 A B C F)))  &  ( ((k5_vectsp_2 A B (k1_algstr_0 A C D) E) = (k1_algstr_0 B (k5_vectsp_2 A B C E) (k5_vectsp_2 A B D E)))  &  ( ((k5_vectsp_2 A B (k6_algstr_0 A D C) E) = (k5_vectsp_2 A B C (k5_vectsp_2 A B D E)))  &  ((k5_vectsp_2 A B (k1_group_1 A) E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ( (E = (k6_vectsp_6 A B C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E F) = (k6_algstr_0 A C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m4_vectsp_8 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_lattices A D E)) = (k3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v8_waybel_0 B A) <=> (v5_orders_3 (k1_waybel_0 A B) B A)) ) ) ) ) ).
tt(d9_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v8_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_orders_2 B C D) => (r3_orders_2 A (k2_waybel_0 A B C) (k2_waybel_0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel18,ax, (! [A:$i] :  ( ((v1_pre_topc A) & (l1_pre_topc A))  =>  ( (A = k9_waybel18)  <=>  ( ((u1_struct_0 A) = (k2_tarski k6_numbers 1))  &  ((u1_pre_topc A) = (k1_enumset1 k1_xboole_0 (k1_tarski 1) (k2_tarski k6_numbers 1))) ) ) ) ) ).
tt(d9_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_waybel_1 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  (C = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_waybel23 B A) <=> (r2_hidden (k4_yellow_0 A) B)) ) ) ) ) ).
tt(d9_waybel34,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_waybel34 C A B) <=>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C))) & (m1_subset_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc B (k2_relset_1 (u1_struct_0 B) C)))))) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel35 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r1_yellow_0 A C) =>  ((k1_yellow_0 A C) = (k1_yellow_0 (k5_yellow_0 A B) C)) ) ) ) ) ) ) ) ) ).
tt(d9_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B C) &  ((v3_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k1_tops_1 A D)) &  ((r1_tarski D C) & (v2_compts_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (B = (k4_waybel_4 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C D) B) <=>  (C = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_9 A B C) <=>  (! [D:$i] :  ((m1_connsp_2 D A C) => (r2_waybel_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(d9_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((k9_weierstr A B C) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) C))) ) ) ) ) ) ) ).
tt(d9_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((v2_wellord1 A) & (r4_wellord1 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_wellord1 A B))  <=> (r3_wellord1 A B C)) ) ) ) ) ) ) ) ).
tt(d9_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ((r3_xboole_0 A B) <=>  ((r1_tarski A B) | (r1_tarski B A)) ) ) ) ).
tt(d9_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A B) = (k3_xboolean (k4_xboolean A B))) ) ) ) ) ).
tt(d9_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 A B) = (k3_xcmplx_0 A (k5_xcmplx_0 B))) ) ) ) ) ).
tt(d9_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((r1_xxreal_0 A B) =>  ((k3_xxreal_0 A B) = A) )  &  ( (~ (r1_xxreal_0 A B))  =>  ((k3_xxreal_0 A B) = B) ) ) ) ) ) ) ).
tt(d9_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((v3_xxreal_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) & (m2_xxreal_2 B A)) ) ) ) ) ).
tt(d9_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_0 A B) =>  ( (C = (k1_yellow_0 A B))  <=>  ((r2_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_yellow18 A B) = (k9_xtuple_0 (k8_altcat_1 A B))) ) ) ) ) ).
tt(d9_yellow21,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v5_yellow21 A) <=>  (? [B:$i] :  (! [C:$i] :  ((r2_hidden C (k1_relat_1 A)) => (r2_hidden (k4_tarski C B) A)) ) ) ) ) ) ).
tt(d9_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((m2_yellow_6 C A B) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  &  ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_waybel_0 A C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) D (u1_waybel_0 A B))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r1_orders_2 C F G) => (r1_orders_2 B E (k2_yellow_6 (u1_struct_0 C) B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v4_zf_fund1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (a_3_0_zf_fund1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(d9_zf_lang,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((v1_zf_lang A) <=> (m1_subset_1 A k9_zf_lang)) ) ) ).
tt(d9_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((r5_zfmisc_1 A B C D E F G) <=>  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (A = E) )  &  ( (~  (A = F) )  &  ( (~  (A = G) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (B = G) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(d9_zf_model,ax, (k9_zf_model = (k15_zf_lang (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k7_zf_lang (k5_zf_lang (k2_zf_lang 1) (k2_zf_lang k6_numbers)) (k8_zf_lang (k2_zf_lang 2) (k11_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang k6_numbers)) (k13_zf_lang (k2_zf_lang 3) (k7_zf_lang (k7_zf_lang (k5_zf_lang (k2_zf_lang 3) (k2_zf_lang k6_numbers)) (k6_zf_lang (k4_zf_lang (k2_zf_lang 3) (k2_zf_lang 2)))) (k8_zf_lang (k2_zf_lang 4) (k11_zf_lang (k5_zf_lang (k2_zf_lang 4) (k2_zf_lang 2)) (k5_zf_lang (k2_zf_lang 4) (k2_zf_lang 3))))))))))) ).
tt(d9_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  ((m1_zmodul01 B A) <=>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ((u1_zmodul01 B) = (k2_partfun1 (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_zmodul01 A) (k2_zfmisc_1 k4_numbers (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(dt_g1_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v3_abcmiz_0 (g1_abcmiz_0 A B)) & (l1_abcmiz_0 (g1_abcmiz_0 A B))) ) ) ).
tt(dt_g1_algstr_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k3_zfmisc_1 A A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A A A) A)))) ) ) )  =>  ((v1_algstr_3 (g1_algstr_3 A B C D)) & (l1_algstr_3 (g1_algstr_3 A B C D))) ) ) ).
tt(dt_g1_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  =>  ((v1_analmetr (g1_analmetr A B C)) & (l1_analmetr (g1_analmetr A B C))) ) ) ).
tt(dt_g1_analoaf,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ((v1_analoaf (g1_analoaf A B)) & (l1_analoaf (g1_analoaf A B))) ) ) ).
tt(dt_g1_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k4_card_3 B)))) )  =>  ((v2_armstrng (g1_armstrng A B C)) & (l1_armstrng (g1_armstrng A B C))) ) ) ).
tt(dt_g1_bcialg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 D A)) )  =>  ((v1_bcialg_4 (g1_bcialg_4 A B C D)) & (l1_bcialg_4 (g1_bcialg_4 A B C D))) ) ) ).
tt(dt_g1_bhsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) )  =>  ((v1_bhsp_1 (g1_bhsp_1 A B C D E)) & (l1_bhsp_1 (g1_bhsp_1 A B C D E))) ) ) ).
tt(dt_g1_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) )  =>  ((v1_cat_1 (g1_cat_1 A B C D E)) & (l1_cat_1 (g1_cat_1 A B C D E))) ) ) ).
tt(dt_g1_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  &  ((m1_subset_1 F A) &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) )  &  ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 A A) B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) ) ) ) ) ) ) )  =>  ((v2_cat_4 (g1_cat_4 A B C D E F G H I)) & (l1_cat_4 (g1_cat_4 A B C D E F G H I))) ) ) ).
tt(dt_g1_cfuncdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) )  =>  ((v1_cfuncdom (g1_cfuncdom A B C D E F)) & (l1_cfuncdom (g1_cfuncdom A B C D E F))) ) ) ).
tt(dt_g1_cgames_1,ax, (! [A:$i,B:$i] :  ((v1_cgames_1 (g1_cgames_1 A B)) & (l1_cgames_1 (g1_cgames_1 A B))) ) ).
tt(dt_g1_clopban2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) )  =>  ((v1_clopban2 (g1_clopban2 A B C D E F G)) & (l1_clopban2 (g1_clopban2 A B C D E F G))) ) ) ).
tt(dt_g1_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) B))) )  =>  ((v5_closure1 (g1_closure1 A B C) A) & (l1_closure1 (g1_closure1 A B C) A)) ) ) ).
tt(dt_g1_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) B)))) )  =>  ((v11_closure2 (g1_closure2 A B C) A) & (l1_closure2 (g1_closure2 A B C) A)) ) ) ).
tt(dt_g1_clvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) ) ) )  =>  ((v1_clvect_1 (g1_clvect_1 A B C D)) & (l1_clvect_1 (g1_clvect_1 A B C D))) ) ) ).
tt(dt_g1_collsp,ax, (! [A:$i,B:$i] :  ((m1_collsp B A) =>  ((v1_collsp (g1_collsp A B)) & (l1_collsp (g1_collsp A B))) ) ) ).
tt(dt_g1_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_incsp_1 A) (u1_incsp_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u2_incsp_1 A) (u2_incsp_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u2_incsp_1 A) (u2_incsp_1 B))))) ) ) ) )  =>  ((v5_combgras (g1_combgras A B C D) A B) & (l1_combgras (g1_combgras A B C D) A B)) ) ) ).
tt(dt_g1_compos_1,ax, (! [A:$i] :  ( ((v1_compos_0 A) &  ((v2_compos_0 A) &  ((v3_compos_0 A) & (v5_compos_0 A)) ) )  =>  ((v1_compos_1 (g1_compos_1 A)) & (l1_compos_1 (g1_compos_1 A))) ) ) ).
tt(dt_g1_conlat_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v2_conlat_1 (g1_conlat_1 A B C)) & (l1_conlat_1 (g1_conlat_1 A B C))) ) ) ).
tt(dt_g1_csspace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k2_numbers)))) ) ) ) )  =>  ((v1_csspace (g1_csspace A B C D E)) & (l1_csspace (g1_csspace A B C D E))) ) ) ).
tt(dt_g1_e_siec,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) & (v1_relat_1 C))  =>  ((v1_e_siec (g1_e_siec A B C)) & (l1_e_siec (g1_e_siec A B C))) ) ) ).
tt(dt_g1_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((m1_subset_1 C B) &  ( ((v1_compos_0 D) &  ((v2_compos_0 D) &  ((v3_compos_0 D) & (v5_compos_0 D)) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G D (k1_funct_2 (k4_card_3 (k3_relat_1 E F)) (k4_card_3 (k3_relat_1 E F)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 D (k1_funct_2 (k4_card_3 (k3_relat_1 E F)) (k4_card_3 (k3_relat_1 E F))))))) ) ) ) ) )  =>  ((v1_extpro_1 (g1_extpro_1 A B C D E F G) A) & (l1_extpro_1 (g1_extpro_1 A B C D E F G) A)) ) ) ).
tt(dt_g1_fomodel1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k6_subset_1 A (k1_tarski C)) k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 A (k1_tarski C)) k4_numbers)))) ) ) )  =>  ((v1_fomodel1 (g1_fomodel1 A B C D)) & (l1_fomodel1 (g1_fomodel1 A B C D))) ) ) ).
tt(dt_g1_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C B) C))) & (m1_subset_1 E (k1_zfmisc_1 C))) ) )  =>  ((v1_fsm_3 (g1_fsm_3 A B C D E) A B) & (l1_fsm_3 (g1_fsm_3 A B C D E) A B)) ) ) ).
tt(dt_g1_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) )  =>  ((v1_funcsdom (g1_funcsdom A B C D E F)) & (l1_funcsdom (g1_funcsdom A B C D E F))) ) ) ).
tt(dt_g1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  =>  ((v1_geomtrap (g1_geomtrap A B C)) & (l1_geomtrap (g1_geomtrap A B C))) ) ) ).
tt(dt_g1_graph_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) )  =>  ((v1_graph_1 (g1_graph_1 A B C D)) & (l1_graph_1 (g1_graph_1 A B C D))) ) ) ).
tt(dt_g1_grcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_grcat_1 (g1_grcat_1 A B C)) & (l1_grcat_1 (g1_grcat_1 A B C))) ) ) ).
tt(dt_g1_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) ) )  =>  ((v2_group_9 (g1_group_9 A B C D) A) & (l1_group_9 (g1_group_9 A B C D) A)) ) ) ).
tt(dt_g1_incsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_incsp_1 (g1_incsp_1 A B C)) & (l1_incsp_1 (g1_incsp_1 A B C))) ) ) ).
tt(dt_g1_lang1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 A)))) =>  ((v1_lang1 (g1_lang1 A B)) & (l1_lang1 (g1_lang1 A B))) ) ) ).
tt(dt_g1_lattices,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_lattices (g1_lattices A B)) & (l1_lattices (g1_lattices A B))) ) ) ).
tt(dt_g1_lopban_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) )  =>  ((v1_lopban_2 (g1_lopban_2 A B C D E F G)) & (l1_lopban_2 (g1_lopban_2 A B C D E F G))) ) ) ).
tt(dt_g1_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C B) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) ) ) )  =>  ((v1_memstr_0 (g1_memstr_0 A B C D E) A) & (l1_memstr_0 (g1_memstr_0 A B C D E) A)) ) ) ).
tt(dt_g1_metric_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((v1_metric_1 (g1_metric_1 A B)) & (l1_metric_1 (g1_metric_1 A B))) ) ) ).
tt(dt_g1_midsp_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_midsp_1 (g1_midsp_1 A B)) & (l1_midsp_1 (g1_midsp_1 A B))) ) ) ).
tt(dt_g1_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) ) ) )  =>  ((v1_midsp_3 (g1_midsp_3 A B C D) A) & (l1_midsp_3 (g1_midsp_3 A B C D) A)) ) ) ).
tt(dt_g1_mod_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  ((v2_mod_2 (g1_mod_2 A B C D) A) & (l1_mod_2 (g1_mod_2 A B C D) A)) ) ) ).
tt(dt_g1_modelc_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) ) )  =>  ((v9_modelc_2 (g1_modelc_2 A B C D E F G H)) & (l1_modelc_2 (g1_modelc_2 A B C D E F G H))) ) ) ).
tt(dt_g1_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B (k1_zfmisc_1 (k1_modelc_3 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (k1_modelc_3 A))) & (m1_subset_1 D (k1_zfmisc_1 (k1_modelc_3 A)))) ) )  =>  ((v1_modelc_3 (g1_modelc_3 A B C D) A) & (l1_modelc_3 (g1_modelc_3 A B C D) A)) ) ) ).
tt(dt_g1_msualg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_finseq_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_finseq_2 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) )  =>  ((v1_msualg_1 (g1_msualg_1 A B C D)) & (l1_msualg_1 (g1_msualg_1 A B C D))) ) ) ).
tt(dt_g1_normsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v1_normsp_1 (g1_normsp_1 A B C D E)) & (l1_normsp_1 (g1_normsp_1 A B C D E))) ) ) ).
tt(dt_g1_orders_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_orders_2 (g1_orders_2 A B)) & (l1_orders_2 (g1_orders_2 A B))) ) ) ).
tt(dt_g1_parsp_1,ax, (! [A:$i,B:$i] :  ((m1_parsp_1 B A) =>  ((v1_parsp_1 (g1_parsp_1 A B)) & (l1_parsp_1 (g1_parsp_1 A B))) ) ) ).
tt(dt_g1_pcs_0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v2_pcs_0 (g1_pcs_0 A B)) & (l1_pcs_0 (g1_pcs_0 A B))) ) ) ).
tt(dt_g1_petri,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ((v1_petri (g1_petri A B C D)) & (l1_petri (g1_petri A B C D))) ) ) ).
tt(dt_g1_polyalg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 E B) &  ((m1_subset_1 F B) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) ) ) ) ) ) )  =>  ((v1_polyalg1 (g1_polyalg1 A B C D E F G) A) & (l1_polyalg1 (g1_polyalg1 A B C D E F G) A)) ) ) ).
tt(dt_g1_pre_topc,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_pre_topc (g1_pre_topc A B)) & (l1_pre_topc (g1_pre_topc A B))) ) ) ).
tt(dt_g1_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) (k1_qmax_1 k1_numbers k12_prob_1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k1_qmax_1 k1_numbers k12_prob_1))))) ) ) )  =>  ((v1_qmax_1 (g1_qmax_1 A B C)) & (l1_qmax_1 (g1_qmax_1 A B C))) ) ) ).
tt(dt_g1_rewrite3,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B))) =>  ((v1_rewrite3 (g1_rewrite3 A B C) A) & (l1_rewrite3 (g1_rewrite3 A B C) A)) ) ) ).
tt(dt_g1_ringcat1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v2_ringcat1 (g1_ringcat1 A B C)) & (l1_ringcat1 (g1_ringcat1 A B C))) ) ) ).
tt(dt_g1_rltopsp1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((v5_rltopsp1 (g1_rltopsp1 A B C D E)) & (l1_rltopsp1 (g1_rltopsp1 A B C D E))) ) ) ).
tt(dt_g1_rlvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) )  =>  ((v1_rlvect_1 (g1_rlvect_1 A B C D)) & (l1_rlvect_1 (g1_rlvect_1 A B C D))) ) ) ).
tt(dt_g1_sgraph1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_sgraph1 A))) =>  ((v1_sgraph1 (g1_sgraph1 A B)) & (l1_sgraph1 (g1_sgraph1 A B))) ) ) ).
tt(dt_g1_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_stacks_1 (g1_stacks_1 A B C D E F)) & (l1_stacks_1 (g1_stacks_1 A B C D E F))) ) ) ).
tt(dt_g1_struct_0,ax, (! [A:$i] :  ((v1_struct_0 (g1_struct_0 A)) & (l1_struct_0 (g1_struct_0 A))) ) ).
tt(dt_g1_symsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) )  & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) )  =>  ((v1_symsp_1 (g1_symsp_1 A B C D E F) A) & (l1_symsp_1 (g1_symsp_1 A B C D E F) A)) ) ) ).
tt(dt_g1_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B A) (k3_zfmisc_1 B A (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) (k3_zfmisc_1 B A (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) )  &  ((m1_subset_1 D B) & (m1_subset_1 E B)) ) ) )  =>  ((v1_turing_1 (g1_turing_1 A B C D E)) & (l1_turing_1 (g1_turing_1 A B C D E))) ) ) ).
tt(dt_g1_unialg_1,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)) =>  ((v1_unialg_1 (g1_unialg_1 A B)) & (l1_unialg_1 (g1_unialg_1 A B))) ) ) ).
tt(dt_g1_vectmetr,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  &  ((m1_subset_1 C A) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) ) )  =>  ((v4_vectmetr (g1_vectmetr A B C D E)) & (l1_vectmetr (g1_vectmetr A B C D E))) ) ) ).
tt(dt_g1_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) ) ) ) )  =>  ((v7_vectsp_1 (g1_vectsp_1 A B C D E) A) & (l1_vectsp_1 (g1_vectsp_1 A B C D E) A)) ) ) ).
tt(dt_g1_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) ) ) ) )  =>  ((v2_vectsp_2 (g1_vectsp_2 A B C D E) A) & (l1_vectsp_2 (g1_vectsp_2 A B C D E) A)) ) ) ).
tt(dt_g1_waybel_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) &  ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ((v6_waybel_0 (g1_waybel_0 A B C D) A) & (l1_waybel_0 (g1_waybel_0 A B C D) A)) ) ) ).
tt(dt_g1_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_waybel_9 (g1_waybel_9 A B C)) & (l1_waybel_9 (g1_waybel_9 A B C))) ) ) ).
tt(dt_g1_zmodul01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k4_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers A) A)))) ) ) )  =>  ((v1_zmodul01 (g1_zmodul01 A B C D)) & (l1_zmodul01 (g1_zmodul01 A B C D))) ) ) ).
tt(dt_g2_abcmiz_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A (k5_finsub_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) ) )  =>  ((v7_abcmiz_0 (g2_abcmiz_0 A B C D E)) & (l2_abcmiz_0 (g2_abcmiz_0 A B C D E))) ) ) ).
tt(dt_g2_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  ((v8_algstr_0 (g2_algstr_0 A B C)) & (l2_algstr_0 (g2_algstr_0 A B C))) ) ) ).
tt(dt_g2_altcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  & (m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)))  =>  ((v6_altcat_1 (g2_altcat_1 A B C)) & (l2_altcat_1 (g2_altcat_1 A B C))) ) ) ).
tt(dt_g2_bcialg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  ((v2_bcialg_1 (g2_bcialg_1 A B C)) & (l2_bcialg_1 (g2_bcialg_1 A B C))) ) ) ).
tt(dt_g2_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  &  ((m1_subset_1 F A) &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) )  &  ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 A A) B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) ) ) ) ) ) ) )  =>  ((v5_cat_4 (g2_cat_4 A B C D E F G H I)) & (l2_cat_4 (g2_cat_4 A B C D E F G H I))) ) ) ).
tt(dt_g2_clvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v7_clvect_1 (g2_clvect_1 A B C D E)) & (l2_clvect_1 (g2_clvect_1 A B C D E))) ) ) ).
tt(dt_g2_conlat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l5_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A)))) )  =>  ((v4_conlat_1 (g2_conlat_1 A B C) A) & (l2_conlat_1 (g2_conlat_1 A B C) A)) ) ) ).
tt(dt_g2_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  & (m1_subset_1 F C)) ) )  =>  ((v2_fsm_1 (g2_fsm_1 A B C D E F) A B) & (l2_fsm_1 (g2_fsm_1 A B C D E F) A B)) ) ) ).
tt(dt_g2_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  &  ((m1_subset_1 F C) & (m1_subset_1 G (k1_zfmisc_1 C))) ) ) )  =>  ((v6_fsm_2 (g2_fsm_2 A B C D E F G) A B) & (l2_fsm_2 (g2_fsm_2 A B C D E F G) A B)) ) ) ).
tt(dt_g2_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C B) C))) &  ((m1_subset_1 E (k1_zfmisc_1 C)) & (m1_subset_1 F (k1_zfmisc_1 C))) ) ) )  =>  ((v3_fsm_3 (g2_fsm_3 A B C D E F) A B) & (l2_fsm_3 (g2_fsm_3 A B C D E F) A B)) ) ) ).
tt(dt_g2_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))))) )  & (m1_functor0 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) C (u1_altcat_1 A) (u1_altcat_1 B))) ) )  =>  ((v9_functor0 (g2_functor0 A B C D) A B) & (l2_functor0 (g2_functor0 A B C D) A B)) ) ) ).
tt(dt_g2_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 A)))))  =>  ((v2_lang1 (g2_lang1 A B C)) & (l2_lang1 (g2_lang1 A B C))) ) ) ).
tt(dt_g2_lattices,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_lattices (g2_lattices A B)) & (l2_lattices (g2_lattices A B))) ) ) ).
tt(dt_g2_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) )  =>  ((v9_modelc_1 (g2_modelc_1 A B C D E F G)) & (l2_modelc_1 (g2_modelc_1 A B C D E F G))) ) ) ).
tt(dt_g2_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B))) &  ((m1_subset_1 D (k1_zfmisc_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  ((v7_modelc_3 (g2_modelc_3 A B C D E) A) & (l2_modelc_3 (g2_modelc_3 A B C D E) A)) ) ) ).
tt(dt_g2_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((v12_pcs_0 (g2_pcs_0 A B C)) & (l2_pcs_0 (g2_pcs_0 A B C))) ) ) ).
tt(dt_g2_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v3_qmax_1 (g2_qmax_1 A B C)) & (l2_qmax_1 (g2_qmax_1 A B C))) ) ) ).
tt(dt_g2_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v2_robbins1 (g2_robbins1 A B C)) & (l2_robbins1 (g2_robbins1 A B C))) ) ) ).
tt(dt_g2_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  &  ((m1_subset_1 E C) &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 A) C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) C) C)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C (u1_struct_0 B)) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 B)) C)))) ) ) ) ) ) )  =>  ((v3_vectsp_2 (g2_vectsp_2 A B C D E F G) A B) & (l2_vectsp_2 (g2_vectsp_2 A B C D E F G) A B)) ) ) ).
tt(dt_g3_algstr_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v15_algstr_0 (g3_algstr_0 A B)) & (l3_algstr_0 (g3_algstr_0 A B))) ) ) ).
tt(dt_g3_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  & (m1_subset_1 F C)) ) )  =>  ((v3_fsm_1 (g3_fsm_1 A B C D E F) A B) & (l3_fsm_1 (g3_fsm_1 A B C D E F) A B)) ) ) ).
tt(dt_g3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ((v3_lattices (g3_lattices A B C)) & (l3_lattices (g3_lattices A B C))) ) ) ).
tt(dt_g3_msualg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) B)) (k3_relat_1 (u2_msualg_1 A) B))) )  =>  ((v3_msualg_1 (g3_msualg_1 A B C) A) & (l3_msualg_1 (g3_msualg_1 A B C) A)) ) ) ).
tt(dt_g3_osalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (k3_finseq_2 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (k3_finseq_2 A))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C A)))) ) ) ) )  =>  ((v3_osalg_1 (g3_osalg_1 A B C D E F)) & (l3_osalg_1 (g3_osalg_1 A B C D E F))) ) ) ).
tt(dt_g3_robbins3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v6_robbins3 (g3_robbins3 A B C D)) & (l3_robbins3 (g3_robbins3 A B C D))) ) ) ).
tt(dt_g4_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  ((v22_algstr_0 (g4_algstr_0 A B C)) & (l4_algstr_0 (g4_algstr_0 A B C))) ) ) ).
tt(dt_g4_robbins1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v4_robbins1 (g4_robbins1 A B C D)) & (l4_robbins1 (g4_robbins1 A B C D))) ) ) ).
tt(dt_g5_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  =>  ((v29_algstr_0 (g5_algstr_0 A B C D)) & (l5_algstr_0 (g5_algstr_0 A B C D))) ) ) ).
tt(dt_g6_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) )  =>  ((v36_algstr_0 (g6_algstr_0 A B C D E)) & (l6_algstr_0 (g6_algstr_0 A B C D E))) ) ) ).
tt(dt_k10_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) )  & (m1_subset_1 B (u1_abcmiz_0 A)))  => (m1_subset_1 (k10_abcmiz_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k10_abcmiz_1,ax,$true).
tt(dt_k10_abcmiz_a,ax,$true).
tt(dt_k10_afinsq_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  => (m2_finseq_1 (k10_afinsq_1 A B) A)) ) ).
tt(dt_k10_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~ (v1_xboole_0 (k10_afproj A))) ) ) ).
tt(dt_k10_algstr_4,ax, (! [A:$i] :  ((v1_funct_1 (k10_algstr_4 A)) &  ((v1_funct_2 (k10_algstr_4 A) k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers)))) & (m1_subset_1 (k10_algstr_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k1_yellow_6 (k2_xboole_0 A k5_numbers))))))) ) ) ).
tt(dt_k10_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_ami_2 (k10_ami_3 A)) & (m1_subset_1 (k10_ami_3 A) (u1_struct_0 k1_ami_3))) ) ) ).
tt(dt_k10_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m1_subset_1 (k10_aofa_000 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((v1_funct_1 (k10_aofa_i00 A B C)) &  ((v1_funct_2 (k10_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k10_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k10_armstrng,ax, (! [A:$i,B:$i] : (m1_subset_1 (k10_armstrng A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ).
tt(dt_k10_arytm_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_arytm_3) & (m1_subset_1 B k5_arytm_3))  => (m1_subset_1 (k10_arytm_3 A B) k5_arytm_3)) ) ).
tt(dt_k10_asympt_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k10_asympt_0 A B) k5_numbers k1_numbers)) ) ).
tt(dt_k10_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  => (l2_bcialg_1 (k10_bcialg_6 A B C D))) ) ).
tt(dt_k10_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l2_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) )  => (m1_subset_1 (k10_bilinear A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k10_binarith,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((v3_card_1 (k10_binarith A B) 1) & (m2_finseq_1 (k10_binarith A B) A)) ) ) ).
tt(dt_k10_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k10_binop_2 A B) k1_numbers)) ) ).
tt(dt_k10_bor_cant,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) )  => (m1_prob_1 (k10_bor_cant A B C) A B)) ) ).
tt(dt_k10_borsuk_1,ax, (! [A:$i] :  ((l1_struct_0 A) => (m1_eqrel_1 (k10_borsuk_1 A) (u1_struct_0 A))) ) ).
tt(dt_k10_borsuk_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  & (m1_subset_1 B k1_numbers))  =>  ((v1_funct_1 (k10_borsuk_7 A B)) &  ((v1_funct_2 (k10_borsuk_7 A B) (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A)) (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A))) & (m1_subset_1 (k10_borsuk_7 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A)) (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A)))))) ) ) ) ).
tt(dt_k10_bspace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k10_bspace A B C D) (u1_struct_0 A))) ) ).
tt(dt_k10_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k10_bvfunc_1 A B C)) &  ((v1_funct_2 (k10_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k10_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k10_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k10_c0sp1 A)) &  ((v1_funct_2 (k10_c0sp1 A) (k6_c0sp1 A) k1_numbers) & (m1_subset_1 (k10_c0sp1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_c0sp1 A) k1_numbers)))) ) ) ) ).
tt(dt_k10_card_3,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((v1_relat_1 (k10_card_3 A)) & (v1_funct_1 (k10_card_3 A))) ) ) ).
tt(dt_k10_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m2_cat_1 (k10_cat_1 A) A A)) ) ).
tt(dt_k10_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m1_subset_1 C (u4_struct_0 A)) & (m1_subset_1 D (u4_struct_0 B))) ) )  => (m1_subset_1 (k10_cat_2 A B C D) (u4_struct_0 (k8_cat_2 A B)))) ) ).
tt(dt_k10_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k10_cat_3 A B C) A B C)) ) ).
tt(dt_k10_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k10_cat_4 A B) A (k2_cat_4 A (k1_cat_4 A) B) B)) ) ).
tt(dt_k10_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k10_cat_5 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k10_catalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k10_catalg_1 A B C D) (u4_struct_0 (k3_catalg_1 A)))) ) ).
tt(dt_k10_cgames_1,ax,$true).
tt(dt_k10_chain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B (k2_nat_1 C 1))))) ) )  => (m1_subset_1 (k10_chain_1 A B C D) (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ).
tt(dt_k10_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k9_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k10_clopban1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k10_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B)) &  ((v7_closure2 C (u1_struct_0 A) B) &  ((v8_closure2 C (u1_struct_0 A) B) &  ((v9_closure2 C (u1_struct_0 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B))))) ) ) ) ) ) )  =>  ((v11_closure2 (k10_closure2 A B C) A) & (l1_closure2 (k10_closure2 A B C) A)) ) ) ).
tt(dt_k10_cohsp_1,ax,$true).
tt(dt_k10_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k10_coh_sp A)) &  ((v1_funct_2 (k10_coh_sp A) (k5_coh_sp A) (k3_coh_sp A)) & (m1_subset_1 (k10_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k3_coh_sp A))))) ) ) ).
tt(dt_k10_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (m1_subset_1 (k10_complex1 A) k2_numbers)) ) ).
tt(dt_k10_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((v1_relat_1 (k10_compos_1 A B)) &  ((v4_relat_1 (k10_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k10_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k10_compos_1 A B)) & (v1_finset_1 (k10_compos_1 A B))) ) ) ) ) ) ).
tt(dt_k10_comput_1,ax,(m1_subset_1 k10_comput_1 (k1_zfmisc_1 (k2_comput_1 k5_numbers)))).
tt(dt_k10_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_funct_1 (k10_comseq_3 A)) &  ((v1_funct_2 (k10_comseq_3 A) k5_numbers k2_numbers) & (m1_subset_1 (k10_comseq_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k10_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k10_conlat_1 A)) &  ((v1_funct_2 (k10_conlat_1 A) (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A)) & (m1_subset_1 (k10_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A))))) ) ) ) ).
tt(dt_k10_convex4,ax,$true).
tt(dt_k10_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k10_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k10_cqc_sim1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k1_qc_lang1 A)) & (m1_subset_1 D (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)))) ) )  => (m2_subset_1 (k10_cqc_sim1 A B C D) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k10_csspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k10_csspace A B) B)) ) ).
tt(dt_k10_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k10_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k10_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) & (v7_ordinal1 C)) )  => (m1_subset_1 (k10_descip_1 A B C) k6_margrel1)) ) ).
tt(dt_k10_dickson,ax,(m1_subset_1 k10_dickson (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))).
tt(dt_k10_diff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k10_diff_1 A B C D) k1_numbers)) ) ).
tt(dt_k10_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (m2_subset_1 (k10_dist_1 A) (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A))) ) ).
tt(dt_k10_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  => (m1_subset_1 (k10_domain_1 A B C D E F) (k1_zfmisc_1 A))) ) ).
tt(dt_k10_dtconstr,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k7_dtconstr k5_dtconstr)) & (m1_subset_1 B (k4_dtconstr k5_dtconstr)))  => (m1_dtconstr (k10_dtconstr A B) (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr))) ) ).
tt(dt_k10_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k10_ens_1 A)) & (m1_subset_1 (k10_ens_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) (k2_ens_1 A)) (k2_ens_1 A))))) ) ) ).
tt(dt_k10_eqrel_1,ax, (! [A:$i] : (m1_eqrel_1 (k10_eqrel_1 A) A)) ).
tt(dt_k10_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k10_e_siec A))) ) ).
tt(dt_k10_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (u1_struct_0 (k15_euclid A)))) ) ) )  => (m1_subset_1 (k10_euclid_3 A B C D E) k1_numbers)) ) ).
tt(dt_k10_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  => (m2_finseq_2 (k10_euclid A B) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k10_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((v3_msualg_1 (k10_facirc_1 A B C D) (k8_facirc_1 A B C D)) &  ((v4_msafree2 (k10_facirc_1 A B C D) (k8_facirc_1 A B C D)) &  ((v4_circcomb (k10_facirc_1 A B C D) (k8_facirc_1 A B C D)) &  ((v6_circcomb (k10_facirc_1 A B C D) (k8_facirc_1 A B C D)) & (l3_msualg_1 (k10_facirc_1 A B C D) (k8_facirc_1 A B C D))) ) ) ) ) ) ).
tt(dt_k10_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k10_ff_siec A))) ) ).
tt(dt_k10_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v3_relat_2 (k10_filter_0 A B)) &  ((v8_relat_2 (k10_filter_0 A B)) &  ((v1_partfun1 (k10_filter_0 A B) (u1_struct_0 A)) & (m1_subset_1 (k10_filter_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k10_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (m2_nat_lat (k10_filter_2 A B) A)) ) ).
tt(dt_k10_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D A) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k10_finance1 A B C D E F)) &  ((v1_funct_2 (k10_finance1 A B C D E F) k5_numbers k1_numbers) & (m1_subset_1 (k10_finance1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k10_finseq_1,ax,$true).
tt(dt_k10_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  => (m2_finseq_1 (k10_finseq_4 A B C D E F) A)) ) ).
tt(dt_k10_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k10_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_fintopo3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k10_fintopo3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k10_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_fomodel1,ax,$true).
tt(dt_k10_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_funct_1 (k10_fomodel2 A B C)) &  ((v1_funct_2 (k10_fomodel2 A B C) (k35_fomodel1 A) B) & (m1_subset_1 (k10_fomodel2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) B)))) ) ) ) ).
tt(dt_k10_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_xboole_0 C) & (v7_ordinal1 C)) ) )  => (m1_subset_1 (k10_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A))))) ) ).
tt(dt_k10_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k10_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k10_freealg,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D (u1_struct_0 (k3_freealg A B))) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k9_freealg A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_freealg A B) C)))) ) ) ) ) )  => (m1_subset_1 (k10_freealg A B C D E) C)) ) ).
tt(dt_k10_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k10_ftacell1 A B C D E) (k3_msafree2 (k7_ftacell1 A B C D E)))) ).
tt(dt_k10_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_funct_1 (k10_funcop_1 A B C D E)) &  ((v1_funct_2 (k10_funcop_1 A B C D E) B A) & (m1_subset_1 (k10_funcop_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k10_funcsdom,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k10_funcsdom A)))  &  ((v13_algstr_0 (k10_funcsdom A)) &  ((v1_rlvect_1 (k10_funcsdom A)) &  ((v2_rlvect_1 (k10_funcsdom A)) &  ((v3_rlvect_1 (k10_funcsdom A)) &  ((v4_rlvect_1 (k10_funcsdom A)) &  ((v5_rlvect_1 (k10_funcsdom A)) &  ((v6_rlvect_1 (k10_funcsdom A)) &  ((v7_rlvect_1 (k10_funcsdom A)) &  ((v8_rlvect_1 (k10_funcsdom A)) & (l1_rlvect_1 (k10_funcsdom A))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k10_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  => (m1_subset_1 (k10_funct_2 A B C D) B)) ) ).
tt(dt_k10_funct_3,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k10_funct_3 A B)) &  ((v1_funct_2 (k10_funct_3 A B) (k2_zfmisc_1 A B) B) & (m1_subset_1 (k10_funct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) ) ) ).
tt(dt_k10_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 C))  &  ((m1_funct_2 D B C) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A D)))) )  & (m1_subset_1 F A)) ) ) )  => (m2_funct_2 (k10_funct_5 A B C D E F) B C D)) ) ).
tt(dt_k10_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k10_funct_6 A)) &  ((v1_funct_1 (k10_funct_6 A)) & (v1_funcop_1 (k10_funct_6 A))) ) ) ) ).
tt(dt_k10_funct_7,ax,$true).
tt(dt_k10_functor0,ax, (! [A:$i,B:$i] :  ( ((l2_altcat_1 A) & (m1_altcat_2 B A))  =>  ((v9_functor0 (k10_functor0 A B) B A) & (l2_functor0 (k10_functor0 A B) B A)) ) ) ).
tt(dt_k10_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m2_finseq_2 (k10_fvsum_1 A B C D) (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B)))) ) ).
tt(dt_k10_gate_1,ax,$true).
tt(dt_k10_gate_5,ax,$true).
tt(dt_k10_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) & (m1_subset_1 G k5_numbers)) ) ) ) ) )  => (m1_genealg1 (k10_genealg1 A B C D E F G) A)) ) ).
tt(dt_k10_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k10_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k10_gfacirc1 A B C)))  &  ((v1_msualg_1 (k10_gfacirc1 A B C)) &  ((v1_circcomb (k10_gfacirc1 A B C)) &  ((v2_circcomb (k10_gfacirc1 A B C)) &  ((v3_circcomb (k10_gfacirc1 A B C)) & (l1_msualg_1 (k10_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k10_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_funct_1 (k10_glib_000 A)) &  ((v1_funct_2 (k10_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k10_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) ) ) ) ).
tt(dt_k10_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m3_glib_001 (k10_glib_001 A B C) A)) ) ).
tt(dt_k10_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m3_glib_001 B A))  => (m1_subset_1 (k10_glib_003 A B) k1_numbers)) ) ).
tt(dt_k10_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m2_glib_004 (k10_glib_004 A B) A)) ) ).
tt(dt_k10_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  &  ((v5_glib_001 C A) & (m3_glib_001 C A)) ) )  =>  ((v1_relat_1 (k10_glib_005 A B C)) &  ((v4_relat_1 (k10_glib_005 A B C) (k7_glib_000 A)) &  ((v1_funct_1 (k10_glib_005 A B C)) &  ((v1_partfun1 (k10_glib_005 A B C) (k7_glib_000 A)) & (v4_valued_0 (k10_glib_005 A B C))) ) ) ) ) ) ).
tt(dt_k10_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k10_graph_1 A B) k5_numbers)) ) ).
tt(dt_k10_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k9_graph_3 A))) )  => (m2_finseq_2 (k10_graph_3 A B C) (u4_struct_0 A) (k9_graph_3 A))) ) ).
tt(dt_k10_graph_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_finseq_1 B (u4_struct_0 A)) &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  => (m1_subset_1 (k10_graph_5 A B C) k1_numbers)) ) ).
tt(dt_k10_graphsp,ax,$true).
tt(dt_k10_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  & (m1_subset_1 D (k1_zfmisc_1 B))) ) )  =>  ((v15_algstr_0 (k10_group_10 A B C D)) & (m1_group_2 (k10_group_10 A B C D) A)) ) ) ).
tt(dt_k10_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k10_group_2 A B C)) & (m1_group_2 (k10_group_2 A B C) A)) ) ) ).
tt(dt_k10_group_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v15_algstr_0 (k10_group_3 A B)) & (m1_group_2 (k10_group_3 A B) A)) ) ) ).
tt(dt_k10_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k10_group_4 A)) &  ((v1_funct_2 (k10_group_4 A) (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A)) & (m1_subset_1 (k10_group_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A))))) ) ) ) ).
tt(dt_k10_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k10_group_5 A)) & (m1_group_2 (k10_group_5 A) A)) ) ) ).
tt(dt_k10_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v15_algstr_0 (k10_group_6 A B C)) & (m1_group_2 (k10_group_6 A B C) B)) ) ) ).
tt(dt_k10_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  => (l1_group_9 (k10_group_9 A B C) A)) ) ).
tt(dt_k10_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  ((v1_rlvect_1 (k10_hahnban1 A)) & (l1_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(dt_k10_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) => (m1_subset_1 (k10_heyting1 A B) (k5_finsub_1 (u1_struct_0 (k12_normform A))))) ) ).
tt(dt_k10_idea_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k10_idea_1 A B) k5_numbers)) ) ).
tt(dt_k10_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k10_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_index_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)))  =>  ((v1_cat_1 (k10_index_1 A B)) & (m4_index_1 (k10_index_1 A B) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B)) ) ) ).
tt(dt_k10_integr15,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) ) )  => (m2_finseq_2 (k10_integr15 A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k10_integra1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  => (m1_subset_1 (k10_integra1 A B) k1_numbers)) ) ).
tt(dt_k10_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_interva1 B A)) )  =>  ( (~ (v1_xboole_0 (k10_interva1 A B)))  & (m1_interva1 (k10_interva1 A B) A)) ) ) ).
tt(dt_k10_intpro_1,ax,(m1_subset_1 k10_intpro_1 k1_intpro_1)).
tt(dt_k10_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  & (m2_cat_1 D A (k8_cat_2 B C))) ) )  => (m2_cat_1 (k10_isocat_2 A B C D) A C)) ) ).
tt(dt_k10_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k10_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k10_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k10_jordan6 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k10_jordan,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((v2_xxreal_0 D) & (v1_xreal_0 D)) ) ) )  =>  ((v1_funct_1 (k10_jordan A B C D)) &  ((v1_funct_2 (k10_jordan A B C D) (u1_struct_0 (k7_toprealb A B D)) (u1_struct_0 (k7_toprealb A B D))) & (m1_subset_1 (k10_jordan A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb A B D)) (u1_struct_0 (k7_toprealb A B D)))))) ) ) ) ).
tt(dt_k10_knaster,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k10_knaster A B) (u1_struct_0 A))) ) ).
tt(dt_k10_laplace,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k10_laplace A B) A 1 (k3_finseq_1 B))) ) ).
tt(dt_k10_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k10_lattice3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k10_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_funct_1 (k10_lattice5 A B C)) &  ((v1_funct_2 (k10_lattice5 A B C) (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 (k10_lattice5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k10_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))))  => (m1_subset_1 (k10_lexbfs A B) (k6_glib_000 A))) ) ).
tt(dt_k10_lmod_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) &  ((m1_subset_1 D (k7_lmod_7 A B C)) & (m1_subset_1 E (k7_lmod_7 A B C))) ) ) )  => (m1_subset_1 (k10_lmod_7 A B C D E) (k7_lmod_7 A B C))) ) ).
tt(dt_k10_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k10_lopban_1 A B) (k1_zfmisc_1 (u1_struct_0 (k8_lopban_1 A B))))) ) ).
tt(dt_k10_lopban_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k10_lopban_4 A B) (u1_struct_0 A))) ) ).
tt(dt_k10_lopclset,ax,$true).
tt(dt_k10_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k10_lpspace1 A B C)))  & (l1_rlvect_1 (k10_lpspace1 A B C))) ) ) ).
tt(dt_k10_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v1_rlvect_1 (k10_lpspace2 A B C D)) & (l1_rlvect_1 (k10_lpspace2 A B C D))) ) ) ).
tt(dt_k10_ltlaxio1,ax,(m1_subset_1 k10_ltlaxio1 (k1_zfmisc_1 k1_hilbert1))).
tt(dt_k10_margrel1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k10_margrel1 A B) k6_margrel1)) ) ).
tt(dt_k10_matrix13,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) & (m1_finseq_1 C (u1_struct_0 (k6_prvect_1 A B)))) )  => (m1_matrix_1 (k10_matrix13 A B C) (u1_struct_0 A) (k3_finseq_1 C) B)) ) ).
tt(dt_k10_matrix_1,ax,$true).
tt(dt_k10_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  => (v7_ordinal1 (k10_matrix_2 A))) ) ).
tt(dt_k10_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_subset_1 D (k12_matrix_2 A))) ) )  => (m2_finseq_1 (k10_matrix_3 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k10_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  => (m2_finseq_1 (k10_matrixc1 A) k2_numbers)) ) ).
tt(dt_k10_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  => (m2_finseq_2 (k10_matrixj1 A B) k5_numbers (k4_finseq_2 (k3_finseq_1 B) k5_numbers))) ) ).
tt(dt_k10_matrixr1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v1_matrix_1 (k10_matrixr1 A)) & (m2_finseq_1 (k10_matrixr1 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k10_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_finseq_1 E (u1_struct_0 B)) & (m1_matrlin F A C)) ) ) ) )  =>  ((v1_matrix_1 (k10_matrlin A B C D E F)) & (m2_finseq_1 (k10_matrlin A B C D E F) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k10_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((m1_subset_1 F (k1_zfmisc_1 B)) &  ((m1_subset_1 G (k1_zfmisc_1 C)) & (m1_subset_1 H (k1_zfmisc_1 D))) ) )  => (m1_subset_1 (k10_mcart_1 A B C D E F G H) (k1_zfmisc_1 (k4_zfmisc_1 A B C D)))) ) ).
tt(dt_k10_measure7,ax, ((v1_funct_1 k10_measure7) &  ((v1_funct_2 k10_measure7 (k9_setfam_1 k1_numbers) k7_numbers) & (m1_subset_1 k10_measure7 (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 k1_numbers) k7_numbers)))) ) ).
tt(dt_k10_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_measure8 C A B) &  ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) )  =>  ((v1_funct_1 (k10_measure8 A B C D)) &  ((v1_funct_2 (k10_measure8 A B C D) k5_numbers k7_numbers) & (m1_subset_1 (k10_measure8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k10_member_1,ax,$true).
tt(dt_k10_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k10_memstr_0 A B C D)) &  ((v4_relat_1 (k10_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k10_memstr_0 A B C D)) & (v5_funct_1 (k10_memstr_0 A B C D) (k2_memstr_0 A B))) ) ) ) ) ).
tt(dt_k10_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ((v1_funct_1 (k10_mesfun7c A B)) & (m1_subset_1 (k10_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k10_mesfunc1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) ) )  =>  ((v1_funct_1 (k10_mesfunc1 A B)) & (m1_subset_1 (k10_mesfunc1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k10_mesfunc9,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers)))))) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k10_mesfunc9 A B C)) &  ((v1_funct_2 (k10_mesfunc9 A B C) k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 (k10_mesfunc9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ).
tt(dt_k10_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (m1_subset_1 (k10_metric_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v1_funct_1 (k10_metric_2 A)) &  ((v1_funct_2 (k10_metric_2 A) (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A)) k1_numbers) & (m1_subset_1 (k10_metric_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A)) k1_numbers)))) ) ) ) ).
tt(dt_k10_metric_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) ) )  =>  ((v1_funct_1 (k10_metric_3 A B)) &  ((v1_funct_2 (k10_metric_3 A B) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers) & (m1_subset_1 (k10_metric_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers)))) ) ) ) ).
tt(dt_k10_midsp_1,ax,$true).
tt(dt_k10_midsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((l1_midsp_2 B A) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 (u1_midsp_2 A B)))) ) )  => (m1_subset_1 (k10_midsp_2 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k10_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m2_midsp_3 B A) &  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  & (m1_subset_1 D (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C))))) ) )  => (m1_subset_1 (k10_midsp_3 A B C D) (u1_struct_0 (u1_midsp_2 B C)))) ) ).
tt(dt_k10_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 D)) )  => (m1_subset_1 (k10_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k10_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) => (m1_subset_1 (k10_mod_2 A) (k1_enumset1 k6_numbers 1 2))) ) ).
tt(dt_k10_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) => (m1_subset_1 (k10_modal_1 A) k6_modal_1)) ) ).
tt(dt_k10_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  =>  ((v1_funct_1 (k10_modcat_1 A B)) & (m1_subset_1 (k10_modcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) (k4_modcat_1 A B)) (k4_modcat_1 A B))))) ) ) ).
tt(dt_k10_modelc_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k10_modelc_1 A) k5_numbers)) ) ).
tt(dt_k10_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_2 (k10_modelc_2 A)) & (m2_finseq_1 (k10_modelc_2 A) k5_numbers)) ) ) ).
tt(dt_k10_modelc_3,ax, (! [A:$i,B:$i] :  ( ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers))  =>  ((v1_modelc_3 (k10_modelc_3 A B) B) & (l1_modelc_3 (k10_modelc_3 A B) B)) ) ) ).
tt(dt_k10_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k10_monoid_0 A)))  &  ((v22_algstr_0 (k10_monoid_0 A)) &  ((v4_vectsp_1 (k10_monoid_0 A)) & (m1_monoid_0 (k10_monoid_0 A) (k9_monoid_0 A))) ) ) ) ) ).
tt(dt_k10_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (u1_struct_0 (k9_monoid_1 A B))) & (m1_subset_1 D B)) ) )  => (m1_subset_1 (k10_monoid_1 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k10_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m2_pboole (k10_msafree A B) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)))) ) ).
tt(dt_k10_msualg_1,ax,$true).
tt(dt_k10_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  =>  ((v3_msualg_1 (k10_msualg_2 A B C) A) & (m1_msualg_2 (k10_msualg_2 A B C) A B)) ) ) ).
tt(dt_k10_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v2_msualg_4 (k10_msualg_6 A B C) A B) &  ((v3_msualg_6 (k10_msualg_6 A B C) A B) &  ((v4_msualg_6 (k10_msualg_6 A B C) A B) & (m1_msualg_4 (k10_msualg_6 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ).
tt(dt_k10_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k10_nat_1 A B C)) &  ((v1_funct_2 (k10_nat_1 A B C) k5_numbers A) & (m1_subset_1 (k10_nat_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k10_nat_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k10_nat_3 A B))) ) ).
tt(dt_k10_nat_lat,ax, ((v3_lattices k10_nat_lat) & (l3_lattices k10_nat_lat)) ).
tt(dt_k10_nattra_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (m4_nattra_1 (k10_nattra_1 A B) A B)) ) ).
tt(dt_k10_net_1,ax,$true).
tt(dt_k10_newton,ax,(m1_subset_1 k10_newton (k1_zfmisc_1 k5_numbers))).
tt(dt_k10_normform,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) & (m1_subset_1 C (k5_finsub_1 (k7_normform A))))  => (m1_subset_1 (k10_normform A B C) (k5_finsub_1 (k7_normform A)))) ) ).
tt(dt_k10_openlatt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k10_openlatt A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k10_oppcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k10_oppcat_1 A B C)) &  ((v1_funct_2 (k10_oppcat_1 A B C) (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 (k10_oppcat_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) ) ) ) ).
tt(dt_k10_ordinal2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k10_ordinal2 A B))) ) ).
tt(dt_k10_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k4_dtconstr (k2_osafree A B)))) )  => (m1_subset_1 (k10_osafree A B C) (u1_struct_0 A))) ) ).
tt(dt_k10_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  & (m2_osalg_2 C A B)) )  =>  ((v3_msualg_1 (k10_osalg_2 A B C) A) &  ((v12_osalg_1 (k10_osalg_2 A B C) A) & (m1_msualg_2 (k10_osalg_2 A B C) A B)) ) ) ) ).
tt(dt_k10_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) ) ) ) )  =>  ((v1_funct_1 (k10_osalg_4 A B C D)) &  ((v1_funct_2 (k10_osalg_4 A B C D) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B)) & (m1_subset_1 (k10_osalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B))))) ) ) ) ).
tt(dt_k10_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  & (m1_subset_1 C (u1_struct_0 (k8_pcs_0 A B)))) )  => (m1_subset_1 (k10_pcs_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k10_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B k5_numbers) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (m1_subset_1 D (k1_euclid A))) ) )  => (v1_xreal_0 (k10_pdiff_1 A B C D))) ) ).
tt(dt_k10_petri,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( (~ (v1_xboole_0 (k10_petri A B C)))  & (m1_subset_1 (k10_petri A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ).
tt(dt_k10_pnproc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m2_pnproc_1 B A) &  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B)))) )  => (m1_subset_1 (k10_pnproc_1 A B C D) (k1_zfmisc_1 (k3_finseq_2 B)))) ) ).
tt(dt_k10_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k10_polyform A B)) &  ((v1_funct_1 (k10_polyform A B)) & (v1_finseq_1 (k10_polyform A B))) ) ) ) ).
tt(dt_k10_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k10_polynom1 A B C D)) &  ((v1_funct_2 (k10_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k10_polynom1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k10_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v1_funct_1 (k10_polynom3 A)) &  ((v1_funct_2 (k10_polynom3 A) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k10_polynom3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k10_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k10_poset_1 A)) &  ((v1_funct_2 (k10_poset_1 A) (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A)) & (m1_subset_1 (k10_poset_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k10_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  & (m1_subset_1 C A)) )  => (l1_struct_0 (k10_pralg_1 A B C))) ) ).
tt(dt_k10_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  & (m1_pralg_2 C A B))  =>  ((v1_relat_1 (k10_pralg_2 A B C)) &  ((v4_relat_1 (k10_pralg_2 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k10_pralg_2 A B C)) & (v1_partfun1 (k10_pralg_2 A B C) (u1_struct_0 B))) ) ) ) ) ).
tt(dt_k10_pre_poly,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k3_finseq_2 A)) =>  ((v1_card_3 (k10_pre_poly A B)) & (m2_finseq_1 (k10_pre_poly A B) k5_numbers)) ) ) ).
tt(dt_k10_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k10_prepower A B) k1_numbers)) ) ).
tt(dt_k10_prob_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (m1_subset_1 (k10_prob_1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k10_prob_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v2_prob_3 (k10_prob_3 A B) A) &  ((v3_prob_3 (k10_prob_3 A B) A) & (m1_subset_1 (k10_prob_3 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ).
tt(dt_k10_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m2_prvect_1 B A) & (m1_subset_1 C (k4_finseq_1 A))) )  =>  ((v1_funct_1 (k10_prvect_1 A B C)) &  ((v1_funct_2 (k10_prvect_1 A B C) (k1_funct_1 A C) (k1_funct_1 A C)) & (m1_subset_1 (k10_prvect_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C))))) ) ) ) ).
tt(dt_k10_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k10_prvect_2 A)))  &  ((v1_rlvect_1 (k10_prvect_2 A)) & (l1_rlvect_1 (k10_prvect_2 A))) ) ) ) ).
tt(dt_k10_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k10_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k10_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  & (m4_pua2mss1 B A))  => (m3_pua2mss1 (k10_pua2mss1 A B) A)) ) ).
tt(dt_k10_qc_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k6_qc_lang1 A)) & (m1_finseq_1 C (k2_qc_lang1 A))) )  => (m1_subset_1 (k10_qc_lang1 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k10_qc_lang2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k10_qc_lang2 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k10_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  => (m1_subset_1 (k10_qmax_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)))))) ) ).
tt(dt_k10_quatern2,ax, ((v1_funct_1 k10_quatern2) &  ((v1_funct_2 k10_quatern2 (k2_zfmisc_1 k1_quaterni k1_quaterni) k1_quaterni) & (m1_subset_1 k10_quatern2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_quaterni k1_quaterni) k1_quaterni)))) ) ).
tt(dt_k10_quaterni,ax,$true).
tt(dt_k10_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  & (m1_subset_1 B (k1_quofield A)))  => (m2_subset_1 (k10_quofield A B) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k10_radix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k10_radix_1 A B C) B) & (m2_finseq_1 (k10_radix_1 A B C) (k3_radix_1 A))) ) ) ).
tt(dt_k10_radix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k10_radix_3 A B C) (k2_xcmplx_0 A 1)) & (m2_finseq_1 (k10_radix_3 A B C) (k4_radix_3 B))) ) ) ).
tt(dt_k10_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k10_radix_6 A B C) A) & (m2_finseq_1 (k10_radix_6 A B C) (k3_radix_1 C))) ) ) ).
tt(dt_k10_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  => (v7_ordinal1 (k10_ranknull A B C D))) ) ).
tt(dt_k10_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_ratfunc1 B A) & (m1_ratfunc1 C A)) )  => (m1_ratfunc1 (k10_ratfunc1 A B C) A)) ) ).
tt(dt_k10_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  => (m1_subset_1 (k10_real_1 A B) k1_numbers)) ) ).
tt(dt_k10_relat_1,ax,$true).
tt(dt_k10_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  ( (~ (v1_xboole_0 (k10_ringcat1 A)))  & (v5_ringcat1 (k10_ringcat1 A))) ) ) ).
tt(dt_k10_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  => (m1_rlvect_2 (k10_rlvect_2 A B C) A)) ) ).
tt(dt_k10_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ((v2_vectsp_2 (k10_rmod_4 A B C) A) & (m1_rmod_2 (k10_rmod_4 A B C) A B)) ) ) ).
tt(dt_k10_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k10_robbins1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k10_rsspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k10_rsspace A B) B)) ) ).
tt(dt_k10_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xreal_0 B))  => (m2_finseq_1 (k10_rvsum_1 A B) k1_numbers)) ) ).
tt(dt_k10_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  & (v1_xcmplx_0 C)) )  => (m2_finseq_2 (k10_rvsum_2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k10_scm_comp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k7_dtconstr k1_scm_comp)) &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v1_int_1 (k10_scm_comp A B C))) ) ).
tt(dt_k10_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) => (m1_subset_1 (k10_scmfsa_1 A) k5_numbers)) ) ).
tt(dt_k10_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k10_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k10_scmfsa_m,ax, ((v1_funct_1 k10_scmfsa_m) & (m1_subset_1 k10_scmfsa_m (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 3 k1_scmfsa_2) (k11_memstr_0 3 k1_scmfsa_2))))) ).
tt(dt_k10_scmpds_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m1_subset_1 (k10_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k10_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k10_scmpds_6 A B C)))  &  ((v1_relat_1 (k10_scmpds_6 A B C)) &  ((v4_relat_1 (k10_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k10_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k10_scmpds_6 A B C)) &  ((v1_finset_1 (k10_scmpds_6 A B C)) & (v1_afinsq_1 (k10_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k10_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (m1_subset_1 (k10_scmpds_i A) k2_scm_inst)) ) ).
tt(dt_k10_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  => (v7_ordinal1 (k10_scmyciel A))) ) ).
tt(dt_k10_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  => (m2_finseq_1 (k10_seq_4 A B) k2_numbers)) ) ).
tt(dt_k10_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k10_seqfunc A B C)) &  ((v1_funct_2 (k10_seqfunc A B C) k5_numbers k1_numbers) & (m1_subset_1 (k10_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k10_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k5_finsub_1 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k5_finsub_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) ) )  => (m1_subset_1 (k10_setwiseo A B C D) (k5_finsub_1 B))) ) ).
tt(dt_k10_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_simplex0 B A) &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_pre_topc (k10_simplex0 A B C)) & (m1_simplex0 (k10_simplex0 A B C) A)) ) ) ).
tt(dt_k10_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k10_sincos10 A) k1_numbers)) ) ).
tt(dt_k10_sin_cos,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k2_numbers) & (m1_subset_1 C k2_numbers)) )  =>  ((v1_funct_1 (k10_sin_cos A B C)) &  ((v1_funct_2 (k10_sin_cos A B C) k5_numbers k2_numbers) & (m1_subset_1 (k10_sin_cos A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k10_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  => (m1_subset_1 (k10_stacks_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A))))) ) ).
tt(dt_k10_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  => (m2_subset_1 (k10_sublemma A B) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k10_subset_1,ax, (! [A:$i] : (m1_subset_1 (k10_subset_1 A) A)) ).
tt(dt_k10_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  =>  ((v1_finset_1 (k10_substut1 A B)) & (m1_subset_1 (k10_substut1 A B) (k1_zfmisc_1 (k1_qc_lang1 A)))) ) ) ).
tt(dt_k10_supinf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v2_membered A) &  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) )  => (m1_subset_1 (k10_supinf_2 A B C D) k7_numbers)) ) ).
tt(dt_k10_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k10_tdlat_1 A)) &  ((v1_funct_2 (k10_tdlat_1 A) (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A)) & (m1_subset_1 (k10_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A))))) ) ) ) ).
tt(dt_k10_tmap_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  &  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k10_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_borsuk_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D))) ) ) )  => (m1_borsuk_2 (k10_topalg_4 A B C D E) B D D)) ) ).
tt(dt_k10_toprealb,ax,(m1_subset_1 k10_toprealb (u1_struct_0 (k8_toprealb 2)))).
tt(dt_k10_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k10_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k10_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))))  =>  ((v1_funct_1 (k10_turing_1 A B)) &  ((v1_funct_2 (k10_turing_1 A B) k5_numbers (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) & (m1_subset_1 (k10_turing_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))))))) ) ) ) ).
tt(dt_k10_twoscomp,ax, ((v1_funct_1 k10_twoscomp) &  ((v1_funct_2 k10_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k10_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k10_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_funct_1 (k10_unialg_2 A)) &  ((v1_funct_2 (k10_unialg_2 A) (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A)) & (m1_subset_1 (k10_unialg_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A))))) ) ) ) ).
tt(dt_k10_uproots,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  =>  ((v1_funct_1 (k10_uproots A B)) &  ((v1_funct_2 (k10_uproots A B) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k10_uproots A B) A) & (m1_subset_1 (k10_uproots A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k10_valued_2,ax,$true).
tt(dt_k10_vectsp10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k10_vectsp10 A B C D)) &  ((v1_funct_2 (k10_vectsp10 A B C D) (u1_struct_0 (k6_vectsp10 A B C)) (u1_struct_0 A)) &  ((v13_vectsp_1 (k10_vectsp10 A B C D) (k6_vectsp10 A B C) A) & (m1_subset_1 (k10_vectsp10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B C)) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k10_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k10_waybel34 A)))  &  ((v2_altcat_1 (k10_waybel34 A)) &  ((v6_altcat_1 (k10_waybel34 A)) &  ((v2_altcat_2 (k10_waybel34 A) (k8_waybel34 A)) &  ((v3_altcat_2 (k10_waybel34 A) (k8_waybel34 A)) & (m1_altcat_2 (k10_waybel34 A) (k8_waybel34 A))) ) ) ) ) ) ) ).
tt(dt_k10_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k10_waybel_4 A)) &  ((v1_funct_2 (k10_waybel_4 A) (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A)))) & (m1_subset_1 (k10_waybel_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))))))) ) ) ) ).
tt(dt_k10_weierstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  => (m1_subset_1 (k10_weierstr A B C) k1_numbers)) ) ).
tt(dt_k10_xboolean,ax,$true).
tt(dt_k10_xtuple_0,ax,$true).
tt(dt_k10_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((v1_waybel_0 (k10_yellow_3 A B C D) (k3_yellow_3 A B)) & (m1_subset_1 (k10_yellow_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) ) ) ).
tt(dt_k10_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  => (m1_subset_1 (k10_yellow_6 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k10_zf_lang,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  =>  ((v1_zf_lang (k10_zf_lang A B)) & (m2_finseq_1 (k10_zf_lang A B) k5_numbers)) ) ) ).
tt(dt_k10_zf_model,ax, ((v1_zf_lang k10_zf_model) & (m2_finseq_1 k10_zf_model k5_numbers)) ).
tt(dt_k10_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k10_zmodul01 A)) &  ((v1_funct_2 (k10_zmodul01 A) (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A)) & (m1_subset_1 (k10_zmodul01 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A))))) ) ) ) ).
tt(dt_k11_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  => (m1_subset_1 (k11_abcmiz_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k11_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k11_afinsq_1 A B C)) &  ((v5_relat_1 (k11_afinsq_1 A B C) A) &  ((v5_ordinal1 (k11_afinsq_1 A B C)) &  ((v1_funct_1 (k11_afinsq_1 A B C)) &  ( (~ (v1_xboole_0 (k11_afinsq_1 A B C)))  & (v1_finset_1 (k11_afinsq_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k11_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (m1_subset_1 (k11_afproj A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_afproj A) (k10_afproj A))))) ) ).
tt(dt_k11_algstr_0,ax, (! [A:$i,B:$i] :  ( ((l5_algstr_0 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k11_algstr_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k11_algstr_4,ax,$true).
tt(dt_k11_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k11_ami_3 A B)) &  ((v4_relat_1 (k11_ami_3 A B) (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 (k11_ami_3 A B)) & (v5_funct_1 (k11_ami_3 A B) (k2_memstr_0 2 k1_ami_3))) ) ) ) ) ).
tt(dt_k11_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  => (m1_freealg (k11_aofa_000 A) A)) ) ).
tt(dt_k11_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((v1_funct_1 (k11_aofa_i00 A B C)) &  ((v1_funct_2 (k11_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k11_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k11_armstrng,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (m1_subset_1 (k11_armstrng A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k11_arytm_3,ax,(m1_subset_1 k11_arytm_3 k5_arytm_3)).
tt(dt_k11_asympt_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k11_asympt_0 A B) k5_numbers k1_numbers)) ) ).
tt(dt_k11_bagorder,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  & (m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))))  => (m1_subset_1 (k11_bagorder A B) (u1_struct_0 A))) ) ).
tt(dt_k11_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  &  ((m4_bcialg_2 D A C) &  ((m1_subset_1 E (k7_bcialg_6 A B C D)) & (m1_subset_1 F (k7_bcialg_6 A B C D))) ) ) ) )  => (m2_subset_1 (k11_bcialg_6 A B C D E F) (u1_struct_0 A) (k7_bcialg_6 A B C D))) ) ).
tt(dt_k11_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l2_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) )  => (m1_subset_1 (k11_bilinear A B C D) (k1_zfmisc_1 (u1_struct_0 C)))) ) ).
tt(dt_k11_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k11_binop_2 A B) k1_numbers)) ) ).
tt(dt_k11_bor_cant,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_bor_cant A B C D)) &  ((v1_funct_2 (k11_bor_cant A B C D) k5_numbers k1_numbers) & (m1_subset_1 (k11_bor_cant A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k11_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((v1_pre_topc (k11_borsuk_1 A B)) &  ((v2_pre_topc (k11_borsuk_1 A B)) & (l1_pre_topc (k11_borsuk_1 A B))) ) ) ) ).
tt(dt_k11_borsuk_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  ((v1_funct_1 (k11_borsuk_7 A B C)) &  ((v1_funct_2 (k11_borsuk_7 A B C) (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C))) & (m1_subset_1 (k11_borsuk_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C)))))) ) ) ) ).
tt(dt_k11_bspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B (u1_struct_0 (k7_bspace A))) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k11_bspace A B C) (u1_struct_0 k2_bspace))) ) ).
tt(dt_k11_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k11_bvfunc_1 A)) &  ((v1_funct_2 (k11_bvfunc_1 A) A k6_margrel1) & (m1_subset_1 (k11_bvfunc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k11_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (l1_lopban_2 (k11_c0sp1 A))) ) ).
tt(dt_k11_card_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  & (m1_subset_1 B (k4_card_3 A)))  => (m1_subset_1 (k11_card_3 A B C) (k8_card_3 A))) ) ).
tt(dt_k11_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k11_cat_1 A B C D E)) &  ((v1_funct_2 (k11_cat_1 A B C D E) (k2_cat_1 A D E) (k2_cat_1 B (k8_cat_1 A B C D) (k8_cat_1 A B C E))) & (m1_subset_1 (k11_cat_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A D E) (k2_cat_1 B (k8_cat_1 A B C D) (k8_cat_1 A B C E)))))) ) ) ) ).
tt(dt_k11_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) &  ((m1_subset_1 E (u4_struct_0 A)) & (m1_subset_1 F (u4_struct_0 B))) ) ) ) )  => (m1_subset_1 (k11_cat_2 A B C D E F) (u4_struct_0 C))) ) ).
tt(dt_k11_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k11_cat_3 A B C) A B C)) ) ).
tt(dt_k11_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k11_cat_4 A B) A B (k2_cat_4 A (k1_cat_4 A) B))) ) ).
tt(dt_k11_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k11_cat_5 A B)))  &  ( (~ (v11_struct_0 (k11_cat_5 A B)))  &  ((v1_cat_1 (k11_cat_5 A B)) &  ((v2_cat_1 (k11_cat_5 A B)) &  ((v3_cat_1 (k11_cat_5 A B)) &  ((v4_cat_1 (k11_cat_5 A B)) &  ((v5_cat_1 (k11_cat_5 A B)) &  ((v6_cat_1 (k11_cat_5 A B)) &  ((v1_cat_5 (k11_cat_5 A B)) & (l1_cat_1 (k11_cat_5 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k11_catalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  =>  ((v1_funct_1 (k11_catalg_1 A B C)) &  ((v1_funct_2 (k11_catalg_1 A B C) (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B)))) & (m1_subset_1 (k11_catalg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B))))))) ) ) ) ).
tt(dt_k11_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (m1_subset_1 (k11_cgames_1 A) (k1_zfmisc_1 (k10_cgames_1 A)))) ) ).
tt(dt_k11_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  => (m3_chain_1 (k11_chain_1 A B C) A B C)) ) ).
tt(dt_k11_clopban1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k11_clopban1 A B C)) &  ((v1_funct_2 (k11_clopban1 A B C) (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 (k11_clopban1 A B C) A B) &  ((v1_clopban1 (k11_clopban1 A B C) A B) &  ((v2_clopban1 (k11_clopban1 A B C) A B) & (m1_subset_1 (k11_clopban1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(dt_k11_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v15_closure2 B A) & (l1_closure2 B A))  & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  => (m1_closure2 (k11_closure2 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))) ) ).
tt(dt_k11_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  => (m1_subset_1 (k11_cohsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski B))))) ) ).
tt(dt_k11_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k11_coh_sp A)) &  ((v1_funct_2 (k11_coh_sp A) (k5_coh_sp A) (k3_coh_sp A)) & (m1_subset_1 (k11_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k3_coh_sp A))))) ) ) ).
tt(dt_k11_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  => (m1_subset_1 (k11_complex1 A B) k2_numbers)) ) ).
tt(dt_k11_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) & (m1_subset_1 B (u1_compos_1 A)))  =>  ((v1_relat_1 (k11_compos_1 A B)) &  ((v4_relat_1 (k11_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k11_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k11_compos_1 A B)) & (v1_finset_1 (k11_compos_1 A B))) ) ) ) ) ) ).
tt(dt_k11_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_comput_1 k5_numbers))) => (m1_subset_1 (k11_comput_1 A) (k1_zfmisc_1 (k2_comput_1 k5_numbers)))) ) ).
tt(dt_k11_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (m1_subset_1 (k11_comseq_3 A) k2_numbers)) ) ).
tt(dt_k11_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v3_lattices (k11_conlat_1 A)) & (l3_lattices (k11_conlat_1 A))) ) ) ) ).
tt(dt_k11_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  & (m1_subset_1 B (k10_convex4 A)))  => (m1_convex4 (k11_convex4 A B) A)) ) ).
tt(dt_k11_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k11_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k11_cqc_sim1,ax, (! [A:$i] : (m1_subset_1 (k11_cqc_sim1 A) (k1_funct_2 A A))) ).
tt(dt_k11_csspace,ax,(m1_subset_1 k11_csspace (k1_zfmisc_1 (u1_struct_0 k7_csspace)))).
tt(dt_k11_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k11_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k11_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (l1_orders_2 k11_dickson)) ).
tt(dt_k11_diff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) & (v1_xreal_0 E)) ) ) )  => (m1_subset_1 (k11_diff_1 A B C D E) k1_numbers)) ) ).
tt(dt_k11_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  => (m1_dist_1 (k11_dist_1 A) A)) ) ).
tt(dt_k11_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) & (m1_subset_1 G A)) ) ) ) ) )  => (m1_subset_1 (k11_domain_1 A B C D E F G) (k1_zfmisc_1 A))) ) ).
tt(dt_k11_dtconstr,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m1_subset_1 (k11_dtconstr A) k5_numbers)) ) ).
tt(dt_k11_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_ens_1 A)))  &  ( (~ (v11_struct_0 (k11_ens_1 A)))  &  ((v1_cat_1 (k11_ens_1 A)) & (l1_cat_1 (k11_ens_1 A))) ) ) ) ) ).
tt(dt_k11_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_eqrel_1 C A)) )  => (m1_subset_1 (k11_eqrel_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k11_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k11_e_siec A))) ) ).
tt(dt_k11_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (u1_struct_0 (k15_euclid A)))) ) ) )  => (m1_subset_1 (k11_euclid_3 A B C D E) k1_numbers)) ) ).
tt(dt_k11_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  => (m2_finseq_2 (k11_euclid A B) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k11_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msafree2 B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k11_facirc_1 A B C D) k6_margrel1)) ) ).
tt(dt_k11_ff_siec,ax,$true).
tt(dt_k11_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m2_nat_lat B A))  =>  ((v3_lattices (k11_filter_2 A B)) & (m2_nat_lat (k11_filter_2 A B) (k1_lattice2 A))) ) ) ).
tt(dt_k11_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  &  ( (~ (v1_xboole_0 E))  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers E)))) )  & (m1_subset_1 G C)) ) ) ) ) )  => (m1_subset_1 (k11_finance1 A B C D E F G) k1_numbers)) ) ).
tt(dt_k11_finseq_1,ax,$true).
tt(dt_k11_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k11_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k11_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_fomodel0,ax, (! [A:$i,B:$i] : (m1_subset_1 (k11_fomodel0 A B) (k1_zfmisc_1 A))) ).
tt(dt_k11_fomodel1,ax,$true).
tt(dt_k11_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k11_fomodel2 A B C)) & (v1_funct_1 (k11_fomodel2 A B C))) ) ) ).
tt(dt_k11_fomodel3,ax,$true).
tt(dt_k11_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k11_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k11_freealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  & (m1_subset_1 C (u1_struct_0 (k3_freealg A B))))  => (m1_subset_1 (k11_freealg A B C) k5_numbers)) ) ).
tt(dt_k11_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) ) ) )  =>  ((v2_fsm_1 (k11_fsm_1 A B C) A B) & (l2_fsm_1 (k11_fsm_1 A B C) A B)) ) ) ).
tt(dt_k11_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k11_ftacell1 A B C D E) (k3_msafree2 (k7_ftacell1 A B C D E)))) ).
tt(dt_k11_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  => (m1_subset_1 (k11_funcop_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ).
tt(dt_k11_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v36_algstr_0 (k11_funcsdom A)) & (l6_algstr_0 (k11_funcsdom A))) ) ) ).
tt(dt_k11_funct_3,ax, (! [A:$i] :  ((v1_relat_1 (k11_funct_3 A)) & (v1_funct_1 (k11_funct_3 A))) ) ).
tt(dt_k11_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((v1_funct_1 (k11_funct_5 A B C D)) &  ((v1_funct_2 (k11_funct_5 A B C D) A (k9_funct_2 B C)) & (m1_subset_1 (k11_funct_5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) ).
tt(dt_k11_funct_7,ax,$true).
tt(dt_k11_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  ((v9_functor0 (k11_functor0 A) A A) & (l2_functor0 (k11_functor0 A) A A)) ) ) ).
tt(dt_k11_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k11_fvsum_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k11_gate_1,ax,$true).
tt(dt_k11_gate_5,ax,$true).
tt(dt_k11_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) & (m1_subset_1 H k5_numbers)) ) ) ) ) ) )  => (m1_genealg1 (k11_genealg1 A B C D E F G H) A)) ) ).
tt(dt_k11_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k11_gfacirc1 A B C) (k10_gfacirc1 A B C)) &  ((v4_msafree2 (k11_gfacirc1 A B C) (k10_gfacirc1 A B C)) &  ((v4_circcomb (k11_gfacirc1 A B C) (k10_gfacirc1 A B C)) &  ((v6_circcomb (k11_gfacirc1 A B C) (k10_gfacirc1 A B C)) & (l3_msualg_1 (k11_gfacirc1 A B C) (k10_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k11_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_funct_1 (k11_glib_000 A)) &  ((v1_funct_2 (k11_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k11_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) ) ) ) ).
tt(dt_k11_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m1_glib_001 (k11_glib_001 A B) A)) ) ).
tt(dt_k11_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  => (m1_subset_1 (k11_glib_003 A) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k11_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k11_glib_004 A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k11_glib_005,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  &  ((m1_subset_1 C (k6_glib_000 A)) & (m1_subset_1 D (k6_glib_000 A))) ) )  =>  ((v1_relat_1 (k11_glib_005 A B C D)) &  ((v4_relat_1 (k11_glib_005 A B C D) (k7_glib_000 A)) &  ((v1_funct_1 (k11_glib_005 A B C D)) &  ((v1_partfun1 (k11_glib_005 A B C D) (k7_glib_000 A)) & (v4_valued_0 (k11_glib_005 A B C D))) ) ) ) ) ) ).
tt(dt_k11_graph_1,ax,$true).
tt(dt_k11_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (k9_graph_3 A)) & (m1_subset_1 C (k9_graph_3 A))) )  => (m2_finseq_2 (k11_graph_3 A B C) (u4_struct_0 A) (k9_graph_3 A))) ) ).
tt(dt_k11_graphsp,ax,$true).
tt(dt_k11_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  => (m1_grcat_1 (k11_grcat_1 A) A A)) ) ).
tt(dt_k11_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  & (m1_subset_1 D B)) ) )  =>  ((v15_algstr_0 (k11_group_10 A B C D)) & (m1_group_2 (k11_group_10 A B C D) A)) ) ) ).
tt(dt_k11_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k11_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_group_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  =>  ((v15_algstr_0 (k11_group_3 A B)) & (m1_group_2 (k11_group_3 A B) A)) ) ) ).
tt(dt_k11_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (~ (v2_struct_0 (k11_group_4 A)))  &  ((v3_lattices (k11_group_4 A)) &  ((v10_lattices (k11_group_4 A)) & (l3_lattices (k11_group_4 A))) ) ) ) ) ).
tt(dt_k11_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) &  ((v3_group_9 D A) & (l1_group_9 D A)) ) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v1_group_6 F C D) &  ((v7_group_9 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k11_group_9 A B C D E F)) &  ((v1_funct_2 (k11_group_9 A B C D E F) (u1_struct_0 B) (u1_struct_0 D)) &  ((v1_group_6 (k11_group_9 A B C D E F) B D) &  ((v7_group_9 (k11_group_9 A B C D E F) A B D) & (m1_subset_1 (k11_group_9 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ).
tt(dt_k11_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_funct_1 (k11_hahnban1 A B)) &  ((v1_funct_2 (k11_hahnban1 A B) (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 (k11_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ).
tt(dt_k11_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  ((v1_funct_1 (k11_heyting1 A B)) &  ((v1_funct_2 (k11_heyting1 A B) (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) & (m1_subset_1 (k11_heyting1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)))))) ) ) ) ).
tt(dt_k11_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_finseq_1 B k5_numbers) & (m1_finseq_1 C k5_numbers)) )  => (m2_finseq_1 (k11_idea_1 A B C) k5_numbers)) ) ).
tt(dt_k11_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k11_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_integr15,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) )  => (m2_finseq_2 (k11_integr15 A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k11_integra1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  => (m1_subset_1 (k11_integra1 A B) k1_numbers)) ) ).
tt(dt_k11_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (m1_subset_1 (k11_intpro_1 A) (k1_zfmisc_1 k1_intpro_1))) ) ).
tt(dt_k11_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A (k8_cat_2 B C)) &  ((m2_cat_1 E A (k8_cat_2 B C)) & (m2_nattra_1 F A (k8_cat_2 B C) D E)) ) ) ) )  => (m2_nattra_1 (k11_isocat_2 A B C D E F) A B (k9_isocat_2 A B C D) (k9_isocat_2 A B C E))) ) ).
tt(dt_k11_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k11_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k11_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k11_jordan6 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k11_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_finseq_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) )  => (m2_finseq_2 (k11_lang1 A B C D) B (k3_finseq_2 B))) ) ).
tt(dt_k11_laplace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_finseq_1 C (u1_struct_0 A))) )  =>  ((v1_matrix_1 (k11_laplace A B C)) & (m2_finseq_1 (k11_laplace A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k11_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k11_lattice3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k11_lattice5,ax,$true).
tt(dt_k11_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) &  ((m1_subset_1 C (k6_glib_000 A)) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k11_lexbfs A B C D) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers))))) ) ).
tt(dt_k11_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_lopban_1 A B)))  &  ((v13_algstr_0 (k11_lopban_1 A B)) &  ((v2_rlvect_1 (k11_lopban_1 A B)) &  ((v3_rlvect_1 (k11_lopban_1 A B)) &  ((v4_rlvect_1 (k11_lopban_1 A B)) &  ((v5_rlvect_1 (k11_lopban_1 A B)) &  ((v6_rlvect_1 (k11_lopban_1 A B)) &  ((v7_rlvect_1 (k11_lopban_1 A B)) &  ((v8_rlvect_1 (k11_lopban_1 A B)) & (l1_rlvect_1 (k11_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k11_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((v1_pre_topc (k11_lopclset A)) &  ((v2_pre_topc (k11_lopclset A)) & (l1_pre_topc (k11_lopclset A))) ) ) ) ).
tt(dt_k11_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k11_lpspace1 A B C)))  & (m1_subset_1 (k11_lpspace1 A B C) (k1_zfmisc_1 (u1_struct_0 (k10_lpspace1 A B C))))) ) ) ).
tt(dt_k11_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v1_funct_1 (k11_lpspace2 A B C D)) &  ((v1_funct_2 (k11_lpspace2 A B C D) (u1_struct_0 (k10_lpspace2 A B C D)) k1_numbers) & (m1_subset_1 (k11_lpspace2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_lpspace2 A B C D)) k1_numbers)))) ) ) ) ).
tt(dt_k11_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((v1_funct_1 (k11_ltlaxio1 A)) &  ((v1_funct_2 (k11_ltlaxio1 A) (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1) & (m1_subset_1 (k11_ltlaxio1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1)))) ) ) ) ).
tt(dt_k11_margrel1,ax,$true).
tt(dt_k11_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) & (m1_matrix_1 D (u1_struct_0 A) B C)) ) )  => (m2_finseq_1 (k11_matrix13 A B C D) (u1_struct_0 (k6_prvect_1 A C)))) ) ).
tt(dt_k11_matrix_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (v7_ordinal1 B))  => (m1_matrix_1 (k11_matrix_1 A B) (u1_struct_0 A) B B)) ) ).
tt(dt_k11_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  => (m1_subset_1 (k11_matrix_2 A) k5_numbers)) ) ).
tt(dt_k11_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  =>  ((v1_funct_1 (k11_matrix_3 A B C)) &  ((v1_funct_2 (k11_matrix_3 A B C) (k12_matrix_2 A) (u1_struct_0 B)) & (m1_subset_1 (k11_matrix_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k11_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  => (m2_finseq_1 (k11_matrixc1 A) k2_numbers)) ) ).
tt(dt_k11_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  => (m2_finseq_2 (k11_matrixj1 A B) k5_numbers (k4_finseq_2 (k3_finseq_1 B) k5_numbers))) ) ).
tt(dt_k11_matrixr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  & (m1_finseq_1 B k1_numbers))  => (m2_finseq_1 (k11_matrixr1 A B) k1_numbers)) ) ).
tt(dt_k11_mcart_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k11_mcart_1 A)) & (v1_funct_1 (k11_mcart_1 A))) ) ) ).
tt(dt_k11_measure7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  &  ((m2_measure7 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))))) ) ) )  => (m1_measure7 (k11_measure7 A B C) (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) A)))) ) ).
tt(dt_k11_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) )  =>  ((v1_funct_1 (k11_measure8 A B C D)) &  ((v1_funct_2 (k11_measure8 A B C D) k5_numbers k7_numbers) & (m1_subset_1 (k11_measure8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k11_member_1,ax,$true).
tt(dt_k11_memstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v2_memstr_0 B A) & (l1_memstr_0 B A)) )  => (m1_subset_1 (k11_memstr_0 A B) (k1_zfmisc_1 (k8_card_3 (k2_memstr_0 A B))))) ) ).
tt(dt_k11_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ((v1_funct_1 (k11_mesfun7c A B)) &  ((v1_funct_2 (k11_mesfun7c A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k11_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k11_mesfunc1,ax,$true).
tt(dt_k11_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (m1_subset_1 (k11_metric_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (k10_midsp_1 A)) & (m1_subset_1 C (k10_midsp_1 A))) )  => (m1_subset_1 (k11_midsp_1 A B C) (k10_midsp_1 A))) ) ).
tt(dt_k11_midsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((v4_midsp_2 B A) & (l1_midsp_2 B A)) )  => (m1_subset_1 (k11_midsp_2 A B) (u1_struct_0 (u1_midsp_2 A B)))) ) ).
tt(dt_k11_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 D)) )  => (m1_subset_1 (k11_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k11_mod_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 B (k1_enumset1 k6_numbers 1 2)))  => (m1_subset_1 (k11_mod_2 A B) (k1_enumset1 k6_numbers 1 2))) ) ).
tt(dt_k11_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) => (m1_subset_1 (k11_modal_1 A) k6_modal_1)) ) ).
tt(dt_k11_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ((v1_cat_1 (k11_modcat_1 A B)) & (l1_cat_1 (k11_modcat_1 A B))) ) ) ).
tt(dt_k11_modelc_1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k11_modelc_1 A B) k5_numbers)) ) ).
tt(dt_k11_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_2 (k11_modelc_2 A)) & (m2_finseq_1 (k11_modelc_2 A) k5_numbers)) ) ) ).
tt(dt_k11_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_3 (k11_modelc_3 A) A) &  ((v3_modelc_3 (k11_modelc_3 A) A) & (l1_modelc_3 (k11_modelc_3 A) A)) ) ) ) ).
tt(dt_k11_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k11_monoid_0 A)) &  ((v1_funct_2 (k11_monoid_0 A) (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A)) & (m1_subset_1 (k11_monoid_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A))))) ) ) ) ).
tt(dt_k11_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ( (~ (v2_struct_0 (k11_monoid_1 A B)))  &  ((v22_algstr_0 (k11_monoid_1 A B)) &  ((v4_vectsp_1 (k11_monoid_1 A B)) &  ((v1_monoid_0 (k11_monoid_1 A B)) & (l4_algstr_0 (k11_monoid_1 A B))) ) ) ) ) ) ).
tt(dt_k11_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (l3_msualg_1 (k11_msafree A B) A)) ) ).
tt(dt_k11_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  => (m2_finseq_1 (k11_msualg_1 A B) (k4_partfun1 (k3_finseq_2 (k10_msualg_1 A B)) (k10_msualg_1 A B)))) ) ).
tt(dt_k11_msualg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((m1_msualg_2 C A B) & (m1_msualg_2 D A B)) ) )  =>  ((v3_msualg_1 (k11_msualg_2 A B C D) A) & (m1_msualg_2 (k11_msualg_2 A B C D) A B)) ) ) ).
tt(dt_k11_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) ) ) ) )  =>  ((v1_funct_1 (k11_msualg_4 A B C D)) &  ((v1_funct_2 (k11_msualg_4 A B C D) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B)) & (m1_subset_1 (k11_msualg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B))))) ) ) ) ).
tt(dt_k11_nat_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k11_nat_3 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k11_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) => (m2_subset_1 (k11_nat_lat A) k5_numbers k6_nat_lat)) ) ).
tt(dt_k11_nattra_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_nattra_1 A B)))  &  ( (~ (v11_struct_0 (k11_nattra_1 A B)))  &  ((v1_cat_1 (k11_nattra_1 A B)) &  ((v2_cat_1 (k11_nattra_1 A B)) &  ((v3_cat_1 (k11_nattra_1 A B)) &  ((v4_cat_1 (k11_nattra_1 A B)) &  ((v5_cat_1 (k11_nattra_1 A B)) &  ((v6_cat_1 (k11_nattra_1 A B)) & (l1_cat_1 (k11_nattra_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k11_net_1,ax,$true).
tt(dt_k11_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k11_newton A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k11_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  => (m1_subset_1 (k11_openlatt A B C) (k9_openlatt A))) ) ).
tt(dt_k11_oppcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k11_oppcat_1 A B C)) &  ((v1_funct_2 (k11_oppcat_1 A B C) (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B))) & (m1_subset_1 (k11_oppcat_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)))))) ) ) ) ).
tt(dt_k11_ordinal2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k11_ordinal2 A B))) ) ).
tt(dt_k11_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((v1_relat_1 (k11_ordinal6 A)) &  ((v1_funct_1 (k11_ordinal6 A)) &  ((v5_ordinal1 (k11_ordinal6 A)) & (v3_ordinal6 (k11_ordinal6 A))) ) ) ) ) ).
tt(dt_k11_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_finseq_1 C (k4_dtconstr (k2_osafree A B)))) )  => (m2_finseq_2 (k11_osafree A B C) (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))) ) ).
tt(dt_k11_osalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) ) ) )  =>  ((v3_msualg_1 (k11_osalg_2 A B C D) A) &  ((v12_osalg_1 (k11_osalg_2 A B C D) A) & (m1_msualg_2 (k11_osalg_2 A B C D) A B)) ) ) ) ).
tt(dt_k11_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  & (m1_subset_1 C (u1_struct_0 (k8_pcs_0 A B)))) )  => (m1_subset_1 (k11_pcs_0 A B C) (u1_struct_0 B))) ) ).
tt(dt_k11_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B k5_numbers) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (m1_subset_1 D (k1_euclid A))) ) )  => (m1_subset_1 (k11_pdiff_1 A B C D) k1_numbers)) ) ).
tt(dt_k11_petri,ax, (! [A:$i] :  ((l1_petri A) =>  ((v1_petri (k11_petri A)) & (l1_petri (k11_petri A))) ) ) ).
tt(dt_k11_pnproc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m2_pnproc_1 B A) &  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B)))) )  => (m1_subset_1 (k11_pnproc_1 A B C D) (k1_zfmisc_1 (k3_finseq_2 B)))) ) ).
tt(dt_k11_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  => (m2_subset_1 (k11_polyform A B) k1_numbers k5_numbers)) ) ).
tt(dt_k11_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (l6_algstr_0 (k11_polynom1 A B))) ) ) ) ).
tt(dt_k11_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k11_polynom3 A B C)) &  ((v1_funct_2 (k11_polynom3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k11_polynom3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k11_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  & (m1_pralg_2 C A B))  =>  ((v1_relat_1 (k11_pralg_2 A B C)) &  ((v4_relat_1 (k11_pralg_2 A B C) A) &  ((v1_funct_1 (k11_pralg_2 A B C)) &  ((v1_partfun1 (k11_pralg_2 A B C) A) & (v1_funcop_1 (k11_pralg_2 A B C))) ) ) ) ) ) ).
tt(dt_k11_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k11_pre_poly A B C)) &  ((v4_relat_1 (k11_pre_poly A B C) A) &  ((v1_funct_1 (k11_pre_poly A B C)) & (v1_partfun1 (k11_pre_poly A B C) A)) ) ) ) ) ).
tt(dt_k11_prob_1,ax,(m1_subset_1 k11_prob_1 (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers)))).
tt(dt_k11_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  & (m2_prvect_1 B A))  =>  ((v1_funct_1 (k11_prvect_1 A B)) &  ((v1_funct_2 (k11_prvect_1 A B) (k4_card_3 A) (k4_card_3 A)) & (m1_subset_1 (k11_prvect_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A))))) ) ) ) ).
tt(dt_k11_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ( (~ (v2_struct_0 (k11_prvect_2 A B)))  &  ((v13_algstr_0 (k11_prvect_2 A B)) &  ((v2_rlvect_1 (k11_prvect_2 A B)) &  ((v3_rlvect_1 (k11_prvect_2 A B)) &  ((v4_rlvect_1 (k11_prvect_2 A B)) &  ((v5_rlvect_1 (k11_prvect_2 A B)) &  ((v6_rlvect_1 (k11_prvect_2 A B)) &  ((v7_rlvect_1 (k11_prvect_2 A B)) &  ((v8_rlvect_1 (k11_prvect_2 A B)) &  ((v3_normsp_0 (k11_prvect_2 A B)) &  ((v4_normsp_0 (k11_prvect_2 A B)) &  ((v2_normsp_1 (k11_prvect_2 A B)) & (l1_normsp_1 (k11_prvect_2 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k11_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k11_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k11_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  & (m3_pua2mss1 B A))  =>  ((v1_msualg_1 (k11_pua2mss1 A B)) & (l1_msualg_1 (k11_pua2mss1 A B))) ) ) ).
tt(dt_k11_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m2_finseq_1 (k11_qc_lang1 A B) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ).
tt(dt_k11_qc_lang2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k11_qc_lang2 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k11_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  ((v1_funct_1 (k11_qmax_1 A)) &  ((v1_funct_2 (k11_qmax_1 A) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) & (m1_subset_1 (k11_qmax_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)))))) ) ) ) ).
tt(dt_k11_quaterni,ax,(m1_subset_1 k11_quaterni k1_quaterni)).
tt(dt_k11_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (m2_subset_1 (k11_quofield A) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k11_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_int_1 (k11_radix_1 A))) ) ).
tt(dt_k11_radix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k4_radix_3 B))) ) ) )  => (m1_subset_1 (k11_radix_3 A B C D) k4_numbers)) ) ).
tt(dt_k11_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  => (v7_ordinal1 (k11_ranknull A B C D))) ) ).
tt(dt_k11_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_ratfunc1 B A))  => (m1_ratfunc1 (k11_ratfunc1 A B) A)) ) ).
tt(dt_k11_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  & (m1_subset_1 B (k10_ringcat1 A)))  => (m2_ringcat1 (k11_ringcat1 A B) A)) ) ).
tt(dt_k11_rlvect_2,ax,$true).
tt(dt_k11_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k11_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k11_rsspace,ax,(m1_subset_1 k11_rsspace (k1_zfmisc_1 (u1_struct_0 k7_rsspace)))).
tt(dt_k11_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (v1_xreal_0 C)) )  => (m2_finseq_2 (k11_rvsum_1 A B C) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k11_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  => (m2_finseq_1 (k11_rvsum_2 A B) k2_numbers)) ) ).
tt(dt_k11_scmfsa_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_scmfsa_i) & (m1_subset_1 B (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))))  => (m1_subset_1 (k11_scmfsa_1 A B) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) ) ).
tt(dt_k11_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k11_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k11_scmpds_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m1_subset_1 (k11_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k11_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (m1_subset_1 (k11_scmpds_i A) k2_scm_inst)) ) ).
tt(dt_k11_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v12_scmyciel A))  => (v7_ordinal1 (k11_scmyciel A))) ) ).
tt(dt_k11_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k11_seq_4 A) k2_numbers)) ) ).
tt(dt_k11_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k11_seqfunc A B C)) & (m1_subset_1 (k11_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k11_setwiseo,ax, (! [A:$i] :  ((v1_funct_1 (k11_setwiseo A)) &  ((v1_funct_2 (k11_setwiseo A) A (k5_finsub_1 A)) & (m1_subset_1 (k11_setwiseo A) (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 A))))) ) ) ).
tt(dt_k11_simplex0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_simplex0 B A) &  ( ((v1_relat_1 C) & (v1_funct_1 C))  & (v7_ordinal1 D)) )  => (m1_simplex0 (k11_simplex0 A B C D) A)) ) ).
tt(dt_k11_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k11_sincos10 A) k1_numbers)) ) ).
tt(dt_k11_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k11_stacks_1 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k11_sublemma,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k11_sublemma A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k11_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_substut1 A))) )  =>  ((v1_finset_1 (k11_substut1 A B)) & (m1_subset_1 (k11_substut1 A B) (k1_zfmisc_1 (k1_qc_lang1 A)))) ) ) ).
tt(dt_k11_supinf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v2_membered A) &  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) )  => (m1_subset_1 (k11_supinf_2 A B C D) k7_numbers)) ) ).
tt(dt_k11_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k11_tdlat_1 A)) &  ((v1_funct_2 (k11_tdlat_1 A) (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A)) & (m1_subset_1 (k11_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_tdlat_1 A) (k9_tdlat_1 A)) (k9_tdlat_1 A))))) ) ) ) ).
tt(dt_k11_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k11_topalg_4 A B C D)) &  ((v1_funct_2 (k11_topalg_4 A B C D) (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) & (m1_subset_1 (k11_topalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))))))) ) ) ) ).
tt(dt_k11_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  ((v1_pre_topc (k11_toprealb A)) & (m1_pre_topc (k11_toprealb A) (k8_toprealb 2))) ) ) ).
tt(dt_k11_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k11_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k11_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~ (v1_xboole_0 (k11_trees_3 A)))  & (v1_trees_1 (k11_trees_3 A))) ) ) ).
tt(dt_k11_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))))  => (m1_subset_1 (k11_turing_1 A B) (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))))) ) ).
tt(dt_k11_twoscomp,ax, ((v1_funct_1 k11_twoscomp) &  ((v1_funct_2 k11_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k11_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k11_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_funct_1 (k11_unialg_2 A)) &  ((v1_funct_2 (k11_unialg_2 A) (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A)) & (m1_subset_1 (k11_unialg_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_unialg_2 A) (k9_unialg_2 A)) (k9_unialg_2 A))))) ) ) ) ).
tt(dt_k11_valued_2,ax,$true).
tt(dt_k11_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_vectsp10 A B C)) &  ((v1_funct_2 (k11_vectsp10 A B C) (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C))) (u1_struct_0 A)) &  ((v13_vectsp_1 (k11_vectsp10 A B C) (k6_vectsp10 A B (k9_vectsp10 A B C)) A) &  ((v1_hahnban1 (k11_vectsp10 A B C) A (k6_vectsp10 A B (k9_vectsp10 A B C))) & (m1_subset_1 (k11_vectsp10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C))) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k11_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k11_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k11_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k11_waybel34 A)))  &  ((v2_altcat_1 (k11_waybel34 A)) &  ((v6_altcat_1 (k11_waybel34 A)) &  ((v2_altcat_2 (k11_waybel34 A) (k9_waybel34 A)) &  ((v3_altcat_2 (k11_waybel34 A) (k9_waybel34 A)) & (m1_altcat_2 (k11_waybel34 A) (k9_waybel34 A))) ) ) ) ) ) ) ).
tt(dt_k11_waybel_4,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v1_funct_1 (k11_waybel_4 A B)) &  ((v1_funct_2 (k11_waybel_4 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 (k11_waybel_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) ) ) ) ).
tt(dt_k11_xboolean,ax,$true).
tt(dt_k11_xtuple_0,ax,$true).
tt(dt_k11_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v3_yellow_6 B A) & (l1_waybel_0 B A)) ) ) ) )  => (m1_subset_1 (k11_yellow_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k11_zf_lang,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  =>  ((v1_zf_lang (k11_zf_lang A B)) & (m2_finseq_1 (k11_zf_lang A B) k5_numbers)) ) ) ).
tt(dt_k11_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k11_zf_model A)) & (m2_finseq_1 (k11_zf_model A) k5_numbers)) ) ) ).
tt(dt_k11_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k11_zmodul01 A)) &  ((v1_funct_2 (k11_zmodul01 A) (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A)) & (m1_subset_1 (k11_zmodul01 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_zmodul01 A) (k8_zmodul01 A)) (k8_zmodul01 A))))) ) ) ) ).
tt(dt_k12_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) &  ((v14_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k12_abcmiz_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k12_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m1_subset_1 (k12_abcmiz_1 A) (u1_struct_0 A))) ) ).
tt(dt_k12_abcmiz_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v2_abcmiz_1 B A) &  ((v4_abcmiz_a B A) & (m2_abcmiz_1 B A (k12_abcmiz_1 A))) ) )  =>  ((v9_abcmiz_1 (k12_abcmiz_a A B) A) & (m1_abcmiz_1 (k12_abcmiz_a A B) A (k12_abcmiz_1 A))) ) ) ).
tt(dt_k12_afinsq_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  => (m2_finseq_1 (k12_afinsq_1 A B) A)) ) ).
tt(dt_k12_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (m1_subset_1 (k12_afproj A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_afproj A) (k8_afproj A))))) ) ).
tt(dt_k12_algstr_4,ax,$true).
tt(dt_k12_ami_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ((v1_relat_1 (k12_ami_3 A B C D)) &  ((v4_relat_1 (k12_ami_3 A B C D) (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 (k12_ami_3 A B C D)) & (v5_funct_1 (k12_ami_3 A B C D) (k2_memstr_0 2 k1_ami_3))) ) ) ) ) ).
tt(dt_k12_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) & (l1_unialg_1 A)) )  => (m1_subset_1 (k12_aofa_000 A) (u1_struct_0 A))) ) ).
tt(dt_k12_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((v1_funct_1 (k12_aofa_i00 A B C)) &  ((v1_funct_2 (k12_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k12_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k12_armstrng,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ((v6_armstrng (k12_armstrng A B) A) & (m1_subset_1 (k12_armstrng A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) ) ).
tt(dt_k12_arytm_3,ax, ( (~ (v1_xboole_0 k12_arytm_3))  &  ((v3_ordinal1 k12_arytm_3) & (m1_subset_1 k12_arytm_3 k5_arytm_3)) ) ).
tt(dt_k12_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k12_asympt_0 A B)) &  ((v1_funct_2 (k12_asympt_0 A B) k5_numbers k1_numbers) & (m1_subset_1 (k12_asympt_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k12_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k12_bagorder A)) &  ((v1_funct_2 (k12_bagorder A) k5_numbers (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A))))) & (m1_subset_1 (k12_bagorder A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))))))) ) ) ) ).
tt(dt_k12_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ((l2_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k12_bilinear A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k12_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k12_binop_2 A B) k1_numbers)) ) ).
tt(dt_k12_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A))) )  =>  ((v1_funct_1 (k12_borsuk_1 A B)) &  ((v1_funct_2 (k12_borsuk_1 A B) (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B))) &  ((v5_pre_topc (k12_borsuk_1 A B) A (k11_borsuk_1 A B)) & (m1_subset_1 (k12_borsuk_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)))))) ) ) ) ) ).
tt(dt_k12_borsuk_7,ax, ((v1_funct_1 k12_borsuk_7) &  ((v1_funct_2 k12_borsuk_7 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 3))) & (m1_subset_1 k12_borsuk_7 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 3)))))) ) ).
tt(dt_k12_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k12_bvfunc_1 A)) &  ((v1_funct_2 (k12_bvfunc_1 A) A k6_margrel1) & (m1_subset_1 (k12_bvfunc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k12_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k12_card_3 A B)) & (v1_funct_1 (k12_card_3 A B))) ) ) ).
tt(dt_k12_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  => (m2_cat_1 (k12_cat_2 A B C D E) B C)) ) ).
tt(dt_k12_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k12_cat_4 A B) A (k2_cat_4 A B (k1_cat_4 A)) B)) ) ).
tt(dt_k12_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k12_cat_5 A B)))  &  ( (~ (v11_struct_0 (k12_cat_5 A B)))  &  ((v1_cat_1 (k12_cat_5 A B)) &  ((v2_cat_1 (k12_cat_5 A B)) &  ((v3_cat_1 (k12_cat_5 A B)) &  ((v4_cat_1 (k12_cat_5 A B)) &  ((v5_cat_1 (k12_cat_5 A B)) &  ((v6_cat_1 (k12_cat_5 A B)) &  ((v1_cat_5 (k12_cat_5 A B)) & (l1_cat_1 (k12_cat_5 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k12_catalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  =>  ((v1_funct_1 (k12_catalg_1 A B C)) &  ((v1_funct_2 (k12_catalg_1 A B C) (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B)))) & (m1_subset_1 (k12_catalg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B))))))) ) ) ) ).
tt(dt_k12_cgames_1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k2_cgames_1 A)))  => (m1_subset_1 (k12_cgames_1 A B) (k1_zfmisc_1 (k2_cgames_1 A)))) ) ).
tt(dt_k12_clopban1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k12_clopban1 A B C)))  & (m1_subset_1 (k12_clopban1 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k12_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v15_closure2 B A) & (l1_closure2 B A)) )  =>  ((v1_funct_1 (k12_closure2 A B)) &  ((v1_funct_2 (k12_closure2 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) &  ((v7_closure2 (k12_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v8_closure2 (k12_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v9_closure2 (k12_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 (k12_closure2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))))) ) ) ) ) ) ) ).
tt(dt_k12_cohsp_1,ax,$true).
tt(dt_k12_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k12_coh_sp A)) & (m1_subset_1 (k12_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_coh_sp A) (k5_coh_sp A)) (k5_coh_sp A))))) ) ).
tt(dt_k12_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (m1_subset_1 (k12_complex1 A) k2_numbers)) ) ).
tt(dt_k12_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_comput_1 k5_numbers))) => (m1_subset_1 (k12_comput_1 A) (k1_zfmisc_1 (k2_comput_1 k5_numbers)))) ) ).
tt(dt_k12_conlat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (m1_subset_1 B (u1_struct_0 (k11_conlat_1 A))))  =>  ((v4_conlat_1 (k12_conlat_1 A B) A) &  ( (~ (v5_conlat_1 (k12_conlat_1 A B) A))  &  ((v7_conlat_1 (k12_conlat_1 A B) A) & (l2_conlat_1 (k12_conlat_1 A B) A)) ) ) ) ) ).
tt(dt_k12_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  & (m1_convex4 B A))  => (m1_subset_1 (k12_convex4 A B) (k10_convex4 A))) ) ).
tt(dt_k12_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k12_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k12_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m1_subset_1 (k12_cqc_sim1 A B) (k1_zfmisc_1 (k1_qc_lang1 A)))) ) ).
tt(dt_k12_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_csspace A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_xcmplx_0 (k12_csspace A B C))) ) ).
tt(dt_k12_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k12_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k12_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 C (k4_finseq_2 A k6_margrel1))) )  => (m2_finseq_2 (k12_descip_1 A B C) k6_margrel1 (k4_finseq_2 A k6_margrel1))) ) ).
tt(dt_k12_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k4_partfun1 k1_numbers k1_numbers)) &  ((v1_diff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k12_diff_1 A B)) &  ((v1_funct_2 (k12_diff_1 A B) k5_numbers k1_numbers) & (m1_subset_1 (k12_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k12_dtconstr,ax, ((v1_funct_1 k12_dtconstr) &  ((v1_funct_2 k12_dtconstr (k4_dtconstr k5_dtconstr) k5_numbers) & (m1_subset_1 k12_dtconstr (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k5_dtconstr) k5_numbers)))) ) ).
tt(dt_k12_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k12_ens_1 A B) (u1_struct_0 (k11_ens_1 A)))) ) ).
tt(dt_k12_eqrel_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_eqrel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) ) )  =>  ( (~ (v1_xboole_0 (k12_eqrel_1 A B)))  & (m1_eqrel_1 (k12_eqrel_1 A B) A)) ) ) ).
tt(dt_k12_e_siec,ax,$true).
tt(dt_k12_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (u1_struct_0 (k15_euclid A)))) ) ) )  => (m1_subset_1 (k12_euclid_3 A B C D E) k1_numbers)) ) ).
tt(dt_k12_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  => (m1_subset_1 (k12_euclid A) k1_numbers)) ) ).
tt(dt_k12_facirc_1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k12_facirc_1 A B C) (u1_struct_0 (k8_facirc_1 A B C k1_facirc_1)) (k3_msafree2 (k8_facirc_1 A B C k1_facirc_1)))) ).
tt(dt_k12_ff_siec,ax,$true).
tt(dt_k12_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  &  ( (~ (v1_xboole_0 E))  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers E)))) )  & (m1_subset_1 G C)) ) ) ) ) )  => (m1_subset_1 (k12_finance1 A B C D E F G) k1_numbers)) ) ).
tt(dt_k12_finseq_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m2_finseq_1 (k12_finseq_1 A B) A)) ) ).
tt(dt_k12_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k12_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k12_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k12_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k12_fomodel0,ax, (! [A:$i,B:$i] : (m1_subset_1 (k12_fomodel0 A B) (k1_zfmisc_1 B))) ).
tt(dt_k12_fomodel1,ax, (! [A:$i,B:$i] :  ( ((l4_struct_0 A) & (m1_subset_1 B (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A)))))  => (v1_int_1 (k12_fomodel1 A B))) ) ).
tt(dt_k12_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_fomodel2 D A B C)) )  &  ((v10_fomodel1 E A) & (m1_subset_1 E (k1_fomodel1 A))) ) ) ) )  => (m2_fomodel2 (k12_fomodel2 A B C D E) A B E)) ) ).
tt(dt_k12_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  & (v1_relat_1 E)) ) ) )  => (m1_subset_1 (k12_fomodel3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A C) (k8_eqrel_1 B D))))) ) ).
tt(dt_k12_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k12_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k12_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ((v2_freealg (k12_freealg A B) (k7_freealg A B)) & (m1_freealg (k12_freealg A B) (k7_freealg A B))) ) ) ).
tt(dt_k12_fsm_1,ax,$true).
tt(dt_k12_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k12_ftacell1 A B C D E) (k3_msafree2 (k7_ftacell1 A B C D E)))) ).
tt(dt_k12_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((v1_funct_1 (k12_funcop_1 A B C D)) &  ((v1_funct_2 (k12_funcop_1 A B C D) A (k2_zfmisc_1 C B)) & (m1_subset_1 (k12_funcop_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 C B))))) ) ) ) ).
tt(dt_k12_funcsdom,ax, (! [A:$i] :  ((v1_funcsdom (k12_funcsdom A)) & (l1_funcsdom (k12_funcsdom A))) ) ).
tt(dt_k12_funct_3,ax, (! [A:$i] :  ((v1_funct_1 (k12_funct_3 A)) &  ((v1_funct_2 (k12_funct_3 A) A (k2_zfmisc_1 A A)) & (m1_subset_1 (k12_funct_3 A) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 A A))))) ) ) ).
tt(dt_k12_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((v1_funct_1 (k12_funct_5 A B C D)) &  ((v1_funct_2 (k12_funct_5 A B C D) B (k9_funct_2 A C)) & (m1_subset_1 (k12_funct_5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (k9_funct_2 A C))))) ) ) ) ).
tt(dt_k12_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k12_funct_7 A B C)) &  ((v1_funct_2 (k12_funct_7 A B C) k5_numbers A) & (m1_subset_1 (k12_funct_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k12_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ((v9_functor0 (k12_functor0 A) A A) &  ((v15_functor0 (k12_functor0 A) A A) & (m2_functor0 (k12_functor0 A) A A)) ) ) ) ).
tt(dt_k12_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  => (m2_finseq_2 (k12_fvsum_1 A B C D) (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B)))) ) ).
tt(dt_k12_gate_1,ax,$true).
tt(dt_k12_gate_5,ax,$true).
tt(dt_k12_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) &  ((m1_subset_1 H k5_numbers) & (m1_subset_1 I k5_numbers)) ) ) ) ) ) ) )  => (m1_genealg1 (k12_genealg1 A B C D E F G H I) A)) ) ).
tt(dt_k12_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k12_gfacirc1 A B C) (u1_struct_0 (k10_gfacirc1 A B C)) (k3_msafree2 (k10_gfacirc1 A B C)))) ).
tt(dt_k12_glib_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) )  =>  ((v1_relat_1 (k12_glib_000 A B C D)) &  ((v4_relat_1 (k12_glib_000 A B C D) k5_numbers) &  ((v1_funct_1 (k12_glib_000 A B C D)) &  ((v1_finset_1 (k12_glib_000 A B C D)) & (v1_glib_000 (k12_glib_000 A B C D))) ) ) ) ) ) ).
tt(dt_k12_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m2_glib_001 (k12_glib_001 A B) A)) ) ).
tt(dt_k12_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) & (v2_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ).
tt(dt_k12_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))))  => (m1_subset_1 (k12_glib_004 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k12_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k6_glib_000 A))) )  => (m3_glib_005 (k12_glib_005 A B C) A)) ) ).
tt(dt_k12_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k12_graph_3 A B C)))  & (m1_finseq_2 (k12_graph_3 A B C) (u4_struct_0 A))) ) ) ).
tt(dt_k12_graphsp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k8_graph_5)))) ) ) ) )  => (m1_subset_1 (k12_graphsp A B C D) k1_numbers)) ) ).
tt(dt_k12_group_10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) ) )  => (m1_subset_1 (k12_group_10 A B C) (k1_zfmisc_1 B))) ) ).
tt(dt_k12_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k12_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k12_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  ((v1_funct_1 (k12_group_9 A B C)) &  ((v1_funct_2 (k12_group_9 A B C) (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B C))) &  ((v1_group_6 (k12_group_9 A B C) B (k10_group_9 A B C)) &  ((v7_group_9 (k12_group_9 A B C) A B (k10_group_9 A B C)) & (m1_subset_1 (k12_group_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B C)))))) ) ) ) ) ) ).
tt(dt_k12_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_funct_1 (k12_hahnban1 A B)) &  ((v1_funct_2 (k12_hahnban1 A B) (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 (k12_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ).
tt(dt_k12_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_finseq_1 B k5_numbers) & (m1_finseq_1 C k5_numbers)) )  => (m2_finseq_1 (k12_idea_1 A B C) k5_numbers)) ) ).
tt(dt_k12_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k12_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k12_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((m1_subset_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid C))))) ) ) )  => (m2_finseq_2 (k12_integr15 A B C D) k1_numbers (k1_euclid C))) ) ).
tt(dt_k12_integra1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  => (m1_subset_1 (k12_integra1 A B) k1_numbers)) ) ).
tt(dt_k12_intpro_1,ax,(m1_subset_1 k12_intpro_1 (k1_zfmisc_1 k1_intpro_1))).
tt(dt_k12_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A (k8_cat_2 B C)) &  ((m2_cat_1 E A (k8_cat_2 B C)) & (m2_nattra_1 F A (k8_cat_2 B C) D E)) ) ) ) )  => (m2_nattra_1 (k12_isocat_2 A B C D E F) A C (k10_isocat_2 A B C D) (k10_isocat_2 A B C E))) ) ).
tt(dt_k12_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k12_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k12_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((v1_funct_1 (k12_lang1 A B C)) &  ((v1_funct_2 (k12_lang1 A B C) (k3_finseq_2 A) (k3_finseq_2 B)) & (m1_subset_1 (k12_lang1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 B))))) ) ) ) ).
tt(dt_k12_laplace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_finseq_1 C (u1_struct_0 A))) )  =>  ((v1_matrix_1 (k12_laplace A B C)) & (m2_finseq_1 (k12_laplace A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k12_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k12_lattice3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k12_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  =>  ((v1_funct_1 (k12_lattice5 A B C D E)) &  ((v1_funct_2 (k12_lattice5 A B C D E) (k2_zfmisc_1 (k8_lattice5 A E) (k8_lattice5 A E)) (u1_struct_0 B)) & (m1_subset_1 (k12_lattice5 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_lattice5 A E) (k8_lattice5 A E)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k12_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))))  => (m1_subset_1 (k12_lexbfs A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers))))) ) ).
tt(dt_k12_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v1_funct_1 (k12_lmod_7 A B C)) &  ((v1_funct_2 (k12_lmod_7 A B C) (k2_zfmisc_1 (k7_lmod_7 A B C) (k7_lmod_7 A B C)) (k7_lmod_7 A B C)) & (m1_subset_1 (k12_lmod_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_lmod_7 A B C) (k7_lmod_7 A B C)) (k7_lmod_7 A B C))))) ) ) ) ).
tt(dt_k12_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k11_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k12_lopban_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k12_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ( (~ (v2_struct_0 (k12_lopclset A)))  &  ((v10_lattices (k12_lopclset A)) & (l3_lattices (k12_lopclset A))) ) ) ) ).
tt(dt_k12_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k12_lpspace1 A B C)))  & (l1_rlvect_1 (k12_lpspace1 A B C))) ) ) ).
tt(dt_k12_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v2_struct_0 (k12_lpspace2 A B C D)))  & (l1_normsp_1 (k12_lpspace2 A B C D))) ) ) ).
tt(dt_k12_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_hilbert1 k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  ((v1_funct_1 (k12_ltlaxio1 A)) &  ((v1_funct_2 (k12_ltlaxio1 A) k1_hilbert1 k6_margrel1) & (m1_subset_1 (k12_ltlaxio1 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) ) ) ) ).
tt(dt_k12_margrel1,ax, (! [A:$i] : (m1_subset_1 (k12_margrel1 A) k6_margrel1)) ).
tt(dt_k12_matrix_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (v7_ordinal1 B))  => (m1_matrix_1 (k12_matrix_1 A B) (u1_struct_0 A) B B)) ) ).
tt(dt_k12_matrix_2,ax,$true).
tt(dt_k12_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_subset_1 (k12_matrix_3 A B C) (u1_struct_0 B))) ) ).
tt(dt_k12_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  => (m1_subset_1 (k12_matrixc1 A) k2_numbers)) ) ).
tt(dt_k12_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v1_matrix_1 (k12_matrixj1 A B C)) & (m2_finseq_1 (k12_matrixj1 A B C) (k3_finseq_2 A))) ) ) ).
tt(dt_k12_matrixr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  & (m1_finseq_1 B k1_numbers))  => (m2_finseq_1 (k12_matrixr1 A B) k1_numbers)) ) ).
tt(dt_k12_mcart_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k12_mcart_1 A)) & (v1_funct_1 (k12_mcart_1 A))) ) ) ).
tt(dt_k12_member_1,ax,$true).
tt(dt_k12_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ((v1_funct_1 (k12_mesfun7c A B)) &  ((v1_funct_2 (k12_mesfun7c A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k12_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k12_mesfunc1,ax,$true).
tt(dt_k12_metric_1,ax, ((v1_funct_1 k12_metric_1) &  ((v1_funct_2 k12_metric_1 (k2_zfmisc_1 2 2) k1_numbers) & (m1_subset_1 k12_metric_1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 2 2) k1_numbers)))) ) ).
tt(dt_k12_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v1_funct_1 (k12_midsp_1 A)) &  ((v1_funct_2 (k12_midsp_1 A) (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A)) (k10_midsp_1 A)) & (m1_subset_1 (k12_midsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A)) (k10_midsp_1 A))))) ) ) ) ).
tt(dt_k12_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 D)) )  => (m1_subset_1 (k12_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k12_mod_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 B (k1_enumset1 k6_numbers 1 2)))  => (m1_subset_1 (k12_mod_2 A B) (k1_enumset1 k6_numbers 1 2))) ) ).
tt(dt_k12_modal_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_modal_1) & (m1_subset_1 B k6_modal_1))  => (m1_subset_1 (k12_modal_1 A B) k6_modal_1)) ) ).
tt(dt_k12_modelc_1,ax, (~ (v1_xboole_0 k12_modelc_1)) ).
tt(dt_k12_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_2 (k12_modelc_2 A)) & (m2_finseq_1 (k12_modelc_2 A) k5_numbers)) ) ) ).
tt(dt_k12_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (l1_modelc_3 B A))  =>  ((v1_modelc_3 (k12_modelc_3 A B) A) & (l1_modelc_3 (k12_modelc_3 A B) A)) ) ) ).
tt(dt_k12_monoid_0,ax, (! [A:$i] :  ((v15_algstr_0 (k12_monoid_0 A)) &  ((v1_monoid_0 (k12_monoid_0 A)) & (l3_algstr_0 (k12_monoid_0 A))) ) ) ).
tt(dt_k12_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v16_monoid_0 A) &  ((v17_monoid_0 A) & (l3_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k12_monoid_1 A B)))  &  ((v22_algstr_0 (k12_monoid_1 A B)) &  ((v3_group_1 (k12_monoid_1 A B)) &  ((v5_group_1 (k12_monoid_1 A B)) &  ((v4_vectsp_1 (k12_monoid_1 A B)) &  ((v1_monoid_0 (k12_monoid_1 A B)) &  ((v16_monoid_0 (k12_monoid_1 A B)) &  ((v17_monoid_0 (k12_monoid_1 A B)) & (l4_algstr_0 (k12_monoid_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k12_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k12_msafree A B C) (k1_zfmisc_1 (k1_funct_1 (k8_msafree A B) C)))) ) ).
tt(dt_k12_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k12_msualg_1 A B)))  &  ((v1_unialg_1 (k12_msualg_1 A B)) &  ((v2_unialg_1 (k12_msualg_1 A B)) &  ((v3_unialg_1 (k12_msualg_1 A B)) &  ((v4_unialg_1 (k12_msualg_1 A B)) & (l1_unialg_1 (k12_msualg_1 A B))) ) ) ) ) ) ) ).
tt(dt_k12_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  =>  ((v3_msualg_1 (k12_msualg_2 A B C) A) & (m1_msualg_2 (k12_msualg_2 A B C) A B)) ) ) ).
tt(dt_k12_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) )  => (m2_pboole (k12_msualg_4 A B C) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A B C)))) ) ).
tt(dt_k12_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k12_nat_3 A)) &  ((v4_relat_1 (k12_nat_3 A) k10_newton) &  ((v1_funct_1 (k12_nat_3 A)) & (v1_partfun1 (k12_nat_3 A) k10_newton)) ) ) ) ) ).
tt(dt_k12_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v1_cat_1 (k12_nattra_1 A)) &  ((v2_nattra_1 (k12_nattra_1 A)) & (m3_cat_2 (k12_nattra_1 A) A)) ) ) ) ).
tt(dt_k12_net_1,ax,$true).
tt(dt_k12_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 (k12_newton A)) & (m2_subset_1 (k12_newton A) k1_numbers k5_numbers)) ) ) ).
tt(dt_k12_normform,ax, (! [A:$i] :  ((v3_lattices (k12_normform A)) & (l3_lattices (k12_normform A))) ) ).
tt(dt_k12_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  => (m1_subset_1 (k12_openlatt A B C) (k9_openlatt A))) ) ).
tt(dt_k12_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m1_oppcat_1 (k12_oppcat_1 A) A (k2_oppcat_1 A))) ) ).
tt(dt_k12_ordinal2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k12_ordinal2 A B))) ) ).
tt(dt_k12_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k12_ordinal6 A B))) ) ).
tt(dt_k12_osafree,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (u4_struct_0 A)) & (m1_finseq_1 D (k4_dtconstr (k2_osafree A B)))) ) )  => (m1_dtconstr (k12_osafree A B C D) (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ).
tt(dt_k12_osalg_2,ax,$true).
tt(dt_k12_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  & (m1_subset_1 E (k1_euclid A))) ) ) )  => (m2_finseq_2 (k12_pdiff_1 A B C D E) k1_numbers (k1_euclid B))) ) ).
tt(dt_k12_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k12_petri A B) (k1_zfmisc_1 (u1_struct_0 (k11_petri A))))) ) ).
tt(dt_k12_pnproc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k12_pnproc_1 A B)) &  ((v1_funct_1 (k12_pnproc_1 A B)) & (v2_finseq_1 (k12_pnproc_1 A B))) ) ) ) ).
tt(dt_k12_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_subset_1 (k12_polyform A) k1_numbers k5_numbers)) ) ).
tt(dt_k12_polynom3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_finseq_2 (k12_polynom3 A) k5_numbers (k4_finseq_2 1 k5_numbers))) ) ).
tt(dt_k12_pralg_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  =>  ((v1_relat_1 (k12_pralg_1 A B)) &  ((v4_relat_1 (k12_pralg_1 A B) A) &  ((v1_funct_1 (k12_pralg_1 A B)) & (v1_partfun1 (k12_pralg_1 A B) A)) ) ) ) ) ).
tt(dt_k12_pralg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_pralg_2 C A B) & (m1_subset_1 D (u4_struct_0 B))) )  =>  ((v1_relat_1 (k12_pralg_2 A B C D)) &  ((v4_relat_1 (k12_pralg_2 A B C D) A) &  ((v1_funct_1 (k12_pralg_2 A B C D)) &  ((v1_partfun1 (k12_pralg_2 A B C D) A) & (v1_funcop_1 (k12_pralg_2 A B C D))) ) ) ) ) ) ).
tt(dt_k12_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k12_pre_poly A B C)) &  ((v4_relat_1 (k12_pre_poly A B C) A) &  ((v1_funct_1 (k12_pre_poly A B C)) & (v1_partfun1 (k12_pre_poly A B C) A)) ) ) ) ) ).
tt(dt_k12_prob_1,ax, ( (~ (v1_xboole_0 k12_prob_1))  &  ((v1_prob_1 k12_prob_1 k1_numbers) &  ((v4_prob_1 k12_prob_1 k1_numbers) & (m1_subset_1 k12_prob_1 (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers)))) ) ) ).
tt(dt_k12_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v4_funct_1 A) &  (~ (v1_xboole_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k12_prvect_1 A B C D) A)) ) ).
tt(dt_k12_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_card_3 (k4_prvect_2 A))))  => (m2_finseq_2 (k12_prvect_2 A B) k1_numbers (k1_euclid (k3_finseq_1 A)))) ) ).
tt(dt_k12_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k12_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k12_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  &  ((m3_pua2mss1 B A) & (m1_subset_1 C (u4_struct_0 (k11_pua2mss1 A B)))) )  => (m2_subset_1 (k12_pua2mss1 A B C) k5_numbers (k4_finseq_1 (u1_unialg_1 A)))) ) ).
tt(dt_k12_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k12_qc_lang1 A) (k9_qc_lang1 A))) ) ).
tt(dt_k12_qc_lang2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k12_qc_lang2 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k12_quatern2,ax, ((v1_funct_1 k12_quatern2) &  ((v1_funct_2 k12_quatern2 (k2_zfmisc_1 k1_quaterni k1_quaterni) k1_quaterni) & (m1_subset_1 k12_quatern2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_quaterni k1_quaterni) k1_quaterni)))) ) ).
tt(dt_k12_quaterni,ax,(m1_subset_1 k12_quaterni k1_quaterni)).
tt(dt_k12_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (m2_subset_1 (k12_quofield A) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k12_radix_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (v1_int_1 (k12_radix_1 A B))) ) ).
tt(dt_k12_radix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k4_radix_3 B))) ) ) )  => (m1_subset_1 (k12_radix_3 A B C D) k4_numbers)) ) ).
tt(dt_k12_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_ratfunc1 B A))  => (v1_int_1 (k12_ratfunc1 A B))) ) ).
tt(dt_k12_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (v1_xreal_0 D)) ) )  => (m2_rfunct_3 (k12_rfunct_3 A B C D) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k12_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  & (m1_subset_1 B (k10_ringcat1 A)))  => (m2_ringcat1 (k12_ringcat1 A B) A)) ) ).
tt(dt_k12_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k11_rlvect_2 A)))  => (m1_rlvect_2 (k12_rlvect_2 A B) A)) ) ).
tt(dt_k12_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k12_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k12_rsspace,ax, ((v1_funct_1 k12_rsspace) &  ((v1_funct_2 k12_rsspace (k2_zfmisc_1 k11_rsspace k11_rsspace) k1_numbers) & (m1_subset_1 k12_rsspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k11_rsspace k11_rsspace) k1_numbers)))) ) ).
tt(dt_k12_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 (k12_rvsum_1 A) k1_numbers)) ) ).
tt(dt_k12_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  => (m2_finseq_2 (k12_rvsum_2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k12_scm_comp,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (v1_int_1 (k12_scm_comp A B))) ) ).
tt(dt_k12_scmfsa_1,ax, ((v1_funct_1 k12_scmfsa_1) &  ((v1_funct_2 k12_scmfsa_1 k2_scmfsa_i (k1_funct_2 (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) & (m1_subset_1 k12_scmfsa_1 (k1_zfmisc_1 (k2_zfmisc_1 k2_scmfsa_i (k1_funct_2 (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))))))) ) ).
tt(dt_k12_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k12_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k12_scmpds_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (m1_subset_1 (k12_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k12_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k12_scmpds_i A))) ) ).
tt(dt_k12_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) => (v4_scmyciel (k12_scmyciel A))) ) ).
tt(dt_k12_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (v1_xcmplx_0 B))  => (m2_finseq_1 (k12_seq_4 A B) k2_numbers)) ) ).
tt(dt_k12_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k12_sincos10 A) k1_numbers)) ) ).
tt(dt_k12_sin_cos,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k2_numbers) &  ((m1_subset_1 B k2_numbers) & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k12_sin_cos A B C)) &  ((v1_funct_2 (k12_sin_cos A B C) k5_numbers k2_numbers) & (m1_subset_1 (k12_sin_cos A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k12_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  => (m1_subset_1 (k12_stacks_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A))))) ) ).
tt(dt_k12_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D B)) ) )  =>  ((v1_funct_1 (k12_sublemma A B C D)) & (m1_subset_1 (k12_sublemma A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) ).
tt(dt_k12_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) &  ((v1_finset_1 C) & (m1_subset_1 C (k1_substut1 A))) ) )  =>  ( (~ (v1_xboole_0 (k12_substut1 A B C)))  & (m1_subset_1 (k12_substut1 A B C) (k1_zfmisc_1 (k1_qc_lang1 A)))) ) ) ).
tt(dt_k12_supinf_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  => (m1_subset_1 (k12_supinf_2 A B) k7_numbers)) ) ).
tt(dt_k12_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (k12_tdlat_1 A)))  &  ((v10_lattices (k12_tdlat_1 A)) &  ((v17_lattices (k12_tdlat_1 A)) & (l3_lattices (k12_tdlat_1 A))) ) ) ) ) ).
tt(dt_k12_toprealb,ax, ((v1_funct_1 k12_toprealb) &  ((v1_funct_2 k12_toprealb (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 k12_toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)))))) ) ).
tt(dt_k12_toprealc,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  => (m1_subset_1 (k12_toprealc A B) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k12_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (~ (v1_xboole_0 (k12_trees_3 A)))  & (v1_trees_1 (k12_trees_3 A))) ) ) ).
tt(dt_k12_trees_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  => (m1_subset_1 (k12_trees_9 A B) (k1_zfmisc_1 (k9_trees_9 A)))) ) ).
tt(dt_k12_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k12_turing_1 A B C)) &  ((v1_funct_2 (k12_turing_1 A B C) A (k2_zfmisc_1 A B)) & (m1_subset_1 (k12_turing_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 A B))))) ) ) ) ).
tt(dt_k12_twoscomp,ax, ((v1_funct_1 k12_twoscomp) &  ((v1_funct_2 k12_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k12_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k12_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k12_unialg_2 A)))  &  ((v3_lattices (k12_unialg_2 A)) &  ((v10_lattices (k12_unialg_2 A)) & (l3_lattices (k12_unialg_2 A))) ) ) ) ) ).
tt(dt_k12_valued_2,ax,$true).
tt(dt_k12_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k12_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k12_waybel_4,ax,$true).
tt(dt_k12_xtuple_0,ax,$true).
tt(dt_k12_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v13_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((v13_waybel_0 (k12_yellow_3 A B C D) (k3_yellow_3 A B)) & (m1_subset_1 (k12_yellow_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) ) ) ).
tt(dt_k12_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m4_yellow_6 (k12_yellow_6 A) A)) ) ).
tt(dt_k12_zf_lang,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  =>  ((v1_zf_lang (k12_zf_lang A B)) & (m2_finseq_1 (k12_zf_lang A B) k5_numbers)) ) ) ).
tt(dt_k12_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k12_zmodul01 A)) &  ((v1_funct_2 (k12_zmodul01 A) (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k12_zmodul01 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k13_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m1_subset_1 (k13_abcmiz_1 A) (u1_struct_0 A))) ) ).
tt(dt_k13_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((v2_abcmiz_1 (k13_abcmiz_a A) k27_abcmiz_1) & (m1_subset_1 (k13_abcmiz_a A) (u4_struct_0 k27_abcmiz_1))) ) ) ).
tt(dt_k13_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v1_incsp_1 (k13_afproj A)) & (l1_incsp_1 (k13_afproj A))) ) ) ).
tt(dt_k13_algstr_4,ax, (! [A:$i] :  ((v1_funct_1 (k13_algstr_4 A)) &  ((v1_funct_2 (k13_algstr_4 A) (k2_zfmisc_1 (k12_algstr_4 A) (k12_algstr_4 A)) (k12_algstr_4 A)) & (m1_subset_1 (k13_algstr_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k12_algstr_4 A) (k12_algstr_4 A)) (k12_algstr_4 A))))) ) ) ).
tt(dt_k13_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_unialg_1 A) &  ((v4_aofa_000 A) & (l1_unialg_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k13_aofa_000 A B C) (u1_struct_0 A))) ) ).
tt(dt_k13_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((v1_funct_1 (k13_aofa_i00 A B C)) &  ((v1_funct_2 (k13_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k13_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k13_armstrng,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (m1_subset_1 (k13_armstrng A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k13_asympt_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_funct_2 B A k1_numbers) & (m1_funct_2 C A k1_numbers)) )  => (m1_funct_2 (k13_asympt_0 A B C) A k1_numbers)) ) ).
tt(dt_k13_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_partfun1 (k13_bagorder A) (k5_finsub_1 (u1_struct_0 A))) &  ((v1_relat_2 (k13_bagorder A)) &  ((v4_relat_2 (k13_bagorder A)) &  ((v8_relat_2 (k13_bagorder A)) & (m1_subset_1 (k13_bagorder A) (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))))) ) ) ) ) ) ).
tt(dt_k13_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k13_bilinear A B C D)))  &  ((v7_vectsp_1 (k13_bilinear A B C D) A) & (m1_vectsp_4 (k13_bilinear A B C D) A B)) ) ) ) ).
tt(dt_k13_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) => (m1_subset_1 (k13_binop_2 A) k3_numbers)) ) ).
tt(dt_k13_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B))) ) )  =>  ( (~ (v1_xboole_0 (k13_borsuk_1 A B C)))  & (m1_eqrel_1 (k13_borsuk_1 A B C) (u1_struct_0 A))) ) ) ).
tt(dt_k13_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k13_borsuk_7 A)) &  ((v1_funct_2 (k13_borsuk_7 A) (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 3))) & (m1_subset_1 (k13_borsuk_7 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k8_toprealb 3)))))) ) ) ) ).
tt(dt_k13_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((v1_funct_1 (k13_bvfunc_1 A B)) &  ((v1_funct_2 (k13_bvfunc_1 A B) A k6_margrel1) & (m1_subset_1 (k13_bvfunc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k13_card_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_funct_1 C B) & (v1_partfun1 C A)) ) ) ) )  => (m1_subset_1 (k13_card_3 A B C) (k4_card_3 B))) ) ).
tt(dt_k13_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (m2_cat_1 (k13_cat_2 A B C D E) A C)) ) ).
tt(dt_k13_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k13_cat_4 A B) A B (k2_cat_4 A B (k1_cat_4 A)))) ) ).
tt(dt_k13_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  => (m1_subset_1 (k13_cat_5 A B C) (u4_struct_0 A))) ) ).
tt(dt_k13_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v3_msualg_1 (k13_catalg_1 A) (k3_catalg_1 (u1_struct_0 A))) & (l3_msualg_1 (k13_catalg_1 A) (k3_catalg_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k13_cgames_1,ax,$true).
tt(dt_k13_classes2,ax, ( (~ (v1_xboole_0 k13_classes2))  & (v1_classes2 k13_classes2)) ).
tt(dt_k13_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k13_clopban1 A B)) &  ((v1_funct_2 (k13_clopban1 A B) (k8_clopban1 A B) k1_numbers) & (m1_subset_1 (k13_clopban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k8_clopban1 A B) k1_numbers)))) ) ) ) ).
tt(dt_k13_cohsp_1,ax,$true).
tt(dt_k13_coh_sp,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k13_coh_sp A)))  &  ( (~ (v11_struct_0 (k13_coh_sp A)))  &  ((v1_cat_1 (k13_coh_sp A)) & (l1_cat_1 (k13_coh_sp A))) ) ) ) ).
tt(dt_k13_complex1,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k13_complex1 A B) k2_numbers)) ) ).
tt(dt_k13_comput_1,ax, ((v1_funct_1 k13_comput_1) &  ((v1_funct_2 k13_comput_1 k5_numbers (k9_setfam_1 (k2_comput_1 k5_numbers))) & (m1_subset_1 k13_comput_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_comput_1 k5_numbers)))))) ) ).
tt(dt_k13_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v1_funct_1 (k13_convex4 A)) &  ((v1_funct_2 (k13_convex4 A) (k2_zfmisc_1 (k10_convex4 A) (k10_convex4 A)) (k10_convex4 A)) & (m1_subset_1 (k13_convex4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_convex4 A) (k10_convex4 A)) (k10_convex4 A))))) ) ) ) ).
tt(dt_k13_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  => (m1_subset_1 (k13_cqc_lang A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k13_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m1_subset_1 (k13_cqc_sim1 A B) (k1_qc_lang1 A))) ) ).
tt(dt_k13_csspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k13_csspace A B) k1_numbers)) ) ).
tt(dt_k13_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k13_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k13_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C (k4_finseq_2 B (k4_finseq_2 A k6_margrel1))) & (m1_subset_1 D (k2_finseq_1 B))) ) )  => (m2_finseq_2 (k13_descip_1 A B C D) k6_margrel1 (k4_finseq_2 A k6_margrel1))) ) ).
tt(dt_k13_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((m1_subset_1 G A) &  ((m1_subset_1 H A) & (m1_subset_1 I A)) ) ) ) ) ) ) )  => (m1_subset_1 (k13_domain_1 A B C D E F G H I) (k1_zfmisc_1 A))) ) ).
tt(dt_k13_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A (k4_dtconstr k5_dtconstr)) => (m1_dtconstr (k13_dtconstr A) (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr))) ) ).
tt(dt_k13_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u1_struct_0 (k11_ens_1 A))))  => (m1_subset_1 (k13_ens_1 A B) A)) ) ).
tt(dt_k13_eqrel_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A)) )  =>  ((v1_funct_1 (k13_eqrel_1 A B)) &  ((v1_funct_2 (k13_eqrel_1 A B) A B) & (m1_subset_1 (k13_eqrel_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k13_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k13_e_siec A))) ) ).
tt(dt_k13_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k13_euclid A)) &  ((v1_funct_2 (k13_euclid A) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers) & (m1_subset_1 (k13_euclid A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers)))) ) ) ) ).
tt(dt_k13_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k13_facirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v4_msafree2 (k13_facirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v4_circcomb (k13_facirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v6_circcomb (k13_facirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) & (l3_msualg_1 (k13_facirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1))) ) ) ) ) ).
tt(dt_k13_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k13_ff_siec A))) ) ).
tt(dt_k13_finseq_1,ax,$true).
tt(dt_k13_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k13_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k13_fomodel0,ax,$true).
tt(dt_k13_fomodel1,ax, (! [A:$i,B:$i] :  ( ((l4_struct_0 A) & (m1_subset_1 B (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A)))))  => (m1_subset_1 (k13_fomodel1 A B) k4_numbers)) ) ).
tt(dt_k13_fomodel2,ax,$true).
tt(dt_k13_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (v7_ordinal1 C)) )  =>  ((v1_partfun1 (k13_fomodel3 A B C) (k4_finseq_2 C A)) &  ((v3_relat_2 (k13_fomodel3 A B C)) &  ((v8_relat_2 (k13_fomodel3 A B C)) & (m1_subset_1 (k13_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A))))) ) ) ) ) ).
tt(dt_k13_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k13_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k13_freealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  &  ((v1_freealg B) & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k13_freealg A B C)))  &  ((v1_funct_1 (k13_freealg A B C)) &  ((v2_margrel1 (k13_freealg A B C)) &  ((v3_margrel1 (k13_freealg A B C) (k4_dtconstr (k3_freealg A B))) & (m1_subset_1 (k13_freealg A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))))) ) ) ) ) ) ).
tt(dt_k13_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B)) ) )  =>  ((v2_fsm_1 (k13_fsm_1 A B C D) A B) & (l2_fsm_1 (k13_fsm_1 A B C D) A B)) ) ) ).
tt(dt_k13_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( (~ (v2_struct_0 (k13_ftacell1 A B C D E)))  &  ( (~ (v11_struct_0 (k13_ftacell1 A B C D E)))  &  ((v1_msualg_1 (k13_ftacell1 A B C D E)) &  ((v1_circcomb (k13_ftacell1 A B C D E)) &  ((v2_circcomb (k13_ftacell1 A B C D E)) &  ((v3_circcomb (k13_ftacell1 A B C D E)) & (l1_msualg_1 (k13_ftacell1 A B C D E))) ) ) ) ) ) ) ).
tt(dt_k13_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_relat_1 (k13_funcop_1 A B C)) & (v1_funct_1 (k13_funcop_1 A B C))) ) ).
tt(dt_k13_funct_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k13_funct_3 A B)) & (v1_funct_1 (k13_funct_3 A B))) ) ) ).
tt(dt_k13_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) )  =>  ((v1_funct_1 (k13_funct_5 A B C D)) &  ((v1_funct_2 (k13_funct_5 A B C D) (k2_zfmisc_1 A B) C) & (m1_subset_1 (k13_funct_5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) ).
tt(dt_k13_funct_7,ax,$true).
tt(dt_k13_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  & (l2_functor0 E B C)) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (l2_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(dt_k13_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k13_fvsum_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k13_gate_1,ax,$true).
tt(dt_k13_gate_5,ax,$true).
tt(dt_k13_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k13_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k13_gfacirc1 A B C)))  &  ((v1_msualg_1 (k13_gfacirc1 A B C)) &  ((v1_circcomb (k13_gfacirc1 A B C)) &  ((v2_circcomb (k13_gfacirc1 A B C)) &  ((v3_circcomb (k13_gfacirc1 A B C)) & (l1_msualg_1 (k13_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k13_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k13_glib_000 A B C)) &  ((v4_relat_1 (k13_glib_000 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A B C)) & (v1_finset_1 (k13_glib_000 A B C))) ) ) ) ) ).
tt(dt_k13_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ((v1_finset_1 (k13_glib_001 A B)) & (m1_subset_1 (k13_glib_001 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ).
tt(dt_k13_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) & (v3_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ).
tt(dt_k13_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  => (m1_subset_1 (k13_glib_004 A) (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k13_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k6_glib_000 A))) )  =>  ((v1_relat_1 (k13_glib_005 A B C)) &  ((v4_relat_1 (k13_glib_005 A B C) (k7_glib_000 A)) &  ((v1_funct_1 (k13_glib_005 A B C)) &  ((v1_partfun1 (k13_glib_005 A B C) (k7_glib_000 A)) & (v4_valued_0 (k13_glib_005 A B C))) ) ) ) ) ) ).
tt(dt_k13_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k13_graph_3 A B C)))  & (m1_subset_1 (k13_graph_3 A B C) (k1_zfmisc_1 (k9_graph_3 A)))) ) ) ).
tt(dt_k13_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k13_graphsp A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k13_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_grcat_1 A) & (l1_grcat_1 A))  &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  ((v1_grcat_1 (k13_grcat_1 A B)) &  ((v2_grcat_1 (k13_grcat_1 A B)) & (l1_grcat_1 (k13_grcat_1 A B))) ) ) ) ).
tt(dt_k13_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  & (m1_subset_1 D B)) ) )  => (m1_subset_1 (k13_group_10 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k13_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k13_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k13_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v2_group_9 (k13_group_9 A B C D) A) & (m1_group_9 (k13_group_9 A B C D) A B)) ) ) ).
tt(dt_k13_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) )  =>  ((v1_funct_1 (k13_hahnban1 A B)) &  ((v1_funct_2 (k13_hahnban1 A B) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (k13_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_k13_idea_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k13_idea_1 A) k5_numbers)) ) ).
tt(dt_k13_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k13_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k13_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  => (m5_index_1 (k13_index_1 A B C) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A))) ) ).
tt(dt_k13_integra1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((m1_integra1 B A) &  ((m1_integra1 C A) & (v7_ordinal1 D)) ) )  => (m2_subset_1 (k13_integra1 A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k13_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (m1_subset_1 (k13_intpro_1 A) (k1_zfmisc_1 k1_intpro_1))) ) ).
tt(dt_k13_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m2_cat_1 F A C) &  ((m2_cat_1 G A C) &  ((m1_nattra_1 H A B D E) & (m1_nattra_1 I A C F G)) ) ) ) ) ) ) )  => (m1_nattra_1 (k13_isocat_2 A B C D E F G H I) A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G))) ) ).
tt(dt_k13_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k13_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k13_lang1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k13_lang1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k13_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k13_lattice3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k13_lattice5,ax,$true).
tt(dt_k13_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m2_lexbfs B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k13_lexbfs A B C) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers))))) ) ).
tt(dt_k13_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v8_algstr_0 (k13_lmod_7 A B C)) & (l2_algstr_0 (k13_lmod_7 A B C))) ) ) ).
tt(dt_k13_lopban_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k13_lopban_1 A B C)) &  ((v1_funct_2 (k13_lopban_1 A B C) (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 (k13_lopban_1 A B C) A B) &  ((v1_lopban_1 (k13_lopban_1 A B C) A B) &  ((v2_lopban_1 (k13_lopban_1 A B C) A B) & (m1_subset_1 (k13_lopban_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(dt_k13_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  => (m1_lattice4 (k13_lopclset A) A (k12_lopclset A))) ) ).
tt(dt_k13_lpspace1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  => (m1_subset_1 (k13_lpspace1 A B C D) (k1_zfmisc_1 (k9_lpspace1 A B C)))) ) ).
tt(dt_k13_ltlaxio1,ax,(m1_subset_1 k13_ltlaxio1 (k1_zfmisc_1 k1_hilbert1))).
tt(dt_k13_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  =>  ((v1_relat_1 (k13_margrel1 A)) &  ((v1_funct_1 (k13_margrel1 A)) & (v1_margrel1 (k13_margrel1 A))) ) ) ) ).
tt(dt_k13_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((v7_ordinal1 B) & (m1_matrix_1 C (u1_struct_0 A) B B)) )  => (m1_matrix_1 (k13_matrix_1 A B C) (u1_struct_0 A) B B)) ) ).
tt(dt_k13_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v15_algstr_0 (k13_matrix_2 A)) & (l3_algstr_0 (k13_matrix_2 A))) ) ) ).
tt(dt_k13_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m2_finseq_1 (k13_matrix_3 A B C) (u1_struct_0 B))) ) ).
tt(dt_k13_matrixc1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A k2_numbers) &  ((m1_finseq_1 B k2_numbers) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 k2_numbers))) ) )  =>  ((v1_matrix_1 (k13_matrixc1 A B C)) & (m2_finseq_1 (k13_matrixc1 A B C) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k13_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  => (m1_matrix_1 (k13_matrixj1 A B C) A (k2_wsierp_1 (k10_matrixj1 A C)) (k2_wsierp_1 (k11_matrixj1 A C)))) ) ).
tt(dt_k13_mcart_1,ax,$true).
tt(dt_k13_member_1,ax,$true).
tt(dt_k13_mesfunc1,ax,$true).
tt(dt_k13_metric_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) ) ) )  =>  ((v1_funct_1 (k13_metric_3 A B C)) &  ((v1_funct_2 (k13_metric_3 A B C) (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers) & (m1_subset_1 (k13_metric_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers)))) ) ) ) ).
tt(dt_k13_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v1_funct_1 (k13_midsp_1 A)) &  ((v1_funct_2 (k13_midsp_1 A) (k10_midsp_1 A) (k10_midsp_1 A)) & (m1_subset_1 (k13_midsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A))))) ) ) ) ).
tt(dt_k13_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 D)) )  => (m1_subset_1 (k13_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k13_mod_2,ax, ((v1_funct_1 k13_mod_2) &  ((v1_funct_2 k13_mod_2 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 k13_mod_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2))))) ) ).
tt(dt_k13_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_1 B) & (m1_finseq_1 B k5_numbers)) )  =>  ((v1_modelc_1 (k13_modelc_1 A B)) & (m2_finseq_1 (k13_modelc_1 A B) k5_numbers)) ) ) ).
tt(dt_k13_modelc_2,ax,$true).
tt(dt_k13_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (m1_subset_1 B (k1_zfmisc_1 (k1_modelc_3 A))))  => (m1_subset_1 (k13_modelc_3 A B) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k13_monoid_1,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k13_monoid_1 A)))  &  ((v22_algstr_0 (k13_monoid_1 A)) &  ((v3_group_1 (k13_monoid_1 A)) &  ((v5_group_1 (k13_monoid_1 A)) &  ((v4_vectsp_1 (k13_monoid_1 A)) &  ((v1_monoid_0 (k13_monoid_1 A)) &  ((v16_monoid_0 (k13_monoid_1 A)) &  ((v17_monoid_0 (k13_monoid_1 A)) & (l4_algstr_0 (k13_monoid_1 A))) ) ) ) ) ) ) ) ) ).
tt(dt_k13_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m1_msafree (k13_msafree A B) A (k11_msafree A B))) ) ).
tt(dt_k13_msualg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((m1_msualg_2 C A B) & (m1_msualg_2 D A B)) ) )  =>  ((v3_msualg_1 (k13_msualg_2 A B C D) A) & (m1_msualg_2 (k13_msualg_2 A B C D) A B)) ) ) ).
tt(dt_k13_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) )  => (l3_msualg_1 (k13_msualg_4 A B C) A)) ) ).
tt(dt_k13_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k13_nat_3 A)) &  ((v4_relat_1 (k13_nat_3 A) k10_newton) &  ((v1_funct_1 (k13_nat_3 A)) & (v1_partfun1 (k13_nat_3 A) k10_newton)) ) ) ) ) ).
tt(dt_k13_net_1,ax,$true).
tt(dt_k13_newton,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k13_newton A B) k1_numbers k5_numbers)) ) ).
tt(dt_k13_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (k13_openlatt A)) &  ((v1_funct_2 (k13_openlatt A) (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A)) & (m1_subset_1 (k13_openlatt A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A))))) ) ) ) ).
tt(dt_k13_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m1_oppcat_1 (k13_oppcat_1 A) (k2_oppcat_1 A) A)) ) ).
tt(dt_k13_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k13_ordinal6 A B))) ) ).
tt(dt_k13_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 (k2_osafree A B)))) )  => (m1_subset_1 (k13_osafree A B C) (u4_struct_0 A))) ) ).
tt(dt_k13_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (m1_subset_1 (k13_osalg_2 A B) (k1_zfmisc_1 (k14_msualg_2 A B)))) ) ).
tt(dt_k13_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D k5_numbers) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  & (m1_subset_1 F (u1_struct_0 (k4_real_ns1 A)))) ) ) ) )  => (m1_subset_1 (k13_pdiff_1 A B C D E F) (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 1))))) ) ).
tt(dt_k13_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k13_petri A B) (u1_struct_0 (k11_petri A)))) ) ).
tt(dt_k13_pnproc_1,ax, (! [A:$i,B:$i] :  ((m2_pnproc_1 B A) =>  ( (~ (v1_xboole_0 (k13_pnproc_1 A B)))  & (m1_subset_1 (k13_pnproc_1 A B) (k1_zfmisc_1 (k3_finseq_2 B)))) ) ) ).
tt(dt_k13_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_subset_1 (k13_polyform A) k1_numbers k5_numbers)) ) ).
tt(dt_k13_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k13_polynom3 A B C)) &  ((v1_funct_2 (k13_polynom3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k13_polynom3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k13_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  & (m1_pralg_2 C A B))  => (m2_pboole (k13_pralg_2 A B C) (u4_struct_0 B) (k3_relat_1 (u1_msualg_1 B) (k6_finseq_2 (u1_struct_0 B) (k10_pralg_2 A B C))) (k3_relat_1 (u2_msualg_1 B) (k10_pralg_2 A B C)))) ) ).
tt(dt_k13_pre_poly,ax,$true).
tt(dt_k13_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v1_funct_1 D) &  ((v1_funct_2 D B (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k9_setfam_1 C))))) ) )  => (m1_subset_1 (k13_prob_1 A B C D E) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k13_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  & (m1_prvect_1 B A))  =>  ((v1_funct_1 (k13_prvect_1 A B)) &  ((v1_funct_2 (k13_prvect_1 A B) (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 (k13_prvect_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A))))) ) ) ) ).
tt(dt_k13_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ((v1_funct_1 (k13_prvect_2 A)) &  ((v1_funct_2 (k13_prvect_2 A) (k4_card_3 (k4_prvect_2 A)) k1_numbers) & (m1_subset_1 (k13_prvect_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k4_prvect_2 A)) k1_numbers)))) ) ) ) ).
tt(dt_k13_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k13_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k13_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  &  ((m3_pua2mss1 B A) & (m1_subset_1 C (u4_struct_0 (k11_pua2mss1 A B)))) )  => (m2_finseq_2 (k13_pua2mss1 A B C) B (k3_finseq_2 B))) ) ).
tt(dt_k13_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k13_qc_lang1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k13_qc_lang2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k13_qc_lang2 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k13_quaterni,ax,$true).
tt(dt_k13_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k7_quofield A)))  => (m2_subset_1 (k13_quofield A B) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k13_radix_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 A)))  &  ((v3_card_1 E C) & (m1_finseq_1 E (k3_radix_1 A))) ) ) ) )  => (m2_subset_1 (k13_radix_1 A B C D E) k4_numbers (k3_radix_1 A))) ) ).
tt(dt_k13_radix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C (k4_radix_3 B))) ) )  =>  ((v3_card_1 (k13_radix_3 A B C) A) & (m2_finseq_1 (k13_radix_3 A B C) k4_numbers)) ) ) ).
tt(dt_k13_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_ratfunc1 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k13_ratfunc1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k13_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k13_rfunct_3 A)) &  ((v1_funct_2 (k13_rfunct_3 A) (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 (k13_rfunct_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) ) ) ) ).
tt(dt_k13_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  & (m1_subset_1 B A))  =>  ((v2_ringcat1 (k13_ringcat1 A B)) & (m3_ringcat1 (k13_ringcat1 A B) (k10_ringcat1 A))) ) ) ).
tt(dt_k13_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlvect_2 B A))  => (m1_subset_1 (k13_rlvect_2 A B) (k11_rlvect_2 A))) ) ).
tt(dt_k13_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k13_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k13_rsspace,ax, ( (~ (v2_struct_0 k13_rsspace))  & (l1_bhsp_1 k13_rsspace)) ).
tt(dt_k13_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k4_finseq_2 A k1_numbers)))  => (m2_finseq_2 (k13_rvsum_1 A B) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k13_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k7_dtconstr k1_scm_comp)) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k13_scm_comp A B)) &  ((v5_relat_1 (k13_scm_comp A B) (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 (k13_scm_comp A B)) &  ((v5_ordinal1 (k13_scm_comp A B)) & (v1_finset_1 (k13_scm_comp A B))) ) ) ) ) ) ).
tt(dt_k13_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k13_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k13_scmpds_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (m1_subset_1 (k13_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k13_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k13_scmpds_i A))) ) ).
tt(dt_k13_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((v1_relat_1 (k13_scmyciel A)) &  ((v4_relat_1 (k13_scmyciel A) k5_numbers) &  ((v1_funct_1 (k13_scmyciel A)) & (v1_partfun1 (k13_scmyciel A) k5_numbers)) ) ) ) ) ).
tt(dt_k13_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k13_seq_4 A) k1_numbers)) ) ).
tt(dt_k13_sin_cos,ax, ((v1_funct_1 k13_sin_cos) &  ((v1_funct_2 k13_sin_cos k2_numbers k2_numbers) & (m1_subset_1 k13_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k13_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k13_stacks_1 A B) (u4_struct_0 A))) ) ).
tt(dt_k13_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) &  ((m1_substut1 D A (k7_sublemma A B C)) &  ( (~ (v1_xboole_0 E))  & (m1_subset_1 F (k2_valuat_1 A E))) ) ) ) )  =>  ((v1_funct_1 (k13_sublemma A B C D E F)) & (m1_subset_1 (k13_sublemma A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) E)))) ) ) ).
tt(dt_k13_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_substut1 A)))  & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k13_substut1 A B C) (k1_qc_lang1 A))) ) ).
tt(dt_k13_supinf_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) )  =>  ((v1_funct_1 (k13_supinf_2 A B C D E)) &  ((v1_funct_2 (k13_supinf_2 A B C D E) A (k5_supinf_2 B C)) & (m1_subset_1 (k13_supinf_2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A (k5_supinf_2 B C))))) ) ) ) ).
tt(dt_k13_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_topalg_2)) =>  ((v1_funct_1 (k13_toprealb A)) &  ((v1_funct_2 (k13_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 A (k3_real_1 A 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)))) & (m1_subset_1 (k13_toprealb A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 A (k3_real_1 A 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A))))))) ) ) ) ).
tt(dt_k13_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k13_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k13_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k13_trees_3 A B)))  & (v1_trees_1 (k13_trees_3 A B))) ) ) ).
tt(dt_k13_trees_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  ((v1_funct_1 (k13_trees_9 A B)) &  ((v1_funct_2 (k13_trees_9 A B) (k12_trees_9 A B) (k3_finseq_2 (k9_trees_9 A))) & (m1_subset_1 (k13_trees_9 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k12_trees_9 A B) (k3_finseq_2 (k9_trees_9 A)))))) ) ) ) ).
tt(dt_k13_turing_1,ax, ((v1_funct_1 k13_turing_1) &  ((v1_funct_2 k13_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 k13_turing_1 (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 5) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ).
tt(dt_k13_twoscomp,ax, ((v1_funct_1 k13_twoscomp) &  ((v1_funct_2 k13_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k13_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k13_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) & (v1_funct_1 (k13_valued_1 A B))) ) ) ).
tt(dt_k13_valued_2,ax,$true).
tt(dt_k13_xtuple_0,ax,$true).
tt(dt_k13_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v12_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((v12_waybel_0 (k13_yellow_3 A B C D) (k3_yellow_3 A B)) & (m1_subset_1 (k13_yellow_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) ) ) ).
tt(dt_k13_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m4_yellow_6 B A))  =>  ((v1_pre_topc (k13_yellow_6 A B)) & (l1_pre_topc (k13_yellow_6 A B))) ) ) ).
tt(dt_k13_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  =>  ((v1_zf_lang (k13_zf_lang A B)) & (m2_finseq_1 (k13_zf_lang A B) k5_numbers)) ) ) ).
tt(dt_k14_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m1_subset_1 (k14_abcmiz_1 A) (u1_struct_0 A))) ) ).
tt(dt_k14_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k5_abcmiz_a) =>  ((v2_abcmiz_1 (k14_abcmiz_a A) k27_abcmiz_1) & (m2_abcmiz_1 (k14_abcmiz_a A) k27_abcmiz_1 (k12_abcmiz_1 k27_abcmiz_1))) ) ) ).
tt(dt_k14_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  & (m1_subset_1 C (k8_afinsq_1 A)))  => (m1_subset_1 (k14_afinsq_1 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k14_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v1_incsp_1 (k14_afproj A)) & (l1_incsp_1 (k14_afproj A))) ) ) ).
tt(dt_k14_algstr_4,ax, (! [A:$i] : (l3_algstr_0 (k14_algstr_4 A))) ).
tt(dt_k14_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v4_unialg_1 A) &  ((v5_aofa_000 A) & (l1_unialg_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k14_aofa_000 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k14_armstrng,ax,$true).
tt(dt_k14_asympt_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_funct_2 B A k1_numbers) & (m1_funct_2 C A k1_numbers)) )  => (m1_funct_2 (k14_asympt_0 A B C) A k1_numbers)) ) ).
tt(dt_k14_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_orders_2 (k14_bagorder A)) &  ((v4_orders_2 (k14_bagorder A)) &  ((v5_orders_2 (k14_bagorder A)) & (l1_orders_2 (k14_bagorder A))) ) ) ) ) ).
tt(dt_k14_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_bilinear A B C D)))  &  ((v7_vectsp_1 (k14_bilinear A B C D) A) & (m1_vectsp_4 (k14_bilinear A B C D) A C)) ) ) ) ).
tt(dt_k14_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) => (m1_subset_1 (k14_binop_2 A) k3_numbers)) ) ).
tt(dt_k14_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_borsuk_2 (k14_borsuk_7 A) (k8_toprealb 3) k8_borsuk_7 k8_borsuk_7)) ) ).
tt(dt_k14_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((v1_funct_1 (k14_bvfunc_1 A B)) &  ((v1_funct_2 (k14_bvfunc_1 A B) A k6_margrel1) & (m1_subset_1 (k14_bvfunc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k14_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (m2_cat_1 (k14_cat_2 A B) (k8_cat_2 A B) A)) ) ).
tt(dt_k14_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k14_cat_4 A B C) A (k2_cat_4 A B C) (k2_cat_4 A C B))) ) ).
tt(dt_k14_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  => (m2_subset_1 (k14_cat_5 A B C) (u4_struct_0 A) (k9_cat_5 A B))) ) ).
tt(dt_k14_classes2,ax, ( (~ (v1_xboole_0 k14_classes2))  & (v1_classes2 k14_classes2)) ).
tt(dt_k14_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_clopban1 A B)))  & (l2_clvect_1 (k14_clopban1 A B))) ) ) ).
tt(dt_k14_cohsp_1,ax,$true).
tt(dt_k14_coh_sp,ax,$true).
tt(dt_k14_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xcmplx_0 (k14_complex1 A))) ) ).
tt(dt_k14_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k14_comput_1 A)) & (v1_funct_1 (k14_comput_1 A))) ) ) ).
tt(dt_k14_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ((v1_funct_1 (k14_convex4 A)) &  ((v1_funct_2 (k14_convex4 A) (k2_zfmisc_1 k2_numbers (k10_convex4 A)) (k10_convex4 A)) & (m1_subset_1 (k14_convex4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k10_convex4 A)) (k10_convex4 A))))) ) ) ) ).
tt(dt_k14_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k14_cqc_sim1 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k14_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k14_csspace A B C) k1_numbers)) ) ).
tt(dt_k14_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k14_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k14_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_finseq_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 A B))))) )  & (v7_ordinal1 D)) ) )  => (m2_finseq_2 (k14_descip_1 A B C D) B (k4_finseq_2 A B))) ) ).
tt(dt_k14_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k2_zfmisc_1 A B) C))) ) )  => (m1_subset_1 (k14_domain_1 A B C D) A)) ) ).
tt(dt_k14_dtconstr,ax, ((v1_funct_1 k14_dtconstr) &  ((v1_funct_2 k14_dtconstr k5_numbers (k4_dtconstr k5_dtconstr)) & (m1_subset_1 k14_dtconstr (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_dtconstr k5_dtconstr))))) ) ).
tt(dt_k14_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k2_ens_1 A)))  => (m1_subset_1 (k14_ens_1 A B) (u4_struct_0 (k11_ens_1 A)))) ) ).
tt(dt_k14_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k14_e_siec A))) ) ).
tt(dt_k14_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_metric_1 (k14_euclid A)) &  ((v6_metric_1 (k14_euclid A)) &  ((v7_metric_1 (k14_euclid A)) &  ((v8_metric_1 (k14_euclid A)) &  ((v9_metric_1 (k14_euclid A)) & (l1_metric_1 (k14_euclid A))) ) ) ) ) ) ) ).
tt(dt_k14_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k14_facirc_1 A B C)))  &  ( (~ (v11_struct_0 (k14_facirc_1 A B C)))  &  ((v1_msualg_1 (k14_facirc_1 A B C)) &  ((v1_circcomb (k14_facirc_1 A B C)) &  ((v2_circcomb (k14_facirc_1 A B C)) &  ((v3_circcomb (k14_facirc_1 A B C)) & (l1_msualg_1 (k14_facirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k14_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k14_ff_siec A))) ) ).
tt(dt_k14_finseq_1,ax, (! [A:$i] : (m2_finseq_1 (k14_finseq_1 A) k5_numbers)) ).
tt(dt_k14_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k14_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k14_fomodel0,ax, (! [A:$i,B:$i] : (m1_subset_1 (k14_fomodel0 A B) (k1_zfmisc_1 A))) ).
tt(dt_k14_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  =>  ((v1_funct_1 (k14_fomodel1 A)) &  ((v1_funct_2 (k14_fomodel1 A) (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))) k4_numbers) & (m1_subset_1 (k14_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))) k4_numbers)))) ) ) ) ).
tt(dt_k14_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (m1_subset_1 (k14_fomodel2 A B C D) k6_margrel1)) ) ).
tt(dt_k14_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k10_eqrel_1 A)))  => (m1_subset_1 (k14_fomodel3 A B) A)) ) ).
tt(dt_k14_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k14_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k14_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  & (v1_freealg B))  => (m2_finseq_1 (k14_freealg A B) (k4_partfun1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B))))) ) ).
tt(dt_k14_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ((v3_msualg_1 (k14_ftacell1 A B C D E) (k13_ftacell1 A B C D E)) &  ((v4_msafree2 (k14_ftacell1 A B C D E) (k13_ftacell1 A B C D E)) &  ((v4_circcomb (k14_ftacell1 A B C D E) (k13_ftacell1 A B C D E)) &  ((v6_circcomb (k14_ftacell1 A B C D E) (k13_ftacell1 A B C D E)) & (l3_msualg_1 (k14_ftacell1 A B C D E) (k13_ftacell1 A B C D E))) ) ) ) ) ).
tt(dt_k14_funcop_1,ax,$true).
tt(dt_k14_funct_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k14_funct_3 A B C D E)) &  ((v1_funct_2 (k14_funct_3 A B C D E) A (k2_zfmisc_1 B C)) & (m1_subset_1 (k14_funct_3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) ).
tt(dt_k14_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((v1_funct_1 (k14_funct_7 A B C D)) &  ((v1_funct_2 (k14_funct_7 A B C D) k5_numbers A) & (m1_subset_1 (k14_funct_7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k14_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l2_altcat_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  & (m1_altcat_2 C A))  & (l2_functor0 D A B)) ) )  => (l2_functor0 (k14_functor0 A B C D) C B)) ) ).
tt(dt_k14_gate_1,ax,$true).
tt(dt_k14_gate_5,ax,$true).
tt(dt_k14_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k14_gfacirc1 A B C) (k13_gfacirc1 A B C)) &  ((v4_msafree2 (k14_gfacirc1 A B C) (k13_gfacirc1 A B C)) &  ((v4_circcomb (k14_gfacirc1 A B C) (k13_gfacirc1 A B C)) &  ((v6_circcomb (k14_gfacirc1 A B C) (k13_gfacirc1 A B C)) & (l3_msualg_1 (k14_gfacirc1 A B C) (k13_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k14_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (v1_card_1 (k14_glib_000 A))) ) ).
tt(dt_k14_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ((v1_finset_1 (k14_glib_001 A B)) & (m1_subset_1 (k14_glib_001 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ) ).
tt(dt_k14_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  => (m1_subset_1 (k14_glib_003 A) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k14_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))))  => (m1_subset_1 (k14_glib_004 A B) (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k14_graph_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  & (m1_subset_1 B (k9_graph_3 A)))  => (m2_finseq_2 (k14_graph_3 A B) (u4_struct_0 A) (k9_graph_3 A))) ) ).
tt(dt_k14_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k14_graphsp A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k14_grcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ((m1_grcat_1 D B C) & (m1_grcat_1 E A B)) ) ) )  =>  ((v1_grcat_1 (k14_grcat_1 A B C D E)) & (m1_grcat_1 (k14_grcat_1 A B C D E) A C)) ) ) ).
tt(dt_k14_group_10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) ) ) )  => (m1_eqrel_1 (k14_group_10 A B C) B)) ) ).
tt(dt_k14_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k14_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k14_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v2_group_9 (k14_group_9 A B C D) A) & (m1_group_9 (k14_group_9 A B C D) A C)) ) ) ).
tt(dt_k14_idea_1,ax,$true).
tt(dt_k14_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k14_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k14_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m5_index_1 E (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) (u1_cat_1 C) (k7_isocat_1 C))) ) ) )  => (m5_index_1 (k14_index_1 A B C D E) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A))) ) ).
tt(dt_k14_integra1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m2_finseq_1 (k14_integra1 A) k1_numbers)) ) ).
tt(dt_k14_interva1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  & (m2_interva1 B A))  => (m1_subset_1 (k14_interva1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k14_intpro_1,ax,(m1_subset_1 k14_intpro_1 (k1_zfmisc_1 k1_intpro_1))).
tt(dt_k14_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m2_cat_1 F A C) &  ((m2_cat_1 G A C) &  ((m2_nattra_1 H A B D E) & (m2_nattra_1 I A C F G)) ) ) ) ) ) ) )  => (m2_nattra_1 (k14_isocat_2 A B C D E F G H I) A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G))) ) ).
tt(dt_k14_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k14_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k14_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v2_struct_0 (k14_lattice3 A)))  &  ((v3_lattices (k14_lattice3 A)) &  ((v10_lattices (k14_lattice3 A)) & (l3_lattices (k14_lattice3 A))) ) ) ) ) ).
tt(dt_k14_lattice5,ax,$true).
tt(dt_k14_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m2_lexbfs B A))  => (m1_subset_1 (k14_lexbfs A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers))))) ) ).
tt(dt_k14_lmod_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k14_lmod_7 A B C D) (u1_struct_0 (k13_lmod_7 A B C)))) ) ).
tt(dt_k14_lopban_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k14_lopban_1 A B C)))  & (m1_subset_1 (k14_lopban_1 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k14_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k14_lpspace1 A B C)))  & (m1_subset_1 (k14_lpspace1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (k9_lpspace1 A B C))))) ) ) ).
tt(dt_k14_margrel1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k14_margrel1 A B)) &  ((v1_funct_1 (k14_margrel1 A B)) & (v1_margrel1 (k14_margrel1 A B))) ) ) ) ).
tt(dt_k14_matrix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((v7_ordinal1 B) &  ((m1_matrix_1 C (u1_struct_0 A) B B) & (m1_matrix_1 D (u1_struct_0 A) B B)) ) )  => (m1_matrix_1 (k14_matrix_1 A B C D) (u1_struct_0 A) B B)) ) ).
tt(dt_k14_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k12_matrix_2 B))) ) )  => (m1_subset_1 (k14_matrix_2 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k14_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  => (m1_matrix_1 (k14_matrixj1 A B C) A (k3_finseq_1 (k2_matrixj1 A B C)) (k3_finseq_1 (k2_matrixj1 A B C)))) ) ).
tt(dt_k14_mcart_1,ax,$true).
tt(dt_k14_member_1,ax,$true).
tt(dt_k14_mesfunc1,ax,$true).
tt(dt_k14_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k14_metric_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k14_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (m1_subset_1 (k14_midsp_1 A) (k10_midsp_1 A))) ) ).
tt(dt_k14_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 D)) )  => (m1_subset_1 (k14_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k14_mod_2,ax, ((v1_funct_1 k14_mod_2) &  ((v1_funct_2 k14_mod_2 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2)) & (m1_subset_1 k14_mod_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2))))) ) ).
tt(dt_k14_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_1 (k14_modelc_1 A)) & (m2_finseq_1 (k14_modelc_1 A) k5_numbers)) ) ) ).
tt(dt_k14_modelc_2,ax, (! [A:$i] :  ((v1_modelc_2 (k14_modelc_2 A)) & (m2_finseq_1 (k14_modelc_2 A) k5_numbers)) ) ).
tt(dt_k14_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_3 B A) & (l1_modelc_3 B A)) )  => (m1_subset_1 (k14_modelc_3 A B) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k14_monoid_0,ax, (! [A:$i] :  ((v1_funct_1 (k14_monoid_0 A)) &  ((v1_funct_2 (k14_monoid_0 A) (k2_zfmisc_1 (k4_partfun1 A A) (k4_partfun1 A A)) (k4_partfun1 A A)) & (m1_subset_1 (k14_monoid_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_partfun1 A A) (k4_partfun1 A A)) (k4_partfun1 A A))))) ) ) ).
tt(dt_k14_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))))  => (m1_subset_1 (k14_monoid_1 A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k14_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k14_msafree A B C)) &  ((v1_funct_2 (k14_msafree A B C) (k12_msafree A B C) (k1_funct_1 B C)) & (m1_subset_1 (k14_msafree A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k12_msafree A B C) (k1_funct_1 B C))))) ) ) ) ).
tt(dt_k14_msualg_2,ax,$true).
tt(dt_k14_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((v1_funct_1 (k14_msualg_4 A B C D)) &  ((v1_funct_2 (k14_msualg_4 A B C D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (k4_msualg_4 A B C) D)) & (m1_subset_1 (k14_msualg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (k4_msualg_4 A B C) D))))) ) ) ) ).
tt(dt_k14_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (k14_openlatt A)) &  ((v1_funct_2 (k14_openlatt A) (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A)) & (m1_subset_1 (k14_openlatt A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_openlatt A) (k9_openlatt A)) (k9_openlatt A))))) ) ) ) ).
tt(dt_k14_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 (k2_osafree A B)))) )  => (m1_dtconstr (k14_osafree A B C) (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ).
tt(dt_k14_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  ((v1_funct_1 (k14_osalg_2 A B)) &  ((v1_funct_2 (k14_osalg_2 A B) (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B)) & (m1_subset_1 (k14_osalg_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B))))) ) ) ) ).
tt(dt_k14_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) ) ) ) )  =>  ((v1_funct_1 (k14_osalg_4 A B C D)) &  ((v1_funct_2 (k14_osalg_4 A B C D) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B)) & (m1_subset_1 (k14_osalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A C D)) B))))) ) ) ) ).
tt(dt_k14_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D k5_numbers) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  & (m1_subset_1 F (k1_euclid A))) ) ) ) )  => (v1_xreal_0 (k14_pdiff_1 A B C D E F))) ) ).
tt(dt_k14_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_subset_1 (k14_polyform A) k1_numbers k5_numbers)) ) ).
tt(dt_k14_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (l6_algstr_0 (k14_polynom3 A))) ) ) ) ).
tt(dt_k14_pralg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ((m1_pralg_1 C A B) & (m1_subset_1 D A)) ) )  =>  ((v1_funct_1 (k14_pralg_1 A B C D)) &  ( (~ (v1_xboole_0 (k14_pralg_1 A B C D)))  &  ((v2_margrel1 (k14_pralg_1 A B C D)) &  ((v3_margrel1 (k14_pralg_1 A B C D) (k1_funct_1 B D)) & (m1_subset_1 (k14_pralg_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k1_funct_1 B D)) (k1_funct_1 B D))))) ) ) ) ) ) ).
tt(dt_k14_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  & (m1_pralg_2 C A B))  => (l3_msualg_1 (k14_pralg_2 A B C) B)) ) ).
tt(dt_k14_pre_poly,ax,$true).
tt(dt_k14_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k14_prvect_2 A)))  &  ((v1_normsp_1 (k14_prvect_2 A)) & (l1_normsp_1 (k14_prvect_2 A))) ) ) ) ).
tt(dt_k14_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k14_pscomp_1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k14_qc_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k14_qc_lang1 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k14_qc_lang2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k14_qc_lang2 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k14_quaterni,ax,$true).
tt(dt_k14_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k7_quofield A)))  => (m2_subset_1 (k14_quofield A B) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k14_radix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v3_card_1 C A) & (m1_finseq_1 C (k3_radix_1 B)))  &  ((v3_card_1 D A) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  =>  ((v3_card_1 (k14_radix_1 A B C D) A) & (m2_finseq_1 (k14_radix_1 A B C D) (k3_radix_1 B))) ) ) ).
tt(dt_k14_radix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C (k4_radix_3 B))) ) )  => (v1_int_1 (k14_radix_3 A B C))) ) ).
tt(dt_k14_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k3_rfunct_3 A k1_numbers)))  => (m2_rfunct_3 (k14_rfunct_3 A B) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k14_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  ((v1_funct_1 (k14_ringcat1 A)) &  ((v1_funct_2 (k14_ringcat1 A) (k10_ringcat1 A) A) & (m1_subset_1 (k14_ringcat1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) A)))) ) ) ) ).
tt(dt_k14_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k14_rlvect_2 A)) &  ((v1_funct_2 (k14_rlvect_2 A) (k2_zfmisc_1 (k11_rlvect_2 A) (k11_rlvect_2 A)) (k11_rlvect_2 A)) & (m1_subset_1 (k14_rlvect_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k11_rlvect_2 A) (k11_rlvect_2 A)) (k11_rlvect_2 A))))) ) ) ) ).
tt(dt_k14_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k14_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k14_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  => (m2_finseq_1 (k14_rvsum_1 A B) k1_numbers)) ) ).
tt(dt_k14_scm_comp,ax, ((v1_funct_1 k14_scm_comp) &  ((v1_funct_2 k14_scm_comp (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3)))) & (m1_subset_1 k14_scm_comp (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k1_scm_comp) (k9_funct_2 k5_numbers (k8_afinsq_1 (u1_compos_1 k1_ami_3))))))) ) ).
tt(dt_k14_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (m1_subset_1 (k14_scmfsa_2 A B C) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k14_scmpds_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (m1_subset_1 (k14_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k14_scmpds_i,ax,(m2_subset_1 k14_scmpds_i k1_numbers k5_numbers)).
tt(dt_k14_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_finseq_2 (k14_seq_4 A) k2_numbers)) ) ).
tt(dt_k14_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xcmplx_0 (k14_sin_cos A))) ) ).
tt(dt_k14_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (l1_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(dt_k14_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  =>  ((v1_funct_1 (k14_sublemma A B C D)) & (m1_subset_1 (k14_sublemma A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) ).
tt(dt_k14_substut1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k9_qc_lang1 A)) &  ((v1_finset_1 D) & (m1_subset_1 D (k1_substut1 A))) ) ) )  => (m1_subset_1 (k14_substut1 A B C D) (k1_substut1 A))) ) ).
tt(dt_k14_supinf_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((v1_funct_1 (k14_supinf_2 A B C)) &  ((v1_funct_2 (k14_supinf_2 A B C) A (k6_supinf_2 B)) & (m1_subset_1 (k14_supinf_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_supinf_2 B))))) ) ) ) ).
tt(dt_k14_toprealb,ax, ((v1_funct_1 k14_toprealb) &  ((v1_funct_2 k14_toprealb (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) & (m1_subset_1 k14_toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) ) ).
tt(dt_k14_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 D)) )  => (m1_subset_1 (k14_toprealc A B C D) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k14_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k14_trees_3 A)) &  ((v1_funct_1 (k14_trees_3 A)) & (v1_finseq_1 (k14_trees_3 A))) ) ) ) ).
tt(dt_k14_turing_1,ax, ((v1_turing_1 k14_turing_1) & (l1_turing_1 k14_turing_1)) ).
tt(dt_k14_twoscomp,ax, ((v1_funct_1 k14_twoscomp) &  ((v1_funct_2 k14_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k14_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k14_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k14_valued_1 A B C D)) & (m1_subset_1 (k14_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k14_valued_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k14_valued_2 A B)) & (v1_funct_1 (k14_valued_2 A B))) ) ) ).
tt(dt_k14_xtuple_0,ax,$true).
tt(dt_k14_zf_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((m1_subset_1 B k1_zf_lang) &  ((v1_zf_lang C) & (m1_finseq_1 C k5_numbers)) ) )  =>  ((v1_zf_lang (k14_zf_lang A B C)) & (m2_finseq_1 (k14_zf_lang A B C) k5_numbers)) ) ) ).
tt(dt_k15_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m1_subset_1 (k15_abcmiz_1 A) (u4_struct_0 A))) ) ).
tt(dt_k15_abcmiz_a,ax,(m3_abcmiz_1 k15_abcmiz_a k27_abcmiz_1)).
tt(dt_k15_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_subset_1 C (k8_afinsq_1 A)))  => (m1_subset_1 (k15_afinsq_1 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k15_algstr_4,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) => (v7_ordinal1 (k15_algstr_4 A B))) ) ).
tt(dt_k15_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v5_aofa_000 A) & (l1_unialg_1 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k15_aofa_000 A B C) (u1_struct_0 A))) ) ).
tt(dt_k15_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) )  =>  ((v1_funct_1 (k15_aofa_i00 A B C)) &  ((v1_funct_2 (k15_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k15_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k15_asympt_0,ax, (! [A:$i,B:$i] :  ( ((m1_funct_2 A k5_numbers k1_numbers) & (m1_funct_2 B k5_numbers k1_numbers))  => (m1_funct_2 (k15_asympt_0 A B) k5_numbers k1_numbers)) ) ).
tt(dt_k15_bagorder,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (l1_orders_2 A)) )  &  (~ (v1_xboole_0 B)) )  => (m1_subset_1 (k15_bagorder A B) (u1_struct_0 A))) ) ).
tt(dt_k15_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_bilinear A B C D)) &  ((v1_funct_2 (k15_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  ((v4_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) & (m1_subset_1 (k15_bilinear A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k15_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (m1_subset_1 (k15_binop_2 A B) k3_numbers)) ) ).
tt(dt_k15_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  &  ((v2_borsuk_1 C B) & (m1_borsuk_1 C B)) ) )  =>  ((v2_borsuk_1 (k15_borsuk_1 A B C) A) & (m1_borsuk_1 (k15_borsuk_1 A B C) A)) ) ) ).
tt(dt_k15_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  => (m1_subset_1 (k15_borsuk_7 A B) (u1_struct_0 (k7_toprealb A (k4_struct_0 (k15_euclid A)) 1)))) ) ).
tt(dt_k15_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_eqrel_1 C A)) )  => (m1_bvfunc_1 (k15_bvfunc_1 A B C) A C)) ) ).
tt(dt_k15_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (m2_cat_1 (k15_cat_2 A B) (k8_cat_2 A B) B)) ) ).
tt(dt_k15_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k15_cat_4 A B) A B (k2_cat_4 A B B))) ) ).
tt(dt_k15_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  => (m2_subset_1 (k15_cat_5 A B C) (u4_struct_0 A) (k9_cat_5 A B))) ) ).
tt(dt_k15_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v2_struct_0 (k15_chain_1 A B C)))  &  ((v8_algstr_0 (k15_chain_1 A B C)) &  ((v13_algstr_0 (k15_chain_1 A B C)) &  ((v2_rlvect_1 (k15_chain_1 A B C)) &  ((v3_rlvect_1 (k15_chain_1 A B C)) &  ((v4_rlvect_1 (k15_chain_1 A B C)) & (l2_algstr_0 (k15_chain_1 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k15_classes2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k15_classes2 A)))  & (v1_classes2 (k15_classes2 A))) ) ).
tt(dt_k15_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k15_clopban1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k15_cohsp_1,ax,$true).
tt(dt_k15_coh_sp,ax,$true).
tt(dt_k15_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k15_complex1 A) k2_numbers)) ) ).
tt(dt_k15_comput_1,ax, ((v1_relat_1 k15_comput_1) &  ((v1_funct_1 k15_comput_1) &  ((v7_comput_1 k15_comput_1) & (v8_comput_1 k15_comput_1 2)) ) ) ).
tt(dt_k15_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ( (~ (v2_struct_0 (k15_convex4 A)))  &  ((v13_algstr_0 (k15_convex4 A)) &  ((v2_rlvect_1 (k15_convex4 A)) &  ((v3_rlvect_1 (k15_convex4 A)) &  ((v4_rlvect_1 (k15_convex4 A)) &  ((v2_clvect_1 (k15_convex4 A)) &  ((v3_clvect_1 (k15_convex4 A)) &  ((v4_clvect_1 (k15_convex4 A)) &  ((v5_clvect_1 (k15_convex4 A)) & (l1_clvect_1 (k15_convex4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k15_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m1_subset_1 (k15_cqc_sim1 A B) (k1_zfmisc_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)))))) ) ).
tt(dt_k15_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k15_csspace A B C) k1_numbers)) ) ).
tt(dt_k15_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k15_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k15_descip_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A 64 16) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 64 16)))) )  => (m1_subset_1 (k15_descip_1 A B) 16)) ) ).
tt(dt_k15_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k2_zfmisc_1 A B) C))) ) )  => (m1_subset_1 (k15_domain_1 A B C D) B)) ) ).
tt(dt_k15_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m2_finseq_1 (k15_dtconstr A B) (k1_lang1 A))) ) ).
tt(dt_k15_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u4_struct_0 (k11_ens_1 A))))  => (m1_subset_1 (k15_ens_1 A B) (k2_ens_1 A))) ) ).
tt(dt_k15_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k15_e_siec A))) ) ).
tt(dt_k15_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (l1_rltopsp1 (k15_euclid A))) ) ) ).
tt(dt_k15_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k15_facirc_1 A B C)))  &  ( (~ (v11_struct_0 (k15_facirc_1 A B C)))  &  ((v1_msualg_1 (k15_facirc_1 A B C)) &  ((v1_circcomb (k15_facirc_1 A B C)) &  ((v2_circcomb (k15_facirc_1 A B C)) &  ((v3_circcomb (k15_facirc_1 A B C)) & (l1_msualg_1 (k15_facirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k15_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k15_ff_siec A))) ) ).
tt(dt_k15_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 (k15_finseq_1 A)) & (v1_funct_1 (k15_finseq_1 A))) ) ) ).
tt(dt_k15_fomodel0,ax, (! [A:$i,B:$i] : (m1_subset_1 (k15_fomodel0 A B) (k1_zfmisc_1 (k2_xboole_0 A B)))) ).
tt(dt_k15_fomodel1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fomodel1 A))  =>  (~ (v1_xboole_0 (k15_fomodel1 A))) ) ) ).
tt(dt_k15_fomodel2,ax,$true).
tt(dt_k15_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k15_fomodel3 A)) &  ((v1_funct_2 (k15_fomodel3 A) (k10_eqrel_1 A) A) & (m1_subset_1 (k15_fomodel3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k10_eqrel_1 A) A)))) ) ) ) ).
tt(dt_k15_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k15_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k15_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  & (v1_freealg B))  =>  ( (~ (v2_struct_0 (k15_freealg A B)))  &  ((v1_unialg_1 (k15_freealg A B)) &  ((v2_unialg_1 (k15_freealg A B)) &  ((v3_unialg_1 (k15_freealg A B)) &  ((v4_unialg_1 (k15_freealg A B)) & (l1_unialg_1 (k15_freealg A B))) ) ) ) ) ) ) ).
tt(dt_k15_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k15_ftacell1 A B C D E) (k3_msafree2 (k13_ftacell1 A B C D E)))) ).
tt(dt_k15_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D A) & (m1_subset_1 E A))  => (m1_subset_1 (k15_funcop_1 A B C D E) A)) ) ).
tt(dt_k15_funct_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k15_funct_3 A B)) & (v1_funct_1 (k15_funct_3 A B))) ) ) ).
tt(dt_k15_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 E B))  =>  ((v1_funct_1 (k15_funct_7 A B C D E)) &  ((v1_funct_2 (k15_funct_7 A B C D E) A B) & (m1_subset_1 (k15_funct_7 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k15_functor0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  & (l2_functor0 C A B)) )  =>  ((v9_functor0 (k15_functor0 A B C) B A) & (l2_functor0 (k15_functor0 A B C) B A)) ) ) ).
tt(dt_k15_gate_1,ax,$true).
tt(dt_k15_gate_5,ax,$true).
tt(dt_k15_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 (k15_glib_000 A)))  & (m1_subset_1 (k15_glib_000 A) k5_numbers)) ) ) ).
tt(dt_k15_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m1_subset_1 (k15_glib_001 A B) k5_numbers)) ) ).
tt(dt_k15_glib_004,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ((m3_glib_004 B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k15_glib_004 A B C) (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k15_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  &  ((m1_subset_1 B (k3_finseq_2 k1_numbers)) & (m1_subset_1 C k5_numbers)) )  => (m2_subset_1 (k15_graphsp A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k15_group_10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (v7_ordinal1 B))  => (m1_subset_1 (k15_group_10 A B) (k1_zfmisc_1 (k1_group_3 A)))) ) ).
tt(dt_k15_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (m1_subset_1 (k15_group_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k15_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  & (m1_group_9 C A B))  => (m1_subset_1 (k15_group_9 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k15_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  ((v1_funct_1 (k15_hahnban1 A B)) &  ((v1_funct_2 (k15_hahnban1 A B) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (k15_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_k15_idea_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_finseq_1 B k5_numbers))  =>  ((v1_funct_1 (k15_idea_1 A B)) &  ((v1_funct_2 (k15_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k15_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k15_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k15_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k15_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  & (m2_cat_1 E C D)) ) ) )  => (m5_index_1 (k15_index_1 A B C D E) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A))) ) ).
tt(dt_k15_interva1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  & (m2_interva1 B A))  => (m1_subset_1 (k15_interva1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k15_isocat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  => (m2_cat_1 (k15_isocat_2 A B C) (k11_nattra_1 A (k8_cat_2 B C)) (k8_cat_2 (k11_nattra_1 A B) (k11_nattra_1 A C)))) ) ).
tt(dt_k15_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k15_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k15_lattice3,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  => (m1_subset_1 (k15_lattice3 A B) (u1_struct_0 A))) ) ).
tt(dt_k15_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  & (m1_lattice5 D A B C)) ) )  =>  ((v1_funct_1 (k15_lattice5 A B C D)) &  ((v1_funct_2 (k15_lattice5 A B C D) (k2_zfmisc_1 (k13_lattice5 A B C) (k13_lattice5 A B C)) (u1_struct_0 B)) &  ((v1_lattice5 (k15_lattice5 A B C D) (k13_lattice5 A B C) B) &  ((v2_lattice5 (k15_lattice5 A B C D) (k13_lattice5 A B C) B) &  ((v3_lattice5 (k15_lattice5 A B C D) (k13_lattice5 A B C) B) & (m1_subset_1 (k15_lattice5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k13_lattice5 A B C) (k13_lattice5 A B C)) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(dt_k15_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m2_lexbfs B A))  => (m1_lexbfs (k15_lexbfs A B) A)) ) ).
tt(dt_k15_lmod_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 (k13_lmod_7 A B C)))) ) ) )  => (m1_subset_1 (k15_lmod_7 A B C D E) (u1_struct_0 (k13_lmod_7 A B C)))) ) ).
tt(dt_k15_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_lopban_1 A B)) &  ((v1_funct_2 (k15_lopban_1 A B) (k10_lopban_1 A B) k1_numbers) & (m1_subset_1 (k15_lopban_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k10_lopban_1 A B) k1_numbers)))) ) ) ) ).
tt(dt_k15_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_lpspace1 A B C)) &  ((v1_funct_2 (k15_lpspace1 A B C) (k2_zfmisc_1 (k14_lpspace1 A B C) (k14_lpspace1 A B C)) (k14_lpspace1 A B C)) & (m1_subset_1 (k15_lpspace1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_lpspace1 A B C) (k14_lpspace1 A B C)) (k14_lpspace1 A B C))))) ) ) ) ).
tt(dt_k15_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((v1_funct_1 (k15_margrel1 A B)) &  ((v1_funct_2 (k15_margrel1 A B) A k6_margrel1) & (m1_subset_1 (k15_margrel1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k15_matrix_2,ax, (! [A:$i] : (m1_subset_1 (k15_matrix_2 A) (k5_finsub_1 A))) ).
tt(dt_k15_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v2_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v2_matrixj1 (k15_matrixj1 A B C) A) & (m2_finseq_1 (k15_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k15_mcart_1,ax,$true).
tt(dt_k15_member_1,ax,$true).
tt(dt_k15_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  => (m1_subset_1 (k15_mesfunc1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k15_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k15_metric_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k15_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (l2_algstr_0 (k15_midsp_1 A))) ) ).
tt(dt_k15_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k15_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k15_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_1 (k15_modelc_1 A)) & (m2_finseq_1 (k15_modelc_1 A) k5_numbers)) ) ) ).
tt(dt_k15_modelc_2,ax,(m1_subset_1 k15_modelc_2 (k1_zfmisc_1 k9_modelc_2))).
tt(dt_k15_monoid_0,ax, (! [A:$i] :  ((v15_algstr_0 (k15_monoid_0 A)) & (m2_monoid_0 (k15_monoid_0 A) (k12_monoid_0 A))) ) ).
tt(dt_k15_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))) & (m1_subset_1 C A)) )  => (m1_subset_1 (k15_monoid_1 A B C) k5_numbers)) ) ).
tt(dt_k15_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m2_pboole (k15_msafree A B) (u1_struct_0 A) (k13_msafree A B) B)) ) ).
tt(dt_k15_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v1_funct_1 (k15_msualg_2 A B)) &  ((v1_funct_2 (k15_msualg_2 A B) (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B)) & (m1_subset_1 (k15_msualg_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B))))) ) ) ) ).
tt(dt_k15_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) )  => (m2_pboole (k15_msualg_4 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C)))) ) ).
tt(dt_k15_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ( (~ (v2_struct_0 (k15_openlatt A)))  &  ((v10_lattices (k15_openlatt A)) & (l3_lattices (k15_openlatt A))) ) ) ) ).
tt(dt_k15_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v2_msualg_4 (k15_osafree A B) A (k8_osafree A B)) &  ((v3_msualg_4 (k15_osafree A B) A (k8_osafree A B)) &  ((v3_osalg_4 (k15_osafree A B) A (k8_osafree A B)) & (m1_osalg_4 (k15_osafree A B) A (k8_osafree A B))) ) ) ) ) ).
tt(dt_k15_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  ((v1_funct_1 (k15_osalg_2 A B)) &  ((v1_funct_2 (k15_osalg_2 A B) (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B)) & (m1_subset_1 (k15_osalg_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k13_osalg_2 A B) (k13_osalg_2 A B)) (k13_osalg_2 A B))))) ) ) ) ).
tt(dt_k15_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) ) ) )  => (m2_pboole (k15_osalg_4 A B C) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A B C))) (k3_relat_1 (u2_msualg_1 A) (k7_osalg_4 A B C)))) ) ).
tt(dt_k15_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  & (m1_subset_1 C A)) )  => (l2_pcs_0 (k15_pcs_0 A B C))) ) ).
tt(dt_k15_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) )  =>  ((v1_funct_1 (k15_pdiff_1 A B C D E)) & (m1_subset_1 (k15_pdiff_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B))))))) ) ) ).
tt(dt_k15_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_struct_0 (k11_petri A))))  => (m1_subset_1 (k15_petri A B) (u1_struct_0 A))) ) ).
tt(dt_k15_polyform,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  &  ((v1_int_1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k15_polyform A B C) (k8_polyform A B))) ) ).
tt(dt_k15_pralg_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k15_pralg_1 A B)) & (v1_funct_1 (k15_pralg_1 A B))) ) ) ).
tt(dt_k15_pre_poly,ax, (! [A:$i] : (m1_subset_1 (k15_pre_poly A) (k1_zfmisc_1 (k14_pre_poly A)))) ).
tt(dt_k15_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k15_pscomp_1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k15_qc_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k15_qc_lang1 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k15_qc_lang2,ax,$true).
tt(dt_k15_quatern2,ax, ((v8_algstr_0 k15_quatern2) & (l2_algstr_0 k15_quatern2)) ).
tt(dt_k15_quaterni,ax,$true).
tt(dt_k15_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_quofield A)) &  ((v1_funct_2 (k15_quofield A) (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A)) & (m1_subset_1 (k15_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A))))) ) ) ) ).
tt(dt_k15_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  => (m2_finseq_1 (k15_rfunct_3 A B) (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k15_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  ((v1_funct_1 (k15_ringcat1 A)) &  ((v1_funct_2 (k15_ringcat1 A) (k10_ringcat1 A) A) & (m1_subset_1 (k15_ringcat1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) A)))) ) ) ) ).
tt(dt_k15_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_rlvect_2 A)) &  ((v1_funct_2 (k15_rlvect_2 A) (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A)) & (m1_subset_1 (k15_rlvect_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A))))) ) ) ) ).
tt(dt_k15_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k15_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k15_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  => (m2_finseq_2 (k15_rvsum_1 A B C) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k15_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k15_scm_comp A B)) &  ((v5_relat_1 (k15_scm_comp A B) (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 (k15_scm_comp A B)) &  ((v5_ordinal1 (k15_scm_comp A B)) & (v1_finset_1 (k15_scm_comp A B))) ) ) ) ) ) ).
tt(dt_k15_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (m1_subset_1 (k15_scmfsa_2 A B C) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k15_scmpds_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (m1_subset_1 (k15_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k15_scmpds_i,ax,(m2_subset_1 k15_scmpds_i k1_numbers k5_numbers)).
tt(dt_k15_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k14_seq_4 A))) )  => (m2_finseq_2 (k15_seq_4 A B C) k2_numbers (k14_seq_4 A))) ) ).
tt(dt_k15_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k15_sin_cos A) k2_numbers)) ) ).
tt(dt_k15_sublemma,ax,$true).
tt(dt_k15_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v1_relat_1 (k15_substut1 A)) & (v1_funct_1 (k15_substut1 A))) ) ) ).
tt(dt_k15_supinf_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) )  & (m1_supinf_2 B A))  =>  ((v1_funct_1 (k15_supinf_2 A B)) &  ((v1_funct_2 (k15_supinf_2 A B) k5_numbers k7_numbers) & (m1_subset_1 (k15_supinf_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k15_toprealb,ax, ((v1_funct_1 k15_toprealb) &  ((v1_funct_2 k15_toprealb (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) & (m1_subset_1 k15_toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))))))) ) ).
tt(dt_k15_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ((v3_membered C) &  ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) )  =>  ((v1_funct_1 (k15_toprealc A B C D)) &  ((v1_funct_2 (k15_toprealc A B C D) B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k15_toprealc A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k15_turing_1,ax, ((v1_funct_1 k15_turing_1) &  ((v1_funct_2 k15_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 k15_turing_1 (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ).
tt(dt_k15_twoscomp,ax, ((v1_funct_1 k15_twoscomp) &  ((v1_funct_2 k15_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k15_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k15_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k15_valued_1 A B C D)) & (m1_subset_1 (k15_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k15_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  ((v1_relat_1 (k15_valued_2 A)) & (v1_funct_1 (k15_valued_2 A))) ) ) ).
tt(dt_k15_zf_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((m1_subset_1 B k1_zf_lang) &  ((v1_zf_lang C) & (m1_finseq_1 C k5_numbers)) ) )  =>  ((v1_zf_lang (k15_zf_lang A B C)) & (m2_finseq_1 (k15_zf_lang A B C) k5_numbers)) ) ) ).
tt(dt_k16_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m1_subset_1 (k16_abcmiz_1 A) (u4_struct_0 A))) ) ).
tt(dt_k16_abcmiz_a,ax, (! [A:$i] :  ((m1_finseq_1 A k2_abcmiz_1) => (m1_trees_4 (k16_abcmiz_a A) (k3_card_3 (u3_msualg_1 k27_abcmiz_1 (k1_msafree3 k27_abcmiz_1 (k28_abcmiz_1 k27_abcmiz_1)))) (k34_abcmiz_1 k27_abcmiz_1))) ) ).
tt(dt_k16_afinsq_1,ax,$true).
tt(dt_k16_algstr_4,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) =>  ((v1_funct_1 (k16_algstr_4 A B)) &  ((v1_funct_2 (k16_algstr_4 A B) (k11_algstr_4 A B) (u1_struct_0 (k14_algstr_4 A))) & (m1_subset_1 (k16_algstr_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A B) (u1_struct_0 (k14_algstr_4 A)))))) ) ) ) ).
tt(dt_k16_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_unialg_1 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k16_aofa_000 A B C) (u1_struct_0 A))) ) ).
tt(dt_k16_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) )  =>  ((v1_funct_1 (k16_aofa_i00 A B C)) &  ((v1_funct_2 (k16_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k16_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k16_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_bilinear A B C D)) &  ((v1_funct_2 (k16_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) & (m1_subset_1 (k16_bilinear A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k16_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (m1_subset_1 (k16_binop_2 A B) k3_numbers)) ) ).
tt(dt_k16_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  &  ((v2_borsuk_1 C B) & (m1_borsuk_1 C B)) ) )  =>  ((v1_pre_topc (k16_borsuk_1 A B C)) &  ((v1_borsuk_1 (k16_borsuk_1 A B C) (k11_borsuk_1 A (k15_borsuk_1 A B C))) & (m1_pre_topc (k16_borsuk_1 A B C) (k11_borsuk_1 A (k15_borsuk_1 A B C)))) ) ) ) ).
tt(dt_k16_borsuk_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) ) )  =>  ((v1_funct_1 (k16_borsuk_7 A B)) &  ((v1_funct_2 (k16_borsuk_7 A B) (u1_struct_0 (k8_toprealb (k1_nat_1 A 1))) (u1_struct_0 (k8_toprealb A))) & (m1_subset_1 (k16_borsuk_7 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_toprealb (k1_nat_1 A 1))) (u1_struct_0 (k8_toprealb A)))))) ) ) ) ).
tt(dt_k16_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  & (m1_eqrel_1 C A)) )  =>  ((v1_funct_1 (k16_bvfunc_1 A B C)) &  ((v1_funct_2 (k16_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k16_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k16_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E A C)) ) ) )  => (m2_cat_1 (k16_cat_2 A B C D E) A (k8_cat_2 B C))) ) ).
tt(dt_k16_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_cat_1 (k16_cat_4 A B C D) A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B (k2_cat_4 A C D)))) ) ).
tt(dt_k16_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  => (m1_subset_1 (k16_cat_5 A B C) (u4_struct_0 A))) ) ).
tt(dt_k16_classes2,ax,$true).
tt(dt_k16_cohsp_1,ax,$true).
tt(dt_k16_coh_sp,ax,$true).
tt(dt_k16_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xreal_0 (k16_complex1 A))) ) ).
tt(dt_k16_comput_1,ax, ((v1_relat_1 k16_comput_1) &  ((v1_funct_1 k16_comput_1) &  ((v7_comput_1 k16_comput_1) & (v8_comput_1 k16_comput_1 2)) ) ) ).
tt(dt_k16_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k16_csspace A B C)) &  ((v1_funct_2 (k16_csspace A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k16_csspace A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k16_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k16_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k16_descip_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  & (m1_subset_1 B A))  => (m2_subset_1 (k16_descip_1 A B) k5_numbers (k2_finseq_1 A))) ) ).
tt(dt_k16_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) ) )  => (m1_subset_1 (k16_domain_1 A B C D) B)) ) ).
tt(dt_k16_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m2_finseq_1 (k16_dtconstr A B) (u1_struct_0 A))) ) ).
tt(dt_k16_ens_1,ax,$true).
tt(dt_k16_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k16_e_siec A))) ) ).
tt(dt_k16_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k16_euclid A) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k16_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k16_facirc_1 A B C) (k14_facirc_1 A B C)) &  ((v4_msafree2 (k16_facirc_1 A B C) (k14_facirc_1 A B C)) &  ((v4_circcomb (k16_facirc_1 A B C) (k14_facirc_1 A B C)) &  ((v6_circcomb (k16_facirc_1 A B C) (k14_facirc_1 A B C)) & (l3_msualg_1 (k16_facirc_1 A B C) (k14_facirc_1 A B C))) ) ) ) ) ).
tt(dt_k16_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k16_ff_siec A))) ) ).
tt(dt_k16_finseq_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k16_finseq_1 A B)) &  ((v1_funct_1 (k16_finseq_1 A B)) & (v1_finseq_1 (k16_finseq_1 A B))) ) ) ) ).
tt(dt_k16_fomodel0,ax, ((v1_funct_1 k16_fomodel0) &  ((v1_funct_2 k16_fomodel0 k2_numbers k2_numbers) & (m1_subset_1 k16_fomodel0 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k16_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ( (~ (v1_xboole_0 (k16_fomodel1 A)))  & (m1_subset_1 (k16_fomodel1 A) (k1_zfmisc_1 (k15_fomodel1 A)))) ) ) ).
tt(dt_k16_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  => (m1_subset_1 (k16_fomodel2 A B) (k1_zfmisc_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1)))))) ) ).
tt(dt_k16_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v1_fomodel3 E C D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_fomodel3 A B C D E)) &  ((v1_funct_2 (k16_fomodel3 A B C D E) (k8_eqrel_1 A C) (k8_eqrel_1 B D)) & (m1_subset_1 (k16_fomodel3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A C) (k8_eqrel_1 B D))))) ) ) ) ).
tt(dt_k16_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k16_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k16_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  & (v1_freealg B))  => (m1_subset_1 (k16_freealg A B) (k1_zfmisc_1 (u1_struct_0 (k15_freealg A B))))) ) ).
tt(dt_k16_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k16_ftacell1 A B C D E) (k3_msafree2 (k13_ftacell1 A B C D E)))) ).
tt(dt_k16_funcop_1,ax,$true).
tt(dt_k16_funct_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) )  =>  ((v1_funct_1 (k16_funct_3 A B C D E F)) &  ((v1_funct_2 (k16_funct_3 A B C D E F) (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) & (m1_subset_1 (k16_funct_3 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D))))) ) ) ) ).
tt(dt_k16_gate_1,ax,$true).
tt(dt_k16_gate_5,ax,$true).
tt(dt_k16_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (v1_card_1 (k16_glib_000 A))) ) ).
tt(dt_k16_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ( (~ (v1_abian (k16_glib_001 A B C)))  & (m1_subset_1 (k16_glib_001 A B C) k5_numbers)) ) ) ).
tt(dt_k16_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  => (m3_glib_004 (k16_glib_004 A) A)) ) ).
tt(dt_k16_graphsp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_funct_2 (k16_graphsp A) (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)))) ) ).
tt(dt_k16_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( ((v7_ordinal1 B) & (v1_int_2 B))  &  ((m1_group_2 C A) & (m1_subset_1 D (u1_struct_0 C))) ) )  =>  ((v1_funct_1 (k16_group_10 A B C D)) &  ((v1_funct_2 (k16_group_10 A B C D) (k15_group_10 A B) (k15_group_10 A B)) & (m1_subset_1 (k16_group_10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_group_10 A B) (k15_group_10 A B))))) ) ) ) ).
tt(dt_k16_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (m1_subset_1 (k16_group_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k16_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((m1_group_9 C A B) & (m1_group_9 D A B)) )  => (m1_subset_1 (k16_group_9 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k16_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) )  =>  ((v1_funct_1 (k16_hahnban1 A B)) &  ((v1_funct_2 (k16_hahnban1 A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 (k16_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) ) ).
tt(dt_k16_idea_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_finseq_1 B k5_numbers))  =>  ((v1_funct_1 (k16_idea_1 A B)) &  ((v1_funct_2 (k16_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k16_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k16_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k16_ideal_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k16_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m5_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) & (m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B))) ) )  => (m5_index_1 (k16_index_1 A B C D) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A))) ) ).
tt(dt_k16_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m2_interva1 B A) & (m2_interva1 C A)) )  => (m2_interva1 (k16_interva1 A B C) A)) ) ).
tt(dt_k16_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k16_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k16_lattice3,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  => (m1_subset_1 (k16_lattice3 A B) (u1_struct_0 A))) ) ).
tt(dt_k16_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k16_lattice5 A)) &  ((v1_funct_2 (k16_lattice5 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) &  ((v1_lattice5 (k16_lattice5 A) (u1_struct_0 A) A) &  ((v2_lattice5 (k16_lattice5 A) (u1_struct_0 A) A) &  ((v3_lattice5 (k16_lattice5 A) (u1_struct_0 A) A) & (m1_subset_1 (k16_lattice5 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_k16_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (m2_lexbfs (k16_lexbfs A) A)) ) ).
tt(dt_k16_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v1_funct_1 (k16_lmod_7 A B C)) &  ((v1_funct_2 (k16_lmod_7 A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k13_lmod_7 A B C))) (u1_struct_0 (k13_lmod_7 A B C))) & (m1_subset_1 (k16_lmod_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k13_lmod_7 A B C))) (u1_struct_0 (k13_lmod_7 A B C)))))) ) ) ) ).
tt(dt_k16_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_lopban_1 A B)))  & (l1_normsp_1 (k16_lopban_1 A B))) ) ) ).
tt(dt_k16_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  => (m2_subset_1 (k16_lpspace1 A B C) (k1_zfmisc_1 (k9_lpspace1 A B C)) (k14_lpspace1 A B C))) ) ).
tt(dt_k16_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k16_margrel1 A B C)) &  ((v1_funct_2 (k16_margrel1 A B C) A k6_margrel1) & (m1_subset_1 (k16_margrel1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k16_matrix_1,ax,$true).
tt(dt_k16_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_matrix_1 C A B B)) )  =>  ((v2_matrixj1 (k16_matrixj1 A B C) A) & (m2_finseq_1 (k16_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k16_mcart_1,ax,$true).
tt(dt_k16_member_1,ax,$true).
tt(dt_k16_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  => (m1_subset_1 (k16_mesfunc1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k16_metric_3,ax, ((v1_funct_1 k16_metric_3) &  ((v1_funct_2 k16_metric_3 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 k16_metric_3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers)))) ) ).
tt(dt_k16_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k16_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k16_mod_2,ax,(m1_subset_1 k16_mod_2 (k1_enumset1 k6_numbers 1 2))).
tt(dt_k16_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) => (m1_subset_1 (k16_modal_1 A) k6_modal_1)) ) ).
tt(dt_k16_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_1 (k16_modelc_1 A)) & (m2_finseq_1 (k16_modelc_1 A) k5_numbers)) ) ) ).
tt(dt_k16_modelc_2,ax,$true).
tt(dt_k16_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v1_funct_1 (k16_modelc_3 A B C)) &  ((v1_funct_2 (k16_modelc_3 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k16_modelc_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k16_monoid_0,ax, (! [A:$i] :  ((v22_algstr_0 (k16_monoid_0 A)) &  ((v4_vectsp_1 (k16_monoid_0 A)) & (m1_monoid_0 (k16_monoid_0 A) (k15_monoid_0 A))) ) ) ).
tt(dt_k16_monoid_1,ax, (! [A:$i,B:$i] : (m1_subset_1 (k16_monoid_1 A B) (u1_struct_0 (k13_monoid_1 B)))) ).
tt(dt_k16_msafree,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  &  ((m2_pboole D (u1_struct_0 A) (k13_msafree A B) C) & (m1_subset_1 E (u1_struct_0 (k5_msafree A B)))) ) ) )  => (m1_subset_1 (k16_msafree A B C D E) (k3_card_3 C))) ) ).
tt(dt_k16_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v1_funct_1 (k16_msualg_2 A B)) &  ((v1_funct_2 (k16_msualg_2 A B) (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B)) & (m1_subset_1 (k16_msualg_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k14_msualg_2 A B) (k14_msualg_2 A B)) (k14_msualg_2 A B))))) ) ) ) ).
tt(dt_k16_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v3_relat_2 (k16_msualg_4 A B C D E)) &  ((v8_relat_2 (k16_msualg_4 A B C D E)) &  ((v1_partfun1 (k16_msualg_4 A B C D E) (k1_funct_1 (u3_msualg_1 A B) E)) & (m1_subset_1 (k16_msualg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) E))))) ) ) ) ) ).
tt(dt_k16_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  => (m1_lattice4 (k16_openlatt A) A (k15_openlatt A))) ) ).
tt(dt_k16_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v3_msualg_1 (k16_osafree A B) A) &  ((v4_msualg_1 (k16_osafree A B) A) &  ((v12_osalg_1 (k16_osafree A B) A) &  ((v13_osalg_1 (k16_osafree A B) A) & (l3_msualg_1 (k16_osafree A B) A)) ) ) ) ) ) ).
tt(dt_k16_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  ( (~ (v2_struct_0 (k16_osalg_2 A B)))  &  ((v3_lattices (k16_osalg_2 A B)) &  ((v10_lattices (k16_osalg_2 A B)) & (l3_lattices (k16_osalg_2 A B))) ) ) ) ) ).
tt(dt_k16_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) ) ) )  =>  ((v12_osalg_1 (k16_osalg_4 A B C) A) & (l3_msualg_1 (k16_osalg_4 A B C) A)) ) ) ).
tt(dt_k16_polyform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  &  ((v1_int_1 B) &  ((m1_subset_1 C (k8_polyform A (k6_xcmplx_0 B 1))) & (m1_subset_1 D (k8_polyform A B))) ) )  => (m1_subset_1 (k16_polyform A B C D) (u1_struct_0 k2_bspace))) ) ).
tt(dt_k16_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k16_pralg_1 A B C)) & (v1_funct_1 (k16_pralg_1 A B C))) ) ) ).
tt(dt_k16_pre_poly,ax, (! [A:$i] : (m2_subset_1 (k16_pre_poly A) (k14_pre_poly A) (k15_pre_poly A))) ).
tt(dt_k16_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k16_pscomp_1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k16_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k16_qc_lang1 A B) (k6_qc_lang1 A))) ) ).
tt(dt_k16_quatern2,ax, ((v36_algstr_0 k16_quatern2) & (l6_algstr_0 k16_quatern2)) ).
tt(dt_k16_quaterni,ax,$true).
tt(dt_k16_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_quofield A)) &  ((v1_funct_2 (k16_quofield A) (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A)) & (m1_subset_1 (k16_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A))))) ) ) ) ).
tt(dt_k16_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B (k3_rfunct_3 A k1_numbers)) & (m1_finseq_1 C k1_numbers)) )  => (m2_finseq_1 (k16_rfunct_3 A B C) (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k16_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  ((v1_funct_1 (k16_ringcat1 A)) & (m1_subset_1 (k16_ringcat1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_ringcat1 A) (k10_ringcat1 A)) (k10_ringcat1 A))))) ) ) ).
tt(dt_k16_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (l1_rlvect_1 (k16_rlvect_2 A))) ) ).
tt(dt_k16_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k16_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k16_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  => (v1_xcmplx_0 (k16_rvsum_1 A))) ) ).
tt(dt_k16_scm_comp,ax, (! [A:$i] :  ((m1_subset_1 A (k6_dtconstr k1_scm_comp)) => (m2_subset_1 (k16_scm_comp A) k1_numbers k5_numbers)) ) ).
tt(dt_k16_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (m1_subset_1 (k16_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k16_scmpds_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (m1_subset_1 (k16_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k16_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_finseq_1 (k16_seq_4 A) k2_numbers)) ) ).
tt(dt_k16_sin_cos,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos k1_numbers k1_numbers) & (m1_subset_1 k16_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k16_sublemma,ax,$true).
tt(dt_k16_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k16_substut1 A))) ) ) ).
tt(dt_k16_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k16_toprealc A)) &  ((v1_funct_2 (k16_toprealc A) (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k16_toprealc A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k16_turing_1,ax, ((v1_turing_1 k16_turing_1) & (l1_turing_1 k16_turing_1)) ).
tt(dt_k16_twoscomp,ax, ((v1_funct_1 k16_twoscomp) &  ((v1_funct_2 k16_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k16_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k16_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k16_valued_2 A B C)) & (m1_subset_1 (k16_valued_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k16_zf_lang,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((m1_subset_1 B k1_zf_lang) &  ((m1_subset_1 C k1_zf_lang) &  ((v1_zf_lang D) & (m1_finseq_1 D k5_numbers)) ) ) )  =>  ((v1_zf_lang (k16_zf_lang A B C D)) & (m2_finseq_1 (k16_zf_lang A B C D) k5_numbers)) ) ) ).
tt(dt_k17_abcmiz_1,ax,$true).
tt(dt_k17_algstr_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  &  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k11_algstr_4 A C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (u1_struct_0 B))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (k11_algstr_4 A D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A D) (u1_struct_0 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k17_algstr_4 A B C D E F)) &  ((v1_funct_2 (k17_algstr_4 A B C D E F) (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C)) (u1_struct_0 B)) & (m1_subset_1 (k17_algstr_4 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A C) (k11_algstr_4 A D)) (k1_tarski C)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k17_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k17_aofa_000 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k17_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_relat_1 (k17_aofa_i00 A B C)) & (v1_funct_1 (k17_aofa_i00 A B C))) ) ) ).
tt(dt_k17_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k17_bilinear A B C D)) &  ((v1_funct_2 (k17_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear (k17_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v2_bilinear (k17_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear (k17_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v4_bilinear (k17_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D))) & (m1_subset_1 (k17_bilinear A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(dt_k17_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (m1_subset_1 (k17_binop_2 A B) k3_numbers)) ) ).
tt(dt_k17_borsuk_1,ax,(l1_pre_topc k17_borsuk_1)).
tt(dt_k17_borsuk_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) &  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) & (m1_borsuk_2 D (k8_toprealb 2) A B)) )  =>  ((v1_funct_1 (k17_borsuk_7 A B C D)) &  ((v1_funct_2 (k17_borsuk_7 A B C D) (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k17_borsuk_7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k17_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  & (m1_eqrel_1 C A)) )  =>  ((v1_funct_1 (k17_bvfunc_1 A B C)) &  ((v1_funct_2 (k17_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k17_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k17_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  &  ((m2_cat_1 E A C) & (m2_cat_1 F B D)) ) ) ) )  => (m2_cat_1 (k17_cat_2 A B C D E F) (k8_cat_2 A B) (k8_cat_2 C D))) ) ).
tt(dt_k17_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_cat_1 (k17_cat_4 A B C D) A (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A (k2_cat_4 A B C) D))) ) ).
tt(dt_k17_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  => (m2_subset_1 (k17_cat_5 A B C) (u4_struct_0 A) (k10_cat_5 A B))) ) ).
tt(dt_k17_cohsp_1,ax,$true).
tt(dt_k17_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) => (m1_subset_1 (k17_coh_sp A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k17_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k17_complex1 A) k1_numbers)) ) ).
tt(dt_k17_comput_1,ax, ((v1_relat_1 k17_comput_1) &  ((v1_funct_1 k17_comput_1) &  ((v7_comput_1 k17_comput_1) & (v8_comput_1 k17_comput_1 1)) ) ) ).
tt(dt_k17_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_clvect_1 B A))  => (m1_subset_1 (k17_convex4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k17_csspace,ax, ((v1_funct_1 k17_csspace) &  ((v1_funct_2 k17_csspace (k2_zfmisc_1 k11_csspace k11_csspace) k2_numbers) & (m1_subset_1 k17_csspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k11_csspace k11_csspace) k2_numbers)))) ) ).
tt(dt_k17_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k17_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k17_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) ) )  => (m1_subset_1 (k17_domain_1 A B C D) C)) ) ).
tt(dt_k17_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m2_finseq_1 (k17_dtconstr A B) (u1_struct_0 A))) ) ).
tt(dt_k17_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((v1_funct_1 (k17_ens_1 A B C)) &  ((v1_funct_2 (k17_ens_1 A B C) (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C))) & (m1_subset_1 (k17_ens_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C)))))) ) ) ) ).
tt(dt_k17_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k17_e_siec A))) ) ).
tt(dt_k17_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k17_euclid A) k1_numbers)) ) ).
tt(dt_k17_facirc_1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k17_facirc_1 A B C) (u1_struct_0 (k15_facirc_1 A B C)) (k3_msafree2 (k15_facirc_1 A B C)))) ).
tt(dt_k17_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k17_ff_siec A))) ) ).
tt(dt_k17_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  => (m2_finseq_1 (k17_finseq_1 A B C) A)) ) ).
tt(dt_k17_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((v1_relat_1 (k17_fomodel0 A B C)) &  ((v1_funct_1 (k17_fomodel0 A B C)) & (v1_finseq_1 (k17_fomodel0 A B C))) ) ) ) ).
tt(dt_k17_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  =>  ( (~ (v1_xboole_0 (k17_fomodel1 A)))  & (m1_subset_1 (k17_fomodel1 A) (k1_zfmisc_1 (k15_fomodel1 A)))) ) ) ).
tt(dt_k17_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k17_fomodel2 A B)) &  ((v1_funct_2 (k17_fomodel2 A B) (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k16_fomodel2 A B) (k32_fomodel1 A)) k6_margrel1) & (m1_subset_1 (k17_fomodel2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k16_fomodel2 A B) (k32_fomodel1 A)) k6_margrel1)))) ) ) ) ).
tt(dt_k17_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_funct_1 (k17_fomodel3 A B)) &  ((v1_funct_2 (k17_fomodel3 A B) A (k8_eqrel_1 A B)) & (m1_subset_1 (k17_fomodel3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A (k8_eqrel_1 A B))))) ) ) ) ).
tt(dt_k17_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k17_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k17_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  & (v1_freealg B))  => (m1_freealg (k17_freealg A B) (k15_freealg A B))) ) ).
tt(dt_k17_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k17_ftacell1 A B C D E) (k3_msafree2 (k13_ftacell1 A B C D E)))) ).
tt(dt_k17_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_funct_1 (k17_funcop_1 A B C)) &  ((v1_funct_2 (k17_funcop_1 A B C) (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C)) & (m1_subset_1 (k17_funcop_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C))))) ) ) ).
tt(dt_k17_gate_1,ax,$true).
tt(dt_k17_gate_5,ax,$true).
tt(dt_k17_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k17_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k17_gfacirc1 A B C)))  &  ((v1_msualg_1 (k17_gfacirc1 A B C)) &  ((v1_circcomb (k17_gfacirc1 A B C)) &  ((v2_circcomb (k17_gfacirc1 A B C)) &  ((v3_circcomb (k17_gfacirc1 A B C)) & (l1_msualg_1 (k17_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k17_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (m1_subset_1 (k17_glib_000 A) k5_numbers)) ) ).
tt(dt_k17_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_abian (k17_glib_001 A B C)))  & (m1_subset_1 (k17_glib_001 A B C) k5_numbers)) ) ) ).
tt(dt_k17_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  => (m1_subset_1 (k17_glib_004 A) (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k17_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k17_graphsp A B C) k1_numbers)) ) ).
tt(dt_k17_grcat_1,ax,$true).
tt(dt_k17_group_10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( ((v7_ordinal1 B) & (v1_int_2 B))  & (m1_group_2 C A)) )  =>  ((v1_funct_1 (k17_group_10 A B C)) &  ((v1_funct_2 (k17_group_10 A B C) (u1_struct_0 C) (k1_funct_2 (k15_group_10 A B) (k15_group_10 A B))) &  ((v1_group_10 (k17_group_10 A B C) C (k15_group_10 A B)) & (m1_subset_1 (k17_group_10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 (k15_group_10 A B) (k15_group_10 A B)))))) ) ) ) ) ).
tt(dt_k17_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (v1_card_1 (k17_group_2 A B))) ) ).
tt(dt_k17_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((m1_group_9 C A B) & (m1_group_9 D A B)) )  =>  ((v2_group_9 (k17_group_9 A B C D) A) & (m1_group_9 (k17_group_9 A B C D) A B)) ) ) ).
tt(dt_k17_idea_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  & (m1_matrix_1 D k5_numbers B 6)) ) )  =>  ((v1_relat_1 (k17_idea_1 A B C D)) &  ((v1_funct_1 (k17_idea_1 A B C D)) & (v1_finseq_1 (k17_idea_1 A B C D))) ) ) ) ).
tt(dt_k17_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k17_ideal_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k17_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m2_interva1 B A) & (m2_interva1 C A)) )  => (m2_interva1 (k17_interva1 A B C) A)) ) ).
tt(dt_k17_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  ((v1_finset_1 (k17_lexbfs A B C D)) & (m1_subset_1 (k17_lexbfs A B C D) (k1_zfmisc_1 B))) ) ) ).
tt(dt_k17_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v7_vectsp_1 (k17_lmod_7 A B C) A) & (l1_vectsp_1 (k17_lmod_7 A B C) A)) ) ) ).
tt(dt_k17_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k17_lopban_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k17_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k17_lpspace1 A B C)) &  ((v1_funct_2 (k17_lpspace1 A B C) (k2_zfmisc_1 k1_numbers (k14_lpspace1 A B C)) (k14_lpspace1 A B C)) & (m1_subset_1 (k17_lpspace1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k14_lpspace1 A B C)) (k14_lpspace1 A B C))))) ) ) ) ).
tt(dt_k17_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k4_partfun1 (k3_finseq_2 A) A)))  => (m2_finseq_1 (k17_margrel1 A B) (k4_partfun1 (k3_finseq_2 A) A))) ) ).
tt(dt_k17_matrixj1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((m1_matrix_1 D A B B) & (m1_matrix_1 E A C C)) ) ) )  =>  ((v2_matrixj1 (k17_matrixj1 A B C D E) A) & (m2_finseq_1 (k17_matrixj1 A B C D E) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k17_member_1,ax,$true).
tt(dt_k17_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  => (m1_subset_1 (k17_mesfunc1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k17_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k17_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k17_mod_2,ax,(m1_subset_1 k17_mod_2 (k1_enumset1 k6_numbers 1 2))).
tt(dt_k17_modal_1,ax,(m1_subset_1 k17_modal_1 k6_modal_1)).
tt(dt_k17_modelc_1,ax, (! [A:$i] :  ((v1_modelc_1 (k17_modelc_1 A)) & (m2_finseq_1 (k17_modelc_1 A) k5_numbers)) ) ).
tt(dt_k17_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (m1_subset_1 (k17_modelc_3 A B C) k1_numbers)) ) ).
tt(dt_k17_monoid_0,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k17_monoid_0 A)))  &  ((v15_algstr_0 (k17_monoid_0 A)) & (m5_monoid_0 (k17_monoid_0 A) (k12_monoid_0 A) (k15_monoid_0 A))) ) ) ).
tt(dt_k17_monoid_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B k5_numbers) => (m1_subset_1 (k17_monoid_1 A B) (u1_struct_0 (k13_monoid_1 A)))) ) ).
tt(dt_k17_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 (k5_msafree A B)))) )  => (m1_subset_1 (k17_msafree A B C) (u4_struct_0 A))) ) ).
tt(dt_k17_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k17_msualg_2 A B)))  &  ((v3_lattices (k17_msualg_2 A B)) &  ((v10_lattices (k17_msualg_2 A B)) & (l3_lattices (k17_msualg_2 A B))) ) ) ) ) ).
tt(dt_k17_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  & (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) )  =>  ((v2_msualg_4 (k17_msualg_4 A B C D) A B) &  ((v3_msualg_4 (k17_msualg_4 A B C D) A B) & (m1_msualg_4 (k17_msualg_4 A B C D) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_k17_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ((v1_pre_topc (k17_openlatt A)) & (l1_pre_topc (k17_openlatt A))) ) ) ).
tt(dt_k17_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 (k2_osafree A B)))) )  => (m1_subset_1 (k17_osafree A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))))) ) ).
tt(dt_k17_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((v1_funct_1 (k17_osalg_4 A B C D)) &  ((v1_funct_2 (k17_osalg_4 A B C D) (k1_funct_1 (u3_msualg_1 A B) D) (k6_osalg_4 A B C D)) & (m1_subset_1 (k17_osalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k6_osalg_4 A B C D))))) ) ) ) ).
tt(dt_k17_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  ((v12_pcs_0 (k17_pcs_0 A B)) & (l2_pcs_0 (k17_pcs_0 A B))) ) ) ).
tt(dt_k17_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ( (~ (v2_struct_0 (k17_polyform A B)))  &  ((v13_algstr_0 (k17_polyform A B)) &  ((v8_vectsp_1 (k17_polyform A B) k2_bspace) &  ((v9_vectsp_1 (k17_polyform A B) k2_bspace) &  ((v10_vectsp_1 (k17_polyform A B) k2_bspace) &  ((v11_vectsp_1 (k17_polyform A B) k2_bspace) &  ((v2_rlvect_1 (k17_polyform A B)) &  ((v3_rlvect_1 (k17_polyform A B)) &  ((v4_rlvect_1 (k17_polyform A B)) &  ((v1_matrlin (k17_polyform A B) k2_bspace) & (l1_vectsp_1 (k17_polyform A B) k2_bspace)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k17_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k17_pre_poly A) (k15_pre_poly A)) &  ((v1_relat_2 (k17_pre_poly A)) &  ((v4_relat_2 (k17_pre_poly A)) &  ((v8_relat_2 (k17_pre_poly A)) & (m1_subset_1 (k17_pre_poly A) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k17_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k17_pscomp_1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k17_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m2_finseq_1 (k17_qc_lang1 A B) (k2_qc_lang1 A))) ) ).
tt(dt_k17_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) => (m1_subset_1 (k17_quatern2 A) (u1_struct_0 k16_quatern2))) ) ).
tt(dt_k17_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k17_quaterni A) k1_numbers)) ) ).
tt(dt_k17_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k17_quofield A)) &  ((v1_funct_2 (k17_quofield A) (k7_quofield A) (k7_quofield A)) & (m1_subset_1 (k17_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A))))) ) ) ) ).
tt(dt_k17_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k17_rfunct_3 A B C) k1_numbers)) ) ).
tt(dt_k17_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (l1_cat_1 (k17_ringcat1 A))) ) ).
tt(dt_k17_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k17_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k17_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m1_subset_1 (k17_rvsum_1 A) k2_numbers)) ) ).
tt(dt_k17_scm_comp,ax, (! [A:$i] :  ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) => (m2_subset_1 (k17_scm_comp A) k1_numbers k5_numbers)) ) ).
tt(dt_k17_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (m1_subset_1 (k17_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k17_scmpds_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  & (v1_int_1 B))  => (m1_subset_1 (k17_scmpds_2 A B) k5_numbers)) ) ).
tt(dt_k17_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_finseq_2 (k17_seq_4 A) k2_numbers (k14_seq_4 A))) ) ).
tt(dt_k17_sin_cos,ax,$true).
tt(dt_k17_substut1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k6_qc_lang1 A)) &  ((m1_finseq_1 C (k2_qc_lang1 A)) & (m1_subset_1 D (k1_substut1 A))) ) )  => (m1_subset_1 (k17_substut1 A B C D) (k16_substut1 A))) ) ).
tt(dt_k17_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (~ (v1_xboole_0 (k17_supinf_2 A)))  &  ((v4_card_3 (k17_supinf_2 A)) & (m1_subset_1 (k17_supinf_2 A) (k1_zfmisc_1 k7_numbers))) ) ) ) ).
tt(dt_k17_toprealc,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k17_toprealc A B)) &  ((v1_funct_2 (k17_toprealc A B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k17_toprealc A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k17_turing_1,ax, ((v1_funct_1 k17_turing_1) &  ((v1_funct_2 k17_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 k17_turing_1 (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 4) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ).
tt(dt_k17_twoscomp,ax, ((v1_funct_1 k17_twoscomp) &  ((v1_funct_2 k17_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k17_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k17_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k17_valued_2 A B C)) & (m1_subset_1 (k17_valued_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k17_zf_lang,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((m1_subset_1 B k1_zf_lang) &  ((m1_subset_1 C k1_zf_lang) &  ((v1_zf_lang D) & (m1_finseq_1 D k5_numbers)) ) ) )  =>  ((v1_zf_lang (k17_zf_lang A B C D)) & (m2_finseq_1 (k17_zf_lang A B C D) k5_numbers)) ) ) ).
tt(dt_k18_abcmiz_1,ax,$true).
tt(dt_k18_abcmiz_a,ax,$true).
tt(dt_k18_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((v1_funct_1 (k18_algstr_4 A B C)) &  ((v1_funct_2 (k18_algstr_4 A B C) (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B))) & (m1_subset_1 (k18_algstr_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B)))))) ) ) ) ).
tt(dt_k18_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  => (m1_subset_1 (k18_aofa_000 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k18_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ((m1_subset_1 E (k9_funct_2 (k9_funct_2 A B) C)) &  ((v1_funct_1 F) &  ((v1_funct_2 F A D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A D)))) ) ) ) ) ) )  => (m2_funct_2 (k18_aofa_i00 A B C D E F) (k9_funct_2 D B) C (k9_funct_2 (k9_funct_2 D B) C))) ) ).
tt(dt_k18_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (m1_subset_1 (k18_binop_2 A B) k3_numbers)) ) ).
tt(dt_k18_borsuk_1,ax,(m1_subset_1 k18_borsuk_1 (u1_struct_0 k17_borsuk_1))).
tt(dt_k18_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  => (m1_eqrel_1 (k18_bvfunc_1 A B) A)) ) ).
tt(dt_k18_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) &  ((m1_cat_1 F A B C) & (m1_cat_1 G A D E)) ) ) ) ) )  => (m1_cat_1 (k18_cat_4 A B C D E F G) A (k2_cat_4 A B D) (k2_cat_4 A C E))) ) ).
tt(dt_k18_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  => (m2_subset_1 (k18_cat_5 A B C) (u4_struct_0 A) (k10_cat_5 A B))) ) ).
tt(dt_k18_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  ((v1_partfun1 (k18_coh_sp A B) (k2_xtuple_0 B)) &  ((v1_relat_2 (k18_coh_sp A B)) &  ((v3_relat_2 (k18_coh_sp A B)) & (m1_subset_1 (k18_coh_sp A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_xtuple_0 B) (k2_xtuple_0 B))))) ) ) ) ) ).
tt(dt_k18_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k18_complex1 A) k1_numbers)) ) ).
tt(dt_k18_comput_1,ax, ((v1_relat_1 k18_comput_1) &  ((v1_funct_1 k18_comput_1) &  ((v7_comput_1 k18_comput_1) & (v8_comput_1 k18_comput_1 2)) ) ) ).
tt(dt_k18_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_clvect_1 (k18_convex4 A)) & (m1_clvect_1 (k18_convex4 A) A)) ) ) ).
tt(dt_k18_csspace,ax, ( (~ (v2_struct_0 k18_csspace))  & (l1_csspace k18_csspace)) ).
tt(dt_k18_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k18_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k18_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k18_dtconstr A B) (k1_zfmisc_1 (k3_finseq_2 (k1_lang1 A))))) ) ).
tt(dt_k18_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((v1_funct_1 (k18_ens_1 A B C)) &  ((v1_funct_2 (k18_ens_1 A B C) (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B)) & (m1_subset_1 (k18_ens_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B))))) ) ) ) ).
tt(dt_k18_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) => (v1_relat_1 (k18_e_siec A))) ) ).
tt(dt_k18_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k18_euclid A) k1_numbers)) ) ).
tt(dt_k18_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k18_facirc_1 A B C) (k15_facirc_1 A B C)) &  ((v4_msafree2 (k18_facirc_1 A B C) (k15_facirc_1 A B C)) &  ((v4_circcomb (k18_facirc_1 A B C) (k15_facirc_1 A B C)) &  ((v6_circcomb (k18_facirc_1 A B C) (k15_facirc_1 A B C)) & (l3_msualg_1 (k18_facirc_1 A B C) (k15_facirc_1 A B C))) ) ) ) ) ).
tt(dt_k18_finseq_1,ax, (! [A:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k18_finseq_1 A))) ) ).
tt(dt_k18_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  ((v1_relat_1 (k18_fomodel0 A B C D)) &  ((v1_funct_1 (k18_fomodel0 A B C D)) & (v1_finseq_1 (k18_fomodel0 A B C D))) ) ) ) ).
tt(dt_k18_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  => (m2_subset_1 (k18_fomodel1 A) (k15_fomodel1 A) (k17_fomodel1 A))) ) ).
tt(dt_k18_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (m1_subset_1 (k18_fomodel2 A B C D E) k6_margrel1)) ) ).
tt(dt_k18_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  => (m1_subset_1 (k18_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B (k8_eqrel_1 A C)) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B)))))) ) ).
tt(dt_k18_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k18_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k18_freealg,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  &  ((v1_freealg B) &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D (u1_struct_0 (k3_freealg A B))) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k17_freealg A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k17_freealg A B) C)))) ) ) ) ) )  => (m1_subset_1 (k18_freealg A B C D E) C)) ) ).
tt(dt_k18_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k18_ftacell1 A B C D E) (k3_msafree2 (k13_ftacell1 A B C D E)))) ).
tt(dt_k18_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k18_funcop_1 A B)) &  ((v1_funct_2 (k18_funcop_1 A B) (k1_tarski A) (k1_tarski B)) & (m1_subset_1 (k18_funcop_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski B))))) ) ) ).
tt(dt_k18_gate_1,ax,$true).
tt(dt_k18_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k18_gfacirc1 A B C) (k17_gfacirc1 A B C)) &  ((v4_msafree2 (k18_gfacirc1 A B C) (k17_gfacirc1 A B C)) &  ((v4_circcomb (k18_gfacirc1 A B C) (k17_gfacirc1 A B C)) &  ((v6_circcomb (k18_gfacirc1 A B C) (k17_gfacirc1 A B C)) & (l3_msualg_1 (k18_gfacirc1 A B C) (k17_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k18_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k18_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k18_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ( (~ (v1_abian (k18_glib_001 A B C)))  & (m1_subset_1 (k18_glib_001 A B C) k5_numbers)) ) ) ).
tt(dt_k18_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (m1_subset_1 B k5_numbers))  => (m2_finseq_2 (k18_graphsp A B) k1_numbers (k3_finseq_2 k1_numbers))) ) ).
tt(dt_k18_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  ( (~ (v1_xboole_0 (k18_grcat_1 A)))  & (v4_grcat_1 (k18_grcat_1 A))) ) ) ).
tt(dt_k18_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (m1_subset_1 (k18_group_2 A B) k5_numbers)) ) ).
tt(dt_k18_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v2_group_9 (k18_group_9 A B C) A) & (m1_group_9 (k18_group_9 A B C) A B)) ) ) ).
tt(dt_k18_idea_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  & (m1_matrix_1 D k5_numbers B 6)) ) )  =>  ((v1_relat_1 (k18_idea_1 A B C D)) &  ((v1_funct_1 (k18_idea_1 A B C D)) & (v1_finseq_1 (k18_idea_1 A B C D))) ) ) ) ).
tt(dt_k18_interva1,ax,$true).
tt(dt_k18_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (m1_subset_1 (k18_lexbfs A) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers)))) ) ).
tt(dt_k18_lmod_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k18_lmod_7 A B C D) (u1_struct_0 (k17_lmod_7 A B C)))) ) ).
tt(dt_k18_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k18_lpspace1 A B C)))  &  ((v13_algstr_0 (k18_lpspace1 A B C)) &  ((v1_rlvect_1 (k18_lpspace1 A B C)) &  ((v2_rlvect_1 (k18_lpspace1 A B C)) &  ((v3_rlvect_1 (k18_lpspace1 A B C)) &  ((v4_rlvect_1 (k18_lpspace1 A B C)) &  ((v5_rlvect_1 (k18_lpspace1 A B C)) &  ((v6_rlvect_1 (k18_lpspace1 A B C)) &  ((v7_rlvect_1 (k18_lpspace1 A B C)) &  ((v8_rlvect_1 (k18_lpspace1 A B C)) & (l1_rlvect_1 (k18_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k18_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_margrel1 A))  => (v7_ordinal1 (k18_margrel1 A))) ) ).
tt(dt_k18_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v2_matrixj1 (k18_matrixj1 A B C) A) & (m2_finseq_1 (k18_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k18_member_1,ax,$true).
tt(dt_k18_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  => (m1_subset_1 (k18_mesfunc1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k18_metric_3,ax, ((v1_funct_1 k18_metric_3) &  ((v1_funct_2 k18_metric_3 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 k18_metric_3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers)) k1_numbers)))) ) ).
tt(dt_k18_mmlquery,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (m1_subset_1 (k18_mmlquery A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k18_mod_2,ax, ((v36_algstr_0 k18_mod_2) & (l6_algstr_0 k18_mod_2)) ).
tt(dt_k18_modelc_1,ax,(m1_subset_1 k18_modelc_1 (k1_zfmisc_1 k12_modelc_1))).
tt(dt_k18_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  & (v7_ordinal1 C)) )  =>  (~ (v1_xboole_0 (k18_modelc_2 A B C))) ) ) ).
tt(dt_k18_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))))  => (m1_subset_1 (k18_modelc_3 A B) k1_numbers)) ) ).
tt(dt_k18_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k18_monoid_1 A B) (u1_struct_0 (k13_monoid_1 A)))) ) ).
tt(dt_k18_msafree,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((m1_subset_1 C (u4_struct_0 A)) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m1_subset_1 (k18_msafree A B C D) (k3_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k18_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k18_msualg_4 A B C D E)) &  ((v1_funct_2 (k18_msualg_4 A B C D E) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E)) & (m1_subset_1 (k18_msualg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E))))) ) ) ) ).
tt(dt_k18_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (m1_lattice4 (k18_openlatt A) A (k6_openlatt (k17_openlatt A)))) ) ).
tt(dt_k18_osafree,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) & (m1_finseq_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))))) ) )  => (m1_subset_1 (k18_osafree A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))))) ) ).
tt(dt_k18_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) ) ) )  => (m2_pboole (k18_osalg_4 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k16_osalg_4 A B C)))) ) ).
tt(dt_k18_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (l2_pcs_0 (k18_pcs_0 A B))) ) ).
tt(dt_k18_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ( (~ (v1_xboole_0 (k18_polyform A B)))  & (v1_finset_1 (k18_polyform A B))) ) ) ).
tt(dt_k18_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (m1_subset_1 (k18_pre_poly A B) (k1_zfmisc_1 (k9_funct_2 A k5_numbers)))) ) ).
tt(dt_k18_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k18_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k18_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k18_qc_lang1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k18_quatern2,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (m1_subset_1 (k18_quatern2 A B) k1_quaterni)) ) ).
tt(dt_k18_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k18_quaterni A) k1_numbers)) ) ).
tt(dt_k18_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k18_quofield A)) &  ((v1_funct_2 (k18_quofield A) (k7_quofield A) (k7_quofield A)) & (m1_subset_1 (k18_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_quofield A) (k7_quofield A))))) ) ) ) ).
tt(dt_k18_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k18_rfunct_3 A B)) & (m1_subset_1 (k18_rfunct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k18_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k18_rvsum_1 A) k1_numbers)) ) ).
tt(dt_k18_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  & (m1_scmfsa_2 B))  => (m2_finseq_1 (k18_scmfsa_2 A B) k4_numbers)) ) ).
tt(dt_k18_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  => (m2_finseq_2 (k18_seq_4 A B) k2_numbers (k14_seq_4 A))) ) ).
tt(dt_k18_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k18_sin_cos A) k1_numbers)) ) ).
tt(dt_k18_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k18_substut1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k18_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_funct_1 (k18_supinf_2 A)) &  ((v1_funct_2 (k18_supinf_2 A) k5_numbers k7_numbers) & (m1_subset_1 (k18_supinf_2 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k18_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))))) )  => (m1_subset_1 (k18_toprealc A B C) (k1_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))))) ) ).
tt(dt_k18_turing_1,ax, ((v1_turing_1 k18_turing_1) & (l1_turing_1 k18_turing_1)) ).
tt(dt_k18_twoscomp,ax, ((v1_funct_1 k18_twoscomp) &  ((v1_funct_2 k18_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k18_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k18_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) & (v1_funct_1 (k18_valued_1 A B))) ) ) ).
tt(dt_k18_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (m2_subset_1 (k18_zf_lang A) k5_numbers k1_zf_lang)) ) ).
tt(dt_k19_abcmiz_1,ax,$true).
tt(dt_k19_aofa_000,ax, ( (~ (v1_xboole_0 k19_aofa_000))  & (m2_finseq_1 k19_aofa_000 k5_numbers)) ).
tt(dt_k19_binop_2,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k19_binop_2 A) k4_numbers)) ) ).
tt(dt_k19_borsuk_1,ax,(m1_subset_1 k19_borsuk_1 (u1_struct_0 k17_borsuk_1))).
tt(dt_k19_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k19_bvfunc_1 A B) k6_margrel1)) ) ).
tt(dt_k19_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  => (m1_subset_1 (k19_cat_4 A) (u1_struct_0 A))) ) ).
tt(dt_k19_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_cat_1 (k19_cat_5 A B) (k11_cat_5 A (k3_graph_1 A B)) (k11_cat_5 A (k4_graph_1 A B)))) ) ).
tt(dt_k19_coh_sp,ax,$true).
tt(dt_k19_comput_1,ax, ((v1_relat_1 k19_comput_1) &  ((v1_funct_1 k19_comput_1) &  ((v7_comput_1 k19_comput_1) & (v8_comput_1 k19_comput_1 1)) ) ) ).
tt(dt_k19_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v1_xcmplx_0 C)) )  => (m1_subset_1 (k19_convex4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k19_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k19_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k19_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k19_dtconstr A B) (k1_zfmisc_1 (k3_finseq_2 (u1_struct_0 A))))) ) ).
tt(dt_k19_ens_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k19_ens_1 A B)) &  ((v1_funct_2 (k19_ens_1 A B) (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 (k19_ens_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)))))) ) ) ) ).
tt(dt_k19_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) => (v1_relat_1 (k19_e_siec A))) ) ).
tt(dt_k19_euclid,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k19_euclid A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k19_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k19_facirc_1 A B C)))  &  ( (~ (v11_struct_0 (k19_facirc_1 A B C)))  &  ((v1_msualg_1 (k19_facirc_1 A B C)) &  ((v1_circcomb (k19_facirc_1 A B C)) &  ((v2_circcomb (k19_facirc_1 A B C)) &  ((v3_circcomb (k19_facirc_1 A B C)) & (l1_msualg_1 (k19_facirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k19_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C A) &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m2_finseq_1 (k19_fomodel0 A B C D) A)) ) ).
tt(dt_k19_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  => (m1_subset_1 (k19_fomodel1 A B) k4_numbers)) ) ).
tt(dt_k19_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))) )  =>  ((v1_funct_1 (k19_fomodel2 A B C)) & (m1_subset_1 (k19_fomodel2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)))) ) ) ).
tt(dt_k19_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ((v1_funct_1 (k19_fomodel3 A B C)) &  ((v1_funct_2 (k19_fomodel3 A B C) (k4_finseq_2 B (k8_eqrel_1 A C)) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B))) & (m1_subset_1 (k19_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B (k8_eqrel_1 A C)) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B)))))) ) ) ) ).
tt(dt_k19_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k19_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k19_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( (~ (v2_struct_0 (k19_ftacell1 A B C D E)))  &  ( (~ (v11_struct_0 (k19_ftacell1 A B C D E)))  &  ((v1_msualg_1 (k19_ftacell1 A B C D E)) &  ((v1_circcomb (k19_ftacell1 A B C D E)) &  ((v2_circcomb (k19_ftacell1 A B C D E)) &  ((v3_circcomb (k19_ftacell1 A B C D E)) & (l1_msualg_1 (k19_ftacell1 A B C D E))) ) ) ) ) ) ) ).
tt(dt_k19_gate_1,ax,$true).
tt(dt_k19_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k19_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k19_gfacirc1 A B C)))  &  ((v1_msualg_1 (k19_gfacirc1 A B C)) &  ((v1_circcomb (k19_gfacirc1 A B C)) &  ((v2_circcomb (k19_gfacirc1 A B C)) &  ((v3_circcomb (k19_gfacirc1 A B C)) & (l1_msualg_1 (k19_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k19_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k19_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k19_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_abian (k19_glib_001 A B C)))  & (m1_subset_1 (k19_glib_001 A B C) k5_numbers)) ) ) ).
tt(dt_k19_graphsp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_funct_2 (k19_graphsp A) (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)))) ) ).
tt(dt_k19_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  & (m1_subset_1 B (k18_grcat_1 A)))  =>  ((v8_algstr_0 (k19_grcat_1 A B)) & (m2_grcat_1 (k19_grcat_1 A B) A)) ) ) ).
tt(dt_k19_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((m1_group_9 C A B) & (m1_group_9 D A B)) )  =>  ((v2_group_9 (k19_group_9 A B C D) A) & (m1_group_9 (k19_group_9 A B C D) A B)) ) ) ).
tt(dt_k19_idea_1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k19_idea_1 A B)) &  ((v1_funct_2 (k19_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k19_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k19_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))))  => (m1_subset_1 (k19_lexbfs A B) (k6_glib_000 A))) ) ).
tt(dt_k19_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k19_lpspace1 A B C)) &  ((v1_funct_2 (k19_lpspace1 A B C) (u1_struct_0 (k18_lpspace1 A B C)) k1_numbers) & (m1_subset_1 (k19_lpspace1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k18_lpspace1 A B C)) k1_numbers)))) ) ) ) ).
tt(dt_k19_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  => (m1_subset_1 (k19_margrel1 A) k5_numbers)) ) ).
tt(dt_k19_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v2_matrixj1 (k19_matrixj1 A B C) A) & (m2_finseq_1 (k19_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k19_member_1,ax,$true).
tt(dt_k19_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  => (m1_subset_1 (k19_mesfunc1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k19_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k19_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k19_modelc_1,ax,$true).
tt(dt_k19_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k19_modelc_2 A B C)) &  ((v1_funct_2 (k19_modelc_2 A B C) k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 (k19_modelc_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) ) ) ) ).
tt(dt_k19_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (m1_subset_1 (k19_modelc_3 A B) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k19_monoid_1,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k19_monoid_1 A)))  &  ((v22_algstr_0 (k19_monoid_1 A)) & (m3_monoid_0 (k19_monoid_1 A) (k13_monoid_1 A))) ) ) ).
tt(dt_k19_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  & (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) )  => (m2_pboole (k19_msualg_4 A B C D) (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) (u3_msualg_1 A C))) ) ).
tt(dt_k19_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_funct_1 (k19_osafree A B)) &  ((v1_funct_2 (k19_osafree A B) (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A)))) & (m1_subset_1 (k19_osafree A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))))))) ) ) ) ).
tt(dt_k19_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  & (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) )  =>  ((v2_msualg_4 (k19_osalg_4 A B C D) A B) &  ((v3_msualg_4 (k19_osalg_4 A B C D) A B) & (m1_osalg_4 (k19_osalg_4 A B C D) A B)) ) ) ) ).
tt(dt_k19_pcs_0,ax, (! [A:$i,B:$i] :  ((l2_pcs_0 A) =>  ((v12_pcs_0 (k19_pcs_0 A B)) & (l2_pcs_0 (k19_pcs_0 A B))) ) ) ).
tt(dt_k19_polyform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  &  ((v1_int_1 B) &  ((m1_subset_1 C (k8_polyform A (k6_xcmplx_0 B 1))) & (m1_subset_1 D (u1_struct_0 (k17_polyform A B)))) ) )  => (m2_finseq_1 (k19_polyform A B C D) (u1_struct_0 k2_bspace))) ) ).
tt(dt_k19_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) &  ((v2_pre_poly B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  => (m1_subset_1 (k19_pre_poly A B) (k5_finsub_1 A))) ) ).
tt(dt_k19_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k19_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k19_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k19_qc_lang1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k19_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k19_quaterni A) k1_numbers)) ) ).
tt(dt_k19_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v36_algstr_0 (k19_quofield A)) & (l6_algstr_0 (k19_quofield A))) ) ) ).
tt(dt_k19_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k19_rfunct_3 A B)) & (m1_subset_1 (k19_rfunct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k19_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  => (v1_xcmplx_0 (k19_rvsum_1 A))) ) ).
tt(dt_k19_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k14_seq_4 A))) )  => (m2_finseq_2 (k19_seq_4 A B C) k2_numbers (k14_seq_4 A))) ) ).
tt(dt_k19_sin_cos,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos k1_numbers k1_numbers) & (m1_subset_1 k19_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k19_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k19_substut1 A B) (k1_substut1 A))) ) ).
tt(dt_k19_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k19_supinf_2 A) k7_numbers)) ) ).
tt(dt_k19_turing_1,ax, ((v1_funct_1 k19_turing_1) &  ((v1_funct_2 k19_turing_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 k19_turing_1 (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 k5_numbers k5_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1)) (k9_mcart_1 k5_numbers k5_numbers k1_numbers (k3_turing_1 3) (k7_domain_1 k5_numbers k6_numbers 1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ).
tt(dt_k19_twoscomp,ax, ((v1_funct_1 k19_twoscomp) &  ((v1_funct_2 k19_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k19_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k19_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k19_valued_1 A B C D E)) & (m1_subset_1 (k19_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k19_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (m2_subset_1 (k19_zf_lang A) k5_numbers k1_zf_lang)) ) ).
tt(dt_k1_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ((l1_abcmiz_0 A) & (m1_subset_1 B (u1_abcmiz_0 A)))  => (m1_subset_1 (k1_abcmiz_0 A B) (u1_abcmiz_0 A))) ) ).
tt(dt_k1_abcmiz_1,ax,$true).
tt(dt_k1_abian,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (m1_subset_1 C k5_numbers))  =>  ((v1_funct_1 (k1_abian A B C)) &  ((v1_funct_2 (k1_abian A B C) A A) & (m1_subset_1 (k1_abian A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(dt_k1_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k1_absvalue A))) ) ).
tt(dt_k1_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_aff_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_aff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_aff_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  => (m2_subset_1 (k1_afinsq_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 (k1_afinsq_2 A)) &  ((v1_funct_1 (k1_afinsq_2 A)) &  ((v5_ordinal1 (k1_afinsq_2 A)) & (v1_finset_1 (k1_afinsq_2 A))) ) ) ) ) ).
tt(dt_k1_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (m1_subset_1 (k1_afproj A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_afvect0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_afvect0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_alg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_unialg_1 (k1_alg_1 A B C)) & (m1_unialg_2 (k1_alg_1 A B C) B)) ) ) ).
tt(dt_k1_algseq_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k1_algseq_1 A B) k5_numbers)) ) ).
tt(dt_k1_algspec1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_relat_1 (k1_algspec1 A B)) &  ((v4_relat_1 (k1_algspec1 A B) A) &  ((v1_funct_1 (k1_algspec1 A B)) & (v1_partfun1 (k1_algspec1 A B) A)) ) ) ) ) ).
tt(dt_k1_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_algstr_0 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_algstr_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_algstr_1,ax, (! [A:$i] : (m1_subset_1 (k1_algstr_1 A) (k1_tarski A))) ).
tt(dt_k1_algstr_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v3_algstr_1 A) & (l2_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_algstr_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_algstr_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_algstr_3 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k1_algstr_3 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_altcat_1,ax,$true).
tt(dt_k1_altcat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_altcat_1 A B C))) ) )  => (m1_subset_1 (k1_altcat_3 A B C D) (k1_altcat_1 A C B))) ) ).
tt(dt_k1_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k1_altcat_4 A)))  &  ((v2_altcat_1 (k1_altcat_4 A)) &  ((v6_altcat_1 (k1_altcat_4 A)) & (m1_altcat_2 (k1_altcat_4 A) A)) ) ) ) ) ).
tt(dt_k1_ami_2,ax,$true).
tt(dt_k1_ami_3,ax, ((v1_extpro_1 k1_ami_3 2) & (l1_extpro_1 k1_ami_3 2)) ).
tt(dt_k1_ami_4,ax, ((v1_relat_1 k1_ami_4) &  ((v4_relat_1 k1_ami_4 k5_numbers) &  ((v5_relat_1 k1_ami_4 (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 k1_ami_4) & (v1_finset_1 k1_ami_4)) ) ) ) ).
tt(dt_k1_amistd_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ((v7_ordinal1 C) & (m1_subset_1 D (u1_compos_1 B))) ) )  => (m1_subset_1 (k1_amistd_1 A B C D) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k1_amistd_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ((v1_relat_1 (k1_amistd_3 A B C)) &  ((v5_relat_1 (k1_amistd_3 A B C) k5_numbers) &  ((v5_ordinal1 (k1_amistd_3 A B C)) & (v1_funct_1 (k1_amistd_3 A B C))) ) ) ) ) ).
tt(dt_k1_amistd_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (k4_memstr_0 A B D))) ) ) )  =>  ((v1_relat_1 (k1_amistd_4 A B C D E)) &  ((v4_relat_1 (k1_amistd_4 A B C D E) (u1_struct_0 B)) &  ((v1_funct_1 (k1_amistd_4 A B C D E)) &  ((v5_funct_1 (k1_amistd_4 A B C D E) (k2_memstr_0 A B)) & (v1_partfun1 (k1_amistd_4 A B C D E) (u1_struct_0 B))) ) ) ) ) ) ).
tt(dt_k1_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  & (v7_ordinal1 C)) )  => (m2_subset_1 (k1_ami_wstd A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k1_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_analmetr A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k1_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (m1_subset_1 (k1_analoaf A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k1_analort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k1_analort A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v3_relat_2 (k1_anproj_1 A)) &  ((v8_relat_2 (k1_anproj_1 A)) &  ((v1_partfun1 (k1_anproj_1 A) (k8_struct_0 A)) & (m1_subset_1 (k1_anproj_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 A) (k8_struct_0 A))))) ) ) ) ) ).
tt(dt_k1_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((m1_finseq_2 C A) & (m1_subset_1 D B)) )  =>  ((v1_funct_1 (k1_aofa_000 A B C D)) & (m1_subset_1 (k1_aofa_000 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) B)))) ) ) ).
tt(dt_k1_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_funct_1 A))  => (m1_subset_1 (k1_aofa_i00 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_armstrng,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) => (m1_subset_1 (k1_armstrng A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_arrow,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B)))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  & (m1_subset_1 E A)) ) ) )  => (m2_subset_1 (k1_arrow A B C D E) B C)) ) ).
tt(dt_k1_arytm_0,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k1_arytm_0 A B) k1_numbers)) ) ).
tt(dt_k1_arytm_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  => (m1_subset_1 (k1_arytm_1 A B) k2_arytm_2)) ) ).
tt(dt_k1_arytm_2,ax,(m1_subset_1 k1_arytm_2 (k1_zfmisc_1 (k1_zfmisc_1 k5_arytm_3)))).
tt(dt_k1_arytm_3,ax,$true).
tt(dt_k1_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_asympt_0 A B)) &  ((v1_funct_2 (k1_asympt_0 A B) k5_numbers k1_numbers) &  ((v2_asympt_0 (k1_asympt_0 A B)) & (m1_subset_1 (k1_asympt_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ).
tt(dt_k1_asympt_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k1_asympt_1 A B C)) &  ((v1_funct_2 (k1_asympt_1 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k1_asympt_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m1_funct_2 (k1_autalg_1 A) (u1_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k1_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (m1_funct_2 (k1_autgroup A) (u1_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k1_bagorder,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) ) ) )  =>  ((v1_relat_1 (k1_bagorder A B C D)) &  ((v4_relat_1 (k1_bagorder A B C D) (k7_nat_d C B)) &  ((v1_funct_1 (k1_bagorder A B C D)) & (v1_partfun1 (k1_bagorder A B C D) (k7_nat_d C B))) ) ) ) ) ).
tt(dt_k1_bcialg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_bcialg_1 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_bcialg_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_bcialg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D k5_numbers)) ) )  => (m1_subset_1 (k1_bcialg_2 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_bcialg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_bcialg_4 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_bcialg_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_bcialg_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E k5_numbers)) ) ) )  => (m1_subset_1 (k1_bcialg_5 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k1_bciideal,ax,$true).
tt(dt_k1_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_bhsp_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_bhsp_1 A B C) k1_numbers)) ) ).
tt(dt_k1_bhsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_bhsp_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_bhsp_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k1_bhsp_4 A B)) &  ((v1_funct_2 (k1_bhsp_4 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k1_bhsp_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_bhsp_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_bhsp_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((l1_vectsp_1 B A) & (l1_vectsp_1 C A)) )  =>  ((v1_funct_1 (k1_bilinear A B C)) &  ((v1_funct_2 (k1_bilinear A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k1_bilinear A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_binari_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v3_card_1 (k1_binari_2 A) A) & (m2_finseq_1 (k1_binari_2 A) k6_margrel1)) ) ) ).
tt(dt_k1_binari_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v3_card_1 (k1_binari_3 A B) A) & (m2_finseq_1 (k1_binari_3 A B) k6_margrel1)) ) ) ).
tt(dt_k1_binari_4,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k1_binari_4 A B))) ) ).
tt(dt_k1_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k1_binarith A B) k6_margrel1)) ) ).
tt(dt_k1_binom,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k1_binom A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_binop_1,ax,$true).
tt(dt_k1_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k1_binop_2 A) k2_numbers)) ) ).
tt(dt_k1_bintree1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m1_subset_1 (k1_bintree1 A B) A)) ) ).
tt(dt_k1_bintree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  &  ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  ((v1_funct_1 (k1_bintree2 A B)) &  ((v1_funct_2 (k1_bintree2 A B) (k2_trees_2 A B) k5_numbers) & (m1_subset_1 (k1_bintree2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_trees_2 A B) k5_numbers)))) ) ) ) ).
tt(dt_k1_birkhoff,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  & (m2_pboole D (u1_struct_0 A) B (u3_msualg_1 A C))) ) )  => (m2_pboole (k1_birkhoff A B C D) (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)) (u3_msualg_1 A C))) ) ).
tt(dt_k1_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_boolealg A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_boolmark,ax, (! [A:$i] :  ((l1_petri A) => (m1_funct_2 (k1_boolmark A) (u1_struct_0 A) k6_margrel1)) ) ).
tt(dt_k1_bor_cant,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xxreal_0 B) &  ((v1_xxreal_0 C) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) )  => (m1_subset_1 (k1_bor_cant A B C D E) A)) ) ).
tt(dt_k1_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (m1_connsp_2 E B C)) ) ) )  => (m2_connsp_2 (k1_borsuk_1 A B C D E) A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k6_domain_1 (u1_struct_0 B) C)))) ) ).
tt(dt_k1_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_borsuk_2 E A B C) & (m1_borsuk_2 F A C D)) ) ) ) )  => (m1_borsuk_2 (k1_borsuk_2 A B C D E F) A B D)) ) ).
tt(dt_k1_borsuk_4,ax, ((v1_pre_topc k1_borsuk_4) & (m1_pre_topc k1_borsuk_4 k5_topmetr)) ).
tt(dt_k1_borsuk_5,ax,(m1_subset_1 k1_borsuk_5 (k1_zfmisc_1 k1_numbers))).
tt(dt_k1_borsuk_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ((v1_funct_1 (k1_borsuk_6 A B C D)) &  ((v1_funct_2 (k1_borsuk_6 A B C D) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 (k1_borsuk_6 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) ) ) ) ).
tt(dt_k1_borsuk_7,ax,$true).
tt(dt_k1_brouwer,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  => (m1_subset_1 (k1_brouwer A B) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) ) ).
tt(dt_k1_bspace,ax, (! [A:$i] :  ((l1_struct_0 A) => (m2_finseq_1 (k1_bspace A) (u1_struct_0 A))) ) ).
tt(dt_k1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((v1_funct_1 (k1_bvfunc_1 A B)) &  ((v1_funct_2 (k1_bvfunc_1 A B) A k6_margrel1) & (m1_subset_1 (k1_bvfunc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k1_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k1_bvfunc26 A B)) & (v1_funct_1 (k1_bvfunc26 A B))) ) ) ).
tt(dt_k1_bvfunc_2,ax, (! [A:$i] :  ((v1_eqrel_1 (k1_bvfunc_2 A) A) & (m1_subset_1 (k1_bvfunc_2 A) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) ) ).
tt(dt_k1_c0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k1_c0sp1 A B)) &  ((v1_funct_2 (k1_c0sp1 A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k1_c0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k1_c0sp2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_c0sp2 A B)) &  ((v1_funct_2 (k1_c0sp2 A B) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (k1_c0sp2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_k1_calcul_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m2_finseq_1 (k1_calcul_1 A B) A)) ) ).
tt(dt_k1_calcul_2,ax,$true).
tt(dt_k1_cantor_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k1_cantor_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k1_card_1,ax, (! [A:$i] : (v1_card_1 (k1_card_1 A))) ).
tt(dt_k1_card_2,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  => (v1_card_1 (k1_card_2 A B))) ) ).
tt(dt_k1_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_card_3 A)) &  ((v1_funct_1 (k1_card_3 A)) & (v1_card_3 (k1_card_3 A))) ) ) ) ).
tt(dt_k1_card_5,ax, (! [A:$i] :  ((v1_card_1 A) => (v1_card_1 (k1_card_5 A))) ) ).
tt(dt_k1_card_fil,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_card_fil B A))  => (m2_card_fil (k1_card_fil A B) A)) ) ).
tt(dt_k1_cardfin2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_int_1 (k1_cardfin2 A))) ) ).
tt(dt_k1_card_fin,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_finset_1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k1_card_fin A B C D) (k1_zfmisc_1 (k9_funct_2 A (k2_tarski C D))))) ) ).
tt(dt_k1_card_lar,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (v3_ordinal1 C)) )  => (m1_subset_1 (k1_card_lar A B C) B)) ) ).
tt(dt_k1_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_cat_1 A) &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  => (m1_subset_1 (k1_cat_1 A B C) (u4_struct_0 A))) ) ).
tt(dt_k1_cat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (m2_cat_1 (k1_cat_2 A B C) A B)) ) ).
tt(dt_k1_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k1_cat_3 A B C)) &  ((v1_funct_2 (k1_cat_3 A B C) (k1_tarski B) A) & (m1_subset_1 (k1_cat_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski B) A)))) ) ) ) ).
tt(dt_k1_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  => (m1_subset_1 (k1_cat_4 A) (u1_struct_0 A))) ) ).
tt(dt_k1_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_5 A) & (l1_cat_1 A)) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k1_cat_5 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_catalan1 A) k1_numbers)) ) ).
tt(dt_k1_catalan2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v5_ordinal1 (k1_catalan2 A B)) &  ((v1_relat_1 (k1_catalan2 A B)) &  ((v5_relat_1 (k1_catalan2 A B) k5_numbers) &  ((v1_funct_1 (k1_catalan2 A B)) & (v1_finset_1 (k1_catalan2 A B))) ) ) ) ) ) ).
tt(dt_k1_catalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_relat_1 (k1_catalg_1 A B C)) &  ((v4_relat_1 (k1_catalg_1 A B C) A) &  ((v1_funct_1 (k1_catalg_1 A B C)) &  ((v1_partfun1 (k1_catalg_1 A B C) A) & (v1_funcop_1 (k1_catalg_1 A B C))) ) ) ) ) ) ).
tt(dt_k1_cayley,ax,$true).
tt(dt_k1_cc0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k1_cc0sp1 A B)) &  ((v1_funct_2 (k1_cc0sp1 A B) (k2_zfmisc_1 k2_numbers B) B) & (m1_subset_1 (k1_cc0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers B) B)))) ) ) ) ).
tt(dt_k1_cc0sp2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (v1_xcmplx_0 B))  =>  ((v1_funct_1 (k1_cc0sp2 A B)) &  ((v1_funct_2 (k1_cc0sp2 A B) (u1_struct_0 A) k2_numbers) & (m1_subset_1 (k1_cc0sp2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) ) ) ).
tt(dt_k1_cfdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k1_cfdiff_1 A)) &  ((v1_funct_2 (k1_cfdiff_1 A) k5_numbers k2_numbers) & (m1_subset_1 (k1_cfdiff_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k1_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k1_cfuncdom A)) &  ((v1_funct_2 (k1_cfuncdom A) (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 (k1_cfuncdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) ) ) ) ).
tt(dt_k1_cfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((v1_funct_1 (k1_cfunct_1 A B C)) & (m1_subset_1 (k1_cfunct_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k1_cgames_1,ax,$true).
tt(dt_k1_chain_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (k1_chain_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k1_chord,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  & (v7_ordinal1 B))  => (v1_finset_1 (k1_chord A B))) ) ).
tt(dt_k1_circcmb3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (k4_card_3 (u3_msualg_1 A B)))) )  => (m1_subset_1 (k1_circcmb3 A B C) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k1_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v4_relat_1 E D) &  ((v1_funct_1 E) & (v1_partfun1 E D)) ) ) )  &  ( ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v4_relat_1 F D) &  ((v1_funct_1 F) & (v1_partfun1 F D)) ) ) )  &  ((m2_pboole G A B C) & (m2_pboole H D E F)) ) ) ) )  => (m2_pboole (k1_circcomb A B C D E F G H) (k2_xboole_0 A D) (k1_funct_4 B E) (k1_funct_4 C F))) ) ).
tt(dt_k1_circled1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_circled1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B)))) ) )  =>  ( (~ (v2_struct_0 (k1_circtrm1 A B C)))  &  ((v1_msualg_1 (k1_circtrm1 A B C)) & (l1_msualg_1 (k1_circtrm1 A B C))) ) ) ) ).
tt(dt_k1_circuit1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) ) )  =>  ((v1_relat_1 (k1_circuit1 A B)) &  ((v4_relat_1 (k1_circuit1 A B) (k1_msafree2 A)) &  ((v1_funct_1 (k1_circuit1 A B)) & (v1_partfun1 (k1_circuit1 A B) (k1_msafree2 A))) ) ) ) ) ).
tt(dt_k1_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_msafree2 D A B)) ) )  => (m1_subset_1 (k1_circuit2 A B C D) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k1_classes1,ax,$true).
tt(dt_k1_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k1_classes2 A B) A)) ) ).
tt(dt_k1_clopban2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_clopban1 B A A) &  ((v2_clopban1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_clopban1 C A A) &  ((v2_clopban1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_clopban2 A B C)) &  ((v1_funct_2 (k1_clopban2 A B C) (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 (k1_clopban2 A B C) A A) &  ((v1_clopban1 (k1_clopban2 A B C) A A) &  ((v2_clopban1 (k1_clopban2 A B C) A A) & (m1_subset_1 (k1_clopban2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_k1_clopban3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_clopban3 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_clopban4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_clopban4 A B)) &  ((v1_funct_2 (k1_clopban4 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k1_clopban4 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ((m2_pboole D A B C) & (m1_pboole E A B)) ) )  => (m1_pboole (k1_closure1 A B C D E) A C)) ) ).
tt(dt_k1_closure2,ax,$true).
tt(dt_k1_closure3,ax,$true).
tt(dt_k1_clvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xcmplx_0 C)) )  => (m1_subset_1 (k1_clvect_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_clvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_clvect_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_clvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_clvect_3 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_cohsp_1,ax,$true).
tt(dt_k1_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ((v1_partfun1 (k1_coh_sp A) (k3_tarski A)) &  ((v1_relat_2 (k1_coh_sp A)) &  ((v3_relat_2 (k1_coh_sp A)) & (m1_subset_1 (k1_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) ) ) ) ).
tt(dt_k1_collsp,ax,$true).
tt(dt_k1_combgras,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  (~ (v1_xboole_0 B)) )  =>  ((v1_incsp_1 (k1_combgras A B)) &  ((v5_incsp_1 (k1_combgras A B)) &  ((v7_incsp_1 (k1_combgras A B)) & (l1_incsp_1 (k1_combgras A B))) ) ) ) ) ).
tt(dt_k1_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) & (m2_cat_1 E B C)) ) ) )  =>  ( (~ (v1_xboole_0 (k1_commacat A B C D E)))  & (m1_subset_1 (k1_commacat A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C))))) ) ) ).
tt(dt_k1_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_pre_topc (k1_compact1 A)) & (l1_pre_topc (k1_compact1 A))) ) ) ).
tt(dt_k1_complex1,ax,$true).
tt(dt_k1_complex2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k1_complex2 A B) k2_numbers)) ) ).
tt(dt_k1_complfld,ax, ((v36_algstr_0 k1_complfld) & (l6_algstr_0 k1_complfld)) ).
tt(dt_k1_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_pre_topc (k1_complsp1 A)) &  ((v2_pre_topc (k1_complsp1 A)) & (l1_pre_topc (k1_complsp1 A))) ) ) ) ).
tt(dt_k1_complsp2,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k1_complsp2 A) k2_numbers)) ) ).
tt(dt_k1_compl_sp,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  =>  ((v1_funct_1 (k1_compl_sp A B)) &  ((v1_funct_2 (k1_compl_sp A B) k5_numbers k1_numbers) & (m1_subset_1 (k1_compl_sp A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_compos_0,ax,$true).
tt(dt_k1_compos_1,ax, ((v1_compos_1 k1_compos_1) & (l1_compos_1 k1_compos_1)) ).
tt(dt_k1_compos_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_amistd_4 A) & (l1_compos_1 A))  &  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_compos_2 A B C)))  &  ((v1_relat_1 (k1_compos_2 A B C)) &  ((v4_relat_1 (k1_compos_2 A B C) k5_numbers) &  ((v5_relat_1 (k1_compos_2 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k1_compos_2 A B C)) &  ((v1_finset_1 (k1_compos_2 A B C)) &  ((v1_afinsq_1 (k1_compos_2 A B C)) &  ((v3_compos_1 (k1_compos_2 A B C) A) & (v4_compos_1 (k1_compos_2 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(dt_k1_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k1_comptrig A) k1_numbers)) ) ).
tt(dt_k1_compts_1,ax, (! [A:$i] : (l1_pre_topc (k1_compts_1 A))) ).
tt(dt_k1_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_comput_1 A))  => (m1_subset_1 (k1_comput_1 A) k5_numbers)) ) ).
tt(dt_k1_comseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k1_comseq_2 A)) &  ((v1_funct_1 (k1_comseq_2 A)) & (v1_valued_0 (k1_comseq_2 A))) ) ) ) ).
tt(dt_k1_comseq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_funct_1 (k1_comseq_3 A)) &  ((v1_funct_2 (k1_comseq_3 A) k5_numbers k2_numbers) & (m1_subset_1 (k1_comseq_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k1_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k1_conlat_1 A)) &  ((v1_funct_2 (k1_conlat_1 A) (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A))) & (m1_subset_1 (k1_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)))))) ) ) ) ).
tt(dt_k1_conlat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  &  ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) ) )  => (m1_subset_1 (k1_conlat_2 A B) (u1_struct_0 (k11_conlat_1 A)))) ) ).
tt(dt_k1_connsp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_connsp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_connsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_connsp_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_connsp_3,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_connsp_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_convex1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k1_convex1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_convex3,ax,$true).
tt(dt_k1_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k9_funct_2 (u1_struct_0 A) k2_numbers)))  => (m1_subset_1 (k1_convex4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  =>  ((v1_funct_1 (k1_convfun1 A B)) &  ((v1_funct_2 (k1_convfun1 A B) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 (k1_convfun1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k1_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_finseq_1 B (k2_qc_lang1 A)) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A))))) ) )  => (m2_finseq_1 (k1_cqc_lang A B C) (k2_qc_lang1 A))) ) ).
tt(dt_k1_cqc_the1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  => (m1_subset_1 (k1_cqc_the1 A B) (k1_zfmisc_1 (k3_cqc_lang A)))) ) ).
tt(dt_k1_csspace3,ax,(m1_subset_1 k1_csspace3 (k1_zfmisc_1 (u1_struct_0 k7_csspace)))).
tt(dt_k1_csspace4,ax,(m1_subset_1 k1_csspace4 (k1_zfmisc_1 (u1_struct_0 k7_csspace)))).
tt(dt_k1_csspace,ax, (~ (v1_xboole_0 k1_csspace)) ).
tt(dt_k1_decomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_decomp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 B A))) )  => (m2_finseq_2 (k1_descip_1 A B C) A (k4_finseq_2 B A))) ) ).
tt(dt_k1_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_partfun1 (k1_dickson A) (u1_struct_0 A)) &  ((v3_relat_2 (k1_dickson A)) &  ((v8_relat_2 (k1_dickson A)) & (m1_subset_1 (k1_dickson A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k1_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_diff_1 A B)) & (m1_subset_1 (k1_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k1_diff_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) &  ((v1_xreal_0 E) & (v1_xreal_0 F)) ) ) ) )  => (m1_subset_1 (k1_diff_2 A B C D E F) k1_numbers)) ) ).
tt(dt_k1_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  => (v7_ordinal1 (k1_dilworth A))) ) ).
tt(dt_k1_diraf,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  => (m1_subset_1 (k1_diraf A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A))))) ) ).
tt(dt_k1_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 B A) => (m1_subset_1 (k1_dist_1 A B C) (k1_zfmisc_1 (k9_xtuple_0 B)))) ) ).
tt(dt_k1_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D B)) ) )  => (m1_subset_1 (k1_domain_1 A B C D) (k2_zfmisc_1 A B))) ) ).
tt(dt_k1_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_trees_3 B A) & (m1_finseq_1 C B)) )  => (m2_finseq_1 (k1_dtconstr A B C) A)) ) ).
tt(dt_k1_dynkin,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 A))) ) )  =>  ((v1_funct_1 (k1_dynkin A B C D)) &  ((v1_funct_2 (k1_dynkin A B C D) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k1_dynkin A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k1_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  => (m2_subset_1 (k1_ec_pf_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  => (m1_subset_1 (k1_ec_pf_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))))) ) ).
tt(dt_k1_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m1_funct_2 (k1_endalg A) (u1_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k1_ens_1,ax,$true).
tt(dt_k1_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v1_entropy1 (k1_entropy1 A) (k3_finseq_1 A)) & (m1_matrix_1 (k1_entropy1 A) k1_numbers (k3_finseq_1 A) (k3_finseq_1 A))) ) ) ).
tt(dt_k1_enumset1,ax,$true).
tt(dt_k1_eqrel_1,ax, (! [A:$i] : (m1_subset_1 (k1_eqrel_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ).
tt(dt_k1_equation,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) ) )  =>  ((v1_relat_1 (k1_equation A B C)) &  ((v4_relat_1 (k1_equation A B C) A) &  ((v1_funct_1 (k1_equation A B C)) & (v1_partfun1 (k1_equation A B C) A)) ) ) ) ) ).
tt(dt_k1_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k1_euclid_3 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  => (m1_subset_1 (k1_euclid_4 A B C) (k1_zfmisc_1 (k1_euclid A)))) ) ).
tt(dt_k1_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) => (m1_subset_1 (k1_euclid_5 A) k1_numbers)) ) ).
tt(dt_k1_euclid_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (v1_xreal_0 (k1_euclid_6 A B C))) ) ).
tt(dt_k1_euclid_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_1 (k1_euclid_7 A B C) (k2_zfmisc_1 A A))) ) ).
tt(dt_k1_euclid_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m2_finseq_2 (k1_euclid_8 A B C) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k1_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  => (v7_ordinal1 (k1_euclid_9 A B C))) ) ).
tt(dt_k1_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_finseq_2 (k1_euclid A) k1_numbers)) ) ).
tt(dt_k1_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k1_euclidlp A) (k1_zfmisc_1 (k1_zfmisc_1 (k1_euclid A))))) ) ).
tt(dt_k1_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_euler_1 A) k5_numbers)) ) ).
tt(dt_k1_euler_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  => (m1_trees_4 (k1_euler_2 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_ordinal1 (k1_exchsort A))) ) ).
tt(dt_k1_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k1_extpro_1 A) A) & (l1_extpro_1 (k1_extpro_1 A) A)) ) ) ).
tt(dt_k1_extreal1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k1_extreal1 A B) k7_numbers)) ) ).
tt(dt_k1_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k1_extreal2 A B) k7_numbers)) ) ).
tt(dt_k1_facirc_1,ax, ((v1_funct_1 k1_facirc_1) &  ((v1_funct_2 k1_facirc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k1_facirc_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k1_facirc_2,ax, (! [A:$i] :  ((v11_struct_0 (k1_facirc_2 A)) &  ((v1_msualg_1 (k1_facirc_2 A)) & (l1_msualg_1 (k1_facirc_2 A))) ) ) ).
tt(dt_k1_fcont_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_fcont_1 A B)) &  ((v1_funct_2 (k1_fcont_1 A B) k1_numbers k1_numbers) & (m1_subset_1 (k1_fcont_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_fdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  => (m1_subset_1 (k1_fdiff_1 A B) k1_numbers)) ) ).
tt(dt_k1_fdiff_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (m1_subset_1 (k1_fdiff_3 A B) k1_numbers)) ) ).
tt(dt_k1_fdiff_9,ax, ((v1_funct_1 k1_fdiff_9) & (m1_subset_1 k1_fdiff_9 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k1_ff_siec,ax, (! [A:$i,B:$i] :  ((v1_petri (k1_ff_siec A B)) &  ((v1_net_1 (k1_ff_siec A B)) & (l1_petri (k1_ff_siec A B))) ) ) ).
tt(dt_k1_fib_fusc,ax, ((v5_ordinal1 k1_fib_fusc) &  ((v1_relat_1 k1_fib_fusc) &  ((v5_relat_1 k1_fib_fusc (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 k1_fib_fusc) & (v1_finset_1 k1_fib_fusc)) ) ) ) ).
tt(dt_k1_fib_num2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v1_finset_1 B) &  ((v1_setfam_1 B) & (v6_membered B)) ) )  => (m1_trees_4 (k1_fib_num2 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_fib_num3 A) k5_numbers)) ) ).
tt(dt_k1_fib_num,ax,(v1_xreal_0 k1_fib_num)).
tt(dt_k1_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_xboole_0 (k1_filter_0 A)))  &  ((v19_lattices (k1_filter_0 A) A) &  ((v20_lattices (k1_filter_0 A) A) & (m1_subset_1 (k1_filter_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k1_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_filter_2 A B) (u1_struct_0 (k1_lattice2 A)))) ) ).
tt(dt_k1_finance1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k1_finance1 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_finseq_1,ax,$true).
tt(dt_k1_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k1_finseq_2 A)) &  ((v1_funct_1 (k1_finseq_2 A)) & (v1_finseq_1 (k1_finseq_2 A))) ) ) ) ).
tt(dt_k1_finseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k1_finseq_3 A B)) &  ((v1_funct_1 (k1_finseq_3 A B)) & (v1_finseq_1 (k1_finseq_3 A B))) ) ) ) ).
tt(dt_k1_finseq_4,ax,$true).
tt(dt_k1_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m2_finseq_1 (k1_finseq_5 A B C) A)) ) ).
tt(dt_k1_finseq_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k1_finseq_6 A B C) A)) ) ).
tt(dt_k1_finseq_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (m1_subset_1 D A)) ) )  => (m2_finseq_1 (k1_finseq_7 A B C D) A)) ) ).
tt(dt_k1_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_1 (k1_finseq_8 A B C) A)) ) ).
tt(dt_k1_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_finseq_1 E A) & (m1_finseq_1 F B)) ) ) ) )  => (m2_finseq_1 (k1_finseqop A B C D E F) C)) ) ).
tt(dt_k1_finsop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) )  => (m1_subset_1 (k1_finsop_1 A B C) A)) ) ).
tt(dt_k1_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k1_finsub_1 A B C) A)) ) ).
tt(dt_k1_fintopo2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k1_fintopo2 A B C D) k6_margrel1)) ) ).
tt(dt_k1_fintopo3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_fintopo3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_fintopo4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ).
tt(dt_k1_fintopo5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k1_fintopo5 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k1_fintopo6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k1_fintopo6 A B)))  &  ((v1_orders_2 (k1_fintopo6 A B)) & (m1_fintopo6 (k1_fintopo6 A B) A)) ) ) ) ).
tt(dt_k1_fin_topo,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k3_catalan2 A)) & (m1_subset_1 C (k3_catalan2 A)))  => (m1_subset_1 (k1_flang_1 A B C) (k3_catalan2 A))) ) ).
tt(dt_k1_flang_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m1_subset_1 (k1_flang_2 A B C D) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k1_flang_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) & (v7_ordinal1 C))  => (m1_subset_1 (k1_flang_3 A B C) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k1_fomodel0,ax, (! [A:$i] :  ((v1_funct_1 (k1_fomodel0 A)) &  ((v1_funct_2 (k1_fomodel0 A) (k2_zfmisc_1 A A) A) & (m1_subset_1 (k1_fomodel0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ).
tt(dt_k1_fomodel1,ax,$true).
tt(dt_k1_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k1_fomodel2 A) (k1_fomodel1 A))) ) ).
tt(dt_k1_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_fomodel1 A)) & (m1_subset_1 C (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) )  => (m2_subset_1 (k1_fomodel3 A B C) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k1_fomodel4,ax,$true).
tt(dt_k1_frechet2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_frechet2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_frechet,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  & (m1_subset_1 B (u1_struct_0 (k3_pcomps_1 A))))  => (m1_subset_1 (k1_frechet A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))) ) ).
tt(dt_k1_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  & (m1_subset_1 B k5_numbers))  => (m5_margrel1 (k1_freealg A B) (u1_struct_0 A) (k1_unialg_2 A))) ) ).
tt(dt_k1_fscirc_1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k1_fscirc_1 A B C) (u1_struct_0 (k8_facirc_1 A B C k1_facirc_1)) (k3_msafree2 (k8_facirc_1 A B C k1_facirc_1)))) ).
tt(dt_k1_fscirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ( (~ (v2_struct_0 (k1_fscirc_2 A B C)))  &  ( (~ (v11_struct_0 (k1_fscirc_2 A B C)))  &  ((v1_msualg_1 (k1_fscirc_2 A B C)) &  ((v1_circcomb (k1_fscirc_2 A B C)) &  ((v2_circcomb (k1_fscirc_2 A B C)) &  ((v3_circcomb (k1_fscirc_2 A B C)) & (l1_msualg_1 (k1_fscirc_2 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k1_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  &  ((m1_subset_1 C A) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k1_fsm_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k1_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_tarski C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski C D) B)))) ) ) )  =>  ( (~ (v2_struct_0 (k1_fsm_2 A B C D E)))  &  ((v6_fsm_2 (k1_fsm_2 A B C D E) A B) & (l2_fsm_2 (k1_fsm_2 A B C D E) A B)) ) ) ) ).
tt(dt_k1_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B)) ) )  =>  ((v1_rewrite3 (k1_fsm_3 A B C) (k9_flang_1 A)) & (l1_rewrite3 (k1_fsm_3 A B C) (k9_flang_1 A))) ) ) ).
tt(dt_k1_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( (~ (v2_struct_0 (k1_ftacell1 A B C D E)))  &  ( (~ (v11_struct_0 (k1_ftacell1 A B C D E)))  &  ((v1_msualg_1 (k1_ftacell1 A B C D E)) &  ((v1_circcomb (k1_ftacell1 A B C D E)) &  ((v2_circcomb (k1_ftacell1 A B C D E)) &  ((v3_circcomb (k1_ftacell1 A B C D E)) & (l1_msualg_1 (k1_ftacell1 A B C D E))) ) ) ) ) ) ) ).
tt(dt_k1_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_funcop_1 A)) & (v1_funct_1 (k1_funcop_1 A))) ) ) ).
tt(dt_k1_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B)) (k9_funct_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B)) (k9_funct_2 A B))))) )  &  ((m1_subset_1 D (k9_funct_2 A B)) & (m1_subset_1 E (k9_funct_2 A B))) ) )  => (m2_funct_2 (k1_funcsdom A B C D E) A B (k9_funct_2 A B))) ) ).
tt(dt_k1_funct_1,ax,$true).
tt(dt_k1_funct_2,ax,$true).
tt(dt_k1_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_funct_3 A)) & (v1_funct_1 (k1_funct_3 A))) ) ) ).
tt(dt_k1_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k1_funct_4 A B)) & (v1_funct_1 (k1_funct_4 A B))) ) ) ).
tt(dt_k1_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_funct_5 A)) & (v1_funct_1 (k1_funct_5 A))) ) ) ).
tt(dt_k1_funct_6,ax,$true).
tt(dt_k1_funct_7,ax, (! [A:$i,B:$i] : (m1_subset_1 (k1_funct_7 A B) B)) ).
tt(dt_k1_funct_8,ax, ((v1_funct_1 k1_funct_8) &  ((v1_funct_2 k1_funct_8 k1_numbers k1_numbers) & (m1_subset_1 k1_funct_8 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k1_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ((v1_funct_1 (k1_functor0 A B C D)) &  ((v1_funct_2 (k1_functor0 A B C D) (k2_zfmisc_1 B A) C) & (m1_subset_1 (k1_functor0 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ) ).
tt(dt_k1_functor2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  & (m2_functor0 C A B)) )  => (m1_functor2 (k1_functor2 A B C) A B C C)) ) ).
tt(dt_k1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ((v15_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k1_functor3 A B C D E) A C) &  ((v15_functor0 (k1_functor3 A B C D E) A C) & (m2_functor0 (k1_functor3 A B C D E) A C)) ) ) ) ).
tt(dt_k1_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k1_fuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k1_fuzzy_1 A B C)) &  ((v1_funct_2 (k1_fuzzy_1 A B C) A k1_numbers) & (m1_subset_1 (k1_fuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k1_fuzzy_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k1_fuzzy_2 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k1_fuzzy_2 A B C)) &  ((v1_funct_2 (k1_fuzzy_2 A B C) A k1_numbers) & (m1_subset_1 (k1_fuzzy_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k1_fuzzy_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) )  => (m1_subset_1 (k1_fuzzy_4 A B C D E) k1_numbers)) ) ).
tt(dt_k1_fvaluat1,ax, (! [A:$i] :  ((v2_membered A) =>  ((v2_xxreal_0 (k1_fvaluat1 A)) & (v1_fvaluat1 (k1_fvaluat1 A))) ) ) ).
tt(dt_k1_fvsum_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_fvsum_1 A B)) &  ((v1_funct_2 (k1_fvsum_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k1_fvsum_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_gate_1,ax,$true).
tt(dt_k1_gate_5,ax,$true).
tt(dt_k1_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_gcd_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) & (m1_subset_1 D k5_numbers)) ) )  => (m2_finseq_1 (k1_genealg1 A B C D) (k3_card_3 A))) ) ).
tt(dt_k1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_geomtrap A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_gfacirc1,ax, ((v1_funct_1 k1_gfacirc1) &  ((v1_funct_2 k1_gfacirc1 (k4_finseq_2 1 k6_margrel1) k6_margrel1) & (m1_subset_1 k1_gfacirc1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k1_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ( (~ (v2_struct_0 (k1_gfacirc2 A B C)))  &  ( (~ (v11_struct_0 (k1_gfacirc2 A B C)))  &  ((v1_msualg_1 (k1_gfacirc2 A B C)) &  ((v1_circcomb (k1_gfacirc2 A B C)) &  ((v2_circcomb (k1_gfacirc2 A B C)) &  ((v3_circcomb (k1_gfacirc2 A B C)) & (l1_msualg_1 (k1_gfacirc2 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k1_glib_000,ax,(m1_subset_1 k1_glib_000 k5_numbers)).
tt(dt_k1_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m3_glib_001 (k1_glib_001 A B) A)) ) ).
tt(dt_k1_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ( (~ (v1_xboole_0 (k1_glib_002 A B)))  & (m1_subset_1 (k1_glib_002 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ).
tt(dt_k1_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_subset_1 C (k1_zfmisc_1 B)))  => (m2_finseq_1 (k1_glib_003 A B C) A)) ) ).
tt(dt_k1_glib_004,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  => (m1_subset_1 (k1_glib_004 A B C) k1_numbers)) ) ).
tt(dt_k1_glib_005,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) ) )  => (v1_xreal_0 (k1_glib_005 A B C D))) ) ).
tt(dt_k1_goboard1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (m2_finseq_1 (k1_goboard1 A) k1_numbers)) ) ).
tt(dt_k1_goboard2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k1_numbers) & (m1_finseq_1 B k1_numbers))  =>  ((v1_matrix_1 (k1_goboard2 A B)) & (m2_finseq_1 (k1_goboard2 A B) (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ).
tt(dt_k1_goboard5,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  & (v7_ordinal1 B))  => (m1_subset_1 (k1_goboard5 A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k1_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_goboard9 A)))  &  ((v1_finseq_6 (k1_goboard9 A) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_goboard9 A)) &  ((v2_topreal1 (k1_goboard9 A)) &  ((v1_goboard5 (k1_goboard9 A)) &  ((v2_goboard5 (k1_goboard9 A)) & (m2_finseq_1 (k1_goboard9 A) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ).
tt(dt_k1_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k1_goedelcp A) (k1_zfmisc_1 (k3_cqc_lang A)))) ) ).
tt(dt_k1_graph_1,ax, (! [A:$i,B:$i] :  ( ((l1_graph_1 A) & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k1_graph_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_graph_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k1_graph_2 A B C)) &  ((v1_funct_1 (k1_graph_2 A B C)) & (v1_finseq_1 (k1_graph_2 A B C))) ) ) ) ).
tt(dt_k1_graph_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (m1_subset_1 (k1_graph_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_graph_4,ax,$true).
tt(dt_k1_graph_5,ax,$true).
tt(dt_k1_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A k1_numbers) & (m1_subset_1 C k1_numbers))  => (m2_finseq_1 (k1_graphsp A B C) k1_numbers)) ) ).
tt(dt_k1_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_grcat_1 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k1_gr_cy_1,ax, (! [A:$i] :  ((m1_finseq_1 A k4_numbers) => (m1_subset_1 (k1_gr_cy_1 A) k4_numbers)) ) ).
tt(dt_k1_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v7_ordinal1 (k1_gr_cy_3 A))) ) ).
tt(dt_k1_grnilp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k1_grnilp_1 A B C)) & (m1_group_2 (k1_grnilp_1 A B C) A)) ) ) ).
tt(dt_k1_groeb_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  => (m1_subset_1 (k1_groeb_1 A B C) (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B))))) ) ).
tt(dt_k1_groeb_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k1_groeb_2 A B C)) &  ((v4_relat_1 (k1_groeb_2 A B C) A) &  ((v1_funct_1 (k1_groeb_2 A B C)) &  ((v1_partfun1 (k1_groeb_2 A B C) A) &  ((v4_valued_0 (k1_groeb_2 A B C)) & (v2_pre_poly (k1_groeb_2 A B C))) ) ) ) ) ) ) ).
tt(dt_k1_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  => (m1_subset_1 (k1_groeb_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B))))) ) ).
tt(dt_k1_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) )  & (m1_subset_1 D (u1_struct_0 A))) )  =>  ((v1_funct_1 (k1_group_10 A B C D)) &  ((v1_funct_2 (k1_group_10 A B C D) B B) & (m1_subset_1 (k1_group_10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(dt_k1_group_11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_group_2 C A)) )  => (m1_subset_1 (k1_group_11 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  & (m1_subset_1 C A)) )  => (m1_subset_1 (k1_group_12 A B C) (k1_zfmisc_1 (u1_struct_0 (k2_group_7 A B))))) ) ).
tt(dt_k1_group_1,ax, (! [A:$i] :  ((l3_algstr_0 A) => (m1_subset_1 (k1_group_1 A) (u1_struct_0 A))) ) ).
tt(dt_k1_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_group_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_group_3,ax,$true).
tt(dt_k1_group_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m2_finseq_1 (k1_group_4 A B C) A)) ) ).
tt(dt_k1_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k1_group_5 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) &  ((v1_group_3 C A) & (m1_group_2 C A)) ) )  =>  ((v15_algstr_0 (k1_group_6 A B C)) &  ((v1_group_3 (k1_group_6 A B C) B) & (m1_group_6 (k1_group_6 A B C) A B)) ) ) ) ).
tt(dt_k1_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (k1_group_7 A B C)))  & (l3_algstr_0 (k1_group_7 A B C))) ) ) ).
tt(dt_k1_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  & (m1_subset_1 D (k1_zfmisc_1 B)))  => (m1_subset_1 (k1_group_9 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k1_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  => (v7_ordinal1 (k1_groupp_1 A B))) ) ).
tt(dt_k1_grsolv_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (m1_group_2 D A)) ) )  =>  ((v1_funct_1 (k1_grsolv_1 A B C D)) &  ((v1_funct_2 (k1_grsolv_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v1_group_6 (k1_grsolv_1 A B C D) D B) & (m1_subset_1 (k1_grsolv_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k1_hahnban1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k1_hahnban1 A B) (u1_struct_0 k1_complfld))) ) ).
tt(dt_k1_hallmar1,ax,$true).
tt(dt_k1_hausdorf,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  => (m1_subset_1 (k1_hausdorf A B C) k1_numbers)) ) ).
tt(dt_k1_heine,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k1_heine A B)) &  ((v1_funct_2 (k1_heine A B) k5_numbers k1_numbers) & (m1_subset_1 (k1_heine A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_helly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k1_helly A B)) &  ((v1_funct_1 (k1_helly A B)) & (v1_finseq_1 (k1_helly A B))) ) ) ) ).
tt(dt_k1_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k1_henmodel A))) ) ) ).
tt(dt_k1_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_funct_1 (k1_hermitan A B)) &  ((v1_funct_2 (k1_hermitan A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 (k1_hermitan A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) ) ).
tt(dt_k1_heyting1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_heyting1 A))) ) ).
tt(dt_k1_heyting2,ax,$true).
tt(dt_k1_heyting3,ax, (! [A:$i,B:$i] : (l1_orders_2 (k1_heyting3 A B))) ).
tt(dt_k1_hilbasis,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) )  => (m2_subset_1 (k1_hilbasis A B C) (k14_pre_poly (k1_nat_1 A 1)) (k15_pre_poly (k1_nat_1 A 1)))) ) ).
tt(dt_k1_hilbert1,ax,$true).
tt(dt_k1_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k1_hilbert2 A) k1_hilbert1)) ) ).
tt(dt_k1_hilbert3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) )  =>  ((v1_funct_1 (k1_hilbert3 A B C D)) &  ((v1_funct_2 (k1_hilbert3 A B C D) (k9_funct_2 A B) (k9_funct_2 A B)) & (m1_subset_1 (k1_hilbert3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B))))) ) ) ) ).
tt(dt_k1_hurwitz,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ((m1_finseq_1 B (u1_struct_0 (k14_polynom3 A))) & (m1_subset_1 C k5_numbers)) )  => (m2_finseq_1 (k1_hurwitz A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v3_card_1 (k1_idea_1 A) A) & (m2_finseq_1 (k1_idea_1 A) k6_margrel1)) ) ) ).
tt(dt_k1_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_funct_1 (k1_ideal_1 A B)) &  ((v1_funct_2 (k1_ideal_1 A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k1_ideal_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k1_incproj,ax,$true).
tt(dt_k1_incsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v15_incsp_1 A) & (l2_incsp_1 A))  &  ((m1_subset_1 B (u1_incsp_1 A)) & (m1_subset_1 C (u1_incsp_1 A))) )  => (m1_subset_1 (k1_incsp_1 A B C) (u2_incsp_1 A))) ) ).
tt(dt_k1_index_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_cat_1 (k1_index_1 A B) (k5_cat_5 A B) (k6_cat_5 A B))) ) ).
tt(dt_k1_instalg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ((l3_msualg_1 C B) &  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ((v1_relat_1 E) & (v1_funct_1 E)) ) ) ) )  =>  ((v3_msualg_1 (k1_instalg1 A B C D E) A) & (l3_msualg_1 (k1_instalg1 A B C D E) A)) ) ) ).
tt(dt_k1_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_int_1 (k1_int_1 A))) ) ).
tt(dt_k1_int_2,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k1_int_2 A) k5_numbers)) ) ).
tt(dt_k1_int_3,ax,(l6_algstr_0 k1_int_3)).
tt(dt_k1_int_4,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k1_int_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers)))) ) ).
tt(dt_k1_int_5,ax, (! [A:$i] :  ((m1_finseq_1 A k4_numbers) =>  ((v1_funct_1 (k1_int_5 A)) &  ((v1_funct_2 (k1_int_5 A) k4_numbers k4_numbers) & (m1_subset_1 (k1_int_5 A) (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers)))) ) ) ) ).
tt(dt_k1_int_6,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k1_int_6 A B)) &  ((v1_funct_1 (k1_int_6 A B)) & (v1_finseq_1 (k1_int_6 A B))) ) ) ) ).
tt(dt_k1_int_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k1_int_7 A)))  &  ((v1_finset_1 (k1_int_7 A)) & (m1_subset_1 (k1_int_7 A) (k1_zfmisc_1 k5_numbers))) ) ) ) ).
tt(dt_k1_integr10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k1_integr10 A B C) k1_numbers)) ) ).
tt(dt_k1_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((m1_integra1 C A) & (m1_integr15 D A B C)) ) )  => (m1_subset_1 (k1_integr15 A B C D) k1_numbers)) ) ).
tt(dt_k1_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k1_integr16 A) k1_numbers)) ) ).
tt(dt_k1_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ((m1_integra1 D B) & (m1_integr18 E A B C D)) ) ) )  => (m1_subset_1 (k1_integr18 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k1_integr1c,ax, ((v1_funct_1 k1_integr1c) &  ((v1_funct_2 k1_integr1c (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers) & (m1_subset_1 k1_integr1c (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k2_numbers)))) ) ).
tt(dt_k1_integra1,ax,$true).
tt(dt_k1_integra2,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (m1_subset_1 (k1_integra2 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_integra3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  & (m1_integra1 B A))  => (m1_subset_1 (k1_integra3 A B) k1_numbers)) ) ).
tt(dt_k1_integra5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((v1_funct_1 (k1_integra5 A B)) & (m1_subset_1 (k1_integra5 A B) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ).
tt(dt_k1_integra7,ax,$true).
tt(dt_k1_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k1_integra8 A)) &  ((v1_funct_2 (k1_integra8 A) k1_numbers k1_numbers) & (m1_subset_1 (k1_integra8 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_integra9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  => (m1_subset_1 (k1_integra9 A B C) k1_numbers)) ) ).
tt(dt_k1_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k1_interva1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k1_intpro_1,ax,$true).
tt(dt_k1_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_irrat_1 A)) &  ((v1_funct_2 (k1_irrat_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k1_irrat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_isocat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  => (m2_cat_1 (k1_isocat_1 A B C) B A)) ) ).
tt(dt_k1_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) )  =>  ((v1_funct_1 (k1_isocat_2 A B C D)) &  ((v1_funct_2 (k1_isocat_2 A B C D) (k2_zfmisc_1 A B) C) & (m1_subset_1 (k1_isocat_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) ).
tt(dt_k1_isomichi,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_isomichi A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_jct_misc,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  => (v1_xreal_0 (k1_jct_misc A B))) ) ).
tt(dt_k1_jgraph_1,ax, (! [A:$i] : (l1_graph_1 (k1_jgraph_1 A))) ).
tt(dt_k1_jgraph_2,ax, ((v1_funct_1 k1_jgraph_2) &  ((v1_funct_2 k1_jgraph_2 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2))) & (m1_subset_1 k1_jgraph_2 (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)))))) ) ).
tt(dt_k1_jgraph_3,ax, ((v1_funct_1 k1_jgraph_3) &  ((v1_funct_2 k1_jgraph_3 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 k1_jgraph_3 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(dt_k1_jgraph_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_jgraph_4 A)) &  ((v1_funct_2 (k1_jgraph_4 A) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k1_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k1_jgraph_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k1_jgraph_6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k1_jordan10,ax,$true).
tt(dt_k1_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m2_subset_1 (k1_jordan11 A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_jordan13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  &  ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k1_jordan13 A B)))  &  ( (~ (v3_funct_1 (k1_jordan13 A B)))  &  ((v1_finseq_6 (k1_jordan13 A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_jordan13 A B)) &  ((v2_topreal1 (k1_jordan13 A B)) &  ((v1_goboard5 (k1_jordan13 A B)) &  ((v2_goboard5 (k1_jordan13 A B)) &  ((v1_sprect_2 (k1_jordan13 A B)) & (m2_finseq_1 (k1_jordan13 A B) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k1_jordan14,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k1_jordan14 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan18,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k1_jordan18 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k1_jordan19 A)) &  ((v1_funct_2 (k1_jordan19 A) k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 (k1_jordan19 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) ) ) ) ).
tt(dt_k1_jordan1a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (m2_subset_1 (k1_jordan1a A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (v7_ordinal1 B))  => (m2_finseq_1 (k1_jordan1e A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan1h,ax,(m1_subset_1 k1_jordan1h (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))).
tt(dt_k1_jordan1k,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (m1_subset_1 (k1_jordan1k A B C) k1_numbers)) ) ).
tt(dt_k1_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k1_jordan21 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k1_jordan24 A)) &  ((v1_funct_2 (k1_jordan24 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k1_jordan24 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k1_jordan2b,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_jordan2b A) (u1_struct_0 (k15_euclid 1)))) ) ).
tt(dt_k1_jordan2c,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  => (m1_subset_1 (k1_jordan2c A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k1_jordan3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m1_subset_1 (k1_jordan3 A B) k5_numbers)) ) ).
tt(dt_k1_jordan4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  => (m1_subset_1 (k1_jordan4 A B) k5_numbers)) ) ).
tt(dt_k1_jordan5c,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (u1_struct_0 (k15_euclid 2)))) ) )  => (m1_subset_1 (k1_jordan5c A B C D) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k1_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_jordan6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (m1_subset_1 (k1_jordan6 A B C) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_jordan7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (m1_subset_1 (k1_jordan7 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k1_jordan8,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) & (v7_ordinal1 B))  =>  ((v1_matrix_1 (k1_jordan8 A B)) & (m2_finseq_1 (k1_jordan8 A B) (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ).
tt(dt_k1_jordan9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (v7_ordinal1 B))  =>  ( (~ (v1_xboole_0 (k1_jordan9 A B)))  &  ( (~ (v3_funct_1 (k1_jordan9 A B)))  &  ((v1_finseq_6 (k1_jordan9 A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_jordan9 A B)) &  ((v2_topreal1 (k1_jordan9 A B)) &  ((v1_goboard5 (k1_jordan9 A B)) &  ((v2_goboard5 (k1_jordan9 A B)) &  ((v1_sprect_2 (k1_jordan9 A B)) & (m2_finseq_1 (k1_jordan9 A B) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k1_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  => (m1_subset_1 (k1_jordan A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_knaster,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  => (m1_subset_1 (k1_knaster A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 B)) & (m2_prob_1 D A B)) ) )  => (m1_subset_1 (k1_kolmog01 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k1_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k1_kurato_0 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_kurato_1,ax,$true).
tt(dt_k1_kurato_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  => (m1_subset_1 (k1_kurato_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_lang1,ax,$true).
tt(dt_k1_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k1_laplace A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k1_latsubgr A)) &  ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k1_latsubgr A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k1_latsum_1,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  ((v1_orders_2 (k1_latsum_1 A B)) & (l1_orders_2 (k1_latsum_1 A B))) ) ) ).
tt(dt_k1_lattice2,ax, (! [A:$i] :  ((l3_lattices A) =>  ((v3_lattices (k1_lattice2 A)) & (l3_lattices (k1_lattice2 A))) ) ) ).
tt(dt_k1_lattice3,ax, (! [A:$i] :  ((v3_lattices (k1_lattice3 A)) & (l3_lattices (k1_lattice3 A))) ) ).
tt(dt_k1_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_lattice4 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_lattice5,ax, (! [A:$i] :  ((v3_orders_2 (k1_lattice5 A)) &  ((v4_orders_2 (k1_lattice5 A)) &  ((v5_orders_2 (k1_lattice5 A)) & (l1_orders_2 (k1_lattice5 A))) ) ) ) ).
tt(dt_k1_lattice6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_lattice6 A B) (k1_zfmisc_1 (u1_struct_0 (k3_lattice3 A))))) ) ).
tt(dt_k1_lattice7,ax, (! [A:$i,B:$i] :  ( ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_lattice7 A B) k5_numbers)) ) ).
tt(dt_k1_lattice8,ax,$true).
tt(dt_k1_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_lattices A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k1_lexbfs A B)) & (v1_funct_1 (k1_lexbfs A B))) ) ) ).
tt(dt_k1_lfuzzy_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_orders_2 (k1_lfuzzy_0 A)) &  ((v1_lfuzzy_0 (k1_lfuzzy_0 A)) & (l1_orders_2 (k1_lfuzzy_0 A))) ) ) ) ).
tt(dt_k1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k1_lfuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k1_lfuzzy_1 A B C)) &  ((v1_funct_2 (k1_lfuzzy_1 A B C) A k1_numbers) & (m1_subset_1 (k1_lfuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k1_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_limfunc1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_limfunc2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k1_limfunc2 A B) k1_numbers)) ) ).
tt(dt_k1_limfunc3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k1_limfunc3 A B) k1_numbers)) ) ).
tt(dt_k1_lmod_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ((v7_vectsp_1 (k1_lmod_5 A B C) A) & (m1_vectsp_4 (k1_lmod_5 A B C) A B)) ) ) ).
tt(dt_k1_lmod_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B)) ) )  => (m1_subset_1 (k1_lmod_6 A B C) (k3_vectsp_5 A B))) ) ).
tt(dt_k1_lmod_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (m1_lmod_7 (k1_lmod_7 A B) A B)) ) ).
tt(dt_k1_lopban_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_lopban_1 B A A) &  ((v2_lopban_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_lopban_1 C A A) &  ((v2_lopban_1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_lopban_2 A B C)) &  ((v1_funct_2 (k1_lopban_2 A B C) (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 (k1_lopban_2 A B C) A A) &  ((v1_lopban_1 (k1_lopban_2 A B C) A A) &  ((v2_lopban_1 (k1_lopban_2 A B C) A A) & (m1_subset_1 (k1_lopban_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_k1_lopban_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_lopban_3 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_lopban_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_lopban_4 A B)) &  ((v1_funct_2 (k1_lopban_4 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k1_lopban_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_lopban_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (m1_subset_1 (k1_lopban_5 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  => (m1_subset_1 (k1_lopclset A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_lpspace1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_lpspace1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_funct_1 (k1_lpspace1 A B)) &  ((v1_funct_2 (k1_lpspace1 A B) (k2_zfmisc_1 k1_numbers B) B) & (m1_subset_1 (k1_lpspace1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers B) B)))) ) ) ) ).
tt(dt_k1_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k1_lpspace2 A B C D)))  & (m1_subset_1 (k1_lpspace2 A B C D) (k1_zfmisc_1 (u1_struct_0 (k7_lpspace1 A))))) ) ) ).
tt(dt_k1_lp_space,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (m1_subset_1 B k1_numbers))  =>  ((v1_funct_1 (k1_lp_space A B)) &  ((v1_funct_2 (k1_lp_space A B) k5_numbers k1_numbers) & (m1_subset_1 (k1_lp_space A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (m1_subset_1 (k1_ltlaxio1 A) k1_hilbert1)) ) ).
tt(dt_k1_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k1_margrel1 A B C)) &  ((v1_funct_2 (k1_margrel1 A B C) B A) & (m1_subset_1 (k1_margrel1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k1_mathmorp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_mathmorp A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_matrix10,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v1_matrix_1 (k1_matrix10 A)) & (m2_finseq_1 (k1_matrix10 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k1_matrix11,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k12_matrix_2 (k1_nat_1 A 2)))) )  =>  ((v1_funct_1 (k1_matrix11 A B C)) &  ((v1_funct_2 (k1_matrix11 A B C) (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B)) & (m1_subset_1 (k1_matrix11 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k1_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) & (v7_ordinal1 F)) ) ) ) )  => (m1_matrix_1 (k1_matrix12 A B C D E F) (u1_struct_0 C) A B)) ) ).
tt(dt_k1_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((m1_subset_1 E (k4_finseq_2 C k5_numbers)) & (m1_subset_1 F (k4_finseq_2 D k5_numbers))) ) ) ) )  => (m1_matrix_1 (k1_matrix13 A B C D E F) A C D)) ) ).
tt(dt_k1_matrix14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  & (m1_subset_1 B k5_numbers))  => (m2_finseq_1 (k1_matrix14 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_matrix15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((m1_matrix_1 E A B C) & (m1_matrix_1 F A B D)) ) ) ) )  => (m1_matrix_1 (k1_matrix15 A B C D E F) A B (k2_nat_1 (k1_matrix_1 E) (k1_matrix_1 F)))) ) ).
tt(dt_k1_matrix16,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k1_matrix16 A B) A (k3_finseq_1 B) (k3_finseq_1 B))) ) ).
tt(dt_k1_matrix17,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k1_matrix17 A B) A (k3_finseq_1 B) (k3_finseq_1 B))) ) ).
tt(dt_k1_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_matrix_1 A)) ) )  => (m1_subset_1 (k1_matrix_1 A) k5_numbers)) ) ).
tt(dt_k1_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_matrix_2 A B C)) &  ((v1_funct_1 (k1_matrix_2 A B C)) &  ((v1_finseq_1 (k1_matrix_2 A B C)) & (v1_matrix_1 (k1_matrix_2 A B C))) ) ) ) ) ).
tt(dt_k1_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_matrix_1 (k1_matrix_3 A B C) (u1_struct_0 A) B C)) ) ).
tt(dt_k1_matrix_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((v1_matrix_1 (k1_matrix_4 A B C)) & (m2_finseq_1 (k1_matrix_4 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k1_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((v1_matrix_1 (k1_matrix_5 A)) & (m2_finseq_1 (k1_matrix_5 A) (k3_finseq_2 (u1_struct_0 k1_complfld)))) ) ) ).
tt(dt_k1_matrix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_matrix_1 (k1_matrix_6 A B C) (u1_struct_0 B) A A)) ) ).
tt(dt_k1_matrix_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_matrix_1 (k1_matrix_7 A B C D) (u1_struct_0 B) A A)) ) ).
tt(dt_k1_matrix_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_subset_1 (k1_matrix_8 A B C) (u1_struct_0 B))) ) ).
tt(dt_k1_matrix_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  =>  ((v1_funct_1 (k1_matrix_9 A B C)) &  ((v1_funct_2 (k1_matrix_9 A B C) (k12_matrix_2 A) (u1_struct_0 B)) & (m1_subset_1 (k1_matrix_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k1_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((v1_matrix_1 (k1_matrixc1 A)) & (m2_finseq_1 (k1_matrixc1 A) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k1_matrixj1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  => (m1_subset_1 (k1_matrixj1 A B) k5_numbers)) ) ).
tt(dt_k1_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v7_ordinal1 C)) )  =>  ((v1_matrix_1 (k1_matrixj2 A B C)) & (m2_finseq_1 (k1_matrixj2 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k1_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v1_matrix_1 (k1_matrixr1 A)) & (m2_finseq_1 (k1_matrixr1 A) (k3_finseq_2 (u1_struct_0 k2_vectsp_1)))) ) ) ).
tt(dt_k1_matrixr2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  => (m1_matrix_1 (k1_matrixr2 A B C) k1_numbers A A)) ) ).
tt(dt_k1_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_finseq_1 E (u1_struct_0 B)) & (m1_matrlin F A C)) ) ) ) )  => (m1_matrix_1 (k1_matrlin2 A B C D E F) (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 F))) ) ).
tt(dt_k1_matrlin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((v1_matrix_1 (k1_matrlin A B C)) & (m2_finseq_1 (k1_matrlin A B C) (k3_finseq_2 A))) ) ) ).
tt(dt_k1_matroid0,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k1_matroid0 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_matrprob,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k3_finseq_2 A)) & (v7_ordinal1 C))  => (m2_finseq_1 (k1_matrprob A B C) A)) ) ).
tt(dt_k1_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  => (m2_finseq_1 (k1_matrtop1 A) (u1_struct_0 k2_vectsp_1))) ) ).
tt(dt_k1_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_matrix_6 (k1_matrtop3 A B) A k2_vectsp_1) & (m1_matrix_1 (k1_matrtop3 A B) (u1_struct_0 k2_vectsp_1) A A)) ) ) ).
tt(dt_k1_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_mazurulm A B)) &  ((v1_funct_2 (k1_mazurulm A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k1_mazurulm A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_mboolean,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k1_mboolean A B)) &  ((v4_relat_1 (k1_mboolean A B) A) &  ((v1_funct_1 (k1_mboolean A B)) & (v1_partfun1 (k1_mboolean A B) A)) ) ) ) ) ).
tt(dt_k1_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  => (m1_subset_1 (k1_mcart_1 A B C D) A)) ) ).
tt(dt_k1_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m2_subset_1 (k1_measure1 A B C D) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k1_measure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  => (m2_subset_1 (k1_measure2 A B C) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k1_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  => (m1_measure2 (k1_measure3 A B C) A B)) ) ).
tt(dt_k1_measure4,ax, (! [A:$i,B:$i] :  ((m1_measure4 B A) =>  ( (~ (v1_xboole_0 (k1_measure4 A B)))  & (m1_subset_1 (k1_measure4 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k1_measure5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k1_measure5 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_measure6,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (m1_subset_1 (k1_measure6 A) k7_numbers)) ) ).
tt(dt_k1_measure7,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) )  =>  ((v1_funct_1 (k1_measure7 A B)) &  ((v1_funct_2 (k1_measure7 A B) k5_numbers k7_numbers) & (m1_subset_1 (k1_measure7 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k1_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_measure8 C A B) & (v7_ordinal1 D)) )  => (m2_subset_1 (k1_measure8 A B C D) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k1_member_1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (m1_subset_1 (k1_member_1 A) k7_numbers)) ) ).
tt(dt_k1_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_memstr_0 (k1_memstr_0 A) A) & (l1_memstr_0 (k1_memstr_0 A) A)) ) ) ).
tt(dt_k1_mesfun6c,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) )  => (v1_xcmplx_0 (k1_mesfun6c A B C D))) ) ).
tt(dt_k1_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k1_mesfun7c A B)) &  ((v1_funct_2 (k1_mesfun7c A B) k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 (k1_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ).
tt(dt_k1_mesfun9c,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ((v1_funct_1 (k1_mesfun9c A B C D)) &  ((v1_funct_2 (k1_mesfun9c A B C D) k5_numbers (k4_partfun1 A B)) & (m1_subset_1 (k1_mesfun9c A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) ) ) ) ).
tt(dt_k1_mesfunc1,ax,(m1_subset_1 k1_mesfunc1 (k1_zfmisc_1 k1_numbers))).
tt(dt_k1_mesfunc2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) )  =>  ((v1_funct_1 (k1_mesfunc2 A B)) & (m1_subset_1 (k1_mesfunc2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k1_mesfunc3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) )  => (m1_subset_1 (k1_mesfunc3 A B C D) k7_numbers)) ) ).
tt(dt_k1_mesfunc5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k1_mesfunc5 A B)) & (m1_subset_1 (k1_mesfunc5 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k1_mesfunc6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  => (m1_subset_1 (k1_mesfunc6 A B C D) k7_numbers)) ) ).
tt(dt_k1_mesfunc7,ax, ((v1_funct_1 k1_mesfunc7) &  ((v1_funct_2 k1_mesfunc7 (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers) & (m1_subset_1 k1_mesfunc7 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers)))) ) ).
tt(dt_k1_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k1_mesfunc8 A B)) & (m1_subset_1 (k1_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k1_mesfunc9,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  => (m1_subset_1 (k1_mesfunc9 A B) k7_numbers)) ) ).
tt(dt_k1_metric_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers))))  &  ((m1_subset_1 D A) & (m1_subset_1 E B)) )  => (m1_subset_1 (k1_metric_1 A B C D E) k1_numbers)) ) ).
tt(dt_k1_metric_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_metric_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_metric_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) ) )  =>  ((v1_funct_1 (k1_metric_3 A B)) &  ((v1_funct_2 (k1_metric_3 A B) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers) & (m1_subset_1 (k1_metric_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) k1_numbers)))) ) ) ) ).
tt(dt_k1_metric_6,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v1_funct_1 (k1_metric_6 A B)) &  ((v1_funct_2 (k1_metric_6 A B) (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 (k1_metric_6 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ).
tt(dt_k1_mfold_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_pre_topc (k1_mfold_1 A B C) (k15_euclid A))) ) ).
tt(dt_k1_mfold_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  =>  ((v1_funct_1 (k1_mfold_2 A B)) &  ((v1_funct_2 (k1_mfold_2 A B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k1_mfold_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k1_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_midsp_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_midsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_midsp_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C (k4_finseq_2 B A)) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E A)) ) ) )  => (m2_finseq_2 (k1_midsp_3 A B C D E) A (k4_finseq_2 B A))) ) ).
tt(dt_k1_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C A))  => (m1_subset_1 (k1_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_mod_2 A)))  &  ((v13_algstr_0 (k1_mod_2 A)) &  ((v7_vectsp_1 (k1_mod_2 A) A) &  ((v8_vectsp_1 (k1_mod_2 A) A) &  ((v9_vectsp_1 (k1_mod_2 A) A) &  ((v10_vectsp_1 (k1_mod_2 A) A) &  ((v11_vectsp_1 (k1_mod_2 A) A) &  ((v2_rlvect_1 (k1_mod_2 A)) &  ((v3_rlvect_1 (k1_mod_2 A)) &  ((v4_rlvect_1 (k1_mod_2 A)) & (l1_vectsp_1 (k1_mod_2 A) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k1_mod_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ((v7_vectsp_1 (k1_mod_3 A B C) A) & (m1_vectsp_4 (k1_mod_3 A B C) A B)) ) ) ).
tt(dt_k1_mod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((v1_funct_1 (k1_mod_4 A B C D)) &  ((v1_funct_2 (k1_mod_4 A B C D) (k2_zfmisc_1 B A) C) & (m1_subset_1 (k1_mod_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ) ).
tt(dt_k1_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (m1_trees_1 (k1_modal_1 A) A)) ) ).
tt(dt_k1_modelc_2,ax, (! [A:$i] : (v7_ordinal1 (k1_modelc_2 A))) ).
tt(dt_k1_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k1_modelc_3 A) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k1_moebius1,ax,(m1_subset_1 k1_moebius1 (k1_zfmisc_1 k5_numbers))).
tt(dt_k1_monoid_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_2 (k1_monoid_0 A B C) A (k3_finseq_2 A))) ) ).
tt(dt_k1_monoid_1,ax,$true).
tt(dt_k1_morph_01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_morph_01 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_msafree1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_prob_2 B)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  & (m2_pboole D A B C)) ) )  =>  ((v1_funct_1 (k1_msafree1 A B C D)) &  ((v1_funct_2 (k1_msafree1 A B C D) (k3_card_3 B) (k3_card_3 C)) & (m1_subset_1 (k1_msafree1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 B) (k3_card_3 C))))) ) ) ) ).
tt(dt_k1_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (m1_subset_1 (k1_msafree2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((v3_msualg_1 (k1_msafree3 A B) A) & (l3_msualg_1 (k1_msafree3 A B) A)) ) ) ).
tt(dt_k1_msafree,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m3_pboole D A B) & (m2_pboole E A B C)) ) )  => (m2_pboole (k1_msafree A B C D E) A D C)) ) ).
tt(dt_k1_msalimit,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_msalimit C A B) &  ((m2_msalimit D A B C) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m2_pboole (k1_msalimit A B C D E F) (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C E)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F)))) ) ).
tt(dt_k1_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k1_msaterm A B) (k1_zfmisc_1 (k5_trees_3 (u1_struct_0 (k5_msafree A B)))))) ) ).
tt(dt_k1_msinst_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k1_msinst_1 A)))  &  ((v6_altcat_1 (k1_msinst_1 A)) & (l2_altcat_1 (k1_msinst_1 A))) ) ) ) ).
tt(dt_k1_msscyc_2,ax,$true).
tt(dt_k1_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (m3_pboole (k1_mssubfam A B) A (k1_mboolean A B))) ) ).
tt(dt_k1_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_finseq_2 (k1_msualg_1 A B) (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))) ) ).
tt(dt_k1_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_msualg_2 A B C) (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C)))) ) ).
tt(dt_k1_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m2_pboole D A B C) & (m1_subset_1 E A)) ) ) )  =>  ((v1_funct_1 (k1_msualg_3 A B C D E)) &  ((v1_funct_2 (k1_msualg_3 A B C D E) (k1_funct_1 B E) (k1_funct_1 C E)) & (m1_subset_1 (k1_msualg_3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))))) ) ) ) ).
tt(dt_k1_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m1_msualg_4 D A B C) & (m1_subset_1 E A)) ) ) )  => (m1_subset_1 (k1_msualg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))))) ) ).
tt(dt_k1_msualg_5,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_partfun1 (k1_msualg_5 A B) A) &  ((v3_relat_2 (k1_msualg_5 A B)) &  ((v8_relat_2 (k1_msualg_5 A B)) & (m1_subset_1 (k1_msualg_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k1_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A B B) & (m2_pboole D A B B)) )  => (m2_pboole (k1_msualg_6 A B C D) A B B)) ) ).
tt(dt_k1_msualg_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ( (~ (v2_struct_0 (k1_msualg_7 A B)))  &  ((v3_lattices (k1_msualg_7 A B)) &  ((v10_lattices (k1_msualg_7 A B)) & (l3_lattices (k1_msualg_7 A B))) ) ) ) ) ).
tt(dt_k1_msualg_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_subset_1 C (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B))))) )  =>  ((v2_msualg_4 (k1_msualg_8 A B C) A B) &  ((v3_msualg_4 (k1_msualg_8 A B C) A B) & (m1_msualg_4 (k1_msualg_8 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_k1_msualg_9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  & (m2_pboole E A B (k6_pboole A C D))) ) )  => (m2_pboole (k1_msualg_9 A B C D E) A B C)) ) ).
tt(dt_k1_msuhom_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_msualg_1 A) & (l1_msualg_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_msualg_1 B) & (l1_msualg_1 B)) ) )  &  ((v3_msualg_1 C B) &  ((v4_msualg_1 C B) & (l3_msualg_1 C B)) ) ) )  =>  ((v3_msualg_1 (k1_msuhom_1 A B C) A) &  ((v4_msualg_1 (k1_msuhom_1 A B C) A) & (l3_msualg_1 (k1_msuhom_1 A B C) A)) ) ) ) ).
tt(dt_k1_multop_1,ax,$true).
tt(dt_k1_mycielsk,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_eqrel_1 B A) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_eqrel_1 (k1_mycielsk A B C) C)) ) ).
tt(dt_k1_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k1_nagata_1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_nagata_2,ax, ((v1_funct_1 k1_nagata_2) &  ((v1_funct_2 k1_nagata_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 k1_nagata_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) ) ).
tt(dt_k1_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k1_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_nat_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_nat_3 A B)) &  ((v1_funct_1 (k1_nat_3 A B)) & (v1_finseq_1 (k1_nat_3 A B))) ) ) ) ).
tt(dt_k1_nat_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) &  ((v7_ordinal1 B) & (v1_int_2 B)) )  => (m1_trees_4 (k1_nat_4 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_nat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((v1_relat_1 (k1_nat_5 A B C)) &  ((v4_relat_1 (k1_nat_5 A B C) C) &  ((v1_funct_1 (k1_nat_5 A B C)) &  ((v1_partfun1 (k1_nat_5 A B C) C) &  ((v4_valued_0 (k1_nat_5 A B C)) & (v2_pre_poly (k1_nat_5 A B C))) ) ) ) ) ) ) ).
tt(dt_k1_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k1_nat_d A B))) ) ).
tt(dt_k1_nat_lat,ax, ((v1_funct_1 k1_nat_lat) &  ((v1_funct_2 k1_nat_lat (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 k1_nat_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) ) ).
tt(dt_k1_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k1_zfmisc_1 A))) )  =>  ((v1_funct_1 (k1_nattra_1 A B C D)) &  ((v1_funct_2 (k1_nattra_1 A B C D) D B) & (m1_subset_1 (k1_nattra_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 D B)))) ) ) ) ).
tt(dt_k1_ndiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_ndiff_1 A B C)) &  ((v1_funct_2 (k1_ndiff_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k1_ndiff_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_ndiff_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  & (v1_xreal_0 C)) )  => (m1_subset_1 (k1_ndiff_3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_ndiff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  & (v1_xreal_0 C)) )  => (m2_finseq_2 (k1_ndiff_4 A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k1_ndiff_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  &  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) & (m1_subset_1 C (k4_finseq_1 A))) )  => (m1_subset_1 (k1_ndiff_5 A B C) (u1_struct_0 (k3_prvect_2 A C)))) ) ).
tt(dt_k1_neckla_2,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  ((v1_orders_2 (k1_neckla_2 A B)) & (l1_orders_2 (k1_neckla_2 A B))) ) ) ).
tt(dt_k1_neckla_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_neckla_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_orders_2 (k1_necklace A)) & (l1_orders_2 (k1_necklace A))) ) ) ).
tt(dt_k1_net_1,ax,$true).
tt(dt_k1_newton,ax,$true).
tt(dt_k1_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ((v1_funct_1 (k1_nfcont_4 A B C)) & (m1_subset_1 (k1_nfcont_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ).
tt(dt_k1_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  => (m1_subset_1 (k1_normform A B C D) (k2_zfmisc_1 A B))) ) ).
tt(dt_k1_normsp_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_normsp_0 A B) k1_numbers)) ) ).
tt(dt_k1_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k1_normsp_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_normsp_2 A)) &  ((v1_funct_2 (k1_normsp_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 (k1_normsp_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) ) ) ) ).
tt(dt_k1_ntalgo_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k4_numbers) & (m1_subset_1 B k4_numbers))  => (m2_subset_1 (k1_ntalgo_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_numbers,ax,$true).
tt(dt_k1_numeral1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  & (v7_ordinal1 B))  => (v7_ordinal1 (k1_numeral1 A B))) ) ).
tt(dt_k1_openlatt,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k1_openlatt A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (l2_qmax_1 k1_oposet_1)) ).
tt(dt_k1_oppcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) )  =>  ((v1_funct_1 (k1_oppcat_1 A B C D)) & (m1_subset_1 (k1_oppcat_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ).
tt(dt_k1_orders_1,ax,$true).
tt(dt_k1_orders_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_orders_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_orders_3,ax,$true).
tt(dt_k1_ordinal1,ax,$true).
tt(dt_k1_ordinal2,ax,$true).
tt(dt_k1_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) ) )  =>  ((v5_ordinal1 (k1_ordinal3 A B)) &  ((v1_relat_1 (k1_ordinal3 A B)) &  ((v1_funct_1 (k1_ordinal3 A B)) & (v1_ordinal2 (k1_ordinal3 A B))) ) ) ) ) ).
tt(dt_k1_ordinal4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_ordinal1 B) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v5_ordinal1 (k1_ordinal4 A B)) & (v1_funct_1 (k1_ordinal4 A B))) ) ) ) ).
tt(dt_k1_ordinal5,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k1_ordinal5 A B))) ) ).
tt(dt_k1_ordinal6,ax, (! [A:$i] : (v3_ordinal1 (k1_ordinal6 A))) ).
tt(dt_k1_ortsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (m1_subset_1 (k1_ortsp_1 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k1_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k1_osafree A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B)))))))) ) ).
tt(dt_k1_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ( (~ (v2_struct_0 (k1_osalg_1 A)))  &  ( (~ (v11_struct_0 (k1_osalg_1 A)))  &  ((v3_osalg_1 (k1_osalg_1 A)) &  ((v4_osalg_1 (k1_osalg_1 A)) & (l3_osalg_1 (k1_osalg_1 A))) ) ) ) ) ) ).
tt(dt_k1_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_osalg_2 A B C) (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C)))) ) ).
tt(dt_k1_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_partfun1 (k1_osalg_4 A) (u1_struct_0 A)) &  ((v3_relat_2 (k1_osalg_4 A)) &  ((v8_relat_2 (k1_osalg_4 A)) & (m1_subset_1 (k1_osalg_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k1_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_parsp_1 A)) &  ((v1_funct_2 (k1_parsp_1 A) (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 (k1_parsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k1_partfun1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) )  =>  ((v1_funct_1 (k1_partfun1 A B C D E F)) & (m1_subset_1 (k1_partfun1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 A D)))) ) ) ).
tt(dt_k1_partfun2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k1_partfun2 A B)) & (m1_subset_1 (k1_partfun2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ).
tt(dt_k1_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k1_partfun3 A)) & (v1_funct_1 (k1_partfun3 A))) ) ) ).
tt(dt_k1_partit1,ax,$true).
tt(dt_k1_partit_2,ax, (! [A:$i,B:$i] : (m1_subset_1 (k1_partit_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ).
tt(dt_k1_pboole,ax, (! [A:$i] :  ((v1_relat_1 (k1_pboole A)) &  ((v4_relat_1 (k1_pboole A) A) &  ((v1_funct_1 (k1_pboole A)) & (v1_partfun1 (k1_pboole A) A)) ) ) ) ).
tt(dt_k1_pcomps_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (m1_subset_1 (k1_pcomps_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_pcomps_2,ax,$true).
tt(dt_k1_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k1_pcs_0 A B C) (k1_zfmisc_1 (k2_xboole_0 A B)))) ) ).
tt(dt_k1_pdiff_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k1_pdiff_1 A B)) &  ((v1_funct_2 (k1_pdiff_1 A B) (k1_euclid B) k1_numbers) & (m1_subset_1 (k1_pdiff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) k1_numbers)))) ) ) ) ).
tt(dt_k1_pdiff_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (m1_subset_1 D (k1_euclid A))) ) )  =>  ((v1_funct_1 (k1_pdiff_2 A B C D)) & (m1_subset_1 (k1_pdiff_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k1_pdiff_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) k1_numbers)))) ) )  =>  ((v1_funct_1 (k1_pdiff_3 A B C)) &  ((v1_funct_2 (k1_pdiff_3 A B C) (k1_euclid B) k1_numbers) & (m1_subset_1 (k1_pdiff_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) k1_numbers)))) ) ) ) ).
tt(dt_k1_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k1_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k1_pdiff_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  & (m1_subset_1 D (k1_euclid A))) ) )  => (m2_finseq_2 (k1_pdiff_6 A B C D) k1_numbers (k1_euclid B))) ) ).
tt(dt_k1_pdiff_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (m1_subset_1 C (k1_euclid A))) )  =>  ((v1_funct_1 (k1_pdiff_7 A B C)) &  ((v1_funct_2 (k1_pdiff_7 A B C) (k1_euclid A) k1_numbers) & (m1_subset_1 (k1_pdiff_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) ) ) ).
tt(dt_k1_pdiff_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) )  =>  ((v1_funct_1 (k1_pdiff_9 A B C D)) & (m1_subset_1 (k1_pdiff_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k9_funct_2 (k1_euclid A) (k1_euclid B)))))) ) ) ).
tt(dt_k1_pencil_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v11_pencil_1 B)) ) ) )  & (m1_subset_1 C A)) )  => (l1_pre_topc (k1_pencil_1 A B C))) ) ).
tt(dt_k1_pencil_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m2_finseq_1 (k1_pencil_2 A B C D) A)) ) ).
tt(dt_k1_pencil_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  => (v7_ordinal1 (k1_pencil_3 A B C))) ) ).
tt(dt_k1_pencil_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_vectsp_4 D A B)) ) )  => (m1_subset_1 (k1_pencil_4 A B C D) (k1_zfmisc_1 (k3_vectsp_5 A B)))) ) ).
tt(dt_k1_pepin,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k1_pepin A) k5_numbers)) ) ).
tt(dt_k1_petri_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A)))) ) )  =>  ( (~ (v1_xboole_0 (k1_petri_2 A B C D)))  & (m1_subset_1 (k1_petri_2 A B C D) (k1_zfmisc_1 (k9_funct_2 B A)))) ) ) ).
tt(dt_k1_pnproc_1,ax, (! [A:$i] :  ((v1_funct_1 (k1_pnproc_1 A)) &  ((v1_funct_2 (k1_pnproc_1 A) A k5_numbers) & (m1_subset_1 (k1_pnproc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ).
tt(dt_k1_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (~ (v2_struct_0 (k1_polyalg1 A)))  &  ((v1_polyalg1 (k1_polyalg1 A) A) & (l1_polyalg1 (k1_polyalg1 A) A)) ) ) ) ).
tt(dt_k1_polyeq_1,ax,$true).
tt(dt_k1_polyeq_2,ax,$true).
tt(dt_k1_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (m1_subset_1 (k1_polyeq_3 A) k2_numbers)) ) ).
tt(dt_k1_polyeq_4,ax,$true).
tt(dt_k1_polyeq_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  & (v1_xcmplx_0 B))  => (v1_xcmplx_0 (k1_polyeq_5 A B))) ) ).
tt(dt_k1_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k1_polyform A B) k4_numbers)) ) ).
tt(dt_k1_polynom1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k1_polynom1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_polynom2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((v1_finset_1 (k1_polynom2 A B)) & (m1_subset_1 (k1_polynom2 A B) (k1_zfmisc_1 A))) ) ) ).
tt(dt_k1_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k1_polynom3 A B C) A)) ) ).
tt(dt_k1_polynom4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k1_polynom4 A B)) &  ((v1_funct_2 (k1_polynom4 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k1_polynom4 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_polynom5,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 k1_complfld)) => (m2_finseq_1 (k1_polynom5 A) k1_numbers)) ) ).
tt(dt_k1_polynom6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ((v3_ordinal1 B) &  ((m1_subset_1 C (k15_pre_poly A)) & (m1_subset_1 D (k15_pre_poly B))) ) )  => (m2_subset_1 (k1_polynom6 A B C D) (k14_pre_poly (k10_ordinal2 A B)) (k15_pre_poly (k10_ordinal2 A B)))) ) ).
tt(dt_k1_polynom7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_polynom7 A B C D)) &  ((v1_funct_2 (k1_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 (k1_polynom7 A B C D) A B) & (m1_subset_1 (k1_polynom7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k1_polynom8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k1_polynom8 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) )  =>  ((v1_funct_1 (k1_polyred A B C D)) &  ((v1_funct_2 (k1_polyred A B C D) (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 (k1_polyred A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k1_poset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k1_poset_1 A B C))) ) ) ).
tt(dt_k1_power,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k1_power A B))) ) ).
tt(dt_k1_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k2_zfmisc_1 A B))) )  => (m2_finseq_1 (k1_pralg_1 A B C) A)) ) ).
tt(dt_k1_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_pralg_2 A)) & (v1_funct_1 (k1_pralg_2 A))) ) ) ).
tt(dt_k1_pralg_3,ax,$true).
tt(dt_k1_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_pre_ff A) k5_numbers)) ) ).
tt(dt_k1_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_prelamb A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k3_finseq_2 A)) & (m1_subset_1 C (k3_finseq_2 A)))  => (m2_finseq_2 (k1_pre_poly A B C) A (k3_finseq_2 A))) ) ).
tt(dt_k1_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k1_prepower A)) &  ((v1_funct_2 (k1_prepower A) k5_numbers k1_numbers) & (m1_subset_1 (k1_prepower A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_pre_topc,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k1_pre_topc A B)) & (m1_pre_topc (k1_pre_topc A B) A)) ) ) ).
tt(dt_k1_prgcor_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k1_prgcor_1 A B))) ) ).
tt(dt_k1_prgcor_2,ax,$true).
tt(dt_k1_prob_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k1_prob_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_prob_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  & (m1_subset_1 D k5_numbers)) )  => (m1_prob_1 (k1_prob_2 A B C D) A B)) ) ).
tt(dt_k1_prob_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k1_prob_3 A B)) &  ((v1_funct_2 (k1_prob_3 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k1_prob_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k1_prob_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  & (m1_subset_1 D k5_numbers)) )  => (m2_subset_1 (k1_prob_4 A B C D) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k1_projpl_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  &  ((m1_subset_1 B (u1_incsp_1 A)) & (m1_subset_1 C (u1_incsp_1 A))) )  => (m1_subset_1 (k1_projpl_1 A B C) (u2_incsp_1 A))) ) ).
tt(dt_k1_projred1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u2_incsp_1 A)) &  ((m1_subset_1 C (u2_incsp_1 A)) & (m1_subset_1 D (u1_incsp_1 A))) ) )  =>  ((v1_funct_1 (k1_projred1 A B C D)) & (m1_subset_1 (k1_projred1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 A))))) ) ) ).
tt(dt_k1_projred2,ax, (! [A:$i,B:$i] :  ( ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  & (m1_subset_1 B (u2_incsp_1 A)))  => (m1_subset_1 (k1_projred2 A B) (k1_zfmisc_1 (u1_incsp_1 A)))) ) ).
tt(dt_k1_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D (k4_finseq_2 B A)) & (m1_subset_1 E (k4_finseq_2 B A))) ) ) )  => (m2_finseq_2 (k1_prvect_1 A B C D E) A (k4_finseq_2 B A))) ) ).
tt(dt_k1_prvect_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m1_prvect_2 C A B) & (m1_subset_1 D (k4_finseq_1 A))) )  =>  ((v1_funct_1 (k1_prvect_2 A B C D)) &  ((v1_funct_2 (k1_prvect_2 A B C D) (k2_zfmisc_1 B (k1_funct_1 A D)) (k1_funct_1 A D)) & (m1_subset_1 (k1_prvect_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (k1_funct_1 A D)) (k1_funct_1 A D))))) ) ) ) ).
tt(dt_k1_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_algstr_0 B)) )  =>  ((v1_funct_1 (k1_prvect_3 A B)) &  ((v1_funct_2 (k1_prvect_3 A B) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 (k1_prvect_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k1_pscomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  => (m1_subset_1 (k1_pscomp_1 A B) k1_numbers)) ) ).
tt(dt_k1_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)))  => (m1_subset_1 (k1_pua2mss1 A B) (k1_zfmisc_1 (k4_partfun1 (k3_finseq_2 A) A)))) ) ).
tt(dt_k1_pzfmisc1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k1_pzfmisc1 A B)) &  ((v4_relat_1 (k1_pzfmisc1 A B) A) &  ((v1_funct_1 (k1_pzfmisc1 A B)) & (v1_partfun1 (k1_pzfmisc1 A B) A)) ) ) ) ) ).
tt(dt_k1_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k1_qc_lang1 A))) ) ) ).
tt(dt_k1_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k1_qc_lang2 A) (k9_qc_lang1 A))) ) ).
tt(dt_k1_qc_lang3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_finseq_1 B (k2_qc_lang1 A)) &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A)))) ) )  => (m1_subset_1 (k1_qc_lang3 A B C) (k1_zfmisc_1 C))) ) ).
tt(dt_k1_qc_lang4,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m2_finseq_1 (k1_qc_lang4 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k1_qmax_1,ax,$true).
tt(dt_k1_quantal1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_quantal1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_quatern2,ax,(m1_subset_1 k1_quatern2 k1_quaterni)).
tt(dt_k1_quatern3,ax,$true).
tt(dt_k1_quaterni,ax,$true).
tt(dt_k1_quin_1,ax,$true).
tt(dt_k1_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  => (m1_subset_1 (k1_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k1_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_radix_1 A) k5_numbers)) ) ).
tt(dt_k1_radix_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D k5_numbers)) ) ) )  => (m2_subset_1 (k1_radix_2 A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k1_radix_3,ax,$true).
tt(dt_k1_radix_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ((v3_card_1 D B) & (m1_finseq_1 D (k4_radix_3 C)))  &  ((v3_card_1 E B) & (m1_finseq_1 E (k4_radix_3 C))) ) ) ) )  => (m2_subset_1 (k1_radix_4 A B C D E) k4_numbers (k4_radix_3 C))) ) ).
tt(dt_k1_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k1_radix_5 A B C) k4_numbers (k3_radix_1 C))) ) ).
tt(dt_k1_radix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m1_finseq_1 D (k3_radix_1 C))) ) ) )  => (m1_subset_1 (k1_radix_6 A B C D) (k3_radix_1 C))) ) ).
tt(dt_k1_ramsey_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) )  =>  ((v1_funct_1 (k1_ramsey_1 A B C D)) &  ((v1_funct_2 (k1_ramsey_1 A B C D) (k3_group_10 B A) (k3_group_10 C A)) & (m1_subset_1 (k1_ramsey_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 B A) (k3_group_10 C A))))) ) ) ) ).
tt(dt_k1_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k1_random_1 A)))  &  ((v1_prob_1 (k1_random_1 A) A) &  ((v4_prob_1 (k1_random_1 A) A) & (m1_subset_1 (k1_random_1 A) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(dt_k1_random_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) & (m1_random_1 D A B)) ) )  => (m1_subset_1 (k1_random_2 A B C D) k1_numbers)) ) ).
tt(dt_k1_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v7_vectsp_1 (k1_ranknull A B C D) A) & (m1_vectsp_4 (k1_ranknull A B C D) A B)) ) ) ).
tt(dt_k1_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (m2_subset_1 (k1_rat_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k1_rcomp_1 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k1_real_1 A) k1_numbers)) ) ).
tt(dt_k1_real_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k1_real_3 A B)) &  ((v1_funct_2 (k1_real_3 A B) k5_numbers k5_numbers) & (m1_subset_1 (k1_real_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k1_real_lat,ax, ((v1_funct_1 k1_real_lat) &  ((v1_funct_2 k1_real_lat (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k1_real_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k1_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_real_ns1 A)) &  ((v1_funct_2 (k1_real_ns1 A) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A)) & (m1_subset_1 (k1_real_ns1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A))))) ) ) ) ).
tt(dt_k1_realset1,ax,$true).
tt(dt_k1_realset2,ax, ((v1_funct_1 k1_realset2) &  ((v1_funct_2 k1_realset2 (k2_zfmisc_1 2 2) 2) & (m1_subset_1 k1_realset2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 2 2) 2)))) ) ).
tt(dt_k1_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_realset3 A)) &  ((v1_funct_2 (k1_realset3 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k1_realset3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_rearran1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (m1_subset_1 D k1_numbers)) ) )  => (m2_rfunct_3 (k1_rearran1 A B C D) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k1_recdef_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  => (m2_subset_1 (k1_recdef_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k1_relat_1,ax,$true).
tt(dt_k1_relset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  => (m1_subset_1 (k1_relset_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k1_relset_2 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k1_rewrite1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k1_rewrite1 A B)) &  ((v1_funct_1 (k1_rewrite1 A B)) & (v1_finseq_1 (k1_rewrite1 A B))) ) ) ) ).
tt(dt_k1_rewrite2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_rewrite2 B)) ) )  =>  ((v1_relat_1 (k1_rewrite2 A B)) &  ((v1_funct_1 (k1_rewrite2 A B)) & (v1_rewrite2 (k1_rewrite2 A B))) ) ) ) ).
tt(dt_k1_rewrite3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B)) ) )  => (m1_subset_1 (k1_rewrite3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k8_afinsq_1 A)) (k2_zfmisc_1 (u1_struct_0 C) (k8_afinsq_1 A)))))) ) ).
tt(dt_k1_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k1_rfinseq2 A) k5_numbers)) ) ).
tt(dt_k1_rfinseq,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k1_rfinseq A B)) &  ((v1_funct_1 (k1_rfinseq A B)) & (v1_finseq_1 (k1_rfinseq A B))) ) ) ) ).
tt(dt_k1_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_rfunct_1 A B)) & (v1_funct_1 (k1_rfunct_1 A B))) ) ) ).
tt(dt_k1_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_rfunct_3 A) k1_numbers)) ) ).
tt(dt_k1_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k1_rinfsup1 A) k1_numbers)) ) ).
tt(dt_k1_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k1_rinfsup2 A) k7_numbers)) ) ).
tt(dt_k1_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  => (m1_subset_1 (k1_ring_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k1_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ( (~ (v2_struct_0 (k1_ringcat1 A)))  &  ((v13_algstr_0 (k1_ringcat1 A)) &  ((v2_rlvect_1 (k1_ringcat1 A)) &  ((v3_rlvect_1 (k1_ringcat1 A)) &  ((v4_rlvect_1 (k1_ringcat1 A)) &  ((v3_group_1 (k1_ringcat1 A)) &  ((v4_vectsp_1 (k1_ringcat1 A)) &  ((v5_vectsp_1 (k1_ringcat1 A)) & (l6_algstr_0 (k1_ringcat1 A))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k1_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  &  ((m1_rlvect_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_rlvect_2 (k1_rlaffin1 A B C) A)) ) ).
tt(dt_k1_rlaffin2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_rlaffin2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_rlaffin3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_rlaffin3 C B)) )  => (m2_finseq_1 (k1_rlaffin3 A B C D) k1_numbers)) ) ).
tt(dt_k1_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_1 (k1_rlsub_1 A)) & (m1_rlsub_1 (k1_rlsub_1 A) A)) ) ) ).
tt(dt_k1_rlsub_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_rlsub_1 B A) & (m1_rlsub_1 C A)) )  =>  ((v1_rlvect_1 (k1_rlsub_2 A B C)) & (m1_rlsub_1 (k1_rlsub_2 A B C) A)) ) ) ).
tt(dt_k1_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_rltopsp1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_rlvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (m1_subset_1 (k1_rlvect_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_rlvect_2,ax, (! [A:$i,B:$i] :  ((l1_struct_0 A) => (m1_subset_1 (k1_rlvect_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_rlvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_rlvect_1 (k1_rlvect_3 A B)) & (m1_rlsub_1 (k1_rlvect_3 A B) A)) ) ) ).
tt(dt_k1_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (m2_subset_1 (k1_rlvect_5 A) k1_numbers k5_numbers)) ) ).
tt(dt_k1_rlvect_x,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v1_int_1 B) & (m1_rlvect_2 C A)) )  => (m1_rlvect_2 (k1_rlvect_x A B C) A)) ) ).
tt(dt_k1_rmod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((v2_vectsp_2 (k1_rmod_2 A B) A) & (m1_rmod_2 (k1_rmod_2 A B) A B)) ) ) ).
tt(dt_k1_rmod_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_2 C A B) & (m1_rmod_2 D A B)) ) )  =>  ((v2_vectsp_2 (k1_rmod_3 A B C D) A) & (m1_rmod_2 (k1_rmod_3 A B C D) A B)) ) ) ).
tt(dt_k1_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m1_subset_1 (k1_rmod_4 A B C) (u1_struct_0 B))) ) ).
tt(dt_k1_robbins3,ax,(l3_robbins3 k1_robbins3)).
tt(dt_k1_robbins4,ax,(l1_orders_2 k1_robbins4)).
tt(dt_k1_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k1_zfmisc_1 A)) & (v7_ordinal1 C))  => (m1_subset_1 (k1_roughs_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_rpr_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 B (k1_zfmisc_1 A)))  => (m1_subset_1 (k1_rpr_1 A B) k1_numbers)) ) ).
tt(dt_k1_rsspace3,ax,(m1_subset_1 k1_rsspace3 (k1_zfmisc_1 (u1_struct_0 k7_rsspace)))).
tt(dt_k1_rsspace4,ax,(m1_subset_1 k1_rsspace4 (k1_zfmisc_1 (u1_struct_0 k7_rsspace)))).
tt(dt_k1_rsspace,ax, (~ (v1_xboole_0 k1_rsspace)) ).
tt(dt_k1_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_bhsp_1 (k1_rusub_1 A)) & (m1_rusub_1 (k1_rusub_1 A) A)) ) ) ).
tt(dt_k1_rusub_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_rusub_1 B A) & (m1_rusub_1 C A)) )  =>  ((v1_bhsp_1 (k1_rusub_2 A B C)) & (m1_rusub_1 (k1_rusub_2 A B C) A)) ) ) ).
tt(dt_k1_rusub_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_bhsp_1 (k1_rusub_3 A B)) & (m1_rusub_1 (k1_rusub_3 A B) A)) ) ) ).
tt(dt_k1_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k1_rusub_4 A) k5_numbers)) ) ).
tt(dt_k1_rusub_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_rusub_5 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  => (m1_subset_1 (k1_rvsum_1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  => (m1_subset_1 (k1_rvsum_2 A) (k1_zfmisc_1 k2_numbers))) ) ).
tt(dt_k1_scmbsort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((v1_relat_1 (k1_scmbsort A)) &  ((v4_relat_1 (k1_scmbsort A) k5_numbers) &  ((v5_relat_1 (k1_scmbsort A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmbsort A)) &  ( (~ (v1_xboole_0 (k1_scmbsort A)))  &  ((v1_finset_1 (k1_scmbsort A)) & (v1_afinsq_1 (k1_scmbsort A))) ) ) ) ) ) ) ) ).
tt(dt_k1_scm_comp,ax, ( (~ (v2_struct_0 k1_scm_comp))  &  ((v1_lang1 k1_scm_comp) &  ((v1_dtconstr k1_scm_comp) &  ((v2_dtconstr k1_scm_comp) &  ((v3_dtconstr k1_scm_comp) &  ((v3_bintree1 k1_scm_comp) & (l1_lang1 k1_scm_comp)) ) ) ) ) ) ).
tt(dt_k1_scmfsa_1,ax,$true).
tt(dt_k1_scmfsa_2,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (l1_extpro_1 k1_scmfsa_2 3)) ).
tt(dt_k1_scmfsa_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmfsa_3 A B)) &  ((v4_relat_1 (k1_scmfsa_3 A B) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_3 A B)) &  ((v5_funct_1 (k1_scmfsa_3 A B) (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 (k1_scmfsa_3 A B))) ) ) ) ) ) ).
tt(dt_k1_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k1_scmfsa6a A B)) &  ((v4_relat_1 (k1_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6a A B)) & (v1_finset_1 (k1_scmfsa6a A B))) ) ) ) ) ) ).
tt(dt_k1_scmfsa6b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) ) ) )  =>  ((v1_relat_1 (k1_scmfsa6b A B C)) &  ((v4_relat_1 (k1_scmfsa6b A B C) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6b A B C)) &  ((v5_funct_1 (k1_scmfsa6b A B C) (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 (k1_scmfsa6b A B C) (u1_struct_0 k1_scmfsa_2))) ) ) ) ) ) ).
tt(dt_k1_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa6c A B)))  &  ((v1_relat_1 (k1_scmfsa6c A B)) &  ((v4_relat_1 (k1_scmfsa6c A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6c A B)) &  ((v1_finset_1 (k1_scmfsa6c A B)) & (v1_afinsq_1 (k1_scmfsa6c A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmfsa_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmfsa_7 A B)) &  ((v4_relat_1 (k1_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_7 A B)) & (v1_finset_1 (k1_scmfsa_7 A B))) ) ) ) ) ) ).
tt(dt_k1_scmfsa8a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k1_scmfsa8a A)))  &  ((v1_relat_1 (k1_scmfsa8a A)) &  ((v4_relat_1 (k1_scmfsa8a A) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8a A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8a A)) &  ((v1_finset_1 (k1_scmfsa8a A)) & (v1_afinsq_1 (k1_scmfsa8a A))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8b A B C)))  &  ((v1_relat_1 (k1_scmfsa8b A B C)) &  ((v4_relat_1 (k1_scmfsa8b A B C) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8b A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8b A B C)) &  ((v1_finset_1 (k1_scmfsa8b A B C)) & (v1_afinsq_1 (k1_scmfsa8b A B C))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8c A)))  &  ((v1_relat_1 (k1_scmfsa8c A)) &  ((v4_relat_1 (k1_scmfsa8c A) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8c A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8c A)) &  ((v1_finset_1 (k1_scmfsa8c A)) &  ((v1_afinsq_1 (k1_scmfsa8c A)) & (v2_compos_1 (k1_scmfsa8c A) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(dt_k1_scmfsa9a,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  => (m2_subset_1 (k1_scmfsa9a A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k1_scmfsa_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_scmfsa_9 A B)) &  ((v4_relat_1 (k1_scmfsa_9 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_9 A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k1_scmfsa_9 A B)))  &  ((v1_funct_1 (k1_scmfsa_9 A B)) &  ((v1_finset_1 (k1_scmfsa_9 A B)) & (v1_afinsq_1 (k1_scmfsa_9 A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmfsa_i,ax,$true).
tt(dt_k1_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k1_scmfsa_m A)) &  ((v4_relat_1 (k1_scmfsa_m A) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_m A)) & (v5_funct_1 (k1_scmfsa_m A) (k2_memstr_0 3 k1_scmfsa_2))) ) ) ) ) ).
tt(dt_k1_scm_inst,ax,(m1_subset_1 k1_scm_inst (k7_card_1 9))).
tt(dt_k1_scmisort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_scmisort A B C D)) &  ((v1_funct_2 (k1_scmisort A B C D) k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 (k1_scmisort A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) ) ) ) ).
tt(dt_k1_scmpds_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) &  ((m1_subset_1 B k2_ami_2) & (v1_int_1 C)) )  => (m2_subset_1 (k1_scmpds_1 A B C) k1_ami_2 k2_ami_2)) ) ).
tt(dt_k1_scmpds_2,ax, ((v1_extpro_1 k1_scmpds_2 2) & (l1_extpro_1 k1_scmpds_2 2)) ).
tt(dt_k1_scmpds_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmpds_3 A B)) &  ((v4_relat_1 (k1_scmpds_3 A B) (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_3 A B)) &  ((v5_funct_1 (k1_scmpds_3 A B) (k2_memstr_0 2 k1_scmpds_2)) & (v1_finset_1 (k1_scmpds_3 A B))) ) ) ) ) ) ).
tt(dt_k1_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmpds_4 A B)))  &  ((v1_relat_1 (k1_scmpds_4 A B)) &  ((v4_relat_1 (k1_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k1_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_4 A B)) &  ((v1_finset_1 (k1_scmpds_4 A B)) & (v1_afinsq_1 (k1_scmpds_4 A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmpds_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (v1_xboole_0 (k1_scmpds_6 A)))  &  ((v1_relat_1 (k1_scmpds_6 A)) &  ((v4_relat_1 (k1_scmpds_6 A) k5_numbers) &  ((v5_relat_1 (k1_scmpds_6 A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_6 A)) &  ((v1_finset_1 (k1_scmpds_6 A)) & (v1_afinsq_1 (k1_scmpds_6 A))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmpds_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ((m1_subset_1 C k5_numbers) &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmpds_7 A B C D)))  &  ((v1_relat_1 (k1_scmpds_7 A B C D)) &  ((v4_relat_1 (k1_scmpds_7 A B C D) k5_numbers) &  ((v5_relat_1 (k1_scmpds_7 A B C D) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_7 A B C D)) &  ((v1_finset_1 (k1_scmpds_7 A B C D)) & (v1_afinsq_1 (k1_scmpds_7 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmpds_8 A B C)))  &  ((v1_relat_1 (k1_scmpds_8 A B C)) &  ((v4_relat_1 (k1_scmpds_8 A B C) k5_numbers) &  ((v5_relat_1 (k1_scmpds_8 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_8 A B C)) &  ((v1_finset_1 (k1_scmpds_8 A B C)) & (v1_afinsq_1 (k1_scmpds_8 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k1_scmpds_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ((v1_relat_1 (k1_scmpds_9 A B C D)) &  ((v4_relat_1 (k1_scmpds_9 A B C D) (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_9 A B C D)) & (v5_funct_1 (k1_scmpds_9 A B C D) (k2_memstr_0 2 k1_scmpds_2))) ) ) ) ) ).
tt(dt_k1_scmpds_i,ax,$true).
tt(dt_k1_scmp_gcd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_ami_2 (k1_scmp_gcd A)) & (m1_subset_1 (k1_scmp_gcd A) (u1_struct_0 k1_scmpds_2))) ) ) ).
tt(dt_k1_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((v1_relat_1 (k1_scmring1 A)) &  ((v4_relat_1 (k1_scmring1 A) 2) &  ((v1_funct_1 (k1_scmring1 A)) & (v1_partfun1 (k1_scmring1 A) 2)) ) ) ) ) ).
tt(dt_k1_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (l1_extpro_1 (k1_scmring2 A) 2)) ) ) ).
tt(dt_k1_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_xboole_0 (k1_scmringi A))) ) ) ).
tt(dt_k1_scmyciel,ax, (! [A:$i] : (m1_subset_1 (k1_scmyciel A) (k1_zfmisc_1 A))) ).
tt(dt_k1_scpinvar,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k1_scpinvar A B)))  &  ((v1_relat_1 (k1_scpinvar A B)) &  ((v4_relat_1 (k1_scpinvar A B) k5_numbers) &  ((v5_relat_1 (k1_scpinvar A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scpinvar A B)) &  ((v1_finset_1 (k1_scpinvar A B)) & (v1_afinsq_1 (k1_scpinvar A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_scpisort,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k1_scpisort A B)))  &  ((v1_relat_1 (k1_scpisort A B)) &  ((v4_relat_1 (k1_scpisort A B) k5_numbers) &  ((v5_relat_1 (k1_scpisort A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scpisort A B)) &  ((v1_finset_1 (k1_scpisort A B)) & (v1_afinsq_1 (k1_scpisort A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_scpqsort,ax, ( (~ (v1_xboole_0 k1_scpqsort))  &  ((v1_relat_1 k1_scpqsort) &  ((v4_relat_1 k1_scpqsort k5_numbers) &  ((v5_relat_1 k1_scpqsort (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 k1_scpqsort) &  ((v1_finset_1 k1_scpqsort) & (v1_afinsq_1 k1_scpqsort)) ) ) ) ) ) ).
tt(dt_k1_semi_af1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k1_semi_af1 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_seq_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  => (m1_subset_1 (k1_seq_1 A B) k1_numbers)) ) ).
tt(dt_k1_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (v1_xreal_0 (k1_seq_2 A))) ) ).
tt(dt_k1_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_seq_4 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_seqfunc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  & (v7_ordinal1 D))  =>  ((v1_funct_1 (k1_seqfunc A B C D)) & (m1_subset_1 (k1_seqfunc A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k1_series_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_membered A) & (v7_membered A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  ((v1_funct_1 (k1_series_1 A B C)) &  ((v1_funct_2 (k1_series_1 A B C) k5_numbers A) & (m1_subset_1 (k1_series_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k1_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k1_series_3 A)) &  ((v1_funct_2 (k1_series_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k1_series_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_setfam_1,ax,$true).
tt(dt_k1_setlim_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k1_setlim_1 A)) & (v1_funct_1 (k1_setlim_1 A))) ) ) ).
tt(dt_k1_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_funct_1 (k1_setlim_2 A B C)) &  ((v1_funct_2 (k1_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k1_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k1_setwiseo,ax, (! [A:$i] :  ((v1_xboole_0 (k1_setwiseo A)) & (m1_subset_1 (k1_setwiseo A) (k5_finsub_1 A))) ) ).
tt(dt_k1_setwop_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k1_setwop_2 A B C)) &  ((v1_funct_2 (k1_setwop_2 A B C) k5_numbers A) & (m1_subset_1 (k1_setwop_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k1_sfmastr1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v1_ami_2 (k1_sfmastr1 A B)) & (m1_subset_1 (k1_sfmastr1 A B) (u1_struct_0 k1_scmfsa_2))) ) ) ).
tt(dt_k1_sfmastr2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_sfmastr2 A B)))  &  ((v1_relat_1 (k1_sfmastr2 A B)) &  ((v4_relat_1 (k1_sfmastr2 A B) k5_numbers) &  ((v5_relat_1 (k1_sfmastr2 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_sfmastr2 A B)) &  ((v1_finset_1 (k1_sfmastr2 A B)) & (v1_afinsq_1 (k1_sfmastr2 A B))) ) ) ) ) ) ) ) ).
tt(dt_k1_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  &  ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 F (u1_struct_0 k1_scmfsa_2))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_sfmastr3 A B C D E F)) &  ((v1_funct_2 (k1_sfmastr3 A B C D E F) k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 (k1_sfmastr3 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) ) ) ) ).
tt(dt_k1_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) => (m1_subset_1 (k1_sf_mastr A) (k5_finsub_1 k2_scmfsa_2))) ) ).
tt(dt_k1_sgraph1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k1_sgraph1 A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k1_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  => (m1_subset_1 (k1_sheffer1 A) (u1_struct_0 A))) ) ).
tt(dt_k1_simplex0,ax, (! [A:$i] : (v1_classes1 (k1_simplex0 A))) ).
tt(dt_k1_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_simplex0 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  => (m1_subset_1 (k1_simplex1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_simplex2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  & (l1_pre_topc B))  => (m1_subset_1 (k1_simplex2 A B) k1_numbers)) ) ).
tt(dt_k1_sincos10,ax, ((v1_funct_1 k1_sincos10) & (m1_subset_1 k1_sincos10 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k1_sin_cos2,ax, ((v1_funct_1 k1_sin_cos2) &  ((v1_funct_2 k1_sin_cos2 k1_numbers k1_numbers) & (m1_subset_1 k1_sin_cos2 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k1_sin_cos3,ax, ((v1_funct_1 k1_sin_cos3) &  ((v1_funct_2 k1_sin_cos3 k2_numbers k2_numbers) & (m1_subset_1 k1_sin_cos3 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k1_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_sin_cos4 A) k1_numbers)) ) ).
tt(dt_k1_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k1_sin_cos5 A) k1_numbers)) ) ).
tt(dt_k1_sin_cos6,ax, ((v1_funct_1 k1_sin_cos6) & (m1_subset_1 k1_sin_cos6 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k1_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k1_sin_cos7 A))) ) ).
tt(dt_k1_sin_cos9,ax, ((v1_funct_1 k1_sin_cos9) & (m1_subset_1 k1_sin_cos9 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k1_sppol_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k1_sppol_2 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k1_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m2_finseq_1 (k1_sprect_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k1_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k1_square_1 A B) k1_numbers)) ) ).
tt(dt_k1_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_2 (k1_stacks_1 A B C) A (k3_finseq_2 A))) ) ).
tt(dt_k1_stirl2_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (m1_subset_1 (k1_stirl2_1 A B C D) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k1_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) => (m1_subset_1 (k1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_valuat_1 A B)) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  => (m2_funct_2 (k1_sublemma A B C D) (k3_qc_lang1 A) B (k2_valuat_1 A B))) ) ).
tt(dt_k1_subset_1,ax, (! [A:$i] : (m1_subset_1 (k1_subset_1 A) (k1_zfmisc_1 A))) ).
tt(dt_k1_substlat,ax, (! [A:$i,B:$i] : (m1_subset_1 (k1_substlat A B) (k1_zfmisc_1 (k5_finsub_1 (k4_partfun1 A B))))) ).
tt(dt_k1_substut1,ax,$true).
tt(dt_k1_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k1_substut1 A))) )  => (m1_subset_1 (k1_substut2 A B C) (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A)))) ) ).
tt(dt_k1_supinf_1,ax,(m1_subset_1 k1_supinf_1 k7_numbers)).
tt(dt_k1_supinf_2,ax,(m1_subset_1 k1_supinf_2 k7_numbers)).
tt(dt_k1_symsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (m1_subset_1 (k1_symsp_1 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k1_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k1_sysrel A))) ) ).
tt(dt_k1_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v1_partfun1 (k1_t_0topsp A) (u1_struct_0 A)) &  ((v3_relat_2 (k1_t_0topsp A)) &  ((v8_relat_2 (k1_t_0topsp A)) & (m1_subset_1 (k1_t_0topsp A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k1_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k1_t_1topsp A)))  &  ((v1_eqrel_1 (k1_t_1topsp A) (u1_struct_0 A)) & (m1_subset_1 (k1_t_1topsp A) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k1_tarski,ax,$true).
tt(dt_k1_taxonom1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  & (v1_xreal_0 C)) )  => (m1_subset_1 (k1_taxonom1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k1_taylor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_funct_1 (k1_taylor_1 A)) &  ((v1_funct_2 (k1_taylor_1 A) k1_numbers k1_numbers) & (m1_subset_1 (k1_taylor_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_taylor_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k1_taylor_2 A B C)) &  ((v1_funct_2 (k1_taylor_2 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k1_taylor_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k1_tbsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k1_tbsp_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (m1_subset_1 (k1_tdgroup A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k1_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k1_tdlat_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_tdlat_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (m1_subset_1 (k1_tdlat_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_termord A B C D)) &  ((v4_relat_1 (k1_termord A B C D) A) &  ((v1_funct_1 (k1_termord A B C D)) &  ((v1_partfun1 (k1_termord A B C D) A) &  ((v4_valued_0 (k1_termord A B C D)) & (v2_pre_poly (k1_termord A B C D))) ) ) ) ) ) ) ).
tt(dt_k1_tex_1,ax, (! [A:$i] : (m1_subset_1 (k1_tex_1 A) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ).
tt(dt_k1_tex_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k1_tex_2 A B)))  &  ((v1_pre_topc (k1_tex_2 A B)) & (m1_pre_topc (k1_tex_2 A B) A)) ) ) ) ).
tt(dt_k1_tex_4,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_tex_4 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_tmap_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  &  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_tmap_1 A B C D E F)) &  ((v1_funct_2 (k1_tmap_1 A B C D E F) (k4_subset_1 A C D) B) & (m1_subset_1 (k1_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k4_subset_1 A C D) B)))) ) ) ) ).
tt(dt_k1_toler_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (m1_subset_1 (k1_toler_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ).
tt(dt_k1_topalg_1,ax,$true).
tt(dt_k1_topalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_topalg_2 A B C D)) &  ((v1_funct_2 (k1_topalg_2 A B C D) (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 B)) & (m1_subset_1 (k1_topalg_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k1_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_borsuk_2 E A C D) &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) )  => (m1_borsuk_2 (k1_topalg_3 A B C D E F) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F D))) ) ).
tt(dt_k1_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  &  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_topalg_4 A B C D E F)) &  ((v1_funct_2 (k1_topalg_4 A B C D E F) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D)))) & (m1_subset_1 (k1_topalg_4 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))))))) ) ) ) ).
tt(dt_k1_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k1_topalg_5 A)) &  ((v1_funct_2 (k1_topalg_5 A) (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 (k1_topalg_5 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2))))) ) ) ) ).
tt(dt_k1_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k1_topalg_6 A) (k1_zfmisc_1 (k4_partfun1 k1_numbers (k2_struct_0 A))))) ) ).
tt(dt_k1_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k1_topdim_1 A)) &  ((v1_funct_2 (k1_topdim_1 A) k5_numbers (k9_setfam_1 (k9_setfam_1 (u1_struct_0 A)))) & (m1_subset_1 (k1_topdim_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k9_setfam_1 (u1_struct_0 A))))))) ) ) ) ).
tt(dt_k1_topdim_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (v1_xxreal_0 (k1_topdim_2 A B))) ) ).
tt(dt_k1_topgen_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (m1_subset_1 (k1_topgen_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_topgen_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_card_1 (k1_topgen_2 A B))) ) ).
tt(dt_k1_topgen_3,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 B)))) => (m1_subset_1 (k1_topgen_3 A B C) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ).
tt(dt_k1_topgen_4,ax, (! [A:$i] :  ((l1_struct_0 A) => (m1_subset_1 (k1_topgen_4 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_topgen_5,ax,(m1_subset_1 k1_topgen_5 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))).
tt(dt_k1_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_topgrp_1 A B)) &  ((v1_funct_2 (k1_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k1_topgrp_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_topmetr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_metric_1 (k1_topmetr A B)) & (m1_topmetr (k1_topmetr A B) A)) ) ) ).
tt(dt_k1_topreal1,ax,(m1_subset_1 k1_topreal1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))).
tt(dt_k1_topreal6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k1_topreal6 A B C) k1_numbers)) ) ).
tt(dt_k1_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_metric_1 B)) )  =>  ((v1_metric_1 (k1_topreal7 A B)) & (l1_metric_1 (k1_topreal7 A B))) ) ) ).
tt(dt_k1_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k1_topreal9 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k1_topreala,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_pre_topc (k1_topreala A B C D) (k15_euclid 2))) ) ).
tt(dt_k1_toprealb,ax,$true).
tt(dt_k1_toprns_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v1_funct_1 (k1_toprns_1 A B C)) &  ((v1_funct_2 (k1_toprns_1 A B C) k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k1_toprns_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k1_tops_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_tops_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_tops_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (m1_subset_1 (k1_tops_2 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))))) ) ).
tt(dt_k1_transgeo,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_funct_1 (k1_transgeo A B C)) &  ((v1_funct_2 (k1_transgeo A B C) A A) &  ((v3_funct_2 (k1_transgeo A B C) A A) & (m1_subset_1 (k1_transgeo A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k1_treal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k1_treal_1 A B) (u1_struct_0 (k4_topmetr A B)))) ) ).
tt(dt_k1_trees_1,ax,$true).
tt(dt_k1_trees_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k1_trees_2 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k1_trees_3,ax,$true).
tt(dt_k1_trees_4,ax, (! [A:$i] :  ((v1_relat_1 (k1_trees_4 A)) &  ((v1_funct_1 (k1_trees_4 A)) & (v3_trees_2 (k1_trees_4 A))) ) ) ).
tt(dt_k1_trees_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  & (m1_subset_1 B A))  =>  ((v2_funct_1 (k1_trees_9 A B)) & (m2_finseq_1 (k1_trees_9 A B) A)) ) ) ).
tt(dt_k1_trees_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  & (m4_trees_1 C A)) )  =>  ( (~ (v1_xboole_0 (k1_trees_a A B C)))  & (v1_trees_1 (k1_trees_a A B C))) ) ) ).
tt(dt_k1_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  => (m1_subset_1 (k1_triang_1 A) (k1_zfmisc_1 (k5_finsub_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ( (~ (v2_struct_0 (k1_tsep_1 A B C)))  &  ((v1_pre_topc (k1_tsep_1 A B C)) & (m1_pre_topc (k1_tsep_1 A B C) A)) ) ) ) ).
tt(dt_k1_tsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) ) )  =>  ((v1_funct_1 (k1_tsp_2 A B)) &  ((v1_funct_2 (k1_tsp_2 A B) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_tsp_2 A B) A B) & (m1_subset_1 (k1_tsp_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k1_twoscomp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msafree2 B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k1_twoscomp A B C D) k6_margrel1)) ) ).
tt(dt_k1_unialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) )  => (m2_finseq_1 (k1_unialg_1 A) k5_numbers)) ) ).
tt(dt_k1_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m4_margrel1 (k1_unialg_2 A) (u1_struct_0 A))) ) ).
tt(dt_k1_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( (~ (v1_xboole_0 (k1_unialg_3 A)))  & (m1_unialg_3 (k1_unialg_3 A) A)) ) ) ).
tt(dt_k1_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_uniroots A)))  &  ((v15_algstr_0 (k1_uniroots A)) &  ((v2_group_1 (k1_uniroots A)) &  ((v3_group_1 (k1_uniroots A)) & (l3_algstr_0 (k1_uniroots A))) ) ) ) ) ) ).
tt(dt_k1_uproots,ax, (! [A:$i] :  ((v1_finset_1 A) => (m2_finseq_1 (k1_uproots A) A)) ) ).
tt(dt_k1_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_urysohn1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  & (m1_subset_1 D k5_numbers)) ) )  => (m1_subset_1 (k1_urysohn3 A B C D) (k4_partfun1 A B))) ) ).
tt(dt_k1_valuat_1,ax,$true).
tt(dt_k1_valued_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C)) )  => (m2_valued_0 (k1_valued_0 A B C) A B)) ) ).
tt(dt_k1_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) & (v1_funct_1 (k1_valued_1 A B))) ) ) ).
tt(dt_k1_valued_2,ax,$true).
tt(dt_k1_vectmetr,ax,$true).
tt(dt_k1_vectsp11,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k1_vectsp11 A B C)) &  ((v1_funct_2 (k1_vectsp11 A B C) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k1_vectsp11 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_vectsp_1,ax, ((v8_algstr_0 k1_vectsp_1) & (l2_algstr_0 k1_vectsp_1)) ).
tt(dt_k1_vectsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_vectsp_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_vectsp_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v7_vectsp_1 (k1_vectsp_4 A B) A) & (m1_vectsp_4 (k1_vectsp_4 A B) A B)) ) ) ).
tt(dt_k1_vectsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_vectsp_4 D A B)) ) )  =>  ((v7_vectsp_1 (k1_vectsp_5 A B C D) A) & (m1_vectsp_4 (k1_vectsp_5 A B C D) A B)) ) ) ).
tt(dt_k1_vectsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  & (m1_vectsp_6 C A B)) )  =>  ((v1_finset_1 (k1_vectsp_6 A B C)) & (m1_subset_1 (k1_vectsp_6 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ).
tt(dt_k1_vectsp_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ((v7_vectsp_1 (k1_vectsp_7 A B C) A) & (m1_vectsp_4 (k1_vectsp_7 A B C) A B)) ) ) ).
tt(dt_k1_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_vectsp_8 A B)))  &  ((v3_lattices (k1_vectsp_8 A B)) &  ((v10_lattices (k1_vectsp_8 A B)) &  ((v15_lattices (k1_vectsp_8 A B)) & (l3_lattices (k1_vectsp_8 A B))) ) ) ) ) ) ).
tt(dt_k1_vectsp_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (v7_ordinal1 (k1_vectsp_9 A B))) ) ).
tt(dt_k1_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k1_vfunct_1 A B C D)) & (m1_subset_1 (k1_vfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k1_vfunct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k1_vfunct_2 A B C D)) & (m1_subset_1 (k1_vfunct_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k1_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  ((v1_funct_1 (k1_waybel_0 A B)) &  ((v1_funct_2 (k1_waybel_0 A B) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k1_waybel_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_waybel10,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v1_orders_2 (k1_waybel10 A B)) &  ((v4_yellow_0 (k1_waybel10 A B) (k7_lattice3 A)) & (m1_yellow_0 (k1_waybel10 A B) (k7_lattice3 A))) ) ) ) ).
tt(dt_k1_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  => (m1_subset_1 (k1_waybel11 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k1_waybel15 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k1_waybel16 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_waybel17,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k1_waybel17 A B C)) &  ((v1_funct_2 (k1_waybel17 A B C) k5_numbers A) & (m1_subset_1 (k1_waybel17 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k1_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k1_waybel19 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k1_waybel_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  => (m1_waybel_1 (k1_waybel_1 A B C D) A B)) ) ).
tt(dt_k1_waybel20,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ((l1_orders_2 C) &  ((l1_orders_2 D) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_waybel20 A B C D E F)) &  ((v1_funct_2 (k1_waybel20 A B C D E F) (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 (k3_yellow_3 C D))) & (m1_subset_1 (k1_waybel20 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 (k3_yellow_3 C D)))))) ) ) ) ).
tt(dt_k1_waybel22,ax, (! [A:$i] : (m1_subset_1 (k1_waybel22 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)))))) ).
tt(dt_k1_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))  => (m1_subset_1 (k1_waybel23 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k1_waybel24 A B C D E)) &  ((v1_funct_2 (k1_waybel24 A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 (k1_waybel24 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k1_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_waybel_9 (k1_waybel25 A)) & (l1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(dt_k1_waybel26,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ( (~ (v2_struct_0 (k1_waybel26 A B)))  &  ((v1_orders_2 (k1_waybel26 A B)) & (l1_orders_2 (k1_waybel26 A B))) ) ) ) ).
tt(dt_k1_waybel27,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k1_waybel27 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k1_waybel28,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel28 A B C)))  &  ((v6_waybel_0 (k1_waybel28 A B C) A) & (l1_waybel_0 (k1_waybel28 A B C) A)) ) ) ) ).
tt(dt_k1_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_waybel_9 (k1_waybel29 A)) &  ((v4_waybel11 (k1_waybel29 A)) & (m1_yellow_9 (k1_waybel29 A) A)) ) ) ) ).
tt(dt_k1_waybel_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (l1_waybel_0 B A))  => (m1_subset_1 (k1_waybel_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_waybel30,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k1_waybel30 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  => (v1_card_1 (k1_waybel31 A))) ) ).
tt(dt_k1_waybel32,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel32 A B C)))  &  ((v6_waybel_0 (k1_waybel32 A B C) A) & (l1_waybel_0 (k1_waybel32 A B C) A)) ) ) ) ).
tt(dt_k1_waybel33,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) ) ) )  => (m1_subset_1 (k1_waybel33 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k1_waybel34 A B C)) &  ((v1_funct_2 (k1_waybel34 A B C) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k1_waybel34 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_waybel_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (m1_subset_1 (k1_waybel_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k1_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m2_pboole D A C (k7_funcop_1 A B)) & (m1_subset_1 E A)) ) ) )  =>  ((v1_funct_1 (k1_waybel_5 A B C D E)) &  ((v1_funct_2 (k1_waybel_5 A B C D E) (k1_funct_1 C E) B) & (m1_subset_1 (k1_waybel_5 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 C E) B)))) ) ) ) ).
tt(dt_k1_waybel_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  & (m1_subset_1 D k5_numbers)) ) )  =>  ((v1_funct_1 (k1_waybel_6 A B C D)) &  ((v1_funct_2 (k1_waybel_6 A B C D) B B) & (m1_subset_1 (k1_waybel_6 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(dt_k1_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k1_waybel_8 A)) &  ((v4_yellow_0 (k1_waybel_8 A) A) & (m1_yellow_0 (k1_waybel_8 A) A)) ) ) ) ).
tt(dt_k1_waybel_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (l1_waybel_0 B A))  => (m1_subset_1 (k1_waybel_9 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v15_algstr_0 (k1_weddwitt A B)) & (m1_group_2 (k1_weddwitt A B) A)) ) ) ).
tt(dt_k1_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) => (m1_subset_1 (k1_weierstr A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k1_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k1_wellfnd1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_wellord1,ax,$true).
tt(dt_k1_wellord2,ax, (! [A:$i] : (v1_relat_1 (k1_wellord2 A))) ).
tt(dt_k1_wsierp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  &  ((m1_finseq_1 C B) & (m1_finseq_1 D B)) ) )  => (m1_trees_4 (k1_wsierp_1 A B C D) A B)) ) ).
tt(dt_k1_xboole_0,ax,$true).
tt(dt_k1_xboolean,ax,$true).
tt(dt_k1_xcmplx_0,ax,$true).
tt(dt_k1_xreal_0,ax,$true).
tt(dt_k1_xtuple_0,ax,$true).
tt(dt_k1_xxreal_0,ax,$true).
tt(dt_k1_xxreal_1,ax,$true).
tt(dt_k1_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) => (v1_xxreal_0 (k1_xxreal_2 A))) ) ).
tt(dt_k1_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k1_xxreal_3 A B))) ) ).
tt(dt_k1_yellow_0,ax, (! [A:$i,B:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k1_yellow_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k1_yellow11,ax,(l1_orders_2 k1_yellow11)).
tt(dt_k1_yellow12,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k1_yellow12 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k1_yellow14,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k1_yellow14 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k1_yellow15,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k9_setfam_1 A)) & (m1_finseq_1 C k6_margrel1))  => (m2_finseq_1 (k1_yellow15 A B C) (k9_setfam_1 A))) ) ).
tt(dt_k1_yellow16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_yellow_1 A B))))) ) )  => (m1_subset_1 (k1_yellow16 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k1_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  ( (~ (v2_struct_0 (k1_yellow18 A)))  &  ((v2_altcat_1 (k1_yellow18 A)) &  ((v6_altcat_1 (k1_yellow18 A)) & (l2_altcat_1 (k1_yellow18 A))) ) ) ) ) ).
tt(dt_k1_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k1_yellow19 A B) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ).
tt(dt_k1_yellow_1,ax, (! [A:$i] :  ((v1_relat_2 (k1_yellow_1 A)) &  ((v4_relat_2 (k1_yellow_1 A)) &  ((v8_relat_2 (k1_yellow_1 A)) &  ((v1_partfun1 (k1_yellow_1 A) A) & (m1_subset_1 (k1_yellow_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k1_yellow20,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k1_yellow20 A B)) & (v1_funct_1 (k1_yellow20 A B))) ) ) ).
tt(dt_k1_yellow21,ax, (! [A:$i] : (l1_struct_0 (k1_yellow21 A))) ).
tt(dt_k1_yellow_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A B C)) &  ((v4_yellow_0 (k1_yellow_2 A B C) B) & (m1_yellow_0 (k1_yellow_2 A B C) B)) ) ) ) ).
tt(dt_k1_yellow_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  => (v1_relat_1 (k1_yellow_3 A B))) ) ).
tt(dt_k1_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k1_yellow_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k1_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k1_yellow_5 A B C) (u1_struct_0 A))) ) ).
tt(dt_k1_yellow_6,ax,$true).
tt(dt_k1_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_funct_1 (k1_yellow_7 A)) &  ((v1_funct_2 (k1_yellow_7 A) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 A))) & (m1_subset_1 (k1_yellow_7 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 A)))))) ) ) ) ).
tt(dt_k1_yellow_8,ax, (! [A:$i] :  ((v1_pre_topc (k1_yellow_8 A)) & (l1_pre_topc (k1_yellow_8 A))) ) ).
tt(dt_k1_yellow_9,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_struct_0 B))  =>  ((v1_funct_1 (k1_yellow_9 A B)) &  ((v1_funct_2 (k1_yellow_9 A B) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k1_yellow_9 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k1_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_yoneda_1 A)))  &  ( (~ (v11_struct_0 (k1_yoneda_1 A)))  &  ((v2_cat_1 (k1_yoneda_1 A)) &  ((v3_cat_1 (k1_yoneda_1 A)) &  ((v4_cat_1 (k1_yoneda_1 A)) &  ((v5_cat_1 (k1_yoneda_1 A)) &  ((v6_cat_1 (k1_yoneda_1 A)) & (l1_cat_1 (k1_yoneda_1 A))) ) ) ) ) ) ) ) ) ).
tt(dt_k1_zf_colla,ax,$true).
tt(dt_k1_zf_fund1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((v1_relat_1 (k1_zf_fund1 A B C)) & (m1_subset_1 (k1_zf_fund1 A B C) A)) ) ) ).
tt(dt_k1_zf_fund2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) ) ) )  => (m1_subset_1 (k1_zf_fund2 A B C) (k1_zfmisc_1 B))) ) ).
tt(dt_k1_zf_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) )  =>  ((v1_funct_1 (k1_zf_lang1 A B C D)) &  ((v1_funct_2 (k1_zf_lang1 A B C D) A C) & (m1_subset_1 (k1_zf_lang1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ).
tt(dt_k1_zf_lang,ax,(m1_subset_1 k1_zf_lang (k1_zfmisc_1 k5_numbers))).
tt(dt_k1_zfmisc_1,ax,$true).
tt(dt_k1_zfmodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) ) ) )  =>  ((v1_funct_1 (k1_zfmodel1 A B C)) &  ((v1_funct_2 (k1_zfmodel1 A B C) B B) & (m1_subset_1 (k1_zfmodel1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(dt_k1_zf_model,ax,$true).
tt(dt_k1_zfrefle1,ax,$true).
tt(dt_k1_zf_refle,ax,$true).
tt(dt_k1_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_zmodul01 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_int_1 C)) )  => (m1_subset_1 (k1_zmodul01 A B C) (u1_struct_0 A))) ) ).
tt(dt_k20_abcmiz_1,ax, (~ (v1_xboole_0 k20_abcmiz_1)) ).
tt(dt_k20_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D C) &  ((m1_subset_1 E (k1_zfmisc_1 C)) & (m1_aofa_000 F A C E)) ) ) ) )  => (m1_subset_1 (k20_aofa_000 A B C D E F) k7_numbers)) ) ).
tt(dt_k20_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (m1_subset_1 (k20_binop_2 A B) k4_numbers)) ) ).
tt(dt_k20_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k20_bvfunc_1 A B) k6_margrel1)) ) ).
tt(dt_k20_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k20_cat_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k20_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_cat_1 (k20_cat_5 A B) (k12_cat_5 A (k4_graph_1 A B)) (k12_cat_5 A (k3_graph_1 A B)))) ) ).
tt(dt_k20_coh_sp,ax,$true).
tt(dt_k20_comput_1,ax, ((v1_relat_1 k20_comput_1) &  ((v1_funct_1 k20_comput_1) &  ((v7_comput_1 k20_comput_1) & (v8_comput_1 k20_comput_1 2)) ) ) ).
tt(dt_k20_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k20_convex4 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k20_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k20_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k20_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k20_dtconstr A B) (k1_zfmisc_1 (k3_finseq_2 (u1_struct_0 A))))) ) ).
tt(dt_k20_ens_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k20_ens_1 A B)) &  ((v1_funct_2 (k20_ens_1 A B) (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 (k20_ens_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k2_ens_1 (k16_ens_1 A)))))) ) ) ) ).
tt(dt_k20_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_1 (k20_euclid A) k1_numbers)) ) ).
tt(dt_k20_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k20_facirc_1 A B C) (k19_facirc_1 A B C)) &  ((v4_msafree2 (k20_facirc_1 A B C) (k19_facirc_1 A B C)) &  ((v4_circcomb (k20_facirc_1 A B C) (k19_facirc_1 A B C)) &  ((v6_circcomb (k20_facirc_1 A B C) (k19_facirc_1 A B C)) & (l3_msualg_1 (k20_facirc_1 A B C) (k19_facirc_1 A B C))) ) ) ) ) ).
tt(dt_k20_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k20_fomodel0 A B C)) &  ((v1_funct_2 (k20_fomodel0 A B C) (k3_finseq_2 A) (k3_finseq_2 A)) & (m1_subset_1 (k20_fomodel0 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A))))) ) ) ) ).
tt(dt_k20_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k20_fomodel1 A)) &  ((v1_funct_2 (k20_fomodel1 A) (k2_zfmisc_1 (k3_finseq_2 (k15_fomodel1 A)) (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A))) & (m1_subset_1 (k20_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k15_fomodel1 A)) (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)))))) ) ) ) ).
tt(dt_k20_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))  &  ((m1_subset_1 D (k16_fomodel2 A B)) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (m1_subset_1 (k20_fomodel2 A B C D E) k6_margrel1)) ) ).
tt(dt_k20_fomodel3,ax,$true).
tt(dt_k20_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k20_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k20_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ((v3_msualg_1 (k20_ftacell1 A B C D E) (k19_ftacell1 A B C D E)) &  ((v4_msafree2 (k20_ftacell1 A B C D E) (k19_ftacell1 A B C D E)) &  ((v4_circcomb (k20_ftacell1 A B C D E) (k19_ftacell1 A B C D E)) &  ((v6_circcomb (k20_ftacell1 A B C D E) (k19_ftacell1 A B C D E)) & (l3_msualg_1 (k20_ftacell1 A B C D E) (k19_ftacell1 A B C D E))) ) ) ) ) ).
tt(dt_k20_gate_1,ax,$true).
tt(dt_k20_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k20_gfacirc1 A B C) (k19_gfacirc1 A B C)) &  ((v4_msafree2 (k20_gfacirc1 A B C) (k19_gfacirc1 A B C)) &  ((v4_circcomb (k20_gfacirc1 A B C) (k19_gfacirc1 A B C)) &  ((v6_circcomb (k20_gfacirc1 A B C) (k19_gfacirc1 A B C)) & (l3_msualg_1 (k20_gfacirc1 A B C) (k19_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k20_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k20_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k20_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (m4_glib_001 (k20_glib_001 A B C D) A B)) ) ).
tt(dt_k20_graphsp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_funct_2 (k20_graphsp A) (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)))) ) ).
tt(dt_k20_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  & (m1_subset_1 B (k18_grcat_1 A)))  =>  ((v8_algstr_0 (k20_grcat_1 A B)) & (m2_grcat_1 (k20_grcat_1 A B) A)) ) ) ).
tt(dt_k20_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v8_group_9 C A B) & (m1_finseq_1 C (k6_group_9 A B))) )  =>  ((v1_relat_1 (k20_group_9 A B C)) &  ((v1_funct_1 (k20_group_9 A B C)) & (v1_finseq_1 (k20_group_9 A B C))) ) ) ) ).
tt(dt_k20_idea_1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k20_idea_1 A B)) &  ((v1_funct_2 (k20_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k20_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k20_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))))  => (m1_subset_1 (k20_lexbfs A B C) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers)))) ) ).
tt(dt_k20_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k20_lpspace1 A B C)))  & (l1_normsp_1 (k20_lpspace1 A B C))) ) ) ).
tt(dt_k20_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  => (m1_matrix_1 (k20_matrixj1 A B C) A (k2_wsierp_1 (k10_matrixj1 A C)) (k2_wsierp_1 (k10_matrixj1 A C)))) ) ).
tt(dt_k20_member_1,ax,$true).
tt(dt_k20_metric_3,ax, ((v1_funct_1 k20_metric_3) &  ((v1_funct_2 k20_metric_3 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 k20_metric_3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers)))) ) ).
tt(dt_k20_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k20_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k20_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) ) )  =>  (~ (v1_xboole_0 (k20_modelc_2 A B))) ) ) ).
tt(dt_k20_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (m1_subset_1 (k20_modelc_3 A B) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k20_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_subset_1 (k20_monoid_1 A B) (u1_struct_0 (k13_monoid_1 A)))) ) ).
tt(dt_k20_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v2_msualg_4 (k20_osafree A B) A (k8_osafree A B)) & (m1_osalg_4 (k20_osafree A B) A (k8_osafree A B))) ) ) ).
tt(dt_k20_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k20_osalg_4 A B C D E)) &  ((v1_funct_2 (k20_osalg_4 A B C D E) (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E)) & (m1_subset_1 (k20_osalg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) E) (k1_funct_1 (u3_msualg_1 A C) E))))) ) ) ) ).
tt(dt_k20_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((v12_pcs_0 (k20_pcs_0 A)) & (l2_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(dt_k20_polyform,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  &  ((v1_int_1 B) & (m1_subset_1 C (u1_struct_0 (k17_polyform A B)))) )  => (m1_subset_1 (k20_polyform A B C) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1))))) ) ).
tt(dt_k20_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  => (m2_finseq_1 (k20_pre_poly A B) (k15_pre_poly A))) ) ).
tt(dt_k20_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k20_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k20_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k20_qc_lang1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k20_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k20_quaterni A) k1_numbers)) ) ).
tt(dt_k20_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k20_quofield A B C) (u1_struct_0 A))) ) ).
tt(dt_k20_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v8_valued_0 (k20_rfunct_3 A B C)) & (m2_finseq_1 (k20_rfunct_3 A B C) k1_numbers)) ) ) ).
tt(dt_k20_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m1_subset_1 (k20_rvsum_1 A) k2_numbers)) ) ).
tt(dt_k20_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C k2_numbers)) )  => (m2_finseq_2 (k20_seq_4 A B C) k2_numbers (k14_seq_4 A))) ) ).
tt(dt_k20_sin_cos,ax,$true).
tt(dt_k20_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k20_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k20_turing_1,ax, ((v1_turing_1 k20_turing_1) & (l1_turing_1 k20_turing_1)) ).
tt(dt_k20_twoscomp,ax, ((v1_funct_1 k20_twoscomp) &  ((v1_funct_2 k20_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k20_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k20_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k20_valued_1 A B C D E)) & (m1_subset_1 (k20_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k20_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_relat_1 (k20_valued_2 A B C)) & (v1_funct_1 (k20_valued_2 A B C))) ) ) ).
tt(dt_k20_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k20_zf_lang A)) & (m2_finseq_1 (k20_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k21_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k4_abcmiz_1 k5_numbers)) => (m2_finseq_2 (k21_abcmiz_1 A) k2_abcmiz_1 k4_abcmiz_1)) ) ).
tt(dt_k21_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 B)) & (m1_aofa_000 D A B C)) ) )  => (m1_subset_1 (k21_aofa_000 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ).
tt(dt_k21_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k9_funct_2 A B)) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k21_aofa_i00 A B C D) B)) ) ).
tt(dt_k21_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (m1_subset_1 (k21_binop_2 A B) k4_numbers)) ) ).
tt(dt_k21_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k21_bvfunc_1 A B) k6_margrel1)) ) ).
tt(dt_k21_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k21_cat_4 A B C) (u4_struct_0 A))) ) ).
tt(dt_k21_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) => (m1_subset_1 (k21_coh_sp A B) (k16_coh_sp A))) ) ).
tt(dt_k21_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_convex4 (k21_convex4 A B) A) & (m1_subset_1 (k21_convex4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k21_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((v1_funct_1 (k21_ens_1 A B C)) &  ((v1_funct_2 (k21_ens_1 A B C) (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C))) & (m1_subset_1 (k21_ens_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C)))))) ) ) ) ).
tt(dt_k21_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_2 (k21_euclid A) k1_numbers (k1_euclid A))) ) ).
tt(dt_k21_fomodel0,ax,$true).
tt(dt_k21_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k21_fomodel1 A)) &  ((v1_funct_2 (k21_fomodel1 A) (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A))) & (m1_subset_1 (k21_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k3_finseq_2 (k15_fomodel1 A)))))) ) ) ) ).
tt(dt_k21_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))) )  =>  ((v1_funct_1 (k21_fomodel2 A B C)) & (m1_subset_1 (k21_fomodel2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)))) ) ) ).
tt(dt_k21_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v2_fomodel3 E A B C D) & (m1_fomodel2 E A B C)) ) ) ) )  => (m2_fomodel2 (k21_fomodel3 A B C D E) A (k8_eqrel_1 B D) C)) ) ).
tt(dt_k21_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))))  => (m2_funct_2 (k21_fomodel4 A B) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k21_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k21_ftacell1 A B C D E) (k3_msafree2 (k19_ftacell1 A B C D E)))) ).
tt(dt_k21_gate_1,ax,$true).
tt(dt_k21_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k21_gfacirc1 A B C) (u1_struct_0 (k19_gfacirc1 A B C)) (k3_msafree2 (k19_gfacirc1 A B C)))) ).
tt(dt_k21_glib_000,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k21_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k21_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  & (m1_subset_1 B A))  =>  ((v1_grcat_1 (k21_grcat_1 A B)) & (m3_grcat_1 (k21_grcat_1 A B) (k18_grcat_1 A))) ) ) ).
tt(dt_k21_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ((v8_group_9 C A B) & (m1_finseq_1 C (k6_group_9 A B)))  &  ((v8_group_9 D A B) & (m1_finseq_1 D (k6_group_9 A B))) ) )  =>  ((v8_group_9 (k21_group_9 A B C D) A B) & (m2_finseq_1 (k21_group_9 A B C D) (k6_group_9 A B))) ) ) ).
tt(dt_k21_idea_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_finseq_1 B k5_numbers))  =>  ((v1_funct_1 (k21_idea_1 A B)) &  ((v1_funct_2 (k21_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k21_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k21_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((v3_lattices (k21_interva1 A)) & (l3_lattices (k21_interva1 A))) ) ) ).
tt(dt_k21_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) &  ((m1_subset_1 C (k6_glib_000 A)) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k21_lexbfs A B C D) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers)))) ) ).
tt(dt_k21_matrixj1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v2_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) )  => (m2_finseq_1 (k21_matrixj1 A B) (u1_struct_0 A))) ) ).
tt(dt_k21_member_1,ax,$true).
tt(dt_k21_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k21_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k21_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  & (m1_subset_1 C k5_numbers)) )  =>  (~ (v1_xboole_0 (k21_modelc_1 A B C))) ) ) ).
tt(dt_k21_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  &  ((v1_modelc_2 C) & (m1_finseq_1 C k5_numbers)) ) )  => (m1_subset_1 (k21_modelc_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k21_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_3 B A) & (l1_modelc_3 B A)) )  => (v7_ordinal1 (k21_modelc_3 A B))) ) ).
tt(dt_k21_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((v1_funct_1 (k21_monoid_1 A B C D)) &  ((v1_funct_2 (k21_monoid_1 A B C D) (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B)) (k1_zfmisc_1 C)) & (m1_subset_1 (k21_monoid_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B)) (k1_zfmisc_1 C))))) ) ) ) ).
tt(dt_k21_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k21_osafree A B C) (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) C)))) ) ).
tt(dt_k21_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  & (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) )  => (m2_pboole (k21_osalg_4 A B C D) (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B (k19_osalg_4 A B C D))) (u3_msualg_1 A C))) ) ).
tt(dt_k21_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (l2_pcs_0 (k21_pcs_0 A B))) ) ).
tt(dt_k21_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ((v1_funct_1 (k21_polyform A B)) &  ((v1_funct_2 (k21_polyform A B) (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) & (m1_subset_1 (k21_polyform A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1))))))) ) ) ) ).
tt(dt_k21_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  => (m2_finseq_1 (k21_pre_poly A B) (k4_finseq_2 2 (k15_pre_poly A)))) ) ).
tt(dt_k21_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k21_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k21_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m2_subset_1 (k21_qc_lang1 A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k21_quaterni,ax,(v1_quaterni k21_quaterni)).
tt(dt_k21_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k21_quofield A B C) (k1_quofield A))) ) ).
tt(dt_k21_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  => (m1_subset_1 (k21_rfunct_3 A B C) k1_numbers)) ) ).
tt(dt_k21_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k21_rvsum_1 A) k1_numbers)) ) ).
tt(dt_k21_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  => (m2_finseq_2 (k21_seq_4 A B) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k21_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k21_sin_cos A) k1_numbers)) ) ).
tt(dt_k21_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k16_substut1 A)) & (m1_subset_1 C (k16_substut1 A))) )  => (m1_subset_1 (k21_substut1 A B C) (k16_substut1 A))) ) ).
tt(dt_k21_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (l1_turing_1 B))  =>  ( (~ (v1_xboole_0 (k21_turing_1 A B)))  & (v1_finset_1 (k21_turing_1 A B))) ) ) ).
tt(dt_k21_twoscomp,ax, ((v1_funct_1 k21_twoscomp) &  ((v1_funct_2 k21_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k21_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k21_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  ((v1_relat_1 (k21_valued_2 A)) & (v1_funct_1 (k21_valued_2 A))) ) ) ).
tt(dt_k21_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k21_zf_lang A)) & (m2_finseq_1 (k21_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k22_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k4_abcmiz_1 k5_numbers)) => (m1_subset_1 (k22_abcmiz_1 A) k5_numbers)) ) ).
tt(dt_k22_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((v1_funct_1 (k22_aofa_i00 A B)) &  ((v1_funct_2 (k22_aofa_i00 A B) (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 (k22_aofa_i00 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) ) ) ) ).
tt(dt_k22_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (m1_subset_1 (k22_binop_2 A B) k4_numbers)) ) ).
tt(dt_k22_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l2_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k22_cat_4 A B C) (u4_struct_0 A))) ) ).
tt(dt_k22_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) => (m1_subset_1 (k22_coh_sp A B) (k16_coh_sp A))) ) ).
tt(dt_k22_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v1_funct_1 (k22_ens_1 A)) &  ((v1_funct_2 (k22_ens_1 A) (u4_struct_0 (k8_cat_2 A A)) (k2_ens_1 (k16_ens_1 A))) & (m1_subset_1 (k22_ens_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k8_cat_2 A A)) (k2_ens_1 (k16_ens_1 A)))))) ) ) ) ).
tt(dt_k22_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k22_euclid A) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k22_fomodel0,ax,$true).
tt(dt_k22_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k22_fomodel1 A)) &  ((v1_funct_2 (k22_fomodel1 A) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A)) & (m1_subset_1 (k22_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A))))) ) ) ) ).
tt(dt_k22_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k22_fomodel2 A B)) &  ((v1_funct_2 (k22_fomodel2 A B) k5_numbers (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1)) & (m1_subset_1 (k22_fomodel2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))))) ) ) ) ).
tt(dt_k22_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) ) ) ) )  =>  ((v1_relat_1 (k22_fomodel3 A B C D)) & (v1_funct_1 (k22_fomodel3 A B C D))) ) ) ).
tt(dt_k22_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k22_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k22_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k22_ftacell1 A B C D E) (k3_msafree2 (k19_ftacell1 A B C D E)))) ).
tt(dt_k22_gate_1,ax,$true).
tt(dt_k22_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k22_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k22_gfacirc1 A B C)))  &  ((v1_msualg_1 (k22_gfacirc1 A B C)) &  ((v1_circcomb (k22_gfacirc1 A B C)) &  ((v2_circcomb (k22_gfacirc1 A B C)) &  ((v3_circcomb (k22_gfacirc1 A B C)) & (l1_msualg_1 (k22_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k22_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k22_glib_000 A B C) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k22_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  ((v1_funct_1 (k22_grcat_1 A)) &  ((v1_funct_2 (k22_grcat_1 A) (k18_grcat_1 A) A) & (m1_subset_1 (k22_grcat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) A)))) ) ) ) ).
tt(dt_k22_idea_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_finseq_1 B k5_numbers))  =>  ((v1_funct_1 (k22_idea_1 A B)) &  ((v1_funct_2 (k22_idea_1 A B) k14_idea_1 k14_idea_1) & (m1_subset_1 (k22_idea_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k14_idea_1 k14_idea_1)))) ) ) ) ).
tt(dt_k22_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  => (m2_interva1 (k22_interva1 A) A)) ) ).
tt(dt_k22_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))))  => (m1_subset_1 (k22_lexbfs A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers)))) ) ).
tt(dt_k22_matrixj1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v2_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) )  => (m2_finseq_2 (k22_matrixj1 A B) (u1_struct_0 A) (k4_finseq_2 (k3_finseq_1 B) (u1_struct_0 A)))) ) ).
tt(dt_k22_member_1,ax,$true).
tt(dt_k22_metric_3,ax, ((v1_funct_1 k22_metric_3) &  ((v1_funct_2 k22_metric_3 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers) & (m1_subset_1 k22_metric_3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) k1_numbers)))) ) ).
tt(dt_k22_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k22_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k22_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k22_modelc_1 A B C)) &  ((v1_funct_2 (k22_modelc_1 A B C) k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 (k22_modelc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_k22_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k22_modelc_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k22_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k22_modelc_3 A))) ) ) ).
tt(dt_k22_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  => (l3_algstr_0 (k22_monoid_1 A))) ) ).
tt(dt_k22_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m3_pboole (k22_osafree A B) (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)))) ) ).
tt(dt_k22_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) &  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_osalg_4 E A B)) )  & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  =>  ((v1_funct_1 (k22_osalg_4 A B C D E F)) &  ((v1_funct_2 (k22_osalg_4 A B C D E F) (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B E)) F) (k1_funct_1 (u3_msualg_1 A C) F)) & (m1_subset_1 (k22_osalg_4 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osalg_4 A B E)) F) (k1_funct_1 (u3_msualg_1 A C) F))))) ) ) ) ).
tt(dt_k22_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (l2_pcs_0 (k22_pcs_0 A B))) ) ).
tt(dt_k22_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  => (m1_vectsp_4 (k22_polyform A B) k2_bspace (k17_polyform A B))) ) ).
tt(dt_k22_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k22_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k22_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k22_qc_lang1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k22_quaterni,ax,(v1_quaterni k22_quaterni)).
tt(dt_k22_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k22_quofield A)) &  ((v1_funct_2 (k22_quofield A) (u1_struct_0 A) (u1_struct_0 (k19_quofield A))) & (m1_subset_1 (k22_quofield A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k19_quofield A)))))) ) ) ) ).
tt(dt_k22_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  => (v1_xreal_0 (k22_rvsum_1 A B))) ) ).
tt(dt_k22_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m1_subset_1 (k22_seq_4 A) k1_numbers)) ) ).
tt(dt_k22_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k22_sin_cos A)) &  ((v1_funct_2 (k22_sin_cos A) k5_numbers k1_numbers) & (m1_subset_1 (k22_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k22_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  => (m1_subset_1 (k22_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k22_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) )  => (m1_subset_1 (k22_turing_1 A B C) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) ) ).
tt(dt_k22_twoscomp,ax, ((v1_funct_1 k22_twoscomp) &  ((v1_funct_2 k22_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k22_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k22_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v5_membered B) &  ((v5_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k22_valued_1 A B C D E)) & (m1_subset_1 (k22_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ).
tt(dt_k22_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k22_valued_2 A B C)) & (m1_subset_1 (k22_valued_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k22_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k22_zf_lang A)) & (m2_finseq_1 (k22_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k23_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) => (m1_subset_1 (k23_abcmiz_1 A) (k1_enumset1 k6_abcmiz_1 k7_abcmiz_1 k8_abcmiz_1))) ) ).
tt(dt_k23_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 A k4_numbers) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) A)))) ) )  =>  ((v1_funct_1 (k23_aofa_i00 A B)) &  ((v1_funct_2 (k23_aofa_i00 A B) (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 (k23_aofa_i00 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) ) ) ) ).
tt(dt_k23_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k23_binop_2 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k23_cat_4,ax, (! [A:$i,B:$i] :  ((v5_cat_4 (k23_cat_4 A B)) & (l2_cat_4 (k23_cat_4 A B))) ) ).
tt(dt_k23_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) => (m1_subset_1 (k23_coh_sp A B) (k20_coh_sp A))) ) ).
tt(dt_k23_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (m2_cat_1 (k23_ens_1 A B C) B (k11_ens_1 A))) ) ).
tt(dt_k23_fomodel0,ax,$true).
tt(dt_k23_fomodel1,ax,$true).
tt(dt_k23_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  (~ (v1_xboole_0 C)) ) )  => (m2_rfunct_3 (k23_fomodel2 A B C) (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) k6_margrel1))) ) ).
tt(dt_k23_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_fomodel2 D A B) & (v3_fomodel3 D A B C)) ) ) ) ) )  => (m2_subset_1 (k23_fomodel3 A B C D) (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 (k8_eqrel_1 B C)) (k2_xboole_0 (k8_eqrel_1 B C) k6_margrel1))) (k16_fomodel2 A (k8_eqrel_1 B C)))) ) ).
tt(dt_k23_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k23_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k23_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k23_ftacell1 A B C D E) (k3_msafree2 (k19_ftacell1 A B C D E)))) ).
tt(dt_k23_gate_1,ax,$true).
tt(dt_k23_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k23_gfacirc1 A B C) (k22_gfacirc1 A B C)) &  ((v4_msafree2 (k23_gfacirc1 A B C) (k22_gfacirc1 A B C)) &  ((v4_circcomb (k23_gfacirc1 A B C) (k22_gfacirc1 A B C)) &  ((v6_circcomb (k23_gfacirc1 A B C) (k22_gfacirc1 A B C)) & (l3_msualg_1 (k23_gfacirc1 A B C) (k22_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k23_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k23_glib_000 A B C) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k23_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  ((v1_funct_1 (k23_grcat_1 A)) &  ((v1_funct_2 (k23_grcat_1 A) (k18_grcat_1 A) A) & (m1_subset_1 (k23_grcat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) A)))) ) ) ) ).
tt(dt_k23_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  => (m2_interva1 (k23_interva1 A) A)) ) ).
tt(dt_k23_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_lexbfs B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k23_lexbfs A B C) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers)))) ) ).
tt(dt_k23_matrixj1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_finseq_1 B k5_numbers))  =>  ((v2_matrixj1 (k23_matrixj1 A B) (u1_struct_0 A)) & (m2_finseq_1 (k23_matrixj1 A B) (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(dt_k23_member_1,ax,$true).
tt(dt_k23_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k23_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k23_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) ) )  =>  (~ (v1_xboole_0 (k23_modelc_1 A B))) ) ) ).
tt(dt_k23_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k23_modelc_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k23_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k23_modelc_3 A))) ) ) ).
tt(dt_k23_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ( (~ (v2_struct_0 (k23_monoid_1 A)))  &  ((v22_algstr_0 (k23_monoid_1 A)) &  ((v4_vectsp_1 (k23_monoid_1 A)) & (l4_algstr_0 (k23_monoid_1 A))) ) ) ) ) ).
tt(dt_k23_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k23_osafree A B C) (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A (k16_osafree A B)) C)))) ) ).
tt(dt_k23_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) &  ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_osalg_4 E A B)) ) ) ) ) )  => (m2_pboole (k23_osalg_4 A B C D E) (u1_struct_0 A) (u3_msualg_1 A (k16_osalg_4 A B E)) (u3_msualg_1 A C))) ) ).
tt(dt_k23_pcs_0,ax, (! [A:$i,B:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k23_pcs_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ).
tt(dt_k23_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ( (~ (v1_xboole_0 (k23_polyform A B)))  & (m1_subset_1 (k23_polyform A B) (k1_zfmisc_1 (k18_polyform A B)))) ) ) ).
tt(dt_k23_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k23_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k23_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k2_qc_lang1 A)))  => (m1_subset_1 (k23_qc_lang1 A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k23_quaterni,ax,$true).
tt(dt_k23_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  => (m1_subset_1 (k23_rvsum_1 A B) k1_numbers)) ) ).
tt(dt_k23_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k23_seq_4 A B C) (k1_zfmisc_1 (k14_seq_4 A)))) ) ).
tt(dt_k23_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k23_sin_cos A)) &  ((v1_funct_2 (k23_sin_cos A) k5_numbers k1_numbers) & (m1_subset_1 (k23_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k23_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  => (m2_subset_1 (k23_substut1 A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k23_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) )  => (m1_subset_1 (k23_turing_1 A B C) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) ) ).
tt(dt_k23_twoscomp,ax, ((v1_funct_1 k23_twoscomp) &  ((v1_funct_2 k23_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k23_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k23_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (m2_subset_1 (k23_zf_lang A) k5_numbers k1_zf_lang)) ) ).
tt(dt_k24_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) => (m1_subset_1 (k24_abcmiz_1 A) (k2_zfmisc_1 k4_abcmiz_1 k5_numbers))) ) ).
tt(dt_k24_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((v1_funct_1 (k24_aofa_i00 A B)) &  ((v1_funct_2 (k24_aofa_i00 A B) (k9_funct_2 A k4_numbers) A) & (m1_subset_1 (k24_aofa_i00 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) A)))) ) ) ) ).
tt(dt_k24_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k24_binop_2 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k24_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k24_cat_4 A B) A (k19_cat_4 A) B)) ) ).
tt(dt_k24_coh_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k20_coh_sp A)) & (m1_subset_1 C (k20_coh_sp A)))  => (m1_subset_1 (k24_coh_sp A B C) (k20_coh_sp A))) ) ).
tt(dt_k24_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (m1_oppcat_1 (k24_ens_1 A B C) B (k11_ens_1 A))) ) ).
tt(dt_k24_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  => (m2_subset_1 (k24_fomodel1 A B C) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k24_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v7_ordinal1 C) & (m1_subset_1 D (k16_fomodel2 A B))) ) )  => (m2_rfunct_3 (k24_fomodel2 A B C D) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) k6_margrel1 (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)) k6_margrel1))) ) ).
tt(dt_k24_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 C (k1_fomodel1 A)) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m2_subset_1 (k24_fomodel3 A B C D) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k24_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k24_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k24_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k24_ftacell1 A B C D E) (k3_msafree2 (k19_ftacell1 A B C D E)))) ).
tt(dt_k24_gate_1,ax,$true).
tt(dt_k24_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k24_gfacirc1 A B C) (u1_struct_0 (k22_gfacirc1 A B C)) (k3_msafree2 (k22_gfacirc1 A B C)))) ).
tt(dt_k24_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_glib_000 B A))  =>  ( (~ (v1_xboole_0 (k24_glib_000 A B)))  & (m1_subset_1 (k24_glib_000 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ).
tt(dt_k24_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  ((v1_funct_1 (k24_grcat_1 A)) & (m1_subset_1 (k24_grcat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k18_grcat_1 A) (k18_grcat_1 A)) (k18_grcat_1 A))))) ) ) ).
tt(dt_k24_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  & (m1_finseq_1 C (u1_struct_0 A))) )  =>  ((v1_matrixj1 (k24_matrixj1 A B C) (u1_struct_0 A)) & (m2_finseq_1 (k24_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(dt_k24_member_1,ax,$true).
tt(dt_k24_mmlquery,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v7_ordinal1 (k24_mmlquery A B))) ) ).
tt(dt_k24_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  &  ((v1_modelc_1 C) & (m1_finseq_1 C k5_numbers)) ) )  => (m1_subset_1 (k24_modelc_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k24_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k24_modelc_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k24_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((m1_orders_1 B (k1_orders_1 (k1_modelc_3 A))) &  ((v1_modelc_3 C A) & (l1_modelc_3 C A)) ) )  =>  ((v1_modelc_2 (k24_modelc_3 A B C)) & (m2_finseq_1 (k24_modelc_3 A B C) k5_numbers)) ) ) ).
tt(dt_k24_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m1_osafree (k24_osafree A B) A (k16_osafree A B))) ) ).
tt(dt_k24_pcs_0,ax, (! [A:$i,B:$i] :  ((l1_pcs_0 A) => (m1_subset_1 (k24_pcs_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ).
tt(dt_k24_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  => (m1_vectsp_4 (k24_polyform A B) k2_bspace (k17_polyform A B))) ) ).
tt(dt_k24_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k24_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k24_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k24_qc_lang1 A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k24_quaterni,ax,$true).
tt(dt_k24_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A)))) )  => (m1_subset_1 (k24_seq_4 A B C) k1_numbers)) ) ).
tt(dt_k24_sin_cos,ax, ((v1_funct_1 k24_sin_cos) &  ((v1_funct_2 k24_sin_cos k1_numbers k1_numbers) & (m1_subset_1 k24_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k24_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) & (m1_substut1 C A B)) )  => (m1_subset_1 (k24_substut1 A B C) (k16_substut1 A))) ) ).
tt(dt_k24_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k21_turing_1 A B))) )  => (m1_subset_1 (k24_turing_1 A B C) (u2_turing_1 A))) ) ).
tt(dt_k24_twoscomp,ax, ((v1_funct_1 k24_twoscomp) &  ((v1_funct_2 k24_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k24_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k24_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) & (v1_funct_1 (k24_valued_1 A B))) ) ) ).
tt(dt_k24_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k24_zf_lang A)) & (m2_finseq_1 (k24_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k25_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) => (m2_finseq_2 (k25_abcmiz_1 A) k2_abcmiz_1 k4_abcmiz_1)) ) ).
tt(dt_k25_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 B))  =>  ((v1_funct_1 (k25_aofa_i00 A B)) &  ((v1_funct_2 (k25_aofa_i00 A B) (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 (k25_aofa_i00 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) ) ) ) ).
tt(dt_k25_binop_2,ax, ((v1_funct_1 k25_binop_2) &  ((v1_funct_2 k25_binop_2 k2_numbers k2_numbers) & (m1_subset_1 k25_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k25_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k25_cat_4 A B C) A B (k20_cat_4 A B C))) ) ).
tt(dt_k25_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k25_coh_sp A)) &  ((v1_funct_2 (k25_coh_sp A) (k20_coh_sp A) (k16_coh_sp A)) & (m1_subset_1 (k25_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k16_coh_sp A))))) ) ) ).
tt(dt_k25_descip_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_finseq_2 64 k6_margrel1)) => (m2_finseq_2 (k25_descip_1 A) k6_margrel1 (k4_finseq_2 64 k6_margrel1))) ) ).
tt(dt_k25_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (m2_cat_1 (k25_ens_1 A B) (k8_cat_2 (k2_oppcat_1 B) B) (k11_ens_1 A))) ) ).
tt(dt_k25_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_relat_1 (k25_fomodel1 A)) & (v1_funct_1 (k25_fomodel1 A))) ) ) ).
tt(dt_k25_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  => (m1_subset_1 (k25_fomodel2 A B) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k25_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m2_subset_1 (k25_fomodel3 A B C) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k25_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k25_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k25_gate_1,ax,$true).
tt(dt_k25_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k25_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k25_gfacirc1 A B C)))  &  ((v1_msualg_1 (k25_gfacirc1 A B C)) &  ((v1_circcomb (k25_gfacirc1 A B C)) &  ((v2_circcomb (k25_gfacirc1 A B C)) &  ((v3_circcomb (k25_gfacirc1 A B C)) & (l1_msualg_1 (k25_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k25_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_glib_000 B A))  => (m1_subset_1 (k25_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k25_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v2_struct_0 (k25_grcat_1 A)))  &  ( (~ (v11_struct_0 (k25_grcat_1 A)))  &  ((v1_cat_1 (k25_grcat_1 A)) & (l1_cat_1 (k25_grcat_1 A))) ) ) ) ) ).
tt(dt_k25_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m3_lexbfs B A))  => (m1_lexbfs (k25_lexbfs A B) A)) ) ).
tt(dt_k25_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  &  ((v1_matrixj1 C (u1_struct_0 A)) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) )  =>  ((v1_matrixj1 (k25_matrixj1 A B C) (u1_struct_0 A)) & (m2_finseq_1 (k25_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(dt_k25_member_1,ax,$true).
tt(dt_k25_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v7_ordinal1 (k25_mmlquery A))) ) ).
tt(dt_k25_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k25_modelc_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k25_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k25_modelc_2 A))) ) ) ).
tt(dt_k25_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) &  ( ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers))  &  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) &  ((v1_modelc_3 D B) & (l1_modelc_3 D B)) ) ) )  =>  ((v1_modelc_3 (k25_modelc_3 A B C D) B) & (l1_modelc_3 (k25_modelc_3 A B C D) B)) ) ) ).
tt(dt_k25_osafree,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  & (m1_subset_1 D (k4_dtconstr (k2_osafree A B)))) ) )  => (m1_subset_1 (k25_osafree A B C D) (k6_osalg_4 A (k8_osafree A B) C (k10_osafree A B D)))) ) ).
tt(dt_k25_pcs_0,ax, (! [A:$i,B:$i] :  ((l2_pcs_0 A) => (l2_pcs_0 (k25_pcs_0 A B))) ) ).
tt(dt_k25_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ( (~ (v1_xboole_0 (k25_polyform A B)))  & (m1_subset_1 (k25_polyform A B) (k1_zfmisc_1 (k18_polyform A B)))) ) ) ).
tt(dt_k25_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k25_pscomp_1 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k25_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_qc_lang1 A)))) )  => (m1_subset_1 (k25_qc_lang1 A B) (k1_qc_lang1 A))) ) ).
tt(dt_k25_quaterni,ax,$true).
tt(dt_k25_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k25_seq_4 A B C) (k1_zfmisc_1 (k14_seq_4 A)))) ) ).
tt(dt_k25_sin_cos,ax,$true).
tt(dt_k25_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k16_substut1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  => (m1_subset_1 (k25_substut1 A B C) (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A)))) ) ).
tt(dt_k25_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k21_turing_1 A B))) )  => (m1_subset_1 (k25_turing_1 A B C) (u2_turing_1 B))) ) ).
tt(dt_k25_twoscomp,ax, ((v1_funct_1 k25_twoscomp) &  ((v1_funct_2 k25_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k25_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k25_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k25_valued_1 A B C D)) & (m1_subset_1 (k25_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k25_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  ((v1_relat_1 (k25_valued_2 A)) & (v1_funct_1 (k25_valued_2 A))) ) ) ).
tt(dt_k25_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k25_zf_lang A)) & (m2_finseq_1 (k25_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k26_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) => (v7_ordinal1 (k26_abcmiz_1 A))) ) ).
tt(dt_k26_aofa_i00,ax, ( (~ (v1_finset_1 k26_aofa_i00))  & (v1_freealg k26_aofa_i00)) ).
tt(dt_k26_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k26_cat_4 A B C) A C (k20_cat_4 A B C))) ) ).
tt(dt_k26_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k26_coh_sp A)) &  ((v1_funct_2 (k26_coh_sp A) (k20_coh_sp A) (k16_coh_sp A)) & (m1_subset_1 (k26_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k16_coh_sp A))))) ) ) ).
tt(dt_k26_descip_1,ax, ((v1_funct_1 k26_descip_1) &  ((v1_funct_2 k26_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 k26_descip_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) ) ).
tt(dt_k26_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k26_fomodel1 A) (k1_zfmisc_1 (k3_finseq_2 (k15_fomodel1 A))))) ) ).
tt(dt_k26_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (m1_subset_1 (k26_fomodel2 A B C D) k6_margrel1)) ) ).
tt(dt_k26_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((v1_relat_1 (k26_fomodel3 A B C D)) &  ((v1_funct_1 (k26_fomodel3 A B C D)) & (v1_finseq_1 (k26_fomodel3 A B C D))) ) ) ) ).
tt(dt_k26_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k26_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k26_gate_1,ax,$true).
tt(dt_k26_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k26_gfacirc1 A B C) (k25_gfacirc1 A B C)) &  ((v4_msafree2 (k26_gfacirc1 A B C) (k25_gfacirc1 A B C)) &  ((v4_circcomb (k26_gfacirc1 A B C) (k25_gfacirc1 A B C)) &  ((v6_circcomb (k26_gfacirc1 A B C) (k25_gfacirc1 A B C)) & (l3_msualg_1 (k26_gfacirc1 A B C) (k25_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k26_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k26_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k26_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (m1_subset_1 (k26_grcat_1 A) (k1_zfmisc_1 (u1_struct_0 (k25_grcat_1 A))))) ) ).
tt(dt_k26_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (m3_lexbfs (k26_lexbfs A) A)) ) ).
tt(dt_k26_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  &  ((v1_matrixj1 C (u1_struct_0 A)) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) )  =>  ((v1_matrixj1 (k26_matrixj1 A B C) (u1_struct_0 A)) & (m2_finseq_1 (k26_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(dt_k26_member_1,ax,$true).
tt(dt_k26_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k9_setfam_1 A)) & (v7_ordinal1 C))  => (m1_subset_1 (k26_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k26_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k26_modelc_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k26_modelc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) )  => (m1_subset_1 (k26_modelc_2 A B) (k25_modelc_2 A))) ) ).
tt(dt_k26_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) &  ( ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers))  & (m1_orders_1 C (k1_orders_1 (k1_modelc_3 B)))) )  =>  ((v1_funct_1 (k26_modelc_3 A B C)) &  ((v1_funct_2 (k26_modelc_3 A B C) (k22_modelc_3 B) (k22_modelc_3 B)) & (m1_subset_1 (k26_modelc_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 B) (k22_modelc_3 B))))) ) ) ) ).
tt(dt_k26_osafree,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  &  ((m2_pboole D (u1_struct_0 A) (k22_osafree A B) C) & (m1_subset_1 E (u1_struct_0 (k2_osafree A B)))) ) ) )  => (m1_subset_1 (k26_osafree A B C D E) (k3_card_3 C))) ) ).
tt(dt_k26_pcs_0,ax,$true).
tt(dt_k26_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k26_qc_lang1 A) (k1_qc_lang1 A))) ) ).
tt(dt_k26_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (m1_subset_1 (k26_quaterni A B) k1_quaterni)) ) ).
tt(dt_k26_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) & (m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A)))) )  => (m1_subset_1 (k26_seq_4 A B C) k1_numbers)) ) ).
tt(dt_k26_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k26_sin_cos A) k1_numbers)) ) ).
tt(dt_k26_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m2_finseq_1 (k26_substut1 A B) (k2_qc_lang1 A))) ) ).
tt(dt_k26_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))))) )  => (m1_subset_1 (k26_turing_1 A B C) (u2_turing_1 A))) ) ).
tt(dt_k26_twoscomp,ax, ((v1_funct_1 k26_twoscomp) &  ((v1_funct_2 k26_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k26_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k26_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k26_valued_1 A B C D)) & (m1_subset_1 (k26_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k26_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k26_valued_2 A B C)) & (m1_subset_1 (k26_valued_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k26_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k26_zf_lang A)) & (m2_finseq_1 (k26_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k27_abcmiz_1,ax, ((v1_msualg_1 k27_abcmiz_1) &  ((v1_instalg1 k27_abcmiz_1) &  ((v1_abcmiz_1 k27_abcmiz_1) & (l1_msualg_1 k27_abcmiz_1)) ) ) ).
tt(dt_k27_binop_2,ax, ((v1_funct_1 k27_binop_2) &  ((v1_funct_2 k27_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 k27_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) ) ).
tt(dt_k27_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k27_cat_4 A B C) A B (k20_cat_4 A B C))) ) ).
tt(dt_k27_coh_sp,ax, (! [A:$i] :  ((v1_funct_1 (k27_coh_sp A)) & (m1_subset_1 (k27_coh_sp A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k20_coh_sp A) (k20_coh_sp A)) (k20_coh_sp A))))) ) ).
tt(dt_k27_descip_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_finseq_2 64 k6_margrel1)) => (m2_finseq_2 (k27_descip_1 A) k6_margrel1 (k4_finseq_2 64 k6_margrel1))) ) ).
tt(dt_k27_fomodel1,ax,$true).
tt(dt_k27_fomodel2,ax,$true).
tt(dt_k27_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (m2_subset_1 (k27_fomodel3 A B C D) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k27_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k27_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k27_gate_1,ax,$true).
tt(dt_k27_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k27_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k27_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (m3_cat_2 (k27_grcat_1 A) (k25_grcat_1 A))) ) ).
tt(dt_k27_member_1,ax,$true).
tt(dt_k27_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B (k9_setfam_1 A)) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m1_subset_1 (k27_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k27_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k27_modelc_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k27_modelc_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k27_modelc_2 A B)) &  ((v1_funct_2 (k27_modelc_2 A B) k5_numbers A) & (m1_subset_1 (k27_modelc_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k27_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  &  ((v1_modelc_3 B A) & (l1_modelc_3 B A)) )  => (m1_subset_1 (k27_modelc_3 A B) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k27_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_qc_lang1 A)))  =>  ( (~ (v1_xboole_0 (k27_qc_lang1 A B)))  & (m1_subset_1 (k27_qc_lang1 A B) (k1_zfmisc_1 (k1_qc_lang1 A)))) ) ) ).
tt(dt_k27_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (m1_subset_1 (k27_quaterni A B) k1_quaterni)) ) ).
tt(dt_k27_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k27_seq_4 A) (k1_zfmisc_1 (k1_zfmisc_1 (k14_seq_4 A))))) ) ).
tt(dt_k27_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_funct_1 (k27_sin_cos A)) &  ((v1_funct_2 (k27_sin_cos A) k5_numbers k2_numbers) & (m1_subset_1 (k27_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k27_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k27_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k27_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))))) )  => (m1_subset_1 (k27_turing_1 A B C) (u2_turing_1 B))) ) ).
tt(dt_k27_twoscomp,ax, ((v1_funct_1 k27_twoscomp) &  ((v1_funct_2 k27_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k27_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k27_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k27_zf_lang A)) & (m2_finseq_1 (k27_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k28_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v1_relat_1 (k28_abcmiz_1 A)) &  ((v4_relat_1 (k28_abcmiz_1 A) (u1_struct_0 A)) &  ((v1_funct_1 (k28_abcmiz_1 A)) & (v1_partfun1 (k28_abcmiz_1 A) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_k28_binop_2,ax, ((v1_funct_1 k28_binop_2) &  ((v1_funct_2 k28_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 k28_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) ) ).
tt(dt_k28_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k28_cat_4 A B C) A C (k20_cat_4 A B C))) ) ).
tt(dt_k28_coh_sp,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k28_coh_sp A)))  &  ( (~ (v11_struct_0 (k28_coh_sp A)))  &  ((v1_cat_1 (k28_coh_sp A)) & (l1_cat_1 (k28_coh_sp A))) ) ) ) ).
tt(dt_k28_descip_1,ax, ((v1_funct_1 k28_descip_1) &  ((v1_funct_2 k28_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 k28_descip_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) ) ).
tt(dt_k28_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k28_fomodel1 A)) &  ((v1_funct_2 (k28_fomodel1 A) k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 A)))) & (m1_subset_1 (k28_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 A))))))) ) ) ) ).
tt(dt_k28_fomodel2,ax,$true).
tt(dt_k28_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v7_ordinal1 D) &  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_pre_poly E)) )  &  ((v4_fomodel2 F A) & (m1_subset_1 F (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) )  =>  ((v1_relat_1 (k28_fomodel3 A B C D E F)) &  ((v1_funct_1 (k28_fomodel3 A B C D E F)) & (v1_finseq_1 (k28_fomodel3 A B C D E F))) ) ) ) ).
tt(dt_k28_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k28_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k28_gate_1,ax,$true).
tt(dt_k28_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k28_glib_000 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k28_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (m1_subset_1 (k28_grcat_1 A) (k1_zfmisc_1 (u1_struct_0 (k27_grcat_1 A))))) ) ).
tt(dt_k28_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k28_modelc_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k28_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 C))  => (m1_subset_1 (k28_modelc_2 A B C) (k25_modelc_2 A))) ) ).
tt(dt_k28_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  &  ((v1_modelc_3 B A) & (l1_modelc_3 B A)) )  => (m1_subset_1 (k28_modelc_3 A B) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k28_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_finseq_1 (k28_polyform A) k4_numbers)) ) ).
tt(dt_k28_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_qc_lang1 A)))  => (m1_subset_1 (k28_qc_lang1 A B) (k1_qc_lang1 A))) ) ).
tt(dt_k28_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k28_quaterni A) k1_quaterni)) ) ).
tt(dt_k28_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v5_valued_0 (k28_seq_4 A)) & (m2_finseq_1 (k28_seq_4 A) k1_numbers)) ) ) ).
tt(dt_k28_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k28_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k28_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_xboole_0 B C)))) ) )  => (m1_subset_1 (k28_turing_1 A B C D) B)) ) ).
tt(dt_k28_twoscomp,ax, ((v1_funct_1 k28_twoscomp) &  ((v1_funct_2 k28_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k28_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k28_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_zf_lang (k28_zf_lang A)) & (m2_finseq_1 (k28_zf_lang A) k5_numbers)) ) ) ).
tt(dt_k29_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A))) )  => (m1_subset_1 (k29_abcmiz_1 A B) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ).
tt(dt_k29_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (v1_int_1 F)) ) ) ) )  => (m3_aofa_i00 (k29_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k29_binop_2,ax, ((v1_funct_1 k29_binop_2) &  ((v1_funct_2 k29_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 k29_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) ) ).
tt(dt_k29_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_cat_1 E A B D) & (m1_cat_1 F A C D)) ) ) ) )  => (m1_cat_1 (k29_cat_4 A B C D E F) A (k20_cat_4 A B C) D)) ) ).
tt(dt_k29_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ( (~ (v1_xboole_0 (k29_fomodel1 A)))  & (m1_subset_1 (k29_fomodel1 A) (k1_zfmisc_1 (k3_finseq_2 (k15_fomodel1 A))))) ) ) ).
tt(dt_k29_fomodel2,ax,$true).
tt(dt_k29_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v7_ordinal1 D) &  ((m1_subset_1 E (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) &  ((v4_fomodel2 F A) & (m1_subset_1 F (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) )  =>  ((v4_fomodel2 (k29_fomodel3 A B C D E F) A) & (m2_subset_1 (k29_fomodel3 A B C D E F) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ).
tt(dt_k29_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k29_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k29_gate_1,ax,$true).
tt(dt_k29_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k29_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k29_gfacirc1 A B C)))  &  ((v1_msualg_1 (k29_gfacirc1 A B C)) &  ((v1_circcomb (k29_gfacirc1 A B C)) &  ((v2_circcomb (k29_gfacirc1 A B C)) &  ((v3_circcomb (k29_gfacirc1 A B C)) & (l1_msualg_1 (k29_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k29_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k29_glib_000 A B C) (k6_glib_000 A))) ) ).
tt(dt_k29_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (m3_cat_2 (k29_grcat_1 A) (k27_grcat_1 A))) ) ).
tt(dt_k29_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  => (m1_subset_1 (k29_mmlquery A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k29_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C))  =>  ((v1_funct_1 (k29_modelc_1 A B C)) &  ((v1_funct_2 (k29_modelc_1 A B C) A A) & (m1_subset_1 (k29_modelc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(dt_k29_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k25_modelc_2 A)) & (v7_ordinal1 C)) )  => (m1_subset_1 (k29_modelc_2 A B C) (k25_modelc_2 A))) ) ).
tt(dt_k29_modelc_3,ax,$true).
tt(dt_k29_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_funct_1 (k29_osafree A B)) &  ((v1_funct_2 (k29_osafree A B) (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B))) & (m1_subset_1 (k29_osafree A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)))))) ) ) ) ).
tt(dt_k29_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_finseq_1 (k29_polyform A) k4_numbers)) ) ).
tt(dt_k29_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (m1_subset_1 (k29_quaterni A B) k1_quaterni)) ) ).
tt(dt_k29_sin_cos,ax, ((v1_funct_1 k29_sin_cos) & (m1_subset_1 k29_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k29_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k29_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k29_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_xboole_0 B C)))) ) )  => (m1_subset_1 (k29_turing_1 A B C D) C)) ) ).
tt(dt_k29_twoscomp,ax, ((v1_funct_1 k29_twoscomp) &  ((v1_funct_2 k29_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k29_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k29_zf_lang,ax,$true).
tt(dt_k2_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ((l2_abcmiz_0 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_abcmiz_0 A B) (k1_zfmisc_1 (u1_abcmiz_0 A)))) ) ).
tt(dt_k2_abcmiz_1,ax,$true).
tt(dt_k2_abian,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_partfun1 (k2_abian A B) A) &  ((v3_relat_2 (k2_abian A B)) &  ((v8_relat_2 (k2_abian A B)) & (m1_subset_1 (k2_abian A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k2_absvalue,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k2_absvalue A) k1_numbers)) ) ).
tt(dt_k2_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_aff_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_aff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_aff_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  => (m1_subset_1 (k2_afinsq_1 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k2_afinsq_2 A B)) &  ((v1_funct_1 (k2_afinsq_2 A B)) &  ((v5_ordinal1 (k2_afinsq_2 A B)) & (v1_finset_1 (k2_afinsq_2 A B))) ) ) ) ) ).
tt(dt_k2_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (m1_subset_1 (k2_afproj A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_afvect0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k2_afvect0 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k2_alg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ((m1_alg_1 B A) & (m1_subset_1 C (k1_unialg_2 A))) )  =>  ( (~ (v1_xboole_0 (k2_alg_1 A B C)))  &  ((v1_funct_1 (k2_alg_1 A B C)) &  ((v2_margrel1 (k2_alg_1 A B C)) &  ((v3_margrel1 (k2_alg_1 A B C) (k8_eqrel_1 (u1_struct_0 A) B)) & (m1_subset_1 (k2_alg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))))) ) ) ) ) ) ).
tt(dt_k2_algseq_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k2_algseq_1 A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_algspec1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  =>  ( (~ (v2_struct_0 (k2_algspec1 A B C)))  &  ( (~ (v11_struct_0 (k2_algspec1 A B C)))  &  ((v1_msualg_1 (k2_algspec1 A B C)) & (l1_msualg_1 (k2_algspec1 A B C))) ) ) ) ) ).
tt(dt_k2_algstr_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v3_algstr_1 A) & (l2_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_algstr_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_algstr_3,ax, ((v1_funct_1 k2_algstr_3) &  ((v1_funct_2 k2_algstr_3 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k2_algstr_3 (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k2_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k8_afinsq_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) A)))) )  &  ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) )  => (m1_subset_1 (k2_algstr_4 A B C) A)) ) ).
tt(dt_k2_altcat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  ((v1_relat_1 (k2_altcat_1 A B)) &  ((v4_relat_1 (k2_altcat_1 A B) (k3_zfmisc_1 A A A)) &  ((v1_funct_1 (k2_altcat_1 A B)) & (v1_partfun1 (k2_altcat_1 A B) (k3_zfmisc_1 A A A))) ) ) ) ) ).
tt(dt_k2_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  ((v1_relat_1 (k2_altcat_2 A)) &  ((v4_relat_1 (k2_altcat_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ((v1_funct_1 (k2_altcat_2 A)) & (v1_partfun1 (k2_altcat_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k2_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_altcat_4 A)))  &  ((v2_altcat_1 (k2_altcat_4 A)) &  ((v6_altcat_1 (k2_altcat_4 A)) & (m1_altcat_2 (k2_altcat_4 A) A)) ) ) ) ) ).
tt(dt_k2_ami_2,ax,(m1_subset_1 k2_ami_2 (k1_zfmisc_1 k1_ami_2))).
tt(dt_k2_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k2_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k2_ami_4,ax, ((v1_funct_1 k2_ami_4) & (m1_subset_1 k2_ami_4 (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 2 k1_ami_3) (k11_memstr_0 2 k1_ami_3))))) ).
tt(dt_k2_amistd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  & (m1_subset_1 C (u1_compos_1 B))) )  => (m1_subset_1 (k2_amistd_1 A B C) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_amistd_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  & (v1_finset_1 C)) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_amistd_3 A B C)) &  ((v5_relat_1 (k2_amistd_3 A B C) k5_numbers) &  ((v1_funct_1 (k2_amistd_3 A B C)) & (v3_trees_2 (k2_amistd_3 A B C))) ) ) ) ) ).
tt(dt_k2_amistd_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_extpro_1 B A)) )  & (m1_subset_1 C (u1_compos_1 B))) )  => (m1_subset_1 (k2_amistd_4 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k2_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  & (v7_ordinal1 C)) )  => (v7_ordinal1 (k2_ami_wstd A B C))) ) ).
tt(dt_k2_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_analmetr (k2_analmetr A B C)) & (l1_analmetr (k2_analmetr A B C))) ) ) ).
tt(dt_k2_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_analoaf (k2_analoaf A)) & (l1_analoaf (k2_analoaf A))) ) ) ).
tt(dt_k2_analort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k2_analort A B C D) (u1_struct_0 A))) ) ).
tt(dt_k2_anproj_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_anproj_1 A B) (k1_zfmisc_1 (k8_struct_0 A)))) ) ).
tt(dt_k2_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k2_aofa_000 A B C)) & (v1_funct_1 (k2_aofa_000 A B C))) ) ) ).
tt(dt_k2_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k2_aofa_i00 A B)) &  ((v5_relat_1 (k2_aofa_i00 A B) k4_numbers) & (v1_funct_1 (k2_aofa_i00 A B))) ) ) ) ).
tt(dt_k2_armstrng,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k2_armstrng A) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_arrow,ax,$true).
tt(dt_k2_arytm_0,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k2_arytm_0 A B) k1_numbers)) ) ).
tt(dt_k2_arytm_1,ax,$true).
tt(dt_k2_arytm_2,ax,$true).
tt(dt_k2_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (m1_subset_1 (k2_arytm_3 A B) k4_ordinal1)) ) ).
tt(dt_k2_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v2_xxreal_0 B) & (m1_subset_1 B k1_numbers)) )  =>  ((v1_funct_1 (k2_asympt_0 A B)) &  ((v1_funct_2 (k2_asympt_0 A B) k5_numbers k1_numbers) &  ((v2_asympt_0 (k2_asympt_0 A B)) & (m1_subset_1 (k2_asympt_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ).
tt(dt_k2_asympt_1,ax, ((v1_funct_1 k2_asympt_1) &  ((v1_funct_2 k2_asympt_1 k5_numbers k1_numbers) & (m1_subset_1 k2_asympt_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(dt_k2_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_funct_1 (k2_autalg_1 A)) &  ((v1_funct_2 (k2_autalg_1 A) (k2_zfmisc_1 (k1_autalg_1 A) (k1_autalg_1 A)) (k1_autalg_1 A)) & (m1_subset_1 (k2_autalg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_autalg_1 A) (k1_autalg_1 A)) (k1_autalg_1 A))))) ) ) ) ).
tt(dt_k2_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v1_funct_1 (k2_autgroup A)) &  ((v1_funct_2 (k2_autgroup A) (k2_zfmisc_1 (k1_autgroup A) (k1_autgroup A)) (k1_autgroup A)) & (m1_subset_1 (k2_autgroup A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_autgroup A) (k1_autgroup A)) (k1_autgroup A))))) ) ) ) ).
tt(dt_k2_bcialg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_bcialg_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k2_bcialg_2 A B)))  & (m1_subset_1 (k2_bcialg_2 A B) k5_numbers)) ) ) ).
tt(dt_k2_bcialg_4,ax,(l1_bcialg_4 k2_bcialg_4)).
tt(dt_k2_bcialg_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v1_xxreal_0 (k2_bcialg_5 A B C D))) ) ).
tt(dt_k2_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ((v1_funct_1 (k2_bcialg_6 A)) &  ((v1_funct_2 (k2_bcialg_6 A) (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 (k2_bcialg_6 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_bhsp_1 A B C) k1_numbers)) ) ).
tt(dt_k2_bhsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k2_bhsp_2 A B)) &  ((v1_funct_2 (k2_bhsp_2 A B) k5_numbers k1_numbers) & (m1_subset_1 (k2_bhsp_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_bhsp_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k2_bhsp_4 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_bhsp_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_bhsp_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k2_bilinear A B C D E)) &  ((v1_funct_2 (k2_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k2_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_binari_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1)) )  =>  ((v3_card_1 (k2_binari_2 A B) A) & (m2_finseq_1 (k2_binari_2 A B) k6_margrel1)) ) ) ).
tt(dt_k2_binari_4,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_int_1 B))  =>  ((v3_card_1 (k2_binari_4 A B) A) & (m2_finseq_1 (k2_binari_4 A B) k6_margrel1)) ) ) ).
tt(dt_k2_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  => (m1_subset_1 (k2_binarith A B) k6_margrel1)) ) ).
tt(dt_k2_binom,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v7_ordinal1 C)) )  => (m1_subset_1 (k2_binom A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F B)) ) ) )  => (m1_subset_1 (k2_binop_1 A B C D E F) C)) ) ).
tt(dt_k2_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k2_binop_2 A) k2_numbers)) ) ).
tt(dt_k2_bintree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  &  ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  => (m2_finseq_1 (k2_bintree2 A B) (k2_trees_2 A B))) ) ).
tt(dt_k2_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_boolealg A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_boolmark,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  &  ((m1_subset_1 B (k1_boolmark A)) & (m1_subset_1 C (u4_struct_0 A))) )  => (m2_funct_2 (k2_boolmark A B C) (u1_struct_0 A) k6_margrel1 (k1_boolmark A))) ) ).
tt(dt_k2_bor_cant,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k2_bor_cant A)) &  ((v1_funct_2 (k2_bor_cant A) k5_numbers k1_numbers) & (m1_subset_1 (k2_bor_cant A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (l1_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(dt_k2_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_borsuk_2 D A B C)) ) )  => (m1_borsuk_2 (k2_borsuk_2 A B C D) A C B)) ) ).
tt(dt_k2_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k2_borsuk_5 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k2_borsuk_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E k5_topmetr k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) ) ) ) ) )  => (m1_borsuk_2 (k2_borsuk_6 A B C D E) A B C)) ) ).
tt(dt_k2_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) & (v1_xreal_0 B))  => (m1_subset_1 (k2_borsuk_7 A B) (u1_struct_0 k3_topmetr))) ) ).
tt(dt_k2_brouwer,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_pre_topc (k2_brouwer A B C) (k15_euclid A))) ) ).
tt(dt_k2_bspace,ax, ( (~ (v2_struct_0 k2_bspace))  &  ( (~ (v6_struct_0 k2_bspace))  &  ((v13_algstr_0 k2_bspace) &  ((v33_algstr_0 k2_bspace) &  ((v3_group_1 k2_bspace) &  ((v5_group_1 k2_bspace) &  ((v4_vectsp_1 k2_bspace) &  ((v5_vectsp_1 k2_bspace) &  ((v2_rlvect_1 k2_bspace) &  ((v3_rlvect_1 k2_bspace) &  ((v4_rlvect_1 k2_bspace) & (l6_algstr_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k2_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k2_bvfunc_1 A B C)) &  ((v1_funct_2 (k2_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k2_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k2_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k2_bvfunc26 A B)) & (v1_funct_1 (k2_bvfunc26 A B))) ) ) ).
tt(dt_k2_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))))  => (m1_eqrel_1 (k2_bvfunc_2 A B) A)) ) ).
tt(dt_k2_c0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k2_c0sp1 A B)) &  ((v1_funct_2 (k2_c0sp1 A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k2_c0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k2_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_subset_1 (k2_c0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))))) ) ).
tt(dt_k2_calcul_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k2_calcul_1 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k2_calcul_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k2_calcul_2 A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_cantor_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k2_cantor_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k2_card_1,ax, (! [A:$i] : (v1_card_1 (k2_card_1 A))) ).
tt(dt_k2_card_2,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  => (v1_card_1 (k2_card_2 A B))) ) ).
tt(dt_k2_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_card_3 A)) & (v1_funct_1 (k2_card_3 A))) ) ) ).
tt(dt_k2_card_5,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  =>  ((v1_relat_1 (k2_card_5 A B)) &  ((v1_funct_1 (k2_card_5 A B)) & (v1_card_3 (k2_card_5 A B))) ) ) ) ).
tt(dt_k2_card_fil,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_card_fil B A) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ( (~ (v1_xboole_0 (k2_card_fil A B C)))  & (m1_subset_1 (k2_card_fil A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k2_cardfin2,ax,$true).
tt(dt_k2_card_fin,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  => (m1_subset_1 (k2_card_fin A B C) (k1_zfmisc_1 (k3_tarski (k10_xtuple_0 A))))) ) ).
tt(dt_k2_card_lar,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 A)))  => (m1_subset_1 (k2_card_lar A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_cat_1 A B C) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k2_cat_2,ax,$true).
tt(dt_k2_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) )  =>  ((v1_funct_1 (k2_cat_3 A B C)) &  ((v1_funct_2 (k2_cat_3 A B C) B (u1_struct_0 A)) & (m1_subset_1 (k2_cat_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_cat_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_5 A) & (l1_cat_1 A)) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k2_cat_5 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_catalan2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k2_catalan2 A B) (k1_zfmisc_1 (k8_afinsq_1 (k7_domain_1 k5_numbers k6_numbers 1))))) ) ).
tt(dt_k2_catalg_1,ax, (! [A:$i] :  ((v1_msualg_1 (k2_catalg_1 A)) & (l1_msualg_1 (k2_catalg_1 A))) ) ).
tt(dt_k2_cayley,ax, (! [A:$i] :  ((v15_algstr_0 (k2_cayley A)) &  ((v1_monoid_0 (k2_cayley A)) & (l3_algstr_0 (k2_cayley A))) ) ) ).
tt(dt_k2_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k2_cc0sp1 A)))  & (m1_subset_1 (k2_cc0sp1 A) (k1_zfmisc_1 (u1_struct_0 (k8_cfuncdom A))))) ) ) ).
tt(dt_k2_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_subset_1 (k2_cc0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))))) ) ).
tt(dt_k2_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  & (v1_xcmplx_0 B))  => (m1_subset_1 (k2_cfdiff_1 A B) k2_numbers)) ) ).
tt(dt_k2_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k2_cfuncdom A)) &  ((v1_funct_2 (k2_cfuncdom A) (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 (k2_cfuncdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k2_numbers) (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) ) ) ) ).
tt(dt_k2_cfunct_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_funct_1 (k2_cfunct_1 A B)) & (m1_subset_1 (k2_cfunct_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k2_cgames_1,ax,$true).
tt(dt_k2_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C (k2_finseq_1 A))) )  =>  ( (~ (v1_zfmisc_1 (k2_chain_1 A B C)))  &  ((v1_finset_1 (k2_chain_1 A B C)) & (m1_subset_1 (k2_chain_1 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(dt_k2_chord,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k2_chord A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k2_circcmb3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (k4_card_3 (u3_msualg_1 A B)))) )  => (m1_subset_1 (k2_circcmb3 A B C) k5_numbers)) ) ).
tt(dt_k2_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v1_msualg_1 (k2_circcomb A B)) & (l1_msualg_1 (k2_circcomb A B))) ) ) ) ).
tt(dt_k2_circled1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_rltopsp1 (k2_circled1 A B) A) & (m1_subset_1 (k2_circled1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k2_circtrm1,ax,$true).
tt(dt_k2_circuit1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) & (m1_subset_1 D k5_numbers)) ) )  => (m1_msafree2 (k2_circuit1 A B C D) A B)) ) ).
tt(dt_k2_circuit2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_msafree2 C A B)) )  => (m2_pboole (k2_circuit2 A B C) (u1_struct_0 A) (k13_msafree A (u3_msualg_1 A B)) (u3_msualg_1 A (k5_msafree2 A B)))) ) ).
tt(dt_k2_classes1,ax,$true).
tt(dt_k2_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k2_classes2 A B) A)) ) ).
tt(dt_k2_clopban1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k2_clopban1 A B)) &  ((v1_funct_2 (k2_clopban1 A B) (k2_zfmisc_1 k2_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 (k2_clopban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k2_clopban2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k8_clopban1 A A)) & (m1_subset_1 C (k8_clopban1 A A))) )  => (m2_subset_1 (k2_clopban2 A B C) (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A))) ) ).
tt(dt_k2_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k2_clopban3 A B C)) &  ((v1_funct_2 (k2_clopban3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_clopban3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_clopban4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k2_clopban4 A B C D)) &  ((v1_funct_2 (k2_clopban4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k2_clopban4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) & (m1_pboole D A (k5_mssubfam A B))) )  => (m1_pboole (k2_closure1 A B C D) A (k5_mssubfam A B))) ) ).
tt(dt_k2_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (m1_subset_1 (k2_closure2 A B) (k1_zfmisc_1 (k1_closure2 A B)))) ) ).
tt(dt_k2_closure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))))  => (m3_pboole (k2_closure3 A B C) A B)) ) ).
tt(dt_k2_clvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k2_clvect_2 A B)) &  ((v1_funct_2 (k2_clvect_2 A B) k5_numbers k1_numbers) & (m1_subset_1 (k2_clvect_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_clvect_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k2_clvect_3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_cohsp_1,ax, (! [A:$i] : (m1_subset_1 (k2_cohsp_1 A) (k1_zfmisc_1 A))) ).
tt(dt_k2_coh_sp,ax, (! [A:$i,B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (~ (v1_xboole_0 (k2_coh_sp A B)))  &  ((v1_classes1 (k2_coh_sp A B)) & (v1_coh_sp (k2_coh_sp A B))) ) ) ) ).
tt(dt_k2_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ((l1_combgras C A B) & (m1_subset_1 D (u1_incsp_1 A))) ) )  => (m1_subset_1 (k2_combgras A B C D) (u1_incsp_1 B))) ) ).
tt(dt_k2_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) & (m2_cat_1 E B C)) ) ) )  =>  ( (~ (v1_xboole_0 (k2_commacat A B C D E)))  & (m1_subset_1 (k2_commacat A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)))))) ) ) ).
tt(dt_k2_complex1,ax,$true).
tt(dt_k2_complex2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k2_complex2 A B) k2_numbers)) ) ).
tt(dt_k2_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) => (m1_subset_1 (k2_complfld A) (u1_struct_0 k1_complfld))) ) ).
tt(dt_k2_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  => (m2_finseq_2 (k2_complsp2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k2_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k2_compl_sp A B C)) &  ((v1_funct_2 (k2_compl_sp A B C) (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) k1_numbers) & (m1_subset_1 (k2_compl_sp A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B))) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) k1_numbers)))) ) ) ) ).
tt(dt_k2_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k2_compos_0 A B) (k1_compos_0 A))) ) ).
tt(dt_k2_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) => (m1_subset_1 (k2_compos_1 A) (u1_compos_1 A))) ) ).
tt(dt_k2_compos_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_amistd_4 A) & (l1_compos_1 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  &  ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A))) ) )  =>  ( (~ (v1_xboole_0 (k2_compos_2 A B C)))  &  ((v1_relat_1 (k2_compos_2 A B C)) &  ((v4_relat_1 (k2_compos_2 A B C) k5_numbers) &  ((v5_relat_1 (k2_compos_2 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k2_compos_2 A B C)) &  ((v1_finset_1 (k2_compos_2 A B C)) &  ((v1_afinsq_1 (k2_compos_2 A B C)) &  ((v3_compos_1 (k2_compos_2 A B C) A) & (v4_compos_1 (k2_compos_2 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(dt_k2_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k2_comput_1 A)))  & (m1_rfunct_3 (k2_comput_1 A) (k3_finseq_2 A) A)) ) ).
tt(dt_k2_comseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((v1_funct_1 (k2_comseq_2 A B)) &  ((v1_funct_2 (k2_comseq_2 A B) A k2_numbers) & (m1_subset_1 (k2_comseq_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ) ).
tt(dt_k2_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v7_ordinal1 B))  => (m1_subset_1 (k2_comseq_3 A B) k2_numbers)) ) ).
tt(dt_k2_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k2_conlat_1 A)) &  ((v1_funct_2 (k2_conlat_1 A) (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k2_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k2_conlat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A)))))  =>  ( (~ (v5_conlat_1 (k2_conlat_2 A B) A))  &  ((v7_conlat_1 (k2_conlat_2 A B) A) & (l2_conlat_1 (k2_conlat_2 A B) A)) ) ) ) ).
tt(dt_k2_connsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_connsp_3 A B C) (u1_struct_0 (k1_pre_topc A B)))) ) ).
tt(dt_k2_convex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_convex1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (m1_convex4 (k2_convex4 A) A)) ) ).
tt(dt_k2_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  =>  ((v1_funct_1 (k2_convfun1 A B)) &  ((v1_funct_2 (k2_convfun1 A B) (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 (k2_convfun1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k2_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k5_qc_lang1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((v1_funct_1 (k2_cqc_lang A B C)) & (m1_subset_1 (k2_cqc_lang A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A))))) ) ) ).
tt(dt_k2_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_cqc_lang A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_cqc_lang A))))) ) ) )  => (m2_funct_2 (k2_cqc_sim1 A B C) B (k3_cqc_lang A) (k9_funct_2 B (k3_cqc_lang A)))) ) ).
tt(dt_k2_cqc_the1,ax,$true).
tt(dt_k2_csspace3,ax, ((v1_funct_1 k2_csspace3) &  ((v1_funct_2 k2_csspace3 k1_csspace3 k1_numbers) & (m1_subset_1 k2_csspace3 (k1_zfmisc_1 (k2_zfmisc_1 k1_csspace3 k1_numbers)))) ) ).
tt(dt_k2_csspace4,ax, ((v1_funct_1 k2_csspace4) &  ((v1_funct_2 k2_csspace4 k1_csspace4 k1_numbers) & (m1_subset_1 k2_csspace4 (k1_zfmisc_1 (k2_zfmisc_1 k1_csspace4 k1_numbers)))) ) ).
tt(dt_k2_csspace,ax, (! [A:$i] :  ((v1_funct_1 (k2_csspace A)) &  ((v1_funct_2 (k2_csspace A) k5_numbers k2_numbers) & (m1_subset_1 (k2_csspace A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ).
tt(dt_k2_decomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_decomp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k2_descip_1 A B C) A)) ) ).
tt(dt_k2_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k2_dickson A) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) (k1_dickson A)) (k8_eqrel_1 (u1_struct_0 A) (k1_dickson A)))))) ) ).
tt(dt_k2_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k2_diff_1 A B)) &  ((v1_funct_2 (k2_diff_1 A B) k1_numbers k1_numbers) & (m1_subset_1 (k2_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_diff_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) &  ((v1_xreal_0 E) &  ((v1_xreal_0 F) & (v1_xreal_0 G)) ) ) ) ) )  => (m1_subset_1 (k2_diff_2 A B C D E F G) k1_numbers)) ) ).
tt(dt_k2_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  => (v7_ordinal1 (k2_dilworth A))) ) ).
tt(dt_k2_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ((v1_analoaf (k2_diraf A)) & (l1_analoaf (k2_diraf A))) ) ) ).
tt(dt_k2_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  => (v7_ordinal1 (k2_dist_1 A B C))) ) ).
tt(dt_k2_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  => (m1_subset_1 (k2_domain_1 A B C) A)) ) ).
tt(dt_k2_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 C (k2_zfmisc_1 A B)) => (m2_finseq_1 (k2_dtconstr A B C) A)) ) ).
tt(dt_k2_dynkin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((v1_funct_1 (k2_dynkin A B C)) &  ((v1_funct_2 (k2_dynkin A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k2_dynkin A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k2_ec_pf_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  & (m1_subset_1 B (u1_struct_0 (k9_int_3 A))))  => (v1_int_1 (k2_ec_pf_1 A B))) ) ).
tt(dt_k2_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  & (m1_subset_1 B (k1_ec_pf_2 A)))  => (m1_subset_1 (k2_ec_pf_2 A B) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k2_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_funct_1 (k2_endalg A)) &  ((v1_funct_2 (k2_endalg A) (k2_zfmisc_1 (k1_endalg A) (k1_endalg A)) (k1_endalg A)) & (m1_subset_1 (k2_endalg A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_endalg A) (k1_endalg A)) (k1_endalg A))))) ) ) ) ).
tt(dt_k2_ens_1,ax,$true).
tt(dt_k2_entropy1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A))) )  => (m2_finseq_1 (k2_entropy1 A B) A)) ) ).
tt(dt_k2_enumset1,ax,$true).
tt(dt_k2_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k2_eqrel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k2_equation,ax,$true).
tt(dt_k2_e_siec,ax, (! [A:$i] :  ((v1_e_siec (k2_e_siec A)) &  ((v2_e_siec (k2_e_siec A)) &  ((v3_e_siec (k2_e_siec A)) & (l1_e_siec (k2_e_siec A))) ) ) ) ).
tt(dt_k2_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k2_euclid_3 A) k2_numbers)) ) ).
tt(dt_k2_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  => (m1_subset_1 (k2_euclid_4 A B C) (k1_zfmisc_1 (k1_euclid A)))) ) ).
tt(dt_k2_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) => (m1_subset_1 (k2_euclid_5 A) k1_numbers)) ) ).
tt(dt_k2_euclid_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (v1_xreal_0 (k2_euclid_6 A B C))) ) ).
tt(dt_k2_euclid_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) ) )  => (m2_finseq_1 (k2_euclid_7 A B C) A)) ) ).
tt(dt_k2_euclid_8,ax,(m2_finseq_2 k2_euclid_8 k1_numbers (k1_euclid 3))).
tt(dt_k2_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k14_euclid A))))  => (m1_subset_1 (k2_euclid_9 A B) (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) ) ).
tt(dt_k2_euclid,ax, ((v1_funct_1 k2_euclid) &  ((v1_funct_2 k2_euclid k1_numbers k1_numbers) & (m1_subset_1 k2_euclid (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k2_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclidlp A))) )  => (m1_subset_1 (k2_euclidlp A B C) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k2_euler_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  => (m1_trees_4 (k2_euler_2 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k2_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_ordinal1 (k2_exchsort A))) ) ).
tt(dt_k2_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ((v2_memstr_0 B A) & (l1_extpro_1 B A))  &  ((m1_subset_1 C (u1_compos_1 B)) &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_extpro_1 A B C D)) &  ((v4_relat_1 (k2_extpro_1 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k2_extpro_1 A B C D)) &  ((v5_funct_1 (k2_extpro_1 A B C D) (k2_memstr_0 A B)) & (v1_partfun1 (k2_extpro_1 A B C D) (u1_struct_0 B))) ) ) ) ) ) ).
tt(dt_k2_extreal1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k2_extreal1 A B) k7_numbers)) ) ).
tt(dt_k2_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k2_extreal2 A B) k7_numbers)) ) ).
tt(dt_k2_facirc_1,ax, ((v1_funct_1 k2_facirc_1) &  ((v1_funct_2 k2_facirc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k2_facirc_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k2_facirc_2,ax, (! [A:$i] :  ((v3_msualg_1 (k2_facirc_2 A) (k1_facirc_2 A)) &  ((v6_circcomb (k2_facirc_2 A) (k1_facirc_2 A)) & (l3_msualg_1 (k2_facirc_2 A) (k1_facirc_2 A))) ) ) ).
tt(dt_k2_fdiff_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_funct_1 (k2_fdiff_1 A B)) & (m1_subset_1 (k2_fdiff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k2_fdiff_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (m1_subset_1 (k2_fdiff_3 A B) k1_numbers)) ) ).
tt(dt_k2_fdiff_9,ax, ((v1_funct_1 k2_fdiff_9) & (m1_subset_1 k2_fdiff_9 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k2_ff_siec,ax, (! [A:$i] :  ((v1_petri (k2_ff_siec A)) &  ((v1_net_1 (k2_ff_siec A)) & (l1_petri (k2_ff_siec A))) ) ) ).
tt(dt_k2_fib_fusc,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k2_fib_fusc A) k5_numbers)) ) ).
tt(dt_k2_fib_num2,ax, ((v1_funct_1 k2_fib_num2) &  ((v1_funct_2 k2_fib_num2 k5_numbers k5_numbers) & (m1_subset_1 k2_fib_num2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ).
tt(dt_k2_fib_num3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k2_fib_num3 A B) (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))) ) ).
tt(dt_k2_fib_num,ax,(v1_xreal_0 k2_fib_num)).
tt(dt_k2_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k2_filter_0 A B)))  &  ((v19_lattices (k2_filter_0 A B) A) &  ((v20_lattices (k2_filter_0 A B) A) & (m1_subset_1 (k2_filter_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k2_filter_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_funct_1 (k2_filter_1 A B C)) &  ((v1_funct_2 (k2_filter_1 A B C) (k8_eqrel_1 A B) (k8_eqrel_1 A B)) & (m1_subset_1 (k2_filter_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B))))) ) ) ) ).
tt(dt_k2_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 (k1_lattice2 A))))  => (m1_subset_1 (k2_filter_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_finance1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_funct_1 (k2_finance1 A B)) &  ((v1_funct_2 (k2_finance1 A B) k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 (k2_finance1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) ) ) ) ).
tt(dt_k2_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k2_finseq_1 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_finseq_2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) & (v1_finseq_1 (k2_finseq_2 A B))) ) ) ) ).
tt(dt_k2_finseq_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k2_finseq_3 A B)) &  ((v1_funct_1 (k2_finseq_3 A B)) & (v1_finseq_1 (k2_finseq_3 A B))) ) ) ) ).
tt(dt_k2_finseq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k2_finseq_4 A B C) A)) ) ).
tt(dt_k2_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k2_finseq_5 A B C) A)) ) ).
tt(dt_k2_finseq_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k2_finseq_6 A B C)) &  ((v1_funct_1 (k2_finseq_6 A B C)) & (v1_finseq_1 (k2_finseq_6 A B C))) ) ) ) ).
tt(dt_k2_finseq_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (m2_finseq_1 (k2_finseq_7 A B C D) A)) ) ).
tt(dt_k2_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k2_finseq_8 A B C)) &  ((v1_funct_1 (k2_finseq_8 A B C)) & (v1_finseq_1 (k2_finseq_8 A B C))) ) ) ) ).
tt(dt_k2_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_finseq_1 E A) & (m1_subset_1 F B)) ) ) ) )  => (m2_finseq_1 (k2_finseqop A B C D E F) C)) ) ).
tt(dt_k2_finsop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (m1_finseq_1 C A)) )  =>  ((v1_funct_1 (k2_finsop_1 A B C)) &  ((v1_funct_2 (k2_finsop_1 A B C) k5_numbers A) & (m1_subset_1 (k2_finsop_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k2_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k2_finsub_1 A B C) A)) ) ).
tt(dt_k2_fintopo2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k2_fintopo2 A B C D) k6_margrel1)) ) ).
tt(dt_k2_fintopo3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k2_fintopo3 A B)) &  ((v1_funct_2 (k2_fintopo3 A B) k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 (k2_fintopo3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k2_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k2_fintopo4 A)))  & (l1_orders_2 (k2_fintopo4 A))) ) ) ).
tt(dt_k2_fintopo5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k2_fintopo5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)))))) ) ).
tt(dt_k2_flang_1,ax, (! [A:$i] : (m1_subset_1 (k2_flang_1 A) (k3_catalan2 A))) ).
tt(dt_k2_flang_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) => (m1_subset_1 (k2_flang_2 A B) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k2_flang_3,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) => (m1_subset_1 (k2_flang_3 A B) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k2_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (~ (v1_xboole_0 (k2_fomodel0 A B)))  & (m1_subset_1 (k2_fomodel0 A B) (k1_zfmisc_1 (k3_finseq_2 A)))) ) ) ).
tt(dt_k2_fomodel1,ax,$true).
tt(dt_k2_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k2_fomodel2 A)) &  ((v1_funct_2 (k2_fomodel2 A) (k4_finseq_2 2 A) k6_margrel1) & (m1_subset_1 (k2_fomodel2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 A) k6_margrel1)))) ) ) ) ).
tt(dt_k2_fomodel3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_fomodel1 A)))  =>  ((v1_funct_1 (k2_fomodel3 A B)) &  ((v1_funct_2 (k2_fomodel3 A B) (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) & (m1_subset_1 (k2_fomodel3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_fomodel0 (k3_finseq_2 (k1_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))))) ) ) ) ).
tt(dt_k2_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  => (m2_funct_2 (k2_fomodel4 A B) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k2_frechet2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k2_frechet2 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_frechet,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k2_frechet A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_freealg,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k2_freealg A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k4_finseq_1 A) B) (k3_finseq_2 (k2_xboole_0 (k4_finseq_1 A) B)))))) ) ).
tt(dt_k2_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k2_fscirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v4_msafree2 (k2_fscirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v4_circcomb (k2_fscirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) &  ((v6_circcomb (k2_fscirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1)) & (l3_msualg_1 (k2_fscirc_1 A B C) (k8_facirc_1 A B C k1_facirc_1))) ) ) ) ) ).
tt(dt_k2_fscirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v3_msualg_1 (k2_fscirc_2 A B C) (k1_fscirc_2 A B C)) &  ((v4_msafree2 (k2_fscirc_2 A B C) (k1_fscirc_2 A B C)) &  ((v4_circcomb (k2_fscirc_2 A B C) (k1_fscirc_2 A B C)) &  ((v6_circcomb (k2_fscirc_2 A B C) (k1_fscirc_2 A B C)) & (l3_msualg_1 (k2_fscirc_2 A B C) (k1_fscirc_2 A B C))) ) ) ) ) ) ).
tt(dt_k2_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_finseq_1 D A)) ) )  => (m2_finseq_1 (k2_fsm_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k2_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  &  ((v1_fsm_2 C A) &  ((v5_fsm_2 C A) & (l2_fsm_2 C A B)) ) )  & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k2_fsm_2 A B C D) B)) ) ).
tt(dt_k2_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B)) ) )  =>  ((v1_fsm_3 (k2_fsm_3 A B C) A (k9_flang_1 A)) & (l1_fsm_3 (k2_fsm_3 A B C) A (k9_flang_1 A))) ) ) ).
tt(dt_k2_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ((v3_msualg_1 (k2_ftacell1 A B C D E) (k1_ftacell1 A B C D E)) &  ((v4_msafree2 (k2_ftacell1 A B C D E) (k1_ftacell1 A B C D E)) &  ((v4_circcomb (k2_ftacell1 A B C D E) (k1_ftacell1 A B C D E)) &  ((v6_circcomb (k2_ftacell1 A B C D E) (k1_ftacell1 A B C D E)) & (l3_msualg_1 (k2_ftacell1 A B C D E) (k1_ftacell1 A B C D E))) ) ) ) ) ).
tt(dt_k2_funcop_1,ax,$true).
tt(dt_k2_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C D) (k9_funct_2 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C D) (k9_funct_2 A B))))) )  & (m1_subset_1 F (k2_zfmisc_1 C D))) ) ) ) )  => (m2_funct_2 (k2_funcsdom A B C D E F) A B (k9_funct_2 A B))) ) ).
tt(dt_k2_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_funct_1 A)) & (v1_funct_1 (k2_funct_1 A))) ) ) ).
tt(dt_k2_funct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v1_funct_1 (k2_funct_2 A B)) &  ((v1_funct_2 (k2_funct_2 A B) A A) &  ((v3_funct_2 (k2_funct_2 A B) A A) & (m1_subset_1 (k2_funct_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k2_funct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k2_funct_3 A B C)) &  ((v1_funct_2 (k2_funct_3 A B C) (k1_zfmisc_1 A) (k1_zfmisc_1 B)) & (m1_subset_1 (k2_funct_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B))))) ) ) ) ).
tt(dt_k2_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_funct_4 A)) & (v1_funct_1 (k2_funct_4 A))) ) ) ).
tt(dt_k2_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_funct_5 A)) & (v1_funct_1 (k2_funct_5 A))) ) ) ).
tt(dt_k2_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_funct_6 A)) & (v1_funct_1 (k2_funct_6 A))) ) ) ).
tt(dt_k2_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k2_funct_7 A B C)) & (v1_funct_1 (k2_funct_7 A B C))) ) ) ).
tt(dt_k2_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((m2_functor0 C A B) &  ((m2_functor0 D A B) &  ((m1_functor2 E A B C D) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k2_functor2 A B C D E F) (k1_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B D F)))) ) ).
tt(dt_k2_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  &  ((v16_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k2_functor3 A B C D E) A C) &  ((v15_functor0 (k2_functor3 A B C D E) A C) & (m2_functor0 (k2_functor3 A B C D E) A C)) ) ) ) ).
tt(dt_k2_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k2_fuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k2_fuzzy_1 A B C)) &  ((v1_funct_2 (k2_fuzzy_1 A B C) A k1_numbers) & (m1_subset_1 (k2_fuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k2_fuzzy_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k2_fuzzy_2 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k2_fuzzy_2 A B C)) &  ((v1_funct_2 (k2_fuzzy_2 A B C) A k1_numbers) & (m1_subset_1 (k2_fuzzy_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k2_fuzzy_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k2_fuzzy_4 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k2_fuzzy_4 A B C)) &  ((v1_funct_2 (k2_fuzzy_4 A B C) (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 (k2_fuzzy_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) ).
tt(dt_k2_fvaluat1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k2_fvaluat1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k2_fvsum_1 A)) &  ((v1_funct_2 (k2_fvsum_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k2_fvsum_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_gate_1,ax,$true).
tt(dt_k2_gate_5,ax,$true).
tt(dt_k2_gcd_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_gcd_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E k5_numbers)) ) ) )  => (m2_finseq_1 (k2_genealg1 A B C D E) (k3_card_3 A))) ) ).
tt(dt_k2_geomtrap,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k2_geomtrap A B C D) k1_numbers)) ) ).
tt(dt_k2_gfacirc1,ax, ((v1_funct_1 k2_gfacirc1) &  ((v1_funct_2 k2_gfacirc1 (k4_finseq_2 1 k6_margrel1) k6_margrel1) & (m1_subset_1 k2_gfacirc1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k2_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v3_msualg_1 (k2_gfacirc2 A B C) (k1_gfacirc2 A B C)) &  ((v4_msafree2 (k2_gfacirc2 A B C) (k1_gfacirc2 A B C)) &  ((v4_circcomb (k2_gfacirc2 A B C) (k1_gfacirc2 A B C)) &  ((v6_circcomb (k2_gfacirc2 A B C) (k1_gfacirc2 A B C)) & (l3_msualg_1 (k2_gfacirc2 A B C) (k1_gfacirc2 A B C))) ) ) ) ) ) ).
tt(dt_k2_glib_000,ax,(m1_subset_1 k2_glib_000 k5_numbers)).
tt(dt_k2_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m3_glib_001 (k2_glib_001 A B C D) A)) ) ).
tt(dt_k2_glib_002,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ( (~ (v1_xboole_0 (k2_glib_002 A B)))  & (m1_subset_1 (k2_glib_002 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ).
tt(dt_k2_glib_003,ax,(m2_subset_1 k2_glib_003 k1_numbers k5_numbers)).
tt(dt_k2_glib_004,ax, ( (~ (v1_xboole_0 k2_glib_004))  &  ((v1_finset_1 k2_glib_004) & (m1_subset_1 k2_glib_004 (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k2_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m1_glib_005 C A B)) )  => (m1_subset_1 (k2_glib_005 A B C) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k2_goboard1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (m2_finseq_1 (k2_goboard1 A) k1_numbers)) ) ).
tt(dt_k2_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ((v1_matrix_1 (k2_goboard2 A)) & (m2_finseq_1 (k2_goboard2 A) (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ).
tt(dt_k2_goboard5,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  & (v7_ordinal1 B))  => (m1_subset_1 (k2_goboard5 A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k2_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m1_subset_1 (k2_goboard9 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k2_gobrd13,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k2_gobrd13 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k2_goedelcp,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m2_subset_1 (k2_goedelcp A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k2_graph_1,ax, (! [A:$i,B:$i] :  ( ((l1_graph_1 A) & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k2_graph_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_graph_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m2_finseq_1 (k2_graph_2 A B C D) A)) ) ).
tt(dt_k2_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_graph_3 A B C) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k2_graph_4,ax,$true).
tt(dt_k2_graph_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_finseq_1 B (u4_struct_0 A)))  => (m1_subset_1 (k2_graph_5 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_graphsp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_finseq_1 C k1_numbers) & (m1_subset_1 D k1_numbers)) ) )  => (m2_finseq_1 (k2_graphsp A B C D) k1_numbers)) ) ).
tt(dt_k2_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k2_grcat_1 A B)) &  ((v1_funct_2 (k2_grcat_1 A B) (k1_grcat_1 A B) B) & (m1_subset_1 (k2_grcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_grcat_1 A B) B)))) ) ) ) ).
tt(dt_k2_gr_cy_1,ax, ( (~ (v2_struct_0 k2_gr_cy_1))  &  ((v15_algstr_0 k2_gr_cy_1) & (l3_algstr_0 k2_gr_cy_1)) ) ).
tt(dt_k2_grnilp_1,ax,$true).
tt(dt_k2_groeb_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  => (m1_subset_1 (k2_groeb_1 A B C D) (k1_zfmisc_1 (k15_pre_poly A)))) ) ).
tt(dt_k2_groeb_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k2_groeb_2 A B C)) &  ((v4_relat_1 (k2_groeb_2 A B C) A) &  ((v1_funct_1 (k2_groeb_2 A B C)) &  ((v1_partfun1 (k2_groeb_2 A B C) A) &  ((v4_valued_0 (k2_groeb_2 A B C)) & (v2_pre_poly (k2_groeb_2 A B C))) ) ) ) ) ) ) ).
tt(dt_k2_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A)))) )  =>  ((v1_funct_1 (k2_groeb_3 A B C D)) &  ((v1_funct_2 (k2_groeb_3 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k2_groeb_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k2_group_10 A)) &  ((v1_funct_2 (k2_group_10 A) (u1_struct_0 A) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 A))) &  ((v1_group_10 (k2_group_10 A) A (u1_struct_0 A)) & (m1_subset_1 (k2_group_10 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 A)))))) ) ) ) ) ).
tt(dt_k2_group_11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_group_2 C A)) )  => (m1_subset_1 (k2_group_11 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  & (m1_subset_1 C A)) )  =>  ((v15_algstr_0 (k2_group_12 A B C)) & (m1_group_2 (k2_group_12 A B C) (k2_group_7 A B))) ) ) ).
tt(dt_k2_group_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_group_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_group_3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_group_4,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k2_group_4 A) k4_numbers)) ) ).
tt(dt_k2_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_group_5 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) &  ((v1_group_3 C A) & (m1_group_2 C A)) ) )  =>  ((v15_algstr_0 (k2_group_6 A B C)) &  ((v1_group_3 (k2_group_6 A B C) B) & (m1_group_6 (k2_group_6 A B C) A B)) ) ) ) ).
tt(dt_k2_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v15_algstr_0 (k2_group_7 A B)) & (l3_algstr_0 (k2_group_7 A B))) ) ) ).
tt(dt_k2_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  & (m1_finseq_1 D A))  =>  ((v1_funct_1 (k2_group_9 A B C D)) &  ((v1_funct_2 (k2_group_9 A B C D) B B) & (m1_subset_1 (k2_group_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(dt_k2_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  => (m1_subset_1 (k2_groupp_1 A B) k5_numbers)) ) ).
tt(dt_k2_grsolv_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (m1_group_2 D A)) ) )  =>  ((v15_algstr_0 (k2_grsolv_1 A B C D)) & (m1_group_2 (k2_grsolv_1 A B C D) B)) ) ) ).
tt(dt_k2_hahnban1,ax,(m1_subset_1 k2_hahnban1 (u1_struct_0 k1_complfld))).
tt(dt_k2_hallmar1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_finset_1 A) &  ((m1_finseq_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C k5_numbers)) )  => (m2_finseq_1 (k2_hallmar1 A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_helly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k6_glib_000 A))) )  =>  ((v5_glib_001 (k2_helly A B C) A) & (m3_glib_001 (k2_helly A B C) A)) ) ) ).
tt(dt_k2_henmodel,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k6_qc_lang1 A)) &  ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C (k7_qc_lang1 A B)) & (m1_finseq_1 C (k2_qc_lang1 A))) ) ) )  => (m2_subset_1 (k2_henmodel A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k2_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k2_hermitan A B)) &  ((v1_funct_2 (k2_hermitan A B) (u1_struct_0 (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B)))) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 (k2_hermitan A B) (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B))) k1_complfld) &  ((v1_hermitan (k2_hermitan A B) (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B)))) & (m1_subset_1 (k2_hermitan A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B)))) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ).
tt(dt_k2_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k7_normform A)) => (m2_subset_1 (k2_heyting1 A B) (k5_finsub_1 (k7_normform A)) (k8_normform A))) ) ).
tt(dt_k2_heyting2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))))  => (m1_subset_1 (k2_heyting2 A B C) (k5_finsub_1 (k4_partfun1 A B)))) ) ).
tt(dt_k2_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k2_heyting3 A B) (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B)))) ) ).
tt(dt_k2_hilbasis,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B A) => (m2_subset_1 (k2_hilbasis A B) (k14_pre_poly A) (k15_pre_poly A))) ) ).
tt(dt_k2_hilbert1,ax,(m1_subset_1 k2_hilbert1 k1_hilbert1)).
tt(dt_k2_hilbert2,ax, ((v1_relat_1 k2_hilbert2) &  ((v4_relat_1 k2_hilbert2 k1_hilbert1) &  ((v1_funct_1 k2_hilbert2) & (v1_partfun1 k2_hilbert2 k1_hilbert1)) ) ) ).
tt(dt_k2_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((v1_relat_1 (k2_hilbert3 A)) &  ((v4_relat_1 (k2_hilbert3 A) k1_hilbert1) &  ((v1_funct_1 (k2_hilbert3 A)) & (v1_partfun1 (k2_hilbert3 A) k1_hilbert1)) ) ) ) ) ).
tt(dt_k2_hurwitz,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (v1_int_1 (k2_hurwitz A B))) ) ).
tt(dt_k2_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k2_idea_1 A B C) A) & (m2_finseq_1 (k2_idea_1 A B C) k6_margrel1)) ) ) ).
tt(dt_k2_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  => (m1_subset_1 (k2_incproj A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_incproj A))))) ) ).
tt(dt_k2_incsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v15_incsp_1 A) & (l2_incsp_1 A))  &  ((m1_subset_1 B (u1_incsp_1 A)) &  ((m1_subset_1 C (u1_incsp_1 A)) & (m1_subset_1 D (u1_incsp_1 A))) ) )  => (m1_subset_1 (k2_incsp_1 A B C D) (u4_incsp_1 A))) ) ).
tt(dt_k2_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (k2_index_1 A B C)))  &  ( (~ (v11_struct_0 (k2_index_1 A B C)))  &  ((v2_cat_1 (k2_index_1 A B C)) &  ((v3_cat_1 (k2_index_1 A B C)) &  ((v4_cat_1 (k2_index_1 A B C)) &  ((v5_cat_1 (k2_index_1 A B C)) &  ((v6_cat_1 (k2_index_1 A B C)) & (l1_cat_1 (k2_index_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(dt_k2_instalg1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  & (l3_msualg_1 C A)) )  =>  ((v3_msualg_1 (k2_instalg1 A B C) B) & (l3_msualg_1 (k2_instalg1 A B C) B)) ) ) ).
tt(dt_k2_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_int_1 (k2_int_1 A))) ) ).
tt(dt_k2_int_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v7_ordinal1 (k2_int_2 A B))) ) ).
tt(dt_k2_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) => (m1_subset_1 (k2_int_3 A) (u1_struct_0 k1_int_3))) ) ).
tt(dt_k2_int_5,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) &  ((v7_ordinal1 B) & (v1_int_2 B)) )  => (v1_int_1 (k2_int_5 A B))) ) ).
tt(dt_k2_int_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) ) )  => (v1_int_1 (k2_int_6 A B))) ) ).
tt(dt_k2_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((v1_funct_1 (k2_int_7 A)) &  ((v1_funct_2 (k2_int_7 A) (k2_zfmisc_1 (k1_int_7 A) (k1_int_7 A)) (k1_int_7 A)) & (m1_subset_1 (k2_int_7 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_int_7 A) (k1_int_7 A)) (k1_int_7 A))))) ) ) ) ).
tt(dt_k2_integr10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k2_integr10 A B C) k1_numbers)) ) ).
tt(dt_k2_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  &  ((m2_integr15 D A B C) & (m1_subset_1 E k5_numbers)) ) ) )  => (m1_integr15 (k2_integr15 A B C D E) A B (k2_integra2 A C E))) ) ).
tt(dt_k2_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k2_integr16 A) k1_numbers)) ) ).
tt(dt_k2_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  &  ((m2_integr18 E A B C D) & (m1_subset_1 F k5_numbers)) ) ) ) )  => (m1_integr18 (k2_integr18 A B C D E F) A B C (k2_integra2 B D F))) ) ).
tt(dt_k2_integr1c,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) ) ) )  => (v1_xcmplx_0 (k2_integr1c A B C D E F))) ) ).
tt(dt_k2_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((m1_integra1 B A) & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k2_integra1 A B C)))  &  ((v2_measure5 (k2_integra1 A B C)) & (m1_subset_1 (k2_integra1 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(dt_k2_integra2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_integra1 (k2_integra2 A B C) A)) ) ).
tt(dt_k2_integra3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) ) )  =>  ((v1_funct_1 (k2_integra3 A B)) &  ((v1_funct_2 (k2_integra3 A B) k5_numbers k1_numbers) & (m1_subset_1 (k2_integra3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_integra5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (m1_subset_1 (k2_integra5 A B) k1_numbers)) ) ).
tt(dt_k2_integra9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (m1_subset_1 (k2_integra9 A B) k1_numbers)) ) ).
tt(dt_k2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_interva1 (k2_interva1 A B C) A)) ) ).
tt(dt_k2_intpro_1,ax,(m1_subset_1 k2_intpro_1 k1_intpro_1)).
tt(dt_k2_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k2_irrat_1 A)) &  ((v1_funct_2 (k2_irrat_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k2_irrat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_isocat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m1_nattra_1 F A B D E) & (m2_cat_1 G B C)) ) ) ) ) )  => (m1_nattra_1 (k2_isocat_1 A B C D E F G) A C (k9_cat_1 A B C D G) (k9_cat_1 A B C E G))) ) ).
tt(dt_k2_isocat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_cat_1 (k2_isocat_2 A B C) (k11_nattra_1 A B) B)) ) ).
tt(dt_k2_jgraph_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k2_jgraph_1 A)) &  ((v1_funct_1 (k2_jgraph_1 A)) & (v1_finseq_1 (k2_jgraph_1 A))) ) ) ) ).
tt(dt_k2_jgraph_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ((v1_funct_1 (k2_jgraph_2 A B C D)) &  ((v1_funct_2 (k2_jgraph_2 A B C D) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k2_jgraph_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k2_jgraph_4,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m1_subset_1 (k2_jgraph_4 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jgraph_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k2_jgraph_6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k2_jordan10,ax,$true).
tt(dt_k2_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m2_subset_1 (k2_jordan11 A) k1_numbers k5_numbers)) ) ).
tt(dt_k2_jordan18,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k2_jordan18 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k2_jordan19 A)) &  ((v1_funct_2 (k2_jordan19 A) k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 (k2_jordan19 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) ) ) ) ).
tt(dt_k2_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (v7_ordinal1 B))  => (m2_finseq_1 (k2_jordan1e A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan1h,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k3_finseq_2 A)))  => (m1_subset_1 (k2_jordan1h A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k2_jordan21 A) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan2c,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  => (m1_subset_1 (k2_jordan2c A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k2_jordan3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m2_finseq_1 (k2_jordan3 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan5c,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (u1_struct_0 (k15_euclid 2)))) ) )  => (m1_subset_1 (k2_jordan5c A B C D) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k2_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k2_jordan6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (m1_subset_1 (k2_jordan6 A B C) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k2_jordan_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((v7_ordinal1 B) & (m1_jordan_a C A)) )  => (m1_subset_1 (k2_jordan_a A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k2_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  => (m1_subset_1 (k2_jordan A B C) (u1_struct_0 B))) ) ).
tt(dt_k2_knaster,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  => (m1_subset_1 (k2_knaster A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ((m1_kolmog01 D A B C) & (m1_subset_1 E (k1_zfmisc_1 A))) ) )  =>  ((v1_funct_1 (k2_kolmog01 A B C D E)) &  ((v1_funct_2 (k2_kolmog01 A B C D E) E (k9_setfam_1 C)) & (m1_subset_1 (k2_kolmog01 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 E (k9_setfam_1 C))))) ) ) ) ).
tt(dt_k2_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k2_kurato_0 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_kurato_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_kurato_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  => (m1_subset_1 (k2_kurato_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_lang1,ax,$true).
tt(dt_k2_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 E (u1_struct_0 D) C C)) ) ) )  => (m1_matrix_1 (k2_laplace A B C D E) (u1_struct_0 D) (k7_nat_d C 1) (k7_nat_d C 1))) ) ).
tt(dt_k2_latsubgr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_group_3 A)))) )  =>  ((v15_algstr_0 (k2_latsubgr A B)) & (m1_group_2 (k2_latsubgr A B) A)) ) ) ).
tt(dt_k2_lattice2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  &  ((m1_subset_1 C (k5_finsub_1 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  => (m1_subset_1 (k2_lattice2 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k2_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_partfun1 (k2_lattice3 A) (u1_struct_0 A)) &  ((v1_relat_2 (k2_lattice3 A)) &  ((v4_relat_2 (k2_lattice3 A)) &  ((v8_relat_2 (k2_lattice3 A)) & (m1_subset_1 (k2_lattice3 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k2_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_lattice4 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_lattice5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_yellow_0 B (k1_lattice5 A)) &  ((v6_yellow_0 B (k1_lattice5 A)) & (m1_yellow_0 B (k1_lattice5 A))) ) )  => (m1_subset_1 (k2_lattice5 A B) k5_numbers)) ) ).
tt(dt_k2_lattice6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_lattice3 A)))))  => (m1_subset_1 (k2_lattice6 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_lattice7,ax, (! [A:$i,B:$i] :  ( ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k2_lattice7 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B)))) ) )  =>  ((v1_funct_1 (k2_lattice8 A B C D)) &  ((v1_funct_2 (k2_lattice8 A B C D) (k2_zfmisc_1 (k1_lattice8 A) (k1_lattice8 A)) (u1_struct_0 B)) & (m1_subset_1 (k2_lattice8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lattice8 A) (k1_lattice8 A)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_lattices A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_lfuzzy_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k2_lfuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k2_lfuzzy_1 A B C)) &  ((v1_funct_2 (k2_lfuzzy_1 A B C) A k1_numbers) & (m1_subset_1 (k2_lfuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k2_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k2_limfunc1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k2_limfunc2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k2_limfunc2 A B) k1_numbers)) ) ).
tt(dt_k2_lmod_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) )  => (m1_subset_1 (k2_lmod_6 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k2_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_algstr_0 B)) )  =>  ((v1_funct_1 (k2_lopban_1 A B)) &  ((v1_funct_2 (k2_lopban_1 A B) (k2_zfmisc_1 (k9_funct_2 A (u1_struct_0 B)) (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 (k2_lopban_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A (u1_struct_0 B)) (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k2_lopban_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k10_lopban_1 A A)) & (m1_subset_1 C (k10_lopban_1 A A))) )  => (m2_subset_1 (k2_lopban_2 A B C) (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A))) ) ).
tt(dt_k2_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k2_lopban_3 A B C)) &  ((v1_funct_2 (k2_lopban_3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_lopban_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_lopban_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k2_lopban_4 A)) &  ((v1_funct_2 (k2_lopban_4 A) k5_numbers k1_numbers) & (m1_subset_1 (k2_lopban_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_lopban_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k16_lopban_1 A B)))))) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((v1_funct_1 (k2_lopban_5 A B C D)) &  ((v1_funct_2 (k2_lopban_5 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k2_lopban_5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  => (m2_subset_1 (k2_lopclset A B C) (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A))) ) ).
tt(dt_k2_lpspace1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_rfunct_3 A B) (k3_rfunct_3 A B)) (k3_rfunct_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A B) (k3_rfunct_3 A B)) (k3_rfunct_3 A B))))) )  &  ((m1_subset_1 D (k3_rfunct_3 A B)) & (m1_subset_1 E (k3_rfunct_3 A B))) ) ) )  => (m2_rfunct_3 (k2_lpspace1 A B C D E) A B (k3_rfunct_3 A B))) ) ).
tt(dt_k2_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v2_struct_0 (k2_lpspace2 A B C D)))  &  ((v1_rlvect_1 (k2_lpspace2 A B C D)) &  ((v2_rlvect_1 (k2_lpspace2 A B C D)) &  ((v3_rlvect_1 (k2_lpspace2 A B C D)) &  ((v4_rlvect_1 (k2_lpspace2 A B C D)) &  ((v5_rlvect_1 (k2_lpspace2 A B C D)) &  ((v6_rlvect_1 (k2_lpspace2 A B C D)) &  ((v7_rlvect_1 (k2_lpspace2 A B C D)) &  ((v8_rlvect_1 (k2_lpspace2 A B C D)) & (l1_rlvect_1 (k2_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k2_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (v1_xboole_0 (k2_lp_space A)))  & (m1_subset_1 (k2_lp_space A) (k1_zfmisc_1 (u1_struct_0 k7_rsspace)))) ) ) ).
tt(dt_k2_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (m1_subset_1 (k2_ltlaxio1 A) k1_hilbert1)) ) ).
tt(dt_k2_mathmorp,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_mathmorp A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_matrix10,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_matrix_1 B k1_numbers A A))  => (m1_matrix_1 (k2_matrix10 A B) k1_numbers A A)) ) ).
tt(dt_k2_matrix11,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k12_matrix_2 (k1_nat_1 A 2)))) )  => (m1_subset_1 (k2_matrix11 A B C) (u1_struct_0 B))) ) ).
tt(dt_k2_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) & (m1_subset_1 F (u1_struct_0 C))) ) ) ) )  => (m1_matrix_1 (k2_matrix12 A B C D E F) (u1_struct_0 C) A B)) ) ).
tt(dt_k2_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) & (m1_subset_1 E (u1_struct_0 C))) ) ) )  => (m1_matrix_1 (k2_matrix13 A B C D E) (u1_struct_0 C) A B)) ) ).
tt(dt_k2_matrix14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  & (m1_subset_1 B k5_numbers))  => (m2_finseq_2 (k2_matrix14 A B) (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A)))) ) ).
tt(dt_k2_matrix15,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k2_matrix15 A B) A 1 (k3_finseq_1 B))) ) ).
tt(dt_k2_matrix16,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k2_matrix16 A B) A (k3_finseq_1 B) (k3_finseq_1 B))) ) ).
tt(dt_k2_matrix_1,ax,$true).
tt(dt_k2_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) & (m1_subset_1 D A)) ) )  => (m1_matrix_1 (k2_matrix_2 A B C D) A B C)) ) ).
tt(dt_k2_matrix_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  =>  ((v1_matrix_1 (k2_matrix_3 A B)) & (m2_finseq_1 (k2_matrix_3 A B) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k2_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 k1_complfld))))  =>  ((v1_matrix_1 (k2_matrix_5 A)) & (m2_finseq_1 (k2_matrix_5 A) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k2_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (m1_matrix_1 (k2_matrix_6 A B C D) (u1_struct_0 B) A A)) ) ).
tt(dt_k2_matrix_7,ax,$true).
tt(dt_k2_matrix_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_subset_1 (k2_matrix_9 A B C) (u1_struct_0 B))) ) ).
tt(dt_k2_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((v1_matrix_1 (k2_matrixc1 A)) & (m2_finseq_1 (k2_matrixc1 A) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k2_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  =>  ((v1_matrix_1 (k2_matrixj1 A B C)) & (m2_finseq_1 (k2_matrixj1 A B C) (k3_finseq_2 A))) ) ) ).
tt(dt_k2_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v7_ordinal1 C)) )  =>  ((v1_matrix_2 (k2_matrixj2 A B C) C A) & (m1_matrix_1 (k2_matrixj2 A B C) (u1_struct_0 A) C C)) ) ) ).
tt(dt_k2_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 k2_vectsp_1))))  =>  ((v1_matrix_1 (k2_matrixr1 A)) & (m2_finseq_1 (k2_matrixr1 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k2_matrixr2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_matrix_1 B k1_numbers A A))  => (m1_matrix_1 (k2_matrixr2 A B) (u1_struct_0 k2_vectsp_1) A A)) ) ).
tt(dt_k2_matrlin2,ax,$true).
tt(dt_k2_matrlin,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k2_matrlin A B) A 1 (k3_finseq_1 B))) ) ).
tt(dt_k2_matroid0,ax, (! [A:$i] :  ((v1_pre_topc (k2_matroid0 A)) & (l1_pre_topc (k2_matroid0 A))) ) ).
tt(dt_k2_matrprob,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m2_finseq_1 (k2_matrprob A) k1_numbers)) ) ).
tt(dt_k2_matrtop1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 k2_vectsp_1)) => (m2_finseq_1 (k2_matrtop1 A) k1_numbers)) ) ).
tt(dt_k2_matrtop3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_xreal_0 B) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  =>  ((v1_matrix_6 (k2_matrtop3 A B C D) A k2_vectsp_1) & (m1_matrix_1 (k2_matrtop3 A B C D) (u1_struct_0 k2_vectsp_1) A A)) ) ) ).
tt(dt_k2_mboolean,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k2_mboolean A B)) &  ((v4_relat_1 (k2_mboolean A B) A) &  ((v1_funct_1 (k2_mboolean A B)) & (v1_partfun1 (k2_mboolean A B) A)) ) ) ) ) ).
tt(dt_k2_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  => (m1_subset_1 (k2_mcart_1 A B C D) B)) ) ).
tt(dt_k2_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m2_subset_1 (k2_measure1 A B C D) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k2_measure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  => (m2_subset_1 (k2_measure2 A B C) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k2_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_measure3 A B C)))  & (m1_subset_1 (k2_measure3 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k2_measure4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  => (m2_subset_1 (k2_measure4 A B C) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k2_measure5,ax, (! [A:$i] :  ((v2_membered A) => (m1_subset_1 (k2_measure5 A) k7_numbers)) ) ).
tt(dt_k2_measure6,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (m1_subset_1 (k2_measure6 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k2_measure7,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) &  ((m1_measure7 B A) & (m1_subset_1 C k5_numbers)) )  =>  ((v6_xxreal_2 (k2_measure7 A B C)) & (m1_subset_1 (k2_measure7 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k2_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  & (m2_measure8 D A B)) )  =>  ((v1_funct_1 (k2_measure8 A B C D)) &  ((v1_funct_2 (k2_measure8 A B C D) k5_numbers k7_numbers) & (m1_subset_1 (k2_measure8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k2_member_1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (m1_subset_1 (k2_member_1 A) k7_numbers)) ) ).
tt(dt_k2_memstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  & (l1_memstr_0 B A))  =>  ((v1_relat_1 (k2_memstr_0 A B)) &  ((v4_relat_1 (k2_memstr_0 A B) (u1_struct_0 B)) &  ((v1_funct_1 (k2_memstr_0 A B)) & (v1_partfun1 (k2_memstr_0 A B) (u1_struct_0 B))) ) ) ) ) ).
tt(dt_k2_mesfun6c,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) )  =>  ((v1_funct_1 (k2_mesfun6c A B C)) & (m1_subset_1 (k2_mesfun6c A B C) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ).
tt(dt_k2_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k2_mesfun7c A B)) & (m1_subset_1 (k2_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k2_mesfun9c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k2_mesfun9c A B)) &  ((v1_funct_2 (k2_mesfun9c A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k2_mesfun9c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k2_mesfunc1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k2_mesfunc1 A) (k1_zfmisc_1 k3_numbers))) ) ).
tt(dt_k2_mesfunc2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) )  =>  ((v1_funct_1 (k2_mesfunc2 A B)) & (m1_subset_1 (k2_mesfunc2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k2_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k2_mesfunc5 A) k7_numbers)) ) ).
tt(dt_k2_mesfunc6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_subset_1 E B)) ) ) )  => (m1_subset_1 (k2_mesfunc6 A B C D E) k7_numbers)) ) ).
tt(dt_k2_mesfunc7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_valued_0 A)) ) )  => (m1_subset_1 (k2_mesfunc7 A) k7_numbers)) ) ).
tt(dt_k2_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k2_mesfunc8 A B)) & (m1_subset_1 (k2_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k2_mesfunc9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((v1_funct_1 (k2_mesfunc9 A)) &  ((v1_funct_2 (k2_mesfunc9 A) k5_numbers k7_numbers) & (m1_subset_1 (k2_mesfunc9 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k2_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_metric_1 A B C) k1_numbers)) ) ).
tt(dt_k2_metric_2,ax,$true).
tt(dt_k2_metric_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k2_metric_6 A B C)) &  ((v1_funct_2 (k2_metric_6 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k2_metric_6 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k2_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_pre_topc (k2_mfold_1 A) (k15_euclid A))) ) ).
tt(dt_k2_mfold_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k2_mfold_2 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k2_midsp_1,ax,(l1_midsp_1 k2_midsp_1)).
tt(dt_k2_midsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (m1_subset_1 (k2_midsp_2 A B C D E) A)) ) ).
tt(dt_k2_midsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (m2_finseq_2 (k2_midsp_3 A B C) (u1_struct_0 B) (k4_finseq_2 1 (u1_struct_0 B)))) ) ).
tt(dt_k2_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k2_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ( (~ (v2_struct_0 (k2_mod_2 A B)))  &  ((v13_algstr_0 (k2_mod_2 A B)) &  ((v8_vectsp_1 (k2_mod_2 A B) A) &  ((v9_vectsp_1 (k2_mod_2 A B) A) &  ((v10_vectsp_1 (k2_mod_2 A B) A) &  ((v11_vectsp_1 (k2_mod_2 A B) A) &  ((v2_rlvect_1 (k2_mod_2 A B)) &  ((v3_rlvect_1 (k2_mod_2 A B)) &  ((v4_rlvect_1 (k2_mod_2 A B)) & (l1_vectsp_1 (k2_mod_2 A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k2_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v36_algstr_0 (k2_mod_4 A)) & (l6_algstr_0 (k2_mod_4 A))) ) ) ).
tt(dt_k2_modal_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m1_subset_1 (k2_modal_1 A B) A)) ) ).
tt(dt_k2_modcat_1,ax,$true).
tt(dt_k2_modelc_1,ax, (! [A:$i] : (m1_subset_1 (k2_modelc_1 A) k5_numbers)) ).
tt(dt_k2_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_1 (k2_modelc_2 A) k5_numbers)) ) ).
tt(dt_k2_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k2_modelc_3 A) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k2_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_xreal_0 (k2_moebius1 A))) ) ).
tt(dt_k2_monoid_0,ax, ( (~ (v2_struct_0 k2_monoid_0))  & (l3_algstr_0 k2_monoid_0)) ).
tt(dt_k2_morph_01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_morph_01 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v3_msualg_1 (k2_msafree1 A) A) & (l3_msualg_1 (k2_msafree1 A) A)) ) ) ).
tt(dt_k2_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (m1_subset_1 (k2_msafree2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_msafree3,ax, (! [A:$i,B:$i] :  ( ((l1_msualg_1 A) &  ( (~ (v1_xboole_0 B))  & (v1_relat_1 B)) )  =>  ((v1_relat_1 (k2_msafree3 A B)) &  ((v4_relat_1 (k2_msafree3 A B) (u1_struct_0 A)) &  ((v1_funct_1 (k2_msafree3 A B)) & (v1_partfun1 (k2_msafree3 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_k2_msafree,ax,$true).
tt(dt_k2_msalimit,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_msalimit C A B) & (m2_msalimit D A B C)) ) )  => (m2_msalimit (k2_msalimit A B C D) A B C)) ) ).
tt(dt_k2_msaterm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  => (m2_subset_1 (k2_msaterm A B C) (u1_struct_0 (k5_msafree A B)) (k7_dtconstr (k5_msafree A B)))) ) ).
tt(dt_k2_msinst_1,ax,$true).
tt(dt_k2_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_funct_1 (k2_msscyc_2 A)) &  ((v1_funct_2 (k2_msscyc_2 A) (k1_msscyc_2 A) (u1_struct_0 A)) & (m1_subset_1 (k2_msscyc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_msscyc_2 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_mssubfam,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m3_pboole C A (k1_mboolean A B)) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k2_mssubfam A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (k1_funct_1 B D))))) ) ).
tt(dt_k2_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k2_msualg_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  => (m3_pboole (k2_msualg_2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(dt_k2_msualg_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (m2_pboole (k2_msualg_3 A B) A B B)) ) ).
tt(dt_k2_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((v3_relat_2 (k2_msualg_4 A B C D)) &  ((v8_relat_2 (k2_msualg_4 A B C D)) &  ((v1_partfun1 (k2_msualg_4 A B C D) (k1_funct_1 (u3_msualg_1 A B) D)) & (m1_subset_1 (k2_msualg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D))))) ) ) ) ) ).
tt(dt_k2_msualg_5,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k2_msualg_5 A)))  &  ((v3_lattices (k2_msualg_5 A)) &  ((v10_lattices (k2_msualg_5 A)) & (l3_lattices (k2_msualg_5 A))) ) ) ) ).
tt(dt_k2_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((m1_msualg_6 C A B) & (m1_msualg_6 D A B)) ) )  => (m1_msualg_6 (k2_msualg_6 A B C D) A B)) ) ).
tt(dt_k2_msualg_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))))) )  =>  ((v2_msualg_4 (k2_msualg_8 A B C) A B) &  ((v3_msualg_4 (k2_msualg_8 A B C) A B) & (m1_msualg_4 (k2_msualg_8 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_k2_msualg_9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  & (m2_pboole E A B (k6_pboole A C D))) ) )  => (m2_pboole (k2_msualg_9 A B C D E) A B D)) ) ).
tt(dt_k2_msuhom_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  => (m2_pboole (k2_msuhom_1 A B C) (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B))))) ) ).
tt(dt_k2_multop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_zfmisc_1 A B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  &  ((m1_subset_1 F A) &  ((m1_subset_1 G B) & (m1_subset_1 H C)) ) ) ) ) ) )  => (m1_subset_1 (k2_multop_1 A B C D E F G H) D)) ) ).
tt(dt_k2_mycielsk,ax, (! [A:$i] :  ( ((v1_mycielsk A) & (l1_orders_2 A))  => (v7_ordinal1 (k2_mycielsk A))) ) ).
tt(dt_k2_nagata_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) ) )  => (m1_subset_1 (k2_nagata_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_nagata_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k2_nagata_2 A B C)) &  ((v1_funct_2 (k2_nagata_2 A B C) A k1_numbers) & (m1_subset_1 (k2_nagata_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k2_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  => (m2_subset_1 (k2_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k2_nat_3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k1_numbers) & (v7_ordinal1 B))  => (m2_finseq_1 (k2_nat_3 A B) k1_numbers)) ) ).
tt(dt_k2_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k2_nat_5 A)) &  ((v1_funct_2 (k2_nat_5 A) k5_numbers k5_numbers) & (m1_subset_1 (k2_nat_5 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k2_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k2_nat_d A B))) ) ).
tt(dt_k2_nat_lat,ax, ((v1_funct_1 k2_nat_lat) &  ((v1_funct_2 k2_nat_lat (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 k2_nat_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) ) ).
tt(dt_k2_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  &  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 A A C C) C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 B B D D) D)))) ) ) ) ) )  =>  ((v1_funct_1 (k2_nattra_1 A B C D E F)) & (m1_subset_1 (k2_nattra_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 A B) (k8_mcart_1 A B C D) (k8_mcart_1 A B C D)) (k8_mcart_1 A B C D))))) ) ) ).
tt(dt_k2_ndiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k2_ndiff_1 A B C)) &  ((v1_funct_2 (k2_ndiff_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_ndiff_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_ndiff_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 E (u1_struct_0 (k16_lopban_1 B C)))) ) ) )  => (m1_subset_1 (k2_ndiff_2 A B C D E) (u1_struct_0 (k16_lopban_1 A C)))) ) ).
tt(dt_k2_ndiff_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ((v1_funct_1 (k2_ndiff_3 A B C)) & (m1_subset_1 (k2_ndiff_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) ).
tt(dt_k2_ndiff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  =>  ((v1_funct_1 (k2_ndiff_4 A B C)) & (m1_subset_1 (k2_ndiff_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) ) ).
tt(dt_k2_ndiff_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_ndiff_5 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_neckla_2,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  ((v1_orders_2 (k2_neckla_2 A B)) & (l1_orders_2 (k2_neckla_2 A B))) ) ) ).
tt(dt_k2_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k2_necklace A)) & (l1_orders_2 (k2_necklace A))) ) ) ).
tt(dt_k2_net_1,ax,$true).
tt(dt_k2_newton,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v7_ordinal1 B))  => (m1_subset_1 (k2_newton A B) k1_numbers)) ) ).
tt(dt_k2_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k2_nfcont_4 A B C)) & (m1_subset_1 (k2_nfcont_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) ) ).
tt(dt_k2_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  => (m1_subset_1 (k2_normform A B C D) (k2_zfmisc_1 A B))) ) ).
tt(dt_k2_normsp_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k2_normsp_0 A B)) & (v1_funct_1 (k2_normsp_0 A B))) ) ) ).
tt(dt_k2_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_normsp_1 A B C)) &  ((v1_funct_2 (k2_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_normsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_normsp_2 A)))  &  ((v6_metric_1 (k2_normsp_2 A)) &  ((v7_metric_1 (k2_normsp_2 A)) &  ((v8_metric_1 (k2_normsp_2 A)) &  ((v9_metric_1 (k2_normsp_2 A)) & (l1_metric_1 (k2_normsp_2 A))) ) ) ) ) ) ) ).
tt(dt_k2_ntalgo_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k4_numbers) & (m1_subset_1 B k4_numbers))  => (m1_subset_1 (k2_ntalgo_1 A B) (k3_zfmisc_1 k4_numbers k4_numbers k4_numbers))) ) ).
tt(dt_k2_numbers,ax,$true).
tt(dt_k2_numeral1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_relat_1 (k2_numeral1 A B)) &  ((v5_relat_1 (k2_numeral1 A B) k5_numbers) &  ((v1_funct_1 (k2_numeral1 A B)) &  ((v5_ordinal1 (k2_numeral1 A B)) & (v1_finset_1 (k2_numeral1 A B))) ) ) ) ) ) ).
tt(dt_k2_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  => (m2_subset_1 (k2_openlatt A B C) (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A))) ) ).
tt(dt_k2_oposet_1,ax, ((v3_qmax_1 k2_oposet_1) & (l2_qmax_1 k2_oposet_1)) ).
tt(dt_k2_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_oppcat_1 A)))  &  ( (~ (v11_struct_0 (k2_oppcat_1 A)))  &  ((v1_cat_1 (k2_oppcat_1 A)) & (l1_cat_1 (k2_oppcat_1 A))) ) ) ) ) ).
tt(dt_k2_orders_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_orders_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_orders_3,ax,$true).
tt(dt_k2_ordinal1,ax,$true).
tt(dt_k2_ordinal2,ax, (! [A:$i] : (v3_ordinal1 (k2_ordinal2 A))) ).
tt(dt_k2_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((v3_ordinal1 (k2_ordinal4 A)) & (m1_subset_1 (k2_ordinal4 A) A)) ) ) ).
tt(dt_k2_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v3_ordinal1 (k2_ordinal5 A)) & (v4_ordinal5 (k2_ordinal5 A))) ) ) ).
tt(dt_k2_ordinal6,ax, (! [A:$i] :  ((v1_relat_1 (k2_ordinal6 A)) &  ((v1_funct_1 (k2_ordinal6 A)) &  ((v5_ordinal1 (k2_ordinal6 A)) & (v1_ordinal2 (k2_ordinal6 A))) ) ) ) ).
tt(dt_k2_ortsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m1_subset_1 E (u1_struct_0 B)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  => (m1_subset_1 (k2_ortsp_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k2_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (l1_lang1 (k2_osafree A B))) ) ).
tt(dt_k2_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (k3_finseq_2 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_osalg_1 A B C) (u4_struct_0 A))) ) ).
tt(dt_k2_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((v1_relat_1 (k2_osalg_2 A B)) &  ((v4_relat_1 (k2_osalg_2 A B) (u1_struct_0 A)) &  ((v1_funct_1 (k2_osalg_2 A B)) &  ((v1_partfun1 (k2_osalg_2 A B) (u1_struct_0 A)) & (v11_osalg_1 (k2_osalg_2 A B) A)) ) ) ) ) ) ).
tt(dt_k2_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ( (~ (v1_xboole_0 (k2_osalg_4 A)))  & (m1_subset_1 (k2_osalg_4 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ).
tt(dt_k2_parsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))) )  => (m1_subset_1 (k2_parsp_1 A B C) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(dt_k2_partfun1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k2_partfun1 A B C D)) & (m1_subset_1 (k2_partfun1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k2_partfun2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k2_partfun2 A B C)) & (m1_subset_1 (k2_partfun2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ).
tt(dt_k2_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k2_partfun3 A B C)) & (m1_subset_1 (k2_partfun3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k2_partit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_eqrel_1 B A) & (m1_eqrel_1 C A)) )  => (m1_eqrel_1 (k2_partit1 A B C) A)) ) ).
tt(dt_k2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k2_pboole A B C)) &  ((v4_relat_1 (k2_pboole A B C) A) &  ((v1_funct_1 (k2_pboole A B C)) & (v1_partfun1 (k2_pboole A B C) A)) ) ) ) ) ).
tt(dt_k2_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) => (m1_subset_1 (k2_pcomps_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  => (m1_subset_1 (k2_pcs_0 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A C) (k2_xboole_0 B D))))) ) ).
tt(dt_k2_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_funct_1 (k2_pdiff_1 A)) & (m1_subset_1 (k2_pdiff_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 1) (k1_euclid 1))))) ) ) ).
tt(dt_k2_pdiff_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  & (m1_subset_1 B (k1_euclid 2)))  => (m1_subset_1 (k2_pdiff_3 A B) k1_numbers)) ) ).
tt(dt_k2_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k2_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k2_pdiff_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) )  =>  ((v1_funct_1 (k2_pdiff_7 A B C D E)) & (m1_subset_1 (k2_pdiff_7 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) ).
tt(dt_k2_pdiff_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) )  =>  ((v1_funct_1 (k2_pdiff_9 A B C)) & (m1_subset_1 (k2_pdiff_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k9_funct_2 (k1_euclid A) k1_numbers))))) ) ) ).
tt(dt_k2_pencil_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (k2_pencil_1 A B C)))  &  ( (~ (v3_pencil_1 (k2_pencil_1 A B C)))  &  ( (~ (v4_pencil_1 (k2_pencil_1 A B C)))  &  ((v5_pencil_1 (k2_pencil_1 A B C)) &  ((v6_pencil_1 (k2_pencil_1 A B C)) & (l1_pre_topc (k2_pencil_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k2_pencil_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_pre_topc A))) )  => (m1_subset_1 (k2_pencil_2 A B C) (u1_pre_topc A))) ) ).
tt(dt_k2_pencil_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) ) ) )  =>  ((v1_funct_1 (k2_pencil_3 A B C)) &  ((v1_funct_2 (k2_pencil_3 A B C) A A) &  ((v3_funct_2 (k2_pencil_3 A B C) A A) & (m1_subset_1 (k2_pencil_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k2_pencil_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_vectsp_4 D A B)) ) )  => (m1_subset_1 (k2_pencil_4 A B C D) (k1_zfmisc_1 (k3_vectsp_5 A B)))) ) ).
tt(dt_k2_pepin,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k2_pepin A B C) k5_numbers)) ) ).
tt(dt_k2_petri_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k2_petri_2 A B)))  & (m1_subset_1 (k2_petri_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (k9_funct_2 B A))))) ) ) ).
tt(dt_k2_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_petri A)))  => (m1_subset_1 (k2_petri A B) (u1_struct_0 A))) ) ).
tt(dt_k2_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((v1_funct_1 (k2_pnproc_1 A B C)) &  ((v1_funct_2 (k2_pnproc_1 A B C) A k5_numbers) & (m1_subset_1 (k2_pnproc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(dt_k2_polyalg1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ( (~ (v2_struct_0 (k2_polyalg1 A B C)))  &  ((v1_polyalg1 (k2_polyalg1 A B C) A) & (m1_polyalg1 (k2_polyalg1 A B C) A B)) ) ) ) ).
tt(dt_k2_polyeq_2,ax,$true).
tt(dt_k2_polyeq_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k2_numbers)) ) )  => (m1_subset_1 (k2_polyeq_3 A B C D) k2_numbers)) ) ).
tt(dt_k2_polyeq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xcmplx_0 (k2_polyeq_5 A B C))) ) ).
tt(dt_k2_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k2_polyform A B) k4_numbers)) ) ).
tt(dt_k2_polynom1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((l2_struct_0 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  => (m1_subset_1 (k2_polynom1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_funct_1 (k2_polynom2 A B C)) & (m1_subset_1 (k2_polynom2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ).
tt(dt_k2_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m2_finseq_2 (k2_polynom3 A B C) A (k4_finseq_2 2 A))) ) ).
tt(dt_k2_polynom4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_polynom4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v3_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k2_polynom5 A B C)) &  ((v1_funct_2 (k2_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_polynom5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_polynom6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 A)) )  &  ( ((v3_ordinal1 B) &  (~ (v1_xboole_0 B)) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 (k11_polynom1 B C))) &  ((v1_polynom1 D (k15_pre_poly A) (k11_polynom1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 (k11_polynom1 B C)))))) ) ) ) ) )  =>  ((v1_funct_1 (k2_polynom6 A B C D)) &  ((v1_funct_2 (k2_polynom6 A B C D) (k15_pre_poly (k10_ordinal2 A B)) (u1_struct_0 C)) &  ((v1_polynom1 (k2_polynom6 A B C D) (k15_pre_poly (k10_ordinal2 A B)) C) & (m1_subset_1 (k2_polynom6 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k10_ordinal2 A B)) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k2_polynom7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((v1_relat_1 (k2_polynom7 A B C)) &  ((v4_relat_1 (k2_polynom7 A B C) A) &  ((v1_funct_1 (k2_polynom7 A B C)) &  ((v1_partfun1 (k2_polynom7 A B C) A) &  ((v4_valued_0 (k2_polynom7 A B C)) & (v2_pre_poly (k2_polynom7 A B C))) ) ) ) ) ) ) ).
tt(dt_k2_polynom8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_polynom8 A B C)) &  ((v1_funct_2 (k2_polynom8 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_polynom8 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  => (m1_subset_1 (k2_polyred A B C D) (k5_finsub_1 (u1_struct_0 (g1_orders_2 (k15_pre_poly A) B))))) ) ).
tt(dt_k2_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v1_xboole_0 (k2_poset_1 A B)))  &  ((v6_orders_2 (k2_poset_1 A B) A) & (m1_subset_1 (k2_poset_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_k2_power,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k2_power A B) k1_numbers)) ) ).
tt(dt_k2_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k2_zfmisc_1 A B))) )  => (m2_finseq_1 (k2_pralg_1 A B C) B)) ) ).
tt(dt_k2_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k2_pralg_2 A)) &  ((v4_relat_1 (k2_pralg_2 A) (k4_card_3 (k2_funct_6 A))) &  ((v1_funct_1 (k2_pralg_2 A)) &  ((v1_partfun1 (k2_pralg_2 A) (k4_card_3 (k2_funct_6 A))) & (v1_funcop_1 (k2_pralg_2 A))) ) ) ) ) ) ).
tt(dt_k2_pralg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_pralg_2 C A B) & (m1_subset_1 D A)) ) )  => (m2_pboole (k2_pralg_3 A B C D) (u1_struct_0 B) (u3_msualg_1 B (k14_pralg_2 A B C)) (u3_msualg_1 B (k5_pralg_2 A B C D)))) ) ).
tt(dt_k2_pre_ff,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k3_finseq_2 k5_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k5_numbers))))) )  & (m1_subset_1 B k5_numbers))  => (m2_finseq_1 (k2_pre_ff A B) k5_numbers)) ) ).
tt(dt_k2_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_prelamb A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_pre_poly,ax, (! [A:$i] :  ((v1_xboole_0 (k2_pre_poly A)) & (m2_finseq_2 (k2_pre_poly A) A (k3_finseq_2 A))) ) ).
tt(dt_k2_prepower,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k2_prepower A B))) ) ).
tt(dt_k2_pre_topc,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_pre_topc A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_prgcor_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k2_prgcor_1 A B))) ) ).
tt(dt_k2_prgcor_2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  => (m1_subset_1 (k2_prgcor_2 A B) k1_numbers)) ) ).
tt(dt_k2_prob_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k2_prob_1 A B)) &  ((v1_funct_2 (k2_prob_1 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k2_prob_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k2_prob_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  => (m1_prob_1 (k2_prob_2 A B C) A B)) ) ).
tt(dt_k2_prob_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k2_prob_3 A B)) &  ((v1_funct_2 (k2_prob_3 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k2_prob_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k2_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  ((v1_funct_1 (k2_prob_4 A B C)) &  ((v1_funct_2 (k2_prob_4 A B C) B k7_numbers) &  ((v10_valued_0 (k2_prob_4 A B C)) &  ((v6_supinf_2 (k2_prob_4 A B C)) &  ((v4_measure1 (k2_prob_4 A B C) A B) & (m1_subset_1 (k2_prob_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) ) ).
tt(dt_k2_projpl_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  &  ((m1_subset_1 B (u2_incsp_1 A)) & (m1_subset_1 C (u2_incsp_1 A))) )  => (m1_subset_1 (k2_projpl_1 A B C) (u1_incsp_1 A))) ) ).
tt(dt_k2_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k2_prvect_1 A B C)) &  ((v1_funct_2 (k2_prvect_1 A B C) (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A)) (k4_finseq_2 C A)) & (m1_subset_1 (k2_prvect_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A)) (k4_finseq_2 C A))))) ) ) ) ).
tt(dt_k2_prvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_prvect_2 C A B)) )  =>  ((v1_funct_1 (k2_prvect_2 A B C)) &  ((v1_funct_2 (k2_prvect_2 A B C) (k2_zfmisc_1 B (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 (k2_prvect_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (k4_card_3 A)) (k4_card_3 A))))) ) ) ) ).
tt(dt_k2_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  =>  ((v1_funct_1 (k2_prvect_3 A B)) &  ((v1_funct_2 (k2_prvect_3 A B) (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 (k2_prvect_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k2_pscomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  => (m1_subset_1 (k2_pscomp_1 A B) k1_numbers)) ) ).
tt(dt_k2_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v4_unialg_1 A) & (l1_unialg_1 A))  & (m1_subset_1 B (k4_finseq_1 (u1_unialg_1 A))))  => (m1_pua2mss1 (k2_pua2mss1 A B) (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A)))) ) ).
tt(dt_k2_pzfmisc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k2_pzfmisc1 A B C)) &  ((v4_relat_1 (k2_pzfmisc1 A B C) A) &  ((v1_funct_1 (k2_pzfmisc1 A B C)) & (v1_partfun1 (k2_pzfmisc1 A B C) A)) ) ) ) ) ).
tt(dt_k2_qc_lang1,ax,$true).
tt(dt_k2_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k2_qc_lang2 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k2_qc_lang3,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_qc_lang1 A)))  => (m2_subset_1 (k2_qc_lang3 A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k2_qc_lang4,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  =>  ((v1_relat_1 (k2_qc_lang4 A B)) &  ((v5_relat_1 (k2_qc_lang4 A B) (k9_qc_lang1 A)) &  ((v1_funct_1 (k2_qc_lang4 A B)) &  ((v1_finset_1 (k2_qc_lang4 A B)) & (v3_trees_2 (k2_qc_lang4 A B))) ) ) ) ) ) ).
tt(dt_k2_qmax_1,ax,$true).
tt(dt_k2_quantal1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_quantal1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_quatern2,ax,(m1_subset_1 k2_quatern2 k1_quaterni)).
tt(dt_k2_quatern3,ax, (! [A:$i] :  ((m1_subset_1 A k1_quaterni) => (m1_subset_1 (k2_quatern3 A) k1_quaterni)) ) ).
tt(dt_k2_quaterni,ax,$true).
tt(dt_k2_quin_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k2_quin_1 A B C) k1_numbers)) ) ).
tt(dt_k2_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  => (m2_subset_1 (k2_quofield A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A))) ) ).
tt(dt_k2_radix_1,ax,$true).
tt(dt_k2_radix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C k5_numbers)) ) )  =>  ((v3_card_1 (k2_radix_2 A B C) A) & (m2_finseq_1 (k2_radix_2 A B C) k5_numbers)) ) ) ).
tt(dt_k2_radix_3,ax,$true).
tt(dt_k2_radix_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v3_card_1 C A) & (m1_finseq_1 C (k4_radix_3 B)))  &  ((v3_card_1 D A) & (m1_finseq_1 D (k4_radix_3 B))) ) ) )  =>  ((v3_card_1 (k2_radix_4 A B C D) A) & (m2_finseq_1 (k2_radix_4 A B C D) (k4_radix_3 B))) ) ) ).
tt(dt_k2_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k2_radix_5 A B C) A) & (m2_finseq_1 (k2_radix_5 A B C) (k3_radix_1 C))) ) ) ).
tt(dt_k2_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k2_radix_6 A B C) (k2_xcmplx_0 A 2)) & (m2_finseq_1 (k2_radix_6 A B C) (k3_radix_1 B))) ) ) ).
tt(dt_k2_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  => (m2_prob_1 (k2_random_1 A) A (k1_random_1 A))) ) ).
tt(dt_k2_random_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ((m2_prob_1 C A (k1_random_1 A)) & (m2_prob_1 D B (k1_random_1 B))) ) )  => (m2_prob_1 (k2_random_2 A B C D) (k2_zfmisc_1 A B) (k1_random_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k2_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k2_ranknull A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k2_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (v1_int_1 (k2_rat_1 A))) ) ).
tt(dt_k2_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k2_ratfunc1 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (m1_subset_1 (k2_rcomp_1 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k2_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k2_real_1 A) k1_numbers)) ) ).
tt(dt_k2_real_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k2_real_3 A B)) &  ((v1_funct_2 (k2_real_3 A B) k5_numbers k5_numbers) & (m1_subset_1 (k2_real_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k2_real_lat,ax, ((v1_funct_1 k2_real_lat) &  ((v1_funct_2 k2_real_lat (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k2_real_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k2_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k2_real_ns1 A)) &  ((v1_funct_2 (k2_real_ns1 A) (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A)) & (m1_subset_1 (k2_real_ns1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)) (k1_euclid A))))) ) ) ) ).
tt(dt_k2_realset2,ax, ((v1_funct_1 k2_realset2) &  ((v1_funct_2 k2_realset2 (k2_zfmisc_1 2 2) 2) & (m1_subset_1 k2_realset2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 2 2) 2)))) ) ).
tt(dt_k2_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k2_realset3 A)) &  ((v1_funct_2 (k2_realset3 A) (k2_zfmisc_1 (u1_struct_0 A) (k8_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k2_realset3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k8_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_rearran1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((v1_rearran1 B) &  ((v2_rearran1 B) &  ((v3_rearran1 B (k1_zfmisc_1 A)) & (m1_finseq_1 B (k1_zfmisc_1 A))) ) ) )  =>  ((v1_rearran1 (k2_rearran1 A B)) &  ((v2_rearran1 (k2_rearran1 A B)) &  ((v3_rearran1 (k2_rearran1 A B) (k1_zfmisc_1 A)) & (m2_finseq_1 (k2_rearran1 A B) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(dt_k2_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k2_relat_1 A))) ) ).
tt(dt_k2_relset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  => (m1_subset_1 (k2_relset_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_rewrite1,ax,$true).
tt(dt_k2_rewrite2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_rewrite2 B)) ) )  =>  ((v1_relat_1 (k2_rewrite2 A B)) &  ((v1_funct_1 (k2_rewrite2 A B)) & (v1_rewrite2 (k2_rewrite2 A B))) ) ) ) ).
tt(dt_k2_rewrite3,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  => (m1_subset_1 (k2_rewrite3 A B) (k8_afinsq_1 B))) ) ).
tt(dt_k2_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k2_rfinseq2 A) k5_numbers)) ) ).
tt(dt_k2_rfinseq,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  => (m2_finseq_1 (k2_rfinseq A B C) A)) ) ).
tt(dt_k2_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k2_rfunct_3 A) k1_numbers)) ) ).
tt(dt_k2_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k2_rinfsup1 A) k1_numbers)) ) ).
tt(dt_k2_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k2_rinfsup2 A) k7_numbers)) ) ).
tt(dt_k2_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ((v36_algstr_0 (k2_ring_1 A B)) & (l6_algstr_0 (k2_ring_1 A B))) ) ) ).
tt(dt_k2_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ( (~ (v2_struct_0 (k2_ringcat1 A)))  &  ((v13_algstr_0 (k2_ringcat1 A)) &  ((v2_rlvect_1 (k2_ringcat1 A)) &  ((v3_rlvect_1 (k2_ringcat1 A)) &  ((v4_rlvect_1 (k2_ringcat1 A)) &  ((v3_group_1 (k2_ringcat1 A)) &  ((v4_vectsp_1 (k2_ringcat1 A)) &  ((v5_vectsp_1 (k2_ringcat1 A)) & (l6_algstr_0 (k2_ringcat1 A))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k2_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  &  ((m1_rlvect_2 B A) & (m1_subset_1 C k1_numbers)) )  => (m1_rlvect_2 (k2_rlaffin1 A B C) A)) ) ).
tt(dt_k2_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k2_rlaffin2 A)) &  ((v1_funct_2 (k2_rlaffin2 A) (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k2_rlaffin2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_rlaffin3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k2_rlaffin3 A B C)) &  ((v1_funct_2 (k2_rlaffin3 A B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k2_rlaffin3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k2_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_1 (k2_rlsub_1 A)) & (m1_rlsub_1 (k2_rlsub_1 A) A)) ) ) ).
tt(dt_k2_rlsub_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_rlsub_1 B A) & (m1_rlsub_1 C A)) )  =>  ((v1_rlvect_1 (k2_rlsub_2 A B C)) & (m1_rlsub_1 (k2_rlsub_2 A B C) A)) ) ) ).
tt(dt_k2_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_rltopsp1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_rlvect_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_rlvect_5,ax,$true).
tt(dt_k2_rlvect_x,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_rlvect_x A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_rmod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((v2_vectsp_2 (k2_rmod_2 A B) A) & (m1_rmod_2 (k2_rmod_2 A B) A B)) ) ) ).
tt(dt_k2_rmod_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_2 C A B) & (m1_rmod_2 D A B)) ) )  =>  ((v2_vectsp_2 (k2_rmod_3 A B C D) A) & (m1_rmod_2 (k2_rmod_3 A B C D) A B)) ) ) ).
tt(dt_k2_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_rmod_4 C A B)) )  =>  ((v1_finset_1 (k2_rmod_4 A B C)) & (m1_subset_1 (k2_rmod_4 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ).
tt(dt_k2_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_partfun1 (k2_robbins3 A) (u1_struct_0 A)) &  ((v1_relat_2 (k2_robbins3 A)) &  ((v4_relat_2 (k2_robbins3 A)) &  ((v8_relat_2 (k2_robbins3 A)) & (m1_subset_1 (k2_robbins3 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k2_robbins4,ax, ((v4_robbins1 k2_robbins4) & (l4_robbins1 k2_robbins4)) ).
tt(dt_k2_roughs_1,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (k2_roughs_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k2_rpr_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A))) )  => (m1_subset_1 (k2_rpr_1 A B C) k1_numbers)) ) ).
tt(dt_k2_rsspace3,ax, ((v1_funct_1 k2_rsspace3) &  ((v1_funct_2 k2_rsspace3 k1_rsspace3 k1_numbers) & (m1_subset_1 k2_rsspace3 (k1_zfmisc_1 (k2_zfmisc_1 k1_rsspace3 k1_numbers)))) ) ).
tt(dt_k2_rsspace4,ax, ((v1_funct_1 k2_rsspace4) &  ((v1_funct_2 k2_rsspace4 k1_rsspace4 k1_numbers) & (m1_subset_1 k2_rsspace4 (k1_zfmisc_1 (k2_zfmisc_1 k1_rsspace4 k1_numbers)))) ) ).
tt(dt_k2_rsspace,ax, (! [A:$i] :  ((v1_funct_1 (k2_rsspace A)) &  ((v1_funct_2 (k2_rsspace A) k5_numbers k1_numbers) & (m1_subset_1 (k2_rsspace A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ).
tt(dt_k2_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_bhsp_1 (k2_rusub_1 A)) & (m1_rusub_1 (k2_rusub_1 A) A)) ) ) ).
tt(dt_k2_rusub_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_rusub_1 B A) & (m1_rusub_1 C A)) )  =>  ((v1_bhsp_1 (k2_rusub_2 A B C)) & (m1_rusub_1 (k2_rusub_2 A B C) A)) ) ) ).
tt(dt_k2_rusub_4,ax,$true).
tt(dt_k2_rusub_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_rusub_1 B A))  =>  ((v1_bhsp_1 (k2_rusub_5 A B)) & (m1_rusub_1 (k2_rusub_5 A B) A)) ) ) ).
tt(dt_k2_rvsum_1,ax, ((v1_funct_1 k2_rvsum_1) &  ((v1_funct_2 k2_rvsum_1 k1_numbers k1_numbers) & (m1_subset_1 k2_rvsum_1 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k2_rvsum_2,ax, ((v1_funct_1 k2_rvsum_2) &  ((v1_funct_2 k2_rvsum_2 k2_numbers k2_numbers) & (m1_subset_1 k2_rvsum_2 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k2_scmbsort,ax, ((v1_relat_1 k2_scmbsort) &  ((v4_relat_1 k2_scmbsort k5_numbers) &  ((v5_relat_1 k2_scmbsort (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 k2_scmbsort) &  ( (~ (v1_xboole_0 k2_scmbsort))  &  ((v1_finset_1 k2_scmbsort) & (v1_afinsq_1 k2_scmbsort)) ) ) ) ) ) ).
tt(dt_k2_scm_comp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k7_dtconstr k1_scm_comp)) &  ((m1_subset_1 B (k4_dtconstr k1_scm_comp)) & (m1_subset_1 C (k4_dtconstr k1_scm_comp))) )  => (m1_dtconstr (k2_scm_comp A B C) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k2_scmfsa_1,ax,(m1_subset_1 k2_scmfsa_1 (k1_zfmisc_1 k1_scmfsa_1))).
tt(dt_k2_scmfsa_2,ax,(m1_subset_1 k2_scmfsa_2 (k1_zfmisc_1 (u1_struct_0 k1_scmfsa_2)))).
tt(dt_k2_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 (k2_scmfsa6a A)) &  ((v4_relat_1 (k2_scmfsa6a A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa6a A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa6a A)) & (v1_finset_1 (k2_scmfsa6a A))) ) ) ) ) ) ).
tt(dt_k2_scmfsa_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((v5_ordinal1 (k2_scmfsa_7 A B)) &  ((v1_relat_1 (k2_scmfsa_7 A B)) &  ((v5_relat_1 (k2_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa_7 A B)) & (v1_finset_1 (k2_scmfsa_7 A B))) ) ) ) ) ) ).
tt(dt_k2_scmfsa8a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  => (m2_subset_1 (k2_scmfsa8a A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k2_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8b A B C)))  &  ((v1_relat_1 (k2_scmfsa8b A B C)) &  ((v4_relat_1 (k2_scmfsa8b A B C) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8b A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8b A B C)) &  ((v1_finset_1 (k2_scmfsa8b A B C)) & (v1_afinsq_1 (k2_scmfsa8b A B C))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmfsa8c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8c A B)))  &  ((v1_relat_1 (k2_scmfsa8c A B)) &  ((v4_relat_1 (k2_scmfsa8c A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8c A B)) &  ((v1_finset_1 (k2_scmfsa8c A B)) & (v1_afinsq_1 (k2_scmfsa8c A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmfsa9a,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  => (m2_subset_1 (k2_scmfsa9a A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k2_scmfsa_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_scmfsa_9 A B)) &  ((v4_relat_1 (k2_scmfsa_9 A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa_9 A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k2_scmfsa_9 A B)))  &  ((v1_funct_1 (k2_scmfsa_9 A B)) &  ((v1_finset_1 (k2_scmfsa_9 A B)) & (v1_afinsq_1 (k2_scmfsa_9 A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmfsa_i,ax, (~ (v1_xboole_0 k2_scmfsa_i)) ).
tt(dt_k2_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  ((v1_ami_2 (k2_scmfsa_m A)) & (m1_subset_1 (k2_scmfsa_m A) (u1_struct_0 k1_scmfsa_2))) ) ) ).
tt(dt_k2_scm_inst,ax,$true).
tt(dt_k2_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ( (~ (v1_xboole_0 (k2_scmisort A)))  &  ((v1_relat_1 (k2_scmisort A)) &  ((v4_relat_1 (k2_scmisort A) k5_numbers) &  ((v5_relat_1 (k2_scmisort A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmisort A)) &  ((v1_finset_1 (k2_scmisort A)) & (v1_afinsq_1 (k2_scmisort A))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmpds_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) & (v1_int_1 B))  => (m1_subset_1 (k2_scmpds_1 A B) k5_numbers)) ) ).
tt(dt_k2_scmpds_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((v1_ami_2 (k2_scmpds_2 A B)) & (m1_subset_1 (k2_scmpds_2 A B) (u1_struct_0 k1_scmpds_2))) ) ) ).
tt(dt_k2_scmpds_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_4 A B)))  &  ((v1_relat_1 (k2_scmpds_4 A B)) &  ((v4_relat_1 (k2_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_4 A B)) &  ((v1_finset_1 (k2_scmpds_4 A B)) & (v1_afinsq_1 (k2_scmpds_4 A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_6 A B C D)))  &  ((v1_relat_1 (k2_scmpds_6 A B C D)) &  ((v4_relat_1 (k2_scmpds_6 A B C D) k5_numbers) &  ((v5_relat_1 (k2_scmpds_6 A B C D) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_6 A B C D)) &  ((v1_finset_1 (k2_scmpds_6 A B C D)) & (v1_afinsq_1 (k2_scmpds_6 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmpds_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ((m1_subset_1 C k5_numbers) &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_7 A B C D)))  &  ((v1_relat_1 (k2_scmpds_7 A B C D)) &  ((v4_relat_1 (k2_scmpds_7 A B C D) k5_numbers) &  ((v5_relat_1 (k2_scmpds_7 A B C D) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_7 A B C D)) &  ((v1_finset_1 (k2_scmpds_7 A B C D)) & (v1_afinsq_1 (k2_scmpds_7 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_8 A B C)))  &  ((v1_relat_1 (k2_scmpds_8 A B C)) &  ((v4_relat_1 (k2_scmpds_8 A B C) k5_numbers) &  ((v5_relat_1 (k2_scmpds_8 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_8 A B C)) &  ((v1_finset_1 (k2_scmpds_8 A B C)) & (v1_afinsq_1 (k2_scmpds_8 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k2_scmpds_i,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_scm_inst) & (v1_int_1 B))  => (m2_finseq_1 (k2_scmpds_i A B) (k2_xboole_0 k2_scm_inst k4_numbers))) ) ).
tt(dt_k2_scmp_gcd,ax, ((v1_ami_2 k2_scmp_gcd) & (m1_subset_1 k2_scmp_gcd (u1_struct_0 k1_scmpds_2))) ).
tt(dt_k2_scmring1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))))  => (m1_subset_1 (k2_scmring1 A B) k5_numbers)) ) ).
tt(dt_k2_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 B (u1_struct_0 (k1_scmring2 A)))) ) ) )  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k2_scmring2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_ami_2 (k2_scmring3 A B)) & (m1_subset_1 (k2_scmring3 A B) (u1_struct_0 (k1_scmring2 A)))) ) ) ).
tt(dt_k2_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k2_scmringi A B) k2_scm_inst)) ) ).
tt(dt_k2_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v5_finset_1 A))  => (v7_ordinal1 (k2_scmyciel A))) ) ).
tt(dt_k2_scpinvar,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) ) )  => (m2_subset_1 (k2_scpinvar A B) k1_numbers k5_numbers)) ) ).
tt(dt_k2_scpqsort,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k2_scpqsort A B)))  &  ((v1_relat_1 (k2_scpqsort A B)) &  ((v4_relat_1 (k2_scpqsort A B) k5_numbers) &  ((v5_relat_1 (k2_scpqsort A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scpqsort A B)) &  ((v1_finset_1 (k2_scpqsort A B)) & (v1_afinsq_1 (k2_scpqsort A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_semi_af1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_semi_af1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k2_seq_2 A) k1_numbers)) ) ).
tt(dt_k2_seq_4,ax, (! [A:$i] :  ((v3_membered A) => (v1_xreal_0 (k2_seq_4 A))) ) ).
tt(dt_k2_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k2_seqfunc A B C)) &  ((v1_funct_2 (k2_seqfunc A B C) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k2_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k2_series_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v1_valued_0 A)) ) ) )  =>  ((v1_relat_1 (k2_series_1 A)) &  ((v4_relat_1 (k2_series_1 A) k5_numbers) &  ((v1_funct_1 (k2_series_1 A)) &  ((v1_partfun1 (k2_series_1 A) k5_numbers) & (v1_valued_0 (k2_series_1 A))) ) ) ) ) ) ).
tt(dt_k2_setfam_1,ax,$true).
tt(dt_k2_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k2_setlim_1 A B)) &  ((v1_funct_2 (k2_setlim_1 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k2_setlim_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k2_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_funct_1 (k2_setlim_2 A B C)) &  ((v1_funct_2 (k2_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k2_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k2_setwiseo,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k2_setwiseo A B) (k5_finsub_1 A))) ) ).
tt(dt_k2_setwop_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k2_setwop_2 A) (k5_finsub_1 k5_numbers))) ) ).
tt(dt_k2_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k2_sfmastr1 A B)))  &  ((v1_relat_1 (k2_sfmastr1 A B)) &  ((v4_relat_1 (k2_sfmastr1 A B) k5_numbers) &  ((v5_relat_1 (k2_sfmastr1 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_sfmastr1 A B)) &  ((v1_finset_1 (k2_sfmastr1 A B)) & (v1_afinsq_1 (k2_sfmastr1 A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_sfmastr2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_sfmastr2 A B)))  &  ((v1_relat_1 (k2_sfmastr2 A B)) &  ((v4_relat_1 (k2_sfmastr2 A B) k5_numbers) &  ((v5_relat_1 (k2_sfmastr2 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_sfmastr2 A B)) &  ((v1_finset_1 (k2_sfmastr2 A B)) & (v1_afinsq_1 (k2_sfmastr2 A B))) ) ) ) ) ) ) ) ).
tt(dt_k2_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_sfmastr3 A B C D)) &  ((v4_relat_1 (k2_sfmastr3 A B C D) k5_numbers) &  ((v5_relat_1 (k2_sfmastr3 A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_sfmastr3 A B C D)) &  ( (~ (v1_xboole_0 (k2_sfmastr3 A B C D)))  &  ((v1_finset_1 (k2_sfmastr3 A B C D)) & (v1_afinsq_1 (k2_sfmastr3 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k2_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (m1_subset_1 (k2_sf_mastr A) (k1_zfmisc_1 k2_scmfsa_2))) ) ).
tt(dt_k2_sgraph1,ax,$true).
tt(dt_k2_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  => (m1_subset_1 (k2_sheffer1 A) (u1_struct_0 A))) ) ).
tt(dt_k2_simplex0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_classes1 (k2_simplex0 A B)) & (m1_subset_1 (k2_simplex0 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k2_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_simplex0 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  => (m1_subset_1 (k2_simplex1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_simplex2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v1_simplex2 B A) & (l1_pre_topc B)) ) ) )  => (m1_subset_1 (k2_simplex2 A B) k1_numbers)) ) ).
tt(dt_k2_sincos10,ax, ((v1_funct_1 k2_sincos10) & (m1_subset_1 k2_sincos10 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k2_sin_cos2,ax,$true).
tt(dt_k2_sin_cos3,ax, ((v1_funct_1 k2_sin_cos3) &  ((v1_funct_2 k2_sin_cos3 k2_numbers k2_numbers) & (m1_subset_1 k2_sin_cos3 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k2_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k2_sin_cos4 A) k1_numbers)) ) ).
tt(dt_k2_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k2_sin_cos5 A) k1_numbers)) ) ).
tt(dt_k2_sin_cos6,ax,$true).
tt(dt_k2_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k2_sin_cos7 A))) ) ).
tt(dt_k2_sin_cos9,ax, ((v1_funct_1 k2_sin_cos9) & (m1_subset_1 k2_sin_cos9 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k2_sin_cos,ax, ((v1_funct_1 k2_sin_cos) &  ((v1_funct_2 k2_sin_cos k5_numbers k1_numbers) & (m1_subset_1 k2_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(dt_k2_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k2_square_1 A B) k1_numbers)) ) ).
tt(dt_k2_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  => (m2_finseq_2 (k2_stacks_1 A B C) A (k3_finseq_2 A))) ) ).
tt(dt_k2_stirl2_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (m1_subset_1 (k2_stirl2_1 A B C D) B)) ) ).
tt(dt_k2_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) => (m1_subset_1 (k2_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  => (m2_subset_1 (k2_sublemma A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k2_subset_1,ax, (! [A:$i] : (m1_subset_1 (k2_subset_1 A) (k1_zfmisc_1 A))) ).
tt(dt_k2_substlat,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_substlat A B)) & (m1_subset_1 D (k1_substlat A B)))  => (m1_subset_1 (k2_substlat A B C D) (k5_finsub_1 (k4_partfun1 A B)))) ) ).
tt(dt_k2_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_substut1 A)))  =>  ((v1_funct_1 (k2_substut1 A B)) & (m1_subset_1 (k2_substut1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) (k3_qc_lang1 A))))) ) ) ).
tt(dt_k2_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k1_substut1 A))) )  => (m2_subset_1 (k2_substut2 A B C) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k2_supinf_1,ax,(m1_subset_1 k2_supinf_1 k7_numbers)).
tt(dt_k2_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (m1_subset_1 (k2_supinf_2 A) k7_numbers)) ) ).
tt(dt_k2_symsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m1_subset_1 E (u1_struct_0 B)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  => (m1_subset_1 (k2_symsp_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k2_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ( (~ (v1_xboole_0 (k2_t_0topsp A)))  & (m1_eqrel_1 (k2_t_0topsp A) (u1_struct_0 A))) ) ) ).
tt(dt_k2_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_pre_topc (k2_t_1topsp A)) & (l1_pre_topc (k2_t_1topsp A))) ) ) ).
tt(dt_k2_tarski,ax,$true).
tt(dt_k2_taxonom1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  => (m1_subset_1 (k2_taxonom1 A B) (k1_zfmisc_1 (k1_partit1 A)))) ) ).
tt(dt_k2_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k2_taylor_1 A)) & (m1_subset_1 (k2_taylor_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k2_tbsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k2_tbsp_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_analoaf (k2_tdgroup A)) & (l1_analoaf (k2_tdgroup A))) ) ) ).
tt(dt_k2_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k2_tdlat_1 A)) &  ((v1_funct_2 (k2_tdlat_1 A) (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A)) & (m1_subset_1 (k2_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A))))) ) ) ) ).
tt(dt_k2_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_termord A B C D)) &  ((v4_relat_1 (k2_termord A B C D) A) &  ((v1_funct_1 (k2_termord A B C D)) &  ((v1_partfun1 (k2_termord A B C D) A) &  ((v4_valued_0 (k2_termord A B C D)) & (v2_pre_poly (k2_termord A B C D))) ) ) ) ) ) ) ).
tt(dt_k2_tex_1,ax, (! [A:$i] : (l1_pre_topc (k2_tex_1 A))) ).
tt(dt_k2_tex_4,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_tex_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_tmap_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (l1_struct_0 D)) ) )  =>  ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_toler_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_relat_2 (k2_toler_1 A B C)) &  ((v3_relat_2 (k2_toler_1 A B C)) &  ((v1_partfun1 (k2_toler_1 A B C) C) & (m1_subset_1 (k2_toler_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) ) ) ) ).
tt(dt_k2_topalg_1,ax,$true).
tt(dt_k2_topalg_2,ax, ((v2_topalg_2 k2_topalg_2) & (m1_pre_topc k2_topalg_2 k3_topmetr)) ).
tt(dt_k2_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A C C) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) )  => (m1_borsuk_2 (k2_topalg_3 A B C D E) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C))) ) ).
tt(dt_k2_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k2_topalg_4 A B C D E)) &  ((v1_funct_2 (k2_topalg_4 A B C D E) (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B))) & (m1_subset_1 (k2_topalg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) ).
tt(dt_k2_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_borsuk_2 (k2_topalg_5 A) k2_topalg_2 (k4_toprealb k6_numbers) (k4_toprealb A))) ) ).
tt(dt_k2_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v5_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  => (m1_subset_1 (k2_topalg_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_topdim_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_int_1 (k2_topdim_1 A B))) ) ).
tt(dt_k2_topgen_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_topgen_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  => (v1_card_1 (k2_topgen_2 A))) ) ).
tt(dt_k2_topgen_3,ax, ( (~ (v2_struct_0 k2_topgen_3))  &  ((v1_pre_topc k2_topgen_3) &  ((v2_pre_topc k2_topgen_3) & (l1_pre_topc k2_topgen_3)) ) ) ).
tt(dt_k2_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (m1_subset_1 (k2_topgen_4 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k2_topgen_5,ax,(m1_subset_1 k2_topgen_5 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))).
tt(dt_k2_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k2_topgrp_1 A B)) &  ((v1_funct_2 (k2_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k2_topgrp_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_topmetr,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (~ (v2_struct_0 (k2_topmetr A B)))  &  ((v1_metric_1 (k2_topmetr A B)) & (m1_topmetr (k2_topmetr A B) k8_metric_1)) ) ) ) ).
tt(dt_k2_topreal1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_finseq_1 B (u1_struct_0 (k15_euclid A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k2_topreal1 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k2_topreal7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k2_topreal7 A B C D) (u1_struct_0 (k1_topreal7 A B)))) ) ).
tt(dt_k2_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k2_topreal9 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k2_topreala,ax, ((v1_funct_1 k2_topreala) &  ((v1_funct_2 k2_topreala (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 k2_topreala (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(dt_k2_toprealc,ax, (! [A:$i] :  ((v1_valued_2 A) => (v1_valued_2 (k2_toprealc A))) ) ).
tt(dt_k2_toprns_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((v7_ordinal1 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid B)))))) ) ) )  =>  ((v1_funct_1 (k2_toprns_1 A B C)) &  ((v1_funct_2 (k2_toprns_1 A B C) k5_numbers (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k2_toprns_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid B)))))) ) ) ) ).
tt(dt_k2_tops_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k2_tops_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_tops_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k2_tops_2 A B C)) &  ((v1_funct_2 (k2_tops_2 A B C) B A) & (m1_subset_1 (k2_tops_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k2_transgeo,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ((v1_funct_1 (k2_transgeo A B C)) &  ((v1_funct_2 (k2_transgeo A B C) A A) &  ((v3_funct_2 (k2_transgeo A B C) A A) & (m1_subset_1 (k2_transgeo A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k2_treal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k2_treal_1 A B) (u1_struct_0 (k4_topmetr A B)))) ) ).
tt(dt_k2_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k2_trees_1 A)))  & (v1_trees_1 (k2_trees_1 A))) ) ) ).
tt(dt_k2_trees_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  & (v7_ordinal1 B))  => (m2_trees_2 (k2_trees_2 A B) A)) ) ).
tt(dt_k2_trees_3,ax,(m1_subset_1 k2_trees_3 (k1_zfmisc_1 k1_trees_3))).
tt(dt_k2_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k2_trees_4 A B) (k5_trees_3 A))) ) ).
tt(dt_k2_trees_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k2_trees_9 A B)) &  ((v1_funct_1 (k2_trees_9 A B)) & (v1_finseq_1 (k2_trees_9 A B))) ) ) ) ).
tt(dt_k2_trees_a,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  & (m1_subset_1 B A))  => (m4_trees_1 (k2_trees_a A B) A)) ) ).
tt(dt_k2_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ( (~ (v2_struct_0 (k2_tsep_1 A B C)))  &  ((v1_pre_topc (k2_tsep_1 A B C)) & (m1_pre_topc (k2_tsep_1 A B C) A)) ) ) ) ).
tt(dt_k2_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D B)) ) )  =>  ((v1_funct_1 (k2_turing_1 A B C D)) & (m1_subset_1 (k2_turing_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k2_twoscomp,ax, ((v1_funct_1 k2_twoscomp) &  ((v1_funct_2 k2_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k2_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k2_unialg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (k1_unialg_2 A))) )  =>  ( (~ (v1_xboole_0 (k2_unialg_2 A B C)))  &  ((v1_funct_1 (k2_unialg_2 A B C)) &  ((v2_margrel1 (k2_unialg_2 A B C)) &  ((v3_margrel1 (k2_unialg_2 A B C) B) & (m1_subset_1 (k2_unialg_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 B) B)))) ) ) ) ) ) ).
tt(dt_k2_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  => (m1_subset_1 (k2_uniroots A) (k1_zfmisc_1 (u1_struct_0 k1_complfld)))) ) ).
tt(dt_k2_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  & (m1_subset_1 C k5_numbers))  => (m2_subset_1 (k2_uproots A B C) (k14_pre_poly A) (k15_pre_poly A))) ) ).
tt(dt_k2_urysohn1,ax,(m1_subset_1 k2_urysohn1 (k1_zfmisc_1 k1_numbers))).
tt(dt_k2_urysohn3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m2_subset_1 (k2_urysohn3 A) k1_numbers k5_numbers)) ) ).
tt(dt_k2_valuat_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  (~ (v1_xboole_0 B)) )  => (m1_funct_2 (k2_valuat_1 A B) (k3_qc_lang1 A) B)) ) ).
tt(dt_k2_valued_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  => (m2_valued_0 (k2_valued_0 A B C) A C)) ) ).
tt(dt_k2_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k2_valued_1 A B C D E)) & (m1_subset_1 (k2_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k2_valued_2,ax,$true).
tt(dt_k2_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k2_vectmetr A) (k1_zfmisc_1 (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k2_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ( (~ (v1_xboole_0 (k2_vectsp10 A B C)))  & (m1_subset_1 (k2_vectsp10 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ).
tt(dt_k2_vectsp11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v7_vectsp_1 (k2_vectsp11 A B C) A) & (m1_vectsp_4 (k2_vectsp11 A B C) A B)) ) ) ).
tt(dt_k2_vectsp_1,ax, ((v36_algstr_0 k2_vectsp_1) & (l6_algstr_0 k2_vectsp_1)) ).
tt(dt_k2_vectsp_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v7_vectsp_1 (k2_vectsp_4 A B) A) & (m1_vectsp_4 (k2_vectsp_4 A B) A B)) ) ) ).
tt(dt_k2_vectsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_vectsp_4 D A B)) ) )  =>  ((v7_vectsp_1 (k2_vectsp_5 A B C D) A) & (m1_vectsp_4 (k2_vectsp_5 A B C D) A B)) ) ) ).
tt(dt_k2_vectsp_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  => (m1_vectsp_6 (k2_vectsp_6 A B) A B)) ) ).
tt(dt_k2_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_vectsp_8 A B)))  & (m1_vectsp_8 (k2_vectsp_8 A B) A B)) ) ) ).
tt(dt_k2_vectsp_9,ax,$true).
tt(dt_k2_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k2_vfunct_1 A B C D)) & (m1_subset_1 (k2_vfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k2_vfunct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  & (v1_xcmplx_0 D)) ) )  =>  ((v1_funct_1 (k2_vfunct_2 A B C D)) & (m1_subset_1 (k2_vfunct_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k2_waybel_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  & (m1_subset_1 C (u1_struct_0 B))) )  => (m1_subset_1 (k2_waybel_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ( (~ (v2_struct_0 (k2_waybel10 A)))  &  ((v1_orders_2 (k2_waybel10 A)) &  ((v4_yellow_0 (k2_waybel10 A) (k7_yellow_1 A A)) & (m1_yellow_0 (k2_waybel10 A) (k7_yellow_1 A A))) ) ) ) ) ).
tt(dt_k2_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (m4_yellow_6 (k2_waybel11 A) A)) ) ).
tt(dt_k2_waybel17,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k2_waybel17 A B)) &  ((v4_yellow_0 (k2_waybel17 A B) (k7_yellow_1 A B)) & (m1_yellow_0 (k2_waybel17 A B) (k7_yellow_1 A B))) ) ) ) ).
tt(dt_k2_waybel18,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_waybel18 B)) ) ) )  => (m1_subset_1 (k2_waybel18 A B) (k1_zfmisc_1 (k1_zfmisc_1 (k4_card_3 (k12_pralg_1 A B)))))) ) ).
tt(dt_k2_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (m1_subset_1 (k2_waybel19 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k2_waybel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k2_waybel_1 A B C)) &  ((v1_funct_2 (k2_waybel_1 A B C) (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A B C))) & (m1_subset_1 (k2_waybel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A B C)))))) ) ) ) ).
tt(dt_k2_waybel20,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_partfun1 (k2_waybel20 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k2_waybel20 A B)) &  ((v8_relat_2 (k2_waybel20 A B)) & (m1_subset_1 (k2_waybel20 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k2_waybel22,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k2_waybel22 A B C)) &  ((v1_funct_2 (k2_waybel22 A B C) (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B)) & (m1_subset_1 (k2_waybel22 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_waybel23,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_card_1 (k2_waybel23 A))) ) ).
tt(dt_k2_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k2_waybel24 A B C D E)) &  ((v1_funct_2 (k2_waybel24 A B C D E) (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 (k2_waybel24 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k2_waybel25,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  &  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D C)) ) )  & (m1_subset_1 E A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel25 A B C D E)))  &  ((v4_orders_2 (k2_waybel25 A B C D E)) &  ((v6_waybel_0 (k2_waybel25 A B C D E) B) &  ((v7_waybel_0 (k2_waybel25 A B C D E)) & (l1_waybel_0 (k2_waybel25 A B C D E) B)) ) ) ) ) ) ).
tt(dt_k2_waybel26,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_waybel26 A B))))) ) )  => (m1_subset_1 (k2_waybel26 A B C D) (k1_zfmisc_1 (u1_struct_0 (k1_waybel25 B))))) ) ).
tt(dt_k2_waybel27,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k2_waybel27 A B)) & (l1_orders_2 (k2_waybel27 A B))) ) ) ).
tt(dt_k2_waybel28,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_waybel28 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) )  =>  ((v6_waybel_0 (k2_waybel28 A B C) A) & (m2_yellow_6 (k2_waybel28 A B C) A B)) ) ) ).
tt(dt_k2_waybel29,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k2_waybel29 A B C)) &  ((v1_funct_2 (k2_waybel29 A B C) (u1_struct_0 (k1_waybel29 A)) (u1_struct_0 (k1_waybel29 B))) & (m1_subset_1 (k2_waybel29 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel29 A)) (u1_struct_0 (k1_waybel29 B)))))) ) ) ) ).
tt(dt_k2_waybel_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) )  =>  ( (~ (v2_struct_0 (k2_waybel_2 A B C)))  &  ((v7_waybel_0 (k2_waybel_2 A B C)) & (l1_waybel_0 (k2_waybel_2 A B C) A)) ) ) ) ).
tt(dt_k2_waybel31,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_waybel31 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_waybel32,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ( (~ (v2_struct_0 (k2_waybel32 A B)))  &  ((v6_waybel_0 (k2_waybel32 A B) A) &  ((v7_waybel_0 (k2_waybel32 A B)) & (l1_waybel_0 (k2_waybel32 A B) A)) ) ) ) ) ).
tt(dt_k2_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_waybel34 A B C)) &  ((v1_funct_2 (k2_waybel34 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k2_waybel34 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k2_waybel35,ax,$true).
tt(dt_k2_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_waybel_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k2_waybel_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k2_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (m2_pboole D A C (k7_funcop_1 A B)))  => (m2_pboole (k2_waybel_5 A B C D) (k4_card_3 (k2_funct_6 D)) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) A) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) B))) ) ).
tt(dt_k2_waybel_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  & (m1_subset_1 E B)) ) ) )  => (m1_subset_1 (k2_waybel_6 A B C D E) (u1_struct_0 A))) ) ).
tt(dt_k2_waybel_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k2_waybel_8 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v6_waybel_0 (k2_waybel_9 A) A) & (l1_waybel_0 (k2_waybel_9 A) A)) ) ) ).
tt(dt_k2_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k2_weddwitt A B)) &  ((v1_funct_2 (k2_weddwitt A B) (u1_struct_0 A) (k7_group_3 A B)) & (m1_subset_1 (k2_weddwitt A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k7_group_3 A B))))) ) ) ) ).
tt(dt_k2_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) => (m1_subset_1 (k2_weierstr A) k1_numbers)) ) ).
tt(dt_k2_wellord1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k2_wellord1 A B))) ) ).
tt(dt_k2_wellord2,ax, (! [A:$i] :  ((v1_relat_1 A) => (v3_ordinal1 (k2_wellord2 A))) ) ).
tt(dt_k2_wsierp_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_subset_1 (k2_wsierp_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k2_xboole_0,ax,$true).
tt(dt_k2_xboolean,ax,$true).
tt(dt_k2_xcmplx_0,ax,$true).
tt(dt_k2_xtuple_0,ax,$true).
tt(dt_k2_xxreal_0,ax,$true).
tt(dt_k2_xxreal_1,ax,$true).
tt(dt_k2_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) => (v1_xxreal_0 (k2_xxreal_2 A))) ) ).
tt(dt_k2_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v1_xxreal_0 (k2_xxreal_3 A))) ) ).
tt(dt_k2_yellow_0,ax, (! [A:$i,B:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k2_yellow_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k2_yellow11,ax,(l1_orders_2 k2_yellow11)).
tt(dt_k2_yellow14,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A B)))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k2_yellow14 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k2_yellow15,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (m1_subset_1 (k2_yellow15 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k2_yellow16,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (k2_yellow16 A B C)))  &  ((v3_orders_2 (k2_yellow16 A B C)) &  ((v4_orders_2 (k2_yellow16 A B C)) &  ((v5_orders_2 (k2_yellow16 A B C)) & (l1_orders_2 (k2_yellow16 A B C))) ) ) ) ) ) ).
tt(dt_k2_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) ) )  =>  ((v9_functor0 (k2_yellow18 A B) A B) &  ((v16_functor0 (k2_yellow18 A B) A B) & (m2_functor0 (k2_yellow18 A B) A B)) ) ) ) ).
tt(dt_k2_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  => (m1_subset_1 (k2_yellow19 A B) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ).
tt(dt_k2_yellow_1,ax, (! [A:$i] :  ((v1_orders_2 (k2_yellow_1 A)) & (l1_orders_2 (k2_yellow_1 A))) ) ).
tt(dt_k2_yellow20,ax, (! [A:$i,B:$i] :  ( ((l2_altcat_1 A) & (l2_altcat_1 B))  =>  ((v6_altcat_1 (k2_yellow20 A B)) & (l2_altcat_1 (k2_yellow20 A B))) ) ) ).
tt(dt_k2_yellow21,ax,$true).
tt(dt_k2_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_funct_1 (k2_yellow_2 A)) &  ((v1_funct_2 (k2_yellow_2 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A)) & (m1_subset_1 (k2_yellow_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k2_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  => (m1_subset_1 (k2_yellow_3 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))))) ) ).
tt(dt_k2_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k2_yellow_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k2_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k2_yellow_5 A B C) (u1_struct_0 A))) ) ).
tt(dt_k2_yellow_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k2_yellow_6 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k2_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k2_yellow_9 A B)))  &  ((v6_waybel_0 (k2_yellow_9 A B) A) & (l1_waybel_0 (k2_yellow_9 A B) A)) ) ) ) ).
tt(dt_k2_yoneda_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m2_cat_1 (k2_yoneda_1 A B) A (k1_yoneda_1 A))) ) ).
tt(dt_k2_zf_fund1,ax, ((v1_funct_1 k2_zf_fund1) &  ((v1_funct_2 k2_zf_fund1 k4_ordinal1 k1_zf_lang) & (m1_subset_1 k2_zf_fund1 (k1_zfmisc_1 (k2_zfmisc_1 k4_ordinal1 k1_zf_lang)))) ) ).
tt(dt_k2_zf_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  &  ((m1_subset_1 C k1_zf_lang) & (m1_subset_1 D A)) ) )  =>  ((v1_funct_1 (k2_zf_lang1 A B C D)) &  ((v1_funct_2 (k2_zf_lang1 A B C D) k1_zf_lang A) & (m1_subset_1 (k2_zf_lang1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) ) ) ) ).
tt(dt_k2_zf_lang,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_subset_1 (k2_zf_lang A) k5_numbers k1_zf_lang)) ) ).
tt(dt_k2_zfmisc_1,ax,$true).
tt(dt_k2_zfmodel1,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k2_zfmodel1 A B)) &  ((v1_funct_2 (k2_zfmodel1 A B) B B) & (m1_subset_1 (k2_zfmodel1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(dt_k2_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k2_zf_model A) (k1_zfmisc_1 k1_zf_lang))) ) ).
tt(dt_k2_zfrefle1,ax,(m1_subset_1 k2_zfrefle1 (k1_zfmisc_1 k9_zf_lang))).
tt(dt_k2_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  &  ((v3_ordinal1 C) & (m1_subset_1 C B)) ) )  =>  ((v3_ordinal1 (k2_zf_refle A B C)) & (m1_subset_1 (k2_zf_refle A B C) B)) ) ) ).
tt(dt_k30_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  => (m1_subset_1 (k30_abcmiz_1 A B C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ).
tt(dt_k30_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k30_cat_4 A B) A (k20_cat_4 A B B) B)) ) ).
tt(dt_k30_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m1_subset_1 (k30_fomodel1 A B) k4_numbers)) ) ).
tt(dt_k30_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m2_subset_1 (k30_fomodel2 A B C) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k30_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k30_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k30_gate_1,ax,$true).
tt(dt_k30_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k30_gfacirc1 A B C) (k29_gfacirc1 A B C)) &  ((v4_msafree2 (k30_gfacirc1 A B C) (k29_gfacirc1 A B C)) &  ((v4_circcomb (k30_gfacirc1 A B C) (k29_gfacirc1 A B C)) &  ((v6_circcomb (k30_gfacirc1 A B C) (k29_gfacirc1 A B C)) & (l3_msualg_1 (k30_gfacirc1 A B C) (k29_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k30_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (v1_card_1 (k30_glib_000 A B))) ) ).
tt(dt_k30_mmlquery,ax, (! [A:$i,B:$i] :  ( ((l1_mmlquery A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k30_mmlquery A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k30_modelc_1,ax,$true).
tt(dt_k30_modelc_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k30_modelc_2 A B) (k30_modelc_1 (k25_modelc_2 A)))) ) ).
tt(dt_k30_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  => (m1_subset_1 (k30_modelc_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k23_modelc_3 A) k43_modelc_2) (k23_modelc_3 A))))) ) ).
tt(dt_k30_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k30_osafree A B) (k1_zfmisc_1 (k4_dtconstr (k2_osafree A B))))) ) ).
tt(dt_k30_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_finseq_1 (k30_polyform A) k4_numbers)) ) ).
tt(dt_k30_qc_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k1_qc_lang1 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k30_qc_lang1 A B C) (k1_qc_lang1 A))) ) ).
tt(dt_k30_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_quaterni (k30_quaterni A))) ) ).
tt(dt_k30_sin_cos,ax, ((v1_funct_1 k30_sin_cos) & (m1_subset_1 k30_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k30_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m2_subset_1 (k30_substut1 A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k30_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))))) )  => (m1_subset_1 (k30_turing_1 A B C) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) ) ).
tt(dt_k30_twoscomp,ax, ((v1_funct_1 k30_twoscomp) &  ((v1_funct_2 k30_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k30_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k30_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) & (v1_valued_0 (k30_valued_1 A))) ) ) ) ).
tt(dt_k30_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (v1_xcmplx_0 C)) )  =>  ((v1_relat_1 (k30_valued_2 A B C)) & (v1_funct_1 (k30_valued_2 A B C))) ) ) ).
tt(dt_k31_abcmiz_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) & (m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) )  => (m1_subset_1 (k31_abcmiz_1 A B C D) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ).
tt(dt_k31_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (v1_int_1 F)) ) ) ) )  => (m3_aofa_i00 (k31_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k31_binop_2,ax, ((v1_funct_1 k31_binop_2) &  ((v1_funct_2 k31_binop_2 k1_numbers k1_numbers) & (m1_subset_1 k31_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k31_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) &  ((m1_cat_1 F A B D) & (m1_cat_1 G A C E)) ) ) ) ) )  => (m1_cat_1 (k31_cat_4 A B C D E F G) A (k20_cat_4 A B C) (k20_cat_4 A D E))) ) ).
tt(dt_k31_descip_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_finseq_2 48 k6_margrel1)) => (m2_finseq_2 (k31_descip_1 A) (k4_finseq_2 6 k6_margrel1) (k4_finseq_2 8 (k4_finseq_2 6 k6_margrel1)))) ) ).
tt(dt_k31_fomodel1,ax,$true).
tt(dt_k31_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_fomodel1 A)))  => (m2_subset_1 (k31_fomodel2 A B) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k31_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v7_ordinal1 D) & (m1_subset_1 E (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))) ) ) )  => (m2_funct_2 (k31_fomodel3 A B C D E) (k33_fomodel2 A) (k33_fomodel2 A) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))) ) ).
tt(dt_k31_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k31_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k31_gate_1,ax,$true).
tt(dt_k31_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k31_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k31_gfacirc1 A B C)))  &  ((v1_msualg_1 (k31_gfacirc1 A B C)) &  ((v1_circcomb (k31_gfacirc1 A B C)) &  ((v2_circcomb (k31_gfacirc1 A B C)) &  ((v3_circcomb (k31_gfacirc1 A B C)) & (l1_msualg_1 (k31_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k31_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (v1_card_1 (k31_glib_000 A B))) ) ).
tt(dt_k31_mmlquery,ax, (! [A:$i,B:$i] :  ( ((l1_mmlquery A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k31_mmlquery A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k31_modelc_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k31_modelc_1 A B)) &  ((v1_funct_2 (k31_modelc_1 A B) A k6_margrel1) & (m1_subset_1 (k31_modelc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k31_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k31_modelc_2 A)) &  ((v1_funct_2 (k31_modelc_2 A) (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k31_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k31_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  => (m1_subset_1 (k31_modelc_3 A) (k1_zfmisc_1 (k23_modelc_3 A)))) ) ).
tt(dt_k31_qc_lang1,ax, (! [A:$i,B:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k31_qc_lang1 A B) (k1_qc_lang1 A))) ) ).
tt(dt_k31_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k31_quaterni A) k1_quaterni)) ) ).
tt(dt_k31_sin_cos,ax,(v1_xreal_0 k31_sin_cos)).
tt(dt_k31_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k31_substut1 A B) (k16_substut1 A))) ) ).
tt(dt_k31_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (l1_turing_1 B))  =>  ((v1_funct_1 (k31_turing_1 A B)) &  ((v1_funct_2 (k31_turing_1 A B) (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 (k31_turing_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B))) (k3_zfmisc_1 (k21_turing_1 A B) (k2_xboole_0 (u1_turing_1 A) (u1_turing_1 B)) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ) ) ).
tt(dt_k31_twoscomp,ax, ((v1_funct_1 k31_twoscomp) &  ((v1_funct_2 k31_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k31_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k31_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k31_valued_1 A B C)) & (m1_subset_1 (k31_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k31_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k31_valued_2 A B C D)) & (m1_subset_1 (k31_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k32_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m2_abcmiz_1 (k32_abcmiz_1 A) A (k13_abcmiz_1 A))) ) ).
tt(dt_k32_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k32_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k32_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k32_fomodel1 A) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k32_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v7_ordinal1 (k32_fomodel2 A B))) ) ).
tt(dt_k32_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  & (m1_subset_1 D (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))) ) )  =>  ((v1_funct_1 (k32_fomodel3 A B C D)) &  ((v1_funct_2 (k32_fomodel3 A B C D) k5_numbers (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) & (m1_subset_1 (k32_fomodel3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))))) ) ) ) ).
tt(dt_k32_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k32_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k32_gate_1,ax,$true).
tt(dt_k32_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k32_gfacirc1 A B C) (k31_gfacirc1 A B C)) &  ((v4_msafree2 (k32_gfacirc1 A B C) (k31_gfacirc1 A B C)) &  ((v4_circcomb (k32_gfacirc1 A B C) (k31_gfacirc1 A B C)) &  ((v6_circcomb (k32_gfacirc1 A B C) (k31_gfacirc1 A B C)) & (l3_msualg_1 (k32_gfacirc1 A B C) (k31_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k32_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k32_glib_000 A B) k5_numbers)) ) ).
tt(dt_k32_mmlquery,ax, (! [A:$i,B:$i] :  ( ((l1_mmlquery A) & (m1_finseq_1 B (u1_mmlquery A)))  => (m1_subset_1 (k32_mmlquery A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k32_modelc_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k32_modelc_1 A B) (k30_modelc_1 A))) ) ).
tt(dt_k32_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) ) )  => (m1_subset_1 (k32_modelc_2 A B C) k6_margrel1)) ) ).
tt(dt_k32_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (m1_subset_1 (k32_modelc_3 A B) (k1_zfmisc_1 (k23_modelc_3 A)))) ) ).
tt(dt_k32_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_xreal_0 (k32_quaterni A))) ) ).
tt(dt_k32_sin_cos,ax,(m1_subset_1 k32_sin_cos k1_numbers)).
tt(dt_k32_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k32_substut1 A B) (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A)))) ) ).
tt(dt_k32_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (l1_turing_1 B))  =>  ((v1_turing_1 (k32_turing_1 A B)) & (l1_turing_1 (k32_turing_1 A B))) ) ) ).
tt(dt_k32_twoscomp,ax, ((v1_funct_1 k32_twoscomp) &  ((v1_funct_2 k32_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k32_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k32_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k32_valued_1 A B C)) & (m1_subset_1 (k32_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k32_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k32_valued_2 A B C D)) & (m1_subset_1 (k32_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k33_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (m2_abcmiz_1 (k33_abcmiz_1 A) A (k12_abcmiz_1 A))) ) ).
tt(dt_k33_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k33_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k33_binop_2,ax, ((v1_funct_1 k33_binop_2) &  ((v1_funct_2 k33_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k33_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k33_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m2_subset_1 (k33_fomodel1 A B) (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A)))) ) ).
tt(dt_k33_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k33_fomodel2 A) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k33_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((v1_funct_1 (k33_fomodel3 A B C)) &  ((v1_funct_2 (k33_fomodel3 A B C) (k32_fomodel1 A) (k32_fomodel1 A)) & (m1_subset_1 (k33_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k32_fomodel1 A) (k32_fomodel1 A))))) ) ) ) ).
tt(dt_k33_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k33_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k33_gate_1,ax,$true).
tt(dt_k33_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k33_gfacirc1 A B C) (u1_struct_0 (k31_gfacirc1 A B C)) (k3_msafree2 (k31_gfacirc1 A B C)))) ).
tt(dt_k33_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k33_glib_000 A B) k5_numbers)) ) ).
tt(dt_k33_mmlquery,ax, (! [A:$i,B:$i] :  ( ((l1_mmlquery A) & (m1_finseq_1 B (u1_mmlquery A)))  => (m1_subset_1 (k33_mmlquery A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k33_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k33_modelc_1 A)) &  ((v1_funct_2 (k33_modelc_1 A) (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 (k33_modelc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) ) ) ) ).
tt(dt_k33_modelc_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k33_modelc_2 A B) (k30_modelc_1 (k25_modelc_2 A)))) ) ).
tt(dt_k33_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  => (m1_subset_1 (k33_modelc_3 A) (k1_zfmisc_1 (k1_zfmisc_1 (k23_modelc_3 A))))) ) ).
tt(dt_k33_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))))  => (m1_subset_1 (k33_substut1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k33_twoscomp,ax, ((v1_funct_1 k33_twoscomp) &  ((v1_funct_2 k33_twoscomp (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k33_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k34_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  => (m1_subset_1 (k34_abcmiz_1 A) (k1_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))) ) ).
tt(dt_k34_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k34_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k34_binop_2,ax, ((v1_funct_1 k34_binop_2) &  ((v1_funct_2 k34_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k34_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k34_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v3_card_1 (k34_fomodel1 A B) (k1_int_2 (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)))) & (m2_subset_1 (k34_fomodel1 A B) (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 A))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A)))) ) ) ).
tt(dt_k34_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k34_fomodel2 A) (k1_fomodel1 A))) ) ).
tt(dt_k34_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((v1_relat_1 (k34_fomodel3 A B C)) & (v1_funct_1 (k34_fomodel3 A B C))) ) ) ).
tt(dt_k34_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_funct_2 (k34_fomodel4 A) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k34_gate_1,ax,$true).
tt(dt_k34_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k34_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k34_gfacirc1 A B C)))  &  ((v1_msualg_1 (k34_gfacirc1 A B C)) &  ((v1_circcomb (k34_gfacirc1 A B C)) &  ((v2_circcomb (k34_gfacirc1 A B C)) &  ((v3_circcomb (k34_gfacirc1 A B C)) & (l1_msualg_1 (k34_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k34_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (v1_card_1 (k34_glib_000 A B))) ) ).
tt(dt_k34_mmlquery,ax, (! [A:$i,B:$i] :  ( ((l1_mmlquery A) & (m1_finseq_1 B (u1_mmlquery A)))  => (m1_subset_1 (k34_mmlquery A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k34_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  => (m1_subset_1 (k34_modelc_1 A B C D) k6_margrel1)) ) ).
tt(dt_k34_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k34_modelc_2 A)) &  ((v1_funct_2 (k34_modelc_2 A) (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k34_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k34_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m1_finseq_1 A k5_numbers)) )  => (l2_modelc_3 (k34_modelc_3 A) k43_modelc_2)) ) ).
tt(dt_k34_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))))  => (m1_subset_1 (k34_substut1 A B) (k1_substut1 A))) ) ).
tt(dt_k34_twoscomp,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k34_twoscomp A B)))  &  ( (~ (v11_struct_0 (k34_twoscomp A B)))  &  ((v1_msualg_1 (k34_twoscomp A B)) &  ((v1_circcomb (k34_twoscomp A B)) &  ((v2_circcomb (k34_twoscomp A B)) &  ((v3_circcomb (k34_twoscomp A B)) & (l1_msualg_1 (k34_twoscomp A B))) ) ) ) ) ) ) ).
tt(dt_k34_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v5_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k34_valued_1 A B C)) & (m1_subset_1 (k34_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ).
tt(dt_k35_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_abcmiz_1) &  ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) ) )  => (m1_abcmiz_1 (k35_abcmiz_1 A B) B (k14_abcmiz_1 B))) ) ).
tt(dt_k35_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k35_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k35_binop_2,ax, ((v1_funct_1 k35_binop_2) &  ((v1_funct_2 k35_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k35_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k35_descip_1,ax, ((v1_funct_1 k35_descip_1) &  ((v1_funct_2 k35_descip_1 (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1)) & (m1_subset_1 k35_descip_1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1))))) ) ).
tt(dt_k35_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_subset_1 (k35_fomodel1 A) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k35_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  => (m1_subset_1 (k35_fomodel2 A B) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k35_fomodel4,ax,$true).
tt(dt_k35_gate_1,ax,$true).
tt(dt_k35_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k35_gfacirc1 A B C) (k34_gfacirc1 A B C)) &  ((v4_msafree2 (k35_gfacirc1 A B C) (k34_gfacirc1 A B C)) &  ((v4_circcomb (k35_gfacirc1 A B C) (k34_gfacirc1 A B C)) &  ((v6_circcomb (k35_gfacirc1 A B C) (k34_gfacirc1 A B C)) & (l3_msualg_1 (k35_gfacirc1 A B C) (k34_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k35_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k35_glib_000 A B) k5_numbers)) ) ).
tt(dt_k35_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_mmlquery A) &  ((m1_finseq_1 B (u1_mmlquery A)) & (v7_ordinal1 C)) )  => (m1_subset_1 (k35_mmlquery A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k35_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k35_modelc_1 A B C) (k30_modelc_1 A))) ) ).
tt(dt_k35_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k35_modelc_2 A B C) (k30_modelc_1 (k25_modelc_2 A)))) ) ).
tt(dt_k35_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) &  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m1_finseq_1 B k5_numbers)) )  &  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) &  ((v1_modelc_3 D B) & (l1_modelc_3 D B)) ) ) )  => (v7_ordinal1 (k35_modelc_3 A B C D))) ) ).
tt(dt_k35_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))))  => (m2_subset_1 (k35_substut1 A B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k35_twoscomp,ax, (! [A:$i,B:$i] :  ((v3_msualg_1 (k35_twoscomp A B) (k34_twoscomp A B)) &  ((v4_msafree2 (k35_twoscomp A B) (k34_twoscomp A B)) &  ((v4_circcomb (k35_twoscomp A B) (k34_twoscomp A B)) &  ((v6_circcomb (k35_twoscomp A B) (k34_twoscomp A B)) & (l3_msualg_1 (k35_twoscomp A B) (k34_twoscomp A B))) ) ) ) ) ).
tt(dt_k35_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k35_valued_1 A)) &  ((v1_funct_1 (k35_valued_1 A)) & (v1_valued_0 (k35_valued_1 A))) ) ) ) ).
tt(dt_k36_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  & (m1_finseq_1 C (k34_abcmiz_1 A))) )  =>  ((v5_abcmiz_1 (k36_abcmiz_1 A B C) A (k28_abcmiz_1 A)) & (m1_subset_1 (k36_abcmiz_1 A B C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ) ).
tt(dt_k36_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k36_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k36_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k36_fomodel1 A)) &  ((v1_funct_2 (k36_fomodel1 A) (k35_fomodel1 A) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))) & (m1_subset_1 (k36_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))))) ) ) ) ).
tt(dt_k36_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  => (m1_subset_1 (k36_fomodel2 A B) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k36_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (m2_funct_2 (k36_fomodel3 A B C) (k33_fomodel2 A) (k33_fomodel2 A) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))) ) ).
tt(dt_k36_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  &  ( ((v3_card_1 C B) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  &  ((v3_card_1 D B) & (m1_subset_1 D (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) ) )  => (m1_subset_1 (k36_fomodel4 A B C D) (k1_zfmisc_1 (k33_fomodel2 A)))) ) ).
tt(dt_k36_gate_1,ax,$true).
tt(dt_k36_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k36_gfacirc1 A B C) (u1_struct_0 (k34_gfacirc1 A B C)) (k3_msafree2 (k34_gfacirc1 A B C)))) ).
tt(dt_k36_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k36_glib_000 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k36_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_mmlquery A) & (l1_mmlquery A))  &  ((m1_finseq_1 B (u1_mmlquery A)) & (v7_ordinal1 C)) )  => (m1_subset_1 (k36_mmlquery A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k36_modelc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_funct_1 (k36_modelc_1 A B)) &  ((v1_funct_2 (k36_modelc_1 A B) (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 (k36_modelc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) ) ) ) ).
tt(dt_k36_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k36_modelc_2 A)) &  ((v1_funct_2 (k36_modelc_2 A) (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k36_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k36_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) &  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m1_finseq_1 B k5_numbers)) )  &  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 B))) &  ((v1_modelc_3 D B) & (l1_modelc_3 D B)) ) ) )  =>  ((v1_modelc_3 (k36_modelc_3 A B C D) B) &  ((v3_modelc_3 (k36_modelc_3 A B C D) B) & (l1_modelc_3 (k36_modelc_3 A B C D) B)) ) ) ) ).
tt(dt_k36_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k16_substut1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k36_substut1 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k36_twoscomp,ax, (! [A:$i,B:$i] : (m1_subset_1 (k36_twoscomp A B) (k3_msafree2 (k34_twoscomp A B)))) ).
tt(dt_k36_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k36_valued_1 A B C)) & (m1_subset_1 (k36_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k36_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (v1_xcmplx_0 C)) )  =>  ((v1_relat_1 (k36_valued_2 A B C)) & (v1_funct_1 (k36_valued_2 A B C))) ) ) ).
tt(dt_k37_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  => (m1_abcmiz_1 (k37_abcmiz_1 A B) A (k13_abcmiz_1 A))) ) ).
tt(dt_k37_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k37_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k37_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k37_fomodel1 A) (k1_zfmisc_1 (k15_fomodel1 A)))) ) ).
tt(dt_k37_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ( ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  & (m1_subset_1 E B)) ) ) )  => (m2_subset_1 (k37_fomodel2 A B C D E) (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B))) ) ).
tt(dt_k37_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((v4_fomodel2 (k37_fomodel3 A B C D) A) & (m2_subset_1 (k37_fomodel3 A B C D) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ).
tt(dt_k37_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k37_fomodel4 A) (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) ) ).
tt(dt_k37_gate_1,ax,$true).
tt(dt_k37_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k37_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k37_gfacirc1 A B C)))  &  ((v1_msualg_1 (k37_gfacirc1 A B C)) &  ((v1_circcomb (k37_gfacirc1 A B C)) &  ((v2_circcomb (k37_gfacirc1 A B C)) &  ((v3_circcomb (k37_gfacirc1 A B C)) & (l1_msualg_1 (k37_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k37_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k37_glib_000 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k37_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_mmlquery A) & (l1_mmlquery A))  &  ((m1_finseq_1 B (u1_mmlquery A)) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k37_mmlquery A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k37_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  => (m1_subset_1 (k37_modelc_1 A B C D) k6_margrel1)) ) ).
tt(dt_k37_modelc_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k25_modelc_2 A) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k25_modelc_2 A) k6_margrel1)))) ) ) )  => (m1_subset_1 (k37_modelc_2 A B C D) k6_margrel1)) ) ).
tt(dt_k37_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) &  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m1_finseq_1 B k5_numbers)) )  & (m1_orders_1 C (k1_orders_1 (k1_modelc_3 B)))) )  =>  ((v1_funct_1 (k37_modelc_3 A B C)) &  ((v1_funct_2 (k37_modelc_3 A B C) k5_numbers (k23_modelc_3 B)) & (m1_subset_1 (k37_modelc_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 B))))) ) ) ) ).
tt(dt_k37_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k37_substut1 A B) (k9_qc_lang1 A))) ) ).
tt(dt_k37_twoscomp,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k37_twoscomp A B)))  &  ( (~ (v11_struct_0 (k37_twoscomp A B)))  &  ((v1_msualg_1 (k37_twoscomp A B)) &  ((v1_circcomb (k37_twoscomp A B)) &  ((v2_circcomb (k37_twoscomp A B)) &  ((v3_circcomb (k37_twoscomp A B)) & (l1_msualg_1 (k37_twoscomp A B))) ) ) ) ) ) ) ).
tt(dt_k37_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k37_valued_1 A B C)) & (m1_subset_1 (k37_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k37_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k37_valued_2 A B C D)) & (m1_subset_1 (k37_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k38_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  => (m1_subset_1 (k38_abcmiz_1 A) (k1_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))) ) ).
tt(dt_k38_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m3_aofa_i00 (k38_aofa_i00 A B C D E F) A B C D)) ) ).
tt(dt_k38_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v7_ordinal1 (k38_fomodel1 A B))) ) ).
tt(dt_k38_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  => (m2_subset_1 (k38_fomodel2 A B) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k38_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  & (v10_fomodel4 C A B)) )  =>  ((v1_relat_1 (k38_fomodel4 A B C)) & (v1_funct_1 (k38_fomodel4 A B C))) ) ) ).
tt(dt_k38_gate_1,ax,$true).
tt(dt_k38_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k38_gfacirc1 A B C) (k37_gfacirc1 A B C)) &  ((v4_msafree2 (k38_gfacirc1 A B C) (k37_gfacirc1 A B C)) &  ((v4_circcomb (k38_gfacirc1 A B C) (k37_gfacirc1 A B C)) &  ((v6_circcomb (k38_gfacirc1 A B C) (k37_gfacirc1 A B C)) & (l3_msualg_1 (k38_gfacirc1 A B C) (k37_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k38_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k38_glib_000 A B) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k38_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k38_modelc_1 A B C) (k30_modelc_1 A))) ) ).
tt(dt_k38_modelc_2,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k38_modelc_2 A B C) (k30_modelc_1 (k25_modelc_2 A)))) ) ).
tt(dt_k38_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k38_substut1 A) (k1_zfmisc_1 (k16_substut1 A)))) ) ).
tt(dt_k38_twoscomp,ax, (! [A:$i,B:$i] :  ((v3_msualg_1 (k38_twoscomp A B) (k37_twoscomp A B)) &  ((v4_msafree2 (k38_twoscomp A B) (k37_twoscomp A B)) &  ((v4_circcomb (k38_twoscomp A B) (k37_twoscomp A B)) &  ((v6_circcomb (k38_twoscomp A B) (k37_twoscomp A B)) & (l3_msualg_1 (k38_twoscomp A B) (k37_twoscomp A B))) ) ) ) ) ).
tt(dt_k38_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k38_valued_2 A B C D)) & (m1_subset_1 (k38_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k39_abcmiz_1,ax,$true).
tt(dt_k39_binop_2,ax, ((v1_funct_1 k39_binop_2) &  ((v1_funct_2 k39_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (m1_subset_1 k39_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers)))) ) ).
tt(dt_k39_descip_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_finseq_2 64 k6_margrel1)) => (m2_finseq_2 (k39_descip_1 A) (k4_finseq_2 48 k6_margrel1) (k4_finseq_2 16 (k4_finseq_2 48 k6_margrel1)))) ) ).
tt(dt_k39_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k39_fomodel1 A)) &  ((v1_funct_2 (k39_fomodel1 A) k5_numbers (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) & (m1_subset_1 (k39_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))))) ) ) ) ).
tt(dt_k39_fomodel2,ax,$true).
tt(dt_k39_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) &  ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  & (v10_fomodel4 C A B)) )  => (m2_subset_1 (k39_fomodel4 A B C) (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A B C))) (k2_xboole_0 (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A B C)) k6_margrel1))) (k16_fomodel2 A (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A B C))))) ) ).
tt(dt_k39_gate_1,ax,$true).
tt(dt_k39_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  => (m1_subset_1 (k39_glib_000 A) k5_numbers)) ) ).
tt(dt_k39_modelc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_funct_1 (k39_modelc_1 A B)) &  ((v1_funct_2 (k39_modelc_1 A B) (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 (k39_modelc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) ) ) ) ).
tt(dt_k39_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k39_modelc_2 A)) &  ((v1_funct_2 (k39_modelc_2 A) (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k39_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k39_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  => (m2_subset_1 (k39_substut1 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k39_twoscomp,ax, (! [A:$i,B:$i] : (m1_subset_1 (k39_twoscomp A B) (k3_msafree2 (k37_twoscomp A B)))) ).
tt(dt_k39_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) & (v1_funct_1 (k39_valued_1 A))) ) ) ).
tt(dt_k3_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ((l2_abcmiz_0 A) & (m1_subset_1 B (u1_abcmiz_0 A)))  => (m1_subset_1 (k3_abcmiz_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) => (m1_subset_1 (k3_abcmiz_1 A) (k1_zfmisc_1 k2_abcmiz_1))) ) ).
tt(dt_k3_aff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k3_aff_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_afinsq_1,ax,$true).
tt(dt_k3_afinsq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k3_afinsq_2 A B C)) &  ((v1_funct_1 (k3_afinsq_2 A B C)) &  ((v5_ordinal1 (k3_afinsq_2 A B C)) & (v1_finset_1 (k3_afinsq_2 A B C))) ) ) ) ) ).
tt(dt_k3_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v3_relat_2 (k3_afproj A)) &  ((v8_relat_2 (k3_afproj A)) &  ((v1_partfun1 (k3_afproj A) (k1_afproj A)) & (m1_subset_1 (k3_afproj A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_afproj A) (k1_afproj A))))) ) ) ) ) ).
tt(dt_k3_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k3_afvect0 A B)) &  ((v1_funct_2 (k3_afvect0 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k3_afvect0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_alg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  & (m1_alg_1 B A))  => (m2_finseq_1 (k3_alg_1 A B) (k4_partfun1 (k3_finseq_2 (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B)))) ) ).
tt(dt_k3_algseq_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k3_algseq_1 A B)) &  ((v1_funct_2 (k3_algseq_1 A B) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k3_algseq_1 A B) A) & (m1_subset_1 (k3_algseq_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k3_algstr_0,ax,(l2_algstr_0 k3_algstr_0)).
tt(dt_k3_algstr_1,ax, ((v29_algstr_0 k3_algstr_1) & (l5_algstr_0 k3_algstr_1)) ).
tt(dt_k3_algstr_3,ax, ((v1_algstr_3 k3_algstr_3) & (l1_algstr_3 k3_algstr_3)) ).
tt(dt_k3_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_algstr_4 A B)) &  ((v1_funct_2 (k3_algstr_4 A B) (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B)) & (m1_subset_1 (k3_algstr_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))))) ) ) ) ).
tt(dt_k3_altcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A A))) ) ) )  =>  ((v1_relat_1 (k3_altcat_1 A B C)) &  ((v4_relat_1 (k3_altcat_1 A B C) (k3_zfmisc_1 A A A)) &  ((v1_funct_1 (k3_altcat_1 A B C)) & (v1_partfun1 (k3_altcat_1 A B C) (k3_zfmisc_1 A A A))) ) ) ) ) ).
tt(dt_k3_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m2_pboole (k3_altcat_2 A) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_altcat_1 (u1_struct_0 A) (k2_altcat_2 A) (k2_altcat_2 A)) (k2_altcat_1 (u1_struct_0 A) (k2_altcat_2 A)))) ) ).
tt(dt_k3_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_altcat_4 A)))  &  ((v2_altcat_1 (k3_altcat_4 A)) &  ((v6_altcat_1 (k3_altcat_4 A)) & (m1_altcat_2 (k3_altcat_4 A) A)) ) ) ) ) ).
tt(dt_k3_ami_2,ax, ((v1_funct_1 k3_ami_2) &  ((v1_funct_2 k3_ami_2 k1_ami_2 2) & (m1_subset_1 k3_ami_2 (k1_zfmisc_1 (k2_zfmisc_1 k1_ami_2 2)))) ) ).
tt(dt_k3_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k3_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k3_amistd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_amistd_1 A B C) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k3_amistd_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  & (m1_subset_1 C (u1_compos_1 B))) )  => (m1_subset_1 (k3_amistd_4 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k3_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  & (v7_ordinal1 C)) )  => (m2_subset_1 (k3_ami_wstd A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k3_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ((v1_analoaf (k3_analmetr A)) & (l1_analoaf (k3_analmetr A))) ) ) ).
tt(dt_k3_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_analort A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k3_anproj_1,ax,$true).
tt(dt_k3_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k9_funct_2 A B)) & (m1_subset_1 D (k9_funct_2 A B))) ) )  => (m2_funct_2 (k3_aofa_000 A B C D E) A B (k9_funct_2 A B))) ) ).
tt(dt_k3_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k3_aofa_i00 A B)) &  ((v5_relat_1 (k3_aofa_i00 A B) k4_numbers) & (v1_funct_1 (k3_aofa_i00 A B))) ) ) ) ).
tt(dt_k3_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k3_armstrng A B C) A) & (m2_finseq_1 (k3_armstrng A B C) k6_margrel1)) ) ) ).
tt(dt_k3_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k3_arrow A) (k1_zfmisc_1 (k2_arrow A)))) ) ).
tt(dt_k3_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k3_arytm_0 A) k1_numbers)) ) ).
tt(dt_k3_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) => (m2_subset_1 (k3_arytm_2 A) (k1_zfmisc_1 k5_arytm_3) k1_arytm_2)) ) ).
tt(dt_k3_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (m1_subset_1 (k3_arytm_3 A B) k4_ordinal1)) ) ).
tt(dt_k3_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ( (~ (v3_xxreal_0 B))  & (m1_subset_1 B k1_numbers)) )  =>  ((v1_funct_1 (k3_asympt_0 A B)) &  ((v1_funct_2 (k3_asympt_0 A B) k5_numbers k1_numbers) &  ((v2_asympt_0 (k3_asympt_0 A B)) & (m1_subset_1 (k3_asympt_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ).
tt(dt_k3_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k3_asympt_1 A)) &  ((v1_funct_2 (k3_asympt_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_asympt_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_autalg_1 A)))  &  ((v2_group_1 (k3_autalg_1 A)) &  ((v3_group_1 (k3_autalg_1 A)) & (l3_algstr_0 (k3_autalg_1 A))) ) ) ) ) ).
tt(dt_k3_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_autgroup A)))  &  ((v15_algstr_0 (k3_autgroup A)) &  ((v2_group_1 (k3_autgroup A)) &  ((v3_group_1 (k3_autgroup A)) & (l3_algstr_0 (k3_autgroup A))) ) ) ) ) ) ).
tt(dt_k3_bagorder,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  => (v7_ordinal1 (k3_bagorder A B))) ) ).
tt(dt_k3_bcialg_2,ax,$true).
tt(dt_k3_bcialg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 (k3_bcialg_4 A B C)))  & (m1_subset_1 (k3_bcialg_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k3_bcialg_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v1_xxreal_0 (k3_bcialg_5 A B C D))) ) ).
tt(dt_k3_bcialg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((v1_int_1 B) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_bcialg_6 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_bhsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_bhsp_1 A B) k1_numbers)) ) ).
tt(dt_k3_bhsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_bhsp_2 A B C)) &  ((v1_funct_2 (k3_bhsp_2 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k3_bhsp_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_bhsp_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k3_bhsp_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_bhsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  => (m1_subset_1 (k3_bhsp_6 A B C) k1_numbers)) ) ).
tt(dt_k3_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k3_bilinear A B C D E)) &  ((v1_funct_2 (k3_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k3_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_binari_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1)) )  => (v1_int_1 (k3_binari_2 A B))) ) ).
tt(dt_k3_binarith,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1)) )  =>  ((v3_card_1 (k3_binarith A B) A) & (m2_finseq_1 (k3_binarith A B) k6_margrel1)) ) ) ).
tt(dt_k3_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k3_binom A)) &  ((v1_funct_2 (k3_binom A) (k2_zfmisc_1 k5_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k3_binom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  => (m1_subset_1 (k3_binop_1 A B C D) A)) ) ).
tt(dt_k3_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k3_binop_2 A B) k2_numbers)) ) ).
tt(dt_k3_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_boolealg A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_boolmark,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  &  ((m1_subset_1 B (k1_boolmark A)) & (m1_finseq_1 C (u4_struct_0 A))) )  => (m2_funct_2 (k3_boolmark A B C) (u1_struct_0 A) k6_margrel1 (k1_boolmark A))) ) ).
tt(dt_k3_bor_cant,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k3_bor_cant A B)) &  ((v1_funct_2 (k3_bor_cant A B) k5_numbers k5_numbers) & (m1_subset_1 (k3_bor_cant A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k3_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m1_subset_1 (k3_borsuk_1 A B C D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) ) ).
tt(dt_k3_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_borsuk_2 A B C D E F)) &  ((v1_funct_2 (k3_borsuk_2 A B C D E F) (u1_struct_0 (k2_borsuk_1 A C)) (u1_struct_0 (k2_borsuk_1 B D))) & (m1_subset_1 (k3_borsuk_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A C)) (u1_struct_0 (k2_borsuk_1 B D)))))) ) ) ) ).
tt(dt_k3_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k3_borsuk_5 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k3_borsuk_6,ax, ((v1_funct_1 k3_borsuk_6) &  ((v1_funct_2 k3_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 k3_borsuk_6 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) ).
tt(dt_k3_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) & (v1_xreal_0 B))  => (m1_subset_1 (k3_borsuk_7 A B) (u1_struct_0 k3_topmetr))) ) ).
tt(dt_k3_brouwer,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) &  ( (~ (v3_xxreal_0 E))  & (v1_xreal_0 E)) ) ) ) )  => (m1_subset_1 (k3_brouwer A B C D E) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k3_bspace,ax, (! [A:$i,B:$i] : (m1_subset_1 (k3_bspace A B) (u1_struct_0 k2_bspace))) ).
tt(dt_k3_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k3_bvfunc_1 A B)) &  ((v1_funct_1 (k3_bvfunc_1 A B)) & (v1_margrel1 (k3_bvfunc_1 A B))) ) ) ) ).
tt(dt_k3_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k3_bvfunc26 A B C)) &  ((v1_funct_2 (k3_bvfunc26 A B C) A k6_margrel1) & (m1_subset_1 (k3_bvfunc26 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k3_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))))  => (m1_eqrel_1 (k3_bvfunc_2 A B) A)) ) ).
tt(dt_k3_c0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_c0sp1 A B) B)) ) ).
tt(dt_k3_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (l1_funcsdom (k3_c0sp2 A))) ) ).
tt(dt_k3_calcul_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_cqc_lang A)))  => (m1_subset_1 (k3_calcul_1 A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k3_calcul_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) ) ) )  => (m2_finseq_1 (k3_calcul_2 A B C) A)) ) ).
tt(dt_k3_card_1,ax,$true).
tt(dt_k3_card_2,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) & (v1_card_1 B))  => (v1_card_1 (k3_card_2 A B))) ) ).
tt(dt_k3_card_3,ax,$true).
tt(dt_k3_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k3_card_fil A)))  & (m1_subset_1 (k3_card_fil A) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) ) ) ).
tt(dt_k3_cardfin2,ax, ((v1_funct_1 k3_cardfin2) &  ((v1_funct_2 k3_cardfin2 k5_numbers k4_numbers) & (m1_subset_1 k3_cardfin2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) ) ).
tt(dt_k3_card_fin,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finset_1 B)) ) )  => (m2_subset_1 (k3_card_fin A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_cat_1,ax, (! [A:$i,B:$i] :  ((v1_cat_1 (k3_cat_1 A B)) & (l1_cat_1 (k3_cat_1 A B))) ) ).
tt(dt_k3_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m1_cat_2 D B C) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A D)))) )  & (m1_subset_1 F A)) ) ) ) )  => (m2_cat_2 (k3_cat_2 A B C D E F) B C D)) ) ).
tt(dt_k3_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) )  =>  ((v1_funct_1 (k3_cat_3 A B C)) &  ((v1_funct_2 (k3_cat_3 A B C) B (u1_struct_0 A)) & (m1_subset_1 (k3_cat_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_cat_4 A B C) (u4_struct_0 A))) ) ).
tt(dt_k3_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_cat_5 A B)))  &  ( (~ (v11_struct_0 (k3_cat_5 A B)))  &  ((v1_cat_1 (k3_cat_5 A B)) &  ((v2_cat_1 (k3_cat_5 A B)) &  ((v3_cat_1 (k3_cat_5 A B)) &  ((v4_cat_1 (k3_cat_5 A B)) &  ((v5_cat_1 (k3_cat_5 A B)) &  ((v6_cat_1 (k3_cat_5 A B)) & (l1_cat_1 (k3_cat_5 A B))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_catalan2,ax, (! [A:$i] : (m1_catalan2 (k3_catalan2 A) A)) ).
tt(dt_k3_catalg_1,ax, (! [A:$i] :  ((v1_msualg_1 (k3_catalg_1 A)) & (m1_catalg_1 (k3_catalg_1 A) A)) ) ).
tt(dt_k3_cayley,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k3_cayley A B C)) &  ((v1_funct_2 (k3_cayley A B C) (u1_struct_0 (k2_cayley A)) (u1_struct_0 (k2_cayley B))) & (m1_subset_1 (k3_cayley A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_cayley A)) (u1_struct_0 (k2_cayley B)))))) ) ) ) ).
tt(dt_k3_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k3_cc0sp1 A)))  &  ((v13_algstr_0 (k3_cc0sp1 A)) &  ((v2_rlvect_1 (k3_cc0sp1 A)) &  ((v3_rlvect_1 (k3_cc0sp1 A)) &  ((v4_rlvect_1 (k3_cc0sp1 A)) &  ((v3_group_1 (k3_cc0sp1 A)) &  ((v5_group_1 (k3_cc0sp1 A)) &  ((v1_vectsp_1 (k3_cc0sp1 A)) &  ((v3_vectsp_1 (k3_cc0sp1 A)) &  ((v2_clvect_1 (k3_cc0sp1 A)) &  ((v3_clvect_1 (k3_cc0sp1 A)) &  ((v4_clvect_1 (k3_cc0sp1 A)) &  ((v2_cfuncdom (k3_cc0sp1 A)) & (l1_cfuncdom (k3_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k3_cc0sp2 A)))  &  ((v13_algstr_0 (k3_cc0sp2 A)) &  ((v2_rlvect_1 (k3_cc0sp2 A)) &  ((v3_rlvect_1 (k3_cc0sp2 A)) &  ((v4_rlvect_1 (k3_cc0sp2 A)) &  ((v3_group_1 (k3_cc0sp2 A)) &  ((v5_group_1 (k3_cc0sp2 A)) &  ((v1_vectsp_1 (k3_cc0sp2 A)) &  ((v3_vectsp_1 (k3_cc0sp2 A)) &  ((v2_clvect_1 (k3_cc0sp2 A)) &  ((v3_clvect_1 (k3_cc0sp2 A)) &  ((v4_clvect_1 (k3_cc0sp2 A)) &  ((v2_cfuncdom (k3_cc0sp2 A)) & (l1_cfuncdom (k3_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v1_funct_1 (k3_cfdiff_1 A B)) & (m1_subset_1 (k3_cfdiff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) ).
tt(dt_k3_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k3_cfuncdom A)) &  ((v1_funct_2 (k3_cfuncdom A) (k2_zfmisc_1 k2_numbers (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers)) & (m1_subset_1 (k3_cfuncdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k9_funct_2 A k2_numbers)) (k9_funct_2 A k2_numbers))))) ) ) ) ).
tt(dt_k3_cgames_1,ax,(m1_subset_1 k3_cgames_1 (k2_cgames_1 k1_xboole_0))).
tt(dt_k3_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ( (~ (v1_xboole_0 (k3_chain_1 A B C)))  & (m1_subset_1 (k3_chain_1 A B C) (k1_zfmisc_1 (k1_euclid A)))) ) ) ).
tt(dt_k3_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m3_chord B A) & (m1_subset_1 C (k6_glib_000 A))) )  =>  ( (~ (v1_xboole_0 (k3_chord A B C)))  & (m2_subset_1 (k3_chord A B C) k1_numbers k5_numbers)) ) ) ).
tt(dt_k3_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  => (m1_subset_1 (k3_circcmb3 A) (u1_struct_0 A))) ) ).
tt(dt_k3_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ((v4_msualg_1 D B) & (l3_msualg_1 D B)) ) ) )  =>  ((v3_msualg_1 (k3_circcomb A B C D) (k2_circcomb A B)) &  ((v4_msualg_1 (k3_circcomb A B C D) (k2_circcomb A B)) & (l3_msualg_1 (k3_circcomb A B C D) (k2_circcomb A B))) ) ) ) ).
tt(dt_k3_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  &  ((m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C))) & (l3_msualg_1 E A)) ) ) )  =>  ((v1_relat_1 (k3_circtrm1 A B C D E)) & (v1_funct_1 (k3_circtrm1 A B C D E))) ) ) ).
tt(dt_k3_circuit1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 D (u4_struct_0 A))) ) )  => (m1_subset_1 (k3_circuit1 A B C D) (k3_msualg_1 A D B))) ) ).
tt(dt_k3_circuit2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_msafree2 C A B)) )  => (m2_pboole (k3_circuit2 A B C) (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)))) ) ).
tt(dt_k3_classes1,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 B) => (m1_subset_1 (k3_classes1 A B) (k1_zfmisc_1 (k1_classes1 A)))) ) ).
tt(dt_k3_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k3_classes2 A B) A)) ) ).
tt(dt_k3_clopban1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_clopban1 A B)))  &  ((v13_algstr_0 (k3_clopban1 A B)) &  ((v2_rlvect_1 (k3_clopban1 A B)) &  ((v3_rlvect_1 (k3_clopban1 A B)) &  ((v4_rlvect_1 (k3_clopban1 A B)) &  ((v2_clvect_1 (k3_clopban1 A B)) &  ((v3_clvect_1 (k3_clopban1 A B)) &  ((v4_clvect_1 (k3_clopban1 A B)) &  ((v5_clvect_1 (k3_clopban1 A B)) & (l1_clvect_1 (k3_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_clopban2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k8_clopban1 A A)) & (m1_subset_1 C (k8_clopban1 A A))) )  => (m2_subset_1 (k3_clopban2 A B C) (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A))) ) ).
tt(dt_k3_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_clopban3 A B C)) &  ((v1_funct_2 (k3_clopban3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k3_clopban3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_clopban4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k3_clopban4 A B C D)) &  ((v1_funct_2 (k3_clopban4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k3_clopban4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k3_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) & (m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B))) )  => (m2_pboole (k3_closure1 A B C D) A (k5_mssubfam A B) (k5_mssubfam A B))) ) ).
tt(dt_k3_closure2,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ((v1_relat_1 (k3_closure2 A)) & (v1_funct_1 (k3_closure2 A))) ) ) ).
tt(dt_k3_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  => (m1_subset_1 (k3_closure3 A B C D) (k1_zfmisc_1 (k1_closure2 A B)))) ) ).
tt(dt_k3_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_clvect_1 (k3_clvect_1 A)) & (m1_clvect_1 (k3_clvect_1 A) A)) ) ) ).
tt(dt_k3_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_clvect_2 A B C)) &  ((v1_funct_2 (k3_clvect_2 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k3_clvect_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_clvect_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (m1_subset_1 (k3_clvect_3 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k3_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  & (m1_subset_1 B A))  =>  ( (~ (v1_xboole_0 (k3_cohsp_1 A B)))  &  ((v4_finsub_1 (k3_cohsp_1 A B)) & (m1_subset_1 (k3_cohsp_1 A B) (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_k3_coh_sp,ax,$true).
tt(dt_k3_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ((l1_combgras C A B) & (m1_subset_1 D (u2_incsp_1 A))) ) )  => (m1_subset_1 (k3_combgras A B C D) (u2_incsp_1 B))) ) ).
tt(dt_k3_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) &  ((m2_cat_1 E B C) & (m1_subset_1 F (k2_commacat A B C D E))) ) ) ) )  => (m2_subset_1 (k3_commacat A B C D E F) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E))) ) ).
tt(dt_k3_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k3_complex1 A) k1_numbers)) ) ).
tt(dt_k3_complex2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k3_complex2 A B) k1_numbers)) ) ).
tt(dt_k3_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  => (m2_finseq_2 (k3_complsp2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k3_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_metric_1 (k3_compl_sp A B C)) & (l1_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(dt_k3_compos_0,ax,$true).
tt(dt_k3_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_compos_1 A B C) (u1_compos_1 A))) ) ).
tt(dt_k3_compos_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_amistd_4 A) & (l1_compos_1 A))  &  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  &  ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A))) ) )  =>  ( (~ (v1_xboole_0 (k3_compos_2 A B C)))  &  ((v1_relat_1 (k3_compos_2 A B C)) &  ((v4_relat_1 (k3_compos_2 A B C) k5_numbers) &  ((v5_relat_1 (k3_compos_2 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k3_compos_2 A B C)) &  ((v1_finset_1 (k3_compos_2 A B C)) &  ((v1_afinsq_1 (k3_compos_2 A B C)) &  ((v3_compos_1 (k3_compos_2 A B C) A) & (v4_compos_1 (k3_compos_2 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k3_comput_1 A B)) &  ((v4_relat_1 (k3_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 A B)) &  ((v4_valued_0 (k3_comput_1 A B)) & (v2_margrel1 (k3_comput_1 A B))) ) ) ) ) ) ).
tt(dt_k3_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (m1_subset_1 (k3_comseq_2 A) k2_numbers)) ) ).
tt(dt_k3_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k3_comseq_3 A)) & (v1_funct_1 (k3_comseq_3 A))) ) ) ).
tt(dt_k3_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k3_conlat_1 A)) &  ((v1_funct_2 (k3_conlat_1 A) (u1_struct_0 (k3_yellow_1 (u1_struct_0 A))) (u1_struct_0 (k3_yellow_1 (u4_struct_0 A)))) & (m1_subset_1 (k3_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u1_struct_0 A))) (u1_struct_0 (k3_yellow_1 (u4_struct_0 A))))))) ) ) ) ).
tt(dt_k3_conlat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A)))))  =>  ( (~ (v5_conlat_1 (k3_conlat_2 A B) A))  &  ((v7_conlat_1 (k3_conlat_2 A B) A) & (l2_conlat_1 (k3_conlat_2 A B) A)) ) ) ) ).
tt(dt_k3_convex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_convex1 (k3_convex1 A B) A) & (m1_subset_1 (k3_convex1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k3_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) ) )  => (m2_finseq_1 (k3_convex4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  => (l1_rlvect_1 (k3_convfun1 A B))) ) ).
tt(dt_k3_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k3_cqc_lang A) (k1_zfmisc_1 (k9_qc_lang1 A)))) ) ).
tt(dt_k3_cqc_sim1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  & (m1_subset_1 D k5_numbers)) ) )  => (m2_funct_2 (k3_cqc_sim1 A B C D) (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))) ) ).
tt(dt_k3_cqc_the1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)))  => (m2_subset_1 (k3_cqc_the1 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k3_csspace3,ax, ( (~ (v2_struct_0 k3_csspace3))  & (l2_clvect_1 k3_csspace3)) ).
tt(dt_k3_csspace4,ax, ( (~ (v2_struct_0 k3_csspace4))  & (l2_clvect_1 k3_csspace4)) ).
tt(dt_k3_csspace,ax, (! [A:$i] : (v1_xcmplx_0 (k3_csspace A))) ).
tt(dt_k3_decomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_decomp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k3_descip_1 A B C) A)) ) ).
tt(dt_k3_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k3_dickson A))) ) ).
tt(dt_k3_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k3_diff_1 A B)) & (m1_subset_1 (k3_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k3_dilworth,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_dilworth A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  => (m1_subset_1 (k3_dist_1 A B C) k1_numbers)) ) ).
tt(dt_k3_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  => (m1_subset_1 (k3_domain_1 A B C) B)) ) ).
tt(dt_k3_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 C (k2_zfmisc_1 A B)) => (m2_finseq_1 (k3_dtconstr A B C) B)) ) ).
tt(dt_k3_dynkin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_dynkin A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_ec_pf_1 A)))  & (m1_subset_1 (k3_ec_pf_1 A) (k1_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))))) ) ) ).
tt(dt_k3_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  & (m1_subset_1 B (k1_ec_pf_2 A)))  => (m1_subset_1 (k3_ec_pf_2 A B) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k3_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v22_algstr_0 (k3_endalg A)) & (l4_algstr_0 (k3_endalg A))) ) ) ).
tt(dt_k3_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k2_ens_1 A)))  => (m1_subset_1 (k3_ens_1 A B) A)) ) ).
tt(dt_k3_entropy1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_finseq_1 B k1_numbers))  => (m2_finseq_1 (k3_entropy1 A B) k1_numbers)) ) ).
tt(dt_k3_enumset1,ax,$true).
tt(dt_k3_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k3_eqrel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k3_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  => (l3_msualg_1 (k3_equation A) A)) ) ).
tt(dt_k3_e_siec,ax, (! [A:$i] :  ((v1_e_siec (k3_e_siec A)) &  ((v2_e_siec (k3_e_siec A)) &  ((v3_e_siec (k3_e_siec A)) & (l1_e_siec (k3_e_siec A))) ) ) ) ).
tt(dt_k3_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k3_euclid_3 A) k1_numbers)) ) ).
tt(dt_k3_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k3_euclid_4 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k3_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) => (m1_subset_1 (k3_euclid_5 A) k1_numbers)) ) ).
tt(dt_k3_euclid_8,ax,(m2_finseq_2 k3_euclid_8 k1_numbers (k1_euclid 3))).
tt(dt_k3_euclid_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k3_euclid_9 A B)) & (v1_funct_1 (k3_euclid_9 A B))) ) ) ).
tt(dt_k3_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  => (m2_finseq_1 (k3_euclid A) k1_numbers)) ) ).
tt(dt_k3_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclidlp A))) )  => (m1_subset_1 (k3_euclidlp A B C) k1_numbers)) ) ).
tt(dt_k3_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_ordinal1 (k3_exchsort A))) ) ).
tt(dt_k3_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  => (m1_subset_1 (k3_extpro_1 A B C D) (u1_compos_1 B))) ) ).
tt(dt_k3_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (m1_subset_1 (k3_extreal1 A) k7_numbers)) ) ).
tt(dt_k3_facirc_1,ax, ((v1_funct_1 k3_facirc_1) &  ((v1_funct_2 k3_facirc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k3_facirc_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k3_facirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ( (~ (v2_struct_0 (k3_facirc_2 A B C)))  &  ( (~ (v11_struct_0 (k3_facirc_2 A B C)))  &  ((v1_msualg_1 (k3_facirc_2 A B C)) &  ((v1_circcomb (k3_facirc_2 A B C)) &  ((v2_circcomb (k3_facirc_2 A B C)) &  ((v3_circcomb (k3_facirc_2 A B C)) & (l1_msualg_1 (k3_facirc_2 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k3_ff_siec,ax, (! [A:$i] :  ((v1_petri (k3_ff_siec A)) &  ((v1_net_1 (k3_ff_siec A)) & (l1_petri (k3_ff_siec A))) ) ) ).
tt(dt_k3_fib_fusc,ax, ((v5_ordinal1 k3_fib_fusc) &  ((v1_relat_1 k3_fib_fusc) &  ((v5_relat_1 k3_fib_fusc (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 k3_fib_fusc) & (v1_finset_1 k3_fib_fusc)) ) ) ) ).
tt(dt_k3_fib_num2,ax,(m1_subset_1 k3_fib_num2 (k1_zfmisc_1 k5_numbers))).
tt(dt_k3_fib_num3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_fib_num3 A B C) k5_numbers)) ) ).
tt(dt_k3_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v1_xboole_0 (k3_filter_0 A B)))  &  ((v19_lattices (k3_filter_0 A B) A) &  ((v20_lattices (k3_filter_0 A B) A) & (m1_subset_1 (k3_filter_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k3_filter_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) )  =>  ((v1_funct_1 (k3_filter_1 A B C)) &  ((v1_funct_2 (k3_filter_1 A B C) (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B)) (k8_eqrel_1 A B)) & (m1_subset_1 (k3_filter_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 A B) (k8_eqrel_1 A B)) (k8_eqrel_1 A B))))) ) ) ) ).
tt(dt_k3_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_filter_2 A B) (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) ) ).
tt(dt_k3_finance1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k3_finance1 A B)) &  ((v1_funct_2 (k3_finance1 A B) k5_numbers k1_numbers) & (m1_subset_1 (k3_finance1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (m2_subset_1 (k3_finseq_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k3_finseq_2,ax, (! [A:$i] : (m1_finseq_2 (k3_finseq_2 A) A)) ).
tt(dt_k3_finseq_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (m1_subset_1 (k3_finseq_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A))))) ) ).
tt(dt_k3_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (m2_finseq_1 (k3_finseq_4 A B C D) A)) ) ).
tt(dt_k3_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ).
tt(dt_k3_finseq_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (m2_finseq_1 (k3_finseq_6 A B C D) A)) ) ).
tt(dt_k3_finseq_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m2_finseq_1 (k3_finseq_8 A B C D) A)) ) ).
tt(dt_k3_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_subset_1 E A) & (m1_finseq_1 F B)) ) ) ) )  => (m2_finseq_1 (k3_finseqop A B C D E F) C)) ) ).
tt(dt_k3_finsop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (m1_subset_1 (k3_finsop_1 A) (k5_finsub_1 k5_numbers))) ) ).
tt(dt_k3_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k3_finsub_1 A B C) A)) ) ).
tt(dt_k3_fintopo2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_fintopo2 A B C) k6_margrel1)) ) ).
tt(dt_k3_fintopo3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_fintopo3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_fintopo4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ).
tt(dt_k3_fintopo5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_orders_2 (k3_fintopo5 A B)) & (l1_orders_2 (k3_fintopo5 A B))) ) ) ).
tt(dt_k3_fin_topo,ax, (! [A:$i] : (m1_subset_1 (k3_fin_topo A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski A))))) ).
tt(dt_k3_flang_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k3_flang_1 A B) (k3_catalan2 A))) ) ).
tt(dt_k3_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_finseq_1 C A)) )  =>  ((v1_relat_1 (k3_fomodel0 A B C)) & (v1_funct_1 (k3_fomodel0 A B C))) ) ) ).
tt(dt_k3_fomodel1,ax,$true).
tt(dt_k3_fomodel2,ax, (! [A:$i] :  ((v1_partfun1 (k3_fomodel2 A) A) &  ((v3_relat_2 (k3_fomodel2 A)) &  ((v8_relat_2 (k3_fomodel2 A)) & (m1_subset_1 (k3_fomodel2 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(dt_k3_fomodel3,ax,$true).
tt(dt_k3_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) & (v7_ordinal1 C)) )  => (m2_funct_2 (k3_fomodel4 A B C) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ).
tt(dt_k3_frechet,ax, ( (~ (v2_struct_0 k3_frechet))  &  ((v1_pre_topc k3_frechet) &  ((v2_pre_topc k3_frechet) & (l1_pre_topc k3_frechet)) ) ) ).
tt(dt_k3_freealg,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  =>  ((v1_lang1 (k3_freealg A B)) & (l1_lang1 (k3_freealg A B))) ) ) ).
tt(dt_k3_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k3_fscirc_1 A B C)))  &  ( (~ (v11_struct_0 (k3_fscirc_1 A B C)))  &  ((v1_msualg_1 (k3_fscirc_1 A B C)) &  ((v1_circcomb (k3_fscirc_1 A B C)) &  ((v2_circcomb (k3_fscirc_1 A B C)) &  ((v3_circcomb (k3_fscirc_1 A B C)) & (l1_msualg_1 (k3_fscirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k3_fscirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (m2_subset_1 (k3_fscirc_2 A B C) (u1_struct_0 (k1_fscirc_2 A B C)) (k3_msafree2 (k1_fscirc_2 A B C)))) ) ).
tt(dt_k3_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_finseq_1 D A)) ) )  => (m1_subset_1 (k3_fsm_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) )  => (m1_subset_1 (k3_fsm_3 A B C D) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k3_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k3_ftacell1 A B C D E) (k3_msafree2 (k1_ftacell1 A B C D E)))) ).
tt(dt_k3_funcop_1,ax,$true).
tt(dt_k3_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  => (m2_funct_2 (k3_funcsdom A B C D E) B A (k9_funct_2 B A))) ) ).
tt(dt_k3_funct_1,ax,$true).
tt(dt_k3_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D A)) )  => (m1_subset_1 (k3_funct_2 A B C D) B)) ) ).
tt(dt_k3_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k3_funct_3 A)) & (v1_funct_1 (k3_funct_3 A))) ) ) ).
tt(dt_k3_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k3_funct_4 A B)) & (v1_funct_1 (k3_funct_4 A B))) ) ) ).
tt(dt_k3_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k3_funct_5 A)) & (v1_funct_1 (k3_funct_5 A))) ) ) ).
tt(dt_k3_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k3_funct_6 A)) & (v1_funct_1 (k3_funct_6 A))) ) ) ).
tt(dt_k3_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D A)) )  => (m2_finseq_1 (k3_funct_7 A B C D) A)) ) ).
tt(dt_k3_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ((l1_functor0 C A B) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_functor0 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((m2_functor0 C A B) &  ((m2_functor0 D A B) &  ((m2_functor0 E A B) &  ((m1_functor2 F A B C D) & (m1_functor2 G A B D E)) ) ) ) ) )  => (m1_functor2 (k3_functor2 A B C D E F G) A B C E)) ) ).
tt(dt_k3_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ((v16_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k3_functor3 A B C D E) A C) &  ((v16_functor0 (k3_functor3 A B C D E) A C) & (m2_functor0 (k3_functor3 A B C D E) A C)) ) ) ) ).
tt(dt_k3_fuzzy_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v5_relat_1 (k3_fuzzy_1 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k3_fuzzy_1 A B)) &  ((v1_funct_2 (k3_fuzzy_1 A B) A k1_numbers) & (m1_subset_1 (k3_fuzzy_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k3_fuzzy_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k3_fuzzy_2 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k3_fuzzy_2 A B C)) &  ((v1_funct_2 (k3_fuzzy_2 A B C) A k1_numbers) & (m1_subset_1 (k3_fuzzy_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k3_fuzzy_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) ) ) ) ) )  =>  ((v5_relat_1 (k3_fuzzy_4 A B C D E F G) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k3_fuzzy_4 A B C D E F G)) &  ((v1_funct_2 (k3_fuzzy_4 A B C D E F G) B k1_numbers) & (m1_subset_1 (k3_fuzzy_4 A B C D E F G) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ) ) ).
tt(dt_k3_fvaluat1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_int_1 C)) )  => (m1_subset_1 (k3_fvaluat1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k3_fvsum_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_gate_1,ax,$true).
tt(dt_k3_gate_5,ax,$true).
tt(dt_k3_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  => (m1_subset_1 (k3_gcd_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k3_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) & (m1_subset_1 F k5_numbers)) ) ) ) )  => (m2_finseq_1 (k3_genealg1 A B C D E F) (k3_card_3 A))) ) ).
tt(dt_k3_geomtrap,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_geomtrap A B C D) k1_numbers)) ) ).
tt(dt_k3_gfacirc1,ax, ((v1_funct_1 k3_gfacirc1) &  ((v1_funct_2 k3_gfacirc1 (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k3_gfacirc1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k3_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (m2_subset_1 (k3_gfacirc2 A B C) (u1_struct_0 (k1_gfacirc2 A B C)) (k3_msafree2 (k1_gfacirc2 A B C)))) ) ).
tt(dt_k3_glib_000,ax,(m1_subset_1 k3_glib_000 k5_numbers)).
tt(dt_k3_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m1_subset_1 (k3_glib_001 A B) (k6_glib_000 A))) ) ).
tt(dt_k3_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( (~ (v1_xboole_0 (k3_glib_002 A)))  & (m1_subset_1 (k3_glib_002 A) (k1_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A))))) ) ) ).
tt(dt_k3_glib_003,ax,(m2_subset_1 k3_glib_003 k1_numbers k5_numbers)).
tt(dt_k3_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (~ (v1_xboole_0 (k3_glib_004 A))) ) ) ).
tt(dt_k3_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m1_glib_005 C A B)) )  => (m1_glib_005 (k3_glib_005 A B C) A B)) ) ).
tt(dt_k3_goboard1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v3_relat_1 (k3_goboard1 A B)))  &  ((v1_matrix_1 (k3_goboard1 A B)) &  ((v2_goboard1 (k3_goboard1 A B)) &  ((v3_goboard1 (k3_goboard1 A B)) &  ((v4_goboard1 (k3_goboard1 A B)) &  ((v5_goboard1 (k3_goboard1 A B)) & (m2_finseq_1 (k3_goboard1 A B) (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ) ) ) ).
tt(dt_k3_goboard5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_goboard5 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m1_subset_1 (k3_goboard9 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_gobrd13,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k3_gobrd13 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_goedelcp,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k3_goedelcp A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k3_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k3_graph_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_graph_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k3_graph_2 A B)) &  ((v1_funct_1 (k3_graph_2 A B)) & (v1_finseq_1 (k3_graph_2 A B))) ) ) ) ).
tt(dt_k3_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_graph_3 A B C) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k3_graph_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_graph_5 A B C) (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 A))))) ) ).
tt(dt_k3_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_funct_2 A A)) & (m1_subset_1 C (k1_funct_2 A A)))  => (m1_subset_1 (k3_graphsp A B C) (k1_funct_2 A A))) ) ).
tt(dt_k3_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k3_grcat_1 A B)) &  ((v1_funct_2 (k3_grcat_1 A B) (k1_grcat_1 A B) B) & (m1_subset_1 (k3_grcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_grcat_1 A B) B)))) ) ) ) ).
tt(dt_k3_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k3_gr_cy_1 A)) &  ((v1_funct_2 (k3_gr_cy_1 A) (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A)) & (m1_subset_1 (k3_gr_cy_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A))))) ) ) ) ).
tt(dt_k3_groeb_1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k1_zfmisc_1 (k15_pre_poly A))))  => (m1_subset_1 (k3_groeb_1 A B) (k1_zfmisc_1 (k15_pre_poly A)))) ) ).
tt(dt_k3_groeb_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_groeb_2 A B C D E)) &  ((v1_funct_2 (k3_groeb_2 A B C D E) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k3_groeb_2 A B C D E) (k15_pre_poly A) C) & (m1_subset_1 (k3_groeb_2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k3_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_finset_1 (k3_groeb_3 A B C D E)) & (m1_subset_1 (k3_groeb_3 A B C D E) (k1_zfmisc_1 (k15_pre_poly A)))) ) ) ).
tt(dt_k3_group_10,ax, (! [A:$i,B:$i] : (m1_subset_1 (k3_group_10 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ).
tt(dt_k3_group_11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  => (m1_subset_1 (k3_group_11 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k3_group_1 A)) &  ((v1_funct_2 (k3_group_1 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k3_group_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k3_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k3_group_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_group_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_finseq_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_group_4 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_group_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_group_5 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k3_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v1_group_3 B A) & (m1_group_2 B A))  & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k3_group_6 A B C)) &  ((v1_group_3 (k3_group_6 A B C) C) & (m1_group_6 (k3_group_6 A B C) A C)) ) ) ) ).
tt(dt_k3_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  ((v15_algstr_0 (k3_group_7 A B)) & (m1_group_2 (k3_group_7 A B) (k2_group_7 A B))) ) ) ).
tt(dt_k3_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k3_group_9 A B C)) &  ((v1_funct_2 (k3_group_9 A B C) (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_group_6 (k3_group_9 A B C) B B) & (m1_subset_1 (k3_group_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k3_hahnban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_hahnban1 A B C D)) &  ((v1_funct_2 (k3_hahnban1 A B C D) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k3_hahnban1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_hausdorf,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (m1_subset_1 (k3_hausdorf A B C) k1_numbers)) ) ).
tt(dt_k3_helly,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) &  ((m1_subset_1 C (k6_glib_000 A)) & (m1_subset_1 D (k6_glib_000 A))) ) )  => (m1_subset_1 (k3_helly A B C D) (k6_glib_000 A))) ) ).
tt(dt_k3_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m2_funct_2 (k3_henmodel A) (k3_qc_lang1 A) (k1_henmodel A) (k2_valuat_1 A (k1_henmodel A)))) ) ).
tt(dt_k3_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ((v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 (k3_hermitan A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ).
tt(dt_k3_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) => (m2_subset_1 (k3_heyting1 A B) (k5_finsub_1 (k7_normform A)) (k8_normform A))) ) ).
tt(dt_k3_heyting2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_finset_1 B) &  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) & (m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B)))) )  => (m1_subset_1 (k3_heyting2 A B C D) (k5_finsub_1 (k4_partfun1 A B)))) ) ).
tt(dt_k3_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k3_heyting3 A B) (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B)))) ) ).
tt(dt_k3_hilbasis,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B A) &  ( (~ (v2_struct_0 C))  &  ((v1_group_1 C) & (l5_algstr_0 C)) ) )  =>  ((v1_funct_1 (k3_hilbasis A B C)) &  ((v1_funct_2 (k3_hilbasis A B C) (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 (k3_hilbasis A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k3_hilbert1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k3_hilbert1 A B) k1_hilbert1)) ) ).
tt(dt_k3_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((v1_relat_1 (k3_hilbert2 A)) &  ((v5_relat_1 (k3_hilbert2 A) k1_hilbert1) &  ((v1_funct_1 (k3_hilbert2 A)) & (v3_trees_2 (k3_hilbert2 A))) ) ) ) ) ).
tt(dt_k3_hilbert3,ax,$true).
tt(dt_k3_hurwitz,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k3_hurwitz A B C)) &  ((v1_funct_2 (k3_hurwitz A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k3_hurwitz A B C) A) & (m1_subset_1 (k3_hurwitz A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k3_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k3_idea_1 A B C) A) & (m2_finseq_1 (k3_idea_1 A B C) k6_margrel1)) ) ) ).
tt(dt_k3_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  => (l1_incsp_1 (k3_incproj A))) ) ).
tt(dt_k3_incsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v15_incsp_1 A) & (l2_incsp_1 A))  &  ((m1_subset_1 B (u1_incsp_1 A)) & (m1_subset_1 C (u2_incsp_1 A))) )  => (m1_subset_1 (k3_incsp_1 A B C) (u4_incsp_1 A))) ) ).
tt(dt_k3_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_index_1 A)) )  =>  ((v1_relat_1 (k3_index_1 A)) &  ((v2_relat_1 (k3_index_1 A)) & (v1_funct_1 (k3_index_1 A))) ) ) ) ).
tt(dt_k3_instalg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_relat_1 E) & (v1_funct_1 E)) ) ) ) )  => (m2_pboole (k3_instalg1 A B C D E) (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k3_relat_1 D C))) (u3_msualg_1 A (k1_instalg1 A B (k11_msafree B C) D E)))) ) ).
tt(dt_k3_int_1,ax,$true).
tt(dt_k3_int_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v7_ordinal1 (k3_int_2 A B))) ) ).
tt(dt_k3_int_3,ax, ((v1_funct_1 k3_int_3) &  ((v1_funct_2 k3_int_3 (u1_struct_0 k1_int_3) k5_numbers) & (m1_subset_1 k3_int_3 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k1_int_3) k5_numbers)))) ) ).
tt(dt_k3_int_5,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B (k1_zfmisc_1 A)))  =>  ((v1_card_3 (k3_int_5 A B)) & (m2_finseq_1 (k3_int_5 A B) k5_numbers)) ) ) ).
tt(dt_k3_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v2_struct_0 (k3_int_7 A)))  &  ((v2_group_1 (k3_int_7 A)) &  ((v3_group_1 (k3_int_7 A)) &  ((v5_group_1 (k3_int_7 A)) & (l3_algstr_0 (k3_int_7 A))) ) ) ) ) ) ).
tt(dt_k3_integr10,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  => (m1_subset_1 (k3_integr10 A B) k1_numbers)) ) ).
tt(dt_k3_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  & (m2_integr15 D A B C)) ) )  =>  ((v1_funct_1 (k3_integr15 A B C D)) &  ((v1_funct_2 (k3_integr15 A B C D) k5_numbers k1_numbers) & (m1_subset_1 (k3_integr15 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_integr16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  &  ((m1_integra1 C A) & (m1_integr16 D A B C)) ) )  => (m1_subset_1 (k3_integr16 A B C D) k2_numbers)) ) ).
tt(dt_k3_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  & (m2_integr18 E A B C D)) ) ) )  =>  ((v1_funct_1 (k3_integr18 A B C D E)) &  ((v1_funct_2 (k3_integr18 A B C D E) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k3_integr18 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_integr1c,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  &  ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) ) )  => (v1_xcmplx_0 (k3_integr1c A B))) ) ).
tt(dt_k3_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k3_integra1 A) k1_numbers)) ) ).
tt(dt_k3_integra2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) ) ) )  =>  ((v1_funct_1 (k3_integra2 A B C)) &  ((v1_funct_2 (k3_integra2 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k3_integra2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_integra5,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (~ (v1_xboole_0 (k3_integra5 A B)))  &  ((v2_measure5 (k3_integra5 A B)) & (m1_subset_1 (k3_integra5 A B) (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(dt_k3_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  => (m1_interva1 (k3_interva1 A B C) A)) ) ).
tt(dt_k3_intpro_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_intpro_1) & (m1_subset_1 B k1_intpro_1))  => (m1_subset_1 (k3_intpro_1 A B) k1_intpro_1)) ) ).
tt(dt_k3_irrat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k3_irrat_1 A)) &  ((v1_funct_2 (k3_irrat_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_irrat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_isocat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D B C) &  ((m2_cat_1 E B C) &  ((m2_cat_1 F A B) & (m1_nattra_1 G B C D E)) ) ) ) ) )  => (m1_nattra_1 (k3_isocat_1 A B C D E F G) A C (k9_cat_1 A B C F D) (k9_cat_1 A B C F E))) ) ).
tt(dt_k3_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) & (m1_subset_1 E (u4_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k3_isocat_2 A B C D E)) &  ((v1_funct_2 (k3_isocat_2 A B C D E) (u4_struct_0 B) (u4_struct_0 C)) & (m1_subset_1 (k3_isocat_2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C))))) ) ) ) ).
tt(dt_k3_jgraph_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m2_finseq_1 (k3_jgraph_1 A B) (u4_struct_0 (k1_jgraph_1 A)))) ) ).
tt(dt_k3_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k3_jgraph_4 A)) &  ((v1_funct_2 (k3_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k3_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k3_jgraph_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k3_jgraph_6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (m1_subset_1 (k3_jordan10 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(dt_k3_jordan11,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k3_jordan11 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k3_jordan19 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_jordan1h,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k3_jordan1h A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_jordan3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m2_finseq_1 (k3_jordan3 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k3_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k3_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k3_jordan6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (u1_struct_0 (k15_euclid 2)))) ) )  => (m1_subset_1 (k3_jordan6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k3_jordan_a,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  => (m1_subset_1 (k3_jordan_a A B) k1_numbers)) ) ).
tt(dt_k3_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k3_jordan A)) &  ((v1_funct_2 (k3_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 (k3_jordan A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ) ) ).
tt(dt_k3_knaster,ax,$true).
tt(dt_k3_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B (k9_setfam_1 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k9_setfam_1 D))))) ) ) ) )  => (m1_subset_1 (k3_kolmog01 A B C D E) (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) ).
tt(dt_k3_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k3_kurato_0 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_kurato_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k3_lang1,ax,$true).
tt(dt_k3_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( (~ (v1_xboole_0 D))  &  ((m1_matrix_1 E D B C) & (m1_finseq_1 F D)) ) ) ) )  => (m1_matrix_1 (k3_laplace A B C D E F) D B C)) ) ).
tt(dt_k3_latsubgr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_latsubgr A B C)) &  ((v1_funct_2 (k3_latsubgr A B C) (u1_struct_0 (k11_group_4 A)) (u1_struct_0 (k11_group_4 B))) & (m1_subset_1 (k3_latsubgr A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_group_4 A)) (u1_struct_0 (k11_group_4 B)))))) ) ) ) ).
tt(dt_k3_lattice2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  &  ((m1_subset_1 C (k5_finsub_1 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  => (m1_subset_1 (k3_lattice2 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) & (l1_orders_2 (k3_lattice3 A))) ) ) ) ) ) ).
tt(dt_k3_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m2_lattice4 (k3_lattice4 A B) A)) ) ).
tt(dt_k3_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  => (m1_subset_1 (k3_lattice5 A B C D E) (u1_struct_0 B))) ) ).
tt(dt_k3_lattice6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_lattice6 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (m1_subset_1 (k3_lattice7 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_lattice8,ax,$true).
tt(dt_k3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_lattices A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k3_lexbfs A B C)) &  ((v1_funct_1 (k3_lexbfs A B C)) & (v4_valued_0 (k3_lexbfs A B C))) ) ) ) ).
tt(dt_k3_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_lfuzzy_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_lfuzzy_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((v5_relat_1 (k3_lfuzzy_1 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k3_lfuzzy_1 A B)) &  ((v1_funct_2 (k3_lfuzzy_1 A B) B k1_numbers) & (m1_subset_1 (k3_lfuzzy_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ) ) ).
tt(dt_k3_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k3_limfunc1 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k3_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_lopban_1 A B)) &  ((v1_funct_2 (k3_lopban_1 A B) (k2_zfmisc_1 k1_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B))) & (m1_subset_1 (k3_lopban_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k3_lopban_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k10_lopban_1 A A)) & (m1_subset_1 C (k10_lopban_1 A A))) )  => (m2_subset_1 (k3_lopban_2 A B C) (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A))) ) ).
tt(dt_k3_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_lopban_3 A B C)) &  ((v1_funct_2 (k3_lopban_3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k3_lopban_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_lopban_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k3_lopban_4 A)) &  ((v1_funct_2 (k3_lopban_4 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_lopban_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  => (m2_subset_1 (k3_lopclset A B C) (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A))) ) ).
tt(dt_k3_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k3_lpspace1 A)) &  ((v1_funct_2 (k3_lpspace1 A) (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 (k3_lpspace1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) ) ) ) ).
tt(dt_k3_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k3_lpspace2 A B C D)))  & (m1_subset_1 (k3_lpspace2 A B C D) (k1_zfmisc_1 (u1_struct_0 (k2_lpspace2 A B C D))))) ) ) ).
tt(dt_k3_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k3_lp_space A)) &  ((v1_funct_2 (k3_lp_space A) (k2_lp_space A) k1_numbers) & (m1_subset_1 (k3_lp_space A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_lp_space A) k1_numbers)))) ) ) ) ).
tt(dt_k3_ltlaxio1,ax,(m1_subset_1 k3_ltlaxio1 k1_hilbert1)).
tt(dt_k3_margrel1,ax,$true).
tt(dt_k3_mathmorp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k3_mathmorp A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  => (m1_matrix_1 (k3_matrix10 A B C) k1_numbers A A)) ) ).
tt(dt_k3_matrix11,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( (~ (v1_xboole_0 D))  &  ((m1_matrix_1 E D B C) & (m1_finseq_1 F D)) ) ) ) )  => (m1_matrix_1 (k3_matrix11 A B C D E F) D B C)) ) ).
tt(dt_k3_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) &  ((v7_ordinal1 F) & (m1_subset_1 G (u1_struct_0 C))) ) ) ) ) )  => (m1_matrix_1 (k3_matrix12 A B C D E F G) (u1_struct_0 C) A B)) ) ).
tt(dt_k3_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_matrix13 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k3_matrix14,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_finseq_1 (k3_matrix14 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_matrix15,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  => (m1_matrix_1 (k3_matrix15 A B) A (k3_finseq_1 B) 1)) ) ).
tt(dt_k3_matrix16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_finseq_1 B (u1_struct_0 A)))  => (m1_matrix_1 (k3_matrix16 A B) (u1_struct_0 A) (k3_finseq_1 B) (k3_finseq_1 B))) ) ).
tt(dt_k3_matrix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  => (m1_subset_1 (k3_matrix_1 A B C D) A)) ) ).
tt(dt_k3_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((v1_relat_1 (k3_matrix_2 A B C D)) &  ((v1_funct_1 (k3_matrix_2 A B C D)) &  ((v1_finseq_1 (k3_matrix_2 A B C D)) & (v1_matrix_1 (k3_matrix_2 A B C D))) ) ) ) ).
tt(dt_k3_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((v1_matrix_1 (k3_matrix_3 A B C)) & (m2_finseq_1 (k3_matrix_3 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k3_matrix_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k2_numbers))) )  =>  ((v1_matrix_1 (k3_matrix_5 A B)) & (m2_finseq_1 (k3_matrix_5 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k3_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (m1_matrix_1 (k3_matrix_6 A B C D) (u1_struct_0 B) A A)) ) ).
tt(dt_k3_matrix_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k12_matrix_2 A)))  => (m1_matrix_2 (k3_matrix_7 A B) (k12_matrix_2 A))) ) ).
tt(dt_k3_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v1_matrixj1 (k3_matrixj1 A B C) A) & (m2_finseq_1 (k3_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k3_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrixj2 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  &  ((v1_matrixj2 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) )  =>  ((v1_matrixj2 (k3_matrixj2 A B C) A) & (m2_finseq_1 (k3_matrixj2 A B C) (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(dt_k3_matrixr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k1_numbers))) )  =>  ((v1_matrix_1 (k3_matrixr1 A B)) & (m2_finseq_1 (k3_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k3_matrixr2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_matrix_1 B k1_numbers A A))  => (m1_subset_1 (k3_matrixr2 A B) k1_numbers)) ) ).
tt(dt_k3_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_finseq_1 E (u1_struct_0 B)) & (m1_matrlin F A C)) ) ) ) )  => (m1_matrix_1 (k3_matrlin2 A B C D E F) (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 E))) ) ).
tt(dt_k3_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k3_matrlin A B C D E)) &  ((v1_funct_2 (k3_matrlin A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 (k3_matrlin A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k3_matroid0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_pre_topc (k3_matroid0 A B)) & (l1_pre_topc (k3_matroid0 A B))) ) ) ).
tt(dt_k3_matrprob,ax, (! [A:$i] :  ((m1_finseq_1 A (k3_finseq_2 k1_numbers)) => (m2_finseq_1 (k3_matrprob A) k1_numbers)) ) ).
tt(dt_k3_matrtop1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B)) )  =>  ((v1_funct_1 (k3_matrtop1 A B C)) &  ((v1_funct_2 (k3_matrtop1 A B C) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k3_matrtop1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) ) ) ) ).
tt(dt_k3_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) ) )  => (m1_matrix_1 (k3_matrtop3 A B) (u1_struct_0 k2_vectsp_1) A A)) ) ).
tt(dt_k3_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  => (m1_subset_1 (k3_mcart_1 A B C D) C)) ) ).
tt(dt_k3_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m2_subset_1 (k3_measure1 A B C D) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k3_measure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  & (m1_subset_1 D (k2_measure3 A B C))) )  =>  ( (~ (v1_xboole_0 (k3_measure3 A B C D)))  & (m1_subset_1 (k3_measure3 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k3_measure4,ax, (! [A:$i,B:$i] :  ((m1_measure4 B A) =>  ((v1_funct_1 (k3_measure4 A B)) &  ((v1_funct_2 (k3_measure4 A B) (k1_measure4 A B) k7_numbers) & (m1_subset_1 (k3_measure4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_measure4 A B) k7_numbers)))) ) ) ) ).
tt(dt_k3_measure6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k3_measure6 A B C)) &  ((v1_funct_2 (k3_measure6 A B C) (k9_setfam_1 B) (k9_setfam_1 A)) & (m1_subset_1 (k3_measure6 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 B) (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k3_measure7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) & (m1_measure7 B A))  =>  ((v1_funct_1 (k3_measure7 A B)) &  ((v1_funct_2 (k3_measure7 A B) k5_numbers k7_numbers) & (m1_subset_1 (k3_measure7 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k3_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((m4_measure8 D A B C) & (v7_ordinal1 E)) ) )  => (m3_measure8 (k3_measure8 A B C D E) A (k8_nat_1 (k9_setfam_1 A) C E) B)) ) ).
tt(dt_k3_member_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k3_member_1 A B) k7_numbers)) ) ).
tt(dt_k3_mesfun6c,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  & (m1_subset_1 E B)) ) ) )  => (v1_xcmplx_0 (k3_mesfun6c A B C D E))) ) ).
tt(dt_k3_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k3_mesfun7c A B)) & (m1_subset_1 (k3_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k3_mesfun9c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ((v1_funct_1 (k3_mesfun9c A B)) &  ((v1_funct_2 (k3_mesfun9c A B) k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 (k3_mesfun9c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) ) ) ).
tt(dt_k3_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) ) ) )  =>  ((v1_funct_1 (k3_mesfunc1 A B C)) & (m1_subset_1 (k3_mesfunc1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k3_mesfunc2,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k3_mesfunc2 A B)) & (m1_subset_1 (k3_mesfunc2 A B) (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ).
tt(dt_k3_mesfunc5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k3_mesfunc5 A B C)) &  ((v1_funct_2 (k3_mesfunc5 A B C) k5_numbers k7_numbers) & (m1_subset_1 (k3_mesfunc5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k3_mesfunc7,ax,$true).
tt(dt_k3_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k3_mesfunc8 A B)) &  ((v1_funct_2 (k3_mesfunc8 A B) k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 (k3_mesfunc8 A B) A k7_numbers) & (m1_subset_1 (k3_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ) ).
tt(dt_k3_mesfunc9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  => (m1_subset_1 (k3_mesfunc9 A) k7_numbers)) ) ).
tt(dt_k3_metric_1,ax, ((v1_funct_1 k3_metric_1) &  ((v1_funct_2 k3_metric_1 (k2_zfmisc_1 1 1) k1_numbers) & (m1_subset_1 k3_metric_1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 1 1) k1_numbers)))) ) ).
tt(dt_k3_metric_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ((m1_subset_1 B (k2_metric_2 A)) & (m1_subset_1 C (k2_metric_2 A))) )  => (m1_subset_1 (k3_metric_2 A B C) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k3_metric_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k3_metric_6 A B C)) &  ((v1_funct_2 (k3_metric_6 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k3_metric_6 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_mfold_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ( (~ (v2_struct_0 (k3_mfold_2 A B C)))  & (m1_pre_topc (k3_mfold_2 A B C) (k15_euclid A))) ) ) ).
tt(dt_k3_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_midsp_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_midsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_midsp_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E (k4_finseq_2 C (u1_struct_0 B))) & (m1_subset_1 F (k4_finseq_2 D (u1_struct_0 B)))) ) ) ) )  => (m2_finseq_2 (k3_midsp_3 A B C D E F) (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 C D) (u1_struct_0 B)))) ) ).
tt(dt_k3_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k3_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ( (~ (v2_struct_0 (k3_mod_2 A B)))  &  ((v13_algstr_0 (k3_mod_2 A B)) &  ((v8_vectsp_1 (k3_mod_2 A B) A) &  ((v9_vectsp_1 (k3_mod_2 A B) A) &  ((v10_vectsp_1 (k3_mod_2 A B) A) &  ((v11_vectsp_1 (k3_mod_2 A B) A) &  ((v2_rlvect_1 (k3_mod_2 A B)) &  ((v3_rlvect_1 (k3_mod_2 A B)) &  ((v4_rlvect_1 (k3_mod_2 A B)) & (l1_vectsp_1 (k3_mod_2 A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v2_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A)) & (l1_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A))) ) ) ).
tt(dt_k3_modal_1,ax,$true).
tt(dt_k3_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  => (m1_modcat_1 (k3_modcat_1 A B) B)) ) ).
tt(dt_k3_modelc_1,ax,$true).
tt(dt_k3_modelc_2,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k3_modelc_2 A) k5_numbers)) ) ).
tt(dt_k3_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k3_modelc_3 A) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k3_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_moebius1 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k3_monoid_0,ax, ( (~ (v2_struct_0 k3_monoid_0))  &  ((v15_algstr_0 k3_monoid_0) & (m2_monoid_0 k3_monoid_0 k2_monoid_0)) ) ).
tt(dt_k3_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) )  => (m2_funct_2 (k3_monoid_1 A B C D E F G) A D (k9_funct_2 A D))) ) ).
tt(dt_k3_morph_01,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k3_morph_01 A B)) &  ((v1_funct_2 (k3_morph_01 A B) (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k3_morph_01 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k3_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (m1_subset_1 (k3_msafree2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_msafree3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_msualg_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ( (~ (v1_xboole_0 C))  & (v1_relat_1 C)) ) )  => (m3_pboole (k3_msafree3 A B C) (u1_struct_0 A) B)) ) ).
tt(dt_k3_msafree,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k3_msafree A B)) & (v1_funct_1 (k3_msafree A B))) ) ) ).
tt(dt_k3_msalimit,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_msalimit C A B) & (m2_msalimit D A B C)) ) )  =>  ((v3_msualg_1 (k3_msalimit A B C D) B) & (m1_msualg_2 (k3_msalimit A B C D) B (k14_pralg_2 (u1_struct_0 A) B C))) ) ) ).
tt(dt_k3_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k1_msaterm A B)) & (m1_subset_1 D (k9_xtuple_0 C))) ) )  => (m1_subset_1 (k3_msaterm A B C D) (u1_struct_0 (k5_msafree A B)))) ) ).
tt(dt_k3_msinst_1,ax,$true).
tt(dt_k3_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_funct_1 (k3_msscyc_2 A)) &  ((v1_funct_2 (k3_msscyc_2 A) (k1_msscyc_2 A) (u1_struct_0 A)) & (m1_subset_1 (k3_msscyc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_msscyc_2 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m3_pboole C A (k1_mboolean A B)))  =>  ((v1_relat_1 (k3_mssubfam A B C)) &  ((v4_relat_1 (k3_mssubfam A B C) A) &  ((v1_funct_1 (k3_mssubfam A B C)) & (v1_partfun1 (k3_mssubfam A B C) A)) ) ) ) ) ).
tt(dt_k3_msualg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (l3_msualg_1 C A)) )  => (m1_subset_1 (k3_msualg_1 A B C) (k10_xtuple_0 (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A C))))) ) ).
tt(dt_k3_msualg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((m1_subset_1 C (u4_struct_0 A)) & (m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B))) ) )  =>  ((v1_funct_1 (k3_msualg_2 A B C D)) &  ((v1_funct_2 (k3_msualg_2 A B C D) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) D)) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) D) C)) & (m1_subset_1 (k3_msualg_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) D)) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) D) C))))) ) ) ) ).
tt(dt_k3_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  &  ((m2_pboole E A B C) & (m2_pboole F A C D)) ) ) )  => (m2_pboole (k3_msualg_3 A B C D E F) A B D)) ) ).
tt(dt_k3_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D))) ) ) )  => (m1_subset_1 (k3_msualg_4 A B C D E) (k1_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D)))) ) ).
tt(dt_k3_msualg_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_msualg_4 C A B B)) )  =>  ((v1_msualg_4 (k3_msualg_5 A B C) A B) & (m1_msualg_4 (k3_msualg_5 A B C) A B B)) ) ) ).
tt(dt_k3_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  => (m1_subset_1 (k3_msualg_6 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k3_msualg_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 A B))))) ) )  => (m1_subset_1 (k3_msualg_8 A B C D) (k1_zfmisc_1 (u1_struct_0 (k2_msualg_5 (k1_funct_1 B C)))))) ) ).
tt(dt_k3_multop_1,ax,$true).
tt(dt_k3_mycielsk,ax, (! [A:$i] :  ( ((v2_mycielsk A) & (l1_orders_2 A))  => (v7_ordinal1 (k3_mycielsk A))) ) ).
tt(dt_k3_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k3_nagata_1 A B C)) &  ((v1_funct_2 (k3_nagata_1 A B C) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (k3_nagata_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_k3_nagata_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((v1_funct_1 (k3_nagata_2 A B C)) &  ((v1_funct_2 (k3_nagata_2 A B C) A k1_numbers) & (m1_subset_1 (k3_nagata_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k3_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k3_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_nat_3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  => (m1_trees_4 (k3_nat_3 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_nat_5,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k3_nat_5 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k3_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k3_nat_d A B) k5_numbers)) ) ).
tt(dt_k3_nat_lat,ax, ( (~ (v2_struct_0 k3_nat_lat))  &  ((v3_lattices k3_nat_lat) & (l3_lattices k3_nat_lat)) ) ).
tt(dt_k3_nattra_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  => (m1_nattra_1 (k3_nattra_1 A B C) A B C C)) ) ).
tt(dt_k3_ndiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_ndiff_1 A B C D) (u1_struct_0 (k16_lopban_1 A B)))) ) ).
tt(dt_k3_ndiff_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k3_ndiff_2 A B C D E) (u1_struct_0 B))) ) ).
tt(dt_k3_ndiff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  & (m1_subset_1 C (u1_struct_0 (k4_real_ns1 A)))) )  =>  ((v1_funct_1 (k3_ndiff_4 A B C)) &  ((v1_funct_2 (k3_ndiff_4 A B C) (u1_struct_0 (k4_real_ns1 A)) k1_numbers) & (m1_subset_1 (k3_ndiff_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers)))) ) ) ) ).
tt(dt_k3_ndiff_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ((v1_funct_1 (k3_ndiff_5 A B)) &  ((v1_funct_2 (k3_ndiff_5 A B) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B))) & (m1_subset_1 (k3_ndiff_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)))))) ) ) ) ).
tt(dt_k3_neckla_2,ax,$true).
tt(dt_k3_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k3_necklace A)) & (l1_orders_2 (k3_necklace A))) ) ) ).
tt(dt_k3_net_1,ax,$true).
tt(dt_k3_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_newton A) k1_numbers)) ) ).
tt(dt_k3_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  => (m1_subset_1 (k3_normform A B C D) (k2_zfmisc_1 A B))) ) ).
tt(dt_k3_normsp_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_normsp_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k3_normsp_0 A B C)) & (m1_subset_1 (k3_normsp_0 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k3_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k3_normsp_1 A B C)) &  ((v1_funct_2 (k3_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k3_normsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_normsp_2 A)))  &  ((v2_pre_topc (k3_normsp_2 A)) & (l1_pre_topc (k3_normsp_2 A))) ) ) ) ).
tt(dt_k3_ntalgo_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k4_numbers) & (m1_subset_1 B k4_numbers))  => (m1_subset_1 (k3_ntalgo_1 A B) k4_numbers)) ) ).
tt(dt_k3_numbers,ax,$true).
tt(dt_k3_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  => (m2_subset_1 (k3_openlatt A B C) (k1_zfmisc_1 (u1_struct_0 A)) (k1_openlatt A))) ) ).
tt(dt_k3_oppcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_oppcat_1 A B) (u1_struct_0 (k2_oppcat_1 A)))) ) ).
tt(dt_k3_orders_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_orders_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_ordinal1,ax,$true).
tt(dt_k3_ordinal2,ax, (! [A:$i] : (v3_ordinal1 (k3_ordinal2 A))) ).
tt(dt_k3_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((v3_ordinal1 (k3_ordinal4 A)) &  ( (~ (v1_xboole_0 (k3_ordinal4 A)))  & (m1_subset_1 (k3_ordinal4 A) A)) ) ) ) ).
tt(dt_k3_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v3_ordinal1 (k3_ordinal5 A))) ) ).
tt(dt_k3_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((v1_relat_1 (k3_ordinal6 A)) &  ((v1_funct_1 (k3_ordinal6 A)) &  ((v5_ordinal1 (k3_ordinal6 A)) & (v1_ordinal2 (k3_ordinal6 A))) ) ) ) ) ).
tt(dt_k3_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  => (m1_subset_1 (k3_osafree A B C) (u1_struct_0 (k2_osafree A B)))) ) ).
tt(dt_k3_osalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_relat_1 (k3_osalg_1 A B)) &  ((v4_relat_1 (k3_osalg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (k3_osalg_1 A B)) & (v1_partfun1 (k3_osalg_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_k3_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (m2_osalg_2 (k3_osalg_2 A B) A B)) ) ).
tt(dt_k3_osalg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m2_subset_1 (k3_osalg_4 A B) (k1_zfmisc_1 (u1_struct_0 A)) (k2_osalg_4 A))) ) ).
tt(dt_k3_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_parsp_1 A)) &  ((v1_funct_2 (k3_parsp_1 A) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 (k3_parsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k3_partfun1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_funct_1 (k3_partfun1 A B C)) & (m1_subset_1 (k3_partfun1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ).
tt(dt_k3_partfun2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k3_partfun2 A B C D)) & (m1_subset_1 (k3_partfun2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k3_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k3_partfun3 A B)) &  ((v1_funct_2 (k3_partfun3 A B) A k1_numbers) & (m1_subset_1 (k3_partfun3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k3_partit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_eqrel_1 B A) & (m1_eqrel_1 C A)) )  => (m1_eqrel_1 (k3_partit1 A B C) A)) ) ).
tt(dt_k3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k3_pboole A B C)) &  ((v4_relat_1 (k3_pboole A B C) A) &  ((v1_funct_1 (k3_pboole A B C)) & (v1_partfun1 (k3_pboole A B C) A)) ) ) ) ) ).
tt(dt_k3_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) => (l1_pre_topc (k3_pcomps_1 A))) ) ).
tt(dt_k3_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  => (m1_subset_1 (k3_pcs_0 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))))) ) ).
tt(dt_k3_pdiff_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) )  =>  ((v1_funct_1 (k3_pdiff_1 A B)) & (m1_subset_1 (k3_pdiff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1))))) ) ) ).
tt(dt_k3_pdiff_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  & (m1_subset_1 B (k1_euclid 2)))  => (m1_subset_1 (k3_pdiff_3 A B) k1_numbers)) ) ).
tt(dt_k3_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k3_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k3_pdiff_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) )  =>  ((v1_funct_1 (k3_pdiff_9 A B C D)) & (m1_subset_1 (k3_pdiff_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) ) ).
tt(dt_k3_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) ) )  => (m1_subset_1 (k3_pencil_1 A B) A)) ) ).
tt(dt_k3_pencil_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_pre_topc A))) )  => (m1_subset_1 (k3_pencil_2 A B C) (u1_pre_topc A))) ) ).
tt(dt_k3_pencil_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  &  ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) ) ) ) )  =>  ((v1_funct_1 (k3_pencil_3 A B C D)) &  ((v1_funct_2 (k3_pencil_3 A B C D) (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D))))) & (m1_subset_1 (k3_pencil_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D)))))))) ) ) ) ).
tt(dt_k3_pencil_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) &  ((m1_vectsp_4 D A B) & (v7_ordinal1 E)) ) ) )  => (m1_subset_1 (k3_pencil_4 A B C D E) (k1_zfmisc_1 (k2_vectsp_9 A B E)))) ) ).
tt(dt_k3_pepin,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k3_pepin A B) k5_numbers)) ) ).
tt(dt_k3_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_petri A)))  => (m1_subset_1 (k3_petri A B) (u4_struct_0 A))) ) ).
tt(dt_k3_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((v1_funct_1 (k3_pnproc_1 A B C)) &  ((v1_funct_2 (k3_pnproc_1 A B C) A k5_numbers) & (m1_subset_1 (k3_pnproc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(dt_k3_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_polyalg1 A)))  &  ((v1_polyalg1 (k3_polyalg1 A) A) & (l1_polyalg1 (k3_polyalg1 A) A)) ) ) ) ).
tt(dt_k3_polyeq_1,ax,$true).
tt(dt_k3_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k3_polyeq_3 A) k2_numbers)) ) ).
tt(dt_k3_polyeq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xcmplx_0 (k3_polyeq_5 A B C))) ) ).
tt(dt_k3_polyform,ax, (! [A:$i] :  ((v1_int_1 A) => (m2_finseq_1 (k3_polyform A) k4_numbers)) ) ).
tt(dt_k3_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) ) ) )  => (m1_subset_1 (k3_polynom1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_polynom2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v4_vectsp_1 C) & (l6_algstr_0 C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) ) ) ) )  => (m1_subset_1 (k3_polynom2 A B C D) (u1_struct_0 C))) ) ).
tt(dt_k3_polynom3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D (k4_finseq_2 B A)) & (m1_subset_1 E (k4_finseq_2 C A))) ) ) )  => (m2_finseq_2 (k3_polynom3 A B C D E) A (k4_finseq_2 (k2_nat_1 B C) A))) ) ).
tt(dt_k3_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_polynom5 A B C)) &  ((v1_funct_2 (k3_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k3_polynom5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_polynom7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  => (m1_subset_1 (k3_polynom7 A B C) (u1_struct_0 B))) ) ).
tt(dt_k3_polynom8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_int_1 C)) )  => (m1_subset_1 (k3_polynom8 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  => (m1_subset_1 (k3_polyred A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 (k11_polynom1 A C)) (u1_struct_0 (k11_polynom1 A C)))))) ) ).
tt(dt_k3_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k3_poset_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_power,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k3_power A B))) ) ).
tt(dt_k3_pralg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v2_margrel1 C) &  ((v3_margrel1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) )  &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v2_margrel1 D) &  ((v3_margrel1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 B) B)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_pralg_1 A B C D)) &  ( (~ (v1_xboole_0 (k3_pralg_1 A B C D)))  &  ((v2_margrel1 (k3_pralg_1 A B C D)) &  ((v3_margrel1 (k3_pralg_1 A B C D) (k2_zfmisc_1 A B)) & (m1_subset_1 (k3_pralg_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k2_zfmisc_1 A B)) (k2_zfmisc_1 A B))))) ) ) ) ) ) ).
tt(dt_k3_pralg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_pralg_2 C A B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) )  => (m1_pralg_3 (k3_pralg_3 A B C D) (k8_eqrel_1 A D) (k6_partfun1 (k8_eqrel_1 A D)) B)) ) ).
tt(dt_k3_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_pre_ff A) k5_numbers)) ) ).
tt(dt_k3_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_prelamb A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m2_finseq_2 (k3_pre_poly A B) A (k3_finseq_2 A))) ) ).
tt(dt_k3_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k3_prepower A B) k1_numbers)) ) ).
tt(dt_k3_prob_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k3_prob_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_prob_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) & (m1_subset_1 D B)) ) )  => (m2_prob_1 (k3_prob_2 A B C D) A B)) ) ).
tt(dt_k3_prob_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k3_prob_3 A B)) &  ((v1_funct_2 (k3_prob_3 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k3_prob_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k3_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k3_prvect_1 A B C)) &  ((v1_funct_2 (k3_prvect_1 A B C) (k4_finseq_2 C A) (k4_finseq_2 C A)) & (m1_subset_1 (k3_prvect_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A))))) ) ) ) ).
tt(dt_k3_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ( (~ (v2_struct_0 (k3_prvect_2 A B)))  &  ((v13_algstr_0 (k3_prvect_2 A B)) &  ((v2_rlvect_1 (k3_prvect_2 A B)) &  ((v3_rlvect_1 (k3_prvect_2 A B)) &  ((v4_rlvect_1 (k3_prvect_2 A B)) &  ((v5_rlvect_1 (k3_prvect_2 A B)) &  ((v6_rlvect_1 (k3_prvect_2 A B)) &  ((v7_rlvect_1 (k3_prvect_2 A B)) &  ((v8_rlvect_1 (k3_prvect_2 A B)) & (l1_rlvect_1 (k3_prvect_2 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k3_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_algstr_0 B)) )  => (m1_subset_1 (k3_prvect_3 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))) ) ).
tt(dt_k3_pscomp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k3_pscomp_1 A B C)) &  ((v1_funct_2 (k3_pscomp_1 A B C) (u1_struct_0 (k1_pre_topc A C)) k1_numbers) & (m1_subset_1 (k3_pscomp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) k1_numbers)))) ) ) ) ).
tt(dt_k3_pua2mss1,ax, (! [A:$i,B:$i] :  ((m2_pua2mss1 B A) => (m1_eqrel_1 (k3_pua2mss1 A B) A)) ) ).
tt(dt_k3_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k3_qc_lang1 A) (k1_zfmisc_1 (k2_qc_lang1 A)))) ) ).
tt(dt_k3_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k3_qc_lang2 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k3_qc_lang3,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k3_qc_lang3 A B) (k2_qc_lang1 A) (k5_qc_lang1 A))) ) ).
tt(dt_k3_qc_lang4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m4_trees_1 (k3_qc_lang4 A B C) (k9_xtuple_0 (k2_qc_lang4 A B)))) ) ).
tt(dt_k3_qmax_1,ax,$true).
tt(dt_k3_quantal1,ax, (! [A:$i] :  ((l3_quantal1 A) => (m1_subset_1 (k3_quantal1 A) (u1_struct_0 A))) ) ).
tt(dt_k3_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k3_quatern2 A) k1_numbers)) ) ).
tt(dt_k3_quatern3,ax,$true).
tt(dt_k3_quaterni,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 F A) &  ((m1_subset_1 G A) &  ((m1_subset_1 H A) & (m1_subset_1 I A)) ) ) )  =>  ((v1_funct_1 (k3_quaterni A B C D E F G H I)) &  ((v1_funct_2 (k3_quaterni A B C D E F G H I) (k2_enumset1 B C D E) A) & (m1_subset_1 (k3_quaterni A B C D E F G H I) (k1_zfmisc_1 (k2_zfmisc_1 (k2_enumset1 B C D E) A)))) ) ) ) ).
tt(dt_k3_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  => (m2_subset_1 (k3_quofield A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A))) ) ).
tt(dt_k3_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k3_radix_1 A)))  & (m1_subset_1 (k3_radix_1 A) (k1_zfmisc_1 k4_numbers))) ) ) ).
tt(dt_k3_radix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C k5_numbers)) ) )  => (m2_subset_1 (k3_radix_2 A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k3_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k3_radix_3 A)))  & (m1_subset_1 (k3_radix_3 A) (k1_zfmisc_1 k4_numbers))) ) ) ).
tt(dt_k3_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k3_radix_5 A B C) k4_numbers (k3_radix_1 C))) ) ).
tt(dt_k3_radix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m1_finseq_1 D (k3_radix_1 C))) ) ) )  => (m1_subset_1 (k3_radix_6 A B C D) (k3_radix_1 C))) ) ).
tt(dt_k3_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  => (m1_random_1 (k3_random_1 A B C D) A B)) ) ).
tt(dt_k3_random_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  ( (~ (v1_xboole_0 (k3_random_2 A B)))  & (m1_subset_1 (k3_random_2 A B) (k1_zfmisc_1 (u1_struct_0 (k12_funcsdom A))))) ) ) ).
tt(dt_k3_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v7_vectsp_1 (k3_ranknull A B C D) A) & (m1_vectsp_4 (k3_ranknull A B C D) A C)) ) ) ).
tt(dt_k3_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ( (~ (v1_ratfunc1 C A))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) )  => (m1_ratfunc1 (k3_ratfunc1 A B C) A)) ) ).
tt(dt_k3_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  => (m1_subset_1 (k3_rcomp_1 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k3_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k3_real_1 A B) k1_numbers)) ) ).
tt(dt_k3_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k3_real_3 A)) &  ((v1_funct_2 (k3_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_real_lat,ax, ((v3_lattices k3_real_lat) & (l3_lattices k3_real_lat)) ).
tt(dt_k3_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k3_real_ns1 A)) &  ((v1_funct_2 (k3_real_ns1 A) (k1_euclid A) k1_numbers) & (m1_subset_1 (k3_real_ns1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) ) ) ).
tt(dt_k3_rearran1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_rearran1 C) &  ((v2_rearran1 C) &  ((v3_rearran1 C (k1_zfmisc_1 B)) & (m1_finseq_1 C (k1_zfmisc_1 B))) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k3_rearran1 A B C D)) & (m1_subset_1 (k3_rearran1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ).
tt(dt_k3_relat_1,ax, (! [A:$i,B:$i] : (v1_relat_1 (k3_relat_1 A B))) ).
tt(dt_k3_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k3_relset_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ).
tt(dt_k3_relset_2,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) =>  ((v1_relat_1 (k3_relset_2 A B)) & (v1_funct_1 (k3_relset_2 A B))) ) ) ).
tt(dt_k3_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k8_afinsq_1 A)) & (v7_ordinal1 C))  => (m1_subset_1 (k3_rewrite2 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k3_rewrite3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B)) ) )  => (m1_subset_1 (k3_rewrite3 A B C D E) (k1_zfmisc_1 (u1_struct_0 C)))) ) ).
tt(dt_k3_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k3_rfinseq2 A) k1_numbers)) ) ).
tt(dt_k3_rfinseq,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m2_finseq_1 (k3_rfinseq A) k1_numbers)) ) ).
tt(dt_k3_rfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k3_rfunct_1 A B C D)) & (m1_subset_1 (k3_rfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k3_rfunct_3,ax, (! [A:$i,B:$i] : (m1_rfunct_3 (k3_rfunct_3 A B) A B)) ).
tt(dt_k3_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k3_rinfsup1 A)) &  ((v1_funct_2 (k3_rinfsup1 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_rinfsup1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_funct_1 (k3_rinfsup2 A)) &  ((v1_funct_2 (k3_rinfsup2 A) k5_numbers k7_numbers) & (m1_subset_1 (k3_rinfsup2 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k3_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((v1_funct_1 (k3_ringcat1 A)) &  ((v1_funct_2 (k3_ringcat1 A) (u1_struct_0 (u1_ringcat1 A)) (u1_struct_0 (u2_ringcat1 A))) & (m1_subset_1 (k3_ringcat1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (u1_ringcat1 A)) (u1_struct_0 (u2_ringcat1 A)))))) ) ) ) ).
tt(dt_k3_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_rlvect_2 B A))  => (m1_subset_1 (k3_rlaffin1 A B) k1_numbers)) ) ).
tt(dt_k3_rlsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_rlsub_1 C A)) )  => (m1_subset_1 (k3_rlsub_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_rlsub_2,ax,$true).
tt(dt_k3_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k3_rltopsp1 A B)) &  ((v1_funct_2 (k3_rltopsp1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k3_rltopsp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_rlvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_rlvect_1 A) & (l1_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_rlvect_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k9_funct_2 (u1_struct_0 A) k1_numbers)))  => (m1_subset_1 (k3_rlvect_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_rlvect_x,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_finseq_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_rlvect_x A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_rmod_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_rmod_2 D A B)) ) )  => (m1_subset_1 (k3_rmod_2 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k3_rmod_3,ax,$true).
tt(dt_k3_rmod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  => (m1_rmod_4 (k3_rmod_4 A B) A B)) ) ).
tt(dt_k3_robbins1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_robbins1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_robbins1 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_roughs_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_rsspace3,ax, ( (~ (v2_struct_0 k3_rsspace3))  & (l1_normsp_1 k3_rsspace3)) ).
tt(dt_k3_rsspace4,ax, ( (~ (v2_struct_0 k3_rsspace4))  & (l1_normsp_1 k3_rsspace4)) ).
tt(dt_k3_rsspace,ax, (! [A:$i] : (m1_subset_1 (k3_rsspace A) k1_numbers)) ).
tt(dt_k3_rusub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_rusub_1 C A)) )  => (m1_subset_1 (k3_rusub_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_rusub_2,ax,$true).
tt(dt_k3_rusub_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlsub_1 B A))  =>  ( (~ (v1_xboole_0 (k3_rusub_4 A B)))  & (m1_subset_1 (k3_rusub_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k3_rusub_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_bhsp_1 (k3_rusub_5 A B)) & (m1_rusub_1 (k3_rusub_5 A B) A)) ) ) ).
tt(dt_k3_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k3_rvsum_1 A)) &  ((v1_funct_2 (k3_rvsum_1 A) k1_numbers k1_numbers) & (m1_subset_1 (k3_rvsum_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  => (m2_finseq_1 (k3_rvsum_2 A B) k2_numbers)) ) ).
tt(dt_k3_scm_comp,ax, (! [A:$i] :  ((m1_subset_1 A (k6_dtconstr k1_scm_comp)) => (m1_dtconstr (k3_scm_comp A) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k3_scmfsa_1,ax,(m1_subset_1 k3_scmfsa_1 (k1_zfmisc_1 k1_scmfsa_1))).
tt(dt_k3_scmfsa_2,ax,(m1_subset_1 k3_scmfsa_2 (k1_zfmisc_1 (u1_struct_0 k1_scmfsa_2)))).
tt(dt_k3_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) & (v1_afinsq_1 (k3_scmfsa6a A B))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmfsa_7,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  =>  ((v5_ordinal1 (k3_scmfsa_7 A B)) &  ((v1_relat_1 (k3_scmfsa_7 A B)) &  ((v5_relat_1 (k3_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa_7 A B)) & (v1_finset_1 (k3_scmfsa_7 A B))) ) ) ) ) ) ).
tt(dt_k3_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_scmfsa8b A B C)))  &  ((v1_relat_1 (k3_scmfsa8b A B C)) &  ((v4_relat_1 (k3_scmfsa8b A B C) k5_numbers) &  ((v5_relat_1 (k3_scmfsa8b A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa8b A B C)) &  ((v1_finset_1 (k3_scmfsa8b A B C)) & (v1_afinsq_1 (k3_scmfsa8b A B C))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmfsa9a,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k3_scmfsa9a A B)))  &  ((v1_relat_1 (k3_scmfsa9a A B)) &  ((v4_relat_1 (k3_scmfsa9a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa9a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa9a A B)) &  ((v1_finset_1 (k3_scmfsa9a A B)) & (v1_afinsq_1 (k3_scmfsa9a A B))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmfsa_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_scmfsa_9 A B)) &  ((v4_relat_1 (k3_scmfsa_9 A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa_9 A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k3_scmfsa_9 A B)))  &  ((v1_funct_1 (k3_scmfsa_9 A B)) &  ((v1_finset_1 (k3_scmfsa_9 A B)) & (v1_afinsq_1 (k3_scmfsa_9 A B))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k3_scmfsa_i A) k2_scm_inst)) ) ).
tt(dt_k3_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k3_scmfsa_2)))  => (m1_scmfsa_2 (k3_scmfsa_m A))) ) ).
tt(dt_k3_scm_inst,ax, (~ (v1_xboole_0 k3_scm_inst)) ).
tt(dt_k3_scmisort,ax, ( (~ (v1_xboole_0 k3_scmisort))  &  ((v1_relat_1 k3_scmisort) &  ((v4_relat_1 k3_scmisort k5_numbers) &  ((v5_relat_1 k3_scmisort (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 k3_scmisort) &  ((v1_finset_1 k3_scmisort) & (v1_afinsq_1 k3_scmisort)) ) ) ) ) ) ).
tt(dt_k3_scmpds_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_ami_2) & (v1_int_1 B))  => (m2_finseq_1 (k3_scmpds_1 A B) (k2_xboole_0 k2_ami_2 k4_numbers))) ) ).
tt(dt_k3_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k3_scmpds_2 A) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k3_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  & (m1_subset_1 B (u1_compos_1 k1_scmpds_2)))  =>  ( (~ (v1_xboole_0 (k3_scmpds_4 A B)))  &  ((v1_relat_1 (k3_scmpds_4 A B)) &  ((v4_relat_1 (k3_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_4 A B)) &  ((v1_finset_1 (k3_scmpds_4 A B)) & (v1_afinsq_1 (k3_scmpds_4 A B))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_6 A B C D)))  &  ((v1_relat_1 (k3_scmpds_6 A B C D)) &  ((v4_relat_1 (k3_scmpds_6 A B C D) k5_numbers) &  ((v5_relat_1 (k3_scmpds_6 A B C D) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_6 A B C D)) &  ((v1_finset_1 (k3_scmpds_6 A B C D)) & (v1_afinsq_1 (k3_scmpds_6 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmpds_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k3_scmpds_7 A)))  &  ((v1_relat_1 (k3_scmpds_7 A)) &  ((v4_relat_1 (k3_scmpds_7 A) k5_numbers) &  ((v5_relat_1 (k3_scmpds_7 A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_7 A)) &  ((v1_finset_1 (k3_scmpds_7 A)) & (v1_afinsq_1 (k3_scmpds_7 A))) ) ) ) ) ) ) ) ).
tt(dt_k3_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (m1_subset_1 (k3_scmpds_i A) k2_scm_inst)) ) ).
tt(dt_k3_scmp_gcd,ax, ((v1_ami_2 k3_scmp_gcd) & (m1_subset_1 k3_scmp_gcd (u1_struct_0 k1_scmpds_2))) ).
tt(dt_k3_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k3_scmring1 A B C) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) ) ).
tt(dt_k3_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k3_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k3_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k3_scmringi A B) k2_scm_inst)) ) ).
tt(dt_k3_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) => (v7_ordinal1 (k3_scmyciel A))) ) ).
tt(dt_k3_scpinvar,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k3_scpinvar A)))  &  ((v1_relat_1 (k3_scpinvar A)) &  ((v4_relat_1 (k3_scpinvar A) k5_numbers) &  ((v5_relat_1 (k3_scpinvar A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scpinvar A)) &  ((v1_finset_1 (k3_scpinvar A)) & (v1_afinsq_1 (k3_scpinvar A))) ) ) ) ) ) ) ) ).
tt(dt_k3_semi_af1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_semi_af1 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k3_seq_4,ax, (! [A:$i] :  ((v3_membered A) => (v1_xreal_0 (k3_seq_4 A))) ) ).
tt(dt_k3_seqfunc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k3_seqfunc A B)) &  ((v1_funct_2 (k3_seqfunc A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k3_seqfunc A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k3_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k3_series_1 A)) &  ((v1_funct_2 (k3_series_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k3_series_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k3_setfam_1,ax,$true).
tt(dt_k3_setlim_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k3_setlim_1 A)) & (v1_funct_1 (k3_setlim_1 A))) ) ) ).
tt(dt_k3_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_funct_1 (k3_setlim_2 A B C)) &  ((v1_funct_2 (k3_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k3_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k3_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k3_setwiseo A B C) (k5_finsub_1 A))) ) ).
tt(dt_k3_sfmastr2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((v1_funct_1 (k3_sfmastr2 A B C D)) &  ((v1_funct_2 (k3_sfmastr2 A B C D) k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 (k3_sfmastr2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) ) ) ) ).
tt(dt_k3_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 D)) ) )  =>  ((v1_relat_1 (k3_sfmastr3 A B C D)) &  ((v4_relat_1 (k3_sfmastr3 A B C D) k5_numbers) &  ((v5_relat_1 (k3_sfmastr3 A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_sfmastr3 A B C D)) &  ( (~ (v1_xboole_0 (k3_sfmastr3 A B C D)))  &  ((v1_finset_1 (k3_sfmastr3 A B C D)) & (v1_afinsq_1 (k3_sfmastr3 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k3_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) => (m1_subset_1 (k3_sf_mastr A) (k5_finsub_1 k3_scmfsa_2))) ) ).
tt(dt_k3_sgraph1,ax,$true).
tt(dt_k3_sheffer1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_sheffer1 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_simplex0,ax, (! [A:$i,B:$i,C:$i] : (m1_subset_1 (k3_simplex0 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ).
tt(dt_k3_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_simplex0 B (u1_struct_0 A)))  => (m1_subset_1 (k3_simplex1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_simplex2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_simplex0 B (u1_struct_0 (k15_euclid A))))  => (m1_subset_1 (k3_simplex2 A B) k1_numbers)) ) ).
tt(dt_k3_sincos10,ax, ((v1_funct_1 k3_sincos10) & (m1_subset_1 k3_sincos10 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k3_sin_cos2,ax, (! [A:$i] : (m1_subset_1 (k3_sin_cos2 A) k1_numbers)) ).
tt(dt_k3_sin_cos3,ax, ((v1_funct_1 k3_sin_cos3) &  ((v1_funct_2 k3_sin_cos3 k2_numbers k2_numbers) & (m1_subset_1 k3_sin_cos3 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k3_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k3_sin_cos4 A) k1_numbers)) ) ).
tt(dt_k3_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k3_sin_cos5 A) k1_numbers)) ) ).
tt(dt_k3_sin_cos6,ax, (! [A:$i] : (m1_subset_1 (k3_sin_cos6 A) k1_numbers)) ).
tt(dt_k3_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k3_sin_cos7 A))) ) ).
tt(dt_k3_sin_cos9,ax,$true).
tt(dt_k3_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_funct_1 (k3_sin_cos A)) &  ((v1_funct_2 (k3_sin_cos A) k5_numbers k2_numbers) & (m1_subset_1 (k3_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k3_square_1,ax,$true).
tt(dt_k3_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) ) ) ) )  =>  ((v1_funct_1 (k3_stacks_1 A B C D)) &  ((v1_funct_2 (k3_stacks_1 A B C D) (k2_zfmisc_1 A (k8_eqrel_1 B C)) (k8_eqrel_1 B C)) & (m1_subset_1 (k3_stacks_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A (k8_eqrel_1 B C)) (k8_eqrel_1 B C))))) ) ) ) ).
tt(dt_k3_stirl2_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k3_stirl2_1 A B) k5_numbers)) ) ).
tt(dt_k3_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k3_struct_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_valuat_1 A C))) ) )  =>  ((v1_funct_1 (k3_sublemma A B C D)) & (m1_subset_1 (k3_sublemma A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) C)))) ) ) ).
tt(dt_k3_subset_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (k3_subset_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_substlat,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) => (m2_subset_1 (k3_substlat A B C) (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B))) ) ).
tt(dt_k3_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_finseq_1 B (k2_qc_lang1 A)) & (m1_subset_1 C (k1_substut1 A))) )  => (m2_finseq_1 (k3_substut1 A B C) (k2_qc_lang1 A))) ) ).
tt(dt_k3_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  => (m1_subset_1 (k3_substut2 A B C) (k1_substut1 A))) ) ).
tt(dt_k3_supinf_1,ax, (! [A:$i] :  ((v2_membered A) => (v2_membered (k3_supinf_1 A))) ) ).
tt(dt_k3_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k3_supinf_2 A B) k7_numbers)) ) ).
tt(dt_k3_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_pre_topc (k3_t_0topsp A)) & (l1_pre_topc (k3_t_0topsp A))) ) ) ).
tt(dt_k3_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k3_t_1topsp A)) &  ((v1_funct_2 (k3_t_1topsp A) (u1_struct_0 A) (u1_struct_0 (k2_t_1topsp A))) &  ((v5_pre_topc (k3_t_1topsp A) A (k2_t_1topsp A)) & (m1_subset_1 (k3_t_1topsp A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_t_1topsp A)))))) ) ) ) ) ).
tt(dt_k3_tarski,ax,$true).
tt(dt_k3_taxonom1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  & (v1_xreal_0 B))  => (m1_subset_1 (k3_taxonom1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k3_taylor_1,ax, ((v1_funct_1 k3_taylor_1) & (m1_subset_1 k3_taylor_1 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k3_tbsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_tbsp_1 A B) k1_numbers)) ) ).
tt(dt_k3_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k3_tdlat_1 A)) &  ((v1_funct_2 (k3_tdlat_1 A) (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A)) & (m1_subset_1 (k3_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tdlat_1 A) (k1_tdlat_1 A)) (k1_tdlat_1 A))))) ) ) ) ).
tt(dt_k3_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  => (m2_subset_1 (k3_termord A B C D) (k14_pre_poly A) (k15_pre_poly A))) ) ).
tt(dt_k3_tex_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B A) => (l1_pre_topc (k3_tex_1 A B))) ) ).
tt(dt_k3_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_tex_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_tmap_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_pre_topc C A) &  ((m1_pre_topc D A) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k3_tmap_1 A B C D E)) &  ((v1_funct_2 (k3_tmap_1 A B C D E) (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 (k3_tmap_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k3_toler_1,ax,$true).
tt(dt_k3_topalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_topalg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C))))) ) ).
tt(dt_k3_topalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k3_topalg_2 A B C)) &  ((v1_funct_2 (k3_topalg_2 A B C) (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 (k3_topalg_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k3_topalg_3 A B C D)) &  ((v1_funct_2 (k3_topalg_3 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)))) & (m1_subset_1 (k3_topalg_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C))))))) ) ) ) ).
tt(dt_k3_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) )  =>  ((v1_funct_1 (k3_topalg_4 A B C D)) &  ((v1_funct_2 (k3_topalg_4 A B C D) (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 (k3_topalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_topalg_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k3_topalg_5 A B C D E)) &  ((v1_funct_2 (k3_topalg_5 A B C D E) (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 (k3_topalg_5 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k3_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v6_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  => (m1_subset_1 (k3_topalg_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k3_topdim_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (v1_int_1 (k3_topdim_1 A B))) ) ).
tt(dt_k3_topgen_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (m1_subset_1 (k3_topgen_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k3_topgen_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_topgen_2 B A))  =>  ((v1_tops_2 (k3_topgen_2 A B) A) &  ((v1_cantor_1 (k3_topgen_2 A B) A) & (m1_subset_1 (k3_topgen_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_topgen_3,ax, ( (~ (v1_finset_1 k3_topgen_3))  & (v1_card_1 k3_topgen_3)) ).
tt(dt_k3_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (m1_subset_1 (k3_topgen_4 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k3_topgen_5,ax, ( (~ (v2_struct_0 k3_topgen_5))  &  ((v1_pre_topc k3_topgen_5) &  ((v2_pre_topc k3_topgen_5) & (l1_pre_topc k3_topgen_5)) ) ) ).
tt(dt_k3_topmetr,ax, ((v2_pre_topc k3_topmetr) & (l1_pre_topc k3_topmetr)) ).
tt(dt_k3_topreal1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_finseq_1 B (u1_struct_0 (k15_euclid A))))  => (m1_subset_1 (k3_topreal1 A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k3_topreal7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  & (m1_subset_1 C (u1_struct_0 (k1_topreal7 A B)))) )  => (m1_subset_1 (k3_topreal7 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k3_topreal9 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k3_toprealb,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_tops_2 (k3_toprealb A B) k2_topalg_2) & (m1_subset_1 (k3_toprealb A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))))) ) ) ).
tt(dt_k3_toprns_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) )  =>  ((v1_funct_1 (k3_toprns_1 A B)) &  ((v1_funct_2 (k3_toprns_1 A B) k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k3_toprns_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k3_treal_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((m1_subset_1 C (u1_struct_0 (k4_topmetr A B))) & (m1_subset_1 D (u1_struct_0 (k4_topmetr A B)))) ) )  =>  ((v1_funct_1 (k3_treal_1 A B C D)) &  ((v1_funct_2 (k3_treal_1 A B C D) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B))) & (m1_subset_1 (k3_treal_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)))))) ) ) ) ).
tt(dt_k3_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (m1_subset_1 (k3_trees_1 A) (k1_zfmisc_1 A))) ) ).
tt(dt_k3_trees_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  & (m1_subset_1 C (k9_xtuple_0 B))) )  => (m1_subset_1 (k3_trees_2 A B C) A)) ) ).
tt(dt_k3_trees_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_relat_1 (k3_trees_4 A B)) &  ((v1_funct_1 (k3_trees_4 A B)) & (v3_trees_2 (k3_trees_4 A B))) ) ) ) ).
tt(dt_k3_trees_9,ax,$true).
tt(dt_k3_trees_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((m4_trees_1 B (k9_xtuple_0 A)) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) )  =>  ((v1_relat_1 (k3_trees_a A B C)) &  ((v1_funct_1 (k3_trees_a A B C)) & (v3_trees_2 (k3_trees_a A B C))) ) ) ) ).
tt(dt_k3_turing_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k3_turing_1 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k3_twoscomp,ax, ((v1_funct_1 k3_twoscomp) &  ((v1_funct_2 k3_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k3_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k3_unialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m2_finseq_1 (k3_unialg_2 A B) (k4_partfun1 (k3_finseq_2 B) B))) ) ).
tt(dt_k3_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_funct_1 (k3_unialg_3 A)) &  ((v1_funct_2 (k3_unialg_3 A) (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k3_unialg_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k3_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  ( (~ (v2_struct_0 (k3_uniroots A)))  &  ((v15_algstr_0 (k3_uniroots A)) &  ((v2_group_1 (k3_uniroots A)) &  ((v3_group_1 (k3_uniroots A)) & (l3_algstr_0 (k3_uniroots A))) ) ) ) ) ) ).
tt(dt_k3_uproots,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (v1_xreal_0 (k3_uproots A B))) ) ).
tt(dt_k3_urysohn1,ax,(m1_subset_1 k3_urysohn1 (k1_zfmisc_1 k1_numbers))).
tt(dt_k3_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m2_urysohn3 D A B C)) ) )  =>  ((v1_funct_1 (k3_urysohn3 A B C D)) &  ((v1_funct_2 (k3_urysohn3 A B C D) k3_urysohn1 (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k3_urysohn3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k3_urysohn1 (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k3_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))) ) )  => (m2_funct_2 (k3_valuat_1 A B C D) (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))) ) ).
tt(dt_k3_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k3_valued_1 A B C D E)) & (m1_subset_1 (k3_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k3_valued_2,ax,$true).
tt(dt_k3_vectmetr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectmetr A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k3_vectmetr A B) k1_numbers)) ) ).
tt(dt_k3_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v1_funct_1 (k3_vectsp10 A B C)) &  ((v1_funct_2 (k3_vectsp10 A B C) (k2_zfmisc_1 (k2_vectsp10 A B C) (k2_vectsp10 A B C)) (k2_vectsp10 A B C)) & (m1_subset_1 (k3_vectsp10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_vectsp10 A B C) (k2_vectsp10 A B C)) (k2_vectsp10 A B C))))) ) ) ) ).
tt(dt_k3_vectsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_vectsp_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_vectsp_2 A)))  &  ((v13_algstr_0 (k3_vectsp_2 A)) &  ((v7_vectsp_1 (k3_vectsp_2 A) A) &  ((v2_rlvect_1 (k3_vectsp_2 A)) &  ((v3_rlvect_1 (k3_vectsp_2 A)) &  ((v4_rlvect_1 (k3_vectsp_2 A)) & (l1_vectsp_1 (k3_vectsp_2 A) A)) ) ) ) ) ) ) ) ).
tt(dt_k3_vectsp_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_vectsp_4 D A B)) ) )  => (m1_subset_1 (k3_vectsp_4 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k3_vectsp_5,ax,$true).
tt(dt_k3_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_finseq_1 C (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  => (m2_finseq_1 (k3_vectsp_6 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_vfunct_1 A B C D)) & (m1_subset_1 (k3_vfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k3_vfunct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_vfunct_2 A B C D)) & (m1_subset_1 (k3_vfunct_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k3_waybel_0,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k3_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v2_struct_0 (k3_waybel10 A)))  &  ((v1_orders_2 (k3_waybel10 A)) & (l1_orders_2 (k3_waybel10 A))) ) ) ) ).
tt(dt_k3_waybel11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k3_waybel11 A B C)))  &  ((v6_waybel_0 (k3_waybel11 A B C) A) & (l1_waybel_0 (k3_waybel11 A B C) A)) ) ) ) ).
tt(dt_k3_waybel17,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k3_waybel17 A B C)))  &  ((v6_waybel_0 (k3_waybel17 A B C) A) & (l1_waybel_0 (k3_waybel17 A B C) A)) ) ) ) ).
tt(dt_k3_waybel18,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ((v1_pre_topc (k3_waybel18 A B)) &  ((v2_pre_topc (k3_waybel18 A B)) & (l1_pre_topc (k3_waybel18 A B))) ) ) ) ).
tt(dt_k3_waybel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_waybel_1 A B C)) &  ((v1_funct_2 (k3_waybel_1 A B C) (u1_struct_0 (k1_yellow_2 A B C)) (u1_struct_0 B)) & (m1_subset_1 (k3_waybel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_yellow_2 A B C)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k3_waybel20,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((v1_funct_1 (k3_waybel20 A B)) &  ((v1_funct_2 (k3_waybel20 A B) (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 (k3_waybel20 A B) A) & (m1_subset_1 (k3_waybel20 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k3_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v1_funct_1 (k3_waybel23 A B)) &  ((v1_funct_2 (k3_waybel23 A B) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A)) & (m1_subset_1 (k3_waybel23 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k3_waybel24,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ( (~ (v2_struct_0 B))  & (l1_waybel_9 B)) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (l1_orders_2 (k3_waybel24 A B))) ) ) ).
tt(dt_k3_waybel26,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k3_waybel26 A B C D)) &  ((v1_funct_2 (k3_waybel26 A B C D) (u1_struct_0 (k1_waybel26 A B)) (u1_struct_0 (k1_waybel26 A C))) & (m1_subset_1 (k3_waybel26 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A B)) (u1_struct_0 (k1_waybel26 A C)))))) ) ) ) ).
tt(dt_k3_waybel27,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  &  ((m1_subset_1 C (u1_struct_0 (k2_waybel27 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k3_waybel27 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k3_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m4_yellow_6 (k3_waybel28 A) A)) ) ).
tt(dt_k3_waybel29,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_funct_1 (k3_waybel29 A B)) &  ((v1_funct_2 (k3_waybel29 A B) (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k3_waybel24 A (k1_waybel29 (k2_yellow_1 (u1_pre_topc B)))))) & (m1_subset_1 (k3_waybel29 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k3_waybel24 A (k1_waybel29 (k2_yellow_1 (u1_pre_topc B))))))))) ) ) ) ).
tt(dt_k3_waybel_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A)) ) )  =>  ((v6_waybel_0 (k3_waybel_2 A B C) A) & (l1_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(dt_k3_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_waybel34 A B C)) &  ((v1_funct_2 (k3_waybel34 A B C) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 (k3_waybel34 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)))))) ) ) ) ).
tt(dt_k3_waybel35,ax,$true).
tt(dt_k3_waybel_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  & (m1_subset_1 C A)) )  => (l1_orders_2 (k3_waybel_3 A B C))) ) ).
tt(dt_k3_waybel_4,ax,$true).
tt(dt_k3_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ((m2_pboole D A C (k7_funcop_1 A B)) &  ((m2_pboole E (k4_card_3 (k2_funct_6 D)) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) A) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) B)) & (m1_subset_1 F (k4_card_3 (k2_funct_6 D)))) ) ) ) )  =>  ((v1_funct_1 (k3_waybel_5 A B C D E F)) &  ((v1_funct_2 (k3_waybel_5 A B C D E F) A B) & (m1_subset_1 (k3_waybel_5 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k3_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k3_waybel_6 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v6_waybel_0 (k3_waybel_9 A) A) & (l1_waybel_0 (k3_waybel_9 A) A)) ) ) ).
tt(dt_k3_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (m1_eqrel_1 (k3_weddwitt A) (u1_struct_0 A))) ) ).
tt(dt_k3_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) => (m1_subset_1 (k3_weierstr A) k1_numbers)) ) ).
tt(dt_k3_wellord1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  =>  ((v1_relat_1 (k3_wellord1 A B)) & (v1_funct_1 (k3_wellord1 A B))) ) ) ).
tt(dt_k3_wsierp_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_subset_1 (k3_wsierp_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k3_xboole_0,ax,$true).
tt(dt_k3_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) => (v1_xboolean (k3_xboolean A))) ) ).
tt(dt_k3_xcmplx_0,ax,$true).
tt(dt_k3_xtuple_0,ax,$true).
tt(dt_k3_xxreal_0,ax,$true).
tt(dt_k3_xxreal_1,ax,$true).
tt(dt_k3_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k3_xxreal_3 A B))) ) ).
tt(dt_k3_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k3_yellow_0 A) (u1_struct_0 A))) ) ).
tt(dt_k3_yellow11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_yellow11 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_yellow18,ax,$true).
tt(dt_k3_yellow19,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_yellow19 A B C)))  &  ((v6_waybel_0 (k3_yellow19 A B C) A) & (l1_waybel_0 (k3_yellow19 A B C) A)) ) ) ) ).
tt(dt_k3_yellow_1,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (l1_orders_2 (k3_yellow_1 A))) ) ).
tt(dt_k3_yellow20,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) ) )  =>  ((v9_functor0 (k3_yellow20 A B) B A) &  ((v15_functor0 (k3_yellow20 A B) B A) & (m2_functor0 (k3_yellow20 A B) B A)) ) ) ) ).
tt(dt_k3_yellow21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v3_orders_2 (k3_yellow21 A B)) &  ((v4_orders_2 (k3_yellow21 A B)) &  ((v5_orders_2 (k3_yellow21 A B)) &  ((v1_lattice3 (k3_yellow21 A B)) &  ((v2_lattice3 (k3_yellow21 A B)) & (l1_orders_2 (k3_yellow21 A B))) ) ) ) ) ) ) ).
tt(dt_k3_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_funct_1 (k3_yellow_2 A)) &  ((v1_funct_2 (k3_yellow_2 A) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 (k3_yellow_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) ) ) ) ).
tt(dt_k3_yellow_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (l1_orders_2 (k3_yellow_3 A B))) ) ) ).
tt(dt_k3_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k3_yellow_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k3_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k3_yellow_5 A B C) (u1_struct_0 A))) ) ).
tt(dt_k3_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v6_waybel_0 (k3_yellow_6 A B C) B) & (l1_waybel_0 (k3_yellow_6 A B C) B)) ) ) ).
tt(dt_k3_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k3_yellow_9 A B)))  &  ((v6_waybel_0 (k3_yellow_9 A B) A) & (l1_waybel_0 (k3_yellow_9 A B) A)) ) ) ) ).
tt(dt_k3_yoneda_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_nattra_1 (k3_yoneda_1 A B) A (k1_yoneda_1 A) (k2_yoneda_1 A (k4_graph_1 A B)) (k2_yoneda_1 A (k3_graph_1 A B)))) ) ).
tt(dt_k3_zf_fund1,ax, (! [A:$i] :  ((m1_subset_1 A k1_zf_lang) => (m1_subset_1 (k3_zf_fund1 A) k5_numbers)) ) ).
tt(dt_k3_zf_lang1,ax,$true).
tt(dt_k3_zf_lang,ax, (! [A:$i] :  ((m1_subset_1 A k1_zf_lang) => (m2_finseq_1 (k3_zf_lang A) k5_numbers)) ) ).
tt(dt_k3_zfmisc_1,ax,$true).
tt(dt_k3_zf_model,ax,$true).
tt(dt_k3_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((v3_ordinal1 (k3_zf_refle A B C)) & (m1_subset_1 (k3_zf_refle A B C) A)) ) ) ).
tt(dt_k3_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((v1_zmodul01 (k3_zmodul01 A)) & (m1_zmodul01 (k3_zmodul01 A) A)) ) ) ).
tt(dt_k40_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))))  &  ((v9_abcmiz_1 C A) & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) ) )  => (m3_abcmiz_1 (k40_abcmiz_1 A B C) A)) ) ).
tt(dt_k40_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  & (m2_aofa_i00 E A B C D)) ) ) )  => (m3_aofa_i00 (k40_aofa_i00 A B C D E) A B C D)) ) ).
tt(dt_k40_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  &  ((m1_subset_1 D (k4_finseq_2 C (k4_finseq_2 B k6_margrel1))) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1))))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) &  ((v3_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1))))) ) )  & (m1_subset_1 G (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1))) ) ) ) ) )  => (m2_finseq_2 (k40_descip_1 A B C D E F G) k6_margrel1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1))) ) ).
tt(dt_k40_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ( (~ (v2_struct_0 B))  & (l1_fomodel1 B)) )  =>  ( (~ (v2_struct_0 (k40_fomodel1 A B)))  &  ((v1_fomodel1 (k40_fomodel1 A B)) & (l1_fomodel1 (k40_fomodel1 A B))) ) ) ) ).
tt(dt_k40_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v4_fomodel2 (k40_fomodel2 A B) A) & (m2_subset_1 (k40_fomodel2 A B) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ).
tt(dt_k40_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) & (v13_fomodel4 C A)) )  => (m1_subset_1 (k40_fomodel4 A B C) (k1_zfmisc_1 (k33_fomodel2 A)))) ) ).
tt(dt_k40_gate_1,ax,$true).
tt(dt_k40_glib_000,ax,$true).
tt(dt_k40_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k40_modelc_1 A B C) (k30_modelc_1 A))) ) ).
tt(dt_k40_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k40_modelc_2 A)) &  ((v1_funct_2 (k40_modelc_2 A) (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k40_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k40_twoscomp,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k40_twoscomp A B)))  &  ( (~ (v11_struct_0 (k40_twoscomp A B)))  &  ((v1_msualg_1 (k40_twoscomp A B)) &  ((v1_circcomb (k40_twoscomp A B)) &  ((v2_circcomb (k40_twoscomp A B)) &  ((v3_circcomb (k40_twoscomp A B)) & (l1_msualg_1 (k40_twoscomp A B))) ) ) ) ) ) ) ).
tt(dt_k41_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  => (m1_subset_1 (k41_abcmiz_1 A B) (k1_zfmisc_1 (k38_abcmiz_1 A)))) ) ).
tt(dt_k41_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  & (m1_subset_1 E B)) ) ) )  => (m2_aofa_i00 (k41_aofa_i00 A B C D E) A B C D)) ) ).
tt(dt_k41_binop_2,ax, ((v1_funct_1 k41_binop_2) &  ((v1_funct_2 k41_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (m1_subset_1 k41_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers)))) ) ).
tt(dt_k41_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k4_finseq_2 16 (k4_finseq_2 48 k6_margrel1))) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1))))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) &  ((v3_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) ) )  & (m1_subset_1 D (k4_finseq_2 64 k6_margrel1))) ) )  => (m2_finseq_2 (k41_descip_1 A B C D) k6_margrel1 (k4_finseq_2 64 k6_margrel1))) ) ).
tt(dt_k41_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v4_funct_1 B))  =>  ( (~ (v6_struct_0 (k41_fomodel1 A B)))  &  ((v11_fomodel1 (k41_fomodel1 A B)) &  ((v16_fomodel1 (k41_fomodel1 A B) A) & (l1_fomodel1 (k41_fomodel1 A B))) ) ) ) ) ).
tt(dt_k41_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (m2_finseq_2 (k41_fomodel2 A B) (k1_fomodel1 A) (k3_finseq_2 (k1_fomodel1 A)))) ) ).
tt(dt_k41_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  => (m1_subset_1 (k41_fomodel4 A B C) (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) ) ).
tt(dt_k41_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k41_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k41_gfacirc1 A B C)))  &  ((v1_msualg_1 (k41_gfacirc1 A B C)) &  ((v1_circcomb (k41_gfacirc1 A B C)) &  ((v2_circcomb (k41_gfacirc1 A B C)) &  ((v3_circcomb (k41_gfacirc1 A B C)) & (l1_msualg_1 (k41_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k41_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k41_modelc_1 A)) &  ((v1_funct_2 (k41_modelc_1 A) (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 (k41_modelc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) ) ) ) ).
tt(dt_k41_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k41_modelc_2 A)) &  ((v1_funct_2 (k41_modelc_2 A) (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 (k41_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) ) ) ) ).
tt(dt_k41_twoscomp,ax, (! [A:$i,B:$i] :  ((v3_msualg_1 (k41_twoscomp A B) (k40_twoscomp A B)) &  ((v4_msafree2 (k41_twoscomp A B) (k40_twoscomp A B)) &  ((v4_circcomb (k41_twoscomp A B) (k40_twoscomp A B)) &  ((v6_circcomb (k41_twoscomp A B) (k40_twoscomp A B)) & (l3_msualg_1 (k41_twoscomp A B) (k40_twoscomp A B))) ) ) ) ) ).
tt(dt_k41_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k41_valued_1 A B C)) & (m1_subset_1 (k41_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k41_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (v1_xcmplx_0 C)) )  =>  ((v1_relat_1 (k41_valued_2 A B C)) & (v1_funct_1 (k41_valued_2 A B C))) ) ) ).
tt(dt_k42_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  =>  ((v9_abcmiz_1 (k42_abcmiz_1 A B) A) & (m1_abcmiz_1 (k42_abcmiz_1 A B) A (k12_abcmiz_1 A))) ) ) ).
tt(dt_k42_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  & (m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) )  => (m3_aofa_i00 (k42_aofa_i00 A B C D E) A B C D)) ) ).
tt(dt_k42_descip_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 B (k4_finseq_2 64 k6_margrel1)))  => (m2_finseq_2 (k42_descip_1 A B) k6_margrel1 (k4_finseq_2 64 k6_margrel1))) ) ).
tt(dt_k42_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) &  ( (~ (v5_fomodel2 B A))  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((v4_fomodel2 (k42_fomodel2 A B) A) & (m2_subset_1 (k42_fomodel2 A B) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ).
tt(dt_k42_fomodel4,ax,$true).
tt(dt_k42_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k42_gfacirc1 A B C) (k41_gfacirc1 A B C)) &  ((v4_msafree2 (k42_gfacirc1 A B C) (k41_gfacirc1 A B C)) &  ((v4_circcomb (k42_gfacirc1 A B C) (k41_gfacirc1 A B C)) &  ((v6_circcomb (k42_gfacirc1 A B C) (k41_gfacirc1 A B C)) & (l3_msualg_1 (k42_gfacirc1 A B C) (k41_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k42_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) )  => (m1_subset_1 (k42_modelc_1 A B C D E) k6_margrel1)) ) ).
tt(dt_k42_modelc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A))))) )  => (l1_modelc_2 (k42_modelc_2 A B))) ) ).
tt(dt_k42_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k42_valued_2 A B C D)) & (m1_subset_1 (k42_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k43_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m3_abcmiz_1 B A) &  ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) ) )  => (m3_abcmiz_1 (k43_abcmiz_1 A B C) A)) ) ).
tt(dt_k43_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  & (v1_int_1 E)) ) ) )  => (m3_aofa_i00 (k43_aofa_i00 A B C D E) A B C D)) ) ).
tt(dt_k43_descip_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 B (k4_finseq_2 64 k6_margrel1)))  => (m2_finseq_2 (k43_descip_1 A B) k6_margrel1 (k4_finseq_2 64 k6_margrel1))) ) ).
tt(dt_k43_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k43_fomodel2 A) (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))))) ) ).
tt(dt_k43_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) &  ((v4_funct_1 C) & (m1_subset_1 D (k43_fomodel2 A))) ) )  => (m1_subset_1 (k43_fomodel4 A B C D) (k1_zfmisc_1 (k2_xboole_0 C (k33_fomodel2 A))))) ) ).
tt(dt_k43_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k43_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k43_gfacirc1 A B C)))  &  ((v1_msualg_1 (k43_gfacirc1 A B C)) &  ((v1_circcomb (k43_gfacirc1 A B C)) &  ((v2_circcomb (k43_gfacirc1 A B C)) &  ((v3_circcomb (k43_gfacirc1 A B C)) & (l1_msualg_1 (k43_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k43_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k43_modelc_1 A B C D) (k30_modelc_1 A))) ) ).
tt(dt_k43_modelc_2,ax, (~ (v1_xboole_0 k43_modelc_2)) ).
tt(dt_k43_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k43_valued_2 A B C D)) & (m1_subset_1 (k43_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k44_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k44_abcmiz_1 A B C)) &  ((v1_funct_2 (k44_abcmiz_1 A B C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k9_setfam_1 (k1_funct_1 B C))) & (m1_subset_1 (k44_abcmiz_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k9_setfam_1 (k1_funct_1 B C)))))) ) ) ) ).
tt(dt_k44_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m2_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (m1_subset_1 (k44_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k44_binop_2,ax, ((v1_funct_1 k44_binop_2) &  ((v1_funct_2 k44_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (m1_subset_1 k44_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers)))) ) ).
tt(dt_k44_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v4_funct_1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) ) ) ) )  =>  ((v1_funct_1 (k44_fomodel4 A B C D)) &  ((v1_funct_2 (k44_fomodel4 A B C D) k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B)))) & (m1_subset_1 (k44_fomodel4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))))))) ) ) ) ).
tt(dt_k44_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k44_gfacirc1 A B C) (k43_gfacirc1 A B C)) &  ((v4_msafree2 (k44_gfacirc1 A B C) (k43_gfacirc1 A B C)) &  ((v4_circcomb (k44_gfacirc1 A B C) (k43_gfacirc1 A B C)) &  ((v6_circcomb (k44_gfacirc1 A B C) (k43_gfacirc1 A B C)) & (l3_msualg_1 (k44_gfacirc1 A B C) (k43_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k44_modelc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_funct_1 (k44_modelc_1 A B)) &  ((v1_funct_2 (k44_modelc_1 A B) (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 (k44_modelc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) ) ) ) ).
tt(dt_k44_modelc_2,ax, (! [A:$i,B:$i] : (m1_subset_1 (k44_modelc_2 A B) k6_margrel1)) ).
tt(dt_k45_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  => (m1_subset_1 (k45_abcmiz_1 A B) (k1_zfmisc_1 k2_abcmiz_1))) ) ).
tt(dt_k45_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v4_funct_1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) ) ) ) )  => (m1_subset_1 (k45_fomodel4 A B C D) (k1_zfmisc_1 (k2_xboole_0 A (k33_fomodel2 B))))) ) ).
tt(dt_k45_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k45_gfacirc1 A B C) (u1_struct_0 (k43_gfacirc1 A B C)) (k3_msafree2 (k43_gfacirc1 A B C)))) ).
tt(dt_k45_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 A)))) )  => (m1_subset_1 (k45_modelc_1 A B C) (k1_zfmisc_1 B))) ) ).
tt(dt_k45_modelc_2,ax, (! [A:$i] : (m1_subset_1 (k45_modelc_2 A) (k30_modelc_1 (k25_modelc_2 k43_modelc_2)))) ).
tt(dt_k45_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) & (v1_funct_1 (k45_valued_1 A B))) ) ) ).
tt(dt_k46_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  =>  ((v1_finset_1 (k46_abcmiz_1 A B)) & (m1_subset_1 (k46_abcmiz_1 A B) (k1_zfmisc_1 k2_abcmiz_1))) ) ) ).
tt(dt_k46_binop_2,ax, ((v1_funct_1 k46_binop_2) &  ((v1_funct_2 k46_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (m1_subset_1 k46_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers)))) ) ).
tt(dt_k46_fomodel4,ax,$true).
tt(dt_k46_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k46_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k46_gfacirc1 A B C)))  &  ((v1_msualg_1 (k46_gfacirc1 A B C)) &  ((v1_circcomb (k46_gfacirc1 A B C)) &  ((v2_circcomb (k46_gfacirc1 A B C)) &  ((v3_circcomb (k46_gfacirc1 A B C)) & (l1_msualg_1 (k46_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k46_modelc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 A)))) )  =>  ((v1_funct_1 (k46_modelc_1 A B)) &  ((v1_funct_2 (k46_modelc_1 A B) A (k1_zfmisc_1 B)) & (m1_subset_1 (k46_modelc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_zfmisc_1 B))))) ) ) ) ).
tt(dt_k46_modelc_2,ax, ( (~ (v1_xboole_0 k46_modelc_2))  & (m1_subset_1 k46_modelc_2 (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 k43_modelc_2))))) ).
tt(dt_k46_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k46_valued_1 A B C D E)) & (m1_subset_1 (k46_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k47_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  => (m1_subset_1 (k47_abcmiz_1 A B) (k1_zfmisc_1 k2_abcmiz_1))) ) ).
tt(dt_k47_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_subset_1 E B) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((v15_aofa_000 (k47_aofa_i00 A B C D E F) A) & (m1_subset_1 (k47_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k47_binop_2,ax, ((v1_funct_1 k47_binop_2) &  ((v1_funct_2 k47_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 k47_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) ) ).
tt(dt_k47_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) & (m1_subset_1 D (k33_fomodel2 B))) )  => (m1_subset_1 (k47_fomodel4 A B C D) (k1_zfmisc_1 (k2_xboole_0 A (k33_fomodel2 B))))) ) ).
tt(dt_k47_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k47_gfacirc1 A B C) (k46_gfacirc1 A B C)) &  ((v4_msafree2 (k47_gfacirc1 A B C) (k46_gfacirc1 A B C)) &  ((v4_circcomb (k47_gfacirc1 A B C) (k46_gfacirc1 A B C)) &  ((v6_circcomb (k47_gfacirc1 A B C) (k46_gfacirc1 A B C)) & (l3_msualg_1 (k47_gfacirc1 A B C) (k46_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k47_modelc_2,ax, ((v1_funct_1 k47_modelc_2) &  ((v1_funct_2 k47_modelc_2 k15_modelc_2 (u1_modelc_2 (k42_modelc_2 k43_modelc_2 k46_modelc_2))) & (m1_subset_1 k47_modelc_2 (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 (k42_modelc_2 k43_modelc_2 k46_modelc_2)))))) ) ).
tt(dt_k47_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k47_valued_1 A B C D E)) & (m1_subset_1 (k47_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k47_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (v1_xcmplx_0 C)) )  =>  ((v1_relat_1 (k47_valued_2 A B C)) & (v1_funct_1 (k47_valued_2 A B C))) ) ) ).
tt(dt_k48_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  =>  ((v1_finset_1 (k48_abcmiz_1 A B)) & (m1_subset_1 (k48_abcmiz_1 A B) (k1_zfmisc_1 k2_abcmiz_1))) ) ) ).
tt(dt_k48_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_subset_1 E B) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k48_aofa_i00 A B C D E F) A) & (m1_subset_1 (k48_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k48_binop_2,ax, ((v1_funct_1 k48_binop_2) &  ((v1_funct_2 k48_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (m1_subset_1 k48_binop_2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)))) ) ).
tt(dt_k48_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) ) ) )  =>  ((v1_funct_1 (k48_fomodel4 A B C D)) &  ((v1_funct_2 (k48_fomodel4 A B C D) k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B)))) & (m1_subset_1 (k48_fomodel4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_xboole_0 A (k33_fomodel2 B))))))) ) ) ) ).
tt(dt_k48_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k48_gfacirc1 A B C) (u1_struct_0 (k46_gfacirc1 A B C)) (k3_msafree2 (k46_gfacirc1 A B C)))) ).
tt(dt_k48_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A)))) ) )  => (l2_modelc_1 (k48_modelc_1 A B C))) ) ).
tt(dt_k48_modelc_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k9_modelc_2)) => (m1_subset_1 (k48_modelc_2 A) (k1_zfmisc_1 k9_modelc_2))) ) ).
tt(dt_k48_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k48_valued_2 A B C D)) & (m1_subset_1 (k48_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k49_abcmiz_1,ax, ( (~ (v2_struct_0 k49_abcmiz_1))  &  ((v1_orders_2 k49_abcmiz_1) &  ((v3_orders_2 k49_abcmiz_1) &  ((v4_orders_2 k49_abcmiz_1) &  ((v5_orders_2 k49_abcmiz_1) & (l1_orders_2 k49_abcmiz_1)) ) ) ) ) ).
tt(dt_k49_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) ) ) )  => (m1_subset_1 (k49_fomodel4 A B C D) (k1_zfmisc_1 (k2_xboole_0 A (k33_fomodel2 B))))) ) ).
tt(dt_k49_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k49_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k49_gfacirc1 A B C)))  &  ((v1_msualg_1 (k49_gfacirc1 A B C)) &  ((v1_circcomb (k49_gfacirc1 A B C)) &  ((v2_circcomb (k49_gfacirc1 A B C)) &  ((v3_circcomb (k49_gfacirc1 A B C)) & (l1_msualg_1 (k49_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k49_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((m1_subset_1 C A) & (m1_modelc_1 D A B)) ) )  => (m1_subset_1 (k49_modelc_1 A B C D E) A)) ) ).
tt(dt_k49_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k49_valued_2 A B C D)) & (m1_subset_1 (k49_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k4_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_abcmiz_0 A))))  => (m1_subset_1 (k4_abcmiz_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_abcmiz_1,ax,(m1_finseq_2 k4_abcmiz_1 k2_abcmiz_1)).
tt(dt_k4_abcmiz_a,ax,$true).
tt(dt_k4_afinsq_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_afinsq_1 A)) &  ((v5_relat_1 (k4_afinsq_1 A) A) &  ((v5_ordinal1 (k4_afinsq_1 A)) &  ((v1_funct_1 (k4_afinsq_1 A)) & (v1_finset_1 (k4_afinsq_1 A))) ) ) ) ) ).
tt(dt_k4_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  ((v1_relat_1 (k4_afinsq_2 A)) &  ((v5_relat_1 (k4_afinsq_2 A) k5_numbers) &  ((v1_funct_1 (k4_afinsq_2 A)) &  ((v5_ordinal1 (k4_afinsq_2 A)) & (v1_finset_1 (k4_afinsq_2 A))) ) ) ) ) ) ).
tt(dt_k4_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v3_relat_2 (k4_afproj A)) &  ((v8_relat_2 (k4_afproj A)) &  ((v1_partfun1 (k4_afproj A) (k2_afproj A)) & (m1_subset_1 (k4_afproj A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_afproj A) (k2_afproj A))))) ) ) ) ) ).
tt(dt_k4_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_afvect0 A B)) &  ((v1_funct_2 (k4_afvect0 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k4_afvect0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_alg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  & (m1_alg_1 B A))  =>  ( (~ (v2_struct_0 (k4_alg_1 A B)))  &  ((v1_unialg_1 (k4_alg_1 A B)) &  ((v2_unialg_1 (k4_alg_1 A B)) &  ((v3_unialg_1 (k4_alg_1 A B)) &  ((v4_unialg_1 (k4_alg_1 A B)) & (l1_unialg_1 (k4_alg_1 A B))) ) ) ) ) ) ) ).
tt(dt_k4_algstr_0,ax, (! [A:$i,B:$i] :  ( ((l2_algstr_0 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_algstr_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  => (l3_algstr_0 (k4_algstr_4 A B))) ) ).
tt(dt_k4_altcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  &  ((m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  =>  ((v1_funct_1 (k4_altcat_1 A B C D E F)) &  ((v1_funct_2 (k4_altcat_1 A B C D E F) (k2_zfmisc_1 (k1_binop_1 B E F) (k1_binop_1 B D E)) (k1_binop_1 B D F)) & (m1_subset_1 (k4_altcat_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_binop_1 B E F) (k1_binop_1 B D E)) (k1_binop_1 B D F))))) ) ) ) ).
tt(dt_k4_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_altcat_2 A)))  &  ((v6_altcat_1 (k4_altcat_2 A)) & (l2_altcat_1 (k4_altcat_2 A))) ) ) ) ).
tt(dt_k4_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k4_altcat_4 A)))  &  ((v2_altcat_1 (k4_altcat_4 A)) &  ((v6_altcat_1 (k4_altcat_4 A)) & (m1_altcat_2 (k4_altcat_4 A) A)) ) ) ) ) ).
tt(dt_k4_ami_2,ax, ((v1_relat_1 k4_ami_2) &  ((v4_relat_1 k4_ami_2 2) &  ((v1_funct_1 k4_ami_2) & (v1_partfun1 k4_ami_2 2)) ) ) ).
tt(dt_k4_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k4_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k4_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (l1_extpro_1 (k4_amistd_1 A) A)) ) ) ).
tt(dt_k4_amistd_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  & (m1_subset_1 C (u1_compos_1 B))) )  => (m1_subset_1 (k4_amistd_4 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k4_ami_wstd,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  &  ((m1_subset_1 C k5_numbers) & (v7_ordinal1 D)) ) )  => (m2_subset_1 (k4_ami_wstd A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k4_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_analmetr A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_analort A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k4_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (m1_collsp (k4_anproj_1 A) (k3_anproj_1 A))) ) ).
tt(dt_k4_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D (k9_funct_2 A B)) & (m1_subset_1 E (k9_funct_2 B C))) ) ) )  => (m2_funct_2 (k4_aofa_000 A B C D E) A C (k9_funct_2 A C))) ) ).
tt(dt_k4_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k4_aofa_i00 A B)) &  ((v5_relat_1 (k4_aofa_i00 A B) k4_numbers) & (v1_funct_1 (k4_aofa_i00 A B))) ) ) ) ).
tt(dt_k4_armstrng,ax, (! [A:$i] : (m1_subset_1 (k4_armstrng A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ).
tt(dt_k4_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k4_arytm_0 A) k1_numbers)) ) ).
tt(dt_k4_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_arytm_2) => (m1_subset_1 (k4_arytm_2 A) k2_arytm_2)) ) ).
tt(dt_k4_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (m1_subset_1 (k4_arytm_3 A B) k4_ordinal1)) ) ).
tt(dt_k4_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k4_asympt_1 A)) &  ((v1_funct_2 (k4_asympt_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k4_asympt_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_autalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (~ (v1_xboole_0 (k4_autalg_1 A B C))) ) ) ).
tt(dt_k4_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (m1_funct_2 (k4_autgroup A) (u1_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k4_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k4_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k4_bagorder A)) &  ((v4_relat_2 (k4_bagorder A)) &  ((v8_relat_2 (k4_bagorder A)) & (m1_subset_1 (k4_bagorder A) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k4_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_bcialg_1 A)))  & (m1_subset_1 (k4_bcialg_1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k4_bcialg_2,ax,$true).
tt(dt_k4_bcialg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_bcialg_6 A B) k5_numbers)) ) ).
tt(dt_k4_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_bhsp_1 A B C) k1_numbers)) ) ).
tt(dt_k4_bhsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k4_bhsp_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_bhsp_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (m1_subset_1 (k4_bhsp_4 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k4_bhsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m1_finseq_1 D B)) ) )  => (m2_finseq_1 (k4_bhsp_5 A B C D) A)) ) ).
tt(dt_k4_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k4_bilinear A B C D)) &  ((v1_funct_2 (k4_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k4_bilinear A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_binari_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  => (m1_subset_1 (k4_binari_2 A B C) k6_margrel1)) ) ).
tt(dt_k4_binarith,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k4_binarith A B C) A) & (m2_finseq_1 (k4_binarith A B C) k6_margrel1)) ) ) ).
tt(dt_k4_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k4_binom A)) &  ((v1_funct_2 (k4_binom A) (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 (k4_binom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_binop_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  => (m1_subset_1 (k4_binop_1 A B) A)) ) ).
tt(dt_k4_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k4_binop_2 A B) k2_numbers)) ) ).
tt(dt_k4_bor_cant,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k4_bor_cant A)) &  ((v1_funct_2 (k4_bor_cant A) k5_numbers k5_numbers) & (m1_subset_1 (k4_bor_cant A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k4_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k4_borsuk_1 A B C D) (u1_struct_0 (k2_borsuk_1 A B)))) ) ).
tt(dt_k4_borsuk_6,ax, ((v1_funct_1 k4_borsuk_6) &  ((v1_funct_2 k4_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 k4_borsuk_6 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) ).
tt(dt_k4_brouwer,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ( ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C))  &  ((m1_subset_1 D (u1_struct_0 (k2_brouwer A B C))) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_brouwer A B C)) (u1_struct_0 (k2_brouwer A B C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A B C)) (u1_struct_0 (k2_brouwer A B C)))))) ) ) ) ) )  => (m1_subset_1 (k4_brouwer A B C D E) (u1_struct_0 (k7_toprealb A B C)))) ) ).
tt(dt_k4_bspace,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (u1_struct_0 k2_bspace)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k4_bspace A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k4_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k4_bvfunc_1 A B)) & (v1_funct_1 (k4_bvfunc_1 A B))) ) ) ).
tt(dt_k4_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k4_bvfunc26 A B C)) &  ((v1_funct_2 (k4_bvfunc26 A B C) A k6_margrel1) & (m1_subset_1 (k4_bvfunc26 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k4_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_eqrel_1 B A))  => (m1_subset_1 (k4_bvfunc_2 A B) (k1_zfmisc_1 (k1_bvfunc_2 A)))) ) ).
tt(dt_k4_c0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_c0sp1 A B) B)) ) ).
tt(dt_k4_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v1_funct_1 (k4_c0sp2 A)) &  ((v1_funct_2 (k4_c0sp2 A) (k2_c0sp2 A) k1_numbers) & (m1_subset_1 (k4_c0sp2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_c0sp2 A) k1_numbers)))) ) ) ) ).
tt(dt_k4_calcul_1,ax,$true).
tt(dt_k4_calcul_2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k4_calcul_2 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k4_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k4_card_1 A) k4_ordinal1)) ) ).
tt(dt_k4_card_3,ax,$true).
tt(dt_k4_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  => (m1_card_fil (k4_card_fil A) A)) ) ).
tt(dt_k4_cardfin2,ax, (! [A:$i,B:$i] : (m1_subset_1 (k4_cardfin2 A B) (k1_zfmisc_1 (k1_funct_2 A B)))) ).
tt(dt_k4_cat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k4_cat_1 A B) A B B)) ) ).
tt(dt_k4_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (m1_cat_2 (k4_cat_2 A B) A B)) ) ).
tt(dt_k4_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) )  =>  ((v1_funct_1 (k4_cat_3 A B C)) &  ((v1_funct_2 (k4_cat_3 A B C) B (u4_struct_0 (k2_oppcat_1 A))) & (m1_subset_1 (k4_cat_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 (k2_oppcat_1 A)))))) ) ) ) ).
tt(dt_k4_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_4 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_cat_4 A B C) (u4_struct_0 A))) ) ).
tt(dt_k4_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  =>  ((v1_cat_1 (k4_cat_5 A B C)) & (m3_cat_2 (k4_cat_5 A B C) B)) ) ) ).
tt(dt_k4_catalan2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k4_catalan2 A B)) &  ((v1_funct_2 (k4_catalan2 A B) k5_numbers k1_numbers) & (m1_subset_1 (k4_catalan2 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_catalg_1,ax,$true).
tt(dt_k4_cayley,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k4_cayley A)) &  ((v1_funct_2 (k4_cayley A) (u1_struct_0 A) (u1_struct_0 (k2_cayley (u1_struct_0 A)))) & (m1_subset_1 (k4_cayley A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_cayley (u1_struct_0 A))))))) ) ) ) ).
tt(dt_k4_cc0sp1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k4_cc0sp1 A B)) &  ((v1_funct_2 (k4_cc0sp1 A B) A k2_numbers) & (m1_subset_1 (k4_cc0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ) ).
tt(dt_k4_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v1_funct_1 (k4_cc0sp2 A)) &  ((v1_funct_2 (k4_cc0sp2 A) (k2_cc0sp2 A) k1_numbers) & (m1_subset_1 (k4_cc0sp2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cc0sp2 A) k1_numbers)))) ) ) ) ).
tt(dt_k4_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m2_funct_2 (k4_cfuncdom A) A k2_numbers (k9_funct_2 A k2_numbers))) ) ).
tt(dt_k4_cgames_1,ax,(m1_subset_1 k4_cgames_1 (k2_cgames_1 1))).
tt(dt_k4_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_xboole_0 (k4_chain_1 A B C)))  &  ((v1_finset_1 (k4_chain_1 A B C)) & (m1_subset_1 (k4_chain_1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (k1_euclid A))))) ) ) ) ).
tt(dt_k4_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m3_chord B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k4_chord A B C) (k1_zfmisc_1 (k6_glib_000 A)))) ) ).
tt(dt_k4_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v1_msualg_1 (k4_circcmb3 A B C D)) & (m1_circcmb3 (k4_circcmb3 A B C D) B)) ) ) ).
tt(dt_k4_circcomb,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v11_struct_0 (k4_circcomb A B C)))  &  ((v1_msualg_1 (k4_circcomb A B C)) & (l1_msualg_1 (k4_circcomb A B C))) ) ) ) ).
tt(dt_k4_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  & (l3_msualg_1 D A)) ) )  =>  ((v1_relat_1 (k4_circtrm1 A B C D)) &  ((v4_relat_1 (k4_circtrm1 A B C D) (u1_struct_0 (k1_circtrm1 A B C))) &  ((v1_funct_1 (k4_circtrm1 A B C D)) & (v1_partfun1 (k4_circtrm1 A B C D) (u1_struct_0 (k1_circtrm1 A B C)))) ) ) ) ) ).
tt(dt_k4_circuit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (v7_ordinal1 (k4_circuit1 A B C))) ) ).
tt(dt_k4_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_msafree2 D A B)) ) )  => (m1_subset_1 (k4_circuit2 A B C D) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C))) ) ).
tt(dt_k4_classes1,ax,$true).
tt(dt_k4_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k3_clopban1 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k4_clopban1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k4_clopban2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k8_clopban1 A A)) & (v1_xcmplx_0 C)) )  => (m2_subset_1 (k4_clopban2 A B C) (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A))) ) ).
tt(dt_k4_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clopban2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k4_clopban3 A B C)) &  ((v1_funct_2 (k4_clopban3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k4_clopban3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_clopban4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v2_cfuncdom B) &  ((v5_clopban2 B) & (l1_clopban2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k4_clopban4 A B C D)) &  ((v1_funct_2 (k4_clopban4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k4_clopban4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k4_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))))  =>  ((v1_relat_1 (k4_closure2 A B C)) &  ((v4_relat_1 (k4_closure2 A B C) A) &  ((v1_funct_1 (k4_closure2 A B C)) & (v1_partfun1 (k4_closure2 A B C) A)) ) ) ) ) ).
tt(dt_k4_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  => (m1_subset_1 (k4_closure3 A B C D) (k1_zfmisc_1 (k1_closure2 A B)))) ) ).
tt(dt_k4_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_clvect_1 (k4_clvect_1 A)) & (m1_clvect_1 (k4_clvect_1 A) A)) ) ) ).
tt(dt_k4_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k4_clvect_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_cohsp_1 A))  &  ((v1_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  => (m1_subset_1 (k4_cohsp_1 A B) A)) ) ).
tt(dt_k4_coh_sp,ax,$true).
tt(dt_k4_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ((l1_combgras C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A)))) ) )  => (m1_subset_1 (k4_combgras A B C D) (k1_zfmisc_1 (u1_incsp_1 B)))) ) ).
tt(dt_k4_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) &  ((m2_cat_1 E B C) & (m1_subset_1 F (k2_commacat A B C D E))) ) ) ) )  => (m2_subset_1 (k4_commacat A B C D E F) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E))) ) ).
tt(dt_k4_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (m1_subset_1 (k4_complex1 A) k1_numbers)) ) ).
tt(dt_k4_complex2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xreal_0 (k4_complex2 A B C))) ) ).
tt(dt_k4_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (v1_xcmplx_0 C)) )  => (m2_finseq_2 (k4_complsp2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k4_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) & (v1_finset_1 (k4_compos_1 A))) ) ) ) ) ) ).
tt(dt_k4_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k4_comput_1 A B)) &  ((v4_relat_1 (k4_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 A B)) &  ((v4_valued_0 (k4_comput_1 A B)) & (v2_margrel1 (k4_comput_1 A B))) ) ) ) ) ) ).
tt(dt_k4_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k4_comseq_3 A)) & (v1_funct_1 (k4_comseq_3 A))) ) ) ).
tt(dt_k4_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k4_conlat_1 A)) &  ((v1_funct_2 (k4_conlat_1 A) (u1_struct_0 (k3_yellow_1 (u4_struct_0 A))) (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))) & (m1_subset_1 (k4_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u4_struct_0 A))) (u1_struct_0 (k3_yellow_1 (u1_struct_0 A))))))) ) ) ) ).
tt(dt_k4_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k4_conlat_2 A)) &  ((v1_funct_2 (k4_conlat_2 A) (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A))) & (m1_subset_1 (k4_conlat_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)))))) ) ) ) ).
tt(dt_k4_connsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_connsp_3 A B C) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C))))) ) ).
tt(dt_k4_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_clvect_1 A)) ) ) ) )  & (m1_convex4 B A))  => (m1_subset_1 (k4_convex4 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_convfun1,ax, ( (~ (v2_struct_0 k4_convfun1))  & (l1_rlvect_1 k4_convfun1)) ).
tt(dt_k4_cqc_lang,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_qc_lang1 B) &  ((m1_subset_1 C (k8_qc_lang1 B A)) &  ((v5_relat_1 D (k3_qc_lang1 B)) &  ((v3_card_1 D A) & (m1_finseq_1 D (k2_qc_lang1 B))) ) ) ) )  => (m2_subset_1 (k4_cqc_lang A B C D) (k9_qc_lang1 B) (k3_cqc_lang B))) ) ).
tt(dt_k4_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))))) )  & (m1_subset_1 C (k3_qc_lang1 A))) )  => (m2_funct_2 (k4_cqc_sim1 A B C) (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))) ) ).
tt(dt_k4_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k4_cqc_the1 A) (k1_zfmisc_1 (k3_cqc_lang A)))) ) ).
tt(dt_k4_csspace3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_clvect_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_csspace3 A B C) k1_numbers)) ) ).
tt(dt_k4_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k4_csspace4 A B) (k1_zfmisc_1 (u1_struct_0 (k3_clopban1 A B))))) ) ).
tt(dt_k4_csspace,ax, ((v1_funct_1 k4_csspace) &  ((v1_funct_2 k4_csspace (k2_zfmisc_1 k1_csspace k1_csspace) k1_csspace) & (m1_subset_1 k4_csspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_csspace k1_csspace) k1_csspace)))) ) ).
tt(dt_k4_decomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_decomp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 (k4_nat_1 2 B) A))) )  => (m2_finseq_2 (k4_descip_1 A B C) A (k4_finseq_2 B A))) ) ).
tt(dt_k4_dickson,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (m1_subset_1 (k4_dickson A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k4_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k4_diff_1 A B)) & (m1_subset_1 (k4_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k4_dilworth,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_dilworth A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_dist_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  => (m2_finseq_1 (k4_dist_1 A B) k1_numbers)) ) ).
tt(dt_k4_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D A) &  ((m1_subset_1 E B) & (m1_subset_1 F C)) ) ) ) )  => (m1_subset_1 (k4_domain_1 A B C D E F) (k3_zfmisc_1 A B C))) ) ).
tt(dt_k4_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  => (m1_subset_1 (k4_dtconstr A) (k1_zfmisc_1 (k5_trees_3 (u1_struct_0 A))))) ) ).
tt(dt_k4_dynkin,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_funct_1 (k4_dynkin A B)) &  ((v1_funct_2 (k4_dynkin A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k4_dynkin A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k4_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 C (u1_struct_0 (k9_int_3 A)))) )  => (m1_subset_1 (k4_ec_pf_1 A B C) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k4_ec_pf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) &  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 D (k6_ec_pf_1 A B C))) ) )  => (m1_subset_1 (k4_ec_pf_2 A B C D) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k4_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v1_xboole_0 (k4_endalg A B)))  & (m1_subset_1 (k4_endalg A B) (k1_zfmisc_1 (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))))) ) ) ).
tt(dt_k4_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k2_ens_1 A)))  => (m1_subset_1 (k4_ens_1 A B) A)) ) ).
tt(dt_k4_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m2_finseq_1 (k4_entropy1 A) k1_numbers)) ) ).
tt(dt_k4_enumset1,ax,$true).
tt(dt_k4_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v3_relat_2 (k4_eqrel_1 A B C)) &  ((v8_relat_2 (k4_eqrel_1 A B C)) &  ((v1_partfun1 (k4_eqrel_1 A B C) A) & (m1_subset_1 (k4_eqrel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k4_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v1_relat_1 (k4_equation A)) &  ((v4_relat_1 (k4_equation A) (u1_struct_0 A)) &  ((v1_funct_1 (k4_equation A)) & (v1_partfun1 (k4_equation A) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_k4_e_siec,ax, (! [A:$i] :  ((v1_e_siec (k4_e_siec A)) &  ((v2_e_siec (k4_e_siec A)) &  ((v3_e_siec (k4_e_siec A)) & (l1_e_siec (k4_e_siec A))) ) ) ) ).
tt(dt_k4_euclid_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (m1_subset_1 (k4_euclid_3 A B C) k1_numbers)) ) ).
tt(dt_k4_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k4_euclid_4 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k4_euclid_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k4_euclid_5 A B C) (u1_struct_0 (k15_euclid 3)))) ) ).
tt(dt_k4_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_finseq_1 B (k1_euclid A)))  => (m2_finseq_1 (k4_euclid_7 A B) (k1_euclid A))) ) ).
tt(dt_k4_euclid_8,ax,(m2_finseq_2 k4_euclid_8 k1_numbers (k1_euclid 3))).
tt(dt_k4_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k4_euclid_9 A B C) (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A)))))) ) ).
tt(dt_k4_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k4_euclid A)) &  ((v1_funct_1 (k4_euclid A)) &  ((v1_finseq_1 (k4_euclid A)) & (v3_valued_0 (k4_euclid A))) ) ) ) ) ).
tt(dt_k4_euclidlp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) &  ((m1_subset_1 C (k1_euclid A)) & (m1_subset_1 D (k1_euclid A))) ) )  => (m1_subset_1 (k4_euclidlp A B C D) (k1_zfmisc_1 (k1_euclid A)))) ) ).
tt(dt_k4_exchsort,ax,$true).
tt(dt_k4_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D (u1_compos_1 B)) & (v1_funct_1 D)) ) ) ) )  =>  ((v1_relat_1 (k4_extpro_1 A B C D)) &  ((v4_relat_1 (k4_extpro_1 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k4_extpro_1 A B C D)) &  ((v5_funct_1 (k4_extpro_1 A B C D) (k2_memstr_0 A B)) & (v1_partfun1 (k4_extpro_1 A B C D) (u1_struct_0 B))) ) ) ) ) ) ).
tt(dt_k4_extreal1,ax, (! [A:$i] :  ((m1_finseq_1 A k7_numbers) => (m1_subset_1 (k4_extreal1 A) k7_numbers)) ) ).
tt(dt_k4_facirc_1,ax, ((v1_funct_1 k4_facirc_1) &  ((v1_funct_2 k4_facirc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 k4_facirc_1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k4_facirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v3_msualg_1 (k4_facirc_2 A B C) (k3_facirc_2 A B C)) &  ((v4_msafree2 (k4_facirc_2 A B C) (k3_facirc_2 A B C)) &  ((v4_circcomb (k4_facirc_2 A B C) (k3_facirc_2 A B C)) &  ((v6_circcomb (k4_facirc_2 A B C) (k3_facirc_2 A B C)) & (l3_msualg_1 (k4_facirc_2 A B C) (k3_facirc_2 A B C))) ) ) ) ) ) ).
tt(dt_k4_ff_siec,ax, (! [A:$i] :  ((v1_petri (k4_ff_siec A)) &  ((v1_net_1 (k4_ff_siec A)) & (l1_petri (k4_ff_siec A))) ) ) ).
tt(dt_k4_fib_num2,ax,(m1_subset_1 k4_fib_num2 (k1_zfmisc_1 k5_numbers))).
tt(dt_k4_filter_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_filter_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v2_struct_0 (k4_filter_1 A B)))  &  ((v3_lattices (k4_filter_1 A B)) &  ((v10_lattices (k4_filter_1 A B)) & (l3_lattices (k4_filter_1 A B))) ) ) ) ) ).
tt(dt_k4_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A)))))  => (m1_subset_1 (k4_filter_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_finance1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  => (m1_subset_1 (k4_finance1 A B C) k1_numbers)) ) ).
tt(dt_k4_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (m1_subset_1 (k4_finseq_1 A) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k4_finseq_2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (m1_finseq_2 (k4_finseq_2 A B) B)) ) ).
tt(dt_k4_finseq_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (m1_subset_1 (k4_finseq_4 A B) k5_numbers)) ) ).
tt(dt_k4_finseq_5,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B A) => (m2_finseq_1 (k4_finseq_5 A B) A)) ) ).
tt(dt_k4_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k4_finseq_8 A B C) A)) ) ).
tt(dt_k4_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (m2_finseq_1 (k4_finseqop A B C D) B)) ) ).
tt(dt_k4_fintopo2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_fintopo2 A B C) k6_margrel1)) ) ).
tt(dt_k4_fintopo3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k4_fintopo3 A B)) &  ((v1_funct_2 (k4_fintopo3 A B) k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 (k4_fintopo3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k4_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_fintopo4 A)))  & (l1_orders_2 (k4_fintopo4 A))) ) ) ).
tt(dt_k4_fintopo5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k4_fintopo5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)))))) ) ).
tt(dt_k4_fin_topo,ax, ((v1_orders_2 k4_fin_topo) & (l1_orders_2 k4_fin_topo)) ).
tt(dt_k4_flang_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k3_catalan2 A)) => (m1_subset_1 (k4_flang_1 A B) (k1_zfmisc_1 (k3_catalan2 A)))) ) ).
tt(dt_k4_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)))) )  =>  ((v1_relat_1 (k4_fomodel0 A B C)) & (v1_funct_1 (k4_fomodel0 A B C))) ) ) ).
tt(dt_k4_fomodel1,ax,$true).
tt(dt_k4_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  => (m2_fomodel2 (k4_fomodel2 A B C D) A B D)) ) ).
tt(dt_k4_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  => (m2_fomodel2 (k4_fomodel3 A B C) A (k35_fomodel1 A) B)) ) ).
tt(dt_k4_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  => (m1_subset_1 (k4_fomodel4 A B) (k1_zfmisc_1 (k1_zfmisc_1 (k8_mcart_1 (k1_zfmisc_1 (k1_fomodel4 A)) (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))) ) ).
tt(dt_k4_freealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  & (v7_ordinal1 C))  => (m1_subset_1 (k4_freealg A B C) (u1_struct_0 (k3_freealg A B)))) ) ).
tt(dt_k4_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k4_fscirc_1 A B C)))  &  ( (~ (v11_struct_0 (k4_fscirc_1 A B C)))  &  ((v1_msualg_1 (k4_fscirc_1 A B C)) &  ((v1_circcomb (k4_fscirc_1 A B C)) &  ((v2_circcomb (k4_fscirc_1 A B C)) &  ((v3_circcomb (k4_fscirc_1 A B C)) & (l1_msualg_1 (k4_fscirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k4_fscirc_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m2_subset_1 (k4_fscirc_2 A B C D) (u1_struct_0 (k1_fscirc_2 B C D)) (k3_msafree2 (k1_fscirc_2 B C D)))) ) ).
tt(dt_k4_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ((m1_subset_1 D (u1_struct_0 C)) & (m1_finseq_1 E A)) ) ) )  => (m2_finseq_1 (k4_fsm_1 A B C D E) B)) ) ).
tt(dt_k4_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B)) ) )  =>  ((v3_fsm_3 (k4_fsm_3 A B C) A (k9_flang_1 A)) & (l2_fsm_3 (k4_fsm_3 A B C) A (k9_flang_1 A))) ) ) ).
tt(dt_k4_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k4_ftacell1 A B C D E) (k3_msafree2 (k1_ftacell1 A B C D E)))) ).
tt(dt_k4_funcop_1,ax,$true).
tt(dt_k4_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  => (m2_funct_2 (k4_funcsdom A B C D E) B A (k9_funct_2 B A))) ) ).
tt(dt_k4_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((v1_funct_1 (k4_funct_2 A B C D)) &  ((v1_funct_2 (k4_funct_2 A B C D) A B) & (m1_subset_1 (k4_funct_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k4_funct_3,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k4_funct_3 A B)) & (v1_funct_1 (k4_funct_3 A B))) ) ).
tt(dt_k4_funct_4,ax,$true).
tt(dt_k4_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k4_funct_5 A)) & (v1_funct_1 (k4_funct_5 A))) ) ) ).
tt(dt_k4_funct_6,ax,$true).
tt(dt_k4_funct_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k4_funct_7 A B)) & (v1_funct_1 (k4_funct_7 A B))) ) ) ).
tt(dt_k4_functor0,ax,$true).
tt(dt_k4_functor2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((v15_functor0 C A B) & (m2_functor0 C A B)) ) )  => (m2_functor2 (k4_functor2 A B C) A B C C)) ) ).
tt(dt_k4_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  &  ((v15_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k4_functor3 A B C D E) A C) &  ((v16_functor0 (k4_functor3 A B C D E) A C) & (m2_functor0 (k4_functor3 A B C D E) A C)) ) ) ) ).
tt(dt_k4_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_relat_1 (k4_fuzzy_1 A) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k4_fuzzy_1 A)) &  ((v1_funct_2 (k4_fuzzy_1 A) A k1_numbers) & (m1_subset_1 (k4_fuzzy_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k4_fuzzy_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v5_relat_1 (k4_fuzzy_2 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k4_fuzzy_2 A B)) &  ((v1_funct_2 (k4_fuzzy_2 A B) (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 (k4_fuzzy_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) ).
tt(dt_k4_fuzzy_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) ) ) ) ) )  =>  ((v5_relat_1 (k4_fuzzy_4 A B C D E) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k4_fuzzy_4 A B C D E)) &  ((v1_funct_2 (k4_fuzzy_4 A B C D E) (k2_zfmisc_1 A C) k1_numbers) & (m1_subset_1 (k4_fuzzy_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) k1_numbers)))) ) ) ) ) ).
tt(dt_k4_fvaluat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_fvaluat1 B A))  => (m1_subset_1 (k4_fvaluat1 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  => (m2_finseq_2 (k4_fvsum_1 A B C D) (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B)))) ) ).
tt(dt_k4_gate_1,ax,$true).
tt(dt_k4_gate_5,ax,$true).
tt(dt_k4_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  &  ((m2_gcd_1 B A) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_gcd_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) & (m1_subset_1 G k5_numbers)) ) ) ) ) )  => (m2_finseq_1 (k4_genealg1 A B C D E F G) (k3_card_3 A))) ) ).
tt(dt_k4_geomtrap,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k4_geomtrap A B C D E) k1_numbers)) ) ).
tt(dt_k4_gfacirc1,ax, ((v1_funct_1 k4_gfacirc1) &  ((v1_funct_2 k4_gfacirc1 (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k4_gfacirc1 (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k4_gfacirc2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m2_subset_1 (k4_gfacirc2 A B C D) (u1_struct_0 (k1_gfacirc2 B C D)) (k3_msafree2 (k1_gfacirc2 B C D)))) ) ).
tt(dt_k4_glib_000,ax,(m1_subset_1 k4_glib_000 k5_numbers)).
tt(dt_k4_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m1_subset_1 (k4_glib_001 A B) (k6_glib_000 A))) ) ).
tt(dt_k4_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (v1_card_1 (k4_glib_002 A))) ) ).
tt(dt_k4_glib_003,ax,(m2_subset_1 k4_glib_003 k1_numbers k5_numbers)).
tt(dt_k4_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  => (m1_subset_1 (k4_glib_004 A) k1_numbers)) ) ).
tt(dt_k4_glib_005,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  &  ((m2_glib_005 C A B) & (v7_ordinal1 D)) ) )  => (m1_glib_005 (k4_glib_005 A B C D) A B)) ) ).
tt(dt_k4_goboard5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k4_goboard5 A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_gobrd13,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k4_gobrd13 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_goedelcp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_cqc_lang A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m2_subset_1 (k4_goedelcp A B C) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ).
tt(dt_k4_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k4_graph_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_graph_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_1 (k4_graph_2 A B C) A)) ) ).
tt(dt_k4_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_graph_3 A B C) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k4_graph_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_graph_5 A B C) (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 A))))) ) ).
tt(dt_k4_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_funct_2 A A)) & (m1_subset_1 C A))  => (m1_subset_1 (k4_graphsp A B C) A)) ) ).
tt(dt_k4_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k4_grcat_1 A B)) & (m1_subset_1 (k4_grcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (u4_struct_0 A) (u4_struct_0 A) (k1_grcat_1 A B) (k1_grcat_1 A B)) (k1_grcat_1 A B))))) ) ) ).
tt(dt_k4_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ( (~ (v2_struct_0 (k4_gr_cy_1 A)))  &  ((v15_algstr_0 (k4_gr_cy_1 A)) & (l3_algstr_0 (k4_gr_cy_1 A))) ) ) ) ).
tt(dt_k4_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k4_groeb_1 A) (k15_pre_poly A)) &  ((v1_relat_2 (k4_groeb_1 A)) &  ((v4_relat_2 (k4_groeb_1 A)) &  ((v8_relat_2 (k4_groeb_1 A)) & (m1_subset_1 (k4_groeb_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k4_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_finset_1 (k4_groeb_3 A B C D E)) & (m1_subset_1 (k4_groeb_3 A B C D E) (k1_zfmisc_1 (k15_pre_poly A)))) ) ) ).
tt(dt_k4_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  &  ((m1_subset_1 D (u1_struct_0 C)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (k1_funct_2 A A)) &  ((v1_group_10 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 A A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_group_10 A B C D E)) &  ((v1_funct_2 (k4_group_10 A B C D E) (k3_group_10 A B) (k3_group_10 A B)) & (m1_subset_1 (k4_group_10 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 A B) (k3_group_10 A B))))) ) ) ) ).
tt(dt_k4_group_11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  => (m1_subset_1 (k4_group_11 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_funct_1 (k4_group_1 A)) &  ((v1_funct_2 (k4_group_1 A) (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 (k4_group_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_group_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_group_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_finseq_1 B k4_numbers) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k4_group_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_group_5 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ((v1_funct_1 (k4_group_6 A B)) &  ((v1_funct_2 (k4_group_6 A B) (k2_zfmisc_1 (k15_group_2 A B) (k15_group_2 A B)) (k15_group_2 A B)) & (m1_subset_1 (k4_group_6 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k15_group_2 A B) (k15_group_2 A B)) (k15_group_2 A B))))) ) ) ) ).
tt(dt_k4_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_group_7 A B) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))))) ) ).
tt(dt_k4_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((v2_group_9 (k4_group_9 A B) A) & (m1_group_9 (k4_group_9 A B) A B)) ) ) ).
tt(dt_k4_hahnban1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k4_hahnban1 A B C)) &  ((v1_funct_2 (k4_hahnban1 A B C) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k4_hahnban1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_xreal_0 (k4_hermitan A B C))) ) ).
tt(dt_k4_heyting1,ax, (! [A:$i] :  ((v1_funct_1 (k4_heyting1 A)) &  ((v1_funct_2 (k4_heyting1 A) (k7_normform A) (u1_struct_0 (k12_normform A))) & (m1_subset_1 (k4_heyting1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_normform A) (u1_struct_0 (k12_normform A)))))) ) ) ).
tt(dt_k4_heyting2,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) =>  ((v1_funct_1 (k4_heyting2 A B)) &  ((v1_funct_2 (k4_heyting2 A B) (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 (k4_heyting2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)))))) ) ) ) ).
tt(dt_k4_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k4_heyting3 A B) (k5_finsub_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B))))) ) ).
tt(dt_k4_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_polynom3 A))))) )  =>  ( (~ (v1_xboole_0 (k4_hilbasis A B)))  & (m1_subset_1 (k4_hilbasis A B) (k1_zfmisc_1 B))) ) ) ).
tt(dt_k4_hilbert1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k4_hilbert1 A B) k1_hilbert1)) ) ).
tt(dt_k4_hilbert3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  & (m1_hilbert3 B A))  => (m2_pboole (k4_hilbert3 A B) k1_hilbert1 (k2_hilbert3 A) (k2_hilbert3 A))) ) ).
tt(dt_k4_hurwitz,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k4_hurwitz A B C)) &  ((v1_funct_2 (k4_hurwitz A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k4_hurwitz A B C) A) & (m1_subset_1 (k4_hurwitz A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k4_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k4_idea_1 A B C) k5_numbers)) ) ).
tt(dt_k4_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m1_ideal_1 D A B) & (m1_ideal_1 E A C)) ) ) )  => (m1_ideal_1 (k4_ideal_1 A B C D E) A (k4_subset_1 (u1_struct_0 A) B C))) ) ).
tt(dt_k4_incsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v15_incsp_1 A) & (l2_incsp_1 A))  &  ((m1_subset_1 B (u2_incsp_1 A)) & (m1_subset_1 C (u2_incsp_1 A))) )  => (m1_subset_1 (k4_incsp_1 A B C) (u4_incsp_1 A))) ) ).
tt(dt_k4_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_index_1 A)) )  =>  ((v1_relat_1 (k4_index_1 A)) &  ((v2_relat_1 (k4_index_1 A)) & (v1_funct_1 (k4_index_1 A))) ) ) ) ).
tt(dt_k4_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k4_int_1 A) k1_numbers)) ) ).
tt(dt_k4_int_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_int_3)) & (m1_subset_1 B (u1_struct_0 k1_int_3)))  => (m1_subset_1 (k4_int_3 A B) (u1_struct_0 k1_int_3))) ) ).
tt(dt_k4_integr10,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  => (m1_subset_1 (k4_integr10 A B) k1_numbers)) ) ).
tt(dt_k4_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  &  ((m1_integra1 D B) & (m3_integr15 E A B C D)) ) ) )  => (m2_finseq_2 (k4_integr15 A B C D E) k1_numbers (k1_euclid A))) ) ).
tt(dt_k4_integr16,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  &  ((m2_integr16 D A B C) & (m1_subset_1 E k5_numbers)) ) ) )  => (m1_integr16 (k4_integr16 A B C D E) A B (k2_integra2 A C E))) ) ).
tt(dt_k4_integr18,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k4_integr18 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  => (m2_finseq_1 (k4_integra1 A B C) k1_numbers)) ) ).
tt(dt_k4_integra2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) ) ) )  =>  ((v1_funct_1 (k4_integra2 A B C)) &  ((v1_funct_2 (k4_integra2 A B C) k5_numbers k1_numbers) & (m1_subset_1 (k4_integra2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_integra5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  => (m1_subset_1 (k4_integra5 A B C) k1_numbers)) ) ).
tt(dt_k4_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  => (m1_interva1 (k4_interva1 A B C) A)) ) ).
tt(dt_k4_intpro_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_intpro_1) & (m1_subset_1 B k1_intpro_1))  => (m1_subset_1 (k4_intpro_1 A B) k1_intpro_1)) ) ).
tt(dt_k4_irrat_1,ax, ((v1_funct_1 k4_irrat_1) &  ((v1_funct_2 k4_irrat_1 k5_numbers k1_numbers) & (m1_subset_1 k4_irrat_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(dt_k4_isocat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m2_nattra_1 F A B D E) & (m2_cat_1 G B C)) ) ) ) ) )  => (m2_nattra_1 (k4_isocat_1 A B C D E F G) A C (k9_cat_1 A B C D G) (k9_cat_1 A B C E G))) ) ).
tt(dt_k4_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) & (m1_subset_1 E (u4_struct_0 A))) ) ) )  => (m2_nattra_1 (k4_isocat_2 A B C D E) B C (k12_cat_2 A B C D (k3_graph_1 A E)) (k12_cat_2 A B C D (k4_graph_1 A E)))) ) ).
tt(dt_k4_jgraph_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((v7_graph_1 (k4_jgraph_1 A B) (k1_jgraph_1 A)) & (m2_graph_1 (k4_jgraph_1 A B) (k1_jgraph_1 A))) ) ) ).
tt(dt_k4_jgraph_4,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m1_subset_1 (k4_jgraph_4 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k4_jgraph_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k4_jgraph_6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (m1_subset_1 (k4_jordan10 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(dt_k4_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (m1_subset_1 (k4_jordan19 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_jordan1k,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ) )  => (m1_subset_1 (k4_jordan1k A B C) k1_numbers)) ) ).
tt(dt_k4_jordan3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 2)))) )  => (m2_finseq_1 (k4_jordan3 A B C) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k4_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k4_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k4_jordan6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (u1_struct_0 (k15_euclid 2)))) ) )  => (m1_subset_1 (k4_jordan6 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_jordan_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (m1_jordan_a B A))  => (m1_subset_1 (k4_jordan_a A B) k1_numbers)) ) ).
tt(dt_k4_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k4_jordan A)) &  ((v1_funct_2 (k4_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 (k4_jordan A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ) ) ).
tt(dt_k4_knaster,ax,$true).
tt(dt_k4_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ((m1_kolmog01 D A B C) & (m1_subset_1 E (k1_zfmisc_1 A))) ) )  =>  ( (~ (v1_xboole_0 (k4_kolmog01 A B C D E)))  &  ((v1_prob_1 (k4_kolmog01 A B C D E) B) &  ((v4_prob_1 (k4_kolmog01 A B C D E) B) & (m1_subset_1 (k4_kolmog01 A B C D E) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ).
tt(dt_k4_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k4_kurato_0 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k4_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_kurato_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k4_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  => (m1_subset_1 (k4_lang1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k4_laplace,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (m1_subset_1 C (k12_matrix_2 (k1_nat_1 B 1)))) )  => (m1_matrix_2 (k4_laplace A B C) (k12_matrix_2 B))) ) ).
tt(dt_k4_lattice3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_lattice3 A B) (u1_struct_0 (k3_lattice3 A)))) ) ).
tt(dt_k4_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_lattice4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_lattice5 A B C)) &  ((v1_funct_2 (k4_lattice5 A B C) (u1_struct_0 B) (u1_struct_0 (k1_lattice5 A))) & (m1_subset_1 (k4_lattice5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k1_lattice5 A)))))) ) ) ) ).
tt(dt_k4_lattice6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_lattice6 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_lattice7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (~ (v1_xboole_0 (k4_lattice7 A))) ) ) ).
tt(dt_k4_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  => (m1_subset_1 (k4_lattice8 A B C D E) (k4_zfmisc_1 (k3_lattice8 A E) (k3_lattice8 A E) (u1_struct_0 B) (u1_struct_0 B)))) ) ).
tt(dt_k4_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_lattices A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k15_pre_poly A)))) ) ) )  =>  ((v1_relat_1 (k4_lexbfs A B C)) &  ((v4_relat_1 (k4_lexbfs A B C) A) &  ((v1_funct_1 (k4_lexbfs A B C)) &  ((v1_partfun1 (k4_lexbfs A B C) A) &  ((v4_valued_0 (k4_lexbfs A B C)) & (v2_pre_poly (k4_lexbfs A B C))) ) ) ) ) ) ) ).
tt(dt_k4_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v3_orders_2 (k4_lfuzzy_0 A)) &  ((v4_orders_2 (k4_lfuzzy_0 A)) &  ((v5_orders_2 (k4_lfuzzy_0 A)) &  ((v1_lattice3 (k4_lfuzzy_0 A)) &  ((v2_lattice3 (k4_lfuzzy_0 A)) &  ((v3_lattice3 (k4_lfuzzy_0 A)) &  ((v9_waybel_1 (k4_lfuzzy_0 A)) & (l1_orders_2 (k4_lfuzzy_0 A))) ) ) ) ) ) ) ) ) ).
tt(dt_k4_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  & (v7_ordinal1 C)) )  =>  ((v5_relat_1 (k4_lfuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k4_lfuzzy_1 A B C)) &  ((v1_funct_2 (k4_lfuzzy_1 A B C) (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 (k4_lfuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ) ).
tt(dt_k4_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (m1_subset_1 (k4_limfunc1 A) k1_numbers)) ) ).
tt(dt_k4_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  => (m2_funct_2 (k4_lopban_1 A B) A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B)))) ) ).
tt(dt_k4_lopban_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k10_lopban_1 A A)) & (m1_subset_1 C k1_numbers)) )  => (m2_subset_1 (k4_lopban_2 A B C) (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A))) ) ).
tt(dt_k4_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_lopban_2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k4_lopban_3 A B C)) &  ((v1_funct_2 (k4_lopban_3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k4_lopban_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_lopban_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k4_lopban_4 A B)) &  ((v1_funct_2 (k4_lopban_4 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k4_lopban_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k4_lopclset A)) &  ((v1_funct_2 (k4_lopclset A) (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A)) & (m1_subset_1 (k4_lopclset A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A))))) ) ) ) ).
tt(dt_k4_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k4_lpspace1 A)) &  ((v1_funct_2 (k4_lpspace1 A) (k2_zfmisc_1 k1_numbers (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers)) & (m1_subset_1 (k4_lpspace1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k3_rfunct_3 A k1_numbers)) (k3_rfunct_3 A k1_numbers))))) ) ) ) ).
tt(dt_k4_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v2_struct_0 (k4_lpspace2 A B C D)))  & (l1_rlvect_1 (k4_lpspace2 A B C D))) ) ) ).
tt(dt_k4_ltlaxio1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k4_ltlaxio1 A B) k1_hilbert1)) ) ).
tt(dt_k4_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_subset_1 (k4_margrel1 A) (k3_margrel1 A))) ) ).
tt(dt_k4_mathmorp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_mathmorp A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  => (m1_matrix_1 (k4_matrix10 A B C) k1_numbers A A)) ) ).
tt(dt_k4_matrix11,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  & (m1_matrix_1 E C A B)) ) ) )  => (m1_matrix_1 (k4_matrix11 A B C D E) C A B)) ) ).
tt(dt_k4_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) & (v7_ordinal1 F)) ) ) ) )  => (m1_matrix_1 (k4_matrix12 A B C D E F) (u1_struct_0 C) A B)) ) ).
tt(dt_k4_matrix13,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k4_matrix13 A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k4_matrix14,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B k5_numbers) & (v7_ordinal1 C)) )  => (m1_matrix_1 (k4_matrix14 A B C) (u1_struct_0 A) B B)) ) ).
tt(dt_k4_matrix15,ax,$true).
tt(dt_k4_matrix_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A))) )  =>  ((v1_matrix_1 (k4_matrix_1 A B)) & (m2_finseq_1 (k4_matrix_1 A B) (k3_finseq_2 A))) ) ) ).
tt(dt_k4_matrix_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m2_finseq_2 (k4_matrix_2 A B) A (k4_finseq_2 1 A))) ) ).
tt(dt_k4_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((v1_matrix_1 (k4_matrix_3 A B C)) & (m2_finseq_1 (k4_matrix_3 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k4_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((v1_matrix_1 (k4_matrix_5 A)) & (m2_finseq_1 (k4_matrix_5 A) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k4_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (m1_matrix_1 (k4_matrix_6 A B C D) (u1_struct_0 B) A A)) ) ).
tt(dt_k4_matrix_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_finseq_1 B (u1_struct_0 A)))  => (m2_finseq_1 (k4_matrix_7 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A))) )  =>  ((v1_matrixj1 (k4_matrixj1 A B) A) & (m2_finseq_1 (k4_matrixj1 A B) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k4_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v1_matrix_1 (k4_matrixr1 A)) & (m2_finseq_1 (k4_matrixr1 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k4_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_matrix_1 (k4_matrixr2 A) k1_numbers A A)) ) ).
tt(dt_k4_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ((m1_matrlin D A B) &  ((m1_finseq_1 E (u1_struct_0 C)) & (m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E))) ) ) ) )  =>  ((v1_funct_1 (k4_matrlin2 A B C D E F)) &  ((v1_funct_2 (k4_matrlin2 A B C D E F) (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 (k4_matrlin2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k4_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k4_matrlin A B C D E)) &  ((v1_funct_2 (k4_matrlin A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 (k4_matrlin A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k4_matroid0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v7_ordinal1 (k4_matroid0 A B))) ) ).
tt(dt_k4_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  => (m2_finseq_1 (k4_matrprob A) k1_numbers)) ) ).
tt(dt_k4_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  => (m1_subset_1 (k4_mcart_1 A B C D E) A)) ) ).
tt(dt_k4_measure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  ( (~ (v1_xboole_0 (k4_measure1 A B C)))  & (m1_subset_1 (k4_measure1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k4_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  ((v1_funct_1 (k4_measure3 A B C)) &  ((v1_funct_2 (k4_measure3 A B C) (k2_measure3 A B C) k7_numbers) &  ((v10_valued_0 (k4_measure3 A B C)) &  ((v6_supinf_2 (k4_measure3 A B C)) &  ((v4_measure1 (k4_measure3 A B C) A (k2_measure3 A B C)) & (m1_subset_1 (k4_measure3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_measure3 A B C) k7_numbers)))) ) ) ) ) ) ) ).
tt(dt_k4_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k4_measure6 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k4_measure7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  &  ((m2_measure7 B A) & (m1_subset_1 C k5_numbers)) )  => (m1_measure7 (k4_measure7 A B C) (k8_nat_1 (k9_setfam_1 k1_numbers) A C))) ) ).
tt(dt_k4_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v2_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  & (m4_measure8 E A B C)) ) )  =>  ((v1_funct_1 (k4_measure8 A B C D E)) &  ((v1_funct_2 (k4_measure8 A B C D E) k5_numbers k7_numbers) & (m1_subset_1 (k4_measure8 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k4_member_1,ax, (! [A:$i] :  ((v2_membered A) => (v2_membered (k4_member_1 A))) ) ).
tt(dt_k4_memstr_0,ax,$true).
tt(dt_k4_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k4_mesfun7c A B)) &  ((v1_funct_2 (k4_mesfun7c A B) k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 (k4_mesfun7c A B) A k7_numbers) & (m1_subset_1 (k4_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ) ).
tt(dt_k4_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) ) ) )  =>  ((v1_funct_1 (k4_mesfunc1 A B C)) & (m1_subset_1 (k4_mesfunc1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k4_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k3_rfunct_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_rfunct_3 A B))))) )  & (v7_ordinal1 D))  =>  ((v1_funct_1 (k4_mesfunc5 A B C D)) & (m1_subset_1 (k4_mesfunc5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k4_mesfunc7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (v7_ordinal1 B))  => (m1_subset_1 (k4_mesfunc7 A B) k7_numbers)) ) ).
tt(dt_k4_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k4_mesfunc8 A B)) &  ((v1_funct_2 (k4_mesfunc8 A B) k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 (k4_mesfunc8 A B) A k7_numbers) & (m1_subset_1 (k4_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ) ).
tt(dt_k4_mesfunc9,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k4_mesfunc9 A B)) &  ((v1_funct_2 (k4_mesfunc9 A B) k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 (k4_mesfunc9 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ).
tt(dt_k4_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v8_metric_1 A) & (l1_metric_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_metric_1 A B C) k1_numbers)) ) ).
tt(dt_k4_metric_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k4_metric_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A))))) ) ).
tt(dt_k4_metric_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_metric_3 A B C)) &  ((v1_funct_2 (k4_metric_3 A B C) (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers) & (m1_subset_1 (k4_metric_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) k1_numbers)))) ) ) ) ).
tt(dt_k4_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_pre_topc (k4_mfold_2 A)) & (l1_pre_topc (k4_mfold_2 A))) ) ) ).
tt(dt_k4_midsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  & (m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))  => (m1_subset_1 (k4_midsp_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k4_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B)))) ) )  => (m1_subset_1 (k4_midsp_3 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k4_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k4_mmlquery A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k4_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ((v1_funct_1 (k4_mod_2 A B)) &  ((v1_funct_2 (k4_mod_2 A B) (u1_struct_0 (k2_mod_2 A B)) (u1_struct_0 (k3_mod_2 A B))) & (m1_subset_1 (k4_mod_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_mod_2 A B)) (u1_struct_0 (k3_mod_2 A B)))))) ) ) ) ).
tt(dt_k4_mod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k4_mod_4 A B C)) &  ((v1_funct_2 (k4_mod_4 A B C) (k2_zfmisc_1 (u1_struct_0 (k3_mod_4 A B)) (u1_struct_0 (k2_mod_4 A))) (u1_struct_0 (k3_mod_4 A B))) & (m1_subset_1 (k4_mod_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_mod_4 A B)) (u1_struct_0 (k2_mod_4 A))) (u1_struct_0 (k3_mod_4 A B)))))) ) ) ) ).
tt(dt_k4_modal_1,ax,$true).
tt(dt_k4_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  => (m3_modcat_1 (k4_modcat_1 A B) A)) ) ).
tt(dt_k4_modelc_1,ax, (! [A:$i] : (v1_xboolean (k4_modelc_1 A))) ).
tt(dt_k4_modelc_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k4_modelc_2 A B) k5_numbers)) ) ).
tt(dt_k4_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k4_modelc_3 A) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k4_moebius1,ax, (! [A:$i] :  ((v1_relat_1 (k4_moebius1 A)) &  ((v4_relat_1 (k4_moebius1 A) k5_numbers) &  ((v1_funct_1 (k4_moebius1 A)) & (v1_partfun1 (k4_moebius1 A) k5_numbers)) ) ) ) ).
tt(dt_k4_monoid_0,ax, ( (~ (v2_struct_0 k4_monoid_0))  &  ((v15_algstr_0 k4_monoid_0) &  ((v1_group_1 k4_monoid_0) &  ((v17_monoid_0 k4_monoid_0) & (m5_monoid_0 k4_monoid_0 k2_monoid_0 k3_monoid_0)) ) ) ) ).
tt(dt_k4_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k4_monoid_1 A B C) A)) ) ).
tt(dt_k4_morph_01,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k4_morph_01 A B)) &  ((v1_funct_2 (k4_morph_01 A B) (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k4_morph_01 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k4_msafree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_msafree2 A B) (u4_struct_0 A))) ) ).
tt(dt_k4_msafree3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k1_msaterm A B))) )  => (m3_pboole (k4_msafree3 A B C) (u1_struct_0 A) B)) ) ).
tt(dt_k4_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k4_msafree A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B)))))))) ) ).
tt(dt_k4_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D))) ) ) )  => (m1_dtconstr (k4_msaterm A B C D E) (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) ) ).
tt(dt_k4_msinst_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  ( (~ (v2_struct_0 (k4_msinst_1 A B)))  &  ((v6_altcat_1 (k4_msinst_1 A B)) & (l2_altcat_1 (k4_msinst_1 A B))) ) ) ) ).
tt(dt_k4_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ( (~ (v2_struct_0 (k4_msscyc_2 A)))  & (l1_graph_1 (k4_msscyc_2 A))) ) ) ).
tt(dt_k4_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m3_pboole C A (k1_mboolean A B)))  => (m3_pboole (k4_mssubfam A B C) A B)) ) ).
tt(dt_k4_msualg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (l3_msualg_1 C A)) )  => (m1_subset_1 (k4_msualg_1 A B C) (k10_xtuple_0 (u3_msualg_1 A C)))) ) ).
tt(dt_k4_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  => (m2_pboole (k4_msualg_2 A B C) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) C)) (k3_relat_1 (u2_msualg_1 A) C))) ) ).
tt(dt_k4_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (m2_pboole D A B C)) )  => (m2_pboole (k4_msualg_3 A B C D) A C B)) ) ).
tt(dt_k4_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) )  =>  ((v1_relat_1 (k4_msualg_4 A B C)) &  ((v2_relat_1 (k4_msualg_4 A B C)) &  ((v4_relat_1 (k4_msualg_4 A B C) (u1_struct_0 A)) &  ((v1_funct_1 (k4_msualg_4 A B C)) & (v1_partfun1 (k4_msualg_4 A B C) (u1_struct_0 A))) ) ) ) ) ) ).
tt(dt_k4_msualg_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  &  ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B)) ) ) )  =>  ((v1_msualg_4 (k4_msualg_5 A B C D) A B) & (m1_msualg_4 (k4_msualg_5 A B C D) A B B)) ) ) ).
tt(dt_k4_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ((m1_subset_1 C k5_numbers) &  ((l3_msualg_1 D A) &  ((v1_relat_1 E) & (v1_funct_1 E)) ) ) ) )  =>  ((v1_relat_1 (k4_msualg_6 A B C D E)) & (v1_funct_1 (k4_msualg_6 A B C D E))) ) ) ).
tt(dt_k4_multop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_zfmisc_1 A B C D) E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 A B C D) E)))) )  &  ((m1_subset_1 G A) &  ((m1_subset_1 H B) &  ((m1_subset_1 I C) & (m1_subset_1 J D)) ) ) ) ) ) ) ) )  => (m1_subset_1 (k4_multop_1 A B C D E F G H I J) E)) ) ).
tt(dt_k4_mycielsk,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_mycielsk A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (k9_funct_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 A B))))) ) ) )  =>  ((v1_funct_1 (k4_nagata_1 A B C)) &  ((v1_funct_2 (k4_nagata_1 A B C) A B) & (m1_subset_1 (k4_nagata_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k4_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  => (m2_subset_1 (k4_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k4_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k4_nat_3 A B C)) &  ((v4_relat_1 (k4_nat_3 A B C) A) &  ((v1_funct_1 (k4_nat_3 A B C)) & (v1_partfun1 (k4_nat_3 A B C) A)) ) ) ) ) ).
tt(dt_k4_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k4_nat_5 A)) &  ((v1_funct_2 (k4_nat_5 A) k5_numbers k5_numbers) & (m1_subset_1 (k4_nat_5 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k4_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k4_nat_d A B) k5_numbers)) ) ).
tt(dt_k4_nat_lat,ax,(m1_subset_1 k4_nat_lat (u1_struct_0 k3_nat_lat))).
tt(dt_k4_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m2_cat_1 D A B) &  ((m1_nattra_1 E A B C D) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_cat_1 (k4_nattra_1 A B C D E F) B (k8_cat_1 A B C F) (k8_cat_1 A B D F))) ) ).
tt(dt_k4_ndiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k4_ndiff_1 A B C D)) & (m1_subset_1 (k4_ndiff_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k16_lopban_1 A B)))))) ) ) ).
tt(dt_k4_ndiff_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  &  ((m1_subset_1 B (k4_finseq_1 A)) & (m1_subset_1 C (u1_struct_0 (k14_prvect_2 A)))) )  =>  ((v1_funct_1 (k4_ndiff_5 A B C)) &  ((v1_funct_2 (k4_ndiff_5 A B C) (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A))) & (m1_subset_1 (k4_ndiff_5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)))))) ) ) ) ).
tt(dt_k4_neckla_2,ax,(m1_subset_1 k4_neckla_2 (k1_zfmisc_1 k3_neckla_2))).
tt(dt_k4_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_orders_2 (k4_necklace A)) & (l1_orders_2 (k4_necklace A))) ) ) ).
tt(dt_k4_net_1,ax,$true).
tt(dt_k4_newton,ax,$true).
tt(dt_k4_normsp_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k4_normsp_0 A B)) &  ((v1_funct_2 (k4_normsp_0 A B) k5_numbers k1_numbers) & (m1_subset_1 (k4_normsp_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k4_normsp_1 A B C)) &  ((v1_funct_2 (k4_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k4_normsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v5_rltopsp1 (k4_normsp_2 A)) & (l1_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(dt_k4_ntalgo_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A (k2_zfmisc_1 k4_numbers k4_numbers)))  => (m1_subset_1 (k4_ntalgo_1 A) k4_numbers)) ) ).
tt(dt_k4_numbers,ax,$true).
tt(dt_k4_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k4_openlatt A)) &  ((v1_funct_2 (k4_openlatt A) (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A)) & (m1_subset_1 (k4_openlatt A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A))))) ) ) ) ).
tt(dt_k4_oppcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))))  => (m1_subset_1 (k4_oppcat_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_orders_2,ax,$true).
tt(dt_k4_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  ((v6_altcat_1 (k4_orders_3 A)) & (l2_altcat_1 (k4_orders_3 A))) ) ) ).
tt(dt_k4_ordinal1,ax,$true).
tt(dt_k4_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  => (v3_ordinal1 (k4_ordinal2 A))) ) ).
tt(dt_k4_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) ) )  =>  ((v5_ordinal1 (k4_ordinal3 A B)) &  ((v1_relat_1 (k4_ordinal3 A B)) &  ((v1_funct_1 (k4_ordinal3 A B)) & (v1_ordinal2 (k4_ordinal3 A B))) ) ) ) ) ).
tt(dt_k4_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((v3_ordinal1 (k4_ordinal4 A B C)) & (m1_subset_1 (k4_ordinal4 A B C) A)) ) ) ).
tt(dt_k4_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_finset_1 A) & (v1_ordinal2 A)) ) ) )  => (v3_ordinal1 (k4_ordinal5 A))) ) ).
tt(dt_k4_ordinal6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v3_ordinal1 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C B (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k2_ordinal1 A))))) ) ) )  =>  ((v3_ordinal1 (k4_ordinal6 A B C D)) & (m1_subset_1 (k4_ordinal6 A B C D) A)) ) ) ).
tt(dt_k4_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_osafree A B C) (k1_zfmisc_1 (k4_dtconstr (k2_osafree A B))))) ) ).
tt(dt_k4_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k3_osalg_1 A B))) (k3_relat_1 (u2_msualg_1 A) (k3_osalg_1 A B)))) )  =>  ((v3_msualg_1 (k4_osalg_1 A B C) A) &  ((v4_msualg_1 (k4_osalg_1 A B C) A) & (l3_msualg_1 (k4_osalg_1 A B C) A)) ) ) ) ).
tt(dt_k4_osalg_4,ax,$true).
tt(dt_k4_parsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))))  => (m1_subset_1 (k4_parsp_1 A B) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(dt_k4_partfun1,ax,$true).
tt(dt_k4_partfun2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D B)) ) )  =>  ((v1_funct_1 (k4_partfun2 A B C D)) & (m1_subset_1 (k4_partfun2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k4_partit1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_eqrel_1 B A))  =>  ((v1_partfun1 (k4_partit1 A B) A) &  ((v3_relat_2 (k4_partit1 A B)) &  ((v8_relat_2 (k4_partit1 A B)) & (m1_subset_1 (k4_partit1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k4_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k4_pboole A B C)) &  ((v4_relat_1 (k4_pboole A B C) A) &  ((v1_funct_1 (k4_pboole A B C)) & (v1_partfun1 (k4_pboole A B C) A)) ) ) ) ) ).
tt(dt_k4_pcomps_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((v1_metric_1 (k4_pcomps_1 A B)) &  ((v6_metric_1 (k4_pcomps_1 A B)) &  ((v7_metric_1 (k4_pcomps_1 A B)) &  ((v8_metric_1 (k4_pcomps_1 A B)) &  ((v9_metric_1 (k4_pcomps_1 A B)) & (l1_metric_1 (k4_pcomps_1 A B))) ) ) ) ) ) ) ).
tt(dt_k4_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  ((v1_relat_1 (k4_pcs_0 A B)) &  ((v4_relat_1 (k4_pcs_0 A B) A) &  ((v1_funct_1 (k4_pcs_0 A B)) & (v1_partfun1 (k4_pcs_0 A B) A)) ) ) ) ) ).
tt(dt_k4_pdiff_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k4_pdiff_1 A B)) &  ((v1_funct_2 (k4_pdiff_1 A B) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 (k4_pdiff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)))))) ) ) ) ).
tt(dt_k4_pdiff_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  & (m1_subset_1 B (k1_euclid 2)))  => (m1_subset_1 (k4_pdiff_3 A B) k1_numbers)) ) ).
tt(dt_k4_pdiff_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m2_finseq_2 (k4_pdiff_4 A B) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k4_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k4_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k4_pdiff_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_finseq_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) )  =>  ((v1_funct_1 (k4_pdiff_9 A B C D)) &  ((v1_funct_2 (k4_pdiff_9 A B C D) k5_numbers (k4_partfun1 (k1_euclid A) k1_numbers)) & (m1_subset_1 (k4_pdiff_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (k1_euclid A) k1_numbers))))) ) ) ) ).
tt(dt_k4_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) ) )  => (m1_subset_1 (k4_pencil_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (k4_card_3 (k12_pralg_1 A B)))))) ) ).
tt(dt_k4_pencil_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  & (m1_subset_1 D A)) ) )  =>  ((v1_funct_1 (k4_pencil_3 A B C D)) &  ((v1_funct_2 (k4_pencil_3 A B C D) (u1_struct_0 (k2_pencil_1 A B D)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) D)))) & (m1_subset_1 (k4_pencil_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B D)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) D))))))) ) ) ) ).
tt(dt_k4_pencil_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 C)) )  => (m1_subset_1 (k4_pencil_4 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (k2_vectsp_9 A B C))))) ) ).
tt(dt_k4_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k4_pepin A) k5_numbers)) ) ).
tt(dt_k4_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u2_petri A)))  => (m1_subset_1 (k4_petri A B) (u4_struct_0 A))) ) ).
tt(dt_k4_pnproc_1,ax, (! [A:$i,B:$i] :  ((m1_pnproc_1 B A) =>  ((v1_funct_1 (k4_pnproc_1 A B)) &  ((v1_funct_2 (k4_pnproc_1 A B) A k5_numbers) & (m1_subset_1 (k4_pnproc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(dt_k4_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k1_numbers)) ) )  => (m1_subset_1 (k4_polyeq_1 A B C D) k1_numbers)) ) ).
tt(dt_k4_polyeq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xcmplx_0 (k4_polyeq_5 A B C))) ) ).
tt(dt_k4_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (m2_finseq_1 (k4_polyform A B) k4_numbers)) ) ).
tt(dt_k4_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k4_polynom1 A B C D)) &  ((v1_funct_2 (k4_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k4_polynom1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k4_polynom2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k15_pre_poly A)))  =>  ((v1_relat_1 (k4_polynom2 A B)) &  ((v4_relat_1 (k4_polynom2 A B) A) &  ((v1_funct_1 (k4_polynom2 A B)) &  ((v1_partfun1 (k4_polynom2 A B) A) &  ((v4_valued_0 (k4_polynom2 A B)) & (v2_pre_poly (k4_polynom2 A B))) ) ) ) ) ) ) ).
tt(dt_k4_polynom3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((m1_finseq_1 D (k4_finseq_2 B A)) & (m1_finseq_1 E (k4_finseq_2 C A))) ) ) )  => (m2_finseq_2 (k4_polynom3 A B C D E) (k4_finseq_2 (k2_nat_1 B C) A) (k3_finseq_2 (k4_finseq_2 (k2_nat_1 B C) A)))) ) ).
tt(dt_k4_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k4_polynom5 A B C)) &  ((v1_funct_2 (k4_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k4_polynom5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_polynom7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B)))  =>  ((v1_funct_1 (k4_polynom7 A B C)) &  ((v1_funct_2 (k4_polynom7 A B C) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k4_polynom7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k4_polynom8,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) )  => (m1_matrix_1 (k4_polynom8 A B C) (u1_struct_0 B) A 1)) ) ).
tt(dt_k4_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k4_poset_1 A B))) ) ) ).
tt(dt_k4_power,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k4_power A B) k1_numbers)) ) ).
tt(dt_k4_pralg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) )  => (m2_finseq_1 (k4_pralg_1 A B) (k4_partfun1 (k3_finseq_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ).
tt(dt_k4_pralg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  & (m1_pralg_3 D A C B)) ) )  => (m1_pralg_2 (k4_pralg_3 A B C D) A B)) ) ).
tt(dt_k4_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m2_finseq_2 (k4_pre_poly A B C) A (k3_finseq_2 A))) ) ).
tt(dt_k4_prepower,ax,$true).
tt(dt_k4_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m1_prob_1 (k4_prob_1 A B) A B)) ) ).
tt(dt_k4_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k9_setfam_1 A)) & (v7_ordinal1 C))  => (m1_subset_1 (k4_prob_3 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k4_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  ( (~ (v1_xboole_0 (k4_prob_4 A B C)))  & (m1_subset_1 (k4_prob_4 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k4_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (v7_ordinal1 B))  =>  ( (~ (v2_struct_0 (k4_prvect_1 A B)))  &  ((v8_algstr_0 (k4_prvect_1 A B)) &  ((v13_algstr_0 (k4_prvect_1 A B)) &  ((v2_rlvect_1 (k4_prvect_1 A B)) &  ((v3_rlvect_1 (k4_prvect_1 A B)) &  ((v4_rlvect_1 (k4_prvect_1 A B)) & (l2_algstr_0 (k4_prvect_1 A B))) ) ) ) ) ) ) ) ).
tt(dt_k4_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ((v1_relat_1 (k4_prvect_2 A)) &  ((v2_relat_1 (k4_prvect_2 A)) &  ((v1_funct_1 (k4_prvect_2 A)) &  ( (~ (v1_xboole_0 (k4_prvect_2 A)))  & (v1_finseq_1 (k4_prvect_2 A))) ) ) ) ) ) ).
tt(dt_k4_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_algstr_0 B)) )  =>  ( (~ (v2_struct_0 (k4_prvect_3 A B)))  &  ((v8_algstr_0 (k4_prvect_3 A B)) & (l2_algstr_0 (k4_prvect_3 A B))) ) ) ) ).
tt(dt_k4_pscomp_1,ax, ((v1_funct_1 k4_pscomp_1) &  ((v1_funct_2 k4_pscomp_1 (u1_struct_0 (k15_euclid 2)) k1_numbers) & (m1_subset_1 k4_pscomp_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) k1_numbers)))) ) ).
tt(dt_k4_pua2mss1,ax, (! [A:$i,B:$i] :  ((m1_eqrel_1 B A) => (m2_pua2mss1 (k4_pua2mss1 A B) A)) ) ).
tt(dt_k4_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k4_qc_lang1 A) (k1_zfmisc_1 (k2_qc_lang1 A)))) ) ).
tt(dt_k4_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k4_qc_lang2 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k4_qc_lang3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_qc_lang1 A))))  & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k4_qc_lang3 A B C) (k1_zfmisc_1 B))) ) ).
tt(dt_k4_qc_lang4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_qc_lang4 C A B)) )  =>  ( (~ (v1_xboole_0 (k4_qc_lang4 A B C)))  & (m4_trees_1 (k4_qc_lang4 A B C) (k9_xtuple_0 (k2_qc_lang4 A B)))) ) ) ).
tt(dt_k4_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_qmax_1 A) &  ((m1_subset_1 B (k2_qmax_1 A)) & (m1_subset_1 C (k3_qmax_1 A))) )  => (m2_prob_1 (k4_qmax_1 A B C) k1_numbers k12_prob_1)) ) ).
tt(dt_k4_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  => (m1_subset_1 (k4_quantal1 A) (u1_struct_0 A))) ) ).
tt(dt_k4_quatern2,ax,(m1_subset_1 k4_quatern2 k1_quaterni)).
tt(dt_k4_quatern3,ax, (! [A:$i] :  ((m1_subset_1 A k1_quaterni) => (m1_subset_1 (k4_quatern3 A) k1_quaterni)) ) ).
tt(dt_k4_quaterni,ax,$true).
tt(dt_k4_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  => (m2_subset_1 (k4_quofield A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A))) ) ).
tt(dt_k4_radix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  => (v1_int_1 (k4_radix_1 A B C D))) ) ).
tt(dt_k4_radix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k4_radix_2 A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k4_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k4_radix_3 A)))  & (m1_subset_1 (k4_radix_3 A) (k1_zfmisc_1 k4_numbers))) ) ) ).
tt(dt_k4_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k4_radix_5 A B C) A) & (m2_finseq_1 (k4_radix_5 A B C) (k3_radix_1 C))) ) ) ).
tt(dt_k4_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k4_radix_6 A B C) (k2_xcmplx_0 A 2)) & (m2_finseq_1 (k4_radix_6 A B C) (k3_radix_1 B))) ) ) ).
tt(dt_k4_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  => (m1_random_1 (k4_random_1 A B C D) A B)) ) ).
tt(dt_k4_ranknull,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_ranknull A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  & (m1_ratfunc1 B A))  =>  ((v1_funct_1 (k4_ratfunc1 A B)) &  ((v1_funct_2 (k4_ratfunc1 A B) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k4_ratfunc1 A B) A) & (m1_subset_1 (k4_ratfunc1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k4_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k4_rcomp_1 A B) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k4_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k4_real_1 A B) k1_numbers)) ) ).
tt(dt_k4_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v5_relat_1 (k4_real_3 A) k4_numbers) &  ((v1_funct_1 (k4_real_3 A)) &  ((v1_funct_2 (k4_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k4_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ).
tt(dt_k4_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k4_real_lat A)) &  ((v1_funct_2 (k4_real_lat A) (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 (k4_real_lat A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) ) ) ) ).
tt(dt_k4_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_real_ns1 A)))  &  ((v1_normsp_1 (k4_real_ns1 A)) & (l1_normsp_1 (k4_real_ns1 A))) ) ) ) ).
tt(dt_k4_realset1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((m1_subset_1 B A) & (m3_realset1 C A B)) )  =>  ((v1_funct_1 (k4_realset1 A B C)) &  ((v1_funct_2 (k4_realset1 A B C) (k2_zfmisc_1 (k6_subset_1 A (k6_domain_1 A B)) (k6_subset_1 A (k6_domain_1 A B))) (k6_subset_1 A (k6_domain_1 A B))) & (m1_subset_1 (k4_realset1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 A (k6_domain_1 A B)) (k6_subset_1 A (k6_domain_1 A B))) (k6_subset_1 A (k6_domain_1 A B)))))) ) ) ) ).
tt(dt_k4_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  => (m3_realset1 (k4_realset2 A) (u1_struct_0 A) (k4_struct_0 A))) ) ).
tt(dt_k4_rearran1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_rearran1 C) &  ((v2_rearran1 C) &  ((v3_rearran1 C (k1_zfmisc_1 B)) & (m1_finseq_1 C (k1_zfmisc_1 B))) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k4_rearran1 A B C D)) & (m1_subset_1 (k4_rearran1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ).
tt(dt_k4_relat_1,ax, (! [A:$i] : (v1_relat_1 (k4_relat_1 A))) ).
tt(dt_k4_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  => (m1_subset_1 (k4_relset_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 A D)))) ) ).
tt(dt_k4_relset_2,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((v1_funct_1 (k4_relset_2 A B C)) &  ((v1_funct_2 (k4_relset_2 A B C) (k9_setfam_1 B) (k9_setfam_1 A)) & (m1_subset_1 (k4_relset_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 B) (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k4_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_finseq_1 C (k8_afinsq_1 A)))  => (m2_finseq_1 (k4_rewrite2 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k4_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k4_rfinseq2 A) k1_numbers)) ) ).
tt(dt_k4_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k4_rfunct_1 A)) & (v1_funct_1 (k4_rfunct_1 A))) ) ) ).
tt(dt_k4_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D B)) ) )  => (m2_rfunct_3 (k4_rfunct_3 A B C D) A B (k3_rfunct_3 A B))) ) ).
tt(dt_k4_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k4_rinfsup1 A)) &  ((v1_funct_2 (k4_rinfsup1 A) k5_numbers k1_numbers) & (m1_subset_1 (k4_rinfsup1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_funct_1 (k4_rinfsup2 A)) &  ((v1_funct_2 (k4_rinfsup2 A) k5_numbers k7_numbers) & (m1_subset_1 (k4_rinfsup2 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k4_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v3_ringcat1 (k4_ringcat1 A)) & (l1_ringcat1 (k4_ringcat1 A))) ) ) ).
tt(dt_k4_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_rlaffin1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_rlsub_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_rlsub_1 C A) & (m1_rlsub_1 D A)) ) )  => (m1_subset_1 (k4_rlsub_2 A B C D) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(dt_k4_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  & (m1_subset_1 B k1_numbers))  =>  ((v1_funct_1 (k4_rltopsp1 A B)) &  ((v1_funct_2 (k4_rltopsp1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k4_rltopsp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_rlvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  => (m1_subset_1 (k4_rlvect_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (m1_rlvect_2 (k4_rlvect_2 A) A)) ) ).
tt(dt_k4_rmod_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_rmod_2 D A B) & (m1_rmod_2 E A B)) ) ) )  => (m1_subset_1 (k4_rmod_3 A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))) ) ).
tt(dt_k4_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_finseq_1 C (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  => (m2_finseq_1 (k4_rmod_4 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k4_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_robbins1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_robbins3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k4_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_roughs_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_rsspace3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k4_rsspace3 A B C) k1_numbers)) ) ).
tt(dt_k4_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k4_rsspace4 A B) (k1_zfmisc_1 (u1_struct_0 (k5_lopban_1 A B))))) ) ).
tt(dt_k4_rsspace,ax, ((v1_funct_1 k4_rsspace) &  ((v1_funct_2 k4_rsspace (k2_zfmisc_1 k1_rsspace k1_rsspace) k1_rsspace) & (m1_subset_1 k4_rsspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_rsspace k1_rsspace) k1_rsspace)))) ) ).
tt(dt_k4_rusub_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_rusub_1 C A) & (m1_rusub_1 D A)) ) )  => (m1_subset_1 (k4_rusub_2 A B C D) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(dt_k4_rusub_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_rusub_1 B A))  =>  ( (~ (v1_xboole_0 (k4_rusub_4 A B)))  & (m1_subset_1 (k4_rusub_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k4_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k4_rusub_5 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k4_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  => (m2_finseq_1 (k4_rvsum_1 A B) k1_numbers)) ) ).
tt(dt_k4_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  => (m2_finseq_2 (k4_rvsum_2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k4_scm_comp,ax, (! [A:$i] :  ((m1_subset_1 A (k6_dtconstr k1_scm_comp)) =>  ((v1_ami_2 (k4_scm_comp A)) & (m1_subset_1 (k4_scm_comp A) (u1_struct_0 k1_ami_3))) ) ) ).
tt(dt_k4_scmfsa_1,ax, ((v1_funct_1 k4_scmfsa_1) &  ((v1_funct_2 k4_scmfsa_1 k1_scmfsa_1 3) & (m1_subset_1 k4_scmfsa_1 (k1_zfmisc_1 (k2_zfmisc_1 k1_scmfsa_1 3)))) ) ).
tt(dt_k4_scmfsa_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_ami_2 (k4_scmfsa_2 A)) & (m1_subset_1 (k4_scmfsa_2 A) (u1_struct_0 k1_scmfsa_2))) ) ) ).
tt(dt_k4_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) & (v1_afinsq_1 (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ).
tt(dt_k4_scmfsa_7,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  =>  ((v1_relat_1 (k4_scmfsa_7 A B)) &  ((v4_relat_1 (k4_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa_7 A B)) & (v1_finset_1 (k4_scmfsa_7 A B))) ) ) ) ) ) ).
tt(dt_k4_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa8b A B C D)))  &  ((v1_relat_1 (k4_scmfsa8b A B C D)) &  ((v4_relat_1 (k4_scmfsa8b A B C D) k5_numbers) &  ((v5_relat_1 (k4_scmfsa8b A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa8b A B C D)) &  ((v1_finset_1 (k4_scmfsa8b A B C D)) & (v1_afinsq_1 (k4_scmfsa8b A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k4_scmfsa_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_scmfsa_9 A B C D)) &  ((v1_funct_2 (k4_scmfsa_9 A B C D) k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 (k4_scmfsa_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) ) ) ) ).
tt(dt_k4_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k4_scmfsa_i A) k2_scm_inst)) ) ).
tt(dt_k4_scmfsa_m,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  => (m1_subset_1 (k4_scmfsa_m A) (k1_zfmisc_1 k2_scmfsa_2))) ) ).
tt(dt_k4_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (m1_subset_1 (k4_scm_inst A) k2_scm_inst)) ) ).
tt(dt_k4_scmpds_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) & (m1_subset_1 B k2_ami_2))  => (m1_subset_1 (k4_scmpds_1 A B) k5_numbers)) ) ).
tt(dt_k4_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  => (m1_subset_1 (k4_scmpds_2 A) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k4_scmpds_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2)))  =>  ( (~ (v1_xboole_0 (k4_scmpds_4 A B)))  &  ((v1_relat_1 (k4_scmpds_4 A B)) &  ((v4_relat_1 (k4_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_4 A B)) &  ((v1_finset_1 (k4_scmpds_4 A B)) & (v1_afinsq_1 (k4_scmpds_4 A B))) ) ) ) ) ) ) ) ).
tt(dt_k4_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_6 A B C D)))  &  ((v1_relat_1 (k4_scmpds_6 A B C D)) &  ((v4_relat_1 (k4_scmpds_6 A B C D) k5_numbers) &  ((v5_relat_1 (k4_scmpds_6 A B C D) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_6 A B C D)) &  ((v1_finset_1 (k4_scmpds_6 A B C D)) & (v1_afinsq_1 (k4_scmpds_6 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k4_scmpds_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E k5_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_7 A B C D E)))  &  ((v1_relat_1 (k4_scmpds_7 A B C D E)) &  ((v4_relat_1 (k4_scmpds_7 A B C D E) k5_numbers) &  ((v5_relat_1 (k4_scmpds_7 A B C D E) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_7 A B C D E)) &  ((v1_finset_1 (k4_scmpds_7 A B C D E)) & (v1_afinsq_1 (k4_scmpds_7 A B C D E))) ) ) ) ) ) ) ) ).
tt(dt_k4_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k4_scmpds_i A))) ) ).
tt(dt_k4_scmp_gcd,ax, ( (~ (v1_xboole_0 k4_scmp_gcd))  &  ((v1_relat_1 k4_scmp_gcd) &  ((v4_relat_1 k4_scmp_gcd k5_numbers) &  ((v5_relat_1 k4_scmp_gcd (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 k4_scmp_gcd) &  ((v1_finset_1 k4_scmp_gcd) & (v1_afinsq_1 k4_scmp_gcd)) ) ) ) ) ) ).
tt(dt_k4_scmring1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) &  ((m1_subset_1 C k2_ami_2) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k4_scmring1 A B C D) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) ) ).
tt(dt_k4_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k4_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k4_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k4_scmringi A B) k5_numbers)) ) ).
tt(dt_k4_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v4_scmyciel A) & (m1_subset_1 B (k3_tarski A)))  => (m1_subset_1 (k4_scmyciel A B) (k1_zfmisc_1 (k3_tarski A)))) ) ).
tt(dt_k4_scpinvar,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scpinvar A B C)))  &  ((v1_relat_1 (k4_scpinvar A B C)) &  ((v4_relat_1 (k4_scpinvar A B C) k5_numbers) &  ((v5_relat_1 (k4_scpinvar A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scpinvar A B C)) &  ((v1_finset_1 (k4_scpinvar A B C)) & (v1_afinsq_1 (k4_scpinvar A B C))) ) ) ) ) ) ) ) ).
tt(dt_k4_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k4_seq_4 A) k1_numbers)) ) ).
tt(dt_k4_seqfunc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k4_seqfunc A B)) &  ((v1_funct_2 (k4_seqfunc A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k4_seqfunc A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k4_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k4_series_1 A) k1_numbers)) ) ).
tt(dt_k4_setfam_1,ax,$true).
tt(dt_k4_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k4_setlim_1 A B)) &  ((v1_funct_2 (k4_setlim_1 A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k4_setlim_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k4_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_funct_1 (k4_setlim_2 A B C)) &  ((v1_funct_2 (k4_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k4_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k4_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k4_setwiseo A B C D) (k5_finsub_1 A))) ) ).
tt(dt_k4_sfmastr2,ax, (! [A:$i] :  ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k4_sfmastr2 A)))  &  ((v1_relat_1 (k4_sfmastr2 A)) &  ((v4_relat_1 (k4_sfmastr2 A) k5_numbers) &  ((v5_relat_1 (k4_sfmastr2 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_sfmastr2 A)) &  ((v1_finset_1 (k4_sfmastr2 A)) & (v1_afinsq_1 (k4_sfmastr2 A))) ) ) ) ) ) ) ) ).
tt(dt_k4_sfmastr3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_scmfsa_2 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k4_sfmastr3 A B C)) &  ((v4_relat_1 (k4_sfmastr3 A B C) k5_numbers) &  ((v5_relat_1 (k4_sfmastr3 A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_sfmastr3 A B C)) &  ( (~ (v1_xboole_0 (k4_sfmastr3 A B C)))  &  ((v1_finset_1 (k4_sfmastr3 A B C)) & (v1_afinsq_1 (k4_sfmastr3 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k4_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (m1_subset_1 (k4_sf_mastr A) (k1_zfmisc_1 k3_scmfsa_2))) ) ).
tt(dt_k4_sgraph1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_sgraph1 B A) => (m1_subset_1 (k4_sgraph1 A B C) k5_numbers)) ) ).
tt(dt_k4_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k4_simplex0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) ) )  =>  ( (~ (v3_pencil_1 (k4_simplex1 A B)))  &  ((v1_matroid0 (k4_simplex1 A B)) &  ((v3_matroid0 (k4_simplex1 A B)) & (m1_simplex1 (k4_simplex1 A B) A B)) ) ) ) ) ).
tt(dt_k4_sincos10,ax, ((v1_funct_1 k4_sincos10) & (m1_subset_1 k4_sincos10 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k4_sin_cos2,ax, ((v1_funct_1 k4_sin_cos2) &  ((v1_funct_2 k4_sin_cos2 k1_numbers k1_numbers) & (m1_subset_1 k4_sin_cos2 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k4_sin_cos3,ax, ((v1_funct_1 k4_sin_cos3) &  ((v1_funct_2 k4_sin_cos3 k2_numbers k2_numbers) & (m1_subset_1 k4_sin_cos3 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(dt_k4_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k4_sin_cos4 A) k1_numbers)) ) ).
tt(dt_k4_sin_cos6,ax, ((v1_funct_1 k4_sin_cos6) & (m1_subset_1 k4_sin_cos6 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(dt_k4_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k4_sin_cos7 A))) ) ).
tt(dt_k4_sin_cos9,ax,$true).
tt(dt_k4_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k4_sin_cos A)) &  ((v1_funct_2 (k4_sin_cos A) k5_numbers k1_numbers) & (m1_subset_1 (k4_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (m1_subset_1 (k4_square_1 A) k2_numbers)) ) ).
tt(dt_k4_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((m1_subset_1 D (k1_zfmisc_1 B)) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_stacks_1 A B C D E F)) &  ((v1_funct_2 (k4_stacks_1 A B C D E F) A B) & (m1_subset_1 (k4_stacks_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k4_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) => (m1_subset_1 (k4_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k4_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_qc_lang1 B) &  ((m1_subset_1 C (k8_qc_lang1 B A)) &  ( ((v5_relat_1 D (k3_qc_lang1 B)) &  ((v3_card_1 D A) & (m1_finseq_1 D (k2_qc_lang1 B))) )  & (m1_subset_1 E (k1_substut1 B))) ) ) )  => (m2_subset_1 (k4_sublemma A B C D E) (k16_substut1 B) (k38_substut1 B))) ) ).
tt(dt_k4_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k4_subset_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k4_substlat,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) & (m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))))  => (m1_subset_1 (k4_substlat A B C D) (k5_finsub_1 (k4_partfun1 A B)))) ) ).
tt(dt_k4_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_qc_lang1 A)))  => (m2_finseq_1 (k4_substut1 A B) (k2_qc_lang1 A))) ) ).
tt(dt_k4_substut2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k3_qc_lang1 A))) ) )  => (m2_subset_1 (k4_substut2 A B C D) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k4_supinf_1,ax, (! [A:$i] :  ((v2_membered A) => (v2_membered (k4_supinf_1 A))) ) ).
tt(dt_k4_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  => (m1_subset_1 (k4_supinf_2 A B) k7_numbers)) ) ).
tt(dt_k4_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k4_t_0topsp A)) &  ((v1_funct_2 (k4_t_0topsp A) (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A))) &  ((v5_pre_topc (k4_t_0topsp A) A (k3_t_0topsp A)) & (m1_subset_1 (k4_t_0topsp A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A)))))) ) ) ) ) ).
tt(dt_k4_tarski,ax,$true).
tt(dt_k4_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  => (m1_subset_1 (k4_taxonom1 A) (k1_zfmisc_1 (k1_partit1 (u1_struct_0 A))))) ) ).
tt(dt_k4_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k4_taylor_1 A)) & (m1_subset_1 (k4_taylor_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k4_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (k4_tdlat_1 A)))  &  ((v10_lattices (k4_tdlat_1 A)) &  ((v15_lattices (k4_tdlat_1 A)) &  ((v16_lattices (k4_tdlat_1 A)) & (l3_lattices (k4_tdlat_1 A))) ) ) ) ) ) ).
tt(dt_k4_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  => (m1_subset_1 (k4_termord A B C D) (u1_struct_0 C))) ) ).
tt(dt_k4_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k4_tex_4 A B)))  & (m1_subset_1 (k4_tex_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k4_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_pre_topc B A))  =>  ((v1_funct_1 (k4_tmap_1 A B)) &  ((v1_funct_2 (k4_tmap_1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k4_tmap_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_toler_1,ax,$true).
tt(dt_k4_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k4_topalg_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_topalg_1 A B) (k2_topalg_1 A B))))) ) ).
tt(dt_k4_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) )  =>  ((v1_funct_1 (k4_topalg_4 A B C D)) &  ((v1_funct_2 (k4_topalg_4 A B C D) (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 (k4_topalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k4_topalg_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k4_topalg_5 A B C D E)) &  ((v1_funct_2 (k4_topalg_5 A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 (k4_topalg_5 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k4_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_topalg_6 A)) & (m1_subset_1 C (k1_topalg_6 A))) )  => (m2_subset_1 (k4_topalg_6 A B C) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ).
tt(dt_k4_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v1_int_1 (k4_topdim_1 A))) ) ).
tt(dt_k4_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v1_card_1 (k4_topgen_1 A))) ) ).
tt(dt_k4_topgen_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_topgen_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_tops_2 (k4_topgen_2 A B C) A) &  ((v1_yellow_8 (k4_topgen_2 A B C) A C) & (m1_subset_1 (k4_topgen_2 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_topgen_3,ax, (! [A:$i,B:$i] :  ((v1_xreal_0 B) =>  ((v1_funct_1 (k4_topgen_3 A B)) &  ((v1_funct_2 (k4_topgen_3 A B) k5_numbers k1_numbers) & (m1_subset_1 (k4_topgen_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k4_topgen_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_topgen_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_topgen_5,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  ((v1_funct_1 (k4_topgen_5 A B)) &  ((v1_funct_2 (k4_topgen_5 A B) (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (m1_subset_1 (k4_topgen_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr))))) ) ) ) ).
tt(dt_k4_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m3_topgrp_1 (k4_topgrp_1 A) A)) ) ).
tt(dt_k4_topmetr,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (~ (v2_struct_0 (k4_topmetr A B)))  &  ((v1_pre_topc (k4_topmetr A B)) & (m1_pre_topc (k4_topmetr A B) k3_topmetr)) ) ) ) ).
tt(dt_k4_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k4_topreal1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k4_topreal7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  & (m1_subset_1 C (u1_struct_0 (k1_topreal7 A B)))) )  => (m1_subset_1 (k4_topreal7 A B C) (u1_struct_0 B))) ) ).
tt(dt_k4_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (m1_subset_1 (k4_topreal9 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k4_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k4_toprealb A) (u1_struct_0 k2_topalg_2))) ) ).
tt(dt_k4_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  => (m1_subset_1 (k4_toprealc A B C) k1_numbers)) ) ).
tt(dt_k4_toprns_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v1_funct_1 (k4_toprns_1 A B C)) &  ((v1_funct_2 (k4_toprns_1 A B C) k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k4_toprns_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k4_treal_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((m1_subset_1 C (u1_struct_0 (k4_topmetr k6_numbers 1))) & (m1_subset_1 D (u1_struct_0 (k4_topmetr k6_numbers 1)))) ) )  =>  ((v1_funct_1 (k4_treal_1 A B C D)) &  ((v1_funct_2 (k4_treal_1 A B C D) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1))) & (m1_subset_1 (k4_treal_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)))))) ) ) ) ).
tt(dt_k4_trees_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  & (m1_finseq_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k4_trees_1 A B)))  & (v1_trees_1 (k4_trees_1 A B))) ) ) ).
tt(dt_k4_trees_2,ax,$true).
tt(dt_k4_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_trees_3 (k4_trees_3 A) A)) ) ).
tt(dt_k4_trees_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_relat_1 (k4_trees_4 A B)) &  ((v1_funct_1 (k4_trees_4 A B)) & (v3_trees_2 (k4_trees_4 A B))) ) ) ) ).
tt(dt_k4_turing_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k4_turing_1 A B) k4_numbers)) ) ).
tt(dt_k4_twoscomp,ax, ((v1_funct_1 k4_twoscomp) &  ((v1_funct_2 k4_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k4_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k4_unialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_unialg_1 (k4_unialg_2 A B)) & (m1_unialg_2 (k4_unialg_2 A B) A)) ) ) ).
tt(dt_k4_unialg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_unialg_3 A)))) )  =>  ((v1_unialg_1 (k4_unialg_3 A B)) & (m1_unialg_2 (k4_unialg_3 A B) A)) ) ) ).
tt(dt_k4_uniroots,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v6_vectsp_1 B) & (l6_algstr_0 B)) ) )  =>  ((v1_funct_1 (k4_uniroots A B)) &  ((v1_funct_2 (k4_uniroots A B) k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 (k4_uniroots A B) B) & (m1_subset_1 (k4_uniroots A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k4_uproots,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (m2_subset_1 (k4_uproots A B) k1_numbers k5_numbers)) ) ).
tt(dt_k4_urysohn1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_zfmisc_1 (u1_struct_0 A)))))) )  & (m1_subset_1 D B)) ) )  => (m1_subset_1 (k4_urysohn1 A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 (u1_struct_0 B)))))) )  & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k4_urysohn3 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k4_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C k5_numbers) &  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m1_finseq_1 D (k2_qc_lang1 A))) )  & (m1_subset_1 E (k2_valuat_1 A B))) ) ) )  => (m2_finseq_1 (k4_valuat_1 A B C D E) B)) ) ).
tt(dt_k4_valued_2,ax,$true).
tt(dt_k4_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k4_vectmetr A)))  &  ((v13_algstr_0 (k4_vectmetr A)) &  ((v6_metric_1 (k4_vectmetr A)) &  ((v7_metric_1 (k4_vectmetr A)) &  ((v8_metric_1 (k4_vectmetr A)) &  ((v9_metric_1 (k4_vectmetr A)) &  ((v2_rlvect_1 (k4_vectmetr A)) &  ((v3_rlvect_1 (k4_vectmetr A)) &  ((v4_rlvect_1 (k4_vectmetr A)) &  ((v5_rlvect_1 (k4_vectmetr A)) &  ((v6_rlvect_1 (k4_vectmetr A)) &  ((v7_rlvect_1 (k4_vectmetr A)) &  ((v8_rlvect_1 (k4_vectmetr A)) &  ((v4_vectmetr (k4_vectmetr A)) &  ((v5_vectmetr (k4_vectmetr A)) &  ((v6_vectmetr (k4_vectmetr A)) & (l1_vectmetr (k4_vectmetr A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k4_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  => (m2_subset_1 (k4_vectsp10 A B C) (k1_zfmisc_1 (u1_struct_0 B)) (k2_vectsp10 A B C))) ) ).
tt(dt_k4_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k4_vectsp_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k4_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_vectsp_2 A)))  &  ((v13_algstr_0 (k4_vectsp_2 A)) &  ((v2_rlvect_1 (k4_vectsp_2 A)) &  ((v3_rlvect_1 (k4_vectsp_2 A)) &  ((v4_rlvect_1 (k4_vectsp_2 A)) &  ((v2_vectsp_2 (k4_vectsp_2 A) A) & (l1_vectsp_2 (k4_vectsp_2 A) A)) ) ) ) ) ) ) ) ).
tt(dt_k4_vectsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((m1_vectsp_4 D A B) & (m1_vectsp_4 E A B)) ) ) )  => (m1_subset_1 (k4_vectsp_5 A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))) ) ).
tt(dt_k4_vectsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  & (m1_vectsp_6 C A B)) )  => (m1_subset_1 (k4_vectsp_6 A B C) (u1_struct_0 B))) ) ).
tt(dt_k4_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_vectsp_8 A B)) &  ((v1_funct_2 (k4_vectsp_8 A B) (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 (k4_vectsp_8 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k4_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  & (m1_subset_1 D k1_numbers)) ) )  =>  ((v1_funct_1 (k4_vfunct_1 A B C D)) & (m1_subset_1 (k4_vfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k4_waybel_0,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k4_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k4_waybel10 A)))  &  ((v1_orders_2 (k4_waybel10 A)) &  ((v4_yellow_0 (k4_waybel10 A) (k3_waybel10 A)) & (m1_yellow_0 (k4_waybel10 A) (k3_waybel10 A))) ) ) ) ) ).
tt(dt_k4_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v6_waybel_0 (k4_waybel11 A B) A) & (l1_waybel_0 (k4_waybel11 A B) A)) ) ) ).
tt(dt_k4_waybel17,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v6_waybel_0 (k4_waybel17 A B) A) & (l1_waybel_0 (k4_waybel17 A B) A)) ) ) ).
tt(dt_k4_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (k4_waybel18 A B C)))  & (l1_pre_topc (k4_waybel18 A B C))) ) ) ).
tt(dt_k4_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_waybel_1 A B)) &  ((v1_funct_2 (k4_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k4_waybel_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_waybel20,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v1_xboole_0 (k4_waybel20 A B)))  & (m1_subset_1 (k4_waybel20 A B) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) ) ) ).
tt(dt_k4_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v1_funct_1 (k4_waybel23 A B)) &  ((v1_funct_2 (k4_waybel23 A B) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 (k4_waybel23 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) ) ) ) ).
tt(dt_k4_waybel26,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k4_waybel26 A B C D)) &  ((v1_funct_2 (k4_waybel26 A B C D) (u1_struct_0 (k1_waybel26 C A)) (u1_struct_0 (k1_waybel26 B A))) & (m1_subset_1 (k4_waybel26 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 C A)) (u1_struct_0 (k1_waybel26 B A)))))) ) ) ) ).
tt(dt_k4_waybel27,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k4_waybel27 A B C D E F)) &  ((v1_funct_2 (k4_waybel27 A B C D E F) (u1_struct_0 (k2_waybel27 B C)) (u1_struct_0 (k2_waybel27 A D))) & (m1_subset_1 (k4_waybel27 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel27 B C)) (u1_struct_0 (k2_waybel27 A D)))))) ) ) ) ).
tt(dt_k4_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k4_waybel28 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k4_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k4_waybel29 A)) &  ((v1_funct_2 (k4_waybel29 A) (u1_struct_0 (k1_waybel26 A k9_waybel18)) (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) & (m1_subset_1 (k4_waybel29 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A k9_waybel18)) (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))))))) ) ) ) ).
tt(dt_k4_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_funct_1 (k4_waybel_2 A)) &  ((v1_funct_2 (k4_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 (k4_waybel_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k4_waybel34 A)))  &  ((v2_altcat_1 (k4_waybel34 A)) &  ((v6_altcat_1 (k4_waybel34 A)) &  ((v11_altcat_1 (k4_waybel34 A)) &  ((v12_altcat_1 (k4_waybel34 A)) &  ((v2_yellow21 (k4_waybel34 A)) & (l2_altcat_1 (k4_waybel34 A))) ) ) ) ) ) ) ) ).
tt(dt_k4_waybel35,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (m1_subset_1 (k4_waybel35 A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_waybel_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k4_waybel_3 A B C D) (u1_struct_0 (k3_waybel_3 A B D)))) ) ).
tt(dt_k4_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k4_waybel_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k4_waybel_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) )  =>  ((v1_funct_1 (k4_waybel_5 A B)) &  ((v1_funct_2 (k4_waybel_5 A B) (k9_xtuple_0 B) (u1_struct_0 A)) & (m1_subset_1 (k4_waybel_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k4_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (m1_subset_1 (k4_waybel_6 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v6_waybel_0 (k4_waybel_9 A B C) A) & (l1_waybel_0 (k4_waybel_9 A B C) A)) ) ) ).
tt(dt_k4_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_weddwitt A)))  &  ( (~ (v6_struct_0 (k4_weddwitt A)))  &  ((v13_algstr_0 (k4_weddwitt A)) &  ((v33_algstr_0 (k4_weddwitt A)) &  ((v36_algstr_0 (k4_weddwitt A)) &  ((v2_rlvect_1 (k4_weddwitt A)) &  ((v3_rlvect_1 (k4_weddwitt A)) &  ((v4_rlvect_1 (k4_weddwitt A)) &  ((v3_group_1 (k4_weddwitt A)) &  ((v5_group_1 (k4_weddwitt A)) &  ((v4_vectsp_1 (k4_weddwitt A)) &  ((v5_vectsp_1 (k4_weddwitt A)) & (l6_algstr_0 (k4_weddwitt A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k4_weierstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_weierstr A B)) &  ((v1_funct_2 (k4_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k4_weierstr A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k4_wsierp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k4_wsierp_1 A B C) A)) ) ).
tt(dt_k4_xboole_0,ax,$true).
tt(dt_k4_xboolean,ax,$true).
tt(dt_k4_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xcmplx_0 (k4_xcmplx_0 A))) ) ).
tt(dt_k4_xtuple_0,ax,$true).
tt(dt_k4_xxreal_0,ax,$true).
tt(dt_k4_xxreal_1,ax,$true).
tt(dt_k4_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k4_xxreal_3 A B))) ) ).
tt(dt_k4_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k4_yellow_0 A) (u1_struct_0 A))) ) ).
tt(dt_k4_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k4_yellow18 A)))  &  ((v2_altcat_1 (k4_yellow18 A)) &  ((v6_altcat_1 (k4_yellow18 A)) &  ((v11_altcat_1 (k4_yellow18 A)) &  ((v12_altcat_1 (k4_yellow18 A)) &  ((v4_yellow18 (k4_yellow18 A)) & (l2_altcat_1 (k4_yellow18 A))) ) ) ) ) ) ) ) ).
tt(dt_k4_yellow_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  & (m1_subset_1 C A)) )  => (l1_orders_2 (k4_yellow_1 A B C))) ) ).
tt(dt_k4_yellow20,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  ((v9_functor0 (k4_yellow20 A B C D) C B) &  ((v15_functor0 (k4_yellow20 A B C D) C B) & (m2_functor0 (k4_yellow20 A B C D) C B)) ) ) ) ).
tt(dt_k4_yellow21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v3_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v3_orders_2 (k4_yellow21 A B)) &  ((v4_orders_2 (k4_yellow21 A B)) &  ((v5_orders_2 (k4_yellow21 A B)) &  ((v1_lattice3 (k4_yellow21 A B)) &  ((v2_lattice3 (k4_yellow21 A B)) &  ((v3_lattice3 (k4_yellow21 A B)) & (l1_orders_2 (k4_yellow21 A B))) ) ) ) ) ) ) ) ).
tt(dt_k4_yellow_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (v1_relat_1 B))  => (m1_subset_1 (k4_yellow_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  => (m1_subset_1 (k4_yellow_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k4_yellow_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k4_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (l1_waybel_0 B A))  => (m1_subset_1 (k4_yellow_6 A B) (u1_struct_0 A))) ) ).
tt(dt_k4_zf_fund1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)) => (m1_subset_1 (k4_zf_fund1 A) (k1_zfmisc_1 k4_ordinal1))) ) ).
tt(dt_k4_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ( (~ (v1_xboole_0 (k4_zf_lang1 A)))  & (m1_subset_1 (k4_zf_lang1 A) (k1_zfmisc_1 k1_zf_lang))) ) ) ).
tt(dt_k4_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) & (m1_subset_1 B k1_zf_lang))  => (m2_finseq_1 (k4_zf_lang A B) k5_numbers)) ) ).
tt(dt_k4_zfmisc_1,ax,$true).
tt(dt_k4_zf_model,ax,$true).
tt(dt_k4_zf_refle,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_zf_refle A B)))  & (m1_subset_1 (k4_zf_refle A B) (k1_zfmisc_1 A))) ) ) ).
tt(dt_k4_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((v1_zmodul01 (k4_zmodul01 A)) & (m1_zmodul01 (k4_zmodul01 A) A)) ) ) ).
tt(dt_k50_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k50_gfacirc1 A B C) (k49_gfacirc1 A B C)) &  ((v4_msafree2 (k50_gfacirc1 A B C) (k49_gfacirc1 A B C)) &  ((v4_circcomb (k50_gfacirc1 A B C) (k49_gfacirc1 A B C)) &  ((v6_circcomb (k50_gfacirc1 A B C) (k49_gfacirc1 A B C)) & (l3_msualg_1 (k50_gfacirc1 A B C) (k49_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k50_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  & (m1_subset_1 C (k1_zfmisc_1 A))) )  => (m1_subset_1 (k50_modelc_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k50_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k50_valued_1 A B)) & (v1_funct_1 (k50_valued_1 A B))) ) ) ).
tt(dt_k51_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  => (m1_subset_1 (k51_abcmiz_1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k51_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k51_aofa_i00 A B C D E F) A) & (m1_subset_1 (k51_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k51_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  & (m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C)))) ) )  => (m1_subset_1 (k51_modelc_1 A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k51_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k51_valued_1 A B C D E)) & (m1_subset_1 (k51_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k51_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k51_valued_2 A B C)) & (v1_funct_1 (k51_valued_2 A B C))) ) ) ).
tt(dt_k52_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  => (m1_subset_1 (k52_abcmiz_1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k52_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  & (m1_subset_1 D (k1_zfmisc_1 A))) ) )  => (m1_subset_1 (k52_modelc_1 A B C D) (u1_struct_0 (k48_modelc_1 A B C)))) ) ).
tt(dt_k52_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((v1_funct_1 (k52_valued_1 A B C D E)) & (m1_subset_1 (k52_valued_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k52_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k52_valued_2 A B C D)) & (m1_subset_1 (k52_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k53_abcmiz_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D A) & (m1_subset_1 E A))  => (m1_subset_1 (k53_abcmiz_1 A B C D E) A)) ) ).
tt(dt_k53_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((v15_aofa_000 (k53_aofa_i00 A B C D E F) A) & (m1_subset_1 (k53_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k53_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  &  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) & (m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C)))) ) ) )  => (m1_subset_1 (k53_modelc_1 A B C D E) (u1_struct_0 (k48_modelc_1 A B C)))) ) ).
tt(dt_k53_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k53_valued_2 A B C D)) & (m1_subset_1 (k53_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k54_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)))  =>  ((v1_funct_1 (k54_abcmiz_1 A B)) & (m1_subset_1 (k54_abcmiz_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) ) ).
tt(dt_k54_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((v15_aofa_000 (k54_aofa_i00 A B C D E F) A) & (m1_subset_1 (k54_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k54_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  &  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) & (m1_subset_1 E (k1_zfmisc_1 A))) ) ) )  => (m1_subset_1 (k54_modelc_1 A B C D E) (k1_zfmisc_1 A))) ) ).
tt(dt_k54_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) & (v3_valued_0 (k54_valued_1 A))) ) ) ) ).
tt(dt_k55_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) )  => (m4_abcmiz_1 (k55_abcmiz_1 A B) A (k28_abcmiz_1 A))) ) ).
tt(dt_k55_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((v15_aofa_000 (k55_aofa_i00 A B C D E F) A) & (m1_subset_1 (k55_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k55_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((m1_modelc_1 C A B) & (m1_subset_1 D k5_numbers)) ) )  => (m1_modelc_1 (k55_modelc_1 A B C D) A B)) ) ).
tt(dt_k55_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k55_valued_1 A B C)) & (m1_subset_1 (k55_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k56_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  => (m1_subset_1 (k56_abcmiz_1 A B C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ).
tt(dt_k56_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((v15_aofa_000 (k56_aofa_i00 A B C D E F) A) & (m1_subset_1 (k56_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k56_modelc_1,ax,$true).
tt(dt_k56_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k56_valued_1 A B C)) & (m1_subset_1 (k56_valued_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k57_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v1_relat_1 (k57_abcmiz_1 A B C)) &  ((v1_funct_1 (k57_abcmiz_1 A B C)) & (v1_finseq_1 (k57_abcmiz_1 A B C))) ) ) ) ).
tt(dt_k57_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k57_aofa_i00 A B C D E F) A) & (m1_subset_1 (k57_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k57_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((m1_modelc_1 C A B) &  ((m1_modelc_1 D A B) & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_funct_1 (k57_modelc_1 A B C D E)) &  ((v1_funct_2 (k57_modelc_1 A B C D E) k5_numbers A) & (m1_subset_1 (k57_modelc_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(dt_k57_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k57_valued_2 A B C)) & (v1_funct_1 (k57_valued_2 A B C))) ) ) ).
tt(dt_k58_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_finseq_1 C (k34_abcmiz_1 A))) )  => (m1_trees_4 (k58_abcmiz_1 A B C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A))) ) ).
tt(dt_k58_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k58_aofa_i00 A B C D E F) A) & (m1_subset_1 (k58_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k58_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  & (m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C)))) ) )  =>  ((v1_funct_1 (k58_modelc_1 A B C D)) &  ((v1_funct_2 (k58_modelc_1 A B C D) (k1_zfmisc_1 A) (k1_zfmisc_1 A)) &  ((v6_cohsp_1 (k58_modelc_1 A B C D)) & (m1_subset_1 (k58_modelc_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A))))) ) ) ) ) ).
tt(dt_k58_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k58_valued_2 A B C D)) & (m1_subset_1 (k58_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k59_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k14_abcmiz_1 A))) )  => (m1_abcmiz_1 (k59_abcmiz_1 A B C) A (k14_abcmiz_1 A))) ) ).
tt(dt_k59_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k59_aofa_i00 A B C D E F) A) & (m1_subset_1 (k59_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k59_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  &  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) &  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) & (m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C)))) ) ) ) )  => (m1_subset_1 (k59_modelc_1 A B C D E F) (u1_struct_0 (k48_modelc_1 A B C)))) ) ).
tt(dt_k59_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k59_valued_2 A B C D)) & (m1_subset_1 (k59_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k5_abcmiz_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l2_abcmiz_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_abcmiz_0 A))) )  => (m1_subset_1 (k5_abcmiz_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_abcmiz_a,ax, ( (~ (v1_xboole_0 k5_abcmiz_a))  & (m1_subset_1 k5_abcmiz_a (k1_zfmisc_1 k20_abcmiz_1))) ).
tt(dt_k5_afinsq_1,ax, (! [A:$i] :  ((v1_relat_1 (k5_afinsq_1 A)) & (v1_funct_1 (k5_afinsq_1 A))) ) ).
tt(dt_k5_afinsq_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 (k5_afinsq_2 A B)) &  ((v1_funct_1 (k5_afinsq_2 A B)) &  ((v5_ordinal1 (k5_afinsq_2 A B)) & (v1_finset_1 (k5_afinsq_2 A B))) ) ) ) ) ).
tt(dt_k5_afproj,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_afproj A B) (k1_zfmisc_1 (k1_afproj A)))) ) ).
tt(dt_k5_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v8_algstr_0 (k5_afvect0 A B)) & (l2_algstr_0 (k5_afvect0 A B))) ) ) ).
tt(dt_k5_alg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  & (m1_alg_1 B A))  =>  ((v1_funct_1 (k5_alg_1 A B)) &  ((v1_funct_2 (k5_alg_1 A B) (u1_struct_0 A) (u1_struct_0 (k4_alg_1 A B))) & (m1_subset_1 (k5_alg_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_alg_1 A B)))))) ) ) ) ).
tt(dt_k5_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l2_algstr_0 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_algstr_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_algstr_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_algstr_4 A B)) &  ((v1_funct_2 (k5_algstr_4 A B) (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B))) & (m1_subset_1 (k5_algstr_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B)))))) ) ) ) ).
tt(dt_k5_altcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (k1_altcat_1 A B C)) & (m1_subset_1 F (k1_altcat_1 A C D))) ) ) ) )  => (m1_subset_1 (k5_altcat_1 A B C D E F) (k1_altcat_1 A B D))) ) ).
tt(dt_k5_altcat_2,ax, ((v6_altcat_1 k5_altcat_2) & (l2_altcat_1 k5_altcat_2)) ).
tt(dt_k5_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_altcat_4 A)))  &  ((v2_altcat_1 (k5_altcat_4 A)) &  ((v6_altcat_1 (k5_altcat_4 A)) & (m1_altcat_2 (k5_altcat_4 A) A)) ) ) ) ) ).
tt(dt_k5_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) => (m1_subset_1 (k5_ami_2 A) k5_numbers)) ) ).
tt(dt_k5_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k5_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k5_amistd_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  & (m1_subset_1 C (u1_compos_1 B))) )  => (m1_subset_1 (k5_amistd_4 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k5_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m2_subset_1 (k5_ami_wstd A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k5_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_analoaf (k5_analort A B C)) & (l1_analoaf (k5_analort A B C))) ) ) ).
tt(dt_k5_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) & (l1_collsp (k5_anproj_1 A))) ) ) ).
tt(dt_k5_aofa_000,ax,$true).
tt(dt_k5_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k5_aofa_i00 A B)) &  ((v5_relat_1 (k5_aofa_i00 A B) k4_numbers) & (v1_funct_1 (k5_aofa_i00 A B))) ) ) ) ).
tt(dt_k5_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) => (m1_subset_1 (k5_armstrng A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_armstrng A)) (k9_setfam_1 (u1_armstrng A)))))) ) ).
tt(dt_k5_arytm_0,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k5_arytm_0 A B) k2_numbers)) ) ).
tt(dt_k5_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_arytm_2) & (m1_subset_1 B k1_arytm_2))  => (m2_subset_1 (k5_arytm_2 A B) (k1_zfmisc_1 k5_arytm_3) k1_arytm_2)) ) ).
tt(dt_k5_arytm_3,ax,$true).
tt(dt_k5_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k5_asympt_0 A B)) &  ((v1_funct_2 (k5_asympt_0 A B) k5_numbers k1_numbers) & (m1_subset_1 (k5_asympt_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k5_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k5_asympt_1 A)) &  ((v1_funct_2 (k5_asympt_1 A) k5_numbers k1_numbers) & (m1_subset_1 (k5_asympt_1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k5_autalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v1_xboole_0 (k5_autalg_1 A B)))  & (m1_subset_1 (k5_autalg_1 A B) (k1_zfmisc_1 (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))))) ) ) ).
tt(dt_k5_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v15_algstr_0 (k5_autgroup A)) &  ((v1_group_3 (k5_autgroup A) (k3_autgroup A)) & (m1_group_2 (k5_autgroup A) (k3_autgroup A))) ) ) ) ).
tt(dt_k5_bagorder,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  ((v1_partfun1 (k5_bagorder A B) (k15_pre_poly A)) &  ((v1_relat_2 (k5_bagorder A B)) &  ((v4_relat_2 (k5_bagorder A B)) &  ((v8_relat_2 (k5_bagorder A B)) & (m1_subset_1 (k5_bagorder A B) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k5_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_bcialg_1 A)))  & (m1_subset_1 (k5_bcialg_1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k5_bcialg_2,ax,$true).
tt(dt_k5_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  ((v1_funct_1 (k5_bcialg_4 A)) &  ((v1_funct_2 (k5_bcialg_4 A) (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 (k5_bcialg_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_bcialg_6,ax,$true).
tt(dt_k5_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k5_bhsp_1 A B C)) &  ((v1_funct_2 (k5_bhsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_bhsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_bhsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k5_bhsp_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_bhsp_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k5_bhsp_4 A B C)) &  ((v1_funct_2 (k5_bhsp_4 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_bhsp_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_bhsp_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) )  => (m1_subset_1 (k5_bhsp_5 A B C D E) A)) ) ).
tt(dt_k5_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k5_bilinear A B C D E)) &  ((v1_funct_2 (k5_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k5_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_binari_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  => (m1_subset_1 (k5_binari_2 A B C) k6_margrel1)) ) ).
tt(dt_k5_binarith,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1)) )  =>  ((v3_card_1 (k5_binarith A B) A) & (m2_finseq_1 (k5_binarith A B) k5_numbers)) ) ) ).
tt(dt_k5_binom,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k5_binom A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  => (m1_subset_1 (k5_binop_1 A B C D) A)) ) ).
tt(dt_k5_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k5_binop_2 A B) k2_numbers)) ) ).
tt(dt_k5_bor_cant,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k5_bor_cant A)) &  ((v1_funct_2 (k5_bor_cant A) k5_numbers k5_numbers) & (m1_subset_1 (k5_bor_cant A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k5_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m1_connsp_2 E A C) & (m1_connsp_2 F B D)) ) ) ) )  => (m1_connsp_2 (k5_borsuk_1 A B C D E F) (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) ) ).
tt(dt_k5_borsuk_6,ax, ((v1_funct_1 k5_borsuk_6) &  ((v1_funct_2 k5_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (m1_subset_1 k5_borsuk_6 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) ).
tt(dt_k5_borsuk_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  & (v1_xreal_0 C))  =>  ((v1_funct_1 (k5_borsuk_7 A B C)) &  ((v1_funct_2 (k5_borsuk_7 A B C) A (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k5_borsuk_7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k5_brouwer,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k2_brouwer A C B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k2_brouwer A C B)))))) ) ) ) )  =>  ((v1_funct_1 (k5_brouwer A B C D)) &  ((v1_funct_2 (k5_brouwer A B C D) (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k7_toprealb A C B))) & (m1_subset_1 (k5_brouwer A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer A C B)) (u1_struct_0 (k7_toprealb A C B)))))) ) ) ) ).
tt(dt_k5_bspace,ax, (! [A:$i] :  ((v1_funct_1 (k5_bspace A)) &  ((v1_funct_2 (k5_bspace A) (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A)) (k1_zfmisc_1 A)) & (m1_subset_1 (k5_bspace A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A)) (k1_zfmisc_1 A))))) ) ) ).
tt(dt_k5_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k5_bvfunc_1 A B C)) &  ((v1_funct_2 (k5_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k5_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k5_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k5_bvfunc26 A B C)) &  ((v1_funct_2 (k5_bvfunc26 A B C) A k6_margrel1) & (m1_subset_1 (k5_bvfunc26 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k5_bvfunc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_eqrel_1 B A) & (m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A)))) )  => (m1_eqrel_1 (k5_bvfunc_2 A B C) A)) ) ).
tt(dt_k5_c0sp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k5_c0sp1 A B)) &  ((v1_funct_2 (k5_c0sp1 A B) (k2_zfmisc_1 k1_numbers B) B) & (m1_subset_1 (k5_c0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers B) B)))) ) ) ) ).
tt(dt_k5_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  => (l1_lopban_2 (k5_c0sp2 A))) ) ).
tt(dt_k5_calcul_2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k5_calcul_2 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k5_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (m1_subset_1 (k5_card_1 A) k4_ordinal1)) ) ).
tt(dt_k5_card_3,ax,$true).
tt(dt_k5_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  => (m2_card_fil (k5_card_fil A) A)) ) ).
tt(dt_k5_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_cat_1 E A B C) & (m1_cat_1 F A C D)) ) ) ) )  => (m1_cat_1 (k5_cat_1 A B C D E F) A B D)) ) ).
tt(dt_k5_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m3_cat_2 B A))  => (m2_cat_1 (k5_cat_2 A B) B A)) ) ).
tt(dt_k5_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 (k2_oppcat_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 (k2_oppcat_1 A)))))) ) )  =>  ((v1_funct_1 (k5_cat_3 A B C)) &  ((v1_funct_2 (k5_cat_3 A B C) B (u4_struct_0 A)) & (m1_subset_1 (k5_cat_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) ) ) ).
tt(dt_k5_cat_4,ax, (! [A:$i,B:$i] :  ((v2_cat_4 (k5_cat_4 A B)) & (l1_cat_4 (k5_cat_4 A B))) ) ).
tt(dt_k5_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_cat_5 A B)))  &  ( (~ (v11_struct_0 (k5_cat_5 A B)))  &  ((v2_cat_1 (k5_cat_5 A B)) &  ((v3_cat_1 (k5_cat_5 A B)) &  ((v4_cat_1 (k5_cat_5 A B)) &  ((v5_cat_1 (k5_cat_5 A B)) &  ((v6_cat_1 (k5_cat_5 A B)) & (l1_cat_1 (k5_cat_5 A B))) ) ) ) ) ) ) ) ) ).
tt(dt_k5_catalg_1,ax,$true).
tt(dt_k5_cc0sp1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ( (~ (v1_xboole_0 (k5_cc0sp1 A B)))  & (m1_subset_1 (k5_cc0sp1 A B) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k5_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  => (l1_clopban2 (k5_cc0sp2 A))) ) ).
tt(dt_k5_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m2_funct_2 (k5_cfuncdom A) A k2_numbers (k9_funct_2 A k2_numbers))) ) ).
tt(dt_k5_cgames_1,ax,(m1_subset_1 k5_cgames_1 (k2_cgames_1 1))).
tt(dt_k5_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k5_chain_1 A B C) (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ).
tt(dt_k5_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v3_msualg_1 (k5_circcmb3 A B C D) (k4_circcmb3 A B C D)) & (m2_circcmb3 (k5_circcmb3 A B C D) B (k4_circcmb3 A B C D))) ) ) ).
tt(dt_k5_circcomb,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v11_struct_0 (k5_circcomb A B)))  &  ((v1_msualg_1 (k5_circcomb A B)) & (l1_msualg_1 (k5_circcomb A B))) ) ) ) ).
tt(dt_k5_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  &  ((v4_msualg_1 D A) & (l3_msualg_1 D A)) ) ) )  => (m2_pboole (k5_circtrm1 A B C D) (u4_struct_0 (k1_circtrm1 A B C)) (k3_relat_1 (u1_msualg_1 (k1_circtrm1 A B C)) (k6_finseq_2 (u1_struct_0 (k1_circtrm1 A B C)) (k4_circtrm1 A B C D))) (k3_relat_1 (u2_msualg_1 (k1_circtrm1 A B C)) (k4_circtrm1 A B C D)))) ) ).
tt(dt_k5_circuit1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C))) ) )  => (m2_subset_1 (k5_circuit1 A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k5_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_msafree2 D A B)) ) )  => (m1_subset_1 (k5_circuit2 A B C D) (k1_funct_1 (u3_msualg_1 A B) C))) ) ).
tt(dt_k5_classes1,ax,$true).
tt(dt_k5_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k5_classes2 A B C) A)) ) ).
tt(dt_k5_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k5_clopban1 A B) (k1_zfmisc_1 (u1_struct_0 (k3_clopban1 (u1_struct_0 A) B))))) ) ).
tt(dt_k5_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_clopban2 A)) &  ((v1_funct_2 (k5_clopban2 A) (k2_zfmisc_1 (k8_clopban1 A A) (k8_clopban1 A A)) (k8_clopban1 A A)) & (m1_subset_1 (k5_clopban2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_clopban1 A A) (k8_clopban1 A A)) (k8_clopban1 A A))))) ) ) ) ).
tt(dt_k5_clopban3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k5_clopban3 A B)) &  ((v1_funct_2 (k5_clopban3 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_clopban3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_clopban4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D k5_numbers)) ) )  =>  ((v1_funct_1 (k5_clopban4 A B C D)) &  ((v1_funct_2 (k5_clopban4 A B C D) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_clopban4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m2_pboole C A B B))  => (m3_pboole (k5_closure1 A B C) A B)) ) ).
tt(dt_k5_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))))  => (m3_pboole (k5_closure2 A B C) A (k1_mboolean A B))) ) ).
tt(dt_k5_clvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_clvect_1 C A)) )  => (m1_subset_1 (k5_clvect_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k5_clvect_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_cohsp_1,ax,$true).
tt(dt_k5_coh_sp,ax,$true).
tt(dt_k5_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ((l1_combgras C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 B)))) ) )  => (m1_subset_1 (k5_combgras A B C D) (k1_zfmisc_1 (u1_incsp_1 A)))) ) ).
tt(dt_k5_complex1,ax,(m1_subset_1 k5_complex1 k2_numbers)).
tt(dt_k5_complsp2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k4_finseq_2 A k2_numbers)))  => (m2_finseq_2 (k5_complsp2 A B) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k5_compos_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) &  ((v2_compos_0 A) & (v3_compos_0 A)) ) )  &  ((m1_subset_1 B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k5_compos_0 A B C) A)) ) ).
tt(dt_k5_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k5_compos_1 A B C)) &  ((v4_relat_1 (k5_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k5_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k5_compos_1 A B C)) & (v1_finset_1 (k5_compos_1 A B C))) ) ) ) ) ) ).
tt(dt_k5_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k5_comput_1 A B)) &  ((v4_relat_1 (k5_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 A B)) &  ((v4_valued_0 (k5_comput_1 A B)) & (v2_margrel1 (k5_comput_1 A B))) ) ) ) ) ) ).
tt(dt_k5_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_funct_1 (k5_comseq_3 A B)) & (m1_subset_1 (k5_comseq_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k5_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v4_conlat_1 (k5_conlat_1 A) A) &  ( (~ (v5_conlat_1 (k5_conlat_1 A) A))  &  ((v7_conlat_1 (k5_conlat_1 A) A) &  ((v8_conlat_1 (k5_conlat_1 A) A) & (l2_conlat_1 (k5_conlat_1 A) A)) ) ) ) ) ) ).
tt(dt_k5_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k5_conlat_2 A)) &  ((v1_funct_2 (k5_conlat_2 A) (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A))) & (m1_subset_1 (k5_conlat_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)))))) ) ) ) ).
tt(dt_k5_connsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B))))) )  => (m1_subset_1 (k5_connsp_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  => (m1_convex4 (k5_convex4 A B C) A)) ) ).
tt(dt_k5_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) ) )  => (m1_subset_1 (k5_convfun1 A B) (k1_zfmisc_1 (u1_struct_0 (k3_convfun1 A k4_convfun1))))) ) ).
tt(dt_k5_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m2_subset_1 (k5_cqc_lang A) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k5_cqc_sim1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m1_finseq_1 C (k2_qc_lang1 A))) )  & (m1_subset_1 D (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)))) ) )  =>  ((v5_relat_1 (k5_cqc_sim1 A B C D) (k3_qc_lang1 A)) &  ((v3_card_1 (k5_cqc_sim1 A B C D) B) & (m2_finseq_1 (k5_cqc_sim1 A B C D) (k2_qc_lang1 A))) ) ) ) ).
tt(dt_k5_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_csspace4 A B)))  &  ((v13_algstr_0 (k5_csspace4 A B)) &  ((v2_rlvect_1 (k5_csspace4 A B)) &  ((v3_rlvect_1 (k5_csspace4 A B)) &  ((v4_rlvect_1 (k5_csspace4 A B)) &  ((v2_clvect_1 (k5_csspace4 A B)) &  ((v3_clvect_1 (k5_csspace4 A B)) &  ((v4_clvect_1 (k5_csspace4 A B)) &  ((v5_clvect_1 (k5_csspace4 A B)) & (l1_clvect_1 (k5_csspace4 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_csspace,ax, ((v1_funct_1 k5_csspace) &  ((v1_funct_2 k5_csspace (k2_zfmisc_1 k2_numbers k1_csspace) k1_csspace) & (m1_subset_1 k5_csspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k1_csspace) k1_csspace)))) ) ).
tt(dt_k5_decomp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_decomp_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  & (m1_subset_1 C (k4_finseq_2 (k4_nat_1 2 B) A))) )  => (m2_finseq_2 (k5_descip_1 A B C) A (k4_finseq_2 B A))) ) ).
tt(dt_k5_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k5_dickson A)) & (l1_orders_2 (k5_dickson A))) ) ) ).
tt(dt_k5_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k5_diff_1 A B)) & (m1_subset_1 (k5_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k5_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k5_dilworth A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_dist_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  => (m1_subset_1 (k5_dist_1 A B) (k1_zfmisc_1 (k3_finseq_2 A)))) ) ).
tt(dt_k5_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ((m1_subset_1 E A) &  ((m1_subset_1 F B) &  ((m1_subset_1 G C) & (m1_subset_1 H D)) ) ) ) ) ) )  => (m1_subset_1 (k5_domain_1 A B C D E F G H) (k4_zfmisc_1 A B C D))) ) ).
tt(dt_k5_dtconstr,ax, ( (~ (v2_struct_0 k5_dtconstr))  &  ((v1_lang1 k5_dtconstr) & (l1_lang1 k5_dtconstr)) ) ).
tt(dt_k5_dynkin,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (m1_dynkin (k5_dynkin A B) A)) ) ).
tt(dt_k5_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 C (u1_struct_0 (k9_int_3 A)))) )  =>  ((v1_funct_1 (k5_ec_pf_1 A B C)) &  ((v1_funct_2 (k5_ec_pf_1 A B C) (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 (k5_ec_pf_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)))))) ) ) ) ).
tt(dt_k5_ec_pf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) &  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 D (k6_ec_pf_1 A B C))) ) )  => (m1_subset_1 (k5_ec_pf_2 A B C D) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k5_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v1_funct_1 (k5_endalg A B)) &  ((v1_funct_2 (k5_endalg A B) (k2_zfmisc_1 (k4_endalg A B) (k4_endalg A B)) (k4_endalg A B)) & (m1_subset_1 (k5_endalg A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_endalg A B) (k4_endalg A B)) (k4_endalg A B))))) ) ) ) ).
tt(dt_k5_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k5_ens_1 A B) (k2_ens_1 A))) ) ).
tt(dt_k5_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v1_matrix_1 (k5_entropy1 A)) & (m2_finseq_1 (k5_entropy1 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k5_enumset1,ax,$true).
tt(dt_k5_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v3_relat_2 (k5_eqrel_1 A B C)) &  ((v8_relat_2 (k5_eqrel_1 A B C)) &  ((v1_partfun1 (k5_eqrel_1 A B C) A) & (m1_subset_1 (k5_eqrel_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k5_e_siec,ax, (! [A:$i] :  ((v1_e_siec (k5_e_siec A)) &  ((v2_e_siec (k5_e_siec A)) &  ((v3_e_siec (k5_e_siec A)) & (l1_e_siec (k5_e_siec A))) ) ) ) ).
tt(dt_k5_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (u1_struct_0 (k15_euclid A)))) ) )  => (m1_subset_1 (k5_euclid_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k5_euclid_5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 3))))  => (m1_subset_1 (k5_euclid_5 A B) (u1_struct_0 (k15_euclid 3)))) ) ).
tt(dt_k5_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_finseq_1 B (k1_euclid A)))  => (m2_finseq_2 (k5_euclid_7 A B) k1_numbers (k1_euclid A))) ) ).
tt(dt_k5_euclid_8,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_euclid 3)) & (m1_subset_1 B (k1_euclid 3)))  => (m2_finseq_2 (k5_euclid_8 A B) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k5_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k14_euclid A))))  => (m1_subset_1 (k5_euclid_9 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))))) ) ).
tt(dt_k5_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_2 (k5_euclid A) k1_numbers (k1_euclid A))) ) ).
tt(dt_k5_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k5_euclidlp A) (k1_zfmisc_1 (k1_zfmisc_1 (k1_euclid A))))) ) ).
tt(dt_k5_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((v1_funct_1 (k5_exchsort A B C D E)) &  ((v1_funct_2 (k5_exchsort A B C D E) A B) & (m1_subset_1 (k5_exchsort A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k5_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  &  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  & (v7_ordinal1 E)) ) ) )  =>  ((v1_relat_1 (k5_extpro_1 A B C D E)) &  ((v4_relat_1 (k5_extpro_1 A B C D E) (u1_struct_0 B)) &  ((v1_funct_1 (k5_extpro_1 A B C D E)) &  ((v5_funct_1 (k5_extpro_1 A B C D E) (k2_memstr_0 A B)) & (v1_partfun1 (k5_extpro_1 A B C D E) (u1_struct_0 B))) ) ) ) ) ) ).
tt(dt_k5_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k5_facirc_1 A B C D) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k5_facirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (m2_subset_1 (k5_facirc_2 A B C) (u1_struct_0 (k3_facirc_2 A B C)) (k3_msafree2 (k3_facirc_2 A B C)))) ) ).
tt(dt_k5_ff_siec,ax, (! [A:$i] :  ((v1_petri (k5_ff_siec A)) &  ((v1_net_1 (k5_ff_siec A)) & (l1_petri (k5_ff_siec A))) ) ) ).
tt(dt_k5_fib_num2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_trees_4 (k5_fib_num2 A) k1_numbers k5_numbers)) ) ).
tt(dt_k5_filter_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k5_filter_0 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_filter_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_filter_1 A B C) (u1_struct_0 (k4_filter_1 A B)))) ) ).
tt(dt_k5_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_xboole_0 (k5_filter_2 A)))  &  ((v18_lattices (k5_filter_2 A) A) &  ((v21_lattices (k5_filter_2 A) A) & (m1_subset_1 (k5_filter_2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k5_finance1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  => (m1_subset_1 (k5_finance1 A B C) k1_numbers)) ) ).
tt(dt_k5_finseq_1,ax,$true).
tt(dt_k5_finseq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C A)) )  => (m2_finseq_2 (k5_finseq_2 A B C) A (k4_finseq_2 B A))) ) ).
tt(dt_k5_finseq_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k5_finseq_4 A B)) &  ((v1_funct_1 (k5_finseq_4 A B)) & (v1_finseq_1 (k5_finseq_4 A B))) ) ) ) ).
tt(dt_k5_finseq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((m1_subset_1 C A) & (v7_ordinal1 D)) ) )  => (m2_finseq_1 (k5_finseq_5 A B C D) A)) ) ).
tt(dt_k5_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k5_finseq_8 A B C) A)) ) ).
tt(dt_k5_finseqop,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ((v1_funct_1 (k5_finseqop A B)) &  ((v1_funct_2 (k5_finseqop A B) A A) & (m1_subset_1 (k5_finseqop A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(dt_k5_finsub_1,ax, (! [A:$i] : (v4_finsub_1 (k5_finsub_1 A))) ).
tt(dt_k5_fintopo2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_fintopo2 A B C) k6_margrel1)) ) ).
tt(dt_k5_fintopo3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k5_fintopo3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_fintopo5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_orders_2 (k5_fintopo5 A B)) & (l1_orders_2 (k5_fintopo5 A B))) ) ) ).
tt(dt_k5_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (v7_ordinal1 C))  => (m1_subset_1 (k5_flang_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k5_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ((v1_funct_1 (k5_fomodel0 A B)) &  ((v1_funct_2 (k5_fomodel0 A B) (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A) & (m1_subset_1 (k5_fomodel0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A)))) ) ) ) ).
tt(dt_k5_fomodel1,ax,$true).
tt(dt_k5_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k5_fomodel2 A B C)) & (v1_funct_1 (k5_fomodel2 A B C))) ) ) ).
tt(dt_k5_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_relat_1 (k5_fomodel3 A B)) & (v1_funct_1 (k5_fomodel3 A B))) ) ) ).
tt(dt_k5_fomodel4,ax,$true).
tt(dt_k5_freealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k5_freealg A B C)))  &  ((v1_funct_1 (k5_freealg A B C)) &  ((v2_margrel1 (k5_freealg A B C)) &  ((v3_margrel1 (k5_freealg A B C) (k4_dtconstr (k3_freealg A B))) & (m1_subset_1 (k5_freealg A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B)))))) ) ) ) ) ) ).
tt(dt_k5_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k5_fscirc_1 A B C) (k3_fscirc_1 A B C)) &  ((v4_msafree2 (k5_fscirc_1 A B C) (k3_fscirc_1 A B C)) &  ((v4_circcomb (k5_fscirc_1 A B C) (k3_fscirc_1 A B C)) &  ((v6_circcomb (k5_fscirc_1 A B C) (k3_fscirc_1 A B C)) & (l3_msualg_1 (k5_fscirc_1 A B C) (k3_fscirc_1 A B C))) ) ) ) ) ).
tt(dt_k5_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l3_fsm_1 C A B))  &  ((m1_subset_1 D (u1_struct_0 C)) & (m1_finseq_1 E A)) ) ) )  => (m2_finseq_1 (k5_fsm_1 A B C D E) B)) ) ).
tt(dt_k5_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) )  => (m1_subset_1 (k5_fsm_3 A B C D) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k5_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k5_ftacell1 A B C D E) (k3_msafree2 (k1_ftacell1 A B C D E)))) ).
tt(dt_k5_funcop_1,ax,$true).
tt(dt_k5_funcsdom,ax, (! [A:$i] :  ((v1_funct_1 (k5_funcsdom A)) &  ((v1_funct_2 (k5_funcsdom A) (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 (k5_funcsdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) ) ) ).
tt(dt_k5_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((v1_funct_1 (k5_funct_2 A B C D)) &  ((v1_funct_2 (k5_funct_2 A B C D) A C) & (m1_subset_1 (k5_funct_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ).
tt(dt_k5_funct_3,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k5_funct_3 A B)) &  ((v1_funct_2 (k5_funct_3 A B) B (k2_tarski k1_xboole_0 1)) & (m1_subset_1 (k5_funct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 B (k2_tarski k1_xboole_0 1))))) ) ) ).
tt(dt_k5_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) )  =>  ((v1_funct_1 (k5_funct_4 A B C D E)) &  ((v1_funct_2 (k5_funct_4 A B C D E) (k2_tarski B C) A) & (m1_subset_1 (k5_funct_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski B C) A)))) ) ) ) ).
tt(dt_k5_funct_5,ax,(m1_subset_1 k5_funct_5 1)).
tt(dt_k5_funct_6,ax,$true).
tt(dt_k5_funct_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funcop_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k5_funct_7 A B)) &  ((v1_funct_1 (k5_funct_7 A B)) & (v1_finseq_1 (k5_funct_7 A B))) ) ) ) ).
tt(dt_k5_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k5_functor0 A B C D E)) &  ((v1_funct_2 (k5_functor0 A B C D E) (k1_altcat_1 A D E) (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E))) & (m1_subset_1 (k5_functor0 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_altcat_1 A D E) (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)))))) ) ) ) ).
tt(dt_k5_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  &  ((m2_functor2 F A B C D) & (m2_functor2 G A B D E)) ) ) ) ) )  => (m2_functor2 (k5_functor2 A B C D E F G) A B C E)) ) ).
tt(dt_k5_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  &  ((m1_functor2 F A B D E) &  ((v15_functor0 G B C) & (m2_functor0 G B C)) ) ) ) ) ) )  => (m1_functor2 (k5_functor3 A B C D E F G) A C (k1_functor3 A B C D G) (k1_functor3 A B C E G))) ) ).
tt(dt_k5_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_relat_1 (k5_fuzzy_1 A) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_fuzzy_1 A)) &  ((v1_funct_2 (k5_fuzzy_1 A) A k1_numbers) & (m1_subset_1 (k5_fuzzy_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k5_fuzzy_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v5_relat_1 (k5_fuzzy_2 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_fuzzy_2 A B)) &  ((v1_funct_2 (k5_fuzzy_2 A B) (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 (k5_fuzzy_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) ).
tt(dt_k5_fuzzy_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v5_relat_1 (k5_fuzzy_4 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_fuzzy_4 A B)) &  ((v1_funct_2 (k5_fuzzy_4 A B) (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 (k5_fuzzy_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) ).
tt(dt_k5_fvaluat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_fvaluat1 B A))  => (m1_fvaluat1 (k5_fvaluat1 A B) A)) ) ).
tt(dt_k5_fvsum_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_finseq_1 B (u1_struct_0 A)))  => (m2_finseq_1 (k5_fvsum_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k5_gate_1,ax,$true).
tt(dt_k5_gate_5,ax,$true).
tt(dt_k5_gcd_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v3_gcd_1 A) & (l4_algstr_0 A)) ) ) )  &  ((m2_gcd_1 B A) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k5_gcd_1 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k5_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) & (m1_subset_1 H k5_numbers)) ) ) ) ) ) )  => (m2_finseq_1 (k5_genealg1 A B C D E F G H) (k3_card_3 A))) ) ).
tt(dt_k5_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_geomtrap A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_k5_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k5_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k5_gfacirc1 A B C)))  &  ((v1_msualg_1 (k5_gfacirc1 A B C)) &  ((v1_circcomb (k5_gfacirc1 A B C)) &  ((v2_circcomb (k5_gfacirc1 A B C)) &  ((v3_circcomb (k5_gfacirc1 A B C)) & (l1_msualg_1 (k5_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k5_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ( (~ (v2_struct_0 (k5_gfacirc2 A B C)))  &  ( (~ (v11_struct_0 (k5_gfacirc2 A B C)))  &  ((v1_msualg_1 (k5_gfacirc2 A B C)) &  ((v1_circcomb (k5_gfacirc2 A B C)) &  ((v2_circcomb (k5_gfacirc2 A B C)) &  ((v3_circcomb (k5_gfacirc2 A B C)) & (l1_msualg_1 (k5_gfacirc2 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k5_glib_000,ax, ( (~ (v1_xboole_0 k5_glib_000))  & (m1_subset_1 k5_glib_000 (k1_zfmisc_1 k5_numbers))) ).
tt(dt_k5_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k5_glib_001 A B C) (k6_glib_000 A))) ) ).
tt(dt_k5_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_glib_002 A)))  & (m1_subset_1 (k5_glib_002 A) k5_numbers)) ) ) ).
tt(dt_k5_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k5_glib_003 A)) &  ((v4_relat_1 (k5_glib_003 A) (k7_glib_000 A)) &  ((v1_funct_1 (k5_glib_003 A)) & (v1_partfun1 (k5_glib_003 A) (k7_glib_000 A))) ) ) ) ) ).
tt(dt_k5_glib_004,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k3_rfunct_3 A B) C)))  => (m2_rfunct_3 (k5_glib_004 A B C D) A B (k3_rfunct_3 A B))) ) ).
tt(dt_k5_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m1_subset_1 C (k6_glib_000 A))) )  => (m2_glib_005 (k5_glib_005 A B C) A B)) ) ).
tt(dt_k5_goboard5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k5_goboard5 A B) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k5_gobrd13,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k5_gobrd13 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k5_goedelcp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k3_cqc_lang A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_cqc_lang A))))) )  & (m1_subset_1 C k5_numbers)) )  => (m2_subset_1 (k5_goedelcp A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k5_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_graph_1 B)) )  =>  ( (~ (v2_struct_0 (k5_graph_1 A B)))  &  ((v1_graph_1 (k5_graph_1 A B)) & (l1_graph_1 (k5_graph_1 A B))) ) ) ) ).
tt(dt_k5_graph_2,ax,$true).
tt(dt_k5_graph_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k5_graph_3 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k5_graph_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_graph_5 A B C D) (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 A))))) ) ).
tt(dt_k5_graphsp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_funct_2 A A)) =>  ((v1_funct_1 (k5_graphsp A B)) &  ((v1_funct_2 (k5_graphsp A B) k5_numbers (k1_funct_2 A A)) & (m1_subset_1 (k5_graphsp A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_funct_2 A A))))) ) ) ) ).
tt(dt_k5_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m3_cat_2 (k5_grcat_1 A B) A)) ) ).
tt(dt_k5_gr_cy_1,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_subset_1 (k5_gr_cy_1 A) (u1_struct_0 k2_gr_cy_1))) ) ).
tt(dt_k5_groeb_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)))))  &  ((m2_ideal_1 D (k11_polynom1 A B) C) & (m2_ideal_1 E (k11_polynom1 A B) C)) ) ) )  => (m2_ideal_1 (k5_groeb_2 A B C D E) (k11_polynom1 A B) C)) ) ).
tt(dt_k5_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_funct_1 (k5_groeb_3 A B C D E)) &  ((v1_funct_2 (k5_groeb_3 A B C D E) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k5_groeb_3 A B C D E) (k15_pre_poly A) C) & (m1_subset_1 (k5_groeb_3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k5_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (k1_funct_2 A A)) &  ((v1_group_10 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 A A))))) ) ) ) ) )  =>  ((v1_funct_1 (k5_group_10 A B C D)) &  ((v1_funct_2 (k5_group_10 A B C D) (u1_struct_0 C) (k1_funct_2 (k3_group_10 A B) (k3_group_10 A B))) &  ((v1_group_10 (k5_group_10 A B C D) C (k3_group_10 A B)) & (m1_subset_1 (k5_group_10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (k1_funct_2 (k3_group_10 A B) (k3_group_10 A B)))))) ) ) ) ) ).
tt(dt_k5_group_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_int_1 B) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_group_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k5_group_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_group_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_group_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v15_algstr_0 (k5_group_4 A B)) & (m1_group_2 (k5_group_4 A B) A)) ) ) ).
tt(dt_k5_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  => (m1_subset_1 (k5_group_5 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  => (l3_algstr_0 (k5_group_6 A B))) ) ).
tt(dt_k5_group_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k5_group_7 A B C D) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))))) ) ).
tt(dt_k5_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((v2_group_9 (k5_group_9 A B) A) & (m1_group_9 (k5_group_9 A B) A B)) ) ) ).
tt(dt_k5_hahnban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_hahnban1 A B C D)) &  ((v1_funct_2 (k5_hahnban1 A B C D) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k5_hahnban1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_heyting1,ax, (! [A:$i] :  ((v1_funct_1 (k5_heyting1 A)) &  ((v1_funct_2 (k5_heyting1 A) (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 (k5_heyting1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) ) ) ).
tt(dt_k5_heyting2,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) =>  ((v1_funct_1 (k5_heyting2 A B)) &  ((v1_funct_2 (k5_heyting2 A B) (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 (k5_heyting2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) (u1_struct_0 (k5_substlat A B)))))) ) ) ) ).
tt(dt_k5_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k5_heyting3 A) (k1_zfmisc_1 (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))))) ) ).
tt(dt_k5_hilbasis,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((v7_ordinal1 B) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k5_hilbasis A B C)) &  ((v1_funct_2 (k5_hilbasis A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_hilbasis A B C) A) & (m1_subset_1 (k5_hilbasis A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) => (m1_subset_1 (k5_hilbert1 A) (k1_zfmisc_1 k1_hilbert1))) ) ).
tt(dt_k5_hilbert3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ((m1_hilbert3 B A) & (m1_subset_1 C k1_hilbert1)) )  =>  ((v1_funct_1 (k5_hilbert3 A B C)) &  ((v1_funct_2 (k5_hilbert3 A B C) (k3_hilbert3 A C) (k3_hilbert3 A C)) & (m1_subset_1 (k5_hilbert3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 A C) (k3_hilbert3 A C))))) ) ) ) ).
tt(dt_k5_hurwitz,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_hurwitz A B C)) &  ((v1_funct_2 (k5_hurwitz A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_hurwitz A B C) A) & (m1_subset_1 (k5_hurwitz A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_idea_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k5_idea_1 A B) k5_numbers)) ) ).
tt(dt_k5_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m2_ideal_1 D A B) & (m2_ideal_1 E A C)) ) ) )  => (m2_ideal_1 (k5_ideal_1 A B C D E) A (k4_subset_1 (u1_struct_0 A) B C))) ) ).
tt(dt_k5_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  => (m1_index_1 (k5_index_1 A B C D) A B)) ) ).
tt(dt_k5_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k5_int_1 A B))) ) ).
tt(dt_k5_int_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_int_3)) & (m1_subset_1 B (u1_struct_0 k1_int_3)))  => (m1_subset_1 (k5_int_3 A B) (u1_struct_0 k1_int_3))) ) ).
tt(dt_k5_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  &  ((m4_integr15 E A B C D) & (m1_subset_1 F k5_numbers)) ) ) ) )  => (m3_integr15 (k5_integr15 A B C D E F) A B C (k2_integra2 B D F))) ) ).
tt(dt_k5_integr16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  & (m2_integr16 D A B C)) ) )  =>  ((v1_funct_1 (k5_integr16 A B C D)) &  ((v1_funct_2 (k5_integr16 A B C D) k5_numbers k2_numbers) & (m1_subset_1 (k5_integr16 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k5_integr18,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k5_integr18 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  => (m2_finseq_1 (k5_integra1 A B C) k1_numbers)) ) ).
tt(dt_k5_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_interva1 B A)) )  => (m1_subset_1 (k5_interva1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k5_intpro_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_intpro_1) & (m1_subset_1 B k1_intpro_1))  => (m1_subset_1 (k5_intpro_1 A B) k1_intpro_1)) ) ).
tt(dt_k5_irrat_1,ax, ((v1_funct_1 k5_irrat_1) &  ((v1_funct_2 k5_irrat_1 k5_numbers k1_numbers) & (m1_subset_1 k5_irrat_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(dt_k5_isocat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D B C) &  ((m2_cat_1 E B C) &  ((m2_cat_1 F A B) & (m2_nattra_1 G B C D E)) ) ) ) ) )  => (m2_nattra_1 (k5_isocat_1 A B C D E F G) A C (k9_cat_1 A B C F D) (k9_cat_1 A B C F E))) ) ).
tt(dt_k5_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  & (m2_cat_1 D (k8_cat_2 A B) C)) ) )  => (m2_cat_1 (k5_isocat_2 A B C D) A (k11_nattra_1 B C))) ) ).
tt(dt_k5_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k5_jgraph_4 A)) &  ((v1_funct_2 (k5_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k5_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k5_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k5_jgraph_6 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k5_jordan1k,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (m1_subset_1 (k5_jordan1k A B C) k1_numbers)) ) ).
tt(dt_k5_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k5_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k5_jordan6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (u1_struct_0 (k15_euclid 2)))) ) ) )  => (m1_subset_1 (k5_jordan6 A B C D E) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k5_jordan_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (m1_jordan_a B A))  => (m1_subset_1 (k5_jordan_a A B) k1_numbers)) ) ).
tt(dt_k5_jordan,ax, ((v1_funct_1 k5_jordan) &  ((v1_funct_2 k5_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 k5_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ).
tt(dt_k5_knaster,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v3_ordinal1 D)) ) )  => (m1_subset_1 (k5_knaster A B C D) (u1_struct_0 A))) ) ).
tt(dt_k5_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_kolmog01 D A B C)) )  => (m1_subset_1 (k5_kolmog01 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 B))))) ) ).
tt(dt_k5_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_kurato_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k5_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  => (m1_subset_1 (k5_lang1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k5_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 E (u1_struct_0 D) C C)) ) ) )  => (m1_subset_1 (k5_laplace A B C D E) (u1_struct_0 D))) ) ).
tt(dt_k5_lattice3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 (k3_lattice3 A))))  => (m1_subset_1 (k5_lattice3 A B) (u1_struct_0 A))) ) ).
tt(dt_k5_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (k5_lattice4 A)) &  ((v1_funct_2 (k5_lattice4 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k5_lattice4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_lattice5,ax,$true).
tt(dt_k5_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  => (m1_subset_1 (k5_lattice6 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_lattice8,ax,$true).
tt(dt_k5_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  => (m1_subset_1 (k5_lattices A) (u1_struct_0 A))) ) ).
tt(dt_k5_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m1_lexbfs B A) & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k5_lexbfs A B C)) & (m1_subset_1 (k5_lexbfs A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) k5_numbers)))) ) ) ).
tt(dt_k5_lfuzzy_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))))  =>  ((v5_relat_1 (k5_lfuzzy_0 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_lfuzzy_0 A B)) &  ((v1_funct_2 (k5_lfuzzy_0 A B) A k1_numbers) & (m1_subset_1 (k5_lfuzzy_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k5_lfuzzy_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) )  =>  ((v5_relat_1 (k5_lfuzzy_1 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_lfuzzy_1 A B)) &  ((v1_funct_2 (k5_lfuzzy_1 A B) (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 (k5_lfuzzy_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ) ).
tt(dt_k5_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (m1_subset_1 (k5_limfunc1 A) k1_numbers)) ) ).
tt(dt_k5_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_lopban_1 A B)))  &  ((v13_algstr_0 (k5_lopban_1 A B)) &  ((v2_rlvect_1 (k5_lopban_1 A B)) &  ((v3_rlvect_1 (k5_lopban_1 A B)) &  ((v4_rlvect_1 (k5_lopban_1 A B)) &  ((v5_rlvect_1 (k5_lopban_1 A B)) &  ((v6_rlvect_1 (k5_lopban_1 A B)) &  ((v7_rlvect_1 (k5_lopban_1 A B)) &  ((v8_rlvect_1 (k5_lopban_1 A B)) & (l1_rlvect_1 (k5_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_lopban_2 A)) &  ((v1_funct_2 (k5_lopban_2 A) (k2_zfmisc_1 (k10_lopban_1 A A) (k10_lopban_1 A A)) (k10_lopban_1 A A)) & (m1_subset_1 (k5_lopban_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k10_lopban_1 A A) (k10_lopban_1 A A)) (k10_lopban_1 A A))))) ) ) ) ).
tt(dt_k5_lopban_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k5_lopban_3 A B)) &  ((v1_funct_2 (k5_lopban_3 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_lopban_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_lopban_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k5_lopban_4 A B C D)) &  ((v1_funct_2 (k5_lopban_4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k5_lopban_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k5_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k5_lopclset A)) &  ((v1_funct_2 (k5_lopclset A) (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A)) & (m1_subset_1 (k5_lopclset A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_lopclset A) (k1_lopclset A)) (k1_lopclset A))))) ) ) ) ).
tt(dt_k5_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m2_rfunct_3 (k5_lpspace1 A) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k5_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers)) ) ) ) )  => (m1_subset_1 (k5_lpspace2 A B C D E) (k1_zfmisc_1 (k1_lpspace2 A B C E)))) ) ).
tt(dt_k5_ltlaxio1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k5_ltlaxio1 A B) k1_hilbert1)) ) ).
tt(dt_k5_mathmorp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k5_mathmorp A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B k1_numbers) & (m1_matrix_1 C k1_numbers A A)) )  => (m1_matrix_1 (k5_matrix10 A B C) k1_numbers A A)) ) ).
tt(dt_k5_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k5_matrix11 A)) &  ((v1_funct_2 (k5_matrix11 A) (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 (k5_matrix11 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k5_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) & (m1_subset_1 F (u1_struct_0 C))) ) ) ) )  => (m1_matrix_1 (k5_matrix12 A B C D E F) (u1_struct_0 C) A B)) ) ).
tt(dt_k5_matrix13,ax, (! [A:$i] :  ( ((v1_finset_1 A) &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  => (m2_finseq_2 (k5_matrix13 A) k5_numbers (k4_finseq_2 (k5_card_1 A) k5_numbers))) ) ).
tt(dt_k5_matrix15,ax,$true).
tt(dt_k5_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  & (m1_matrix_1 C B A A)) )  => (m1_matrix_1 (k5_matrix_1 A B C) B A A)) ) ).
tt(dt_k5_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 B A))) )  => (m1_matrix_1 (k5_matrix_2 A B C) A 1 B)) ) ).
tt(dt_k5_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 E (u1_struct_0 D) A B) & (m1_matrix_1 F (u1_struct_0 D) (k1_matrix_1 E) C)) ) ) ) )  => (m1_matrix_1 (k5_matrix_3 A B C D E F) (u1_struct_0 D) (k3_finseq_1 E) (k1_matrix_1 F))) ) ).
tt(dt_k5_matrix_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k2_numbers))) )  =>  ((v1_matrix_1 (k5_matrix_5 A B)) & (m2_finseq_1 (k5_matrix_5 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k5_matrix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_matrix_1 (k5_matrix_6 A B C) (u1_struct_0 B) A A)) ) ).
tt(dt_k5_matrixc1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  => (m2_finseq_1 (k5_matrixc1 A B) k2_numbers)) ) ).
tt(dt_k5_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((v1_matrixj1 (k5_matrixj1 A B C) A) & (m2_finseq_1 (k5_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k5_matrixr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k1_numbers))) )  =>  ((v1_matrix_1 (k5_matrixr1 A B)) & (m2_finseq_1 (k5_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k5_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_matrix_1 (k5_matrixr2 A) k1_numbers A A)) ) ).
tt(dt_k5_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v1_matrix_1 E) & (m1_finseq_1 E (k3_finseq_2 (u1_struct_0 C)))) ) ) ) )  => (m1_matrix_1 (k5_matrlin2 A B C D E) (u1_struct_0 C) A B)) ) ).
tt(dt_k5_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_finseq_1 C (u1_struct_0 A)) & (m1_finseq_1 D (u1_struct_0 B))) ) )  => (m2_finseq_1 (k5_matrlin A B C D) (u1_struct_0 B))) ) ).
tt(dt_k5_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  => (m1_subset_1 (k5_matrprob A) k1_numbers)) ) ).
tt(dt_k5_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  => (m1_subset_1 (k5_mcart_1 A B C D E) B)) ) ).
tt(dt_k5_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k5_measure6 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k5_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  & (m1_subset_1 D (k1_zfmisc_1 A))) )  => (m1_subset_1 (k5_measure8 A B C D) (k1_zfmisc_1 k7_numbers))) ) ).
tt(dt_k5_member_1,ax, (! [A:$i] :  ((v1_membered A) => (v1_membered (k5_member_1 A))) ) ).
tt(dt_k5_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  => (m2_subset_1 (k5_memstr_0 A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k5_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k5_mesfun7c A B)) &  ((v1_funct_2 (k5_mesfun7c A B) k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 (k5_mesfun7c A B) A k7_numbers) & (m1_subset_1 (k5_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) ) ) ) ).
tt(dt_k5_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C k7_numbers) & (v1_funct_1 C)) ) ) ) )  =>  ((v1_funct_1 (k5_mesfunc1 A B C)) & (m1_subset_1 (k5_mesfunc1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k5_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) )  => (m1_subset_1 (k5_mesfunc5 A B C D) k7_numbers)) ) ).
tt(dt_k5_mesfunc7,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) )  =>  ((v1_funct_1 (k5_mesfunc7 A B C)) & (m1_subset_1 (k5_mesfunc7 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ).
tt(dt_k5_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k5_mesfunc8 A B)) & (m1_subset_1 (k5_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k5_mesfunc9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) (k4_partfun1 C k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k4_partfun1 C k7_numbers))))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F B)) ) ) ) )  =>  ((v1_funct_1 (k5_mesfunc9 A B C D E F)) & (m1_subset_1 (k5_mesfunc9 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ).
tt(dt_k5_metric_1,ax, (! [A:$i] :  ((v1_funct_1 (k5_metric_1 A)) &  ((v1_funct_2 (k5_metric_1 A) (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 (k5_metric_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ).
tt(dt_k5_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k5_metric_2 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k5_mfold_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_pre_topc C (k15_euclid A))) )  =>  ((v1_funct_1 (k5_mfold_2 A B C)) &  ((v1_funct_2 (k5_mfold_2 A B C) (u1_struct_0 C) (u1_struct_0 (k3_mfold_2 A B (k4_struct_0 (k15_euclid A))))) & (m1_subset_1 (k5_mfold_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k3_mfold_2 A B (k4_struct_0 (k15_euclid A)))))))) ) ) ) ).
tt(dt_k5_midsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  & (m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))  => (m1_midsp_1 (k5_midsp_1 A B) A)) ) ).
tt(dt_k5_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v1_funct_1 (k5_midsp_2 A)) &  ((v1_funct_2 (k5_midsp_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (k15_midsp_1 A))) & (m1_subset_1 (k5_midsp_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (k15_midsp_1 A)))))) ) ) ) ).
tt(dt_k5_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k4_finseq_2 (k2_nat_1 A 1) B)) & (m1_midsp_3 D A)) ) )  => (m1_subset_1 (k5_midsp_3 A B C D) B)) ) ).
tt(dt_k5_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A)) )  =>  ((v7_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) & (l1_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A))) ) ) ).
tt(dt_k5_modal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  & (m1_subset_1 B A))  => (m1_subset_1 (k5_modal_1 A B) k5_numbers)) ) ).
tt(dt_k5_modcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_modcat_1 B A) & (m1_subset_1 C (k4_modcat_1 A B))) )  => (m2_modcat_1 (k5_modcat_1 A B C) A B)) ) ).
tt(dt_k5_modelc_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k5_modelc_2 A B) k5_numbers)) ) ).
tt(dt_k5_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((l1_modelc_3 B A) &  ((v1_modelc_2 C) & (m1_finseq_1 C k5_numbers)) ) )  =>  ((v1_modelc_3 (k5_modelc_3 A B C) A) & (l1_modelc_3 (k5_modelc_3 A B C) A)) ) ) ).
tt(dt_k5_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k5_moebius1 A)) &  ((v4_relat_1 (k5_moebius1 A) k10_newton) &  ((v1_funct_1 (k5_moebius1 A)) & (v1_partfun1 (k5_moebius1 A) k10_newton)) ) ) ) ) ).
tt(dt_k5_monoid_0,ax, ( (~ (v2_struct_0 k5_monoid_0))  &  ((v22_algstr_0 k5_monoid_0) &  ((v4_vectsp_1 k5_monoid_0) & (m1_monoid_0 k5_monoid_0 k4_monoid_0)) ) ) ).
tt(dt_k5_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  => (m2_funct_2 (k5_monoid_1 A B C) B A (k9_funct_2 B A))) ) ).
tt(dt_k5_msafree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v3_msualg_1 (k5_msafree2 A B) A) &  ((v4_msualg_1 (k5_msafree2 A B) A) &  ((v2_msafree (k5_msafree2 A B) A) & (l3_msualg_1 (k5_msafree2 A B) A)) ) ) ) ) ).
tt(dt_k5_msafree3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) ) )  => (m3_pboole (k5_msafree3 A B C) (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)))) ) ).
tt(dt_k5_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (l1_lang1 (k5_msafree A B))) ) ).
tt(dt_k5_msalimit,ax,$true).
tt(dt_k5_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (k1_funct_1 C D))) ) ) )  => (m1_dtconstr (k5_msaterm A B C D E) (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) ) ).
tt(dt_k5_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_mssubfam (k5_mssubfam A B) A B) &  ((v2_mssubfam (k5_mssubfam A B) A B) &  ((v3_mssubfam (k5_mssubfam A B) A B) &  ((v4_mssubfam (k5_mssubfam A B) A B) &  ((v5_mssubfam (k5_mssubfam A B) A B) &  ((v6_mssubfam (k5_mssubfam A B) A B) & (m3_pboole (k5_mssubfam A B) A (k1_mboolean A B))) ) ) ) ) ) ) ) ).
tt(dt_k5_msualg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (l3_msualg_1 C A)) )  =>  ((v1_funct_1 (k5_msualg_1 A B C)) &  ((v1_funct_2 (k5_msualg_1 A B C) (k3_msualg_1 A B C) (k4_msualg_1 A B C)) & (m1_subset_1 (k5_msualg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k3_msualg_1 A B C) (k4_msualg_1 A B C))))) ) ) ) ).
tt(dt_k5_msualg_2,ax,$true).
tt(dt_k5_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((l3_msualg_1 C A) &  ((m1_subset_1 D (u4_struct_0 A)) &  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (m1_subset_1 F (k3_msualg_1 A D B))) ) ) ) )  => (m1_subset_1 (k5_msualg_3 A B C D E F) (k3_msualg_1 A D C))) ) ).
tt(dt_k5_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u4_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u4_struct_0 A))) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u4_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u4_struct_0 A))) ) )  &  ((m2_pboole D (u4_struct_0 A) B C) & (m1_subset_1 E (u4_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k5_msualg_4 A B C D E)) &  ((v1_funct_2 (k5_msualg_4 A B C D E) (k1_funct_1 B E) (k1_funct_1 C E)) & (m1_subset_1 (k5_msualg_4 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B E) (k1_funct_1 C E))))) ) ) ) ).
tt(dt_k5_msualg_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_msualg_5 A B)))  &  ((v3_lattices (k5_msualg_5 A B)) &  ((v10_lattices (k5_msualg_5 A B)) & (l3_lattices (k5_msualg_5 A B))) ) ) ) ) ).
tt(dt_k5_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_mycielsk (k5_mycielsk A) A)) ) ).
tt(dt_k5_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B k1_numbers) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_funct_1 (k5_nagata_1 A B C)) &  ((v1_funct_2 (k5_nagata_1 A B C) A k1_numbers) & (m1_subset_1 (k5_nagata_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k5_nat_1,ax, (! [A:$i] : (m2_subset_1 (k5_nat_1 A) k1_numbers k5_numbers)) ).
tt(dt_k5_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k5_nat_3 A B C)) &  ((v4_relat_1 (k5_nat_3 A B C) A) &  ((v1_funct_1 (k5_nat_3 A B C)) & (v1_partfun1 (k5_nat_3 A B C) A)) ) ) ) ) ).
tt(dt_k5_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_subset_1 (k5_nat_5 A) k1_numbers k5_numbers)) ) ).
tt(dt_k5_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k5_nat_d A B) k5_numbers)) ) ).
tt(dt_k5_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m1_nattra_1 F A B C D) & (m1_nattra_1 G A B D E)) ) ) ) ) )  => (m1_nattra_1 (k5_nattra_1 A B C D E F G) A B C E)) ) ).
tt(dt_k5_ndiff_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  => (m2_subset_1 (k5_ndiff_5 A B) k5_numbers (k4_finseq_1 A))) ) ).
tt(dt_k5_net_1,ax,$true).
tt(dt_k5_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k5_newton A B) k1_numbers)) ) ).
tt(dt_k5_normform,ax, (! [A:$i] :  ((v1_funct_1 (k5_normform A)) &  ((v1_funct_2 (k5_normform A) (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 (k5_normform A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) ) ) ).
tt(dt_k5_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k5_normsp_1 A B C)) &  ((v1_funct_2 (k5_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k5_normsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_numbers,ax,(m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers))).
tt(dt_k5_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k5_openlatt A)) &  ((v1_funct_2 (k5_openlatt A) (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A)) & (m1_subset_1 (k5_openlatt A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_openlatt A) (k1_openlatt A)) (k1_openlatt A))))) ) ) ) ).
tt(dt_k5_oppcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k5_oppcat_1 A B) (u4_struct_0 (k2_oppcat_1 A)))) ) ).
tt(dt_k5_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  => (v3_ordinal1 (k5_ordinal2 A))) ) ).
tt(dt_k5_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k5_ordinal3 A B))) ) ).
tt(dt_k5_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) )  =>  ((v1_funct_1 (k5_ordinal4 A B C)) &  ((v1_funct_2 (k5_ordinal4 A B C) (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 (k5_ordinal4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ).
tt(dt_k5_ordinal5,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k5_ordinal5 A B))) ) ).
tt(dt_k5_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (k5_osafree A B)) &  ((v4_relat_1 (k5_osafree A B) (u1_struct_0 A)) &  ((v1_funct_1 (k5_osafree A B)) &  ((v1_partfun1 (k5_osafree A B) (u1_struct_0 A)) & (v11_osalg_1 (k5_osafree A B) A)) ) ) ) ) ) ).
tt(dt_k5_osalg_2,ax,$true).
tt(dt_k5_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  & (m1_subset_1 D (k2_osalg_4 A))) ) )  =>  ((v1_partfun1 (k5_osalg_4 A B C D) (k4_osalg_4 A (u3_msualg_1 A B) D)) &  ((v3_relat_2 (k5_osalg_4 A B C D)) &  ((v8_relat_2 (k5_osalg_4 A B C D)) & (m1_subset_1 (k5_osalg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k4_osalg_4 A (u3_msualg_1 A B) D) (k4_osalg_4 A (u3_msualg_1 A B) D))))) ) ) ) ) ).
tt(dt_k5_parsp_1,ax,$true).
tt(dt_k5_partfun1,ax,$true).
tt(dt_k5_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v1_funct_1 (k5_partfun3 A B C)) &  ((v1_funct_2 (k5_partfun3 A B C) A k1_numbers) & (m1_subset_1 (k5_partfun3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k5_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k5_pboole A B C)) &  ((v4_relat_1 (k5_pboole A B C) A) &  ((v1_funct_1 (k5_pboole A B C)) & (v1_partfun1 (k5_pboole A B C) A)) ) ) ) ) ).
tt(dt_k5_pcs_0,ax,(l1_pcs_0 k5_pcs_0)).
tt(dt_k5_pdiff_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_finseq_1 B k1_numbers))  =>  ((v1_relat_1 (k5_pdiff_1 A B)) & (v1_funct_1 (k5_pdiff_1 A B))) ) ) ).
tt(dt_k5_pdiff_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  & (m1_subset_1 B (k1_euclid 2)))  => (m1_subset_1 (k5_pdiff_3 A B) k1_numbers)) ) ).
tt(dt_k5_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_euclid 3)) => (m2_finseq_2 (k5_pdiff_4 A) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k5_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k5_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k5_pdiff_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_finseq_1 C k5_numbers) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) )  =>  ((v1_funct_1 (k5_pdiff_9 A B C D)) & (m1_subset_1 (k5_pdiff_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers)))) ) ) ).
tt(dt_k5_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_pencil_1 A B)))  & (l1_pre_topc (k5_pencil_1 A B))) ) ) ).
tt(dt_k5_pencil_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_pre_topc (k5_pencil_4 A B C)) & (l1_pre_topc (k5_pencil_4 A B C))) ) ) ).
tt(dt_k5_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u2_petri A)))  => (m1_subset_1 (k5_petri A B) (u1_struct_0 A))) ) ).
tt(dt_k5_pnproc_1,ax, (! [A:$i,B:$i] :  ((m1_pnproc_1 B A) =>  ((v1_funct_1 (k5_pnproc_1 A B)) &  ((v1_funct_2 (k5_pnproc_1 A B) A k5_numbers) & (m1_subset_1 (k5_pnproc_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(dt_k5_polyeq_1,ax,$true).
tt(dt_k5_polyeq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_xcmplx_0 (k5_polyeq_5 A B C D))) ) ).
tt(dt_k5_polyform,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m2_finseq_1 (k5_polyform A B C) k4_numbers)) ) ).
tt(dt_k5_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k5_polynom1 A B C D)) &  ((v1_funct_2 (k5_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k5_polynom1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k5_polynom2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  => (m1_subset_1 (k5_polynom2 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k5_polynom3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_partfun1 (k5_polynom3 A) (k4_finseq_2 A k5_numbers)) &  ((v1_relat_2 (k5_polynom3 A)) &  ((v4_relat_2 (k5_polynom3 A)) &  ((v8_relat_2 (k5_polynom3 A)) & (m1_subset_1 (k5_polynom3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k5_numbers) (k4_finseq_2 A k5_numbers))))) ) ) ) ) ) ).
tt(dt_k5_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_polynom5 A B C)) &  ((v1_funct_2 (k5_polynom5 A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_polynom5 A B C) A) & (m1_subset_1 (k5_polynom5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_polynom7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l5_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  & (m1_subset_1 D (u1_struct_0 B))) )  =>  ((v1_funct_1 (k5_polynom7 A B C D)) &  ((v1_funct_2 (k5_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k5_polynom7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k5_polynom8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k5_polynom8 A B)) &  ((v1_funct_2 (k5_polynom8 A B) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_polynom8 A B) A) & (m1_subset_1 (k5_polynom8 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (m1_subset_1 (k5_poset_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_poset_1 A B) (k4_poset_1 A B))))) ) ).
tt(dt_k5_power,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k5_power A B))) ) ).
tt(dt_k5_pralg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_pralg_1 A B)))  &  ((v1_unialg_1 (k5_pralg_1 A B)) &  ((v2_unialg_1 (k5_pralg_1 A B)) &  ((v3_unialg_1 (k5_pralg_1 A B)) &  ((v4_unialg_1 (k5_pralg_1 A B)) & (l1_unialg_1 (k5_pralg_1 A B))) ) ) ) ) ) ) ).
tt(dt_k5_pralg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ((m1_pralg_2 C A B) & (m1_subset_1 D A)) ) )  =>  ((v4_msualg_1 (k5_pralg_2 A B C D) B) & (l3_msualg_1 (k5_pralg_2 A B C D) B)) ) ) ).
tt(dt_k5_pre_poly,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k3_finseq_2 A)) => (m2_finseq_2 (k5_pre_poly A B) A (k3_finseq_2 A))) ) ).
tt(dt_k5_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_int_1 B))  => (m1_subset_1 (k5_prepower A B) k1_numbers)) ) ).
tt(dt_k5_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m1_prob_1 (k5_prob_1 A B C D) A B)) ) ).
tt(dt_k5_prob_3,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k9_setfam_1 A)) => (m1_subset_1 (k5_prob_3 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k5_prob_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) & (m1_subset_1 D (k4_prob_4 A B C))) ) )  => (m2_subset_1 (k5_prob_4 A B C D) (k1_zfmisc_1 A) (k2_measure3 A B (k2_prob_4 A B C)))) ) ).
tt(dt_k5_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ((v1_funct_1 (k5_prvect_1 A B)) &  ((v1_funct_2 (k5_prvect_1 A B) (k2_zfmisc_1 (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A))) (k4_finseq_2 B (u1_struct_0 A))) & (m1_subset_1 (k5_prvect_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k4_finseq_2 B (u1_struct_0 A))) (k4_finseq_2 B (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k5_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 (k4_prvect_2 A))))  =>  ( (~ (v2_struct_0 (k5_prvect_2 A B)))  &  ((v13_algstr_0 (k5_prvect_2 A B)) &  ((v2_rlvect_1 (k5_prvect_2 A B)) &  ((v3_rlvect_1 (k5_prvect_2 A B)) &  ((v4_rlvect_1 (k5_prvect_2 A B)) &  ((v5_rlvect_1 (k5_prvect_2 A B)) &  ((v6_rlvect_1 (k5_prvect_2 A B)) &  ((v7_rlvect_1 (k5_prvect_2 A B)) &  ((v8_rlvect_1 (k5_prvect_2 A B)) & (l1_rlvect_1 (k5_prvect_2 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (l1_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(dt_k5_pscomp_1,ax, ((v1_funct_1 k5_pscomp_1) &  ((v1_funct_2 k5_pscomp_1 (u1_struct_0 (k15_euclid 2)) k1_numbers) & (m1_subset_1 k5_pscomp_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) k1_numbers)))) ) ).
tt(dt_k5_pua2mss1,ax,$true).
tt(dt_k5_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k5_qc_lang1 A) (k1_zfmisc_1 (k2_qc_lang1 A)))) ) ).
tt(dt_k5_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (m1_subset_1 (k5_qc_lang2 A B C) (k9_qc_lang1 A))) ) ).
tt(dt_k5_qc_lang3,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k5_qc_lang3 A B) (k1_zfmisc_1 (k5_qc_lang1 A)))) ) ).
tt(dt_k5_qmax_1,ax,$true).
tt(dt_k5_quantal1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k5_quantal1 A B) (u1_struct_0 A))) ) ).
tt(dt_k5_quatern2,ax,$true).
tt(dt_k5_quaterni,ax,$true).
tt(dt_k5_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  => (m2_subset_1 (k5_quofield A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A))) ) ).
tt(dt_k5_radix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  => (m1_subset_1 (k5_radix_1 A B C D) k4_numbers)) ) ).
tt(dt_k5_radix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k5_radix_2 A B C) B) & (m2_finseq_1 (k5_radix_2 A B C) k5_numbers)) ) ) ).
tt(dt_k5_radix_3,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (v1_int_1 (k5_radix_3 A B))) ) ).
tt(dt_k5_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k5_radix_5 A B C) k4_numbers (k3_radix_1 C))) ) ).
tt(dt_k5_radix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m1_finseq_1 D (k3_radix_1 C))) ) ) )  => (m1_subset_1 (k5_radix_6 A B C D) (k3_radix_1 C))) ) ).
tt(dt_k5_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_subset_1 D k1_numbers)) ) )  => (m1_random_1 (k5_random_1 A B C D) A B)) ) ).
tt(dt_k5_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m1_subset_1 (k5_ranknull A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  & (m1_ratfunc1 B A))  =>  ((v1_funct_1 (k5_ratfunc1 A B)) &  ((v1_funct_2 (k5_ratfunc1 A B) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_ratfunc1 A B) A) &  ( (~ (v1_ratfunc1 (k5_ratfunc1 A B) A))  & (m1_subset_1 (k5_ratfunc1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_k5_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k5_real_1 A B) k1_numbers)) ) ).
tt(dt_k5_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k5_real_3 A)) &  ((v1_funct_2 (k5_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k5_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k5_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k5_real_lat A)) &  ((v1_funct_2 (k5_real_lat A) (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 (k5_real_lat A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) ) ) ) ).
tt(dt_k5_real_ns1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_euclid A))))) )  & (v7_ordinal1 C)) )  => (m2_finseq_2 (k5_real_ns1 A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k5_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_realset2 A)) &  ((v1_funct_2 (k5_realset2 A) (k8_struct_0 A) (k8_struct_0 A)) & (m1_subset_1 (k5_realset2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k8_struct_0 A) (k8_struct_0 A))))) ) ) ) ).
tt(dt_k5_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k5_relat_1 A B))) ) ).
tt(dt_k5_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k5_relset_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k5_relset_2,ax,$true).
tt(dt_k5_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_finseq_1 C (k8_afinsq_1 A)))  => (m2_finseq_1 (k5_rewrite2 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k5_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v8_valued_0 (k5_rfinseq2 A)) & (m2_finseq_1 (k5_rfinseq2 A) k1_numbers)) ) ) ).
tt(dt_k5_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  => (m2_rfunct_3 (k5_rfunct_3 A B C D) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k5_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k5_rinfsup1 A) k1_numbers)) ) ).
tt(dt_k5_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k5_rinfsup2 A) k7_numbers)) ) ).
tt(dt_k5_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v2_ringcat1 (k5_ringcat1 A)) & (m1_ringcat1 (k5_ringcat1 A) A A)) ) ) ).
tt(dt_k5_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m2_rlvect_2 (k5_rlaffin1 A B C) A B)) ) ).
tt(dt_k5_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_rlsub_2 A)) &  ((v1_funct_2 (k5_rlsub_2 A) (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A)) & (m1_subset_1 (k5_rlsub_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A))))) ) ) ) ).
tt(dt_k5_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_finseq_1 B (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  => (m2_finseq_1 (k5_rlvect_2 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_rmod_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_rmod_3 A B)) &  ((v1_funct_2 (k5_rmod_3 A B) (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B)) & (m1_subset_1 (k5_rmod_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B))))) ) ) ) ).
tt(dt_k5_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_rmod_4 C A B)) )  => (m1_subset_1 (k5_rmod_4 A B C) (u1_struct_0 B))) ) ).
tt(dt_k5_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_robbins1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_robbins1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_robbins3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_roughs_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_rsspace4 A B)))  &  ((v13_algstr_0 (k5_rsspace4 A B)) &  ((v2_rlvect_1 (k5_rsspace4 A B)) &  ((v3_rlvect_1 (k5_rsspace4 A B)) &  ((v4_rlvect_1 (k5_rsspace4 A B)) &  ((v5_rlvect_1 (k5_rsspace4 A B)) &  ((v6_rlvect_1 (k5_rsspace4 A B)) &  ((v7_rlvect_1 (k5_rsspace4 A B)) &  ((v8_rlvect_1 (k5_rsspace4 A B)) & (l1_rlvect_1 (k5_rsspace4 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_rsspace,ax, ((v1_funct_1 k5_rsspace) &  ((v1_funct_2 k5_rsspace (k2_zfmisc_1 k1_numbers k1_rsspace) k1_rsspace) & (m1_subset_1 k5_rsspace (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_rsspace) k1_rsspace)))) ) ).
tt(dt_k5_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_rusub_2 A)) &  ((v1_funct_2 (k5_rusub_2 A) (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A)) & (m1_subset_1 (k5_rusub_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A))))) ) ) ) ).
tt(dt_k5_rusub_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_rusub_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (l1_pre_topc (k5_rusub_5 A))) ) ).
tt(dt_k5_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  => (m2_finseq_2 (k5_rvsum_1 A B C) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k5_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  => (m2_finseq_1 (k5_rvsum_2 A) k2_numbers)) ) ).
tt(dt_k5_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (m1_dtconstr (k5_scm_comp A B) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k5_scmfsa_1,ax, ((v1_relat_1 k5_scmfsa_1) &  ((v4_relat_1 k5_scmfsa_1 3) &  ((v1_funct_1 k5_scmfsa_1) & (v1_partfun1 k5_scmfsa_1 3)) ) ) ).
tt(dt_k5_scmfsa_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_scmfsa_2 (k5_scmfsa_2 A))) ) ).
tt(dt_k5_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k5_scmfsa6a A B)) &  ((v4_relat_1 (k5_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k5_scmfsa6a A B)))  &  ((v1_funct_1 (k5_scmfsa6a A B)) &  ((v1_finset_1 (k5_scmfsa6a A B)) & (v1_afinsq_1 (k5_scmfsa6a A B))) ) ) ) ) ) ) ) ).
tt(dt_k5_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa8b A B C D)))  &  ((v1_relat_1 (k5_scmfsa8b A B C D)) &  ((v4_relat_1 (k5_scmfsa8b A B C D) k5_numbers) &  ((v5_relat_1 (k5_scmfsa8b A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa8b A B C D)) &  ((v1_finset_1 (k5_scmfsa8b A B C D)) & (v1_afinsq_1 (k5_scmfsa8b A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k5_scmfsa_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_scmfsa_9 A B C D)) &  ((v1_funct_2 (k5_scmfsa_9 A B C D) k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2))) & (m1_subset_1 (k5_scmfsa_9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)))))) ) ) ) ).
tt(dt_k5_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k5_scmfsa_i A) k1_scmfsa_i)) ) ).
tt(dt_k5_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k5_scmfsa_m A B) (k1_zfmisc_1 k2_scmfsa_2))) ) ).
tt(dt_k5_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (m1_subset_1 (k5_scm_inst A) k2_scm_inst)) ) ).
tt(dt_k5_scmpds_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_scmpds_i) & (m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))  => (m1_subset_1 (k5_scmpds_1 A B) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) ) ).
tt(dt_k5_scmpds_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  => (m1_subset_1 (k5_scmpds_2 A B) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k5_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmpds_6 A B C)))  &  ((v1_relat_1 (k5_scmpds_6 A B C)) &  ((v4_relat_1 (k5_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k5_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k5_scmpds_6 A B C)) &  ((v1_finset_1 (k5_scmpds_6 A B C)) & (v1_afinsq_1 (k5_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k5_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (m1_subset_1 (k5_scmpds_i A) k2_scm_inst)) ) ).
tt(dt_k5_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) & (m1_subset_1 C k2_ami_2)) )  => (m1_subset_1 (k5_scmring1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k5_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k5_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k5_scmringi A B) k5_numbers)) ) ).
tt(dt_k5_scmyciel,ax, (! [A:$i] : (m1_scmyciel (k5_scmyciel A) A)) ).
tt(dt_k5_scpinvar,ax, ( (~ (v1_xboole_0 k5_scpinvar))  &  ((v1_relat_1 k5_scpinvar) &  ((v4_relat_1 k5_scpinvar k5_numbers) &  ((v5_relat_1 k5_scpinvar (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 k5_scpinvar) &  ((v1_finset_1 k5_scpinvar) & (v1_afinsq_1 k5_scpinvar)) ) ) ) ) ) ).
tt(dt_k5_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k5_seq_4 A) k1_numbers)) ) ).
tt(dt_k5_seqfunc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k5_seqfunc A B)) &  ((v1_funct_2 (k5_seqfunc A B) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k5_seqfunc A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k5_series_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k5_series_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k5_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k5_setfam_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k5_setlim_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k5_setlim_1 A B C) B) &  ((v1_funct_1 (k5_setlim_1 A B C)) &  ((v1_funct_2 (k5_setlim_1 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k5_setlim_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) ).
tt(dt_k5_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k5_setlim_2 A B C)) &  ((v1_funct_2 (k5_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k5_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k5_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  => (m1_subset_1 (k5_setwiseo A B C) (k5_finsub_1 A))) ) ).
tt(dt_k5_sfmastr2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k5_sfmastr2 A B)))  &  ((v1_relat_1 (k5_sfmastr2 A B)) &  ((v4_relat_1 (k5_sfmastr2 A B) k5_numbers) &  ((v5_relat_1 (k5_sfmastr2 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_sfmastr2 A B)) &  ((v1_finset_1 (k5_sfmastr2 A B)) & (v1_afinsq_1 (k5_sfmastr2 A B))) ) ) ) ) ) ) ) ).
tt(dt_k5_sfmastr3,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((v1_relat_1 (k5_sfmastr3 A)) &  ((v4_relat_1 (k5_sfmastr3 A) k5_numbers) &  ((v5_relat_1 (k5_sfmastr3 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_sfmastr3 A)) &  ( (~ (v1_xboole_0 (k5_sfmastr3 A)))  &  ((v1_finset_1 (k5_sfmastr3 A)) & (v1_afinsq_1 (k5_sfmastr3 A))) ) ) ) ) ) ) ) ).
tt(dt_k5_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_ami_2 (k5_sf_mastr A)) & (m1_subset_1 (k5_sf_mastr A) (u1_struct_0 k1_scmfsa_2))) ) ) ).
tt(dt_k5_sgraph1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_sgraph1 B A) &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) )  => (m1_subset_1 (k5_sgraph1 A B C D) (k1_zfmisc_1 (k3_finseq_2 (u1_struct_0 B))))) ) ).
tt(dt_k5_sheffer1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k5_sheffer1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k5_simplex0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_pre_topc (k5_simplex0 A B)) & (m1_simplex0 (k5_simplex0 A B) A)) ) ) ).
tt(dt_k5_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) ) ) )  =>  ( (~ (v3_pencil_1 (k5_simplex1 A B C)))  &  ((v1_matroid0 (k5_simplex1 A B C)) &  ((v3_matroid0 (k5_simplex1 A B C)) & (m1_simplex1 (k5_simplex1 A B C) B C)) ) ) ) ) ).
tt(dt_k5_sincos10,ax,$true).
tt(dt_k5_sin_cos2,ax,$true).
tt(dt_k5_sin_cos6,ax,$true).
tt(dt_k5_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k5_sin_cos7 A))) ) ).
tt(dt_k5_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k5_sin_cos9 A) k1_numbers)) ) ).
tt(dt_k5_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k5_sin_cos A)) &  ((v1_funct_2 (k5_sin_cos A) k5_numbers k2_numbers) & (m1_subset_1 (k5_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k5_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k5_square_1 A) k1_numbers)) ) ).
tt(dt_k5_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  & (l1_stacks_1 A))  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k5_stacks_1 A B) (u4_struct_0 A))) ) ).
tt(dt_k5_struct_0,ax, (! [A:$i] :  ((l3_struct_0 A) => (m1_subset_1 (k5_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_k5_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  => (m2_subset_1 (k5_sublemma A B) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k5_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k5_subset_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k5_substlat,ax, (! [A:$i,B:$i] :  ((v3_lattices (k5_substlat A B)) & (l3_lattices (k5_substlat A B))) ) ).
tt(dt_k5_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_finseq_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k1_substut1 A))) )  => (m2_finseq_1 (k5_substut1 A B C) (k3_qc_lang1 A))) ) ).
tt(dt_k5_substut2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (m1_subset_1 (k5_substut2 A B) (k1_substut1 A))) ) ).
tt(dt_k5_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  => (v2_membered (k5_supinf_1 A))) ) ).
tt(dt_k5_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  => (m1_subset_1 (k5_supinf_2 A B) (k1_zfmisc_1 k7_numbers))) ) ).
tt(dt_k5_taylor_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((v1_funct_1 (k5_taylor_1 A B)) &  ((v1_funct_2 (k5_taylor_1 A B) k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 (k5_taylor_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) ) ) ).
tt(dt_k5_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k5_tdlat_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k5_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k5_termord A B C D)) &  ((v1_funct_2 (k5_termord A B C D) (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 (k5_termord A B C D) A C) & (m1_subset_1 (k5_termord A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k5_tex_4,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_pre_topc (k5_tex_4 A B)) & (m1_pre_topc (k5_tex_4 A B) A)) ) ) ).
tt(dt_k5_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k5_tmap_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k5_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v15_algstr_0 (k5_topalg_1 A B)) & (l3_algstr_0 (k5_topalg_1 A B))) ) ) ).
tt(dt_k5_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k5_topalg_5 A)) &  ((v1_funct_2 (k5_topalg_5 A) (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 (k5_topalg_5 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)))))) ) ) ) ).
tt(dt_k5_topalg_6,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_finseq_1 B (k1_topalg_6 A)))  => (m2_finseq_1 (k5_topalg_6 A B) (k1_topalg_6 A))) ) ).
tt(dt_k5_topgen_2,ax, (! [A:$i,B:$i] :  ((v1_pre_topc (k5_topgen_2 A B)) & (l1_pre_topc (k5_topgen_2 A B))) ) ).
tt(dt_k5_topgen_3,ax, (! [A:$i] :  ((v1_pre_topc (k5_topgen_3 A)) &  ((v2_pre_topc (k5_topgen_3 A)) & (l1_pre_topc (k5_topgen_3 A))) ) ) ).
tt(dt_k5_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_prob_1 (k5_topgen_4 A) (u1_struct_0 A)) &  ((v1_topgen_4 (k5_topgen_4 A) A) &  ((v3_topgen_4 (k5_topgen_4 A) (u1_struct_0 A)) & (m1_subset_1 (k5_topgen_4 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_topgen_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  ((v1_funct_1 (k5_topgen_5 A B C)) &  ((v1_funct_2 (k5_topgen_5 A B C) (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (m1_subset_1 (k5_topgen_5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr))))) ) ) ) ).
tt(dt_k5_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v15_algstr_0 (k5_topgrp_1 A)) & (l3_algstr_0 (k5_topgrp_1 A))) ) ) ).
tt(dt_k5_topmetr,ax,(m1_pre_topc k5_topmetr k3_topmetr)).
tt(dt_k5_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k5_topreal1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k5_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k5_toprealb A) (k1_zfmisc_1 (u1_struct_0 k2_topalg_2)))) ) ).
tt(dt_k5_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 (k2_borsuk_1 A B)))) ) ) )  => (m1_subset_1 (k5_toprealc A B C D E) (u1_struct_0 C))) ) ).
tt(dt_k5_toprns_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) )  =>  ((v1_funct_1 (k5_toprns_1 A B)) &  ((v1_funct_2 (k5_toprns_1 A B) k5_numbers k1_numbers) & (m1_subset_1 (k5_toprns_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k5_trees_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ((m1_finseq_1 B k5_numbers) &  ( (~ (v1_xboole_0 C))  & (v1_trees_1 C)) ) )  =>  ( (~ (v1_xboole_0 (k5_trees_1 A B C)))  & (v1_trees_1 (k5_trees_1 A B C))) ) ) ).
tt(dt_k5_trees_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  & (m1_finseq_1 B k5_numbers))  =>  ((v1_relat_1 (k5_trees_2 A B)) &  ((v1_funct_1 (k5_trees_2 A B)) & (v3_trees_2 (k5_trees_2 A B))) ) ) ) ).
tt(dt_k5_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_trees_3 (k5_trees_3 A) A)) ) ).
tt(dt_k5_trees_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((v1_relat_1 (k5_trees_4 A B)) &  ((v1_funct_1 (k5_trees_4 A B)) & (v3_trees_2 (k5_trees_4 A B))) ) ) ) ).
tt(dt_k5_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_turing_1 A) &  ((m1_subset_1 B (k9_funct_2 k4_numbers (u1_turing_1 A))) &  ((v1_int_1 C) & (m1_subset_1 D (u1_turing_1 A))) ) )  => (m2_funct_2 (k5_turing_1 A B C D) k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A)))) ) ).
tt(dt_k5_twoscomp,ax, ((v1_funct_1 k5_twoscomp) &  ((v1_funct_2 k5_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k5_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k5_unialg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ((m1_unialg_2 B A) & (m1_unialg_2 C A)) )  =>  ((v1_unialg_1 (k5_unialg_2 A B C)) & (m1_unialg_2 (k5_unialg_2 A B C) A)) ) ) ).
tt(dt_k5_unialg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) &  ((v2_unialg_2 B) & (l1_unialg_1 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k5_unialg_3 A B C)) &  ((v1_funct_2 (k5_unialg_3 A B C) (u1_struct_0 (k12_unialg_2 A)) (u1_struct_0 (k12_unialg_2 B))) & (m1_subset_1 (k5_unialg_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_unialg_2 A)) (u1_struct_0 (k12_unialg_2 B)))))) ) ) ) ).
tt(dt_k5_uniroots,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((v1_funct_1 (k5_uniroots A)) &  ((v1_funct_2 (k5_uniroots A) k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 (k5_uniroots A) k1_complfld) & (m1_subset_1 (k5_uniroots A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) ) ) ) ).
tt(dt_k5_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k5_uproots A B C)) &  ((v1_funct_2 (k5_uproots A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k5_uproots A B C) A) & (m1_subset_1 (k5_uproots A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k5_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k5_urysohn1 A)) &  ((v1_funct_1 (k5_urysohn1 A)) & (v1_finseq_1 (k5_urysohn1 A))) ) ) ) ).
tt(dt_k5_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((m2_urysohn3 D A B C) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  => (m1_subset_1 (k5_urysohn3 A B C D E) (k1_zfmisc_1 k7_numbers))) ) ).
tt(dt_k5_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C k5_numbers) &  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m1_finseq_1 D (k2_qc_lang1 A))) )  & (m1_subset_1 E (k3_margrel1 B))) ) ) )  => (m2_funct_2 (k5_valuat_1 A B C D E) (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))) ) ).
tt(dt_k5_valued_2,ax,$true).
tt(dt_k5_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v15_algstr_0 (k5_vectmetr A)) & (l3_algstr_0 (k5_vectmetr A))) ) ) ).
tt(dt_k5_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v1_funct_1 (k5_vectsp10 A B C)) &  ((v1_funct_2 (k5_vectsp10 A B C) (k2_zfmisc_1 (u1_struct_0 A) (k2_vectsp10 A B C)) (k2_vectsp10 A B C)) & (m1_subset_1 (k5_vectsp10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k2_vectsp10 A B C)) (k2_vectsp10 A B C))))) ) ) ) ).
tt(dt_k5_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((v1_funct_1 (k5_vectsp_1 A)) &  ((v1_funct_2 (k5_vectsp_1 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k5_vectsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k5_vectsp_2 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k5_vectsp_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_vectsp_5 A B)) &  ((v1_funct_2 (k5_vectsp_5 A B) (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B)) & (m1_subset_1 (k5_vectsp_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B))))) ) ) ) ).
tt(dt_k5_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_vectsp_6 D A B)) ) )  => (m1_vectsp_6 (k5_vectsp_6 A B C D) A B)) ) ).
tt(dt_k5_vectsp_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_vectsp_8 A B)))) ) )  =>  ((v7_vectsp_1 (k5_vectsp_8 A B C) A) & (m1_vectsp_4 (k5_vectsp_8 A B C) A B)) ) ) ).
tt(dt_k5_vfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k5_vfunct_1 A B C)) & (m1_subset_1 (k5_vfunct_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k5_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k5_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_funct_1 (k5_waybel10 A)) &  ((v1_funct_2 (k5_waybel10 A) (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)))) & (m1_subset_1 (k5_waybel10 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A))))))) ) ) ) ).
tt(dt_k5_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (m1_subset_1 (k5_waybel11 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k5_waybel18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k5_waybel18 A B C D) (u1_struct_0 (k4_waybel18 A B D)))) ) ).
tt(dt_k5_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k5_waybel_1 A B)) &  ((v1_funct_2 (k5_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k5_waybel_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_waybel20,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((v1_orders_2 (k5_waybel20 A B)) &  ((v3_orders_2 (k5_waybel20 A B)) &  ((v4_orders_2 (k5_waybel20 A B)) &  ((v5_orders_2 (k5_waybel20 A B)) &  ((v1_lattice3 (k5_waybel20 A B)) &  ((v2_lattice3 (k5_waybel20 A B)) &  ((v3_lattice3 (k5_waybel20 A B)) &  ((v3_waybel_3 (k5_waybel20 A B)) & (l1_orders_2 (k5_waybel20 A B))) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v6_waybel23 B A) & (m1_waybel23 B A)) )  =>  ((v1_funct_1 (k5_waybel23 A B)) &  ((v1_funct_2 (k5_waybel23 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) & (m1_subset_1 (k5_waybel23 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))))))) ) ) ) ).
tt(dt_k5_waybel26,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_relat_1 (k5_waybel26 A))) ) ).
tt(dt_k5_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_funct_1 (k5_waybel_2 A)) &  ((v1_funct_2 (k5_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 (k5_waybel_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k5_waybel34 A)))  &  ((v2_altcat_1 (k5_waybel34 A)) &  ((v6_altcat_1 (k5_waybel34 A)) &  ((v11_altcat_1 (k5_waybel34 A)) &  ((v12_altcat_1 (k5_waybel34 A)) &  ((v2_yellow21 (k5_waybel34 A)) & (l2_altcat_1 (k5_waybel34 A))) ) ) ) ) ) ) ) ).
tt(dt_k5_waybel35,ax,$true).
tt(dt_k5_waybel_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B))))) ) )  => (m1_subset_1 (k5_waybel_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k3_waybel_3 A B C))))) ) ).
tt(dt_k5_waybel_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (m1_subset_1 (k5_waybel_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k5_waybel_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) )  =>  ((v1_funct_1 (k5_waybel_5 A B)) &  ((v1_funct_2 (k5_waybel_5 A B) (k9_xtuple_0 B) (u1_struct_0 A)) & (m1_subset_1 (k5_waybel_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k5_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v6_waybel_0 (k5_waybel_9 A B C) A) & (m2_yellow_6 (k5_waybel_9 A B C) A B)) ) ) ).
tt(dt_k5_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_weddwitt A B)))  &  ( (~ (v6_struct_0 (k5_weddwitt A B)))  &  ((v13_algstr_0 (k5_weddwitt A B)) &  ((v33_algstr_0 (k5_weddwitt A B)) &  ((v36_algstr_0 (k5_weddwitt A B)) &  ((v2_rlvect_1 (k5_weddwitt A B)) &  ((v3_rlvect_1 (k5_weddwitt A B)) &  ((v4_rlvect_1 (k5_weddwitt A B)) &  ((v3_group_1 (k5_weddwitt A B)) &  ((v4_vectsp_1 (k5_weddwitt A B)) &  ((v5_vectsp_1 (k5_weddwitt A B)) & (l6_algstr_0 (k5_weddwitt A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k5_weierstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((v1_funct_1 (k5_weierstr A B)) &  ((v1_funct_2 (k5_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k5_weierstr A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k5_wsierp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  &  ((v7_ordinal1 C) & (m1_finseq_1 D B)) ) )  => (m1_trees_4 (k5_wsierp_1 A B C D) A B)) ) ).
tt(dt_k5_xboole_0,ax,$true).
tt(dt_k5_xboolean,ax,$true).
tt(dt_k5_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xcmplx_0 (k5_xcmplx_0 A))) ) ).
tt(dt_k5_xtuple_0,ax,$true).
tt(dt_k5_xxreal_0,ax,$true).
tt(dt_k5_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v1_xxreal_0 (k5_xxreal_3 A))) ) ).
tt(dt_k5_yellow_0,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (m1_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(dt_k5_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v9_functor0 (k5_yellow18 A) A (k4_yellow18 A)) &  ((v15_functor0 (k5_yellow18 A) A (k4_yellow18 A)) & (m2_functor0 (k5_yellow18 A) A (k4_yellow18 A))) ) ) ) ).
tt(dt_k5_yellow_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 A B)) & (l1_orders_2 (k5_yellow_1 A B))) ) ) ).
tt(dt_k5_yellow20,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  &  ((v16_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  ((v9_functor0 (k5_yellow20 A B C D) C B) &  ((v16_functor0 (k5_yellow20 A B C D) C B) & (m2_functor0 (k5_yellow20 A B C D) C B)) ) ) ) ).
tt(dt_k5_yellow21,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_altcat_1 A B C))) ) )  =>  ((v1_funct_1 (k5_yellow21 A B C D)) &  ((v1_funct_2 (k5_yellow21 A B C D) (u1_struct_0 (k3_yellow21 A B)) (u1_struct_0 (k3_yellow21 A C))) &  ((v5_orders_3 (k5_yellow21 A B C D) (k3_yellow21 A B) (k3_yellow21 A C)) & (m1_subset_1 (k5_yellow21 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow21 A B)) (u1_struct_0 (k3_yellow21 A C)))))) ) ) ) ) ).
tt(dt_k5_yellow_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (v1_relat_1 B))  => (m1_subset_1 (k5_yellow_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k5_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  => (m1_subset_1 (k5_yellow_3 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k5_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) & (l1_waybel_0 B A))  =>  ((v6_waybel_0 (k5_yellow_6 A B C) A) & (m1_yellow_6 (k5_yellow_6 A B C) A B)) ) ) ).
tt(dt_k5_zf_fund1,ax,$true).
tt(dt_k5_zf_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B k1_zf_lang) & (m1_subset_1 C k1_zf_lang)) )  =>  ((v1_relat_1 (k5_zf_lang1 A B C)) & (v1_funct_1 (k5_zf_lang1 A B C))) ) ) ).
tt(dt_k5_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) & (m1_subset_1 B k1_zf_lang))  => (m2_finseq_1 (k5_zf_lang A B) k5_numbers)) ) ).
tt(dt_k5_zf_model,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  (~ (v1_xboole_0 B)) )  => (m1_subset_1 (k5_zf_model A B) (k1_zfmisc_1 (k3_zf_model B)))) ) ).
tt(dt_k5_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) )  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ( (~ (v1_xboole_0 (k5_zf_refle A B C)))  & (m1_subset_1 (k5_zf_refle A B C) A)) ) ) ).
tt(dt_k5_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_zmodul01 C A)) )  => (m1_subset_1 (k5_zmodul01 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k60_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) )  => (m1_abcmiz_1 (k60_abcmiz_1 A B C) A (k13_abcmiz_1 A))) ) ).
tt(dt_k60_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k60_aofa_i00 A B C D E F) A) & (m1_subset_1 (k60_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k60_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  &  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) &  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) & (m1_subset_1 F (k1_zfmisc_1 A))) ) ) ) )  => (m1_subset_1 (k60_modelc_1 A B C D E F) (k1_zfmisc_1 A))) ) ).
tt(dt_k61_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) ) )  =>  ((v8_abcmiz_1 (k61_abcmiz_1 A B C) A) & (m1_abcmiz_1 (k61_abcmiz_1 A B C) A (k13_abcmiz_1 A))) ) ) ).
tt(dt_k61_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  &  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) & (m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C)))) ) ) )  =>  ((v1_funct_1 (k61_modelc_1 A B C D E)) &  ((v1_funct_2 (k61_modelc_1 A B C D E) (k1_zfmisc_1 A) (k1_zfmisc_1 A)) &  ((v6_cohsp_1 (k61_modelc_1 A B C D E)) & (m1_subset_1 (k61_modelc_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A))))) ) ) ) ) ).
tt(dt_k61_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k61_valued_1 A B)) & (v1_funct_1 (k61_valued_1 A B))) ) ) ).
tt(dt_k62_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) )  => (m1_abcmiz_1 (k62_abcmiz_1 A B C) A (k12_abcmiz_1 A))) ) ).
tt(dt_k62_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  => (m2_subset_1 (k62_valued_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k62_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k62_valued_2 A B C)) & (v1_funct_1 (k62_valued_2 A B C))) ) ) ).
tt(dt_k63_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A)))) )  => (m1_subset_1 (k63_abcmiz_1 A B C) (k1_zfmisc_1 (k38_abcmiz_1 A)))) ) ).
tt(dt_k63_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 (k63_valued_1 A)) & (v1_funct_1 (k63_valued_1 A))) ) ) ).
tt(dt_k63_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k63_valued_2 A B C D)) & (m1_subset_1 (k63_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k64_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m3_abcmiz_1 C A)) )  => (m3_abcmiz_1 (k64_abcmiz_1 A B C) A)) ) ).
tt(dt_k64_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  => (m2_subset_1 (k64_valued_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k64_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k64_valued_2 A B C D)) & (m1_subset_1 (k64_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k65_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  =>  ((v1_funct_1 (k65_abcmiz_1 A B C)) & (m1_subset_1 (k65_abcmiz_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) ) ).
tt(dt_k65_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  & (m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) )  =>  ((v15_aofa_000 (k65_aofa_i00 A B C D E) A) & (m1_subset_1 (k65_aofa_i00 A B C D E) (u1_struct_0 A))) ) ) ).
tt(dt_k66_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  & (m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) )  =>  ((v15_aofa_000 (k66_aofa_i00 A B C D E) A) & (m1_subset_1 (k66_aofa_i00 A B C D E) (u1_struct_0 A))) ) ) ).
tt(dt_k67_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) & (m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k67_aofa_i00 A B C D E F) A) & (m1_subset_1 (k67_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k68_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m3_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D) & (m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k68_aofa_i00 A B C D E F) A) & (m1_subset_1 (k68_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k68_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k68_valued_2 A B C)) & (v1_funct_1 (k68_valued_2 A B C))) ) ) ).
tt(dt_k69_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k69_valued_2 A B C D)) & (m1_subset_1 (k69_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k6_abcmiz_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l2_abcmiz_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A)))) )  => (m1_subset_1 (k6_abcmiz_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_abcmiz_1,ax,$true).
tt(dt_k6_afinsq_1,ax,$true).
tt(dt_k6_afinsq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) )  => (m1_subset_1 (k6_afinsq_2 A B C) A)) ) ).
tt(dt_k6_afproj,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k6_afproj A B) (k1_zfmisc_1 (k2_afproj A)))) ) ).
tt(dt_k6_alg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  => (m1_alg_1 (k6_alg_1 A B C) A)) ) ).
tt(dt_k6_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l3_algstr_0 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_algstr_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (v1_funct_1 B)) ) )  =>  ((v1_partfun1 (k6_algstr_4 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k6_algstr_4 A B)) &  ((v8_relat_2 (k6_algstr_4 A B)) & (m1_subset_1 (k6_algstr_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k6_altcat_1,ax, (! [A:$i,B:$i] :  ( ((v4_funct_1 A) & (v4_funct_1 B))  =>  ((v1_relat_1 (k6_altcat_1 A B)) &  ((v4_relat_1 (k6_altcat_1 A B) (k2_zfmisc_1 B A)) &  ((v1_funct_1 (k6_altcat_1 A B)) &  ((v1_partfun1 (k6_altcat_1 A B) (k2_zfmisc_1 B A)) &  ((v1_funcop_1 (k6_altcat_1 A B)) & (v7_altcat_1 (k6_altcat_1 A B))) ) ) ) ) ) ) ).
tt(dt_k6_altcat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v6_altcat_1 (k6_altcat_2 A B)) & (m1_altcat_2 (k6_altcat_2 A B) A)) ) ) ).
tt(dt_k6_ami_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) & (v7_ordinal1 B))  => (m1_subset_1 (k6_ami_2 A B) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) ) ).
tt(dt_k6_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k6_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k6_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) ) )  => (m2_subset_1 (k6_ami_wstd A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k6_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_analoaf (k6_analort A B C)) & (l1_analoaf (k6_analort A B C))) ) ) ).
tt(dt_k6_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k6_armstrng A B C) (k4_armstrng A))) ) ).
tt(dt_k6_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_arytm_2) & (m1_subset_1 B k1_arytm_2))  => (m2_subset_1 (k6_arytm_2 A B) (k1_zfmisc_1 k5_arytm_3) k1_arytm_2)) ) ).
tt(dt_k6_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) => (m1_subset_1 (k6_arytm_3 A) k4_ordinal1)) ) ).
tt(dt_k6_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k6_asympt_0 A) k5_numbers k1_numbers)) ) ).
tt(dt_k6_asympt_1,ax, ( (~ (v1_xboole_0 k6_asympt_1))  & (m1_subset_1 k6_asympt_1 (k1_zfmisc_1 k5_numbers))) ).
tt(dt_k6_autalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v1_funct_1 (k6_autalg_1 A B)) &  ((v1_funct_2 (k6_autalg_1 A B) (k2_zfmisc_1 (k5_autalg_1 A B) (k5_autalg_1 A B)) (k5_autalg_1 A B)) & (m1_subset_1 (k6_autalg_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_autalg_1 A B) (k5_autalg_1 A B)) (k5_autalg_1 A B))))) ) ) ) ).
tt(dt_k6_autgroup,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m2_funct_2 (k6_autgroup A B) (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A))) ) ).
tt(dt_k6_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k6_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k6_bagorder A)) &  ((v4_relat_2 (k6_bagorder A)) &  ((v8_relat_2 (k6_bagorder A)) & (m1_subset_1 (k6_bagorder A) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k6_bcialg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_subset_1 B (k5_bcialg_1 A)) & (m1_subset_1 C (k5_bcialg_1 A))) )  => (m2_subset_1 (k6_bcialg_1 A B C) (u1_struct_0 A) (k5_bcialg_1 A))) ) ).
tt(dt_k6_bcialg_2,ax,$true).
tt(dt_k6_bcialg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k6_bcialg_4 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_bcialg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m2_bcialg_1 B A) & (m4_bcialg_2 C A B)) )  =>  ((v1_funct_1 (k6_bcialg_6 A B C)) &  ((v1_funct_2 (k6_bcialg_6 A B C) (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A C))) &  ((v2_bcialg_6 (k6_bcialg_6 A B C) A (k9_bcialg_2 A C)) & (m1_subset_1 (k6_bcialg_6 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A C)))))) ) ) ) ) ).
tt(dt_k6_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k6_bhsp_1 A B C)) &  ((v1_funct_2 (k6_bhsp_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k6_bhsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_bhsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k6_bhsp_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_bilinear A B C D E)) &  ((v1_funct_2 (k6_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k6_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_binari_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k6_binari_2 A B C) A) & (m2_finseq_1 (k6_binari_2 A B C) k6_margrel1)) ) ) ).
tt(dt_k6_binarith,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1)) )  => (m2_subset_1 (k6_binarith A B) k1_numbers k5_numbers)) ) ).
tt(dt_k6_binom,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k6_binom A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (m1_subset_1 (k6_binop_2 A B) k2_numbers)) ) ).
tt(dt_k6_bor_cant,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_bor_cant A B)) &  ((v1_funct_2 (k6_bor_cant A B) k5_numbers k5_numbers) & (m1_subset_1 (k6_bor_cant A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ).
tt(dt_k6_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m2_connsp_2 E A C) & (m1_connsp_2 F B D)) ) ) ) )  => (m2_connsp_2 (k6_borsuk_1 A B C D E F) (k2_borsuk_1 A B) (k3_borsuk_1 A B C (k6_domain_1 (u1_struct_0 B) D)))) ) ).
tt(dt_k6_borsuk_6,ax,(m1_subset_1 k6_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))).
tt(dt_k6_bspace,ax, (! [A:$i] :  ((v1_funct_1 (k6_bspace A)) &  ((v1_funct_2 (k6_bspace A) (k2_zfmisc_1 (u1_struct_0 k2_bspace) (k1_zfmisc_1 A)) (k1_zfmisc_1 A)) & (m1_subset_1 (k6_bspace A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_bspace) (k1_zfmisc_1 A)) (k1_zfmisc_1 A))))) ) ) ).
tt(dt_k6_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k6_bvfunc_1 A B C)) &  ((v1_funct_2 (k6_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k6_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k6_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k6_bvfunc26 A B C)) &  ((v1_funct_2 (k6_bvfunc26 A B C) A k6_margrel1) & (m1_subset_1 (k6_bvfunc26 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k6_bvfunc_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) & (m1_eqrel_1 D A)) ) )  =>  ((v1_funct_1 (k6_bvfunc_2 A B C D)) &  ((v1_funct_2 (k6_bvfunc_2 A B C D) A k6_margrel1) & (m1_subset_1 (k6_bvfunc_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k6_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k6_c0sp1 A)))  & (m1_subset_1 (k6_c0sp1 A) (k1_zfmisc_1 (u1_struct_0 (k12_funcsdom A))))) ) ) ).
tt(dt_k6_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_c0sp2 A)))  & (m1_subset_1 (k6_c0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (u1_struct_0 A)))))) ) ) ).
tt(dt_k6_calcul_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C A)) )  => (m2_finseq_1 (k6_calcul_2 A B C) A)) ) ).
tt(dt_k6_card_1,ax,$true).
tt(dt_k6_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  => (v1_card_1 (k6_card_3 A))) ) ).
tt(dt_k6_card_fil,ax, (! [A:$i] :  ( ((v1_card_1 A) &  (~ (v2_card_1 A)) )  => (v1_card_1 (k6_card_fil A))) ) ).
tt(dt_k6_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_cat_1 D A B C)) ) )  => (m1_cat_1 (k6_cat_1 A B C D) A C B)) ) ).
tt(dt_k6_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_cat_2 A B C D E F)) &  ((v1_funct_2 (k6_cat_2 A B C D E F) (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) & (m1_subset_1 (k6_cat_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D))))) ) ) ) ).
tt(dt_k6_cat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  & (m1_subset_1 D (u4_struct_0 A))) )  =>  ((v1_funct_1 (k6_cat_3 A B C D)) &  ((v1_funct_2 (k6_cat_3 A B C D) B (u4_struct_0 A)) & (m1_subset_1 (k6_cat_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) ) ) ).
tt(dt_k6_cat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_cat_1 (k6_cat_4 A B) A B (k1_cat_4 A))) ) ).
tt(dt_k6_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ( (~ (v2_struct_0 (k6_cat_5 A B)))  &  ( (~ (v11_struct_0 (k6_cat_5 A B)))  &  ((v2_cat_1 (k6_cat_5 A B)) &  ((v3_cat_1 (k6_cat_5 A B)) &  ((v4_cat_1 (k6_cat_5 A B)) &  ((v5_cat_1 (k6_cat_5 A B)) &  ((v6_cat_1 (k6_cat_5 A B)) & (l1_cat_1 (k6_cat_5 A B))) ) ) ) ) ) ) ) ) ).
tt(dt_k6_catalg_1,ax,$true).
tt(dt_k6_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k6_cc0sp1 A)) &  ((v1_funct_2 (k6_cc0sp1 A) (k2_cc0sp1 A) k1_numbers) & (m1_subset_1 (k6_cc0sp1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cc0sp1 A) k1_numbers)))) ) ) ) ).
tt(dt_k6_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_cc0sp2 A)))  & (m1_subset_1 (k6_cc0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k6_cfuncdom (u1_struct_0 A)))))) ) ) ).
tt(dt_k6_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_cfuncdom A)))  &  ((v1_clvect_1 (k6_cfuncdom A)) & (l1_clvect_1 (k6_cfuncdom A))) ) ) ) ).
tt(dt_k6_cgames_1,ax,$true).
tt(dt_k6_chain_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_chain_1 B A))  => (m1_subset_1 (k6_chain_1 A B) (k1_zfmisc_1 (k4_chain_1 A B A)))) ) ).
tt(dt_k6_circcmb3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_circcmb3 B A) & (m1_circcmb3 C A)) )  =>  ((v1_msualg_1 (k6_circcmb3 A B C)) & (m1_circcmb3 (k6_circcmb3 A B C) A)) ) ) ).
tt(dt_k6_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  &  ((v4_msualg_1 D A) & (l3_msualg_1 D A)) ) ) )  =>  ((v3_msualg_1 (k6_circtrm1 A B C D) (k1_circtrm1 A B C)) &  ((v4_msualg_1 (k6_circtrm1 A B C D) (k1_circtrm1 A B C)) & (l3_msualg_1 (k6_circtrm1 A B C D) (k1_circtrm1 A B C))) ) ) ) ).
tt(dt_k6_circuit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (v7_ordinal1 (k6_circuit1 A B C))) ) ).
tt(dt_k6_circuit2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (k4_card_3 (u3_msualg_1 A B)))) )  => (m1_subset_1 (k6_circuit2 A B C) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k6_classes1,ax, (! [A:$i] : (v3_ordinal1 (k6_classes1 A))) ).
tt(dt_k6_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k6_classes2 A B C) A)) ) ).
tt(dt_k6_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_clopban1 A B)))  &  ((v13_algstr_0 (k6_clopban1 A B)) &  ((v2_rlvect_1 (k6_clopban1 A B)) &  ((v3_rlvect_1 (k6_clopban1 A B)) &  ((v4_rlvect_1 (k6_clopban1 A B)) &  ((v2_clvect_1 (k6_clopban1 A B)) &  ((v3_clvect_1 (k6_clopban1 A B)) &  ((v4_clvect_1 (k6_clopban1 A B)) &  ((v5_clvect_1 (k6_clopban1 A B)) & (l1_clvect_1 (k6_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k6_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (m2_subset_1 (k6_clopban2 A) (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A))) ) ).
tt(dt_k6_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k6_clopban3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_clopban4 A)) &  ((v1_funct_2 (k6_clopban4 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k6_clopban4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) &  ((v3_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) ) ) ) )  =>  ((v9_closure1 (k6_closure1 A B C) A) & (l1_closure1 (k6_closure1 A B C) A)) ) ) ).
tt(dt_k6_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_closure2 (k6_closure2 A B) A B) &  ((v2_closure2 (k6_closure2 A B) A B) &  ((v3_closure2 (k6_closure2 A B) A B) &  ((v4_closure2 (k6_closure2 A B) A B) &  ((v5_closure2 (k6_closure2 A B) A B) &  ((v6_closure2 (k6_closure2 A B) A B) & (m1_subset_1 (k6_closure2 A B) (k1_zfmisc_1 (k1_closure2 A B)))) ) ) ) ) ) ) ) ).
tt(dt_k6_clvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (v1_xcmplx_0 C)) )  =>  ((v1_funct_1 (k6_clvect_1 A B C)) &  ((v1_funct_2 (k6_clvect_1 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k6_clvect_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  => (m1_subset_1 (k6_clvect_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_clvect_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k6_clvect_3 A B C)) &  ((v1_funct_2 (k6_clvect_3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k6_clvect_3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  => (m1_subset_1 (k6_cohsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B))))) ) ).
tt(dt_k6_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) => (m1_subset_1 (k6_coh_sp A B) (k3_coh_sp A))) ) ).
tt(dt_k6_combgras,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) => (m1_subset_1 (k6_combgras A B) (k1_zfmisc_1 (k9_setfam_1 A)))) ) ).
tt(dt_k6_complex1,ax,(m1_subset_1 k6_complex1 k2_numbers)).
tt(dt_k6_complsp2,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k6_complsp2 A) k1_numbers)) ) ).
tt(dt_k6_compos_0,ax, (! [A:$i] :  ((v5_compos_0 A) => (m1_subset_1 (k6_compos_0 A) A)) ) ).
tt(dt_k6_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k6_compos_1 A B C)) &  ((v4_relat_1 (k6_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k6_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k6_compos_1 A B C)) & (v1_finset_1 (k6_compos_1 A B C))) ) ) ) ) ) ).
tt(dt_k6_comput_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  &  ((m1_subset_1 C k5_numbers) & (m1_finseq_1 D k5_numbers)) ) )  => (m2_rfunct_3 (k6_comput_1 A B C D) (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers))) ) ).
tt(dt_k6_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_funct_1 (k6_comseq_3 A B)) & (m1_subset_1 (k6_comseq_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k6_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v4_conlat_1 (k6_conlat_1 A) A) &  ( (~ (v5_conlat_1 (k6_conlat_1 A) A))  &  ((v7_conlat_1 (k6_conlat_1 A) A) &  ((v9_conlat_1 (k6_conlat_1 A) A) & (l2_conlat_1 (k6_conlat_1 A) A)) ) ) ) ) ) ).
tt(dt_k6_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_conlat_1 (k6_conlat_2 A)))  &  ((v2_conlat_1 (k6_conlat_2 A)) & (l1_conlat_1 (k6_conlat_2 A))) ) ) ) ).
tt(dt_k6_connsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_connsp_3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_cqc_lang,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m2_subset_1 (k6_cqc_lang A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k6_cqc_sim1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C (k8_qc_lang1 A B)) &  ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m1_finseq_1 D (k2_qc_lang1 A))) ) ) ) )  => (m2_funct_2 (k6_cqc_sim1 A B C D) (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))) ) ).
tt(dt_k6_csspace4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_csspace4 A B C)) &  ((v1_funct_2 (k6_csspace4 A B C) A (u1_struct_0 B)) &  ((v1_csspace4 (k6_csspace4 A B C) A B) & (m1_subset_1 (k6_csspace4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k6_csspace,ax,(m1_subset_1 k6_csspace k1_csspace)).
tt(dt_k6_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k6_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k6_descip_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k6_descip_1 A)) &  ((v1_funct_1 (k6_descip_1 A)) & (v1_finseq_1 (k6_descip_1 A))) ) ) ) ).
tt(dt_k6_dickson,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k6_dickson A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k6_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k6_diff_1 A B)) &  ((v1_funct_2 (k6_diff_1 A B) k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 (k6_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) ) ) ).
tt(dt_k6_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (k6_dilworth A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (m1_subset_1 (k6_dist_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (k3_finseq_2 A))))) ) ).
tt(dt_k6_domain_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k6_domain_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k6_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) & (l1_lang1 A)) )  =>  ( (~ (v1_xboole_0 (k6_dtconstr A)))  & (m1_subset_1 (k6_dtconstr A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k6_dynkin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C (k1_zfmisc_1 A)))  => (m1_subset_1 (k6_dynkin A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k6_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 C (u1_struct_0 (k9_int_3 A)))) )  =>  ( (~ (v1_xboole_0 (k6_ec_pf_1 A B C)))  & (m1_subset_1 (k6_ec_pf_1 A B C) (k1_zfmisc_1 (k3_ec_pf_1 (k9_int_3 A))))) ) ) ).
tt(dt_k6_ec_pf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) &  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 D (k6_ec_pf_1 A B C))) ) )  => (m1_subset_1 (k6_ec_pf_2 A B C D) (u1_struct_0 (k9_int_3 A)))) ) ).
tt(dt_k6_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v22_algstr_0 (k6_endalg A B)) & (l4_algstr_0 (k6_endalg A B))) ) ) ).
tt(dt_k6_ens_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k2_ens_1 A)) & (m1_subset_1 C (k2_ens_1 A))) )  => (m1_subset_1 (k6_ens_1 A B C) (k2_ens_1 A))) ) ).
tt(dt_k6_entropy1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m1_subset_1 (k6_entropy1 A) k1_numbers)) ) ).
tt(dt_k6_enumset1,ax,$true).
tt(dt_k6_eqrel_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k6_eqrel_1 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k6_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (u1_struct_0 (k15_euclid A)))) ) )  => (m1_subset_1 (k6_euclid_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k6_euclid_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) & (m1_subset_1 C (u1_struct_0 (k15_euclid 3)))) )  => (v1_xreal_0 (k6_euclid_5 A B C))) ) ).
tt(dt_k6_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_finseq_2 (k6_euclid_7 A B) k1_numbers (k1_euclid A))) ) ).
tt(dt_k6_euclid_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k6_euclid_8 A B C)) &  ((v1_funct_2 (k6_euclid_8 A B C) k1_numbers (k1_euclid 3)) & (m1_subset_1 (k6_euclid_8 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 3))))) ) ) ) ).
tt(dt_k6_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  => (m2_finseq_2 (k6_euclid A B) k1_numbers (k1_euclid A))) ) ).
tt(dt_k6_exchsort,ax,$true).
tt(dt_k6_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  =>  ((v1_relat_1 (k6_extpro_1 A B C D)) &  ((v4_relat_1 (k6_extpro_1 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k6_extpro_1 A B C D)) &  ((v5_funct_1 (k6_extpro_1 A B C D) (k2_memstr_0 A B)) & (v1_partfun1 (k6_extpro_1 A B C D) (u1_struct_0 B))) ) ) ) ) ) ).
tt(dt_k6_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((v3_msualg_1 (k6_facirc_1 A B C) (k5_circcomb C (k10_finseq_1 A B))) &  ((v4_msafree2 (k6_facirc_1 A B C) (k5_circcomb C (k10_finseq_1 A B))) &  ((v4_circcomb (k6_facirc_1 A B C) (k5_circcomb C (k10_finseq_1 A B))) &  ((v6_circcomb (k6_facirc_1 A B C) (k5_circcomb C (k10_finseq_1 A B))) & (l3_msualg_1 (k6_facirc_1 A B C) (k5_circcomb C (k10_finseq_1 A B)))) ) ) ) ) ) ).
tt(dt_k6_facirc_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m2_subset_1 (k6_facirc_2 A B C D) (u1_struct_0 (k3_facirc_2 B C D)) (k3_msafree2 (k3_facirc_2 B C D)))) ) ).
tt(dt_k6_ff_siec,ax, ((v1_petri k6_ff_siec) &  ((v1_net_1 k6_ff_siec) & (l1_petri k6_ff_siec)) ) ).
tt(dt_k6_fib_num2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_trees_4 (k6_fib_num2 A) k1_numbers k5_numbers)) ) ).
tt(dt_k6_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v2_struct_0 (k6_filter_0 A B)))  &  ((v10_lattices (k6_filter_0 A B)) & (l3_lattices (k6_filter_0 A B))) ) ) ) ).
tt(dt_k6_filter_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) )  =>  ((v1_funct_1 (k6_filter_1 A B C D)) &  ((v1_funct_2 (k6_filter_1 A B C D) (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 A B)) (k2_zfmisc_1 A B)) & (m1_subset_1 (k6_filter_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 A B)) (k2_zfmisc_1 A B))))) ) ) ) ).
tt(dt_k6_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k6_filter_2 A B)))  &  ((v18_lattices (k6_filter_2 A B) A) &  ((v21_lattices (k6_filter_2 A B) A) & (m1_subset_1 (k6_filter_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k6_finance1,ax,$true).
tt(dt_k6_finseq_1,ax, (! [A:$i] : (m2_finseq_1 (k6_finseq_1 A) A)) ).
tt(dt_k6_finseq_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k6_finseq_2 A B)) &  ((v4_relat_1 (k6_finseq_2 A B) (k3_finseq_2 A)) &  ((v1_funct_1 (k6_finseq_2 A B)) & (v1_partfun1 (k6_finseq_2 A B) (k3_finseq_2 A))) ) ) ) ) ).
tt(dt_k6_finseq_4,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k6_finseq_4 A B)) &  ((v1_funct_1 (k6_finseq_4 A B)) & (v1_finseq_1 (k6_finseq_4 A B))) ) ) ) ).
tt(dt_k6_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k6_finseq_8 A B C) A)) ) ).
tt(dt_k6_finseqop,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k6_finseqop A B C)) & (v1_funct_1 (k6_finseqop A B C))) ) ) ).
tt(dt_k6_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k6_fintopo2 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k6_fintopo3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k6_fintopo3 A B)) &  ((v1_funct_2 (k6_fintopo3 A B) k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 (k6_fintopo3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k6_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k6_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))))  => (m1_subset_1 (k6_flang_1 A B C) (k1_zfmisc_1 (k3_catalan2 A)))) ) ).
tt(dt_k6_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k6_fomodel0 A)) &  ((v1_funct_2 (k6_fomodel0 A) (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A) & (m1_subset_1 (k6_fomodel0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A)))) ) ) ) ).
tt(dt_k6_fomodel1,ax,$true).
tt(dt_k6_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k6_fomodel2 A B)) & (v1_funct_1 (k6_fomodel2 A B))) ) ) ).
tt(dt_k6_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  => (m1_subset_1 (k6_fomodel4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) (k35_fomodel1 A))))) ) ).
tt(dt_k6_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  => (m2_finseq_1 (k6_freealg A B) (k4_partfun1 (k3_finseq_2 (k4_dtconstr (k3_freealg A B))) (k4_dtconstr (k3_freealg A B))))) ) ).
tt(dt_k6_fscirc_1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k6_fscirc_1 A B C) (u1_struct_0 (k4_fscirc_1 A B C)) (k3_msafree2 (k4_fscirc_1 A B C)))) ).
tt(dt_k6_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  & (v7_ordinal1 D)) ) )  =>  ((v1_partfun1 (k6_fsm_1 A B C D) (u1_struct_0 C)) &  ((v3_relat_2 (k6_fsm_1 A B C D)) &  ((v8_relat_2 (k6_fsm_1 A B C D)) & (m1_subset_1 (k6_fsm_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k6_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B)) ) )  => (m1_subset_1 (k6_fsm_3 A B C) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k6_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k6_ftacell1 A B C D E) (k3_msafree2 (k1_ftacell1 A B C D E)))) ).
tt(dt_k6_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_funct_1 (k6_funcop_1 A B C D E)) &  ((v1_funct_2 (k6_funcop_1 A B C D E) B A) & (m1_subset_1 (k6_funcop_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k6_funcsdom,ax, (! [A:$i] :  ((v1_funct_1 (k6_funcsdom A)) &  ((v1_funct_2 (k6_funcsdom A) (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 (k6_funcsdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) ) ) ).
tt(dt_k6_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  => (m1_subset_1 (k6_funct_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k6_funct_3,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_funct_1 (k6_funct_3 A B)) &  ((v1_funct_2 (k6_funct_3 A B) B A) & (m1_subset_1 (k6_funct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k6_funct_4,ax,$true).
tt(dt_k6_funct_5,ax,$true).
tt(dt_k6_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k6_funct_6 A)) & (v1_funct_1 (k6_funct_6 A))) ) ) ).
tt(dt_k6_funct_7,ax,$true).
tt(dt_k6_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (k1_altcat_1 A D E))) ) ) ) )  => (m1_subset_1 (k6_functor0 A B C D E F) (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)))) ) ).
tt(dt_k6_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  &  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  &  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  &  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  & (m1_functor2 G B C D E)) ) ) ) ) )  => (m1_functor2 (k6_functor3 A B C D E F G) A C (k1_functor3 A B C F D) (k1_functor3 A B C F E))) ) ).
tt(dt_k6_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((v5_relat_1 (k6_fuzzy_1 A B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k6_fuzzy_1 A B C)) &  ((v1_funct_2 (k6_fuzzy_1 A B C) A k1_numbers) & (m1_subset_1 (k6_fuzzy_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(dt_k6_fvaluat1,ax,$true).
tt(dt_k6_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  & (m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B)))) )  => (m2_finseq_2 (k6_fvsum_1 A B C) (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B)))) ) ).
tt(dt_k6_gate_1,ax,$true).
tt(dt_k6_gate_5,ax,$true).
tt(dt_k6_gcd_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m2_gcd_1 B A) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k6_gcd_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k6_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_finseq_1 B (k3_card_3 A)) &  ((m1_finseq_1 C (k3_card_3 A)) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) &  ((m1_subset_1 H k5_numbers) & (m1_subset_1 I k5_numbers)) ) ) ) ) ) ) )  => (m2_finseq_1 (k6_genealg1 A B C D E F G H I) (k3_card_3 A))) ) ).
tt(dt_k6_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_geomtrap A)) &  ((v1_funct_2 (k6_geomtrap A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (k6_geomtrap A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k6_gfacirc1 A B C) (k5_gfacirc1 A B C)) &  ((v4_msafree2 (k6_gfacirc1 A B C) (k5_gfacirc1 A B C)) &  ((v4_circcomb (k6_gfacirc1 A B C) (k5_gfacirc1 A B C)) &  ((v6_circcomb (k6_gfacirc1 A B C) (k5_gfacirc1 A B C)) & (l3_msualg_1 (k6_gfacirc1 A B C) (k5_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k6_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  ((v3_msualg_1 (k6_gfacirc2 A B C) (k5_gfacirc2 A B C)) &  ((v4_msafree2 (k6_gfacirc2 A B C) (k5_gfacirc2 A B C)) &  ((v4_circcomb (k6_gfacirc2 A B C) (k5_gfacirc2 A B C)) &  ((v6_circcomb (k6_gfacirc2 A B C) (k5_gfacirc2 A B C)) & (l3_msualg_1 (k6_gfacirc2 A B C) (k5_gfacirc2 A B C))) ) ) ) ) ) ).
tt(dt_k6_glib_000,ax,$true).
tt(dt_k6_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  => (m3_glib_001 (k6_glib_001 A B) A)) ) ).
tt(dt_k6_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k6_glib_003 A)) & (v1_funct_1 (k6_glib_003 A))) ) ) ).
tt(dt_k6_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))))  => (m1_subset_1 (k6_glib_004 A B) (k1_zfmisc_1 (k7_glib_000 A)))) ) ).
tt(dt_k6_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m1_subset_1 C (k6_glib_000 A))) )  => (m1_glib_005 (k6_glib_005 A B C) A B)) ) ).
tt(dt_k6_goedelcp,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  => (m1_subset_1 (k6_goedelcp A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k6_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  => (m1_subset_1 (k6_graph_1 A) k5_numbers)) ) ).
tt(dt_k6_graph_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_graph_1 B A))  => (m2_finseq_1 (k6_graph_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k6_graph_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k6_graph_3 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k6_graph_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  => (m1_subset_1 (k6_graph_5 A B) (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 A))))) ) ).
tt(dt_k6_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) & (m1_subset_1 B (k3_finseq_2 k1_numbers)))  => (m2_finseq_2 (k6_graphsp A B) k1_numbers (k3_finseq_2 k1_numbers))) ) ).
tt(dt_k6_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_struct_0 B)) )  =>  ((v1_funct_1 (k6_grcat_1 A B)) &  ((v1_funct_2 (k6_grcat_1 A B) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k6_grcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_funct_1 (k6_groeb_3 A B C D E)) &  ((v1_funct_2 (k6_groeb_3 A B C D E) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k6_groeb_3 A B C D E) (k15_pre_poly A) C) & (m1_subset_1 (k6_groeb_3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k6_group_10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  (~ (v1_xboole_0 C)) ) )  =>  ((v1_funct_1 (k6_group_10 A B C)) &  ((v1_funct_2 (k6_group_10 A B C) (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C)) & (m1_subset_1 (k6_group_10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C))))) ) ) ) ).
tt(dt_k6_group_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m2_subset_1 (k6_group_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k6_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k6_group_2 A)) & (m1_group_2 (k6_group_2 A) A)) ) ) ).
tt(dt_k6_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v15_algstr_0 (k6_group_3 A B C)) & (m1_group_2 (k6_group_3 A B C) A)) ) ) ).
tt(dt_k6_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k6_group_4 A)) & (m1_group_2 (k6_group_4 A) A)) ) ) ).
tt(dt_k6_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (m1_subset_1 (k6_group_5 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v1_group_3 B A) & (m1_group_2 B A))  & (m1_subset_1 C (u1_struct_0 (k5_group_6 A B)))) )  => (m1_subset_1 (k6_group_6 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_group_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) & (m1_subset_1 F (u1_struct_0 C))) ) ) ) )  => (m1_subset_1 (k6_group_7 A B C D E F) (u1_struct_0 (k2_group_7 (k1_enumset1 1 2 3) (k11_finseq_1 A B C))))) ) ).
tt(dt_k6_group_9,ax,$true).
tt(dt_k6_hahnban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k6_hahnban1 A B C D)) &  ((v1_funct_2 (k6_hahnban1 A B C D) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k6_hahnban1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_hermitan A B C)) &  ((v1_funct_2 (k6_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_hermitan (k6_hermitan A B C) A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) & (m1_subset_1 (k6_hermitan A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ).
tt(dt_k6_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) => (m1_subset_1 (k6_heyting1 A B) (k5_finsub_1 (k7_normform A)))) ) ).
tt(dt_k6_heyting2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 C (u1_struct_0 (k5_substlat A B))))  => (m1_subset_1 (k6_heyting2 A B C) (k5_finsub_1 (u1_struct_0 (k5_substlat A B))))) ) ).
tt(dt_k6_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_hilbasis A B)) &  ((v1_funct_2 (k6_hilbasis A B) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (m1_subset_1 (k6_hilbasis A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)))))) ) ) ) ).
tt(dt_k6_hilbert1,ax,(m1_subset_1 k6_hilbert1 (k1_zfmisc_1 k1_hilbert1))).
tt(dt_k6_hurwitz,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k6_hurwitz A B C)) &  ((v1_funct_2 (k6_hurwitz A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k6_hurwitz A B C) A) & (m1_subset_1 (k6_hurwitz A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k6_idea_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k6_idea_1 A B) k5_numbers)) ) ).
tt(dt_k6_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m3_ideal_1 D A B) & (m3_ideal_1 E A C)) ) ) )  => (m3_ideal_1 (k6_ideal_1 A B C D E) A (k4_subset_1 (u1_struct_0 A) B C))) ) ).
tt(dt_k6_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_partfun1 D B) & (v1_funcop_1 D)) ) ) ) )  =>  ((v2_index_1 (k6_index_1 A B C D) A B) &  ((v3_index_1 (k6_index_1 A B C D) A B) & (m1_index_1 (k6_index_1 A B C D) A B)) ) ) ) ).
tt(dt_k6_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k6_int_1 A B))) ) ).
tt(dt_k6_integr10,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k6_integr10 A)) &  ((v1_funct_2 (k6_integr10 A) k1_numbers k1_numbers) & (m1_subset_1 (k6_integr10 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(dt_k6_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  & (m4_integr15 E A B C D)) ) ) )  =>  ((v1_funct_1 (k6_integr15 A B C D E)) &  ((v1_funct_2 (k6_integr15 A B C D E) k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 (k6_integr15 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) ) ) ).
tt(dt_k6_integr16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  => (m1_subset_1 (k6_integr16 A B) k2_numbers)) ) ).
tt(dt_k6_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k6_integr18 A B C D) (u1_struct_0 A))) ) ).
tt(dt_k6_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  => (m1_subset_1 (k6_integra1 A B C) k1_numbers)) ) ).
tt(dt_k6_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_interva1 B A)) )  => (m1_subset_1 (k6_interva1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k6_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) => (m1_subset_1 (k6_intpro_1 A) k1_intpro_1)) ) ).
tt(dt_k6_isocat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m2_cat_1 F B C) &  ((m2_cat_1 G B C) &  ((m2_nattra_1 H A B D E) & (m2_nattra_1 I B C F G)) ) ) ) ) ) ) )  => (m2_nattra_1 (k6_isocat_1 A B C D E F G H I) A C (k9_cat_1 A B C D F) (k9_cat_1 A B C E G))) ) ).
tt(dt_k6_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) &  ((m2_cat_1 E (k8_cat_2 A B) C) & (m2_nattra_1 F (k8_cat_2 A B) C D E)) ) ) ) )  => (m2_nattra_1 (k6_isocat_2 A B C D E F) A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E))) ) ).
tt(dt_k6_jgraph_4,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m1_subset_1 (k6_jgraph_4 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k6_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k6_jgraph_6 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k6_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k6_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k6_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k6_jordan6 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k6_jordan,ax, ((v1_funct_1 k6_jordan) &  ((v1_funct_2 k6_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 k6_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ).
tt(dt_k6_knaster,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v3_ordinal1 D)) ) )  => (m1_subset_1 (k6_knaster A B C D) (u1_struct_0 A))) ) ).
tt(dt_k6_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_kolmog01 D A B C)) )  => (m1_subset_1 (k6_kolmog01 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ).
tt(dt_k6_kurato_1,ax,(m1_subset_1 k6_kurato_1 (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))).
tt(dt_k6_lang1,ax, (! [A:$i] :  ((v2_lang1 (k6_lang1 A)) & (l2_lang1 (k6_lang1 A))) ) ).
tt(dt_k6_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 E (u1_struct_0 D) C C)) ) ) )  => (m1_subset_1 (k6_laplace A B C D E) (u1_struct_0 D))) ) ).
tt(dt_k6_lattice3,ax, (! [A:$i,B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_partfun1 (k6_lattice3 A B) A) &  ((v1_relat_2 (k6_lattice3 A B)) &  ((v4_relat_2 (k6_lattice3 A B)) &  ((v8_relat_2 (k6_lattice3 A B)) & (m1_subset_1 (k6_lattice3 A B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(dt_k6_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B)))) ) )  =>  ((v1_funct_1 (k6_lattice5 A B C D)) &  ((v1_funct_2 (k6_lattice5 A B C D) (k2_zfmisc_1 (k5_lattice5 A) (k5_lattice5 A)) (u1_struct_0 B)) & (m1_subset_1 (k6_lattice5 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_lattice5 A) (k5_lattice5 A)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  => (m1_subset_1 (k6_lattice6 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  =>  ((v1_funct_1 (k6_lattice8 A B C D E)) &  ((v1_funct_2 (k6_lattice8 A B C D E) (k2_zfmisc_1 (k3_lattice8 A E) (k3_lattice8 A E)) (u1_struct_0 B)) & (m1_subset_1 (k6_lattice8 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_lattice8 A E) (k3_lattice8 A E)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  => (m1_subset_1 (k6_lattices A) (u1_struct_0 A))) ) ).
tt(dt_k6_lexbfs,ax,$true).
tt(dt_k6_lfuzzy_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  => (m1_subset_1 (k6_lfuzzy_0 A B) (u1_struct_0 (k4_lfuzzy_0 A)))) ) ).
tt(dt_k6_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k5_lopban_1 A B))) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k6_lopban_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k6_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (m2_subset_1 (k6_lopban_2 A) (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A))) ) ).
tt(dt_k6_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k6_lopban_3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_lopban_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k6_lopban_4 A B C D)) &  ((v1_funct_2 (k6_lopban_4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k6_lopban_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k6_lopclset A)))  &  ((v10_lattices (k6_lopclset A)) & (l3_lattices (k6_lopclset A))) ) ) ) ).
tt(dt_k6_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m2_rfunct_3 (k6_lpspace1 A) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k6_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k6_lpspace2 A B C D)))  & (m1_subset_1 (k6_lpspace2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (k1_lpspace2 A B C D))))) ) ) ).
tt(dt_k6_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (m1_subset_1 (k6_ltlaxio1 A) k1_hilbert1)) ) ).
tt(dt_k6_margrel1,ax,$true).
tt(dt_k6_mathmorp,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  => (m1_subset_1 (k6_mathmorp A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k6_matrix12,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v7_ordinal1 E) &  ((v7_ordinal1 F) & (m1_subset_1 G (u1_struct_0 C))) ) ) ) ) )  => (m1_matrix_1 (k6_matrix12 A B C D E F G) (u1_struct_0 C) A B)) ) ).
tt(dt_k6_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  &  ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) ) ) ) )  => (m1_matrix_1 (k6_matrix13 A B C D) A (k5_card_1 C) (k5_card_1 D))) ) ).
tt(dt_k6_matrix15,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_finseq_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_matrix15 A B C) (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 A (k1_matrix_1 B)))))) ) ).
tt(dt_k6_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  => (m2_finseq_1 (k6_matrix_1 A B C) A)) ) ).
tt(dt_k6_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  => (m1_matrix_1 (k6_matrix_2 A B C D E) A 2 2)) ) ).
tt(dt_k6_matrix_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_matrix_1 (k6_matrix_3 A B C)) & (m2_finseq_1 (k6_matrix_3 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k6_matrix_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k2_numbers))) )  =>  ((v1_matrix_1 (k6_matrix_5 A B)) & (m2_finseq_1 (k6_matrix_5 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k6_matrixc1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  & (m1_finseq_1 B k2_numbers))  => (m2_finseq_1 (k6_matrixc1 A B) k2_numbers)) ) ).
tt(dt_k6_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v1_matrixj1 (k6_matrixj1 A B C) A) & (m2_finseq_1 (k6_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k6_matrixj2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_matrixj2 C A B) & (m1_matrixj2 D A B)) ) )  => (m1_matrixj2 (k6_matrixj2 A B C D) A B)) ) ).
tt(dt_k6_matrixr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k1_numbers))) )  =>  ((v1_matrix_1 (k6_matrixr1 A B)) & (m2_finseq_1 (k6_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k6_matrixr2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_finseq_1 (k6_matrixr2 A B) k1_numbers)) ) ).
tt(dt_k6_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v13_vectsp_1 F C D) &  ((v1_mod_2 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_matrlin2 A B C D E F)) &  ((v1_funct_2 (k6_matrlin2 A B C D E F) (u1_struct_0 B) (u1_struct_0 D)) &  ((v13_vectsp_1 (k6_matrlin2 A B C D E F) B D) &  ((v1_mod_2 (k6_matrlin2 A B C D E F) A B D) & (m1_subset_1 (k6_matrlin2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ).
tt(dt_k6_matrlin,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  => (m2_finseq_1 (k6_matrlin A B) (u1_struct_0 A))) ) ).
tt(dt_k6_matroid0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k6_matroid0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_matrprob,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A k1_numbers) &  ((m1_finseq_1 B k1_numbers) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 k1_numbers))) ) )  =>  ((v1_matrix_1 (k6_matrprob A B C)) & (m2_finseq_1 (k6_matrprob A B C) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k6_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  => (m1_subset_1 (k6_mcart_1 A B C D E) C)) ) ).
tt(dt_k6_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k6_measure6 A) (k1_zfmisc_1 k1_numbers))) ) ).
tt(dt_k6_measure7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) & (m1_measure7 B A))  => (m1_subset_1 (k6_measure7 A B) k7_numbers)) ) ).
tt(dt_k6_measure8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  ((v1_funct_1 (k6_measure8 A B C)) &  ((v1_funct_2 (k6_measure8 A B C) (k9_setfam_1 A) k7_numbers) & (m1_subset_1 (k6_measure8 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) k7_numbers)))) ) ) ) ).
tt(dt_k6_member_1,ax, (! [A:$i] :  ((v2_membered A) => (v2_membered (k6_member_1 A))) ) ).
tt(dt_k6_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((l1_memstr_0 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((v1_relat_1 (k6_memstr_0 A B C)) &  ((v4_relat_1 (k6_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k6_memstr_0 A B C)) & (v5_funct_1 (k6_memstr_0 A B C) (k2_memstr_0 A B))) ) ) ) ) ).
tt(dt_k6_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k6_mesfun7c A B)) & (m1_subset_1 (k6_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k6_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k6_mesfunc1 A B C)) & (m1_subset_1 (k6_mesfunc1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k6_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) )  => (m1_subset_1 (k6_mesfunc5 A B C D) k7_numbers)) ) ).
tt(dt_k6_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k6_mesfunc8 A B)) & (m1_subset_1 (k6_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k6_metric_1,ax, (! [A:$i] :  ((v1_metric_1 (k6_metric_1 A)) & (l1_metric_1 (k6_metric_1 A))) ) ).
tt(dt_k6_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k6_metric_2 A) (k1_zfmisc_1 (k2_metric_2 A)))) ) ).
tt(dt_k6_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (m1_midsp_1 (k6_midsp_1 A) A)) ) ).
tt(dt_k6_midsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_midsp_2 A B C)) &  ((v1_funct_2 (k6_midsp_2 A B C) (k2_zfmisc_1 A A) A) & (m1_subset_1 (k6_midsp_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ).
tt(dt_k6_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ((m1_subset_1 C (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (m2_finseq_2 (k6_midsp_3 A B C D E) (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B)))) ) ).
tt(dt_k6_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k6_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k6_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v2_mod_2 (k6_mod_2 A B) A) & (m1_mod_2 (k6_mod_2 A B) A B B)) ) ) ).
tt(dt_k6_mod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_mod_4 A B C)) &  ((v1_funct_2 (k6_mod_4 A B C) (k2_zfmisc_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k5_mod_4 A B))) (u1_struct_0 (k5_mod_4 A B))) & (m1_subset_1 (k6_mod_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k5_mod_4 A B))) (u1_struct_0 (k5_mod_4 A B)))))) ) ) ) ).
tt(dt_k6_modal_1,ax,(m1_trees_3 k6_modal_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))).
tt(dt_k6_modcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_modcat_1 B A) & (m1_subset_1 C (k4_modcat_1 A B))) )  => (m2_modcat_1 (k6_modcat_1 A B C) A B)) ) ).
tt(dt_k6_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_finseq_1 (k6_modelc_1 A) k5_numbers)) ) ).
tt(dt_k6_modelc_2,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k6_modelc_2 A) k5_numbers)) ) ).
tt(dt_k6_modelc_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((l1_modelc_3 B A) &  ((v1_modelc_2 C) & (m1_finseq_1 C k5_numbers)) ) )  =>  ((v1_modelc_3 (k6_modelc_3 A B C) A) & (l1_modelc_3 (k6_modelc_3 A B C) A)) ) ) ).
tt(dt_k6_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  => (m2_subset_1 (k6_moebius1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k6_monoid_0,ax, ( (~ (v2_struct_0 k6_monoid_0))  &  ((v15_algstr_0 k6_monoid_0) &  ((v1_group_1 k6_monoid_0) &  ((v3_group_1 k6_monoid_0) &  ((v5_group_1 k6_monoid_0) & (l3_algstr_0 k6_monoid_0)) ) ) ) ) ).
tt(dt_k6_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ((m1_subset_1 F B) &  ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) )  => (m2_funct_2 (k6_monoid_1 A B C D E F G) A D (k9_funct_2 A D))) ) ).
tt(dt_k6_msafree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  => (m2_pboole (k6_msafree2 A B) (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A B))) ) ).
tt(dt_k6_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  => (m1_subset_1 (k6_msafree A B C) (u1_struct_0 (k5_msafree A B)))) ) ).
tt(dt_k6_msalimit,ax,$true).
tt(dt_k6_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k7_dtconstr (k5_msafree A B))) & (m1_msaterm D A B C)) ) )  => (m1_dtconstr (k6_msaterm A B C D) (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ).
tt(dt_k6_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v7_struct_0 (k6_msualg_1 A)) &  ( (~ (v11_struct_0 (k6_msualg_1 A)))  &  ((v1_msualg_1 (k6_msualg_1 A)) &  ((v5_msualg_1 (k6_msualg_1 A)) & (l1_msualg_1 (k6_msualg_1 A))) ) ) ) ) ) ).
tt(dt_k6_msualg_2,ax,$true).
tt(dt_k6_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  & (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C))) ) )  =>  ((v3_msualg_1 (k6_msualg_3 A B C D) A) &  ((v4_msualg_1 (k6_msualg_3 A B C D) A) & (m1_msualg_2 (k6_msualg_3 A B C D) A C)) ) ) ) ).
tt(dt_k6_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) )  & (m1_subset_1 E (k3_msualg_1 A B C))) ) ) )  => (m1_subset_1 (k6_msualg_4 A B C D E) (k4_card_3 (k3_relat_1 (k1_msualg_1 A B) (k4_msualg_4 A C D))))) ) ).
tt(dt_k6_msualg_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v3_lattices (k6_msualg_5 A B)) & (m2_nat_lat (k6_msualg_5 A B) (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ).
tt(dt_k6_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v3_msualg_6 (k6_msualg_6 A B C) A B) & (m1_msualg_4 (k6_msualg_6 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ).
tt(dt_k6_mycielsk,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_mycielsk B A))  => (m1_mycielsk (k6_mycielsk A B) (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1))) ) ).
tt(dt_k6_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k6_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k6_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k6_nat_3 A B C)) &  ((v4_relat_1 (k6_nat_3 A B C) A) &  ((v1_funct_1 (k6_nat_3 A B C)) & (v1_partfun1 (k6_nat_3 A B C) A)) ) ) ) ) ).
tt(dt_k6_nat_5,ax, ((v1_funct_1 k6_nat_5) &  ((v1_funct_2 k6_nat_5 k5_numbers k5_numbers) & (m1_subset_1 k6_nat_5 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ).
tt(dt_k6_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k6_nat_d A B) k5_numbers)) ) ).
tt(dt_k6_nat_lat,ax,(m1_subset_1 k6_nat_lat (k1_zfmisc_1 k5_numbers))).
tt(dt_k6_nattra_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  => (m2_nattra_1 (k6_nattra_1 A B C) A B C C)) ) ).
tt(dt_k6_ndiff_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  & (m1_subset_1 E (u1_struct_0 (k14_prvect_2 A)))) ) )  => (m1_subset_1 (k6_ndiff_5 A B C D E) (u1_struct_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B)))) ) ).
tt(dt_k6_net_1,ax,$true).
tt(dt_k6_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m2_subset_1 (k6_newton A B) k1_numbers k5_numbers)) ) ).
tt(dt_k6_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k5_finsub_1 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B)))))) ) ) )  => (m1_subset_1 (k6_normform A B C D) (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 B)))) ) ).
tt(dt_k6_normsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k6_normsp_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k6_numbers,ax,(m2_subset_1 k6_numbers k1_numbers k5_numbers)).
tt(dt_k6_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k6_openlatt A)))  &  ((v10_lattices (k6_openlatt A)) & (l3_lattices (k6_openlatt A))) ) ) ) ).
tt(dt_k6_oppcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 (k2_oppcat_1 A))))  => (m1_subset_1 (k6_oppcat_1 A B) (u4_struct_0 A))) ) ).
tt(dt_k6_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k6_ordinal3 A B))) ) ).
tt(dt_k6_ordinal4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v3_ordinal1 B) & (m1_subset_1 B A)) )  =>  ((v3_ordinal1 (k6_ordinal4 A B)) &  ( (~ (v1_xboole_0 (k6_ordinal4 A B)))  & (m1_subset_1 (k6_ordinal4 A B) A)) ) ) ) ).
tt(dt_k6_ordinal6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (v3_ordinal1 B))  =>  ((v1_funct_1 (k6_ordinal6 A B)) &  ((v1_funct_2 (k6_ordinal6 A B) (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 (k6_ordinal6 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ).
tt(dt_k6_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((v1_funct_1 (k6_osafree A B C)) &  ((v1_funct_2 (k6_osafree A B C) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) C)) & (m1_subset_1 (k6_osafree A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)) C))))) ) ) ) ).
tt(dt_k6_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C B)) )  =>  ((v3_msualg_1 (k6_osalg_1 A B C) A) &  ((v12_osalg_1 (k6_osalg_1 A B C) A) & (l3_msualg_1 (k6_osalg_1 A B C) A)) ) ) ) ).
tt(dt_k6_osalg_2,ax,$true).
tt(dt_k6_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k6_osalg_4 A B C D) (k1_zfmisc_1 (k8_eqrel_1 (k4_osalg_4 A (u3_msualg_1 A B) (k3_osalg_4 A D)) (k5_osalg_4 A B C (k3_osalg_4 A D)))))) ) ).
tt(dt_k6_parsp_1,ax,$true).
tt(dt_k6_partfun1,ax, (! [A:$i] :  ((v1_partfun1 (k6_partfun1 A) A) & (m1_subset_1 (k6_partfun1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ).
tt(dt_k6_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_eqrel_1 (k6_partit1 A) A)) ) ).
tt(dt_k6_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k6_pboole A B C)) &  ((v4_relat_1 (k6_pboole A B C) A) &  ((v1_funct_1 (k6_pboole A B C)) & (v1_partfun1 (k6_pboole A B C) A)) ) ) ) ) ).
tt(dt_k6_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v7_pcs_0 B)) ) ) )  & (m1_subset_1 C A)) )  => (l1_pcs_0 (k6_pcs_0 A B C))) ) ).
tt(dt_k6_pdiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C (k1_euclid A))) )  =>  ((v1_funct_1 (k6_pdiff_1 A B C)) &  ((v1_funct_2 (k6_pdiff_1 A B C) k1_numbers (k1_euclid A)) & (m1_subset_1 (k6_pdiff_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) ) ) ).
tt(dt_k6_pdiff_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  &  ((m1_subset_1 B (k1_euclid 3)) & (m1_subset_1 C (k1_euclid 3))) )  => (m1_subset_1 (k6_pdiff_4 A B C) k1_numbers)) ) ).
tt(dt_k6_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k6_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k6_pencil_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k6_pencil_4 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (k2_vectsp_9 A B C))))) ) ).
tt(dt_k6_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k6_petri A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k6_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  & (m1_pnproc_1 C A))  =>  ((v1_funct_1 (k6_pnproc_1 A B C)) &  ((v1_funct_2 (k6_pnproc_1 A B C) A k5_numbers) & (m1_subset_1 (k6_pnproc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(dt_k6_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k1_numbers)) ) )  => (m1_subset_1 (k6_polyeq_1 A B C D) k1_numbers)) ) ).
tt(dt_k6_polyeq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_xcmplx_0 (k6_polyeq_5 A B C D))) ) ).
tt(dt_k6_polyform,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k4_numbers) & (m1_finseq_1 B k4_numbers))  => (m2_finseq_1 (k6_polyform A B) k4_numbers)) ) ).
tt(dt_k6_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom1 A B C D)) &  ((v1_funct_2 (k6_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k6_polynom1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom2 A B C)) &  ((v1_funct_2 (k6_polynom2 A B C) (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (m1_subset_1 (k6_polynom2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_polynom3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_subset_1 B k5_numbers))  => (m2_finseq_1 (k6_polynom3 A B) (k4_finseq_2 A k5_numbers))) ) ).
tt(dt_k6_polynom5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k6_polynom5 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_polynom7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l5_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  & (m1_subset_1 D (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_polynom7 A B C D)) &  ((v1_funct_2 (k6_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k6_polynom7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_polynom8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k6_polynom8 A B C D)) &  ((v1_funct_2 (k6_polynom8 A B C D) k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 (k6_polynom8 A B C D) B) & (m1_subset_1 (k6_polynom8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k6_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_poset_1 A B)))  &  ((v1_orders_2 (k6_poset_1 A B)) &  ((v3_orders_2 (k6_poset_1 A B)) &  ((v4_orders_2 (k6_poset_1 A B)) &  ((v5_orders_2 (k6_poset_1 A B)) & (l1_orders_2 (k6_poset_1 A B))) ) ) ) ) ) ) ).
tt(dt_k6_power,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k6_power A B) k1_numbers)) ) ).
tt(dt_k6_pralg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k6_pralg_1 A B)) &  ((v1_funct_2 (k6_pralg_1 A B) (k2_zfmisc_1 A B) (k2_zfmisc_1 B A)) & (m1_subset_1 (k6_pralg_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A))))) ) ) ) ).
tt(dt_k6_pralg_2,ax,$true).
tt(dt_k6_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_prelamb A B C) (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)))) ) ).
tt(dt_k6_prepower,ax,$true).
tt(dt_k6_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m1_prob_1 (k6_prob_1 A B C D) A B)) ) ).
tt(dt_k6_prob_3,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k9_setfam_1 A)) => (m2_finseq_1 (k6_prob_3 A B) (k9_setfam_1 A))) ) ).
tt(dt_k6_prob_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) & (m1_subset_1 D (k4_prob_4 A B C))) ) )  =>  ( (~ (v1_xboole_0 (k6_prob_4 A B C D)))  & (m1_subset_1 (k6_prob_4 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_k6_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ((v7_vectsp_1 (k6_prvect_1 A B) A) & (l1_vectsp_1 (k6_prvect_1 A B) A)) ) ) ).
tt(dt_k6_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  => (m1_prvect_1 (k6_prvect_2 A) (k4_prvect_2 A))) ) ).
tt(dt_k6_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_normsp_1 B)) )  =>  ((v1_funct_1 (k6_prvect_3 A B)) &  ((v1_funct_2 (k6_prvect_3 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) k1_numbers) & (m1_subset_1 (k6_prvect_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) k1_numbers)))) ) ) ) ).
tt(dt_k6_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k6_pscomp_1 A) k1_numbers)) ) ).
tt(dt_k6_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  => (m1_subset_1 (k6_pua2mss1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k6_qc_lang1,ax,$true).
tt(dt_k6_qc_lang2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k9_qc_lang1 A))) ) )  => (m1_subset_1 (k6_qc_lang2 A B C D) (k9_qc_lang1 A))) ) ).
tt(dt_k6_qc_lang3,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k6_qc_lang3 A B) (k1_zfmisc_1 (k4_qc_lang1 A)))) ) ).
tt(dt_k6_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  => (m1_subset_1 (k6_qmax_1 A B) (k2_qmax_1 A))) ) ).
tt(dt_k6_quatern2,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (m1_subset_1 (k6_quatern2 A B) k1_quaterni)) ) ).
tt(dt_k6_quaterni,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (m1_subset_1 (k6_quaterni A B C D) k1_quaterni)) ) ).
tt(dt_k6_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  & (m1_subset_1 B (k1_quofield A)))  => (m1_subset_1 (k6_quofield A B) (k1_zfmisc_1 (k1_quofield A)))) ) ).
tt(dt_k6_radix_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  => (m1_subset_1 (k6_radix_1 A B C D) k4_numbers)) ) ).
tt(dt_k6_radix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_int_1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((v7_ordinal1 E) &  ((v3_card_1 F E) & (m1_finseq_1 F (k3_radix_1 D))) ) ) ) ) )  => (v1_int_1 (k6_radix_2 A B C D E F))) ) ).
tt(dt_k6_radix_3,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (v1_int_1 (k6_radix_3 A B))) ) ).
tt(dt_k6_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k6_radix_5 A B C) A) & (m2_finseq_1 (k6_radix_5 A B C) (k3_radix_1 C))) ) ) ).
tt(dt_k6_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k6_radix_6 A B C) (k2_xcmplx_0 A 2)) & (m2_finseq_1 (k6_radix_6 A B C) (k3_radix_1 B))) ) ) ).
tt(dt_k6_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  => (m1_random_1 (k6_random_1 A B C D) A B)) ) ).
tt(dt_k6_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m2_vectsp_6 (k6_ranknull A B C D) A B D)) ) ).
tt(dt_k6_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_ratfunc1 B A))  => (m1_ratfunc1 (k6_ratfunc1 A B) A)) ) ).
tt(dt_k6_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  => (m1_subset_1 (k6_real_1 A B) k1_numbers)) ) ).
tt(dt_k6_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k6_real_3 A)) &  ((v1_funct_2 (k6_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k6_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k6_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_real_lat A)))  &  ((v3_lattices (k6_real_lat A)) & (l3_lattices (k6_real_lat A))) ) ) ) ).
tt(dt_k6_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k6_real_ns1 A)) &  ((v1_funct_2 (k6_real_ns1 A) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers) & (m1_subset_1 (k6_real_ns1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) k1_numbers)))) ) ) ) ).
tt(dt_k6_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) => (v1_relat_1 (k6_relat_1 A B))) ) ).
tt(dt_k6_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k6_relset_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k6_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  => (m1_subset_1 (k6_relset_2 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k6_rewrite2,ax, (! [A:$i] : (m1_subset_1 (k6_rewrite2 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ).
tt(dt_k6_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v1_integra2 (k6_rfinseq2 A)) & (m2_finseq_1 (k6_rfinseq2 A) k1_numbers)) ) ) ).
tt(dt_k6_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k6_rfunct_1 A B C)) & (m1_subset_1 (k6_rfunct_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k6_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (m1_subset_1 (k6_rinfsup1 A) k1_numbers)) ) ).
tt(dt_k6_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (m1_subset_1 (k6_rinfsup2 A) k7_numbers)) ) ).
tt(dt_k6_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ((v3_ringcat1 A) & (l1_ringcat1 A))  &  ((v3_ringcat1 B) & (l1_ringcat1 B)) )  =>  ((v2_ringcat1 (k6_ringcat1 A B)) &  ((v3_ringcat1 (k6_ringcat1 A B)) & (l1_ringcat1 (k6_ringcat1 A B))) ) ) ) ).
tt(dt_k6_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_rlsub_2 A)) &  ((v1_funct_2 (k6_rlsub_2 A) (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A)) & (m1_subset_1 (k6_rlsub_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rlsub_2 A) (k3_rlsub_2 A)) (k3_rlsub_2 A))))) ) ) ) ).
tt(dt_k6_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlvect_2 B A))  => (m1_subset_1 (k6_rlvect_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k6_rmod_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_rmod_3 A B)) &  ((v1_funct_2 (k6_rmod_3 A B) (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B)) & (m1_subset_1 (k6_rmod_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rmod_3 A B) (k3_rmod_3 A B)) (k3_rmod_3 A B))))) ) ) ) ).
tt(dt_k6_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_4 C A B) & (m1_rmod_4 D A B)) ) )  => (m1_rmod_4 (k6_rmod_4 A B C D) A B)) ) ).
tt(dt_k6_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (l2_robbins1 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_robbins1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k6_roughs_1 A B)) &  ((v1_funct_2 (k6_roughs_1 A B) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (k6_roughs_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_k6_rsspace4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_rsspace4 A B C)) &  ((v1_funct_2 (k6_rsspace4 A B C) A (u1_struct_0 B)) &  ((v1_rsspace4 (k6_rsspace4 A B C) A B) & (m1_subset_1 (k6_rsspace4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ).
tt(dt_k6_rsspace,ax,(m1_subset_1 k6_rsspace k1_rsspace)).
tt(dt_k6_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_rusub_2 A)) &  ((v1_funct_2 (k6_rusub_2 A) (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A)) & (m1_subset_1 (k6_rusub_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rusub_2 A) (k3_rusub_2 A)) (k3_rusub_2 A))))) ) ) ) ).
tt(dt_k6_rusub_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k6_rusub_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 (k6_rvsum_1 A) k1_numbers)) ) ).
tt(dt_k6_rvsum_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers)) )  => (m2_finseq_2 (k6_rvsum_2 A B) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k6_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (m1_dtconstr (k6_scm_comp A B) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k6_scmfsa_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) & (v7_ordinal1 B))  => (m1_subset_1 (k6_scmfsa_1 A B) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) ) ).
tt(dt_k6_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k6_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k6_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k6_scmfsa6a A B)) &  ((v4_relat_1 (k6_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k6_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k6_scmfsa6a A B)))  &  ((v1_funct_1 (k6_scmfsa6a A B)) &  ((v1_finset_1 (k6_scmfsa6a A B)) & (v1_afinsq_1 (k6_scmfsa6a A B))) ) ) ) ) ) ) ) ).
tt(dt_k6_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k6_scmfsa_i A) k2_scm_inst)) ) ).
tt(dt_k6_scmfsa_m,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  => (m1_subset_1 (k6_scmfsa_m A B C) (k1_zfmisc_1 k2_scmfsa_2))) ) ).
tt(dt_k6_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (m1_subset_1 (k6_scm_inst A) k5_numbers)) ) ).
tt(dt_k6_scmpds_1,ax, ((v1_funct_1 k6_scmpds_1) &  ((v1_funct_2 k6_scmpds_1 k1_scmpds_i (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) & (m1_subset_1 k6_scmpds_1 (k1_zfmisc_1 (k2_zfmisc_1 k1_scmpds_i (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))))) ) ).
tt(dt_k6_scmpds_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  => (m1_subset_1 (k6_scmpds_2 A B) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k6_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) ) ) )  =>  ((v1_relat_1 (k6_scmpds_4 A B C)) &  ((v4_relat_1 (k6_scmpds_4 A B C) (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 (k6_scmpds_4 A B C)) &  ((v5_funct_1 (k6_scmpds_4 A B C) (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 (k6_scmpds_4 A B C) (u1_struct_0 k1_scmpds_2))) ) ) ) ) ) ).
tt(dt_k6_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k6_scmpds_6 A B C)))  &  ((v1_relat_1 (k6_scmpds_6 A B C)) &  ((v4_relat_1 (k6_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k6_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k6_scmpds_6 A B C)) &  ((v1_finset_1 (k6_scmpds_6 A B C)) & (v1_afinsq_1 (k6_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k6_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k6_scmpds_i A))) ) ).
tt(dt_k6_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B k2_ami_2) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k6_scmring1 A B C) (k2_xboole_0 k2_ami_2 (u1_struct_0 A)))) ) ).
tt(dt_k6_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k6_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k6_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k6_scmringi A B) k2_scm_inst)) ) ).
tt(dt_k6_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) => (v4_scmyciel (k6_scmyciel A))) ) ).
tt(dt_k6_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v6_membered A))  => (m2_subset_1 (k6_seq_4 A) k1_numbers k5_numbers)) ) ).
tt(dt_k6_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) )  =>  ((v1_funct_1 (k6_seqfunc A B C)) &  ((v1_funct_2 (k6_seqfunc A B C) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k6_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k6_series_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (v7_ordinal1 B))  => (m1_subset_1 (k6_series_1 A B) k1_numbers)) ) ).
tt(dt_k6_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k6_setfam_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k6_setlim_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k6_setlim_1 A B C) B) &  ((v1_funct_1 (k6_setlim_1 A B C)) &  ((v1_funct_2 (k6_setlim_1 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k6_setlim_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) ).
tt(dt_k6_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k6_setlim_2 A B C)) &  ((v1_funct_2 (k6_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k6_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k6_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  => (m1_subset_1 (k6_setwiseo A B C) (k5_finsub_1 A))) ) ).
tt(dt_k6_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  => (m1_scmfsa_2 (k6_sf_mastr A))) ) ).
tt(dt_k6_sheffer1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k6_sheffer1 A B) (u1_struct_0 A))) ) ).
tt(dt_k6_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_xxreal_0 (k6_simplex0 A))) ) ).
tt(dt_k6_sincos10,ax,$true).
tt(dt_k6_sin_cos2,ax, (! [A:$i] : (m1_subset_1 (k6_sin_cos2 A) k1_numbers)) ).
tt(dt_k6_sin_cos6,ax, (! [A:$i] : (m1_subset_1 (k6_sin_cos6 A) k1_numbers)) ).
tt(dt_k6_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k6_sin_cos7 A))) ) ).
tt(dt_k6_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k6_sin_cos9 A) k1_numbers)) ) ).
tt(dt_k6_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k6_sin_cos A)) &  ((v1_funct_2 (k6_sin_cos A) k5_numbers k2_numbers) & (m1_subset_1 (k6_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k6_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k6_square_1 A))) ) ).
tt(dt_k6_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  & (l1_stacks_1 A))  & (m1_subset_1 B (u4_struct_0 A)))  => (m1_subset_1 (k6_stacks_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k6_struct_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_struct_0 A B C)) &  ((v1_funct_2 (k6_struct_0 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k6_struct_0 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k6_sublemma,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) & (m1_subset_1 C (k38_substut1 A))) )  => (m2_subset_1 (k6_sublemma A B C) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k6_subset_1,ax, (! [A:$i,B:$i] : (m1_subset_1 (k6_subset_1 A B) (k1_zfmisc_1 A))) ).
tt(dt_k6_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_substut1 A)))  => (m1_subset_1 (k6_substut1 A B C) (k1_substut1 A))) ) ).
tt(dt_k6_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v1_funct_1 (k6_substut2 A)) &  ((v1_funct_2 (k6_substut2 A) (k38_substut1 A) (k1_substut1 A)) & (m1_subset_1 (k6_substut2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k38_substut1 A) (k1_substut1 A))))) ) ) ) ).
tt(dt_k6_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  => (v2_membered (k6_supinf_1 A))) ) ).
tt(dt_k6_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) => (m1_subset_1 (k6_supinf_2 A) (k1_zfmisc_1 k7_numbers))) ) ).
tt(dt_k6_taylor_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ((v1_funct_1 (k6_taylor_1 A B C D)) &  ((v1_funct_2 (k6_taylor_1 A B C D) k5_numbers k1_numbers) & (m1_subset_1 (k6_taylor_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k6_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k6_tdlat_1 A)) &  ((v1_funct_2 (k6_tdlat_1 A) (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A)) & (m1_subset_1 (k6_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A))))) ) ) ) ).
tt(dt_k6_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_termord A B C D)) &  ((v1_funct_2 (k6_termord A B C D) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k6_termord A B C D) (k15_pre_poly A) C) & (m1_subset_1 (k6_termord A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ).
tt(dt_k6_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k6_tex_4 A B)) & (m1_pre_topc (k6_tex_4 A B) A)) ) ) ).
tt(dt_k6_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k6_tmap_1 A B)) &  ((v2_pre_topc (k6_tmap_1 A B)) & (l1_pre_topc (k6_tmap_1 A B))) ) ) ) ).
tt(dt_k6_topalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_borsuk_2 D A B C)) ) )  =>  ((v1_funct_1 (k6_topalg_1 A B C D)) &  ((v1_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) & (m1_subset_1 (k6_topalg_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))))) ) ) ) ).
tt(dt_k6_topalg_5,ax, (! [A:$i] :  ((v1_int_1 A) => (m1_borsuk_2 (k6_topalg_5 A) (k8_toprealb 2) k9_toprealb k9_toprealb)) ) ).
tt(dt_k6_topalg_6,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_finseq_1 B (k1_topalg_6 A)))  => (m2_subset_1 (k6_topalg_6 A B) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ).
tt(dt_k6_topgen_3,ax, (! [A:$i,B:$i] :  ((v1_pre_topc (k6_topgen_3 A B)) &  ((v2_pre_topc (k6_topgen_3 A B)) & (l1_pre_topc (k6_topgen_3 A B))) ) ) ).
tt(dt_k6_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m3_topgrp_1 (k6_topgrp_1 A B) A)) ) ).
tt(dt_k6_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k6_topreal1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k6_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_funct_1 (k6_toprealb A)) &  ((v1_funct_2 (k6_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A))))) & (m1_subset_1 (k6_toprealb A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A)))))))) ) ) ) ).
tt(dt_k6_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  => (m1_subset_1 (k6_toprealc A B C D E F) (u1_struct_0 C))) ) ).
tt(dt_k6_toprns_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) ) )  => (m1_subset_1 (k6_toprns_1 A B) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k6_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  => (m1_subset_1 (k6_trees_1 A) k5_numbers)) ) ).
tt(dt_k6_trees_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  => (m1_subset_1 (k6_trees_2 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k6_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k6_trees_3 A B)) &  ((v1_funct_2 (k6_trees_3 A B) (k2_zfmisc_1 A B) A) & (m1_subset_1 (k6_trees_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) A)))) ) ) ) ).
tt(dt_k6_trees_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((v1_relat_1 (k6_trees_4 A B C)) &  ((v1_funct_1 (k6_trees_4 A B C)) & (v3_trees_2 (k6_trees_4 A B C))) ) ) ) ).
tt(dt_k6_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  => (m1_subset_1 (k6_trees_9 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 A) (k3_trees_9 A))))) ) ).
tt(dt_k6_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))))  => (v1_int_1 (k6_turing_1 A B))) ) ).
tt(dt_k6_twoscomp,ax, ((v1_funct_1 k6_twoscomp) &  ((v1_funct_2 k6_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k6_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k6_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m1_subset_1 (k6_unialg_2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k6_uproots A B C)) &  ((v1_funct_2 (k6_uproots A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k6_uproots A B C) A) & (m1_subset_1 (k6_uproots A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k6_urysohn1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_urysohn1 A)))  => (m1_subset_1 (k6_urysohn1 A B) k5_numbers)) ) ).
tt(dt_k6_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m2_urysohn3 D A B C)) ) )  =>  ((v1_funct_1 (k6_urysohn3 A B C D)) &  ((v1_funct_2 (k6_urysohn3 A B C D) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k6_urysohn3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k6_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))))) )  & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (m2_funct_2 (k6_valuat_1 A B C D) (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))) ) ).
tt(dt_k6_valued_2,ax,$true).
tt(dt_k6_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ( (~ (v2_struct_0 (k6_vectsp10 A B C)))  &  ((v13_algstr_0 (k6_vectsp10 A B C)) &  ((v2_rlvect_1 (k6_vectsp10 A B C)) &  ((v3_rlvect_1 (k6_vectsp10 A B C)) &  ((v4_rlvect_1 (k6_vectsp10 A B C)) &  ((v7_vectsp_1 (k6_vectsp10 A B C) A) &  ((v8_vectsp_1 (k6_vectsp10 A B C) A) &  ((v9_vectsp_1 (k6_vectsp10 A B C) A) &  ((v10_vectsp_1 (k6_vectsp10 A B C) A) &  ((v11_vectsp_1 (k6_vectsp10 A B C) A) & (l1_vectsp_1 (k6_vectsp10 A B C) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k6_vectsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_vectsp_2 A B)))  &  ((v13_algstr_0 (k6_vectsp_2 A B)) &  ((v2_rlvect_1 (k6_vectsp_2 A B)) &  ((v3_rlvect_1 (k6_vectsp_2 A B)) &  ((v4_rlvect_1 (k6_vectsp_2 A B)) &  ((v3_vectsp_2 (k6_vectsp_2 A B) A B) & (l2_vectsp_2 (k6_vectsp_2 A B) A B)) ) ) ) ) ) ) ) ).
tt(dt_k6_vectsp_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_vectsp_5 A B)) &  ((v1_funct_2 (k6_vectsp_5 A B) (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B)) & (m1_subset_1 (k6_vectsp_5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B))))) ) ) ) ).
tt(dt_k6_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_vectsp_6 D A B)) ) )  => (m1_vectsp_6 (k6_vectsp_6 A B C D) A B)) ) ).
tt(dt_k6_vectsp_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  ((v1_funct_1 (k6_vectsp_8 A B C D)) &  ((v1_funct_2 (k6_vectsp_8 A B C D) (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A C))) & (m1_subset_1 (k6_vectsp_8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A C)))))) ) ) ) ).
tt(dt_k6_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_vfunct_1 A B C D)) & (m1_subset_1 (k6_vfunct_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ).
tt(dt_k6_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k6_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_waybel10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_yellow_0 B A))  =>  ((v1_funct_1 (k6_waybel10 A B)) &  ((v1_funct_2 (k6_waybel10 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k6_waybel10 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k6_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k6_waybel18 A B C)) &  ((v1_funct_2 (k6_waybel18 A B C) (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C))) & (m1_subset_1 (k6_waybel18 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)))))) ) ) ) ).
tt(dt_k6_waybel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k6_waybel_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k6_waybel26,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) =>  ((v1_relat_1 (k6_waybel26 A B)) & (v1_funct_1 (k6_waybel26 A B))) ) ) ).
tt(dt_k6_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((v9_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A)) &  ((v16_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A)) & (m2_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A))) ) ) ) ).
tt(dt_k6_waybel35,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (m1_subset_1 (k6_waybel35 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_waybel_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (m1_subset_1 (k6_waybel_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k6_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  => (m2_pboole (k6_waybel_5 A B C D) A (k7_funcop_1 A B) (k7_funcop_1 A C))) ) ).
tt(dt_k6_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (l1_waybel_0 D A)) ) )  =>  ((v6_waybel_0 (k6_waybel_9 A B C D) B) & (l1_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(dt_k6_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_weddwitt A)))  &  ((v13_algstr_0 (k6_weddwitt A)) &  ((v2_rlvect_1 (k6_weddwitt A)) &  ((v3_rlvect_1 (k6_weddwitt A)) &  ((v4_rlvect_1 (k6_weddwitt A)) &  ((v7_vectsp_1 (k6_weddwitt A) (k4_weddwitt A)) &  ((v8_vectsp_1 (k6_weddwitt A) (k4_weddwitt A)) &  ((v9_vectsp_1 (k6_weddwitt A) (k4_weddwitt A)) &  ((v10_vectsp_1 (k6_weddwitt A) (k4_weddwitt A)) &  ((v11_vectsp_1 (k6_weddwitt A) (k4_weddwitt A)) & (l1_vectsp_1 (k6_weddwitt A) (k4_weddwitt A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k6_weierstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((v1_funct_1 (k6_weierstr A B)) &  ((v1_funct_2 (k6_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k6_weierstr A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(dt_k6_xboolean,ax,$true).
tt(dt_k6_xcmplx_0,ax,$true).
tt(dt_k6_xtuple_0,ax,$true).
tt(dt_k6_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k6_xxreal_3 A B))) ) ).
tt(dt_k6_yellow_1,ax, (! [A:$i,B:$i] :  ((l1_orders_2 B) =>  ((v1_orders_2 (k6_yellow_1 A B)) & (l1_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(dt_k6_yellow21,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_yellow21 A)))  &  ((v2_altcat_1 (k6_yellow21 A)) &  ((v6_altcat_1 (k6_yellow21 A)) &  ((v11_altcat_1 (k6_yellow21 A)) &  ((v12_altcat_1 (k6_yellow21 A)) &  ((v2_yellow21 (k6_yellow21 A)) & (l2_altcat_1 (k6_yellow21 A))) ) ) ) ) ) ) ) ).
tt(dt_k6_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m1_subset_1 (k6_yellow_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) ) ).
tt(dt_k6_yellow_6,ax,$true).
tt(dt_k6_zf_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B k1_zf_lang) & (m1_subset_1 C k1_zf_lang)) )  =>  ((v1_zf_lang (k6_zf_lang1 A B C)) & (m2_finseq_1 (k6_zf_lang1 A B C) k5_numbers)) ) ) ).
tt(dt_k6_zf_lang,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k6_zf_lang A) k5_numbers)) ) ).
tt(dt_k6_zf_model,ax, ((v1_zf_lang k6_zf_model) & (m2_finseq_1 k6_zf_model k5_numbers)) ).
tt(dt_k6_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_zmodul01 B A) & (m1_zmodul01 C A)) )  =>  ((v1_zmodul01 (k6_zmodul01 A B C)) & (m1_zmodul01 (k6_zmodul01 A B C) A)) ) ) ).
tt(dt_k70_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((v1_funct_1 (k70_valued_2 A B C D)) & (m1_subset_1 (k70_valued_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k6_valued_2 (k1_valued_2 B)))))) ) ) ).
tt(dt_k72_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  & (m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) )  =>  ((v15_aofa_000 (k72_aofa_i00 A B C D E) A) & (m1_subset_1 (k72_aofa_i00 A B C D E) (u1_struct_0 A))) ) ) ).
tt(dt_k72_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 A) &  ((v1_valued_2 B) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) ) ) ) )  =>  ((v1_relat_1 (k72_valued_2 A B C D)) & (v1_funct_1 (k72_valued_2 A B C D))) ) ) ).
tt(dt_k73_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  & (m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) )  =>  ((v15_aofa_000 (k73_aofa_i00 A B C D E) A) & (m1_subset_1 (k73_aofa_i00 A B C D E) (u1_struct_0 A))) ) ) ).
tt(dt_k73_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k73_valued_2 A B C D E F)) & (m1_subset_1 (k73_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k2_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k74_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k74_aofa_i00 A B C D E F) A) & (m1_subset_1 (k74_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k74_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k74_valued_2 A B C D E F)) & (m1_subset_1 (k74_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k6_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k75_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k75_aofa_i00 A B C D E F) A) & (m1_subset_1 (k75_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k76_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k76_aofa_i00 A B C D E F) A) & (m1_subset_1 (k76_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k77_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k77_aofa_i00 A B C D E F) A) & (m1_subset_1 (k77_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k78_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k78_aofa_i00 A B C D E F) A) & (m1_subset_1 (k78_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k78_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 A) &  ((v1_valued_2 B) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) ) ) ) )  =>  ((v1_relat_1 (k78_valued_2 A B C D)) & (v1_funct_1 (k78_valued_2 A B C D))) ) ) ).
tt(dt_k79_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C B) &  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (v1_int_1 F)) ) ) ) )  =>  ((v15_aofa_000 (k79_aofa_i00 A B C D E F) A) & (m1_subset_1 (k79_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k79_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k79_valued_2 A B C D E F)) & (m1_subset_1 (k79_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k2_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k7_abcmiz_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_abcmiz_0 A))) )  => (m2_finseq_1 (k7_abcmiz_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k7_abcmiz_1,ax,$true).
tt(dt_k7_abcmiz_a,ax, ( (~ (v1_xboole_0 k7_abcmiz_a))  & (m1_subset_1 k7_abcmiz_a (k1_zfmisc_1 k20_abcmiz_1))) ).
tt(dt_k7_afinsq_1,ax,$true).
tt(dt_k7_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  => (m1_subset_1 (k7_afinsq_2 A) k2_numbers)) ) ).
tt(dt_k7_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~ (v1_xboole_0 (k7_afproj A))) ) ) ).
tt(dt_k7_alg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k7_alg_1 A B C)) &  ((v1_funct_2 (k7_alg_1 A B C) (u1_struct_0 (k4_alg_1 A (k6_alg_1 A B C))) (u1_struct_0 B)) & (m1_subset_1 (k7_alg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_alg_1 A (k6_alg_1 A B C))) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_algstr_0,ax,(l3_algstr_0 k7_algstr_0)).
tt(dt_k7_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_partfun1 (k7_algstr_4 A B C) A) &  ((v3_relat_2 (k7_algstr_4 A B C)) &  ((v8_relat_2 (k7_algstr_4 A B C)) & (m1_subset_1 (k7_algstr_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ).
tt(dt_k7_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_altcat_1 A)))  &  ((v6_altcat_1 (k7_altcat_1 A)) &  ((v10_altcat_1 (k7_altcat_1 A)) & (l2_altcat_1 (k7_altcat_1 A))) ) ) ) ) ).
tt(dt_k7_ami_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) &  ((m1_subset_1 B k2_ami_2) & (v1_int_1 C)) )  => (m1_subset_1 (k7_ami_2 A B C) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) ) ).
tt(dt_k7_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k7_ami_3 A) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k7_ami_wstd,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  &  ((m1_subset_1 C k5_numbers) & (v7_ordinal1 D)) ) )  => (m2_subset_1 (k7_ami_wstd A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k7_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_relat_1 (k7_aofa_000 A B C)) & (v1_funct_1 (k7_aofa_000 A B C))) ) ) ).
tt(dt_k7_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  & (v1_int_1 C)) )  =>  ((v1_funct_1 (k7_aofa_i00 A B C)) &  ((v1_funct_2 (k7_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k7_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k7_armstrng,ax, (! [A:$i] : (m1_subset_1 (k7_armstrng A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_armstrng A) (k4_armstrng A))))) ).
tt(dt_k7_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  => (m1_subset_1 (k7_arytm_2 A B) k2_arytm_2)) ) ).
tt(dt_k7_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) => (m1_subset_1 (k7_arytm_3 A) k4_ordinal1)) ) ).
tt(dt_k7_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k7_asympt_0 A) k5_numbers k1_numbers)) ) ).
tt(dt_k7_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m2_subset_1 (k7_asympt_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k7_autalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k7_autalg_1 A B)))  &  ((v2_group_1 (k7_autalg_1 A B)) &  ((v3_group_1 (k7_autalg_1 A B)) & (l3_algstr_0 (k7_autalg_1 A B))) ) ) ) ) ).
tt(dt_k7_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k7_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k7_bagorder A)) &  ((v4_relat_2 (k7_bagorder A)) &  ((v8_relat_2 (k7_bagorder A)) & (m1_subset_1 (k7_bagorder A) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) ) ).
tt(dt_k7_bcialg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_subset_1 B (k5_bcialg_1 A)))  =>  ( (~ (v1_xboole_0 (k7_bcialg_1 A B)))  & (m1_subset_1 (k7_bcialg_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k7_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_bcialg_2 B A))  =>  ((v1_funct_1 (k7_bcialg_2 A B)) &  ((v1_funct_2 (k7_bcialg_2 A B) (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B)) & (m1_subset_1 (k7_bcialg_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_eqrel_1 (u1_struct_0 A) B) (k8_eqrel_1 (u1_struct_0 A) B)) (k8_eqrel_1 (u1_struct_0 A) B))))) ) ) ) ).
tt(dt_k7_bcialg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  & (m1_finseq_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_bcialg_4 A B) (u1_struct_0 A))) ) ).
tt(dt_k7_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  =>  ( (~ (v1_xboole_0 (k7_bcialg_6 A B C D)))  & (m1_subset_1 (k7_bcialg_6 A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k7_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k7_bilinear A B C D E)) &  ((v1_funct_2 (k7_bilinear A B C D E) (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 (k7_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k7_binarith,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((v3_card_1 (k7_binarith A B C) A) & (m2_finseq_1 (k7_binarith A B C) k6_margrel1)) ) ) ).
tt(dt_k7_binom,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k7_binom A B) k5_numbers)) ) ).
tt(dt_k7_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k7_binop_2 A) k1_numbers)) ) ).
tt(dt_k7_bor_cant,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k7_bor_cant A B)) &  ((v1_funct_2 (k7_bor_cant A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k7_bor_cant A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k7_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) )  => (m1_subset_1 (k7_borsuk_1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))) ) ).
tt(dt_k7_borsuk_6,ax,(m1_subset_1 k7_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))).
tt(dt_k7_borsuk_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) &  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) &  ((m1_borsuk_2 C k3_topmetr A B) & (v1_xreal_0 D)) ) )  => (m1_borsuk_2 (k7_borsuk_7 A B C D) k3_topmetr (k3_borsuk_7 A D) (k3_borsuk_7 B D))) ) ).
tt(dt_k7_bspace,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k7_bspace A)))  & (l1_vectsp_1 (k7_bspace A) k2_bspace)) ) ).
tt(dt_k7_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k7_bvfunc_1 A B)) & (v1_funct_1 (k7_bvfunc_1 A B))) ) ) ).
tt(dt_k7_bvfunc_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) & (m1_eqrel_1 D A)) ) )  =>  ((v1_funct_1 (k7_bvfunc_2 A B C D)) &  ((v1_funct_2 (k7_bvfunc_2 A B C D) A k6_margrel1) & (m1_subset_1 (k7_bvfunc_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k7_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_c0sp1 A)))  &  ((v13_algstr_0 (k7_c0sp1 A)) &  ((v2_rlvect_1 (k7_c0sp1 A)) &  ((v3_rlvect_1 (k7_c0sp1 A)) &  ((v4_rlvect_1 (k7_c0sp1 A)) &  ((v5_rlvect_1 (k7_c0sp1 A)) &  ((v6_rlvect_1 (k7_c0sp1 A)) &  ((v7_rlvect_1 (k7_c0sp1 A)) &  ((v2_funcsdom (k7_c0sp1 A)) &  ((v3_group_1 (k7_c0sp1 A)) &  ((v5_group_1 (k7_c0sp1 A)) &  ((v1_vectsp_1 (k7_c0sp1 A)) &  ((v3_vectsp_1 (k7_c0sp1 A)) & (l1_funcsdom (k7_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k7_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k7_c0sp2 A)))  &  ((v13_algstr_0 (k7_c0sp2 A)) &  ((v2_rlvect_1 (k7_c0sp2 A)) &  ((v3_rlvect_1 (k7_c0sp2 A)) &  ((v4_rlvect_1 (k7_c0sp2 A)) &  ((v5_rlvect_1 (k7_c0sp2 A)) &  ((v6_rlvect_1 (k7_c0sp2 A)) &  ((v7_rlvect_1 (k7_c0sp2 A)) &  ((v8_rlvect_1 (k7_c0sp2 A)) & (l1_rlvect_1 (k7_c0sp2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k7_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k7_card_1 A) (k1_zfmisc_1 k4_ordinal1))) ) ).
tt(dt_k7_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  => (v1_card_1 (k7_card_3 A))) ) ).
tt(dt_k7_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k7_cat_1 A B C)) &  ((v1_funct_2 (k7_cat_1 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k7_cat_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) )  =>  ((v1_funct_1 (k7_cat_2 A B C D)) & (m1_subset_1 (k7_cat_2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 A B)) (k2_zfmisc_1 A B))))) ) ) ).
tt(dt_k7_cat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  & (m1_subset_1 D (u4_struct_0 A))) )  =>  ((v1_funct_1 (k7_cat_3 A B C D)) &  ((v1_funct_2 (k7_cat_3 A B C D) B (u4_struct_0 A)) & (m1_subset_1 (k7_cat_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) ) ) ).
tt(dt_k7_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k7_cat_4 A B C) A (k2_cat_4 A B C) B)) ) ).
tt(dt_k7_cat_5,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k7_cat_5 A)))  &  ( (~ (v11_struct_0 (k7_cat_5 A)))  &  ((v2_cat_1 (k7_cat_5 A)) &  ((v3_cat_1 (k7_cat_5 A)) &  ((v4_cat_1 (k7_cat_5 A)) &  ((v5_cat_1 (k7_cat_5 A)) &  ((v6_cat_1 (k7_cat_5 A)) & (l1_cat_1 (k7_cat_5 A))) ) ) ) ) ) ) ) ).
tt(dt_k7_catalg_1,ax,$true).
tt(dt_k7_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (l1_clopban2 (k7_cc0sp1 A))) ) ).
tt(dt_k7_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k7_cc0sp2 A)))  &  ((v13_algstr_0 (k7_cc0sp2 A)) &  ((v2_rlvect_1 (k7_cc0sp2 A)) &  ((v3_rlvect_1 (k7_cc0sp2 A)) &  ((v4_rlvect_1 (k7_cc0sp2 A)) &  ((v2_clvect_1 (k7_cc0sp2 A)) &  ((v3_clvect_1 (k7_cc0sp2 A)) &  ((v4_clvect_1 (k7_cc0sp2 A)) &  ((v5_clvect_1 (k7_cc0sp2 A)) & (l1_clvect_1 (k7_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k7_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (l6_algstr_0 (k7_cfuncdom A))) ) ).
tt(dt_k7_cgames_1,ax,$true).
tt(dt_k7_chain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B C))) & (m1_subset_1 E (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ) )  => (m1_subset_1 (k7_chain_1 A B C D E) (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ).
tt(dt_k7_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_circcmb3 B A) &  ((m1_circcmb3 C A) &  ((m2_circcmb3 D A B) & (m2_circcmb3 E A C)) ) ) )  =>  ((v3_msualg_1 (k7_circcmb3 A B C D E) (k6_circcmb3 A B C)) & (m2_circcmb3 (k7_circcmb3 A B C D E) A (k6_circcmb3 A B C))) ) ) ).
tt(dt_k7_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) &  ((v4_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) & (l3_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D))) ) ) ) ).
tt(dt_k7_circtrm1,ax,$true).
tt(dt_k7_circuit1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  &  ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) ) )  => (v7_ordinal1 (k7_circuit1 A B))) ) ).
tt(dt_k7_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_msafree2 D A B)) ) )  => (m1_subset_1 (k7_circuit2 A B C D) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k7_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k7_classes2 A B C) A)) ) ).
tt(dt_k7_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k6_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k7_clopban1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k7_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l6_algstr_0 (k7_clopban2 A))) ) ).
tt(dt_k7_clopban4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_clopban4 A B) (u1_struct_0 A))) ) ).
tt(dt_k7_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v9_closure1 B A) & (l1_closure1 B A)) )  =>  ((v1_closure1 (k7_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v2_closure1 (k7_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v3_closure1 (k7_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B)) & (m2_pboole (k7_closure1 A B) (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ) ) ).
tt(dt_k7_closure2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  & (m1_subset_1 D (k6_closure2 A B))) )  => (m1_closure2 (k7_closure2 A B C D) A B (k6_closure2 A B))) ) ).
tt(dt_k7_clvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (m1_subset_1 (k7_clvect_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k7_cohsp_1,ax,$true).
tt(dt_k7_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) => (m1_subset_1 (k7_coh_sp A B) (k3_coh_sp A))) ) ).
tt(dt_k7_combgras,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  & (v1_finset_1 C)) )  => (m1_subset_1 (k7_combgras A B C) (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B))))) ) ).
tt(dt_k7_complex1,ax,(m1_subset_1 k7_complex1 k2_numbers)).
tt(dt_k7_complsp2,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) => (m2_finseq_1 (k7_complsp2 A) k1_numbers)) ) ).
tt(dt_k7_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) & (v1_finset_1 (k7_compos_1 A B C))) ) ) ) ) ) ).
tt(dt_k7_comput_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  & (m1_subset_1 C k5_numbers)) )  => (m2_rfunct_3 (k7_comput_1 A B C) (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers))) ) ).
tt(dt_k7_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_funct_1 (k7_comseq_3 A)) &  ((v1_funct_2 (k7_comseq_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k7_comseq_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k7_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (~ (v1_xboole_0 (k7_conlat_1 A))) ) ) ).
tt(dt_k7_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v1_conlat_1 (k7_conlat_2 A)))  &  ((v2_conlat_1 (k7_conlat_2 A)) & (l1_conlat_1 (k7_conlat_2 A))) ) ) ) ).
tt(dt_k7_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  &  ((v1_xcmplx_0 B) & (m1_convex4 C A)) )  => (m1_convex4 (k7_convex4 A B C) A)) ) ).
tt(dt_k7_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k7_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k7_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (m1_subset_1 (k7_cqc_sim1 A B) k5_numbers)) ) ).
tt(dt_k7_csspace4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ( (~ (v1_xboole_0 (k7_csspace4 A B C)))  & (m1_subset_1 (k7_csspace4 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k7_csspace,ax, ( (~ (v2_struct_0 k7_csspace))  &  ((v1_clvect_1 k7_csspace) & (l1_clvect_1 k7_csspace)) ) ).
tt(dt_k7_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k7_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k7_descip_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k7_descip_1 A)) &  ((v1_funct_1 (k7_descip_1 A)) & (v1_finseq_1 (k7_descip_1 A))) ) ) ) ).
tt(dt_k7_dickson,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (m1_subset_1 (k7_dickson A B) k5_numbers)) ) ).
tt(dt_k7_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k7_diff_1 A B)) &  ((v1_funct_2 (k7_diff_1 A B) k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 (k7_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) ) ) ).
tt(dt_k7_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_funct_1 (k7_dist_1 A)) &  ((v1_funct_2 (k7_dist_1 A) (k6_dist_1 A) (k3_finseq_2 k1_numbers)) & (m1_subset_1 (k7_dist_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_dist_1 A) (k3_finseq_2 k1_numbers))))) ) ) ) ).
tt(dt_k7_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k7_domain_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k7_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  =>  ( (~ (v1_xboole_0 (k7_dtconstr A)))  & (m1_subset_1 (k7_dtconstr A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k7_dynkin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_dynkin B A) & (m1_subset_1 C B)) )  => (m1_dynkin (k7_dynkin A B C) A)) ) ).
tt(dt_k7_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  => (m1_subset_1 (k7_ec_pf_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_ec_pf_1 (k9_int_3 A)) (k3_ec_pf_1 (k9_int_3 A)))))) ) ).
tt(dt_k7_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  & (m1_subset_1 B (k3_ec_pf_1 (k9_int_3 A))))  => (m2_subset_1 (k7_ec_pf_2 A B) (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A)))) ) ).
tt(dt_k7_ens_1,ax,$true).
tt(dt_k7_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  => (m1_subset_1 (k7_entropy1 A) k1_numbers)) ) ).
tt(dt_k7_enumset1,ax,$true).
tt(dt_k7_eqrel_1,ax, (! [A:$i,B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (m1_subset_1 (k7_eqrel_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k7_e_siec,ax,$true).
tt(dt_k7_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (u1_struct_0 (k15_euclid A)))) ) )  => (m1_subset_1 (k7_euclid_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k7_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  => (m2_finseq_1 (k7_euclid_7 A B) (k1_euclid A))) ) ).
tt(dt_k7_euclid_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k1_euclid 3)) &  ((m1_subset_1 B (k1_euclid 3)) & (m1_subset_1 C (k1_euclid 3))) )  => (v1_xreal_0 (k7_euclid_8 A B C))) ) ).
tt(dt_k7_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  => (m2_finseq_2 (k7_euclid A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k7_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  ((v1_relat_1 (k7_exchsort A B C D)) & (v1_funct_1 (k7_exchsort A B C D))) ) ) ).
tt(dt_k7_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_extpro_1 A B C D)) &  ((v4_relat_1 (k7_extpro_1 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k7_extpro_1 A B C D)) &  ((v5_funct_1 (k7_extpro_1 A B C D) (k2_memstr_0 A B)) & (v1_finset_1 (k7_extpro_1 A B C D))) ) ) ) ) ) ).
tt(dt_k7_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  ((v3_msualg_1 (k7_facirc_1 A B C D) (k5_circcomb D (k11_finseq_1 A B C))) &  ((v4_msafree2 (k7_facirc_1 A B C D) (k5_circcomb D (k11_finseq_1 A B C))) &  ((v4_circcomb (k7_facirc_1 A B C D) (k5_circcomb D (k11_finseq_1 A B C))) &  ((v6_circcomb (k7_facirc_1 A B C D) (k5_circcomb D (k11_finseq_1 A B C))) & (l3_msualg_1 (k7_facirc_1 A B C D) (k5_circcomb D (k11_finseq_1 A B C)))) ) ) ) ) ) ).
tt(dt_k7_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k7_ff_siec A))) ) ).
tt(dt_k7_filter_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k7_filter_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k7_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  &  ( (~ (v2_struct_0 B))  & (l3_lattices B)) )  =>  ((v3_lattices (k7_filter_1 A B)) & (l3_lattices (k7_filter_1 A B))) ) ) ).
tt(dt_k7_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v1_xboole_0 (k7_filter_2 A B)))  &  ((v18_lattices (k7_filter_2 A B) A) &  ((v21_lattices (k7_filter_2 A B) A) & (m1_subset_1 (k7_filter_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k7_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_subset_1 F E)) ) ) )  =>  ((v1_funct_1 (k7_finance1 A B C D E F)) &  ((v1_funct_2 (k7_finance1 A B C D E F) A B) & (m1_subset_1 (k7_finance1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k7_finseq_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ).
tt(dt_k7_finseq_2,ax, (! [A:$i] :  ((v1_funct_1 (k7_finseq_2 A)) &  ((v1_funct_2 (k7_finseq_2 A) k5_numbers (k3_finseq_2 (k1_tarski A))) & (m1_subset_1 (k7_finseq_2 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (k1_tarski A)))))) ) ) ).
tt(dt_k7_finseq_4,ax,$true).
tt(dt_k7_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k7_finseq_8 A B C) A)) ) ).
tt(dt_k7_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ((v1_funct_1 (k7_finseqop A B C D)) &  ((v1_funct_2 (k7_finseqop A B C D) (k2_zfmisc_1 A A) A) & (m1_subset_1 (k7_finseqop A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ).
tt(dt_k7_fintopo3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k7_fintopo3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k7_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) & (v7_ordinal1 C))  => (m1_subset_1 (k7_flang_1 A B C) (k1_zfmisc_1 (k3_catalan2 A)))) ) ).
tt(dt_k7_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_relat_1 (k7_fomodel0 A)) & (v1_funct_1 (k7_fomodel0 A))) ) ) ).
tt(dt_k7_fomodel1,ax,$true).
tt(dt_k7_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k7_fomodel2 A B)) & (v1_funct_1 (k7_fomodel2 A B))) ) ) ).
tt(dt_k7_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m2_subset_1 (k7_fomodel3 A B) (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 (k35_fomodel1 A)) (k2_xboole_0 (k35_fomodel1 A) k6_margrel1))) (k16_fomodel2 A (k35_fomodel1 A)))) ) ).
tt(dt_k7_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v1_xboole_0 B) &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (m1_subset_1 (k7_fomodel4 A B C) (k1_fomodel4 A))) ) ).
tt(dt_k7_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ( (~ (v2_struct_0 (k7_freealg A B)))  &  ((v1_unialg_1 (k7_freealg A B)) &  ((v2_unialg_1 (k7_freealg A B)) &  ((v3_unialg_1 (k7_freealg A B)) &  ((v4_unialg_1 (k7_freealg A B)) & (l1_unialg_1 (k7_freealg A B))) ) ) ) ) ) ) ).
tt(dt_k7_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k7_fscirc_1 A B C) (k4_fscirc_1 A B C)) &  ((v4_msafree2 (k7_fscirc_1 A B C) (k4_fscirc_1 A B C)) &  ((v4_circcomb (k7_fscirc_1 A B C) (k4_fscirc_1 A B C)) &  ((v6_circcomb (k7_fscirc_1 A B C) (k4_fscirc_1 A B C)) & (l3_msualg_1 (k7_fscirc_1 A B C) (k4_fscirc_1 A B C))) ) ) ) ) ).
tt(dt_k7_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  & (v7_ordinal1 D)) ) )  =>  ( (~ (v1_xboole_0 (k7_fsm_1 A B C D)))  & (m1_eqrel_1 (k7_fsm_1 A B C D) (u1_struct_0 C))) ) ) ).
tt(dt_k7_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_subset_1 C (k8_afinsq_1 A))) )  => (m1_subset_1 (k7_fsm_3 A B C) (k8_afinsq_1 A))) ) ).
tt(dt_k7_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( (~ (v2_struct_0 (k7_ftacell1 A B C D E)))  &  ( (~ (v11_struct_0 (k7_ftacell1 A B C D E)))  &  ((v1_msualg_1 (k7_ftacell1 A B C D E)) &  ((v1_circcomb (k7_ftacell1 A B C D E)) &  ((v2_circcomb (k7_ftacell1 A B C D E)) &  ((v3_circcomb (k7_ftacell1 A B C D E)) & (l1_msualg_1 (k7_ftacell1 A B C D E))) ) ) ) ) ) ) ).
tt(dt_k7_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k7_funcop_1 A B)) &  ((v1_funct_2 (k7_funcop_1 A B) A (k1_tarski B)) & (m1_subset_1 (k7_funcop_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))))) ) ) ).
tt(dt_k7_funcsdom,ax, (! [A:$i] :  ((v1_funct_1 (k7_funcsdom A)) &  ((v1_funct_2 (k7_funcsdom A) (k2_zfmisc_1 k1_numbers (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers)) & (m1_subset_1 (k7_funcsdom A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers))))) ) ) ).
tt(dt_k7_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m1_subset_1 (k7_funct_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ).
tt(dt_k7_funct_3,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k7_funct_3 A B)) & (v1_funct_1 (k7_funct_3 A B))) ) ).
tt(dt_k7_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k7_funct_4 A B C D)) & (m1_subset_1 (k7_funct_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ).
tt(dt_k7_funct_5,ax,$true).
tt(dt_k7_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k7_funct_6 A)) & (v1_funct_1 (k7_funct_6 A))) ) ) ).
tt(dt_k7_funct_7,ax,$true).
tt(dt_k7_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k7_functor0 A B C D E)) &  ((v1_funct_2 (k7_functor0 A B C D E) (k1_altcat_1 A D E) (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D))) & (m1_subset_1 (k7_functor0 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_altcat_1 A D E) (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D)))))) ) ) ) ).
tt(dt_k7_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  &  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  &  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  &  ((m1_functor2 H A B D E) & (m1_functor2 I B C F G)) ) ) ) ) ) ) )  => (m1_functor2 (k7_functor3 A B C D E F G H I) A C (k1_functor3 A B C D F) (k1_functor3 A B C E G))) ) ).
tt(dt_k7_fvaluat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_fvaluat1 B A))  =>  ( (~ (v2_struct_0 (k7_fvaluat1 A B)))  &  ( (~ (v6_struct_0 (k7_fvaluat1 A B)))  &  ((v13_algstr_0 (k7_fvaluat1 A B)) &  ((v36_algstr_0 (k7_fvaluat1 A B)) &  ((v3_group_1 (k7_fvaluat1 A B)) &  ((v5_group_1 (k7_fvaluat1 A B)) &  ((v4_vectsp_1 (k7_fvaluat1 A B)) &  ((v5_vectsp_1 (k7_fvaluat1 A B)) &  ((v2_rlvect_1 (k7_fvaluat1 A B)) &  ((v3_rlvect_1 (k7_fvaluat1 A B)) &  ((v4_rlvect_1 (k7_fvaluat1 A B)) & (l6_algstr_0 (k7_fvaluat1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k7_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k7_fvsum_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k7_gate_1,ax,$true).
tt(dt_k7_gate_5,ax,$true).
tt(dt_k7_gcd_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m2_gcd_1 B A) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k7_gcd_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k7_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) & (m1_subset_1 D k5_numbers)) ) )  => (m1_genealg1 (k7_genealg1 A B C D) A)) ) ).
tt(dt_k7_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_geomtrap (k7_geomtrap A B C)) & (l1_geomtrap (k7_geomtrap A B C))) ) ) ).
tt(dt_k7_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k7_gfacirc1 A B C)))  &  ( (~ (v11_struct_0 (k7_gfacirc1 A B C)))  &  ((v1_msualg_1 (k7_gfacirc1 A B C)) &  ((v1_circcomb (k7_gfacirc1 A B C)) &  ((v2_circcomb (k7_gfacirc1 A B C)) &  ((v3_circcomb (k7_gfacirc1 A B C)) & (l1_msualg_1 (k7_gfacirc1 A B C))) ) ) ) ) ) ) ).
tt(dt_k7_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (m2_subset_1 (k7_gfacirc2 A B C) (u1_struct_0 (k5_gfacirc2 A B C)) (k3_msafree2 (k5_gfacirc2 A B C)))) ) ).
tt(dt_k7_glib_000,ax,$true).
tt(dt_k7_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) & (m3_glib_001 C A)) )  => (m3_glib_001 (k7_glib_001 A B C) A)) ) ).
tt(dt_k7_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k7_glib_003 A)) & (v1_funct_1 (k7_glib_003 A))) ) ) ).
tt(dt_k7_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))))  => (m1_subset_1 (k7_glib_004 A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k7_glib_005,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  &  ((m1_subset_1 C (k6_glib_000 A)) & (m1_subset_1 D (k6_glib_000 A))) ) )  =>  ((v5_glib_001 (k7_glib_005 A B C D) A) &  ((v6_glib_001 (k7_glib_005 A B C D) A) & (m3_glib_001 (k7_glib_005 A B C D) A)) ) ) ) ).
tt(dt_k7_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  => (m1_subset_1 (k7_graph_1 A) k5_numbers)) ) ).
tt(dt_k7_graph_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  => (m2_finseq_1 (k7_graph_2 A B) (u1_struct_0 A))) ) ).
tt(dt_k7_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_graph_3 A B C) k5_numbers)) ) ).
tt(dt_k7_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (m1_subset_1 (k7_graph_5 A) (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 A))))) ) ).
tt(dt_k7_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (v7_ordinal1 B))  => (m1_subset_1 (k7_graphsp A B) (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_k7_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ( (~ (v2_struct_0 (k7_grcat_1 A)))  &  ((v13_algstr_0 (k7_grcat_1 A)) &  ((v3_rlvect_1 (k7_grcat_1 A)) &  ((v4_rlvect_1 (k7_grcat_1 A)) & (l2_algstr_0 (k7_grcat_1 A))) ) ) ) ) ) ).
tt(dt_k7_group_10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k7_group_10 A B)) &  ((v1_funct_2 (k7_group_10 A B) (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) B) (k2_zfmisc_1 (u1_struct_0 A) B))) &  ((v1_group_10 (k7_group_10 A B) A (k2_zfmisc_1 (u1_struct_0 A) B)) & (m1_subset_1 (k7_group_10 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) B) (k2_zfmisc_1 (u1_struct_0 A) B)))))) ) ) ) ) ).
tt(dt_k7_group_1,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  => (m2_subset_1 (k7_group_1 A) k1_numbers k5_numbers)) ) ).
tt(dt_k7_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k7_group_2 A)) & (m1_group_2 (k7_group_2 A) A)) ) ) ).
tt(dt_k7_group_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_group_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_group_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  => (m1_subset_1 (k7_group_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v15_algstr_0 (k7_group_5 A B C)) & (m1_group_2 (k7_group_5 A B C) A)) ) ) ).
tt(dt_k7_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((v1_funct_1 (k7_group_6 A B)) &  ((v1_funct_2 (k7_group_6 A B) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k7_group_6 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_group_9,ax,$true).
tt(dt_k7_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  & (l1_vectsp_1 B A))  =>  ((v1_funct_1 (k7_hahnban1 A B)) &  ((v1_funct_2 (k7_hahnban1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k7_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k7_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k7_hermitan A B C)) &  ((v1_funct_2 (k7_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v4_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_hermitan (k7_hermitan A B C) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) & (m1_subset_1 (k7_hermitan A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) ) ).
tt(dt_k7_heyting1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) & (m1_subset_1 C (k5_finsub_1 (k7_normform A))))  => (m1_subset_1 (k7_heyting1 A B C) (k5_finsub_1 (k7_normform A)))) ) ).
tt(dt_k7_heyting2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 C (u1_struct_0 (k5_substlat A B))))  =>  ((v1_funct_1 (k7_heyting2 A B C)) &  ((v1_funct_2 (k7_heyting2 A B C) (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 (k7_heyting2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)))))) ) ) ) ).
tt(dt_k7_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k7_hilbasis A B)) &  ((v1_funct_2 (k7_hilbasis A B) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A)))) & (m1_subset_1 (k7_hilbasis A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))))))) ) ) ) ).
tt(dt_k7_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_funct_1 (k7_hurwitz A)) &  ((v1_funct_2 (k7_hurwitz A) k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 (k7_hurwitz A) k1_complfld) & (m1_subset_1 (k7_hurwitz A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) ) ) ) ).
tt(dt_k7_idea_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k7_idea_1 A B) k5_numbers)) ) ).
tt(dt_k7_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k7_ideal_1 A B)))  &  ((v1_ideal_1 (k7_ideal_1 A B) A) &  ((v2_ideal_1 (k7_ideal_1 A B) A) &  ((v3_ideal_1 (k7_ideal_1 A B) A) & (m1_subset_1 (k7_ideal_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(dt_k7_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) )  &  ((m2_index_1 D A B C) & (m1_subset_1 E A)) ) ) )  => (m2_cat_1 (k7_index_1 A B C D E) (k2_index_1 A B E) (k2_index_1 A C E))) ) ).
tt(dt_k7_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k7_int_3 A)) &  ((v1_funct_2 (k7_int_3 A) (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A)) & (m1_subset_1 (k7_int_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A)) (k7_card_1 A))))) ) ) ) ).
tt(dt_k7_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_funct_1 (k7_integr10 A)) & (m1_subset_1 (k7_integr10 A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ).
tt(dt_k7_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k7_integr15 A B C D)) & (m1_subset_1 (k7_integr15 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) ) ).
tt(dt_k7_integr16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  => (m1_subset_1 (k7_integr16 A B) k2_numbers)) ) ).
tt(dt_k7_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  => (m1_subset_1 (k7_integra1 A B C) k1_numbers)) ) ).
tt(dt_k7_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  => (m2_subset_1 (k7_interva1 A B) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k7_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (m1_subset_1 (k7_intpro_1 A) (k1_zfmisc_1 k1_intpro_1))) ) ).
tt(dt_k7_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v1_funct_1 (k7_isocat_1 A)) &  ((v1_funct_2 (k7_isocat_1 A) (u1_struct_0 A) (u4_struct_0 A)) & (m1_subset_1 (k7_isocat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A))))) ) ) ) ).
tt(dt_k7_isocat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  => (m2_cat_1 (k7_isocat_2 A B C) (k11_nattra_1 (k8_cat_2 A B) C) (k11_nattra_1 A (k11_nattra_1 B C)))) ) ).
tt(dt_k7_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k7_jgraph_4 A)) &  ((v1_funct_2 (k7_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k7_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k7_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k7_jgraph_6 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k7_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k7_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k7_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k7_jordan6 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k7_jordan,ax, ((v1_funct_1 k7_jordan) &  ((v1_funct_2 k7_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 k7_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ).
tt(dt_k7_knaster,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_knaster B A) &  ((v3_knaster B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v2_struct_0 (k7_knaster A B)))  &  ((v3_lattices (k7_knaster A B)) &  ((v10_lattices (k7_knaster A B)) & (l3_lattices (k7_knaster A B))) ) ) ) ) ).
tt(dt_k7_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 C)))  & (m1_kolmog01 E C A B)) ) ) )  => (m1_subset_1 (k7_kolmog01 A B C D E) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k7_lang1,ax, (! [A:$i,B:$i] :  ((v2_lang1 (k7_lang1 A B)) & (l2_lang1 (k7_lang1 A B))) ) ).
tt(dt_k7_laplace,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (m1_matrix_1 (k7_laplace A B C) (u1_struct_0 B) A A)) ) ).
tt(dt_k7_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k7_lattice3 A)) & (l1_orders_2 (k7_lattice3 A))) ) ) ).
tt(dt_k7_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  => (v1_card_1 (k7_lattice5 A B C))) ) ).
tt(dt_k7_lattice8,ax,$true).
tt(dt_k7_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_lattices A B) (u1_struct_0 A))) ) ).
tt(dt_k7_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k3_rfunct_3 A B) C)))  => (m2_rfunct_3 (k7_lexbfs A B C D) A B (k3_rfunct_3 A B))) ) ).
tt(dt_k7_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  & (m1_subset_1 C A)) )  => (m1_subset_1 (k7_lfuzzy_0 A B C) (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1))))) ) ).
tt(dt_k7_lmod_7,ax,$true).
tt(dt_k7_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k7_lopban_1 A B) (k1_zfmisc_1 (u1_struct_0 (k5_lopban_1 (u1_struct_0 A) B))))) ) ).
tt(dt_k7_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l6_algstr_0 (k7_lopban_2 A))) ) ).
tt(dt_k7_lopban_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v5_lopban_2 B) & (l1_lopban_2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k7_lopban_4 A B C D)) &  ((v1_funct_2 (k7_lopban_4 A B C D) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k7_lopban_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  => (m1_subset_1 (k7_lopclset A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k7_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_lpspace1 A)))  & (l1_rlvect_1 (k7_lpspace1 A))) ) ) ).
tt(dt_k7_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v1_funct_1 (k7_lpspace2 A B C D)) &  ((v1_funct_2 (k7_lpspace2 A B C D) (k2_zfmisc_1 (k6_lpspace2 A B C D) (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D)) & (m1_subset_1 (k7_lpspace2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k6_lpspace2 A B C D) (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D))))) ) ) ) ).
tt(dt_k7_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (m1_subset_1 (k7_ltlaxio1 A) k1_hilbert1)) ) ).
tt(dt_k7_margrel1,ax,(m1_subset_1 k7_margrel1 k6_margrel1)).
tt(dt_k7_mathmorp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k7_mathmorp A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  &  ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) ) ) ) )  => (m1_matrix_1 (k7_matrix13 A B C D) A (k5_card_1 C) (k5_card_1 C))) ) ).
tt(dt_k7_matrix15,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  =>  ((v7_vectsp_1 (k7_matrix15 A B) A) & (m1_vectsp_4 (k7_matrix15 A B) A (k6_prvect_1 A (k1_matrix_1 B)))) ) ) ).
tt(dt_k7_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  => (m2_finseq_1 (k7_matrix_1 A B C) A)) ) ).
tt(dt_k7_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 B)))) ) )  =>  ((v1_matrix_1 (k7_matrix_2 A B C)) & (m2_finseq_1 (k7_matrix_2 A B C) (k3_finseq_2 (u1_struct_0 B)))) ) ) ).
tt(dt_k7_matrix_5,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k2_numbers))) )  =>  ((v1_matrix_1 (k7_matrix_5 A B)) & (m2_finseq_1 (k7_matrix_5 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k7_matrixc1,ax, (! [A:$i,B:$i] :  ( ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  & (v1_xcmplx_0 B))  =>  ((v1_matrix_1 (k7_matrixc1 A B)) & (m2_finseq_1 (k7_matrixc1 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k7_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((v1_matrixj1 (k7_matrixj1 A B C) A) & (m2_finseq_1 (k7_matrixj1 A B C) (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(dt_k7_matrixj2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v7_ordinal1 C) & (m1_matrixj2 D A B)) ) )  => (m1_matrixj2 (k7_matrixj2 A B C D) A B)) ) ).
tt(dt_k7_matrixr1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 k1_numbers))) )  =>  ((v1_matrix_1 (k7_matrixr1 A B)) & (m2_finseq_1 (k7_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k7_matrixr2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_matrix_1 B k1_numbers A A))  => (m1_matrix_1 (k7_matrixr2 A B) k1_numbers A A)) ) ).
tt(dt_k7_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 D A B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k7_matrlin2 A B C D E)) &  ((v1_funct_2 (k7_matrlin2 A B C D E) (u1_struct_0 D) (u1_struct_0 C)) & (m1_subset_1 (k7_matrlin2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C))))) ) ) ) ).
tt(dt_k7_matrlin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((v1_matrix_1 (k7_matrlin A B C)) & (m2_finseq_1 (k7_matrlin A B C) (k3_finseq_2 A))) ) ) ).
tt(dt_k7_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  => (m1_subset_1 (k7_mcart_1 A B C D E) D)) ) ).
tt(dt_k7_measure6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k7_measure6 A B C)) & (m1_subset_1 (k7_measure6 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k7_measure7,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  & (m2_measure7 B A))  =>  ((v1_funct_1 (k7_measure7 A B)) &  ((v1_funct_2 (k7_measure7 A B) k5_numbers k7_numbers) & (m1_subset_1 (k7_measure7 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ).
tt(dt_k7_measure8,ax, ((v1_funct_1 k7_measure8) &  ((v1_funct_2 k7_measure8 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers)) & (m1_subset_1 k7_measure8 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))))) ) ).
tt(dt_k7_member_1,ax, (! [A:$i] :  ((v1_membered A) => (v1_membered (k7_member_1 A))) ) ).
tt(dt_k7_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k7_memstr_0 A B C)) &  ((v4_relat_1 (k7_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k7_memstr_0 A B C)) & (v5_funct_1 (k7_memstr_0 A B C) (k2_memstr_0 A B))) ) ) ) ) ).
tt(dt_k7_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k7_mesfun7c A B)) & (m1_subset_1 (k7_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k7_mesfunc1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) ) )  =>  ((v1_funct_1 (k7_mesfunc1 A B)) & (m1_subset_1 (k7_mesfunc1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k7_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) )  => (m1_subset_1 (k7_mesfunc5 A B C D) k7_numbers)) ) ).
tt(dt_k7_mesfunc8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  ((v1_funct_1 (k7_mesfunc8 A B)) & (m1_subset_1 (k7_mesfunc8 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k7_metric_1,ax, ((v1_funct_1 k7_metric_1) &  ((v1_funct_2 k7_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 k7_metric_1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) ) ).
tt(dt_k7_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k7_metric_2 A) (k1_zfmisc_1 (k2_metric_2 A)))) ) ).
tt(dt_k7_metric_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  &  ( (~ (v2_struct_0 D))  &  ((v6_metric_1 D) &  ((v7_metric_1 D) &  ((v8_metric_1 D) &  ((v9_metric_1 D) & (l1_metric_1 D)) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k7_metric_3 A B C D)) &  ((v1_funct_2 (k7_metric_3 A B C D) (k2_zfmisc_1 (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) k1_numbers) & (m1_subset_1 (k7_metric_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D)) (k4_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D))) k1_numbers)))) ) ) ) ).
tt(dt_k7_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_midsp_1 B A) & (m1_midsp_1 C A)) )  => (m1_midsp_1 (k7_midsp_1 A B C) A)) ) ).
tt(dt_k7_midsp_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k7_midsp_2 A B C)) &  ((v1_funct_2 (k7_midsp_2 A B C) (k2_zfmisc_1 (u1_struct_0 (g1_midsp_1 A (k6_midsp_2 A B C))) (u1_struct_0 (g1_midsp_1 A (k6_midsp_2 A B C)))) (u1_struct_0 B)) & (m1_subset_1 (k7_midsp_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (g1_midsp_1 A (k6_midsp_2 A B C))) (u1_struct_0 (g1_midsp_1 A (k6_midsp_2 A B C)))) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C))))) ) ) )  => (m2_finseq_2 (k7_midsp_3 A B C D E) (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B)))) ) ).
tt(dt_k7_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k7_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k7_mod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k7_mod_4 A B C)) &  ((v1_funct_2 (k7_mod_4 A B C) (u1_struct_0 A) (u1_struct_0 (k2_mod_4 B))) & (m1_subset_1 (k7_mod_4 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_mod_4 B)))))) ) ) ) ).
tt(dt_k7_modal_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_modal_1) & (m1_subset_1 B (k9_xtuple_0 A)))  => (m1_subset_1 (k7_modal_1 A B) k6_modal_1)) ) ).
tt(dt_k7_modelc_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k7_modelc_1 A) k5_numbers)) ) ).
tt(dt_k7_modelc_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k7_modelc_2 A B) k5_numbers)) ) ).
tt(dt_k7_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k7_modelc_3 A) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k7_monoid_0,ax, ( (~ (v2_struct_0 k7_monoid_0))  &  ((v15_algstr_0 k7_monoid_0) &  ((v1_group_1 k7_monoid_0) &  ((v17_monoid_0 k7_monoid_0) & (m2_monoid_0 k7_monoid_0 k6_monoid_0)) ) ) ) ).
tt(dt_k7_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 G C)) ) ) ) )  => (m2_funct_2 (k7_monoid_1 A B C D E F G) A D (k9_funct_2 A D))) ) ).
tt(dt_k7_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v3_msualg_1 (k7_msafree2 A) A) & (l3_msualg_1 (k7_msafree2 A) A)) ) ) ).
tt(dt_k7_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k7_msafree A B C) (k1_zfmisc_1 (k4_dtconstr (k5_msafree A B))))) ) ).
tt(dt_k7_msaterm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k1_msaterm A B))) )  => (m1_subset_1 (k7_msaterm A B C) (u1_struct_0 A))) ) ).
tt(dt_k7_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v1_relat_1 (k7_msualg_1 A)) &  ((v2_relat_1 (k7_msualg_1 A)) &  ((v4_relat_1 (k7_msualg_1 A) (u1_struct_0 (k6_msualg_1 A))) &  ((v1_funct_1 (k7_msualg_1 A)) & (v1_partfun1 (k7_msualg_1 A) (u1_struct_0 (k6_msualg_1 A)))) ) ) ) ) ) ).
tt(dt_k7_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) ) ) ) )  =>  ((v1_funct_1 (k7_msualg_4 A B C D)) &  ((v1_funct_2 (k7_msualg_4 A B C D) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B)) & (m1_subset_1 (k7_msualg_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A C)) B) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k4_msualg_4 A C D)) B))))) ) ) ) ).
tt(dt_k7_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v4_msualg_6 (k7_msualg_6 A B C) A B) & (m1_msualg_4 (k7_msualg_6 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ).
tt(dt_k7_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_mycielsk (k7_mycielsk A) (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 A)) 1))) ) ).
tt(dt_k7_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m2_subset_1 (k7_nat_1 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k7_nat_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (v1_xcmplx_0 (k7_nat_3 A B))) ) ).
tt(dt_k7_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (m1_subset_1 (k7_nat_d A B) k5_numbers)) ) ).
tt(dt_k7_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m2_cat_1 D A B) &  ((m2_cat_1 E A B) &  ((m2_nattra_1 F A B C D) & (m2_nattra_1 G A B D E)) ) ) ) ) )  => (m2_nattra_1 (k7_nattra_1 A B C D E F G) A B C E)) ) ).
tt(dt_k7_ndiff_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k7_ndiff_5 A B C D E)) & (m1_subset_1 (k7_ndiff_5 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A C)) B)))))) ) ) ).
tt(dt_k7_newton,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v7_ordinal1 C)) )  => (m2_finseq_1 (k7_newton A B C) k1_numbers)) ) ).
tt(dt_k7_normform,ax, (! [A:$i] : (m1_subset_1 (k7_normform A) (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))))) ).
tt(dt_k7_numbers,ax,$true).
tt(dt_k7_openlatt,ax,$true).
tt(dt_k7_oppcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_cat_1 D A B C)) ) )  => (m1_cat_1 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B))) ) ).
tt(dt_k7_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k7_ordinal3 A B))) ) ).
tt(dt_k7_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((v3_ordinal1 (k7_ordinal4 A B C)) & (m1_subset_1 (k7_ordinal4 A B C) A)) ) ) ).
tt(dt_k7_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  ((v1_relat_1 (k7_ordinal6 A)) &  ((v1_funct_1 (k7_ordinal6 A)) &  ((v5_ordinal1 (k7_ordinal6 A)) & (v1_ordinal2 (k7_ordinal6 A))) ) ) ) ) ).
tt(dt_k7_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (m2_pboole (k7_osafree A B) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) (k3_relat_1 (u2_msualg_1 A) (k5_osafree A B)))) ) ).
tt(dt_k7_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  ( (~ (v1_xboole_0 (k7_osalg_1 A)))  & (m1_subset_1 (k7_osalg_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A))))) ) ) ).
tt(dt_k7_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) & (m1_osalg_4 C A B)) ) )  =>  ((v1_relat_1 (k7_osalg_4 A B C)) &  ((v4_relat_1 (k7_osalg_4 A B C) (u1_struct_0 A)) &  ((v1_funct_1 (k7_osalg_4 A B C)) &  ((v1_partfun1 (k7_osalg_4 A B C) (u1_struct_0 A)) & (v11_osalg_1 (k7_osalg_4 A B C) A)) ) ) ) ) ) ).
tt(dt_k7_parsp_1,ax,$true).
tt(dt_k7_partfun1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  => (m1_subset_1 (k7_partfun1 A B C) A)) ) ).
tt(dt_k7_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k7_pboole A B C)) &  ((v4_relat_1 (k7_pboole A B C) A) &  ((v1_funct_1 (k7_pboole A B C)) & (v1_partfun1 (k7_pboole A B C) A)) ) ) ) ) ).
tt(dt_k7_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v7_pcs_0 B)) ) ) )  =>  ((v1_relat_1 (k7_pcs_0 A B)) &  ((v4_relat_1 (k7_pcs_0 A B) A) &  ((v1_funct_1 (k7_pcs_0 A B)) & (v1_partfun1 (k7_pcs_0 A B) A)) ) ) ) ) ).
tt(dt_k7_pdiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C (u1_struct_0 (k4_real_ns1 A)))) )  =>  ((v1_funct_1 (k7_pdiff_1 A B C)) &  ((v1_funct_2 (k7_pdiff_1 A B C) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 (k7_pdiff_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) ) ) ) ).
tt(dt_k7_pdiff_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 D (k1_euclid 3))) ) )  => (m2_finseq_2 (k7_pdiff_4 A B C D) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k7_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k7_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k7_pencil_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  =>  ((v1_pre_topc (k7_pencil_4 A B C D)) & (l1_pre_topc (k7_pencil_4 A B C D))) ) ) ).
tt(dt_k7_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k7_petri A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k7_pnproc_1,ax, (! [A:$i,B:$i] :  ((m1_pnproc_1 B A) =>  ((v1_relat_1 (k7_pnproc_1 A B)) & (v1_funct_1 (k7_pnproc_1 A B))) ) ) ).
tt(dt_k7_polyeq_1,ax,$true).
tt(dt_k7_polyeq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_xcmplx_0 (k7_polyeq_5 A B C D))) ) ).
tt(dt_k7_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m2_subset_1 (k7_polyform A) k1_numbers k5_numbers)) ) ).
tt(dt_k7_polynom1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((v1_funct_1 (k7_polynom1 A B)) &  ((v1_funct_2 (k7_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k7_polynom1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k7_polynom3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_finseq_1 E (k4_finseq_2 3 k5_numbers))) ) ) )  => (m2_finseq_2 (k7_polynom3 A B C D E) (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))) ) ).
tt(dt_k7_polynom5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k7_polynom5 A B)) &  ((v1_funct_2 (k7_polynom5 A B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k7_polynom5 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k7_polynom8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((v7_ordinal1 B) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_matrix_1 (k7_polynom8 A B C) (u1_struct_0 A) B B)) ) ).
tt(dt_k7_poset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ( (~ (v1_xboole_0 (k7_poset_1 A B C D)))  &  ((v6_orders_2 (k7_poset_1 A B C D) B) & (m1_subset_1 (k7_poset_1 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(dt_k7_power,ax,(v1_xreal_0 k7_power)).
tt(dt_k7_pralg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k7_pralg_1 A)) & (m1_subset_1 (k7_pralg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k1_tarski k1_xboole_0)) (k1_tarski k1_xboole_0))))) ) ) ).
tt(dt_k7_pralg_2,ax,$true).
tt(dt_k7_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  &  ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  => (m2_finseq_1 (k7_pre_poly A B C) A)) ) ).
tt(dt_k7_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_rat_1 B))  => (m1_subset_1 (k7_prepower A B) k1_numbers)) ) ).
tt(dt_k7_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  => (m1_prob_1 (k7_prob_1 A B C D) A B)) ) ).
tt(dt_k7_prob_3,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k9_setfam_1 A)) => (m1_subset_1 (k7_prob_3 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k7_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  => (m2_prob_1 (k7_prob_4 A B C) A (k4_prob_4 A B C))) ) ).
tt(dt_k7_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E (k4_finseq_2 B A))) ) ) )  => (m2_finseq_2 (k7_prvect_1 A B C D E) A (k4_finseq_2 B A))) ) ).
tt(dt_k7_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_normsp_1 B)) )  =>  ( (~ (v2_struct_0 (k7_prvect_3 A B)))  &  ((v1_normsp_1 (k7_prvect_3 A B)) & (l1_normsp_1 (k7_prvect_3 A B))) ) ) ) ).
tt(dt_k7_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k7_pscomp_1 A) k1_numbers)) ) ).
tt(dt_k7_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (m1_subset_1 (k7_pua2mss1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k7_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k6_qc_lang1 A)))  => (m1_subset_1 (k7_qc_lang1 A B) k5_numbers)) ) ).
tt(dt_k7_qc_lang2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k9_qc_lang1 A))) ) )  => (m1_subset_1 (k7_qc_lang2 A B C D) (k9_qc_lang1 A))) ) ).
tt(dt_k7_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  => (m1_prob_1 (k7_qmax_1 A B) k1_numbers k12_prob_1)) ) ).
tt(dt_k7_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_quaterni (k7_quatern2 A))) ) ).
tt(dt_k7_quaterni,ax,$true).
tt(dt_k7_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  => (m1_subset_1 (k7_quofield A) (k1_zfmisc_1 (k1_zfmisc_1 (k1_quofield A))))) ) ).
tt(dt_k7_radix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k7_radix_1 A B C) A) & (m2_finseq_1 (k7_radix_1 A B C) k4_numbers)) ) ) ).
tt(dt_k7_radix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_int_1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((v3_card_1 E D) & (m1_finseq_1 E (k3_radix_1 B))) ) ) ) )  =>  ((v3_card_1 (k7_radix_2 A B C D E) D) & (m2_finseq_1 (k7_radix_2 A B C D E) k4_numbers)) ) ) ).
tt(dt_k7_radix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k4_radix_3 B))) ) ) )  => (v1_int_1 (k7_radix_3 A B C D))) ) ).
tt(dt_k7_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k7_radix_5 A B C) k4_numbers (k3_radix_1 C))) ) ).
tt(dt_k7_radix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D (k2_xcmplx_0 B 2)) & (m1_finseq_1 D (k3_radix_1 C))) ) ) )  => (m1_subset_1 (k7_radix_6 A B C D) (k3_radix_1 C))) ) ).
tt(dt_k7_random_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_random_1 C A B)) )  => (m1_random_1 (k7_random_1 A B C) A B)) ) ).
tt(dt_k7_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (m1_subset_1 (k7_ranknull A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  => (m1_ratfunc1 (k7_ratfunc1 A) A)) ) ).
tt(dt_k7_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  => (m1_subset_1 (k7_real_1 A B) k1_numbers)) ) ).
tt(dt_k7_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k7_real_3 A)) &  ((v1_funct_2 (k7_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k7_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k7_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ((v1_bhsp_1 (k7_real_ns1 A)) & (l1_bhsp_1 (k7_real_ns1 A))) ) ) ) ).
tt(dt_k7_relat_1,ax,$true).
tt(dt_k7_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k7_relset_1 A B C D) (k1_zfmisc_1 B))) ) ).
tt(dt_k7_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  => (m1_subset_1 (k7_relset_2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ).
tt(dt_k7_rewrite2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) => (m1_subset_1 (k7_rewrite2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A))))) ) ).
tt(dt_k7_rfunct_1,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k7_rfunct_1 A B)) & (m1_subset_1 (k7_rfunct_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ).
tt(dt_k7_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  => (m2_rfunct_3 (k7_rfunct_3 A B C D) A k1_numbers (k3_rfunct_3 A k1_numbers))) ) ).
tt(dt_k7_ringcat1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  &  ((m1_ringcat1 D B C) & (m1_ringcat1 E A B)) ) ) )  =>  ((v2_ringcat1 (k7_ringcat1 A B C D E)) & (m1_ringcat1 (k7_ringcat1 A B C D E) A C)) ) ) ).
tt(dt_k7_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  => (m1_rlvect_2 (k7_rlvect_2 A B C) A)) ) ).
tt(dt_k7_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_rmod_4 D A B)) ) )  => (m1_rmod_4 (k7_rmod_4 A B C D) A B)) ) ).
tt(dt_k7_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) &  ((v7_robbins1 A) & (l2_robbins1 A)) ) ) ) )  => (m1_subset_1 (k7_robbins1 A) (u1_struct_0 A))) ) ).
tt(dt_k7_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  &  ((m1_finseq_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k7_roughs_1 A B C) k1_numbers)) ) ).
tt(dt_k7_rsspace4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ( (~ (v1_xboole_0 (k7_rsspace4 A B C)))  & (m1_subset_1 (k7_rsspace4 A B C) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k7_rsspace,ax,(l1_rlvect_1 k7_rsspace)).
tt(dt_k7_rusub_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_subset_1 (k7_rusub_4 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k7_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k4_finseq_2 A k1_numbers)))  => (m2_finseq_2 (k7_rvsum_1 A B) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k7_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  => (m2_finseq_1 (k7_rvsum_2 A B) k2_numbers)) ) ).
tt(dt_k7_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (m1_dtconstr (k7_scm_comp A B) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k7_scmfsa_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) &  ((m1_subset_1 B k2_scmfsa_1) & (v1_int_1 C)) )  => (m1_subset_1 (k7_scmfsa_1 A B C) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) ) ).
tt(dt_k7_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k7_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k7_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k7_scmfsa_i A) k2_scm_inst)) ) ).
tt(dt_k7_scmfsa_m,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  => (m1_subset_1 (k7_scmfsa_m A B C D) (k1_zfmisc_1 k2_scmfsa_2))) ) ).
tt(dt_k7_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (m1_subset_1 (k7_scm_inst A) k5_numbers)) ) ).
tt(dt_k7_scmpds_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m1_subset_1 (k7_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k7_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k7_scmpds_6 A B C)))  &  ((v1_relat_1 (k7_scmpds_6 A B C)) &  ((v4_relat_1 (k7_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k7_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k7_scmpds_6 A B C)) &  ((v1_finset_1 (k7_scmpds_6 A B C)) & (v1_afinsq_1 (k7_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k7_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (m1_subset_1 (k7_scmpds_i A) k2_scm_inst)) ) ).
tt(dt_k7_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_scmringi A)) & (m1_subset_1 C (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) )  => (m1_subset_1 (k7_scmring1 A B C) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) ) ).
tt(dt_k7_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k7_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k7_scmringi,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B k2_scm_inst) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k7_scmringi A B C) (k2_xboole_0 k2_scm_inst (u1_struct_0 A)))) ) ).
tt(dt_k7_scmyciel,ax, (! [A:$i,B:$i] :  ((v4_scmyciel A) => (m1_subset_1 (k7_scmyciel A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k7_seq_4,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_funct_1 (k7_seq_4 A)) &  ((v1_funct_2 (k7_seq_4 A) k2_numbers k2_numbers) & (m1_subset_1 (k7_seq_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) ) ).
tt(dt_k7_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) )  =>  ((v1_funct_1 (k7_seqfunc A B C)) &  ((v1_funct_2 (k7_seqfunc A B C) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k7_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k7_series_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k7_series_1 A B C) k1_numbers)) ) ).
tt(dt_k7_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k7_setfam_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k7_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k7_setlim_2 A B C)) &  ((v1_funct_2 (k7_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k7_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k7_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D (k5_finsub_1 A)) &  ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) )  => (m1_subset_1 (k7_setwiseo A B C D E) B)) ) ).
tt(dt_k7_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_sgraph1 (k7_sgraph1 A) k5_numbers)) ) ).
tt(dt_k7_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_matroid0 B) & (m1_simplex0 B A))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v1_pre_topc (k7_simplex0 A B C)) &  ((v7_simplex0 (k7_simplex0 A B C) A B) & (m2_simplex0 (k7_simplex0 A B C) A B)) ) ) ) ).
tt(dt_k7_sincos10,ax,$true).
tt(dt_k7_sin_cos2,ax, ((v1_funct_1 k7_sin_cos2) &  ((v1_funct_2 k7_sin_cos2 k1_numbers k1_numbers) & (m1_subset_1 k7_sin_cos2 (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(dt_k7_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k7_sin_cos7 A))) ) ).
tt(dt_k7_sin_cos,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_funct_1 (k7_sin_cos A)) &  ((v1_funct_2 (k7_sin_cos A) k5_numbers k2_numbers) & (m1_subset_1 (k7_sin_cos A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k7_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k7_square_1 A) k1_numbers)) ) ).
tt(dt_k7_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k7_stacks_1 A B C) (u4_struct_0 A))) ) ).
tt(dt_k7_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) => (v1_card_1 (k7_struct_0 A))) ) ).
tt(dt_k7_sublemma,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((v1_sublemma (k7_sublemma A B C) A) & (m1_subset_1 (k7_sublemma A B C) (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A)))) ) ) ).
tt(dt_k7_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (k7_subset_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k7_substut1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k9_qc_lang1 A)) & (m1_subset_1 D (k1_substut1 A))) ) )  =>  ((v1_finset_1 (k7_substut1 A B C D)) & (m1_subset_1 (k7_substut1 A B C D) (k1_substut1 A))) ) ) ).
tt(dt_k7_substut2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k1_substut1 A))) ) )  =>  ((v1_sublemma (k7_substut2 A B C D) A) & (m1_subset_1 (k7_substut2 A B C D) (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A)))) ) ) ).
tt(dt_k7_supinf_2,ax, (! [A:$i] :  ((v2_membered A) => (m1_subset_1 (k7_supinf_2 A) k7_numbers)) ) ).
tt(dt_k7_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k7_tdlat_1 A)) &  ((v1_funct_2 (k7_tdlat_1 A) (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A)) & (m1_subset_1 (k7_tdlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_tdlat_1 A) (k5_tdlat_1 A)) (k5_tdlat_1 A))))) ) ) ) ).
tt(dt_k7_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k7_tmap_1 A B)) &  ((v1_funct_2 (k7_tmap_1 A B) (u1_struct_0 A) (u1_struct_0 (k6_tmap_1 A B))) & (m1_subset_1 (k7_tmap_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_tmap_1 A B)))))) ) ) ) ).
tt(dt_k7_topalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v1_funct_1 (k7_topalg_1 A B C)) &  ((v1_funct_2 (k7_topalg_1 A B C) (u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k7_topalg_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) (u1_struct_0 (k15_euclid A)))))) ) ) ) ).
tt(dt_k7_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) &  ((m1_subset_1 F (u1_struct_0 B)) & (m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) )  => (m1_borsuk_2 (k7_topalg_4 A B C D E F G) A C D)) ) ).
tt(dt_k7_topalg_5,ax, ((v1_funct_1 k7_topalg_5) &  ((v1_funct_2 k7_topalg_5 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb))) & (m1_subset_1 k7_topalg_5 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb)))))) ) ).
tt(dt_k7_topgen_3,ax, (! [A:$i,B:$i] :  ((v1_pre_topc (k7_topgen_3 A B)) &  ((v2_pre_topc (k7_topgen_3 A B)) & (l1_pre_topc (k7_topgen_3 A B))) ) ) ).
tt(dt_k7_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m3_topgrp_1 (k7_topgrp_1 A B) A)) ) ).
tt(dt_k7_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (k7_topreal1 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k7_toprealb,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_pre_topc (k7_toprealb A B C) (k15_euclid A))) ) ).
tt(dt_k7_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k7_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k7_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  => (m1_subset_1 (k7_trees_1 A) k5_numbers)) ) ).
tt(dt_k7_trees_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((m1_finseq_1 B k5_numbers) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) )  =>  ((v1_relat_1 (k7_trees_2 A B C)) &  ((v1_funct_1 (k7_trees_2 A B C)) & (v3_trees_2 (k7_trees_2 A B C))) ) ) ) ).
tt(dt_k7_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((v1_funct_1 (k7_trees_3 A B)) &  ((v1_funct_2 (k7_trees_3 A B) (k2_zfmisc_1 A B) B) & (m1_subset_1 (k7_trees_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) ) ) ) ).
tt(dt_k7_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k5_trees_3 A)))  => (m2_finseq_1 (k7_trees_4 A B) k2_trees_3)) ) ).
tt(dt_k7_trees_9,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  => (m1_subset_1 (k7_trees_9 A B) (k1_zfmisc_1 (k3_trees_9 A)))) ) ).
tt(dt_k7_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))))  => (v1_int_1 (k7_turing_1 A B))) ) ).
tt(dt_k7_twoscomp,ax, ((v1_funct_1 k7_twoscomp) &  ((v1_funct_2 k7_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k7_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k7_unialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_unialg_1 (k7_unialg_2 A B)) & (m1_unialg_2 (k7_unialg_2 A B) A)) ) ) ).
tt(dt_k7_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) )  => (m2_subset_1 (k7_uproots A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k7_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C k5_numbers) &  ((m1_valuat_1 D A B) & (m1_subset_1 E (k8_qc_lang1 A C))) ) ) )  => (m1_subset_1 (k7_valuat_1 A B C D E) (k3_margrel1 B))) ) ).
tt(dt_k7_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) & (v1_funct_1 (k7_valued_1 A B))) ) ) ).
tt(dt_k7_valued_2,ax,$true).
tt(dt_k7_vectsp10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_vectsp_5 D A B (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) ) )  =>  ((v1_funct_1 (k7_vectsp10 A B C D)) &  ( (~ (v3_funct_1 (k7_vectsp10 A B C D)))  &  ( (~ (v1_zfmisc_1 (k7_vectsp10 A B C D)))  &  ((v1_funct_2 (k7_vectsp10 A B C D) (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 (k7_vectsp10 A B C D) B A) &  ((v1_hahnban1 (k7_vectsp10 A B C D) A B) & (m1_subset_1 (k7_vectsp10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(dt_k7_vectsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_6 C A B)) )  => (m1_vectsp_6 (k7_vectsp_6 A B C) A B)) ) ).
tt(dt_k7_waybel_0,ax,$true).
tt(dt_k7_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ( (~ (v2_struct_0 (k7_waybel10 A)))  &  ((v1_orders_2 (k7_waybel10 A)) &  ((v4_yellow_0 (k7_waybel10 A) (k2_waybel10 A)) & (m1_yellow_0 (k7_waybel10 A) (k2_waybel10 A))) ) ) ) ) ).
tt(dt_k7_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l1_pre_topc B) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  => (m1_pre_topc (k7_waybel18 A B C) B)) ) ).
tt(dt_k7_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k7_waybel_1 A B) (u1_struct_0 A))) ) ).
tt(dt_k7_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((v9_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A)) &  ((v16_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A)) & (m2_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A))) ) ) ) ).
tt(dt_k7_waybel_4,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) &  ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k7_waybel_4 A B)) &  ((v1_funct_2 (k7_waybel_4 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 (k7_waybel_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) ) ) ) ).
tt(dt_k7_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (m2_pboole (k7_waybel_5 A B C D) C (k7_funcop_1 C A) (k7_funcop_1 C B))) ) ).
tt(dt_k7_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k7_weddwitt A B)))  &  ((v13_algstr_0 (k7_weddwitt A B)) &  ((v2_rlvect_1 (k7_weddwitt A B)) &  ((v3_rlvect_1 (k7_weddwitt A B)) &  ((v4_rlvect_1 (k7_weddwitt A B)) &  ((v7_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A)) &  ((v8_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A)) &  ((v9_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A)) &  ((v10_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A)) &  ((v11_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A)) & (l1_vectsp_1 (k7_weddwitt A B) (k4_weddwitt A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k7_weierstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  => (m1_subset_1 (k7_weierstr A B C) k1_numbers)) ) ).
tt(dt_k7_xboolean,ax,$true).
tt(dt_k7_xcmplx_0,ax,$true).
tt(dt_k7_xtuple_0,ax,$true).
tt(dt_k7_yellow_1,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  =>  ((v1_orders_2 (k7_yellow_1 A B)) &  ((v4_yellow_0 (k7_yellow_1 A B) (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 (k7_yellow_1 A B) (k6_yellow_1 (u1_struct_0 A) B))) ) ) ) ).
tt(dt_k7_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k7_yellow21 A)))  &  ((v2_altcat_1 (k7_yellow21 A)) &  ((v6_altcat_1 (k7_yellow21 A)) &  ((v2_altcat_2 (k7_yellow21 A) (k6_yellow21 A)) &  ((v3_altcat_2 (k7_yellow21 A) (k6_yellow21 A)) & (m1_altcat_2 (k7_yellow21 A) (k6_yellow21 A))) ) ) ) ) ) ) ).
tt(dt_k7_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k7_yellow_3 A B C D) (u1_struct_0 (k3_yellow_3 A B)))) ) ).
tt(dt_k7_yellow_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((l1_struct_0 B) &  ((m3_yellow_6 C A B) & (m1_subset_1 D A)) ) )  =>  ( (~ (v2_struct_0 (k7_yellow_6 A B C D)))  &  ((v4_orders_2 (k7_yellow_6 A B C D)) &  ((v7_waybel_0 (k7_yellow_6 A B C D)) & (l1_waybel_0 (k7_yellow_6 A B C D) B)) ) ) ) ) ).
tt(dt_k7_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k7_zf_lang A B) k5_numbers)) ) ).
tt(dt_k7_zf_model,ax, ((v1_zf_lang k7_zf_model) & (m2_finseq_1 k7_zf_model k5_numbers)) ).
tt(dt_k7_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_zmodul01 B A) & (m1_zmodul01 C A)) )  =>  ((v1_zmodul01 (k7_zmodul01 A B C)) & (m1_zmodul01 (k7_zmodul01 A B C) A)) ) ) ).
tt(dt_k80_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k80_valued_2 A B C D E F)) & (m1_subset_1 (k80_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k6_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k81_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k81_aofa_i00 A B C D E F) A) & (m1_subset_1 (k81_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k82_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k82_aofa_i00 A B C D E F) A) & (m1_subset_1 (k82_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k83_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k83_aofa_i00 A B C D E F) A) & (m1_subset_1 (k83_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k83_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 A) &  ((v1_valued_2 B) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) ) ) ) )  =>  ((v1_relat_1 (k83_valued_2 A B C D)) & (v1_funct_1 (k83_valued_2 A B C D))) ) ) ).
tt(dt_k84_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) & (m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D)) ) ) ) )  =>  ((v15_aofa_000 (k84_aofa_i00 A B C D E F) A) & (m1_subset_1 (k84_aofa_i00 A B C D E F) (u1_struct_0 A))) ) ) ).
tt(dt_k84_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k84_valued_2 A B C D E F)) & (m1_subset_1 (k84_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k2_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k85_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k85_valued_2 A B C D E F)) & (m1_subset_1 (k85_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k6_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k89_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_card_3 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) &  ((v3_aofa_000 B) &  ((v4_aofa_000 B) &  ((v5_aofa_000 B) &  ((v6_aofa_000 B) &  ((v2_aofa_i00 B) & (l1_unialg_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) &  ( ((v1_aofa_i00 D B A C) & (m1_aofa_000 D B (k9_funct_2 A k4_numbers) C))  &  ((m1_subset_1 E (k9_funct_2 A k4_numbers)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  => (m2_funct_2 (k89_aofa_i00 A B C D E F) A k4_numbers (k9_funct_2 A k4_numbers))) ) ).
tt(dt_k89_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 A) &  ((v1_valued_2 B) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D B) & (v1_funct_1 D)) ) ) ) )  =>  ((v1_relat_1 (k89_valued_2 A B C D)) & (v1_funct_1 (k89_valued_2 A B C D))) ) ) ).
tt(dt_k8_abcmiz_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_abcmiz_0 A))) )  => (m1_subset_1 (k8_abcmiz_0 A B C) (u1_struct_0 A))) ) ).
tt(dt_k8_abcmiz_1,ax,$true).
tt(dt_k8_abcmiz_a,ax,(m2_subset_1 k8_abcmiz_a k20_abcmiz_1 k5_abcmiz_a)).
tt(dt_k8_afinsq_1,ax,$true).
tt(dt_k8_afinsq_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k8_afinsq_1 A)) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  => (m1_subset_1 (k8_afinsq_2 A B) (k8_afinsq_1 A))) ) ).
tt(dt_k8_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~ (v1_xboole_0 (k8_afproj A))) ) ) ).
tt(dt_k8_algstr_0,ax,(l4_algstr_0 k8_algstr_0)).
tt(dt_k8_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v2_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k8_algstr_4 A B)) &  ((v1_funct_2 (k8_algstr_4 A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k8_algstr_4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k8_altcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k8_altcat_1 A B) (k1_altcat_1 A B B))) ) ).
tt(dt_k8_ami_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k3_scm_inst) & (m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))  => (m1_subset_1 (k8_ami_2 A B) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) ) ).
tt(dt_k8_ami_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k8_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k8_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k9_funct_2 A A)) & (m1_subset_1 D (k9_funct_2 A A))) )  => (m2_funct_2 (k8_aofa_000 A B C D) A A (k9_funct_2 A A))) ) ).
tt(dt_k8_armstrng,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (m1_subset_1 (k8_armstrng A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) ).
tt(dt_k8_arytm_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_arytm_2) & (m1_subset_1 B k2_arytm_2))  => (m1_subset_1 (k8_arytm_2 A B) k2_arytm_2)) ) ).
tt(dt_k8_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (m1_subset_1 (k8_arytm_3 A B) k5_arytm_3)) ) ).
tt(dt_k8_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k8_asympt_0 A) k5_numbers k1_numbers)) ) ).
tt(dt_k8_bagorder,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_partfun1 C (k15_pre_poly (k1_nat_1 A 1))) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k1_nat_1 A 1)) (k15_pre_poly (k1_nat_1 A 1)))))) ) ) )  &  ((v1_partfun1 D (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1)))) &  ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))) (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))))))) ) ) ) ) ) )  =>  ((v1_partfun1 (k8_bagorder A B C D) (k15_pre_poly B)) &  ((v1_relat_2 (k8_bagorder A B C D)) &  ((v4_relat_2 (k8_bagorder A B C D)) &  ((v8_relat_2 (k8_bagorder A B C D)) & (m1_subset_1 (k8_bagorder A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (k15_pre_poly B))))) ) ) ) ) ) ).
tt(dt_k8_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_bcialg_2 B A))  => (m2_subset_1 (k8_bcialg_2 A B) (k1_zfmisc_1 (u1_struct_0 A)) (k8_eqrel_1 (u1_struct_0 A) B))) ) ).
tt(dt_k8_bcialg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k8_bcialg_4 A B)))  & (m1_subset_1 (k8_bcialg_4 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(dt_k8_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  =>  ((v1_funct_1 (k8_bcialg_6 A B C D)) &  ((v1_funct_2 (k8_bcialg_6 A B C D) (k2_zfmisc_1 (k7_bcialg_6 A B C D) (k7_bcialg_6 A B C D)) (k7_bcialg_6 A B C D)) & (m1_subset_1 (k8_bcialg_6 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_bcialg_6 A B C D) (k7_bcialg_6 A B C D)) (k7_bcialg_6 A B C D))))) ) ) ) ).
tt(dt_k8_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  & (m1_subset_1 E (u1_struct_0 C))) ) ) )  =>  ((v1_funct_1 (k8_bilinear A B C D E)) &  ((v1_funct_2 (k8_bilinear A B C D E) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k8_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k8_binarith,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  => (m1_subset_1 (k8_binarith A B C) k6_margrel1)) ) ).
tt(dt_k8_binom,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D k5_numbers)) ) )  => (m2_finseq_1 (k8_binom A B C D) (u1_struct_0 A))) ) ).
tt(dt_k8_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_subset_1 (k8_binop_2 A) k1_numbers)) ) ).
tt(dt_k8_bor_cant,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) )  => (m1_prob_1 (k8_bor_cant A B C) A B)) ) ).
tt(dt_k8_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_funct_1 (k8_borsuk_1 A B)) &  ((v1_funct_2 (k8_borsuk_1 A B) (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 (k8_borsuk_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k8_borsuk_6,ax,(m1_subset_1 k8_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))).
tt(dt_k8_borsuk_7,ax,(m1_subset_1 k8_borsuk_7 (u1_struct_0 (k8_toprealb 3)))).
tt(dt_k8_bspace,ax,$true).
tt(dt_k8_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k8_bvfunc_1 A B)) & (v1_funct_1 (k8_bvfunc_1 A B))) ) ) ).
tt(dt_k8_c0sp1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k8_c0sp1 A B)) &  ((v1_funct_2 (k8_c0sp1 A B) A k1_numbers) & (m1_subset_1 (k8_c0sp1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k8_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k8_c0sp2 A)) &  ((v1_funct_2 (k8_c0sp2 A) (k6_c0sp2 A) k1_numbers) & (m1_subset_1 (k8_c0sp2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_c0sp2 A) k1_numbers)))) ) ) ) ).
tt(dt_k8_card_3,ax,$true).
tt(dt_k8_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k8_cat_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k8_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_cat_2 A B)))  &  ( (~ (v11_struct_0 (k8_cat_2 A B)))  &  ((v2_cat_1 (k8_cat_2 A B)) &  ((v3_cat_1 (k8_cat_2 A B)) &  ((v4_cat_1 (k8_cat_2 A B)) &  ((v5_cat_1 (k8_cat_2 A B)) &  ((v6_cat_1 (k8_cat_2 A B)) & (l1_cat_1 (k8_cat_2 A B))) ) ) ) ) ) ) ) ) ).
tt(dt_k8_cat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k8_cat_3 A B C D)) &  ((v1_funct_2 (k8_cat_3 A B C D) B (u4_struct_0 A)) & (m1_subset_1 (k8_cat_3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (u4_struct_0 A))))) ) ) ) ).
tt(dt_k8_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_cat_1 (k8_cat_4 A B C) A (k2_cat_4 A B C) C)) ) ).
tt(dt_k8_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_cat_1 (k8_cat_5 A B) (k7_cat_5 (k3_graph_1 A B)) (k7_cat_5 (k4_graph_1 A B)))) ) ).
tt(dt_k8_catalg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (m1_subset_1 (k8_catalg_1 A B) (u4_struct_0 (k3_catalg_1 A)))) ) ).
tt(dt_k8_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k8_cc0sp2 A)) &  ((v1_funct_2 (k8_cc0sp2 A) (k6_cc0sp2 A) k1_numbers) & (m1_subset_1 (k8_cc0sp2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_cc0sp2 A) k1_numbers)))) ) ) ) ).
tt(dt_k8_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_cfuncdom (k8_cfuncdom A)) & (l1_cfuncdom (k8_cfuncdom A))) ) ) ).
tt(dt_k8_cgames_1,ax,$true).
tt(dt_k8_chain_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_chain_1 B A))  => (m2_subset_1 (k8_chain_1 A B) (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A B A))) ) ).
tt(dt_k8_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) & (m1_subset_1 D (k4_card_3 (u3_msualg_1 A B)))) ) )  => (m1_subset_1 (k8_circuit2 A B C D) (k4_card_3 (u3_msualg_1 A B)))) ) ).
tt(dt_k8_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  => (m1_subset_1 (k8_clopban1 A B) (k1_zfmisc_1 (u1_struct_0 (k6_clopban1 A B))))) ) ).
tt(dt_k8_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l1_cfuncdom (k8_clopban2 A))) ) ).
tt(dt_k8_closure2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) )  =>  ((v1_funct_1 (k8_closure2 A B C D)) &  ((v1_funct_2 (k8_closure2 A B C D) (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 (k8_closure2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) ) ).
tt(dt_k8_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  => (m1_subset_1 (k8_cohsp_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B))))) ) ).
tt(dt_k8_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k3_coh_sp A)) => (m1_subset_1 (k8_coh_sp A B) (k5_coh_sp A))) ) ).
tt(dt_k8_combgras,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B B) &  ((v3_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) )  =>  ((v5_combgras (k8_combgras A B C) (k1_combgras A B) (k1_combgras A B)) & (l1_combgras (k8_combgras A B C) (k1_combgras A B) (k1_combgras A B))) ) ) ).
tt(dt_k8_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  => (m1_subset_1 (k8_complex1 A B) k2_numbers)) ) ).
tt(dt_k8_complsp2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  => (m1_subset_1 (k8_complsp2 A B) k2_numbers)) ) ).
tt(dt_k8_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k8_compos_1 A B C)))  &  ((v1_relat_1 (k8_compos_1 A B C)) &  ((v4_relat_1 (k8_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k8_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k8_compos_1 A B C)) &  ((v1_finset_1 (k8_compos_1 A B C)) &  ((v1_afinsq_1 (k8_compos_1 A B C)) &  ((v3_compos_1 (k8_compos_1 A B C) A) & (v4_compos_1 (k8_compos_1 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(dt_k8_comput_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k5_numbers)) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (m2_finseq_2 (k8_comput_1 A B C D) k5_numbers (k4_finseq_2 A k5_numbers))) ) ).
tt(dt_k8_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_funct_1 (k8_comseq_3 A)) &  ((v1_funct_2 (k8_comseq_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k8_comseq_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k8_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  => (m1_conlat_1 (k8_conlat_1 A) A)) ) ).
tt(dt_k8_conlat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (l2_conlat_1 B A))  =>  ((v4_conlat_1 (k8_conlat_2 A B) (k7_conlat_2 A)) & (l2_conlat_1 (k8_conlat_2 A B) (k7_conlat_2 A))) ) ) ).
tt(dt_k8_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  & (m1_convex4 B A))  => (m1_convex4 (k8_convex4 A B) A)) ) ).
tt(dt_k8_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k8_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k8_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))))) )  & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_funct_2 (k8_cqc_sim1 A B C) (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))) ) ).
tt(dt_k8_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_csspace4 A B)) &  ((v1_funct_2 (k8_csspace4 A B) (k4_csspace4 A B) k1_numbers) & (m1_subset_1 (k8_csspace4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_csspace4 A B) k1_numbers)))) ) ) ) ).
tt(dt_k8_csspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k8_csspace A B)) &  ((v1_funct_2 (k8_csspace A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k8_csspace A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k8_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k8_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k8_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (v1_int_1 C)) )  => (m2_finseq_1 (k8_descip_1 A B C) A)) ) ).
tt(dt_k8_dickson,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 D k5_numbers)) )  => (m1_subset_1 (k8_dickson A B C D) k5_numbers)) ) ).
tt(dt_k8_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k8_diff_1 A B)) &  ((v1_funct_2 (k8_diff_1 A B) k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 (k8_diff_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) ) ) ).
tt(dt_k8_dist_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) &  ((v1_matrprob B) & (m1_finseq_1 B k1_numbers)) )  => (m2_subset_1 (k8_dist_1 A B) (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A))) ) ).
tt(dt_k8_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (m1_subset_1 (k8_domain_1 A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k8_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) & (l1_lang1 A)) )  & (m1_subset_1 B (k6_dtconstr A)))  => (m1_dtconstr (k8_dtconstr A B) (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A))) ) ).
tt(dt_k8_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) & (m1_subset_1 C (u1_struct_0 (k9_int_3 A)))) )  =>  ((v1_partfun1 (k8_ec_pf_1 A B C) (k6_ec_pf_1 A B C)) &  ((v3_relat_2 (k8_ec_pf_1 A B C)) &  ((v8_relat_2 (k8_ec_pf_1 A B C)) & (m1_subset_1 (k8_ec_pf_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C))))) ) ) ) ) ).
tt(dt_k8_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  & (m1_subset_1 B (k1_ec_pf_2 A)))  =>  ((v1_funct_1 (k8_ec_pf_2 A B)) &  ((v1_funct_2 (k8_ec_pf_2 A B) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) & (m1_subset_1 (k8_ec_pf_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))))) ) ) ) ).
tt(dt_k8_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k8_ens_1 A)) &  ((v1_funct_2 (k8_ens_1 A) (k2_ens_1 A) A) & (m1_subset_1 (k8_ens_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) A)))) ) ) ) ).
tt(dt_k8_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers)))  => (m2_finseq_1 (k8_entropy1 A) k1_numbers)) ) ).
tt(dt_k8_enumset1,ax,$true).
tt(dt_k8_eqrel_1,ax, (! [A:$i,B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (m1_eqrel_1 (k8_eqrel_1 A B) A)) ) ).
tt(dt_k8_e_siec,ax,$true).
tt(dt_k8_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (u1_struct_0 (k15_euclid A)))) ) )  => (m1_subset_1 (k8_euclid_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k8_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k8_euclid_7 A) (k1_zfmisc_1 (k1_euclid A)))) ) ).
tt(dt_k8_euclid_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (m1_subset_1 D k1_numbers)) ) )  => (m2_finseq_2 (k8_euclid_8 A B C D) k1_numbers (k1_euclid 3))) ) ).
tt(dt_k8_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  => (m2_finseq_2 (k8_euclid A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k8_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  => (m2_subset_1 (k8_extpro_1 A B C D) k1_numbers k5_numbers)) ) ).
tt(dt_k8_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (~ (v2_struct_0 (k8_facirc_1 A B C D)))  &  ( (~ (v11_struct_0 (k8_facirc_1 A B C D)))  &  ((v1_msualg_1 (k8_facirc_1 A B C D)) &  ((v1_circcomb (k8_facirc_1 A B C D)) &  ((v2_circcomb (k8_facirc_1 A B C D)) &  ((v3_circcomb (k8_facirc_1 A B C D)) & (l1_msualg_1 (k8_facirc_1 A B C D))) ) ) ) ) ) ) ) ).
tt(dt_k8_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k8_ff_siec A))) ) ).
tt(dt_k8_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v1_relat_1 (k8_filter_0 A B))) ) ).
tt(dt_k8_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (v1_relat_1 (k8_filter_1 A))) ) ).
tt(dt_k8_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k8_filter_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D C)) ) )  =>  ((v1_funct_1 (k8_finance1 A B C D)) &  ((v1_funct_2 (k8_finance1 A B C D) A k1_numbers) & (m1_subset_1 (k8_finance1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ).
tt(dt_k8_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  => (m2_finseq_1 (k8_finseq_1 A B C) A)) ) ).
tt(dt_k8_finseq_4,ax,$true).
tt(dt_k8_finseq_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((m1_finseq_1 C A) & (m1_subset_1 D k5_numbers)) ) )  => (m1_subset_1 (k8_finseq_8 A B C D) k5_numbers)) ) ).
tt(dt_k8_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k8_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_fintopo3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k8_fintopo3 A B)) &  ((v1_funct_2 (k8_fintopo3 A B) k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 (k8_fintopo3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_k8_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k8_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_flang_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) => (m1_subset_1 (k8_flang_1 A B) (k1_zfmisc_1 (k3_catalan2 A)))) ) ).
tt(dt_k8_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k8_fomodel0 A)) &  ((v1_funct_2 (k8_fomodel0 A) (k3_finseq_2 (k3_finseq_2 A)) (k3_finseq_2 A)) & (m1_subset_1 (k8_fomodel0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (k3_finseq_2 A)) (k3_finseq_2 A))))) ) ) ) ).
tt(dt_k8_fomodel1,ax,$true).
tt(dt_k8_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C B) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) ) ) ) )  =>  ((v1_funct_1 (k8_fomodel2 A B C D)) &  ((v1_funct_2 (k8_fomodel2 A B C D) k5_numbers (k9_funct_2 (k35_fomodel1 A) B)) & (m1_subset_1 (k8_fomodel2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 (k35_fomodel1 A) B))))) ) ) ) ).
tt(dt_k8_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (v7_ordinal1 D)) ) )  => (m1_subset_1 (k8_fomodel3 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 D A) (k4_finseq_2 D B))))) ) ).
tt(dt_k8_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k8_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k8_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  => (m1_subset_1 (k8_freealg A B) (k1_zfmisc_1 (u1_struct_0 (k7_freealg A B))))) ) ).
tt(dt_k8_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v2_struct_0 (k8_fscirc_1 A B C)))  &  ( (~ (v11_struct_0 (k8_fscirc_1 A B C)))  &  ((v1_msualg_1 (k8_fscirc_1 A B C)) &  ((v1_circcomb (k8_fscirc_1 A B C)) &  ((v2_circcomb (k8_fscirc_1 A B C)) &  ((v3_circcomb (k8_fscirc_1 A B C)) & (l1_msualg_1 (k8_fscirc_1 A B C))) ) ) ) ) ) ) ).
tt(dt_k8_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) ) ) )  => (m1_eqrel_1 (k8_fsm_1 A B C) (u1_struct_0 C))) ) ).
tt(dt_k8_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ((v3_msualg_1 (k8_ftacell1 A B C D E) (k7_ftacell1 A B C D E)) &  ((v4_msafree2 (k8_ftacell1 A B C D E) (k7_ftacell1 A B C D E)) &  ((v4_circcomb (k8_ftacell1 A B C D E) (k7_ftacell1 A B C D E)) &  ((v6_circcomb (k8_ftacell1 A B C D E) (k7_ftacell1 A B C D E)) & (l3_msualg_1 (k8_ftacell1 A B C D E) (k7_ftacell1 A B C D E))) ) ) ) ) ).
tt(dt_k8_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((v1_funct_1 (k8_funcop_1 A B C)) &  ((v1_funct_2 (k8_funcop_1 A B C) B A) & (m1_subset_1 (k8_funcop_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k8_funcsdom,ax, (! [A:$i] : (m2_funct_2 (k8_funcsdom A) A k1_numbers (k9_funct_2 A k1_numbers))) ).
tt(dt_k8_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_relat_1 E) &  ((v5_relat_1 E B) & (v1_funct_1 E)) ) ) )  =>  ((v1_funct_1 (k8_funct_2 A B C D E)) &  ((v1_funct_2 (k8_funct_2 A B C D E) A B) & (m1_subset_1 (k8_funct_2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ).
tt(dt_k8_funct_3,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k8_funct_3 A B)) & (v1_funct_1 (k8_funct_3 A B))) ) ).
tt(dt_k8_funct_5,ax, ((v1_funct_1 k8_funct_5) &  ((v1_funct_2 k8_funct_5 1 1) & (m1_subset_1 k8_funct_5 (k1_zfmisc_1 (k2_zfmisc_1 1 1)))) ) ).
tt(dt_k8_funct_6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k8_funct_6 A B)) & (v1_funct_1 (k8_funct_6 A B))) ) ) ).
tt(dt_k8_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (k1_altcat_1 A D E))) ) ) ) )  => (m1_subset_1 (k8_functor0 A B C D E F) (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D)))) ) ).
tt(dt_k8_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  & (m1_functor3 E A B C D)) ) ) )  => (m1_functor3 (k8_functor3 A B C D E) A B D C)) ) ).
tt(dt_k8_fvaluat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_fvaluat1 B A))  =>  ( (~ (v1_xboole_0 (k8_fvaluat1 A B)))  &  ((v1_ideal_1 (k8_fvaluat1 A B) (k7_fvaluat1 A B)) &  ((v2_ideal_1 (k8_fvaluat1 A B) (k7_fvaluat1 A B)) &  ((v3_ideal_1 (k8_fvaluat1 A B) (k7_fvaluat1 A B)) & (m1_subset_1 (k8_fvaluat1 A B) (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B))))) ) ) ) ) ) ).
tt(dt_k8_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  => (m2_finseq_2 (k8_fvsum_1 A B C D) (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B)))) ) ).
tt(dt_k8_gate_1,ax,$true).
tt(dt_k8_gate_5,ax,$true).
tt(dt_k8_gcd_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m2_gcd_1 B A) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k8_gcd_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k8_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E k5_numbers)) ) ) )  => (m1_genealg1 (k8_genealg1 A B C D E) A)) ) ).
tt(dt_k8_geomtrap,ax, (! [A:$i] :  ((l1_geomtrap A) =>  ((v1_analoaf (k8_geomtrap A)) & (l1_analoaf (k8_geomtrap A))) ) ) ).
tt(dt_k8_gfacirc1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k8_gfacirc1 A B C) (k7_gfacirc1 A B C)) &  ((v4_msafree2 (k8_gfacirc1 A B C) (k7_gfacirc1 A B C)) &  ((v4_circcomb (k8_gfacirc1 A B C) (k7_gfacirc1 A B C)) &  ((v6_circcomb (k8_gfacirc1 A B C) (k7_gfacirc1 A B C)) & (l3_msualg_1 (k8_gfacirc1 A B C) (k7_gfacirc1 A B C))) ) ) ) ) ).
tt(dt_k8_gfacirc2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  => (m2_subset_1 (k8_gfacirc2 A B C D) (u1_struct_0 (k5_gfacirc2 B C D)) (k3_msafree2 (k5_gfacirc2 B C D)))) ) ).
tt(dt_k8_glib_000,ax,$true).
tt(dt_k8_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (m3_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(dt_k8_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  & (m3_glib_001 B A))  =>  ((v1_relat_1 (k8_glib_003 A B)) &  ((v1_funct_1 (k8_glib_003 A B)) & (v1_finseq_1 (k8_glib_003 A B))) ) ) ) ).
tt(dt_k8_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (m1_subset_1 (k8_glib_004 A B) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k8_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m3_glib_001 C A)) )  => (m2_finseq_1 (k8_glib_005 A B C) k5_numbers)) ) ).
tt(dt_k8_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k8_graph_1 A B) k5_numbers)) ) ).
tt(dt_k8_graph_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A k4_numbers) &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C k5_numbers)) )  => (m2_subset_1 (k8_graph_2 A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k8_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k8_graph_3 A B C)))  &  ((v1_graph_1 (k8_graph_3 A B C)) & (l1_graph_1 (k8_graph_3 A B C))) ) ) ) ).
tt(dt_k8_graph_5,ax,(m1_subset_1 k8_graph_5 (k1_zfmisc_1 k1_numbers))).
tt(dt_k8_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) &  ((m1_subset_1 B (k3_finseq_2 k1_numbers)) & (v7_ordinal1 C)) )  => (m2_subset_1 (k8_graphsp A B C) k1_numbers k5_numbers)) ) ).
tt(dt_k8_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ( (~ (v2_struct_0 (k8_grcat_1 A)))  &  ((v13_algstr_0 (k8_grcat_1 A)) &  ((v3_rlvect_1 (k8_grcat_1 A)) &  ((v4_rlvect_1 (k8_grcat_1 A)) & (l2_algstr_0 (k8_grcat_1 A))) ) ) ) ) ) ).
tt(dt_k8_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) &  ((m1_group_2 C A) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k8_group_10 A B C D)) &  ((v1_funct_2 (k8_group_10 A B C D) (k15_group_2 A C) (k15_group_2 A C)) & (m1_subset_1 (k8_group_10 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_group_2 A C) (k15_group_2 A C))))) ) ) ) ).
tt(dt_k8_group_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k8_group_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k8_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (m1_subset_1 (k8_group_2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_group_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k8_group_3 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k8_group_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k8_group_4 A B C)) & (m1_group_2 (k8_group_4 A B C) A)) ) ) ).
tt(dt_k8_group_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k8_group_5 A B C)) & (m1_group_2 (k8_group_5 A B C) A)) ) ) ).
tt(dt_k8_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ((v1_funct_1 (k8_group_6 A B)) &  ((v1_funct_2 (k8_group_6 A B) (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B))) & (m1_subset_1 (k8_group_6 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B)))))) ) ) ) ).
tt(dt_k8_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  ((v1_funct_1 (k8_group_9 A B C)) &  ((v1_funct_2 (k8_group_9 A B C) (k2_zfmisc_1 (k7_group_9 A B C) (k7_group_9 A B C)) (k7_group_9 A B C)) & (m1_subset_1 (k8_group_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_group_9 A B C) (k7_group_9 A B C)) (k7_group_9 A B C))))) ) ) ) ).
tt(dt_k8_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_hermitan A B)) &  ((v1_funct_2 (k8_hermitan A B) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)))) (u1_struct_0 k1_complfld)) &  ((v2_bilinear (k8_hermitan A B) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) &  ((v4_bilinear (k8_hermitan A B) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) &  ((v3_hermitan (k8_hermitan A B) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) &  ((v5_hermitan (k8_hermitan A B) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) & (m1_subset_1 (k8_hermitan A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)))) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) ) ).
tt(dt_k8_heyting1,ax, (! [A:$i] :  ((v1_funct_1 (k8_heyting1 A)) &  ((v1_funct_2 (k8_heyting1 A) (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) & (m1_subset_1 (k8_heyting1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)))))) ) ) ).
tt(dt_k8_heyting2,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) =>  ((v1_funct_1 (k8_heyting2 A B)) &  ((v1_funct_2 (k8_heyting2 A B) (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B))) & (m1_subset_1 (k8_heyting2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)))))) ) ) ) ).
tt(dt_k8_hurwitz,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  & (m1_subset_1 B (u1_struct_0 k1_complfld)))  =>  ((v1_funct_1 (k8_hurwitz A B)) &  ((v1_funct_2 (k8_hurwitz A B) k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 (k8_hurwitz A B) k1_complfld) & (m1_subset_1 (k8_hurwitz A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) ) ) ) ).
tt(dt_k8_idea_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k8_idea_1 A B) k5_numbers)) ) ).
tt(dt_k8_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k8_ideal_1 A B)))  &  ((v1_ideal_1 (k8_ideal_1 A B) A) &  ((v2_ideal_1 (k8_ideal_1 A B) A) & (m1_subset_1 (k8_ideal_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k8_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m3_index_1 E A B C D)) ) ) )  => (m2_index_1 (k8_index_1 A B C D E) B (k3_relat_1 C (k1_xtuple_0 E)) (k3_relat_1 D (k1_xtuple_0 E)))) ) ).
tt(dt_k8_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k8_int_3 A)) &  ((v1_funct_2 (k8_int_3 A) (k7_card_1 A) (k7_card_1 A)) & (m1_subset_1 (k8_int_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_card_1 A) (k7_card_1 A))))) ) ) ) ).
tt(dt_k8_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k8_integr15 A B C D)) & (m1_subset_1 (k8_integr15 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) ) ).
tt(dt_k8_integr16,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) ) )  => (m1_subset_1 (k8_integr16 A B C) k2_numbers)) ) ).
tt(dt_k8_integra1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k8_integra1 A B)) &  ((v1_funct_2 (k8_integra1 A B) (k1_integra1 A) k1_numbers) & (m1_subset_1 (k8_integra1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_integra1 A) k1_numbers)))) ) ) ) ).
tt(dt_k8_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  => (m2_subset_1 (k8_interva1 A B) (k1_zfmisc_1 A) B)) ) ).
tt(dt_k8_intpro_1,ax,(m1_subset_1 k8_intpro_1 (k1_zfmisc_1 k1_intpro_1))).
tt(dt_k8_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E A C)) ) ) )  => (m2_cat_1 (k8_isocat_2 A B C D E) A (k8_cat_2 B C))) ) ).
tt(dt_k8_jgraph_4,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (m1_subset_1 (k8_jgraph_4 A B) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(dt_k8_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k8_jgraph_6 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k8_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k8_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k8_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (~ (v1_xboole_0 (k8_jordan6 A)))  & (m1_subset_1 (k8_jordan6 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ).
tt(dt_k8_jordan,ax, ((v1_funct_1 k8_jordan) &  ((v1_funct_2 k8_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (m1_subset_1 k8_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers)))) ) ).
tt(dt_k8_knaster,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (~ (v2_struct_0 (k8_knaster A B)))  &  ((v3_lattices (k8_knaster A B)) &  ((v10_lattices (k8_knaster A B)) & (l3_lattices (k8_knaster A B))) ) ) ) ) ).
tt(dt_k8_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_kolmog01 D A B C)) )  => (m1_subset_1 (k8_kolmog01 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ).
tt(dt_k8_lang1,ax, (! [A:$i,B:$i] :  ((v2_lang1 (k8_lang1 A B)) & (l2_lang1 (k8_lang1 A B))) ) ).
tt(dt_k8_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 D (u1_struct_0 C) A A)) ) )  => (m2_finseq_1 (k8_laplace A B C D) (u1_struct_0 C))) ) ).
tt(dt_k8_lattice3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k8_lattice3 A B) (u1_struct_0 (k7_lattice3 A)))) ) ).
tt(dt_k8_lattice5,ax,$true).
tt(dt_k8_lattice8,ax,$true).
tt(dt_k8_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 D (k2_zfmisc_1 A (k9_funct_2 C B)))) )  => (m2_funct_2 (k8_lexbfs A B C D) C B (k9_funct_2 C B))) ) ).
tt(dt_k8_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((m1_subset_1 D A) & (m1_subset_1 E B)) ) ) )  => (m1_subset_1 (k8_lfuzzy_0 A B C D E) (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1))))) ) ).
tt(dt_k8_lmod_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k8_lmod_7 A B C D) (k7_lmod_7 A B C))) ) ).
tt(dt_k8_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_lopban_1 A B)))  &  ((v13_algstr_0 (k8_lopban_1 A B)) &  ((v2_rlvect_1 (k8_lopban_1 A B)) &  ((v3_rlvect_1 (k8_lopban_1 A B)) &  ((v4_rlvect_1 (k8_lopban_1 A B)) &  ((v5_rlvect_1 (k8_lopban_1 A B)) &  ((v6_rlvect_1 (k8_lopban_1 A B)) &  ((v7_rlvect_1 (k8_lopban_1 A B)) &  ((v8_rlvect_1 (k8_lopban_1 A B)) & (l1_rlvect_1 (k8_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k8_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l1_funcsdom (k8_lopban_2 A))) ) ).
tt(dt_k8_lopban_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D k5_numbers)) ) )  =>  ((v1_funct_1 (k8_lopban_4 A B C D)) &  ((v1_funct_2 (k8_lopban_4 A B C D) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k8_lopban_4 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k8_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((v1_relat_1 (k8_lopclset A)) & (v1_funct_1 (k8_lopclset A))) ) ) ).
tt(dt_k8_lpspace1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B k1_numbers))  =>  ((v1_funct_1 (k8_lpspace1 A B)) & (m1_subset_1 (k8_lpspace1 A B) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k8_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  => (m2_subset_1 (k8_lpspace2 A B C D) (k1_zfmisc_1 (k1_lpspace2 A B C D)) (k6_lpspace2 A B C D))) ) ).
tt(dt_k8_ltlaxio1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k8_ltlaxio1 A B) k1_hilbert1)) ) ).
tt(dt_k8_margrel1,ax,(m1_subset_1 k8_margrel1 k6_margrel1)).
tt(dt_k8_mathmorp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k8_mathmorp A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_matrix13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  => (m1_subset_1 (k8_matrix13 A B) k5_numbers)) ) ).
tt(dt_k8_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  => (m2_finseq_2 (k8_matrix_1 A B C) A (k4_finseq_2 (k1_matrix_1 B) A))) ) ).
tt(dt_k8_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((v1_matrix_1 (k8_matrix_2 A B C)) & (m2_finseq_1 (k8_matrix_2 A B C) (k3_finseq_2 (u1_struct_0 A)))) ) ) ).
tt(dt_k8_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k5_finsub_1 A)) & (m1_subset_1 D (k5_finsub_1 B))) ) )  => (m1_subset_1 (k8_matrix_3 A B C D) (k5_finsub_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k8_matrix_5,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_matrix_1 (k8_matrix_5 A B)) & (m2_finseq_1 (k8_matrix_5 A B) (k3_finseq_2 k2_numbers))) ) ) ).
tt(dt_k8_matrixc1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  => (m2_finseq_2 (k8_matrixc1 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k8_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  => (m2_finseq_1 (k8_matrixj1 A B) k5_numbers)) ) ).
tt(dt_k8_matrixr1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_matrix_1 (k8_matrixr1 A B)) & (m2_finseq_1 (k8_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k8_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 D A B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_matrlin2 A B C D E)) &  ((v1_funct_2 (k8_matrlin2 A B C D E) (u1_struct_0 D) (u1_struct_0 C)) &  ((v13_vectsp_1 (k8_matrlin2 A B C D E) D C) &  ((v1_mod_2 (k8_matrlin2 A B C D E) A D C) & (m1_subset_1 (k8_matrlin2 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C))))) ) ) ) ) ) ).
tt(dt_k8_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((m1_matrix_1 E A B D) & (m1_matrix_1 F A C D)) ) ) ) )  => (m1_matrix_1 (k8_matrlin A B C D E F) A (k2_xcmplx_0 B C) D)) ) ).
tt(dt_k8_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 B)))  => (m1_subset_1 (k8_mcart_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(dt_k8_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k8_measure7 A) (k1_zfmisc_1 k7_numbers))) ) ).
tt(dt_k8_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m4_measure8 D A B C)) )  => (m3_measure8 (k8_measure8 A B C D) A (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) C)) B)) ) ).
tt(dt_k8_member_1,ax,$true).
tt(dt_k8_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((v1_relat_1 (k8_memstr_0 A B C)) &  ((v4_relat_1 (k8_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k8_memstr_0 A B C)) & (v5_funct_1 (k8_memstr_0 A B C) (k2_memstr_0 A B))) ) ) ) ) ).
tt(dt_k8_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((v1_funct_1 (k8_mesfun7c A B)) & (m1_subset_1 (k8_mesfun7c A B) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k8_mesfunc1,ax,(m1_subset_1 k8_mesfunc1 k7_numbers)).
tt(dt_k8_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (m1_subset_1 E B)) ) ) )  => (m1_subset_1 (k8_mesfunc5 A B C D E) k7_numbers)) ) ).
tt(dt_k8_mesfunc9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B))))) )  & (v7_ordinal1 D))  =>  ((v1_funct_1 (k8_mesfunc9 A B C D)) &  ((v1_funct_2 (k8_mesfunc9 A B C D) k5_numbers (k4_partfun1 A B)) & (m1_subset_1 (k8_mesfunc9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) ) ) ) ).
tt(dt_k8_metric_1,ax, ((v1_metric_1 k8_metric_1) & (l1_metric_1 k8_metric_1)) ).
tt(dt_k8_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k8_metric_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A))))) ) ).
tt(dt_k8_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_midsp_1 (k8_midsp_1 A B C) A)) ) ).
tt(dt_k8_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B)))) ) ) )  => (m2_finseq_2 (k8_midsp_3 A B C D E) (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C))))) ) ).
tt(dt_k8_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k8_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k8_mod_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v3_mod_2 B A) & (l1_mod_2 B A))  &  ((v3_mod_2 C A) & (l1_mod_2 C A)) ) )  =>  ((v2_mod_2 (k8_mod_2 A B C) A) &  ((v3_mod_2 (k8_mod_2 A B C) A) & (l1_mod_2 (k8_mod_2 A B C) A)) ) ) ) ).
tt(dt_k8_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  =>  ((v1_funct_1 (k8_modcat_1 A B)) &  ((v1_funct_2 (k8_modcat_1 A B) (k4_modcat_1 A B) B) & (m1_subset_1 (k8_modcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) B)))) ) ) ) ).
tt(dt_k8_modelc_1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k8_modelc_1 A B) k5_numbers)) ) ).
tt(dt_k8_modelc_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k8_modelc_2 A B) k5_numbers)) ) ).
tt(dt_k8_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (m1_subset_1 (k8_modelc_3 A) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_k8_monoid_0,ax, ( (~ (v2_struct_0 k8_monoid_0))  &  ((v22_algstr_0 k8_monoid_0) &  ((v4_vectsp_1 k8_monoid_0) & (m1_monoid_0 k8_monoid_0 k7_monoid_0)) ) ) ).
tt(dt_k8_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((v1_funct_1 (k8_monoid_1 A B C D E)) &  ((v1_funct_2 (k8_monoid_1 A B C D E) (k2_zfmisc_1 (k9_funct_2 E A) (k9_funct_2 E B)) (k9_funct_2 E C)) & (m1_subset_1 (k8_monoid_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 E A) (k9_funct_2 E B)) (k9_funct_2 E C))))) ) ) ) ).
tt(dt_k8_msafree2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C))) ) )  => (v7_ordinal1 (k8_msafree2 A B C D))) ) ).
tt(dt_k8_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (k8_msafree A B)) &  ((v4_relat_1 (k8_msafree A B) (u1_struct_0 A)) &  ((v1_funct_1 (k8_msafree A B)) & (v1_partfun1 (k8_msafree A B) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_k8_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k1_msaterm A B)) & (m1_subset_1 D (k9_xtuple_0 C))) ) )  => (m1_dtconstr (k8_msaterm A B C D) (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ).
tt(dt_k8_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (m2_pboole (k8_msualg_1 A) (u4_struct_0 (k6_msualg_1 A)) (k3_relat_1 (u1_msualg_1 (k6_msualg_1 A)) (k6_finseq_2 (u1_struct_0 (k6_msualg_1 A)) (k7_msualg_1 A))) (k3_relat_1 (u2_msualg_1 (k6_msualg_1 A)) (k7_msualg_1 A)))) ) ).
tt(dt_k8_msualg_2,ax,$true).
tt(dt_k8_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v3_msualg_6 (k8_msualg_6 A B C) A B) &  ((v4_msualg_6 (k8_msualg_6 A B C) A B) & (m1_msualg_4 (k8_msualg_6 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_k8_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C))  => (m1_subset_1 (k8_nat_1 A B C) A)) ) ).
tt(dt_k8_nat_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (m2_subset_1 (k8_nat_3 A B) k1_numbers k5_numbers)) ) ).
tt(dt_k8_nat_lat,ax, ((v1_funct_1 k8_nat_lat) &  ((v1_funct_2 k8_nat_lat (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat) & (m1_subset_1 k8_nat_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat)))) ) ).
tt(dt_k8_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m2_cat_1 D A B) & (m1_nattra_1 E A B C D)) ) ) )  => (m1_nattra_1 (k8_nattra_1 A B C D E) A B D C)) ) ).
tt(dt_k8_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_1 (k8_newton A) k1_numbers)) ) ).
tt(dt_k8_normform,ax, (! [A:$i] : (m1_subset_1 (k8_normform A) (k1_zfmisc_1 (k5_finsub_1 (k7_normform A))))) ).
tt(dt_k8_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((v1_relat_1 (k8_openlatt A)) & (v1_funct_1 (k8_openlatt A))) ) ) ).
tt(dt_k8_oppcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_cat_1 D (k2_oppcat_1 A) (k3_oppcat_1 A B) (k3_oppcat_1 A C))) ) )  => (m1_cat_1 (k8_oppcat_1 A B C D) A C B)) ) ).
tt(dt_k8_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  => (v3_ordinal1 (k8_ordinal2 A))) ) ).
tt(dt_k8_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (v3_ordinal1 (k8_ordinal3 A B))) ) ).
tt(dt_k8_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  ((v1_relat_1 (k8_ordinal6 A)) &  ((v1_funct_1 (k8_ordinal6 A)) &  ((v5_ordinal1 (k8_ordinal6 A)) & (v1_ordinal2 (k8_ordinal6 A))) ) ) ) ) ).
tt(dt_k8_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v12_osalg_1 (k8_osafree A B) A) & (l3_msualg_1 (k8_osafree A B) A)) ) ) ).
tt(dt_k8_osalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_subset_1 (k8_osalg_1 A B) (k1_zfmisc_1 (u4_struct_0 A)) (k7_osalg_1 A))) ) ).
tt(dt_k8_osalg_2,ax,$true).
tt(dt_k8_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D))) ) ) )  => (m1_subset_1 (k8_osalg_4 A B C D E) (k6_osalg_4 A B C D))) ) ).
tt(dt_k8_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (m1_parsp_1 (k8_parsp_1 A) (k5_parsp_1 A))) ) ).
tt(dt_k8_pboole,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) )  =>  ((v1_relat_1 (k8_pboole A B)) & (v1_funct_1 (k8_pboole A B))) ) ) ).
tt(dt_k8_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l1_pcs_0 A) & (l1_pcs_0 B))  => (l1_pcs_0 (k8_pcs_0 A B))) ) ).
tt(dt_k8_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  & (m1_subset_1 D (k1_euclid A))) ) )  =>  ((v1_funct_1 (k8_pdiff_1 A B C D)) &  ((v1_funct_2 (k8_pdiff_1 A B C D) (k1_euclid A) (k1_euclid B)) & (m1_subset_1 (k8_pdiff_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) ) ).
tt(dt_k8_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k8_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k8_petri_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri_2 A)) ) ) )  => (m1_subset_1 (k8_petri_2 A) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k8_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))))  => (m1_subset_1 (k8_petri A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m2_pnproc_1 B A) & (m1_subset_1 C (k3_finseq_2 B)))  =>  ((v1_relat_1 (k8_pnproc_1 A B C)) & (v1_funct_1 (k8_pnproc_1 A B C))) ) ) ).
tt(dt_k8_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) &  ((m1_subset_1 D k1_numbers) & (m1_subset_1 E k1_numbers)) ) ) )  => (m1_subset_1 (k8_polyeq_1 A B C D E) k1_numbers)) ) ).
tt(dt_k8_polyeq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_xcmplx_0 (k8_polyeq_5 A B C D))) ) ).
tt(dt_k8_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  => (v1_finset_1 (k8_polyform A B))) ) ).
tt(dt_k8_polynom1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_vectsp_1 B) & (l5_algstr_0 B)) )  =>  ((v1_funct_1 (k8_polynom1 A B)) &  ((v1_funct_2 (k8_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k8_polynom1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k8_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k8_polynom3 A B C)) &  ((v1_funct_2 (k8_polynom3 A B C) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k8_polynom3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k8_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k8_polynom5 A B C)) &  ((v1_funct_2 (k8_polynom5 A B C) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k8_polynom5 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k8_poset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) ) ) )  =>  ((v1_funct_1 (k8_poset_1 A B C)) &  ((v1_funct_2 (k8_poset_1 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k8_poset_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k8_power,ax,(m1_subset_1 k8_power k1_numbers)).
tt(dt_k8_pralg_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k8_pralg_1 A) (k4_partfun1 (k3_finseq_2 (k1_tarski k1_xboole_0)) (k1_tarski k1_xboole_0)))) ) ).
tt(dt_k8_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) )  => (m2_finseq_1 (k8_prelamb A B C) k1_numbers)) ) ).
tt(dt_k8_pre_poly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_pre_poly B)) ) )  =>  ((v1_relat_1 (k8_pre_poly A B)) &  ((v1_funct_1 (k8_pre_poly A B)) & (v1_pre_poly (k8_pre_poly A B))) ) ) ) ).
tt(dt_k8_prepower,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v5_relat_1 B k3_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k8_prepower A B)) &  ((v1_funct_2 (k8_prepower A B) k5_numbers k1_numbers) & (m1_subset_1 (k8_prepower A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k8_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k8_prob_1 A B C D)) &  ((v1_funct_2 (k8_prob_1 A B C D) k5_numbers k1_numbers) & (m1_subset_1 (k8_prob_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k8_prob_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_finseq_1 C B) & (v7_ordinal1 D)) )  => (m1_prob_1 (k8_prob_3 A B C D) A B)) ) ).
tt(dt_k8_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  &  ((m1_subset_1 B (k4_card_3 A)) & (m1_subset_1 C (k9_xtuple_0 A))) )  => (m1_subset_1 (k8_prvect_1 A B C) (k1_funct_1 A C))) ) ).
tt(dt_k8_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  => (m1_subset_1 (k8_prvect_2 A) (k4_card_3 (k4_prvect_2 A)))) ) ).
tt(dt_k8_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k8_pscomp_1 A) k1_numbers)) ) ).
tt(dt_k8_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) & (m1_subset_1 C k5_numbers)) )  => (m1_subset_1 (k8_pua2mss1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k8_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k8_qc_lang1 A B) (k1_zfmisc_1 (k6_qc_lang1 A)))) ) ).
tt(dt_k8_qc_lang2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) &  ((m1_subset_1 D (k3_qc_lang1 A)) & (m1_subset_1 E (k9_qc_lang1 A))) ) ) )  => (m1_subset_1 (k8_qc_lang2 A B C D E) (k9_qc_lang1 A))) ) ).
tt(dt_k8_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  => (m1_subset_1 (k8_qmax_1 A B) (k5_qmax_1 A))) ) ).
tt(dt_k8_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) => (m1_subset_1 (k8_quatern2 A) k1_quaterni)) ) ).
tt(dt_k8_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_quaterni (k8_quaterni A))) ) ).
tt(dt_k8_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k7_quofield A)) & (m1_subset_1 C (k7_quofield A))) )  => (m2_subset_1 (k8_quofield A B C) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k8_radix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C A) & (m1_finseq_1 C (k3_radix_1 B))) ) )  => (v1_int_1 (k8_radix_1 A B C))) ) ).
tt(dt_k8_radix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((v3_card_1 E A) & (m1_finseq_1 E k5_numbers)) ) ) ) )  => (m2_subset_1 (k8_radix_2 A B C D E) k1_numbers k5_numbers)) ) ).
tt(dt_k8_radix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  => (v1_int_1 (k8_radix_3 A B C D))) ) ).
tt(dt_k8_radix_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  ((v3_card_1 (k8_radix_5 A B C) A) & (m2_finseq_1 (k8_radix_5 A B C) (k3_radix_1 C))) ) ) ).
tt(dt_k8_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m1_finseq_1 C (k3_radix_1 B))) ) )  =>  ((v3_card_1 (k8_radix_6 A B C) (k2_xcmplx_0 A 2)) & (m2_finseq_1 (k8_radix_6 A B C) (k3_radix_1 B))) ) ) ).
tt(dt_k8_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_prob_1 C A B) & (m1_random_1 D A B)) ) )  => (m1_subset_1 (k8_random_1 A B C D) k1_numbers)) ) ).
tt(dt_k8_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 D A B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) )  => (m1_vectsp_6 (k8_ranknull A B C D E) A C)) ) ).
tt(dt_k8_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  => (m1_ratfunc1 (k8_ratfunc1 A) A)) ) ).
tt(dt_k8_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  => (m1_subset_1 (k8_real_1 A B) k1_numbers)) ) ).
tt(dt_k8_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k8_real_3 A)) &  ((v1_funct_2 (k8_real_3 A) k5_numbers k1_numbers) & (m1_subset_1 (k8_real_3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_k8_relat_1,ax,$true).
tt(dt_k8_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (k8_relset_1 A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k8_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) & (m1_subset_1 C (k8_afinsq_1 A)))  => (m1_subset_1 (k8_rewrite2 A B C) (k1_zfmisc_1 (k8_afinsq_1 A)))) ) ).
tt(dt_k8_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B k1_numbers) & (m1_rlvect_2 C A)) )  => (m1_rlvect_2 (k8_rlvect_2 A B C) A)) ) ).
tt(dt_k8_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_rmod_4 C A B)) )  => (m1_rmod_4 (k8_rmod_4 A B C) A B)) ) ).
tt(dt_k8_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ((v4_robbins1 (k8_robbins1 A)) & (l4_robbins1 (k8_robbins1 A))) ) ) ).
tt(dt_k8_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_rsspace4 A B)) &  ((v1_funct_2 (k8_rsspace4 A B) (k4_rsspace4 A B) k1_numbers) & (m1_subset_1 (k8_rsspace4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_rsspace4 A B) k1_numbers)))) ) ) ) ).
tt(dt_k8_rsspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k8_rsspace A B)) &  ((v1_funct_2 (k8_rsspace A B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k8_rsspace A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ).
tt(dt_k8_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  => (m2_finseq_1 (k8_rvsum_1 A B) k1_numbers)) ) ).
tt(dt_k8_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  => (m2_finseq_2 (k8_rvsum_2 A B C) k2_numbers (k4_finseq_2 A k2_numbers))) ) ).
tt(dt_k8_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (m1_dtconstr (k8_scm_comp A B) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k8_scmfsa_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) &  ((m1_subset_1 B k3_scmfsa_1) & (m1_finseq_1 C k4_numbers)) )  => (m1_subset_1 (k8_scmfsa_1 A B C) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) ) ).
tt(dt_k8_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k8_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k8_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (m1_subset_1 (k8_scmfsa_i A) k1_scmfsa_i)) ) ).
tt(dt_k8_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  ((v1_funct_1 (k8_scmfsa_m A)) &  ((v1_funct_2 (k8_scmfsa_m A) k5_numbers (k1_zfmisc_1 k5_numbers)) & (m1_subset_1 (k8_scmfsa_m A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k5_numbers))))) ) ) ) ).
tt(dt_k8_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (m1_subset_1 (k8_scm_inst A) k2_scm_inst)) ) ).
tt(dt_k8_scmpds_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m1_subset_1 (k8_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k8_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k8_scmpds_6 A B C)))  &  ((v1_relat_1 (k8_scmpds_6 A B C)) &  ((v4_relat_1 (k8_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k8_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k8_scmpds_6 A B C)) &  ((v1_finset_1 (k8_scmpds_6 A B C)) & (v1_afinsq_1 (k8_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k8_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k8_scmpds_i A))) ) ).
tt(dt_k8_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_scmring1 A)) &  ((v1_funct_2 (k8_scmring1 A) (k1_scmringi A) (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))))) & (m1_subset_1 (k8_scmring1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_scmringi A) (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))))))) ) ) ) ).
tt(dt_k8_scmring2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (m1_subset_1 (k8_scmring2 A B) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k8_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k8_scmringi A B) k2_scm_inst)) ) ).
tt(dt_k8_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  => (v7_ordinal1 (k8_scmyciel A))) ) ).
tt(dt_k8_seq_4,ax, ((v1_funct_1 k8_seq_4) &  ((v1_funct_2 k8_seq_4 k2_numbers k1_numbers) & (m1_subset_1 k8_seq_4 (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k1_numbers)))) ) ).
tt(dt_k8_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) )  =>  ((v1_funct_1 (k8_seqfunc A B C)) &  ((v1_funct_2 (k8_seqfunc A B C) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k8_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k8_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k8_setfam_1 A B) (k1_zfmisc_1 A))) ) ).
tt(dt_k8_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k8_setlim_2 A B C)) &  ((v1_funct_2 (k8_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k8_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k8_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k5_finsub_1 A))) ) )  => (m1_subset_1 (k8_setwiseo A B C D) (k5_finsub_1 B))) ) ).
tt(dt_k8_sgraph1,ax,(m1_sgraph1 k8_sgraph1 k5_numbers)).
tt(dt_k8_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_simplex0 B A) & (v1_xreal_0 C))  => (m1_simplex0 (k8_simplex0 A B C) A)) ) ).
tt(dt_k8_sincos10,ax,$true).
tt(dt_k8_sin_cos2,ax,$true).
tt(dt_k8_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k8_sin_cos7 A))) ) ).
tt(dt_k8_sin_cos,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k2_numbers) & (m1_subset_1 C k2_numbers)) )  =>  ((v1_funct_1 (k8_sin_cos A B C)) &  ((v1_funct_2 (k8_sin_cos A B C) k5_numbers k2_numbers) & (m1_subset_1 (k8_sin_cos A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k8_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (l1_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(dt_k8_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) => (m1_subset_1 (k8_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k8_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A)))) )  => (m2_subset_1 (k8_sublemma A B) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k8_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (k8_subset_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k8_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k2_qc_lang1 A)))  => (m1_subset_1 (k8_substut1 A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k8_substut2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D (k1_substut1 A))) ) )  => (m1_substut1 (k8_substut2 A B C D) A (k7_substut2 A B C D))) ) ).
tt(dt_k8_supinf_2,ax, (! [A:$i] :  ((v2_membered A) => (m1_subset_1 (k8_supinf_2 A) k7_numbers)) ) ).
tt(dt_k8_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (k8_tdlat_1 A)))  &  ((v10_lattices (k8_tdlat_1 A)) &  ((v17_lattices (k8_tdlat_1 A)) & (l3_lattices (k8_tdlat_1 A))) ) ) ) ) ).
tt(dt_k8_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_pre_topc B A))  =>  ((v1_pre_topc (k8_tmap_1 A B)) &  ((v2_pre_topc (k8_tmap_1 A B)) & (l1_pre_topc (k8_tmap_1 A B))) ) ) ) ).
tt(dt_k8_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) &  ((m1_subset_1 F (u1_struct_0 B)) & (m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) )  => (m1_borsuk_2 (k8_topalg_4 A B C D E F G) B E F)) ) ).
tt(dt_k8_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  => (m3_topgrp_1 (k8_topgrp_1 A) A)) ) ).
tt(dt_k8_toprealb,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_pre_topc (k8_toprealb A) (k15_euclid A))) ) ).
tt(dt_k8_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k8_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k8_trees_1,ax,$true).
tt(dt_k8_trees_2,ax,$true).
tt(dt_k8_trees_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) )  =>  ((v1_relat_1 (k8_trees_3 A B C)) &  ((v5_relat_1 (k8_trees_3 A B C) A) &  ((v1_funct_1 (k8_trees_3 A B C)) & (v3_trees_2 (k8_trees_3 A B C))) ) ) ) ) ).
tt(dt_k8_trees_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_finseq_1 C (k5_trees_3 A))) )  => (m1_subset_1 (k8_trees_4 A B C) (k5_trees_3 A))) ) ).
tt(dt_k8_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))))  => (m1_subset_1 (k8_turing_1 A B) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))) ) ).
tt(dt_k8_twoscomp,ax, ((v1_funct_1 k8_twoscomp) &  ((v1_funct_2 k8_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k8_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k8_unialg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ((m1_unialg_2 B A) & (m1_unialg_2 C A)) )  =>  ((v1_unialg_1 (k8_unialg_2 A B C)) & (m1_unialg_2 (k8_unialg_2 A B C) A)) ) ) ).
tt(dt_k8_uproots,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_relat_1 (k8_uproots A B)) &  ((v4_relat_1 (k8_uproots A B) (u1_struct_0 A)) &  ((v1_funct_1 (k8_uproots A B)) &  ((v1_partfun1 (k8_uproots A B) (u1_struct_0 A)) &  ((v4_valued_0 (k8_uproots A B)) & (v2_pre_poly (k8_uproots A B))) ) ) ) ) ) ) ).
tt(dt_k8_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_valuat_1 C A B) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (m2_funct_2 (k8_valuat_1 A B C D) (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))) ) ).
tt(dt_k8_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k8_valued_1 A B C D)) & (m1_subset_1 (k8_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) ) ).
tt(dt_k8_valued_2,ax,$true).
tt(dt_k8_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k8_vectsp10 A B C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_k8_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_vectsp_6 D A B)) ) )  => (m1_vectsp_6 (k8_vectsp_6 A B C D) A B)) ) ).
tt(dt_k8_waybel_0,ax,$true).
tt(dt_k8_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k8_waybel10 A)))  &  ((v1_orders_2 (k8_waybel10 A)) &  ((v4_yellow_0 (k8_waybel10 A) (k4_waybel10 A)) & (m1_yellow_0 (k8_waybel10 A) (k4_waybel10 A))) ) ) ) ) ).
tt(dt_k8_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k8_waybel18 A B C)) &  ((v1_funct_2 (k8_waybel18 A B C) (u1_struct_0 A) (u1_struct_0 (k7_waybel18 A B C))) & (m1_subset_1 (k8_waybel18 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_waybel18 A B C)))))) ) ) ) ).
tt(dt_k8_waybel34,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_waybel34 A)))  &  ((v2_altcat_1 (k8_waybel34 A)) &  ((v6_altcat_1 (k8_waybel34 A)) &  ((v3_altcat_2 (k8_waybel34 A) (k4_waybel34 A)) & (m1_altcat_2 (k8_waybel34 A) (k4_waybel34 A))) ) ) ) ) ) ).
tt(dt_k8_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_orders_2 (k8_waybel_4 A)) & (l1_orders_2 (k8_waybel_4 A))) ) ) ).
tt(dt_k8_weierstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  => (m1_subset_1 (k8_weierstr A B C) k1_numbers)) ) ).
tt(dt_k8_xboolean,ax,$true).
tt(dt_k8_xtuple_0,ax,$true).
tt(dt_k8_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k8_yellow21 A)))  &  ((v2_altcat_1 (k8_yellow21 A)) &  ((v6_altcat_1 (k8_yellow21 A)) &  ((v2_altcat_2 (k8_yellow21 A) (k7_yellow21 A)) &  ((v3_altcat_2 (k8_yellow21 A) (k7_yellow21 A)) & (m1_altcat_2 (k8_yellow21 A) (k7_yellow21 A))) ) ) ) ) ) ) ).
tt(dt_k8_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  & (m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B)))) )  => (m1_subset_1 (k8_yellow_3 A B C) (u1_struct_0 A))) ) ).
tt(dt_k8_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m3_yellow_6 C (u1_struct_0 B) A)) )  =>  ( (~ (v2_struct_0 (k8_yellow_6 A B C)))  &  ((v4_orders_2 (k8_yellow_6 A B C)) &  ((v6_waybel_0 (k8_yellow_6 A B C) A) &  ((v7_waybel_0 (k8_yellow_6 A B C)) & (l1_waybel_0 (k8_yellow_6 A B C) A)) ) ) ) ) ) ).
tt(dt_k8_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) & (m1_finseq_1 B k5_numbers))  => (m2_finseq_1 (k8_zf_lang A B) k5_numbers)) ) ).
tt(dt_k8_zf_model,ax, ((v1_zf_lang k8_zf_model) & (m2_finseq_1 k8_zf_model k5_numbers)) ).
tt(dt_k8_zmodul01,ax,$true).
tt(dt_k90_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k90_valued_2 A B C D E F)) & (m1_subset_1 (k90_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k2_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k91_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((v1_funct_1 (k91_valued_2 A B C D E F)) & (m1_subset_1 (k91_valued_2 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A B) (k6_valued_2 (k3_xboole_0 (k1_valued_2 C) (k1_valued_2 D))))))) ) ) ).
tt(dt_k9_abcmiz_1,ax,$true).
tt(dt_k9_abcmiz_a,ax,$true).
tt(dt_k9_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~ (v1_xboole_0 (k9_afproj A))) ) ) ).
tt(dt_k9_algstr_0,ax, (! [A:$i,B:$i] :  ( ((l4_algstr_0 A) & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k9_algstr_0 A B) (u1_struct_0 A))) ) ).
tt(dt_k9_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v15_algstr_0 (k9_algstr_4 A B)) & (m1_algstr_4 (k9_algstr_4 A B) A)) ) ) ).
tt(dt_k9_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k9_altcat_1 A)))  &  ((v6_altcat_1 (k9_altcat_1 A)) &  ((v13_altcat_1 (k9_altcat_1 A)) & (l2_altcat_1 (k9_altcat_1 A))) ) ) ) ) ).
tt(dt_k9_ami_2,ax, ((v1_funct_1 k9_ami_2) &  ((v1_funct_2 k9_ami_2 k3_scm_inst (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) & (m1_subset_1 k9_ami_2 (k1_zfmisc_1 (k2_zfmisc_1 k3_scm_inst (k1_funct_2 (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))))))) ) ).
tt(dt_k9_ami_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (m1_subset_1 (k9_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(dt_k9_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_unialg_1 A) & (l1_unialg_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_aofa_000 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  & (v1_int_1 C)) )  =>  ((v1_funct_1 (k9_aofa_i00 A B C)) &  ((v1_funct_2 (k9_aofa_i00 A B C) A k4_numbers) & (m1_subset_1 (k9_aofa_i00 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) ) ).
tt(dt_k9_armstrng,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (m1_subset_1 (k9_armstrng A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(dt_k9_arytm_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_arytm_3) & (m1_subset_1 B k5_arytm_3))  => (m1_subset_1 (k9_arytm_3 A B) k5_arytm_3)) ) ).
tt(dt_k9_asympt_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (m1_funct_2 (k9_asympt_0 A B) k5_numbers k1_numbers)) ) ).
tt(dt_k9_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_orders_2 (k9_bagorder A)) & (l1_orders_2 (k9_bagorder A))) ) ) ).
tt(dt_k9_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_bcialg_2 B A))  => (l2_bcialg_1 (k9_bcialg_2 A B))) ) ).
tt(dt_k9_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  => (m2_subset_1 (k9_bcialg_6 A B C D) (u1_struct_0 A) (k7_bcialg_6 A B C D))) ) ).
tt(dt_k9_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ((v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 (k9_bilinear A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k9_binarith,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( (~ (v1_xboole_0 C))  &  ( ((v3_card_1 D A) & (m1_finseq_1 D C))  &  ((v3_card_1 E B) & (m1_finseq_1 E C)) ) ) ) )  =>  ((v3_card_1 (k9_binarith A B C D E) (k23_binop_2 A B)) & (m2_finseq_1 (k9_binarith A B C D E) C)) ) ) ).
tt(dt_k9_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (m1_subset_1 (k9_binop_2 A B) k1_numbers)) ) ).
tt(dt_k9_bor_cant,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k9_bor_cant A B)) &  ((v1_funct_2 (k9_bor_cant A B) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k9_bor_cant A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k9_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_funct_1 (k9_borsuk_1 A B)) &  ((v1_funct_2 (k9_borsuk_1 A B) (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 (k9_borsuk_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)))))) ) ) ) ).
tt(dt_k9_borsuk_7,ax,(m1_subset_1 k9_borsuk_7 (u1_struct_0 (k8_toprealb 3)))).
tt(dt_k9_bspace,ax, (! [A:$i] : (m1_subset_1 (k9_bspace A) (k1_zfmisc_1 (u1_struct_0 (k7_bspace A))))) ).
tt(dt_k9_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((v1_funct_1 (k9_bvfunc_1 A B C)) &  ((v1_funct_2 (k9_bvfunc_1 A B C) A k6_margrel1) & (m1_subset_1 (k9_bvfunc_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) ) ).
tt(dt_k9_c0sp1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (~ (v1_xboole_0 (k9_c0sp1 A B)))  & (m1_subset_1 (k9_c0sp1 A B) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(dt_k9_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_c0sp2 A)))  & (l1_normsp_1 (k9_c0sp2 A))) ) ) ).
tt(dt_k9_card_3,ax,$true).
tt(dt_k9_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E B C)) ) ) )  => (m2_cat_1 (k9_cat_1 A B C D E) A C)) ) ).
tt(dt_k9_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k9_cat_2 A B C D) (u1_struct_0 (k8_cat_2 A B)))) ) ).
tt(dt_k9_cat_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  &  ((m2_cat_1 E A D) & (m1_cat_1 F A B C)) ) ) ) )  => (m1_cat_1 (k9_cat_3 A B C D E F) D (k8_cat_1 A D E B) (k8_cat_1 A D E C))) ) ).
tt(dt_k9_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_cat_1 E A D B) & (m1_cat_1 F A D C)) ) ) ) )  => (m1_cat_1 (k9_cat_4 A B C D E F) A D (k2_cat_4 A B C))) ) ).
tt(dt_k9_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k9_cat_5 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_k9_catalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k9_catalg_1 A B C) (u1_struct_0 (k3_catalg_1 A)))) ) ).
tt(dt_k9_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (l2_clvect_1 (k9_cc0sp2 A))) ) ).
tt(dt_k9_cgames_1,ax, (! [A:$i] : (v3_ordinal1 (k9_cgames_1 A))) ).
tt(dt_k9_chain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D (k4_chain_1 A B C))) ) )  => (m1_subset_1 (k9_chain_1 A B C D) (k1_zfmisc_1 (k4_chain_1 A B (k2_nat_1 C 1))))) ) ).
tt(dt_k9_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) & (m1_subset_1 D (k4_card_3 (u3_msualg_1 A B)))) ) )  =>  ((v1_funct_1 (k9_circuit2 A B C D)) &  ((v1_funct_2 (k9_circuit2 A B C D) k5_numbers (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 (k9_circuit2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_card_3 (u3_msualg_1 A B)))))) ) ) ) ).
tt(dt_k9_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (m1_subset_1 (k9_classes2 A B C) A)) ) ).
tt(dt_k9_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_clopban1 A B)))  &  ((v13_algstr_0 (k9_clopban1 A B)) &  ((v2_rlvect_1 (k9_clopban1 A B)) &  ((v3_rlvect_1 (k9_clopban1 A B)) &  ((v4_rlvect_1 (k9_clopban1 A B)) &  ((v2_clvect_1 (k9_clopban1 A B)) &  ((v3_clvect_1 (k9_clopban1 A B)) &  ((v4_clvect_1 (k9_clopban1 A B)) &  ((v5_clvect_1 (k9_clopban1 A B)) & (l1_clvect_1 (k9_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_k9_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l1_clopban2 (k9_clopban2 A))) ) ).
tt(dt_k9_cohsp_1,ax,$true).
tt(dt_k9_coh_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_coh_sp A)) & (m1_subset_1 C (k5_coh_sp A)))  => (m1_subset_1 (k9_coh_sp A B C) (k5_coh_sp A))) ) ).
tt(dt_k9_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  => (m1_subset_1 (k9_complex1 A B) k2_numbers)) ) ).
tt(dt_k9_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) & (m1_subset_1 B (u1_compos_1 A)))  =>  ((v1_relat_1 (k9_compos_1 A B)) &  ((v4_relat_1 (k9_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k9_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k9_compos_1 A B)) & (v1_finset_1 (k9_compos_1 A B))) ) ) ) ) ) ).
tt(dt_k9_comput_1,ax,(m1_subset_1 k9_comput_1 (k1_zfmisc_1 (k2_comput_1 k5_numbers)))).
tt(dt_k9_comseq_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k9_comseq_3 A B)) &  ((v1_funct_2 (k9_comseq_3 A B) k5_numbers k2_numbers) & (m1_subset_1 (k9_comseq_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k9_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v1_funct_1 (k9_conlat_1 A)) &  ((v1_funct_2 (k9_conlat_1 A) (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A)) & (m1_subset_1 (k9_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_conlat_1 A) (k8_conlat_1 A)) (k8_conlat_1 A))))) ) ) ) ).
tt(dt_k9_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  => (m1_lattice4 (k9_conlat_2 A) (k1_lattice2 (k11_conlat_1 A)) (k11_conlat_1 (k7_conlat_2 A)))) ) ).
tt(dt_k9_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  => (m1_convex4 (k9_convex4 A B C) A)) ) ).
tt(dt_k9_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (m2_subset_1 (k9_cqc_lang A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ).
tt(dt_k9_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v1_funct_1 (k9_cqc_sim1 A)) &  ((v1_funct_2 (k9_cqc_sim1 A) (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) & (m1_subset_1 (k9_cqc_sim1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))))) ) ) ) ).
tt(dt_k9_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_csspace4 A B)))  & (l2_clvect_1 (k9_csspace4 A B))) ) ) ).
tt(dt_k9_csspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k9_csspace A B)) &  ((v1_funct_2 (k9_csspace A B) (k2_zfmisc_1 k2_numbers B) B) & (m1_subset_1 (k9_csspace A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers B) B)))) ) ) ) ).
tt(dt_k9_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m1_subset_1 (k9_decomp_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k9_dickson,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k9_dickson A B)))  & (m1_subset_1 (k9_dickson A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ).
tt(dt_k9_diff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k9_diff_1 A B C) k1_numbers)) ) ).
tt(dt_k9_dist_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  => (m2_finseq_1 (k9_dist_1 A B) k5_numbers)) ) ).
tt(dt_k9_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  => (m1_subset_1 (k9_domain_1 A B C D E) (k1_zfmisc_1 A))) ) ).
tt(dt_k9_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) &  ((v3_dtconstr A) & (l1_lang1 A)) ) )  &  ((m1_subset_1 B (k7_dtconstr A)) & (m2_dtconstr C A B)) )  => (m1_dtconstr (k9_dtconstr A B C) (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A))) ) ).
tt(dt_k9_ec_pf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  &  ((m1_subset_1 B (k1_ec_pf_2 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))))) )  & (m1_subset_1 D (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))) ) )  => (m2_subset_1 (k9_ec_pf_2 A B C D) (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))) ) ).
tt(dt_k9_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k9_ens_1 A)) &  ((v1_funct_2 (k9_ens_1 A) (k2_ens_1 A) A) & (m1_subset_1 (k9_ens_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ens_1 A) A)))) ) ) ) ).
tt(dt_k9_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (m1_subset_1 C A)) )  => (m2_subset_1 (k9_eqrel_1 A B C) (k1_zfmisc_1 A) (k8_eqrel_1 A B))) ) ).
tt(dt_k9_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (v1_relat_1 (k9_e_siec A))) ) ).
tt(dt_k9_euclid_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (u1_struct_0 (k15_euclid A)))) ) )  => (m1_subset_1 (k9_euclid_3 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ).
tt(dt_k9_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (v1_xreal_0 C)) )  => (m2_finseq_2 (k9_euclid A B C) k1_numbers (k1_euclid A))) ) ).
tt(dt_k9_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  => (m2_subset_1 (k9_facirc_1 A B C D) (u1_struct_0 (k8_facirc_1 A B C D)) (k3_msafree2 (k8_facirc_1 A B C D)))) ) ).
tt(dt_k9_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  => (v1_relat_1 (k9_ff_siec A))) ) ).
tt(dt_k9_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v3_relat_2 (k9_filter_0 A B)) &  ((v8_relat_2 (k9_filter_0 A B)) &  ((v1_partfun1 (k9_filter_0 A B) (u1_struct_0 A)) & (m1_subset_1 (k9_filter_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_k9_filter_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k9_filter_1 A B C D) (u1_struct_0 (k7_filter_1 A B)))) ) ).
tt(dt_k9_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 (k9_filter_2 A B C)))  &  ((v20_lattices (k9_filter_2 A B C) A) &  ((v21_lattices (k9_filter_2 A B C) A) & (m1_subset_1 (k9_filter_2 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k9_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ( ( (~ (v1_xboole_0 E))  &  ((v1_prob_1 E C) &  ((v4_prob_1 E C) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers F)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_finance1 A B C D E F G)) &  ((v1_funct_2 (k9_finance1 A B C D E F G) B C) & (m1_subset_1 (k9_finance1 A B C D E F G) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ).
tt(dt_k9_finseq_1,ax, (! [A:$i] :  ((v1_relat_1 (k9_finseq_1 A)) & (v1_funct_1 (k9_finseq_1 A))) ) ).
tt(dt_k9_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  => (m2_finseq_1 (k9_finseq_4 A B C D E) A)) ) ).
tt(dt_k9_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (m2_finseq_1 (k9_finseq_8 A B C) A)) ) ).
tt(dt_k9_fintopo2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k9_fintopo2 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_fintopo3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_fintopo3 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_fin_topo,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (m1_subset_1 (k9_fin_topo A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_flang_1,ax, (! [A:$i] : (m1_subset_1 (k9_flang_1 A) (k1_zfmisc_1 (k3_catalan2 A)))) ).
tt(dt_k9_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k9_fomodel0 A B)) &  ((v1_funct_2 (k9_fomodel0 A B) B k6_margrel1) & (m1_subset_1 (k9_fomodel0 A B) (k1_zfmisc_1 (k2_zfmisc_1 B k6_margrel1)))) ) ) ).
tt(dt_k9_fomodel1,ax,$true).
tt(dt_k9_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  & (m1_subset_1 D (k35_fomodel1 A))) ) )  => (m1_subset_1 (k9_fomodel2 A B C D) B)) ) ).
tt(dt_k9_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_fomodel3 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) (k4_finseq_2 C A))))) ) ).
tt(dt_k9_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (m1_subset_1 (k9_fomodel4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A))))) ) ).
tt(dt_k9_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  => (m1_freealg (k9_freealg A B) (k7_freealg A B))) ) ).
tt(dt_k9_fscirc_1,ax, (! [A:$i,B:$i,C:$i] :  ((v3_msualg_1 (k9_fscirc_1 A B C) (k8_fscirc_1 A B C)) &  ((v4_msafree2 (k9_fscirc_1 A B C) (k8_fscirc_1 A B C)) &  ((v4_circcomb (k9_fscirc_1 A B C) (k8_fscirc_1 A B C)) &  ((v6_circcomb (k9_fscirc_1 A B C) (k8_fscirc_1 A B C)) & (l3_msualg_1 (k9_fscirc_1 A B C) (k8_fscirc_1 A B C))) ) ) ) ) ).
tt(dt_k9_ftacell1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (m1_subset_1 (k9_ftacell1 A B C D E) (k3_msafree2 (k7_ftacell1 A B C D E)))) ).
tt(dt_k9_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m1_subset_1 E A)) ) )  =>  ((v1_funct_1 (k9_funcop_1 A B C D E)) &  ((v1_funct_2 (k9_funcop_1 A B C D E) B A) & (m1_subset_1 (k9_funcop_1 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ).
tt(dt_k9_funcsdom,ax, (! [A:$i] : (m2_funct_2 (k9_funcsdom A) A k1_numbers (k9_funct_2 A k1_numbers))) ).
tt(dt_k9_funct_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  => (m1_funct_2 (k9_funct_2 A B) A B)) ) ).
tt(dt_k9_funct_3,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k9_funct_3 A B)) &  ((v1_funct_2 (k9_funct_3 A B) (k2_zfmisc_1 A B) A) & (m1_subset_1 (k9_funct_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) A)))) ) ) ).
tt(dt_k9_funct_5,ax, ((v1_funct_1 k9_funct_5) &  ((v1_funct_2 k9_funct_5 (k2_zfmisc_1 1 1) 1) & (m1_subset_1 k9_funct_5 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 1 1) 1)))) ) ).
tt(dt_k9_funct_6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_relat_1 (k9_funct_6 A B)) & (v1_funct_1 (k9_funct_6 A B))) ) ) ).
tt(dt_k9_funct_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v7_ordinal1 B))  => (v1_relat_1 (k9_funct_7 A B))) ) ).
tt(dt_k9_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (k1_altcat_1 B C C))) ) )  =>  ((v9_functor0 (k9_functor0 A B C D) A B) & (l2_functor0 (k9_functor0 A B C D) A B)) ) ) ).
tt(dt_k9_functor3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ((v15_functor0 C A B) & (m2_functor0 C A B)) ) )  => (m1_functor3 (k9_functor3 A B C) A B C C)) ) ).
tt(dt_k9_fvaluat1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ((m1_fvaluat1 B A) &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k9_fvaluat1 A B C) (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B))))) ) ).
tt(dt_k9_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m2_finseq_1 (k9_fvsum_1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k9_gate_1,ax,$true).
tt(dt_k9_gate_5,ax,$true).
tt(dt_k9_gcd_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m2_gcd_1 B A) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 A))) ) ) ) )  => (m1_subset_1 (k9_gcd_1 A B C D E F) (u1_struct_0 A))) ) ).
tt(dt_k9_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) & (m1_subset_1 F k5_numbers)) ) ) ) )  => (m1_genealg1 (k9_genealg1 A B C D E F) A)) ) ).
tt(dt_k9_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_geomtrap A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k9_geomtrap A B C) (u1_struct_0 A))) ) ).
tt(dt_k9_gfacirc1,ax, (! [A:$i,B:$i,C:$i] : (m2_subset_1 (k9_gfacirc1 A B C) (u1_struct_0 (k7_gfacirc1 A B C)) (k3_msafree2 (k7_gfacirc1 A B C)))) ).
tt(dt_k9_glib_000,ax,$true).
tt(dt_k9_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (m3_glib_001 (k9_glib_001 A B C D) A)) ) ).
tt(dt_k9_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m3_glib_001 B A))  => (m2_finseq_1 (k9_glib_003 A B) k1_numbers)) ) ).
tt(dt_k9_glib_004,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ((m2_glib_004 B A) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_glib_004 A B C) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A))))) ) ).
tt(dt_k9_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  & (m3_glib_001 C A)) )  => (v7_ordinal1 (k9_glib_005 A B C))) ) ).
tt(dt_k9_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (m1_subset_1 (k9_graph_1 A B) k5_numbers)) ) ).
tt(dt_k9_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (m1_finseq_2 (k9_graph_3 A) (u4_struct_0 A))) ) ).
tt(dt_k9_graph_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_finseq_1 B (u4_struct_0 A)) &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  => (m2_finseq_1 (k9_graph_5 A B C) k1_numbers)) ) ).
tt(dt_k9_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) & (m1_subset_1 B k5_numbers))  => (m2_funct_2 (k9_graphsp A B) (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)))) ) ).
tt(dt_k9_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((v1_funct_1 (k9_grcat_1 A)) &  ((v1_funct_2 (k9_grcat_1 A) (u1_struct_0 (k7_grcat_1 A)) (u1_struct_0 (k8_grcat_1 A))) & (m1_subset_1 (k9_grcat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_grcat_1 A)) (u1_struct_0 (k8_grcat_1 A)))))) ) ) ) ).
tt(dt_k9_group_10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v1_funct_1 (k9_group_10 A B C)) &  ((v1_funct_2 (k9_group_10 A B C) (u1_struct_0 B) (k1_funct_2 (k15_group_2 A C) (k15_group_2 A C))) &  ((v1_group_10 (k9_group_10 A B C) B (k15_group_2 A C)) & (m1_subset_1 (k9_group_10 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (k1_funct_2 (k15_group_2 A C) (k15_group_2 A C)))))) ) ) ) ) ).
tt(dt_k9_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((v15_algstr_0 (k9_group_2 A B C)) & (m1_group_2 (k9_group_2 A B C) A)) ) ) ).
tt(dt_k9_group_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  => (m1_subset_1 (k9_group_3 A B) (k1_zfmisc_1 (k1_group_3 A)))) ) ).
tt(dt_k9_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k9_group_4 A)) &  ((v1_funct_2 (k9_group_4 A) (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A)) & (m1_subset_1 (k9_group_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_group_3 A) (k1_group_3 A)) (k1_group_3 A))))) ) ) ) ).
tt(dt_k9_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k9_group_5 A)) &  ((v1_group_3 (k9_group_5 A) A) & (m1_group_2 (k9_group_5 A) A)) ) ) ) ).
tt(dt_k9_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v15_algstr_0 (k9_group_6 A B C)) & (m1_group_2 (k9_group_6 A B C) A)) ) ) ).
tt(dt_k9_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  ((v1_funct_1 (k9_group_9 A B C)) &  ((v1_funct_2 (k9_group_9 A B C) A (k1_funct_2 (k7_group_9 A B C) (k7_group_9 A B C))) & (m1_subset_1 (k9_group_9 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 (k7_group_9 A B C) (k7_group_9 A B C)))))) ) ) ) ).
tt(dt_k9_heyting1,ax, (! [A:$i] :  ((v1_funct_1 (k9_heyting1 A)) &  ((v1_funct_2 (k9_heyting1 A) (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) (u1_struct_0 (k12_normform A))) & (m1_subset_1 (k9_heyting1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A))) (u1_struct_0 (k12_normform A)))))) ) ) ).
tt(dt_k9_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_idea_1 A B C) k5_numbers)) ) ).
tt(dt_k9_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k9_ideal_1 A B)))  &  ((v1_ideal_1 (k9_ideal_1 A B) A) &  ((v3_ideal_1 (k9_ideal_1 A B) A) & (m1_subset_1 (k9_ideal_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_k9_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) & (m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B)) )  => (m2_cat_1 (k9_index_1 A B C) A C)) ) ).
tt(dt_k9_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (l6_algstr_0 (k9_int_3 A))) ) ).
tt(dt_k9_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_xreal_0 B) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k9_integr15 A B C D)) & (m1_subset_1 (k9_integr15 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 C (k1_euclid A))))) ) ) ).
tt(dt_k9_integra1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_funct_1 (k9_integra1 A B)) &  ((v1_funct_2 (k9_integra1 A B) (k1_integra1 A) k1_numbers) & (m1_subset_1 (k9_integra1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_integra1 A) k1_numbers)))) ) ) ) ).
tt(dt_k9_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  => (m1_interva1 (k9_interva1 A B C) A)) ) ).
tt(dt_k9_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  & (m2_cat_1 D A (k8_cat_2 B C))) ) )  => (m2_cat_1 (k9_isocat_2 A B C D) A B)) ) ).
tt(dt_k9_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k9_jgraph_4 A)) &  ((v1_funct_2 (k9_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k9_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(dt_k9_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (m1_subset_1 (k9_jgraph_6 A B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(dt_k9_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (m2_subset_1 (k9_jordan5d A) k1_numbers k5_numbers)) ) ).
tt(dt_k9_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (~ (v1_xboole_0 (k9_jordan6 A)))  & (m1_subset_1 (k9_jordan6 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ).
tt(dt_k9_jordan,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ((v2_xxreal_0 D) & (v1_xreal_0 D)) ) ) )  =>  ((v1_funct_1 (k9_jordan A B C D)) &  ((v1_funct_2 (k9_jordan A B C D) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D))) & (m1_subset_1 (k9_jordan A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D)))))) ) ) ) ).
tt(dt_k9_knaster,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  => (m1_subset_1 (k9_knaster A B) (u1_struct_0 A))) ) ).
tt(dt_k9_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_lang1 (k9_lang1 A)) & (l2_lang1 (k9_lang1 A))) ) ) ).
tt(dt_k9_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 D (u1_struct_0 C) A A)) ) )  => (m2_finseq_1 (k9_laplace A B C D) (u1_struct_0 C))) ) ).
tt(dt_k9_lattice3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (m1_subset_1 B (u1_struct_0 (k7_lattice3 A))))  => (m1_subset_1 (k9_lattice3 A B) (u1_struct_0 A))) ) ).
tt(dt_k9_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  => (m1_subset_1 (k9_lattice5 A B C D E) (k4_zfmisc_1 (k8_lattice5 A E) (k8_lattice5 A E) (u1_struct_0 B) (u1_struct_0 B)))) ) ).
tt(dt_k9_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  & (m1_lattice5 D A B C)) ) )  =>  ((v1_funct_1 (k9_lattice8 A B C D)) &  ((v1_funct_2 (k9_lattice8 A B C D) (k2_zfmisc_1 (k7_lattice8 A B C) (k7_lattice8 A B C)) (u1_struct_0 B)) &  ((v1_lattice5 (k9_lattice8 A B C D) (k7_lattice8 A B C) B) &  ((v2_lattice5 (k9_lattice8 A B C D) (k7_lattice8 A B C) B) &  ((v3_lattice5 (k9_lattice8 A B C D) (k7_lattice8 A B C) B) & (m1_subset_1 (k9_lattice8 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k7_lattice8 A B C) (k7_lattice8 A B C)) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(dt_k9_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_subset_1 (k9_lexbfs A) (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers))))) ) ).
tt(dt_k9_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) & (m1_subset_1 C A)) )  => (m1_subset_1 (k9_lfuzzy_0 A B C) (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1))))) ) ).
tt(dt_k9_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k8_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k9_lopban_1 A B C D) (u1_struct_0 B))) ) ).
tt(dt_k9_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (l1_lopban_2 (k9_lopban_2 A))) ) ).
tt(dt_k9_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_lopban_4 A)) &  ((v1_funct_2 (k9_lopban_4 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k9_lopban_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k9_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((v1_funct_1 (k9_lopclset A)) &  ((v1_funct_2 (k9_lopclset A) (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A))) & (m1_subset_1 (k9_lopclset A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)))))) ) ) ) ).
tt(dt_k9_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k9_lpspace1 A B C)))  & (m1_subset_1 (k9_lpspace1 A B C) (k1_zfmisc_1 (u1_struct_0 (k7_lpspace1 A))))) ) ) ).
tt(dt_k9_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v1_funct_1 (k9_lpspace2 A B C D)) &  ((v1_funct_2 (k9_lpspace2 A B C D) (k2_zfmisc_1 k1_numbers (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D)) & (m1_subset_1 (k9_lpspace2 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (k6_lpspace2 A B C D)) (k6_lpspace2 A B C D))))) ) ) ) ).
tt(dt_k9_ltlaxio1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (m1_subset_1 (k9_ltlaxio1 A B) k1_hilbert1)) ) ).
tt(dt_k9_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) => (m1_subset_1 (k9_margrel1 A) k6_margrel1)) ) ).
tt(dt_k9_mathmorp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k9_mathmorp A B C D) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) & (m1_matrix_1 D (u1_struct_0 A) B C)) ) )  => (m1_subset_1 (k9_matrix13 A B C D) (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 A C))))) ) ).
tt(dt_k9_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  => (m2_finseq_2 (k9_matrix_1 A B C) A (k4_finseq_2 (k3_finseq_1 B) A))) ) ).
tt(dt_k9_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 E (u1_struct_0 D) C C)) ) ) )  =>  ((v1_matrix_1 (k9_matrix_2 A B C D E)) & (m2_finseq_1 (k9_matrix_2 A B C D E) (k3_finseq_2 (u1_struct_0 D)))) ) ) ).
tt(dt_k9_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_matrix_3 A B C D E F)) &  ((v1_funct_2 (k9_matrix_3 A B C D E F) (k2_zfmisc_1 A B) C) & (m1_subset_1 (k9_matrix_3 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) ).
tt(dt_k9_matrix_5,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  => (m1_subset_1 (k9_matrix_5 A B) k2_numbers)) ) ).
tt(dt_k9_matrixc1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) => (m2_finseq_1 (k9_matrixc1 A) k2_numbers)) ) ).
tt(dt_k9_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  => (m2_finseq_1 (k9_matrixj1 A B) k5_numbers)) ) ).
tt(dt_k9_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l6_algstr_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) )  => (v7_ordinal1 (k9_matrixj2 A B C))) ) ).
tt(dt_k9_matrixr1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((v1_matrix_1 (k9_matrixr1 A)) & (m2_finseq_1 (k9_matrixr1 A) (k3_finseq_2 k1_numbers))) ) ) ).
tt(dt_k9_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((m1_matrlin C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m2_finseq_1 (k9_matrlin A B C D) (u1_struct_0 A))) ) ).
tt(dt_k9_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 D (k1_zfmisc_1 A)) &  ((m1_subset_1 E (k1_zfmisc_1 B)) & (m1_subset_1 F (k1_zfmisc_1 C))) )  => (m1_subset_1 (k9_mcart_1 A B C D E F) (k1_zfmisc_1 (k3_zfmisc_1 A B C)))) ) ).
tt(dt_k9_measure8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  => (m1_measure4 (k9_measure8 A B C) A)) ) ).
tt(dt_k9_member_1,ax,$true).
tt(dt_k9_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k9_memstr_0 A B C D)) &  ((v4_relat_1 (k9_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k9_memstr_0 A B C D)) & (v5_funct_1 (k9_memstr_0 A B C D) (k2_memstr_0 A B))) ) ) ) ) ).
tt(dt_k9_mesfun7c,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  & (m1_subset_1 C A)) )  =>  ((v1_funct_1 (k9_mesfun7c A B C)) &  ((v1_funct_2 (k9_mesfun7c A B C) k5_numbers k2_numbers) & (m1_subset_1 (k9_mesfun7c A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k9_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v5_relat_1 B k7_numbers) & (v1_funct_1 B)) ) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k9_mesfunc1 A B C)) & (m1_subset_1 (k9_mesfunc1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) ) ) ).
tt(dt_k9_mesfunc9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k4_partfun1 A B))))) )  & (v7_ordinal1 D))  =>  ((v1_funct_1 (k9_mesfunc9 A B C D)) &  ((v1_funct_2 (k9_mesfunc9 A B C D) k5_numbers (k4_partfun1 A B)) & (m1_subset_1 (k9_mesfunc9 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) ) ) ) ).
tt(dt_k9_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (m1_subset_1 (k9_metric_1 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  => (m1_subset_1 (k9_metric_2 A) (k1_zfmisc_1 (k3_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A) k1_numbers)))) ) ).
tt(dt_k9_midsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((l1_midsp_2 B A) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  => (m1_subset_1 (k9_midsp_2 A B C D) (u1_struct_0 (u1_midsp_2 A B)))) ) ).
tt(dt_k9_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C))))) ) ) )  => (m1_subset_1 (k9_midsp_3 A B C D E) (u1_struct_0 (u1_midsp_2 B C)))) ) ).
tt(dt_k9_mmlquery,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (m1_subset_1 (k9_mmlquery A B C D) (k1_zfmisc_1 A))) ) ).
tt(dt_k9_mod_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  &  ((m1_mod_2 E A C D) & (m1_mod_2 F A B C)) ) ) ) )  =>  ((v2_mod_2 (k9_mod_2 A B C D E F) A) & (m1_mod_2 (k9_mod_2 A B C D E F) A B D)) ) ) ).
tt(dt_k9_modal_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  & (m1_finseq_1 D k5_numbers)) ) )  =>  ((v1_relat_1 (k9_modal_1 A B C D)) &  ((v5_relat_1 (k9_modal_1 A B C D) A) &  ((v1_funct_1 (k9_modal_1 A B C D)) & (v3_trees_2 (k9_modal_1 A B C D))) ) ) ) ) ).
tt(dt_k9_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  =>  ((v1_funct_1 (k9_modcat_1 A B)) &  ((v1_funct_2 (k9_modcat_1 A B) (k4_modcat_1 A B) B) & (m1_subset_1 (k9_modcat_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_modcat_1 A B) B)))) ) ) ) ).
tt(dt_k9_modelc_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) => (m2_finseq_1 (k9_modelc_1 A) k5_numbers)) ) ).
tt(dt_k9_modelc_2,ax, (~ (v1_xboole_0 k9_modelc_2)) ).
tt(dt_k9_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((v1_modelc_3 (k9_modelc_3 A) A) &  ((v3_modelc_3 (k9_modelc_3 A) A) & (l1_modelc_3 (k9_modelc_3 A) A)) ) ) ) ).
tt(dt_k9_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k9_monoid_0 A)))  &  ((v15_algstr_0 (k9_monoid_0 A)) &  ((v1_group_1 (k9_monoid_0 A)) &  ((v3_group_1 (k9_monoid_0 A)) &  ((v2_monoid_0 (k9_monoid_0 A)) &  ((v16_monoid_0 (k9_monoid_0 A)) &  ((v17_monoid_0 (k9_monoid_0 A)) & (l3_algstr_0 (k9_monoid_0 A))) ) ) ) ) ) ) ) ) ).
tt(dt_k9_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  => (l3_algstr_0 (k9_monoid_1 A B))) ) ).
tt(dt_k9_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((v1_funct_1 (k9_msafree A B C)) &  ((v1_funct_2 (k9_msafree A B C) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)) C)) & (m1_subset_1 (k9_msafree A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) C) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k8_msafree A B)) C))))) ) ) ) ).
tt(dt_k9_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((m4_msaterm C A B) &  ((m1_subset_1 D (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) & (m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B))) ) ) )  => (m1_subset_1 (k9_msaterm A B C D E) (k1_funct_1 (u3_msualg_1 A B) (k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) D)))) ) ).
tt(dt_k9_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v3_msualg_1 (k9_msualg_1 A) (k6_msualg_1 A)) & (l3_msualg_1 (k9_msualg_1 A) (k6_msualg_1 A))) ) ) ).
tt(dt_k9_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  => (m3_pboole (k9_msualg_2 A B C) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(dt_k9_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v2_msualg_4 (k9_msualg_6 A B C) A B) & (m1_msualg_4 (k9_msualg_6 A B C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ).
tt(dt_k9_nat_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k9_nat_1 A B)) &  ((v4_relat_1 (k9_nat_1 A B) k5_numbers) &  ((v1_funct_1 (k9_nat_1 A B)) & (v1_partfun1 (k9_nat_1 A B) k5_numbers)) ) ) ) ) ).
tt(dt_k9_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  &  ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k9_nat_3 A B C)) &  ((v4_relat_1 (k9_nat_3 A B C) A) &  ((v1_funct_1 (k9_nat_3 A B C)) & (v1_partfun1 (k9_nat_3 A B C) A)) ) ) ) ) ).
tt(dt_k9_nat_lat,ax, ((v1_funct_1 k9_nat_lat) &  ((v1_funct_2 k9_nat_lat (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat) & (m1_subset_1 k9_nat_lat (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k6_nat_lat k6_nat_lat) k6_nat_lat)))) ) ).
tt(dt_k9_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) &  ((m2_cat_1 D A B) & (m2_nattra_1 E A B C D)) ) ) )  => (m2_nattra_1 (k9_nattra_1 A B C D E) A B D C)) ) ).
tt(dt_k9_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_subset_1 (k9_newton A) k1_numbers k5_numbers)) ) ).
tt(dt_k9_normform,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) => (m2_subset_1 (k9_normform A B) (k5_finsub_1 (k7_normform A)) (k8_normform A))) ) ).
tt(dt_k9_openlatt,ax,$true).
tt(dt_k9_oppcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k9_oppcat_1 A B C)) &  ((v1_funct_2 (k9_oppcat_1 A B C) (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 (k9_oppcat_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) ) ).
tt(dt_k9_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  => (v3_ordinal1 (k9_ordinal3 A B))) ) ).
tt(dt_k9_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  => (m2_subset_1 (k9_osafree A B C) (u1_struct_0 (k2_osafree A B)) (k7_dtconstr (k2_osafree A B)))) ) ).
tt(dt_k9_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  & (m2_osalg_2 C A B)) )  => (m2_osalg_2 (k9_osalg_2 A B C) A B)) ) ).
tt(dt_k9_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) &  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  &  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) )  & (m1_subset_1 E (k3_msualg_1 A B C))) ) ) )  => (m1_subset_1 (k9_osalg_4 A B C D E) (k4_card_3 (k3_relat_1 (k1_msualg_1 A B) (k7_osalg_4 A C D))))) ) ).
tt(dt_k9_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (l1_parsp_1 (k9_parsp_1 A))) ) ).
tt(dt_k9_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) ) )  =>  ((v1_relat_1 (k9_pboole A B C)) &  ((v4_relat_1 (k9_pboole A B C) A) &  ((v1_funct_1 (k9_pboole A B C)) & (v1_partfun1 (k9_pboole A B C) A)) ) ) ) ) ).
tt(dt_k9_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (m1_subset_1 (k9_pcs_0 A B C D) (u1_struct_0 (k8_pcs_0 A B)))) ) ).
tt(dt_k9_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C k5_numbers) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  & (m1_subset_1 E (u1_struct_0 (k4_real_ns1 A)))) ) ) )  => (m1_subset_1 (k9_pdiff_1 A B C D E) (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B))))) ) ).
tt(dt_k9_pdiff_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  & (m1_subset_1 B (k1_euclid 3)))  => (m1_subset_1 (k9_pdiff_5 A B) k1_numbers)) ) ).
tt(dt_k9_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))))  => (m1_subset_1 (k9_petri A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_k9_polyeq_1,ax,$true).
tt(dt_k9_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  => (m2_funct_2 (k9_polyform A B) (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)) (k9_funct_2 (k2_zfmisc_1 (k8_polyform A (k6_xcmplx_0 B 1)) (k8_polyform A B)) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace))))) ) ).
tt(dt_k9_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k9_polynom1 A B C D)) &  ((v1_funct_2 (k9_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 (k9_polynom1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k9_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((v1_funct_1 (k9_polynom3 A)) &  ((v1_funct_2 (k9_polynom3 A) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k9_polynom3 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ).
tt(dt_k9_polynom5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k9_polynom5 A B)) &  ((v1_funct_2 (k9_polynom5 A B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k9_polynom5 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_k9_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_poset_1 A B)) &  ((v1_funct_2 (k9_poset_1 A B) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k9_poset_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_k9_pralg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_pralg_2 D A B)) )  =>  ((v1_relat_1 (k9_pralg_2 A B C D)) &  ((v4_relat_1 (k9_pralg_2 A B C D) A) &  ((v1_funct_1 (k9_pralg_2 A B C D)) & (v1_partfun1 (k9_pralg_2 A B C D) A)) ) ) ) ) ).
tt(dt_k9_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 C))  & (m1_finseq_2 C A))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  => (m2_finseq_2 (k9_pre_poly A B C D E) A C)) ) ).
tt(dt_k9_prepower,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k9_prepower A B))) ) ).
tt(dt_k9_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (~ (v1_xboole_0 (k9_prob_1 A B)))  &  ((v1_prob_1 (k9_prob_1 A B) A) &  ((v4_prob_1 (k9_prob_1 A B) A) & (m1_subset_1 (k9_prob_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(dt_k9_prob_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_finseq_1 C B) & (m2_prob_1 D A B)) ) )  => (m2_finseq_1 (k9_prob_3 A B C D) k1_numbers)) ) ).
tt(dt_k9_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m1_prvect_1 B A) & (m1_subset_1 C (k4_finseq_1 A))) )  =>  ((v1_funct_1 (k9_prvect_1 A B C)) &  ((v1_funct_2 (k9_prvect_1 A B C) (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C)) & (m1_subset_1 (k9_prvect_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C))))) ) ) ) ).
tt(dt_k9_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  => (m1_prvect_2 (k9_prvect_2 A) (k4_prvect_2 A) k1_numbers)) ) ).
tt(dt_k9_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (m1_subset_1 (k9_pscomp_1 A) k1_numbers)) ) ).
tt(dt_k9_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  => (m1_subset_1 (k9_pua2mss1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_k9_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k9_qc_lang1 A))) ) ) ).
tt(dt_k9_qc_lang2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) &  ((m1_subset_1 C (k3_qc_lang1 A)) &  ((m1_subset_1 D (k3_qc_lang1 A)) & (m1_subset_1 E (k9_qc_lang1 A))) ) ) )  => (m1_subset_1 (k9_qc_lang2 A B C D E) (k9_qc_lang1 A))) ) ).
tt(dt_k9_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  ((v3_relat_2 (k9_qmax_1 A)) &  ((v8_relat_2 (k9_qmax_1 A)) &  ((v1_partfun1 (k9_qmax_1 A) (k5_qmax_1 A)) & (m1_subset_1 (k9_qmax_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k5_qmax_1 A) (k5_qmax_1 A))))) ) ) ) ) ).
tt(dt_k9_quantal1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k9_quantal1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k9_quaterni,ax,$true).
tt(dt_k9_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k7_quofield A)) & (m1_subset_1 C (k7_quofield A))) )  => (m2_subset_1 (k9_quofield A B C) (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A))) ) ).
tt(dt_k9_radix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m2_subset_1 (k9_radix_1 A B C) k4_numbers (k3_radix_1 B))) ) ).
tt(dt_k9_radix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((v3_card_1 E D) & (m1_finseq_1 E k5_numbers)) ) ) ) )  =>  ((v3_card_1 (k9_radix_2 A B C D E) D) & (m2_finseq_1 (k9_radix_2 A B C D E) k5_numbers)) ) ) ).
tt(dt_k9_radix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D C) & (m1_finseq_1 D (k3_radix_1 B))) ) ) )  => (m2_subset_1 (k9_radix_3 A B C D) k4_numbers (k4_radix_3 B))) ) ).
tt(dt_k9_radix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (m1_subset_1 (k9_radix_6 A B C) (k3_radix_1 C))) ) ).
tt(dt_k9_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  & (m2_vectsp_6 F A C (k2_ranknull B C E D))) ) ) ) )  => (m2_vectsp_6 (k9_ranknull A B C D E F) A B D)) ) ).
tt(dt_k9_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_ratfunc1 B A) & (m1_ratfunc1 C A)) )  => (m1_ratfunc1 (k9_ratfunc1 A B C) A)) ) ).
tt(dt_k9_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  => (m1_subset_1 (k9_real_1 A B) k1_numbers)) ) ).
tt(dt_k9_relat_1,ax,$true).
tt(dt_k9_ringcat1,ax,$true).
tt(dt_k9_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlvect_2 B A))  => (m1_rlvect_2 (k9_rlvect_2 A B) A)) ) ).
tt(dt_k9_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_4 C A B) & (m1_rmod_4 D A B)) ) )  => (m1_rmod_4 (k9_rmod_4 A B C D) A B)) ) ).
tt(dt_k9_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (m1_subset_1 (k9_robbins1 A B C) (u1_struct_0 A))) ) ).
tt(dt_k9_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_rsspace4 A B)))  & (l1_normsp_1 (k9_rsspace4 A B))) ) ) ).
tt(dt_k9_rsspace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k9_rsspace A B)) &  ((v1_funct_2 (k9_rsspace A B) (k2_zfmisc_1 k1_numbers B) B) & (m1_subset_1 (k9_rsspace A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers B) B)))) ) ) ) ).
tt(dt_k9_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  => (m2_finseq_2 (k9_rvsum_1 A B C) k1_numbers (k4_finseq_2 A k1_numbers))) ) ).
tt(dt_k9_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  & (v1_xcmplx_0 B))  => (m2_finseq_1 (k9_rvsum_2 A B) k2_numbers)) ) ).
tt(dt_k9_scm_comp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_dtconstr k1_scm_comp)) & (m1_subset_1 B (k4_dtconstr k1_scm_comp)))  => (m1_dtconstr (k9_scm_comp A B) (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp))) ) ).
tt(dt_k9_scmfsa_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) & (m1_subset_1 B k3_scmfsa_1))  => (m2_finseq_1 (k9_scmfsa_1 A B) k4_numbers)) ) ).
tt(dt_k9_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (m1_subset_1 (k9_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(dt_k9_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2))) )  =>  ((v1_ami_2 (k9_scmfsa_m A B)) & (m1_subset_1 (k9_scmfsa_m A B) (u1_struct_0 k1_scmfsa_2))) ) ) ).
tt(dt_k9_scmpds_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (m1_subset_1 (k9_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(dt_k9_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k9_scmpds_6 A B C)))  &  ((v1_relat_1 (k9_scmpds_6 A B C)) &  ((v4_relat_1 (k9_scmpds_6 A B C) k5_numbers) &  ((v5_relat_1 (k9_scmpds_6 A B C) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k9_scmpds_6 A B C)) &  ((v1_finset_1 (k9_scmpds_6 A B C)) & (v1_afinsq_1 (k9_scmpds_6 A B C))) ) ) ) ) ) ) ) ).
tt(dt_k9_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (v1_int_1 (k9_scmpds_i A))) ) ).
tt(dt_k9_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B k5_numbers) &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (m1_subset_1 (k9_scmring2 A B C) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(dt_k9_scmringi,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (k1_scmringi A)))  => (m1_subset_1 (k9_scmringi A B) (u1_struct_0 A))) ) ).
tt(dt_k9_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v8_scmyciel A))  => (v7_ordinal1 (k9_scmyciel A))) ) ).
tt(dt_k9_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  => (m2_finseq_1 (k9_seq_4 A B) k2_numbers)) ) ).
tt(dt_k9_seqfunc,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) )  =>  ((v1_funct_1 (k9_seqfunc A B C)) &  ((v1_funct_2 (k9_seqfunc A B C) k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 (k9_seqfunc A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) ) ).
tt(dt_k9_setfam_1,ax, (! [A:$i] : (m1_subset_1 (k9_setfam_1 A) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ).
tt(dt_k9_setlim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_funct_1 (k9_setlim_2 A B C)) &  ((v1_funct_2 (k9_setlim_2 A B C) k5_numbers (k9_setfam_1 A)) & (m1_subset_1 (k9_setlim_2 A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ).
tt(dt_k9_setwiseo,ax, (! [A:$i] :  ((v1_funct_1 (k9_setwiseo A)) &  ((v1_funct_2 (k9_setwiseo A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_finsub_1 A)) & (m1_subset_1 (k9_setwiseo A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_finsub_1 A))))) ) ) ).
tt(dt_k9_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_matroid0 B) & (m1_simplex0 B A))  & (v1_int_1 C))  => (m2_simplex0 (k9_simplex0 A B C) A B)) ) ).
tt(dt_k9_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (k9_sincos10 A) k1_numbers)) ) ).
tt(dt_k9_sin_cos2,ax, (! [A:$i] : (m1_subset_1 (k9_sin_cos2 A) k1_numbers)) ).
tt(dt_k9_sin_cos,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k2_numbers) & (m1_subset_1 C k2_numbers)) )  =>  ((v1_funct_1 (k9_sin_cos A B C)) &  ((v1_funct_2 (k9_sin_cos A B C) k5_numbers k2_numbers) & (m1_subset_1 (k9_sin_cos A B C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) ) ).
tt(dt_k9_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  => (m2_finseq_2 (k9_stacks_1 A B) (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))) ) ).
tt(dt_k9_sublemma,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  & (m1_substut1 C A B)) )  => (m2_subset_1 (k9_sublemma A B C) (k16_substut1 A) (k38_substut1 A))) ) ).
tt(dt_k9_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (m1_subset_1 (k9_subset_1 A B C) (k1_zfmisc_1 A))) ) ).
tt(dt_k9_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (m1_subset_1 (k9_substut1 A B) (k1_zfmisc_1 (k3_qc_lang1 A)))) ) ).
tt(dt_k9_supinf_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ( (~ (v1_xboole_0 (k9_supinf_2 A B C)))  & (m1_subset_1 (k9_supinf_2 A B C) (k1_zfmisc_1 k7_numbers))) ) ) ).
tt(dt_k9_tdlat_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (k9_tdlat_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_k9_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_pre_topc B A))  =>  ((v1_funct_1 (k9_tmap_1 A B)) &  ((v1_funct_2 (k9_tmap_1 A B) (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B))) & (m1_subset_1 (k9_tmap_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B)))))) ) ) ) ).
tt(dt_k9_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_borsuk_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D))) ) ) )  => (m1_borsuk_2 (k9_topalg_4 A B C D E) A C C)) ) ).
tt(dt_k9_toprealb,ax,(m1_subset_1 k9_toprealb (u1_struct_0 (k8_toprealb 2)))).
tt(dt_k9_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (m1_subset_1 (k9_toprealc A B C) (u1_struct_0 (k15_euclid A)))) ) ).
tt(dt_k9_trees_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) )  =>  ((v1_relat_1 (k9_trees_3 A B C)) &  ((v5_relat_1 (k9_trees_3 A B C) B) &  ((v1_funct_1 (k9_trees_3 A B C)) & (v3_trees_2 (k9_trees_3 A B C))) ) ) ) ) ).
tt(dt_k9_trees_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((v1_relat_1 (k9_trees_4 A B C)) &  ((v1_funct_1 (k9_trees_4 A B C)) & (v3_trees_2 (k9_trees_4 A B C))) ) ) ) ).
tt(dt_k9_trees_9,ax,$true).
tt(dt_k9_turing_1,ax, (! [A:$i,B:$i] :  ( ((l1_turing_1 A) & (m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))))  => (m1_subset_1 (k9_turing_1 A B) (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))))) ) ).
tt(dt_k9_twoscomp,ax, ((v1_funct_1 k9_twoscomp) &  ((v1_funct_2 k9_twoscomp (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 k9_twoscomp (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) ) ).
tt(dt_k9_unialg_2,ax,$true).
tt(dt_k9_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  => (m2_finseq_1 (k9_uproots A B C) (u1_struct_0 (k14_polynom3 A)))) ) ).
tt(dt_k9_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k9_valued_1 A B C D)) & (m1_subset_1 (k9_valued_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ).
tt(dt_k9_valued_2,ax,$true).
tt(dt_k9_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_vectsp10 A B C)))  &  ((v7_vectsp_1 (k9_vectsp10 A B C) A) & (m1_vectsp_4 (k9_vectsp10 A B C) A B)) ) ) ) ).
tt(dt_k9_waybel18,ax, ((v1_pre_topc k9_waybel18) & (l1_pre_topc k9_waybel18)) ).
tt(dt_k9_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k9_waybel34 A)))  &  ((v2_altcat_1 (k9_waybel34 A)) &  ((v6_altcat_1 (k9_waybel34 A)) &  ((v3_altcat_2 (k9_waybel34 A) (k5_waybel34 A)) & (m1_altcat_2 (k9_waybel34 A) (k5_waybel34 A))) ) ) ) ) ) ).
tt(dt_k9_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k9_waybel_4 A)) &  ((v1_funct_2 (k9_waybel_4 A) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A))) & (m1_subset_1 (k9_waybel_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A)))))) ) ) ) ).
tt(dt_k9_weierstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  => (m1_subset_1 (k9_weierstr A B C) k1_numbers)) ) ).
tt(dt_k9_xboolean,ax,$true).
tt(dt_k9_xtuple_0,ax,$true).
tt(dt_k9_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  & (m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B)))) )  => (m1_subset_1 (k9_yellow_3 A B C) (u1_struct_0 B))) ) ).
tt(dt_k9_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (l1_orders_2 (k9_yellow_6 A B))) ) ).
tt(dt_k9_zf_lang,ax, (~ (v1_xboole_0 k9_zf_lang)) ).
tt(dt_k9_zf_model,ax, ((v1_zf_lang k9_zf_model) & (m2_finseq_1 k9_zf_model k5_numbers)) ).
tt(dt_k9_zmodul01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_zmodul01 C A) & (m1_zmodul01 D A)) ) )  => (m1_subset_1 (k9_zmodul01 A B C D) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(dt_l1_abcmiz_0,ax,$true).
tt(dt_l1_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_algstr_3,ax, (! [A:$i] :  ((l1_algstr_3 A) => (l4_struct_0 A)) ) ).
tt(dt_l1_altcat_1,ax, (! [A:$i] :  ((l1_altcat_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_analmetr,ax, (! [A:$i] :  ((l1_analmetr A) => (l1_analoaf A)) ) ).
tt(dt_l1_analoaf,ax, (! [A:$i] :  ((l1_analoaf A) => (l1_struct_0 A)) ) ).
tt(dt_l1_armstrng,ax,$true).
tt(dt_l1_bcialg_1,ax, (! [A:$i] :  ((l1_bcialg_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_bcialg_4,ax, (! [A:$i] :  ((l1_bcialg_4 A) =>  ((l2_bcialg_1 A) & (l2_struct_0 A)) ) ) ).
tt(dt_l1_bhsp_1,ax, (! [A:$i] :  ((l1_bhsp_1 A) => (l1_rlvect_1 A)) ) ).
tt(dt_l1_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) => (l1_graph_1 A)) ) ).
tt(dt_l1_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) => (l1_cat_1 A)) ) ).
tt(dt_l1_cfuncdom,ax, (! [A:$i] :  ((l1_cfuncdom A) =>  ((l6_algstr_0 A) & (l1_clvect_1 A)) ) ) ).
tt(dt_l1_cgames_1,ax,$true).
tt(dt_l1_clopban2,ax, (! [A:$i] :  ((l1_clopban2 A) =>  ((l1_cfuncdom A) & (l2_clvect_1 A)) ) ) ).
tt(dt_l1_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure1 B A) => (l2_msualg_1 B A)) ) ) ) ).
tt(dt_l1_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_closure2 B A) => (l2_msualg_1 B A)) ) ) ) ).
tt(dt_l1_clvect_1,ax, (! [A:$i] :  ((l1_clvect_1 A) => (l2_algstr_0 A)) ) ).
tt(dt_l1_collsp,ax, (! [A:$i] :  ((l1_collsp A) => (l1_struct_0 A)) ) ).
tt(dt_l1_combgras,ax,$true).
tt(dt_l1_compos_1,ax,$true).
tt(dt_l1_conlat_1,ax, (! [A:$i] :  ((l1_conlat_1 A) => (l5_struct_0 A)) ) ).
tt(dt_l1_csspace,ax, (! [A:$i] :  ((l1_csspace A) => (l1_clvect_1 A)) ) ).
tt(dt_l1_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) => (l1_struct_0 A)) ) ).
tt(dt_l1_extpro_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_extpro_1 B A) =>  ((l1_memstr_0 B A) & (l1_compos_1 B)) ) ) ) ).
tt(dt_l1_fintopo2,ax, (! [A:$i] :  ((l1_fintopo2 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) => (l4_struct_0 A)) ) ).
tt(dt_l1_fsm_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_fsm_1 B A) => (l1_struct_0 B)) ) ) ).
tt(dt_l1_fsm_2,ax, (! [A:$i] :  (! [B:$i] :  ((l1_fsm_2 B A) => (l1_fsm_1 B A)) ) ) ).
tt(dt_l1_fsm_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))))  =>  (! [C:$i] :  ((l1_fsm_3 C A B) => (l1_rewrite3 C B)) ) ) ) ).
tt(dt_l1_funcsdom,ax, (! [A:$i] :  ((l1_funcsdom A) =>  ((l6_algstr_0 A) & (l1_rlvect_1 A)) ) ) ).
tt(dt_l1_functor0,ax,$true).
tt(dt_l1_geomtrap,ax, (! [A:$i] :  ((l1_geomtrap A) =>  ((l1_analoaf A) & (l1_midsp_1 A)) ) ) ).
tt(dt_l1_graph_1,ax, (! [A:$i] :  ((l1_graph_1 A) => (l5_struct_0 A)) ) ).
tt(dt_l1_grcat_1,ax,$true).
tt(dt_l1_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((l1_group_9 B A) => (l3_algstr_0 B)) ) ) ).
tt(dt_l1_incsp_1,ax,$true).
tt(dt_l1_lang1,ax, (! [A:$i] :  ((l1_lang1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_lattices,ax, (! [A:$i] :  ((l1_lattices A) => (l1_struct_0 A)) ) ).
tt(dt_l1_lopban_2,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  ((l1_funcsdom A) & (l1_normsp_1 A)) ) ) ).
tt(dt_l1_memstr_0,ax, (! [A:$i] :  (! [B:$i] :  ((l1_memstr_0 B A) => (l2_struct_0 B)) ) ) ).
tt(dt_l1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_midsp_1,ax, (! [A:$i] :  ((l1_midsp_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_midsp_2,ax,$true).
tt(dt_l1_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((l1_midsp_3 B A) => (l1_midsp_1 B)) ) ) ) ).
tt(dt_l1_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) => (l1_struct_0 A)) ) ).
tt(dt_l1_mod_2,ax,$true).
tt(dt_l1_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) => (l4_robbins1 A)) ) ).
tt(dt_l1_modelc_3,ax,$true).
tt(dt_l1_msualg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) => (l5_struct_0 A)) ) ).
tt(dt_l1_normsp_0,ax, (! [A:$i] :  ((l1_normsp_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_normsp_1,ax, (! [A:$i] :  ((l1_normsp_1 A) =>  ((l1_rlvect_1 A) & (l2_normsp_0 A)) ) ) ).
tt(dt_l1_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_osalg_1,ax, (! [A:$i] :  ((l1_osalg_1 A) => (l1_msualg_1 A)) ) ).
tt(dt_l1_parsp_1,ax, (! [A:$i] :  ((l1_parsp_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_petri_2,ax, (! [A:$i] :  ((l1_petri_2 A) => (l1_petri A)) ) ).
tt(dt_l1_petri,ax, (! [A:$i] :  ((l1_petri A) => (l5_struct_0 A)) ) ).
tt(dt_l1_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) =>  ((l6_algstr_0 B) & (l1_vectsp_1 B A)) ) ) ) ) ).
tt(dt_l1_polyform,ax,$true).
tt(dt_l1_prelamb,ax, (! [A:$i] :  ((l1_prelamb A) => (l1_struct_0 A)) ) ).
tt(dt_l1_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) => (l1_struct_0 A)) ) ).
tt(dt_l1_qmax_1,ax,$true).
tt(dt_l1_quantal1,ax, (! [A:$i] :  ((l1_quantal1 A) =>  ((l3_lattices A) & (l3_algstr_0 A)) ) ) ).
tt(dt_l1_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ((l1_rewrite3 B A) => (l1_struct_0 B)) ) ) ).
tt(dt_l1_ringcat1,ax,$true).
tt(dt_l1_rltopsp1,ax, (! [A:$i] :  ((l1_rltopsp1 A) =>  ((l1_rlvect_1 A) & (l1_pre_topc A)) ) ) ).
tt(dt_l1_rlvect_1,ax, (! [A:$i] :  ((l1_rlvect_1 A) => (l2_algstr_0 A)) ) ).
tt(dt_l1_robbins1,ax, (! [A:$i] :  ((l1_robbins1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_robbins3,ax, (! [A:$i] :  ((l1_robbins3 A) =>  ((l2_lattices A) & (l1_orders_2 A)) ) ) ).
tt(dt_l1_sgraph1,ax, (! [A:$i] :  ((l1_sgraph1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_sheffer1,ax, (! [A:$i] :  ((l1_sheffer1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) => (l5_struct_0 A)) ) ).
tt(dt_l1_struct_0,ax,$true).
tt(dt_l1_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((l1_symsp_1 B A) =>  ((l1_orders_2 B) & (l1_vectsp_1 B A)) ) ) ) ) ).
tt(dt_l1_topgrp_1,ax, (! [A:$i] :  ((l1_topgrp_1 A) =>  ((l3_algstr_0 A) & (l1_pre_topc A)) ) ) ).
tt(dt_l1_turing_1,ax,$true).
tt(dt_l1_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) => (l1_struct_0 A)) ) ).
tt(dt_l1_vectmetr,ax, (! [A:$i] :  ((l1_vectmetr A) =>  ((l1_rlvect_1 A) & (l1_metric_1 A)) ) ) ).
tt(dt_l1_vectsp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_vectsp_1 B A) => (l2_algstr_0 B)) ) ) ) ).
tt(dt_l1_vectsp_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_vectsp_2 B A) => (l2_algstr_0 B)) ) ) ) ).
tt(dt_l1_waybel_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) => (l1_orders_2 B)) ) ) ) ).
tt(dt_l1_waybel_9,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  ((l1_pre_topc A) & (l1_orders_2 A)) ) ) ).
tt(dt_l1_zmodul01,ax, (! [A:$i] :  ((l1_zmodul01 A) => (l2_algstr_0 A)) ) ).
tt(dt_l2_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  ((l1_orders_2 A) & (l1_abcmiz_0 A)) ) ) ).
tt(dt_l2_algstr_0,ax, (! [A:$i] :  ((l2_algstr_0 A) =>  ((l2_struct_0 A) & (l1_algstr_0 A)) ) ) ).
tt(dt_l2_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) => (l1_altcat_1 A)) ) ).
tt(dt_l2_bcialg_1,ax, (! [A:$i] :  ((l2_bcialg_1 A) =>  ((l1_bcialg_1 A) & (l2_struct_0 A)) ) ) ).
tt(dt_l2_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) => (l1_cat_1 A)) ) ).
tt(dt_l2_clvect_1,ax, (! [A:$i] :  ((l2_clvect_1 A) =>  ((l1_clvect_1 A) & (l2_normsp_0 A)) ) ) ).
tt(dt_l2_conlat_1,ax,$true).
tt(dt_l2_fsm_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((l2_fsm_1 C A B) => (l1_fsm_1 C A)) ) ) ) ).
tt(dt_l2_fsm_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((l2_fsm_2 C A B) =>  ((l1_fsm_2 C A) & (l3_fsm_1 C A B)) ) ) ) ) ).
tt(dt_l2_fsm_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))))  =>  (! [C:$i] :  ((l2_fsm_3 C A B) => (l1_fsm_3 C A B)) ) ) ) ).
tt(dt_l2_functor0,ax, (! [A:$i,B:$i] :  ( ((l1_altcat_1 A) & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) => (l1_functor0 C A B)) ) ) ) ).
tt(dt_l2_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) => (l1_incsp_1 A)) ) ).
tt(dt_l2_lang1,ax, (! [A:$i] :  ((l2_lang1 A) => (l1_lang1 A)) ) ).
tt(dt_l2_lattices,ax, (! [A:$i] :  ((l2_lattices A) => (l1_struct_0 A)) ) ).
tt(dt_l2_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) => (l3_robbins1 A)) ) ).
tt(dt_l2_modelc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l2_modelc_3 B A) => (l1_struct_0 B)) ) ) ) ).
tt(dt_l2_msualg_1,ax,$true).
tt(dt_l2_normsp_0,ax, (! [A:$i] :  ((l2_normsp_0 A) =>  ((l1_normsp_0 A) & (l2_struct_0 A)) ) ) ).
tt(dt_l2_osalg_1,ax, (! [A:$i] :  ((l2_osalg_1 A) =>  ((l1_msualg_1 A) & (l1_orders_2 A)) ) ) ).
tt(dt_l2_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  ((l1_orders_2 A) & (l1_pcs_0 A)) ) ) ).
tt(dt_l2_prelamb,ax, (! [A:$i] :  ((l2_prelamb A) => (l1_prelamb A)) ) ).
tt(dt_l2_qmax_1,ax, (! [A:$i] :  ((l2_qmax_1 A) =>  ((l1_orders_2 A) & (l1_robbins1 A)) ) ) ).
tt(dt_l2_quantal1,ax, (! [A:$i] :  ((l2_quantal1 A) =>  ((l1_quantal1 A) & (l4_algstr_0 A)) ) ) ).
tt(dt_l2_robbins1,ax, (! [A:$i] :  ((l2_robbins1 A) =>  ((l2_lattices A) & (l1_robbins1 A)) ) ) ).
tt(dt_l2_robbins3,ax, (! [A:$i] :  ((l2_robbins3 A) =>  ((l1_lattices A) & (l1_orders_2 A)) ) ) ).
tt(dt_l2_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l2_vectsp_2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_struct_0 B))  =>  (! [C:$i] :  ((l2_vectsp_2 C A B) =>  ((l1_vectsp_1 C A) & (l1_vectsp_2 C B)) ) ) ) ) ).
tt(dt_l3_abcmiz_0,ax, (! [A:$i] :  ((l3_abcmiz_0 A) => (l2_abcmiz_0 A)) ) ).
tt(dt_l3_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l3_fsm_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((l3_fsm_1 C A B) => (l1_fsm_1 C A)) ) ) ) ).
tt(dt_l3_lattices,ax, (! [A:$i] :  ((l3_lattices A) =>  ((l1_lattices A) & (l2_lattices A)) ) ) ).
tt(dt_l3_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (l2_msualg_1 B A)) ) ) ) ).
tt(dt_l3_osalg_1,ax, (! [A:$i] :  ((l3_osalg_1 A) =>  ((l1_osalg_1 A) & (l2_osalg_1 A)) ) ) ).
tt(dt_l3_quantal1,ax, (! [A:$i] :  ((l3_quantal1 A) => (l2_quantal1 A)) ) ).
tt(dt_l3_robbins1,ax, (! [A:$i] :  ((l3_robbins1 A) =>  ((l1_lattices A) & (l1_robbins1 A)) ) ) ).
tt(dt_l3_robbins3,ax, (! [A:$i] :  ((l3_robbins3 A) =>  ((l2_robbins3 A) &  ((l1_robbins3 A) & (l3_lattices A)) ) ) ) ).
tt(dt_l3_sheffer1,ax, (! [A:$i] :  ((l3_sheffer1 A) =>  ((l1_sheffer1 A) & (l4_robbins1 A)) ) ) ).
tt(dt_l3_struct_0,ax, (! [A:$i] :  ((l3_struct_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l4_algstr_0,ax, (! [A:$i] :  ((l4_algstr_0 A) =>  ((l3_struct_0 A) & (l3_algstr_0 A)) ) ) ).
tt(dt_l4_robbins1,ax, (! [A:$i] :  ((l4_robbins1 A) =>  ((l2_robbins1 A) & (l3_lattices A)) ) ) ).
tt(dt_l4_robbins3,ax, (! [A:$i] :  ((l4_robbins3 A) =>  ((l3_robbins3 A) &  ((l4_robbins1 A) & (l2_qmax_1 A)) ) ) ) ).
tt(dt_l4_struct_0,ax, (! [A:$i] :  ((l4_struct_0 A) =>  ((l2_struct_0 A) & (l3_struct_0 A)) ) ) ).
tt(dt_l5_algstr_0,ax, (! [A:$i] :  ((l5_algstr_0 A) =>  ((l4_algstr_0 A) & (l4_struct_0 A)) ) ) ).
tt(dt_l5_struct_0,ax, (! [A:$i] :  ((l5_struct_0 A) => (l1_struct_0 A)) ) ).
tt(dt_l6_algstr_0,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  ((l2_algstr_0 A) & (l5_algstr_0 A)) ) ) ).
tt(dt_m1_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_abcmiz_1 C A B) => (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ) ) ).
tt(dt_m1_abcmiz_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  =>  (! [C:$i] :  ((m1_abcmiz_a C A B) => (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) ) ) ) ).
tt(dt_m1_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) =>  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_m1_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_algspec1 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(dt_m1_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_algstr_4 B A) => (l3_algstr_0 B)) ) ) ) ).
tt(dt_m1_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((m1_altcat_2 B A) => (l2_altcat_1 B)) ) ) ) ).
tt(dt_m1_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k1_zfmisc_1 B))) )  =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) ) ) ) ) ) ).
tt(dt_m1_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k9_funct_2 A k4_numbers) B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) B) C)))) )  =>  (! [E:$i] :  ((m1_aofa_i00 E A B C D) => (m1_subset_1 E A)) ) ) ) ).
tt(dt_m1_armstrng,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  (! [C:$i] :  ((m1_armstrng C A B) => (m1_subset_1 C (k4_armstrng A))) ) ) ) ).
tt(dt_m1_autalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_autalg_1 A B B)))) )  =>  (! [D:$i] :  ((m1_autalg_1 D A B C) => (m2_pboole D A B B)) ) ) ) ).
tt(dt_m1_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) ) ) ) ) ) ).
tt(dt_m1_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_m1_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_3 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m1_bcialg_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  =>  (! [E:$i] :  ((m1_bcialg_5 E A B C D) =>  ( (~ (v2_struct_0 E))  &  ((v3_bcialg_1 E) &  ((v4_bcialg_1 E) &  ((v5_bcialg_1 E) &  ((v7_bcialg_1 E) & (l2_bcialg_1 E)) ) ) ) ) ) ) ) ) ).
tt(dt_m1_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bciideal B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m1_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_bhsp_5 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  (! [B:$i] :  ((m1_bintree2 B A) => (m2_finseq_1 B k6_margrel1)) ) ) ) ).
tt(dt_m1_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_borsuk_1 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(dt_m1_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_m1_borsuk_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  =>  (! [F:$i] :  ((m1_borsuk_6 F A B C D E) =>  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_m1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m1_bvfunc_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_eqrel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_bvfunc_2 C A B) => (m1_eqrel_1 C A)) ) ) ) ).
tt(dt_m1_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_c0sp1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(dt_m1_card_lar,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_card_lar C A B) => (m1_subset_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) => (m1_subset_1 D (u4_struct_0 A))) ) ) ) ).
tt(dt_m1_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_cat_2 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(dt_m1_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [D:$i] :  ((m1_cat_3 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) ) ) ) ) ) ).
tt(dt_m1_cat_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_cat_5 A))  =>  (! [B:$i] :  ((m1_cat_5 B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_catalan2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_catalan2 B A) =>  ( (~ (v1_xboole_0 B))  & (v4_funct_1 B)) ) ) ) ).
tt(dt_m1_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_catalg_1 B A) =>  ((v1_instalg1 B) & (l1_msualg_1 B)) ) ) ) ).
tt(dt_m1_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_cc0sp1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v2_cfuncdom B) & (l1_cfuncdom B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_cfdiff_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_cfdiff_1 B A) => (m1_subset_1 B (k1_zfmisc_1 k2_numbers))) ) ) ) ).
tt(dt_m1_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) (k1_zfmisc_1 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k1_zfmisc_1 k1_numbers))))) ) ) ) ) ) ).
tt(dt_m1_chord,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [C:$i] :  ((m1_chord C A B) => (m1_glib_000 C A)) ) ) ) ).
tt(dt_m1_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v5_circcomb B) & (l1_msualg_1 B)) ) ) ) ) ) ) ) ) ).
tt(dt_m1_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m3_msaterm C A B) &  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  & (m1_subset_1 E (k4_card_3 (u3_msualg_1 (k1_circtrm1 A B C) (k6_circtrm1 A B C D))))) ) ) )  =>  (! [F:$i] :  ((m1_circtrm1 F A B C D E) => (m2_pboole F (u1_struct_0 A) B (u3_msualg_1 A D))) ) ) ) ).
tt(dt_m1_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  (! [D:$i] :  ((m1_closure2 D A B C) => (m3_pboole D A B)) ) ) ) ).
tt(dt_m1_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_collsp,ax,$true).
tt(dt_m1_complfld,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_complfld)) &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  (! [C:$i] :  ((m1_complfld C A B) => (m1_subset_1 C (u1_struct_0 k1_complfld))) ) ) ) ).
tt(dt_m1_comptrig,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  =>  (! [C:$i] :  ((m1_comptrig C A B) => (v1_xcmplx_0 C)) ) ) ) ).
tt(dt_m1_comput_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_rfunct_3 C A B))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 C))) ) ) )  =>  (! [E:$i] :  ((m1_comput_1 E A B C D) => (m2_rfunct_3 E A B C)) ) ) ) ).
tt(dt_m1_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_conlat_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(dt_m1_connsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_connsp_2 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_connsp_3 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (m2_funct_2 B (u1_struct_0 A) k2_numbers (k9_funct_2 (u1_struct_0 A) k2_numbers))) ) ) ) ).
tt(dt_m1_decomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_decomp_1 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_dist_1 B A) =>  ((v1_matrprob B) & (m2_finseq_1 B k1_numbers)) ) ) ) ) ).
tt(dt_m1_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_trees_3 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B))) ) )  =>  (! [D:$i] :  ((m1_dtconstr D A B C) => (m1_subset_1 D B)) ) ) ) ).
tt(dt_m1_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_dynkin B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ).
tt(dt_m1_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ec_pf_1 B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_m1_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  (! [B:$i] :  ((m1_exchsort B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) ) ) ) ).
tt(dt_m1_extpro_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_extpro_1 D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) ) ) ) ) ) ).
tt(dt_m1_filter_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 B))  =>  (! [C:$i] :  ((m1_filter_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(dt_m1_finance1,ax, (! [A:$i] :  ((m1_finance1 A) =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ).
tt(dt_m1_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_1 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ).
tt(dt_m1_finseq_2,ax,$true).
tt(dt_m1_fintopo6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_fintopo6 B A) => (l1_orders_2 B)) ) ) ) ).
tt(dt_m1_fomodel2,ax,$true).
tt(dt_m1_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_funct_2,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_funct_2 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ).
tt(dt_m1_funct_7,ax, (! [A:$i,B:$i] :  (! [C:$i] :  ((m1_funct_7 C A B) =>  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_funct_7 C)) ) ) ) ) ) ).
tt(dt_m1_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) ) ) )  =>  (! [F:$i] :  ((m1_functor0 F A B C D E) =>  ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) ) ) ) ) ) ).
tt(dt_m1_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((m2_functor0 C A B) & (m2_functor0 D A B)) ) )  =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 A)) &  ((v1_funct_1 E) & (v1_partfun1 E (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(dt_m1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  (! [E:$i] :  ((m1_functor3 E A B C D) => (m2_functor2 E A B C D)) ) ) ) ).
tt(dt_m1_fvaluat1,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) &  ((v2_fvaluat1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) ) ) ) ) ) ) ).
tt(dt_m1_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_gcd_1 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m1_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_genealg1 B A) => (m2_finseq_1 B (k3_card_3 A))) ) ) ) ).
tt(dt_m1_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) ) ) ) ) ) ).
tt(dt_m1_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_001 B A) => (m2_finseq_1 B (k6_glib_000 A))) ) ) ) ).
tt(dt_m1_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k3_glib_004 A)))) )  =>  (! [C:$i] :  ((m1_glib_004 C A B) =>  ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m1_glib_000 C A)) ) ) ) ) ) ).
tt(dt_m1_glib_005,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_glib_005 C A B) =>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) (k2_xboole_0 (k6_domain_1 k5_numbers 1) (k7_glib_000 A)))))) ) ) ) ) ).
tt(dt_m1_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(dt_m1_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (m1_finseq_2 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B))) )  =>  (! [D:$i] :  ((m1_graph_3 D A B C) => (m2_finseq_1 D A)) ) ) ) ).
tt(dt_m1_graph_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k3_finseq_2 A))))  =>  (! [C:$i] :  ((m1_graph_5 C A B) => (m2_finseq_1 C A)) ) ) ) ).
tt(dt_m1_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_grcat_1 C A B) =>  ((v2_grcat_1 C) & (l1_grcat_1 C)) ) ) ) ) ).
tt(dt_m1_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) ) ) ) ) ) ).
tt(dt_m1_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_group_6 C A B) => (m1_group_2 C A)) ) ) ) ).
tt(dt_m1_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) ) ) ) ) ).
tt(dt_m1_hallmar1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_hallmar1 D A B C) => (m2_finseq_1 D (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_henmodel,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A)))) )  =>  (! [C:$i] :  ((m1_henmodel C A B) => (m1_valuat_1 C A (k1_henmodel A))) ) ) ) ).
tt(dt_m1_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_hilbert3 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(dt_m1_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_ideal_1 C A B) => (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ).
tt(dt_m1_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_incproj B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_index_1,ax,$true).
tt(dt_m1_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) => (l1_msualg_1 B)) ) ) ) ).
tt(dt_m1_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_int_3 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_int_3 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers)))) ) ) ) ) ) ).
tt(dt_m1_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_int_6 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(dt_m1_integr15,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  & (m1_integra1 C A)) )  =>  (! [D:$i] :  ((m1_integr15 D A B C) => (m2_finseq_1 D k1_numbers)) ) ) ) ).
tt(dt_m1_integr16,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  & (m1_integra1 C A)) )  =>  (! [D:$i] :  ((m1_integr16 D A B C) => (m2_finseq_1 D k2_numbers)) ) ) ) ).
tt(dt_m1_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  & (m1_integra1 D B)) ) )  =>  (! [E:$i] :  ((m1_integr18 E A B C D) => (m2_finseq_1 E (u1_struct_0 A))) ) ) ) ).
tt(dt_m1_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ( (~ (v1_xboole_0 B))  &  ((v5_valued_0 B) & (m2_finseq_1 B k1_numbers)) ) ) ) ) ) ).
tt(dt_m1_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_interva1 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_m1_isocat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_isocat_1 C A B) => (m2_cat_1 C A B)) ) ) ) ).
tt(dt_m1_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) => (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ).
tt(dt_m1_kolmog01,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 C))))) ) ) ) ) ) ).
tt(dt_m1_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  ((v1_relat_1 D) &  ((v5_relat_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) &  ((v1_funct_1 D) & (v5_ordinal1 D)) ) ) ) ) ) ) ).
tt(dt_m1_lattice7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (! [D:$i] :  ((m1_lattice7 D A B C) =>  ( (~ (v1_xboole_0 D))  &  ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(dt_m1_lattice8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_lattice8 D A B C) =>  ((v1_relat_1 D) & (v1_funct_1 D)) ) ) ) ) ).
tt(dt_m1_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_lexbfs B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m1_lmod_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_lmod_7 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(dt_m1_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_margrel1 B A) =>  ((v3_finseq_1 B) & (v2_card_3 B)) ) ) ) ) ).
tt(dt_m1_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  =>  (! [D:$i] :  ((m1_matrix_1 D A B C) =>  ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A))) ) ) ) ) ).
tt(dt_m1_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  =>  (! [B:$i] :  ((m1_matrix_2 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 (k11_matrix_2 A)) (k2_finseq_1 (k11_matrix_2 A))) &  ((v3_funct_2 B (k2_finseq_1 (k11_matrix_2 A)) (k2_finseq_1 (k11_matrix_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k11_matrix_2 A)) (k2_finseq_1 (k11_matrix_2 A)))))) ) ) ) ) ) ) ).
tt(dt_m1_matrixj2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_matrixj2 C A B) =>  ((v1_matrixj2 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_m1_matrlin,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) => (m2_finseq_1 C (u1_struct_0 B))) ) ) ) ).
tt(dt_m1_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v4_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_matroid0 B A) =>  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m1_measure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  (! [D:$i] :  ((m1_measure1 D A B C) => (m2_subset_1 D (k1_zfmisc_1 A) B)) ) ) ) ).
tt(dt_m1_measure2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_measure2 C A B) =>  ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ).
tt(dt_m1_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  (! [D:$i] :  ((m1_measure3 D A B C) => (m1_subset_1 D (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) k7_numbers)))) ) ) ) ) ).
tt(dt_m1_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_measure7 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) ) ) ) ) ) ).
tt(dt_m1_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_metric_2 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(dt_m1_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) => (m1_subset_1 B k5_numbers)) ) ) ) ).
tt(dt_m1_mod_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_mod_2 D A B C) =>  ((v3_mod_2 D A) & (l1_mod_2 D A)) ) ) ) ) ).
tt(dt_m1_mod_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_mod_3 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(dt_m1_mod_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E B) &  ((v9_vectsp_1 E B) &  ((v10_vectsp_1 E B) &  ((v11_vectsp_1 E B) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_mod_4 F A B C D E) =>  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) ) ) ) ) ) ).
tt(dt_m1_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(dt_m1_modelc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ((m1_modelc_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ) ) ).
tt(dt_m1_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_monoid_0 B A) => (l4_algstr_0 B)) ) ) ) ).
tt(dt_m1_msafree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C (k2_msafree2 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_msafree2 A))) ) ) ) ) ) ) ).
tt(dt_m1_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msafree C A B) => (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_m1_msalimit,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ((m1_msalimit C A B) => (m1_pralg_2 C (u1_struct_0 A) B)) ) ) ) ).
tt(dt_m1_msaterm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k7_dtconstr (k5_msafree A B)))) )  =>  (! [D:$i] :  ((m1_msaterm D A B C) => (m1_trees_4 D (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ).
tt(dt_m1_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) => (l3_msualg_1 C A)) ) ) ) ).
tt(dt_m1_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m1_msualg_4 D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) ) ) ) ) ).
tt(dt_m1_msualg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_6 C A B) => (m2_pboole C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_m1_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  ((v1_orders_2 B) & (l1_orders_2 B)) ) ) ) ) ).
tt(dt_m1_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_ncfcont1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_ncfcont1 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_nfcont_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_nfcont_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_oppcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_orders_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_orders_1 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B A (k3_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski A))))) ) ) ) ) ) ).
tt(dt_m1_orders_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_orders_2 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ((m1_orders_3 B A) =>  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ).
tt(dt_m1_orders_4,ax, (! [A:$i] :  ((m1_orders_4 A) => (l1_orders_2 A)) ) ).
tt(dt_m1_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_osafree C A B) => (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_m1_osalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  & (m1_subset_1 B (k7_osalg_1 A)))  =>  (! [C:$i] :  ((m1_osalg_1 C A B) => (m1_subset_1 C (u4_struct_0 A))) ) ) ) ).
tt(dt_m1_osalg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_osalg_4 C A B) => (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_m1_parsp_1,ax,$true).
tt(dt_m1_partit_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A)))) )  =>  (! [C:$i] :  ((m1_partit_2 C A B) => (m1_eqrel_1 C A)) ) ) ) ).
tt(dt_m1_pboole,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_pboole C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) ) ) ) ).
tt(dt_m1_pencil_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v11_pencil_1 B) & (v14_pencil_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B))))) ) ) ) ).
tt(dt_m1_petri_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [C:$i] :  ((m1_petri_2 C A B) =>  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B A)))) ) ) ) ) ).
tt(dt_m1_petri,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_petri D A B C) => (m1_subset_1 D (k2_zfmisc_1 A B))) ) ) ) ).
tt(dt_m1_pnproc_1,ax,$true).
tt(dt_m1_polyalg1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_polyalg1 B A))  =>  (! [C:$i] :  ((m1_polyalg1 C A B) => (l1_polyalg1 C A)) ) ) ) ).
tt(dt_m1_pralg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_pralg_1 C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) ) ) ) ) ) ).
tt(dt_m1_pralg_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) ) ) ) ).
tt(dt_m1_pralg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_msualg_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_pralg_3 D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) ) ) ) ) ).
tt(dt_m1_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) ) ) ) ) ) ) ).
tt(dt_m1_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k5_finsub_1 A))))  =>  (! [C:$i] :  ((m1_pre_poly C A B) => (m1_subset_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) => (l1_pre_topc B)) ) ) ) ).
tt(dt_m1_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_prob_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_3 C A B) => (m2_finseq_1 C (k9_setfam_1 A))) ) ) ) ).
tt(dt_m1_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  (! [D:$i] :  ((m1_prob_4 D A B C) => (m1_subset_1 D (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_projred2 B A) =>  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 A))))) ) ) ) ) ).
tt(dt_m1_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(dt_m1_prvect_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [C:$i] :  ((m1_prvect_2 C A B) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(dt_m1_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_partfun1 A B)))) ) )  =>  (! [D:$i] :  ((m1_pua2mss1 D A B C) =>  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(dt_m1_pythtrip,ax, (! [A:$i] :  ((m1_pythtrip A) => (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) ) ).
tt(dt_m1_qc_lang1,ax,$true).
tt(dt_m1_qc_lang4,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  =>  (! [C:$i] :  ((m1_qc_lang4 C A B) => (m1_subset_1 C (k9_qc_lang1 A))) ) ) ) ).
tt(dt_m1_random_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ).
tt(dt_m1_ratfunc1,ax,$true).
tt(dt_m1_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_rcomp_1 B A) => (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(dt_m1_rcomp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))) )  =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) => (m2_finseq_1 D (k9_setfam_1 k1_numbers))) ) ) ) ).
tt(dt_m1_realset1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_realset1 C A B) => (m1_subset_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_rewrite1 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(dt_m1_rfunct_3,ax,$true).
tt(dt_m1_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_ringcat1 C A B) =>  ((v2_ringcat1 C) &  ((v3_ringcat1 C) & (l1_ringcat1 C)) ) ) ) ) ) ).
tt(dt_m1_rlaffin3,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_rlaffin3 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(dt_m1_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_rlsub_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ((m1_rlsub_2 C A B) => (m1_rlsub_1 C A)) ) ) ) ).
tt(dt_m1_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (m2_funct_2 B (u1_struct_0 A) k1_numbers (k9_funct_2 (u1_struct_0 A) k1_numbers))) ) ) ) ).
tt(dt_m1_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_3 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_rmod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_rmod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) => (m2_funct_2 C (u1_struct_0 B) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_rusub_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_rusub_1 B A))  =>  (! [C:$i] :  ((m1_rusub_2 C A B) => (m1_rusub_1 C A)) ) ) ) ).
tt(dt_m1_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_3 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_scm_1 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) ) ) ) ) ) ).
tt(dt_m1_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) => (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) ) ).
tt(dt_m1_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((m1_scmyciel B A) => (v4_scmyciel B)) ) ) ).
tt(dt_m1_setfam_1,ax,$true).
tt(dt_m1_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  ((v1_sgraph1 B) & (l1_sgraph1 B)) ) ) ) ).
tt(dt_m1_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) => (l1_pre_topc B)) ) ) ).
tt(dt_m1_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_simplex0 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_simplex1 C A B) => (m1_simplex0 C (u1_struct_0 A))) ) ) ) ).
tt(dt_m1_simplex2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [C:$i] :  ((m1_simplex2 C A B) =>  ((v2_xxreal_0 C) & (m1_subset_1 C k1_numbers)) ) ) ) ) ).
tt(dt_m1_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_relat_1 C)) )  =>  (! [D:$i] :  ((m1_stacks_1 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) ) ) ) ) ) ).
tt(dt_m1_subset_1,ax,$true).
tt(dt_m1_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) => (m1_subset_1 C (k1_substut1 A))) ) ) ) ).
tt(dt_m1_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  =>  (! [D:$i] :  ((m1_substut2 D A B C) =>  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) ) ) ).
tt(dt_m1_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) )  =>  (! [B:$i] :  ((m1_supinf_2 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ) ) ).
tt(dt_m1_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_taxonom1 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A)))) ) ) ) ).
tt(dt_m1_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_taxonom2 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(dt_m1_toler_1,ax,$true).
tt(dt_m1_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_topgen_2 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(dt_m1_topgrp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_topgrp_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_topmetr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_topmetr B A) =>  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) ) ) ) ) ).
tt(dt_m1_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) => (m2_finseq_1 B k5_numbers)) ) ) ) ).
tt(dt_m1_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) => (m1_subset_1 B (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m1_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_trees_3 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(dt_m1_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_trees_4 C A B) => (m2_finseq_1 C A)) ) ) ) ).
tt(dt_m1_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) ) ) ) ) ).
tt(dt_m1_unialg_3,ax,$true).
tt(dt_m1_urysohn1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_urysohn1 D A B C) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D k5_numbers)) ) )  =>  (! [E:$i] :  ((m1_urysohn3 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) ) ) ).
tt(dt_m1_valuat_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k6_qc_lang1 A) (k3_margrel1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_qc_lang1 A) (k3_margrel1 B))))) ) ) ) ) ) ).
tt(dt_m1_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ((m1_valued_0 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m1_vectsp11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_vectsp11 D A B C) => (m1_subset_1 D (u1_struct_0 A))) ) ) ) ).
tt(dt_m1_vectsp_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m1_vectsp_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) => (m1_vectsp_4 D A B)) ) ) ) ).
tt(dt_m1_vectsp_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) => (m2_funct_2 C (u1_struct_0 B) (u1_struct_0 A) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_vectsp_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_7 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(dt_m1_vectsp_8,ax,$true).
tt(dt_m1_waybel12,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_waybel12 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_waybel16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel16 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_waybel_1,ax,$true).
tt(dt_m1_waybel21,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel21 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m1_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_waybel23 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_waybel35,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((m1_xxreal_2 B A) => (v1_xxreal_0 B)) ) ) ) ).
tt(dt_m1_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_0 B A) => (l1_orders_2 B)) ) ) ) ).
tt(dt_m1_yellow13,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_yellow13 C A B) => (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_m1_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ((m1_yellow19 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m1_yellow_6,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_yellow_6 C A B) => (l1_waybel_0 C A)) ) ) ) ).
tt(dt_m1_yellow_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_9 B A) => (l1_waybel_9 B)) ) ) ) ).
tt(dt_m1_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m2_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m2_abcmiz_1 C A B) => (m1_subset_1 C (u4_struct_0 A))) ) ) ) ).
tt(dt_m2_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k4_abcmiz_1) =>  (! [B:$i] :  ((m2_abcmiz_a B A) =>  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 k4_abcmiz_a)))) ) ) ) ) ).
tt(dt_m2_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m2_algspec1 B A) =>  ((v1_instalg1 B) & (l1_msualg_1 B)) ) ) ) ) ).
tt(dt_m2_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C)) ) )  =>  (! [E:$i] :  ((m2_aofa_i00 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 B k4_numbers) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) B)))) ) ) ) ) ) ).
tt(dt_m2_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m2_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_2 B A) =>  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_m2_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bciideal B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m2_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bhsp_5 B A) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m2_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_c0sp1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) & (l1_funcsdom B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m2_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_card_fil B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(dt_m2_cat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m2_cat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_cat_2 C A B)) )  =>  (! [D:$i] :  ((m2_cat_2 D A B C) => (m2_cat_1 D A B)) ) ) ) ).
tt(dt_m2_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (! [D:$i] :  ((m2_cat_3 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D C (u4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u4_struct_0 A))))) ) ) ) ) ) ).
tt(dt_m2_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m2_chain_1 B A) => (m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers))) ) ) ) ).
tt(dt_m2_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k6_glib_000 A))) )  =>  (! [D:$i] :  ((m2_chord D A B C) => (m1_subset_1 D (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ) ).
tt(dt_m2_circcmb3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  & (m1_circcmb3 B A))  =>  (! [C:$i] :  ((m2_circcmb3 C A B) =>  ((v4_msafree2 C B) & (l3_msualg_1 C B)) ) ) ) ) ).
tt(dt_m2_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  &  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A B))))  &  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  &  ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) ) ) ) ) ) )  =>  (! [G:$i] :  ((m2_circtrm1 G A B C D E F) =>  ((v1_relat_1 G) &  ((v1_funct_1 G) & (v2_funct_1 G)) ) ) ) ) ) ).
tt(dt_m2_clvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_clvect_1 B A))  =>  (! [C:$i] :  ((m2_clvect_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m2_collsp,ax,$true).
tt(dt_m2_conlat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (m1_conlat_1 B A))  =>  (! [C:$i] :  ((m2_conlat_1 C A B) =>  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) ) ) ) ) ).
tt(dt_m2_connsp_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_connsp_2 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m2_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_convex4 C A B) => (m1_convex4 C A)) ) ) ) ).
tt(dt_m2_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) &  ((v3_dtconstr A) & (l1_lang1 A)) ) )  & (m1_subset_1 B (k7_dtconstr A)))  =>  (! [C:$i] :  ((m2_dtconstr C A B) => (m1_trees_4 C (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A))) ) ) ) ).
tt(dt_m2_exchsort,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m2_exchsort C A B) =>  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) ) ) ) ) ) ) ).
tt(dt_m2_filter_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 B))  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) ).
tt(dt_m2_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ) ).
tt(dt_m2_finseq_2,ax, (! [A:$i,B:$i] :  ((m1_finseq_2 B A) =>  (! [C:$i] :  ((m2_finseq_2 C A B) => (m2_finseq_1 C A)) ) ) ) ).
tt(dt_m2_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (! [D:$i] :  ((m2_fomodel2 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k2_xboole_0 B k6_margrel1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 A C)) B) (k2_xboole_0 B k6_margrel1))))) ) ) ) ) ) ).
tt(dt_m2_funct_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_funct_2 C A B))  =>  (! [D:$i] :  ((m2_funct_2 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ).
tt(dt_m2_funct_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_7 B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(dt_m2_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) => (l2_functor0 C A B)) ) ) ) ).
tt(dt_m2_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  (! [E:$i] :  ((m2_functor2 E A B C D) => (m1_functor2 E A B C D)) ) ) ) ).
tt(dt_m2_fvaluat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m2_fvaluat1 C A B) => (m1_rmod_2 C A (k4_vectsp_2 A))) ) ) ) ).
tt(dt_m2_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m2_glib_000,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [D:$i] :  ((m2_glib_000 D A B C) => (m1_glib_000 D A)) ) ) ) ).
tt(dt_m2_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_glib_001 B A) => (m2_finseq_1 B (k7_glib_000 A))) ) ) ) ).
tt(dt_m2_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_glib_004 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m2_glib_005,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_glib_005 C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m2_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) => (m2_finseq_1 B (u4_struct_0 A))) ) ) ) ).
tt(dt_m2_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ((m2_grcat_1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) ) ) ) ) ).
tt(dt_m2_hallmar1,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_hallmar1 C A B) => (m2_finseq_1 C (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m2_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_ideal_1 C A B) => (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ).
tt(dt_m2_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m2_index_1 D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) ) ) ) ) ) ).
tt(dt_m2_integr15,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) ) ) )  =>  (! [D:$i] :  ((m2_integr15 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k3_finseq_2 k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k1_numbers))))) ) ) ) ) ) ).
tt(dt_m2_integr16,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) ) ) )  =>  (! [D:$i] :  ((m2_integr16 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k3_finseq_2 k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k2_numbers))))) ) ) ) ) ) ).
tt(dt_m2_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) ) ) ) )  =>  (! [E:$i] :  ((m2_integr18 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (u1_struct_0 A)))))) ) ) ) ) ) ).
tt(dt_m2_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) => (m2_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 A))) (k8_mcart_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_m2_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 D (k1_zfmisc_1 C)) & (m1_kolmog01 E C A B)) ) )  =>  (! [F:$i] :  ((m2_kolmog01 F A B C D E) =>  ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) ) ) ) ) ) ).
tt(dt_m2_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_lattice4 B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m2_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_lattice5 D A B C) =>  ((v1_relat_1 D) & (v1_funct_1 D)) ) ) ) ) ).
tt(dt_m2_lattice7,ax,$true).
tt(dt_m2_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m2_lexbfs B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m2_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_lmod_7 C A B)) )  =>  (! [D:$i] :  ((m2_lmod_7 D A B C) =>  ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B)) ) ) ) ) ).
tt(dt_m2_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_margrel1 B A) =>  ((v3_finseq_1 B) & (v2_card_3 B)) ) ) ) ).
tt(dt_m2_measure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_measure1 D A B C) => (m2_subset_1 D (k1_zfmisc_1 A) B)) ) ) ) ).
tt(dt_m2_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ((m2_measure7 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 k1_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 k1_numbers)))))) ) ) ) ) ) ).
tt(dt_m2_measure8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_measure8 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) ) ).
tt(dt_m2_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) ) ) ) ) ) ).
tt(dt_m2_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  =>  (! [C:$i] :  ((m2_modcat_1 C A B) =>  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m2_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m2_monoid_0 B A) => (l3_algstr_0 B)) ) ) ) ).
tt(dt_m2_msalimit,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  & (m1_msalimit C A B)) )  =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_orders_2 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (u1_orders_2 A)) & (v1_funcop_1 D)) ) ) ) ) ) ) ) ).
tt(dt_m2_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m2_msaterm C A B) => (m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ).
tt(dt_m2_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  (! [E:$i] :  ((m2_msualg_6 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D))))) ) ) ) ) ) ).
tt(dt_m2_nat_lat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) ) ) ) ) ).
tt(dt_m2_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) => (m1_nattra_1 E A B C D)) ) ) ) ).
tt(dt_m2_orders_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_orders_1 B (k1_orders_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_orders_2 C A B) =>  ((v6_orders_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m2_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m2_osafree C A B) => (m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ) ) ).
tt(dt_m2_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ).
tt(dt_m2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) ) ) ) ) ).
tt(dt_m2_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ).
tt(dt_m2_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) ) ) ) ).
tt(dt_m2_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  (! [D:$i] :  ((m2_prob_4 D A B C) => (m1_prob_1 D A (k4_prob_4 A B C))) ) ) ) ).
tt(dt_m2_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_prvect_1 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(dt_m2_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pua2mss1 B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ).
tt(dt_m2_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_qc_lang1 B A) => (v1_relat_1 B)) ) ) ) ).
tt(dt_m2_qc_lang4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_qc_lang4 C A B)) )  =>  (! [D:$i] :  ((m2_qc_lang4 D A B C) => (m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B)))) ) ) ) ).
tt(dt_m2_rcomp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) & (m1_rcomp_3 D A B C)) ) )  =>  (! [E:$i] :  ((m2_rcomp_3 E A B C D) => (m2_finseq_1 E k1_numbers)) ) ) ) ).
tt(dt_m2_realset1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_realset1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) ).
tt(dt_m2_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m2_rewrite1 B A) =>  ((v1_relat_1 B) & (v10_rewrite1 B)) ) ) ) ) ).
tt(dt_m2_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_rfunct_3 C A B))  =>  (! [D:$i] :  ((m2_rfunct_3 D A B C) =>  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(dt_m2_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ((m2_ringcat1 B A) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m2_rlaffin3,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_rlaffin3 C A B) =>  ((v2_funct_1 C) & (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ) ).
tt(dt_m2_rlsub_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ((m2_rlsub_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m2_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_rlvect_2 C A B) => (m1_rlvect_2 C A)) ) ) ) ).
tt(dt_m2_rmod_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_rmod_2 C A B)) )  =>  (! [D:$i] :  ((m2_rmod_2 D A B C) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(dt_m2_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ((m2_rmod_4 D A B C) => (m1_rmod_4 D A B)) ) ) ) ).
tt(dt_m2_rusub_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  & (m1_rusub_1 B A))  =>  (! [C:$i] :  ((m2_rusub_1 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m2_simplex0,ax, (! [A:$i,B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C A)) ) ) ) ) ) ).
tt(dt_m2_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m2_subset_1 C A B) => (m1_subset_1 C A)) ) ) ) ).
tt(dt_m2_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_taxonom1 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A)))) ) ) ) ).
tt(dt_m2_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_topgrp_1 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(dt_m2_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_trees_1 B A) => (m1_trees_1 B A)) ) ) ) ).
tt(dt_m2_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_trees_2 B A) => (m1_subset_1 B (k1_zfmisc_1 A))) ) ) ) ).
tt(dt_m2_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m2_trees_3 C A B) => (m1_trees_1 C A)) ) ) ) ).
tt(dt_m2_unialg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_unialg_3 B A)) )  =>  (! [C:$i] :  ((m2_unialg_3 C A B) => (m1_unialg_2 C A)) ) ) ) ).
tt(dt_m2_urysohn3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A))))))) ) ) ) ) ) ).
tt(dt_m2_valued_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) )  =>  (! [C:$i] :  ((m2_valued_0 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ) ) ).
tt(dt_m2_vectsp11,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  (! [E:$i] :  ((m2_vectsp11 E A B C D) => (m1_subset_1 E (u1_struct_0 B))) ) ) ) ).
tt(dt_m2_vectsp_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  (! [D:$i] :  ((m2_vectsp_4 D A B C) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(dt_m2_vectsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ((m2_vectsp_6 D A B C) => (m1_vectsp_6 D A B)) ) ) ) ).
tt(dt_m2_vectsp_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_vectsp_8 C A B)) ) )  =>  (! [D:$i] :  ((m2_vectsp_8 D A B C) => (m1_vectsp_4 D A B)) ) ) ) ).
tt(dt_m2_waybel21,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  &  ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m2_waybel21 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m2_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((m2_xxreal_2 B A) => (v1_xxreal_0 B)) ) ) ) ).
tt(dt_m2_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_yellow13 B A) => (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(dt_m2_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) ) ) ) ) ) ).
tt(dt_m2_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_yellow_9 B A) =>  ((v2_pre_topc B) & (l1_pre_topc B)) ) ) ) ) ).
tt(dt_m2_zmodul01,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m2_zmodul01 C A B) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(dt_m3_abcmiz_1,ax,$true).
tt(dt_m3_algspec1,ax,$true).
tt(dt_m3_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C)) ) )  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 B k4_numbers) k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B k4_numbers) k4_numbers)))) ) ) ) ) ) ).
tt(dt_m3_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_bcialg_2 B A) =>  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(dt_m3_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_bciideal B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m3_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m3_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  =>  (! [D:$i] :  ((m3_chain_1 D A B C) => (m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ) ) ).
tt(dt_m3_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) => (m2_finseq_1 B (k6_glib_000 A))) ) ) ) ).
tt(dt_m3_conlat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A))))) )  =>  (! [C:$i] :  ((m3_conlat_1 C A B) =>  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) ) ) ) ) ).
tt(dt_m3_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((m3_fomodel2 C A B) =>  ((v1_relat_1 C) & (v1_funct_1 C)) ) ) ) ) ).
tt(dt_m3_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (m2_finseq_1 B (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)))) ) ) ) ).
tt(dt_m3_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_004 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m3_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_005 B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m3_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m3_graph_1 B A) =>  ( (~ (v2_struct_0 B))  & (l1_graph_1 B)) ) ) ) ) ).
tt(dt_m3_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_grcat_1 A))  =>  (! [B:$i] :  ((m3_grcat_1 B A) =>  ((v2_grcat_1 B) & (l1_grcat_1 B)) ) ) ) ) ).
tt(dt_m3_hallmar1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m3_hallmar1 D A B C) => (m2_hallmar1 D A B)) ) ) ) ).
tt(dt_m3_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m3_ideal_1 C A B) => (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ).
tt(dt_m3_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  (! [E:$i] :  ((m3_index_1 E A B C D) =>  ((v2_index_1 E A B) & (m1_index_1 E A B)) ) ) ) ) ).
tt(dt_m3_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  & (m1_integra1 D B)) ) )  =>  (! [E:$i] :  ((m3_integr15 E A B C D) => (m2_finseq_1 E (k1_euclid A))) ) ) ) ).
tt(dt_m3_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_lexbfs B A) =>  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) ) ) ) ) ).
tt(dt_m3_measure8,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v2_finsub_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  (! [D:$i] :  ((m3_measure8 D A B C) => (m2_measure8 D A C)) ) ) ) ).
tt(dt_m3_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_modcat_1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(dt_m3_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m3_monoid_0 B A) => (l4_algstr_0 B)) ) ) ) ).
tt(dt_m3_msalimit,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_msalimit A))  =>  (! [B:$i] :  ((m3_msalimit B A) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_msualg_1 B) & (l1_msualg_1 B)) ) ) ) ) ) ) ).
tt(dt_m3_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ((m3_msaterm C A B) =>  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B)))) ) ) ) ) ).
tt(dt_m3_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  =>  (! [E:$i] :  ((m3_nattra_1 E A B C D) => (m2_nattra_1 E A B C D)) ) ) ) ).
tt(dt_m3_pboole,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) ) ) ) ).
tt(dt_m3_pnproc_1,ax, (! [A:$i,B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) => (m1_pnproc_1 C A)) ) ) ) ).
tt(dt_m3_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m3_pua2mss1 B A) => (m1_eqrel_1 B (u1_struct_0 A))) ) ) ) ).
tt(dt_m3_realset1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m3_realset1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) ).
tt(dt_m3_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v5_ringcat1 A))  =>  (! [B:$i] :  ((m3_ringcat1 B A) =>  ((v3_ringcat1 B) & (l1_ringcat1 B)) ) ) ) ) ).
tt(dt_m3_robbins3,ax, (! [A:$i] :  ((l4_robbins1 A) =>  (! [B:$i] :  ((m3_robbins3 B A) => (l4_robbins3 B)) ) ) ) ).
tt(dt_m3_simplex0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m3_simplex0 C A B) =>  ((v1_finset_1 C) &  ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(dt_m3_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) => (m1_topgrp_1 B A A)) ) ) ) ).
tt(dt_m3_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m3_trees_3 B A) => (m2_trees_3 B A (k3_trees_1 A))) ) ) ) ).
tt(dt_m3_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m3_vectsp_8 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m3_yellow_6,ax, (! [A:$i,B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((m3_yellow_6 C A B) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) ) ) ) ).
tt(dt_m3_yellow_9,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  ((v2_pre_topc C) & (l1_pre_topc C)) ) ) ) ) ).
tt(dt_m3_zmodul01,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) => (m1_zmodul01 C A)) ) ) ) ).
tt(dt_m4_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m4_abcmiz_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))))))) ) ) ) ) ) ).
tt(dt_m4_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m4_algspec1 B A) => (m3_algspec1 B)) ) ) ) ).
tt(dt_m4_aofa_i00,ax, (! [A:$i] :  ((m4_aofa_i00 A) => (m1_aofa_000 A (k7_freealg k19_aofa_000 k26_aofa_i00) (k9_funct_2 k5_numbers k4_numbers) (k1_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k6_numbers k6_numbers))) ) ).
tt(dt_m4_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m2_bcialg_1 B A))  =>  (! [C:$i] :  ((m4_bcialg_2 C A B) => (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_m4_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m4_bciideal B A) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_m4_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m4_glib_001 C A B) => (m3_glib_001 C A)) ) ) ) ).
tt(dt_m4_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m4_grcat_1 C A B) =>  ( (~ (v1_xboole_0 C))  & (v4_grcat_1 C)) ) ) ) ) ).
tt(dt_m4_hallmar1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m4_hallmar1 C A B) => (m2_hallmar1 C A B)) ) ) ) ).
tt(dt_m4_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m3_index_1 E A B C D)) ) ) )  =>  (! [F:$i] :  ((m4_index_1 F A B C D E) =>  ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) &  ((v3_cat_5 F) & (l1_cat_1 F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_m4_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) ) ) ) )  =>  (! [E:$i] :  ((m4_integr15 E A B C D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k3_finseq_2 (k1_euclid A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (k1_euclid A)))))) ) ) ) ) ) ).
tt(dt_m4_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m4_margrel1 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(dt_m4_measure8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m4_measure8 D A B C) =>  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k9_setfam_1 A)))))) ) ) ) ) ) ).
tt(dt_m4_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m3_modcat_1 B A))  =>  (! [C:$i] :  ((m4_modcat_1 C A B) =>  ((v3_mod_2 C A) & (l1_mod_2 C A)) ) ) ) ) ).
tt(dt_m4_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(dt_m4_nattra_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m4_nattra_1 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ).
tt(dt_m4_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m4_pua2mss1 B A) => (m2_pua2mss1 B (u1_struct_0 A))) ) ) ) ).
tt(dt_m4_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m4_ringcat1 C A B) =>  ( (~ (v1_xboole_0 C))  & (v5_ringcat1 C)) ) ) ) ) ).
tt(dt_m4_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  &  ((v1_xreal_0 B) & (m3_simplex0 C A B)) )  =>  (! [D:$i] :  ((m4_simplex0 D A B C) => (m3_simplex0 D A (k4_xxreal_0 (k3_xxreal_3 B 1) (k2_xxreal_3 1)))) ) ) ) ).
tt(dt_m4_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m4_trees_1 B A) => (v2_trees_1 B)) ) ) ) ).
tt(dt_m4_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m4_trees_3 B A) =>  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(dt_m4_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m4_vectsp_8 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(dt_m4_yellow_6,ax,$true).
tt(dt_m5_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m2_bcialg_1 B A))  =>  (! [C:$i] :  ((m5_bcialg_2 C A B) => (m1_bcialg_2 C A)) ) ) ) ).
tt(dt_m5_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  &  ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) )  =>  (! [G:$i] :  ((m5_index_1 G A B C D E F) => (m3_index_1 G A B C D)) ) ) ) ).
tt(dt_m5_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m4_margrel1 B A))  =>  (! [C:$i] :  ((m5_margrel1 C A B) =>  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v2_margrel1 C) &  ((v3_margrel1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) ) ) ) ) ) ).
tt(dt_m5_modcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m5_modcat_1 D A B C) => (m3_modcat_1 D A)) ) ) ) ).
tt(dt_m5_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m2_monoid_0 B A))  =>  (! [C:$i] :  ((m5_monoid_0 C A B) => (m2_monoid_0 C A)) ) ) ) ).
tt(dt_m6_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) &  ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C A (k1_card_1 A)) &  ((v2_funct_2 C (k1_card_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) ) ) )  =>  (! [D:$i] :  ((m6_aofa_i00 D A B C) => (m1_aofa_000 D (k7_freealg k19_aofa_000 k26_aofa_i00) (k9_funct_2 A k4_numbers) B)) ) ) ) ).
tt(dt_m6_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m3_monoid_0 B A))  =>  (! [C:$i] :  ((m6_monoid_0 C A B) => (m2_monoid_0 C A)) ) ) ) ).
tt(dt_m7_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m3_monoid_0 B A))  =>  (! [C:$i] :  ((m7_monoid_0 C A B) => (m3_monoid_0 C A)) ) ) ) ).
tt(dt_m9_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ((m9_lmod_7 D A B C) => (m1_subset_1 D (u1_struct_0 B))) ) ) ) ).
tt(dt_u1_abcmiz_0,ax,$true).
tt(dt_u1_algstr_0,ax, (! [A:$i] :  ((l1_algstr_0 A) =>  ((v1_funct_1 (u1_algstr_0 A)) &  ((v1_funct_2 (u1_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_algstr_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_algstr_3,ax, (! [A:$i] :  ((l1_algstr_3 A) =>  ((v1_funct_1 (u1_algstr_3 A)) &  ((v1_funct_2 (u1_algstr_3 A) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_algstr_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_altcat_1,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  ((v1_relat_1 (u1_altcat_1 A)) &  ((v4_relat_1 (u1_altcat_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ((v1_funct_1 (u1_altcat_1 A)) & (v1_partfun1 (u1_altcat_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ) ) ) ).
tt(dt_u1_analmetr,ax, (! [A:$i] :  ((l1_analmetr A) => (m1_subset_1 (u1_analmetr A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_u1_analoaf,ax, (! [A:$i] :  ((l1_analoaf A) => (m1_subset_1 (u1_analoaf A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))) ) ).
tt(dt_u1_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  ( (~ (v1_xboole_0 (u1_armstrng A)))  & (v1_finset_1 (u1_armstrng A))) ) ) ).
tt(dt_u1_bcialg_1,ax, (! [A:$i] :  ((l1_bcialg_1 A) =>  ((v1_funct_1 (u1_bcialg_1 A)) &  ((v1_funct_2 (u1_bcialg_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_bcialg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_bcialg_4,ax, (! [A:$i] :  ((l1_bcialg_4 A) =>  ((v1_funct_1 (u1_bcialg_4 A)) &  ((v1_funct_2 (u1_bcialg_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_bcialg_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_bhsp_1,ax, (! [A:$i] :  ((l1_bhsp_1 A) =>  ((v1_funct_1 (u1_bhsp_1 A)) &  ((v1_funct_2 (u1_bhsp_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 (u1_bhsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) ) ) ) ).
tt(dt_u1_cat_1,ax, (! [A:$i] :  ((l1_cat_1 A) =>  ((v1_funct_1 (u1_cat_1 A)) & (m1_subset_1 (u1_cat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A)) (u4_struct_0 A))))) ) ) ).
tt(dt_u1_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) => (m1_subset_1 (u1_cat_4 A) (u1_struct_0 A))) ) ).
tt(dt_u1_cgames_1,ax,$true).
tt(dt_u1_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_closure1 B A))  => (m3_pboole (u1_closure1 A B) (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) ).
tt(dt_u1_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_closure2 B A))  => (m1_subset_1 (u1_closure2 A B) (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) ).
tt(dt_u1_clvect_1,ax, (! [A:$i] :  ((l1_clvect_1 A) =>  ((v1_funct_1 (u1_clvect_1 A)) &  ((v1_funct_2 (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_clvect_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_collsp,ax, (! [A:$i] :  ((l1_collsp A) => (m1_collsp (u1_collsp A) (u1_struct_0 A))) ) ).
tt(dt_u1_combgras,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) & (l1_combgras C A B)) )  =>  ((v1_funct_1 (u1_combgras A B C)) &  ((v1_funct_2 (u1_combgras A B C) (u1_incsp_1 A) (u1_incsp_1 B)) & (m1_subset_1 (u1_combgras A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 B))))) ) ) ) ).
tt(dt_u1_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((v1_compos_0 (u1_compos_1 A)) &  ((v2_compos_0 (u1_compos_1 A)) &  ((v3_compos_0 (u1_compos_1 A)) & (v5_compos_0 (u1_compos_1 A))) ) ) ) ) ).
tt(dt_u1_conlat_1,ax, (! [A:$i] :  ((l1_conlat_1 A) => (m1_subset_1 (u1_conlat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A))))) ) ).
tt(dt_u1_csspace,ax, (! [A:$i] :  ((l1_csspace A) =>  ((v1_funct_1 (u1_csspace A)) &  ((v1_funct_2 (u1_csspace A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k2_numbers) & (m1_subset_1 (u1_csspace A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k2_numbers)))) ) ) ) ).
tt(dt_u1_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) => (v1_relat_1 (u1_e_siec A))) ) ).
tt(dt_u1_extpro_1,ax, (! [A:$i,B:$i] :  ((l1_extpro_1 B A) =>  ((v1_funct_1 (u1_extpro_1 A B)) &  ((v1_funct_2 (u1_extpro_1 A B) (u1_compos_1 B) (k1_funct_2 (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))))) & (m1_subset_1 (u1_extpro_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_compos_1 B) (k1_funct_2 (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B)))))))) ) ) ) ).
tt(dt_u1_fintopo2,ax, (! [A:$i] :  ((l1_fintopo2 A) =>  ((v1_funct_1 (u1_fintopo2 A)) &  ((v1_funct_2 (u1_fintopo2 A) (u1_struct_0 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 (u1_fintopo2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) ) ) ) ).
tt(dt_u1_fomodel1,ax, (! [A:$i] :  ((l1_fomodel1 A) =>  ((v1_funct_1 (u1_fomodel1 A)) &  ((v1_funct_2 (u1_fomodel1 A) (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers) & (m1_subset_1 (u1_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers)))) ) ) ) ).
tt(dt_u1_fsm_1,ax, (! [A:$i,B:$i] :  ((l1_fsm_1 B A) =>  ((v1_funct_1 (u1_fsm_1 A B)) &  ((v1_funct_2 (u1_fsm_1 A B) (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B)) & (m1_subset_1 (u1_fsm_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B))))) ) ) ) ).
tt(dt_u1_fsm_2,ax, (! [A:$i,B:$i] :  ((l1_fsm_2 B A) => (m1_subset_1 (u1_fsm_2 A B) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_u1_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) & (l1_fsm_3 C A B)) )  => (m1_subset_1 (u1_fsm_3 A B C) (k1_zfmisc_1 (u1_struct_0 C)))) ) ).
tt(dt_u1_functor0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) & (l1_functor0 C A B)) )  =>  ((v1_funct_1 (u1_functor0 A B C)) &  ((v1_funct_2 (u1_functor0 A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) & (m1_subset_1 (u1_functor0 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_u1_graph_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ((v1_funct_1 (u1_graph_1 A)) &  ((v1_funct_2 (u1_graph_1 A) (u4_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u1_graph_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ( (~ (v2_struct_0 (u1_grcat_1 A)))  &  ((v13_algstr_0 (u1_grcat_1 A)) &  ((v3_rlvect_1 (u1_grcat_1 A)) &  ((v4_rlvect_1 (u1_grcat_1 A)) & (l2_algstr_0 (u1_grcat_1 A))) ) ) ) ) ) ).
tt(dt_u1_group_9,ax, (! [A:$i,B:$i] :  ((l1_group_9 B A) =>  ((v1_funct_1 (u1_group_9 A B)) &  ((v1_funct_2 (u1_group_9 A B) A (k1_funct_2 (u1_struct_0 B) (u1_struct_0 B))) & (m1_subset_1 (u1_group_9 A B) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 (u1_struct_0 B) (u1_struct_0 B)))))) ) ) ) ).
tt(dt_u1_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (~ (v1_xboole_0 (u1_incsp_1 A))) ) ) ).
tt(dt_u1_lang1,ax, (! [A:$i] :  ((l1_lang1 A) => (m1_subset_1 (u1_lang1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))))) ) ).
tt(dt_u1_lattices,ax, (! [A:$i] :  ((l1_lattices A) =>  ((v1_funct_1 (u1_lattices A)) &  ((v1_funct_2 (u1_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_lattices A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_memstr_0,ax, (! [A:$i,B:$i] :  ((l1_memstr_0 B A) =>  ((v1_funct_1 (u1_memstr_0 A B)) &  ((v1_funct_2 (u1_memstr_0 A B) (u1_struct_0 B) A) & (m1_subset_1 (u1_memstr_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) A)))) ) ) ) ).
tt(dt_u1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v1_funct_1 (u1_metric_1 A)) &  ((v1_funct_2 (u1_metric_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 (u1_metric_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) ) ) ) ).
tt(dt_u1_midsp_1,ax, (! [A:$i] :  ((l1_midsp_1 A) =>  ((v1_funct_1 (u1_midsp_1 A)) &  ((v1_funct_2 (u1_midsp_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_midsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_midsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  & (l1_midsp_2 B A))  =>  ( (~ (v2_struct_0 (u1_midsp_2 A B)))  & (l2_algstr_0 (u1_midsp_2 A B))) ) ) ).
tt(dt_u1_midsp_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (l1_midsp_3 B A))  =>  ((v1_funct_1 (u1_midsp_3 A B)) &  ((v1_funct_2 (u1_midsp_3 A B) (k4_finseq_2 A (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 (u1_midsp_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A (u1_struct_0 B)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_u1_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) => (m1_subset_1 (u1_mmlquery A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_u1_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ( (~ (v2_struct_0 (u1_mod_2 A B)))  &  ((v13_algstr_0 (u1_mod_2 A B)) &  ((v8_vectsp_1 (u1_mod_2 A B) A) &  ((v9_vectsp_1 (u1_mod_2 A B) A) &  ((v10_vectsp_1 (u1_mod_2 A B) A) &  ((v11_vectsp_1 (u1_mod_2 A B) A) &  ((v2_rlvect_1 (u1_mod_2 A B)) &  ((v3_rlvect_1 (u1_mod_2 A B)) &  ((v4_rlvect_1 (u1_mod_2 A B)) & (l1_vectsp_1 (u1_mod_2 A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_u1_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) => (m1_subset_1 (u1_modelc_2 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_u1_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (l1_modelc_3 B A))  => (m1_subset_1 (u1_modelc_3 A B) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_u1_msualg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_funct_1 (u1_msualg_1 A)) &  ((v1_funct_2 (u1_msualg_1 A) (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 (u1_msualg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)))))) ) ) ) ).
tt(dt_u1_normsp_0,ax, (! [A:$i] :  ((l1_normsp_0 A) =>  ((v1_funct_1 (u1_normsp_0 A)) &  ((v1_funct_2 (u1_normsp_0 A) (u1_struct_0 A) k1_numbers) & (m1_subset_1 (u1_normsp_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ).
tt(dt_u1_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_subset_1 (u1_orders_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_u1_osalg_1,ax, (! [A:$i] :  ((l1_osalg_1 A) =>  ((v3_relat_2 (u1_osalg_1 A)) &  ((v8_relat_2 (u1_osalg_1 A)) &  ((v1_partfun1 (u1_osalg_1 A) (u4_struct_0 A)) & (m1_subset_1 (u1_osalg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A))))) ) ) ) ) ).
tt(dt_u1_parsp_1,ax, (! [A:$i] :  ((l1_parsp_1 A) => (m1_parsp_1 (u1_parsp_1 A) (u1_struct_0 A))) ) ).
tt(dt_u1_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) => (m1_subset_1 (u1_pcs_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_u1_petri_2,ax, (! [A:$i] :  ((l1_petri_2 A) =>  ( (~ (v1_xboole_0 (u1_petri_2 A)))  & (v1_finset_1 (u1_petri_2 A))) ) ) ).
tt(dt_u1_petri,ax, (! [A:$i] :  ((l1_petri A) => (m1_subset_1 (u1_petri A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A))))) ) ).
tt(dt_u1_polyform,ax, (! [A:$i] :  ((l1_polyform A) =>  ((v1_relat_1 (u1_polyform A)) &  ((v1_funct_1 (u1_polyform A)) &  ((v1_finseq_1 (u1_polyform A)) & (v1_pre_poly (u1_polyform A))) ) ) ) ) ).
tt(dt_u1_prelamb,ax, (! [A:$i] :  ((l1_prelamb A) =>  ((v1_funct_1 (u1_prelamb A)) &  ((v1_funct_2 (u1_prelamb A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_prelamb A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ).
tt(dt_u1_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  (~ (v1_xboole_0 (u1_qmax_1 A))) ) ) ).
tt(dt_u1_quantal1,ax, (! [A:$i] :  ((l3_quantal1 A) => (m1_subset_1 (u1_quantal1 A) (u1_struct_0 A))) ) ).
tt(dt_u1_rewrite3,ax, (! [A:$i,B:$i] :  ((l1_rewrite3 B A) => (m1_subset_1 (u1_rewrite3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B))))) ) ).
tt(dt_u1_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ( (~ (v2_struct_0 (u1_ringcat1 A)))  &  ((v13_algstr_0 (u1_ringcat1 A)) &  ((v2_rlvect_1 (u1_ringcat1 A)) &  ((v3_rlvect_1 (u1_ringcat1 A)) &  ((v4_rlvect_1 (u1_ringcat1 A)) &  ((v3_group_1 (u1_ringcat1 A)) &  ((v4_vectsp_1 (u1_ringcat1 A)) &  ((v5_vectsp_1 (u1_ringcat1 A)) & (l6_algstr_0 (u1_ringcat1 A))) ) ) ) ) ) ) ) ) ) ).
tt(dt_u1_rlvect_1,ax, (! [A:$i] :  ((l1_rlvect_1 A) =>  ((v1_funct_1 (u1_rlvect_1 A)) &  ((v1_funct_2 (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_rlvect_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_robbins1,ax, (! [A:$i] :  ((l1_robbins1 A) =>  ((v1_funct_1 (u1_robbins1 A)) &  ((v1_funct_2 (u1_robbins1 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u1_robbins1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_sgraph1,ax, (! [A:$i] :  ((l1_sgraph1 A) => (m1_subset_1 (u1_sgraph1 A) (k1_zfmisc_1 (k2_sgraph1 (u1_struct_0 A))))) ) ).
tt(dt_u1_sheffer1,ax, (! [A:$i] :  ((l1_sheffer1 A) =>  ((v1_funct_1 (u1_sheffer1 A)) &  ((v1_funct_2 (u1_sheffer1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_sheffer1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) => (m1_subset_1 (u1_stacks_1 A) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_u1_struct_0,ax,$true).
tt(dt_u1_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  ( (~ (v1_xboole_0 (u1_turing_1 A)))  & (v1_finset_1 (u1_turing_1 A))) ) ) ).
tt(dt_u1_unialg_1,ax, (! [A:$i] :  ((l1_unialg_1 A) => (m2_finseq_1 (u1_unialg_1 A) (k4_partfun1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)))) ) ).
tt(dt_u1_vectsp_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_vectsp_1 B A))  =>  ((v1_funct_1 (u1_vectsp_1 A B)) &  ((v1_funct_2 (u1_vectsp_1 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 (u1_vectsp_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_u1_vectsp_2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_vectsp_2 B A))  =>  ((v1_funct_1 (u1_vectsp_2 A B)) &  ((v1_funct_2 (u1_vectsp_2 A B) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 (u1_vectsp_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B))))) ) ) ) ).
tt(dt_u1_waybel_0,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_waybel_0 B A))  =>  ((v1_funct_1 (u1_waybel_0 A B)) &  ((v1_funct_2 (u1_waybel_0 A B) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (u1_waybel_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u1_zmodul01,ax, (! [A:$i] :  ((l1_zmodul01 A) =>  ((v1_funct_1 (u1_zmodul01 A)) &  ((v1_funct_2 (u1_zmodul01 A) (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u1_zmodul01 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  ((v1_funct_1 (u2_abcmiz_0 A)) &  ((v1_funct_2 (u2_abcmiz_0 A) (u1_abcmiz_0 A) (u1_abcmiz_0 A)) & (m1_subset_1 (u2_abcmiz_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_abcmiz_0 A) (u1_abcmiz_0 A))))) ) ) ) ).
tt(dt_u2_algstr_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u2_algstr_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_altcat_1,ax, (! [A:$i] :  ((l2_altcat_1 A) => (m2_pboole (u2_altcat_1 A) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u1_altcat_1 A)) (k2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A)))) ) ).
tt(dt_u2_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  ((v1_relat_1 (u2_armstrng A)) &  ((v2_relat_1 (u2_armstrng A)) &  ((v4_relat_1 (u2_armstrng A) (u1_armstrng A)) &  ((v1_funct_1 (u2_armstrng A)) & (v1_partfun1 (u2_armstrng A) (u1_armstrng A))) ) ) ) ) ) ).
tt(dt_u2_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) =>  ((v1_funct_1 (u2_cat_4 A)) &  ((v1_funct_2 (u2_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u2_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_cgames_1,ax,$true).
tt(dt_u2_combgras,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) & (l1_combgras C A B)) )  =>  ((v1_funct_1 (u2_combgras A B C)) &  ((v1_funct_2 (u2_combgras A B C) (u2_incsp_1 A) (u2_incsp_1 B)) & (m1_subset_1 (u2_combgras A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u2_incsp_1 A) (u2_incsp_1 B))))) ) ) ) ).
tt(dt_u2_conlat_1,ax, (! [A:$i,B:$i] :  ( ((l5_struct_0 A) & (l2_conlat_1 B A))  => (m1_subset_1 (u2_conlat_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_u2_e_siec,ax, (! [A:$i] :  ((l1_e_siec A) => (v1_relat_1 (u2_e_siec A))) ) ).
tt(dt_u2_fsm_1,ax, (! [A:$i,B:$i] :  ((l1_fsm_1 B A) => (m1_subset_1 (u2_fsm_1 A B) (u1_struct_0 B))) ) ).
tt(dt_u2_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) & (l2_fsm_3 C A B)) )  => (m1_subset_1 (u2_fsm_3 A B C) (k1_zfmisc_1 (u1_struct_0 C)))) ) ).
tt(dt_u2_functor0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) & (l2_functor0 C A B)) )  => (m1_functor0 (u2_functor0 A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) (u1_altcat_1 A) (u1_altcat_1 B))) ) ).
tt(dt_u2_graph_1,ax, (! [A:$i] :  ((l1_graph_1 A) =>  ((v1_funct_1 (u2_graph_1 A)) &  ((v1_funct_2 (u2_graph_1 A) (u4_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u2_graph_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ( (~ (v2_struct_0 (u2_grcat_1 A)))  &  ((v13_algstr_0 (u2_grcat_1 A)) &  ((v3_rlvect_1 (u2_grcat_1 A)) &  ((v4_rlvect_1 (u2_grcat_1 A)) & (l2_algstr_0 (u2_grcat_1 A))) ) ) ) ) ) ).
tt(dt_u2_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (~ (v1_xboole_0 (u2_incsp_1 A))) ) ) ).
tt(dt_u2_lang1,ax, (! [A:$i] :  ((l2_lang1 A) => (m1_subset_1 (u2_lang1 A) (u1_struct_0 A))) ) ).
tt(dt_u2_lattices,ax, (! [A:$i] :  ((l2_lattices A) =>  ((v1_funct_1 (u2_lattices A)) &  ((v1_funct_2 (u2_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u2_lattices A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_memstr_0,ax, (! [A:$i,B:$i] :  ((l1_memstr_0 B A) =>  ((v1_relat_1 (u2_memstr_0 A B)) &  ((v4_relat_1 (u2_memstr_0 A B) A) &  ((v1_funct_1 (u2_memstr_0 A B)) & (v1_partfun1 (u2_memstr_0 A B) A)) ) ) ) ) ).
tt(dt_u2_midsp_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  & (l1_midsp_2 B A))  =>  ((v1_funct_1 (u2_midsp_2 A B)) &  ((v1_funct_2 (u2_midsp_2 A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (u1_midsp_2 A B))) & (m1_subset_1 (u2_midsp_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (u1_midsp_2 A B)))))) ) ) ) ).
tt(dt_u2_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) => (m1_subset_1 (u2_mmlquery A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_mmlquery A))))) ) ).
tt(dt_u2_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ( (~ (v2_struct_0 (u2_mod_2 A B)))  &  ((v13_algstr_0 (u2_mod_2 A B)) &  ((v8_vectsp_1 (u2_mod_2 A B) A) &  ((v9_vectsp_1 (u2_mod_2 A B) A) &  ((v10_vectsp_1 (u2_mod_2 A B) A) &  ((v11_vectsp_1 (u2_mod_2 A B) A) &  ((v2_rlvect_1 (u2_mod_2 A B)) &  ((v3_rlvect_1 (u2_mod_2 A B)) &  ((v4_rlvect_1 (u2_mod_2 A B)) & (l1_vectsp_1 (u2_mod_2 A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(dt_u2_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  ((v1_funct_1 (u2_modelc_2 A)) &  ((v1_funct_2 (u2_modelc_2 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u2_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (l1_modelc_3 B A))  => (m1_subset_1 (u2_modelc_3 A B) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_u2_msualg_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  ((v1_funct_1 (u2_msualg_1 A)) &  ((v1_funct_2 (u2_msualg_1 A) (u4_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u2_msualg_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_petri_2,ax, (! [A:$i] :  ((l1_petri_2 A) =>  ((v1_relat_1 (u2_petri_2 A)) & (v1_funct_1 (u2_petri_2 A))) ) ) ).
tt(dt_u2_petri,ax, (! [A:$i] :  ((l1_petri A) => (m1_subset_1 (u2_petri A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ).
tt(dt_u2_polyform,ax, (! [A:$i] :  ((l1_polyform A) =>  ((v1_relat_1 (u2_polyform A)) &  ((v1_funct_1 (u2_polyform A)) &  ((v1_finseq_1 (u2_polyform A)) & (v1_funcop_1 (u2_polyform A))) ) ) ) ) ).
tt(dt_u2_prelamb,ax, (! [A:$i] :  ((l1_prelamb A) =>  ((v1_funct_1 (u2_prelamb A)) &  ((v1_funct_2 (u2_prelamb A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u2_prelamb A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u2_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  (~ (v1_xboole_0 (u2_qmax_1 A))) ) ) ).
tt(dt_u2_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ( (~ (v2_struct_0 (u2_ringcat1 A)))  &  ((v13_algstr_0 (u2_ringcat1 A)) &  ((v2_rlvect_1 (u2_ringcat1 A)) &  ((v3_rlvect_1 (u2_ringcat1 A)) &  ((v4_rlvect_1 (u2_ringcat1 A)) &  ((v3_group_1 (u2_ringcat1 A)) &  ((v4_vectsp_1 (u2_ringcat1 A)) &  ((v5_vectsp_1 (u2_ringcat1 A)) & (l6_algstr_0 (u2_ringcat1 A))) ) ) ) ) ) ) ) ) ) ).
tt(dt_u2_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) =>  ((v1_funct_1 (u2_stacks_1 A)) &  ((v1_funct_2 (u2_stacks_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A)) (u4_struct_0 A)) & (m1_subset_1 (u2_stacks_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u4_struct_0 A)) (u4_struct_0 A))))) ) ) ) ).
tt(dt_u2_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) => (m1_subset_1 (u2_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_u2_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  ( (~ (v1_xboole_0 (u2_turing_1 A)))  & (v1_finset_1 (u2_turing_1 A))) ) ) ).
tt(dt_u3_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  ((v1_funct_1 (u3_abcmiz_0 A)) &  ((v1_funct_2 (u3_abcmiz_0 A) (u1_struct_0 A) (k5_finsub_1 (u1_abcmiz_0 A))) & (m1_subset_1 (u3_abcmiz_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k5_finsub_1 (u1_abcmiz_0 A)))))) ) ) ) ).
tt(dt_u3_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) => (m1_subset_1 (u3_armstrng A) (k1_zfmisc_1 (k4_card_3 (u2_armstrng A))))) ) ).
tt(dt_u3_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) =>  ((v1_funct_1 (u3_cat_4 A)) &  ((v1_funct_2 (u3_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A)) & (m1_subset_1 (u3_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A))))) ) ) ) ).
tt(dt_u3_conlat_1,ax, (! [A:$i,B:$i] :  ( ((l5_struct_0 A) & (l2_conlat_1 B A))  => (m1_subset_1 (u3_conlat_1 A B) (k1_zfmisc_1 (u4_struct_0 A)))) ) ).
tt(dt_u3_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (l2_fsm_1 C A B))  =>  ((v1_funct_1 (u3_fsm_1 A B C)) &  ((v1_funct_2 (u3_fsm_1 A B C) (k2_zfmisc_1 (u1_struct_0 C) A) B) & (m1_subset_1 (u3_fsm_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) A) B)))) ) ) ) ).
tt(dt_u3_grcat_1,ax, (! [A:$i] :  ((l1_grcat_1 A) =>  ((v1_funct_1 (u3_grcat_1 A)) &  ((v1_funct_2 (u3_grcat_1 A) (u1_struct_0 (u1_grcat_1 A)) (u1_struct_0 (u2_grcat_1 A))) & (m1_subset_1 (u3_grcat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (u1_grcat_1 A)) (u1_struct_0 (u2_grcat_1 A)))))) ) ) ) ).
tt(dt_u3_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) => (m1_subset_1 (u3_incsp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u2_incsp_1 A))))) ) ).
tt(dt_u3_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (l1_mod_2 B A))  =>  ((v1_funct_1 (u3_mod_2 A B)) &  ((v1_funct_2 (u3_mod_2 A B) (u1_struct_0 (u1_mod_2 A B)) (u1_struct_0 (u2_mod_2 A B))) & (m1_subset_1 (u3_mod_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (u1_mod_2 A B)) (u1_struct_0 (u2_mod_2 A B)))))) ) ) ) ).
tt(dt_u3_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) => (m1_subset_1 (u3_modelc_1 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ).
tt(dt_u3_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  ((v1_funct_1 (u3_modelc_2 A)) &  ((v1_funct_2 (u3_modelc_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u3_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u3_modelc_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  & (l1_modelc_3 B A))  => (m1_subset_1 (u3_modelc_3 A B) (k1_zfmisc_1 (k1_modelc_3 A)))) ) ).
tt(dt_u3_msualg_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l2_msualg_1 B A))  =>  ((v1_relat_1 (u3_msualg_1 A B)) &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) & (v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(dt_u3_prelamb,ax, (! [A:$i] :  ((l1_prelamb A) =>  ((v1_funct_1 (u3_prelamb A)) &  ((v1_funct_2 (u3_prelamb A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u3_prelamb A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u3_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  ((v1_funct_1 (u3_qmax_1 A)) &  ((v1_funct_2 (u3_qmax_1 A) (k2_zfmisc_1 (u1_qmax_1 A) (u2_qmax_1 A)) (k1_qmax_1 k1_numbers k12_prob_1)) & (m1_subset_1 (u3_qmax_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_qmax_1 A) (u2_qmax_1 A)) (k1_qmax_1 k1_numbers k12_prob_1))))) ) ) ) ).
tt(dt_u3_ringcat1,ax, (! [A:$i] :  ((l1_ringcat1 A) =>  ((v1_funct_1 (u3_ringcat1 A)) &  ((v1_funct_2 (u3_ringcat1 A) (u1_struct_0 (u1_ringcat1 A)) (u1_struct_0 (u2_ringcat1 A))) & (m1_subset_1 (u3_ringcat1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (u1_ringcat1 A)) (u1_struct_0 (u2_ringcat1 A)))))) ) ) ) ).
tt(dt_u3_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) =>  ((v1_funct_1 (u3_stacks_1 A)) &  ((v1_funct_2 (u3_stacks_1 A) (u4_struct_0 A) (u4_struct_0 A)) & (m1_subset_1 (u3_stacks_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 A))))) ) ) ) ).
tt(dt_u3_struct_0,ax, (! [A:$i] :  ((l3_struct_0 A) => (m1_subset_1 (u3_struct_0 A) (u1_struct_0 A))) ) ).
tt(dt_u3_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  ((v1_funct_1 (u3_turing_1 A)) &  ((v1_funct_2 (u3_turing_1 A) (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 (u3_turing_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) ) ) ) ).
tt(dt_u4_abcmiz_0,ax, (! [A:$i] :  ((l3_abcmiz_0 A) =>  ((v1_funct_1 (u4_abcmiz_0 A)) &  ((v1_funct_2 (u4_abcmiz_0 A) (u1_abcmiz_0 A) (u1_struct_0 A)) & (m1_subset_1 (u4_abcmiz_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_abcmiz_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u4_cat_4,ax, (! [A:$i] :  ((l1_cat_4 A) =>  ((v1_funct_1 (u4_cat_4 A)) &  ((v1_funct_2 (u4_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A)) & (m1_subset_1 (u4_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A))))) ) ) ) ).
tt(dt_u4_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (l3_fsm_1 C A B))  =>  ((v1_funct_1 (u4_fsm_1 A B C)) &  ((v1_funct_2 (u4_fsm_1 A B C) (u1_struct_0 C) B) & (m1_subset_1 (u4_fsm_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) B)))) ) ) ) ).
tt(dt_u4_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (~ (v1_xboole_0 (u4_incsp_1 A))) ) ) ).
tt(dt_u4_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  ((v1_funct_1 (u4_modelc_1 A)) &  ((v1_funct_2 (u4_modelc_1 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u4_modelc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u4_modelc_2,ax, (! [A:$i] :  ((l1_modelc_2 A) =>  ((v1_funct_1 (u4_modelc_2 A)) &  ((v1_funct_2 (u4_modelc_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u4_modelc_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u4_modelc_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (l2_modelc_3 B A))  => (m1_subset_1 (u4_modelc_3 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B))))) ) ).
tt(dt_u4_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  & (l3_msualg_1 B A))  => (m2_pboole (u4_msualg_1 A B) (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A B))) (k3_relat_1 (u2_msualg_1 A) (u3_msualg_1 A B)))) ) ).
tt(dt_u4_stacks_1,ax, (! [A:$i] :  ((l1_stacks_1 A) =>  ((v1_funct_1 (u4_stacks_1 A)) &  ((v1_funct_2 (u4_stacks_1 A) (u4_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u4_stacks_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u4_struct_0,ax,$true).
tt(dt_u4_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) => (m1_subset_1 (u4_turing_1 A) (u2_turing_1 A))) ) ).
tt(dt_u5_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) => (m1_subset_1 (u5_cat_4 A) (u1_struct_0 A))) ) ).
tt(dt_u5_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  ((v1_funct_1 (u5_modelc_1 A)) &  ((v1_funct_2 (u5_modelc_1 A) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (u5_modelc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u5_modelc_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (l2_modelc_3 B A))  => (m1_subset_1 (u5_modelc_3 A B) (k1_zfmisc_1 (u1_struct_0 B)))) ) ).
tt(dt_u5_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) => (m1_subset_1 (u5_turing_1 A) (u2_turing_1 A))) ) ).
tt(dt_u6_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) =>  ((v1_funct_1 (u6_cat_4 A)) &  ((v1_funct_2 (u6_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u6_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u6_modelc_1,ax, (! [A:$i] :  ((l2_modelc_1 A) =>  ((v1_funct_1 (u6_modelc_1 A)) &  ((v1_funct_2 (u6_modelc_1 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 (u6_modelc_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ) ).
tt(dt_u6_modelc_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (l2_modelc_3 B A))  => (m1_subset_1 (u6_modelc_3 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ).
tt(dt_u7_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) =>  ((v1_funct_1 (u7_cat_4 A)) &  ((v1_funct_2 (u7_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A)) & (m1_subset_1 (u7_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A))))) ) ) ) ).
tt(dt_u8_cat_4,ax, (! [A:$i] :  ((l2_cat_4 A) =>  ((v1_funct_1 (u8_cat_4 A)) &  ((v1_funct_2 (u8_cat_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A)) & (m1_subset_1 (u8_cat_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u4_struct_0 A))))) ) ) ) ).
tt(fc100_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k24_member_1 A B))) ) ) ).
tt(fc100_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k54_valued_1 C)) & (v1_partfun1 (k54_valued_1 C) A)) ) ) ).
tt(fc101_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k24_member_1 A B))) ) ).
tt(fc101_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k54_valued_1 C)) & (v1_partfun1 (k54_valued_1 C) A)) ) ) ).
tt(fc102_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k25_member_1 A B))) ) ).
tt(fc102_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v1_finseq_1 (k54_valued_1 A))) ) ) ) ) ).
tt(fc103_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k25_member_1 A B))) ) ) ).
tt(fc103_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k61_valued_1 A B)) &  ((v4_relat_1 (k61_valued_1 A B) k5_numbers) & (v1_funct_1 (k61_valued_1 A B))) ) ) ) ).
tt(fc104_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k25_member_1 A B))) ) ).
tt(fc104_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k61_valued_1 A B)) &  ((v1_funct_1 (k61_valued_1 A B)) & (v1_finset_1 (k61_valued_1 A B))) ) ) ) ).
tt(fc105_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k25_member_1 A B))) ) ).
tt(fc105_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k61_valued_1 B C)) &  ((v5_relat_1 (k61_valued_1 B C) A) & (v1_funct_1 (k61_valued_1 B C))) ) ) ) ).
tt(fc106_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k25_member_1 A B))) ) ).
tt(fc106_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k61_valued_1 A B)) &  ((v1_funct_1 (k61_valued_1 A B)) & (v1_xboole_0 (k61_valued_1 A B))) ) ) ) ).
tt(fc107_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k26_member_1 A B))) ) ).
tt(fc107_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k61_valued_1 A B)) &  ((v1_funct_1 (k61_valued_1 A B)) &  (~ (v1_xboole_0 (k61_valued_1 A B))) ) ) ) ) ).
tt(fc108_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k26_member_1 A B))) ) ) ).
tt(fc108_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_relat_1 A k5_numbers))  => (v6_membered (k9_xtuple_0 A))) ) ).
tt(fc109_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k26_member_1 A B))) ) ).
tt(fc109_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 (k63_valued_1 A)) &  ((v4_relat_1 (k63_valued_1 A) k5_numbers) &  ((v1_funct_1 (k63_valued_1 A)) & (v1_finset_1 (k63_valued_1 A))) ) ) ) ) ).
tt(fc10_abcmiz_1,ax, ((v1_msualg_1 k27_abcmiz_1) &  ((v1_instalg1 k27_abcmiz_1) &  ((v1_abcmiz_1 k27_abcmiz_1) & (v3_abcmiz_1 k27_abcmiz_1)) ) ) ).
tt(fc10_abcmiz_a,ax, ((v2_abcmiz_1 (k13_abcmiz_a k8_abcmiz_a) k27_abcmiz_1) & (v4_abcmiz_a (k13_abcmiz_a k8_abcmiz_a) k27_abcmiz_1)) ).
tt(fc10_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  =>  (~ (v1_abian (k2_xcmplx_0 A B))) ) ) ).
tt(fc10_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_relat_1 (k7_afinsq_1 A B C)) & (v1_funct_1 (k7_afinsq_1 A B C))) ) ).
tt(fc10_algstr_0,ax,(v7_algstr_0 k3_algstr_0)).
tt(fc10_algstr_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  =>  (~ (v1_xboole_0 (k11_algstr_4 A B))) ) ) ).
tt(fc10_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k5_ami_3 A B)))) ) ).
tt(fc10_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v9_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (~ (v1_finset_1 (k18_aofa_000 A))) ) ) ).
tt(fc10_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_orders_2 (k14_bagorder A)) &  ((v4_orders_2 (k14_bagorder A)) &  ((v5_orders_2 (k14_bagorder A)) & (v16_waybel_0 (k14_bagorder A))) ) ) ) ) ).
tt(fc10_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ((v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v2_bilinear (k9_bilinear A B C D E) A B C)) ) ) ) ).
tt(fc10_binop_2,ax, ((v1_funct_1 k48_binop_2) &  ((v1_funct_2 k48_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) &  ((v1_binop_1 k48_binop_2 k5_numbers) & (v2_binop_1 k48_binop_2 k5_numbers)) ) ) ).
tt(fc10_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_rat_1 A))  &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k3_xcmplx_0 A B))) ) ) ).
tt(fc10_borsuk_6,ax, ( (~ (v1_xboole_0 k8_borsuk_6))  & (v4_pre_topc k8_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr))) ).
tt(fc10_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v3_normsp_0 (k5_c0sp2 A)) &  ((v4_normsp_0 (k5_c0sp2 A)) & (v2_normsp_1 (k5_c0sp2 A))) ) ) ) ).
tt(fc10_card_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_finset_1 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_finset_1 (k2_zfmisc_1 A B))) ) ) ).
tt(fc10_card_3,ax,(v5_card_3 k4_ordinal1)).
tt(fc10_card_5,ax, (! [A:$i,B:$i] :  ((v6_membered A) => (v7_ordinal1 (k1_funct_1 (k3_wellord1 (k1_wellord2 (k2_wellord2 (k1_wellord2 A))) (k1_wellord2 A)) B))) ) ).
tt(fc10_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v3_catalg_1 A) & (l1_msualg_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  => (v1_finseq_1 (k2_xtuple_0 B))) ) ).
tt(fc10_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v3_normsp_0 (k5_cc0sp2 A)) &  ((v4_normsp_0 (k5_cc0sp2 A)) & (v8_clvect_1 (k5_cc0sp2 A))) ) ) ) ).
tt(fc10_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v3_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) &  ((v1_partfun1 (k18_valued_1 A B) k2_numbers) & (v2_cfdiff_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc10_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (v2_cgames_1 (k13_cgames_1 A))) ) ).
tt(fc10_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  => (v1_relat_1 (k3_msafree2 A))) ) ).
tt(fc10_circcomb,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v11_struct_0 (k5_circcomb A B)))  &  ((v1_msualg_1 (k5_circcomb A B)) &  ((v1_circcomb (k5_circcomb A B)) & (v2_circcomb (k5_circcomb A B))) ) ) ) ) ).
tt(fc10_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_clopban1 A B)))  &  ((v13_algstr_0 (k14_clopban1 A B)) &  ((v2_rlvect_1 (k14_clopban1 A B)) &  ((v3_rlvect_1 (k14_clopban1 A B)) &  ((v4_rlvect_1 (k14_clopban1 A B)) &  ((v3_normsp_0 (k14_clopban1 A B)) &  ((v4_normsp_0 (k14_clopban1 A B)) &  ((v2_clvect_1 (k14_clopban1 A B)) &  ((v3_clvect_1 (k14_clopban1 A B)) &  ((v4_clvect_1 (k14_clopban1 A B)) &  ((v5_clvect_1 (k14_clopban1 A B)) & (v8_clvect_1 (k14_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc10_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k9_clopban2 A))) ) ).
tt(fc10_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) B))) )  =>  ((v4_msualg_1 (g1_closure1 A B C) A) & (v5_closure1 (g1_closure1 A B C) A)) ) ) ).
tt(fc10_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v15_closure2 B A) & (l1_closure2 B A)) )  => (v4_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc10_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  ( (~ (v1_xboole_0 (k9_cohsp_1 A B)))  &  ((v1_classes1 (k9_cohsp_1 A B)) & (v1_coh_sp (k9_cohsp_1 A B))) ) ) ) ).
tt(fc10_coh_sp,ax, (! [A:$i] :  ((v4_funct_1 (k19_coh_sp A)) &  (~ (v1_xboole_0 (k19_coh_sp A))) ) ) ).
tt(fc10_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B (k1_compos_0 A)))  =>  ( (~ (v1_xboole_0 (k3_compos_0 A B)))  & (v4_funct_1 (k3_compos_0 A B))) ) ) ).
tt(fc10_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k7_compos_1 A B C)))  &  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) &  ((v1_finset_1 (k7_compos_1 A B C)) & (v1_afinsq_1 (k7_compos_1 A B C))) ) ) ) ) ) ) ) ).
tt(fc10_comput_1,ax, ( (~ (v1_xboole_0 k9_comput_1))  & (v6_comput_1 k9_comput_1)) ).
tt(fc10_comseq_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v1_comseq_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) &  ((v1_funct_2 (k1_valued_1 A B) k5_numbers k2_numbers) & (v1_comseq_3 (k1_valued_1 A B))) ) ) ) ).
tt(fc10_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v16_waybel_0 k11_dickson)) ).
tt(fc10_dilworth,ax, (! [A:$i,B:$i] :  ( ( ((v3_dilworth A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v3_dilworth (k5_yellow_0 A B))) ) ) ) ).
tt(fc10_euclid_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ((v2_monoid_0 (k7_real_ns1 A)) & (v1_bhsp_1 (k7_real_ns1 A))) ) ) ) ).
tt(fc10_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v3_card_1 (k45_valued_1 B C) A)) ) ) ) ).
tt(fc10_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_valued_2 (k1_euclid A))) ) ).
tt(fc10_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  => (v1_exchsort (k10_funct_7 A B C))) ) ).
tt(fc10_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xtuple_0 A) &  ((v1_xtuple_0 B) & (v1_xtuple_0 C)) )  => (v1_relat_1 (k1_enumset1 A B C))) ) ).
tt(fc10_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v2_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) & (v2_fcont_1 (k45_valued_1 A B))) ) ) ).
tt(fc10_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v18_lattices B (k1_lattice2 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) )  => (v19_lattices (k3_filter_2 (k1_lattice2 A) B) A)) ) ).
tt(fc10_finseq_1,ax, (! [A:$i,B:$i] : (v1_finseq_1 (k10_finseq_1 A B))) ).
tt(fc10_finset_1,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) => (v1_finset_1 (k3_xboole_0 A B))) ) ).
tt(fc10_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  => (v3_fomodel0 (k3_xboole_0 B A) A)) ) ).
tt(fc10_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k27_fomodel1 A))) ) ) ).
tt(fc10_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k11_fomodel2 A B C)) &  ((v1_funct_1 (k11_fomodel2 A B C)) & (v1_fomodel2 (k11_fomodel2 A B C) A B)) ) ) ) ).
tt(fc10_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) &  ((v1_xboole_0 D) & (v7_ordinal1 D)) ) ) )  => (v1_funct_1 (k8_fomodel3 A B C D))) ) ).
tt(fc10_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k33_fomodel2 A))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_fomodel4 (k4_tarski B C) A)) ) ).
tt(fc10_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_3 C A B)) ) ) )  =>  ((v8_struct_0 (k4_fsm_3 A B C)) & (v3_fsm_3 (k4_fsm_3 A B C) A (k9_flang_1 A))) ) ) ).
tt(fc10_funcop_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  => (v2_relat_1 (k2_funcop_1 A B))) ) ).
tt(fc10_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  => (v1_setfam_1 (k10_xtuple_0 A))) ) ).
tt(fc10_funct_2,ax, (! [A:$i,B:$i] : (v4_funct_1 (k1_funct_2 A B))) ).
tt(fc10_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k1_funct_4 B C)) &  ((v5_relat_1 (k1_funct_4 B C) A) & (v1_funct_1 (k1_funct_4 B C))) ) ) ) ).
tt(fc10_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (k2_zfmisc_1 A A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_zfmisc_1 A A)))))) )  & (v7_ordinal1 C))  => (v1_relat_1 (k1_funct_1 B C))) ) ).
tt(fc10_funct_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_funct_9 A)) ) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v2_funct_9 (k54_valued_1 A))) ) ) ) ) ).
tt(fc10_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) )  => (v1_xboole_0 (k5_gate_1 A B))) ) ).
tt(fc10_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v2_glib_001 B A) & (m3_glib_001 B A))  &  ((v2_glib_001 C A) & (m3_glib_001 C A)) ) )  => (v2_glib_001 (k7_glib_001 A B C) A)) ) ).
tt(fc10_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k8_graph_3 A B C)))  &  ((v1_graph_1 (k8_graph_3 A B C)) & (v6_graph_1 (k8_graph_3 A B C))) ) ) ) ).
tt(fc10_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ( (~ (v2_struct_0 (k4_gr_cy_1 A)))  &  ((v15_algstr_0 (k4_gr_cy_1 A)) & (v1_gr_cy_1 (k4_gr_cy_1 A))) ) ) ) ).
tt(fc10_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v15_algstr_0 (k9_group_6 A B C)) & (v1_group_3 (k9_group_6 A B C) A)) ) ) ).
tt(fc10_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  => (v3_group_7 (k5_finseq_1 A) (k1_tarski 1))) ) ).
tt(fc10_hilbert3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (v1_hilbert3 (k3_hilbert1 A (k3_hilbert1 B A)))) ) ).
tt(fc10_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l6_algstr_0 A)) )  &  ( ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v3_ideal_1 (k10_ideal_1 A B C) A)) ) ).
tt(fc10_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) => (v4_relat_1 (k1_xtuple_0 C) A)) ) ).
tt(fc10_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((v3_lattices (k21_interva1 A)) & (v11_lattices (k21_interva1 A))) ) ) ).
tt(fc10_jordan23,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k1_jordan9 A B)))  &  ( (~ (v3_funct_1 (k1_jordan9 A B)))  &  ((v1_finseq_6 (k1_jordan9 A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_jordan9 A B)) &  ((v2_topreal1 (k1_jordan9 A B)) &  ((v1_goboard5 (k1_jordan9 A B)) &  ((v2_goboard5 (k1_jordan9 A B)) &  ((v1_sprect_2 (k1_jordan9 A B)) & (v1_jordan23 (k1_jordan9 A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc10_jordan,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v9_rltopsp1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (v9_rltopsp1 (k2_pre_topc (k15_euclid A) B) (k15_euclid A))) ) ).
tt(fc10_kurato_1,ax,(v1_setfam_1 (k4_kurato_1 k3_topmetr k6_kurato_1))).
tt(fc10_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (u1_lattices A)) &  ((v1_funct_2 (u1_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_setwiseo (u1_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc10_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_lopban_1 A B)))  &  ((v13_algstr_0 (k16_lopban_1 A B)) &  ((v2_rlvect_1 (k16_lopban_1 A B)) &  ((v3_rlvect_1 (k16_lopban_1 A B)) &  ((v4_rlvect_1 (k16_lopban_1 A B)) &  ((v5_rlvect_1 (k16_lopban_1 A B)) &  ((v6_rlvect_1 (k16_lopban_1 A B)) &  ((v7_rlvect_1 (k16_lopban_1 A B)) &  ((v8_rlvect_1 (k16_lopban_1 A B)) &  ((v3_normsp_0 (k16_lopban_1 A B)) &  ((v4_normsp_0 (k16_lopban_1 A B)) & (v2_normsp_1 (k16_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc10_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k9_lopban_2 A))) ) ).
tt(fc10_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A C) (k6_cqc_lang A B))) A)) ) ).
tt(fc10_matrtop1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B)) )  =>  ((v1_relat_1 (k1_funct_1 (k3_matrtop1 A B C) D)) & (v1_funct_1 (k1_funct_1 (k3_matrtop1 A B C) D))) ) ) ).
tt(fc10_mazurulm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_mazurulm C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 B C)) &  ((v1_funct_2 (k3_relat_1 B C) (u1_struct_0 A) (u1_struct_0 A)) & (v1_mazurulm (k3_relat_1 B C) A A)) ) ) ) ).
tt(fc10_member_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k6_member_1 A)) & (v2_membered (k6_member_1 A))) ) ) ).
tt(fc10_membered,ax, (! [A:$i] :  ((v1_rat_1 A) => (v4_membered (k1_tarski A))) ) ).
tt(fc10_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k7_memstr_0 A B C)))  &  ((v1_relat_1 (k7_memstr_0 A B C)) &  ((v4_relat_1 (k7_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k7_memstr_0 A B C)) &  ((v5_funct_1 (k7_memstr_0 A B C) (k2_memstr_0 A B)) & (v5_memstr_0 (k7_memstr_0 A B C) A B C)) ) ) ) ) ) ) ).
tt(fc10_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) &  ((v1_metrizts A) & (l1_pre_topc A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_metrizts (k1_pre_topc A B))) ) ) ).
tt(fc10_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v5_vectsp_1 (k2_mod_4 A))) ) ) ).
tt(fc10_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (~ (v1_xboole_0 (u1_modelc_2 A))) ) ) ).
tt(fc10_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k12_msafree A B C))) ) ) ).
tt(fc10_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v2_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k9_pboole A C B)) &  ((v4_relat_1 (k9_pboole A C B) A) &  ((v1_funct_1 (k9_pboole A C B)) &  ((v1_partfun1 (k9_pboole A C B) A) & (v2_finset_1 (k9_pboole A C B))) ) ) ) ) ) ).
tt(fc10_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_relat_1 C) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) ) )  =>  ((v3_msualg_1 (k12_msualg_2 A B C) A) & (v4_msualg_1 (k12_msualg_2 A B C) A)) ) ) ).
tt(fc10_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k3_necklace A)) & (v3_dilworth (k3_necklace A))) ) ) ).
tt(fc10_nat_1,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 A) => (v5_ordinal1 (k2_funcop_1 A B))) ) ).
tt(fc10_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k5_nat_3 A B C)) &  ((v4_relat_1 (k5_nat_3 A B C) A) &  ((v1_funct_1 (k5_nat_3 A B C)) &  ((v1_partfun1 (k5_nat_3 A B C) A) & (v2_pre_poly (k5_nat_3 A B C))) ) ) ) ) ) ).
tt(fc10_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k3_necklace A)) & (v3_necklace (k3_necklace A))) ) ) ).
tt(fc10_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k4_newton A B))) ) ).
tt(fc10_nfcont_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v2_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k2_normsp_0 A B)) & (v2_fcont_1 (k2_normsp_0 A B))) ) ) ).
tt(fc10_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ( (~ (v2_struct_0 (k17_openlatt A)))  &  ((v1_pre_topc (k17_openlatt A)) & (v2_pre_topc (k17_openlatt A))) ) ) ) ).
tt(fc10_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (v4_oposet_1 k1_oposet_1)) ).
tt(fc10_ordinal6,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v3_ordinal1 (k2_wellord2 A)) & (v1_xboole_0 (k2_wellord2 A))) ) ) ).
tt(fc10_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (v2_relat_1 (k24_osafree A B))) ) ).
tt(fc10_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) )  => (v4_partfun3 (k2_funcop_1 A B))) ) ).
tt(fc10_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v13_algstr_0 (k11_polynom1 A B)) & (v36_algstr_0 (k11_polynom1 A B))) ) ) ) ).
tt(fc10_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v3_rlvect_1 (k14_polynom3 A))) ) ) ) ).
tt(fc10_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A B))) ) ) )  =>  ((v1_relat_1 (k1_funct_5 C)) &  ((v4_relat_1 (k1_funct_5 C) A) & (v1_funct_1 (k1_funct_5 C))) ) ) ) ).
tt(fc10_pre_poly,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k16_finseq_1 B A)) &  ((v1_funct_1 (k16_finseq_1 B A)) &  ((v1_card_3 (k16_finseq_1 B A)) & (v1_finseq_1 (k16_finseq_1 B A))) ) ) ) ) ).
tt(fc10_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v13_algstr_0 (k5_prvect_3 A B)) & (v1_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc10_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_xreal_0 (k15_quaterni A))) ) ).
tt(fc10_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v36_algstr_0 (k19_quofield A)) &  ((v1_vectsp_1 (k19_quofield A)) &  ((v3_vectsp_1 (k19_quofield A)) & (v1_vectsp_2 (k19_quofield A))) ) ) ) ) ).
tt(fc10_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ( (~ (v1_ratfunc1 B A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ( (~ (v9_struct_0 C A))  & (m1_subset_1 C (u1_struct_0 A))) ) )  =>  ((v1_funct_1 (k3_polynom5 A B C)) &  ((v1_funct_2 (k3_polynom5 A B C) k5_numbers (u1_struct_0 A)) &  (~ (v1_ratfunc1 (k3_polynom5 A B C) A)) ) ) ) ) ).
tt(fc10_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v3_xxreal_2 (k3_limfunc1 A)) &  ( (~ (v4_xxreal_2 (k3_limfunc1 A)))  & (v6_xxreal_2 (k3_limfunc1 A))) ) ) ) ).
tt(fc10_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k9_xtuple_0 A))) ) ).
tt(fc10_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_relat_2 A))  &  ((v1_relat_1 B) & (v3_relat_2 B)) )  => (v3_relat_2 (k2_xboole_0 A B))) ) ).
tt(fc10_relset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k9_xtuple_0 A)))) )  =>  ( (~ (v1_xboole_0 (k5_relat_1 A B)))  & (v1_relat_1 (k5_relat_1 A B))) ) ) ).
tt(fc10_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_seq_2 A)) ) )  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) &  ((v3_valued_0 (k24_valued_1 A B)) & (v2_seq_2 (k24_valued_1 A B))) ) ) ) ) ).
tt(fc10_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k4_rlaffin1 A B))) ) ) ).
tt(fc10_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k1_numbers)) )  =>  ((v1_funct_1 (k4_rltopsp1 A B)) &  ((v1_funct_2 (k4_rltopsp1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v3_tops_2 (k4_rltopsp1 A B) A A)) ) ) ) ).
tt(fc10_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) & (l2_robbins1 A)) )  =>  ((v5_lattices (k8_robbins1 A)) & (v4_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc10_rvsum_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_valued_0 (k5_finseq_1 A))) ) ).
tt(fc10_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k9_scmfsa_2 A B)))) ) ).
tt(fc10_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v2_extpro_1 (k10_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc10_scmfsa_4,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v2_amistd_5 k1_scmfsa_2 3)) ).
tt(fc10_scmfsa6c,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  =>  ((v1_scmfsa6c (k15_scmfsa_2 B A C)) & (v2_scmfsa6c (k15_scmfsa_2 B A C))) ) ) ).
tt(fc10_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2))) )  =>  ((v1_ami_2 (k9_scmfsa_m A B)) &  (~ (v1_scmfsa_m (k9_scmfsa_m A B))) ) ) ) ).
tt(fc10_scm_halt,ax, ((v1_relat_1 (k4_compos_1 k1_scmfsa_2)) &  ((v4_relat_1 (k4_compos_1 k1_scmfsa_2) k5_numbers) &  ((v5_relat_1 (k4_compos_1 k1_scmfsa_2) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_compos_1 k1_scmfsa_2)) &  ((v1_finset_1 (k4_compos_1 k1_scmfsa_2)) &  ((v1_scmfsa7b (k4_compos_1 k1_scmfsa_2)) & (v2_scm_halt (k4_compos_1 k1_scmfsa_2))) ) ) ) ) ) ).
tt(fc10_scmpds_4,ax, (! [A:$i] :  ( ((v4_scmpds_4 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  =>  ( (~ (v1_xboole_0 (k3_afinsq_1 A)))  &  ((v1_relat_1 (k3_afinsq_1 A)) &  ((v4_relat_1 (k3_afinsq_1 A) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 A)) &  ((v1_finset_1 (k3_afinsq_1 A)) &  ((v1_afinsq_1 (k3_afinsq_1 A)) & (v3_scmpds_4 (k3_afinsq_1 A))) ) ) ) ) ) ) ) ) ).
tt(fc10_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v6_compos_0 (k13_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc10_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k6_scmpds_6 B C A)))  &  ((v1_relat_1 (k6_scmpds_6 B C A)) &  ((v4_relat_1 (k6_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k6_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k6_scmpds_6 B C A)) &  ((v1_finset_1 (k6_scmpds_6 B C A)) &  ((v1_afinsq_1 (k6_scmpds_6 B C A)) & (v2_compos_1 (k6_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc10_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v2_extpro_1 (k7_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc10_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k6_scmring2 A B C)))) ) ).
tt(fc10_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k5_scmyciel A))) ) ).
tt(fc10_sfmastr1,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  => (v1_sfmastr1 (k16_scmfsa_2 B A))) ) ).
tt(fc10_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ((v1_classes1 B) => (v1_classes1 (k3_simplex0 A B C))) ) ).
tt(fc10_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  & (v7_ordinal1 C)) )  =>  ( (~ (v3_pencil_1 (k5_simplex1 C A B)))  &  ((v1_matroid0 (k5_simplex1 C A B)) &  ((v3_matroid0 (k5_simplex1 C A B)) & (v2_simplex1 (k5_simplex1 C A B) A)) ) ) ) ) ).
tt(fc10_sincos10,ax, ((v1_relat_1 (k5_relat_1 k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)))) ).
tt(fc10_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc10_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v1_topreal1 (k1_rfinseq B A))) ) ).
tt(fc10_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (v1_sprect_1 (k1_sprect_1 A))) ) ).
tt(fc10_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v7_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc10_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) => (v9_struct_0 (k4_struct_0 A) A)) ) ).
tt(fc10_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k2_zfmisc_1 A B))) ) ) ).
tt(fc10_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k3_tex_4 A B))) ) ) ).
tt(fc10_topalg_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_toprealb A) & (m1_pre_topc A (k15_euclid 2)))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v8_struct_0 (k5_topalg_1 A B)))  & (v15_algstr_0 (k5_topalg_1 A B))) ) ) ).
tt(fc10_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v5_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  =>  ((v1_xreal_0 (k2_xxreal_2 (k9_xtuple_0 B))) & (v1_xxreal_0 (k2_xxreal_2 (k9_xtuple_0 B)))) ) ) ).
tt(fc10_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v9_rltopsp1 (k3_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc10_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k2_xxreal_1 A B))) ) ) ).
tt(fc10_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~ (v1_xboole_0 (k5_toprealb A))) ) ) ).
tt(fc10_toprealc,ax, ((v7_struct_0 (k15_euclid k6_numbers)) & (v5_rltopsp1 (k15_euclid k6_numbers))) ).
tt(fc10_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v3_pre_topc (k2_struct_0 A) A)) ) ).
tt(fc10_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k10_finseq_1 A B)))  & (v4_trees_3 (k10_finseq_1 A B))) ) ) ).
tt(fc10_trees_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  & (m1_subset_1 B (k9_xtuple_0 A)))  =>  ((v1_relat_1 (k5_trees_2 A B)) &  ((v1_funct_1 (k5_trees_2 A B)) &  ((v3_trees_2 (k5_trees_2 A B)) & (v3_trees_9 (k5_trees_2 A B))) ) ) ) ) ).
tt(fc10_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  &  ((v1_relat_1 B) & (v5_relat_1 B k3_numbers)) )  => (v5_relat_1 (k2_xboole_0 A B) k3_numbers)) ) ).
tt(fc10_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v5_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 D E)) & (v1_partfun1 (k1_valued_1 D E) A)) ) ) ).
tt(fc10_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v1_xboole_0 (k8_vectsp10 A B C))) ) ) ).
tt(fc10_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v12_waybel_0 (k3_waybel_0 A B) A)) ) ).
tt(fc10_waybel10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v1_funct_1 (k6_waybel10 A B)) &  ((v1_funct_2 (k6_waybel10 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v7_waybel_1 (k6_waybel10 A B) A)) ) ) ) ).
tt(fc10_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (v4_yellow_6 (k2_waybel11 A) A)) ) ).
tt(fc10_waybel18,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A B))) & (v5_orders_2 (k5_yellow_1 A (k7_funcop_1 A B)))) ) ) ).
tt(fc10_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  &  ((v6_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v1_yellow_0 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc10_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v5_orders_2 B) & (l1_waybel_9 B)) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v5_orders_2 (k3_waybel24 A B))) ) ) ).
tt(fc10_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  =>  ((v3_lattice3 (k1_waybel25 A)) &  ((v1_waybel_9 (k1_waybel25 A)) & (v3_waybel_3 (k1_waybel25 A))) ) ) ) ).
tt(fc10_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k2_yellow_2 A)) &  ((v1_funct_2 (k2_yellow_2 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A)) &  ((v19_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) & (v20_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ) ) ).
tt(fc10_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v3_waybel_3 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k5_waybel11 A))) & (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ).
tt(fc10_waybel34,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v6_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A A B)) &  ((v4_yellow_0 (k1_yellow_2 A A B) A) & (v3_lattice3 (k1_yellow_2 A A B))) ) ) ) ).
tt(fc10_waybel_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v5_waybel_3 B)) ) ) ) )  & (m1_subset_1 C A)) )  => (v3_orders_2 (k1_funct_1 B C))) ) ).
tt(fc10_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k3_waybel_4 A))) & (v3_lattice3 (k2_yellow_1 (k3_waybel_4 A)))) ) ) ).
tt(fc10_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) )  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v24_waybel_0 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc10_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  ((v3_orders_2 (k2_waybel_9 A)) & (v6_waybel_0 (k2_waybel_9 A) A)) ) ) ).
tt(fc10_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k11_xboolean A B))) ) ).
tt(fc10_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k2_xcmplx_0 A B))) ) ) ).
tt(fc10_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  => (v3_membered (k2_xxreal_1 A B))) ) ).
tt(fc10_xxreal_2,ax, (! [A:$i] :  ( ((v6_membered A) & (v2_xxreal_2 A))  =>  ((v1_xxreal_0 (k1_xxreal_2 A)) & (v7_ordinal1 (k1_xxreal_2 A))) ) ) ).
tt(fc10_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) & (v2_xxreal_0 (k1_xxreal_3 A B))) ) ) ).
tt(fc10_yellow10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v1_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v24_waybel_0 B) &  ((v1_lattice3 B) &  ((v1_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v1_waybel_8 (k3_yellow_3 A B))) ) ) ).
tt(fc10_yellow_1,ax, (! [A:$i,B:$i] :  ((l1_orders_2 B) => (v1_yellow_1 (k2_funcop_1 A B))) ) ).
tt(fc10_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v3_lattice3 (k3_yellow_3 A B))) ) ) ).
tt(fc10_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ((v7_waybel_0 A) & (l1_orders_2 A))  &  ((v7_waybel_0 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v7_waybel_0 (k3_yellow_3 A B))) ) ) ).
tt(fc10_yellow_7,ax, (! [A:$i] :  ( ((v2_yellow_0 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v1_yellow_0 (k7_lattice3 A))) ) ) ).
tt(fc110_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k27_member_1 A B))) ) ).
tt(fc110_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_card_1 A 1)) ) ) )  =>  ((v1_relat_1 (k63_valued_1 A)) &  ((v1_funct_1 (k63_valued_1 A)) & (v1_xboole_0 (k63_valued_1 A))) ) ) ) ).
tt(fc111_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k27_member_1 A B))) ) ) ).
tt(fc111_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v4_relat_1 (k30_valued_1 B) A) &  ((v1_funct_1 (k30_valued_1 B)) & (v1_valued_0 (k30_valued_1 B))) ) ) ) ) ).
tt(fc112_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k27_member_1 A B))) ) ).
tt(fc112_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v4_relat_1 (k35_valued_1 B) A) &  ((v1_funct_1 (k35_valued_1 B)) & (v1_valued_0 (k35_valued_1 B))) ) ) ) ) ).
tt(fc113_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k27_member_1 A B))) ) ).
tt(fc113_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k39_valued_1 B)) &  ((v4_relat_1 (k39_valued_1 B) A) & (v1_funct_1 (k39_valued_1 B))) ) ) ) ).
tt(fc114_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k27_member_1 A B))) ) ).
tt(fc114_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v4_relat_1 (k54_valued_1 B) A) &  ((v1_funct_1 (k54_valued_1 B)) & (v3_valued_0 (k54_valued_1 B))) ) ) ) ) ).
tt(fc115_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_partfun1 (k30_valued_1 B) A) & (v1_valued_0 (k30_valued_1 B))) ) ) ) ) ).
tt(fc116_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_partfun1 (k35_valued_1 B) A) & (v1_valued_0 (k35_valued_1 B))) ) ) ) ) ).
tt(fc117_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k39_valued_1 B)) &  ((v1_funct_1 (k39_valued_1 B)) & (v1_partfun1 (k39_valued_1 B) A)) ) ) ) ).
tt(fc118_valued_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v1_partfun1 (k54_valued_1 B) A) & (v3_valued_0 (k54_valued_1 B))) ) ) ) ) ).
tt(fc119_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k7_valued_1 B C)) &  ((v4_relat_1 (k7_valued_1 B C) A) & (v1_funct_1 (k7_valued_1 B C))) ) ) ) ).
tt(fc11_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v1_relat_1 (k28_abcmiz_1 A)) &  ( (~ (v3_relat_1 (k28_abcmiz_1 A)))  &  ((v4_relat_1 (k28_abcmiz_1 A) (u1_struct_0 A)) &  ((v1_funct_1 (k28_abcmiz_1 A)) & (v1_partfun1 (k28_abcmiz_1 A) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc11_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  =>  (~ (v1_abian (k2_xcmplx_0 B A))) ) ) ).
tt(fc11_afinsq_1,ax, (! [A:$i,B:$i] :  ((v5_ordinal1 (k6_afinsq_1 A B)) & (v1_finset_1 (k6_afinsq_1 A B))) ) ).
tt(fc11_algstr_0,ax,(v14_algstr_0 k3_algstr_0)).
tt(fc11_algstr_4,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k12_algstr_4 A))) ) ).
tt(fc11_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k6_ami_3 A B)))) ) ).
tt(fc11_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  => (v15_aofa_000 (k12_aofa_000 A) A)) ) ).
tt(fc11_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) &  ((v1_hahnban1 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ((v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v3_bilinear (k9_bilinear A B C D E) A B C)) ) ) ) ).
tt(fc11_binop_2,ax, ((v1_funct_1 k27_binop_2) &  ((v1_funct_2 k27_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (v1_setwiseo k27_binop_2 k2_numbers)) ) ).
tt(fc11_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_rat_1 A))  &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k3_xcmplx_0 B A))) ) ) ).
tt(fc11_card_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_finset_1 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_finset_1 (k2_zfmisc_1 B A))) ) ) ).
tt(fc11_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k12_card_3 A B)) &  ((v4_relat_1 (k12_card_3 A B) (k4_card_3 A)) & (v1_funct_1 (k12_card_3 A B))) ) ) ) ).
tt(fc11_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v3_msualg_1 (k13_catalg_1 A) (k3_catalg_1 (u1_struct_0 A))) &  ((v1_msafree1 (k13_catalg_1 A) (k3_catalg_1 (u1_struct_0 A))) & (v1_msualg_6 (k13_catalg_1 A) (k3_catalg_1 (u1_struct_0 A)))) ) ) ) ).
tt(fc11_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v2_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) &  ((v1_partfun1 (k18_valued_1 A B) k2_numbers) & (v2_cfdiff_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc11_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v5_circcomb A) & (l1_msualg_1 A)) ) ) )  => (v1_relat_1 (k3_msafree2 A))) ) ).
tt(fc11_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) & (l1_msualg_1 B)) ) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v1_msualg_1 (k2_circcomb A B)) & (v1_circcomb (k2_circcomb A B))) ) ) ) ).
tt(fc11_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k9_clopban2 A)) &  ((v2_rlvect_1 (k9_clopban2 A)) &  ((v3_rlvect_1 (k9_clopban2 A)) &  ((v4_rlvect_1 (k9_clopban2 A)) &  ((v3_normsp_0 (k9_clopban2 A)) &  ((v4_normsp_0 (k9_clopban2 A)) &  ((v2_clvect_1 (k9_clopban2 A)) &  ((v3_clvect_1 (k9_clopban2 A)) &  ((v4_clvect_1 (k9_clopban2 A)) &  ((v5_clvect_1 (k9_clopban2 A)) &  ((v8_clvect_1 (k9_clopban2 A)) &  ((v3_group_1 (k9_clopban2 A)) &  ((v1_vectsp_1 (k9_clopban2 A)) &  ((v3_vectsp_1 (k9_clopban2 A)) & (v2_cfuncdom (k9_clopban2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc11_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v1_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v6_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc11_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v16_closure2 B A) & (l1_closure2 B A)) )  => (v5_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc11_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_relat_1 (k10_cohsp_1 A))) ) ).
tt(fc11_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k20_coh_sp A))) ) ).
tt(fc11_compos_0,ax, ((v2_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))) & (v3_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)))) ).
tt(fc11_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_compos_1 C A)) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) &  ((v1_finset_1 (k7_compos_1 A B C)) & (v3_compos_1 (k7_compos_1 A B C) A)) ) ) ) ) ) ) ).
tt(fc11_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  ((v1_relat_1 (k5_comput_1 A 1)) &  ((v4_relat_1 (k5_comput_1 A 1) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 A 1)) &  ((v4_valued_0 (k5_comput_1 A 1)) &  ((v2_margrel1 (k5_comput_1 A 1)) & (v7_comput_1 (k5_comput_1 A 1))) ) ) ) ) ) ) ).
tt(fc11_comseq_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v1_comseq_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) &  ((v1_funct_2 (k45_valued_1 A B) k5_numbers k2_numbers) & (v1_comseq_3 (k45_valued_1 A B))) ) ) ) ).
tt(fc11_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v4_dickson k11_dickson)) ).
tt(fc11_dilworth,ax, (! [A:$i,B:$i] :  ( ( ((v4_dilworth A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v4_dilworth (k5_yellow_0 A B))) ) ) ) ).
tt(fc11_euclid_7,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k10_funcsdom A)))  &  ((v13_algstr_0 (k10_funcsdom A)) &  ((v1_monoid_0 (k10_funcsdom A)) &  ((v1_rlvect_1 (k10_funcsdom A)) &  ((v2_rlvect_1 (k10_funcsdom A)) &  ((v3_rlvect_1 (k10_funcsdom A)) &  ((v4_rlvect_1 (k10_funcsdom A)) &  ((v5_rlvect_1 (k10_funcsdom A)) &  ((v6_rlvect_1 (k10_funcsdom A)) &  ((v7_rlvect_1 (k10_funcsdom A)) & (v8_rlvect_1 (k10_funcsdom A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc11_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v3_card_1 (k18_valued_1 B C) A)) ) ) ) ).
tt(fc11_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_exchsort A)) ) )  =>  ((v1_relat_1 (k10_funct_7 A B C)) &  ((v1_funct_1 (k10_funct_7 A B C)) &  ((v3_valued_0 (k10_funct_7 A B C)) & (v1_exchsort (k10_funct_7 A B C))) ) ) ) ) ).
tt(fc11_facirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  => (v2_facirc_1 (k5_finseq_1 A))) ) ).
tt(fc11_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_comseq_2 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_comseq_2 B) &  ((v2_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) & (v2_fcont_1 (k18_valued_1 A B))) ) ) ).
tt(fc11_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v1_xboole_0 (k8_filter_2 A B C))) ) ) ).
tt(fc11_finseq_1,ax, (! [A:$i,B:$i,C:$i] : (v1_finseq_1 (k11_finseq_1 A B C))) ).
tt(fc11_finset_1,ax, (! [A:$i,B:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k3_xboole_0 A B))) ) ).
tt(fc11_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  => (v1_xboole_0 (k1_funct_1 (k8_fomodel0 A) B))) ) ).
tt(fc11_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k1_funct_1 (k28_fomodel1 A) B))) ) ) ).
tt(fc11_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k5_relat_1 C (k37_fomodel1 A))) &  ((v5_relat_1 (k5_relat_1 C (k37_fomodel1 A)) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) & (v1_funct_1 (k5_relat_1 C (k37_fomodel1 A)))) ) ) ) ).
tt(fc11_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C)) )  => (v1_partfun1 (k9_fomodel3 A B C) (k4_finseq_2 C A))) ) ).
tt(fc11_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_fomodel4 (k4_tarski (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B) C) A)) ) ).
tt(fc11_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k16_funcop_1 A B)) & (v1_funct_1 (k16_funcop_1 A B))) ) ).
tt(fc11_funct_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) ) )  & (m1_subset_1 B (k9_xtuple_0 A)))  =>  (~ (v1_xboole_0 (k1_funct_1 A B))) ) ) ).
tt(fc11_funct_2,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) &  ((v4_relat_1 (k4_relat_1 A) A) &  ((v1_funct_1 (k4_relat_1 A)) & (v1_partfun1 (k4_relat_1 A) A)) ) ) ) ).
tt(fc11_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_funct_1 B A)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_funct_1 C A)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 B C)) &  ((v1_funct_1 (k1_funct_4 B C)) & (v5_funct_1 (k1_funct_4 B C) A)) ) ) ) ).
tt(fc11_funct_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k9_funct_7 A B)) & (v1_funct_1 (k9_funct_7 A B))) ) ) ).
tt(fc11_functor0,ax, (! [A:$i,B:$i] :  ( ((l2_altcat_1 A) & (m1_altcat_2 B A))  =>  ((v9_functor0 (k10_functor0 A B) B A) & (v10_functor0 (k10_functor0 A B) B A)) ) ) ).
tt(fc11_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  =>  (~ (v1_xboole_0 (k5_gate_1 A B))) ) ) ).
tt(fc11_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v3_glib_001 B A) & (m3_glib_001 B A))  &  ((v3_glib_001 C A) & (m3_glib_001 C A)) ) )  => (v3_glib_001 (k7_glib_001 A B C) A)) ) ).
tt(fc11_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k8_graph_3 A B C)))  &  ((v1_graph_1 (k8_graph_3 A B C)) & (v5_graph_1 (k8_graph_3 A B C))) ) ) ) ).
tt(fc11_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~ (v1_xboole_0 (k17_grcat_1 A))) ) ) ).
tt(fc11_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v8_struct_0 (k10_group_6 A B C)) & (v15_algstr_0 (k10_group_6 A B C))) ) ) ).
tt(fc11_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  => (v4_group_7 (k5_finseq_1 A) (k1_tarski 1))) ) ).
tt(fc11_hilbert3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (v1_hilbert3 (k3_hilbert1 (k4_hilbert1 A B) A))) ) ).
tt(fc11_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v1_xboole_0 (k11_ideal_1 A B C))) ) ) ).
tt(fc11_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) => (v4_relat_1 (k2_xtuple_0 C) B)) ) ).
tt(fc11_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((v3_lattices (k21_interva1 A)) & (v15_lattices (k21_interva1 A))) ) ) ).
tt(fc11_jordan23,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k1_jordan9 A B)))  &  ( (~ (v3_funct_1 (k1_jordan9 A B)))  &  ((v1_finseq_6 (k1_jordan9 A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_jordan9 A B)) &  ((v2_topreal1 (k1_jordan9 A B)) &  ((v1_goboard5 (k1_jordan9 A B)) &  ((v2_goboard5 (k1_jordan9 A B)) &  ((v1_sprect_2 (k1_jordan9 A B)) & (v2_jordan23 (k1_jordan9 A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc11_jordan,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v9_rltopsp1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (v9_rltopsp1 (k2_tops_1 (k15_euclid A) B) (k15_euclid A))) ) ).
tt(fc11_kurato_1,ax,(v2_tops_2 (k3_kurato_1 k3_topmetr k6_kurato_1) k3_topmetr)).
tt(fc11_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v3_lopban_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_lopban_1 A B)))  & (v3_lopban_1 (k16_lopban_1 A B))) ) ) ).
tt(fc11_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k9_lopban_2 A)) &  ((v2_rlvect_1 (k9_lopban_2 A)) &  ((v3_rlvect_1 (k9_lopban_2 A)) &  ((v4_rlvect_1 (k9_lopban_2 A)) &  ((v5_rlvect_1 (k9_lopban_2 A)) &  ((v6_rlvect_1 (k9_lopban_2 A)) &  ((v7_rlvect_1 (k9_lopban_2 A)) &  ((v8_rlvect_1 (k9_lopban_2 A)) &  ((v2_funcsdom (k9_lopban_2 A)) &  ((v3_normsp_0 (k9_lopban_2 A)) &  ((v4_normsp_0 (k9_lopban_2 A)) &  ((v2_normsp_1 (k9_lopban_2 A)) &  ((v3_group_1 (k9_lopban_2 A)) &  ((v1_vectsp_1 (k9_lopban_2 A)) & (v3_vectsp_1 (k9_lopban_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc11_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C)) (k8_cqc_lang A C B)) A)) ) ).
tt(fc11_matrtop1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B)) )  =>  ((v1_finseq_1 (k1_funct_1 (k3_matrtop1 A B C) D)) & (v3_valued_0 (k1_funct_1 (k3_matrtop1 A B C) D))) ) ) ).
tt(fc11_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) & (v1_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A A)) ) ) ) ).
tt(fc11_member_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  =>  ( (~ (v1_xboole_0 (k6_member_1 A)))  & (v2_membered (k6_member_1 A))) ) ) ).
tt(fc11_membered,ax, (! [A:$i] :  ((v1_int_1 A) => (v5_membered (k1_tarski A))) ) ).
tt(fc11_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v7_ordinal1 C) &  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v5_memstr_0 E A B C)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_4 D E)) &  ((v1_funct_1 (k1_funct_4 D E)) & (v5_memstr_0 (k1_funct_4 D E) A B C)) ) ) ) ).
tt(fc11_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v6_struct_0 (k2_mod_4 A)))  &  ((v13_algstr_0 (k2_mod_4 A)) &  ((v33_algstr_0 (k2_mod_4 A)) &  ((v36_algstr_0 (k2_mod_4 A)) &  ((v1_group_1 (k2_mod_4 A)) &  ((v3_group_1 (k2_mod_4 A)) &  ((v5_vectsp_1 (k2_mod_4 A)) &  ((v2_rlvect_1 (k2_mod_4 A)) &  ((v3_rlvect_1 (k2_mod_4 A)) & (v4_rlvect_1 (k2_mod_4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc11_modelc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A))))) )  =>  ( (~ (v2_struct_0 (k42_modelc_2 A B)))  &  ((v9_modelc_2 (k42_modelc_2 A B)) & (v10_modelc_2 (k42_modelc_2 A B))) ) ) ) ).
tt(fc11_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v2_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k6_pboole A B C)) &  ((v4_relat_1 (k6_pboole A B C) A) &  ((v1_funct_1 (k6_pboole A B C)) &  ((v1_partfun1 (k6_pboole A B C) A) & (v2_finset_1 (k6_pboole A B C))) ) ) ) ) ) ).
tt(fc11_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (~ (v1_xboole_0 (k14_msualg_2 A B))) ) ) ).
tt(fc11_mycielsk,ax, (! [A:$i] :  ( ((v1_mycielsk A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k3_necklace A)) & (v2_mycielsk (k3_necklace A))) ) ) ).
tt(fc11_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k6_nat_3 A B C)) &  ((v4_relat_1 (k6_nat_3 A B C) A) &  ((v1_funct_1 (k6_nat_3 A B C)) &  ((v1_partfun1 (k6_nat_3 A B C) A) & (v3_valued_0 (k6_nat_3 A B C))) ) ) ) ) ) ).
tt(fc11_neckla_3,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k3_necklace A)) & (v1_necklace (k3_necklace A))) ) ) ).
tt(fc11_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (k11_newton A))) ) ).
tt(fc11_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (v5_oposet_1 k1_oposet_1)) ).
tt(fc11_ordinal6,ax, (! [A:$i] :  ((v1_relat_1 (k2_ordinal6 A)) &  ((v1_funct_1 (k2_ordinal6 A)) &  ((v5_ordinal1 (k2_ordinal6 A)) &  ((v1_ordinal2 (k2_ordinal6 A)) & (v2_ordinal2 (k2_ordinal6 A))) ) ) ) ) ).
tt(fc11_partfun3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_relat_1 (k2_funcop_1 A k6_numbers))) ) ) ).
tt(fc11_pcs_0,ax, ((v2_struct_0 k5_pcs_0) & (v2_pcs_0 k5_pcs_0)) ).
tt(fc11_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v5_group_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc11_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v4_rlvect_1 (k14_polynom3 A))) ) ) ) ).
tt(fc11_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A B))) ) ) )  =>  ((v1_relat_1 (k1_funct_5 C)) &  ((v4_relat_1 (k1_funct_5 C) A) &  ((v1_funct_1 (k1_funct_5 C)) & (v1_partfun1 (k1_funct_5 C) A)) ) ) ) ) ).
tt(fc11_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 (k1_card_3 A)) &  ((v1_funct_1 (k1_card_3 A)) &  ((v1_xboole_0 (k1_card_3 A)) & (v1_card_3 (k1_card_3 A))) ) ) ) ) ).
tt(fc11_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v5_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc11_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_xreal_0 (k16_quaterni A))) ) ).
tt(fc11_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ( (~ (v1_ratfunc1 B A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ( (~ (v1_ratfunc1 C A))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_polynom3 A B C)) &  ((v1_funct_2 (k11_polynom3 A B C) k5_numbers (u1_struct_0 A)) &  (~ (v1_ratfunc1 (k11_polynom3 A B C) A)) ) ) ) ) ).
tt(fc11_rcomp_3,ax, ( (~ (v3_xxreal_2 (k2_subset_1 k1_numbers)))  &  ( (~ (v4_xxreal_2 (k2_subset_1 k1_numbers)))  & (v6_xxreal_2 (k2_subset_1 k1_numbers))) ) ).
tt(fc11_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k10_xtuple_0 A))) ) ).
tt(fc11_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_relat_2 A))  &  ((v1_relat_1 B) & (v3_relat_2 B)) )  => (v3_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc11_relset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k9_xtuple_0 A)))) )  =>  (~ (v1_xboole_0 (k7_relat_1 A B))) ) ) ).
tt(fc11_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_seq_2 A)) ) )  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) &  ((v3_valued_0 (k24_valued_1 A B)) & (v1_seq_2 (k24_valued_1 A B))) ) ) ) ) ).
tt(fc11_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C k1_numbers)) )  => (v9_rltopsp1 (k1_convex1 A B C) A)) ) ).
tt(fc11_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (l2_robbins1 A)) ) )  =>  ((v6_lattices (k8_robbins1 A)) & (v4_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc11_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_valued_0 (k10_finseq_1 A B))) ) ).
tt(fc11_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B)))) ) ).
tt(fc11_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v2_extpro_1 (k11_scmfsa_2 A) 3 k1_scmfsa_2)) ) ) ).
tt(fc11_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v1_scmfsa6c (k16_scmfsa_2 A B))) ) ).
tt(fc11_scmfsa_m,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_ami_2 (k4_scmfsa_2 (k2_nat_1 A 1))) &  (~ (v1_scmfsa_m (k4_scmfsa_2 (k2_nat_1 A 1)))) ) ) ) ).
tt(fc11_scm_halt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scm_halt A)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_scm_halt B)) ) ) ) ) ) )  &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8b C A B)))  &  ((v1_relat_1 (k1_scmfsa8b C A B)) &  ((v4_relat_1 (k1_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8b C A B)) &  ((v1_finset_1 (k1_scmfsa8b C A B)) &  ((v1_afinsq_1 (k1_scmfsa8b C A B)) & (v2_scm_halt (k1_scmfsa8b C A B))) ) ) ) ) ) ) ) ) ).
tt(fc11_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ((v4_scmpds_4 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_4 A B)))  &  ((v1_relat_1 (k2_scmpds_4 A B)) &  ((v4_relat_1 (k2_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_4 A B)) &  ((v1_finset_1 (k2_scmpds_4 A B)) &  ((v1_afinsq_1 (k2_scmpds_4 A B)) & (v3_scmpds_4 (k2_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc11_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v6_compos_0 (k14_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc11_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scmpds_4 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_6 C D A B)))  &  ((v1_relat_1 (k3_scmpds_6 C D A B)) &  ((v4_relat_1 (k3_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_6 C D A B)) &  ((v1_finset_1 (k3_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k3_scmpds_6 C D A B)) &  ((v2_scmpds_4 (k3_scmpds_6 C D A B)) & (v3_scmpds_4 (k3_scmpds_6 C D A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc11_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v3_extpro_1 (k1_scmring2 A) 2)) ) ) ).
tt(fc11_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k7_scmring2 A B C)))) ) ).
tt(fc11_scmyciel,ax, (! [A:$i,B:$i] :  ((v4_scmyciel A) => (v4_scmyciel (k7_scmyciel A B))) ) ).
tt(fc11_sfmastr1,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_sfmastr1 (k17_scmfsa_2 B A))) ) ).
tt(fc11_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_setfam_1 B))  =>  (~ (v1_setfam_1 (k3_simplex0 A B C))) ) ) ).
tt(fc11_sincos10,ax, ((v1_relat_1 (k5_relat_1 k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))))) & (v2_funct_1 (k5_relat_1 k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))))) ).
tt(fc11_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))) ).
tt(fc11_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v1_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ).
tt(fc11_sprect_1,ax, (! [A:$i] :  ( ((v1_sprect_1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (v1_jordan1 (k3_topreal1 2 A))) ) ).
tt(fc11_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_partfun1 (k10_stacks_1 A) (u4_struct_0 A)) &  ((v3_relat_2 (k10_stacks_1 A)) & (v8_relat_2 (k10_stacks_1 A))) ) ) ) ).
tt(fc11_struct_0,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  =>  (~ (v9_struct_0 (k5_struct_0 A) A)) ) ) ).
tt(fc11_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k3_zfmisc_1 A B C))) ) ) ).
tt(fc11_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k3_tex_4 A B))) ) ).
tt(fc11_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v6_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  =>  (~ (v1_xboole_0 (k9_xtuple_0 B))) ) ) ).
tt(fc11_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v1_convex1 (k1_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc11_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k3_xxreal_1 A B))) ) ) ).
tt(fc11_toprealb,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v3_pre_topc (k5_toprealb A) k2_topalg_2)) ) ).
tt(fc11_toprealc,ax, (! [A:$i] :  ( ((v1_toprealc A) & (l1_struct_0 A))  => (v1_valued_2 (u1_struct_0 A))) ) ).
tt(fc11_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v4_pre_topc (k2_tops_1 A B) A)) ) ).
tt(fc11_trees_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v1_finseq_1 (k2_finseq_2 A B)) & (v4_trees_3 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc11_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  &  ((v1_relat_1 B) & (v5_relat_1 B k4_numbers)) )  => (v5_relat_1 (k2_xboole_0 A B) k4_numbers)) ) ).
tt(fc11_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v6_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v6_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 D E)) & (v1_partfun1 (k1_valued_1 D E) A)) ) ) ).
tt(fc11_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ( (~ (v3_funct_1 C))  &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k11_vectsp10 A B C)) &  ( (~ (v3_funct_1 (k11_vectsp10 A B C)))  &  ((v1_funct_2 (k11_vectsp10 A B C) (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C))) (u1_struct_0 A)) &  ((v13_vectsp_1 (k11_vectsp10 A B C) (k6_vectsp10 A B (k9_vectsp10 A B C)) A) & (v1_hahnban1 (k11_vectsp10 A B C) A (k6_vectsp10 A B (k9_vectsp10 A B C)))) ) ) ) ) ) ).
tt(fc11_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v13_waybel_0 (k4_waybel_0 A B) A)) ) ).
tt(fc11_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k5_waybel10 A)) &  ((v2_funct_1 (k5_waybel10 A)) & (v1_funct_2 (k5_waybel10 A) (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A))))) ) ) ) ).
tt(fc11_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (v5_yellow_6 (k2_waybel11 A) A)) ) ).
tt(fc11_waybel18,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) & (l1_orders_2 B)) ) )  =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A B))) & (v4_orders_2 (k5_yellow_1 A (k7_funcop_1 A B)))) ) ) ).
tt(fc11_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v3_orders_2 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc11_waybel24,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((v1_monoid_0 (k6_yellow_1 A B)) & (v1_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(fc11_waybel25,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 (k1_waybel25 A))))  =>  ( (~ (v1_xboole_0 (k2_pre_topc (k1_waybel25 A) (k6_domain_1 (u1_struct_0 (k1_waybel25 A)) B))))  &  ((v1_waybel_0 (k2_pre_topc (k1_waybel25 A) (k6_domain_1 (u1_struct_0 (k1_waybel25 A)) B)) (k1_waybel25 A)) & (v12_waybel_0 (k2_pre_topc (k1_waybel25 A) (k6_domain_1 (u1_struct_0 (k1_waybel25 A)) B)) (k1_waybel25 A))) ) ) ) ).
tt(fc11_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k4_waybel_2 A)) &  ((v1_funct_2 (k4_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (v22_waybel_0 (k4_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ) ).
tt(fc11_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel_8 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k5_waybel11 A))) & (v2_waybel_8 (k2_yellow_1 (k5_waybel11 A)))) ) ) ).
tt(fc11_waybel_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 A B)) & (v3_orders_2 (k5_yellow_1 A B))) ) ) ).
tt(fc11_waybel_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v4_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~ (v1_xboole_0 (k5_waybel_4 A B C))) ) ) ).
tt(fc11_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v2_waybel_8 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc11_waybel_9,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v5_orders_2 (k2_waybel_9 A)) & (v6_waybel_0 (k2_waybel_9 A) A)) ) ) ).
tt(fc11_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v2_xxreal_0 (k2_xcmplx_0 A B))) ) ).
tt(fc11_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  => (v3_membered (k3_xxreal_1 B A))) ) ).
tt(fc11_xxreal_2,ax, ( (~ (v3_xxreal_2 k1_numbers))  &  (~ (v4_xxreal_2 k1_numbers)) ) ).
tt(fc11_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 B A)) & (v2_xxreal_0 (k1_xxreal_3 B A))) ) ) ).
tt(fc11_yellow10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v3_lattice3 B) &  ((v2_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v2_waybel_8 (k3_yellow_3 A B))) ) ) ).
tt(fc11_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( (~ (v2_struct_0 (k6_yellow_1 A B)))  & (v1_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(fc11_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v6_waybel_0 (k3_yellow_6 A B C) B) & (v1_yellow_6 (k3_yellow_6 A B C) B)) ) ) ).
tt(fc11_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) &  ((v10_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v1_orders_2 (k7_lattice3 A)) & (v10_waybel_1 (k7_lattice3 A))) ) ) ).
tt(fc120_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k13_valued_1 B C)) &  ((v4_relat_1 (k13_valued_1 B C) A) & (v1_funct_1 (k13_valued_1 B C))) ) ) ) ).
tt(fc121_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k24_valued_1 B C)) &  ((v4_relat_1 (k24_valued_1 B C) A) & (v1_funct_1 (k24_valued_1 B C))) ) ) ) ).
tt(fc122_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k7_valued_1 B C)) &  ((v1_funct_1 (k7_valued_1 B C)) & (v1_partfun1 (k7_valued_1 B C) A)) ) ) ) ).
tt(fc123_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k13_valued_1 B C)) &  ((v1_funct_1 (k13_valued_1 B C)) & (v1_partfun1 (k13_valued_1 B C) A)) ) ) ) ).
tt(fc124_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k24_valued_1 B C)) &  ((v1_funct_1 (k24_valued_1 B C)) & (v1_partfun1 (k24_valued_1 B C) A)) ) ) ) ).
tt(fc125_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v4_relat_1 (k1_valued_1 B C) A) & (v1_funct_1 (k1_valued_1 B C))) ) ) ) ).
tt(fc126_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v4_relat_1 (k45_valued_1 B C) A) & (v1_funct_1 (k45_valued_1 B C))) ) ) ) ).
tt(fc127_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v4_relat_1 (k18_valued_1 B C) A) & (v1_funct_1 (k18_valued_1 B C))) ) ) ) ).
tt(fc128_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_valued_0 C)) ) ) )  =>  ((v1_relat_1 (k50_valued_1 B C)) &  ((v4_relat_1 (k50_valued_1 B C) A) & (v1_funct_1 (k50_valued_1 B C))) ) ) ) ).
tt(fc129_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v1_partfun1 (k1_valued_1 B C) A)) ) ) ) ).
tt(fc12_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ((v3_msualg_1 (k1_msafree3 A (k28_abcmiz_1 A)) A) & (v4_msualg_1 (k1_msafree3 A (k28_abcmiz_1 A)) A)) ) ) ).
tt(fc12_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) &  (~ (v1_abian A)) )  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  => (v1_abian (k2_xcmplx_0 A B))) ) ).
tt(fc12_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ((v5_ordinal1 (k7_afinsq_1 A B C)) & (v1_finset_1 (k7_afinsq_1 A B C))) ) ).
tt(fc12_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v1_finset_1 (k54_valued_1 A))) ) ) ) ) ).
tt(fc12_algstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ( (~ (v2_struct_0 (g3_algstr_0 A B)))  & (v15_algstr_0 (g3_algstr_0 A B))) ) ) ).
tt(fc12_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k12_algstr_4 A))) ) ) ).
tt(fc12_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v3_card_1 (k2_amistd_1 2 k1_ami_3 (k7_ami_3 A)) 1)) ) ).
tt(fc12_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( ((v15_aofa_000 B A) & (m1_subset_1 B (u1_struct_0 A)))  &  ((v15_aofa_000 C A) & (m1_subset_1 C (u1_struct_0 A))) ) )  => (v15_aofa_000 (k13_aofa_000 A B C) A)) ) ).
tt(fc12_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_hahnban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ((v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v4_bilinear (k9_bilinear A B C D E) A B C)) ) ) ) ).
tt(fc12_binop_2,ax, ((v1_funct_1 k33_binop_2) &  ((v1_funct_2 k33_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (v1_setwiseo k33_binop_2 k1_numbers)) ) ).
tt(fc12_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_rat_1 A))  &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k7_xcmplx_0 A B))) ) ) ).
tt(fc12_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_relat_1 (k1_wellord2 A)) & (v1_finset_1 (k1_wellord2 A))) ) ) ).
tt(fc12_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k12_card_3 A B)) &  ((v1_funct_1 (k12_card_3 A B)) & (v1_partfun1 (k12_card_3 A B) (k4_card_3 A))) ) ) ) ).
tt(fc12_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v2_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 B A)) &  ((v1_partfun1 (k18_valued_1 B A) k2_numbers) & (v2_cfdiff_1 (k18_valued_1 B A))) ) ) ) ).
tt(fc12_circcmb3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v6_circcmb3 A) & (l1_msualg_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v6_circcmb3 B) & (l1_msualg_1 B)) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v1_msualg_1 (k2_circcomb A B)) & (v6_circcmb3 (k2_circcomb A B))) ) ) ) ).
tt(fc12_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_circcomb A) & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v1_msualg_1 (k2_circcomb A B)) & (v2_circcomb (k2_circcomb A B))) ) ) ) ).
tt(fc12_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v2_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v7_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc12_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v17_closure2 B A) & (l1_closure2 B A)) )  => (v6_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc12_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  ( (~ (v1_xboole_0 (k12_cohsp_1 A B)))  &  ((v1_classes1 (k12_cohsp_1 A B)) & (v1_coh_sp (k12_cohsp_1 A B))) ) ) ) ).
tt(fc12_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc12_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) & (v2_compos_0 A)) )  & (m1_subset_1 B (k1_compos_0 A)))  => (v2_card_3 (k3_compos_0 A B))) ) ).
tt(fc12_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) &  ((v1_finset_1 (k7_compos_1 A B C)) & (v4_compos_1 (k7_compos_1 A B C) A)) ) ) ) ) ) ) ).
tt(fc12_comput_1,ax, ((v1_relat_1 (k5_comput_1 2 2)) &  ((v4_relat_1 (k5_comput_1 2 2) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 2 2)) &  ((v4_valued_0 (k5_comput_1 2 2)) &  ((v2_margrel1 (k5_comput_1 2 2)) & (v7_comput_1 (k5_comput_1 2 2))) ) ) ) ) ).
tt(fc12_comseq_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v1_comseq_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k24_valued_1 B A)) &  ((v1_funct_2 (k24_valued_1 B A) k5_numbers k2_numbers) & (v1_comseq_3 (k24_valued_1 B A))) ) ) ) ).
tt(fc12_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v3_dickson k11_dickson)) ).
tt(fc12_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k10_funcsdom (k2_finseq_1 A))))  &  ((v13_algstr_0 (k10_funcsdom (k2_finseq_1 A))) &  ((v2_monoid_0 (k10_funcsdom (k2_finseq_1 A))) &  ((v1_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v2_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v3_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v4_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v5_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v6_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v7_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) & (v8_rlvect_1 (k10_funcsdom (k2_finseq_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc12_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k50_valued_1 B C)) &  ((v1_funct_1 (k50_valued_1 B C)) & (v3_card_1 (k50_valued_1 B C) A)) ) ) ) ).
tt(fc12_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((v4_relat_1 (k10_funct_7 (k6_partfun1 A) B C) A) &  ((v5_relat_1 (k10_funct_7 (k6_partfun1 A) B C) A) & (v2_funct_1 (k10_funct_7 (k6_partfun1 A) B C))) ) ) ) ).
tt(fc12_facirc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xtuple_0 A))  &  (~ (v1_xtuple_0 B)) )  => (v2_facirc_1 (k10_finseq_1 A B))) ) ).
tt(fc12_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k24_valued_1 A B)) & (v2_fcont_1 (k24_valued_1 A B))) ) ) ).
tt(fc12_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ((v18_lattices (k8_filter_2 A B C) A) & (v21_lattices (k8_filter_2 A B C) A)) ) ) ).
tt(fc12_finseq_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k13_finseq_1 A))) ) ).
tt(fc12_finset_1,ax, (! [A:$i,B:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k4_xboole_0 A B))) ) ).
tt(fc12_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v14_fomodel1 B k6_numbers A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v4_fomodel1 (k1_funct_1 (k22_fomodel1 A) B) A)) ) ).
tt(fc12_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k5_relat_1 C (k37_fomodel1 A))) &  ((v1_funct_1 (k5_relat_1 C (k37_fomodel1 A))) & (v1_fomodel2 (k5_relat_1 C (k37_fomodel1 A)) A B)) ) ) ) ).
tt(fc12_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C)) )  => (v3_relat_2 (k9_fomodel3 A B C))) ) ).
tt(fc12_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v1_fomodel4 (k4_tarski (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B C) D) A)) ) ).
tt(fc12_funcop_1,ax, (! [A:$i,B:$i] : (v2_funct_1 (k16_funcop_1 A B))) ).
tt(fc12_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_funct_1 A)) )  => (v1_zfmisc_1 (k10_xtuple_0 A))) ) ).
tt(fc12_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (v4_relat_1 (k4_funct_4 B C D E) A)) ) ).
tt(fc12_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k10_funct_7 A B C)) & (v1_funct_1 (k10_funct_7 A B C))) ) ) ).
tt(fc12_funct_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_funct_9 A)) ) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v2_funct_9 (k39_valued_1 A))) ) ) ) ).
tt(fc12_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  &  ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A)) )  =>  ((v8_functor0 (k10_functor0 A B) B A) & (v9_functor0 (k10_functor0 A B) B A)) ) ) ).
tt(fc12_gate_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k5_gate_1 A B))) ) ) ).
tt(fc12_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v2_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v2_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(fc12_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (~ (v1_xboole_0 (k9_graph_3 A))) ) ) ).
tt(fc12_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v3_grcat_1 (k17_grcat_1 A))) ) ).
tt(fc12_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l3_algstr_0 B)) )  => (v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ).
tt(fc12_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld)) )  =>  ((v1_funct_1 (k1_bilinear k1_complfld A B)) &  ((v1_funct_2 (k1_bilinear k1_complfld A B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (v2_hermitan (k1_bilinear k1_complfld A B) A B)) ) ) ) ).
tt(fc12_hilbert3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (v1_hilbert3 (k3_hilbert1 (k4_hilbert1 A B) B))) ) ).
tt(fc12_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  &  ( ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_ideal_1 (k11_ideal_1 A B C) A)) ) ).
tt(fc12_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) =>  ((v1_relat_1 (k1_xtuple_0 C)) &  ((v4_relat_1 (k1_xtuple_0 C) A) &  ((v1_funct_1 (k1_xtuple_0 C)) & (v1_partfun1 (k1_xtuple_0 C) A)) ) ) ) ) ).
tt(fc12_jordan,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (v1_xreal_0 B))  => (v1_borsuk_1 (k2_brouwer 2 A B) (k15_euclid 2))) ) ).
tt(fc12_kurato_1,ax,(v1_tops_2 (k4_kurato_1 k3_topmetr k6_kurato_1) k3_topmetr)).
tt(fc12_lukasi_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (v2_cqc_the1 (k2_qc_lang2 A B (k6_cqc_lang A (k6_cqc_lang A B))) A)) ) ).
tt(fc12_matrix17,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (v3_matrix17 (k1_matrix_2 A A C) B A)) ) ).
tt(fc12_matrtop1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) ) ) ) )  => (v3_card_1 (k1_funct_1 (k3_matrtop1 A B C) D) B)) ) ).
tt(fc12_mazurulm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_mazurulm C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 B C)) &  ((v1_funct_2 (k3_relat_1 B C) (u1_struct_0 A) (u1_struct_0 A)) & (v3_mazurulm (k3_relat_1 B C) A A)) ) ) ) ).
tt(fc12_member_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k7_member_1 A)) & (v1_membered (k7_member_1 A))) ) ) ).
tt(fc12_membered,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v6_membered (k1_tarski A))) ) ).
tt(fc12_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v7_ordinal1 C) &  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v5_memstr_0 D A B C)) ) ) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v4_memstr_0 E A B)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_4 D E)) &  ((v1_funct_1 (k1_funct_4 D E)) & (v5_memstr_0 (k1_funct_4 D E) A B C)) ) ) ) ).
tt(fc12_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A)))) ) )  =>  ( (~ (v2_struct_0 (k48_modelc_1 A B C)))  & (v10_modelc_1 (k48_modelc_1 A B C))) ) ) ).
tt(fc12_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) )  =>  ((v1_relat_1 (k1_mboolean A B)) &  ((v4_relat_1 (k1_mboolean A B) A) &  ((v1_funct_1 (k1_mboolean A B)) &  ((v1_partfun1 (k1_mboolean A B) A) & (v2_finset_1 (k1_mboolean A B))) ) ) ) ) ) ).
tt(fc12_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k17_msualg_2 A B)))  &  ((v3_lattices (k17_msualg_2 A B)) &  ((v10_lattices (k17_msualg_2 A B)) & (v15_lattices (k17_msualg_2 A B))) ) ) ) ) ).
tt(fc12_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v2_mycielsk A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k3_necklace A)) & (v1_mycielsk (k3_necklace A))) ) ) ).
tt(fc12_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k6_nat_3 A B C)) &  ((v4_relat_1 (k6_nat_3 A B C) A) &  ((v1_funct_1 (k6_nat_3 A B C)) &  ((v1_partfun1 (k6_nat_3 A B C) A) & (v4_valued_0 (k6_nat_3 A B C))) ) ) ) ) ) ).
tt(fc12_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k1_neckla_3 A B))) ) ) ).
tt(fc12_newton,ax, (~ (v1_xboole_0 k10_newton)) ).
tt(fc12_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (v7_oposet_1 k1_oposet_1)) ).
tt(fc12_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v1_ordinal6 A) & (v1_ordinal6 B))  => (v1_ordinal6 (k2_xboole_0 A B))) ) ).
tt(fc12_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v3_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc12_pcs_0,ax, (! [A:$i] :  ( ((v3_pcs_0 A) & (l1_pcs_0 A))  => (v1_partfun1 (u1_pcs_0 A) (u1_struct_0 A))) ) ).
tt(fc12_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v4_algstr_1 (k14_polynom3 A))) ) ) ) ).
tt(fc12_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v3_group_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc12_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v13_algstr_0 (k14_polynom3 A)) & (v36_algstr_0 (k14_polynom3 A))) ) ) ) ).
tt(fc12_pre_poly,ax, (! [A:$i] : (v1_pre_poly (k6_finseq_1 A))) ).
tt(fc12_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v6_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v6_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc12_quaterni,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_quaterni B))  => (v1_quaterni (k23_quaterni A B))) ) ).
tt(fc12_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ( (~ (v1_ratfunc1 B A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v7_ordinal1 (k2_hurwitz A B)) & (v1_int_1 (k2_hurwitz A B))) ) ) ).
tt(fc12_rcomp_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_topmetr A) & (l1_pre_topc A))  &  ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v2_topalg_2 (k1_pre_topc A B))) ) ) ).
tt(fc12_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 B))  =>  ((v1_xboole_0 (k3_relat_1 A B)) & (v1_relat_1 (k3_relat_1 A B))) ) ) ).
tt(fc12_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_relat_2 A))  &  ((v1_relat_1 B) & (v3_relat_2 B)) )  => (v3_relat_2 (k4_xboole_0 A B))) ) ).
tt(fc12_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v2_seq_2 (k54_valued_1 A))) ) ) ) ) ).
tt(fc12_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_convex1 (k2_pre_topc A B) A)) ) ).
tt(fc12_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ((v7_lattices (k8_robbins1 A)) &  ((v8_lattices (k8_robbins1 A)) &  ((v9_lattices (k8_robbins1 A)) & (v4_robbins1 (k8_robbins1 A))) ) ) ) ) ).
tt(fc12_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_valued_0 (k11_finseq_1 A B C))) ) ).
tt(fc12_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v3_card_1 (k2_amistd_1 3 k1_scmfsa_2 (k11_scmfsa_2 A)) 1)) ) ).
tt(fc12_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  =>  (~ (v2_extpro_1 (k12_scmfsa_2 B A) 3 k1_scmfsa_2)) ) ) ).
tt(fc12_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  ((v1_scmfsa6c (k17_scmfsa_2 A B)) & (v2_scmfsa6c (k17_scmfsa_2 A B))) ) ) ).
tt(fc12_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  => (v5_funct_1 (k16_funcop_1 A B) (k2_memstr_0 3 k1_scmfsa_2))) ) ).
tt(fc12_scm_halt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scm_halt A)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_scm_halt B)) ) ) ) ) ) )  &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8b C A B)))  &  ((v1_relat_1 (k2_scmfsa8b C A B)) &  ((v4_relat_1 (k2_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8b C A B)) &  ((v1_finset_1 (k2_scmfsa8b C A B)) &  ((v1_afinsq_1 (k2_scmfsa8b C A B)) & (v2_scm_halt (k2_scmfsa8b C A B))) ) ) ) ) ) ) ) ) ).
tt(fc12_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ((v4_scmpds_4 B) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_4 A B)))  &  ((v1_relat_1 (k3_scmpds_4 A B)) &  ((v4_relat_1 (k3_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_4 A B)) &  ((v1_finset_1 (k3_scmpds_4 A B)) &  ((v1_afinsq_1 (k3_scmpds_4 A B)) & (v3_scmpds_4 (k3_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc12_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v6_compos_0 (k15_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc12_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_6 C D A B)))  &  ((v1_relat_1 (k3_scmpds_6 C D A B)) &  ((v4_relat_1 (k3_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_6 C D A B)) &  ((v1_finset_1 (k3_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k3_scmpds_6 C D A B)) & (v2_compos_1 (k3_scmpds_6 C D A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc12_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (v3_card_1 (k2_amistd_1 2 (k1_scmring2 A) (k8_scmring2 A B)) 1)) ) ).
tt(fc12_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  => (v1_finset_1 (k7_scmyciel A B))) ) ).
tt(fc12_setfam_1,ax, (! [A:$i,B:$i] :  ( ((v1_setfam_1 A) & (v1_setfam_1 B))  => (v1_setfam_1 (k2_xboole_0 A B))) ) ).
tt(fc12_sfmastr1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_scmfsa_2 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  => (v1_sfmastr1 (k15_scmfsa_2 C B A))) ) ).
tt(fc12_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_setfam_1 B))  &  ((v1_classes1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v2_setfam_1 (k3_simplex0 A B C))) ) ) ).
tt(fc12_sincos10,ax, ((v1_relat_1 (k5_relat_1 k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))))) ).
tt(fc12_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc12_sppol_2,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (v4_topreal1 (k3_finseq_5 A))) ) ).
tt(fc12_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k2_goboard9 A))) ) ) ).
tt(fc12_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_stacks_1 A)))  &  ( (~ (v11_struct_0 (k14_stacks_1 A)))  & (v1_stacks_1 (k14_stacks_1 A))) ) ) ) ).
tt(fc12_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (~ (v1_subset_1 (k2_struct_0 A) (u1_struct_0 A))) ) ) ).
tt(fc12_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) )  =>  (~ (v1_xboole_0 (k4_zfmisc_1 A B C D))) ) ) ).
tt(fc12_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_subset_1 B (u1_struct_0 A)))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_subset_1 (k3_tex_4 A B) (u1_struct_0 A))) ) ) ).
tt(fc12_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v6_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  =>  ((v1_xreal_0 (k1_xxreal_2 (k9_xtuple_0 B))) & (v1_xxreal_0 (k1_xxreal_2 (k9_xtuple_0 B)))) ) ) ).
tt(fc12_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_topgrp_1 A B)) &  ((v1_funct_2 (k1_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v5_pre_topc (k1_topgrp_1 A B) A A)) ) ) ) ).
tt(fc12_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v1_convex1 (k2_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc12_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k1_xxreal_1 A B))) ) ) ).
tt(fc12_toprealb,ax, (! [A:$i] :  ( ((v2_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v4_pre_topc (k5_toprealb A) k2_topalg_2)) ) ).
tt(fc12_toprealc,ax, (! [A:$i] :  ( ((v2_toprealc A) & (l1_struct_0 A))  => (v3_valued_2 (u1_struct_0 A))) ) ).
tt(fc12_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_tops_1 (k2_struct_0 A) A)) ) ).
tt(fc12_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  => (v5_trees_3 (k5_finseq_1 A))) ) ).
tt(fc12_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_valued_0 A))  &  ((v1_relat_1 B) & (v4_valued_0 B)) )  => (v4_valued_0 (k2_xboole_0 A B))) ) ).
tt(fc12_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v1_finseq_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc12_vectsp10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_vectsp10 A B C)) &  ((v1_funct_2 (k11_vectsp10 A B C) (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C))) (u1_struct_0 A)) &  ((v13_vectsp_1 (k11_vectsp10 A B C) (k6_vectsp10 A B (k9_vectsp10 A B C)) A) &  ((v1_hahnban1 (k11_vectsp10 A B C) A (k6_vectsp10 A B (k9_vectsp10 A B C))) &  (~ (v2_vectsp10 (k11_vectsp10 A B C) A (k6_vectsp10 A B (k9_vectsp10 A B C)))) ) ) ) ) ) ) ).
tt(fc12_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v12_waybel_0 (k5_waybel_0 A B) A)) ) ).
tt(fc12_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k5_waybel10 A)) &  ((v1_funct_2 (k5_waybel10 A) (u1_struct_0 (k2_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)))) & (v23_waybel_0 (k5_waybel10 A) (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)))) ) ) ) ).
tt(fc12_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v8_yellow_6 (k2_waybel11 A) A)) ) ).
tt(fc12_waybel18,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A B))) &  ((v1_lattice3 (k5_yellow_1 A (k7_funcop_1 A B))) & (v3_lattice3 (k5_yellow_1 A (k7_funcop_1 A B)))) ) ) ) ).
tt(fc12_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_orders_2 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc12_waybel24,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_struct_0 A B C)) &  ((v1_funct_2 (k6_struct_0 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v22_waybel_0 (k6_struct_0 A B C) A B)) ) ) ) ).
tt(fc12_waybel25,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 (k1_waybel25 A))))  => (v4_pre_topc (k5_waybel_0 (k1_waybel25 A) B) (k1_waybel25 A))) ) ).
tt(fc12_waybel_2,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_waybel_1 A B)) &  ((v1_funct_2 (k4_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v22_waybel_0 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(fc12_waybel_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v2_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (v12_waybel_0 (k5_waybel_4 A B C) A)) ) ).
tt(fc12_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v3_waybel_8 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc12_waybel_9,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  ((v4_orders_2 (k2_waybel_9 A)) & (v6_waybel_0 (k2_waybel_9 A) A)) ) ) ).
tt(fc12_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v2_xxreal_0 (k2_xcmplx_0 B A))) ) ).
tt(fc12_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v3_membered (k1_xxreal_1 A B))) ) ).
tt(fc12_xxreal_2,ax,(v6_xxreal_2 k7_numbers)).
tt(fc12_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) & (v3_xxreal_0 (k1_xxreal_3 A B))) ) ) ).
tt(fc12_yellow10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v3_waybel_8 (k3_yellow_3 A B))) ) ) ).
tt(fc12_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v3_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(fc12_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ( (~ (v2_struct_0 (k3_yellow_6 A B C)))  & (v6_waybel_0 (k3_yellow_6 A B C) B)) ) ) ).
tt(fc12_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k1_yellow_7 A)) &  ((v2_funct_1 (k1_yellow_7 A)) & (v1_funct_2 (k1_yellow_7 A) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 A)))) ) ) ) ).
tt(fc130_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v1_partfun1 (k45_valued_1 B C) A)) ) ) ) ).
tt(fc131_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v1_partfun1 (k18_valued_1 B C) A)) ) ) ) ).
tt(fc132_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k50_valued_1 B C)) &  ((v1_funct_1 (k50_valued_1 B C)) & (v1_partfun1 (k50_valued_1 B C) A)) ) ) ) ).
tt(fc133_valued_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) ) ) )  =>  ((v1_relat_1 (k63_valued_1 B)) &  ((v5_relat_1 (k63_valued_1 B) A) & (v1_funct_1 (k63_valued_1 B))) ) ) ) ).
tt(fc13_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  => (v5_abcmiz_1 (k30_abcmiz_1 A (k15_abcmiz_1 A) B) A (k28_abcmiz_1 A))) ) ).
tt(fc13_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  =>  (~ (v1_abian (k6_xcmplx_0 A B))) ) ) ).
tt(fc13_afinsq_1,ax, (! [A:$i] : (v3_card_1 (k3_afinsq_1 A) 1)) ).
tt(fc13_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v1_finset_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc13_algstr_0,ax, (! [A:$i,B:$i] :  ( ((v1_zfmisc_1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ((v7_struct_0 (g3_algstr_0 A B)) & (v15_algstr_0 (g3_algstr_0 A B))) ) ) ).
tt(fc13_algstr_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k12_algstr_4 A)))  =>  ( (~ (v1_xboole_0 (k2_xtuple_0 B)))  & (v7_ordinal1 (k2_xtuple_0 B))) ) ) ).
tt(fc13_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  => (v3_card_1 (k2_amistd_1 2 k1_ami_3 (k8_ami_3 B A)) 1)) ) ).
tt(fc13_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( ((v15_aofa_000 B A) & (m1_subset_1 B (u1_struct_0 A)))  &  ( ((v15_aofa_000 C A) & (m1_subset_1 C (u1_struct_0 A)))  &  ((v15_aofa_000 D A) & (m1_subset_1 D (u1_struct_0 A))) ) ) )  => (v15_aofa_000 (k14_aofa_000 A B C D) A)) ) ).
tt(fc13_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l6_algstr_0 A)) )  &  ( ( (~ (v7_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) )  =>  ( (~ (v1_zfmisc_1 (k9_bilinear A B C D E)))  &  ((v1_funct_1 (k9_bilinear A B C D E)) & (v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))) ) ) ) ).
tt(fc13_binop_2,ax, ((v1_funct_1 k39_binop_2) &  ((v1_funct_2 k39_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (v1_setwiseo k39_binop_2 k3_numbers)) ) ).
tt(fc13_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_rat_1 A))  &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k7_xcmplx_0 B A))) ) ) ).
tt(fc13_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_c0sp2 A)))  & (v1_rlsub_1 (k6_c0sp2 A) (k10_funcsdom (u1_struct_0 A)))) ) ) ).
tt(fc13_card_1,ax, (! [A:$i] : (v3_card_1 (k1_tarski A) 1)) ).
tt(fc13_card_3,ax, (! [A:$i,B:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_finset_1 (k2_funcop_1 A B))) ) ) ).
tt(fc13_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_cc0sp2 A)))  & (v6_clvect_1 (k6_cc0sp2 A) (k6_cfuncdom (u1_struct_0 A)))) ) ) ).
tt(fc13_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k9_nat_1 A B)) &  ((v2_relat_1 (k9_nat_1 A B)) &  ((v4_relat_1 (k9_nat_1 A B) k5_numbers) &  ((v1_funct_1 (k9_nat_1 A B)) & (v1_partfun1 (k9_nat_1 A B) k5_numbers)) ) ) ) ) ) ).
tt(fc13_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) &  ((v4_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) & (v4_circcomb (k7_circcomb A B C D) (k5_circcomb C D))) ) ) ) ).
tt(fc13_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v3_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v8_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc13_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) B)))) )  =>  ((v4_msualg_1 (g1_closure2 A B C) A) & (v11_closure2 (g1_closure2 A B C) A)) ) ) ).
tt(fc13_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ( (~ (v1_xboole_0 (k13_cohsp_1 A)))  &  ((v1_classes1 (k13_cohsp_1 A)) & (v1_coh_sp (k13_cohsp_1 A))) ) ) ) ).
tt(fc13_coh_sp,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k28_coh_sp A)))  &  ( (~ (v11_struct_0 (k28_coh_sp A)))  &  ((v1_cat_1 (k28_coh_sp A)) &  ((v2_cat_1 (k28_coh_sp A)) &  ((v3_cat_1 (k28_coh_sp A)) &  ((v4_cat_1 (k28_coh_sp A)) & (v5_cat_1 (k28_coh_sp A))) ) ) ) ) ) ) ).
tt(fc13_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  =>  ((v1_relat_1 (k5_xtuple_0 B)) &  ((v5_relat_1 (k5_xtuple_0 B) k5_numbers) & (v1_funct_1 (k5_xtuple_0 B))) ) ) ) ).
tt(fc13_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k10_compos_1 A B)))  &  ((v1_relat_1 (k10_compos_1 A B)) &  ((v4_relat_1 (k10_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k10_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k10_compos_1 A B)) &  ((v1_finset_1 (k10_compos_1 A B)) & (v1_afinsq_1 (k10_compos_1 A B))) ) ) ) ) ) ) ) ).
tt(fc13_comput_1,ax, ((v1_relat_1 (k4_comput_1 1 1)) &  ((v4_relat_1 (k4_comput_1 1 1) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 1 1)) &  ((v4_valued_0 (k4_comput_1 1 1)) &  ((v2_margrel1 (k4_comput_1 1 1)) & (v7_comput_1 (k4_comput_1 1 1))) ) ) ) ) ).
tt(fc13_comseq_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k9_nat_1 A B)) &  ((v1_funct_2 (k9_nat_1 A B) k5_numbers k2_numbers) & (v1_comseq_3 (k9_nat_1 A B))) ) ) ) ).
tt(fc13_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v5_orders_2 k11_dickson)) ).
tt(fc13_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (k8_euclid_7 A))) ) ).
tt(fc13_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k7_valued_1 C A)) &  ((v1_funct_1 (k7_valued_1 C A)) & (v3_card_1 (k7_valued_1 C A) B)) ) ) ) ).
tt(fc13_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((v1_partfun1 (k10_funct_7 (k6_partfun1 A) B C) A) & (v2_funct_2 (k10_funct_7 (k6_partfun1 A) B C) A)) ) ) ).
tt(fc13_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xtuple_0 A))  &  ( (~ (v1_xtuple_0 B))  &  (~ (v1_xtuple_0 C)) ) )  => (v2_facirc_1 (k11_finseq_1 A B C))) ) ).
tt(fc13_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k54_valued_1 A)) & (v2_fcont_1 (k54_valued_1 A))) ) ) ).
tt(fc13_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  ((v3_lattices (k1_lattice2 A)) &  ((v10_lattices (k1_lattice2 A)) & (v17_lattices (k1_lattice2 A))) ) ) ) ).
tt(fc13_finseq_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_finseq_1 (k5_relat_1 A B))) ) ) ).
tt(fc13_finset_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  & (v1_finset_1 B))  => (v1_finset_1 (k7_relat_1 A B))) ) ).
tt(fc13_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v8_fomodel1 (k1_funct_1 (k22_fomodel1 A) B) A)) ) ).
tt(fc13_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k5_relat_1 C (k37_fomodel1 A))) &  ((v4_relat_1 (k5_relat_1 C (k37_fomodel1 A)) (k37_fomodel1 A)) & (v1_partfun1 (k5_relat_1 C (k37_fomodel1 A)) (k37_fomodel1 A))) ) ) ) ).
tt(fc13_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C)) )  =>  ((v1_partfun1 (k9_fomodel3 A B C) (k4_finseq_2 C A)) & (v3_relat_2 (k9_fomodel3 A B C))) ) ) ).
tt(fc13_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k33_fomodel2 A)))) ) ) )  => (v1_fomodel4 (k4_tarski (k2_xboole_0 D (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B)) C) A)) ) ).
tt(fc13_funcop_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_funcop_1 (k5_relat_1 A B))) ) ) ).
tt(fc13_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  (~ (v3_funct_1 A)) ) )  =>  (~ (v1_zfmisc_1 (k10_xtuple_0 A))) ) ) ).
tt(fc13_funct_4,ax, (! [A:$i,B:$i] : (v1_zfmisc_1 (k16_funcop_1 A B))) ).
tt(fc13_funct_7,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k11_funct_7 A B)) & (v1_funct_1 (k11_funct_7 A B))) ) ).
tt(fc13_funct_9,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos k1_numbers k1_numbers) & (v2_funct_9 k16_sin_cos)) ) ).
tt(fc13_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  ((v8_functor0 (k11_functor0 A) A A) &  ((v9_functor0 (k11_functor0 A) A A) & (v10_functor0 (k11_functor0 A) A A)) ) ) ) ).
tt(fc13_gate_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) =>  (~ (v1_xboole_0 (k6_gate_1 A B))) ) ) ).
tt(fc13_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v3_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v3_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(fc13_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v2_struct_0 (k25_grcat_1 A)))  &  ( (~ (v11_struct_0 (k25_grcat_1 A)))  & (v1_cat_1 (k25_grcat_1 A))) ) ) ) ).
tt(fc13_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l3_algstr_0 B)) )  =>  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) & (v1_group_7 (k10_finseq_1 A B))) ) ) ).
tt(fc13_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  ((v1_funct_1 (k1_bilinear k1_complfld A A)) &  ((v1_funct_2 (k1_bilinear k1_complfld A A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v3_hermitan (k1_bilinear k1_complfld A A) A)) ) ) ) ).
tt(fc13_hilbert3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_hilbert1) & (m1_subset_1 B k1_hilbert1))  => (v1_hilbert3 (k3_hilbert1 A (k3_hilbert1 B (k4_hilbert1 A B))))) ) ).
tt(fc13_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) )  &  ( ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_ideal_1 (k11_ideal_1 A B C) A)) ) ).
tt(fc13_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) =>  ((v1_relat_1 (k2_xtuple_0 C)) &  ((v4_relat_1 (k2_xtuple_0 C) B) &  ((v1_funct_1 (k2_xtuple_0 C)) & (v1_partfun1 (k2_xtuple_0 C) B)) ) ) ) ) ).
tt(fc13_jordan,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (v1_xreal_0 B))  => (v1_compts_1 (k2_brouwer 2 A B))) ) ).
tt(fc13_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_finset_1 (k3_kurato_1 A B))) ) ).
tt(fc13_lukasi_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (v2_cqc_the1 (k2_qc_lang2 A (k6_cqc_lang A (k6_cqc_lang A B)) B) A)) ) ).
tt(fc13_matrtop1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_matrix_6 B A k2_vectsp_1) & (m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A)) )  =>  ((v1_funct_1 (k3_matrtop1 A A B)) &  ((v1_funct_2 (k3_matrtop1 A A B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_tops_2 (k3_matrtop1 A A B) (k15_euclid A) (k15_euclid A))) ) ) ) ).
tt(fc13_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) & (v3_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A A)) ) ) ) ).
tt(fc13_member_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  =>  ( (~ (v1_xboole_0 (k7_member_1 A)))  & (v1_membered (k7_member_1 A))) ) ) ).
tt(fc13_membered,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_membered (k2_tarski A B))) ) ).
tt(fc13_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((v1_relat_1 (k8_memstr_0 A B C)) &  ((v4_relat_1 (k8_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k8_memstr_0 A B C)) &  ((v5_funct_1 (k8_memstr_0 A B C) (k2_memstr_0 A B)) & (v5_memstr_0 (k8_memstr_0 A B C) A B k6_numbers)) ) ) ) ) ) ).
tt(fc13_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ( (~ (v2_struct_0 (k3_mod_4 A B)))  & (v2_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A))) ) ) ).
tt(fc13_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_necklace (k5_mycielsk A)) & (v3_necklace (k5_mycielsk A))) ) ) ).
tt(fc13_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k6_nat_3 A B C)) &  ((v4_relat_1 (k6_nat_3 A B C) A) &  ((v1_funct_1 (k6_nat_3 A B C)) &  ((v1_partfun1 (k6_nat_3 A B C) A) & (v2_pre_poly (k6_nat_3 A B C))) ) ) ) ) ) ).
tt(fc13_newton,ax,(v1_xboole_0 (k11_newton 2))).
tt(fc13_ordinal6,ax, (! [A:$i,B:$i] :  ((v1_ordinal6 A) => (v1_ordinal6 (k4_xboole_0 A B))) ) ).
tt(fc13_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v4_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc13_pcs_0,ax, (! [A:$i] :  ( ((v4_pcs_0 A) & (l1_pcs_0 A))  => (v1_relat_2 (u1_pcs_0 A))) ) ).
tt(fc13_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) &  ((v1_vectsp_1 (k11_polynom1 A B)) & (v4_vectsp_1 (k11_polynom1 A B))) ) ) ) ) ).
tt(fc13_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v5_group_1 (k14_polynom3 A))) ) ) ) ).
tt(fc13_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v1_pre_poly (k5_finseq_1 A))) ) ).
tt(fc13_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v7_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v7_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v7_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc13_quaterni,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_quaterni B))  => (v1_quaterni (k25_quaterni A B))) ) ).
tt(fc13_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l6_algstr_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ( (~ (v1_ratfunc1 B A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  (~ (v9_struct_0 (k2_ratfunc1 A B) A)) ) ) ).
tt(fc13_rcomp_3,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v6_xxreal_2 (k5_toprealb A))) ) ).
tt(fc13_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 B))  =>  ((v1_xboole_0 (k3_relat_1 B A)) & (v1_relat_1 (k3_relat_1 B A))) ) ) ).
tt(fc13_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v5_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc13_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_comseq_2 A)) ) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v1_comseq_2 (k54_valued_1 A))) ) ) ) ) ).
tt(fc13_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_convex1 (k1_tops_1 A B) A)) ) ).
tt(fc13_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_robbins1 A) & (l2_robbins1 A)) )  =>  ((v4_robbins1 (k8_robbins1 A)) & (v6_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc13_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_valued_0 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc13_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v3_card_1 (k2_amistd_1 3 k1_scmfsa_2 (k12_scmfsa_2 B A)) 1)) ) ).
tt(fc13_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  =>  (~ (v2_extpro_1 (k13_scmfsa_2 B A) 3 k1_scmfsa_2)) ) ) ).
tt(fc13_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v2_scmfsa6c (k6_scmfsa_2 A B))) ) ).
tt(fc13_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ((v4_scmpds_4 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ((v4_scmpds_4 B) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_4 A B)))  &  ((v1_relat_1 (k4_scmpds_4 A B)) &  ((v4_relat_1 (k4_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_4 A B)) &  ((v1_finset_1 (k4_scmpds_4 A B)) &  ((v1_afinsq_1 (k4_scmpds_4 A B)) & (v3_scmpds_4 (k4_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc13_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v6_compos_0 (k16_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc13_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k7_scmpds_6 B C A)))  &  ((v1_relat_1 (k7_scmpds_6 B C A)) &  ((v4_relat_1 (k7_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k7_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k7_scmpds_6 B C A)) &  ((v1_finset_1 (k7_scmpds_6 B C A)) &  ((v1_afinsq_1 (k7_scmpds_6 B C A)) &  ((v2_scmpds_4 (k7_scmpds_6 B C A)) & (v3_scmpds_4 (k7_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc13_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  => (v3_card_1 (k2_amistd_1 2 (k1_scmring2 A) (k9_scmring2 A C B)) 1)) ) ).
tt(fc13_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v4_scmyciel A) & (v1_finset_1 B))  => (v1_finset_1 (k7_scmyciel A B))) ) ).
tt(fc13_setfam_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  =>  (~ (v1_xboole_0 (k3_tarski A))) ) ) ).
tt(fc13_sfmastr1,ax, (! [A:$i] :  ( ((v1_sfmastr1 A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v4_relat_1 (k11_compos_1 k1_scmfsa_2 A) k5_numbers) &  ((v5_relat_1 (k11_compos_1 k1_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v1_finset_1 (k11_compos_1 k1_scmfsa_2 A)) & (v1_scmfsa7b (k11_compos_1 k1_scmfsa_2 A))) ) ) ) ) ) ) ).
tt(fc13_simplex0,ax, (! [A:$i] :  ( ( (~ (v4_simplex0 A))  & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (k4_simplex0 A))) ) ) ).
tt(fc13_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(fc13_sppol_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v2_compts_1 (k1_rltopsp1 (k15_euclid A) B C) (k15_euclid A))) ) ).
tt(fc13_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_goboard9 A))) ) ) ).
tt(fc13_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (v2_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(fc13_struct_0,ax, (! [A:$i] :  ( ((v11_struct_0 A) & (l5_struct_0 A))  => (v1_xboole_0 (u4_struct_0 A))) ) ).
tt(fc13_subset_1,ax, (! [A:$i] : (v1_xboole_0 (k1_subset_1 A))) ).
tt(fc13_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_zfmisc_1 (k3_tex_4 A B))) ) ) ).
tt(fc13_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k2_topgrp_1 A B)) &  ((v1_funct_2 (k2_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v5_pre_topc (k2_topgrp_1 A B) A A)) ) ) ) ).
tt(fc13_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k6_struct_0 (k15_euclid A) (k15_euclid A) (k4_struct_0 (k15_euclid A)))) &  ((v1_funct_2 (k6_struct_0 (k15_euclid A) (k15_euclid A) (k4_struct_0 (k15_euclid A))) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 (k6_struct_0 (k15_euclid A) (k15_euclid A) (k4_struct_0 (k15_euclid A))) (k15_euclid A) (k15_euclid A)) & (v1_topreal9 (k6_struct_0 (k15_euclid A) (k15_euclid A) (k4_struct_0 (k15_euclid A))) A)) ) ) ) ) ).
tt(fc13_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  (~ (v1_xboole_0 (k4_xxreal_1 A B))) ) ) ).
tt(fc13_toprealb,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((v1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb A))) & (v1_tsep_1 (k1_pre_topc k2_topalg_2 (k5_toprealb A)) k2_topalg_2)) ) ) ).
tt(fc13_toprealc,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k2_toprealc A)) & (v1_valued_2 (k2_toprealc A))) ) ) ).
tt(fc13_tops_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ((v2_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k1_tops_1 A B))) ) ).
tt(fc13_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) )  => (v5_trees_3 (k10_finseq_1 A B))) ) ).
tt(fc13_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_valued_0 A))  & (v1_relat_1 B))  => (v1_valued_0 (k3_xboole_0 A B))) ) ).
tt(fc13_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v1_valued_0 (k7_valued_1 A B))) ) ) ) ).
tt(fc13_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v13_waybel_0 (k6_waybel_0 A B) A)) ) ).
tt(fc13_waybel10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) ) )  =>  ((v1_funct_1 (k6_waybel10 A B)) &  ((v1_funct_2 (k6_waybel10 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v22_waybel_0 (k6_waybel10 A B) A A)) ) ) ) ).
tt(fc13_waybel18,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v2_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A B))) & (v2_waybel_8 (k5_yellow_1 A (k7_funcop_1 A B)))) ) ) ).
tt(fc13_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v5_orders_2 A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v5_orders_2 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc13_waybel24,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v3_lattice3 (k3_waybel24 A B))) ) ) ).
tt(fc13_waybel25,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v10_waybel_0 C (k3_waybel24 A (k1_waybel25 B))) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) ) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ( (~ (v2_struct_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D)))  &  ((v4_orders_2 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D)) &  ((v6_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D) (k1_waybel25 B)) &  ((v7_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D)) & (v10_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D) (k1_waybel25 B))) ) ) ) ) ) ).
tt(fc13_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k10_waybel34 A)))  &  ((v2_altcat_1 (k10_waybel34 A)) &  ((v6_altcat_1 (k10_waybel34 A)) &  ((v2_altcat_2 (k10_waybel34 A) (k8_waybel34 A)) &  ((v3_altcat_2 (k10_waybel34 A) (k8_waybel34 A)) & (v3_yellow21 (k10_waybel34 A))) ) ) ) ) ) ) ).
tt(fc13_waybel_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v3_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (v1_waybel_0 (k5_waybel_4 A B C) A)) ) ).
tt(fc13_waybel_8,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  ((v1_waybel_0 (k2_waybel_8 (k3_yellow_1 A) B) (k3_yellow_1 A)) & (v12_waybel_0 (k2_waybel_8 (k3_yellow_1 A) B) (k3_yellow_1 A))) ) ) ).
tt(fc13_waybel_9,ax, (! [A:$i] :  ( ((v1_lattice3 A) & (l1_orders_2 A))  =>  ((v6_waybel_0 (k2_waybel_9 A) A) & (v7_waybel_0 (k2_waybel_9 A))) ) ) ).
tt(fc13_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v3_xxreal_0 (k2_xcmplx_0 A B))) ) ).
tt(fc13_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v6_xxreal_2 (k1_xxreal_1 A B))) ) ).
tt(fc13_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 B A)) & (v3_xxreal_0 (k1_xxreal_3 B A))) ) ) ).
tt(fc13_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v13_struct_0 (k6_yellow_1 k1_xboole_0 A) 1) & (v1_orders_2 (k6_yellow_1 k1_xboole_0 A))) ) ) ).
tt(fc13_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v7_waybel_0 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v6_waybel_0 (k3_yellow_6 A B C) B) & (v7_waybel_0 (k3_yellow_6 A B C))) ) ) ).
tt(fc13_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k1_yellow_7 A)) &  ((v1_funct_2 (k1_yellow_7 A) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 A))) & (v23_waybel_0 (k1_yellow_7 A) A (k7_lattice3 A))) ) ) ) ).
tt(fc14_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) )  => (v5_abcmiz_1 (k31_abcmiz_1 A (k16_abcmiz_1 A) B C) A (k28_abcmiz_1 A))) ) ).
tt(fc14_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  =>  (~ (v1_abian (k6_xcmplx_0 B A))) ) ) ).
tt(fc14_afinsq_1,ax, (! [A:$i,B:$i] : (v3_card_1 (k6_afinsq_1 A B) 2)) ).
tt(fc14_algstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ( (~ (v7_struct_0 (g3_algstr_0 A B)))  & (v15_algstr_0 (g3_algstr_0 A B))) ) ) ).
tt(fc14_algstr_4,ax, (! [A:$i] : (v15_algstr_0 (k14_algstr_4 A))) ).
tt(fc14_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  => (v3_card_1 (k2_amistd_1 2 k1_ami_3 (k9_ami_3 B A)) 1)) ) ).
tt(fc14_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  &  ( ((v15_aofa_000 B A) & (m1_subset_1 B (u1_struct_0 A)))  &  ((v15_aofa_000 C A) & (m1_subset_1 C (u1_struct_0 A))) ) )  => (v15_aofa_000 (k15_aofa_000 A B C) A)) ) ).
tt(fc14_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l6_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v7_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) )  =>  ( (~ (v1_zfmisc_1 (k9_bilinear A B C D E)))  &  ((v1_funct_1 (k9_bilinear A B C D E)) & (v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))) ) ) ) ).
tt(fc14_binop_2,ax, ((v1_funct_1 k44_binop_2) &  ((v1_funct_2 k44_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (v1_setwiseo k44_binop_2 k4_numbers)) ) ).
tt(fc14_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  &  ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  => (v3_rcomp_1 (k3_xboole_0 A B))) ) ).
tt(fc14_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_c0sp2 A)))  & (v1_normsp_1 (k9_c0sp2 A))) ) ) ).
tt(fc14_card_1,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_card_1 B A)) ) )  => (v3_card_1 (k9_xtuple_0 B) A)) ) ).
tt(fc14_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  (~ (v1_finset_1 A)) )  =>  (~ (v1_finset_1 (k1_relat_1 A))) ) ) ).
tt(fc14_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_cc0sp2 A)))  & (v7_clvect_1 (k9_cc0sp2 A))) ) ) ).
tt(fc14_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_cfdiff_1 A k6_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k9_nat_1 A B)) &  ((v1_funct_2 (k9_nat_1 A B) k5_numbers k2_numbers) & (v1_cfdiff_1 (k9_nat_1 A B) k6_numbers)) ) ) ) ).
tt(fc14_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ( (~ (v11_struct_0 (k5_circcomb C D)))  &  ((v1_msualg_1 (k5_circcomb C D)) & (v5_circcomb (k5_circcomb C D))) ) ) ) ).
tt(fc14_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v4_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v9_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc14_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v1_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v12_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc14_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  ( (~ (v1_xboole_0 (k15_cohsp_1 A B)))  &  ((v1_classes1 (k15_cohsp_1 A B)) & (v1_coh_sp (k15_cohsp_1 A B))) ) ) ) ).
tt(fc14_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) &  ((v2_compos_0 A) & (v3_compos_0 A)) ) )  & (m1_subset_1 B (k1_compos_0 A)))  => (v3_card_3 (k3_compos_0 A B))) ) ).
tt(fc14_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) & (m1_subset_1 B (u1_compos_1 A)))  =>  ( (~ (v1_xboole_0 (k11_compos_1 A B)))  &  ((v1_relat_1 (k11_compos_1 A B)) &  ((v4_relat_1 (k11_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k11_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k11_compos_1 A B)) &  ((v1_finset_1 (k11_compos_1 A B)) & (v1_afinsq_1 (k11_compos_1 A B))) ) ) ) ) ) ) ) ).
tt(fc14_comput_1,ax, ((v1_relat_1 (k4_comput_1 3 3)) &  ((v4_relat_1 (k4_comput_1 3 3) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 3 3)) &  ((v4_valued_0 (k4_comput_1 3 3)) &  ((v2_margrel1 (k4_comput_1 3 3)) & (v7_comput_1 (k4_comput_1 3 3))) ) ) ) ) ).
tt(fc14_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A))) &  ((v1_funct_2 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A)) k5_numbers k1_numbers) & (v1_seq_2 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A)))) ) ) ) ).
tt(fc14_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v4_orders_2 k11_dickson)) ).
tt(fc14_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k10_funcsdom (k2_finseq_1 A))))  &  ((v13_algstr_0 (k10_funcsdom (k2_finseq_1 A))) &  ((v1_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v2_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v3_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v4_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v5_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v6_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v7_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) &  ((v8_rlvect_1 (k10_funcsdom (k2_finseq_1 A))) & (v1_rlvect_5 (k10_funcsdom (k2_finseq_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc14_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k13_valued_1 C A)) &  ((v1_funct_1 (k13_valued_1 C A)) & (v3_card_1 (k13_valued_1 C A) B)) ) ) ) ).
tt(fc14_exchsort,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v1_xboole_0 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) ) )  => (v1_xboole_0 (k6_exchsort A B))) ) ).
tt(fc14_facirc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_facirc_1 A)) )  =>  (~ (v1_facirc_1 (k10_xtuple_0 A))) ) ) ).
tt(fc14_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_funct_1 (k4_relat_1 A)) & (v2_fcont_1 (k4_relat_1 A))) ) ) ).
tt(fc14_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v3_lattices (k10_filter_2 A B))) ) ).
tt(fc14_finseq_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 (k6_relat_1 B A)) & (v2_finseq_1 (k6_relat_1 B A))) ) ) ).
tt(fc14_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k2_zfmisc_1 A B))) ) ).
tt(fc14_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  => (v12_fomodel1 (k1_funct_1 (k28_fomodel1 A) B) A)) ) ).
tt(fc14_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k15_fomodel2 A B))) ) ) ).
tt(fc14_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C)) )  =>  ((v1_partfun1 (k9_fomodel3 A B C) (k4_finseq_2 C A)) & (v8_relat_2 (k9_fomodel3 A B C))) ) ) ).
tt(fc14_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v7_fomodel4 (k1_tarski (k4_tarski k1_xboole_0 (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) B))) A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k24_fomodel4 A)))) ) ).
tt(fc14_funcop_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (v1_funcop_1 (k2_funcop_1 A B))) ) ).
tt(fc14_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v4_funct_1 (k1_tarski A))) ) ).
tt(fc14_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ((v1_relat_1 (k13_funct_7 A B C)) & (v1_funct_1 (k13_funct_7 A B C))) ) ).
tt(fc14_funct_9,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos k1_numbers k1_numbers) & (v2_funct_9 k19_sin_cos)) ) ).
tt(fc14_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ((v9_functor0 (k11_functor0 A) A A) &  ((v12_functor0 (k11_functor0 A) A A) & (v13_functor0 (k11_functor0 A) A A)) ) ) ) ).
tt(fc14_gate_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (v1_xboole_0 (k6_gate_1 A B))) ) ).
tt(fc14_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v4_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(fc14_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v2_struct_0 (k25_grcat_1 A)))  &  ( (~ (v11_struct_0 (k25_grcat_1 A)))  &  ((v1_cat_1 (k25_grcat_1 A)) &  ((v2_cat_1 (k25_grcat_1 A)) & (v5_cat_1 (k25_grcat_1 A))) ) ) ) ) ) ).
tt(fc14_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) ) )  => (v2_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ).
tt(fc14_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  ((v1_funct_1 (k1_bilinear k1_complfld A A)) &  ((v1_funct_2 (k1_bilinear k1_complfld A A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (v5_hermitan (k1_bilinear k1_complfld A A) A)) ) ) ) ).
tt(fc14_hilbert3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_hilbert1) &  ((m1_subset_1 B k1_hilbert1) & (m1_subset_1 C k1_hilbert1)) )  => (v1_hilbert3 (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B C)) (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 A C))))) ) ).
tt(fc14_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) )  &  ( ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_ideal_1 (k11_ideal_1 A B C) A)) ) ).
tt(fc14_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v2_index_1 C A B) & (m1_index_1 C A B))  => (v1_index_1 (k1_xtuple_0 C))) ) ).
tt(fc14_jordan,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v4_pre_topc (k2_jgraph_6 A B C D) (k15_euclid 2))) ) ).
tt(fc14_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_finset_1 (k4_kurato_1 A B))) ) ).
tt(fc14_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C) (k8_cqc_lang A B C)) A)) ) ).
tt(fc14_mazurulm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_mazurulm C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 B C)) &  ((v1_funct_2 (k3_relat_1 B C) (u1_struct_0 A) (u1_struct_0 A)) & (v2_mazurulm (k3_relat_1 B C) A A)) ) ) ) ).
tt(fc14_member_1,ax, (! [A:$i] :  ((v3_membered A) =>  ((v1_membered (k7_member_1 A)) & (v3_membered (k7_member_1 A))) ) ) ).
tt(fc14_membered,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v2_membered (k2_tarski A B))) ) ).
tt(fc14_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) ) ) )  =>  ((v1_relat_1 (k8_memstr_0 A B C)) &  ((v4_relat_1 (k8_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k8_memstr_0 A B C)) &  ((v5_funct_1 (k8_memstr_0 A B C) (k2_memstr_0 A B)) & (v1_partfun1 (k8_memstr_0 A B C) (u1_struct_0 B))) ) ) ) ) ) ).
tt(fc14_mod_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A)) )  =>  ( (~ (v2_struct_0 (k5_mod_4 A B)))  & (v7_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A))) ) ) ).
tt(fc14_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_dilworth (k2_struct_0 (k5_mycielsk A)) (k5_mycielsk A))) ) ).
tt(fc14_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k9_nat_3 A B C)) &  ((v4_relat_1 (k9_nat_3 A B C) A) &  ((v1_funct_1 (k9_nat_3 A B C)) &  ((v1_partfun1 (k9_nat_3 A B C) A) & (v4_valued_0 (k9_nat_3 A B C))) ) ) ) ) ) ).
tt(fc14_newton,ax, ( (~ (v1_xboole_0 k10_newton))  &  (~ (v1_finset_1 k10_newton)) ) ).
tt(fc14_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (v10_oposet_1 k1_oposet_1)) ).
tt(fc14_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((v1_relat_1 (k3_ordinal6 A)) &  ((v1_funct_1 (k3_ordinal6 A)) &  ((v5_ordinal1 (k3_ordinal6 A)) &  ((v1_ordinal2 (k3_ordinal6 A)) & (v2_ordinal2 (k3_ordinal6 A))) ) ) ) ) ) ).
tt(fc14_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v1_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc14_pcs_0,ax, (! [A:$i] :  ( ((v5_pcs_0 A) & (l1_pcs_0 A))  => (v2_relat_2 (u1_pcs_0 A))) ) ).
tt(fc14_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v3_group_1 (k14_polynom3 A))) ) ) ) ).
tt(fc14_pre_poly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_pre_poly A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_pre_poly B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v1_pre_poly (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc14_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v8_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc14_quaterni,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_quaterni B))  => (v1_quaterni (k24_quaterni A B))) ) ).
tt(fc14_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ( (~ (v1_ratfunc1 B A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_polynom5 A B (k3_vectsp_1 A (k5_struct_0 A) (k2_ratfunc1 A B)))) &  ((v1_funct_2 (k3_polynom5 A B (k3_vectsp_1 A (k5_struct_0 A) (k2_ratfunc1 A B))) k5_numbers (u1_struct_0 A)) & (v3_ratfunc1 (k3_polynom5 A B (k3_vectsp_1 A (k5_struct_0 A) (k2_ratfunc1 A B))) A)) ) ) ) ).
tt(fc14_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (v2_struct_0 (k4_topmetr A A)))  &  ((v13_struct_0 (k4_topmetr A A) 1) & (v1_pre_topc (k4_topmetr A A))) ) ) ) ).
tt(fc14_relat_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k2_relat_1 A)) & (v1_relat_1 (k2_relat_1 A))) ) ) ).
tt(fc14_relat_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v5_relat_2 B)) )  => (v5_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc14_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_seq_2 A)) ) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) &  ((v3_valued_0 (k30_valued_1 A)) & (v2_seq_2 (k30_valued_1 A))) ) ) ) ) ).
tt(fc14_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_rltopsp1 (k2_pre_topc A B) A)) ) ).
tt(fc14_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ((v13_lattices (k8_robbins1 A)) & (v4_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc14_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v3_card_1 (k2_amistd_1 3 k1_scmfsa_2 (k13_scmfsa_2 B A)) 1)) ) ).
tt(fc14_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((m1_scmfsa_2 B) &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  (~ (v2_extpro_1 (k14_scmfsa_2 A C B) 3 k1_scmfsa_2)) ) ) ).
tt(fc14_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v2_scmfsa6c (k7_scmfsa_2 A B))) ) ).
tt(fc14_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8c A B)))  &  ((v1_relat_1 (k2_scmfsa8c A B)) &  ((v4_relat_1 (k2_scmfsa8c A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8c A B)) &  ((v1_finset_1 (k2_scmfsa8c A B)) &  ((v1_afinsq_1 (k2_scmfsa8c A B)) & (v1_scmfsa7b (k2_scmfsa8c A B))) ) ) ) ) ) ) ) ) ).
tt(fc14_scmpds_4,ax, ((v1_relat_1 (k4_compos_1 k1_scmpds_2)) &  ((v4_relat_1 (k4_compos_1 k1_scmpds_2) k5_numbers) &  ((v5_relat_1 (k4_compos_1 k1_scmpds_2) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_compos_1 k1_scmpds_2)) &  ((v1_finset_1 (k4_compos_1 k1_scmpds_2)) &  ((v2_scmpds_4 (k4_compos_1 k1_scmpds_2)) & (v3_scmpds_4 (k4_compos_1 k1_scmpds_2))) ) ) ) ) ) ).
tt(fc14_scmpds_5,ax,(v1_scmpds_5 (k2_compos_1 k1_scmpds_2))).
tt(fc14_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k7_scmpds_6 B C A)))  &  ((v1_relat_1 (k7_scmpds_6 B C A)) &  ((v4_relat_1 (k7_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k7_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k7_scmpds_6 B C A)) &  ((v1_finset_1 (k7_scmpds_6 B C A)) &  ((v1_afinsq_1 (k7_scmpds_6 B C A)) & (v2_compos_1 (k7_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc14_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v3_amistd_1 (k1_scmring2 A) 2)) ) ) ).
tt(fc14_scmyciel,ax, (! [A:$i] : (v5_scmyciel (k5_scmyciel A))) ).
tt(fc14_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_sfmastr1 A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ((v1_sfmastr1 B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k6_scmfsa6a A B)))  &  ((v1_relat_1 (k6_scmfsa6a A B)) &  ((v4_relat_1 (k6_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k6_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k6_scmfsa6a A B)) &  ((v1_finset_1 (k6_scmfsa6a A B)) &  ((v1_afinsq_1 (k6_scmfsa6a A B)) & (v1_scmfsa7b (k6_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc14_simplex0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_pre_topc (k5_simplex0 A B)) &  ((v1_matroid0 (k5_simplex0 A B)) & (v6_simplex0 (k5_simplex0 A B) A)) ) ) ) ).
tt(fc14_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc14_sppol_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ( (~ (v1_xboole_0 (k1_sppol_2 A B C D)))  & (v2_compts_1 (k1_sppol_2 A B C D) (k15_euclid 2))) ) ) ).
tt(fc14_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (v3_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(fc14_struct_0,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  & (l5_struct_0 A))  =>  (~ (v1_xboole_0 (u4_struct_0 A))) ) ) ).
tt(fc14_subset_1,ax, (! [A:$i] :  (~ (v1_subset_1 (k2_subset_1 A) A)) ) ).
tt(fc14_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_tex_4 A B)))  & (v1_pre_topc (k5_tex_4 A B))) ) ) ).
tt(fc14_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v4_pre_topc (k5_group_2 A C B) A)) ) ).
tt(fc14_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  (~ (v1_xboole_0 (k2_xxreal_1 A B))) ) ) ).
tt(fc14_toprealb,ax, (! [A:$i] :  ( ((v2_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((v1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb A))) & (v1_borsuk_1 (k1_pre_topc k2_topalg_2 (k5_toprealb A)) k2_topalg_2)) ) ) ).
tt(fc14_toprealc,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_valued_2 A))  =>  ( (~ (v1_xboole_0 (k2_toprealc A)))  & (v1_valued_2 (k2_toprealc A))) ) ) ).
tt(fc14_tops_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~ (v2_tops_1 (k2_struct_0 A) A)) ) ) ).
tt(fc14_trees_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) )  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v1_finseq_1 (k2_finseq_2 A B)) & (v5_trees_3 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc14_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_valued_0 A))  & (v1_relat_1 B))  => (v1_valued_0 (k4_xboole_0 A B))) ) ).
tt(fc14_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v3_valued_0 (k7_valued_1 A B))) ) ) ) ).
tt(fc14_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((v1_relat_1 (k1_funct_1 D B)) & (v1_funct_1 (k1_funct_1 D B))) ) ) ).
tt(fc14_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v12_waybel_0 (k2_struct_0 A) A) & (v13_waybel_0 (k2_struct_0 A) A)) ) ) ).
tt(fc14_waybel10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v22_waybel_0 B A A) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A A B)) &  ((v4_yellow_0 (k1_yellow_2 A A B) A) & (v4_waybel_0 (k1_yellow_2 A A B) A)) ) ) ) ).
tt(fc14_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v1_funct_1 (k3_waybel23 A B)) &  ((v1_funct_2 (k3_waybel23 A B) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A)) & (v5_orders_3 (k3_waybel23 A B) (k2_yellow_1 (k7_waybel_0 B)) A)) ) ) ) ).
tt(fc14_waybel25,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v4_waybel11 B) & (m1_yellow_9 B A)) )  =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) & (v1_waybel25 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ).
tt(fc14_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k1_waybel_8 A)) &  ((v1_yellow_0 (k1_waybel_8 A)) & (v4_yellow_0 (k1_waybel_8 A) A)) ) ) ) ).
tt(fc14_waybel_4,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) &  ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k7_waybel_4 A B)) &  ((v1_funct_2 (k7_waybel_4 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (v5_orders_3 (k7_waybel_4 A B) A (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(fc14_waybel_8,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v2_waybel_8 (k3_yellow_1 A))) ) ).
tt(fc14_waybel_9,ax, (! [A:$i] :  ( ((v7_waybel_0 A) & (l1_orders_2 A))  =>  ((v6_waybel_0 (k2_waybel_9 A) A) & (v7_waybel_0 (k2_waybel_9 A))) ) ) ).
tt(fc14_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v3_xxreal_0 (k2_xcmplx_0 B A))) ) ).
tt(fc14_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v6_xxreal_2 (k3_xxreal_1 A B))) ) ).
tt(fc14_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  =>  ((v1_xxreal_0 (k2_xxreal_3 A)) &  (~ (v3_xxreal_0 (k2_xxreal_3 A))) ) ) ) ).
tt(fc14_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k6_yellow_1 k1_xboole_0 A)) &  ((v5_orders_2 (k6_yellow_1 k1_xboole_0 A)) &  ((v1_lattice3 (k6_yellow_1 k1_xboole_0 A)) & (v2_lattice3 (k6_yellow_1 k1_xboole_0 A))) ) ) ) ) ).
tt(fc14_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v4_orders_2 (k3_yellow_6 A B C)) & (v6_waybel_0 (k3_yellow_6 A B C) B)) ) ) ).
tt(fc15_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ( (~ (v1_xboole_0 (k34_abcmiz_1 A)))  & (v3_trees_3 (k34_abcmiz_1 A))) ) ) ).
tt(fc15_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) &  (~ (v1_abian A)) )  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  => (v1_abian (k6_xcmplx_0 A B))) ) ).
tt(fc15_afinsq_1,ax, (! [A:$i,B:$i,C:$i] : (v3_card_1 (k7_afinsq_1 A B C) 3)) ).
tt(fc15_algstr_4,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v2_struct_0 (k14_algstr_4 A))) ) ).
tt(fc15_ami_6,ax, ((v1_extpro_1 k1_ami_3 2) & (v3_amistd_1 k1_ami_3 2)) ).
tt(fc15_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ( (~ (v3_funct_1 D))  &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_hahnban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  &  ((v1_funct_1 E) &  ( (~ (v3_funct_1 E))  &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) &  ((v2_hahnban1 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ( (~ (v3_funct_1 (k9_bilinear A B C D E)))  & (v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))) ) ) ) ).
tt(fc15_binop_2,ax, ((v1_funct_1 k47_binop_2) &  ((v1_funct_2 k47_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (v1_setwiseo k47_binop_2 k5_numbers)) ) ).
tt(fc15_borsuk_5,ax, (! [A:$i,B:$i] :  ( ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  &  ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  => (v3_rcomp_1 (k2_xboole_0 A B))) ) ).
tt(fc15_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_c0sp2 A)))  &  ((v13_algstr_0 (k9_c0sp2 A)) &  ((v2_rlvect_1 (k9_c0sp2 A)) &  ((v3_rlvect_1 (k9_c0sp2 A)) &  ((v4_rlvect_1 (k9_c0sp2 A)) &  ((v5_rlvect_1 (k9_c0sp2 A)) &  ((v6_rlvect_1 (k9_c0sp2 A)) &  ((v7_rlvect_1 (k9_c0sp2 A)) &  ((v8_rlvect_1 (k9_c0sp2 A)) &  ((v3_normsp_0 (k9_c0sp2 A)) &  ((v4_normsp_0 (k9_c0sp2 A)) & (v2_normsp_1 (k9_c0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc15_card_3,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((v1_relat_1 (k1_wellord2 A)) &  (~ (v1_finset_1 (k1_wellord2 A))) ) ) ) ).
tt(fc15_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v13_algstr_0 (k9_cc0sp2 A)) &  ((v2_rlvect_1 (k9_cc0sp2 A)) &  ((v3_rlvect_1 (k9_cc0sp2 A)) &  ((v4_rlvect_1 (k9_cc0sp2 A)) &  ((v3_normsp_0 (k9_cc0sp2 A)) &  ((v4_normsp_0 (k9_cc0sp2 A)) &  ((v2_clvect_1 (k9_cc0sp2 A)) &  ((v3_clvect_1 (k9_cc0sp2 A)) &  ((v4_clvect_1 (k9_cc0sp2 A)) &  ((v5_clvect_1 (k9_cc0sp2 A)) & (v8_clvect_1 (k9_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc15_circcomb,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_2 A k6_margrel1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) k6_margrel1)))) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) )  =>  ( (~ (v11_struct_0 (k5_circcomb B C)))  &  ((v1_msualg_1 (k5_circcomb B C)) & (v3_circcomb (k5_circcomb B C))) ) ) ) ).
tt(fc15_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v5_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v10_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc15_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v2_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v13_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc15_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  ( (~ (v1_xboole_0 (k16_cohsp_1 A B)))  &  ((v1_classes1 (k16_cohsp_1 A B)) & (v1_coh_sp (k16_cohsp_1 A B))) ) ) ) ).
tt(fc15_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  =>  ((v1_relat_1 (k5_xtuple_0 B)) &  ((v1_funct_1 (k5_xtuple_0 B)) & (v4_valued_0 (k5_xtuple_0 B))) ) ) ) ).
tt(fc15_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) &  ((v1_finset_1 (k4_compos_1 A)) &  (~ (v2_compos_1 (k4_compos_1 A) A)) ) ) ) ) ) ) ) ).
tt(fc15_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k3_comput_1 k6_numbers A)) &  ((v4_relat_1 (k3_comput_1 k6_numbers A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 k6_numbers A)) &  ((v4_valued_0 (k3_comput_1 k6_numbers A)) &  ((v2_margrel1 (k3_comput_1 k6_numbers A)) & (v8_comput_1 (k3_comput_1 k6_numbers A) k6_numbers)) ) ) ) ) ) ) ).
tt(fc15_dickson,ax, ( (~ (v2_struct_0 k11_dickson))  & (v1_wellfnd1 k11_dickson)) ).
tt(fc15_euclid_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ((v1_bhsp_1 (k7_real_ns1 A)) & (v1_rusub_4 (k7_real_ns1 A))) ) ) ) ).
tt(fc15_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k24_valued_1 C A)) &  ((v1_funct_1 (k24_valued_1 C A)) & (v3_card_1 (k24_valued_1 C A) B)) ) ) ) ).
tt(fc15_exchsort,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_exchsort B)) ) ) ) )  => (v1_finset_1 (k6_exchsort A B))) ) ).
tt(fc15_facirc_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_circcomb A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc15_fcont_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_fcont_1 A B)) &  ((v1_funct_2 (k1_fcont_1 A B) k1_numbers k1_numbers) & (v1_fcont_1 (k1_fcont_1 A B))) ) ) ) ).
tt(fc15_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v14_lattices (k10_filter_2 A (k6_filter_2 A B)))) ) ).
tt(fc15_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((v1_relat_1 (k15_finseq_1 A)) &  ((v1_funct_1 (k15_finseq_1 A)) & (v1_finseq_1 (k15_finseq_1 A))) ) ) ) ).
tt(fc15_finset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((v1_finset_1 B) & (v1_finset_1 C)) )  => (v1_finset_1 (k3_zfmisc_1 A B C))) ) ).
tt(fc15_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A))))  => (v1_relat_1 (k1_funct_1 (k21_fomodel1 A) B))) ) ).
tt(fc15_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k25_fomodel2 A B))) ) ) ).
tt(fc15_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (v7_ordinal1 C)) )  =>  ((v1_partfun1 (k9_fomodel3 A B C) (k4_finseq_2 C A)) &  ((v3_relat_2 (k9_fomodel3 A B C)) & (v8_relat_2 (k9_fomodel3 A B C))) ) ) ) ).
tt(fc15_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k24_fomodel4 A) A)) ) ).
tt(fc15_funcop_1,ax, (! [A:$i,B:$i] : (v3_funct_1 (k2_funcop_1 A B))) ).
tt(fc15_funct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  => (v4_funct_1 (k2_tarski A B))) ) ).
tt(fc15_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  & (m1_subset_1 D A)) )  =>  ((v1_relat_1 (k2_funct_7 B C D)) &  ((v5_relat_1 (k2_funct_7 B C D) A) & (v1_funct_1 (k2_funct_7 B C D))) ) ) ) ).
tt(fc15_funct_9,ax, ((v1_funct_1 k2_fdiff_9) & (v2_funct_9 k2_fdiff_9)) ).
tt(fc15_functor0,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  ((v9_functor0 (k11_functor0 A) A A) & (v21_functor0 (k11_functor0 A) A A)) ) ) ).
tt(fc15_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  =>  (~ (v1_xboole_0 (k7_gate_1 A B))) ) ) ).
tt(fc15_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v5_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(fc15_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v2_struct_0 (k25_grcat_1 A)))  &  ( (~ (v11_struct_0 (k25_grcat_1 A)))  &  ((v1_cat_1 (k25_grcat_1 A)) &  ((v3_cat_1 (k25_grcat_1 A)) &  ((v4_cat_1 (k25_grcat_1 A)) & (v6_cat_1 (k25_grcat_1 A))) ) ) ) ) ) ) ).
tt(fc15_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  => (v3_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ).
tt(fc15_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (~ (v1_xboole_0 (k3_xboole_0 B C))) ) ) ).
tt(fc15_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_index_1 C A B) & (m1_index_1 C A B))  => (v1_funcop_1 (k2_xtuple_0 C))) ) ).
tt(fc15_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k3_jordan A)) &  ((v1_funct_2 (k3_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 (k3_jordan A) (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ) ) ).
tt(fc15_kurato_1,ax, (~ (v1_xboole_0 k6_kurato_1)) ).
tt(fc15_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A C))) (k8_cqc_lang A B C)) A)) ) ).
tt(fc15_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_mazurulm B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) & (v2_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A A)) ) ) ) ).
tt(fc15_member_1,ax, (! [A:$i] :  ((v4_membered A) =>  ((v1_membered (k7_member_1 A)) & (v4_membered (k7_member_1 A))) ) ) ).
tt(fc15_membered,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v3_membered (k2_tarski A B))) ) ).
tt(fc15_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k9_memstr_0 A B C D)) &  ((v4_relat_1 (k9_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k9_memstr_0 A B C D)) &  ((v5_funct_1 (k9_memstr_0 A B C D) (k2_memstr_0 A B)) & (v1_partfun1 (k9_memstr_0 A B C D) (u1_struct_0 B))) ) ) ) ) ) ).
tt(fc15_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_necklace (k7_mycielsk A))) ) ).
tt(fc15_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k9_nat_3 A B C)) &  ((v4_relat_1 (k9_nat_3 A B C) A) &  ((v1_funct_1 (k9_nat_3 A B C)) &  ((v1_partfun1 (k9_nat_3 A B C) A) & (v2_pre_poly (k9_nat_3 A B C))) ) ) ) ) ) ).
tt(fc15_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v2_ordinal6 A)) ) ) )  =>  ((v1_relat_1 (k3_ordinal6 A)) &  ((v1_funct_1 (k3_ordinal6 A)) &  ((v5_ordinal1 (k3_ordinal6 A)) &  ((v1_ordinal2 (k3_ordinal6 A)) & (v3_ordinal2 (k3_ordinal6 A))) ) ) ) ) ) ).
tt(fc15_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v1_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc15_pcs_0,ax, (! [A:$i] :  ( ((v6_pcs_0 A) & (l1_pcs_0 A))  => (v3_relat_2 (u1_pcs_0 A))) ) ).
tt(fc15_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v4_vectsp_1 (k14_polynom3 A))) ) ) ) ).
tt(fc15_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 B) & (m1_finseq_1 B (k3_finseq_2 A)))  => (v1_xboole_0 (k5_pre_poly A B))) ) ).
tt(fc15_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v1_prvect_2 (k5_finseq_1 A))) ) ).
tt(fc15_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v2_relat_1 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v2_relat_1 (k3_relat_1 A B))) ) ) ).
tt(fc15_relat_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v5_relat_2 B)) )  => (v5_relat_2 (k3_xboole_0 B A))) ) ).
tt(fc15_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_seq_2 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_seq_2 B)) ) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) &  ((v3_valued_0 (k1_valued_1 A B)) & (v1_seq_2 (k1_valued_1 A B))) ) ) ) ) ).
tt(fc15_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v9_rltopsp1 (k2_pre_topc A B) A)) ) ).
tt(fc15_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v4_amistd_1 (k14_scmfsa_2 A B C) 3 k1_scmfsa_2)) ) ).
tt(fc15_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((m1_scmfsa_2 B) &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  (~ (v2_extpro_1 (k15_scmfsa_2 A C B) 3 k1_scmfsa_2)) ) ) ).
tt(fc15_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v2_scmfsa6c (k8_scmfsa_2 A B))) ) ).
tt(fc15_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k10_compos_1 k1_scmpds_2 A)) &  ((v4_relat_1 (k10_compos_1 k1_scmpds_2 A) k5_numbers) &  ((v5_relat_1 (k10_compos_1 k1_scmpds_2 A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k10_compos_1 k1_scmpds_2 A)) &  ((v1_finset_1 (k10_compos_1 k1_scmpds_2 A)) & (v3_scmpds_4 (k10_compos_1 k1_scmpds_2 A))) ) ) ) ) ) ) ).
tt(fc15_scmpds_5,ax, (! [A:$i] :  ( ((v1_scmpds_5 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  =>  ( (~ (v1_xboole_0 (k3_afinsq_1 A)))  &  ((v1_relat_1 (k3_afinsq_1 A)) &  ((v4_relat_1 (k3_afinsq_1 A) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 A)) &  ((v1_finset_1 (k3_afinsq_1 A)) &  ((v1_afinsq_1 (k3_afinsq_1 A)) & (v2_scmpds_4 (k3_afinsq_1 A))) ) ) ) ) ) ) ) ) ).
tt(fc15_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k8_scmpds_6 B C A)))  &  ((v1_relat_1 (k8_scmpds_6 B C A)) &  ((v4_relat_1 (k8_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k8_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k8_scmpds_6 B C A)) &  ((v1_finset_1 (k8_scmpds_6 B C A)) &  ((v1_afinsq_1 (k8_scmpds_6 B C A)) &  ((v2_scmpds_4 (k8_scmpds_6 B C A)) & (v3_scmpds_4 (k8_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc15_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (v1_amistd_1 (k4_xtuple_0 (k2_compos_1 (k1_scmring2 A))) 2 (k1_scmring2 A))) ) ).
tt(fc15_scmyciel,ax, (! [A:$i,B:$i] :  ( ( ((v4_scmyciel A) & (v8_scmyciel A))  & (m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))))  => (v8_scmyciel (k7_scmyciel A B))) ) ).
tt(fc15_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_sfmastr1 A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) & (v1_scmfsa7b (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc15_simplex0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_pre_topc (k5_simplex0 A B)) &  (~ (v5_simplex0 (k5_simplex0 A B))) ) ) ) ).
tt(fc15_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))))) ).
tt(fc15_sppol_2,ax,(v1_topreal4 k1_topreal1)).
tt(fc15_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (v4_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(fc15_struct_0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l2_struct_0 A))  =>  (~ (v1_xboole_0 (k8_struct_0 A))) ) ) ).
tt(fc15_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_pre_topc (k5_tex_4 A B)) & (v4_tex_4 (k5_tex_4 A B) A)) ) ) ).
tt(fc15_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v4_pre_topc (k4_group_2 A C B) A)) ) ).
tt(fc15_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  (~ (v1_xboole_0 (k4_topreal9 A B C))) ) ) ).
tt(fc15_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  (~ (v1_xboole_0 (k3_xxreal_1 A B))) ) ) ).
tt(fc15_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_funct_1 (k6_toprealb A)) &  ((v1_funct_2 (k6_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A))))) & (v2_funct_2 (k6_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A)))))) ) ) ) ).
tt(fc15_toprealc,ax, (! [A:$i] :  ((v3_valued_2 A) =>  ((v1_valued_2 (k2_toprealc A)) & (v3_valued_2 (k2_toprealc A))) ) ) ).
tt(fc15_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v3_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc15_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ( (~ (v1_xboole_0 (k5_finseq_1 A)))  & (v6_trees_3 (k5_finseq_1 A))) ) ) ).
tt(fc15_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_valued_0 A))  & (v1_relat_1 B))  => (v2_valued_0 (k3_xboole_0 A B))) ) ).
tt(fc15_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  & (v1_rat_1 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v5_relat_1 (k7_valued_1 A B) k3_numbers) & (v1_funct_1 (k7_valued_1 A B))) ) ) ) ).
tt(fc15_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v2_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((v1_relat_1 (k1_funct_1 D B)) & (v1_funct_1 (k1_funct_1 D B))) ) ) ).
tt(fc15_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_waybel_0 (k3_waybel_0 A B) A)) ) ).
tt(fc15_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k2_waybel_1 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A)))) &  ((v1_funct_2 (k2_waybel_1 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A))) (u1_struct_0 (k7_waybel10 A)) (u1_struct_0 (k1_yellow_2 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A))))) & (v23_waybel_0 (k2_waybel_1 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A))) (k7_waybel10 A) (k1_yellow_2 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A))))) ) ) ) ).
tt(fc15_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v1_funct_1 (k4_waybel23 A B)) &  ((v1_funct_2 (k4_waybel23 A B) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (v5_orders_3 (k4_waybel23 A B) (k2_yellow_1 (k7_waybel_0 B)) (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(fc15_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  =>  ((v24_waybel_0 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc15_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_orders_2 (k1_waybel_8 A)) &  ((v4_yellow_0 (k1_waybel_8 A) A) & (v6_waybel34 (k1_waybel_8 A) A)) ) ) ) ).
tt(fc15_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_waybel_4 A)))  & (v1_orders_2 (k8_waybel_4 A))) ) ) ).
tt(fc15_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v6_waybel_0 (k2_waybel_9 A) A) &  ((v8_waybel_0 (k2_waybel_9 A) A) & (v10_waybel_0 (k2_waybel_9 A) A)) ) ) ) ).
tt(fc15_xreal_0,ax, (! [A:$i] :  ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) &  (~ (v3_xxreal_0 (k4_xcmplx_0 A))) ) ) ) ).
tt(fc15_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v6_xxreal_2 (k2_xxreal_1 A B))) ) ).
tt(fc15_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  =>  ((v1_xxreal_0 (k2_xxreal_3 A)) &  (~ (v2_xxreal_0 (k2_xxreal_3 A))) ) ) ) ).
tt(fc15_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v4_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(fc15_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  ((v1_funct_1 (u1_waybel_0 A B)) &  ( (~ (v1_xboole_0 (u1_waybel_0 A B)))  & (v1_funct_2 (u1_waybel_0 A B) (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ).
tt(fc16_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_abcmiz_1) &  ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) ) )  =>  (~ (v5_abcmiz_1 (k35_abcmiz_1 A B) B (k28_abcmiz_1 B))) ) ) ).
tt(fc16_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  => (v1_abian (k2_xcmplx_0 A 2))) ) ).
tt(fc16_afinsq_1,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) =>  ((v5_ordinal1 (k2_funcop_1 A B)) & (v1_finset_1 (k2_funcop_1 A B))) ) ) ).
tt(fc16_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k14_algstr_4 A))) ) ) ).
tt(fc16_ami_6,ax,(v1_amistd_1 (k4_xtuple_0 (k2_compos_1 k1_ami_3)) 2 k1_ami_3)).
tt(fc16_binop_2,ax, ((v1_funct_1 k29_binop_2) &  ((v1_funct_2 k29_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (v1_setwiseo k29_binop_2 k2_numbers)) ) ).
tt(fc16_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v1_xboole_0 (k4_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(fc16_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_circcomb A) & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v3_circcomb B) & (l1_msualg_1 B)) ) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v1_msualg_1 (k2_circcomb A B)) & (v3_circcomb (k2_circcomb A B))) ) ) ) ).
tt(fc16_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v6_mssubfam C (u1_struct_0 A) (u3_msualg_1 A B)) & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B)))) ) )  =>  ((v5_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A) & (v11_closure1 (g1_closure1 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc16_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v3_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v14_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc16_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  (~ (v1_xboole_0 (k17_cohsp_1 A B))) ) ) ).
tt(fc16_compos_0,ax,(v1_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)))).
tt(fc16_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_4 B C)) &  ((v1_funct_1 (k1_funct_4 B C)) &  (~ (v2_compos_1 (k1_funct_4 B C) A)) ) ) ) ) ).
tt(fc16_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k3_comput_1 1 A)) &  ((v4_relat_1 (k3_comput_1 1 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 1 A)) &  ((v4_valued_0 (k3_comput_1 1 A)) &  ((v2_margrel1 (k3_comput_1 1 A)) & (v8_comput_1 (k3_comput_1 1 A) 1)) ) ) ) ) ) ) ).
tt(fc16_dickson,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))))  & (v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson)))) ) ) ).
tt(fc16_euclid_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  => (v3_valued_2 (k1_tarski A))) ) ).
tt(fc16_exchsort,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  => (v1_relat_1 (k6_exchsort A B))) ) ).
tt(fc16_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  => (v1_xtuple_0 (k9_facirc_1 A B C D))) ) ).
tt(fc16_finseq_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k5_finseq_1 A))) ) ).
tt(fc16_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_finset_1 A) &  ((v1_finset_1 B) &  ((v1_finset_1 C) & (v1_finset_1 D)) ) )  => (v1_finset_1 (k4_zfmisc_1 A B C D))) ) ).
tt(fc16_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 A)) (k29_fomodel1 A))))  =>  ((v1_relat_1 (k1_funct_1 (k21_fomodel1 A) B)) & (v1_funct_1 (k1_funct_1 (k21_fomodel1 A) B))) ) ) ).
tt(fc16_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k27_fomodel2 A))) ) ) ).
tt(fc16_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel3 E C D)) ) ) ) ) )  =>  ((v1_relat_1 (k11_fomodel3 A B C D E)) & (v1_funct_1 (k11_fomodel3 A B C D E))) ) ) ).
tt(fc16_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k26_fomodel4 A) A)) ) ).
tt(fc16_funcop_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_funct_1 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v3_funct_1 (k5_relat_1 A B))) ) ) ).
tt(fc16_funct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_funct_1 C B)) ) )  =>  ((v1_relat_1 (k5_relat_1 C A)) & (v5_funct_1 (k5_relat_1 C A) B)) ) ) ).
tt(fc16_funct_9,ax, ((v1_funct_1 k1_fdiff_9) & (v2_funct_9 k1_fdiff_9)) ).
tt(fc16_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) &  ((v10_functor0 D A B) & (l2_functor0 D A B)) )  &  ((v10_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v10_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc16_gate_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  => (v1_xboole_0 (k7_gate_1 A B))) ) ).
tt(fc16_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v6_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v6_glib_001 (k8_glib_001 A B C D) A)) ) ).
tt(fc16_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~ (v1_xboole_0 (k26_grcat_1 A))) ) ) ).
tt(fc16_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l3_algstr_0 B)) ) )  => (v4_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ).
tt(fc16_hermitan,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) )  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((v1_funct_1 (k7_bilinear k1_complfld A B C D)) &  ((v1_funct_2 (k7_bilinear k1_complfld A B C D) (u1_struct_0 B) (u1_struct_0 k1_complfld)) & (v1_hermitan (k7_bilinear k1_complfld A B C D) B)) ) ) ) ).
tt(fc16_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_ideal_1 (k3_xboole_0 B C) A)) ) ).
tt(fc16_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  => (v4_funct_1 (k10_xtuple_0 A))) ) ).
tt(fc16_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k4_jordan A)) &  ((v1_funct_2 (k4_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 (k4_jordan A) (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ) ) ).
tt(fc16_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B (k6_cqc_lang A C)) (k8_cqc_lang A C (k6_cqc_lang A B))) A)) ) ).
tt(fc16_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_mazurulm A B)) &  ((v1_funct_2 (k1_mazurulm A B) (u1_struct_0 A) (u1_struct_0 A)) & (v3_funct_2 (k1_mazurulm A B) (u1_struct_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc16_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k8_member_1 A B))) ) ).
tt(fc16_membered,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (v4_membered (k2_tarski A B))) ) ).
tt(fc16_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k10_memstr_0 A B C D)) &  ((v4_relat_1 (k10_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k10_memstr_0 A B C D)) &  ((v5_funct_1 (k10_memstr_0 A B C D) (k2_memstr_0 A B)) & (v1_partfun1 (k10_memstr_0 A B C D) (u1_struct_0 B))) ) ) ) ) ) ).
tt(fc16_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_necklace (k7_mycielsk A))) ) ).
tt(fc16_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k12_nat_3 A)) &  ((v4_relat_1 (k12_nat_3 A) k10_newton) &  ((v1_funct_1 (k12_nat_3 A)) &  ((v1_partfun1 (k12_nat_3 A) k10_newton) & (v4_valued_0 (k12_nat_3 A))) ) ) ) ) ) ).
tt(fc16_ordinal6,ax, (~ (v1_zfmisc_1 k4_ordinal1)) ).
tt(fc16_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v2_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc16_pcs_0,ax, (! [A:$i] :  ( ((v3_pcs_0 A) & (l1_pcs_0 A))  =>  ((v2_pcs_0 (g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A))) & (v3_pcs_0 (g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A)))) ) ) ).
tt(fc16_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v5_vectsp_1 (k14_polynom3 A))) ) ) ) ).
tt(fc16_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v4_valued_0 (k2_funct_7 A B C))) ) ) ) ).
tt(fc16_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  => (v1_prvect_2 (k10_finseq_1 A B))) ) ).
tt(fc16_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_ratfunc1 B A))  =>  (~ (v9_struct_0 (k2_ratfunc1 A (k5_ratfunc1 A B)) A)) ) ) ).
tt(fc16_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 B))  =>  ((v1_xboole_0 (k5_relat_1 A B)) & (v1_relat_1 (k5_relat_1 A B))) ) ) ).
tt(fc16_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_2 A))  & (v1_relat_1 B))  => (v5_relat_2 (k4_xboole_0 A B))) ) ).
tt(fc16_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_seq_2 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v2_seq_2 B)) ) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) &  ((v3_valued_0 (k1_valued_1 A B)) & (v2_seq_2 (k1_valued_1 A B))) ) ) ) ) ).
tt(fc16_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k14_scmfsa_2 A B C)))) ) ).
tt(fc16_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v2_extpro_1 (k16_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc16_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v2_scmfsa6c (k9_scmfsa_2 A B))) ) ).
tt(fc16_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k3_afinsq_1 (k3_scmpds_2 A))))  &  ((v1_relat_1 (k3_afinsq_1 (k3_scmpds_2 A))) &  ((v4_relat_1 (k3_afinsq_1 (k3_scmpds_2 A)) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 (k3_scmpds_2 A)) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 (k3_scmpds_2 A))) &  ((v1_finset_1 (k3_afinsq_1 (k3_scmpds_2 A))) &  ((v1_afinsq_1 (k3_afinsq_1 (k3_scmpds_2 A))) & (v3_scmpds_4 (k3_afinsq_1 (k3_scmpds_2 A)))) ) ) ) ) ) ) ) ) ).
tt(fc16_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  => (v1_scmpds_5 (k5_scmpds_2 A B))) ) ).
tt(fc16_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k8_scmpds_6 B C A)))  &  ((v1_relat_1 (k8_scmpds_6 B C A)) &  ((v4_relat_1 (k8_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k8_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k8_scmpds_6 B C A)) &  ((v1_finset_1 (k8_scmpds_6 B C A)) &  ((v1_afinsq_1 (k8_scmpds_6 B C A)) & (v2_compos_1 (k8_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc16_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (v2_amistd_1 (k2_compos_1 (k1_scmring2 A)) 2 (k1_scmring2 A))) ) ).
tt(fc16_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  => (v11_scmyciel (k7_scmyciel A B))) ) ).
tt(fc16_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_sfmastr1 A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa6a B A)))  &  ((v1_relat_1 (k5_scmfsa6a B A)) &  ((v4_relat_1 (k5_scmfsa6a B A) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a B A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa6a B A)) &  ((v1_finset_1 (k5_scmfsa6a B A)) &  ((v1_afinsq_1 (k5_scmfsa6a B A)) & (v1_scmfsa7b (k5_scmfsa6a B A))) ) ) ) ) ) ) ) ) ).
tt(fc16_simplex0,ax, (! [A:$i,B:$i] :  ( ((v5_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_pre_topc (k5_simplex0 A B)) & (v3_matroid0 (k5_simplex0 A B))) ) ) ).
tt(fc16_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos)))) ).
tt(fc16_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (v5_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(fc16_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) & (l2_struct_0 A)) )  => (v1_xboole_0 (k8_struct_0 A))) ) ).
tt(fc16_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v7_struct_0 (k1_pre_topc A B)))  & (v1_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc16_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v4_pre_topc (k1_group_2 A B) A)) ) ).
tt(fc16_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v1_convex1 (k4_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc16_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  (~ (v1_xboole_0 (k1_xxreal_1 A B))) ) ) ).
tt(fc16_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k6_toprealb A)) &  ((v2_funct_1 (k6_toprealb A)) & (v1_funct_2 (k6_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A)))))) ) ) ) ).
tt(fc16_toprealc,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_pre_topc B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (v3_pre_topc (k2_toprealc B) (k15_euclid A))) ) ).
tt(fc16_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_tops_1 (k2_tops_1 A B) A)) ) ).
tt(fc16_trees_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ( (~ (v1_xboole_0 (k10_finseq_1 A B)))  & (v6_trees_3 (k10_finseq_1 A B))) ) ) ).
tt(fc16_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_valued_0 A))  & (v1_relat_1 B))  => (v2_valued_0 (k4_xboole_0 A B))) ) ).
tt(fc16_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v5_relat_1 (k7_valued_1 A B) k4_numbers) & (v1_funct_1 (k7_valued_1 A B))) ) ) ) ).
tt(fc16_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v1_valued_0 (k1_funct_1 D B))) ) ).
tt(fc16_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_waybel_0 (k4_waybel_0 A B) A)) ) ).
tt(fc16_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v6_waybel23 B A) & (m1_waybel23 B A)) )  =>  ((v1_funct_1 (k5_waybel23 A B)) &  ((v1_funct_2 (k5_waybel23 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) & (v5_orders_3 (k5_waybel23 A B) A (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ).
tt(fc16_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k8_waybel_4 A)) & (v2_yellow_0 (k8_waybel_4 A))) ) ) ).
tt(fc16_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k3_waybel_9 A)))  & (v6_waybel_0 (k3_waybel_9 A) A)) ) ) ).
tt(fc16_xreal_0,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) &  (~ (v2_xxreal_0 (k4_xcmplx_0 A))) ) ) ) ).
tt(fc16_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v6_xxreal_2 (k4_xxreal_1 A B))) ) ).
tt(fc16_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  =>  ((v1_xxreal_0 (k2_xxreal_3 A)) & (v3_xxreal_0 (k2_xxreal_3 A))) ) ) ).
tt(fc16_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v5_orders_2 (k6_yellow_1 A B))) ) ) ).
tt(fc16_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) )  =>  ((v1_funct_1 (u1_waybel_0 A B)) &  ((v3_funct_1 (u1_waybel_0 A B)) & (v1_funct_2 (u1_waybel_0 A B) (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ).
tt(fc17_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v6_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A))) )  =>  ( (~ (v6_abcmiz_1 (k37_abcmiz_1 A B) A))  & (v7_abcmiz_1 (k37_abcmiz_1 A B) A)) ) ) ).
tt(fc17_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  (~ (v1_abian (k2_xcmplx_0 A 2))) ) ) ).
tt(fc17_afinsq_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (v5_relat_1 (k3_afinsq_1 B) A)) ) ).
tt(fc17_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (g4_algstr_0 A B C)))  & (v22_algstr_0 (g4_algstr_0 A B C))) ) ) ).
tt(fc17_algstr_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))))  =>  ( (~ (v1_xboole_0 (k2_xtuple_0 B)))  & (v7_ordinal1 (k2_xtuple_0 B))) ) ) ).
tt(fc17_ami_6,ax,(v2_amistd_1 (k2_compos_1 k1_ami_3) 2 k1_ami_3)).
tt(fc17_binop_2,ax, ((v1_funct_1 k35_binop_2) &  ((v1_funct_2 k35_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (v1_setwiseo k35_binop_2 k1_numbers)) ) ).
tt(fc17_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v1_xboole_0 (k3_xxreal_1 k2_xxreal_0 A))) ) ) ).
tt(fc17_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) &  ((v4_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) & (v4_msafree2 (k7_circcomb A B C D) (k5_circcomb C D))) ) ) ) ).
tt(fc17_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v3_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  & (m2_pboole C A B B))  => (v3_relat_1 (k5_closure1 A B C))) ) ).
tt(fc17_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v4_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v15_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc17_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) ) )  =>  ((v1_classes1 (k17_cohsp_1 A B)) & (v1_coh_sp (k17_cohsp_1 A B))) ) ) ).
tt(fc17_compos_0,ax, ((v2_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0))) & (v3_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)))) ).
tt(fc17_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  (~ (v2_compos_1 B A)) ) ) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k6_compos_1 A B C)) &  ((v4_relat_1 (k6_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k6_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k6_compos_1 A B C)) &  ((v1_finset_1 (k6_compos_1 A B C)) &  (~ (v2_compos_1 (k6_compos_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(fc17_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k3_comput_1 2 A)) &  ((v4_relat_1 (k3_comput_1 2 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 2 A)) &  ((v4_valued_0 (k3_comput_1 2 A)) &  ((v2_margrel1 (k3_comput_1 2 A)) & (v8_comput_1 (k3_comput_1 2 A) 2)) ) ) ) ) ) ) ).
tt(fc17_dickson,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) & (v4_dickson (k5_yellow_1 A (k7_funcop_1 A k11_dickson)))) ) ) ).
tt(fc17_euclid_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  => (v3_valued_2 (k2_tarski A B))) ) ).
tt(fc17_exchsort,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  ((v1_relat_1 (k6_exchsort A B)) &  ((v5_relat_2 (k6_exchsort A B)) & (v8_relat_2 (k6_exchsort A B))) ) ) ) ).
tt(fc17_finseq_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ( (~ (v1_xboole_0 (k7_finseq_1 A B)))  & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc17_finset_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k1_zfmisc_1 A))) ) ).
tt(fc17_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v7_fomodel1 (k1_funct_1 (k22_fomodel1 A) B) A)) ) ).
tt(fc17_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k31_fomodel1 A) A)) ) ).
tt(fc17_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_partfun1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) )  => (v1_partfun1 (k11_fomodel3 A B C D E) (k8_eqrel_1 A C))) ) ).
tt(fc17_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v13_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k33_fomodel2 A)))) ) ) ) )  => (v4_fomodel4 (k4_tarski (k2_xboole_0 E (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) C) D))) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) D)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k25_fomodel4 A)) (k4_lang1 (k1_zfmisc_1 (k33_fomodel2 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_domain_1 (k1_zfmisc_1 (k33_fomodel2 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) E (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C))))) ) ).
tt(fc17_funcop_1,ax, (! [A:$i,B:$i] : (v4_relat_1 (k2_funcop_1 A B) A)) ).
tt(fc17_funct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v4_funct_1 A) &  ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k1_funct_1 C B)) & (v1_funct_1 (k1_funct_1 C B))) ) ) ).
tt(fc17_funct_9,ax, ((v1_funct_1 k29_sin_cos) & (v2_funct_9 k29_sin_cos)) ).
tt(fc17_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) &  ((v11_functor0 D A B) & (l2_functor0 D A B)) )  &  ((v10_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v11_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc17_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k8_gate_1 A B C))) ) ) ).
tt(fc17_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v1_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v1_glib_001 (k9_glib_001 A B C D) A)) ) ).
tt(fc17_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v1_cat_1 (k27_grcat_1 A))) ) ).
tt(fc17_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( (~ (v2_struct_0 C))  & (l3_algstr_0 C)) ) )  => (v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ).
tt(fc17_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_ideal_1 (k3_xboole_0 B C) A)) ) ).
tt(fc17_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  =>  ((v1_funct_1 (k7_cat_1 A B C)) &  ((v1_funct_2 (k7_cat_1 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v1_index_1 (k7_cat_1 A B C))) ) ) ) ).
tt(fc17_jordan,ax, ((v1_funct_1 k5_jordan) &  ((v1_funct_2 k5_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 k5_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ).
tt(fc17_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A (k6_cqc_lang A B) C) (k8_cqc_lang A (k6_cqc_lang A C) B)) A)) ) ).
tt(fc17_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_mazurulm A B)) &  ((v1_funct_2 (k1_mazurulm A B) (u1_struct_0 A) (u1_struct_0 A)) & (v1_mazurulm (k1_mazurulm A B) A A)) ) ) ) ).
tt(fc17_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k8_member_1 B A))) ) ).
tt(fc17_membered,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v5_membered (k2_tarski A B))) ) ).
tt(fc17_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v7_ordinal1 C) &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v5_memstr_0 D A B C)) ) ) ) ) ) )  =>  ((v1_relat_1 (k10_memstr_0 A B D C)) &  ((v4_relat_1 (k10_memstr_0 A B D C) (u1_struct_0 B)) &  ((v1_funct_1 (k10_memstr_0 A B D C)) &  ((v5_funct_1 (k10_memstr_0 A B D C) (k2_memstr_0 A B)) & (v5_memstr_0 (k10_memstr_0 A B D C) A B k6_numbers)) ) ) ) ) ) ).
tt(fc17_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v7_mod_4 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc17_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k12_nat_3 A)) &  ((v4_relat_1 (k12_nat_3 A) k10_newton) &  ((v1_funct_1 (k12_nat_3 A)) &  ((v1_partfun1 (k12_nat_3 A) k10_newton) & (v2_pre_poly (k12_nat_3 A))) ) ) ) ) ) ).
tt(fc17_ordinal6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v3_ordinal1 B) &  ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B A)) ) )  =>  ((v1_funct_1 (k6_ordinal6 A B)) &  ((v1_funct_2 (k6_ordinal6 A B) (k2_ordinal1 A) (k2_ordinal1 A)) & (v2_ordinal6 (k6_ordinal6 A B))) ) ) ) ).
tt(fc17_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v2_partfun3 (k1_valued_1 B C))) ) ) ) ).
tt(fc17_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 C))  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v3_valued_0 (k2_funct_7 A B C))) ) ) ) ).
tt(fc17_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_prvect_2 B)) ) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v1_prvect_2 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc17_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A)) )  =>  (~ (v4_ratfunc1 (k6_ratfunc1 A B) A)) ) ) ).
tt(fc17_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_xboole_0 (k5_relat_1 A B)) & (v1_relat_1 (k5_relat_1 A B))) ) ) ).
tt(fc17_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v4_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc17_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_comseq_2 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_comseq_2 B)) ) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v1_funct_1 (k18_valued_1 A B)) &  ((v3_valued_0 (k18_valued_1 A B)) & (v1_comseq_2 (k18_valued_1 A B))) ) ) ) ) ).
tt(fc17_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v4_amistd_1 (k15_scmfsa_2 A B C) 3 k1_scmfsa_2)) ) ).
tt(fc17_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v2_extpro_1 (k17_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc17_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  => (v2_scmfsa6c (k10_scmfsa_2 A B))) ) ).
tt(fc17_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_xboole_0 (k3_afinsq_1 (k7_scmpds_2 B A C))))  &  ((v1_relat_1 (k3_afinsq_1 (k7_scmpds_2 B A C))) &  ((v4_relat_1 (k3_afinsq_1 (k7_scmpds_2 B A C)) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 (k7_scmpds_2 B A C)) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 (k7_scmpds_2 B A C))) &  ((v1_finset_1 (k3_afinsq_1 (k7_scmpds_2 B A C))) &  ((v1_afinsq_1 (k3_afinsq_1 (k7_scmpds_2 B A C))) & (v3_scmpds_4 (k3_afinsq_1 (k7_scmpds_2 B A C)))) ) ) ) ) ) ) ) ) ).
tt(fc17_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v1_scmpds_5 (k10_scmpds_2 A B C))) ) ).
tt(fc17_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scmpds_4 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_6 C D A B)))  &  ((v1_relat_1 (k4_scmpds_6 C D A B)) &  ((v4_relat_1 (k4_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_6 C D A B)) &  ((v1_finset_1 (k4_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k4_scmpds_6 C D A B)) &  ((v2_scmpds_4 (k4_scmpds_6 C D A B)) & (v3_scmpds_4 (k4_scmpds_6 C D A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc17_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (v1_amistd_1 (k4_xtuple_0 (k8_scmring2 A B)) 2 (k1_scmring2 A))) ) ).
tt(fc17_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa6c A B)))  &  ((v1_relat_1 (k1_scmfsa6c A B)) &  ((v4_relat_1 (k1_scmfsa6c A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6c A B)) &  ((v1_finset_1 (k1_scmfsa6c A B)) &  ((v1_afinsq_1 (k1_scmfsa6c A B)) & (v1_scmfsa7b (k1_scmfsa6c A B))) ) ) ) ) ) ) ) ) ).
tt(fc17_simplex0,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 B) &  ((v5_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((v1_pre_topc (k5_simplex0 A B)) & (v2_simplex0 (k5_simplex0 A B))) ) ) ).
tt(fc17_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))))) ).
tt(fc17_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  ((v1_stacks_1 (k14_stacks_1 A)) & (v6_stacks_1 (k14_stacks_1 A))) ) ) ).
tt(fc17_struct_0,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  =>  ((v7_ordinal1 (k7_struct_0 A)) & (v1_card_1 (k7_struct_0 A))) ) ) ).
tt(fc17_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_subset_1 B (u1_struct_0 A)))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) &  (~ (v1_tex_2 (k1_pre_topc A B) A)) ) ) ) ).
tt(fc17_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v3_pre_topc (k5_group_2 A C B) A)) ) ).
tt(fc17_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) & (v3_xxreal_0 C)) ) )  => (v1_xboole_0 (k3_topreal9 A B C))) ) ).
tt(fc17_topreala,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ( ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) )  &  ( ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) )  &  ((v1_xreal_0 D) &  (~ (v3_xxreal_0 D)) ) ) ) )  =>  (~ (v2_struct_0 (k1_topreala A C B D))) ) ) ).
tt(fc17_toprealb,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k6_toprealb A)) &  ((v1_funct_2 (k6_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A))))) & (v5_pre_topc (k6_toprealb A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers A))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers A))))) ) ) ) ).
tt(fc17_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_metric_1 (k14_euclid A)) &  ((v6_metric_1 (k14_euclid A)) &  ((v7_metric_1 (k14_euclid A)) &  ((v8_metric_1 (k14_euclid A)) &  ((v9_metric_1 (k14_euclid A)) & (v2_toprealc (k14_euclid A))) ) ) ) ) ) ) ).
tt(fc17_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_tops_1 (k2_tops_1 A B) A)) ) ).
tt(fc17_trees_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v1_finseq_1 (k2_finseq_2 A B)) & (v6_trees_3 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc17_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_valued_0 A))  & (v1_relat_1 B))  => (v3_valued_0 (k3_xboole_0 A B))) ) ).
tt(fc17_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v4_valued_0 (k7_valued_1 A B))) ) ) ) ).
tt(fc17_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v2_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v2_valued_0 (k1_funct_1 D B))) ) ).
tt(fc17_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k11_waybel_0 A B))) ) ) ).
tt(fc17_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v6_waybel23 B A) & (m1_waybel23 B A)) )  =>  ((v1_funct_1 (k3_waybel23 A (k5_yellow_0 A B))) &  ((v1_funct_2 (k3_waybel23 A (k5_yellow_0 A B)) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))) (u1_struct_0 A)) &  ((v17_waybel_0 (k3_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A) & (v18_waybel_0 (k3_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A)) ) ) ) ) ).
tt(fc17_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k9_waybel_4 A)) &  ((v1_funct_2 (k9_waybel_4 A) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A))) & (v5_orders_3 (k9_waybel_4 A) (k2_yellow_1 (k3_waybel_4 A)) (k8_waybel_4 A))) ) ) ) ).
tt(fc17_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  ((v3_orders_2 (k3_waybel_9 A)) & (v6_waybel_0 (k3_waybel_9 A) A)) ) ) ).
tt(fc17_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k6_xcmplx_0 A B))) ) ) ).
tt(fc17_xxreal_2,ax,(v6_xxreal_2 k1_numbers)).
tt(fc17_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  =>  ((v1_xxreal_0 (k2_xxreal_3 A)) & (v2_xxreal_0 (k2_xxreal_3 A))) ) ) ).
tt(fc17_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v2_lattice3 (k6_yellow_1 A B))) ) ) ).
tt(fc17_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((v4_orders_2 B) & (l1_waybel_0 B A)) )  =>  ((v4_orders_2 (k5_yellow_6 A B C)) &  ((v6_waybel_0 (k5_yellow_6 A B C) A) & (v2_yellow_6 (k5_yellow_6 A B C) A B)) ) ) ) ).
tt(fc18_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v7_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A))) )  => (v6_abcmiz_1 (k37_abcmiz_1 A B) A)) ) ).
tt(fc18_abian,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_setfam_1 B))  &  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  & (m1_subset_1 D A)) ) )  =>  (~ (v1_xboole_0 (k1_funct_1 C D))) ) ) ).
tt(fc18_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  => (v5_relat_1 (k6_afinsq_1 B C) A)) ) ).
tt(fc18_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_zfmisc_1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ((v7_struct_0 (g4_algstr_0 A B C)) & (v22_algstr_0 (g4_algstr_0 A B C))) ) ) ).
tt(fc18_algstr_4,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) =>  ((v1_funct_1 (k16_algstr_4 A B)) &  ((v2_funct_1 (k16_algstr_4 A B)) & (v1_funct_2 (k16_algstr_4 A B) (k11_algstr_4 A B) (u1_struct_0 (k14_algstr_4 A)))) ) ) ) ).
tt(fc18_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_amistd_1 (k4_xtuple_0 (k7_ami_3 A)) 2 k1_ami_3)) ) ).
tt(fc18_binop_2,ax, ((v1_funct_1 k41_binop_2) &  ((v1_funct_2 k41_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) & (v1_setwiseo k41_binop_2 k3_numbers)) ) ).
tt(fc18_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v1_xboole_0 (k4_xxreal_1 k2_xxreal_0 A))) ) ) ).
tt(fc18_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) )  &  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  &  ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) ) ) ) )  =>  ((v3_msualg_1 (k3_circcomb A B C D) (k2_circcomb A B)) &  ((v4_msualg_1 (k3_circcomb A B C D) (k2_circcomb A B)) &  ((v4_circcomb (k3_circcomb A B C D) (k2_circcomb A B)) & (v6_circcomb (k3_circcomb A B C D) (k2_circcomb A B))) ) ) ) ) ).
tt(fc18_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) &  ((v3_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) ) ) ) )  =>  ((v5_closure1 (k6_closure1 A B C) A) & (v9_closure1 (k6_closure1 A B C) A)) ) ) ).
tt(fc18_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v5_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v16_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc18_compos_0,ax,(v5_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)))).
tt(fc18_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k10_compos_1 A B)) &  ((v4_relat_1 (k10_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k10_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k10_compos_1 A B)) &  ((v1_finset_1 (k10_compos_1 A B)) & (v4_compos_1 (k10_compos_1 A B) A)) ) ) ) ) ) ) ).
tt(fc18_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k3_comput_1 3 A)) &  ((v4_relat_1 (k3_comput_1 3 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 3 A)) &  ((v4_valued_0 (k3_comput_1 3 A)) &  ((v2_margrel1 (k3_comput_1 3 A)) & (v8_comput_1 (k3_comput_1 3 A) 3)) ) ) ) ) ) ) ).
tt(fc18_dickson,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) & (v3_dickson (k5_yellow_1 A (k7_funcop_1 A k11_dickson)))) ) ) ).
tt(fc18_euclid_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) )  =>  ((v1_relat_1 (k2_funct_7 D B C)) &  ((v1_funct_1 (k2_funct_7 D B C)) & (v3_card_1 (k2_funct_7 D B C) A)) ) ) ) ).
tt(fc18_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  => (v1_relat_1 (k7_relat_1 (k7_exchsort A B C D) E))) ) ).
tt(fc18_finseq_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 B A)) &  ((v1_funct_1 (k7_finseq_1 B A)) &  ( (~ (v1_xboole_0 (k7_finseq_1 B A)))  & (v1_finseq_1 (k7_finseq_1 B A))) ) ) ) ) ).
tt(fc18_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k5_xboole_0 A B))) ) ).
tt(fc18_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k31_fomodel1 A))) ) ) ).
tt(fc18_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k25_fomodel2 A k6_numbers) A)) ) ).
tt(fc18_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_funct_1 (k17_fomodel3 A B)) &  ((v1_funct_2 (k17_fomodel3 A B) A (k8_eqrel_1 A B)) & (v2_funct_2 (k17_fomodel3 A B) (k8_eqrel_1 A B))) ) ) ) ).
tt(fc18_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v13_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 E A) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v4_fomodel4 (k4_tarski (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) E (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) C) D)) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) D)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k25_fomodel4 A)) (k4_lang1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_domain_1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) E) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C))))) ) ).
tt(fc18_funcop_1,ax, (! [A:$i,B:$i] : (v4_relat_1 (k16_funcop_1 A B) (k1_tarski A))) ).
tt(fc18_funct_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  (~ (v1_zfmisc_1 (k9_xtuple_0 A))) ) ) ).
tt(fc18_funct_9,ax, ((v1_funct_1 k30_sin_cos) & (v2_funct_9 k30_sin_cos)) ).
tt(fc18_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) &  ((v10_functor0 D A B) & (l2_functor0 D A B)) )  &  ((v11_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v11_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc18_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k8_gate_1 A B C))) ) ).
tt(fc18_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~ (v1_xboole_0 (k28_grcat_1 A))) ) ) ).
tt(fc18_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( (~ (v2_struct_0 C))  & (l3_algstr_0 C)) ) )  =>  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) & (v1_group_7 (k11_finseq_1 A B C))) ) ) ).
tt(fc18_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_ideal_1 (k3_xboole_0 B C) A)) ) ).
tt(fc18_jordan,ax, ((v1_funct_1 k6_jordan) &  ((v1_funct_2 k6_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 k6_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ).
tt(fc18_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  &  ( (~ (v1_xboole_0 B))  & (v2_membered B)) )  =>  (~ (v1_xboole_0 (k8_member_1 A B))) ) ) ).
tt(fc18_membered,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v6_membered (k2_tarski A B))) ) ).
tt(fc18_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k7_memstr_0 A B C)) &  ((v4_relat_1 (k7_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k7_memstr_0 A B C)) &  ((v5_funct_1 (k7_memstr_0 A B C) (k2_memstr_0 A B)) & (v1_finset_1 (k7_memstr_0 A B C))) ) ) ) ) ) ).
tt(fc18_nat_3,ax,(v1_xboole_0 (k13_pre_poly (k12_nat_3 1)))).
tt(fc18_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  => (v3_ordinal6 (k3_afinsq_1 A))) ) ).
tt(fc18_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v4_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc18_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v4_valued_0 (k1_valued_1 B C))) ) ) ) ).
tt(fc18_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_prvect_3 A B)))  &  ((v3_normsp_0 (k7_prvect_3 A B)) &  ((v4_normsp_0 (k7_prvect_3 A B)) &  ((v1_normsp_1 (k7_prvect_3 A B)) & (v2_normsp_1 (k7_prvect_3 A B))) ) ) ) ) ) ).
tt(fc18_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  => (v6_ratfunc1 (k7_ratfunc1 A) A)) ) ).
tt(fc18_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 B))  =>  ((v1_xboole_0 (k6_relat_1 B A)) & (v1_relat_1 (k6_relat_1 B A))) ) ) ).
tt(fc18_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_relat_2 A))  & (v1_relat_1 B))  => (v4_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc18_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v3_funct_1 (k1_valued_1 B C))) ) ) ) ).
tt(fc18_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k15_scmfsa_2 A B C)))) ) ).
tt(fc18_scmfsa_2,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v3_extpro_1 k1_scmfsa_2 3)) ).
tt(fc18_scmfsa6c,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((m1_scmfsa_2 B) &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  => (v2_scmfsa6c (k14_scmfsa_2 C A B))) ) ).
tt(fc18_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_xboole_0 (k3_afinsq_1 (k8_scmpds_2 B A C))))  &  ((v1_relat_1 (k3_afinsq_1 (k8_scmpds_2 B A C))) &  ((v4_relat_1 (k3_afinsq_1 (k8_scmpds_2 B A C)) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 (k8_scmpds_2 B A C)) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 (k8_scmpds_2 B A C))) &  ((v1_finset_1 (k3_afinsq_1 (k8_scmpds_2 B A C))) &  ((v1_afinsq_1 (k3_afinsq_1 (k8_scmpds_2 B A C))) & (v3_scmpds_4 (k3_afinsq_1 (k8_scmpds_2 B A C)))) ) ) ) ) ) ) ) ) ).
tt(fc18_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v1_scmpds_5 (k11_scmpds_2 A B C))) ) ).
tt(fc18_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_6 C D A B)))  &  ((v1_relat_1 (k4_scmpds_6 C D A B)) &  ((v4_relat_1 (k4_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_6 C D A B)) &  ((v1_finset_1 (k4_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k4_scmpds_6 C D A B)) & (v2_compos_1 (k4_scmpds_6 C D A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc18_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  => (v2_amistd_1 (k8_scmring2 A B) 2 (k1_scmring2 A))) ) ).
tt(fc18_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ((v4_scmyciel (k6_scmyciel A)) & (v12_scmyciel (k6_scmyciel A))) ) ) ).
tt(fc18_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8c B A)))  &  ((v1_relat_1 (k2_scmfsa8c B A)) &  ((v4_relat_1 (k2_scmfsa8c B A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8c B A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8c B A)) &  ((v1_finset_1 (k2_scmfsa8c B A)) &  ((v1_afinsq_1 (k2_scmfsa8c B A)) & (v1_scmfsa7b (k2_scmfsa8c B A))) ) ) ) ) ) ) ) ) ).
tt(fc18_simplex0,ax, (! [A:$i] :  ( ((v4_matroid0 A) & (l1_pre_topc A))  =>  ((v1_xxreal_0 (k1_xxreal_3 (k6_simplex0 A) 1)) & (v7_ordinal1 (k1_xxreal_3 (k6_simplex0 A) 1))) ) ) ).
tt(fc18_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc18_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (l1_struct_0 A)) )  =>  ( (~ (v1_xboole_0 (k7_struct_0 A)))  & (v7_ordinal1 (k7_struct_0 A))) ) ) ).
tt(fc18_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k6_tex_4 A B)))  & (v1_pre_topc (k6_tex_4 A B))) ) ) ).
tt(fc18_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v3_pre_topc (k4_group_2 A C B) A)) ) ).
tt(fc18_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  (~ (v1_xboole_0 (k3_topreal9 A B C))) ) ) ).
tt(fc18_toprealb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k6_toprealb (k1_fcont_1 A B))) &  ((v1_funct_2 (k6_toprealb (k1_fcont_1 A B)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 A B))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 A B)))))) & (v1_t_0topsp (k6_toprealb (k1_fcont_1 A B)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 A B)))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 A B)))))) ) ) ) ).
tt(fc18_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  =>  ((v1_relat_1 (k72_valued_2 A A B C)) &  ((v1_funct_1 (k72_valued_2 A A B C)) & (v1_finseq_1 (k72_valued_2 A A B C))) ) ) ) ).
tt(fc18_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v6_trees_3 A)) ) )  =>  ((v1_relat_1 (k2_funct_6 A)) &  ((v1_funct_1 (k2_funct_6 A)) &  ((v1_finseq_1 (k2_funct_6 A)) & (v4_trees_3 (k2_funct_6 A))) ) ) ) ) ).
tt(fc18_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_valued_0 A))  & (v1_relat_1 B))  => (v3_valued_0 (k4_xboole_0 A B))) ) ).
tt(fc18_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k7_valued_1 C D)) & (v1_partfun1 (k7_valued_1 C D) A)) ) ) ).
tt(fc18_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v3_valued_0 (k1_funct_1 D B))) ) ).
tt(fc18_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k12_waybel_0 A B))) ) ) ).
tt(fc18_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v6_waybel23 B A) & (m1_waybel23 B A)) )  =>  ((v1_funct_1 (k5_waybel23 A B)) &  ((v1_funct_2 (k5_waybel23 A B) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) & (v18_waybel_0 (k5_waybel23 A B) A (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ).
tt(fc18_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k10_waybel_4 A)) &  ((v1_funct_2 (k10_waybel_4 A) (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A)))) & (v5_orders_3 (k10_waybel_4 A) (k8_waybel_4 A) (k2_yellow_1 (k3_waybel_4 A)))) ) ) ) ).
tt(fc18_waybel_9,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v5_orders_2 (k3_waybel_9 A)) & (v6_waybel_0 (k3_waybel_9 A) A)) ) ) ).
tt(fc18_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k6_xcmplx_0 B A))) ) ) ).
tt(fc18_xxreal_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_membered A) & (v6_xxreal_2 A))  &  ((v2_membered B) & (v6_xxreal_2 B)) )  => (v6_xxreal_2 (k3_xboole_0 A B))) ) ).
tt(fc18_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k3_xxreal_3 A B))) ) ) ) ).
tt(fc18_yellow_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v1_lattice3 (k6_yellow_1 A B))) ) ) ).
tt(fc18_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_xboole_0 (k6_yellow_6 A))) ) ) ).
tt(fc19_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  ( (~ (v1_xboole_0 (k38_abcmiz_1 A)))  & (v3_trees_3 (k38_abcmiz_1 A))) ) ) ).
tt(fc19_abian,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_setfam_1 (k1_zfmisc_1 A))) ) ) ).
tt(fc19_afinsq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  => (v5_relat_1 (k7_afinsq_1 B C D) A)) ) ).
tt(fc19_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ( (~ (v7_struct_0 (g4_algstr_0 A B C)))  & (v22_algstr_0 (g4_algstr_0 A B C))) ) ) ).
tt(fc19_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((v1_funct_1 (k18_algstr_4 A B C)) &  ((v1_funct_2 (k18_algstr_4 A B C) (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B))) & (v1_group_6 (k18_algstr_4 A B C) (k14_algstr_4 A) (k14_algstr_4 B))) ) ) ) ).
tt(fc19_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v4_compos_0 (k7_ami_3 A) (u1_compos_1 k1_ami_3)))  &  ((v2_amistd_1 (k7_ami_3 A) 2 k1_ami_3) &  (~ (v4_amistd_1 (k7_ami_3 A) 2 k1_ami_3)) ) ) ) ) ).
tt(fc19_binop_2,ax, ((v1_funct_1 k46_binop_2) &  ((v1_funct_2 k46_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) & (v1_setwiseo k46_binop_2 k4_numbers)) ) ).
tt(fc19_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v1_xboole_0 (k2_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(fc19_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) &  ((v4_msualg_1 (k7_circcomb A B C D) (k5_circcomb C D)) & (v4_circcomb (k7_circcomb A B C D) (k5_circcomb C D))) ) ) ) ).
tt(fc19_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) &  ((v3_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) ) ) ) )  =>  ((v4_msualg_1 (k6_closure1 A B C) A) & (v9_closure1 (k6_closure1 A B C) A)) ) ) ).
tt(fc19_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((l2_msualg_1 B A) &  ((v6_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) )  =>  ((v11_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A) & (v17_closure2 (g1_closure2 A (u3_msualg_1 A B) C) A)) ) ) ).
tt(fc19_compos_0,ax,(v5_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)))).
tt(fc19_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  (~ (v2_compos_1 C A)) ) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) &  ((v1_finset_1 (k7_compos_1 A B C)) &  (~ (v2_compos_1 (k7_compos_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(fc19_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k5_comput_1 1 A)) &  ((v4_relat_1 (k5_comput_1 1 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 1 A)) &  ((v4_valued_0 (k5_comput_1 1 A)) &  ((v2_margrel1 (k5_comput_1 1 A)) & (v8_comput_1 (k5_comput_1 1 A) 1)) ) ) ) ) ) ) ).
tt(fc19_dickson,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) & (v5_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson)))) ) ) ).
tt(fc19_euclid_9,ax,(v7_struct_0 (k3_pcomps_1 (k14_euclid k6_numbers)))).
tt(fc19_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  => (v1_finset_1 (k10_funct_7 A B C))) ) ).
tt(fc19_finseq_1,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k10_finseq_1 A B))) ) ).
tt(fc19_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_finset_1 A))  => (v1_finset_1 (k9_xtuple_0 A))) ) ).
tt(fc19_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 D C)) & (v1_finseq_1 (k3_relat_1 D C))) ) ) ).
tt(fc19_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k27_fomodel1 A) A)) ) ).
tt(fc19_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  ( ((v3_fomodel2 C A B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v3_fomodel2 D A B) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v3_fomodel2 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D) A (k1_nat_1 B 1))) ) ).
tt(fc19_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) & (v5_relat_1 B A)) )  =>  ((v1_relat_1 (k2_relat_1 B)) & (v4_relat_1 (k2_relat_1 B) A)) ) ) ).
tt(fc19_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k33_fomodel2 A)))) ) )  => (v4_fomodel4 (k4_tarski (k2_xboole_0 C (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B)) B) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc19_funcop_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (v1_funcop_1 (k16_funcop_1 A B))) ) ).
tt(fc19_funct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v3_relat_1 A) & (v1_funct_1 A)) )  => (v1_xboole_0 (k1_funct_1 A B))) ) ).
tt(fc19_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) &  ((v11_functor0 D A B) & (l2_functor0 D A B)) )  &  ((v11_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v10_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc19_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k8_gate_1 B A C))) ) ).
tt(fc19_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v3_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v3_glib_001 (k9_glib_001 A B C D) A)) ) ).
tt(fc19_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v1_cat_1 (k29_grcat_1 A))) ) ).
tt(fc19_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  &  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) ) ) )  => (v2_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ).
tt(fc19_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  ( (~ (v2_struct_0 (k10_hahnban1 A)))  & (v1_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(fc19_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k14_ideal_1 A B C))) ) ) ).
tt(fc19_jordan,ax, ((v1_funct_1 k7_jordan) &  ((v1_funct_2 k7_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 k7_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ).
tt(fc19_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k8_member_1 A B))) ) ).
tt(fc19_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_membered (k1_enumset1 A B C))) ) ).
tt(fc19_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((l1_memstr_0 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_finset_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k6_memstr_0 A B C)) &  ((v4_relat_1 (k6_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k6_memstr_0 A B C)) &  ((v5_funct_1 (k6_memstr_0 A B C) (k2_memstr_0 A B)) & (v1_finset_1 (k6_memstr_0 A B C))) ) ) ) ) ) ).
tt(fc19_nat_3,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  => (v3_card_1 (k13_pre_poly (k12_nat_3 (k1_newton A B))) 1)) ) ).
tt(fc19_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v2_card_3 (k1_tarski A))) ) ).
tt(fc19_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v3_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc19_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k12_pre_poly A B C)) &  ((v4_relat_1 (k12_pre_poly A B C) A) &  ((v1_funct_1 (k12_pre_poly A B C)) &  ((v1_partfun1 (k12_pre_poly A B C) A) & (v4_valued_0 (k12_pre_poly A B C))) ) ) ) ) ) ).
tt(fc19_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_prvect_3 A B)))  &  ((v13_algstr_0 (k7_prvect_3 A B)) &  ((v2_rlvect_1 (k7_prvect_3 A B)) &  ((v3_rlvect_1 (k7_prvect_3 A B)) &  ((v4_rlvect_1 (k7_prvect_3 A B)) &  ((v5_rlvect_1 (k7_prvect_3 A B)) &  ((v6_rlvect_1 (k7_prvect_3 A B)) &  ((v7_rlvect_1 (k7_prvect_3 A B)) &  ((v8_rlvect_1 (k7_prvect_3 A B)) &  ((v3_normsp_0 (k7_prvect_3 A B)) &  ((v4_normsp_0 (k7_prvect_3 A B)) &  ((v1_normsp_1 (k7_prvect_3 A B)) & (v2_normsp_1 (k7_prvect_3 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc19_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  =>  (~ (v4_ratfunc1 (k8_ratfunc1 A) A)) ) ) ).
tt(fc19_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k7_relat_1 A B))) ) ).
tt(fc19_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_relat_2 A))  & (v1_relat_1 B))  => (v4_relat_2 (k3_xboole_0 B A))) ) ).
tt(fc19_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v3_funct_1 (k45_valued_1 B C))) ) ) ) ).
tt(fc19_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v4_amistd_1 (k16_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc19_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  =>  ((v1_relat_1 (k16_funcop_1 A B)) &  ((v4_relat_1 (k16_funcop_1 A B) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k16_funcop_1 A B)) &  ((v5_funct_1 (k16_funcop_1 A B) (k2_memstr_0 3 k1_scmfsa_2)) & (v4_memstr_0 (k16_funcop_1 A B) 3 k1_scmfsa_2)) ) ) ) ) ) ).
tt(fc19_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  => (v2_scmfsa6c (k16_scmfsa_2 B A))) ) ).
tt(fc19_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_xboole_0 (k3_afinsq_1 (k9_scmpds_2 B A C))))  &  ((v1_relat_1 (k3_afinsq_1 (k9_scmpds_2 B A C))) &  ((v4_relat_1 (k3_afinsq_1 (k9_scmpds_2 B A C)) k5_numbers) &  ((v5_relat_1 (k3_afinsq_1 (k9_scmpds_2 B A C)) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_afinsq_1 (k9_scmpds_2 B A C))) &  ((v1_finset_1 (k3_afinsq_1 (k9_scmpds_2 B A C))) &  ((v1_afinsq_1 (k3_afinsq_1 (k9_scmpds_2 B A C))) & (v3_scmpds_4 (k3_afinsq_1 (k9_scmpds_2 B A C)))) ) ) ) ) ) ) ) ) ).
tt(fc19_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v1_scmpds_5 (k12_scmpds_2 A B C D))) ) ).
tt(fc19_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k9_scmpds_6 B C A)))  &  ((v1_relat_1 (k9_scmpds_6 B C A)) &  ((v4_relat_1 (k9_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k9_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k9_scmpds_6 B C A)) &  ((v1_finset_1 (k9_scmpds_6 B C A)) &  ((v1_afinsq_1 (k9_scmpds_6 B C A)) &  ((v2_scmpds_4 (k9_scmpds_6 B C A)) & (v3_scmpds_4 (k9_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc19_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  => (v1_amistd_1 (k4_xtuple_0 (k9_scmring2 A C B)) 2 (k1_scmring2 A))) ) ).
tt(fc19_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v12_scmyciel A))  =>  ((v4_scmyciel (k6_scmyciel A)) & (v6_scmyciel (k6_scmyciel A))) ) ) ).
tt(fc19_sfmastr1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v1_ami_2 (k1_sfmastr1 A B)) &  (~ (v1_scmfsa_m (k1_sfmastr1 A B))) ) ) ) ).
tt(fc19_simplex0,ax, (! [A:$i] :  ( ((v4_matroid0 A) & (l1_pre_topc A))  =>  ((v1_xxreal_0 (k6_simplex0 A)) & (v1_int_1 (k6_simplex0 A))) ) ) ).
tt(fc19_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(fc19_struct_0,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) &  ((v13_struct_0 B A) & (l1_struct_0 B)) )  => (v3_card_1 (u1_struct_0 B) A)) ) ).
tt(fc19_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v7_struct_0 (k6_tex_4 A B)))  & (v1_pre_topc (k6_tex_4 A B))) ) ) ).
tt(fc19_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k1_group_2 A B) A)) ) ).
tt(fc19_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  (~ (v1_xboole_0 (k6_jgraph_6 A B C))) ) ) ).
tt(fc19_toprealb,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v1_topreal2 (k3_topreal9 2 B A))) ) ).
tt(fc19_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 A) &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  =>  ((v1_relat_1 (k78_valued_2 A A B C)) &  ((v1_funct_1 (k78_valued_2 A A B C)) & (v1_finseq_1 (k78_valued_2 A A B C))) ) ) ) ).
tt(fc19_trees_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((v1_relat_1 (k13_funct_3 A B)) &  ((v1_funct_1 (k13_funct_3 A B)) & (v3_trees_2 (k13_funct_3 A B))) ) ) ) ).
tt(fc19_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  & (v1_relat_1 B))  => (v5_relat_1 (k3_xboole_0 A B) k3_numbers)) ) ).
tt(fc19_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k7_valued_1 C D)) & (v1_partfun1 (k7_valued_1 C D) A)) ) ) ).
tt(fc19_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v4_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v5_relat_1 (k1_funct_1 D B) k3_numbers)) ) ).
tt(fc19_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k11_waybel_0 A B))) ) ) ).
tt(fc19_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k9_waybel_4 A)) &  ((v2_funct_1 (k9_waybel_4 A)) & (v1_funct_2 (k9_waybel_4 A) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A)))) ) ) ) ).
tt(fc19_waybel_9,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  ((v4_orders_2 (k3_waybel_9 A)) & (v6_waybel_0 (k3_waybel_9 A) A)) ) ) ).
tt(fc19_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v2_xxreal_0 (k6_xcmplx_0 A B))) ) ).
tt(fc19_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  (~ (v1_xxreal_2 (k3_xxreal_1 A B))) ) ) ).
tt(fc19_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 B A)) &  (~ (v2_xxreal_0 (k3_xxreal_3 B A))) ) ) ) ).
tt(fc19_yellow_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m3_yellow_6 C (u1_struct_0 B) A)) )  =>  ((v1_orders_2 (k5_yellow_1 (u1_struct_0 B) C)) &  ((v4_orders_2 (k5_yellow_1 (u1_struct_0 B) C)) & (v7_waybel_0 (k5_yellow_1 (u1_struct_0 B) C))) ) ) ) ).
tt(fc1_abcmiz_0,ax, (! [A:$i] :  ( ((v1_abcmiz_0 A) & (l1_orders_2 A))  => (v1_rewrite1 (u1_orders_2 A))) ) ).
tt(fc1_abcmiz_1,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k1_abcmiz_1 A))) ) ).
tt(fc1_abcmiz_a,ax, ((v1_msualg_1 k27_abcmiz_1) &  ((v1_instalg1 k27_abcmiz_1) &  ((v1_abcmiz_1 k27_abcmiz_1) & (v1_abcmiz_a k27_abcmiz_1)) ) ) ).
tt(fc1_abian,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_abian (k3_xcmplx_0 2 A))) ) ).
tt(fc1_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xreal_0 (k1_absvalue A)) & (v1_int_1 (k1_absvalue A))) ) ) ).
tt(fc1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  => (v7_ordinal1 (k9_xtuple_0 A))) ) ).
tt(fc1_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v1_incsp_1 (k13_afproj A)) &  ((v6_incsp_1 (k13_afproj A)) &  ((v1_incproj (k13_afproj A)) &  ((v2_incproj (k13_afproj A)) &  ((v3_incproj (k13_afproj A)) & (v4_incproj (k13_afproj A))) ) ) ) ) ) ) ).
tt(fc1_afvect01,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  =>  ( (~ (v2_struct_0 (g1_analoaf A B)))  & (v1_analoaf (g1_analoaf A B))) ) ) ).
tt(fc1_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_afvect0 A B)))  & (v8_algstr_0 (k5_afvect0 A B))) ) ) ).
tt(fc1_algspec1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_finseq_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_finseq_2 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) )  =>  ( (~ (v11_struct_0 (g1_msualg_1 A B C D)))  & (v1_msualg_1 (g1_msualg_1 A B C D))) ) ) ).
tt(fc1_algstr_1,ax, ((v3_rlvect_1 k3_algstr_0) &  ((v4_rlvect_1 k3_algstr_0) &  ((v1_algstr_1 k3_algstr_0) & (v4_algstr_1 k3_algstr_0)) ) ) ).
tt(fc1_algstr_3,ax, ( (~ (v2_struct_0 k3_algstr_3))  & (v1_algstr_3 k3_algstr_3)) ).
tt(fc1_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C))  =>  ((v5_ordinal1 (k5_relat_1 B C)) & (v1_relat_1 (k5_relat_1 B C))) ) ) ).
tt(fc1_altcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  & (m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B))) )  =>  ( (~ (v2_struct_0 (g2_altcat_1 A B C)))  & (v6_altcat_1 (g2_altcat_1 A B C))) ) ) ).
tt(fc1_altcat_2,ax, (! [A:$i] :  ((v1_relat_1 (k1_pboole A)) &  ((v4_relat_1 (k1_pboole A) A) &  ((v1_funct_1 (k1_pboole A)) &  ((v1_partfun1 (k1_pboole A) A) & (v1_funcop_1 (k1_pboole A))) ) ) ) ) ).
tt(fc1_altcat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k1_altcat_1 A B B))) ) ) ).
tt(fc1_ami_2,ax, (~ (v1_xboole_0 k1_ami_2)) ).
tt(fc1_ami_3,ax, ( (~ (v2_struct_0 k1_ami_3))  & (v1_extpro_1 k1_ami_3 2)) ).
tt(fc1_ami_4,ax, ((v1_relat_1 k1_ami_4) &  ((v4_relat_1 k1_ami_4 k5_numbers) &  ((v5_relat_1 k1_ami_4 (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 k1_ami_4) & (v1_finset_1 k1_ami_4)) ) ) ) ).
tt(fc1_ami_5,ax, (~ (v1_finset_1 (k8_struct_0 k1_ami_3))) ).
tt(fc1_ami_6,ax,(v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k2_compos_1 k1_ami_3)))).
tt(fc1_amistd_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ((v2_memstr_0 B A) & (l1_extpro_1 B A))  &  ((m1_subset_1 C (u1_compos_1 B)) &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_1 (k3_funct_2 (u1_compos_1 B) (k1_funct_2 (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B)))) (u1_extpro_1 A B) C) D)) & (v1_funct_1 (k1_funct_1 (k3_funct_2 (u1_compos_1 B) (k1_funct_2 (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B))) (k4_card_3 (k3_relat_1 (u1_memstr_0 A B) (u2_memstr_0 A B)))) (u1_extpro_1 A B) C) D))) ) ) ).
tt(fc1_amistd_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ((v1_relat_1 (k1_amistd_3 A B C)) &  ((v5_relat_1 (k1_amistd_3 A B C) k5_numbers) &  ((v5_ordinal1 (k1_amistd_3 A B C)) &  ((v1_funct_1 (k1_amistd_3 A B C)) & (v2_funct_1 (k1_amistd_3 A B C))) ) ) ) ) ) ).
tt(fc1_amistd_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  &  ( ((v3_amistd_2 C A B) & (m1_subset_1 C (u1_compos_1 B)))  & (m1_subset_1 D k5_numbers)) ) )  => (v3_amistd_2 (k5_compos_0 (u1_compos_1 B) C D) A B)) ) ).
tt(fc1_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v2_ami_wstd (k4_amistd_1 A) A)) ) ) ).
tt(fc1_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k2_analmetr A B C)))  & (v1_analmetr (k2_analmetr A B C))) ) ) ).
tt(fc1_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_analoaf A)))  & (v1_analoaf (k2_analoaf A))) ) ) ).
tt(fc1_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k5_analort A B C)))  & (v1_analoaf (k5_analort A B C))) ) ) ).
tt(fc1_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_anproj_1 A))) ) ) ).
tt(fc1_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) &  ((v2_collsp (k5_anproj_1 A)) & (v3_collsp (k5_anproj_1 A))) ) ) ) ).
tt(fc1_aofa_000,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (v2_relat_1 (k10_finseq_1 A B))) ) ).
tt(fc1_aofa_i00,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_finset_1 B)) )  =>  (~ (v1_finset_1 (k1_funct_2 A B))) ) ) ).
tt(fc1_armstrng,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) )  => (v1_finseq_1 (k1_funct_1 A B))) ) ).
tt(fc1_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_arrow A))) ) ) ).
tt(fc1_arytm_2,ax, (~ (v1_xboole_0 k1_arytm_2)) ).
tt(fc1_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((v3_ordinal1 (k6_ordinal3 A B)) & (v7_ordinal1 (k6_ordinal3 A B))) ) ) ).
tt(fc1_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k5_asympt_0 A B)) &  ((v1_funct_2 (k5_asympt_0 A B) k5_numbers k1_numbers) & (v2_asympt_0 (k5_asympt_0 A B))) ) ) ) ).
tt(fc1_asympt_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_xxreal_0 A) & (m1_subset_1 A k1_numbers))  &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k1_asympt_1 A B C)) &  ((v1_funct_2 (k1_asympt_1 A B C) k5_numbers k1_numbers) & (v4_asympt_0 (k1_asympt_1 A B C))) ) ) ) ).
tt(fc1_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_autalg_1 A)))  &  ((v15_algstr_0 (k3_autalg_1 A)) &  ((v2_group_1 (k3_autalg_1 A)) & (v3_group_1 (k3_autalg_1 A))) ) ) ) ) ).
tt(fc1_bagorder,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pre_poly A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_pre_poly (k5_relat_1 A B))) ) ) ).
tt(fc1_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v10_bcialg_1 (k4_struct_0 A) A) & (v1_bcialg_2 (k4_struct_0 A) A)) ) ) ).
tt(fc1_bcialg_4,ax, ((v13_struct_0 k2_bcialg_4 1) & (v1_bcialg_4 k2_bcialg_4)) ).
tt(fc1_bcialg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (~ (v1_xboole_0 (k5_bcialg_6 A B C))) ) ) ).
tt(fc1_bhsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_bhsp_1 A B C D E)))  & (v1_bhsp_1 (g1_bhsp_1 A B C D E))) ) ) ).
tt(fc1_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A)) ) )  =>  ((v1_funct_1 (k1_bilinear A B C)) &  ((v1_funct_2 (k1_bilinear A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v1_bilinear (k1_bilinear A B C) A B C)) ) ) ) ).
tt(fc1_binop_2,ax, ((v1_funct_1 k27_binop_2) &  ((v1_funct_2 k27_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) &  ((v1_binop_1 k27_binop_2 k2_numbers) & (v2_binop_1 k27_binop_2 k2_numbers)) ) ) ).
tt(fc1_bintree1,ax, ( (~ (v1_xboole_0 (k2_trees_1 k6_numbers)))  &  ((v1_trees_1 (k2_trees_1 k6_numbers)) & (v1_bintree1 (k2_trees_1 k6_numbers))) ) ).
tt(fc1_bintree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  ((v1_funct_1 (k1_bintree2 A B)) &  ((v2_funct_1 (k1_bintree2 A B)) & (v1_funct_2 (k1_bintree2 A B) (k2_trees_2 A B) k5_numbers)) ) ) ) ).
tt(fc1_bor_cant,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k3_bor_cant A B)) &  ((v2_funct_1 (k3_bor_cant A B)) & (v1_funct_2 (k3_bor_cant A B) k5_numbers k5_numbers)) ) ) ) ).
tt(fc1_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 D E)) &  ((v1_funct_2 (k3_relat_1 D E) (u1_struct_0 A) (u1_struct_0 C)) & (v5_pre_topc (k3_relat_1 D E) A C)) ) ) ) ).
tt(fc1_borsuk_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_pre_topc (k3_struct_0 A) A A) & (v1_t_0topsp (k3_struct_0 A) A A)) ) ) ) ) ).
tt(fc1_borsuk_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v3_tops_2 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc1_borsuk_4,ax, ( (~ (v2_struct_0 k1_borsuk_4))  & (v1_pre_topc k1_borsuk_4)) ).
tt(fc1_borsuk_5,ax, ((v2_pre_topc k3_topmetr) & (v1_borsuk_2 k3_topmetr)) ).
tt(fc1_borsuk_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_topmetr A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_topmetr B) & (l1_pre_topc B)) ) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  => (v1_xreal_0 (k1_xtuple_0 C))) ) ).
tt(fc1_borsuk_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) & (v1_valued_0 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v2_funct_1 (k7_valued_1 A B))) ) ) ) ).
tt(fc1_brouwer2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v9_rltopsp1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v9_rltopsp1 (k5_rusub_4 (k15_euclid A) B C) (k15_euclid A))) ) ).
tt(fc1_brouwer,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (~ (v1_xboole_0 (k1_brouwer A B))) ) ) ).
tt(fc1_bspace,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k7_bspace A)))  &  ((v13_algstr_0 (k7_bspace A)) &  ((v8_vectsp_1 (k7_bspace A) k2_bspace) &  ((v9_vectsp_1 (k7_bspace A) k2_bspace) &  ((v10_vectsp_1 (k7_bspace A) k2_bspace) &  ((v11_vectsp_1 (k7_bspace A) k2_bspace) &  ((v2_rlvect_1 (k7_bspace A)) &  ((v3_rlvect_1 (k7_bspace A)) & (v4_rlvect_1 (k7_bspace A))) ) ) ) ) ) ) ) ) ).
tt(fc1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k4_bvfunc_1 A B)) &  ((v1_funct_1 (k4_bvfunc_1 A B)) & (v1_margrel1 (k4_bvfunc_1 A B))) ) ) ) ).
tt(fc1_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k1_bvfunc26 A B)) &  ((v1_funct_1 (k1_bvfunc26 A B)) & (v1_margrel1 (k1_bvfunc26 A B))) ) ) ) ).
tt(fc1_c0sp2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_c0sp2 A B)) &  ((v1_funct_2 (k1_c0sp2 A B) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k1_c0sp2 A B) A)) ) ) ) ).
tt(fc1_calcul_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k1_calcul_2 A B))) ) ).
tt(fc1_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_cantor_1 (u1_pre_topc A) A)) ) ).
tt(fc1_card_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k1_card_1 A)) & (v1_card_1 (k1_card_1 A))) ) ) ).
tt(fc1_card_2,ax, (! [A:$i,B:$i] :  (~ (v7_ordinal1 (k4_tarski A B))) ) ).
tt(fc1_card_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_card_3 (k5_relat_1 A B))) ) ) ).
tt(fc1_card_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  => (v3_ordinal1 (k3_card_3 A))) ) ).
tt(fc1_card_fil,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (~ (v1_xboole_0 (k7_setfam_1 A B))) ) ) ).
tt(fc1_cardfin2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v2_xxreal_0 (k25_sin_cos A))) ) ).
tt(fc1_card_fin,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_finset_1 (k5_relat_1 A B))) ) ) ).
tt(fc1_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~ (v1_xboole_0 (k4_classes1 A))) ) ) ).
tt(fc1_cat_1,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k3_cat_1 A B)))  &  ((v7_struct_0 (k3_cat_1 A B)) &  ( (~ (v11_struct_0 (k3_cat_1 A B)))  &  ((v15_struct_0 (k3_cat_1 A B)) & (v1_cat_1 (k3_cat_1 A B))) ) ) ) ) ).
tt(fc1_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k2_cat_2 A B))) ) ) ).
tt(fc1_cat_4,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k5_cat_4 A B)))  &  ((v7_struct_0 (k5_cat_4 A B)) &  ( (~ (v11_struct_0 (k5_cat_4 A B)))  &  ((v15_struct_0 (k5_cat_4 A B)) & (v2_cat_4 (k5_cat_4 A B))) ) ) ) ) ).
tt(fc1_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k9_cat_5 A B))) ) ) ).
tt(fc1_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v7_ordinal1 (k1_catalan1 A))) ) ).
tt(fc1_catalan2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) => (v5_relat_1 (k2_funcop_1 A B) k5_numbers)) ) ).
tt(fc1_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v1_catalg_1 B A))  & (l3_msualg_1 B A)) )  =>  ((v1_relat_1 (u3_msualg_1 A B)) &  ( (~ (v3_relat_1 (u3_msualg_1 A B)))  &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) & (v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc1_cayley,ax, (! [A:$i] : (v2_funct_2 (k1_partit_2 A k1_xboole_0) k1_xboole_0)) ).
tt(fc1_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_clvect_1 (k8_cfuncdom A)) & (v1_cfuncdom (k8_cfuncdom A))) ) ) ).
tt(fc1_cc0sp2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (v1_xcmplx_0 B))  =>  ((v1_funct_1 (k1_cc0sp2 A B)) &  ((v1_funct_2 (k1_cc0sp2 A B) (u1_struct_0 A) k2_numbers) & (v1_cc0sp2 (k1_cc0sp2 A B) A)) ) ) ) ).
tt(fc1_cfdiff_1,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  ((v1_funct_1 (k1_cfdiff_1 A)) &  ((v1_funct_2 (k1_cfdiff_1 A) k5_numbers k2_numbers) & (v2_comseq_2 (k1_cfdiff_1 A))) ) ) ) ).
tt(fc1_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_cfuncdom A)))  &  ((v13_algstr_0 (k6_cfuncdom A)) &  ((v2_rlvect_1 (k6_cfuncdom A)) &  ((v3_rlvect_1 (k6_cfuncdom A)) &  ((v4_rlvect_1 (k6_cfuncdom A)) &  ((v1_clvect_1 (k6_cfuncdom A)) &  ((v2_clvect_1 (k6_cfuncdom A)) &  ((v3_clvect_1 (k6_cfuncdom A)) &  ((v4_clvect_1 (k6_cfuncdom A)) & (v5_clvect_1 (k6_cfuncdom A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc1_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~ (v1_xboole_0 (k2_cgames_1 A))) ) ) ).
tt(fc1_chain_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (~ (v1_zfmisc_1 (k2_xboole_0 A B))) ) ) ).
tt(fc1_circcmb2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_2 A k6_margrel1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) k6_margrel1)))) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb A k6_margrel1 B C) (k5_circcomb B C)) &  ((v4_msualg_1 (k7_circcomb A k6_margrel1 B C) (k5_circcomb B C)) & (v6_circcomb (k7_circcomb A k6_margrel1 B C) (k5_circcomb B C))) ) ) ) ).
tt(fc1_circcmb3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v8_struct_0 (k5_circcomb B A)) &  ( (~ (v11_struct_0 (k5_circcomb B A)))  & (v1_msualg_1 (k5_circcomb B A))) ) ) ) ).
tt(fc1_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 C D)) &  ((v4_relat_1 (k1_funct_4 C D) (k2_xboole_0 A B)) & (v1_funct_1 (k1_funct_4 C D))) ) ) ) ).
tt(fc1_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B)))) ) )  =>  ( (~ (v2_struct_0 (k1_circtrm1 A B C)))  &  ((v1_msualg_1 (k1_circtrm1 A B C)) & (v1_circcomb (k1_circtrm1 A B C))) ) ) ) ).
tt(fc1_circuit1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_finset_1 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C))) ) ).
tt(fc1_classes1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_classes1 A))) ) ).
tt(fc1_classes2,ax, (! [A:$i] : (v2_classes1 (k1_classes1 A))) ).
tt(fc1_clopban1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_clopban1 A B)))  &  ((v13_algstr_0 (k3_clopban1 A B)) &  ((v2_rlvect_1 (k3_clopban1 A B)) &  ((v3_rlvect_1 (k3_clopban1 A B)) &  ((v4_rlvect_1 (k3_clopban1 A B)) &  ((v1_clvect_1 (k3_clopban1 A B)) &  ((v2_clvect_1 (k3_clopban1 A B)) &  ((v3_clvect_1 (k3_clopban1 A B)) &  ((v4_clvect_1 (k3_clopban1 A B)) & (v5_clvect_1 (k3_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc1_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_clopban2 A)))  & (v36_algstr_0 (k7_clopban2 A))) ) ) ).
tt(fc1_clopban3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v2_clopban3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_normsp_0 A B)) &  ((v1_funct_2 (k2_normsp_0 A B) k5_numbers k1_numbers) & (v1_series_1 (k2_normsp_0 A B))) ) ) ) ).
tt(fc1_clopban4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_clopban4 A B)) &  ((v1_funct_2 (k1_clopban4 A B) k5_numbers (u1_struct_0 A)) & (v2_clopban3 (k1_clopban4 A B) A)) ) ) ) ).
tt(fc1_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k15_pralg_1 B C)) &  ((v4_relat_1 (k15_pralg_1 B C) A) &  ((v1_funct_1 (k15_pralg_1 B C)) & (v1_partfun1 (k15_pralg_1 B C) A)) ) ) ) ) ).
tt(fc1_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ( (~ (v1_xboole_0 (k1_closure2 A B)))  &  ((v4_funct_1 (k1_closure2 A B)) & (v2_card_3 (k1_closure2 A B))) ) ) ) ).
tt(fc1_clvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_clvect_1 A B C D)))  & (v1_clvect_1 (g1_clvect_1 A B C D))) ) ) ).
tt(fc1_cohsp_1,ax, ((v1_classes1 (k1_tarski k1_xboole_0)) & (v1_coh_sp (k1_tarski k1_xboole_0))) ).
tt(fc1_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k3_coh_sp A))) ) ).
tt(fc1_compact1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_compact1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_compts_1 (k2_pre_topc A B) A)) ) ).
tt(fc1_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xreal_0 (k1_complex1 A))) ) ).
tt(fc1_complfld,ax, ( (~ (v2_struct_0 k1_complfld))  & (v36_algstr_0 k1_complfld)) ).
tt(fc1_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k1_complsp1 A)))  &  ((v1_pre_topc (k1_complsp1 A)) & (v2_pre_topc (k1_complsp1 A))) ) ) ) ).
tt(fc1_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_metric_1 A) & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k3_compl_sp A B C)))  & (v1_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(fc1_compos_0,ax,(v1_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)))).
tt(fc1_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ( (~ (v1_xboole_0 (k4_compos_1 A)))  &  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) &  ((v1_finset_1 (k4_compos_1 A)) & (v1_afinsq_1 (k4_compos_1 A))) ) ) ) ) ) ) ) ).
tt(fc1_compos_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_amistd_4 A) & (l1_compos_1 A))  &  ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A))) )  =>  ((v1_relat_1 (k11_compos_1 A B)) &  ((v4_relat_1 (k11_compos_1 A B) k5_numbers) &  ((v5_relat_1 (k11_compos_1 A B) (u1_compos_1 A)) &  ((v1_funct_1 (k11_compos_1 A B)) &  ((v1_finset_1 (k11_compos_1 A B)) &  ((v3_compos_1 (k11_compos_1 A B) A) & (v4_compos_1 (k11_compos_1 A B) A)) ) ) ) ) ) ) ) ).
tt(fc1_comptrig,ax, ((v1_xreal_0 k31_sin_cos) &  (~ (v3_xxreal_0 k31_sin_cos)) ) ).
tt(fc1_compts_1,ax, (! [A:$i] :  ((v1_pre_topc (k1_compts_1 A)) & (v2_pre_topc (k1_compts_1 A))) ) ).
tt(fc1_comput_1,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v1_comput_1 A))  =>  ((v1_relat_1 (k3_tarski A)) & (v1_funct_1 (k3_tarski A))) ) ) ).
tt(fc1_comseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) ) )  =>  ((v1_relat_1 (k1_comseq_2 B)) &  ((v4_relat_1 (k1_comseq_2 B) A) &  ((v1_funct_1 (k1_comseq_2 B)) & (v1_valued_0 (k1_comseq_2 B))) ) ) ) ) ).
tt(fc1_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k3_comseq_3 A)) &  ((v1_funct_1 (k3_comseq_3 A)) & (v3_valued_0 (k3_comseq_3 A))) ) ) ) ).
tt(fc1_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l5_struct_0 A))  =>  (~ (v1_xboole_0 (u4_struct_0 A))) ) ) ).
tt(fc1_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v3_lattices (k11_conlat_1 A)) & (v15_lattices (k11_conlat_1 A))) ) ) ) ).
tt(fc1_connsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_connsp_1 (k1_tarski B) A)) ) ).
tt(fc1_convex1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_convex1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_convex1 (k3_xboole_0 B C) A)) ) ).
tt(fc1_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_convex4 B A))  => (v1_finset_1 (k13_pre_poly B))) ) ).
tt(fc1_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B)) )  =>  (~ (v2_struct_0 (k3_convfun1 A B))) ) ) ).
tt(fc1_cqc_lang,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ( ((v3_card_1 C B) & (m1_finseq_1 C (k2_qc_lang1 A)))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A))))) ) ) )  => (v3_card_1 (k1_cqc_lang A C D) B)) ) ).
tt(fc1_cqc_sim1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  =>  (~ (v1_xboole_0 (k12_cqc_sim1 A B))) ) ) ).
tt(fc1_cqc_the1,ax, (~ (v1_xboole_0 k2_cqc_the1)) ).
tt(fc1_csspace3,ax, (~ (v1_xboole_0 k1_csspace3)) ).
tt(fc1_csspace4,ax, (~ (v1_xboole_0 k1_csspace4)) ).
tt(fc1_csspace,ax, ((v2_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace)) & (v1_clvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) ).
tt(fc1_descip_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k3_finseq_5 B)) &  ((v1_funct_1 (k3_finseq_5 B)) &  ((v3_card_1 (k3_finseq_5 B) A) & (v1_finseq_1 (k3_finseq_5 B))) ) ) ) ) ).
tt(fc1_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_1 (k3_dickson A)) & (v5_relat_2 (k3_dickson A))) ) ) ).
tt(fc1_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k3_diff_1 A B)) & (v1_funct_2 (k3_diff_1 A B) k1_numbers k1_numbers)) ) ) ).
tt(fc1_dilworth,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  ((v1_xboole_0 (k1_dilworth A)) & (v7_ordinal1 (k1_dilworth A))) ) ) ).
tt(fc1_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( (~ (v2_struct_0 (k2_diraf A)))  & (v1_analoaf (k2_diraf A))) ) ) ).
tt(fc1_dist_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B A))  =>  (~ (v1_xboole_0 (k5_dist_1 A B))) ) ) ).
tt(fc1_dtconstr,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 A)))))  =>  ( (~ (v2_struct_0 (g1_lang1 A B)))  & (v1_lang1 (g1_lang1 A B))) ) ) ).
tt(fc1_dynkin,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_finset_1 (k6_card_1 A))) ) ).
tt(fc1_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  => (v8_struct_0 (k9_int_3 A))) ) ).
tt(fc1_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (~ (v1_xboole_0 (k1_ec_pf_2 A))) ) ) ).
tt(fc1_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_endalg A)))  & (v22_algstr_0 (k3_endalg A))) ) ) ).
tt(fc1_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v4_funct_1 (k1_ens_1 A)) &  (~ (v1_xboole_0 (k1_ens_1 A))) ) ) ) ).
tt(fc1_eqrel_1,ax, (! [A:$i] :  ((v1_relat_2 (k1_eqrel_1 A)) & (v1_partfun1 (k1_eqrel_1 A) A)) ) ).
tt(fc1_equation,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m1_msualg_2 C A B)) )  =>  (~ (v1_xboole_0 (k2_equation A B C))) ) ) ).
tt(fc1_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  (~ (v1_xboole_0 (k1_euclid_4 A B C))) ) ) ).
tt(fc1_euclid_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k13_funct_3 A B)) &  ((v1_funct_1 (k13_funct_3 A B)) & (v1_finseq_1 (k13_funct_3 A B))) ) ) ) ).
tt(fc1_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v1_xboole_0 (k4_xxreal_1 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)))) ) ).
tt(fc1_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k1_euclid A))) ) ) ).
tt(fc1_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v1_xboole_0 (k1_euclidlp A))) ) ) ).
tt(fc1_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  => (v1_ordinal6 (k9_xtuple_0 A))) ) ).
tt(fc1_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v13_struct_0 (k1_extpro_1 A) 1) & (v1_extpro_1 (k1_extpro_1 A) A)) ) ) ).
tt(fc1_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (~ (v3_xxreal_0 (k3_extreal1 A))) ) ) ).
tt(fc1_facirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (~ (v1_facirc_1 (k1_tarski A))) ) ) ).
tt(fc1_facirc_2,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k1_facirc_2 A)))  &  ((v11_struct_0 (k1_facirc_2 A)) & (v1_msualg_1 (k1_facirc_2 A))) ) ) ).
tt(fc1_fcont_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v1_fcont_1 (k5_relat_1 A B))) ) ) ).
tt(fc1_fcont_3,ax,(v2_rcomp_1 (k2_subset_1 k1_numbers))).
tt(fc1_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v1_fdiff_1 A k6_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_xboole_0 (k1_seq_2 A)) & (v1_xreal_0 (k1_seq_2 A))) ) ) ).
tt(fc1_fdiff_2,ax, (! [A:$i] :  ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v1_fdiff_1 A k6_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v2_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) &  ((v1_valued_0 (k30_valued_1 A)) & (v2_comseq_2 (k30_valued_1 A))) ) ) ) ) ) ).
tt(fc1_fib_num2,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) &  (~ (v1_abian (k4_xcmplx_0 A))) ) ) ) ).
tt(fc1_fib_num3,ax, ((v2_xxreal_0 k1_fib_num) & (v1_xreal_0 k1_fib_num)) ).
tt(fc1_filter_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v1_xboole_0 (k5_filter_0 A B C))) ) ) ).
tt(fc1_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v2_struct_0 (k4_filter_1 A B)))  &  ((v3_lattices (k4_filter_1 A B)) &  ((v10_lattices (k4_filter_1 A B)) & (v3_filter_0 (k4_filter_1 A B))) ) ) ) ) ).
tt(fc1_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k3_filter_2 A B))) ) ) ).
tt(fc1_finance1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k6_finance1 A B C D))) ) ) ).
tt(fc1_finseq_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_xboole_0 A))  => (v1_xboole_0 (k1_finseq_1 A))) ) ).
tt(fc1_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k1_finseq_2 A)) &  ((v1_funct_1 (k1_finseq_2 A)) &  ((v3_card_1 (k1_finseq_2 A) A) & (v1_finseq_1 (k1_finseq_2 A))) ) ) ) ) ).
tt(fc1_finseq_3,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (v2_card_3 (k4_finseq_2 A B))) ) ).
tt(fc1_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((v1_relat_1 (k7_finseq_4 A B C D)) &  ((v1_funct_1 (k7_finseq_4 A B C D)) &  (~ (v1_xboole_0 (k7_finseq_4 A B C D))) ) ) ) ).
tt(fc1_finseq_5,ax, (! [A:$i] : (v1_zfmisc_1 (k5_finseq_1 A))) ).
tt(fc1_finseq_6,ax, (! [A:$i,B:$i,C:$i] :  (~ (v1_zfmisc_1 (k11_finseq_1 A B C))) ) ).
tt(fc1_finseq_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (v1_finseq_1 (k10_funct_7 A B C))) ) ).
tt(fc1_finset_1,ax, (! [A:$i] : (v1_finset_1 (k1_tarski A))) ).
tt(fc1_finsub_1,ax, (! [A:$i] : (v4_finsub_1 (k1_zfmisc_1 A))) ).
tt(fc1_fintopo5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  ( (~ (v2_struct_0 (k3_fintopo5 A B)))  & (v1_orders_2 (k3_fintopo5 A B))) ) ) ).
tt(fc1_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v1_xboole_0 (k9_fin_topo A (k1_struct_0 A)))) ) ).
tt(fc1_fin_topo,ax, ( (~ (v2_struct_0 k4_fin_topo))  & (v1_orders_2 k4_fin_topo)) ).
tt(fc1_flang_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (~ (v1_xboole_0 (k2_flang_2 A B))) ) ) ).
tt(fc1_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k1_fomodel0 A)) &  ((v1_funct_2 (k1_fomodel0 A) (k2_zfmisc_1 A A) A) & (v2_binop_1 (k1_fomodel0 A) A)) ) ) ) ).
tt(fc1_fomodel1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_int_1 A))  =>  ((v1_xboole_0 (k16_complex1 A)) & (v1_int_1 (k16_complex1 A))) ) ) ).
tt(fc1_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ( ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  & (m1_fomodel2 E A B D)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 C (k16_funcop_1 D E))) &  ((v1_funct_1 (k1_funct_4 C (k16_funcop_1 D E))) & (v1_fomodel2 (k1_funct_4 C (k16_funcop_1 D E)) A B)) ) ) ) ).
tt(fc1_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B k5_numbers) &  ( ((v8_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v3_card_1 D (k1_int_2 (k19_fomodel1 A C))) & (m1_subset_1 D (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) B)))) ) ) )  => (v14_fomodel1 (k1_fomodel3 A C D) (k2_nat_1 B 1) A)) ) ).
tt(fc1_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k1_fomodel4 A))) ) ) ).
tt(fc1_fraenkel,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k1_funct_2 A B))) ) ).
tt(fc1_frechet,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 (k3_pcomps_1 A))))  =>  ((v1_tops_2 (k1_frechet A B) (k3_pcomps_1 A)) & (v1_yellow_8 (k1_frechet A B) (k3_pcomps_1 A) B)) ) ) ).
tt(fc1_freealg,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  =>  ( (~ (v2_struct_0 (k3_freealg A B)))  & (v1_lang1 (k3_freealg A B))) ) ) ).
tt(fc1_fscirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (v1_xtuple_0 (k3_fscirc_2 A B C))) ) ).
tt(fc1_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_finseq_1 D A)) ) )  =>  (~ (v1_xboole_0 (k2_fsm_1 A B C D))) ) ) ).
tt(fc1_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k9_flang_1 A))) ) ) ).
tt(fc1_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k2_funcop_1 A B)) & (v1_funct_1 (k2_funcop_1 A B))) ) ).
tt(fc1_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_funcsdom A)))  & (v36_algstr_0 (k11_funcsdom A))) ) ) ).
tt(fc1_funct_1,ax, (! [A:$i,B:$i] : (v1_funct_1 (k1_tarski (k4_tarski A B)))) ).
tt(fc1_funct_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~ (v1_xboole_0 (k1_funct_2 A B))) ) ) ).
tt(fc1_funct_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k13_funct_3 A B)) &  ((v1_funct_1 (k13_funct_3 A B)) & (v1_xboole_0 (k13_funct_3 A B))) ) ) ) ).
tt(fc1_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((v1_relat_1 (k4_funct_4 A B C D)) & (v1_funct_1 (k4_funct_4 A B C D))) ) ).
tt(fc1_funct_7,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k16_funcop_1 A B))) ) ).
tt(fc1_funct_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_funct_8 A))  => (v1_funct_8 (k9_xtuple_0 A))) ) ).
tt(fc1_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  => (v1_funct_9 (k2_funcop_1 k1_numbers A) A)) ) ).
tt(fc1_functor0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  =>  ((v1_relat_1 (k2_funct_4 A)) &  ((v1_funct_1 (k2_funct_4 A)) & (v1_xboole_0 (k2_funct_4 A))) ) ) ) ).
tt(fc1_functor1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l2_altcat_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  &  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  &  ( (~ (v2_struct_0 D))  &  ((v1_altcat_2 D) & (m1_altcat_2 D A)) ) ) ) )  => (v8_functor0 (k14_functor0 A B D C) D B)) ) ).
tt(fc1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v8_functor0 D A B) &  ((v10_functor0 D A B) &  ((v13_functor0 D A B) & (l2_functor0 D A B)) ) )  &  ((v8_functor0 E B C) &  ((v10_functor0 E B C) &  ((v13_functor0 E B C) & (l2_functor0 E B C)) ) ) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v13_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc1_fuzzy_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k4_funct_3 A B)) &  ((v5_relat_1 (k4_funct_3 A B) (k1_rcomp_1 k6_numbers 1)) & (v1_funct_1 (k4_funct_3 A B))) ) ) ).
tt(fc1_fuzzy_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 B))) ) ) ).
tt(fc1_fvaluat1,ax,(v1_fvaluat1 k1_xxreal_0)).
tt(fc1_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  =>  ((v1_funct_1 (u1_algstr_0 A)) &  ((v1_funct_2 (u1_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc1_gate_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (~ (v1_xboole_0 (k1_gate_1 A))) ) ) ).
tt(fc1_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) ) )  =>  (~ (v1_xboole_0 (k3_card_3 A))) ) ) ).
tt(fc1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k7_geomtrap A B C)))  & (v1_geomtrap (k7_geomtrap A B C))) ) ) ).
tt(fc1_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (v1_xtuple_0 (k3_gfacirc2 A B C))) ) ).
tt(fc1_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (~ (v1_xboole_0 (k6_glib_000 A))) ) ) ).
tt(fc1_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ( (~ (v1_xboole_0 (k1_card_1 B)))  &  ((v1_card_1 (k1_card_1 B)) &  (~ (v1_abian (k1_card_1 B))) ) ) ) ) ).
tt(fc1_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v1_glib_000 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc1_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k5_relat_1 A k2_glib_004)) &  ((v1_glib_000 (k5_relat_1 A k2_glib_004)) & (v1_glib_003 (k5_relat_1 A k2_glib_004))) ) ) ) ).
tt(fc1_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) )  =>  ((v1_relat_1 (k5_glib_003 A)) &  ((v4_relat_1 (k5_glib_003 A) (k7_glib_000 A)) &  ((v1_funct_1 (k5_glib_003 A)) &  ((v1_partfun1 (k5_glib_003 A) (k7_glib_000 A)) & (v4_valued_0 (k5_glib_003 A))) ) ) ) ) ) ).
tt(fc1_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (~ (v1_xboole_0 (k1_goboard1 A))) ) ) ).
tt(fc1_goboard9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v3_funct_1 A))  & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) &  ( (~ (v3_funct_1 (k3_finseq_5 A)))  & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc1_gobrd11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) ) ) ).
tt(fc1_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v1_jordan1 (k3_topreal1 2 A))) ) ).
tt(fc1_graph_1,ax, (! [A:$i] :  ( ((v6_graph_1 A) & (l1_graph_1 A))  => (v1_finset_1 (u1_struct_0 A))) ) ).
tt(fc1_graph_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) & (v1_abian B)) )  => (v1_abian (k6_xcmplx_0 A B))) ) ).
tt(fc1_graph_5,ax, (~ (v1_xboole_0 k2_arytm_2)) ).
tt(fc1_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k13_graphsp A B))) ) ).
tt(fc1_grcat_1,ax,(v2_midsp_2 k3_algstr_0)).
tt(fc1_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~ (v1_xboole_0 (k6_card_1 A))) ) ) ).
tt(fc1_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k10_group_5 A)) & (v1_group_3 (k10_group_5 A) A)) ) ) ).
tt(fc1_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_uniroots A)))  &  ((v15_algstr_0 (k1_uniroots A)) &  ((v2_group_1 (k1_uniroots A)) &  ((v3_group_1 (k1_uniroots A)) & (v5_group_1 (k1_uniroots A))) ) ) ) ) ) ).
tt(fc1_grfunc_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_funct_1 (k3_xboole_0 A B))) ) ).
tt(fc1_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (~ (v1_xboole_0 (k2_grnilp_1 A))) ) ) ).
tt(fc1_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_orders_2 (g1_orders_2 (k15_pre_poly A) (k4_groeb_1 A))) & (v4_dickson (g1_orders_2 (k15_pre_poly A) (k4_groeb_1 A)))) ) ) ).
tt(fc1_groeb_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( (~ (v9_struct_0 B A))  & (m1_subset_1 B (u1_struct_0 A))) )  =>  (~ (v9_struct_0 (k4_algstr_0 A B) A)) ) ) ).
tt(fc1_groeb_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  => (v1_finset_1 (k2_polynom1 (k15_pre_poly A) B C))) ) ).
tt(fc1_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (k1_funct_2 A A)) &  ((v1_group_10 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (k1_funct_2 A A))))) ) ) ) ) )  =>  ((v1_funct_1 (k1_funct_1 D C)) &  ((v2_funct_1 (k1_funct_1 D C)) & (v1_funct_2 (k1_funct_1 D C) A A)) ) ) ) ).
tt(fc1_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v2_group_7 B A)) ) ) ) )  & (m1_subset_1 C A)) )  => (v2_group_1 (k1_funct_1 B C))) ) ).
tt(fc1_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v2_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc1_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k1_group_2 A B))) ) ).
tt(fc1_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (~ (v1_xboole_0 (k1_group_3 A))) ) ) ).
tt(fc1_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (~ (v2_struct_0 (k11_group_4 A)))  &  ((v3_lattices (k11_group_4 A)) &  ((v10_lattices (k11_group_4 A)) &  ((v13_lattices (k11_group_4 A)) & (v14_lattices (k11_group_4 A))) ) ) ) ) ) ).
tt(fc1_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k6_group_2 A)) & (v1_group_3 (k6_group_2 A) A)) ) ) ).
tt(fc1_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ((v1_relat_1 (k12_pralg_1 A B)) &  ((v2_relat_1 (k12_pralg_1 A B)) &  ((v4_relat_1 (k12_pralg_1 A B) A) &  ((v1_funct_1 (k12_pralg_1 A B)) & (v1_partfun1 (k12_pralg_1 A B) A)) ) ) ) ) ) ).
tt(fc1_group_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  =>  (~ (v1_xboole_0 (k15_group_2 A B))) ) ) ).
tt(fc1_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((v2_group_9 (k4_group_9 A B) A) & (v4_group_9 (k4_group_9 A B) A B)) ) ) ).
tt(fc1_groupp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ((v1_groupp_1 C A B) & (m1_subset_1 C (u1_struct_0 B))) ) )  => (v1_groupp_1 (k2_group_1 B C) A B)) ) ).
tt(fc1_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k7_hahnban1 A B)) &  ((v1_funct_2 (k7_hahnban1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v13_vectsp_1 (k7_hahnban1 A B) B A)) ) ) ) ).
tt(fc1_hallmar1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((m1_finseq_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C k5_numbers)) )  => (v1_finset_1 (k1_funct_1 B C))) ) ).
tt(fc1_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  => (v8_pre_topc (k3_pcomps_1 A))) ) ).
tt(fc1_helly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((v1_glib_001 (k2_helly A B B) A) & (v5_glib_001 (k2_helly A B B) A)) ) ) ).
tt(fc1_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  ((v1_funct_1 (k7_hahnban1 k1_complfld A)) &  ((v1_funct_2 (k7_hahnban1 k1_complfld A) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v1_hermitan (k7_hahnban1 k1_complfld A) A)) ) ) ) ).
tt(fc1_heyting1,ax, (! [A:$i] :  ((v3_lattices (k12_normform A)) & (v3_filter_0 (k12_normform A))) ) ).
tt(fc1_heyting2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))))  => (v1_finset_1 (k1_heyting2 A B C))) ) ).
tt(fc1_heyting3,ax, (! [A:$i,B:$i] : (v1_funct_1 (k2_zfmisc_1 A (k1_tarski B)))) ).
tt(fc1_hilbasis,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ((m1_subset_1 B A) &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_1 C) &  ((v4_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_hilbasis A B C)) &  ((v1_funct_2 (k3_hilbasis A B C) (k15_pre_poly A) (u1_struct_0 C)) & (v1_polynom1 (k3_hilbasis A B C) (k15_pre_poly A) C)) ) ) ) ).
tt(fc1_hilbert1,ax,(v5_hilbert1 k1_hilbert1)).
tt(fc1_hilbert3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  => (v2_funct_1 (k4_funct_4 k6_numbers B A k6_numbers))) ) ).
tt(fc1_idea_1,ax, (~ (v1_xboole_0 k14_idea_1)) ).
tt(fc1_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  => (v1_ideal_1 (k1_tarski (k4_struct_0 A)) A)) ) ).
tt(fc1_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (~ (v1_xboole_0 (k1_incproj A))) ) ) ).
tt(fc1_index_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  => (v1_index_1 (k2_funcop_1 A B))) ) ).
tt(fc1_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k2_xcmplx_0 A B))) ) ).
tt(fc1_int_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v7_ordinal1 (k4_xcmplx_0 A)))  & (v1_xcmplx_0 (k4_xcmplx_0 A))) ) ) ).
tt(fc1_int_3,ax, ( (~ (v2_struct_0 k1_int_3))  & (v36_algstr_0 k1_int_3)) ).
tt(fc1_int_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_finset_1 A) & (v3_membered A))  & (v1_xreal_0 B))  => (v1_finset_1 (k17_member_1 A B))) ) ).
tt(fc1_int_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k16_finseq_1 B A)) &  ((v1_funct_1 (k16_finseq_1 B A)) &  ((v1_finseq_1 (k16_finseq_1 B A)) & (v1_valued_0 (k16_finseq_1 B A))) ) ) ) ) ).
tt(fc1_int_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k13_nat_3 A)) &  ((v4_relat_1 (k13_nat_3 A) k10_newton) &  ((v1_funct_1 (k13_nat_3 A)) &  ((v1_partfun1 (k13_nat_3 A) k10_newton) & (v1_int_7 (k13_nat_3 A))) ) ) ) ) ) ).
tt(fc1_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((v1_relat_1 (k3_comseq_3 A)) &  ((v1_funct_1 (k3_comseq_3 A)) & (v1_finseq_1 (k3_comseq_3 A))) ) ) ) ).
tt(fc1_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (~ (v1_xboole_0 (k1_integra1 A))) ) ) ).
tt(fc1_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  =>  (~ (v1_xboole_0 (k3_interva1 A B C))) ) ) ).
tt(fc1_intpro_1,ax,(v7_intpro_1 k1_intpro_1)).
tt(fc1_isocat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  => (v12_cat_1 (k7_isocat_2 A B C) (k11_nattra_1 (k8_cat_2 A B) C) (k11_nattra_1 A (k11_nattra_1 B C)))) ) ).
tt(fc1_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k1_jgraph_1 A))) ) ) ).
tt(fc1_jgraph_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ((v1_funct_1 (k2_jgraph_2 A B C D)) &  ((v1_funct_2 (k2_jgraph_2 A B C D) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (v5_pre_topc (k2_jgraph_2 A B C D) (k15_euclid 2) (k15_euclid 2))) ) ) ) ).
tt(fc1_jgraph_3,ax, ((v1_funct_1 k1_jgraph_3) &  ((v2_funct_1 k1_jgraph_3) & (v1_funct_2 k1_jgraph_3 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))) ) ).
tt(fc1_jgraph_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_jgraph_4 A)) &  ((v1_funct_2 (k1_jgraph_4 A) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k1_jgraph_4 A) (k15_euclid A) k3_topmetr)) ) ) ) ).
tt(fc1_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (v2_compts_1 (k5_jgraph_6 A B C) (k15_euclid 2))) ) ).
tt(fc1_jgraph_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v1_convex1 (k2_jgraph_6 A B C D) (k15_euclid 2))) ) ).
tt(fc1_jordan10,ax, (! [A:$i,B:$i] :  ( ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (m1_subset_1 B k5_numbers))  => (v2_compts_1 (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan9 A B))) (k15_euclid 2))) ) ).
tt(fc1_jordan14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v2_connsp_1 (k1_jordan2c 2 (k3_topreal1 2 A)) (k15_euclid 2))) ) ).
tt(fc1_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k7_relat_1 k5_pscomp_1 (k4_topreal1 A)))) ) ) ).
tt(fc1_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v1_convex1 (k4_topreal1 A) (k15_euclid 2))) ) ).
tt(fc1_jordan1d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  => (v1_abian (k1_newton 2 A))) ) ).
tt(fc1_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k1_jordan1e A B))) ) ) ).
tt(fc1_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ( (~ (v1_zfmisc_1 (k3_finseq_5 A)))  &  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc1_jordan1j,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ( (~ (v1_xboole_0 (k3_graph_2 A B)))  &  ((v1_relat_1 (k3_graph_2 A B)) &  ((v1_funct_1 (k3_graph_2 A B)) & (v1_finseq_1 (k3_graph_2 A B))) ) ) ) ) ).
tt(fc1_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k9_jordan6 A)))  & (v1_jordan21 (k9_jordan6 A))) ) ) ).
tt(fc1_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k8_jordan6 A)))  & (v2_connsp_1 (k8_jordan6 A) (k15_euclid 2))) ) ) ).
tt(fc1_jordan23,ax, (! [A:$i] : (v2_funct_1 (k5_finseq_1 A))) ).
tt(fc1_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) &  ((v6_rltopsp1 (k15_euclid A)) & (v7_rltopsp1 (k15_euclid A))) ) ) ) ).
tt(fc1_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v5_rltopsp1 (k15_euclid A)) & (v1_borsuk_2 (k15_euclid A))) ) ) ).
tt(fc1_jordan6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k9_jordan6 A)))  & (v2_compts_1 (k9_jordan6 A) (k15_euclid 2))) ) ) ).
tt(fc1_jordan8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (v7_ordinal1 B))  =>  ( (~ (v3_relat_1 (k1_jordan8 A B)))  &  ((v1_matrix_1 (k1_jordan8 A B)) &  ((v2_goboard1 (k1_jordan8 A B)) & (v3_goboard1 (k1_jordan8 A B))) ) ) ) ) ).
tt(fc1_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v3_xxreal_0 (k2_metric_1 A B C))) ) ) ).
tt(fc1_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_kolmog01 D A B C)) )  =>  (~ (v1_xboole_0 (k5_kolmog01 A B C D))) ) ) ).
tt(fc1_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_finset_1 (k1_kurato_1 A B))) ) ).
tt(fc1_kurato_2,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k3_topreal1 2 A) (k15_euclid 2))) ) ).
tt(fc1_lang1,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k6_lang1 A)))  & (v2_lang1 (k6_lang1 A))) ) ).
tt(fc1_latsum_1,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ( (~ (v2_struct_0 (k1_latsum_1 A B)))  & (v1_orders_2 (k1_latsum_1 A B))) ) ) ).
tt(fc1_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( (~ (v2_struct_0 (k1_lattice2 A)))  & (v3_lattices (k1_lattice2 A))) ) ) ).
tt(fc1_lattice3,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k1_lattice3 A)))  & (v3_lattices (k1_lattice3 A))) ) ).
tt(fc1_lattice5,ax, (! [A:$i] :  ((v3_orders_2 (k1_lattice5 A)) &  ((v4_orders_2 (k1_lattice5 A)) &  ((v5_orders_2 (k1_lattice5 A)) &  ((v1_lattice3 (k1_lattice5 A)) & (v2_lattice3 (k1_lattice5 A))) ) ) ) ) ).
tt(fc1_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) & (v1_wellfnd1 (k3_lattice3 A))) ) ) ) ) ) ).
tt(fc1_lattice7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_lattice7 A))  =>  ((v1_orders_2 (k2_yellow_1 A)) &  ((v2_waybel_1 (k2_yellow_1 A)) &  ((v1_lattice3 (k2_yellow_1 A)) & (v2_lattice3 (k2_yellow_1 A))) ) ) ) ) ).
tt(fc1_lattice8,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_lattice8 A))) ) ).
tt(fc1_lattices,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ( (~ (v2_struct_0 (g2_lattices A B)))  & (v2_lattices (g2_lattices A B))) ) ) ).
tt(fc1_lexbfs,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k4_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k4_bagorder A)) &  ((v4_relat_2 (k4_bagorder A)) &  ((v6_relat_2 (k4_bagorder A)) & (v8_relat_2 (k4_bagorder A))) ) ) ) ) ) ).
tt(fc1_lfuzzy_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (v2_struct_0 (k1_lfuzzy_0 A)))  &  ((v1_orders_2 (k1_lfuzzy_0 A)) & (v1_lfuzzy_0 (k1_lfuzzy_0 A))) ) ) ) ).
tt(fc1_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_relat_1 (k5_fuzzy_4 A A) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_fuzzy_4 A A)) &  ((v1_funct_2 (k5_fuzzy_4 A A) (k2_zfmisc_1 A A) k1_numbers) &  ((v1_lfuzzy_1 (k5_fuzzy_4 A A) A) &  ((v2_lfuzzy_1 (k5_fuzzy_4 A A) A) &  ((v3_lfuzzy_1 (k5_fuzzy_4 A A) A) & (v4_lfuzzy_1 (k5_fuzzy_4 A A) A)) ) ) ) ) ) ) ) ).
tt(fc1_lmod_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 C A B) &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) ) )  =>  (~ (v1_xboole_0 (k2_lmod_6 A B C D))) ) ) ).
tt(fc1_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  (~ (v1_xboole_0 (k7_lmod_7 A B C))) ) ) ).
tt(fc1_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_lopban_1 A B)))  &  ((v13_algstr_0 (k5_lopban_1 A B)) &  ((v1_rlvect_1 (k5_lopban_1 A B)) &  ((v2_rlvect_1 (k5_lopban_1 A B)) &  ((v3_rlvect_1 (k5_lopban_1 A B)) &  ((v4_rlvect_1 (k5_lopban_1 A B)) &  ((v5_rlvect_1 (k5_lopban_1 A B)) &  ((v6_rlvect_1 (k5_lopban_1 A B)) &  ((v7_rlvect_1 (k5_lopban_1 A B)) & (v8_rlvect_1 (k5_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc1_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_lopban_2 A)))  & (v36_algstr_0 (k7_lopban_2 A))) ) ) ).
tt(fc1_lopban_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v2_lopban_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_normsp_0 A B)) &  ((v1_funct_2 (k2_normsp_0 A B) k5_numbers k1_numbers) & (v1_series_1 (k2_normsp_0 A B))) ) ) ) ).
tt(fc1_lopban_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_lopban_4 A B)) &  ((v1_funct_2 (k1_lopban_4 A B) k5_numbers (u1_struct_0 A)) & (v2_lopban_3 (k1_lopban_4 A B) A)) ) ) ) ).
tt(fc1_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_normsp_2 A)))  &  ((v6_metric_1 (k2_normsp_2 A)) &  ((v7_metric_1 (k2_normsp_2 A)) &  ((v8_metric_1 (k2_normsp_2 A)) &  ((v9_metric_1 (k2_normsp_2 A)) & (v4_tbsp_1 (k2_normsp_2 A))) ) ) ) ) ) ) ).
tt(fc1_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~ (v1_xboole_0 (k1_lopclset A))) ) ) ).
tt(fc1_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_lpspace1 A)))  &  ((v1_rlvect_1 (k7_lpspace1 A)) &  ((v2_rlvect_1 (k7_lpspace1 A)) &  ((v3_rlvect_1 (k7_lpspace1 A)) &  ((v4_rlvect_1 (k7_lpspace1 A)) &  ((v5_rlvect_1 (k7_lpspace1 A)) &  ((v6_rlvect_1 (k7_lpspace1 A)) &  ((v7_rlvect_1 (k7_lpspace1 A)) & (v8_rlvect_1 (k7_lpspace1 A))) ) ) ) ) ) ) ) ) ) ).
tt(fc1_lpspace2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v3_valued_0 (k54_valued_1 B)) & (v6_supinf_2 (k54_valued_1 B))) ) ) ) ) ).
tt(fc1_ltlaxio1,ax,(v2_ltlaxio1 k13_ltlaxio1)).
tt(fc1_lukasi_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_cqc_lang A)) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A B D))) A)) ) ).
tt(fc1_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k3_margrel1 A))) ) ) ).
tt(fc1_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2)))))  & (v1_finset_1 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))))) ) ) ).
tt(fc1_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_setfam_1 (k1_finseq_1 A))) ) ).
tt(fc1_matrix15,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_subset_1 C k5_numbers)) )  => (v1_vectsp_4 (k5_matrix15 A B (k5_finseq_2 (u1_struct_0 A) C (k4_struct_0 A))) A (k6_prvect_1 A (k1_matrix_1 B)))) ) ).
tt(fc1_matrix17,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  => (v1_matrix17 (k1_matrix_2 A A C) B A)) ) ).
tt(fc1_matrix_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k10_matrix_1 A B))) ) ) ).
tt(fc1_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((v1_relat_1 (k2_finseq_3 B C)) &  ((v1_funct_1 (k2_finseq_3 B C)) &  ((v1_finseq_1 (k2_finseq_3 B C)) & (v1_matrix_1 (k2_finseq_3 B C))) ) ) ) ) ).
tt(fc1_matrix_6,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  => (v2_matrix_6 (k12_matrix_1 B A) A B)) ) ).
tt(fc1_matrix_8,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_matrix_8 (k12_matrix_1 B A) A B) & (v3_matrix_8 (k12_matrix_1 B A) A B)) ) ) ).
tt(fc1_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k4_relat_1 (k2_finseq_1 A))) & (v1_finseq_1 (k4_relat_1 (k2_finseq_1 A)))) ) ) ).
tt(fc1_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v2_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  & (m1_finseq_1 C (u1_struct_0 A))) )  =>  ((v1_matrixj1 (k24_matrixj1 A B C) (u1_struct_0 A)) & (v2_matrixj1 (k24_matrixj1 A B C) (u1_struct_0 A))) ) ) ).
tt(fc1_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_matrixr2 (k4_matrixr2 A) A)) ) ).
tt(fc1_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ((m1_matrlin D A B) &  ((m1_finseq_1 E (u1_struct_0 C)) & (m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E))) ) ) ) )  =>  ((v1_funct_1 (k4_matrlin2 A B C D E F)) &  ((v1_funct_2 (k4_matrlin2 A B C D E F) (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 (k4_matrlin2 A B C D E F) B C) & (v1_mod_2 (k4_matrlin2 A B C D E F) A B C)) ) ) ) ) ).
tt(fc1_matroid0,ax, (! [A:$i] :  ( ((v1_matroid0 A) & (l1_pre_topc A))  => (v1_classes1 (k1_matroid0 A))) ) ).
tt(fc1_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v4_matrprob A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  ( (~ (v1_xboole_0 (k3_matrprob A)))  & (v1_matrprob (k3_matrprob A))) ) ) ).
tt(fc1_matrtop2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 B A))))) )  =>  ((v7_vectsp_1 (k1_vectsp_7 B (k6_prvect_1 B A) C) B) & (v1_matrlin (k1_vectsp_7 B (k6_prvect_1 B A) C) B)) ) ) ).
tt(fc1_matrtop3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_matrtop3 C A)) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funcop_1 D) & (v1_matrtop3 D B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 D C)) & (v1_matrtop3 (k3_relat_1 D C) (k2_xboole_0 A B))) ) ) ).
tt(fc1_mazurulm,ax,(v1_borsuk_1 k17_borsuk_1 k3_topmetr)).
tt(fc1_mboolean,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k1_mboolean A B)) &  ((v2_relat_1 (k1_mboolean A B)) &  ((v4_relat_1 (k1_mboolean A B) A) &  ((v1_funct_1 (k1_mboolean A B)) & (v1_partfun1 (k1_mboolean A B) A)) ) ) ) ) ) ).
tt(fc1_measure1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (~ (v1_xboole_0 (k7_setfam_1 A B))) ) ) ).
tt(fc1_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_measure3 A B C)))  &  ((v1_prob_1 (k2_measure3 A B C) A) & (v3_measure1 (k2_measure3 A B C) A)) ) ) ) ).
tt(fc1_measure4,ax, (! [A:$i,B:$i] :  ((m1_measure4 B A) =>  ( (~ (v1_xboole_0 (k1_measure4 A B)))  &  ((v1_prob_1 (k1_measure4 A B) A) & (v3_measure1 (k1_measure4 A B) A)) ) ) ) ).
tt(fc1_measure6,ax, (~ (v1_setfam_1 k1_numbers)) ).
tt(fc1_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (~ (v1_xboole_0 (k8_measure7 A))) ) ) ).
tt(fc1_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v2_finsub_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v2_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k5_measure8 A C D B))) ) ) ).
tt(fc1_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_membered (k2_enumset1 A B C D))) ) ).
tt(fc1_membered,ax,(v1_membered k2_numbers)).
tt(fc1_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v13_struct_0 (k1_memstr_0 A) 1) & (v1_memstr_0 (k1_memstr_0 A) A)) ) ) ).
tt(fc1_mesfun6c,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v6_supinf_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k2_mesfun6c A B C)) & (v6_supinf_2 (k2_mesfun6c A B C))) ) ) ).
tt(fc1_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_funct_1 (k1_mesfunc5 A B)) & (v1_partfun1 (k1_mesfunc5 A B) A)) ) ) ).
tt(fc1_mesfunc1,ax, (~ (v1_xboole_0 k1_mesfunc1)) ).
tt(fc1_mesfunc7,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers)))) )  =>  ((v1_funct_1 (k10_mesfunc1 A B)) & (v6_supinf_2 (k10_mesfunc1 A B))) ) ) ).
tt(fc1_mesfunc8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) &  ((v1_mesfunc8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) ) )  & (m1_subset_1 D k5_numbers))  =>  ((v1_funct_1 (k9_nat_1 C D)) &  ((v1_funct_2 (k9_nat_1 C D) k5_numbers (k4_partfun1 A B)) & (v1_mesfunc8 (k9_nat_1 C D) A B)) ) ) ) ).
tt(fc1_metric_1,ax, ((v1_relat_1 k7_funct_5) &  ((v1_funct_1 k7_funct_5) & (v4_valued_0 k7_funct_5)) ) ).
tt(fc1_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (~ (v1_xboole_0 (k2_metric_2 A))) ) ) ).
tt(fc1_metric_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( (~ (v2_struct_0 (g1_metric_1 A B)))  & (v1_metric_1 (g1_metric_1 A B))) ) ) ).
tt(fc1_metrizts,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  => (v3_pcomps_1 (k3_pcomps_1 A))) ) ).
tt(fc1_mfold_1,ax, (! [A:$i,B:$i] : (v2_funct_1 (k1_tarski (k4_tarski A B)))) ).
tt(fc1_mfold_2,ax,(v5_relat_1 k1_xboole_0 k1_xboole_0)).
tt(fc1_midsp_1,ax, ( (~ (v2_struct_0 k2_midsp_1))  & (v1_midsp_1 k2_midsp_1)) ).
tt(fc1_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v13_algstr_0 (k15_midsp_1 A)) &  ((v2_rlvect_1 (k15_midsp_1 A)) &  ((v3_rlvect_1 (k15_midsp_1 A)) & (v4_rlvect_1 (k15_midsp_1 A))) ) ) ) ) ).
tt(fc1_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_midsp_3 A B C D)))  & (v1_midsp_3 (g1_midsp_3 A B C D) A)) ) ) ).
tt(fc1_mmlquery,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (v1_mmlquery (k18_mmlquery A B) A)) ) ).
tt(fc1_mod_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_grcat_1 B C)) &  ((v1_funct_2 (k6_grcat_1 B C) (u1_struct_0 B) (u1_struct_0 C)) & (v1_mod_2 (k6_grcat_1 B C) A B C)) ) ) ) ).
tt(fc1_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v3_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc1_modal_1,ax, (~ (v1_xboole_0 k3_modal_1)) ).
tt(fc1_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k2_modcat_1 A B))) ) ) ).
tt(fc1_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_modelc_1 (k6_modelc_1 A))) ) ).
tt(fc1_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_modelc_2 (k2_modelc_2 A))) ) ).
tt(fc1_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (v1_finset_1 (k13_modelc_2 A))) ) ).
tt(fc1_moebius1,ax,(v1_xboole_0 (k1_uproots k1_xboole_0))).
tt(fc1_monoid_0,ax, ( (~ (v2_struct_0 k2_monoid_0))  &  ((v15_algstr_0 k2_monoid_0) &  ((v1_group_1 k2_monoid_0) &  ((v3_group_1 k2_monoid_0) &  ((v5_group_1 k2_monoid_0) &  ((v13_monoid_0 k2_monoid_0) & (v16_monoid_0 k2_monoid_0)) ) ) ) ) ) ).
tt(fc1_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (~ (v2_struct_0 (k9_monoid_1 A B))) ) ) ).
tt(fc1_msafree1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 B))) ) ) ).
tt(fc1_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_msafree2 A) & (l1_msualg_1 A)) )  =>  (~ (v1_xboole_0 (k2_msafree2 A))) ) ) ).
tt(fc1_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v1_catalg_1 B A))  & (l3_msualg_1 B A)) )  =>  (~ (v1_xboole_0 (k3_card_3 (u3_msualg_1 A B)))) ) ) ).
tt(fc1_msafree,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k2_card_3 B)) &  ((v4_relat_1 (k2_card_3 B) A) & (v1_funct_1 (k2_card_3 B))) ) ) ) ).
tt(fc1_msaterm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  (~ (v1_xboole_0 (k1_msaterm A B))) ) ) ).
tt(fc1_msinst_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k1_msinst_1 A)))  &  ((v2_altcat_1 (k1_msinst_1 A)) &  ((v6_altcat_1 (k1_msinst_1 A)) &  ((v11_altcat_1 (k1_msinst_1 A)) & (v12_altcat_1 (k1_msinst_1 A))) ) ) ) ) ) ).
tt(fc1_msscyc_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) ) )  =>  (~ (v1_xboole_0 (k7_graph_2 A B))) ) ) ).
tt(fc1_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_relat_1 (k2_funct_6 B)) &  ((v4_relat_1 (k2_funct_6 B) A) & (v1_funct_1 (k2_funct_6 B))) ) ) ) ).
tt(fc1_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  ((v7_struct_0 (k6_msualg_1 A)) &  ( (~ (v11_struct_0 (k6_msualg_1 A)))  &  ((v1_msualg_1 (k6_msualg_1 A)) &  ((v5_msualg_1 (k6_msualg_1 A)) & (v2_msualg_2 (k6_msualg_1 A))) ) ) ) ) ) ).
tt(fc1_msualg_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v4_msualg_1 B A) & (l2_msualg_1 B A)) )  =>  ((v1_relat_1 (u3_msualg_1 A B)) &  ((v2_relat_1 (u3_msualg_1 A B)) &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) & (v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc1_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((v1_relat_1 (k2_pboole A B C)) &  ((v2_relat_1 (k2_pboole A B C)) &  ((v4_relat_1 (k2_pboole A B C) A) &  ((v1_funct_1 (k2_pboole A B C)) & (v1_partfun1 (k2_pboole A B C) A)) ) ) ) ) ) ).
tt(fc1_msualg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  & (m1_subset_1 C (u4_struct_0 A))) )  => (v4_funct_1 (k3_msualg_1 A C B))) ) ).
tt(fc1_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 B C)) &  ((v4_relat_1 (k3_relat_1 B C) (k4_finseq_1 B)) & (v1_funct_1 (k3_relat_1 B C))) ) ) ) ).
tt(fc1_msualg_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v3_lattices (k6_msualg_5 A B)) & (v15_lattices (k6_msualg_5 A B))) ) ) ).
tt(fc1_msualg_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k4_relat_1 A)))  & (v1_relat_1 (k4_relat_1 A))) ) ) ).
tt(fc1_msualg_7,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_msualg_5 A B)))  &  ((v3_lattices (k5_msualg_5 A B)) &  ((v10_lattices (k5_msualg_5 A B)) & (v15_lattices (k5_msualg_5 A B))) ) ) ) ) ).
tt(fc1_msualg_8,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k2_msualg_5 A)))  &  ((v3_lattices (k2_msualg_5 A)) &  ((v10_lattices (k2_msualg_5 A)) & (v15_lattices (k2_msualg_5 A))) ) ) ) ).
tt(fc1_msualg_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v2_relat_1 (k13_msafree A B)) & (v1_msafree (k13_msafree A B) A (k11_msafree A B))) ) ) ).
tt(fc1_mycielsk,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_finset_1 B) & (m1_eqrel_1 B A))  & (m1_subset_1 C (k1_zfmisc_1 A)))  => (v1_finset_1 (k1_mycielsk A B C))) ) ).
tt(fc1_nagata_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_nagata_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (v1_nagata_1 (k1_pcomps_1 A B) A)) ) ).
tt(fc1_nagata_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A B)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) k1_numbers)))) )  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  => (v1_xreal_0 (k1_binop_1 C D E))) ) ).
tt(fc1_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k2_xcmplx_0 A B))) ) ).
tt(fc1_nat_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k1_newton A B))) ) ) ).
tt(fc1_nat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A))) )  => (v7_ordinal1 (k3_uproots C (k1_nat_5 A B C)))) ) ).
tt(fc1_nat_lat,ax,(v6_membered (u1_struct_0 k3_nat_lat))).
tt(fc1_ndiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v12_struct_0 B k5_numbers A) &  ((v1_ndiff_1 B A (k4_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k9_nat_1 B C)) &  ((v1_funct_2 (k9_nat_1 B C) k5_numbers (u1_struct_0 A)) &  ((v12_struct_0 (k9_nat_1 B C) k5_numbers A) & (v1_ndiff_1 (k9_nat_1 B C) A (k4_struct_0 A))) ) ) ) ) ).
tt(fc1_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  ((v1_funct_1 (k2_funcop_1 k1_numbers (k5_euclid A))) &  ((v1_funct_2 (k2_funcop_1 k1_numbers (k5_euclid A)) k1_numbers (k1_euclid A)) & (v1_ndiff_4 (k2_funcop_1 k1_numbers (k5_euclid A)) A)) ) ) ) ).
tt(fc1_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k14_prvect_2 A)))  &  ((v1_normsp_1 (k14_prvect_2 A)) & (v2_monoid_0 (k14_prvect_2 A))) ) ) ) ).
tt(fc1_neckla_2,ax, (~ (v1_xboole_0 k3_neckla_2)) ).
tt(fc1_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (l1_orders_2 B))  =>  ( (~ (v2_struct_0 (k1_neckla_2 A B)))  & (v1_orders_2 (k1_neckla_2 A B))) ) ) ).
tt(fc1_net_1,ax, (! [A:$i] :  ((l1_petri A) => (v1_relat_1 (k1_net_1 A))) ) ).
tt(fc1_newton,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v7_ordinal1 B))  =>  ((v1_relat_1 (k2_finseq_2 B A)) &  ((v1_funct_1 (k2_finseq_2 B A)) &  ((v1_finseq_1 (k2_finseq_2 B A)) & (v1_valued_0 (k2_finseq_2 B A))) ) ) ) ) ).
tt(fc1_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v1_nfcont_3 (k5_relat_1 B C) A)) ) ) ).
tt(fc1_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_funct_1 B) &  ((v1_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v1_nfcont_4 (k5_relat_1 B C) A)) ) ) ).
tt(fc1_normform,ax, (! [A:$i] :  ((v1_funct_1 (k5_normform A)) &  ((v1_funct_2 (k5_normform A) (k2_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) &  ((v1_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) &  ((v2_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (v3_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) ) ) ) ) ).
tt(fc1_normsp_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k2_normsp_0 A B)) &  ((v5_relat_1 (k2_normsp_0 A B) k1_numbers) & (v1_funct_1 (k2_normsp_0 A B))) ) ) ) ).
tt(fc1_normsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v3_xxreal_0 (k1_normsp_0 A B))) ) ) ).
tt(fc1_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_normsp_2 A)))  &  ((v2_pre_topc (k3_normsp_2 A)) & (v4_frechet (k3_normsp_2 A))) ) ) ) ).
tt(fc1_numbers,ax, (~ (v1_xboole_0 k1_numbers)) ).
tt(fc1_openlatt,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (k1_openlatt A))) ) ) ).
tt(fc1_oposet_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( (~ (v2_struct_0 (g2_qmax_1 A B C)))  & (v3_qmax_1 (g2_qmax_1 A B C))) ) ) ).
tt(fc1_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_oppcat_1 A)))  &  ( (~ (v11_struct_0 (k2_oppcat_1 A)))  &  ((v1_cat_1 (k2_oppcat_1 A)) &  ((v2_cat_1 (k2_oppcat_1 A)) &  ((v3_cat_1 (k2_oppcat_1 A)) &  ((v4_cat_1 (k2_oppcat_1 A)) &  ((v5_cat_1 (k2_oppcat_1 A)) & (v6_cat_1 (k2_oppcat_1 A))) ) ) ) ) ) ) ) ) ).
tt(fc1_orders_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k1_orders_1 A))) ) ) ).
tt(fc1_orders_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ( (~ (v2_struct_0 (g1_orders_2 A B)))  & (v1_orders_2 (g1_orders_2 A B))) ) ) ).
tt(fc1_ordinal1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_ordinal1 A))) ) ).
tt(fc1_ordinal2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  & (v3_ordinal1 B))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_ordinal2 (k5_relat_1 A B))) ) ) ).
tt(fc1_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k2_xboole_0 A B))) ) ).
tt(fc1_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  => (v3_ordinal1 (k1_ordinal2 A))) ) ).
tt(fc1_ordinal5,ax,(v4_ordinal1 k4_ordinal1)).
tt(fc1_ordinal6,ax, (! [A:$i] : (v1_ordinal6 (k2_ordinal1 A))) ).
tt(fc1_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ( (~ (v2_struct_0 (k2_osafree A B)))  & (v1_lang1 (k2_osafree A B))) ) ) ).
tt(fc1_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_finseq_1 C A))  =>  ((v1_relat_1 (k3_relat_1 C B)) & (v1_finseq_1 (k3_relat_1 C B))) ) ) ).
tt(fc1_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  & (m2_osalg_2 C A B)) )  =>  (~ (v1_xboole_0 (k5_osalg_2 A B C))) ) ) ).
tt(fc1_osalg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) ) )  => (v1_osalg_3 (k2_msualg_3 (u1_struct_0 A) B) A)) ) ).
tt(fc1_osalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  (~ (v1_xboole_0 (k6_osalg_4 A B C D))) ) ) ).
tt(fc1_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ( (~ (v7_struct_0 (k2_diraf A)))  &  ((v1_analoaf (k2_diraf A)) & (v1_diraf (k2_diraf A))) ) ) ) ).
tt(fc1_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k5_parsp_1 A))) ) ) ).
tt(fc1_partfun1,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k4_partfun1 A B))) ) ).
tt(fc1_partfun3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v3_xxreal_0 (k7_xcmplx_0 A A))) ) ) ).
tt(fc1_partfun4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 B C)) &  ((v1_funct_2 (k1_valued_1 B C) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k1_valued_1 B C) A)) ) ) ) ).
tt(fc1_partit1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_partit1 A))) ) ).
tt(fc1_partit_2,ax, (! [A:$i,B:$i] : (v1_xboole_0 (k1_partit_2 A B))) ).
tt(fc1_pboole,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C D)) &  ((v4_relat_1 (k3_relat_1 C D) A) &  ((v1_funct_1 (k3_relat_1 C D)) & (v1_partfun1 (k3_relat_1 C D) A)) ) ) ) ) ).
tt(fc1_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v1_pre_topc (k3_pcomps_1 A)) & (v2_pre_topc (k3_pcomps_1 A))) ) ) ).
tt(fc1_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_partfun1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v1_partfun1 (k2_xboole_0 C D) (k2_xboole_0 A B))) ) ).
tt(fc1_pdiff_1,ax, ((v1_funct_1 (k1_pdiff_1 1 1)) &  ((v1_funct_2 (k1_pdiff_1 1 1) (k1_euclid 1) k1_numbers) & (v3_funct_2 (k1_pdiff_1 1 1) (k1_euclid 1) k1_numbers)) ) ).
tt(fc1_pdiff_6,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_funct_1 (k2_funcop_1 (k1_euclid B) (k5_euclid A))) &  ((v1_funct_2 (k2_funcop_1 (k1_euclid B) (k5_euclid A)) (k1_euclid B) (k1_euclid A)) &  ((v1_pdiff_6 (k2_funcop_1 (k1_euclid B) (k5_euclid A)) A B) & (v2_pdiff_6 (k2_funcop_1 (k1_euclid B) (k5_euclid A)) A B)) ) ) ) ) ).
tt(fc1_pencil_1,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (u1_pre_topc A))) ) ) ).
tt(fc1_pepin,ax, (! [A:$i] :  ((v1_int_1 A) => (v7_ordinal1 (k3_square_1 A))) ) ).
tt(fc1_pnproc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m2_pnproc_1 B A) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B)))) ) )  =>  (~ (v1_xboole_0 (k10_pnproc_1 A B C D))) ) ) ).
tt(fc1_polyeq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xcmplx_0 (k1_polyeq_1 A B C))) ) ).
tt(fc1_polyeq_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) &  ((v1_xcmplx_0 D) &  ((v1_xcmplx_0 E) & (v1_xcmplx_0 F)) ) ) ) )  => (v1_xcmplx_0 (k1_polyeq_2 A B C D E F))) ) ).
tt(fc1_polyeq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) &  ((v1_xcmplx_0 D) &  ((v1_xcmplx_0 E) &  ((v1_xcmplx_0 F) & (v1_xcmplx_0 G)) ) ) ) ) )  => (v1_xcmplx_0 (k1_polyeq_4 A B C D E F G))) ) ).
tt(fc1_polyform,ax, (! [A:$i,B:$i] :  ( ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  & (v1_int_1 B))  =>  ((v1_funct_1 (k21_polyform A B)) &  ((v1_funct_2 (k21_polyform A B) (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) &  ((v13_vectsp_1 (k21_polyform A B) (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1))) & (v1_mod_2 (k21_polyform A B) k2_bspace (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1)))) ) ) ) ) ).
tt(fc1_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k4_polynom1 A B C D)) &  ((v1_funct_2 (k4_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k4_polynom1 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc1_polynom2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_polynom1 A B C D)) &  ((v1_funct_2 (k6_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k6_polynom1 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc1_polynom3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_partfun1 (k5_polynom3 A) (k4_finseq_2 A k5_numbers)) &  ((v1_relat_2 (k5_polynom3 A)) &  ((v4_relat_2 (k5_polynom3 A)) &  ((v8_relat_2 (k5_polynom3 A)) & (v3_orders_1 (k5_polynom3 A))) ) ) ) ) ) ).
tt(fc1_polynom4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k1_polynom4 A B)) &  ((v1_funct_2 (k1_polynom4 A B) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k1_polynom4 A B) A)) ) ) ) ).
tt(fc1_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v3_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k2_polynom5 A B C)) &  ((v1_funct_2 (k2_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k2_polynom5 A B C) A)) ) ) ) ).
tt(fc1_polynom6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v3_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  ((v3_ordinal1 (k10_ordinal2 A B)) &  (~ (v1_xboole_0 (k10_ordinal2 A B))) ) ) ) ).
tt(fc1_polynom7,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((v1_funct_1 (k7_polynom1 A B)) &  ((v1_funct_2 (k7_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (v4_polynom7 (k7_polynom1 A B) A B)) ) ) ) ).
tt(fc1_polynom8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_polynom8 A B C)) &  ((v1_funct_2 (k2_polynom8 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k2_polynom8 A B C) A)) ) ) ) ).
tt(fc1_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_2 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom7 C A B) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom7 D A B) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_polynom1 A B C D)) &  ((v1_funct_2 (k9_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom7 (k9_polynom1 A B C D) A B)) ) ) ) ).
tt(fc1_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (v1_relat_2 (k5_poset_1 A B))) ) ).
tt(fc1_pralg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k7_pralg_1 A)) &  ( (~ (v1_xboole_0 (k7_pralg_1 A)))  &  ((v2_margrel1 (k7_pralg_1 A)) & (v3_margrel1 (k7_pralg_1 A) (k1_tarski k1_xboole_0))) ) ) ) ) ).
tt(fc1_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((v1_relat_1 (k6_pboole A B C)) &  ((v2_relat_1 (k6_pboole A B C)) &  ((v4_relat_1 (k6_pboole A B C) A) &  ((v1_funct_1 (k6_pboole A B C)) & (v1_partfun1 (k6_pboole A B C) A)) ) ) ) ) ) ).
tt(fc1_pralg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  & (m1_pralg_2 C A B))  => (v4_msualg_1 (k14_pralg_2 A B C) B)) ) ).
tt(fc1_pre_circ,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_relat_1 (k5_relat_1 B C)) &  ((v4_relat_1 (k5_relat_1 B C) C) &  ((v1_funct_1 (k5_relat_1 B C)) & (v1_partfun1 (k5_relat_1 B C) C)) ) ) ) ) ).
tt(fc1_pre_poly,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k1_finseq_1 (k1_nat_1 A 1)))) ) ) ).
tt(fc1_prepower,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v7_ordinal1 (k16_complex1 A)) & (v1_xreal_0 (k16_complex1 A))) ) ) ).
tt(fc1_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (u1_pre_topc A))) ) ) ).
tt(fc1_prob_1,ax, (! [A:$i] : (v2_finsub_1 (k1_zfmisc_1 A))) ).
tt(fc1_prob_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k2_prob_1 A C) B) &  ((v1_funct_1 (k2_prob_1 A C)) & (v1_funct_2 (k2_prob_1 A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc1_prob_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k3_prob_3 A B)) &  ((v1_funct_2 (k3_prob_3 A B) k5_numbers (k9_setfam_1 A)) & (v1_prob_2 (k3_prob_3 A B))) ) ) ) ).
tt(fc1_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  ( (~ (v1_xboole_0 (k4_prob_4 A B C)))  &  ((v1_prob_1 (k4_prob_4 A B C) A) & (v4_prob_1 (k4_prob_4 A B C) A)) ) ) ) ).
tt(fc1_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  & (v7_ordinal1 B))  =>  ( (~ (v2_struct_0 (k4_prvect_1 A B)))  &  ((v8_algstr_0 (k4_prvect_1 A B)) &  ((v13_algstr_0 (k4_prvect_1 A B)) &  ((v2_rlvect_1 (k4_prvect_1 A B)) &  ((v3_rlvect_1 (k4_prvect_1 A B)) & (v4_rlvect_1 (k4_prvect_1 A B))) ) ) ) ) ) ) ).
tt(fc1_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k10_prvect_2 A)))  &  ((v13_algstr_0 (k10_prvect_2 A)) &  ((v1_rlvect_1 (k10_prvect_2 A)) &  ((v2_rlvect_1 (k10_prvect_2 A)) &  ((v3_rlvect_1 (k10_prvect_2 A)) &  ((v4_rlvect_1 (k10_prvect_2 A)) &  ((v5_rlvect_1 (k10_prvect_2 A)) &  ((v6_rlvect_1 (k10_prvect_2 A)) &  ((v7_rlvect_1 (k10_prvect_2 A)) & (v8_rlvect_1 (k10_prvect_2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc1_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v2_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc1_pscomp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_funct_1 (k5_relat_1 B C)) &  ((v1_funct_2 (k5_relat_1 B C) (u1_struct_0 (k1_pre_topc A C)) k1_numbers) & (v1_pscomp_1 (k5_relat_1 B C) (k1_pre_topc A C))) ) ) ) ).
tt(fc1_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  ((v1_partfun1 (k6_pua2mss1 A) (u1_struct_0 A)) &  ((v3_relat_2 (k6_pua2mss1 A)) & (v8_relat_2 (k6_pua2mss1 A))) ) ) ) ).
tt(fc1_pythtrip,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_pythtrip (k3_square_1 A))) ) ).
tt(fc1_pzfmisc1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k1_pzfmisc1 A B)) &  ((v2_relat_1 (k1_pzfmisc1 A B)) &  ((v4_relat_1 (k1_pzfmisc1 A B) A) &  ((v1_funct_1 (k1_pzfmisc1 A B)) &  ((v1_partfun1 (k1_pzfmisc1 A B) A) & (v2_finset_1 (k1_pzfmisc1 A B))) ) ) ) ) ) ) ).
tt(fc1_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k1_qc_lang1 A))) ) ) ).
tt(fc1_qmax_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  (~ (v1_xboole_0 (k1_qmax_1 A B))) ) ) ).
tt(fc1_quatern2,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (v1_quaterni (k5_quatern2 A B))) ) ).
tt(fc1_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_quaterni (k1_quatern3 A))) ) ).
tt(fc1_quaterni,ax, (~ (v1_xboole_0 k1_quaterni)) ).
tt(fc1_quin_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) & (v1_xcmplx_0 C)) )  => (v1_xcmplx_0 (k1_quin_1 A B C))) ) ).
tt(fc1_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (~ (v1_xboole_0 (k1_quofield A))) ) ) ).
tt(fc1_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k2_radix_1 A))) ) ) ).
tt(fc1_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k1_radix_3 A))) ) ) ).
tt(fc1_ramsey_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_finset_1 B)) )  =>  (~ (v1_xboole_0 (k3_group_10 B A))) ) ) ).
tt(fc1_random_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_random_1 C A B)) )  =>  ((v1_relat_1 (k54_valued_1 C)) &  ((v1_funct_1 (k54_valued_1 C)) &  ((v3_valued_0 (k54_valued_1 C)) & (v6_supinf_2 (k54_valued_1 C))) ) ) ) ) ).
tt(fc1_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (v1_finset_1 (k7_relat_1 C D))) ) ).
tt(fc1_rat_1,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (v1_rat_1 (k3_xcmplx_0 A B))) ) ).
tt(fc1_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v9_struct_0 B A))  & (m1_subset_1 B (u1_struct_0 A)))  &  ( (~ (v9_struct_0 C A))  & (m1_subset_1 C (u1_struct_0 A))) ) )  =>  (~ (v9_struct_0 (k3_vectsp_1 A B C) A)) ) ) ).
tt(fc1_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v3_rcomp_1 (k4_xxreal_1 A B))) ) ).
tt(fc1_rcomp_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_subset_1 A))) ) ) ).
tt(fc1_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_xboole_0 (k5_int_1 A k6_numbers)) & (v1_int_1 (k5_int_1 A k6_numbers))) ) ) ).
tt(fc1_real_lat,ax,(v3_membered (u1_struct_0 k3_real_lat))).
tt(fc1_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_real_ns1 A)) &  ((v1_funct_2 (k1_real_ns1 A) (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A)) &  ((v1_binop_1 (k1_real_ns1 A) (k1_euclid A)) & (v2_binop_1 (k1_real_ns1 A) (k1_euclid A))) ) ) ) ) ).
tt(fc1_realset1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k1_realset1 A B))) ) ).
tt(fc1_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k3_xboole_0 A B))) ) ).
tt(fc1_relat_2,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) &  ((v3_relat_2 (k4_relat_1 A)) &  ((v4_relat_2 (k4_relat_1 A)) & (v8_relat_2 (k4_relat_1 A))) ) ) ) ).
tt(fc1_reloc,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_compos_0 (k2_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(fc1_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v4_relat_1 B A))  &  ((v1_relat_1 C) & (v4_relat_1 C A)) )  => (v4_relat_1 (k2_xboole_0 B C) A)) ) ).
tt(fc1_revrot_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((m1_subset_1 B A) &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C A) & (m1_finseq_1 C A)) ) ) )  =>  (~ (v3_funct_1 (k1_finseq_6 A C B))) ) ) ).
tt(fc1_rewrite2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  => (v1_rewrite2 (k5_finseq_1 A))) ) ).
tt(fc1_rfinseq,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v1_finset_1 (k10_relat_1 A B))) ) ).
tt(fc1_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_rfunct_1 A B)) &  ((v1_funct_1 (k1_rfunct_1 A B)) & (v1_valued_0 (k1_rfunct_1 A B))) ) ) ) ).
tt(fc1_rfunct_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_funct_1 B)) )  =>  ((v1_relat_1 (k5_relat_1 B A)) & (v2_funct_1 (k5_relat_1 B A))) ) ) ).
tt(fc1_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_funct_1 (k18_rfunct_3 A B)) & (v1_finset_1 (k18_rfunct_3 A B))) ) ) ).
tt(fc1_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_funct_1 (k4_rinfsup2 A)) &  ((v1_funct_2 (k4_rinfsup2 A) k5_numbers k7_numbers) & (v8_valued_0 (k4_rinfsup2 A))) ) ) ) ).
tt(fc1_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (v1_ideal_1 (k2_struct_0 A) A)) ) ).
tt(fc1_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v1_ringcat1 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc1_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_xboole_0 (k3_convex1 A B)) & (v1_convex1 (k3_convex1 A B) A)) ) ) ).
tt(fc1_rlaffin2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k1_rlaffin2 A B))) ) ).
tt(fc1_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) &  ((v6_rltopsp1 (k15_euclid A)) & (v7_rltopsp1 (k15_euclid A))) ) ) ) ).
tt(fc1_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_rlsub_2 A))) ) ) ).
tt(fc1_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_xboole_0 (k3_convex1 A B)) & (v1_convex1 (k3_convex1 A B) A)) ) ) ).
tt(fc1_rlvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_rlvect_1 A B C D)))  & (v1_rlvect_1 (g1_rlvect_1 A B C D))) ) ) ).
tt(fc1_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_rlvect_2 B A))  => (v1_finset_1 (k13_pre_poly B))) ) ).
tt(fc1_rmod_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_rmod_3 A B))) ) ) ).
tt(fc1_robbins3,ax,(v13_struct_0 k1_robbins3 1)).
tt(fc1_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v3_lattices (g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A))) & (v10_lattices (g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)))) ) ) ).
tt(fc1_rsspace3,ax, (~ (v1_xboole_0 k1_rsspace3)) ).
tt(fc1_rsspace4,ax, (~ (v1_xboole_0 k1_rsspace4)) ).
tt(fc1_rsspace,ax, ((v1_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace)) & (v2_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) ).
tt(fc1_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_rusub_2 A))) ) ) ).
tt(fc1_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (v2_pre_topc (k5_rusub_5 A))) ) ).
tt(fc1_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers A)))) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C B)) & (v1_finseq_1 (k3_relat_1 C B))) ) ) ).
tt(fc1_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k2_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers A)))) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C B)) & (v1_finseq_1 (k3_relat_1 C B))) ) ) ).
tt(fc1_scm_1,ax, (! [A:$i] :  ((v1_int_1 A) => (v5_relat_1 (k3_afinsq_1 A) k4_numbers)) ) ).
tt(fc1_scmbsort,ax, ((v1_relat_1 k2_scmbsort) &  ((v4_relat_1 k2_scmbsort k5_numbers) &  ((v5_relat_1 k2_scmbsort (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 k2_scmbsort) &  ( (~ (v1_xboole_0 k2_scmbsort))  &  ((v1_finset_1 k2_scmbsort) &  ((v1_afinsq_1 k2_scmbsort) &  (~ (v2_compos_1 k2_scmbsort k1_scmfsa_2)) ) ) ) ) ) ) ) ).
tt(fc1_scm_comp,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  & (m1_subset_1 B (k6_dtconstr k1_scm_comp)))  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc1_scmfsa10,ax,(v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k2_compos_1 k1_scmfsa_2)))).
tt(fc1_scmfsa_1,ax, (~ (v1_xboole_0 k1_scmfsa_1)) ).
tt(fc1_scmfsa_2,ax, ( (~ (v2_struct_0 k1_scmfsa_2))  &  ((v2_memstr_0 k1_scmfsa_2 3) & (v1_extpro_1 k1_scmfsa_2 3)) ) ).
tt(fc1_scmfsa_3,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v3_amistd_5 k1_scmfsa_2 3)) ).
tt(fc1_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_compos_0 (k6_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc1_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_relat_1 (k2_scmfsa6a A)) &  ((v4_relat_1 (k2_scmfsa6a A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa6a A) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k2_scmfsa6a A)))  &  ((v1_funct_1 (k2_scmfsa6a A)) &  ((v1_finset_1 (k2_scmfsa6a A)) & (v1_afinsq_1 (k2_scmfsa6a A))) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa6b,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) & (v7_amistd_1 (k3_scmfsa6a A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa6c,ax, ((v1_scmfsa6c (k2_compos_1 k1_scmfsa_2)) & (v2_scmfsa6c (k2_compos_1 k1_scmfsa_2))) ).
tt(fc1_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ( (~ (v1_xboole_0 (k1_scmfsa_7 A B)))  &  ((v1_relat_1 (k1_scmfsa_7 A B)) &  ((v4_relat_1 (k1_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_7 A B)) &  ((v1_finset_1 (k1_scmfsa_7 A B)) & (v1_afinsq_1 (k1_scmfsa_7 A B))) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa8a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_scmfsa7b A)) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k1_scmfsa6a A B)) &  ((v4_relat_1 (k1_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6a A B)) &  ((v1_finset_1 (k1_scmfsa6a A B)) & (v1_scmfsa7b (k1_scmfsa6a A B))) ) ) ) ) ) ) ).
tt(fc1_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8b C A B)))  &  ((v1_relat_1 (k1_scmfsa8b C A B)) &  ((v4_relat_1 (k1_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8b C A B)) &  ((v1_finset_1 (k1_scmfsa8b C A B)) &  ((v1_afinsq_1 (k1_scmfsa8b C A B)) & (v7_amistd_1 (k1_scmfsa8b C A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8c A)))  &  ((v1_relat_1 (k1_scmfsa8c A)) &  ((v4_relat_1 (k1_scmfsa8c A) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8c A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8c A)) &  ((v1_finset_1 (k1_scmfsa8c A)) &  ((v1_afinsq_1 (k1_scmfsa8c A)) &  ((v2_compos_1 (k1_scmfsa8c A) k1_scmfsa_2) & (v1_scmfsa7b (k1_scmfsa8c A))) ) ) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) )  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k1_scmfsa8b C A B)) &  ((v4_relat_1 (k1_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k1_scmfsa8b C A B)))  &  ((v1_funct_1 (k1_scmfsa8b C A B)) &  ((v1_finset_1 (k1_scmfsa8b C A B)) &  ((v1_afinsq_1 (k1_scmfsa8b C A B)) & (v1_scmfsa7b (k1_scmfsa8b C A B))) ) ) ) ) ) ) ) ) ).
tt(fc1_scmfsa_i,ax, (~ (v1_xboole_0 k1_scmfsa_i)) ).
tt(fc1_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_int_1 B))  => (v5_funct_1 (k16_funcop_1 (k4_scmfsa_2 A) B) (k2_memstr_0 3 k1_scmfsa_2))) ) ).
tt(fc1_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scm_halt A) & (v3_scm_halt A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_scm_halt B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) & (v2_scm_halt (k3_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc1_scm_inst,ax, (~ (v1_xboole_0 k2_scm_inst)) ).
tt(fc1_scmisort,ax, ( (~ (v1_xboole_0 k3_scmisort))  &  ((v1_relat_1 k3_scmisort) &  ((v4_relat_1 k3_scmisort k5_numbers) &  ((v5_relat_1 k3_scmisort (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 k3_scmisort) &  ((v1_finset_1 k3_scmisort) &  ((v1_afinsq_1 k3_scmisort) &  (~ (v2_compos_1 k3_scmisort k1_scmfsa_2)) ) ) ) ) ) ) ) ).
tt(fc1_scmpds_2,ax, ( (~ (v2_struct_0 k1_scmpds_2))  & (v1_extpro_1 k1_scmpds_2 2)) ).
tt(fc1_scmpds_3,ax, ((v1_extpro_1 k1_scmpds_2 2) & (v3_amistd_5 k1_scmpds_2 2)) ).
tt(fc1_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  => (v4_scmpds_4 (k5_scmpds_2 A B))) ) ).
tt(fc1_scmpds_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  => (v6_compos_0 (k4_scmpds_2 A) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc1_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v6_compos_0 (k3_scmpds_2 (k2_nat_1 A 1)) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc1_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k1_scmpds_8 B C A)))  &  ((v1_relat_1 (k1_scmpds_8 B C A)) &  ((v4_relat_1 (k1_scmpds_8 B C A) k5_numbers) &  ((v5_relat_1 (k1_scmpds_8 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_8 B C A)) &  ((v1_finset_1 (k1_scmpds_8 B C A)) &  ((v1_afinsq_1 (k1_scmpds_8 B C A)) & (v3_scmpds_4 (k1_scmpds_8 B C A))) ) ) ) ) ) ) ) ) ).
tt(fc1_scmpds_9,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_xboole_0 (k2_amistd_1 2 k1_scmpds_2 (k3_scmpds_2 A)))) ) ).
tt(fc1_scmpds_i,ax, (~ (v1_xboole_0 k1_scmpds_i)) ).
tt(fc1_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((v1_relat_1 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) & (v2_relat_1 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) ) ) ).
tt(fc1_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_scmring2 A)))  & (v1_extpro_1 (k1_scmring2 A) 2)) ) ) ).
tt(fc1_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k2_compos_1 (k1_scmring2 A))))) ) ).
tt(fc1_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v2_amistd_5 (k1_scmring2 A) 2)) ) ) ).
tt(fc1_scmringi,ax, ( (~ (v1_xboole_0 k3_scm_inst))  &  (~ (v1_zfmisc_1 k3_scm_inst)) ) ).
tt(fc1_scmyciel,ax,(v1_xboole_0 (k3_tarski (k1_tarski k1_xboole_0)))).
tt(fc1_scpinvar,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k4_scpinvar B C A)))  &  ((v1_relat_1 (k4_scpinvar B C A)) &  ((v4_relat_1 (k4_scpinvar B C A) k5_numbers) &  ((v5_relat_1 (k4_scpinvar B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scpinvar B C A)) &  ((v1_finset_1 (k4_scpinvar B C A)) &  ((v1_afinsq_1 (k4_scpinvar B C A)) & (v3_scmpds_4 (k4_scpinvar B C A))) ) ) ) ) ) ) ) ) ).
tt(fc1_scpqsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v3_scmpds_4 B)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_6 C D A B)))  &  ((v1_relat_1 (k3_scmpds_6 C D A B)) &  ((v4_relat_1 (k3_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_6 C D A B)) &  ((v1_finset_1 (k3_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k3_scmpds_6 C D A B)) & (v3_scmpds_4 (k3_scmpds_6 C D A B))) ) ) ) ) ) ) ) ) ).
tt(fc1_seq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) &  ((v1_funct_2 (k1_valued_1 A B) k5_numbers k1_numbers) & (v2_comseq_2 (k1_valued_1 A B))) ) ) ) ).
tt(fc1_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k54_valued_1 A)) &  ((v1_funct_2 (k54_valued_1 A) k5_numbers k1_numbers) & (v2_comseq_2 (k54_valued_1 A))) ) ) ) ).
tt(fc1_seqm_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k9_nat_1 A B)) &  ((v1_funct_1 (k9_nat_1 A B)) &  ((v2_valued_0 (k9_nat_1 A B)) &  ((v4_valued_0 (k9_nat_1 A B)) & (v5_valued_0 (k9_nat_1 A B))) ) ) ) ) ) ).
tt(fc1_series_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v3_valued_0 A)) ) ) )  =>  ((v1_relat_1 (k2_series_1 A)) &  ((v4_relat_1 (k2_series_1 A) k5_numbers) &  ((v1_funct_1 (k2_series_1 A)) &  ((v1_partfun1 (k2_series_1 A) k5_numbers) &  ((v1_valued_0 (k2_series_1 A)) & (v3_valued_0 (k2_series_1 A))) ) ) ) ) ) ) ).
tt(fc1_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xreal_0 (k16_complex1 A)) &  (~ (v3_xxreal_0 (k16_complex1 A))) ) ) ) ).
tt(fc1_setfam_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (v1_xboole_0 (k7_setfam_1 A B))) ) ).
tt(fc1_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k1_setlim_1 B)) &  ((v1_funct_2 (k1_setlim_1 B) k5_numbers (k9_setfam_1 A)) & (v3_prob_1 (k1_setlim_1 B))) ) ) ) ).
tt(fc1_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_sfmastr1 (k6_scmfsa_2 A B))) ) ).
tt(fc1_sfmastr2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k2_sfmastr2 B A)))  &  ((v1_relat_1 (k2_sfmastr2 B A)) &  ((v4_relat_1 (k2_sfmastr2 B A) k5_numbers) &  ((v5_relat_1 (k2_sfmastr2 B A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_sfmastr2 B A)) &  ((v1_finset_1 (k2_sfmastr2 B A)) &  ((v1_afinsq_1 (k2_sfmastr2 B A)) & (v1_scmfsa7b (k2_sfmastr2 B A))) ) ) ) ) ) ) ) ) ).
tt(fc1_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k5_scmfsa8b A B C D)) &  ((v4_relat_1 (k5_scmfsa8b A B C D) k5_numbers) &  ((v5_relat_1 (k5_scmfsa8b A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa8b A B C D)) &  ( (~ (v1_xboole_0 (k5_scmfsa8b A B C D)))  &  ((v1_finset_1 (k5_scmfsa8b A B C D)) &  ((v1_afinsq_1 (k5_scmfsa8b A B C D)) & (v1_scmfsa7b (k5_scmfsa8b A B C D))) ) ) ) ) ) ) ) ) ).
tt(fc1_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  => (v1_finset_1 (k2_sf_mastr A))) ) ).
tt(fc1_sgraph1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v1_finset_1 (k1_sgraph1 A B))) ) ).
tt(fc1_simplex0,ax, (! [A:$i] : (v5_finset_1 (k2_cohsp_1 A))) ).
tt(fc1_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v6_simplex0 C (u1_struct_0 B)) & (m1_simplex0 C (u1_struct_0 B))) ) ) ) ) )  =>  ( (~ (v3_pencil_1 (k5_simplex1 A B C)))  &  ((v1_matroid0 (k5_simplex1 A B C)) &  ((v3_matroid0 (k5_simplex1 A B C)) & (v6_simplex0 (k5_simplex1 A B C) (u1_struct_0 B))) ) ) ) ) ).
tt(fc1_simplex2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ( ((v1_matroid0 C) &  ((v1_simplex2 C A) & (m1_simplex0 C B)) )  & (v1_int_1 D)) )  => (v1_simplex2 (k8_simplex0 B C D) A)) ) ).
tt(fc1_sincos10,ax, ((v1_relat_1 (k5_relat_1 k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc1_sin_cos6,ax, ((v1_xreal_0 k31_sin_cos) & (v2_xxreal_0 k31_sin_cos)) ).
tt(fc1_sin_cos9,ax, ((v1_relat_1 (k5_relat_1 k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))) ).
tt(fc1_sppol_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v2_compts_1 (k1_rltopsp1 (k15_euclid A) B C) (k15_euclid A))) ) ).
tt(fc1_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v2_topreal1 (k16_finseq_1 B A))) ) ).
tt(fc1_sprect_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_zfmisc_1 B))  & (m1_finseq_1 B (u1_struct_0 (k15_euclid A)))) )  =>  (~ (v1_xboole_0 (k3_topreal1 A B))) ) ) ).
tt(fc1_sprect_2,ax,(v2_compts_1 k1_topreal1 (k15_euclid 2))).
tt(fc1_sprect_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(fc1_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_rfinseq 1 A)) &  ((v1_funct_1 (k1_rfinseq 1 A)) &  ((v2_funct_1 (k1_rfinseq 1 A)) & (v1_finseq_1 (k1_rfinseq 1 A))) ) ) ) ) ).
tt(fc1_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xcmplx_0 (k3_square_1 A))) ) ).
tt(fc1_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k1_zfmisc_1 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_stacks_1 A B C D E F)))  & (v1_stacks_1 (g1_stacks_1 A B C D E F))) ) ) ).
tt(fc1_struct_0,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_struct_0 A))  => (v1_xboole_0 (u1_struct_0 A))) ) ).
tt(fc1_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m1_finseq_1 C (k2_qc_lang1 A))) )  & (m1_subset_1 D (k1_substut1 A))) ) )  =>  ((v5_relat_1 (k3_substut1 A C D) (k3_qc_lang1 A)) & (v3_card_1 (k3_substut1 A C D) B)) ) ) ).
tt(fc1_subset_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_zfmisc_1 A))) ) ).
tt(fc1_substlat,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k1_substlat A B))) ) ).
tt(fc1_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k1_substut1 A))) ) ) ).
tt(fc1_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  ( (~ (v1_xboole_0 (k3_supinf_1 A)))  & (v2_membered (k3_supinf_1 A))) ) ) ).
tt(fc1_symsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) )  & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_symsp_1 A B C D E F)))  & (v1_symsp_1 (g1_symsp_1 A B C D E F) A)) ) ) ).
tt(fc1_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k3_t_0topsp A)))  & (v2_pre_topc (k3_t_0topsp A))) ) ) ).
tt(fc1_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k2_t_1topsp A)))  &  ((v1_pre_topc (k2_t_1topsp A)) & (v2_pre_topc (k2_t_1topsp A))) ) ) ) ).
tt(fc1_taxonom1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v6_tbsp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v3_xxreal_0 (k3_tbsp_1 A B))) ) ) ).
tt(fc1_taylor_1,ax, ((v1_funct_1 k24_sin_cos) &  ((v2_funct_1 k24_sin_cos) & (v1_funct_2 k24_sin_cos k1_numbers k1_numbers)) ) ).
tt(fc1_tbsp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_metric_1 (k6_metric_1 A)) & (v5_tbsp_1 (k6_metric_1 A))) ) ) ).
tt(fc1_tdgroup,ax, ((v8_algstr_0 k1_vectsp_1) &  ((v12_vectsp_1 k1_vectsp_1) & (v1_tdgroup k1_vectsp_1)) ) ).
tt(fc1_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (k1_tdlat_1 A))) ) ) ).
tt(fc1_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_polynom1 A B C D)) &  ((v1_funct_2 (k9_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v3_polynom7 (k9_polynom1 A B C D) A B)) ) ) ) ).
tt(fc1_tex_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_tex_1 A))) ) ).
tt(fc1_tex_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_subset_1 B A) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (~ (v1_xboole_0 (k3_subset_1 A B))) ) ) ).
tt(fc1_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k2_pre_topc A B))) ) ) ).
tt(fc1_tietze,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_borsuk_1 (k1_pre_topc A B) A)) ) ) ).
tt(fc1_tmap_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ( (~ (v2_struct_0 (k1_tsep_1 A B C)))  &  ((v1_pre_topc (k1_tsep_1 A B C)) & (v2_pre_topc (k1_tsep_1 A B C))) ) ) ) ).
tt(fc1_topalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k1_topalg_1 A B C))) ) ) ).
tt(fc1_topalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v7_struct_0 (k5_topalg_1 B C)) & (v15_algstr_0 (k5_topalg_1 B C))) ) ) ).
tt(fc1_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_connsp_1 A) & (l1_pre_topc A)) )  =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (v1_connsp_1 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(fc1_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) & (l3_algstr_0 D)) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v1_group_6 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) &  ((v1_group_6 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_topalg_4 A B C D E F)) &  ((v1_funct_2 (k1_topalg_4 A B C D E F) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D)))) & (v1_group_6 (k1_topalg_4 A B C D E F) (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)) (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D)))) ) ) ) ).
tt(fc1_topalg_5,ax, ( (~ (v2_struct_0 k2_gr_cy_1))  &  ( (~ (v8_struct_0 k2_gr_cy_1))  & (v15_algstr_0 k2_gr_cy_1)) ) ).
tt(fc1_topalg_6,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v2_xxreal_0 A))  =>  ( (~ (v8_struct_0 (k15_euclid A)))  & (v5_rltopsp1 (k15_euclid A))) ) ) ).
tt(fc1_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_funct_1 (k1_topdim_1 A)) &  ((v1_funct_2 (k1_topdim_1 A) k5_numbers (k9_setfam_1 (k9_setfam_1 (u1_struct_0 A)))) & (v3_prob_1 (k1_topdim_1 A))) ) ) ) ).
tt(fc1_topdim_2,ax, (! [A:$i,B:$i] :  ( ((v1_topdim_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v7_ordinal1 (k1_xxreal_3 (k1_topdim_2 A B) 1)) & (v1_xxreal_0 (k1_xxreal_3 (k1_topdim_2 A B) 1))) ) ) ).
tt(fc1_topgen_1,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  => (v1_finset_1 (k2_struct_0 A))) ) ).
tt(fc1_topgen_2,ax, (! [A:$i,B:$i] :  ((v1_pre_topc (k5_topgen_2 A B)) & (v2_pre_topc (k5_topgen_2 A B))) ) ).
tt(fc1_topgen_3,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( (~ (v1_finset_1 (k3_card_2 2 A)))  & (v1_card_1 (k3_card_2 2 A))) ) ) ).
tt(fc1_topgen_4,ax,(v4_card_3 k3_numbers)).
tt(fc1_topgen_5,ax, (~ (v1_xboole_0 k1_topgen_5)) ).
tt(fc1_topgrp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A))) &  ((v2_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A))) & (v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc1_topmetr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k1_topmetr A B)))  & (v1_metric_1 (k1_topmetr A B))) ) ) ).
tt(fc1_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v4_funct_1 (u1_struct_0 (k15_euclid A)))) ) ).
tt(fc1_topreal2,ax,(v1_topreal2 k1_topreal1)).
tt(fc1_topreal6,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v8_struct_0 (k1_pre_topc A B)) & (v1_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc1_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_metric_1 B)) )  =>  ( (~ (v2_struct_0 (k1_topreal7 A B)))  & (v1_metric_1 (k1_topreal7 A B))) ) ) ).
tt(fc1_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) &  (~ (v2_xxreal_0 C)) ) ) )  => (v1_xboole_0 (k1_topreal9 A B C))) ) ).
tt(fc1_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k4_xxreal_1 A (k2_xcmplx_0 A B)))) ) ) ).
tt(fc1_toprealb,ax, (~ (v1_xboole_0 (k4_xxreal_1 k6_numbers 1))) ).
tt(fc1_toprealc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v3_xxreal_0 (k3_square_1 A))) ) ) ).
tt(fc1_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v4_pre_topc (k2_pre_topc A B) A)) ) ).
tt(fc1_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_tops_2 (u1_pre_topc A) A)) ) ).
tt(fc1_trees_1,ax,(v1_trees_1 (k1_tarski k1_xboole_0))).
tt(fc1_trees_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_2 A)) )  & (m1_subset_1 B A))  => (v1_finset_1 (k1_trees_2 A B))) ) ).
tt(fc1_trees_3,ax, (~ (v1_xboole_0 k1_trees_3)) ).
tt(fc1_trees_9,ax, (! [A:$i] :  ((v1_relat_1 (k1_trees_4 A)) &  ((v1_zfmisc_1 (k1_trees_4 A)) &  ((v1_funct_1 (k1_trees_4 A)) &  ((v1_finset_1 (k1_trees_4 A)) & (v3_trees_2 (k1_trees_4 A))) ) ) ) ) ).
tt(fc1_turing_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k1_ordinal1 A)))  & (v1_finset_1 (k1_ordinal1 A))) ) ) ).
tt(fc1_unialg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)))  =>  ( (~ (v2_struct_0 (g1_unialg_1 A B)))  & (v1_unialg_1 (g1_unialg_1 A B))) ) ) ).
tt(fc1_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (~ (v1_xboole_0 (k6_unialg_2 A))) ) ) ).
tt(fc1_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k12_unialg_2 A)))  &  ((v3_lattices (k12_unialg_2 A)) &  ((v10_lattices (k12_unialg_2 A)) & (v15_lattices (k12_unialg_2 A))) ) ) ) ) ).
tt(fc1_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_uniroots A)))  &  ((v8_struct_0 (k1_uniroots A)) &  ((v15_algstr_0 (k1_uniroots A)) &  ((v2_group_1 (k1_uniroots A)) & (v3_group_1 (k1_uniroots A))) ) ) ) ) ) ).
tt(fc1_uproots,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v2_funct_1 (k1_uproots A)) & (v2_funct_2 (k1_uproots A) A)) ) ) ).
tt(fc1_urysohn1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k1_urysohn1 A))) ) ) ).
tt(fc1_urysohn2,ax, (! [A:$i,B:$i] :  ( ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  & (m1_subset_1 B k1_numbers))  => (v6_xxreal_2 (k23_member_1 A B))) ) ).
tt(fc1_valuat_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  (~ (v1_xboole_0 B)) )  =>  ((v4_funct_1 (k1_valuat_1 A B)) &  (~ (v1_xboole_0 (k1_valuat_1 A B))) ) ) ) ).
tt(fc1_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  => (v1_membered (k10_xtuple_0 A))) ) ).
tt(fc1_valued_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((v1_xreal_0 (k16_complex1 A)) & (v1_rat_1 (k16_complex1 A))) ) ) ).
tt(fc1_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  => (v1_valued_2 (k1_tarski A))) ) ).
tt(fc1_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 (k3_struct_0 A) (u1_struct_0 A)) & (v3_vectmetr (k3_struct_0 A) A)) ) ) ) ) ).
tt(fc1_vectsp11,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_funct_1 (k1_vectsp11 B C D)) &  ((v1_funct_2 (k1_vectsp11 B C D) (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 (k1_vectsp11 B C D) B B) & (v1_mod_2 (k1_vectsp11 B C D) A B B)) ) ) ) ) ).
tt(fc1_vectsp_1,ax, ( (~ (v2_struct_0 k1_vectsp_1))  & (v8_algstr_0 k1_vectsp_1)) ).
tt(fc1_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_vectsp_2 A B C D E)))  & (v2_vectsp_2 (g1_vectsp_2 A B C D E) A)) ) ) ).
tt(fc1_vectsp_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k3_vectsp_5 A B))) ) ) ).
tt(fc1_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_vfunct_1 A B C D)) & (v1_partfun1 (k1_vfunct_1 A B C D) A)) ) ) ).
tt(fc1_waybel_0,ax, (! [A:$i] :  ( ((v1_lattice3 A) & (l1_orders_2 A))  => (v1_waybel_0 (k2_struct_0 A) A)) ) ).
tt(fc1_waybel10,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  => (v4_waybel_3 (k2_funcop_1 A B))) ) ).
tt(fc1_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((v3_waybel11 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_waybel11 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc1_waybel12,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel_6 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A)) ) ).
tt(fc1_waybel14,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel_0 (k2_waybel_8 A B) A)) ) ).
tt(fc1_waybel15,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v3_waybel_8 (k3_yellow_1 A))) ) ).
tt(fc1_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (~ (v1_xboole_0 (k8_waybel_0 A))) ) ) ).
tt(fc1_waybel17,ax, (! [A:$i,B:$i] :  ( ((v3_orders_2 B) & (l1_orders_2 B))  => (v5_waybel_3 (k2_funcop_1 A B))) ) ).
tt(fc1_waybel18,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_waybel18 A B)))  &  ((v1_pre_topc (k3_waybel18 A B)) & (v2_pre_topc (k3_waybel18 A B))) ) ) ) ).
tt(fc1_waybel_1,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v2_waybel_1 (k3_yellow_1 A))) ) ).
tt(fc1_waybel21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B))))  &  ((v4_orders_2 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B))) &  ((v6_waybel_0 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B)) A) &  ((v7_waybel_0 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B))) &  ((v8_waybel_0 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B)) A) & (v9_waybel_0 (k3_yellow_9 A (k6_domain_1 (u1_struct_0 A) B)) A)) ) ) ) ) ) ) ).
tt(fc1_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k8_waybel_0 A))) & (v3_waybel_3 (k2_yellow_1 (k8_waybel_0 A)))) ) ) ).
tt(fc1_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v2_lattice3 (k5_yellow_0 A B))) ) ) ) ).
tt(fc1_waybel24,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_struct_0 A B C)) &  ((v1_funct_2 (k6_struct_0 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v5_orders_3 (k6_struct_0 A B C) A B)) ) ) ) ).
tt(fc1_waybel25,ax, ((v1_pre_topc k9_waybel18) &  (~ (v7_pre_topc k9_waybel18)) ) ).
tt(fc1_waybel26,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ( (~ (v2_struct_0 (k1_waybel26 A B)))  &  ((v1_monoid_0 (k1_waybel26 A B)) &  ((v1_orders_2 (k1_waybel26 A B)) &  ((v3_orders_2 (k1_waybel26 A B)) & (v4_orders_2 (k1_waybel26 A B))) ) ) ) ) ) ).
tt(fc1_waybel27,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_waybel27 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_waybel27 (k5_relat_1 A B))) ) ) ).
tt(fc1_waybel28,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_orders_2 B)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) C)))  &  ((v4_orders_2 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) C)) &  ((v6_waybel_0 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) C) A) & (v7_waybel_0 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) C))) ) ) ) ) ).
tt(fc1_waybel29,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v24_waybel_0 (k3_waybel24 A B))) ) ) ).
tt(fc1_waybel_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A))) ) ) )  =>  (~ (v1_xboole_0 (k7_relat_1 C D))) ) ) ).
tt(fc1_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 A))) & (v24_waybel_0 (k2_yellow_1 (k7_waybel_0 A)))) ) ) ).
tt(fc1_waybel31,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v6_waybel23 B A) & (m1_waybel23 B A)) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))) & (v2_waybel_8 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ).
tt(fc1_waybel32,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) & (l1_orders_2 B)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel32 A B C)))  &  ((v4_orders_2 (k1_waybel32 A B C)) & (v6_waybel_0 (k1_waybel32 A B C) A)) ) ) ) ).
tt(fc1_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_waybel34 A B C)) &  ((v1_funct_2 (k1_waybel34 A B C) (u1_struct_0 B) (u1_struct_0 A)) & (v5_waybel_1 (k1_waybel34 A B C) A B)) ) ) ) ).
tt(fc1_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k1_waybel_3 A B))) ) ) ).
tt(fc1_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) => (v1_waybel_4 (k2_waybel_4 A) A)) ) ).
tt(fc1_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ((m2_pboole D A C (k7_funcop_1 A B)) & (m1_subset_1 E A)) ) ) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 (k1_waybel_5 A B C D E)))) ) ) ).
tt(fc1_waybel_7,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v11_waybel_1 (k3_yellow_1 A))) ) ).
tt(fc1_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel_8 A)))  &  ((v1_orders_2 (k1_waybel_8 A)) & (v4_yellow_0 (k1_waybel_8 A) A)) ) ) ) ).
tt(fc1_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v5_orders_3 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc1_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v8_struct_0 (k10_group_5 A)) & (v15_algstr_0 (k10_group_5 A))) ) ) ).
tt(fc1_wellfnd1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k2_card_1 A)))  & (v1_card_1 (k2_card_1 A))) ) ).
tt(fc1_wellord2,ax, (! [A:$i] :  ((v1_relat_1 (k1_wellord2 A)) & (v1_relat_2 (k1_wellord2 A))) ) ).
tt(fc1_wsierp_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  => (v1_int_1 (k1_newton A B))) ) ).
tt(fc1_xboole_0,ax,(v1_xboole_0 k1_xboole_0)).
tt(fc1_xboolean,ax,(v1_xboolean k1_xboolean)).
tt(fc1_xcmplx_0,ax,(v1_xcmplx_0 k1_xcmplx_0)).
tt(fc1_xreal_0,ax, (~ (v1_xreal_0 k2_xxreal_0)) ).
tt(fc1_xtuple_0,ax, (! [A:$i,B:$i] : (v1_xtuple_0 (k4_tarski A B))) ).
tt(fc1_xxreal_0,ax,(v1_xxreal_0 k1_xxreal_0)).
tt(fc1_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v2_membered (k1_xxreal_1 A B))) ) ).
tt(fc1_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) &  ( (~ (v1_xboole_0 A))  & (v4_xxreal_2 A)) )  =>  ((v1_xxreal_0 (k1_xxreal_2 A)) & (v1_xreal_0 (k1_xxreal_2 A))) ) ) ).
tt(fc1_xxreal_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xxreal_0 (k2_xxreal_3 A)) & (v1_xreal_0 (k2_xxreal_3 A))) ) ) ).
tt(fc1_yellow_0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski A)))) =>  ((v13_struct_0 (g1_orders_2 (k1_tarski A) B) 1) & (v1_orders_2 (g1_orders_2 (k1_tarski A) B))) ) ) ).
tt(fc1_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_yellow_0 A) & (l1_orders_2 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v2_yellow_0 (k3_yellow_3 A B))) ) ) ).
tt(fc1_yellow11,ax, ((v1_orders_2 k1_yellow11) &  ((v3_orders_2 k1_yellow11) &  ((v4_orders_2 k1_yellow11) & (v5_orders_2 k1_yellow11)) ) ) ).
tt(fc1_yellow12,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k3_tarski A))) ) ).
tt(fc1_yellow13,ax, (! [A:$i] :  ( ((v1_compts_1 A) & (l1_pre_topc A))  => (v2_compts_1 (k2_struct_0 A) A)) ) ).
tt(fc1_yellow14,ax, (! [A:$i,B:$i] :  ( ( ((v1_monoid_0 A) & (l1_struct_0 A))  &  ((v1_yellow14 B A) & (l1_waybel_0 B A)) )  =>  ((v1_funct_1 (u1_waybel_0 A B)) &  ((v1_funct_2 (u1_waybel_0 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v1_funcop_1 (u1_waybel_0 A B))) ) ) ) ).
tt(fc1_yellow15,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (v1_finset_1 (k2_yellow15 A B))) ) ).
tt(fc1_yellow16,ax, (! [A:$i,B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  => (v1_yellow16 (k2_funcop_1 A B))) ) ).
tt(fc1_yellow18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k1_multop_1 A B C D)) & (v1_funct_1 (k1_multop_1 A B C D))) ) ) ).
tt(fc1_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k1_yellow19 A B)))  &  ((v1_subset_1 (k1_yellow19 A B) (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 (k1_yellow19 A B) (k3_yellow_1 (k2_struct_0 A))) & (v13_waybel_0 (k1_yellow19 A B) (k3_yellow_1 (k2_struct_0 A)))) ) ) ) ) ).
tt(fc1_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) &  ((v1_lattice3 (k3_lattice3 A)) & (v2_lattice3 (k3_lattice3 A))) ) ) ) ) ) ) ).
tt(fc1_yellow20,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k1_binop_1 A B C)) & (v1_funct_1 (k1_binop_1 A B C))) ) ) ).
tt(fc1_yellow21,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_yellow21 A))) ) ) ).
tt(fc1_yellow_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k5_yellow_0 A B)))  &  ((v1_orders_2 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc1_yellow_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k3_waybel_0 A B))) ) ).
tt(fc1_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v1_xboole_0 (k1_yellow_4 A B C))) ) ) ).
tt(fc1_yellow_6,ax, (! [A:$i] :  ((v1_ordinal1 (k1_yellow_6 A)) & (v2_classes1 (k1_yellow_6 A))) ) ).
tt(fc1_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v3_orders_2 (k7_lattice3 A))) ) ) ).
tt(fc1_yellow_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k1_yellow_8 A)))  & (v1_pre_topc (k1_yellow_8 A))) ) ) ).
tt(fc1_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A)) )  =>  ((v1_funct_1 (k1_yellow_9 A B)) &  ((v1_funct_2 (k1_yellow_9 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v5_orders_3 (k1_yellow_9 A B) B A)) ) ) ) ).
tt(fc1_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)))  => (v1_finset_1 (k4_zf_fund1 A))) ) ).
tt(fc1_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (v1_finset_1 (k1_zf_model A))) ) ).
tt(fc1_zf_lang,ax, (~ (v1_xboole_0 k1_zf_lang)) ).
tt(fc1_zfmisc_1,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k4_tarski A B))) ) ).
tt(fc1_zfmodel2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (v1_finset_1 (k3_zf_lang1 A))) ) ).
tt(fc1_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k3_zf_model A))) ) ) ).
tt(fc1_zmodul01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k4_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers A) A)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_zmodul01 A B C D)))  & (v1_zmodul01 (g1_zmodul01 A B C D))) ) ) ).
tt(fc20_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A))) )  => (v8_abcmiz_1 (k37_abcmiz_1 A B) A)) ) ).
tt(fc20_afinsq_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k8_afinsq_1 A))) ) ).
tt(fc20_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_valued_0 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v5_ordinal1 (k24_valued_1 A B))) ) ) ) ).
tt(fc20_algstr_0,ax, ((v13_struct_0 k8_algstr_0 1) & (v22_algstr_0 k8_algstr_0)) ).
tt(fc20_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  => (v1_amistd_1 (k4_xtuple_0 (k8_ami_3 B A)) 2 k1_ami_3)) ) ).
tt(fc20_binop_2,ax, ((v1_funct_1 k48_binop_2) &  ((v1_funct_2 k48_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) & (v1_setwiseo k48_binop_2 k5_numbers)) ) ).
tt(fc20_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B)) &  ((v7_closure2 C (u1_struct_0 A) B) &  ((v8_closure2 C (u1_struct_0 A) B) &  ((v9_closure2 C (u1_struct_0 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B))))) ) ) ) ) ) )  =>  ((v11_closure2 (k10_closure2 A B C) A) & (v15_closure2 (k10_closure2 A B C) A)) ) ) ).
tt(fc20_compos_0,ax, (! [A:$i] :  ( ((v1_compos_0 A) & (v5_compos_0 A))  => (v4_compos_0 (k6_compos_0 A) A)) ) ).
tt(fc20_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k5_comput_1 2 A)) &  ((v4_relat_1 (k5_comput_1 2 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 2 A)) &  ((v4_valued_0 (k5_comput_1 2 A)) &  ((v2_margrel1 (k5_comput_1 2 A)) & (v8_comput_1 (k5_comput_1 2 A) 2)) ) ) ) ) ) ) ).
tt(fc20_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_monoid_0 (k14_euclid A)) &  ((v1_metric_1 (k14_euclid A)) &  ((v6_metric_1 (k14_euclid A)) &  ((v7_metric_1 (k14_euclid A)) &  ((v8_metric_1 (k14_euclid A)) & (v9_metric_1 (k14_euclid A))) ) ) ) ) ) ) ).
tt(fc20_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  & (m2_exchsort C A B)) )  =>  ((v1_relat_1 (k1_funct_1 C D)) &  ((v1_funct_1 (k1_funct_1 C D)) & (v1_exchsort (k1_funct_1 C D))) ) ) ) ).
tt(fc20_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  (~ (v1_xboole_0 (k11_finseq_1 A B C))) ) ).
tt(fc20_finset_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((v1_relat_1 (k3_relat_1 B A)) & (v1_finset_1 (k3_relat_1 B A))) ) ) ).
tt(fc20_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v7_ordinal1 C) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) &  ((v3_card_1 E C) & (v1_finseq_1 E)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 E D)) & (v3_card_1 (k3_relat_1 E D) C)) ) ) ).
tt(fc20_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v3_card_1 (k33_fomodel1 A B) (k1_int_2 (k30_fomodel1 A B)))) ) ).
tt(fc20_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel2 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C) A)) ) ).
tt(fc20_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v2_funct_2 B A)) ) )  =>  ((v1_relat_1 (k2_relat_1 B)) &  ((v4_relat_1 (k2_relat_1 B) A) & (v1_partfun1 (k2_relat_1 B) A)) ) ) ) ).
tt(fc20_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel4 (k4_tarski (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B C) B) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc20_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k2_funcop_1 A B)) &  ((v4_relat_1 (k2_funcop_1 A B) A) &  ((v1_funct_1 (k2_funcop_1 A B)) & (v1_partfun1 (k2_funcop_1 A B) A)) ) ) ) ).
tt(fc20_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  &  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  &  ((v8_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v8_functor0 (k13_functor0 A B C D E) A C) & (v9_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc20_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k8_gate_1 B C A))) ) ).
tt(fc20_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v4_glib_001 (k9_glib_001 A B C D) A)) ) ).
tt(fc20_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  &  ( (~ (v2_struct_0 C))  &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) )  => (v3_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ).
tt(fc20_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l1_vectsp_1 A k1_complfld)) )  =>  ((v1_rlvect_1 (k10_hahnban1 A)) & (v2_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(fc20_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_ideal_1 (k14_ideal_1 A B C) A)) ) ).
tt(fc20_jordan,ax, ((v1_funct_1 k8_jordan) &  ((v1_funct_2 k8_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) k1_numbers) & (v1_pscomp_1 k8_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) ) ).
tt(fc20_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k9_member_1 A B))) ) ).
tt(fc20_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xxreal_0 A) &  ((v1_xxreal_0 B) & (v1_xxreal_0 C)) )  => (v2_membered (k1_enumset1 A B C))) ) ).
tt(fc20_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_finset_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k8_memstr_0 A B C)) &  ((v4_relat_1 (k8_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k8_memstr_0 A B C)) &  ((v5_funct_1 (k8_memstr_0 A B C) (k2_memstr_0 A B)) & (v1_finset_1 (k8_memstr_0 A B C))) ) ) ) ) ) ).
tt(fc20_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  => (v3_card_1 (k13_pre_poly (k12_nat_3 A)) 1)) ) ).
tt(fc20_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v4_ordinal6 (k3_afinsq_1 A))) ) ).
tt(fc20_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v1_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc20_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pre_poly A)) )  => (v1_finset_1 (k13_pre_poly A))) ) ).
tt(fc20_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v2_prvect_2 (k5_finseq_1 A))) ) ).
tt(fc20_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  => (v5_ratfunc1 (k8_ratfunc1 A) A)) ) ).
tt(fc20_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  => (v1_xboole_0 (k7_relat_1 A B))) ) ).
tt(fc20_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_relat_2 A))  & (v1_relat_1 B))  => (v4_relat_2 (k4_xboole_0 A B))) ) ).
tt(fc20_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v3_funct_1 (k18_valued_1 B C))) ) ) ) ).
tt(fc20_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k16_scmfsa_2 A B)))) ) ).
tt(fc20_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k16_funcop_1 A B)) &  ((v4_relat_1 (k16_funcop_1 A B) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k16_funcop_1 A B)) &  ((v5_funct_1 (k16_funcop_1 A B) (k2_memstr_0 3 k1_scmfsa_2)) & (v4_memstr_0 (k16_funcop_1 A B) 3 k1_scmfsa_2)) ) ) ) ) ) ).
tt(fc20_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) & (v7_amistd_1 (k4_scmfsa6a A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc20_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v1_scmpds_5 (k13_scmpds_2 A B C D))) ) ).
tt(fc20_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k9_scmpds_6 B C A)))  &  ((v1_relat_1 (k9_scmpds_6 B C A)) &  ((v4_relat_1 (k9_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k9_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k9_scmpds_6 B C A)) &  ((v1_finset_1 (k9_scmpds_6 B C A)) &  ((v1_afinsq_1 (k9_scmpds_6 B C A)) & (v2_compos_1 (k9_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc20_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  => (v2_amistd_1 (k9_scmring2 A C B) 2 (k1_scmring2 A))) ) ).
tt(fc20_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  =>  ((v4_scmyciel (k6_scmyciel A)) & (v8_scmyciel (k6_scmyciel A))) ) ) ).
tt(fc20_simplex0,ax, (! [A:$i,B:$i] :  ((m1_simplex0 B A) => (v4_simplex0 (k8_simplex0 A B (k2_xxreal_3 1)))) ) ).
tt(fc20_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc20_struct_0,ax, (! [A:$i] :  ( ((v15_struct_0 A) & (l5_struct_0 A))  => (v1_zfmisc_1 (u4_struct_0 A))) ) ).
tt(fc20_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_subset_1 B (u1_struct_0 A)))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k6_tex_4 A B)) &  (~ (v1_tex_2 (k6_tex_4 A B) A)) ) ) ) ).
tt(fc20_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k2_group_2 A B C) A)) ) ).
tt(fc20_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  (~ (v1_xboole_0 (k7_jgraph_6 A B C))) ) ) ).
tt(fc20_toprealb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  ( (~ (v2_struct_0 (k7_toprealb A B C)))  & (v1_pre_topc (k7_toprealb A B C))) ) ) ).
tt(fc20_trees_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) ) ) ) )  =>  ((v1_relat_1 (k13_funct_3 C D)) &  ((v5_relat_1 (k13_funct_3 C D) (k2_zfmisc_1 A B)) & (v1_funct_1 (k13_funct_3 C D))) ) ) ) ).
tt(fc20_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  & (v1_relat_1 B))  => (v5_relat_1 (k4_xboole_0 A B) k3_numbers)) ) ).
tt(fc20_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_rat_1 D)) )  =>  ((v1_funct_1 (k7_valued_1 C D)) & (v1_partfun1 (k7_valued_1 C D) A)) ) ) ).
tt(fc20_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v5_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v5_relat_1 (k1_funct_1 D B) k4_numbers)) ) ).
tt(fc20_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k12_waybel_0 A B))) ) ) ).
tt(fc20_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  => (v1_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc20_waybel_9,ax, (! [A:$i] :  ( ((v2_lattice3 A) & (l1_orders_2 A))  =>  ((v6_waybel_0 (k3_waybel_9 A) A) & (v7_waybel_0 (k3_waybel_9 A))) ) ) ).
tt(fc20_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v3_xxreal_0 (k6_xcmplx_0 B A))) ) ).
tt(fc20_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  (~ (v2_xxreal_2 (k2_xxreal_1 A B))) ) ) ).
tt(fc20_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 A B)) & (v2_xxreal_0 (k3_xxreal_3 A B))) ) ) ).
tt(fc20_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v2_struct_0 (k9_yellow_6 A B))) ) ) ).
tt(fc21_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (~ (v1_xboole_0 (k39_abcmiz_1 A))) ) ) ).
tt(fc21_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v5_ordinal1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v1_finset_1 (k2_funct_7 A B C))) ) ) ) ) ).
tt(fc21_algstr_0,ax,(v21_algstr_0 k8_algstr_0)).
tt(fc21_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  => (v1_amistd_1 (k4_xtuple_0 (k9_ami_3 B A)) 2 k1_ami_3)) ) ).
tt(fc21_compos_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_compos_0 A) & (v5_compos_0 A))  &  ((v4_compos_0 B A) & (m1_subset_1 B A)) )  => (v1_xboole_0 (k5_xtuple_0 B))) ) ).
tt(fc21_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k5_comput_1 3 A)) &  ((v4_relat_1 (k5_comput_1 3 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 3 A)) &  ((v4_valued_0 (k5_comput_1 3 A)) &  ((v2_margrel1 (k5_comput_1 3 A)) & (v8_comput_1 (k5_comput_1 3 A) 3)) ) ) ) ) ) ) ).
tt(fc21_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) &  ( (~ (v2_xxreal_0 C))  & (v1_xreal_0 C)) ) )  => (v1_xboole_0 (k9_metric_1 (k14_euclid A) B C))) ) ).
tt(fc21_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  & (m2_exchsort C A B)) )  => (v5_relat_1 (k1_funct_1 C D) (u1_struct_0 A))) ) ).
tt(fc21_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k16_finseq_1 k6_numbers A)) &  ((v1_funct_1 (k16_finseq_1 k6_numbers A)) &  ((v1_xboole_0 (k16_finseq_1 k6_numbers A)) & (v1_finseq_1 (k16_finseq_1 k6_numbers A))) ) ) ) ) ).
tt(fc21_finset_1,ax, (! [A:$i,B:$i] : (v1_finset_1 (k16_funcop_1 A B))) ).
tt(fc21_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v14_fomodel1 B k6_numbers A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v1_xboole_0 (k33_fomodel1 A B))) ) ).
tt(fc21_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  ( ((v3_fomodel2 C A B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  => (v3_fomodel2 (k7_finseq_1 (k31_fomodel2 A D) C) A (k1_nat_1 B 1))) ) ).
tt(fc21_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v2_funct_2 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (v1_partfun1 (k2_relat_1 C) B)) ) ).
tt(fc21_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v4_fomodel4 (k4_tarski (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B) B) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc21_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  => (v5_relat_1 (k16_funcop_1 B C) A)) ) ).
tt(fc21_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v6_functor0 D A B) &  ((v8_functor0 D A B) &  ((v12_functor0 D A B) & (l2_functor0 D A B)) ) )  &  ((v12_functor0 E B C) & (l2_functor0 E B C)) ) ) ) )  =>  ((v9_functor0 (k13_functor0 A B C D E) A C) & (v12_functor0 (k13_functor0 A B C D E) A C)) ) ) ).
tt(fc21_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) )  => (v1_xboole_0 (k9_gate_1 A B C))) ) ).
tt(fc21_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  => (v5_glib_001 (k9_glib_001 A B C D) A)) ) ).
tt(fc21_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l3_algstr_0 B)) )  &  ( (~ (v2_struct_0 C))  &  ((v5_group_1 C) & (l3_algstr_0 C)) ) ) )  => (v4_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ).
tt(fc21_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l1_vectsp_1 A k1_complfld)) )  =>  ((v1_rlvect_1 (k10_hahnban1 A)) & (v3_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(fc21_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ((v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (v1_bilinear (k3_hermitan A B C) k1_complfld A B)) ) ) ) ).
tt(fc21_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_ideal_1 (k14_ideal_1 A B C) A)) ) ).
tt(fc21_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (v1_xboole_0 (k1_jordan2c 2 A))) ) ) ).
tt(fc21_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k9_member_1 B A))) ) ).
tt(fc21_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (v3_membered (k1_enumset1 A B C))) ) ).
tt(fc21_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_finset_1 C)) ) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k9_memstr_0 A B C D)) &  ((v4_relat_1 (k9_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k9_memstr_0 A B C D)) &  ((v5_funct_1 (k9_memstr_0 A B C D) (k2_memstr_0 A B)) & (v1_finset_1 (k9_memstr_0 A B C D))) ) ) ) ) ) ).
tt(fc21_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k13_nat_3 A)) &  ((v4_relat_1 (k13_nat_3 A) k10_newton) &  ((v1_funct_1 (k13_nat_3 A)) &  ((v1_partfun1 (k13_nat_3 A) k10_newton) &  ((v4_valued_0 (k13_nat_3 A)) & (v2_pre_poly (k13_nat_3 A))) ) ) ) ) ) ) ).
tt(fc21_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_ordinal6 A)) )  =>  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) ).
tt(fc21_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v2_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc21_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_pre_poly A)) )  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v2_pre_poly (k2_funct_7 A B C))) ) ) ) ).
tt(fc21_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  => (v2_prvect_2 (k10_finseq_1 A B))) ) ).
tt(fc21_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v4_ratfunc1 (k4_tarski (k3_hurwitz A B 1) (k3_hurwitz A B 1)) A))  &  (~ (v5_ratfunc1 (k4_tarski (k3_hurwitz A B 1) (k3_hurwitz A B 1)) A)) ) ) ) ).
tt(fc21_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k8_relat_1 A B))) ) ).
tt(fc21_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v8_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v8_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc21_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v3_funct_1 (k30_valued_1 B)) & (v1_valued_0 (k30_valued_1 B))) ) ) ) ) ).
tt(fc21_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v4_amistd_1 (k17_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc21_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k6_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc21_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ((v1_scmfsa6c B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa6a A B)))  &  ((v1_relat_1 (k5_scmfsa6a A B)) &  ((v4_relat_1 (k5_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa6a A B)) &  ((v1_finset_1 (k5_scmfsa6a A B)) &  ((v1_afinsq_1 (k5_scmfsa6a A B)) & (v7_amistd_1 (k5_scmfsa6a A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc21_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v1_scmpds_5 (k14_scmpds_2 A B C D))) ) ).
tt(fc21_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k10_scmpds_6 B C A)))  &  ((v1_relat_1 (k10_scmpds_6 B C A)) &  ((v4_relat_1 (k10_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k10_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k10_scmpds_6 B C A)) &  ((v1_finset_1 (k10_scmpds_6 B C A)) &  ((v1_afinsq_1 (k10_scmpds_6 B C A)) &  ((v2_scmpds_4 (k10_scmpds_6 B C A)) & (v3_scmpds_4 (k10_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc21_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k3_scmring2 A B C)) 2 (k1_scmring2 A))) ) ) ).
tt(fc21_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v8_scmyciel A))  =>  ((v4_scmyciel (k6_scmyciel A)) & (v11_scmyciel (k6_scmyciel A))) ) ) ).
tt(fc21_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_simplex0 B A) & (v1_int_1 C))  => (v4_matroid0 (k8_simplex0 A B C))) ) ).
tt(fc21_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k1_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))))) ).
tt(fc21_struct_0,ax, (! [A:$i] :  ( ( (~ (v15_struct_0 A))  & (l5_struct_0 A))  =>  (~ (v1_zfmisc_1 (u4_struct_0 A))) ) ) ).
tt(fc21_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k2_group_2 A C B) A)) ) ).
tt(fc21_toprealb,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xboole_0 C) & (v1_xreal_0 C)) ) )  => (v7_struct_0 (k7_toprealb A B C))) ) ).
tt(fc21_trees_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C D)) & (v3_trees_2 (k3_relat_1 C D))) ) ) ).
tt(fc21_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  & (v1_relat_1 B))  => (v5_relat_1 (k3_xboole_0 A B) k4_numbers)) ) ).
tt(fc21_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_int_1 D)) )  =>  ((v1_funct_1 (k7_valued_1 C D)) & (v1_partfun1 (k7_valued_1 C D) A)) ) ) ).
tt(fc21_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v6_valued_2 C) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (v4_valued_0 (k1_funct_1 D B))) ) ).
tt(fc21_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_waybel_0 (k11_waybel_0 A B) A)) ) ).
tt(fc21_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  => (v2_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc21_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v6_waybel_0 (k3_waybel_9 A) A) &  ((v9_waybel_0 (k3_waybel_9 A) A) & (v11_waybel_0 (k3_waybel_9 A) A)) ) ) ) ).
tt(fc21_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v3_xxreal_0 (k6_xcmplx_0 A B))) ) ).
tt(fc21_xxreal_2,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ( (~ (v1_xxreal_2 (k4_xxreal_1 A B)))  &  (~ (v2_xxreal_2 (k4_xxreal_1 A B))) ) ) ) ).
tt(fc21_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 B A)) & (v3_xxreal_0 (k3_xxreal_3 B A))) ) ) ).
tt(fc21_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v4_orders_2 (k9_yellow_6 A B)) & (v7_waybel_0 (k9_yellow_6 A B))) ) ) ).
tt(fc22_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  => (v1_finset_1 (k1_xtuple_0 B))) ) ).
tt(fc22_afinsq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D A)) ) )  =>  ((v1_relat_1 (k2_funct_7 B C D)) &  ((v5_relat_1 (k2_funct_7 B C D) A) & (v1_funct_1 (k2_funct_7 B C D))) ) ) ) ).
tt(fc22_algstr_0,ax,(v28_algstr_0 k8_algstr_0)).
tt(fc22_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v4_compos_0 (k8_ami_3 B A) (u1_compos_1 k1_ami_3)))  &  ((v2_amistd_1 (k8_ami_3 B A) 2 k1_ami_3) &  (~ (v4_amistd_1 (k8_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(fc22_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k4_comput_1 1 A)) &  ((v4_relat_1 (k4_comput_1 1 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 1 A)) &  ((v4_valued_0 (k4_comput_1 1 A)) &  ((v2_margrel1 (k4_comput_1 1 A)) & (v8_comput_1 (k4_comput_1 1 A) 1)) ) ) ) ) ) ) ).
tt(fc22_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) &  ((v2_xxreal_0 C) & (v1_xreal_0 C)) ) )  =>  (~ (v1_xboole_0 (k9_metric_1 (k14_euclid A) B C))) ) ) ).
tt(fc22_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  & (m2_exchsort C A B)) )  =>  ((v1_relat_1 (k4_exchsort C)) &  ((v1_funct_1 (k4_exchsort C)) & (v1_exchsort (k4_exchsort C))) ) ) ) ).
tt(fc22_finseq_1,ax, (! [A:$i] : (v4_funct_1 (k13_finseq_1 A))) ).
tt(fc22_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_finset_1 A))  => (v1_finset_1 (k10_xtuple_0 A))) ) ).
tt(fc22_fomodel0,ax, (! [A:$i,B:$i,C:$i] : (v1_xboole_0 (k3_xboole_0 (k6_subset_1 B A) (k3_xboole_0 A C)))) ).
tt(fc22_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((v14_fomodel1 C (k2_xcmplx_0 A 1) B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) )  => (v5_relat_1 (k33_fomodel1 B C) (k3_funct_2 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 B))) (k28_fomodel1 B) A))) ) ).
tt(fc22_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel2 (k7_finseq_1 (k31_fomodel2 A B) C) A)) ) ).
tt(fc22_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v2_funct_2 B A)) ) )  =>  ((v1_relat_1 (k2_relat_1 B)) &  ((v4_relat_1 (k2_relat_1 B) A) & (v1_partfun1 (k2_relat_1 B) A)) ) ) ) ).
tt(fc22_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v3_fomodel4 (k1_tarski (k1_domain_1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B) B)) A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc22_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 C B))  => (v5_relat_1 (k2_funcop_1 A C) B)) ) ).
tt(fc22_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k9_gate_1 A B C))) ) ) ).
tt(fc22_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l1_vectsp_1 A k1_complfld)) )  =>  ((v1_rlvect_1 (k10_hahnban1 A)) & (v4_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(fc22_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear C k1_complfld A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ((v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (v2_bilinear (k3_hermitan A B C) k1_complfld A B)) ) ) ) ).
tt(fc22_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_ideal_1 (k14_ideal_1 A B C) A)) ) ).
tt(fc22_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  &  ( (~ (v1_xboole_0 B))  & (v1_membered B)) )  =>  (~ (v1_xboole_0 (k9_member_1 A B))) ) ) ).
tt(fc22_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_rat_1 A) &  ((v1_rat_1 B) & (v1_rat_1 C)) )  => (v4_membered (k1_enumset1 A B C))) ) ).
tt(fc22_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_finset_1 C)) ) ) )  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k10_memstr_0 A B C D)) &  ((v4_relat_1 (k10_memstr_0 A B C D) (u1_struct_0 B)) &  ((v1_funct_1 (k10_memstr_0 A B C D)) &  ((v5_funct_1 (k10_memstr_0 A B C D) (k2_memstr_0 A B)) & (v1_finset_1 (k10_memstr_0 A B C D))) ) ) ) ) ) ).
tt(fc22_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_ordinal6 A)) )  =>  ((v5_ordinal1 (k1_funct_1 A B)) & (v1_ordinal2 (k1_funct_1 A B))) ) ) ).
tt(fc22_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v2_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc22_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v2_pre_poly (k1_valued_1 B C))) ) ) ) ).
tt(fc22_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_prvect_2 B)) ) ) ) )  =>  ( (~ (v1_xboole_0 (k7_finseq_1 A B)))  &  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v2_prvect_2 (k7_finseq_1 A B))) ) ) ) ) ) ).
tt(fc22_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  => (v4_ratfunc1 (k7_ratfunc1 A) A)) ) ).
tt(fc22_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  => (v1_xboole_0 (k8_relat_1 A B))) ) ).
tt(fc22_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v8_relat_2 A))  &  ((v1_relat_1 B) & (v8_relat_2 B)) )  => (v8_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc22_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v3_funct_1 (k54_valued_1 B)) & (v3_valued_0 (k54_valued_1 B))) ) ) ) ) ).
tt(fc22_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k17_scmfsa_2 A B)))) ) ).
tt(fc22_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k7_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc22_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ((v1_scmfsa6c B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k6_scmfsa6a A B)))  &  ((v1_relat_1 (k6_scmfsa6a A B)) &  ((v4_relat_1 (k6_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k6_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k6_scmfsa6a A B)) &  ((v1_finset_1 (k6_scmfsa6a A B)) &  ((v1_afinsq_1 (k6_scmfsa6a A B)) & (v7_amistd_1 (k6_scmfsa6a A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc22_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v1_scmpds_5 (k15_scmpds_2 A B C D))) ) ).
tt(fc22_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k10_scmpds_6 B C A)))  &  ((v1_relat_1 (k10_scmpds_6 B C A)) &  ((v4_relat_1 (k10_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k10_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k10_scmpds_6 B C A)) &  ((v1_finset_1 (k10_scmpds_6 B C A)) &  ((v1_afinsq_1 (k10_scmpds_6 B C A)) & (v2_compos_1 (k10_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc22_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_amistd_1 (k3_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc22_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  ((v1_finset_1 (k12_scmyciel A)) & (v4_scmyciel (k12_scmyciel A))) ) ) ).
tt(fc22_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_simplex0 B) & (m1_simplex0 B A))  & (v1_int_1 C))  => (v4_simplex0 (k8_simplex0 A B C))) ) ).
tt(fc22_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)))) ).
tt(fc22_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_tops_1 (k1_group_2 A B) A)) ) ).
tt(fc22_toprealb,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  => (v1_toprealb (k7_toprealb 2 A B))) ) ).
tt(fc22_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( (~ (v1_xboole_0 (k3_trees_1 A)))  & (v1_finset_1 (k3_trees_1 A))) ) ) ).
tt(fc22_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  & (v1_relat_1 B))  => (v5_relat_1 (k4_xboole_0 A B) k4_numbers)) ) ).
tt(fc22_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v6_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v7_ordinal1 D)) )  =>  ((v1_funct_1 (k7_valued_1 C D)) & (v1_partfun1 (k7_valued_1 C D) A)) ) ) ).
tt(fc22_valued_2,ax, (! [A:$i,B:$i] :  ((v1_membered B) => (v1_valued_2 (k4_partfun1 A B))) ) ).
tt(fc22_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_waybel_0 (k12_waybel_0 A B) A)) ) ).
tt(fc22_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  => (v3_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc22_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_waybel_0 B A)) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ( (~ (v2_struct_0 (k4_waybel_9 A B C)))  &  ((v3_orders_2 (k4_waybel_9 A B C)) & (v6_waybel_0 (k4_waybel_9 A B C) A)) ) ) ) ).
tt(fc22_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_xxreal_0 A) & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v2_xxreal_0 (k6_xcmplx_0 B A))) ) ).
tt(fc22_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 A B)) & (v3_xxreal_0 (k3_xxreal_3 A B))) ) ) ).
tt(fc22_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  => (v1_zfmisc_1 (k10_yellow_6 A B))) ) ).
tt(fc23_abcmiz_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  & (m1_subset_1 D (k1_msaterm A C))) ) )  => (v1_finset_1 (k1_funct_1 (k4_msafree3 A C D) B))) ) ).
tt(fc23_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) )  =>  ((v1_relat_1 (k63_valued_1 A)) &  ((v1_funct_1 (k63_valued_1 A)) & (v1_afinsq_1 (k63_valued_1 A))) ) ) ) ).
tt(fc23_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v1_finset_1 (k24_valued_1 A B))) ) ) ) ).
tt(fc23_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ( (~ (v2_struct_0 (g5_algstr_0 A B C D)))  & (v29_algstr_0 (g5_algstr_0 A B C D))) ) ) ).
tt(fc23_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v4_compos_0 (k9_ami_3 B A) (u1_compos_1 k1_ami_3)))  &  ((v2_amistd_1 (k9_ami_3 B A) 2 k1_ami_3) &  (~ (v4_amistd_1 (k9_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(fc23_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k4_comput_1 2 A)) &  ((v4_relat_1 (k4_comput_1 2 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 2 A)) &  ((v4_valued_0 (k4_comput_1 2 A)) &  ((v2_margrel1 (k4_comput_1 2 A)) & (v8_comput_1 (k4_comput_1 2 A) 2)) ) ) ) ) ) ) ).
tt(fc23_euclid_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_relat_1 (k3_euclid_9 k1_xboole_0 A)) &  ((v1_funct_1 (k3_euclid_9 k1_xboole_0 A)) & (v1_xboole_0 (k3_euclid_9 k1_xboole_0 A))) ) ) ) ).
tt(fc23_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  & (m2_exchsort C A B)) )  => (v5_relat_1 (k4_exchsort C) (u1_struct_0 A))) ) ).
tt(fc23_finseq_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~ (v1_xboole_0 (k1_finseq_1 A))) ) ) ).
tt(fc23_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  => (v1_finset_1 (k8_relat_1 A B))) ) ).
tt(fc23_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_1 (k18_finseq_1 A)) & (v8_relat_2 (k18_finseq_1 A))) ) ) ).
tt(fc23_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v1_relat_1 (k34_fomodel1 A B)) &  ((v1_funct_1 (k34_fomodel1 A B)) &  ((v3_card_1 (k34_fomodel1 A B) (k1_int_2 (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B)))) & (v1_finseq_1 (k34_fomodel1 A B))) ) ) ) ) ).
tt(fc23_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ( (~ (v7_fomodel1 C A))  & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (~ (v15_fomodel1 (k7_finseq_1 (k31_fomodel2 A C) B) A)) ) ) ).
tt(fc23_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  => (v1_funct_1 (k18_fomodel3 A B C))) ) ).
tt(fc23_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k22_fomodel4 A) A)) ) ).
tt(fc23_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (v4_relat_1 (k16_funcop_1 B C) A)) ) ).
tt(fc23_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k9_gate_1 B A C))) ) ) ).
tt(fc23_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (l1_vectsp_1 A k1_complfld)) )  =>  ((v13_algstr_0 (k10_hahnban1 A)) & (v1_rlvect_1 (k10_hahnban1 A))) ) ) ).
tt(fc23_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v3_bilinear C k1_complfld A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ((v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (v2_hermitan (k3_hermitan A B C) A B)) ) ) ) ).
tt(fc23_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (~ (v1_xboole_0 (k16_ideal_1 A B C))) ) ) ).
tt(fc23_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k9_member_1 A B))) ) ).
tt(fc23_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v5_membered (k1_enumset1 A B C))) ) ).
tt(fc23_memstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v2_memstr_0 B A) & (l1_memstr_0 B A)) )  =>  (~ (v1_xboole_0 (k11_memstr_0 A B))) ) ) ).
tt(fc23_ordinal6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  & (v3_ordinal1 B))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v5_ordinal1 (k5_relat_1 A B))) ) ) ).
tt(fc23_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k45_valued_1 B C)) &  ((v1_funct_1 (k45_valued_1 B C)) & (v1_partfun3 (k45_valued_1 B C))) ) ) ) ).
tt(fc23_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v7_pcs_0 B)) ) ) )  =>  ((v1_relat_1 (k7_pcs_0 A B)) &  ((v4_relat_1 (k7_pcs_0 A B) A) &  ((v1_funct_1 (k7_pcs_0 A B)) &  ((v1_partfun1 (k7_pcs_0 A B) A) & (v2_funcop_1 (k7_pcs_0 A B))) ) ) ) ) ) ).
tt(fc23_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((v1_relat_1 (k12_pre_poly A B C)) &  ((v4_relat_1 (k12_pre_poly A B C) A) &  ((v1_funct_1 (k12_pre_poly A B C)) &  ((v1_partfun1 (k12_pre_poly A B C) A) & (v2_pre_poly (k12_pre_poly A B C))) ) ) ) ) ) ).
tt(fc23_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  => (v6_ratfunc1 (k8_ratfunc1 A) A)) ) ).
tt(fc23_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v3_relat_1 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v3_relat_1 (k5_relat_1 A B))) ) ) ).
tt(fc23_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  & (v1_xreal_0 C)) )  =>  ((v1_relat_1 (k24_valued_1 B C)) &  ((v1_funct_1 (k24_valued_1 B C)) & (v3_funct_1 (k24_valued_1 B C))) ) ) ) ).
tt(fc23_scmfsa10,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v3_amistd_1 k1_scmfsa_2 3)) ).
tt(fc23_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k8_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc23_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa6b B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) & (v1_scmfsa6b (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc23_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v1_scmpds_5 (k16_scmpds_2 A B C D))) ) ).
tt(fc23_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k4_scmring2 A B C)) 2 (k1_scmring2 A))) ) ) ).
tt(fc23_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ((v4_scmyciel (k12_scmyciel A)) & (v6_scmyciel (k12_scmyciel A))) ) ) ).
tt(fc23_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) & (m1_simplex0 B A)) )  & (v1_int_1 C)) )  =>  (~ (v3_pencil_1 (k8_simplex0 A B C))) ) ) ).
tt(fc23_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))))) ).
tt(fc23_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_tops_1 (k5_group_2 A C B) A)) ) ).
tt(fc23_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v2_struct_0 (k8_toprealb A))) ) ) ).
tt(fc23_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k2_xboole_0 A B)))  & (v1_trees_1 (k2_xboole_0 A B))) ) ) ).
tt(fc23_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_valued_0 A))  & (v1_relat_1 B))  => (v4_valued_0 (k3_xboole_0 A B))) ) ).
tt(fc23_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v1_finseq_1 (k7_valued_1 A B))) ) ) ) ).
tt(fc23_valued_2,ax, (! [A:$i,B:$i] :  ((v2_membered B) => (v2_valued_2 (k4_partfun1 A B))) ) ).
tt(fc23_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k7_lattice3 A)) & (v16_waybel_0 (k7_lattice3 A))) ) ) ).
tt(fc23_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  => (v3_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc23_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ( (~ (v2_struct_0 (k4_waybel_9 A B C)))  & (v6_waybel_0 (k4_waybel_9 A B C) A)) ) ) ).
tt(fc23_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k3_xcmplx_0 A B))) ) ) ).
tt(fc23_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k3_xxreal_3 B A)) & (v2_xxreal_0 (k3_xxreal_3 B A))) ) ) ).
tt(fc23_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_yellow_6 (k12_yellow_6 A) A) &  ((v5_yellow_6 (k12_yellow_6 A) A) &  ((v6_yellow_6 (k12_yellow_6 A) A) & (v7_yellow_6 (k12_yellow_6 A) A)) ) ) ) ) ).
tt(fc24_abcmiz_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( ((v1_relat_1 C) &  ( (~ (v3_relat_1 C))  &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  & (m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A C))))) ) )  => (v1_finset_1 (k1_funct_1 (k2_msafree3 A D) B))) ) ).
tt(fc24_afinsq_1,ax, (! [A:$i] : (v4_funct_1 (k8_afinsq_1 A))) ).
tt(fc24_afinsq_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_relat_1 (k1_afinsq_2 B)) &  ((v5_relat_1 (k1_afinsq_2 B) A) &  ((v1_funct_1 (k1_afinsq_2 B)) &  ((v5_ordinal1 (k1_afinsq_2 B)) & (v1_finset_1 (k1_afinsq_2 B))) ) ) ) ) ) ).
tt(fc24_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_zfmisc_1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((v7_struct_0 (g5_algstr_0 A B C D)) & (v29_algstr_0 (g5_algstr_0 A B C D))) ) ) ).
tt(fc24_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k2_ami_3 A B)) 2 k1_ami_3)) ) ) ).
tt(fc24_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_relat_1 (k4_comput_1 3 A)) &  ((v4_relat_1 (k4_comput_1 3 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 3 A)) &  ((v4_valued_0 (k4_comput_1 3 A)) &  ((v2_margrel1 (k4_comput_1 3 A)) & (v8_comput_1 (k4_comput_1 3 A) 3)) ) ) ) ) ) ) ).
tt(fc24_euclid_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k3_euclid_9 A B)) &  ((v1_funct_1 (k3_euclid_9 A B)) & (v1_finseq_1 (k3_euclid_9 A B))) ) ) ) ).
tt(fc24_finseq_1,ax, (! [A:$i] : (v3_card_1 (k5_finseq_1 A) 1)) ).
tt(fc24_finset_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v1_finset_1 (k1_funct_4 A B))) ) ) ) ).
tt(fc24_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_1 (k18_finseq_1 A)) & (v1_relat_2 (k18_finseq_1 A))) ) ) ).
tt(fc24_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v5_fomodel1 (k8_fomodel1 A) A)) ) ) ).
tt(fc24_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ( (~ (v7_fomodel1 D A))  & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  =>  (~ (v15_fomodel1 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A D) B) C) A)) ) ) ).
tt(fc24_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  => (v1_partfun1 (k18_fomodel3 A B C) (k4_finseq_2 B (k8_eqrel_1 A C)))) ) ).
tt(fc24_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k25_fomodel4 A) A)) ) ).
tt(fc24_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k9_gate_1 B C A))) ) ) ).
tt(fc24_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) )  =>  ((v1_rlvect_1 (k10_hahnban1 A)) &  ((v5_rlvect_1 (k10_hahnban1 A)) &  ((v6_rlvect_1 (k10_hahnban1 A)) &  ((v7_rlvect_1 (k10_hahnban1 A)) & (v8_rlvect_1 (k10_hahnban1 A))) ) ) ) ) ) ).
tt(fc24_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ((v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (v3_bilinear (k3_hermitan A B C) k1_complfld A B)) ) ) ) ).
tt(fc24_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  => (v1_ideal_1 (k16_ideal_1 A B C) A)) ) ).
tt(fc24_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k9_member_1 A B))) ) ).
tt(fc24_membered,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (v7_ordinal1 C)) )  => (v6_membered (k1_enumset1 A B C))) ) ).
tt(fc24_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_ordinal6 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v3_ordinal6 (k5_relat_1 A B))) ) ) ).
tt(fc24_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v4_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc24_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v7_pcs_0 B) & (v9_pcs_0 B)) ) ) ) )  & (m1_subset_1 C A)) )  => (v4_pcs_0 (k1_funct_1 B C))) ) ).
tt(fc24_pre_poly,ax, (! [A:$i] :  (~ (v1_xboole_0 (k14_pre_poly A))) ) ).
tt(fc24_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_ratfunc1 B A))  =>  ((v5_ratfunc1 (k11_ratfunc1 A B) A) & (v6_ratfunc1 (k11_ratfunc1 A B) A)) ) ) ).
tt(fc24_relat_1,ax, (! [A:$i] :  ( ((v1_zfmisc_1 A) & (v1_relat_1 A))  => (v1_zfmisc_1 (k9_xtuple_0 A))) ) ).
tt(fc24_scmfsa10,ax,(v1_amistd_1 (k4_xtuple_0 (k2_compos_1 k1_scmfsa_2)) 3 k1_scmfsa_2)).
tt(fc24_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k9_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc24_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa6b A)) ) ) ) ) ) )  &  ((v2_scmfsa6c B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa6a A B)))  &  ((v1_relat_1 (k5_scmfsa6a A B)) &  ((v4_relat_1 (k5_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa6a A B)) &  ((v1_finset_1 (k5_scmfsa6a A B)) &  ((v1_afinsq_1 (k5_scmfsa6a A B)) & (v1_scmfsa6b (k5_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc24_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) ) )  =>  ((v5_ordinal1 (k1_ordinal4 A B)) &  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) & (v2_compos_1 (k1_ordinal4 A B) k1_scmpds_2)) ) ) ) ) ).
tt(fc24_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_amistd_1 (k4_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc24_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  =>  ((v4_scmyciel (k12_scmyciel A)) & (v11_scmyciel (k12_scmyciel A))) ) ) ).
tt(fc24_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_simplex0 B A) &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_pre_topc (k10_simplex0 A B C)) &  ((v1_matroid0 (k10_simplex0 A B C)) &  ((v3_matroid0 (k10_simplex0 A B C)) &  (~ (v5_simplex0 (k10_simplex0 A B C))) ) ) ) ) ) ).
tt(fc24_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc24_topgrp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  &  ( ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_tops_1 (k4_group_2 A C B) A)) ) ).
tt(fc24_toprealb,ax,(v1_toprealb (k8_toprealb 2))).
tt(fc24_toprealc,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) )  =>  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_funct_2 (k30_valued_1 B) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k30_valued_1 B) A k3_topmetr)) ) ) ) ).
tt(fc24_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v5_trees_3 A)) ) )  =>  ( (~ (v1_xboole_0 (k11_trees_3 A)))  &  ((v1_finset_1 (k11_trees_3 A)) & (v1_trees_1 (k11_trees_3 A))) ) ) ) ).
tt(fc24_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_valued_0 A))  & (v1_relat_1 B))  => (v4_valued_0 (k4_xboole_0 A B))) ) ).
tt(fc24_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v1_funct_1 (k13_valued_1 A B)) & (v1_valued_0 (k13_valued_1 A B))) ) ) ) ).
tt(fc24_valued_2,ax, (! [A:$i,B:$i] :  ((v3_membered B) => (v3_valued_2 (k4_partfun1 A B))) ) ).
tt(fc24_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  => (v4_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc24_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v5_orders_2 (k4_waybel_9 A B C)) & (v6_waybel_0 (k4_waybel_9 A B C) A)) ) ) ).
tt(fc24_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k3_xcmplx_0 B A))) ) ) ).
tt(fc24_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) & (v3_xxreal_0 B)) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) & (v3_xxreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc24_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m4_yellow_6 B A))  =>  ( (~ (v2_struct_0 (k13_yellow_6 A B)))  & (v1_pre_topc (k13_yellow_6 A B))) ) ) ).
tt(fc25_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  => (v1_finset_1 (k45_abcmiz_1 A B))) ) ).
tt(fc25_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) )  =>  ((v1_relat_1 (k63_valued_1 A)) &  ((v1_funct_1 (k63_valued_1 A)) & (v1_afinsq_1 (k63_valued_1 A))) ) ) ) ).
tt(fc25_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k2_afinsq_2 A B)) &  ((v1_funct_1 (k2_afinsq_2 A B)) &  ((v2_funct_1 (k2_afinsq_2 A B)) &  ((v5_ordinal1 (k2_afinsq_2 A B)) & (v1_finset_1 (k2_afinsq_2 A B))) ) ) ) ) ) ).
tt(fc25_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ( (~ (v7_struct_0 (g5_algstr_0 A B C D)))  & (v29_algstr_0 (g5_algstr_0 A B C D))) ) ) ).
tt(fc25_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k3_ami_3 A B)) 2 k1_ami_3)) ) ) ).
tt(fc25_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k3_comput_1 A B)) &  ((v4_relat_1 (k3_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 A B)) &  ((v4_valued_0 (k3_comput_1 A B)) &  ((v2_margrel1 (k3_comput_1 A B)) & (v7_comput_1 (k3_comput_1 A B))) ) ) ) ) ) ) ).
tt(fc25_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) &  ( (~ (v2_xxreal_0 C))  & (v1_xreal_0 C)) ) )  => (v1_xboole_0 (k4_euclid_9 A B C))) ) ).
tt(fc25_finseq_1,ax, (! [A:$i,B:$i] : (v3_card_1 (k10_finseq_1 A B) 2)) ).
tt(fc25_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_finset_1 B))  =>  ((v1_relat_1 (k6_relat_1 A B)) & (v1_finset_1 (k6_relat_1 A B))) ) ) ).
tt(fc25_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) => (v1_relat_1 (k3_tarski A))) ) ).
tt(fc25_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v9_fomodel1 (k8_fomodel1 A) A)) ) ) ).
tt(fc25_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v7_fomodel1 (k8_fomodel1 A) A)) ) ) ).
tt(fc25_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) )  =>  ((v1_relat_1 (k8_fomodel3 B C D A)) & (v1_funct_1 (k8_fomodel3 B C D A))) ) ) ).
tt(fc25_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k27_fomodel4 A) A)) ) ).
tt(fc25_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) )  => (v1_xboole_0 (k10_gate_1 A B C))) ) ).
tt(fc25_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v2_hahnban B (k10_hahnban1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k13_hahnban1 A B)) &  ((v1_funct_2 (k13_hahnban1 A B) (u1_struct_0 A) k1_numbers) & (v4_hahnban1 (k13_hahnban1 A B) k1_complfld A)) ) ) ) ).
tt(fc25_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ( (~ (v3_funct_1 C))  &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((v1_funct_1 (k3_hermitan A B C)) &  ( (~ (v3_funct_1 (k3_hermitan A B C)))  & (v1_funct_2 (k3_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))) ) ) ) ).
tt(fc25_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v2_ideal_1 (k16_ideal_1 A B C) A)) ) ).
tt(fc25_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k9_member_1 A B))) ) ).
tt(fc25_membered,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k2_xboole_0 A B))) ) ).
tt(fc25_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~ (v4_card_3 (k1_classes1 (k2_xboole_0 A k4_ordinal1)))) ) ) ).
tt(fc25_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v4_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc25_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v7_pcs_0 B) & (v10_pcs_0 B)) ) ) ) )  & (m1_subset_1 C A)) )  => (v5_pcs_0 (k1_funct_1 B C))) ) ).
tt(fc25_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k17_pre_poly A) (k15_pre_poly A)) &  ((v1_relat_2 (k17_pre_poly A)) &  ((v4_relat_2 (k17_pre_poly A)) &  ((v8_relat_2 (k17_pre_poly A)) & (v3_orders_1 (k17_pre_poly A))) ) ) ) ) ) ).
tt(fc25_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A)) )  =>  (~ (v4_ratfunc1 (k11_ratfunc1 A B) A)) ) ) ).
tt(fc25_relat_1,ax, (! [A:$i] :  ( ((v1_zfmisc_1 A) & (v1_relat_1 A))  => (v1_zfmisc_1 (k10_xtuple_0 A))) ) ).
tt(fc25_scmfsa10,ax,(v2_amistd_1 (k2_compos_1 k1_scmfsa_2) 3 k1_scmfsa_2)).
tt(fc25_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k10_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc25_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ((v2_scmfsa6c B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k6_scmfsa6a A B)))  &  ((v1_relat_1 (k6_scmfsa6a A B)) &  ((v4_relat_1 (k6_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k6_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k6_scmfsa6a A B)) &  ((v1_finset_1 (k6_scmfsa6a A B)) &  ((v1_afinsq_1 (k6_scmfsa6a A B)) & (v1_scmfsa6b (k6_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc25_scmpds_5,ax, (! [A:$i] :  ( ((v6_compos_0 A (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  => (v2_compos_1 (k3_afinsq_1 A) k1_scmpds_2)) ) ).
tt(fc25_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k5_scmring2 A B C)) 2 (k1_scmring2 A))) ) ) ).
tt(fc25_scmyciel,ax, (! [A:$i,B:$i] :  ( ((v4_scmyciel A) & (v7_ordinal1 B))  => (v4_scmyciel (k1_funct_1 (k13_scmyciel A) B))) ) ).
tt(fc25_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_pencil_1 B) & (m1_simplex0 B A))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_pre_topc (k10_simplex0 A B C)) & (v4_simplex0 (k10_simplex0 A B C))) ) ) ).
tt(fc25_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(fc25_toprealb,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  => (v1_borsuk_2 (k7_toprealb 2 A B))) ) ).
tt(fc25_toprealc,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) )  =>  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_funct_2 (k35_valued_1 B) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k35_valued_1 B) A k3_topmetr)) ) ) ) ).
tt(fc25_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( (~ (v1_xboole_0 (k12_trees_3 A)))  &  ((v1_finset_1 (k12_trees_3 A)) & (v1_trees_1 (k12_trees_3 A))) ) ) ) ).
tt(fc25_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_valued_0 A))  &  ((v1_relat_1 B) & (v1_valued_0 B)) )  => (v1_valued_0 (k5_xboole_0 A B))) ) ).
tt(fc25_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v1_funct_1 (k13_valued_1 A B)) & (v3_valued_0 (k13_valued_1 A B))) ) ) ) ).
tt(fc25_valued_2,ax, (! [A:$i,B:$i] :  ((v4_membered B) => (v4_valued_2 (k4_partfun1 A B))) ) ).
tt(fc25_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v6_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc25_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v5_orders_2 (k4_waybel_9 A B C)) & (v6_waybel_0 (k4_waybel_9 A B C) A)) ) ) ).
tt(fc25_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k3_xcmplx_0 A B))) ) ) ).
tt(fc25_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v3_xxreal_0 A))  &  ((v1_xxreal_0 B) & (v3_xxreal_0 B)) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) & (v2_xxreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc25_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m4_yellow_6 B A))  =>  ((v1_pre_topc (k13_yellow_6 A B)) & (v2_pre_topc (k13_yellow_6 A B))) ) ) ).
tt(fc26_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  => (v1_finset_1 (k47_abcmiz_1 A B))) ) ).
tt(fc26_afinsq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((v1_relat_1 (k16_afinsq_1 A B C D)) & (v1_funct_1 (k16_afinsq_1 A B C D))) ) ).
tt(fc26_afinsq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k2_afinsq_2 B C)) &  ((v5_relat_1 (k2_afinsq_2 B C) A) &  ((v1_funct_1 (k2_afinsq_2 B C)) &  ((v5_ordinal1 (k2_afinsq_2 B C)) & (v1_finset_1 (k2_afinsq_2 B C))) ) ) ) ) ) ).
tt(fc26_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k4_ami_3 A B)) 2 k1_ami_3)) ) ) ).
tt(fc26_comput_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A k6_numbers)) ) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 2)) ) ) )  =>  ((v7_comput_1 (k7_comput_1 A B 1)) & (v8_comput_1 (k7_comput_1 A B 1) 1)) ) ) ).
tt(fc26_euclid_9,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k14_euclid k6_numbers))) & (v1_xreal_0 B))  =>  (~ (v1_xboole_0 (k4_euclid_9 k6_numbers A B))) ) ) ).
tt(fc26_finseq_1,ax, (! [A:$i,B:$i,C:$i] : (v3_card_1 (k11_finseq_1 A B C) 3)) ).
tt(fc26_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_finset_1 B))  =>  ((v1_relat_1 (k5_relat_1 B A)) & (v1_finset_1 (k5_relat_1 B A))) ) ) ).
tt(fc26_fomodel0,ax, (! [A:$i] : (v1_xboole_0 (k4_xboole_0 A A))) ).
tt(fc26_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v1_xboole_0 B) &  ((v14_fomodel1 C B A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_xboole_0 (k38_fomodel1 A C))) ) ).
tt(fc26_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (~ (v15_fomodel1 (k7_finseq_1 (k31_fomodel2 A (k1_fomodel2 A)) B) A)) ) ) ).
tt(fc26_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_xboole_0 C) & (v7_ordinal1 C))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (v1_xboole_0 (k5_xboole_0 (k8_fomodel3 A B D C) (k3_fomodel2 (k1_tarski k1_xboole_0))))) ) ).
tt(fc26_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k28_fomodel4 A) A)) ) ).
tt(fc26_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k10_gate_1 A B C))) ) ) ).
tt(fc26_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v3_ideal_1 (k16_ideal_1 A B C) A)) ) ).
tt(fc26_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v5_membered B))  => (v5_membered (k9_member_1 A B))) ) ).
tt(fc26_membered,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k2_xboole_0 A B))) ) ).
tt(fc26_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v3_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc26_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v7_pcs_0 B) & (v11_pcs_0 B)) ) ) ) )  & (m1_subset_1 C A)) )  => (v6_pcs_0 (k1_funct_1 B C))) ) ).
tt(fc26_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((v4_funct_1 (k18_pre_poly A B)) &  (~ (v1_xboole_0 (k18_pre_poly A B))) ) ) ) ).
tt(fc26_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) & (v5_relat_1 C B))  =>  ((v1_relat_1 (k5_relat_1 C A)) & (v5_relat_1 (k5_relat_1 C A) B)) ) ) ).
tt(fc26_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_amistd_1 (k4_xtuple_0 (k11_scmfsa_2 A)) 3 k1_scmfsa_2)) ) ).
tt(fc26_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v6_compos_0 (k11_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc26_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa6c A B)))  &  ((v1_relat_1 (k1_scmfsa6c A B)) &  ((v4_relat_1 (k1_scmfsa6c A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6c A B)) &  ((v1_finset_1 (k1_scmfsa6c A B)) &  ((v1_afinsq_1 (k1_scmfsa6c A B)) & (v7_amistd_1 (k1_scmfsa6c A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc26_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v6_compos_0 A (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_4 A B)))  &  ((v1_relat_1 (k2_scmpds_4 A B)) &  ((v4_relat_1 (k2_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_4 A B)) &  ((v1_finset_1 (k2_scmpds_4 A B)) &  ((v1_afinsq_1 (k2_scmpds_4 A B)) & (v2_compos_1 (k2_scmpds_4 A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc26_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_amistd_1 (k5_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc26_scmyciel,ax, (! [A:$i,B:$i] :  ( ( ((v4_scmyciel A) & (v6_scmyciel A))  & (v7_ordinal1 B))  => (v6_scmyciel (k1_funct_1 (k13_scmyciel A) B))) ) ).
tt(fc26_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_matroid0 B) & (m1_simplex0 B A))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_pre_topc (k10_simplex0 A B C)) & (v4_matroid0 (k10_simplex0 A B C))) ) ) ).
tt(fc26_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc26_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  ( (~ (v2_struct_0 (k11_toprealb A)))  & (v1_pre_topc (k11_toprealb A))) ) ) ).
tt(fc26_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k7_valued_1 B C)) &  ((v1_funct_2 (k7_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k7_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc26_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) )  =>  ( (~ (v1_xboole_0 (k13_trees_3 A B)))  &  ((v1_finset_1 (k13_trees_3 A B)) & (v1_trees_1 (k13_trees_3 A B))) ) ) ) ).
tt(fc26_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_valued_0 A))  &  ((v1_relat_1 B) & (v2_valued_0 B)) )  => (v2_valued_0 (k5_xboole_0 A B))) ) ).
tt(fc26_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  & (v1_rat_1 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v5_relat_1 (k13_valued_1 A B) k3_numbers) & (v1_funct_1 (k13_valued_1 A B))) ) ) ) ).
tt(fc26_valued_2,ax, (! [A:$i,B:$i] :  ((v5_membered B) => (v5_valued_2 (k4_partfun1 A B))) ) ).
tt(fc26_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~ (v1_xboole_0 (k12_waybel_4 A))) ) ) ).
tt(fc26_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v4_orders_2 (k4_waybel_9 A B C)) & (v6_waybel_0 (k4_waybel_9 A B C) A)) ) ) ).
tt(fc26_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k3_xcmplx_0 A B))) ) ) ).
tt(fc26_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) & (v2_xxreal_0 A))  &  ((v1_xxreal_0 B) & (v2_xxreal_0 B)) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) & (v2_xxreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc27_afinsq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((v5_ordinal1 (k16_afinsq_1 A B C D)) & (v1_finset_1 (k16_afinsq_1 A B C D))) ) ).
tt(fc27_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k5_ami_3 A B)) 2 k1_ami_3)) ) ) ).
tt(fc27_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 1)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 3)) ) ) )  =>  ((v7_comput_1 (k7_comput_1 A B 1)) & (v8_comput_1 (k7_comput_1 A B 1) 2)) ) ) ).
tt(fc27_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) &  ((v2_xxreal_0 C) & (v1_xreal_0 C)) ) )  =>  (~ (v1_xboole_0 (k4_euclid_9 A B C))) ) ) ).
tt(fc27_finseq_1,ax, (! [A:$i] : (v3_finseq_1 (k13_finseq_1 A))) ).
tt(fc27_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k5_relat_1 B A)) & (v1_finset_1 (k5_relat_1 B A))) ) ) ).
tt(fc27_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (v1_xboole_0 (k4_xboole_0 (k6_domain_1 A (k3_funct_2 A A (k6_partfun1 A) B)) (k6_domain_1 A B)))) ) ).
tt(fc27_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v5_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  (~ (v1_xboole_0 (k19_fomodel1 A B))) ) ) ).
tt(fc27_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  (~ (v15_fomodel1 (k7_finseq_1 (k31_fomodel2 A B) C) A)) ) ) ).
tt(fc27_fomodel3,ax, (! [A:$i,B:$i] :  ((v4_funct_1 B) => (v4_funct_1 (k3_xboole_0 A B))) ) ).
tt(fc27_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v6_fomodel4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  &  ((v6_fomodel4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) ) )  => (v6_fomodel4 (k2_xboole_0 B C) A)) ) ).
tt(fc27_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k10_gate_1 A C B))) ) ) ).
tt(fc27_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v3_hahnban B (k10_hahnban1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k13_hahnban1 A B)) &  ((v1_funct_2 (k13_hahnban1 A B) (u1_struct_0 A) k1_numbers) & (v5_hahnban1 (k13_hahnban1 A B) A)) ) ) ) ).
tt(fc27_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k17_ideal_1 A B))) ) ) ).
tt(fc27_member_1,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v6_membered B))  => (v6_membered (k9_member_1 A B))) ) ).
tt(fc27_membered,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k2_xboole_0 A B))) ) ).
tt(fc27_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v3_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc27_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) & (v4_relat_1 C B))  =>  ((v1_relat_1 (k5_relat_1 C A)) &  ((v4_relat_1 (k5_relat_1 C A) A) & (v4_relat_1 (k5_relat_1 C A) B)) ) ) ) ).
tt(fc27_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v4_compos_0 (k11_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2)))  &  ((v2_amistd_1 (k11_scmfsa_2 A) 3 k1_scmfsa_2) &  (~ (v4_amistd_1 (k11_scmfsa_2 A) 3 k1_scmfsa_2)) ) ) ) ) ).
tt(fc27_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k12_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc27_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa6c A B)))  &  ((v1_relat_1 (k1_scmfsa6c A B)) &  ((v4_relat_1 (k1_scmfsa6c A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6c A B)) &  ((v1_finset_1 (k1_scmfsa6c A B)) &  ((v1_afinsq_1 (k1_scmfsa6c A B)) & (v1_scmfsa6b (k1_scmfsa6c A B))) ) ) ) ) ) ) ) ) ).
tt(fc27_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ((v6_compos_0 B (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_4 A B)))  &  ((v1_relat_1 (k3_scmpds_4 A B)) &  ((v4_relat_1 (k3_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_4 A B)) &  ((v1_finset_1 (k3_scmpds_4 A B)) &  ((v1_afinsq_1 (k3_scmpds_4 A B)) & (v2_compos_1 (k3_scmpds_4 A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc27_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k6_scmring2 A B C)) 2 (k1_scmring2 A))) ) ) ).
tt(fc27_scmyciel,ax, (! [A:$i,B:$i] :  ( ( ((v4_scmyciel A) & (v11_scmyciel A))  & (v7_ordinal1 B))  => (v11_scmyciel (k1_funct_1 (k13_scmyciel A) B))) ) ).
tt(fc27_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_simplex0 B) & (m1_simplex0 B A))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_pre_topc (k10_simplex0 A B C)) & (v2_simplex0 (k10_simplex0 A B C))) ) ) ).
tt(fc27_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k19_sin_cos (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))))) ).
tt(fc27_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  ((v1_pre_topc (k11_toprealb A)) & (v1_tsep_1 (k11_toprealb A) (k8_toprealb 2))) ) ) ).
tt(fc27_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k13_valued_1 B C)) &  ((v1_funct_2 (k13_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k13_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc27_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k5_trees_3 A)))  => (v1_finset_1 (k9_xtuple_0 B))) ) ).
tt(fc27_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_valued_0 A))  &  ((v1_relat_1 B) & (v3_valued_0 B)) )  => (v3_valued_0 (k5_xboole_0 A B))) ) ).
tt(fc27_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v5_relat_1 (k13_valued_1 A B) k4_numbers) & (v1_funct_1 (k13_valued_1 A B))) ) ) ) ).
tt(fc27_valued_2,ax, (! [A:$i,B:$i] :  ((v6_membered B) => (v6_valued_2 (k4_partfun1 A B))) ) ).
tt(fc27_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v8_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(fc27_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v4_orders_2 (k4_waybel_9 A B C)) &  ((v6_waybel_0 (k4_waybel_9 A B C) A) & (v7_waybel_0 (k4_waybel_9 A B C))) ) ) ) ).
tt(fc27_xreal_0,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) & (v2_xxreal_0 (k5_xcmplx_0 A))) ) ) ).
tt(fc27_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) &  (~ (v2_xxreal_0 (k4_xxreal_3 A B))) ) ) ) ).
tt(fc28_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  ((v1_relat_1 (k4_afinsq_2 A)) &  ((v5_relat_1 (k4_afinsq_2 A) k5_numbers) &  ((v1_funct_1 (k4_afinsq_2 A)) &  ((v2_funct_1 (k4_afinsq_2 A)) &  ((v5_ordinal1 (k4_afinsq_2 A)) & (v1_finset_1 (k4_afinsq_2 A))) ) ) ) ) ) ) ).
tt(fc28_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k6_ami_3 A B)) 2 k1_ami_3)) ) ) ).
tt(fc28_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 1)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 3)) ) ) )  =>  ((v7_comput_1 (k7_comput_1 A B 2)) & (v8_comput_1 (k7_comput_1 A B 2) 2)) ) ) ).
tt(fc28_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) & (v1_xreal_0 C)) )  => (v3_pre_topc (k4_euclid_9 A B C) (k3_pcomps_1 (k14_euclid A)))) ) ).
tt(fc28_finseq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B k5_numbers) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 C D)) &  ((v1_funct_1 (k7_finseq_1 C D)) &  ((v3_card_1 (k7_finseq_1 C D) (k1_nat_1 A B)) & (v1_finseq_1 (k7_finseq_1 C D))) ) ) ) ) ).
tt(fc28_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_finset_1 A))  => (v1_finset_1 (k1_relat_1 A))) ) ).
tt(fc28_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 B C)) &  ((v5_relat_1 (k7_finseq_1 B C) A) &  ((v1_funct_1 (k7_finseq_1 B C)) & (v1_finseq_1 (k7_finseq_1 B C))) ) ) ) ) ).
tt(fc28_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v8_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((v1_xxreal_0 (k19_fomodel1 A B)) &  (~ (v3_xxreal_0 (k19_fomodel1 A B))) ) ) ) ).
tt(fc28_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  => (v5_fomodel2 (k7_finseq_1 (k31_fomodel2 A C) B) A)) ) ).
tt(fc28_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) )  =>  ((v1_relat_1 (k22_fomodel3 A B D C)) &  ((v4_relat_1 (k22_fomodel3 A B D C) (k37_fomodel1 A)) & (v1_funct_1 (k22_fomodel3 A B D C))) ) ) ) ).
tt(fc28_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v3_fomodel2 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C) A k6_numbers)) ) ).
tt(fc28_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k10_gate_1 C A B))) ) ) ).
tt(fc28_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v1_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc28_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_hermitan B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) )  =>  (~ (v1_xboole_0 (k12_bilinear k1_complfld A B))) ) ) ).
tt(fc28_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  => (v1_ideal_1 (k17_ideal_1 A B) A)) ) ).
tt(fc28_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k10_member_1 A B))) ) ).
tt(fc28_membered,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k2_xboole_0 A B))) ) ).
tt(fc28_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v2_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc28_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  =>  ((v2_funct_1 (k20_pre_poly A B)) &  (~ (v1_xboole_0 (k20_pre_poly A B))) ) ) ) ).
tt(fc28_relat_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) &  ((v4_relat_1 (k4_relat_1 A) A) & (v5_relat_1 (k4_relat_1 A) A)) ) ) ).
tt(fc28_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v1_amistd_1 (k4_xtuple_0 (k12_scmfsa_2 B A)) 3 k1_scmfsa_2)) ) ).
tt(fc28_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k13_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc28_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v6_compos_0 A (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ((v6_compos_0 B (u1_compos_1 k1_scmpds_2)) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_4 A B)))  &  ((v1_relat_1 (k4_scmpds_4 A B)) &  ((v4_relat_1 (k4_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_4 A B)) &  ((v1_finset_1 (k4_scmpds_4 A B)) &  ((v1_afinsq_1 (k4_scmpds_4 A B)) & (v2_compos_1 (k4_scmpds_4 A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc28_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_amistd_1 (k6_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc28_scmyciel,ax, (! [A:$i,B:$i] :  ( ( ((v1_finset_1 A) & (v4_scmyciel A))  & (v7_ordinal1 B))  => (v1_finset_1 (k1_funct_1 (k13_scmyciel A) B))) ) ).
tt(fc28_sin_cos6,ax, ((v1_funct_1 k1_sin_cos6) & (v2_funct_1 k1_sin_cos6)) ).
tt(fc28_toprealb,ax, ((v1_funct_1 k12_toprealb) &  ((v1_funct_2 k12_toprealb (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2))) & (v5_pre_topc k12_toprealb k2_topalg_2 (k8_toprealb 2))) ) ).
tt(fc28_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k24_valued_1 B C)) &  ((v1_funct_2 (k24_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k24_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc28_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  &  ((v1_relat_1 B) & (v5_relat_1 B k3_numbers)) )  => (v5_relat_1 (k5_xboole_0 A B) k3_numbers)) ) ).
tt(fc28_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k13_valued_1 C D)) & (v1_partfun1 (k13_valued_1 C D) A)) ) ) ).
tt(fc28_valued_2,ax, (! [A:$i,B:$i] :  ((v1_membered B) => (v1_valued_2 (k1_funct_2 A B))) ) ).
tt(fc28_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( (~ (v2_struct_0 D))  & (l1_waybel_0 D A)) ) ) )  =>  ( (~ (v2_struct_0 (k6_waybel_9 A B C D)))  & (v6_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc28_xreal_0,ax, (! [A:$i] :  ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) &  (~ (v2_xxreal_0 (k5_xcmplx_0 A))) ) ) ) ).
tt(fc28_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k4_xxreal_3 A B))) ) ) ) ).
tt(fc29_abcmiz_1,ax, ( (~ (v2_struct_0 k49_abcmiz_1))  &  ((v1_orders_2 k49_abcmiz_1) &  ((v3_orders_2 k49_abcmiz_1) &  ((v4_orders_2 k49_abcmiz_1) &  ((v5_orders_2 k49_abcmiz_1) &  ((v1_lattice3 k49_abcmiz_1) & (v2_lattice3 k49_abcmiz_1)) ) ) ) ) ) ).
tt(fc29_afinsq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_relat_1 (k5_afinsq_2 B C)) &  ((v5_relat_1 (k5_afinsq_2 B C) A) &  ((v1_funct_1 (k5_afinsq_2 B C)) &  ((v5_ordinal1 (k5_afinsq_2 B C)) & (v1_finset_1 (k5_afinsq_2 B C))) ) ) ) ) ) ).
tt(fc29_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ( (~ (v2_struct_0 (g6_algstr_0 A B C D E)))  & (v36_algstr_0 (g6_algstr_0 A B C D E))) ) ) ).
tt(fc29_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v2_amistd_1 (k2_ami_3 A B) 2 k1_ami_3)) ) ) ).
tt(fc29_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v4_valued_0 A)) ) )  =>  ((v1_relat_1 (k14_comput_1 A)) &  ((v4_relat_1 (k14_comput_1 A) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k14_comput_1 A)) & (v4_valued_0 (k14_comput_1 A))) ) ) ) ) ).
tt(fc29_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k14_euclid A))))  =>  ( (~ (v1_xboole_0 (k5_euclid_9 A B)))  &  ((v1_tops_2 (k5_euclid_9 A B) (k3_pcomps_1 (k14_euclid A))) & (v1_yellow_8 (k5_euclid_9 A B) (k3_pcomps_1 (k14_euclid A)) (k2_euclid_9 A B))) ) ) ) ).
tt(fc29_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_finseq_1 A) &  ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) ) )  => (v1_finseq_1 (k1_funct_1 B C))) ) ).
tt(fc29_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v1_finset_1 (k4_funct_4 A B C D))) ).
tt(fc29_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (v3_fomodel0 C A)) )  => (v3_fomodel0 (k7_relat_1 (k8_fomodel0 A) (k4_finseq_2 B C)) A)) ) ).
tt(fc29_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((v1_xxreal_0 (k19_fomodel1 A B)) & (v3_xxreal_0 (k19_fomodel1 A B))) ) ) ).
tt(fc29_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ( (~ (v1_xboole_0 (k32_fomodel2 A B)))  & (v7_ordinal1 (k32_fomodel2 A B))) ) ) ).
tt(fc29_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ( ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_fomodel2 E A B) & (v3_fomodel3 E A B C)) ) ) ) ) ) )  => (v2_fomodel3 (k1_funct_1 E D) A B D C)) ) ).
tt(fc29_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  &  ( ((v3_card_1 C B) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  &  ((v3_card_1 D B) & (m1_subset_1 D (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) ) )  => (v1_finset_1 (k35_fomodel4 A B C D))) ) ).
tt(fc29_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 C)) )  => (v1_xboole_0 (k10_gate_1 A B C))) ) ).
tt(fc29_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v1_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc29_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_bilinear k1_complfld A B C)) &  ((v1_funct_2 (k15_bilinear k1_complfld A B C) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k15_bilinear k1_complfld A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B) &  ((v2_bilinear (k15_bilinear k1_complfld A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B) &  ((v4_bilinear (k15_bilinear k1_complfld A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B) & (v2_hermitan (k15_bilinear k1_complfld A B C) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B)) ) ) ) ) ) ) ).
tt(fc29_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_ideal_1 (k17_ideal_1 A B) A)) ) ).
tt(fc29_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k10_member_1 B A))) ) ).
tt(fc29_membered,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v5_membered B))  => (v5_membered (k2_xboole_0 A B))) ) ).
tt(fc29_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v2_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc29_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) ) )  =>  ((v2_funct_1 (k21_pre_poly A B)) &  ( (~ (v1_xboole_0 (k21_pre_poly A B)))  & (v1_pre_poly (k21_pre_poly A B))) ) ) ) ).
tt(fc29_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v5_relat_1 B A))  & (v1_relat_1 C))  =>  ((v1_relat_1 (k3_relat_1 C B)) & (v5_relat_1 (k3_relat_1 C B) A)) ) ) ).
tt(fc29_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v1_amistd_1 (k4_xtuple_0 (k13_scmfsa_2 B A)) 3 k1_scmfsa_2)) ) ).
tt(fc29_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_scmfsa_2 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  => (v6_compos_0 (k14_scmfsa_2 C B A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc29_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scmpds_4 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scmpds_4 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_ordinal4 A B)))  &  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v4_relat_1 (k1_ordinal4 A B) k5_numbers) &  ((v5_relat_1 (k1_ordinal4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_ordinal4 A B)) &  ((v1_finset_1 (k1_ordinal4 A B)) &  ((v1_afinsq_1 (k1_ordinal4 A B)) & (v2_scmpds_4 (k1_ordinal4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc29_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k7_scmring2 A B C)) 2 (k1_scmring2 A))) ) ) ).
tt(fc29_sin_cos6,ax, ((v1_funct_1 k4_sin_cos6) & (v2_funct_1 k4_sin_cos6)) ).
tt(fc29_toprealb,ax, ((v1_funct_1 k12_toprealb) &  ((v1_funct_2 k12_toprealb (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2))) & (v2_funct_2 k12_toprealb (u1_struct_0 (k8_toprealb 2)))) ) ).
tt(fc29_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k14_valued_2 B C)) &  ((v1_funct_2 (k14_valued_2 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k14_valued_2 B C) A k3_topmetr)) ) ) ) ).
tt(fc29_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  &  ((v1_relat_1 B) & (v5_relat_1 B k4_numbers)) )  => (v5_relat_1 (k5_xboole_0 A B) k4_numbers)) ) ).
tt(fc29_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k13_valued_1 C D)) & (v1_partfun1 (k13_valued_1 C D) A)) ) ) ).
tt(fc29_valued_2,ax, (! [A:$i,B:$i] :  ((v2_membered B) => (v2_valued_2 (k1_funct_2 A B))) ) ).
tt(fc29_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v3_orders_2 D) & (l1_waybel_0 D A)) ) ) )  =>  ((v3_orders_2 (k6_waybel_9 A B C D)) & (v6_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc29_xreal_0,ax, (! [A:$i] :  ( ((v3_xxreal_0 A) & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) & (v3_xxreal_0 (k5_xcmplx_0 A))) ) ) ).
tt(fc29_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k4_xxreal_3 A B))) ) ) ) ).
tt(fc2_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v4_abcmiz_0 A))  & (l1_abcmiz_0 A))  =>  (~ (v1_xboole_0 (u1_abcmiz_0 A))) ) ) ).
tt(fc2_abcmiz_1,ax, (~ (v1_xboole_0 k2_abcmiz_1)) ).
tt(fc2_abcmiz_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  => (v1_xtuple_0 (k1_funct_1 B k1_xboole_0))) ) ).
tt(fc2_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  =>  (~ (v1_abian (k2_xcmplx_0 A 1))) ) ) ).
tt(fc2_afinsq_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_finset_1 (k5_relat_1 A B))) ) ) ).
tt(fc2_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_incsp_1 (k13_afproj A)) & (v5_incproj (k13_afproj A))) ) ) ).
tt(fc2_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v8_algstr_0 (k5_afvect0 A B)) &  ((v13_algstr_0 (k5_afvect0 A B)) &  ((v2_rlvect_1 (k5_afvect0 A B)) &  ((v3_rlvect_1 (k5_afvect0 A B)) & (v4_rlvect_1 (k5_afvect0 A B))) ) ) ) ) ) ).
tt(fc2_algspec1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) &  ((v1_msafree1 B A) & (l3_msualg_1 B A)) ) )  =>  ((v1_relat_1 (u3_msualg_1 A B)) &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) &  ((v2_funct_1 (u3_msualg_1 A B)) & (v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc2_algstr_1,ax,(v2_rlvect_1 k3_algstr_0)).
tt(fc2_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_altcat_1 A)))  &  ((v2_altcat_1 (k7_altcat_1 A)) &  ((v6_altcat_1 (k7_altcat_1 A)) &  ((v10_altcat_1 (k7_altcat_1 A)) &  ((v11_altcat_1 (k7_altcat_1 A)) & (v12_altcat_1 (k7_altcat_1 A))) ) ) ) ) ) ) ).
tt(fc2_altcat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k2_funct_4 A)) &  ((v1_funct_1 (k2_funct_4 A)) & (v1_funcop_1 (k2_funct_4 A))) ) ) ) ).
tt(fc2_altcat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_altcat_3 (k8_altcat_1 A B) A B B) &  ((v2_altcat_3 (k8_altcat_1 A B) A B B) &  ((v4_altcat_3 (k8_altcat_1 A B) A B B) & (v5_altcat_3 (k8_altcat_1 A B) A B B)) ) ) ) ) ).
tt(fc2_ami_2,ax, ((v1_relat_1 (k3_relat_1 k3_ami_2 k4_ami_2)) & (v2_relat_1 (k3_relat_1 k3_ami_2 k4_ami_2))) ).
tt(fc2_ami_3,ax, ((v2_memstr_0 k1_ami_3 2) & (v1_extpro_1 k1_ami_3 2)) ).
tt(fc2_ami_4,ax, ((v1_relat_1 k1_ami_4) &  ((v4_relat_1 k1_ami_4 k5_numbers) &  ((v5_relat_1 k1_ami_4 (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 k1_ami_4) &  ((v1_finset_1 k1_ami_4) &  (~ (v2_compos_1 k1_ami_4 k1_ami_3)) ) ) ) ) ) ).
tt(fc2_ami_5,ax, ((v1_extpro_1 k1_ami_3 2) & (v3_amistd_5 k1_ami_3 2)) ).
tt(fc2_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_amistd_1 (k2_ami_3 A B) 2 k1_ami_3)) ) ).
tt(fc2_amistd_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ((m1_subset_1 C (u1_compos_1 B)) & (m1_subset_1 D k5_numbers)) ) )  =>  (~ (v1_xboole_0 (k1_amistd_1 A B D C))) ) ) ).
tt(fc2_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v2_amistd_2 (k4_amistd_1 A) A)) ) ) ).
tt(fc2_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  => (v1_xboole_0 (k8_struct_0 (k4_amistd_1 A)))) ) ).
tt(fc2_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ( (~ (v2_struct_0 (k3_analmetr A)))  & (v1_analoaf (k3_analmetr A))) ) ) ).
tt(fc2_analort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k6_analort A B C)))  & (v1_analoaf (k6_analort A B C))) ) ) ).
tt(fc2_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_anproj_1 A)))  & (v1_collsp (k5_anproj_1 A))) ) ) ).
tt(fc2_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) & (v2_anproj_2 (k5_anproj_1 A))) ) ) ).
tt(fc2_aofa_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v2_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc2_armstrng,ax, (! [A:$i] :  (~ (v1_xboole_0 (k4_armstrng A))) ) ).
tt(fc2_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k3_arrow A))) ) ) ).
tt(fc2_arytm_2,ax, (~ (v1_xboole_0 k2_arytm_2)) ).
tt(fc2_arytm_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((v3_ordinal1 (k7_ordinal3 A B)) & (v7_ordinal1 (k7_ordinal3 A B))) ) ) ).
tt(fc2_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k5_asympt_0 A B)) &  ((v1_funct_2 (k5_asympt_0 A B) k5_numbers k1_numbers) & (v4_asympt_0 (k5_asympt_0 A B))) ) ) ) ).
tt(fc2_asympt_1,ax, ((v1_funct_1 k2_asympt_1) &  ((v1_funct_2 k2_asympt_1 k5_numbers k1_numbers) & (v4_asympt_0 k2_asympt_1)) ) ).
tt(fc2_bagorder,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v4_valued_0 D)) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_bagorder A B C D)) &  ((v4_relat_1 (k1_bagorder A B C D) (k7_nat_d C B)) &  ((v1_funct_1 (k1_bagorder A B C D)) &  ((v1_partfun1 (k1_bagorder A B C D) (k7_nat_d C B)) & (v4_valued_0 (k1_bagorder A B C D))) ) ) ) ) ) ).
tt(fc2_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (v5_bcialg_2 (k4_struct_0 A) A)) ) ).
tt(fc2_bcialg_4,ax, ((v3_bcialg_1 k2_bcialg_4) &  ((v4_bcialg_1 k2_bcialg_4) &  ((v5_bcialg_1 k2_bcialg_4) &  ((v7_bcialg_1 k2_bcialg_4) &  ((v8_bcialg_1 k2_bcialg_4) & (v2_bcialg_4 k2_bcialg_4)) ) ) ) ) ).
tt(fc2_bcialg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (v12_bcialg_1 (k5_bcialg_6 A B C) A)) ) ).
tt(fc2_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A)) ) )  =>  ((v1_funct_1 (k1_bilinear A B C)) &  ((v1_funct_2 (k1_bilinear A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v2_bilinear (k1_bilinear A B C) A B C)) ) ) ) ).
tt(fc2_binop_2,ax, ((v1_funct_1 k29_binop_2) &  ((v1_funct_2 k29_binop_2 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) &  ((v1_binop_1 k29_binop_2 k2_numbers) & (v2_binop_1 k29_binop_2 k2_numbers)) ) ) ).
tt(fc2_bintree1,ax, ( (~ (v1_xboole_0 (k2_trees_1 2)))  &  ((v1_trees_1 (k2_trees_1 2)) & (v1_bintree1 (k2_trees_1 2))) ) ).
tt(fc2_bintree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k2_trees_2 A B))) ) ).
tt(fc2_bor_cant,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_bor_cant A B)) &  ((v2_funct_1 (k6_bor_cant A B)) & (v1_funct_2 (k6_bor_cant A B) k5_numbers k5_numbers)) ) ) ) ).
tt(fc2_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_compts_1 (k1_tarski B) A)) ) ).
tt(fc2_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v3_funct_1 C) & (m1_borsuk_2 C A B B)) ) )  => (v3_funct_1 (k1_borsuk_2 A B B B C C))) ) ).
tt(fc2_borsuk_3,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v2_struct_0 (k1_pre_topc A B)) & (v1_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc2_borsuk_4,ax, ((v1_pre_topc k1_borsuk_4) & (v1_tsep_1 k1_borsuk_4 k5_topmetr)) ).
tt(fc2_borsuk_5,ax, ((v1_xreal_0 k7_power) &  (~ (v1_rat_1 k7_power)) ) ).
tt(fc2_borsuk_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_topmetr A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_topmetr B) & (l1_pre_topc B)) ) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  => (v1_xreal_0 (k2_xtuple_0 C))) ) ).
tt(fc2_borsuk_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) & (v1_valued_0 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v1_funct_1 (k13_valued_1 A B)) & (v2_funct_1 (k13_valued_1 A B))) ) ) ) ).
tt(fc2_brouwer,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v7_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (~ (v1_xboole_0 (k1_brouwer A B))) ) ) ).
tt(fc2_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k8_bspace A))) ) ) ).
tt(fc2_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k7_bvfunc_1 A B)) &  ((v1_funct_1 (k7_bvfunc_1 A B)) & (v1_margrel1 (k7_bvfunc_1 A B))) ) ) ) ).
tt(fc2_bvfunc26,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k2_bvfunc26 A B)) &  ((v1_funct_1 (k2_bvfunc26 A B)) & (v1_margrel1 (k2_bvfunc26 A B))) ) ) ) ).
tt(fc2_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v13_algstr_0 (k12_funcsdom A)) &  ((v2_rlvect_1 (k12_funcsdom A)) &  ((v3_rlvect_1 (k12_funcsdom A)) &  ((v4_rlvect_1 (k12_funcsdom A)) &  ((v5_rlvect_1 (k12_funcsdom A)) &  ((v6_rlvect_1 (k12_funcsdom A)) &  ((v7_rlvect_1 (k12_funcsdom A)) &  ((v1_funcsdom (k12_funcsdom A)) &  ((v2_funcsdom (k12_funcsdom A)) &  ((v3_group_1 (k12_funcsdom A)) &  ((v5_group_1 (k12_funcsdom A)) &  ((v1_vectsp_1 (k12_funcsdom A)) & (v3_vectsp_1 (k12_funcsdom A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~ (v1_xboole_0 (k2_c0sp2 A))) ) ) ).
tt(fc2_calcul_2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_finseq_1 B (k3_cqc_lang A)))  =>  ((v1_finset_1 (k1_card_1 B)) & (v1_card_1 (k1_card_1 B))) ) ) ).
tt(fc2_cantor_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~ (v1_xboole_0 (k2_cantor_1 A B))) ) ) ).
tt(fc2_card_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k1_card_1 A)))  & (v1_card_1 (k1_card_1 A))) ) ) ).
tt(fc2_card_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) )  => (v1_finset_1 (k3_card_3 C))) ) ).
tt(fc2_card_3,ax, (! [A:$i,B:$i] :  ((v1_card_1 B) => (v1_card_3 (k2_funcop_1 A B))) ) ).
tt(fc2_card_5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~ (v1_finset_1 (k3_card_1 A))) ) ) ).
tt(fc2_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v1_card_1 (k2_card_1 A)) &  (~ (v2_card_1 (k2_card_1 A))) ) ) ) ).
tt(fc2_cardfin2,ax, ((v1_xreal_0 k7_power) & (v2_xxreal_0 k7_power)) ).
tt(fc2_card_fin,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k3_relat_1 B A)) & (v2_finset_1 (k3_relat_1 B A))) ) ) ).
tt(fc2_cat_1,ax, (! [A:$i,B:$i] :  ((v1_cat_1 (k3_cat_1 A B)) & (v2_cat_1 (k3_cat_1 A B))) ) ).
tt(fc2_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_cat_1 A B C D E)))  &  ( (~ (v11_struct_0 (g1_cat_1 A B C D E)))  & (v1_cat_1 (g1_cat_1 A B C D E))) ) ) ) ).
tt(fc2_cat_4,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k5_cat_4 A B)))  &  ( (~ (v11_struct_0 (k5_cat_4 A B)))  &  ((v2_cat_1 (k5_cat_4 A B)) &  ((v3_cat_1 (k5_cat_4 A B)) &  ((v4_cat_1 (k5_cat_4 A B)) &  ((v5_cat_1 (k5_cat_4 A B)) &  ((v6_cat_1 (k5_cat_4 A B)) & (v2_cat_4 (k5_cat_4 A B))) ) ) ) ) ) ) ) ).
tt(fc2_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k10_cat_5 A B))) ) ) ).
tt(fc2_catalan1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v1_xboole_0 (k1_catalan1 A))) ) ) ).
tt(fc2_catalan2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v1_finset_1 (k2_catalan2 A B))) ) ).
tt(fc2_catalg_1,ax, (! [A:$i] :  ((v1_msualg_1 (k2_catalg_1 A)) & (v1_instalg1 (k2_catalg_1 A))) ) ).
tt(fc2_cayley,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k1_cayley A)))  & (v4_funct_1 (k1_cayley A))) ) ).
tt(fc2_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k2_cc0sp1 A)))  &  ((v3_c0sp1 (k2_cc0sp1 A) (k8_cfuncdom A)) & (v1_cc0sp1 (k2_cc0sp1 A) (k8_cfuncdom A))) ) ) ) ).
tt(fc2_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~ (v1_xboole_0 (k2_cc0sp2 A))) ) ) ).
tt(fc2_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_cfuncdom A)))  & (v36_algstr_0 (k7_cfuncdom A))) ) ) ).
tt(fc2_cgames_1,ax,(v2_cgames_1 k1_cgames_1)).
tt(fc2_chain_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (~ (v1_zfmisc_1 (k2_xboole_0 B A))) ) ) ).
tt(fc2_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_subset_1 B k5_numbers) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 B A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B A) A)))) ) ) ) )  =>  ( (~ (v11_struct_0 (k5_circcomb D C)))  &  ((v1_msualg_1 (k5_circcomb D C)) & (v4_circcmb3 (k5_circcomb D C))) ) ) ) ).
tt(fc2_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 C D)) &  ((v4_relat_1 (k1_funct_4 C D) (k2_xboole_0 A B)) &  ((v1_funct_1 (k1_funct_4 C D)) & (v1_partfun1 (k1_funct_4 C D) (k2_xboole_0 A B))) ) ) ) ) ).
tt(fc2_circled1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k1_circled1 A B))) ) ) ).
tt(fc2_circtrm1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m3_msaterm C A B)) )  =>  ( (~ (v2_struct_0 (k1_circtrm1 A B C)))  &  ( (~ (v11_struct_0 (k1_circtrm1 A B C)))  & (v1_msualg_1 (k1_circtrm1 A B C))) ) ) ) ).
tt(fc2_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_ordinal1 (k4_classes1 A))) ) ).
tt(fc2_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v3_ordinal1 (k2_ordinal1 A))) ) ).
tt(fc2_clopban1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_clopban1 A B)))  &  ((v13_algstr_0 (k3_clopban1 A B)) &  ((v2_rlvect_1 (k3_clopban1 A B)) &  ((v3_rlvect_1 (k3_clopban1 A B)) &  ((v4_rlvect_1 (k3_clopban1 A B)) &  ((v1_monoid_0 (k3_clopban1 A B)) &  ((v2_clvect_1 (k3_clopban1 A B)) &  ((v3_clvect_1 (k3_clopban1 A B)) &  ((v4_clvect_1 (k3_clopban1 A B)) & (v5_clvect_1 (k3_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k7_clopban2 A))) ) ).
tt(fc2_closure2,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v4_funct_1 A))  =>  ((v1_xboole_0 (k3_closure2 A)) &  ((v1_relat_1 (k3_closure2 A)) & (v1_funct_1 (k3_closure2 A))) ) ) ) ).
tt(fc2_closure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_xboole_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B)))) )  => (v3_relat_1 (k2_closure3 A B C))) ) ).
tt(fc2_cohsp_1,ax, (! [A:$i] :  ((v1_classes1 (k1_zfmisc_1 A)) & (v1_coh_sp (k1_zfmisc_1 A))) ) ).
tt(fc2_coh_sp,ax, (! [A:$i] :  ((v4_funct_1 (k4_coh_sp A)) &  (~ (v1_xboole_0 (k4_coh_sp A))) ) ) ).
tt(fc2_compact1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v5_compact1 A) & (l1_pre_topc A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v5_compact1 (k1_pre_topc A B))) ) ) ).
tt(fc2_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xreal_0 (k2_complex1 A))) ) ).
tt(fc2_complfld,ax, ((v36_algstr_0 k1_complfld) & (v4_vectsp_1 k1_complfld)) ).
tt(fc2_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_metric_1 A) & (l1_metric_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_metric_1 (k3_compl_sp A B C)) & (v6_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(fc2_compos_0,ax,(v1_compos_0 (k1_tarski (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)))).
tt(fc2_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ( (~ (v1_xboole_0 (k4_compos_1 A)))  &  ((v1_zfmisc_1 (k4_compos_1 A)) &  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) &  ((v1_finset_1 (k4_compos_1 A)) & (v1_afinsq_1 (k4_compos_1 A))) ) ) ) ) ) ) ) ) ).
tt(fc2_compos_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_amistd_4 A) & (l1_compos_1 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v4_compos_1 B A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k63_valued_1 B)) &  ((v1_funct_1 (k63_valued_1 B)) & (v2_compos_1 (k63_valued_1 B) A)) ) ) ) ).
tt(fc2_compts_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k1_compts_1 A))) ) ) ).
tt(fc2_comput_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~ (v1_xboole_0 (k16_funcop_1 A B)))  & (v2_margrel1 (k16_funcop_1 A B))) ) ) ).
tt(fc2_comseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) ) )  =>  ((v1_relat_1 (k1_comseq_2 B)) &  ((v4_relat_1 (k1_comseq_2 B) A) &  ((v1_funct_1 (k1_comseq_2 B)) & (v1_partfun1 (k1_comseq_2 B) A)) ) ) ) ) ).
tt(fc2_comseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k4_comseq_3 A)) &  ((v1_funct_1 (k4_comseq_3 A)) & (v3_valued_0 (k4_comseq_3 A))) ) ) ) ).
tt(fc2_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l5_struct_0 A))  =>  (~ (v1_xboole_0 (u1_struct_0 A))) ) ) ).
tt(fc2_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((v3_lattices (k1_lattice2 A)) & (v4_lattice3 (k1_lattice2 A))) ) ) ).
tt(fc2_connsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k1_connsp_1 A B)))  & (v2_connsp_1 (k1_connsp_1 A B) A)) ) ) ).
tt(fc2_convex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k2_convex1 A B))) ) ) ).
tt(fc2_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (v1_xboole_0 (k13_pre_poly (k2_convex4 A)))) ) ).
tt(fc2_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_rlvect_1 B) & (l1_rlvect_1 B)) ) )  => (v2_rlvect_1 (k3_convfun1 A B))) ) ).
tt(fc2_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k3_cqc_lang A))) ) ) ).
tt(fc2_csspace3,ax,(v6_clvect_1 k1_csspace3 k7_csspace)).
tt(fc2_csspace4,ax,(v6_clvect_1 k1_csspace4 k7_csspace)).
tt(fc2_csspace,ax, ( (~ (v2_struct_0 k7_csspace))  &  ((v13_algstr_0 k7_csspace) &  ((v2_rlvect_1 k7_csspace) &  ((v3_rlvect_1 k7_csspace) &  ((v4_rlvect_1 k7_csspace) &  ((v1_clvect_1 k7_csspace) &  ((v2_clvect_1 k7_csspace) &  ((v3_clvect_1 k7_csspace) &  ((v4_clvect_1 k7_csspace) & (v5_clvect_1 k7_csspace)) ) ) ) ) ) ) ) ) ).
tt(fc2_descip_1,ax, ((v1_funct_1 k26_descip_1) &  ((v1_funct_2 k26_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (v3_funct_2 k26_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))) ) ).
tt(fc2_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k5_dickson A)))  & (v1_orders_2 (k5_dickson A))) ) ) ).
tt(fc2_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k4_diff_1 A B)) & (v1_funct_2 (k4_diff_1 A B) k1_numbers k1_numbers)) ) ) ).
tt(fc2_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_dilworth A) & (l1_orders_2 A)) )  =>  ((v2_xxreal_0 (k1_dilworth A)) & (v7_ordinal1 (k1_dilworth A))) ) ) ).
tt(fc2_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (~ (v1_xboole_0 (k6_dist_1 A))) ) ) ).
tt(fc2_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) & (l1_lang1 A)) )  =>  (~ (v1_xboole_0 (k4_dtconstr A))) ) ) ).
tt(fc2_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  => (v1_ec_pf_1 (k9_int_3 A))) ) ).
tt(fc2_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v22_algstr_0 (k3_endalg A)) &  ((v3_group_1 (k3_endalg A)) & (v4_vectsp_1 (k3_endalg A))) ) ) ) ).
tt(fc2_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_ens_1 A))) ) ) ).
tt(fc2_eqrel_1,ax, (! [A:$i] :  ((v3_relat_2 (k1_eqrel_1 A)) &  ((v8_relat_2 (k1_eqrel_1 A)) & (v1_partfun1 (k1_eqrel_1 A) A)) ) ) ).
tt(fc2_equation,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_relat_1 C) &  ((v2_finset_1 C) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) )  =>  ((v3_msualg_1 (k12_msualg_2 A B C) A) & (v3_msafree2 (k12_msualg_2 A B C) A)) ) ) ).
tt(fc2_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  (~ (v1_xboole_0 (k3_euclid_4 A B C))) ) ) ).
tt(fc2_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v2_euclid_7 A) & (v2_euclid_7 B))  => (v2_euclid_7 (k2_xboole_0 A B))) ) ).
tt(fc2_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (~ (v3_xxreal_0 (k12_euclid A))) ) ) ).
tt(fc2_euclidlp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) &  ((m1_subset_1 C (k1_euclid A)) & (m1_subset_1 D (k1_euclid A))) ) )  =>  (~ (v1_xboole_0 (k4_euclidlp A B C D))) ) ) ).
tt(fc2_exchsort,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 A) => (v1_exchsort (k1_tarski (k4_tarski A B)))) ) ).
tt(fc2_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v2_memstr_0 (k1_extpro_1 A) A) & (v1_extpro_1 (k1_extpro_1 A) A)) ) ) ).
tt(fc2_facirc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xtuple_0 A))  &  (~ (v1_xtuple_0 B)) )  =>  (~ (v1_facirc_1 (k2_tarski A B))) ) ) ).
tt(fc2_facirc_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_facirc_1 A)) )  =>  (~ (v1_xtuple_0 (k1_funct_1 A B))) ) ) ).
tt(fc2_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  & (v1_zfmisc_1 B))  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v1_fcont_1 (k5_relat_1 A B))) ) ) ).
tt(fc2_fcont_3,ax,(v3_rcomp_1 (k2_subset_1 k1_numbers))).
tt(fc2_fdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v1_fdiff_1 A k6_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v2_relat_1 (k9_nat_1 A B)) &  ((v1_funct_1 (k9_nat_1 A B)) &  ((v1_funct_2 (k9_nat_1 A B) k5_numbers k1_numbers) & (v1_fdiff_1 (k9_nat_1 A B) k6_numbers)) ) ) ) ) ).
tt(fc2_fib_num2,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) & (v1_abian (k4_xcmplx_0 A))) ) ) ).
tt(fc2_fib_num3,ax, ((v3_xxreal_0 k2_fib_num) & (v1_xreal_0 k2_fib_num)) ).
tt(fc2_filter_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ((v19_lattices (k5_filter_0 A B C) A) & (v20_lattices (k5_filter_0 A B C) A)) ) ) ).
tt(fc2_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  &  ( (~ (v2_struct_0 B))  & (l3_lattices B)) )  =>  ( (~ (v2_struct_0 (k7_filter_1 A B)))  & (v3_lattices (k7_filter_1 A B))) ) ) ).
tt(fc2_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) )  =>  (~ (v1_xboole_0 (k4_filter_2 A B))) ) ) ).
tt(fc2_finseq_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~ (v1_xboole_0 (k1_finseq_1 A))) ) ) ).
tt(fc2_finseq_2,ax, ((v1_relat_1 (k1_finseq_2 k6_numbers)) &  ((v1_funct_1 (k1_finseq_2 k6_numbers)) &  ((v1_xboole_0 (k1_finseq_2 k6_numbers)) & (v1_finseq_1 (k1_finseq_2 k6_numbers))) ) ) ).
tt(fc2_finseq_3,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (v3_card_3 (k4_finseq_2 A B))) ) ).
tt(fc2_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ((v1_relat_1 (k8_finseq_4 A B C D E)) &  ((v1_funct_1 (k8_finseq_4 A B C D E)) &  (~ (v1_xboole_0 (k8_finseq_4 A B C D E))) ) ) ) ).
tt(fc2_finseq_5,ax, (! [A:$i,B:$i] :  (~ (v1_zfmisc_1 (k10_finseq_1 A B))) ) ).
tt(fc2_finseq_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ( (~ (v1_xboole_0 (k3_finseq_5 A)))  &  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc2_finset_1,ax, (! [A:$i,B:$i] : (v1_finset_1 (k2_tarski A B))) ).
tt(fc2_finsub_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k5_finsub_1 A)))  & (v4_finsub_1 (k5_finsub_1 A))) ) ).
tt(fc2_fintopo5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  ( (~ (v2_struct_0 (k5_fintopo5 A B)))  & (v1_orders_2 (k5_fintopo5 A B))) ) ) ).
tt(fc2_fintopo6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (v4_fin_topo (k1_tarski B) A)) ) ).
tt(fc2_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k11_monoid_0 A)) &  ((v1_funct_2 (k11_monoid_0 A) (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A)) & (v2_binop_1 (k11_monoid_0 A) (k3_finseq_2 A))) ) ) ) ).
tt(fc2_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  =>  (~ (v1_xboole_0 (k4_xboole_0 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (u3_struct_0 A))))) ) ) ).
tt(fc2_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ( ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  & (m1_subset_1 E B)) ) ) )  =>  ((v1_relat_1 (k5_fomodel2 C D E)) &  ((v1_funct_1 (k5_fomodel2 C D E)) & (v1_fomodel2 (k5_fomodel2 C D E) A B)) ) ) ) ).
tt(fc2_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v8_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v3_card_1 C (k1_int_2 (k19_fomodel1 A B))) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) )  => (v13_fomodel1 (k1_fomodel3 A B C) A)) ) ).
tt(fc2_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_relat_1 (k1_fomodel4 A))) ) ).
tt(fc2_frechet,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 (k3_pcomps_1 A))))  => (v4_card_3 (k1_frechet A B))) ) ).
tt(fc2_freealg,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  =>  ((v1_lang1 (k3_freealg A B)) & (v2_dtconstr (k3_freealg A B))) ) ) ).
tt(fc2_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  & (m1_subset_1 F C)) ) ) )  =>  ( (~ (v2_struct_0 (g2_fsm_1 A B C D E F)))  &  ((v8_struct_0 (g2_fsm_1 A B C D E F)) & (v2_fsm_1 (g2_fsm_1 A B C D E F) A B)) ) ) ) ).
tt(fc2_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_tarski C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski C D) B)))) ) ) )  =>  ( (~ (v2_struct_0 (k1_fsm_2 A B C D E)))  &  ((v1_fsm_2 (k1_fsm_2 A B C D E) A) & (v6_fsm_2 (k1_fsm_2 A B C D E) A B)) ) ) ) ).
tt(fc2_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B)) ) )  =>  ( (~ (v2_struct_0 (k1_fsm_3 A B C)))  &  ((v1_rewrite3 (k1_fsm_3 A B C) (k9_flang_1 A)) & (v2_rewrite3 (k1_fsm_3 A B C) A (k9_flang_1 A))) ) ) ) ).
tt(fc2_funcop_1,ax, (! [A:$i] : (v1_xboole_0 (k2_funcop_1 k1_xboole_0 A))) ).
tt(fc2_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v36_algstr_0 (k11_funcsdom A)) & (v1_group_1 (k11_funcsdom A))) ) ) ).
tt(fc2_funct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v1_funct_1 (k3_relat_1 A B))) ) ) ).
tt(fc2_funct_2,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_funct_2 A A))) ) ).
tt(fc2_funct_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k13_funct_3 B A)) &  ((v1_funct_1 (k13_funct_3 B A)) & (v1_xboole_0 (k13_funct_3 B A))) ) ) ) ).
tt(fc2_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k6_funct_4 A B C)) & (v1_funct_1 (k6_funct_4 A B C))) ) ) ).
tt(fc2_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  (~ (v1_xboole_0 (k4_funct_4 A B C D))) ) ).
tt(fc2_funct_8,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos k1_numbers k1_numbers) & (v6_funct_8 k16_sin_cos k1_numbers k1_numbers)) ) ).
tt(fc2_funct_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_funct_9 B A)) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_funct_9 C A)) ) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v1_funct_9 (k1_valued_1 B C) A)) ) ) ) ).
tt(fc2_functor0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k15_funct_3 A B)) &  ((v1_funct_1 (k15_funct_3 A B)) & (v1_xboole_0 (k15_funct_3 A B))) ) ) ) ).
tt(fc2_functor1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) & (v2_funct_2 (k4_relat_1 A) A)) ) ).
tt(fc2_fvaluat1,ax, (~ (v1_fvaluat1 k2_xxreal_0)) ).
tt(fc2_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  ((v1_funct_1 (u1_algstr_0 A)) &  ((v1_funct_2 (u1_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc2_gate_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_xboole_0 (k1_gate_1 A))) ) ).
tt(fc2_gcd_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k2_gcd_1 A B))) ) ) ).
tt(fc2_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_geomtrap A))  =>  ( (~ (v2_struct_0 (k8_geomtrap A)))  & (v1_analoaf (k8_geomtrap A))) ) ) ).
tt(fc2_gfacirc2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (v1_xtuple_0 (k7_gfacirc2 A B C))) ) ).
tt(fc2_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((v1_glib_001 (k1_glib_001 A B) A) &  ((v2_glib_001 (k1_glib_001 A B) A) & (v3_glib_001 (k1_glib_001 A B) A)) ) ) ) ).
tt(fc2_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v1_glib_000 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc2_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v1_glib_003 A)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_glib_004 A)))  & (v1_finset_1 (k3_glib_004 A))) ) ) ).
tt(fc2_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_005 B A) & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k1_funct_1 B C)) & (v1_funct_1 (k1_funct_1 B C))) ) ) ).
tt(fc2_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (~ (v1_xboole_0 (k2_goboard1 A))) ) ) ).
tt(fc2_graph_1,ax, (! [A:$i] :  ( ((v6_graph_1 A) & (l1_graph_1 A))  => (v1_finset_1 (u4_struct_0 A))) ) ).
tt(fc2_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k2_graph_3 A B C))) ) ).
tt(fc2_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  => (v1_finset_1 (k7_graph_5 A))) ) ).
tt(fc2_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k3_finseq_2 k1_numbers)) & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k7_graphsp A B))) ) ).
tt(fc2_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k1_grcat_1 A B))) ) ) ).
tt(fc2_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  ((v15_algstr_0 (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) & (v3_group_1 (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)))) ) ) ).
tt(fc2_grfunc_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_funct_1 (k4_xboole_0 A B))) ) ).
tt(fc2_groeb_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v7_algstr_0 B) &  ((v5_vectsp_1 B) &  ((v4_rlvect_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  & (m1_subset_1 D (u1_struct_0 B))) )  =>  ((v1_funct_1 (k5_polynom7 A B C D)) &  ((v1_funct_2 (k5_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v3_polynom7 (k5_polynom7 A B C D) A B)) ) ) ) ).
tt(fc2_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  & (m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A)))) ) )  =>  ((v1_funct_1 (k2_groeb_3 A B C D)) &  ((v1_funct_2 (k2_groeb_3 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k2_groeb_3 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc2_group_10,ax, (! [A:$i,B:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k3_group_10 A B))) ) ).
tt(fc2_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v3_group_7 B A)) ) ) ) )  & (m1_subset_1 C A)) )  => (v3_group_1 (k1_funct_1 B C))) ) ).
tt(fc2_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_setwiseo (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc2_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k1_group_2 A B))) ) ) ).
tt(fc2_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v8_struct_0 C) & (m1_group_2 C A)) ) )  =>  ((v8_struct_0 (k6_group_3 A C B)) & (v15_algstr_0 (k6_group_3 A C B))) ) ) ).
tt(fc2_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k7_group_2 A)) & (v1_group_3 (k7_group_2 A) A)) ) ) ).
tt(fc2_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  =>  ( (~ (v2_struct_0 (k2_group_7 A B)))  &  ((v15_algstr_0 (k2_group_7 A B)) & (v1_monoid_0 (k2_group_7 A B))) ) ) ) ).
tt(fc2_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  ((v2_group_9 (k5_group_9 A B) A) & (v4_group_9 (k5_group_9 A B) A B)) ) ) ).
tt(fc2_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k7_hahnban1 A B)) &  ((v1_funct_2 (k7_hahnban1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v1_hahnban1 (k7_hahnban1 A B) A B)) ) ) ) ).
tt(fc2_hallmar1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B (k1_zfmisc_1 A)))  => (v1_finset_1 (k1_hallmar1 A B C))) ) ).
tt(fc2_hausdorf,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_weierstr A B)) &  ((v1_funct_2 (k4_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k4_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ).
tt(fc2_helly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((v3_glib_001 (k2_helly A B B) A) & (v5_glib_001 (k2_helly A B B) A)) ) ) ).
tt(fc2_heyting2,ax, (! [A:$i,B:$i] :  ((v1_finset_1 B) =>  ((v3_lattices (k5_substlat A B)) & (v3_filter_0 (k5_substlat A B))) ) ) ).
tt(fc2_heyting3,ax, (! [A:$i,B:$i] :  ((v1_lattice3 (k1_heyting3 A B)) & (v2_lattice3 (k1_heyting3 A B))) ) ).
tt(fc2_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_hilbasis A B)) &  ((v1_funct_2 (k6_hilbasis A B) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (v13_vectsp_1 (k6_hilbasis A B) (k14_polynom3 (k11_polynom1 B A)) (k11_polynom1 (k2_nat_1 B 1) A))) ) ) ) ).
tt(fc2_hilbert1,ax,(v4_funct_1 k1_hilbert1)).
tt(fc2_hilbert3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  => (v2_funct_1 (k4_funct_4 B k6_numbers k6_numbers A))) ) ).
tt(fc2_idea_1,ax,(v4_funct_1 k14_idea_1)).
tt(fc2_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) )  => (v2_ideal_1 (k1_tarski (k4_struct_0 A)) A)) ) ).
tt(fc2_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  => (v1_incsp_1 (k3_incproj A))) ) ).
tt(fc2_index_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_index_1 A)) )  => (v2_cat_5 (k10_xtuple_0 A))) ) ).
tt(fc2_instalg1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (v2_relat_1 (k13_msafree A B))) ) ).
tt(fc2_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k3_xcmplx_0 A B))) ) ).
tt(fc2_int_3,ax,(v5_membered (u1_struct_0 k1_int_3))).
tt(fc2_int_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_finset_1 A) & (v3_membered A))  & (v1_xreal_0 B))  => (v1_finset_1 (k23_member_1 A B))) ) ).
tt(fc2_int_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k16_finseq_1 B A)) &  ((v5_relat_1 (k16_finseq_1 B A) k4_numbers) &  ((v1_funct_1 (k16_finseq_1 B A)) & (v1_finseq_1 (k16_finseq_1 B A))) ) ) ) ) ).
tt(fc2_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v2_struct_0 (k3_int_7 A)))  &  ((v8_struct_0 (k3_int_7 A)) &  ((v2_group_1 (k3_int_7 A)) &  ((v3_group_1 (k3_int_7 A)) & (v5_group_1 (k3_int_7 A))) ) ) ) ) ) ).
tt(fc2_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((v1_relat_1 (k4_comseq_3 A)) &  ((v1_funct_1 (k4_comseq_3 A)) & (v1_finseq_1 (k4_comseq_3 A))) ) ) ) ).
tt(fc2_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  =>  (~ (v1_xboole_0 (k4_integra1 A B C))) ) ) ).
tt(fc2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  =>  (~ (v1_xboole_0 (k4_interva1 A B C))) ) ) ).
tt(fc2_intpro_1,ax,(v4_funct_1 k1_intpro_1)).
tt(fc2_isocat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  => (v12_cat_1 (k15_isocat_2 A B C) (k11_nattra_1 A (k8_cat_2 B C)) (k8_cat_2 (k11_nattra_1 A B) (k11_nattra_1 A C)))) ) ).
tt(fc2_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v5_tops_1 (k2_struct_0 A) A) & (v6_tops_1 (k2_struct_0 A) A)) ) ) ).
tt(fc2_jgraph_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  (~ (v1_xboole_0 (k5_jgraph_6 A B C))) ) ) ).
tt(fc2_jgraph_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v1_topalg_2 (k1_topreala A B C D) 2)) ) ).
tt(fc2_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (v1_xboole_0 (k1_jordan10 A))) ) ) ).
tt(fc2_jordan14,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  & (m1_subset_1 B k5_numbers))  => (v2_compts_1 (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan13 A B))) (k15_euclid 2))) ) ).
tt(fc2_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k7_relat_1 k5_pscomp_1 (k6_topreal1 A)))) ) ) ).
tt(fc2_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v1_convex1 (k5_topreal1 A) (k15_euclid 2))) ) ).
tt(fc2_jordan1d,ax, (! [A:$i,B:$i] :  ( ( ((v1_abian A) & (m1_subset_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  => (v1_abian (k1_newton A B))) ) ).
tt(fc2_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k2_jordan1e A B))) ) ) ).
tt(fc2_jordan1g,ax, (! [A:$i,B:$i] :  ( ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (m1_subset_1 B k5_numbers))  => (v2_goboard5 (k1_jordan1e A B))) ) ).
tt(fc2_jordan1h,ax, ((v1_partfun1 k1_jordan1h k1_numbers) &  ((v1_relat_2 k1_jordan1h) &  ((v4_relat_2 k1_jordan1h) &  ((v8_relat_2 k1_jordan1h) & (v3_orders_1 k1_jordan1h)) ) ) ) ).
tt(fc2_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k8_jordan6 A)))  & (v1_jordan21 (k8_jordan6 A))) ) ) ).
tt(fc2_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k9_jordan6 A)))  & (v2_connsp_1 (k9_jordan6 A) (k15_euclid 2))) ) ) ).
tt(fc2_jordan23,ax, (! [A:$i] : (v2_jordan23 (k5_finseq_1 A))) ).
tt(fc2_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_convex1 (k2_struct_0 (k15_euclid A)) (k15_euclid A))) ) ).
tt(fc2_jordan5a,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_rcomp_1 (k1_xxreal_1 A B))) ) ).
tt(fc2_jordan6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k8_jordan6 A)))  & (v2_compts_1 (k8_jordan6 A) (k15_euclid 2))) ) ) ).
tt(fc2_jordan8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (v7_ordinal1 B))  =>  ((v1_matrix_1 (k1_jordan8 A B)) &  ((v4_goboard1 (k1_jordan8 A B)) & (v5_goboard1 (k1_jordan8 A B))) ) ) ) ).
tt(fc2_jordan_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((m1_jordan_a B A) & (m1_subset_1 C k5_numbers)) )  =>  ( (~ (v1_xboole_0 (k2_jordan_a A C B)))  & (v2_compts_1 (k2_jordan_a A C B) (k15_euclid 2))) ) ) ).
tt(fc2_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  (~ (v3_xxreal_0 (k1_topreal6 A B C))) ) ) ).
tt(fc2_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  & (m1_kolmog01 D A B C)) )  =>  (~ (v1_xboole_0 (k6_kolmog01 A B C D))) ) ) ).
tt(fc2_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_finset_1 (k2_kurato_1 A B))) ) ).
tt(fc2_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  => (v1_frechet (k3_pcomps_1 A))) ) ).
tt(fc2_lang1,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k7_lang1 A B)))  & (v2_lang1 (k7_lang1 A B))) ) ).
tt(fc2_latsum_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (l1_orders_2 B))  =>  ( (~ (v2_struct_0 (k1_latsum_1 A B)))  & (v1_orders_2 (k1_latsum_1 A B))) ) ) ).
tt(fc2_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_funct_1 (u2_lattices A)) &  ((v1_funct_2 (u2_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v3_binop_1 (u2_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc2_lattice3,ax, (! [A:$i] :  ((v3_lattices (k1_lattice3 A)) & (v10_lattices (k1_lattice3 A))) ) ).
tt(fc2_lattice4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k4_lattice4 A B))) ) ) ).
tt(fc2_lattice5,ax, (! [A:$i] :  ((v3_orders_2 (k1_lattice5 A)) &  ((v4_orders_2 (k1_lattice5 A)) &  ((v5_orders_2 (k1_lattice5 A)) & (v3_lattice3 (k1_lattice5 A))) ) ) ) ).
tt(fc2_lattice8,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_ordinal1 B))  =>  (~ (v1_xboole_0 (k3_lattice8 A B))) ) ) ).
tt(fc2_lattices,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ( (~ (v2_struct_0 (g1_lattices A B)))  & (v1_lattices (g1_lattices A B))) ) ) ).
tt(fc2_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))))  => (v1_finset_1 (k1_xtuple_0 B))) ) ).
tt(fc2_lfuzzy_0,ax, (~ (v1_xboole_0 (k1_xxreal_1 k6_numbers 1))) ).
tt(fc2_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) &  ((v2_lfuzzy_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) &  ((v2_lfuzzy_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ) )  =>  ((v5_relat_1 (k1_fuzzy_1 (k2_zfmisc_1 A A) B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k1_fuzzy_1 (k2_zfmisc_1 A A) B C)) &  ((v1_funct_2 (k1_fuzzy_1 (k2_zfmisc_1 A A) B C) (k2_zfmisc_1 A A) k1_numbers) & (v2_lfuzzy_1 (k1_fuzzy_1 (k2_zfmisc_1 A A) B C) A)) ) ) ) ) ).
tt(fc2_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ( (~ (v2_struct_0 (k13_lmod_7 A B C)))  & (v8_algstr_0 (k13_lmod_7 A B C))) ) ) ).
tt(fc2_lopban_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_lopban_1 A B)))  &  ((v13_algstr_0 (k5_lopban_1 A B)) &  ((v2_rlvect_1 (k5_lopban_1 A B)) &  ((v3_rlvect_1 (k5_lopban_1 A B)) &  ((v4_rlvect_1 (k5_lopban_1 A B)) &  ((v5_rlvect_1 (k5_lopban_1 A B)) &  ((v6_rlvect_1 (k5_lopban_1 A B)) &  ((v7_rlvect_1 (k5_lopban_1 A B)) &  ((v8_rlvect_1 (k5_lopban_1 A B)) & (v1_monoid_0 (k5_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k7_lopban_2 A))) ) ).
tt(fc2_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k6_lopclset A)))  &  ((v10_lattices (k6_lopclset A)) & (v17_lattices (k6_lopclset A))) ) ) ) ).
tt(fc2_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k9_lpspace1 A B C)))  &  ((v1_ideal_1 (k9_lpspace1 A B C) (k7_lpspace1 A)) & (v1_lpspace1 (k9_lpspace1 A B C) (k7_lpspace1 A))) ) ) ) ).
tt(fc2_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k1_lpspace2 A B C D)))  &  ((v1_ideal_1 (k1_lpspace2 A B C D) (k7_lpspace1 A)) & (v1_lpspace1 (k1_lpspace2 A B C D) (k7_lpspace1 A))) ) ) ) ).
tt(fc2_ltlaxio1,ax, (~ (v1_xboole_0 k13_ltlaxio1)) ).
tt(fc2_lukasi_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  => (v2_cqc_the1 (k2_qc_lang2 A B B) A)) ) ).
tt(fc2_margrel1,ax, (~ (v1_xboole_0 k6_margrel1)) ).
tt(fc2_matrix11,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 C (k12_matrix_2 A)))  => (v7_ordinal1 (k1_funct_1 C B))) ) ).
tt(fc2_matrix13,ax, (! [A:$i,B:$i] :  ((v1_setfam_1 A) => (v1_setfam_1 (k4_xboole_0 A B))) ) ).
tt(fc2_matrix_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k3_finseq_2 A)))  => (v1_finset_1 (k16_matrix_1 B))) ) ).
tt(fc2_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_xboole_0 (k12_matrix_2 A)))  & (v3_matrix_2 (k12_matrix_2 A))) ) ) ).
tt(fc2_matrix_8,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_matrix_8 (k11_matrix_1 B A) A B) & (v2_matrix_8 (k11_matrix_1 B A) A B)) ) ) ).
tt(fc2_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v2_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  &  ((v1_matrixj1 C (u1_struct_0 A)) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) )  =>  ((v1_matrixj1 (k25_matrixj1 A B C) (u1_struct_0 A)) & (v2_matrixj1 (k25_matrixj1 A B C) (u1_struct_0 A))) ) ) ).
tt(fc2_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_matrlin A B C D E)) &  ((v1_funct_2 (k3_matrlin A B C D E) (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 (k3_matrlin A B C D E) B C) & (v1_mod_2 (k3_matrlin A B C D E) A B C)) ) ) ) ) ).
tt(fc2_matroid0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k3_xboole_0 B C) A)) ) ).
tt(fc2_matrtop3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) & (m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B)) )  =>  ((v1_funct_1 (k3_matrtop1 A B C)) &  ((v1_funct_2 (k3_matrtop1 A B C) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (v13_vectsp_1 (k3_matrtop1 A B C) (k15_euclid A) (k15_euclid B))) ) ) ) ).
tt(fc2_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ((v3_membered A) & (v4_xxreal_2 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  => (v4_xxreal_2 (k23_member_1 A B))) ) ).
tt(fc2_mboolean,ax, (! [A:$i] :  ((v1_relat_1 (k2_mboolean A (k1_pboole A))) &  ((v3_relat_1 (k2_mboolean A (k1_pboole A))) &  ((v4_relat_1 (k2_mboolean A (k1_pboole A)) A) &  ((v1_funct_1 (k2_mboolean A (k1_pboole A))) & (v1_partfun1 (k2_mboolean A (k1_pboole A)) A)) ) ) ) ) ).
tt(fc2_measure4,ax, (! [A:$i,B:$i] :  ((m1_measure4 B A) =>  ((v1_funct_1 (k3_measure4 A B)) &  ((v1_funct_2 (k3_measure4 A B) (k1_measure4 A B) k7_numbers) &  ((v10_valued_0 (k3_measure4 A B)) &  ((v6_supinf_2 (k3_measure4 A B)) & (v4_measure1 (k3_measure4 A B) A (k1_measure4 A B))) ) ) ) ) ) ).
tt(fc2_measure6,ax, (~ (v1_setfam_1 k4_ordinal1)) ).
tt(fc2_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xxreal_0 A) &  ((v1_xxreal_0 B) &  ((v1_xxreal_0 C) & (v1_xxreal_0 D)) ) )  => (v2_membered (k2_enumset1 A B C D))) ) ).
tt(fc2_membered,ax,(v2_membered k7_numbers)).
tt(fc2_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_memstr_0 (k1_memstr_0 A) A) & (v2_memstr_0 (k1_memstr_0 A) A)) ) ) ).
tt(fc2_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) ) )  =>  ((v1_funct_1 (k1_mesfun7c A B)) &  ((v1_funct_2 (k1_mesfun7c A B) k5_numbers (k4_partfun1 A k7_numbers)) & (v1_mesfunc8 (k1_mesfun7c A B) A k7_numbers)) ) ) ) ).
tt(fc2_mesfunc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k2_mesfunc1 (k1_nat_1 A 1)))) ) ) ).
tt(fc2_mesfunc7,ax, ((v1_funct_1 k1_mesfunc7) &  ((v1_funct_2 k1_mesfunc7 (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers) &  ((v1_binop_1 k1_mesfunc7 k7_numbers) & (v2_binop_1 k1_mesfunc7 k7_numbers)) ) ) ).
tt(fc2_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  => (v7_ordinal1 (k1_binop_1 A B C))) ) ).
tt(fc2_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v3_pcomps_1 (k1_pre_topc A B))) ) ) ).
tt(fc2_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v2_struct_0 (k2_mfold_1 A))) ) ) ).
tt(fc2_mfold_2,ax,(v2_funct_2 k1_xboole_0 k1_xboole_0)).
tt(fc2_midsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  & (m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k4_midsp_1 A B))) ) ) ).
tt(fc2_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (v2_midsp_2 (k15_midsp_1 A))) ) ).
tt(fc2_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (v1_mmlquery (k3_xboole_0 B C) A)) ) ).
tt(fc2_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (~ (v2_struct_0 (k2_mod_4 A)))  & (v36_algstr_0 (k2_mod_4 A))) ) ) ).
tt(fc2_modal_1,ax, (~ (v1_xboole_0 k4_modal_1)) ).
tt(fc2_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_modcat_1 A B)))  &  ( (~ (v11_struct_0 (k11_modcat_1 A B)))  & (v1_cat_1 (k11_modcat_1 A B))) ) ) ) ).
tt(fc2_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  => (v1_modelc_1 (k7_modelc_1 A))) ) ).
tt(fc2_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (v1_modelc_2 (k3_modelc_2 A))) ) ).
tt(fc2_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ( (~ (v1_xboole_0 (k22_modelc_3 A)))  & (v1_finset_1 (k22_modelc_3 A))) ) ) ).
tt(fc2_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_moebius1 A)) )  =>  ( (~ (v1_xboole_0 (k2_moebius1 A)))  & (v1_xreal_0 (k2_moebius1 A))) ) ) ).
tt(fc2_monoid_0,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k12_monoid_0 A)))  &  ((v15_algstr_0 (k12_monoid_0 A)) &  ((v1_group_1 (k12_monoid_0 A)) &  ((v3_group_1 (k12_monoid_0 A)) & (v1_monoid_0 (k12_monoid_0 A))) ) ) ) ) ).
tt(fc2_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  => (v1_monoid_0 (k9_monoid_1 A B))) ) ).
tt(fc2_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (~ (v1_xboole_0 (k3_msafree2 A))) ) ) ).
tt(fc2_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v3_msualg_1 (k1_msafree3 A B) A) &  (~ (v1_catalg_1 (k1_msafree3 A B) A)) ) ) ) ).
tt(fc2_msafree,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k2_card_3 B)) &  ((v1_funct_1 (k2_card_3 B)) & (v1_partfun1 (k2_card_3 B) A)) ) ) ) ).
tt(fc2_msalimit,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_pralg_2 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  => (v4_funct_1 (k1_funct_1 (k10_pralg_2 A B C) D))) ) ).
tt(fc2_msinst_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k2_msinst_1 A B))) ) ) ).
tt(fc2_msscyc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v2_finset_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_finset_1 (k12_msafree A B C))) ) ).
tt(fc2_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_relat_1 (k3_funct_6 B)) &  ((v4_relat_1 (k3_funct_6 B) A) & (v1_funct_1 (k3_funct_6 B))) ) ) ) ).
tt(fc2_mssublat,ax, (! [A:$i] :  ( ((v3_unialg_1 A) & (l1_unialg_1 A))  =>  ((v1_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) & (v3_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A)))) ) ) ).
tt(fc2_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v7_struct_0 (k6_msualg_1 A)) &  ( (~ (v11_struct_0 (k6_msualg_1 A)))  &  ((v13_struct_0 (k6_msualg_1 A) 1) &  ((v1_msualg_1 (k6_msualg_1 A)) & (v5_msualg_1 (k6_msualg_1 A))) ) ) ) ) ) ).
tt(fc2_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((v1_relat_1 (k2_pboole A C B)) &  ((v2_relat_1 (k2_pboole A C B)) &  ((v4_relat_1 (k2_pboole A C B) A) &  ((v1_funct_1 (k2_pboole A C B)) & (v1_partfun1 (k2_pboole A C B) A)) ) ) ) ) ) ).
tt(fc2_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 B C)) &  ((v4_relat_1 (k3_relat_1 B C) (k4_finseq_1 B)) &  ((v1_funct_1 (k3_relat_1 B C)) & (v1_partfun1 (k3_relat_1 B C) (k4_finseq_1 B))) ) ) ) ) ).
tt(fc2_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_relat_1 C) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((v2_relat_1 (k6_msualg_6 A B C)) & (v3_msualg_6 (k6_msualg_6 A B C) A B)) ) ) ).
tt(fc2_msualg_7,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_msualg_5 A B)))  &  ((v3_lattices (k5_msualg_5 A B)) &  ((v10_lattices (k5_msualg_5 A B)) & (v4_lattice3 (k5_msualg_5 A B))) ) ) ) ) ).
tt(fc2_msualg_8,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k2_msualg_5 A)))  &  ((v3_lattices (k2_msualg_5 A)) &  ((v10_lattices (k2_msualg_5 A)) & (v4_lattice3 (k2_msualg_5 A))) ) ) ) ).
tt(fc2_msualg_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (v2_msafree (k11_msafree A B) A)) ) ).
tt(fc2_mycielsk,ax, (! [A:$i,B:$i] :  ( ( ((v1_mycielsk A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v1_mycielsk (k5_yellow_0 A B))) ) ) ) ).
tt(fc2_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k3_xcmplx_0 A B))) ) ).
tt(fc2_nat_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_nat_3 A B)) &  ((v1_funct_1 (k1_nat_3 A B)) &  ((v1_finseq_1 (k1_nat_3 A B)) & (v3_valued_0 (k1_nat_3 A B))) ) ) ) ) ).
tt(fc2_nat_lat,ax, ( (~ (v2_struct_0 k3_nat_lat))  &  ((v3_lattices k3_nat_lat) & (v10_lattices k3_nat_lat)) ) ).
tt(fc2_ndiff_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ( (~ (v2_struct_0 (k1_funct_1 A B)))  &  ( (~ (v7_struct_0 (k1_funct_1 A B)))  &  ((v13_algstr_0 (k1_funct_1 A B)) &  ((v2_rlvect_1 (k1_funct_1 A B)) &  ((v3_rlvect_1 (k1_funct_1 A B)) &  ((v4_rlvect_1 (k1_funct_1 A B)) &  ((v5_rlvect_1 (k1_funct_1 A B)) &  ((v6_rlvect_1 (k1_funct_1 A B)) &  ((v7_rlvect_1 (k1_funct_1 A B)) &  ((v8_rlvect_1 (k1_funct_1 A B)) &  ((v3_normsp_0 (k1_funct_1 A B)) &  ((v4_normsp_0 (k1_funct_1 A B)) & (v2_normsp_1 (k1_funct_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_neckla_2,ax, (~ (v1_xboole_0 k4_neckla_2)) ).
tt(fc2_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (l1_orders_2 B))  =>  ( (~ (v2_struct_0 (k2_neckla_2 A B)))  & (v1_orders_2 (k2_neckla_2 A B))) ) ) ).
tt(fc2_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k2_necklace A)) & (v1_necklace (k2_necklace A))) ) ) ).
tt(fc2_net_1,ax, ((v1_petri (g1_petri k1_xboole_0 k1_xboole_0 (k1_partit_2 k1_xboole_0 k1_xboole_0) (k1_partit_2 k1_xboole_0 k1_xboole_0))) & (v1_net_1 (g1_petri k1_xboole_0 k1_xboole_0 (k1_partit_2 k1_xboole_0 k1_xboole_0) (k1_partit_2 k1_xboole_0 k1_xboole_0)))) ).
tt(fc2_newton,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v7_ordinal1 B))  => (v1_xreal_0 (k1_newton A B))) ) ).
tt(fc2_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  & (v1_zfmisc_1 C)) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v1_nfcont_3 (k5_relat_1 B C) A)) ) ) ).
tt(fc2_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  & (v1_zfmisc_1 C)) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v1_nfcont_4 (k5_relat_1 B C) A)) ) ) ).
tt(fc2_normform,ax, (! [A:$i] :  (~ (v1_xboole_0 (k7_normform A))) ) ).
tt(fc2_normsp_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_normsp_0 A) & (l2_normsp_0 A)) )  => (v1_xboole_0 (k1_normsp_0 A (k4_struct_0 A)))) ) ).
tt(fc2_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v2_pre_topc (k4_normsp_2 A)) &  ((v13_algstr_0 (k4_normsp_2 A)) &  ((v2_rlvect_1 (k4_normsp_2 A)) &  ((v3_rlvect_1 (k4_normsp_2 A)) &  ((v4_rlvect_1 (k4_normsp_2 A)) &  ((v5_rlvect_1 (k4_normsp_2 A)) &  ((v6_rlvect_1 (k4_normsp_2 A)) &  ((v7_rlvect_1 (k4_normsp_2 A)) &  ((v8_rlvect_1 (k4_normsp_2 A)) &  ((v5_rltopsp1 (k4_normsp_2 A)) &  ((v6_rltopsp1 (k4_normsp_2 A)) & (v7_rltopsp1 (k4_normsp_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_numbers,ax, (~ (v1_xboole_0 k2_numbers)) ).
tt(fc2_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k6_openlatt A)))  &  ((v10_lattices (k6_openlatt A)) & (v3_filter_0 (k6_openlatt A))) ) ) ) ).
tt(fc2_oposet_1,ax, ((v13_struct_0 k1_oposet_1 1) & (v3_qmax_1 k1_oposet_1)) ).
tt(fc2_orders_1,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  => (v1_xboole_0 (k1_relat_1 A))) ) ).
tt(fc2_orders_2,ax, (! [A:$i] :  ( ((v2_orders_2 A) & (l1_orders_2 A))  => (v1_partfun1 (u1_orders_2 A) (u1_struct_0 A))) ) ).
tt(fc2_orders_3,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  => (v1_xboole_0 (u1_orders_2 A))) ) ).
tt(fc2_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (~ (v1_xboole_0 (k1_ordinal1 A)))  & (v3_ordinal1 (k1_ordinal1 A))) ) ) ).
tt(fc2_ordinal2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  & (v3_ordinal1 B))  => (v3_ordinal1 (k1_funct_1 A B))) ) ).
tt(fc2_ordinal3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v3_ordinal1 (k3_xboole_0 A B))) ) ).
tt(fc2_ordinal4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  &  ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v5_ordinal1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) & (v1_ordinal2 (k1_ordinal4 A B))) ) ) ) ) ).
tt(fc2_ordinal5,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v5_ordinal1 B)) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) &  ( (~ (v1_xboole_0 (k1_ordinal4 A B)))  & (v5_ordinal1 (k1_ordinal4 A B))) ) ) ) ) ).
tt(fc2_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (v1_ordinal6 (k4_xboole_0 A B))) ) ).
tt(fc2_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_dtconstr (k2_osafree A B)) &  ((v2_dtconstr (k2_osafree A B)) & (v3_dtconstr (k2_osafree A B))) ) ) ) ).
tt(fc2_osalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (k3_finseq_2 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (k3_finseq_2 A))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C A)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_osalg_1 A B C D E F)))  &  ((v3_orders_2 (g3_osalg_1 A B C D E F)) &  ((v4_orders_2 (g3_osalg_1 A B C D E F)) &  ((v5_orders_2 (g3_osalg_1 A B C D E F)) & (v3_osalg_1 (g3_osalg_1 A B C D E F))) ) ) ) ) ) ).
tt(fc2_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (~ (v1_xboole_0 (k6_osalg_2 A B))) ) ) ).
tt(fc2_osalg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v3_msualg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A) & (v12_osalg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A)) ) ) ).
tt(fc2_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) & (m1_osalg_4 C A B)) ) )  =>  ((v1_relat_1 (k7_osalg_4 A B C)) &  ((v2_relat_1 (k7_osalg_4 A B C)) &  ((v4_relat_1 (k7_osalg_4 A B C) (u1_struct_0 A)) &  ((v1_funct_1 (k7_osalg_4 A B C)) &  ((v1_partfun1 (k7_osalg_4 A B C) (u1_struct_0 A)) & (v11_osalg_1 (k7_osalg_4 A B C) A)) ) ) ) ) ) ) ).
tt(fc2_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k6_parsp_1 A))) ) ) ).
tt(fc2_partfun1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_xboole_0 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (v1_xboole_0 (k5_partfun1 A B C))) ) ).
tt(fc2_partfun3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v3_xxreal_0 (k3_xcmplx_0 A A))) ) ) ).
tt(fc2_partfun4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 B C)) &  ((v1_funct_2 (k45_valued_1 B C) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k45_valued_1 B C) A)) ) ) ) ).
tt(fc2_partit_2,ax, ((v1_relat_1 k6_funct_5) &  ((v1_funct_1 k6_funct_5) & (v1_partit_2 k6_funct_5)) ) ).
tt(fc2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  & (m1_subset_1 C A)) )  =>  (~ (v1_xboole_0 (k1_funct_1 B C))) ) ) ).
tt(fc2_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (~ (v2_struct_0 (k3_pcomps_1 A))) ) ) ).
tt(fc2_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v1_relat_2 (k2_xboole_0 C D))) ) ).
tt(fc2_pencil_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k1_pzfmisc1 A B)) &  ((v4_relat_1 (k1_pzfmisc1 A B) A) &  ((v1_funct_1 (k1_pzfmisc1 A B)) &  ((v1_partfun1 (k1_pzfmisc1 A B) A) & (v13_pencil_1 (k1_pzfmisc1 A B))) ) ) ) ) ) ).
tt(fc2_petri,ax, (! [A:$i] :  ( ((v2_petri A) & (l1_petri A))  =>  (~ (v1_xboole_0 (u1_petri A))) ) ) ).
tt(fc2_pnproc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m2_pnproc_1 B A) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B)))) ) )  =>  (~ (v1_xboole_0 (k11_pnproc_1 A B C D))) ) ) ).
tt(fc2_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l6_algstr_0 A)) )  =>  ( (~ (v2_struct_0 (k1_polyalg1 A)))  &  ((v3_rlvect_1 (k1_polyalg1 A)) & (v1_polyalg1 (k1_polyalg1 A) A)) ) ) ) ).
tt(fc2_polyeq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (v1_xreal_0 (k1_polyeq_1 A B C))) ) ).
tt(fc2_polyeq_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) &  ((v1_xreal_0 E) & (v1_xreal_0 F)) ) ) ) )  => (v1_xreal_0 (k1_polyeq_2 A B C D E F))) ) ).
tt(fc2_polyeq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) &  ((v1_xreal_0 E) &  ((v1_xreal_0 F) & (v1_xreal_0 G)) ) ) ) ) )  => (v1_xreal_0 (k1_polyeq_4 A B C D E F G))) ) ).
tt(fc2_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ( (~ (v1_xboole_0 (k8_polyform A (k6_xcmplx_0 (k7_polyform A) 1))))  & (v1_finset_1 (k8_polyform A (k6_xcmplx_0 (k7_polyform A) 1)))) ) ) ).
tt(fc2_polynom1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k5_vfunct_1 (k15_pre_poly A) B C)) & (v1_polynom1 (k5_vfunct_1 (k15_pre_poly A) B C) (k15_pre_poly A) B)) ) ) ).
tt(fc2_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  => (v1_finset_1 (k2_polynom1 (k15_pre_poly A) B C))) ) ).
tt(fc2_polynom3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  & (m1_subset_1 B k5_numbers))  =>  ((v2_funct_1 (k6_polynom3 A B)) &  ( (~ (v1_xboole_0 (k6_polynom3 A B)))  & (v1_pre_poly (k6_polynom3 A B))) ) ) ) ).
tt(fc2_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k3_polynom5 A B C)) &  ((v1_funct_2 (k3_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k3_polynom5 A B C) A)) ) ) ) ).
tt(fc2_polynom6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v3_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  ((v3_ordinal1 (k10_ordinal2 B A)) &  (~ (v1_xboole_0 (k10_ordinal2 B A))) ) ) ) ).
tt(fc2_polynom7,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  =>  ((v1_funct_1 (k8_polynom1 A B)) &  ((v1_funct_2 (k8_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (v4_polynom7 (k8_polynom1 A B) A B)) ) ) ) ).
tt(fc2_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v1_funct_1 (k1_polyred A B C D)) &  ((v1_funct_2 (k1_polyred A B C D) (k15_pre_poly A) (u1_struct_0 C)) & (v1_polynom1 (k1_polyred A B C D) (k15_pre_poly A) C)) ) ) ) ).
tt(fc2_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (v8_relat_2 (k5_poset_1 A B))) ) ).
tt(fc2_pralg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (~ (v1_xboole_0 (k6_pralg_2 A B))) ) ) ).
tt(fc2_pralg_3,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v2_relat_1 (k4_relat_1 A))) ) ) ).
tt(fc2_pre_circ,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_relat_1 (k5_relat_1 B C)) & (v1_partfun1 (k5_relat_1 B C) C)) ) ) ).
tt(fc2_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k2_funct_7 B C D)) &  ((v4_relat_1 (k2_funct_7 B C D) A) & (v1_funct_1 (k2_funct_7 B C D))) ) ) ) ).
tt(fc2_prepower,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_int_1 B))  => (v1_xreal_0 (k4_prepower A B))) ) ).
tt(fc2_pre_topc,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k1_pre_topc A B)))  & (v1_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc2_prob_1,ax, (! [A:$i] : (v1_prob_1 (k1_zfmisc_1 A) A)) ).
tt(fc2_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k1_prob_3 A C) B) &  ((v1_funct_1 (k1_prob_3 A C)) & (v1_funct_2 (k1_prob_3 A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc2_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ( (~ (v2_struct_0 (k6_prvect_1 A B)))  & (v7_vectsp_1 (k6_prvect_1 A B) A)) ) ) ).
tt(fc2_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ( (~ (v2_struct_0 (k14_prvect_2 A)))  &  ((v13_algstr_0 (k14_prvect_2 A)) &  ((v2_rlvect_1 (k14_prvect_2 A)) &  ((v3_rlvect_1 (k14_prvect_2 A)) &  ((v4_rlvect_1 (k14_prvect_2 A)) &  ((v5_rlvect_1 (k14_prvect_2 A)) &  ((v6_rlvect_1 (k14_prvect_2 A)) &  ((v7_rlvect_1 (k14_prvect_2 A)) &  ((v8_rlvect_1 (k14_prvect_2 A)) &  ((v3_normsp_0 (k14_prvect_2 A)) &  ((v4_normsp_0 (k14_prvect_2 A)) &  ((v1_normsp_1 (k14_prvect_2 A)) & (v2_normsp_1 (k14_prvect_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc2_pscomp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_compts_1 (k1_pre_topc A B))) ) ) ).
tt(fc2_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  ((v1_partfun1 (k9_pua2mss1 A) (u1_struct_0 A)) &  ((v3_relat_2 (k9_pua2mss1 A)) & (v8_relat_2 (k9_pua2mss1 A))) ) ) ) ).
tt(fc2_pythtrip,ax, (! [A:$i,B:$i] :  ( ((v1_pythtrip A) & (v1_pythtrip B))  => (v1_pythtrip (k3_xcmplx_0 A B))) ) ).
tt(fc2_pzfmisc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k2_pzfmisc1 A B C)) &  ((v2_relat_1 (k2_pzfmisc1 A B C)) &  ((v4_relat_1 (k2_pzfmisc1 A B C) A) &  ((v1_funct_1 (k2_pzfmisc1 A B C)) &  ((v1_partfun1 (k2_pzfmisc1 A B C) A) & (v2_finset_1 (k2_pzfmisc1 A B C))) ) ) ) ) ) ) ).
tt(fc2_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k2_qc_lang1 A))) ) ) ).
tt(fc2_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  (~ (v1_xboole_0 (k2_qmax_1 A))) ) ) ).
tt(fc2_quatern2,ax, ( (~ (v2_struct_0 k15_quatern2))  & (v8_algstr_0 k15_quatern2)) ).
tt(fc2_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_quaterni (k3_quatern3 A))) ) ).
tt(fc2_quaterni,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ((v1_relat_1 (k2_quaterni A B C D E F G H)) & (v1_funct_1 (k2_quaterni A B C D E F G H))) ) ).
tt(fc2_quin_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (v1_xreal_0 (k1_quin_1 A B C))) ) ).
tt(fc2_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v5_group_1 A) & (l5_algstr_0 A)) ) )  & (m1_subset_1 B (k1_quofield A)))  =>  (~ (v1_xboole_0 (k6_quofield A B))) ) ) ).
tt(fc2_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_xboole_0 (k2_radix_3 A))) ) ) ).
tt(fc2_ramsey_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_finset_1 (k2_xboole_0 A B))) ) ) ).
tt(fc2_rat_1,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (v1_rat_1 (k2_xcmplx_0 A B))) ) ).
tt(fc2_ratfunc1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k4_xxreal_0 A B))) ) ).
tt(fc2_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v2_rcomp_1 (k1_xxreal_1 A B))) ) ).
tt(fc2_rcomp_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  => (v3_xxreal_2 (k2_xxreal_1 A B))) ) ).
tt(fc2_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_xboole_0 (k6_int_1 A k6_numbers)) & (v1_int_1 (k6_int_1 A k6_numbers))) ) ) ).
tt(fc2_real_lat,ax, ( (~ (v2_struct_0 k3_real_lat))  & (v3_lattices k3_real_lat)) ).
tt(fc2_real_ns1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v2_struct_0 (k4_real_ns1 A)))  &  ( (~ (v7_struct_0 (k4_real_ns1 A)))  & (v1_normsp_1 (k4_real_ns1 A))) ) ) ) ).
tt(fc2_realset1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_funct_1 (k1_realset1 A B))) ) ).
tt(fc2_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k4_xboole_0 A B))) ) ).
tt(fc2_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v1_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc2_reloc,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_compos_0 (k3_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(fc2_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v4_relat_1 B A))  & (v1_relat_1 C))  => (v4_relat_1 (k3_xboole_0 B C) A)) ) ).
tt(fc2_revrot_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v7_struct_0 (k15_euclid A)))  & (v5_rltopsp1 (k15_euclid A))) ) ) ).
tt(fc2_rewrite2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_rewrite2 A)) )  =>  ((v1_relat_1 (k1_funct_1 A B)) &  ((v1_funct_1 (k1_funct_1 A B)) & (v1_finset_1 (k1_funct_1 A B))) ) ) ) ).
tt(fc2_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_rfunct_1 A B)) &  ((v1_funct_1 (k1_rfunct_1 A B)) & (v3_valued_0 (k1_rfunct_1 A B))) ) ) ) ).
tt(fc2_rfunct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v5_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc2_rfunct_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_funct_1 (k19_rfunct_3 A B)) & (v1_finset_1 (k19_rfunct_3 A B))) ) ) ).
tt(fc2_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v1_funct_1 (k3_rinfsup2 A)) &  ((v1_funct_2 (k3_rinfsup2 A) k5_numbers k7_numbers) & (v7_valued_0 (k3_rinfsup2 A))) ) ) ) ).
tt(fc2_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v2_ideal_1 (k2_struct_0 A) A) & (v3_ideal_1 (k2_struct_0 A) A)) ) ) ).
tt(fc2_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v2_ringcat1 (k4_ringcat1 A)) & (v3_ringcat1 (k4_ringcat1 A))) ) ) ).
tt(fc2_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v1_xboole_0 (k3_convex1 A B)))  & (v1_convex1 (k3_convex1 A B) A)) ) ) ).
tt(fc2_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v1_rlvect_5 (k15_euclid A))) ) ) ).
tt(fc2_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v3_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) & (v10_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ) ).
tt(fc2_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v1_xboole_0 (k1_rltopsp1 A B C)))  & (v1_convex1 (k1_rltopsp1 A B C) A)) ) ) ).
tt(fc2_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k11_rlvect_2 A))) ) ) ).
tt(fc2_robbins3,ax,(v3_orders_2 k1_robbins3)).
tt(fc2_robbins4,ax, (~ (v2_struct_0 k1_robbins4)) ).
tt(fc2_rsspace3,ax,(v1_rlsub_1 k1_rsspace3 k7_rsspace)).
tt(fc2_rsspace4,ax,(v1_rlsub_1 k1_rsspace4 k7_rsspace)).
tt(fc2_rsspace,ax, ( (~ (v2_struct_0 k7_rsspace))  & (v1_rlvect_1 k7_rsspace)) ).
tt(fc2_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v3_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) & (v10_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ) ).
tt(fc2_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (~ (v2_struct_0 (k5_rusub_5 A))) ) ) ).
tt(fc2_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v3_valued_0 (k5_finseq_1 A))) ) ).
tt(fc2_scm_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v5_relat_1 (k6_afinsq_1 A B) k4_numbers)) ) ).
tt(fc2_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_amistd_1 (k6_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc2_scmfsa_1,ax, (~ (v1_xboole_0 k1_scmfsa_i)) ).
tt(fc2_scmfsa_2,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v1_amistd_4 k1_scmfsa_2)) ).
tt(fc2_scmfsa_3,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v4_amistd_5 k1_scmfsa_2 3)) ).
tt(fc2_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_compos_0 (k7_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc2_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  (~ (v2_compos_1 B k1_scmfsa_2)) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) &  (~ (v2_compos_1 (k3_scmfsa6a A B) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc2_scmfsa6b,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa6b A)) ) ) ) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa6b B)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) & (v1_scmfsa6b (k3_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc2_scmfsa6c,ax, (! [A:$i] :  ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v4_relat_1 (k11_compos_1 k1_scmfsa_2 A) k5_numbers) &  ((v5_relat_1 (k11_compos_1 k1_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v1_finset_1 (k11_compos_1 k1_scmfsa_2 A)) & (v7_amistd_1 (k11_compos_1 k1_scmfsa_2 A) 3 k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(fc2_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmfsa_7 A B)) &  ((v4_relat_1 (k1_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_7 A B)) &  ((v1_finset_1 (k1_scmfsa_7 A B)) & (v7_amistd_1 (k1_scmfsa_7 A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(fc2_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_scmfsa6a A)) &  ((v4_relat_1 (k2_scmfsa6a A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa6a A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa6a A)) &  ((v1_finset_1 (k2_scmfsa6a A)) & (v1_scmfsa7b (k2_scmfsa6a A))) ) ) ) ) ) ) ).
tt(fc2_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8b C A B)))  &  ((v1_relat_1 (k2_scmfsa8b C A B)) &  ((v4_relat_1 (k2_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8b C A B)) &  ((v1_finset_1 (k2_scmfsa8b C A B)) &  ((v1_afinsq_1 (k2_scmfsa8b C A B)) & (v7_amistd_1 (k2_scmfsa8b C A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc2_scmfsa8c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8c A B)))  &  ((v1_relat_1 (k2_scmfsa8c A B)) &  ((v4_relat_1 (k2_scmfsa8c A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8c A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8c A B)) &  ((v1_finset_1 (k2_scmfsa8c A B)) &  ((v1_afinsq_1 (k2_scmfsa8c A B)) &  (~ (v2_compos_1 (k2_scmfsa8c A B) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc2_scmfsa_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ((v1_relat_1 (k1_scmfsa_9 B A)) &  ((v4_relat_1 (k1_scmfsa_9 B A) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_9 B A) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k1_scmfsa_9 B A)))  &  ((v1_funct_1 (k1_scmfsa_9 B A)) &  ((v1_finset_1 (k1_scmfsa_9 B A)) &  ((v1_afinsq_1 (k1_scmfsa_9 B A)) & (v1_scmfsa7b (k1_scmfsa_9 B A))) ) ) ) ) ) ) ) ) ).
tt(fc2_scmfsa_i,ax,(v3_finseq_1 (k10_xtuple_0 k2_scmfsa_i))).
tt(fc2_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k1_scmfsa_m A)) &  ((v4_relat_1 (k1_scmfsa_m A) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_m A)) &  ((v5_funct_1 (k1_scmfsa_m A) (k2_memstr_0 3 k1_scmfsa_2)) & (v5_memstr_0 (k1_scmfsa_m A) 3 k1_scmfsa_2 k6_numbers)) ) ) ) ) ) ).
tt(fc2_scm_halt,ax, (! [A:$i] :  ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v4_relat_1 (k11_compos_1 k1_scmfsa_2 A) k5_numbers) &  ((v5_relat_1 (k11_compos_1 k1_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v1_finset_1 (k11_compos_1 k1_scmfsa_2 A)) & (v2_scm_halt (k11_compos_1 k1_scmfsa_2 A))) ) ) ) ) ) ) ).
tt(fc2_scm_inst,ax, (~ (v1_xboole_0 k3_scm_inst)) ).
tt(fc2_scmpds_2,ax, ((v2_memstr_0 k1_scmpds_2 2) &  ((v3_memstr_0 k1_scmpds_2 2) & (v1_extpro_1 k1_scmpds_2 2)) ) ).
tt(fc2_scmpds_3,ax, ((v1_extpro_1 k1_scmpds_2 2) & (v4_amistd_5 k1_scmpds_2 2)) ).
tt(fc2_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v4_scmpds_4 (k10_scmpds_2 A B C))) ) ).
tt(fc2_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  => (v6_compos_0 (k5_scmpds_2 A B) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc2_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v6_compos_0 (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 A 1))) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc2_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k1_scmpds_8 B C A)))  &  ((v1_relat_1 (k1_scmpds_8 B C A)) &  ((v4_relat_1 (k1_scmpds_8 B C A) k5_numbers) &  ((v5_relat_1 (k1_scmpds_8 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_8 B C A)) &  ((v1_finset_1 (k1_scmpds_8 B C A)) &  ((v1_afinsq_1 (k1_scmpds_8 B C A)) & (v2_compos_1 (k1_scmpds_8 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc2_scmpds_i,ax,(v3_finseq_1 (k10_xtuple_0 k1_scmpds_i))).
tt(fc2_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v2_memstr_0 (k1_scmring2 A) 2) & (v1_extpro_1 (k1_scmring2 A) 2)) ) ) ).
tt(fc2_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v4_amistd_1 (k3_scmring2 A B C) 2 (k1_scmring2 A))) ) ).
tt(fc2_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v3_amistd_5 (k1_scmring2 A) 2)) ) ) ).
tt(fc2_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ( (~ (v1_xboole_0 (k1_scmringi A)))  &  (~ (v1_zfmisc_1 (k1_scmringi A))) ) ) ) ).
tt(fc2_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k1_scmyciel A))) ) ).
tt(fc2_scpinvar,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k4_scpinvar B C A)))  &  ((v1_relat_1 (k4_scpinvar B C A)) &  ((v4_relat_1 (k4_scpinvar B C A) k5_numbers) &  ((v5_relat_1 (k4_scpinvar B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scpinvar B C A)) &  ((v1_finset_1 (k4_scpinvar B C A)) &  ((v1_afinsq_1 (k4_scpinvar B C A)) & (v2_compos_1 (k4_scpinvar B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc2_seq_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k24_valued_1 B A)) &  ((v1_funct_2 (k24_valued_1 B A) k5_numbers k1_numbers) & (v2_comseq_2 (k24_valued_1 B A))) ) ) ) ).
tt(fc2_seq_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k9_nat_1 A B)) &  ((v1_funct_2 (k9_nat_1 A B) k5_numbers k1_numbers) & (v2_comseq_2 (k9_nat_1 A B))) ) ) ) ).
tt(fc2_seqm_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k9_nat_1 A B)) &  ((v4_relat_1 (k9_nat_1 A B) k5_numbers) &  ((v1_funct_1 (k9_nat_1 A B)) &  ((v1_partfun1 (k9_nat_1 A B) k5_numbers) & (v3_valued_0 (k9_nat_1 A B))) ) ) ) ) ) ).
tt(fc2_series_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v7_ordinal1 (k3_power A B)) & (v1_xreal_0 (k3_power A B))) ) ) ).
tt(fc2_setfam_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_setfam_1 (k1_tarski A))) ) ).
tt(fc2_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_funct_1 (k3_setlim_1 B)) &  ((v1_funct_2 (k3_setlim_1 B) k5_numbers (k9_setfam_1 A)) & (v2_prob_1 (k3_setlim_1 B))) ) ) ) ).
tt(fc2_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_sfmastr1 (k7_scmfsa_2 A B))) ) ).
tt(fc2_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_sfmastr3 A B C D)) &  ((v4_relat_1 (k2_sfmastr3 A B C D) k5_numbers) &  ((v5_relat_1 (k2_sfmastr3 A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_sfmastr3 A B C D)) &  ( (~ (v1_xboole_0 (k2_sfmastr3 A B C D)))  &  ((v1_finset_1 (k2_sfmastr3 A B C D)) &  ((v1_afinsq_1 (k2_sfmastr3 A B C D)) & (v1_scmfsa7b (k2_sfmastr3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(fc2_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  => (v1_finset_1 (k4_sf_mastr A))) ) ).
tt(fc2_sgraph1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k3_sgraph1 A))) ) ).
tt(fc2_simplex0,ax, (! [A:$i] :  ((v1_classes1 A) => (v1_classes1 (k2_cohsp_1 A))) ) ).
tt(fc2_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v2_simplex0 C) &  ((v6_simplex0 C (u1_struct_0 B)) & (m1_simplex0 C (u1_struct_0 B))) ) ) ) ) ) )  =>  ( (~ (v3_pencil_1 (k5_simplex1 A B C)))  &  ((v1_matroid0 (k5_simplex1 A B C)) &  ((v3_matroid0 (k5_simplex1 A B C)) & (v2_simplex0 (k5_simplex1 A B C))) ) ) ) ) ).
tt(fc2_simplex2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  ((v2_compts_1 (k3_convex1 (k15_euclid A) B) (k15_euclid A)) & (v1_convex1 (k3_convex1 (k15_euclid A) B) (k15_euclid A))) ) ) ).
tt(fc2_sincos10,ax, ((v1_relat_1 (k5_relat_1 k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(fc2_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))) ).
tt(fc2_sin_cos9,ax, ((v1_relat_1 (k5_relat_1 k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)))) ).
tt(fc2_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_funct_1 (k3_sin_cos A)) &  ((v1_funct_2 (k3_sin_cos A) k5_numbers k2_numbers) & (v2_comseq_3 (k3_sin_cos A))) ) ) ) ).
tt(fc2_sppol_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v4_pre_topc (k1_rltopsp1 (k15_euclid A) B C) (k15_euclid A))) ) ).
tt(fc2_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v2_topreal1 (k1_rfinseq B A))) ) ).
tt(fc2_sprect_1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v2_compts_1 (k3_topreal1 2 A) (k15_euclid 2))) ) ).
tt(fc2_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (v1_sprect_2 (k1_sprect_1 A))) ) ).
tt(fc2_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( (~ (v1_sppol_1 (k3_topreal1 2 A)))  &  (~ (v2_sppol_1 (k3_topreal1 2 A))) ) ) ) ).
tt(fc2_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k3_square_1 A))) ) ).
tt(fc2_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) )  =>  ( (~ (v11_struct_0 (g1_stacks_1 A B C D E F)))  & (v1_stacks_1 (g1_stacks_1 A B C D E F))) ) ) ).
tt(fc2_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_xboole_0 (u1_struct_0 A))) ) ) ).
tt(fc2_subset_1,ax, (! [A:$i,B:$i,C:$i] :  (~ (v1_xboole_0 (k1_enumset1 A B C))) ) ).
tt(fc2_substlat,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k5_substlat A B)))  & (v3_lattices (k5_substlat A B))) ) ).
tt(fc2_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (v4_funct_1 (k1_substut1 A))) ) ).
tt(fc2_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  ( (~ (v1_xboole_0 (k4_supinf_1 A)))  & (v2_membered (k4_supinf_1 A))) ) ) ).
tt(fc2_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_pre_topc (k2_t_1topsp A)) & (v7_pre_topc (k2_t_1topsp A))) ) ) ).
tt(fc2_taylor_1,ax, (~ (v1_xboole_0 (k3_limfunc1 k6_numbers))) ).
tt(fc2_tbsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xreal_0 C)) )  => (v6_tbsp_1 (k9_metric_1 A B C) A)) ) ).
tt(fc2_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ( (~ (v2_struct_0 (k2_tdgroup A)))  & (v1_analoaf (k2_tdgroup A))) ) ) ).
tt(fc2_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (k5_tdlat_1 A))) ) ) ).
tt(fc2_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_polynom1 A B C D)) &  ((v1_funct_2 (k9_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v4_polynom7 (k9_polynom1 A B C D) A B)) ) ) ) ).
tt(fc2_tex_1,ax, (! [A:$i] :  ((v1_pre_topc (k2_tex_1 A)) &  ((v2_pre_topc (k2_tex_1 A)) & (v2_tdlat_3 (k2_tex_1 A))) ) ) ).
tt(fc2_tex_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k1_tex_2 A B)))  &  ((v13_struct_0 (k1_tex_2 A B) 1) & (v1_pre_topc (k1_tex_2 A B))) ) ) ) ).
tt(fc2_tex_4,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k2_pre_topc A B))) ) ).
tt(fc2_tmap_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ( (~ (v2_struct_0 D))  & (m1_pre_topc D A)) ) ) )  =>  ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) & (v5_pre_topc (k2_tmap_1 A B C D) D B)) ) ) ) ).
tt(fc2_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k2_topalg_1 A B))) ) ) ).
tt(fc2_topalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v7_struct_0 (k5_topalg_1 A B)) & (v15_algstr_0 (k5_topalg_1 A B))) ) ) ).
tt(fc2_topalg_3,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v1_connsp_1 A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v1_connsp_1 B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v1_connsp_1 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc2_topalg_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v1_borsuk_2 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc2_topalg_5,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_tsep_1 (k1_pre_topc A B) A)) ) ) ).
tt(fc2_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ( (~ (v2_struct_0 (k3_mfold_2 A B C)))  & (v1_topalg_2 (k3_mfold_2 A B C) A)) ) ) ).
tt(fc2_topdim_1,ax, (! [A:$i] : (v3_topdim_1 (k1_compts_1 A))) ).
tt(fc2_topdim_2,ax, (! [A:$i,B:$i] :  ( ((v1_topdim_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_xxreal_0 (k1_topdim_2 A B)) & (v1_int_1 (k1_topdim_2 A B))) ) ) ).
tt(fc2_topgen_1,ax, (! [A:$i] :  ( ((v1_orders_4 A) & (l1_struct_0 A))  => (v4_card_3 (k2_struct_0 A))) ) ).
tt(fc2_topgen_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k5_topgen_2 A B)))  & (v1_pre_topc (k5_topgen_2 A B))) ) ) ).
tt(fc2_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k5_topgen_3 A)))  &  ((v1_pre_topc (k5_topgen_3 A)) & (v2_pre_topc (k5_topgen_3 A))) ) ) ) ).
tt(fc2_topgen_4,ax, (~ (v4_card_3 k1_numbers)) ).
tt(fc2_topgen_5,ax, (~ (v1_xboole_0 k2_topgen_5)) ).
tt(fc2_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k3_group_1 A)) &  ((v2_funct_1 (k3_group_1 A)) &  ((v1_funct_2 (k3_group_1 A) (u1_struct_0 A) (u1_struct_0 A)) & (v2_funct_2 (k3_group_1 A) (u1_struct_0 A))) ) ) ) ) ).
tt(fc2_topmetr,ax, ( (~ (v2_struct_0 k3_topmetr))  &  ((v1_pre_topc k3_topmetr) & (v2_pre_topc k3_topmetr)) ) ).
tt(fc2_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v8_pre_topc (k15_euclid A)) & (v5_rltopsp1 (k15_euclid A))) ) ) ).
tt(fc2_topreal6,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v2_connsp_1 (k1_rltopsp1 (k15_euclid 2) A B) (k15_euclid 2))) ) ).
tt(fc2_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) & (l1_metric_1 B)) ) )  =>  ((v1_metric_1 (k1_topreal7 A B)) & (v6_metric_1 (k1_topreal7 A B))) ) ) ).
tt(fc2_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  (~ (v1_xboole_0 (k1_topreal9 A B C))) ) ) ).
tt(fc2_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k2_xxreal_1 A (k2_xcmplx_0 A B)))) ) ) ).
tt(fc2_toprealb,ax, (~ (v1_xboole_0 (k1_xxreal_1 (k1_real_1 1) 1))) ).
tt(fc2_toprealc,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  => (v2_xxreal_0 (k3_square_1 A))) ) ).
tt(fc2_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc2_trees_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  => (v1_trees_1 (k2_xboole_0 A B))) ) ).
tt(fc2_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ( (~ (v1_xboole_0 (k9_xtuple_0 A)))  & (v1_trees_1 (k9_xtuple_0 A))) ) ) ).
tt(fc2_trees_3,ax, (~ (v1_xboole_0 k2_trees_3)) ).
tt(fc2_trees_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_trees_3 B A))  &  ((m1_subset_1 C A) & (m1_finseq_1 D B)) ) )  =>  ((v1_relat_1 (k4_trees_4 C D)) &  ((v5_relat_1 (k4_trees_4 C D) A) &  ((v1_funct_1 (k4_trees_4 C D)) & (v3_trees_2 (k4_trees_4 C D))) ) ) ) ) ).
tt(fc2_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v2_trees_9 A)) ) )  => (v1_trees_2 (k9_xtuple_0 A))) ) ).
tt(fc2_unialg_1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) & (l1_unialg_1 A))  => (v4_margrel1 (u1_unialg_1 A) (u1_struct_0 A))) ) ).
tt(fc2_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (~ (v1_xboole_0 (k9_unialg_2 A))) ) ) ).
tt(fc2_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k2_uniroots A))) ) ) ).
tt(fc2_uproots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (~ (v1_xboole_0 (k1_uproots A))) ) ) ).
tt(fc2_urysohn1,ax, (~ (v1_xboole_0 k2_urysohn1)) ).
tt(fc2_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_valued_0 A))  => (v2_membered (k10_xtuple_0 A))) ) ).
tt(fc2_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v1_valued_0 (k1_valued_1 A B))) ) ) ) ).
tt(fc2_valued_2,ax, (! [A:$i] : (v1_valued_2 (k2_valued_2 A))) ).
tt(fc2_vectmetr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 B (u1_struct_0 A)) &  ((v3_vectmetr B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A)) & (v3_vectmetr (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(fc2_vectsp_1,ax,(v3_membered (u1_struct_0 k1_vectsp_1))).
tt(fc2_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  &  ((m1_subset_1 E C) &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 A) C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) C) C)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C (u1_struct_0 B)) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 B)) C)))) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g2_vectsp_2 A B C D E F G)))  & (v3_vectsp_2 (g2_vectsp_2 A B C D E F G) A B)) ) ) ).
tt(fc2_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k2_vfunct_1 A B C D)) & (v1_partfun1 (k2_vfunct_1 A B C D) A)) ) ) ).
tt(fc2_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_yellow_0 A) & (l1_orders_2 A)) )  => (v1_waybel_0 (k2_struct_0 A) A)) ) ).
tt(fc2_waybel10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k2_waybel_1 A B C)) &  ((v1_funct_2 (k2_waybel_1 A B C) (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A B C))) & (v5_orders_3 (k2_waybel_1 A B C) A (k1_yellow_2 A B C))) ) ) ) ).
tt(fc2_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_waybel11 (k2_struct_0 A) A) & (v2_waybel11 (k2_struct_0 A) A)) ) ) ).
tt(fc2_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v2_waybel12 (k4_yellow_0 A) A)) ) ).
tt(fc2_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_orders_2 (k2_yellow_1 (u1_pre_topc A))) & (v2_waybel_1 (k2_yellow_1 (u1_pre_topc A)))) ) ) ).
tt(fc2_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k8_waybel_0 A))) & (v3_lattice3 (k2_yellow_1 (k8_waybel_0 A)))) ) ) ).
tt(fc2_waybel17,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v3_lattice3 (k6_yellow_1 A B))) ) ) ).
tt(fc2_waybel18,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ((v1_pre_topc (k3_waybel18 A B)) &  ((v2_pre_topc (k3_waybel18 A B)) & (v1_monoid_0 (k3_waybel18 A B))) ) ) ) ).
tt(fc2_waybel_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v23_waybel_0 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc2_waybel21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k3_yellow_9 A B)))  &  ((v6_waybel_0 (k3_yellow_9 A B) A) & (v9_waybel_0 (k3_yellow_9 A B) A)) ) ) ) ).
tt(fc2_waybel22,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k2_waybel22 A B C)) &  ((v1_funct_2 (k2_waybel22 A B C) (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B)) & (v22_waybel_0 (k2_waybel22 A B C) (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B)) ) ) ) ).
tt(fc2_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v1_lattice3 (k5_yellow_0 A B))) ) ) ) ).
tt(fc2_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v5_orders_3 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k1_waybel24 A B C D E)) &  ((v1_funct_2 (k1_waybel24 A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (v5_orders_3 (k1_waybel24 A B C D E) B C)) ) ) ) ).
tt(fc2_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) )  =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (v2_waybel18 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(fc2_waybel26,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel26 A B)))  &  ((v1_orders_2 (k1_waybel26 A B)) & (v5_orders_2 (k1_waybel26 A B))) ) ) ) ).
tt(fc2_waybel27,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_waybel27 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_waybel27 (k5_relat_1 A B))) ) ) ).
tt(fc2_waybel28,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel28 A B C)))  &  ((v4_orders_2 (k1_waybel28 A B C)) &  ((v6_waybel_0 (k1_waybel28 A B C) A) & (v7_waybel_0 (k1_waybel28 A B C))) ) ) ) ) ).
tt(fc2_waybel29,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v1_yellow_0 (k6_yellow_1 A B))) ) ) ).
tt(fc2_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  => (v1_waybel_0 (k2_struct_0 A) A)) ) ).
tt(fc2_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 A))) & (v1_waybel_2 (k2_yellow_1 (k7_waybel_0 A)))) ) ) ).
tt(fc2_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k5_waybel11 A))) &  ((v1_lattice3 (k2_yellow_1 (k5_waybel11 A))) & (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(fc2_waybel32,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_orders_2 B)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_waybel32 A B C)))  &  ((v6_waybel_0 (k1_waybel32 A B C) A) & (v7_waybel_0 (k1_waybel32 A B C))) ) ) ) ).
tt(fc2_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v18_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_waybel34 A B C)) &  ((v1_funct_2 (k2_waybel34 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v4_waybel_1 (k2_waybel34 A B C) A B)) ) ) ) ).
tt(fc2_waybel35,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) & (m1_waybel35 C A B)) )  =>  (~ (v1_xboole_0 (k2_waybel35 A B C))) ) ) ).
tt(fc2_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v12_waybel_0 (k1_waybel_3 A B) A)) ) ).
tt(fc2_waybel_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  => (v2_waybel_4 (k2_waybel_4 A) A)) ) ).
tt(fc2_waybel_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k2_funct_6 A)) &  ((v2_relat_1 (k2_funct_6 A)) & (v1_funct_1 (k2_funct_6 A))) ) ) ) ).
tt(fc2_waybel_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v7_struct_0 (k3_yellow_1 A)))  & (v1_orders_2 (k3_yellow_1 A))) ) ) ).
tt(fc2_waybel_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k2_waybel_8 A B))) ) ) ).
tt(fc2_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ((v6_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C) A) & (v7_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C))) ) ) ).
tt(fc2_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v8_struct_0 (k1_weddwitt A B)) & (v15_algstr_0 (k1_weddwitt A B))) ) ) ).
tt(fc2_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v12_waybel_0 (k1_wellfnd1 A) A) & (v2_wellfnd1 (k1_wellfnd1 A) A)) ) ) ).
tt(fc2_wellord2,ax, (! [A:$i] :  ((v1_relat_1 (k1_wellord2 A)) & (v8_relat_2 (k1_wellord2 A))) ) ).
tt(fc2_wsierp_1,ax, (! [A:$i] :  ((m1_finseq_1 A k4_numbers) =>  ((v1_xcmplx_0 (k19_rvsum_1 A)) & (v1_int_1 (k19_rvsum_1 A))) ) ) ).
tt(fc2_xboole_0,ax, (! [A:$i] :  (~ (v1_xboole_0 (k1_tarski A))) ) ).
tt(fc2_xboolean,ax,(v1_xboolean k2_xboolean)).
tt(fc2_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_xcmplx_0 (k2_xcmplx_0 A B))) ) ).
tt(fc2_xreal_0,ax, (~ (v1_xreal_0 k1_xxreal_0)) ).
tt(fc2_xtuple_0,ax, (! [A:$i,B:$i,C:$i] : (v2_xtuple_0 (k3_xtuple_0 A B C))) ).
tt(fc2_xxreal_0,ax,(v1_xxreal_0 k2_xxreal_0)).
tt(fc2_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v2_membered (k2_xxreal_1 A B))) ) ).
tt(fc2_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) &  ( (~ (v1_xboole_0 A))  & (v3_xxreal_2 A)) )  =>  ((v1_xxreal_0 (k2_xxreal_2 A)) & (v1_xreal_0 (k2_xxreal_2 A))) ) ) ).
tt(fc2_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) & (v1_xreal_0 (k1_xxreal_3 A B))) ) ) ).
tt(fc2_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (~ (v1_xboole_0 (k2_struct_0 A))) ) ) ).
tt(fc2_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_yellow_0 A) & (l1_orders_2 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v1_yellow_0 (k3_yellow_3 A B))) ) ) ).
tt(fc2_yellow11,ax, ((v1_lattice3 k1_yellow11) & (v2_lattice3 k1_yellow11)) ).
tt(fc2_yellow12,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B))) &  ((v1_funct_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B))) & (v2_funct_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B)))) ) ) ).
tt(fc2_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_funct_1 (k3_yellow_2 A)) &  ((v2_funct_1 (k3_yellow_2 A)) & (v1_funct_2 (k3_yellow_2 A) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))) ) ) ) ).
tt(fc2_yellow14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 (u1_waybel_0 A B)))) ) ) ).
tt(fc2_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_waybel23 (k2_struct_0 A) A) &  ((v4_waybel23 (k2_struct_0 A) A) &  ((v6_waybel23 (k2_struct_0 A) A) & (v7_waybel23 (k2_struct_0 A) A)) ) ) ) ) ).
tt(fc2_yellow16,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 A B)) &  ((v4_orders_2 (k5_yellow_1 A B)) & (v5_orders_2 (k5_yellow_1 A B))) ) ) ) ).
tt(fc2_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ( (~ (v2_struct_0 (k1_yellow18 A)))  &  ((v2_altcat_1 (k1_yellow18 A)) &  ((v6_altcat_1 (k1_yellow18 A)) & (v11_altcat_1 (k1_yellow18 A))) ) ) ) ) ).
tt(fc2_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  ( (~ (v1_xboole_0 (k2_yellow19 A B)))  & (v13_waybel_0 (k2_yellow19 A B) (k3_yellow_1 (k2_struct_0 A)))) ) ) ).
tt(fc2_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) & (v2_yellow_0 (k3_lattice3 A))) ) ) ) ) ) ).
tt(fc2_yellow20,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) ) )  =>  ((v9_functor0 (k10_functor0 A B) B A) &  ((v12_functor0 (k10_functor0 A B) B A) & (v13_functor0 (k10_functor0 A B) B A)) ) ) ) ).
tt(fc2_yellow21,ax, (! [A:$i] :  ((v1_setfam_1 A) => (v4_orders_3 (k2_yellow21 A))) ) ).
tt(fc2_yellow_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ( (~ (v2_struct_0 (k1_yellow_2 A B C)))  &  ((v1_orders_2 (k1_yellow_2 A B C)) & (v4_yellow_0 (k1_yellow_2 A B C) B)) ) ) ) ).
tt(fc2_yellow_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k4_waybel_0 A B))) ) ).
tt(fc2_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  &  ( ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_waybel_0 (k1_yellow_4 A B C) A)) ) ).
tt(fc2_yellow_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k1_yellow_6 A)))  & (v1_classes2 (k1_yellow_6 A))) ) ).
tt(fc2_yellow_7,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v4_orders_2 (k7_lattice3 A))) ) ) ).
tt(fc2_yellow_8,ax, (! [A:$i] :  ((v1_pre_topc (k1_yellow_8 A)) & (v2_pre_topc (k1_yellow_8 A))) ) ).
tt(fc2_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k2_yellow_9 A B)))  &  ((v3_orders_2 (k2_yellow_9 A B)) & (v6_waybel_0 (k2_yellow_9 A B) A)) ) ) ) ).
tt(fc2_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) & (m1_subset_1 B k1_zf_lang))  => (v1_zf_lang (k4_zf_lang A B))) ) ).
tt(fc2_zfmisc_1,ax, (! [A:$i] : (v1_zfmisc_1 (k1_tarski A))) ).
tt(fc30_abcmiz_1,ax, ( (~ (v2_struct_0 k49_abcmiz_1))  &  ((v1_orders_2 k49_abcmiz_1) &  ((v3_orders_2 k49_abcmiz_1) &  ((v4_orders_2 k49_abcmiz_1) &  ((v5_orders_2 k49_abcmiz_1) & (v24_waybel_0 k49_abcmiz_1)) ) ) ) ) ).
tt(fc30_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v1_relat_1 (k5_afinsq_2 A k1_xboole_0)) &  ((v1_funct_1 (k5_afinsq_2 A k1_xboole_0)) &  ((v1_xboole_0 (k5_afinsq_2 A k1_xboole_0)) &  ((v5_ordinal1 (k5_afinsq_2 A k1_xboole_0)) & (v1_finset_1 (k5_afinsq_2 A k1_xboole_0))) ) ) ) ) ) ).
tt(fc30_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_zfmisc_1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((v7_struct_0 (g6_algstr_0 A B C D E)) & (v36_algstr_0 (g6_algstr_0 A B C D E))) ) ) ).
tt(fc30_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v2_amistd_1 (k3_ami_3 A B) 2 k1_ami_3)) ) ) ).
tt(fc30_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  =>  ((v1_relat_1 (k14_comput_1 A)) &  ((v1_funct_1 (k14_comput_1 A)) & (v2_margrel1 (k14_comput_1 A))) ) ) ) ).
tt(fc30_finset_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v5_finset_1 (k1_tarski A))) ) ).
tt(fc30_fomodel0,ax, (! [A:$i] : (v1_xboole_0 (k5_xboole_0 (k6_partfun1 (k1_tarski A)) (k1_tarski (k4_tarski A A))))) ).
tt(fc30_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_relat_1 (k21_fomodel1 A)) &  ((v1_funct_1 (k21_fomodel1 A)) & (v1_pre_poly (k21_fomodel1 A))) ) ) ) ).
tt(fc30_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  (~ (v7_fomodel1 (k1_funct_1 (k22_fomodel1 A) B) A)) ) ) ).
tt(fc30_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_fomodel2 D A B) & (v3_fomodel3 D A B C)) ) ) ) ) )  =>  ((v1_relat_1 (k22_fomodel3 A B C D)) &  ((v1_funct_1 (k22_fomodel3 A B C D)) & (v1_fomodel2 (k22_fomodel3 A B C D) A (k8_eqrel_1 B C))) ) ) ) ).
tt(fc30_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v7_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v3_card_1 C (k1_int_2 (k19_fomodel1 A B))) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  &  ((v3_card_1 D (k1_int_2 (k19_fomodel1 A B))) & (m1_subset_1 D (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) ) )  => (v3_fomodel4 (k1_tarski (k4_tarski (k2_xboole_0 (k36_fomodel4 A (k1_int_2 (k19_fomodel1 A B)) C D) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_fomodel3 A B C))) (k1_fomodel3 A B D))) A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k28_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc30_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 C)) )  => (v1_xboole_0 (k10_gate_1 A C B))) ) ).
tt(fc30_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k7_glib_000 A))) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v1_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc30_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_hermitan A B C)) &  ((v1_funct_2 (k6_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v4_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) & (v2_hermitan (k6_hermitan A B C) A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) ) ) ) ) ) ) ).
tt(fc30_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_ideal_1 (k17_ideal_1 A B) A)) ) ).
tt(fc30_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  &  ( (~ (v1_xboole_0 B))  & (v2_membered B)) )  =>  (~ (v1_xboole_0 (k10_member_1 A B))) ) ) ).
tt(fc30_membered,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v6_membered B))  => (v6_membered (k2_xboole_0 A B))) ) ).
tt(fc30_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v1_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc30_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k15_pre_poly A)))  =>  ((v2_funct_1 (k21_pre_poly A B)) &  ( (~ (v1_xboole_0 (k21_pre_poly A B)))  & (v1_pre_poly (k21_pre_poly A B))) ) ) ) ).
tt(fc30_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v4_relat_1 B A))  & (v1_relat_1 C))  =>  ((v1_relat_1 (k3_relat_1 B C)) & (v4_relat_1 (k3_relat_1 B C) A)) ) ) ).
tt(fc30_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v4_compos_0 (k12_scmfsa_2 B A) (u1_compos_1 k1_scmfsa_2)))  &  ((v2_amistd_1 (k12_scmfsa_2 B A) 3 k1_scmfsa_2) &  (~ (v4_amistd_1 (k12_scmfsa_2 B A) 3 k1_scmfsa_2)) ) ) ) ) ).
tt(fc30_scmfsa_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_scmfsa_2 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  => (v6_compos_0 (k15_scmfsa_2 C B A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc30_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmpds_5 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scmpds_4 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_4 A B)))  &  ((v1_relat_1 (k2_scmpds_4 A B)) &  ((v4_relat_1 (k2_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_4 A B)) &  ((v1_finset_1 (k2_scmpds_4 A B)) &  ((v1_afinsq_1 (k2_scmpds_4 A B)) & (v2_scmpds_4 (k2_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc30_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v2_amistd_1 (k7_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc30_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_relat_1 (k5_relat_1 k12_toprealb (k3_rcomp_1 A (k3_real_1 A 1)))) & (v2_funct_1 (k5_relat_1 k12_toprealb (k3_rcomp_1 A (k3_real_1 A 1))))) ) ) ).
tt(fc30_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc C A k3_topmetr) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 B C)) &  ((v1_funct_2 (k1_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k1_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc30_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v4_valued_0 A))  &  ((v1_relat_1 B) & (v4_valued_0 B)) )  => (v4_valued_0 (k5_xboole_0 A B))) ) ).
tt(fc30_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_rat_1 D)) )  =>  ((v1_funct_1 (k13_valued_1 C D)) & (v1_partfun1 (k13_valued_1 C D) A)) ) ) ).
tt(fc30_valued_2,ax, (! [A:$i,B:$i] :  ((v3_membered B) => (v3_valued_2 (k1_funct_2 A B))) ) ).
tt(fc30_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v5_orders_2 D) & (l1_waybel_0 D A)) ) ) )  =>  ((v5_orders_2 (k6_waybel_9 A B C D)) & (v6_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc30_xreal_0,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) &  (~ (v3_xxreal_0 (k5_xcmplx_0 A))) ) ) ) ).
tt(fc30_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  =>  ((v1_xxreal_0 (k5_xxreal_3 A)) &  (~ (v2_xxreal_0 (k5_xxreal_3 A))) ) ) ) ).
tt(fc31_afinsq_2,ax, (! [A:$i] :  ((v1_relat_1 (k5_afinsq_2 k1_xboole_0 A)) &  ((v1_funct_1 (k5_afinsq_2 k1_xboole_0 A)) &  ((v1_xboole_0 (k5_afinsq_2 k1_xboole_0 A)) &  ((v5_ordinal1 (k5_afinsq_2 k1_xboole_0 A)) & (v1_finset_1 (k5_afinsq_2 k1_xboole_0 A))) ) ) ) ) ).
tt(fc31_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ( (~ (v7_struct_0 (g6_algstr_0 A B C D E)))  & (v36_algstr_0 (g6_algstr_0 A B C D E))) ) ) ).
tt(fc31_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v2_amistd_1 (k4_ami_3 A B) 2 k1_ami_3)) ) ) ).
tt(fc31_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) &  ((v2_margrel1 A) &  ((v2_comput_1 A) & (v8_comput_1 A 2)) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k14_comput_1 A)))  &  ((v1_relat_1 (k14_comput_1 A)) &  ((v1_funct_1 (k14_comput_1 A)) &  ((v2_comput_1 (k14_comput_1 A)) & (v8_comput_1 (k14_comput_1 A) 3)) ) ) ) ) ) ).
tt(fc31_finset_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v5_finset_1 (k1_zfmisc_1 A))) ) ).
tt(fc31_fomodel0,ax, (! [A:$i,B:$i] : (v1_xboole_0 (k5_xboole_0 (k16_funcop_1 A B) (k1_tarski (k4_tarski A B))))) ).
tt(fc31_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) )  =>  (~ (v1_xboole_0 (k1_funct_1 (k21_fomodel1 A) B))) ) ) ).
tt(fc31_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  => (v12_fomodel1 (k25_fomodel2 A B) A)) ) ).
tt(fc31_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v7_ordinal1 D) &  ((v14_fomodel1 E D A) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v14_fomodel1 (k17_fomodel0 B C E) D A)) ) ).
tt(fc31_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel4 (k37_fomodel4 A) 2 A)) ) ).
tt(fc31_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 C)) )  => (v1_xboole_0 (k10_gate_1 C A B))) ) ).
tt(fc31_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k7_glib_000 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) B)))) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 C)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 C) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 C)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 C)) & (v1_glib_003 (k13_glib_000 A k2_glib_003 C))) ) ) ) ) ) ).
tt(fc31_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ( (~ (v3_funct_1 C))  &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k7_hermitan A B C)) &  ( (~ (v3_funct_1 (k7_hermitan A B C)))  &  ((v1_funct_2 (k7_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v4_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) & (v2_hermitan (k7_hermitan A B C) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) ) ) ) ) ) ) ) ).
tt(fc31_ideal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v1_xboole_0 (k7_ideal_1 A B)))  &  ((v1_ideal_1 (k7_ideal_1 A B) A) &  ((v2_ideal_1 (k7_ideal_1 A B) A) &  ((v3_ideal_1 (k7_ideal_1 A B) A) & (v5_ideal_1 (k7_ideal_1 A B) A)) ) ) ) ) ) ).
tt(fc31_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k10_member_1 A B))) ) ).
tt(fc31_membered,ax, (! [A:$i,B:$i] :  ((v1_membered A) => (v1_membered (k3_xboole_0 A B))) ) ).
tt(fc31_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v1_partfun3 (k18_valued_1 B C))) ) ) ) ).
tt(fc31_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k4_finseq_2 A B))) )  =>  ((v1_relat_1 (k7_partfun1 (k4_finseq_2 A B) C D)) & (v1_funct_1 (k7_partfun1 (k4_finseq_2 A B) C D))) ) ) ).
tt(fc31_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) & (v4_relat_1 C A))  =>  ((v1_relat_1 (k6_relat_1 B C)) & (v4_relat_1 (k6_relat_1 B C) A)) ) ) ).
tt(fc31_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  =>  ( (~ (v4_compos_0 (k13_scmfsa_2 B A) (u1_compos_1 k1_scmfsa_2)))  &  ((v2_amistd_1 (k13_scmfsa_2 B A) 3 k1_scmfsa_2) &  (~ (v4_amistd_1 (k13_scmfsa_2 B A) 3 k1_scmfsa_2)) ) ) ) ) ).
tt(fc31_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k16_scmfsa_2 B A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc31_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_scmpds_4 A)) ) ) ) ) ) )  &  ((v4_scmpds_4 B) &  ((v1_scmpds_5 B) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) ) )  =>  ( (~ (v1_xboole_0 (k3_scmpds_4 A B)))  &  ((v1_relat_1 (k3_scmpds_4 A B)) &  ((v4_relat_1 (k3_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k3_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k3_scmpds_4 A B)) &  ((v1_finset_1 (k3_scmpds_4 A B)) &  ((v1_afinsq_1 (k3_scmpds_4 A B)) & (v2_scmpds_4 (k3_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc31_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  (~ (v4_amistd_1 (k8_scmring2 A B) 2 (k1_scmring2 A))) ) ) ).
tt(fc31_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_relat_1 (k5_relat_1 k12_toprealb (k2_rcomp_1 A (k3_real_1 A 1)))) & (v2_funct_1 (k5_relat_1 k12_toprealb (k2_rcomp_1 A (k3_real_1 A 1))))) ) ) ).
tt(fc31_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc C A k3_topmetr) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 B C)) &  ((v1_funct_2 (k45_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k45_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc31_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  => (v1_membered (k7_relat_1 A B))) ) ).
tt(fc31_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_int_1 D)) )  =>  ((v1_funct_1 (k13_valued_1 C D)) & (v1_partfun1 (k13_valued_1 C D) A)) ) ) ).
tt(fc31_valued_2,ax, (! [A:$i,B:$i] :  ((v4_membered B) => (v4_valued_2 (k1_funct_2 A B))) ) ).
tt(fc31_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v4_orders_2 D) & (l1_waybel_0 D A)) ) ) )  =>  ((v4_orders_2 (k6_waybel_9 A B C D)) & (v6_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc31_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k7_xcmplx_0 A B))) ) ) ).
tt(fc31_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  =>  ((v1_xxreal_0 (k5_xxreal_3 A)) &  (~ (v3_xxreal_0 (k5_xxreal_3 A))) ) ) ) ).
tt(fc32_abcmiz_1,ax, ((v1_msualg_1 k27_abcmiz_1) &  ((v1_instalg1 k27_abcmiz_1) &  ((v1_abcmiz_1 k27_abcmiz_1) & (v12_abcmiz_1 k27_abcmiz_1)) ) ) ).
tt(fc32_afinsq_2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (v5_ordinal1 (k2_funcop_1 A B))) ) ).
tt(fc32_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v2_amistd_1 (k5_ami_3 A B) 2 k1_ami_3)) ) ) ).
tt(fc32_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k10_bilinear A B C D))) ) ) ).
tt(fc32_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_margrel1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 2)) ) ) )  =>  ((v1_relat_1 (k14_comput_1 A)) &  ((v1_funct_1 (k14_comput_1 A)) &  ((v7_comput_1 (k14_comput_1 A)) & (v8_comput_1 (k14_comput_1 A) 3)) ) ) ) ) ).
tt(fc32_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v5_finset_1 (k2_tarski A B))) ) ).
tt(fc32_fomodel0,ax, (! [A:$i] : (v1_xboole_0 (k5_xboole_0 (k6_partfun1 (k1_tarski A)) (k16_funcop_1 A A)))) ).
tt(fc32_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  => (v14_fomodel1 (k5_finseq_1 B) k6_numbers A)) ) ).
tt(fc32_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k27_fomodel2 A) A)) ) ).
tt(fc32_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  => (v13_fomodel1 (k17_fomodel0 C D B) A)) ) ).
tt(fc32_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  &  ((v10_fomodel4 C A B) &  ((v10_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  => (v2_fomodel3 (k3_fomodel3 A D C) A (k35_fomodel1 A) D (k6_fomodel4 A B C))) ) ).
tt(fc32_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  =>  (~ (v1_xboole_0 (k10_gate_1 A B C))) ) ) ).
tt(fc32_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v2_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc32_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l1_vectsp_1 A k1_complfld)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_hermitan A B C)) &  ((v1_funct_2 (k6_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ( (~ (v6_bilinear (k6_hermitan A B C) k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))))  & (v2_hermitan (k6_hermitan A B C) A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) ) ) ) ) ) ).
tt(fc32_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k11_member_1 A B))) ) ).
tt(fc32_membered,ax, (! [A:$i,B:$i] :  ((v1_membered A) => (v1_membered (k3_xboole_0 B A))) ) ).
tt(fc32_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_relat_1 B) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v2_relat_1 (k18_valued_1 B C)) & (v1_funct_1 (k18_valued_1 B C))) ) ) ) ).
tt(fc32_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k4_finseq_2 A B))) )  =>  ((v5_relat_1 (k7_partfun1 (k4_finseq_2 A B) C D) B) & (v1_finseq_1 (k7_partfun1 (k4_finseq_2 A B) C D))) ) ) ).
tt(fc32_relat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) & (v5_relat_1 C B))  =>  ((v1_relat_1 (k6_relat_1 A C)) &  ((v5_relat_1 (k6_relat_1 A C) A) & (v5_relat_1 (k6_relat_1 A C) B)) ) ) ) ).
tt(fc32_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k6_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc32_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v6_compos_0 (k17_scmfsa_2 B A) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc32_scmpds_5,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmpds_5 A) & (m1_subset_1 A (u1_compos_1 k1_scmpds_2)))  &  ((v4_scmpds_4 B) &  ((v1_scmpds_5 B) & (m1_subset_1 B (u1_compos_1 k1_scmpds_2))) ) )  =>  ( (~ (v1_xboole_0 (k4_scmpds_4 A B)))  &  ((v1_relat_1 (k4_scmpds_4 A B)) &  ((v4_relat_1 (k4_scmpds_4 A B) k5_numbers) &  ((v5_relat_1 (k4_scmpds_4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k4_scmpds_4 A B)) &  ((v1_finset_1 (k4_scmpds_4 A B)) &  ((v1_afinsq_1 (k4_scmpds_4 A B)) & (v2_scmpds_4 (k4_scmpds_4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc32_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  =>  (~ (v4_amistd_1 (k9_scmring2 A C B) 2 (k1_scmring2 A))) ) ) ).
tt(fc32_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_topalg_2)) =>  ((v1_funct_1 (k13_toprealb A)) &  ((v2_funct_1 (k13_toprealb A)) &  ((v1_funct_2 (k13_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 A (k3_real_1 A 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)))) &  ((v2_funct_2 (k13_toprealb A) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)))) & (v5_pre_topc (k13_toprealb A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 A (k3_real_1 A 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)))) ) ) ) ) ) ).
tt(fc32_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc B A k3_topmetr) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc C A k3_topmetr) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 B C)) &  ((v1_funct_2 (k18_valued_1 B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k18_valued_1 B C) A k3_topmetr)) ) ) ) ).
tt(fc32_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v2_valued_0 A))  => (v2_membered (k7_relat_1 A B))) ) ).
tt(fc32_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v1_funct_1 (k13_valued_1 A B)) & (v1_finseq_1 (k13_valued_1 A B))) ) ) ) ).
tt(fc32_valued_2,ax, (! [A:$i,B:$i] :  ((v5_membered B) => (v5_valued_2 (k1_funct_2 A B))) ) ).
tt(fc32_waybel_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) ) )  =>  ((v6_waybel_0 (k6_waybel_9 A B C D) B) & (v7_waybel_0 (k6_waybel_9 A B C D))) ) ) ).
tt(fc32_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v2_xxreal_0 (k7_xcmplx_0 B A))) ) ) ).
tt(fc32_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k6_xxreal_3 A B)) &  (~ (v2_xxreal_0 (k6_xxreal_3 A B))) ) ) ) ).
tt(fc33_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v1_relat_1 (k28_abcmiz_1 A)) &  ((v4_relat_1 (k28_abcmiz_1 A) (u1_struct_0 A)) &  ((v1_funct_1 (k28_abcmiz_1 A)) &  ((v1_partfun1 (k28_abcmiz_1 A) (u1_struct_0 A)) & (v13_abcmiz_1 (k28_abcmiz_1 A) A)) ) ) ) ) ) ).
tt(fc33_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_xboole_0 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) ) )  => (v1_xboole_0 (k7_afinsq_2 A))) ) ).
tt(fc33_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  =>  (~ (v2_amistd_1 (k6_ami_3 A B) 2 k1_ami_3)) ) ) ).
tt(fc33_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k10_bilinear A B C D))) ) ) ).
tt(fc33_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_margrel1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 2)) ) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_margrel1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 2)) ) ) ) )  => (v3_comput_1 (k10_finseq_1 A B))) ) ).
tt(fc33_finset_1,ax, (! [A:$i,B:$i] :  ( ((v5_finset_1 A) & (v5_finset_1 B))  => (v5_finset_1 (k2_xboole_0 A B))) ) ).
tt(fc33_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v1_finseq_1 (k6_funct_4 A B C))) ) ).
tt(fc33_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v1_relat_1 (k33_fomodel1 A B)) & (v5_relat_1 (k33_fomodel1 A B) (k3_finseq_2 (k10_xtuple_0 B)))) ) ) ).
tt(fc33_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_xboole_0 (k2_xcmplx_0 (k19_fomodel1 A (k34_fomodel2 A)) 2))) ) ).
tt(fc33_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v15_fomodel1 (k17_fomodel0 B C D) A)) ) ).
tt(fc33_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  & (v10_fomodel4 C A B)) )  =>  ((v1_partfun1 (k5_fomodel4 A B C) (k35_fomodel1 A)) &  ((v3_relat_2 (k5_fomodel4 A B C)) & (v8_relat_2 (k5_fomodel4 A B C))) ) ) ) ).
tt(fc33_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k11_gate_1 A B C))) ) ) ).
tt(fc33_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v2_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc33_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A))) ) ) )  =>  ( (~ (v1_xboole_0 (k5_relat_1 C D)))  & (v1_relat_1 (k5_relat_1 C D))) ) ) ).
tt(fc33_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k11_member_1 B A))) ) ).
tt(fc33_membered,ax, (! [A:$i,B:$i] :  ((v2_membered A) => (v2_membered (k3_xboole_0 A B))) ) ).
tt(fc33_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_relat_1 (k18_valued_1 B B)) &  ((v1_funct_1 (k18_valued_1 B B)) & (v4_partfun3 (k18_valued_1 B B))) ) ) ) ).
tt(fc33_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k7_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc33_scmring3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  (~ (v4_compos_0 (k8_scmring2 A B) (u1_compos_1 (k1_scmring2 A)))) ) ) ).
tt(fc33_toprealb,ax, ((v1_funct_1 k14_toprealb) &  ((v2_funct_1 k14_toprealb) &  ((v1_funct_2 k14_toprealb (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) &  ((v2_funct_2 k14_toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) & (v5_pre_topc k14_toprealb (k11_toprealb k9_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) ) ) ) ).
tt(fc33_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  => (v3_membered (k7_relat_1 A B))) ) ).
tt(fc33_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v1_funct_1 (k18_valued_1 A B)) & (v1_valued_0 (k18_valued_1 A B))) ) ) ) ).
tt(fc33_valued_2,ax, (! [A:$i,B:$i] :  ((v6_membered B) => (v6_valued_2 (k1_funct_2 A B))) ) ).
tt(fc33_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( (~ (v2_struct_0 (g1_waybel_9 A B C)))  & (v1_waybel_9 (g1_waybel_9 A B C))) ) ) ).
tt(fc33_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k7_xcmplx_0 A B))) ) ) ).
tt(fc33_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k6_xxreal_3 B A)) &  (~ (v2_xxreal_0 (k6_xxreal_3 B A))) ) ) ) ).
tt(fc34_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)))  =>  ((v1_funct_1 (k54_abcmiz_1 A B)) &  ((v2_funct_1 (k54_abcmiz_1 A B)) & (v15_abcmiz_1 (k54_abcmiz_1 A B) A)) ) ) ) ).
tt(fc34_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  => (v1_xreal_0 (k7_afinsq_2 A))) ) ).
tt(fc34_ami_6,ax, ((v1_extpro_1 k1_ami_3 2) & (v2_amistd_2 k1_ami_3 2)) ).
tt(fc34_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k11_bilinear A B C D))) ) ) ).
tt(fc34_comput_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 2)) ) )  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 2)) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v7_comput_1 C) & (v8_comput_1 C 2)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 (k6_funct_6 (k10_finseq_1 B C)) A)) & (v7_comput_1 (k3_relat_1 (k6_funct_6 (k10_finseq_1 B C)) A))) ) ) ).
tt(fc34_finset_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v5_finset_1 A))  => (v1_finset_1 (k3_tarski A))) ) ).
tt(fc34_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 C) &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D C) & (v1_finseq_1 D)) ) ) )  =>  ((v1_relat_1 (k17_fomodel0 A B D)) &  ((v1_funct_1 (k17_fomodel0 A B D)) &  ((v3_card_1 (k17_fomodel0 A B D) C) & (v1_finseq_1 (k17_fomodel0 A B D))) ) ) ) ) ).
tt(fc34_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v1_relat_1 (k34_fomodel1 A B)) & (v5_relat_1 (k34_fomodel1 A B) (k3_finseq_2 (k10_xtuple_0 B)))) ) ) ).
tt(fc34_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_xboole_0 (k6_xcmplx_0 (k1_int_2 (k19_fomodel1 A (k34_fomodel2 A))) 2))) ) ).
tt(fc34_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v1_xboole_0 B) &  ((v3_fomodel2 C A B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_xboole_0 (k32_fomodel2 A C))) ) ).
tt(fc34_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v1_fomodel4 B A))  => (v2_fomodel4 (k1_tarski B) A)) ) ).
tt(fc34_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k11_gate_1 A C B))) ) ) ).
tt(fc34_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) B)))) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 C)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 C) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 C)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 C)) & (v2_glib_003 (k13_glib_000 A k3_glib_003 C))) ) ) ) ) ) ).
tt(fc34_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  &  ( (~ (v1_xboole_0 B))  & (v1_membered B)) )  =>  (~ (v1_xboole_0 (k11_member_1 A B))) ) ) ).
tt(fc34_membered,ax, (! [A:$i,B:$i] :  ((v2_membered A) => (v2_membered (k3_xboole_0 B A))) ) ).
tt(fc34_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v4_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc34_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k8_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc34_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  =>  (~ (v4_compos_0 (k9_scmring2 A C B) (u1_compos_1 (k1_scmring2 A)))) ) ) ).
tt(fc34_toprealb,ax, ((v1_funct_1 k15_toprealb) &  ((v2_funct_1 k15_toprealb) &  ((v1_funct_2 k15_toprealb (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) &  ((v2_funct_2 k15_toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) & (v5_pre_topc k15_toprealb (k11_toprealb k10_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) ) ) ) ).
tt(fc34_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  => (v4_membered (k7_relat_1 A B))) ) ).
tt(fc34_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v1_funct_1 (k18_valued_1 A B)) & (v3_valued_0 (k18_valued_1 A B))) ) ) ) ).
tt(fc34_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v7_valued_2 A))  => (v1_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc34_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski A)))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k1_tarski A)))))  =>  ((v13_struct_0 (g1_waybel_9 (k1_tarski A) B C) 1) & (v1_waybel_9 (g1_waybel_9 (k1_tarski A) B C))) ) ) ).
tt(fc34_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k7_xcmplx_0 A B))) ) ) ).
tt(fc34_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k6_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k6_xxreal_3 A B))) ) ) ) ).
tt(fc35_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1))) )  =>  ((v1_xboole_0 (k54_abcmiz_1 A B)) & (v1_funct_1 (k54_abcmiz_1 A B))) ) ) ).
tt(fc35_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  => (v1_rat_1 (k7_afinsq_2 A))) ) ).
tt(fc35_ami_6,ax, ((v1_extpro_1 k1_ami_3 2) & (v4_amistd_2 k1_ami_3 2)) ).
tt(fc35_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k11_bilinear A B C D))) ) ) ).
tt(fc35_comput_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 2)) ) )  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 2)) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v7_comput_1 C) & (v8_comput_1 C 2)) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 (k6_funct_6 (k10_finseq_1 B C)) A)) & (v8_comput_1 (k3_relat_1 (k6_funct_6 (k10_finseq_1 B C)) A) 2)) ) ) ).
tt(fc35_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  => (v1_finset_1 (k1_funct_1 A B))) ) ).
tt(fc35_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C B) &  ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  =>  ((v1_relat_1 (k17_fomodel0 A C D)) &  ((v5_relat_1 (k17_fomodel0 A C D) B) &  ((v1_funct_1 (k17_fomodel0 A C D)) & (v1_finseq_1 (k17_fomodel0 A C D))) ) ) ) ) ).
tt(fc35_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B k5_numbers))  => (v1_setfam_1 (k1_funct_1 (k39_fomodel1 A) B))) ) ).
tt(fc35_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k28_fomodel2 A B))) ) ) ).
tt(fc35_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  & (v7_ordinal1 C)) )  => (v3_fomodel2 (k13_fomodel0 C B) A (k2_xcmplx_0 (k32_fomodel2 A B) C))) ) ).
tt(fc35_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v2_fomodel4 B A) & (v2_fomodel4 C A)) )  => (v2_fomodel4 (k2_xboole_0 B C) A)) ) ).
tt(fc35_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k11_gate_1 C A B))) ) ) ).
tt(fc35_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k7_glib_000 A))) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v2_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc35_hermitan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k7_hermitan A B C)) &  ((v1_funct_2 (k7_hermitan A B C) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld)) &  ((v1_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v2_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ((v4_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) &  ( (~ (v5_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))))  &  ( (~ (v6_bilinear (k7_hermitan A B C) k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C)))))  & (v2_hermitan (k7_hermitan A B C) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) ) ) ) ) ) ) ) ) ).
tt(fc35_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k11_member_1 A B))) ) ).
tt(fc35_membered,ax, (! [A:$i,B:$i] :  ((v3_membered A) => (v3_membered (k3_xboole_0 A B))) ) ).
tt(fc35_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v4_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc35_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k9_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc35_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v2_amistd_2 (k1_scmring2 A) 2)) ) ) ).
tt(fc35_toprealb,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_funct_1 (k13_toprealb (k4_toprealb A))) &  ((v1_funct_2 (k13_toprealb (k4_toprealb A)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb A) (k3_real_1 (k4_toprealb A) 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb A))))) & (v1_t_0topsp (k13_toprealb (k4_toprealb A)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb A) (k3_real_1 (k4_toprealb A) 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb A))))) ) ) ) ).
tt(fc35_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C B (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc D B (k15_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) ) ) ) ) )  =>  ((v1_funct_1 (k78_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C D)) &  ((v1_funct_2 (k78_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C D) (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (v5_pre_topc (k78_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C D) B (k15_euclid A))) ) ) ) ).
tt(fc35_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  => (v5_membered (k7_relat_1 A B))) ) ).
tt(fc35_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k3_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v5_relat_1 (k18_valued_1 A B) k3_numbers) & (v1_funct_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc35_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v8_valued_2 A))  => (v2_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc35_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k3_xxreal_0 A B))) ) ).
tt(fc35_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k6_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k6_xxreal_3 A B))) ) ) ) ).
tt(fc36_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) )  => (v14_abcmiz_1 (k55_abcmiz_1 A B) A (k28_abcmiz_1 A))) ) ).
tt(fc36_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  => (v1_int_1 (k7_afinsq_2 A))) ) ).
tt(fc36_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v1_bilinear C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v1_xboole_0 (k12_bilinear A B C))) ) ) ).
tt(fc36_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 1)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v7_comput_1 B)) ) )  =>  ((v1_relat_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 B)) A)) & (v7_comput_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 B)) A))) ) ) ).
tt(fc36_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_finset_1 A))  => (v5_finset_1 (k10_xtuple_0 A))) ) ).
tt(fc36_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((v1_relat_1 (k20_fomodel0 A B C)) &  ((v1_funct_1 (k20_fomodel0 A B C)) & (v1_pre_poly (k20_fomodel0 A B C))) ) ) ) ).
tt(fc36_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v14_fomodel1 (k13_fomodel0 B C) (k2_xcmplx_0 (k38_fomodel1 A C) B) A)) ) ).
tt(fc36_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  (~ (v1_xboole_0 (k29_fomodel2 A B))) ) ) ).
tt(fc36_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  ((v3_fomodel2 C A B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((v1_xxreal_0 (k6_xcmplx_0 B (k32_fomodel2 A C))) &  (~ (v3_xxreal_0 (k6_xcmplx_0 B (k32_fomodel2 A C)))) ) ) ) ).
tt(fc36_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v1_fomodel4 B A) & (v1_fomodel4 C A)) )  => (v2_fomodel4 (k2_tarski B C) A)) ) ).
tt(fc36_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k11_gate_1 A B C))) ) ).
tt(fc36_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v3_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc36_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k11_member_1 A B))) ) ).
tt(fc36_membered,ax, (! [A:$i,B:$i] :  ((v3_membered A) => (v3_membered (k3_xboole_0 B A))) ) ).
tt(fc36_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v3_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc36_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k10_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc36_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v4_amistd_2 (k1_scmring2 A) 2)) ) ) ).
tt(fc36_toprealb,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_funct_1 (k13_toprealb (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)))) &  ((v1_funct_2 (k13_toprealb (k4_toprealb (k7_real_1 (k10_real_1 1 2) A))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)) (k3_real_1 (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)) 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)))))) & (v1_t_0topsp (k13_toprealb (k4_toprealb (k7_real_1 (k10_real_1 1 2) A))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)) (k3_real_1 (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)) 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k7_real_1 (k10_real_1 1 2) A)))))) ) ) ) ).
tt(fc36_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  => (v6_membered (k7_relat_1 A B))) ) ).
tt(fc36_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v5_relat_1 (k18_valued_1 A B) k4_numbers) & (v1_funct_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc36_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v9_valued_2 A))  => (v3_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc36_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k4_xxreal_0 A B))) ) ).
tt(fc36_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xxreal_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xxreal_0 B)) )  =>  ( (~ (v1_xboole_0 (k4_xxreal_3 A B)))  & (v1_xxreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc37_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v6_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) ) )  => (v6_abcmiz_1 (k56_abcmiz_1 A B C) A)) ) ).
tt(fc37_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v4_valued_0 A) & (v1_finset_1 A)) ) ) )  => (v7_ordinal1 (k7_afinsq_2 A))) ) ).
tt(fc37_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v2_bilinear C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v1_xboole_0 (k12_bilinear A B C))) ) ) ).
tt(fc37_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v7_comput_1 A) & (v8_comput_1 A 1)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v7_comput_1 B) & (v8_comput_1 B 2)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 B)) A)) & (v8_comput_1 (k3_relat_1 (k6_funct_6 (k9_finseq_1 B)) A) 2)) ) ) ).
tt(fc37_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_pre_poly A)) )  => (v1_finseq_1 (k1_funct_1 A B))) ) ).
tt(fc37_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_xboole_0 (k4_xboole_0 (k35_fomodel1 A) (k3_finseq_2 (k5_fomodel1 A))))) ) ).
tt(fc37_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v5_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v4_fomodel1 (k1_funct_1 (k22_fomodel1 A) B) A)) ) ).
tt(fc37_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v7_ordinal1 D) &  ((v3_fomodel2 E A D) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v3_fomodel2 (k17_fomodel0 B C E) A D)) ) ).
tt(fc37_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel4 (k4_tarski (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k38_fomodel2 A B) (k38_fomodel2 A C)) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k31_fomodel4 A)) (k5_lang1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_domain_1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k38_fomodel2 A B) (k38_fomodel2 A C)) (k38_fomodel2 A B)) (k1_domain_1 (k1_zfmisc_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k38_fomodel2 A B) (k38_fomodel2 A C)) (k38_fomodel2 A C))))) ) ).
tt(fc37_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k11_gate_1 A C B))) ) ).
tt(fc37_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v3_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc37_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k11_member_1 A B))) ) ).
tt(fc37_membered,ax, (! [A:$i,B:$i] :  ((v4_membered A) => (v4_membered (k3_xboole_0 A B))) ) ).
tt(fc37_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v3_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc37_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k14_scmfsa_2 B A C)) 3 k1_scmfsa_2)) ) ) ).
tt(fc37_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  => (v1_membered (k9_relat_1 A B))) ) ).
tt(fc37_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v4_valued_0 B)) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v1_funct_1 (k18_valued_1 A B)) & (v4_valued_0 (k18_valued_1 A B))) ) ) ) ).
tt(fc37_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v10_valued_2 A))  => (v4_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc37_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k1_xreal_0 A B))) ) ).
tt(fc37_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xboole_0 A) & (v1_xxreal_0 A))  & (v1_xxreal_0 B))  =>  ((v1_xboole_0 (k4_xxreal_3 A B)) & (v1_xxreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc38_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v7_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) ) )  => (v7_abcmiz_1 (k56_abcmiz_1 A B C) A)) ) ).
tt(fc38_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) &  ( (~ (v1_xboole_0 (k1_ordinal4 A B)))  & (v5_ordinal1 (k1_ordinal4 A B))) ) ) ) ) ).
tt(fc38_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v3_bilinear C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v1_xboole_0 (k12_bilinear A B C))) ) ) ).
tt(fc38_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C A) &  ((v7_ordinal1 D) &  ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) &  ((v3_card_1 E D) & (v1_finseq_1 E)) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_1 (k20_fomodel0 A B C) E)) &  ((v1_funct_1 (k1_funct_1 (k20_fomodel0 A B C) E)) &  ((v3_card_1 (k1_funct_1 (k20_fomodel0 A B C) E) D) & (v1_finseq_1 (k1_funct_1 (k20_fomodel0 A B C) E))) ) ) ) ) ).
tt(fc38_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((v5_relat_1 (k34_fomodel1 A B) (k3_finseq_2 (k5_fomodel1 A))) & (v3_card_1 (k34_fomodel1 A B) (k1_int_2 (k19_fomodel1 A (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B))))) ) ) ).
tt(fc38_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ( (~ (v4_fomodel1 C A))  & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (~ (v5_fomodel2 (k7_finseq_1 (k31_fomodel2 A C) B) A)) ) ) ).
tt(fc38_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel2 (k17_fomodel0 B C D) A)) ) ).
tt(fc38_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel4 (k4_tarski (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B C) C) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc38_gate_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k11_gate_1 C A B))) ) ).
tt(fc38_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) B)))) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 C)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 C) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 C)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 C)) & (v3_glib_003 (k13_glib_000 A k4_glib_003 C))) ) ) ) ) ) ).
tt(fc38_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v5_membered B))  => (v5_membered (k11_member_1 A B))) ) ).
tt(fc38_membered,ax, (! [A:$i,B:$i] :  ((v4_membered A) => (v4_membered (k3_xboole_0 B A))) ) ).
tt(fc38_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v2_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc38_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k15_scmfsa_2 B A C)) 3 k1_scmfsa_2)) ) ) ).
tt(fc38_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v2_valued_0 A))  => (v2_membered (k9_relat_1 A B))) ) ).
tt(fc38_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 D E)) & (v1_partfun1 (k18_valued_1 D E) A)) ) ) ).
tt(fc38_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v11_valued_2 A))  => (v5_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc38_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ( (~ (v3_xxreal_0 (k1_xreal_0 A B)))  & (v1_xreal_0 (k1_xreal_0 A B))) ) ) ).
tt(fc38_xxreal_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xxreal_0 (k5_xxreal_3 A)) & (v1_xreal_0 (k5_xxreal_3 A))) ) ) ).
tt(fc39_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v9_abcmiz_1 C A) & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) ) )  => (v9_abcmiz_1 (k56_abcmiz_1 A B C) A)) ) ).
tt(fc39_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 B A)) &  ((v1_funct_1 (k1_ordinal4 B A)) &  ( (~ (v1_xboole_0 (k1_ordinal4 B A)))  & (v5_ordinal1 (k1_ordinal4 B A))) ) ) ) ) ).
tt(fc39_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v4_bilinear C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v1_xboole_0 (k12_bilinear A B C))) ) ) ).
tt(fc39_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C A) & (v1_xboole_0 D)) )  => (v1_xboole_0 (k1_funct_1 (k20_fomodel0 A B C) D))) ) ).
tt(fc39_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k9_fomodel1 A))) ) ) ).
tt(fc39_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ((m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) &  ( (~ (v4_fomodel1 D A))  & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  =>  (~ (v5_fomodel2 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A D) B) C) A)) ) ) ).
tt(fc39_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k32_fomodel2 A (k24_fomodel3 A B C D)) (k32_fomodel2 A D)))) ) ).
tt(fc39_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k31_fomodel4 A) A)) ) ).
tt(fc39_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k6_glib_000 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k6_glib_000 A))) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v3_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc39_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k12_member_1 A B))) ) ).
tt(fc39_membered,ax, (! [A:$i,B:$i] :  ((v5_membered A) => (v5_membered (k3_xboole_0 A B))) ) ).
tt(fc39_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) & (v3_xxreal_0 B))  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v2_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc39_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v5_waybel_3 B) & (v16_pcs_0 B)) ) ) ) )  =>  ((v3_orders_2 (k17_pcs_0 A B)) & (v12_pcs_0 (k17_pcs_0 A B))) ) ) ).
tt(fc39_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  =>  (~ (v2_amistd_1 (k14_scmfsa_2 B A C) 3 k1_scmfsa_2)) ) ) ).
tt(fc39_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C B (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc D B k3_topmetr) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) ) ) ) ) )  =>  ((v1_funct_1 (k62_valued_2 (u1_struct_0 (k15_euclid A)) C D)) &  ((v1_funct_2 (k62_valued_2 (u1_struct_0 (k15_euclid A)) C D) (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (v5_pre_topc (k62_valued_2 (u1_struct_0 (k15_euclid A)) C D) B (k15_euclid A))) ) ) ) ).
tt(fc39_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  => (v3_membered (k9_relat_1 A B))) ) ).
tt(fc39_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v3_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 D E)) & (v1_partfun1 (k18_valued_1 D E) A)) ) ) ).
tt(fc39_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v12_valued_2 A))  => (v6_valued_2 (k10_xtuple_0 A))) ) ).
tt(fc39_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_xxreal_0 (k4_xxreal_3 A B)) & (v1_xreal_0 (k4_xxreal_3 A B))) ) ) ).
tt(fc3_abcmiz_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A (k5_finsub_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) ) ) )  =>  ( (~ (v2_struct_0 (g2_abcmiz_0 A B C D E)))  & (v7_abcmiz_0 (g2_abcmiz_0 A B C D E))) ) ) ).
tt(fc3_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) => (v1_finset_1 (k1_xtuple_0 A))) ) ).
tt(fc3_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  => (v1_abian (k2_xcmplx_0 A 1))) ) ).
tt(fc3_afinsq_1,ax, (! [A:$i] :  (~ (v1_xboole_0 (k3_afinsq_1 A))) ) ).
tt(fc3_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v8_algstr_0 (k5_afvect0 A B)) & (v1_tdgroup (k5_afvect0 A B))) ) ) ).
tt(fc3_algstr_1,ax, (~ (v2_struct_0 k8_algstr_0)) ).
tt(fc3_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  => (v15_algstr_0 (k4_algstr_4 A B))) ) ).
tt(fc3_altcat_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  ((v1_relat_1 (k2_funct_4 B)) &  ((v4_relat_1 (k2_funct_4 B) (k2_zfmisc_1 A A)) & (v1_funct_1 (k2_funct_4 B))) ) ) ) ).
tt(fc3_altcat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( ((v3_altcat_3 C A B B) & (m1_subset_1 C (k1_altcat_1 A B B)))  &  ((v3_altcat_3 D A B B) & (m1_subset_1 D (k1_altcat_1 A B B))) ) ) )  => (v3_altcat_3 (k5_altcat_1 A B B B D C) A B B)) ) ).
tt(fc3_altcat_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v3_altcat_3 (k8_altcat_1 A B) A B B)) ) ).
tt(fc3_ami_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) & (m1_subset_1 B k2_ami_2))  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc3_ami_3,ax, ((v3_memstr_0 k1_ami_3 2) & (v1_extpro_1 k1_ami_3 2)) ).
tt(fc3_ami_5,ax, ((v1_extpro_1 k1_ami_3 2) & (v4_amistd_5 k1_ami_3 2)) ).
tt(fc3_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_amistd_1 (k3_ami_3 A B) 2 k1_ami_3)) ) ).
tt(fc3_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ( (~ (v2_struct_0 (k4_amistd_1 A)))  &  ((v8_struct_0 (k4_amistd_1 A)) & (v1_extpro_1 (k4_amistd_1 A) A)) ) ) ) ).
tt(fc3_amistd_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v2_amistd_4 B A) & (l1_extpro_1 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  (~ (v1_zfmisc_1 (k4_memstr_0 A B C))) ) ) ).
tt(fc3_amistd_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 B) & (v5_funct_1 B (k2_memstr_0 A (k4_amistd_1 A)))) ) ) )  =>  ((v1_relat_1 (k6_memstr_0 A (k4_amistd_1 A) B)) &  ((v4_relat_1 (k6_memstr_0 A (k4_amistd_1 A) B) (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 (k6_memstr_0 A (k4_amistd_1 A) B)) &  ((v5_funct_1 (k6_memstr_0 A (k4_amistd_1 A) B) (k2_memstr_0 A (k4_amistd_1 A))) & (v1_xboole_0 (k6_memstr_0 A (k4_amistd_1 A) B))) ) ) ) ) ) ).
tt(fc3_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ( (~ (v7_struct_0 (k3_analmetr A)))  &  ((v1_analoaf (k3_analmetr A)) & (v1_diraf (k3_analmetr A))) ) ) ) ).
tt(fc3_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) & (v4_collsp (k5_anproj_1 A))) ) ) ).
tt(fc3_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k2_funcop_1 (k4_finseq_2 C A) B)))  &  ((v1_funct_1 (k2_funcop_1 (k4_finseq_2 C A) B)) &  ((v2_margrel1 (k2_funcop_1 (k4_finseq_2 C A) B)) & (v3_margrel1 (k2_funcop_1 (k4_finseq_2 C A) B) A)) ) ) ) ) ).
tt(fc3_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m2_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  => (v15_aofa_000 (k44_aofa_i00 A B C D E F) A)) ) ).
tt(fc3_armstrng,ax, (! [A:$i] :  (~ (v1_xboole_0 (k7_armstrng A))) ) ).
tt(fc3_arytm_3,ax, (~ (v1_xboole_0 k5_arytm_3)) ).
tt(fc3_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_funct_1 (k3_asympt_1 A)) &  ((v1_funct_2 (k3_asympt_1 A) k5_numbers k1_numbers) & (v4_asympt_0 (k3_asympt_1 A))) ) ) ) ).
tt(fc3_autalg_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (v2_msualg_3 (k2_msualg_3 A B) A B B)) ) ).
tt(fc3_bagorder,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v2_pre_poly D)) ) ) ) ) ) )  =>  ((v1_relat_1 (k1_bagorder A B C D)) &  ((v4_relat_1 (k1_bagorder A B C D) (k7_nat_d C B)) &  ((v1_funct_1 (k1_bagorder A B C D)) &  ((v1_partfun1 (k1_bagorder A B C D) (k7_nat_d C B)) & (v2_pre_poly (k1_bagorder A B C D))) ) ) ) ) ) ).
tt(fc3_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_bcialg_2 B A))  =>  (~ (v1_xboole_0 (k7_eqrel_1 (u1_struct_0 A) B))) ) ) ).
tt(fc3_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  ((v1_funct_1 (u1_bcialg_4 A)) &  ((v1_funct_2 (u1_bcialg_4 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) &  ((v1_binop_1 (u1_bcialg_4 A) (u1_struct_0 A)) & (v2_binop_1 (u1_bcialg_4 A) (u1_struct_0 A))) ) ) ) ) ).
tt(fc3_bcialg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m2_bcialg_1 B A) & (m4_bcialg_2 C A B)) )  =>  ((v2_bcialg_1 (k9_bcialg_2 A C)) &  ((v3_bcialg_1 (k9_bcialg_2 A C)) &  ((v4_bcialg_1 (k9_bcialg_2 A C)) &  ((v5_bcialg_1 (k9_bcialg_2 A C)) & (v7_bcialg_1 (k9_bcialg_2 A C))) ) ) ) ) ) ).
tt(fc3_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A)) ) )  =>  ((v1_funct_1 (k1_bilinear A B C)) &  ((v1_funct_2 (k1_bilinear A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v3_bilinear (k1_bilinear A B C) A B C)) ) ) ) ).
tt(fc3_binop_2,ax, ((v1_funct_1 k33_binop_2) &  ((v1_funct_2 k33_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) &  ((v1_binop_1 k33_binop_2 k1_numbers) & (v2_binop_1 k33_binop_2 k1_numbers)) ) ) ).
tt(fc3_bintree1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v3_trees_2 C) & (v2_bintree1 C)) ) ) ) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v3_trees_2 D) & (v2_bintree1 D)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k6_trees_4 B C D)) &  ((v5_relat_1 (k6_trees_4 B C D) A) &  ((v1_funct_1 (k6_trees_4 B C D)) &  ((v1_finset_1 (k6_trees_4 B C D)) &  ((v3_trees_2 (k6_trees_4 B C D)) & (v2_bintree1 (k6_trees_4 B C D))) ) ) ) ) ) ) ).
tt(fc3_bintree2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  => (v2_funct_1 (k2_bintree2 A B))) ) ).
tt(fc3_bor_cant,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k4_bor_cant A)) &  ((v2_funct_1 (k4_bor_cant A)) & (v1_funct_2 (k4_bor_cant A) k5_numbers k5_numbers)) ) ) ) ).
tt(fc3_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_struct_0 B) &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v2_struct_0 (k2_borsuk_1 A B)) &  ((v1_pre_topc (k2_borsuk_1 A B)) & (v2_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(fc3_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v3_funct_1 C) & (m1_borsuk_2 C A B B)) ) )  => (v3_funct_1 (k2_borsuk_2 A B B C))) ) ).
tt(fc3_borsuk_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_pre_topc (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) &  ((v2_pre_topc (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) & (v1_compts_1 (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C))))) ) ) ) ).
tt(fc3_borsuk_5,ax, (~ (v1_xboole_0 k1_borsuk_5)) ).
tt(fc3_borsuk_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (m1_pre_topc A (k2_borsuk_1 k5_topmetr k5_topmetr)))  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_xreal_0 (k1_xtuple_0 B))) ) ).
tt(fc3_borsuk_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ((v1_relat_1 (k1_borsuk_7 A B C D E F)) & (v1_funct_1 (k1_borsuk_7 A B C D E F))) ) ).
tt(fc3_brouwer,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C)) ) )  =>  (~ (v2_struct_0 (k2_brouwer A B C))) ) ) ).
tt(fc3_bspace,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k8_bspace A))) ) ).
tt(fc3_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((v1_relat_1 (k8_bvfunc_1 A B)) &  ((v1_funct_1 (k8_bvfunc_1 A B)) & (v1_margrel1 (k8_bvfunc_1 A B))) ) ) ) ).
tt(fc3_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k6_c0sp1 A)))  &  ((v3_c0sp1 (k6_c0sp1 A) (k12_funcsdom A)) & (v4_c0sp1 (k6_c0sp1 A) (k12_funcsdom A))) ) ) ) ).
tt(fc3_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_c0sp1 (k2_c0sp2 A) (k12_funcsdom (u1_struct_0 A))) & (v4_c0sp1 (k2_c0sp2 A) (k12_funcsdom (u1_struct_0 A)))) ) ) ).
tt(fc3_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v2_cantor_1 (u1_pre_topc A) A)) ) ).
tt(fc3_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_card_1 (k3_card_1 A))) ) ).
tt(fc3_card_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v2_finset_1 A)) ) )  => (v1_finset_1 (k4_card_3 A))) ) ).
tt(fc3_card_3,ax, (! [A:$i,B:$i] :  ((v1_card_1 B) => (v1_card_3 (k16_funcop_1 A B))) ) ).
tt(fc3_card_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  & (v1_card_1 B))  =>  ( (~ (v1_finset_1 (k1_card_2 A B)))  & (v1_card_1 (k1_card_2 A B))) ) ) ).
tt(fc3_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  ( (~ (v1_finset_1 (k6_card_fil A)))  & (v1_card_1 (k6_card_fil A))) ) ) ).
tt(fc3_cardfin2,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k2_cardfin2 A))) ) ).
tt(fc3_card_fin,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k1_yellow20 A B)) &  ((v1_funct_1 (k1_yellow20 A B)) & (v2_finset_1 (k1_yellow20 A B))) ) ) ) ).
tt(fc3_cat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_cat_1 A) & (l1_cat_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k2_cat_1 A B B))) ) ) ).
tt(fc3_cat_4,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k23_cat_4 A B)))  &  ((v7_struct_0 (k23_cat_4 A B)) &  ( (~ (v11_struct_0 (k23_cat_4 A B)))  &  ((v15_struct_0 (k23_cat_4 A B)) & (v5_cat_4 (k23_cat_4 A B))) ) ) ) ) ).
tt(fc3_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k2_catalg_1 A)))  &  ( (~ (v11_struct_0 (k2_catalg_1 A)))  & (v1_msualg_1 (k2_catalg_1 A))) ) ) ) ).
tt(fc3_cayley,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k1_cayley A))) ) ).
tt(fc3_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k3_cc0sp1 A)))  &  ((v13_algstr_0 (k3_cc0sp1 A)) &  ((v2_rlvect_1 (k3_cc0sp1 A)) &  ((v3_rlvect_1 (k3_cc0sp1 A)) &  ((v4_rlvect_1 (k3_cc0sp1 A)) &  ((v3_group_1 (k3_cc0sp1 A)) &  ((v5_group_1 (k3_cc0sp1 A)) &  ((v1_vectsp_1 (k3_cc0sp1 A)) &  ((v3_vectsp_1 (k3_cc0sp1 A)) &  ((v2_clvect_1 (k3_cc0sp1 A)) &  ((v3_clvect_1 (k3_cc0sp1 A)) &  ((v4_clvect_1 (k3_cc0sp1 A)) &  ((v5_clvect_1 (k3_cc0sp1 A)) & (v2_cfuncdom (k3_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc3_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_c0sp1 (k2_cc0sp2 A) (k8_cfuncdom (u1_struct_0 A))) & (v1_cc0sp1 (k2_cc0sp2 A) (k8_cfuncdom (u1_struct_0 A)))) ) ) ).
tt(fc3_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v3_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) &  ((v1_partfun1 (k1_valued_1 A B) k2_numbers) & (v3_cfdiff_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc3_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_group_1 (k7_cfuncdom A))) ) ).
tt(fc3_cgames_1,ax,(v1_xboole_0 (k6_cgames_1 k3_cgames_1))).
tt(fc3_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_subset_1 B k5_numbers) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 B A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B A) A)))) ) ) ) )  =>  ((v3_msualg_1 (k7_circcomb B A D C) (k5_circcomb D C)) &  ((v4_msualg_1 (k7_circcomb B A D C) (k5_circcomb D C)) & (v5_circcmb3 (k7_circcomb B A D C) (k5_circcomb D C))) ) ) ) ).
tt(fc3_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m3_msaterm C A B) & (m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C)))) ) )  => (v6_trees_3 (k1_msualg_1 (k1_circtrm1 A B C) D))) ) ).
tt(fc3_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v1_classes2 (k1_classes1 A))) ) ).
tt(fc3_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_clopban1 A B)))  & (v4_funct_1 (k5_clopban1 A B))) ) ) ).
tt(fc3_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k7_clopban2 A)) &  ((v2_rlvect_1 (k7_clopban2 A)) &  ((v3_rlvect_1 (k7_clopban2 A)) &  ((v4_rlvect_1 (k7_clopban2 A)) &  ((v3_group_1 (k7_clopban2 A)) &  ((v4_vectsp_1 (k7_clopban2 A)) & (v5_vectsp_1 (k7_clopban2 A))) ) ) ) ) ) ) ) ).
tt(fc3_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_clopban3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_clopban3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_normsp_1 A B C)) &  ((v1_funct_2 (k3_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (v1_clopban3 (k3_normsp_1 A B C) A)) ) ) ) ).
tt(fc3_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_xboole_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((v1_relat_1 (k4_closure2 A B C)) &  ((v3_relat_1 (k4_closure2 A B C)) &  ((v4_relat_1 (k4_closure2 A B C) A) &  ((v1_funct_1 (k4_closure2 A B C)) & (v1_partfun1 (k4_closure2 A B C) A)) ) ) ) ) ) ).
tt(fc3_cohsp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k1_cohsp_1 A)))  &  ((v1_classes1 (k1_cohsp_1 A)) & (v1_coh_sp (k1_cohsp_1 A))) ) ) ).
tt(fc3_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k5_coh_sp A))) ) ).
tt(fc3_compact1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v9_pre_topc A) &  ((v5_compact1 A) & (l1_pre_topc A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v5_compact1 (k1_pre_topc A B))) ) ) ).
tt(fc3_complex1,ax, ((v1_xboole_0 (k16_complex1 k6_numbers)) & (v1_xreal_0 (k16_complex1 k6_numbers))) ).
tt(fc3_complfld,ax, ( (~ (v6_struct_0 k1_complfld))  &  ((v13_algstr_0 k1_complfld) &  ((v33_algstr_0 k1_complfld) &  ((v36_algstr_0 k1_complfld) &  ((v3_group_1 k1_complfld) &  ((v5_group_1 k1_complfld) &  ((v3_vectsp_1 k1_complfld) &  ((v5_vectsp_1 k1_complfld) &  ((v6_vectsp_1 k1_complfld) &  ((v2_rlvect_1 k1_complfld) &  ((v3_rlvect_1 k1_complfld) & (v4_rlvect_1 k1_complfld)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc3_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v8_metric_1 A) & (l1_metric_1 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_metric_1 (k3_compl_sp A B C)) & (v8_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(fc3_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc3_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) &  ((v1_finset_1 (k4_compos_1 A)) &  ((v3_compos_1 (k4_compos_1 A) A) & (v4_compos_1 (k4_compos_1 A) A)) ) ) ) ) ) ) ) ).
tt(fc3_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  ((v1_relat_1 (k4_compos_1 A)) &  ((v4_relat_1 (k4_compos_1 A) k5_numbers) &  ((v5_relat_1 (k4_compos_1 A) (u1_compos_1 A)) &  ((v1_funct_1 (k4_compos_1 A)) &  ((v1_finset_1 (k4_compos_1 A)) & (v1_compos_2 (k4_compos_1 A) A)) ) ) ) ) ) ) ).
tt(fc3_compts_1,ax, (! [A:$i] : (v8_pre_topc (k1_compts_1 (k1_tarski A)))) ).
tt(fc3_comput_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v2_margrel1 (k3_relat_1 A B))) ) ) ).
tt(fc3_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k1_comseq_2 A)) &  ((v1_funct_2 (k1_comseq_2 A) k5_numbers k2_numbers) & (v2_comseq_2 (k1_comseq_2 A))) ) ) ) ).
tt(fc3_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_funct_1 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A))) &  ((v1_funct_2 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A)) k5_numbers k1_numbers) & (v7_valued_0 (k2_series_1 (k55_valued_1 k5_numbers k2_numbers A)))) ) ) ) ).
tt(fc3_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (~ (v1_xboole_0 (k7_conlat_1 A))) ) ) ).
tt(fc3_conlat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((v4_conlat_1 (k8_conlat_2 A B) (k7_conlat_2 A)) &  ( (~ (v5_conlat_1 (k8_conlat_2 A B) (k7_conlat_2 A)))  & (v7_conlat_1 (k8_conlat_2 A B) (k7_conlat_2 A))) ) ) ) ).
tt(fc3_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (~ (v1_xboole_0 (k10_convex4 A))) ) ) ).
tt(fc3_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v3_rlvect_1 B) & (l1_rlvect_1 B)) ) )  => (v3_rlvect_1 (k3_convfun1 A B))) ) ).
tt(fc3_csspace3,ax, ((v13_algstr_0 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v2_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v3_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v4_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v1_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v2_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v3_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v4_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) & (v5_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3)))) ) ) ) ) ) ) ) ).
tt(fc3_csspace4,ax, ((v13_algstr_0 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v2_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v3_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v4_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v1_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v2_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v3_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v4_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) & (v5_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4)))) ) ) ) ) ) ) ) ).
tt(fc3_csspace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k2_numbers)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_csspace A B C D E)))  & (v1_csspace (g1_csspace A B C D E))) ) ) ).
tt(fc3_descip_1,ax, ((v1_funct_1 k28_descip_1) &  ((v1_funct_2 k28_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (v3_funct_2 k28_descip_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))) ) ).
tt(fc3_dickson,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k5_dickson A)) & (v4_orders_2 (k5_dickson A))) ) ) ).
tt(fc3_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k5_diff_1 A B)) & (v1_funct_2 (k5_diff_1 A B) k1_numbers k1_numbers)) ) ) ).
tt(fc3_dilworth,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  ((v1_xboole_0 (k2_dilworth A)) & (v7_ordinal1 (k2_dilworth A))) ) ) ).
tt(fc3_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_funct_1 (k7_dist_1 A)) &  ((v2_funct_1 (k7_dist_1 A)) & (v1_funct_2 (k7_dist_1 A) (k6_dist_1 A) (k3_finseq_2 k1_numbers))) ) ) ) ).
tt(fc3_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_dtconstr A) & (l1_lang1 A)) )  =>  (~ (v1_xboole_0 (k4_dtconstr A))) ) ) ).
tt(fc3_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v2_struct_0 (k1_uniroots (k9_int_3 A))))  &  ((v15_algstr_0 (k1_uniroots (k9_int_3 A))) &  ((v2_group_1 (k1_uniroots (k9_int_3 A))) &  ((v3_group_1 (k1_uniroots (k9_int_3 A))) & (v1_gr_cy_1 (k1_uniroots (k9_int_3 A)))) ) ) ) ) ) ).
tt(fc3_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k6_endalg A B)))  & (v22_algstr_0 (k6_endalg A B))) ) ) ).
tt(fc3_ens_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k2_ens_1 A)))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc3_eqrel_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (~ (v1_xboole_0 (k7_eqrel_1 A B))) ) ) ).
tt(fc3_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v3_msualg_1 (k3_equation A) A) &  ((v4_msualg_1 (k3_equation A) A) & (v2_msafree (k3_equation A) A)) ) ) ) ).
tt(fc3_euclid_7,ax,(v3_euclid_7 (k1_tarski (k12_finseq_1 k5_numbers 1)))).
tt(fc3_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ( (~ (v2_xxreal_0 B))  & (v1_xreal_0 B)) )  => (v1_xboole_0 (k3_xxreal_1 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)))) ) ).
tt(fc3_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  => (v1_xboole_0 (k12_euclid (k8_euclid A B B)))) ) ).
tt(fc3_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v1_xboole_0 (k5_euclidlp A))) ) ) ).
tt(fc3_exchsort,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_tarski (k4_tarski A B))) &  ((v1_funct_1 (k1_tarski (k4_tarski A B))) &  ((v4_valued_0 (k1_tarski (k4_tarski A B))) & (v1_exchsort (k1_tarski (k4_tarski A B)))) ) ) ) ) ).
tt(fc3_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k1_extpro_1 A) A) & (v3_extpro_1 (k1_extpro_1 A) A)) ) ) ).
tt(fc3_facirc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xtuple_0 A))  &  ( (~ (v1_xtuple_0 B))  &  (~ (v1_xtuple_0 C)) ) )  =>  (~ (v1_facirc_1 (k1_enumset1 A B C))) ) ) ).
tt(fc3_facirc_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  => (v1_xtuple_0 (k5_facirc_2 A B C))) ) ).
tt(fc3_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) & (v1_fcont_1 (k1_valued_1 A B))) ) ) ).
tt(fc3_fcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v2_rcomp_1 (k2_limfunc1 A))) ) ).
tt(fc3_fib_num2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v1_finset_1 B) &  ((v1_setfam_1 B) & (v6_membered B)) ) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_finseq_1 (k5_relat_1 A B))) ) ) ).
tt(fc3_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v2_xxreal_0 (k1_fib_num3 A))) ) ).
tt(fc3_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v2_struct_0 (k6_filter_0 A B)))  &  ((v3_lattices (k6_filter_0 A B)) & (v10_lattices (k6_filter_0 A B))) ) ) ) ).
tt(fc3_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  ((v3_lattices (k7_filter_1 A B)) & (v10_lattices (k7_filter_1 A B))) ) ) ).
tt(fc3_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v21_lattices (k3_filter_2 A B) (k1_lattice2 A))) ) ).
tt(fc3_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (k1_finseq_1 A))) ) ).
tt(fc3_finseq_2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (v1_finseq_1 (k2_funcop_1 (k2_finseq_1 A) B))) ) ).
tt(fc3_finseq_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_finset_1 B))  => (v1_finset_1 (k4_finseq_2 A B))) ) ).
tt(fc3_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v1_finseq_1 (k7_finseq_4 A B C D))) ).
tt(fc3_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ((v2_funct_1 C) & (m1_finseq_1 C B)) ) )  =>  ((v1_relat_1 (k16_finseq_1 A C)) &  ((v1_funct_1 (k16_finseq_1 A C)) &  ((v2_funct_1 (k16_finseq_1 A C)) & (v1_finseq_1 (k16_finseq_1 A C))) ) ) ) ) ).
tt(fc3_finseq_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k5_relat_1 A (k2_finseq_1 B))) & (v1_finseq_1 (k5_relat_1 A (k2_finseq_1 B)))) ) ) ).
tt(fc3_finset_1,ax, (! [A:$i,B:$i,C:$i] : (v1_finset_1 (k1_enumset1 A B C))) ).
tt(fc3_fintopo6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_fintopo6 (k5_finseq_1 B) A)) ) ).
tt(fc3_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k4_xboole_0 (k3_finseq_2 A) (k1_tarski k1_xboole_0)))) ) ) ).
tt(fc3_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ( (~ (v8_struct_0 A))  & (l4_struct_0 A)) )  =>  (~ (v1_finset_1 (k8_relat_1 (k14_fomodel1 A) (k6_domain_1 k5_numbers k6_numbers)))) ) ) ).
tt(fc3_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k1_fomodel1 A))) ) ) ).
tt(fc3_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v7_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v3_card_1 C (k1_int_2 (k19_fomodel1 A B))) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) )  => (v15_fomodel1 (k1_fomodel3 A B C) A)) ) ).
tt(fc3_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_funct_2 A B))) => (v1_relat_1 (k3_tarski C))) ) ).
tt(fc3_frechet,ax, ((v2_pre_topc k3_topmetr) & (v1_frechet k3_topmetr)) ).
tt(fc3_freealg,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  =>  ((v1_lang1 (k3_freealg A B)) &  ((v2_dtconstr (k3_freealg A B)) & (v3_dtconstr (k3_freealg A B))) ) ) ) ).
tt(fc3_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  & (m1_subset_1 F C)) ) ) )  =>  ( (~ (v2_struct_0 (g3_fsm_1 A B C D E F)))  &  ((v8_struct_0 (g3_fsm_1 A B C D E F)) & (v3_fsm_1 (g3_fsm_1 A B C D E F) A B)) ) ) ) ).
tt(fc3_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_tarski C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski C D) B)))) ) ) )  =>  ( (~ (v2_struct_0 (k1_fsm_2 A B C D E)))  &  ((v5_fsm_2 (k1_fsm_2 A B C D E) A) & (v6_fsm_2 (k1_fsm_2 A B C D E) A B)) ) ) ) ).
tt(fc3_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l1_rewrite3 C B)) ) ) )  =>  ((v8_struct_0 (k1_fsm_3 A B C)) & (v1_rewrite3 (k1_fsm_3 A B C) (k9_flang_1 A))) ) ) ).
tt(fc3_funcop_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 B) => (v1_xboole_0 (k2_funcop_1 B A))) ) ).
tt(fc3_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k12_funcsdom A)))  & (v1_funcsdom (k12_funcsdom A))) ) ) ).
tt(fc3_funct_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) & (v1_funct_1 (k4_relat_1 A))) ) ).
tt(fc3_funct_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  => (v1_xboole_0 (k1_funct_2 A B))) ) ).
tt(fc3_funct_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_funct_1 B)) ) )  =>  ((v1_relat_1 (k15_funct_3 A B)) &  ((v1_funct_1 (k15_funct_3 A B)) & (v2_funct_1 (k15_funct_3 A B))) ) ) ) ).
tt(fc3_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  (~ (v1_xboole_0 B)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) &  (~ (v1_xboole_0 (k1_funct_4 A B))) ) ) ) ) ).
tt(fc3_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_funcop_1 (k5_finseq_1 A))) ) ).
tt(fc3_funct_8,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos k1_numbers k1_numbers) & (v4_funct_8 k19_sin_cos k1_numbers k1_numbers)) ) ).
tt(fc3_functor0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_xboole_0 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k15_funct_3 B A)) &  ((v1_funct_1 (k15_funct_3 B A)) & (v1_xboole_0 (k15_funct_3 B A))) ) ) ) ).
tt(fc3_fvaluat1,ax, ((v1_xreal_0 k8_mesfunc1) &  ((v2_xxreal_0 k8_mesfunc1) & (v1_fvaluat1 k8_mesfunc1)) ) ).
tt(fc3_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc3_gate_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k2_gate_1 A B))) ) ) ).
tt(fc3_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (~ (v1_xboole_0 (k3_gcd_1 A))) ) ) ).
tt(fc3_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v1_finset_1 (k6_glib_000 A))) ) ).
tt(fc3_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (v5_glib_001 (k2_glib_001 A B D C) A)) ) ).
tt(fc3_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v1_glib_000 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc3_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))))  => (v1_finset_1 (k1_xtuple_0 B))) ) ).
tt(fc3_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_005 B A) & (v7_ordinal1 C)) )  => (v4_relat_1 (k1_funct_1 B C) (k7_glib_000 A))) ) ).
tt(fc3_goboard2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k1_numbers))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 B k1_numbers)) )  =>  ( (~ (v3_relat_1 (k1_goboard2 A B)))  &  ((v1_matrix_1 (k1_goboard2 A B)) &  ((v2_goboard1 (k1_goboard2 A B)) & (v3_goboard1 (k1_goboard2 A B))) ) ) ) ) ).
tt(fc3_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k3_graph_3 A B C))) ) ).
tt(fc3_graph_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  => (v1_finset_1 (k6_graph_5 A B))) ) ).
tt(fc3_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_cat_1 (k5_grcat_1 A B))) ) ).
tt(fc3_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) & (v2_group_1 (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)))) ) ) ).
tt(fc3_grnilp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_grnilp_1 A) & (l3_algstr_0 A)) ) ) ) )  &  ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) ) )  => (v1_grnilp_1 (k5_group_6 A B))) ) ).
tt(fc3_groeb_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v7_algstr_0 B) &  ((v5_vectsp_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_2 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom7 C A B) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  &  ( (~ (v9_struct_0 D B))  & (m1_subset_1 D (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k5_polynom7 A B C D)) &  ((v1_funct_2 (k5_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom7 (k5_polynom7 A B C D) A B)) ) ) ) ).
tt(fc3_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_groeb_3 A B C D k6_numbers)) &  ((v1_funct_2 (k5_groeb_3 A B C D k6_numbers) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k5_groeb_3 A B C D k6_numbers) (k15_pre_poly A) C) & (v3_polynom7 (k5_groeb_3 A B C D k6_numbers) A C)) ) ) ) ) ).
tt(fc3_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C B) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k13_group_10 A B D C))) ) ) ).
tt(fc3_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v4_group_7 B A)) ) ) ) )  & (m1_subset_1 C A)) )  => (v5_group_1 (k1_funct_1 B C))) ) ).
tt(fc3_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_finseqop (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc3_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v8_struct_0 (k6_group_2 A)) & (v15_algstr_0 (k6_group_2 A))) ) ) ).
tt(fc3_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v7_struct_0 (k6_group_2 A)) & (v15_algstr_0 (k6_group_2 A))) ) ) ).
tt(fc3_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v2_group_7 B A)) ) ) ) )  =>  ((v15_algstr_0 (k2_group_7 A B)) & (v2_group_1 (k2_group_7 A B))) ) ) ).
tt(fc3_group_9,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (~ (v1_xboole_0 (k6_group_9 A B))) ) ) ).
tt(fc3_groupp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  &  ( ((v1_groupp_1 C A B) & (m1_subset_1 C (u1_struct_0 B)))  &  ((v1_groupp_1 D A B) & (m1_subset_1 D (u1_struct_0 B))) ) ) )  => (v1_groupp_1 (k6_algstr_0 B C D) A B)) ) ).
tt(fc3_hahnban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k7_hahnban1 A B)) &  ((v1_funct_2 (k7_hahnban1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v2_hahnban1 (k7_hahnban1 A B) A B)) ) ) ) ).
tt(fc3_hausdorf,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) ) )  =>  ((v1_funct_1 (k5_weierstr A B)) &  ((v1_funct_2 (k5_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k5_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ).
tt(fc3_heyting3,ax, (! [A:$i,B:$i] :  ((v3_orders_2 (k1_heyting3 A B)) &  ((v4_orders_2 (k1_heyting3 A B)) & (v5_orders_2 (k1_heyting3 A B))) ) ) ).
tt(fc3_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_hilbasis A B)) &  ((v1_funct_2 (k6_hilbasis A B) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (v1_group_6 (k6_hilbasis A B) (k14_polynom3 (k11_polynom1 B A)) (k11_polynom1 (k2_nat_1 B 1) A))) ) ) ) ).
tt(fc3_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) => (v6_hilbert1 (k5_hilbert1 A))) ) ).
tt(fc3_hilbert2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((v1_relat_1 (k6_trees_4 A B C)) &  ((v1_funct_1 (k6_trees_4 A B C)) &  ( (~ (v1_zfmisc_1 (k6_trees_4 A B C)))  & (v3_trees_2 (k6_trees_4 A B C))) ) ) ) ) ).
tt(fc3_hilbert3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_funct_1 B)) ) )  =>  ((v1_relat_1 (k15_funct_3 A B)) &  ((v1_funct_1 (k15_funct_3 A B)) & (v2_funct_1 (k15_funct_3 A B))) ) ) ) ).
tt(fc3_idea_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  & (m1_matrix_1 D k5_numbers B 6)) ) )  =>  ((v1_relat_1 (k17_idea_1 A B C D)) &  ((v1_funct_1 (k17_idea_1 A B C D)) &  ((v1_funcop_1 (k17_idea_1 A B C D)) & (v1_finseq_1 (k17_idea_1 A B C D))) ) ) ) ) ).
tt(fc3_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  => (v3_ideal_1 (k1_tarski (k4_struct_0 A)) A)) ) ).
tt(fc3_index_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_index_1 B)) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v1_index_1 (k3_relat_1 A B))) ) ) ).
tt(fc3_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) & (v1_int_1 (k4_xcmplx_0 A))) ) ) ).
tt(fc3_int_3,ax,(v4_vectsp_1 k1_int_3)).
tt(fc3_int_4,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_partfun1 (k1_int_4 A) k4_numbers)) ) ).
tt(fc3_int_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_rfinseq B A)) &  ((v5_relat_1 (k1_rfinseq B A) k4_numbers) &  ((v1_funct_1 (k1_rfinseq B A)) & (v1_finseq_1 (k1_rfinseq B A))) ) ) ) ) ).
tt(fc3_integr16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((v1_funct_1 (k3_comseq_3 B)) & (v1_funct_2 (k3_comseq_3 B) A k1_numbers)) ) ) ).
tt(fc3_integra1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (m1_integra1 C A)) )  =>  (~ (v1_xboole_0 (k5_integra1 A B C))) ) ) ).
tt(fc3_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  =>  (~ (v1_xboole_0 (k9_interva1 A B C))) ) ) ).
tt(fc3_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v8_intpro_1 (k7_intpro_1 A))) ) ).
tt(fc3_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v6_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v5_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc3_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (v1_xboole_0 (k2_jordan10 A))) ) ) ).
tt(fc3_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k7_relat_1 k4_pscomp_1 (k7_topreal1 A)))) ) ) ).
tt(fc3_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v1_convex1 (k6_topreal1 A) (k15_euclid 2))) ) ).
tt(fc3_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v2_funct_1 (k1_jordan1e A B)) &  ((v1_topreal1 (k1_jordan1e A B)) &  ((v2_topreal1 (k1_jordan1e A B)) & (v3_topreal1 (k1_jordan1e A B))) ) ) ) ) ).
tt(fc3_jordan1g,ax, (! [A:$i,B:$i] :  ( ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  & (m1_subset_1 B k5_numbers))  => (v2_goboard5 (k2_jordan1e A B))) ) ).
tt(fc3_jordan1h,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v5_valued_0 (k7_pre_poly k1_numbers A k1_jordan1h))) ) ).
tt(fc3_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v2_compts_1 (k3_jordan19 A) (k15_euclid 2))) ) ).
tt(fc3_jordan23,ax, (! [A:$i,B:$i] : (v3_jordan23 (k10_finseq_1 A B))) ).
tt(fc3_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v3_connsp_1 (k2_struct_0 (k15_euclid A)) (k15_euclid A))) ) ).
tt(fc3_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)))) ) ).
tt(fc3_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ((m1_kolmog01 D A B C) &  ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A))) ) ) ) )  => (v2_finsub_1 (k7_kolmog01 B C A E D))) ) ).
tt(fc3_kurato_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_finset_1 (k5_kurato_1 A B))) ) ).
tt(fc3_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v5_rltopsp1 (k15_euclid A)) & (v1_frechet (k15_euclid A))) ) ) ).
tt(fc3_lang1,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k8_lang1 A B)))  & (v2_lang1 (k8_lang1 A B))) ) ).
tt(fc3_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  =>  ((v1_funct_1 (u2_lattices A)) &  ((v1_funct_2 (u2_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_binop_1 (u2_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc3_lattice3,ax, (! [A:$i] :  ((v3_lattices (k1_lattice3 A)) & (v17_lattices (k1_lattice3 A))) ) ).
tt(fc3_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v19_waybel_0 C A B) &  ((v20_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A B C)) &  ((v4_yellow_0 (k1_yellow_2 A B C) B) &  ((v5_yellow_0 (k1_yellow_2 A B C) B) & (v6_yellow_0 (k1_yellow_2 A B C) B)) ) ) ) ) ).
tt(fc3_lattice8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  =>  (~ (v1_xboole_0 (k7_lattice8 A B C))) ) ) ).
tt(fc3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices A B C)))  & (v3_lattices (g3_lattices A B C))) ) ) ).
tt(fc3_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))))  => (v1_finset_1 (k2_xtuple_0 B))) ) ).
tt(fc3_lfuzzy_0,ax, ((v1_orders_2 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1))) &  ((v1_lfuzzy_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1))) & (v2_lfuzzy_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)))) ) ).
tt(fc3_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) &  ((v2_lfuzzy_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) &  ((v2_lfuzzy_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) ) )  =>  ((v5_relat_1 (k2_fuzzy_1 (k2_zfmisc_1 A A) B C) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k2_fuzzy_1 (k2_zfmisc_1 A A) B C)) &  ((v1_funct_2 (k2_fuzzy_1 (k2_zfmisc_1 A A) B C) (k2_zfmisc_1 A A) k1_numbers) & (v2_lfuzzy_1 (k2_fuzzy_1 (k2_zfmisc_1 A A) B C) A)) ) ) ) ) ).
tt(fc3_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ((v8_algstr_0 (k13_lmod_7 A B C)) &  ((v13_algstr_0 (k13_lmod_7 A B C)) &  ((v2_rlvect_1 (k13_lmod_7 A B C)) &  ((v3_rlvect_1 (k13_lmod_7 A B C)) & (v4_rlvect_1 (k13_lmod_7 A B C))) ) ) ) ) ) ).
tt(fc3_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k7_lopban_1 A B)))  & (v4_funct_1 (k7_lopban_1 A B))) ) ) ).
tt(fc3_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k7_lopban_2 A)) &  ((v2_rlvect_1 (k7_lopban_2 A)) &  ((v3_rlvect_1 (k7_lopban_2 A)) &  ((v4_rlvect_1 (k7_lopban_2 A)) &  ((v3_group_1 (k7_lopban_2 A)) &  ((v3_vectsp_1 (k7_lopban_2 A)) &  ((v5_vectsp_1 (k7_lopban_2 A)) & (v6_vectsp_1 (k7_lopban_2 A))) ) ) ) ) ) ) ) ) ).
tt(fc3_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_lopban_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_lopban_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_normsp_1 A B C)) &  ((v1_funct_2 (k3_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (v1_lopban_3 (k3_normsp_1 A B C) A)) ) ) ) ).
tt(fc3_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (~ (v1_xboole_0 (k7_lopclset A))) ) ) ).
tt(fc3_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k10_lpspace1 A B C)))  &  ((v1_rlvect_1 (k10_lpspace1 A B C)) &  ((v2_rlvect_1 (k10_lpspace1 A B C)) &  ((v3_rlvect_1 (k10_lpspace1 A B C)) &  ((v4_rlvect_1 (k10_lpspace1 A B C)) &  ((v5_rlvect_1 (k10_lpspace1 A B C)) &  ((v6_rlvect_1 (k10_lpspace1 A B C)) &  ((v7_rlvect_1 (k10_lpspace1 A B C)) & (v8_rlvect_1 (k10_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(fc3_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v1_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v2_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v3_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v4_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v5_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v6_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v7_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) & (v8_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D))))) ) ) ) ) ) ) ) ) ).
tt(fc3_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A B (k8_cqc_lang A C B)) A)) ) ).
tt(fc3_margrel1,ax, (! [A:$i] : (v1_xboolean (k11_margrel1 A))) ).
tt(fc3_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_setwiseo (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc3_matrix13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ((v13_algstr_0 (k6_prvect_1 A B)) &  ((v2_rlvect_1 (k6_prvect_1 A B)) &  ((v3_rlvect_1 (k6_prvect_1 A B)) &  ((v4_rlvect_1 (k6_prvect_1 A B)) & (v7_vectsp_1 (k6_prvect_1 A B) A)) ) ) ) ) ) ).
tt(fc3_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k13_matrix_2 A)))  & (v15_algstr_0 (k13_matrix_2 A))) ) ) ).
tt(fc3_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k4_matrlin A B C D E)) &  ((v1_funct_2 (k4_matrlin A B C D E) (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 (k4_matrlin A B C D E) B C) & (v1_mod_2 (k4_matrlin A B C D E) A B C)) ) ) ) ) ).
tt(fc3_matroid0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k3_xboole_0 C B) A)) ) ).
tt(fc3_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k1_numbers))) )  =>  ( (~ (v3_relat_1 (k4_matrix_1 k1_numbers A)))  & (v1_matrix_1 (k4_matrix_1 k1_numbers A))) ) ) ).
tt(fc3_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A))  =>  ((v1_funct_1 (k3_matrtop1 A A B)) &  ((v1_funct_2 (k3_matrtop1 A A B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v1_topreal9 (k3_matrtop1 A A B) A)) ) ) ) ).
tt(fc3_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ((v3_membered A) & (v4_xxreal_2 A))  &  ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  => (v3_xxreal_2 (k23_member_1 A B))) ) ).
tt(fc3_measure6,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  (~ (v1_xboole_0 (k7_relat_1 C A))) ) ) ).
tt(fc3_member_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k4_member_1 A)) & (v2_membered (k4_member_1 A))) ) ) ).
tt(fc3_membered,ax,(v3_membered k1_numbers)).
tt(fc3_memstr_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v2_memstr_0 B A) & (l1_memstr_0 B A)) )  =>  ((v1_relat_1 (k2_memstr_0 A B)) &  ((v2_relat_1 (k2_memstr_0 A B)) &  ((v4_relat_1 (k2_memstr_0 A B) (u1_struct_0 B)) &  ((v1_funct_1 (k2_memstr_0 A B)) & (v1_partfun1 (k2_memstr_0 A B) (u1_struct_0 B))) ) ) ) ) ) ).
tt(fc3_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) ) )  =>  ((v1_funct_1 (k11_mesfun7c A B)) &  ((v1_funct_2 (k11_mesfun7c A B) k5_numbers (k4_partfun1 A k1_numbers)) & (v1_mesfunc8 (k11_mesfun7c A B) A k1_numbers)) ) ) ) ).
tt(fc3_mesfunc7,ax, ((v1_funct_1 k1_mesfunc7) &  ((v1_funct_2 k1_mesfunc7 (k2_zfmisc_1 k7_numbers k7_numbers) k7_numbers) & (v1_setwiseo k1_mesfunc7 k7_numbers)) ) ).
tt(fc3_metric_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_metric_1 A)))  & (v1_metric_1 (k6_metric_1 A))) ) ) ).
tt(fc3_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v3_pcomps_1 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc3_mfold_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  (~ (v2_struct_0 (k1_mfold_1 A B C))) ) ) ).
tt(fc3_mfold_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  =>  ((v1_funct_1 (k1_mfold_2 A B)) &  ((v1_funct_2 (k1_mfold_2 A B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k1_mfold_2 A B) (k15_euclid A) k3_topmetr)) ) ) ) ).
tt(fc3_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (~ (v1_xboole_0 (k10_midsp_1 A))) ) ) ).
tt(fc3_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v1_funct_1 (k5_midsp_2 A)) &  ((v1_funct_2 (k5_midsp_2 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 (k15_midsp_1 A))) & (v1_midsp_2 (k5_midsp_2 A) A (k15_midsp_1 A))) ) ) ) ).
tt(fc3_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (v1_mmlquery (k3_xboole_0 C B) A)) ) ).
tt(fc3_mod_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_struct_0 B)) &  ((v1_funct_2 (k3_struct_0 B) (u1_struct_0 B) (u1_struct_0 B)) & (v1_mod_2 (k3_struct_0 B) A B B)) ) ) ) ).
tt(fc3_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v4_vectsp_1 (k2_mod_4 A))) ) ) ).
tt(fc3_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  => (v1_modelc_1 (k9_modelc_1 A))) ) ).
tt(fc3_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  => (v1_modelc_2 (k6_modelc_2 A))) ) ).
tt(fc3_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ( (~ (v1_xboole_0 (k23_modelc_3 A)))  & (v1_finset_1 (k23_modelc_3 A))) ) ) ).
tt(fc3_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_finset_1 (k3_moebius1 A)) & (v1_setfam_1 (k3_moebius1 A))) ) ) ).
tt(fc3_monoid_0,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k15_monoid_0 A)))  &  ((v15_algstr_0 (k15_monoid_0 A)) & (v1_group_1 (k15_monoid_0 A))) ) ) ).
tt(fc3_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (u1_struct_0 (k9_monoid_1 A B)))) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 C))) ) ) ).
tt(fc3_msafree1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ((v1_msafree1 B A) & (l3_msualg_1 B A)) )  =>  ((v1_relat_1 (u3_msualg_1 A B)) &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) &  ((v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A)) & (v1_prob_2 (u3_msualg_1 A B))) ) ) ) ) ) ).
tt(fc3_msafree3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((v3_msualg_1 (k1_msafree3 A B) A) &  ((v2_msafree (k1_msafree3 A B) A) & (v1_msualg_6 (k1_msafree3 A B) A)) ) ) ) ).
tt(fc3_msafree,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) )  =>  ((v1_relat_1 (k2_card_3 B)) &  ((v2_relat_1 (k2_card_3 B)) & (v1_funct_1 (k2_card_3 B))) ) ) ) ).
tt(fc3_msalimit,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ((m1_msalimit C A B) & (m2_msalimit D A B C)) ) )  => (v1_msalimit (k2_msalimit A B C D) A B C)) ) ).
tt(fc3_msinst_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  ( (~ (v2_struct_0 (k4_msinst_1 A B)))  &  ((v2_altcat_1 (k4_msinst_1 A B)) &  ((v6_altcat_1 (k4_msinst_1 A B)) &  ((v11_altcat_1 (k4_msinst_1 A B)) & (v12_altcat_1 (k4_msinst_1 A B))) ) ) ) ) ) ).
tt(fc3_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_relat_1 (k2_funct_6 B)) &  ((v4_relat_1 (k2_funct_6 B) A) &  ((v1_funct_1 (k2_funct_6 B)) & (v1_partfun1 (k2_funct_6 B) A)) ) ) ) ) ).
tt(fc3_mssublat,ax, (! [A:$i] :  ( ((v2_unialg_1 A) & (l1_unialg_1 A))  =>  ((v1_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) & (v2_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A)))) ) ) ).
tt(fc3_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((v3_msualg_1 (k9_msualg_1 A) (k6_msualg_1 A)) & (v4_msualg_1 (k9_msualg_1 A) (k6_msualg_1 A))) ) ) ).
tt(fc3_msualg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_finseq_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_finseq_2 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) )  =>  ( (~ (v2_struct_0 (g1_msualg_1 A B C D)))  & (v1_msualg_1 (g1_msualg_1 A B C D))) ) ) ).
tt(fc3_msualg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) )  =>  ((v3_msualg_1 (k13_msualg_4 A B C) A) & (v4_msualg_1 (k13_msualg_4 A B C) A)) ) ) ).
tt(fc3_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_relat_1 C) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((v2_relat_1 (k7_msualg_6 A B C)) & (v4_msualg_6 (k7_msualg_6 A B C) A B)) ) ) ).
tt(fc3_mycielsk,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  ((v1_xboole_0 (k2_mycielsk A)) & (v7_ordinal1 (k2_mycielsk A))) ) ) ).
tt(fc3_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  =>  (~ (v1_xboole_0 (k2_xcmplx_0 A B))) ) ) ).
tt(fc3_nat_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_valued_0 A)) ) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k1_nat_3 A B)) &  ((v1_funct_1 (k1_nat_3 A B)) &  ((v1_finseq_1 (k1_nat_3 A B)) & (v4_valued_0 (k1_nat_3 A B))) ) ) ) ) ).
tt(fc3_nat_lat,ax, ( (~ (v2_struct_0 k3_nat_lat))  & (v3_lattices k3_nat_lat)) ).
tt(fc3_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_prvect_2 A)))  &  ( (~ (v7_struct_0 (k14_prvect_2 A)))  & (v1_normsp_1 (k14_prvect_2 A))) ) ) ) ).
tt(fc3_neckla_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ( (~ (v2_struct_0 (k1_neckla_2 A B)))  & (v1_orders_2 (k1_neckla_2 A B))) ) ) ).
tt(fc3_necklace,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  => (v3_relat_2 (u1_orders_2 A))) ) ).
tt(fc3_newton,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v7_ordinal1 B))  => (v1_xcmplx_0 (k1_newton A B))) ) ).
tt(fc3_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_nfcont_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k1_vfunct_1 k1_numbers A B C)) & (v1_nfcont_3 (k1_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc3_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) &  ((v1_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  &  ((v1_funct_1 C) &  ((v1_nfcont_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) ) )  =>  ((v1_funct_1 (k7_integr15 A k1_numbers B C)) & (v1_nfcont_4 (k7_integr15 A k1_numbers B C) A)) ) ) ).
tt(fc3_normform,ax, (! [A:$i] :  (~ (v1_xboole_0 (k8_normform A))) ) ).
tt(fc3_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v8_pre_topc (k4_normsp_2 A)) & (v5_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(fc3_numbers,ax, (~ (v1_xboole_0 k3_numbers)) ).
tt(fc3_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k6_openlatt A)))  &  ((v10_lattices (k6_openlatt A)) & (v1_lattice2 (k6_openlatt A))) ) ) ) ).
tt(fc3_oposet_1,ax, ( (~ (v2_struct_0 k2_oposet_1))  & (v3_qmax_1 k2_oposet_1)) ).
tt(fc3_orders_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) &  ((v1_orders_1 (k4_relat_1 A)) & (v2_orders_1 (k4_relat_1 A))) ) ) ).
tt(fc3_orders_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  => (v1_relat_2 (u1_orders_2 A))) ) ).
tt(fc3_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (~ (v1_xboole_0 (k1_orders_3 A A))) ) ) ).
tt(fc3_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v3_ordinal1 (k3_tarski A))) ) ).
tt(fc3_ordinal2,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 B) => (v1_ordinal2 (k2_funcop_1 A B))) ) ).
tt(fc3_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((v3_ordinal1 (k5_ordinal3 A B)) & (v7_ordinal1 (k5_ordinal3 A B))) ) ) ).
tt(fc3_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~ (v1_xboole_0 (k2_ordinal1 A))) ) ) ).
tt(fc3_ordinal5,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v5_ordinal1 B)) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 B A)) &  ((v1_funct_1 (k1_ordinal4 B A)) &  ( (~ (v1_xboole_0 (k1_ordinal4 B A)))  & (v5_ordinal1 (k1_ordinal4 B A))) ) ) ) ) ).
tt(fc3_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) => (v3_ordinal1 (k3_tarski A))) ) ).
tt(fc3_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k4_osafree A B C))) ) ) ).
tt(fc3_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ( (~ (v2_struct_0 (k1_osalg_1 A)))  &  ( (~ (v11_struct_0 (k1_osalg_1 A)))  &  ((v1_orders_3 (k1_osalg_1 A)) &  ((v3_osalg_1 (k1_osalg_1 A)) &  ((v4_osalg_1 (k1_osalg_1 A)) & (v6_osalg_1 (k1_osalg_1 A))) ) ) ) ) ) ) ).
tt(fc3_osalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ((m2_osalg_2 C A B) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  (~ (v1_xboole_0 (k8_osalg_2 A B C D))) ) ) ).
tt(fc3_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) ) ) )  =>  ((v3_msualg_1 (k16_osalg_4 A B C) A) &  ((v4_msualg_1 (k16_osalg_4 A B C) A) & (v12_osalg_1 (k16_osalg_4 A B C) A)) ) ) ) ).
tt(fc3_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ((v1_analoaf (k2_diraf A)) & (v1_translac (k2_diraf A))) ) ) ).
tt(fc3_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_parsp_1 A)))  & (v1_parsp_1 (k9_parsp_1 A))) ) ) ).
tt(fc3_partfun1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) &  ((v3_relat_2 (k4_relat_1 A)) &  ((v4_relat_2 (k4_relat_1 A)) & (v8_relat_2 (k4_relat_1 A))) ) ) ) ).
tt(fc3_partfun3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v3_xxreal_0 (k3_xcmplx_0 A (k5_xcmplx_0 A)))) ) ) ).
tt(fc3_partfun4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 B C)) &  ((v1_funct_2 (k18_valued_1 B C) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k18_valued_1 B C) A)) ) ) ) ).
tt(fc3_partit_2,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) & (v1_partit_2 (k4_relat_1 A))) ) ).
tt(fc3_pboole,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) )  =>  ((v1_relat_1 (k8_pboole A B)) &  ((v1_funct_1 (k8_pboole A B)) & (v1_funcop_1 (k8_pboole A B))) ) ) ) ).
tt(fc3_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v3_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v3_relat_2 (k2_xboole_0 C D))) ) ).
tt(fc3_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 (k1_pzfmisc1 A B)) &  ((v4_relat_1 (k1_pzfmisc1 A B) A) &  ((v1_funct_1 (k1_pzfmisc1 A B)) &  ((v1_partfun1 (k1_pzfmisc1 A B) A) & (v16_pencil_1 (k1_pzfmisc1 A B) A)) ) ) ) ) ) ).
tt(fc3_petri,ax, (! [A:$i] :  ( ((v3_petri A) & (l1_petri A))  =>  (~ (v1_xboole_0 (u2_petri A))) ) ) ).
tt(fc3_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) )  =>  ( (~ (v2_struct_0 (k1_polyalg1 A)))  &  ((v4_rlvect_1 (k1_polyalg1 A)) & (v1_polyalg1 (k1_polyalg1 A) A)) ) ) ) ).
tt(fc3_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v1_xreal_0 (k3_polyeq_1 A B C D))) ) ).
tt(fc3_polyeq_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) &  ((v1_xreal_0 E) & (v1_xreal_0 F)) ) ) ) )  => (v1_xreal_0 (k2_polyeq_2 A B C D E F))) ) ).
tt(fc3_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k6_polynom1 A B C D)) &  ((v1_funct_2 (k6_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k6_polynom1 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc3_polynom2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v4_vectsp_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc3_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k2_normsp_1 A B C)) &  ((v1_funct_2 (k2_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k2_normsp_1 A B C) A)) ) ) ) ).
tt(fc3_polynom5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_funct_1 (k4_polynom5 A B C)) &  ((v1_funct_2 (k4_polynom5 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k4_polynom5 A B C) A)) ) ) ) ).
tt(fc3_polynom6,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ( (~ (v7_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v5_vectsp_1 (k11_polynom1 A B))) ) ) ) ) ).
tt(fc3_polynom7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  & (m1_subset_1 C (u1_struct_0 B)))  =>  ((v1_funct_1 (k4_polynom7 A B C)) &  ((v1_funct_2 (k4_polynom7 A B C) (k15_pre_poly A) (u1_struct_0 B)) & (v4_polynom7 (k4_polynom7 A B C) A B)) ) ) ) ).
tt(fc3_polyred,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  ((v1_orders_2 (g1_orders_2 (k15_pre_poly A) B)) & (v16_waybel_0 (g1_orders_2 (k15_pre_poly A) B))) ) ) ).
tt(fc3_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (v4_relat_2 (k5_poset_1 A B))) ) ).
tt(fc3_pralg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) )  =>  (~ (v1_xboole_0 (k4_card_3 B))) ) ) ).
tt(fc3_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  & (m1_pralg_2 C A B)) )  =>  (~ (v1_xboole_0 (k7_pralg_2 A B C))) ) ) ).
tt(fc3_pralg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (u4_struct_0 A)) & (m1_pralg_2 D B A)) ) )  =>  ((v1_relat_1 (k1_pralg_3 A (k14_pralg_2 B A D) C)) & (v1_funct_1 (k1_pralg_3 A (k14_pralg_2 B A D) C))) ) ) ).
tt(fc3_pre_circ,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_relat_1 (k5_relat_1 A B))) ) ) ).
tt(fc3_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_relat_1 (k2_funct_7 B C D)) &  ((v4_relat_1 (k2_funct_7 B C D) A) &  ((v1_funct_1 (k2_funct_7 B C D)) & (v1_partfun1 (k2_funct_7 B C D) A)) ) ) ) ) ).
tt(fc3_prepower,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_rat_1 B))  => (v1_xreal_0 (k6_prepower A B))) ) ).
tt(fc3_pre_topc,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v2_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc3_prob_1,ax, (! [A:$i] : (v2_finsub_1 (k2_tarski k1_xboole_0 A))) ).
tt(fc3_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k2_prob_3 A C) B) &  ((v1_funct_1 (k2_prob_3 A C)) & (v1_funct_2 (k2_prob_3 A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc3_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ((v7_vectsp_1 (k6_prvect_1 A B) A) &  ((v8_vectsp_1 (k6_prvect_1 A B) A) &  ((v9_vectsp_1 (k6_prvect_1 A B) A) &  ((v10_vectsp_1 (k6_prvect_1 A B) A) & (v11_vectsp_1 (k6_prvect_1 A B) A)) ) ) ) ) ) ).
tt(fc3_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v3_rlvect_1 B) & (l2_algstr_0 B)) ) )  =>  ( (~ (v2_struct_0 (k4_prvect_3 A B)))  &  ((v8_algstr_0 (k4_prvect_3 A B)) & (v3_rlvect_1 (k4_prvect_3 A B))) ) ) ) ).
tt(fc3_pscomp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) )  => (v2_compts_1 (k3_xboole_0 B C) (k15_euclid A))) ) ).
tt(fc3_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  & (m3_pua2mss1 B A))  =>  ( (~ (v2_struct_0 (k11_pua2mss1 A B)))  &  ( (~ (v11_struct_0 (k11_pua2mss1 A B)))  & (v1_msualg_1 (k11_pua2mss1 A B))) ) ) ) ).
tt(fc3_pythtrip,ax, (! [A:$i] :  ((v1_int_1 A) => (v1_int_1 (k3_square_1 A))) ) ).
tt(fc3_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k3_qc_lang1 A))) ) ) ).
tt(fc3_qmax_1,ax, (! [A:$i] :  ((l1_qmax_1 A) =>  (~ (v1_xboole_0 (k3_qmax_1 A))) ) ) ).
tt(fc3_quatern2,ax, ((v8_algstr_0 k15_quatern2) &  ((v13_algstr_0 k15_quatern2) &  ((v2_rlvect_1 k15_quatern2) &  ((v3_rlvect_1 k15_quatern2) & (v4_rlvect_1 k15_quatern2)) ) ) ) ).
tt(fc3_quaterni,ax,(v1_quaterni k1_xcmplx_0)).
tt(fc3_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (~ (v1_xboole_0 (k7_quofield A))) ) ) ).
tt(fc3_ramsey_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_finset_1 B))  =>  (~ (v1_finset_1 (k4_xboole_0 A B))) ) ) ).
tt(fc3_rat_1,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (v1_rat_1 (k6_xcmplx_0 A B))) ) ).
tt(fc3_rcomp_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  => (v4_xxreal_2 (k3_xxreal_1 B A))) ) ).
tt(fc3_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_xboole_0 (k5_int_1 k6_numbers A)) & (v1_int_1 (k5_int_1 k6_numbers A))) ) ) ).
tt(fc3_real_lat,ax, ((v3_lattices k3_real_lat) & (v10_lattices k3_real_lat)) ).
tt(fc3_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_real_ns1 A)))  &  ((v13_algstr_0 (k4_real_ns1 A)) &  ((v2_rlvect_1 (k4_real_ns1 A)) &  ((v3_rlvect_1 (k4_real_ns1 A)) &  ((v4_rlvect_1 (k4_real_ns1 A)) &  ((v5_rlvect_1 (k4_real_ns1 A)) &  ((v6_rlvect_1 (k4_real_ns1 A)) &  ((v7_rlvect_1 (k4_real_ns1 A)) &  ((v8_rlvect_1 (k4_real_ns1 A)) &  ((v3_normsp_0 (k4_real_ns1 A)) &  ((v4_normsp_0 (k4_real_ns1 A)) &  ((v1_normsp_1 (k4_real_ns1 A)) & (v2_normsp_1 (k4_real_ns1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc3_realset1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (~ (v1_xboole_0 (k4_xboole_0 A B))) ) ) ).
tt(fc3_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  => (v1_relat_1 (k2_xboole_0 A B))) ) ).
tt(fc3_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v2_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc3_reloc,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_compos_0 (k4_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(fc3_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v4_relat_1 B A))  & (v1_relat_1 C))  => (v4_relat_1 (k4_xboole_0 B C) A)) ) ).
tt(fc3_revrot_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) & (m1_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) )  => (v1_topreal1 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A))) ) ).
tt(fc3_rewrite2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_rewrite2 A)) )  => (v5_ordinal1 (k1_funct_1 A B))) ) ).
tt(fc3_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k4_rfunct_1 A)) &  ((v1_funct_1 (k4_rfunct_1 A)) & (v1_valued_0 (k4_rfunct_1 A))) ) ) ) ).
tt(fc3_rfunct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v6_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v6_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc3_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_ring_1 A B)))  &  ((v1_partfun1 (k1_ring_1 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k1_ring_1 A B)) & (v8_relat_2 (k1_ring_1 A B))) ) ) ) ) ).
tt(fc3_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~ (v1_xboole_0 (k9_ringcat1 A))) ) ) ).
tt(fc3_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_rlaffin1 (k1_tarski B) A)) ) ).
tt(fc3_rlaffin3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_finset_1 (k5_rusub_4 A B C))) ) ).
tt(fc3_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v3_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) &  ((v12_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) &  ((v13_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) &  ((v14_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) & (v16_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ) ) ) ) ).
tt(fc3_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_rltopsp1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_rltopsp1 (k6_rusub_4 A B C) A)) ) ).
tt(fc3_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_rlvect_2 A)))  & (v1_rlvect_1 (k16_rlvect_2 A))) ) ) ).
tt(fc3_robbins3,ax,(v3_robbins3 k1_robbins3)).
tt(fc3_robbins4,ax, ((v3_orders_2 k1_robbins4) &  ((v4_orders_2 k1_robbins4) & (v5_orders_2 k1_robbins4)) ) ).
tt(fc3_rsspace3,ax, ((v13_algstr_0 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v1_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v2_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v3_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v4_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v5_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v6_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v7_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) & (v8_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3)))) ) ) ) ) ) ) ) ).
tt(fc3_rsspace4,ax, ((v13_algstr_0 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v1_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v2_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v3_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v4_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v5_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v6_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v7_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) & (v8_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4)))) ) ) ) ) ) ) ) ).
tt(fc3_rsspace,ax, ((v13_algstr_0 k7_rsspace) &  ((v2_rlvect_1 k7_rsspace) &  ((v3_rlvect_1 k7_rsspace) &  ((v4_rlvect_1 k7_rsspace) &  ((v5_rlvect_1 k7_rsspace) &  ((v6_rlvect_1 k7_rsspace) &  ((v7_rlvect_1 k7_rsspace) & (v8_rlvect_1 k7_rsspace)) ) ) ) ) ) ) ).
tt(fc3_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v3_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) &  ((v12_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) &  ((v13_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) &  ((v14_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) & (v16_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ) ) ) ) ).
tt(fc3_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v3_valued_0 (k10_finseq_1 A B))) ) ).
tt(fc3_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_amistd_1 (k7_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc3_scmfsa_1,ax, ((v1_relat_1 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) & (v2_relat_1 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) ).
tt(fc3_scmfsa_2,ax, (~ (v1_finset_1 k3_scmfsa_2)) ).
tt(fc3_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_compos_0 (k8_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc3_scmfsa6a,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k1_scmfsa6a A B)) &  ((v4_relat_1 (k1_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6a A B)) &  ((v1_finset_1 (k1_scmfsa6a A B)) & (v2_compos_1 (k1_scmfsa6a A B) k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(fc3_scmfsa6c,ax, (! [A:$i] :  ( ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  =>  ((v1_relat_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v4_relat_1 (k11_compos_1 k1_scmfsa_2 A) k5_numbers) &  ((v5_relat_1 (k11_compos_1 k1_scmfsa_2 A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k11_compos_1 k1_scmfsa_2 A)) &  ((v1_finset_1 (k11_compos_1 k1_scmfsa_2 A)) & (v1_scmfsa6b (k11_compos_1 k1_scmfsa_2 A))) ) ) ) ) ) ) ).
tt(fc3_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  =>  ( (~ (v1_xboole_0 (k4_scmfsa_7 A B)))  &  ((v1_relat_1 (k4_scmfsa_7 A B)) &  ((v4_relat_1 (k4_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa_7 A B)) &  ((v1_finset_1 (k4_scmfsa_7 A B)) & (v1_afinsq_1 (k4_scmfsa_7 A B))) ) ) ) ) ) ) ) ).
tt(fc3_scmfsa8a,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_relat_1 (k1_scmfsa6a A B)) &  ((v4_relat_1 (k1_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa6a A B)) &  ((v1_finset_1 (k1_scmfsa6a A B)) & (v1_afinsq_1 (k1_scmfsa6a A B))) ) ) ) ) ) ) ).
tt(fc3_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmfsa8b A B C)))  &  ((v1_relat_1 (k1_scmfsa8b A B C)) &  ((v4_relat_1 (k1_scmfsa8b A B C) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8b A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8b A B C)) &  ((v1_finset_1 (k1_scmfsa8b A B C)) &  ((v1_afinsq_1 (k1_scmfsa8b A B C)) &  (~ (v2_compos_1 (k1_scmfsa8b A B C) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc3_scmfsa_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) )  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k2_scmfsa8b C A B)) &  ((v4_relat_1 (k2_scmfsa8b C A B) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8b C A B) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k2_scmfsa8b C A B)))  &  ((v1_funct_1 (k2_scmfsa8b C A B)) &  ((v1_finset_1 (k2_scmfsa8b C A B)) &  ((v1_afinsq_1 (k2_scmfsa8b C A B)) & (v1_scmfsa7b (k2_scmfsa8b C A B))) ) ) ) ) ) ) ) ) ).
tt(fc3_scmfsa_i,ax, ( (~ (v1_xboole_0 k2_scmfsa_i))  & (v1_compos_0 k2_scmfsa_i)) ).
tt(fc3_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 (k1_scmfsa_m A)) &  ((v4_relat_1 (k1_scmfsa_m A) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_m A)) &  ((v5_funct_1 (k1_scmfsa_m A) (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 (k1_scmfsa_m A))) ) ) ) ) ) ).
tt(fc3_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) & (v2_scm_halt (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc3_scm_inst,ax,(v3_finseq_1 (k10_xtuple_0 k3_scm_inst))).
tt(fc3_scmpds_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2))) )  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc3_scmpds_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v4_scmpds_4 (k11_scmpds_2 A B C))) ) ).
tt(fc3_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k1_scmpds_6 (k2_nat_1 A 1))))  &  ((v1_relat_1 (k1_scmpds_6 (k2_nat_1 A 1))) &  ((v4_relat_1 (k1_scmpds_6 (k2_nat_1 A 1)) k5_numbers) &  ((v5_relat_1 (k1_scmpds_6 (k2_nat_1 A 1)) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_6 (k2_nat_1 A 1))) &  ((v1_finset_1 (k1_scmpds_6 (k2_nat_1 A 1))) &  ((v1_afinsq_1 (k1_scmpds_6 (k2_nat_1 A 1))) & (v2_compos_1 (k1_scmpds_6 (k2_nat_1 A 1)) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc3_scmpds_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (m1_subset_1 D k5_numbers)) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_7 B C D A)))  &  ((v1_relat_1 (k2_scmpds_7 B C D A)) &  ((v4_relat_1 (k2_scmpds_7 B C D A) k5_numbers) &  ((v5_relat_1 (k2_scmpds_7 B C D A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_7 B C D A)) &  ((v1_finset_1 (k2_scmpds_7 B C D A)) &  ((v1_afinsq_1 (k2_scmpds_7 B C D A)) & (v3_scmpds_4 (k2_scmpds_7 B C D A))) ) ) ) ) ) ) ) ) ).
tt(fc3_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_8 B C A)))  &  ((v1_relat_1 (k2_scmpds_8 B C A)) &  ((v4_relat_1 (k2_scmpds_8 B C A) k5_numbers) &  ((v5_relat_1 (k2_scmpds_8 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_8 B C A)) &  ((v1_finset_1 (k2_scmpds_8 B C A)) &  ((v1_afinsq_1 (k2_scmpds_8 B C A)) & (v3_scmpds_4 (k2_scmpds_8 B C A))) ) ) ) ) ) ) ) ) ).
tt(fc3_scmpds_i,ax,(v1_compos_0 k1_scmpds_i)).
tt(fc3_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v3_memstr_0 (k1_scmring2 A) 2) & (v1_extpro_1 (k1_scmring2 A) 2)) ) ) ).
tt(fc3_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v4_amistd_1 (k4_scmring2 A B C) 2 (k1_scmring2 A))) ) ).
tt(fc3_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  ((v1_extpro_1 (k1_scmring2 A) 2) & (v4_amistd_5 (k1_scmring2 A) 2)) ) ) ).
tt(fc3_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  => (v3_finseq_1 (k10_xtuple_0 (k1_scmringi A)))) ) ).
tt(fc3_scmyciel,ax, (! [A:$i] :  ((v1_scmyciel A) => (v1_xboole_0 (k3_tarski A))) ) ).
tt(fc3_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k30_valued_1 A)) &  ((v1_funct_2 (k30_valued_1 A) k5_numbers k1_numbers) & (v2_comseq_2 (k30_valued_1 A))) ) ) ) ).
tt(fc3_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v1_xboole_0 (k14_seq_4 A))) ) ) ).
tt(fc3_setfam_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (v1_setfam_1 (k2_tarski A B))) ) ).
tt(fc3_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_sfmastr1 (k8_scmfsa_2 A B))) ) ).
tt(fc3_sfmastr3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  & (m1_scmfsa_2 D)) ) )  =>  ((v1_relat_1 (k3_sfmastr3 A B C D)) &  ((v4_relat_1 (k3_sfmastr3 A B C D) k5_numbers) &  ((v5_relat_1 (k3_sfmastr3 A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_sfmastr3 A B C D)) &  ( (~ (v1_xboole_0 (k3_sfmastr3 A B C D)))  &  ((v1_finset_1 (k3_sfmastr3 A B C D)) &  ((v1_afinsq_1 (k3_sfmastr3 A B C D)) & (v1_scmfsa7b (k3_sfmastr3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(fc3_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_ami_2 (k5_sf_mastr A)) &  (~ (v1_scmfsa_m (k5_sf_mastr A))) ) ) ) ).
tt(fc3_simplex0,ax, (! [A:$i,B:$i] :  ( ((v1_classes1 A) & (v1_classes1 B))  => (v1_classes1 (k2_xboole_0 A B))) ) ).
tt(fc3_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v2_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_pre_topc (k5_simplex0 (u1_struct_0 A) B)) & (v1_simplex1 (k5_simplex0 (u1_struct_0 A) B) A)) ) ) ).
tt(fc3_sincos10,ax, ((v1_relat_1 (k5_relat_1 k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) & (v2_funct_1 (k5_relat_1 k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))) ).
tt(fc3_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc3_sin_cos9,ax, ((v1_funct_1 k1_sin_cos9) & (v2_funct_1 k1_sin_cos9)) ).
tt(fc3_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k17_sin_cos A))) ) ).
tt(fc3_sppol_1,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B k5_numbers))  => (v4_pre_topc (k2_topreal1 2 A B) (k15_euclid 2))) ) ).
tt(fc3_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v2_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ).
tt(fc3_sprect_1,ax, ((v1_topreal4 k1_topreal1) &  ( (~ (v1_sppol_1 k1_topreal1))  &  (~ (v2_sppol_1 k1_topreal1)) ) ) ).
tt(fc3_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v1_topreal2 (k3_topreal1 2 A))) ) ).
tt(fc3_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v2_topreal4 (k2_goboard9 A) (k15_euclid 2))) ) ).
tt(fc3_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v4_funct_1 (u4_struct_0 (k8_stacks_1 A)))) ) ).
tt(fc3_struct_0,ax, (! [A:$i] :  ((l1_struct_0 A) => (v1_xboole_0 (k1_struct_0 A))) ) ).
tt(fc3_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  (~ (v1_xboole_0 (k2_enumset1 A B C D))) ) ).
tt(fc3_substlat,ax, (! [A:$i,B:$i] :  ((v3_lattices (k5_substlat A B)) & (v10_lattices (k5_substlat A B))) ) ).
tt(fc3_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k9_qc_lang1 A)))  => (v1_finset_1 (k9_substut1 A B))) ) ).
tt(fc3_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  ( (~ (v1_xboole_0 (k5_supinf_1 A)))  & (v2_membered (k5_supinf_1 A))) ) ) ).
tt(fc3_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_tbsp_1 A) & (l1_metric_1 A)) )  => (v6_tbsp_1 (k2_struct_0 A) A)) ) ).
tt(fc3_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (~ (v1_xboole_0 (k9_tdlat_1 A))) ) ) ).
tt(fc3_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_termord A B C D)) &  ((v1_funct_2 (k5_termord A B C D) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 (k5_termord A B C D) A C) & (v3_polynom7 (k5_termord A B C D) A C)) ) ) ) ) ).
tt(fc3_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k2_tex_1 A))) ) ) ).
tt(fc3_tex_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k1_tex_2 A B)))  &  ((v1_pre_topc (k1_tex_2 A B)) & (v2_pre_topc (k1_tex_2 A B))) ) ) ) ).
tt(fc3_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_subset_1 B (u1_struct_0 A)))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_subset_1 (k2_pre_topc A B) (u1_struct_0 A))) ) ) ).
tt(fc3_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v5_pre_topc (k3_struct_0 A) A A)) ) ) ) ).
tt(fc3_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k4_topalg_1 A B)))  &  ((v1_partfun1 (k4_topalg_1 A B) (k2_topalg_1 A B)) &  ((v3_relat_2 (k4_topalg_1 A B)) & (v8_relat_2 (k4_topalg_1 A B))) ) ) ) ) ).
tt(fc3_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  ((v7_struct_0 (k5_topalg_1 k5_topmetr A)) & (v15_algstr_0 (k5_topalg_1 k5_topmetr A))) ) ) ).
tt(fc3_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k3_topalg_3 A B C D)) &  ((v1_funct_2 (k3_topalg_3 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)))) & (v1_group_6 (k3_topalg_3 A B C D) (k5_topalg_1 A C) (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ).
tt(fc3_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k11_topalg_4 A B C D)) &  ((v2_funct_1 (k11_topalg_4 A B C D)) &  ((v1_funct_2 (k11_topalg_4 A B C D) (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) & (v2_funct_2 (k11_topalg_4 A B C D) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))))) ) ) ) ) ).
tt(fc3_topalg_5,ax,(v1_connsp_2 k17_borsuk_1)).
tt(fc3_topalg_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v1_topalg_6 (k15_euclid A))) ) ) ).
tt(fc3_topdim_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v7_ordinal1 (k2_topdim_1 A B)) & (v1_int_1 (k2_topdim_1 A B))) ) ) ).
tt(fc3_topdim_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) &  ((v5_waybel23 A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) ) )  &  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_topdim_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_topdim_1 (k2_xboole_0 B C) A)) ) ).
tt(fc3_topgen_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v4_pre_topc (k2_topgen_1 A B) A)) ) ).
tt(fc3_topgen_3,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_topgen_3 A B)))  &  ((v1_pre_topc (k6_topgen_3 A B)) & (v2_pre_topc (k6_topgen_3 A B))) ) ) ) ).
tt(fc3_topgen_4,ax, (! [A:$i,B:$i] :  ( ((v4_card_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (v4_card_3 (k7_setfam_1 A B))) ) ).
tt(fc3_topgen_5,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  ((v1_funct_1 (k4_topgen_5 A B)) &  ((v1_funct_2 (k4_topgen_5 A B) (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (v5_pre_topc (k4_topgen_5 A B) k3_topgen_5 k5_topmetr)) ) ) ) ).
tt(fc3_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k1_topgrp_1 A B)) &  ((v2_funct_1 (k1_topgrp_1 A B)) &  ((v1_funct_2 (k1_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v2_funct_2 (k1_topgrp_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(fc3_topmetr,ax,(v3_topmetr k17_borsuk_1)).
tt(fc3_topreal1,ax, (~ (v1_xboole_0 k1_topreal1)) ).
tt(fc3_topreal6,ax,(v2_connsp_1 k1_topreal1 (k15_euclid 2))).
tt(fc3_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) & (l1_metric_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v8_metric_1 B) & (l1_metric_1 B)) ) )  =>  ((v1_metric_1 (k1_topreal7 A B)) & (v8_metric_1 (k1_topreal7 A B))) ) ) ).
tt(fc3_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) & (v3_xxreal_0 C)) ) )  => (v1_xboole_0 (k2_topreal9 A B C))) ) ).
tt(fc3_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k3_xxreal_1 A (k2_xcmplx_0 A B)))) ) ) ).
tt(fc3_toprealb,ax, (~ (v1_xboole_0 (k4_xxreal_1 (k10_real_1 1 2) (k10_real_1 3 2)))) ).
tt(fc3_toprealc,ax, ((v1_xboole_0 (k6_square_1 k6_numbers)) & (v1_xreal_0 (k6_square_1 k6_numbers))) ).
tt(fc3_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v4_pre_topc (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc3_trees_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k3_xboole_0 A B)))  & (v1_trees_1 (k3_xboole_0 A B))) ) ) ).
tt(fc3_trees_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  & (m1_subset_1 C (k9_xtuple_0 B))) )  =>  ((v1_relat_1 (k5_trees_2 B C)) &  ((v5_relat_1 (k5_trees_2 B C) A) &  ((v1_funct_1 (k5_trees_2 B C)) & (v3_trees_2 (k5_trees_2 B C))) ) ) ) ) ).
tt(fc3_trees_3,ax,(v1_trees_3 k1_trees_3)).
tt(fc3_trees_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) )  =>  ((v1_relat_1 (k5_trees_4 B C)) &  ((v5_relat_1 (k5_trees_4 B C) A) &  ((v1_funct_1 (k5_trees_4 B C)) & (v3_trees_2 (k5_trees_4 B C))) ) ) ) ) ).
tt(fc3_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  => (v1_trees_9 (k9_xtuple_0 A))) ) ).
tt(fc3_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (~ (v2_setfam_1 (k1_triang_1 A))) ) ) ).
tt(fc3_unialg_1,ax, (! [A:$i] :  ( ((v3_unialg_1 A) & (l1_unialg_1 A))  => (v5_margrel1 (u1_unialg_1 A) (u1_struct_0 A))) ) ).
tt(fc3_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  => (v1_finset_1 (k2_uniroots A))) ) ).
tt(fc3_uproots,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_polynom5 A B (k5_struct_0 A))) &  ((v1_funct_2 (k4_polynom5 A B (k5_struct_0 A)) k5_numbers (u1_struct_0 A)) & (v1_uproots (k4_polynom5 A B (k5_struct_0 A)) A)) ) ) ) ).
tt(fc3_urysohn1,ax, (~ (v1_xboole_0 k3_urysohn1)) ).
tt(fc3_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  => (v3_membered (k10_xtuple_0 A))) ) ).
tt(fc3_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v3_valued_0 (k1_valued_1 A B))) ) ) ) ).
tt(fc3_vectmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 B (u1_struct_0 A)) &  ((v3_vectmetr B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v3_vectmetr C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 C B)) &  ((v1_funct_2 (k3_relat_1 C B) (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 (k3_relat_1 C B) (u1_struct_0 A)) & (v3_vectmetr (k3_relat_1 C B) A)) ) ) ) ) ).
tt(fc3_vectsp_1,ax, ((v8_algstr_0 k1_vectsp_1) &  ((v13_algstr_0 k1_vectsp_1) &  ((v2_rlvect_1 k1_vectsp_1) &  ((v3_rlvect_1 k1_vectsp_1) & (v4_rlvect_1 k1_vectsp_1)) ) ) ) ).
tt(fc3_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k3_vfunct_1 A B C D)) & (v1_partfun1 (k3_vfunct_1 A B C D) A)) ) ) ).
tt(fc3_waybel_0,ax, (! [A:$i] :  ( ((v2_lattice3 A) & (l1_orders_2 A))  => (v2_waybel_0 (k2_struct_0 A) A)) ) ).
tt(fc3_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) &  ((v17_waybel_0 (k3_struct_0 A) A A) & (v18_waybel_0 (k3_struct_0 A) A A)) ) ) ) ) ).
tt(fc3_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((v1_waybel11 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_waybel11 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc3_waybel14,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~ (v1_xboole_0 (k5_waybel11 A))) ) ) ).
tt(fc3_waybel17,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel17 A B)))  &  ((v1_orders_2 (k2_waybel17 A B)) & (v4_yellow_0 (k2_waybel17 A B) (k7_yellow_1 A B))) ) ) ) ).
tt(fc3_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (~ (v2_struct_0 (k7_waybel18 A B C))) ) ) ).
tt(fc3_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v6_waybel_1 (k3_struct_0 A) A)) ) ) ) ).
tt(fc3_waybel21,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ( (~ (v2_struct_0 D))  &  ((v9_waybel_0 D A) & (l1_waybel_0 D A)) ) ) ) )  =>  ((v6_waybel_0 (k6_waybel_9 A B C D) B) & (v9_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc3_waybel22,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k2_waybel22 A B C)) &  ((v1_funct_2 (k2_waybel22 A B C) (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B)) & (v17_waybel_0 (k2_waybel22 A B C) (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B)) ) ) ) ).
tt(fc3_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_waybel23 (k5_waybel_0 A B) A)) ) ).
tt(fc3_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v5_orders_3 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k2_waybel24 A B C D E)) &  ((v1_funct_2 (k2_waybel24 A B C D E) (u1_struct_0 A) (u1_struct_0 C)) & (v5_orders_3 (k2_waybel24 A B C D E) A C)) ) ) ) ).
tt(fc3_waybel25,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_pre_topc A))  =>  ((v2_struct_0 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc3_waybel26,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_waybel26 A B))))) ) )  =>  (~ (v1_xboole_0 (k5_card_3 C D))) ) ) ).
tt(fc3_waybel27,ax, (! [A:$i] :  ( ((v1_monoid_0 A) & (l1_struct_0 A))  => (v4_funct_1 (u1_struct_0 A))) ) ).
tt(fc3_waybel29,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_waybel_9 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v1_yellow_0 (k3_waybel24 A B))) ) ) ).
tt(fc3_waybel_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v24_waybel_0 (k3_yellow_3 A B))) ) ) ).
tt(fc3_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~ (v1_xboole_0 (k2_waybel19 A))) ) ) ).
tt(fc3_waybel32,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel32 A B)))  &  ((v4_orders_2 (k2_waybel32 A B)) &  ((v6_waybel_0 (k2_waybel32 A B) A) & (v7_waybel_0 (k2_waybel32 A B))) ) ) ) ) ).
tt(fc3_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k3_waybel34 A B C)) &  ((v1_funct_2 (k3_waybel34 A B C) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (v5_waybel_1 (k3_waybel34 A B C) (k7_lattice3 B) (k7_lattice3 A))) ) ) ) ).
tt(fc3_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v13_waybel_0 (k2_waybel_3 A B) A)) ) ).
tt(fc3_waybel_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  => (v3_waybel_4 (k2_waybel_4 A) A)) ) ).
tt(fc3_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  & (m2_pboole D A B (k7_funcop_1 A (u1_struct_0 C)))) ) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 (k4_waybel_5 C D)))) ) ) ).
tt(fc3_waybel_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v13_waybel_0 (k6_waybel_4 A C B) A)) ) ).
tt(fc3_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k1_waybel_8 A)) &  ((v4_yellow_0 (k1_waybel_8 A) A) & (v6_yellow_0 (k1_waybel_8 A) A)) ) ) ) ).
tt(fc3_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ((v4_orders_2 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)) & (v6_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C) A)) ) ) ).
tt(fc3_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k7_group_3 A B))) ) ) ).
tt(fc3_wellord2,ax, (! [A:$i] :  ((v1_relat_1 (k1_wellord2 A)) & (v4_relat_2 (k1_wellord2 A))) ) ).
tt(fc3_xboole_0,ax, (! [A:$i,B:$i] :  (~ (v1_xboole_0 (k2_tarski A B))) ) ).
tt(fc3_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k4_xboolean A B))) ) ).
tt(fc3_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_xcmplx_0 (k3_xcmplx_0 A B))) ) ).
tt(fc3_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) & (v1_xreal_0 (k4_xcmplx_0 A))) ) ) ).
tt(fc3_xtuple_0,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v3_xtuple_0 (k6_xtuple_0 A B C D))) ).
tt(fc3_xxreal_0,ax,(v2_xxreal_0 k1_xxreal_0)).
tt(fc3_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v2_membered (k3_xxreal_1 A B))) ) ).
tt(fc3_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) & (v1_xxreal_2 A))  =>  ((v1_xxreal_0 (k2_xxreal_2 A)) & (v1_xreal_0 (k2_xxreal_2 A))) ) ) ).
tt(fc3_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_xxreal_0 (k3_xxreal_3 A B)) & (v1_xreal_0 (k3_xxreal_3 A B))) ) ) ).
tt(fc3_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) )  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v25_waybel_0 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc3_yellow11,ax, ((v1_orders_2 k2_yellow11) &  ((v3_orders_2 k2_yellow11) &  ((v4_orders_2 k2_yellow11) & (v5_orders_2 k2_yellow11)) ) ) ).
tt(fc3_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k4_waybel_2 A)) &  ((v1_funct_2 (k4_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (v17_waybel_0 (k4_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ) ).
tt(fc3_yellow13,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k2_yellow_2 A)) &  ((v2_funct_1 (k2_yellow_2 A)) & (v1_funct_2 (k2_yellow_2 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A))) ) ) ) ).
tt(fc3_yellow14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A)) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 (k1_waybel_0 A B)))) ) ) ).
tt(fc3_yellow16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_yellow_1 A B))))) )  =>  (~ (v1_xboole_0 (k5_card_3 D C))) ) ) ).
tt(fc3_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ( (~ (v2_struct_0 (k1_yellow18 A)))  &  ((v2_altcat_1 (k1_yellow18 A)) &  ((v6_altcat_1 (k1_yellow18 A)) & (v12_altcat_1 (k1_yellow18 A))) ) ) ) ) ).
tt(fc3_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  ((v1_subset_1 (k2_yellow19 A B) (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) & (v2_waybel_0 (k2_yellow19 A B) (k3_yellow_1 (k2_struct_0 A)))) ) ) ).
tt(fc3_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) & (v1_yellow_0 (k3_lattice3 A))) ) ) ) ) ) ).
tt(fc3_yellow20,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) ) )  =>  ((v9_functor0 (k10_functor0 A B) B A) & (v10_functor0 (k10_functor0 A B) B A)) ) ) ).
tt(fc3_yellow21,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) & (v1_relat_2 B)) )  =>  ((v1_relat_1 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A))) & (v1_relat_2 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A)))) ) ) ).
tt(fc3_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (~ (v1_xboole_0 (k7_waybel_0 A))) ) ) ).
tt(fc3_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ( (~ (v2_struct_0 (k3_yellow_3 A B)))  & (v1_orders_2 (k3_yellow_3 A B))) ) ) ).
tt(fc3_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  &  ( ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_waybel_0 (k1_yellow_4 A B C) A)) ) ).
tt(fc3_yellow_6,ax, (! [A:$i,B:$i] :  ((l1_struct_0 B) => (v2_pralg_1 (k2_funcop_1 A B))) ) ).
tt(fc3_yellow_7,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v5_orders_2 (k7_lattice3 A))) ) ) ).
tt(fc3_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k3_yellow_9 A B)))  &  ((v3_orders_2 (k3_yellow_9 A B)) & (v6_waybel_0 (k3_yellow_9 A B) A)) ) ) ) ).
tt(fc3_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) & (m1_subset_1 B k1_zf_lang))  => (v1_zf_lang (k5_zf_lang A B))) ) ).
tt(fc3_zfmisc_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 B) => (v1_xboole_0 (k2_zfmisc_1 A B))) ) ).
tt(fc3_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  => (v7_zmodul01 (k1_tarski (k4_struct_0 A)) A)) ) ).
tt(fc40_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A)))) ) )  => (v1_finset_1 (k63_abcmiz_1 A B C))) ) ).
tt(fc40_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_bilinear A B C D)) &  ((v1_funct_2 (k15_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  ((v2_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  ((v3_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) & (v4_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C)) ) ) ) ) ) ) ).
tt(fc40_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_relat_1 (k7_fomodel0 A)) &  ((v1_funct_1 (k7_fomodel0 A)) & (v1_pre_poly (k7_fomodel0 A))) ) ) ) ).
tt(fc40_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v16_fomodel1 (k22_fomodel0 A) A)) ) ).
tt(fc40_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v4_fomodel1 (k8_fomodel1 A) A)) ) ) ).
tt(fc40_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v15_fomodel1 (k26_fomodel3 A B C D) A)) ) ).
tt(fc40_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k33_fomodel4 A) A)) ) ).
tt(fc40_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 k1_xboole_0) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) & (v2_glib_003 (k13_glib_000 A k3_glib_003 k1_xboole_0))) ) ) ) ) ) ).
tt(fc40_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k12_member_1 B A))) ) ).
tt(fc40_membered,ax, (! [A:$i,B:$i] :  ((v5_membered A) => (v5_membered (k3_xboole_0 B A))) ) ).
tt(fc40_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v1_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc40_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v9_pcs_0 B) & (v16_pcs_0 B)) ) ) ) )  =>  ((v4_pcs_0 (k17_pcs_0 A B)) & (v12_pcs_0 (k17_pcs_0 A B))) ) ) ).
tt(fc40_scmfsa10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  =>  (~ (v2_amistd_1 (k15_scmfsa_2 B A C) 3 k1_scmfsa_2)) ) ) ).
tt(fc40_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C B (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc D B k3_topmetr) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k68_valued_2 (u1_struct_0 (k15_euclid A)) C D)) &  ((v1_funct_2 (k68_valued_2 (u1_struct_0 (k15_euclid A)) C D) (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (v5_pre_topc (k68_valued_2 (u1_struct_0 (k15_euclid A)) C D) B (k15_euclid A))) ) ) ) ).
tt(fc40_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  => (v4_membered (k9_relat_1 A B))) ) ).
tt(fc40_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v4_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 D E)) & (v1_partfun1 (k18_valued_1 D E) A)) ) ) ).
tt(fc40_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  =>  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) ).
tt(fc40_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_xxreal_0 (k6_xxreal_3 A B)) & (v1_xreal_0 (k6_xxreal_3 A B))) ) ) ).
tt(fc41_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) &  ((v15_abcmiz_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) )  &  ((v1_funct_1 C) &  ((v15_abcmiz_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) ) )  =>  ((v1_funct_1 (k65_abcmiz_1 A B C)) & (v15_abcmiz_1 (k65_abcmiz_1 A B C) A)) ) ) ).
tt(fc41_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_bilinear A B C D)) &  ((v1_funct_2 (k16_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v2_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) & (v4_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D)))) ) ) ) ) ) ) ).
tt(fc41_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  &  ((v7_ordinal1 C) &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) &  ((v3_card_1 D (k2_xcmplx_0 B C)) & (v1_finseq_1 D)) ) ) ) ) ) )  => (v1_xboole_0 (k4_xboole_0 (k1_tarski (k1_funct_1 D B)) A))) ) ).
tt(fc41_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) &  ((v16_fomodel1 B A) & (l1_fomodel1 B)) ) ) )  => (v1_xboole_0 (k4_xboole_0 (k37_fomodel1 A) (k37_fomodel1 B)))) ) ).
tt(fc41_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  (~ (v3_fomodel2 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C) A (k4_xxreal_0 (k32_fomodel2 A B) (k32_fomodel2 A C)))) ) ) ).
tt(fc41_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  & (v7_ordinal1 D)) ) )  =>  ((v1_relat_1 (k5_relat_1 (k20_fomodel0 (k1_fomodel1 A) B C) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) D))) & (v5_relat_1 (k5_relat_1 (k20_fomodel0 (k1_fomodel1 A) B C) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) D)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) D))) ) ) ).
tt(fc41_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k23_fomodel4 A) A)) ) ).
tt(fc41_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 k1_xboole_0) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) & (v3_glib_003 (k13_glib_000 A k4_glib_003 k1_xboole_0))) ) ) ) ) ) ).
tt(fc41_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k12_member_1 A B))) ) ).
tt(fc41_membered,ax, (! [A:$i,B:$i] :  ((v6_membered A) => (v6_membered (k3_xboole_0 A B))) ) ).
tt(fc41_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_xreal_0 B) & (v3_xxreal_0 B))  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v1_funct_1 (k24_valued_1 C B)) & (v1_partfun3 (k24_valued_1 C B))) ) ) ) ).
tt(fc41_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v11_pcs_0 B) & (v16_pcs_0 B)) ) ) ) )  =>  ((v6_pcs_0 (k17_pcs_0 A B)) & (v12_pcs_0 (k17_pcs_0 A B))) ) ) ).
tt(fc41_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k16_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc41_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  => (v5_membered (k9_relat_1 A B))) ) ).
tt(fc41_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v5_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 D E)) & (v1_partfun1 (k18_valued_1 D E) A)) ) ) ).
tt(fc41_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_valued_2 A)) )  =>  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) ).
tt(fc41_xxreal_3,ax, ((v1_xboole_0 (k5_xxreal_3 k2_xxreal_0)) & (v1_xxreal_0 (k5_xxreal_3 k2_xxreal_0))) ).
tt(fc42_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_bilinear A B C D)) &  ((v1_funct_2 (k15_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  ((v4_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C) &  (~ (v5_bilinear (k15_bilinear A B C D) A (k6_vectsp10 A B (k13_bilinear A B C D)) C)) ) ) ) ) ) ) ).
tt(fc42_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v3_card_1 D (k2_xcmplx_0 (k2_xcmplx_0 B 1) C)) & (m1_subset_1 D (k3_finseq_2 A))) ) ) )  => (v1_xboole_0 (k4_xboole_0 (k1_tarski (k1_funct_1 D (k2_xcmplx_0 B 1))) A))) ) ).
tt(fc42_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_fomodel1 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ( (~ (v2_struct_0 (k40_fomodel1 B A)))  &  ((v1_fomodel1 (k40_fomodel1 B A)) & (v16_fomodel1 (k40_fomodel1 B A) A)) ) ) ) ).
tt(fc42_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (~ (v3_fomodel2 (k7_finseq_1 (k31_fomodel2 A C) B) A (k32_fomodel2 A B))) ) ) ).
tt(fc42_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  ((v1_relat_1 (k5_relat_1 (k20_fomodel0 (k1_fomodel1 A) B C) (k35_fomodel1 A))) & (v5_relat_1 (k5_relat_1 (k20_fomodel0 (k1_fomodel1 A) B C) (k35_fomodel1 A)) (k35_fomodel1 A))) ) ) ).
tt(fc42_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k32_fomodel4 A) A)) ) ).
tt(fc42_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k7_glib_000 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) k1_numbers)))) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v7_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc42_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  &  ( (~ (v1_xboole_0 B))  & (v2_membered B)) )  =>  (~ (v1_xboole_0 (k12_member_1 A B))) ) ) ).
tt(fc42_membered,ax, (! [A:$i,B:$i] :  ((v6_membered A) => (v6_membered (k3_xboole_0 B A))) ) ).
tt(fc42_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_xreal_0 B))  &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k24_valued_1 C B)) &  ((v2_relat_1 (k24_valued_1 C B)) & (v1_funct_1 (k24_valued_1 C B))) ) ) ) ).
tt(fc42_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v1_amistd_1 (k4_xtuple_0 (k17_scmfsa_2 A B)) 3 k1_scmfsa_2)) ) ) ).
tt(fc42_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  => (v6_membered (k9_relat_1 A B))) ) ).
tt(fc42_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v6_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v6_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k18_valued_1 D E)) & (v1_partfun1 (k18_valued_1 D E) A)) ) ) ).
tt(fc42_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v7_valued_2 A)) )  => (v1_valued_0 (k1_funct_1 A B))) ) ).
tt(fc42_xxreal_3,ax, ((v1_xboole_0 (k5_xxreal_3 k1_xxreal_0)) & (v1_xxreal_0 (k5_xxreal_3 k1_xxreal_0))) ).
tt(fc43_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_bilinear A B C D)) &  ((v1_funct_2 (k16_bilinear A B C D) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v1_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v3_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D))) &  (~ (v6_bilinear (k16_bilinear A B C D) A B (k6_vectsp10 A C (k14_bilinear A B C D)))) ) ) ) ) ) ) ).
tt(fc43_fomodel0,ax, (! [A:$i] : (v1_xboole_0 (k5_xboole_0 (k9_finseq_1 A) (k1_tarski (k4_tarski 1 A))))) ).
tt(fc43_fomodel1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_relat_1 A))  =>  ((v1_xboole_0 (k6_relat_1 B A)) & (v1_relat_1 (k6_relat_1 B A))) ) ) ).
tt(fc43_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  => (v3_fomodel2 (k7_finseq_1 (k31_fomodel2 A C) B) A (k2_nat_1 1 (k32_fomodel2 A B)))) ) ).
tt(fc43_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v7_ordinal1 D) &  ((m1_subset_1 E (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) &  ((v4_fomodel2 F A) & (m1_subset_1 F (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) )  => (v4_fomodel2 (k28_fomodel3 A B C D E F) A)) ) ).
tt(fc43_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) &  ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  & (v10_fomodel4 C A B)) )  =>  ((v1_relat_1 (k5_fomodel3 A C)) &  ((v1_funct_1 (k5_fomodel3 A C)) &  ((v1_fomodel2 (k5_fomodel3 A C) A (k35_fomodel1 A)) & (v3_fomodel3 (k5_fomodel3 A C) A (k35_fomodel1 A) (k6_fomodel4 A B C))) ) ) ) ) ).
tt(fc43_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) k1_numbers)))) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v9_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc43_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k13_member_1 A B))) ) ).
tt(fc43_membered,ax, (! [A:$i,B:$i] :  ((v1_membered A) => (v1_membered (k4_xboole_0 A B))) ) ).
tt(fc43_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v4_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc43_pcs_0,ax, (! [A:$i,B:$i] : (v4_relat_1 (k6_afinsq_1 A B) (k2_tarski k6_numbers 1))) ).
tt(fc43_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v2_amistd_1 (k16_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc43_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc43_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k18_valued_1 A B)) &  ((v1_funct_1 (k18_valued_1 A B)) & (v1_finseq_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc43_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_valued_2 A)) )  => (v2_valued_0 (k1_funct_1 A B))) ) ).
tt(fc44_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_xcmplx_0 A 1)) & (v1_finseq_1 B)) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k7_finseq_1 (k5_relat_1 B (k2_finseq_1 A)) (k9_finseq_1 (k1_funct_1 B (k2_xcmplx_0 A 1)))) B))) ) ).
tt(fc44_fomodel1,ax, (! [A:$i,B:$i] :  ((v1_int_1 B) => (v5_relat_1 (k2_funcop_1 A B) k4_numbers)) ) ).
tt(fc44_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) &  ((v3_fomodel2 C A B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v3_fomodel2 (k38_fomodel2 A C) A (k1_nat_1 B 1))) ) ).
tt(fc44_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel2 (k37_fomodel3 A B C D) A)) ) ).
tt(fc44_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  & (v10_fomodel4 C A B)) )  =>  ((v1_relat_1 (k38_fomodel4 A B C)) &  ((v4_relat_1 (k38_fomodel4 A B C) (k37_fomodel1 A)) & (v1_funct_1 (k38_fomodel4 A B C))) ) ) ) ).
tt(fc44_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v3_valued_0 B)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v9_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc44_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k13_member_1 B A))) ) ).
tt(fc44_membered,ax, (! [A:$i,B:$i] :  ((v2_membered A) => (v2_membered (k4_xboole_0 A B))) ) ).
tt(fc44_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v4_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc44_pcs_0,ax, (! [A:$i,B:$i] : (v1_partfun1 (k6_afinsq_1 A B) (k2_tarski k6_numbers 1))) ).
tt(fc44_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  =>  (~ (v2_amistd_1 (k17_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc44_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v2_valued_0 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc44_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v1_valued_0 (k24_valued_1 A B))) ) ) ) ).
tt(fc44_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v9_valued_2 A)) )  => (v3_valued_0 (k1_funct_1 A B))) ) ).
tt(fc45_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) &  ((v1_funct_2 (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))))) (u1_struct_0 A)) &  ((v1_bilinear (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)))) &  ((v3_bilinear (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)))) &  ( (~ (v5_bilinear (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)))))  &  (~ (v6_bilinear (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))))) ) ) ) ) ) ) ) ).
tt(fc45_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C (k2_xcmplx_0 A B)) & (v1_finseq_1 C)) ) ) ) )  =>  ((v1_relat_1 (k5_relat_1 C (k2_finseq_1 A))) &  ((v1_funct_1 (k5_relat_1 C (k2_finseq_1 A))) &  ((v3_card_1 (k5_relat_1 C (k2_finseq_1 A)) A) & (v1_finseq_1 (k5_relat_1 C (k2_finseq_1 A)))) ) ) ) ) ).
tt(fc45_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v4_funct_1 B))  =>  (~ (v1_finset_1 (k4_xboole_0 (k16_fomodel1 (k41_fomodel1 A B)) (k21_fomodel0 B)))) ) ) ).
tt(fc45_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v4_fomodel2 (k38_fomodel2 A B) A)) ) ).
tt(fc45_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  &  ( ((v13_fomodel1 D B) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((v3_fomodel2 E B A) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v3_fomodel2 (k37_fomodel3 B C D E) B A)) ) ).
tt(fc45_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) &  ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  & (v10_fomodel4 C A B)) )  =>  ((v1_relat_1 (k38_fomodel4 A B C)) &  ((v1_funct_1 (k38_fomodel4 A B C)) & (v1_fomodel2 (k38_fomodel4 A B C) A (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A B C)))) ) ) ) ).
tt(fc45_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) k1_numbers)))) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v10_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc45_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  &  ( (~ (v1_xboole_0 B))  & (v1_membered B)) )  =>  (~ (v1_xboole_0 (k13_member_1 A B))) ) ) ).
tt(fc45_membered,ax, (! [A:$i,B:$i] :  ((v3_membered A) => (v3_membered (k4_xboole_0 A B))) ) ).
tt(fc45_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v3_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc45_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_struct_0 B))  => (v2_pralg_1 (k6_afinsq_1 A B))) ) ).
tt(fc45_scmfsa10,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v2_amistd_2 k1_scmfsa_2 3)) ).
tt(fc45_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  &  ((v3_pre_topc C (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))))) ) )  => (v3_pre_topc (k2_toprealc C) (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))) ) ).
tt(fc45_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v3_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc45_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v3_valued_0 (k24_valued_1 A B))) ) ) ) ).
tt(fc45_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v10_valued_2 A)) )  => (v5_relat_1 (k1_funct_1 A B) k3_numbers)) ) ).
tt(fc46_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) &  ((v1_funct_2 (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A)) &  ((v2_bilinear (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ((v4_bilinear (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D))) &  ( (~ (v5_bilinear (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D))))  &  (~ (v6_bilinear (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)) A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D)))) ) ) ) ) ) ) ) ).
tt(fc46_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_partfun1 C A)) ) )  =>  ((v1_relat_1 (k5_relat_1 C B)) &  ((v4_relat_1 (k5_relat_1 C B) B) & (v1_partfun1 (k5_relat_1 C B) B)) ) ) ) ).
tt(fc46_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v1_orders_4 A) &  ((v11_fomodel1 A) & (l1_fomodel1 A)) ) )  => (v4_card_3 (k1_fomodel1 A))) ) ).
tt(fc46_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v9_fomodel1 (k7_fomodel1 A) A)) ) ) ).
tt(fc46_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v8_fomodel4 (k7_finseq_1 (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C) A (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k31_fomodel4 A))) (k7_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k38_fomodel2 A B) (k38_fomodel2 A C)))) ) ).
tt(fc46_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k6_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k6_glib_000 A)) & (v3_valued_0 B)) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v10_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc46_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k13_member_1 A B))) ) ).
tt(fc46_membered,ax, (! [A:$i,B:$i] :  ((v4_membered A) => (v4_membered (k4_xboole_0 A B))) ) ).
tt(fc46_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v3_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v3_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc46_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  => (v1_yellow_1 (k6_afinsq_1 A B))) ) ).
tt(fc46_scmfsa10,ax, ((v1_extpro_1 k1_scmfsa_2 3) & (v4_amistd_2 k1_scmfsa_2 3)) ).
tt(fc46_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v5_relat_1 (k5_relat_1 A B) k3_numbers)) ) ) ).
tt(fc46_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  & (v1_rat_1 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v5_relat_1 (k24_valued_1 A B) k3_numbers) & (v1_funct_1 (k24_valued_1 A B))) ) ) ) ).
tt(fc46_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v11_valued_2 A)) )  => (v5_relat_1 (k1_funct_1 A B) k4_numbers)) ) ).
tt(fc47_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C B)) )  => (v1_xboole_0 (k5_xboole_0 (k1_funct_1 (k5_relat_1 A B) C) (k1_funct_1 A C)))) ) ).
tt(fc47_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v1_orders_4 A) &  ((v11_fomodel1 A) & (l1_fomodel1 A)) ) )  => (v4_card_3 (k4_xboole_0 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ).
tt(fc47_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  => (v13_fomodel4 (k1_tarski B) A)) ) ).
tt(fc47_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 k1_xboole_0) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 k1_xboole_0)) & (v9_glib_003 (k13_glib_000 A k3_glib_003 k1_xboole_0))) ) ) ) ) ) ).
tt(fc47_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k13_member_1 A B))) ) ).
tt(fc47_membered,ax, (! [A:$i,B:$i] :  ((v5_membered A) => (v5_membered (k4_xboole_0 A B))) ) ).
tt(fc47_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v2_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc47_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l1_pcs_0 A) & (l1_pcs_0 B))  => (v7_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc47_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v5_relat_1 (k5_relat_1 A B) k4_numbers)) ) ) ).
tt(fc47_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v5_relat_1 (k24_valued_1 A B) k4_numbers) & (v1_funct_1 (k24_valued_1 A B))) ) ) ) ).
tt(fc47_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v12_valued_2 A)) )  => (v4_valued_0 (k1_funct_1 A B))) ) ).
tt(fc48_bilinear,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k1_bilinear A B B)) &  ((v1_funct_2 (k1_bilinear A B B) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (v7_bilinear (k1_bilinear A B B) A B)) ) ) ) ).
tt(fc48_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k1_funct_1 (k3_relat_1 E A) D) (k1_funct_1 A (k3_funct_2 B C E D))))) ) ).
tt(fc48_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_xboole_0 (k4_xboole_0 (k32_fomodel1 A) (k33_fomodel2 A)))) ) ).
tt(fc48_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v1_xboole_0 B))  => (v13_fomodel4 (k13_fomodel0 A B) A)) ) ).
tt(fc48_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 k1_xboole_0) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 k1_xboole_0)) & (v10_glib_003 (k13_glib_000 A k4_glib_003 k1_xboole_0))) ) ) ) ) ) ).
tt(fc48_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k13_member_1 A B))) ) ).
tt(fc48_membered,ax, (! [A:$i,B:$i] :  ((v6_membered A) => (v6_membered (k4_xboole_0 A B))) ) ).
tt(fc48_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v2_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc48_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (v16_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc48_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v4_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc48_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v4_valued_0 (k24_valued_1 A B))) ) ) ) ).
tt(fc48_valued_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k14_valued_2 A B)) &  ((v1_funct_1 (k14_valued_2 A B)) & (v1_valued_0 (k14_valued_2 A B))) ) ) ) ).
tt(fc49_bilinear,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k1_bilinear A B B)) &  ((v1_funct_2 (k1_bilinear A B B) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (v8_bilinear (k1_bilinear A B B) A B)) ) ) ) ).
tt(fc49_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((v1_xxreal_0 (k6_xcmplx_0 (k4_xxreal_0 A B) A)) &  (~ (v3_xxreal_0 (k6_xcmplx_0 (k4_xxreal_0 A B) A))) ) ) ) ).
tt(fc49_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v1_orders_4 A) &  ((v11_fomodel1 A) & (l1_fomodel1 A)) ) )  & (v4_funct_1 B))  => (v1_orders_4 (k41_fomodel1 A B))) ) ).
tt(fc49_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) &  ((v5_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_xboole_0 (k41_fomodel2 A B))) ) ).
tt(fc49_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v13_fomodel4 B A))  => (v13_fomodel4 (k13_fomodel0 C B) A)) ) ).
tt(fc49_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (v1_xreal_0 C)) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C)) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) & (v3_glib_003 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C)))) ) ) ) ) ) ).
tt(fc49_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v5_membered B))  => (v5_membered (k13_member_1 A B))) ) ).
tt(fc49_membered,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k5_xboole_0 A B))) ) ).
tt(fc49_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v1_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc49_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) & (l2_pcs_0 A))  &  ((v3_orders_2 B) & (l2_pcs_0 B)) )  => (v5_waybel_3 (k6_afinsq_1 A B))) ) ).
tt(fc49_valued_0,ax, (! [A:$i] :  ((v1_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v1_valued_0 (k4_relat_1 A))) ) ) ).
tt(fc49_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xcmplx_0 D)) )  =>  ((v1_funct_1 (k24_valued_1 C D)) & (v1_partfun1 (k24_valued_1 C D) A)) ) ) ).
tt(fc49_valued_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k14_valued_2 A B)) &  ((v1_funct_1 (k14_valued_2 A B)) & (v3_valued_0 (k14_valued_2 A B))) ) ) ) ).
tt(fc4_abcmiz_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A (k5_finsub_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) ) ) )  =>  ( (~ (v4_abcmiz_0 (g2_abcmiz_0 A B C D E)))  & (v7_abcmiz_0 (g2_abcmiz_0 A B C D E))) ) ) ).
tt(fc4_abcmiz_1,ax, (~ (v1_xboole_0 k4_abcmiz_1)) ).
tt(fc4_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  =>  (~ (v1_abian (k6_xcmplx_0 A 1))) ) ) ).
tt(fc4_afinsq_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_afinsq_1 A)) &  ((v5_relat_1 (k4_afinsq_1 A) A) &  ((v5_ordinal1 (k4_afinsq_1 A)) &  ((v1_funct_1 (k4_afinsq_1 A)) &  ((v1_xboole_0 (k4_afinsq_1 A)) & (v1_finset_1 (k4_afinsq_1 A))) ) ) ) ) ) ).
tt(fc4_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_valued_0 A)) ) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v5_ordinal1 (k54_valued_1 A)) & (v3_valued_0 (k54_valued_1 A))) ) ) ) ) ).
tt(fc4_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v8_algstr_0 (k5_afvect0 A B)) & (v12_vectsp_1 (k5_afvect0 A B))) ) ) ).
tt(fc4_algstr_1,ax, ((v21_algstr_0 k8_algstr_0) &  ((v4_vectsp_1 k8_algstr_0) & (v5_algstr_1 k8_algstr_0)) ) ).
tt(fc4_algstr_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (~ (v2_struct_0 (k4_algstr_4 A B))) ) ) ).
tt(fc4_altcat_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  =>  ((v1_relat_1 (k2_funct_4 B)) &  ((v4_relat_1 (k2_funct_4 B) (k2_zfmisc_1 A A)) &  ((v1_funct_1 (k2_funct_4 B)) & (v1_partfun1 (k2_funct_4 B) (k2_zfmisc_1 A A))) ) ) ) ) ).
tt(fc4_altcat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( ((v1_altcat_3 C A B B) & (m1_subset_1 C (k1_altcat_1 A B B)))  &  ((v1_altcat_3 D A B B) & (m1_subset_1 D (k1_altcat_1 A B B))) ) ) )  => (v1_altcat_3 (k5_altcat_1 A B B B D C) A B B)) ) ).
tt(fc4_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k1_altcat_4 A)))  &  ((v2_altcat_1 (k1_altcat_4 A)) &  ((v6_altcat_1 (k1_altcat_4 A)) & (v3_altcat_2 (k1_altcat_4 A) A)) ) ) ) ) ).
tt(fc4_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc4_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_amistd_1 (k4_ami_3 A B) 2 k1_ami_3)) ) ).
tt(fc4_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v2_memstr_0 (k4_amistd_1 A) A) & (v1_extpro_1 (k4_amistd_1 A) A)) ) ) ).
tt(fc4_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k1_extpro_1 A) A) & (v2_amistd_2 (k1_extpro_1 A) A)) ) ) ).
tt(fc4_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) &  ((v2_amistd_5 (k4_amistd_1 A) A) & (v3_amistd_5 (k4_amistd_1 A) A)) ) ) ) ).
tt(fc4_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( (~ (v7_struct_0 (k3_analmetr A)))  &  ((v1_analoaf (k3_analmetr A)) &  ((v1_diraf (k3_analmetr A)) & (v2_diraf (k3_analmetr A))) ) ) ) ) ).
tt(fc4_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) & (v3_anproj_2 (k5_anproj_1 A))) ) ) ).
tt(fc4_aofa_000,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (v7_ordinal1 C)) )  =>  ((v1_funct_1 (k2_funcop_1 (k4_finseq_2 C A) B)) &  ((v2_margrel1 (k2_funcop_1 (k4_finseq_2 C A) B)) & (v8_comput_1 (k2_funcop_1 (k4_finseq_2 C A) B) C)) ) ) ) ).
tt(fc4_armstrng,ax, (! [A:$i] :  ((v1_partfun1 (k7_armstrng A) (k4_armstrng A)) &  ((v1_relat_2 (k7_armstrng A)) &  ((v4_relat_2 (k7_armstrng A)) & (v8_relat_2 (k7_armstrng A))) ) ) ) ).
tt(fc4_asympt_1,ax, ((v1_funct_1 (k4_asympt_1 1)) &  ((v1_funct_2 (k4_asympt_1 1) k5_numbers k1_numbers) & (v2_asympt_0 (k4_asympt_1 1))) ) ).
tt(fc4_autalg_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (v1_msualg_3 (k2_msualg_3 A B))) ) ).
tt(fc4_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m1_bcialg_2 B A))  =>  (~ (v2_struct_0 (k9_bcialg_2 A B))) ) ) ).
tt(fc4_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  =>  (~ (v2_struct_0 (k10_bcialg_6 A B C D))) ) ) ).
tt(fc4_bilinear,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A)) ) )  =>  ((v1_funct_1 (k1_bilinear A B C)) &  ((v1_funct_2 (k1_bilinear A B C) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v4_bilinear (k1_bilinear A B C) A B C)) ) ) ) ).
tt(fc4_binop_2,ax, ((v1_funct_1 k35_binop_2) &  ((v1_funct_2 k35_binop_2 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) &  ((v1_binop_1 k35_binop_2 k1_numbers) & (v2_binop_1 k35_binop_2 k1_numbers)) ) ) ).
tt(fc4_bor_cant,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C k5_numbers) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) )  =>  ((v1_relat_1 (k9_nat_1 D C)) &  ((v4_relat_1 (k9_nat_1 D C) k5_numbers) &  ((v5_relat_1 (k9_nat_1 D C) B) &  ((v1_funct_1 (k9_nat_1 D C)) & (v1_partfun1 (k9_nat_1 D C) k5_numbers)) ) ) ) ) ) ).
tt(fc4_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_struct_0 B) &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v2_struct_0 (k2_borsuk_1 B A)) &  ((v1_pre_topc (k2_borsuk_1 B A)) & (v2_pre_topc (k2_borsuk_1 B A))) ) ) ) ).
tt(fc4_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k15_funct_3 E F)) &  ((v1_funct_2 (k15_funct_3 E F) (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 C D))) & (v5_pre_topc (k15_funct_3 E F) (k2_borsuk_1 A B) (k2_borsuk_1 C D))) ) ) ) ).
tt(fc4_borsuk_3,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v1_compts_1 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc4_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k2_xcmplx_0 A B))) ) ) ).
tt(fc4_borsuk_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (m1_pre_topc A (k2_borsuk_1 k5_topmetr k5_topmetr)))  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_xreal_0 (k2_xtuple_0 B))) ) ).
tt(fc4_borsuk_7,ax,(v1_borsuk_7 k1_xboole_0)).
tt(fc4_brouwer,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v1_topalg_2 (k2_brouwer A B C) A)) ) ).
tt(fc4_bspace,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k8_bspace A))) ) ).
tt(fc4_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k11_bvfunc_1 A)) &  ((v3_funct_1 (k11_bvfunc_1 A)) & (v1_funct_2 (k11_bvfunc_1 A) A k6_margrel1)) ) ) ) ).
tt(fc4_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k11_c0sp1 A))) ) ) ).
tt(fc4_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k3_c0sp2 A)))  & (v1_funcsdom (k3_c0sp2 A))) ) ) ).
tt(fc4_card_1,ax,(v1_card_1 k4_ordinal1)).
tt(fc4_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v4_funct_1 (k4_card_3 A))) ) ).
tt(fc4_card_5,ax, (! [A:$i,B:$i] :  ( ((v1_card_1 A) &  ( (~ (v1_finset_1 B))  & (v1_card_1 B)) )  =>  ( (~ (v1_finset_1 (k1_card_2 A B)))  & (v1_card_1 (k1_card_2 A B))) ) ) ).
tt(fc4_cardfin2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((v5_ordinal1 (k24_valued_1 B A)) &  ((v1_relat_1 (k24_valued_1 B A)) &  ((v5_relat_1 (k24_valued_1 B A) k4_numbers) &  ((v1_funct_1 (k24_valued_1 B A)) & (v1_finset_1 (k24_valued_1 B A))) ) ) ) ) ) ).
tt(fc4_cat_4,ax, (! [A:$i,B:$i] :  ( (~ (v2_struct_0 (k23_cat_4 A B)))  &  ( (~ (v11_struct_0 (k23_cat_4 A B)))  &  ((v2_cat_1 (k23_cat_4 A B)) &  ((v3_cat_1 (k23_cat_4 A B)) &  ((v4_cat_1 (k23_cat_4 A B)) &  ((v5_cat_1 (k23_cat_4 A B)) &  ((v6_cat_1 (k23_cat_4 A B)) & (v5_cat_4 (k23_cat_4 A B))) ) ) ) ) ) ) ) ).
tt(fc4_catalg_1,ax, (! [A:$i] :  ((v1_msualg_1 (k2_catalg_1 A)) & (v3_catalg_1 (k2_catalg_1 A))) ) ).
tt(fc4_cayley,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k2_cayley A)))  &  ((v15_algstr_0 (k2_cayley A)) &  ((v2_group_1 (k2_cayley A)) &  ((v3_group_1 (k2_cayley A)) & (v1_monoid_0 (k2_cayley A))) ) ) ) ) ).
tt(fc4_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_struct_0 (k7_cc0sp1 A))) ) ) ).
tt(fc4_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k3_cc0sp2 A)))  &  ((v13_algstr_0 (k3_cc0sp2 A)) &  ((v2_rlvect_1 (k3_cc0sp2 A)) &  ((v3_rlvect_1 (k3_cc0sp2 A)) &  ((v4_rlvect_1 (k3_cc0sp2 A)) &  ((v3_group_1 (k3_cc0sp2 A)) &  ((v5_group_1 (k3_cc0sp2 A)) &  ((v1_vectsp_1 (k3_cc0sp2 A)) &  ((v3_vectsp_1 (k3_cc0sp2 A)) &  ((v2_clvect_1 (k3_cc0sp2 A)) &  ((v3_clvect_1 (k3_cc0sp2 A)) &  ((v4_clvect_1 (k3_cc0sp2 A)) &  ((v1_cfuncdom (k3_cc0sp2 A)) & (v2_cfuncdom (k3_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc4_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v3_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) &  ((v1_partfun1 (k45_valued_1 A B) k2_numbers) & (v3_cfdiff_1 (k45_valued_1 A B))) ) ) ) ).
tt(fc4_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_cfuncdom A)))  & (v1_cfuncdom (k8_cfuncdom A))) ) ) ).
tt(fc4_cgames_1,ax,(v1_xboole_0 (k7_cgames_1 k3_cgames_1))).
tt(fc4_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  => (v1_xtuple_0 (k3_circcmb3 A))) ) ).
tt(fc4_circtrm1,ax, (! [A:$i,B:$i] :  ( ((v3_trees_3 A) & (v3_trees_3 B))  => (v3_trees_3 (k2_xboole_0 A B))) ) ).
tt(fc4_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_classes2 (k1_classes1 A))) ) ).
tt(fc4_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v2_rlvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v3_rlvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v4_rlvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v1_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v2_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v3_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) &  ((v4_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)))) & (v5_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc4_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_clopban2 A)))  & (v1_cfuncdom (k8_clopban2 A))) ) ) ).
tt(fc4_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v6_closure1 B A) & (l1_closure1 B A)) )  => (v1_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc4_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((v1_relat_1 (k4_closure2 A B C)) &  ((v2_relat_1 (k4_closure2 A B C)) &  ((v4_relat_1 (k4_closure2 A B C) A) &  ((v1_funct_1 (k4_closure2 A B C)) & (v1_partfun1 (k4_closure2 A B C) A)) ) ) ) ) ) ).
tt(fc4_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  =>  ( (~ (v1_xboole_0 (k2_cohsp_1 A)))  & (v1_classes1 (k2_cohsp_1 A))) ) ) ).
tt(fc4_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc4_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (~ (v2_struct_0 (k1_compact1 A)))  & (v1_pre_topc (k1_compact1 A))) ) ) ).
tt(fc4_complex1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  =>  ( (~ (v1_xboole_0 (k16_complex1 A)))  & (v1_xreal_0 (k16_complex1 A))) ) ) ).
tt(fc4_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_metric_1 (k3_compl_sp A B C)) & (v9_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(fc4_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  =>  ((v1_relat_1 (k5_xtuple_0 B)) & (v1_funct_1 (k5_xtuple_0 B))) ) ) ).
tt(fc4_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k5_compos_1 A B C)) &  ((v4_relat_1 (k5_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k5_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k5_compos_1 A B C)) & (v1_finset_1 (k5_compos_1 A B C))) ) ) ) ) ) ).
tt(fc4_compts_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v8_struct_0 (k1_compts_1 A))) ) ).
tt(fc4_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k3_comput_1 A B)))  &  ((v1_relat_1 (k3_comput_1 A B)) &  ((v4_relat_1 (k3_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k3_comput_1 A B)) &  ((v4_valued_0 (k3_comput_1 A B)) &  ((v2_margrel1 (k3_comput_1 A B)) & (v2_comput_1 (k3_comput_1 A B))) ) ) ) ) ) ) ) ).
tt(fc4_comseq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) &  ((v1_funct_2 (k1_valued_1 A B) k5_numbers k2_numbers) & (v2_comseq_2 (k1_valued_1 A B))) ) ) ) ).
tt(fc4_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k3_comseq_3 A)) &  ((v1_funct_2 (k3_comseq_3 A) k5_numbers k1_numbers) & (v2_comseq_2 (k3_comseq_3 A))) ) ) ) ).
tt(fc4_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v3_lattices (k11_conlat_1 A)) & (v10_lattices (k11_conlat_1 A))) ) ) ) ).
tt(fc4_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  ( (~ (v2_struct_0 (k15_convex4 A)))  &  ((v13_algstr_0 (k15_convex4 A)) &  ((v2_rlvect_1 (k15_convex4 A)) &  ((v3_rlvect_1 (k15_convex4 A)) &  ((v4_rlvect_1 (k15_convex4 A)) &  ((v1_clvect_1 (k15_convex4 A)) &  ((v2_clvect_1 (k15_convex4 A)) &  ((v3_clvect_1 (k15_convex4 A)) &  ((v4_clvect_1 (k15_convex4 A)) & (v5_clvect_1 (k15_convex4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc4_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_rlvect_1 B)) ) )  => (v4_rlvect_1 (k3_convfun1 A B))) ) ).
tt(fc4_csspace3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g2_clvect_1 A B C D E)))  & (v7_clvect_1 (g2_clvect_1 A B C D E))) ) ) ).
tt(fc4_csspace4,ax, ((v13_algstr_0 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v2_rlvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v3_rlvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v4_rlvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v2_clvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v3_clvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v4_clvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) &  ((v5_clvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4)) & (v7_clvect_1 (g2_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4) k2_csspace4))) ) ) ) ) ) ) ) ).
tt(fc4_csspace,ax, ( (~ (v2_struct_0 (g1_csspace k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace) k17_csspace)))  & (v1_csspace (g1_csspace k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace) k17_csspace))) ).
tt(fc4_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_2 (k5_dickson A)) & (v5_orders_2 (k5_dickson A))) ) ) ).
tt(fc4_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  ((v2_xxreal_0 (k2_dilworth A)) & (v7_ordinal1 (k2_dilworth A))) ) ) ).
tt(fc4_dist_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 B A)) )  => (v1_matrprob (k4_dist_1 A B))) ) ).
tt(fc4_dtconstr,ax, ( (~ (v2_struct_0 k5_dtconstr))  &  ((v1_lang1 k5_dtconstr) &  ((v1_dtconstr k5_dtconstr) &  ((v2_dtconstr k5_dtconstr) & (v3_dtconstr k5_dtconstr)) ) ) ) ).
tt(fc4_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  => (v2_ec_pf_1 (k5_struct_0 (k9_int_3 A)) A)) ) ).
tt(fc4_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v22_algstr_0 (k6_endalg A B)) &  ((v3_group_1 (k6_endalg A B)) & (v4_vectsp_1 (k6_endalg A B))) ) ) ) ).
tt(fc4_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_ens_1 A)))  &  ( (~ (v11_struct_0 (k11_ens_1 A)))  &  ((v1_cat_1 (k11_ens_1 A)) &  ((v2_cat_1 (k11_ens_1 A)) &  ((v3_cat_1 (k11_ens_1 A)) &  ((v4_cat_1 (k11_ens_1 A)) &  ((v5_cat_1 (k11_ens_1 A)) & (v6_cat_1 (k11_ens_1 A))) ) ) ) ) ) ) ) ) ).
tt(fc4_eqrel_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  => (v1_setfam_1 (k7_eqrel_1 A B))) ) ).
tt(fc4_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v1_relat_1 (k4_equation A)) &  ((v2_relat_1 (k4_equation A)) &  ((v4_relat_1 (k4_equation A) (u1_struct_0 A)) &  ((v1_funct_1 (k4_equation A)) & (v1_partfun1 (k4_equation A) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc4_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v3_xxreal_0 B) & (v1_xreal_0 B)) )  => (v1_xboole_0 (k1_xxreal_1 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)))) ) ).
tt(fc4_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k14_euclid A)))  &  ((v1_metric_1 (k14_euclid A)) &  ((v6_metric_1 (k14_euclid A)) &  ((v7_metric_1 (k14_euclid A)) &  ((v8_metric_1 (k14_euclid A)) & (v9_metric_1 (k14_euclid A))) ) ) ) ) ) ) ).
tt(fc4_exchsort,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v1_xreal_0 B))  =>  ((v1_relat_1 (k1_tarski (k4_tarski A B))) &  ((v1_funct_1 (k1_tarski (k4_tarski A B))) &  ((v3_valued_0 (k1_tarski (k4_tarski A B))) & (v1_exchsort (k1_tarski (k4_tarski A B)))) ) ) ) ) ).
tt(fc4_extpro_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v2_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) )  => (v2_extpro_1 (k2_compos_1 B) A B)) ) ).
tt(fc4_facirc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_facirc_1 A))  &  (~ (v1_facirc_1 B)) )  =>  (~ (v1_facirc_1 (k2_xboole_0 A B))) ) ) ).
tt(fc4_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) & (v1_fcont_1 (k45_valued_1 A B))) ) ) ).
tt(fc4_fcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v2_rcomp_1 (k1_limfunc1 A))) ) ).
tt(fc4_fib_num2,ax,(v3_xxreal_2 k4_ordinal1)).
tt(fc4_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k6_filter_0 A (k2_filter_0 A B))))  &  ((v10_lattices (k6_filter_0 A (k2_filter_0 A B))) & (v13_lattices (k6_filter_0 A (k2_filter_0 A B)))) ) ) ) ).
tt(fc4_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v20_lattices (k3_filter_2 A B) (k1_lattice2 A))) ) ).
tt(fc4_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_card_1 (k1_finseq_1 A) A)) ) ).
tt(fc4_finseq_2,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v3_card_1 (k2_finseq_2 A B) A) & (v1_finseq_1 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc4_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (v1_finseq_1 (k8_finseq_4 A B C D E))) ).
tt(fc4_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  &  ((v2_funct_1 C) & (m1_finseq_1 C B)) ) )  =>  ((v1_relat_1 (k1_rfinseq A C)) &  ((v1_funct_1 (k1_rfinseq A C)) &  ((v2_funct_1 (k1_rfinseq A C)) & (v1_finseq_1 (k1_rfinseq A C))) ) ) ) ) ).
tt(fc4_finseq_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_finseq_1 B A))  & (m1_subset_1 C A)) )  =>  (~ (v1_xboole_0 (k1_finseq_6 A B C))) ) ) ).
tt(fc4_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v1_finset_1 (k2_enumset1 A B C D))) ).
tt(fc4_fintopo6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (u1_struct_0 A)))  => (v3_fintopo6 (k1_tarski B) A)) ) ).
tt(fc4_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k5_relat_1 A (k1_tarski B))) & (v2_funct_1 (k5_relat_1 A (k1_tarski B)))) ) ) ).
tt(fc4_fomodel1,ax, (! [A:$i] :  ( ((v11_fomodel1 A) & (l1_fomodel1 A))  =>  (~ (v1_finset_1 (k2_fomodel1 A))) ) ) ).
tt(fc4_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ((v1_xboole_0 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_xboole_0 (k6_fomodel2 A B)) &  ((v1_relat_1 (k6_fomodel2 A B)) & (v1_funct_1 (k6_fomodel2 A B))) ) ) ) ).
tt(fc4_fomodel3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v8_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((v1_relat_1 (k5_relat_1 (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A)))) & (v5_relat_1 (k5_relat_1 (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A))) (k35_fomodel1 A))) ) ) ).
tt(fc4_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  => (v1_relat_1 (k3_tarski B))) ) ).
tt(fc4_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ((v1_lang1 (k3_freealg A B)) &  ((v1_dtconstr (k3_freealg A B)) &  ((v2_dtconstr (k3_freealg A B)) & (v3_dtconstr (k3_freealg A B))) ) ) ) ) ).
tt(fc4_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) ) ) )  =>  ( (~ (v2_struct_0 (k11_fsm_1 A B C)))  &  ((v8_struct_0 (k11_fsm_1 A B C)) & (v2_fsm_1 (k11_fsm_1 A B C) A B)) ) ) ) ).
tt(fc4_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B)) ) )  =>  ( (~ (v2_struct_0 (g1_rewrite3 B (u1_struct_0 C) (u1_rewrite3 B C))))  & (v1_rewrite3 (g1_rewrite3 B (u1_struct_0 C) (u1_rewrite3 B C)) B)) ) ) ).
tt(fc4_funcop_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~ (v1_xboole_0 (k2_funcop_1 B A))) ) ) ).
tt(fc4_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_group_1 (k12_funcsdom A)) & (v1_funcsdom (k12_funcsdom A))) ) ) ).
tt(fc4_funct_1,ax, (! [A:$i] :  ((v1_relat_1 (k4_relat_1 A)) & (v2_funct_1 (k4_relat_1 A))) ) ).
tt(fc4_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v1_funct_1 (k3_relat_1 D C)) & (v1_funct_2 (k3_relat_1 D C) A B)) ) ) ).
tt(fc4_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  (~ (v1_xboole_0 B)) ) ) )  =>  ((v1_relat_1 (k1_funct_4 B A)) &  ((v1_funct_1 (k1_funct_4 B A)) &  (~ (v1_xboole_0 (k1_funct_4 B A))) ) ) ) ) ).
tt(fc4_funct_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  => (v1_funcop_1 (k10_finseq_1 A B))) ) ).
tt(fc4_funct_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_funct_9 B A)) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_funct_9 C A)) ) ) ) )  =>  ((v1_relat_1 (k18_valued_1 B C)) &  ((v1_funct_1 (k18_valued_1 B C)) & (v1_funct_9 (k18_valued_1 B C) A)) ) ) ) ).
tt(fc4_functor0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k2_funct_4 A)) &  ((v1_funct_1 (k2_funct_4 A)) & (v1_funcop_1 (k2_funct_4 A))) ) ) ) ).
tt(fc4_fvaluat1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_fvaluat1 A)) )  => (v1_fvaluat1 (k1_funct_1 A B))) ) ).
tt(fc4_gate_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k2_gate_1 A B))) ) ).
tt(fc4_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v1_finset_1 (k7_glib_000 A))) ) ).
tt(fc4_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (v1_glib_001 (k2_glib_001 A B B C) A)) ) ).
tt(fc4_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))))  => (v1_finset_1 (k2_xtuple_0 B))) ) ).
tt(fc4_glib_005,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_005 B A) & (v7_ordinal1 C)) )  =>  ((v1_partfun1 (k1_funct_1 B C) (k7_glib_000 A)) & (v4_valued_0 (k1_funct_1 B C))) ) ) ).
tt(fc4_goboard2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v5_valued_0 A) & (m1_finseq_1 A k1_numbers)) )  &  ( (~ (v1_xboole_0 B))  &  ((v5_valued_0 B) & (m1_finseq_1 B k1_numbers)) ) )  =>  ((v1_matrix_1 (k1_goboard2 A B)) &  ((v4_goboard1 (k1_goboard2 A B)) & (v5_goboard1 (k1_goboard2 A B))) ) ) ) ).
tt(fc4_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k4_graph_3 A B C))) ) ).
tt(fc4_graph_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_finset_1 (k4_graph_5 A B C))) ) ).
tt(fc4_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  =>  ((v1_funct_1 (k6_grcat_1 A B)) &  ((v1_funct_2 (k6_grcat_1 A B) (u1_struct_0 A) (u1_struct_0 B)) & (v13_vectsp_1 (k6_grcat_1 A B) A B)) ) ) ) ).
tt(fc4_gr_cy_1,ax, ( (~ (v2_struct_0 k2_gr_cy_1))  &  ((v15_algstr_0 k2_gr_cy_1) &  ((v2_group_1 k2_gr_cy_1) & (v3_group_1 k2_gr_cy_1)) ) ) ).
tt(fc4_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k5_groeb_3 A B C D 1)) &  ((v1_funct_2 (k5_groeb_3 A B C D 1) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k5_groeb_3 A B C D 1) (k15_pre_poly A) C) &  ((v1_polynom7 (k5_groeb_3 A B C D 1) A C) & (v3_polynom7 (k5_groeb_3 A B C D 1) A C)) ) ) ) ) ) ).
tt(fc4_group_10,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ( (~ (v2_struct_0 (k4_gr_cy_1 A)))  &  ((v15_algstr_0 (k4_gr_cy_1 A)) & (v2_group_10 (k4_gr_cy_1 A) A)) ) ) ) ).
tt(fc4_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  & (m1_subset_1 C A)) )  =>  (~ (v1_xboole_0 (k1_group_12 A B C))) ) ) ).
tt(fc4_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (~ (v4_group_1 (k1_group_1 A) A)) ) ) ).
tt(fc4_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (~ (v1_xboole_0 (k15_group_2 A B))) ) ) ).
tt(fc4_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v3_group_7 B A)) ) ) ) )  =>  ((v15_algstr_0 (k2_group_7 A B)) & (v3_group_1 (k2_group_7 A B))) ) ) ).
tt(fc4_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (~ (v2_struct_0 (k10_group_9 A B C))) ) ) ).
tt(fc4_hausdorf,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) ) )  =>  ((v1_funct_1 (k6_weierstr A B)) &  ((v1_funct_2 (k6_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k6_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ).
tt(fc4_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k2_heyting3 A B))) ) ).
tt(fc4_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_hilbasis A B)) &  ((v1_funct_2 (k6_hilbasis A B) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (v6_group_1 (k6_hilbasis A B) (k14_polynom3 (k11_polynom1 B A)) (k11_polynom1 (k2_nat_1 B 1) A))) ) ) ) ).
tt(fc4_hilbert1,ax,(v6_hilbert1 k6_hilbert1)).
tt(fc4_hilbert3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) )  =>  ((v1_funct_1 (k15_funct_3 C D)) &  ((v1_funct_2 (k15_funct_3 C D) (k2_zfmisc_1 A B) (k2_zfmisc_1 A B)) & (v3_funct_2 (k15_funct_3 C D) (k2_zfmisc_1 A B) (k2_zfmisc_1 A B))) ) ) ) ).
tt(fc4_idea_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  & (m1_matrix_1 D k5_numbers B 6)) ) )  =>  ((v1_relat_1 (k18_idea_1 A B C D)) &  ((v1_funct_1 (k18_idea_1 A B C D)) &  ((v1_funcop_1 (k18_idea_1 A B C D)) & (v1_finseq_1 (k18_idea_1 A B C D))) ) ) ) ) ).
tt(fc4_index_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) ) )  =>  ((v1_relat_1 (k3_index_1 B)) &  ((v2_relat_1 (k3_index_1 B)) &  ((v4_relat_1 (k3_index_1 B) A) & (v1_funct_1 (k3_index_1 B))) ) ) ) ) ).
tt(fc4_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (v1_int_1 (k6_xcmplx_0 A B))) ) ).
tt(fc4_int_3,ax, ( (~ (v6_struct_0 k1_int_3))  &  ((v13_algstr_0 k1_int_3) &  ((v3_group_1 k1_int_3) &  ((v5_group_1 k1_int_3) &  ((v2_rlvect_1 k1_int_3) &  ((v3_rlvect_1 k1_int_3) &  ((v4_rlvect_1 k1_int_3) &  ((v5_vectsp_1 k1_int_3) & (v1_vectsp_2 k1_int_3)) ) ) ) ) ) ) ) ).
tt(fc4_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_relat_2 (k1_int_4 A)) &  ((v3_relat_2 (k1_int_4 A)) & (v8_relat_2 (k1_int_4 A))) ) ) ) ).
tt(fc4_int_6,ax, (! [A:$i] :  ((v1_int_1 A) => (v5_relat_1 (k5_finseq_1 A) k4_numbers)) ) ).
tt(fc4_integr16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((v1_funct_1 (k4_comseq_3 B)) & (v1_funct_2 (k4_comseq_3 B) A k1_numbers)) ) ) ).
tt(fc4_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k1_interva1 A (k2_subset_1 A) (k2_subset_1 A)))) ) ) ).
tt(fc4_intpro_1,ax,(v8_intpro_1 k8_intpro_1)).
tt(fc4_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v5_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v6_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc4_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k7_relat_1 k4_pscomp_1 (k5_topreal1 A)))) ) ) ).
tt(fc4_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v1_convex1 (k7_topreal1 A) (k15_euclid 2))) ) ).
tt(fc4_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v2_funct_1 (k2_jordan1e A B)) &  ((v1_topreal1 (k2_jordan1e A B)) &  ((v2_topreal1 (k2_jordan1e A B)) & (v3_topreal1 (k2_jordan1e A B))) ) ) ) ) ).
tt(fc4_jordan1h,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  &  ( (~ (v1_xboole_0 B))  &  ((v2_relat_1 B) & (m1_finseq_1 B (k3_finseq_2 A))) ) )  =>  (~ (v1_xboole_0 (k16_matrix_1 B))) ) ) ).
tt(fc4_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v2_compts_1 (k4_jordan19 A) (k15_euclid 2))) ) ).
tt(fc4_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_jordan23 A)) ) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) &  ((v1_finseq_1 (k3_finseq_5 A)) & (v1_jordan23 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc4_jordan2c,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v2_tops_1 (k1_rltopsp1 (k15_euclid 2) A B) (k15_euclid 2))) ) ).
tt(fc4_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k10_pscomp_1 A)))) ) ).
tt(fc4_kurato_1,ax, ( (~ (v3_pre_topc k6_kurato_1 k3_topmetr))  &  (~ (v4_pre_topc k6_kurato_1 k3_topmetr)) ) ).
tt(fc4_kurato_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  => (v4_pre_topc (k1_kurato_2 A B) A)) ) ).
tt(fc4_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k9_lang1 A)))  & (v2_lang1 (k9_lang1 A))) ) ) ).
tt(fc4_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) & (l2_lattices A)) )  =>  ((v1_funct_1 (u2_lattices A)) &  ((v1_funct_2 (u2_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v2_binop_1 (u2_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc4_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v2_struct_0 (k3_lattice3 A)))  &  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) & (v5_orders_2 (k3_lattice3 A))) ) ) ) ) ) ).
tt(fc4_lattice5,ax, (! [A:$i] :  (~ (v1_xboole_0 (k5_lattice5 A))) ) ).
tt(fc4_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_xboole_0 (k2_struct_0 A)))  &  ((v18_lattices (k2_struct_0 A) A) & (v19_lattices (k2_struct_0 A) A)) ) ) ) ).
tt(fc4_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v2_lexbfs (k16_lexbfs A))) ) ).
tt(fc4_lfuzzy_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v9_waybel_1 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k6_yellow_1 A B)) & (v9_waybel_1 (k6_yellow_1 A B))) ) ) ).
tt(fc4_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_4 C A B)) )  =>  ( (~ (v2_struct_0 (k17_lmod_7 A B C)))  & (v7_vectsp_1 (k17_lmod_7 A B C) A)) ) ) ).
tt(fc4_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v1_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v2_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v3_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v4_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v5_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v6_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) &  ((v7_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)))) & (v8_rlvect_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc4_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_lopban_2 A)))  & (v1_funcsdom (k8_lopban_2 A))) ) ) ).
tt(fc4_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (~ (v1_xboole_0 (k10_lopclset A))) ) ) ).
tt(fc4_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k11_lpspace1 A B C)))  &  ((v1_ideal_1 (k11_lpspace1 A B C) (k10_lpspace1 A B C)) & (v1_lpspace1 (k11_lpspace1 A B C) (k10_lpspace1 A B C))) ) ) ) ).
tt(fc4_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v1_xboole_0 (k3_lpspace2 A B C D)))  &  ((v1_ideal_1 (k3_lpspace2 A B C D) (k2_lpspace2 A B C D)) & (v1_lpspace1 (k3_lpspace2 A B C D) (k2_lpspace2 A B C D))) ) ) ) ).
tt(fc4_lukasi_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_cqc_lang A)) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A D (k8_cqc_lang A C B)) (k8_cqc_lang A C (k8_cqc_lang A D B))) A)) ) ).
tt(fc4_margrel1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  => (v1_xboolean (k1_funct_1 A B))) ) ).
tt(fc4_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (u2_algstr_0 A)) &  ((v1_funct_2 (u2_algstr_0 A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v2_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ).
tt(fc4_matrix13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (v7_ordinal1 B))  =>  ((v7_vectsp_1 (k6_prvect_1 A B) A) & (v1_matrlin (k6_prvect_1 A B) A)) ) ) ).
tt(fc4_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v15_algstr_0 (k13_matrix_2 A)) &  ((v2_group_1 (k13_matrix_2 A)) & (v3_group_1 (k13_matrix_2 A))) ) ) ) ).
tt(fc4_matroid0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k4_xboole_0 B C) A)) ) ).
tt(fc4_matrtop1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v4_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_relat_1 (k5_relat_1 C B)) & (v4_partfun3 (k5_relat_1 C B))) ) ) ).
tt(fc4_matrtop3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v1_topreal9 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 C B)) &  ((v1_funct_2 (k3_relat_1 C B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v1_topreal9 (k3_relat_1 C B) A)) ) ) ) ).
tt(fc4_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ((v3_membered A) & (v3_xxreal_2 A))  &  ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  => (v3_xxreal_2 (k23_member_1 A B))) ) ).
tt(fc4_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~ (v1_xboole_0 (k5_measure6 A))) ) ) ).
tt(fc4_member_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  =>  ( (~ (v1_xboole_0 (k4_member_1 A)))  & (v2_membered (k4_member_1 A))) ) ) ).
tt(fc4_membered,ax,(v4_membered k3_numbers)).
tt(fc4_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_memstr_0 (k1_memstr_0 A) A) & (v3_memstr_0 (k1_memstr_0 A) A)) ) ) ).
tt(fc4_mesfun7c,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) ) )  =>  ((v1_funct_1 (k12_mesfun7c A B)) &  ((v1_funct_2 (k12_mesfun7c A B) k5_numbers (k4_partfun1 A k1_numbers)) & (v1_mesfunc8 (k12_mesfun7c A B) A k1_numbers)) ) ) ) ).
tt(fc4_mesfunc7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (v7_ordinal1 B))  =>  ((v1_relat_1 (k2_finseq_2 B A)) &  ((v1_funct_1 (k2_finseq_2 B A)) &  ((v1_finseq_1 (k2_finseq_2 B A)) & (v2_valued_0 (k2_finseq_2 B A))) ) ) ) ) ).
tt(fc4_metric_1,ax, (! [A:$i] :  ((v1_metric_1 (k6_metric_1 A)) &  ((v6_metric_1 (k6_metric_1 A)) &  ((v7_metric_1 (k6_metric_1 A)) &  ((v8_metric_1 (k6_metric_1 A)) & (v9_metric_1 (k6_metric_1 A))) ) ) ) ) ).
tt(fc4_metrizts,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_xboole_0 (k2_waybel23 A)) & (v1_card_1 (k2_waybel23 A))) ) ) ).
tt(fc4_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v2_mfold_1 (k15_euclid A) A)) ) ) ).
tt(fc4_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_mfold_2 A)))  & (v2_pre_topc (k4_mfold_2 A))) ) ) ).
tt(fc4_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ( (~ (v2_struct_0 (k15_midsp_1 A)))  & (v8_algstr_0 (k15_midsp_1 A))) ) ) ).
tt(fc4_midsp_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  ( (~ (v2_struct_0 (g1_midsp_1 A B)))  & (v1_midsp_1 (g1_midsp_1 A B))) ) ) ).
tt(fc4_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (v1_mmlquery (k4_xboole_0 B C) A)) ) ).
tt(fc4_mod_2,ax, ( (~ (v2_struct_0 k18_mod_2))  & (v36_algstr_0 k18_mod_2)) ).
tt(fc4_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  ((v13_algstr_0 (k2_mod_4 A)) &  ((v36_algstr_0 (k2_mod_4 A)) &  ((v3_rlvect_1 (k2_mod_4 A)) & (v4_rlvect_1 (k2_mod_4 A))) ) ) ) ) ).
tt(fc4_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  => (v1_modelc_1 (k10_modelc_1 A))) ) ).
tt(fc4_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_2 (k4_modelc_2 A B))) ) ).
tt(fc4_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k3_tarski (k1_orders_1 (k1_modelc_3 A))))) ) ) ).
tt(fc4_moebius1,ax, (! [A:$i] :  ((v1_relat_1 (k4_moebius1 A)) &  ((v4_relat_1 (k4_moebius1 A) k5_numbers) &  ((v1_funct_1 (k4_moebius1 A)) &  ((v1_partfun1 (k4_moebius1 A) k5_numbers) & (v3_valued_0 (k4_moebius1 A))) ) ) ) ) ).
tt(fc4_monoid_0,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k17_monoid_0 A)))  &  ((v15_algstr_0 (k17_monoid_0 A)) &  ((v1_group_1 (k17_monoid_0 A)) & (v13_monoid_0 (k17_monoid_0 A))) ) ) ) ).
tt(fc4_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (~ (v2_struct_0 (k22_monoid_1 A))) ) ) ).
tt(fc4_msafree1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (k8_msafree A B)) &  ((v4_relat_1 (k8_msafree A B) (u1_struct_0 A)) &  ((v1_funct_1 (k8_msafree A B)) &  ((v1_partfun1 (k8_msafree A B) (u1_struct_0 A)) & (v1_prob_2 (k8_msafree A B))) ) ) ) ) ) ).
tt(fc4_msafree,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) ) )  =>  (~ (v1_xboole_0 (k3_card_3 B))) ) ) ).
tt(fc4_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_relat_1 (k3_funct_6 B)) &  ((v4_relat_1 (k3_funct_6 B) A) &  ((v1_funct_1 (k3_funct_6 B)) & (v1_partfun1 (k3_funct_6 B) A)) ) ) ) ) ).
tt(fc4_mssublat,ax, (! [A:$i] :  ( ((v4_unialg_1 A) & (l1_unialg_1 A))  =>  ((v1_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) & (v4_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A)))) ) ) ).
tt(fc4_msualg_1,ax, (! [A:$i,B:$i] :  ( ( ((v13_struct_0 A 1) & (l1_msualg_1 A))  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (~ (v1_xboole_0 (k10_msualg_1 A B))) ) ) ).
tt(fc4_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v2_relat_1 C) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((v2_relat_1 (k8_msualg_6 A B C)) &  ((v3_msualg_6 (k8_msualg_6 A B C) A B) & (v4_msualg_6 (k8_msualg_6 A B C) A B)) ) ) ) ).
tt(fc4_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v1_relat_1 (u3_msualg_1 A (k7_msafree2 A))) &  ((v2_relat_1 (u3_msualg_1 A (k7_msafree2 A))) &  ((v4_relat_1 (u3_msualg_1 A (k7_msafree2 A)) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A (k7_msafree2 A))) &  ((v1_partfun1 (u3_msualg_1 A (k7_msafree2 A)) (u1_struct_0 A)) & (v2_finset_1 (u3_msualg_1 A (k7_msafree2 A)))) ) ) ) ) ) ) ).
tt(fc4_mycielsk,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_mycielsk A) & (l1_orders_2 A)) )  =>  ((v7_ordinal1 (k2_mycielsk A)) & (v2_xxreal_0 (k2_mycielsk A))) ) ) ).
tt(fc4_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  =>  (~ (v1_xboole_0 (k2_xcmplx_0 B A))) ) ) ).
tt(fc4_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k4_nat_3 A B C)) &  ((v4_relat_1 (k4_nat_3 A B C) A) &  ((v1_funct_1 (k4_nat_3 A B C)) &  ((v1_partfun1 (k4_nat_3 A B C) A) & (v3_valued_0 (k4_nat_3 A B C))) ) ) ) ) ) ).
tt(fc4_nat_lat,ax, ( (~ (v2_struct_0 k3_nat_lat))  &  ((v3_lattices k3_nat_lat) & (v13_lattices k3_nat_lat)) ) ).
tt(fc4_neckla_3,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ( (~ (v2_struct_0 (k2_neckla_2 A B)))  & (v1_orders_2 (k2_neckla_2 A B))) ) ) ).
tt(fc4_necklace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k3_necklace A)))  & (v1_orders_2 (k3_necklace A))) ) ) ).
tt(fc4_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k1_newton A B))) ) ).
tt(fc4_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_nfcont_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_vfunct_1 k1_numbers A B C)) & (v1_nfcont_3 (k2_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc4_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) &  ((v1_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k9_integr15 A C k1_numbers B)) & (v1_nfcont_4 (k9_integr15 A C k1_numbers B) A)) ) ) ).
tt(fc4_normform,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k12_normform A)))  & (v3_lattices (k12_normform A))) ) ).
tt(fc4_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v4_yellow_8 (k4_normsp_2 A)) & (v5_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(fc4_numbers,ax, (~ (v1_xboole_0 k4_numbers)) ).
tt(fc4_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (~ (v1_xboole_0 (k9_openlatt A))) ) ) ).
tt(fc4_oposet_1,ax, ((v3_qmax_1 k1_oposet_1) & (v1_oposet_1 k1_oposet_1)) ).
tt(fc4_orders_1,ax, ((v1_xboole_0 (k2_wellord2 k1_xboole_0)) & (v3_ordinal1 (k2_wellord2 k1_xboole_0))) ).
tt(fc4_orders_2,ax, (! [A:$i] :  ( ((v2_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  => (v4_relat_2 (u1_orders_2 A))) ) ).
tt(fc4_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (~ (v1_xboole_0 (k2_orders_3 A))) ) ) ).
tt(fc4_ordinal1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  => (v3_ordinal1 (k9_xtuple_0 A))) ) ).
tt(fc4_ordinal2,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 A) => (v5_ordinal1 (k2_funcop_1 A B))) ) ).
tt(fc4_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((v3_ordinal1 (k11_ordinal2 A B)) & (v7_ordinal1 (k11_ordinal2 A B))) ) ) ).
tt(fc4_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) & (v1_funct_1 B)) ) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v5_ordinal1 C) & (v1_funct_1 C)) ) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 B C)) &  ((v5_relat_1 (k1_ordinal4 B C) A) &  ((v5_ordinal1 (k1_ordinal4 B C)) & (v1_funct_1 (k1_ordinal4 B C))) ) ) ) ) ).
tt(fc4_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_ordinal2 (k3_afinsq_1 A))) ) ).
tt(fc4_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) )  => (v1_ordinal6 (k10_xtuple_0 A))) ) ).
tt(fc4_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (k5_osafree A B)) &  ((v2_relat_1 (k5_osafree A B)) &  ((v4_relat_1 (k5_osafree A B) (u1_struct_0 A)) &  ((v1_funct_1 (k5_osafree A B)) &  ((v1_partfun1 (k5_osafree A B) (u1_struct_0 A)) & (v11_osalg_1 (k5_osafree A B) A)) ) ) ) ) ) ) ).
tt(fc4_osalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_relat_1 (k3_osalg_1 A B)) &  ((v4_relat_1 (k3_osalg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (k3_osalg_1 A B)) &  ((v1_partfun1 (k3_osalg_1 A B) (u1_struct_0 A)) & (v11_osalg_1 (k3_osalg_1 A B) A)) ) ) ) ) ) ).
tt(fc4_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  & (m2_osalg_2 C A B)) )  => (v3_msualg_2 (k9_osalg_2 A B C) A B)) ) ).
tt(fc4_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) &  ((v3_osalg_4 C A B) & (m1_osalg_4 C A B)) ) ) ) )  =>  ((v12_osalg_1 (k16_osalg_4 A B C) A) & (v13_osalg_1 (k16_osalg_4 A B C) A)) ) ) ).
tt(fc4_partfun1,ax, (! [A:$i,B:$i] : (v4_funct_1 (k4_partfun1 A B))) ).
tt(fc4_partfun3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  =>  ((v1_xreal_0 (k6_square_1 A)) &  (~ (v3_xxreal_0 (k6_square_1 A))) ) ) ) ).
tt(fc4_partfun4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_funct_2 (k30_valued_1 B) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k30_valued_1 B) A)) ) ) ) ).
tt(fc4_pboole,ax, (! [A:$i] :  ((v1_relat_1 (k1_pboole A)) &  ((v3_relat_1 (k1_pboole A)) &  ((v4_relat_1 (k1_pboole A) A) &  ((v1_funct_1 (k1_pboole A)) & (v1_partfun1 (k1_pboole A) A)) ) ) ) ) ).
tt(fc4_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_partfun1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v1_partfun1 (k3_pcs_0 A A B B C D) (k2_zfmisc_1 A B))) ) ).
tt(fc4_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) ) )  =>  (~ (v1_zfmisc_1 (k4_card_3 B))) ) ) ).
tt(fc4_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ( (~ (v2_struct_0 (k11_petri A)))  &  ( (~ (v11_struct_0 (k11_petri A)))  &  ((v1_petri (k11_petri A)) &  ((v2_petri (k11_petri A)) & (v3_petri (k11_petri A))) ) ) ) ) ) ).
tt(fc4_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  ( (~ (v2_struct_0 (k1_polyalg1 A)))  &  ((v13_algstr_0 (k1_polyalg1 A)) & (v1_polyalg1 (k1_polyalg1 A) A)) ) ) ) ).
tt(fc4_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  => (v1_xcmplx_0 (k3_polyeq_1 A B C D))) ) ).
tt(fc4_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v2_struct_0 B))  & (l2_struct_0 B)) )  =>  ((v1_funct_1 (k7_polynom1 A B)) &  ((v1_funct_2 (k7_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k7_polynom1 A B) (k15_pre_poly A) B)) ) ) ) ).
tt(fc4_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom2 A B C)) &  ((v1_funct_2 (k6_polynom2 A B C) (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (v6_group_1 (k6_polynom2 A B C) (k11_polynom1 A B) B)) ) ) ) ).
tt(fc4_polynom3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k5_vfunct_1 k5_numbers A B)) & (v1_algseq_1 (k5_vfunct_1 k5_numbers A B) A)) ) ) ).
tt(fc4_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  ((v1_funct_1 (k9_polynom3 A)) &  ((v1_funct_2 (k9_polynom3 A) k5_numbers (u1_struct_0 A)) & (v1_polynom5 (k9_polynom3 A) A)) ) ) ) ).
tt(fc4_polynom7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v7_algstr_0 B) &  ((v4_rlvect_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  & (m1_subset_1 D (u1_struct_0 B))) )  =>  ((v1_funct_1 (k5_polynom7 A B C D)) &  ((v1_funct_2 (k5_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k5_polynom7 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc4_polyred,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  ((v1_orders_2 (g1_orders_2 (k15_pre_poly A) B)) & (v1_wellfnd1 (g1_orders_2 (k15_pre_poly A) B))) ) ) ).
tt(fc4_poset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) ) ) )  =>  ((v1_funct_1 (k8_poset_1 A B C)) &  ((v1_funct_2 (k8_poset_1 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v2_poset_1 (k8_poset_1 A B C) A B)) ) ) ) ).
tt(fc4_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k15_pralg_1 B C)) &  ((v4_relat_1 (k15_pralg_1 B C) A) & (v1_funct_1 (k15_pralg_1 B C))) ) ) ) ).
tt(fc4_pre_circ,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  & (m1_subset_1 B (k9_xtuple_0 A)))  =>  ((v1_relat_1 (k5_trees_2 A B)) &  ((v1_funct_1 (k5_trees_2 A B)) &  ((v1_finset_1 (k5_trees_2 A B)) & (v3_trees_2 (k5_trees_2 A B))) ) ) ) ) ).
tt(fc4_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  &  ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) &  ((v3_orders_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) )  =>  ((v2_funct_1 (k7_pre_poly A B C)) &  (~ (v1_xboole_0 (k7_pre_poly A B C))) ) ) ) ).
tt(fc4_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v4_pre_topc (k2_struct_0 A) A)) ) ).
tt(fc4_prob_1,ax, (! [A:$i] : (v4_prob_1 (k1_zfmisc_1 A) A)) ).
tt(fc4_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((v5_relat_1 (k3_prob_3 A C) B) &  ((v1_funct_1 (k3_prob_3 A C)) & (v1_funct_2 (k3_prob_3 A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc4_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  =>  ( (~ (v2_struct_0 (k4_prvect_3 A B)))  &  ((v8_algstr_0 (k4_prvect_3 A B)) & (v4_rlvect_1 (k4_prvect_3 A B))) ) ) ) ).
tt(fc4_pscomp_1,ax, ((v1_funct_1 k4_pscomp_1) &  ((v1_funct_2 k4_pscomp_1 (u1_struct_0 (k15_euclid 2)) k1_numbers) & (v1_pscomp_1 k4_pscomp_1 (k15_euclid 2))) ) ).
tt(fc4_pythtrip,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  => (v1_abian (k3_square_1 A))) ) ).
tt(fc4_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k4_qc_lang1 A))) ) ) ).
tt(fc4_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (~ (v1_xboole_0 (k5_qmax_1 A))) ) ) ).
tt(fc4_quatern2,ax, ( (~ (v2_struct_0 k16_quatern2))  & (v36_algstr_0 k16_quatern2)) ).
tt(fc4_quaterni,ax,(v1_quaterni k4_quaterni)).
tt(fc4_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k19_quofield A)))  & (v36_algstr_0 (k19_quofield A))) ) ) ).
tt(fc4_rat_1,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  => (v1_rat_1 (k7_xcmplx_0 A B))) ) ).
tt(fc4_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((v1_funct_1 (k9_polynom3 A)) &  ((v1_funct_2 (k9_polynom3 A) k5_numbers (u1_struct_0 A)) &  ((v1_ratfunc1 (k9_polynom3 A) A) & (v2_ratfunc1 (k9_polynom3 A) A)) ) ) ) ) ).
tt(fc4_rcomp_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v5_xxreal_2 (k2_xxreal_1 A B))) ) ).
tt(fc4_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_xboole_0 (k6_int_1 k6_numbers A)) & (v1_int_1 (k6_int_1 k6_numbers A))) ) ) ).
tt(fc4_real_lat,ax, ((v3_lattices k3_real_lat) & (v11_lattices k3_real_lat)) ).
tt(fc4_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_real_ns1 A)))  &  ((v1_normsp_1 (k4_real_ns1 A)) & (v3_lopban_1 (k4_real_ns1 A))) ) ) ) ).
tt(fc4_realset2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 E A)) ) ) )  =>  ( (~ (v2_struct_0 (g6_algstr_0 A B D E C)))  & (v36_algstr_0 (g6_algstr_0 A B D E C))) ) ) ).
tt(fc4_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  => (v1_relat_1 (k5_xboole_0 A B))) ) ).
tt(fc4_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_relat_2 A))  &  ((v1_relat_1 B) & (v1_relat_2 B)) )  => (v1_relat_2 (k2_xboole_0 A B))) ) ).
tt(fc4_reloc,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_compos_0 (k5_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(fc4_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v5_relat_1 B A))  &  ((v1_relat_1 C) & (v5_relat_1 C A)) )  => (v5_relat_1 (k2_xboole_0 B C) A)) ) ).
tt(fc4_revrot_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 B) & (m1_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) )  => (v1_goboard5 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A))) ) ).
tt(fc4_rewrite2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_rewrite2 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_rewrite2 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v1_rewrite2 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc4_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k4_rfunct_1 A)) &  ((v1_funct_1 (k4_rfunct_1 A)) & (v3_valued_0 (k4_rfunct_1 A))) ) ) ) ).
tt(fc4_rfunct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v7_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v7_valued_0 (k5_relat_1 A B))) ) ) ).
tt(fc4_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_ring_1 A B)))  & (v36_algstr_0 (k2_ring_1 A B))) ) ) ).
tt(fc4_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v4_ringcat1 (k9_ringcat1 A))) ) ).
tt(fc4_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_rlaffin1 (k2_tarski B C) A)) ) ).
tt(fc4_rlaffin3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C k1_numbers)) )  => (v1_finset_1 (k1_convex1 A B C))) ) ).
tt(fc4_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_convex1 (k3_convex1 A B) A) & (v3_rltopsp1 (k3_convex1 A B) A)) ) ) ).
tt(fc4_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k16_rlvect_2 A)) &  ((v2_rlvect_1 (k16_rlvect_2 A)) &  ((v3_rlvect_1 (k16_rlvect_2 A)) &  ((v4_rlvect_1 (k16_rlvect_2 A)) &  ((v5_rlvect_1 (k16_rlvect_2 A)) &  ((v6_rlvect_1 (k16_rlvect_2 A)) &  ((v7_rlvect_1 (k16_rlvect_2 A)) & (v8_rlvect_1 (k16_rlvect_2 A))) ) ) ) ) ) ) ) ) ).
tt(fc4_robbins4,ax, ((v1_lattice3 k1_robbins4) & (v2_lattice3 k1_robbins4)) ).
tt(fc4_rsspace3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_normsp_1 A B C D E)))  & (v1_normsp_1 (g1_normsp_1 A B C D E))) ) ) ).
tt(fc4_rsspace4,ax, ((v13_algstr_0 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v2_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v3_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v4_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v5_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v6_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v7_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) &  ((v8_rlvect_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4)) & (v1_normsp_1 (g1_normsp_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4) k2_rsspace4))) ) ) ) ) ) ) ) ).
tt(fc4_rsspace,ax, ( (~ (v1_xboole_0 k11_rsspace))  & (v1_rlsub_1 k11_rsspace k7_rsspace)) ).
tt(fc4_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  => (v3_valued_0 (k11_finseq_1 A B C))) ) ).
tt(fc4_scm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_int_1 A) &  ((v1_int_1 B) &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v5_relat_1 (k16_afinsq_1 A B C D) k4_numbers)) ) ).
tt(fc4_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_amistd_1 (k8_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc4_scmfsa_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) & (m1_subset_1 B k2_scmfsa_1))  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc4_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc4_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_compos_0 (k9_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc4_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_relat_1 (k2_scmfsa6a A)) &  ((v4_relat_1 (k2_scmfsa6a A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa6a A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa6a A)) &  ((v1_finset_1 (k2_scmfsa6a A)) & (v2_compos_1 (k2_scmfsa6a A) k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(fc4_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_scmfsa6c (k6_scmfsa_2 A B))) ) ).
tt(fc4_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ((m1_scmfsa_2 A) & (m1_finseq_1 B k4_numbers))  =>  ((v1_relat_1 (k4_scmfsa_7 A B)) &  ((v4_relat_1 (k4_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa_7 A B)) &  ((v1_finset_1 (k4_scmfsa_7 A B)) & (v7_amistd_1 (k4_scmfsa_7 A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(fc4_scmfsa8a,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) & (v1_scmfsa7b (k3_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc4_scmfsa8b,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k2_scmfsa8b A B C)))  &  ((v1_relat_1 (k2_scmfsa8b A B C)) &  ((v4_relat_1 (k2_scmfsa8b A B C) k5_numbers) &  ((v5_relat_1 (k2_scmfsa8b A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa8b A B C)) &  ((v1_finset_1 (k2_scmfsa8b A B C)) &  ((v1_afinsq_1 (k2_scmfsa8b A B C)) &  (~ (v2_compos_1 (k2_scmfsa8b A B C) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc4_scmfsa_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v1_scmfsa7b A)) ) ) ) ) ) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ((v1_relat_1 (k2_scmfsa_9 B A)) &  ((v4_relat_1 (k2_scmfsa_9 B A) k5_numbers) &  ((v5_relat_1 (k2_scmfsa_9 B A) (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 (k2_scmfsa_9 B A)))  &  ((v1_funct_1 (k2_scmfsa_9 B A)) &  ((v1_finset_1 (k2_scmfsa_9 B A)) &  ((v1_afinsq_1 (k2_scmfsa_9 B A)) & (v1_scmfsa7b (k2_scmfsa_9 B A))) ) ) ) ) ) ) ) ) ).
tt(fc4_scmfsa_i,ax, ( (~ (v1_xboole_0 k2_scmfsa_i))  & (v2_compos_0 k2_scmfsa_i)) ).
tt(fc4_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((v1_relat_1 (k1_scmfsa_m A)) &  ((v4_relat_1 (k1_scmfsa_m A) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_m A)) &  ((v5_funct_1 (k1_scmfsa_m A) (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 (k1_scmfsa_m A) (u1_struct_0 k1_scmfsa_2))) ) ) ) ) ) ).
tt(fc4_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) &  ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_scm_halt B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) & (v2_scm_halt (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc4_scm_inst,ax, ( (~ (v1_xboole_0 k3_scm_inst))  & (v1_compos_0 k3_scm_inst)) ).
tt(fc4_scmpds_2,ax, ((v1_extpro_1 k1_scmpds_2 2) & (v3_extpro_1 k1_scmpds_2 2)) ).
tt(fc4_scmpds_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v4_scmpds_4 (k12_scmpds_2 A B C D))) ) ).
tt(fc4_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v6_compos_0 (k7_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc4_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1)))))  &  ((v1_relat_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1)))) &  ((v4_relat_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1))) k5_numbers) &  ((v5_relat_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1))) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1)))) &  ((v1_finset_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1)))) &  ((v1_afinsq_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1)))) & (v2_compos_1 (k1_scmpds_6 (k4_xcmplx_0 (k2_nat_1 A 1))) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc4_scmpds_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (m1_subset_1 D k5_numbers)) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_7 B C D A)))  &  ((v1_relat_1 (k2_scmpds_7 B C D A)) &  ((v4_relat_1 (k2_scmpds_7 B C D A) k5_numbers) &  ((v5_relat_1 (k2_scmpds_7 B C D A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_7 B C D A)) &  ((v1_finset_1 (k2_scmpds_7 B C D A)) &  ((v1_afinsq_1 (k2_scmpds_7 B C D A)) & (v2_compos_1 (k2_scmpds_7 B C D A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc4_scmpds_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_8 B C A)))  &  ((v1_relat_1 (k2_scmpds_8 B C A)) &  ((v4_relat_1 (k2_scmpds_8 B C A) k5_numbers) &  ((v5_relat_1 (k2_scmpds_8 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_8 B C A)) &  ((v1_finset_1 (k2_scmpds_8 B C A)) &  ((v1_afinsq_1 (k2_scmpds_8 B C A)) & (v2_compos_1 (k2_scmpds_8 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc4_scmpds_i,ax,(v2_compos_0 k1_scmpds_i)).
tt(fc4_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_extpro_1 (k3_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc4_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v4_amistd_1 (k5_scmring2 A B C) 2 (k1_scmring2 A))) ) ).
tt(fc4_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmringi A)))  & (v1_compos_0 (k1_scmringi A))) ) ) ).
tt(fc4_scmyciel,ax, (! [A:$i,B:$i] :  ((v5_finset_1 A) => (v5_finset_1 (k3_xboole_0 A B))) ) ).
tt(fc4_seq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) &  ((v1_funct_2 (k45_valued_1 A B) k5_numbers k1_numbers) & (v2_comseq_2 (k45_valued_1 A B))) ) ) ) ).
tt(fc4_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k1_numbers))  =>  ( (~ (v1_xboole_0 (k28_seq_4 A)))  & (v5_valued_0 (k28_seq_4 A))) ) ) ).
tt(fc4_setfam_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  => (v1_setfam_1 (k1_enumset1 A B C))) ) ).
tt(fc4_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_sfmastr1 (k9_scmfsa_2 A B))) ) ).
tt(fc4_sfmastr3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_scmfsa_2 A) &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  ((v1_relat_1 (k4_sfmastr3 A B C)) &  ((v4_relat_1 (k4_sfmastr3 A B C) k5_numbers) &  ((v5_relat_1 (k4_sfmastr3 A B C) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_sfmastr3 A B C)) &  ( (~ (v1_xboole_0 (k4_sfmastr3 A B C)))  &  ((v1_finset_1 (k4_sfmastr3 A B C)) &  ((v1_afinsq_1 (k4_sfmastr3 A B C)) &  ((v1_scmfsa7b (k4_sfmastr3 A B C)) & (v7_amistd_1 (k4_sfmastr3 A B C) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc4_simplex0,ax, (! [A:$i,B:$i] :  ( ((v1_classes1 A) & (v1_classes1 B))  => (v1_classes1 (k3_xboole_0 A B))) ) ).
tt(fc4_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))) & (v2_simplex1 (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B)) A)) ) ) ).
tt(fc4_sincos10,ax, ((v1_relat_1 (k5_relat_1 k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc4_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))) ).
tt(fc4_sin_cos9,ax, ((v1_funct_1 k2_sin_cos9) & (v2_funct_1 k2_sin_cos9)) ).
tt(fc4_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k20_sin_cos A))) ) ).
tt(fc4_sppol_1,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k3_topreal1 2 A) (k15_euclid 2))) ) ).
tt(fc4_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v3_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v3_topreal1 (k16_finseq_1 B A))) ) ).
tt(fc4_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (v3_funct_1 (k1_sprect_1 A))) ) ) ).
tt(fc4_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v2_topreal4 (k3_goboard9 A) (k15_euclid 2))) ) ).
tt(fc4_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v2_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc4_struct_0,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_struct_0 A))  => (v1_xboole_0 (k2_struct_0 A))) ) ).
tt(fc4_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  (~ (v1_xboole_0 (k3_enumset1 A B C D E))) ) ).
tt(fc4_substlat,ax, (! [A:$i,B:$i] :  ((v3_lattices (k5_substlat A B)) &  ((v11_lattices (k5_substlat A B)) & (v15_lattices (k5_substlat A B))) ) ) ).
tt(fc4_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ( (~ (v1_xboole_0 (k16_substut1 A)))  & (v1_substut1 (k16_substut1 A) A)) ) ) ).
tt(fc4_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  ( (~ (v1_xboole_0 (k6_supinf_1 A)))  & (v2_membered (k6_supinf_1 A))) ) ) ).
tt(fc4_termord,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  (~ (v9_struct_0 (k4_termord A B C D) C)) ) ) ).
tt(fc4_tex_1,ax, (! [A:$i] : (v1_tdlat_3 (k1_compts_1 A))) ).
tt(fc4_tex_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k1_tex_2 A B)))  &  ((v1_pre_topc (k1_tex_2 A B)) &  ((v1_tdlat_3 (k1_tex_2 A B)) & (v2_tdlat_3 (k1_tex_2 A B))) ) ) ) ) ).
tt(fc4_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_zfmisc_1 (k2_pre_topc A B))) ) ) ).
tt(fc4_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v2_struct_0 (k6_tmap_1 A B)))  &  ((v1_pre_topc (k6_tmap_1 A B)) & (v2_pre_topc (k6_tmap_1 A B))) ) ) ) ).
tt(fc4_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_topalg_1 A B)))  & (v15_algstr_0 (k5_topalg_1 A B))) ) ) ).
tt(fc4_topalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 B)) &  ((v5_pre_topc C k5_topmetr B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 B)) &  ((v5_pre_topc D k5_topmetr B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k1_topalg_2 A B C D)) &  ((v1_funct_2 (k1_topalg_2 A B C D) (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 B)) & (v5_pre_topc (k1_topalg_2 A B C D) (k2_borsuk_1 k5_topmetr k5_topmetr) B)) ) ) ) ).
tt(fc4_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((v1_funct_1 (k11_topalg_4 A B C D)) &  ((v1_funct_2 (k11_topalg_4 A B C D) (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) & (v1_group_6 (k11_topalg_4 A B C D) (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) ) ) ) ).
tt(fc4_topalg_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_pre_topc A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) )  =>  ((v1_pre_topc (k1_pre_topc k5_topmetr A)) & (v1_connsp_2 (k1_pre_topc k5_topmetr A))) ) ) ).
tt(fc4_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topalg_6 A) & (l1_pre_topc A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v7_struct_0 (k5_topalg_1 A B)) & (v15_algstr_0 (k5_topalg_1 A B))) ) ) ).
tt(fc4_topdim_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  &  ((v2_topdim_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  => (v2_topdim_1 (k2_xboole_0 B C) A)) ) ).
tt(fc4_topdim_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v5_waybel23 A) &  ((v3_topdim_1 A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) ) ) )  &  ((v2_pre_topc B) &  ((v5_waybel23 B) &  ((v3_topdim_1 B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) ) ) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v3_topdim_1 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc4_topgen_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v3_pre_topc B A) &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_xboole_0 (k2_tops_1 A B))) ) ).
tt(fc4_topgen_3,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_topgen_3 A B)))  &  ((v1_pre_topc (k7_topgen_3 A B)) & (v2_pre_topc (k7_topgen_3 A B))) ) ) ) ).
tt(fc4_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v5_topgen_4 (k2_struct_0 A) A) & (v6_topgen_4 (k2_struct_0 A) A)) ) ) ).
tt(fc4_topgen_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  ((v1_funct_1 (k5_topgen_5 A B C)) &  ((v1_funct_2 (k5_topgen_5 A B C) (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr)) & (v5_pre_topc (k5_topgen_5 A B C) k3_topgen_5 k5_topmetr)) ) ) ) ).
tt(fc4_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k2_topgrp_1 A B)) &  ((v2_funct_1 (k2_topgrp_1 A B)) &  ((v1_funct_2 (k2_topgrp_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v2_funct_2 (k2_topgrp_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(fc4_topmetr,ax, (! [A:$i] :  ( ((v3_topmetr A) & (l1_struct_0 A))  => (v3_membered (u1_struct_0 A))) ) ).
tt(fc4_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k4_topreal1 A))) ) ) ).
tt(fc4_topreal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~ (v1_xboole_0 (k6_measure6 A))) ) ) ).
tt(fc4_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v9_metric_1 A) & (l1_metric_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v9_metric_1 B) & (l1_metric_1 B)) ) )  =>  ((v1_metric_1 (k1_topreal7 A B)) & (v9_metric_1 (k1_topreal7 A B))) ) ) ).
tt(fc4_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) ) ) )  =>  (~ (v1_xboole_0 (k2_topreal9 A B C))) ) ) ).
tt(fc4_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k1_xxreal_1 A (k2_xcmplx_0 A B)))) ) ) ).
tt(fc4_toprealb,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos k1_numbers k1_numbers) & (v1_fcont_1 k16_sin_cos)) ) ).
tt(fc4_toprealc,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v1_xboole_0 (k39_valued_1 A))) ) ) ) ).
tt(fc4_tops_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v4_pre_topc (k3_xboole_0 B C) A)) ) ).
tt(fc4_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k2_trees_1 A)))  &  ((v1_finset_1 (k2_trees_1 A)) & (v1_trees_1 (k2_trees_1 A))) ) ) ) ).
tt(fc4_trees_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (v3_trees_2 (k2_funcop_1 A B))) ) ).
tt(fc4_trees_3,ax,(v2_trees_3 k2_trees_3)).
tt(fc4_trees_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) ) ) ) )  =>  ((v1_relat_1 (k6_trees_4 B C D)) &  ((v5_relat_1 (k6_trees_4 B C D) A) &  ((v1_funct_1 (k6_trees_4 B C D)) & (v3_trees_2 (k6_trees_4 B C D))) ) ) ) ) ).
tt(fc4_trees_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  & (m1_subset_1 B A))  => (v1_finset_1 (k1_trees_2 A B))) ) ).
tt(fc4_unialg_1,ax, (! [A:$i] :  ( ((v4_unialg_1 A) & (l1_unialg_1 A))  =>  ((v2_relat_1 (u1_unialg_1 A)) &  (~ (v1_xboole_0 (u1_unialg_1 A))) ) ) ) ).
tt(fc4_uniroots,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  ((v1_funct_1 (k4_uniroots B A)) &  ((v1_funct_2 (k4_uniroots B A) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k4_uniroots B A) A) & (v1_uproots (k4_uniroots B A) A)) ) ) ) ) ).
tt(fc4_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v1_vectsp_2 (k14_polynom3 A))) ) ) ) ).
tt(fc4_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k3_numbers))  => (v4_membered (k10_xtuple_0 A))) ) ).
tt(fc4_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k3_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v5_relat_1 (k1_valued_1 A B) k3_numbers) & (v1_funct_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc4_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (~ (v1_xboole_0 (k1_vectmetr A))) ) ) ).
tt(fc4_vectsp_1,ax, ( (~ (v2_struct_0 k2_vectsp_1))  & (v36_algstr_0 k2_vectsp_1)) ).
tt(fc4_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_vectsp_2 A)))  &  ((v13_algstr_0 (k4_vectsp_2 A)) &  ((v2_rlvect_1 (k4_vectsp_2 A)) &  ((v3_rlvect_1 (k4_vectsp_2 A)) &  ((v4_rlvect_1 (k4_vectsp_2 A)) &  ((v2_vectsp_2 (k4_vectsp_2 A) A) & (v4_vectsp_2 (k4_vectsp_2 A) A)) ) ) ) ) ) ) ) ).
tt(fc4_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  & (m1_subset_1 D k1_numbers)) ) )  =>  ((v1_funct_1 (k4_vfunct_1 A B C D)) & (v1_partfun1 (k4_vfunct_1 A B C D) A)) ) ) ).
tt(fc4_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_yellow_0 A) & (l1_orders_2 A)) )  => (v2_waybel_0 (k2_struct_0 A) A)) ) ).
tt(fc4_waybel10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (m1_yellow_0 D A)) ) )  =>  ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) & (v5_orders_3 (k2_tmap_1 A B C D) D B)) ) ) ) ).
tt(fc4_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((v2_waybel11 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_waybel11 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc4_waybel17,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ( (~ (v2_struct_0 (k3_waybel17 A B C)))  &  ((v3_orders_2 (k3_waybel17 A B C)) &  ((v4_orders_2 (k3_waybel17 A B C)) &  ((v5_orders_2 (k3_waybel17 A B C)) &  ((v6_waybel_0 (k3_waybel17 A B C) A) & (v7_waybel_0 (k3_waybel17 A B C))) ) ) ) ) ) ) ).
tt(fc4_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k8_waybel18 A B C)) &  ((v1_funct_2 (k8_waybel18 A B C) (u1_struct_0 A) (u1_struct_0 (k7_waybel18 A B C))) & (v2_funct_2 (k8_waybel18 A B C) (u1_struct_0 (k7_waybel18 A B C)))) ) ) ) ).
tt(fc4_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v7_waybel_1 (k3_struct_0 A) A)) ) ) ) ).
tt(fc4_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_waybel23 (k6_waybel_0 A B) A)) ) ).
tt(fc4_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v5_waybel_0 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k1_waybel24 A B C D E)) &  ((v1_funct_2 (k1_waybel24 A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (v5_waybel_0 (k1_waybel24 A B C D E) B C)) ) ) ) ).
tt(fc4_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (k1_waybel25 A)))  & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc4_waybel26,ax, ( (~ (v7_struct_0 k9_waybel18))  &  ((v1_pre_topc k9_waybel18) & (v1_waybel25 k9_waybel18)) ) ).
tt(fc4_waybel27,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel27 A B)))  &  ((v1_monoid_0 (k2_waybel27 A B)) &  ((v1_orders_2 (k2_waybel27 A B)) &  ((v3_orders_2 (k2_waybel27 A B)) & (v5_orders_2 (k2_waybel27 A B))) ) ) ) ) ) ).
tt(fc4_waybel_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) )  =>  ( (~ (v2_struct_0 (k2_waybel_2 A B C)))  &  ((v7_waybel_0 (k2_waybel_2 A B C)) & (v8_waybel_0 (k2_waybel_2 A B C) A)) ) ) ) ).
tt(fc4_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_yellow_1 (k5_waybel11 A))))  &  ((v1_orders_2 (k2_yellow_1 (k5_waybel11 A))) & (v3_lattice3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(fc4_waybel32,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel32 A B)))  &  ((v6_waybel_0 (k2_waybel32 A B) A) & (v7_waybel_0 (k2_waybel32 A B))) ) ) ) ).
tt(fc4_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v18_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k3_waybel34 A B C)) &  ((v1_funct_2 (k3_waybel34 A B C) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (v4_waybel_1 (k3_waybel34 A B C) (k7_lattice3 A) (k7_lattice3 B))) ) ) ) ).
tt(fc4_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel_0 (k1_waybel_3 A B) A)) ) ).
tt(fc4_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  => (v4_waybel_4 (k2_waybel_4 A) A)) ) ).
tt(fc4_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  & (m2_pboole D A B (k7_funcop_1 A (u1_struct_0 C)))) ) )  =>  (~ (v1_xboole_0 (k10_xtuple_0 (k5_waybel_5 C D)))) ) ) ).
tt(fc4_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))))  & (v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc4_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) ) ) )  =>  ((v4_orders_2 (k3_waybel_2 A B C)) & (v6_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(fc4_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_weddwitt A)))  &  ( (~ (v6_struct_0 (k4_weddwitt A)))  &  ((v8_struct_0 (k4_weddwitt A)) &  ((v13_algstr_0 (k4_weddwitt A)) &  ((v33_algstr_0 (k4_weddwitt A)) &  ((v36_algstr_0 (k4_weddwitt A)) &  ((v2_rlvect_1 (k4_weddwitt A)) &  ((v3_rlvect_1 (k4_weddwitt A)) &  ((v4_rlvect_1 (k4_weddwitt A)) &  ((v3_group_1 (k4_weddwitt A)) &  ((v5_group_1 (k4_weddwitt A)) &  ((v4_vectsp_1 (k4_weddwitt A)) & (v5_vectsp_1 (k4_weddwitt A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc4_wellord2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k1_wellord2 A)) & (v6_relat_2 (k1_wellord2 A))) ) ) ).
tt(fc4_xboole_0,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_xboole_0 A B))) ) ) ).
tt(fc4_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k5_xboolean A B))) ) ).
tt(fc4_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_xcmplx_0 (k6_xcmplx_0 A B))) ) ).
tt(fc4_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) & (v1_xreal_0 (k5_xcmplx_0 A))) ) ) ).
tt(fc4_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k9_xtuple_0 A))) ) ).
tt(fc4_xxreal_0,ax,(v3_xxreal_0 k2_xxreal_0)).
tt(fc4_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v2_membered (k4_xxreal_1 A B))) ) ).
tt(fc4_xxreal_2,ax, (! [A:$i] :  ( ((v4_membered A) & (v1_xxreal_2 A))  =>  ((v1_xxreal_0 (k2_xxreal_2 A)) & (v1_rat_1 (k2_xxreal_2 A))) ) ) ).
tt(fc4_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xxreal_0 B) &  (~ (v1_xreal_0 B)) ) )  =>  (~ (v1_xreal_0 (k1_xxreal_3 A B))) ) ) ).
tt(fc4_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v25_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v25_waybel_0 (k3_yellow_3 A B))) ) ) ).
tt(fc4_yellow11,ax, ((v1_lattice3 k2_yellow11) & (v2_lattice3 k2_yellow11)) ).
tt(fc4_yellow13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_waybel_1 A B)) &  ((v1_funct_2 (k4_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v19_waybel_0 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(fc4_yellow14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  & (m1_pre_topc B A)) )  =>  ((v1_funct_1 (k4_tmap_1 A B)) &  ((v1_funct_2 (k4_tmap_1 A B) (u1_struct_0 B) (u1_struct_0 A)) & (v5_pre_topc (k4_tmap_1 A B) B A)) ) ) ) ).
tt(fc4_yellow16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B))))) ) )  =>  (~ (v1_xboole_0 (k5_card_3 D C))) ) ) ).
tt(fc4_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v9_functor0 (k2_yellow18 A (k1_yellow18 A)) A (k1_yellow18 A)) &  ((v16_functor0 (k2_yellow18 A (k1_yellow18 A)) A (k1_yellow18 A)) & (v21_functor0 (k2_yellow18 A (k1_yellow18 A)) A (k1_yellow18 A))) ) ) ) ).
tt(fc4_yellow19,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_yellow19 A B C)))  &  ((v3_orders_2 (k3_yellow19 A B C)) &  ((v4_orders_2 (k3_yellow19 A B C)) & (v6_waybel_0 (k3_yellow19 A B C) A)) ) ) ) ) ).
tt(fc4_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((v1_orders_2 (k3_lattice3 A)) &  ((v3_orders_2 (k3_lattice3 A)) &  ((v4_orders_2 (k3_lattice3 A)) &  ((v5_orders_2 (k3_lattice3 A)) & (v3_lattice3 (k3_lattice3 A))) ) ) ) ) ) ).
tt(fc4_yellow21,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) & (v4_relat_2 B)) )  =>  ((v1_relat_1 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A))) & (v4_relat_2 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A)))) ) ) ).
tt(fc4_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 A))) & (v2_lattice3 (k2_yellow_1 (k7_waybel_0 A)))) ) ) ).
tt(fc4_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) & (l1_orders_2 A))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v3_orders_2 (k3_yellow_3 A B))) ) ) ).
tt(fc4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v13_waybel_0 (k1_yellow_4 A B C) A)) ) ).
tt(fc4_yellow_6,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) ) )  => (v4_funct_1 (u1_struct_0 (k5_yellow_1 A B)))) ) ).
tt(fc4_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v16_waybel_0 A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k7_lattice3 A)) & (v16_waybel_0 (k7_lattice3 A))) ) ) ).
tt(fc4_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k2_yellow_9 A B)))  &  ((v4_orders_2 (k2_yellow_9 A B)) & (v6_waybel_0 (k2_yellow_9 A B) A)) ) ) ) ).
tt(fc4_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  => (v1_zf_lang (k6_zf_lang A))) ) ).
tt(fc4_zfmisc_1,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k2_zfmisc_1 A B))) ) ).
tt(fc4_zmodul01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  &  ( ((v7_zmodul01 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v7_zmodul01 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v7_zmodul01 (k3_xboole_0 B C) A)) ) ).
tt(fc50_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v1_xboole_0 (k4_xboole_0 B A))) ) ).
tt(fc50_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) &  ( (~ (v5_fomodel2 B A))  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel2 (k41_fomodel2 A B) A)) ) ).
tt(fc50_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) & (v13_fomodel4 C A)) )  => (v13_fomodel4 (k2_xboole_0 B C) A)) ) ).
tt(fc50_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (v1_xreal_0 C)) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C)) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C))) & (v10_glib_003 (k13_glib_000 A k4_glib_003 (k16_funcop_1 B C)))) ) ) ) ) ) ).
tt(fc50_member_1,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v6_membered B))  => (v6_membered (k13_member_1 A B))) ) ).
tt(fc50_membered,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k5_xboole_0 A B))) ) ).
tt(fc50_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v2_partfun3 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v1_funct_1 (k1_rfunct_1 B C)) & (v1_partfun3 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc50_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) & (l2_pcs_0 A))  &  ((v4_orders_2 B) & (l2_pcs_0 B)) )  => (v1_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc50_valued_0,ax, (! [A:$i] :  ((v2_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v2_valued_0 (k4_relat_1 A))) ) ) ).
tt(fc50_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_xreal_0 D)) )  =>  ((v1_funct_1 (k24_valued_1 C D)) & (v1_partfun1 (k24_valued_1 C D) A)) ) ) ).
tt(fc50_valued_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  & (v1_rat_1 B))  =>  ((v1_relat_1 (k14_valued_2 A B)) &  ((v5_relat_1 (k14_valued_2 A B) k3_numbers) & (v1_funct_1 (k14_valued_2 A B))) ) ) ) ).
tt(fc51_fomodel0,ax, (! [A:$i,B:$i] : (v1_xboole_0 (k4_xboole_0 (k1_tarski A) (k2_tarski A B)))) ).
tt(fc51_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) &  ( (~ (v5_fomodel2 B A))  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B) (k1_fomodel2 A)))) ) ).
tt(fc51_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_fomodel4 (k4_tarski B C) A)) ) ).
tt(fc51_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v1_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k5_glib_003 A)) &  ((v4_relat_1 (k5_glib_003 A) (k7_glib_000 A)) &  ((v1_funct_1 (k5_glib_003 A)) &  ((v1_partfun1 (k5_glib_003 A) (k7_glib_000 A)) & (v1_finset_1 (k5_glib_003 A))) ) ) ) ) ) ).
tt(fc51_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k14_member_1 A B))) ) ).
tt(fc51_membered,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k5_xboole_0 A B))) ) ).
tt(fc51_partfun3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_relat_1 (k1_rfunct_1 B B)) &  ((v1_funct_1 (k1_rfunct_1 B B)) & (v4_partfun3 (k1_rfunct_1 B B))) ) ) ) ).
tt(fc51_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v4_pcs_0 A) & (l2_pcs_0 A))  &  ((v4_pcs_0 B) & (l2_pcs_0 B)) )  => (v9_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc51_valued_0,ax, (! [A:$i] :  ((v3_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v3_valued_0 (k4_relat_1 A))) ) ) ).
tt(fc51_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_rat_1 D)) )  =>  ((v1_funct_1 (k24_valued_1 C D)) & (v1_partfun1 (k24_valued_1 C D) A)) ) ) ).
tt(fc51_valued_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k14_valued_2 A B)) &  ((v1_funct_1 (k14_valued_2 A B)) & (v1_finseq_1 (k14_valued_2 A B))) ) ) ) ).
tt(fc52_fomodel0,ax, (! [A:$i,B:$i] : (v1_xboole_0 (k5_xboole_0 (k1_xtuple_0 (k4_tarski A B)) A))) ).
tt(fc52_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((v3_fomodel2 C B (k1_nat_1 A 1)) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) )  => (v3_fomodel2 (k40_fomodel2 B C) B A)) ) ).
tt(fc52_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ((v13_fomodel4 C A) &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel4 (k4_tarski (k2_xboole_0 B C) D) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k23_fomodel4 A)) (k1_tarski (k4_tarski B D)))) ) ).
tt(fc52_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v2_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k6_glib_003 A)) &  ((v1_funct_1 (k6_glib_003 A)) & (v1_finset_1 (k6_glib_003 A))) ) ) ) ).
tt(fc52_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v2_membered B))  => (v1_xboole_0 (k14_member_1 B A))) ) ).
tt(fc52_membered,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k5_xboole_0 A B))) ) ).
tt(fc52_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v2_relat_1 B) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((v1_relat_1 (k1_rfunct_1 B C)) &  ((v2_relat_1 (k1_rfunct_1 B C)) & (v1_funct_1 (k1_rfunct_1 B C))) ) ) ) ).
tt(fc52_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v6_pcs_0 A) & (l2_pcs_0 A))  &  ((v6_pcs_0 B) & (l2_pcs_0 B)) )  => (v11_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc52_valued_0,ax, (! [A:$i] :  ((v4_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v5_relat_1 (k4_relat_1 A) k3_numbers)) ) ) ).
tt(fc52_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v1_int_1 D)) )  =>  ((v1_funct_1 (k24_valued_1 C D)) & (v1_partfun1 (k24_valued_1 C D) A)) ) ) ).
tt(fc52_valued_2,ax, (! [A:$i,B:$i] :  ( ((v1_valued_2 A) & (m1_finseq_1 B A))  =>  ((v1_relat_1 (k15_valued_2 B)) &  ((v1_funct_1 (k15_valued_2 B)) & (v1_finseq_1 (k15_valued_2 B))) ) ) ) ).
tt(fc53_fomodel0,ax, (! [A:$i,B:$i] : (v1_xboole_0 (k5_xboole_0 (k2_xtuple_0 (k4_tarski A B)) B))) ).
tt(fc53_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( (~ (v15_fomodel1 C B))  &  ((v3_fomodel2 C B (k1_nat_1 A 1)) &  ( (~ (v5_fomodel2 C B))  & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v3_fomodel2 (k41_fomodel2 B C) B A)) ) ).
tt(fc53_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 E A) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v4_fomodel4 (k4_tarski (k13_fomodel0 (k30_fomodel2 A D E) B) (k38_fomodel2 A C)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k33_fomodel4 A)) (k2_tarski (k4_tarski (k2_xboole_0 B (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C)) D) (k4_tarski (k2_xboole_0 B (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C)) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) D) E))))) ) ).
tt(fc53_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v3_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k7_glib_003 A)) &  ((v1_funct_1 (k7_glib_003 A)) & (v1_finset_1 (k7_glib_003 A))) ) ) ) ).
tt(fc53_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  &  ( (~ (v1_xboole_0 B))  & (v2_membered B)) )  =>  (~ (v1_xboole_0 (k14_member_1 A B))) ) ) ).
tt(fc53_membered,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v5_membered B))  => (v5_membered (k5_xboole_0 A B))) ) ).
tt(fc53_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_valued_0 (k35_valued_1 B)) & (v3_partfun3 (k35_valued_1 B))) ) ) ) ) ).
tt(fc53_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v14_pcs_0 A) & (l2_pcs_0 A))  &  ((v14_pcs_0 B) & (l2_pcs_0 B)) )  => (v17_pcs_0 (k6_afinsq_1 A B))) ) ).
tt(fc53_valued_0,ax, (! [A:$i] :  ((v5_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v5_relat_1 (k4_relat_1 A) k4_numbers)) ) ) ).
tt(fc53_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v6_membered B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (v7_ordinal1 D)) )  =>  ((v1_funct_1 (k24_valued_1 C D)) & (v1_partfun1 (k24_valued_1 C D) A)) ) ) ).
tt(fc54_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) => (v1_relat_1 (k13_fomodel0 B A))) ) ).
tt(fc54_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  (~ (v1_xboole_0 (k3_xboole_0 (k2_relset_1 (k5_fomodel1 A) B) (k16_fomodel1 A)))) ) ) ).
tt(fc54_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v2_fomodel4 (k13_fomodel0 A k1_xboole_0) A)) ) ).
tt(fc54_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k5_glib_003 A)) &  ((v4_relat_1 (k5_glib_003 A) (k7_glib_000 A)) &  ((v1_funct_1 (k5_glib_003 A)) &  ((v1_partfun1 (k5_glib_003 A) (k7_glib_000 A)) & (v3_valued_0 (k5_glib_003 A))) ) ) ) ) ) ).
tt(fc54_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v2_membered B))  => (v2_membered (k14_member_1 A B))) ) ).
tt(fc54_membered,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v6_membered B))  => (v6_membered (k5_xboole_0 A B))) ) ).
tt(fc54_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_valued_0 (k35_valued_1 B)) & (v4_partfun3 (k35_valued_1 B))) ) ) ) ) ).
tt(fc54_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) & (l2_pcs_0 A))  &  ((v3_orders_2 B) & (l2_pcs_0 B)) )  => (v3_orders_2 (k18_pcs_0 A B))) ) ).
tt(fc54_valued_0,ax, (! [A:$i] :  ((v6_membered A) =>  ((v1_relat_1 (k4_relat_1 A)) & (v4_valued_0 (k4_relat_1 A))) ) ) ).
tt(fc54_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xcmplx_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v1_finseq_1 (k24_valued_1 A B))) ) ) ) ).
tt(fc55_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_funct_1 A) => (v1_funct_1 (k13_fomodel0 B A))) ) ).
tt(fc55_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  (~ (v1_xboole_0 (k3_xboole_0 (k10_xtuple_0 B) (k16_fomodel1 A)))) ) ) ).
tt(fc55_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel4 (k4_tarski (k2_xboole_0 B (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C)) C) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc55_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v9_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k6_glib_003 A)) &  ((v1_funct_1 (k6_glib_003 A)) & (v3_valued_0 (k6_glib_003 A))) ) ) ) ).
tt(fc55_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k15_member_1 A B))) ) ).
tt(fc55_membered,ax,(v7_membered k2_numbers)).
tt(fc55_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_valued_0 (k35_valued_1 B)) & (v1_partfun3 (k35_valued_1 B))) ) ) ) ) ).
tt(fc55_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v4_pcs_0 A) & (l2_pcs_0 A))  &  ((v4_pcs_0 B) & (l2_pcs_0 B)) )  => (v4_pcs_0 (k18_pcs_0 A B))) ) ).
tt(fc55_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v1_valued_0 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v1_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc55_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) & (v1_valued_0 (k30_valued_1 A))) ) ) ) ).
tt(fc56_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_finseq_1 A))  =>  ((v1_relat_1 (k13_fomodel0 B A)) & (v1_finseq_1 (k13_fomodel0 B A))) ) ) ).
tt(fc56_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  => (v1_xboole_0 (k4_xboole_0 (k37_fomodel1 A) (k9_xtuple_0 C)))) ) ).
tt(fc56_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel4 (k4_tarski (k13_fomodel0 D B) (k38_fomodel2 A C)) 2 A (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k23_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k33_fomodel4 A))) (k1_tarski (k4_tarski B (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D))))) ) ).
tt(fc56_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_003 A) & (v10_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k7_glib_003 A)) &  ((v1_funct_1 (k7_glib_003 A)) & (v3_valued_0 (k7_glib_003 A))) ) ) ) ).
tt(fc56_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_membered B))  => (v1_xboole_0 (k15_member_1 B A))) ) ).
tt(fc56_membered,ax,(v7_membered k1_numbers)).
tt(fc56_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_valued_0 (k35_valued_1 B)) & (v2_partfun3 (k35_valued_1 B))) ) ) ) ) ).
tt(fc56_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v6_pcs_0 A) & (l2_pcs_0 A))  &  ((v6_pcs_0 B) & (l2_pcs_0 B)) )  => (v6_pcs_0 (k18_pcs_0 A B))) ) ).
tt(fc56_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v2_valued_0 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v2_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc56_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) &  ((v1_valued_0 (k30_valued_1 A)) & (v3_valued_0 (k30_valued_1 A))) ) ) ) ) ).
tt(fc57_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k13_fomodel0 B A)) &  ((v1_funct_1 (k13_fomodel0 B A)) &  ((v3_card_1 (k13_fomodel0 B A) (k3_finseq_1 A)) & (v1_finseq_1 (k13_fomodel0 B A))) ) ) ) ) ).
tt(fc57_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( ( (~ (v15_fomodel1 C B))  &  ((v4_fomodel2 C B) &  ( (~ (v5_fomodel2 C B))  & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) )  & (m1_subset_1 D (k16_fomodel2 B A))) ) )  => (v1_xboole_0 (k5_xboole_0 (k26_fomodel2 B A D C) (k9_xboolean (k26_fomodel2 B A D (k40_fomodel2 B C)) (k26_fomodel2 B A D (k42_fomodel2 B C)))))) ) ).
tt(fc57_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel4 (k4_tarski B (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) D) C)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k32_fomodel4 A)) (k1_tarski (k4_tarski B (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D))))) ) ).
tt(fc57_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v7_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc57_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  &  ( (~ (v1_xboole_0 B))  & (v1_membered B)) )  =>  (~ (v1_xboole_0 (k15_member_1 A B))) ) ) ).
tt(fc57_membered,ax,(v7_membered k3_numbers)).
tt(fc57_partfun3,ax, (! [A:$i,B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v2_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) & (v1_valued_0 (k35_valued_1 B))) ) ) ) ) ).
tt(fc57_pcs_0,ax, (! [A:$i,B:$i] :  ((l2_pcs_0 A) =>  ( (~ (v2_struct_0 (k19_pcs_0 A B)))  & (v12_pcs_0 (k19_pcs_0 A B))) ) ) ).
tt(fc57_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v3_valued_0 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v3_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc57_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v5_relat_1 (k30_valued_1 A) k3_numbers) &  ((v1_funct_1 (k30_valued_1 A)) & (v1_valued_0 (k30_valued_1 A))) ) ) ) ) ).
tt(fc58_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) )  =>  (~ (v1_xboole_0 (k1_card_1 A))) ) ) ).
tt(fc58_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k43_fomodel2 A))) ) ) ).
tt(fc58_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel4 (k4_tarski (k13_fomodel0 C B) (k38_fomodel2 A D)) 3 A (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k22_fomodel4 A)) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k23_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k33_fomodel4 A))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k32_fomodel4 A))) (k1_tarski (k4_tarski B (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D))))) ) ).
tt(fc58_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v7_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc58_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_membered B))  => (v1_membered (k15_member_1 A B))) ) ).
tt(fc58_membered,ax,(v7_membered k4_numbers)).
tt(fc58_partfun3,ax, (! [A:$i,B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v2_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) & (v1_valued_0 (k30_valued_1 B))) ) ) ) ) ).
tt(fc58_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v3_orders_2 A) & (l2_pcs_0 A))  =>  ((v3_orders_2 (k19_pcs_0 A B)) & (v12_pcs_0 (k19_pcs_0 A B))) ) ) ).
tt(fc58_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v5_relat_1 B k3_numbers)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v5_relat_1 (k3_relat_1 A B) k3_numbers)) ) ) ).
tt(fc58_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v5_relat_1 (k30_valued_1 A) k4_numbers) &  ((v1_funct_1 (k30_valued_1 A)) & (v1_valued_0 (k30_valued_1 A))) ) ) ) ) ).
tt(fc59_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) =>  ((v1_relat_1 (k5_relat_1 A B)) & (v4_relat_1 (k5_relat_1 A B) B)) ) ) ).
tt(fc59_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v1_xboole_0 (k4_xboole_0 (k43_fomodel2 A) (k33_fomodel2 A)))) ) ).
tt(fc59_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v1_fomodel4 B A))  => (v13_fomodel4 (k1_xtuple_0 B) A)) ) ).
tt(fc59_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v3_membered B))  => (v3_membered (k15_member_1 A B))) ) ).
tt(fc59_membered,ax,(v7_membered k4_ordinal1)).
tt(fc59_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v3_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_valued_0 (k30_valued_1 B)) & (v4_partfun3 (k30_valued_1 B))) ) ) ) ) ).
tt(fc59_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v4_pcs_0 A) & (l2_pcs_0 A))  =>  ((v4_pcs_0 (k19_pcs_0 A B)) & (v12_pcs_0 (k19_pcs_0 A B))) ) ) ).
tt(fc59_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v5_relat_1 B k4_numbers)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v5_relat_1 (k3_relat_1 A B) k4_numbers)) ) ) ).
tt(fc59_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k30_valued_1 C)) & (v1_partfun1 (k30_valued_1 C) A)) ) ) ).
tt(fc5_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) )  & (m1_subset_1 B (u1_abcmiz_0 A)))  =>  ((v1_waybel_0 (k3_abcmiz_0 A B) A) & (v12_waybel_0 (k3_abcmiz_0 A B) A)) ) ) ).
tt(fc5_abcmiz_a,ax, (~ (v1_xboole_0 k4_abcmiz_a)) ).
tt(fc5_abian,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  => (v1_abian (k6_xcmplx_0 A 1))) ) ).
tt(fc5_afinsq_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v5_ordinal1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) & (v1_finset_1 (k1_ordinal4 A B))) ) ) ) ) ).
tt(fc5_afinsq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v5_ordinal1 (k1_valued_1 A B))) ) ) ) ).
tt(fc5_afvect0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v7_struct_0 (k5_afvect0 A B)))  & (v8_algstr_0 (k5_afvect0 A B))) ) ) ).
tt(fc5_algstr_1,ax,(v3_group_1 k8_algstr_0)).
tt(fc5_algstr_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_algstr_4 A B)) &  ((v1_funct_2 (k5_algstr_4 A B) (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B))) & (v1_group_6 (k5_algstr_4 A B) A (k4_algstr_4 A B))) ) ) ) ).
tt(fc5_altcat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) ) )  =>  ((v1_relat_1 (k8_pboole B C)) &  ((v4_relat_1 (k8_pboole B C) A) & (v1_funct_1 (k8_pboole B C))) ) ) ) ).
tt(fc5_altcat_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( ((v2_altcat_3 C A B B) & (m1_subset_1 C (k1_altcat_1 A B B)))  &  ((v2_altcat_3 D A B B) & (m1_subset_1 D (k1_altcat_1 A B B))) ) ) )  => (v2_altcat_3 (k5_altcat_1 A B B B D C) A B B)) ) ).
tt(fc5_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_altcat_4 A)))  &  ((v2_altcat_1 (k2_altcat_4 A)) &  ((v6_altcat_1 (k2_altcat_4 A)) & (v3_altcat_2 (k2_altcat_4 A) A)) ) ) ) ) ).
tt(fc5_ami_3,ax, ((v1_extpro_1 k1_ami_3 2) & (v3_extpro_1 k1_ami_3 2)) ).
tt(fc5_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_amistd_1 (k5_ami_3 A B) 2 k1_ami_3)) ) ).
tt(fc5_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v3_memstr_0 (k4_amistd_1 A) A) & (v1_extpro_1 (k4_amistd_1 A) A)) ) ) ).
tt(fc5_amistd_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  &  ((v2_extpro_1 C A B) & (m1_subset_1 C (u1_compos_1 B))) ) )  => (v1_xboole_0 (k2_amistd_1 A B C))) ) ).
tt(fc5_amistd_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) ) )  =>  (~ (v1_zfmisc_1 (k4_memstr_0 A B (k4_struct_0 B)))) ) ) ).
tt(fc5_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v4_amistd_5 (k4_amistd_1 A) A)) ) ) ).
tt(fc5_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_collsp (k5_anproj_1 A)) &  ((v4_anproj_2 (k5_anproj_1 A)) &  ((v5_anproj_2 (k5_anproj_1 A)) & (v6_anproj_2 (k5_anproj_1 A))) ) ) ) ) ).
tt(fc5_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  => (v2_freealg (k10_aofa_000 A) A)) ) ).
tt(fc5_armstrng,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((v6_armstrng B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) )  =>  (~ (v1_xboole_0 (k8_armstrng A B))) ) ) ).
tt(fc5_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v1_funct_1 (k5_asympt_1 A)) &  ((v1_funct_2 (k5_asympt_1 A) k5_numbers k1_numbers) & (v4_asympt_0 (k5_asympt_1 A))) ) ) ) ).
tt(fc5_autalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ( (~ (v2_struct_0 (k7_autalg_1 A B)))  &  ((v15_algstr_0 (k7_autalg_1 A B)) &  ((v2_group_1 (k7_autalg_1 A B)) & (v3_group_1 (k7_autalg_1 A B))) ) ) ) ) ).
tt(fc5_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k17_pre_poly A) (k15_pre_poly A)) &  ((v1_relat_2 (k17_pre_poly A)) &  ((v4_relat_2 (k17_pre_poly A)) &  ((v8_relat_2 (k17_pre_poly A)) & (v2_bagorder (k17_pre_poly A) A)) ) ) ) ) ) ).
tt(fc5_bcialg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m2_bcialg_1 B A) & (m4_bcialg_2 C A B)) )  =>  ((v2_bcialg_1 (k9_bcialg_2 A C)) &  ((v3_bcialg_1 (k9_bcialg_2 A C)) &  ((v4_bcialg_1 (k9_bcialg_2 A C)) &  ((v5_bcialg_1 (k9_bcialg_2 A C)) & (v7_bcialg_1 (k9_bcialg_2 A C))) ) ) ) ) ) ).
tt(fc5_bcialg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_bcialg_1 B A) &  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  & (m4_bcialg_2 D A C)) ) )  =>  ((v2_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v3_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v4_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v5_bcialg_1 (k10_bcialg_6 A B C D)) & (v7_bcialg_1 (k10_bcialg_6 A B C D))) ) ) ) ) ) ).
tt(fc5_binop_2,ax, ((v1_funct_1 k39_binop_2) &  ((v1_funct_2 k39_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) &  ((v1_binop_1 k39_binop_2 k3_numbers) & (v2_binop_1 k39_binop_2 k3_numbers)) ) ) ).
tt(fc5_bor_cant,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) )  =>  ((v5_relat_1 (k7_bor_cant A C) B) &  ((v1_funct_1 (k7_bor_cant A C)) & (v1_funct_2 (k7_bor_cant A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc5_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  ( (~ (v2_struct_0 (k2_borsuk_1 A B)))  &  ((v1_pre_topc (k2_borsuk_1 A B)) & (v2_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(fc5_borsuk_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v6_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(fc5_borsuk_3,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_compts_1 (k1_pre_topc A B))) ) ) ).
tt(fc5_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k2_xcmplx_0 B A))) ) ) ).
tt(fc5_borsuk_6,ax, ((v1_funct_1 k3_borsuk_6) &  ((v1_funct_2 k3_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (v5_pre_topc k3_borsuk_6 k5_topmetr k5_topmetr)) ) ).
tt(fc5_borsuk_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_connsp_1 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (v1_connsp_1 (k7_waybel18 A B C))) ) ).
tt(fc5_bspace,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ( (~ (v2_struct_0 (k7_bspace A)))  & (v1_matrlin (k7_bspace A) k2_bspace)) ) ) ).
tt(fc5_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_funct_1 (k12_bvfunc_1 A)) &  ((v3_funct_1 (k12_bvfunc_1 A)) & (v1_funct_2 (k12_bvfunc_1 A) A k6_margrel1)) ) ) ) ).
tt(fc5_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_group_1 (k11_c0sp1 A))) ) ).
tt(fc5_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v13_algstr_0 (k3_c0sp2 A)) &  ((v2_rlvect_1 (k3_c0sp2 A)) &  ((v3_rlvect_1 (k3_c0sp2 A)) &  ((v4_rlvect_1 (k3_c0sp2 A)) &  ((v5_rlvect_1 (k3_c0sp2 A)) &  ((v6_rlvect_1 (k3_c0sp2 A)) &  ((v7_rlvect_1 (k3_c0sp2 A)) &  ((v8_rlvect_1 (k3_c0sp2 A)) &  ((v3_group_1 (k3_c0sp2 A)) &  ((v5_group_1 (k3_c0sp2 A)) &  ((v1_vectsp_1 (k3_c0sp2 A)) &  ((v3_vectsp_1 (k3_c0sp2 A)) & (v2_funcsdom (k3_c0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_card_1,ax,(v2_card_1 k4_ordinal1)).
tt(fc5_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  (~ (v1_xboole_0 (k4_card_3 A))) ) ) ).
tt(fc5_card_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  &  ( (~ (v1_finset_1 B))  & (v1_card_1 B)) )  =>  ( (~ (v1_finset_1 (k2_card_2 A B)))  & (v1_card_1 (k2_card_2 A B))) ) ) ).
tt(fc5_cardfin2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xboole_0 B) &  ((v1_relat_1 B) & (v1_funct_1 B)) ) )  =>  ((v1_xboole_0 (k24_valued_1 B A)) &  ((v1_relat_1 (k24_valued_1 B A)) & (v1_funct_1 (k24_valued_1 B A))) ) ) ) ).
tt(fc5_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) &  ((v2_catalg_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc5_cayley,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v15_algstr_0 (k13_matrix_2 A)) & (v1_monoid_0 (k13_matrix_2 A))) ) ) ).
tt(fc5_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_group_1 (k7_cc0sp1 A))) ) ).
tt(fc5_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k3_cc0sp2 A)))  &  ((v13_algstr_0 (k3_cc0sp2 A)) &  ((v2_rlvect_1 (k3_cc0sp2 A)) &  ((v3_rlvect_1 (k3_cc0sp2 A)) &  ((v4_rlvect_1 (k3_cc0sp2 A)) &  ((v3_group_1 (k3_cc0sp2 A)) &  ((v5_group_1 (k3_cc0sp2 A)) &  ((v1_vectsp_1 (k3_cc0sp2 A)) &  ((v3_vectsp_1 (k3_cc0sp2 A)) &  ((v2_clvect_1 (k3_cc0sp2 A)) &  ((v3_clvect_1 (k3_cc0sp2 A)) &  ((v4_clvect_1 (k3_cc0sp2 A)) &  ((v5_clvect_1 (k3_cc0sp2 A)) & (v2_cfuncdom (k3_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v3_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k24_valued_1 B A)) &  ((v1_partfun1 (k24_valued_1 B A) k2_numbers) & (v3_cfdiff_1 (k24_valued_1 B A))) ) ) ) ).
tt(fc5_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_group_1 (k8_cfuncdom A)) & (v1_cfuncdom (k8_cfuncdom A))) ) ) ).
tt(fc5_circcmb3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) & (l1_msualg_1 B)) ) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ((v8_struct_0 (k2_circcomb A B)) & (v1_msualg_1 (k2_circcomb A B))) ) ) ) ).
tt(fc5_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  &  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) &  ((v4_msualg_1 E A) & (l3_msualg_1 E A)) ) ) ) )  =>  (~ (v1_xboole_0 (k2_circtrm1 A B C D E))) ) ) ).
tt(fc5_classes2,ax, (! [A:$i] : (v1_ordinal1 (k5_classes1 A))) ).
tt(fc5_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_clopban1 A B)))  &  ((v13_algstr_0 (k6_clopban1 A B)) &  ((v2_rlvect_1 (k6_clopban1 A B)) &  ((v3_rlvect_1 (k6_clopban1 A B)) &  ((v4_rlvect_1 (k6_clopban1 A B)) &  ((v1_clvect_1 (k6_clopban1 A B)) &  ((v2_clvect_1 (k6_clopban1 A B)) &  ((v3_clvect_1 (k6_clopban1 A B)) &  ((v4_clvect_1 (k6_clopban1 A B)) & (v5_clvect_1 (k6_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k8_clopban2 A))) ) ).
tt(fc5_clopban3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_clopban3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k9_nat_1 B C)) &  ((v1_funct_2 (k9_nat_1 B C) k5_numbers (u1_struct_0 A)) & (v1_clopban3 (k9_nat_1 B C) A)) ) ) ) ).
tt(fc5_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v7_closure1 B A) & (l1_closure1 B A)) )  => (v2_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc5_cohsp_1,ax, (! [A:$i] :  ((v4_finsub_1 (k5_finsub_1 A)) &  ((v1_cohsp_1 (k5_finsub_1 A)) & (v2_cohsp_1 (k5_finsub_1 A))) ) ) ).
tt(fc5_coh_sp,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k13_coh_sp A)))  &  ( (~ (v11_struct_0 (k13_coh_sp A)))  &  ((v1_cat_1 (k13_coh_sp A)) &  ((v2_cat_1 (k13_coh_sp A)) &  ((v3_cat_1 (k13_coh_sp A)) &  ((v4_cat_1 (k13_coh_sp A)) & (v5_cat_1 (k13_coh_sp A))) ) ) ) ) ) ) ).
tt(fc5_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_pre_topc (k1_compact1 A)) & (v2_pre_topc (k1_compact1 A))) ) ) ).
tt(fc5_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((v1_xreal_0 (k16_complex1 A)) &  (~ (v3_xxreal_0 (k16_complex1 A))) ) ) ) ).
tt(fc5_compl_sp,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_metric_1 (k3_compl_sp A B C)) & (v7_metric_1 (k3_compl_sp A B C))) ) ) ).
tt(fc5_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  => (v1_finseq_1 (k2_xtuple_0 B))) ) ).
tt(fc5_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_xboole_0 B) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_xboole_0 (k5_compos_1 A B C)) &  ((v1_relat_1 (k5_compos_1 A B C)) &  ((v4_relat_1 (k5_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k5_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k5_compos_1 A B C)) & (v1_finset_1 (k5_compos_1 A B C))) ) ) ) ) ) ) ).
tt(fc5_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_tops_2 (u1_pre_topc A) A)) ) ).
tt(fc5_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k4_comput_1 A B)))  &  ((v1_relat_1 (k4_comput_1 A B)) &  ((v4_relat_1 (k4_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k4_comput_1 A B)) &  ((v4_valued_0 (k4_comput_1 A B)) &  ((v2_margrel1 (k4_comput_1 A B)) & (v2_comput_1 (k4_comput_1 A B))) ) ) ) ) ) ) ) ).
tt(fc5_comseq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  & (v1_xcmplx_0 B))  =>  ((v1_funct_1 (k24_valued_1 A B)) &  ((v1_funct_2 (k24_valued_1 A B) k5_numbers k2_numbers) & (v2_comseq_2 (k24_valued_1 A B))) ) ) ) ).
tt(fc5_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k4_comseq_3 A)) &  ((v1_funct_2 (k4_comseq_3 A) k5_numbers k1_numbers) & (v2_comseq_2 (k4_comseq_3 A))) ) ) ) ).
tt(fc5_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v3_lattices (k11_conlat_1 A)) & (v4_lattice3 (k11_conlat_1 A))) ) ) ) ).
tt(fc5_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  & (m1_clvect_1 B A))  =>  (~ (v1_xboole_0 (k17_convex4 A B))) ) ) ).
tt(fc5_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) & (l1_rlvect_1 B)) ) )  => (v13_algstr_0 (k3_convfun1 A B))) ) ).
tt(fc5_csspace3,ax, ( (~ (v2_struct_0 k3_csspace3))  &  ((v13_algstr_0 k3_csspace3) &  ((v2_rlvect_1 k3_csspace3) &  ((v3_rlvect_1 k3_csspace3) &  ((v4_rlvect_1 k3_csspace3) &  ((v3_normsp_0 k3_csspace3) &  ((v4_normsp_0 k3_csspace3) &  ((v2_clvect_1 k3_csspace3) &  ((v3_clvect_1 k3_csspace3) &  ((v4_clvect_1 k3_csspace3) &  ((v5_clvect_1 k3_csspace3) & (v8_clvect_1 k3_csspace3)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_csspace4,ax, ( (~ (v2_struct_0 k3_csspace4))  &  ((v13_algstr_0 k3_csspace4) &  ((v2_rlvect_1 k3_csspace4) &  ((v3_rlvect_1 k3_csspace4) &  ((v4_rlvect_1 k3_csspace4) &  ((v3_normsp_0 k3_csspace4) &  ((v4_normsp_0 k3_csspace4) &  ((v2_clvect_1 k3_csspace4) &  ((v3_clvect_1 k3_csspace4) &  ((v4_clvect_1 k3_csspace4) &  ((v5_clvect_1 k3_csspace4) & (v8_clvect_1 k3_csspace4)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_csspace,ax, ( (~ (v2_struct_0 k18_csspace))  &  ((v13_algstr_0 k18_csspace) &  ((v2_rlvect_1 k18_csspace) &  ((v3_rlvect_1 k18_csspace) &  ((v4_rlvect_1 k18_csspace) &  ((v2_clvect_1 k18_csspace) &  ((v3_clvect_1 k18_csspace) &  ((v4_clvect_1 k18_csspace) & (v5_clvect_1 k18_csspace)) ) ) ) ) ) ) ) ).
tt(fc5_dickson,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((v1_relat_1 (k5_relat_1 B C)) & (v1_yellow_1 (k5_relat_1 B C))) ) ) ).
tt(fc5_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (~ (v1_xboole_0 (k6_dilworth A))) ) ) ).
tt(fc5_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_dist_1 (k1_uproots A) A)) ) ).
tt(fc5_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((v1_partfun1 (k7_ec_pf_1 A) (k3_ec_pf_1 (k9_int_3 A))) &  ((v3_relat_2 (k7_ec_pf_1 A)) & (v8_relat_2 (k7_ec_pf_1 A))) ) ) ) ).
tt(fc5_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k16_ens_1 A))) ) ) ).
tt(fc5_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v6_euclid_7 (k1_tarski (k5_euclid A)) A)) ) ).
tt(fc5_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_valued_0 (k30_valued_1 B)) & (v3_card_1 (k30_valued_1 B) A)) ) ) ) ) ).
tt(fc5_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k15_euclid A)))  & (v5_rltopsp1 (k15_euclid A))) ) ) ).
tt(fc5_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C B)) )  =>  ((v1_relat_1 (k1_tarski (k4_tarski A C))) &  ((v5_relat_1 (k1_tarski (k4_tarski A C)) B) &  ((v1_funct_1 (k1_tarski (k4_tarski A C))) & (v1_exchsort (k1_tarski (k4_tarski A C)))) ) ) ) ) ).
tt(fc5_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v3_memstr_0 (k1_extpro_1 A) A) & (v1_extpro_1 (k1_extpro_1 A) A)) ) ) ).
tt(fc5_facirc_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_facirc_1 A))  =>  (~ (v1_facirc_1 (k4_xboole_0 A B))) ) ) ).
tt(fc5_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) & (v1_fcont_1 (k18_valued_1 A B))) ) ) ).
tt(fc5_fcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v3_rcomp_1 (k3_limfunc1 A))) ) ).
tt(fc5_fib_num2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_setfam_1 (k1_finseq_1 A))) ) ).
tt(fc5_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v20_lattices B (k1_lattice2 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) )  => (v21_lattices (k4_filter_2 A B) A)) ) ).
tt(fc5_finseq_1,ax, (! [A:$i] : (v1_xboole_0 (k6_finseq_1 A))) ).
tt(fc5_finseq_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k4_finseq_2 A B))) ) ) ).
tt(fc5_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v3_card_1 (k7_finseq_4 A B C D) 4)) ).
tt(fc5_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v2_funct_1 C) & (m1_finseq_1 C A)) ) )  => (v2_funct_1 (k1_finseq_5 A C B))) ) ).
tt(fc5_finseq_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C A) & (m1_finseq_1 C A)) ) ) )  => (v1_finseq_6 (k1_finseq_6 A C B) A)) ) ).
tt(fc5_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (v1_finset_1 (k3_enumset1 A B C D E))) ).
tt(fc5_fomodel0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v2_setfam_1 (k1_tarski A))) ) ).
tt(fc5_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v7_fomodel1 (k7_fomodel1 A) A)) ) ).
tt(fc5_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_xboole_0 B) &  ((v1_relat_1 B) & (v1_funct_1 B)) ) )  =>  ((v1_xboole_0 (k7_fomodel2 A B)) &  ((v1_relat_1 (k7_fomodel2 A B)) & (v1_funct_1 (k7_fomodel2 A B))) ) ) ) ).
tt(fc5_fomodel3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((v1_relat_1 (k5_relat_1 (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A)))) & (v5_relat_1 (k5_relat_1 (k2_fomodel3 A B) (k4_finseq_2 (k1_int_2 (k19_fomodel1 A B)) (k35_fomodel1 A))) (k32_fomodel1 A))) ) ) ).
tt(fc5_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v5_fomodel4 B A) & (m1_subset_1 B (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) )  => (v6_fomodel4 (k1_tarski B) A)) ) ).
tt(fc5_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ( (~ (v2_struct_0 (k7_freealg A B)))  &  ((v1_unialg_1 (k7_freealg A B)) &  ((v2_unialg_1 (k7_freealg A B)) &  ((v3_unialg_1 (k7_freealg A B)) &  ((v4_unialg_1 (k7_freealg A B)) & (v3_freealg (k7_freealg A B))) ) ) ) ) ) ) ).
tt(fc5_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) ) ) )  =>  ((v2_fsm_1 (k11_fsm_1 A B C) A B) & (v5_fsm_1 (k11_fsm_1 A B C) A B)) ) ) ).
tt(fc5_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B)) ) )  =>  ( (~ (v2_struct_0 (k2_fsm_3 A B C)))  &  ((v1_fsm_3 (k2_fsm_3 A B C) A (k9_flang_1 A)) & (v2_fsm_3 (k2_fsm_3 A B C) A (k9_flang_1 A))) ) ) ) ).
tt(fc5_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k3_funcop_1 A B C)) & (v1_funct_1 (k3_funcop_1 A B C))) ) ) ).
tt(fc5_funcsdom,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k12_funcsdom A)))  & (v1_funcsdom (k12_funcsdom A))) ) ).
tt(fc5_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  ((v1_relat_1 (k2_relat_1 A)) & (v1_funct_1 (k2_relat_1 A))) ) ) ).
tt(fc5_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k3_relat_1 D C)) & (v1_funct_2 (k3_relat_1 D C) A B)) ) ) ).
tt(fc5_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v2_relat_1 (k1_funct_4 A B)) & (v1_funct_1 (k1_funct_4 A B))) ) ) ) ).
tt(fc5_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((v1_relat_1 C) & (v1_funct_1 C)) ) )  => (v1_funcop_1 (k11_finseq_1 A B C))) ) ).
tt(fc5_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) &  ((l2_functor0 C A B) &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_relat_1 (k4_functor0 A B C D E)) & (v1_funct_1 (k4_functor0 A B C D E))) ) ) ).
tt(fc5_gate_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~ (v1_xboole_0 (k3_gate_1 A B))) ) ) ).
tt(fc5_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  => (v1_finset_1 (k6_glib_000 A))) ) ).
tt(fc5_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_glib_001 B A) & (m3_glib_001 B A)) )  => (v1_glib_001 (k6_glib_001 A B) A)) ) ).
tt(fc5_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  => (v13_glib_000 (k10_glib_004 A B))) ) ).
tt(fc5_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ( (~ (v3_relat_1 (k2_goboard2 A)))  &  ((v1_matrix_1 (k2_goboard2 A)) &  ((v2_goboard1 (k2_goboard2 A)) &  ((v3_goboard1 (k2_goboard2 A)) &  ((v4_goboard1 (k2_goboard2 A)) & (v5_goboard1 (k2_goboard2 A))) ) ) ) ) ) ) ).
tt(fc5_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xboole_0 C)) )  => (v1_xboole_0 (k2_graph_3 A B C))) ) ).
tt(fc5_graph_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_finset_1 (k5_graph_5 A B C D))) ) ).
tt(fc5_grcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 D E)) &  ((v1_funct_2 (k3_relat_1 D E) (u1_struct_0 A) (u1_struct_0 C)) & (v13_vectsp_1 (k3_relat_1 D E) A C)) ) ) ) ).
tt(fc5_gr_cy_1,ax,(v5_membered (u1_struct_0 k2_gr_cy_1))).
tt(fc5_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  &  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)))) &  ((v1_funct_2 (k6_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k6_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) (k15_pre_poly A) C) & (v3_polynom7 (k6_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) A C)) ) ) ) ) ).
tt(fc5_group_10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ((v7_ordinal1 B) & (v1_int_2 B)) )  =>  ( (~ (v1_xboole_0 (k15_group_10 A B)))  & (v1_finset_1 (k15_group_10 A B))) ) ) ).
tt(fc5_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ( (~ (v2_struct_0 (k5_group_6 A B)))  & (v15_algstr_0 (k5_group_6 A B))) ) ) ).
tt(fc5_group_7,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) & (v4_group_7 B A)) ) ) ) )  =>  ((v15_algstr_0 (k2_group_7 A B)) & (v5_group_1 (k2_group_7 A B))) ) ) ).
tt(fc5_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  ((v2_group_1 (k10_group_9 A B C)) &  ((v3_group_1 (k10_group_9 A B C)) & (v3_group_9 (k10_group_9 A B C) A)) ) ) ) ).
tt(fc5_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  => (v1_finset_1 (k3_heyting3 A B))) ) ).
tt(fc5_hilbasis,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  ((v1_funct_1 (k6_hilbasis A B)) &  ((v2_funct_1 (k6_hilbasis A B)) & (v1_funct_2 (k6_hilbasis A B) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)))) ) ) ) ).
tt(fc5_hilbert3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) )  =>  ((v1_funct_1 (k1_hilbert3 A B C D)) &  ((v1_funct_2 (k1_hilbert3 A B C D) (k9_funct_2 A B) (k9_funct_2 A B)) & (v3_funct_2 (k1_hilbert3 A B C D) (k9_funct_2 A B) (k9_funct_2 A B))) ) ) ) ).
tt(fc5_index_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) ) )  =>  ((v1_relat_1 (k4_index_1 B)) &  ((v2_relat_1 (k4_index_1 B)) &  ((v4_relat_1 (k4_index_1 B) A) & (v1_funct_1 (k4_index_1 B))) ) ) ) ) ).
tt(fc5_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k3_int_1 A))) ) ).
tt(fc5_int_3,ax,(v1_int_3 k1_int_3)).
tt(fc5_int_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v5_relat_1 (k7_finseq_1 A B) k4_numbers) &  ((v1_funct_1 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc5_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k1_interva1 A (k1_subset_1 A) (k1_subset_1 A)))) ) ) ).
tt(fc5_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v9_intpro_1 (k11_intpro_1 A))) ) ).
tt(fc5_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v6_tops_1 (k1_tops_1 A (k2_pre_topc A B)) A)) ) ).
tt(fc5_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k4_topreal1 A) (k15_euclid 2))) ) ).
tt(fc5_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  => (v4_topreal1 (k1_jordan1e A B))) ) ).
tt(fc5_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m1_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~ (v1_xboole_0 (k16_matrix_1 A))) ) ) ).
tt(fc5_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_jordan23 A)) ) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) &  ((v1_finseq_1 (k3_finseq_5 A)) & (v2_jordan23 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc5_jordan2c,ax, (! [A:$i] :  ((m1_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v2_tops_1 (k3_topreal1 2 A) (k15_euclid 2))) ) ).
tt(fc5_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k12_pscomp_1 A) (k13_pscomp_1 A)))) ) ).
tt(fc5_kurato_1,ax,(v3_setfam_1 (k3_kurato_1 k3_topmetr k6_kurato_1) (u1_struct_0 k3_topmetr))).
tt(fc5_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_funct_1 (u1_lattices A)) &  ((v1_funct_2 (u1_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v3_binop_1 (u1_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc5_lattice3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  ((v1_orders_2 (k7_lattice3 A)) &  ((v3_orders_2 (k7_lattice3 A)) &  ((v4_orders_2 (k7_lattice3 A)) & (v5_orders_2 (k7_lattice3 A))) ) ) ) ) ).
tt(fc5_lattice5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_ordinal1 B))  =>  (~ (v1_xboole_0 (k8_lattice5 A B))) ) ) ).
tt(fc5_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v3_lexbfs (k16_lexbfs A))) ) ).
tt(fc5_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v3_orders_2 (k4_lfuzzy_0 A)) &  ((v4_orders_2 (k4_lfuzzy_0 A)) &  ((v5_orders_2 (k4_lfuzzy_0 A)) &  ((v1_lattice3 (k4_lfuzzy_0 A)) &  ((v2_lattice3 (k4_lfuzzy_0 A)) &  ((v3_lattice3 (k4_lfuzzy_0 A)) &  ((v1_monoid_0 (k4_lfuzzy_0 A)) & (v9_waybel_1 (k4_lfuzzy_0 A))) ) ) ) ) ) ) ) ) ).
tt(fc5_lfuzzy_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) )  =>  ((v5_relat_1 (k5_lfuzzy_1 A B) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k5_lfuzzy_1 A B)) &  ((v1_funct_2 (k5_lfuzzy_1 A B) (k2_zfmisc_1 A A) k1_numbers) & (v3_lfuzzy_1 (k5_lfuzzy_1 A B) A)) ) ) ) ) ).
tt(fc5_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_lopban_1 A B)))  &  ((v13_algstr_0 (k8_lopban_1 A B)) &  ((v1_rlvect_1 (k8_lopban_1 A B)) &  ((v2_rlvect_1 (k8_lopban_1 A B)) &  ((v3_rlvect_1 (k8_lopban_1 A B)) &  ((v4_rlvect_1 (k8_lopban_1 A B)) &  ((v5_rlvect_1 (k8_lopban_1 A B)) &  ((v6_rlvect_1 (k8_lopban_1 A B)) &  ((v7_rlvect_1 (k8_lopban_1 A B)) & (v8_rlvect_1 (k8_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v1_group_1 (k8_lopban_2 A))) ) ).
tt(fc5_lopban_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_lopban_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k9_nat_1 B C)) &  ((v1_funct_2 (k9_nat_1 B C) k5_numbers (u1_struct_0 A)) & (v1_lopban_3 (k9_nat_1 B C) A)) ) ) ) ).
tt(fc5_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ( (~ (v2_struct_0 (k11_lopclset A)))  &  ((v1_pre_topc (k11_lopclset A)) & (v2_pre_topc (k11_lopclset A))) ) ) ) ).
tt(fc5_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k10_lpspace1 A B C)))  &  ((v1_rlvect_1 (k10_lpspace1 A B C)) &  ((v2_rlvect_1 (k10_lpspace1 A B C)) &  ((v3_rlvect_1 (k10_lpspace1 A B C)) &  ((v4_rlvect_1 (k10_lpspace1 A B C)) &  ((v5_rlvect_1 (k10_lpspace1 A B C)) &  ((v6_rlvect_1 (k10_lpspace1 A B C)) &  ((v7_rlvect_1 (k10_lpspace1 A B C)) & (v8_rlvect_1 (k10_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(fc5_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v2_struct_0 (k2_lpspace2 A B C D)))  &  ((v1_rlvect_1 (k2_lpspace2 A B C D)) &  ((v2_rlvect_1 (k2_lpspace2 A B C D)) &  ((v3_rlvect_1 (k2_lpspace2 A B C D)) &  ((v4_rlvect_1 (k2_lpspace2 A B C D)) &  ((v5_rlvect_1 (k2_lpspace2 A B C D)) &  ((v6_rlvect_1 (k2_lpspace2 A B C D)) &  ((v7_rlvect_1 (k2_lpspace2 A B C D)) & (v8_rlvect_1 (k2_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(fc5_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A B (k8_cqc_lang A (k8_cqc_lang A B C) C)) A)) ) ).
tt(fc5_margrel1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v2_card_3 B))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v2_margrel1 (k5_relat_1 A B))) ) ) ).
tt(fc5_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  =>  ((v1_funct_1 (k5_matrix11 A)) &  ((v1_funct_2 (k5_matrix11 A) (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A))) & (v1_binop_1 (k5_matrix11 A) (k3_finseq_2 (u1_struct_0 A)))) ) ) ) ).
tt(fc5_matroid0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  =>  ( (~ (v2_struct_0 (k2_matroid0 A)))  & (v1_pre_topc (k2_matroid0 A))) ) ) ).
tt(fc5_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((v1_relat_1 (k1_partfun3 A)) &  ((v1_funct_1 (k1_partfun3 A)) & (v1_finseq_1 (k1_partfun3 A))) ) ) ) ).
tt(fc5_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k3_struct_0 (k15_euclid A))) &  ((v1_funct_2 (k3_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_matrtop3 (k3_struct_0 (k15_euclid A)) A)) ) ) ) ).
tt(fc5_mazurulm,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v3_membered A) & (v3_xxreal_2 A)) )  &  ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  => (v4_xxreal_2 (k23_member_1 A B))) ) ).
tt(fc5_measure6,ax, (! [A:$i] :  ( ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v1_setfam_1 (k5_measure6 A))) ) ).
tt(fc5_member_1,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((v1_xboole_0 (k5_member_1 A)) & (v1_membered (k5_member_1 A))) ) ) ).
tt(fc5_membered,ax,(v5_membered k4_numbers)).
tt(fc5_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_memstr_0 B A)) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  (~ (v1_xboole_0 (k4_memstr_0 A B C))) ) ) ).
tt(fc5_mesfunc7,ax,(v2_valued_0 (k6_finseq_1 k7_numbers))).
tt(fc5_metric_1,ax, ( (~ (v2_struct_0 k8_metric_1))  & (v1_metric_1 k8_metric_1)) ).
tt(fc5_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v5_waybel23 A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v5_waybel23 B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v5_waybel23 (k2_borsuk_1 A B))) ) ) ) ).
tt(fc5_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v5_waybel23 (k15_euclid A))) ) ) ).
tt(fc5_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_pre_topc (k4_mfold_2 A)) & (v5_waybel23 (k4_mfold_2 A))) ) ) ).
tt(fc5_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_mmlquery C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (v1_mmlquery (k2_xboole_0 B C) A)) ) ).
tt(fc5_mod_2,ax, ((v36_algstr_0 k18_mod_2) & (v4_vectsp_1 k18_mod_2)) ).
tt(fc5_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v2_rlvect_1 (k2_mod_4 A))) ) ) ).
tt(fc5_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_1 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_1 (k8_modelc_1 A B))) ) ).
tt(fc5_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_2 (k5_modelc_2 A B))) ) ).
tt(fc5_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k1_orders_1 (k1_modelc_3 A)))) ) ) ).
tt(fc5_moebius1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_relat_1 (k4_moebius1 A)) &  ((v4_relat_1 (k4_moebius1 A) k5_numbers) &  ((v1_funct_1 (k4_moebius1 A)) &  ((v1_partfun1 (k4_moebius1 A) k5_numbers) & (v2_pre_poly (k4_moebius1 A))) ) ) ) ) ) ).
tt(fc5_msafree1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (v4_msualg_1 (k11_msafree A B) A)) ) ).
tt(fc5_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ( (~ (v2_struct_0 (k5_msafree A B)))  & (v1_lang1 (k5_msafree A B))) ) ) ).
tt(fc5_msalimit,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k5_msalimit A)))  & (v2_msalimit (k5_msalimit A))) ) ) ).
tt(fc5_mssubfam,ax, (! [A:$i] :  ((v1_relat_1 (k1_pboole A)) &  ((v3_relat_1 (k1_pboole A)) &  ((v4_relat_1 (k1_pboole A) A) &  ((v1_funct_1 (k1_pboole A)) &  ((v1_partfun1 (k1_pboole A) A) & (v2_finset_1 (k1_pboole A))) ) ) ) ) ) ).
tt(fc5_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  ((v1_unialg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) & (v2_unialg_2 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A)))) ) ) ).
tt(fc5_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msualg_2 A) & (l1_msualg_1 A)) ) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  => (v2_relat_1 (k2_msualg_2 A B))) ) ).
tt(fc5_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((v2_msualg_4 (k9_msualg_6 A B C) A B) & (v4_msualg_6 (k9_msualg_6 A B C) A B)) ) ) ).
tt(fc5_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v3_msualg_1 (k7_msafree2 A) A) &  ((v4_msualg_1 (k7_msafree2 A) A) & (v4_msafree2 (k7_msafree2 A) A)) ) ) ) ).
tt(fc5_mycielsk,ax, (! [A:$i,B:$i] :  ( ( ((v2_mycielsk A) & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v2_mycielsk (k5_yellow_0 A B))) ) ) ) ).
tt(fc5_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k3_xxreal_0 A B))) ) ).
tt(fc5_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k4_nat_3 A B C)) &  ((v4_relat_1 (k4_nat_3 A B C) A) &  ((v1_funct_1 (k4_nat_3 A B C)) &  ((v1_partfun1 (k4_nat_3 A B C) A) & (v4_valued_0 (k4_nat_3 A B C))) ) ) ) ) ) ).
tt(fc5_nat_lat,ax, (~ (v1_xboole_0 k6_nat_lat)) ).
tt(fc5_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ((v8_struct_0 A) & (l1_orders_2 A))  &  ((v8_struct_0 B) & (l1_orders_2 B)) )  =>  ((v8_struct_0 (k1_neckla_2 A B)) & (v1_orders_2 (k1_neckla_2 A B))) ) ) ).
tt(fc5_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_orders_2 (k4_necklace A)) & (v1_necklace (k4_necklace A))) ) ) ).
tt(fc5_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k1_finseq_2 A)) &  ((v1_funct_1 (k1_finseq_2 A)) &  ((v1_finseq_1 (k1_finseq_2 A)) & (v4_valued_0 (k1_finseq_2 A))) ) ) ) ) ).
tt(fc5_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k4_vfunct_1 k1_numbers A B C)) & (v1_nfcont_3 (k4_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc5_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_funct_1 B) &  ((v2_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v2_nfcont_4 (k5_relat_1 B C) A)) ) ) ).
tt(fc5_normform,ax, (! [A:$i] :  ((v3_lattices (k12_normform A)) & (v10_lattices (k12_normform A))) ) ).
tt(fc5_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v1_frechet (k4_normsp_2 A)) & (v5_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(fc5_numbers,ax, (~ (v1_xboole_0 k7_numbers)) ).
tt(fc5_openlatt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k10_openlatt A B))) ) ) ).
tt(fc5_oposet_1,ax, ((v3_orders_2 k1_oposet_1) & (v3_qmax_1 k1_oposet_1)) ).
tt(fc5_orders_2,ax, (! [A:$i] :  ( ((v2_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) )  => (v8_relat_2 (u1_orders_2 A))) ) ).
tt(fc5_orders_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) ) )  => (v4_funct_1 (k1_orders_3 A B))) ) ).
tt(fc5_ordinal1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  & (v3_ordinal1 B))  =>  ((v1_relat_1 (k5_relat_1 A B)) &  ((v5_relat_1 (k5_relat_1 A B) (k10_xtuple_0 A)) & (v5_ordinal1 (k5_relat_1 A B))) ) ) ) ).
tt(fc5_ordinal2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v3_ordinal1 (k10_ordinal2 A B)) & (v7_ordinal1 (k10_ordinal2 A B))) ) ) ).
tt(fc5_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v2_ordinal2 (k3_afinsq_1 A)) & (v1_ordinal5 (k3_afinsq_1 A))) ) ) ).
tt(fc5_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k4_relat_1 A)) &  ((v5_ordinal1 (k4_relat_1 A)) & (v1_ordinal2 (k4_relat_1 A))) ) ) ) ).
tt(fc5_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v3_msualg_1 (k8_osafree A B) A) &  ((v4_msualg_1 (k8_osafree A B) A) & (v12_osalg_1 (k8_osafree A B) A)) ) ) ) ).
tt(fc5_osalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ((v3_msualg_2 C A B) & (m2_osalg_2 C A B)) ) )  =>  ((v3_msualg_1 (k10_msualg_2 A B C) A) & (v12_osalg_1 (k10_msualg_2 A B C) A)) ) ) ).
tt(fc5_partfun3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  ((v1_xreal_0 (k6_square_1 A)) & (v2_xxreal_0 (k6_square_1 A))) ) ) ).
tt(fc5_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v1_relat_2 (k3_pcs_0 A A B B C D))) ) ).
tt(fc5_pencil_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_pencil_1 A B)))  &  ( (~ (v3_pencil_1 (k5_pencil_1 A B)))  &  ( (~ (v4_pencil_1 (k5_pencil_1 A B)))  &  ((v5_pencil_1 (k5_pencil_1 A B)) & (v6_pencil_1 (k5_pencil_1 A B))) ) ) ) ) ) ).
tt(fc5_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v1_xreal_0 (k5_polyeq_1 A B C D))) ) ).
tt(fc5_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_polynom1 A B)) &  ((v1_funct_2 (k8_polynom1 A B) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k8_polynom1 A B) (k15_pre_poly A) B)) ) ) ) ).
tt(fc5_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom2 A B C)) &  ((v1_funct_2 (k6_polynom2 A B C) (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (v13_vectsp_1 (k6_polynom2 A B C) (k11_polynom1 A B) B)) ) ) ) ).
tt(fc5_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_normsp_1 A B C)) &  ((v1_funct_2 (k3_normsp_1 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k3_normsp_1 A B C) A)) ) ) ) ).
tt(fc5_polynom5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k7_polynom5 A B)) &  ((v1_funct_2 (k7_polynom5 A B) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k7_polynom5 A B) A)) ) ) ) ).
tt(fc5_polynom7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v7_algstr_0 B) &  ((v4_rlvect_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  & (m1_subset_1 D (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_polynom7 A B C D)) &  ((v1_funct_2 (k6_polynom7 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k6_polynom7 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc5_polyred,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  => (v3_rewrite1 (k3_polyred A B C D))) ) ).
tt(fc5_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_poset_1 A B)) &  ((v1_funct_2 (k9_poset_1 A B) (u1_struct_0 A) (u1_struct_0 B)) & (v2_poset_1 (k9_poset_1 A B) A B)) ) ) ) ).
tt(fc5_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((v1_relat_1 (k15_pralg_1 B C)) &  ((v4_relat_1 (k15_pralg_1 B C) A) &  ((v1_funct_1 (k15_pralg_1 B C)) & (v1_partfun1 (k15_pralg_1 B C) A)) ) ) ) ) ).
tt(fc5_pralg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_pralg_2 D A B)) )  =>  ((v1_relat_1 (k9_pralg_2 A B C D)) &  ((v2_relat_1 (k9_pralg_2 A B C D)) &  ((v4_relat_1 (k9_pralg_2 A B C D) A) &  ((v1_funct_1 (k9_pralg_2 A B C D)) & (v1_partfun1 (k9_pralg_2 A B C D) A)) ) ) ) ) ) ).
tt(fc5_pre_circ,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  &  ((m1_subset_1 B (k9_xtuple_0 A)) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v3_trees_2 C)) ) ) ) )  =>  ((v1_relat_1 (k7_trees_2 A B C)) &  ((v1_funct_1 (k7_trees_2 A B C)) &  ((v1_finset_1 (k7_trees_2 A B C)) & (v3_trees_2 (k7_trees_2 A B C))) ) ) ) ) ).
tt(fc5_pre_poly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_pre_poly A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_pre_poly B)) ) ) )  =>  ((v1_relat_1 (k8_pre_poly A B)) &  ((v1_funct_1 (k8_pre_poly A B)) &  ((v1_finseq_1 (k8_pre_poly A B)) & (v1_pre_poly (k8_pre_poly A B))) ) ) ) ) ).
tt(fc5_pre_topc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((v1_funct_1 (k6_struct_0 A B C)) &  ((v1_funct_2 (k6_struct_0 A B C) (u1_struct_0 A) (u1_struct_0 B)) & (v5_pre_topc (k6_struct_0 A B C) A B)) ) ) ) ).
tt(fc5_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_finseq_1 C B))  => (v5_relat_1 (k6_prob_3 A C) B)) ) ).
tt(fc5_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (l2_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) & (l2_algstr_0 B)) ) )  =>  ( (~ (v2_struct_0 (k4_prvect_3 A B)))  &  ((v8_algstr_0 (k4_prvect_3 A B)) & (v13_algstr_0 (k4_prvect_3 A B))) ) ) ) ).
tt(fc5_pscomp_1,ax, ((v1_funct_1 k5_pscomp_1) &  ((v1_funct_2 k5_pscomp_1 (u1_struct_0 (k15_euclid 2)) k1_numbers) & (v1_pscomp_1 k5_pscomp_1 (k15_euclid 2))) ) ).
tt(fc5_pythtrip,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  (~ (v1_abian (k3_square_1 A))) ) ) ).
tt(fc5_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k5_qc_lang1 A))) ) ) ).
tt(fc5_quatern2,ax, ((v36_algstr_0 k16_quatern2) & (v4_vectsp_1 k16_quatern2)) ).
tt(fc5_quaterni,ax,(v1_quaterni k5_quaterni)).
tt(fc5_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k19_quofield A)) &  ((v36_algstr_0 (k19_quofield A)) &  ((v3_rlvect_1 (k19_quofield A)) & (v4_rlvect_1 (k19_quofield A))) ) ) ) ) ).
tt(fc5_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) & (v1_rat_1 (k4_xcmplx_0 A))) ) ) ).
tt(fc5_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l5_algstr_0 A))  =>  ((v1_funct_1 (k10_polynom3 A)) &  ((v1_funct_2 (k10_polynom3 A) k5_numbers (u1_struct_0 A)) &  (~ (v1_ratfunc1 (k10_polynom3 A) A)) ) ) ) ) ).
tt(fc5_rcomp_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v5_xxreal_2 (k3_xxreal_1 A B))) ) ).
tt(fc5_real_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xboole_0 (k6_xcmplx_0 A A))) ) ).
tt(fc5_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_real_lat A)))  &  ((v4_lattices (k6_real_lat A)) &  ((v5_lattices (k6_real_lat A)) &  ((v6_lattices (k6_real_lat A)) &  ((v7_lattices (k6_real_lat A)) &  ((v8_lattices (k6_real_lat A)) & (v9_lattices (k6_real_lat A))) ) ) ) ) ) ) ) ).
tt(fc5_real_ns1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ( (~ (v7_struct_0 (k7_real_ns1 A)))  & (v1_bhsp_1 (k7_real_ns1 A))) ) ) ) ).
tt(fc5_relat_1,ax, (! [A:$i,B:$i] : (v1_relat_1 (k1_tarski (k4_tarski A B)))) ).
tt(fc5_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_relat_2 A))  &  ((v1_relat_1 B) & (v1_relat_2 B)) )  => (v1_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc5_reloc,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_compos_0 (k6_ami_3 A B) (u1_compos_1 k1_ami_3))) ) ).
tt(fc5_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v5_relat_1 B A))  & (v1_relat_1 C))  => (v5_relat_1 (k3_xboole_0 B C) A)) ) ).
tt(fc5_revrot_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m1_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  => (v2_topreal1 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A))) ) ).
tt(fc5_rewrite2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_rewrite2 B)) ) ) )  =>  ((v1_relat_1 (k1_rewrite2 A B)) &  ((v1_funct_1 (k1_rewrite2 A B)) &  ((v1_finseq_1 (k1_rewrite2 A B)) & (v1_rewrite2 (k1_rewrite2 A B))) ) ) ) ) ).
tt(fc5_rfunct_1,ax, (! [A:$i,B:$i] :  ((v1_funct_1 (k4_funct_3 A B)) & (v1_partfun1 (k4_funct_3 A B) B)) ) ).
tt(fc5_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ((v13_algstr_0 (k2_ring_1 A B)) &  ((v36_algstr_0 (k2_ring_1 A B)) &  ((v3_group_1 (k2_ring_1 A B)) &  ((v4_vectsp_1 (k2_ring_1 A B)) &  ((v5_vectsp_1 (k2_ring_1 A B)) &  ((v2_rlvect_1 (k2_ring_1 A B)) &  ((v3_rlvect_1 (k2_ring_1 A B)) & (v4_rlvect_1 (k2_ring_1 A B))) ) ) ) ) ) ) ) ) ).
tt(fc5_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v2_struct_0 (k17_ringcat1 A)))  &  ( (~ (v11_struct_0 (k17_ringcat1 A)))  & (v1_cat_1 (k17_ringcat1 A))) ) ) ) ).
tt(fc5_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_rlaffin1 (k5_rusub_4 A B C) A)) ) ).
tt(fc5_rlaffin3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k4_vfunct_1 k5_numbers A B C)) & (v1_finseq_1 (k4_vfunct_1 k5_numbers A B C))) ) ) ).
tt(fc5_rltopsp1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) )  =>  ( (~ (v2_struct_0 (g1_rltopsp1 A B C D E)))  & (v5_rltopsp1 (g1_rltopsp1 A B C D E))) ) ) ).
tt(fc5_robbins4,ax, ( (~ (v2_struct_0 k2_robbins4))  & (v4_robbins1 k2_robbins4)) ).
tt(fc5_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((v1_relat_2 (u1_orders_2 A)) &  ((v3_relat_2 (u1_orders_2 A)) & (v1_partfun1 (u1_orders_2 A) (u1_struct_0 A))) ) ) ) ).
tt(fc5_rsspace3,ax, ( (~ (v2_struct_0 k3_rsspace3))  &  ((v13_algstr_0 k3_rsspace3) &  ((v2_rlvect_1 k3_rsspace3) &  ((v3_rlvect_1 k3_rsspace3) &  ((v4_rlvect_1 k3_rsspace3) &  ((v5_rlvect_1 k3_rsspace3) &  ((v6_rlvect_1 k3_rsspace3) &  ((v7_rlvect_1 k3_rsspace3) &  ((v8_rlvect_1 k3_rsspace3) &  ((v3_normsp_0 k3_rsspace3) &  ((v4_normsp_0 k3_rsspace3) & (v2_normsp_1 k3_rsspace3)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_rsspace4,ax, ( (~ (v2_struct_0 k3_rsspace4))  &  ((v13_algstr_0 k3_rsspace4) &  ((v2_rlvect_1 k3_rsspace4) &  ((v3_rlvect_1 k3_rsspace4) &  ((v4_rlvect_1 k3_rsspace4) &  ((v5_rlvect_1 k3_rsspace4) &  ((v6_rlvect_1 k3_rsspace4) &  ((v7_rlvect_1 k3_rsspace4) &  ((v8_rlvect_1 k3_rsspace4) &  ((v3_normsp_0 k3_rsspace4) &  ((v4_normsp_0 k3_rsspace4) & (v2_normsp_1 k3_rsspace4)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_rsspace,ax, ( (~ (v2_struct_0 (g1_bhsp_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace) k12_rsspace)))  & (v1_bhsp_1 (g1_bhsp_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace) k12_rsspace))) ).
tt(fc5_rvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  => (v3_valued_0 (k7_finseq_4 A B C D))) ) ).
tt(fc5_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_amistd_1 (k9_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc5_scmfsa_2,ax, ((v3_memstr_0 k1_scmfsa_2 3) & (v1_extpro_1 k1_scmfsa_2 3)) ).
tt(fc5_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_compos_0 (k10_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc5_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_scmfsa6c (k7_scmfsa_2 A B))) ) ).
tt(fc5_scmfsa7b,ax, ((v1_relat_1 (k4_compos_1 k1_scmfsa_2)) &  ((v4_relat_1 (k4_compos_1 k1_scmfsa_2) k5_numbers) &  ((v5_relat_1 (k4_compos_1 k1_scmfsa_2) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_compos_1 k1_scmfsa_2)) &  ((v1_finset_1 (k4_compos_1 k1_scmfsa_2)) &  ((v7_amistd_1 (k4_compos_1 k1_scmfsa_2) 3 k1_scmfsa_2) & (v1_scmfsa7b (k4_compos_1 k1_scmfsa_2))) ) ) ) ) ) ).
tt(fc5_scmfsa8a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v1_xboole_0 (k1_scmfsa8a A)))  &  ((v1_relat_1 (k1_scmfsa8a A)) &  ((v4_relat_1 (k1_scmfsa8a A) k5_numbers) &  ((v5_relat_1 (k1_scmfsa8a A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa8a A)) &  ((v1_finset_1 (k1_scmfsa8a A)) &  ((v1_afinsq_1 (k1_scmfsa8a A)) &  ((v2_compos_1 (k1_scmfsa8a A) k1_scmfsa_2) & (v1_scmfsa7b (k1_scmfsa8a A))) ) ) ) ) ) ) ) ) ) ).
tt(fc5_scmfsa_i,ax, ( (~ (v1_xboole_0 k2_scmfsa_i))  & (v3_compos_0 k2_scmfsa_i)) ).
tt(fc5_scmfsa_m,ax, (~ (v1_xboole_0 k2_scm_inst)) ).
tt(fc5_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scm_halt A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v3_scm_halt B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k3_scmfsa6a A B)))  &  ((v1_relat_1 (k3_scmfsa6a A B)) &  ((v4_relat_1 (k3_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa6a A B)) &  ((v1_finset_1 (k3_scmfsa6a A B)) &  ((v1_afinsq_1 (k3_scmfsa6a A B)) & (v3_scm_halt (k3_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc5_scm_inst,ax, ( (~ (v1_xboole_0 k3_scm_inst))  & (v2_compos_0 k3_scm_inst)) ).
tt(fc5_scmpds_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v4_scmpds_4 (k13_scmpds_2 A B C D))) ) ).
tt(fc5_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v6_compos_0 (k8_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc5_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scmpds_4 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_6 C D A B)))  &  ((v1_relat_1 (k2_scmpds_6 C D A B)) &  ((v4_relat_1 (k2_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_6 C D A B)) &  ((v1_finset_1 (k2_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k2_scmpds_6 C D A B)) &  ((v2_scmpds_4 (k2_scmpds_6 C D A B)) & (v3_scmpds_4 (k2_scmpds_6 C D A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc5_scmpds_i,ax,(v3_compos_0 k1_scmpds_i)).
tt(fc5_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_extpro_1 (k4_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc5_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v4_amistd_1 (k6_scmring2 A B C) 2 (k1_scmring2 A))) ) ).
tt(fc5_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmringi A)))  & (v2_compos_0 (k1_scmringi A))) ) ) ).
tt(fc5_scmyciel,ax, (! [A:$i,B:$i] :  ((v5_finset_1 A) => (v5_finset_1 (k4_xboole_0 A B))) ) ).
tt(fc5_seq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) &  ((v1_funct_2 (k18_valued_1 A B) k5_numbers k1_numbers) & (v2_comseq_2 (k18_valued_1 A B))) ) ) ) ).
tt(fc5_setfam_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) )  => (v1_setfam_1 (k2_enumset1 A B C D))) ) ).
tt(fc5_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) ) )  => (v1_sfmastr1 (k10_scmfsa_2 A B))) ) ).
tt(fc5_simplex0,ax, ((v1_xboole_0 (k1_simplex0 k1_xboole_0)) & (v1_classes1 (k1_simplex0 k1_xboole_0))) ).
tt(fc5_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) )  &  ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (v1_rlaffin1 (k1_simplex1 A B C) A)) ) ).
tt(fc5_sincos10,ax, ((v1_funct_1 k1_sincos10) & (v2_funct_1 k1_sincos10)) ).
tt(fc5_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(fc5_sin_cos9,ax, ((v1_relat_1 (k5_relat_1 k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) & (v2_funct_1 (k5_relat_1 k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))))) ).
tt(fc5_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v1_xreal_0 (k25_sin_cos A))) ) ).
tt(fc5_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v3_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v3_topreal1 (k1_rfinseq B A))) ) ).
tt(fc5_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (v3_funct_1 (k1_sprect_1 A))) ) ) ).
tt(fc5_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v3_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc5_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_xboole_0 (k2_struct_0 A))) ) ) ).
tt(fc5_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  (~ (v1_xboole_0 (k4_enumset1 A B C D E F))) ) ).
tt(fc5_substut1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C (k8_qc_lang1 A B)) &  ( ((v3_card_1 D B) & (m1_finseq_1 D (k2_qc_lang1 A)))  & (m1_subset_1 E (k1_substut1 A))) ) ) )  => (v4_substut1 (k17_substut1 A C D E) A)) ) ).
tt(fc5_tex_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B A) =>  ((v1_pre_topc (k3_tex_1 A B)) & (v2_pre_topc (k3_tex_1 A B))) ) ) ).
tt(fc5_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v1_subset_1 B (u1_struct_0 A)))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_subset_1 (k1_tops_1 A B) (u1_struct_0 A))) ) ) ).
tt(fc5_tmap_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_pre_topc B A))  =>  ( (~ (v2_struct_0 (k8_tmap_1 A B)))  &  ((v1_pre_topc (k8_tmap_1 A B)) & (v2_pre_topc (k8_tmap_1 A B))) ) ) ) ).
tt(fc5_topalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v15_algstr_0 (k5_topalg_1 A B)) &  ((v2_group_1 (k5_topalg_1 A B)) & (v3_group_1 (k5_topalg_1 A B))) ) ) ) ).
tt(fc5_topalg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 A)) &  ((v5_pre_topc B k5_topmetr A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 A)) &  ((v5_pre_topc C k5_topmetr A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k3_topalg_2 A B C)) &  ((v1_funct_2 (k3_topalg_2 A B C) (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A)) & (v5_pre_topc (k3_topalg_2 A B C) (k2_borsuk_1 k5_topmetr k5_topmetr) A)) ) ) ) ).
tt(fc5_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_funct_1 (k1_topalg_5 A)) &  ((v1_funct_2 (k1_topalg_5 A) (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2)) & (v5_pre_topc (k1_topalg_5 A) k5_topmetr k2_topalg_2)) ) ) ) ).
tt(fc5_topalg_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ( ((v3_topalg_6 D A C) & (m1_borsuk_2 D A C C))  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) )  => (v3_topalg_6 (k3_relat_1 D E) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C))) ) ).
tt(fc5_topdim_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_topdim_1 A) & (l1_pre_topc A)) ) )  =>  ((v7_ordinal1 (k4_topdim_1 A)) & (v1_int_1 (k4_topdim_1 A))) ) ) ).
tt(fc5_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v3_topdim_1 (k15_euclid A))) ) ) ).
tt(fc5_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A))) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A)) & (v5_pre_topc (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A)) A A)) ) ) ) ).
tt(fc5_topmetr,ax, ((v2_pre_topc k3_topmetr) & (v3_topmetr k3_topmetr)) ).
tt(fc5_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k5_topreal1 A))) ) ) ).
tt(fc5_topreal6,ax, (! [A:$i] :  ( ((v3_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v3_xxreal_2 (k6_measure6 A))) ) ).
tt(fc5_topreal7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) ) )  =>  ((v1_metric_1 (k1_topreal7 A B)) & (v7_metric_1 (k1_topreal7 A B))) ) ) ).
tt(fc5_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v3_pre_topc (k1_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc5_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k4_xxreal_1 (k6_xcmplx_0 A B) A))) ) ) ).
tt(fc5_toprealb,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos k1_numbers k1_numbers) & (v1_fcont_1 k19_sin_cos)) ) ).
tt(fc5_toprealc,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k12_euclid A))) ) ).
tt(fc5_tops_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v4_pre_topc (k2_xboole_0 B C) A)) ) ).
tt(fc5_trees_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  & (m1_subset_1 B A))  =>  ( (~ (v1_xboole_0 (k4_trees_1 A B)))  &  ((v1_finset_1 (k4_trees_1 A B)) & (v1_trees_1 (k4_trees_1 A B))) ) ) ) ).
tt(fc5_trees_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  & (m1_subset_1 B A))  => (v1_finset_1 (k1_trees_2 A B))) ) ).
tt(fc5_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k4_trees_3 A))) ) ) ).
tt(fc5_trees_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) )  =>  ((v1_relat_1 (k9_trees_4 B C D)) &  ((v5_relat_1 (k9_trees_4 B C D) A) &  ((v1_funct_1 (k9_trees_4 B C D)) & (v3_trees_2 (k9_trees_4 B C D))) ) ) ) ) ).
tt(fc5_trees_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  & (m1_subset_1 B (k9_xtuple_0 A)))  =>  ((v1_relat_1 (k5_trees_2 A B)) &  ((v1_funct_1 (k5_trees_2 A B)) &  ((v1_finset_1 (k5_trees_2 A B)) & (v3_trees_2 (k5_trees_2 A B))) ) ) ) ) ).
tt(fc5_unialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (v1_funcop_1 (u1_unialg_1 A))) ) ).
tt(fc5_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_polynom3 A B C)) &  ((v1_funct_2 (k11_polynom3 A B C) k5_numbers (u1_struct_0 A)) & (v1_uproots (k11_polynom3 A B C) A)) ) ) ) ).
tt(fc5_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v5_relat_1 A k4_numbers))  => (v5_membered (k10_xtuple_0 A))) ) ).
tt(fc5_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v5_relat_1 (k1_valued_1 A B) k4_numbers) & (v1_funct_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc5_vectmetr,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  &  ((m1_subset_1 C A) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_vectmetr A B C D E)))  & (v4_vectmetr (g1_vectmetr A B C D E))) ) ) ).
tt(fc5_vectsp_1,ax,(v3_membered (u1_struct_0 k2_vectsp_1))).
tt(fc5_vfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k5_vfunct_1 A B C)) & (v1_partfun1 (k5_vfunct_1 A B C) A)) ) ) ).
tt(fc5_waybel_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) &  ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_waybel_0 A B C D)))  & (v6_waybel_0 (g1_waybel_0 A B C D) A)) ) ) ).
tt(fc5_waybel10,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) ) )  =>  ( (~ (v2_struct_0 (k7_yellow_1 A B)))  &  ((v1_orders_2 (k7_yellow_1 A B)) & (v4_yellow_0 (k7_yellow_1 A B) (k6_yellow_1 (u1_struct_0 A) B))) ) ) ) ).
tt(fc5_waybel11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k3_waybel11 A B C)))  &  ((v6_waybel_0 (k3_waybel11 A B C) A) & (v8_waybel_0 (k3_waybel11 A B C) A)) ) ) ) ).
tt(fc5_waybel17,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v2_struct_0 (k4_waybel17 A B)))  &  ((v3_orders_2 (k4_waybel17 A B)) &  ((v6_waybel_0 (k4_waybel17 A B) A) & (v7_waybel_0 (k4_waybel17 A B))) ) ) ) ) ).
tt(fc5_waybel18,ax, ( (~ (v2_struct_0 k9_waybel18))  &  ((v1_pre_topc k9_waybel18) & (v2_pre_topc k9_waybel18)) ) ).
tt(fc5_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v8_waybel_1 (k3_struct_0 A) A)) ) ) ) ).
tt(fc5_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel23 (k5_waybel_0 A B) A)) ) ).
tt(fc5_waybel24,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v5_waybel_0 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k2_waybel24 A B C D E)) &  ((v1_funct_2 (k2_waybel24 A B C D E) (u1_struct_0 A) (u1_struct_0 C)) & (v5_waybel_0 (k2_waybel24 A B C D E) A C)) ) ) ) ).
tt(fc5_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v2_pre_topc (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc5_waybel26,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_relat_1 (k3_card_3 (k2_card_3 A)))) ) ).
tt(fc5_waybel27,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) ) )  =>  ((v1_orders_2 (k2_waybel27 A B)) & (v4_orders_2 (k2_waybel27 A B))) ) ) ).
tt(fc5_waybel_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A)) ) )  =>  ( (~ (v2_struct_0 (k3_waybel_2 A B C)))  & (v6_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(fc5_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_yellow_1 (k5_waybel11 A))))  &  ((v1_orders_2 (k2_yellow_1 (k5_waybel11 A))) & (v3_lattice3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(fc5_waybel32,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel32 A B)))  &  ((v6_waybel_0 (k2_waybel32 A B) A) &  ((v7_waybel_0 (k2_waybel32 A B)) & (v8_waybel_0 (k2_waybel32 A B) A)) ) ) ) ) ).
tt(fc5_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k4_waybel34 A)))  &  ((v2_altcat_1 (k4_waybel34 A)) &  ((v6_altcat_1 (k4_waybel34 A)) &  ((v11_altcat_1 (k4_waybel34 A)) &  ((v12_altcat_1 (k4_waybel34 A)) &  ((v2_yellow21 (k4_waybel34 A)) & (v3_yellow21 (k4_waybel34 A))) ) ) ) ) ) ) ) ).
tt(fc5_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel_0 (k1_waybel_3 A B) A)) ) ).
tt(fc5_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (~ (v1_xboole_0 (k3_waybel_4 A))) ) ) ).
tt(fc5_waybel_5,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k2_funcop_1 A B)) &  ((v4_relat_1 (k2_funcop_1 A B) A) &  ((v1_funct_1 (k2_funcop_1 A B)) & (v1_partfun1 (k2_funcop_1 A B) A)) ) ) ) ).
tt(fc5_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v3_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc5_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_waybel_0 C A)) ) ) )  =>  ((v3_orders_2 (k3_waybel_2 A B C)) & (v6_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(fc5_weddwitt,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k5_weddwitt A B)))  &  ( (~ (v6_struct_0 (k5_weddwitt A B)))  &  ((v8_struct_0 (k5_weddwitt A B)) &  ((v13_algstr_0 (k5_weddwitt A B)) &  ((v33_algstr_0 (k5_weddwitt A B)) &  ((v36_algstr_0 (k5_weddwitt A B)) &  ((v2_rlvect_1 (k5_weddwitt A B)) &  ((v3_rlvect_1 (k5_weddwitt A B)) &  ((v4_rlvect_1 (k5_weddwitt A B)) &  ((v3_group_1 (k5_weddwitt A B)) &  ((v4_vectsp_1 (k5_weddwitt A B)) & (v5_vectsp_1 (k5_weddwitt A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc5_wellord2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k1_wellord2 A)) & (v1_wellord1 (k1_wellord2 A))) ) ) ).
tt(fc5_xboole_0,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k2_xboole_0 B A))) ) ) ).
tt(fc5_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k6_xboolean A B))) ) ).
tt(fc5_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  => (v1_xcmplx_0 (k7_xcmplx_0 A B))) ) ).
tt(fc5_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k2_xcmplx_0 A B))) ) ).
tt(fc5_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k10_xtuple_0 A))) ) ).
tt(fc5_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k3_xxreal_0 A B))) ) ).
tt(fc5_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (~ (v1_xboole_0 (k1_xxreal_1 A A))) ) ) ).
tt(fc5_xxreal_2,ax, (! [A:$i] :  ( ((v5_membered A) & (v1_xxreal_2 A))  =>  ((v1_xxreal_0 (k2_xxreal_2 A)) & (v1_int_1 (k2_xxreal_2 A))) ) ) ).
tt(fc5_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  ((v2_xxreal_0 A) &  (~ (v1_xreal_0 A)) ) )  &  ((v1_xxreal_0 B) &  ((v2_xxreal_0 B) &  (~ (v1_xreal_0 B)) ) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) &  (~ (v1_xreal_0 (k1_xxreal_3 A B))) ) ) ) ).
tt(fc5_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_yellow_0 A) &  ((v10_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v3_yellow_0 B) &  ((v10_waybel_1 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v10_waybel_1 (k3_yellow_3 A B))) ) ) ).
tt(fc5_yellow11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (v2_yellow11 (k3_yellow11 A B C) A)) ) ).
tt(fc5_yellow13,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_yellow13 A) & (l1_waybel_9 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_waybel_1 A B)) &  ((v1_funct_2 (k4_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v5_pre_topc (k4_waybel_1 A B) A A)) ) ) ) ).
tt(fc5_yellow14,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) ) )  =>  ((v1_pre_topc (k3_waybel18 A (k7_funcop_1 A B))) &  ((v2_pre_topc (k3_waybel18 A (k7_funcop_1 A B))) & (v6_pre_topc (k3_waybel18 A (k7_funcop_1 A B)))) ) ) ) ).
tt(fc5_yellow16,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  (~ (v1_xboole_0 B)) )  =>  ((v1_orders_2 (k6_yellow_1 B A)) & (v24_waybel_0 (k6_yellow_1 B A))) ) ) ).
tt(fc5_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v9_functor0 (k2_yellow18 (k1_yellow18 A) A) (k1_yellow18 A) A) &  ((v16_functor0 (k2_yellow18 (k1_yellow18 A) A) (k1_yellow18 A) A) & (v21_functor0 (k2_yellow18 (k1_yellow18 A) A) (k1_yellow18 A) A)) ) ) ) ).
tt(fc5_yellow19,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  &  ((v1_subset_1 C (u1_struct_0 (k3_yellow_1 B))) &  ((v2_waybel_0 C (k3_yellow_1 B)) &  ((v13_waybel_0 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 B))))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_yellow19 A B C)))  &  ((v6_waybel_0 (k3_yellow19 A B C) A) & (v7_waybel_0 (k3_yellow19 A B C))) ) ) ) ).
tt(fc5_yellow_1,ax, (! [A:$i] :  ((v1_orders_2 (k2_yellow_1 A)) &  ((v3_orders_2 (k2_yellow_1 A)) &  ((v4_orders_2 (k2_yellow_1 A)) & (v5_orders_2 (k2_yellow_1 A))) ) ) ) ).
tt(fc5_yellow21,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) & (v8_relat_2 B)) )  =>  ((v1_relat_1 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A))) & (v8_relat_2 (k3_relat_1 (k3_relat_1 A B) (k2_funct_1 A)))) ) ) ).
tt(fc5_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 A))) & (v1_lattice3 (k2_yellow_1 (k7_waybel_0 A)))) ) ) ).
tt(fc5_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ((v5_orders_2 A) & (l1_orders_2 A))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v5_orders_2 (k3_yellow_3 A B))) ) ) ).
tt(fc5_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (v1_xboole_0 (k3_yellow_4 A B C))) ) ) ).
tt(fc5_yellow_6,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v2_pralg_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ((v1_relat_1 (k12_pralg_1 A B)) &  ((v2_relat_1 (k12_pralg_1 A B)) &  ((v4_relat_1 (k12_pralg_1 A B) A) &  ((v1_funct_1 (k12_pralg_1 A B)) & (v1_partfun1 (k12_pralg_1 A B) A)) ) ) ) ) ) ).
tt(fc5_yellow_7,ax, (! [A:$i] :  ( ((v2_lattice3 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v1_lattice3 (k7_lattice3 A))) ) ) ).
tt(fc5_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v2_struct_0 (k3_yellow_9 A B)))  &  ((v4_orders_2 (k3_yellow_9 A B)) & (v6_waybel_0 (k3_yellow_9 A B) A)) ) ) ) ).
tt(fc5_zf_lang,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  => (v1_zf_lang (k7_zf_lang A B))) ) ).
tt(fc5_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k8_zmodul01 A))) ) ) ).
tt(fc60_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 B) => (v1_xboole_0 (k13_fomodel0 A B))) ) ).
tt(fc60_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) &  ((v16_fomodel1 C B) & (l1_fomodel1 C)) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D C A)) ) ) ) )  =>  ((v1_relat_1 (k5_relat_1 D (k37_fomodel1 B))) &  ((v1_funct_1 (k5_relat_1 D (k37_fomodel1 B))) & (v1_fomodel2 (k5_relat_1 D (k37_fomodel1 B)) B A)) ) ) ) ).
tt(fc60_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  &  ((v13_fomodel4 E A) &  ((v4_fomodel1 F A) &  ( (~ (v7_fomodel2 F (k2_xboole_0 (k2_xboole_0 E (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) B)) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C)) A))  & (m1_subset_1 F (k1_fomodel1 A))) ) ) ) ) ) )  => (v4_fomodel4 (k4_tarski (k13_fomodel0 F (k2_xboole_0 E (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k30_fomodel2 A (k31_fomodel2 A D) B)))) C) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k30_fomodel4 A)) (k1_tarski (k4_tarski (k2_xboole_0 E (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k24_fomodel3 A D F B))) C)))) ) ).
tt(fc60_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v4_membered B))  => (v4_membered (k15_member_1 A B))) ) ).
tt(fc60_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_valued_0 (k30_valued_1 B)) & (v3_partfun3 (k30_valued_1 B))) ) ) ) ) ).
tt(fc60_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v6_pcs_0 A) & (l2_pcs_0 A))  =>  ((v6_pcs_0 (k19_pcs_0 A B)) & (v12_pcs_0 (k19_pcs_0 A B))) ) ) ).
tt(fc60_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_relat_1 B) & (v4_valued_0 B)) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v4_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc60_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k30_valued_1 C)) & (v1_partfun1 (k30_valued_1 C) A)) ) ) ).
tt(fc61_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 B) =>  ((v1_relat_1 (k13_fomodel0 A B)) & (v5_relat_1 (k13_fomodel0 A B) A)) ) ) ).
tt(fc61_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) &  ((v16_fomodel1 C B) & (l1_fomodel1 C)) ) )  &  ((m1_subset_1 D (k16_fomodel2 B A)) &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel2 E C A)) ) ) ) ) )  =>  ((v1_relat_1 (k1_funct_4 E D)) &  ((v1_funct_1 (k1_funct_4 E D)) & (v1_fomodel2 (k1_funct_4 E D) C A)) ) ) ) ).
tt(fc61_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((v13_fomodel4 C B) &  ((v13_fomodel4 D B) &  ((v4_fomodel2 E B) & (m1_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) )  => (v4_fomodel4 (k4_tarski (k13_fomodel0 A (k2_xboole_0 C D)) E) A B (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k23_fomodel4 B)) (k1_tarski (k4_tarski C E)))) ) ).
tt(fc61_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v9_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v9_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc61_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k16_member_1 A B))) ) ).
tt(fc61_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_valued_0 (k30_valued_1 B)) & (v2_partfun3 (k30_valued_1 B))) ) ) ) ) ).
tt(fc61_pcs_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  =>  ( (~ (v2_struct_0 (k20_pcs_0 A)))  & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc61_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  => (v1_xcmplx_0 (k1_funct_1 A B))) ) ).
tt(fc61_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k30_valued_1 C)) & (v1_partfun1 (k30_valued_1 C) A)) ) ) ).
tt(fc62_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) )  =>  ((v1_relat_1 (k13_fomodel0 B C)) & (v4_relat_1 (k13_fomodel0 B C) (k2_finseq_1 (k2_xcmplx_0 A B)))) ) ) ).
tt(fc62_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((v1_xboole_0 C) & (m1_subset_1 D (k16_fomodel2 B A))) ) )  => (v10_fomodel2 (k13_fomodel0 D C) A B D)) ) ).
tt(fc62_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k30_fomodel4 A) A)) ) ).
tt(fc62_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v9_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k4_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k4_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k4_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k4_glib_003 B)) & (v9_glib_003 (k13_glib_000 A k4_glib_003 B))) ) ) ) ) ) ).
tt(fc62_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k16_member_1 A B))) ) ) ).
tt(fc62_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v2_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k30_valued_1 B)) &  ((v1_funct_1 (k30_valued_1 B)) &  ((v1_valued_0 (k30_valued_1 B)) & (v1_partfun3 (k30_valued_1 B))) ) ) ) ) ).
tt(fc62_pcs_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l2_pcs_0 A))  =>  ((v3_orders_2 (k20_pcs_0 A)) & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc62_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  => (v1_xxreal_0 (k1_funct_1 A B))) ) ).
tt(fc62_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k30_valued_1 C)) & (v1_partfun1 (k30_valued_1 C) A)) ) ) ).
tt(fc63_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 C D)) &  ((v1_funct_1 (k7_finseq_1 C D)) &  ((v3_card_1 (k7_finseq_1 C D) (k2_xcmplx_0 A B)) & (v1_finseq_1 (k7_finseq_1 C D))) ) ) ) ) ).
tt(fc63_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k16_fomodel2 B A)) &  ((v10_fomodel2 D A B C) & (v10_fomodel2 E A B C)) ) ) )  => (v10_fomodel2 (k2_xboole_0 D E) A B C)) ) ).
tt(fc63_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v4_fomodel2 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  => (v4_fomodel4 (k4_tarski (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k37_fomodel3 A B C D)) (k30_fomodel2 A (k31_fomodel2 A B) D)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k29_fomodel4 A)) k1_xboole_0)) ) ).
tt(fc63_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_003 A) & (v10_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k2_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k2_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k2_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k2_glib_003 B)) & (v10_glib_003 (k13_glib_000 A k2_glib_003 B))) ) ) ) ) ) ).
tt(fc63_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k16_member_1 A B))) ) ).
tt(fc63_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v3_valued_0 (k54_valued_1 B)) & (v4_partfun3 (k54_valued_1 B))) ) ) ) ) ).
tt(fc63_pcs_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l2_pcs_0 A))  =>  ((v4_orders_2 (k20_pcs_0 A)) & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc63_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  => (v1_xreal_0 (k1_funct_1 A B))) ) ).
tt(fc63_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k30_valued_1 A)) &  ((v1_funct_1 (k30_valued_1 A)) &  ((v1_valued_0 (k30_valued_1 A)) & (v1_finseq_1 (k30_valued_1 A))) ) ) ) ) ).
tt(fc64_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  => (v1_xboole_0 (k5_xboole_0 (k3_funct_2 A A (k6_partfun1 A) B) B))) ) ).
tt(fc64_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k16_fomodel2 B A)) & (v10_fomodel2 D A B C)) ) )  => (v11_fomodel2 (k13_fomodel0 D C) B A D)) ) ).
tt(fc64_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k29_fomodel4 A) A)) ) ).
tt(fc64_glib_003,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_003 A) & (v10_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_000 A k3_glib_003 B)) &  ((v4_relat_1 (k13_glib_000 A k3_glib_003 B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A k3_glib_003 B)) &  ((v1_finset_1 (k13_glib_000 A k3_glib_003 B)) & (v10_glib_003 (k13_glib_000 A k3_glib_003 B))) ) ) ) ) ) ).
tt(fc64_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k17_member_1 A B))) ) ).
tt(fc64_partfun3,ax, (! [A:$i,B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v3_valued_0 (k54_valued_1 B)) & (v1_partfun3 (k54_valued_1 B))) ) ) ) ) ).
tt(fc64_pcs_0,ax, (! [A:$i] :  ( ((v4_pcs_0 A) & (l2_pcs_0 A))  =>  ((v5_pcs_0 (k20_pcs_0 A)) & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc64_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  => (v1_rat_1 (k1_funct_1 A B))) ) ).
tt(fc64_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k35_valued_1 A)) &  ((v1_funct_1 (k35_valued_1 A)) &  ((v1_valued_0 (k35_valued_1 A)) & (v3_valued_0 (k35_valued_1 A))) ) ) ) ) ).
tt(fc65_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) ) )  => (v1_xboole_0 (k4_xboole_0 (k1_tarski (k1_funct_1 B 1)) A))) ) ).
tt(fc65_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel2 (k13_fomodel0 A k1_xboole_0) A)) ) ).
tt(fc65_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) &  ((v4_funct_1 C) & (m1_subset_1 D (k43_fomodel2 A))) ) )  => (v1_xboole_0 (k4_xboole_0 C (k42_fomodel4 A B C D)))) ) ).
tt(fc65_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v2_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v2_glib_000 (k12_glib_003 A B C)) & (v2_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc65_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k17_member_1 A B))) ) ) ).
tt(fc65_pcs_0,ax, (! [A:$i] :  ( ((v5_pcs_0 A) & (l2_pcs_0 A))  =>  ((v4_pcs_0 (k20_pcs_0 A)) & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc65_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  => (v1_int_1 (k1_funct_1 A B))) ) ).
tt(fc65_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k35_valued_1 A)) &  ((v5_relat_1 (k35_valued_1 A) k3_numbers) &  ((v1_funct_1 (k35_valued_1 A)) & (v1_valued_0 (k35_valued_1 A))) ) ) ) ) ).
tt(fc66_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C B) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) & (v1_partfun1 D B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C D)) &  ((v4_relat_1 (k3_relat_1 C D) A) & (v1_partfun1 (k3_relat_1 C D) A)) ) ) ) ).
tt(fc66_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ( ((v4_fomodel2 C B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ( ((v4_fomodel2 D B) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  & (m1_subset_1 E (k16_fomodel2 B A))) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k26_fomodel2 B A E (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) C) D)) (k9_xboolean (k26_fomodel2 B A E C) (k26_fomodel2 B A E D))))) ) ).
tt(fc66_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) &  ((v4_funct_1 C) & (m1_subset_1 D (k43_fomodel2 A))) ) )  => (v1_zfmisc_1 (k4_xboole_0 (k42_fomodel4 A B C D) C))) ) ).
tt(fc66_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k17_member_1 A B))) ) ).
tt(fc66_pcs_0,ax, (! [A:$i] :  ( ((v6_pcs_0 A) & (l2_pcs_0 A))  =>  ((v6_pcs_0 (k20_pcs_0 A)) & (v12_pcs_0 (k20_pcs_0 A))) ) ) ).
tt(fc66_valued_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  => (v7_ordinal1 (k1_funct_1 A B))) ) ).
tt(fc66_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k35_valued_1 C)) & (v1_partfun1 (k35_valued_1 C) A)) ) ) ).
tt(fc67_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) =>  ((v1_relat_1 (k13_fomodel0 A B)) & (v5_relat_1 (k13_fomodel0 A B) (k2_xboole_0 A (k10_xtuple_0 B)))) ) ) ).
tt(fc67_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k16_fomodel2 A C))) ) )  => (v1_xboole_0 (k5_xboole_0 (k26_fomodel2 A C D (k38_fomodel2 A B)) (k9_margrel1 (k26_fomodel2 A C D B))))) ) ).
tt(fc67_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v13_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v1_xboole_0 (k5_xboole_0 (k34_fomodel1 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C)) (k10_finseq_1 B C)))) ) ).
tt(fc67_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k17_member_1 A B))) ) ).
tt(fc67_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xcmplx_0 B) => (v1_valued_0 (k2_funcop_1 A B))) ) ).
tt(fc67_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k35_valued_1 C)) & (v1_partfun1 (k35_valued_1 C) A)) ) ) ).
tt(fc68_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v4_funct_1 A) & (v4_funct_1 B))  => (v4_funct_1 (k2_xboole_0 A B))) ) ).
tt(fc68_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k22_fomodel4 A) A)) ) ).
tt(fc68_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k17_member_1 A B))) ) ).
tt(fc68_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (v12_pcs_0 (k21_pcs_0 A B))) ) ).
tt(fc68_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xxreal_0 B) => (v2_valued_0 (k2_funcop_1 A B))) ) ).
tt(fc68_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k35_valued_1 C)) & (v1_partfun1 (k35_valued_1 C) A)) ) ) ).
tt(fc69_fomodel0,ax, (! [A:$i] :  ( ((v4_funct_1 A) &  ((v1_finset_1 A) & (v5_finset_1 A)) )  => (v1_finset_1 (k21_fomodel0 A))) ) ).
tt(fc69_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k23_fomodel4 A) A)) ) ).
tt(fc69_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v1_int_1 B))  => (v5_membered (k17_member_1 A B))) ) ).
tt(fc69_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_pcs_0 B)) )  =>  (~ (v2_struct_0 (k21_pcs_0 A B))) ) ) ).
tt(fc69_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xreal_0 B) => (v3_valued_0 (k2_funcop_1 A B))) ) ).
tt(fc69_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k35_valued_1 A)) &  ((v1_funct_1 (k35_valued_1 A)) &  ((v1_valued_0 (k35_valued_1 A)) & (v1_finseq_1 (k35_valued_1 A))) ) ) ) ) ).
tt(fc6_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_abcmiz_0 A))))  =>  ((v1_waybel_0 (k4_abcmiz_0 A B) A) & (v12_waybel_0 (k4_abcmiz_0 A B) A)) ) ) ).
tt(fc6_abcmiz_1,ax, (~ (v1_xboole_0 k17_abcmiz_1)) ).
tt(fc6_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))))) )  => (v1_relat_1 (k10_xtuple_0 C))) ) ).
tt(fc6_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  & (v1_int_1 B))  => (v1_abian (k3_xcmplx_0 A B))) ) ).
tt(fc6_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k1_ordinal4 B C)) &  ((v5_relat_1 (k1_ordinal4 B C) A) &  ((v5_ordinal1 (k1_ordinal4 B C)) & (v1_funct_1 (k1_ordinal4 B C))) ) ) ) ) ).
tt(fc6_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_tdgroup A)))  &  ((v1_analoaf (k2_tdgroup A)) & (v2_tdgroup (k2_tdgroup A))) ) ) ) ).
tt(fc6_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ( (~ (v2_struct_0 (g2_algstr_0 A B C)))  & (v8_algstr_0 (g2_algstr_0 A B C))) ) ) ).
tt(fc6_algstr_1,ax, ( (~ (v2_struct_0 k3_algstr_1))  & (v29_algstr_0 k3_algstr_1)) ).
tt(fc6_algstr_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k5_algstr_4 A B)) &  ((v1_funct_2 (k5_algstr_4 A B) (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A B))) & (v2_funct_2 (k5_algstr_4 A B) (u1_struct_0 (k4_algstr_4 A B)))) ) ) ) ).
tt(fc6_altcat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) ) )  =>  ((v1_relat_1 (k8_pboole B C)) &  ((v1_funct_1 (k8_pboole B C)) & (v1_partfun1 (k8_pboole B C) A)) ) ) ) ).
tt(fc6_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_altcat_4 A)))  &  ((v2_altcat_1 (k3_altcat_4 A)) &  ((v6_altcat_1 (k3_altcat_4 A)) & (v3_altcat_2 (k3_altcat_4 A) A)) ) ) ) ) ).
tt(fc6_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v4_amistd_1 (k6_ami_3 A B) 2 k1_ami_3)) ) ).
tt(fc6_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v3_amistd_1 (k4_amistd_1 A) A)) ) ) ).
tt(fc6_amistd_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  ((v1_relat_1 (k4_compos_1 B)) &  ((v4_relat_1 (k4_compos_1 B) k5_numbers) &  ((v5_relat_1 (k4_compos_1 B) (u1_compos_1 B)) &  ((v1_funct_1 (k4_compos_1 B)) &  ((v1_finset_1 (k4_compos_1 B)) & (v5_amistd_1 (k4_compos_1 B) A B)) ) ) ) ) ) ) ).
tt(fc6_aofa_000,ax, (! [A:$i,B:$i] : (v1_freealg (k2_zfmisc_1 A B))) ).
tt(fc6_armstrng,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  => (v1_finset_1 (k9_armstrng A B))) ) ).
tt(fc6_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k4_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k4_bagorder A)) &  ((v4_relat_2 (k4_bagorder A)) &  ((v8_relat_2 (k4_bagorder A)) & (v2_bagorder (k4_bagorder A) A)) ) ) ) ) ) ).
tt(fc6_binop_2,ax, ((v1_funct_1 k41_binop_2) &  ((v1_funct_2 k41_binop_2 (k2_zfmisc_1 k3_numbers k3_numbers) k3_numbers) &  ((v1_binop_1 k41_binop_2 k3_numbers) & (v2_binop_1 k41_binop_2 k3_numbers)) ) ) ).
tt(fc6_bor_cant,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) )  =>  ((v5_relat_1 (k9_bor_cant A C) B) &  ((v1_funct_1 (k9_bor_cant A C)) & (v1_funct_2 (k9_bor_cant A C) k5_numbers (k9_setfam_1 A))) ) ) ) ).
tt(fc6_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) )  => (v1_tops_2 (k7_borsuk_1 A B C) (k2_borsuk_1 A B))) ) ).
tt(fc6_borsuk_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v7_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v7_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(fc6_borsuk_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v1_rat_1 A)) )  =>  ((v1_xcmplx_0 (k4_xcmplx_0 A)) &  (~ (v1_rat_1 (k4_xcmplx_0 A))) ) ) ) ).
tt(fc6_borsuk_6,ax, ((v1_funct_1 k4_borsuk_6) &  ((v1_funct_2 k4_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (v5_pre_topc k4_borsuk_6 k5_topmetr k5_topmetr)) ) ).
tt(fc6_borsuk_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  & (m1_subset_1 B k1_numbers))  =>  ((v1_funct_1 (k10_borsuk_7 A B)) &  ((v1_funct_2 (k10_borsuk_7 A B) (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A)) (u1_struct_0 (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A))) & (v3_tops_2 (k10_borsuk_7 A B) (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A) (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A))) ) ) ) ).
tt(fc6_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v13_algstr_0 (k11_c0sp1 A)) &  ((v2_rlvect_1 (k11_c0sp1 A)) &  ((v3_rlvect_1 (k11_c0sp1 A)) &  ((v4_rlvect_1 (k11_c0sp1 A)) &  ((v5_rlvect_1 (k11_c0sp1 A)) &  ((v6_rlvect_1 (k11_c0sp1 A)) &  ((v7_rlvect_1 (k11_c0sp1 A)) &  ((v8_rlvect_1 (k11_c0sp1 A)) &  ((v3_normsp_0 (k11_c0sp1 A)) &  ((v4_normsp_0 (k11_c0sp1 A)) & (v2_normsp_1 (k11_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 (k5_c0sp2 A)))  & (v1_lopban_2 (k5_c0sp2 A))) ) ) ).
tt(fc6_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_finset_1 (k1_card_1 A)) & (v1_card_1 (k1_card_1 A))) ) ) ).
tt(fc6_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (~ (v1_xboole_0 (k8_card_3 A)))  & (v4_funct_1 (k8_card_3 A))) ) ) ).
tt(fc6_card_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  &  ( (~ (v1_finset_1 B))  & (v1_card_1 B)) )  =>  ( (~ (v1_finset_1 (k3_card_2 A B)))  & (v1_card_1 (k3_card_2 A B))) ) ) ).
tt(fc6_cardfin2,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k4_cardfin2 A B))) ) ).
tt(fc6_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_catalg_1 A) & (l1_msualg_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc6_cayley,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v8_struct_0 (k2_cayley A)) &  ((v15_algstr_0 (k2_cayley A)) & (v1_monoid_0 (k2_cayley A))) ) ) ) ).
tt(fc6_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v13_algstr_0 (k7_cc0sp1 A)) &  ((v2_rlvect_1 (k7_cc0sp1 A)) &  ((v3_rlvect_1 (k7_cc0sp1 A)) &  ((v4_rlvect_1 (k7_cc0sp1 A)) &  ((v3_normsp_0 (k7_cc0sp1 A)) &  ((v4_normsp_0 (k7_cc0sp1 A)) &  ((v2_clvect_1 (k7_cc0sp1 A)) &  ((v3_clvect_1 (k7_cc0sp1 A)) &  ((v4_clvect_1 (k7_cc0sp1 A)) &  ((v5_clvect_1 (k7_cc0sp1 A)) & (v8_clvect_1 (k7_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 (k5_cc0sp2 A)))  & (v1_clopban2 (k5_cc0sp2 A))) ) ) ).
tt(fc6_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v2_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v2_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) &  ((v1_partfun1 (k1_valued_1 A B) k2_numbers) & (v2_cfdiff_1 (k1_valued_1 A B))) ) ) ) ).
tt(fc6_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v13_algstr_0 (k8_cfuncdom A)) &  ((v2_rlvect_1 (k8_cfuncdom A)) &  ((v3_rlvect_1 (k8_cfuncdom A)) &  ((v4_rlvect_1 (k8_cfuncdom A)) &  ((v2_clvect_1 (k8_cfuncdom A)) &  ((v3_clvect_1 (k8_cfuncdom A)) &  ((v4_clvect_1 (k8_cfuncdom A)) &  ((v3_group_1 (k8_cfuncdom A)) &  ((v5_group_1 (k8_cfuncdom A)) &  ((v1_vectsp_1 (k8_cfuncdom A)) &  ((v3_vectsp_1 (k8_cfuncdom A)) &  ((v1_cfuncdom (k8_cfuncdom A)) & (v2_cfuncdom (k8_cfuncdom A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (v3_cgames_1 (k5_finseq_1 A))) ) ).
tt(fc6_circcmb3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_circcmb3 B A) & (m1_circcmb3 C A)) )  =>  ( (~ (v2_struct_0 (k2_circcomb B C)))  &  ((v1_msualg_1 (k2_circcomb B C)) & (v5_circcomb (k2_circcomb B C))) ) ) ) ).
tt(fc6_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  =>  ( (~ (v2_struct_0 (k2_circcomb A B)))  &  ( (~ (v11_struct_0 (k2_circcomb A B)))  & (v1_msualg_1 (k2_circcomb A B))) ) ) ) ).
tt(fc6_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  &  ((v4_msualg_1 D A) & (l3_msualg_1 D A)) ) ) )  =>  ((v1_relat_1 (k4_circtrm1 A B C D)) &  ((v2_relat_1 (k4_circtrm1 A B C D)) &  ((v4_relat_1 (k4_circtrm1 A B C D) (u1_struct_0 (k1_circtrm1 A B C))) &  ((v1_funct_1 (k4_circtrm1 A B C D)) & (v1_partfun1 (k4_circtrm1 A B C D) (u1_struct_0 (k1_circtrm1 A B C)))) ) ) ) ) ) ).
tt(fc6_classes2,ax, (! [A:$i] :  ((v1_ordinal1 A) => (v1_ordinal1 (k1_classes1 A))) ) ).
tt(fc6_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_clopban1 A B)))  &  ((v13_algstr_0 (k6_clopban1 A B)) &  ((v2_rlvect_1 (k6_clopban1 A B)) &  ((v3_rlvect_1 (k6_clopban1 A B)) &  ((v4_rlvect_1 (k6_clopban1 A B)) &  ((v1_monoid_0 (k6_clopban1 A B)) &  ((v2_clvect_1 (k6_clopban1 A B)) &  ((v3_clvect_1 (k6_clopban1 A B)) &  ((v4_clvect_1 (k6_clopban1 A B)) & (v5_clvect_1 (k6_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k8_clopban2 A)) &  ((v2_rlvect_1 (k8_clopban2 A)) &  ((v3_rlvect_1 (k8_clopban2 A)) &  ((v4_rlvect_1 (k8_clopban2 A)) &  ((v2_clvect_1 (k8_clopban2 A)) &  ((v3_clvect_1 (k8_clopban2 A)) &  ((v4_clvect_1 (k8_clopban2 A)) &  ((v3_group_1 (k8_clopban2 A)) &  ((v1_vectsp_1 (k8_clopban2 A)) &  ((v3_vectsp_1 (k8_clopban2 A)) & (v2_cfuncdom (k8_clopban2 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_clopban3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v2_clopban3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_series_1 (k4_normsp_0 A B))) &  ((v1_funct_2 (k2_series_1 (k4_normsp_0 A B)) k5_numbers k1_numbers) & (v1_seq_2 (k2_series_1 (k4_normsp_0 A B)))) ) ) ) ).
tt(fc6_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v8_closure1 B A) & (l1_closure1 B A)) )  => (v3_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc6_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_cohsp_1 A)) )  => (v3_cohsp_1 (k9_xtuple_0 A))) ) ).
tt(fc6_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_pre_topc (k1_compact1 A)) & (v1_compts_1 (k1_compact1 A))) ) ) ).
tt(fc6_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  => (v1_finseq_1 (k5_xtuple_0 B))) ) ).
tt(fc6_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  & (v7_ordinal1 C)) )  =>  ( (~ (v1_xboole_0 (k5_compos_1 A B C)))  &  ((v1_relat_1 (k5_compos_1 A B C)) &  ((v4_relat_1 (k5_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k5_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k5_compos_1 A B C)) & (v1_finset_1 (k5_compos_1 A B C))) ) ) ) ) ) ) ).
tt(fc6_comput_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ( (~ (v1_xboole_0 (k5_comput_1 A B)))  &  ((v1_relat_1 (k5_comput_1 A B)) &  ((v4_relat_1 (k5_comput_1 A B) (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 (k5_comput_1 A B)) &  ((v4_valued_0 (k5_comput_1 A B)) &  ((v2_margrel1 (k5_comput_1 A B)) & (v2_comput_1 (k5_comput_1 A B))) ) ) ) ) ) ) ) ).
tt(fc6_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k30_valued_1 A)) &  ((v1_funct_2 (k30_valued_1 A) k5_numbers k2_numbers) & (v2_comseq_2 (k30_valued_1 A))) ) ) ) ).
tt(fc6_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k2_series_1 A)) &  ((v1_funct_2 (k2_series_1 A) k5_numbers k2_numbers) & (v2_comseq_2 (k2_series_1 A))) ) ) ) ).
tt(fc6_convfun1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) )  =>  ((v5_rlvect_1 (k3_convfun1 A B)) &  ((v6_rlvect_1 (k3_convfun1 A B)) &  ((v7_rlvect_1 (k3_convfun1 A B)) & (v8_rlvect_1 (k3_convfun1 A B))) ) ) ) ) ).
tt(fc6_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k4_csspace4 A B))) ) ) ).
tt(fc6_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_yellow_1 k1_xboole_0 A)))  & (v1_orders_2 (k5_yellow_1 k1_xboole_0 A))) ) ) ).
tt(fc6_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (~ (v1_xboole_0 (k5_dilworth A))) ) ) ).
tt(fc6_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  => (v3_funct_1 (k11_dist_1 A))) ) ).
tt(fc6_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) )  =>  ((v1_relat_1 (k35_valued_1 B)) &  ((v1_funct_1 (k35_valued_1 B)) &  ((v1_valued_0 (k35_valued_1 B)) & (v3_card_1 (k35_valued_1 B) A)) ) ) ) ) ).
tt(fc6_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_pre_topc (k15_euclid A)) &  ((v13_algstr_0 (k15_euclid A)) &  ((v2_rlvect_1 (k15_euclid A)) &  ((v3_rlvect_1 (k15_euclid A)) &  ((v4_rlvect_1 (k15_euclid A)) &  ((v5_rlvect_1 (k15_euclid A)) &  ((v6_rlvect_1 (k15_euclid A)) &  ((v7_rlvect_1 (k15_euclid A)) &  ((v8_rlvect_1 (k15_euclid A)) & (v5_rltopsp1 (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_exchsort,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k1_tarski (k4_tarski A B))) &  ((v1_funct_1 (k1_tarski (k4_tarski A B))) &  ((v1_exchsort (k1_tarski (k4_tarski A B))) &  ((v2_exchsort (k1_tarski (k4_tarski A B)) A) & (v3_exchsort (k1_tarski (k4_tarski A B)) (k1_ordinal1 A))) ) ) ) ) ) ).
tt(fc6_facirc_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_facirc_1 A))  =>  (~ (v1_facirc_1 (k3_xboole_0 A B))) ) ) ).
tt(fc6_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k24_valued_1 A B)) & (v1_fcont_1 (k24_valued_1 A B))) ) ) ).
tt(fc6_fcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v3_rcomp_1 (k10_prob_1 A))) ) ).
tt(fc6_fib_num2,ax, (! [A:$i,B:$i] :  ((v1_setfam_1 A) => (v1_setfam_1 (k3_xboole_0 A B))) ) ).
tt(fc6_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v21_lattices B (k1_lattice2 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) )  => (v20_lattices (k4_filter_2 A B) A)) ) ).
tt(fc6_finseq_1,ax, (! [A:$i] :  ((v1_relat_1 (k5_finseq_1 A)) & (v1_funct_1 (k5_finseq_1 A))) ) ).
tt(fc6_finseq_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((v1_relat_1 (k6_finseq_2 A B)) &  ((v2_relat_1 (k6_finseq_2 A B)) &  ((v4_relat_1 (k6_finseq_2 A B) (k3_finseq_2 A)) &  ((v1_funct_1 (k6_finseq_2 A B)) & (v1_partfun1 (k6_finseq_2 A B) (k3_finseq_2 A))) ) ) ) ) ) ).
tt(fc6_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] : (v3_card_1 (k8_finseq_4 A B C D E) 5)) ).
tt(fc6_finseq_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_finseq_1 C A)) )  =>  (~ (v1_xboole_0 (k2_finseq_5 A C B))) ) ) ).
tt(fc6_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] : (v1_finset_1 (k4_enumset1 A B C D E F))) ).
tt(fc6_fomodel0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  => (v1_setfam_1 (k4_finseq_2 B A))) ) ).
tt(fc6_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k5_fomodel1 A))) ) ) ).
tt(fc6_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v5_relat_1 C B) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 C D)) &  ((v1_funct_1 (k3_relat_1 C D)) &  ((v3_card_1 (k3_relat_1 C D) (k3_finseq_1 C)) & (v1_finseq_1 (k3_relat_1 C D))) ) ) ) ) ).
tt(fc6_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_relat_1 (k5_fomodel3 A B)) &  ((v1_funct_1 (k5_fomodel3 A B)) & (v1_funcop_1 (k5_fomodel3 A B))) ) ) ) ).
tt(fc6_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel2 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k33_fomodel2 A))))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k33_fomodel2 A)))) ) ) )  => (v1_fomodel4 (k4_tarski (k4_subset_1 (k33_fomodel2 A) C D) B) A)) ) ).
tt(fc6_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v7_fsm_1 C A B) & (l2_fsm_1 C A B)) ) ) ) )  =>  ((v2_fsm_1 (k11_fsm_1 A B C) A B) & (v7_fsm_1 (k11_fsm_1 A B C) A B)) ) ) ).
tt(fc6_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l1_fsm_3 C A B)) ) ) )  =>  ((v8_struct_0 (k2_fsm_3 A B C)) & (v1_fsm_3 (k2_fsm_3 A B C) A (k9_flang_1 A))) ) ) ).
tt(fc6_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k4_funcop_1 A B C)) & (v1_funct_1 (k4_funcop_1 A B C))) ) ) ).
tt(fc6_funcsdom,ax, (! [A:$i] :  ((v13_algstr_0 (k12_funcsdom A)) &  ((v3_group_1 (k12_funcsdom A)) &  ((v5_group_1 (k12_funcsdom A)) &  ((v1_vectsp_1 (k12_funcsdom A)) &  ((v3_vectsp_1 (k12_funcsdom A)) &  ((v2_rlvect_1 (k12_funcsdom A)) &  ((v3_rlvect_1 (k12_funcsdom A)) &  ((v4_rlvect_1 (k12_funcsdom A)) &  ((v5_rlvect_1 (k12_funcsdom A)) &  ((v6_rlvect_1 (k12_funcsdom A)) &  ((v7_rlvect_1 (k12_funcsdom A)) &  ((v1_funcsdom (k12_funcsdom A)) & (v2_funcsdom (k12_funcsdom A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  ((v1_relat_1 (k2_funct_1 A)) &  ((v1_funct_1 (k2_funct_1 A)) & (v2_funct_1 (k2_funct_1 A))) ) ) ) ).
tt(fc6_funct_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v2_funct_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ((v1_funct_1 C) &  ((v2_funct_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v1_funct_1 (k3_relat_1 C B)) & (v2_funct_2 (k3_relat_1 C B) A)) ) ) ).
tt(fc6_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v1_funcop_1 (k1_funct_4 A B))) ) ) ) ).
tt(fc6_funct_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v1_funcop_1 (k2_finseq_2 A B)) & (v1_finseq_1 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc6_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (k1_altcat_1 B C C))) ) )  =>  ((v8_functor0 (k9_functor0 A B C D) A B) &  ((v9_functor0 (k9_functor0 A B C D) A B) &  ((v10_functor0 (k9_functor0 A B C D) A B) & (v11_functor0 (k9_functor0 A B C D) A B)) ) ) ) ) ).
tt(fc6_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k3_gate_1 A B))) ) ).
tt(fc6_glib_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((v1_finset_1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_relat_1 (k12_glib_000 A B C D)) &  ((v4_relat_1 (k12_glib_000 A B C D) k5_numbers) &  ((v1_funct_1 (k12_glib_000 A B C D)) &  ((v1_finset_1 (k12_glib_000 A B C D)) &  ((v1_glib_000 (k12_glib_000 A B C D)) & (v2_glib_000 (k12_glib_000 A B C D))) ) ) ) ) ) ) ).
tt(fc6_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v3_glib_001 B A) & (m3_glib_001 B A)) )  => (v3_glib_001 (k6_glib_001 A B) A)) ) ).
tt(fc6_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))))  => (v1_finset_1 (k1_xtuple_0 B))) ) ).
tt(fc6_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xboole_0 C)) )  => (v1_xboole_0 (k3_graph_3 A B C))) ) ).
tt(fc6_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v6_membered (k6_card_1 A))) ) ).
tt(fc6_group_12,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  & (m1_subset_1 C A)) )  =>  ((v15_algstr_0 (k2_group_12 A B C)) & (v1_group_3 (k2_group_12 A B C) (k2_group_7 A B))) ) ) ).
tt(fc6_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ((v2_group_1 (k5_group_6 A B)) & (v3_group_1 (k5_group_6 A B))) ) ) ).
tt(fc6_group_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k3_group_7 A B))) & (m1_subset_1 D (u1_struct_0 (k3_group_7 A B)))) )  =>  ((v1_relat_1 (k1_binop_1 (u2_algstr_0 (k3_group_7 A B)) C D)) & (v1_funct_1 (k1_binop_1 (u2_algstr_0 (k3_group_7 A B)) C D))) ) ) ).
tt(fc6_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((v2_group_9 (k13_group_9 A B C D) A) & (v4_group_9 (k13_group_9 A B C D) A B)) ) ) ).
tt(fc6_groupp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_10 B A) & (l3_algstr_0 B)) ) ) ) )  &  ((v1_group_3 C B) & (m1_group_2 C B)) ) )  => (v2_group_10 (k5_group_6 B C) A)) ) ).
tt(fc6_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k1_hermitan A B)) &  ((v1_funct_2 (k1_hermitan A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v13_vectsp_1 (k1_hermitan A B) A k1_complfld)) ) ) ) ).
tt(fc6_heyting3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  (~ (v1_xboole_0 (k2_heyting3 A B))) ) ) ).
tt(fc6_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v6_ideal_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v6_ideal_1 (k14_polynom3 A))) ) ) ) ).
tt(fc6_hilbert3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  & (m1_subset_1 B k1_hilbert1))  =>  (~ (v1_xboole_0 (k3_hilbert3 A B))) ) ) ).
tt(fc6_index_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) ) )  =>  ((v1_relat_1 (k3_index_1 B)) &  ((v2_relat_1 (k3_index_1 B)) &  ((v1_funct_1 (k3_index_1 B)) & (v1_partfun1 (k3_index_1 B) A)) ) ) ) ) ).
tt(fc6_int_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v2_struct_0 (k9_int_3 A)))  & (v36_algstr_0 (k9_int_3 A))) ) ) ).
tt(fc6_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_xcmplx_0 (k16_rvsum_1 A)) & (v1_int_1 (k16_rvsum_1 A))) ) ) ).
tt(fc6_intpro_1,ax,(v9_intpro_1 k12_intpro_1)).
tt(fc6_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v5_tops_1 (k2_pre_topc A (k1_tops_1 A B)) A)) ) ).
tt(fc6_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k6_topreal1 A) (k15_euclid 2))) ) ).
tt(fc6_jordan1e,ax, (! [A:$i,B:$i] :  ( ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  & (m1_subset_1 B k5_numbers))  => (v4_topreal1 (k2_jordan1e A B))) ) ).
tt(fc6_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_jordan23 A)) ) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) &  ((v1_finseq_1 (k3_finseq_5 A)) & (v3_jordan23 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc6_jordan2c,ax, (! [A:$i] :  ( ((v4_pre_topc A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v3_pre_topc (k1_jordan2c 2 A) (k15_euclid 2))) ) ).
tt(fc6_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k10_pscomp_1 A)))) ) ).
tt(fc6_kurato_1,ax,(v3_setfam_1 (k4_kurato_1 k3_topmetr k6_kurato_1) (u1_struct_0 k3_topmetr))).
tt(fc6_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  =>  ((v1_funct_1 (u1_lattices A)) &  ((v1_funct_2 (u1_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_binop_1 (u1_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc6_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k7_lattice3 A)))  & (v1_orders_2 (k7_lattice3 A))) ) ) ).
tt(fc6_lattice5,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) )  =>  (~ (v1_xboole_0 (k13_lattice5 A B C))) ) ) ).
tt(fc6_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v4_lexbfs (k15_lexbfs A (k16_lexbfs A)) A)) ) ).
tt(fc6_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_lopban_1 A B)))  &  ((v13_algstr_0 (k8_lopban_1 A B)) &  ((v2_rlvect_1 (k8_lopban_1 A B)) &  ((v3_rlvect_1 (k8_lopban_1 A B)) &  ((v4_rlvect_1 (k8_lopban_1 A B)) &  ((v5_rlvect_1 (k8_lopban_1 A B)) &  ((v6_rlvect_1 (k8_lopban_1 A B)) &  ((v7_rlvect_1 (k8_lopban_1 A B)) &  ((v8_rlvect_1 (k8_lopban_1 A B)) & (v1_monoid_0 (k8_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (k8_lopban_2 A)) &  ((v2_rlvect_1 (k8_lopban_2 A)) &  ((v3_rlvect_1 (k8_lopban_2 A)) &  ((v4_rlvect_1 (k8_lopban_2 A)) &  ((v5_rlvect_1 (k8_lopban_2 A)) &  ((v6_rlvect_1 (k8_lopban_2 A)) &  ((v7_rlvect_1 (k8_lopban_2 A)) &  ((v1_funcsdom (k8_lopban_2 A)) &  ((v2_funcsdom (k8_lopban_2 A)) &  ((v3_group_1 (k8_lopban_2 A)) &  ((v1_vectsp_1 (k8_lopban_2 A)) & (v3_vectsp_1 (k8_lopban_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_lopban_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v2_lopban_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_series_1 (k4_normsp_0 A B))) &  ((v1_funct_2 (k2_series_1 (k4_normsp_0 A B)) k5_numbers k1_numbers) & (v1_seq_2 (k2_series_1 (k4_normsp_0 A B)))) ) ) ) ).
tt(fc6_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((v1_relat_1 (k8_lopclset A)) &  ((v1_funct_1 (k8_lopclset A)) & (v2_funct_1 (k8_lopclset A))) ) ) ) ).
tt(fc6_lpspace1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k20_lpspace1 A B C)))  &  ((v13_algstr_0 (k20_lpspace1 A B C)) &  ((v2_rlvect_1 (k20_lpspace1 A B C)) &  ((v3_rlvect_1 (k20_lpspace1 A B C)) &  ((v4_rlvect_1 (k20_lpspace1 A B C)) &  ((v5_rlvect_1 (k20_lpspace1 A B C)) &  ((v6_rlvect_1 (k20_lpspace1 A B C)) &  ((v7_rlvect_1 (k20_lpspace1 A B C)) &  ((v8_rlvect_1 (k20_lpspace1 A B C)) & (v2_normsp_1 (k20_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ( (~ (v2_struct_0 (k10_lpspace2 A B C D)))  & (v1_rlvect_1 (k10_lpspace2 A B C D))) ) ) ).
tt(fc6_lukasi_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B (k8_cqc_lang A B C)) (k8_cqc_lang A B C)) A)) ) ).
tt(fc6_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) )  => (v3_finseq_1 (k9_xtuple_0 B))) ) ).
tt(fc6_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  ((v1_funct_1 (k5_matrix11 A)) &  ((v1_funct_2 (k5_matrix11 A) (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A))) (k3_finseq_2 (u1_struct_0 A))) & (v2_binop_1 (k5_matrix11 A) (k3_finseq_2 (u1_struct_0 A)))) ) ) ) ).
tt(fc6_matroid0,ax, (! [A:$i] :  ((v1_pre_topc (k2_matroid0 A)) &  ( (~ (v3_pencil_1 (k2_matroid0 A)))  & (v1_matroid0 (k2_matroid0 A))) ) ) ).
tt(fc6_matrtop1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((v1_relat_1 (k1_finseq_3 A B)) &  ((v1_funct_1 (k1_finseq_3 A B)) &  ((v1_finseq_1 (k1_finseq_3 A B)) & (v1_valued_0 (k1_finseq_3 A B))) ) ) ) ) ).
tt(fc6_matrtop3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v3_matrtop3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v3_matrtop3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 C B)) &  ((v1_funct_2 (k3_relat_1 C B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_matrtop3 (k3_relat_1 C B) A)) ) ) ) ).
tt(fc6_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (v2_rcomp_1 (k6_measure6 A))) ) ).
tt(fc6_member_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  =>  ( (~ (v1_xboole_0 (k5_member_1 A)))  & (v1_membered (k5_member_1 A))) ) ) ).
tt(fc6_membered,ax,(v6_membered k4_ordinal1)).
tt(fc6_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (k4_memstr_0 A B C))) ) )  => (v5_funct_1 (k16_funcop_1 C D) (k2_memstr_0 A B))) ) ).
tt(fc6_mesfunc7,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (v2_valued_0 (k5_finseq_1 A))) ) ).
tt(fc6_metric_1,ax, ((v1_metric_1 k8_metric_1) &  ((v6_metric_1 k8_metric_1) &  ((v7_metric_1 k8_metric_1) &  ((v8_metric_1 k8_metric_1) & (v9_metric_1 k8_metric_1)) ) ) ) ).
tt(fc6_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v5_waybel23 A) & (l1_pre_topc A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v5_waybel23 (k1_pre_topc A B))) ) ) ).
tt(fc6_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_pre_topc (k4_mfold_2 A)) & (v2_mfold_1 (k4_mfold_2 A) A)) ) ) ).
tt(fc6_mmlquery,ax, (! [A:$i,B:$i] :  ( ( ((v3_mmlquery A) & (l1_mmlquery A))  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k30_mmlquery A B))) ) ).
tt(fc6_mod_2,ax, ((v13_algstr_0 k18_mod_2) &  ((v36_algstr_0 k18_mod_2) &  ((v3_rlvect_1 k18_mod_2) & (v4_rlvect_1 k18_mod_2)) ) ) ).
tt(fc6_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v3_rlvect_1 (k2_mod_4 A))) ) ) ).
tt(fc6_modelc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_1 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_1 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_1 (k11_modelc_1 A B))) ) ).
tt(fc6_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_2 (k7_modelc_2 A B))) ) ).
tt(fc6_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_relat_1 (k5_moebius1 A)) &  ((v4_relat_1 (k5_moebius1 A) k10_newton) &  ((v1_funct_1 (k5_moebius1 A)) &  ((v1_partfun1 (k5_moebius1 A) k10_newton) &  ((v4_valued_0 (k5_moebius1 A)) & (v2_pre_poly (k5_moebius1 A))) ) ) ) ) ) ) ).
tt(fc6_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_dtconstr (k5_msafree A B)) &  ((v2_dtconstr (k5_msafree A B)) & (v3_dtconstr (k5_msafree A B))) ) ) ) ).
tt(fc6_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v2_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k2_pboole A B C)) &  ((v4_relat_1 (k2_pboole A B C) A) &  ((v1_funct_1 (k2_pboole A B C)) &  ((v1_partfun1 (k2_pboole A B C) A) & (v2_finset_1 (k2_pboole A B C))) ) ) ) ) ) ).
tt(fc6_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v3_msualg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A) & (v4_msualg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A)) ) ) ).
tt(fc6_msualg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  &  ((v3_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) )  =>  ((v2_msualg_4 (k9_msualg_6 A B C) A B) & (v3_msualg_6 (k9_msualg_6 A B C) A B)) ) ) ).
tt(fc6_mycielsk,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_orders_2 A))  =>  ((v1_xboole_0 (k3_mycielsk A)) & (v7_ordinal1 (k3_mycielsk A))) ) ) ).
tt(fc6_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v7_ordinal1 (k4_xxreal_0 A B))) ) ).
tt(fc6_nat_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  => (v1_xboole_0 (k13_pre_poly (k4_nat_3 A B k6_numbers)))) ) ).
tt(fc6_nat_lat,ax, ( (~ (v2_struct_0 k10_nat_lat))  & (v3_lattices k10_nat_lat)) ).
tt(fc6_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ((v8_struct_0 A) & (l1_orders_2 A))  &  ((v8_struct_0 B) & (l1_orders_2 B)) )  =>  ((v8_struct_0 (k2_neckla_2 A B)) & (v1_orders_2 (k2_neckla_2 A B))) ) ) ).
tt(fc6_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_orders_2 (k4_necklace A)) & (v3_necklace (k4_necklace A))) ) ) ).
tt(fc6_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_xreal_0 (k3_newton A))) ) ).
tt(fc6_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v2_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k5_relat_1 B C)) & (v2_nfcont_3 (k5_relat_1 B C) A)) ) ) ).
tt(fc6_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) &  ((v2_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  &  ((v1_funct_1 C) &  ((v2_nfcont_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) ) )  =>  ((v1_funct_1 (k7_integr15 A k1_numbers B C)) & (v2_nfcont_4 (k7_integr15 A k1_numbers B C) A)) ) ) ).
tt(fc6_normform,ax, (! [A:$i] :  ((v3_lattices (k12_normform A)) &  ((v11_lattices (k12_normform A)) & (v13_lattices (k12_normform A))) ) ) ).
tt(fc6_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v3_frechet (k4_normsp_2 A)) & (v5_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(fc6_numbers,ax, (~ (v1_finset_1 k4_numbers)) ).
tt(fc6_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((v1_relat_1 (k8_openlatt A)) &  ((v1_funct_1 (k8_openlatt A)) & (v2_funct_1 (k8_openlatt A))) ) ) ) ).
tt(fc6_oposet_1,ax, ((v3_necklace k2_oposet_1) & (v3_qmax_1 k2_oposet_1)) ).
tt(fc6_orders_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_orders_2 (g1_orders_2 A B)) & (v3_orders_2 (g1_orders_2 A B))) ) ) ).
tt(fc6_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  ( (~ (v2_struct_0 (k4_orders_3 A)))  &  ((v2_altcat_1 (k4_orders_3 A)) & (v6_altcat_1 (k4_orders_3 A))) ) ) ) ).
tt(fc6_ordinal1,ax, ( (~ (v1_xboole_0 k4_ordinal1))  & (v3_ordinal1 k4_ordinal1)) ).
tt(fc6_ordinal5,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v3_ordinal1 (k12_ordinal2 A B)) & (v7_ordinal1 (k12_ordinal2 A B))) ) ) ).
tt(fc6_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k4_relat_1 A)) &  ((v1_funct_1 (k4_relat_1 A)) &  ((v5_ordinal1 (k4_relat_1 A)) &  ((v1_ordinal2 (k4_relat_1 A)) & (v2_ordinal2 (k4_relat_1 A))) ) ) ) ) ) ).
tt(fc6_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  (~ (v1_xboole_0 (k3_msualg_1 A C (k8_osafree A B)))) ) ) ).
tt(fc6_osalg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  &  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) ) ) )  =>  ((v3_msualg_1 (k11_msualg_2 A B C D) A) & (v12_osalg_1 (k11_msualg_2 A B C D) A)) ) ) ).
tt(fc6_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  => (v1_xboole_0 (k8_relat_1 A (k1_tarski k6_numbers)))) ) ).
tt(fc6_partfun4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  =>  ((v1_funct_1 (k1_partfun3 B)) &  ((v1_funct_2 (k1_partfun3 B) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k1_partfun3 B) A)) ) ) ) ).
tt(fc6_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_partfun1 D B) &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  => (v1_relat_2 (k3_pcs_0 A A B B C D))) ) ).
tt(fc6_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((v1_xcmplx_0 C) &  ((v1_xcmplx_0 D) & (v1_xcmplx_0 E)) ) ) )  => (v1_xcmplx_0 (k7_polyeq_1 A B C D E))) ) ).
tt(fc6_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((v1_funct_1 (k9_polynom1 A B C D)) &  ((v1_funct_2 (k9_polynom1 A B C D) (k15_pre_poly A) (u1_struct_0 B)) & (v1_polynom1 (k9_polynom1 A B C D) (k15_pre_poly A) B)) ) ) ) ).
tt(fc6_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom2 A B C)) &  ((v1_funct_2 (k6_polynom2 A B C) (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (v1_group_6 (k6_polynom2 A B C) (k11_polynom1 A B) B)) ) ) ) ).
tt(fc6_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((v1_funct_1 (k9_polynom3 A)) &  ((v1_funct_2 (k9_polynom3 A) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k9_polynom3 A) A)) ) ) ) ).
tt(fc6_polynom5,ax, ((v36_algstr_0 k1_complfld) & (v2_polynom5 k1_complfld)) ).
tt(fc6_poset_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_poset_1 A B)))  &  ((v1_orders_2 (k6_poset_1 A B)) &  ((v3_orders_2 (k6_poset_1 A B)) &  ((v4_orders_2 (k6_poset_1 A B)) &  ((v5_orders_2 (k6_poset_1 A B)) & (v1_poset_1 (k6_poset_1 A B))) ) ) ) ) ) ) ).
tt(fc6_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  & (m1_pralg_2 C A B))  =>  ((v1_relat_1 (k10_pralg_2 A B C)) &  ((v2_relat_1 (k10_pralg_2 A B C)) &  ((v4_relat_1 (k10_pralg_2 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k10_pralg_2 A B C)) & (v1_partfun1 (k10_pralg_2 A B C) (u1_struct_0 B))) ) ) ) ) ) ).
tt(fc6_pre_circ,ax, (! [A:$i] :  ((v1_relat_1 (k1_trees_4 A)) &  ((v1_funct_1 (k1_trees_4 A)) &  ((v1_finset_1 (k1_trees_4 A)) & (v3_trees_2 (k1_trees_4 A))) ) ) ) ).
tt(fc6_pre_poly,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v1_finseq_1 (k2_finseq_2 A B)) & (v1_pre_poly (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc6_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (v2_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(fc6_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k14_pscomp_1 A)))  & (v2_compts_1 (k14_pscomp_1 A) (k15_euclid 2))) ) ) ).
tt(fc6_pythtrip,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) &  ( (~ (v1_abian A))  & (v1_pythtrip A)) )  &  ((v1_int_1 B) &  ( (~ (v1_abian B))  & (v1_pythtrip B)) ) )  =>  (~ (v1_pythtrip (k2_xcmplx_0 A B))) ) ) ).
tt(fc6_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k6_qc_lang1 A))) ) ) ).
tt(fc6_quatern2,ax, ( (~ (v6_struct_0 k16_quatern2))  &  ((v13_algstr_0 k16_quatern2) &  ((v34_algstr_0 k16_quatern2) &  ((v36_algstr_0 k16_quatern2) &  ((v2_rlvect_1 k16_quatern2) &  ((v3_rlvect_1 k16_quatern2) &  ((v4_rlvect_1 k16_quatern2) &  ((v3_group_1 k16_quatern2) &  ((v3_vectsp_1 k16_quatern2) &  ((v5_vectsp_1 k16_quatern2) & (v6_vectsp_1 k16_quatern2)) ) ) ) ) ) ) ) ) ) ).
tt(fc6_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (v1_quaterni (k7_quaterni A B))) ) ).
tt(fc6_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v36_algstr_0 (k19_quofield A)) & (v5_group_1 (k19_quofield A))) ) ) ).
tt(fc6_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((v1_xcmplx_0 (k5_xcmplx_0 A)) & (v1_rat_1 (k5_xcmplx_0 A))) ) ) ).
tt(fc6_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v1_funct_1 (k10_polynom3 A)) &  ((v1_funct_2 (k10_polynom3 A) k5_numbers (u1_struct_0 A)) & (v2_ratfunc1 (k10_polynom3 A) A)) ) ) ) ).
tt(fc6_rcomp_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v5_xxreal_2 (k4_xxreal_1 A B))) ) ).
tt(fc6_real_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_xboole_0 (k7_xcmplx_0 A k6_numbers))) ) ).
tt(fc6_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ((v13_algstr_0 (k7_real_ns1 A)) &  ((v2_rlvect_1 (k7_real_ns1 A)) &  ((v3_rlvect_1 (k7_real_ns1 A)) &  ((v4_rlvect_1 (k7_real_ns1 A)) &  ((v5_rlvect_1 (k7_real_ns1 A)) &  ((v6_rlvect_1 (k7_real_ns1 A)) &  ((v7_rlvect_1 (k7_real_ns1 A)) &  ((v8_rlvect_1 (k7_real_ns1 A)) &  ((v1_bhsp_1 (k7_real_ns1 A)) & (v2_bhsp_1 (k7_real_ns1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc6_relat_1,ax, (! [A:$i,B:$i] : (v1_relat_1 (k2_zfmisc_1 A B))) ).
tt(fc6_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_relat_2 A))  &  ((v1_relat_1 B) & (v2_relat_2 B)) )  => (v2_relat_2 (k2_xboole_0 A B))) ) ).
tt(fc6_reloc,ax, ((v1_extpro_1 k1_ami_3 2) & (v2_amistd_5 k1_ami_3 2)) ).
tt(fc6_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) & (v5_relat_1 B A))  & (v1_relat_1 C))  => (v5_relat_1 (k4_xboole_0 B C) A)) ) ).
tt(fc6_revrot_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v2_goboard5 B) & (m1_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) )  => (v2_goboard5 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A))) ) ).
tt(fc6_rewrite2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_rewrite2 B)) ) ) )  =>  ((v1_relat_1 (k2_rewrite2 A B)) &  ((v1_funct_1 (k2_rewrite2 A B)) &  ((v1_finseq_1 (k2_rewrite2 A B)) & (v1_rewrite2 (k2_rewrite2 A B))) ) ) ) ) ).
tt(fc6_rfunct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_seq_2 A)) ) )  =>  ((v1_relat_1 (k5_relat_1 A B)) &  ((v1_funct_1 (k5_relat_1 A B)) &  ((v3_valued_0 (k5_relat_1 A B)) & (v1_seq_2 (k5_relat_1 A B))) ) ) ) ) ).
tt(fc6_ring_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) )  =>  ((v36_algstr_0 (k2_ring_1 A B)) & (v5_group_1 (k2_ring_1 A B))) ) ) ).
tt(fc6_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((v2_cat_1 (k17_ringcat1 A)) &  ((v3_cat_1 (k17_ringcat1 A)) &  ((v4_cat_1 (k17_ringcat1 A)) & (v5_cat_1 (k17_ringcat1 A))) ) ) ) ) ).
tt(fc6_rlaffin1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C k1_numbers)) )  => (v1_rlaffin1 (k1_convex1 A B C) A)) ) ).
tt(fc6_rlaffin3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  => (v4_pre_topc (k4_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc6_rltopsp1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k3_rltopsp1 A B)) &  ((v1_funct_2 (k3_rltopsp1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v3_tops_2 (k3_rltopsp1 A B) A A)) ) ) ) ).
tt(fc6_robbins4,ax, ((v10_lattices k2_robbins4) & (v4_robbins1 k2_robbins4)) ).
tt(fc6_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  => (v8_relat_2 (u1_orders_2 A))) ) ).
tt(fc6_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k4_rsspace4 A B))) ) ) ).
tt(fc6_rsspace,ax, ( (~ (v2_struct_0 k13_rsspace))  &  ((v13_algstr_0 k13_rsspace) &  ((v2_rlvect_1 k13_rsspace) &  ((v3_rlvect_1 k13_rsspace) &  ((v4_rlvect_1 k13_rsspace) &  ((v5_rlvect_1 k13_rsspace) &  ((v6_rlvect_1 k13_rsspace) &  ((v7_rlvect_1 k13_rsspace) & (v8_rlvect_1 k13_rsspace)) ) ) ) ) ) ) ) ).
tt(fc6_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v1_xreal_0 B))  =>  ((v1_relat_1 (k2_finseq_2 A B)) &  ((v1_funct_1 (k2_finseq_2 A B)) &  ((v3_valued_0 (k2_finseq_2 A B)) & (v1_finseq_1 (k2_finseq_2 A B))) ) ) ) ) ).
tt(fc6_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v4_amistd_1 (k10_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ).
tt(fc6_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v2_extpro_1 (k6_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc6_scmfsa_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v4_compos_0 (k14_scmfsa_2 B A C) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc6_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_scmfsa6c (k8_scmfsa_2 A B))) ) ).
tt(fc6_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmfsa_7 A B)) &  ((v4_relat_1 (k1_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_7 A B)) &  ((v1_finset_1 (k1_scmfsa_7 A B)) & (v1_scmfsa7b (k1_scmfsa_7 A B))) ) ) ) ) ) ) ).
tt(fc6_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa8b A B C D)))  &  ((v1_relat_1 (k4_scmfsa8b A B C D)) &  ((v4_relat_1 (k4_scmfsa8b A B C D) k5_numbers) &  ((v5_relat_1 (k4_scmfsa8b A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa8b A B C D)) &  ((v1_finset_1 (k4_scmfsa8b A B C D)) &  ((v1_afinsq_1 (k4_scmfsa8b A B C D)) &  (~ (v2_compos_1 (k4_scmfsa8b A B C D) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc6_scmfsa_i,ax, ( (~ (v1_xboole_0 k2_scmfsa_i))  & (v5_compos_0 k2_scmfsa_i)) ).
tt(fc6_scmfsa_m,ax, ((v1_ami_2 (k4_scmfsa_2 k6_numbers)) & (v1_scmfsa_m (k4_scmfsa_2 k6_numbers))) ).
tt(fc6_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) &  ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scm_halt B) & (v3_scm_halt B)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa6a B A)))  &  ((v1_relat_1 (k5_scmfsa6a B A)) &  ((v4_relat_1 (k5_scmfsa6a B A) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a B A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa6a B A)) &  ((v1_finset_1 (k5_scmfsa6a B A)) &  ((v1_afinsq_1 (k5_scmfsa6a B A)) &  ((v2_scm_halt (k5_scmfsa6a B A)) & (v3_scm_halt (k5_scmfsa6a B A))) ) ) ) ) ) ) ) ) ) ).
tt(fc6_scm_inst,ax, ( (~ (v1_xboole_0 k3_scm_inst))  & (v3_compos_0 k3_scm_inst)) ).
tt(fc6_scmpds_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v4_scmpds_4 (k14_scmpds_2 A B C D))) ) ).
tt(fc6_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v6_compos_0 (k9_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc6_scmpds_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 D)) ) )  =>  ( (~ (v1_xboole_0 (k2_scmpds_6 C D A B)))  &  ((v1_relat_1 (k2_scmpds_6 C D A B)) &  ((v4_relat_1 (k2_scmpds_6 C D A B) k5_numbers) &  ((v5_relat_1 (k2_scmpds_6 C D A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k2_scmpds_6 C D A B)) &  ((v1_finset_1 (k2_scmpds_6 C D A B)) &  ((v1_afinsq_1 (k2_scmpds_6 C D A B)) & (v2_compos_1 (k2_scmpds_6 C D A B) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc6_scmpds_i,ax,(v5_compos_0 k1_scmpds_i)).
tt(fc6_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_extpro_1 (k5_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc6_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v4_amistd_1 (k7_scmring2 A B C) 2 (k1_scmring2 A))) ) ).
tt(fc6_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_scmringi A)))  & (v3_compos_0 (k1_scmringi A))) ) ) ).
tt(fc6_scmyciel,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v3_scmyciel B A) & (v3_scmyciel C A)) )  => (v3_scmyciel (k2_xboole_0 B C) A)) ) ).
tt(fc6_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k54_valued_1 A)) &  ((v1_funct_2 (k54_valued_1 A) k5_numbers k1_numbers) & (v2_comseq_2 (k54_valued_1 A))) ) ) ) ).
tt(fc6_setfam_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) )  => (v1_setfam_1 (k3_enumset1 A B C D E))) ) ).
tt(fc6_sfmastr1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_sfmastr1 (k11_scmfsa_2 A))) ) ).
tt(fc6_simplex0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k1_simplex0 A)))  & (v1_classes1 (k1_simplex0 A))) ) ) ).
tt(fc6_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  =>  ( (~ (v3_pencil_1 (k4_simplex1 A B)))  &  ((v1_matroid0 (k4_simplex1 A B)) &  ((v3_matroid0 (k4_simplex1 A B)) & (v1_simplex1 (k4_simplex1 A B) A)) ) ) ) ) ).
tt(fc6_sincos10,ax, ((v1_funct_1 k2_sincos10) & (v2_funct_1 k2_sincos10)) ).
tt(fc6_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(fc6_sin_cos9,ax, ((v1_relat_1 (k5_relat_1 k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))))) ).
tt(fc6_sin_cos,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos k1_numbers k1_numbers) & (v1_fcont_1 k16_sin_cos)) ) ).
tt(fc6_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v3_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B (u1_struct_0 (k15_euclid 2))))  => (v3_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ).
tt(fc6_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((v1_finseq_6 (k1_sprect_1 A) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k1_sprect_1 A)) &  ((v2_topreal1 (k1_sprect_1 A)) &  ((v1_goboard5 (k1_sprect_1 A)) & (v2_goboard5 (k1_sprect_1 A))) ) ) ) ) ) ).
tt(fc6_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v4_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc6_struct_0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_zfmisc_1 (u1_struct_0 A))) ) ) ).
tt(fc6_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  (~ (v1_xboole_0 (k5_enumset1 A B C D E F G))) ) ).
tt(fc6_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  => (v5_substut1 (k20_substut1 A B) A)) ) ).
tt(fc6_tex_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  (~ (v2_struct_0 (k3_tex_1 A B))) ) ) ).
tt(fc6_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_subset_1 (k1_tops_1 A B) (u1_struct_0 A))) ) ).
tt(fc6_topalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_borsuk_2 D A B C)) ) )  =>  ((v1_funct_1 (k6_topalg_1 A B C D)) &  ((v1_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) & (v1_group_6 (k6_topalg_1 A B C D) (k5_topalg_1 A C) (k5_topalg_1 A B))) ) ) ) ).
tt(fc6_topalg_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) &  ((v5_pre_topc D (k2_borsuk_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((v1_funct_1 (k3_topalg_5 A B C D E)) &  ((v1_funct_2 (k3_topalg_5 A B C D E) (u1_struct_0 A) (u1_struct_0 C)) & (v5_pre_topc (k3_topalg_5 A B C D E) A C)) ) ) ) ).
tt(fc6_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ( (~ (v2_struct_0 (k3_mfold_2 A B C)))  & (v1_topalg_6 (k3_mfold_2 A B C))) ) ) ).
tt(fc6_topdim_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v3_topdim_1 (k1_pre_topc A B))) ) ) ).
tt(fc6_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k1_topgen_4 A)))  &  ((v1_prob_1 (k1_topgen_4 A) (u1_struct_0 A)) &  ((v1_topgen_4 (k1_topgen_4 A) A) & (v3_topgen_4 (k1_topgen_4 A) (u1_struct_0 A))) ) ) ) ) ).
tt(fc6_topgrp_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_tops_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) & (v3_tops_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A A)) ) ) ) ).
tt(fc6_topmetr,ax, ((v1_metric_1 k8_metric_1) & (v3_topmetr k8_metric_1)) ).
tt(fc6_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k6_topreal1 A))) ) ) ).
tt(fc6_topreal6,ax, (! [A:$i] :  ( ((v4_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (v4_xxreal_2 (k6_measure6 A))) ) ).
tt(fc6_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v4_pre_topc (k2_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc6_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k2_xxreal_1 (k6_xcmplx_0 A B) A))) ) ) ).
tt(fc6_toprealb,ax, ((v1_funct_1 k1_sin_cos6) & (v1_fcont_1 k1_sin_cos6)) ).
tt(fc6_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  & (v1_xcmplx_0 C))  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v1_valued_0 (k2_funct_7 A B C))) ) ) ) ).
tt(fc6_tops_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_pre_topc (k3_xboole_0 B C) A)) ) ).
tt(fc6_trees_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  &  ((m1_subset_1 B A) &  ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (v1_trees_1 C)) ) ) )  =>  ( (~ (v1_xboole_0 (k5_trees_1 A B C)))  &  ((v1_finset_1 (k5_trees_1 A B C)) & (v1_trees_1 (k5_trees_1 A B C))) ) ) ) ).
tt(fc6_trees_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v4_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc6_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ( (~ (v1_xboole_0 (k3_trees_9 A)))  & (v3_trees_3 (k3_trees_9 A))) ) ) ).
tt(fc6_uproots,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k2_polynom5 A (k4_polynom5 A B (k5_struct_0 A)) C)) &  ((v1_funct_2 (k2_polynom5 A (k4_polynom5 A B (k5_struct_0 A)) C) k5_numbers (u1_struct_0 A)) & (v1_uproots (k2_polynom5 A (k4_polynom5 A B (k5_struct_0 A)) C) A)) ) ) ) ).
tt(fc6_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_valued_0 A))  => (v6_membered (k10_xtuple_0 A))) ) ).
tt(fc6_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v4_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_valued_1 A B)) &  ((v1_funct_1 (k1_valued_1 A B)) & (v4_valued_0 (k1_valued_1 A B))) ) ) ) ).
tt(fc6_valued_2,ax, (! [A:$i] : (v3_valued_2 (k6_valued_2 A))) ).
tt(fc6_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k5_vectmetr A)))  & (v15_algstr_0 (k5_vectmetr A))) ) ) ).
tt(fc6_vectsp_1,ax, ((v36_algstr_0 k2_vectsp_1) & (v4_vectsp_1 k2_vectsp_1)) ).
tt(fc6_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k3_waybel_0 A B))) ) ) ).
tt(fc6_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v2_struct_0 (k3_waybel10 A)))  &  ((v1_orders_2 (k3_waybel10 A)) &  ((v3_orders_2 (k3_waybel10 A)) &  ((v4_orders_2 (k3_waybel10 A)) & (v5_orders_2 (k3_waybel10 A))) ) ) ) ) ) ).
tt(fc6_waybel11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k3_waybel11 A B C)))  &  ((v4_orders_2 (k3_waybel11 A B C)) & (v6_waybel_0 (k3_waybel11 A B C) A)) ) ) ) ).
tt(fc6_waybel17,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v4_orders_2 (k4_waybel17 A B)) & (v6_waybel_0 (k4_waybel17 A B) A)) ) ) ).
tt(fc6_waybel18,ax, ((v1_pre_topc k9_waybel18) & (v6_pre_topc k9_waybel18)) ).
tt(fc6_waybel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k2_waybel_1 A B C)) &  ((v1_funct_2 (k2_waybel_1 A B C) (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A B C))) & (v2_funct_2 (k2_waybel_1 A B C) (u1_struct_0 (k1_yellow_2 A B C)))) ) ) ) ).
tt(fc6_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel23 (k6_waybel_0 A B) A)) ) ).
tt(fc6_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_waybel_9 B)) ) )  =>  ( (~ (v2_struct_0 (k3_waybel24 A B)))  & (v1_orders_2 (k3_waybel24 A B))) ) ) ).
tt(fc6_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v3_orders_2 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc6_waybel27,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k2_waybel27 A B)) & (v3_lattice3 (k2_waybel27 A B))) ) ) ).
tt(fc6_waybel_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) ) )  =>  ((v6_waybel_0 (k3_waybel_2 A B C) A) & (v7_waybel_0 (k3_waybel_2 A B C))) ) ) ).
tt(fc6_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_yellow_1 (k2_waybel19 A))))  &  ((v1_orders_2 (k2_yellow_1 (k2_waybel19 A))) & (v3_lattice3 (k2_yellow_1 (k2_waybel19 A)))) ) ) ) ).
tt(fc6_waybel32,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) ) )  =>  ( (~ (v2_struct_0 (k2_waybel32 A B)))  &  ((v6_waybel_0 (k2_waybel32 A B) A) &  ((v7_waybel_0 (k2_waybel32 A B)) & (v10_waybel_0 (k2_waybel32 A B) A)) ) ) ) ) ).
tt(fc6_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k5_waybel34 A)))  &  ((v2_altcat_1 (k5_waybel34 A)) &  ((v6_altcat_1 (k5_waybel34 A)) &  ((v11_altcat_1 (k5_waybel34 A)) &  ((v12_altcat_1 (k5_waybel34 A)) &  ((v2_yellow21 (k5_waybel34 A)) & (v3_yellow21 (k5_waybel34 A))) ) ) ) ) ) ) ) ).
tt(fc6_waybel_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  & (v1_waybel_0 (k1_waybel_3 A B) A)) ) ) ).
tt(fc6_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k3_waybel_4 A))) & (v2_yellow_0 (k2_yellow_1 (k3_waybel_4 A)))) ) ) ).
tt(fc6_waybel_8,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v4_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc6_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  &  ((v5_orders_2 C) & (l1_waybel_0 C A)) ) ) )  =>  ((v5_orders_2 (k3_waybel_2 A B C)) & (v6_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(fc6_wellord2,ax, ((v1_relat_1 (k1_wellord2 k1_xboole_0)) & (v1_xboole_0 (k1_wellord2 k1_xboole_0))) ).
tt(fc6_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k7_xboolean A B))) ) ).
tt(fc6_xcmplx_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  =>  ( (~ (v1_xboole_0 (k4_xcmplx_0 A)))  & (v1_xcmplx_0 (k4_xcmplx_0 A))) ) ) ).
tt(fc6_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k3_xcmplx_0 A B))) ) ).
tt(fc6_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k11_xtuple_0 A))) ) ).
tt(fc6_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v1_xxreal_0 (k4_xxreal_0 A B))) ) ).
tt(fc6_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v1_xboole_0 (k2_xxreal_1 A A))) ) ).
tt(fc6_xxreal_2,ax, (! [A:$i] :  ( ((v6_membered A) & (v1_xxreal_2 A))  =>  ((v1_xxreal_0 (k2_xxreal_2 A)) & (v7_ordinal1 (k2_xxreal_2 A))) ) ) ).
tt(fc6_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  ((v3_xxreal_0 A) &  (~ (v1_xreal_0 A)) ) )  &  ((v1_xxreal_0 B) &  ((v3_xxreal_0 B) &  (~ (v1_xreal_0 B)) ) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) &  (~ (v1_xreal_0 (k1_xxreal_3 A B))) ) ) ) ).
tt(fc6_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v2_waybel_1 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v2_waybel_1 (k3_yellow_3 A B))) ) ) ).
tt(fc6_yellow11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_orders_2 (k5_yellow_0 A (k3_yellow11 A B C))) &  ((v4_yellow_0 (k5_yellow_0 A (k3_yellow11 A B C)) A) & (v5_yellow_0 (k5_yellow_0 A (k3_yellow11 A B C)) A)) ) ) ) ).
tt(fc6_yellow14,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v7_pre_topc B) & (l1_pre_topc B)) ) ) )  =>  ((v1_pre_topc (k3_waybel18 A (k7_funcop_1 A B))) &  ((v2_pre_topc (k3_waybel18 A (k7_funcop_1 A B))) & (v7_pre_topc (k3_waybel18 A (k7_funcop_1 A B)))) ) ) ) ).
tt(fc6_yellow19,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_yellow19 A (k2_struct_0 A) B)))  &  ((v6_waybel_0 (k3_yellow19 A (k2_struct_0 A) B) A) & (v1_yellow19 (k3_yellow19 A (k2_struct_0 A) B) A)) ) ) ) ).
tt(fc6_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k2_yellow_1 A)))  & (v1_orders_2 (k2_yellow_1 A))) ) ) ).
tt(fc6_yellow21,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_wellord1 B) &  ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v5_yellow21 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) )  =>  ((v1_orders_2 (g1_orders_2 A B)) &  ((v2_waybel_8 (g1_orders_2 A B)) &  ((v3_lattice3 (g1_orders_2 A B)) &  ((v16_waybel_0 (g1_orders_2 A B)) & (v3_waybel_3 (g1_orders_2 A B))) ) ) ) ) ) ).
tt(fc6_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k7_waybel_0 A))) & (v3_lattice3 (k2_yellow_1 (k7_waybel_0 A)))) ) ) ).
tt(fc6_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) & (l1_orders_2 A))  &  ((v4_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v4_orders_2 (k3_yellow_3 A B))) ) ) ).
tt(fc6_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ( ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v1_waybel_0 (k3_yellow_4 A B C) A)) ) ).
tt(fc6_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v13_waybel_0 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc6_yellow_7,ax, (! [A:$i] :  ( ((v1_lattice3 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v2_lattice3 (k7_lattice3 A))) ) ) ).
tt(fc6_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_orders_2 (k5_yellow_0 A B)) &  ((v4_yellow_0 (k5_yellow_0 A B) A) & (v7_waybel_0 (k5_yellow_0 A B))) ) ) ) ).
tt(fc6_zf_lang,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_zf_lang) &  ((v1_zf_lang B) & (m1_finseq_1 B k5_numbers)) )  => (v1_zf_lang (k8_zf_lang A B))) ) ).
tt(fc6_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((v3_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))) & (v10_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ) ).
tt(fc70_fomodel0,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v3_finseq_1 A))  => (v1_finset_1 (k21_fomodel0 A))) ) ).
tt(fc70_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k24_fomodel4 A) A)) ) ).
tt(fc70_member_1,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v7_ordinal1 B))  => (v6_membered (k17_member_1 A B))) ) ).
tt(fc70_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k1_partfun3 A)) &  ((v1_funct_1 (k1_partfun3 A)) & (v3_valued_0 (k1_partfun3 A))) ) ) ) ).
tt(fc70_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) & (l2_pcs_0 A))  &  ((v3_orders_2 B) & (l2_pcs_0 B)) )  => (v3_orders_2 (k21_pcs_0 A B))) ) ).
tt(fc70_valued_0,ax, (! [A:$i,B:$i] :  ((v1_rat_1 B) => (v5_relat_1 (k2_funcop_1 A B) k3_numbers)) ) ).
tt(fc70_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v1_valued_0 (k39_valued_1 A))) ) ) ) ).
tt(fc71_fomodel0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  =>  ((v1_xxreal_0 (k16_complex1 A)) & (v2_xxreal_0 (k16_complex1 A))) ) ) ).
tt(fc71_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k25_fomodel4 A) A)) ) ).
tt(fc71_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k18_member_1 A B))) ) ).
tt(fc71_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v4_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_partfun3 B)) &  ((v1_funct_1 (k1_partfun3 B)) & (v4_partfun3 (k1_partfun3 B))) ) ) ) ).
tt(fc71_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v4_orders_2 A) & (l2_pcs_0 A))  &  ((v4_orders_2 B) & (l2_pcs_0 B)) )  => (v4_orders_2 (k21_pcs_0 A B))) ) ).
tt(fc71_valued_0,ax, (! [A:$i,B:$i] :  ((v1_int_1 B) => (v5_relat_1 (k2_funcop_1 A B) k4_numbers)) ) ).
tt(fc71_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v3_valued_0 (k39_valued_1 A))) ) ) ) ).
tt(fc72_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_setfam_1 A))) => (v1_xboole_0 (k4_xboole_0 (k5_setfam_1 A B) A))) ) ).
tt(fc72_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k26_fomodel4 A) A)) ) ).
tt(fc72_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k18_member_1 A B))) ) ) ).
tt(fc72_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) &  ((v1_partfun3 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v1_relat_1 (k1_partfun3 B)) &  ((v1_funct_1 (k1_partfun3 B)) & (v1_partfun3 (k1_partfun3 B))) ) ) ) ).
tt(fc72_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) &  ((v4_pcs_0 B) & (l2_pcs_0 B)) )  => (v4_pcs_0 (k21_pcs_0 A B))) ) ).
tt(fc72_valued_0,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) => (v4_valued_0 (k2_funcop_1 A B))) ) ).
tt(fc72_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v5_relat_1 (k39_valued_1 A) k3_numbers) & (v1_funct_1 (k39_valued_1 A))) ) ) ) ).
tt(fc73_fomodel0,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 A))  => (v5_relat_1 (k1_funct_1 (k8_fomodel0 A) B) A)) ) ).
tt(fc73_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k27_fomodel4 A) A)) ) ).
tt(fc73_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v2_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v1_glib_003 (k12_glib_003 A B C)) & (v2_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc73_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k18_member_1 A B))) ) ).
tt(fc73_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v4_pcs_0 A) & (l2_pcs_0 A))  & (l2_pcs_0 B))  => (v4_pcs_0 (k21_pcs_0 A B))) ) ).
tt(fc73_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v1_valued_0 (k1_funct_4 A B))) ) ) ) ).
tt(fc73_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v5_relat_1 (k39_valued_1 A) k4_numbers) & (v1_funct_1 (k39_valued_1 A))) ) ) ) ).
tt(fc74_fomodel0,ax, (! [A:$i] : (v1_setfam_1 (k4_xboole_0 A (k1_tarski k1_xboole_0)))) ).
tt(fc74_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k28_fomodel4 A) A)) ) ).
tt(fc74_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v2_glib_003 (k12_glib_003 A B C)) & (v3_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc74_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k19_member_1 A B))) ) ).
tt(fc74_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ((v6_pcs_0 A) & (l2_pcs_0 A))  &  ((v6_pcs_0 B) & (l2_pcs_0 B)) )  => (v6_pcs_0 (k21_pcs_0 A B))) ) ).
tt(fc74_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v2_valued_0 (k1_funct_4 A B))) ) ) ) ).
tt(fc74_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v4_valued_0 (k39_valued_1 A))) ) ) ) ).
tt(fc75_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_finset_1 (k13_finseq_1 A))) ) ) ).
tt(fc75_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k29_fomodel4 A) A)) ) ).
tt(fc75_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) &  ((v2_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v2_glib_003 (k12_glib_003 A B C)) & (v7_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc75_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k19_member_1 A B))) ) ) ).
tt(fc75_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v3_valued_0 (k1_funct_4 A B))) ) ) ) ).
tt(fc75_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k39_valued_1 C)) & (v1_partfun1 (k39_valued_1 C) A)) ) ) ).
tt(fc76_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v2_setfam_1 (k13_finseq_1 A))) ) ) ).
tt(fc76_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k30_fomodel4 A) A)) ) ).
tt(fc76_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k19_member_1 A B))) ) ).
tt(fc76_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (v12_pcs_0 (k22_pcs_0 A B))) ) ).
tt(fc76_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k3_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v5_relat_1 (k1_funct_4 A B) k3_numbers) & (v1_funct_1 (k1_funct_4 A B))) ) ) ) ).
tt(fc76_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k39_valued_1 C)) & (v1_partfun1 (k39_valued_1 C) A)) ) ) ).
tt(fc77_fomodel0,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) => (v1_xboole_0 (k4_xboole_0 (k4_finseq_2 B A) (k3_finseq_2 A)))) ) ).
tt(fc77_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k31_fomodel4 A) A)) ) ).
tt(fc77_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v9_glib_003 A)) ) ) ) ) )  & (m1_subset_1 C k1_numbers))  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v2_glib_003 (k12_glib_003 A B C)) & (v9_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc77_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k19_member_1 A B))) ) ).
tt(fc77_pcs_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  &  ( (~ (v2_struct_0 B))  & (l2_pcs_0 B)) )  =>  (~ (v2_struct_0 (k22_pcs_0 A B))) ) ) ).
tt(fc77_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v5_relat_1 (k1_funct_4 A B) k4_numbers) & (v1_funct_1 (k1_funct_4 A B))) ) ) ) ).
tt(fc77_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k39_valued_1 C)) & (v1_partfun1 (k39_valued_1 C) A)) ) ) ).
tt(fc78_fomodel0,ax, (! [A:$i] :  (~ (v1_xboole_0 (k4_xboole_0 (k9_setfam_1 A) A))) ) ).
tt(fc78_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k32_fomodel4 A) A)) ) ).
tt(fc78_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) &  ((v3_glib_003 A) & (v10_glib_003 A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k12_glib_003 A B C)) &  ((v4_relat_1 (k12_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k12_glib_003 A B C)) &  ((v1_finset_1 (k12_glib_003 A B C)) &  ((v1_glib_000 (k12_glib_003 A B C)) &  ((v2_glib_003 (k12_glib_003 A B C)) & (v10_glib_003 (k12_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc78_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k19_member_1 A B))) ) ).
tt(fc78_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v4_valued_0 B)) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v1_funct_1 (k1_funct_4 A B)) & (v4_valued_0 (k1_funct_4 A B))) ) ) ) ).
tt(fc78_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k39_valued_1 C)) & (v1_partfun1 (k39_valued_1 C) A)) ) ) ).
tt(fc79_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) =>  ((v1_relat_1 (k13_fomodel0 A B)) & (v4_relat_1 (k13_fomodel0 A B) (k2_xboole_0 A (k9_xtuple_0 B)))) ) ) ).
tt(fc79_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k33_fomodel4 A) A)) ) ).
tt(fc79_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v3_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v2_glib_000 (k13_glib_003 A B C)) & (v3_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc79_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v1_int_1 B))  => (v5_membered (k19_member_1 A B))) ) ).
tt(fc79_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xcmplx_0 B) => (v1_valued_0 (k16_funcop_1 A B))) ) ).
tt(fc79_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v6_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k39_valued_1 C)) & (v1_partfun1 (k39_valued_1 C) A)) ) ) ).
tt(fc7_abcmiz_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_finseq_1 C (u1_abcmiz_0 A))) )  =>  (~ (v1_xboole_0 (k7_abcmiz_0 A B C))) ) ) ).
tt(fc7_abcmiz_1,ax, (~ (v1_xboole_0 k18_abcmiz_1)) ).
tt(fc7_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (v5_abcmiz_a (k15_abcmiz_1 A) A)) ) ).
tt(fc7_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  & (v1_int_1 B))  => (v1_abian (k3_xcmplx_0 B A))) ) ).
tt(fc7_afinsq_1,ax, (! [A:$i] :  ((v1_relat_1 (k3_afinsq_1 A)) & (v1_funct_1 (k3_afinsq_1 A))) ) ).
tt(fc7_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_zfmisc_1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ((v7_struct_0 (g2_algstr_0 A B C)) & (v8_algstr_0 (g2_algstr_0 A B C))) ) ) ).
tt(fc7_algstr_1,ax, ((v29_algstr_0 k3_algstr_1) & (v4_vectsp_1 k3_algstr_1)) ).
tt(fc7_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (v1_funct_1 B)) ) )  =>  ((v1_partfun1 (k6_algstr_4 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k6_algstr_4 A B)) &  ((v8_relat_2 (k6_algstr_4 A B)) & (v1_algstr_4 (k6_algstr_4 A B) A)) ) ) ) ) ).
tt(fc7_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k4_altcat_4 A)))  &  ((v2_altcat_1 (k4_altcat_4 A)) &  ((v6_altcat_1 (k4_altcat_4 A)) & (v3_altcat_2 (k4_altcat_4 A) A)) ) ) ) ) ).
tt(fc7_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k2_ami_3 A B)))) ) ).
tt(fc7_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v3_extpro_1 (k4_amistd_1 A) A)) ) ) ).
tt(fc7_amistd_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  &  ( ((v2_extpro_1 C A B) & (m1_subset_1 C (u1_compos_1 B)))  & (v7_ordinal1 D)) ) )  => (v2_extpro_1 (k5_compos_0 (u1_compos_1 B) C D) A B)) ) ).
tt(fc7_amistd_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) &  ((v5_amistd_5 B A) &  ((v6_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  &  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) &  ((v4_extpro_1 D A B C) & (v5_extpro_1 D A B C)) ) ) ) ) ) )  & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((v1_relat_1 (k9_memstr_0 A B D E)) &  ((v4_relat_1 (k9_memstr_0 A B D E) (u1_struct_0 B)) &  ((v1_funct_1 (k9_memstr_0 A B D E)) &  ((v5_funct_1 (k9_memstr_0 A B D E) (k2_memstr_0 A B)) & (v5_extpro_1 (k9_memstr_0 A B D E) A B (k6_compos_1 B C E))) ) ) ) ) ) ).
tt(fc7_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  ( (~ (v2_struct_0 (k7_freealg k19_aofa_000 A)))  &  ((v1_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v2_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v3_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v4_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v3_aofa_000 (k7_freealg k19_aofa_000 A)) &  ((v4_aofa_000 (k7_freealg k19_aofa_000 A)) &  ((v5_aofa_000 (k7_freealg k19_aofa_000 A)) & (v6_aofa_000 (k7_freealg k19_aofa_000 A))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k6_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k6_bagorder A)) &  ((v4_relat_2 (k6_bagorder A)) &  ((v8_relat_2 (k6_bagorder A)) & (v2_bagorder (k6_bagorder A) A)) ) ) ) ) ) ).
tt(fc7_binop_2,ax, ((v1_funct_1 k44_binop_2) &  ((v1_funct_2 k44_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) &  ((v1_binop_1 k44_binop_2 k4_numbers) & (v2_binop_1 k44_binop_2 k4_numbers)) ) ) ).
tt(fc7_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_xboole_0 (k10_borsuk_1 A))) ) ) ).
tt(fc7_borsuk_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) )  &  ((v2_pre_topc B) &  ((v8_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((v1_pre_topc (k2_borsuk_1 A B)) &  ((v2_pre_topc (k2_borsuk_1 A B)) & (v8_pre_topc (k2_borsuk_1 A B))) ) ) ) ).
tt(fc7_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k6_xcmplx_0 A B))) ) ) ).
tt(fc7_borsuk_6,ax, ((v1_funct_1 k5_borsuk_6) &  ((v1_funct_2 k5_borsuk_6 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) & (v5_pre_topc k5_borsuk_6 k5_topmetr k5_topmetr)) ) ).
tt(fc7_borsuk_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_xreal_0 C) & (v2_xxreal_0 C)) ) )  =>  ((v1_funct_1 (k11_borsuk_7 A B C)) &  ((v1_funct_2 (k11_borsuk_7 A B C) (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A B C))) & (v3_tops_2 (k11_borsuk_7 A B C) (k8_toprealb A) (k7_toprealb A B C))) ) ) ) ).
tt(fc7_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v3_lopban_1 (k11_c0sp1 A))) ) ).
tt(fc7_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  => (v1_group_1 (k5_c0sp2 A))) ) ).
tt(fc7_card_1,ax, (~ (v1_finset_1 k4_ordinal1)) ).
tt(fc7_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v2_card_3 (k1_tarski A))) ) ).
tt(fc7_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( (~ (v1_finset_1 (k2_card_1 A)))  & (v1_card_1 (k2_card_1 A))) ) ) ).
tt(fc7_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v11_struct_0 A))  &  ((v3_catalg_1 A) & (l1_msualg_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((v1_relat_1 (k2_xtuple_0 B)) & (v1_funct_1 (k2_xtuple_0 B))) ) ) ).
tt(fc7_cayley,ax, ((v7_struct_0 (k2_cayley k1_xboole_0)) &  ((v15_algstr_0 (k2_cayley k1_xboole_0)) & (v1_monoid_0 (k2_cayley k1_xboole_0))) ) ).
tt(fc7_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v3_clopban1 (k7_cc0sp1 A))) ) ).
tt(fc7_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  => (v1_group_1 (k5_cc0sp2 A))) ) ).
tt(fc7_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v2_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v2_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) &  ((v1_partfun1 (k45_valued_1 A B) k2_numbers) & (v2_cfdiff_1 (k45_valued_1 A B))) ) ) ) ).
tt(fc7_cgames_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v3_cgames_1 A)) ) )  & (m1_subset_1 B (k9_xtuple_0 A)))  => (v2_cgames_1 (k1_funct_1 A B))) ) ).
tt(fc7_circcmb3,ax, (~ (v1_facirc_1 k4_ordinal1)) ).
tt(fc7_circcomb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  =>  ( (~ (v2_struct_0 (k2_circcomb B A)))  &  ( (~ (v11_struct_0 (k2_circcomb B A)))  & (v1_msualg_1 (k2_circcomb B A))) ) ) ) ).
tt(fc7_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m3_msaterm C A B) &  ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) ) ) ) )  =>  ((v3_msualg_1 (k6_circtrm1 A B C D) (k1_circtrm1 A B C)) &  ((v4_msualg_1 (k6_circtrm1 A B C D) (k1_circtrm1 A B C)) & (v4_msafree2 (k6_circtrm1 A B C D) (k1_circtrm1 A B C))) ) ) ) ).
tt(fc7_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (~ (v1_xboole_0 (k16_classes2 A)))  & (v1_classes2 (k16_classes2 A))) ) ) ).
tt(fc7_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k8_clopban1 A B))) ) ) ).
tt(fc7_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v9_closure1 B A) & (l1_closure1 B A)) )  => (v4_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc7_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v12_closure2 B A) & (l1_closure2 B A)) )  => (v1_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc7_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v9_cohsp_1 A)) )  => (v2_finsub_1 (k9_xtuple_0 A))) ) ).
tt(fc7_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k14_coh_sp A))) ) ).
tt(fc7_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  => (v7_ordinal1 (k4_xtuple_0 B))) ) ).
tt(fc7_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k5_compos_1 A B C)) &  ((v4_relat_1 (k5_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k5_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k5_compos_1 A B C)) &  ((v1_finset_1 (k5_compos_1 A B C)) & (v1_afinsq_1 (k5_compos_1 A B C))) ) ) ) ) ) ) ).
tt(fc7_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k2_comput_1 A)))  & (v4_funct_1 (k2_comput_1 A))) ) ).
tt(fc7_comseq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k45_valued_1 A B)) &  ((v1_funct_2 (k45_valued_1 A B) k5_numbers k2_numbers) & (v2_comseq_2 (k45_valued_1 A B))) ) ) ) ).
tt(fc7_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k54_valued_1 A)) &  ((v1_funct_2 (k54_valued_1 A) k5_numbers k1_numbers) & (v1_series_1 (k54_valued_1 A))) ) ) ) ).
tt(fc7_convfun1,ax, ( (~ (v2_struct_0 k4_convfun1))  &  ((v13_algstr_0 k4_convfun1) &  ((v2_rlvect_1 k4_convfun1) &  ((v3_rlvect_1 k4_convfun1) &  ((v4_rlvect_1 k4_convfun1) &  ((v5_rlvect_1 k4_convfun1) &  ((v6_rlvect_1 k4_convfun1) &  ((v7_rlvect_1 k4_convfun1) & (v8_rlvect_1 k4_convfun1)) ) ) ) ) ) ) ) ).
tt(fc7_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v2_rlvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v3_rlvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v4_rlvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v1_clvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v2_clvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v3_clvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) &  ((v4_clvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B)))) & (v5_clvect_1 (g1_clvect_1 (k4_csspace4 A B) (k10_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k8_csspace (k3_clopban1 A B) (k4_csspace4 A B)) (k9_csspace (k3_clopban1 A B) (k4_csspace4 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 k1_xboole_0 A)) & (v5_orders_2 (k5_yellow_1 k1_xboole_0 A))) ) ) ).
tt(fc7_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) => (v2_dilworth (k5_dilworth A) A)) ) ).
tt(fc7_euclid_7,ax,(v1_xboole_0 (k8_euclid_7 k6_numbers))).
tt(fc7_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) )  =>  ((v1_relat_1 (k39_valued_1 B)) &  ((v1_funct_1 (k39_valued_1 B)) & (v3_card_1 (k39_valued_1 B) A)) ) ) ) ).
tt(fc7_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_monoid_0 (k15_euclid A)) & (v5_rltopsp1 (k15_euclid A))) ) ) ).
tt(fc7_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  => (v4_relat_1 (k10_funct_7 B C D) A)) ) ).
tt(fc7_facirc_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_facirc_1 A))  =>  (~ (v1_facirc_1 (k3_xboole_0 B A))) ) ) ).
tt(fc7_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k3_relat_1 A B)) & (v1_fcont_1 (k3_relat_1 A B))) ) ) ).
tt(fc7_fib_num2,ax, (! [A:$i,B:$i] :  ((v1_setfam_1 A) => (v1_setfam_1 (k3_xboole_0 B A))) ) ).
tt(fc7_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v19_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v18_lattices (k3_filter_2 A B) (k1_lattice2 A))) ) ).
tt(fc7_finseq_1,ax, (! [A:$i] : (v1_finseq_1 (k5_finseq_1 A))) ).
tt(fc7_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_relat_1 (k2_finseq_2 A k6_numbers)) &  ((v3_relat_1 (k2_finseq_2 A k6_numbers)) &  ((v1_funct_1 (k2_finseq_2 A k6_numbers)) & (v1_finseq_1 (k2_finseq_2 A k6_numbers))) ) ) ) ) ).
tt(fc7_finseq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k13_finseq_1 A)) & (v7_ordinal1 C))  =>  ((v1_relat_1 (k7_partfun1 (k13_finseq_1 A) B C)) & (v1_funct_1 (k7_partfun1 (k13_finseq_1 A) B C))) ) ) ).
tt(fc7_finseq_5,ax, (! [A:$i] :  ( ((v1_xboole_0 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_xboole_0 (k3_finseq_5 A)) &  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc7_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] : (v1_finset_1 (k5_enumset1 A B C D E F G))) ).
tt(fc7_fomodel0,ax, (! [A:$i,B:$i] :  ((v1_xboole_0 B) => (v2_setfam_1 (k4_finseq_2 B A))) ) ).
tt(fc7_fomodel1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  => (v1_xboole_0 (k19_fomodel1 A B))) ) ).
tt(fc7_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((v1_relat_1 (k3_relat_1 D C)) & (v1_finseq_1 (k3_relat_1 D C))) ) ) ).
tt(fc7_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_relat_1 (k5_fomodel3 A B)) &  ((v1_funct_1 (k5_fomodel3 A B)) & (v1_fomodel2 (k5_fomodel3 A B) A (k35_fomodel1 A))) ) ) ) ).
tt(fc7_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v2_fomodel4 (k3_xboole_0 k1_xboole_0 A) A)) ) ).
tt(fc7_fsm_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) ) ) )  =>  ( (~ (v1_xboole_0 (k12_fsm_1 A B C)))  & (v1_finset_1 (k12_fsm_1 A B C))) ) ) ).
tt(fc7_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B)) ) )  =>  ( (~ (v2_struct_0 (g1_rewrite3 B (u1_struct_0 C) (u1_rewrite3 B C))))  & (v1_rewrite3 (g1_rewrite3 B (u1_struct_0 C) (u1_rewrite3 B C)) B)) ) ) ).
tt(fc7_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ((v1_relat_1 (k5_funcop_1 A B C)) & (v1_funct_1 (k5_funcop_1 A B C))) ) ) ).
tt(fc7_funct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_funct_1 B)) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v2_funct_1 (k3_relat_1 A B))) ) ) ).
tt(fc7_funct_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v1_funct_1 (k3_relat_1 B C)) &  ((v1_funct_2 (k3_relat_1 B C) A A) & (v3_funct_2 (k3_relat_1 B C) A A)) ) ) ) ).
tt(fc7_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k1_funct_4 B C)) &  ((v4_relat_1 (k1_funct_4 B C) A) & (v1_funct_1 (k1_funct_4 B C))) ) ) ) ).
tt(fc7_funct_7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funcop_1 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_funcop_1 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc7_funct_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_funct_9 A)) ) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) & (v2_funct_9 (k24_valued_1 A B))) ) ) ) ).
tt(fc7_functor0,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) & (l2_functor0 C A B)) )  => (v1_funcop_1 (u2_functor0 A B C))) ) ).
tt(fc7_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) )  =>  (~ (v1_xboole_0 (k4_gate_1 A B))) ) ) ).
tt(fc7_glib_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_xboole_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((v1_relat_1 (k12_glib_000 A B C D)) &  ((v4_relat_1 (k12_glib_000 A B C D) k5_numbers) &  ((v1_funct_1 (k12_glib_000 A B C D)) &  ((v1_finset_1 (k12_glib_000 A B C D)) &  ((v1_glib_000 (k12_glib_000 A B C D)) & (v7_glib_000 (k12_glib_000 A B C D))) ) ) ) ) ) ) ).
tt(fc7_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v4_glib_001 B A) & (m3_glib_001 B A)) )  => (v4_glib_001 (k6_glib_001 A B) A)) ) ).
tt(fc7_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))))  => (v1_finset_1 (k2_xtuple_0 B))) ) ).
tt(fc7_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (v1_xboole_0 C)) )  => (v1_xboole_0 (k4_graph_3 A B C))) ) ).
tt(fc7_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ( (~ (v2_struct_0 (k4_gr_cy_1 A)))  &  ((v8_struct_0 (k4_gr_cy_1 A)) &  ((v15_algstr_0 (k4_gr_cy_1 A)) &  ((v2_group_1 (k4_gr_cy_1 A)) & (v3_group_1 (k4_gr_cy_1 A))) ) ) ) ) ) ).
tt(fc7_group_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 D E)) &  ((v1_funct_2 (k3_relat_1 D E) (u1_struct_0 A) (u1_struct_0 C)) & (v1_group_6 (k3_relat_1 D E) A C)) ) ) ) ).
tt(fc7_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  => (v4_relat_1 (k5_finseq_1 A) (k1_tarski 1))) ) ).
tt(fc7_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v1_hahnban1 B k1_complfld A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k1_hermitan A B)) &  ((v1_funct_2 (k1_hermitan A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v1_hermitan (k1_hermitan A B) A)) ) ) ) ).
tt(fc7_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v1_xboole_0 (k4_heyting3 1 A))) ) ) ).
tt(fc7_hilbert3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ((m1_subset_1 B k1_hilbert1) & (m1_subset_1 C k1_hilbert1)) )  => (v4_funct_1 (k3_hilbert3 A (k3_hilbert1 B C)))) ) ).
tt(fc7_index_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) ) )  =>  ((v1_relat_1 (k4_index_1 B)) &  ((v2_relat_1 (k4_index_1 B)) &  ((v1_funct_1 (k4_index_1 B)) & (v1_partfun1 (k4_index_1 B) A)) ) ) ) ) ).
tt(fc7_int_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v6_struct_0 (k9_int_3 A)))  &  ((v13_algstr_0 (k9_int_3 A)) &  ((v33_algstr_0 (k9_int_3 A)) &  ((v3_group_1 (k9_int_3 A)) &  ((v5_group_1 (k9_int_3 A)) &  ((v2_rlvect_1 (k9_int_3 A)) &  ((v3_rlvect_1 (k9_int_3 A)) &  ((v4_rlvect_1 (k9_int_3 A)) &  ((v4_vectsp_1 (k9_int_3 A)) & (v5_vectsp_1 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc7_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_xcmplx_0 (k19_rvsum_1 A)) & (v1_int_1 (k19_rvsum_1 A))) ) ) ).
tt(fc7_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (~ (v1_xboole_0 (k18_interva1 A))) ) ) ).
tt(fc7_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v10_intpro_1 (k13_intpro_1 A))) ) ).
tt(fc7_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v6_tops_1 (k1_isomichi A B) A)) ) ).
tt(fc7_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k5_topreal1 A) (k15_euclid 2))) ) ).
tt(fc7_jordan23,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_jordan23 B) & (m1_finseq_1 B A))  & (m1_subset_1 C A)) )  => (v1_jordan23 (k1_finseq_6 A B C))) ) ).
tt(fc7_jordan2c,ax, (! [A:$i] :  ( ((v4_pre_topc A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v3_pre_topc (k2_jordan2c 2 A) (k15_euclid 2))) ) ).
tt(fc7_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)))) ) ).
tt(fc7_kurato_1,ax,(v3_setfam_1 (k2_kurato_1 k3_topmetr k6_kurato_1) (u1_struct_0 k3_topmetr))).
tt(fc7_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_lattices A) & (l1_lattices A)) )  =>  ((v1_funct_1 (u1_lattices A)) &  ((v1_funct_2 (u1_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v2_binop_1 (u1_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc7_lattice3,ax, (! [A:$i] :  ((v3_lattices (k1_lattice3 A)) & (v4_lattice3 (k1_lattice3 A))) ) ).
tt(fc7_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v2_lexbfs (k26_lexbfs A))) ) ).
tt(fc7_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (~ (v1_xboole_0 (k10_lopban_1 A B))) ) ) ).
tt(fc7_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((v1_funct_1 (k8_lopclset A)) &  ((v1_funct_2 (k8_lopclset A) (u1_struct_0 A) (u1_struct_0 (k12_lopclset A))) & (v3_funct_2 (k8_lopclset A) (u1_struct_0 A) (u1_struct_0 (k12_lopclset A)))) ) ) ) ).
tt(fc7_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  &  ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers)) ) ) )  =>  ((v13_algstr_0 (k10_lpspace2 A B C D)) &  ((v1_rlvect_1 (k10_lpspace2 A B C D)) &  ((v2_rlvect_1 (k10_lpspace2 A B C D)) &  ((v3_rlvect_1 (k10_lpspace2 A B C D)) &  ((v4_rlvect_1 (k10_lpspace2 A B C D)) &  ((v5_rlvect_1 (k10_lpspace2 A B C D)) &  ((v6_rlvect_1 (k10_lpspace2 A B C D)) &  ((v7_rlvect_1 (k10_lpspace2 A B C D)) & (v8_rlvect_1 (k10_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_lukasi_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_cqc_lang A)) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B (k8_cqc_lang A C D)) (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B D))) A)) ) ).
tt(fc7_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_margrel1 A))  => (v2_card_3 (k9_xtuple_0 A))) ) ).
tt(fc7_matrtop1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((v1_relat_1 (k1_finseq_3 A B)) &  ((v1_funct_1 (k1_finseq_3 A B)) &  ((v1_finseq_1 (k1_finseq_3 A B)) & (v3_valued_0 (k1_finseq_3 A B))) ) ) ) ) ).
tt(fc7_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v3_matrtop3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v3_matrtop3 (k2_tops_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B) A)) ) ) ) ).
tt(fc7_member_1,ax, (! [A:$i] :  ((v3_membered A) =>  ((v1_membered (k5_member_1 A)) & (v3_membered (k5_member_1 A))) ) ) ).
tt(fc7_membered,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v1_membered (k1_tarski A))) ) ).
tt(fc7_mesfunc7,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v2_valued_0 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc7_metrizts,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) )  =>  ((v1_funct_1 (k6_weierstr A B)) &  ((v1_funct_2 (k6_weierstr A B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr)) & (v5_pre_topc (k6_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ).
tt(fc7_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v2_pre_topc (k4_mfold_2 A)) & (v3_mfold_1 (k4_mfold_2 A) A)) ) ) ).
tt(fc7_mod_2,ax, ((v13_algstr_0 k18_mod_2) &  ((v33_algstr_0 k18_mod_2) &  ((v36_algstr_0 k18_mod_2) &  ((v3_group_1 k18_mod_2) &  ((v5_group_1 k18_mod_2) &  ((v4_vectsp_1 k18_mod_2) &  ((v5_vectsp_1 k18_mod_2) &  ((v12_vectsp_1 k18_mod_2) &  ((v2_rlvect_1 k18_mod_2) &  ((v3_rlvect_1 k18_mod_2) & (v4_rlvect_1 k18_mod_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc7_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v4_rlvect_1 (k2_mod_4 A))) ) ) ).
tt(fc7_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (v1_modelc_2 (k8_modelc_2 A B))) ) ).
tt(fc7_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v1_xboole_0 (k6_moebius1 A))) ) ) ).
tt(fc7_msafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k7_msafree A B C))) ) ) ).
tt(fc7_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v2_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k3_pboole A B C)) &  ((v4_relat_1 (k3_pboole A B C) A) &  ((v1_funct_1 (k3_pboole A B C)) &  ((v1_partfun1 (k3_pboole A B C) A) & (v2_finset_1 (k3_pboole A B C))) ) ) ) ) ) ).
tt(fc7_msualg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B))) )  =>  (~ (v1_xboole_0 (k5_msualg_2 A B C))) ) ) ).
tt(fc7_mycielsk,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_mycielsk A) & (l1_orders_2 A)) )  =>  ((v7_ordinal1 (k3_mycielsk A)) & (v2_xxreal_0 (k3_mycielsk A))) ) ) ).
tt(fc7_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  & (v7_ordinal1 C)) )  =>  ((v1_relat_1 (k9_nat_1 B C)) &  ((v4_relat_1 (k9_nat_1 B C) k5_numbers) &  ((v5_relat_1 (k9_nat_1 B C) A) &  ((v1_funct_1 (k9_nat_1 B C)) & (v1_partfun1 (k9_nat_1 B C) k5_numbers)) ) ) ) ) ) ).
tt(fc7_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  & (v7_ordinal1 C))  =>  ((v1_relat_1 (k4_nat_3 A B C)) &  ((v4_relat_1 (k4_nat_3 A B C) A) &  ((v1_funct_1 (k4_nat_3 A B C)) &  ((v1_partfun1 (k4_nat_3 A B C) A) & (v2_pre_poly (k4_nat_3 A B C))) ) ) ) ) ) ).
tt(fc7_nat_lat,ax, ((v3_lattices k10_nat_lat) &  ((v4_lattices k10_nat_lat) &  ((v5_lattices k10_nat_lat) &  ((v6_lattices k10_nat_lat) &  ((v7_lattices k10_nat_lat) &  ((v8_lattices k10_nat_lat) & (v9_lattices k10_nat_lat)) ) ) ) ) ) ).
tt(fc7_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_necklace A) & (l1_orders_2 A))  &  ((v1_necklace B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k1_neckla_2 A B)) & (v1_necklace (k1_neckla_2 A B))) ) ) ).
tt(fc7_necklace,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v2_struct_0 (k4_necklace A)))  & (v1_orders_2 (k4_necklace A))) ) ) ).
tt(fc7_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v7_ordinal1 (k3_newton A))) ) ).
tt(fc7_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v2_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v2_nfcont_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k1_vfunct_1 k1_numbers A B C)) & (v2_nfcont_3 (k1_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc7_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) &  ((v2_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  &  ((v1_funct_1 C) &  ((v2_nfcont_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) ) )  =>  ((v1_funct_1 (k8_integr15 A k1_numbers B C)) & (v2_nfcont_4 (k8_integr15 A k1_numbers B C) A)) ) ) ).
tt(fc7_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k4_normsp_2 A)))  &  ((v4_frechet (k4_normsp_2 A)) & (v5_rltopsp1 (k4_normsp_2 A))) ) ) ) ).
tt(fc7_numbers,ax, (~ (v1_finset_1 k3_numbers)) ).
tt(fc7_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (k8_openlatt A)) &  ((v1_funct_2 (k8_openlatt A) (u1_struct_0 A) (u1_struct_0 (k15_openlatt A))) & (v3_funct_2 (k8_openlatt A) (u1_struct_0 A) (u1_struct_0 (k15_openlatt A)))) ) ) ) ).
tt(fc7_oposet_1,ax, ((v1_necklace k1_oposet_1) & (v3_qmax_1 k1_oposet_1)) ).
tt(fc7_orders_2,ax, (! [A:$i,B:$i] :  ( ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_orders_2 (g1_orders_2 A B)) & (v4_orders_2 (g1_orders_2 A B))) ) ) ).
tt(fc7_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  ((v6_altcat_1 (k4_orders_3 A)) &  ((v11_altcat_1 (k4_orders_3 A)) & (v12_altcat_1 (k4_orders_3 A))) ) ) ) ).
tt(fc7_ordinal1,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  => (v7_ordinal1 (k1_ordinal1 A))) ) ).
tt(fc7_ordinal5,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((v3_ordinal1 (k1_ordinal5 A B)) & (v7_ordinal1 (k1_ordinal5 A B))) ) ) ).
tt(fc7_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_relat_1 (k4_relat_1 A)) &  ((v1_funct_1 (k4_relat_1 A)) &  ((v5_ordinal1 (k4_relat_1 A)) &  ((v1_ordinal2 (k4_relat_1 A)) & (v3_ordinal2 (k4_relat_1 A))) ) ) ) ) ) ).
tt(fc7_osafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v2_msualg_4 (k20_osafree A B) A (k8_osafree A B)) & (v3_osalg_4 (k20_osafree A B) A (k8_osafree A B))) ) ) ).
tt(fc7_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (~ (v1_xboole_0 (k12_osalg_2 A B))) ) ) ).
tt(fc7_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (v1_partfun3 (k2_funcop_1 A B))) ) ).
tt(fc7_partfun4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  & (v1_xreal_0 C)) )  =>  ((v1_funct_1 (k24_valued_1 B C)) &  ((v1_funct_2 (k24_valued_1 B C) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k24_valued_1 B C) A)) ) ) ) ).
tt(fc7_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_partfun1 C A) &  ((v1_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B))))  => (v1_relat_2 (k3_pcs_0 A A B B C D))) ) ).
tt(fc7_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k1_polyalg1 A)))  &  ((v4_vectsp_1 (k1_polyalg1 A)) & (v1_polyalg1 (k1_polyalg1 A) A)) ) ) ) ).
tt(fc7_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) & (v1_xreal_0 E)) ) ) )  => (v1_xreal_0 (k7_polyeq_1 A B C D E))) ) ).
tt(fc7_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v2_rlvect_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc7_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k6_polynom2 A B C)) &  ((v1_funct_2 (k6_polynom2 A B C) (u1_struct_0 (k11_polynom1 A B)) (u1_struct_0 B)) & (v1_quofield (k6_polynom2 A B C) (k11_polynom1 A B) B)) ) ) ) ).
tt(fc7_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v1_funct_1 (k10_polynom3 A)) &  ((v1_funct_2 (k10_polynom3 A) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k10_polynom3 A) A)) ) ) ) ).
tt(fc7_pralg_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  & (m1_pralg_2 C A B))  => (v3_msualg_1 (k14_pralg_2 A B C) B)) ) ).
tt(fc7_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_pre_poly A)) ) )  => (v1_finseq_1 (k1_funct_1 A B))) ) ).
tt(fc7_pre_topc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))  & (v1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(fc7_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v2_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc7_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k15_pscomp_1 A)))  & (v2_compts_1 (k15_pscomp_1 A) (k15_euclid 2))) ) ) ).
tt(fc7_qc_lang1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_qc_lang1 B))  =>  (~ (v1_xboole_0 (k8_qc_lang1 B A))) ) ) ).
tt(fc7_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  => (v1_quaterni (k10_quaterni A B))) ) ).
tt(fc7_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v36_algstr_0 (k19_quofield A)) & (v4_vectsp_1 (k19_quofield A))) ) ) ).
tt(fc7_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C k5_numbers)) )  =>  ((v1_funct_1 (k3_hurwitz A B C)) &  ((v1_funct_2 (k3_hurwitz A B C) k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 (k3_hurwitz A B C) A) &  (~ (v1_ratfunc1 (k3_hurwitz A B C) A)) ) ) ) ) ) ).
tt(fc7_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (v3_xxreal_2 (k1_limfunc1 A)))  &  ((v4_xxreal_2 (k1_limfunc1 A)) & (v6_xxreal_2 (k1_limfunc1 A))) ) ) ) ).
tt(fc7_real_3,ax, ((v1_xboole_0 (k1_int_1 k6_numbers)) & (v1_int_1 (k1_int_1 k6_numbers))) ).
tt(fc7_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k7_real_ns1 A)))  &  ((v1_bhsp_1 (k7_real_ns1 A)) & (v3_bhsp_3 (k7_real_ns1 A))) ) ) ) ).
tt(fc7_relat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] : (v1_relat_1 (k2_tarski (k4_tarski A B) (k4_tarski C D)))) ).
tt(fc7_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_relat_2 A))  &  ((v1_relat_1 B) & (v2_relat_2 B)) )  => (v2_relat_2 (k3_xboole_0 A B))) ) ).
tt(fc7_reloc,ax, ((v1_extpro_1 k1_ami_3 2) &  ((v5_amistd_5 k1_ami_3 2) & (v6_amistd_5 k1_ami_3 2)) ) ).
tt(fc7_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k4_relat_1 A)))  & (v1_relat_1 (k4_relat_1 A))) ) ) ).
tt(fc7_revrot_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) &  ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m1_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) )  => (v1_sprect_2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A))) ) ).
tt(fc7_rfunct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_seq_2 A)) ) )  =>  ((v1_relat_1 (k5_relat_1 A B)) &  ((v1_funct_1 (k5_relat_1 A B)) &  ((v3_valued_0 (k5_relat_1 A B)) & (v2_seq_2 (k5_relat_1 A B))) ) ) ) ) ).
tt(fc7_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v6_cat_1 (k17_ringcat1 A))) ) ).
tt(fc7_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_rlaffin1 (k1_tarski B) A)) ) ).
tt(fc7_rlaffin3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  ((v1_convex1 (k3_convex1 (k15_euclid A) B) (k15_euclid A)) & (v4_pre_topc (k3_convex1 (k15_euclid A) B) (k15_euclid A))) ) ) ).
tt(fc7_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v3_pre_topc (k5_rusub_4 A B C) A)) ) ).
tt(fc7_robbins4,ax, ((v13_lattices k2_robbins4) & (v4_robbins1 k2_robbins4)) ).
tt(fc7_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v4_roughs_1 (k3_roughs_1 A B) A)) ) ) ).
tt(fc7_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v1_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v2_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v3_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v4_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v5_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v6_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) &  ((v7_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)))) & (v8_rlvect_1 (g1_rlvect_1 (k4_rsspace4 A B) (k10_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k8_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B)) (k9_rsspace (k5_lopban_1 A B) (k4_rsspace4 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v3_valued_0 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc7_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k6_scmfsa_2 A B)))) ) ).
tt(fc7_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v2_extpro_1 (k7_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc7_scmfsa_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v4_compos_0 (k15_scmfsa_2 B A C) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc7_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_scmfsa6c (k9_scmfsa_2 A B))) ) ).
tt(fc7_scmfsa7b,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  & (v1_int_1 B))  =>  ((v1_relat_1 (k1_scmfsa_7 A B)) &  ((v4_relat_1 (k1_scmfsa_7 A B) k5_numbers) &  ((v5_relat_1 (k1_scmfsa_7 A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k1_scmfsa_7 A B)) &  ((v1_finset_1 (k1_scmfsa_7 A B)) & (v1_scmfsa6b (k1_scmfsa_7 A B))) ) ) ) ) ) ) ).
tt(fc7_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  &  ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa8b A B C D)))  &  ((v1_relat_1 (k5_scmfsa8b A B C D)) &  ((v4_relat_1 (k5_scmfsa8b A B C D) k5_numbers) &  ((v5_relat_1 (k5_scmfsa8b A B C D) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa8b A B C D)) &  ((v1_finset_1 (k5_scmfsa8b A B C D)) &  ((v1_afinsq_1 (k5_scmfsa8b A B C D)) &  (~ (v2_compos_1 (k5_scmfsa8b A B C D) k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
tt(fc7_scmfsa_m,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 C)) )  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v5_funct_1 (k2_funct_7 A B C) (k2_memstr_0 3 k1_scmfsa_2))) ) ) ) ).
tt(fc7_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) &  ((v2_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scm_halt B) & (v3_scm_halt B)) ) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa6a A B)))  &  ((v1_relat_1 (k4_scmfsa6a A B)) &  ((v4_relat_1 (k4_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa6a A B)) &  ((v1_finset_1 (k4_scmfsa6a A B)) &  ((v1_afinsq_1 (k4_scmfsa6a A B)) &  ((v2_scm_halt (k4_scmfsa6a A B)) & (v3_scm_halt (k4_scmfsa6a A B))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_scm_inst,ax, ( (~ (v1_xboole_0 k3_scm_inst))  & (v5_compos_0 k3_scm_inst)) ).
tt(fc7_scmpds_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v4_scmpds_4 (k15_scmpds_2 A B C D))) ) ).
tt(fc7_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v6_compos_0 (k10_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc7_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k5_scmpds_6 B C A)))  &  ((v1_relat_1 (k5_scmpds_6 B C A)) &  ((v4_relat_1 (k5_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k5_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k5_scmpds_6 B C A)) &  ((v1_finset_1 (k5_scmpds_6 B C A)) &  ((v1_afinsq_1 (k5_scmpds_6 B C A)) &  ((v2_scmpds_4 (k5_scmpds_6 B C A)) & (v3_scmpds_4 (k5_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc7_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  (~ (v2_extpro_1 (k6_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ).
tt(fc7_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k3_scmring2 A B C)))) ) ).
tt(fc7_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ( (~ (v1_xboole_0 (k1_scmringi A)))  & (v5_compos_0 (k1_scmringi A))) ) ) ).
tt(fc7_scmyciel,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (v3_scmyciel B A))  => (v3_scmyciel (k3_xboole_0 B C) A)) ) ).
tt(fc7_setfam_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) )  => (v1_setfam_1 (k4_enumset1 A B C D E F))) ) ).
tt(fc7_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v1_sfmastr1 (k12_scmfsa_2 B A))) ) ).
tt(fc7_simplex0,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_setfam_1 (k1_simplex0 A)))  & (v1_classes1 (k1_simplex0 A))) ) ) ).
tt(fc7_simplex1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) )  & (v7_ordinal1 C)) )  =>  ( (~ (v3_pencil_1 (k5_simplex1 C A B)))  &  ((v1_matroid0 (k5_simplex1 C A B)) &  ((v3_matroid0 (k5_simplex1 C A B)) & (v1_simplex1 (k5_simplex1 C A B) A)) ) ) ) ) ).
tt(fc7_sincos10,ax, ((v1_funct_1 k3_sincos10) & (v2_funct_1 k3_sincos10)) ).
tt(fc7_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))) ).
tt(fc7_sin_cos,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos k1_numbers k1_numbers) & (v1_fcont_1 k19_sin_cos)) ) ).
tt(fc7_sppol_2,ax,(v1_topreal1 (k6_finseq_1 (u1_struct_0 (k15_euclid 2))))).
tt(fc7_sprect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  => (v3_xxreal_2 (k7_relat_1 C B))) ) ).
tt(fc7_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v5_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc7_struct_0,ax, (! [A:$i] :  ( ((v7_struct_0 A) & (l1_struct_0 A))  => (v1_zfmisc_1 (u1_struct_0 A))) ) ).
tt(fc7_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  (~ (v1_xboole_0 (k6_enumset1 A B C D E F G H))) ) ).
tt(fc7_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (~ (v1_xboole_0 (k38_substut1 A))) ) ) ).
tt(fc7_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k1_tops_1 A B))) ) ).
tt(fc7_topalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_borsuk_2 D A B C)) ) )  =>  ((v1_funct_1 (k6_topalg_1 A B C D)) &  ((v2_funct_1 (k6_topalg_1 A B C D)) &  ((v1_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) & (v2_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A B)))) ) ) ) ) ).
tt(fc7_topalg_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) &  ((v5_pre_topc D (k2_borsuk_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) ) )  & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((v1_funct_1 (k4_topalg_5 A B C D E)) &  ((v1_funct_2 (k4_topalg_5 A B C D E) (u1_struct_0 B) (u1_struct_0 C)) & (v5_pre_topc (k4_topalg_5 A B C D E) B C)) ) ) ) ).
tt(fc7_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (~ (v1_xboole_0 (k1_topalg_6 A))) ) ) ).
tt(fc7_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (~ (v2_struct_0 (k5_topgrp_1 A)))  & (v15_algstr_0 (k5_topgrp_1 A))) ) ) ).
tt(fc7_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v1_xboole_0 (k7_topreal1 A))) ) ) ).
tt(fc7_topreal6,ax, ((v2_pre_topc k3_topmetr) & (v8_pre_topc k3_topmetr)) ).
tt(fc7_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v4_pre_topc (k3_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc7_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k3_xxreal_1 (k6_xcmplx_0 A B) A))) ) ) ).
tt(fc7_toprealb,ax, ((v1_funct_1 k4_sin_cos6) & (v1_fcont_1 k4_sin_cos6)) ).
tt(fc7_tops_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v3_pre_topc (k2_xboole_0 B C) A)) ) ).
tt(fc7_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v1_finset_1 (k1_trees_1 A))) ) ).
tt(fc7_trees_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v5_trees_3 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v5_trees_3 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v5_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc7_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (~ (v1_xboole_0 (k6_trees_9 A))) ) ) ).
tt(fc7_uproots,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  => (v1_finset_1 (k6_polynom5 A B))) ) ).
tt(fc7_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_valued_0 A))  &  ((v1_relat_1 B) & (v1_valued_0 B)) )  => (v1_valued_0 (k2_xboole_0 A B))) ) ).
tt(fc7_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 D E)) & (v1_partfun1 (k1_valued_1 D E) A)) ) ) ).
tt(fc7_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((v15_algstr_0 (k5_vectmetr A)) &  ((v2_group_1 (k5_vectmetr A)) & (v3_group_1 (k5_vectmetr A))) ) ) ) ).
tt(fc7_vectsp_1,ax, ((v36_algstr_0 k2_vectsp_1) & (v1_group_1 k2_vectsp_1)) ).
tt(fc7_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (v1_xboole_0 (k4_waybel_0 A B))) ) ) ).
tt(fc7_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (~ (v2_struct_0 (k3_waybel10 A)))  &  ((v1_orders_2 (k3_waybel10 A)) & (v3_lattice3 (k3_waybel10 A))) ) ) ) ).
tt(fc7_waybel11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  ( (~ (v2_struct_0 (k3_waybel11 A B C)))  &  ((v3_orders_2 (k3_waybel11 A B C)) & (v6_waybel_0 (k3_waybel11 A B C) A)) ) ) ) ).
tt(fc7_waybel17,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v6_waybel_0 (k4_waybel17 A B) A) & (v8_waybel_0 (k4_waybel17 A B) A)) ) ) ).
tt(fc7_waybel18,ax, ((v1_pre_topc k9_waybel18) & (v2_waybel18 k9_waybel18)) ).
tt(fc7_waybel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k3_waybel_1 A B C)) &  ((v2_funct_1 (k3_waybel_1 A B C)) &  ((v1_funct_2 (k3_waybel_1 A B C) (u1_struct_0 (k1_yellow_2 A B C)) (u1_struct_0 B)) & (v5_orders_3 (k3_waybel_1 A B C) (k1_yellow_2 A B C) B)) ) ) ) ) ).
tt(fc7_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_waybel23 (k1_waybel_3 A B) A)) ) ).
tt(fc7_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_waybel_9 B)) ) )  =>  ((v1_monoid_0 (k3_waybel24 A B)) & (v1_orders_2 (k3_waybel24 A B))) ) ) ).
tt(fc7_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v4_orders_2 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc7_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  =>  ((v1_waybel_9 (k1_waybel25 A)) & (v4_waybel11 (k1_waybel25 A))) ) ) ).
tt(fc7_waybel_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  ((v1_funct_1 (k4_waybel_2 A)) &  ((v1_funct_2 (k4_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (v5_orders_3 (k4_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ) ).
tt(fc7_waybel30,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) )  &  ((v3_waybel11 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_waybel11 (k4_waybel_0 A B) A)) ) ).
tt(fc7_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((v9_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A)) &  ((v16_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A)) & (v21_functor0 (k6_waybel34 A) (k4_waybel34 A) (k5_waybel34 A))) ) ) ) ).
tt(fc7_waybel_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_yellow_1 A B)))  & (v1_orders_2 (k5_yellow_1 A B))) ) ) ).
tt(fc7_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v5_waybel_4 (k4_waybel_4 A) A)) ) ).
tt(fc7_waybel_8,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v5_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc7_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) & (l1_waybel_0 C A)) ) ) )  =>  ((v4_orders_2 (k3_waybel_2 A B C)) & (v6_waybel_0 (k3_waybel_2 A B C) A)) ) ) ).
tt(fc7_wellord2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_relat_1 (k1_wellord2 A)) &  (~ (v1_xboole_0 (k1_wellord2 A))) ) ) ) ).
tt(fc7_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k8_xboolean A B))) ) ).
tt(fc7_xcmplx_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  =>  ( (~ (v1_xboole_0 (k5_xcmplx_0 A)))  & (v1_xcmplx_0 (k5_xcmplx_0 A))) ) ) ).
tt(fc7_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k6_xcmplx_0 A B))) ) ).
tt(fc7_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k12_xtuple_0 A))) ) ).
tt(fc7_xxreal_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xxreal_0 A) &  ((v1_xxreal_0 B) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  => (v7_ordinal1 (k5_xxreal_0 A B C D))) ) ).
tt(fc7_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v1_xboole_0 (k3_xxreal_1 A A))) ) ).
tt(fc7_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) & (v2_xxreal_2 A))  =>  ((v1_xxreal_0 (k1_xxreal_2 A)) & (v1_xreal_0 (k1_xxreal_2 A))) ) ) ).
tt(fc7_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  ((v3_xxreal_0 A) &  (~ (v1_xreal_0 A)) ) )  &  ((v1_xxreal_0 B) &  ((v2_xxreal_0 B) &  (~ (v1_xreal_0 B)) ) ) )  =>  ((v1_xboole_0 (k1_xxreal_3 A B)) & (v1_xxreal_0 (k1_xxreal_3 A B))) ) ) ).
tt(fc7_yellow10,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) &  ((v2_waybel_2 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v1_waybel_2 (k3_yellow_3 A B))) ) ) ).
tt(fc7_yellow11,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((v1_orders_2 (k5_yellow_0 A (k3_yellow11 A B C))) &  ((v4_yellow_0 (k5_yellow_0 A (k3_yellow11 A B C)) A) & (v6_yellow_0 (k5_yellow_0 A (k3_yellow11 A B C)) A)) ) ) ) ).
tt(fc7_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k3_yellow18 (k4_yellow18 A) B))) ) ) ).
tt(fc7_yellow_1,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k3_yellow_1 A)))  &  ((v1_orders_2 (k3_yellow_1 A)) &  ((v3_orders_2 (k3_yellow_1 A)) &  ((v4_orders_2 (k3_yellow_1 A)) & (v5_orders_2 (k3_yellow_1 A))) ) ) ) ) ).
tt(fc7_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( (~ (v2_struct_0 (k6_yellow21 A)))  &  ((v2_altcat_1 (k6_yellow21 A)) &  ((v6_altcat_1 (k6_yellow21 A)) &  ((v11_altcat_1 (k6_yellow21 A)) &  ((v12_altcat_1 (k6_yellow21 A)) &  ((v2_yellow21 (k6_yellow21 A)) &  ((v3_yellow21 (k6_yellow21 A)) & (v4_yellow21 (k6_yellow21 A))) ) ) ) ) ) ) ) ) ).
tt(fc7_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k2_yellow_2 A)) &  ((v1_funct_2 (k2_yellow_2 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A)) & (v5_orders_3 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ) ).
tt(fc7_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_lattice3 A) & (l1_orders_2 A))  &  ((v1_lattice3 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v1_lattice3 (k3_yellow_3 A B))) ) ) ).
tt(fc7_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ( ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_waybel_0 (k3_yellow_4 A B C) A)) ) ).
tt(fc7_yellow_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v12_waybel_0 (k3_subset_1 (u1_struct_0 A) B) A)) ) ).
tt(fc7_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_lattice3 A) & (l1_orders_2 A)) )  =>  ((v1_orders_2 (k7_lattice3 A)) & (v3_lattice3 (k7_lattice3 A))) ) ) ).
tt(fc7_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v2_struct_0 (k2_yellow_9 A B)))  &  ((v6_waybel_0 (k2_yellow_9 A B) A) & (v7_waybel_0 (k2_yellow_9 A B))) ) ) ) ).
tt(fc80_fomodel0,ax, (! [A:$i] :  (~ (v1_finset_1 (k23_fomodel0 A))) ) ).
tt(fc80_fomodel4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v17_fomodel4 B A) & (m1_subset_1 B (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) )  => (v16_fomodel4 (k1_tarski B) A)) ) ).
tt(fc80_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k20_member_1 A B))) ) ).
tt(fc80_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xxreal_0 B) => (v2_valued_0 (k16_funcop_1 A B))) ) ).
tt(fc80_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k39_valued_1 A)) &  ((v1_funct_1 (k39_valued_1 A)) & (v1_finseq_1 (k39_valued_1 A))) ) ) ) ).
tt(fc81_fomodel0,ax, (! [A:$i] : (v1_xboole_0 (k3_xboole_0 (k23_fomodel0 A) A))) ).
tt(fc81_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v16_fomodel4 (k37_fomodel4 A) A)) ) ).
tt(fc81_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k20_member_1 A B))) ) ) ).
tt(fc81_valued_0,ax, (! [A:$i,B:$i] :  ((v1_xreal_0 B) => (v3_valued_0 (k16_funcop_1 A B))) ) ).
tt(fc81_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) &  ((v1_funct_1 (k45_valued_1 A B)) & (v1_valued_0 (k45_valued_1 A B))) ) ) ) ).
tt(fc82_fomodel0,ax, (! [A:$i] : (v4_card_3 (k23_fomodel0 A))) ).
tt(fc82_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v5_fomodel4 (k34_fomodel4 A) A)) ) ).
tt(fc82_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k20_member_1 A B))) ) ).
tt(fc82_valued_0,ax, (! [A:$i,B:$i] :  ((v1_rat_1 B) => (v5_relat_1 (k16_funcop_1 A B) k3_numbers)) ) ).
tt(fc82_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) &  ((v1_funct_1 (k45_valued_1 A B)) & (v3_valued_0 (k45_valued_1 A B))) ) ) ) ).
tt(fc83_fomodel0,ax,(v1_xboole_0 (k4_xboole_0 k5_numbers k4_numbers))).
tt(fc83_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  => (v4_fomodel4 (k13_fomodel0 1 (k4_tarski B C)) 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k34_fomodel4 A)) (k1_tarski (k4_tarski B (k38_fomodel2 A (k38_fomodel2 A C)))))) ) ).
tt(fc83_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k21_member_1 A B))) ) ).
tt(fc83_valued_0,ax, (! [A:$i,B:$i] :  ((v1_int_1 B) => (v5_relat_1 (k16_funcop_1 A B) k4_numbers)) ) ).
tt(fc83_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k3_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) &  ((v5_relat_1 (k45_valued_1 A B) k3_numbers) & (v1_funct_1 (k45_valued_1 A B))) ) ) ) ).
tt(fc84_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (v1_xboole_0 (k5_xboole_0 (k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) B) 1) A))) ) ).
tt(fc84_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v4_fomodel2 C A) &  ((v13_fomodel2 C B A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((v4_fomodel2 (k38_fomodel2 A (k38_fomodel2 A C)) A) & (v13_fomodel2 (k38_fomodel2 A (k38_fomodel2 A C)) B A)) ) ) ).
tt(fc84_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k21_member_1 A B))) ) ) ).
tt(fc84_valued_0,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 B) => (v4_valued_0 (k16_funcop_1 A B))) ) ).
tt(fc84_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) &  ((v5_relat_1 (k45_valued_1 A B) k4_numbers) & (v1_funct_1 (k45_valued_1 A B))) ) ) ) ).
tt(fc85_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((v1_xboole_0 B) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) )  =>  ((v1_relat_1 (k13_fomodel0 B C)) &  ((v4_relat_1 (k13_fomodel0 B C) (k2_finseq_1 (k2_xcmplx_0 A B))) & (v1_partfun1 (k13_fomodel0 B C) (k2_finseq_1 (k2_xcmplx_0 A B)))) ) ) ) ).
tt(fc85_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v4_funct_1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) ) ) ) )  => (v1_xboole_0 (k4_xboole_0 A (k45_fomodel4 A B C D)))) ) ).
tt(fc85_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k21_member_1 A B))) ) ).
tt(fc85_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) &  (~ (v1_xboole_0 B)) )  =>  (~ (v2_struct_0 (k25_pcs_0 A B))) ) ) ).
tt(fc85_valued_0,ax, (! [A:$i,B:$i] :  ((v1_membered B) => (v1_valued_0 (k2_zfmisc_1 A B))) ) ).
tt(fc85_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 D E)) & (v1_partfun1 (k45_valued_1 D E) A)) ) ) ).
tt(fc86_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) ) )  => (v1_xboole_0 (k5_xboole_0 (k1_funct_1 (k8_fomodel0 A) (k10_finseq_1 B C)) (k7_finseq_1 B C)))) ) ).
tt(fc86_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) & (m1_subset_1 D (k33_fomodel2 B))) )  => (v1_xboole_0 (k4_xboole_0 A (k47_fomodel4 A B C D)))) ) ).
tt(fc86_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k21_member_1 A B))) ) ).
tt(fc86_valued_0,ax, (! [A:$i,B:$i] :  ((v2_membered B) => (v2_valued_0 (k2_zfmisc_1 A B))) ) ).
tt(fc86_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v3_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 D E)) & (v1_partfun1 (k45_valued_1 D E) A)) ) ) ).
tt(fc87_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) ) ) )  => (v1_xboole_0 (k4_xboole_0 A (k49_fomodel4 A B C D)))) ) ).
tt(fc87_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v1_glib_003 (k13_glib_003 A B C)) & (v3_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc87_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k21_member_1 A B))) ) ).
tt(fc87_valued_0,ax, (! [A:$i,B:$i] :  ((v3_membered B) => (v3_valued_0 (k2_zfmisc_1 A B))) ) ).
tt(fc87_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v4_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 D E)) & (v1_partfun1 (k45_valued_1 D E) A)) ) ) ).
tt(fc88_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v5_fomodel4 B A) & (m1_subset_1 B (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))  &  ((v5_fomodel4 C A) & (m1_subset_1 C (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) )  => (v6_fomodel4 (k2_tarski B C) A)) ) ).
tt(fc88_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v2_glib_003 (k13_glib_003 A B C)) & (v3_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc88_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v1_int_1 B))  => (v5_membered (k21_member_1 A B))) ) ).
tt(fc88_valued_0,ax, (! [A:$i,B:$i] :  ((v4_membered B) => (v5_relat_1 (k2_zfmisc_1 A B) k3_numbers)) ) ).
tt(fc88_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v5_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v5_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k45_valued_1 D E)) & (v1_partfun1 (k45_valued_1 D E) A)) ) ) ).
tt(fc89_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v5_fomodel4 B A) & (m1_subset_1 B (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))  &  ( ((v5_fomodel4 C A) & (m1_subset_1 C (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))  &  ( ((v5_fomodel4 D A) & (m1_subset_1 D (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))  &  ((v5_fomodel4 E A) & (m1_subset_1 E (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) ) ) ) )  => (v6_fomodel4 (k2_enumset1 B C D E) A)) ) ).
tt(fc89_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) &  ((v3_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v3_glib_003 (k13_glib_003 A B C)) & (v7_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc89_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k22_member_1 A B))) ) ).
tt(fc89_valued_0,ax, (! [A:$i,B:$i] :  ((v5_membered B) => (v5_relat_1 (k2_zfmisc_1 A B) k4_numbers)) ) ).
tt(fc89_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k45_valued_1 A B)) &  ((v1_funct_1 (k45_valued_1 A B)) & (v1_finseq_1 (k45_valued_1 A B))) ) ) ) ).
tt(fc8_abcmiz_1,ax, (~ (v1_xboole_0 k19_abcmiz_1)) ).
tt(fc8_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  => (v6_abcmiz_a (k16_abcmiz_1 A) A)) ) ).
tt(fc8_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) &  (~ (v1_abian A)) )  &  ((v1_int_1 B) &  (~ (v1_abian B)) ) )  =>  (~ (v1_abian (k3_xcmplx_0 A B))) ) ) ).
tt(fc8_afinsq_1,ax, (! [A:$i] :  ((v5_ordinal1 (k3_afinsq_1 A)) & (v1_finset_1 (k3_afinsq_1 A))) ) ).
tt(fc8_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A)) )  =>  ( (~ (v7_struct_0 (g2_algstr_0 A B C)))  & (v8_algstr_0 (g2_algstr_0 A B C))) ) ) ).
tt(fc8_algstr_1,ax, ((v29_algstr_0 k3_algstr_1) &  ((v4_vectsp_1 k3_algstr_1) & (v7_algstr_1 k3_algstr_1)) ) ).
tt(fc8_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m1_algstr_4 B A))  => (v2_algstr_4 (u1_struct_0 B) A)) ) ).
tt(fc8_altcat_2,ax, ((v2_struct_0 k5_altcat_2) & (v6_altcat_1 k5_altcat_2)) ).
tt(fc8_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_altcat_4 A)))  &  ((v2_altcat_1 (k5_altcat_4 A)) &  ((v6_altcat_1 (k5_altcat_4 A)) & (v3_altcat_2 (k5_altcat_4 A) A)) ) ) ) ) ).
tt(fc8_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k3_ami_3 A B)))) ) ).
tt(fc8_amistd_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 B) & (v5_funct_1 B (k2_memstr_0 A (k4_amistd_1 A)))) ) ) )  =>  ((v1_relat_1 (k6_memstr_0 A (k4_amistd_1 A) B)) &  ((v4_relat_1 (k6_memstr_0 A (k4_amistd_1 A) B) (u1_struct_0 (k4_amistd_1 A))) &  ((v1_xboole_0 (k6_memstr_0 A (k4_amistd_1 A) B)) &  ((v1_funct_1 (k6_memstr_0 A (k4_amistd_1 A) B)) & (v5_funct_1 (k6_memstr_0 A (k4_amistd_1 A) B) (k2_memstr_0 A (k4_amistd_1 A)))) ) ) ) ) ) ).
tt(fc8_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((v1_extpro_1 (k4_amistd_1 A) A) & (v4_amistd_2 (k4_amistd_1 A) A)) ) ) ).
tt(fc8_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_freealg A))  =>  ( (~ (v2_struct_0 (k7_freealg k19_aofa_000 A)))  &  ((v1_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v2_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v3_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v4_unialg_1 (k7_freealg k19_aofa_000 A)) & (v9_aofa_000 (k7_freealg k19_aofa_000 A))) ) ) ) ) ) ) ).
tt(fc8_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_partfun1 (k7_bagorder A) (k15_pre_poly A)) &  ((v1_relat_2 (k7_bagorder A)) &  ((v4_relat_2 (k7_bagorder A)) &  ((v8_relat_2 (k7_bagorder A)) & (v2_bagorder (k7_bagorder A) A)) ) ) ) ) ) ).
tt(fc8_binop_2,ax, ((v1_funct_1 k46_binop_2) &  ((v1_funct_2 k46_binop_2 (k2_zfmisc_1 k4_numbers k4_numbers) k4_numbers) &  ((v1_binop_1 k46_binop_2 k4_numbers) & (v2_binop_1 k46_binop_2 k4_numbers)) ) ) ).
tt(fc8_borsuk_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k11_borsuk_1 A B)))  &  ((v1_pre_topc (k11_borsuk_1 A B)) & (v2_pre_topc (k11_borsuk_1 A B))) ) ) ) ).
tt(fc8_borsuk_2,ax, ((v8_pre_topc k17_borsuk_1) & (v1_compts_1 k17_borsuk_1)) ).
tt(fc8_borsuk_5,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) &  ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) ) )  =>  (~ (v1_rat_1 (k6_xcmplx_0 B A))) ) ) ).
tt(fc8_borsuk_6,ax, ( (~ (v1_xboole_0 k6_borsuk_6))  & (v4_pre_topc k6_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr))) ).
tt(fc8_borsuk_7,ax, ((v1_funct_1 k12_borsuk_7) &  ((v1_funct_2 k12_borsuk_7 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 3))) & (v5_pre_topc k12_borsuk_7 k3_topmetr (k8_toprealb 3))) ) ).
tt(fc8_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v13_algstr_0 (k5_c0sp2 A)) &  ((v2_rlvect_1 (k5_c0sp2 A)) &  ((v3_rlvect_1 (k5_c0sp2 A)) &  ((v4_rlvect_1 (k5_c0sp2 A)) &  ((v5_rlvect_1 (k5_c0sp2 A)) &  ((v6_rlvect_1 (k5_c0sp2 A)) &  ((v7_rlvect_1 (k5_c0sp2 A)) &  ((v3_group_1 (k5_c0sp2 A)) &  ((v5_group_1 (k5_c0sp2 A)) &  ((v1_vectsp_1 (k5_c0sp2 A)) &  ((v3_vectsp_1 (k5_c0sp2 A)) & (v2_funcsdom (k5_c0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_card_1,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ( (~ (v1_finset_1 (k1_card_1 A)))  & (v1_card_1 (k1_card_1 A))) ) ) ).
tt(fc8_card_3,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k9_card_3 A))) ) ).
tt(fc8_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( (~ (v1_finset_1 (k1_card_5 A)))  & (v1_card_1 (k1_card_5 A))) ) ) ).
tt(fc8_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) &  ((v2_catalg_1 A) & (l1_msualg_1 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finseq_1 (k2_xtuple_0 B))) ) ).
tt(fc8_cayley,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k4_cayley A)) &  ((v1_funct_2 (k4_cayley A) (u1_struct_0 A) (u1_struct_0 (k2_cayley (u1_struct_0 A)))) & (v1_group_6 (k4_cayley A) A (k2_cayley (u1_struct_0 A)))) ) ) ) ).
tt(fc8_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v13_algstr_0 (k5_cc0sp2 A)) &  ((v2_rlvect_1 (k5_cc0sp2 A)) &  ((v3_rlvect_1 (k5_cc0sp2 A)) &  ((v4_rlvect_1 (k5_cc0sp2 A)) &  ((v3_group_1 (k5_cc0sp2 A)) &  ((v5_group_1 (k5_cc0sp2 A)) &  ((v1_vectsp_1 (k5_cc0sp2 A)) &  ((v3_vectsp_1 (k5_cc0sp2 A)) &  ((v2_clvect_1 (k5_cc0sp2 A)) &  ((v3_clvect_1 (k5_cc0sp2 A)) &  ((v4_clvect_1 (k5_cc0sp2 A)) & (v2_cfuncdom (k5_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_partfun1 A k2_numbers) &  ((v2_cfdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v2_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) &  ((v1_partfun1 (k18_valued_1 A B) k2_numbers) & (v2_cfdiff_1 (k18_valued_1 A B))) ) ) ) ).
tt(fc8_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (v4_cgames_1 (k5_finseq_1 A))) ) ).
tt(fc8_circcmb3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_facirc_1 A)) ) )  =>  ( (~ (v11_struct_0 (k5_circcomb B A)))  &  ((v1_msualg_1 (k5_circcomb B A)) & (v6_circcmb3 (k5_circcomb B A))) ) ) ) ).
tt(fc8_circcomb,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v2_struct_0 (k4_circcomb A B C)))  &  ( (~ (v11_struct_0 (k4_circcomb A B C)))  & (v1_msualg_1 (k4_circcomb A B C))) ) ) ) ).
tt(fc8_circtrm1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  & (m1_finseq_1 D (k1_msaterm B C))) )  =>  ((v1_relat_1 (k4_trees_4 A D)) &  ((v1_funct_1 (k4_trees_4 A D)) &  ((v1_finset_1 (k4_trees_4 A D)) & (v3_trees_2 (k4_trees_4 A D))) ) ) ) ) ).
tt(fc8_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v2_rlvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v3_rlvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v4_rlvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v1_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v2_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v3_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) &  ((v4_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B)))) & (v5_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc8_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v10_closure1 B A) & (l1_closure1 B A)) )  => (v5_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc8_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v13_closure2 B A) & (l1_closure2 B A)) )  => (v2_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc8_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_relat_1 (k5_cohsp_1 A))) ) ).
tt(fc8_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k15_coh_sp A))) ) ).
tt(fc8_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  (~ (v1_xboole_0 (k1_compos_0 A))) ) ) ).
tt(fc8_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k7_compos_1 A B C)))  &  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) & (v1_finset_1 (k7_compos_1 A B C))) ) ) ) ) ) ) ).
tt(fc8_comput_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_comput_1 B) & (m1_finseq_1 B (k2_comput_1 A))) )  =>  ((v1_relat_1 (k6_funct_6 B)) &  ((v1_funct_1 (k6_funct_6 B)) & (v2_margrel1 (k6_funct_6 B))) ) ) ) ).
tt(fc8_comseq_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k18_valued_1 A B)) &  ((v1_funct_2 (k18_valued_1 A B) k5_numbers k2_numbers) & (v2_comseq_2 (k18_valued_1 A B))) ) ) ) ).
tt(fc8_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k3_comseq_3 A)) &  ((v1_funct_2 (k3_comseq_3 A) k5_numbers k1_numbers) & (v1_series_1 (k3_comseq_3 A))) ) ) ) ).
tt(fc8_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_csspace4 A B)))  &  ((v13_algstr_0 (k5_csspace4 A B)) &  ((v2_rlvect_1 (k5_csspace4 A B)) &  ((v3_rlvect_1 (k5_csspace4 A B)) &  ((v4_rlvect_1 (k5_csspace4 A B)) &  ((v1_clvect_1 (k5_csspace4 A B)) &  ((v2_clvect_1 (k5_csspace4 A B)) &  ((v3_clvect_1 (k5_csspace4 A B)) &  ((v4_clvect_1 (k5_csspace4 A B)) & (v5_clvect_1 (k5_csspace4 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 k1_xboole_0 A)) & (v3_dickson (k5_yellow_1 k1_xboole_0 A))) ) ) ).
tt(fc8_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) => (v2_dilworth (k6_dilworth A) A)) ) ).
tt(fc8_euclid_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v1_xboole_0 (k8_euclid_7 A))) ) ) ).
tt(fc8_euclid_9,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) )  =>  ((v1_relat_1 (k54_valued_1 B)) &  ((v1_funct_1 (k54_valued_1 B)) &  ((v3_valued_0 (k54_valued_1 B)) & (v3_card_1 (k54_valued_1 B) A)) ) ) ) ) ).
tt(fc8_euclid,ax, (! [A:$i,B:$i] :  ((v7_ordinal1 A) => (v3_finseq_1 (k4_finseq_2 A B))) ) ).
tt(fc8_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  => (v5_relat_1 (k10_funct_7 B C D) A)) ) ).
tt(fc8_facirc_1,ax, (! [A:$i] :  ((v1_xtuple_0 A) => (v1_relat_1 (k1_tarski A))) ) ).
tt(fc8_fcont_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k5_relat_1 A B)) & (v2_fcont_1 (k5_relat_1 A B))) ) ) ).
tt(fc8_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v18_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v19_lattices (k3_filter_2 A B) (k1_lattice2 A))) ) ).
tt(fc8_finseq_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k10_finseq_1 A B)) & (v1_funct_1 (k10_finseq_1 A B))) ) ).
tt(fc8_finseq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k13_finseq_1 A)) & (v7_ordinal1 C))  =>  ((v1_relat_1 (k7_partfun1 (k13_finseq_1 A) B C)) &  ((v5_relat_1 (k7_partfun1 (k13_finseq_1 A) B C) A) &  ((v1_funct_1 (k7_partfun1 (k13_finseq_1 A) B C)) & (v1_finseq_1 (k7_partfun1 (k13_finseq_1 A) B C))) ) ) ) ) ).
tt(fc8_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((v1_relat_1 (k3_finseq_5 A)) &  ((v1_funct_1 (k3_finseq_5 A)) &  ((v2_funct_1 (k3_finseq_5 A)) & (v1_finseq_1 (k3_finseq_5 A))) ) ) ) ) ).
tt(fc8_finset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] : (v1_finset_1 (k6_enumset1 A B C D E F G H))) ).
tt(fc8_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) &  ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B)) )  => (v1_xboole_0 (k4_finseq_2 B A))) ) ).
tt(fc8_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_xboole_0 (k4_xboole_0 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ).
tt(fc8_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v7_ordinal1 C) &  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v3_card_1 D C) & (v1_finseq_1 D)) ) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) )  => (v3_card_1 (k3_relat_1 D E) C)) ) ).
tt(fc8_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D)) ) ) )  => (v1_partfun1 (k8_fomodel3 A B C D) (k4_finseq_2 D A))) ) ).
tt(fc8_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)))))) )  => (v2_fomodel4 (k1_funct_1 (k3_fomodel4 B C A) D) B)) ) ).
tt(fc8_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  &  ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) ) ) )  =>  ( (~ (v2_struct_0 (k13_fsm_1 A B C D)))  &  ((v8_struct_0 (k13_fsm_1 A B C D)) & (v2_fsm_1 (k13_fsm_1 A B C D) A B)) ) ) ) ).
tt(fc8_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B)) ) )  =>  ( (~ (v2_struct_0 (g1_fsm_3 A B (u1_struct_0 C) (u1_rewrite3 B C) (u1_fsm_3 A B C))))  & (v1_fsm_3 (g1_fsm_3 A B (u1_struct_0 C) (u1_rewrite3 B C) (u1_fsm_3 A B C)) A B)) ) ) ).
tt(fc8_funcop_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) ).
tt(fc8_funct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_relat_1 (k5_relat_1 A B)) & (v1_funct_1 (k5_relat_1 A B))) ) ) ).
tt(fc8_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) )  =>  ((v1_funct_1 (k3_relat_1 D E)) & (v1_funct_2 (k3_relat_1 D E) A C)) ) ) ).
tt(fc8_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k1_funct_4 B C)) &  ((v4_relat_1 (k1_funct_4 B C) A) &  ((v1_funct_1 (k1_funct_4 B C)) & (v1_partfun1 (k1_funct_4 B C) A)) ) ) ) ) ).
tt(fc8_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k2_funct_7 A B C)) &  ((v1_funct_1 (k2_funct_7 A B C)) & (v1_finseq_1 (k2_funct_7 A B C))) ) ) ) ).
tt(fc8_funct_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_funct_9 A)) ) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k7_valued_1 A B)) &  ((v1_funct_1 (k7_valued_1 A B)) & (v2_funct_9 (k7_valued_1 A B))) ) ) ) ).
tt(fc8_gate_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xboole_0 B))  => (v1_xboole_0 (k4_gate_1 A B))) ) ).
tt(fc8_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v5_glib_001 B A) & (m3_glib_001 B A)) )  => (v5_glib_001 (k6_glib_001 A B) A)) ) ).
tt(fc8_graph_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k5_graph_3 A B))) ) ).
tt(fc8_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v13_vectsp_1 (k3_struct_0 A) A A)) ) ) ) ).
tt(fc8_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v15_algstr_0 (k6_group_2 A)) & (v1_gr_cy_1 (k6_group_2 A))) ) ) ).
tt(fc8_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((v1_funct_1 (k7_group_6 A B)) &  ((v1_funct_2 (k7_group_6 A B) (u1_struct_0 A) (u1_struct_0 B)) & (v1_group_6 (k7_group_6 A B) A B)) ) ) ) ).
tt(fc8_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_partfun1 (k5_finseq_1 A) (k1_tarski 1)) & (v1_group_7 (k5_finseq_1 A))) ) ) ).
tt(fc8_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v1_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k1_hermitan A B)) &  ((v1_funct_2 (k1_hermitan A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (v1_hahnban1 (k1_hermitan A B) k1_complfld A)) ) ) ) ).
tt(fc8_hilbert3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  &  ((m1_hilbert3 B A) & (m1_subset_1 C k1_hilbert1)) )  =>  ((v1_funct_1 (k5_hilbert3 A B C)) &  ((v1_funct_2 (k5_hilbert3 A B C) (k3_hilbert3 A C) (k3_hilbert3 A C)) & (v3_funct_2 (k5_hilbert3 A B C) (k3_hilbert3 A C) (k3_hilbert3 A C))) ) ) ) ).
tt(fc8_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k10_ideal_1 A B C))) ) ) ).
tt(fc8_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) =>  ((v1_relat_1 (k1_xtuple_0 C)) & (v1_funct_1 (k1_xtuple_0 C))) ) ) ).
tt(fc8_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  ((v7_ordinal1 (k19_rvsum_1 A)) &  ((v1_xcmplx_0 (k19_rvsum_1 A)) & (v2_xxreal_0 (k19_rvsum_1 A))) ) ) ) ).
tt(fc8_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ( (~ (v2_struct_0 (k21_interva1 A)))  & (v3_lattices (k21_interva1 A))) ) ) ).
tt(fc8_intpro_1,ax,(v10_intpro_1 k14_intpro_1)).
tt(fc8_isomichi,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_xboole_0 (k1_isomichi A (k1_isomichi A B)))) ) ).
tt(fc8_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_pre_topc (k7_topreal1 A) (k15_euclid 2))) ) ).
tt(fc8_jordan23,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_finseq_6 B A) &  ((v2_jordan23 B) & (m1_finseq_1 B A)) )  & (m1_subset_1 C A)) )  => (v2_jordan23 (k1_finseq_6 A B C))) ) ).
tt(fc8_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v2_connsp_1 (k2_jordan2c 2 A) (k15_euclid 2))) ) ).
tt(fc8_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(fc8_kurato_1,ax,(v1_setfam_1 (k2_kurato_1 k3_topmetr k6_kurato_1))).
tt(fc8_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v3_lattices (k1_lattice2 A)) & (v10_lattices (k1_lattice2 A))) ) ) ).
tt(fc8_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_lattice3 A)))  &  ((v3_lattices (k14_lattice3 A)) &  ((v10_lattices (k14_lattice3 A)) & (v4_lattice3 (k14_lattice3 A))) ) ) ) ) ).
tt(fc8_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v3_lexbfs (k26_lexbfs A))) ) ).
tt(fc8_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v13_algstr_0 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v1_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v2_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v3_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v4_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v5_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v6_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) &  ((v7_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)))) & (v8_rlvect_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(fc8_lpspace2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_lpspace2 A) & (m1_subset_1 A k1_numbers))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k12_lpspace2 B C D A)))  &  ((v13_algstr_0 (k12_lpspace2 B C D A)) &  ((v2_rlvect_1 (k12_lpspace2 B C D A)) &  ((v3_rlvect_1 (k12_lpspace2 B C D A)) &  ((v4_rlvect_1 (k12_lpspace2 B C D A)) &  ((v5_rlvect_1 (k12_lpspace2 B C D A)) &  ((v6_rlvect_1 (k12_lpspace2 B C D A)) &  ((v7_rlvect_1 (k12_lpspace2 B C D A)) &  ((v8_rlvect_1 (k12_lpspace2 B C D A)) &  ((v3_normsp_0 (k12_lpspace2 B C D A)) &  ((v4_normsp_0 (k12_lpspace2 B C D A)) & (v2_normsp_1 (k12_lpspace2 B C D A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_lukasi_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_cqc_lang A)) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A (k8_cqc_lang A B C) D) (k8_cqc_lang A C D)) A)) ) ).
tt(fc8_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_margrel1 B A) & (m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A))) )  => (v2_margrel1 (k1_funct_1 B C))) ) ).
tt(fc8_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((v1_relat_1 (k15_finseq_1 A)) &  ((v1_funct_1 (k15_finseq_1 A)) & (v1_valued_0 (k15_finseq_1 A))) ) ) ) ).
tt(fc8_matrtop3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v2_matrtop3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v2_matrtop3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) ) )  =>  ((v1_funct_1 (k3_relat_1 C B)) &  ((v1_funct_2 (k3_relat_1 C B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (v2_matrtop3 (k3_relat_1 C B) A)) ) ) ) ).
tt(fc8_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_normsp_1 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v1_mazurulm (k3_struct_0 A) A A)) ) ) ) ).
tt(fc8_member_1,ax, (! [A:$i] :  ((v4_membered A) =>  ((v1_membered (k5_member_1 A)) & (v4_membered (k5_member_1 A))) ) ) ).
tt(fc8_membered,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v2_membered (k1_tarski A))) ) ).
tt(fc8_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((l1_memstr_0 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((v1_relat_1 (k6_memstr_0 A B C)) &  ((v4_relat_1 (k6_memstr_0 A B C) (u1_struct_0 B)) &  ((v1_funct_1 (k6_memstr_0 A B C)) &  ((v5_funct_1 (k6_memstr_0 A B C) (k2_memstr_0 A B)) & (v4_memstr_0 (k6_memstr_0 A B C) A B)) ) ) ) ) ) ).
tt(fc8_metrizts,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 (k15_euclid A)) (u1_pre_topc (k15_euclid A)))) & (v5_waybel23 (g1_pre_topc (u1_struct_0 (k15_euclid A)) (u1_pre_topc (k15_euclid A))))) ) ) ).
tt(fc8_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) & (l6_algstr_0 A)) )  =>  ((v13_algstr_0 (k2_mod_4 A)) & (v36_algstr_0 (k2_mod_4 A))) ) ) ).
tt(fc8_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (~ (v1_xboole_0 (u3_modelc_1 A))) ) ) ).
tt(fc8_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  (~ (v1_xboole_0 (k13_modelc_2 A))) ) ) ).
tt(fc8_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v1_moebius1 (k6_moebius1 A))) ) ) ).
tt(fc8_msafree1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (u3_msualg_1 A (k11_msafree A B))) &  ((v4_relat_1 (u3_msualg_1 A (k11_msafree A B)) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A (k11_msafree A B))) &  ((v1_partfun1 (u3_msualg_1 A (k11_msafree A B)) (u1_struct_0 A)) & (v1_prob_2 (u3_msualg_1 A (k11_msafree A B)))) ) ) ) ) ) ).
tt(fc8_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v1_relat_1 (k8_msafree A B)) &  ((v2_relat_1 (k8_msafree A B)) &  ((v4_relat_1 (k8_msafree A B) (u1_struct_0 A)) &  ((v1_funct_1 (k8_msafree A B)) & (v1_partfun1 (k8_msafree A B) (u1_struct_0 A))) ) ) ) ) ) ).
tt(fc8_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v2_finset_1 C)) ) ) ) )  =>  ((v1_relat_1 (k3_pboole A C B)) &  ((v4_relat_1 (k3_pboole A C B) A) &  ((v1_funct_1 (k3_pboole A C B)) &  ((v1_partfun1 (k3_pboole A C B) A) & (v2_finset_1 (k3_pboole A C B))) ) ) ) ) ) ).
tt(fc8_msualg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  & (l3_msualg_1 B A))  =>  (~ (v1_xboole_0 (k6_msualg_2 A B))) ) ) ).
tt(fc8_mycielsk,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  =>  ((v8_struct_0 (k3_necklace A)) & (v1_orders_2 (k3_necklace A))) ) ) ).
tt(fc8_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A C)) &  ((v4_relat_1 (k3_relat_1 A C) k5_numbers) &  ((v5_relat_1 (k3_relat_1 A C) B) & (v1_funct_1 (k3_relat_1 A C))) ) ) ) ) ).
tt(fc8_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k5_nat_3 A B C)) &  ((v4_relat_1 (k5_nat_3 A B C) A) &  ((v1_funct_1 (k5_nat_3 A B C)) &  ((v1_partfun1 (k5_nat_3 A B C) A) & (v3_valued_0 (k5_nat_3 A B C))) ) ) ) ) ) ).
tt(fc8_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_necklace A) & (l1_orders_2 A))  &  ((v1_necklace B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k2_neckla_2 A B)) & (v1_necklace (k2_neckla_2 A B))) ) ) ).
tt(fc8_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (u1_struct_0 (k4_necklace A)))) ) ).
tt(fc8_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v2_xxreal_0 (k3_newton A))) ) ).
tt(fc8_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v2_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v2_nfcont_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_funct_1 (k2_vfunct_1 k1_numbers A B C)) & (v2_nfcont_3 (k2_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc8_nfcont_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 B) &  ((v2_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k9_integr15 A C k1_numbers B)) & (v2_nfcont_4 (k9_integr15 A C k1_numbers B) A)) ) ) ).
tt(fc8_numbers,ax, (~ (v1_finset_1 k1_numbers)) ).
tt(fc8_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ( (~ (v2_struct_0 (k15_openlatt A)))  &  ((v10_lattices (k15_openlatt A)) & (v11_lattices (k15_openlatt A))) ) ) ) ).
tt(fc8_oposet_1,ax, ((v2_necklace k2_oposet_1) & (v3_qmax_1 k2_oposet_1)) ).
tt(fc8_orders_2,ax, (! [A:$i,B:$i] :  ( ((v4_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_orders_2 (g1_orders_2 A B)) & (v5_orders_2 (g1_orders_2 A B))) ) ) ).
tt(fc8_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v3_ordinal1 (k3_ordinal5 A)) & (v4_ordinal5 (k3_ordinal5 A))) ) ) ).
tt(fc8_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  ((v1_relat_1 (k1_wellord2 A)) & (v2_wellord1 (k1_wellord2 A))) ) ) ).
tt(fc8_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k21_osafree A B C))) ) ) ).
tt(fc8_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  ( (~ (v2_struct_0 (k16_osalg_2 A B)))  &  ((v3_lattices (k16_osalg_2 A B)) &  ((v10_lattices (k16_osalg_2 A B)) & (v15_lattices (k16_osalg_2 A B))) ) ) ) ) ).
tt(fc8_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 B) & (v3_xxreal_0 B))  => (v2_partfun3 (k2_funcop_1 A B))) ) ).
tt(fc8_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  &  ((v3_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  => (v3_relat_2 (k3_pcs_0 A A B B C D))) ) ).
tt(fc8_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xreal_0 C) &  ((v1_xreal_0 D) & (v1_xreal_0 E)) ) ) )  => (v1_xreal_0 (k9_polyeq_1 A B C D E))) ) ).
tt(fc8_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v3_rlvect_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc8_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) )  =>  ((v1_funct_1 (k11_polynom3 A B C)) &  ((v1_funct_2 (k11_polynom3 A B C) k5_numbers (u1_struct_0 A)) & (v1_algseq_1 (k11_polynom3 A B C) A)) ) ) ) ).
tt(fc8_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A B))) ) )  =>  ((v1_relat_1 (k2_funct_4 C)) &  ((v4_relat_1 (k2_funct_4 C) (k2_zfmisc_1 B A)) & (v1_funct_1 (k2_funct_4 C))) ) ) ) ).
tt(fc8_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_relat_1 (k1_card_3 A)) &  ((v1_funct_1 (k1_card_3 A)) &  ((v1_card_3 (k1_card_3 A)) & (v1_finseq_1 (k1_card_3 A))) ) ) ) ) ).
tt(fc8_pre_topc,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v2_struct_0 (k1_pre_topc A B)) & (v1_pre_topc (k1_pre_topc A B))) ) ) ).
tt(fc8_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v3_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v3_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc8_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k16_pscomp_1 A)))  & (v2_compts_1 (k16_pscomp_1 A) (k15_euclid 2))) ) ) ).
tt(fc8_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_xreal_0 (k13_quaterni A))) ) ).
tt(fc8_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v6_struct_0 (k19_quofield A)))  &  ((v33_algstr_0 (k19_quofield A)) &  ((v36_algstr_0 (k19_quofield A)) &  ((v2_rlvect_1 (k19_quofield A)) &  ((v3_group_1 (k19_quofield A)) & (v5_vectsp_1 (k19_quofield A))) ) ) ) ) ) ) ).
tt(fc8_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ( (~ (v6_struct_0 (k14_polynom3 A)))  & (v36_algstr_0 (k14_polynom3 A))) ) ) ) ).
tt(fc8_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (v3_xxreal_2 (k10_prob_1 A)))  &  ((v4_xxreal_2 (k10_prob_1 A)) & (v6_xxreal_2 (k10_prob_1 A))) ) ) ) ).
tt(fc8_relat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 A))  =>  (~ (v1_xboole_0 (k9_xtuple_0 A))) ) ) ).
tt(fc8_relat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_relat_2 A))  & (v1_relat_1 B))  => (v2_relat_2 (k4_xboole_0 A B))) ) ).
tt(fc8_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))) => (v1_relat_1 (k9_xtuple_0 D))) ) ).
tt(fc8_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) & (m1_subset_1 C (k8_afinsq_1 A))) )  =>  (~ (v1_xboole_0 (k8_rewrite2 A B C))) ) ) ).
tt(fc8_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_seq_2 A)) ) )  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) &  ((v3_valued_0 (k24_valued_1 A B)) & (v1_seq_2 (k24_valued_1 A B))) ) ) ) ) ).
tt(fc8_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_rusub_4 (k4_rlaffin1 A B) A)) ) ).
tt(fc8_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v3_pre_topc (k6_rusub_4 A C B) A)) ) ).
tt(fc8_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ( (~ (v2_struct_0 (k8_robbins1 A)))  & (v4_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc8_robbins4,ax, ((v14_lattices k2_robbins4) & (v4_robbins1 k2_robbins4)) ).
tt(fc8_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v4_roughs_1 (k4_roughs_1 A B) A)) ) ) ).
tt(fc8_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_rsspace4 A B)))  &  ((v13_algstr_0 (k5_rsspace4 A B)) &  ((v1_rlvect_1 (k5_rsspace4 A B)) &  ((v2_rlvect_1 (k5_rsspace4 A B)) &  ((v3_rlvect_1 (k5_rsspace4 A B)) &  ((v4_rlvect_1 (k5_rsspace4 A B)) &  ((v5_rlvect_1 (k5_rsspace4 A B)) &  ((v6_rlvect_1 (k5_rsspace4 A B)) &  ((v7_rlvect_1 (k5_rsspace4 A B)) & (v8_rlvect_1 (k5_rsspace4 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_xcmplx_0 (k16_rvsum_1 A)) & (v1_xreal_0 (k16_rvsum_1 A))) ) ) ).
tt(fc8_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k7_scmfsa_2 A B)))) ) ).
tt(fc8_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v2_extpro_1 (k8_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc8_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v4_compos_0 (k16_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc8_scmfsa6c,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_scmfsa6c (k10_scmfsa_2 A B))) ) ).
tt(fc8_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) ) ) ) )  =>  ( (~ (v1_xboole_0 (k4_scmfsa8b C D A B)))  &  ((v1_relat_1 (k4_scmfsa8b C D A B)) &  ((v4_relat_1 (k4_scmfsa8b C D A B) k5_numbers) &  ((v5_relat_1 (k4_scmfsa8b C D A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k4_scmfsa8b C D A B)) &  ((v1_finset_1 (k4_scmfsa8b C D A B)) &  ((v1_afinsq_1 (k4_scmfsa8b C D A B)) & (v7_amistd_1 (k4_scmfsa8b C D A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc8_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v7_ordinal1 B))  =>  ((v1_relat_1 (k16_funcop_1 A B)) &  ((v4_relat_1 (k16_funcop_1 A B) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k16_funcop_1 A B)) &  ((v5_funct_1 (k16_funcop_1 A B) (k2_memstr_0 3 k1_scmfsa_2)) & (v4_memstr_0 (k16_funcop_1 A B) 3 k1_scmfsa_2)) ) ) ) ) ) ).
tt(fc8_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa6a B A)))  &  ((v1_relat_1 (k5_scmfsa6a B A)) &  ((v4_relat_1 (k5_scmfsa6a B A) k5_numbers) &  ((v5_relat_1 (k5_scmfsa6a B A) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa6a B A)) &  ((v1_finset_1 (k5_scmfsa6a B A)) &  ((v1_afinsq_1 (k5_scmfsa6a B A)) & (v2_scm_halt (k5_scmfsa6a B A))) ) ) ) ) ) ) ) ) ).
tt(fc8_scmpds_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v4_scmpds_4 (k16_scmpds_2 A B C D))) ) ).
tt(fc8_scmpds_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 B) & (v1_int_1 C)) )  => (v6_compos_0 (k11_scmpds_2 A B C) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc8_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v2_compos_1 A k1_scmpds_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k5_scmpds_6 B C A)))  &  ((v1_relat_1 (k5_scmpds_6 B C A)) &  ((v4_relat_1 (k5_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k5_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k5_scmpds_6 B C A)) &  ((v1_finset_1 (k5_scmpds_6 B C A)) &  ((v1_afinsq_1 (k5_scmpds_6 B C A)) & (v2_compos_1 (k5_scmpds_6 B C A) k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(fc8_scmring2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_subset_1 B k5_numbers))  =>  (~ (v2_extpro_1 (k8_scmring2 A B) 2 (k1_scmring2 A))) ) ) ).
tt(fc8_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k4_scmring2 A B C)))) ) ).
tt(fc8_scmyciel,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (v3_scmyciel B A))  => (v3_scmyciel (k4_xboole_0 B C) A)) ) ).
tt(fc8_setfam_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) )  => (v1_setfam_1 (k5_enumset1 A B C D E F G))) ) ).
tt(fc8_sfmastr1,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  => (v1_sfmastr1 (k13_scmfsa_2 B A))) ) ).
tt(fc8_simplex0,ax, (! [A:$i] :  ((v5_finset_1 A) =>  ((v5_finset_1 (k1_simplex0 A)) & (v1_classes1 (k1_simplex0 A))) ) ) ).
tt(fc8_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  =>  ((v1_relat_1 (k5_relat_1 (k2_rlaffin2 A) (u1_pre_topc B))) & (v2_funct_1 (k5_relat_1 (k2_rlaffin2 A) (u1_pre_topc B)))) ) ) ).
tt(fc8_sincos10,ax, ((v1_funct_1 k4_sincos10) & (v2_funct_1 k4_sincos10)) ).
tt(fc8_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k1_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))))) ).
tt(fc8_sin_cos,ax, ((v1_funct_1 k24_sin_cos) &  ((v1_funct_2 k24_sin_cos k1_numbers k1_numbers) & (v1_fcont_1 k24_sin_cos)) ) ).
tt(fc8_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v1_topreal1 (k5_finseq_1 A))) ) ).
tt(fc8_sprect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) )  => (v4_xxreal_2 (k7_relat_1 C B))) ) ).
tt(fc8_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_stacks_1 A)))  &  ( (~ (v11_struct_0 (k8_stacks_1 A)))  &  ((v1_stacks_1 (k8_stacks_1 A)) & (v6_stacks_1 (k8_stacks_1 A))) ) ) ) ) ).
tt(fc8_struct_0,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  => (v1_finset_1 (u1_struct_0 A))) ) ).
tt(fc8_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  (~ (v1_xboole_0 (k7_enumset1 A B C D E F G H I))) ) ).
tt(fc8_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k1_tex_4 A B))) ) ) ).
tt(fc8_topalg_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  =>  ((v7_struct_0 (k5_topalg_1 (k15_euclid A) B)) & (v15_algstr_0 (k5_topalg_1 (k15_euclid A) B))) ) ) ).
tt(fc8_topalg_5,ax, ((v1_funct_1 k7_topalg_5) &  ((v1_funct_2 k7_topalg_5 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb))) & (v1_group_6 k7_topalg_5 k2_gr_cy_1 (k5_topalg_1 (k8_toprealb 2) k9_toprealb))) ) ).
tt(fc8_topalg_6,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_topalg_6 A)))  => (v3_membered (k9_xtuple_0 B))) ) ).
tt(fc8_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_tops_2 (k1_openlatt A) A) & (v1_topgen_4 (k1_openlatt A) A)) ) ) ).
tt(fc8_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v15_algstr_0 (k5_topgrp_1 A)) &  ((v2_group_1 (k5_topgrp_1 A)) & (v3_group_1 (k5_topgrp_1 A))) ) ) ) ).
tt(fc8_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v9_rltopsp1 (k1_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc8_topreala,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k1_xxreal_1 (k6_xcmplx_0 A B) A))) ) ) ).
tt(fc8_toprealb,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  & (v1_xreal_0 B))  =>  ((v1_funct_1 (k1_fcont_1 A B)) &  ((v2_funct_1 (k1_fcont_1 A B)) &  ((v1_funct_2 (k1_fcont_1 A B) k1_numbers k1_numbers) & (v2_funct_2 (k1_fcont_1 A B) k1_numbers)) ) ) ) ) ).
tt(fc8_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v5_rltopsp1 (k15_euclid A)) & (v2_toprealc (k15_euclid A))) ) ) ).
tt(fc8_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_xboole_0 (k1_tops_1 A (k1_struct_0 A)))) ) ).
tt(fc8_trees_1,ax, ( (~ (v1_xboole_0 k8_trees_1))  & (v1_trees_1 k8_trees_1)) ).
tt(fc8_trees_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v6_trees_3 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v6_trees_3 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_finseq_1 (k7_finseq_1 A B)) & (v6_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc8_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  ( (~ (v1_xboole_0 (k9_trees_9 A)))  & (v3_trees_3 (k9_trees_9 A))) ) ) ).
tt(fc8_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v2_valued_0 A))  &  ((v1_relat_1 B) & (v2_valued_0 B)) )  => (v2_valued_0 (k2_xboole_0 A B))) ) ).
tt(fc8_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v3_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 D E)) & (v1_partfun1 (k1_valued_1 D E) A)) ) ) ).
tt(fc8_vectsp10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A)) )  =>  ((v1_funct_1 (k7_hahnban1 A B)) &  ((v3_funct_1 (k7_hahnban1 A B)) & (v1_funct_2 (k7_hahnban1 A B) (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ).
tt(fc8_vectsp_1,ax, ( (~ (v6_struct_0 k2_vectsp_1))  &  ((v13_algstr_0 k2_vectsp_1) &  ((v33_algstr_0 k2_vectsp_1) &  ((v36_algstr_0 k2_vectsp_1) &  ((v2_rlvect_1 k2_vectsp_1) &  ((v3_rlvect_1 k2_vectsp_1) &  ((v4_rlvect_1 k2_vectsp_1) &  ((v3_group_1 k2_vectsp_1) &  ((v5_group_1 k2_vectsp_1) &  ((v3_vectsp_1 k2_vectsp_1) &  ((v5_vectsp_1 k2_vectsp_1) & (v6_vectsp_1 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ).
tt(fc8_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k5_waybel_0 A B)))  & (v1_waybel_0 (k5_waybel_0 A B) A)) ) ) ).
tt(fc8_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_orders_2 (k5_yellow_0 A (k2_struct_0 A))) &  ((v4_yellow_0 (k5_yellow_0 A (k2_struct_0 A)) A) &  ((v7_yellow_0 (k5_yellow_0 A (k2_struct_0 A)) A) & (v8_yellow_0 (k5_yellow_0 A (k2_struct_0 A)) A)) ) ) ) ) ).
tt(fc8_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v2_struct_0 (k4_waybel11 A B)))  & (v6_waybel_0 (k4_waybel11 A B) A)) ) ) ).
tt(fc8_waybel17,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ( (~ (v2_struct_0 D))  &  ((v8_waybel_0 D A) & (l1_waybel_0 D A)) ) ) ) )  =>  ((v6_waybel_0 (k6_waybel_9 A B C D) B) & (v8_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ).
tt(fc8_waybel18,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  => (v4_waybel_3 (k2_funcop_1 A B))) ) ).
tt(fc8_waybel_1,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v1_funct_1 (k4_waybel_1 A B)) &  ((v1_funct_2 (k4_waybel_1 A B) (u1_struct_0 A) (u1_struct_0 A)) & (v5_orders_3 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(fc8_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v2_waybel23 (k2_waybel_3 A B) A)) ) ).
tt(fc8_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) & (l1_waybel_9 B)) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v3_orders_2 (k3_waybel24 A B))) ) ) ).
tt(fc8_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v5_orders_2 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc8_waybel_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  ((v1_funct_1 (k5_waybel_2 A)) &  ((v1_funct_2 (k5_waybel_2 A) (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (v5_orders_3 (k5_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ) ).
tt(fc8_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((v9_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A)) &  ((v16_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A)) & (v21_functor0 (k7_waybel34 A) (k5_waybel34 A) (k4_waybel34 A))) ) ) ) ).
tt(fc8_waybel_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  (~ (v2_struct_0 (k1_funct_1 B C))) ) ) ).
tt(fc8_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k3_waybel_4 A))) & (v1_yellow_0 (k2_yellow_1 (k3_waybel_4 A)))) ) ) ).
tt(fc8_waybel_8,ax, (! [A:$i] :  ( ((v2_lattice3 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v2_lattice3 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc8_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k9_xboolean A B))) ) ).
tt(fc8_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xcmplx_0 B)) )  =>  (~ (v1_xboole_0 (k3_xcmplx_0 A B))) ) ) ).
tt(fc8_xreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v1_xreal_0 (k7_xcmplx_0 A B))) ) ).
tt(fc8_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k13_xtuple_0 A))) ) ).
tt(fc8_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (v1_xboole_0 (k4_xxreal_1 A A))) ) ).
tt(fc8_xxreal_2,ax, (! [A:$i] :  ( ((v4_membered A) & (v2_xxreal_2 A))  =>  ((v1_xxreal_0 (k1_xxreal_2 A)) & (v1_rat_1 (k1_xxreal_2 A))) ) ) ).
tt(fc8_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v3_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v3_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) &  (~ (v3_xxreal_0 (k1_xxreal_3 A B))) ) ) ) ).
tt(fc8_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v25_waybel_0 B) &  ((v2_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v2_waybel_3 (k3_yellow_3 A B))) ) ) ).
tt(fc8_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v9_functor0 (k5_yellow18 A) A (k4_yellow18 A)) &  ((v15_functor0 (k5_yellow18 A) A (k4_yellow18 A)) & (v21_functor0 (k5_yellow18 A) A (k4_yellow18 A))) ) ) ) ).
tt(fc8_yellow_1,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v3_lattice3 (k3_yellow_1 A))) ) ).
tt(fc8_yellow21,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v2_setfam_1 A))  &  ((m1_subset_1 B (u1_struct_0 (k6_yellow21 A))) & (m1_subset_1 C (u1_struct_0 (k6_yellow21 A)))) )  =>  (~ (v1_xboole_0 (k1_altcat_1 (k6_yellow21 A) B C))) ) ) ).
tt(fc8_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_funct_1 (k3_yellow_2 A)) &  ((v1_funct_2 (k3_yellow_2 A) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (v5_orders_3 (k3_yellow_2 A) A (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(fc8_yellow_3,ax, (! [A:$i,B:$i] :  ( ( ((v2_lattice3 A) & (l1_orders_2 A))  &  ((v2_lattice3 B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v2_lattice3 (k3_yellow_3 A B))) ) ) ).
tt(fc8_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  &  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v12_waybel_0 (k3_yellow_4 A B C) A)) ) ).
tt(fc8_yellow_6,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v7_waybel_0 (k3_yellow_1 A))) ) ).
tt(fc8_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_orders_2 (k7_lattice3 A)) & (v2_waybel_1 (k7_lattice3 A))) ) ) ).
tt(fc8_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v6_waybel_0 (k3_waybel_9 (k5_yellow_0 A B)) (k5_yellow_0 A B)) & (v7_waybel_0 (k3_waybel_9 (k5_yellow_0 A B)))) ) ) ).
tt(fc90_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v6_fomodel4 (k37_fomodel4 A) A)) ) ).
tt(fc90_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  & (v1_xxreal_0 B))  =>  (~ (v1_xboole_0 (k22_member_1 A B))) ) ) ).
tt(fc90_valued_0,ax, (! [A:$i,B:$i] :  ((v6_membered B) => (v4_valued_0 (k2_zfmisc_1 A B))) ) ).
tt(fc90_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) ) )  =>  ((v1_relat_1 (k50_valued_1 A B)) &  ((v1_funct_1 (k50_valued_1 A B)) & (v1_valued_0 (k50_valued_1 A B))) ) ) ) ).
tt(fc91_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v1_orders_4 A) &  ((v11_fomodel1 A) & (l1_fomodel1 A)) ) )  => (v4_card_3 (k27_fomodel2 A))) ) ).
tt(fc91_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) &  ((v3_glib_003 A) & (v9_glib_003 A)) ) ) ) ) ) )  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v3_glib_003 (k13_glib_003 A B C)) & (v9_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc91_member_1,ax, (! [A:$i,B:$i] :  ( ((v2_membered A) & (v1_xxreal_0 B))  => (v2_membered (k22_member_1 A B))) ) ).
tt(fc91_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v5_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v5_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v5_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc91_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  =>  ((v1_relat_1 (k50_valued_1 A B)) &  ((v1_funct_1 (k50_valued_1 A B)) & (v3_valued_0 (k50_valued_1 A B))) ) ) ) ).
tt(fc92_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_003 A) & (v10_glib_003 A)) ) ) ) ) )  & (m1_subset_1 C k1_numbers))  =>  ((v1_relat_1 (k13_glib_003 A B C)) &  ((v4_relat_1 (k13_glib_003 A B C) k5_numbers) &  ((v1_funct_1 (k13_glib_003 A B C)) &  ((v1_finset_1 (k13_glib_003 A B C)) &  ((v1_glib_000 (k13_glib_003 A B C)) &  ((v3_glib_003 (k13_glib_003 A B C)) & (v10_glib_003 (k13_glib_003 A B C))) ) ) ) ) ) ) ) ).
tt(fc92_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xcmplx_0 B))  => (v1_xboole_0 (k23_member_1 A B))) ) ).
tt(fc92_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v7_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v7_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v7_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc92_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B k3_numbers) & (v1_funct_1 B)) ) )  =>  ((v1_relat_1 (k50_valued_1 A B)) &  ((v5_relat_1 (k50_valued_1 A B) k3_numbers) & (v1_funct_1 (k50_valued_1 A B))) ) ) ) ).
tt(fc93_member_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_membered A))  & (v1_xcmplx_0 B))  =>  (~ (v1_xboole_0 (k23_member_1 A B))) ) ) ).
tt(fc93_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v6_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v6_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v5_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc93_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k50_valued_1 D E)) & (v1_partfun1 (k50_valued_1 D E) A)) ) ) ).
tt(fc94_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_membered A) & (v1_xcmplx_0 B))  => (v1_membered (k23_member_1 A B))) ) ).
tt(fc94_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v8_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v8_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v7_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc94_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v3_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k50_valued_1 D E)) & (v1_partfun1 (k50_valued_1 D E) A)) ) ) ).
tt(fc95_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  => (v3_membered (k23_member_1 A B))) ) ).
tt(fc95_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v6_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v5_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v6_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc95_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v4_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k50_valued_1 D E)) & (v1_partfun1 (k50_valued_1 D E) A)) ) ) ).
tt(fc96_member_1,ax, (! [A:$i,B:$i] :  ( ((v4_membered A) & (v1_rat_1 B))  => (v4_membered (k23_member_1 A B))) ) ).
tt(fc96_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v6_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v5_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 B A)) & (v6_valued_0 (k3_relat_1 B A))) ) ) ).
tt(fc96_valued_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k50_valued_1 A B)) &  ((v1_funct_1 (k50_valued_1 A B)) & (v1_finseq_1 (k50_valued_1 A B))) ) ) ) ).
tt(fc97_member_1,ax, (! [A:$i,B:$i] :  ( ((v5_membered A) & (v1_int_1 B))  => (v5_membered (k23_member_1 A B))) ) ).
tt(fc97_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v8_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v7_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A B)) & (v8_valued_0 (k3_relat_1 A B))) ) ) ).
tt(fc97_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v5_relat_1 (k54_valued_1 A) k3_numbers) &  ((v1_funct_1 (k54_valued_1 A)) & (v3_valued_0 (k54_valued_1 A))) ) ) ) ) ).
tt(fc98_member_1,ax, (! [A:$i,B:$i] :  ( ((v6_membered A) & (v7_ordinal1 B))  => (v6_membered (k23_member_1 A B))) ) ).
tt(fc98_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_valued_0 A) & (v8_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_valued_0 B) & (v7_valued_0 B)) ) ) )  =>  ((v1_relat_1 (k3_relat_1 B A)) & (v8_valued_0 (k3_relat_1 B A))) ) ) ).
tt(fc98_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) & (v1_funct_1 A)) )  =>  ((v1_relat_1 (k54_valued_1 A)) &  ((v1_funct_1 (k54_valued_1 A)) &  ((v3_valued_0 (k54_valued_1 A)) & (v4_valued_0 (k54_valued_1 A))) ) ) ) ) ).
tt(fc99_member_1,ax, (! [A:$i,B:$i] :  ( ((v1_xboole_0 A) & (v1_xxreal_0 B))  => (v1_xboole_0 (k24_member_1 A B))) ) ).
tt(fc99_valued_0,ax, (! [A:$i] :  ((v2_membered A) =>  ((v1_funct_1 (k4_relat_1 A)) &  ((v1_funct_2 (k4_relat_1 A) A A) & (v5_valued_0 (k4_relat_1 A))) ) ) ) ).
tt(fc99_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v1_funct_1 (k54_valued_1 C)) & (v1_partfun1 (k54_valued_1 C) A)) ) ) ).
tt(fc9_abcmiz_a,ax, ((v1_msualg_1 k27_abcmiz_1) &  ((v1_instalg1 k27_abcmiz_1) &  ((v1_abcmiz_1 k27_abcmiz_1) & (v3_abcmiz_a k27_abcmiz_1)) ) ) ).
tt(fc9_abian,ax, (! [A:$i,B:$i] :  ( ( ((v1_int_1 A) & (v1_abian A))  &  ((v1_int_1 B) & (v1_abian B)) )  => (v1_abian (k2_xcmplx_0 A B))) ) ).
tt(fc9_afinsq_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 (k6_afinsq_1 A B)) & (v1_funct_1 (k6_afinsq_1 A B))) ) ).
tt(fc9_algstr_0,ax, ((v13_struct_0 k3_algstr_0 1) & (v8_algstr_0 k3_algstr_0)) ).
tt(fc9_algstr_1,ax, ((v29_algstr_0 k3_algstr_1) & (v3_group_1 k3_algstr_1)) ).
tt(fc9_algstr_4,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v2_struct_0 (k9_algstr_4 A B)) & (v15_algstr_0 (k9_algstr_4 A B))) ) ) ).
tt(fc9_ami_6,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3))) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 (k4_ami_3 A B)))) ) ).
tt(fc9_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  ( (~ (v2_struct_0 (k7_freealg k19_aofa_000 A)))  &  ((v1_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v2_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v3_unialg_1 (k7_freealg k19_aofa_000 A)) &  ((v4_unialg_1 (k7_freealg k19_aofa_000 A)) & (v12_aofa_000 (k7_freealg k19_aofa_000 A))) ) ) ) ) ) ) ).
tt(fc9_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_bagorder A)))  &  ((v3_orders_2 (k14_bagorder A)) &  ((v4_orders_2 (k14_bagorder A)) & (v5_orders_2 (k14_bagorder A))) ) ) ) ) ).
tt(fc9_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) &  ((v13_vectsp_1 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k9_bilinear A B C D E)) &  ((v1_funct_2 (k9_bilinear A B C D E) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (v1_bilinear (k9_bilinear A B C D E) A B C)) ) ) ) ).
tt(fc9_binop_2,ax, ((v1_funct_1 k47_binop_2) &  ((v1_funct_2 k47_binop_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers) &  ((v1_binop_1 k47_binop_2 k5_numbers) & (v2_binop_1 k47_binop_2 k5_numbers)) ) ) ).
tt(fc9_borsuk_1,ax, ( (~ (v2_struct_0 k17_borsuk_1))  &  ((v1_pre_topc k17_borsuk_1) & (v2_pre_topc k17_borsuk_1)) ) ).
tt(fc9_borsuk_2,ax,(v1_borsuk_2 k17_borsuk_1)).
tt(fc9_borsuk_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v1_rat_1 A)) )  =>  (~ (v1_rat_1 (k3_int_1 A))) ) ) ).
tt(fc9_borsuk_6,ax, ( (~ (v1_xboole_0 k7_borsuk_6))  & (v4_pre_topc k7_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr))) ).
tt(fc9_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) => (v3_topalg_6 (k13_borsuk_7 A) (k8_toprealb 3) k8_borsuk_7)) ) ).
tt(fc9_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v5_rlvect_1 (k5_c0sp2 A)) &  ((v6_rlvect_1 (k5_c0sp2 A)) &  ((v7_rlvect_1 (k5_c0sp2 A)) & (v8_rlvect_1 (k5_c0sp2 A))) ) ) ) ) ).
tt(fc9_card_1,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (~ (v1_finset_1 (k1_zfmisc_1 A))) ) ) ).
tt(fc9_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_card_3 (k4_card_3 A))) ) ).
tt(fc9_card_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k1_zfmisc_1 A)))  => (v3_ordinal1 (k1_funct_1 (k3_wellord1 (k1_wellord2 (k2_wellord2 (k1_wellord2 B))) (k1_wellord2 B)) C))) ) ).
tt(fc9_catalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_catalg_1 A) & (l1_msualg_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finseq_1 (k2_xtuple_0 B))) ) ).
tt(fc9_cayley,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_funct_1 (k4_cayley A)) &  ((v2_funct_1 (k4_cayley A)) & (v1_funct_2 (k4_cayley A) (u1_struct_0 A) (u1_struct_0 (k2_cayley (u1_struct_0 A))))) ) ) ) ).
tt(fc9_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((v2_clvect_1 (k5_cc0sp2 A)) &  ((v3_clvect_1 (k5_cc0sp2 A)) &  ((v4_clvect_1 (k5_cc0sp2 A)) & (v5_clvect_1 (k5_cc0sp2 A))) ) ) ) ) ).
tt(fc9_cfdiff_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) &  ((v1_funct_1 B) &  ((v1_partfun1 B k2_numbers) &  ((v2_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ) )  =>  ((v1_funct_1 (k24_valued_1 B A)) &  ((v1_partfun1 (k24_valued_1 B A) k2_numbers) & (v2_cfdiff_1 (k24_valued_1 B A))) ) ) ) ).
tt(fc9_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (~ (v1_xboole_0 (k10_cgames_1 A))) ) ) ).
tt(fc9_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_circcmb3 A) & (l1_msualg_1 A)) )  =>  (~ (v1_facirc_1 (k2_msafree2 A))) ) ) ).
tt(fc9_circcomb,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v2_struct_0 (k5_circcomb A B)))  &  ( (~ (v11_struct_0 (k5_circcomb A B)))  & (v1_msualg_1 (k5_circcomb A B))) ) ) ) ).
tt(fc9_clopban1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_clopban1 A B)))  &  ((v13_algstr_0 (k9_clopban1 A B)) &  ((v2_rlvect_1 (k9_clopban1 A B)) &  ((v3_rlvect_1 (k9_clopban1 A B)) &  ((v4_rlvect_1 (k9_clopban1 A B)) &  ((v1_clvect_1 (k9_clopban1 A B)) &  ((v2_clvect_1 (k9_clopban1 A B)) &  ((v3_clvect_1 (k9_clopban1 A B)) &  ((v4_clvect_1 (k9_clopban1 A B)) & (v5_clvect_1 (k9_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc9_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_clopban2 A)))  & (v1_clopban2 (k9_clopban2 A))) ) ) ).
tt(fc9_closure1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v11_closure1 B A) & (l1_closure1 B A)) )  => (v6_mssubfam (u1_closure1 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc9_closure2,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v14_closure2 B A) & (l1_closure2 B A)) )  => (v3_closure2 (u1_closure2 A B) (u1_struct_0 A) (u3_msualg_1 A B))) ) ).
tt(fc9_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_relat_1 (k7_cohsp_1 A))) ) ).
tt(fc9_coh_sp,ax, (! [A:$i] :  (~ (v1_xboole_0 (k16_coh_sp A))) ) ).
tt(fc9_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) ) ) )  =>  ((v1_relat_1 (k7_compos_1 A B C)) &  ((v4_relat_1 (k7_compos_1 A B C) k5_numbers) &  ((v5_relat_1 (k7_compos_1 A B C) (u1_compos_1 A)) &  ((v1_funct_1 (k7_compos_1 A B C)) &  ((v1_finset_1 (k7_compos_1 A B C)) & (v1_afinsq_1 (k7_compos_1 A B C))) ) ) ) ) ) ) ).
tt(fc9_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v2_margrel1 A)) ) )  => (v3_comput_1 (k5_finseq_1 A))) ) ).
tt(fc9_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v1_comseq_3 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v1_funct_1 (k4_comseq_3 A)) &  ((v1_funct_2 (k4_comseq_3 A) k5_numbers k1_numbers) & (v1_series_1 (k4_comseq_3 A))) ) ) ) ).
tt(fc9_csspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_csspace4 A B)))  &  ((v13_algstr_0 (k9_csspace4 A B)) &  ((v2_rlvect_1 (k9_csspace4 A B)) &  ((v3_rlvect_1 (k9_csspace4 A B)) &  ((v4_rlvect_1 (k9_csspace4 A B)) &  ((v3_normsp_0 (k9_csspace4 A B)) &  ((v4_normsp_0 (k9_csspace4 A B)) &  ((v2_clvect_1 (k9_csspace4 A B)) &  ((v3_clvect_1 (k9_csspace4 A B)) &  ((v4_clvect_1 (k9_csspace4 A B)) &  ((v5_clvect_1 (k9_csspace4 A B)) & (v8_clvect_1 (k9_csspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc9_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ((v1_orders_2 (k5_yellow_1 k1_xboole_0 A)) & (v4_dickson (k5_yellow_1 k1_xboole_0 A))) ) ) ).
tt(fc9_dilworth,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v8_struct_0 (k5_yellow_0 A B)) &  ((v1_orders_2 (k5_yellow_0 A B)) & (v4_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ).
tt(fc9_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v5_euclid_7 (k8_euclid_7 A) A)) ) ).
tt(fc9_euclid_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) ) ) )  =>  ((v1_relat_1 (k1_valued_1 B C)) &  ((v1_funct_1 (k1_valued_1 B C)) & (v3_card_1 (k1_valued_1 B C) A)) ) ) ) ).
tt(fc9_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_finseq_1 (k1_euclid A))) ) ).
tt(fc9_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v2_funct_2 B A)) ) ) )  &  ((m1_subset_1 C (k9_xtuple_0 B)) & (m1_subset_1 D (k9_xtuple_0 B))) ) )  => (v2_funct_2 (k10_funct_7 B C D) A)) ) ).
tt(fc9_facirc_1,ax, (! [A:$i,B:$i] :  ( ((v1_xtuple_0 A) & (v1_xtuple_0 B))  => (v1_relat_1 (k2_tarski A B))) ) ).
tt(fc9_fcont_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v2_fcont_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v2_fcont_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) )  =>  ((v1_funct_1 (k1_valued_1 A B)) & (v2_fcont_1 (k1_valued_1 A B))) ) ) ).
tt(fc9_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((v19_lattices B (k1_lattice2 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) )  => (v18_lattices (k4_filter_2 A B) A)) ) ).
tt(fc9_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ((v1_relat_1 (k11_finseq_1 A B C)) & (v1_funct_1 (k11_finseq_1 A B C))) ) ).
tt(fc9_finseq_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (m1_subset_1 D A)) ) )  =>  (~ (v1_xboole_0 (k5_finseq_5 A B D C))) ) ) ).
tt(fc9_finset_1,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k2_xboole_0 A B))) ) ).
tt(fc9_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (v1_xboole_0 C)) )  => (v2_fomodel0 (k3_xboole_0 C B) A B)) ) ).
tt(fc9_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (~ (v1_finset_1 (k1_fomodel1 A))) ) ) ).
tt(fc9_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) ) ) )  =>  ((v1_relat_1 (k11_fomodel2 A B C)) &  ((v1_funct_1 (k11_fomodel2 A B C)) & (v2_fomodel2 (k11_fomodel2 A B C) A B C)) ) ) ) ).
tt(fc9_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v7_ordinal1 D)) ) )  => (v1_partfun1 (k8_fomodel3 A B C D) (k4_finseq_2 D A))) ) ).
tt(fc9_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v2_fomodel4 C A))  => (v2_fomodel4 (k3_xboole_0 C B) A)) ) ).
tt(fc9_fsm_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B)) ) )  =>  ( (~ (v2_struct_0 (k4_fsm_3 A B C)))  &  ((v3_fsm_3 (k4_fsm_3 A B C) A (k9_flang_1 A)) & (v4_fsm_3 (k4_fsm_3 A B C) A (k9_flang_1 A))) ) ) ) ).
tt(fc9_funcop_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((v1_relat_1 (k3_relat_1 B A)) & (v1_funcop_1 (k3_relat_1 B A))) ) ) ).
tt(fc9_funct_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_relat_1 (k6_relat_1 A B)) & (v1_funct_1 (k6_relat_1 A B))) ) ) ).
tt(fc9_funct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v1_funct_1 (k3_partfun1 B A A)) & (v1_partfun1 (k3_partfun1 B A A) A)) ) ) ).
tt(fc9_funct_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) ) )  =>  ((v1_relat_1 (k1_funct_4 C B)) &  ((v4_relat_1 (k1_funct_4 C B) A) &  ((v1_funct_1 (k1_funct_4 C B)) & (v1_partfun1 (k1_funct_4 C B) A)) ) ) ) ) ).
tt(fc9_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v1_funct_7 (k5_finseq_1 A))) ) ).
tt(fc9_funct_9,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_funct_9 A)) ) )  & (v1_xreal_0 B))  =>  ((v1_relat_1 (k13_valued_1 A B)) &  ((v1_funct_1 (k13_valued_1 A B)) & (v2_funct_9 (k13_valued_1 A B))) ) ) ) ).
tt(fc9_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  &  ((m1_subset_1 C (u1_struct_0 B)) & (m1_subset_1 D (k1_altcat_1 B C C))) ) )  =>  ((v6_functor0 (k9_functor0 A B C D) A B) & (v9_functor0 (k9_functor0 A B C D) A B)) ) ) ).
tt(fc9_gate_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (v1_xboole_0 (k4_gate_1 A B))) ) ).
tt(fc9_glib_001,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v1_glib_001 B A) & (m3_glib_001 B A))  &  ((v1_glib_001 C A) & (m3_glib_001 C A)) ) )  => (v1_glib_001 (k7_glib_001 A B C) A)) ) ).
tt(fc9_graph_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_finset_1 (k6_graph_3 A B))) ) ).
tt(fc9_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  => (v1_grcat_1 (k11_grcat_1 A))) ) ).
tt(fc9_gr_cy_1,ax, ( (~ (v2_struct_0 k2_gr_cy_1))  &  ((v15_algstr_0 k2_gr_cy_1) & (v1_gr_cy_1 k2_gr_cy_1)) ) ).
tt(fc9_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ((v1_funct_1 (k8_group_6 A B)) &  ((v1_funct_2 (k8_group_6 A B) (u1_struct_0 A) (u1_struct_0 (k5_group_6 A B))) & (v1_group_6 (k8_group_6 A B) A (k5_group_6 A B))) ) ) ) ).
tt(fc9_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  => (v2_group_7 (k5_finseq_1 A) (k1_tarski 1))) ) ).
tt(fc9_hermitan,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) ) )  &  ((v1_funct_1 B) &  ( (~ (v3_funct_1 B))  &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k1_hermitan A B)) &  ( (~ (v3_funct_1 (k1_hermitan A B)))  & (v1_funct_2 (k1_hermitan A B) (u1_struct_0 A) (u1_struct_0 k1_complfld))) ) ) ) ).
tt(fc9_hilbert3,ax,(v1_hilbert3 k2_hilbert1)).
tt(fc9_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) )  &  ( ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v1_ideal_1 (k10_ideal_1 A B C) A)) ) ).
tt(fc9_index_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_index_1 C A B) =>  ((v1_relat_1 (k2_xtuple_0 C)) & (v1_funct_1 (k2_xtuple_0 C))) ) ) ).
tt(fc9_int_6,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k1_int_6 A B)) &  ((v5_relat_1 (k1_int_6 A B) k4_numbers) &  ((v1_funct_1 (k1_int_6 A B)) & (v1_finseq_1 (k1_int_6 A B))) ) ) ) ) ).
tt(fc9_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((v3_lattices (k21_interva1 A)) & (v10_lattices (k21_interva1 A))) ) ) ).
tt(fc9_jordan23,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_finseq_6 B A) &  ((v3_jordan23 B) & (m1_finseq_1 B A)) )  & (m1_subset_1 C A)) )  => (v3_jordan23 (k1_finseq_6 A B C))) ) ).
tt(fc9_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (v1_xboole_0 (k2_jordan2c 2 A))) ) ) ).
tt(fc9_jordan,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (u1_struct_0 (k15_euclid B)))) ) )  =>  (~ (v1_xboole_0 (k4_xboole_0 (k2_topreal9 B C A) (k6_domain_1 (u1_struct_0 (k15_euclid B)) D)))) ) ) ).
tt(fc9_kurato_1,ax,(v1_setfam_1 (k3_kurato_1 k3_topmetr k6_kurato_1))).
tt(fc9_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((v1_funct_1 (u2_lattices A)) &  ((v1_funct_2 (u2_lattices A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (v1_setwiseo (u2_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(fc9_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v4_lexbfs (k25_lexbfs A (k26_lexbfs A)) A)) ) ).
tt(fc9_lopban_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_lopban_1 A B)))  &  ((v13_algstr_0 (k11_lopban_1 A B)) &  ((v1_rlvect_1 (k11_lopban_1 A B)) &  ((v2_rlvect_1 (k11_lopban_1 A B)) &  ((v3_rlvect_1 (k11_lopban_1 A B)) &  ((v4_rlvect_1 (k11_lopban_1 A B)) &  ((v5_rlvect_1 (k11_lopban_1 A B)) &  ((v6_rlvect_1 (k11_lopban_1 A B)) &  ((v7_rlvect_1 (k11_lopban_1 A B)) & (v8_rlvect_1 (k11_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(fc9_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_lopban_2 A)))  & (v1_lopban_2 (k9_lopban_2 A))) ) ) ).
tt(fc9_lukasi_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) &  ((m1_subset_1 C (k3_cqc_lang A)) & (m1_subset_1 D (k3_cqc_lang A))) ) )  => (v2_cqc_the1 (k2_qc_lang2 A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A D B) (k8_cqc_lang A D C))) A)) ) ).
tt(fc9_matroid0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_matroid0 A B)))  &  ((v1_pre_topc (k3_matroid0 A B)) &  ( (~ (v3_pencil_1 (k3_matroid0 A B)))  & (v1_matroid0 (k3_matroid0 A B))) ) ) ) ) ).
tt(fc9_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v2_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((v1_relat_1 (k15_finseq_1 A)) &  ((v1_funct_1 (k15_finseq_1 A)) & (v3_valued_0 (k15_finseq_1 A))) ) ) ) ).
tt(fc9_matrtop3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) &  ((v2_matrtop3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) ) ) )  => (v4_matrix_6 (k3_matrtop3 A B) A k2_vectsp_1)) ) ).
tt(fc9_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_mazurulm (k3_struct_0 A) A A) & (v3_mazurulm (k3_struct_0 A) A A)) ) ) ) ) ).
tt(fc9_member_1,ax, (! [A:$i] :  ((v5_membered A) =>  ((v1_membered (k5_member_1 A)) & (v5_membered (k5_member_1 A))) ) ) ).
tt(fc9_membered,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v3_membered (k1_tarski A))) ) ).
tt(fc9_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((m1_subset_1 C k5_numbers) &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  =>  ((v1_relat_1 (k2_funct_7 D (k4_struct_0 B) C)) &  ((v1_funct_1 (k2_funct_7 D (k4_struct_0 B) C)) & (v5_funct_1 (k2_funct_7 D (k4_struct_0 B) C) (k2_memstr_0 A B))) ) ) ) ).
tt(fc9_metrizts,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) &  ((v1_metrizts A) & (l1_pre_topc A)) )  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_pre_topc (k1_pre_topc A B)) & (v1_metrizts (k1_pre_topc A B))) ) ) ).
tt(fc9_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l6_algstr_0 A)) )  =>  ((v36_algstr_0 (k2_mod_4 A)) & (v3_group_1 (k2_mod_4 A))) ) ) ).
tt(fc9_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (v1_xboole_0 (k30_modelc_1 A))) ) ) ).
tt(fc9_msafree1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  => (v1_msafree1 (k11_msafree A B) A)) ) ).
tt(fc9_msafree,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) ) )  =>  ((v3_msualg_1 (k11_msafree A B) A) & (v4_msualg_1 (k11_msafree A B) A)) ) ) ).
tt(fc9_msualg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  (~ (v1_xboole_0 (k8_msualg_2 A B C D))) ) ) ).
tt(fc9_mycielsk,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k3_necklace A)) & (v4_dilworth (k3_necklace A))) ) ) ).
tt(fc9_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) ) )  =>  ((v1_relat_1 (k3_relat_1 A C)) & (v1_partfun1 (k3_relat_1 A C) k5_numbers)) ) ) ).
tt(fc9_nat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) ) )  =>  ((v1_relat_1 (k5_nat_3 A B C)) &  ((v4_relat_1 (k5_nat_3 A B C) A) &  ((v1_funct_1 (k5_nat_3 A B C)) &  ((v1_partfun1 (k5_nat_3 A B C) A) & (v4_valued_0 (k5_nat_3 A B C))) ) ) ) ) ) ).
tt(fc9_neckla_3,ax, (! [A:$i,B:$i] :  ( ( ((v3_necklace A) & (l1_orders_2 A))  &  ((v3_necklace B) & (l1_orders_2 B)) )  =>  ((v1_orders_2 (k1_neckla_2 A B)) & (v3_necklace (k1_neckla_2 A B))) ) ) ).
tt(fc9_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (v1_xreal_0 (k4_newton A B))) ) ).
tt(fc9_nfcont_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v2_nfcont_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k1_numbers)) )  =>  ((v1_funct_1 (k4_vfunct_1 k1_numbers A B C)) & (v2_nfcont_3 (k4_vfunct_1 k1_numbers A B C) A)) ) ) ).
tt(fc9_nfcont_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((v1_funct_1 B) &  ((v2_nfcont_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) ) )  =>  ((v1_funct_1 (k1_nfcont_4 A k1_numbers B)) & (v2_fcont_1 (k1_nfcont_4 A k1_numbers B))) ) ) ).
tt(fc9_numbers,ax, (~ (v1_finset_1 k2_numbers)) ).
tt(fc9_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  (~ (v1_xboole_0 (k7_openlatt A))) ) ) ).
tt(fc9_orders_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  & (m1_orders_1 B (k1_orders_1 (u1_struct_0 A))))  =>  (~ (v1_xboole_0 (k4_orders_2 A B))) ) ) ).
tt(fc9_ordinal6,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k2_ordinal1 A))) ) ).
tt(fc9_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (v1_xboole_0 (k23_osafree A B C))) ) ) ).
tt(fc9_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 B) &  (~ (v2_xxreal_0 B)) )  => (v3_partfun3 (k2_funcop_1 A B))) ) ).
tt(fc9_partfun4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  &  ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ) )  =>  ((v1_funct_1 (k1_rfunct_1 B C)) &  ((v1_funct_2 (k1_rfunct_1 B C) (u1_struct_0 A) k1_numbers) & (v1_pscomp_1 (k1_rfunct_1 B C) A)) ) ) ) ).
tt(fc9_pcs_0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  ((v1_relat_1 (k4_pcs_0 A B)) &  ((v4_relat_1 (k4_pcs_0 A B) A) &  ((v1_funct_1 (k4_pcs_0 A B)) &  ((v1_partfun1 (k4_pcs_0 A B) A) & (v2_funcop_1 (k4_pcs_0 A B))) ) ) ) ) ) ).
tt(fc9_polynom1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k11_polynom1 A B)))  &  ((v36_algstr_0 (k11_polynom1 A B)) & (v4_rlvect_1 (k11_polynom1 A B))) ) ) ) ).
tt(fc9_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v2_rlvect_1 (k14_polynom3 A))) ) ) ) ).
tt(fc9_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A B))) ) )  =>  ((v1_relat_1 (k2_funct_4 C)) &  ((v4_relat_1 (k2_funct_4 C) (k2_zfmisc_1 B A)) &  ((v1_funct_1 (k2_funct_4 C)) & (v1_partfun1 (k2_funct_4 C) (k2_zfmisc_1 B A))) ) ) ) ) ).
tt(fc9_pre_poly,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_card_3 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_card_3 B) & (v1_finseq_1 B)) ) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ((v1_card_3 (k7_finseq_1 A B)) & (v1_finseq_1 (k7_finseq_1 A B))) ) ) ) ) ).
tt(fc9_pre_topc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (~ (v2_struct_0 (g1_pre_topc A B)))  & (v1_pre_topc (g1_pre_topc A B))) ) ) ).
tt(fc9_prvect_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_rlvect_1 B)) ) )  =>  ( (~ (v2_struct_0 (k5_prvect_3 A B)))  &  ((v1_rlvect_1 (k5_prvect_3 A B)) & (v4_rlvect_1 (k5_prvect_3 A B))) ) ) ) ).
tt(fc9_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (v1_xboole_0 (k17_pscomp_1 A)))  & (v2_compts_1 (k17_pscomp_1 A) (k15_euclid 2))) ) ) ).
tt(fc9_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (v1_xreal_0 (k14_quaterni A))) ) ).
tt(fc9_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v1_funct_1 (k3_struct_0 A)) &  ((v1_funct_2 (k3_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) & (v1_quofield (k3_struct_0 A) A A)) ) ) ) ).
tt(fc9_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_polynom3 A)))  &  ((v36_algstr_0 (k14_polynom3 A)) & (v1_vectsp_2 (k14_polynom3 A))) ) ) ) ).
tt(fc9_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v3_xxreal_2 (k2_limfunc1 A)) &  ( (~ (v4_xxreal_2 (k2_limfunc1 A)))  & (v6_xxreal_2 (k2_limfunc1 A))) ) ) ) ).
tt(fc9_relat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_relat_1 A))  =>  (~ (v1_xboole_0 (k10_xtuple_0 A))) ) ) ).
tt(fc9_relat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_relat_2 A))  =>  ((v1_relat_1 (k2_relat_1 A)) & (v3_relat_2 (k2_relat_1 A))) ) ) ).
tt(fc9_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) => (v1_relat_1 (k10_xtuple_0 D))) ) ).
tt(fc9_rfunct_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v2_seq_2 A)) ) )  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  ((v1_relat_1 (k24_valued_1 A B)) &  ((v1_funct_1 (k24_valued_1 A B)) &  ((v3_valued_0 (k24_valued_1 A B)) & (v2_seq_2 (k24_valued_1 A B))) ) ) ) ) ).
tt(fc9_rlaffin1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k4_rlaffin1 A B))) ) ).
tt(fc9_rltopsp1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  & (m1_subset_1 C (u1_struct_0 A))) )  => (v4_pre_topc (k5_rusub_4 A B C) A)) ) ).
tt(fc9_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_robbins1 A)) )  =>  ((v4_lattices (k8_robbins1 A)) & (v4_robbins1 (k8_robbins1 A))) ) ) ).
tt(fc9_roughs_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k1_card_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) B))))  & (v1_card_1 (k1_card_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) B)))) ) ) ).
tt(fc9_rsspace4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_rsspace4 A B)))  &  ((v13_algstr_0 (k9_rsspace4 A B)) &  ((v2_rlvect_1 (k9_rsspace4 A B)) &  ((v3_rlvect_1 (k9_rsspace4 A B)) &  ((v4_rlvect_1 (k9_rsspace4 A B)) &  ((v5_rlvect_1 (k9_rsspace4 A B)) &  ((v6_rlvect_1 (k9_rsspace4 A B)) &  ((v7_rlvect_1 (k9_rsspace4 A B)) &  ((v8_rlvect_1 (k9_rsspace4 A B)) &  ((v3_normsp_0 (k9_rsspace4 A B)) &  ((v4_normsp_0 (k9_rsspace4 A B)) & (v2_normsp_1 (k9_rsspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(fc9_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((v1_xcmplx_0 (k19_rvsum_1 A)) & (v1_xreal_0 (k19_rvsum_1 A))) ) ) ).
tt(fc9_scmfsa10,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 (k8_scmfsa_2 A B)))) ) ).
tt(fc9_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (~ (v2_extpro_1 (k9_scmfsa_2 A B) 3 k1_scmfsa_2)) ) ) ).
tt(fc9_scmfsa_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 B))  => (v4_compos_0 (k17_scmfsa_2 A B) (u1_compos_1 k1_scmfsa_2))) ) ).
tt(fc9_scmfsa6c,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  & (m1_scmfsa_2 C)) )  => (v1_scmfsa6c (k14_scmfsa_2 B A C))) ) ).
tt(fc9_scmfsa8b,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  &  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) ) ) ) )  =>  ( (~ (v1_xboole_0 (k5_scmfsa8b C D A B)))  &  ((v1_relat_1 (k5_scmfsa8b C D A B)) &  ((v4_relat_1 (k5_scmfsa8b C D A B) k5_numbers) &  ((v5_relat_1 (k5_scmfsa8b C D A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k5_scmfsa8b C D A B)) &  ((v1_finset_1 (k5_scmfsa8b C D A B)) &  ((v1_afinsq_1 (k5_scmfsa8b C D A B)) & (v7_amistd_1 (k5_scmfsa8b C D A B) 3 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(fc9_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  & (m1_subset_1 B k5_numbers))  =>  (~ (v1_xboole_0 (k1_funct_1 (k8_scmfsa_m A) B))) ) ) ).
tt(fc9_scm_halt,ax, (! [A:$i,B:$i] :  ( ( ((v1_scmfsa6c A) & (m1_subset_1 A (u1_compos_1 k1_scmfsa_2)))  &  ((v1_scmfsa6c B) & (m1_subset_1 B (u1_compos_1 k1_scmfsa_2))) )  =>  ( (~ (v1_xboole_0 (k6_scmfsa6a A B)))  &  ((v1_relat_1 (k6_scmfsa6a A B)) &  ((v4_relat_1 (k6_scmfsa6a A B) k5_numbers) &  ((v5_relat_1 (k6_scmfsa6a A B) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k6_scmfsa6a A B)) &  ((v1_finset_1 (k6_scmfsa6a A B)) &  ((v1_afinsq_1 (k6_scmfsa6a A B)) & (v2_scm_halt (k6_scmfsa6a A B))) ) ) ) ) ) ) ) ) ).
tt(fc9_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v3_scmpds_4 B)) ) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (k1_ordinal4 A B)))  &  ((v1_relat_1 (k1_ordinal4 A B)) &  ((v4_relat_1 (k1_ordinal4 A B) k5_numbers) &  ((v5_relat_1 (k1_ordinal4 A B) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k1_ordinal4 A B)) &  ((v1_finset_1 (k1_ordinal4 A B)) &  ((v1_afinsq_1 (k1_ordinal4 A B)) & (v3_scmpds_4 (k1_ordinal4 A B))) ) ) ) ) ) ) ) ) ).
tt(fc9_scmpds_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  => (v6_compos_0 (k12_scmpds_2 A B C D) (u1_compos_1 k1_scmpds_2))) ) ).
tt(fc9_scmpds_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scmpds_4 A) & (v3_scmpds_4 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 C)) )  =>  ( (~ (v1_xboole_0 (k6_scmpds_6 B C A)))  &  ((v1_relat_1 (k6_scmpds_6 B C A)) &  ((v4_relat_1 (k6_scmpds_6 B C A) k5_numbers) &  ((v5_relat_1 (k6_scmpds_6 B C A) (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 (k6_scmpds_6 B C A)) &  ((v1_finset_1 (k6_scmpds_6 B C A)) &  ((v1_afinsq_1 (k6_scmpds_6 B C A)) &  ((v2_scmpds_4 (k6_scmpds_6 B C A)) & (v3_scmpds_4 (k6_scmpds_6 B C A))) ) ) ) ) ) ) ) ) ) ).
tt(fc9_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  & (m1_subset_1 C k5_numbers)) )  =>  (~ (v2_extpro_1 (k9_scmring2 A C B) 2 (k1_scmring2 A))) ) ) ).
tt(fc9_scmring3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) (k5_scmring2 A B C)))) ) ).
tt(fc9_scmyciel,ax,(v4_scmyciel (k1_tarski k1_xboole_0))).
tt(fc9_setfam_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) )  => (v1_setfam_1 (k6_enumset1 A B C D E F G H))) ) ).
tt(fc9_sfmastr1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((m1_scmfsa_2 B) &  ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  => (v1_sfmastr1 (k14_scmfsa_2 C A B))) ) ).
tt(fc9_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ((v1_finset_1 C) => (v5_finset_1 (k3_simplex0 A B C))) ) ).
tt(fc9_simplex1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) ) )  =>  ( (~ (v3_pencil_1 (k4_simplex1 A B)))  &  ((v1_matroid0 (k4_simplex1 A B)) &  ((v3_matroid0 (k4_simplex1 A B)) & (v2_simplex1 (k4_simplex1 A B) A)) ) ) ) ) ).
tt(fc9_sincos10,ax, ((v1_relat_1 (k5_relat_1 k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)))) & (v2_funct_1 (k5_relat_1 k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))))) ).
tt(fc9_sin_cos6,ax, ((v1_relat_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) & (v2_funct_1 (k5_relat_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))) ).
tt(fc9_sppol_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_topreal1 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2))))  & (m1_subset_1 B k5_numbers))  => (v1_topreal1 (k16_finseq_1 B A))) ) ).
tt(fc9_sprect_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  => (v5_xxreal_2 (k1_xxreal_1 A B))) ) ).
tt(fc9_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) & (l1_stacks_1 A)) ) )  =>  (~ (v1_xboole_0 (u1_stacks_1 A))) ) ) ).
tt(fc9_struct_0,ax, (! [A:$i] :  ( ( (~ (v8_struct_0 A))  & (l1_struct_0 A))  =>  (~ (v1_finset_1 (u1_struct_0 A))) ) ) ).
tt(fc9_subset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i] :  (~ (v1_xboole_0 (k8_enumset1 A B C D E F G H I J))) ) ).
tt(fc9_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  (~ (v1_xboole_0 (k2_tex_4 A B))) ) ) ).
tt(fc9_topalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc B k17_borsuk_1 (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C k17_borsuk_1 (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) ) ) )  =>  ((v1_funct_1 (k7_topalg_1 A B C)) &  ((v1_funct_2 (k7_topalg_1 A B C) (u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) (u1_struct_0 (k15_euclid A))) & (v5_pre_topc (k7_topalg_1 A B C) (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1) (k15_euclid A))) ) ) ) ).
tt(fc9_topalg_5,ax, ((v1_funct_1 k7_topalg_5) &  ((v2_funct_1 k7_topalg_5) &  ((v1_funct_2 k7_topalg_5 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb))) & (v2_funct_2 k7_topalg_5 (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb)))) ) ) ).
tt(fc9_topalg_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((v5_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A))) )  =>  (~ (v1_xboole_0 (k9_xtuple_0 B))) ) ) ).
tt(fc9_topreal9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  => (v9_rltopsp1 (k2_topreal9 A B C) (k15_euclid A))) ) ).
tt(fc9_topreala,ax, (! [A:$i,B:$i] :  ( ( ((v1_xreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xreal_0 B) & (v2_xxreal_0 B)) )  =>  (~ (v1_xboole_0 (k4_xxreal_1 A B))) ) ) ).
tt(fc9_toprealb,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  (~ (v1_xboole_0 (k1_toprealb A B))) ) ) ).
tt(fc9_toprealc,ax, ((v5_rltopsp1 (k15_euclid k6_numbers)) & (v3_topmetr (k15_euclid k6_numbers))) ).
tt(fc9_tops_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_pre_topc (k1_tops_1 A B) A)) ) ).
tt(fc9_trees_1,ax, (~ (v1_finset_1 k8_trees_1)) ).
tt(fc9_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (~ (v1_xboole_0 (k5_finseq_1 A)))  & (v4_trees_3 (k5_finseq_1 A))) ) ) ).
tt(fc9_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  => (v3_trees_3 (k1_tarski A))) ) ).
tt(fc9_valued_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v3_valued_0 A))  &  ((v1_relat_1 B) & (v3_valued_0 B)) )  => (v3_valued_0 (k2_xboole_0 A B))) ) ).
tt(fc9_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (v4_membered B))  &  ( ( (~ (v1_xboole_0 C))  & (v4_membered C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((v1_funct_1 (k1_valued_1 D E)) & (v1_partfun1 (k1_valued_1 D E) A)) ) ) ).
tt(fc9_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_vectsp_1 A B C D E)))  & (v7_vectsp_1 (g1_vectsp_1 A B C D E) A)) ) ) ).
tt(fc9_waybel_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 (k6_waybel_0 A B)))  & (v2_waybel_0 (k6_waybel_0 A B) A)) ) ) ).
tt(fc9_waybel10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A A B)) &  ((v4_yellow_0 (k1_yellow_2 A A B) A) & (v7_yellow_0 (k1_yellow_2 A A B) A)) ) ) ) ).
tt(fc9_waybel11,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((v3_orders_2 (k4_waybel11 A B)) &  ((v4_orders_2 (k4_waybel11 A B)) &  ((v5_orders_2 (k4_waybel11 A B)) &  ((v6_waybel_0 (k4_waybel11 A B) A) & (v7_waybel_0 (k4_waybel11 A B))) ) ) ) ) ) ).
tt(fc9_waybel18,ax, (! [A:$i,B:$i] :  ((l1_pre_topc B) => (v1_waybel18 (k2_funcop_1 A B))) ) ).
tt(fc9_waybel_1,ax, (! [A:$i] :  ((v1_orders_2 (k3_yellow_1 A)) & (v10_waybel_1 (k3_yellow_1 A))) ) ).
tt(fc9_waybel23,ax, (! [A:$i,B:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  => (v1_waybel23 (k1_waybel_3 A B) A)) ) ).
tt(fc9_waybel24,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v4_orders_2 B) & (l1_waybel_9 B)) ) ) )  =>  ((v1_orders_2 (k3_waybel24 A B)) & (v4_orders_2 (k3_waybel24 A B))) ) ) ).
tt(fc9_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_lattice3 (k1_waybel25 A)) & (v1_waybel_9 (k1_waybel25 A))) ) ) ).
tt(fc9_waybel29,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v2_waybel18 B) & (l1_pre_topc B)) ) ) ) )  =>  ((v1_pre_topc (k3_waybel18 A (k2_funcop_1 A B))) &  ((v2_pre_topc (k3_waybel18 A (k2_funcop_1 A B))) & (v2_waybel18 (k3_waybel18 A (k2_funcop_1 A B)))) ) ) ) ).
tt(fc9_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k2_yellow_2 A)) &  ((v1_funct_2 (k2_yellow_2 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A)) & (v20_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ) ).
tt(fc9_waybel30,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  &  ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_xboole_0 (k1_waybel30 A B))) ) ).
tt(fc9_waybel34,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v18_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_orders_2 (k1_yellow_2 A B C)) &  ((v4_yellow_0 (k1_yellow_2 A B C) B) & (v3_lattice3 (k1_yellow_2 A B C))) ) ) ) ).
tt(fc9_waybel_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ((v1_monoid_0 (k5_yellow_1 A B)) & (v1_orders_2 (k5_yellow_1 A B))) ) ) ).
tt(fc9_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_orders_2 (k2_yellow_1 (k3_waybel_4 A))) & (v2_lattice3 (k2_yellow_1 (k3_waybel_4 A)))) ) ) ).
tt(fc9_waybel_8,ax, (! [A:$i] :  ( ((v1_lattice3 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) & (v1_lattice3 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(fc9_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (~ (v2_struct_0 (k2_waybel_9 A)))  & (v6_waybel_0 (k2_waybel_9 A) A)) ) ) ).
tt(fc9_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  => (v1_xboolean (k10_xboolean A B))) ) ).
tt(fc9_xcmplx_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_xcmplx_0 A))  &  ( (~ (v1_xboole_0 B))  & (v1_xcmplx_0 B)) )  =>  (~ (v1_xboole_0 (k7_xcmplx_0 A B))) ) ) ).
tt(fc9_xreal_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (~ (v3_xxreal_0 (k2_xcmplx_0 A B))) ) ) ).
tt(fc9_xtuple_0,ax, (! [A:$i] :  ((v1_xboole_0 A) => (v1_xboole_0 (k14_xtuple_0 A))) ) ).
tt(fc9_xxreal_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (v3_membered (k4_xxreal_1 A B))) ) ).
tt(fc9_xxreal_2,ax, (! [A:$i] :  ( ((v5_membered A) & (v2_xxreal_2 A))  =>  ((v1_xxreal_0 (k1_xxreal_2 A)) & (v1_int_1 (k1_xxreal_2 A))) ) ) ).
tt(fc9_xxreal_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_xxreal_0 A) &  (~ (v2_xxreal_0 A)) )  &  ((v1_xxreal_0 B) &  (~ (v2_xxreal_0 B)) ) )  =>  ((v1_xxreal_0 (k1_xxreal_3 A B)) &  (~ (v2_xxreal_0 (k1_xxreal_3 A B))) ) ) ) ).
tt(fc9_yellow10,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v25_waybel_0 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((v1_orders_2 (k3_yellow_3 A B)) & (v3_waybel_3 (k3_yellow_3 A B))) ) ) ).
tt(fc9_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v7_struct_0 (k2_yellow_1 (u1_pre_topc A))))  &  ((v1_orders_2 (k2_yellow_1 (u1_pre_topc A))) & (v3_lattice3 (k2_yellow_1 (u1_pre_topc A)))) ) ) ) ).
tt(fc9_yellow_3,ax, (! [A:$i] :  ( ( (~ (v1_yellow_3 A))  & (l1_orders_2 A))  =>  (~ (v1_xboole_0 (u1_orders_2 A))) ) ) ).
tt(fc9_yellow_6,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_yellow_1 A B)))  & (v1_orders_2 (k5_yellow_1 A B))) ) ) ).
tt(fc9_yellow_7,ax, (! [A:$i] :  ( ((v1_yellow_0 A) & (l1_orders_2 A))  =>  ((v1_orders_2 (k7_lattice3 A)) & (v2_yellow_0 (k7_lattice3 A))) ) ) ).
tt(fc9_yellow_9,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v2_struct_0 (k3_yellow_9 A B)))  &  ((v6_waybel_0 (k3_yellow_9 A B) A) & (v7_waybel_0 (k3_yellow_9 A B))) ) ) ) ).
tt(free_g1_abcmiz_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i,D:$i] :  ( ((g1_abcmiz_0 A B) = (g1_abcmiz_0 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_algstr_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k3_zfmisc_1 A A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A A A) A)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_algstr_3 A B C D) = (g1_algstr_3 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_analmetr A B C) = (g1_analmetr D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_analoaf,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  (! [C:$i,D:$i] :  ( ((g1_analoaf A B) = (g1_analoaf C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k4_card_3 B)))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_armstrng A B C) = (g1_armstrng D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_bcialg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 D A)) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_bcialg_4 A B C D) = (g1_bcialg_4 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_bhsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_bhsp_1 A B C D E) = (g1_bhsp_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_cat_1 A B C D E) = (g1_cat_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  &  ((m1_subset_1 F A) &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) )  &  ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 A A) B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) ) ) ) ) ) ) )  =>  (! [J:$i,K:$i,L:$i,M:$i,N:$i,O:$i,P:$i,Q:$i,R:$i] :  ( ((g1_cat_4 A B C D E F G H I) = (g1_cat_4 J K L M N O P Q R))  =>  ( (A = J)  &  ( (B = K)  &  ( (C = L)  &  ( (D = M)  &  ( (E = N)  &  ( (F = O)  &  ( (G = P)  &  ( (H = Q)  &  (I = R) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_cfuncdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g1_cfuncdom A B C D E F) = (g1_cfuncdom G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_cgames_1,ax, (! [A:$i,B:$i] :  (! [C:$i,D:$i] :  ( ((g1_cgames_1 A B) = (g1_cgames_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ).
tt(free_g1_clopban2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g1_clopban2 A B C D E F G) = (g1_clopban2 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_closure1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m3_pboole C (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) B))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_closure1 A B C) = (g1_closure1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) B)))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_closure2 A B C) = (g1_closure2 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_clvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_clvect_1 A B C D) = (g1_clvect_1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_collsp,ax, (! [A:$i,B:$i] :  ((m1_collsp B A) =>  (! [C:$i,D:$i] :  ( ((g1_collsp A B) = (g1_collsp C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_combgras,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_incsp_1 A) &  ((l1_incsp_1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_incsp_1 A) (u1_incsp_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_incsp_1 A) (u1_incsp_1 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u2_incsp_1 A) (u2_incsp_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u2_incsp_1 A) (u2_incsp_1 B))))) ) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_combgras A B C D) = (g1_combgras E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_compos_1,ax, (! [A:$i] :  ( ((v1_compos_0 A) &  ((v2_compos_0 A) &  ((v3_compos_0 A) & (v5_compos_0 A)) ) )  =>  (! [B:$i] :  ( ((g1_compos_1 A) = (g1_compos_1 B))  =>  (A = B) ) ) ) ) ).
tt(free_g1_conlat_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_conlat_1 A B C) = (g1_conlat_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_csspace,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k2_numbers)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_csspace A B C D E) = (g1_csspace F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_e_siec,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_relat_1 B) & (v1_relat_1 C))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_e_siec A B C) = (g1_e_siec D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((m1_subset_1 C B) &  ( ((v1_compos_0 D) &  ((v2_compos_0 D) &  ((v3_compos_0 D) & (v5_compos_0 D)) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G D (k1_funct_2 (k4_card_3 (k3_relat_1 E F)) (k4_card_3 (k3_relat_1 E F)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 D (k1_funct_2 (k4_card_3 (k3_relat_1 E F)) (k4_card_3 (k3_relat_1 E F))))))) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g1_extpro_1 A B C D E F G) = (g1_extpro_1 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_fomodel1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k6_subset_1 A (k1_tarski C)) k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_subset_1 A (k1_tarski C)) k4_numbers)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_fomodel1 A B C D) = (g1_fomodel1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C B) C))) & (m1_subset_1 E (k1_zfmisc_1 C))) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_fsm_3 A B C D E) = (g1_fsm_3 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g1_funcsdom A B C D E F) = (g1_funcsdom G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_geomtrap A B C) = (g1_geomtrap D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_graph_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_graph_1 A B C D) = (g1_graph_1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_grcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_grcat_1 A B C) = (g1_grcat_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_group_9 A B C D) = (g1_group_9 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_incsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_incsp_1 A B C) = (g1_incsp_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_lang1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 A)))) =>  (! [C:$i,D:$i] :  ( ((g1_lang1 A B) = (g1_lang1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_lattices,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i,D:$i] :  ( ((g1_lattices A B) = (g1_lattices C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_lopban_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g1_lopban_2 A B C D E F G) = (g1_lopban_2 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_memstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C B) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_memstr_0 A B C D E) = (g1_memstr_0 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_metric_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i,D:$i] :  ( ((g1_metric_1 A B) = (g1_metric_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_midsp_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i,D:$i] :  ( ((g1_midsp_1 A B) = (g1_midsp_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_midsp_3 A B C D) = (g1_midsp_3 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_mod_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_mod_2 A B C D) = (g1_mod_2 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_modelc_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) ) )  =>  (! [I:$i,J:$i,K:$i,L:$i,M:$i,N:$i,O:$i,P:$i] :  ( ((g1_modelc_2 A B C D E F G H) = (g1_modelc_2 I J K L M N O P))  =>  ( (A = I)  &  ( (B = J)  &  ( (C = K)  &  ( (D = L)  &  ( (E = M)  &  ( (F = N)  &  ( (G = O)  &  (H = P) ) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B (k1_zfmisc_1 (k1_modelc_3 A))) &  ((m1_subset_1 C (k1_zfmisc_1 (k1_modelc_3 A))) & (m1_subset_1 D (k1_zfmisc_1 (k1_modelc_3 A)))) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_modelc_3 A B C D) = (g1_modelc_3 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_msualg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k3_finseq_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k3_finseq_2 A))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_msualg_1 A B C D) = (g1_msualg_1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_normsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_normsp_1 A B C D E) = (g1_normsp_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_orders_2,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i,D:$i] :  ( ((g1_orders_2 A B) = (g1_orders_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_parsp_1,ax, (! [A:$i,B:$i] :  ((m1_parsp_1 B A) =>  (! [C:$i,D:$i] :  ( ((g1_parsp_1 A B) = (g1_parsp_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_pcs_0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i,D:$i] :  ( ((g1_pcs_0 A B) = (g1_pcs_0 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_petri,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_petri A B C D) = (g1_petri E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_polyalg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 E B) &  ((m1_subset_1 F B) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) ) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g1_polyalg1 A B C D E F G) = (g1_polyalg1 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_pre_topc,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i,D:$i] :  ( ((g1_pre_topc A B) = (g1_pre_topc C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) (k1_qmax_1 k1_numbers k12_prob_1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k1_qmax_1 k1_numbers k12_prob_1))))) ) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_qmax_1 A B C) = (g1_qmax_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_rewrite3,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B))) =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_rewrite3 A B C) = (g1_rewrite3 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_ringcat1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_ringcat1 A B C) = (g1_ringcat1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_rltopsp1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_rltopsp1 A B C D E) = (g1_rltopsp1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_rlvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_rlvect_1 A B C D) = (g1_rlvect_1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_sgraph1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_sgraph1 A))) =>  (! [C:$i,D:$i] :  ( ((g1_sgraph1 A B) = (g1_sgraph1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g1_stacks_1 A B C D E F) = (g1_stacks_1 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_struct_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((g1_struct_0 A) = (g1_struct_0 B))  =>  (A = B) ) ) ) ).
tt(free_g1_symsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) )  & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g1_symsp_1 A B C D E F) = (g1_symsp_1 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g1_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B A) (k3_zfmisc_1 B A (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) (k3_zfmisc_1 B A (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)))))) )  &  ((m1_subset_1 D B) & (m1_subset_1 E B)) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_turing_1 A B C D E) = (g1_turing_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_unialg_1,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)) =>  (! [C:$i,D:$i] :  ( ((g1_unialg_1 A B) = (g1_unialg_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g1_vectmetr,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  &  ((m1_subset_1 C A) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_vectmetr A B C D E) = (g1_vectmetr F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B) B)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_vectsp_1 A B C D E) = (g1_vectsp_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((l1_struct_0 A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((m1_subset_1 D B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g1_vectsp_2 A B C D E) = (g1_vectsp_2 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g1_waybel_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) &  ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_waybel_0 A B C D) = (g1_waybel_0 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g1_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g1_waybel_9 A B C) = (g1_waybel_9 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g1_zmodul01,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k4_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers A) A)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g1_zmodul01 A B C D) = (g1_zmodul01 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g2_abcmiz_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A (k5_finsub_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g2_abcmiz_0 A B C D E) = (g2_abcmiz_0 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g2_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_algstr_0 A B C) = (g2_algstr_0 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_altcat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  & (m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_altcat_1 A B C) = (g2_altcat_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_bcialg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_bcialg_1 A B C) = (g2_bcialg_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_cat_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  &  ((m1_subset_1 F A) &  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) )  &  ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 A A) B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) B)))) ) ) ) ) ) ) )  =>  (! [J:$i,K:$i,L:$i,M:$i,N:$i,O:$i,P:$i,Q:$i,R:$i] :  ( ((g2_cat_4 A B C D E F G H I) = (g2_cat_4 J K L M N O P Q R))  =>  ( (A = J)  &  ( (B = K)  &  ( (C = L)  &  ( (D = M)  &  ( (E = N)  &  ( (F = O)  &  ( (G = P)  &  ( (H = Q)  &  (I = R) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g2_clvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B A) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g2_clvect_1 A B C D E) = (g2_clvect_1 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g2_conlat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l5_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A)))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_conlat_1 A B C) = (g2_conlat_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  & (m1_subset_1 F C)) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g2_fsm_1 A B C D E F) = (g2_fsm_1 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g2_fsm_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  &  ((m1_subset_1 F C) & (m1_subset_1 G (k1_zfmisc_1 C))) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g2_fsm_2 A B C D E F G) = (g2_fsm_2 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g2_fsm_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) &  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C B) C))) &  ((m1_subset_1 E (k1_zfmisc_1 C)) & (m1_subset_1 F (k1_zfmisc_1 C))) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g2_fsm_3 A B C D E F) = (g2_fsm_3 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g2_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_altcat_1 A) &  ((l1_altcat_1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))))) )  & (m1_functor0 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) C (u1_altcat_1 A) (u1_altcat_1 B))) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g2_functor0 A B C D) = (g2_functor0 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g2_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 A)))))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_lang1 A B C) = (g2_lang1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_lattices,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i,D:$i] :  ( ((g2_lattices A B) = (g2_lattices C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g2_modelc_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g2_modelc_1 A B C D E F G) = (g2_modelc_1 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g2_modelc_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B))) &  ((m1_subset_1 D (k1_zfmisc_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g2_modelc_3 A B C D E) = (g2_modelc_3 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(free_g2_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_pcs_0 A B C) = (g2_pcs_0 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_qmax_1 A B C) = (g2_qmax_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g2_robbins1 A B C) = (g2_robbins1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g2_vectsp_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ((l1_struct_0 A) &  ((l1_struct_0 B) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  &  ((m1_subset_1 E C) &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 A) C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) C) C)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C (u1_struct_0 B)) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 B)) C)))) ) ) ) ) ) )  =>  (! [H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i] :  ( ((g2_vectsp_2 A B C D E F G) = (g2_vectsp_2 H I J K L M N))  =>  ( (A = H)  &  ( (B = I)  &  ( (C = J)  &  ( (D = K)  &  ( (E = L)  &  ( (F = M)  &  (G = N) ) ) ) ) ) ) ) ) ) ) ).
tt(free_g3_algstr_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i,D:$i] :  ( ((g3_algstr_0 A B) = (g3_algstr_0 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ).
tt(free_g3_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  & (m1_subset_1 F C)) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g3_fsm_1 A B C D E F) = (g3_fsm_1 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g3_lattices A B C) = (g3_lattices D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g3_msualg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  & (m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) B)) (k3_relat_1 (u2_msualg_1 A) B))) )  =>  (! [D:$i,E:$i,F:$i] :  ( ((g3_msualg_1 A B C) = (g3_msualg_1 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g3_osalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (k3_finseq_2 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (k3_finseq_2 A))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C A)))) ) ) ) )  =>  (! [G:$i,H:$i,I:$i,J:$i,K:$i,L:$i] :  ( ((g3_osalg_1 A B C D E F) = (g3_osalg_1 G H I J K L))  =>  ( (A = G)  &  ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  ( (E = K)  &  (F = L) ) ) ) ) ) ) ) ) ) ).
tt(free_g3_robbins3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g3_robbins3 A B C D) = (g3_robbins3 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g4_algstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  & (m1_subset_1 C A))  =>  (! [D:$i,E:$i,F:$i] :  ( ((g4_algstr_0 A B C) = (g4_algstr_0 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ).
tt(free_g4_robbins1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g4_robbins1 A B C D) = (g4_robbins1 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g5_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  =>  (! [E:$i,F:$i,G:$i,H:$i] :  ( ((g5_algstr_0 A B C D) = (g5_algstr_0 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ).
tt(free_g6_algstr_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) )  =>  (! [F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ((g6_algstr_0 A B C D E) = (g6_algstr_0 F G H I J))  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) ).
tt(idempotence_k10_margrel1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k10_margrel1 A A) = A) ) ) ).
tt(idempotence_k11_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k11_openlatt A B B) = B) ) ) ).
tt(idempotence_k12_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k12_openlatt A B B) = B) ) ) ).
tt(idempotence_k13_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k13_ideal_1 A B B) = B) ) ) ).
tt(idempotence_k14_margrel1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k14_margrel1 A A) = A) ) ) ).
tt(idempotence_k14_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  =>  ((k14_sublemma A B C C) = C) ) ) ).
tt(idempotence_k15_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k15_mmlquery A B B) = B) ) ) ).
tt(idempotence_k16_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k16_margrel1 A B B) = B) ) ) ).
tt(idempotence_k16_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k16_mmlquery A B B) = B) ) ) ).
tt(idempotence_k19_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k19_mmlquery A B B) = B) ) ) ).
tt(idempotence_k1_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k1_binarith A A) = A) ) ) ).
tt(idempotence_k1_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v4_relat_1 E D) &  ((v1_funct_1 E) & (v1_partfun1 E D)) ) ) )  &  ( ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v4_relat_1 F D) &  ((v1_funct_1 F) & (v1_partfun1 F D)) ) ) )  &  ((m2_pboole G A B C) & (m2_pboole H D E F)) ) ) ) )  =>  ((k1_circcomb A B C D E F G G) = G) ) ) ).
tt(idempotence_k1_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_msafree2 D A B)) ) )  =>  ((k1_circuit2 A B C C) = C) ) ) ).
tt(idempotence_k1_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_extreal2 A A) = A) ) ) ).
tt(idempotence_k1_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k1_finsub_1 A B B) = B) ) ) ).
tt(idempotence_k1_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((k1_funct_4 A A) = A) ) ) ).
tt(idempotence_k1_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k1_fuzzy_1 A B B) = B) ) ) ).
tt(idempotence_k1_geomtrap,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k1_geomtrap A B B) = B) ) ) ).
tt(idempotence_k1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k1_lfuzzy_1 A B B) = B) ) ) ).
tt(idempotence_k1_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k1_measure1 A B C C) = C) ) ) ).
tt(idempotence_k1_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k1_normform A B C C) = C) ) ) ).
tt(idempotence_k1_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k1_square_1 A A) = A) ) ) ).
tt(idempotence_k1_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_valuat_1 A B)) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  =>  ((k1_sublemma A B C C) = C) ) ) ).
tt(idempotence_k20_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k20_mmlquery A B B) = B) ) ) ).
tt(idempotence_k2_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k2_bvfunc_1 A B B) = B) ) ) ).
tt(idempotence_k2_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k2_eqrel_1 A B B) = B) ) ) ).
tt(idempotence_k2_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k2_extreal2 A A) = A) ) ) ).
tt(idempotence_k2_finsop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (m1_finseq_1 C A)) )  =>  ((k2_finsop_1 A B B) = B) ) ) ).
tt(idempotence_k2_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_fuzzy_1 A B B) = B) ) ) ).
tt(idempotence_k2_groeb_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((k2_groeb_2 A B B) = B) ) ) ).
tt(idempotence_k2_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_lfuzzy_0 A B B) = B) ) ) ).
tt(idempotence_k2_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_lfuzzy_1 A B B) = B) ) ) ).
tt(idempotence_k2_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k2_lopclset A B B) = B) ) ) ).
tt(idempotence_k2_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k2_measure1 A B C C) = C) ) ) ).
tt(idempotence_k2_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k2_normform A B C C) = C) ) ) ).
tt(idempotence_k2_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k2_openlatt A B B) = B) ) ) ).
tt(idempotence_k2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k2_pboole A B B) = B) ) ) ).
tt(idempotence_k2_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((k2_pcs_0 A B C D E E) = E) ) ) ).
tt(idempotence_k2_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k2_square_1 A A) = A) ) ) ).
tt(idempotence_k2_substlat,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_substlat A B)) & (m1_subset_1 D (k1_substlat A B)))  =>  ((k2_substlat A B C C) = C) ) ) ).
tt(idempotence_k2_xboole_0,ax, (! [A:$i,B:$i] :  ((k2_xboole_0 A A) = A) ) ).
tt(idempotence_k3_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_margrel1 B)) ) )  =>  ((k3_bvfunc_1 A A) = A) ) ) ).
tt(idempotence_k3_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k3_closure3 A B C C) = C) ) ) ).
tt(idempotence_k3_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k3_eqrel_1 A B B) = B) ) ) ).
tt(idempotence_k3_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k3_finsub_1 A B B) = B) ) ) ).
tt(idempotence_k3_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_lfuzzy_0 A B B) = B) ) ) ).
tt(idempotence_k3_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k3_lopclset A B B) = B) ) ) ).
tt(idempotence_k3_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k3_openlatt A B B) = B) ) ) ).
tt(idempotence_k3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k3_pboole A B B) = B) ) ) ).
tt(idempotence_k3_xboole_0,ax, (! [A:$i,B:$i] :  ((k3_xboole_0 A A) = A) ) ).
tt(idempotence_k3_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k3_xxreal_0 A A) = A) ) ) ).
tt(idempotence_k3_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k3_zf_refle A B B) = B) ) ) ).
tt(idempotence_k4_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k4_closure3 A B C C) = C) ) ) ).
tt(idempotence_k4_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k4_eqrel_1 A B B) = B) ) ) ).
tt(idempotence_k4_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((m1_subset_1 D (k1_zfmisc_1 B)) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) )  =>  ((k4_stacks_1 A B C D E E) = E) ) ) ).
tt(idempotence_k4_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k4_subset_1 A B B) = B) ) ) ).
tt(idempotence_k4_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k4_xboolean A A) = A) ) ) ).
tt(idempotence_k4_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k4_xxreal_0 A A) = A) ) ) ).
tt(idempotence_k5_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k5_bvfunc_1 A B B) = B) ) ) ).
tt(idempotence_k5_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k5_eqrel_1 A B B) = B) ) ) ).
tt(idempotence_k5_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k5_prob_1 A B C C) = C) ) ) ).
tt(idempotence_k5_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  =>  ((k5_setwiseo A B B) = B) ) ) ).
tt(idempotence_k5_xboolean,ax, (! [A:$i,B:$i] :  ( ((v1_xboolean A) & (v1_xboolean B))  =>  ((k5_xboolean A A) = A) ) ) ).
tt(idempotence_k6_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k6_nat_1 A A) = A) ) ) ).
tt(idempotence_k6_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k6_prob_1 A B C C) = C) ) ) ).
tt(idempotence_k7_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k7_classes2 A B B) = B) ) ) ).
tt(idempotence_k7_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_funct_4 A B C C) = C) ) ) ).
tt(idempotence_k7_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k7_nat_1 A A) = A) ) ) ).
tt(idempotence_k8_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k8_subset_1 A B B) = B) ) ) ).
tt(idempotence_k9_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k9_subset_1 A B B) = B) ) ) ).
tt(ie10_fomodel0,ax, (! [A:$i,B:$i] :  ((k14_fomodel0 A B) = (k6_subset_1 A B)) ) ).
tt(ie10_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k23_member_1 A C) = (k22_member_1 B D)) ) ) ) ).
tt(ie11_fomodel0,ax, (! [A:$i,B:$i] :  ((k15_fomodel0 A B) = (k13_fomodel0 B A)) ) ).
tt(ie11_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k25_member_1 A C) = (k24_member_1 B D)) ) ) ) ).
tt(ie12_fomodel0,ax, (! [A:$i,B:$i] :  ((k13_fomodel0 B A) = (k15_fomodel0 A B)) ) ).
tt(ie12_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k27_member_1 A C) = (k26_member_1 B D)) ) ) ) ).
tt(ie13_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_xboole_0 A B) = (k13_fomodel0 B A)) ) ) ).
tt(ie14_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k13_fomodel0 B A) = (k2_xboole_0 A B)) ) ) ).
tt(ie15_fomodel0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_xboole_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k7_finseq_1 A B) = (k13_fomodel0 B A)) ) ) ).
tt(ie16_fomodel0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_xboole_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k13_fomodel0 B A) = (k7_finseq_1 A B)) ) ) ).
tt(ie17_fomodel0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_xboole_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k7_finseq_1 B A) = (k13_fomodel0 B A)) ) ) ).
tt(ie18_fomodel0,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_xboole_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k13_fomodel0 B A) = (k7_finseq_1 B A)) ) ) ).
tt(ie19_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((k5_relat_1 B A) = (k13_fomodel0 A B)) ) ) ).
tt(ie1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k1_card_1 A) = (k9_xtuple_0 A)) ) ) ).
tt(ie1_complfld,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((m1_subset_1 C (u1_struct_0 k1_complfld)) & (m1_subset_1 D (u1_struct_0 k1_complfld))) ) )  =>  ( ( (C = A)  &  (D = B) )  =>  ((k1_algstr_0 k1_complfld C D) = (k3_binop_2 A B)) ) ) ) ).
tt(ie1_euclid_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k7_real_ns1 A))) &  ((m1_subset_1 C (u1_struct_0 (k7_real_ns1 A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_valued_0 E)) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k7_real_ns1 A) B C) = (k1_valued_1 D E)) ) ) ) ).
tt(ie1_euclid,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v7_ordinal1 C) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (A = B)  &  (D = E) )  =>  ((k1_rlvect_1 (k15_euclid C) D A) = (k10_rvsum_1 E B)) ) ) ) ).
tt(ie1_fomodel0,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((k3_finseq_2 A) = (k1_tarski A)) ) ) ).
tt(ie1_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v15_fomodel1 B A) & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((k40_fomodel2 A B) = (k22_fomodel0 B)) ) ) ).
tt(ie1_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k37_fomodel3 A B C D) = (k27_fomodel3 A B C D)) ) ) ).
tt(ie1_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D A)) ) )  =>  ((k7_partfun1 B C D) = (k3_funct_2 A B C D)) ) ) ).
tt(ie1_gr_cy_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k2_gr_cy_1)) & (m1_subset_1 B (u1_struct_0 k2_gr_cy_1)))  =>  ((k6_algstr_0 k2_gr_cy_1 A B) = (k20_binop_2 A B)) ) ) ).
tt(ie1_int_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_int_3)) &  ((m1_subset_1 B (u1_struct_0 k1_int_3)) &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_algstr_0 k1_int_3 A B) = (k22_binop_2 C D)) ) ) ) ).
tt(ie1_lattice3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (u1_struct_0 (k1_lattice3 A))) & (m1_subset_1 C (u1_struct_0 (k1_lattice3 A))))  =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_lattices (k1_lattice3 A) B C) = (k2_xboole_0 D E)) ) ) ) ).
tt(ie1_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k13_lattice3 A B C) = (k2_lfuzzy_0 A B C)) ) ) ).
tt(ie1_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v2_membered B))  =>  ( (A = B)  =>  ((k5_member_1 A) = (k4_member_1 B)) ) ) ) ).
tt(ie1_nat_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) & (m1_subset_1 B (u1_struct_0 k3_nat_lat)))  =>  ((k1_lattices k3_nat_lat A B) = (k5_nat_d A B)) ) ) ).
tt(ie1_pdiff_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k15_euclid A) B C) = (k1_valued_1 D E)) ) ) ) ).
tt(ie1_power,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v7_ordinal1 B))  =>  ((k3_power A B) = (k1_newton A B)) ) ) ).
tt(ie1_quatern2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k15_quatern2)) &  ((m1_subset_1 B (u1_struct_0 k15_quatern2)) &  ((v1_quaterni C) & (v1_quaterni D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_algstr_0 k15_quatern2 A B) = (k26_quaterni C D)) ) ) ) ).
tt(ie1_real_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_real_lat)) & (m1_subset_1 B (u1_struct_0 k3_real_lat)))  =>  ((k1_lattices k3_real_lat A B) = (k4_xxreal_0 A B)) ) ) ).
tt(ie1_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered A) & (v3_xxreal_2 A)) )  =>  ((k3_seq_4 A) = (k2_xxreal_2 A)) ) ) ).
tt(ie1_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_vectsp_1)) &  ((m1_subset_1 B (u1_struct_0 k1_vectsp_1)) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_algstr_0 k1_vectsp_1 A B) = (k9_binop_2 C D)) ) ) ) ).
tt(ie1_xxreal_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_xxreal_3 A B) = (k2_xcmplx_0 C D)) ) ) ) ).
tt(ie20_fomodel0,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((k13_fomodel0 A B) = (k5_relat_1 B A)) ) ) ).
tt(ie21_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k1_funct_4 B C) = (k13_fomodel0 B C)) ) ) ).
tt(ie22_fomodel0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k13_fomodel0 B C) = (k1_funct_4 B C)) ) ) ).
tt(ie2_complfld,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xcmplx_0 A) &  ((v1_xcmplx_0 B) &  ((m1_subset_1 C (u1_struct_0 k1_complfld)) & (m1_subset_1 D (u1_struct_0 k1_complfld))) ) )  =>  ( ( (C = A)  &  (D = B) )  =>  ((k6_algstr_0 k1_complfld C D) = (k5_binop_2 A B)) ) ) ) ).
tt(ie2_euclid_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (u1_struct_0 (k7_real_ns1 A))) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  &  ((m1_subset_1 D k1_numbers) & (m1_subset_1 E k1_numbers)) ) ) )  =>  ( ( (B = C)  &  (D = E) )  =>  ((k1_rlvect_1 (k7_real_ns1 A) B D) = (k24_valued_1 C E)) ) ) ) ).
tt(ie2_euclid,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k15_euclid A) B C) = (k4_rvsum_1 D E)) ) ) ) ).
tt(ie2_fomodel0,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  ((k1_tarski A) = (k3_finseq_2 A)) ) ) ).
tt(ie2_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k26_fomodel2 A B C D) = (k14_fomodel2 A B C D)) ) ) ).
tt(ie2_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k27_fomodel3 A B C D) = (k37_fomodel3 A B C D)) ) ) ).
tt(ie2_int_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_int_3)) &  ((m1_subset_1 B (u1_struct_0 k1_int_3)) &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_algstr_0 k1_int_3 A B) = (k20_binop_2 C D)) ) ) ) ).
tt(ie2_lattice3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (u1_struct_0 (k1_lattice3 A))) & (m1_subset_1 C (u1_struct_0 (k1_lattice3 A))))  =>  ( ( (B = D)  &  (C = E) )  =>  ((k2_lattices (k1_lattice3 A) B C) = (k3_xboole_0 D E)) ) ) ) ).
tt(ie2_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k12_lattice3 A B C) = (k3_lfuzzy_0 A B C)) ) ) ).
tt(ie2_member_1,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v2_membered B))  =>  ( (A = B)  =>  ((k7_member_1 A) = (k6_member_1 B)) ) ) ) ).
tt(ie2_nat_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) & (m1_subset_1 B (u1_struct_0 k3_nat_lat)))  =>  ((k2_lattices k3_nat_lat A B) = (k6_nat_d A B)) ) ) ).
tt(ie2_pdiff_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v7_ordinal1 C) &  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (A = B)  &  (D = E) )  =>  ((k1_rlvect_1 (k15_euclid C) D A) = (k10_rvsum_1 E B)) ) ) ) ).
tt(ie2_real_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_real_lat)) & (m1_subset_1 B (u1_struct_0 k3_real_lat)))  =>  ((k2_lattices k3_real_lat A B) = (k3_xxreal_0 A B)) ) ) ).
tt(ie2_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered A) & (v4_xxreal_2 A)) )  =>  ((k2_seq_4 A) = (k1_xxreal_2 A)) ) ) ).
tt(ie2_vectsp_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_vectsp_1)) & (v1_xreal_0 B))  =>  ( (A = B)  =>  ((k4_algstr_0 k1_vectsp_1 A) = (k7_binop_2 B)) ) ) ) ).
tt(ie2_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xcmplx_0 B))  =>  ( (A = B)  =>  ((k2_xxreal_3 A) = (k4_xcmplx_0 B)) ) ) ) ).
tt(ie3_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) ) )  =>  ( (B = C)  =>  ((k4_algstr_0 (k15_euclid A) B) = (k6_rvsum_1 C)) ) ) ) ).
tt(ie3_fomodel0,ax, (! [A:$i,B:$i] :  ((k3_xboole_0 A B) = (k11_fomodel0 A B)) ) ).
tt(ie3_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k14_fomodel2 A B C D) = (k26_fomodel2 A B C D)) ) ) ).
tt(ie3_int_3,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_int_3)) & (v1_int_1 B))  =>  ( (A = B)  =>  ((k4_algstr_0 k1_int_3 A) = (k19_binop_2 B)) ) ) ) ).
tt(ie3_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v3_membered B) &  ((v2_membered C) & (v2_membered D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k9_member_1 A B) = (k8_member_1 C D)) ) ) ) ).
tt(ie3_nat_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) & (m1_subset_1 B (u1_struct_0 k10_nat_lat)))  =>  ((k1_lattices k10_nat_lat A B) = (k5_nat_d A B)) ) ) ).
tt(ie3_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) &  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_algstr_0 k2_vectsp_1 A B) = (k9_binop_2 C D)) ) ) ) ).
tt(ie3_xxreal_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k3_xxreal_3 A B) = (k6_xcmplx_0 C D)) ) ) ) ).
tt(ie4_euclid,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k15_euclid A) B C) = (k8_rvsum_1 D E)) ) ) ) ).
tt(ie4_fomodel0,ax, (! [A:$i,B:$i] :  ((k11_fomodel0 A B) = (k3_xboole_0 A B)) ) ).
tt(ie4_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v3_membered B) &  ((v2_membered C) & (v2_membered D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k11_member_1 A B) = (k10_member_1 C D)) ) ) ) ).
tt(ie4_nat_lat,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) & (m1_subset_1 B (u1_struct_0 k10_nat_lat)))  =>  ((k2_lattices k10_nat_lat A B) = (k6_nat_d A B)) ) ) ).
tt(ie4_pdiff_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) &  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k15_euclid A) B C) = (k45_valued_1 D E)) ) ) ) ).
tt(ie4_vectsp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) &  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) &  ((v1_xreal_0 C) & (v1_xreal_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_algstr_0 k2_vectsp_1 A B) = (k11_binop_2 C D)) ) ) ) ).
tt(ie4_xxreal_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k4_xxreal_3 A B) = (k3_xcmplx_0 C D)) ) ) ) ).
tt(ie5_euclid_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (u1_struct_0 (k10_funcsdom A))) &  ((m1_subset_1 C (u1_struct_0 (k10_funcsdom A))) &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_valued_0 E)) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k10_funcsdom A) B C) = (k1_valued_1 D E)) ) ) ) ).
tt(ie5_fomodel0,ax, (! [A:$i,B:$i] :  ((k3_xboole_0 A B) = (k12_fomodel0 A B)) ) ).
tt(ie5_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v3_membered B) &  ((v2_membered C) & (v2_membered D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k13_member_1 A B) = (k12_member_1 C D)) ) ) ) ).
tt(ie5_quatern2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_quaterni A) &  ((v1_quaterni B) &  ((m1_subset_1 C (u1_struct_0 k16_quatern2)) & (m1_subset_1 D (u1_struct_0 k16_quatern2))) ) )  =>  ( ( (C = A)  &  (D = B) )  =>  ((k6_algstr_0 k16_quatern2 C D) = (k27_quaterni A B)) ) ) ) ).
tt(ie5_vectsp_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) & (v1_xreal_0 B))  =>  ( (A = B)  =>  ((k4_algstr_0 k2_vectsp_1 A) = (k7_binop_2 B)) ) ) ) ).
tt(ie5_xxreal_3,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xcmplx_0 B))  =>  ( (A = B)  =>  ((k5_xxreal_3 A) = (k5_xcmplx_0 B)) ) ) ) ).
tt(ie6_euclid_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (u1_struct_0 (k10_funcsdom A))) &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  &  ((m1_subset_1 D k1_numbers) & (m1_subset_1 E k1_numbers)) ) )  =>  ( ( (B = C)  &  (D = E) )  =>  ((k1_rlvect_1 (k10_funcsdom A) B D) = (k24_valued_1 C E)) ) ) ) ).
tt(ie6_fomodel0,ax, (! [A:$i,B:$i] :  ((k12_fomodel0 A B) = (k3_xboole_0 A B)) ) ).
tt(ie6_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v3_membered B) &  ((v2_membered C) & (v2_membered D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k15_member_1 A B) = (k14_member_1 C D)) ) ) ) ).
tt(ie6_quatern2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k16_quatern2)) & (v1_quaterni B))  =>  ( (A = B)  =>  ((k4_algstr_0 k16_quatern2 A) = (k28_quaterni B)) ) ) ) ).
tt(ie6_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  ((k1_group_1 A) = (k5_struct_0 A)) ) ) ).
tt(ie6_xxreal_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) &  ((v1_xcmplx_0 C) & (v1_xcmplx_0 D)) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_xxreal_3 A B) = (k7_xcmplx_0 C D)) ) ) ) ).
tt(ie7_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k9_subset_1 A A B) = (k13_fomodel0 A B)) ) ) ).
tt(ie7_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k17_member_1 A C) = (k16_member_1 B D)) ) ) ) ).
tt(ie8_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k13_fomodel0 A B) = (k9_subset_1 A A B)) ) ) ).
tt(ie8_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k19_member_1 A C) = (k18_member_1 B D)) ) ) ) ).
tt(ie9_fomodel0,ax, (! [A:$i,B:$i] :  ((k6_subset_1 A B) = (k14_fomodel0 A B)) ) ).
tt(ie9_member_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered A) &  ((v2_membered B) &  ((v1_xreal_0 C) & (v1_xxreal_0 D)) ) )  =>  ( ( (A = B)  &  (C = D) )  =>  ((k21_member_1 A C) = (k20_member_1 B D)) ) ) ) ).
tt(involutiveness_k10_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k10_complex1 (k10_complex1 A)) = A) ) ) ).
tt(involutiveness_k10_petri,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k10_petri A B (k10_petri A B C)) = C) ) ) ).
tt(involutiveness_k11_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k11_seq_4 (k11_seq_4 A)) = A) ) ) ).
tt(involutiveness_k12_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k12_complex1 (k12_complex1 A)) = A) ) ) ).
tt(involutiveness_k12_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((k12_funcop_1 A B C (k12_funcop_1 A B C D)) = D) ) ) ).
tt(involutiveness_k13_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k13_binop_2 (k13_binop_2 A)) = A) ) ) ).
tt(involutiveness_k13_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_margrel1 A)) )  =>  ((k13_margrel1 (k13_margrel1 A)) = A) ) ) ).
tt(involutiveness_k14_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k14_binop_2 (k14_binop_2 A)) = A) ) ) ).
tt(involutiveness_k14_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k14_complex1 (k14_complex1 A)) = A) ) ) ).
tt(involutiveness_k15_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_complex1 (k15_complex1 A)) = A) ) ) ).
tt(involutiveness_k15_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((k15_margrel1 A (k15_margrel1 A B)) = B) ) ) ).
tt(involutiveness_k18_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  =>  ((k18_seq_4 A (k18_seq_4 A B)) = B) ) ) ).
tt(involutiveness_k18_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))))) )  =>  ((k18_toprealc A B (k18_toprealc A B C)) = C) ) ) ).
tt(involutiveness_k19_binop_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k19_binop_2 (k19_binop_2 A)) = A) ) ) ).
tt(involutiveness_k1_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_binop_2 (k1_binop_2 A)) = A) ) ) ).
tt(involutiveness_k1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((k1_bvfunc_1 A (k1_bvfunc_1 A B)) = B) ) ) ).
tt(involutiveness_k1_card_fil,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_card_fil B A))  =>  ((k1_card_fil A (k1_card_fil A B)) = B) ) ) ).
tt(involutiveness_k1_comseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k1_comseq_2 (k1_comseq_2 A)) = A) ) ) ).
tt(involutiveness_k1_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 B A))) )  =>  ((k1_descip_1 A B (k1_descip_1 A B C)) = C) ) ) ).
tt(involutiveness_k1_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_funcop_1 (k1_funcop_1 A)) = A) ) ) ).
tt(involutiveness_k1_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((k1_goboard9 (k1_goboard9 A)) = A) ) ) ).
tt(involutiveness_k1_group_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_group_2 A (k1_group_2 A B)) = B) ) ) ).
tt(involutiveness_k1_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m1_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k1_matrixc1 (k1_matrixc1 A)) = A) ) ) ).
tt(involutiveness_k1_member_1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k1_member_1 (k1_member_1 A)) = A) ) ) ).
tt(involutiveness_k1_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_real_1 (k1_real_1 A)) = A) ) ) ).
tt(involutiveness_k28_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k28_quaterni (k28_quaterni A)) = A) ) ) ).
tt(involutiveness_k2_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_binop_2 (k2_binop_2 A)) = A) ) ) ).
tt(involutiveness_k2_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k2_complfld A)) = A) ) ) ).
tt(involutiveness_k2_comseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((k2_comseq_2 A (k2_comseq_2 A B)) = B) ) ) ).
tt(involutiveness_k2_group_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k2_group_1 A (k2_group_1 A B)) = B) ) ) ).
tt(involutiveness_k2_prob_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k2_prob_1 A (k2_prob_1 A B)) = B) ) ) ).
tt(involutiveness_k2_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k2_real_1 (k2_real_1 A)) = A) ) ) ).
tt(involutiveness_k2_rearran1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((v1_rearran1 B) &  ((v2_rearran1 B) &  ((v3_rearran1 B (k1_zfmisc_1 A)) & (m1_finseq_1 B (k1_zfmisc_1 A))) ) ) )  =>  ((k2_rearran1 A (k2_rearran1 A B)) = B) ) ) ).
tt(involutiveness_k2_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k2_relat_1 (k2_relat_1 A)) = A) ) ) ).
tt(involutiveness_k2_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k2_supinf_2 (k2_supinf_2 A)) = A) ) ) ).
tt(involutiveness_k2_toprealc,ax, (! [A:$i] :  ((v1_valued_2 A) =>  ((k2_toprealc (k2_toprealc A)) = A) ) ) ).
tt(involutiveness_k2_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_3 (k2_xxreal_3 A)) = A) ) ) ).
tt(involutiveness_k30_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k30_valued_1 (k30_valued_1 A)) = A) ) ) ).
tt(involutiveness_k31_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k31_valued_1 A B (k31_valued_1 A B C)) = C) ) ) ).
tt(involutiveness_k32_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k32_valued_1 A B (k32_valued_1 A B C)) = C) ) ) ).
tt(involutiveness_k34_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v5_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k34_valued_1 A B (k34_valued_1 A B C)) = C) ) ) ).
tt(involutiveness_k35_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k35_valued_1 (k35_valued_1 A)) = A) ) ) ).
tt(involutiveness_k36_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k36_valued_1 A B (k36_valued_1 A B C)) = C) ) ) ).
tt(involutiveness_k37_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k37_valued_1 A B (k37_valued_1 A B C)) = C) ) ) ).
tt(involutiveness_k3_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_arytm_0 (k3_arytm_0 A)) = A) ) ) ).
tt(involutiveness_k3_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_finseq_5 (k3_finseq_5 A)) = A) ) ) ).
tt(involutiveness_k3_fuzzy_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) )  =>  ((k3_fuzzy_1 A (k3_fuzzy_1 A B)) = B) ) ) ).
tt(involutiveness_k3_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k3_relset_1 A B (k3_relset_1 A B C)) = C) ) ) ).
tt(involutiveness_k3_subset_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k3_subset_1 A (k3_subset_1 A B)) = B) ) ) ).
tt(involutiveness_k3_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k3_xboolean A)) = A) ) ) ).
tt(involutiveness_k4_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k4_arytm_0 (k4_arytm_0 A)) = A) ) ) ).
tt(involutiveness_k4_finseq_5,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B A) =>  ((k4_finseq_5 A (k4_finseq_5 A B)) = B) ) ) ).
tt(involutiveness_k4_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k4_measure6 (k4_measure6 A)) = A) ) ) ).
tt(involutiveness_k4_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  ((k4_member_1 (k4_member_1 A)) = A) ) ) ).
tt(involutiveness_k4_seqfunc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((k4_seqfunc A (k4_seqfunc A B)) = B) ) ) ).
tt(involutiveness_k4_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k4_xcmplx_0 (k4_xcmplx_0 A)) = A) ) ) ).
tt(involutiveness_k5_complsp2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k4_finseq_2 A k2_numbers)))  =>  ((k5_complsp2 A (k5_complsp2 A B)) = B) ) ) ).
tt(involutiveness_k5_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k5_measure6 (k5_measure6 A)) = A) ) ) ).
tt(involutiveness_k5_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k5_member_1 (k5_member_1 A)) = A) ) ) ).
tt(involutiveness_k5_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k5_rvsum_2 (k5_rvsum_2 A)) = A) ) ) ).
tt(involutiveness_k5_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_xcmplx_0 (k5_xcmplx_0 A)) = A) ) ) ).
tt(involutiveness_k6_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  =>  ((k6_euclid A (k6_euclid A B)) = B) ) ) ).
tt(involutiveness_k6_glib_001,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m3_glib_001 B A))  =>  ((k6_glib_001 A (k6_glib_001 A B)) = B) ) ) ).
tt(involutiveness_k6_lattice3,ax, (! [A:$i,B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k6_lattice3 A (k6_lattice3 A B)) = B) ) ) ).
tt(involutiveness_k6_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k6_rvsum_1 (k6_rvsum_1 A)) = A) ) ) ).
tt(involutiveness_k6_rvsum_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers)) )  =>  ((k6_rvsum_2 A (k6_rvsum_2 A B)) = B) ) ) ).
tt(involutiveness_k6_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k6_scmyciel (k6_scmyciel A)) = A) ) ) ).
tt(involutiveness_k6_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) =>  ((k6_supinf_2 (k6_supinf_2 A)) = A) ) ) ).
tt(involutiveness_k7_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_binop_2 (k7_binop_2 A)) = A) ) ) ).
tt(involutiveness_k7_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((k7_hurwitz (k7_hurwitz A)) = A) ) ) ).
tt(involutiveness_k7_measure6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_measure6 A B (k7_measure6 A B C)) = C) ) ) ).
tt(involutiveness_k7_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k7_member_1 (k7_member_1 A)) = A) ) ) ).
tt(involutiveness_k7_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k4_finseq_2 A k1_numbers)))  =>  ((k7_rvsum_1 A (k7_rvsum_1 A B)) = B) ) ) ).
tt(involutiveness_k7_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k7_setfam_1 A (k7_setfam_1 A B)) = B) ) ) ).
tt(involutiveness_k7_vectsp_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_vectsp_6 C A B)) )  =>  ((k7_vectsp_6 A B (k7_vectsp_6 A B C)) = C) ) ) ).
tt(involutiveness_k8_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k8_binop_2 (k8_binop_2 A)) = A) ) ) ).
tt(involutiveness_k8_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  =>  ((k8_qmax_1 A (k8_qmax_1 A B)) = B) ) ) ).
tt(involutiveness_k8_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_quaterni (k8_quaterni A)) = A) ) ) ).
tt(involutiveness_k8_rmod_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  & (m1_rmod_4 C A B)) )  =>  ((k8_rmod_4 A B (k8_rmod_4 A B C)) = C) ) ) ).
tt(involutiveness_k9_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  ((k9_margrel1 (k9_margrel1 A)) = A) ) ) ).
tt(irreflexivity_r10_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (r10_analmetr A B B)) ) ) ).
tt(irreflexivity_r1_afvect0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (r1_afvect0 A B B)) ) ) ).
tt(irreflexivity_r1_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (r1_exchsort A B B)) ) ) ).
tt(irreflexivity_r1_gobrd10,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  (~ (r1_gobrd10 A A)) ) ) ).
tt(irreflexivity_r1_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (r1_subset_1 A A)) ) ) ).
tt(irreflexivity_r2_orders_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  (~ (r2_orders_2 A B B)) ) ) ).
tt(irreflexivity_r2_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  (~ (r2_subset_1 A A)) ) ) ).
tt(irreflexivity_r2_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~ (r2_tsep_2 A B B)) ) ) ).
tt(irreflexivity_r2_xboole_0,ax, (! [A:$i,B:$i] :  (~ (r2_xboole_0 A A)) ) ).
tt(irreflexivity_r3_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  =>  (~ (r3_modelc_2 A A)) ) ) ).
tt(irreflexivity_r3_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  =>  (~ (r3_qc_lang2 A B B)) ) ) ).
tt(irreflexivity_r4_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  (~ (r4_tsep_2 A B B)) ) ) ).
tt(irreflexivity_r7_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) ) )  =>  (~ (r7_glib_000 A A)) ) ) ).
tt(l100_asympt_1,ax,(v4_asympt_0 (k47_valued_1 k5_numbers k1_numbers k1_numbers (k3_asympt_1 1) (k4_asympt_1 1)))).
tt(l100_finseq_1,ax,(r2_hidden 7 (k2_finseq_1 7))).
tt(l100_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ( (B = C)  =>  ((k1_funct_1 (k20_fomodel0 A C D) (k12_finseq_1 A B)) = (k12_finseq_1 A D)) )  &  ( (~  (B = C) )  =>  ((k1_funct_1 (k20_fomodel0 A C D) (k12_finseq_1 A B)) = (k12_finseq_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l100_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((r2_hidden C B) => (v1_fomodel3 E (k1_tarski (k4_tarski C C)) D)) ) ) ) ) ) ) ) ) ).
tt(l100_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp)))  &  (H = (k1_funct_1 F D)) )  =>  ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k48_gfacirc1 (k48_gfacirc1 A B C) E D)) = (k2_binarith G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l100_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_diraf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_diraf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_diraf A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_diraf A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_diraf A))) =>  ( ((r2_analoaf (k2_diraf A) B C D E) & (r2_analoaf (k2_diraf A) B C F G))  =>  ( (B = C)  | (r2_analoaf (k2_diraf A) D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l100_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_glib_001 B A) <=> (v5_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(l100_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  ((k1_lattices (k21_interva1 A) (k2_lattices (k21_interva1 A) B C) C) = C) ) ) ) ) ) ) ).
tt(l100_jordan,ax, ((k18_euclid (k19_euclid k6_numbers (k1_real_1 3))) = (k1_real_1 3)) ).
tt(l100_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  => (r5_modelc_2 A B C k6_numbers)) ) ) ) ) ) ).
tt(l100_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_3 D C) &  ((v3_modelc_3 D C) & (l1_modelc_3 D C)) )  =>  (! [E:$i] :  ( ((v1_modelc_3 E C) &  ((v3_modelc_3 E C) & (l1_modelc_3 E C)) )  =>  (! [F:$i] :  ( ((v1_modelc_3 F C) &  ((v3_modelc_3 F C) & (l1_modelc_3 F C)) )  =>  (~  ((r6_modelc_3 C E D) &  ((r6_modelc_3 C D F) &  ((r2_hidden (k7_modelc_2 A B) (u1_modelc_3 C D)) &  ( (~ (r2_hidden B (u1_modelc_3 C D)))  &  (~  ((r2_hidden A (u1_modelc_3 C D)) & (r2_hidden (k7_modelc_2 A B) (u1_modelc_3 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l100_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k3_nat_1 (k2_newton 2 A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k3_nat_1 (k2_newton 2 C) (k2_nat_1 (k4_nat_1 2 D) 1)))  => (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ) ).
tt(l100_ordinal6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) =>  ((k13_ordinal6 1 B) = (k3_ordinal5 B)) ) ) )  =>  ((k13_ordinal6 1 A) = (k3_ordinal5 A)) ) ) ) ).
tt(l100_pepin,ax, ((k4_nat_d (k13_newton 3 128) (k4_pepin 4)) = (k4_nat_1 52 289)) ).
tt(l100_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))) (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))))).
tt(l100_toprealb,ax, ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k6_toprealb (k1_fcont_1 (k1_real_1 1) 1)) (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k6_toprealb (k1_fcont_1 (k1_real_1 1) 1)) (k5_toprealb (k2_rcomp_1 k6_numbers 1))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k6_toprealb (k1_fcont_1 (k1_real_1 1) 1)) (k5_toprealb (k2_rcomp_1 k6_numbers 1))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) ) ).
tt(l100_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v9_waybel_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_orders_2 A (k11_lattice3 A B (k6_waybel_1 A B C)) C)) ) ) ) ) ) ) ).
tt(l101_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v5_pre_topc B (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1) (k15_euclid A)) =>  ((v2_borsuk_7 B (k1_nat_1 A 1) A (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1) | (v5_pre_topc (k16_borsuk_7 A B) (k8_toprealb (k1_nat_1 A 1)) (k8_toprealb A))) ) ) ) ) ) ).
tt(l101_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 A) B) & (r1_xxreal_0 B A))  <=> (r1_xxreal_0 (k17_complex1 B) A)) ) ) ) ) ).
tt(l101_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 8)) & (r2_hidden 2 (k2_finseq_1 8))) ).
tt(l101_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E B) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ((k1_funct_1 (k20_fomodel0 B A C) (k7_finseq_1 D E)) = (k7_finseq_1 (k1_funct_1 (k20_fomodel0 B A C) D) (k1_funct_1 (k20_fomodel0 B A C) E))) ) ) ) ) ) ) ) ) ) ).
tt(l101_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v15_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ((k26_fomodel2 A B D C) = (k14_fomodel2 A B D C)) ) ) ) ) ) ) ) ) ).
tt(l101_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [E:$i] :  ((m2_fomodel2 E B A C) => (v2_fomodel3 E B A C D)) ) ) ) ) ) ) ) ) ) ).
tt(l101_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) (k45_gfacirc1 (k48_gfacirc1 A B C) E D)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)) (k9_margrel1 K)) (k10_margrel1 (k9_margrel1 K) (k9_margrel1 J))) (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I))))))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l101_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_diraf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_diraf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_diraf A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_diraf A))) =>  (~  ((r2_analoaf (k2_diraf A) B C D E) &  ((r2_analoaf (k2_diraf A) B C D F) &  ( (~  (B = C) )  &  (~  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l101_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v5_glib_001 B A) => (v5_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(l101_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (m1_group_2 (k10_group_2 A B C) B)) ) ) ) ) ) ).
tt(l101_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) => (m1_group_9 (k17_group_9 A B C D) A C)) ) ) ) ) ) ) ).
tt(l101_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  ((k2_lattices (k21_interva1 A) B C) = (k2_lattices (k21_interva1 A) C B)) ) ) ) ) ) ) ).
tt(l101_jordan,ax, ((k17_euclid (k19_euclid (k1_real_1 1) 3)) = (k1_real_1 1)) ).
tt(l101_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 B))))) )  =>  ((r5_modelc_2 B C D (k1_nat_1 A 1)) => (r5_modelc_2 B C D A)) ) ) ) ) ) ) ) ) ).
tt(l101_pepin,ax, ((k4_nat_d (k13_newton 3 256) (k4_pepin 4)) = 282) ).
tt(l101_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))))).
tt(l101_toprealb,ax, ((k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1)) = k1_numbers) ).
tt(l101_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k7_xcmplx_0 B A) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ).
tt(l102_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A (k13_complex1 1 2)))  =>  ((v2_borsuk_7 B (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) |  ((k1_funct_1 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 B)) (k2_xcmplx_0 A (k13_complex1 1 2))) = (k30_valued_1 (k1_funct_1 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 B)) A))) ) ) ) ) ) ) ).
tt(l102_finseq_1,ax, ((r2_hidden 3 (k2_finseq_1 8)) & (r2_hidden 4 (k2_finseq_1 8))) ).
tt(l102_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v5_relat_1 A (k1_tarski k1_xboole_0)) <=> (v3_relat_1 A)) ) ) ).
tt(l102_fomodel2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D B C)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel2 E B C)) )  =>  ( ((k5_relat_1 D A) = (k5_relat_1 E A))  => (r2_relset_1 (k35_fomodel1 B) C (k5_relset_1 (k35_fomodel1 B) C (k10_fomodel2 B C D) (k3_finseq_2 A)) (k5_relset_1 (k35_fomodel1 B) C (k10_fomodel2 B C E) (k3_finseq_2 A)))) ) ) ) ) ) ) ) ) ) ).
tt(l102_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r1_tarski (k7_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k22_fomodel4 B) (k25_fomodel4 B)) D) &  ((r1_tarski (k7_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B) (k26_fomodel4 B)) D) & (v10_fomodel4 A B D)) )  => (v2_fomodel3 (k4_fomodel3 B C A) B (k35_fomodel1 B) C (k6_fomodel4 B D A))) ) ) ) ) ) ) ) ).
tt(l102_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) (k48_gfacirc1 (k48_gfacirc1 A B C) E D)) = (k9_margrel1 (k2_binarith (k2_binarith (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)) (k9_margrel1 J)) (k9_margrel1 K))))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l102_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ).
tt(l102_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v5_glib_001 B A) &  ((r1_glib_000 A (k4_glib_001 A B) D C) &  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 E 1))  &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = D) ) ) ) ) ) ) )  =>  ((r2_hidden C (k14_glib_001 A B)) |  ( ( (~ (v3_glib_001 B A))  & (v1_glib_001 B A))  | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(l102_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k21_interva1 A))) =>  ((k2_lattices (k21_interva1 A) B (k2_lattices (k21_interva1 A) C D)) = (k2_lattices (k21_interva1 A) (k2_lattices (k21_interva1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(l102_jordan,ax, ((k18_euclid (k19_euclid (k1_real_1 1) 3)) = 3) ).
tt(l102_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v6_supinf_2 D) & (v6_supinf_2 E))  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  &  ( (F = (k1_relset_1 A E))  &  ((r1_mesfunc1 A B D F) & (r1_mesfunc1 A B E F)) ) ) ) ) )  |  ((k6_mesfunc5 A B C (k3_mesfunc1 A D E)) = (k3_supinf_2 (k6_mesfunc5 A B C D) (k6_mesfunc5 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l102_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 B))))) )  =>  ((r4_modelc_2 B C D) => (r5_modelc_2 B C D A)) ) ) ) ) ) ) ) ) ).
tt(l102_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 2)) (k4_pepin 4)) = (k4_nat_1 71 197)) ).
tt(l102_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_finseq_1 D)) )  =>  ( ((r1_tarski C A) & (r1_tarski D B))  =>  ((k14_finseq_1 (k2_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 (k12_pnproc_1 D (k3_finseq_1 A))))) = (k8_finseq_1 k5_numbers (k14_finseq_1 (k9_xtuple_0 C)) (k14_finseq_1 (k9_xtuple_0 (k12_pnproc_1 D (k3_finseq_1 A)))))) ) ) ) ) ) ) ) ) ) ).
tt(l102_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)))).
tt(l102_toprealb,ax, ((k1_pre_topc k2_topalg_2 (k2_struct_0 k2_topalg_2)) = k2_topalg_2) ).
tt(l102_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 B A)))  & (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ).
tt(l103_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) =>  (~  ( ((k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A) = (k30_valued_1 (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 (k8_toprealb 2)) k12_toprealb B)))  &  (! [C:$i] :  ( ((v1_int_1 C) &  (~ (v1_abian C)) )  =>  (~  (A = (k2_borsuk_7 B (k13_complex1 C 2))) ) ) ) ) ) ) ) ) ) ).
tt(l103_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_chord B A) => (v5_chord (k6_glib_001 A B) A)) ) ) ) ) ).
tt(l103_facirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k11_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k17_facirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E F) (k10_margrel1 F G)) (k10_margrel1 G E)))  &  ( ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l103_finseq_1,ax, ((r2_hidden 5 (k2_finseq_1 8)) & (r2_hidden 6 (k2_finseq_1 8))) ).
tt(l103_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v10_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r1_tarski (k7_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k22_fomodel4 B) (k25_fomodel4 B)) D) &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) D (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k27_fomodel4 B))) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k27_fomodel4 B)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B)) D) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k26_fomodel4 B)) D) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k26_fomodel4 B)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) D (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k28_fomodel4 B))) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k28_fomodel4 B)))  & (v10_fomodel4 A B D)) ) ) ) )  => (v2_fomodel3 (k4_fomodel3 B C A) B (k35_fomodel1 B) C (k6_fomodel4 B D A))) ) ) ) ) ) ) ) ).
tt(l103_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_diraf A))) => (r2_analoaf (k2_diraf A) B C C B)) ) ) ) ) ) ).
tt(l103_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) )  => (v5_glib_001 B A)) ) ) ) ) ).
tt(l103_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k18_interva1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k18_interva1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k18_interva1 A)) =>  ((k1_binop_1 (u1_lattices (k21_interva1 A)) B (k1_binop_1 (u2_lattices (k21_interva1 A)) C D)) = (k1_binop_1 (u2_lattices (k21_interva1 A)) (k1_binop_1 (u1_lattices (k21_interva1 A)) B C) (k1_binop_1 (u1_lattices (k21_interva1 A)) B D))) ) ) ) ) ) ) ) ) ).
tt(l103_jordan,ax, ((k17_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))) = (k1_real_1 1)) ).
tt(l103_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  ( ( (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k30_modelc_1 A)) & (r2_hidden F (k30_modelc_1 A)))  =>  ((k1_binop_1 C E F) = (k43_modelc_1 A B E F)) ) ) )  &  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k30_modelc_1 A)) & (r2_hidden F (k30_modelc_1 A)))  =>  ((k1_binop_1 D E F) = (k43_modelc_1 A B E F)) ) ) ) )  => (r8_binop_1 (k30_modelc_1 A) (k30_modelc_1 A) (k30_modelc_1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(l103_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k9_modelc_2 (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 B))))) )  =>  ( ((r5_modelc_2 B C D A) & (r5_modelc_2 B C E A))  =>  (! [F:$i] :  ( ((v1_modelc_2 F) & (m2_finseq_1 F k5_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 F) A) =>  ((k1_funct_1 D F) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l103_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 4)) (k4_pepin 4)) = (k4_nat_1 32 257)) ).
tt(l103_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))))).
tt(l103_toprealb,ax, ((v1_funct_1 c31__toprealb) &  ((v1_funct_2 c31__toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) &  ((v5_pre_topc c31__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) & (m1_subset_1 c31__toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) ) ) ).
tt(l104_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ((v5_pre_topc A (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) (k15_euclid 2)) =>  ((v2_borsuk_7 A (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) |  ((v3_topalg_6 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A)) (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) & (m1_borsuk_2 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A)) (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7))) ) ) ) ) ).
tt(l104_finseq_1,ax, ((r2_hidden 7 (k2_finseq_1 8)) & (r2_hidden 8 (k2_finseq_1 8))) ).
tt(l104_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k19_glib_001 A B C) = C) ) ) )  => (v5_glib_001 B A)) ) ) ) ) ).
tt(l104_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v1_group_3 D B) & (m1_group_2 D B))  =>  ( (D = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)))  =>  ( ((k5_group_6 B D) = (g3_algstr_0 (u1_struct_0 (k10_group_9 A B C)) (u2_algstr_0 (k10_group_9 A B C))))  &  ((k1_group_1 (k5_group_6 B D)) = (k1_group_1 (k10_group_9 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(l104_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  ((k2_lattices (k21_interva1 A) B (k1_lattices (k21_interva1 A) B C)) = B) ) ) ) ) ) ) ).
tt(l104_jordan,ax, ((k18_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))) = (k1_real_1 3)) ).
tt(l104_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  & (r5_modelc_2 A B D C)) ) ) ) ) ) ) ) ).
tt(l104_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 8)) (k4_pepin 4)) = (k4_nat_1 81 809)) ).
tt(l104_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))))).
tt(l104_sin_cos6,ax, ((k2_funct_1 k4_sin_cos6) = (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos))) ).
tt(l104_toprealb,ax, ((v1_funct_1 (k6_toprealb k4_sin_cos6)) &  ((v1_funct_2 (k6_toprealb k4_sin_cos6) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos))))) &  ((v5_pre_topc (k6_toprealb k4_sin_cos6) (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) & (m1_subset_1 (k6_toprealb k4_sin_cos6) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))))))) ) ) ).
tt(l105_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (~  ( (~ (v2_borsuk_7 A (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1))  &  ((v5_pre_topc A (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) (k15_euclid 2)) &  ((r2_hidden C (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k1_tarski (k1_funct_1 (k16_borsuk_7 2 A) k8_borsuk_7)))) &  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 B (k13_complex1 1 2)) &  (! [D:$i] :  ( ((v1_int_1 D) &  (~ (v1_abian D)) )  =>  (? [E:$i] :  ((m1_borsuk_2 E (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) &  ((r2_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) E (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A))) &  (~  ((k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) C E) (k2_xcmplx_0 B (k13_complex1 1 2))) = (k2_xcmplx_0 (k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) C E) B) (k13_complex1 D 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l105_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((v5_relat_1 D (k3_finseq_2 B)) =>  ((k1_funct_1 (k20_fomodel0 B A C) (k1_funct_1 (k8_fomodel0 B) D)) = (k1_funct_1 (k8_fomodel0 B) (k3_relat_1 D (k20_fomodel0 B A C)))) ) ) ) ) ) ) ) ) ).
tt(l105_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  => (v4_geomtrap (k2_diraf A))) ) ).
tt(l105_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_glib_000 A (k4_glib_001 A B) D C) & (v5_glib_001 B A))  =>  ((r2_hidden D (k13_glib_001 A B)) |  ( ( (~ (v3_glib_001 B A))  & (v1_glib_001 B A))  | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(l105_jordan,ax, ((k17_euclid (k19_euclid 1 3)) = 1) ).
tt(l105_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (r5_modelc_2 A B C D)) )  => (r4_modelc_2 A B C)) ) ) ) ) ) ) ).
tt(l105_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 16)) (k4_pepin 4)) = 64) ).
tt(l105_prepower,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  ((v2_comseq_2 C) &  ((r1_xxreal_0 k6_numbers A) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers))  &  ((k1_seq_1 C D) = (k7_prepower (k1_seq_1 B D) A)) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k2_seq_2 B) k6_numbers) |  ((k2_seq_2 C) = (k7_prepower (k2_seq_2 B) A)) ) ) ) ) ) ) ) ) ).
tt(l105_toprealb,ax, ((k1_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c25__toprealb))) = c25__toprealb) ).
tt(l106_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  (~  ( (~ (v2_borsuk_7 A (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1))  &  ((v5_pre_topc A (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) (k15_euclid 2)) &  ((r2_hidden B (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k1_tarski (k1_funct_1 (k16_borsuk_7 2 A) k8_borsuk_7)))) &  (! [C:$i] :  ( ((v1_int_1 C) &  (~ (v1_abian C)) )  =>  (~  (! [D:$i] :  ((m1_borsuk_2 D (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) =>  ((r2_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) D (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r1_xxreal_0 k6_numbers E) & (r1_xxreal_0 E (k13_complex1 1 2)))  =>  ((k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B D) (k2_xcmplx_0 E (k13_complex1 1 2))) = (k2_xcmplx_0 (k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B D) E) (k13_complex1 C 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l106_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  => (r2_hidden C (k4_finseq_2 A B))) ) ) ) ) ) ).
tt(l106_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (~  ((v13_fomodel1 B A) &  ((k9_subset_1 (k15_fomodel1 A) (k10_xtuple_0 B) (k16_fomodel1 A)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(l106_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v10_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((v12_fomodel4 D 1 B) & (v10_fomodel4 A B D))  => (v2_fomodel3 (k4_fomodel3 B C A) B (k35_fomodel1 B) C (k6_fomodel4 B D A))) ) ) ) ) ) ) ) ).
tt(l106_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((r1_xxreal_0 (k3_finseq_1 B) 3) => (v5_glib_001 B A)) ) ) ) ) ).
tt(l106_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  => (r2_hidden (k22_interva1 A) (k18_interva1 A))) ) ).
tt(l106_jordan,ax, ((k18_euclid (k19_euclid 1 3)) = 3) ).
tt(l106_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 32)) (k4_pepin 4)) = (k4_nat_1 256 16)) ).
tt(l106_toprealb,ax,(r1_tarski (k2_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c25__toprealb))) c26__toprealb)).
tt(l107_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) =>  (! [C:$i] :  ((m1_borsuk_2 C (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) =>  ((r2_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) C (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A))) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( (! [E:$i] :  ((m1_borsuk_2 E (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) =>  ((r2_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) E (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A))) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r1_xxreal_0 k6_numbers F) & (r1_xxreal_0 F (k13_complex1 1 2)))  =>  ((k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B E) (k2_xcmplx_0 F (k13_complex1 1 2))) = (k2_xcmplx_0 (k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B E) F) (k13_complex1 D 2))) ) ) ) ) ) )  =>  ((k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B C) 1) = (k2_xcmplx_0 (k1_funct_1 (k17_borsuk_7 (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) B C) k6_numbers) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l107_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (~  ((v4_fomodel2 B A) &  ((k9_subset_1 (k15_fomodel1 A) (k10_xtuple_0 B) (k16_fomodel1 A)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(l107_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((v12_fomodel4 C k6_numbers B) & (v10_fomodel4 A B C))  =>  ((v1_partfun1 (k6_fomodel4 B C A) (k35_fomodel1 B)) &  ((v3_relat_2 (k6_fomodel4 B C A)) &  ((v8_relat_2 (k6_fomodel4 B C A)) & (m1_subset_1 (k6_fomodel4 B C A) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 B) (k35_fomodel1 B))))) ) ) ) ) ) ) ) ) ).
tt(l107_jordan,ax, ((k17_euclid (k19_euclid 1 (k1_real_1 3))) = 1) ).
tt(l107_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski B (k2_finseq_1 A)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((r2_hidden C B) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l107_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 64)) (k4_pepin 4)) = (k4_nat_1 673 97)) ).
tt(l107_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k6_prepower (k9_prepower A B) C) = (k9_prepower A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(l107_toprealb,ax, ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c25__toprealb))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c25__toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c25__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb)))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c25__toprealb)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c25__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))))))) ) ).
tt(l108_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (v2_borsuk_7 A (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1))  &  ((v5_pre_topc A (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) (k15_euclid 2)) &  ((v3_topalg_6 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A)) (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7)) & (m1_borsuk_2 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (u1_struct_0 (k8_toprealb (k1_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k14_borsuk_7 1) (k16_borsuk_7 2 A)) (k8_toprealb 2) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7) (k3_funct_2 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))) (u1_struct_0 (k8_toprealb 2)) (k16_borsuk_7 2 A) c18__borsuk_7))) ) ) ) ) ) ).
tt(l108_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (m4_glib_001 B A B)) ) ) ) ).
tt(l108_jordan,ax, ((k18_euclid (k19_euclid 1 (k1_real_1 3))) = (k1_real_1 3)) ).
tt(l108_pepin,ax, ((k4_nat_d (k13_newton 3 (k4_nat_1 256 128)) (k4_pepin 4)) = (k4_nat_1 256 256)) ).
tt(l108_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 1 A) &  ((v2_comseq_2 B) &  ((v2_comseq_2 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k9_prepower A (k1_seq_1 B D))) ) ) ) ) )  =>  ((k2_seq_2 C) = (k9_prepower A (k2_seq_2 B))) ) ) ) ) ) ) ) ).
tt(l108_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(l108_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k5_xcmplx_0 B) (k5_xcmplx_0 A))) ) ) ) ) ) ) ).
tt(l109_borsuk_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2))) &  ((v5_pre_topc A (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1) (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_nat_1 2 1) (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) (u1_struct_0 (k15_euclid 2)))))) ) )  => (v2_borsuk_7 A (k2_nat_1 2 1) 2 (k4_struct_0 (k15_euclid (k2_nat_1 2 1))) 1)) ) ).
tt(l109_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ( (~ (v6_struct_0 F))  &  ((v11_fomodel1 F) & (l1_fomodel1 F)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [J:$i] :  ((v2_fomodel4 J F) =>  (! [K:$i] :  ((v2_fomodel4 K F) =>  ( ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) F) &  ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) I) F) &  ((v4_fomodel4 C A F G J) &  ((v4_fomodel4 D A F H K) & (v4_fomodel4 E B F I (k2_tarski C D))) ) ) )  => (v4_fomodel4 E (k2_xcmplx_0 A B) F (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) I) (k2_xboole_0 J K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l109_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) =>  (! [D:$i] :  ((m4_glib_001 D A C) => (m4_glib_001 D A B)) ) ) ) ) ) ) ) ).
tt(l109_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  => (r2_hidden (k23_interva1 A) (k18_interva1 A))) ) ).
tt(l109_jordan,ax, ((k19_euclid (k1_real_1 1) (k1_real_1 3)) = (k19_euclid (k17_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))) (k18_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))))) ).
tt(l109_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  => (r2_hidden (k18_modelc_2 B C A) (k20_modelc_2 B C))) ) ) ) ) ) ).
tt(l109_pepin,ax,(r1_nat_d (k4_pepin 3) (k2_nat_1 (k13_newton 3 (k2_nat_1 (k4_nat_1 32 k6_numbers) 128)) 1))).
tt(l109_toprealb,ax,(m1_subset_1 (k5_toprealb c25__toprealb) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1))))))).
tt(l10_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_aff_1 A B C D) =>  ((r1_aff_1 A B D C) & (r1_aff_1 A C B D)) ) ) ) ) ) ) ) ) ) ).
tt(l10_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_diraf A B C C G) &  ((r2_diraf A C D E F) &  ((r2_diraf A C E E D) & (r2_diraf A C F F D)) ) )  => (r2_diraf A B D D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (? [C:$i] :  ((v7_ordinal1 C) & (r1_algseq_1 A B C)) ) ) ) ) ) ).
tt(l10_algstr_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_0)) =>  ( ((k1_algstr_0 k3_algstr_0 A B) = (k1_algstr_0 k3_algstr_0 A C))  =>  (B = C) ) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_0)) =>  ( ((k1_algstr_0 k3_algstr_0 B A) = (k1_algstr_0 k3_algstr_0 C A))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(l10_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  ((k1_algstr_3 k3_algstr_3 A (k4_struct_0 k3_algstr_3) B) = B) ) ) ) ) ).
tt(l10_amistd_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_extpro_1 C B)) ) )  =>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_finseq_1 D k5_numbers))  &  ( ((k7_partfun1 k5_numbers D 1) = A)  &  ( ((k7_partfun1 k5_numbers D (k3_finseq_1 D)) = A)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k3_finseq_1 D) E) | (r2_hidden (k7_partfun1 k5_numbers D (k2_nat_1 E 1)) (k3_amistd_1 B C (k7_partfun1 k5_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 (k4_amistd_1 B))) =>  ( ( (C = A)  &  ((k2_compos_0 (u1_compos_1 (k4_amistd_1 B)) D) = 1) )  =>  ((k1_amistd_1 B (k4_amistd_1 B) C D) = (k6_domain_1 k5_numbers (k1_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ).
tt(l10_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C G) (k1_rlvect_1 A D H)))  &  (D = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C I) (k1_rlvect_1 A E J)) (k1_rlvect_1 A F K))) )  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C (k7_real_1 G (k8_real_1 H I))) (k1_rlvect_1 A E (k8_real_1 H J))) (k1_rlvect_1 A F (k8_real_1 H K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_arytm_2,ax,(r1_tarski k4_ordinal1 (k2_xboole_0 (k6_subset_1 a_0_3_arytm_2 a_0_4_arytm_2) k4_ordinal1))).
tt(l10_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) C) = (k10_real_1 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) ) ) ) ) ).
tt(l10_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc E k5_topmetr A) &  ( (B = (k1_funct_1 E k6_numbers))  &  ( (C = (k1_funct_1 E 1))  &  ((v5_pre_topc F k5_topmetr A) &  ( (C = (k1_funct_1 F k6_numbers))  &  ( (D = (k1_funct_1 F 1))  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc G k5_topmetr A) &  ( (B = (k1_funct_1 G k6_numbers))  &  ( (D = (k1_funct_1 G 1))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) G) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_borsuk_5,ax,(v1_borsuk_2 k3_topmetr)).
tt(l10_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k3_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k5_bvfunc_1 A B C) D E) F) = k8_margrel1)  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G (k15_bvfunc_1 A F (k5_bvfunc_2 A E D))) =>  ((k3_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) G) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_cat_4,ax, (! [A:$i] :  (! [B:$i] : (v2_cat_1 (k5_cat_4 A B))) ) ).
tt(l10_cfdiff_1,ax, ((v1_funct_1 (k8_funcop_1 k2_numbers k2_numbers k5_complex1)) &  ((v1_funct_2 (k8_funcop_1 k2_numbers k2_numbers k5_complex1) k2_numbers k2_numbers) & (m1_subset_1 (k8_funcop_1 k2_numbers k2_numbers k5_complex1) (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) ).
tt(l10_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  ( (D = (k10_finseq_1 A B))  =>  ((k9_euclid 2 D C) = (k10_finseq_1 (k8_real_1 C A) (k8_real_1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(l10_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) & (v2_compos_0 A)) )  =>  ((v3_compos_0 A) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((r2_hidden C (k4_finseq_1 (k5_xtuple_0 B))) => (r1_tarski k5_numbers (k1_funct_1 (k10_card_3 (k3_compos_0 A (k2_compos_0 A B))) C))) ) ) ) ) ) ) ).
tt(l10_comptrig,ax, (~ (r1_xxreal_0 (k7_real_1 k32_sin_cos (k10_real_1 k32_sin_cos 2)) (k7_real_1 (k10_real_1 k32_sin_cos 2) (k10_real_1 k32_sin_cos 2)))) ).
tt(l10_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_convex1 A B k6_numbers) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ).
tt(l10_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k4_convfun1)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_funct_1 A C) = (k1_seq_1 B C)) ) ) ) )  =>  ((k4_rlvect_1 k4_convfun1 A) = (k18_rvsum_1 B)) ) ) ) ) ) ).
tt(l10_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k9_cqc_lang A B C)) A) & (v2_cqc_the1 (k8_cqc_lang A B (k9_cqc_lang A C B)) A)) ) ) ) ) ) ) ).
tt(l10_csspace2,ax, ((k4_struct_0 k18_csspace) = k6_csspace) ).
tt(l10_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 A) => (v1_comseq_2 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(l10_ens_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k4_tarski (k4_tarski A C) E) = (k4_tarski (k4_tarski B D) F))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ).
tt(l10_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_tarski (k1_euclid_4 A B C) (k1_euclid_4 A C B))) ) ) ) ) ) ).
tt(l10_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ( (D = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)))  &  (E = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) C B))) )  =>  ((k4_euclid_3 A B C) = (k3_complex2 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k7_euclid 3 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k1_euclid_8 (k9_binop_2 A D) (k9_binop_2 B E) (k9_binop_2 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_fib_fusc,ax, (~  ((k10_ami_3 1) = (k10_ami_3 2)) ) ).
tt(l10_fib_num4,ax, ((k3_power k1_fib_num 2) = (k13_complex1 (k2_xcmplx_0 3 (k7_square_1 5)) 2)) ).
tt(l10_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((k1_pre_ff (k2_nat_1 A 1)) = k6_numbers) ) ) ) ).
tt(l10_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((k1_funct_1 (k1_finseq_7 A B D C) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(l10_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F A))  =>  (! [G:$i] :  ( ((v3_card_1 G k6_numbers) & (m2_finseq_1 G B))  => (r2_relset_1 k5_numbers C (k1_finseqop B A C E G F) (k6_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_finset_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) &  (! [B:$i] :  ((r2_hidden B A) => (v1_finset_1 B)) ) )  => (v1_finset_1 (k3_tarski A))) ) ).
tt(l10_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo D A) &  ((k3_finseq_1 C) = k6_numbers) )  =>  ((k1_finsop_1 A (k8_finseq_1 A C (k12_finseq_1 A B)) D) = (k5_binop_1 A D (k1_finsop_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(l10_fintopo6,ax, (! [A:$i] :  ((l1_orders_2 A) => (m1_fintopo6 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) A)) ) ).
tt(l10_flang_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (~  ( ((k1_afinsq_1 C) = (k2_xcmplx_0 A B))  &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  (! [E:$i] :  ( ((v5_ordinal1 E) &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) )  =>  (~  ( ((k1_afinsq_1 D) = A)  &  ( ((k1_afinsq_1 E) = B)  &  (C = (k1_ordinal4 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((k4_finseq_2 A B) = (k1_funct_2 (k2_finseq_1 A) B)) ) ) ) ).
tt(l10_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C B A)) )  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((k4_finseq_2 (k1_int_2 (k30_fomodel1 B D)) A) = (k1_relset_1 (k4_finseq_2 (k1_int_2 (k19_fomodel1 B (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) D))) A) (k4_fomodel2 B A C (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) D)))) ) ) ) ) ) ) ) ) ).
tt(l10_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden C (k13_glib_001 A B)) => (r1_tarski (k13_glib_001 A B) (k1_glib_002 A C))) ) ) ) ) ) ) ).
tt(l10_goboard1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ( (~ (v3_relat_1 B))  <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers)) ) ) ) ) ) ) ).
tt(l10_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_3_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l10_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 D (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 E (k1_matrix_1 (k2_goboard2 A))) &  ( (C = E)  & (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_goboard9 A)))) ) ) ) )  =>  ( ( (~  (D = (k2_nat_1 B 1)) )  &  (~  (B = (k2_nat_1 D 1)) ) )  | (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) D E)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_goboard9 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r1_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ( (~ (r1_aff_1 A B C E))  &  ((r1_aff_1 A B E F) & (r2_analoaf A C E D F)) ) )  &  (~  ((r1_aff_1 A B C E) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G D H) &  ((r2_analoaf A G E H F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_1 A B) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (B = (k3_xcmplx_0 A C)) ) ) ) ) ) ) ) ).
tt(l10_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A (k6_xcmplx_0 B C)))  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(l10_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((v1_int_7 B) & (r2_hidden A (k1_polynom2 k10_newton B)))  =>  ((r1_int_1 A (k8_nat_3 k10_newton B)) &  (? [C:$i] :  ((v7_ordinal1 C) & (r1_int_1 (k1_newton A C) (k8_nat_3 k10_newton B))) ) ) ) ) ) ) ) ).
tt(l10_integr16,ax, ((k17_rvsum_1 (k6_finseq_1 k2_numbers)) = k6_numbers) ).
tt(l10_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_3_jordan1 A) (k1_zfmisc_1 (k1_euclid 2)))) ) ).
tt(l10_jordan1d,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 k6_numbers (k9_real_1 (k8_real_1 2 A) 1))) ) ) ).
tt(l10_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_kurato_1 A B) = (k2_xboole_0 (k2_xboole_0 (k4_enumset1 (k2_pre_topc A B) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))))) (k2_tarski B (k3_subset_1 (u1_struct_0 A) B))) (k4_enumset1 (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))) (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))))))))) ) ) ) ) ).
tt(l10_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) D) (k8_cqc_lang A (k8_cqc_lang A E C) D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l10_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((k3_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) B) C)) = (k2_nat_1 (k2_nat_1 1 (k3_finseq_1 B)) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(l10_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r2_modelc_2 A B) & (r2_modelc_2 C B))  => (m1_subset_1 (k2_tarski A C) (k1_zfmisc_1 (k13_modelc_2 B)))) ) ) ) ) ) ) ).
tt(l10_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  ( ((k2_lattices k3_nat_lat k4_nat_lat A) = k4_nat_lat)  &  ((k2_lattices k3_nat_lat A k4_nat_lat) = k4_nat_lat) ) ) ) ).
tt(l10_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ((k4_finseq_1 (k4_prvect_2 A)) = (k4_finseq_1 A)) ) ) ).
tt(l10_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k4_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k4_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers k4_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers k4_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  &  ( ((k8_nat_1 k4_numbers G k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers H k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers E k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers J k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers I k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  ( ((k8_nat_1 k4_numbers F k6_numbers) = k6_numbers)  &  (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers E (k2_nat_1 K 1)) = (k5_int_1 (k8_nat_1 k4_numbers C K) (k8_nat_1 k4_numbers D K)))  &  ( ((k8_nat_1 k4_numbers F (k2_nat_1 K 1)) = (k6_int_1 (k8_nat_1 k4_numbers C K) (k8_nat_1 k4_numbers D K)))  &  ( ((k8_nat_1 k4_numbers G (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers J K))  &  ( ((k8_nat_1 k4_numbers H (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers I K))  &  ( ((k8_nat_1 k4_numbers C (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers D K))  &  ( ((k8_nat_1 k4_numbers J (k2_nat_1 K 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers G K) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 K 1)) (k8_nat_1 k4_numbers J K))))  &  ( ((k8_nat_1 k4_numbers I (k2_nat_1 K 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers H K) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 K 1)) (k8_nat_1 k4_numbers I K))))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers F (k2_nat_1 K 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_numbers,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_tarski A B) = (k1_tarski C))  =>  ( (C = (k1_tarski A))  &  (A = B) ) ) ) ) ) ).
tt(l10_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v2_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l10_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A D E)) = (k3_rlvect_1 A (k3_rlvect_1 A B (k3_rlvect_1 A C D)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k8_group_1 A B (k5_algstr_0 A C D)) (k8_group_1 A E (k5_algstr_0 A C F))) = (k5_algstr_0 A F D))  =>  ((k8_group_1 A (k3_rlvect_1 A B (k4_algstr_0 A (k1_group_1 A))) (k5_algstr_0 A C D)) = (k8_group_1 A (k3_rlvect_1 A E (k4_algstr_0 A (k1_group_1 A))) (k5_algstr_0 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  (~  ((r2_hidden C A) & (r2_hidden C B)) ) )  <=> (r1_xboole_0 A B)) ) ) ).
tt(l10_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  => (m1_subset_1 (k1_funct_1 (k9_funct_7 D A) C) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(l10_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) <=> (v2_prob_1 (k2_prob_1 A B))) ) ) ) ).
tt(l10_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_projdes1 A B C D E) => (r1_projdes1 A C D E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r6_binop_1 (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A))) ) ).
tt(l10_qmax_1,ax, (! [A:$i] :  ( ((v5_relat_1 A k12_prob_1) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) ) )  =>  ((v2_prob_1 A) =>  ((v2_comseq_2 (k8_prob_1 k1_numbers k12_prob_1 A c2__qmax_1)) &  ((k2_seq_2 (k8_prob_1 k1_numbers k12_prob_1 A c2__qmax_1)) = (k1_funct_1 c2__qmax_1 (k3_prob_1 k1_numbers A))) ) ) ) ) ).
tt(l10_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 (k2_xcmplx_0 2 2) (k1_radix_1 A))) ) ) ).
tt(l10_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_group_10 C A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 C A) B)))) )  =>  (~  ( ((k1_card_1 C) = k4_ordinal1)  &  ((r1_tarski C k4_ordinal1) &  ( (~  (B = k6_numbers) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (~  ( (~ (v1_finset_1 E))  & (v3_funct_1 (k2_partfun1 (k3_group_10 C A) B D (k3_group_10 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (? [C:$i] :  ( ((v1_prob_2 C) & (m2_finseq_1 C (k1_random_1 A)))  &  ( ((k1_relset_1 A B) = (k3_tarski (k2_relset_1 (k1_random_1 A) C)))  &  ( ((k4_finseq_1 C) = (k4_finseq_1 (k1_uproots (k1_relset_1 A B))))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k1_tarski (k1_funct_1 (k1_uproots (k1_relset_1 A B)) D))) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ((r2_hidden E (k1_funct_1 C D)) & (r2_hidden F (k1_funct_1 C D))) )  =>  ((k1_seq_1 B E) = (k1_seq_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  &  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F A) & (r2_hidden G B))  =>  ((k1_binop_1 E F G) = (k11_binop_2 (k1_seq_1 C (k1_tarski F)) (k1_seq_1 D (k1_tarski G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v4_xxreal_2 (k3_limfunc1 A))) ) ) ).
tt(l10_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_real_lat)) =>  ((k4_lattices k3_real_lat A (k3_lattices k3_real_lat B C)) = (k3_lattices k3_real_lat (k4_lattices k3_real_lat A B) (k4_lattices k3_real_lat A C))) ) ) ) ) ) ) ).
tt(l10_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 1 k6_numbers 1)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers))) ).
tt(l10_ringcat1,ax, (! [A:$i] :  ( ((v3_ringcat1 A) & (l1_ringcat1 A))  => (v3_ringcat1 (g1_ringcat1 (u1_ringcat1 A) (u2_ringcat1 A) (u3_ringcat1 A)))) ) ).
tt(l10_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_ordinal1 (k1_card_1 (k5_rusub_4 A B C)) (k1_card_1 B))) ) ) ) ) ) ).
tt(l10_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) = (u1_struct_0 (k15_euclid A))) ) ) ).
tt(l10_robbins4,ax,(r1_xboole_0 (k6_subset_1 3 2) 2)).
tt(l10_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ( ((m1_rusub_1 B C) & (m1_rusub_1 B D))  => (m1_rusub_1 B (k2_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(l10_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ).
tt(l10_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k11_complex1 (k13_complex1 1 (k2_nat_1 A 1)) (k13_complex1 2 (k4_nat_1 (k2_nat_1 A 1) (k2_nat_1 A 3)))) = (k13_complex1 1 (k2_nat_1 A 3))) ) ) ).
tt(l10_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ((k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B))) = (k3_xcmplx_0 (k13_complex1 1 2) (k6_square_1 (k2_xcmplx_0 (k3_xcmplx_0 4 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B))) (k3_xcmplx_0 (k3_xcmplx_0 4 A) B))))) ) ) ) ) ).
tt(l10_sin_cos6,ax, ((k1_rcomp_1 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers)) (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers))) = (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))) ).
tt(l10_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ( ((k9_substut1 A (k5_cqc_lang A)) = (k1_subset_1 (k3_qc_lang1 A)))  &  ( ((v2_qc_lang1 B A) =>  ((k9_substut1 A B) = (k8_substut1 A (k17_qc_lang1 A B))) )  &  ( ((v3_qc_lang1 B A) =>  ((k9_substut1 A B) = (k9_substut1 A (k18_qc_lang1 A B))) )  &  ( ((v4_qc_lang1 B A) =>  ((k9_substut1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k9_substut1 A (k19_qc_lang1 A B)) (k9_substut1 A (k20_qc_lang1 A B)))) )  &  ((v5_qc_lang1 B A) =>  ((k9_substut1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k9_substut1 A (k22_qc_lang1 A B)) (k6_domain_1 (k3_qc_lang1 A) (k21_qc_lang1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(l10_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ((k9_prepower (k25_sin_cos A) B) = (k25_sin_cos (k3_xcmplx_0 B A))) ) ) ) ) ).
tt(l10_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) => (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(l10_topalg_4,ax, ((m1_subset_1 k6_numbers (u1_struct_0 k17_borsuk_1)) & (m1_subset_1 1 (u1_struct_0 k17_borsuk_1))) ).
tt(l10_topalg_5,ax,(r1_xxreal_0 (k9_real_1 (k10_real_1 3 2) (k10_real_1 1 2)) 1)).
tt(l10_topdim_1,ax, (! [A:$i] : (r2_hidden A (k13_prob_1 (u1_struct_0 (k1_compts_1 A)) k5_numbers (k9_setfam_1 (u1_struct_0 (k1_compts_1 A))) (k1_topdim_1 (k1_compts_1 A)) 1))) ).
tt(l10_topreal2,ax, ((k17_euclid (k19_euclid 1 1)) = 1) ).
tt(l10_toprealb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (m1_subset_1 D (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(l10_uniform1,ax, (k5_topmetr = (k3_pcomps_1 (k2_topmetr k6_numbers 1))) ).
tt(l10_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  ((r2_funct_2 (k2_valuat_1 A C) k6_margrel1 (k8_valuat_1 A C D (k5_cqc_lang A)) (k1_margrel1 k6_margrel1 (k2_valuat_1 A C) k8_margrel1)) &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v5_relat_1 F (k3_qc_lang1 A)) &  ((v3_card_1 F E) & (m2_finseq_1 F (k2_qc_lang1 A))) )  =>  (! [G:$i] :  ((m2_subset_1 G (k6_qc_lang1 A) (k8_qc_lang1 A E)) => (r2_funct_2 (k2_valuat_1 A C) k6_margrel1 (k8_valuat_1 A C D (k4_cqc_lang E A G F)) (k5_valuat_1 A C E F (k7_valuat_1 A C E D G)))) ) ) ) ) )  &  ( (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_funct_2 (k2_valuat_1 A C) k6_margrel1 (k8_valuat_1 A C D (k6_cqc_lang A E)) (k15_margrel1 (k2_valuat_1 A C) (k8_valuat_1 A C D E)))) )  &  ( (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_funct_2 (k2_valuat_1 A C) k6_margrel1 (k8_valuat_1 A C D (k7_cqc_lang A B E)) (k16_margrel1 (k2_valuat_1 A C) (k8_valuat_1 A C D B) (k8_valuat_1 A C D E)))) )  &  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_funct_2 (k2_valuat_1 A C) k6_margrel1 (k8_valuat_1 A C D (k11_cqc_lang A E B)) (k3_valuat_1 A C E (k8_valuat_1 A C D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_xreal_0,ax,(m1_subset_1 1 k2_arytm_2)).
tt(l10_xxreal_0,ax, (~ (r2_hidden k2_xxreal_0 (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ).
tt(l10_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_2 (k1_tarski A)) = A) ) ) ).
tt(l10_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k2_zf_lang E) (k2_zf_model A)) =>  ((k2_xboole_0 (k1_tarski (k4_tarski E C)) (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 D) (k7_subset_1 k4_ordinal1 (k4_zf_fund1 (k2_zf_model A)) (k1_tarski E)))) = (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 (k2_zf_lang1 B D (k2_zf_lang E) C)) (k4_zf_fund1 (k2_zf_model A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l10_zfmodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_zf_lang E) & (m2_finseq_1 E k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ( ( ((k3_finseq_1 E) = B)  & (r1_zf_model D F E))  =>  ((r2_hidden C (k2_zf_model E)) | (r1_zf_model D F (k8_zf_lang C E))) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ( ( ((k3_finseq_1 D) = A)  & (r1_zf_model C E D))  =>  ((r2_hidden B (k2_zf_model D)) | (r1_zf_model C E (k8_zf_lang B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l110_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ( ((r1_tarski D E) & (v8_fomodel4 A C D B))  =>  ( ( (~ (v6_fomodel4 D C))  &  (~ (v6_fomodel4 E C)) )  | (v8_fomodel4 A C E B)) ) ) ) ) ) ) ) ) ) ).
tt(l110_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(l110_jordan,ax, ((k19_euclid (k1_real_1 1) 3) = (k19_euclid (k17_euclid (k19_euclid (k1_real_1 1) 3)) (k18_euclid (k19_euclid (k1_real_1 1) 3)))) ).
tt(l110_pepin,ax,(r1_nat_d (k4_pepin 4) (k2_nat_1 (k13_newton 3 (k2_nat_1 (k4_nat_1 64 k6_numbers) (k4_nat_1 256 128))) 1))).
tt(l110_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) = (k1_rcomp_1 k6_numbers k32_sin_cos)) ).
tt(l110_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_tarski A (k2_zfmisc_1 B C)) &  ((r1_tarski D (k2_zfmisc_1 E F)) &  (! [G:$i] :  (! [H:$i] :  ((r2_hidden (k4_tarski G H) A) <=> (r2_hidden (k4_tarski G H) D)) ) ) ) )  =>  (A = D) ) ) ) ) ) ) ) ).
tt(l111_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A B) & (v4_card_3 B))  => (v4_card_3 A)) ) ) ).
tt(l111_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v2_margrel1 A) &  ((v3_margrel1 A k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 k5_numbers) k5_numbers)))) ) ) )  =>  ( ((k19_margrel1 A) = 2)  =>  ( ((k9_xtuple_0 (k6_funct_6 (k10_finseq_1 (k5_comput_1 3 1) (k5_comput_1 3 3)))) = (k9_subset_1 (k3_finseq_2 k5_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k5_comput_1 3 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k5_comput_1 3 3))))  &  ( ((k9_xtuple_0 (k6_funct_6 (k10_finseq_1 (k5_comput_1 3 1) (k5_comput_1 3 3)))) = (k4_finseq_2 3 k5_numbers))  &  ( ((k9_xtuple_0 (k3_relat_1 (k6_funct_6 (k10_finseq_1 (k5_comput_1 3 1) (k5_comput_1 3 3))) A)) = (k4_finseq_2 3 k5_numbers))  &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v2_margrel1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 k5_numbers) k5_numbers)))) )  &  ( (B = (k3_relat_1 (k6_funct_6 (k10_finseq_1 (k5_comput_1 3 1) (k5_comput_1 3 3))) A))  &  ((m2_rfunct_3 B (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) &  ( ((k19_margrel1 B) = 3)  &  ((v3_margrel1 B k5_numbers) &  (~ (v1_xboole_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l111_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_convex4 E A (k8_domain_1 (u1_struct_0 A) B C D)) =>  (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (D = B) )  &  (~  ((k4_convex4 A E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_clvect_1 A B (k3_funct_2 (u1_struct_0 A) k2_numbers E B)) (k1_clvect_1 A C (k3_funct_2 (u1_struct_0 A) k2_numbers E C))) (k1_clvect_1 A D (k3_funct_2 (u1_struct_0 A) k2_numbers E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l111_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m2_funct_2 D (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)))) =>  ((r2_hidden A (k1_funct_1 D B)) => (v4_fomodel4 A 1 C (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))) D) B)) ) ) ) ) ) ) ).
tt(l111_jordan,ax, ((k19_euclid 1 (k1_real_1 3)) = (k19_euclid (k17_euclid (k19_euclid 1 (k1_real_1 3))) (k18_euclid (k19_euclid 1 (k1_real_1 3))))) ).
tt(l111_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_xboole_0 A) & (v1_finseq_1 A)) ) )  =>  ((k19_rvsum_1 A) = 1) ) ) ).
tt(l111_toprealb,ax,(m1_subset_1 (k5_toprealb c26__toprealb) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos))))))).
tt(l111_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (! [E:$i] :  (~  (C = (k4_tarski D E)) ) ) ) ) ) )  &  ( (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  (! [E:$i] :  (~  (C = (k4_tarski D E)) ) ) ) ) ) )  &  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) A) <=> (r2_hidden (k4_tarski C D) B)) ) ) ) )  =>  (A = B) ) ) ) ).
tt(l112_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  => (v4_lattice3 (k21_interva1 A))) ) ).
tt(l112_jordan,ax, ((k19_euclid 1 3) = (k19_euclid (k17_euclid (k19_euclid 1 3)) (k18_euclid (k19_euclid 1 3)))) ).
tt(l112_toprealb,ax, ((k1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1))) c36__toprealb) = (k1_pre_topc k2_topalg_2 (k5_toprealb c25__toprealb))) ).
tt(l113_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_bcialg_1 A (k2_bcialg_1 A B) B)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k1_bcialg_1 A B C)) = (k2_bcialg_1 A (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(l113_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((v3_card_1 B A) &  ((v3_card_1 D A) &  ((k7_finseq_1 B C) = (k7_finseq_1 D E)) ) )  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l113_jordan,ax, ((k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3)))))) ).
tt(l113_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) => (m1_subset_1 (k10_xtuple_0 D) (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 C B))))) ) ) ) ) ) ) ) ).
tt(l113_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ((v2_extpro_1 A 3 k1_scmfsa_2) =>  (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ) ) ) ).
tt(l113_toprealb,ax, ((k1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos))) c37__toprealb) = (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) ).
tt(l114_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k1_bcialg_1 A B C)) = (k2_bcialg_1 A (k1_bcialg_1 A C B))) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k2_bcialg_1 A B) C) = (k2_bcialg_1 A (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ).
tt(l114_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3))))).
tt(l114_sin_cos,ax, ( ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 k6_numbers 1))) = (k1_rcomp_1 k6_numbers 1))  &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 k6_numbers 1)) =>  ((k1_seq_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 k6_numbers 1)) A) = (k1_seq_1 k29_sin_cos A)) ) ) ) ) ).
tt(l114_toprealb,ax,(v5_pre_topc c35__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb c25__toprealb)) (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb)))).
tt(l115_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k2_bcialg_1 A B) C) = (k2_bcialg_1 A (k1_bcialg_1 A B C))) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A C B)) (k4_bcialg_1 A))) ) ) ) ) ) ) ).
tt(l115_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (r1_tarski (k11_intpro_1 (k11_intpro_1 A)) (k11_intpro_1 A))) ) ).
tt(l115_jordan,ax,(r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l115_sin_cos,ax, ((r2_fdiff_1 k29_sin_cos (k2_rcomp_1 k6_numbers 1)) &  (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden A (k2_rcomp_1 k6_numbers 1)) & (r1_xxreal_0 (k1_fdiff_1 k29_sin_cos A) k6_numbers)) ) ) ) ) ).
tt(l115_toprealb,ax, ((v1_funct_1 k4_pscomp_1) &  ((v1_funct_2 k4_pscomp_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 k4_pscomp_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k2_topalg_2))))) ) ).
tt(l115_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( ((v2_waybel_1 A) & (v10_waybel_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A (k12_lattice3 A (k13_lattice3 A D C) B) D) & (r3_orders_2 A D (k13_lattice3 A (k12_lattice3 A D B) C))) ) ) ) ) ) ) ) ) ) ).
tt(l115_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 1 (k5_xcmplx_0 A)) = A) ) ) ).
tt(l115_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden A (k2_zfmisc_1 B C)) &  (! [D:$i] :  (! [E:$i] :  (~  ((k4_tarski D E) = A) ) ) ) ) ) ) ) ) ).
tt(l115_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 (k6_zmodul01 A B C)))) ) ) ) ) ) ).
tt(l116_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A C B)) (k4_bcialg_1 A))) ) ) )  => (v14_bcialg_1 A)) ) ) ).
tt(l116_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l116_toprealb,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) c38__toprealb) = (u1_struct_0 (k15_euclid 2))) ).
tt(l116_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A (k12_lattice3 A (k13_lattice3 A D C) B) D) & (r3_orders_2 A D (k13_lattice3 A (k12_lattice3 A D B) C))) ) ) ) ) ) )  =>  ((v9_waybel_1 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_waybel_1 A (k7_waybel_1 A B)) = B) ) ) ) ) ) ) ).
tt(l116_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) =>  ((k6_zmodul01 A B C) = C) ) ) ) ) ) ) ) ).
tt(l117_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_bcialg_1 A (k2_bcialg_1 A B) B)) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) D) (k1_bcialg_1 A B (k1_bcialg_1 A C D)))) ) ) ) ) ) ) ) ) ).
tt(l117_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A))) ) ) ).
tt(l117_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v9_intpro_1 (k11_intpro_1 A))) ) ).
tt(l117_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3))))).
tt(l117_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k23_modelc_3 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 D))))) )  =>  ( ((r2_hidden (k7_modelc_2 B C) (u1_modelc_3 D (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 D) E 1) D))) &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r6_modelc_3 D (k10_modelc_3 (k1_funct_1 E F) D) (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 D) E (k1_nat_1 F 1)) D))) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 A F))  & (r2_hidden C (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 E F) D)))) ) ) ) ) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 A F) |  ((r2_hidden B (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 E F) D))) & (r2_hidden (k7_modelc_2 B C) (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 E F) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l117_toprealb,ax,(v5_pre_topc c38__toprealb (k15_euclid 2) k2_topalg_2)).
tt(l117_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k5_xcmplx_0 B) (k5_xcmplx_0 A))) ) ) ) ) ) ).
tt(l118_jordan,ax,(r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l118_sin_cos,ax, ( ((k1_seq_1 k29_sin_cos k6_numbers) = k6_numbers)  &  (~ (r1_xxreal_0 (k1_seq_1 k29_sin_cos 1) 1)) ) ).
tt(l118_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k11_toprealb k9_toprealb)))) =>  ( (A = a_0_2_toprealb)  => (v5_pre_topc (k2_tmap_1 (k11_toprealb k9_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))) k14_toprealb (k1_pre_topc (k11_toprealb k9_toprealb) A)) (k1_pre_topc (k11_toprealb k9_toprealb) A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) ) ) ).
tt(l118_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B))) ) ) ) ) ) ).
tt(l119_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ( ((v1_finset_1 A) & (v5_finset_1 A))  => (v1_finset_1 (k21_fomodel0 A))) ) ) ).
tt(l119_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3)) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l119_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k23_modelc_3 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 C))))) )  =>  (~  ((r2_hidden (k7_modelc_2 A B) (u1_modelc_3 C (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 C) D 1) C))) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r6_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C) (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 C) D (k1_nat_1 E 1)) C))) )  &  ( (? [E:$i] :  ((v7_ordinal1 E) &  ((r1_xxreal_0 1 E) &  (~  ((r2_hidden (k7_modelc_2 A B) (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C))) &  ((r2_hidden A (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C))) &  (~ (r2_hidden B (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C)))) ) ) ) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 E) &  ((r2_hidden B (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C))) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 E F) |  ((r2_hidden (k7_modelc_2 A B) (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D F) C))) & (r2_hidden A (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l119_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k11_toprealb k9_toprealb)))) =>  ( (A = a_0_3_toprealb)  => (v5_pre_topc (k2_tmap_1 (k11_toprealb k9_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))) k14_toprealb (k1_pre_topc (k11_toprealb k9_toprealb) A)) (k1_pre_topc (k11_toprealb k9_toprealb) A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) ) ) ).
tt(l11_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ((r2_diraf A B C C E) &  ((r2_diraf A B D D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (F = G) )  &  ((r2_diraf A C D F G) &  ((r2_diraf A C F F D) & (r2_diraf A C G G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) &  ((v1_algseq_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) ) )  =>  ( ((r1_algseq_1 C D A) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_algseq_1 C D E) => (r1_xxreal_0 A E)) ) )  &  ((r1_algseq_1 C D B) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_algseq_1 C D E) => (r1_xxreal_0 B E)) ) ) ) ) )  =>  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(l11_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  ((k1_algstr_3 k3_algstr_3 (k4_struct_0 k3_algstr_3) A B) = B) ) ) ) ) ).
tt(l11_ami_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_partfun1 B (u1_struct_0 k1_ami_3)) & (v5_memstr_0 B 2 k1_ami_3 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 C) =>  ((r1_xxreal_0 (k1_funct_1 B (k10_ami_3 k6_numbers)) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B (k10_ami_3 1)) k6_numbers) |  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 k6_numbers)) k6_numbers))  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 1)) k6_numbers))  &  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A))) = k6_numbers) )  |  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 1)) = k6_numbers)  &  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A))) = 4) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k1_rlvect_1 A B (k7_real_1 (k7_real_1 C D) E)) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B C) (k1_rlvect_1 A B D)) (k1_rlvect_1 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 (k8_arytm_2 A B) (k8_arytm_2 A C)) =>  ( (A = k11_arytm_3)  | (r1_arytm_2 B C)) ) ) ) ) ) ) ) ).
tt(l11_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k6_asympt_0 B)) & (r2_hidden B (k6_asympt_0 A)))  <=>  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ).
tt(l11_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) =>  ( ((k9_xtuple_0 B) = (k10_xtuple_0 B))  &  ((k9_xtuple_0 B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(l11_bhsp_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k18_complex1 (k10_binop_2 A B)))) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l11_bintree2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (m2_finseq_1 (k4_finseq_5 A B) A)) ) ) ) ).
tt(l11_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_boolealg A B C) => (r2_boolealg A C B)) ) ) ) ) ) ) ).
tt(l11_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  ( ((k7_relat_1 C B) = (k6_domain_1 k6_margrel1 k7_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r1_boolmark A C D) =>  ((k7_relat_1 (k2_boolmark A C D) B) = (k6_domain_1 k6_margrel1 k7_margrel1)) ) ) ) ) ) )  => (v4_petri B A)) ) ) ) ) ).
tt(l11_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (m1_subset_1 (k10_finseq_1 A B) (u1_struct_0 (k4_real_ns1 2)))) ) ) ) ).
tt(l11_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k1_binop_1 (k2_lopban_1 A B) (k1_funct_1 (k2_clopban1 A B) (k4_tarski E C)) (k1_funct_1 (k2_clopban1 A B) (k4_tarski E D))) = (k1_funct_1 (k2_clopban1 A B) (k4_tarski E (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_complex1,ax, (k6_numbers = (k5_arytm_0 k6_numbers k6_numbers)) ).
tt(l11_comptrig,ax, ((k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k10_real_1 k32_sin_cos 2)) = (k8_real_1 2 k32_sin_cos)) ).
tt(l11_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A B (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(l11_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k3_rusub_4 A (k1_rlsub_2 A B C)) = (k7_rusub_4 A (k3_rusub_4 A B) (k3_rusub_4 A C))) ) ) ) ) ) ) ).
tt(l11_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((k4_extreal1 (k8_finseq_1 k7_numbers A (k12_finseq_1 k7_numbers B))) = (k3_supinf_2 (k4_extreal1 A) B)) ) ) ) ) ).
tt(l11_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A D C) A))  => (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A B D) C) A)) ) ) ) ) ) ) ) ) ).
tt(l11_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (A = (k2_csspace A)) ) ) ).
tt(l11_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 (k55_valued_1 k5_numbers k2_numbers A)) => (v1_comseq_2 A)) ) ) ).
tt(l11_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (B = k6_numbers)  =>  ((k1_comptrig (k2_complex2 B (k1_real_1 (k1_comptrig A)))) = k6_numbers) ) ) ) ) ) ).
tt(l11_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 (k7_euclid 3 A B) (k7_euclid 3 C D)) = (k7_euclid 3 (k7_euclid 3 A C) (k7_euclid 3 B D))) ) ) ) ) ) ) ) ) ).
tt(l11_extreal1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((k4_extreal1 (k8_finseq_1 k7_numbers A (k12_finseq_1 k7_numbers B))) = (k3_supinf_2 (k4_extreal1 A) B)) ) ) ) ) ).
tt(l11_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski A))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers B)))  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers D B))))) ) ) ) )  =>  ( (! [C:$i] :  ((m1_rcomp_1 C A) =>  (~ (r1_tarski C (k1_relset_1 k1_numbers B))) ) )  |  ((r1_fdiff_1 B A) &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski A))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers B)))  =>  ((k1_fdiff_1 B A) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers D B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_fib_fusc,ax, (~  ((k10_ami_3 1) = (k10_ami_3 3)) ) ).
tt(l11_fib_num4,ax, ((k3_power k2_fib_num 2) = (k13_complex1 (k6_xcmplx_0 3 (k7_square_1 5)) 2)) ).
tt(l11_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F k6_numbers) & (m2_finseq_1 F B))  => (r2_relset_1 k5_numbers C (k3_finseqop A B C E D F) (k6_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k3_xboole_0 (k4_finseq_2 C A) (k3_finseq_2 B)) (k4_finseq_2 C B))) ) ) ) ).
tt(l11_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_2_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l11_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 D (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 E (k1_matrix_1 (k2_goboard2 A))) &  ( (B = D)  & (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_goboard9 A)))) ) ) ) )  =>  ( ( (~  (E = (k2_nat_1 C 1)) )  &  (~  (C = (k2_nat_1 E 1)) ) )  | (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) D E)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_goboard9 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (m1_group_6 (k5_group_4 A (k8_group_2 A B)) A B)) ) ) ) ).
tt(l11_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_rewrite1 (k3_polyred A B C F) D E) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  => (m1_group_9 (g1_group_9 A (u1_struct_0 B) (u2_algstr_0 B) (u1_group_9 A B)) A B)) ) ) ).
tt(l11_henmodel,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k2_finseq_1 (k3_finseq_1 (k7_finseq_1 A B))) = (k4_subset_1 k5_numbers (k2_finseq_1 (k3_finseq_1 A)) (k2_calcul_2 (k3_finseq_1 A) (k3_finseq_1 B)))) ) ) ) ) ).
tt(l11_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ((r1_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ( (~ (r1_aff_1 A B C F))  &  ((r1_aff_1 A B F E) & (r2_analoaf A C F D E)) ) )  &  (~  ((r1_aff_1 A B C F) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G D H) &  ((r2_analoaf A G F H E) & (r1_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k5_vfunct_1 k5_numbers A B)) B)) ) ) ) ).
tt(l11_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_int_1 A B) & (r1_int_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(l11_int_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (A = k6_numbers)  | (r1_xxreal_0 1 (k1_funct_1 k2_euclid A))) ) ) ).
tt(l11_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_int_2 A) &  ((r1_int_2 A B) & (r1_nat_d A B)) ) ) ) ) ) ) ).
tt(l11_int_7,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ((v1_int_7 C) &  ( ((k8_finseq_1 k5_numbers A (k3_pre_poly k5_numbers B)) = (k3_relat_1 (k1_uproots (k1_polynom2 k10_newton C)) C))  &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (! [E:$i] :  ( ((v7_ordinal1 E) & (v1_int_2 E))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k10_newton) &  ((v1_funct_1 G) &  ((v1_partfun1 G k10_newton) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ((v1_int_7 G) &  ((r2_hidden E (k1_polynom2 k10_newton C)) &  ( ((k1_polynom2 k10_newton G) = (k7_subset_1 k10_newton (k1_polynom2 k10_newton C) (k1_tarski E)))  &  ( (B = (k1_newton E F))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 A))  &  ( ((k3_wsierp_1 A) = (k3_wsierp_1 D))  &  (D = (k3_relat_1 (k1_uproots (k1_polynom2 k10_newton G)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_integr16,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k17_rvsum_1 (k8_finseq_1 k2_numbers A (k12_finseq_1 k2_numbers B))) = (k3_binop_2 (k17_rvsum_1 A) B)) ) ) ) ) ).
tt(l11_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D))) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 F G)) E)) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k18_complex1 (k4_integra5 C D F)) (k11_binop_2 E (k18_complex1 (k10_binop_2 D C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_0_jordan1 A) (k1_zfmisc_1 (k1_euclid 2)))) ) ).
tt(l11_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 2 A) =>  ((k9_real_1 (k4_nat_1 2 A) 2) = (k7_nat_d (k4_nat_1 2 A) 2)) ) ) ) ).
tt(l11_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( (C = (k5_euclid A))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( ( (F = D)  &  ((k1_rlvect_1 (k15_euclid A) F B) = E) )  =>  ((k8_real_1 B (k4_metric_1 (k14_euclid A) C D)) = (k4_metric_1 (k14_euclid A) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C)) (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l11_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 (k1_nat_1 A 2))) & (r2_hidden E (k2_finseq_1 (k1_nat_1 A 2))))  =>  ((r1_xxreal_0 E D) |  ( ((k1_group_1 B) = (k4_algstr_0 B (k1_group_1 B)))  |  ( (~  ( ((k1_funct_1 (k1_matrix11 A B C) (k2_tarski D E)) = (k1_group_1 B))  & (r1_xxreal_0 (k1_funct_1 C E) (k1_funct_1 C D))) )  &  (~  ( ((k1_funct_1 (k1_matrix11 A B C) (k2_tarski D E)) = (k4_algstr_0 B (k1_group_1 B)))  & (r1_xxreal_0 (k1_funct_1 C D) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 C)) =>  ((k3_matrix_1 k1_numbers (k4_matrixr1 C) A B) = (k1_real_1 (k3_matrix_1 k1_numbers C A B))) ) ) ) ) ) ) ) ).
tt(l11_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ) ) ) ) ).
tt(l11_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v5_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  => (m1_subset_1 (k2_tarski (k11_modelc_2 A) (k12_modelc_2 A)) (k1_zfmisc_1 (k13_modelc_2 A)))) ) ) ).
tt(l11_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = (k6_rusub_4 A C B)) ) ) ) ) ) ) ).
tt(l11_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k4_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k4_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers k4_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers k4_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K k5_numbers k4_numbers) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [L:$i] :  ( ((v1_funct_1 L) &  ((v1_funct_2 L k5_numbers k4_numbers) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [M:$i] :  ( ((v1_funct_1 M) &  ((v1_funct_2 M k5_numbers k4_numbers) & (m1_subset_1 M (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [N:$i] :  ( ((v1_funct_1 N) &  ((v1_funct_2 N k5_numbers k4_numbers) & (m1_subset_1 N (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [O:$i] :  ( ((v1_funct_1 O) &  ((v1_funct_2 O k5_numbers k4_numbers) & (m1_subset_1 O (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [P:$i] :  ( ((v1_funct_1 P) &  ((v1_funct_2 P k5_numbers k4_numbers) & (m1_subset_1 P (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [Q:$i] :  ( ((v1_funct_1 Q) &  ((v1_funct_2 Q k5_numbers k4_numbers) & (m1_subset_1 Q (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [R:$i] :  ( ((v1_funct_1 R) &  ((v1_funct_2 R k5_numbers k4_numbers) & (m1_subset_1 R (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( ( ((k8_nat_1 k4_numbers G k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers H k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers E k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers J k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers I k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  ( ((k8_nat_1 k4_numbers F k6_numbers) = k6_numbers)  &  ( (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers E (k2_nat_1 S 1)) = (k5_int_1 (k8_nat_1 k4_numbers C S) (k8_nat_1 k4_numbers D S)))  &  ( ((k8_nat_1 k4_numbers F (k2_nat_1 S 1)) = (k6_int_1 (k8_nat_1 k4_numbers C S) (k8_nat_1 k4_numbers D S)))  &  ( ((k8_nat_1 k4_numbers G (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers J S))  &  ( ((k8_nat_1 k4_numbers H (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers I S))  &  ( ((k8_nat_1 k4_numbers C (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers D S))  &  ( ((k8_nat_1 k4_numbers J (k2_nat_1 S 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers G S) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 S 1)) (k8_nat_1 k4_numbers J S))))  &  ( ((k8_nat_1 k4_numbers I (k2_nat_1 S 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers H S) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 S 1)) (k8_nat_1 k4_numbers I S))))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers F (k2_nat_1 S 1))) ) ) ) ) ) ) ) ) )  &  ( ((k8_nat_1 k4_numbers O k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers P k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers K k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers M k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers R k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers Q k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers L k6_numbers) = B)  &  ( ((k8_nat_1 k4_numbers N k6_numbers) = k6_numbers)  &  (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers M (k2_nat_1 S 1)) = (k5_int_1 (k8_nat_1 k4_numbers K S) (k8_nat_1 k4_numbers L S)))  &  ( ((k8_nat_1 k4_numbers N (k2_nat_1 S 1)) = (k6_int_1 (k8_nat_1 k4_numbers K S) (k8_nat_1 k4_numbers L S)))  &  ( ((k8_nat_1 k4_numbers O (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers R S))  &  ( ((k8_nat_1 k4_numbers P (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers Q S))  &  ( ((k8_nat_1 k4_numbers K (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers L S))  &  ( ((k8_nat_1 k4_numbers R (k2_nat_1 S 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers O S) (k3_xcmplx_0 (k8_nat_1 k4_numbers M (k2_nat_1 S 1)) (k8_nat_1 k4_numbers R S))))  &  ( ((k8_nat_1 k4_numbers Q (k2_nat_1 S 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers P S) (k3_xcmplx_0 (k8_nat_1 k4_numbers M (k2_nat_1 S 1)) (k8_nat_1 k4_numbers Q S))))  &  ((k8_nat_1 k4_numbers L (k2_nat_1 S 1)) = (k8_nat_1 k4_numbers N (k2_nat_1 S 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_funct_2 k5_numbers k4_numbers C K) &  ((r2_funct_2 k5_numbers k4_numbers D L) &  ((r2_funct_2 k5_numbers k4_numbers E M) &  ((r2_funct_2 k5_numbers k4_numbers F N) &  ((r2_funct_2 k5_numbers k4_numbers G O) &  ((r2_funct_2 k5_numbers k4_numbers H P) &  ((r2_funct_2 k5_numbers k4_numbers I Q) & (r2_funct_2 k5_numbers k4_numbers J R)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_numbers,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r2_hidden (k5_funct_4 k1_numbers k1_xboole_0 k12_arytm_3 A B) k1_numbers)) ) ) ) ) ).
tt(l11_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v3_o_ring_1 B A)) ) ) ) ) ).
tt(l11_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k1_algstr_0 A C B) (k1_algstr_0 A D B)) = (k5_algstr_0 A C D)) ) ) ) ) ) ) ) ) ).
tt(l11_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k5_algstr_0 A D E))  =>  (E = (k5_algstr_0 A (k3_rlvect_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_pnproc_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) => (r1_xboole_0 A B)) ) ) ) ) ).
tt(l11_polyform,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k2_xcmplx_0 k6_numbers 1) A)) ) ) ).
tt(l11_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ( ((k1_funct_1 (k3_relat_1 (k9_funct_7 D A) D) C) = (k1_funct_1 D (k1_funct_1 (k9_funct_7 D A) C)))  &  ((k1_funct_1 (k3_relat_1 D (k9_funct_7 D A)) C) = (k1_funct_1 (k9_funct_7 D A) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ) ).
tt(l11_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k1_newton B C) (k1_newton A C))) ) ) ) ) ) ) ) ) ) ).
tt(l11_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) A)) ) ).
tt(l11_qmax_1,ax,(m2_prob_1 c2__qmax_1 k1_numbers k12_prob_1)).
tt(l11_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  ( ( (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H B))  =>  ((k1_binop_1 E G H) = (k11_binop_2 (k1_seq_1 C (k1_tarski G)) (k1_seq_1 D (k1_tarski H)))) ) ) )  &  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H B))  =>  ((k1_binop_1 F G H) = (k11_binop_2 (k1_seq_1 C (k1_tarski G)) (k1_seq_1 D (k1_tarski H)))) ) ) ) )  => (r8_binop_1 A B k1_numbers E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 k6_numbers 1 1)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers 1))) ).
tt(l11_robbins4,ax,(r1_tarski 1 2)).
tt(l11_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) => (m1_rusub_1 B (k1_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(l11_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((r2_hidden (k2_nat_1 (k5_card_1 B) 4) (k9_xtuple_0 (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)))) &  ((k1_funct_1 (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k2_nat_1 (k5_card_1 B) 4)) = (k11_scmfsa_2 (k2_nat_1 k6_numbers (k2_nat_1 (k5_card_1 B) 4)))) ) ) ) ) ) ).
tt(l11_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_finseq_1 G k4_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k4_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B D) = F)  &  ( ((k3_finseq_1 G) = J)  &  ( ((k3_finseq_1 H) = J)  &  ((r1_scpisort G B I) &  ((r1_scpisort H (k6_scmpds_4 (k2_scmpds_8 D E C) B A) I) &  ( (1 = (k1_funct_1 B (k2_scmpds_2 F E)))  &  ( (K = (k2_nat_1 (k2_nat_1 I J) 1))  &  ( ((k2_nat_1 I 1) = (k1_funct_1 B (k1_scmp_gcd K)))  &  ( ((k2_nat_1 I J) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 K 1))))  &  (! [L:$i] :  ( ((v1_relat_1 L) &  ((v4_relat_1 L (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 L) &  ((v5_funct_1 L (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 L (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 L 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [M:$i] :  ( ((v1_relat_1 M) &  ((v4_relat_1 M k5_numbers) &  ((v5_relat_1 M (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 M) & (v1_partfun1 M k5_numbers)) ) ) )  =>  (! [N:$i] :  ((m2_finseq_1 N k4_numbers) =>  (! [O:$i] :  ((m2_finseq_1 O k4_numbers) =>  (! [P:$i] :  ((m2_subset_1 P k1_numbers k5_numbers) =>  (! [Q:$i] :  ((m2_subset_1 Q k1_numbers k5_numbers) =>  (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 L D) = F)  &  ( ((k2_nat_1 (k4_nat_1 2 P) 1) = (k1_funct_1 L (k2_scmpds_2 F E)))  &  ( (Q = (k2_nat_1 (k2_nat_1 (k2_nat_1 I J) (k4_nat_1 2 P)) 1))  &  ( ((k2_nat_1 I R) = (k1_funct_1 L (k1_scmp_gcd Q)))  &  ((k2_nat_1 I S) = (k1_funct_1 L (k1_scmp_gcd (k2_nat_1 Q 1)))) ) ) ) )  =>  ( ( (~  ((r1_xxreal_0 1 R) & (r1_xxreal_0 S J)) )  &  (~ (r1_xxreal_0 S R)) )  |  ((r1_scmpds_6 C L M) &  ((r2_scmpds_6 C L M) &  ( ((k1_funct_1 (k6_scmpds_4 C L M) D) = (k1_funct_1 L D))  &  ( (! [T:$i] :  ((m2_subset_1 T k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 T) =>  ((r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 P) 1) T) |  ((k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 (k2_nat_1 I J) T))) = (k1_funct_1 L (k1_scmp_gcd (k2_nat_1 (k2_nat_1 I J) T)))) ) ) ) )  &  ( ((r1_xxreal_0 S R) =>  ( ((k1_funct_1 (k6_scmpds_4 C L M) (k2_scmpds_2 F E)) = (k6_xcmplx_0 (k4_nat_1 2 P) 1))  &  (! [T:$i] :  ((m2_subset_1 T k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 T) & (r1_xxreal_0 T J))  =>  ((k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I T))) = (k1_funct_1 L (k1_scmp_gcd (k2_nat_1 I T)))) ) ) ) ) )  &  ( ( (~ (r1_xxreal_0 S R))  =>  ( ((k1_funct_1 (k6_scmpds_4 C L M) (k2_scmpds_2 F E)) = (k2_nat_1 (k4_nat_1 2 P) 3))  &  ( (! [T:$i] :  ((m2_subset_1 T k1_numbers k5_numbers) =>  ( ( ((r1_xxreal_0 1 T) &  (~ (r1_xxreal_0 R T)) )  |  ( (~ (r1_xxreal_0 T S))  & (r1_xxreal_0 T J)) )  =>  ((k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I T))) = (k1_funct_1 L (k1_scmp_gcd (k2_nat_1 I T)))) ) ) )  &  (? [T:$i] :  ((m2_subset_1 T k1_numbers k5_numbers) &  ((r1_xxreal_0 R T) &  ((r1_xxreal_0 T S) &  ( ((k2_nat_1 I R) = (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd Q)))  &  ( ((k6_xcmplx_0 (k2_nat_1 I T) 1) = (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 Q 1))))  &  ( ((k2_nat_1 (k2_nat_1 I T) 1) = (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 Q 2))))  &  ( ((k2_nat_1 I S) = (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 Q 3))))  &  ( (! [U:$i] :  ((m2_subset_1 U k1_numbers k5_numbers) =>  ((r1_xxreal_0 R U) =>  ((r1_xxreal_0 T U) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I U))) (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I T))))) ) ) )  &  (! [U:$i] :  ((m2_subset_1 U k1_numbers k5_numbers) =>  ((r1_xxreal_0 U S) =>  ((r1_xxreal_0 U T) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I T))) (k1_funct_1 (k6_scmpds_4 C L M) (k1_scmp_gcd (k2_nat_1 I U))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r1_scpisort N L I) &  ((r1_scpisort O (k6_scmpds_4 C L M) I) &  ( ((k3_finseq_1 N) = J)  &  ((k3_finseq_1 O) = J) ) ) )  => (r2_classes1 N O)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) &  ((r2_classes1 G H) & (r3_graph_2 H 1 J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  =>  ( ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C B) => (r1_xxreal_0 A C)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D B) => (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 C A)) ) ) )  =>  (A = (k3_seq_4 B)) ) ) ) ) ) ).
tt(l11_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ) ).
tt(l11_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k11_complex1 (k13_complex1 1 (k2_nat_1 A 1)) (k13_complex1 3 (k4_nat_1 (k2_nat_1 A 1) (k2_nat_1 A 4)))) = (k13_complex1 1 (k2_nat_1 A 4))) ) ) ).
tt(l11_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 (k13_complex1 1 2) (k7_square_1 3)) (k2_xcmplx_0 A B)) (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B))))) ) ) ) ).
tt(l11_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) = 1)  =>  ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1)) ) ) ) ) ) ).
tt(l11_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 2 (k2_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))))) ) ).
tt(l11_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ( (! [E:$i] :  ((r2_hidden E C) => (r2_hidden E D)) )  => (r1_tarski C D)) ) ) ) ) ) ) ).
tt(l11_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (~  ((r2_hidden B (k1_tarski (k1_tarski A))) &  ((r2_hidden C (k1_tarski (k1_tarski A))) &  ( (~ (r1_setfam_1 B C))  &  (~ (r1_setfam_1 C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l11_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r1_termord A B C C)) ) ) ) ) ) ).
tt(l11_topreal2,ax, ((k18_euclid (k19_euclid 1 1)) = 1) ).
tt(l11_toprealb,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(l11_uniform1,ax, ((u1_struct_0 k5_topmetr) = (u1_struct_0 (k2_topmetr k6_numbers 1))) ).
tt(l11_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_vectsp11 (k3_struct_0 B) A B) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  ( (~  (C = (k4_struct_0 B)) )  &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k3_struct_0 B) C) = (k4_vectsp_1 A B (k1_group_1 A) C)) ) ) ) ) ) ) ) ) ).
tt(l11_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) => (r2_hidden (k4_tarski C D) (k2_waybel_4 A))) ) ) ) ) ) ) ).
tt(l11_xreal_0,ax,(r1_arytm_2 c1__xreal_0 c2__xreal_0)).
tt(l11_xxreal_0,ax, (~ (r1_xxreal_0 k1_xxreal_0 k2_xxreal_0)) ).
tt(l11_xxreal_3,ax, ((k1_xxreal_3 k1_xxreal_0 k1_xxreal_0) = k1_xxreal_0) ).
tt(l11_zfmodel2,ax, (~  ((k2_zf_lang k6_numbers) = (k2_zf_lang 3)) ) ).
tt(l120_clvect_1,ax, ((u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) = (k6_domain_1 (u1_struct_0 o_0_5_clvect_1) (k4_struct_0 o_0_5_clvect_1))) ).
tt(l120_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k4_finseq_2 A C)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(l120_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3)))))).
tt(l120_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k11_toprealb k9_toprealb))) =>  ( (A = k10_toprealb)  => (r1_tmap_1 (k11_toprealb k9_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))) k14_toprealb A)) ) ) ).
tt(l121_clvect_1,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k6_numbers) (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers)))) ) ).
tt(l121_jordan,ax,(r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3)))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l121_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (~  ( (~  ((k3_finseq_1 A) = k6_numbers) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (~  (A = (k7_finseq_1 B (k9_finseq_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(l121_toprealb,ax, ((v1_funct_1 (k8_funcop_1 k1_numbers k1_numbers 1)) & (m1_subset_1 (k8_funcop_1 k1_numbers k1_numbers 1) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ).
tt(l122_clvect_1,ax,(m1_subset_1 (k4_struct_0 o_0_5_clvect_1) (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)))).
tt(l122_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_tarski (a_2_3_fomodel0 A B) (a_1_4_fomodel0 A))) ) ) ) ).
tt(l122_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A))) ) ) ).
tt(l122_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l122_toprealb,ax,(v5_pre_topc k14_toprealb (k11_toprealb k9_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))).
tt(l122_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B))) ) ) ) ) ) ) ).
tt(l123_clvect_1,ax, ((k1_funct_1 c2__clvect_1 (k4_struct_0 o_0_5_clvect_1)) = k6_numbers) ).
tt(l123_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos))) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) A))) ) ) ).
tt(l123_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3)))))).
tt(l123_toprealb,ax, ( ( (~ (v1_xboole_0 (k4_rcomp_1 (k1_real_1 1) 1)))  & (m1_subset_1 (k4_rcomp_1 (k1_real_1 1) 1) (k1_zfmisc_1 k1_numbers)))  &  ( (~ (v1_xboole_0 (k3_rcomp_1 k6_numbers k32_sin_cos)))  & (m1_subset_1 (k3_rcomp_1 k6_numbers k32_sin_cos) (k1_zfmisc_1 k1_numbers))) ) ).
tt(l124_clvect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1))) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_funct_2 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers c2__clvect_1 (k1_clvect_1 (k3_clvect_1 o_0_5_clvect_1) A B)) = (k8_real_1 (k17_complex1 B) (k3_funct_2 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers c2__clvect_1 A))) ) ) ) ) ).
tt(l124_jordan,ax,(r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3)))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l124_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_xxreal_0 (k5_square_1 A) (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 A) (k5_square_1 B)) (k5_square_1 C)) (k5_square_1 D)))) ) ) ) ) ) ) ) ).
tt(l124_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c44__toprealb))) = (k5_toprealb c44__toprealb)) ).
tt(l124_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_3 A (k1_xxreal_3 B B)) = (k1_xxreal_3 (k4_xxreal_3 A B) (k4_xxreal_3 A B))) ) ) ) ) ).
tt(l125_clvect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1))) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers c2__clvect_1 (k3_rlvect_1 (k3_clvect_1 o_0_5_clvect_1) A B)) (k7_real_1 (k3_funct_2 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers c2__clvect_1 A) (k3_funct_2 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) k1_numbers c2__clvect_1 B)))) ) ) ) ).
tt(l125_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid (k1_real_1 1) (k1_real_1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l125_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((m1_vectsp_7 (k9_matrix13 B A A (k12_matrix_1 B A)) B (k6_prvect_1 B A)) &  ((k8_matrix13 B (k12_matrix_1 B A)) = A) ) ) ) ) ) ).
tt(l125_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 (k3_square_1 C) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)) (k3_square_1 D)))) ) ) ) ) ) ) ) ).
tt(l125_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) = (k5_toprealb c45__toprealb)) ).
tt(l125_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_3 A (k1_xxreal_3 k6_numbers B)) = (k1_xxreal_3 (k4_xxreal_3 A k6_numbers) (k4_xxreal_3 A B))) ) ) ) ) ).
tt(l126_clvect_1,ax, ( (~ (v2_struct_0 (g2_clvect_1 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) (k4_struct_0 (k3_clvect_1 o_0_5_clvect_1)) (u1_algstr_0 (k3_clvect_1 o_0_5_clvect_1)) (u1_clvect_1 (k3_clvect_1 o_0_5_clvect_1)) c2__clvect_1)))  & (l2_clvect_1 (g2_clvect_1 (u1_struct_0 (k3_clvect_1 o_0_5_clvect_1)) (k4_struct_0 (k3_clvect_1 o_0_5_clvect_1)) (u1_algstr_0 (k3_clvect_1 o_0_5_clvect_1)) (u1_clvect_1 (k3_clvect_1 o_0_5_clvect_1)) c2__clvect_1))) ).
tt(l126_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)))).
tt(l126_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_xxreal_0 (k5_square_1 A) (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 B) (k5_square_1 C)) (k5_square_1 D)) (k5_square_1 A)))) ) ) ) ) ) ) ) ).
tt(l126_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))) = (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))) ).
tt(l126_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_3 k6_numbers (k1_xxreal_3 A B)) = (k1_xxreal_3 (k4_xxreal_3 k6_numbers A) (k4_xxreal_3 k6_numbers B))) ) ) ) ) ).
tt(l127_clvect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c3__clvect_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c3__clvect_1)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ( ((k1_normsp_0 c3__clvect_1 A) = k6_numbers)  =>  (A = (k4_struct_0 c3__clvect_1)) )  &  ( ( (A = (k4_struct_0 c3__clvect_1))  =>  ((k1_normsp_0 c3__clvect_1 A) = k6_numbers) )  &  ( ((k1_normsp_0 c3__clvect_1 (k1_clvect_1 c3__clvect_1 A C)) = (k8_real_1 (k17_complex1 C) (k1_normsp_0 c3__clvect_1 A)))  & (r1_xxreal_0 (k1_normsp_0 c3__clvect_1 (k1_algstr_0 c3__clvect_1 A B)) (k7_real_1 (k1_normsp_0 c3__clvect_1 A) (k1_normsp_0 c3__clvect_1 B)))) ) ) ) ) ) ) ) ) ).
tt(l127_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid 1 3)))).
tt(l127_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 A)) =>  ((k29_modelc_2 A B k6_numbers) = B) ) ) ) ) ).
tt(l127_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l127_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 (k5_square_1 B) A) => (r1_xxreal_0 B (k7_square_1 A))) ) ) ) ) ).
tt(l127_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 k6_numbers 1)) => (r1_xxreal_0 k6_numbers (k1_seq_1 k16_sin_cos A))) ) ) ).
tt(l127_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1)) = (u1_struct_0 k2_topalg_2)) ).
tt(l127_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k4_xxreal_3 A (k1_xxreal_3 B C)) = (k1_xxreal_3 (k4_xxreal_3 A B) (k4_xxreal_3 A C))) ) ) ) ) ) ) ) ).
tt(l127_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (r1_tarski (u1_struct_0 (k7_zmodul01 A B C)) (u1_struct_0 B))) ) ) ) ) ) ).
tt(l128_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v20_bcialg_1 A) <=> (v13_bcialg_1 A)) ) ) ).
tt(l128_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) 3)))).
tt(l128_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 C)) =>  ((k29_modelc_2 C (k29_modelc_2 C D A) B) = (k29_modelc_2 C D (k2_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(l128_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l128_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  (! [J:$i] :  ((v1_xreal_0 J) =>  (! [K:$i] :  ((v1_xreal_0 K) =>  (! [L:$i] :  ((v1_xreal_0 L) =>  ( ((r1_xxreal_0 G A) &  ((r1_xxreal_0 H B) &  ((r1_xxreal_0 I C) &  ((r1_xxreal_0 J D) &  ((r1_xxreal_0 K E) & (r1_xxreal_0 L F)) ) ) ) )  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 G H) I) J) K) L) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) D) E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l128_toprealb,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1) (k5_toprealb c45__toprealb))) = (k5_toprealb c45__toprealb)) ).
tt(l128_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_xxreal_0 B))  &  ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B)) )  =>  (k6_numbers = (k3_xcmplx_0 B A)) ) ) ) ) ).
tt(l128_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((v1_xreal_0 A) =>  ((v1_xreal_0 B) |  ((k4_xxreal_3 A (k1_xxreal_3 B C)) = (k1_xxreal_3 (k4_xxreal_3 A B) (k4_xxreal_3 A C))) ) ) ) ) ) ) ) ) ).
tt(l129_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v20_bcialg_1 A) => (v17_bcialg_1 A)) ) ) ).
tt(l129_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v12_fomodel4 B k6_numbers A) &  ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  =>  (! [C:$i] :  ((v10_fomodel4 C A B) =>  (! [D:$i] :  ( ((v15_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( ((k14_fomodel2 A (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A B C)) (k39_fomodel4 A B C) D) = 1)  <=> (r2_hidden D C)) ) ) ) ) ) ) ) ) ).
tt(l129_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) (k1_real_1 3))))).
tt(l129_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l129_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 (k5_square_1 B) (k5_square_1 A))) )  => (r1_xxreal_0 B A)) ) ) ) ) ).
tt(l129_toprealb,ax,(r1_tarski (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1) (k5_toprealb c45__toprealb))) (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))).
tt(l12_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_diraf A B C E F) &  ((r2_diraf A B D G H) &  ((r2_diraf A B E E C) &  ((r2_diraf A B G G D) &  ((r2_diraf A B F F C) &  ((r2_diraf A B H H D) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ((r2_diraf A C D I J) &  ((r2_diraf A C I I D) & (r2_diraf A C J J D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k3_algstr_3)) &  ((k1_algstr_3 k3_algstr_3 A B D) = C) ) ) ) ) ) ) ) ) ).
tt(l12_ami_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_partfun1 B (u1_struct_0 k1_ami_3)) & (v5_memstr_0 B 2 k1_ami_3 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 C) =>  ((r1_xxreal_0 (k1_funct_1 B (k10_ami_3 k6_numbers)) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B (k10_ami_3 1)) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 1)) k6_numbers) |  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 (k2_nat_1 A 1))) (k10_ami_3 k6_numbers)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 1)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 (k2_nat_1 A 1))) (k10_ami_3 1)) = (k6_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 k6_numbers)) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 C B (k4_nat_1 4 A)) (k10_ami_3 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B C) D) (k3_rlvect_1 A (k3_rlvect_1 A E F) G)) = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B E) (k3_rlvect_1 A C F)) (k3_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k2_c0sp2 A)) => (r2_hidden B (k6_c0sp1 (u1_struct_0 A)))) ) ) ) ).
tt(l12_card_2,ax, (! [A:$i] :  (! [B:$i] : (r2_wellord2 (k2_zfmisc_1 A B) (k2_zfmisc_1 (k1_card_1 A) B))) ) ).
tt(l12_card_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ((v2_ordinal2 A) & (v2_ordinal2 B)) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((r2_hidden C (k9_xtuple_0 B)) &  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l12_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 2))) =>  ( ( (E = (k10_finseq_1 A B))  &  (F = (k10_finseq_1 C D)) )  =>  ( ((k3_rlvect_1 (k4_real_ns1 2) E F) = (k10_finseq_1 (k7_real_1 A C) (k7_real_1 B D)))  &  ((k5_algstr_0 (k4_real_ns1 2) E F) = (k10_finseq_1 (k9_real_1 A C) (k9_real_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_classes1,ax, (! [A:$i] :  ( ((k2_classes1 A k1_xboole_0) = (k1_tarski A))  &  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((k2_classes1 A (k1_ordinal1 B)) = (k2_xboole_0 (k2_xboole_0 (a_2_3_classes1 A B) (a_2_4_classes1 A B)) (k8_subset_1 (k1_zfmisc_1 (k2_classes1 A B)) (k9_setfam_1 (k2_classes1 A B)) (k1_classes1 A)))) ) )  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_ordinal1 C)) )  =>  ( ((v4_ordinal1 B) &  ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k2_classes1 A D)) ) ) ) ) )  =>  ( (B = k1_xboole_0)  |  ((k2_classes1 A B) = (k3_xboole_0 (k3_tarski (k10_xtuple_0 C)) (k1_classes1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l12_complex1,ax, (k6_complex1 = (k5_arytm_0 1 k6_numbers)) ).
tt(l12_comptrig,ax, (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) ).
tt(l12_comseq_2,ax, ((v1_funct_1 (k8_funcop_1 k2_numbers k5_numbers k5_complex1)) &  ((v1_funct_2 (k8_funcop_1 k2_numbers k5_numbers k5_complex1) k5_numbers k2_numbers) & (m1_subset_1 (k8_funcop_1 k2_numbers k5_numbers k5_complex1) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ).
tt(l12_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  => (r1_tarski (k9_subset_1 (u1_struct_0 B) (k1_tops_1 A C) (k2_struct_0 B)) (k1_tops_1 B D))) ) ) ) ) ) ) ) ) ).
tt(l12_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_convex1 A (k1_convex1 A B D) C) = (k1_convex1 A B (k8_real_1 C D))) ) ) ) ) ) ) ) ) ).
tt(l12_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k3_rusub_4 A (k2_rlsub_2 A B C)) = (k9_subset_1 (u1_struct_0 A) (k3_rusub_4 A B) (k3_rusub_4 A C))) ) ) ) ) ) ) ).
tt(l12_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (~  ( (~ (r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)))  &  ((k4_extreal1 A) = k2_supinf_1) ) ) ) ) ).
tt(l12_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 B A) & (v2_cqc_the1 C A))  => (v2_cqc_the1 (k7_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(l12_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k1_algstr_0 k18_csspace A B) = (k1_series_1 k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) ) ).
tt(l12_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A))) = k6_numbers) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) ) ) ) ) ).
tt(l12_dtconstr,ax, ((u1_struct_0 k5_dtconstr) = (k7_domain_1 k5_numbers k6_numbers 1)) ).
tt(l12_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k7_euclid A B (k7_euclid A C D)) = (k7_euclid A (k7_euclid A B C) D)) ) ) ) ) ) ) ) ) ).
tt(l12_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ( (B = k6_numbers)  &  ((k1_comptrig A) = k6_numbers) )  =>  ((k3_complex2 A B) = k6_numbers) ) ) ) ) ) ).
tt(l12_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  ((k8_euclid 3 (k7_euclid 3 A B) (k7_euclid 3 C D)) = (k7_euclid 3 (k8_euclid 3 A C) (k8_euclid 3 B D))) ) ) ) ) ) ) ) ) ).
tt(l12_fib_fusc,ax, (~  ((k10_ami_3 2) = (k10_ami_3 3)) ) ).
tt(l12_fib_num4,ax, ((k3_power k2_fib_num 3) = (k6_xcmplx_0 2 (k7_square_1 5))) ).
tt(l12_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_int_2 (k1_pre_ff A) (k1_pre_ff (k2_nat_1 A 1))) = 1) ) ) ).
tt(l12_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F k6_numbers) & (m2_finseq_1 F B))  => (r2_relset_1 k5_numbers C (k2_finseqop B A C E F D) (k6_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k35_fomodel1 A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) B)))) )  =>  ((m2_funct_2 (k7_fomodel2 (k3_relat_1 (k22_fomodel1 A) C) (k6_fomodel2 (k36_fomodel1 A) D)) (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B)) & (r1_tarski (k35_fomodel1 A) (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k3_relat_1 (k22_fomodel1 A) C)))) ) ) ) ) ) ) ) ) ).
tt(l12_fomodel3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k2_finseq_1 A) B (k9_funct_2 (k2_finseq_1 A) B)) =>  (! [D:$i] :  ((m2_funct_2 D (k2_finseq_1 A) B (k9_funct_2 (k2_finseq_1 A) B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  ((r2_hidden (k1_domain_1 (k9_funct_2 (k2_finseq_1 A) B) (k9_funct_2 (k2_finseq_1 A) B) C D) (k9_fomodel3 B E A)) <=>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r2_hidden (k1_domain_1 B B (k3_funct_2 (k2_finseq_1 A) B C F) (k3_funct_2 (k2_finseq_1 A) B D F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  ((k5_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C F) (k3_functor0 A B C F) (k6_functor0 A B C E F G) (k2_functor2 A B C C (k1_functor2 A B C) F)) = (k5_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C E) (k3_functor0 A B C F) (k2_functor2 A B C C (k1_functor2 A B C) E) (k6_functor0 A B C E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  => (r1_tarski (k9_xtuple_0 (k6_glib_003 A)) (k7_glib_000 A))) ) ).
tt(l12_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_1_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l12_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(l12_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (C = D)  =>  ( (B = C)  |  ( ( (~  ( (~ (r1_aff_1 A B C E))  &  ((r1_aff_1 A B E F) & (r2_analoaf A C E D F)) ) )  &  (~  ((r1_aff_1 A B C E) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G D H) &  ((r2_analoaf A G E H F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) )  |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_int_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 1 A))  =>  (A = k6_numbers) ) ) ) ).
tt(l12_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ( (~  (B = (k4_struct_0 k1_int_3)) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (C = B)  &  ((r1_xxreal_0 k6_numbers C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_int_3)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_int_3)) =>  (~  ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 D B) E))  &  (~  ( (~  (E = (k4_struct_0 k1_int_3)) )  & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 k1_int_3) k5_numbers k3_int_3 B) (k3_funct_2 (u1_struct_0 k1_int_3) k5_numbers k3_int_3 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k7_real_1 1 k6_numbers) A)) ) ) ).
tt(l12_int_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) & (v1_int_2 D))  =>  ( ( ((k3_finseq_1 B) = A)  &  ((v1_int_7 C) &  ((r1_int_1 D (k8_nat_3 k10_newton C)) &  ( ((k8_nat_3 k10_newton C) = (k3_wsierp_1 B))  &  (B = (k3_relat_1 (k1_uproots (k1_polynom2 k10_newton C)) C)) ) ) ) )  =>  ( ((k8_nat_3 k10_newton C) = 1)  | (r2_hidden D (k1_polynom2 k10_newton C))) ) ) ) ) ) ) ) ) ) ).
tt(l12_integr19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) =>  ((v1_funct_1 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((v1_funct_2 (k2_partfun1 k1_numbers k1_numbers B A) A k1_numbers) & (m1_subset_1 (k2_partfun1 k1_numbers k1_numbers B A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ) ).
tt(l12_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) A) &  ((k1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) A) = (k1_real_1 (k1_seq_1 k19_sin_cos A))) ) ) ) ).
tt(l12_jgraph_5,ax,(r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1))).
tt(l12_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_2_jordan1 A) (k1_zfmisc_1 (k1_euclid 2)))) ) ).
tt(l12_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r2_hidden A B) & (v9_rltopsp1 B (k15_euclid 2)))  =>  ((r1_xxreal_0 (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 B)) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 B)))) ) ) ) ) ) ).
tt(l12_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k9_real_1 (k4_nat_1 2 A) 1) = (k7_nat_d (k4_nat_1 2 A) 1)) ) ) ) ).
tt(l12_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (D = (k5_euclid A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (E = (k9_metric_1 (k14_euclid A) D C))  =>  ((k1_convex1 (k15_euclid A) E B) = (k9_metric_1 (k14_euclid A) D (k8_real_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_jordan5a,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc A k3_topmetr k3_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ( (A = B)  &  ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_rcomp_1 k6_numbers 1))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_rcomp_1 k6_numbers 1)))) ) ) ) ) ) ) ) ).
tt(l12_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  ((v1_lattice6 A) & (v2_lattice6 A)) ) ) ).
tt(l12_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l12_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k2_wsierp_1 (k17_finseq_1 k5_numbers A B)) = (k2_nat_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d A 1) B)) (k1_funct_1 B A))) ) ) ) ) ) ).
tt(l12_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v5_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  ((m1_subset_1 (k1_tarski (k11_modelc_2 A)) (k1_zfmisc_1 (k13_modelc_2 A))) & (m1_subset_1 (k1_tarski (k12_modelc_2 A)) (k1_zfmisc_1 (k13_modelc_2 A)))) ) ) ) ).
tt(l12_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ( ( (F = G)  &  ((r2_hidden F (k3_msualg_1 A D B)) & (r2_hidden H (k3_msualg_1 A D C))) )  =>  ( ( (H = (k5_msualg_3 A B C D E F))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k9_xtuple_0 G)) =>  ((k1_funct_1 H I) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) I)) (k1_funct_1 G I))) ) ) ) )  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k9_xtuple_0 G)) =>  ((k1_funct_1 H I) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) I)) (k1_funct_1 G I))) ) ) )  =>  (H = (k5_msualg_3 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (r1_xboole_0 B (k2_pre_topc A C)))  & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(l12_neckla_2,ax, ((u1_struct_0 (k4_necklace 4)) = (k2_enumset1 k6_numbers 1 2 3)) ).
tt(l12_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (~  ((v5_orders_3 D A B) &  ((v5_orders_3 E B C) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 C) F (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) & (v5_orders_3 F A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k4_algstr_0 A (k1_algstr_0 A (k4_algstr_0 A C) (k4_algstr_0 A B)))) ) ) ) ) ) ) ).
tt(l12_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (D = (k10_finseq_1 A B))  & (r3_pdiff_1 2 1 E D))  =>  ( (C = (k1_fdiff_1 (k1_pdiff_2 2 1 E D) A))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (D = (k10_finseq_1 F G))  &  (? [H:$i] :  ((m1_rcomp_1 H F) &  ((r1_tarski H (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 E D))) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v3_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v2_fdiff_1 J) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 I 1))  &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ((r2_hidden K H) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 E D) K) (k1_seq_1 (k1_pdiff_2 2 1 E D) F)) = (k7_real_1 (k1_seq_1 I (k9_real_1 K F)) (k1_seq_1 J (k9_real_1 K F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((v3_nfcont_1 C (k4_real_ns1 A)) &  ((r2_hidden B C) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  (! [E:$i] :  ((m1_nfcont_1 E (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D A) B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 1))) &  ((r2_hidden F E) &  (~ (r2_hidden (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D B) F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_polynom1 A B))) =>  ( (C = D)  =>  ((k5_vfunct_1 (k15_pre_poly A) B C) = (k4_algstr_0 (k11_polynom1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(l12_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 G B B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ( ((r3_orders_2 B C D) &  ( (E = (k1_funct_1 (k9_funct_7 G A) C))  &  (F = (k1_funct_1 (k9_funct_7 G A) D)) ) )  => (r3_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_projdes1 A B C D E) & (r1_projdes1 A B C D F))  =>  ((r1_collsp A B C D) | (r1_projdes1 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_qmax_1,ax,(r2_relset_1 k5_numbers k5_numbers (k1_relset_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1))) (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)))).
tt(l12_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k11_radix_1 (k6_xcmplx_0 (k1_radix_1 A) 1)) = 1) ) ) ) ).
tt(l12_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 F G) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_realset2,ax, ((k5_binop_1 2 k1_realset2 (k1_funct_7 k6_numbers 2) (k1_funct_7 k6_numbers 2)) = (k1_funct_7 k6_numbers 2)) ).
tt(l12_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((r1_rfunct_4 B C) => (r1_rfunct_4 (k15_valued_1 k1_numbers k1_numbers B A) C)) ) ) ) ) ) ).
tt(l12_ringcat1,ax, (! [A:$i] :  ( ((v3_ringcat1 A) & (l1_ringcat1 A))  => (v1_ringcat1 (u3_ringcat1 A) (u1_ringcat1 A) (u2_ringcat1 A))) ) ).
tt(l12_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B C) = (k4_struct_0 A))  =>  ((k1_algstr_0 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(l12_robbins4,ax,(r1_xboole_0 (k6_subset_1 3 2) 1)).
tt(l12_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ( ((m1_rusub_1 B D) & (m1_rusub_1 C D))  => (m1_rusub_1 (k1_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(l12_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k2_sf_mastr (k1_funct_4 (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers))))) ) ) ) ) ).
tt(l12_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 2)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 3)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1)) ) ) ) ) ) ) ) ) ).
tt(l12_scpisort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k2_scmpds_7 A B C D))) = (k2_nat_1 (k5_card_1 D) 4)) ) ) ) ) ) ) ) ) ).
tt(l12_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B D) = F)  &  ( (1 = (k1_funct_1 B (k2_scmpds_2 F E)))  &  ( (I = (k2_nat_1 (k2_nat_1 G H) 1))  &  ( ((k2_nat_1 G 1) = (k1_funct_1 B (k1_scmp_gcd I)))  &  ( ((k2_nat_1 G H) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 I 1))))  &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  (! [L:$i] :  ((m2_finseq_1 L k4_numbers) =>  (! [M:$i] :  ((m2_finseq_1 M k4_numbers) =>  (! [N:$i] :  ((m2_subset_1 N k1_numbers k5_numbers) =>  (! [O:$i] :  ((m2_subset_1 O k1_numbers k5_numbers) =>  (! [P:$i] :  ((m2_subset_1 P k1_numbers k5_numbers) =>  (! [Q:$i] :  ((m2_subset_1 Q k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 J D) = F)  &  ( ((k2_nat_1 (k4_nat_1 2 N) 1) = (k1_funct_1 J (k2_scmpds_2 F E)))  &  ( (O = (k2_nat_1 (k2_nat_1 (k2_nat_1 G H) (k4_nat_1 2 N)) 1))  &  ( ((k2_nat_1 G P) = (k1_funct_1 J (k1_scmp_gcd O)))  &  ((k2_nat_1 G Q) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 O 1)))) ) ) ) )  =>  ( ( (~  ((r1_xxreal_0 1 P) & (r1_xxreal_0 Q H)) )  &  (~ (r1_xxreal_0 Q P)) )  |  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) &  ( ((k1_funct_1 (k6_scmpds_4 C J K) D) = (k1_funct_1 J D))  &  ( (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 R) =>  ((r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 N) 1) R) |  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 (k2_nat_1 G H) R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 (k2_nat_1 G H) R)))) ) ) ) )  &  ( ((r1_xxreal_0 Q P) =>  ( ((k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 F E)) = (k6_xcmplx_0 (k4_nat_1 2 N) 1))  &  (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 R) & (r1_xxreal_0 R H))  =>  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 G R)))) ) ) ) ) )  &  ( ( (~ (r1_xxreal_0 Q P))  =>  ( ((k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 F E)) = (k2_nat_1 (k4_nat_1 2 N) 3))  &  ( (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ( ( ((r1_xxreal_0 1 R) &  (~ (r1_xxreal_0 P R)) )  |  ( (~ (r1_xxreal_0 R Q))  & (r1_xxreal_0 R H)) )  =>  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 G R)))) ) ) )  &  (? [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) &  ((r1_xxreal_0 P R) &  ((r1_xxreal_0 R Q) &  ( ((k2_nat_1 G P) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd O)))  &  ( ((k6_xcmplx_0 (k2_nat_1 G R) 1) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 1))))  &  ( ((k2_nat_1 (k2_nat_1 G R) 1) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 2))))  &  ( ((k2_nat_1 G Q) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 3))))  &  ( (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ((r1_xxreal_0 P S) =>  ((r1_xxreal_0 R S) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G S))) (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))))) ) ) )  &  (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ((r1_xxreal_0 S Q) =>  ((r1_xxreal_0 S R) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G S))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r1_scpisort L J G) &  ((r1_scpisort M (k6_scmpds_4 C J K) G) &  ( ((k3_finseq_1 L) = H)  &  ((k3_finseq_1 M) = H) ) ) )  => (r2_classes1 L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_scmpds_6 (k2_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D A) => (r1_xxreal_0 D C)) ) )  => (r1_xxreal_0 B C)) ) ) )  =>  (B = (k2_seq_4 A)) ) ) ) ) ) ).
tt(l12_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ).
tt(l12_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_nat_1 (k2_nat_1 (k13_newton A 2) (k4_nat_1 3 A)) 2) = (k4_nat_1 (k2_nat_1 A 1) (k2_nat_1 A 2))) ) ) ).
tt(l12_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B)) 3)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)))) ) ) ) ).
tt(l12_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) => (m1_subset_1 (k7_relset_1 A B C D) (k5_finsub_1 B))) ) ) ) ) ) ) ) ).
tt(l12_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_binop_1 B A) & (v2_binop_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k5_binop_1 A B (k5_binop_1 A B C D) (k5_binop_1 A B E F)) = (k5_binop_1 A B (k5_binop_1 A B C E) (k5_binop_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_sin_cos6,ax, (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 1) (k10_real_1 k32_sin_cos 2))) ).
tt(l12_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r1_termord A B C D) & (r1_termord A B D C))  => (r6_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(l12_topreal1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v8_pre_topc A) <=> (v8_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(l12_topreal2,ax, (~ (r2_hidden (k19_euclid k6_numbers k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)))) ).
tt(l12_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( (~ (r1_aff_1 A B C D))  &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) )  &  (~  ((r1_aff_1 A B C D) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C F))  &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B F C G) &  ((r2_analoaf A F G D E) & (r2_analoaf A F D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~  ((v3_waybel_3 A) &  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v3_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (~  ((v2_funct_2 C (u1_struct_0 A)) &  ((v17_waybel_0 C B A) & (v22_waybel_0 C B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l12_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C A)) )  => (r1_ordinal1 (k2_waybel23 B) (k2_waybel23 C))) ) ) ) ) ) ).
tt(l12_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v25_waybel_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  => (r1_tarski (u1_pre_topc (k13_yellow_6 A (k3_waybel28 A))) (u1_pre_topc (k13_yellow_6 B (k3_waybel28 B))))) ) ) ) ) ).
tt(l12_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (~ (v2_struct_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)))  &  ((v4_orders_2 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)) &  ((v7_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)) & (l1_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C) A)) ) ) ) ) ) ) ) ) ).
tt(l12_xreal_0,ax,(r1_xxreal_0 k6_numbers 1)).
tt(l12_xxreal_3,ax, ((k1_xxreal_3 k2_xxreal_0 k2_xxreal_0) = k2_xxreal_0) ).
tt(l12_zfmodel1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_relset_1 k5_numbers k5_numbers (k24_zf_lang (k8_zf_lang A B)) B) &  ((k23_zf_lang (k8_zf_lang A B)) = A) ) ) ) ) ) ).
tt(l12_zfmodel2,ax, (~  ((k2_zf_lang k6_numbers) = (k2_zf_lang 4)) ) ).
tt(l130_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 3)))).
tt(l130_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 B D) = (k30_modelc_2 A D)) ) )  &  (! [D:$i] :  ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 C D) = (k30_modelc_2 A D)) ) ) )  => (r2_funct_2 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l130_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l130_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ((k3_square_1 (k2_xcmplx_0 (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 D)) (k3_square_1 C))) (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 E) (k3_square_1 F)) (k3_square_1 G)) (k3_square_1 H))))) = (k3_real_1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 D)) (k3_square_1 C)) (k3_square_1 E)) (k3_square_1 F)) (k3_square_1 G)) (k3_square_1 H)) (k8_real_1 2 (k6_square_1 (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 D)) (k3_square_1 C)) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 E) (k3_square_1 F)) (k3_square_1 G)) (k3_square_1 H))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l130_toprealb,ax, ((v1_funct_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1) (k5_toprealb c45__toprealb))) &  ((v1_funct_2 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1) (k5_toprealb c45__toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))))) & (m1_subset_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1) (k5_toprealb c45__toprealb)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))))))) ) ).
tt(l131_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v5_relat_1 C A) &  ((r1_tarski A (k3_finseq_2 B)) &  ((v1_setfam_1 A) &  ((k1_funct_1 (k8_fomodel0 B) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(l131_jordan,ax,(v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 (k1_real_1 3))))).
tt(l131_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ((k3_square_1 (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 (k2_xcmplx_0 A E)) (k3_square_1 (k2_xcmplx_0 B F))) (k3_square_1 (k2_xcmplx_0 C G))) (k3_square_1 (k2_xcmplx_0 D H))))) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 (k2_xcmplx_0 A E)) (k3_square_1 (k2_xcmplx_0 B F))) (k3_square_1 (k2_xcmplx_0 C G))) (k3_square_1 (k2_xcmplx_0 D H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l131_toprealb,ax, ((k6_toprealb (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1)) = (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1)) ).
tt(l132_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v13_bcialg_1 A) => (v16_bcialg_1 A)) ) ) ).
tt(l132_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))))).
tt(l132_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k51_modelc_1 A B C D) = (a_4_1_modelc_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(l132_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v8_o_ring_1 B A) & (v8_o_ring_1 C A))  => (v8_o_ring_1 (k8_finseq_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(l132_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1)) = k1_numbers) ).
tt(l133_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v19_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v16_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(l133_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))))).
tt(l133_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((a_2_0_modelc_1 A B) = (a_2_0_modelc_1 A C))  => (r2_funct_2 A k6_margrel1 B C)) ) ) ) ) ) ) ).
tt(l133_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ((v8_o_ring_1 D C) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 B (k3_finseq_1 D))) )  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v8_o_ring_1 (k8_finseq_1 (u1_struct_0 C) D (k12_finseq_1 (u1_struct_0 C) (k6_algstr_0 C (k7_partfun1 (u1_struct_0 C) D A) (k7_partfun1 (u1_struct_0 C) D B)))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l133_toprealb,ax, ((k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos))) 1)) = k1_numbers) ).
tt(l134_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid k6_numbers 3)))).
tt(l134_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ((r2_funct_2 A k6_margrel1 (k31_modelc_1 A D) (k31_modelc_1 A E)) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l134_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 B D) = (k33_modelc_2 A D)) ) )  &  (! [D:$i] :  ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) =>  ((k1_funct_1 C D) = (k33_modelc_2 A D)) ) ) )  => (r2_funct_2 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l134_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ((v12_o_ring_1 D C) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 B (k3_finseq_1 D))) )  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 C) D (k12_finseq_1 (u1_struct_0 C) (k6_algstr_0 C (k7_partfun1 (u1_struct_0 C) D A) (k7_partfun1 (u1_struct_0 C) D B)))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l134_toprealb,ax, ((v1_funct_1 c47__toprealb) &  ((v1_funct_2 c47__toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))))) &  ((v5_pre_topc c47__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))) & (m1_subset_1 c47__toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))))))) ) ) ).
tt(l134_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (r1_tarski (u1_struct_0 (k7_zmodul01 A B C)) (u1_struct_0 (k6_zmodul01 A B C)))) ) ) ) ) ) ).
tt(l135_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((v6_fomodel4 D B) &  ((r2_hidden (k23_fomodel4 B) D) &  ((r2_hidden (k33_fomodel4 B) D) & (v14_fomodel4 (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) C)) B D)) ) )  => (v8_fomodel4 (k38_fomodel2 B C) B D A)) ) ) ) ) ) ) ) ).
tt(l135_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid k6_numbers 3)))).
tt(l135_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) & (r1_mesfunc5 A B C E))  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( ((k1_relset_1 A (k3_mesfunc1 A D E)) = F)  & (r1_mesfunc1 A B (k3_mesfunc1 A D E) F)) ) ) )  | (r1_mesfunc5 A B C (k3_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l135_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v4_o_ring_1 C A) & (v1_o_ring_1 B A))  => (v4_o_ring_1 (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l135_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1)) = (u1_struct_0 k2_topalg_2)) ).
tt(l136_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v16_bcialg_1 A) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) = (k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A C (k1_bcialg_1 A C B)) (k1_bcialg_1 A C B)) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ).
tt(l136_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( (~ (v14_fomodel4 A B C))  <=>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (~ (v14_fomodel4 D B C)) ) ) ) ) ) ) ) ) ).
tt(l136_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3)))).
tt(l136_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v8_o_ring_1 B A) & (v8_o_ring_1 C A))  => (v8_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B C) (k12_finseq_1 (u1_struct_0 A) (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))))) A)) ) ) ) ) ) ) ).
tt(l136_toprealb,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1) (k5_toprealb c45__toprealb))) = (k5_toprealb c45__toprealb)) ).
tt(l136_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 (k4_xcmplx_0 A) B)) ) ) ) ) ).
tt(l136_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((u1_struct_0 (k6_zmodul01 A (k7_zmodul01 A B C) C)) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(l137_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v15_bcialg_1 A) <=> (v16_bcialg_1 A)) ) ) ).
tt(l137_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r2_hidden (k22_fomodel4 B) C) & (v9_fomodel2 A B))  =>  ((v14_fomodel4 A B C) |  ((v6_fomodel2 A B) & (v10_fomodel4 A B C)) ) ) ) ) ) ) ) ).
tt(l137_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (r1_tarski (k13_intpro_1 (k13_intpro_1 A)) (k13_intpro_1 A))) ) ).
tt(l137_jordan,ax,(v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid 1 (k1_real_1 3))))).
tt(l137_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  ( ((k1_relset_1 A D) = (k1_relset_1 A E))  &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (! [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) =>  (~  ((r1_tarski F (k1_relset_1 A D)) &  ((r1_tarski G (k1_relset_1 A D)) &  ( (F = (k7_subset_1 A (k1_relset_1 A D) G))  &  ((v3_valued_0 (k2_partfun1 A k7_numbers D F)) &  ( (F = (k1_relset_1 A (k2_partfun1 A k7_numbers D F)))  &  ((r1_mesfunc1 A B (k2_partfun1 A k7_numbers D F) F) &  ((r1_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) &  ( ((k7_mesfunc5 A B C D) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)))  &  ((r1_tarski F (k1_relset_1 A E)) &  ((r1_tarski G (k1_relset_1 A E)) &  ( (F = (k7_subset_1 A (k1_relset_1 A E) G))  &  ((v3_valued_0 (k2_partfun1 A k7_numbers E F)) &  ( (F = (k1_relset_1 A (k2_partfun1 A k7_numbers E F)))  &  ((r1_mesfunc1 A B (k2_partfun1 A k7_numbers E F) F) &  ((r1_mesfunc5 A B C (k2_partfun1 A k7_numbers E F)) &  ( ((k7_mesfunc5 A B C E) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E F)))  &  ((r1_tarski F (k1_relset_1 A (k3_mesfunc1 A D E))) &  ((r1_tarski H (k1_relset_1 A (k3_mesfunc1 A D E))) &  ( (F = (k7_subset_1 A (k1_relset_1 A (k3_mesfunc1 A D E)) H))  &  ( ((k12_supinf_2 C G) = k6_numbers)  &  ( ((k12_supinf_2 C H) = k6_numbers)  &  ( (F = (k1_relset_1 A (k2_partfun1 A k7_numbers (k3_mesfunc1 A D E) F)))  &  ((r1_mesfunc1 A B (k2_partfun1 A k7_numbers (k3_mesfunc1 A D E) F) F) &  ((r1_mesfunc5 A B C (k2_partfun1 A k7_numbers (k3_mesfunc1 A D E) F)) &  ((r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k3_mesfunc1 A D E) F) (k3_mesfunc1 A (k2_partfun1 A k7_numbers D F) (k2_partfun1 A k7_numbers E F))) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k3_mesfunc1 A D E) F)) = (k3_supinf_2 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l137_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B D E) = (k35_modelc_2 A D E)) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 C D E) = (k35_modelc_2 A D E)) ) ) ) )  => (r2_funct_2 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l137_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 B A) & (v12_o_ring_1 C A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B C) (k12_finseq_1 (u1_struct_0 A) (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))))) A)) ) ) ) ) ) ) ).
tt(l137_toprealb,ax,(r1_tarski (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1) (k5_toprealb c45__toprealb))) (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))).
tt(l138_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (~  ((v6_fomodel4 D B) &  ((r2_hidden (k23_fomodel4 B) D) &  ((r2_hidden (k33_fomodel4 B) D) &  ((v8_fomodel4 C B D A) &  ( (~ (v14_fomodel4 A B D))  & (v14_fomodel4 (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) C)) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l138_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)))).
tt(l138_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  ((k1_relset_1 A D) = (k1_relset_1 A E)) ) )  =>  ((r1_mesfunc5 A B C (k3_mesfunc1 A D E)) &  ((k7_mesfunc5 A B C (k3_mesfunc1 A D E)) = (k3_supinf_2 (k7_mesfunc5 A B C D) (k7_mesfunc5 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l138_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (A = (k29_quaterni (k26_quaterni A B) B)) ) ) ) ) ).
tt(l138_toprealb,ax, ((v1_funct_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1) (k5_toprealb c45__toprealb))) &  ((v1_funct_2 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1) (k5_toprealb c45__toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))))) & (m1_subset_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1) (k5_toprealb c45__toprealb)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))))))) ) ).
tt(l138_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((u1_struct_0 (k7_zmodul01 A B (k6_zmodul01 A B C))) = (u1_struct_0 B)) ) ) ) ) ) ) ).
tt(l139_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 C A)) =>  (~  ((v16_fomodel4 D C) &  ((v10_fomodel2 B A C E) & (v14_fomodel4 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l139_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v10_intpro_1 (k13_intpro_1 A))) ) ).
tt(l139_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid (k1_real_1 1) 3)))).
tt(l139_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (A = (k26_quaterni (k29_quaterni A B) B)) ) ) ) ) ).
tt(l139_toprealb,ax, ((k6_toprealb (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1)) = (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1)) ).
tt(l13_afvect01,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01)) (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01))))) &  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) A) <=>  ((r2_hidden B (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01))) &  ((r2_hidden C (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01))) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 o_0_0_afvect01)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 o_0_0_afvect01)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 o_0_0_afvect01)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 o_0_0_afvect01)) &  ( (B = (k4_tarski D E))  &  ( (C = (k4_tarski F G))  & (r2_diraf o_0_0_afvect01 D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k3_algstr_3)) =>  ( ((k1_algstr_3 k3_algstr_3 A B C) = (k1_algstr_3 k3_algstr_3 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(l13_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) &  ((v1_partfun1 A (u1_struct_0 k1_ami_3)) & (v5_memstr_0 A 2 k1_ami_3 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ( ((k1_funct_1 A (k10_ami_3 k6_numbers)) = C)  &  ((k1_funct_1 A (k10_ami_3 1)) = D) )  =>  ((r1_xxreal_0 C D) |  ((r1_xxreal_0 D k6_numbers) |  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 B A) (k10_ami_3 k6_numbers)) = (k3_int_2 C D))  &  (? [E:$i] :  ((m1_subset_1 E k5_numbers) & (r1_compos_1 k1_ami_3 B (k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 C (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = 1)  =>  ((k1_funct_1 (k2_extpro_1 A (k4_amistd_1 A) B C) (k4_struct_0 (k4_amistd_1 A))) = (k1_ordinal1 (k5_memstr_0 A (k4_amistd_1 A) C))) ) ) ) ) ) ) ) ).
tt(l13_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 D E)) (k1_rlvect_1 A C (k8_real_1 D F))) = (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ((k1_arytm_1 A A) = k11_arytm_3) ) ) ).
tt(l13_asympt_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k3_power A C) (k3_power B C))) ) ) ) ) ) ) ) ).
tt(l13_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k4_struct_0 A)) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l13_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v2_tops_1 (k2_topreal9 A (k4_struct_0 (k15_euclid A)) 1) (k15_euclid A))) ) ) ).
tt(l13_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 2))) =>  ( (D = (k10_finseq_1 A B))  =>  ((k1_rlvect_1 (k4_real_ns1 2) D C) = (k10_finseq_1 (k8_real_1 C A) (k8_real_1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(l13_complex2,ax, ((k1_comptrig k6_numbers) = k6_numbers) ).
tt(l13_compl_sp,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  &  ((v4_compl_sp B A) &  ((v5_compl_sp B A) &  ( (~ (v2_struct_0 A))  => (v2_relat_1 B)) ) ) ) ) ) ) ).
tt(l13_comptrig,ax, (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) k6_numbers)) ).
tt(l13_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_convex1 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A (k1_convex1 A B D) (k1_convex1 A C D))) ) ) ) ) ) ) ) ) ).
tt(l13_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  ((r2_hidden k1_supinf_1 (k2_relset_1 k7_numbers A)) =>  ((r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)) |  ((k4_extreal1 A) = k1_supinf_1) ) ) ) ) ).
tt(l13_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A D B) (k7_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(l13_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k1_clvect_1 k18_csspace B A) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace B) A)) ) ) ) ) ).
tt(l13_csspace3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) & (v2_comseq_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B E) A)) (k1_seq_1 C E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)) (k2_seq_2 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_dtconstr,ax, ((m1_subset_1 k6_numbers (u1_struct_0 k5_dtconstr)) & (m1_subset_1 1 (u1_struct_0 k5_dtconstr))) ).
tt(l13_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) => (m1_subset_1 (k1_binop_1 (k4_group_1 A) B C) (u1_struct_0 A))) ) ) ) ) ) ).
tt(l13_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_xboole_0 (k2_tarski A B) (k2_tarski C D))) ) ) ) ) ).
tt(l13_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig B) (k1_comptrig A))) =>  ( (B = k6_numbers)  |  ((k1_comptrig (k2_complex2 B (k1_real_1 (k1_comptrig A)))) = (k9_real_1 (k1_comptrig B) (k1_comptrig A))) ) ) ) ) ) ) ).
tt(l13_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k8_euclid 3 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k1_euclid_8 (k10_binop_2 A D) (k10_binop_2 B E) (k10_binop_2 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_extreal1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (~  ( (~ (r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)))  &  ((k4_extreal1 A) = k2_supinf_1) ) ) ) ) ).
tt(l13_fib_fusc,ax, (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 4)) ) ).
tt(l13_fib_num4,ax, ((k3_power k2_fib_num 6) = (k6_xcmplx_0 9 (k3_xcmplx_0 4 (k7_square_1 5)))) ).
tt(l13_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_wellord2 (k2_finseq_1 A) A)) ) ).
tt(l13_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k10_finseq_1 A B)) = (k2_tarski A B)) ) ) ).
tt(l13_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 (k1_funct_2 A B) (k1_funct_2 A C)) = (k1_funct_2 A (k3_xboole_0 B C))) ) ) ) ).
tt(l13_fomodel3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((v1_partfun1 (k9_fomodel3 B C A) (k4_finseq_2 A B)) &  ((v3_relat_2 (k9_fomodel3 B C A)) & (m1_subset_1 (k9_fomodel3 B C A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) (k4_finseq_2 A B))))) ) ) ) ) ) ) ) ).
tt(l13_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_funct_2 B (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ((m2_funct_2 (k3_fomodel2 (k9_setfam_1 (k1_fomodel4 A))) (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) &  ((r2_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) B (k3_fomodel2 (k9_setfam_1 (k1_fomodel4 A)))) => (v5_fomodel4 B A)) ) ) ) ) ) ).
tt(l13_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_glib_000 A) <=>  ((r1_tarski k5_glib_000 (k1_relset_1 k5_numbers A)) &  ( (~ (v1_xboole_0 (k6_glib_000 A)))  &  ( ((v1_funct_1 (k8_glib_000 A)) &  ((v1_funct_2 (k8_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k8_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) )  &  ((v1_funct_1 (k9_glib_000 A)) &  ((v1_funct_2 (k9_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k9_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) ) ) ) ) ) ) ) ).
tt(l13_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  => (r1_tarski (k9_xtuple_0 (k7_glib_003 A)) (k6_glib_000 A))) ) ).
tt(l13_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_4_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l13_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ((r2_hidden (k1_funct_1 (u1_graph_1 B) (k1_funct_1 C A)) (u1_struct_0 B)) & (r2_hidden (k1_funct_1 (u2_graph_1 B) (k1_funct_1 C A)) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(l13_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 2))  & (r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 A) 1) 5)) ) ) ) ).
tt(l13_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) &  ((v4_aff_2 A) & (r1_aff_1 A B C E)) )  =>  ( (B = C)  |  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H E I F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) )  |  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H E I G) & (r1_aff_1 A B C G)) ) ) ) ) ) ) ) )  |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_polynom3 A))) =>  ( (C = B)  =>  ((k4_algstr_0 (k14_polynom3 A) C) = (k5_vfunct_1 k5_numbers A B)) ) ) ) ) ) ) ) ).
tt(l13_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 1 A)) ) ) ).
tt(l13_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ( (~  (B = (k4_struct_0 k1_int_3)) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (C = B)  &  ((r1_xxreal_0 k6_numbers C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_int_3)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_int_3)) =>  (~  ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 D B) E))  &  ((r1_xxreal_0 (k4_struct_0 k1_int_3) E) &  (~ (r1_xxreal_0 (k2_int_3 B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_integr12,ax, ((k3_limfunc1 k6_numbers) = a_0_0_integr12) ).
tt(l13_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra7 A B C) <=>  ((r2_fdiff_1 B A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 B A) (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) ) ) ).
tt(l13_jgraph_5,ax,(r2_hidden 1 (k1_rcomp_1 k6_numbers 1))).
tt(l13_jordan18,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l13_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (m1_subset_1 (a_4_0_jordan1 A B C D) (k1_zfmisc_1 (k1_euclid 2)))) ) ) ) ) ) ) ) ).
tt(l13_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r2_hidden A B) & (v9_rltopsp1 B (k15_euclid 2)))  =>  ((r1_xxreal_0 (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 B)) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 B)))) ) ) ) ) ) ).
tt(l13_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k2_nat_1 (k7_nat_d (k4_nat_1 2 A) 2) 1) = (k7_nat_d (k4_nat_1 2 A) 1)) ) ) ) ).
tt(l13_jordan24,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))))))) )  =>  ( ( (D = C)  & (v3_tops_2 D (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))))  => (v3_tops_2 C A B)) ) ) ) ) ) ) ) ) ).
tt(l13_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 C k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( (E = (k5_euclid A))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (F = (k9_metric_1 (k14_euclid A) E B))  => (r1_tarski (k1_convex1 (k15_euclid A) F C) (k1_convex1 (k15_euclid A) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_lpspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 (k3_series_1 A) B)) (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B))) ) ) ) ).
tt(l13_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) (k8_cqc_lang A D (k8_cqc_lang A (k8_cqc_lang A C B) B))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(l13_matrix_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k8_matrix_1 (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ).
tt(l13_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_matrixj2 k1_xboole_0 A) & (m2_finseq_1 k1_xboole_0 (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) ) ).
tt(l13_measure7,ax,(r2_hidden k1_numbers (k9_setfam_1 k1_numbers))).
tt(l13_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((k3_finseq_1 (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers A) B) C)) = (k2_nat_1 (k2_nat_1 1 (k3_finseq_1 B)) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(l13_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  => (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 (k13_modelc_2 A)))) ) ).
tt(l13_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (r1_tarski (k2_pre_topc A C) (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(l13_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k4_numbers D E))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 E 1)) = (k6_int_1 (k8_nat_1 k4_numbers C E) (k8_nat_1 k4_numbers D E))) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  ((k8_nat_1 k4_numbers D E) = k6_numbers) )  =>  ((k3_int_2 (k8_nat_1 k4_numbers C E) (k8_nat_1 k4_numbers D E)) = (k3_int_2 (k8_nat_1 k4_numbers C (k2_nat_1 E 1)) (k8_nat_1 k4_numbers D (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_numbers,ax,(r1_tarski k3_numbers k1_numbers)).
tt(l13_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v5_orders_3 (k3_struct_0 A) A A)) ) ).
tt(l13_ordinal1,ax, ((v1_ordinal1 k1_xboole_0) & (v2_ordinal1 k1_xboole_0)) ).
tt(l13_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) (k8_group_1 A (k5_algstr_0 A B F) (k5_algstr_0 A D G))) = (k4_struct_0 A))  =>  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A C B) (k5_algstr_0 A G E)) (k8_group_1 A (k5_algstr_0 A C F) (k5_algstr_0 A G D))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A B D)) = (k3_rlvect_1 A D C))  =>  ((k8_group_1 A (k5_algstr_0 A B (k1_group_1 A)) C) = (k8_group_1 A (k3_rlvect_1 A B (k1_group_1 A)) D)) ) ) ) ) ) ) ) ) ) ).
tt(l13_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (D = (k10_finseq_1 A B))  & (r3_pdiff_1 2 2 E D))  =>  ( (C = (k1_fdiff_1 (k1_pdiff_2 2 2 E D) B))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (D = (k10_finseq_1 F G))  &  (? [H:$i] :  ((m1_rcomp_1 H G) &  ((r1_tarski H (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 E D))) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v3_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v2_fdiff_1 J) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 I 1))  &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ((r2_hidden K H) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 E D) K) (k1_seq_1 (k1_pdiff_2 2 2 E D) G)) = (k7_real_1 (k1_seq_1 I (k9_real_1 K G)) (k1_seq_1 J (k9_real_1 K G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  ( ( (F = (k3_relat_1 C (k4_pdiff_1 E B)))  &  ( (G = (k3_relat_1 D (k4_pdiff_1 E B)))  &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E B)) ) )  =>  ((k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) F G) = (k3_relat_1 (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) C D) (k4_pdiff_1 E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid A))) =>  (~  ((v1_pdiff_7 D A) &  ((r2_hidden C D) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  (! [E:$i] :  ((m1_rcomp_1 E (k1_seq_1 (k1_pdiff_1 B A) C)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ((r2_hidden F E) &  (~ (r2_hidden (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A B C) F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((k4_finseq_1 (k15_finseq_1 A)) = (k4_finseq_1 (k14_finseq_1 (k9_xtuple_0 A)))) ) ) ).
tt(l13_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~  ((k4_finseq_1 B) = k1_xboole_0) )  => (r2_hidden 1 (k4_finseq_1 B))) ) ) ) ).
tt(l13_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_orders_2 C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_poset_1 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 C) (u1_struct_0 C)) &  ((v5_orders_3 H C C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) )  =>  ( ( (D = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 C) H E))  &  ((r3_orders_2 C E D) &  ( (F = (k1_funct_1 (k9_funct_7 H A) E))  &  (G = (k1_funct_1 (k9_funct_7 H (k2_xcmplx_0 A B)) E)) ) ) )  => (r3_orders_2 C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 D) =>  ((v2_comseq_2 (k8_prob_1 A B D C)) &  ((k2_seq_2 (k8_prob_1 A B D C)) = (k1_seq_1 C (k1_prob_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (~  ( (? [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) &  ((r1_incsp_1 A H F) & (r1_incsp_1 A H G)) ) )  &  ((r1_incsp_1 A B F) &  ((r1_incsp_1 A C F) &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A E F) &  ((r2_zfmisc_1 B C D E) &  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A H G) &  ((r1_incsp_1 A I G) &  ((r1_incsp_1 A J G) &  ((r1_incsp_1 A K G) & (r2_zfmisc_1 H I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_qmax_1,ax,(r2_relset_1 k5_numbers k5_numbers (k1_relset_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1))) (k8_mcart_1 k5_numbers k5_numbers (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers)))).
tt(l13_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k3_quatern2 A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(l13_quaterni,ax, (k1_xcmplx_0 = (k5_arytm_0 k6_numbers 1)) ).
tt(l13_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 2 B) & (r2_hidden C (k2_finseq_1 A)))  =>  ((k11_radix_1 (k4_radix_1 C B A (k10_radix_1 B A 1))) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l13_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  =>  ( ( (! [H:$i] :  ( ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 F H) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 H E)) ) )  &  (! [H:$i] :  ( ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 G H) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 H E)) ) ) )  => (r2_funct_2 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_realset2,ax, ((k5_binop_1 2 k1_realset2 (k1_funct_7 k6_numbers 2) (k1_funct_7 1 2)) = (k1_funct_7 1 2)) ).
tt(l13_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_ringcat1 C) & (l1_ringcat1 C))  =>  ( ( ((k1_ringcat1 C) = A)  &  ( ((k2_ringcat1 C) = B)  & (v1_ringcat1 (k3_ringcat1 C) (u1_ringcat1 C) (u2_ringcat1 C))) )  => (m1_ringcat1 C A B)) ) ) ) ) ) ) ).
tt(l13_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k6_rusub_4 A D B) (k6_rusub_4 A D C))) ) ) ) ) ) ) ) ) ).
tt(l13_robbins3,ax,(v10_lattices k1_robbins3)).
tt(l13_rsspace3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) & (v2_comseq_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k18_complex1 (k9_real_1 (k1_seq_1 B E) A)) (k1_seq_1 C E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k18_complex1 (k9_real_1 (k2_seq_2 B) A)) (k2_seq_2 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k4_sf_mastr (k1_funct_4 (k1_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers))))) ) ) ) ) ).
tt(l13_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 1)) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = 1)  &  ((k1_funct_1 B (k1_scmp_gcd 3)) = C) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1)))) B A) (k1_scmp_gcd 1)) = (k1_pre_ff C))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1)))) B A) (k1_scmp_gcd 2)) = (k1_pre_ff (k2_nat_1 C 1)))  &  ((r1_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1)))) B A) & (r2_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 2) (k12_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 4)) (k11_scmpds_2 k2_scmp_gcd 3 (k4_xcmplx_0 1)))) B A)) ) ) ) ) ) ) ) ) ) ).
tt(l13_scpisort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k2_scmpds_7 A B C D) = (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 D) 3)) (k3_scmpds_4 (k3_scmpds_4 D (k11_scmpds_2 A B (k4_xcmplx_0 C))) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 D) 2)))))) ) ) ) ) ) ) ) ) ).
tt(l13_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B D) = F)  &  ( (1 = (k1_funct_1 B (k2_scmpds_2 F E)))  &  ( (I = (k2_nat_1 (k2_nat_1 G H) 1))  &  ( ((k2_nat_1 G 1) = (k1_funct_1 B (k1_scmp_gcd I)))  &  ( ((k2_nat_1 G H) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 I 1))))  &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  (! [L:$i] :  ((m2_finseq_1 L k4_numbers) =>  (! [M:$i] :  ((m2_finseq_1 M k4_numbers) =>  (! [N:$i] :  ((m2_subset_1 N k1_numbers k5_numbers) =>  (! [O:$i] :  ((m2_subset_1 O k1_numbers k5_numbers) =>  (! [P:$i] :  ((m2_subset_1 P k1_numbers k5_numbers) =>  (! [Q:$i] :  ((m2_subset_1 Q k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 J D) = F)  &  ( ((k2_nat_1 (k4_nat_1 2 N) 1) = (k1_funct_1 J (k2_scmpds_2 F E)))  &  ( (O = (k2_nat_1 (k2_nat_1 (k2_nat_1 G H) (k4_nat_1 2 N)) 1))  &  ( ((k2_nat_1 G P) = (k1_funct_1 J (k1_scmp_gcd O)))  &  ((k2_nat_1 G Q) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 O 1)))) ) ) ) )  =>  ( ( (~  ((r1_xxreal_0 1 P) & (r1_xxreal_0 Q H)) )  &  (~ (r1_xxreal_0 Q P)) )  |  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) &  ( ((k1_funct_1 (k6_scmpds_4 C J K) D) = (k1_funct_1 J D))  &  ( (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 R) =>  ((r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 N) 1) R) |  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 (k2_nat_1 G H) R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 (k2_nat_1 G H) R)))) ) ) ) )  &  ( ((r1_xxreal_0 Q P) =>  ( ((k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 F E)) = (k6_xcmplx_0 (k4_nat_1 2 N) 1))  &  (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 R) & (r1_xxreal_0 R H))  =>  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 G R)))) ) ) ) ) )  &  ( ( (~ (r1_xxreal_0 Q P))  =>  ( ((k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 F E)) = (k2_nat_1 (k4_nat_1 2 N) 3))  &  ( (! [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) =>  ( ( ((r1_xxreal_0 1 R) &  (~ (r1_xxreal_0 P R)) )  |  ( (~ (r1_xxreal_0 R Q))  & (r1_xxreal_0 R H)) )  =>  ((k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) = (k1_funct_1 J (k1_scmp_gcd (k2_nat_1 G R)))) ) ) )  &  (? [R:$i] :  ((m2_subset_1 R k1_numbers k5_numbers) &  ((r1_xxreal_0 P R) &  ((r1_xxreal_0 R Q) &  ( ((k2_nat_1 G P) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd O)))  &  ( ((k6_xcmplx_0 (k2_nat_1 G R) 1) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 1))))  &  ( ((k2_nat_1 (k2_nat_1 G R) 1) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 2))))  &  ( ((k2_nat_1 G Q) = (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 O 3))))  &  ( (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ((r1_xxreal_0 P S) =>  ((r1_xxreal_0 R S) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G S))) (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))))) ) ) )  &  (! [S:$i] :  ((m2_subset_1 S k1_numbers k5_numbers) =>  ((r1_xxreal_0 S Q) =>  ((r1_xxreal_0 S R) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G R))) (k1_funct_1 (k6_scmpds_4 C J K) (k1_scmp_gcd (k2_nat_1 G S))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r1_scpisort L J G) &  ((r1_scpisort M (k6_scmpds_4 C J K) G) &  ( ((k3_finseq_1 L) = H)  &  ((k3_finseq_1 M) = H) ) ) )  => (r2_classes1 L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) & (r1_scmpds_6 (k2_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ).
tt(l13_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_nat_1 (k2_nat_1 (k2_nat_1 (k4_nat_1 A (k4_nat_1 4 (k13_newton A 2))) (k4_nat_1 11 A)) (k4_nat_1 12 (k13_newton A 2))) 3) = (k3_xcmplx_0 (k2_nat_1 A 1) (k6_xcmplx_0 (k4_nat_1 4 (k13_newton (k2_nat_1 A 1) 2)) 1))) ) ) ).
tt(l13_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k3_xcmplx_0 2 (k3_square_1 B)) (k8_complex1 (k4_square_1 (k13_complex1 (k3_xcmplx_0 A B) C)) (k4_square_1 (k13_complex1 (k3_xcmplx_0 B C) A))))) ) ) ) ) ) ).
tt(l13_sin_cos6,ax, (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 1 k32_sin_cos))) ).
tt(l13_sysrel,ax, (! [A:$i] : (r1_tarski (k4_relat_1 A) (k2_zfmisc_1 A A))) ).
tt(l13_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r2_hidden C (k1_relat_1 B))) ) ) ) ) ) ).
tt(l13_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) =>  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  (~  ((r2_hidden E D) & (r1_xboole_0 E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_topreal2,ax, (~ (r2_hidden (k19_euclid k6_numbers k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)))) ).
tt(l13_topreal8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k2_nat_1 C 1)) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( ((k2_nat_1 (k3_finseq_1 (k1_graph_2 A B C)) B) = (k2_nat_1 C 1))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_graph_2 A B C)) D))  =>  ((k1_funct_1 (k1_graph_2 A B C) (k2_nat_1 D 1)) = (k1_funct_1 A (k2_nat_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( (~ (r1_aff_1 A B C E))  &  ((r2_analoaf A B C E D) & (r2_analoaf A B E C D)) ) )  &  (~  ((r1_aff_1 A B C E) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C F))  &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B F C G) &  ((r2_analoaf A F G E D) & (r2_analoaf A F E G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l13_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((v5_vectsp_1 A) =>  ((v1_vectsp_1 A) & (v2_vectsp_1 A)) ) ) ) ).
tt(l13_xboole_0,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (A = k1_xboole_0) ) ) ).
tt(l13_xcmplx_0,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 A (k3_xcmplx_0 B C)) = (k3_xcmplx_0 (k3_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(l13_xreal_0,ax, ((k2_xcmplx_0 1 (k4_xcmplx_0 1)) = k6_numbers) ).
tt(l13_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C B)) => (r1_xxreal_0 A C)) ) ) ) ) ) ) ).
tt(l13_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r1_xxreal_0 A k2_xxreal_0) =>  (A = k2_xxreal_0) ) ) ) ).
tt(l13_zfmodel2,ax, (~  ((k2_zf_lang 3) = (k2_zf_lang 4)) ) ).
tt(l140_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v13_fomodel1 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel2 E B A)) )  =>  ( ((k14_fomodel2 B A E (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) C) D)) = 1)  <=>  ((k1_funct_1 (k10_fomodel2 B A E) C) = (k1_funct_1 (k10_fomodel2 B A E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l140_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid 1 3)))).
tt(l140_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l140_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k29_quaterni A B) = (k6_quaterni (k9_real_1 (k17_quaterni A) (k17_quaterni B)) (k9_real_1 (k18_quaterni A) (k18_quaterni B)) (k9_real_1 (k19_quaterni A) (k19_quaterni B)) (k9_real_1 (k20_quaterni A) (k20_quaterni B)))) ) ) ) ) ).
tt(l140_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1)) = k1_numbers) ).
tt(l140_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) => (r1_tarski (u1_struct_0 (k6_zmodul01 A (k7_zmodul01 A B C) (k7_zmodul01 A C D))) (u1_struct_0 (k7_zmodul01 A C (k6_zmodul01 A B D))))) ) ) ) ) ) ) ) ).
tt(l141_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid 1 3)))).
tt(l141_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B D E) = (k38_modelc_2 A D E)) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 C D E) = (k38_modelc_2 A D E)) ) ) ) )  => (r2_funct_2 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l141_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k29_quaterni A B) = (k28_quaterni (k29_quaterni B A))) ) ) ) ) ).
tt(l141_toprealb,ax, ((k2_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) 1)) = k1_numbers) ).
tt(l142_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k22_fomodel4 A) A)) ) ).
tt(l142_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  => (r1_tarski (k2_group_2 A (k8_group_2 A C) (k8_group_2 A B)) (k2_group_2 A (k8_group_2 A B) (k8_group_2 A C)))) ) ) ) ) ) ).
tt(l142_jordan,ax, ((k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3) = a_0_0_jordan) ).
tt(l142_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k29_quaterni A B) = k6_numbers)  =>  (A = B) ) ) ) ) ) ).
tt(l142_toprealb,ax, ((v1_funct_1 c50__toprealb) &  ((v1_funct_2 c50__toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb)))))) &  ((v5_pre_topc c50__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))) & (m1_subset_1 c50__toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k7_real_1 (k10_real_1 1 2) c5__toprealb))))))))) ) ) ).
tt(l142_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((m1_zmodul01 B C) =>  ((u1_struct_0 (k7_zmodul01 A C (k6_zmodul01 A B D))) = (u1_struct_0 (k6_zmodul01 A (k7_zmodul01 A B C) (k7_zmodul01 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l143_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) &  ((v3_freealg C) &  ((v3_aofa_000 C) &  ((v4_aofa_000 C) &  ((v5_aofa_000 C) &  ((v6_aofa_000 C) &  ((v12_aofa_000 C) & (l1_unialg_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_aofa_000 D C A B) =>  (! [E:$i] :  ((m1_aofa_000 E C A B) =>  ((r2_relset_1 (k2_zfmisc_1 A (u1_struct_0 C)) A (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A D (k2_zfmisc_1 A (k18_aofa_000 C))) (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A E (k2_zfmisc_1 A (k18_aofa_000 C)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden (k4_tarski G F) (k21_aofa_000 C A B D)) =>  ((r2_hidden (k4_tarski G F) (k21_aofa_000 C A B E)) &  ((k2_binop_1 A (u1_struct_0 C) A D G F) = (k2_binop_1 A (u1_struct_0 C) A E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l143_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k23_fomodel4 A) A)) ) ).
tt(l143_jordan,ax,(r2_hidden (k19_euclid k6_numbers 3) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l143_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B D E) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k36_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) D) (k1_funct_1 (k31_modelc_2 A) E)))) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 C D E) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k36_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) D) (k1_funct_1 (k31_modelc_2 A) E)))) ) ) ) )  => (r2_funct_2 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l143_toprealb,ax, ((k1_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c44__toprealb))) = c44__toprealb) ).
tt(l143_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~ (r2_hidden A C))  &  ( (~ (r2_hidden B C))  &  (~ (r1_xboole_0 (k2_tarski A B) C)) ) ) ) ) ) ) ).
tt(l144_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ( ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k83_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) E) = (k21_aofa_i00 B k4_numbers H F))  &  ( ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k83_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) F) = (k6_int_1 (k21_aofa_i00 B k4_numbers H E) (k21_aofa_i00 B k4_numbers H F)))  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  (~  ( (J = (k21_aofa_i00 B k4_numbers H F))  &  ( (~  ((r2_hidden H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (r1_xxreal_0 J k6_numbers)) )  &  ( ( (~ (r1_xxreal_0 J k6_numbers))  => (r2_hidden H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  &  (~ (r4_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k83_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)) (k78_aofa_i00 A B C D F k6_numbers)) (k9_funct_2 B k4_numbers) H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l144_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k24_fomodel4 A) A)) ) ).
tt(l144_jordan,ax,(r2_hidden (k19_euclid k6_numbers (k1_real_1 3)) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l144_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)))))) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 B D E) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k39_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) D) (k1_funct_1 (k31_modelc_2 A) E)))) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 (k25_modelc_2 A))) & (r2_hidden E (k30_modelc_1 (k25_modelc_2 A))))  =>  ((k1_binop_1 C D E) = (k1_funct_1 (k31_modelc_2 A) (k1_binop_1 (k39_modelc_2 A) (k1_funct_1 (k31_modelc_2 A) D) (k1_funct_1 (k31_modelc_2 A) E)))) ) ) ) )  => (r2_funct_2 (k2_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)) (k30_modelc_1 (k25_modelc_2 A))) (k30_modelc_1 (k25_modelc_2 A)) B C)) ) ) ) ) ) ) ).
tt(l144_toprealb,ax,(r1_tarski (k2_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c44__toprealb))) c45__toprealb)).
tt(l144_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) => (r1_tarski (u1_struct_0 (k6_zmodul01 A B (k7_zmodul01 A C D))) (u1_struct_0 (k7_zmodul01 A (k6_zmodul01 A C B) (k6_zmodul01 A B D))))) ) ) ) ) ) ) ) ).
tt(l145_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k25_fomodel4 A) A)) ) ).
tt(l145_jordan,ax, ((k5_square_1 (k7_real_1 2 1)) = (k7_real_1 (k7_real_1 4 4) 1)) ).
tt(l145_toprealb,ax, ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c44__toprealb))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c44__toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c44__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb)))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) c33__toprealb (k5_toprealb c44__toprealb)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c44__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))))))) ) ).
tt(l146_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k26_fomodel4 A) A)) ) ).
tt(l146_jordan,ax, ((k7_square_1 9) = 3) ).
tt(l146_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(l146_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((m1_zmodul01 B C) =>  ((u1_struct_0 (k6_zmodul01 A C (k7_zmodul01 A B D))) = (u1_struct_0 (k7_zmodul01 A (k6_zmodul01 A B C) (k6_zmodul01 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l147_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  ( ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k32_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) (k15_aofa_000 A (k79_aofa_i00 A B C D G k6_numbers) (k58_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k4_xcmplx_0 1)))) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) E) = (k21_aofa_i00 B k4_numbers H F))  &  ( ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k32_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) (k15_aofa_000 A (k79_aofa_i00 A B C D G k6_numbers) (k58_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k4_xcmplx_0 1)))) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) F) = (k1_int_2 (k6_xcmplx_0 (k21_aofa_i00 B k4_numbers H E) (k21_aofa_i00 B k4_numbers H F))))  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( (I = (k21_aofa_i00 B k4_numbers H E))  &  (J = (k21_aofa_i00 B k4_numbers H F)) )  =>  ( ((r2_hidden H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (r1_xxreal_0 J k6_numbers))  |  ( ( (~ (r1_xxreal_0 J k6_numbers))  &  (~ (r2_hidden H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers))) )  | (r4_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k32_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) (k15_aofa_000 A (k79_aofa_i00 A B C D G k6_numbers) (k58_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k4_xcmplx_0 1)))) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)) (k78_aofa_i00 A B C D F k6_numbers)) (k9_funct_2 B k4_numbers) H (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l147_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k27_fomodel4 A) A)) ) ).
tt(l147_jordan,ax, ((k1_topreal6 2 (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) = (k1_real_1 (k1_real_1 2))) ).
tt(l147_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k29_quaterni B C) = (k26_quaterni (k29_quaterni B A) (k29_quaterni A C))) ) ) ) ) ) ) ).
tt(l147_toprealb,ax,(m1_subset_1 (k5_toprealb c44__toprealb) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1))))))).
tt(l148_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k28_fomodel4 A) A)) ) ).
tt(l148_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l148_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos)))) = (k1_rcomp_1 k6_numbers k32_sin_cos)) ).
tt(l149_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k29_fomodel4 A) A)) ) ).
tt(l149_toprealb,ax,(m1_subset_1 (k5_toprealb c45__toprealb) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos))))))).
tt(l14_afvect01,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k4_tarski A B) c4__afvect01) <=>  ((r2_hidden A (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01))) &  ((r2_hidden B (k2_zfmisc_1 (u1_struct_0 o_0_0_afvect01) (u1_struct_0 o_0_0_afvect01))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 o_0_0_afvect01)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 o_0_0_afvect01)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 o_0_0_afvect01)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 o_0_0_afvect01)) &  ( (A = (k4_tarski C D))  &  ( (B = (k4_tarski E F))  & (r2_diraf o_0_0_afvect01 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  ( (~  (A = B) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k3_algstr_3)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 k3_algstr_3)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 k3_algstr_3)) &  ( ((k1_algstr_3 k3_algstr_3 E A F) = C)  &  ((k1_algstr_3 k3_algstr_3 E B F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_arytm_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_tarski A B) = (k1_tarski C))  =>  ( (C = (k1_tarski A))  &  (A = B) ) ) ) ) ) ).
tt(l14_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ( (~  ( (~ (r3_arytm_3 A C))  & (r3_arytm_3 B C)) )  &  (~  ( (~ (r3_arytm_3 B C))  & (r3_arytm_3 A C)) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l14_asympt_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 4 A) & (r1_xxreal_0 (k5_series_1 2 A) (k2_nat_1 (k4_nat_1 2 A) 3))) ) ) ) ).
tt(l14_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binom A B (k2_nat_1 C D)) = (k6_algstr_0 A (k2_binom A B C) (k2_binom A B D))) ) ) ) ) ) ) ) ) ).
tt(l14_brouwer2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1)))  =>  (~  ( (B = (k7_toprealb A (k4_struct_0 (k15_euclid A)) 1))  & (r1_borsuk_1 (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1) B)) ) ) ) ) ) ).
tt(l14_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r2_hidden B (k1_relset_1 (k1_euclid 2) A)) =>  ((k1_funct_1 (k3_pdiff_1 2 A) B) = (k12_finseq_1 k1_numbers (k1_seq_1 A B))) ) ) ) ) ) ).
tt(l14_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((k17_complex1 (k8_nat_1 k2_numbers A B)) = (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) B))  & (r1_xxreal_0 k6_numbers (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) B))) ) ) ) ) ).
tt(l14_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_convex1 B A) & (m1_rlvect_2 B A))  =>  (! [C:$i] :  ( ((v2_convex1 C A) & (m1_rlvect_2 C A))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 (k8_real_1 D E) k6_numbers))  =>  ((k3_rlvect_2 A (k7_rlvect_2 A (k8_rlvect_2 A D B) (k8_rlvect_2 A E C))) = (k4_subset_1 (u1_struct_0 A) (k3_rlvect_2 A (k8_rlvect_2 A D B)) (k3_rlvect_2 A (k8_rlvect_2 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  (~  ((r1_xxreal_0 1 (k5_card_1 (k3_rlvect_2 A C))) &  (! [D:$i] :  ((m2_rlvect_2 D A B) =>  (! [E:$i] :  ((m2_rlvect_2 E A B) =>  (~  ( ((k6_rlvect_2 A C) = (k3_rlvect_1 A (k6_rlvect_2 A D) (k6_rlvect_2 A E)))  &  ( ((k5_card_1 (k3_rlvect_2 A D)) = 1)  &  ( ((k5_card_1 (k3_rlvect_2 A E)) = (k5_real_1 (k5_card_1 (k3_rlvect_2 A C)) 1))  &  ((r1_tarski (k3_rlvect_2 A D) (k3_rlvect_2 A C)) &  ((r1_tarski (k3_rlvect_2 A E) (k3_rlvect_2 A C)) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F (k3_rlvect_2 A D)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers D F) = (k3_funct_2 (u1_struct_0 A) k1_numbers C F)) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F (k3_rlvect_2 A E)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers E F) = (k3_funct_2 (u1_struct_0 A) k1_numbers C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k12_supinf_2 A C) = (k1_seq_1 B C)) ) ) ) )  =>  ((k4_extreal1 A) = (k18_rvsum_1 B)) ) ) ) ) ) ).
tt(l14_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) => (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A B D) (k9_cqc_lang A C D)) A)) ) ) ) ) ) ) ) ) ).
tt(l14_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  ( ((k4_algstr_0 k18_csspace A) = (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))  & (r2_funct_2 k5_numbers k2_numbers (k2_csspace (k4_algstr_0 k18_csspace A)) (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))) ) ) ).
tt(l14_dtconstr,ax,(r1_lang1 k5_dtconstr c3__dtconstr (k3_pre_poly (u1_struct_0 k5_dtconstr) c2__dtconstr))).
tt(l14_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  ( ( ((k2_xtuple_0 B) = (k2_xtuple_0 C))  &  ( ((k3_ens_1 A B) = (k3_ens_1 A C))  &  ((k4_ens_1 A B) = (k4_ens_1 A C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l14_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig B) (k1_comptrig A))) =>  ( (B = k6_numbers)  |  ((k3_complex2 A B) = (k9_real_1 (k1_comptrig B) (k1_comptrig A))) ) ) ) ) ) ) ).
tt(l14_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k12_rvsum_1 (k3_euclid A)) = (k12_rvsum_1 A)) ) ) ).
tt(l14_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 C A) & (r1_fdiff_1 B (k1_seq_1 C A)))  =>  ( (! [D:$i] :  ((m1_rcomp_1 D A) =>  (~ (r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C B)))) ) )  |  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C B) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C B) A) = (k8_real_1 (k1_fdiff_1 B (k1_seq_1 C A)) (k1_fdiff_1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(l14_fib_fusc,ax, (~  ((k10_ami_3 1) = (k10_ami_3 4)) ) ).
tt(l14_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_finseq_1 A)) = (k5_card_1 A)) ) ) ).
tt(l14_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 D A) & (v1_binop_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) )  =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C F) = (k1_funct_1 B (k1_funct_1 E F))) ) ) ) ) )  =>  ((k1_finsop_1 A B D) = (k1_finsop_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  (! [E:$i] :  ( ((v13_fomodel1 E A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B C D) (k2_nat_1 F 1)) E) = (k1_funct_1 (k4_fomodel2 A B D (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) E)) (k3_relat_1 (k33_fomodel1 A E) (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B C D) F))))  &  ((v14_fomodel1 E k6_numbers A) =>  ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B C D) (k2_nat_1 F 1)) E) = (k1_funct_1 (k4_fomodel2 A B D (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) E)) k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_fomodel3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((v1_partfun1 (k9_fomodel3 B C A) (k4_finseq_2 A B)) &  ((v8_relat_2 (k9_fomodel3 B C A)) & (m1_subset_1 (k9_fomodel3 B C A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) (k4_finseq_2 A B))))) ) ) ) ) ) ) ) ).
tt(l14_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k10_funcop_1 (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) C (k6_partfun1 (u1_struct_0 A))) B) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ).
tt(l14_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ( (~  (D = (k4_tarski (k10_finseq_1 E F) B)) )  &  ( (~  (E = (k4_tarski (k10_finseq_1 F D) C)) )  &  ( (~  (F = (k4_tarski (k10_finseq_1 D E) A)) )  &  (~  ( (~ (r2_hidden (k4_tarski (k10_finseq_1 D E) A) (k2_tarski E F)))  &  ( (~ (r2_hidden F (k2_tarski (k4_tarski (k10_finseq_1 D E) A) (k4_tarski (k10_finseq_1 E F) B))))  &  ( (~ (r2_hidden D (k2_tarski (k4_tarski (k10_finseq_1 D E) A) (k4_tarski (k10_finseq_1 E F) B))))  &  (~ (r2_hidden (k4_tarski (k10_finseq_1 F D) C) (k1_enumset1 D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r5_glib_000 (k13_glib_000 A k2_glib_003 B) A) &  ((r5_glib_000 (k13_glib_000 A k3_glib_003 B) A) & (r5_glib_000 (k13_glib_000 A k4_glib_003 B) A)) ) ) ) ) ).
tt(l14_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_7_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l14_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (m1_group_6 B A (k7_group_2 A))) ) ) ) ).
tt(l14_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_group_4 A (k5_finseq_2 (u1_struct_0 A) k6_numbers B)) = (k5_group_1 A k6_numbers B)) ) ) ) ) ).
tt(l14_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) & (v4_aff_2 A))  =>  ( (B = C)  |  ( (B = D)  |  ( ( (~  ( (~ (r1_aff_1 A B C E))  &  ((r1_aff_1 A B E F) & (r2_analoaf A C E D F)) ) )  &  (~  ((r1_aff_1 A B C E) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H E I F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) )  |  ( ( (~  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G F) & (r2_analoaf A C G D F)) ) )  &  (~  ((r1_aff_1 A B C G) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H G I F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) )  |  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m3_index_1 E A B C D) =>  (? [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v1_cat_1 F) &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) &  ((v3_cat_5 F) &  ((v4_cat_5 F) & (l1_cat_1 F)) ) ) ) ) ) ) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G A) => (m1_subset_1 (k2_index_1 A (k1_xtuple_0 E) G) (u1_struct_0 F))) )  &  (! [G:$i] :  ((m1_subset_1 G B) => (m1_subset_1 (k4_tarski (k4_tarski (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A C G)) (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A D G))) (k7_index_1 B (k3_relat_1 C (k1_xtuple_0 E)) (k3_relat_1 D (k1_xtuple_0 E)) (k8_index_1 A B C D E) G)) (u4_struct_0 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_1 B A) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(l14_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((v1_int_7 B) & (r1_int_1 A (k8_nat_3 k10_newton B)))  => (r2_hidden A (k1_polynom2 k10_newton B))) ) ) ) ) ).
tt(l14_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 B)) (k4_seq_4 (k1_rvsum_1 B)))) ) ) ) ) ).
tt(l14_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_integra1 A) k6_numbers))  &  (! [C:$i] :  ((m1_integra1 C A) =>  (~  ( ((k3_finseq_1 C) = B)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_seq_1 C D) = (k7_real_1 (k5_seq_4 A) (k8_real_1 (k10_real_1 (k3_integra1 A) B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (m1_subset_1 (a_4_1_jordan1 A B C D) (k1_zfmisc_1 (k1_euclid 2)))) ) ) ) ) ) ) ) ).
tt(l14_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 2 A) =>  ((k8_real_1 (k6_real_1 C (k13_newton 2 B)) (k5_real_1 A 2)) = (k8_real_1 (k6_real_1 C (k13_newton 2 (k2_nat_1 B 1))) (k5_real_1 (k7_nat_d (k4_nat_1 2 A) 2) 2))) ) ) ) ) ) ) ) ).
tt(l14_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) (k2_funcsdom A (u1_struct_0 B) k1_numbers (k9_funct_2 A (u1_struct_0 B)) (k3_lopban_1 A B) (k1_domain_1 k1_numbers (k9_funct_2 A (u1_struct_0 B)) E C)) (k2_funcsdom A (u1_struct_0 B) k1_numbers (k9_funct_2 A (u1_struct_0 B)) (k3_lopban_1 A B) (k1_domain_1 k1_numbers (k9_funct_2 A (u1_struct_0 B)) E D))) (k2_funcsdom A (u1_struct_0 B) k1_numbers (k9_funct_2 A (u1_struct_0 B)) (k3_lopban_1 A B) (k1_domain_1 k1_numbers (k9_funct_2 A (u1_struct_0 B)) E (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D))))) ) ) ) ) ) ) ) ) ) ).
tt(l14_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A C D) D)) E) (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A D) C) E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l14_measure7,ax, ((v1_funct_1 (k7_funcop_1 k5_numbers k1_numbers)) &  ((v1_funct_2 (k7_funcop_1 k5_numbers k1_numbers) k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 (k7_funcop_1 k5_numbers k1_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) ) ).
tt(l14_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_metric_2 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(l14_metrizts,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((v3_pre_topc (a_3_0_metrizts A B C) (k3_pcomps_1 A)) & (m1_subset_1 (a_3_0_metrizts A B C) (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) ) ) ) ) ) ) ).
tt(l14_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  => (m1_subset_1 (k1_tarski (k10_modelc_2 A)) (k1_zfmisc_1 (k13_modelc_2 A)))) ) ) ).
tt(l14_msalimit,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v11_struct_0 A) & (l1_msualg_1 A)) )  => (r3_pua2mss1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)))) ) ).
tt(l14_msualg_1,ax,(m1_subset_1 k6_numbers (k1_tarski k6_numbers))).
tt(l14_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (m1_msualg_2 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A B)) ) ) ) ).
tt(l14_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  ( (~ (v1_int_2 A))  &  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_nat_d B A) &  ( (~ (r1_xxreal_0 B 1))  &  ((r1_xxreal_0 (k4_nat_1 B B) A) & (v1_int_2 B)) ) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_nat_d B A) &  ( (~ (r1_xxreal_0 B 1))  &  ((r1_xxreal_0 (k4_nat_1 B B) A) & (v1_int_2 B)) ) ) ) ) ) ) )  & (v1_int_2 A)) ) ) ) ) ).
tt(l14_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k4_numbers D E))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 E 1)) = (k6_int_1 (k8_nat_1 k4_numbers C E) (k8_nat_1 k4_numbers D E))) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  ((k8_nat_1 k4_numbers D E) = k6_numbers) )  =>  ((k3_int_2 (k8_nat_1 k4_numbers C k6_numbers) (k8_nat_1 k4_numbers D k6_numbers)) = (k3_int_2 (k8_nat_1 k4_numbers C E) (k8_nat_1 k4_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_numbers,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 A k5_arytm_3))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B k5_arytm_3))  =>  (~  ((r2_hidden A B) & (r3_arytm_3 B A)) ) ) ) ) ) ).
tt(l14_oposet_1,ax,(v5_orders_2 k1_oposet_1)).
tt(l14_ordinal3,ax, (1 = (k1_ordinal1 k1_xboole_0)) ).
tt(l14_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v4_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l14_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A B (k3_rlvect_1 A (k3_rlvect_1 A B C) (k4_algstr_0 A D))) = (k5_algstr_0 A D C)) ) ) ) ) ) ) ) ) ).
tt(l14_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((k8_group_1 A B (k5_algstr_0 A C D)) = (k5_algstr_0 A E F))  &  (F = (k5_algstr_0 A (k3_rlvect_1 A C D) E)) )  =>  ((k8_group_1 A (k5_algstr_0 A B (k1_group_1 A)) (k5_algstr_0 A E D)) = (k8_group_1 A (k3_rlvect_1 A B (k1_group_1 A)) (k5_algstr_0 A E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ((v2_bvfunc_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ( ((r1_tarski C B) & (r1_tarski D B))  => (r1_relset_1 A A (k4_relset_1 A A A A (k4_partit1 A (k2_bvfunc_2 A C)) (k4_partit1 A (k2_bvfunc_2 A D))) (k4_relset_1 A A A A (k4_partit1 A (k2_bvfunc_2 A D)) (k4_partit1 A (k2_bvfunc_2 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(l14_pdiff_1,ax, ((v1_funct_1 (k2_funct_1 (k1_pdiff_1 1 1))) &  ((v1_funct_2 (k2_funct_1 (k1_pdiff_1 1 1)) k1_numbers (k1_euclid 1)) & (m1_subset_1 (k2_funct_1 (k1_pdiff_1 1 1)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 1))))) ) ).
tt(l14_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_finseq_1 (k1_finseq_7 k1_numbers B D C)) = A) ) ) ) ) ) ) ) ) ).
tt(l14_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((k10_xtuple_0 A) = (k10_xtuple_0 (k15_finseq_1 A))) ) ) ).
tt(l14_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( (~  (E = (k2_polynom7 A B D)) )  =>  ((k3_polynom1 A B D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_orders_2 C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_poset_1 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 C) (u1_struct_0 C)) &  ((v5_orders_3 H C C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) )  =>  ( ((r1_xxreal_0 A B) &  ( (D = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 C) H E))  &  ((r3_orders_2 C E D) &  ( (F = (k1_funct_1 (k9_funct_7 H A) E))  &  (G = (k1_funct_1 (k9_funct_7 H B) E)) ) ) ) )  => (r3_orders_2 C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_projdes1 A B C D E) &  ((r1_projdes1 A B C D F) & (r1_projdes1 A B C D G)) )  =>  ((r1_collsp A B C D) | (r1_projdes1 A B E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_qmax_1,ax, ( ((k10_xtuple_0 (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1))) = (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) c3__qmax_1))  & (r2_hidden c3__qmax_1 (k1_qmax_1 k1_numbers k12_prob_1))) ).
tt(l14_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) &  ((r2_hidden E B) & (r1_tarski D E)) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C E)) | (r2_hidden (k12_supinf_2 C D) k1_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(l14_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E B) =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  (! [G:$i] :  ((m2_finseq_1 G A) =>  ( ((r2_relset_1 k5_numbers A F (k1_partfun1 k5_numbers B B A D C)) & (r2_relset_1 k5_numbers A G (k1_partfun1 k5_numbers B B A E C)))  => (r2_relset_1 k5_numbers A (k1_partfun1 k5_numbers B B A (k8_finseq_1 B D E) C) (k8_finseq_1 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_realset2,ax, ((k5_binop_1 2 k1_realset2 (k1_funct_7 1 2) (k1_funct_7 k6_numbers 2)) = (k1_funct_7 1 2)) ).
tt(l14_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k1_zfmisc_1 B)) =>  ((r2_hidden A (k4_finseq_1 C)) => (r1_tarski (k1_funct_1 C A) B)) ) ) ) ) ) ) ).
tt(l14_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((r1_rfunct_4 B C) =>  ((r1_xxreal_0 A k6_numbers) | (r1_rfunct_4 (k26_valued_1 k1_numbers k1_numbers B A) C)) ) ) ) ) ) ) ).
tt(l14_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_ringcat1 C A B) => (m1_ringcat1 (g1_ringcat1 A B C) A B)) ) ) ) ) ) ) ).
tt(l14_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (~ (r1_xxreal_0 (k5_card_1 A) k6_numbers)) ) ) ).
tt(l14_scmfsa_1,ax,(r1_subset_1 k3_scmfsa_1 k1_ami_2)).
tt(l14_scmfsa8a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( ((k9_xtuple_0 (k16_funcop_1 k6_numbers (k11_scmfsa_2 A))) = (k1_tarski k6_numbers))  &  ((r2_hidden k6_numbers (k9_xtuple_0 (k16_funcop_1 k6_numbers (k11_scmfsa_2 A)))) &  ( ((k1_funct_1 (k16_funcop_1 k6_numbers (k11_scmfsa_2 A)) k6_numbers) = (k11_scmfsa_2 A))  &  ( ((k5_card_1 (k16_funcop_1 k6_numbers (k11_scmfsa_2 A))) = 1)  &  (~ (r2_hidden (k2_compos_1 k1_scmfsa_2) (k10_xtuple_0 (k16_funcop_1 k6_numbers (k11_scmfsa_2 A))))) ) ) ) ) ) ) ).
tt(l14_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scpinvar C) B A) (k1_scmp_gcd 1)) = (k1_pre_ff C))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scpinvar C) B A) (k1_scmp_gcd 2)) = (k1_pre_ff (k2_nat_1 C 1)))  & (r2_scmpds_6 (k3_scpinvar C) B A)) ) ) ) ) ) ) ) ).
tt(l14_scpisort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k61_valued_1 (k3_scmpds_4 A (k11_scmpds_2 B C (k4_xcmplx_0 D))) 1) (k2_scmpds_7 B C D A))) ) ) ) ) ) ) ) ).
tt(l14_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_xcmplx_0 (k13_newton (k2_nat_1 A 1) 2) (k6_xcmplx_0 (k4_nat_1 2 (k13_newton (k2_nat_1 A 1) 2)) 1)) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_nat_1 (k4_nat_1 (k13_newton A 2) (k13_newton A 2)) 2) (k3_xcmplx_0 (k6_xcmplx_0 12 1) (k13_newton A 2))) (k4_nat_1 8 (k13_newton A 3))) (k4_nat_1 6 A)) 1)) ) ) ).
tt(l14_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k9_complex1 (k13_complex1 (k3_xcmplx_0 A B) C) (k13_complex1 (k3_xcmplx_0 B C) A)) = (k3_square_1 B)) ) ) ) ) ) ) ).
tt(l14_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k3_funct_2 k5_numbers (k9_setfam_1 A) C D) = B)  &  ( ((k1_kurato_0 A C) = B)  &  ((k3_prob_1 A C) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_sin_cos6,ax, (~ (r1_xxreal_0 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) 1)) (k7_real_1 k6_numbers (k8_real_1 (k8_real_1 2 k32_sin_cos) 1)))) ).
tt(l14_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden A (k1_tarski k1_xboole_0)) & (r2_hidden B (k1_tarski k1_xboole_0)))  =>  ( (A = B)  | (r1_xboole_0 A B)) ) ) ) ).
tt(l14_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v7_ordinal1 (k3_real_1 (k2_topdim_1 A B) 1))) ) ) ) ).
tt(l14_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_topdim_1 B A) &  ((v1_topdim_1 C A) & (v5_waybel23 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C)))) )  =>  ((v1_topdim_1 (k4_subset_1 (u1_struct_0 A) B C) A) & (r1_xxreal_0 (k2_topdim_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k1_xxreal_3 (k1_xxreal_3 (k2_topdim_1 A B) (k2_topdim_1 A C)) 1))) ) ) ) ) ) ) ) ).
tt(l14_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  (~  ((r2_hidden E D) & (r1_xboole_0 E B)) ) ) ) )  => (r2_hidden C (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(l14_topreal2,ax, (~ (r2_hidden (k19_euclid k6_numbers 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)))) ).
tt(l14_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v11_aff_2 A) &  ((r1_aff_1 A B C D) &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B C G H) &  ((r2_analoaf A B E C F) &  ((r2_analoaf A B G C H) &  ((r2_analoaf A E F D I) &  ((r2_analoaf A G H D J) &  ((r2_analoaf A E D F I) & (r2_analoaf A G D H J)) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ((r1_aff_1 A B C E) |  ((r1_aff_1 A B C G) |  ((r1_aff_1 A E F G) |  (I = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_waybel35 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (~  ((r1_yellow_0 A D) &  ((v2_waybel35 C A B) &  ( (~ (r2_hidden (k1_yellow_0 A D) C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) &  ((r2_orders_2 A (k1_yellow_0 A D) E) &  ( (~ (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k1_yellow_0 A D) E) B))  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_yellow_0 A C))) &  ( (E = F)  &  ((r2_lattice3 (k5_yellow_0 A C) D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_yellow_0 A C))) =>  ((r2_lattice3 (k5_yellow_0 A C) D G) => (r3_orders_2 (k5_yellow_0 A C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_xcmplx_0,ax,(r1_tarski k1_numbers k2_numbers)).
tt(l14_xreal_0,ax, (? [A:$i] :  ((m1_subset_1 A k1_numbers) &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (1 = (k5_arytm_0 A B))  &  ( ((k4_xcmplx_0 1) = (k5_arytm_0 C D))  &  (k6_numbers = (k5_arytm_0 (k1_arytm_0 A C) (k1_arytm_0 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l14_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r1_xxreal_0 k1_xxreal_0 A) =>  (A = k1_xxreal_0) ) ) ) ).
tt(l150_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k30_fomodel4 A) A)) ) ).
tt(l150_jordan,ax,(r1_tarski (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3) (k2_jgraph_6 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l150_toprealb,ax, ((k1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 (k1_real_1 1) 1))) c54__toprealb) = (k1_pre_topc k2_topalg_2 (k5_toprealb c44__toprealb))) ).
tt(l151_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k31_fomodel4 A) A)) ) ).
tt(l151_jordan,ax, ((k18_euclid (k19_euclid (k1_real_1 1) 3)) = (k18_euclid (k19_euclid (k1_real_1 1) 3))) ).
tt(l151_toprealb,ax, ((k1_pre_topc (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_rcomp_1 k6_numbers k32_sin_cos))) c55__toprealb) = (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb))) ).
tt(l152_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k32_fomodel4 A) A)) ) ).
tt(l152_jordan,ax,(r1_xxreal_0 (k17_euclid (k19_euclid (k1_real_1 1) 3)) (k17_euclid (k19_euclid k6_numbers 3)))).
tt(l152_toprealb,ax,(v5_pre_topc c53__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb c44__toprealb)) (k1_pre_topc k2_topalg_2 (k5_toprealb c45__toprealb)))).
tt(l153_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v17_fomodel4 (k33_fomodel4 A) A)) ) ).
tt(l153_jordan,ax,(r1_xxreal_0 (k17_euclid (k19_euclid k6_numbers 3)) (k17_euclid (k19_euclid 1 3)))).
tt(l153_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) &  ((v5_modelc_3 A) & (m2_finseq_1 A k5_numbers)) )  =>  ((k48_modelc_2 (k13_modelc_3 A (k7_modelc_3 A))) = k1_xboole_0) ) ) ).
tt(l153_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k11_toprealb k10_toprealb)))) =>  ( (A = a_0_4_toprealb)  => (v5_pre_topc (k2_tmap_1 (k11_toprealb k10_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))) k15_toprealb (k1_pre_topc (k11_toprealb k10_toprealb) A)) (k1_pre_topc (k11_toprealb k10_toprealb) A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) ) ) ).
tt(l154_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid k6_numbers 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3)))).
tt(l154_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k11_toprealb k10_toprealb)))) =>  ( (A = a_0_5_toprealb)  => (v5_pre_topc (k2_tmap_1 (k11_toprealb k10_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))) k15_toprealb (k1_pre_topc (k11_toprealb k10_toprealb) A)) (k1_pre_topc (k11_toprealb k10_toprealb) A) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))) ) ) ).
tt(l155_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid k6_numbers 3)) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l155_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k11_toprealb k10_toprealb))) =>  ( (A = k9_toprealb)  => (r1_tmap_1 (k11_toprealb k10_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))) k15_toprealb A)) ) ) ).
tt(l155_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ) ) ) ).
tt(l156_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid k6_numbers 3)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid 1 3)))).
tt(l156_toprealb,ax,(v5_pre_topc k15_toprealb (k11_toprealb k10_toprealb) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))).
tt(l156_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( ((k6_zmodul01 A B C) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l157_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  (! [E:$i] :  ( ((v4_fomodel1 E B) & (m1_subset_1 E (k1_fomodel1 B)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((v6_fomodel4 F B) &  ((r2_hidden (k23_fomodel4 B) F) &  ((r2_hidden (k33_fomodel4 B) F) &  ((r2_hidden (k24_fomodel4 B) F) &  ((r2_hidden (k30_fomodel4 B) F) & (v14_fomodel4 (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k24_fomodel3 B D E C))) B F)) ) ) ) )  =>  ((v7_fomodel2 E (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) C)) B) | (v14_fomodel4 (k2_xboole_0 A (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k30_fomodel2 B (k31_fomodel2 B D) C))) B F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l157_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid k6_numbers 3)) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l157_toprealb,ax,(v1_t_0topsp (k13_toprealb (k4_toprealb k6_numbers)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb k6_numbers) (k3_real_1 (k4_toprealb k6_numbers) 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb k6_numbers))))).
tt(l158_jordan,ax, ((k18_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))) = (k18_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3)))) ).
tt(l158_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k30_modelc_1 A)) &  ((r2_hidden C (k30_modelc_1 A)) & (r2_funct_2 A k6_margrel1 (k31_modelc_1 A B) (k31_modelc_1 A C))) )  =>  (B = C) ) ) ) ) ) ).
tt(l158_toprealb,ax,(v1_t_0topsp (k13_toprealb (k4_toprealb (k10_real_1 1 2))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k10_real_1 1 2)) (k3_real_1 (k4_toprealb (k10_real_1 1 2)) 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k10_real_1 1 2)))))).
tt(l159_jordan,ax,(r1_xxreal_0 (k17_euclid (k19_euclid (k1_real_1 1) (k1_real_1 3))) (k17_euclid (k19_euclid k6_numbers (k1_real_1 3))))).
tt(l159_seq_4,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((k5_card_1 A) = k6_numbers)  =>  ( (A = k1_xboole_0)  |  ((v4_xxreal_2 A) &  ((r2_hidden (k4_seq_4 A) A) &  ((v3_xxreal_2 A) & (r2_hidden (k5_seq_4 A) A)) ) ) ) ) ) ) ).
tt(l159_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_zmodul01 A B C) => (r1_zmodul01 A C B)) ) ) ) ) ) ) ).
tt(l15_afvect01,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 o_0_0_afvect01)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 o_0_0_afvect01)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 o_0_0_afvect01)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 o_0_0_afvect01)) =>  ((r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C D)) c4__afvect01) <=> (r2_diraf o_0_0_afvect01 A B C D)) ) ) ) ) ) ) ) ) ).
tt(l15_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  ( (~  (A = B) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k3_algstr_3)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 k3_algstr_3)) &  ((k1_algstr_3 k3_algstr_3 A E C) = (k1_algstr_3 k3_algstr_3 B E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_amistd_1 2 k1_ami_3 B A) = (k1_tarski (k1_ordinal1 B))) ) )  => (v1_xboole_0 (k2_amistd_1 2 k1_ami_3 A))) ) ) ).
tt(l15_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((k3_rlvect_1 A B (k1_rlvect_1 A C E)) = (k3_rlvect_1 A D (k1_rlvect_1 A C F)))  =>  ((k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 E F)) B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 6 A) & (r1_xxreal_0 (k5_series_1 2 A) (k5_square_1 (k2_nat_1 A 1)))) ) ) ) ).
tt(l15_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( ((k17_sin_cos (k13_complex1 (k6_xcmplx_0 A B) 2)) = k6_numbers)  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k3_real_1 B (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ) ) ) ) ).
tt(l15_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k3_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k9_bvfunc_1 A B C) D E) F) = k8_margrel1)  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G (k15_bvfunc_1 A F (k5_bvfunc_2 A E D))) =>  ((k3_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) G) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_cardfin2,ax, ((m1_subset_1 1 k4_numbers) & (m1_subset_1 k6_numbers k4_numbers)) ).
tt(l15_cfdiff_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_cfdiff_1 B A) =>  (! [C:$i] :  ((m1_cfdiff_1 C A) =>  (? [D:$i] :  ((m1_cfdiff_1 D A) &  ((r1_tarski D B) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ).
tt(l15_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden (k10_finseq_1 B C) (k1_relset_1 (k1_euclid 2) A)) =>  ((k7_partfun1 (k1_euclid 1) (k3_pdiff_1 2 A) (k10_finseq_1 B C)) = (k12_finseq_1 k1_numbers (k7_partfun1 k1_numbers A (k10_finseq_1 B C)))) ) ) ) ) ) ) ) ).
tt(l15_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_abian A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_abian B)) )  =>  (~  ((r1_xxreal_0 A B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((k1_nat_1 A (k4_nat_1 2 C)) = B) ) ) ) ) ) ) ) ) ) ).
tt(l15_convex2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_classes1 A B) =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) &  ((r2_hidden D (k9_xtuple_0 A)) &  ( (~  (C = D) )  &  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden E (k9_xtuple_0 B)) &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  (E = F) )  &  ( ((k1_funct_1 A C) = (k1_funct_1 B E))  &  ((k1_funct_1 A D) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_convfun1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k7_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 k4_convfun1)) =>  ( ( ((k3_finseq_1 B) = A)  &  ( ((k3_finseq_1 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k12_supinf_2 B D) = (k1_funct_1 C D)) ) ) ) ) )  =>  ((k4_extreal1 B) = (k4_rlvect_1 k4_convfun1 C)) ) ) ) ) ) ) ) ).
tt(l15_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A B) C)) A)) ) ) ) ) ) ).
tt(l15_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k5_algstr_0 k18_csspace A B) = (k46_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) ) ).
tt(l15_dtconstr,ax,(r1_lang1 k5_dtconstr c3__dtconstr (k3_pre_poly (u1_struct_0 k5_dtconstr) c3__dtconstr))).
tt(l15_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( (~  (B = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig B) (k1_comptrig A))))  &  (~  ((k1_comptrig (k2_complex2 B (k1_real_1 (k1_comptrig A)))) = (k7_real_1 (k9_real_1 (k8_real_1 2 k32_sin_cos) (k1_comptrig A)) (k1_comptrig B))) ) ) ) ) ) ) ) ) ).
tt(l15_extreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k2_finseq_1 (k1_nat_1 A 1))) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) &  ((v3_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)))))) ) )  =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r2_hidden D (k2_finseq_1 (k1_nat_1 A 1))) &  (~  ( ( (~ (r1_xxreal_0 B D))  =>  ((k12_supinf_2 C D) = D) )  &  ( ( (D = B)  =>  ((k12_supinf_2 C D) = (k1_nat_1 A 1)) )  &  ( (~ (r1_xxreal_0 D B))  =>  ((k12_supinf_2 C D) = (k21_binop_2 D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_fib_fusc,ax, (~  ((k10_ami_3 2) = (k10_ami_3 4)) ) ).
tt(l15_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k3_xcmplx_0 (k3_power (k18_complex1 k2_fib_num) A) (k13_complex1 1 (k7_square_1 5))) k6_numbers)) ) ) ).
tt(l15_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k10_xtuple_0 (k11_finseq_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ).
tt(l15_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) )  =>  ( ((v1_setwiseo D A) &  ( ((k3_finseq_1 B) = k6_numbers)  &  (C = (k3_relat_1 E B)) ) )  =>  ((k1_finsop_1 A B D) = (k1_finsop_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v14_fomodel1 G F A) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B D C) (k1_nat_1 F 1)) G) = (k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 A) B (k9_funct_2 (k35_fomodel1 A) B) (k8_fomodel2 A B E C) (k2_nat_1 (k1_nat_1 F 1) H)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_fomodel3,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  ((v1_partfun1 (k10_fomodel3 B C A) (k4_finseq_2 A B)) &  ((v3_relat_2 (k10_fomodel3 B C A)) &  ((v8_relat_2 (k10_fomodel3 B C A)) & (m1_subset_1 (k10_fomodel3 B C A) (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) (k4_finseq_2 A B))))) ) ) ) ) ) ) ) ) ).
tt(l15_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  ( ((r1_functor2 A B C D) & (r1_functor2 A B D E))  =>  (! [F:$i] :  ((m1_functor2 F A B C D) =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A G H) = k1_xboole_0) )  =>  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A G H)) =>  ((k5_altcat_1 B (k3_functor0 A B C G) (k3_functor0 A B C H) (k3_functor0 A B D H) (k6_functor0 A B C G H I) (k2_functor2 A B C D F H)) = (k5_altcat_1 B (k3_functor0 A B C G) (k3_functor0 A B D G) (k3_functor0 A B D H) (k2_functor2 A B C D F G) (k6_functor0 A B D G H I))) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_functor2 G A B D E) =>  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A H I) = k1_xboole_0) )  =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 A H I)) =>  ((k5_altcat_1 B (k3_functor0 A B D H) (k3_functor0 A B D I) (k3_functor0 A B E I) (k6_functor0 A B D H I J) (k2_functor2 A B D E G I)) = (k5_altcat_1 B (k3_functor0 A B D H) (k3_functor0 A B E H) (k3_functor0 A B E I) (k2_functor2 A B D E G H) (k6_functor0 A B E H I J))) ) ) ) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A H I) = k1_xboole_0) )  =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 A H I)) =>  ((k5_altcat_1 B (k3_functor0 A B C H) (k3_functor0 A B C I) (k3_functor0 A B E I) (k6_functor0 A B C H I J) (k2_functor2 A B C E (k3_functor2 A B C D E F G) I)) = (k5_altcat_1 B (k3_functor0 A B C H) (k3_functor0 A B E H) (k3_functor0 A B E I) (k2_functor2 A B C E (k3_functor2 A B C D E F G) H) (k6_functor0 A B E H I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analoaf A B C C D) =>  ((r1_analoaf A D C C B) &  ((r1_analoaf A B C B D) & (r1_analoaf A C D B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k6_subset_1 (k1_enumset1 E F G) (k1_tarski (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 E F) A) (k4_tarski (k10_finseq_1 F G) B) (k4_tarski (k10_finseq_1 G E) C)) D))) = (k1_enumset1 E F G)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_6_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l15_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (m1_graph_1 k1_xboole_0 A)) ) ).
tt(l15_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ( ( (~  (D = (k1_funct_1 (u1_graph_1 B) (k1_funct_1 C A))) )  &  (~  (D = (k1_funct_1 (u2_graph_1 B) (k1_funct_1 C A))) ) )  | (r2_hidden D (k2_graph_5 B C))) ) ) ) ) ) ) ) ) ) ).
tt(l15_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k3_group_4 A (k5_finseq_2 (u1_struct_0 A) C B)) = (k5_group_1 A C B))  =>  ((k3_group_4 A (k5_finseq_2 (u1_struct_0 A) (k2_nat_1 C 1) B)) = (k5_group_1 A (k2_nat_1 C 1) B)) ) ) ) ) ) ) ) ).
tt(l15_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v4_aff_2 A) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ((r1_aff_1 A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ( (~ (r1_aff_1 A B C F))  &  ((r1_aff_1 A B F G) & (r2_analoaf A C F D G)) )  |  ((r1_aff_1 A B C F) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H F I G) & (r1_aff_1 A B C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ((r1_int_2 A B) | (r1_int_1 B A)) ) ) ) ) ).
tt(l15_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) & (r1_tarski B A))  =>  ((r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 C)) (k5_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B)))) &  ((r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 C)) (k4_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B)))) &  ((r1_xxreal_0 (k4_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B))) (k4_seq_4 (k1_rvsum_1 C))) & (r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B))) (k4_seq_4 (k1_rvsum_1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(l15_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~ (r1_xxreal_0 (k3_integra1 A) k6_numbers))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (~  ((v2_comseq_2 (k2_integra3 A B)) &  ((k2_seq_2 (k2_integra3 A B)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l15_integra8,ax, (~ (r1_xxreal_0 (k21_sin_cos (k10_real_1 k32_sin_cos 4)) k6_numbers)) ).
tt(l15_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) k1_numbers (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) B) = (k1_funct_1 k5_pscomp_1 B)) ) ) ) ) ).
tt(l15_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k1_jordan2c 2 A) = k1_xboole_0) )  &  ( (~ (r1_xxreal_0 B (k6_pscomp_1 (k1_jordan2c 2 A))))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k1_jordan2c 2 A)) => (r1_xxreal_0 B (k17_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 1 (k7_nat_d (k4_nat_1 2 A) 2))) ) ) ).
tt(l15_lattice5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k2_nat_1 B C) A))  &  ( (~  ((r1_xxreal_0 1 A) &  (~ (r1_xxreal_0 B A)) ) )  &  ( (~  ( (B = A)  &  (~ (r1_xxreal_0 (k2_nat_1 B C) A)) ) )  &  (~  ((r1_xxreal_0 (k2_nat_1 B 1) A) &  (~ (r1_xxreal_0 (k2_nat_1 B C) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k15_glib_001 A (k10_glib_001 A B C)) = (k2_nat_1 (k15_glib_001 A B) 1)) ) ) ) ) ) ) ) ).
tt(l15_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ( ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = (a_7_0_lfuzzy_1 A B C D E F G))  &  (~  ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) (k8_cqc_lang A (k8_cqc_lang A C B) B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l15_measure7,ax, ((k2_relset_1 (k9_setfam_1 k1_numbers) c1__measure7) = (k1_tarski k1_numbers)) ).
tt(l15_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (A = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) E H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) A I))) ) )  =>  ((k1_euclid_6 B D F) = (k11_binop_2 (k10_binop_2 (k10_binop_2 1 H) (k11_binop_2 I (k9_binop_2 (k10_binop_2 1 H) (k11_binop_2 G H)))) (k1_euclid_6 E B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ( (C = (k3_finseq_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k12_supinf_2 A D) = B) ) ) ) )  =>  ((k4_extreal1 A) = (k1_extreal1 C B)) ) ) ) ) ) ) ) ).
tt(l15_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_struct_0 A) & (l1_msualg_1 A)) )  => (r3_pua2mss1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)))) ) ).
tt(l15_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 (k1_unialg_1 A)) (k3_finseq_2 (k1_tarski k6_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 (k1_unialg_1 A)) (k3_finseq_2 (k1_tarski k6_numbers)))))) )  =>  ((v5_msualg_1 (g1_msualg_1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) B (k1_margrel1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) c1__msualg_1))) &  ((v13_struct_0 (g1_msualg_1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) B (k1_margrel1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) c1__msualg_1)) 1) &  ( (~ (v11_struct_0 (g1_msualg_1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) B (k1_margrel1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) c1__msualg_1))))  & (v1_msualg_1 (g1_msualg_1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) B (k1_margrel1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) c1__msualg_1)))) ) ) ) ) ) ) ).
tt(l15_numbers,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 A k5_arytm_3))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B k5_arytm_3))  =>  ((r1_ordinal1 A B) => (r3_arytm_3 A B)) ) ) ) ) ).
tt(l15_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v5_o_ring_1 B A)) ) ) ) ) ).
tt(l15_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D (k3_rlvect_1 A (k3_rlvect_1 A D E) (k4_algstr_0 A F)))) (k8_group_1 A (k5_algstr_0 A G (k3_rlvect_1 A (k3_rlvect_1 A G C) (k4_algstr_0 A B))) (k5_algstr_0 A F E))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (B = (k5_algstr_0 A (k3_rlvect_1 A C D) E))  &  (F = (k5_algstr_0 A (k3_rlvect_1 A C G) E)) )  =>  ((k8_group_1 A (k1_group_1 A) (k5_algstr_0 A D G)) = (k5_algstr_0 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ( ( (C = D)  =>  ((k1_seq_1 (k1_finseq_7 k1_numbers (k5_euclid A) C B) D) = B) )  &  ( (~  (C = D) )  =>  ((k1_seq_1 (k1_finseq_7 k1_numbers (k5_euclid A) C B) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ((r2_abian (u1_struct_0 B) C D) =>  ((k1_funct_1 (k9_funct_7 D A) C) = C) ) ) ) ) ) ) ) ) ) ).
tt(l15_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v8_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) &  (? [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) &  (? [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) &  (? [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) &  (? [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) &  (? [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) &  (? [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) &  (? [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) &  (? [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) &  (? [Q:$i] :  ((m1_subset_1 Q (u1_incsp_1 A)) &  ( (~ (r1_incsp_1 A C M))  &  ( (~ (r1_incsp_1 A D M))  &  ( (~ (r1_incsp_1 A B L))  &  ( (~ (r1_incsp_1 A E L))  &  ( (~ (r1_incsp_1 A B N))  &  ( (~ (r1_incsp_1 A D N))  &  ( (~ (r1_incsp_1 A C O))  &  ( (~ (r1_incsp_1 A E O))  &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F B E) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F C D) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G C E) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G B D) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H B C) I) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H D E) J) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) F G) K) &  ( (~ (r1_incsp_1 A H K))  &  ((r1_incsp_1 A G P) &  ((r1_incsp_1 A H P) &  ((r2_zfmisc_1 K P N O) &  ((r1_incsp_1 A Q I) & (r2_zfmisc_1 H Q B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_prvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)))  =>  ((v2_rlvect_1 A) & (v3_rlvect_1 A)) ) ) ) ).
tt(l15_qmax_1,ax,(r1_tarski (k10_xtuple_0 (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1))) (k1_qmax_1 k1_numbers k12_prob_1))).
tt(l15_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k6_quaterni A B k6_numbers k6_numbers) = (k5_arytm_0 A B)) ) ) ) ) ).
tt(l15_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (m2_finseq_1 (k1_partfun1 k5_numbers (k1_relset_1 A B) A k1_numbers (k1_uproots (k1_relset_1 A B)) B) k1_numbers)) ) ) ) ).
tt(l15_realset2,ax, ((k5_binop_1 2 k1_realset2 (k1_funct_7 1 2) (k1_funct_7 1 2)) = (k1_funct_7 k6_numbers 2)) ).
tt(l15_ringcat1,ax, (! [A:$i] :  ( ((v3_ringcat1 A) & (l1_ringcat1 A))  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  &  ((r1_ringcat1 B C) &  ( ((k1_ringcat1 A) = B)  &  ( ((k2_ringcat1 A) = C)  & (m1_ringcat1 (g1_ringcat1 (u1_ringcat1 A) (u2_ringcat1 A) (u3_ringcat1 A)) B C)) ) ) ) ) ) ) ) ) ).
tt(l15_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_ordinal1 (k1_card_1 (k1_convex1 A B C)) (k1_card_1 B))) ) ) ) ) ) ).
tt(l15_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  ( ((k1_rmod_3 A B E C) = (k1_rmod_3 A B E D))  &  ((k1_rmod_3 A B C E) = (k1_rmod_3 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((u1_struct_0 B) = C)  => (v1_rlsub_1 C A)) ) ) ) ) ) ) ) ) ).
tt(l15_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 A k1_numbers)) ) ).
tt(l15_scmfsa_1,ax,(r1_tarski (k9_xtuple_0 k3_ami_2) (k9_xtuple_0 k4_scmfsa_1))).
tt(l15_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k1_scmfsa8b A B C))) &  ((r2_hidden 1 (k9_xtuple_0 (k1_scmfsa8b A B C))) &  ((r2_hidden k6_numbers (k9_xtuple_0 (k2_scmfsa8b A B C))) & (r2_hidden 1 (k9_xtuple_0 (k2_scmfsa8b A B C)))) ) ) ) ) ) ) ) ) ).
tt(l15_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k4_scmp_gcd A) =>  ( ((k3_compos_1 k1_scmpds_2 A k6_numbers) = (k5_scmpds_2 k2_scmp_gcd k6_numbers))  &  ( ((k3_compos_1 k1_scmpds_2 A 1) = (k5_scmpds_2 k3_scmp_gcd 7))  &  ( ((k3_compos_1 k1_scmpds_2 A 2) = (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i))  &  ( ((k3_compos_1 k1_scmpds_2 A 3) = (k3_scmpds_2 2))  &  ( ((k3_compos_1 k1_scmpds_2 A 4) = (k2_compos_1 k1_scmpds_2))  &  ( ((k3_compos_1 k1_scmpds_2 A 5) = (k8_scmpds_2 k3_scmp_gcd 3 9))  &  ( ((k3_compos_1 k1_scmpds_2 A 6) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 6 3))  &  ( ((k3_compos_1 k1_scmpds_2 A 7) = (k15_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 3))  &  ( ((k3_compos_1 k1_scmpds_2 A 8) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 7 3))  &  ( ((k3_compos_1 k1_scmpds_2 A 9) = (k16_scmpds_2 k3_scmp_gcd k2_scmp_gcd (k2_nat_1 4 k14_scmpds_i) 1))  &  ( ((k3_compos_1 k1_scmpds_2 A 10) = (k11_scmpds_2 k2_scmp_gcd 1 4))  &  ( ((k3_compos_1 k1_scmpds_2 A 11) = (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i))  &  ( ((k3_compos_1 k1_scmpds_2 A 12) = (k3_scmpds_2 (k4_xcmplx_0 7)))  &  ( ((k3_compos_1 k1_scmpds_2 A 13) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 6))  &  ((k3_compos_1 k1_scmpds_2 A 14) = (k4_scmpds_2 k3_scmp_gcd)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_xcmplx_0 (k2_nat_1 A 2) (k6_xcmplx_0 (k2_nat_1 (k13_newton (k2_nat_1 A 1) 2) (k2_nat_1 A 1)) 1)) = (k2_nat_1 (k2_nat_1 (k2_nat_1 (k13_newton A 3) (k4_nat_1 5 (k13_newton A 2))) (k4_nat_1 7 A)) 2)) ) ) ).
tt(l15_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 (k13_complex1 (k3_xcmplx_0 A B) C)) (k13_complex1 (k3_xcmplx_0 B C) A)) (k3_xcmplx_0 (k3_xcmplx_0 2 (k13_complex1 (k3_xcmplx_0 A B) C)) (k13_complex1 (k3_xcmplx_0 C A) B))) (k3_xcmplx_0 (k3_xcmplx_0 2 (k13_complex1 (k3_xcmplx_0 B C) A)) (k13_complex1 (k3_xcmplx_0 C A) B))) = (k3_xcmplx_0 2 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 A)) (k3_square_1 B)))) ) ) ) ) ) ) ).
tt(l15_sin_cos6,ax, (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) ).
tt(l15_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 A 1) (k10_binop_2 1 A)) k6_numbers)) ) ) ) ).
tt(l15_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_t_0topsp A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_t_0topsp A))) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_t_0topsp A)))) =>  (~  ((v3_pre_topc D (k3_t_0topsp A)) &  ( ((r2_hidden B D) &  (~ (r2_hidden C D)) )  |  ((r2_hidden C D) &  (~ (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r1_termord A B C D) | (r1_termord A B D C)) ) ) ) ) ) ) ) ) ).
tt(l15_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v5_pre_topc C B (k15_euclid A)) &  ((v5_pre_topc D B (k15_euclid A)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) E F) = (k3_rlvect_1 (k15_euclid A) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C F) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) D F))) ) ) ) )  => (v5_pre_topc E B (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_topgen_3,ax, ((u1_struct_0 k2_topgen_3) = k1_numbers) ).
tt(l15_topreal2,ax, (~ (r2_hidden (k19_euclid k6_numbers 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)))) ).
tt(l15_uniform1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 (k7_finseq_1 B (k9_finseq_1 A))) = (k2_nat_1 (k3_finseq_1 B) 1))  &  ( ((k3_finseq_1 (k7_finseq_1 (k9_finseq_1 A) B)) = (k2_nat_1 (k3_finseq_1 B) 1))  &  ( ((k1_funct_1 (k7_finseq_1 B (k9_finseq_1 A)) (k2_nat_1 (k3_finseq_1 B) 1)) = A)  &  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) B) 1) = A) ) ) ) ) ) ) ).
tt(l15_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (? [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  &  ((u1_struct_0 C) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(l15_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  ((k1_waybel11 A (k3_waybel17 A B C)) = B) ) ) ) ) ) ) ) ).
tt(l15_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((u1_struct_0 A) = (u1_struct_0 (k1_waybel25 A))) ) ) ).
tt(l15_waybel_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A C (k7_funcop_1 A B)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k1_relset_1 (k4_card_3 (k2_funct_6 D)) (k2_pralg_2 D))) =>  (! [F:$i] :  ((r2_hidden F A) =>  ( ((k1_funct_1 (k1_funct_1 (k2_pralg_2 D) E) F) = (k1_funct_1 (k1_funct_1 D F) (k1_funct_1 E F)))  & (r2_hidden (k1_funct_1 (k1_funct_1 D F) (k1_funct_1 E F)) (k10_xtuple_0 (k1_funct_1 (k2_pralg_2 D) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C A) &  ((v5_pre_topc B A k3_topmetr) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = (k4_seq_4 (k1_weierstr (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C))))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = (k5_seq_4 (k1_weierstr (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_xreal_0,ax, (1 = (k5_arytm_0 c3__xreal_0 c4__xreal_0)) ).
tt(l15_xreal_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k2_arytm_0 A B) = (k3_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l15_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r2_hidden (k2_xxreal_3 A) k1_numbers) <=> (r2_hidden A k1_numbers)) ) ) ).
tt(l15_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_yellow11 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  &  ( ((k12_lattice3 A B C) = B)  &  ( ((k12_lattice3 A B D) = B)  &  ( ((k12_lattice3 A D F) = D)  &  ( ((k12_lattice3 A E F) = E)  &  ( ((k12_lattice3 A C D) = B)  &  ( ((k12_lattice3 A C E) = C)  &  ( ((k12_lattice3 A D E) = B)  &  ( ((k13_lattice3 A C D) = F)  &  ((k13_lattice3 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l15_yellow21,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) <=>  (B = (k2_xboole_0 (k6_subset_1 B (k1_tarski A)) (k1_tarski A))) ) ) ) ).
tt(l15_zf_fund1,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) =>  (A = (k3_zf_fund1 (k2_zf_lang (k5_card_1 A)))) ) ) ).
tt(l15_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k2_xboole_0 (k1_tarski A) B) B) => (r2_hidden A B)) ) ) ).
tt(l160_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((v4_funct_1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k43_fomodel2 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 A))))) )  =>  (~  ((v6_fomodel4 B A) &  ((r2_hidden (k23_fomodel4 A) B) &  ((r2_hidden (k24_fomodel4 A) B) &  ((r2_hidden (k30_fomodel4 A) B) &  ((r2_hidden (k33_fomodel4 A) B) &  ( (~ (v1_finset_1 (k7_subset_1 (k15_fomodel1 A) (k16_fomodel1 A) (k21_fomodel0 (k9_subset_1 (k3_finseq_2 (k1_fomodel1 A)) C (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))))))  &  ( (~ (v14_fomodel4 C A B))  & (v14_fomodel4 (k45_fomodel4 C A B D) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l160_jordan,ax,(r1_xxreal_0 (k17_euclid (k19_euclid k6_numbers (k1_real_1 3))) (k17_euclid (k19_euclid 1 (k1_real_1 3))))).
tt(l160_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((k5_card_1 B) = A)  =>  ( (B = k1_xboole_0)  |  ((v4_xxreal_2 B) &  ((r2_hidden (k4_seq_4 B) B) &  ((v3_xxreal_2 B) & (r2_hidden (k5_seq_4 B) B)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((k5_card_1 B) = (k2_nat_1 A 1))  =>  ( (B = k1_xboole_0)  |  ((v4_xxreal_2 B) &  ((r2_hidden (k4_seq_4 B) B) &  ((v3_xxreal_2 B) & (r2_hidden (k5_seq_4 B) B)) ) ) ) ) ) ) ) ) ) ).
tt(l160_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ( (A = (k5_zf_lang1 B E F))  &  (C = (k5_zf_lang1 D E F)) )  =>  ((k7_zf_lang A C) = (k5_zf_lang1 (k7_zf_lang B D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l161_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid 1 (k1_real_1 3))))).
tt(l161_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((k5_card_1 B) = A)  =>  ( (B = k1_xboole_0)  |  ((v4_xxreal_2 B) &  ((r2_hidden (k4_seq_4 B) B) &  ((v3_xxreal_2 B) & (r2_hidden (k5_seq_4 B) B)) ) ) ) ) ) ) ) ) ).
tt(l161_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( (A = (k5_zf_lang1 B C D))  =>  ( ( (~  ( (E = F)  &  (~  (F = C) ) ) )  &  (~  ( (E = D)  &  (F = C) ) ) )  |  ((k8_zf_lang E A) = (k5_zf_lang1 (k8_zf_lang F B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l162_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l163_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid 1 (k1_real_1 3))))).
tt(l164_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k33_fomodel2 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 D))))) )  =>  ( ((v6_fomodel4 E D) &  ((r2_hidden (k23_fomodel4 D) E) & (r2_hidden (k33_fomodel4 D) E)) )  =>  ((v14_fomodel4 C D E) |  ((r1_tarski (k8_nat_1 (k9_setfam_1 (k2_xboole_0 C (k33_fomodel2 D))) (k48_fomodel4 C D E F) A) (k8_nat_1 (k9_setfam_1 (k2_xboole_0 C (k33_fomodel2 D))) (k48_fomodel4 C D E F) (k2_xcmplx_0 A B))) &  (~ (v14_fomodel4 (k8_nat_1 (k9_setfam_1 (k2_xboole_0 C (k33_fomodel2 D))) (k48_fomodel4 C D E F) B) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l164_jordan,ax,(r1_tarski (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3))).
tt(l165_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ((r2_hidden A (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3)) &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) 3))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid k6_numbers 3))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 3) (k19_euclid 1 3))))  &  (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid 1 k6_numbers)))) ) ) ) ) ) ) ) ) ).
tt(l166_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) )  =>  ( ((k10_xtuple_0 D) = (k33_fomodel2 B))  => (v9_fomodel2 (k49_fomodel4 A B C D) B)) ) ) ) ) ) ) ) ).
tt(l166_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 (k18_euclid A) k6_numbers) &  ((r2_hidden A (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3)) &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) (k1_real_1 3)))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3)))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers (k1_real_1 3)) (k19_euclid 1 (k1_real_1 3)))))  &  (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid 1 k6_numbers)))) ) ) ) ) ) ) ) ) ).
tt(l167_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k33_fomodel2 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k33_fomodel2 B))))) )  =>  (~  ((v6_fomodel4 C B) &  ((r2_hidden (k23_fomodel4 B) C) &  ((r2_hidden (k33_fomodel4 B) C) &  ( (~ (v14_fomodel4 A B C))  & (v14_fomodel4 (k49_fomodel4 A B C D) B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l168_group_9,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (A = (k6_relat_1 (k10_xtuple_0 A) B))  <=>  ((k2_relat_1 A) = (k5_relat_1 (k2_relat_1 B) (k9_xtuple_0 (k2_relat_1 A)))) ) ) ) ) ) ).
tt(l169_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v12_fomodel4 B 2 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [C:$i] :  ((v4_funct_1 C) =>  (~  ((v4_card_3 (k33_fomodel2 A)) &  ( (~ (v1_finset_1 (k7_subset_1 (k15_fomodel1 A) (k16_fomodel1 A) (k21_fomodel0 (k9_subset_1 (k3_finseq_2 (k1_fomodel1 A)) C (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0)))))))  &  ( (~ (v14_fomodel4 C A B))  &  ((v6_fomodel4 B A) &  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 A D)) =>  (~ (v10_fomodel2 C D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l169_group_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_finset_1 D) =>  (~  ( (D = C)  &  ( ((k5_card_1 D) = A)  &  (! [E:$i] :  ((r2_hidden E B) =>  ( (C = E)  |  ((r2_wellord2 C E) & (r1_xboole_0 C E)) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (k3_tarski B))  &  ((k5_card_1 C) = (k3_nat_1 A (k5_card_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l169_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k3_relat_1 B (k5_relat_1 C A)) = (k3_relat_1 (k6_relat_1 A B) C)) ) ) ) ) ) ).
tt(l169_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (~  ( ((k5_card_1 (k1_rvsum_1 A)) = k6_numbers)  &  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( ((k1_rvsum_1 B) = (k1_rvsum_1 A))  &  ( ((k3_finseq_1 B) = (k5_card_1 (k1_rvsum_1 A)))  & (v5_valued_0 B)) ) ) ) ) ) ) ) ) ).
tt(l169_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_zmodul01 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(l16_afvect01,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 o_0_0_afvect01)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 o_0_0_afvect01)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 o_0_0_afvect01)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 o_0_0_afvect01)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ( ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) )  =>  ((r2_diraf o_0_0_afvect01 A B C D) <=> (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_0)) =>  ((k1_algstr_0 k3_algstr_0 (k1_algstr_0 k3_algstr_0 A B) C) = (k1_algstr_0 k3_algstr_0 A (k1_algstr_0 k3_algstr_0 B C))) ) ) ) ) ) ) ).
tt(l16_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k3_algstr_3)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k3_algstr_3)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k3_algstr_3)) =>  (~  ( ((k1_algstr_3 k3_algstr_3 C A E) = (k1_algstr_3 k3_algstr_3 D A F))  &  ( ((k1_algstr_3 k3_algstr_3 C B E) = (k1_algstr_3 k3_algstr_3 D B F))  &  ( (~  (A = B) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_ami_2,ax, ((k9_xtuple_0 k3_ami_2) = k1_ami_2) ).
tt(l16_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_algstr_0 A (k1_rlvect_1 A B C)) = (k1_rlvect_1 A B (k1_real_1 C))) ) ) ) ) ) ) ).
tt(l16_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  (~  ((r2_hidden B k1_arytm_2) &  ((r2_hidden A B) &  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (~  ((r2_hidden C B) &  (~ (r3_arytm_3 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 6))  & (r1_xxreal_0 (k4_power 2 A) (k5_square_1 A))) ) ) ) ).
tt(l16_borsuk_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  =>  ((r1_xxreal_0 k6_numbers (k9_real_1 1 A)) & (r1_xxreal_0 (k9_real_1 1 A) 1)) ) ) ) ).
tt(l16_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (D = (k6_domain_1 (u1_struct_0 A) C))  => (r2_borsuk_3 (k2_borsuk_1 B (k1_pre_topc A D)) B)) ) ) ) ) ) ) ) ) ).
tt(l16_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  ( (C = (k4_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)))  =>  ( ((k6_algstr_0 (k5_c0sp2 A) B C) = B)  &  ((k6_algstr_0 (k5_c0sp2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l16_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~  (A = B) )  =>  ( ((k2_xboole_0 (a_5_8_card_fin A B C D E) (a_5_9_card_fin A B C D E)) = (k1_card_fin (k2_xboole_0 D (k1_tarski C)) (k23_binop_2 E 1) A B))  & (r1_xboole_0 (a_5_8_card_fin A B C D E) (a_5_9_card_fin A B C D E))) ) ) ) ) ) ) ) ) ).
tt(l16_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 2))) =>  ( ( (C = (k3_binop_2 A (k5_binop_2 B k7_complex1)))  &  (D = (k10_finseq_1 A B)) )  =>  ((k17_complex1 C) = (k1_normsp_0 (k4_real_ns1 2) D)) ) ) ) ) ) ) ) ) ) ).
tt(l16_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_tarski (k1_enumset1 A B (k2_xboole_0 A B))) = (k2_xboole_0 A B)) ) ) ).
tt(l16_complex1,ax, (k7_complex1 = (k5_arytm_0 k6_numbers 1)) ).
tt(l16_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C (k3_rlvect_2 A B)) &  (! [D:$i] :  ((m1_rlvect_2 D A) =>  (~  ((k3_rlvect_2 A D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  ((r1_tarski (k2_relset_1 k7_numbers A) (k6_domain_1 k7_numbers k1_supinf_2)) =>  ((k4_extreal1 A) = k1_supinf_2) ) ) ) ).
tt(l16_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) (k9_cqc_lang A B C)) A)) ) ) ) ) ) ).
tt(l16_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) => (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace A)) (k55_valued_1 k5_numbers k2_numbers (k2_csspace B))))) ) ) ) ).
tt(l16_dtconstr,ax,(r1_lang1 k5_dtconstr c3__dtconstr (k3_pre_poly (u1_struct_0 k5_dtconstr) c2__dtconstr))).
tt(l16_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ( ((k9_xtuple_0 (k2_xtuple_0 B)) = (k3_ens_1 A B))  & (r1_tarski (k10_xtuple_0 (k2_xtuple_0 B)) (k4_ens_1 A B))) ) ) ) ) ).
tt(l16_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((v1_euclid_4 B A) &  ((r2_hidden C B) & (r2_hidden D B)) )  =>  ( (C = D)  |  (B = (k2_euclid_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( (~  (B = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k9_real_1 (k1_comptrig B) (k1_comptrig A))))  &  (~  ((k3_complex2 A B) = (k7_real_1 (k9_real_1 (k8_real_1 2 k32_sin_cos) (k1_comptrig A)) (k1_comptrig B))) ) ) ) ) ) ) ) ) ).
tt(l16_extreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) &  ((v3_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) &  ((v3_funct_2 D (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)))))) ) )  =>  (! [E:$i] :  ((m2_finseq_1 E (k2_finseq_1 (k1_nat_1 A 1))) =>  ( ( (E = C)  &  ( (B = (k12_supinf_2 C (k1_nat_1 A 1)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k2_finseq_1 (k1_nat_1 A 1))) =>  ( ( (~ (r1_xxreal_0 B F))  =>  ((k12_supinf_2 D F) = F) )  &  ( ( (F = B)  =>  ((k12_supinf_2 D F) = (k1_nat_1 A 1)) )  &  ( (~ (r1_xxreal_0 F B))  =>  ((k12_supinf_2 D F) = (k21_binop_2 F 1)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_partfun1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k17_finseq_1 (k2_finseq_1 (k1_nat_1 A 1)) A E) D)) &  ((v1_funct_2 (k1_partfun1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k17_finseq_1 (k2_finseq_1 (k1_nat_1 A 1)) A E) D) (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 (k1_partfun1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k17_finseq_1 (k2_finseq_1 (k1_nat_1 A 1)) A E) D) (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 (k1_partfun1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) (k17_finseq_1 (k2_finseq_1 (k1_nat_1 A 1)) A E) D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_fdiff_9,ax, ((k3_limfunc1 k6_numbers) = a_0_0_fdiff_9) ).
tt(l16_ff_siec,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_xboole_0 B D) &  ((r1_tarski A B) & (r1_tarski C D)) )  => (r1_xboole_0 A C)) ) ) ) ) ).
tt(l16_fib_fusc,ax, (~  ((k10_ami_3 3) = (k10_ami_3 4)) ) ).
tt(l16_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k13_complex1 1 2) (k3_xcmplx_0 (k3_power (k18_complex1 k2_fib_num) A) (k13_complex1 1 (k7_square_1 5))))) ) ) ).
tt(l16_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  <=> (r2_hidden (k3_lattices A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(l16_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k7_partfun1 B (k8_finseq_1 B C D) A) = (k7_partfun1 B C A)) ) ) ) ) ) ) ) ) ) ).
tt(l16_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k1_binop_1 (k11_monoid_0 A) B C) = (k1_monoid_0 A B C)) ) ) ) ) ) ) ).
tt(l16_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H C))  =>  ((k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D (k2_fuzzy_1 (k2_zfmisc_1 B C) E F) G H))) = (k2_square_1 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E G H))) (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D F G H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_gfacirc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (D = (k4_tarski (k10_finseq_1 B C) A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A)))) =>  ( ((k1_twoscomp (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) (k6_circuit2 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) E) (k9_facirc_1 B C D A)) = (k1_funct_1 A (k10_finseq_1 (k1_funct_1 E (k4_tarski (k10_finseq_1 B C) A)) (k1_funct_1 E D))))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) E) (k4_tarski (k10_finseq_1 B C) A)) = (k1_funct_1 A (k10_finseq_1 (k1_funct_1 E B) (k1_funct_1 E C))))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) E) B) = (k1_funct_1 E B))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) E) C) = (k1_funct_1 E C))  &  ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C D A) (k10_facirc_1 B C D A) E) D) = (k1_funct_1 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k1_xtuple_0 (k3_gfacirc2 C A B)) = k1_xboole_0)  &  ( ((k2_xtuple_0 (k3_gfacirc2 C A B)) = (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1))  &  ((k9_xtuple_0 (k2_xtuple_0 (k3_gfacirc2 C A B))) = (k4_finseq_2 k6_numbers k6_margrel1)) ) )  |  ( ((k1_card_1 (k1_xtuple_0 (k3_gfacirc2 C A B))) = 3)  &  ( ((k2_xtuple_0 (k3_gfacirc2 C A B)) = k25_twoscomp)  &  ((k9_xtuple_0 (k2_xtuple_0 (k3_gfacirc2 C A B))) = (k4_finseq_2 3 k6_margrel1)) ) ) ) ) ) ) ) ) ) ).
tt(l16_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v1_glib_002 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ((v11_glib_000 B A) => (v1_glib_002 C)) ) ) ) ) ) ) ).
tt(l16_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  => (r1_tarski k2_glib_004 (k1_relset_1 k5_numbers A))) ) ).
tt(l16_goboard5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_finseq_1 (k1_goboard1 A)) = (k4_finseq_1 A)) ) ) ).
tt(l16_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_5_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l16_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_graph_2 A C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 C)) &  ((r1_xxreal_0 1 (k1_nat_1 D 1)) &  ((r1_xxreal_0 (k1_nat_1 D 1) (k3_finseq_1 C)) &  ( ( ((k1_funct_1 C D) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D)))  &  ((k1_funct_1 C (k1_nat_1 D 1)) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B D))) )  |  ( ((k1_funct_1 C D) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B D)))  &  ((k1_funct_1 C (k1_nat_1 D 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((r3_lattices (k12_normform A) B C) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E C) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((v4_aff_2 A) &  ((r1_aff_1 A B C D) &  ((r1_aff_1 A B E F) &  ((r2_analoaf A C E D F) & (r1_aff_1 A B C G)) ) ) )  =>  ( (B = C)  |  ((r1_aff_1 A B C E) |  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C I))  &  ((r1_aff_1 A B I J) &  ((r2_analoaf A C I D J) &  ((r2_analoaf A I G J H) & (r1_aff_1 A B C H)) ) ) ) ) ) ) ) )  | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( (~  (C = B) )  &  ( (~  ((k1_funct_1 A C) = k6_numbers) )  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k3_xcmplx_0 D (k1_funct_1 A B)) = (k7_xcmplx_0 (k19_rvsum_1 A) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_integra3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  ((r2_hidden A (k4_finseq_1 C)) => (r1_xxreal_0 (k3_integra1 (k2_integra1 B C A)) (k1_integra3 B C))) ) ) ) ) ) ) ).
tt(l16_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( ((k3_integra1 A) = k6_numbers)  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (~  ((v2_comseq_2 (k2_integra3 A B)) &  ((k2_seq_2 (k2_integra3 A B)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l16_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A)) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (k1_pre_topc (k15_euclid 2) A) k3_topmetr) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) ) ) ) ).
tt(l16_jordan1b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k7_nat_d (k3_finseq_1 (k1_jordan8 A k6_numbers)) 1) = 3) ) ) ).
tt(l16_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k1_jordan2c 2 A) = k1_xboole_0) )  &  ( (~ (r1_xxreal_0 (k8_pscomp_1 (k1_jordan2c 2 A)) B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k1_jordan2c 2 A)) => (r1_xxreal_0 (k17_euclid C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 1 (k7_nat_d (k4_nat_1 2 A) 1))) ) ) ).
tt(l16_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k15_glib_001 A B) = (k15_glib_001 A (k6_glib_001 A B))) ) ) ) ) ).
tt(l16_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A C B) B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l16_matrix11,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden A (k2_sgraph1 (k2_finseq_1 B))) & (r2_hidden C A))  =>  ((r2_hidden C (k2_finseq_1 B)) &  (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden D (k2_finseq_1 B)) &  ( (~  (C = D) )  &  (A = (k2_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) => (r1_tarski (k9_matrix13 k2_vectsp_1 A B C) (k2_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B C))))) ) ) ) ) ) ).
tt(l16_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 C) (k2_finseq_1 C)) &  ((v3_funct_2 D (k2_finseq_1 C) (k2_finseq_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))))) ) )  =>  (~  ( ((k1_seq_1 D 1) = A)  &  ( ((k1_seq_1 D 2) = B)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 C)) =>  ((r1_xxreal_0 E 2) |  ( ((r1_xxreal_0 E (k1_nat_1 A 1)) =>  ((k1_seq_1 D E) = (k5_real_1 E 2)) )  &  ( ((r1_xxreal_0 E B) =>  ((r1_xxreal_0 E (k1_nat_1 A 1)) |  ((k1_seq_1 D E) = (k5_real_1 E 1)) ) )  &  ( (~ (r1_xxreal_0 E B))  =>  ((k1_seq_1 D E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_measure7,ax,(r1_tarski k1_numbers (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) c1__measure7)))).
tt(l16_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((r1_tarski A B) => (r1_tarski (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(l16_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B C) &  ( (! [D:$i] :  ((r2_hidden D (k1_relset_1 A C)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 C D))) )  &  ( (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 A C)) &  (k1_supinf_2 = (k12_supinf_2 C D)) ) ) )  &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (~  ((r1_mesfunc3 A B C D E) &  ( ((k12_supinf_2 E 1) = k1_supinf_2)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 2 F) & (r2_hidden F (k4_finseq_1 E)))  =>  ( (~ (r1_xxreal_0 (k12_supinf_2 E F) k1_supinf_2))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v2_mfold_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_connsp_2 D B C) &  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_mfold_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  & (r1_metrizts B (k15_euclid A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) = (u1_struct_0 (k15_euclid A))) ) ) ).
tt(l16_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k4_finseq_1 (k1_unialg_1 A)) = (k4_finseq_1 (u1_unialg_1 A))) ) ) ).
tt(l16_numbers,ax, (2 = (k2_tarski k6_numbers 1)) ).
tt(l16_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 1 F E))  =>  ( (D = (k1_fdiff_1 (k1_pdiff_2 3 1 F E) A))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J G) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 F E) M) (k1_seq_1 (k1_pdiff_2 3 1 F E) G)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M G)) (k1_seq_1 L (k9_real_1 M G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_polyeq_1,ax, (3 = (k2_nat_1 (k4_nat_1 2 1) 1)) ).
tt(l16_poset_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_orders_3 G B B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ( ((r1_yellow_2 (u1_struct_0 B) B F G) &  ( (C = (k1_funct_1 (k9_funct_7 F A) D))  &  (E = (k1_funct_1 (k9_funct_7 G A) D)) ) )  => (r3_orders_2 B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_pre_ff,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k3_finseq_2 k5_numbers)) =>  (? [C:$i] :  ((m2_finseq_2 C k5_numbers (k3_finseq_2 k5_numbers)) &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_nat_1 A 2) = (k4_nat_1 2 D))  =>  (C = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers B D)))) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_nat_1 A 2) = (k2_nat_1 (k4_nat_1 2 D) 1))  =>  (C = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers B D) (k7_partfun1 k5_numbers B (k1_nat_1 D 1)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) (k7_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l16_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) & (r1_projdes1 A E F B C))  =>  ( (B = C)  | (r1_projdes1 A E F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_prvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((r3_binop_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A)) => (v4_rlvect_1 A)) ) ) ).
tt(l16_qmax_1,ax, ((v1_funct_1 (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1))) &  ((v1_funct_2 (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1)) (k8_mcart_1 k5_numbers k5_numbers (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers)) (k1_qmax_1 k1_numbers k12_prob_1)) & (m1_subset_1 (k6_domain_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers))) (k1_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) c3__qmax_1)) (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 k5_numbers k5_numbers (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers)) (k1_qmax_1 k1_numbers k12_prob_1))))) ) ).
tt(l16_quin_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( ((k3_square_1 A) = (k3_square_1 B))  &  ( (~  (A = B) )  &  (~  (A = (k4_xcmplx_0 B)) ) ) ) ) ) ) ) ) ).
tt(l16_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k1_relset_1 k5_numbers (k1_partfun1 k5_numbers (k1_relset_1 A B) A k1_numbers (k1_uproots (k1_relset_1 A B)) B)) = (k4_finseq_1 (k1_uproots (k1_relset_1 A B)))) ) ) ) ) ).
tt(l16_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 1 1 1)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1))) ).
tt(l16_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (v8_valued_0 (k4_rinfsup2 A))) ) ).
tt(l16_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) ).
tt(l16_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) => (m1_rmod_2 C A (k2_rmod_2 A B))) ) ) ) ) ) ).
tt(l16_scmfsa_1,ax,(r2_hidden k5_numbers (k9_xtuple_0 k4_scmfsa_1))).
tt(l16_scmfsa8b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa8b A B C) k6_numbers) = (k12_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A))  &  ( ((k1_funct_1 (k1_scmfsa8b A B C) 1) = (k11_scmfsa_2 2))  &  ( ((k1_funct_1 (k2_scmfsa8b A B C) k6_numbers) = (k13_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A))  &  ((k1_funct_1 (k2_scmfsa8b A B C) 1) = (k11_scmfsa_2 2)) ) ) ) ) ) ) ) ) ) ).
tt(l16_scmpds_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) => (r1_tarski (k61_valued_1 A 1) (k1_scmpds_8 B C A))) ) ) ) ) ) ).
tt(l16_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) => (r1_xxreal_0 (k2_compos_0 (k1_scmringi A) B) 7)) ) ) ) ).
tt(l16_scpqsort,ax, ((k5_card_1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) = 9) ).
tt(l16_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 C D) = (k2_xcmplx_0 (k3_xcmplx_0 A D) B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 (k3_series_1 C) D) = (k2_xcmplx_0 (k2_xcmplx_0 (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 A (k2_nat_1 D 1)) D) 2) (k3_xcmplx_0 D B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(l16_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k4_square_1 (k8_complex1 (k8_complex1 (k13_complex1 (k3_xcmplx_0 A B) C) (k13_complex1 (k3_xcmplx_0 B C) A)) (k13_complex1 (k3_xcmplx_0 C A) B))) = (k2_xcmplx_0 (k8_complex1 (k8_complex1 (k4_square_1 (k13_complex1 (k3_xcmplx_0 B C) A)) (k4_square_1 (k13_complex1 (k3_xcmplx_0 C A) B))) (k4_square_1 (k13_complex1 (k3_xcmplx_0 A B) C))) (k3_xcmplx_0 2 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 A)) (k3_square_1 B))))) ) ) ) ) ) ) ).
tt(l16_sin_cos6,ax, (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k8_real_1 1 k32_sin_cos))) ).
tt(l16_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k3_xcmplx_0 (k2_xcmplx_0 A (k3_xcmplx_0 C k7_complex1)) (k2_xcmplx_0 B (k3_xcmplx_0 D k7_complex1))) = (k2_xcmplx_0 (k9_real_1 (k8_real_1 A B) (k8_real_1 C D)) (k3_xcmplx_0 (k7_real_1 (k8_real_1 A D) (k8_real_1 B C)) k7_complex1)))  &  ((k15_complex1 (k2_xcmplx_0 B (k3_xcmplx_0 D k7_complex1))) = (k2_xcmplx_0 B (k3_xcmplx_0 (k1_real_1 D) k7_complex1))) ) ) ) ) ) ) ) ) ) ).
tt(l16_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 A (k3_square_1 B))) ) ) ) ) ) ) ) ) ).
tt(l16_taylor_1,ax, (~ (r1_xxreal_0 k8_power 1)) ).
tt(l16_topgen_3,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) &  ( ((u1_pre_topc k2_topgen_3) = (k1_cantor_1 k1_numbers A))  &  (A = a_0_0_topgen_3) ) ) ) ).
tt(l16_topreal2,ax, (~ (r2_hidden (k19_euclid 1 k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)))) ).
tt(l16_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v11_aff_2 A) &  ((r1_aff_1 A B C D) &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B C G H) &  ((r2_analoaf A B E C F) &  ((r2_analoaf A B G C H) &  ((r2_analoaf A E F D I) &  ((r2_analoaf A G H D J) &  ((r2_analoaf A E D F I) & (r2_analoaf A G D H J)) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ((r1_aff_1 A B C E) |  ((r1_aff_1 A B C G) |  (I = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_uniform1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ( ((k1_funct_1 (k7_finseq_1 B (k9_finseq_1 A)) 1) = (k1_funct_1 B 1))  &  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) B) (k2_nat_1 (k3_finseq_1 B) 1)) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ).
tt(l16_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  ( ((k1_vectsp_5 A B E C) = (k1_vectsp_5 A B E D))  &  ((k1_vectsp_5 A B C E) = (k1_vectsp_5 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v2_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v17_waybel_0 C B A) & (v22_waybel_0 C B A)) ) ) ) ) )  &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v6_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  =>  (~  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) ) ) ) ) ) ) ) ).
tt(l16_waybel25,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (k1_tarski B))  &  (E = (k1_tarski C)) )  =>  ((r2_hidden B (k2_pre_topc A E)) <=> (r1_tarski (k2_pre_topc A D) (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_waybel_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_pboole D A B (k7_funcop_1 A C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k1_relset_1 (k4_card_3 (k2_funct_6 D)) (k2_pralg_2 D))) =>  (! [F:$i] :  ((r2_hidden F A) => (r2_hidden (k1_funct_1 E F) (k1_funct_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_xreal_0,ax, ( ((k4_xcmplx_0 1) = (k5_arytm_0 c5__xreal_0 c6__xreal_0))  &  (k6_numbers = (k5_arytm_0 (k1_arytm_0 c3__xreal_0 c5__xreal_0) (k1_arytm_0 c4__xreal_0 c6__xreal_0))) ) ).
tt(l16_xreal_1,ax,(m1_subset_1 k6_numbers k2_arytm_2)).
tt(l16_xxreal_3,ax, ((k2_xxreal_3 (k1_xxreal_3 k1_xxreal_0 k2_xxreal_0)) = (k3_xxreal_3 (k2_xxreal_3 k2_xxreal_0) k1_xxreal_0)) ).
tt(l16_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) =>  (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l16_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k4_ordinal1)))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( ((k1_relset_1 A (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A)) = A)  &  ((r1_tarski (k2_relset_1 B (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A)) B) &  ((r2_hidden (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A) (k9_funct_2 A B)) &  ((k1_relset_1 k4_ordinal1 (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C)) = k4_ordinal1) ) ) ) ) ) ) ) ) ) ).
tt(l170_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v12_fomodel4 B 2 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  (! [C:$i] :  ((v4_funct_1 C) =>  (~  ((v1_finset_1 C) &  ((v4_card_3 (k33_fomodel2 A)) &  ( (~ (v14_fomodel4 C A B))  &  ((v6_fomodel4 B A) &  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 A D)) =>  (~ (v10_fomodel2 C D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l170_group_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k2_finseq_1 A)) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)) & (r1_tarski (k7_relset_1 k1_numbers k1_numbers C B) (k7_subset_1 k1_numbers k5_numbers (k1_tarski k6_numbers)))) ) )  =>  ((k14_finseq_1 (k7_relset_1 k1_numbers k1_numbers C B)) = (k1_partfun1 k5_numbers k5_numbers k1_numbers k1_numbers (k14_finseq_1 B) C)) ) ) ) ) ) ) ).
tt(l170_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 3) (k19_euclid k6_numbers 3)) A)) ) ) ).
tt(l170_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( ((k5_card_1 (k1_rvsum_1 B)) = A)  &  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (~  ( ((k1_rvsum_1 C) = (k1_rvsum_1 B))  &  ( ((k3_finseq_1 C) = (k5_card_1 (k1_rvsum_1 B)))  & (v5_valued_0 C)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( ((k5_card_1 (k1_rvsum_1 B)) = (k2_nat_1 A 1))  &  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (~  ( ((k1_rvsum_1 C) = (k1_rvsum_1 B))  &  ( ((k3_finseq_1 C) = (k5_card_1 (k1_rvsum_1 B)))  & (v5_valued_0 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l171_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 C A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 D) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 D A)) =>  ( ((v16_fomodel1 D C) &  ((r1_tarski B (k33_fomodel2 C)) &  ((k5_relat_1 E (k37_fomodel1 C)) = (k5_relat_1 F (k37_fomodel1 C))) ) )  =>  ((v10_fomodel2 B A C E) <=> (v10_fomodel2 B A D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l171_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_tarski A (k2_finseq_1 (k1_nat_1 B 1))) &  ((r2_hidden C (k2_finseq_1 (k1_nat_1 B 1))) &  ( (~ (r2_hidden C A))  &  (! [D:$i] :  (~  ( ((k14_finseq_1 D) = (k3_relat_1 (k14_finseq_1 A) (k2_funct_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k2_finseq_1 (k1_nat_1 B 1)) (k1_tarski C))))))  & (r1_tarski D (k2_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l171_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 3) (k19_euclid k6_numbers 3)) A)) ) ) ).
tt(l171_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( ((k5_card_1 (k1_rvsum_1 B)) = A)  &  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (~  ( ((k1_rvsum_1 C) = (k1_rvsum_1 B))  &  ( ((k3_finseq_1 C) = (k5_card_1 (k1_rvsum_1 B)))  & (v5_valued_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l172_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) A)) ) ) ).
tt(l173_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v1_orders_4 B) &  ((v11_fomodel1 B) & (l1_fomodel1 B)) ) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( ((r1_tarski A (k33_fomodel2 B)) & (v13_fomodel2 (k38_fomodel2 B C) A B))  => (v8_fomodel4 (k38_fomodel2 B C) B (k37_fomodel4 B) A)) ) ) ) ) ) ).
tt(l173_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 3)) (k19_euclid k6_numbers (k1_real_1 3))) A)) ) ) ).
tt(l173_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = k6_numbers)  &  ( ((k3_finseq_1 B) = k6_numbers)  &  ( ((k1_rvsum_1 A) = (k1_rvsum_1 B))  &  ((v5_valued_0 A) & (v5_valued_0 B)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l174_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_jordan24 2 B (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) &  ((r2_hidden A (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) 3)))) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k1_real_1 1) 3)) B)) ) ) ) ) ).
tt(l174_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 B) = A)  &  ( ((k3_finseq_1 C) = A)  &  ( ((k1_rvsum_1 B) = (k1_rvsum_1 C))  &  ((v5_valued_0 B) & (v5_valued_0 C)) ) ) )  =>  (B = C) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 B) = (k2_nat_1 A 1))  &  ( ((k3_finseq_1 C) = (k2_nat_1 A 1))  &  ( ((k1_rvsum_1 B) = (k1_rvsum_1 C))  &  ((v5_valued_0 B) & (v5_valued_0 C)) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(l175_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_jordan24 2 B (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) &  ((r2_hidden A (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 3)))) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) A (k19_euclid 1 3)) B)) ) ) ) ) ).
tt(l175_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 B) = A)  &  ( ((k3_finseq_1 C) = A)  &  ( ((k1_rvsum_1 B) = (k1_rvsum_1 C))  &  ((v5_valued_0 B) & (v5_valued_0 C)) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l176_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_jordan24 2 B (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) &  ((r2_hidden A (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid (k1_real_1 1) (k1_real_1 3))))) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k1_real_1 1) (k1_real_1 3))) B)) ) ) ) ) ).
tt(l177_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_jordan24 2 B (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) &  ((r2_hidden A (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 (k1_real_1 3))))) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) A (k19_euclid 1 (k1_real_1 3))) B)) ) ) ) ) ).
tt(l178_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden (k19_euclid k6_numbers A) (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 3) 3)) &  ( (~  (A = (k1_real_1 3)) )  &  (~  (A = 3) ) ) ) ) ) ) ).
tt(l17_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_aff_4 A B C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_aff_1 A D E B) & (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_afvect01,ax, ( (~  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (A = B) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) => (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B B A)) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B A A) =>  (A = B) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ( ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B E F) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) C D E F))  => (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B C D)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A C C B)) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ( ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) E A E B) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) E C E D))  =>  ( (A = B)  |  ( (C = D)  | (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A C B D)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ( (~  (A = B) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ( (~  ( (~  (A = C) )  & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B B C)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ( (~  (D = E) )  &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B D E) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A D D B) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A E E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  ( ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B B F) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B C D E) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B D D C) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B E E C)) ) )  => (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A C C F)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ( (~  (A = D) )  &  ( (~  (B = C) )  &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B B D) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A C C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ( (~  (E = F) )  &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B C E F) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B E E C) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B F F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A B D E) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A C F G) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A D D B) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A F F C) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A E E B) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) A G G C) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01))) =>  (~  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B C H I) &  ((r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B H H C) & (r2_analoaf (g1_analoaf (u1_struct_0 o_0_0_afvect01) c4__afvect01) B I I C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  ((k1_algstr_0 k3_algstr_0 A B) = (k1_algstr_0 k3_algstr_0 B A)) ) ) ) ) ).
tt(l17_ami_2,ax, ((k1_afinsq_1 (k6_afinsq_1 k5_numbers k4_numbers)) = 2) ).
tt(l17_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( (A = k11_arytm_3)  =>  ((k1_arytm_1 B A) = B) ) ) ) ) ) ).
tt(l17_arytm_2,ax,(r2_hidden k11_arytm_3 k1_arytm_2)).
tt(l17_arytm_3,ax, (1 = (k1_ordinal1 k1_xboole_0)) ).
tt(l17_asympt_1,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k6_power 2 (k4_power C A))) ) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B (k3_asympt_1 A))) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B (k3_asympt_1 A))) = k6_numbers) ) ) ) ) ) ) ).
tt(l17_borsuk_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (u1_struct_0 k5_topmetr)) => (r2_hidden (k9_real_1 1 A) (u1_struct_0 k5_topmetr))) ) ) ).
tt(l17_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k3_binop_2 A (k5_binop_2 B k7_complex1)))  => (r1_xxreal_0 (k17_complex1 C) (k7_real_1 (k18_complex1 A) (k18_complex1 B)))) ) ) ) ) ) ) ).
tt(l17_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((r1_tarski (k1_rvsum_1 A) (k6_domain_1 k1_numbers k6_numbers)) =>  ((k18_rvsum_1 A) = k6_numbers) ) ) ) ).
tt(l17_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((v1_funct_1 (k1_funct_4 D (k16_funcop_1 C (k2_qc_lang3 A B)))) &  ((v1_funct_2 (k1_funct_4 D (k16_funcop_1 C (k2_qc_lang3 A B))) (k3_qc_lang1 A) (k3_qc_lang1 A)) & (m1_subset_1 (k1_funct_4 D (k16_funcop_1 C (k2_qc_lang3 A B))) (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) (k3_qc_lang1 A))))) ) ) ) ) ) ) ) ) ) ).
tt(l17_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k10_cqc_lang A B B) A)) ) ) ) ).
tt(l17_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k12_csspace k18_csspace A B) = (k11_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_comseq_2 k5_numbers (k2_csspace B))))) ) ) ) ) ).
tt(l17_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A D) = (k11_complex1 (k3_funct_2 k5_numbers k2_numbers B D) (k3_funct_2 k5_numbers k2_numbers C D))) ) ) ) ) ) ) ) ) ) ).
tt(l17_dtconstr,ax,(r1_lang1 k5_dtconstr c3__dtconstr (k3_pre_poly (u1_struct_0 k5_dtconstr) c3__dtconstr))).
tt(l17_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_endalg A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_endalg A B))) =>  ( (D = (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)))  =>  ( ((k6_algstr_0 (k6_endalg A B) C D) = C)  &  ((k6_algstr_0 (k6_endalg A B) D C) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_enumset1 A B C D E) = (k2_xboole_0 (k1_enumset1 A B C) (k2_tarski D E))) ) ) ) ) ) ).
tt(l17_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k7_real_1 (k3_complex2 A B) (k3_complex2 B C)) = (k3_complex2 A C))  |  ((k7_real_1 (k3_complex2 A B) (k3_complex2 B C)) = (k7_real_1 (k3_complex2 A C) (k8_real_1 2 k32_sin_cos))) ) ) ) ) ) ) ) ).
tt(l17_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  ( (D = (k1_euclid_8 A B C))  =>  ((k23_rvsum_1 D D) = (k9_binop_2 (k9_binop_2 (k5_square_1 A) (k5_square_1 B)) (k5_square_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(l17_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_conmetr A) <=> (v2_aff_2 (k3_analmetr A))) ) ) ).
tt(l17_extreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) &  ((v3_funct_2 C (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)))))) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k7_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  ( ( (D = (k1_partfun1 (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 (k1_nat_1 A 1)) k5_numbers k7_numbers C E))  &  ((r2_hidden B (k2_finseq_1 (k1_nat_1 A 1))) &  ( ((k3_finseq_1 E) = (k1_nat_1 A 1))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k2_finseq_1 (k1_nat_1 A 1))) =>  ( ( (~ (r1_xxreal_0 B F))  =>  ((k12_supinf_2 C F) = F) )  &  ( ( (F = B)  =>  ((k12_supinf_2 C F) = (k1_nat_1 A 1)) )  &  ( (~ (r1_xxreal_0 F B))  =>  ((k12_supinf_2 C F) = (k21_binop_2 F 1)) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers E)) |  ((k4_extreal1 D) = (k4_extreal1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_fib_num,ax, ( ((k3_square_1 k1_fib_num) = (k2_xcmplx_0 k1_fib_num 1))  &  ((k3_square_1 k2_fib_num) = (k2_xcmplx_0 k2_fib_num 1)) ) ).
tt(l17_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 D A) &  ((v1_binop_1 D A) &  ((v2_funct_1 B) &  ((v2_funct_1 C) &  ( ((k10_xtuple_0 B) = (k10_xtuple_0 C))  & (r1_xxreal_0 1 (k3_finseq_1 B))) ) ) ) )  =>  ((k1_finsop_1 A B D) = (k1_finsop_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(l17_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F))  &  ( ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k12_gfacirc1 A B C)))  &  ( (H = (k1_funct_1 F D))  &  (I = (k1_funct_1 F E)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp)) = (k10_margrel1 G I))  &  ( ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 E D) k2_twoscomp)) = (k10_margrel1 I H))  &  ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) = (k10_margrel1 H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (~  ((k3_gfacirc2 A B C) = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (? [D:$i] :  ((m3_glib_001 D A) & (r1_glib_001 A B C D)) ) ) ) ) )  => (v1_glib_002 A)) ) ) ).
tt(l17_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((r5_glib_000 A (k5_relat_1 A k2_glib_004)) &  ((k5_glib_003 A) = (k5_glib_003 (k5_relat_1 A k2_glib_004))) ) ) ) ).
tt(l17_goboard5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_finseq_1 (k2_goboard1 A)) = (k4_finseq_1 A)) ) ) ).
tt(l17_goboard6,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (g1_pre_topc (u1_struct_0 (k14_euclid 2)) (k2_pcomps_1 (k14_euclid 2)))) ).
tt(l17_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_8_gobrd11 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(l17_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (B = (k2_xboole_0 C D))  =>  ((r2_hidden A (k9_xtuple_0 B)) <=>  ((r2_hidden A (k9_xtuple_0 C)) | (r2_hidden A (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(l17_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  => (m1_group_6 (k1_grnilp_1 A C B) A C)) ) ) ) ) ) ).
tt(l17_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v6_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A E F H) &  ((r1_collsp A C D H) &  ((r1_collsp A F G I) &  ((r1_collsp A D J I) &  ((r1_collsp A E G K) &  ((r1_collsp A C J K) &  ((r1_collsp A B E C) &  ((r1_collsp A B F D) & (r1_collsp A B G J)) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ((r1_collsp A B E F) |  ((r1_collsp A B E G) |  ((r1_collsp A B F G) |  ( ( (~ (r1_collsp A E F G))  &  (~ (r1_collsp A C D J)) )  | (r1_collsp A I K H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ( (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E C) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E D)) ) ) ) ) ) ) )  => (r3_lattices (k12_normform A) B C)) ) ) ) ) ) ).
tt(l17_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((v4_aff_2 A) &  ((r1_aff_1 A B C D) &  ((r1_aff_1 A B C E) &  ((r1_aff_1 A B G H) & (r2_analoaf A C G D H)) ) ) )  =>  ( (B = C)  |  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C I))  &  ((r1_aff_1 A B I J) &  ((r2_analoaf A C I D J) &  ((r2_analoaf A I E J F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) )  |  ((r1_aff_1 A B C G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_integr11,ax, ((k9_xtuple_0 (k1_fcont_1 2 k6_numbers)) = (k2_subset_1 k1_numbers)) ).
tt(l17_integr15,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 C) &  ( ((k2_seq_2 A) = (k2_seq_2 C))  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 C D))) ) ) ) ) )  =>  ((v2_comseq_2 B) &  ( ((k2_seq_2 A) = (k2_seq_2 B))  &  ((k2_seq_2 C) = (k2_seq_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(l17_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( (E = (k9_real_1 (k3_finseq_1 C) 1))  &  ((r2_hidden A (k2_integra1 B C (k3_finseq_1 C))) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r1_integra1 C D) &  ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 C) (k1_seq_4 A))) ) ) ) )  =>  ((k1_rvsum_1 (k17_finseq_1 k1_numbers (k13_integra1 B C D E) D)) = (k1_rvsum_1 (k17_finseq_1 k1_numbers E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) k1_numbers (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) B) = (k1_funct_1 k4_pscomp_1 B)) ) ) ) ) ).
tt(l17_jgraph_6,ax, ((k17_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = (k1_real_1 1)) ).
tt(l17_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k1_jordan2c 2 A) = k1_xboole_0) )  &  ( (~ (r1_xxreal_0 (k7_pscomp_1 (k1_jordan2c 2 A)) B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k1_jordan2c 2 A)) => (r1_xxreal_0 (k18_euclid C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k2_nat_1 (k13_newton 2 B) 3) A))  & (r1_xxreal_0 (k2_nat_1 (k13_newton 2 (k2_nat_1 B 1)) 3) (k7_nat_d (k4_nat_1 2 A) 2))) ) ) ) ) ) ).
tt(l17_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ( ((k1_funct_1 (k10_glib_001 A B C) E) = (k1_funct_1 B E))  & (r2_hidden E (k1_relset_1 k5_numbers (k10_glib_001 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A (k5_algstr_0 A B C) C) = B)  &  ((k5_algstr_0 A (k3_rlvect_1 A B C) C) = B) ) ) ) ) ) ) ) ).
tt(l17_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k4_struct_0 A)) ) ) )  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l17_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  => (v1_matrixj1 (k10_laplace (k3_finseq_2 A) B) A)) ) ) ) ).
tt(l17_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C D) &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) D D) =>  (~  ( ((k12_matrix_3 D k2_vectsp_1 E) = (k5_struct_0 k2_vectsp_1))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E B B) = (k20_sin_cos A))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E C C) = (k20_sin_cos A))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E B C) = (k17_sin_cos A))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E C B) = (k4_xcmplx_0 (k17_sin_cos A)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 E)) =>  ( ( (F = G)  =>  ( (F = B)  |  ( (F = C)  |  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E F F) = (k5_struct_0 k2_vectsp_1)) ) ) )  &  (~  ( (~  (F = G) )  &  ( (~  ((k4_matrix13 F G) = (k4_matrix13 B C)) )  &  (~  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) E F G) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(l17_measure5,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r1_xxreal_0 k6_numbers (k2_measure5 A))) ) ).
tt(l17_measure7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((v6_xxreal_2 (k8_nat_1 (k9_setfam_1 k1_numbers) c1__measure7 A)) & (m1_subset_1 (k8_nat_1 (k9_setfam_1 k1_numbers) c1__measure7 A) (k1_zfmisc_1 k1_numbers))) ) ) ).
tt(l17_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (E = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc1 A C (k4_mesfunc5 A k7_numbers B G) E)) )  &  ((r1_mesfunc5 A C D F) &  ((v6_supinf_2 F) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G E) => (r1_xxreal_0 (k12_supinf_2 (k10_mesfunc1 A (k4_mesfunc5 A k7_numbers B H)) G) (k12_supinf_2 F G))) ) ) ) )  &  ( ((k19_mesfunc1 A F k1_supinf_1) = k1_xboole_0)  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k12_supinf_2 G H) = (k7_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B H))) ) )  &  ((r1_xxreal_0 (k7_mesfunc5 A C D (k5_mesfunc8 A B)) (k6_rinfsup2 G)) &  ((r1_xxreal_0 (k5_rinfsup2 G) (k7_mesfunc5 A C D (k6_mesfunc8 A B))) &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H E) => (v10_mesfunc5 (k3_mesfunc5 A B H))) ) )  =>  ((v10_mesfunc5 G) &  ((k2_mesfunc5 G) = (k7_mesfunc5 A C D (k7_mesfunc8 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B C) &  ( (! [D:$i] :  ((r2_hidden D (k1_relset_1 A C)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 C D))) )  &  ( (? [D:$i] :  ((r2_hidden D (k1_relset_1 A C)) &  (k1_supinf_2 = (k12_supinf_2 C D)) ) )  &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (~  ((r1_mesfunc3 A B C D E) &  ( ((k12_supinf_2 E 1) = k1_supinf_2)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 2 F) & (r2_hidden F (k4_finseq_1 E)))  =>  ( (~ (r1_xxreal_0 (k12_supinf_2 E F) k1_supinf_2))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_struct_0 (k10_funcsdom (k2_finseq_1 A))) = (k4_struct_0 (k15_euclid A))) ) ) ).
tt(l17_nfcont_2,ax, ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) )  &  (B = C) ) )  &  (~  ( (~  (B = C) )  &  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~ (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers))  &  (B = C) ) )  &  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers)) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k5_algstr_0 A C B))) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A D C))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A C D))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k1_normsp_0 A B))) ) ) )  =>  (B = (k4_struct_0 A)) ) ) ) ) )  &  (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_numbers,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (~  ( ((k9_ordinal3 A A) = (k9_ordinal3 2 B))  &  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  (~  (A = (k9_ordinal3 2 C)) ) ) ) ) ) ) ) ) ) ).
tt(l17_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 2 F E))  =>  ( (D = (k1_fdiff_1 (k1_pdiff_2 3 2 F E) B))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J H) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 F E) M) (k1_seq_1 (k1_pdiff_2 3 2 F E) H)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M H)) (k1_seq_1 L (k9_real_1 M H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_nat_d (k3_nat_1 A (k13_newton 2 (k1_nat_1 B 1))) 2) = (k3_xcmplx_0 A (k2_newton 2 B))) ) ) ) ) ).
tt(l17_polyeq_1,ax, (~ (v1_abian 3)) ).
tt(l17_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k3_finseq_2 k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k3_finseq_2 k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k3_finseq_2 k5_numbers)) =>  ( ( ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k1_nat_1 A 2) = (k4_nat_1 2 E))  =>  (C = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers B E)))) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k1_nat_1 A 2) = (k2_nat_1 (k4_nat_1 2 E) 1))  =>  (C = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers B E) (k7_partfun1 k5_numbers B (k2_nat_1 E 1)))))) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k1_nat_1 A 2) = (k4_nat_1 2 E))  =>  (D = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers B E)))) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k1_nat_1 A 2) = (k2_nat_1 (k4_nat_1 2 E) 1))  =>  (D = (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers B E) (k7_partfun1 k5_numbers B (k2_nat_1 E 1)))))) ) ) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(l17_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r2_funct_2 k5_numbers (k1_zfmisc_1 A) (k2_prob_1 A (k12_funct_7 (k1_zfmisc_1 A) B C)) (k12_funct_7 (k1_zfmisc_1 A) (k3_subset_1 A B) (k3_subset_1 A C)))) ) ) ) ) ).
tt(l17_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C) (k7_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l17_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k4_prvect_2 A))) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 (k4_prvect_2 A))) =>  ( ((k8_prvect_1 (k4_prvect_2 A) (k12_prvect_1 (k4_card_3 (k4_prvect_2 A)) (k13_prvect_1 (k4_prvect_2 A) (k6_prvect_2 A)) B C) D) = (k1_binop_1 (u1_algstr_0 (k5_prvect_2 A D)) (k8_prvect_1 (k4_prvect_2 A) B D) (k8_prvect_1 (k4_prvect_2 A) C D)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_2 A D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_prvect_2 A D))) =>  ( ( (E = (k8_prvect_1 (k4_prvect_2 A) B D))  &  (F = (k8_prvect_1 (k4_prvect_2 A) C D)) )  =>  ((k8_prvect_1 (k4_prvect_2 A) (k12_prvect_1 (k4_card_3 (k4_prvect_2 A)) (k13_prvect_1 (k4_prvect_2 A) (k6_prvect_2 A)) B C) D) = (k3_rlvect_1 (k5_prvect_2 A D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_qmax_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (k2_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (! [B:$i] :  ((m1_subset_1 B (k2_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) => (r2_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) A C) (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) B C))) )  =>  (A = B) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (! [B:$i] :  ((m1_subset_1 B (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k2_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) => (r2_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) C A) (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) C B))) )  =>  (A = B) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (! [B:$i] :  ((m1_subset_1 B (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 C 1) &  (! [D:$i] :  ((m1_subset_1 D (k3_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (~  (! [E:$i] :  ((m1_subset_1 E (k2_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1))) =>  (! [F:$i] :  ((m1_prob_1 F k1_numbers k12_prob_1) =>  ((k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) E D) F) = (k7_real_1 (k8_real_1 C (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) E A) F)) (k8_real_1 (k9_real_1 1 C) (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 (g1_qmax_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers) c5__qmax_1) E B) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_random_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 A) = (k2_finseq_1 1))  =>  (A = (k9_finseq_1 (k1_funct_1 A 1))) ) ) ) ).
tt(l17_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 1 k6_numbers k6_numbers)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers))) ).
tt(l17_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (v7_valued_0 (k3_rinfsup2 A))) ) ).
tt(l17_scmfsa_1,ax, ((k1_funct_1 k4_scmfsa_1 k5_numbers) = k6_numbers) ).
tt(l17_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) => (r1_xxreal_0 (k2_compos_0 k2_scmfsa_i A) 12)) ) ).
tt(l17_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (k2_scmp_gcd = (k1_scmp_gcd (k2_nat_1 B A))) ) ) ) ) ) ) ).
tt(l17_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( (~  ( (~  ((k4_xtuple_0 B) = 1) )  &  ( (~  ((k4_xtuple_0 B) = 2) )  &  ( (~  ((k4_xtuple_0 B) = 3) )  &  (~  ((k4_xtuple_0 B) = 4) ) ) ) ) )  =>  ((k5_xtuple_0 B) = k1_xboole_0) ) ) ) ) ) ).
tt(l17_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ( ((k1_funct_1 B (k1_scmp_gcd 4)) = D)  &  ((r1_xxreal_0 8 C) &  ((r1_xxreal_0 8 D) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) ) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 3)) = (k1_funct_1 B (k1_scmp_gcd 3)))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 E) =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) )  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd D)) (k1_funct_1 B (k1_scmp_gcd C))))  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 5)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 5)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 4)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) 1))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 7)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 5)) 1)) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd D)) (k1_funct_1 B (k1_scmp_gcd C))) =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 5)) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 4)) = (k1_funct_1 B (k1_scmp_gcd 4)))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))) B A) (k1_scmp_gcd 7)) = (k1_funct_1 B (k1_scmp_gcd 5))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  =>  ((k6_xcmplx_0 (k13_complex1 1 A) 1) = (k13_complex1 (k2_xcmplx_0 B C) A)) ) ) ) ) ) ) ) ).
tt(l17_sincos10,ax, ((r2_hidden k6_numbers (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) & (r2_hidden (k10_real_1 k32_sin_cos 4) (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l17_topalg_2,ax, (! [A:$i] :  ((m1_pre_topc A k3_topmetr) =>  ( (A = k3_topmetr)  => (v2_topalg_2 A)) ) ) ).
tt(l17_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v5_waybel23 A) &  ((v3_topdim_1 A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v5_waybel23 B) &  ((v3_topdim_1 B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) ) ) )  =>  ( (~  ((v2_struct_0 A) & (v2_struct_0 B)) )  =>  ((v3_topdim_1 (k2_borsuk_1 A B)) & (r1_xxreal_0 (k4_topdim_1 (k2_borsuk_1 A B)) (k1_xxreal_3 (k4_topdim_1 A) (k4_topdim_1 B)))) ) ) ) ) ) ).
tt(l17_topgen_3,ax, ((u1_pre_topc k2_topgen_3) = (k1_cantor_1 k1_numbers c1__topgen_3)) ).
tt(l17_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (v3_topgen_4 B A)) ) ) ) ).
tt(l17_topreal2,ax, (~ (r2_hidden (k19_euclid 1 k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)))) ).
tt(l17_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B E C F) & (r2_analoaf A E F D G)) ) )  =>  ( (B = C)  |  ((r1_aff_1 A B C E) |  ( (~  (E = F) )  & (r1_aff_1 A B C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_uniroots,ax,(v8_struct_0 k18_mod_2)).
tt(l17_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (m1_vectsp_4 C A (k2_vectsp_4 A B))) ) ) ) ) ) ).
tt(l17_xreal_0,ax, (c3__xreal_0 = 1) ).
tt(l17_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers C))  => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l17_xxreal_3,ax, ((k2_xxreal_3 k1_xxreal_0) = k2_xxreal_0) ).
tt(l17_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_yellow11 A) =>  ((v2_waybel_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  &  ( ((k12_lattice3 A B C) = B)  &  ( ((k12_lattice3 A B D) = B)  &  ( ((k12_lattice3 A B E) = B)  &  ( ((k12_lattice3 A C F) = C)  &  ( ((k12_lattice3 A D F) = D)  &  ( ((k12_lattice3 A E F) = E)  &  ( ((k12_lattice3 A C D) = B)  &  ( ((k12_lattice3 A C E) = B)  &  ( ((k12_lattice3 A D E) = B)  &  ( ((k13_lattice3 A C D) = F)  &  ( ((k13_lattice3 A C E) = F)  &  ((k13_lattice3 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l17_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ( ((k3_funct_2 k5_numbers k1_zf_lang k2_zf_fund1 (k3_zf_fund1 C)) = C)  &  ( ((k1_funct_1 (k2_funct_1 k2_zf_fund1) C) = (k3_zf_fund1 C))  &  ((k3_funct_2 k5_numbers A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 B) (k3_zf_fund1 C)) = (k3_funct_2 k1_zf_lang A B C)) ) ) ) ) ) ) ) ) ).
tt(l183_group_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B A))  <=> (r1_xxreal_0 A (k6_xcmplx_0 B 1))) ) ) ) ) ).
tt(l184_group_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 (k1_funct_1 B A))) D))  &  ( ((k3_finseq_1 C) = (k6_xcmplx_0 A 1))  &  ((k3_finseq_1 D) = (k6_xcmplx_0 (k3_finseq_1 B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l185_group_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((r2_hidden A (k4_finseq_1 B)) &  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 E)) D))  &  ((k3_finseq_1 C) = (k6_xcmplx_0 A 1)) ) )  =>  ((k2_finseq_3 A B) = (k7_finseq_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l185_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) =>  ((k17_euclid (k19_euclid k6_numbers 3)) = (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) ) ) ) ).
tt(l186_group_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ((k2_finseq_3 A (k7_finseq_1 B C)) = (k7_finseq_1 (k2_finseq_3 A B) C)) )  &  ((r1_xxreal_0 1 A) =>  ((k2_finseq_3 (k2_nat_1 (k3_finseq_1 B) A) (k7_finseq_1 B C)) = (k7_finseq_1 B (k2_finseq_3 A C))) ) ) ) ) ) ) ) ) ).
tt(l186_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) =>  ((k17_euclid (k19_euclid k6_numbers (k1_real_1 3))) = (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) ) ) ) ).
tt(l186_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v4_relat_1 k1_xboole_0 A) & (v5_relat_1 k1_xboole_0 B)) ) ) ).
tt(l187_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  (B = (k2_finseq_3 (k1_nat_1 D 1) (k5_finseq_5 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(l18_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A D (k5_struct_0 A)) = D) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (D = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A D E) = (k5_struct_0 A)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A D E) F) = (k6_algstr_0 A D (k6_algstr_0 A E F))) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A D (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) )  =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(l18_ami_2,ax,(r1_tarski (k10_xtuple_0 k3_ami_2) (k9_xtuple_0 k4_ami_2))).
tt(l18_amistd_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 (k4_amistd_1 B))) =>  ( ( (C = A)  &  ((k2_compos_0 (u1_compos_1 (k4_amistd_1 B)) D) = 1) )  =>  ((k1_amistd_1 B (k4_amistd_1 B) C D) = (k6_domain_1 k5_numbers (k1_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ).
tt(l18_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C (k4_amistd_1 A))) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A (k4_amistd_1 A))) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v4_extpro_1 D A (k4_amistd_1 A) C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 E (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 F (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  ( ((r1_tarski D E) & (r1_tarski (k9_memstr_0 A (k4_amistd_1 A) D B) F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 (k4_amistd_1 A))) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 (k4_amistd_1 A))) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ((r1_tarski C G) & (r1_tarski (k6_compos_1 (k4_amistd_1 A) C B) H))  =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 A (k4_amistd_1 A) (k5_extpro_1 A (k4_amistd_1 A) G E I)) B) = (k5_memstr_0 A (k4_amistd_1 A) (k5_extpro_1 A (k4_amistd_1 A) H F I)))  &  ((k5_compos_0 (u1_compos_1 (k4_amistd_1 A)) (k3_extpro_1 A (k4_amistd_1 A) G (k5_extpro_1 A (k4_amistd_1 A) G E I)) B) = (k3_extpro_1 A (k4_amistd_1 A) H (k5_extpro_1 A (k4_amistd_1 A) H F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((k1_arytm_1 (k7_arytm_2 A B) B) = A) ) ) ) ) ).
tt(l18_arytm_2,ax, ((k8_subset_1 (k1_zfmisc_1 k5_arytm_3) k1_arytm_2 k5_arytm_3) = (k1_tarski k11_arytm_3)) ).
tt(l18_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers k2_asympt_1 (k3_asympt_1 A))) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers k2_asympt_1 (k3_asympt_1 A))) = k6_numbers) ) ) ) ) ).
tt(l18_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_bcialg_6 A (k23_binop_2 C D) B) = (k1_bcialg_1 A (k3_bcialg_6 A D B) (k2_bcialg_1 A (k3_bcialg_6 A C B)))) ) ) ) ) ) ) ) ) ).
tt(l18_brouwer,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (v1_pscomp_1 (k8_funcop_1 k1_numbers (u1_struct_0 A) B) A)) ) ) ) ).
tt(l18_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( (B = C)  =>  ((k1_normsp_0 (k5_c0sp2 A) B) = (k1_normsp_0 (k11_c0sp1 (u1_struct_0 A)) C)) ) ) ) ) ) ) ) ).
tt(l18_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 (k18_complex1 A) (k17_complex1 (k3_binop_2 A (k5_binop_2 B k7_complex1)))) & (r1_xxreal_0 (k18_complex1 B) (k17_complex1 (k3_binop_2 A (k5_binop_2 B k7_complex1))))) ) ) ) ) ).
tt(l18_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (k5_arytm_0 B C))  =>  ( (C = k6_numbers)  &  (A = B) ) ) ) ) ) ) ) ) ).
tt(l18_comseq_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers c1__comseq_2 A) = k5_complex1) ) ) ).
tt(l18_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l18_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_qc_lang1 A) (k9_qc_lang1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k9_qc_lang1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_qc_lang1 A) (k9_qc_lang1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k9_qc_lang1 A))))) )  =>  ( ( (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C (k5_cqc_lang A)) = (k5_cqc_lang A))  &  ( ((v2_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C E) = (k10_qc_lang1 A (k16_qc_lang1 A E) (k1_cqc_lang A (k17_qc_lang1 A E) (k2_cqc_lang A (k3_qc_lang3 A k6_numbers) B)))) )  &  ( ((v3_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C E) = (k13_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C (k18_qc_lang1 A E)))) )  &  ( ((v4_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C E) = (k14_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C (k19_qc_lang1 A E)) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C (k20_qc_lang1 A E)))) )  &  ((v5_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C E) = (k15_funcop_1 (k9_qc_lang1 A) (k21_qc_lang1 A E) B E (k15_qc_lang1 A (k21_qc_lang1 A E) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C (k22_qc_lang1 A E))))) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D (k5_cqc_lang A)) = (k5_cqc_lang A))  &  ( ((v2_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D E) = (k10_qc_lang1 A (k16_qc_lang1 A E) (k1_cqc_lang A (k17_qc_lang1 A E) (k2_cqc_lang A (k3_qc_lang3 A k6_numbers) B)))) )  &  ( ((v3_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D E) = (k13_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D (k18_qc_lang1 A E)))) )  &  ( ((v4_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D E) = (k14_qc_lang1 A (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D (k19_qc_lang1 A E)) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D (k20_qc_lang1 A E)))) )  &  ((v5_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D E) = (k15_funcop_1 (k9_qc_lang1 A) (k21_qc_lang1 A E) B E (k15_qc_lang1 A (k21_qc_lang1 A E) (k3_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) D (k22_qc_lang1 A E))))) ) ) ) ) ) ) ) )  => (r2_funct_2 (k9_qc_lang1 A) (k9_qc_lang1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(l18_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A C B) A))  <=> (v2_cqc_the1 (k10_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(l18_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers A) (k55_valued_1 k5_numbers k2_numbers (k2_comseq_2 k5_numbers A)))) ) ).
tt(l18_dtconstr,ax, ((k1_lang1 k5_dtconstr) = a_0_10_dtconstr) ).
tt(l18_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_ami_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_ami_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_ami_3)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_compos_1 k1_ami_3)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_compos_1 k1_ami_3)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_compos_1 k1_ami_3)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_compos_1 k1_ami_3)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_compos_1 k1_ami_3)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ((r1_tarski (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)) (k5_afinsq_1 G)) (k5_afinsq_1 H)) (k5_afinsq_1 I)) (k5_afinsq_1 J)) A) =>  ( ((k3_compos_1 k1_ami_3 A k6_numbers) = B)  &  ( ((k3_compos_1 k1_ami_3 A 1) = C)  &  ( ((k3_compos_1 k1_ami_3 A 2) = D)  &  ( ((k3_compos_1 k1_ami_3 A 3) = E)  &  ( ((k3_compos_1 k1_ami_3 A 4) = F)  &  ( ((k3_compos_1 k1_ami_3 A 5) = G)  &  ( ((k3_compos_1 k1_ami_3 A 6) = H)  &  ( ((k3_compos_1 k1_ami_3 A 7) = I)  &  ((k3_compos_1 k1_ami_3 A 8) = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_fib_num,ax, (~ (r1_xxreal_0 (k7_square_1 5) 2)) ).
tt(l18_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ( ((k3_finseq_1 B) = k6_numbers)  &  ((v1_setwiseo D A) &  ((v2_funct_1 B) &  ((v2_funct_1 C) &  ((k10_xtuple_0 B) = (k10_xtuple_0 C)) ) ) ) )  =>  ((k1_finsop_1 A B D) = (k1_finsop_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(l18_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k12_gfacirc1 A B C)))  &  (H = (k1_funct_1 F E)) )  =>  ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp)) = (k2_binarith G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H C))  =>  ((k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C (k2_fuzzy_1 (k2_zfmisc_1 A B) D E) F G H))) = (k2_square_1 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D F G H))) (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C E F G H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analoaf A B C D E) => (r1_geomtrap A B C (k1_geomtrap A B E) (k1_geomtrap A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) <=>  ((r2_glib_000 A C D B) | (r2_glib_000 A D C B)) ) ) ) ) ) ) ).
tt(l18_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  ((k1_glib_002 A B) = (k6_glib_000 A)) ) )  => (v1_glib_002 A)) ) ) ).
tt(l18_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((k1_relset_1 k2_glib_004 (k5_relat_1 A k2_glib_004)) = k2_glib_004) ) ) ).
tt(l18_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A))) => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k2_groeb_3 A B C D)) (k2_polynom1 (k15_pre_poly A) B C))) ) ) ) ) ) ) ).
tt(l18_group_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((m2_subset_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1) k1_numbers k5_numbers) &  ((r1_xxreal_0 1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1)) & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1) (k3_finseq_1 A))) ) ) ) ) ) ) ).
tt(l18_group_9,ax,(v5_group_9 (k13_matrix_2 2))).
tt(l18_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v6_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ((r1_collsp A D F J) &  ((r1_collsp A C E J) &  ((r1_collsp A F H I) &  ((r1_collsp A E G I) &  ((r1_collsp A D H K) &  ((r1_collsp A C G K) &  ((r1_collsp A B D C) &  ((r1_collsp A B F E) &  ((r1_collsp A B H G) &  ((r1_collsp A B F L) & (r1_collsp A D H L)) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = C)  |  ( (B = E)  |  ( (F = E)  |  ( (B = G)  |  ( (H = G)  |  ((r1_collsp A B D F) |  ((r1_collsp A B D H) |  ((r1_collsp A B F H) |  ((r1_collsp A B I J) |  ((r1_collsp A I J L) | (r1_collsp A I K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) & (r1_aff_1 A B C G))  =>  ( (B = C)  |  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C I))  &  ((r1_aff_1 A B I J) &  ((r2_analoaf A C I E J) &  ((r2_analoaf A I D J F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) )  |  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C I))  &  ((r1_aff_1 A B I J) &  ((r2_analoaf A C I E J) &  ((r2_analoaf A I G J H) & (r1_aff_1 A B C H)) ) ) ) ) ) ) ) )  | (r2_analoaf A D G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 A B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k3_real_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l18_integr11,ax, ((k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4)))) = k1_numbers) ).
tt(l18_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) & (r1_tarski A (k1_relset_1 k1_numbers B)))  => (r1_integra5 A B)) ) ) ) ) ).
tt(l18_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 D)) &  ((r1_integra5 (k3_integra5 A B) D) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B))) & (r2_hidden C (k3_integra5 A B))) ) ) )  =>  ( (B = C)  |  ( ((k4_integra5 A B D) = (k7_real_1 (k4_integra5 A C D) (k4_integra5 C B D)))  &  ((r1_integra5 (k3_integra5 A C) D) & (r1_integra5 (k3_integra5 C B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_jgraph_2,ax, ((k4_struct_0 (k15_euclid 2)) = (k16_euclid 2)) ).
tt(l18_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A)) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (k1_pre_topc (k15_euclid 2) A) k3_topmetr) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) ) ) ) ).
tt(l18_jgraph_6,ax, ((k18_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = k6_numbers) ).
tt(l18_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k1_jordan2c 2 A) = k1_xboole_0) )  &  ( (~ (r1_xxreal_0 B (k9_pscomp_1 (k1_jordan2c 2 A))))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k1_jordan2c 2 A)) => (r1_xxreal_0 B (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 2 A) =>  ((k9_real_1 (k2_nat_1 (k7_nat_d (k4_nat_1 2 A) 2) 1) 2) = (k9_real_1 (k4_nat_1 2 A) 3)) ) ) ) ).
tt(l18_jordan5a,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r2_hidden C (u1_struct_0 (k4_topmetr A B))) <=>  ((r1_xxreal_0 A C) & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ).
tt(l18_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A C B) =>  ((k1_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A C) (k3_lattice7 A))) = C) ) ) )  =>  ((k1_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k3_lattice7 A))) = B) ) ) ) ) ) ).
tt(l18_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  ( (~ (v2_struct_0 (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)))  &  ((v10_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)) & (l3_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B))) ) ) ) ) ) ).
tt(l18_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (~  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ((k8_matrix13 C D) = A)  &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) (k7_nat_d B A) B) =>  (~  ((k8_matrix13 C (k8_matrlin (u1_struct_0 C) A (k7_nat_d B A) B D E)) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_measure5,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k2_measure5 A) (k2_measure5 B))) ) ) ) ) ).
tt(l18_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) A H)))  &  ((r1_euclid_6 A D F) & (r1_euclid_6 B E F)) ) )  =>  ((r1_euclid_6 A B C) |  ( (H = 1)  |  ( (~  ((k9_binop_2 (k10_binop_2 1 H) (k11_binop_2 G H)) = k6_numbers) )  &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) D I)))  &  (I = (k12_binop_2 (k10_binop_2 1 H) (k9_binop_2 (k10_binop_2 1 H) (k11_binop_2 G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_metrizts,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((k2_card_2 k4_ordinal1 A) = A) ) ) ).
tt(l18_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k6_msualg_1 A))) => (m5_margrel1 (k5_msualg_1 (k6_msualg_1 A) C (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B))) (u1_struct_0 B) (k1_unialg_2 B))) ) ) ) ) ) ) ).
tt(l18_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  & (v2_nagata_1 B A)) ) ) ) ).
tt(l18_nfcont_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 C (k18_complex1 (k3_xcmplx_0 B (k3_power A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k4_numbers D E))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 E 1)) = (k6_int_1 (k8_nat_1 k4_numbers C E) (k8_nat_1 k4_numbers D E))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (a_1_1_ntalgo_1 D)))  & (m1_subset_1 (a_1_1_ntalgo_1 D) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ) ) ) ) ) ).
tt(l18_numbers,ax,(r2_hidden 1 k4_ordinal1)).
tt(l18_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ((m1_orders_3 B A) => (r2_hidden (u1_struct_0 B) (k2_orders_3 A))) ) ) ) ).
tt(l18_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v6_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l18_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (D = C) )  &  ((r1_analoaf A B C C D) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( ((k5_algstr_0 A C B) = (k1_rlvect_1 A (k5_algstr_0 A D C) E))  &  (~ (r1_xxreal_0 E k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 3 F E))  =>  ( (D = (k1_fdiff_1 (k1_pdiff_2 3 3 F E) C))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J I) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 F E) M) (k1_seq_1 (k1_pdiff_2 3 3 F E) I)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M I)) (k1_seq_1 L (k9_real_1 M I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_nat_d (k1_newton C A) (k1_newton C B))) ) ) ) ) ) ) ).
tt(l18_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) ) ).
tt(l18_pre_ff,ax,(m2_finseq_2 (k12_finseq_1 k5_numbers 1) k5_numbers (k3_finseq_2 k5_numbers))).
tt(l18_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_prob_4 A (k9_setfam_1 A) (k2_prob_3 A B) C) = (k1_prob_4 A (k9_setfam_1 A) B C)) ) ) ) ) ) ) ).
tt(l18_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k4_prvect_2 A))) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 (k4_prvect_2 A))) =>  ( ((k8_prvect_1 (k4_prvect_2 A) (k2_binop_1 k1_numbers (k4_card_3 (k4_prvect_2 A)) (k4_card_3 (k4_prvect_2 A)) (k2_prvect_2 (k4_prvect_2 A) k1_numbers (k9_prvect_2 A)) B C) D) = (k1_binop_1 (u1_rlvect_1 (k5_prvect_2 A D)) B (k8_prvect_1 (k4_prvect_2 A) C D)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_2 A D))) =>  ( (E = (k8_prvect_1 (k4_prvect_2 A) C D))  =>  ((k8_prvect_1 (k4_prvect_2 A) (k2_binop_1 k1_numbers (k4_card_3 (k4_prvect_2 A)) (k4_card_3 (k4_prvect_2 A)) (k2_prvect_2 (k4_prvect_2 A) k1_numbers (k9_prvect_2 A)) B C) D) = (k1_rlvect_1 (k5_prvect_2 A D) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) => (m2_finseq_1 (k9_finseq_1 (k4_tarski B C)) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ) ) ) ) ).
tt(l18_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_random_1 A) k7_numbers) &  ((v10_valued_0 B) &  ((v6_supinf_2 B) &  ((v4_measure1 B A (k1_random_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_random_1 A) k7_numbers)))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 B A)))  &  (! [D:$i] :  ((m2_finseq_1 D k7_numbers) =>  (~  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k12_supinf_2 D E) = (k1_extreal1 (k1_measure6 (k1_seq_1 C (k1_funct_1 (k1_uproots A) E))) (k12_supinf_2 B (k1_tarski (k1_funct_1 (k1_uproots A) E))))) ) ) )  &  ((k1_mesfunc6 A (k1_random_1 A) B C) = (k4_extreal1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v2_struct_0 (k4_real_ns1 A)))  &  ((v13_algstr_0 (k4_real_ns1 A)) &  ((v2_rlvect_1 (k4_real_ns1 A)) &  ((v3_rlvect_1 (k4_real_ns1 A)) &  ((v4_rlvect_1 (k4_real_ns1 A)) &  ((v5_rlvect_1 (k4_real_ns1 A)) &  ((v6_rlvect_1 (k4_real_ns1 A)) &  ((v7_rlvect_1 (k4_real_ns1 A)) &  ((v8_rlvect_1 (k4_real_ns1 A)) &  ((v3_normsp_0 (k4_real_ns1 A)) &  ((v4_normsp_0 (k4_real_ns1 A)) &  ((v2_normsp_1 (k4_real_ns1 A)) &  ((v3_lopban_1 (k4_real_ns1 A)) & (l1_normsp_1 (k4_real_ns1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 k6_numbers 1 k6_numbers)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers 1))) ).
tt(l18_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_classes1 A B) => (r1_xxreal_0 (k3_rfinseq2 A) (k3_rfinseq2 B))) ) ) ) ) ).
tt(l18_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_ringcat1 C A B) =>  (~  ((r1_ringcat1 A B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ( (C = (g1_ringcat1 A B D))  & (v1_ringcat1 D A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( ( ((k2_compos_0 k2_scmfsa_i A) = 9)  |  ((k2_compos_0 k2_scmfsa_i A) = 10) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l18_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( (~  ( (~  ((k2_compos_0 k3_scm_inst A) = 1) )  &  ( (~  ((k2_compos_0 k3_scm_inst A) = 2) )  &  ( (~  ((k2_compos_0 k3_scm_inst A) = 3) )  &  ( (~  ((k2_compos_0 k3_scm_inst A) = 4) )  &  (~  ((k2_compos_0 k3_scm_inst A) = 5) ) ) ) ) ) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l18_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  (k3_scmp_gcd = (k1_scmp_gcd (k2_nat_1 B A))) ) ) ) ) ) ) ).
tt(l18_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( ((k4_xtuple_0 B) = 5)  =>  ((k5_xtuple_0 B) = k1_xboole_0) ) ) ) ) ) ).
tt(l18_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k4_scpinvar A B C))) = (k2_nat_1 (k5_card_1 C) 4)) ) ) ) ) ) ) ).
tt(l18_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 4)) = (k2_xcmplx_0 C (k1_funct_1 B (k1_scmp_gcd 5))))  &  ((r1_xxreal_0 8 C) &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = D)  & (r1_xxreal_0 8 D)) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 5)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 5)) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 3)) = (k1_funct_1 B (k1_scmp_gcd 3)))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 E) =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) )  &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ( (E = (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 7)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd 4)) = (k2_nat_1 C E))  &  ((r1_xxreal_0 E (k1_funct_1 B (k1_scmp_gcd 5))) &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 F (k2_nat_1 C E)))  &  ((r1_xxreal_0 F (k1_funct_1 B (k1_scmp_gcd 4))) & (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd F)) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd D)))) ) ) ) )  &  ( (E = k6_numbers)  | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd (k2_nat_1 C E))) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) (k1_scmp_gcd D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k9_complex1 (k9_complex1 (k13_complex1 (k3_xcmplx_0 2 (k6_square_1 (k3_xcmplx_0 A B))) C) (k13_complex1 (k3_xcmplx_0 2 (k6_square_1 (k3_xcmplx_0 C B))) A)) (k13_complex1 (k3_xcmplx_0 2 (k6_square_1 (k3_xcmplx_0 C A))) B)) = 8) ) ) ) ) ) ) ).
tt(l18_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_struct_0 (k15_euclid A)) = (k2_struct_0 (k14_euclid A))) ) ) ).
tt(l18_sincos10,ax, ((r2_hidden (k8_real_1 (k10_real_1 3 4) k32_sin_cos) (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) & (r2_hidden k32_sin_cos (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) ).
tt(l18_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (v1_zfmisc_1 A))  &  ((v1_sppol_1 A) & (v2_sppol_1 A)) ) ) ) ) ).
tt(l18_substut1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) &  ((k6_subset_1 B A) = k1_xboole_0) ) ) ) ) ).
tt(l18_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_taxonom2 B A) =>  ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ( ((v4_taxonom2 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski C B) &  (! [D:$i] :  ( ((v4_taxonom2 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski D B) & (r1_tarski (k5_setfam_1 A C) (k5_setfam_1 A D)))  =>  (C = D) ) ) ) )  =>  ((k5_setfam_1 A C) = A) ) ) ) ) ) ) ) ).
tt(l18_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v13_struct_0 (k1_tex_2 A B) 1)) ) ) ) ).
tt(l18_topgen_3,ax, (c1__topgen_3 = a_0_0_topgen_3) ).
tt(l18_topreal2,ax, (~ (r2_hidden (k19_euclid 1 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)))) ).
tt(l18_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v11_aff_2 A) &  ((r1_aff_1 A B C D) &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B C G H) &  ((r2_analoaf A B E C F) &  ((r2_analoaf A B G C H) &  ((r2_analoaf A E F D I) &  ((r2_analoaf A E D F I) &  ((r2_analoaf A G H J I) & (r2_analoaf A G J H I)) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ((r1_aff_1 A B C E) |  ((r1_aff_1 A B C G) |  (D = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l18_uniform1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden A (k1_rcomp_1 B C)) <=>  ((r1_xxreal_0 B A) & (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(l18_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_xxreal_2 (k1_integra2 A B)) =>  ((r1_xxreal_0 B k6_numbers) | (v4_xxreal_2 A)) ) ) ) ) ) ).
tt(l18_xreal_0,ax, ( (c5__xreal_0 = (k4_xcmplx_0 1))  &  ((k1_arytm_0 c3__xreal_0 c5__xreal_0) = k6_numbers) ) ).
tt(l18_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k3_xcmplx_0 C A) (k3_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(l18_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r2_hidden A k1_numbers) =>  ((k2_xxreal_3 (k1_xxreal_3 A k1_xxreal_0)) = (k1_xxreal_3 (k2_xxreal_3 k1_xxreal_0) (k2_xxreal_3 A))) ) ) ) ).
tt(l18_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) )  => (r2_hidden C (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(l18_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_zf_lang)))  =>  ((r2_hidden A (k4_zf_fund1 B)) <=>  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  ((r2_hidden C B) &  (A = (k3_zf_fund1 C)) ) ) ) ) ) ) ) ).
tt(l18_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_xboole_0 (k1_tarski A) B) & (r2_hidden A B)) ) ) ) ).
tt(l194_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden E (k2_finseq_1 F)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) 1))  &  ( (F = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 C) 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) 1))  &  ( (~  (E = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 C) 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) 1)) )  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ( (E = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 G 1) (k6_xcmplx_0 (k3_finseq_1 D) 1)) H))  &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k6_xcmplx_0 (k3_finseq_1 C) 1)) &  ((r1_xxreal_0 1 H) & (r1_xxreal_0 H (k6_xcmplx_0 (k3_finseq_1 D) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l195_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v8_group_9 G A B) & (m2_finseq_1 G (k6_group_9 A B)))  =>  (! [H:$i] :  ( ((v8_group_9 H A B) & (m2_finseq_1 H (k6_group_9 A B)))  =>  ( ( ((k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 C 1) (k6_xcmplx_0 (k3_finseq_1 H) 1)) D) = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 E 1) (k6_xcmplx_0 (k3_finseq_1 H) 1)) F))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k6_xcmplx_0 (k3_finseq_1 H) 1)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k6_xcmplx_0 (k3_finseq_1 H) 1))) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 H) 1) |  ( (D = F)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l196_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v8_group_9 F A B) & (m2_finseq_1 F (k6_group_9 A B)))  =>  (! [G:$i] :  ( ((v8_group_9 G A B) & (m2_finseq_1 G (k6_group_9 A B)))  =>  ( ( (C = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 D 1) (k6_xcmplx_0 (k3_finseq_1 G) 1)) E))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k6_xcmplx_0 (k3_finseq_1 F) 1)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k6_xcmplx_0 (k3_finseq_1 G) 1))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 G) 1) |  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 F) 1) (k6_xcmplx_0 (k3_finseq_1 G) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A C (k5_struct_0 A)) = C) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (C = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A C D) = (k5_struct_0 A)) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A C D) E) = (k6_algstr_0 A C (k6_algstr_0 A D E))) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A C (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) )  =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  ((k6_algstr_0 A (k5_struct_0 A) B) = (k6_algstr_0 A B (k5_struct_0 A))) ) ) ) ) ) ) ).
tt(l19_ami_2,ax, ((k9_xtuple_0 (k3_relat_1 k3_ami_2 k4_ami_2)) = k1_ami_2) ).
tt(l19_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) => (v1_xboole_0 (k2_amistd_1 A (k4_amistd_1 A) B))) ) ) ) ).
tt(l19_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_rlvect_1 A B D) = C)  =>  ( (D = k6_numbers)  | (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l19_arytm_0,ax,(m1_subset_1 k6_numbers k1_numbers)).
tt(l19_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k1_arytm_1 B (k1_arytm_1 B A)) = A) ) ) ) ) ) ).
tt(l19_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ( ((k3_arytm_2 A) = k11_arytm_3)  <=>  (A = k11_arytm_3) ) ) ) ).
tt(l19_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_bcialg_6 A D (k3_bcialg_6 A C B)) = (k3_bcialg_6 A (k24_binop_2 C D) B)) ) ) ) ) ) ) ) ) ).
tt(l19_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k3_borsuk_1 B A (k2_struct_0 B) D))  =>  ((g1_pre_topc (u1_struct_0 (k2_borsuk_1 B (k1_pre_topc A D))) (u1_pre_topc (k2_borsuk_1 B (k1_pre_topc A D)))) = (g1_pre_topc (u1_struct_0 (k1_pre_topc (k2_borsuk_1 B A) C)) (u1_pre_topc (k1_pre_topc (k2_borsuk_1 B A) C)))) ) ) ) ) ) ) ) ) ) ).
tt(l19_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) D) (k2_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) D)) (k2_bvfunc_1 A (k2_bvfunc_1 A B C) (k1_bvfunc_1 A D))) (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D))))) ) ) ) ) ) ) ) ).
tt(l19_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_algstr_0 (k5_c0sp2 A) B C) = (k3_rlvect_1 (k11_c0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_comseq_2 (k55_valued_1 A k2_numbers B)) <=> (v1_comseq_2 B)) ) ) ) ) ).
tt(l19_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 2))) =>  ( (C = (k10_finseq_1 A B))  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 2) C) (k7_real_1 (k18_complex1 A) (k18_complex1 B)))) ) ) ) ) ) ) ).
tt(l19_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_clopban2 A))) =>  ( (C = (k6_clopban2 A))  =>  ( ((k6_algstr_0 (k7_clopban2 A) B C) = B)  &  ((k6_algstr_0 (k7_clopban2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l19_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) = (k4_struct_0 A)) ) ) ).
tt(l19_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_arytm_0 A B) = (k2_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l19_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ( ((k2_afinsq_1 (k4_compos_1 A)) = (k6_domain_1 k5_numbers k6_numbers))  & (r2_hidden k6_numbers (k2_afinsq_1 (k4_compos_1 A)))) ) ) ).
tt(l19_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) => (r3_lattices A D E)) ) ) ) )  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(l19_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  => (m2_finseq_1 C (k3_qc_lang1 A))) ) ) ) ) ) ).
tt(l19_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k10_cqc_lang A B C) A) =>  ((v2_cqc_the1 B A) <=> (v2_cqc_the1 C A)) ) ) ) ) ) ) ) ).
tt(l19_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  & (v2_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_comseq_2 k5_numbers (k2_csspace A))))) ) ) ).
tt(l19_dtconstr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~ (r1_lang1 k5_dtconstr c2__dtconstr A)) ) ) ).
tt(l19_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(l19_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k5_euclid_8 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k1_euclid_8 (k10_binop_2 (k11_binop_2 B F) (k11_binop_2 C E)) (k10_binop_2 (k11_binop_2 C D) (k11_binop_2 A F)) (k10_binop_2 (k11_binop_2 A E) (k11_binop_2 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v1_conaffm A) <=> (v4_aff_2 (k3_analmetr A))) ) ) ).
tt(l19_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r4_fdiff_3 A C) & (r4_fdiff_3 B C))  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k1_numbers B)) &  ((r2_hidden E (k1_rcomp_1 (k9_real_1 C D) C)) &  ((k1_seq_1 B E) = k6_numbers) ) ) ) ) ) ) ) ) )  |  ((r4_fdiff_3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) &  ((k1_fdiff_3 C (k3_rfunct_1 k1_numbers k1_numbers A B)) = (k10_real_1 (k9_real_1 (k8_real_1 (k1_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k1_fdiff_3 C B) (k1_seq_1 A C))) (k5_square_1 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(l19_fib_num,ax, (~  ((k7_square_1 5) = k6_numbers) ) ).
tt(l19_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_fomodel0 B A D) & (r1_tarski C B))  => (v2_fomodel0 C A D)) ) ) ) ) ) ) ).
tt(l19_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k13_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp)) = (k10_margrel1 (k2_binarith (k2_binarith G H) I) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 E D) k2_twoscomp)) = (k10_margrel1 K J))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) = (k10_margrel1 J (k2_binarith (k2_binarith G H) I)))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_functor1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m2_pboole E A C B) =>  ( ((v1_msualg_3 D) &  ((v2_msualg_3 D A B C) & (r6_pboole A E (k4_msualg_3 A B C D))) )  =>  ((r6_pboole A (k8_pboole E D) (k2_msualg_3 A C)) & (r6_pboole A (k8_pboole D E) (k2_msualg_3 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k1_geomtrap A B C) = (k1_geomtrap A D E))  =>  ((k5_algstr_0 A D B) = (k4_algstr_0 A (k5_algstr_0 A E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k1_glib_002 A B) = (k6_glib_000 A)) ) ) ) ) ) ).
tt(l19_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v6_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A D F J) &  ((r1_collsp A C E J) &  ((r1_collsp A F H I) &  ((r1_collsp A E G I) &  ((r1_collsp A D H K) &  ((r1_collsp A C G K) &  ((r1_collsp A B D C) &  ((r1_collsp A B F E) & (r1_collsp A B H G)) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = C)  |  ( (B = E)  |  ( (F = E)  |  ( (B = G)  |  ( (H = G)  |  ((r1_collsp A B D F) |  ((r1_collsp A B D H) |  ((r1_collsp A B F H) |  ((r1_collsp A B I J) | (r1_collsp A I K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r1_aff_1 A B C D) &  ((v4_aff_2 A) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ( (~ (r1_aff_1 A B C F))  &  ((r1_aff_1 A B F G) & (r2_analoaf A C F D G)) )  |  ((r1_aff_1 A B C F) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C H))  &  ((r1_aff_1 A B H I) &  ((r2_analoaf A C H D I) &  ((r2_analoaf A H F I G) & (r1_aff_1 A B C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ((v6_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_polynom3 A))) =>  ( (D = C)  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) =>  ( (B = (k4_rlvect_1 (k14_polynom3 A) E))  =>  ((k11_polynom3 A C B) = (k4_rlvect_1 (k14_polynom3 A) (k9_fvsum_1 (k14_polynom3 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (r1_funct_2 (u1_struct_0 A) (u4_struct_0 A) (u1_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 A)) (k7_isocat_1 A) (k7_isocat_1 (k2_oppcat_1 A)))) ) ).
tt(l19_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 A B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k5_real_1 B C) = A) ) ) ) ) ) ) ) ) ) ).
tt(l19_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (D = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (C = (k1_algstr_0 A (k8_group_1 A E D) F))  &  (~  ( (~  (F = (k4_struct_0 A)) )  & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k5_numbers B D) (k3_funct_2 (u1_struct_0 A) k5_numbers B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_jgraph_6,ax, ((k17_euclid (k19_euclid 1 k6_numbers)) = 1) ).
tt(l19_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v9_rltopsp1 A (k15_euclid 2)) & (v1_xboole_0 (k2_jordan2c 2 A))) ) ) ) ).
tt(l19_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_topmetr A B))) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_tmap_1 (k4_topmetr A B) (k4_topmetr C D) E F) &  ( ((k1_funct_1 E A) = C)  &  ( ((k1_funct_1 E B) = D)  &  ((v2_funct_1 E) &  ( (E = G)  &  (F = H) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ( (F = A)  |  ( (F = B)  | (r1_fcont_1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B))))) =>  ((r2_hidden A B) => (r1_xboole_0 (k6_domain_1 (u1_struct_0 (k15_euclid 2)) A) C)) ) ) ) ) ) ) ).
tt(l19_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  ( (~ (v2_struct_0 (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)))  &  ((v10_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)) &  ((v13_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)) & (l3_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B))) ) ) ) ) ) ) ).
tt(l19_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_monoid_0 (k4_lfuzzy_0 A))) ) ).
tt(l19_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lopban_2 A))) =>  ( (C = (k6_lopban_2 A))  =>  ( ((k6_algstr_0 (k7_lopban_2 A) B C) = B)  &  ((k6_algstr_0 (k7_lopban_2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l19_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k12_matrix_1 B A))) &  ((r2_hidden E (k4_finseq_1 (k12_matrix_1 B A))) & (r2_hidden F (k4_finseq_1 (k12_matrix_1 B A)))) )  =>  ( (F = E)  |  ((k3_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) C D) = (k3_matrix_1 (u1_struct_0 B) (k3_matrix12 A A B (k3_matrix12 A A B (k12_matrix_1 B A) E F (k4_algstr_0 B G)) E F G) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) B A) =>  (~  ( ((k5_card_1 (k9_matrix13 k2_vectsp_1 B A D)) = 1)  &  (! [E:$i] :  ((m2_vectsp_6 E k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k9_matrix13 k2_vectsp_1 B A D)) =>  (~  ( ((k4_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) E) = (k1_funct_1 (k3_matrtop1 B A D) C))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 B)) =>  ( ((k1_funct_1 E (k8_matrix_1 (u1_struct_0 k2_vectsp_1) D F)) = (k16_rvsum_1 C))  &  ((k8_relset_1 k5_numbers (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) D (k1_tarski (k8_matrix_1 (u1_struct_0 k2_vectsp_1) D F))) = (k4_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_euclid_6 A B C))  &  ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 F)) (k1_rlvect_1 (k15_euclid 2) C F)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) A G)))  &  ( (~  ((k9_binop_2 (k10_binop_2 1 G) (k11_binop_2 F G)) = k6_numbers) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_euclid_6 A D H) & (r1_euclid_6 B E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_mfold_1,ax, ((k1_pre_topc (k15_euclid k1_xboole_0) (k2_struct_0 (k15_euclid k1_xboole_0))) = (g1_pre_topc (u1_struct_0 (k15_euclid k1_xboole_0)) (u1_pre_topc (k15_euclid k1_xboole_0)))) ).
tt(l19_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k4_vectsp_1 A C (k11_algstr_0 A B) (k4_vectsp_1 A C B D)) = (k4_vectsp_1 A C (k5_struct_0 A) D))  &  ((k4_vectsp_1 A C (k6_algstr_0 A (k11_algstr_0 A B) B) D) = (k4_vectsp_1 A C (k5_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_rlvect_1 A B (k1_rlvect_1 A (k5_algstr_0 A C B) D)) = (k3_rlvect_1 A (k1_rlvect_1 A B (k10_binop_2 1 D)) (k1_rlvect_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(l19_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  ((k3_int_2 A k6_numbers) = (k1_int_2 A)) ) ) ).
tt(l19_numbers,ax,(m1_subset_1 1 k5_arytm_3)).
tt(l19_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v7_o_ring_1 B A)) ) ) ) ) ).
tt(l19_pepin,ax, ((k13_newton 2 8) = 256) ).
tt(l19_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~ (r1_xxreal_0 k6_numbers C))  =>  ((k3_polynom8 A B C) = (k11_algstr_0 A (k3_polynom8 A B (k1_int_2 C)))) ) ) ) ) ) ) ) ).
tt(l19_pre_ff,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k3_finseq_2 k5_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k5_numbers))))) )  &  ( ((k2_pre_ff A k6_numbers) = c1__pre_ff)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_nat_1 B 2) = (k4_nat_1 2 C))  =>  ((k2_pre_ff A (k2_nat_1 B 1)) = (k8_finseq_1 k5_numbers (k2_pre_ff A B) (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers (k2_pre_ff A B) C)))) ) ) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_nat_1 B 2) = (k2_nat_1 (k4_nat_1 2 C) 1))  =>  ((k2_pre_ff A (k2_nat_1 B 1)) = (k8_finseq_1 k5_numbers (k2_pre_ff A B) (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers (k2_pre_ff A B) C) (k7_partfun1 k5_numbers (k2_pre_ff A B) (k1_nat_1 C 1)))))) ) ) ) ) ) ) ) ) ) ).
tt(l19_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  ((v5_rlvect_1 (k10_prvect_2 A)) &  ((v6_rlvect_1 (k10_prvect_2 A)) &  ((v7_rlvect_1 (k10_prvect_2 A)) & (v8_rlvect_1 (k10_prvect_2 A))) ) ) ) ) ).
tt(l19_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k4_card_3 A)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ).
tt(l19_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A)))  => (m2_finseq_1 (k7_finseq_1 (k12_finseq_1 (k8_qc_lang1 A B) C) D) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ) ) ) ) ) ) ).
tt(l19_quantal1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v11_quantal1 B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A B (k3_funct_2 A A B C)) = (k3_funct_2 A A B C)) ) ) ) ) ) ) ) ).
tt(l19_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_tarski A B) = (k1_tarski C))  =>  ( (C = (k1_tarski A))  &  (A = B) ) ) ) ) ) ).
tt(l19_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 (k1_seq_1 (k1_real_3 A B) C) (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) (k1_nat_1 C 1))) &  (~  ((k1_seq_1 (k1_real_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(l19_realset2,ax, ((k5_binop_1 2 k2_realset2 (k1_funct_7 k6_numbers 2) (k1_funct_7 k6_numbers 2)) = (k1_funct_7 k6_numbers 2)) ).
tt(l19_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_ringcat1 C A B) =>  (~  ((r1_ringcat1 A B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  (C = (g1_ringcat1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( ((u1_struct_0 C) = B)  => (v1_rlsub_1 B A)) ) ) ) ) ) ) ).
tt(l19_rlvect_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((r1_struct_0 (k1_rlsub_1 B) A) <=>  (A = (k4_struct_0 B)) ) ) ) ) ).
tt(l19_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( ((u1_struct_0 D) = C)  => (v1_rmod_2 C A B)) ) ) ) ) ) ) ) ) ).
tt(l19_scmfsa_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_scmfsa_1 k2_scmfsa_1) =>  ((k3_funct_2 k1_scmfsa_1 3 k4_scmfsa_1 A) = 1) ) ) ).
tt(l19_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ( ( ((k2_compos_0 k2_scmfsa_i A) = 11)  |  ((k2_compos_0 k2_scmfsa_i A) = 12) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l19_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( ( ((k2_compos_0 k3_scm_inst A) = 7)  |  ((k2_compos_0 k3_scm_inst A) = 8) )  =>  ((k4_finseq_1 (k5_xtuple_0 A)) = (k2_finseq_1 1)) ) ) ) ).
tt(l19_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r1_tarski k4_scmp_gcd C) &  ( ((k5_memstr_0 2 k1_scmpds_2 B) = 5)  &  ( (A = (k1_funct_1 B k3_scmp_gcd))  &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) k6_numbers) |  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C B 7)) = (k2_nat_1 5 7))  &  ( ((k5_extpro_1 2 k1_scmpds_2 C B 8) = (k2_extpro_1 2 k1_scmpds_2 (k3_scmpds_2 (k4_xcmplx_0 7)) (k5_extpro_1 2 k1_scmpds_2 C B 7)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) k3_scmp_gcd) = (k2_nat_1 A 4))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) (k1_scmp_gcd (k2_nat_1 A 7))) = (k6_int_1 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) (k1_scmp_gcd (k2_nat_1 A 6))) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) (k1_scmp_gcd (k2_nat_1 A 4))) = A)  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 C B 7) (k1_scmp_gcd (k2_nat_1 A 5))) = 11) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( ((k2_compos_0 (k1_scmringi A) B) = 6)  =>  ((k4_finseq_1 (k5_xtuple_0 B)) = (k2_finseq_1 1)) ) ) ) ) ) ).
tt(l19_scpisort,ax, ((k5_card_1 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) = 10) ).
tt(l19_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 4)) = (k2_xcmplx_0 C (k1_funct_1 B (k1_scmp_gcd 5))))  &  ((r1_xxreal_0 8 C) &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = D)  & (r1_xxreal_0 8 D)) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A) & (r2_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) B A)) ) ) ) ) ) ) ) ) ) ).
tt(l19_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  =>  ((k2_xcmplx_0 1 (k13_complex1 1 A)) = (k2_xcmplx_0 2 (k13_complex1 (k2_xcmplx_0 B C) A))) ) ) ) ) ) ) ) ).
tt(l19_simplex2,ax, (! [A:$i] : (v6_ordinal1 (k1_tarski A))) ).
tt(l19_sincos10,ax, ((r2_hidden (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) & (r2_hidden (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) ).
tt(l19_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k6_sin_cos2 (k2_xcmplx_0 A B)) = (k2_xcmplx_0 (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) (k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B))))  &  ( ((k6_sin_cos2 (k6_xcmplx_0 A B)) = (k6_xcmplx_0 (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) (k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B))))  &  ( ((k3_sin_cos2 (k2_xcmplx_0 A B)) = (k2_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k3_sin_cos2 B))))  &  ( ((k3_sin_cos2 (k6_xcmplx_0 A B)) = (k6_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k3_sin_cos2 B))))  &  ( ((k9_sin_cos2 (k2_xcmplx_0 A B)) = (k7_xcmplx_0 (k2_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k2_xcmplx_0 1 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)))))  &  ((k9_sin_cos2 (k6_xcmplx_0 A B)) = (k7_xcmplx_0 (k6_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k6_xcmplx_0 1 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B))))) ) ) ) ) ) ) ) ) ) ).
tt(l19_sin_cos9,ax, ((k2_funct_1 k1_sin_cos9) = (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(l19_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((k3_square_1 A) = (k3_square_1 B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l19_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_taxonom2 B A) =>  (! [C:$i] :  ( ((v4_taxonom2 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski C B) &  (! [D:$i] :  ( ((v4_taxonom2 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski D B) & (r1_tarski (k5_setfam_1 A C) (k5_setfam_1 A D)))  =>  (C = D) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D C) &  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_topgen_3,ax,(r1_tarski c1__topgen_3 (u1_pre_topc k2_topgen_3))).
tt(l19_topreal2,ax, (~ (r2_hidden (k19_euclid 1 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)))) ).
tt(l19_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v11_aff_2 A) &  ( (~  (B = C) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v7_transgeo D A) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) => (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(l19_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (? [B:$i] :  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v6_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  &  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l19_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v8_waybel_0 B A) & (l1_waybel_0 B A)) ) ) ) )  =>  ((k1_waybel11 A B) = (k1_waybel_2 A B)) ) ) ) ) ).
tt(l19_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((r2_hidden D (k1_binop_1 (u1_altcat_1 (k4_waybel34 A)) B C)) <=>  ((r2_hidden B (u1_struct_0 (k4_waybel34 A))) &  ((r2_hidden C (u1_struct_0 (k4_waybel34 A))) &  ((v3_lattice3 B) &  ((v3_lattice3 C) & (v17_waybel_0 D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l19_xreal_0,ax, (~ (r2_hidden (k4_xcmplx_0 1) k2_arytm_2)) ).
tt(l19_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r2_hidden A k1_numbers) =>  ((k2_xxreal_3 (k1_xxreal_3 A k2_xxreal_0)) = (k1_xxreal_3 (k2_xxreal_3 k2_xxreal_0) (k2_xxreal_3 A))) ) ) ) ).
tt(l19_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_1 A))) =>  ((r2_hidden (k3_xboole_0 B C) (k9_setfam_1 A)) & (r2_hidden (k2_xboole_0 B C) (k9_setfam_1 A))) ) ) ) ) ) ).
tt(l19_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) => (m1_yellow_6 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) (u1_waybel_0 A B)) A B)) ) ) ) ).
tt(l19_zf_fund1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  ((k4_zf_fund1 (k6_domain_1 k1_zf_lang A)) = (k6_domain_1 k5_numbers (k3_zf_fund1 A))) ) ) ).
tt(l19_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) = (k4_struct_0 A)) ) ) ).
tt(l1_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C B) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(l1_afinsq_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((r1_tarski A B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(l1_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_diraf A B C C D) =>  ( (B = D)  | (r2_analoaf A B C C D)) ) ) ) ) ) ) ) ) ) ).
tt(l1_algstr_2,ax, (k6_numbers = (k4_struct_0 k2_vectsp_1)) ).
tt(l1_ami_4,ax, ( (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 1)) )  &  (~  ((k10_ami_3 1) = (k10_ami_3 2)) ) ) ).
tt(l1_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C F) (k1_rlvect_1 A D G)))  &  (E = (k3_rlvect_1 A (k1_rlvect_1 A C H) (k1_rlvect_1 A D I))) )  =>  ( ((k3_rlvect_1 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k7_real_1 F H)) (k1_rlvect_1 A D (k7_real_1 G I))))  &  ((k5_algstr_0 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 F H)) (k1_rlvect_1 A D (k9_real_1 G I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C F) (k1_rlvect_1 A D G)))  &  (E = (k3_rlvect_1 A (k1_rlvect_1 A C H) (k1_rlvect_1 A D I))) )  =>  ( ((k3_rlvect_1 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k7_real_1 F H)) (k1_rlvect_1 A D (k7_real_1 G I))))  &  ((k5_algstr_0 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 F H)) (k1_rlvect_1 A D (k9_real_1 G I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_armstrng,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  ((k4_finseq_1 C) = (k2_finseq_1 A)) ) ) ) ) ) ) ).
tt(l1_arytm_0,ax,(r2_hidden k11_arytm_3 (k1_tarski k11_arytm_3))).
tt(l1_arytm_3,ax,(r2_hidden k1_xboole_0 k4_ordinal1)).
tt(l1_asympt_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k5_series_1 2 A) (k1_nat_1 A 1))) ) ) ) ).
tt(l1_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 B (k2_group_3 A D C))) ) ) ) )  => (v1_group_3 B A)) ) ) ) ) ).
tt(l1_axioms,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ( (~  ((r2_hidden A k2_arytm_2) &  ((r2_hidden B k2_arytm_2) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = C)  &  ( (B = D)  & (r1_arytm_2 C D)) ) ) ) ) ) ) ) )  &  ( (~  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  ((r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = (k4_tarski k6_numbers C))  &  ( (B = (k4_tarski k6_numbers D))  & (r1_arytm_2 D C)) ) ) ) ) ) ) ) )  &  (~  ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(l1_bhsp_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k10_real_1 D 2) (k18_complex1 (k9_real_1 A B))))  &  ( (~ (r1_xxreal_0 (k10_real_1 D 2) (k18_complex1 (k9_real_1 B C))))  & (r1_xxreal_0 D (k18_complex1 (k9_real_1 A C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_binari_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ( ((k3_finseq_1 B) = A)  &  ( ((k3_finseq_1 C) = A)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 B D) = (k7_partfun1 k6_margrel1 C D)) ) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l1_bintree2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) => (m2_finseq_1 (k8_finseq_1 A B C) A)) ) ) ) ) ).
tt(l1_borsuk_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  <=> (r2_hidden A (u1_struct_0 k5_topmetr))) ) ) ).
tt(l1_borsuk_7,ax,(v7_ordinal1 k6_numbers)).
tt(l1_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k5_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid A) C D)) B) = (k1_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) C B) D)) ) ) ) ) ) ) ) ) ).
tt(l1_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A B C) B)) ) ) ) ) ) ).
tt(l1_card_5,ax, (1 = (k5_card_1 1)) ).
tt(l1_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k2_numbers A B) &  ((v2_comseq_2 A) &  ((k2_seq_2 A) = C) ) )  =>  ((k3_comseq_2 B) = C) ) ) ) ) ) ) ) ).
tt(l1_circcomb,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k4_card_3 (k7_funcop_1 (k2_finseq_1 A) B)) = (k4_finseq_2 A B)) ) ) ) ) ).
tt(l1_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  => (r2_hidden (k5_algstr_0 A D E) (k1_rusub_5 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_circuit2,ax, (! [A:$i] :  (~ (r2_hidden A A)) ) ).
tt(l1_classes2,ax, (! [A:$i] : (v2_classes1 (k1_classes1 A))) ).
tt(l1_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k6_algstr_0 A B (k6_clopban3 A B C)) = (k6_clopban3 A B (k2_nat_1 C 1)))  &  ( ((k6_algstr_0 A (k6_clopban3 A B C) B) = (k6_clopban3 A B (k2_nat_1 C 1)))  &  ((k6_algstr_0 A B (k6_clopban3 A B C)) = (k6_algstr_0 A (k6_clopban3 A B C) B)) ) ) ) ) ) ) ) ) ).
tt(l1_cohsp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((r2_hidden E (k3_funct_2 A B C D)) => (r2_hidden E (k3_tarski B))) ) ) ) ) ) ) ) ) ) ).
tt(l1_comseq_3,ax, (k5_complex1 = (k2_xcmplx_0 k6_numbers (k3_xcmplx_0 k6_numbers k7_complex1))) ).
tt(l1_convex2,ax,(m1_subset_1 1 k1_numbers)).
tt(l1_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (~ (r2_hidden B (k4_qc_lang1 A))) ) ) ) ) ).
tt(l1_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k10_comseq_3 (k2_comseq_2 k5_numbers A)) (k2_comseq_2 k5_numbers (k10_comseq_3 A)))) ) ).
tt(l1_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A C) B)) )  => (r1_xxreal_0 (k4_seq_4 (k2_relset_1 k1_numbers A)) B)) ) ) ) ) ).
tt(l1_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k3_tarski (k2_tarski B (k1_tarski C)))) <=>  ((r2_hidden A B) |  (A = C) ) ) ) ) ) ).
tt(l1_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(l1_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 (k7_xcmplx_0 B A) (k2_xcmplx_0 (k1_int_1 (k7_xcmplx_0 B A)) 1)) =>  ( (A = k6_numbers)  | (r1_xxreal_0 (k6_xcmplx_0 B (k3_xcmplx_0 (k1_int_1 (k7_xcmplx_0 B A)) A)) A)) ) ) ) ) ) ).
tt(l1_euler_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (r1_xxreal_0 1 A))  <=> (r1_xxreal_0 A k1_xboole_0)) ) ) ).
tt(l1_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  ((v1_relat_1 (k8_pboole E F)) &  ((v4_relat_1 (k8_pboole E F) A) &  ((v1_funct_1 (k8_pboole E F)) & (v1_partfun1 (k8_pboole E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = A) ) ) )  &  (D = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) E) = (k8_real_1 2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k9_real_1 1 (k21_sin_cos (k8_real_1 2 A))) = (k8_real_1 2 (k5_square_1 (k18_sin_cos A)))) ) ) ).
tt(l1_fib_fusc,ax, (k6_numbers = (k1_int_1 (k6_power 2 1))) ).
tt(l1_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k4_xcmplx_0 A) (k3_xcmplx_0 A (k3_power (k4_xcmplx_0 1) B)))) ) ) ) ).
tt(l1_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k10_finseq_1 A B)) = (k2_tarski A B)) ) ) ).
tt(l1_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_funct_2 B C))) => (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 B C))))) ) ) ) ).
tt(l1_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) B)) ) )  => (v7_pre_topc A)) ) ) ).
tt(l1_frechet,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k10_real_1 1 B)))  &  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(l1_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((k4_tarski (k4_tarski A B) (k4_tarski C D)) = (k4_tarski (k4_tarski E F) (k4_tarski G H)))  =>  ( (A = E)  &  ( (C = G)  &  ( (B = F)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C))) = (k2_xboole_0 (k9_xtuple_0 A) (k1_tarski B))) ) ) ) ) ).
tt(l1_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C))) = (k2_xboole_0 (k9_xtuple_0 A) (k1_tarski B))) ) ) ) ) ).
tt(l1_goboard3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k2_nat_1 B 1))  & (v2_topreal1 A))  =>  ( (B = k6_numbers)  | (v2_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(l1_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k7_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k7_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(l1_gobrd11,ax, (~ (r1_xxreal_0 (k7_square_1 2) k6_numbers)) ).
tt(l1_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) = (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))))) ) ) ).
tt(l1_gobrd14,ax, ((u1_struct_0 (k15_euclid 2)) = (k1_euclid 2)) ).
tt(l1_gr_cy_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k7_card_1 B)) => (m2_subset_1 A k1_numbers k5_numbers)) ) ) ) ).
tt(l1_group_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) =>  ((k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) (k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) A B) C) = (k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) A (k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) B C))) ) ) ) ) ) )  &  (? [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) =>  ( ((k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) B A) = B)  &  ( ((k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) A B) = B)  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_algstr_0 k1_numbers k33_binop_2))) &  ( ((k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) B C) = A)  &  ((k6_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2) C B) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A C) => (m1_subset_1 A (u1_struct_0 B))) ) ) ) ) ) ).
tt(l1_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_algstr_0 A C)) = (k4_algstr_0 A (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(l1_hermitan,ax, (k6_numbers = (k2_xcmplx_0 k6_numbers (k3_xcmplx_0 k6_numbers k7_complex1))) ).
tt(l1_heyting3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 (k2_zfmisc_1 A (k1_tarski B))) & (v1_funct_1 (k2_zfmisc_1 A (k1_tarski B)))) ) ) ).
tt(l1_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) &  ((r1_aff_1 A B E F) &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C E D F) & (r2_analoaf A C G D H)) ) ) )  =>  ((r1_aff_1 A B C E) |  ((r1_aff_1 A B C G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (C = (k2_partfun1 k5_numbers (u1_struct_0 A) B (k2_finseq_1 D)))  &  ((k3_finseq_1 B) = (k1_nat_1 D 1)) )  =>  ((m2_finseq_1 C (u1_struct_0 A)) &  ((r1_tarski (k4_finseq_1 C) (k4_finseq_1 B)) &  ( ((k3_finseq_1 C) = D)  &  (B = (k7_finseq_1 C (k12_finseq_1 (u1_struct_0 A) (k7_partfun1 (u1_struct_0 A) B (k1_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v1_int_2 B) =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 B A) | (r1_int_2 A B)) ) ) ) ) ) ) ).
tt(l1_int_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k6_subset_1 (k2_zfmisc_1 (k1_tarski k6_numbers) k5_numbers) (k1_tarski (k4_tarski k6_numbers k6_numbers)))) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  (A = (k1_real_1 B)) ) ) ) ) ) ) ).
tt(l1_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 A k4_numbers)) ) ).
tt(l1_int_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_funct_7 (k8_funcop_1 k5_numbers B k6_numbers) A C) D) = k6_numbers) ) ) ) ) ) ).
tt(l1_integr11,ax, ((k2_subset_1 k1_numbers) = (k9_xtuple_0 (k1_fcont_1 (k10_real_1 1 2) k6_numbers))) ).
tt(l1_integr12,ax,(m1_subset_1 (k19_binop_2 1) k1_numbers)).
tt(l1_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden k6_numbers A) =>  ((k8_relset_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_seq_4 k6_numbers)) = (k1_seq_4 k6_numbers)) ) ) ) ).
tt(l1_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden k6_numbers A) =>  ((k8_relset_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_seq_4 k6_numbers)) = (k1_seq_4 k6_numbers)) ) ) ) ).
tt(l1_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  => (r2_relset_1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers B C) (k7_integr15 A k1_numbers B (k2_nfcont_4 A k1_numbers C)))) ) ) ) ) ) ).
tt(l1_integra3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_nat_1 (k7_nat_d A A) 1) = 1) ) ) ).
tt(l1_integra8,ax, (~ (r1_xxreal_0 (k18_sin_cos (k10_real_1 k32_sin_cos 4)) k6_numbers)) ).
tt(l1_integra9,ax, ((k1_relset_1 k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 1) k6_numbers) k24_sin_cos))) = (k2_subset_1 k1_numbers)) ).
tt(l1_jgraph_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k3_real_1 (k3_square_1 A) 1) k6_numbers)) ) ) ).
tt(l1_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  & (r1_xxreal_0 (k12_euclid A) k6_numbers)) ) ) ) ).
tt(l1_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 B k6_numbers) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k4_real_1 A (k7_square_1 (k7_real_1 1 (k3_square_1 B)))) (k4_real_1 B (k7_square_1 (k7_real_1 1 (k3_square_1 A)))))) ) ) ) ) ).
tt(l1_jgraph_8,ax, (k17_borsuk_1 = (k3_pcomps_1 (k2_topmetr k6_numbers 1))) ).
tt(l1_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_topreal2 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k1_jordan8 D A))) &  ((r1_xxreal_0 C B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 D A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) C)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 D A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) B)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) C)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 D A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) C))) ) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) C)) (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan9 D A))))) ) ) ) ) ) ) ) ) ) ).
tt(l1_jordan12,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_zfmisc_1 (k4_finseq_1 A)) => (v1_zfmisc_1 (k3_finseq_1 A))) ) ) ).
tt(l1_jordan18,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k4_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l1_jordan1a,ax, (3 = (k2_nat_1 (k4_nat_1 2 1) 1)) ).
tt(l1_jordan1,ax, ((r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1)) & (r2_hidden 1 (k1_rcomp_1 k6_numbers 1))) ).
tt(l1_jordan1c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k6_xcmplx_0 (k1_int_1 (k2_xcmplx_0 A B)) B) = (k1_int_1 A)) ) ) ) ) ).
tt(l1_jordan1d,ax, (1 = (k2_nat_1 (k4_nat_1 2 k6_numbers) 1)) ).
tt(l1_jordan21,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k5_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l1_jordan22,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r2_hidden A (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) &  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_jordan2b,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m2_finseq_1 E k1_numbers) &  ( (E = C)  &  (D = (k7_partfun1 k1_numbers E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_jordan7,ax, ((k7_nat_d 2 1) = 1) ).
tt(l1_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k2_nat_1 (k7_nat_d A 1) 2) = (k2_nat_1 A 1)) ) ) ) ).
tt(l1_jordan,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A D) &  ((r1_tarski B D) & (r1_tarski C D)) )  => (r1_tarski (k2_xboole_0 (k2_xboole_0 A B) C) D)) ) ) ) ) ).
tt(l1_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_lattice3 A))) =>  (~  ((r2_hidden D B) &  ( (~  (D = C) )  & (r3_orders_2 (k3_lattice3 A) D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C))) = (k2_xboole_0 (k9_xtuple_0 A) (k1_tarski B))) ) ) ) ) ).
tt(l1_limfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 A k6_numbers) |  ( (~ (r1_xxreal_0 C (k6_xcmplx_0 B A)))  &  (~ (r1_xxreal_0 (k2_xcmplx_0 C A) B)) ) ) ) ) ) ) ) ) ) ).
tt(l1_limfunc2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A C) =>  ((r1_xxreal_0 B k6_numbers) |  ( (~ (r1_xxreal_0 C (k6_xcmplx_0 A B)))  &  (~ (r1_xxreal_0 (k2_xcmplx_0 C B) A)) ) ) ) ) ) ) ) ) ) ).
tt(l1_limfunc3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 A k6_numbers) |  ( (~ (r1_xxreal_0 C (k6_xcmplx_0 B A)))  &  (~ (r1_xxreal_0 (k2_xcmplx_0 C A) B)) ) ) ) ) ) ) ) ) ) ).
tt(l1_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( (~ (r1_xxreal_0 B (k9_real_1 B A)))  &  (~ (r1_xxreal_0 (k7_real_1 B A) B)) ) ) ) ) ) ) ).
tt(l1_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k4_algstr_0 A (k5_algstr_0 A B C)) = (k5_algstr_0 A (k4_algstr_0 A B) (k4_algstr_0 A C)))  &  ((k3_rlvect_1 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A (k3_rlvect_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(l1_ltlaxio1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k1_funct_1 B C) = (k7_partfun1 A B C)) ) ) ) ) ) ) ).
tt(l1_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) B A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) B A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 C) B A) =>  (! [I:$i] :  ((m2_finseq_1 I (u1_struct_0 C)) =>  (! [J:$i] :  ((m2_finseq_1 J (u1_struct_0 C)) =>  (! [K:$i] :  ((v7_ordinal1 K) =>  (! [L:$i] :  ((v7_ordinal1 L) =>  ( ((r2_hidden K (k2_finseq_1 B)) &  ((r2_hidden L (k2_finseq_1 (k1_matrix_1 F))) &  ( (I = (k8_matrix_1 (u1_struct_0 C) F E))  &  ( (J = (k8_matrix_1 (u1_struct_0 C) F D))  &  ( (G = (k3_matrix11 D B A (u1_struct_0 C) F I))  &  (H = (k3_matrix11 E B A (u1_struct_0 C) G J)) ) ) ) ) )  =>  ( ( (K = E)  =>  ((k3_matrix_1 (u1_struct_0 C) H K L) = (k3_matrix_1 (u1_struct_0 C) F D L)) )  &  ( ( (K = D)  =>  ((k3_matrix_1 (u1_struct_0 C) H K L) = (k3_matrix_1 (u1_struct_0 C) F E L)) )  &  (~  ( (~  (K = E) )  &  ( (~  (K = D) )  &  (~  ((k3_matrix_1 (u1_struct_0 C) H K L) = (k3_matrix_1 (u1_struct_0 C) F K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 1 B))  =>  ((k6_int_1 (k6_xcmplx_0 B 1) A) = (k6_xcmplx_0 B 1)) ) ) ) ) ) ).
tt(l1_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k2_finseq_1 A)) => (r2_hidden (k6_xcmplx_0 (k2_xcmplx_0 A 1) B) (k2_finseq_1 A))) ) ) ) ) ).
tt(l1_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_finseq_1 (k3_fvsum_1 A B C)) = (k9_subset_1 k5_numbers (k4_finseq_1 B) (k4_finseq_1 C))) ) ) ) ) ) ) ).
tt(l1_matrixj2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_funct_1 C) & (r2_hidden A (k9_xtuple_0 C)))  =>  ((k10_xtuple_0 (k2_funct_7 C A B)) = (k2_xboole_0 (k6_subset_1 (k10_xtuple_0 C) (k1_tarski (k1_funct_1 C A))) (k1_tarski B))) ) ) ) ) ) ).
tt(l1_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_funct_1 (k8_rvsum_1 A B) C) = (k6_xcmplx_0 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(l1_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) = (u1_struct_0 (k15_euclid A))) ) ) ).
tt(l1_mazurulm,ax,(m1_subset_1 k2_urysohn1 (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))).
tt(l1_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))))  &  ((v13_algstr_0 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))) &  ((v7_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A) &  ((v8_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A) &  ((v9_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A) &  ((v10_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A) &  ((v11_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A) &  ((v2_rlvect_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))) &  ((v3_rlvect_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))) &  ((v4_rlvect_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1))) & (l1_vectsp_1 (g1_vectsp_1 A 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k4_algstr_0 A B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l1_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r2_xboole_0 k1_xboole_0 (k12_finseq_1 k5_numbers A))) ) ).
tt(l1_modelc_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k1_nat_1 C 1)) =>  ((r1_xxreal_0 B A) | (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(l1_modelc_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_xboole_0 (k2_xboole_0 B C) D)) <=>  (~  ( (~ (r2_hidden A B))  &  ( (~ (r2_hidden A C))  &  (~ (r2_hidden A D)) ) ) ) ) ) ) ) ) ).
tt(l1_moebius1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r1_xboole_0 A B) &  ((r2_hidden D (k3_xboole_0 A C)) & (r2_hidden D (k3_xboole_0 B C))) ) ) ) ) ) ) ).
tt(l1_msaterm,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (A = (k2_nat_1 C 1))  &  (~ (r1_xxreal_0 (k3_finseq_1 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(l1_nagata_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((r1_xxreal_0 C (k7_real_1 A B)) |  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(l1_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ((v1_int_2 A) =>  ((k11_nat_3 (k6_nat_d B C) A) = (k3_xxreal_0 (k11_nat_3 B A) (k11_nat_3 C A))) ) ) ) ) ) ) ) ).
tt(l1_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (v7_ordinal1 (k5_int_1 A B))) ) ) ) ).
tt(l1_ndiff_3,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) k5_numbers k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(l1_ndiff_4,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) k5_numbers k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(l1_normsp_0,ax,(r1_funct_2 1 1 1 k5_numbers k8_funct_5 (k8_funcop_1 k5_numbers 1 k6_numbers))).
tt(l1_normsp_1,ax, ((u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) = (k6_domain_1 (u1_struct_0 o_0_5_normsp_1) (k4_struct_0 o_0_5_normsp_1))) ).
tt(l1_numbers,ax,(r1_tarski k4_ordinal1 (k2_xboole_0 (k6_subset_1 a_0_1_numbers a_0_2_numbers) k4_ordinal1))).
tt(l1_orders_1,ax, (! [A:$i] :  ( (~  ( (? [B:$i] :  ( (~  (B = k1_xboole_0) )  & (r2_hidden B A)) )  &  ((k3_tarski A) = k1_xboole_0) ) )  &  (~  ( (~  ((k3_tarski A) = k1_xboole_0) )  &  (! [B:$i] :  (~  ( (~  (B = k1_xboole_0) )  & (r2_hidden B A)) ) ) ) ) ) ) ).
tt(l1_ordinal4,ax,(r2_hidden k1_xboole_0 k4_ordinal1)).
tt(l1_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( (B = (k8_finseq_1 (u1_struct_0 A) C D))  <=>  ( ((k4_finseq_1 B) = (k2_finseq_1 (k2_nat_1 (k3_finseq_1 C) (k3_finseq_1 D))))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k7_partfun1 (u1_struct_0 A) B E) = (k7_partfun1 (u1_struct_0 A) C E)) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k7_partfun1 (u1_struct_0 A) B (k2_nat_1 (k3_finseq_1 C) E)) = (k7_partfun1 (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_ortsp_1,ax, (~ (v1_xboole_0 (k1_tarski k6_numbers))) ).
tt(l1_osalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k4_finseq_1 (k3_relat_1 C B)) = (k4_finseq_1 C))  &  ((k3_finseq_1 (k3_relat_1 C B)) = (k3_finseq_1 C)) ) ) ) ) ) ) ).
tt(l1_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k5_algstr_0 A B C)) = (k5_algstr_0 A C B)) ) ) ) ) ) ) ).
tt(l1_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l1_partfun4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (v1_pscomp_1 (k8_funcop_1 k1_numbers (u1_struct_0 A) B) A)) ) ) ) ).
tt(l1_pcs_0,ax, ((m1_subset_1 k6_numbers (k2_tarski k6_numbers 1)) & (m1_subset_1 1 (k2_tarski k6_numbers 1))) ).
tt(l1_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_nfcont_1 C A B) =>  (! [D:$i] :  ((m1_nfcont_1 D A B) => (m1_nfcont_1 (k9_subset_1 (u1_struct_0 A) C D) A B)) ) ) ) ) ) ) ) ).
tt(l1_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) &  (1 = (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 B C) A) B) C)) )  =>  ((r1_xxreal_0 A 1) |  ( (B = 1)  &  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(l1_polyeq_2,ax, (4 = (k3_xcmplx_0 2 2)) ).
tt(l1_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r1_relat_2 C B) &  ((r4_relat_2 C B) & (r8_relat_2 C B)) ) ) ) ) ) ) ).
tt(l1_polynom8,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~  (A = (k4_xcmplx_0 1)) )  & (r1_xxreal_0 (k4_xcmplx_0 1) A)) ) ) ) ) ).
tt(l1_polyred,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v3_orders_1 C) => (r3_orders_1 C B)) ) ) ) ) ) ).
tt(l1_poset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  ((k9_funct_7 A k6_numbers) = (k6_partfun1 (k9_xtuple_0 A))) ) ) ) ).
tt(l1_prob_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C k6_numbers) |  ( (~ (r1_xxreal_0 (k9_binop_2 B C) A))  &  (~ (r1_xxreal_0 B (k10_binop_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(l1_prob_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski C B) =>  ((k6_subset_1 A C) = (k2_xboole_0 (k6_subset_1 A B) (k9_subset_1 B A (k6_subset_1 B C)))) ) ) ) ) ).
tt(l1_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_xxreal_2 A) => (v4_xxreal_2 (k4_measure6 A))) ) ) ).
tt(l1_pua2mss1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 B) = (k4_finseq_1 A))  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(l1_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (A = (k6_quaterni B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k1_radix_1 A) = (k2_xcmplx_0 (k1_radix_1 (k7_nat_d A 1)) (k1_radix_1 (k7_nat_d A 1)))) ) ) ) ).
tt(l1_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_xcmplx_0 A 2) 1)) ) ) ) ).
tt(l1_rat_1,ax,(r1_tarski k4_ordinal1 (k2_xboole_0 (k6_subset_1 a_0_0_rat_1 a_0_1_rat_1) k4_ordinal1))).
tt(l1_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  => (v7_ordinal1 (k5_real_1 A 1))) ) ) ).
tt(l1_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B A))  =>  (A = B) ) ) ) ) ) ).
tt(l1_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid A)) (k1_euclid A))))) )  &  ( (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k5_binop_1 (k1_euclid A) B C D) = (k7_euclid A C D)) ) ) ) )  &  ((v1_binop_1 B (k1_euclid A)) & (v2_binop_1 B (k1_euclid A))) ) ) ) ) ) ).
tt(l1_rearran1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (k10_xtuple_0 A)))  =>  ((k8_relat_1 A (k1_tarski B)) = k1_xboole_0) ) ) ) ) ).
tt(l1_recdef_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 C)))  => (m1_subset_1 (k1_funct_1 C A) B)) ) ) ) ) ) ) ).
tt(l1_rfunct_1,ax, ((k2_real_1 (k1_real_1 1)) = (k1_real_1 1)) ).
tt(l1_rinfsup1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C k6_numbers) |  ( (~ (r1_xxreal_0 (k2_xcmplx_0 B C) A))  &  (~ (r1_xxreal_0 B (k6_xcmplx_0 A C))) ) ) ) ) ) ) ) ) ) ).
tt(l1_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_convex1 A B))) ) ) ) ).
tt(l1_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k3_rlvect_1 B (k1_rlvect_1 B C A) (k1_rlvect_1 B D (k9_real_1 1 A))) = E)  =>  ( (A = 1)  |  (D = (k3_rlvect_1 B (k1_rlvect_1 B E (k10_real_1 1 (k9_real_1 1 A))) (k1_rlvect_1 B C (k9_real_1 1 (k10_real_1 1 (k9_real_1 1 A)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) ) )  => (m1_subset_1 B (u1_struct_0 (k15_euclid A)))) ) ) ) ).
tt(l1_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k5_rlvect_2 A (k8_finseq_1 (u1_struct_0 A) B C) D) = (k8_finseq_1 (u1_struct_0 A) (k5_rlvect_2 A B D) (k5_rlvect_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(l1_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m2_rlvect_2 D A (k6_domain_1 (u1_struct_0 A) B)) &  ((k3_funct_2 (u1_struct_0 A) k1_numbers D B) = C) ) ) ) ) ) ) ) ) ).
tt(l1_rlvect_x,ax,(m1_subset_1 k6_numbers k1_numbers)).
tt(l1_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = (k2_nat_1 (k3_finseq_1 E) 1))  &  ( (E = (k2_partfun1 k5_numbers (u1_struct_0 B) D (k2_finseq_1 (k3_finseq_1 E))))  &  (C = (k1_funct_1 D (k3_finseq_1 D))) ) )  =>  ((k4_rlvect_1 B D) = (k3_rlvect_1 B (k4_rlvect_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A C) B)) )  => (r1_xxreal_0 (k4_seq_4 (k2_relset_1 k1_numbers A)) B)) ) ) ) ) ).
tt(l1_scm_comp,ax, (1 = a_0_0_scm_comp) ).
tt(l1_scmfsa_7,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) = (k1_ordinal4 (k1_ordinal4 A B) (k1_ordinal4 C D)))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) = (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 B C) D)))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) = (k1_ordinal4 A (k1_ordinal4 B (k1_ordinal4 C D))))  &  ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) = (k1_ordinal4 (k1_ordinal4 A (k1_ordinal4 B C)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_scmfsa8b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski (k6_compos_1 k1_scmfsa_2 B (k5_card_1 A)) (k3_scmfsa6a A B))) ) ) ) ).
tt(l1_scmfsa_9,ax, ((k5_card_1 (k4_compos_1 k1_scmfsa_2)) = 1) ).
tt(l1_scm_halt,ax, ((v1_relat_1 k1_xboole_0) &  ((v4_relat_1 k1_xboole_0 (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 k1_xboole_0) & (v5_funct_1 k1_xboole_0 (k2_memstr_0 3 k1_scmfsa_2))) ) ) ).
tt(l1_scmpds_5,ax, ((k5_card_1 (k4_compos_1 k1_scmpds_2)) = 1) ).
tt(l1_scmpds_6,ax, ((k1_funct_1 (k4_compos_1 k1_scmpds_2) k6_numbers) = (k2_compos_1 k1_scmpds_2)) ).
tt(l1_scmpds_9,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k2_amistd_1 2 k1_scmpds_2 (k3_scmpds_2 A)) = k1_xboole_0) ) ) ).
tt(l1_seqfunc,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  <=>  ( ((k9_xtuple_0 C) = k5_numbers)  &  (! [D:$i] :  ((r2_hidden D k5_numbers) =>  ((v1_funct_1 (k1_funct_1 C D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(l1_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  (B = (k2_nat_1 (k2_nat_1 A 1) C)) ) ) ) ) ) ) ) ) ) ).
tt(l1_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_square_1 A) = (k1_newton A 2)) ) ) ).
tt(l1_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (4 = (k13_newton 2 2))  &  ((k1_newton (k2_xcmplx_0 A B) 2) = (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k1_newton B 2))) ) ) ) ) ) ).
tt(l1_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k1_newton A 3) (k1_newton B 3)) = (k3_xcmplx_0 (k6_xcmplx_0 A B) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B)))) ) ) ) ) ).
tt(l1_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 A B) &  ( (~  (A = B) )  &  (~ (r1_xxreal_0 (k2_nat_1 A 1) B)) ) ) ) ) ) ) ) ).
tt(l1_setwop_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k2_finseq_1 A) (k5_finsub_1 k5_numbers))) ) ).
tt(l1_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r2_hidden A (k2_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (A = C)  &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(l1_sincos10,ax,(r1_tarski (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))).
tt(l1_sin_cos7,ax, (~  (k8_power = 1) ) ).
tt(l1_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 (k6_sin_cos2 A)) &  ( ((k6_sin_cos2 k6_numbers) = 1)  &  ((k3_sin_cos2 k6_numbers) = k6_numbers) ) ) ) ) ).
tt(l1_symsp_1,ax,(m1_subset_1 k6_numbers (k1_tarski k6_numbers))).
tt(l1_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ( ((k9_xtuple_0 (k2_zfmisc_1 A B)) = A)  &  ((k10_xtuple_0 (k2_zfmisc_1 A B)) = B) ) ) ) ) ) ) ) ).
tt(l1_topalg_3,ax, ((u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) = (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k17_borsuk_1))) ).
tt(l1_topalg_4,ax,(r2_hidden 1 (k2_tarski 1 2))).
tt(l1_topalg_5,ax,(r2_hidden k6_numbers k4_numbers)).
tt(l1_topreal2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden A B))  =>  ((k3_xboole_0 (k1_tarski A) B) = k1_xboole_0) ) ) ) ).
tt(l1_topreal5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_topreala,ax, ((u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) = (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))) ).
tt(l1_toprealb,ax,(r2_hidden k6_numbers k4_numbers)).
tt(l1_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((r2_hidden C (k1_rcomp_1 A B)) => (m1_subset_1 C k1_numbers)) ) ) ) ) ) ).
tt(l1_trees_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_funct_1 (k7_finseq_1 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ).
tt(l1_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((r2_hidden B (k4_finseq_1 C)) | (r2_hidden B (k4_finseq_1 C)))  => (r2_hidden (k1_funct_1 C B) A)) ) ) ) ) ).
tt(l1_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (A = (k2_nat_1 C 1))  &  (~ (r1_xxreal_0 (k3_finseq_1 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(l1_tsep_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((k7_subset_1 A B C) = k1_xboole_0)  => (r1_xboole_0 B (k7_subset_1 A D C))) ) ) ) ) ) ) ) ).
tt(l1_uniroots,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (v1_xboole_0 A))  <=> (r1_xxreal_0 1 A)) ) ) ).
tt(l1_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_urysohn1 k6_numbers) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 k6_numbers) (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski B (k1_funct_1 D k6_numbers)) &  ( (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_funct_1 D 1)))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers (k1_urysohn1 k6_numbers)) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers (k1_urysohn1 k6_numbers)) =>  ( (~ (r1_xxreal_0 F E))  =>  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 k6_numbers) D E) A) &  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 k6_numbers) D F) A) & (r1_tarski (k2_pre_topc A (k4_urysohn1 A (k1_urysohn1 k6_numbers) D E)) (k4_urysohn1 A (k1_urysohn1 k6_numbers) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 B) = (k4_finseq_1 A))  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(l1_valued_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 A (k3_xboole_0 B C)) = (k3_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(l1_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) =>  ((k5_struct_0 A) = (k1_group_1 A)) ) ) ) ).
tt(l1_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k4_vectsp_1 A B (k5_algstr_0 A C D) E) = (k5_algstr_0 B (k4_vectsp_1 A B C E) (k4_vectsp_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_vectsp_9,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  ((k2_xboole_0 (k6_subset_1 A (k1_tarski B)) (k1_tarski B)) = A) ) ) ) ).
tt(l1_waybel11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  ( (D = F)  &  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (r1_orders_2 A C D)) ) )  => (r1_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l1_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (v1_xboole_0 (a_3_1_waybel12 A B C)))  &  ((v1_finset_1 (a_3_1_waybel12 A B C)) & (m1_subset_1 (a_3_1_waybel12 A B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(l1_waybel22,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((r1_tarski B (k9_setfam_1 (u1_struct_0 A))) =>  ((k2_yellow_0 A (k3_tarski B)) = (k2_yellow_0 A (a_2_2_waybel22 A B))) ) ) ) ) ).
tt(l1_waybel35,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k2_xboole_0 (k1_tarski A) C)) &  ( (~  (B = A) )  &  (~ (r2_hidden B C)) ) ) ) ) ) ) ).
tt(l1_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  &  ((v1_waybel_0 (k1_waybel_3 A B) A) &  ((v12_waybel_0 (k1_waybel_3 A B) A) & (m1_subset_1 (k1_waybel_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A (k1_waybel_3 A B))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) => (r1_tarski (k1_waybel_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(l1_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_2 A) <=>  (! [B:$i] :  ((r2_hidden B (k1_relat_1 A)) => (r2_hidden (k4_tarski B B) A)) ) ) ) ) ).
tt(l1_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ( (~  ((r2_hidden A k2_arytm_2) &  ((r2_hidden B k2_arytm_2) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = C)  &  ( (B = D)  & (r1_arytm_2 C D)) ) ) ) ) ) ) ) )  &  ( (~  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  ((r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = (k4_tarski k6_numbers C))  &  ( (B = (k4_tarski k6_numbers D))  & (r1_arytm_2 D C)) ) ) ) ) ) ) ) )  &  (~  ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(l1_yellow12,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  =>  ((k1_binop_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B)) C D) = (k4_tarski D C)) ) ) ) ) ) ).
tt(l1_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_tarski A) B) <=> (r2_hidden A B)) ) ) ).
tt(l1_zfrefle1,ax,(r2_hidden k1_xboole_0 k4_ordinal1)).
tt(l200_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k2_jgraph_6 (k1_real_1 1) 1 (k1_real_1 3) 3)) => (r1_tarski (k2_jgraph_6 (k1_real_1 1) 1 (k1_real_1 3) 3) (k1_topreal9 2 A 10))) ) ) ).
tt(l202_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) &  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ((v1_jordan21 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ((v1_jordan21 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((r1_topreal1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers) B) &  ((r1_topreal1 (k15_euclid 2) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers) C) &  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k7_domain_1 (u1_struct_0 (k15_euclid 2)) (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)))  &  ((r2_hidden (k1_jordan21 A) B) &  ((r2_hidden (k2_jordan21 A) C) &  ( ((k6_pscomp_1 A) = (k6_pscomp_1 B))  &  ((k8_pscomp_1 A) = (k8_pscomp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l204_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 1 (k5_xcmplx_0 A))) ) ) ) ).
tt(l205_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan24 2 A (k19_euclid (k1_real_1 1) k6_numbers) (k19_euclid 1 k6_numbers)) => (v1_jordan1 A)) ) ) ).
tt(l205_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~  (D = k6_numbers) )  &  (~  ((k1_binop_1 (k12_zmodul01 A) (k3_xcmplx_0 C D) B) = (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l206_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_jordan1 A)) ) ).
tt(l206_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers A))  => (r1_xxreal_0 (k7_xcmplx_0 A B) 1)) ) ) ) ) ).
tt(l206_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ( ( (C = k6_numbers)  |  (D = k6_numbers) )  =>  ((k1_binop_1 (k12_zmodul01 A) (k3_xcmplx_0 C D) B) = (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B))) ) ) ) ) ) ) ) ) ) ).
tt(l207_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k7_xcmplx_0 A B) 1)) ) ) ) ) ).
tt(l20_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) )  =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ( (B = (k3_rlvect_1 A C (k1_rlvect_1 A D G)))  &  ( (E = (k3_rlvect_1 A C (k1_rlvect_1 A F H)))  & (r1_anproj_1 A B E)) )  =>  ( (G = k6_numbers)  | (r2_anproj_1 A C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 (k1_arytm_1 A B) C) <=> (r1_arytm_2 A (k7_arytm_2 C B))) ) ) ) ) ) ) ).
tt(l20_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ( ((k4_arytm_2 A) = k11_arytm_3)  <=>  (A = k11_arytm_3) ) ) ) ).
tt(l20_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) & (l1_funcsdom A)) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_rlvect_1 A B 1) = B) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( (C = D)  =>  ((k1_rlvect_1 (k5_c0sp2 A) C B) = (k1_rlvect_1 (k11_c0sp1 (u1_struct_0 A)) D B)) ) ) ) ) ) ) ) ) ) ).
tt(l20_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k2_cc0sp2 A)) => (r2_hidden B (k2_cc0sp1 (u1_struct_0 A)))) ) ) ) ).
tt(l20_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = k6_numbers)  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l20_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (r1_tarski (k5_finsub_1 B) A)) ) ) ) ).
tt(l20_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_arytm_0 A) = (k1_real_1 A)) ) ) ).
tt(l20_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((k7_nat_d (k5_card_1 (k4_compos_1 A)) 1) = k6_numbers) ) ) ).
tt(l20_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v4_lattice3 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_funct_1 C) &  ( ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_lattices A D E) <=> (r3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) )  => (m1_lattice4 C A B)) ) ) ) ) ) ) ).
tt(l20_connsp_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_connsp_1 C A)) ) )  &  ((k1_struct_0 A) = (k5_setfam_1 (u1_struct_0 A) B)) ) ) ) ) ) ).
tt(l20_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_tarski B C) => (r1_tarski (k1_convex1 A B D) (k1_convex1 A C D))) ) ) ) ) ) ) ) ) ).
tt(l20_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) & (v2_cqc_the1 (k8_cqc_lang A D E) A))  => (v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_dtconstr,ax,(r2_hidden c2__dtconstr (k1_lang1 k5_dtconstr))).
tt(l20_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ( (D = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)))  &  (E = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) C B))) )  =>  ( ((k3_complex1 (k1_complex2 D E)) = (k7_real_1 (k8_real_1 (k9_real_1 (k17_euclid A) (k17_euclid B)) (k9_real_1 (k17_euclid C) (k17_euclid B))) (k8_real_1 (k9_real_1 (k18_euclid A) (k18_euclid B)) (k9_real_1 (k18_euclid C) (k18_euclid B)))))  &  ( ((k4_complex1 (k1_complex2 D E)) = (k7_real_1 (k1_real_1 (k8_real_1 (k9_real_1 (k17_euclid A) (k17_euclid B)) (k9_real_1 (k18_euclid C) (k18_euclid B)))) (k8_real_1 (k9_real_1 (k18_euclid A) (k18_euclid B)) (k9_real_1 (k17_euclid C) (k17_euclid B)))))  &  ( ((k17_complex1 D) = (k7_square_1 (k7_real_1 (k5_square_1 (k9_real_1 (k17_euclid A) (k17_euclid B))) (k5_square_1 (k9_real_1 (k18_euclid A) (k18_euclid B))))))  &  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k17_complex1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ( ((k5_euclid_8 (k9_euclid 3 B A) C) = (k9_euclid 3 (k5_euclid_8 B C) A))  &  ((k5_euclid_8 (k9_euclid 3 B A) C) = (k5_euclid_8 B (k9_euclid 3 C A))) ) ) ) ) ) ) ) ).
tt(l20_euler_1,ax, (! [A:$i] :  ((r2_hidden A a_0_0_euler_1) <=>  (A = 1) ) ) ).
tt(l20_fib_num,ax, (~ (r1_xxreal_0 3 (k7_square_1 5))) ).
tt(l20_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((k3_finseq_1 B) = 1)  =>  ((k1_finsop_1 A B C) = (k1_funct_1 B 1)) ) ) ) ) ) ) ) ).
tt(l20_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  => (v2_fomodel0 k1_xboole_0 A B)) ) ) ) ).
tt(l20_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k13_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp)) = (k2_binarith (k2_binarith (k2_binarith G H) I) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H C))  => (r1_xxreal_0 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D (k1_fuzzy_1 (k2_zfmisc_1 B C) E F) G H))) (k1_square_1 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E G H))) (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D F G H)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r3_analmetr A B C D E F G) => (r3_analmetr A B C E D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( ((r5_glib_000 A B) &  (C = D) )  =>  ((k1_glib_002 A C) = (k1_glib_002 B D)) ) ) ) ) ) ) ) ) ) ).
tt(l20_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 C))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_gr_cy_3,ax, ((k13_newton 2 2) = 4) ).
tt(l20_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_rewrite1 (k3_polyred A B C F) D E) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_rewrite1 (k3_polyred A B C F) D E) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  ((v15_algstr_0 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) &  ((v1_group_3 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) B) & (m1_group_2 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) B)) ) ) ) ) ) ) ).
tt(l20_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( ( (D = (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B))  & (v2_compts_1 B (k3_pcomps_1 A)))  => (v4_xxreal_2 D)) ) ) ) ) ) ) ) ) ).
tt(l20_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  (~  ( (E = (k4_finseqop (k1_euclid A) k1_numbers C (k1_pdiff_1 D A)))  &  ((k1_seq_1 B D) = (k18_rvsum_1 E)) ) ) ) ) ) ) ) )  =>  (B = (k5_euclid_7 A C)) ) ) ) ) ) ) ) ).
tt(l20_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (~  ( (~  ((k3_integra1 B) = k6_numbers) )  &  ((r2_hidden A (k1_rvsum_1 (k9_integra1 B C))) &  (! [D:$i] :  ((m1_integra1 D B) =>  (~  ((r2_hidden D (k9_xtuple_0 (k9_integra1 B C))) &  ( (A = (k1_seq_1 (k9_integra1 B C) D))  &  (~ (r1_xxreal_0 (k1_seq_1 D 1) (k5_seq_4 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A C) & (r1_xxreal_0 C B))  =>  ((r2_hidden C (k3_integra5 A B)) &  ((r1_tarski (k3_integra5 A C) (k3_integra5 A B)) & (r1_tarski (k3_integra5 C B) (k3_integra5 A B))) ) ) ) ) ) ) ) ) ).
tt(l20_jgraph_6,ax, ((k18_euclid (k19_euclid 1 k6_numbers)) = k6_numbers) ).
tt(l20_jordan,ax, ((u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) = (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))) ).
tt(l20_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  ( (~ (v2_struct_0 (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)))  &  ((v10_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)) &  ((v14_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B)) & (l3_lattices (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B))) ) ) ) ) ) ) ).
tt(l20_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r2_funct_2 k5_numbers k1_numbers (k1_lp_space (k2_rsspace (k1_rlvect_1 B C D)) A) (k26_valued_1 k5_numbers k1_numbers (k1_lp_space (k2_rsspace C) A) (k4_power (k18_complex1 D) A)))) ) ) ) ) ) ) ) ) ) ).
tt(l20_matrprob,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) => (r1_xxreal_0 A (k3_matrix_1 k1_numbers B C D))) ) ) ) )  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 (k1_matrprob k1_numbers B C))))  => (r1_xxreal_0 A (k1_seq_1 (k1_matrprob k1_numbers B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l20_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) (k3_struct_0 A))) ) ) ) ) ) ) ).
tt(l20_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  (A = 1) )  &  ( (~  (B = 1) )  &  ( (~  (C = 1) )  &  (~  ( (k6_numbers = (k10_binop_2 (k11_binop_2 (k11_binop_2 A B) C) (k11_binop_2 (k11_binop_2 (k10_binop_2 1 A) (k10_binop_2 1 B)) (k10_binop_2 1 C))))  <=>  ((k11_binop_2 (k11_binop_2 (k12_binop_2 A (k10_binop_2 1 A)) (k12_binop_2 B (k10_binop_2 1 B))) (k12_binop_2 C (k10_binop_2 1 C))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_metric_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ( ((k6_square_1 (k2_xcmplx_0 A B)) = k6_numbers)  <=>  ( (A = k6_numbers)  &  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(l20_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_midsp_1 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_midsp_1 A))) &  ((k1_midsp_2 (k15_midsp_1 A) C) = B) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_midsp_1 A))) =>  ( ((k1_midsp_2 (k15_midsp_1 A) B) = (k4_struct_0 (k15_midsp_1 A)))  =>  (B = (k4_struct_0 (k15_midsp_1 A))) ) ) ) ) ) ) ).
tt(l20_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k4_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k4_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k4_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers k4_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers k4_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k4_numbers)))) )  =>  ( ( ((k8_nat_1 k4_numbers G k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers H k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers C k6_numbers) = A)  &  ( ((k8_nat_1 k4_numbers E k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers J k6_numbers) = k6_numbers)  &  ( ((k8_nat_1 k4_numbers I k6_numbers) = 1)  &  ( ((k8_nat_1 k4_numbers D k6_numbers) = B)  &  ( ((k8_nat_1 k4_numbers F k6_numbers) = k6_numbers)  &  (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ( ((k8_nat_1 k4_numbers E (k2_nat_1 K 1)) = (k5_int_1 (k8_nat_1 k4_numbers C K) (k8_nat_1 k4_numbers D K)))  &  ( ((k8_nat_1 k4_numbers F (k2_nat_1 K 1)) = (k6_int_1 (k8_nat_1 k4_numbers C K) (k8_nat_1 k4_numbers D K)))  &  ( ((k8_nat_1 k4_numbers G (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers J K))  &  ( ((k8_nat_1 k4_numbers H (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers I K))  &  ( ((k8_nat_1 k4_numbers C (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers D K))  &  ( ((k8_nat_1 k4_numbers J (k2_nat_1 K 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers G K) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 K 1)) (k8_nat_1 k4_numbers J K))))  &  ( ((k8_nat_1 k4_numbers I (k2_nat_1 K 1)) = (k6_xcmplx_0 (k8_nat_1 k4_numbers H K) (k3_xcmplx_0 (k8_nat_1 k4_numbers E (k2_nat_1 K 1)) (k8_nat_1 k4_numbers I K))))  &  ((k8_nat_1 k4_numbers D (k2_nat_1 K 1)) = (k8_nat_1 k4_numbers F (k2_nat_1 K 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ( (~  ((k8_nat_1 k4_numbers D K) = k6_numbers) )  =>  ((k2_xcmplx_0 (k3_xcmplx_0 (k8_nat_1 k4_numbers G (k2_nat_1 K 1)) A) (k3_xcmplx_0 (k8_nat_1 k4_numbers H (k2_nat_1 K 1)) B)) = (k8_nat_1 k4_numbers C (k2_nat_1 K 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_numbers,ax,(r2_hidden 2 k4_ordinal1)).
tt(l20_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v6_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l20_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_xxreal_0 B k6_numbers) =>  ((k3_polynom8 A C B) = (k11_algstr_0 A (k3_polynom8 A C (k1_int_2 B)))) ) ) ) ) ) ) ) ).
tt(l20_pre_ff,ax, ((k2_pre_ff c2__pre_ff k6_numbers) = c1__pre_ff) ).
tt(l20_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) => (m2_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 (k4_tarski 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) B)) C) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ) ) ) ) ).
tt(l20_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_hidden C (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(l20_realset2,ax, ((k5_binop_1 2 k2_realset2 (k1_funct_7 k6_numbers 2) (k1_funct_7 1 2)) = (k1_funct_7 k6_numbers 2)) ).
tt(l20_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_classes1 A B) => (r1_xxreal_0 (k4_rfinseq2 B) (k4_rfinseq2 A))) ) ) ) ) ).
tt(l20_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  (! [B:$i] :  ((m1_subset_1 B k3_scm_inst) =>  ( (A = B)  =>  ((k3_compos_0 k2_scmfsa_i (k2_compos_0 k2_scmfsa_i A)) = (k3_compos_0 k3_scm_inst (k2_compos_0 k3_scm_inst B))) ) ) ) ) ) ).
tt(l20_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  ( ((k2_compos_0 k3_scm_inst A) = 6)  =>  ((k4_finseq_1 (k5_xtuple_0 A)) = (k2_finseq_1 1)) ) ) ) ).
tt(l20_scmpds_9,ax, (~ (v1_int_1 (k13_complex1 5 3))) ).
tt(l20_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ( ((r1_tarski k4_scmp_gcd D) &  ( ((k5_memstr_0 2 k1_scmpds_2 C) = 5)  &  ( (A = (k1_funct_1 C k3_scmp_gcd))  &  ( ((k1_funct_1 C k2_scmp_gcd) = k6_numbers)  & (r1_xxreal_0 B (k2_nat_1 A 1))) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 3)) k6_numbers) |  ((r1_xxreal_0 B 1) |  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D C 7) (k1_scmp_gcd B)) = (k1_funct_1 C (k1_scmp_gcd B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l20_scmring3,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k9_xtuple_0 (k9_finseq_1 B))) =>  (A = 1) ) ) ) ).
tt(l20_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_scmringi A)) =>  ( ((k2_compos_0 (k1_scmringi A) B) = 7)  =>  ((k4_finseq_1 (k5_xtuple_0 B)) = (k2_finseq_1 1)) ) ) ) ) ) ).
tt(l20_scpisort,ax, ((k5_card_1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) = 16) ).
tt(l20_scpqsort,ax, ((k5_card_1 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers)))))) = 11) ).
tt(l20_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k3_xcmplx_0 (k2_xcmplx_0 1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 A B)) C)) (k13_complex1 (k6_square_1 (k3_xcmplx_0 A C)) B)) = (k8_complex1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 A C)) B) (k13_complex1 A (k6_square_1 (k3_xcmplx_0 C B))))) ) ) ) ) ) ) ).
tt(l20_sincos10,ax, ((r2_hidden (k10_real_1 k32_sin_cos 4) (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) & (r2_hidden (k10_real_1 k32_sin_cos 2) (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l20_sin_cos9,ax, ((k2_funct_1 k2_sin_cos9) = (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos))) ).
tt(l20_topgen_3,ax, ((v1_tops_2 c1__topgen_3 k2_topgen_3) &  ((v1_cantor_1 c1__topgen_3 k2_topgen_3) & (m1_subset_1 c1__topgen_3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 k2_topgen_3))))) ) ).
tt(l20_topreal2,ax,(r2_hidden (k19_euclid k6_numbers k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)))).
tt(l20_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) A)) ) ).
tt(l20_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v3_xxreal_2 (k1_integra2 A B)) =>  ((r1_xxreal_0 B k6_numbers) | (v3_xxreal_2 A)) ) ) ) ) ) ).
tt(l20_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((u1_struct_0 C) = D)  => (v1_vectsp_4 D A B)) ) ) ) ) ) ) ) ) ).
tt(l20_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((k4_vectsp_6 A B (k2_vectsp_6 A B)) = (k4_struct_0 B)) ) ) ) ) ).
tt(l20_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A))))))  => (r1_tarski (a_2_7_waybel33 A B) (k2_zfmisc_1 (u1_struct_0 A) (k9_setfam_1 (u1_struct_0 A))))) ) ) ) ).
tt(l20_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(l20_zf_fund1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k4_zf_fund1 (k7_domain_1 k1_zf_lang A B)) = (k7_domain_1 k5_numbers (k3_zf_fund1 A) (k3_zf_fund1 B))) ) ) ) ) ).
tt(l20_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden A B))  => (r1_xboole_0 (k1_tarski A) B)) ) ) ).
tt(l20_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = k6_numbers)  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l216_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~  (A = k6_numbers) )  &  ( (A = (k5_xcmplx_0 A))  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ).
tt(l21_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k1_aff_1 A B C) (k1_aff_1 A C B))) ) ) ) ) ) ).
tt(l21_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_algseq_1 A (k4_struct_0 A))) =>  ((k1_algseq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(l21_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_altcat_3 (k8_altcat_1 A B) A B B) & (v4_altcat_3 (k8_altcat_1 A B) A B B)) ) ) ) ) ).
tt(l21_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 A B) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 B))) ) )  & (v2_extpro_1 A 2 k1_ami_3)) ) ) ) ).
tt(l21_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( ((k1_rlvect_1 A B D) = C)  &  ( (~  (D = k6_numbers) )  &  ( (~ (v9_struct_0 B A))  & (v9_struct_0 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((r1_arytm_2 (k7_arytm_2 C A) B) <=> (r1_arytm_2 C (k1_arytm_1 B A))) ) ) ) ) ) ) ) ).
tt(l21_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k3_arytm_2 (k4_arytm_2 A)) = A) ) ) ).
tt(l21_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) => (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) )  => (r1_xxreal_0 k6_numbers (k6_series_1 A B))) ) ) ) ) ).
tt(l21_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k5_c0sp2 A) B C) = (k6_algstr_0 (k11_c0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k1_binop_1 (k1_cfuncdom A) (k1_funct_1 (k3_cfuncdom A) (k4_tarski D B)) (k1_funct_1 (k3_cfuncdom A) (k4_tarski D C))) = (k1_funct_1 (k3_cfuncdom A) (k4_tarski D (k1_funcsdom A k2_numbers (k1_cfuncdom A) B C)))) ) ) ) ) ) ) ) ) ).
tt(l21_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k2_arytm_0 A B) = (k3_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l21_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((k62_valued_1 (k4_compos_1 A)) = k6_numbers) ) ) ).
tt(l21_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  (~  ( ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (u2_conlat_1 A B)) = (u3_conlat_1 A B))  & (v5_conlat_1 B A)) ) ) ) ) ) ).
tt(l21_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_convex1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(l21_convfun1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k9_binop_2 (k11_binop_2 E C) (k11_binop_2 F D)) = (k3_supinf_2 (k1_extreal1 (k1_measure6 E) A) (k1_extreal1 (k1_measure6 F) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (k1_cqc_the1 A (k1_cqc_the1 A B)) (k1_cqc_the1 A B))) ) ) ) ).
tt(l21_dtconstr,ax,(r1_tarski (k1_lang1 k5_dtconstr) (k6_domain_1 (u1_struct_0 k5_dtconstr) c2__dtconstr))).
tt(l21_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = (k1_endalg A))  &  (! [C:$i] :  ((r2_hidden C (k1_endalg A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) ) )  =>  ((k10_xtuple_0 B) = (k4_endalg (k6_msualg_1 A) (k9_msualg_1 A))) ) ) ) ) ) ).
tt(l21_euler_1,ax, ((k5_card_1 (k1_tarski 1)) = (k1_euler_1 1)) ).
tt(l21_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_fdiff_3 A B) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k1_numbers A)) &  ((r2_hidden D (k1_rcomp_1 (k9_real_1 B C) B)) &  ((k1_seq_1 A D) = k6_numbers) ) ) ) ) ) ) ) ) )  |  ((r4_fdiff_3 (k6_rfunct_1 k1_numbers k1_numbers A) B) &  ((k1_fdiff_3 B (k6_rfunct_1 k1_numbers k1_numbers A)) = (k1_real_1 (k10_real_1 (k1_fdiff_3 B A) (k5_square_1 (k1_seq_1 A B))))) ) ) ) ) ) ) ) ).
tt(l21_fib_num,ax, (~ (r1_xxreal_0 k1_fib_num 1)) ).
tt(l21_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 E A) &  ((v1_binop_1 E A) &  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 D F) = (k1_binop_1 E (k1_funct_1 B F) (k1_funct_1 C F))) ) ) ) ) ) ) ) )  =>  ((k1_finsop_1 A D E) = (k5_binop_1 A E (k1_finsop_1 A B E) (k1_finsop_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k9_xtuple_0 (k13_funct_3 A B)) = (k2_finseq_1 (k3_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)))) ) ) ) ) ).
tt(l21_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) (k8_eqrel_1 A B)) =>  ( ((r2_hidden C E) & (r2_hidden D E))  => (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ) ).
tt(l21_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp)))  &  ( (H = (k1_funct_1 F (k4_tarski (k10_finseq_1 E D) k2_twoscomp)))  &  (I = (k1_funct_1 F (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp))) ) )  =>  ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k9_gfacirc1 (k12_gfacirc1 A B C) E D)) = (k1_binarith (k1_binarith G H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_funcsdom,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_funct_2 C B k1_numbers (k9_funct_2 B k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D B k1_numbers (k9_funct_2 B k1_numbers)) =>  ((k1_funcsdom B k1_numbers (k5_funcsdom B) (k2_binop_1 k1_numbers (k9_funct_2 B k1_numbers) (k9_funct_2 B k1_numbers) (k7_funcsdom B) A C) (k2_binop_1 k1_numbers (k9_funct_2 B k1_numbers) (k9_funct_2 B k1_numbers) (k7_funcsdom B) A D)) = (k2_binop_1 k1_numbers (k9_funct_2 B k1_numbers) (k9_funct_2 B k1_numbers) (k7_funcsdom B) A (k1_funcsdom B k1_numbers (k5_funcsdom B) C D))) ) ) ) ) ) ) ) ).
tt(l21_funct_6,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) )  =>  ((k1_funct_6 A) = A) ) ) ).
tt(l21_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r3_analmetr A B C D E F G) => (r3_analmetr A D E B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_002 B) & (m1_glib_000 B A))  =>  ((v9_glib_000 B A) => (v1_glib_002 A)) ) ) ) ) ).
tt(l21_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 C))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_gr_cy_3,ax, ((k13_newton 2 3) = 8) ).
tt(l21_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (~  ((r1_rewrite1 (k3_polyred A B C F) D E) &  ( (~  (E = D) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r5_polyred A B C D G F) & (r1_rewrite1 (k3_polyred A B C F) G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_group_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  (! [F:$i] :  ( ((v15_algstr_0 F) & (m1_group_2 F B))  =>  ( ( ((g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)) = (g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)))  &  ( (C = D)  &  (E = F) ) )  =>  ( ((k11_group_2 A E C) = (k11_group_2 B F D))  &  ((k12_group_2 A E C) = (k12_group_2 B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 B C))) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 B C)) (k1_substlat B C)) =>  (~  ((r2_hidden A (k4_substlat B C D (k3_heyting2 B C D E))) &  (! [F:$i] :  (~  ((r2_hidden F E) & (r1_tarski F A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ((r8_pboole k10_newton C (k15_funct_7 k10_newton k5_numbers (k8_funcop_1 k5_numbers k10_newton k6_numbers) A B)) &  ( ((k1_polynom2 k10_newton C) = (k1_tarski A))  &  ((k8_nat_3 k10_newton C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid A) C E)) (k7_partfun1 k1_numbers D E))) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  (~  ( (F = (k4_finseqop (k1_euclid A) k1_numbers C (k1_pdiff_1 E A)))  &  ((k1_seq_1 B E) = (k18_rvsum_1 F)) ) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid B) (k18_rvsum_1 D))) ) ) ) ) ) ) ) ) ).
tt(l21_jgraph_6,ax, ((k17_euclid (k19_euclid k6_numbers (k1_real_1 1))) = k6_numbers) ).
tt(l21_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 C B)) (k2_nat_1 A 1)))  & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 C (k2_nat_1 B 1))) (k7_nat_d (k4_nat_1 2 A) 1))) ) ) ) ) ) ) ) ).
tt(l21_jordan20,ax, (~  ((k2_struct_0 k5_topmetr) = k1_xboole_0) ) ).
tt(l21_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (r1_xxreal_0 A (k9_real_1 (k5_real_1 A 1) 1))) ) ) ).
tt(l21_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (v1_pscomp_1 (k8_funcop_1 k1_numbers (u1_struct_0 A) B) A)) ) ) ) ).
tt(l21_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) =>  ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ) ).
tt(l21_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k4_series_1 (k1_lp_space (k2_rsspace (k1_rlvect_1 B C D)) A)) = (k8_real_1 (k4_power (k18_complex1 D) A) (k4_series_1 (k1_lp_space (k2_rsspace C) A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_matrprob,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) => (r1_xxreal_0 A (k3_matrix_1 k1_numbers B C D))) ) ) ) )  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 (k8_matrix_1 k1_numbers B C))))  => (r1_xxreal_0 A (k1_seq_1 (k8_matrix_1 k1_numbers B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l21_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) ) )  => (m1_subset_1 B (u1_struct_0 (k15_euclid A)))) ) ) ) ).
tt(l21_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( (k6_numbers = (k10_binop_2 (k11_binop_2 (k11_binop_2 B A) C) (k11_binop_2 (k11_binop_2 (k10_binop_2 1 B) (k10_binop_2 1 A)) (k10_binop_2 1 C))))  &  ((k9_binop_2 (k10_binop_2 1 A) (k11_binop_2 A B)) = k6_numbers) )  =>  ( (A = 1)  |  ((k9_binop_2 (k10_binop_2 1 B) (k11_binop_2 B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l21_ndiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 A B)) ) )  => (r1_xxreal_0 A k6_numbers)) ) ) ).
tt(l21_numbers,ax, ((v3_ordinal1 2) & (m1_subset_1 2 k5_arytm_3)) ).
tt(l21_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v7_o_ring_1 B A)) ) ) ) ) ).
tt(l21_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_geomtrap A B C B D) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( ((k5_algstr_0 A C B) = (k1_rlvect_1 A (k5_algstr_0 A D B) E))  &  (~  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k1_funct_1 (k1_pnproc_1 B) A) = k6_numbers) ) ) ) ).
tt(l21_pre_ff,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_nat_1 A 2) = (k4_nat_1 2 B))  =>  ((k2_pre_ff c2__pre_ff (k2_nat_1 A 1)) = (k8_finseq_1 k5_numbers (k2_pre_ff c2__pre_ff A) (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers (k2_pre_ff c2__pre_ff A) B)))) ) ) )  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_nat_1 A 2) = (k2_nat_1 (k4_nat_1 2 B) 1))  =>  ((k2_pre_ff c2__pre_ff (k2_nat_1 A 1)) = (k8_finseq_1 k5_numbers (k2_pre_ff c2__pre_ff A) (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers (k2_pre_ff c2__pre_ff A) B) (k7_partfun1 k5_numbers (k2_pre_ff c2__pre_ff A) (k1_nat_1 B 1)))))) ) ) ) ) ) ) ).
tt(l21_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) )  => (v1_prvect_2 A)) ) ).
tt(l21_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~ (r2_hidden (k3_quaterni k1_numbers k6_numbers 1 2 3 A B C D) k1_numbers)) ) ) ) ) ) ) ) ) ).
tt(l21_realset2,ax, ((k5_binop_1 2 k2_realset2 (k1_funct_7 1 2) (k1_funct_7 k6_numbers 2)) = (k1_funct_7 k6_numbers 2)) ).
tt(l21_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_tarski (u1_struct_0 (k2_rlsub_2 A B C)) (u1_struct_0 B))) ) ) ) ) ) ).
tt(l21_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k3_convex1 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(l21_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (r1_tarski (u1_struct_0 (k2_rusub_2 A B C)) (u1_struct_0 B))) ) ) ) ) ) ).
tt(l21_scmfsa_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_scmfsa_1 k3_scmfsa_1) =>  ((k3_funct_2 k1_scmfsa_1 3 k4_scmfsa_1 A) = 2) ) ) ).
tt(l21_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 k3_scm_inst)) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  (~  (A = 8) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_scmpds_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 A) (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k18_complex1 A)) 4)) 2) 2) A) = (k4_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 A) (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k18_complex1 A)) 4)) (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k18_complex1 A)) 4)) 2) 2) A))) ) ) ) ).
tt(l21_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  (~  ( (~  (B = k6_numbers) )  &  ( (~  (B = 1) )  &  ( (~  (B = 2) )  &  ( (~  (B = 3) )  &  ( (~  (B = 4) )  &  ( (~  (B = 5) )  &  ( (~  (B = 6) )  &  (~  (B = 7) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k1_scmp_gcd 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 6)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) k2_scmp_gcd) = k6_numbers)  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1))) ) ) ) ) ) ) ) ).
tt(l21_scpqsort,ax, ((k5_card_1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) = 9) ).
tt(l21_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k9_complex1 (k8_complex1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 A B)) C) (k13_complex1 B (k6_square_1 (k3_xcmplx_0 A C)))) (k13_complex1 (k6_square_1 (k3_xcmplx_0 C A)) B)) = (k2_xcmplx_0 (k13_complex1 A (k6_square_1 (k3_xcmplx_0 C B))) 1)) ) ) ) ) ) ) ).
tt(l21_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))).
tt(l21_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k10_binop_2 1 (k3_square_1 A)) k6_numbers)) ) ) ) ) ).
tt(l21_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l21_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (v6_tbsp_1 (k9_metric_1 A B C) A)) ) ) ) ) ) ) ).
tt(l21_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_6 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  ((r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  ((v5_pre_topc (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) (k2_borsuk_1 k5_topmetr k5_topmetr) A) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) J k6_numbers) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 A) (k3_topalg_4 A B k5_topmetr G) J))  &  ( ((k1_binop_1 (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) J 1) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 A) (k3_topalg_4 A B k5_topmetr H) J))  &  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) k6_numbers K) = C)  &  ((k1_binop_1 (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) 1 K) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_topreal2,ax,(r2_hidden (k19_euclid k6_numbers k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)))).
tt(l21_uniform1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  & (r1_xxreal_0 (k7_partfun1 k1_numbers A (k2_nat_1 B 1)) (k7_partfun1 k1_numbers A B))) ) ) ) )  => (v5_valued_0 A)) ) ) ).
tt(l21_waybel18,ax,(v6_pre_topc k9_waybel18)).
tt(l21_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) => (v1_waybel25 B)) ) ) ) ) ) ) ).
tt(l21_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((r2_hidden D (k1_binop_1 (u1_altcat_1 (k5_waybel34 A)) B C)) <=>  ((r2_hidden B (u1_struct_0 (k5_waybel34 A))) &  ((r2_hidden C (u1_struct_0 (k5_waybel34 A))) &  ((v3_lattice3 B) &  ((v3_lattice3 C) & (v18_waybel_0 D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l21_wellord2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ((v2_wellord1 B) &  ((r2_wellord2 A (k1_relat_1 B)) &  (! [C:$i] :  ((v1_relat_1 C) =>  (~ (r2_wellord1 C A)) ) ) ) ) ) ) ) ) ).
tt(l21_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  ((r1_nat_d A B) <=> (m2_subset_1 (k7_xcmplx_0 B A) k1_numbers k5_numbers)) ) ) ) ) ) ).
tt(l21_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(l21_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  ((v4_yellow_0 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) (u1_waybel_0 A B)) B) & (m1_yellow_0 (g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) (u1_waybel_0 A B)) B)) ) ) ) ) ).
tt(l21_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)))  => (r2_tarski A (k4_zf_fund1 A))) ) ).
tt(l22_algstr_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  ((k6_algstr_0 k8_algstr_0 A (k5_struct_0 k8_algstr_0)) = A) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  ((k6_algstr_0 k8_algstr_0 (k5_struct_0 k8_algstr_0) A) = A) ) ) ) ).
tt(l22_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  ( (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))  => (v2_extpro_1 A 2 k1_ami_3)) ) ) ).
tt(l22_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( ((k1_rlvect_1 A (k5_algstr_0 A B C) F) = (k1_rlvect_1 A (k5_algstr_0 A D E) G))  &  ( (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) )  &  ( (~ (r1_analoaf A C B D E))  &  (~ (r1_analoaf A C B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C J) (k1_rlvect_1 A D K)))  &  ( (C = (k3_rlvect_1 A E (k1_rlvect_1 A F H)))  &  (D = (k3_rlvect_1 A E (k1_rlvect_1 A G I))) ) )  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A E (k7_real_1 J K)) (k1_rlvect_1 A F (k8_real_1 J H))) (k1_rlvect_1 A G (k8_real_1 K I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((k1_arytm_1 (k1_arytm_1 A B) C) = (k1_arytm_1 A (k7_arytm_2 C B))) ) ) ) ) ) ) ).
tt(l22_arytm_2,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A a_0_0_arytm_2) &  ((r2_hidden B a_0_0_arytm_2) &  ( (~ (r1_tarski A B))  &  (~ (r1_tarski B A)) ) ) ) ) ) ) ).
tt(l22_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D C) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) )  => (r1_xxreal_0 (k6_series_1 A C) (k6_series_1 B C))) ) ) ) ) ) ) ).
tt(l22_cardfin2,ax, (~ (r1_xxreal_0 (k11_binop_2 2 (k10_binop_2 (k13_newton 365 23) (k12_binop_2 (k3_newton 365) (k3_newton (k7_nat_d 365 23))))) (k13_newton 365 23))) ).
tt(l22_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 2))) =>  ( (B = (k10_finseq_1 A k6_numbers))  =>  ((k1_normsp_0 (k4_real_ns1 2) B) = (k18_complex1 A)) ) ) ) ) ) ).
tt(l22_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k2_xcmplx_0 A B))  =>  ((k3_complex1 C) = (k7_real_1 (k3_complex1 A) (k3_complex1 B))) ) ) ) ) ) ) ) ).
tt(l22_compos_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)))) =>  ((k3_compos_0 (k2_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (k3_xtuple_0 1 k1_xboole_0 k1_xboole_0)) A) = (k6_domain_1 k5_numbers k6_numbers)) ) ) ).
tt(l22_compos_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) =>  (! [C:$i] :  (! [D:$i] :  ( (~ (r2_hidden C (k10_xtuple_0 A)))  => (r1_tarski A (k6_subset_1 B (k16_funcop_1 D C)))) ) ) ) ) ) ) ) ).
tt(l22_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(l22_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k8_real_1 2 (k17_complex1 (k3_xcmplx_0 A B))) (k7_real_1 (k5_square_1 (k17_complex1 A)) (k5_square_1 (k17_complex1 B))))) ) ) ) ).
tt(l22_dtconstr,ax, ((k2_lang1 k5_dtconstr) = a_0_11_dtconstr) ).
tt(l22_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k1_enumset1 A B C) (k1_enumset1 D E F))) ) ) ) ) ) ) ).
tt(l22_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v8_conmetr A) <=> (v11_aff_2 (k3_analmetr A))) ) ) ).
tt(l22_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_nat_1 A 1)) & (v1_finseq_1 B)) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  &  (? [D:$i] :  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ).
tt(l22_fib_num,ax, (~ (r1_xxreal_0 k1_fib_num k6_numbers)) ).
tt(l22_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo E A) &  ( ((k3_finseq_1 B) = k6_numbers)  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 D)) ) ) )  =>  ((k1_finsop_1 A B E) = (k5_binop_1 A E (k1_finsop_1 A C E) (k1_finsop_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) (k8_eqrel_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k8_eqrel_1 A B)) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E C) &  ((r2_hidden F D) & (r2_hidden (k4_tarski E F) B)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  ( ((r1_tarski A B) & (v8_fomodel4 C D E A))  => (v8_fomodel4 C D E B)) ) ) ) ) ) ) ) ).
tt(l22_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k11_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F G)) (k10_margrel1 (k9_margrel1 E) G)))  &  ( ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F))  &  ( ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp)))  &  (H = (k1_funct_1 F D)) )  =>  ((k1_funct_1 (k6_circuit2 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F) (k12_gfacirc1 (k12_gfacirc1 A B C) E D)) = (k2_binarith G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H C))  => (r1_xxreal_0 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C (k1_fuzzy_1 (k2_zfmisc_1 A B) D E) F G H))) (k1_square_1 (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D F G H))) (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C E F G H)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_analmetr A B C) => (r3_analmetr A D E F F B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) <=>  ((k3_glib_002 A) = (k1_tarski (k6_glib_000 A))) ) ) ) ).
tt(l22_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r3_graph_4 A (k12_finseq_1 (u1_struct_0 A) B) k1_xboole_0)) ) ) ) ).
tt(l22_gr_cy_3,ax, ((k13_newton 2 4) = 16) ).
tt(l22_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 A) 1) (k2_nat_1 (k4_nat_1 2 (k2_nat_1 A 1)) 1))) ) ).
tt(l22_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ((v1_int_7 A) &  ((r2_hidden B (k1_polynom2 k10_newton A)) &  ( ((k1_recdef_1 A B) = B)  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k10_newton) &  ((v1_funct_1 D) &  ((v1_partfun1 D k10_newton) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (~  ((v1_int_7 C) &  ( ((k1_polynom2 k10_newton D) = (k1_tarski B))  &  ( ((k8_nat_3 k10_newton D) = B)  &  ( ((k1_polynom2 k10_newton C) = (k7_subset_1 k10_newton (k1_polynom2 k10_newton A) (k1_tarski B)))  &  ( ((k5_relat_1 C (k1_polynom2 k10_newton C)) = (k5_relat_1 A (k1_polynom2 k10_newton C)))  &  ((k8_nat_3 k10_newton A) = (k4_nat_1 (k8_nat_3 k10_newton C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_integr19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_euclid B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_integr15 C B A) &  ((v2_integr15 C B A) &  ((r2_relset_1 A k1_numbers D (k1_nfcont_4 B A C)) & (v3_integra1 D A)) ) )  => (r1_xxreal_0 (k12_euclid (k10_integr15 B A C)) (k12_integra1 A D))) ) ) ) ) ) ) ) ) ).
tt(l22_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ( ((k3_finseq_1 B) = 1)  =>  ( ((k3_integra1 A) = k6_numbers)  |  ( (~ (v1_xboole_0 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B)))  &  ((v5_valued_0 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B)) & (m2_finseq_1 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B) k1_numbers)) ) ) ) ) ) ) ) ).
tt(l22_jgraph_6,ax, ((k18_euclid (k19_euclid k6_numbers (k1_real_1 1))) = (k1_real_1 1)) ).
tt(l22_jordan12,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 B (k3_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k1_goboard5 A B)) &  ((r2_hidden D (k1_goboard5 A B)) & (r1_xxreal_0 (k17_euclid C) (k17_euclid D))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k1_goboard5 A B))) ) ) ) ) ) ) ) ) ) ).
tt(l22_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k2_nat_1 A 1)) &  ( (~  (A = B) )  &  (~  (A = (k7_nat_d B 1)) ) ) ) ) ) ) ) ) ) ).
tt(l22_jordan7,ax,(r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1))).
tt(l22_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k4_power (k4_series_1 (k1_lp_space (k2_rsspace (k1_rlvect_1 B C D)) A)) (k10_real_1 1 A)) = (k8_real_1 (k18_complex1 D) (k4_power (k4_series_1 (k1_lp_space (k2_rsspace C) A)) (k10_real_1 1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A C D)) E) (k8_cqc_lang A (k8_cqc_lang A C (k8_cqc_lang A B D)) E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l22_matrixc1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k12_seq_4 B A) = (k4_finseqop k2_numbers k2_numbers B (k10_funcop_1 k2_numbers k2_numbers k29_binop_2 A (k6_partfun1 k2_numbers)))) ) ) ) ) ).
tt(l22_matrprob,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) => (r1_xxreal_0 A (k3_matrix_1 k1_numbers B C D))) ) ) ) )  <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden D (k2_finseq_1 (k1_matrix_1 B))) & (r2_hidden C (k4_finseq_1 (k9_matrix_1 k1_numbers B D))))  => (r1_xxreal_0 A (k1_seq_1 (k9_matrix_1 k1_numbers B D) C))) ) ) ) ) ) ) ) ) ) ).
tt(l22_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 (k1_mesfunc2 A D)) & (v6_supinf_2 (k2_mesfunc2 A D))) ) ) ) ) ) ) ) ) ).
tt(l22_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_2 A) =>  ((k1_funct_1 A 1) = k6_numbers) ) ) ) ).
tt(l22_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  => (v1_monoid_0 (k9_monoid_1 B A))) ) ) ).
tt(l22_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 (u1_unialg_1 A))) => (m1_subset_1 B (u4_struct_0 (k6_msualg_1 A)))) ) ) ) ) ).
tt(l22_numbers,ax, ((k9_arytm_3 k12_arytm_3 k12_arytm_3) = c2__numbers) ).
tt(l22_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski (k10_xtuple_0 A) C) =>  ((k3_relat_1 A (k5_relat_1 B C)) = (k3_relat_1 A B)) ) ) ) ) ) ) ).
tt(l22_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_o_ring_1 B A) => (v6_o_ring_1 B A)) ) ) ) ) ).
tt(l22_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k5_algstr_0 A B D) (k5_algstr_0 A C D)) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(l22_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A C B))  =>  (B = C) ) ) ) ) ) ) ).
tt(l22_polynom2,ax, (! [A:$i] :  ((k1_polynom2 A (k16_pre_poly A)) = k1_xboole_0) ) ).
tt(l22_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(l22_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_struct_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 D))))) )  =>  ((k3_polynom1 A D (k1_polyred A B D E) (k11_pre_poly A C B)) = (k3_polynom1 A D E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_nat_1 A 2) = (k4_nat_1 2 B))  =>  ((k2_pre_ff c2__pre_ff (k1_nat_1 A 1)) = (k8_finseq_1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) c2__pre_ff A) (k12_finseq_1 k5_numbers (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) c2__pre_ff A) B)))) ) ) )  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_nat_1 A 2) = (k2_nat_1 (k4_nat_1 2 B) 1))  =>  ((k2_pre_ff c2__pre_ff (k1_nat_1 A 1)) = (k8_finseq_1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) c2__pre_ff A) (k12_finseq_1 k5_numbers (k2_nat_1 (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) c2__pre_ff A) B) (k7_partfun1 k5_numbers (k8_nat_1 (k3_finseq_2 k5_numbers) c2__pre_ff A) (k1_nat_1 B 1)))))) ) ) ) ) ) ) ).
tt(l22_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k1_newton (k2_prepower B A) B) = A)  &  ((k2_prepower B (k1_newton A B)) = A) ) ) ) ) ) ) ) ).
tt(l22_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_seq_1 D E) = (k8_real_1 (k1_seq_1 C (k1_funct_1 (k1_uproots A) E)) (k1_seq_1 B (k1_tarski (k1_funct_1 (k1_uproots A) E))))) ) ) )  &  ((k1_mesfunc6 A (k1_random_1 A) (k2_prob_4 A (k1_random_1 A) B) C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_seq_1 (k1_real_3 A B) C) = k6_numbers)  =>  ((k3_funct_2 k5_numbers k5_numbers (k2_real_3 A B) (k1_nat_1 C 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l22_realset2,ax, ((k5_binop_1 2 k2_realset2 (k1_funct_7 1 2) (k1_funct_7 1 2)) = (k1_funct_7 1 2)) ).
tt(l22_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_ring_1 A B))) =>  ( (C = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k1_group_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_ring_1 A B))) =>  ( ((k6_algstr_0 (k2_ring_1 A B) D C) = D)  &  ((k6_algstr_0 (k2_ring_1 A B) C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k1_numbers (k9_funct_2 (u1_struct_0 A) k1_numbers)) => (r1_tarski (k13_pre_poly B) (u1_struct_0 A))) ) ) ) ).
tt(l22_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_rusub_4 A)) &  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (~  ((k1_rusub_4 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l22_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v7_amistd_1 B 3 k1_scmfsa_2) & (v1_scmfsa6b B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski (k3_scmfsa6a B C) A) & (r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) D))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k5_card_1 B))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_funct_4 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D)) (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))  &  ((r1_tarski (k6_compos_1 k1_scmfsa_2 C (k5_card_1 B)) A) &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1)) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r1_extpro_1 3 k1_scmfsa_2 A D) &  ( ((k8_extpro_1 3 k1_scmfsa_2 A D) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A B) C) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))))  &  ((v1_scmfsa6b C) =>  ((k1_funct_1 (k6_extpro_1 3 k1_scmfsa_2 A D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 k3_scm_inst)) =>  ( (A = k6_numbers)  =>  ((k3_compos_0 k3_scm_inst A) = (k6_domain_1 k5_numbers k6_numbers)) ) ) ) ).
tt(l22_scmpds_5,ax,(v2_scmpds_4 (k9_compos_1 k1_scmpds_2 (k5_scmpds_2 (k2_scmpds_2 k6_numbers k6_numbers) k6_numbers)))).
tt(l22_scmpds_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((k2_xcmplx_0 A 1) = (k2_xcmplx_0 A (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k18_complex1 B)) 4) B))) ) ) ) ) ) ).
tt(l22_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k4_scpinvar A B C) = (k2_scmpds_4 (k7_scmpds_2 A B 2) (k3_scmpds_4 (k2_scmpds_4 (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)) C) (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 2)))))) ) ) ) ) ) ) ).
tt(l22_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k1_scmp_gcd 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 6)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 3)) = (k1_funct_1 B (k1_scmp_gcd 3)))  &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 6)) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 6))))  &  ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 6))) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 4))) &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 7 C) =>  ( (C = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) 1))  |  ( (C = (k1_funct_1 B (k1_scmp_gcd 4)))  |  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd C)) = (k1_funct_1 B (k1_scmp_gcd C))) ) ) ) ) )  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers))))  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 6)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 6)) 1))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 4)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) 1)) ) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers))) =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) (k4_xcmplx_0 1))))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd 4)) k6_numbers)))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A) (k1_scmp_gcd 6)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_scpqsort,ax, ((k5_card_1 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) = 11) ).
tt(l22_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 A B)) C)) (k2_xcmplx_0 1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 C B)) A))) (k2_xcmplx_0 1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 C A)) B))) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 2 (k13_complex1 (k6_square_1 (k3_xcmplx_0 C B)) A)) (k13_complex1 A (k6_square_1 (k3_xcmplx_0 C B)))) (k13_complex1 (k6_square_1 (k3_xcmplx_0 C A)) B)) (k13_complex1 B (k6_square_1 (k3_xcmplx_0 A C)))) (k13_complex1 C (k6_square_1 (k3_xcmplx_0 A B)))) (k13_complex1 (k6_square_1 (k3_xcmplx_0 A B)) C))) ) ) ) ) ) ) ).
tt(l22_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers k1_fdiff_9))).
tt(l22_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k4_sin_cos2 (k9_binop_2 A B)) = (k7_real_1 (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ).
tt(l22_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l22_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((v1_finset_1 E) =>  (~  ((r2_hidden E (k4_substlat A B C D)) &  (! [F:$i] :  ((v1_finset_1 F) =>  (~  ((r1_tarski F E) & (r2_hidden F (k4_substlat A B (k3_substlat A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_6 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  ((r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  ((v5_pre_topc (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) (k2_borsuk_1 k5_topmetr k5_topmetr) B) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) J k6_numbers) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 B) (k4_topalg_4 A B k5_topmetr G) J))  &  ( ((k1_binop_1 (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) J 1) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 B) (k4_topalg_4 A B k5_topmetr H) J))  &  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) k6_numbers K) = E)  &  ((k1_binop_1 (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) 1 K) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((v2_topdim_1 B A) &  ((v2_topdim_1 C A) &  ((r1_xxreal_0 (k3_topdim_1 A B) D) & (r1_xxreal_0 (k3_topdim_1 A C) D)) ) )  =>  ((v2_topdim_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A) & (r1_xxreal_0 (k3_topdim_1 A (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(l22_topgen_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ( (~ (v1_topgen_2 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  ((r1_tarski C B) &  ((k1_card_1 C) = (k2_waybel23 A)) ) ) ) ) ) ) ) ).
tt(l22_topreal2,ax,(r2_hidden (k19_euclid k6_numbers 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)))).
tt(l22_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  => (v7_metric_1 (k1_topreal7 A B))) ) ) ) ).
tt(l22_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  => (m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers))) ) ) ) ).
tt(l22_uniform1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  & (r1_xxreal_0 (k7_partfun1 k1_numbers A B) (k7_partfun1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) )  => (v2_uniform1 A)) ) ) ).
tt(l22_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_waybel_9 A)) )  => (v3_waybel11 (k2_struct_0 A) A)) ) ).
tt(l22_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v4_waybel11 C) &  ((v3_waybel_3 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_waybel_9 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D (k3_waybel24 A C)))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)))))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D)))))) )  &  ((v1_waybel27 E) &  ((v2_funct_1 E) &  ((v2_funct_2 E (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) &  ((v2_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 (k3_waybel24 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v4_waybel11 C) &  ((v3_waybel_3 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_waybel_9 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D (k3_waybel24 A C)))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)))))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D)))))) )  &  ((v1_waybel27 E) &  ((v23_waybel_0 E (k3_waybel24 B D) (k3_waybel24 (k2_borsuk_1 B A) C)) &  ((v2_waybel27 F) & (v23_waybel_0 F (k3_waybel24 (k2_borsuk_1 B A) C) (k3_waybel24 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l22_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k6_relat_1 A B)) (k9_xtuple_0 B))) ) ) ).
tt(l22_xreal_0,ax,(m1_subset_1 k6_numbers k2_arytm_2)).
tt(l22_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (~  ( (~ (r2_hidden A k1_numbers))  &  ( (~  (A = k1_xxreal_0) )  &  (~  (A = k2_xxreal_0) ) ) ) ) ) ) ).
tt(l22_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (m1_xxreal_2 B (k2_tarski A B))) ) ) ) ) ).
tt(l22_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k1_xxreal_3 A B) = k1_xxreal_0)  &  ( (~  (A = k1_xxreal_0) )  &  (~  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(l22_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_5_yellow_4 A B C) = (k6_domain_1 (u1_struct_0 A) (k10_lattice3 A B C))) ) ) ) ) ) ) ).
tt(l22_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r2_hidden C (k2_zf_model D)) =>  ((k1_funct_1 (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 B) (k4_zf_fund1 (k2_zf_model D))) (k3_zf_fund1 C)) = (k3_funct_2 k1_zf_lang A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l22_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_xboole_0 A (k1_tarski B)) = (k1_tarski B))  => (r2_hidden B A)) ) ) ).
tt(l230_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_xcmplx_0 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k5_xcmplx_0 A))) ) ) ).
tt(l23_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_algstr_0)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k8_algstr_0)) &  ((k6_algstr_0 k8_algstr_0 A C) = B) ) ) ) ) ) ) ).
tt(l23_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k2_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(l23_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 D E)) (k1_rlvect_1 A C (k8_real_1 D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C F) (k1_rlvect_1 A D G)))  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A E k6_numbers) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((k1_arytm_1 (k1_arytm_1 A B) C) = (k1_arytm_1 (k1_arytm_1 A C) B)) ) ) ) ) ) ) ).
tt(l23_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k6_asympt_0 B)) & (r2_hidden B (k6_asympt_0 A)))  <=>  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ).
tt(l23_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( ((k1_seq_1 A k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 A C) = B) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k6_series_1 A C) = (k8_real_1 B C)) ) ) ) ) ) ) ) ).
tt(l23_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 2))) =>  ( (B = (k10_finseq_1 k6_numbers A))  =>  ((k1_normsp_0 (k4_real_ns1 2) B) = (k18_complex1 A)) ) ) ) ) ) ).
tt(l23_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_clopban2 A))) =>  ( (C = (k6_clopban2 A))  =>  ( ((k6_algstr_0 (k8_clopban2 A) B C) = B)  &  ((k6_algstr_0 (k8_clopban2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l23_collsp,ax,(r1_tarski a_0_2_collsp (k3_zfmisc_1 (k8_domain_1 k5_numbers 1 2 3) (k8_domain_1 k5_numbers 1 2 3) (k8_domain_1 k5_numbers 1 2 3)))).
tt(l23_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k2_xcmplx_0 A B))  =>  ((k4_complex1 C) = (k7_real_1 (k4_complex1 A) (k4_complex1 B))) ) ) ) ) ) ) ) ).
tt(l23_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = B) ) ) ) ) ).
tt(l23_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_xxreal_0 (k8_real_1 (k17_complex1 (k2_xcmplx_0 A B)) (k17_complex1 (k2_xcmplx_0 A B))) (k7_real_1 (k8_real_1 (k8_real_1 2 (k17_complex1 A)) (k17_complex1 A)) (k8_real_1 (k8_real_1 2 (k17_complex1 B)) (k17_complex1 B)))) & (r1_xxreal_0 (k8_real_1 (k17_complex1 A) (k17_complex1 A)) (k7_real_1 (k8_real_1 (k8_real_1 2 (k17_complex1 (k6_xcmplx_0 A B))) (k17_complex1 (k6_xcmplx_0 A B))) (k8_real_1 (k8_real_1 2 (k17_complex1 B)) (k17_complex1 B))))) ) ) ) ) ).
tt(l23_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 3)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  (~  (B = (k1_nat_1 A 3)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_dtconstr,ax,(r2_hidden c3__dtconstr (k2_lang1 k5_dtconstr))).
tt(l23_euler_1,ax, (! [A:$i] :  ((r2_hidden A a_0_1_euler_1) <=>  (A = 1) ) ) ).
tt(l23_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_nat_1 A 1)) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  &  (? [D:$i] :  ( (~ (v1_xtuple_0 D))  &  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ) ).
tt(l23_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k8_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) (k1_tarski k6_numbers)) = (k8_relset_1 k1_numbers k1_numbers A (k1_tarski k6_numbers))) ) ) ).
tt(l23_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ((r2_hidden A (k9_xtuple_0 k3_taylor_1)) & (r1_xxreal_0 A k6_numbers)) ) ) ) ).
tt(l23_fib_num,ax, (~ (r1_xxreal_0 k6_numbers k2_fib_num)) ).
tt(l23_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((v2_funct_1 C) => (v2_funct_1 (k17_finseq_1 B A C))) ) ) ) ) ) ) ).
tt(l23_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ( ((k1_funct_1 (k2_finseq_7 A B C D) C) = (k1_funct_1 B D))  &  ((k1_funct_1 (k2_finseq_7 A B C D) D) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  =>  ((k1_funct_1 (k14_fomodel1 A) (u2_struct_0 A)) = (k4_xcmplx_0 2)) ) ) ).
tt(l23_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ((r1_tarski A (k1_fomodel4 B)) =>  ((k1_funct_1 (k2_fomodel4 B C) A) = (k3_tarski (k3_tarski (a_3_3_fomodel4 A B C)))) ) ) ) ) ) ) ).
tt(l23_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k13_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) (k9_gfacirc1 (k12_gfacirc1 A B C) E D)) = (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith G H) I) K) (k10_margrel1 K J)) (k10_margrel1 J (k2_binarith (k2_binarith G H) I))))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_fvaluat1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_realset2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_fvaluat1 B C (k3_real_1 A 1)) = (k8_group_1 B (k3_fvaluat1 B C A) C)) ) ) ) ) ) ) ).
tt(l23_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r3_analmetr A D E F G B C) & (r3_analmetr A D E F H B C)) )  => (r3_analmetr A D E G H B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  ((k3_glib_002 A) = (k3_glib_002 B)) ) ) ) ) ) ).
tt(l23_gr_cy_3,ax, ((k13_newton 2 8) = 256) ).
tt(l23_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden C (k7_ideal_1 A B))) ) ) ) ) ) ) ).
tt(l23_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((r1_tarski D C) => (r2_hidden D (k1_substlat A B))) ) ) ) ) ) ) ).
tt(l23_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ((v1_int_7 A) &  ((r2_hidden B (k1_polynom2 k10_newton A)) &  ( (~  ((k1_recdef_1 A B) = B) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k10_newton) &  ((v1_funct_1 D) &  ((v1_partfun1 D k10_newton) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (~  ((v1_int_7 C) &  ( ((k1_polynom2 k10_newton D) = (k1_tarski B))  &  ( ((k8_nat_3 k10_newton D) = B)  &  ( ((k1_polynom2 k10_newton C) = (k1_polynom2 k10_newton A))  &  ( ((k5_relat_1 C (k7_subset_1 k10_newton (k1_polynom2 k10_newton C) (k1_tarski B))) = (k5_relat_1 A (k7_subset_1 k10_newton (k1_polynom2 k10_newton C) (k1_tarski B))))  &  ( ((k1_recdef_1 A B) = (k4_nat_1 (k1_recdef_1 C B) B))  &  ((k8_nat_3 k10_newton A) = (k4_nat_1 (k8_nat_3 k10_newton C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) =>  ((v1_funct_1 (k2_partfun1 k1_numbers (k1_euclid A) C B)) &  ((v1_funct_2 (k2_partfun1 k1_numbers (k1_euclid A) C B) B (k1_euclid A)) & (m1_subset_1 (k2_partfun1 k1_numbers (k1_euclid A) C B) (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) ) ) ) ) ) ) ) ) ).
tt(l23_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B 1) (k5_seq_4 A)))  =>  ( (~ (v1_xboole_0 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B)))  &  ((v5_valued_0 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B)) & (m2_finseq_1 (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B) k1_numbers)) ) ) ) ) ) ) ).
tt(l23_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((k4_integra5 A D E) = (k7_real_1 (k4_integra5 A C E) (k4_integra5 C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers A) (k32_valued_1 k1_numbers k1_numbers B)) = (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) ) ) ) ) ).
tt(l23_jgraph_3,ax, ((k16_euclid 2) = (k4_struct_0 (k15_euclid 2))) ).
tt(l23_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A)) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (k1_pre_topc (k15_euclid 2) A) k3_topmetr) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) k1_numbers (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) B) = (k1_funct_1 k4_pscomp_1 B)) ) ) ) ) ) ).
tt(l23_jgraph_6,ax, ((k17_euclid (k19_euclid k6_numbers 1)) = k6_numbers) ).
tt(l23_jordan7,ax,(r2_hidden 1 (k1_rcomp_1 k6_numbers 1))).
tt(l23_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A)))) ) ) ) ).
tt(l23_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_lopban_2 A))) =>  ( (C = (k6_lopban_2 A))  =>  ( ((k6_algstr_0 (k8_lopban_2 A) B C) = B)  &  ((k6_algstr_0 (k8_lopban_2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l23_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) B) B) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(l23_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k2_wsierp_1 (k10_matrixj1 A (k4_matrixj1 A B))) = (k3_finseq_1 B)) ) ) ) ) ).
tt(l23_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  (! [D:$i] :  ((v1_relat_1 (k1_funct_1 (k3_matrtop1 A B C) D)) &  ((v1_funct_1 (k1_funct_1 (k3_matrtop1 A B C) D)) &  ((v1_finseq_1 (k1_funct_1 (k3_matrtop1 A B C) D)) & (v3_valued_0 (k1_funct_1 (k3_matrtop1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l23_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (? [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (~  (C = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) A H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) B I))) ) )  =>  ((r1_euclid_6 A B C) |  ( (G = 1)  |  ( (H = 1)  |  ( (I = 1)  |  ( ( (~  ((k9_binop_2 (k10_binop_2 1 H) (k11_binop_2 G H)) = k6_numbers) )  &  ( (~  ((k9_binop_2 (k10_binop_2 1 G) (k11_binop_2 I G)) = k6_numbers) )  &  (~  ((k9_binop_2 (k10_binop_2 1 I) (k11_binop_2 H I)) = k6_numbers) ) ) )  |  ( ((k11_binop_2 (k11_binop_2 (k12_binop_2 G (k10_binop_2 1 G)) (k12_binop_2 H (k10_binop_2 1 H))) (k12_binop_2 I (k10_binop_2 1 I))) = 1)  <=>  ((r1_xboole_0 (k4_euclid_4 2 A D) (k4_euclid_4 2 B E)) &  ((r1_xboole_0 (k4_euclid_4 2 B E) (k4_euclid_4 2 C F)) & (r1_xboole_0 (k4_euclid_4 2 C F) (k4_euclid_4 2 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers (k11_mesfun7c A (k1_mesfun9c A k2_numbers C B)) D) (k2_partfun1 A k1_numbers (k4_mesfunc5 A k1_numbers (k11_mesfun7c A C) D) B)) & (r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers (k12_mesfun7c A (k1_mesfun9c A k2_numbers C B)) D) (k2_partfun1 A k1_numbers (k4_mesfunc5 A k1_numbers (k12_mesfun7c A C) D) B))) ) ) ) ) ) ) ) ).
tt(l23_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xboole_0 D E)) ) ) ) ) ) )  =>  ((r2_hidden k1_xboole_0 C) | (r1_ordinal1 (k1_card_1 C) B)) ) ) )  => (r1_ordinal1 (k4_topgen_1 A) B)) ) ) ) ) ).
tt(l23_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_2 A) =>  ((k1_funct_1 A 1) = 1) ) ) ) ).
tt(l23_nagata_2,ax, ((k2_tops_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers k1_nagata_2) = (k2_funct_1 k1_nagata_2)) ).
tt(l23_normform,ax, (! [A:$i] : (v3_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) ).
tt(l23_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  ( ( (B = (k6_int_1 A C))  &  ((k3_mcart_1 k4_numbers k4_numbers k4_numbers (k2_ntalgo_1 C B)) = 1) )  =>  ( (C = k6_numbers)  |  ((k6_int_1 (k3_xcmplx_0 (k3_ntalgo_1 A C) A) C) = (k6_int_1 1 C)) ) ) ) ) ) ) ) ) ).
tt(l23_numbers,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((k9_arytm_3 A A) = (k10_arytm_3 c2__numbers A)) ) ) ).
tt(l23_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_o_ring_1 B A) => (v7_o_ring_1 B A)) ) ) ) ) ).
tt(l23_petri_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 C)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 D)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 D)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 D)) = k1_xboole_0)  &  (E = (k1_funct_4 (k1_funct_4 (k1_funct_4 A B) C) D)) ) ) ) ) ) )  =>  ( (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 A)) =>  ((k1_funct_1 E F) = (k1_funct_1 A F)) ) )  &  ( (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 B)) =>  ((k1_funct_1 E F) = (k1_funct_1 B F)) ) )  &  ( (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 C)) =>  ((k1_funct_1 E F) = (k1_funct_1 C F)) ) )  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 D)) =>  ((k1_funct_1 E F) = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( ((k2_polynom7 A B C) = (k16_pre_poly A))  &  ((k3_polynom7 A B C) = (k3_polynom1 A B C (k16_pre_poly A))) ) ) ) ) ) ) ).
tt(l23_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_polynom8 A (k5_struct_0 A) B) = (k5_struct_0 A)) ) ) ) ) ).
tt(l23_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k1_polyred A D B C)) (a_4_0_polyred A B C D))) ) ) ) ) ) ) ) ).
tt(l23_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_projred2 A D E F))  &  ((r1_projred2 A D F G) &  ( (~ (r1_incsp_1 A C G))  &  ( (~  (D = G) )  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  ( (~ (r1_projred2 A E F H))  &  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A I H) &  ( (~ (r1_incsp_1 A I D))  &  ( (~ (r1_incsp_1 A I G))  &  ((k3_relat_1 (k1_projred1 A D F B) (k1_projred1 A F E C)) = (k3_relat_1 (k1_projred1 A D G I) (k1_projred1 A G E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 A))) )  =>  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  &  ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 B))) )  =>  ( ( (! [I:$i] :  (! [J:$i] :  ( ((r2_hidden I A) & (r2_hidden J B))  =>  ((k1_binop_1 E I J) = (k11_binop_2 (k1_seq_1 C (k1_tarski I)) (k1_seq_1 D (k1_tarski J)))) ) ) )  &  (! [I:$i] :  ( ((v1_finset_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 F I) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 I E)) ) ) )  =>  ((k1_seq_1 F (k2_zfmisc_1 G H)) = (k11_binop_2 (k1_seq_1 C G) (k1_seq_1 D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_realset2,ax, ((k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2))) = (k6_domain_1 2 (k1_funct_7 1 2))) ).
tt(l23_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (r1_tarski (u1_struct_0 (k2_rmod_3 A B C D)) (u1_struct_0 C))) ) ) ) ) ) ) ) ).
tt(l23_scmfsa_1,ax, ((k9_xtuple_0 k4_scmfsa_1) = k1_scmfsa_1) ).
tt(l23_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 k3_scm_inst)) =>  ( (~  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  (~  (A = 5) ) ) ) ) ) )  =>  ((k3_compos_0 k3_scm_inst A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(l23_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k2_scmpds_8 A B C))) = (k2_nat_1 (k5_card_1 C) 3)) ) ) ) ) ) ) ).
tt(l23_scmpds_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 B) A) 1) = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 B) A) A) B))) ) ) ) ) ) ) ).
tt(l23_scmyciel,ax, (! [A:$i] :  ((k3_tarski (a_1_3_scmyciel A)) = A) ) ).
tt(l23_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k2_scmp_gcd) 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) & (r2_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A)) ) ) ) ) ) ).
tt(l23_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ( ((k1_funct_1 B (k1_scmp_gcd 3)) = D)  &  ((r1_xxreal_0 8 C) &  ((r1_xxreal_0 8 D) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) ) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 4)) = (k1_funct_1 B (k1_scmp_gcd 4)))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 E) =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) )  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd C)) (k1_funct_1 B (k1_scmp_gcd D))))  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 7)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 7)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 3)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 5)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 7)) 1)) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd C)) (k1_funct_1 B (k1_scmp_gcd D))) =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 7)) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 3)) = (k1_funct_1 B (k1_scmp_gcd 3)))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))) B A) (k1_scmp_gcd 5)) = (k1_funct_1 B (k1_scmp_gcd 7))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l23_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 6 (k8_complex1 (k8_complex1 (k8_complex1 (k8_complex1 (k8_complex1 (k13_complex1 (k6_square_1 (k3_xcmplx_0 A B)) C) (k13_complex1 C (k6_square_1 (k3_xcmplx_0 A B)))) (k13_complex1 (k6_square_1 (k3_xcmplx_0 A C)) B)) (k13_complex1 B (k6_square_1 (k3_xcmplx_0 C A)))) (k13_complex1 A (k6_square_1 (k3_xcmplx_0 C B)))) (k13_complex1 (k6_square_1 (k3_xcmplx_0 C B)) A)))) ) ) ) ) ) ).
tt(l23_sincos10,ax,(r1_tarski (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))).
tt(l23_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k1_sin_cos2 (k9_binop_2 A B)) = (k7_real_1 (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ).
tt(l23_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) = (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))) (k6_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))))  &  ( ((k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) = (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))) (k6_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))))  &  ( ((k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) = (k3_xcmplx_0 (k3_xcmplx_0 2 (k6_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))) (k6_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))))  &  ( ((k6_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) = (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))) (k3_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))))  &  ( ((k2_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) = (k7_xcmplx_0 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))))  &  ((k6_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) = (k7_xcmplx_0 (k3_sin_cos2 (k6_xcmplx_0 A B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)))) ) ) ) ) ) ) ) ) ) ).
tt(l23_sin_cos9,ax,(r2_hidden (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))).
tt(l23_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l23_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_square_1 B) (k6_square_1 A))) ) ) ) ) ) ) ).
tt(l23_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r6_pboole A (k1_termord A B C C) C) & (r6_pboole A (k2_termord A B C C) C)) ) ) ) ) ) ) ).
tt(l23_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 A)) &  ((v5_pre_topc B k5_topmetr A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 A)) &  ((v5_pre_topc C k5_topmetr A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) )  => (v5_pre_topc (k3_topalg_2 A B C) (k2_borsuk_1 k5_topmetr k5_topmetr) A)) ) ) ) ) ) ).
tt(l23_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 A)))))  =>  ( (B = k1_xboole_0)  => (v4_topalg_6 B A)) ) ) ) ) ).
tt(l23_topreal2,ax,(r2_hidden (k19_euclid k6_numbers 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)))).
tt(l23_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_tarski (u1_struct_0 (k2_vectsp_5 A B C D)) (u1_struct_0 C))) ) ) ) ) ) ) ) ).
tt(l23_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k2_funct_6 D))) <=> (r2_hidden E (k1_relset_1 (k4_card_3 (k2_funct_6 D)) (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l23_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k3_xcmplx_0 B C) = A)  =>  ( (A = k6_numbers)  | (m2_subset_1 C k1_numbers k5_numbers)) ) ) ) ) ) ) ) ).
tt(l23_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers C))  => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l23_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k4_xcmplx_0 B) (k4_xcmplx_0 A))) ) ) ) ) ).
tt(l23_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((m1_xxreal_2 C (k2_tarski A B)) => (r1_xxreal_0 B C)) ) ) ) ) ) ).
tt(l23_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k1_xxreal_3 A B) = k2_xxreal_0)  &  ( (~  (A = k2_xxreal_0) )  &  (~  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(l23_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((a_4_0_yellow_4 A B C D) = (k7_domain_1 (u1_struct_0 A) (k10_lattice3 A B C) (k10_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(l23_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r2_relset_1 k4_ordinal1 A (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 C) (k4_zf_fund1 (k2_zf_model B))) (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 D) (k4_zf_fund1 (k2_zf_model B)))) & (r2_hidden C (k5_zf_model B A)))  => (r2_hidden D (k5_zf_model B A))) ) ) ) ) ) ) ) ) ).
tt(l23_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(l24_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B C) &  ((r2_hidden B (k1_aff_4 A D E)) & (r5_aff_1 A D C)) )  => (r1_tarski C (k1_aff_4 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_algstr_0)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k8_algstr_0)) &  ((k6_algstr_0 k8_algstr_0 C A) = B) ) ) ) ) ) ) ).
tt(l24_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k3_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(l24_ami_6,ax, (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 1)) ) ).
tt(l24_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k1_rlvect_1 A B k6_numbers) (k1_rlvect_1 A C k6_numbers)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l24_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  (! [D:$i] :  ((m1_subset_1 D k2_arytm_2) =>  ( ( (C = A)  &  (D = B) )  =>  ((r1_arytm_2 C D) <=> (r3_arytm_3 A B)) ) ) ) ) ) ) ) ) ) ).
tt(l24_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_real_1 (k7_series_1 A B C) (k1_seq_1 A (k1_nat_1 B 1))) = (k7_series_1 A (k1_nat_1 B 1) C)) ) ) ) ) ) ) ).
tt(l24_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k4_struct_0 (k5_c0sp2 A)) = (k4_struct_0 (k11_c0sp1 (u1_struct_0 A)))) ) ) ).
tt(l24_card_1,ax, ( ((k3_card_1 k1_xboole_0) = (k1_card_1 k4_ordinal1))  &  ( (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_card_1 (k1_ordinal1 A)) = (k2_card_1 (k3_tarski (k1_tarski (k3_card_1 A))))) ) )  &  (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k3_card_1 C)) ) ) ) )  =>  ((k3_card_1 A) = (k1_card_1 (k4_ordinal2 B))) ) ) ) ) ) ) ) ) ) ).
tt(l24_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) =>  ( (C = (k4_c0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)))  =>  ( ((k6_algstr_0 (k5_cc0sp2 A) B C) = B)  &  ((k6_algstr_0 (k5_cc0sp2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l24_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  ( (B = (k12_finseq_1 k1_numbers A))  =>  ((k1_normsp_0 (k4_real_ns1 1) B) = (k18_complex1 A)) ) ) ) ) ) ).
tt(l24_collsp,ax, (~ (v1_xboole_0 (k8_domain_1 k5_numbers 1 2 3))) ).
tt(l24_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k3_xcmplx_0 A B))  =>  ((k3_complex1 C) = (k9_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B)))) ) ) ) ) ) ) ) ).
tt(l24_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 A (k4_xcmplx_0 1))) ) ) ).
tt(l24_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_margrel1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) )  =>  ( ((v3_margrel1 B A) &  (~ (v1_xboole_0 B)) )  <=>  ((k1_relset_1 (k3_finseq_2 A) B) = (k4_finseq_2 (k19_margrel1 B) A)) ) ) ) ) ) ).
tt(l24_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 k6_numbers D) & (v1_convex1 B A)) )  => (r1_tarski (k7_rusub_4 A (k1_convex1 A B C) (k1_convex1 A B D)) (k1_convex1 A B (k7_real_1 C D)))) ) ) ) ) ) ) ) ) ).
tt(l24_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)))) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)))) ) ) ) ) ) ) ) ) ) ).
tt(l24_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 7)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  (~  (B = (k1_nat_1 A 7)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_dtconstr,ax,(r1_tarski (k6_domain_1 (u1_struct_0 k5_dtconstr) c3__dtconstr) (k2_lang1 k5_dtconstr))).
tt(l24_euler_1,ax, ((k5_card_1 (k1_tarski 1)) = (k1_euler_1 2)) ).
tt(l24_fib_num4,ax, ((k3_square_1 k2_fib_num) = (k13_complex1 (k6_xcmplx_0 3 (k7_square_1 5)) 2)) ).
tt(l24_fib_num,ax, (~ (r1_xxreal_0 1 (k18_complex1 k2_fib_num))) ).
tt(l24_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_1 B A) =>  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(l24_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 (k2_xcmplx_0 D 1) (k3_finseq_1 C)) => (r2_hidden (k1_funct_1 (k3_fomodel0 A B C) D) A))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 (k2_xcmplx_0 D 1) E) =>  ((k1_funct_1 (k3_fomodel0 A B (k17_finseq_1 A E C)) D) = (k1_funct_1 (k3_fomodel0 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  => (v1_funct_1 (k4_relset_1 (k4_finseq_2 C (k8_eqrel_1 A B)) (k4_finseq_2 C A) (k4_finseq_2 C A) (k8_eqrel_1 (k4_finseq_2 C A) (k13_fomodel3 A B C)) (k8_fomodel3 (k8_eqrel_1 A B) A (k3_relset_1 A (k8_eqrel_1 A B) (k17_fomodel3 A B)) C) (k17_fomodel3 (k4_finseq_2 C A) (k13_fomodel3 A B C))))) ) ) ) ) ) ).
tt(l24_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_funct_2 B (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) => (r2_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) B (k2_fomodel4 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) B)))) ) ) ) ).
tt(l24_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k13_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) (k12_gfacirc1 (k12_gfacirc1 A B C) E D)) = (k2_binarith (k2_binarith (k2_binarith (k2_binarith G H) I) J) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 (k3_relat_1 (k13_funct_3 A B) C))) =>  ((k1_funct_1 (k3_relat_1 (k13_funct_3 A B) C) D) = (k1_binop_1 C (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(l24_funct_9,ax,(v1_funct_9 k16_sin_cos (k8_real_1 2 k32_sin_cos))).
tt(l24_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F A) & (r2_hidden G C))  =>  ((k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 C B A (k2_fuzzy_4 C B E) (k2_fuzzy_4 B A D) G F))) = (k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r3_analmetr A D E D E B C))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k3_glib_002 A)) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ) ) ).
tt(l24_goedelcp,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ((v4_card_3 A) &  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( ((k9_xtuple_0 B) = k5_numbers)  &  (A = (k10_xtuple_0 B)) ) ) ) ) ) ) ) ) ).
tt(l24_graph_2,ax, ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_finseq_4 k5_numbers 1 2)) 1))  &  ( (~  (1 = 2) )  &  ((k10_xtuple_0 (k2_finseq_4 k5_numbers 1 2)) = (k2_tarski 1 2)) ) ) ).
tt(l24_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_polynom1 A C))) =>  ( ( (F = D)  &  (G = E) )  =>  ((k5_algstr_0 (k11_polynom1 A C) F G) = (k6_polynom1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_group_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k15_group_2 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) <=>  (C = (k13_group_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(l24_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_tarski (k3_heyting3 (k2_nat_1 A 1) B) (k3_heyting3 A B))) ) ) ) ) ).
tt(l24_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) => (r1_tarski (k5_hilbert1 (k5_hilbert1 A)) (k5_hilbert1 A))) ) ).
tt(l24_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  ((k7_cat_1 A C (k9_index_1 A B C)) = (k1_xtuple_0 B)) ) ) ) ) ) ) ).
tt(l24_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D A) =>  ( (D = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B))  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k2_finseq_1 (k3_finseq_1 B))) =>  ((k2_integra1 A D (k2_nat_1 E 1)) = (k2_integra1 A B E)) ) ) )  &  ( ((k4_integra1 A C B) = (k2_rfinseq k1_numbers 1 (k4_integra1 A C D)))  &  ((k5_integra1 A C B) = (k2_rfinseq k1_numbers 1 (k5_integra1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_hidden (k4_nattra_1 A B C D E F) (k2_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_jgraph_3,ax, ( ((r1_xxreal_0 (k18_euclid (k22_euclid 2)) (k17_euclid (k22_euclid 2))) & (r1_xxreal_0 (k1_real_1 (k17_euclid (k22_euclid 2))) (k18_euclid (k22_euclid 2))))  |  ((r1_xxreal_0 (k17_euclid (k22_euclid 2)) (k18_euclid (k22_euclid 2))) & (r1_xxreal_0 (k18_euclid (k22_euclid 2)) (k1_real_1 (k17_euclid (k22_euclid 2))))) ) ).
tt(l24_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A)) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (k1_pre_topc (k15_euclid 2) A) k3_topmetr) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) k1_numbers (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) B) = (k1_funct_1 k5_pscomp_1 B)) ) ) ) ) ) ).
tt(l24_jgraph_6,ax, ((k18_euclid (k19_euclid k6_numbers 1)) = 1) ).
tt(l24_jordan12,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 B (k1_matrix_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k2_goboard5 A B)) &  ((r2_hidden D (k2_goboard5 A B)) & (r1_xxreal_0 (k18_euclid C) (k18_euclid D))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k2_goboard5 A B))) ) ) ) ) ) ) ) ) ) ).
tt(l24_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  ( (~  (B = (k1_funct_1 A (k3_finseq_1 A))) )  &  ((v4_topreal1 A) &  ( (~ (r2_hidden B (k3_topreal1 2 (k2_jordan3 A C))))  &  (~ (r2_hidden C (k3_topreal1 2 (k2_jordan3 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k2_lattice2 (u1_struct_0 A) A (k1_setwiseo (u1_struct_0 A)) B) = (k5_lattices A)) ) ) ) ) ).
tt(l24_lattice7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_waybel_0 C A B) => (v19_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(l24_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) D) (k8_cqc_lang A (k8_cqc_lang A B E) (k8_cqc_lang A (k8_cqc_lang A E C) D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l24_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k5_matrix_1 D (u1_struct_0 k2_vectsp_1) (k2_matrtop3 D A B C)) = (k2_matrtop3 D (k4_xcmplx_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k2_measure6 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D A) &  (C = (k3_real_1 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (? [E:$i] :  ((v7_ordinal1 E) &  ((k1_mesfunc9 (k6_measure8 A B C) (k8_nat_1 (k9_setfam_1 A) D E)) = k1_supinf_1) ) )  => (r1_xxreal_0 (k1_mesfunc9 (k6_measure8 A B C) (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) D))) (k19_supinf_2 (k1_partfun1 k5_numbers (k9_setfam_1 A) (k9_setfam_1 A) k7_numbers D (k6_measure8 A B C))))) ) ) ) ) ) ) ) ).
tt(l24_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_2 A) =>  ((k1_funct_1 A 1) = 2) ) ) ) ).
tt(l24_msaterm,ax, (! [A:$i] :  (~ (r2_hidden A A)) ) ).
tt(l24_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) => (r2_hidden (u3_msualg_1 A B) (k5_msualg_2 A B C))) ) ) ) ) ) ).
tt(l24_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers B) = (k1_rcomp_1 k6_numbers 1))  &  ( ((k1_relset_1 k1_numbers C) = (k1_rcomp_1 k6_numbers 1))  &  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) B (k1_rcomp_1 k6_numbers 1)) A) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 k6_numbers 1))) &  ((r2_ndiff_3 A B (k2_rcomp_1 k6_numbers 1)) &  ((r2_fdiff_1 C (k2_rcomp_1 k6_numbers 1)) &  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D (k2_rcomp_1 k6_numbers 1)) => (r1_xxreal_0 (k1_normsp_0 A (k1_ndiff_3 A B D)) (k1_fdiff_1 C D))) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B 1) (k7_partfun1 (u1_struct_0 A) B k6_numbers))) (k10_binop_2 (k7_partfun1 k1_numbers C 1) (k7_partfun1 k1_numbers C k6_numbers)))) ) ) ) ) ) ) ).
tt(l24_necklace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((r5_waybel_1 A B) =>  ((k1_card_1 (u1_orders_2 A)) = (k1_card_1 (u1_orders_2 B))) ) ) ) ) ) ).
tt(l24_normform,ax, (! [A:$i] : (v1_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) ).
tt(l24_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_6_normsp_2 A B C) = (a_3_8_normsp_2 A B C)) ) ) ) ) ) ) ).
tt(l24_petri_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ( ((k3_xboole_0 A B) = k1_xboole_0)  &  ((r1_tarski C A) &  ((r1_tarski D B) &  ((r1_tarski E (k6_subset_1 A C)) &  ((r1_tarski F (k6_subset_1 B D)) &  ( (G = C)  &  (H = D) ) ) ) ) ) )  =>  ( ((k3_xboole_0 E F) = k1_xboole_0)  &  ( ((k3_xboole_0 E G) = k1_xboole_0)  &  ( ((k3_xboole_0 E H) = k1_xboole_0)  &  ( ((k3_xboole_0 F G) = k1_xboole_0)  &  ( ((k3_xboole_0 F H) = k1_xboole_0)  &  ((k3_xboole_0 G H) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_projred2 A D E F))  &  ((r1_projred2 A D F G) &  ( (~ (r1_incsp_1 A C G))  &  ( (~  (D = G) )  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  ((r1_projred2 A E F H) &  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A I H) &  ( (~ (r1_incsp_1 A I D))  &  ( (~ (r1_incsp_1 A I G))  &  ((k3_relat_1 (k1_projred1 A D F B) (k1_projred1 A F E C)) = (k3_relat_1 (k1_projred1 A D G I) (k1_projred1 A G E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  =>  ( ( (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H B))  =>  ((k1_binop_1 E G H) = (k11_binop_2 (k1_seq_1 C (k1_tarski G)) (k1_seq_1 D (k1_tarski H)))) ) ) )  &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 F G) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 G E)) ) ) )  =>  ((k1_seq_1 F (k2_zfmisc_1 A B)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_realset2,ax, ((k2_zfmisc_1 (k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2))) (k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2)))) = (k6_domain_1 (k2_zfmisc_1 2 2) (k1_domain_1 2 2 (k1_funct_7 1 2) (k1_funct_7 1 2)))) ).
tt(l24_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 (k2_rlsub_2 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(l24_scmfsa_1,ax, ((k1_afinsq_1 (k7_afinsq_1 k5_numbers k4_numbers (k3_finseq_2 k4_numbers))) = 3) ).
tt(l24_scmpds_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~  (B = 5) )  &  ((k2_xcmplx_0 (k2_xcmplx_0 A (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k1_int_2 B)) 4)) 1) = (k2_xcmplx_0 A B)) ) ) ) ) ) ) ).
tt(l24_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) => (r1_xxreal_0 (k2_compos_0 k1_scmpds_i A) 14)) ) ).
tt(l24_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_tarski k4_scmp_gcd D) &  ((r1_tarski k4_scmp_gcd E) &  ( ((k5_memstr_0 2 k1_scmpds_2 B) = 5)  &  ( (A = (k1_funct_1 B k3_scmp_gcd))  &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k5_memstr_0 2 k1_scmpds_2 C) = (k5_memstr_0 2 k1_scmpds_2 B))  &  ( ((k1_funct_1 C k3_scmp_gcd) = (k1_funct_1 B k3_scmp_gcd))  &  ( ((k1_funct_1 C k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 C (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)))  &  ((k1_funct_1 C (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) k6_numbers) |  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 D B 7)) = (k2_nat_1 5 7))  &  ( ((k5_extpro_1 2 k1_scmpds_2 D B 8) = (k2_extpro_1 2 k1_scmpds_2 (k3_scmpds_2 (k4_xcmplx_0 7)) (k5_extpro_1 2 k1_scmpds_2 D B 7)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) k3_scmp_gcd) = (k2_nat_1 A 4))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) (k1_scmp_gcd (k2_nat_1 A 7))) = (k6_int_1 (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 2))) (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 3)))))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) (k1_scmp_gcd (k2_nat_1 A 6))) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 3))))  &  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 E C 7)) = (k2_nat_1 5 7))  &  ( ((k5_extpro_1 2 k1_scmpds_2 E C 8) = (k2_extpro_1 2 k1_scmpds_2 (k3_scmpds_2 (k4_xcmplx_0 7)) (k5_extpro_1 2 k1_scmpds_2 E C 7)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) k3_scmp_gcd) = (k2_nat_1 A 4))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) (k1_scmp_gcd (k2_nat_1 A 7))) = (k6_int_1 (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 2))) (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 3)))))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) (k1_scmp_gcd (k2_nat_1 A 6))) = (k1_funct_1 B (k1_scmp_gcd (k2_nat_1 A 3))))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) (k1_scmp_gcd (k2_nat_1 A 4))) = A)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B 7) (k1_scmp_gcd (k2_nat_1 A 5))) = 11)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) (k1_scmp_gcd (k2_nat_1 A 4))) = A)  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C 7) (k1_scmp_gcd (k2_nat_1 A 5))) = 11) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k2_scmp_gcd) 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) (k1_scmp_gcd 3)) = (k1_funct_1 B (k1_scmp_gcd 3))) ) ) ) ) ) ) ) ) ).
tt(l24_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) (k1_funct_1 B (k1_scmp_gcd 7))) = C)  &  ((r1_xxreal_0 8 (k1_funct_1 B (k1_scmp_gcd 3))) &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = D)  & (r1_xxreal_0 8 D)) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 7)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 7)) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 4)) = (k1_funct_1 B (k1_scmp_gcd 4)))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 E) =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) )  &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (E = (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 5)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd 3)) = F)  &  ( ((k2_nat_1 F E) = C)  &  ((r1_xxreal_0 E (k1_funct_1 B (k1_scmp_gcd 7))) &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) G) &  ( (~ (r1_xxreal_0 F G))  & (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd D)) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd G)))) ) ) ) )  &  ( (E = k6_numbers)  | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd D)) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) (k1_scmp_gcd F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_sincos10,ax,(r1_tarski (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) (k1_relset_1 k1_numbers k1_fdiff_9))).
tt(l24_sin_cos9,ax,(r2_hidden (k10_real_1 k32_sin_cos 4) (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))).
tt(l24_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A)) (k3_topreal1 2 A))) ) ) ) ).
tt(l24_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l24_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 (k3_topalg_2 A D E) F k6_numbers) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) D F))  &  ( ((k1_binop_1 (k3_topalg_2 A D E) F 1) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) E F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 (k3_topalg_2 A D E) k6_numbers G) = B)  &  ((k1_binop_1 (k3_topalg_2 A D E) 1 G) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  ((v1_connsp_2 A) => (v1_connsp_2 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ).
tt(l24_topreal2,ax,(r2_hidden (k19_euclid 1 k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)))).
tt(l24_toprealb,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 k16_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2))))) ) ).
tt(l24_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) C D) & (v6_waybel_1 C A)) )  => (v6_waybel_1 D B)) ) ) ) ) ) ) ) ) ).
tt(l24_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) C) =>  ((r1_xxreal_0 A C) & (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(l24_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(l24_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 A) (k4_xcmplx_0 B)) => (r1_xxreal_0 B A)) ) ) ) ) ).
tt(l24_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k4_ordinal1)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A (k9_funct_2 B C)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  (~  (A = (k2_partfun1 k4_ordinal1 C (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang C k2_zf_fund1 D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l24_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k3_xboole_0 B (k1_tarski A)) = (k1_tarski A)) ) ) ) ).
tt(l25_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 D A) &  ((v1_aff_1 E A) &  ((v1_aff_1 F A) &  ((r2_hidden B (k1_aff_4 A D E)) &  ((r2_hidden C (k1_aff_4 A D E)) &  ((r2_hidden B F) & (r2_hidden C F)) ) ) ) ) )  =>  ( (B = C)  | (r1_tarski F (k1_aff_4 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k4_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(l25_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B k6_numbers) (k1_rlvect_1 A C (k8_real_1 E F))) (k1_rlvect_1 A D (k8_real_1 (k1_real_1 E) G))) = (k1_rlvect_1 A (k5_algstr_0 A (k1_rlvect_1 A C F) (k1_rlvect_1 A D G)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_arytm_2,ax, (! [A:$i] :  (~  ((r2_hidden A k1_arytm_2) &  ( (~  (A = k11_arytm_3) )  &  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (~  ((r2_hidden B A) &  (~  (B = k11_arytm_3) ) ) ) ) ) ) ) ) ) ).
tt(l25_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) E) & (r1_xxreal_0 E D))  => (r1_xxreal_0 (k1_seq_1 A E) (k1_seq_1 B E))) ) ) )  => (r1_xxreal_0 (k7_series_1 A D C) (k7_series_1 B D C))) ) ) ) ) ) ) ) ) ).
tt(l25_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  => (v1_binop_1 (u1_bcialg_4 A) (u1_struct_0 A))) ) ).
tt(l25_binop_2,ax,(r2_hidden k6_numbers k5_numbers)).
tt(l25_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  => (v1_compts_1 (k2_borsuk_1 A B))) ) ) ) ).
tt(l25_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k5_struct_0 (k5_c0sp2 A)) = (k5_struct_0 (k11_c0sp1 (u1_struct_0 A)))) ) ) ).
tt(l25_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  => (r1_xboole_0 (k2_zfmisc_1 C (k1_tarski A)) (k2_zfmisc_1 D (k1_tarski B)))) ) ) ) ) ).
tt(l25_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( (B = C)  =>  ((k1_normsp_0 (k5_cc0sp2 A) B) = (k1_normsp_0 (k7_cc0sp1 (u1_struct_0 A)) C)) ) ) ) ) ) ) ) ).
tt(l25_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k4_real_ns1 1))) =>  ((k18_complex1 (k1_seq_1 (k1_pdiff_1 1 1) A)) = (k1_normsp_0 (k4_real_ns1 1) A)) ) ) ).
tt(l25_collsp,ax,(m1_collsp a_0_2_collsp c7__collsp)).
tt(l25_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (C = (k3_xcmplx_0 A B))  =>  ((k4_complex1 C) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B)) (k8_real_1 (k4_complex1 A) (k3_complex1 B)))) ) ) ) ) ) ) ) ).
tt(l25_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 2 C) &  ((r1_xxreal_0 (k6_xcmplx_0 B 1) A) &  ( (~  ((r1_xxreal_0 B A) & (r1_xxreal_0 A (k6_xcmplx_0 (k2_nat_1 B C) 3))) )  &  ( (~  (A = (k6_xcmplx_0 (k2_nat_1 B C) 2)) )  &  ((r1_xxreal_0 A (k6_xcmplx_0 (k2_nat_1 B C) 2)) &  (~  (A = (k6_xcmplx_0 B 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (k4_subset_1 (k3_cqc_lang A) B C) (k4_subset_1 (k3_cqc_lang A) (k1_cqc_the1 A B) (k1_cqc_the1 A C)))) ) ) ) ) ) ).
tt(l25_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v2_comseq_2 B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A))) (k1_seq_1 B E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A))) (k2_seq_2 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 15)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  (~  (B = (k1_nat_1 A 15)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_dtconstr,ax,(r1_tarski (k2_lang1 k5_dtconstr) (k6_domain_1 (u1_struct_0 k5_dtconstr) c3__dtconstr))).
tt(l25_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((k2_binop_1 (u1_struct_0 (k9_int_3 A)) k5_numbers (u1_struct_0 (k9_int_3 A)) (k4_group_1 (k9_int_3 A)) B 1) = B) ) ) ) ) ).
tt(l25_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ).
tt(l25_fomodel1,ax, (? [A:$i] :  ((l1_fomodel1 A) &  ( (~ (v6_struct_0 A))  & (v11_fomodel1 A)) ) ) ).
tt(l25_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_fomodel4 B))) =>  (~  ((v3_fomodel4 (k1_tarski A) B C D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (v4_fomodel4 A E B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_funct_9,ax,(v1_funct_9 k19_sin_cos (k8_real_1 2 k32_sin_cos))).
tt(l25_fvaluat1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_realset2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (C = (k4_struct_0 B)) )  &  ((k3_fvaluat1 B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(l25_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_algstr_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k4_fvsum_1 A B C (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = C) ) ) ) ) ) ) ).
tt(l25_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((r3_analmetr A D E F F B C) & (r3_analmetr A F F D E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  ((k25_glib_000 A B) = (k21_glib_000 A (k24_glib_000 A B))) ) ) ) ) ).
tt(l25_glib_003,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ( ((r2_hidden A C) & (r2_hidden B D))  =>  ((v1_funct_1 (k1_funct_4 E (k16_funcop_1 A B))) & (m1_subset_1 (k1_funct_4 E (k16_funcop_1 A B)) (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) ) ) ).
tt(l25_goboard7,ax, ((k9_real_1 1 (k10_real_1 1 2)) = (k10_real_1 1 2)) ).
tt(l25_graph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_graph_1 C B) => (m2_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B)) ) ) ) ) ) ).
tt(l25_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_group_1 k2_gr_cy_1 A (k5_gr_cy_1 1)) = A) ) ) ).
tt(l25_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ((m1_group_9 D A C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r1_struct_0 D E) => (r1_struct_0 D (k3_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k3_group_9 A C B) E))) ) ) ) ) ) ) ) ) ) ).
tt(l25_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_1 A B C F) =>  ((r2_hidden B F) |  ( ( (~  ((r2_hidden D F) &  (D = E) ) )  &  (~  ( (~ (r2_hidden D F))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r2_hidden G F) &  ((r2_hidden H F) &  ((r2_analoaf A G B H D) &  ((r2_analoaf A G C H E) & (r2_aff_1 A D E F)) ) ) ) ) ) ) ) ) ) )  |  ((r2_aff_1 A C B F) &  ( (~ (r2_hidden C F))  &  ( ((r2_hidden E F) &  (E = D) )  |  ( (~ (r2_hidden E F))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r2_hidden G F) &  ((r2_hidden H F) &  ((r2_analoaf A G C H E) &  ((r2_analoaf A G B H D) & (r2_aff_1 A E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ( (C = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B))  =>  ((k3_integra1 (k2_integra1 A C 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l25_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((r1_tarski (k3_integra5 C D) (k9_xtuple_0 (k56_valued_1 k1_numbers k1_numbers E))) &  ((r1_integra5 (k3_integra5 C D) (k56_valued_1 k1_numbers k1_numbers E)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers E) (k3_integra5 C D))) & (r1_xxreal_0 (k18_complex1 (k4_integra5 C D E)) (k4_integra5 C D (k56_valued_1 k1_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_jgraph_3,ax, (~  ((k22_euclid 2) = (k4_struct_0 (k15_euclid 2))) ) ).
tt(l25_jgraph_4,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) (k1_jgraph_4 2)) = (u1_struct_0 (k15_euclid 2))) ).
tt(l25_jgraph_6,ax, ( ((k12_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = 1)  &  ( ((k12_euclid (k19_euclid 1 k6_numbers)) = 1)  &  ( ((k12_euclid (k19_euclid k6_numbers (k1_real_1 1))) = 1)  &  ((k12_euclid (k19_euclid k6_numbers 1)) = 1) ) ) ) ).
tt(l25_lattice7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v18_waybel_0 C A B) => (v20_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(l25_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) D) (k8_cqc_lang A (k8_cqc_lang A D B) B)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(l25_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A C) =>  (? [E:$i] :  ((m1_vectsp_6 E A B) &  ( ((k1_vectsp_6 A B E) = (k1_vectsp_6 A C D))  &  ( ((k4_vectsp_6 A B E) = (k4_vectsp_6 A C D))  &  ((k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) E (u1_struct_0 C)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k4_topgen_1 A) B) => (r1_ordinal1 (k2_waybel23 A) B)) ) ) ) ) ).
tt(l25_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) & (v1_mod_3 C A B)) ) ) ) ) ) ).
tt(l25_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_1 A) =>  ((k1_funct_1 A 1) = k6_numbers) ) ) ) ).
tt(l25_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_2 A) =>  ((k1_funct_1 A 1) = 3) ) ) ) ).
tt(l25_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r4_msualg_3 A B C D) => (r1_msualg_3 A C B (k4_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D))) ) ) ) ) ) ) ) ) ).
tt(l25_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  <=> (r1_xxreal_0 A (k21_binop_2 B 1))) ) ) ) ) ).
tt(l25_normform,ax, (! [A:$i] : (v2_binop_1 (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) ).
tt(l25_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden B (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_openlatt A C) (k10_openlatt A D))) <=>  ((r2_hidden C B) &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_relat_2 A) => (v6_relat_2 (k2_relat_1 A))) ) ) ).
tt(l25_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ( ((k1_polynom2 A D) = (k2_xboole_0 (k1_polynom2 A C) (k1_tarski E)))  &  (! [F:$i] :  ( (~  (F = E) )  =>  ((k1_recdef_1 D F) = (k1_recdef_1 C F)) ) ) )  =>  ((r2_hidden E (k1_polynom2 A C)) |  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (G = (k1_binop_1 (k4_group_1 B) (k1_funct_1 F E) (k1_recdef_1 D E)))  =>  ((k3_polynom2 A D B F) = (k8_group_1 B G (k3_polynom2 A C B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v2_poset_1 C A A) &  (B = (k1_yellow_0 A (k2_poset_1 A C))) )  => (r2_abian (u1_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(l25_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (m1_subset_1 (k9_qc_lang1 A) (k1_zfmisc_1 (k13_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))))) ) ).
tt(l25_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) k1_numbers)))) )  =>  ( ( (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H B))  =>  ((k1_binop_1 E G H) = (k11_binop_2 (k1_seq_1 C (k1_tarski G)) (k1_seq_1 D (k1_tarski H)))) ) ) )  &  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k1_seq_1 F G) = (k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 G E)) ) ) )  =>  (! [G:$i] :  ((r1_tarski G (k2_zfmisc_1 A B)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 F G)) & (r1_xxreal_0 (k1_seq_1 F G) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_realset2,ax, (! [A:$i] :  ((r2_hidden A (k2_zfmisc_1 (k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2))) (k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2))))) => (r2_hidden (k1_funct_1 k2_realset2 A) (k6_subset_1 c4__realset2 (k6_domain_1 2 (k1_funct_7 k6_numbers 2))))) ) ).
tt(l25_rfinseq2,ax, (! [A:$i] :  ( ((v1_integra2 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_integra2 B) & (m2_finseq_1 B k1_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k2_nat_1 C 1))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  & (r2_classes1 A B)) )  =>  ( ((k1_seq_1 A (k3_finseq_1 A)) = (k1_seq_1 B (k3_finseq_1 B)))  & (r2_classes1 (k17_finseq_1 k1_numbers C A) (k17_finseq_1 k1_numbers C B))) ) ) ) ) ) ) ) ).
tt(l25_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((m1_rlsub_1 B C) & (m1_rlsub_1 B D))  => (m1_rlsub_1 B (k2_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(l25_scmfsa_1,ax,(r1_tarski (k10_xtuple_0 k4_scmfsa_1) (k9_xtuple_0 k5_scmfsa_1))).
tt(l25_scmpds_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 B) A) A) 1) = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k18_complex1 B) A) B))) ) ) ) ) ) ) ).
tt(l25_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( ((k2_compos_0 k1_scmpds_i A) = k6_numbers)  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l25_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_tarski k4_scmp_gcd D) &  ((r1_tarski k4_scmp_gcd E) &  ( ((k5_memstr_0 2 k1_scmpds_2 B) = 5)  &  ( (A = (k1_funct_1 B k3_scmp_gcd))  &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k5_memstr_0 2 k1_scmpds_2 C) = (k5_memstr_0 2 k1_scmpds_2 B))  &  ( ((k1_funct_1 C k3_scmp_gcd) = (k1_funct_1 B k3_scmp_gcd))  &  ( ((k1_funct_1 C k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 C (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)))  &  ((k1_funct_1 C (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) k6_numbers) |  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmpds_2)))  =>  ( ((r1_xxreal_0 F 7) &  ((k1_funct_1 B G) = (k1_funct_1 C G)) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 D B F)) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 E C F)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 D B F) G) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 E C F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v3_scmyciel (k1_tarski k1_xboole_0) A)) ) ).
tt(l25_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd 1)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd 3)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd 4)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd 6)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 1))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 7 C) =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A) (k1_scmp_gcd C)) = (k1_funct_1 B (k1_scmp_gcd C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ((r1_xxreal_0 8 (k1_funct_1 B (k1_scmp_gcd 3))) &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  & (r1_xxreal_0 8 C)) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A) & (r2_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers))))) B A)) ) ) ) ) ) ) ) ).
tt(l25_sincos10,ax,(r1_tarski (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)) (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))).
tt(l25_sin_cos9,ax,(r2_hidden (k10_real_1 k32_sin_cos 4) (k2_rcomp_1 k6_numbers k32_sin_cos))).
tt(l25_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l25_square_1,ax, ((k5_square_1 2) = (k3_xcmplx_0 2 2)) ).
tt(l25_topdim_2,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 1)) (u1_pre_topc (k15_euclid 1))) = (k3_pcomps_1 (k14_euclid 1))) ).
tt(l25_topreal2,ax,(r2_hidden (k19_euclid 1 k6_numbers) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)))).
tt(l25_toprealb,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 k19_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2))))) ) ).
tt(l25_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  ( ((k2_vectsp_5 A B E C) = (k2_vectsp_5 A B E D))  &  ((k2_vectsp_5 A B C E) = (k2_vectsp_5 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_waybel30,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  =>  ((k1_funct_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B)) (k4_tarski C D)) = (k4_tarski D C)) ) ) ) ) ) ).
tt(l25_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v2_waybel19 B) & (m1_yellow_9 B A)) )  => (r1_ordinal1 (k2_waybel23 B) (k1_waybel31 A))) ) ) ) ).
tt(l25_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k4_waybel_0 A (k12_waybel_0 A (k4_subset_1 (u1_struct_0 A) B C)))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r1_orders_2 A (k12_lattice3 A E (k2_yellow_0 A C)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l25_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = (k5_xcmplx_0 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(l25_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(l25_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (E = C)  &  ( (F = D)  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B F E)) &  ( (H = G)  &  (~  ( ((v1_altcat_3 G A C D) => (v2_altcat_3 H B F E))  &  ((v2_altcat_3 G A C D) => (v1_altcat_3 H B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  =>  ( (B = C)  |  (D = (k2_aff_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_algstr_0)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k8_algstr_0)) =>  ((k6_algstr_0 k8_algstr_0 (k6_algstr_0 k8_algstr_0 A B) C) = (k6_algstr_0 k8_algstr_0 A (k6_algstr_0 k8_algstr_0 B C))) ) ) ) ) ) ) ).
tt(l26_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k5_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(l26_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_anproj_1 A B C D))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 E A))  &  ( (~ (v9_struct_0 F A))  &  ( (~ (r1_anproj_1 A E F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) => (r2_anproj_1 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k1_arytm_1 C (k1_arytm_1 B A)) = (k1_arytm_1 (k7_arytm_2 C A) B)) ) ) ) ) ) ) ) ).
tt(l26_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ( ((r2_hidden C k1_arytm_2) &  ((r2_hidden A C) & (r3_arytm_3 B A)) )  => (r2_hidden B C)) ) ) ) ) ) ).
tt(l26_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((r1_xxreal_0 (k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) k6_numbers) | (r2_hidden A (k6_asympt_0 B))) ) ) ) ) ) ).
tt(l26_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (r1_xxreal_0 (k2_int_1 (k10_real_1 A 2)) A)) ) ).
tt(l26_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  => (v2_binop_1 (u1_bcialg_4 A) (u1_struct_0 A))) ) ).
tt(l26_binop_2,ax,(m1_subset_1 k6_numbers k2_numbers)).
tt(l26_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_pre_topc C A) => (m1_pre_topc (k2_borsuk_1 C B) (k2_borsuk_1 A B))) ) ) ) ) ) ).
tt(l26_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cc0sp1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_cc0sp1 A))) =>  ( (C = (k4_c0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)))  =>  ( ((k6_algstr_0 (k7_cc0sp1 A) B C) = B)  &  ((k6_algstr_0 (k7_cc0sp1 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l26_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_algstr_0 (k5_cc0sp2 A) B C) = (k3_rlvect_1 (k7_cc0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_classes2,ax, (! [A:$i] :  ( ((v2_classes1 A) & (r2_hidden k1_xboole_0 (k2_ordinal1 A)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 k1_xboole_0)) (k1_card_1 A)) & (r2_hidden (k4_classes1 k1_xboole_0) A)) ) ) ).
tt(l26_collsp,ax, ( (~ (v2_struct_0 (g1_collsp c7__collsp c8__collsp)))  & (l1_collsp (g1_collsp c7__collsp c8__collsp))) ).
tt(l26_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 A B) = (k5_arytm_0 (k7_real_1 (k3_complex1 A) (k3_complex1 B)) (k7_real_1 (k4_complex1 A) (k4_complex1 B)))) ) ) ) ) ).
tt(l26_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  (~  ( ((k3_finseq_1 E) = C)  &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((k12_supinf_2 B G) = k2_supinf_1) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 C)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 D G)) &  ((k12_supinf_2 E G) = (k1_extreal1 (k1_measure6 (k1_seq_1 D G)) (k12_supinf_2 B (k7_partfun1 (u1_struct_0 A) F G)))) ) ) ) )  & (r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 23)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  ( (~  (B = (k1_nat_1 A 15)) )  &  ( (~  (B = (k1_nat_1 A 16)) )  &  ( (~  (B = (k1_nat_1 A 17)) )  &  ( (~  (B = (k1_nat_1 A 18)) )  &  ( (~  (B = (k1_nat_1 A 19)) )  &  ( (~  (B = (k1_nat_1 A 20)) )  &  ( (~  (B = (k1_nat_1 A 21)) )  &  ( (~  (B = (k1_nat_1 A 22)) )  &  (~  (B = (k1_nat_1 A 23)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_diraf A B C D E) & (r2_diraf A B C F G))  =>  ( (B = C)  | (r2_diraf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_dist_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v1_prob_2 A) => (v1_prob_2 (k5_relat_1 A B))) ) ) ) ).
tt(l26_dtconstr,ax, ((k2_lang1 k5_dtconstr) = (k6_domain_1 (u1_struct_0 k5_dtconstr) c3__dtconstr)) ).
tt(l26_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((k2_binop_1 (u1_struct_0 (k9_int_3 A)) k5_numbers (u1_struct_0 (k9_int_3 A)) (k4_group_1 (k9_int_3 A)) B 2) = (k8_group_1 (k9_int_3 A) B B)) ) ) ) ) ).
tt(l26_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((r2_hidden (k4_tarski D B) C) <=>  ((k6_eqrel_1 A A C D) = (k6_eqrel_1 A A C B)) ) ) ) ) ) ) ) ).
tt(l26_fib_num4,ax, (~ (r1_xxreal_0 (k2_xcmplx_0 (k7_square_1 5) 3) (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) 3))) ).
tt(l26_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k18_complex1 B) 1) => (r1_xxreal_0 (k18_complex1 (k1_newton B A)) 1)) ) ) ) ) ).
tt(l26_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  => (r2_hidden (k7_fomodel1 A) (k6_subset_1 (k15_fomodel1 A) (k1_tarski (k8_fomodel1 A))))) ) ).
tt(l26_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ((r1_tarski B (k1_fomodel4 C)) => (r1_tarski (k1_funct_1 (k3_fomodel4 C D A) B) (k5_setfam_1 (k1_fomodel4 C) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 C)) (k2_fomodel4 C D)) (k1_tarski B))))) ) ) ) ) ) ) ) ).
tt(l26_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F))  &  ( ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k16_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))) ) ).
tt(l26_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( ( (~ (r1_geomtrap A D E F G))  &  (~ (r1_geomtrap A F G D E)) )  |  ( ( (~ (r3_analmetr A H I F G B C))  &  (~ (r3_analmetr A F G H I B C)) )  |  ( (F = G)  |  ((r3_analmetr A D E H I B C) & (r3_analmetr A H I D E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( ((k7_glib_000 A) = k1_xboole_0)  => (v7_glib_000 A)) ) ) ).
tt(l26_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ( ((v4_glib_002 C A) & (m1_glib_000 C A))  =>  ( ((k24_glib_000 A B) = (k24_glib_000 A C))  <=> (r5_glib_000 B C)) ) ) ) ) ) ) ).
tt(l26_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_graph_1 B) & (m3_graph_1 B A))  =>  (! [C:$i] :  ( ((v1_graph_1 C) & (m3_graph_1 C A))  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 C))  &  ((u4_struct_0 B) = (u4_struct_0 C)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l26_graph_2,ax,(v1_graph_2 (k2_finseq_4 k5_numbers 1 2))).
tt(l26_group_10,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((k7_group_1 (k4_gr_cy_1 A)) = A) ) ) ).
tt(l26_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) => (v6_hilbert1 (k5_hilbert1 A))) ) ).
tt(l26_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_1 A B C D) =>  ((r2_hidden B D) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((r2_hidden E D) &  (E = F) ) )  &  (~  ( (~ (r2_hidden E D))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r2_hidden G D) &  ((r2_hidden H D) &  ((r2_analoaf A G B H E) &  ((r2_analoaf A G C H F) & (r2_aff_1 A E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (a_2_4_ideal_1 A B)))  &  ((v1_ideal_1 (a_2_4_ideal_1 A B) A) &  ((v2_ideal_1 (a_2_4_ideal_1 A B) A) &  ((v3_ideal_1 (a_2_4_ideal_1 A B) A) & (m1_subset_1 (a_2_4_ideal_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(l26_int_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ((v1_int_7 B) &  ((v1_int_7 C) &  ((r1_xxreal_0 (k8_nat_3 k10_newton B) (k13_newton 2 A)) &  ((k8_nat_3 k10_newton B) = (k8_nat_3 k10_newton C)) ) ) )  => (r8_pboole k10_newton B C)) ) ) ) ) ) ) ).
tt(l26_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ( (C = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k5_seq_4 A)) B))  =>  ((k1_integra3 A C) = (k1_integra3 A B)) ) ) ) ) ) ) ) ).
tt(l26_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_numbers (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) k5_pscomp_1)) = (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) ) ) ).
tt(l26_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A) (k1_pre_topc (k15_euclid 2) A) k3_topmetr) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A) B) = (k1_funct_1 (k1_jgraph_4 2) B)) ) ) ) ) ) ).
tt(l26_jgraph_6,ax,(r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1))).
tt(l26_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k10_lattice3 A B C))  <=>  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_rfunct_3 C B k1_numbers (k3_rfunct_3 B k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D B k1_numbers (k3_rfunct_3 B k1_numbers)) =>  ((k2_lpspace1 B k1_numbers (k13_rfunct_3 B) (k2_binop_1 k1_numbers (k3_rfunct_3 B k1_numbers) (k3_rfunct_3 B k1_numbers) (k4_lpspace1 B) A C) (k2_binop_1 k1_numbers (k3_rfunct_3 B k1_numbers) (k3_rfunct_3 B k1_numbers) (k4_lpspace1 B) A D)) = (k2_binop_1 k1_numbers (k3_rfunct_3 B k1_numbers) (k3_rfunct_3 B k1_numbers) (k4_lpspace1 B) A (k2_lpspace1 B k1_numbers (k13_rfunct_3 B) C D))) ) ) ) ) ) ) ) ) ).
tt(l26_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k4_power (k18_complex1 (k9_real_1 (k1_seq_1 C E) B)) A)) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k4_power (k18_complex1 (k9_real_1 (k2_seq_2 C) B)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) C) D) (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A C E) B) D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l26_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k5_matrix_6 D k2_vectsp_1 (k2_matrtop3 D A B C)) = (k2_matrtop3 D (k4_xcmplx_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_modal_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_finset_1 (k9_xtuple_0 A)) => (v1_finset_1 A)) ) ) ).
tt(l26_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_1 A) =>  ((k1_funct_1 A 1) = 1) ) ) ) ).
tt(l26_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_2 A) =>  ((k1_funct_1 A 1) = 4) ) ) ) ).
tt(l26_nat_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 (k1_funct_1 B A))) D))  &  ( ((k3_finseq_1 C) = (k21_binop_2 A 1))  &  ((k3_finseq_1 D) = (k21_binop_2 (k3_finseq_1 B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_numbers,ax,(r1_tarski k4_numbers k3_numbers)).
tt(l26_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v8_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l26_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (? [D:$i] :  ((k1_polynom2 A C) = (k1_tarski D)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k3_polynom2 A (k11_pre_poly A C D) B E) = (k8_group_1 B (k3_polynom2 A C B E) (k3_polynom2 A D B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) k6_numbers))  &  ((k3_funct_2 k5_numbers (u1_struct_0 A) B (k7_nat_d (k1_algseq_1 A B) 1)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l26_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_binom A (k5_struct_0 A) B) = (k5_struct_0 A)) ) ) ) ) ).
tt(l26_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (B = (k1_yellow_0 A (k2_poset_1 A C)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_abian (u1_struct_0 A) D C) => (r3_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(l26_prelamb,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (v7_ordinal1 (k18_rvsum_1 (k8_prelamb A B C)))) ) ) ) ) ) ).
tt(l26_prvect_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k12_rvsum_1 (k8_finseq_1 k1_numbers A B)) = (k8_finseq_1 k1_numbers (k12_rvsum_1 A) (k12_rvsum_1 B))) ) ) ) ) ).
tt(l26_quaterni,ax, (k6_numbers = (k6_quaterni k6_numbers k6_numbers k6_numbers k6_numbers)) ).
tt(l26_realset2,ax,(m2_subset_1 (k1_funct_7 1 2) c4__realset2 (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2)))).
tt(l26_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 B (k1_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(l26_scmfsa_1,ax, ((k9_xtuple_0 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) = k1_scmfsa_1) ).
tt(l26_scmpds_4,ax,(v2_scmpds_4 (k9_compos_1 k1_scmpds_2 (k2_compos_1 k1_scmpds_2)))).
tt(l26_scmpds_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ( (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 A B) (k4_struct_0 k1_scmpds_2)) = (k1_ordinal1 (k5_memstr_0 2 k1_scmpds_2 B))) ) )  => (v2_scmpds_4 (k9_compos_1 k1_scmpds_2 A))) ) ) ).
tt(l26_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_amistd_1 2 k1_scmpds_2 (k7_scmpds_2 A B 5)) = k1_xboole_0) ) ) ) ) ).
tt(l26_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( ((k2_compos_0 k1_scmpds_i A) = 14)  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l26_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (~  ((r1_tarski k4_scmp_gcd A) &  ((r1_tarski k4_scmp_gcd B) &  ( ((k5_memstr_0 2 k1_scmpds_2 C) = 5)  &  ( (~ (r1_xxreal_0 (k1_funct_1 C k3_scmp_gcd) k6_numbers))  &  ( ((k1_funct_1 C k2_scmp_gcd) = k6_numbers)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 3))) &  ((r1_xxreal_0 (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 3)) (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 2))) &  ( ((k5_memstr_0 2 k1_scmpds_2 D) = (k5_memstr_0 2 k1_scmpds_2 C))  &  ( ((k1_funct_1 D k3_scmp_gcd) = (k1_funct_1 C k3_scmp_gcd))  &  ( ((k1_funct_1 D k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 D (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 2)) = (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 2)))  &  ( ((k1_funct_1 D (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 3)) = (k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C k3_scmp_gcd) 3)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A C E)) = (k4_scmpds_2 k3_scmp_gcd))  &  ( ((k1_funct_1 C k3_scmp_gcd) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A C E) k3_scmp_gcd))  &  ( ((k3_extpro_1 2 k1_scmpds_2 B (k5_extpro_1 2 k1_scmpds_2 B D E)) = (k4_scmpds_2 k3_scmp_gcd))  &  ( ((k1_funct_1 D k3_scmp_gcd) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B D E) k3_scmp_gcd))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F (k2_xcmplx_0 (k1_funct_1 C k3_scmp_gcd) 1)) =>  ((r1_xxreal_0 F 1) |  ( ((k1_funct_1 C (k1_scmp_gcd F)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A C E) (k1_scmp_gcd F)))  &  ((k1_funct_1 D (k1_scmp_gcd F)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B D E) (k1_scmp_gcd F))) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmpds_2)))  =>  ( ((r1_xxreal_0 F E) &  ((k1_funct_1 C G) = (k1_funct_1 D G)) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A C F)) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D F)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A C F) G) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 7) (k1_funct_1 B (k1_scmp_gcd 3))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 2)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 2)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 3)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd 1)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 1))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~  (C = 2) )  =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A) (k1_scmp_gcd C)) = (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) B A)) A) (k1_scmp_gcd C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_scpqsort,ax, ((k5_card_1 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) = 29) ).
tt(l26_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_xboole_0 (k4_simplex0 A)) <=> (v4_simplex0 A)) ) ) ).
tt(l26_sincos10,ax,(r1_tarski (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos) (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))).
tt(l26_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k15_sin_cos (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k5_binop_2 (k26_sin_cos A) (k3_binop_2 (k21_sin_cos B) (k5_binop_2 (k18_sin_cos B) k7_complex1)))) ) ) ) ) ).
tt(l26_sin_cos9,ax,(r2_hidden (k8_real_1 (k10_real_1 3 4) k32_sin_cos) (k2_rcomp_1 k6_numbers k32_sin_cos))).
tt(l26_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l26_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) => (m2_finseq_1 (k7_finseq_1 (k7_finseq_1 (k12_finseq_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers)) (k12_finseq_1 (k3_qc_lang1 A) B)) C) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ) ) ) ) ).
tt(l26_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topgen_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  ((r1_tarski C B) &  ((k1_card_1 C) = (k2_waybel23 A)) ) ) ) ) ) ) ) ).
tt(l26_topreal2,ax,(r2_hidden (k19_euclid 1 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)))).
tt(l26_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (k2_topalg_2 = (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 A B)))))  &  (k2_topalg_2 = (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 A B))))) ) ) ) ) ) ).
tt(l26_valued_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((k1_relset_1 A (k46_valued_1 A B C D E)) = A) ) ) ) ) ) ) ) ) ) ).
tt(l26_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (m1_subset_1 (a_2_11_waybel12 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(l26_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~  ((v2_waybel_8 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_1 B)) & (m1_yellow_0 C (k3_yellow_1 B)))  =>  (~  ((v7_yellow_0 C (k3_yellow_1 B)) &  ((v4_waybel_0 C (k3_yellow_1 B)) & (r5_waybel_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l26_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) =>  ( ( (C = (a_2_5_waybel14 A B))  &  (D = (k7_setfam_1 (u1_struct_0 A) C)) )  => (v1_waybel_0 D (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) ) ) ).
tt(l26_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 B A))  <=> (r1_xxreal_0 A (k5_real_1 B 1))) ) ) ) ) ).
tt(l26_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k7_xcmplx_0 A (k7_xcmplx_0 B C)) = (k7_xcmplx_0 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(l26_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k4_xcmplx_0 B) (k4_xcmplx_0 A))) ) ) ) ) ).
tt(l26_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (m2_xxreal_2 A (k2_tarski B A))) ) ) ) ) ).
tt(l26_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (C = (a_2_0_yellow13 A B))  => (m1_yellow13 C A B)) ) ) ) ) ) ).
tt(l26_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) B) = (k1_tarski A))  <=>  (~ (r2_hidden A B)) ) ) ) ).
tt(l27_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) & (r1_tarski C (k1_aff_4 A B D)))  => (r1_tarski (k1_aff_4 A B C) (k1_aff_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(l27_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A D (k5_struct_0 A)) = D) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k6_algstr_0 A D E) = (k5_struct_0 A)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A D E) F) = (k6_algstr_0 A D (k6_algstr_0 A E F))) ) ) ) ) ) )  &  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) )  =>  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(l27_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k6_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(l27_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 C A))  =>  ((k1_arytm_1 B (k1_arytm_1 A C)) = (k7_arytm_2 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ).
tt(l27_arytm_2,ax, (! [A:$i] :  ((r2_hidden A k1_arytm_2) =>  ( (A = k11_arytm_3)  | (r2_hidden k11_arytm_3 A)) ) ) ).
tt(l27_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_seq_1 A k6_numbers) = k6_numbers)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  =>  ((k1_seq_1 A D) = B) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k7_series_1 A C D) = (k8_real_1 B (k9_real_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(l27_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (~  ((k1_bcialg_1 A (k3_bcialg_6 A C B) (k3_bcialg_6 A D B)) = (k3_bcialg_6 A (k21_binop_2 C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_binop_2,ax,(r3_binop_1 k2_numbers c1__binop_2 k27_binop_2)).
tt(l27_borsuk_4,ax, ((v1_borsuk_1 k5_topmetr k3_topmetr) & (m1_pre_topc k5_topmetr k3_topmetr)) ).
tt(l27_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = (k3_tarski (a_2_0_cat_2 A B)))  &  ( (D = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C))  &  ( (E = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C))  &  (F = (k1_realset1 (u1_cat_1 A) C)) ) ) )  =>  ( (~ (v2_struct_0 (g1_cat_1 B C D E F)))  &  ( (~ (v11_struct_0 (g1_cat_1 B C D E F)))  &  ((v2_cat_1 (g1_cat_1 B C D E F)) &  ((v3_cat_1 (g1_cat_1 B C D E F)) &  ((v4_cat_1 (g1_cat_1 B C D E F)) &  ((v5_cat_1 (g1_cat_1 B C D E F)) &  ((v6_cat_1 (g1_cat_1 B C D E F)) & (l1_cat_1 (g1_cat_1 B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( (C = D)  =>  ((k1_clvect_1 (k5_cc0sp2 A) C B) = (k1_clvect_1 (k7_cc0sp1 (u1_struct_0 A)) D B)) ) ) ) ) ) ) ) ) ) ).
tt(l27_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A (k2_ordinal1 B)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 A)) (k1_card_1 B)) & (r2_hidden (k4_classes1 A) B)) ) )  =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden (k1_ordinal1 A) (k2_ordinal1 B)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 (k1_ordinal1 A))) (k1_card_1 B)) & (r2_hidden (k4_classes1 (k1_ordinal1 A)) B)) ) ) ) ) ) ).
tt(l27_collsp,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c9__collsp)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c9__collsp)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c9__collsp)) =>  ((r2_hidden (k4_domain_1 (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) A B C) c8__collsp) <=>  ( (~  ( (~  (A = B) )  &  ( (~  (B = C) )  &  (~  (C = A) ) ) ) )  &  ((r2_hidden A c7__collsp) &  ((r2_hidden B c7__collsp) & (r2_hidden C c7__collsp)) ) ) ) ) ) ) ) ) ) ).
tt(l27_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 A B) = (k5_arytm_0 (k9_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))) (k7_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B)) (k8_real_1 (k3_complex1 B) (k4_complex1 A))))) ) ) ) ) ).
tt(l27_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v5_qc_lang1 C A) =>  ((k13_cqc_lang A C B) = (k15_funcop_1 (k9_qc_lang1 A) (k21_qc_lang1 A C) B C (k15_qc_lang1 A (k21_qc_lang1 A C) (k13_cqc_lang A (k22_qc_lang1 A C) B)))) ) ) ) ) ) ) ) ).
tt(l27_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 31)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  ( (~  (B = (k1_nat_1 A 15)) )  &  ( (~  (B = (k1_nat_1 A 16)) )  &  ( (~  (B = (k1_nat_1 A 17)) )  &  ( (~  (B = (k1_nat_1 A 18)) )  &  ( (~  (B = (k1_nat_1 A 19)) )  &  ( (~  (B = (k1_nat_1 A 20)) )  &  ( (~  (B = (k1_nat_1 A 21)) )  &  ( (~  (B = (k1_nat_1 A 22)) )  &  ( (~  (B = (k1_nat_1 A 23)) )  &  ( (~  (B = (k1_nat_1 A 24)) )  &  ( (~  (B = (k1_nat_1 A 25)) )  &  ( (~  (B = (k1_nat_1 A 26)) )  &  ( (~  (B = (k1_nat_1 A 27)) )  &  ( (~  (B = (k1_nat_1 A 28)) )  &  ( (~  (B = (k1_nat_1 A 29)) )  &  ( (~  (B = (k1_nat_1 A 30)) )  &  (~  (B = (k1_nat_1 A 31)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_dist_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((v1_prob_2 B) &  ( ((k9_xtuple_0 B) = (k4_finseq_1 C))  &  ( (A = (k3_finseq_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((v1_finset_1 (k1_funct_1 B D)) &  ((k1_funct_1 C D) = (k1_card_1 (k1_funct_1 B D))) ) ) ) ) ) ) )  =>  ((v1_finset_1 (k3_card_3 B)) &  ((k1_card_1 (k3_card_3 B)) = (k16_rvsum_1 C)) ) ) ) ) ) ) ) ) ).
tt(l27_dtconstr,ax, ( (~ (v1_xboole_0 (k4_dtconstr k5_dtconstr)))  & (m1_subset_1 (k4_dtconstr k5_dtconstr) (k1_zfmisc_1 (k5_trees_3 (u1_struct_0 k5_dtconstr))))) ).
tt(l27_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r3_fdiff_3 A C) & (r3_fdiff_3 B C))  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k1_numbers B)) &  ((r2_hidden E (k1_rcomp_1 C (k7_real_1 C D))) &  ((k1_seq_1 B E) = k6_numbers) ) ) ) ) ) ) ) ) )  |  ((r3_fdiff_3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) &  ((k2_fdiff_3 C (k3_rfunct_1 k1_numbers k1_numbers A B)) = (k10_real_1 (k9_real_1 (k8_real_1 (k2_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k2_fdiff_3 C B) (k1_seq_1 A C))) (k5_square_1 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(l27_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 (k2_xcmplx_0 (k7_square_1 5) 3) 2) (k13_complex1 (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) 3) 2))) ).
tt(l27_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (r1_xxreal_0 1 (k18_complex1 (k13_complex1 (k3_power k2_fib_num A) (k7_square_1 5))))) ) ) ).
tt(l27_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (A = k1_xboole_0)  <=>  ((k3_finseq_1 A) = k6_numbers) ) ) ) ).
tt(l27_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 B) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 B) A)))) ) ) ) ) ) ) ) ).
tt(l27_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k1_funct_1 (k5_fomodel0 A B) (k12_finseq_1 A D)) = D)  &  ((k1_funct_1 (k5_fomodel0 A B) (k1_monoid_0 A C (k12_finseq_1 A D))) = (k1_binop_1 B (k1_funct_1 (k5_fomodel0 A B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(l27_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ((k5_setfam_1 (k1_fomodel4 B) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B C)) (k1_tarski A))) = (k3_tarski (a_3_5_fomodel4 A B C))) ) ) ) ) ) ).
tt(l27_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden C (k24_glib_000 A B)) <=>  ((k24_glib_000 A B) = (k1_glib_002 A C)) ) ) ) ) ) ) ) ).
tt(l27_graph_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k1_nat_1 A 1) (k3_finseq_1 (k2_finseq_4 k5_numbers 1 2))) &  ((k1_recdef_1 (k2_finseq_4 k5_numbers 1 2) A) = (k1_recdef_1 (k2_finseq_4 k5_numbers 1 2) (k1_nat_1 A 1))) ) ) ) ) ) ).
tt(l27_gr_cy_1,ax, (k2_gr_cy_1 = (k5_group_4 k2_gr_cy_1 (k6_domain_1 (u1_struct_0 k2_gr_cy_1) (k5_gr_cy_1 1)))) ).
tt(l27_heyting1,ax, ((k5_finsub_1 (k7_normform k1_xboole_0)) = (k2_tarski k1_xboole_0 (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0)))) ).
tt(l27_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k3_heyting3 A B) (k3_heyting3 (k2_nat_1 A 1) B))) ) ) ) ).
tt(l27_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_1 A B C D) =>  ((r2_hidden B D) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((r2_hidden F D) &  (F = E) ) )  &  (~  ( (~ (r2_hidden F D))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r2_hidden G D) &  ((r2_hidden H D) &  ((r2_analoaf A G B H F) &  ((r2_analoaf A G C H E) & (r2_aff_1 A F E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) k6_numbers))  &  ((k1_funct_1 B (k6_xcmplx_0 (k1_algseq_1 A B) 1)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l27_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k24_binop_2 C B) A) &  (~ (r1_xxreal_0 (k24_binop_2 (k23_binop_2 C 1) B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_relset_1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers (k2_partfun1 k1_numbers k2_numbers A B)) (k2_partfun1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers A) B)) & (r2_relset_1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers (k2_partfun1 k1_numbers k2_numbers A B)) (k2_partfun1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers A) B))) ) ) ) ) ).
tt(l27_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((r1_tarski (k3_integra5 C D) (k9_xtuple_0 (k56_valued_1 k1_numbers k1_numbers E))) &  ((r1_integra5 (k3_integra5 C D) (k56_valued_1 k1_numbers k1_numbers E)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers E) (k3_integra5 C D))) & (r1_xxreal_0 (k18_complex1 (k4_integra5 C D E)) (k4_integra5 C D (k56_valued_1 k1_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_numbers (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) k4_pscomp_1)) = (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) ) ) ).
tt(l27_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (B = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) (k1_jgraph_4 2) A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  (C = (k4_struct_0 (k15_euclid 2))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  (~  ((k3_funct_2 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr) B C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l27_jgraph_6,ax,(r2_hidden 1 (k1_rcomp_1 k6_numbers 1))).
tt(l27_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ( ((r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B)) &  (~  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) ) )  |  ( (B = C)  | (r1_tarski (k3_topreal1 2 (k4_jordan3 A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(l27_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v2_comseq_2 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_seq_1 E F) = (k7_real_1 (k4_power (k18_complex1 (k9_real_1 (k1_seq_1 C F) B)) A) (k1_seq_1 D F))) ) )  =>  ((v2_comseq_2 E) &  ((k2_seq_2 E) = (k7_real_1 (k4_power (k18_complex1 (k9_real_1 (k2_seq_2 C) B)) A) (k2_seq_2 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) D) (k8_cqc_lang A (k8_cqc_lang A B D) D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(l27_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k2_mboolean A (k2_pboole A B C)) D) = (k3_tarski (k2_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l27_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) & (r1_xxreal_0 D C))  => (r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) D)))) ) ) ) ) ) ) ) ) ) ).
tt(l27_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_1 A) =>  ((k1_funct_1 A 1) = 2) ) ) ) ).
tt(l27_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_modelc_2 A) =>  ((k1_funct_1 A 1) = 5) ) ) ) ).
tt(l27_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v5_group_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(l27_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 5 A))  &  ((v1_int_2 A) &  ( (~  (A = 2) )  &  (~  (A = 3) ) ) ) ) ) ) ) ) ).
tt(l27_nat_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((r2_hidden A (k4_finseq_1 B)) &  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 E)) D))  &  ((k3_finseq_1 C) = (k21_binop_2 A 1)) ) )  =>  ((k2_finseq_3 A B) = (k7_finseq_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_nat_lat,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k1_lattices k10_nat_lat A B) = (k1_lattices k10_nat_lat B A)) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k10_nat_lat)) =>  ((k1_lattices k10_nat_lat A (k1_lattices k10_nat_lat B C)) = (k1_lattices k10_nat_lat (k1_lattices k10_nat_lat A B) C)) ) ) ) ) ) ) ) ).
tt(l27_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_oppcat_1 A))) =>  ( ( (~  ((k2_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A B) C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) (k3_oppcat_1 A B) C) =>  ((k1_cat_1 (k2_oppcat_1 A) (k7_oppcat_1 A B B (k4_cat_1 A B)) D) = D) ) ) )  &  ( (~  ((k2_cat_1 (k2_oppcat_1 A) C (k3_oppcat_1 A B)) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) C (k3_oppcat_1 A B)) =>  ((k1_cat_1 (k2_oppcat_1 A) D (k7_oppcat_1 A B B (k4_cat_1 A B))) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k12_ordinal2 k1_xboole_0 C)) ) ) ) )  => (r1_ordinal2 k1_xboole_0 B)) ) ) ) ) ) ) ).
tt(l27_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v9_o_ring_1 B A)) ) ) ) ) ).
tt(l27_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_algseq_1 A C) k6_numbers))  &  (~  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k11_polynom3 A (k1_polynom4 A B) (k1_polynom4 A C)) D) = (k6_algstr_0 A (k6_algstr_0 A (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) (k1_normsp_1 A C (k7_nat_d (k1_algseq_1 A C) 1))) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) D (k7_nat_d (k2_nat_1 (k1_algseq_1 A B) (k1_algseq_1 A C)) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom7 A B (k4_struct_0 B)) (k7_polynom1 A B))) ) ) ).
tt(l27_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k8_group_1 A (k2_binom A C B) (k2_binom A (k11_algstr_0 A C) B)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(l27_real_3,ax, ((k1_relset_1 k5_numbers (k8_funcop_1 k5_numbers k5_numbers k6_numbers)) = k5_numbers) ).
tt(l27_realset2,ax, ((v1_funct_1 k1_realset2) &  ((v1_funct_2 k1_realset2 (k2_zfmisc_1 c4__realset2 c4__realset2) c4__realset2) & (m1_subset_1 k1_realset2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 c4__realset2 c4__realset2) c4__realset2)))) ) ).
tt(l27_rfinseq2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_integra2 B) & (m2_finseq_1 B k1_numbers))  =>  (! [C:$i] :  ( ((v1_integra2 C) & (m2_finseq_1 C k1_numbers))  =>  ( ( (A = (k3_finseq_1 B))  & (r2_classes1 B C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l27_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((m1_rlsub_1 B C) & (m1_rlsub_1 D C))  => (m1_rlsub_1 (k1_rlsub_2 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(l27_scm_comp,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_dtconstr k1_scm_comp) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr k1_scm_comp) k5_numbers)))) )  &  ( ((k17_scm_comp o_0_2_scm_comp) = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers A o_0_2_scm_comp))  &  ( (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers A (k3_scm_comp B)) = (k16_scm_comp B)) ) )  &  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_scm_comp)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k1_scm_comp)) =>  ( ( (E = (k1_bintree1 (u1_struct_0 k1_scm_comp) C))  &  ( (F = (k1_bintree1 (u1_struct_0 k1_scm_comp) D))  & (r1_lang1 k1_scm_comp B (k4_pre_poly (u1_struct_0 k1_scm_comp) E F))) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ( (G = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers A C))  &  (H = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers A D)) )  =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers A (k2_scm_comp B C D)) = (k7_nat_1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (B = 5) )  =>  ((k2_amistd_1 2 k1_scmpds_2 (k7_scmpds_2 A C B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(l27_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( ((k2_compos_0 k1_scmpds_i A) = 1)  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l27_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_tarski (k7_memstr_0 2 k1_scmpds_2 k6_numbers) C) &  ((r1_tarski (k7_memstr_0 2 k1_scmpds_2 k6_numbers) D) &  ((r1_tarski k4_scmp_gcd A) &  ((r1_tarski k4_scmp_gcd B) &  ( ((k1_funct_1 C E) = (k1_funct_1 D E))  & (r1_xxreal_0 F 4)) ) ) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A C F)) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D F)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A C F) E) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_scpinvar,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) => (r1_tarski (k61_valued_1 A 2) (k4_scpinvar B C A))) ) ) ) ) ) ).
tt(l27_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 7) (k1_funct_1 B (k1_scmp_gcd 3))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_scmpds_6 (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) B A) & (r2_scmpds_6 (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) B A)) ) ) ) ) ) ).
tt(l27_scpqsort,ax, ((k5_card_1 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))))) = 31) ).
tt(l27_seqm_3,ax, ((v5_valued_0 (k6_funct_3 k1_numbers k5_numbers)) & (v4_valued_0 (k6_funct_3 k1_numbers k5_numbers))) ).
tt(l27_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C B) & (r2_hidden A C))  => (r2_hidden A (k4_simplex0 B))) ) ) ) ) ) ).
tt(l27_sincos10,ax,(r1_tarski (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))).
tt(l27_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k10_real_1 (k7_real_1 (k11_binop_2 C B) (k11_binop_2 A D)) (k7_real_1 (k11_binop_2 A B) (k11_binop_2 C D))) = (k10_real_1 (k7_real_1 (k12_binop_2 C A) (k12_binop_2 D B)) (k7_real_1 1 (k8_real_1 (k12_binop_2 C A) (k12_binop_2 D B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_sin_cos9,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))) ).
tt(l27_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l27_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) => (r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) (k1_substut1 A) (k12_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)) (k1_domain_1 k5_numbers (k1_qc_lang1 A) B C)) D) (k2_zfmisc_1 (k13_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) (k1_substut1 A)))) ) ) ) ) ) ) ) ).
tt(l27_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A C D) =>  (! [K:$i] :  ((m1_borsuk_2 K B E F) =>  (! [L:$i] :  ((m1_borsuk_2 L B E F) =>  (! [M:$i] :  ((m1_borsuk_6 M A C D I J) =>  (! [N:$i] :  ((m1_borsuk_6 N B E F K L) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) I (k3_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) J (k3_topalg_4 A B k5_topmetr H)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) K (k4_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) L (k4_topalg_4 A B k5_topmetr H)) &  ((r3_borsuk_2 A C D I J) & (r3_borsuk_2 B E F K L)) ) ) ) )  =>  ((v5_pre_topc (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) (k2_borsuk_1 k5_topmetr k5_topmetr) (k2_borsuk_1 A B)) &  (! [O:$i] :  ((m1_subset_1 O (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) O k6_numbers) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k2_borsuk_1 A B)) G O))  &  ( ((k1_binop_1 (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) O 1) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k2_borsuk_1 A B)) H O))  &  (! [P:$i] :  ((m1_subset_1 P (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) k6_numbers P) = (k4_borsuk_1 A B C E))  &  ((k1_binop_1 (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) 1 P) = (k4_borsuk_1 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_topreal2,ax,(r2_hidden (k19_euclid 1 1) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)))).
tt(l27_topreal4,ax, ((k3_pcomps_1 (k14_euclid 2)) = (g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2)))) ).
tt(l27_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) (u1_struct_0 (k3_pcomps_1 (k14_euclid (k2_nat_1 A B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) (u1_struct_0 (k3_pcomps_1 (k14_euclid (k2_nat_1 A B)))))))) )  &  ((v3_tops_2 C (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B))) (k3_pcomps_1 (k14_euclid (k2_nat_1 A B)))) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ((r2_hidden (k4_tarski D E) (k1_relset_1 (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) C)) =>  ((k1_binop_1 C D E) = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) => (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(l27_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) C D E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A D)) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k3_waybel_0 A (k11_waybel_0 A (k4_subset_1 (u1_struct_0 A) B C)))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r3_orders_2 A D (k13_lattice3 A E (k1_yellow_0 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l27_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 (k3_real_1 B 1) A))  <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(l27_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_xcmplx_0 (k7_xcmplx_0 B A) A) = B) ) ) ) ) ) ).
tt(l27_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(l27_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) C) => (r1_xxreal_0 A (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(l27_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((m2_xxreal_2 C (k2_tarski A B)) => (r1_xxreal_0 C B)) ) ) ) ) ) ).
tt(l27_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_yellow13 C A B) =>  ( (C = (a_2_0_yellow13 A B))  => (v1_yellow13 C A B)) ) ) ) ) ) ) ).
tt(l27_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v1_yellow_0 (k2_yellow_1 (u1_pre_topc A)))) ) ).
tt(l28_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A C (k5_struct_0 A)) = C) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A C D) = (k5_struct_0 A)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A C D) E) = (k6_algstr_0 A C (k6_algstr_0 A D E))) ) ) ) ) ) ) ) )  =>  ((k6_algstr_0 A (k5_struct_0 A) B) = (k6_algstr_0 A B (k5_struct_0 A))) ) ) ) ) ) ).
tt(l28_altcat_2,ax, (! [A:$i] :  ( ((v6_altcat_1 A) & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ((v6_altcat_1 B) & (l2_altcat_1 B))  =>  ( ((v1_xboole_0 (u1_struct_0 A)) & (v1_xboole_0 (u1_struct_0 B)))  =>  (A = B) ) ) ) ) ) ).
tt(l28_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v2_extpro_1 (k7_ami_3 A) 2 k1_ami_3)) ) ) ).
tt(l28_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) K) (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C G) (k1_rlvect_1 A D H)) L)) (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B I) (k1_rlvect_1 A D J)) M)) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k7_real_1 (k8_real_1 K E) (k8_real_1 M I))) (k1_rlvect_1 A C (k7_real_1 (k8_real_1 K F) (k8_real_1 L G)))) (k1_rlvect_1 A D (k7_real_1 (k8_real_1 L H) (k8_real_1 M J))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 C B))  =>  ((k1_arytm_1 A (k1_arytm_1 B C)) = (k1_arytm_1 C (k1_arytm_1 B A))) ) ) ) ) ) ) ) ).
tt(l28_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  (~  ((r2_hidden B (k7_subset_1 (k1_zfmisc_1 k5_arytm_3) k1_arytm_2 a_0_1_arytm_2)) &  ( (~ (r2_hidden A B))  &  ( (~  (B = k11_arytm_3) )  &  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (~  ( (~ (r2_hidden C B))  &  (~ (r3_arytm_3 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A C B) =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(l28_binop_2,ax,(r3_binop_1 k1_numbers k6_numbers k33_binop_2)).
tt(l28_borsuk_7,ax,(r1_zfmisc_1 1 2 3)).
tt(l28_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_bspace A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_bspace A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_bspace A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( ((k1_algstr_0 (k7_bspace A) B (k1_algstr_0 (k7_bspace A) C D)) = (k5_subset_1 A E (k5_subset_1 A F G)))  &  ((k1_algstr_0 (k7_bspace A) (k1_algstr_0 (k7_bspace A) B C) D) = (k5_subset_1 A (k5_subset_1 A E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = (k3_tarski (a_2_0_cat_2 A B)))  &  ( (D = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C))  &  ( (E = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C))  &  (F = (k1_realset1 (u1_cat_1 A) C)) ) ) )  => (m3_cat_2 (g1_cat_1 B C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k5_cc0sp2 A) B C) = (k6_algstr_0 (k7_cc0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( ((v4_ordinal1 A) &  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) =>  (! [C:$i] :  ( ((v2_classes1 C) & (r2_hidden B (k2_ordinal1 C)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 B)) (k1_card_1 C)) & (r2_hidden (k4_classes1 B) C)) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A (k2_ordinal1 B)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 A)) (k1_card_1 B)) & (r2_hidden (k4_classes1 A) B)) ) ) ) ) ) ) ).
tt(l28_collsp,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c9__collsp)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c9__collsp)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c9__collsp)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 c9__collsp)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 c9__collsp)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 c9__collsp)) =>  ( ((r2_hidden (k4_domain_1 (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) A B D) (u1_collsp c9__collsp)) &  ((r2_hidden (k4_domain_1 (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) A B E) (u1_collsp c9__collsp)) & (r2_hidden (k4_domain_1 (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) A B F) (u1_collsp c9__collsp))) )  =>  ( (A = B)  | (r2_hidden (k4_domain_1 (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) (u1_struct_0 c9__collsp) D E F) (u1_collsp c9__collsp))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_complex1 (k3_xcmplx_0 A B)) = (k9_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))))  &  ((k4_complex1 (k3_xcmplx_0 A B)) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B)) (k8_real_1 (k3_complex1 B) (k4_complex1 A)))) ) ) ) ) ) ).
tt(l28_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((l2_conlat_1 B A) =>  (~  ( ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (u2_conlat_1 A B)) = (u3_conlat_1 A B))  & (v5_conlat_1 B A)) ) ) ) ) ) ).
tt(l28_convfun1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 A) (k4_finseq_1 A)) &  ((v3_funct_2 B (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) ) )  &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((r2_hidden D (k2_finseq_1 C)) <=>  (~  ((k1_seq_1 A (k1_seq_1 B D)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_csspace,ax, ((u1_struct_0 (k3_clvect_1 o_0_6_csspace)) = (k6_domain_1 (u1_struct_0 o_0_6_csspace) (k4_struct_0 o_0_6_csspace))) ).
tt(l28_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 47)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  ( (~  (B = (k1_nat_1 A 15)) )  &  ( (~  (B = (k1_nat_1 A 16)) )  &  ( (~  (B = (k1_nat_1 A 17)) )  &  ( (~  (B = (k1_nat_1 A 18)) )  &  ( (~  (B = (k1_nat_1 A 19)) )  &  ( (~  (B = (k1_nat_1 A 20)) )  &  ( (~  (B = (k1_nat_1 A 21)) )  &  ( (~  (B = (k1_nat_1 A 22)) )  &  ( (~  (B = (k1_nat_1 A 23)) )  &  ( (~  (B = (k1_nat_1 A 24)) )  &  ( (~  (B = (k1_nat_1 A 25)) )  &  ( (~  (B = (k1_nat_1 A 26)) )  &  ( (~  (B = (k1_nat_1 A 27)) )  &  ( (~  (B = (k1_nat_1 A 28)) )  &  ( (~  (B = (k1_nat_1 A 29)) )  &  ( (~  (B = (k1_nat_1 A 30)) )  &  ( (~  (B = (k1_nat_1 A 31)) )  &  ( (~  (B = (k1_nat_1 A 32)) )  &  ( (~  (B = (k1_nat_1 A 33)) )  &  ( (~  (B = (k1_nat_1 A 34)) )  &  ( (~  (B = (k1_nat_1 A 35)) )  &  ( (~  (B = (k1_nat_1 A 36)) )  &  ( (~  (B = (k1_nat_1 A 37)) )  &  ( (~  (B = (k1_nat_1 A 38)) )  &  ( (~  (B = (k1_nat_1 A 39)) )  &  ( (~  (B = (k1_nat_1 A 40)) )  &  ( (~  (B = (k1_nat_1 A 41)) )  &  ( (~  (B = (k1_nat_1 A 42)) )  &  ( (~  (B = (k1_nat_1 A 43)) )  &  ( (~  (B = (k1_nat_1 A 44)) )  &  ( (~  (B = (k1_nat_1 A 45)) )  &  ( (~  (B = (k1_nat_1 A 46)) )  &  (~  (B = (k1_nat_1 A 47)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden (k4_tarski (k1_domain_1 A A B C) D) (k7_ens_1 A B C)) =>  ( ( (C = k1_xboole_0)  =>  (B = k1_xboole_0) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k2_enumset1 A B C D) (k1_enumset1 E F G))) ) ) ) ) ) ) ) ).
tt(l28_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k5_algstr_0 A B D) (k5_algstr_0 A C D)) = (k5_algstr_0 A B C))  &  ((k5_algstr_0 A (k3_rlvect_1 A B D) (k3_rlvect_1 A C D)) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l28_fib_num4,ax, (~ (r1_xxreal_0 (k3_square_1 k1_fib_num) (k3_square_1 k2_fib_num))) ).
tt(l28_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v1_fomodel0 B (k2_zfmisc_1 C A)) <=>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden D (k3_xboole_0 C A)) &  ((r2_hidden E (k3_xboole_0 C A)) &  ((r2_hidden F A) &  ((r2_hidden G A) &  ((k1_binop_1 B D F) = (k1_binop_1 B E G)) ) ) ) )  =>  ( (D = E)  &  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) => (r1_tarski (k1_funct_1 (k3_fomodel4 C D A) B) (k5_setfam_1 (k1_fomodel4 C) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 C)) (k2_fomodel4 C D)) (k1_tarski B))))) ) ) ) ) ) ) ).
tt(l28_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k11_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F G)) (k10_margrel1 (k9_margrel1 E) G)))  &  ( ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F))  &  ( ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k19_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))) ) ).
tt(l28_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ( ((v4_glib_002 C A) & (m1_glib_000 C A))  =>  (! [D:$i] :  ( ((r2_hidden D (k24_glib_000 A B)) & (r2_hidden D (k24_glib_000 A C)))  => (r5_glib_000 B C)) ) ) ) ) ) ) ) ).
tt(l28_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m3_graph_1 B A) =>  ((r2_hidden (u1_graph_1 B) (k4_partfun1 (u4_struct_0 A) (u1_struct_0 A))) & (r2_hidden (u2_graph_1 B) (k4_partfun1 (u4_struct_0 A) (u1_struct_0 A)))) ) ) ) ) ).
tt(l28_graph_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k2_nat_1 C 1)) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( ((k2_nat_1 (k3_finseq_1 (k1_graph_2 A B C)) B) = (k2_nat_1 C 1))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_graph_2 A B C)) D))  =>  ((k1_funct_1 (k1_graph_2 A B C) (k2_nat_1 D 1)) = (k1_funct_1 A (k2_nat_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_funct_2 A A)) =>  ((k9_xtuple_0 B) = A) ) ) ) ).
tt(l28_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (r1_group_2 B (k3_group_6 A (k7_group_2 A) B) (k7_group_2 B))) ) ) ) ).
tt(l28_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ) ) ) ) ).
tt(l28_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) => (r2_relset_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k2_partfun1 k1_numbers (k1_euclid A) C E) (k1_pdiff_1 D A)) (k2_partfun1 k1_numbers k1_numbers (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers C (k1_pdiff_1 D A)) E))) ) ) ) ) ) ) ) ) ) ).
tt(l28_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  => (r1_xxreal_0 (k18_complex1 (k4_integra5 D C E)) (k4_integra5 C D (k56_valued_1 k1_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_jgraph_3,ax, (~  ((k8_struct_0 (k15_euclid 2)) = k1_xboole_0) ) ).
tt(l28_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A D)) & (r2_hidden C B)) ) ) ) )  =>  ((r1_xboole_0 (k2_topreal1 2 A D) B) | (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) (k1_jordan5c (k2_topreal1 2 A D) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1))) C)) ) ) ) ) ) ) ) ) ) ).
tt(l28_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k11_lattice3 A B C))  <=>  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k3_lattice2 (u1_struct_0 A) A (k1_setwiseo (u1_struct_0 A)) B) = (k6_lattices A)) ) ) ) ) ).
tt(l28_lp_space,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_series_1 k1_numbers A B) B))) ) ) ) ).
tt(l28_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k6_rusub_4 A (k3_mathmorp A B C) C) B)) ) ) ) ) ) ).
tt(l28_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k2_wsierp_1 (k11_matrixj1 A (k4_matrixj1 A B))) = (k1_matrix_1 B)) ) ) ) ) ).
tt(l28_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k2_mboolean A (k3_pboole A B C)) D) = (k3_tarski (k3_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l28_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 J)) (k1_rlvect_1 (k15_euclid 2) C J)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 K)) (k1_rlvect_1 (k15_euclid 2) A K)))  &  ( (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 L)) (k1_rlvect_1 (k15_euclid 2) B L)))  &  ((r1_euclid_6 A D G) &  ((r1_euclid_6 B E G) &  ((r1_euclid_6 B E H) &  ((r1_euclid_6 C F H) &  ((r1_euclid_6 A D I) & (r1_euclid_6 C F I)) ) ) ) ) ) ) )  =>  ((r1_euclid_6 A B C) |  ( (J = 1)  |  ( (K = 1)  |  ( (L = 1)  |  ( ((k11_binop_2 (k11_binop_2 (k12_binop_2 J (k10_binop_2 1 J)) (k12_binop_2 K (k10_binop_2 1 K))) (k12_binop_2 L (k10_binop_2 1 L))) = 1)  <=> (r1_euclid_6 H I G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_1 A) =>  ((k1_funct_1 A 1) = 3) ) ) ) ).
tt(l28_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_2 A) =>  ( (~  ((k1_funct_1 A 1) = k6_numbers) )  &  ( (~  ((k1_funct_1 A 1) = 1) )  &  ( (~  ((k1_funct_1 A 1) = 2) )  &  ( (~  ((k1_funct_1 A 1) = 3) )  &  ( (~  ((k1_funct_1 A 1) = 4) )  &  (~  ((k1_funct_1 A 1) = 5) ) ) ) ) ) ) ) ) ) ).
tt(l28_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v3_group_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(l28_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) => (v3_pre_topc (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(l28_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 25 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ((r1_xxreal_0 (k4_nat_1 B B) A) &  ((v1_int_2 B) &  ( (~  (B = 2) )  &  (~  (B = 3) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_nat_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( (A = (k7_finseq_1 (k9_finseq_1 (k1_funct_1 A 1)) (k2_finseq_3 1 A)))  &  (A = (k7_finseq_1 (k2_finseq_3 (k3_finseq_1 A) A) (k9_finseq_1 (k1_funct_1 A (k3_finseq_1 A))))) ) ) ) ) ).
tt(l28_nat_lat,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k1_lattices k10_nat_lat (k2_lattices k10_nat_lat A B) B) = B) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k2_lattices k10_nat_lat A B) = (k2_lattices k10_nat_lat B A)) ) ) ) ) ) ).
tt(l28_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (m1_subset_1 (k3_funct_2 k5_numbers (u1_struct_0 A) B C) (u1_struct_0 A))) ) ) ) ) ) ).
tt(l28_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (~  (A = k1_xboole_0) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k12_ordinal2 1 C)) ) ) ) )  => (r1_ordinal2 1 B)) ) ) ) ) ) ).
tt(l28_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v8_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l28_polynom4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k11_polynom3 A (k1_polynom4 A B) (k1_polynom4 A C)) D) = (k8_group_1 A (k2_polynom4 A (k1_polynom4 A B) D) (k2_polynom4 A (k1_polynom4 A C) D))) ) ) ) ) ) ) ) ) ).
tt(l28_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C G))  &  ( (~ (r1_incsp_1 A B H))  &  ( (~ (r1_incsp_1 A C H))  &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A D H) &  ( (~  (B = C) )  &  ((r1_incsp_1 A B I) &  ((r1_incsp_1 A C I) &  ((r1_incsp_1 A E I) &  ( (~ (r1_incsp_1 A E F))  &  ( (~  (E = C) )  &  ( (~ (r1_projred2 A F G H))  &  ( (~ (r1_projred2 A G H I))  &  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A D J) &  ( (~ (r1_incsp_1 A C J))  &  ( (~ (r1_incsp_1 A E J))  &  ((k3_relat_1 (k1_projred1 A F H B) (k1_projred1 A H G C)) = (k3_relat_1 (k1_projred1 A F J E) (k1_projred1 A J G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_qc_lang4,ax, (! [A:$i] :  (! [B:$i] :  ((k4_finseq_1 (k10_finseq_1 A B)) = (k2_finseq_1 2)) ) ) ).
tt(l28_realset2,ax, ((v1_funct_1 k2_realset2) &  ((v1_funct_2 k2_realset2 (k2_zfmisc_1 c4__realset2 c4__realset2) c4__realset2) & (m1_subset_1 k2_realset2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 c4__realset2 c4__realset2) c4__realset2)))) ) ).
tt(l28_rfinseq,ax, (! [A:$i] :  ( ((v8_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_real_1 C 1))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  & (r2_classes1 A B)) )  =>  ( ((k1_seq_1 A (k3_finseq_1 A)) = (k1_seq_1 B (k3_finseq_1 B)))  & (r2_classes1 (k17_finseq_1 k1_numbers C A) (k17_finseq_1 k1_numbers C B))) ) ) ) ) ) ) ) ).
tt(l28_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_tarski (u1_struct_0 (k2_rlsub_2 A B C)) (u1_struct_0 (k1_rlsub_2 A B C)))) ) ) ) ) ) ).
tt(l28_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E k4_numbers) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 C))) =>  ((k7_partfun1 (u1_struct_0 A) D F) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) C F) (k1_seq_1 E F))) ) ) ) ) ) )  => (r2_hidden (k4_rlvect_1 A D) (k2_rlvect_x A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (r1_tarski (u1_struct_0 (k2_rusub_2 A B C)) (u1_struct_0 (k1_rusub_2 A B C)))) ) ) ) ) ) ).
tt(l28_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  ((r1_scmfsa8a A B (k2_scmfsa6a C)) &  ((k2_scmfsa8a A B (k2_scmfsa6a C)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1)) ) ) ) ) ) ) ) ) ).
tt(l28_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_compos_1 D k1_scmpds_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v3_scmpds_4 E)) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 F (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 F 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_scmpds_6 D F A) &  ((r2_scmpds_6 D F A) &  ((r1_scmpds_6 E (k6_scmpds_4 D F A) A) &  ((r2_scmpds_6 E (k6_scmpds_4 D F A) A) &  ( (B = (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 D E))))  &  (C = (k1_funct_4 A (k10_compos_1 k1_scmpds_2 D))) ) ) ) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B F (k8_extpro_1 2 k1_scmpds_2 C F))) = (k5_card_1 D))  &  ( ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B F (k8_extpro_1 2 k1_scmpds_2 C F))) = (k6_memstr_0 2 k1_scmpds_2 (k8_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C F (k8_extpro_1 2 k1_scmpds_2 C F)))))  &  ((r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 E) (k5_card_1 D)) B) &  ((k8_extpro_1 2 k1_scmpds_2 B F) = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 C F) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 C (k10_compos_1 k1_scmpds_2 E)) (k8_memstr_0 2 k1_scmpds_2 (k6_extpro_1 2 k1_scmpds_2 C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_amistd_1 2 k1_scmpds_2 (k8_scmpds_2 A B 5)) = k1_xboole_0) ) ) ) ) ).
tt(l28_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( ( ((k2_compos_0 k1_scmpds_i A) = 2)  |  ((k2_compos_0 k1_scmpds_i A) = 3) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l28_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) 7) (k1_funct_1 B (k1_scmp_gcd 3))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 2)) k6_numbers) |  ((k6_scmpds_4 (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) B A) = (k6_scmpds_4 (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k3_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))))) (k11_scmpds_2 k2_scmp_gcd 2 (k4_xcmplx_0 1))) B A)) A)) ) ) ) ) ) ) ).
tt(l28_seqm_3,ax, ((v5_valued_0 (k6_partfun1 k5_numbers)) & (v4_valued_0 (k6_partfun1 k5_numbers))) ).
tt(l28_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) &  ((v1_afinsq_1 F) & (v1_scmfsa7b F)) ) ) ) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~ (r1_sfmastr3 E B C D F A))  &  (~ (v7_amistd_1 F 3 k1_scmfsa_2)) )  |  ((r3_scmfsa9a E (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) D) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) C)) (k7_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 B C)) A E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k5_scmfsa6a (k5_scmfsa6a F (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k4_scmfsa_2 k6_numbers)))) & (r4_scmfsa9a E (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) D) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) C)) (k7_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 B C)) A E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k5_scmfsa6a (k5_scmfsa6a F (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr F))) (k4_scmfsa_2 k6_numbers))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (r1_tarski B (k4_simplex0 A))) ) ) ) ) ).
tt(l28_sincos10,ax,(r1_tarski (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) (k1_relset_1 k1_numbers k2_fdiff_9))).
tt(l28_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k7_sin_cos2 (k9_binop_2 A B)) = (k10_real_1 (k7_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) (k7_real_1 1 (k8_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B))))) ) ) ) ) ).
tt(l28_sin_cos9,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) = (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))) ).
tt(l28_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (v1_finset_1 (a_2_0_sppol_1 A B))) ) ) ) ).
tt(l28_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (v2_topreal1 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ).
tt(l28_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l28_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A)))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) => (r2_hidden (k4_tarski (k7_finseq_1 (k12_finseq_1 (k8_qc_lang1 A B) C) D) E) (k2_zfmisc_1 (k13_finseq_1 (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) (k1_substut1 A)))) ) ) ) ) ) ) ) ) ) ).
tt(l28_taxonom1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C))  =>  (! [D:$i] :  ( ( (~ (v3_xxreal_0 D))  & (v1_xreal_0 D))  =>  ((r1_xxreal_0 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) k1_numbers))))  =>  (! [F:$i] :  ( ((v1_partfun1 F B) &  ((v3_relat_2 F) &  ((v8_relat_2 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [G:$i] :  ( ((v1_partfun1 G B) &  ((v3_relat_2 G) &  ((v8_relat_2 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  ( ((r2_relset_1 B B F (k13_lang1 B (k1_taxonom1 B E C))) & (r2_relset_1 B B G (k13_lang1 B (k1_taxonom1 B E D))))  => (r1_tarski (k6_eqrel_1 B B F A) (k6_eqrel_1 B B G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_topdim_1 (k1_pre_topc A B)) &  ((k4_topdim_1 (k1_pre_topc A B)) = (k2_topdim_1 A B)) ) ) ) ) ) ).
tt(l28_topdim_2,ax, ((v3_topdim_1 (k15_euclid k6_numbers)) &  ((k4_topdim_1 (k15_euclid k6_numbers)) = k6_numbers) ) ).
tt(l28_topreal2,ax,(r2_hidden (k19_euclid k6_numbers k6_numbers) a_0_0_topreal2)).
tt(l28_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( (C = (a_3_4_topreal9 A B D))  => (v1_convex1 C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(l28_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (~  ( (? [B:$i] :  ( (~ (v1_xboole_0 B))  &  (? [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_1 B)) & (m1_yellow_0 C (k3_yellow_1 B)))  &  ((v7_yellow_0 C (k3_yellow_1 B)) &  ((v4_waybel_0 C (k3_yellow_1 B)) & (r5_waybel_1 A C)) ) ) ) ) )  &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v7_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  =>  (~  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) ) ) ) ) ) ) ) ).
tt(l28_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k2_yellow_0 A C)) (k2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ).
tt(l28_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  => (r1_ordinal1 (k1_waybel31 A) (k2_waybel23 B))) ) ) ) ).
tt(l28_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 (k1_funct_1 B A))) D))  &  ( ((k3_finseq_1 C) = (k5_real_1 A 1))  &  ((k3_finseq_1 D) = (k9_real_1 (k3_finseq_1 B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l28_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 1 A) = (k5_xcmplx_0 A)) ) ) ).
tt(l28_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A (k6_xcmplx_0 B C)) => (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(l28_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) B) = k1_xboole_0)  <=> (r2_hidden A B)) ) ) ).
tt(l29_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ( ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k6_algstr_0 A C B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(l29_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (v2_extpro_1 (k8_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(l29_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_rlvect_1 A B D) = C)  =>  ( (D = k6_numbers)  | (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l29_arytm_0,ax,(m1_subset_1 1 k1_numbers)).
tt(l29_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ((r2_hidden (k3_arytm_2 A) a_0_1_arytm_2) => (r2_hidden A k5_arytm_3)) ) ) ).
tt(l29_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (v1_bcialg_2 (k4_struct_0 A) A)) ) ).
tt(l29_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k1_binari_3 (k2_xcmplx_0 A 1) (k5_series_1 2 A)) = (k7_finseq_1 (k5_euclid A) (k10_binarith k6_margrel1 k8_margrel1))) ) ) ).
tt(l29_binop_2,ax,(m1_subset_1 k6_numbers k3_numbers)).
tt(l29_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_bspace A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_bspace A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ( ( (D = F)  &  (E = G) )  =>  ( ((k1_algstr_0 (k7_bspace A) (k4_vectsp_1 k2_bspace (k7_bspace A) B D) (k4_vectsp_1 k2_bspace (k7_bspace A) C E)) = (k5_subset_1 A (k4_bspace A B F) (k4_bspace A C G)))  &  ( ((k4_vectsp_1 k2_bspace (k7_bspace A) B (k1_algstr_0 (k7_bspace A) D E)) = (k4_bspace A B (k5_subset_1 A F G)))  &  ( ((k4_vectsp_1 k2_bspace (k7_bspace A) (k3_rlvect_1 k2_bspace B C) D) = (k4_bspace A (k3_rlvect_1 k2_bspace B C) F))  &  ( ((k4_vectsp_1 k2_bspace (k7_bspace A) (k8_group_1 k2_bspace B C) D) = (k4_bspace A (k8_group_1 k2_bspace B C) F))  &  ((k4_vectsp_1 k2_bspace (k7_bspace A) B (k4_vectsp_1 k2_bspace (k7_bspace A) C D)) = (k4_bspace A B (k4_bspace A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_card_5,ax, (1 = (k5_card_1 1)) ).
tt(l29_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_clopban2 A))) =>  ( (C = (k6_clopban2 A))  =>  ( ((k6_algstr_0 (k9_clopban2 A) B C) = B)  &  ((k6_algstr_0 (k9_clopban2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l29_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_funct_1 B C)) (k9_setfam_1 (k1_funct_1 B C))) =>  ( (D = (k1_funct_4 (k1_pboole A) (k16_funcop_1 C E)))  => (r1_pboole A D (k5_mssubfam A B))) ) ) ) ) ) ) ) ) ).
tt(l29_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  ( ( ((k2_xtuple_0 B) = (k2_xtuple_0 C))  &  ( ((k6_coh_sp A B) = (k6_coh_sp A C))  &  ((k7_coh_sp A B) = (k7_coh_sp A C)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(l29_collsp,ax, (~  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c9__collsp)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c9__collsp)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c9__collsp)) => (r1_collsp c9__collsp A B C)) ) ) ) ) ) ) ).
tt(l29_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k4_complex1 A) (k4_complex1 B))) ) ) ) ) ) ).
tt(l29_csspace,ax, ((v1_funct_1 (k8_funcop_1 k2_numbers (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k5_complex1)) &  ((v1_funct_2 (k8_funcop_1 k2_numbers (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k5_complex1) (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers) & (m1_subset_1 (k8_funcop_1 k2_numbers (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k5_complex1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers)))) ) ).
tt(l29_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 55)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  ( (~  (B = (k1_nat_1 A 15)) )  &  ( (~  (B = (k1_nat_1 A 16)) )  &  ( (~  (B = (k1_nat_1 A 17)) )  &  ( (~  (B = (k1_nat_1 A 18)) )  &  ( (~  (B = (k1_nat_1 A 19)) )  &  ( (~  (B = (k1_nat_1 A 20)) )  &  ( (~  (B = (k1_nat_1 A 21)) )  &  ( (~  (B = (k1_nat_1 A 22)) )  &  ( (~  (B = (k1_nat_1 A 23)) )  &  ( (~  (B = (k1_nat_1 A 24)) )  &  ( (~  (B = (k1_nat_1 A 25)) )  &  ( (~  (B = (k1_nat_1 A 26)) )  &  ( (~  (B = (k1_nat_1 A 27)) )  &  ( (~  (B = (k1_nat_1 A 28)) )  &  ( (~  (B = (k1_nat_1 A 29)) )  &  ( (~  (B = (k1_nat_1 A 30)) )  &  ( (~  (B = (k1_nat_1 A 31)) )  &  ( (~  (B = (k1_nat_1 A 32)) )  &  ( (~  (B = (k1_nat_1 A 33)) )  &  ( (~  (B = (k1_nat_1 A 34)) )  &  ( (~  (B = (k1_nat_1 A 35)) )  &  ( (~  (B = (k1_nat_1 A 36)) )  &  ( (~  (B = (k1_nat_1 A 37)) )  &  ( (~  (B = (k1_nat_1 A 38)) )  &  ( (~  (B = (k1_nat_1 A 39)) )  &  ( (~  (B = (k1_nat_1 A 40)) )  &  ( (~  (B = (k1_nat_1 A 41)) )  &  ( (~  (B = (k1_nat_1 A 42)) )  &  ( (~  (B = (k1_nat_1 A 43)) )  &  ( (~  (B = (k1_nat_1 A 44)) )  &  ( (~  (B = (k1_nat_1 A 45)) )  &  ( (~  (B = (k1_nat_1 A 46)) )  &  ( (~  (B = (k1_nat_1 A 47)) )  &  ( (~  (B = (k1_nat_1 A 48)) )  &  ( (~  (B = (k1_nat_1 A 49)) )  &  ( (~  (B = (k1_nat_1 A 50)) )  &  ( (~  (B = (k1_nat_1 A 51)) )  &  ( (~  (B = (k1_nat_1 A 52)) )  &  ( (~  (B = (k1_nat_1 A 53)) )  &  ( (~  (B = (k1_nat_1 A 54)) )  &  (~  (B = (k1_nat_1 A 55)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((r2_hidden A (k6_jgraph_6 C D E)) &  ((r2_hidden B (k8_jgraph_6 C D E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~ (r2_hidden F (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k5_jgraph_6 C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((k4_geomtrap A B C (k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 F E)) (k1_rlvect_1 A C (k1_real_1 (k8_real_1 F D))))) = k6_numbers)  & (r2_analmetr A (k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 F E)) (k1_rlvect_1 A C (k1_real_1 (k8_real_1 F D)))) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r3_fdiff_3 A B) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k1_numbers A)) &  ((r2_hidden D (k1_rcomp_1 B (k7_real_1 B C))) &  ((k1_seq_1 A D) = k6_numbers) ) ) ) ) ) ) ) ) )  |  ((r3_fdiff_3 (k6_rfunct_1 k1_numbers k1_numbers A) B) &  ((k2_fdiff_3 B (k6_rfunct_1 k1_numbers k1_numbers A)) = (k1_real_1 (k10_real_1 (k2_fdiff_3 B A) (k5_square_1 (k1_seq_1 A B))))) ) ) ) ) ) ) ) ).
tt(l29_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k2_nat_1 (k4_nat_1 2 (k1_nat_1 A 2)) 1)) = (k2_nat_1 (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 3)) (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 4)))) ) ) ).
tt(l29_fib_num4,ax, (~ (r1_xxreal_0 (k6_square_1 (k1_pepin 3)) (k7_square_1 5))) ).
tt(l29_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  ((v4_fomodel4 B A D E C) => (v3_fomodel4 (k1_tarski B) D E C)) ) ) ) ) ) ) ) ) ).
tt(l29_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) <=>  ((k4_glib_002 A) = 1) ) ) ) ).
tt(l29_graph_2,ax,(v2_graph_2 (k2_finseq_4 k5_numbers 1 2))).
tt(l29_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((v1_group_3 B D) & (m1_group_6 B A D))  =>  ((v1_group_3 (k10_group_2 A B C) (k10_group_2 A D C)) & (m1_group_6 (k10_group_2 A B C) A (k10_group_2 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(l29_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (A = (k3_xcmplx_0 (k1_newton B D) C))  &  (~ (r1_nat_d B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) &  ((v3_group_9 D A) & (l1_group_9 D A)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v1_group_6 F C D) &  ((v7_group_9 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) (u1_struct_0 B) (u1_struct_0 D)) &  ((v1_group_6 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) B D) &  ((v7_group_9 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) A B D) & (m1_subset_1 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r2_hidden C (u1_struct_0 B)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) &  ((v1_hahnban D A) &  ((v4_hahnban D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) k1_numbers) &  ((v2_hahnban E B) &  ((v3_hahnban E B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) )  =>  (~  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (F = G)  => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 B) k1_numbers E F) (k3_funct_2 (u1_struct_0 A) k1_numbers D G))) ) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) k1_numbers) &  ((v2_hahnban F (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) &  ((v3_hahnban F (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) k1_numbers)))) ) ) )  =>  (~  ( ((k2_partfun1 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) k1_numbers F (u1_struct_0 B)) = E)  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C))))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( (G = H)  => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)))) k1_numbers F G) (k3_funct_2 (u1_struct_0 A) k1_numbers D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((r2_hidden C (k6_heyting2 A B D)) =>  ((k3_lattices (k5_substlat A B) C (k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k7_heyting2 A B D) C)) = D) ) ) ) ) ) ) ) ) ).
tt(l29_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 C A))  => (r1_tarski (k3_heyting3 A B) (k2_heyting3 C B))) ) ) ) ) ) ) ).
tt(l29_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C J) &  ((v7_aff_2 A) &  ((r2_hidden E J) &  ((r2_hidden F J) &  ((r2_analoaf A E B F D) &  ((r2_analoaf A E C F G) &  ((r2_aff_1 A D G J) &  ((r2_hidden H J) &  ((r2_hidden I J) & (r2_analoaf A H B I D)) ) ) ) ) ) ) ) )  =>  ((r2_hidden B J) |  ((r2_hidden D J) | (r2_analoaf A H C I G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  ((k2_hurwitz A B) = (k4_xcmplx_0 1)) )  &  ((k1_funct_1 B (k2_hurwitz A B)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l29_jordan1,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l29_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r2_hidden (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A D)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A D)) & (r2_hidden C B)) ) ) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) | (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) C)) ) ) ) ) ) ) ) ) ) ).
tt(l29_limfunc1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_recdef_1 (k6_funct_3 k1_numbers k5_numbers) A) = A) ) ) ).
tt(l29_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_lopban_2 A))) =>  ( (C = (k6_lopban_2 A))  =>  ( ((k6_algstr_0 (k9_lopban_2 A) B C) = B)  &  ((k6_algstr_0 (k9_lopban_2 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l29_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_series_1 (k1_lp_space B A)) & (v1_series_1 (k1_lp_space C A)))  => (v1_series_1 (k1_lp_space (k1_series_1 k1_numbers B C) A))) ) ) ) ) ) ) ) ).
tt(l29_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B D) E) (k8_cqc_lang A (k8_cqc_lang A C E) E))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l29_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( (~ (r1_xxreal_0 2 A))  =>  ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) &  (B = (k1_finseq_2 A)) ) ) ) ) ) ) ).
tt(l29_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 (k1_mesfunc2 A D)) &  ((v6_supinf_2 (k2_mesfunc2 A D)) & (v6_supinf_2 (k10_mesfunc1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(l29_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_1 A) =>  ((k1_funct_1 A 1) = 4) ) ) ) ).
tt(l29_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~  ((v2_modelc_2 A) &  ( (~  ((k1_funct_1 A 1) = k6_numbers) )  &  ( (~  ((k1_funct_1 A 1) = 1) )  &  ( (~  ((k1_funct_1 A 1) = 2) )  &  ( (~  ((k1_funct_1 A 1) = 3) )  &  ( (~  ((k1_funct_1 A 1) = 4) )  &  (~  ((k1_funct_1 A 1) = 5) ) ) ) ) ) ) ) )  &  ( (~  ((v3_modelc_2 A) &  ((k1_funct_1 A 1) = k6_numbers) ) )  &  ( (~  ((v4_modelc_2 A) &  ((k1_funct_1 A 1) = 1) ) )  &  ( (~  ((v5_modelc_2 A) &  ((k1_funct_1 A 1) = 2) ) )  &  ( (~  ((v6_modelc_2 A) &  ((k1_funct_1 A 1) = 3) ) )  &  ( (~  ((v7_modelc_2 A) &  ((k1_funct_1 A 1) = 4) ) )  &  (~  ((v8_modelc_2 A) &  ((k1_funct_1 A 1) = 5) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_nat_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k11_binop_2 (k21_rvsum_1 (k4_wsierp_1 k1_numbers A B)) (k1_funct_1 B A)) = (k21_rvsum_1 B)) ) ) ) ) ) ).
tt(l29_nat_lat,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k10_nat_lat)) =>  ((k2_lattices k10_nat_lat A (k2_lattices k10_nat_lat B C)) = (k2_lattices k10_nat_lat (k2_lattices k10_nat_lat A B) C)) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k2_lattices k10_nat_lat A (k1_lattices k10_nat_lat A B)) = A) ) ) ) ) ) ).
tt(l29_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  ((k2_cat_1 B D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F B D E) =>  ((k5_cat_1 A (k8_cat_1 B A C D) (k8_cat_1 B A C E) (k8_cat_1 B A C E) (k9_cat_3 B D E A C F) (k4_nattra_1 B A C C (k3_nattra_1 B A C) E)) = (k5_cat_1 A (k8_cat_1 B A C D) (k8_cat_1 B A C D) (k8_cat_1 B A C E) (k4_nattra_1 B A C C (k3_nattra_1 B A C) D) (k9_cat_3 B D E A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (~  ( (A = (k6_int_1 B C))  &  ( (~  (C = k6_numbers) )  &  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  (~  (A = (k2_xcmplx_0 B (k3_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_cat_1 A B) = (k4_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A B))) ) ) ) ) ).
tt(l29_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v4_ordinal1 B) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  (~  ( ((k9_xtuple_0 C) = B)  &  ( (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k12_ordinal2 A D)) ) ) )  &  (? [D:$i] :  ((v3_ordinal1 D) & (r1_ordinal2 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v9_o_ring_1 B A)) ) ) ) ) ).
tt(l29_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_projdes1 A B F G H) &  ((r1_collsp A B F C) &  ((r1_collsp A B G D) &  ((r1_collsp A B H E) &  ((r1_collsp A F G I) &  ((r1_collsp A C D I) &  ((r1_collsp A G H J) &  ((r1_collsp A D E J) &  ((r1_collsp A F H K) & (r1_collsp A C E K)) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (F = C)  |  ( (G = D)  | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C G))  &  ( (~ (r1_incsp_1 A B H))  &  ( (~ (r1_incsp_1 A C H))  &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A D H) &  ( (~  (B = C) )  &  ((r1_incsp_1 A B I) &  ((r1_incsp_1 A C I) &  ((r1_incsp_1 A E I) &  ( (~ (r1_incsp_1 A E F))  &  ( (~  (E = C) )  &  ( (~ (r1_projred2 A F G H))  &  ((r1_projred2 A G H I) &  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A D J) &  ( (~ (r1_incsp_1 A C J))  &  ( (~ (r1_incsp_1 A E J))  &  ((k3_relat_1 (k1_projred1 A F H B) (k1_projred1 A H G C)) = (k3_relat_1 (k1_projred1 A F J E) (k1_projred1 A J G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ((v4_normsp_0 (k14_prvect_2 A)) &  ((v3_normsp_0 (k14_prvect_2 A)) & (v2_normsp_1 (k14_prvect_2 A))) ) ) ) ).
tt(l29_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (v1_finset_1 (k5_ranknull A B C D))) ) ) ) ) ) ) ) ).
tt(l29_realset2,ax, (! [A:$i] :  ((m1_subset_1 A c4__realset2) =>  (! [B:$i] :  ((m1_subset_1 B c4__realset2) =>  (! [C:$i] :  ((m1_subset_1 C c4__realset2) =>  ((k1_binop_1 k1_realset2 (k1_binop_1 k1_realset2 A B) C) = (k1_binop_1 k1_realset2 A (k1_binop_1 k1_realset2 B C))) ) ) ) ) ) ) ).
tt(l29_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (~  ( (k6_numbers = (k3_finseq_1 A))  &  (! [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  (~ (r2_classes1 A B)) ) ) ) ) ) ) ).
tt(l29_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rlvect_2 E C) =>  (! [F:$i] :  ((m1_rlvect_2 F C) =>  ( (~  ((k3_funct_2 (u1_struct_0 C) k1_numbers E D) = (k3_funct_2 (u1_struct_0 C) k1_numbers F D)) )  =>  ( ((k3_funct_2 (u1_struct_0 C) k1_numbers (k7_rlvect_2 C (k8_rlvect_2 C A E) (k8_rlvect_2 C (k9_real_1 1 A) F)) D) = B)  <=>  (A = (k10_real_1 (k9_real_1 (k3_funct_2 (u1_struct_0 C) k1_numbers F D) B) (k9_real_1 (k3_funct_2 (u1_struct_0 C) k1_numbers F D) (k3_funct_2 (u1_struct_0 C) k1_numbers E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (~  ((r2_hidden C (k2_rlvect_x A B)) &  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v5_relat_1 F k4_numbers) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) )  =>  (~  ( (C = (k4_rlvect_1 A E))  &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) B) &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 F))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k3_finseq_1 D))) =>  ((k7_partfun1 (u1_struct_0 A) E G) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) D G) (k1_seq_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  => (v4_lattices A)) ) ).
tt(l29_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers c8__scm_comp (k3_scm_comp A)) = (k16_scm_comp A)) ) ) ).
tt(l29_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (B = 5) )  =>  ((k2_amistd_1 2 k1_scmpds_2 (k8_scmpds_2 A C B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(l29_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (~  ( (~  ((k2_compos_0 k1_scmpds_i A) = 4) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 5) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 6) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 7) )  &  (~  ((k2_compos_0 k1_scmpds_i A) = 8) ) ) ) ) ) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l29_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 3)) = C)  &  ((k1_funct_1 B (k1_scmp_gcd 4)) = D) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 5)) k6_numbers) |  ((r1_xxreal_0 C 6) |  ((r1_xxreal_0 D 6) |  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd C)) = (k1_funct_1 B (k1_scmp_gcd D)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd D)) = (k1_funct_1 B (k1_scmp_gcd C)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 3)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 4)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 5)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 5)) 2))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 E) =>  ( (E = C)  |  ( (E = D)  |  ((k1_funct_1 (k6_scmpds_4 (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k5_numbers A (k2_nat_1 B 1)) (k8_nat_1 k5_numbers A B))) ) ) ) ) ) ).
tt(l29_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ((k5_binop_1 A C B B) = B) )  => (r2_funct_2 k5_numbers A (k6_funcop_1 A k5_numbers C (k1_setwop_2 A D B) (k1_setwop_2 A E B)) (k1_setwop_2 A (k1_finseqop A A A C D E) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k4_simplex0 A) = (k5_setfam_1 (u1_struct_0 A) (u1_pre_topc A))) ) ) ).
tt(l29_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_struct_0 (k15_euclid A)) = (k2_struct_0 (k3_pcomps_1 (k14_euclid A)))) ) ) ).
tt(l29_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))).
tt(l29_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v2_topreal1 A) => (v2_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l29_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l29_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  (~  ((r2_hidden E (k4_substlat A B C D)) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l29_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_topdim_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_topdim_1 (k1_pre_topc A B)) & (r1_xxreal_0 (k4_topdim_1 (k1_pre_topc A B)) (k4_topdim_1 A))) ) ) ) ) ).
tt(l29_topdim_2,ax, ((v3_topdim_1 (k15_euclid 1)) &  ((k4_topdim_1 (k15_euclid 1)) = 1) ) ).
tt(l29_topgen_5,ax, ((u1_struct_0 k3_topgen_5) = k2_topgen_5) ).
tt(l29_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 (k2_xcmplx_0 A C) B))  => (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(l29_topreal2,ax,(r2_hidden (k19_euclid 1 1) a_0_0_topreal2)).
tt(l29_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( (C = (a_3_5_topreal9 A B D))  => (v1_convex1 C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(l29_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (~  ( (? [B:$i] :  (? [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_1 B)) & (m1_yellow_0 C (k3_yellow_1 B)))  &  ((v7_yellow_0 C (k3_yellow_1 B)) &  ((v4_waybel_0 C (k3_yellow_1 B)) & (r5_waybel_1 A C)) ) ) ) )  &  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v7_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  =>  (~  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) ) ) ) ) ) ) ).
tt(l29_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  => (r2_hidden (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) (k9_funct_2 (u1_struct_0 C) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(l29_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (v23_waybel_0 (k3_waybel29 B A) (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 B A))) (k3_waybel24 B (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_pre_topc (k5_waybel26 D) (k2_borsuk_1 B A)) & (m1_subset_1 (k5_waybel26 D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) ) ) ) ) ).
tt(l29_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k5_waybel_0 A D)) <=> (r2_hidden (k4_tarski C D) (u1_orders_2 A))) ) ) ) ) ) ) ) ).
tt(l29_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) C D E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A D)) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l29_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 A A) = 1) ) ) ) ).
tt(l29_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A (k2_xcmplx_0 B C)) => (r1_xxreal_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(l29_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v3_lattice3 (k2_yellow_1 (u1_pre_topc A)))) ) ).
tt(l2_abian,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) <=>  (? [B:$i] :  ((v1_int_1 B) &  (A = (k3_xcmplx_0 2 B)) ) ) ) ) ) ).
tt(l2_afinsq_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((k5_card_1 A) = (k5_card_1 B))  =>  ((v2_funct_2 C B) <=> (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(l2_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_diraf A B C D E) &  ((r2_diraf A B D D C) & (r2_diraf A B E E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_algstr_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (~  ( (~  (A = (k4_struct_0 k2_vectsp_1)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  (~  ((k8_group_1 k2_vectsp_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l2_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_ami_2) =>  ( (A = k5_numbers)  | (r2_hidden A k2_ami_2)) ) ) ).
tt(l2_ami_3,ax, ((k2_memstr_0 2 k1_ami_3) = (k3_relat_1 k3_ami_2 k4_ami_2)) ).
tt(l2_ami_4,ax, (~  ((k10_ami_3 2) = (k10_ami_3 k6_numbers)) ) ).
tt(l2_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k1_rlvect_1 A B k6_numbers) (k1_rlvect_1 A C k6_numbers)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l2_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D F)))  =>  ((k1_rlvect_1 A B G) = (k3_rlvect_1 A (k1_rlvect_1 A C (k8_real_1 G E)) (k1_rlvect_1 A D (k8_real_1 G F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) )  =>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  (~ (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l2_arithm,ax, ((k4_xcmplx_0 k6_numbers) = k6_numbers) ).
tt(l2_armstrng,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_2 C B (k4_finseq_2 A B)) =>  ((k4_finseq_1 C) = (k2_finseq_1 A)) ) ) ) ) ) ) ).
tt(l2_arytm_1,ax,(m1_subset_1 k12_arytm_3 k2_arytm_2)).
tt(l2_arytm_3,ax,(r2_hidden 1 k4_ordinal1)).
tt(l2_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v1_group_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 B (k2_group_3 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(l2_axioms,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (k5_arytm_0 B C))  =>  ( (C = k6_numbers)  &  (A = B) ) ) ) ) ) ) ) ) ).
tt(l2_bhsp_1,ax, ((u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) = (k6_domain_1 (u1_struct_0 o_0_5_bhsp_1) (k4_struct_0 o_0_5_bhsp_1))) ).
tt(l2_bhsp_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 A (k10_real_1 1 (k2_nat_1 B 1)))) ) ) ) ) ) ).
tt(l2_bintree2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m2_finseq_1 (k10_binarith A B) A)) ) ) ) ).
tt(l2_borsuk_7,ax, ((m1_subset_1 k6_numbers (u1_struct_0 k17_borsuk_1)) & (m1_subset_1 1 (u1_struct_0 k17_borsuk_1))) ).
tt(l2_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 k1_xboole_0 C) => (r2_hidden (k1_rlvect_1 (k15_euclid A) B C) (k4_topreal9 A (k4_struct_0 (k15_euclid A)) B))) ) ) ) ) ) ) ).
tt(l2_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) (k2_bvfunc_1 A C (k1_bvfunc_1 A D))) (k2_bvfunc_1 A D (k1_bvfunc_1 A B))) (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A C (k1_bvfunc_1 A B)) (k2_bvfunc_1 A D (k1_bvfunc_1 A C))) (k2_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(l2_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) C)) ) ) ) ) ) ) ) ) ).
tt(l2_card_5,ax, (2 = (k5_card_1 2)) ).
tt(l2_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ( ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k4_cat_1 A C) = (k4_cat_1 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_cc0sp1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v1_vectsp_1 C) &  ((v3_vectsp_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v2_cfuncdom C) & (l1_cfuncdom C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B B) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 k2_numbers B) B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers B) B)))) )  =>  ( ( (D = B)  &  (I = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 C)) (u1_struct_0 C) (u1_clvect_1 C) (k2_zfmisc_1 k2_numbers D))) )  =>  (! [J:$i] :  ( ( (~ (v2_struct_0 J))  & (l1_cfuncdom J))  =>  ( (J = (g1_cfuncdom B H G I F E))  =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 J)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 C)) =>  ( (K = L)  =>  ((k1_clvect_1 J K A) = (k1_clvect_1 C L A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k2_numbers A B) &  ((v2_comseq_2 B) &  ((k3_comseq_2 B) = C) ) )  =>  ((k2_seq_2 A) = C) ) ) ) ) ) ) ) ).
tt(l2_cgames_1,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (a_2_0_cgames_1 A B)) ) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 (k5_relat_1 A B))) =>  ((k1_funct_1 (k5_relat_1 A B) C) = (a_3_0_cgames_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(l2_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ( ((k6_algstr_0 A D (k6_clopban3 A C B)) = (k6_algstr_0 A (k6_clopban3 A C B) D))  &  ((k6_algstr_0 A C (k6_clopban3 A D B)) = (k6_algstr_0 A (k6_clopban3 A D B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)))) ) ) ) ).
tt(l2_complfld,ax, ((k1_group_1 k1_complfld) = k6_complex1) ).
tt(l2_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k12_seq_4 A B) = (k4_finseqop k2_numbers k2_numbers A (k10_funcop_1 k2_numbers k2_numbers k29_binop_2 B (k6_partfun1 k2_numbers)))) ) ) ) ) ).
tt(l2_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k2_numbers (k9_funct_2 (u1_struct_0 A) k2_numbers)) => (r1_tarski (k13_pre_poly B) (u1_struct_0 A))) ) ) ) ).
tt(l2_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 k6_numbers (k7_real_1 (k5_square_1 A) (k5_square_1 B)))) ) ) ) ).
tt(l2_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k4_seq_4 (k2_relset_1 k1_numbers A)))) ) ) ) ) ).
tt(l2_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) B A))) ) ) ) ) ).
tt(l2_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_euclid 3 A B) = (k1_euclid_8 (k11_binop_2 B (k1_seq_1 A 1)) (k11_binop_2 B (k1_seq_1 A 2)) (k11_binop_2 B (k1_seq_1 A 3)))) ) ) ) ) ).
tt(l2_euler_1,ax, (~ (v1_int_2 1)) ).
tt(l2_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k1_xboole_0) )  => (r1_xxreal_0 k1_xboole_0 (k6_xcmplx_0 A 1))) ) ) ).
tt(l2_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = A) ) ) )  &  (D = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) B) E) = (k1_real_1 (k8_real_1 2 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k7_real_1 1 (k21_sin_cos (k8_real_1 2 A))) = (k8_real_1 2 (k5_square_1 (k21_sin_cos A)))) ) ) ).
tt(l2_fib_fusc,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((m1_subset_1 (k1_int_1 (k5_power 2 A)) k5_numbers) &  (~ (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 A)) 1)) 1) k6_numbers)) ) ) ) ) ).
tt(l2_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k4_xcmplx_0 A) (k4_xcmplx_0 (k3_xcmplx_0 A (k3_power (k4_xcmplx_0 1) B))))) ) ) ) ).
tt(l2_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k10_xtuple_0 (k11_finseq_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ).
tt(l2_finset_1,ax, (! [A:$i] : (v1_finset_1 (k1_tarski A))) ).
tt(l2_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (~  ( (~ (r2_hidden A (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k39_fomodel1 D) (k2_xcmplx_0 B C))))  & (r2_hidden A (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k39_fomodel1 D) B))) ) ) ) ) ) ) ) ) ).
tt(l2_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v13_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((v15_fomodel1 (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C) A) & (m2_subset_1 (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) B) C) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ).
tt(l2_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (~ (v7_pre_topc A))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  & (r2_hidden C (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(l2_freealg,ax, ( (~ (r2_hidden k6_numbers (k10_xtuple_0 (k3_pre_poly k5_numbers 1))))  & (r2_hidden k6_numbers (k10_xtuple_0 (k3_pre_poly k5_numbers k6_numbers)))) ).
tt(l2_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C)))) =>  ((r2_hidden D (k9_xtuple_0 A)) |  (B = D) ) ) ) ) ) ) ) ).
tt(l2_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] : (r2_hidden B (k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C))))) ) ) ) ).
tt(l2_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(l2_gobrd12,ax, ((u1_struct_0 (k15_euclid 2)) = (k1_euclid 2)) ).
tt(l2_graph_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k2_nat_1 C 1)) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( ((k2_nat_1 (k3_finseq_1 (k1_graph_2 A B C)) B) = (k2_nat_1 C 1))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_graph_2 A B C)) D))  =>  ((k1_funct_1 (k1_graph_2 A B C) (k2_nat_1 D 1)) = (k1_funct_1 A (k2_nat_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ) ) ) ) ).
tt(l2_group_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_group_7 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k12_pralg_1 A C))) => (r2_hidden (k1_funct_1 D B) (u1_struct_0 (k1_group_7 A C B)))) ) ) ) ) ) ) ) ).
tt(l2_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r1_group_9 A B C (k2_subset_1 B))) ) ) ) ).
tt(l2_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (A = (k2_xboole_0 B C))  & (r1_tarski A B))  =>  (A = B) ) ) ) ) ).
tt(l2_heyting3,ax, (k6_numbers = (k4_nat_1 2 k6_numbers)) ).
tt(l2_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r2_hidden B C) &  ((r2_hidden D C) &  ((r2_hidden E C) &  ((v1_aff_1 C A) &  ((r1_aff_1 A B F H) &  ((r1_aff_1 A B G I) &  ((r2_aff_1 A F G C) &  ((r2_aff_1 A H I C) & (r2_analoaf A F D H E)) ) ) ) ) ) ) )  =>  ((r2_hidden F C) | (r2_analoaf A G D I E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((v1_int_2 A) &  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 A C))  &  ( (~  (B = k6_numbers) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((k4_nat_d (k4_nat_1 D B) A) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_int_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (A = (k1_real_1 B))  =>  ( (B = A)  | (r2_hidden A (k6_subset_1 (k2_zfmisc_1 (k1_tarski k6_numbers) k5_numbers) (k1_tarski (k4_tarski k6_numbers k6_numbers))))) ) ) ) ) ).
tt(l2_integr11,ax, ((k2_subset_1 k1_numbers) = (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos))) ).
tt(l2_integr13,ax, ((k3_limfunc1 k6_numbers) = a_0_0_integr13) ).
tt(l2_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr15 D A B C) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) & (r2_hidden E (k4_finseq_1 C)))  => (r1_xxreal_0 (k1_seq_1 (k5_integra1 A B C) E) (k1_seq_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_integr16,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k4_finseq_1 A) = (k9_xtuple_0 B))  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(l2_integra3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A 2) &  ( (~  (A = 1) )  &  (~  (A = 2) ) ) ) ) ) ) ) ).
tt(l2_integra8,ax, (~ (r1_xxreal_0 k6_numbers (k18_sin_cos (k1_real_1 (k10_real_1 k32_sin_cos 4))))) ).
tt(l2_jgraph_3,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k4_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l2_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k4_real_1 A (k7_square_1 (k7_real_1 1 (k3_square_1 B)))) (k4_real_1 B (k7_square_1 (k7_real_1 1 (k3_square_1 A)))))) ) ) ) ) ).
tt(l2_jgraph_8,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ( ((k1_funct_1 (k7_finseq_1 B (k9_finseq_1 A)) 1) = (k1_funct_1 B 1))  &  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) B) (k2_nat_1 (k3_finseq_1 B) 1)) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ).
tt(l2_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) & (r1_jordan1h A B)) ) ) ) ).
tt(l2_jordan12,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_zfmisc_1 A) => (v1_zfmisc_1 (k3_finseq_1 A))) ) ) ).
tt(l2_jordan18,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k5_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l2_jordan1a,ax, ((k3_nat_d 3 2) = 1) ).
tt(l2_jordan1c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_xcmplx_0 (k13_complex1 A B) (k3_xcmplx_0 (k13_complex1 C A) B)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_jordan1d,ax, ((k3_nat_d 1 2) = k6_numbers) ).
tt(l2_jordan21,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r2_hidden A (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) &  ((k1_seq_1 k5_pscomp_1 C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_jordan24,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l2_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( ((u1_struct_0 (k14_euclid A)) = (k1_euclid A))  &  ((u1_struct_0 (k15_euclid A)) = (k1_euclid A)) ) ) ) ).
tt(l2_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 (k7_nat_d A C) B) => (r1_xxreal_0 A (k2_nat_1 B C))) ) ) ) ) ) ) ).
tt(l2_jordan,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r1_tarski A E) &  ((r1_tarski B E) &  ((r1_tarski C E) & (r1_tarski D E)) ) )  => (r1_tarski (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D) E)) ) ) ) ) ) ).
tt(l2_kurato_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (m1_subset_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(l2_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_lattice3 A))) =>  (~  ((r2_hidden D B) &  ( (~  (D = C) )  & (r3_orders_2 (k3_lattice3 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) =>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 (k2_funct_1 (k5_relat_1 A B)))) =>  ((k1_funct_1 (k2_funct_1 (k5_relat_1 A B)) D) = (k1_funct_1 (k2_funct_1 (k5_relat_1 A C)) D)) ) ) ) ) ) ) ) ).
tt(l2_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) =>  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))  &  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)) & (r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) ).
tt(l2_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) D)) =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r1_tarski (k2_relset_1 k1_numbers A) D) &  ( ((k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))  &  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)) &  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers C)) &  ((r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) D)) & (r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) D)) =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( ((k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 B)) &  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 C)) &  ((r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 B) D)) & (r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B A))) =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) & (r1_tarski (k2_relset_1 k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers C B)) (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ).
tt(l2_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k6_algstr_0 A B (k6_lopban_3 A B C)) = (k6_lopban_3 A B (k2_nat_1 C 1)))  &  ( ((k6_algstr_0 A (k6_lopban_3 A B C) B) = (k6_lopban_3 A B (k2_nat_1 C 1)))  &  ((k6_algstr_0 A B (k6_lopban_3 A B C)) = (k6_algstr_0 A (k6_lopban_3 A B C) B)) ) ) ) ) ) ) ) ) ).
tt(l2_matrix16,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k2_finseq_1 A)))  => (r2_hidden (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 C B) A) 1) (k2_finseq_1 A))) ) ) ) ) ) ) ).
tt(l2_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k4_tarski B C) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))) =>  ((r2_hidden (k6_xcmplx_0 (k2_xcmplx_0 A 1) C) (k2_finseq_1 A)) & (r2_hidden (k6_xcmplx_0 (k2_xcmplx_0 A 1) B) (k2_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(l2_matrix_9,ax, (~  ((k2_finseq_4 k5_numbers 1 2) = (k2_finseq_4 k5_numbers 2 1)) ) ).
tt(l2_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_struct_0 (k6_prvect_1 k2_vectsp_1 A)) = (k4_struct_0 (k15_euclid A))) ) ) ).
tt(l2_mazurulm,ax, ((k2_pre_topc k5_topmetr c1__mazurulm) = (k2_struct_0 k5_topmetr)) ).
tt(l2_mboolean,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  ((r2_hidden A B) =>  ((k9_xtuple_0 (k1_funct_4 D (k16_funcop_1 A C))) = B) ) ) ) ) ) ) ).
tt(l2_mesfunc1,ax, (k6_numbers = (k1_real_1 k6_numbers)) ).
tt(l2_metric_1,ax, ((k1_binop_1 k9_funct_5 k1_xboole_0 k1_xboole_0) = k6_numbers) ).
tt(l2_metrizts,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_struct_0 B) &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (r1_borsuk_3 A B)) ) ) ) ).
tt(l2_modelc_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k1_nat_1 C 1)) =>  ((r1_xxreal_0 B A) | (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(l2_modelc_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (k2_xboole_0 (k6_subset_1 B C) (k6_subset_1 D E))) <=>  ( ((r2_hidden A B) &  (~ (r2_hidden A C)) )  |  ((r2_hidden A D) &  (~ (r2_hidden A E)) ) ) ) ) ) ) ) ) ).
tt(l2_msaterm,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) A))  => (r2_hidden (k1_funct_1 C (k2_nat_1 A 1)) B)) ) ) ) ) ) ).
tt(l2_nagata_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_xxreal_0 (k18_complex1 (k9_real_1 A D)) (k7_real_1 (k7_real_1 (k18_complex1 (k9_real_1 A B)) (k18_complex1 (k9_real_1 B C))) (k18_complex1 (k9_real_1 C D))))) ) ) ) ) ) ) ) ).
tt(l2_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (v7_ordinal1 (k6_int_1 A B))) ) ) ) ).
tt(l2_ndiff_4,ax, ((u1_struct_0 (k4_real_ns1 1)) = (k1_euclid 1)) ).
tt(l2_normsp_0,ax, ((v1_funct_1 k8_funct_5) &  ((v1_funct_2 k8_funct_5 1 k1_numbers) & (m1_subset_1 k8_funct_5 (k1_zfmisc_1 (k2_zfmisc_1 1 k1_numbers)))) ) ).
tt(l2_normsp_1,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k6_numbers) (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers)))) ) ).
tt(l2_ntalgo_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k6_nat_d A k6_numbers) = A) ) ) ).
tt(l2_numbers,ax, (1 = (k1_ordinal1 k1_xboole_0)) ).
tt(l2_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v1_orders_3 A)) ) ) ).
tt(l2_ordinal4,ax,(v4_ordinal1 k4_ordinal1)).
tt(l2_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (C = (k12_finseq_1 (u1_struct_0 A) B))  <=>  ( ((k3_finseq_1 C) = 1)  &  ((k7_partfun1 (u1_struct_0 A) C 1) = B) ) ) ) ) ) ) ) ) ).
tt(l2_ortsp_1,ax,(m1_subset_1 k6_numbers c1__ortsp_1)).
tt(l2_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) (k8_group_1 A (k5_algstr_0 A C B) (k5_algstr_0 A E D))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k1_algstr_0 A B (k4_algstr_0 A C)) = (k4_struct_0 A))  =>  (B = C) )  &  ( ( (B = C)  =>  ((k1_algstr_0 A B (k4_algstr_0 A C)) = (k4_struct_0 A)) )  &  ( ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  (B = C) )  &  ( (B = C)  =>  ((k5_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B))) =>  ((r1_xboole_0 A B) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden (k4_tarski E F) (k2_pcs_0 A A B B C D)) & (r2_hidden F B))  =>  ((r2_hidden (k4_tarski E F) D) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_pdiff_1,ax, ((v3_funct_2 (k1_pdiff_1 1 1) (k1_euclid 1) k1_numbers) &  ( ((k1_relset_1 (k1_euclid 1) (k1_pdiff_1 1 1)) = (k1_euclid 1))  &  ( ((k1_rvsum_1 (k1_pdiff_1 1 1)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((k1_seq_1 (k1_pdiff_1 1 1) (k12_finseq_1 k1_numbers A)) = A)  &  ((k1_funct_1 (k2_funct_1 (k1_pdiff_1 1 1)) A) = (k12_finseq_1 k1_numbers A)) ) ) ) ) ) ) ).
tt(l2_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  ((k23_binop_2 A (k7_nat_d B A)) = (k7_nat_d (k23_binop_2 A B) A)) ) ) ) ) ) ).
tt(l2_pencil_4,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 B (k5_card_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((k5_card_1 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l2_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k2_newton 2 (k2_newton 2 A)) 1)) ) ) ).
tt(l2_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ( ((k15_finseq_1 A) = k1_xboole_0)  =>  (A = k1_xboole_0) ) ) ) ).
tt(l2_polyeq_2,ax,(r1_int_1 2 4)).
tt(l2_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r6_relat_2 C A) => (r6_relat_2 C B)) ) ) ) ) ) ).
tt(l2_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(l2_polynom8,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ( (~ (r1_xxreal_0 1 A))  &  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(l2_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r2_pre_poly A B C) => (r2_pre_poly A (k11_pre_poly A B D) (k11_pre_poly A C D))) ) ) ) ) ) ) ) ) ).
tt(l2_poset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  ( ((k9_xtuple_0 (k9_funct_7 A B)) = (k9_xtuple_0 A))  & (r1_tarski (k10_xtuple_0 (k9_funct_7 A B)) (k9_xtuple_0 A))) ) ) ) ) ) ).
tt(l2_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k9_cqc_lang A B C) = (k8_cqc_lang A (k6_cqc_lang A B) C)) ) ) ) ) ) ) ).
tt(l2_pscomp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v6_measure6 B A) => (v5_measure6 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(l2_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (m2_finseq_1 (k1_partfun1 k5_numbers A A B C D) B)) ) ) ) ) ) ) ).
tt(l2_quatern2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)) (k3_square_1 D)))) ) ) ) ) ) ) ) ).
tt(l2_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((m1_subset_1 A k1_numbers) =>  ( (A = (k17_quaterni A))  &  ( ((k18_quaterni A) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ((k20_quaterni A) = k6_numbers) ) ) ) ) ) ) ).
tt(l2_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k6_xcmplx_0 (k1_radix_1 A) (k1_radix_1 (k7_nat_d A 1))) = (k1_radix_1 (k7_nat_d A 1))) ) ) ) ).
tt(l2_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r2_hidden B (k3_radix_3 A)) =>  ((r1_xxreal_0 (k4_xcmplx_0 (k1_radix_1 (k7_nat_d A 1))) B) & (r1_xxreal_0 B (k6_xcmplx_0 (k1_radix_1 (k7_nat_d A 1)) 1))) ) ) ) ) ) ).
tt(l2_rat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_arytm_3 A B) = (k10_real_1 A B)) ) ) ) ) ).
tt(l2_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k2_xcmplx_0 (k3_xcmplx_0 B C) D))  =>  ( ((k6_xcmplx_0 (k13_complex1 A B) C) = k6_numbers)  |  ( (D = k6_numbers)  |  ( (B = k6_numbers)  |  ((k10_real_1 1 (k6_xcmplx_0 (k13_complex1 A B) C)) = (k13_complex1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  => (r1_xxreal_0 A C)) ) ) ) ) ) ) ).
tt(l2_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 (k2_nat_1 k6_numbers 1) B) &  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ) ).
tt(l2_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (B = C) )  &  (! [F:$i] :  ((m2_rlvect_2 F A (k7_domain_1 (u1_struct_0 A) B C)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers F B) = D)  &  ((k3_funct_2 (u1_struct_0 A) k1_numbers F C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k4_seq_4 (k2_relset_1 k1_numbers A)))) ) ) ) ) ).
tt(l2_rusub_4,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  ((k2_xboole_0 (k6_subset_1 A (k1_tarski B)) (k1_tarski B)) = A) ) ) ) ).
tt(l2_scm_comp,ax, (5 = a_0_1_scm_comp) ).
tt(l2_scmfsa_7,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  (! [E:$i] :  ( ((v5_ordinal1 E) &  ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) )  =>  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) (k1_ordinal4 D E)))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 A B) (k1_ordinal4 (k1_ordinal4 C D) E)))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 A B) (k1_ordinal4 C (k1_ordinal4 D E))))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 B C) D) E)))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 B C) (k1_ordinal4 D E))))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 A (k1_ordinal4 B (k1_ordinal4 (k1_ordinal4 C D) E))))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 A (k1_ordinal4 B (k1_ordinal4 C (k1_ordinal4 D E)))))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) (k1_ordinal4 C D)) E))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 B C) D)) E))  &  ( ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 (k1_ordinal4 A (k1_ordinal4 B (k1_ordinal4 C D))) E))  &  ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) E) = (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 B (k1_ordinal4 C D)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_scmfsa_9,ax, ((k1_funct_1 (k4_compos_1 k1_scmfsa_2) k6_numbers) = (k2_compos_1 k1_scmfsa_2)) ).
tt(l2_scm_halt,ax, ((k5_memstr_0 3 k1_scmfsa_2 (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1))) = k6_numbers) ).
tt(l2_scmpds_6,ax,(r2_hidden k6_numbers (k9_xtuple_0 (k4_compos_1 k1_scmpds_2)))).
tt(l2_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k2_memstr_0 2 (k1_scmring2 A)) = (k3_relat_1 k3_ami_2 (k1_scmring1 A))) ) ) ).
tt(l2_scpqsort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k2_scmpds_8 A B C) = (k2_scmpds_4 (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)) (k3_scmpds_4 C (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 1)))))) ) ) ) ) ) ) ).
tt(l2_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)) (k8_nat_1 k1_numbers A B))) ) ) ) ) )  &  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)) (k8_nat_1 k1_numbers A B))) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A C) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A C) (k8_nat_1 k1_numbers A B))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(l2_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton A 3) = (k3_xcmplx_0 (k3_xcmplx_0 A A) A)) ) ) ).
tt(l2_series_3,ax, ((k13_newton 1 3) = 1) ).
tt(l2_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_newton (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 2) (k2_nat_1 A 1)) (k13_newton 2 (k2_nat_1 A 1))) 2) = (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 4) (k2_nat_1 A 1)) (k13_newton 4 (k2_nat_1 A 1))) 2)) ) ) ).
tt(l2_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ((k13_complex1 2 (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B))) = (k13_complex1 (k3_xcmplx_0 2 (k3_xcmplx_0 A B)) (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(l2_setwop_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r2_hidden (k1_nat_1 A 1) (k2_finseq_1 A))) ) ) ).
tt(l2_simplex0,ax, (! [A:$i] :  (? [B:$i] :  ((v1_classes1 B) &  ( (B = (k3_tarski (a_1_0_simplex0 A)))  &  ((r1_tarski A B) &  (! [C:$i] :  ( ((r1_tarski A C) & (v1_classes1 C))  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(l2_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  &  ( (~ (r1_xxreal_0 1 B))  & (r1_xxreal_0 1 (k11_binop_2 (k3_square_1 A) B))) ) ) ) ) ) ) ).
tt(l2_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k3_sin_cos2 A) = (k7_xcmplx_0 (k6_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))) 2))  &  ( ((k6_sin_cos2 A) = (k7_xcmplx_0 (k2_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))) 2))  &  ((k9_sin_cos2 A) = (k7_xcmplx_0 (k6_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))) (k2_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))))) ) ) ) ) ).
tt(l2_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((r2_hidden C B) => (r2_hidden C A)) ) ) ) ) ).
tt(l2_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_substlat A B)) & (r2_hidden C D))  => (v1_finset_1 C)) ) ) ) ) ).
tt(l2_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A D)) & (m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A E)))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_symsp_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)) (k1_tarski k6_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)) (k1_tarski k6_numbers))))) )  &  (! [B:$i] :  ((m1_subset_1 B (k1_tarski k6_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_tarski k6_numbers)) =>  ((k5_binop_1 (k1_tarski k6_numbers) A B C) = c2__symsp_1) ) ) ) ) ) ) ).
tt(l2_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_3 B A) &  ((v1_tops_3 C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ).
tt(l2_topalg_3,ax, ((m1_subset_1 k6_numbers (u1_struct_0 k17_borsuk_1)) & (m1_subset_1 1 (u1_struct_0 k17_borsuk_1))) ).
tt(l2_topalg_4,ax,(r2_hidden 2 (k2_tarski 1 2))).
tt(l2_topalg_5,ax,(r2_hidden k6_numbers (u1_struct_0 k5_topmetr))).
tt(l2_topmetr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k7_relat_1 A (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) (k10_xtuple_0 B)) => (r1_tarski (k6_subset_1 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k10_xtuple_0 (k1_funct_4 A B)))) ) ) ) ) ).
tt(l2_topreal2,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1))) = k1_xboole_0) ).
tt(l2_toprealb,ax, ((v1_xreal_0 (k1_real_1 1)) & (v3_xxreal_0 (k1_real_1 1))) ).
tt(l2_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_aff_1 A B C D) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ( (~ (r1_aff_1 A B C E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A E B F) &  ( (~  (E = F) )  &  (~  (B = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr A B))) =>  ((r1_xxreal_0 A B) => (m1_subset_1 C k1_numbers)) ) ) ) ) ) ) ).
tt(l2_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  =>  ((k1_funct_1 A (k2_nat_1 C 1)) = (k1_funct_1 B (k2_nat_1 C 1))) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l2_tsep_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k6_subset_1 (k3_xboole_0 A B) C) = (k9_subset_1 B (k6_subset_1 A C) (k6_subset_1 B C))) ) ) ) ).
tt(l2_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k9_subset_1 k5_numbers (k4_finseq_1 A) (k4_finseq_1 B)))  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(l2_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k1_vectsp_5 A B C D) = (k1_vectsp_5 A B D C)) ) ) ) ) ) ) ) ) ).
tt(l2_waybel14,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k3_subset_1 (u1_struct_0 A) C)) <=> (r1_tarski C (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(l2_waybel15,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v2_funct_2 D B) & (v2_funct_2 E C))  => (v2_funct_2 (k1_partfun1 A B B C D E) C)) ) ) ) ) ) ) ) ) ) ).
tt(l2_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((a_1_5_waybel19 A) = (a_1_5_waybel19 B)) ) ) ) ) ) ).
tt(l2_waybel22,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((r1_tarski B (k9_setfam_1 (u1_struct_0 A))) =>  ((k1_yellow_0 A (k3_tarski B)) = (k1_yellow_0 A (a_2_4_waybel22 A B))) ) ) ) ) ).
tt(l2_waybel23,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 A)))) =>  ((r1_yellow_0 (k2_yellow_1 A) B) => (r1_tarski (k3_tarski B) (k1_yellow_0 (k2_yellow_1 A) B))) ) ) ) ) ).
tt(l2_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  &  ((v1_waybel_0 (k1_waybel_3 A B) A) &  ((v12_waybel_0 (k1_waybel_3 A B) A) & (m1_subset_1 (k1_waybel_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A (k1_waybel_3 A B))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) => (r1_tarski (k1_waybel_3 A B) C)) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l2_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_relat_2 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski C D) A))  => (r2_hidden (k4_tarski B D) A)) ) ) ) ) ) ) ).
tt(l2_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (k5_arytm_0 B C))  =>  ( (C = k6_numbers)  &  (A = B) ) ) ) ) ) ) ) ) ).
tt(l2_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (k5_arytm_0 B C))  =>  ( (C = k6_numbers)  &  (A = B) ) ) ) ) ) ) ) ) ).
tt(l2_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k1_tarski A) = (k2_tarski B C))  =>  (A = B) ) ) ) ) ).
tt(l2_yellow_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (A = (k4_tarski (k4_tarski B C) (k4_tarski D E)))  =>  ( ((k1_xtuple_0 (k1_xtuple_0 A)) = B)  &  ( ((k2_xtuple_0 (k1_xtuple_0 A)) = C)  &  ( ((k1_xtuple_0 (k2_xtuple_0 A)) = D)  &  ((k2_xtuple_0 (k2_xtuple_0 A)) = E) ) ) ) ) ) ) ) ) ) ).
tt(l2_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) =>  ((r2_hidden C A) | (r1_tarski A (k4_xboole_0 B (k1_tarski C)))) ) ) ) ) ).
tt(l2_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (B = (k1_zf_model A))  <=>  (? [C:$i] :  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ((r2_hidden (k4_tarski (k4_zf_lang D E) (k2_tarski D E)) C) & (r2_hidden (k4_tarski (k5_zf_lang D E) (k2_tarski D E)) C)) ) ) ) )  &  ((r2_hidden (k4_tarski A B) C) &  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) =>  ( ((v2_zf_lang D) =>  (E = (k2_tarski (k18_zf_lang D) (k19_zf_lang D))) )  &  ( ((v3_zf_lang D) =>  (E = (k2_tarski (k18_zf_lang D) (k19_zf_lang D))) )  &  ( (~  ((v4_zf_lang D) &  (! [F:$i] :  (~  ( (E = F)  & (r2_hidden (k4_tarski (k20_zf_lang D) F) C)) ) ) ) )  &  ( (~  ((v5_zf_lang D) &  (! [F:$i] :  (! [G:$i] :  (~  ( (E = (k3_tarski (k2_tarski F G)))  &  ((r2_hidden (k4_tarski (k21_zf_lang D) F) C) & (r2_hidden (k4_tarski (k22_zf_lang D) G) C)) ) ) ) ) ) )  &  (~  ((v6_zf_lang D) &  (! [F:$i] :  (~  ( (E = (k6_subset_1 (k3_tarski (k1_tarski F)) (k1_tarski (k23_zf_lang D))))  & (r2_hidden (k4_tarski (k24_zf_lang D) F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l2_zfrefle1,ax,(v4_ordinal1 k4_ordinal1)).
tt(l30_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (v2_extpro_1 (k9_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(l30_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_anproj_1 A B C))  &  ( (D = (k1_rlvect_1 A C E))  &  ( (~  (E = k6_numbers) )  & (r1_anproj_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((r1_tarski (k3_arytm_2 A) (k3_arytm_2 B)) => (r1_arytm_2 A B)) ) ) ) ) ).
tt(l30_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (v10_bcialg_1 (k4_struct_0 A) A)) ) ).
tt(l30_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k5_series_1 2 A) B) =>  ((r1_xxreal_0 (k5_series_1 2 (k2_xcmplx_0 A 1)) B) |  ((k1_funct_1 (k1_binari_3 (k2_xcmplx_0 A 1) B) (k2_xcmplx_0 A 1)) = k8_margrel1) ) ) ) ) ) ) ).
tt(l30_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k4_nat_d B A) = (k4_nat_d C A))  &  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  (B = (k20_binop_2 C (k22_binop_2 D A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_binop_2,ax,(r3_binop_1 k3_numbers c2__binop_2 k39_binop_2)).
tt(l30_collsp,ax, ( (~ (v2_struct_0 c9__collsp))  &  ((v2_collsp c9__collsp) &  ((v3_collsp c9__collsp) & (l1_collsp c9__collsp)) ) ) ).
tt(l30_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_complex1 (k3_xcmplx_0 A k7_complex1)) = k6_numbers) ) ) ).
tt(l30_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A B)) = k5_complex1) ) ) ) ) ).
tt(l30_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 63)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  ( (~  (B = (k1_nat_1 A 4)) )  &  ( (~  (B = (k1_nat_1 A 5)) )  &  ( (~  (B = (k1_nat_1 A 6)) )  &  ( (~  (B = (k1_nat_1 A 7)) )  &  ( (~  (B = (k1_nat_1 A 8)) )  &  ( (~  (B = (k1_nat_1 A 9)) )  &  ( (~  (B = (k1_nat_1 A 10)) )  &  ( (~  (B = (k1_nat_1 A 11)) )  &  ( (~  (B = (k1_nat_1 A 12)) )  &  ( (~  (B = (k1_nat_1 A 13)) )  &  ( (~  (B = (k1_nat_1 A 14)) )  &  ( (~  (B = (k1_nat_1 A 15)) )  &  ( (~  (B = (k1_nat_1 A 16)) )  &  ( (~  (B = (k1_nat_1 A 17)) )  &  ( (~  (B = (k1_nat_1 A 18)) )  &  ( (~  (B = (k1_nat_1 A 19)) )  &  ( (~  (B = (k1_nat_1 A 20)) )  &  ( (~  (B = (k1_nat_1 A 21)) )  &  ( (~  (B = (k1_nat_1 A 22)) )  &  ( (~  (B = (k1_nat_1 A 23)) )  &  ( (~  (B = (k1_nat_1 A 24)) )  &  ( (~  (B = (k1_nat_1 A 25)) )  &  ( (~  (B = (k1_nat_1 A 26)) )  &  ( (~  (B = (k1_nat_1 A 27)) )  &  ( (~  (B = (k1_nat_1 A 28)) )  &  ( (~  (B = (k1_nat_1 A 29)) )  &  ( (~  (B = (k1_nat_1 A 30)) )  &  ( (~  (B = (k1_nat_1 A 31)) )  &  ( (~  (B = (k1_nat_1 A 32)) )  &  ( (~  (B = (k1_nat_1 A 33)) )  &  ( (~  (B = (k1_nat_1 A 34)) )  &  ( (~  (B = (k1_nat_1 A 35)) )  &  ( (~  (B = (k1_nat_1 A 36)) )  &  ( (~  (B = (k1_nat_1 A 37)) )  &  ( (~  (B = (k1_nat_1 A 38)) )  &  ( (~  (B = (k1_nat_1 A 39)) )  &  ( (~  (B = (k1_nat_1 A 40)) )  &  ( (~  (B = (k1_nat_1 A 41)) )  &  ( (~  (B = (k1_nat_1 A 42)) )  &  ( (~  (B = (k1_nat_1 A 43)) )  &  ( (~  (B = (k1_nat_1 A 44)) )  &  ( (~  (B = (k1_nat_1 A 45)) )  &  ( (~  (B = (k1_nat_1 A 46)) )  &  ( (~  (B = (k1_nat_1 A 47)) )  &  ( (~  (B = (k1_nat_1 A 48)) )  &  ( (~  (B = (k1_nat_1 A 49)) )  &  ( (~  (B = (k1_nat_1 A 50)) )  &  ( (~  (B = (k1_nat_1 A 51)) )  &  ( (~  (B = (k1_nat_1 A 52)) )  &  ( (~  (B = (k1_nat_1 A 53)) )  &  ( (~  (B = (k1_nat_1 A 54)) )  &  ( (~  (B = (k1_nat_1 A 55)) )  &  ( (~  (B = (k1_nat_1 A 56)) )  &  ( (~  (B = (k1_nat_1 A 57)) )  &  ( (~  (B = (k1_nat_1 A 58)) )  &  ( (~  (B = (k1_nat_1 A 59)) )  &  ( (~  (B = (k1_nat_1 A 60)) )  &  ( (~  (B = (k1_nat_1 A 61)) )  &  ( (~  (B = (k1_nat_1 A 62)) )  &  (~  (B = (k1_nat_1 A 63)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_euclid_9,ax, ((k3_pcomps_1 (k14_euclid k6_numbers)) = (k3_waybel18 k1_xboole_0 (k7_funcop_1 k1_xboole_0 k3_topmetr))) ).
tt(l30_fib_num4,ax, (~ (r1_xxreal_0 3 (k7_square_1 5))) ).
tt(l30_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 (k2_xcmplx_0 D 1) A)) =>  ((k1_funct_1 (k5_fomodel0 A B) (k1_monoid_0 A (k12_finseq_1 A C) E)) = (k1_binop_1 B C (k1_funct_1 (k5_fomodel0 A B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden B (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k3_finseq_2 (k1_fomodel1 C)) (k16_fomodel2 C D) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k1_tarski k1_xboole_0))) (k23_fomodel2 C A D))) =>  ((r2_hidden B (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k3_finseq_2 (k1_fomodel1 C)) (k16_fomodel2 C D) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k1_tarski k1_xboole_0))) (k23_fomodel2 C (k2_xcmplx_0 A E) D))) &  ((k1_funct_1 (k23_fomodel2 C A D) B) = (k1_funct_1 (k23_fomodel2 C (k2_xcmplx_0 A E) D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_fomodel4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_fomodel4 A))) =>  ( ((r1_tarski D E) & (r1_tarski B C))  =>  ( ( (~ (v6_fomodel4 C A))  &  (~ (v6_fomodel4 B A)) )  | (r1_tarski (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k2_fomodel4 A B) D) (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k2_fomodel4 A C) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_funct_9,ax,(v1_funct_9 k2_fdiff_9 (k8_real_1 2 k32_sin_cos))).
tt(l30_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ( (~ (v5_glib_002 B A))  <=>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) => (r1_ordinal1 (k4_glib_002 C) (k4_glib_002 A))) ) ) ) ) ) ) ).
tt(l30_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) 1)) ) ) ).
tt(l30_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  (! [F:$i] :  ((r1_rewrite1 (k3_polyred A B C D) E F) =>  ( (E = F)  |  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_group_10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k1_card_1 (a_2_2_group_10 A B)) = (k1_card_1 B)) ) ) ) ) ).
tt(l30_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_3 A (k5_group_1 A k1_xboole_0 B) C) = (k5_group_1 A k1_xboole_0 (k2_group_3 A B C))) ) ) ) ) ) ) ).
tt(l30_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))))  &  ((v13_algstr_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v2_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v3_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v4_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v5_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v6_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v7_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v8_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) & (l1_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_partfun1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A B))) =>  (~  ( (E = (k1_tarski D))  &  (! [F:$i] :  ((m2_subset_1 F (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (~  ((r2_hidden F (k6_heyting2 A B C)) &  ( ((k4_substlat A B F E) = k1_xboole_0)  &  (! [G:$i] :  ((m1_subset_1 G (k4_partfun1 A B)) =>  ((r2_hidden G (k1_funct_1 (k7_heyting2 A B C) F)) => (r1_partfun1 G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C K) &  ((v7_aff_2 A) &  ((r2_hidden E K) &  ((r2_hidden F K) &  ((r2_analoaf A E B F D) &  ((r2_analoaf A E C F G) &  ((r2_aff_1 A D G K) &  ((r2_hidden H K) &  ((r2_hidden I K) &  ((r2_analoaf A H B I D) &  ((r2_aff_1 A D J K) & (r2_analoaf A H C I J)) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden B K) |  ((r2_hidden D K) |  (J = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((m1_subset_1 (k2_hurwitz A B) k5_numbers) <=>  (~  (B = (k9_polynom3 A)) ) ) ) ) ) ) ).
tt(l30_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D))) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 F G)) E)) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k18_complex1 (k4_integra5 C D F)) (k4_real_1 E (k18_complex1 (k6_xcmplx_0 D C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_jgraph_3,ax, ( ((r1_xxreal_0 (k17_euclid (k22_euclid 2)) (k18_euclid (k22_euclid 2))) & (r1_xxreal_0 (k1_real_1 (k18_euclid (k22_euclid 2))) (k17_euclid (k22_euclid 2))))  |  ((r1_xxreal_0 (k18_euclid (k22_euclid 2)) (k17_euclid (k22_euclid 2))) & (r1_xxreal_0 (k17_euclid (k22_euclid 2)) (k1_real_1 (k18_euclid (k22_euclid 2))))) ) ).
tt(l30_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A) = (k1_rcomp_1 (k1_real_1 1) 1))  &  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A) = (k1_rcomp_1 (k1_real_1 1) 1)) ) ) ) ) ).
tt(l30_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (? [E:$i] :  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski E)) )  &  ( (~ (r2_hidden D (k3_topreal1 2 C)))  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C)) E) &  ((r2_hidden D E) & (r2_hidden A E)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C)) E) &  ((r2_hidden D E) & (r2_hidden B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_jordan5a,ax, (k3_topmetr = (g1_pre_topc (u1_struct_0 k8_metric_1) (k2_pcomps_1 k8_metric_1))) ).
tt(l30_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A D)) & (r2_hidden C B)) ) ) ) )  =>  ((r1_xboole_0 (k2_topreal1 2 A D) B) | (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) C (k2_jordan5c (k2_topreal1 2 A D) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ).
tt(l30_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) D) (k8_cqc_lang A (k8_cqc_lang A B E) (k8_cqc_lang A (k8_cqc_lang A E D) D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l30_measure7,ax, ((v1_funct_1 (k8_funcop_1 (k1_zfmisc_1 k1_numbers) k5_numbers (k1_subset_1 k1_numbers))) &  ((v1_funct_2 (k8_funcop_1 (k1_zfmisc_1 k1_numbers) k5_numbers (k1_subset_1 k1_numbers)) k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 (k8_funcop_1 (k1_zfmisc_1 k1_numbers) k5_numbers (k1_subset_1 k1_numbers)) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) ) ).
tt(l30_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_1 A) =>  ( (~  ((k1_funct_1 A 1) = k6_numbers) )  &  ( (~  ((k1_funct_1 A 1) = 1) )  &  ( (~  ((k1_funct_1 A 1) = 2) )  &  ( (~  ((k1_funct_1 A 1) = 3) )  &  (~  ((k1_funct_1 A 1) = 4) ) ) ) ) ) ) ) ) ).
tt(l30_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 (k23_binop_2 A 2)) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k2_finseq_1 A)) &  ( (~  (B = 1) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k2_finseq_1 A)) &  ( (~  (C = 1) )  &  ( (~  (C = B) )  &  ((k4_nat_d (k24_binop_2 B C) (k23_binop_2 A 2)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_nat_lat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ((u2_lattices A) = (k1_realset1 (u2_lattices A) (u1_struct_0 A)))  &  ((u1_lattices A) = (k1_realset1 (u1_lattices A) (u1_struct_0 A))) ) ) ) ).
tt(l30_ntalgo_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 A))) &  ((k1_funct_1 A C) = k6_numbers) ) ) ) )  &  ((k1_funct_1 B 1) = 1) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k6_xcmplx_0 (k3_finseq_1 A) 1)) &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D C))  =>  ((k1_funct_1 B (k1_nat_1 D 1)) = (k3_xcmplx_0 (k1_funct_1 B D) (k1_funct_1 A D))) ) ) )  &  ((k1_funct_1 B (k2_nat_1 C 1)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_xxreal_0 (k4_xcmplx_0 1) (k11_radix_1 A)) & (r1_xxreal_0 (k11_radix_1 A) 1)) ) ) ).
tt(l30_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((v4_c0sp1 (k3_random_2 A B) (k12_funcsdom A)) & (v3_c0sp1 (k3_random_2 A B) (k12_funcsdom A))) ) ) ) ) ).
tt(l30_realset2,ax, ( (~ (v2_struct_0 (g6_algstr_0 c4__realset2 c8__realset2 c9__realset2 c7__realset2 c5__realset2)))  & (l6_algstr_0 (g6_algstr_0 c4__realset2 c8__realset2 c9__realset2 c7__realset2 c5__realset2))) ).
tt(l30_rfinseq,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( (A = (k3_finseq_1 B))  &  (! [C:$i] :  ( ((v8_valued_0 C) & (m2_finseq_1 C k1_numbers))  =>  (~ (r2_classes1 B C)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (~  ( ((k3_real_1 A 1) = (k3_finseq_1 B))  &  (! [C:$i] :  ( ((v8_valued_0 C) & (m2_finseq_1 C k1_numbers))  =>  (~ (r2_classes1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l30_rlaffin3,ax,(r2_hidden k1_xboole_0 k1_numbers)).
tt(l30_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((u1_struct_0 (k1_rlsub_2 A (k2_rlsub_2 A B C) C)) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(l30_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((u1_struct_0 (k1_rusub_2 A (k2_rusub_2 A B C) C)) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(l30_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_scm_comp)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_scm_comp)) =>  ( ( (D = (k1_bintree1 (u1_struct_0 k1_scm_comp) B))  &  ( (E = (k1_bintree1 (u1_struct_0 k1_scm_comp) C))  & (r1_lang1 k1_scm_comp A (k4_pre_poly (u1_struct_0 k1_scm_comp) D E))) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (F = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers c8__scm_comp B))  &  (G = (k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers c8__scm_comp C)) )  =>  ((k3_funct_2 (k4_dtconstr k1_scm_comp) k5_numbers c8__scm_comp (k2_scm_comp A B C)) = (k7_nat_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((r2_hidden (k2_nat_1 (k5_card_1 B) 4) (k9_xtuple_0 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)))) &  ((k1_funct_1 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k2_nat_1 (k5_card_1 B) 4)) = (k11_scmfsa_2 (k2_nat_1 k6_numbers (k2_nat_1 (k5_card_1 B) 4)))) ) ) ) ) ) ).
tt(l30_scmpds_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) => (r1_tarski (k61_valued_1 A 1) (k2_scmpds_8 B C A))) ) ) ) ) ) ).
tt(l30_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_amistd_1 2 k1_scmpds_2 (k9_scmpds_2 A B 5)) = k1_xboole_0) ) ) ) ) ).
tt(l30_scmpds_i,ax, (! [A:$i] :  ((m1_subset_1 A k1_scmpds_i) =>  ( (~  ( (~  ((k2_compos_0 k1_scmpds_i A) = 9) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 10) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 11) )  &  ( (~  ((k2_compos_0 k1_scmpds_i A) = 12) )  &  (~  ((k2_compos_0 k1_scmpds_i A) = 13) ) ) ) ) ) )  =>  ((k5_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(l30_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 4)) = (k2_xcmplx_0 D (k1_funct_1 B (k1_scmp_gcd 5))))  &  ( (D = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ((r1_xxreal_0 8 C) & (r1_xxreal_0 C D)) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 5)) k6_numbers) |  ((r1_scmpds_6 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) &  ((r2_scmpds_6 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 2)) = C)  &  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 3))) &  ((r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 4)) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((r1_xxreal_0 D (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 4))) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 5)) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 5))))  &  ((r1_xxreal_0 (k4_xcmplx_0 1) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 5))) &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 4)) = (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 3)) 1) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 5))))  &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (E = (k6_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 3)) 1))  &  ( (F = (k2_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd 4)) 1))  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 G) =>  ( (G = E)  |  ( (G = F)  |  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd G)) = (k1_funct_1 B (k1_scmp_gcd G))) ) ) ) ) )  &  ( ( ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd E)))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd F)) = (k1_funct_1 B (k1_scmp_gcd F))) )  |  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) E) &  ((r1_xxreal_0 F (k1_funct_1 B (k1_scmp_gcd 4))) &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd E)) = (k1_funct_1 B (k1_scmp_gcd F)))  &  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd F)) = (k1_funct_1 B (k1_scmp_gcd E))) ) ) ) )  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) G) & (r1_xxreal_0 G E))  => (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd G)) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd C)))) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 F G) & (r1_xxreal_0 G (k1_funct_1 B (k1_scmp_gcd 4))))  => (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd C)) (k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))))) B A) (k1_scmp_gcd G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((k5_binop_1 A D B C) = B)  => (r2_funct_2 k5_numbers A (k9_funcop_1 A k5_numbers D (k1_setwop_2 A E B) C) (k1_setwop_2 A (k2_finseqop A A A D E C) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_simplex0 A) => (v1_finset_1 (u1_pre_topc A))) ) ) ).
tt(l30_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 A) = A) ) ) ).
tt(l30_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers k2_fdiff_9))).
tt(l30_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k1_sin_cos2 (k8_real_1 2 A)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k1_sin_cos2 A)) (k1_seq_1 k4_sin_cos2 A)))  &  ((k1_seq_1 k4_sin_cos2 (k8_real_1 2 A)) = (k9_real_1 (k8_real_1 2 (k5_square_1 (k1_seq_1 k4_sin_cos2 A))) 1)) ) ) ) ).
tt(l30_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v2_topreal1 A) => (v2_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l30_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l30_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) (k4_substlat A B C D) D)) = (k3_substlat A B D)) ) ) ) ) ) ) ).
tt(l30_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (~  ((r1_tarski A B) & (r1_xboole_0 A B)) ) ) ) ) ).
tt(l30_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_topdim_1 A) => (v1_topdim_1 B A)) ) ) ) ) ).
tt(l30_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v3_topdim_1 (k15_euclid A)) & (r1_xxreal_0 (k4_topdim_1 (k15_euclid A)) A)) ) ) ).
tt(l30_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden B k1_topreal1) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B C) &  ((r1_topreal1 (k15_euclid 2) A B D) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_transgeo A) & (l1_analoaf A)) )  => (r1_relat_2 (u1_analoaf A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(l30_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ((v2_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B)) &  ((v3_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B)) &  ((v4_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B)) & (v13_algstr_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B))) ) ) ) ) ) ) ).
tt(l30_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v2_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) &  ((v3_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) &  ((v4_rlvect_1 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) & (v13_algstr_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A)))) ) ) ) ) ).
tt(l30_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_waybel_3 A D E) => (r1_waybel_3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((r2_hidden A (k4_finseq_1 B)) &  ( (B = (k7_finseq_1 (k7_finseq_1 C (k9_finseq_1 E)) D))  &  ((k3_finseq_1 C) = (k5_real_1 A 1)) ) )  =>  ((k2_finseq_3 A B) = (k7_finseq_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l30_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) C) => (r1_xxreal_0 A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l30_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~ (v7_struct_0 (k2_yellow_1 (u1_pre_topc A)))) ) ) ).
tt(l31_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_algstr_0)) =>  ((k6_algstr_0 k8_algstr_0 A B) = (k6_algstr_0 k8_algstr_0 B A)) ) ) ) ) ).
tt(l31_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) <=>  (~  ( (~  (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k2_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k3_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k4_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k5_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k6_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  (A = (k7_ami_3 B)) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k8_ami_3 C B)) ) ) ) ) )  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k9_ami_3 C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((v5_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r2_hidden (k5_memstr_0 A B D) (k1_relset_1 k5_numbers C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ((r1_tarski C E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B E D F)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C G) (k1_rlvect_1 A D H)))  &  (D = (k3_rlvect_1 A E (k1_rlvect_1 A F I))) )  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A E H) (k1_rlvect_1 A C G)) (k1_rlvect_1 A F (k8_real_1 H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 B A))  =>  (A = B) ) ) ) ) ) ).
tt(l31_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 1 C))  =>  ((r1_xxreal_0 A 1) | (r1_xxreal_0 (k6_power B C) (k6_power A C))) ) ) ) ) ) ) ) ).
tt(l31_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_autalg_1 C (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  ((v1_msualg_3 C) & (v2_msualg_3 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ).
tt(l31_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (r1_tarski (u1_struct_0 A) (k4_bcialg_1 A))) ) ).
tt(l31_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k5_series_1 2 A) B) =>  ((r1_xxreal_0 (k5_series_1 2 (k2_xcmplx_0 A 1)) B) |  ((k1_binari_3 (k2_xcmplx_0 A 1) B) = (k9_binarith A 1 k6_margrel1 (k1_binari_3 A (k7_nat_d B (k5_series_1 2 A))) (k10_binarith k6_margrel1 k8_margrel1))) ) ) ) ) ) ) ).
tt(l31_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k4_nat_d B A) = (k4_nat_d C A))  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  (B = (k20_binop_2 C (k22_binop_2 D A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_binop_2,ax,(m1_subset_1 k6_numbers k4_numbers)).
tt(l31_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A G E))) (k1_bvfunc_1 A (k2_bvfunc_1 A G F)))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_cfuncdom,ax, (? [A:$i] :  ( (~ (v1_xboole_0 A))  &  (? [B:$i] :  (? [C:$i] :  ( (A = (k2_tarski B C))  &  (~  (B = C) ) ) ) ) ) ) ).
tt(l31_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k4_tarski (k4_tarski A C) E) = (k4_tarski (k4_tarski B D) F))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ).
tt(l31_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k4_complex1 (k3_xcmplx_0 A k7_complex1)) = A) ) ) ).
tt(l31_csspace,ax,(r2_hidden (k4_struct_0 o_0_6_csspace) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)))).
tt(l31_dtconstr,ax, ((v1_dtconstr k5_dtconstr) &  ((v2_dtconstr k5_dtconstr) & (v3_dtconstr k5_dtconstr)) ) ).
tt(l31_fib_num4,ax, (~ (r1_xxreal_0 (k6_xcmplx_0 3 3) (k6_xcmplx_0 (k7_square_1 5) 3))) ).
tt(l31_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v2_binop_1 C A) & (v2_fomodel0 B A C))  => (v2_fomodel0 (k7_relset_1 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A (k5_fomodel0 A C) (k4_finseq_2 (k2_xcmplx_0 D 1) B)) A C)) ) ) ) ) ) ) ) ) ).
tt(l31_fomodel2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_xboole_0 (k2_xboole_0 B C) D)) <=>  (~  ( (~ (r2_hidden A B))  &  ( (~ (r2_hidden A C))  &  (~ (r2_hidden A D)) ) ) ) ) ) ) ) ) ).
tt(l31_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_fomodel4 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_fomodel4 B))) =>  ( ((r1_tarski E F) & (r1_tarski C D))  =>  ( ( (~ (v6_fomodel4 D B))  &  (~ (v6_fomodel4 C B)) )  | (r1_tarski (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k3_fomodel4 B C A) E) (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k3_fomodel4 B D A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((k24_gfacirc1 A B C) = (k4_tarski D k3_gfacirc1)) ) ) ) ) ) ).
tt(l31_funct_9,ax,(v1_funct_9 k1_fdiff_9 (k8_real_1 2 k32_sin_cos))).
tt(l31_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E C) & (r2_hidden F B))  =>  ((k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 C A B (k4_fuzzy_2 C A) D E F))) = (k1_seq_1 (k4_fuzzy_2 C B) (k4_tarski E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ( (~ (v5_glib_002 B A))  => (v1_glib_002 C)) ) ) ) ) ) ) ).
tt(l31_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_funct_2 (u1_struct_0 A) (k1_funct_2 B B) (u1_struct_0 A) (k1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) C) (k2_zfmisc_1 (u1_struct_0 A) C)) D (k7_group_10 A C)) &  ( (E = (k7_group_1 A))  &  ( (B = (k2_zfmisc_1 (u1_struct_0 A) C))  & (r1_ordinal1 (k5_card_1 E) (k1_card_1 B))) ) )  =>  ((k12_group_10 A (k3_group_10 B E) (k5_group_10 B E A D)) = (a_2_4_group_10 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_group_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_3 B (k5_group_1 B A C) D) = (k5_group_1 B A (k2_group_3 B C D))) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_3 B (k5_group_1 B (k1_nat_1 A 1) C) D) = (k5_group_1 B (k1_nat_1 A 1) (k2_group_3 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(l31_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  ((r2_group_9 A B C) => (r2_group_9 A C B)) ) ) ) ) ) ).
tt(l31_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  ( (B = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( (C = (g1_rlvect_1 (u1_struct_0 D) (u2_struct_0 D) (u1_algstr_0 D) (u1_rlvect_1 D)))  => (m1_rlsub_1 C B)) ) ) ) ) ) ) ) ) ) ).
tt(l31_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m2_funct_2 D (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k9_funct_2 (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) =>  ((k3_funct_2 (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k6_funcop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A) (k5_heyting1 A) D (k6_funct_3 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))) C) = (k3_normform (k5_finsub_1 A) (k5_finsub_1 A) (k3_funct_2 (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) D C) C)) ) ) ) ) ) ) ) ).
tt(l31_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C G) & (v7_aff_2 A))  =>  ((r2_hidden B G) |  ( ( (~  ((r2_hidden D G) &  (D = E) ) )  &  (~  ( (~ (r2_hidden D G))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H G) &  ((r2_hidden I G) &  ((r2_analoaf A H B I D) &  ((r2_analoaf A H C I E) & (r2_aff_1 A D E G)) ) ) ) ) ) ) ) ) ) )  |  ( ( (~  ((r2_hidden F G) &  (F = E) ) )  &  (~  ( (~ (r2_hidden F G))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H G) &  ((r2_hidden I G) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I E) & (r2_aff_1 A F E G)) ) ) ) ) ) ) ) ) ) )  |  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid E)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 E (k3_integra5 A B) F) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 E k1_numbers F)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid E) F (k3_integra5 A B)) E) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) )  =>  ((r1_integr15 E (k3_integra5 C D) F) &  ((r1_integra5 (k3_integra5 C D) (k1_nfcont_4 E k1_numbers F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 E k1_numbers F) (k3_integra5 C D))) & (r1_xxreal_0 (k12_euclid (k12_integr15 C D E F)) (k4_integra5 C D (k1_nfcont_4 E k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 C D)) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 F G)) E)) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k18_complex1 (k4_integra5 C D F)) (k3_xcmplx_0 E (k6_xcmplx_0 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_jgraph_3,ax, (~  ((k22_euclid 2) = (k4_struct_0 (k15_euclid 2))) ) ).
tt(l31_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((k6_pscomp_1 A) = (k1_real_1 1)) ) ) ) ).
tt(l31_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r2_hidden (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A D)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A D)) & (r2_hidden C B)) ) ) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) | (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) C (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ) ) ) ).
tt(l31_lfuzzy_0,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)))) => (m1_subset_1 A k1_numbers)) ) ).
tt(l31_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( (A = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  (k6_numbers = (k1_funct_1 D E)) ) ) ) )  =>  ((r3_mesfunc6 A B C D) &  ((k1_mesfunc6 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A C (k8_cqc_lang A D (k8_cqc_lang A B E))) (k8_cqc_lang A D (k8_cqc_lang A B E)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l31_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~  ((v2_modelc_1 A) &  ( (~  ((k1_funct_1 A 1) = k6_numbers) )  &  ( (~  ((k1_funct_1 A 1) = 1) )  &  ( (~  ((k1_funct_1 A 1) = 2) )  &  ( (~  ((k1_funct_1 A 1) = 3) )  &  (~  ((k1_funct_1 A 1) = 4) ) ) ) ) ) ) )  &  ( (~  ((v3_modelc_1 A) &  ((k1_funct_1 A 1) = k6_numbers) ) )  &  ( (~  ((v4_modelc_1 A) &  ((k1_funct_1 A 1) = 1) ) )  &  ( (~  ((v5_modelc_1 A) &  ((k1_funct_1 A 1) = 2) ) )  &  ( (~  ((v6_modelc_1 A) &  ((k1_funct_1 A 1) = 3) ) )  &  (~  ((v7_modelc_1 A) &  ((k1_funct_1 A 1) = 4) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (A = (k7_finseq_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(l31_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( ((v1_int_2 (k23_binop_2 A 2)) &  ((r1_tarski (k1_rvsum_1 B) (k2_finseq_1 A)) &  ((v2_funct_1 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k1_rvsum_1 B)) &  ( (~  (C = 1) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k1_rvsum_1 B)) &  ( (~  (D = 1) )  &  ( (~  (D = C) )  &  ((k4_nat_d (k24_binop_2 C D) (k23_binop_2 A 2)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k4_nat_d (k3_wsierp_1 B) (k23_binop_2 A 2)) = 1) ) ) ) ) ) ).
tt(l31_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  (! [E:$i] :  ((m2_cat_1 E B A) =>  ( ((r1_nattra_1 B A C D) & (r1_nattra_1 B A D E))  =>  (! [F:$i] :  ((m1_nattra_1 F B A C D) =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( (~  ((k2_cat_1 B G H) = k1_xboole_0) )  =>  (! [I:$i] :  ((m1_cat_1 I B G H) =>  ((k5_cat_1 A (k8_cat_1 B A C G) (k8_cat_1 B A C H) (k8_cat_1 B A D H) (k9_cat_3 B G H A C I) (k4_nattra_1 B A C D F H)) = (k5_cat_1 A (k8_cat_1 B A C G) (k8_cat_1 B A D G) (k8_cat_1 B A D H) (k4_nattra_1 B A C D F G) (k9_cat_3 B G H A D I))) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_nattra_1 G B A D E) =>  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ( (~  ((k2_cat_1 B H I) = k1_xboole_0) )  =>  (! [J:$i] :  ((m1_cat_1 J B H I) =>  ((k5_cat_1 A (k8_cat_1 B A D H) (k8_cat_1 B A D I) (k8_cat_1 B A E I) (k9_cat_3 B H I A D J) (k4_nattra_1 B A D E G I)) = (k5_cat_1 A (k8_cat_1 B A D H) (k8_cat_1 B A E H) (k8_cat_1 B A E I) (k4_nattra_1 B A D E G H) (k9_cat_3 B H I A E J))) ) ) ) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ( (~  ((k2_cat_1 B H I) = k1_xboole_0) )  =>  (! [J:$i] :  ((m1_cat_1 J B H I) =>  ((k5_cat_1 A (k8_cat_1 B A C H) (k8_cat_1 B A C I) (k8_cat_1 B A E I) (k9_cat_3 B H I A C J) (k4_nattra_1 B A C E (k5_nattra_1 B A C D E F G) I)) = (k5_cat_1 A (k8_cat_1 B A C H) (k8_cat_1 B A E H) (k8_cat_1 B A E I) (k4_nattra_1 B A C E (k5_nattra_1 B A C D E F G) H) (k9_cat_3 B H I A E J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_ntalgo_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_finseq_1 (k3_finseq_1 A))) & (r2_hidden D (k2_finseq_1 (k3_finseq_1 A))))  =>  ( (C = D)  | (r1_int_2 (k1_funct_1 A C) (k1_funct_1 A D))) ) ) ) ) )  &  ((k1_funct_1 B 1) = 1) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k6_xcmplx_0 (k3_finseq_1 A) 1)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D C))  =>  ((k1_funct_1 B (k1_nat_1 D 1)) = (k3_xcmplx_0 (k1_funct_1 B D) (k1_funct_1 A D))) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) D) & (r1_xxreal_0 D (k3_finseq_1 A)))  => (r1_int_2 (k1_funct_1 B (k2_nat_1 C 1)) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((k5_cat_1 A B C D E F) = (k5_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A D) (k3_oppcat_1 A C) (k3_oppcat_1 A B) (k7_oppcat_1 A C D F) (k7_oppcat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (r1_yellow_2 (u1_struct_0 A) B C C)) ) ) ) ) ) ).
tt(l31_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_prelamb A B D) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) E)) F))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A E D))) B) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_prvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = C) )  =>  ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) = k6_numbers) ) )  &  ( ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) = k6_numbers) )  =>  ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(l31_realset2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c10__realset2)) =>  ((k1_algstr_0 c10__realset2 A (k4_struct_0 c10__realset2)) = A) ) ) ).
tt(l31_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k2_sf_mastr (k1_funct_4 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers))))) ) ) ) ) ).
tt(l31_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (B = 5) )  =>  ((k2_amistd_1 2 k1_scmpds_2 (k9_scmpds_2 A C B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(l31_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (~ (v2_extpro_1 (k3_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l31_scpinvar,ax, ((k5_card_1 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))) = 6) ).
tt(l31_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k1_scmp_gcd 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ((k1_funct_1 B k2_scmp_gcd) = k6_numbers) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 6)) k6_numbers) |  ((k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) = (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers)))) B A)) A)) ) ) ) ) ) ) ).
tt(l31_scpqsort,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A k6_numbers) &  ( (~  (A = (k4_xcmplx_0 1)) )  &  (~  (A = k6_numbers) ) ) ) ) ) ) ) ).
tt(l31_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((k5_binop_1 A D B C) = C)  => (r2_funct_2 k5_numbers A (k10_funcop_1 A k5_numbers D B (k1_setwop_2 A E C)) (k1_setwop_2 A (k3_finseqop A A A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_sincos10,ax,(r1_tarski (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))) (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))).
tt(l31_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k2_xcmplx_0 1 (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 A))) = k6_numbers) ) ) ) ).
tt(l31_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (m1_subset_1 (a_2_0_sppol_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))) ) ) ) ).
tt(l31_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k4_termord A B C D) = (k4_struct_0 C))  <=> (r8_pboole (k15_pre_poly A) D (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(l31_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden B k1_topreal1) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B C) &  ((r1_topreal1 (k15_euclid 2) A B D) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_transgeo A) & (l1_analoaf A)) )  => (r3_relat_2 (u1_analoaf A) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(l31_valued_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((k1_relset_1 A (k51_valued_1 A B C D E)) = A) ) ) ) ) ) ) ) ) ) ).
tt(l31_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ((r8_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B (u2_algstr_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B))) =>  ( ((k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) C (k1_algstr_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) E F)) = (k1_algstr_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) C E) (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) C F)))  &  ( ((k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) (k1_algstr_0 A C D) E) = (k1_algstr_0 (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) C E) (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) D E)))  &  ( ((k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) (k6_algstr_0 A C D) E) = (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) C (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) D E)))  &  ((k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) B) (k5_struct_0 A) E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l31_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_waybel11 A D)) (k1_waybel11 B (k6_waybel_9 A B C D)))) )  => (v22_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(l31_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_pre_topc (k5_waybel26 D) (k2_borsuk_1 B A)) & (m1_subset_1 (k5_waybel26 D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (v23_waybel_0 (k3_waybel29 B A) (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 B A))) (k3_waybel24 B (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))))) ) ) ) ) ).
tt(l31_weierstr,ax, (~  ((k2_struct_0 k3_topmetr) = k1_xboole_0) ) ).
tt(l31_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 (k2_finseq_3 A B)) (k4_finseq_1 B))) ) ) ) ).
tt(l31_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_xboole_0 (k2_tarski A B) C) = (k1_tarski A))  <=>  ( (~ (r2_hidden A C))  &  ((r2_hidden B C) |  (A = B) ) ) ) ) ) ) ).
tt(l32_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  ((v2_extpro_1 A 2 k1_ami_3) =>  (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ) ) ) ).
tt(l32_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C G) (k1_rlvect_1 A D H)))  &  (D = (k3_rlvect_1 A E (k1_rlvect_1 A F I))) )  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A E H) (k1_rlvect_1 A F (k8_real_1 H I))) (k1_rlvect_1 A C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((k3_arytm_2 A) = (k3_arytm_2 B))  =>  (A = B) ) ) ) ) ) ).
tt(l32_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( (C = (k5_euclid A))  =>  ( ((k1_binari_3 A B) = (k3_binarith A C))  <=>  (B = (k6_xcmplx_0 (k5_series_1 2 A) 1)) ) ) ) ) ) ) ) ) ) ).
tt(l32_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k4_nat_d B (k5_series_1 2 A)) = (k4_nat_d C (k5_series_1 2 A)))  =>  ((r1_xxreal_0 A D) |  ((k4_nat_d (k3_nat_d B (k5_series_1 2 D)) 2) = (k4_nat_d (k3_nat_d C (k5_series_1 2 D)) 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_binop_2,ax,(r3_binop_1 k4_numbers c3__binop_2 k44_binop_2)).
tt(l32_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A F E))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G)))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k5_c0sp2 A) B C) = (k5_algstr_0 (k11_c0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k5_arytm_0 A B) = (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1))) ) ) ) ) ).
tt(l32_csspace,ax, ((k1_funct_1 c2__csspace (k1_domain_1 (u1_struct_0 o_0_6_csspace) (u1_struct_0 o_0_6_csspace) (k4_struct_0 o_0_6_csspace) (k4_struct_0 o_0_6_csspace))) = k5_complex1) ).
tt(l32_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m2_subset_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D A B) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ( (C = E)  &  (D = F) )  =>  ((k7_ens_1 B C D) = (k7_ens_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k5_algstr_0 A (k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G))) = (k3_rlvect_1 A (k1_rlvect_1 A B (k9_real_1 D F)) (k1_rlvect_1 A C (k9_real_1 E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_fib_num4,ax, (~ (r1_xxreal_0 k6_numbers (k13_complex1 (k6_xcmplx_0 (k7_square_1 5) 3) 2))) ).
tt(l32_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v2_binop_1 C A) & (v2_fomodel0 B A C))  => (v2_fomodel0 (k7_relset_1 (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)) A (k5_fomodel0 A C) (k4_finseq_2 (k2_xcmplx_0 D 1) B)) A C)) ) ) ) ) ) ) ) ).
tt(l32_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 A C)) =>  (! [G:$i] :  ((m2_subset_1 G (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((r2_hidden (k1_domain_1 (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) E G) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k23_fomodel2 A D B))) => (r2_hidden (k1_domain_1 (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) F G) (k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 A)) (k16_fomodel2 A C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 A)) (k1_tarski k1_xboole_0))) (k23_fomodel2 A D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k8_fomodel3 A B D C) = (a_4_6_fomodel3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(l32_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [E:$i] :  ((v2_fomodel4 E B) =>  (! [F:$i] :  ((v2_fomodel4 F B) =>  ( ((r1_tarski E F) & (r1_tarski C D))  =>  ( ( (~ (v6_fomodel4 D B))  &  (~ (v6_fomodel4 C B)) )  | (r1_tarski (k1_funct_1 (k3_fomodel4 B C A) E) (k1_funct_1 (k3_fomodel4 B D A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] : (r1_xboole_0 (k2_msafree2 (k25_gfacirc1 A B C)) (k3_msafree2 (k37_gfacirc1 D E F)))) ) ) ) ) ) ) ) ) ).
tt(l32_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k1_fdiff_9 (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))) ) ).
tt(l32_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ((m2_functor2 H B C F G) =>  (! [I:$i] :  ((m2_functor2 I A B D E) =>  ( ((r2_functor2 A B D E) & (r2_functor2 B C F G))  =>  ((r2_functor2 A C (k1_functor3 A B C D F) (k1_functor3 A B C E G)) & (m2_functor2 (k7_functor3 A B C D E F G I H) A C (k1_functor3 A B C D F) (k1_functor3 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k4_fvsum_1 A B C (k6_fvsum_1 A B C)) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ) ) ).
tt(l32_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v1_glib_002 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) &  ( (~  (B = C) )  &  ( (~ (v5_glib_002 B A))  &  (~ (v5_glib_002 C A)) ) ) ) ) ) ) ) ) ).
tt(l32_goboard1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  => (r1_goboard1 A (k6_finseq_1 A) B)) ) ) ).
tt(l32_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  ( ((k2_polynom1 (k15_pre_poly A) C (k2_groeb_3 A C D (k3_groeb_3 A B C D E))) = (k3_groeb_3 A B C D E))  &  ((k2_polynom1 (k15_pre_poly A) C (k2_groeb_3 A C D (k4_groeb_3 A B C D E))) = (k4_groeb_3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v7_ordinal1 D) & (v1_int_2 D))  =>  (~  ( (A = (k3_xcmplx_0 (k1_newton D C) B))  &  ( (~ (r1_nat_d D B))  &  ((k4_nat_d (k6_newton (k1_newton D C) A) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_group_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_3 B (k5_group_1 B A C) D) = (k5_group_1 B A (k2_group_3 B C D))) ) ) ) ) ) ) ) ) ).
tt(l32_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ( (B = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) &  ((v2_hahnban C B) &  ((v3_hahnban C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v2_hahnban C A) &  ((v3_hahnban C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  ((v1_finset_1 C) =>  ((k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) C) = (k1_tarski C)) ) ) ) ) ) ) ).
tt(l32_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k8_real_1 (k10_real_1 (k3_newton B) (k3_newton A)) A) = (k10_real_1 (k3_newton B) (k3_newton (k7_nat_d A 1)))) ) ) ) ) ) ).
tt(l32_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_aff_1 A B C D) &  ( (~ (r2_hidden B D))  &  ((v7_aff_2 A) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ((r2_hidden F D) &  (F = G) )  |  ( (~ (r2_hidden F D))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H D) &  ((r2_hidden I D) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I G) & (r2_aff_1 A F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_xxreal_0 (k4_xcmplx_0 1) (k2_hurwitz A B))) ) ) ) ).
tt(l32_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m2_cat_1 (k1_funct_1 (k2_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B)))) C) (k2_index_1 (u4_struct_0 A) (k3_relat_1 (u1_graph_1 A) (k1_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))))) C) (k2_index_1 (u4_struct_0 A) (k3_relat_1 (u2_graph_1 A) (k1_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))))) C))) ) ) ) ) ) ).
tt(l32_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k7_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) | (r2_hidden (k21_binop_2 B A) (k7_card_1 B))) ) ) ) ) ) ).
tt(l32_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 C D)) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 F G)) E)) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k18_complex1 (k4_integra5 D C F)) (k3_xcmplx_0 E (k6_xcmplx_0 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski (k2_setfam_1 B (k3_setfam_1 C D)) (k3_setfam_1 (k2_setfam_1 B C) (k2_setfam_1 B D)))) ) ) ) ) ) ) ).
tt(l32_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ( ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = (a_7_0_lfuzzy_0 A B C D E F G))  &  (~  ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((v1_ideal_1 (k1_lpspace2 A B C D) (k7_lpspace1 A)) & (v1_lpspace1 (k1_lpspace2 A B C D) (k7_lpspace1 A))) ) ) ) ) ) ) ) ) ).
tt(l32_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A C (k8_cqc_lang A D E))) (k8_cqc_lang A (k8_cqc_lang A D B) (k8_cqc_lang A C (k8_cqc_lang A D E)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l32_matrix_9,ax, (~  ((k3_finseq_4 k5_numbers 1 2 3) = (k3_finseq_4 k5_numbers 3 2 1)) ) ).
tt(l32_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_membered D) =>  ( (D = (a_3_0_mazurulm A B C))  => (m1_xxreal_2 (k11_binop_2 2 (k1_normsp_0 A (k5_algstr_0 A B (k1_rlvect_1 A (k3_rlvect_1 A B C) (k18_binop_2 1 2))))) D)) ) ) ) ) ) ) ) ) ).
tt(l32_metric_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 k6_numbers D) &  ((r1_xxreal_0 k6_numbers E) & (r1_xxreal_0 k6_numbers F)) ) ) ) )  => (r1_xxreal_0 (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 (k2_xcmplx_0 A C)) (k3_square_1 (k2_xcmplx_0 B D))) (k3_square_1 (k2_xcmplx_0 E F)))) (k2_xcmplx_0 (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 E))) (k6_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 D)) (k3_square_1 F)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_modcat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k11_modcat_1 A B))) =>  ( ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C))  =>  ( ((k3_graph_1 (k11_modcat_1 A B) (k1_cat_1 (k11_modcat_1 A B) C D)) = (k3_graph_1 (k11_modcat_1 A B) C))  &  ((k4_graph_1 (k11_modcat_1 A B) (k1_cat_1 (k11_modcat_1 A B) C D)) = (k4_graph_1 (k11_modcat_1 A B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  => (r1_xxreal_0 1 (k3_finseq_1 A))) ) ).
tt(l32_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k4_modelc_2 A B) = (k4_modelc_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_nat_4,ax, ( (~ (v1_int_2 6))  &  ( (~ (v1_int_2 8))  &  ( (~ (v1_int_2 9))  &  ( (~ (v1_int_2 10))  &  ( (~ (v1_int_2 12))  &  ( (~ (v1_int_2 14))  &  ( (~ (v1_int_2 15))  &  ( (~ (v1_int_2 16))  &  ( (~ (v1_int_2 18))  &  ( (~ (v1_int_2 20))  &  ( (~ (v1_int_2 21))  &  ( (~ (v1_int_2 22))  &  ( (~ (v1_int_2 24))  &  ( (~ (v1_int_2 25))  &  ( (~ (v1_int_2 26))  &  ( (~ (v1_int_2 27))  &  (~ (v1_int_2 28)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_ndiff_3,ax,(v2_rcomp_1 (k1_subset_1 k1_numbers))).
tt(l32_ntalgo_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_funct_1 B 1) = 1) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k6_xcmplx_0 (k3_finseq_1 A) 1)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D C))  =>  ((k1_funct_1 B (k1_nat_1 D 1)) = (k3_xcmplx_0 (k1_funct_1 B D) (k1_funct_1 A D))) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D C))  =>  ((k6_int_1 (k1_funct_1 B (k2_nat_1 C 1)) (k1_funct_1 A D)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v10_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l32_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k2_normsp_1 A B (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ).
tt(l32_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k2_binom A (k11_algstr_0 A C) B) = (k11_algstr_0 A (k2_binom A C B))) ) ) ) ) ) ) ) ).
tt(l32_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_yellow_2 (u1_struct_0 A) B C D) & (r1_yellow_2 (u1_struct_0 A) B D E))  => (r1_yellow_2 (u1_struct_0 A) B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_prelamb A B D) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) E) C) F))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A E D)) B) C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((v7_ordinal1 C) &  ((k1_seq_1 (k1_real_3 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(l32_realset2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c10__realset2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c10__realset2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c10__realset2)) =>  ((k1_algstr_0 c10__realset2 (k1_algstr_0 c10__realset2 A B) C) = (k1_algstr_0 c10__realset2 A (k1_algstr_0 c10__realset2 B C))) ) ) ) ) ) ) ).
tt(l32_rfinseq,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  (! [C:$i] :  ( ((v8_valued_0 C) & (m2_finseq_1 C k1_numbers))  =>  ( ( (A = (k3_finseq_1 B))  & (r2_classes1 B C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l32_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_pre_topc B) &  ((v6_rltopsp1 B) &  ((v7_rltopsp1 B) & (l1_rltopsp1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ((m2_rlaffin3 D B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_rlaffin3 F B (k5_rusub_4 B C E)) =>  ( (F = (k3_fvsum_1 B D (k5_finseq_2 (u1_struct_0 B) (k5_card_1 C) E)))  =>  (! [G:$i] :  ((k7_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k3_rltopsp1 B E) (a_5_3_rlaffin3 A B C D G)) = (a_6_0_rlaffin3 A B C E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((u1_struct_0 (k2_rlsub_2 A B (k1_rlsub_2 A B C))) = (u1_struct_0 B)) ) ) ) ) ) ) ).
tt(l32_rlvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_orders_1 B A) =>  ( (~ (r2_hidden k1_xboole_0 A))  =>  ((k9_xtuple_0 B) = A) ) ) ) ) ) ).
tt(l32_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (r1_tarski (u1_struct_0 (k2_rmod_3 A B C D)) (u1_struct_0 (k1_rmod_3 A B C D)))) ) ) ) ) ) ) ) ).
tt(l32_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((u1_struct_0 (k2_rusub_2 A B (k1_rusub_2 A B C))) = (u1_struct_0 B)) ) ) ) ) ) ) ).
tt(l32_scm_comp,ax, ((k7_dtconstr k1_scm_comp) = (k2_zfmisc_1 1 5)) ).
tt(l32_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k4_sf_mastr (k1_funct_4 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_nat_1 (k5_card_1 B) 4) (k11_scmfsa_2 k6_numbers))))) ) ) ) ) ).
tt(l32_scmpds_4,ax,(v3_scmpds_4 (k9_compos_1 k1_scmpds_2 (k2_compos_1 k1_scmpds_2)))).
tt(l32_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (~ (v2_extpro_1 (k4_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l32_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_amistd_1 2 (k1_scmring2 A) C B) = (k1_tarski (k1_ordinal1 C))) ) )  => (v1_xboole_0 (k2_amistd_1 2 (k1_scmring2 A) B))) ) ) ) ) ).
tt(l32_scpinvar,ax, ((k5_card_1 (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)))) = 9) ).
tt(l32_scpqsort,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A k6_numbers) &  ( (D = (k2_xcmplx_0 B 1))  &  (B = (k2_xcmplx_0 C A)) ) ) )  =>  ((r1_xxreal_0 D E) | (r1_xxreal_0 E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_simplex2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 1)))) =>  ( ((v4_pre_topc A (k15_euclid 1)) & (v9_rltopsp1 A (k15_euclid 1)))  => (v2_compts_1 A (k15_euclid 1))) ) ) ).
tt(l32_sincos10,ax,(r1_tarski (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)) (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))).
tt(l32_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k4_sin_cos2 (k10_binop_2 A B)) = (k9_real_1 (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ).
tt(l32_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k6_sin_cos2 A) 1) k6_numbers))  &  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k6_sin_cos2 A) 1)) &  (~  ((k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 A) 2) (k6_sin_cos2 A)) = k6_numbers) ) ) ) ) ) ).
tt(l32_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((v2_topreal1 A) => (v2_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(l32_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k3_polynom1 A C (k5_termord A B C D) (k3_termord A B C D)) = (k3_polynom1 A C D (k3_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(l32_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden B k1_topreal1) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B C) &  ((r1_topreal1 (k15_euclid 2) A B D) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l32_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v2_rlvect_1 (g1_vectsp_2 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) &  ((v3_rlvect_1 (g1_vectsp_2 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) &  ((v4_rlvect_1 (g1_vectsp_2 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A))) & (v13_algstr_0 (g1_vectsp_2 A (u1_struct_0 A) (u1_algstr_0 A) (k4_struct_0 A) (u2_algstr_0 A)))) ) ) ) ) ).
tt(l32_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (B = (a_2_3_waybel24 A B)) ) ) ) ) ).
tt(l32_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_pre_topc (k5_waybel26 D) (k2_borsuk_1 B A)) & (m1_subset_1 (k5_waybel26 D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  ((v3_pre_topc (a_1_0_waybel29 A) (k2_borsuk_1 B A)) & (m1_subset_1 (a_1_0_waybel29 A) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) ).
tt(l32_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) (k7_funcop_1 B C) (k6_waybel_5 B C (u1_struct_0 A) D) E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) (k7_funcop_1 B C) (k6_waybel_5 B C (u1_struct_0 A) D))))) ) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l32_waybel_9,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (k6_domain_1 k5_numbers k6_numbers)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_domain_1 k5_numbers k6_numbers) (k6_domain_1 k5_numbers k6_numbers)))) =>  ( ( (A = (k2_tarski k1_xboole_0 (k6_domain_1 k5_numbers k6_numbers)))  &  (B = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers))) )  =>  ((v3_orders_2 (g1_waybel_9 (k6_domain_1 k5_numbers k6_numbers) B A)) &  ((v1_tdlat_3 (g1_waybel_9 (k6_domain_1 k5_numbers k6_numbers) B A)) &  ((v8_struct_0 (g1_waybel_9 (k6_domain_1 k5_numbers k6_numbers) B A)) & (v13_struct_0 (g1_waybel_9 (k6_domain_1 k5_numbers k6_numbers) B A) 1)) ) ) ) ) ) ) ) ).
tt(l32_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ((k2_finseq_3 A (k7_finseq_1 B C)) = (k7_finseq_1 (k2_finseq_3 A B) C)) )  &  ((r1_xxreal_0 1 A) =>  ((k2_finseq_3 (k2_nat_1 (k3_finseq_1 B) A) (k7_finseq_1 B C)) = (k7_finseq_1 B (k2_finseq_3 A C))) ) ) ) ) ) ) ) ) ).
tt(l32_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 A B) = k1_xboole_0)  <=> (r1_tarski A B)) ) ) ).
tt(l33_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_altcat_1 (k7_altcat_1 A)) &  ((v11_altcat_1 (k7_altcat_1 A)) & (v12_altcat_1 (k7_altcat_1 A))) ) ) ) ).
tt(l33_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( ((k1_rlvect_1 A B D) = C)  &  ( (~  (D = k6_numbers) )  &  ( (~ (v9_struct_0 B A))  & (v9_struct_0 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((k8_arytm_2 A (k1_arytm_1 B C)) = (k1_arytm_1 (k8_arytm_2 A B) (k8_arytm_2 A C))) ) ) ) ) ) ) ).
tt(l33_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ((k4_arytm_2 (k3_arytm_2 A)) = A) ) ) ).
tt(l33_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k6_int_1 B (k5_series_1 2 A)) = (k6_int_1 C (k5_series_1 2 A)))  =>  ((k6_int_1 (k20_binop_2 (k5_series_1 2 (k1_binari_4 A (k1_int_2 B))) B) (k5_series_1 2 A)) = (k6_int_1 (k20_binop_2 (k5_series_1 2 (k1_binari_4 A (k1_int_2 C))) C) (k5_series_1 2 A))) ) ) ) ) ) ) ) ).
tt(l33_binop_2,ax,(r3_binop_1 k5_numbers k6_numbers k47_binop_2)).
tt(l33_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_connsp_2 C A B) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc D A) &  ((r1_tarski B D) &  ((r1_tarski D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E (k10_borsuk_1 A)) =>  ((r1_xboole_0 E D) | (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_borsuk_5 B C))  =>  ((r1_xxreal_0 C B) |  ((r2_hidden B (k2_pre_topc k3_topmetr A)) & (r2_hidden C (k2_pre_topc k3_topmetr A))) ) ) ) ) ) ) ) ) ).
tt(l33_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A C F) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G)))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k3_relat_1 (k9_finseq_1 A) B) = (k9_finseq_1 (k1_funct_1 B A))) ) ) ) ) ).
tt(l33_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k4_struct_0 (k5_cc0sp2 A)) = (k4_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) ) ) ).
tt(l33_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  ((r1_xxreal_0 k6_numbers (k3_complex1 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A A)))) &  ((k4_complex1 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A A))) = k6_numbers) ) ) ) ).
tt(l33_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C F)) = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C G)))  =>  ( (D = E)  &  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v2_binop_1 C A) & (v2_fomodel0 B A C))  => (v1_fomodel0 (k5_fomodel0 A C) (k4_finseq_2 (k2_xcmplx_0 D 1) B))) ) ) ) ) ) ) ) ) ).
tt(l33_fomodel2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_funct_1 (k1_funct_5 (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) k6_margrel1) (k22_fomodel2 B C) A))) &  ((v1_funct_2 (k1_funct_5 (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) k6_margrel1) (k22_fomodel2 B C) A)) (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1)) & (m1_subset_1 (k1_funct_5 (k8_nat_1 (k3_rfunct_3 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) k6_margrel1) (k22_fomodel2 B C) A)) (k1_zfmisc_1 (k2_zfmisc_1 (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1))))) ) ) ) ) ) ) ) ).
tt(l33_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B E))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C))) => (r1_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D C) (k4_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D E) (k4_finseq_2 D A) (k4_finseq_2 D C) (k8_fomodel3 B E F D) (k8_fomodel3 A C G D)) (k8_fomodel3 B C (k4_relset_1 B E A C F G) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ((r1_tarski D E) =>  ( ( (~ (v6_fomodel4 E C))  &  (~ (v6_fomodel4 D C)) )  | (r1_tarski (k1_funct_1 (k3_fomodel4 C D A) B) (k1_funct_1 (k3_fomodel4 C E A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_funcsdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_funcsdom A))) =>  ( (C = (k9_funcsdom A))  =>  ( ((k6_algstr_0 (k11_funcsdom A) B C) = B)  &  ((k6_algstr_0 (k11_funcsdom A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l33_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E A) & (r2_hidden F C))  =>  ((k4_seq_4 (k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D (k4_fuzzy_2 B C) E F))) = (k1_seq_1 (k4_fuzzy_2 A C) (k4_tarski E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((r2_hidden C (k28_glib_000 A (k4_glib_001 A B))) =>  ((r2_hidden C (k14_glib_001 A B)) | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(l33_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v7_ordinal1 E) & (v1_int_2 E))  =>  ( ((k3_xcmplx_0 (k1_newton E A) B) = (k3_xcmplx_0 C D))  =>  ((r1_nat_d E B) |  ((r1_nat_d E D) | (r1_nat_d (k1_newton E A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k1_group_1 B)) = (k1_group_1 C)) ) ) ) ) ) ) ) ).
tt(l33_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ( (B = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v2_hahnban C A) &  ((v3_hahnban C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) &  ((v2_hahnban C B) &  ((v3_hahnban C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (~  ((r2_hidden B (k10_normform A D (k7_heyting1 A D (k3_heyting1 A C)))) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E C) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r2_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ((r2_hidden F D) &  (F = G) )  |  ( (~ (r2_hidden F D))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H D) &  ((r2_hidden I D) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I G) & (r2_aff_1 A F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden B D) |  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m2_cat_1 (k1_funct_1 (k2_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B)))) C) (k2_index_1 (u4_struct_0 A) (k3_relat_1 (u2_graph_1 A) (k1_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))))) C) (k2_index_1 (u4_struct_0 A) (k3_relat_1 (u1_graph_1 A) (k1_xtuple_0 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))))) C))) ) ) ) ) ) ).
tt(l33_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k5_struct_0 (k9_int_3 A)) = 1) ) ) ) ).
tt(l33_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( ((k3_int_2 A B) = 1)  & (r1_int_1 B A)) ) ) ) ) ) ).
tt(l33_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k19_rvsum_1 A) k6_numbers)) ) ) ).
tt(l33_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( ( (B = D)  &  (E = C) )  =>  ((k8_group_1 (k9_int_3 A) D E) = (k6_algstr_0 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A)) B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid E)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 E (k3_integra5 A B) F) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 E k1_numbers F)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid E) F (k3_integra5 A B)) E) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 C D) (k1_nfcont_4 E k1_numbers F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 E k1_numbers F) (k3_integra5 C D))) & (r1_xxreal_0 (k12_euclid (k12_integr15 C D E F)) (k4_integra5 C D (k1_nfcont_4 E k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (r1_tarski (k7_intpro_1 (k7_intpro_1 A)) (k7_intpro_1 A))) ) ).
tt(l33_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k1_sppol_2 A B C D) = (a_4_4_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(l33_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_lattices A B C) = (k12_lattice3 (k3_lattice3 A) (k4_lattice3 A B) (k4_lattice3 A C)))  &  ((k3_lattices A B C) = (k13_lattice3 (k3_lattice3 A) (k4_lattice3 A B) (k4_lattice3 A C))) ) ) ) ) ) ) ) ).
tt(l33_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ( ((v1_funct_1 (k8_lpspace1 A k6_numbers)) & (m1_subset_1 (k8_lpspace1 A k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (r2_hidden (k8_lpspace1 A k6_numbers) (k9_lpspace1 A B C))) ) ) ) ) ) ) ).
tt(l33_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((v2_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v3_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v4_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v5_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v6_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) &  ((v7_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D)))) & (v8_rlvect_1 (g1_rlvect_1 (k1_lpspace2 A B C D) (k1_funct_7 (k4_struct_0 (k7_lpspace1 A)) (k1_lpspace2 A B C D)) (k1_ideal_1 (k7_lpspace1 A) (k1_lpspace2 A B C D)) (k1_lpspace1 (k7_lpspace1 A) (k1_lpspace2 A B C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) & (r1_xxreal_0 1 A))  => (v5_matrix_2 (k3_matrix_7 A B) (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ).
tt(l33_matrix_9,ax, (~  ((k3_finseq_4 k5_numbers 1 2 3) = (k3_finseq_4 k5_numbers 1 3 2)) ) ).
tt(l33_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrlin E B D) =>  (! [F:$i] :  ((m1_matrixj2 F B C) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) (k3_finseq_1 E) (k3_finseq_1 E)) =>  ( (G = (k20_matrixj1 (u1_struct_0 B) (k4_struct_0 B) F))  =>  ( ((k3_finseq_1 E) = k1_xboole_0)  |  ( ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 D) (k1_vectsp11 D (k4_matrlin2 B D D E E G) A) (k7_partfun1 (u1_struct_0 D) E (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 B) (k7_matrixj2 B C (k1_matrixj1 (k10_matrixj1 (u1_struct_0 B) F) (k3_finseq_1 E)) F))))) = (k4_vectsp_1 B D (k1_laplace B (k4_group_1 B) C A) (k7_partfun1 (u1_struct_0 D) E (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 B) (k7_matrixj2 B C (k1_matrixj1 (k10_matrixj1 (u1_struct_0 B) F) (k3_finseq_1 E)) F))))))  & (r2_hidden (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 B) (k7_matrixj2 B C (k1_matrixj1 (k10_matrixj1 (u1_struct_0 B) F) (k3_finseq_1 E)) F))) (k4_finseq_1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k7_real_1 (k8_real_1 (k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) B) (k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) B)) (k8_real_1 (k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) C) (k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) C))) = (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k1_seq_1 E B)) (k8_real_1 (k1_seq_1 E C) (k1_seq_1 E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_hidden D (a_3_1_mazurulm A B C)) => (r2_hidden (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A (k1_rlvect_1 A (k3_rlvect_1 A B C) (k18_binop_2 1 2))) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) D) (k1_mazurulm A (k1_rlvect_1 A (k3_rlvect_1 A B C) (k18_binop_2 1 2)))))) (a_3_1_mazurulm A B C))) ) ) ) ) ) ) ) ) ).
tt(l33_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_metrizts A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 B A) &  ((m1_setfam_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (r1_ordinal1 (k1_card_1 C) k4_ordinal1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_modcat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k11_modcat_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k11_modcat_1 A B))) =>  ( ( ((k3_graph_1 (k11_modcat_1 A B) E) = (k4_graph_1 (k11_modcat_1 A B) D))  &  ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C)) )  =>  ((k1_cat_1 (k11_modcat_1 A B) (k1_cat_1 (k11_modcat_1 A B) C D) E) = (k1_cat_1 (k11_modcat_1 A B) C (k1_cat_1 (k11_modcat_1 A B) D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (A = (k7_finseq_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(l33_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k5_modelc_2 A B) = (k5_modelc_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_nagata_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_metric_1)) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r2_hidden B (k9_metric_1 k8_metric_1 B A))) ) ) ) ) ).
tt(l33_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) => (r1_tarski A (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)))) ) ).
tt(l33_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v11_o_ring_1 B A)) ) ) ) ) ).
tt(l33_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_square_1 (k2_newton 2 (k2_newton 2 A))) = (k13_newton 2 (k13_newton 2 (k1_nat_1 A 1)))) ) ) ).
tt(l33_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_yellow_2 (u1_struct_0 A) B C D) & (r1_yellow_2 (u1_struct_0 A) B D C))  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) ) ) ) ) ) ) ) ) ).
tt(l33_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_prelamb A B C) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) D) E))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A D C)) B) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden B (k4_cqc_the1 A)) & (r2_hidden C (k4_cqc_the1 A)))  => (r2_hidden (k7_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(l33_realset2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c10__realset2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c10__realset2)) =>  ((k1_algstr_0 c10__realset2 A B) = (k1_algstr_0 c10__realset2 B A)) ) ) ) ) ).
tt(l33_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) => (r2_rewrite1 A C B)) ) ) ) ) ).
tt(l33_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) &  ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) )  =>  ( ((k5_card_1 C) = (k23_binop_2 A 1))  =>  (! [D:$i] :  ((m2_rlaffin3 D (k15_euclid A) C) =>  ( ((k1_funct_1 D (k3_finseq_1 D)) = (k5_euclid A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (F = (a_5_4_rlaffin3 A B C D E))  =>  ((v3_pre_topc E (k15_euclid B)) <=> (v3_pre_topc F (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_rusub_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden B A))  =>  ((k6_subset_1 A (k1_tarski B)) = A) ) ) ) ).
tt(l33_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_amistd_1 3 k1_scmfsa_2 B A) = (k1_tarski (k1_ordinal1 B))) ) )  => (v1_xboole_0 (k2_amistd_1 3 k1_scmfsa_2 A))) ) ) ).
tt(l33_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (~ (v2_extpro_1 (k5_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l33_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = (k6_xcmplx_0 F 1))  &  ( ((k1_funct_1 B (k1_scmp_gcd 3)) = (k2_nat_1 E 1))  &  ( ((k1_funct_1 B (k1_scmp_gcd 1)) = k6_numbers)  &  ((r1_xxreal_0 6 E) &  ((r1_scpisort C B E) &  ((r1_scpisort D (k6_scmpds_4 (k2_scmpds_7 k2_scmp_gcd 2 1 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 4 3)) (k11_scmpds_2 k2_scmp_gcd 1 1)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 6 1)) (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))))) B A) E) &  ( ((k3_finseq_1 C) = F)  &  ((k3_finseq_1 D) = F) ) ) ) ) ) ) ) )  =>  ((r2_classes1 C D) & (r3_graph_2 D 1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_scpqsort,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ( (D = (k2_xcmplx_0 B 1))  &  (B = (k2_xcmplx_0 C A)) ) )  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ).
tt(l33_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_xcmplx_0 (k3_xcmplx_0 (k13_newton A 2) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 2 (k13_newton A 2)) (k4_nat_1 2 A)) 1)) (k4_nat_1 (k13_newton (k2_nat_1 A 1) 3) 12)) = (k3_xcmplx_0 (k13_newton (k2_nat_1 A 2) 2) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 2 (k13_newton (k2_nat_1 A 1) 2)) (k4_nat_1 2 (k2_nat_1 A 1))) 1))) ) ) ).
tt(l33_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v4_pre_topc B (k15_euclid A)) & (v9_rltopsp1 B (k15_euclid A)))  => (v2_compts_1 B (k15_euclid A))) ) ) ) ) ).
tt(l33_sincos10,ax, ((k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) = (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(l33_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (B = (k3_tarski (a_2_0_sppol_1 A C)))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ) ) ).
tt(l33_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( (~  ((k4_termord A B C D) = (k4_struct_0 C)) )  => (r2_hidden (k3_termord A B C D) (k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)))) ) ) ) ) ) ) ) ) ).
tt(l33_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (C = (a_2_3_tex_1 A B))  &  (A = (k6_domain_1 A B)) )  =>  (C = k1_xboole_0) ) ) ) ) ) ) ).
tt(l33_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v5_waybel23 (k1_pre_topc A B)) & (r1_xxreal_0 (k4_topdim_1 (k1_pre_topc A B)) k6_numbers))  =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski B (k4_subset_1 (u1_struct_0 A) C D)) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski E C) &  ((r1_tarski F D) &  ((r1_xboole_0 E F) & (r1_tarski B (k4_subset_1 (u1_struct_0 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden B k1_topreal1) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B C) &  ((r1_topreal1 (k15_euclid 2) A B D) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_toprealb,ax, ((u1_struct_0 (k8_toprealb 2)) = (k3_topreal9 2 (k19_euclid k6_numbers k6_numbers) 1)) ).
tt(l33_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_pre_topc B (k6_domain_1 (u1_struct_0 B) E))) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_tarski (u1_struct_0 (k2_vectsp_5 A B C D)) (u1_struct_0 (k1_vectsp_5 A B C D)))) ) ) ) ) ) ) ) ).
tt(l33_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (B = (k4_waybel_0 A (k12_waybel_0 A B))) ) ) ) ) ).
tt(l33_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_waybel_5 A) =>  ((v3_lattice3 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski C (k1_waybel15 A)) &  (B = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ) ) ).
tt(l33_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_waybel11 A D)) (k1_waybel11 B (k6_waybel_9 A B C D)))) ) ) ) ) ) ) ) ).
tt(l33_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((v1_funct_1 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D)) &  ((v1_funct_2 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D) (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  &  ((v1_funct_1 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D)) &  ((v1_funct_2 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  ((v3_pre_topc (a_1_0_waybel29 A) (k2_borsuk_1 B A)) & (m1_subset_1 (a_1_0_waybel29 A) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A C))  =>  (? [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D E) & (m1_connsp_2 (k1_setfam_1 E) A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l33_wsierp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k2_finseq_3 1 (k7_finseq_1 (k9_finseq_1 B) A)) = A)  &  ((k2_finseq_3 (k2_nat_1 (k3_finseq_1 A) 1) (k7_finseq_1 A (k9_finseq_1 B))) = A) ) ) ) ) ).
tt(l34_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 E A) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ( (~  (B = C) )  &  ( (~ (r2_hidden D E))  & (r1_aff_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k1_tarski (k4_tarski C D))) =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ).
tt(l34_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_binop_1 (u1_altcat_1 A) B D) = k1_xboole_0)  =>  ((k2_zfmisc_1 (k1_binop_1 (u1_altcat_1 A) C D) (k1_binop_1 (u1_altcat_1 A) B C)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(l34_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  ( ((k1_funct_1 (k5_afinsq_1 (k2_compos_1 B)) (k62_valued_1 (k5_afinsq_1 (k2_compos_1 B)))) = (k2_compos_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k1_funct_1 (k5_afinsq_1 (k2_compos_1 B)) C) = (k2_compos_1 B))  & (r2_hidden C (k2_afinsq_1 (k5_afinsq_1 (k2_compos_1 B)))))  =>  (C = (k62_valued_1 (k5_afinsq_1 (k2_compos_1 B)))) ) ) ) ) ) ) ) ) ).
tt(l34_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_anproj_1 A B C))  &  ( (D = (k1_rlvect_1 A C F))  &  ( (~  (F = k6_numbers) )  &  ( (E = (k1_rlvect_1 A B G))  &  ( (~  (G = k6_numbers) )  & (r1_anproj_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) &  ((k6_int_1 B (k5_series_1 2 A)) = (k6_int_1 C (k5_series_1 2 A))) ) )  =>  ((k2_binari_4 A B) = (k2_binari_4 A C)) ) ) ) ) ) ) ) ).
tt(l34_binop_2,ax,(r2_hidden 1 k5_numbers)).
tt(l34_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_borsuk_5 B C))  =>  ((r1_xxreal_0 C B) |  ((r2_hidden B (k2_pre_topc k3_topmetr A)) & (r2_hidden C (k2_pre_topc k3_topmetr A))) ) ) ) ) ) ) ) ) ).
tt(l34_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k5_struct_0 (k5_cc0sp2 A)) = (k5_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) ) ) ).
tt(l34_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cfuncdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_cfuncdom A))) =>  ( (C = (k5_cfuncdom A))  =>  ( ((k6_algstr_0 (k7_cfuncdom A) C B) = B)  &  ((k6_algstr_0 (k7_cfuncdom A) B C) = B) ) ) ) ) ) ) ) ) ).
tt(l34_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_compl_sp A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) & (v1_setfam_1 B))  => (v1_finset_1 B)) ) ) ) ) ) ).
tt(l34_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A B)) = (k15_complex1 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) B A)))) ) ) ) ) ).
tt(l34_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  ((k8_group_1 (k9_int_3 C) (k2_binom (k9_int_3 C) D A) (k2_binom (k9_int_3 C) D B)) = (k2_binom (k9_int_3 C) D (k2_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ).
tt(l34_fdiff_7,ax, ((k3_limfunc1 k6_numbers) = a_0_0_fdiff_7) ).
tt(l34_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v2_binop_1 C A) & (v2_fomodel0 B A C))  => (v1_fomodel0 (k5_fomodel0 A C) (k4_finseq_2 (k2_xcmplx_0 D 1) B))) ) ) ) ) ) ) ) ).
tt(l34_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_funct_1 (k1_funct_5 (k23_fomodel2 B A C))) &  ((v1_funct_2 (k1_funct_5 (k23_fomodel2 B A C)) (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1)) & (m1_subset_1 (k1_funct_5 (k23_fomodel2 B A C)) (k1_zfmisc_1 (k2_zfmisc_1 (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1))))) ) ) ) ) ) ) ) ).
tt(l34_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B E))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C))) => (r1_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D C) (k8_fomodel3 B C (k4_relset_1 B E A C F G) D) (k4_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D E) (k4_finseq_2 D A) (k4_finseq_2 D C) (k8_fomodel3 B E F D) (k8_fomodel3 A C G D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ((r1_tarski C D) =>  ( ( (~ (v6_fomodel4 D B))  &  (~ (v6_fomodel4 C B)) )  | (r1_tarski (k5_setfam_1 (k1_fomodel4 B) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B C)) (k1_tarski A))) (k5_setfam_1 (k1_fomodel4 B) (k7_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k13_lang1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B D)) (k1_tarski A))))) ) ) ) ) ) ) ) ) ).
tt(l34_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k2_fdiff_9 (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))) ) ).
tt(l34_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v2_glib_002 A)) ) ) ) ) ) )  =>  (~  ( (~  ((k7_glib_000 A) = k1_xboole_0) )  &  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ((v11_glib_000 B A) &  ((v11_glib_000 C A) & (r2_hidden C (k1_glib_002 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ( ((r1_tarski E D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden F D) => (r1_rewrite1 (k3_polyred A B C E) F (k7_polynom1 A C))) ) ) )  =>  ((k7_ideal_1 (k11_polynom1 A C) E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_card_1 B) = (k1_card_1 (k5_group_2 A C B))) ) ) ) ) ) ) ).
tt(l34_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E (k2_group_1 B D)) = (k2_group_1 C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ).
tt(l34_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((r2_hidden C (k4_heyting3 A B)) => (v1_finset_1 C)) ) ) ) ) ) ).
tt(l34_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r2_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ((r2_hidden F D) &  (F = G) )  |  ( (~ (r2_hidden F D))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H D) &  ((r2_hidden I D) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I G) & (r2_aff_1 A F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_aff_1 A F (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_partfun1 (k1_int_4 A) k4_numbers) &  ((v3_relat_2 (k1_int_4 A)) &  ((v8_relat_2 (k1_int_4 A)) & (m1_subset_1 (k1_int_4 A) (k1_zfmisc_1 (k2_zfmisc_1 k4_numbers k4_numbers)))) ) ) ) ) ).
tt(l34_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid E)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 E (k3_integra5 A B) F) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 E k1_numbers F)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid E) F (k3_integra5 A B)) E) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 D C E F)) (k4_integra5 C D (k1_nfcont_4 E k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 C D) (k3_valued_1 k1_numbers k1_numbers k1_numbers E F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E F) (k3_integra5 C D))) &  ( ((k4_integra5 C D (k3_valued_1 k1_numbers k1_numbers k1_numbers E F)) = (k7_real_1 (k4_integra5 C D E) (k4_integra5 C D F)))  &  ((r1_integra5 (k3_integra5 C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers E F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers E F) (k3_integra5 C D))) &  ((k4_integra5 C D (k47_valued_1 k1_numbers k1_numbers k1_numbers E F)) = (k9_real_1 (k4_integra5 C D E) (k4_integra5 C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_18_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(l34_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)))) =>  ((k12_lattice3 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (k8_lfuzzy_0 A C (k4_fuzzy_4 A B C D E) F G) H) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_8_0_lfuzzy_0 A B C D E F G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k3_funct_2 B k7_numbers C D) = k6_numbers)  &  ((k3_funct_2 B k7_numbers C E) = k6_numbers) )  =>  ((k3_funct_2 B k7_numbers C (k1_measure1 A B D E)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E C B A) =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  ( ((k2_matrix_1 E) = (k2_matrix_1 (k3_matrix11 D B A C E F)))  &  ( ((k3_finseq_1 E) = (k3_finseq_1 (k3_matrix11 D B A C E F)))  &  ((k1_matrix_1 E) = (k1_matrix_1 (k3_matrix11 D B A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_matrix_9,ax, (~  ((k3_finseq_4 k5_numbers 1 2 3) = (k3_finseq_4 k5_numbers 2 1 3)) ) ).
tt(l34_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v4_xxreal_2 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( (D = (a_3_0_mazurulm A B C))  => (m1_xxreal_2 (k1_xxreal_2 D) (k23_member_1 D 2))) ) ) ) ) ) ) ) ) ).
tt(l34_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid (k23_binop_2 A 1)))) =>  ( (B = (k6_euclid_7 (k23_binop_2 A 1) (k23_binop_2 A 1)))  => (r1_mfold_2 (k15_euclid A) (k3_mfold_2 (k23_binop_2 A 1) B (k4_struct_0 (k15_euclid (k23_binop_2 A 1)))))) ) ) ) ) ).
tt(l34_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (v1_midsp_2 (k5_midsp_2 A) A (k15_midsp_1 A))) ) ).
tt(l34_mod_2,ax, (? [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) &  (A = k6_numbers) ) ) ).
tt(l34_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_1 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k8_modelc_1 A B) = (k8_modelc_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k7_modelc_2 A B) = (k7_modelc_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r5_modelc_3 C B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ((r5_modelc_3 C E) &  ( (B = (k7_finseq_1 D E))  &  ( ((k1_funct_1 E 1) = (k1_funct_1 B A))  &  ((r1_xxreal_0 1 (k3_finseq_1 E)) &  ( ((k3_finseq_1 E) = (k9_real_1 (k3_finseq_1 B) (k5_real_1 A 1)))  &  ((k1_funct_1 E (k3_finseq_1 E)) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_msaterm D A B (k2_msaterm A B C)) =>  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( (F = (k1_funct_1 D E))  &  ( (F = (k7_partfun1 (k1_msaterm A B) D E))  &  ( ((k7_msaterm A B F) = (k1_funct_1 (k1_msualg_1 A C) E))  &  ((k7_msaterm A B F) = (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) => (m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(l34_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ( ( ((k6_int_1 A C) = (k6_int_1 B C))  &  ( ((k6_int_1 A D) = (k6_int_1 B D))  & (r1_int_2 C D)) )  =>  ((k6_int_1 A (k3_xcmplx_0 C D)) = (k6_int_1 B (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(l34_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_2 A) & (r1_tarski B (k1_relat_1 A)))  =>  ((k1_relat_1 (k2_wellord1 A B)) = B) ) ) ) ) ).
tt(l34_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_o_ring_1 B A) => (v10_o_ring_1 B A)) ) ) ) ) ).
tt(l34_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_prelamb A B D) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) E)) F))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C B) (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A D E))) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_rat_1,ax, ((k2_real_1 1) = 1) ).
tt(l34_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  ((k1_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) B (k1_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) C D)) = (k1_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) (k1_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) B C) D)) ) ) ) ) ) ) ) ) ).
tt(l34_realset2,ax,(m3_realset1 k2_realset2 c4__realset2 c5__realset2)).
tt(l34_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) &  ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) )  =>  ( (~ (r1_xxreal_0 (k5_card_1 C) B))  =>  (! [D:$i] :  ((m2_rlaffin3 D (k15_euclid A) C) =>  ( ((k1_funct_1 D (k3_finseq_1 D)) = (k5_euclid A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C))))) =>  ( (F = (a_5_5_rlaffin3 A B C D E))  =>  ((v3_pre_topc E (k15_euclid B)) <=> (v3_pre_topc F (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) => (r1_tarski (u1_struct_0 (k1_rlsub_2 A (k2_rlsub_2 A B C) (k2_rlsub_2 A C D))) (u1_struct_0 (k2_rlsub_2 A C (k1_rlsub_2 A B D))))) ) ) ) ) ) ) ) ).
tt(l34_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((u1_struct_0 (k1_rmod_3 A B (k2_rmod_3 A B C D) D)) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(l34_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) => (r1_tarski (u1_struct_0 (k1_rusub_2 A (k2_rusub_2 A B C) (k2_rusub_2 A C D))) (u1_struct_0 (k2_rusub_2 A C (k1_rusub_2 A B D))))) ) ) ) ) ) ) ) ).
tt(l34_scmbsort,ax, (~  ((k4_scmfsa_2 k6_numbers) = (k4_scmfsa_2 2)) ) ).
tt(l34_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k17_scm_comp (k3_scm_comp A))) =>  ((k1_funct_1 B (k10_ami_3 D)) = (k1_funct_1 C (k10_ami_3 D))) ) ) )  =>  ((k12_scm_comp B (k3_scm_comp A)) = (k12_scm_comp C (k3_scm_comp A))) ) ) ) ) ) ) ) ).
tt(l34_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (~ (v2_extpro_1 (k6_scmring2 A B C) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l34_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) k6_numbers))  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 1)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2))) ) )  &  ( ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 3)) k6_numbers) =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 2)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 2)) (k1_funct_1 B (k1_scmp_gcd 1))))  &  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1))) ) )  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) k2_scmp_gcd) = k6_numbers)  &  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 3)) = (k6_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 1)) (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) B A) (k1_scmp_gcd 2)))) ) ) ) ) ) ) ) ) ).
tt(l34_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k4_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k4_numbers) =>  ( ((r1_scpisort G A C) &  ((r1_scpisort H B C) &  ( ((k3_finseq_1 G) = F)  &  ( ((k3_finseq_1 H) = F)  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 C 1) I) =>  ( (I = D)  |  ( (I = E)  |  ((k1_funct_1 B (k1_scmp_gcd I)) = (k1_funct_1 A (k1_scmp_gcd I))) ) ) ) ) ) ) ) ) )  =>  ( ( (~  ( ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 A (k1_scmp_gcd D)))  &  ((k1_funct_1 B (k1_scmp_gcd E)) = (k1_funct_1 A (k1_scmp_gcd E))) ) )  &  (~  ((r1_xxreal_0 (k2_nat_1 C 1) D) &  ((r1_xxreal_0 (k2_nat_1 C 1) E) &  ((r1_xxreal_0 D (k2_nat_1 C F)) &  ((r1_xxreal_0 E (k2_nat_1 C F)) &  ( ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 A (k1_scmp_gcd E)))  &  ((k1_funct_1 B (k1_scmp_gcd E)) = (k1_funct_1 A (k1_scmp_gcd D))) ) ) ) ) ) ) )  | (r2_classes1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))))).
tt(l34_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k1_sin_cos2 (k10_binop_2 A B)) = (k9_real_1 (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ).
tt(l34_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k9_sin_cos2 A))  &  ( ((k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)) = (k3_xcmplx_0 (k9_sin_cos2 A) (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))))  &  ( ((k3_sin_cos2 A) = (k3_xcmplx_0 (k9_sin_cos2 A) (k6_sin_cos2 A)))  &  ((k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) = (k3_xcmplx_0 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)))) ) ) ) ) ) ) ) ).
tt(l34_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k4_termord A B C D) = (k4_struct_0 C))  =>  ((k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(l34_topalg_5,ax, ((u1_struct_0 (k8_toprealb 2)) = (k3_topreal9 2 (k19_euclid k6_numbers k6_numbers) 1)) ).
tt(l34_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_funct_1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  &  ((v2_funct_1 B) &  ((v2_topreal1 B) &  ((v3_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  ( (~ (r1_xxreal_0 C 1))  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) C) (k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) D))) &  (E = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = k6_numbers)  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l34_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (u1_struct_0 B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k9_subset_1 (u1_struct_0 A) D (k4_tex_4 A E)) = (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (~  ((v3_lattice3 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski C (k1_waybel15 A)) &  (B = (k1_yellow_0 A C)) ) ) ) ) )  &  (! [B:$i] :  (~ (r5_waybel_1 A (k3_yellow_1 B))) ) ) ) ) ) ) ).
tt(l34_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l34_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_relset_1 (u1_struct_0 C) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C)) = (k1_relset_1 (u1_struct_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D)) (u1_waybel_0 (k1_waybel25 B) (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D)))) ) ) ) ) ) ) ) ) ).
tt(l34_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A C))  =>  (? [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D E) & (m1_connsp_2 (k1_setfam_1 E) A C)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_pre_topc (k5_waybel26 D) (k2_borsuk_1 B A)) & (m1_subset_1 (k5_waybel26 D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) ) ) ) ) ).
tt(l34_waybel_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C (k1_funct_2 A (k5_finsub_1 B))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_finset_1 (k1_funct_1 C D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(l34_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D A) => (r1_yellow_0 (k2_yellow16 A B D) (k5_waybel_3 A B D C))) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E A) =>  ((k4_waybel_3 A B D E) = (k1_yellow_0 (k3_waybel_3 A B E) (k5_waybel_3 A B E C))) ) )  &  ((r2_lattice3 (k5_yellow_1 A B) C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_yellow_1 A B))) =>  ((r2_lattice3 (k5_yellow_1 A B) C E) => (r3_orders_2 (k5_yellow_1 A B) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C J) (k1_rlvect_1 A D K)))  &  ( (C = (k3_rlvect_1 A E (k1_rlvect_1 A F H)))  &  (D = (k3_rlvect_1 A E (k1_rlvect_1 A G I))) ) )  =>  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A E (k7_real_1 J K)) (k1_rlvect_1 A F (k8_real_1 J H))) (k1_rlvect_1 A G (k8_real_1 K I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_arytm_2,ax, (! [A:$i] :  (~  ((r2_hidden A k1_arytm_2) &  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) => (r2_hidden B A)) ) ) ) ) ).
tt(l35_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k6_int_1 B (k5_series_1 2 A)) = (k6_int_1 C (k5_series_1 2 A)))  =>  ((r1_xxreal_0 k6_numbers B) |  ((r1_xxreal_0 k6_numbers C) |  ((k2_binari_4 A B) = (k2_binari_4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(l35_binop_2,ax,(m1_subset_1 1 k2_numbers)).
tt(l35_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_closure2 (k2_closure2 A B) A B) &  ((v2_closure2 (k2_closure2 A B) A B) &  ((v3_closure2 (k2_closure2 A B) A B) &  ((v4_closure2 (k2_closure2 A B) A B) &  ((v5_closure2 (k2_closure2 A B) A B) & (v6_closure2 (k2_closure2 A B) A B)) ) ) ) ) ) ) ) ).
tt(l35_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) & (v1_setfam_1 B))  => (v1_finset_1 B)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((k1_card_1 C) = 1) ) ) ) )  => (v1_finset_1 B)) ) ) ) ) ) ).
tt(l35_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k3_rlvect_1 (k3_clvect_1 o_0_6_csspace) A B) C)) = (k8_complex1 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A C)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) B C)))) ) ) ) ) ) ) ).
tt(l35_dtconstr,ax,(m2_subset_1 c2__dtconstr (u1_struct_0 k5_dtconstr) (k6_dtconstr k5_dtconstr))).
tt(l35_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  ((k2_binom (k9_int_3 C) (k2_binom (k9_int_3 C) D A) B) = (k2_binom (k9_int_3 C) D (k3_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ).
tt(l35_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k2_enumset1 A B C D) (k2_enumset1 E F G H))) ) ) ) ) ) ) ) ) ).
tt(l35_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_valued_0 E)) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k15_euclid A) B C) = (k1_valued_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~  (C = D) )  &  ( (~  (E = D) )  &  (~  ((k1_funct_1 (k2_finseq_7 A B C E) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (r1_tarski (k1_funct_1 (k25_fomodel1 B) A) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) ).
tt(l35_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B E))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C))) => (r2_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D C) (k8_fomodel3 B C (k4_relset_1 B E A C F G) D) (k4_relset_1 (k4_finseq_2 D B) (k4_finseq_2 D E) (k4_finseq_2 D A) (k4_finseq_2 D C) (k8_fomodel3 B E F D) (k8_fomodel3 A C G D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ( ((r1_tarski D E) & (v3_fomodel4 A C D B))  =>  ( ( (~ (v6_fomodel4 E C))  &  (~ (v6_fomodel4 D C)) )  | (v3_fomodel4 A C E B)) ) ) ) ) ) ) ) ) ) ).
tt(l35_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v3_glib_002 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) &  ( (~  (B = C) )  &  ((v11_glib_000 B A) & (v11_glib_000 C A)) ) ) ) ) ) ) ) ).
tt(l35_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B (k1_nat_1 A 1) C) = (k6_algstr_0 B (k5_group_1 B A C) C)) ) ) ) ) ) ) ).
tt(l35_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k6_algstr_0 B D E) C)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D C) => (r2_hidden (k2_group_1 B D) C)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E C) => (r2_hidden (k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k3_group_9 A B D) E) C)) ) ) ) )  &  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  (~  ((u1_struct_0 D) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ( (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) )  => (r3_lattices (k5_substlat A B) C D)) ) ) ) ) ) ) ) ).
tt(l35_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r2_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ((r2_hidden F D) &  (F = G) )  |  ( (~ (r2_hidden F D))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H D) &  ((r2_hidden I D) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I G) & (r2_aff_1 A F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden B D) | (v8_transgeo E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_xxreal_0 k6_numbers C) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) => (r2_int_1 C (k1_funct_1 A E) (k1_funct_1 B E))) ) )  &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) => (r2_int_1 D (k1_funct_1 A E) (k1_funct_1 B E))) ) ) ) ) )  =>  ((r1_xxreal_0 (k19_rvsum_1 B) C) |  ((r1_xxreal_0 (k19_rvsum_1 B) D) |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (v8_intpro_1 (k7_intpro_1 A))) ) ).
tt(l35_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_21_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(l35_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k5_binop_1 (u1_struct_0 A) (u2_lattices A) (k7_setwiseo (u1_struct_0 A) (u1_struct_0 A) (u1_lattices A) B D) C) = (k7_setwiseo (u1_struct_0 A) (u1_struct_0 A) (u1_lattices A) B (k9_funcop_1 (u1_struct_0 A) (u1_struct_0 A) (u2_lattices A) D C))) ) ) ) ) ) ) ) ) ).
tt(l35_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)))) =>  ((k12_lattice3 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) H (k8_lfuzzy_0 A C (k4_fuzzy_4 A B C D E) F G)) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_8_2_lfuzzy_0 A B C D E F G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_lopclset A)))) =>  ((r2_hidden B (k10_lopclset A)) => (v3_pre_topc B (k11_lopclset A))) ) ) ) ) ).
tt(l35_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k1_xboole_0))  =>  ( ((k3_finseq_1 (k4_matrix_1 A B)) = (k1_matrix_1 B))  &  ((k1_matrix_1 (k4_matrix_1 A B)) = (k3_finseq_1 B)) ) ) ) ) ) ) ).
tt(l35_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 1 2 3) = (k3_finseq_4 k5_numbers 2 3 1)) )  &  (~  ((k3_finseq_4 k5_numbers 1 2 3) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ).
tt(l35_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_membered D) =>  ( (D = (a_3_0_mazurulm A B C))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_hidden E (a_3_1_mazurulm A B C)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E (k1_rlvect_1 A (k3_rlvect_1 A B C) (k18_binop_2 1 2))) = (k1_rlvect_1 A (k3_rlvect_1 A B C) (k18_binop_2 1 2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  ((v1_metrizts A) <=> (v5_waybel23 A)) ) ) ).
tt(l35_mod_2,ax, (? [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) &  (A = 1) ) ) ).
tt(l35_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_1 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_1 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k11_modelc_1 A B) = (k11_modelc_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k8_modelc_2 A B) = (k8_modelc_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 29 A))  &  ((v1_int_2 A) &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 5) )  &  ( (~  (A = 7) )  &  ( (~  (A = 11) )  &  ( (~  (A = 13) )  &  ( (~  (A = 17) )  &  ( (~  (A = 19) )  &  (~  (A = 23) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_ndiff_3,ax,(v3_rcomp_1 (k2_subset_1 k1_numbers))).
tt(l35_neckla_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ( (A = (k2_xboole_0 B C))  & (r1_subset_1 B C))  => (r2_hidden (k1_card_1 B) (k5_card_1 A))) ) ) ) ) ) ) ).
tt(l35_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_o_ring_1 B A) => (v11_o_ring_1 B A)) ) ) ) ) ).
tt(l35_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 E B A) &  ((v2_pdiff_6 E B A) &  ((v3_pdiff_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) ) )  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (? [G:$i] :  ((m2_finseq_1 G (k1_euclid B)) &  ( ((k4_finseq_1 G) = (k2_finseq_1 A))  &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((r2_hidden H (k2_finseq_1 A)) =>  ((k1_funct_1 G H) = (k9_euclid B (k12_pdiff_1 A B H C D) (k1_seq_1 (k1_pdiff_1 H A) F))) ) ) )  &  ((k1_pdiff_6 A B E F) = (k5_euclid_7 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_polyeq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k2_newton k6_numbers A) = k6_numbers) ) ) ) ).
tt(l35_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r2_hidden (k2_polynom1 (k15_pre_poly A) C D) (k5_finsub_1 (u1_struct_0 (g1_orders_2 (k15_pre_poly A) B))))) ) ) ) ) ) ) ) ).
tt(l35_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  => (r1_tarski (k1_relat_1 (k5_poset_1 A B)) (k4_poset_1 A B))) ) ) ) ).
tt(l35_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_prelamb A B D) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) E) C) F))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A D E))) C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)))) =>  ((k2_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) B (k2_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) C D)) = (k2_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) (k2_lattices (g3_lattices (k9_funct_2 A k1_numbers) (k4_real_lat A) (k5_real_lat A)) B C) D)) ) ) ) ) ) ) ) ) ).
tt(l35_realset2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ( (A = (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2)))  &  (C = c7__realset2) )  =>  ( (~ (v2_struct_0 (g2_algstr_0 A B C)))  &  ((v13_algstr_0 (g2_algstr_0 A B C)) &  ((v2_rlvect_1 (g2_algstr_0 A B C)) &  ((v3_rlvect_1 (g2_algstr_0 A B C)) &  ((v4_rlvect_1 (g2_algstr_0 A B C)) & (l2_algstr_0 (g2_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_scmbsort,ax, (~  ((k4_scmfsa_2 k6_numbers) = (k4_scmfsa_2 4)) ) ).
tt(l35_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ( ((r1_lang1 k1_scm_comp A (k4_pre_poly (u1_struct_0 k1_scm_comp) (k1_bintree1 (u1_struct_0 k1_scm_comp) B) (k1_bintree1 (u1_struct_0 k1_scm_comp) C))) &  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 E (u1_struct_0 k1_ami_3))) ) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 F (k17_scm_comp B)) =>  ((k1_funct_1 D (k10_ami_3 F)) = (k1_funct_1 E (k10_ami_3 F))) ) ) )  =>  ((k12_scm_comp D B) = (k12_scm_comp E B)) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 E (u1_struct_0 k1_ami_3))) ) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 F (k17_scm_comp C)) =>  ((k1_funct_1 D (k10_ami_3 F)) = (k1_funct_1 E (k10_ami_3 F))) ) ) )  =>  ((k12_scm_comp D C) = (k12_scm_comp E C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 E (u1_struct_0 k1_ami_3))) ) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 F (k17_scm_comp (k2_scm_comp A B C))) =>  ((k1_funct_1 D (k10_ami_3 F)) = (k1_funct_1 E (k10_ami_3 F))) ) ) )  =>  ((k12_scm_comp D (k2_scm_comp A B C)) = (k12_scm_comp E (k2_scm_comp A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_scmpds_6 B D A) & (r2_scmpds_6 B D A))  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D) 1))) = (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1))  &  ( ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D))) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D) 1))))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D)) &  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D E)) = (k2_compos_1 k1_scmpds_2)) ) ) ) )  &  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D))) = (k5_card_1 B))  &  ((r1_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D) &  ((k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C))) D) = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k1_scmpds_7 A B C D))) = (k2_nat_1 (k5_card_1 D) 4)) ) ) ) ) ) ) ) ) ).
tt(l35_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (v2_extpro_1 (k8_scmring2 A B) 2 (k1_scmring2 A))) ) ) ) ) ).
tt(l35_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ((k1_funct_1 B (k1_scmp_gcd 3)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2)))) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 1)) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 2)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))) B A) (k1_scmp_gcd 1)) = (k3_int_2 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ( ((k1_funct_1 (k6_scmpds_4 (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))) B A) (k1_scmp_gcd 2)) = (k3_int_2 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ((r1_scmpds_6 (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))) B A) & (r2_scmpds_6 (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2))) B A)) ) ) ) ) ) ) ) ) ) ).
tt(l35_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ( (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r1_xxreal_0 C H) =>  ( (H = D)  |  ( (H = E)  |  ((k1_funct_1 B (k1_scmp_gcd H)) = (k1_funct_1 A (k1_scmp_gcd H))) ) ) ) ) )  & (r1_xxreal_0 D E))  =>  ( ( (~  ( ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 A (k1_scmp_gcd D)))  &  ((k1_funct_1 B (k1_scmp_gcd E)) = (k1_funct_1 A (k1_scmp_gcd E))) ) )  &  (~  ((r1_xxreal_0 F D) &  ((r1_xxreal_0 E G) &  ( ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 A (k1_scmp_gcd E)))  &  ((k1_funct_1 B (k1_scmp_gcd E)) = (k1_funct_1 A (k1_scmp_gcd D))) ) ) ) ) )  |  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r1_xxreal_0 C H) =>  ( ((r1_xxreal_0 F H) & (r1_xxreal_0 H G))  |  ((k1_funct_1 B (k1_scmp_gcd H)) = (k1_funct_1 A (k1_scmp_gcd H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_xcmplx_0 (k4_nat_1 (k2_nat_1 A 2) (k2_nat_1 (k4_nat_1 2 (k2_nat_1 A 1)) 1)) (k2_xcmplx_0 (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton (k2_nat_1 A 1) 4)) (k4_nat_1 6 (k13_newton (k2_nat_1 A 1) 3))) (k4_nat_1 3 (k2_nat_1 A 1))) 1)) = (k2_nat_1 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k4_nat_1 6 (k13_newton A 6)) (k4_nat_1 57 (k13_newton A 5))) (k4_nat_1 216 (k13_newton A 4))) (k4_nat_1 414 (k13_newton A 3))) (k4_nat_1 419 (k13_newton A 2))) (k4_nat_1 211 A)) 42)) ) ) ).
tt(l35_sincos10,ax, ((k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) = (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))) ).
tt(l35_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((k1_lattices (k5_substlat A B) C D) = (k1_lattices (k5_substlat A B) D C)) ) ) ) ) ) ) ).
tt(l35_taylor_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers B) = (k2_subset_1 k1_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k1_seq_1 B C) = (k9_real_1 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_fdiff_1 B D) &  ((k1_fdiff_1 B D) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r6_pboole A (k3_termord A B C D) (k2_polynom7 A C D)) &  ( ((k4_termord A B C D) = (k3_polynom7 A C D))  & (r8_pboole (k15_pre_poly A) (k5_termord A B C D) D)) ) ) ) ) ) ) ) ) ) ).
tt(l35_topalg_5,ax, ((k1_relset_1 (u1_struct_0 k2_topalg_2) k12_toprealb) = k1_numbers) ).
tt(l35_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_funct_1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  &  ((v2_funct_1 B) &  ((v2_topreal1 B) &  ((v3_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D (k3_finseq_1 A)))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) (k2_nat_1 D 1)))  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) C) (k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) D))) &  (E = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (B = C)  =>  ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l35_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  => (r1_tarski (k4_tex_4 A D) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_valuat_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k9_margrel1 (k10_margrel1 (k9_margrel1 (k10_margrel1 A (k9_margrel1 B))) (k10_margrel1 (k9_margrel1 (k10_margrel1 B C)) (k10_margrel1 A C)))) = k8_margrel1) ) ) ) ) ) ) ).
tt(l35_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ((v2_rlvect_1 (g2_vectsp_2 A B 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1) (k9_funct_3 1 (u1_struct_0 B)))) &  ((v3_rlvect_1 (g2_vectsp_2 A B 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1) (k9_funct_3 1 (u1_struct_0 B)))) &  ((v4_rlvect_1 (g2_vectsp_2 A B 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1) (k9_funct_3 1 (u1_struct_0 B)))) & (v13_algstr_0 (g2_vectsp_2 A B 1 k9_funct_5 k5_funct_5 (k10_funct_3 (u1_struct_0 A) 1) (k9_funct_3 1 (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(l35_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((u1_struct_0 (k1_vectsp_5 A B (k2_vectsp_5 A B C D) D)) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(l35_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_waybel12 C A B) => (r1_tarski C B)) ) ) ) ) ) ).
tt(l35_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_pre_topc (k2_waybel_3 A B) A)) ) ) ) ).
tt(l35_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A C))  =>  (? [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D E) & (m1_connsp_2 (k1_setfam_1 E) A C)) ) ) ) ) ) ) ) )  => (v3_waybel_3 (k2_yellow_1 (u1_pre_topc A)))) ) ) ).
tt(l35_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v4_relat_1 G B) &  ((v1_funct_1 G) & (v1_partfun1 G B)) ) ) )  =>  ((r2_hidden G (k1_funct_2 B (k5_finsub_1 C))) =>  (! [H:$i] :  ((m2_pboole H B G (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((r2_hidden J (k1_funct_1 G I)) =>  ((k1_funct_1 (k1_waybel_5 B (u1_struct_0 A) G H I) J) = (k1_binop_1 F I J)) ) ) ) )  =>  ((v1_finset_1 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) G H E))) & (m1_subset_1 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) G H E)) (k1_zfmisc_1 (k2_relset_1 D (k1_waybel_5 B D (k7_funcop_1 B C) (k6_waybel_5 B C D F) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_wsierp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( (A = (k7_finseq_1 (k9_finseq_1 (k1_funct_1 A 1)) (k2_finseq_3 1 A)))  &  (A = (k7_finseq_1 (k2_finseq_3 (k3_finseq_1 A) A) (k9_finseq_1 (k1_funct_1 A (k3_finseq_1 A))))) ) ) ) ) ).
tt(l35_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D A) => (r2_yellow_0 (k2_yellow16 A B D) (k5_waybel_3 A B D C))) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E A) =>  ((k4_waybel_3 A B D E) = (k2_yellow_0 (k3_waybel_3 A B E) (k5_waybel_3 A B E C))) ) )  &  ((r1_lattice3 (k5_yellow_1 A B) C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_yellow_1 A B))) =>  ((r1_lattice3 (k5_yellow_1 A B) C E) => (r1_orders_2 (k5_yellow_1 A B) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l35_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r3_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(l35_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k4_ordinal1) =>  ((v8_zf_fund1 B A) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(l36_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  ( (B = 1)  =>  ( ((k6_algstr_0 k3_algstr_1 A B) = A)  &  ((k6_algstr_0 k3_algstr_1 B A) = A) ) ) ) ) ) ) ).
tt(l36_anproj_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  (A = B) )  &  ( (~  (C = k6_numbers) )  &  ((k9_real_1 (k8_real_1 B C) (k8_real_1 A C)) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(l36_binop_2,ax,(r3_binop_1 k2_numbers c4__binop_2 k29_binop_2)).
tt(l36_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v3_cgames_1 B) & (v4_cgames_1 B)) ) ) ) )  &  ( ((k1_funct_1 B 1) = A)  &  ((k1_funct_1 B (k3_finseq_1 B)) = A) ) ) ) ) ) ).
tt(l36_classes1,ax, ( ((k4_classes1 k1_xboole_0) = k1_xboole_0)  &  ( (! [A:$i] :  ((v3_ordinal1 A) =>  ((k4_classes1 (k1_ordinal1 A)) = (k9_setfam_1 (k4_classes1 A))) ) )  &  (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ( ((v4_ordinal1 A) &  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k4_classes1 C)) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ((k4_classes1 A) = (k3_tarski (k10_xtuple_0 B))) ) ) ) ) ) ) ) ) ).
tt(l36_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((k1_card_1 C) = 1) ) ) ) )  => (v1_finset_1 B)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_finset_1 B))  & (v1_xboole_0 (k2_topgen_1 A B))) ) ) ) ) ) ) ).
tt(l36_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k1_clvect_1 (k3_clvect_1 o_0_6_csspace) A C) B)) = (k3_xcmplx_0 C (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace))) k2_numbers c2__csspace (k1_domain_1 (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) A B)))) ) ) ) ) ) ) ).
tt(l36_dtconstr,ax,(m2_subset_1 c3__dtconstr (u1_struct_0 k5_dtconstr) (k7_dtconstr k5_dtconstr))).
tt(l36_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  ( (B = D)  =>  ((k1_rlvect_1 (k15_euclid A) B C) = (k24_valued_1 D C)) ) ) ) ) ) ) ) ) ) ).
tt(l36_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((v2_funct_1 C) => (v2_funct_1 (k2_rfinseq B A C))) ) ) ) ) ) ) ).
tt(l36_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  ((k1_funct_1 (k6_fomodel0 A) B) = (k1_funct_1 B 1)) ) ) ) ) ).
tt(l36_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  => (r1_tarski (k1_funct_1 (k25_fomodel1 C) A) (k1_funct_1 (k25_fomodel1 C) (k2_xcmplx_0 A B)))) ) ) ) ) ) ).
tt(l36_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 C D)) => (r1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k1_tarski k1_xboole_0)) k6_margrel1 (k24_fomodel2 C D A E) (k24_fomodel2 C D (k2_xcmplx_0 A B) E))) ) ) ) ) ) ) ) ) ) ).
tt(l36_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))) => (r2_relset_1 (k4_finseq_2 D A) (k4_finseq_2 D C) (k8_fomodel3 A C (k4_relset_1 A B B C E F) D) (k4_relset_1 (k4_finseq_2 D A) (k4_finseq_2 D B) (k4_finseq_2 D B) (k4_finseq_2 D C) (k8_fomodel3 A B E D) (k8_fomodel3 B C F D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_funct_2 C (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_fomodel4 B))) =>  ((r1_tarski A (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) C D)) => (v3_fomodel4 A B (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) C) D)) ) ) ) ) ) ) ) ).
tt(l36_funct_9,ax,(v1_funct_9 k29_sin_cos k32_sin_cos)).
tt(l36_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r1_geomtrap A D E D F) &  ((r1_geomtrap A D E D G) &  ((r1_geomtrap A D E D H) & (r1_geomtrap A D E D I)) ) ) )  =>  ( (D = E)  | (r1_geomtrap A F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k1_xtuple_0 (k7_gfacirc2 C A B)) = k1_xboole_0)  &  ( ((k2_xtuple_0 (k7_gfacirc2 C A B)) = (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1))  &  ((k9_xtuple_0 (k2_xtuple_0 (k7_gfacirc2 C A B))) = (k4_finseq_2 k6_numbers k6_margrel1)) ) )  |  ( ((k1_card_1 (k1_xtuple_0 (k7_gfacirc2 C A B))) = 3)  &  ( ((k2_xtuple_0 (k7_gfacirc2 C A B)) = k25_twoscomp)  &  ((k9_xtuple_0 (k2_xtuple_0 (k7_gfacirc2 C A B))) = (k4_finseq_2 3 k6_margrel1)) ) ) ) ) ) ) ) ) ) ).
tt(l36_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_glib_000 A A)) ) ).
tt(l36_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( ((v7_ordinal1 (k6_xcmplx_0 (k1_newton A B) 1)) & (v1_int_2 (k6_xcmplx_0 (k1_newton A B) 1)))  & (r1_xxreal_0 A 1)) ) ) ) ) ) ) ).
tt(l36_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ((r1_nat_d A (k1_newton C B)) =>  ((r1_xxreal_0 A 1) | (r1_nat_d C A)) ) ) ) ) ) ) ) ).
tt(l36_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A k6_numbers B) = (k1_group_1 A)) ) ) ) ) ).
tt(l36_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E F) = (k1_group_1 B)) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k6_algstr_0 A C D)) = (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) (k9_bilinear k1_complfld A A B (k7_hahnban1 k1_complfld A)) C D) = (k4_struct_0 k1_complfld)) ) ) ) ) ) ) ) ) ).
tt(l36_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r2_aff_1 A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E F) = G)  <=>  ( ((r2_hidden F D) &  (F = G) )  |  ( (~ (r2_hidden F D))  &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((r2_hidden H D) &  ((r2_hidden I D) &  ((r2_analoaf A H B I F) &  ((r2_analoaf A H C I G) & (r2_aff_1 A F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden B D) | (r1_homothet A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~  (C = k6_numbers) )  =>  ( ((k1_funct_1 (k1_funct_4 (k9_polynom3 A) (k5_funct_4 (u1_struct_0 A) k6_numbers C (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)) (k1_group_1 A))) k6_numbers) = (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)))  &  ((k1_funct_1 (k1_funct_4 (k9_polynom3 A) (k5_funct_4 (u1_struct_0 A) k6_numbers C (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)) (k1_group_1 A))) C) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ).
tt(l36_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_subset_1 F k1_numbers k5_numbers))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid F)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integr15 F (k3_integra5 A B) G) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 F k1_numbers G)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid F) G (k3_integra5 A B)) F) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers G)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D))) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid F) G H)) E)) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 C D F G)) (k11_binop_2 E (k18_complex1 (k10_binop_2 D C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((k4_integra5 C D (k26_valued_1 k1_numbers k1_numbers F E)) = (k4_real_1 E (k4_integra5 C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ((r2_hidden C B) =>  ( (C = (k7_interva1 A B))  <=>  (! [D:$i] :  ((r2_hidden D B) => (r1_tarski C D)) ) ) ) ) ) ) ) ).
tt(l36_jordan22,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l36_matrix_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) => (m1_matrix_1 (k4_matrix_1 B C) B A A)) ) ) ) ) ) ).
tt(l36_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 3 2 1) = (k3_finseq_4 k5_numbers 2 3 1)) )  &  (~  ((k3_finseq_4 k5_numbers 3 2 1) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ).
tt(l36_matrixc1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k9_matrix_5 (k10_funcop_1 k2_numbers k2_numbers k29_binop_2 A (k6_partfun1 k2_numbers)) B) = (k5_binop_2 A B)) ) ) ) ) ).
tt(l36_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_vectsp_4 F A C) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  ((r1_funct_2 (u1_struct_0 E) (u1_struct_0 F) (u1_struct_0 E) (u1_struct_0 C) G (k8_matrlin2 A B C E D)) =>  ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) &  ((v13_vectsp_1 G E F) &  ((v1_mod_2 G A E F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) &  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (~  (D = (k3_xtuple_0 E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((r1_tarski A B) => (r1_tarski (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(l36_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  ((v1_metrizts A) <=> (v7_topgen_1 A)) ) ) ).
tt(l36_mod_2,ax, (? [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) &  (A = 2) ) ) ).
tt(l36_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_1 A) =>  ( (~ (v3_modelc_1 A))  &  ( (~ (v4_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  ( (~ (v6_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ).
tt(l36_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l36_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D))) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) F)) =>  ( (G = (k3_msualg_4 A B C F H))  =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B D)) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D)) E F) G) = (k3_msualg_4 A B D F H)) ) ) ) ) ) ) )  => (v2_msualg_3 E (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 841 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ((r1_xxreal_0 (k4_nat_1 B B) A) &  ((v1_int_2 B) &  ( (~  (B = 2) )  &  ( (~  (B = 3) )  &  ( (~  (B = 5) )  &  ( (~  (B = 7) )  &  ( (~  (B = 11) )  &  ( (~  (B = 13) )  &  ( (~  (B = 17) )  &  ( (~  (B = 19) )  &  (~  (B = 23) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_oposet_1,ax, ((k6_partfun1 (k1_tarski k1_xboole_0)) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ).
tt(l36_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v10_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l36_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ( ( ((k2_polynom1 (k15_pre_poly A) B D) = (k2_xboole_0 (k2_polynom1 (k15_pre_poly A) B C) (k1_tarski F)))  &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( (~  (G = F) )  =>  ((k3_polynom1 A B D G) = (k3_polynom1 A B C G)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) B C)) |  ((k5_polynom2 A B D E) = (k3_rlvect_1 B (k5_polynom2 A B C E) (k6_algstr_0 B (k3_polynom1 A B D F) (k3_polynom2 A F B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_polynom8 A (k11_algstr_0 A B) C) = (k11_algstr_0 A (k3_polynom8 A B C))) ) ) ) ) ) ) ) ).
tt(l36_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  => (r1_relat_2 (k5_poset_1 A B) (k4_poset_1 A B))) ) ) ) ).
tt(l36_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_prelamb A B C) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) D) E))  => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A C D))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden A B) =>  ((r1_xxreal_0 (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 B)) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 B))) &  ((r1_xxreal_0 (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 B)) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) B) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 B)))) ) ) ) ) ) ) ) ).
tt(l36_realset2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c10__realset2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c10__realset2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c10__realset2)) =>  ( ((k6_algstr_0 c10__realset2 A (k1_algstr_0 c10__realset2 B C)) = (k1_algstr_0 c10__realset2 (k6_algstr_0 c10__realset2 A B) (k6_algstr_0 c10__realset2 A C)))  &  ((k6_algstr_0 c10__realset2 (k1_algstr_0 c10__realset2 B C) A) = (k1_algstr_0 c10__realset2 (k6_algstr_0 c10__realset2 B A) (k6_algstr_0 c10__realset2 C A))) ) ) ) ) ) ) ) ).
tt(l36_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) =>  ((u1_struct_0 (k2_rlsub_2 A C (k1_rlsub_2 A B D))) = (u1_struct_0 (k1_rlsub_2 A (k2_rlsub_2 A B C) (k2_rlsub_2 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l36_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((u1_struct_0 (k2_rmod_3 A B C (k1_rmod_3 A B C D))) = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(l36_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) =>  ((u1_struct_0 (k2_rusub_2 A C (k1_rusub_2 A B D))) = (u1_struct_0 (k1_rusub_2 A (k2_rusub_2 A B C) (k2_rusub_2 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l36_scmbsort,ax, (~  ((k4_scmfsa_2 k6_numbers) = (k4_scmfsa_2 5)) ) ).
tt(l36_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b A C B) & (r6_scmfsa7b A C B))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 C) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B A) (k8_memstr_0 3 k1_scmfsa_2 C)) 1))) = (k5_card_1 A))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B A) (k8_memstr_0 3 k1_scmfsa_2 C) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B A) (k8_memstr_0 3 k1_scmfsa_2 C)))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 C) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B A) (k8_memstr_0 3 k1_scmfsa_2 C)) 1))))  &  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 C)) &  ( ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 C)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B A) (k8_memstr_0 3 k1_scmfsa_2 C)) 1))  &  ((r5_scmfsa7b (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2)) C B) & (r6_scmfsa7b (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2)) C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (v2_extpro_1 (k9_scmring2 A C B) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l36_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 1)) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 2)) k6_numbers))  &  (~  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)))) B A) (k1_scmp_gcd 1)) = (k3_int_2 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)))) B A) (k1_scmp_gcd 2)) = (k3_int_2 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  ((r1_scmpds_6 (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)))) B A) & (r2_scmpds_6 (k1_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k5_scmpds_2 k2_scmp_gcd k6_numbers) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k4_scpinvar k2_scmp_gcd 3 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_6 k2_scmp_gcd 3 (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 1 2)) (k9_compos_1 k1_scmpds_2 (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 2 1))) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 1)) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)))) B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_scpqsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k4_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k4_numbers) =>  ( ( ((k1_funct_1 C k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 C (k1_scmp_gcd 4)) = (k2_xcmplx_0 E (k1_funct_1 C (k1_scmp_gcd 5))))  &  ( (E = (k6_xcmplx_0 (k1_funct_1 C (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 C (k1_scmp_gcd 2)) = D)  &  ((r1_xxreal_0 (k2_nat_1 F 1) D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 (k2_nat_1 F 1) (k1_funct_1 C (k1_scmp_gcd 3))) &  ((r1_xxreal_0 (k1_funct_1 C (k1_scmp_gcd 4)) (k2_nat_1 F A)) &  ((r1_scpisort G C F) &  ((r1_scpisort H (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) F) &  ((r1_xxreal_0 7 F) &  ( ((k3_finseq_1 G) = A)  &  ((k3_finseq_1 H) = A) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 C (k1_scmp_gcd 5)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 1)) = (k1_funct_1 C (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 2)) = D)  &  ((r1_xxreal_0 D (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 4))) &  ((r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 4)) (k1_funct_1 C (k1_scmp_gcd 4))) &  ((r2_classes1 G H) &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k1_funct_1 C (k1_scmp_gcd 3)) I) & (r1_xxreal_0 I (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 4))))  => (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd I)) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd D)))) ) )  &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 I (k1_funct_1 C (k1_scmp_gcd 4))) =>  ((r1_xxreal_0 I (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd 4))) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd D)) (k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd I)))) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 F 1) I) =>  ( ((r1_xxreal_0 (k1_funct_1 C (k1_scmp_gcd 3)) I) & (r1_xxreal_0 I (k1_funct_1 C (k1_scmp_gcd 4))))  |  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) C B) (k1_scmp_gcd I)) = (k1_funct_1 C (k1_scmp_gcd I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_sincos10,ax,(r1_tarski (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))))).
tt(l36_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k7_sin_cos2 (k10_binop_2 A B)) = (k10_real_1 (k9_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) (k9_real_1 1 (k8_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B))))) ) ) ) ) ).
tt(l36_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k9_binop_2 (k3_square_1 A) 1) k6_numbers)) ) ) ).
tt(l36_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_substlat A B))) =>  ((k1_lattices (k5_substlat A B) C (k1_lattices (k5_substlat A B) D E)) = (k1_lattices (k5_substlat A B) (k1_lattices (k5_substlat A B) C D) E)) ) ) ) ) ) ) ) ) ).
tt(l36_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers D) = (k2_subset_1 k1_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k1_seq_1 D E) = (k10_real_1 (k8_real_1 B (k2_newton (k9_real_1 C E) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r1_fdiff_1 D F) &  ((k1_fdiff_1 D F) = (k1_real_1 (k10_real_1 (k8_real_1 B (k2_newton (k9_real_1 C F) A)) (k3_newton A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v2_struct_0 A) => (v3_tops_2 B A A)) ) ) ) ) ).
tt(l36_trees_2,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r2_hidden C A) &  (~ (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ).
tt(l36_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E)) = (k4_tex_4 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (? [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) &  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (H = C) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B E H)) ) ) )  &  ((k3_funct_2 (k3_qc_lang1 A) B G C) = (k3_funct_2 (k3_qc_lang1 A) B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  (! [C:$i] :  ((m1_valued_0 C B) => (r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(l36_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_yellow_8 (a_2_7_waybel17 A B) A B) &  ((v1_tops_2 (a_2_7_waybel17 A B) A) & (m1_subset_1 (a_2_7_waybel17 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(l36_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k2_yellow_1 (u1_pre_topc A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A C))  =>  (? [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D E) & (m1_connsp_2 (k1_setfam_1 E) A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l36_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k8_real_1 (k21_rvsum_1 (k4_wsierp_1 k1_numbers A B)) (k1_seq_1 B A)) = (k21_rvsum_1 B)) ) ) ) ) ) ).
tt(l36_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 A (k3_xboole_0 B C)) = (k2_xboole_0 (k4_xboole_0 A B) (k4_xboole_0 A C))) ) ) ) ).
tt(l36_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C D)) => (r1_xxreal_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ).
tt(l36_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (~  ((r2_hidden B (k6_yellow_6 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r3_waybel_9 A B C)) ) ) ) ) ) )  => (v1_compts_1 A)) ) ) ).
tt(l36_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v8_zf_fund1 B A) =>  ((r2_hidden (k2_ordinal4 A) B) & (r2_hidden (k3_ordinal4 A) B)) ) ) ) ) ) ).
tt(l37_algstr_1,ax, (k6_numbers = (k4_struct_0 k3_algstr_1)) ).
tt(l37_anproj_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ( ((k7_real_1 E G) = (k7_real_1 F H))  &  ( ((k8_real_1 E A) = (k8_real_1 F B))  &  ((k8_real_1 G C) = (k8_real_1 H D)) ) )  =>  ( (A = B)  |  ( (D = k6_numbers)  |  (E = (k8_real_1 (k8_real_1 (k9_real_1 (k8_real_1 B C) (k8_real_1 B D)) (k2_real_1 (k9_real_1 (k8_real_1 B D) (k8_real_1 A D)))) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k5_bhsp_1 A D C))) &  ((k2_seq_2 (k2_bhsp_2 A (k5_bhsp_1 A D C))) = (k3_bhsp_1 A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_binop_2,ax,(r3_binop_1 k1_numbers 1 k35_binop_2)).
tt(l37_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k5_bhsp_1 A D C))) &  ((k2_seq_2 (k2_clvect_2 A (k5_bhsp_1 A D C))) = (k13_csspace A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ( ((v2_convex1 C A) &  ((k3_rlvect_2 A C) = (k6_domain_1 (u1_struct_0 A) B)) )  =>  ( ((k1_funct_1 C B) = 1)  &  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k1_funct_1 C B))) ) ) ) ) ) ) ) ) ).
tt(l37_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace))) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A A) = k5_complex1)  =>  (A = (k4_struct_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace))) )  &  ( ( (A = (k4_struct_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace)))  =>  ((k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A A) = k5_complex1) )  &  ((r1_xxreal_0 k6_numbers (k3_complex1 (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A A))) &  ( (k6_numbers = (k4_complex1 (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A A)))  &  ( ((k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A B) = (k15_complex1 (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) B A)))  &  ( ((k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) (k1_algstr_0 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A B) C) = (k2_xcmplx_0 (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A C) (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) B C)))  &  ((k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) (k1_clvect_1 (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A D) B) = (k3_xcmplx_0 D (k12_csspace (g1_csspace (u1_struct_0 (k3_clvect_1 o_0_6_csspace)) (k4_struct_0 (k3_clvect_1 o_0_6_csspace)) (u1_algstr_0 (k3_clvect_1 o_0_6_csspace)) (u1_clvect_1 (k3_clvect_1 o_0_6_csspace)) c2__csspace) A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_diraf A B C D) =>  ((r3_diraf A B D C) & (r3_diraf A C B D)) ) ) ) ) ) ) ) ) ) ).
tt(l37_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r2_hidden B (k5_dist_1 A (k1_uproots A))) => (v1_dist_1 B A)) ) ) ) ) ).
tt(l37_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r3_euclidlp A B C) &  (B = (k5_euclid A)) ) ) ) ) ) ) ) ) ).
tt(l37_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 B C)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) => (r1_tarski (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k24_fomodel2 B C A E)) (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k24_fomodel2 B D A F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r2_relset_1 (k4_finseq_2 C B) (k4_finseq_2 C A) (k8_fomodel3 B A (k3_relset_1 A B D) C) (k3_relset_1 (k4_finseq_2 C A) (k4_finseq_2 C B) (k8_fomodel3 A B D C)))) ) ) ) ) ) ) ) ).
tt(l37_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  (! [G:$i] :  ((v2_fomodel4 G D) =>  (! [H:$i] :  ((v2_fomodel4 H D) =>  ( ((v6_fomodel4 E D) &  ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) E F) D) &  ((r1_tarski G (k1_funct_1 (k9_funct_7 (k2_fomodel4 D E) A) H)) & (r1_tarski C (k1_funct_1 (k9_funct_7 (k2_fomodel4 D F) B) G))) ) )  => (r1_tarski C (k1_funct_1 (k9_funct_7 (k2_fomodel4 D (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) E F)) (k2_xcmplx_0 A B)) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_frechet,ax,(r1_tarski (k1_tarski k1_numbers) (u1_struct_0 k3_frechet))).
tt(l37_funct_9,ax,(v1_funct_9 k30_sin_cos k32_sin_cos)).
tt(l37_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k4_fvsum_1 A B C D) = (k4_fvsum_1 A B E D))  =>  (C = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (~  ((k7_gfacirc2 A B C) = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r1_glib_000 B C D E) => (r1_glib_000 A C D E)) ) ) ) ) ) ) ) ).
tt(l37_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((k5_group_1 B A (k1_group_1 B)) = (k1_group_1 B)) ) ) ) ) ).
tt(l37_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((v15_algstr_0 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) & (m1_group_2 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) B)) ) ) ) ) ) ).
tt(l37_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  => (v3_hermitan (k9_bilinear k1_complfld A A B (k7_hahnban1 k1_complfld A)) A)) ) ) ) ).
tt(l37_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~  (D = k6_numbers) )  &  ( (~  (D = C) )  &  (~  ((k1_funct_1 (k1_funct_4 (k9_polynom3 A) (k5_funct_4 (u1_struct_0 A) k6_numbers C (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)) (k1_group_1 A))) D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 B A)) ) ) ) ) ).
tt(l37_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_subset_1 F k1_numbers k5_numbers))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid F)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 F (k3_integra5 A B) G) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 F k1_numbers G)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid F) G (k3_integra5 A B)) F) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers G)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 C D)) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid F) G H)) E)) ) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 C D F G)) (k11_binop_2 E (k10_binop_2 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ((r2_hidden C B) =>  ( (C = (k8_interva1 A B))  <=>  (! [D:$i] :  ((r2_hidden D B) => (r1_tarski D C)) ) ) ) ) ) ) ) ).
tt(l37_jgraph_3,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l37_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_23_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(l37_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) => (r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k2_relset_1 (u1_struct_0 A) (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(l37_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_ideal_1 (k9_lpspace1 A B C) (k7_lpspace1 A)) & (v1_lpspace1 (k9_lpspace1 A B C) (k7_lpspace1 A))) ) ) ) ) ) ) ).
tt(l37_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  ( ( ((k10_xtuple_0 B) = (k10_xtuple_0 C))  & (v2_funct_1 B))  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(l37_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 3 2 1) = (k3_finseq_4 k5_numbers 2 1 3)) )  &  (~  ((k3_finseq_4 k5_numbers 1 3 2) = (k3_finseq_4 k5_numbers 2 1 3)) ) ) ).
tt(l37_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_rlvect_1 A (k1_rlvect_1 A B (k10_binop_2 1 D)) (k1_rlvect_1 A C D)) = (k3_rlvect_1 A B (k1_rlvect_1 A (k5_algstr_0 A C B) D))) ) ) ) ) ) ) ) ) ).
tt(l37_metrizts,ax,(v5_waybel23 (g1_pre_topc (u1_struct_0 (k15_euclid 1)) (u1_pre_topc (k15_euclid 1))))).
tt(l37_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_1 A) =>  ( (~ (v2_modelc_1 A))  &  ( (~ (v4_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  ( (~ (v6_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ).
tt(l37_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l37_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (m1_msualg_2 D A C))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D)) =>  ( ((r8_pboole (u1_struct_0 A) E F) & (r1_msualg_3 A B D F))  => (r1_msualg_3 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_ordinal5,ax,(r2_hidden k1_xboole_0 k4_ordinal1)).
tt(l37_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v11_o_ring_1 B A)) ) ) ) ) ).
tt(l37_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  &  ((k2_polynom1 (k15_pre_poly A) B C) = (k1_tarski D)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k5_polynom1 A B C D) E) = (k3_rlvect_1 B (k5_polynom2 A B C E) (k5_polynom2 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  => (r8_relat_2 (k5_poset_1 A B) (k4_poset_1 A B))) ) ) ) ).
tt(l37_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) C) (k12_finseq_1 (u1_struct_0 A) D)) B) E) => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A C D)) B) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_prepower,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k1_seq_1 A C) = (k2_prepower C B)) ) ) ) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = 1) ) ) ) ) ) ) ).
tt(l37_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (v6_supinf_2 (k56_valued_1 A k1_numbers B))) ) ) ) ).
tt(l37_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (~  ((v5_ratfunc1 B A) &  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (~  ( (B = (k3_ratfunc1 A (k13_polynom3 A D (k4_ratfunc1 A C)) (k13_polynom3 A D (k5_ratfunc1 A C))))  &  ((v5_ratfunc1 C A) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) &  ( (D = (k3_group_4 (k14_polynom3 A) E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) G) &  ((k1_funct_1 E F) = (k3_hurwitz A G 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_scmbsort,ax, (~  ((k4_scmfsa_2 k6_numbers) = (k4_scmfsa_2 6)) ) ).
tt(l37_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k3_scmisort A) =>  ( ((k3_compos_1 k1_scmfsa_2 A k6_numbers) = (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 1) = (k11_scmfsa_2 2))  &  ( ((k3_compos_1 k1_scmfsa_2 A 2) = (k6_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 3) = (k11_scmfsa_2 4))  &  ( ((k3_compos_1 k1_scmfsa_2 A 4) = (k6_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 5) = (k11_scmfsa_2 6))  &  ( ((k3_compos_1 k1_scmfsa_2 A 6) = (k6_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 7) = (k11_scmfsa_2 8))  &  ( ((k3_compos_1 k1_scmfsa_2 A 8) = (k6_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 9) = (k11_scmfsa_2 10))  &  ( ((k3_compos_1 k1_scmfsa_2 A 10) = (k16_scmfsa_2 (k4_scmfsa_2 1) (k5_scmfsa_2 k6_numbers)))  &  ((k3_compos_1 k1_scmfsa_2 A 11) = (k11_scmfsa_2 12)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (~ (v2_extpro_1 (k7_scmring2 A C B) 2 (k1_scmring2 A))) ) ) ) ) ) ) ).
tt(l37_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 4)) = (k2_xcmplx_0 D (k1_funct_1 B (k1_scmp_gcd 5))))  &  ( (D = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 3)) 1))  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ((r1_xxreal_0 (k2_nat_1 E 1) C) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 7 E)) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) B A) & (r2_scmpds_6 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 5 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 7 5) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 5 k6_numbers))))) (k2_scmpds_8 k2_scmp_gcd 7 (k1_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 7) (k11_scmpds_2 k2_scmp_gcd 7 (k4_xcmplx_0 1))) (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 2) 6 k6_numbers)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 6 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 6 (k4_scmpds_4 (k11_scmpds_2 k2_scmp_gcd 3 1) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 7 k6_numbers)))))) (k7_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 6 k6_numbers) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 3) k6_numbers k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 3) k2_scmp_gcd k6_numbers 6)) (k11_scmpds_2 k2_scmp_gcd 5 (k4_xcmplx_0 2))) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1)))))) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_xcmplx_0 (k13_newton (k2_nat_1 A 2) 2) (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton (k2_nat_1 A 1) 4)) (k4_nat_1 6 (k13_newton (k2_nat_1 A 1) 3))) (k13_newton (k2_nat_1 A 1) 2)) (k4_nat_1 4 (k2_nat_1 A 1))) 2)) = (k2_xcmplx_0 (k3_xcmplx_0 (k13_newton A 2) (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton A 4)) (k4_nat_1 6 (k13_newton A 3))) (k13_newton A 2)) (k4_nat_1 4 A)) 2)) (k4_nat_1 (k13_newton (k2_nat_1 A 1) 5) 24))) ) ) ).
tt(l37_sincos10,ax, ((k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) = (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))) ).
tt(l37_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k9_complex1 (k11_comseq_3 (k3_sin_cos A)) (k11_comseq_3 (k3_sin_cos B))) = (k11_comseq_3 (k3_sin_cos (k2_xcmplx_0 A B)))) ) ) ) ) ).
tt(l37_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k1_binop_1 (u2_lattices (k5_substlat A B)) (k1_binop_1 (u1_lattices (k5_substlat A B)) C D) D) = D) ) ) ) ) ) ) ).
tt(l37_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( ((k1_relset_1 k1_numbers E) = C)  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 E F) = (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C F D)) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ((r1_borsuk_3 A B) & (v3_topdim_1 A))  =>  ((v3_topdim_1 B) & (r1_xxreal_0 (k4_topdim_1 B) (k4_topdim_1 A))) ) ) ) ) ) ).
tt(l37_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (E = D)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E) = (k3_tex_4 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((u1_struct_0 (k2_vectsp_5 A B C (k1_vectsp_5 A B C D))) = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(l37_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 B (k1_vectsp_9 A C)) &  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A C))  =>  (~  ((k1_vectsp_9 A D) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (? [B:$i] :  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v7_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  &  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) )  => (v2_waybel_8 A)) ) ) ).
tt(l37_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v1_cantor_1 (a_1_0_waybel17 A) A) &  ((v1_tops_2 (a_1_0_waybel17 A) A) & (m1_subset_1 (a_1_0_waybel17 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(l37_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_0_waybel_5 A B C D))  =>  ((k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))) = (k1_yellow_0 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l37_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = (k1_tarski B)) )  &  ( (~  (A = k1_xboole_0) )  &  (! [C:$i] :  (~  ((r2_hidden C A) &  (~  (C = B) ) ) ) ) ) ) ) ) ) ).
tt(l38_algstr_1,ax, (1 = (k1_group_1 k3_algstr_1)) ).
tt(l38_anproj_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = C) )  &  ( (~  (D = k6_numbers) )  &  ((k8_real_1 D (k2_real_1 (k9_real_1 (k8_real_1 C A) (k8_real_1 B A)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_arytm_3,ax,(r1_arytm_3 1 1)).
tt(l38_bcialg_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v2_bcialg_4 B) & (l1_bcialg_4 B)) ) ) ) ) )  =>  ((k6_bcialg_4 B (k4_struct_0 B) (k2_nat_1 A 1)) = (k4_struct_0 B)) ) ) ) ) ).
tt(l38_binop_2,ax,(m1_subset_1 1 k3_numbers)).
tt(l38_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_cfuncdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_cfuncdom A))) =>  ( (C = (k5_cfuncdom A))  =>  ( ((k6_algstr_0 (k8_cfuncdom A) C B) = B)  &  ((k6_algstr_0 (k8_cfuncdom A) B C) = B) ) ) ) ) ) ) ) ) ).
tt(l38_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m2_collsp B A) =>  (! [C:$i] :  ((r2_hidden C B) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(l38_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((v2_convex1 D A) &  ((k3_rlvect_2 A D) = (k7_domain_1 (u1_struct_0 A) B C)) )  =>  ( (B = C)  |  ( ((k2_xcmplx_0 (k1_funct_1 D B) (k1_funct_1 D C)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 D B)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 D C)) &  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 D B)) (k1_rlvect_1 A C (k1_funct_1 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_dist_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((v1_dist_1 C A) => (r2_hidden C (k5_dist_1 A B))) ) ) ) ) ) ) ) ).
tt(l38_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k11_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k17_facirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E F) (k10_margrel1 F G)) (k10_margrel1 G E)))  &  ( ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_fdiff_1,ax,(v2_rcomp_1 (k1_subset_1 k1_numbers))).
tt(l38_fomodel2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 B C)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) =>  ((k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k24_fomodel2 B C A E)) = (k1_relset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k24_fomodel2 B D A F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v1_fomodel3 E C D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (r2_funct_2 A (k8_eqrel_1 B D) (k1_partfun1 A B B (k8_eqrel_1 B D) E (k17_fomodel3 B D)) (k1_partfun1 A (k8_eqrel_1 A C) (k8_eqrel_1 A C) (k8_eqrel_1 B D) (k17_fomodel3 A C) (k16_fomodel3 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(l38_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ( (~ (v6_struct_0 F))  &  ((v11_fomodel1 F) & (l1_fomodel1 F)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  ( ((v6_fomodel4 G F) &  ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) F) &  ((v4_fomodel4 C A F G D) & (v4_fomodel4 E B F H (k1_tarski C))) ) )  => (v4_fomodel4 E (k2_xcmplx_0 A B) F (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_funcsdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_funcsdom A))) =>  ( (C = (k9_funcsdom A))  =>  ( ((k6_algstr_0 (k12_funcsdom A) B C) = B)  &  ((k6_algstr_0 (k12_funcsdom A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l38_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k29_sin_cos (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l38_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) => (r2_hidden (k1_funct_1 B C) (k6_glib_000 A))) ) ) ) ) ) ) ).
tt(l38_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (? [F:$i] :  ( ((v2_group_9 F A) & (m1_group_9 F A C))  &  ((u1_struct_0 F) = (k7_relset_1 (u1_struct_0 B) (u1_struct_0 C) E (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_subset_1 F k1_numbers k5_numbers))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid F)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 F (k3_integra5 A B) G) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 F k1_numbers G)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid F) G (k3_integra5 A B)) F) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers G)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 C D)) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid F) G H)) E)) ) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 D C F G)) (k11_binop_2 E (k10_binop_2 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_isomichi,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k4_subset_1 k1_numbers (k1_rcomp_1 A B) (k1_seq_4 B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(l38_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_26_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(l38_knaster,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~ (r2_xboole_0 A B))  &  ( (~  (A = B) )  &  (~ (r2_xboole_0 B A)) ) ) ) ) ) ) ) ).
tt(l38_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_finseq_1 B) = (k3_finseq_1 (k9_fvsum_1 A B C))) ) ) ) ) ) ) ).
tt(l38_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 1 3 2) = (k3_finseq_4 k5_numbers 2 3 1)) )  &  (~  ((k3_finseq_4 k5_numbers 1 3 2) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ).
tt(l38_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((v3_mazurulm C A B) &  ((r1_xxreal_0 G (k2_newton 2 F)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ( (H = (k21_binop_2 (k2_newton 2 F) G))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_rlvect_1 A D (k1_rlvect_1 A (k5_algstr_0 A E D) (k12_binop_2 G (k13_newton 2 (k23_binop_2 F 1)))))) = (k1_rlvect_1 B (k3_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A D H) (k1_rlvect_1 A E G)) (k12_binop_2 1 (k2_newton 2 F))))) (k18_binop_2 1 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v4_midsp_2 E B) & (l1_midsp_2 E B))  =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B E)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B E)))) =>  ( ((k8_midsp_3 A B E C D) = F)  =>  ((k10_midsp_3 A B E F) = (k9_midsp_2 B E C (k4_midsp_3 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_1 A) =>  ( (~ (v2_modelc_1 A))  &  ( (~ (v3_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  ( (~ (v6_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ).
tt(l38_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l38_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  ((r2_hidden A (u2_modelc_3 B C)) =>  ( ( (~ (v2_modelc_2 A))  &  (~ (v3_modelc_2 A)) )  |  ((k14_modelc_3 B C) = (k14_modelc_3 B (k5_modelc_3 B C A))) ) ) ) ) ) ) ) ) ).
tt(l38_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v13_monoid_0 A) <=>  ((v11_monoid_0 A) & (v12_monoid_0 A)) ) ) ) ).
tt(l38_nat_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 A)))  =>  ( (E = (k1_tarski B))  =>  ((k3_uproots (k8_mcart_1 A A E F) (k1_nat_5 (k2_zfmisc_1 A A) (k1_partfun1 (k2_zfmisc_1 A A) (k2_zfmisc_1 k5_numbers k5_numbers) (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers (k16_funct_3 A A k5_numbers k5_numbers C D) k48_binop_2) (k8_mcart_1 A A E F))) = (k24_binop_2 (k1_recdef_1 C B) (k3_uproots F (k1_nat_5 A D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_o_ring_1 B A) => (v10_o_ring_1 B A)) ) ) ) ) ).
tt(l38_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  => (r4_relat_2 (k5_poset_1 A B) (k4_poset_1 A B))) ) ) ) ).
tt(l38_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) C)) (k12_finseq_1 (u1_struct_0 A) D)) E) => (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A C D))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k4_radix_1 D C (k2_xcmplx_0 A 1) (k10_radix_1 C (k2_xcmplx_0 A 1) B)) = (k4_radix_1 D C A (k10_radix_1 C A (k4_nat_d B (k1_newton (k1_radix_1 C) A))))) ) ) ) ) ) ) ) ) ) ).
tt(l38_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) => (r1_tarski (u1_struct_0 (k1_rlsub_2 A B (k2_rlsub_2 A C D))) (u1_struct_0 (k2_rlsub_2 A (k1_rlsub_2 A C B) (k1_rlsub_2 A B D))))) ) ) ) ) ) ) ) ).
tt(l38_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v3_rltopsp1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_rltopsp1 (k7_rusub_4 A B C) A)) ) ) ) ) ) ).
tt(l38_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k6_rlvect_2 A (k4_rlvect_2 A)) = (k4_struct_0 A)) ) ) ).
tt(l38_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) => (r1_tarski (u1_struct_0 (k1_rmod_3 A B (k2_rmod_3 A B C D) (k2_rmod_3 A B D E))) (u1_struct_0 (k2_rmod_3 A B D (k1_rmod_3 A B C E))))) ) ) ) ) ) ) ) ) ) ).
tt(l38_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ((k5_rmod_4 A B (k3_rmod_4 A B)) = (k4_struct_0 B)) ) ) ) ) ).
tt(l38_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) => (r1_tarski (u1_struct_0 (k1_rusub_2 A C (k2_rusub_2 A B D))) (u1_struct_0 (k2_rusub_2 A (k1_rusub_2 A B C) (k1_rusub_2 A C D))))) ) ) ) ) ) ) ) ).
tt(l38_scmbsort,ax, (~  ((k4_scmfsa_2 1) = (k4_scmfsa_2 2)) ) ).
tt(l38_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k3_scmisort B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 12 C))  &  (~  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A C) (k4_struct_0 k1_scmfsa_2)) = C)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A C) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A C) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ) )  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 1)) = (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 2)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 3)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 4)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 5)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 6)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 E (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 E 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D)) A) &  (B = (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C))) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A E (k8_extpro_1 2 k1_scmpds_2 B E))) = (k5_card_1 C))  &  ( ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A E (k8_extpro_1 2 k1_scmpds_2 B E))) = (k6_memstr_0 2 k1_scmpds_2 (k8_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B E (k8_extpro_1 2 k1_scmpds_2 B E)))))  &  ((r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 D) (k5_card_1 C)) A) &  ((k8_extpro_1 2 k1_scmpds_2 A E) = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 B E) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 D)) (k8_memstr_0 2 k1_scmpds_2 (k6_extpro_1 2 k1_scmpds_2 B E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  ((v2_extpro_1 B 2 (k1_scmring2 A)) =>  (B = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ) ) ) ) ) ).
tt(l38_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 2)) = (k1_funct_1 B (k1_scmp_gcd 2)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 3)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 2)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 4)) = (k1_funct_1 B (k1_scmp_gcd 4)))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 5)) = (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) (k1_funct_1 B (k1_scmp_gcd 2))))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 8 C) =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 4) (k13_scmpds_2 k2_scmp_gcd k2_scmp_gcd 5 2)) (k16_scmpds_2 k2_scmp_gcd k2_scmp_gcd 3 2)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd C)) = (k1_funct_1 B (k1_scmp_gcd C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (r1_xxreal_0 (k2_xcmplx_0 (k13_newton 2 (k2_nat_1 A 2)) (k1_newton (k4_xcmplx_0 1) (k2_nat_1 A 2))) k6_numbers)) ) ) ).
tt(l38_sincos10,ax,(r1_tarski (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))))).
tt(l38_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((k1_lattices (k5_substlat A B) (k2_lattices (k5_substlat A B) C D) D) = D) ) ) ) ) ) ) ).
tt(l38_topalg_5,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2))))) &  ((m1_setfam_1 A (u1_struct_0 (k8_toprealb 2))) &  ((v1_tops_2 A (k8_toprealb 2)) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2)))) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ( ((v4_taxonom2 C) &  ((v1_tops_2 C k2_topalg_2) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))))) )  =>  (~  ( ((k5_setfam_1 (u1_struct_0 k2_topalg_2) C) = (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb B))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((r2_hidden D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc k2_topalg_2 D)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 D)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B)))))) )  =>  ( (E = (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb D))  => (v3_tops_2 E (k1_pre_topc k2_topalg_2 D) (k1_pre_topc (k8_toprealb 2) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l38_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) =>  ( ((v3_topdim_1 A) => (v3_topdim_1 B))  &  ( ((v3_topdim_1 B) => (v3_topdim_1 A))  &  ((v3_topdim_1 A) =>  ((k4_topdim_1 B) = (k4_topdim_1 A)) ) ) ) ) ) ) ) ) ).
tt(l38_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A B) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k2_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_tops_1 A C))))) ) ) ) ) ) ).
tt(l38_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 A 5) => (m1_subset_1 A (u2_turing_1 k14_turing_1))) ) ) ).
tt(l38_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v8_vectsp_1 (k3_vectsp_2 A) A) &  ((v9_vectsp_1 (k3_vectsp_2 A) A) &  ((v10_vectsp_1 (k3_vectsp_2 A) A) & (v11_vectsp_1 (k3_vectsp_2 A) A)) ) ) ) ) ).
tt(l38_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k3_tarski (a_2_8_waybel17 A B))) ) ) ) ) ).
tt(l38_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) C))  =>  (B = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(l38_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_0_waybel_5 A B C D))  =>  ((k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))) = (k1_yellow_0 A E)) ) ) ) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l38_xxreal_3,ax, ((k2_xxreal_3 k1_xxreal_0) = k2_xxreal_0) ).
tt(l38_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) =>  ((r2_hidden C (u1_struct_0 (k5_yellow_1 A (k7_funcop_1 A B)))) &  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ) ) ) ).
tt(l38_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_tarski B C)) <=>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (A = (k1_tarski B)) )  &  ( (~  (A = (k1_tarski C)) )  &  (~  (A = (k2_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(l39_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_tarski (k2_zfmisc_1 (k11_algstr_4 A B) (k1_tarski B)) (k12_algstr_4 A))) ) ) ) ).
tt(l39_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (J = (k8_real_1 (k8_real_1 (k9_real_1 (k8_real_1 F G) (k8_real_1 F H)) (k2_real_1 (k9_real_1 (k8_real_1 F H) (k8_real_1 I H)))) K))  &  (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C (k7_real_1 J K)) (k1_rlvect_1 A D (k8_real_1 J I))) (k1_rlvect_1 A E (k8_real_1 K G)))) )  =>  ( (H = k6_numbers)  |  ( (I = F)  |  (B = (k1_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 (k8_real_1 F G) (k8_real_1 I H))) (k1_rlvect_1 A D (k8_real_1 (k8_real_1 I F) (k9_real_1 G H)))) (k1_rlvect_1 A E (k8_real_1 (k8_real_1 H G) (k9_real_1 F I)))) (k8_real_1 K (k2_real_1 (k9_real_1 (k8_real_1 F H) (k8_real_1 I H)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_arytm_3,ax,(r2_hidden (k4_tarski 1 1) a_0_0_arytm_3)).
tt(l39_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 (k8_real_1 A C) (k8_real_1 B D))) ) ) ) ) ) ) ) ) ).
tt(l39_binop_2,ax,(r3_binop_1 k3_numbers c5__binop_2 k41_binop_2)).
tt(l39_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B (k3_catalg_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) B) (k9_catalg_1 (u1_struct_0 A) C D)) = (k2_cat_1 A C D)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) C D E) B) = (k4_card_3 (k2_finseq_4 (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A D E) (k2_cat_1 A C D))))  &  ((k4_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) C D E) B) = (k2_cat_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v4_normsp_0 (k7_cc0sp1 A)) &  ((v3_normsp_0 (k7_cc0sp1 A)) & (v8_clvect_1 (k7_cc0sp1 A))) ) ) ) ).
tt(l39_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_finset_1 B))  &  ((v4_card_3 B) & (v1_xboole_0 (k2_topgen_1 A B))) ) ) ) )  => (v8_compl_sp A)) ) ) ).
tt(l39_convex1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((v2_funct_1 A) &  ( ((k10_xtuple_0 A) = (k1_enumset1 B C D))  &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (D = B) )  &  ( (~  (A = (k11_finseq_1 B C D)) )  &  ( (~  (A = (k11_finseq_1 B D C)) )  &  ( (~  (A = (k11_finseq_1 C B D)) )  &  ( (~  (A = (k11_finseq_1 C D B)) )  &  ( (~  (A = (k11_finseq_1 D B C)) )  &  (~  (A = (k11_finseq_1 D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A D B) & (r3_cqc_the1 A D C))  => (r3_cqc_the1 A D (k7_cqc_lang A B C))) ) ) ) ) ) ) ) ) ).
tt(l39_fdiff_1,ax,(v3_rcomp_1 (k2_subset_1 k1_numbers))).
tt(l39_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_tarski A (k2_finseq_1 B)) => (v2_funct_1 (k14_finseq_1 A))) ) ) ) ).
tt(l39_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_relset_1 (k3_finseq_2 (k3_finseq_2 A)) (k3_finseq_2 A) (k8_fomodel0 A) (k6_subset_1 (k3_finseq_2 (k3_finseq_2 A)) (k1_tarski k1_xboole_0))) = (k5_fomodel0 (k3_finseq_2 A) (k11_monoid_0 A))) ) ) ).
tt(l39_fomodel1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (~  ((r2_hidden A (k27_fomodel1 B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r2_hidden A (k1_funct_1 (k25_fomodel1 B) C))) ) ) ) ) ) ) ) ).
tt(l39_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) &  ((v3_card_1 D C) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k3_relat_1 D E) = (k1_funct_1 (k8_fomodel3 A B E C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v13_fomodel1 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ((r2_hidden (k1_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) C D) (k6_fomodel4 B E A)) <=> (v8_fomodel4 (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k34_fomodel2 B)) C) D) B E A)) ) ) ) ) ) ) ) ) ) ).
tt(l39_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_gcd_1 A D B) &  ((r2_gcd_1 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_gcd_1 A E B) & (r2_gcd_1 A E C))  => (r2_gcd_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ((v1_abian C) & (m1_subset_1 C k5_numbers))  =>  (~  ((r2_hidden C (k1_relset_1 k5_numbers B)) &  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (~  ( (D = (k6_xcmplx_0 C 1))  &  ((r2_hidden (k6_xcmplx_0 C 1) (k1_relset_1 k5_numbers B)) &  ((r2_hidden (k2_nat_1 C 1) (k1_relset_1 k5_numbers B)) & (r1_glib_000 A (k1_funct_1 B D) (k1_funct_1 B (k2_nat_1 C 1)) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ) ) ) ) ).
tt(l39_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((r2_hidden C (k10_heyting1 A B)) =>  ((k3_lattices (k12_normform A) C (k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k11_heyting1 A B) C)) = B) ) ) ) ) ) ) ).
tt(l39_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 C B)) D) (k3_hilbert1 (k3_hilbert1 C A) D)) k6_hilbert1)) ) ) ) ) ) ) ) ).
tt(l39_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ( (~  (B = D) )  & (r1_incsp_1 A D C)) ) ) ) ) ) ) ) ) ).
tt(l39_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) D B) (k1_jordan2c 2 A)) &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((v1_ideal_1 (k3_lpspace2 A B C D) (k2_lpspace2 A B C D)) & (v1_lpspace1 (k3_lpspace2 A B C D) (k2_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(l39_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k3_finseq_1 B) = (k3_finseq_1 (k3_fvsum_1 A B C))) ) ) ) ) ) ) ) ).
tt(l39_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 3 2 1) = (k3_finseq_4 k5_numbers 1 3 2)) )  &  (~  ((k3_finseq_4 k5_numbers 2 3 1) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ).
tt(l39_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) | (v2_matrtop3 (k3_matrtop1 D D (k2_matrtop3 D A B C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(l39_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((v3_mazurulm C A B) &  ((r1_xxreal_0 (k2_newton 2 F) G) &  (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ( (H = (k21_binop_2 (k23_binop_2 (k2_newton 2 F) G) (k13_newton 2 (k23_binop_2 F 1))))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_rlvect_1 A D (k1_rlvect_1 A (k5_algstr_0 A E D) (k12_binop_2 G (k13_newton 2 (k23_binop_2 F 1)))))) = (k1_rlvect_1 B (k3_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A D (k21_binop_2 (k13_newton 2 (k23_binop_2 F 1)) G)) (k1_rlvect_1 A E H)) (k12_binop_2 1 (k2_newton 2 F))))) (k18_binop_2 1 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_metrizts,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((v3_pre_topc (a_3_5_metrizts A B C) (k3_pcomps_1 A)) & (m1_subset_1 (a_3_5_metrizts A B C) (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) ) ) ) ) ) ) ).
tt(l39_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v4_midsp_2 E B) & (l1_midsp_2 E B))  =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B E)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B E)))) =>  ( ((k7_midsp_3 A B E C F) = D)  =>  ((k10_midsp_3 A B E F) = (k9_midsp_2 B E C (k4_midsp_3 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_1 A) =>  ( (~ (v2_modelc_1 A))  &  ( (~ (v4_modelc_1 A))  &  ( (~ (v3_modelc_1 A))  &  ( (~ (v6_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ).
tt(l39_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l39_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ((r2_hidden A (u2_modelc_3 B C)) =>  ( ( (~ (v4_modelc_2 A))  &  (~ (v6_modelc_2 A)) )  |  ((r8_modelc_2 D (k14_modelc_3 B C)) <=> (r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v16_monoid_0 A) <=>  ((v14_monoid_0 A) & (v15_monoid_0 A)) ) ) ) ).
tt(l39_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((r2_hidden (k4_tarski F G) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D E)) <=>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E))))) )  &  (? [J:$i] :  ((m1_subset_1 J (k1_funct_1 (u3_msualg_1 A B) H)) &  (? [K:$i] :  ((m1_subset_1 K (k1_funct_1 (u3_msualg_1 A B) H)) &  ( ((r1_rewrite1 (k3_msualg_6 A) H E) & (m2_msualg_6 I A B H E))  &  ((r2_hidden (k4_tarski J K) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C H)) &  ( (F = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E) I J))  &  (G = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E) I K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_msualg_6 D A B) &  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ((m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( ((v3_msualg_6 E A B) & (r2_pboole (u1_struct_0 A) C E))  => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) (k3_oppcat_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(l39_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_o_ring_1 B A) => (v11_o_ring_1 B A)) ) ) ) ) ).
tt(l39_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 C 1))  & (r1_xxreal_0 (k1_newton C A) (k1_newton C B))) ) ) ) ) ) ) ) ) ).
tt(l39_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) B) (k12_finseq_1 (u1_struct_0 A) C)) D) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A B C)) D)) ) ) ) ) ) ) ) ) ).
tt(l39_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((v5_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ( (B = (k3_ratfunc1 A (k13_polynom3 A D (k4_ratfunc1 A C)) (k13_polynom3 A D (k5_ratfunc1 A C))))  & (v5_ratfunc1 C A))  =>  ( (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) =>  (~  ( (D = (k3_group_4 (k14_polynom3 A) E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) G) &  ((k1_funct_1 E F) = (k3_hurwitz A G 1)) ) ) ) ) ) ) ) ) ) ) ) )  |  (! [E:$i] :  ((m1_ratfunc1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 F A) &  ( (~ (v1_ratfunc1 F A))  & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ( (B = (k3_ratfunc1 A (k13_polynom3 A F (k4_ratfunc1 A E)) (k13_polynom3 A F (k5_ratfunc1 A E))))  & (v5_ratfunc1 E A))  =>  ( (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k14_polynom3 A))) =>  (~  ( (F = (k3_group_4 (k14_polynom3 A) G))  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 G)) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) I) &  ((k1_funct_1 G H) = (k3_hurwitz A I 1)) ) ) ) ) ) ) ) ) ) ) ) )  |  ((r2_funct_2 k5_numbers (u1_struct_0 A) D (k10_polynom3 A)) &  ((r2_funct_2 k5_numbers (u1_struct_0 A) F (k10_polynom3 A)) &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_realset2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ( (A = (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2)))  &  ( (C = c7__realset2)  & (r1_funct_2 (k2_zfmisc_1 A A) A (k2_zfmisc_1 (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2)) (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2))) (k6_subset_1 c4__realset2 (k6_domain_1 c4__realset2 c5__realset2)) B (k4_realset1 c4__realset2 c5__realset2 c11__realset2))) )  =>  ( (~ (v2_struct_0 (g2_algstr_0 A B C)))  &  ((v13_algstr_0 (g2_algstr_0 A B C)) &  ((v2_rlvect_1 (g2_algstr_0 A B C)) &  ((v3_rlvect_1 (g2_algstr_0 A B C)) &  ((v4_rlvect_1 (g2_algstr_0 A B C)) & (l2_algstr_0 (g2_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_scmbsort,ax, (~  ((k4_scmfsa_2 1) = (k4_scmfsa_2 3)) ) ).
tt(l39_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A (k1_scmfsa_m B) C) & (r6_scmfsa7b A (k1_scmfsa_m B) C))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k5_card_1 A))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))))  &  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 4 1))) k6_numbers))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) B A) (k4_scmfsa_2 (k2_nat_1 1 1))) = k6_numbers) )  &  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 4 1))) k6_numbers) =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) B A) (k4_scmfsa_2 (k2_nat_1 1 1))) = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 1 1))) 1)) ) ) ) ) ) ) ).
tt(l39_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (r1_xxreal_0 (k2_xcmplx_0 (k13_newton 2 (k2_nat_1 A 3)) (k1_newton (k4_xcmplx_0 1) (k2_nat_1 A 3))) k6_numbers)) ) ) ).
tt(l39_sincos10,ax, ((k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) = (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))) ).
tt(l39_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k19_binop_2 1) A)) )  & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 A 1) (k10_binop_2 A 1)) k6_numbers)) ) ) ) ).
tt(l39_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_sppol_1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)) &  ( (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B))  &  ( (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) C D)) &  ( (~  ((k17_euclid E) = (k17_euclid C)) )  &  ( (~  ((k17_euclid E) = (k17_euclid D)) )  &  ( (~  ((k18_euclid E) = (k18_euclid C)) )  &  (~  ((k18_euclid E) = (k18_euclid D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (v3_topreal1 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ).
tt(l39_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((k2_lattices (k5_substlat A B) C D) = (k2_lattices (k5_substlat A B) D C)) ) ) ) ) ) ) ).
tt(l39_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r1_tarski B (k1_relset_1 k1_numbers A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_taylor_1 A C B) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_tarski (k1_rcomp_1 D E) B) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A B) C) (k1_rcomp_1 D E))) & (r1_taylor_1 A (k2_nat_1 C 1) (k2_rcomp_1 D E))) )  =>  ((r1_xxreal_0 E D) |  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers F) = B)  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ((k1_seq_1 F G) = (k9_real_1 (k1_seq_1 A E) (k1_seq_1 (k3_series_1 (k6_taylor_1 A B G E)) C))) ) ) ) )  =>  ( ((k1_seq_1 F E) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 D E))) &  ((r2_fdiff_1 F (k2_rcomp_1 D E)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 F G) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A (k2_rcomp_1 D E)) (k2_nat_1 C 1)) G) (k2_newton (k9_real_1 E G) C)) (k3_newton C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) = k1_xboole_0)  |  ((k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) = (k1_tarski (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(l39_topalg_5,ax, ((k2_struct_0 (k1_tex_2 k17_borsuk_1 k18_borsuk_1)) = (k6_domain_1 k1_numbers k6_numbers)) ).
tt(l39_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_topreal1 (k15_euclid 2) A B D) &  ((r1_topreal1 (k15_euclid 2) A B E) &  ( (C = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) D E))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) D E) = (k2_tarski A B)) ) ) )  => (v1_topreal2 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l39_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k1_algstr_0 A C (k4_algstr_0 A B))) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(l39_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (r1_tarski (u1_struct_0 (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E))) (u1_struct_0 (k2_vectsp_5 A B D (k1_vectsp_5 A B C E))))) ) ) ) ) ) ) ) ) ) ).
tt(l39_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v3_waybel_3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_waybel_3 A F D) & (r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) )  => (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(l39_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r2_hidden A k1_numbers) =>  ((k2_xxreal_3 (k1_xxreal_3 A k2_xxreal_0)) = (k1_xxreal_3 (k2_xxreal_3 k2_xxreal_0) (k2_xxreal_3 A))) ) ) ) ).
tt(l3_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_diraf A B C D E) => (r2_diraf A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_algstr_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (~  ( (~  (A = (k4_struct_0 k2_vectsp_1)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  (~  ((k8_group_1 k2_vectsp_1 C A) = B) ) ) ) ) ) ) ) ) ) ).
tt(l3_ami_2,ax, (~ (r2_hidden k5_numbers k2_ami_2)) ).
tt(l3_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D F)))  =>  ((k1_rlvect_1 A B G) = (k3_rlvect_1 A (k1_rlvect_1 A C (k8_real_1 G E)) (k1_rlvect_1 A D (k8_real_1 G F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_analmetr A B C) &  ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G))) )  =>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_arithm,ax, ((k3_arytm_0 k6_numbers) = k6_numbers) ).
tt(l3_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((k8_arytm_2 A B) = (k8_arytm_2 A C))  =>  ( (A = k11_arytm_3)  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(l3_arytm_2,ax, (! [A:$i] :  (! [B:$i] :  (~ (r2_hidden (k4_tarski A B) a_0_0_arytm_2)) ) ) ).
tt(l3_asympt_1,ax, (! [A:$i] :  ( ((v1_asympt_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k6_power A C)) ) ) )  =>  ((r1_xxreal_0 A 1) | (v4_asympt_0 B)) ) ) ) ) ) ).
tt(l3_axioms,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_arytm_0 A B) = (k2_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l3_bhsp_1,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k6_numbers) (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers)))) ) ).
tt(l3_bhsp_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k10_real_1 1 (k2_nat_1 C 1))))  & (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l3_binom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k5_numbers A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers A) B)))) )  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k2_binop_1 k5_numbers A B E k6_numbers F) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k2_binop_1 k5_numbers A B E (k2_nat_1 G 1) F) = (k2_binop_1 A B B D F (k2_binop_1 k5_numbers A B E G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_borsuk_3,ax, (! [A:$i] :  ((l1_pre_topc A) => (r1_t_0topsp A A)) ) ).
tt(l3_borsuk_7,ax, ((u1_struct_0 (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1)) = (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k17_borsuk_1))) ).
tt(l3_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k9_xtuple_0 (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F))) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(l3_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (v1_ideal_1 (k2_struct_0 A) A)) ) ).
tt(l3_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r1_funct_2 k5_numbers k1_numbers k5_numbers k2_numbers A B) =>  ( ( ((v1_fdiff_1 A k6_numbers) & (v2_relat_1 A))  =>  ((v1_cfdiff_1 B k6_numbers) & (v2_relat_1 B)) )  &  ( ((v1_cfdiff_1 B k6_numbers) & (v2_relat_1 B))  =>  ((v1_fdiff_1 A k6_numbers) & (v2_relat_1 A)) ) ) ) ) ) ) ) ).
tt(l3_chord,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~ (r1_xxreal_0 B (k2_xcmplx_0 A 2)))  & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 C A) 1) (k2_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 C B) 1) 2))) ) ) ) ) ) ) ) ).
tt(l3_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m1_pboole E A B) => (m1_pboole (k16_pralg_1 A D E) A C)) ) ) ) ) ) ) ) ) ).
tt(l3_complfld,ax, ((k5_struct_0 k1_complfld) = k6_complex1) ).
tt(l3_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k8_real_1 (k3_complex1 A) (k4_complex1 B)) = (k8_real_1 (k3_complex1 B) (k4_complex1 A)))  & (r1_xxreal_0 k6_numbers (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B)))))  =>  ((k17_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k17_complex1 A) (k17_complex1 B))) ) ) ) ) ) ).
tt(l3_csspace3,ax,(m1_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3)) k7_csspace)).
tt(l3_dtconstr,ax, ((k4_finseq_1 (k14_trees_3 k1_xboole_0)) = k1_xboole_0) ).
tt(l3_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_funct_1 (k14_funct_7 A B C D)) &  ((v1_funct_2 (k14_funct_7 A B C D) k5_numbers A) & (m1_subset_1 (k14_funct_7 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ) ) ) ) ) ) ).
tt(l3_euclid_7,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ((k1_card_1 A) = (k1_card_1 B)) ) ) ) ) ) ) ).
tt(l3_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 A B) = (k1_euclid_8 (k9_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k9_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k9_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(l3_euler_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k3_int_2 1 A) = 1) ) ) ).
tt(l3_fdiff_1,ax, ((v1_funct_1 (k4_partfun2 k1_numbers k5_numbers k5_numbers k6_numbers)) &  ((v1_funct_2 (k4_partfun2 k1_numbers k5_numbers k5_numbers k6_numbers) k5_numbers k1_numbers) & (m1_subset_1 (k4_partfun2 k1_numbers k5_numbers k5_numbers k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(l3_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k4_taylor_1 (k10_real_1 1 2)))) =>  ((r2_fdiff_1 (k4_taylor_1 (k10_real_1 1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k4_taylor_1 (k10_real_1 1 2)) A) B) = (k8_real_1 (k10_real_1 1 2) (k10_prepower B (k1_real_1 (k10_real_1 1 2))))) ) ) ) ) ) ) ) ).
tt(l3_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos A) k6_numbers))  =>  ((k1_seq_1 k16_sin_cos A) = (k10_prepower (k8_real_1 (k9_real_1 1 (k1_seq_1 k19_sin_cos A)) (k7_real_1 1 (k1_seq_1 k19_sin_cos A))) (k10_real_1 1 2))) ) ) ) ).
tt(l3_fib_fusc,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (A = (k2_nat_1 (k4_nat_1 2 B) 1))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k2_xcmplx_0 6 (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 B)) 1)) 1)) = (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 A)) 1)) 1)) ) ) ) ) ) ) ).
tt(l3_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k2_xboole_0 A B))) ) ) ).
tt(l3_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  ((r2_hidden A (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))) (k39_fomodel1 C) B)) => (r1_tarski (a_2_1_fomodel3 A C) B)) ) ) ) ) ) ).
tt(l3_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (~ (v7_pre_topc A))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r2_funct_2 k5_numbers (u1_struct_0 A) D (k8_funcop_1 (u1_struct_0 A) k5_numbers B)) &  ( (~  (B = C) )  & (r1_frechet A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 B C)) B) = C) ) ) ) ) ).
tt(l3_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k1_rlvect_1 (k15_euclid 2) B A)) = (k8_real_1 A (k17_euclid B)))  &  ((k18_euclid (k1_rlvect_1 (k15_euclid 2) B A)) = (k8_real_1 A (k18_euclid B))) ) ) ) ) ) ).
tt(l3_groeb_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden C (k7_ideal_1 A B))) ) ) ) ) ) ) ).
tt(l3_heyting3,ax, (1 = (k2_nat_1 k6_numbers 1)) ).
tt(l3_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((r2_hidden C B) &  ((r2_hidden F B) &  ((r2_hidden I B) &  ((r1_aff_1 A C D G) &  ((r2_analoaf A D E G H) &  ((r2_analoaf A E F H I) &  ((r2_analoaf A D F G I) & (r2_aff_1 A D E B)) ) ) ) ) ) ) )  =>  ((r2_hidden D B) |  ( (D = E)  | (r1_aff_1 A C E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k4_numbers)) => (r1_tarski (k2_measure6 B A) k4_numbers)) ) ) ) ).
tt(l3_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_int_1 A B) =>  ((k6_int_1 B A) = k6_numbers) )  &  ( ((k6_int_1 B A) = k6_numbers)  =>  ( (A = k6_numbers)  | (r1_int_1 A B)) ) ) ) ) ) ) ).
tt(l3_integr11,ax, ((k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) = (k2_subset_1 k1_numbers)) ).
tt(l3_integr13,ax, ((m1_subset_1 (k1_real_1 1) k1_numbers) &  ((m1_subset_1 (k1_real_1 (k10_real_1 1 2)) k1_numbers) & (m1_subset_1 (k10_real_1 1 2) k1_numbers)) ) ).
tt(l3_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_integr15 E A B C) =>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden F (k4_finseq_1 C)) &  (~  ((r1_xxreal_0 (k1_seq_1 (k5_integra1 A B C) F) (k1_seq_1 E F)) &  (~ (r1_xxreal_0 (k7_real_1 (k1_seq_1 (k5_integra1 A B C) F) D) (k1_seq_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_jgraph_3,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k5_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l3_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B A))  => (r1_xxreal_0 (k4_real_1 B (k7_square_1 (k7_real_1 1 (k3_square_1 A)))) (k4_real_1 A (k7_square_1 (k7_real_1 1 (k3_square_1 B)))))) ) ) ) ) ).
tt(l3_jgraph_8,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  & (r1_xxreal_0 (k7_partfun1 k1_numbers A (k2_nat_1 B 1)) (k7_partfun1 k1_numbers A B))) ) ) ) )  => (v5_valued_0 A)) ) ) ).
tt(l3_jordan1a,ax, (1 = (k2_nat_1 (k4_nat_1 2 k6_numbers) 1)) ).
tt(l3_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 A (u1_struct_0 (k14_euclid 2)))) ) ).
tt(l3_jordan1d,ax, (2 = (k2_nat_1 (k4_nat_1 2 1) k6_numbers)) ).
tt(l3_jordan21,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden A (k2_xboole_0 (k2_xboole_0 B C) D)) &  ( (~ (r2_hidden A B))  &  ( (~ (r2_hidden A C))  &  (~ (r2_hidden A D)) ) ) ) ) ) ) ) ) ).
tt(l3_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 B C) A) => (r1_xxreal_0 C (k7_nat_d A B))) ) ) ) ) ) ) ).
tt(l3_jordan,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r1_xboole_0 A E) &  ((r1_xboole_0 B E) &  ((r1_xboole_0 C E) & (r1_xboole_0 D E)) ) )  => (r1_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D) E)) ) ) ) ) ) ).
tt(l3_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_lattice3 A))) &  ((r2_hidden D B) &  (~ (r3_orders_2 (k3_lattice3 A) D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_lattice8,ax, (~ (v1_abian 1)) ).
tt(l3_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) =>  ( ((k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))  &  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)) & (r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) ).
tt(l3_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A (k9_real_1 A (k10_real_1 1 (k2_nat_1 B 1)))))  &  (~ (r1_xxreal_0 (k7_real_1 A (k10_real_1 1 (k2_nat_1 B 1))) A)) ) ) ) ) ) ).
tt(l3_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A (k9_real_1 A (k10_real_1 1 (k2_nat_1 B 1)))))  &  (~ (r1_xxreal_0 (k7_real_1 A (k10_real_1 1 (k2_nat_1 B 1))) A)) ) ) ) ) ) ).
tt(l3_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ( ((k6_algstr_0 A D (k6_lopban_3 A C B)) = (k6_algstr_0 A (k6_lopban_3 A C B) D))  &  ((k6_algstr_0 A C (k6_lopban_3 A D B)) = (k6_algstr_0 A (k6_lopban_3 A D B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 k6_numbers (k4_power A B))) ) ) ) ) ) ).
tt(l3_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k2_matrix_1 B) = (k2_matrix_1 (k2_matrix_3 A B))) ) ) ) ) ).
tt(l3_matrix16,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden (k4_tarski B C) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))) | (r2_hidden (k4_tarski C B) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))  => (r2_hidden (k2_xcmplx_0 (k6_int_1 (k6_xcmplx_0 C B) A) 1) (k2_finseq_1 A))) ) ) ) ) ) ) ).
tt(l3_matrix_9,ax,(r2_hidden (k2_finseq_4 k5_numbers 2 1) (k12_matrix_2 2))).
tt(l3_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C)))  =>  ((k8_matrix_1 A C B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ).
tt(l3_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) ) )  => (m1_subset_1 B (u1_struct_0 (k15_euclid A)))) ) ) ) ).
tt(l3_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k1_mboolean A (k2_pboole A B C)) D) = (k1_zfmisc_1 (k2_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l3_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  ( ((k5_binop_1 1 k9_funct_5 A B) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(l3_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_mod_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_mod_4 A))) =>  ( (C = (k5_struct_0 A))  =>  ( ((k6_algstr_0 (k2_mod_4 A) B C) = B)  &  ((k6_algstr_0 (k2_mod_4 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l3_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 (k12_finseq_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) A) 1) = A)  &  ((k2_relset_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) (k12_finseq_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) A)) = (k1_tarski A)) ) ) ) ).
tt(l3_normsp_0,ax,(m1_subset_1 k6_numbers 1)).
tt(l3_normsp_1,ax,(m1_subset_1 (k4_struct_0 o_0_5_normsp_1) (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)))).
tt(l3_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v2_metric_1 (u1_metric_1 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))) (u1_struct_0 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))))) ) ).
tt(l3_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( ((k8_nat_1 k5_numbers C k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k5_numbers D E))  &  ((k8_nat_1 k5_numbers D (k2_nat_1 E 1)) = (k4_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_ordinal4,ax, (1 = (k4_card_1 k1_xboole_0)) ).
tt(l3_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k7_partfun1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) (k2_nat_1 (k3_finseq_1 C) 1)) = B) ) ) ) ) ) ) ).
tt(l3_ortsp_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1) c1__ortsp_1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1) c1__ortsp_1)))) )  &  (! [B:$i] :  ((m1_subset_1 B c1__ortsp_1) =>  (! [C:$i] :  ((m1_subset_1 C c1__ortsp_1) =>  ((k5_binop_1 c1__ortsp_1 A B C) = c2__ortsp_1) ) ) ) ) ) ) ).
tt(l3_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_algstr_0 A (k8_group_1 A B (k5_algstr_0 A C C)) (k8_group_1 A (k5_algstr_0 A D D) E)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (? [C:$i] :  ((r1_tarski (k9_xtuple_0 C) A) & (r1_tarski (k10_xtuple_0 C) B)) ) ) ) ).
tt(l3_pdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden A (k2_finseq_1 B)) => (v2_funct_2 (k1_pdiff_1 A B) k1_numbers)) ) ) ) ) ).
tt(l3_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 A 1))) ) ) ).
tt(l3_polyeq_2,ax,(v1_abian 4)).
tt(l3_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v3_orders_1 C) => (r3_orders_1 C B)) ) ) ) ) ) ).
tt(l3_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ((r2_pre_poly A B C) & (r2_pre_poly A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l3_poset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_funct_1 (k9_funct_7 B C)) &  ((v1_funct_2 (k9_funct_7 B C) A A) & (m1_subset_1 (k9_funct_7 B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ).
tt(l3_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r1_finseqop (u1_struct_0 A) (k5_vectsp_1 A) (u1_algstr_0 A))) ) ).
tt(l3_quatern2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)) (k3_square_1 D)) = k6_numbers)  =>  ( (A = k6_numbers)  &  ( (B = k6_numbers)  &  ( (C = k6_numbers)  &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 A)) (k1_radix_1 (k7_nat_d A 1))) = (k4_xcmplx_0 (k1_radix_1 (k7_nat_d A 1)))) ) ) ) ).
tt(l3_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k4_radix_1 D C (k2_xcmplx_0 A 1) (k10_radix_1 C (k2_xcmplx_0 A 1) B)) = (k4_radix_1 D C A (k10_radix_1 C A B))) ) ) ) ) ) ) ) ) ) ).
tt(l3_ramsey_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k3_group_10 A C) (k3_group_10 B C))) ) ) ) ).
tt(l3_rat_1,ax,(r2_hidden k6_numbers k4_ordinal1)).
tt(l3_realset2,ax,(r2_hidden 1 2)).
tt(l3_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden (k1_nat_1 B 1) (k4_finseq_1 A)) & (r1_xxreal_0 (k3_finseq_1 A) B)) ) ) ) ) ) ).
tt(l3_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [H:$i] :  ((m2_rlvect_2 H A (k8_domain_1 (u1_struct_0 A) B C D)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers H B) = E)  &  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers H C) = F)  &  ((k3_funct_2 (u1_struct_0 A) k1_numbers H D) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k9_xtuple_0 D)) =>  ((k1_funct_1 E F) = (k5_vectsp_2 A B C (k7_partfun1 (u1_struct_0 B) D F))) ) ) ) )  =>  ((k4_rlvect_1 B E) = (k5_vectsp_2 A B C (k4_rlvect_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_rsspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 A) B))) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 (k3_series_1 A) B))) )  &  ((v1_series_1 A) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k4_series_1 A))) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k4_series_1 A))) ) ) ) ) ) ) ) ) ).
tt(l3_rsspace3,ax,(m1_rlsub_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3)) k7_rsspace)).
tt(l3_rusub_4,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden B A))  =>  ((k6_subset_1 A (k1_tarski B)) = A) ) ) ) ).
tt(l3_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_funct_1 (k5_funcop_1 k29_binop_2 A (k6_partfun1 k2_numbers)) B) = (k5_binop_2 A B)) ) ) ) ) ).
tt(l3_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 A) = k6_numbers)  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_tarski (k1_scmfsa_7 C D) B) => (r1_extpro_1 3 k1_scmfsa_2 B A)) ) ) ) ) ) ) ) ) ) ).
tt(l3_scmfsa_9,ax,(r2_hidden k6_numbers (k2_afinsq_1 (k4_compos_1 k1_scmfsa_2)))).
tt(l3_scm_halt,ax,(r1_tarski (k7_memstr_0 3 k1_scmfsa_2 k6_numbers) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)))).
tt(l3_scmpds_i,ax,(r2_hidden (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) k1_scmpds_i)).
tt(l3_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k6_subset_1 (u1_struct_0 (k1_scmring2 A)) (k1_tarski k5_numbers)) = k2_ami_2) ) ) ).
tt(l3_scpqsort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) => (r1_tarski (k61_valued_1 A 1) (k2_scmpds_8 B C A))) ) ) ) ) ) ).
tt(l3_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)))) ) ) ) ) )  &  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)))) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A C))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A C))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(l3_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton A 3) = (k3_xcmplx_0 (k1_newton A 2) A)) ) ) ).
tt(l3_series_3,ax, ((k13_newton 2 3) = 8) ).
tt(l3_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_newton (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 3) (k2_nat_1 A 1)) (k13_newton 3 (k2_nat_1 A 1))) 2) = (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 9) (k2_nat_1 A 1)) (k13_newton 9 (k2_nat_1 A 1))) 2)) ) ) ).
tt(l3_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k9_complex1 (k9_complex1 (k13_complex1 1 A) (k13_complex1 1 B)) (k13_complex1 1 C)) = (k13_complex1 1 (k3_xcmplx_0 (k3_xcmplx_0 A B) C))) ) ) ) ) ) ) ).
tt(l3_sincos10,ax,(r1_tarski (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))).
tt(l3_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden A (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) & (r1_xxreal_0 (k1_seq_1 k16_sin_cos A) k6_numbers)) ) ) ) ).
tt(l3_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k6_xcmplx_0 (k5_square_1 (k6_sin_cos2 A)) (k5_square_1 (k3_sin_cos2 A))) = 1)  &  ((k6_xcmplx_0 (k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 A)) (k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 A))) = 1) ) ) ) ).
tt(l3_sin_cos9,ax,(r2_fdiff_1 k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))).
tt(l3_symsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_tarski k6_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_tarski k6_numbers)) =>  ((k5_binop_1 (k1_tarski k6_numbers) c3__symsp_1 A B) = c2__symsp_1) ) ) ) ) ).
tt(l3_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ( ((v1_tops_3 B A) & (v1_tops_1 C A))  |  ((v1_tops_1 B A) & (v1_tops_3 C A)) )  & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(l3_topalg_2,ax, ((u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) = (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))) ).
tt(l3_topalg_5,ax,(r1_tarski (k6_domain_1 k1_numbers k6_numbers) (u1_struct_0 k5_topmetr))).
tt(l3_topgen_4,ax, (! [A:$i] :  ((v4_card_3 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ( ((k9_xtuple_0 B) = k3_numbers)  & (r1_tarski A (k10_xtuple_0 B))) ) ) ) ) ).
tt(l3_topreal2,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1))) = k1_xboole_0) ).
tt(l3_toprealb,ax, ((v1_xreal_0 1) & (v2_xxreal_0 1)) ).
tt(l3_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A B C D) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ( (~ (r1_aff_1 A B C E))  &  ((r1_aff_1 A B C F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_aff_1 A E F G) &  ( (~  (E = G) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l3_trees_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  =>  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B)) & (r2_hidden (k1_funct_1 B (k2_nat_1 A 1)) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(l3_uniroots,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) =>  ((k5_relat_1 (k5_relat_1 A (k2_finseq_1 B)) (k2_finseq_1 C)) = (k5_relat_1 A (k2_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(l3_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k7_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ( (C = (k3_tarski B))  => (r2_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B C)) ) ) ) ) ) ) ).
tt(l3_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_relat_2 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski C B) A))  =>  (B = C) ) ) ) ) ) ) ).
tt(l3_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ( (~  ((r2_hidden A k2_arytm_2) &  ((r2_hidden B k2_arytm_2) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = C)  &  ( (B = D)  & (r1_arytm_2 C D)) ) ) ) ) ) ) ) )  &  ( (~  ((r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  ((r2_hidden B (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2)) &  (? [C:$i] :  ((m1_subset_1 C k2_arytm_2) &  (? [D:$i] :  ((m1_subset_1 D k2_arytm_2) &  ( (A = (k4_tarski k6_numbers C))  &  ( (B = (k4_tarski k6_numbers D))  & (r1_arytm_2 D C)) ) ) ) ) ) ) ) )  &  (~  ((r2_hidden B k2_arytm_2) & (r2_hidden A (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(l3_xreal_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_arytm_0 A B) = (k2_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l3_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k1_tarski A) = (k2_tarski B C))  =>  (B = C) ) ) ) ) ).
tt(l3_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A (k1_tarski B)) <=>  ( (A = k1_xboole_0)  |  (A = (k1_tarski B)) ) ) ) ) ).
tt(l3_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v2_zf_lang A) =>  ((k1_zf_model A) = (k2_tarski (k18_zf_lang A) (k19_zf_lang A))) )  &  ( ((v3_zf_lang A) =>  ((k1_zf_model A) = (k2_tarski (k18_zf_lang A) (k19_zf_lang A))) )  &  ( ((v4_zf_lang A) =>  ((k1_zf_model A) = (k1_zf_model (k20_zf_lang A))) )  &  ( ((v5_zf_lang A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (B = (k1_zf_model (k21_zf_lang A)))  &  (C = (k1_zf_model (k22_zf_lang A))) )  =>  ((k1_zf_model A) = (k3_tarski (k2_tarski B C))) ) ) ) )  &  ((v6_zf_lang A) =>  ((k1_zf_model A) = (k6_subset_1 (k3_tarski (k1_tarski (k1_zf_model (k24_zf_lang A)))) (k1_tarski (k23_zf_lang A)))) ) ) ) ) ) ) ) ).
tt(l40_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B C) D) (k3_rlvect_1 A (k3_rlvect_1 A E F) G)) = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B E) (k3_rlvect_1 A C F)) (k3_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_arytm_3,ax, (~ (v1_xboole_0 a_0_0_arytm_3)) ).
tt(l40_binop_2,ax,(m1_subset_1 1 k4_numbers)).
tt(l40_cfunct_1,ax, ((k12_complex1 (k10_complex1 k6_complex1)) = (k10_complex1 k6_complex1)) ).
tt(l40_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ((k6_algstr_0 A (k1_clopban3 A (k1_clopban4 A B)) (k1_clopban3 A (k1_clopban4 A C))) = (k1_clopban3 A (k1_clopban4 A (k3_rlvect_1 A B C)))) ) ) ) ) ) ) ) ).
tt(l40_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((k1_card_1 C) = 1) ) ) ) )  => (v1_finset_1 B)) ) )  => (v8_compl_sp A)) ) ) ).
tt(l40_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_rlvect_2 E A (k8_domain_1 (u1_struct_0 A) B C D)) =>  (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (D = B) )  &  (~  ((k6_rlvect_2 A E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 E B)) (k1_rlvect_1 A C (k1_funct_1 E C))) (k1_rlvect_1 A D (k1_funct_1 E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (a_2_0_cqc_the1 A B) (k3_cqc_lang A))) ) ) ) ).
tt(l40_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D (k7_cqc_lang A B C)) =>  ((r3_cqc_the1 A D B) & (r3_cqc_the1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(l40_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 4) & (v3_card_1 C 4))  =>  ((v3_card_1 (k8_finseq_1 A B C) 8) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 C 3))  &  ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 C 4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) 1)) ).
tt(l40_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((k5_relset_1 (k3_finseq_2 (k3_finseq_2 A)) (k3_finseq_2 A) (k8_fomodel0 A) (k6_subset_1 B (k1_tarski k1_xboole_0))) = (k5_relset_1 (k6_subset_1 (k3_finseq_2 (k3_finseq_2 A)) (k1_tarski k1_xboole_0)) (k3_finseq_2 A) (k5_fomodel0 (k3_finseq_2 A) (k11_monoid_0 A)) B)) ) ) ) ).
tt(l40_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  => (r1_tarski (k25_fomodel2 C A) (k25_fomodel2 C (k2_xcmplx_0 A B)))) ) ) ) ) ) ).
tt(l40_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_funct_2 (k4_finseq_2 B A) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B)) (k17_fomodel3 (k4_finseq_2 B A) (k13_fomodel3 A C B)) (k1_partfun1 (k4_finseq_2 B A) (k4_finseq_2 B (k8_eqrel_1 A C)) (k4_finseq_2 B (k8_eqrel_1 A C)) (k8_eqrel_1 (k4_finseq_2 B A) (k13_fomodel3 A C B)) (k8_fomodel3 A (k8_eqrel_1 A C) (k17_fomodel3 A C) B) (k19_fomodel3 A B C)))) ) ) ) ) ) ).
tt(l40_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v1_fomodel4 B A) =>  ((v4_fomodel2 (k2_xtuple_0 B) A) & (m2_subset_1 (k2_xtuple_0 B) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) ).
tt(l40_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 k30_sin_cos (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l40_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) &  ((r2_hidden (k2_nat_1 C 1) (k1_relset_1 k5_numbers B)) & (r2_hidden (k2_nat_1 C 2) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ) ).
tt(l40_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((r3_lattices (k5_substlat A B) C D) =>  (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ).
tt(l40_jgraph_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 B D)) (k9_real_1 (k6_real_1 (k6_xcmplx_0 A B) 4) (k1_real_1 (k6_real_1 (k6_xcmplx_0 A B) 4)))) => (r1_xxreal_0 (k6_real_1 (k6_xcmplx_0 A B) 2) (k6_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(l40_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_matrix_9,ax, ( (~  ((k3_finseq_4 k5_numbers 2 3 1) = (k3_finseq_4 k5_numbers 2 1 3)) )  &  (~  ((k3_finseq_4 k5_numbers 2 1 3) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ).
tt(l40_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((v3_mazurulm C A B) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_xxreal_0 F (k2_newton 2 G)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k3_rlvect_1 A (k1_rlvect_1 A D (k10_binop_2 1 (k12_binop_2 F (k2_newton 2 G)))) (k1_rlvect_1 A E (k12_binop_2 F (k2_newton 2 G))))) = (k3_rlvect_1 B (k1_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k10_binop_2 1 (k12_binop_2 F (k2_newton 2 G)))) (k1_rlvect_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k12_binop_2 F (k2_newton 2 G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_connsp_1 A B C) &  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_1 A) =>  ( (~ (v2_modelc_1 A))  &  ( (~ (v4_modelc_1 A))  &  ( (~ (v3_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ).
tt(l40_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l40_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( ((v3_group_1 A) & (v13_monoid_0 A))  => (v2_group_1 A)) ) ) ).
tt(l40_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ( ((r1_nattra_1 A B C D) & (v1_nattra_1 E A B C D))  => (r1_nattra_1 A B D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_o_ring_1 B A) => (v10_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l40_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d (k2_newton 2 A) (k2_newton 2 B)) => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(l40_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ( ( ((k2_polynom1 (k15_pre_poly A) B C) = (k1_tarski E))  &  ((k2_polynom1 (k15_pre_poly A) B D) = (k1_tarski F)) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B C D) G) = (k8_group_1 B (k5_polynom2 A B C G) (k5_polynom2 A B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k2_binom A B C) = (k5_struct_0 A))  =>  ( (B = (k4_struct_0 A))  |  ((k2_binom A (k11_algstr_0 A B) C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(l40_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ( ((k4_qc_lang3 A B (k12_qc_lang1 A)) = k1_xboole_0)  &  ( (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v2_qc_lang1 C A) =>  ((k4_qc_lang3 A B C) = (k1_qc_lang3 A (k17_qc_lang1 A C) B)) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v3_qc_lang1 C A) =>  ((k4_qc_lang3 A B C) = (k4_qc_lang3 A B (k18_qc_lang1 A C))) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v4_qc_lang1 C A) =>  ((k4_qc_lang3 A B C) = (k4_subset_1 B (k4_qc_lang3 A B (k19_qc_lang1 A C)) (k4_qc_lang3 A B (k20_qc_lang1 A C)))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v5_qc_lang1 C A) =>  ((k4_qc_lang3 A B C) = (k4_qc_lang3 A B (k22_qc_lang1 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A))  =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ( (B = (k3_ratfunc1 A (k13_polynom3 A D (k4_ratfunc1 A C)) (k13_polynom3 A D (k5_ratfunc1 A C))))  & (v5_ratfunc1 C A))  =>  ( (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) =>  (~  ( (D = (k3_group_4 (k14_polynom3 A) E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) G) &  ((k1_funct_1 E F) = (k3_hurwitz A G 1)) ) ) ) ) ) ) ) ) ) ) ) )  |  (! [E:$i] :  ((m1_ratfunc1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 F A) &  ( (~ (v1_ratfunc1 F A))  & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ( (B = (k3_ratfunc1 A (k13_polynom3 A F (k4_ratfunc1 A E)) (k13_polynom3 A F (k5_ratfunc1 A E))))  & (v5_ratfunc1 E A))  =>  ( (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k14_polynom3 A))) =>  (~  ( (F = (k3_group_4 (k14_polynom3 A) G))  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 G)) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) I) &  ((k1_funct_1 G H) = (k3_hurwitz A I 1)) ) ) ) ) ) ) ) ) ) ) ) )  |  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_revrot_1,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ( (~ (v1_sprect_2 A))  &  (~ (v1_sprect_2 (k1_goboard9 A))) ) ) ) ) ) ).
tt(l40_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) =>  ((u1_struct_0 (k1_rlsub_2 A C (k2_rlsub_2 A B D))) = (u1_struct_0 (k2_rlsub_2 A (k1_rlsub_2 A B C) (k1_rlsub_2 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l40_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_rltopsp1 B A)) ) ) ) ).
tt(l40_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k1_algstr_0 A B C)) = (k1_algstr_0 A (k4_algstr_0 A C) (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(l40_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) =>  ((u1_struct_0 (k2_rmod_3 A B D (k1_rmod_3 A B C E))) = (u1_struct_0 (k1_rmod_3 A B (k2_rmod_3 A B C D) (k2_rmod_3 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) =>  ((u1_struct_0 (k1_rusub_2 A C (k2_rusub_2 A B D))) = (u1_struct_0 (k2_rusub_2 A (k1_rusub_2 A B C) (k1_rusub_2 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l40_scmbsort,ax, (~  ((k4_scmfsa_2 1) = (k4_scmfsa_2 4)) ) ).
tt(l40_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (~  ((r1_xxreal_0 (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 1 1))) (k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 1 1)))) &  (~ (r1_xxreal_0 (k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 1 1))) k6_numbers)) ) ) ) ) ) ) ).
tt(l40_sincos10,ax,(r1_tarski (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))))).
tt(l40_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)) A)) ) ) ).
tt(l40_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v3_topreal1 A) => (v3_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l40_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_substlat A B))) =>  ((k2_lattices (k5_substlat A B) C (k2_lattices (k5_substlat A B) D E)) = (k2_lattices (k5_substlat A B) (k2_lattices (k5_substlat A B) C D) E)) ) ) ) ) ) ) ) ) ).
tt(l40_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) &  ((r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E)) &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ( ((k1_relset_1 k1_numbers F) = C)  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G C) =>  ((k1_seq_1 F G) = (k9_real_1 (k1_seq_1 B E) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C G E)) A))) ) ) )  &  ( ((k1_seq_1 F E) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 D E))) &  ((r2_fdiff_1 F (k2_rcomp_1 D E)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 F G) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) G) (k2_newton (k9_real_1 E G) A)) (k3_newton A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_tex_2,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_tarski A B) &  ( (~  (A = B) )  &  ((k6_subset_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(l40_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  (! [E:$i] :  ((m2_rcomp_3 E A B C D) =>  (~  ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) &  ((r1_xxreal_0 A B) & (v1_xboole_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l40_turing_1,ax, ((r2_hidden k6_numbers (u1_turing_1 k14_turing_1)) & (r2_hidden 1 (u1_turing_1 k14_turing_1))) ).
tt(l40_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k5_algstr_0 A (k4_algstr_0 A B) C)) = (k1_algstr_0 A C B)) ) ) ) ) ) ) ).
tt(l40_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_waybel11 C A)) ) )  => (v3_waybel11 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l40_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v1_yellow_6 C A) & (l1_waybel_0 C A)) ) ) )  =>  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v1_yellow_6 C B) & (l1_waybel_0 C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  (~  ( (~  (A = (k4_struct_0 k3_algstr_1)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_1)) =>  (~  ((k6_algstr_0 k3_algstr_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l41_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 (k8_real_1 H I) (k8_real_1 J K))) (k1_rlvect_1 A D (k8_real_1 (k8_real_1 J H) (k9_real_1 I K)))) (k1_rlvect_1 A E (k8_real_1 (k8_real_1 K I) (k9_real_1 H J)))))  &  ( (F = (k3_rlvect_1 A (k3_rlvect_1 A C (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)))  &  ( (G = (k3_rlvect_1 A (k3_rlvect_1 A C (k1_rlvect_1 A D J)) (k1_rlvect_1 A E K)))  &  ( ((k7_real_1 L M) = (k9_real_1 (k8_real_1 J K) (k8_real_1 H I)))  &  ( ((k7_real_1 (k8_real_1 L H) (k8_real_1 M J)) = (k8_real_1 (k8_real_1 J H) (k9_real_1 K I)))  &  ((k7_real_1 (k8_real_1 L I) (k8_real_1 M K)) = (k8_real_1 (k8_real_1 K I) (k9_real_1 J H))) ) ) ) ) )  =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B 1) (k1_rlvect_1 A F L)) (k1_rlvect_1 A G M)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) => (r1_tarski (k5_arytm_2 A (k5_arytm_2 B C)) (k5_arytm_2 (k5_arytm_2 A B) C))) ) ) ) ) ) ).
tt(l41_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((r2_hidden (k4_tarski A B) c2__arytm_3) =>  ((r1_arytm_3 A B) &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(l41_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_2 A B C k6_numbers) = (k1_bcialg_1 A B (k6_bcialg_4 A C k6_numbers))) ) ) ) ) ) ) ).
tt(l41_binop_2,ax,(r3_binop_1 k4_numbers c6__binop_2 k46_binop_2)).
tt(l41_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A E F) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_cat_1 G A D E) =>  (! [H:$i] :  ((m1_cat_1 H A E F) =>  ((k9_cat_3 A D F B C (k5_cat_1 A D E F G H)) = (k5_cat_1 B (k8_cat_1 A B C D) (k8_cat_1 A B C E) (k8_cat_1 A B C F) (k9_cat_3 A D E B C G) (k9_cat_3 A E F B C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rlvect_2 E A) =>  ( ((v2_convex1 E A) &  ((k3_rlvect_2 A E) = (k8_domain_1 (u1_struct_0 A) B C D)) )  =>  ( (B = C)  |  ( (C = D)  |  ( (D = B)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k1_funct_1 E B) (k1_funct_1 E C)) (k1_funct_1 E D)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E B)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E C)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E D)) &  ((k6_rlvect_2 A E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 E B)) (k1_rlvect_1 A C (k1_funct_1 E C))) (k1_rlvect_1 A D (k1_funct_1 E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k4_euclid_3 C B A) = (k4_euclid_3 F D E))  &  ((k4_euclid_3 A C B) = (k4_euclid_3 E F D)) )  =>  ( (A = B)  |  ( (A = C)  |  ( (B = C)  |  ( (D = E)  |  ( (D = F)  |  ( (E = F)  |  ( ((k4_euclid_3 C B A) = k32_sin_cos)  |  ( ((k4_euclid_3 B A C) = k32_sin_cos)  |  ( ((k4_euclid_3 A C B) = k32_sin_cos)  |  ( ((k4_euclid_3 F D E) = k32_sin_cos)  |  ( ((k4_euclid_3 D E F) = k32_sin_cos)  |  ( ((k4_euclid_3 E F D) = k32_sin_cos)  |  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) F E))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_fib_num4,ax, (~  ((k6_xcmplx_0 1 (k7_square_1 5)) = k6_numbers) ) ).
tt(l41_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_partfun1 (k16_funcop_1 k1_xboole_0 k1_xboole_0) (k5_fomodel0 (k3_finseq_2 A) (k11_monoid_0 A)))) ) ).
tt(l41_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k25_fomodel2 A k6_numbers) = (k32_fomodel1 A)) ) ) ).
tt(l41_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E B) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 C A) B) &  ((v1_fomodel3 F (k13_fomodel3 A D C) E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C A) B)))) ) )  => (r2_relset_1 (k4_finseq_2 C (k8_eqrel_1 A D)) (k8_eqrel_1 B E) (k1_partfun1 (k4_finseq_2 C (k8_eqrel_1 A D)) (k8_eqrel_1 (k4_finseq_2 C A) (k13_fomodel3 A D C)) (k8_eqrel_1 (k4_finseq_2 C A) (k13_fomodel3 A D C)) (k8_eqrel_1 B E) (k19_fomodel3 A C D) (k16_fomodel3 (k4_finseq_2 C A) B (k13_fomodel3 A D C) E F)) (k4_relset_1 (k4_finseq_2 C (k8_eqrel_1 A D)) (k4_finseq_2 C A) (k4_finseq_2 C A) (k8_eqrel_1 B E) (k8_fomodel3 (k8_eqrel_1 A D) A (k3_relset_1 A (k8_eqrel_1 A D) (k17_fomodel3 A D)) C) (k1_partfun1 (k4_finseq_2 C A) B B (k8_eqrel_1 B E) F (k17_fomodel3 B E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ((v8_fomodel4 A C D B) =>  ((v4_fomodel2 A C) & (m2_subset_1 A (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ).
tt(l41_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v1_glib_001 (k1_glib_001 A B) A) &  ((v2_glib_001 (k1_glib_001 A B) A) &  ((v3_glib_001 (k1_glib_001 A B) A) &  ((v4_glib_001 (k1_glib_001 A B) A) & (v5_glib_001 (k1_glib_001 A B) A)) ) ) ) ) ) ) ) ).
tt(l41_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  ((r2_groeb_2 A C D E F) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((r2_hidden H (k4_finseq_1 F)) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 I A C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 J (k15_pre_poly A) C) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ( ((k1_funct_1 F H) = (k9_polynom1 A C I J))  & (r2_hidden J E))  =>  ((k3_polynom1 A C (k9_polynom1 A C I J) G) = (k4_struct_0 C)) ) ) ) ) ) ) ) )  =>  ((k3_polynom1 A C D G) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) &  ((r2_hidden D (k10_heyting1 A C)) &  ( ((k10_normform A (k3_heyting1 A D) (k2_heyting1 A B)) = k1_xboole_0)  &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((r2_hidden E (k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k11_heyting1 A C) D)) => (r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B) (k7_normform A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 B A D E) =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ( (F = (k1_instalg1 B A C D E))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((r1_rewrite1 (k3_msualg_6 B) G H) =>  ((r1_rewrite1 (k3_msualg_6 A) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D H)) &  (! [I:$i] :  ((m2_msualg_6 I B F G H) => (m2_msualg_6 I A C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ((r1_tarski (k2_rcomp_1 A B) (k9_xtuple_0 D)) &  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden E (k2_rcomp_1 A B)) =>  ((k1_seq_1 D E) = (k4_integra5 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(l41_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 (k1_jordan1a (k1_jordan8 A B))) & (r1_xxreal_0 (k1_jordan1a (k1_jordan8 A B)) (k3_finseq_1 (k1_jordan8 A B)))) ) ) ) ) ).
tt(l41_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) D B) (k1_jordan2c 2 A)) &  (D = (k3_finseq_1 (k1_jordan8 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((k8_matrix_1 (u1_struct_0 A) (k3_matrix_3 A B C) D) = (k3_fvsum_1 A (k8_matrix_1 (u1_struct_0 A) B D) (k8_matrix_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k9_xtuple_0 (k9_matrlin A B C D)) = (k9_xtuple_0 C)) ) ) ) ) ) ) ) ) ).
tt(l41_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v2_matrtop3 B A) & (v2_matrtop3 C A))  => (v2_matrtop3 (k1_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C B) A)) ) ) ) ) ) ) ).
tt(l41_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (v6_supinf_2 (k55_valued_1 A k2_numbers B))) ) ) ) ).
tt(l41_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_modelc_2 A) =>  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  (~ (v7_modelc_2 A)) ) ) ) ) ) ) ) ) ).
tt(l41_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ( ((r2_hidden A (u2_modelc_3 B C)) & (v5_modelc_2 A))  =>  ((r8_modelc_2 D (k14_modelc_3 B C)) <=>  ((r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A))) | (r8_modelc_2 D (k14_modelc_3 B (k6_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_o_ring_1 B A) => (v11_o_ring_1 B A)) ) ) ) ) ).
tt(l41_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_polynom1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_polynom1 A B))) =>  ( (D = (k5_struct_0 (k11_polynom1 A B)))  =>  ( ((k6_algstr_0 (k11_polynom1 A B) C D) = C)  &  ((k6_algstr_0 (k11_polynom1 A B) D C) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  &  ((k2_polynom1 (k15_pre_poly A) B C) = (k1_tarski D)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B D C) E) = (k8_group_1 B (k5_polynom2 A B D E) (k5_polynom2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k2_binom A (k11_algstr_0 A B) C) = (k5_struct_0 A))  =>  ( (B = (k4_struct_0 A))  |  ((k2_binom A B C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(l41_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_polyred A B C (k7_polynom1 A C) D)) ) ) ) ) ) ) ) ).
tt(l41_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  ( ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k10_real_1 1 B)) 1) = B)  &  ( ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k10_real_1 1 B)) (k1_nat_1 A 2)) = k6_numbers)  &  ( ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) k6_numbers) = k6_numbers)  &  ( ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) 1) = B)  &  ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) (k1_nat_1 A 2)) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(l41_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_rltopsp1 (k3_convex1 A B) A)) ) ) ) ).
tt(l41_rlvect_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_rlvect_5 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k1_rlvect_5 B)) &  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C B))  =>  (~  ((k1_rlvect_5 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(l41_rsspace4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(l41_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ((k3_rusub_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(l41_scmbsort,ax, (~  ((k4_scmfsa_2 1) = (k4_scmfsa_2 5)) ) ).
tt(l41_scmisort,ax, ( (~ (v1_xboole_0 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))))  &  ((v1_relat_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) &  ((v4_relat_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))) k5_numbers) &  ((v5_relat_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) &  ((v1_finset_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) &  ((v1_afinsq_1 (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) &  ((v2_scm_halt (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) & (v1_scmfsa7b (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))))) ) ) ) ) ) ) ) ).
tt(l41_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~ (r1_xxreal_0 (k10_binop_2 (k11_binop_2 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)) (k7_square_1 (k9_binop_2 (k3_square_1 B) 1))) (k11_binop_2 A B)) k6_numbers)) ) ) ) ) ).
tt(l41_sin_cos9,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))) (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))))).
tt(l41_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v3_topreal1 A) => (v3_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l41_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l41_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k1_binop_1 (u1_lattices (k5_substlat A B)) C (k1_binop_1 (u2_lattices (k5_substlat A B)) D E)) = (k1_binop_1 (u2_lattices (k5_substlat A B)) (k1_binop_1 (u1_lattices (k5_substlat A B)) C D) (k1_binop_1 (u1_lattices (k5_substlat A B)) C E))) ) ) ) ) ) ) ) ) ).
tt(l41_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (v4_vectsp_2 (k4_vectsp_2 A) A)) ) ).
tt(l41_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) =>  ((u1_struct_0 (k2_vectsp_5 A B D (k1_vectsp_5 A B C E))) = (u1_struct_0 (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l41_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_waybel11 B A) & (v3_waybel11 C A))  => (v3_waybel11 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(l41_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r1_tarski (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)) B)) ) ) ) ).
tt(l41_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  ((k6_yellow_6 A) = (k6_yellow_6 B)) ) ) ) ) ) ).
tt(l42_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 C A) & (r2_hidden B C))  =>  ((k2_aff_4 A B C) = C) ) ) ) ) ) ) ) ).
tt(l42_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  (~  ( (~  (A = (k4_struct_0 k3_algstr_1)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_1)) =>  (~  ((k6_algstr_0 k3_algstr_1 C A) = B) ) ) ) ) ) ) ) ) ) ).
tt(l42_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k3_rlvect_1 A C (k1_rlvect_1 A D G)) (k1_rlvect_1 A E H)))  &  ( (F = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C K) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E (k8_real_1 K H))))  &  ( (K = L)  &  (I = (k8_real_1 L G)) ) ) )  =>  (F = (k1_rlvect_1 A B K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k5_arytm_2 A (k5_arytm_2 B C)) = (k5_arytm_2 (k5_arytm_2 A B) C)) ) ) ) ) ) ) ).
tt(l42_binop_2,ax,(r3_binop_1 k5_numbers 1 k48_binop_2)).
tt(l42_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_c0sp1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_c0sp1 A))) =>  ( (C = (k4_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)))  =>  ( ((k6_algstr_0 (k11_c0sp1 A) B C) = B)  &  ((k6_algstr_0 (k11_c0sp1 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l42_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))) =>  ( ((r2_hidden B (k6_c0sp2 A)) & (r2_hidden C (k6_c0sp2 A)))  => (r2_hidden (k3_rlvect_1 (k12_funcsdom (u1_struct_0 A)) B C) (k6_c0sp2 A))) ) ) ) ) ) ) ).
tt(l42_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k9_cat_3 A D D B C (k4_cat_1 A D)) = (k4_cat_1 B (k8_cat_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(l42_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k5_cqc_lang A) (a_2_0_cqc_the1 A B))) ) ) ) ).
tt(l42_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r5_cqc_the3 A B C) & (r5_cqc_the3 A D E))  => (r1_cqc_the3 A (k7_cqc_lang A B D) (k7_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 8) & (v3_card_1 C 8))  =>  ((v3_card_1 (k8_finseq_1 A B C) 16) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 B 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 B 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 B 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 B 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 9) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 10) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 11) = (k1_funct_1 C 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 12) = (k1_funct_1 C 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 13) = (k1_funct_1 C 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 14) = (k1_funct_1 C 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 15) = (k1_funct_1 C 7))  &  ((k1_funct_1 (k8_finseq_1 A B C) 16) = (k1_funct_1 C 8)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_dtconstr,ax, (k6_numbers = (k3_funct_2 (k4_dtconstr k5_dtconstr) k5_numbers k12_dtconstr (k8_nat_1 (k4_dtconstr k5_dtconstr) k14_dtconstr k6_numbers))) ).
tt(l42_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( ((k3_funct_2 k5_numbers k5_numbers B k6_numbers) = 1)  &  ( ((k3_funct_2 k5_numbers k5_numbers B 1) = 2)  &  ((k3_funct_2 k5_numbers k5_numbers B 2) = A) ) ) ) ) ) ) ).
tt(l42_fib_num4,ax, (~ (r1_xxreal_0 (k3_square_1 (k6_xcmplx_0 1 (k7_square_1 5))) k6_numbers)) ).
tt(l42_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v3_fomodel0 B A) & (r1_tarski C B))  => (v3_fomodel0 C A)) ) ) ) ) ).
tt(l42_fomodel1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v14_fomodel1 C (k2_xcmplx_0 A 1) B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  ( (~ (v14_fomodel1 C A B))  &  (! [D:$i] :  ( ((v8_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  (! [E:$i] :  ((m2_subset_1 E (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 B)) (k3_funct_2 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 B))) (k28_fomodel1 B) A))) =>  (~  ((v3_card_1 E (k1_int_2 (k19_fomodel1 B D))) &  (C = (k7_finseq_1 (k4_matrix_2 (k1_fomodel1 B) D) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k3_finseq_2 (k15_fomodel1 B)) (k21_fomodel1 B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_partfun1 D B) &  ((v1_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (v5_relat_1 C B))  => (v1_fomodel3 C (k3_fomodel2 (k1_tarski A)) D)) ) ) ) ) ) ) ) ).
tt(l42_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) => (v10_fomodel4 (k33_fomodel2 A) A B)) ) ) ) ).
tt(l42_funct_9,ax,(v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) k32_sin_cos)).
tt(l42_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A B D C) =>  ((k3_finseq_1 (k2_glib_001 A B D C)) = 3) ) ) ) ) ) ) ).
tt(l42_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E B) =>  ( ( (D = E)  &  ((r3_group_10 C A D) & (m1_group_2 B A)) )  => (r3_group_10 C B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) => (r1_struct_0 C (k1_group_1 B))) ) ) ) ) ).
tt(l42_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m3_cat_2 C B) =>  (! [D:$i] :  ((m2_cat_1 D A C) => (m2_cat_1 D A B)) ) ) ) ) ) ) ) ).
tt(l42_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (~  ( ((k2_hurwitz A C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (D = (k5_card_1 (k6_polynom5 A C)))  & (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski (k3_setfam_1 B (k2_setfam_1 C D)) (k2_setfam_1 (k3_setfam_1 B C) (k3_setfam_1 B D)))) ) ) ) ) ) ) ).
tt(l42_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))) (k5_square_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))))) ) ) ) ) ).
tt(l42_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))))  => (r2_hidden (k4_tarski (k1_jordan1a (k1_jordan8 A B)) C) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ).
tt(l42_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) &  (D = (k1_matrix_1 (k1_jordan8 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_matrix15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = k1_xboole_0)  &  ((k1_matrix_1 C) = k1_xboole_0) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l42_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers E F) C)) )  =>  ((r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k11_mesfun7c A E) D) C) & (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k12_mesfun7c A E) D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ( ((r2_hidden A (u2_modelc_3 B C)) & (v7_modelc_2 A))  =>  ((r8_modelc_2 D (k14_modelc_3 B C)) <=>  ((r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A))) | (r8_modelc_2 D (k14_modelc_3 B (k6_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ( ((r2_nattra_1 A B C D) & (v1_nattra_1 E A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_cat_1 H A F G) =>  ((k5_cat_1 B (k8_cat_1 A B D F) (k8_cat_1 A B D G) (k8_cat_1 A B C G) (k9_cat_3 A F G B D H) (k4_nattra_1 A B D C (k8_nattra_1 A B C D E) G)) = (k5_cat_1 B (k8_cat_1 A B D F) (k8_cat_1 A B C F) (k8_cat_1 A B C G) (k4_nattra_1 A B D C (k8_nattra_1 A B C D E) F) (k9_cat_3 A F G B C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_ndiff_4,ax, ( ((k1_relset_1 (k1_euclid 1) (k1_pdiff_1 1 1)) = (k1_euclid 1))  &  ( ((k1_rvsum_1 (k1_pdiff_1 1 1)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((k1_seq_1 (k1_pdiff_1 1 1) (k12_finseq_1 k1_numbers A)) = A)  &  ((k1_funct_1 (k2_funct_1 (k1_pdiff_1 1 1)) A) = (k12_finseq_1 k1_numbers A)) ) ) ) ) ) ).
tt(l42_normform,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (a_1_1_normform A))) ).
tt(l42_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l42_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B (k4_polynom7 A B D) C) E) = (k8_group_1 B D (k5_polynom2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  => (v5_orders_3 (k8_poset_1 A B C) A B)) ) ) ) ) ) ).
tt(l42_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  &  ((v5_ratfunc1 B A) & (m1_ratfunc1 B A)) )  =>  ((k11_ratfunc1 A B) = (k6_ratfunc1 A B)) ) ) ) ) ).
tt(l42_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) => (r1_tarski (u1_struct_0 (k1_rmod_3 A B C (k2_rmod_3 A B D E))) (u1_struct_0 (k2_rmod_3 A B (k1_rmod_3 A B D C) (k1_rmod_3 A B C E))))) ) ) ) ) ) ) ) ) ) ).
tt(l42_scmbsort,ax, (~  ((k4_scmfsa_2 1) = (k4_scmfsa_2 6)) ) ).
tt(l42_scmfsa10,ax, (~  ((k4_scmfsa_2 k6_numbers) = (k4_scmfsa_2 1)) ) ).
tt(l42_scmisort,ax, (~ (r4_scmfsa7b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k4_scmfsa_2 (k2_nat_1 3 1)))) ).
tt(l42_scmpds_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_tarski (k61_valued_1 A 1) (k1_scmpds_7 B C D A))) ) ) ) ) ) ) ) ).
tt(l42_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k5_card_1 (k2_scpqsort D C)) = 57)  &  ((r1_xxreal_0 7 C) =>  ((r2_scmpds_6 (k2_scpqsort D C) B A) &  (? [E:$i] :  ((m2_finseq_1 E k4_numbers) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  ( ((k3_finseq_1 E) = D)  &  ((r1_scpisort E B C) &  ( ((k3_finseq_1 F) = D)  &  ((r1_scpisort F (k6_scmpds_4 (k2_scpqsort D C) B A) C) &  ((r2_classes1 E F) & (r3_graph_2 F 1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))) k6_numbers)) ) ) ) ).
tt(l42_sin_cos9,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))) (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))))).
tt(l42_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((v3_topreal1 A) => (v3_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(l42_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l42_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ( (~  (A = B) )  &  ((k6_xcmplx_0 (k3_square_1 (k6_square_1 A)) (k3_square_1 (k6_square_1 B))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l42_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((k2_lattices (k5_substlat A B) C (k1_lattices (k5_substlat A B) C D)) = C) ) ) ) ) ) ) ).
tt(l42_topreal2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_struct_0 A) &  ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B)) )  => (v2_struct_0 B)) ) ) ) ) ) ) ).
tt(l42_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r2_borsuk_3 (k8_toprealb A) (k7_toprealb A C B))) ) ) ) ) ) ).
tt(l42_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k14_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)))) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (A = (k3_xtuple_0 B C D))  =>  ( (B = 5)  |  ((k9_turing_1 k14_turing_1 A) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 k14_turing_1) (u1_turing_1 k14_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k14_turing_1 A)) (k2_xcmplx_0 (k7_turing_1 k14_turing_1 A) (k6_turing_1 k14_turing_1 (k8_turing_1 k14_turing_1 A))) (k5_turing_1 k14_turing_1 (k3_mcart_1 (u2_turing_1 k14_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)) A) (k7_turing_1 k14_turing_1 A) (k2_mcart_1 (u2_turing_1 k14_turing_1) (u1_turing_1 k14_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k14_turing_1 A))))) ) ) ) ) ) ) ) ).
tt(l42_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k6_vectsp_2 A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k6_vectsp_2 A B))) =>  ( ((k4_vectsp_1 A (k6_vectsp_2 A B) C (k3_rlvect_1 (k6_vectsp_2 A B) G H)) = (k3_rlvect_1 (k6_vectsp_2 A B) (k4_vectsp_1 A (k6_vectsp_2 A B) C G) (k4_vectsp_1 A (k6_vectsp_2 A B) C H)))  &  ( ((k4_vectsp_1 A (k6_vectsp_2 A B) (k3_rlvect_1 A C D) G) = (k3_rlvect_1 (k6_vectsp_2 A B) (k4_vectsp_1 A (k6_vectsp_2 A B) C G) (k4_vectsp_1 A (k6_vectsp_2 A B) D G)))  &  ( ((k4_vectsp_1 A (k6_vectsp_2 A B) (k6_algstr_0 A C D) G) = (k4_vectsp_1 A (k6_vectsp_2 A B) C (k4_vectsp_1 A (k6_vectsp_2 A B) D G)))  &  ( ((k4_vectsp_1 A (k6_vectsp_2 A B) (k1_group_1 A) G) = G)  &  ( ((k5_vectsp_2 B (k6_vectsp_2 A B) E (k3_rlvect_1 (k6_vectsp_2 A B) G H)) = (k3_rlvect_1 (k6_vectsp_2 A B) (k5_vectsp_2 B (k6_vectsp_2 A B) E G) (k5_vectsp_2 B (k6_vectsp_2 A B) E H)))  &  ( ((k5_vectsp_2 B (k6_vectsp_2 A B) (k3_rlvect_1 B E F) G) = (k3_rlvect_1 (k6_vectsp_2 A B) (k5_vectsp_2 B (k6_vectsp_2 A B) E G) (k5_vectsp_2 B (k6_vectsp_2 A B) F G)))  &  ( ((k5_vectsp_2 B (k6_vectsp_2 A B) (k6_algstr_0 B F E) G) = (k5_vectsp_2 B (k6_vectsp_2 A B) E (k5_vectsp_2 B (k6_vectsp_2 A B) F G)))  &  ( ((k5_vectsp_2 B (k6_vectsp_2 A B) (k1_group_1 B) G) = G)  &  ((k4_vectsp_1 A (k6_vectsp_2 A B) C (k5_vectsp_2 B (k6_vectsp_2 A B) E G)) = (k5_vectsp_2 B (k6_vectsp_2 A B) E (k4_vectsp_1 A (k6_vectsp_2 A B) C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_3_waybel17 A B C D))) ) )  => (v22_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(l42_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v3_waybel11 (k2_struct_0 A) A)) ) ).
tt(l42_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_orders_2 B) => (r1_yellow_2 (u1_struct_0 A) B C C)) ) ) ) ) ) ) ).
tt(l42_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D C))  =>  ((k5_waybel11 (k3_yellow_3 C A)) = (u1_pre_topc (k2_borsuk_1 D B))) ) ) ) ) ) )  <=>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D C))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E (k3_yellow_3 C A)))  =>  ((g1_pre_topc (u1_struct_0 E) (u1_pre_topc E)) = (k2_borsuk_1 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l42_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (r1_tarski A (k3_tarski B))) ) ) ).
tt(l43_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_1)) =>  ( ((k6_algstr_0 k3_algstr_1 A B) = (k6_algstr_0 k3_algstr_1 A C))  =>  ( (A = (k4_struct_0 k3_algstr_1))  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(l43_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (~  ( ((k5_arytm_2 A B) = k11_arytm_3)  &  ( (~  (A = k11_arytm_3) )  &  (~  (B = k11_arytm_3) ) ) ) ) ) ) ) ) ).
tt(l43_arytm_3,ax,(r1_tarski k4_ordinal1 k5_arytm_3)).
tt(l43_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = (k1_autalg_1 A))  &  (! [C:$i] :  ((r2_hidden C (k1_autalg_1 A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) ) )  =>  ((k10_xtuple_0 B) = (k5_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))) ) ) ) ) ) ).
tt(l43_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))) =>  ((r2_hidden C (k6_c0sp2 A)) => (r2_hidden (k1_rlvect_1 (k12_funcsdom (u1_struct_0 A)) C B) (k6_c0sp2 A))) ) ) ) ) ) ) ).
tt(l43_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_wellord2 A B) =>  (A = B) ) ) ) ) ) ).
tt(l43_card_5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski B A) => (v1_finset_1 (k2_wellord2 (k1_wellord2 B)))) ) ) ) ) ).
tt(l43_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k5_cc0sp2 A) B C) = (k5_algstr_0 (k7_cc0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) B) B) (a_2_0_cqc_the1 A C))) ) ) ) ) ) ).
tt(l43_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (A = (k3_funct_2 (k4_dtconstr k5_dtconstr) k5_numbers k12_dtconstr (k8_nat_1 (k4_dtconstr k5_dtconstr) k14_dtconstr A)))  =>  ((k2_nat_1 A 1) = (k3_funct_2 (k4_dtconstr k5_dtconstr) k5_numbers k12_dtconstr (k8_nat_1 (k4_dtconstr k5_dtconstr) k14_dtconstr (k2_nat_1 A 1)))) ) ) ) ).
tt(l43_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_funct_1 (k4_equation A) B)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_pralg_2 E D A) =>  ( (! [F:$i] :  ((m1_subset_1 F D) => (r1_equation A (k5_pralg_2 D A E F) B C)) )  => (r1_equation A (k14_pralg_2 D A E) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k4_euclid_3 C B A) = (k4_euclid_3 D E F))  &  ((k4_euclid_3 A C B) = (k4_euclid_3 E F D)) )  =>  ( (A = B)  |  ( (A = C)  |  ( (B = C)  |  ( (D = E)  |  ( (D = F)  |  ( (E = F)  |  ( ((k4_euclid_3 C B A) = k32_sin_cos)  |  ( ((k4_euclid_3 B A C) = k32_sin_cos)  |  ( ((k4_euclid_3 A C B) = k32_sin_cos)  |  ( ((k4_euclid_3 D E F) = k32_sin_cos)  |  ( ((k4_euclid_3 E F D) = k32_sin_cos)  |  ( ((k4_euclid_3 F D E) = k32_sin_cos)  |  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D F))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A C)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_fib_num4,ax, (~ (r1_xxreal_0 (k3_power (k6_xcmplx_0 1 (k7_square_1 5)) 2) k6_numbers)) ).
tt(l43_fomodel1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v14_fomodel1 C (k2_xcmplx_0 A 1) B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (? [D:$i] :  ( ((v8_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  &  (? [E:$i] :  ((m2_subset_1 E (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 B)) (k3_funct_2 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 B))) (k28_fomodel1 B) A))) &  ((v3_card_1 E (k1_int_2 (k19_fomodel1 B D))) &  (C = (k7_finseq_1 (k4_matrix_2 (k1_fomodel1 B) D) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k3_finseq_2 (k15_fomodel1 B)) (k21_fomodel1 B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_partfun1 A (k8_eqrel_1 A (k3_fomodel2 A)) (k10_eqrel_1 A) A (k17_fomodel3 A (k3_fomodel2 A)) (k15_fomodel3 A)) = (k3_fomodel2 A)) ) ) ).
tt(l43_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k24_gfacirc1 A B C)))  &  ( (H = (k1_funct_1 F D))  &  (I = (k1_funct_1 F E)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 G) I))  &  ( ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 E D) k3_gfacirc1)) = (k10_margrel1 I (k9_margrel1 H)))  &  ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 H) (k9_margrel1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_funct_9,ax,(v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k19_sin_cos) k32_sin_cos)).
tt(l43_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C F) (k1_rlvect_1 A D G)))  &  (E = (k3_rlvect_1 A (k1_rlvect_1 A C H) (k1_rlvect_1 A D I))) )  =>  ( ((k3_rlvect_1 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k7_real_1 F H)) (k1_rlvect_1 A D (k7_real_1 G I))))  &  ((k5_algstr_0 A B E) = (k3_rlvect_1 A (k1_rlvect_1 A C (k9_real_1 F H)) (k1_rlvect_1 A D (k9_real_1 G I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k10_glib_000 A) B) C) & (r2_hidden (k1_funct_1 (k11_glib_000 A) B) C)) )  <=> (r2_hidden B (k21_glib_000 A C))) ) ) ) ) ).
tt(l43_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A B D C) =>  ( ((k3_glib_001 A (k2_glib_001 A B D C)) = B)  &  ( ((k4_glib_001 A (k2_glib_001 A B D C)) = D)  & (r1_glib_001 A B D (k2_glib_001 A B D C))) ) ) ) ) ) ) ) ).
tt(l43_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~  (A = k6_numbers) )  => (r2_int_1 (k6_int_1 B A) B A)) ) ) ) ) ).
tt(l43_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k5_group_1 C (k23_binop_2 A B) D) = (k6_algstr_0 C (k5_group_1 C A D) (k5_group_1 C B D))) ) ) ) ) ) ) ) ) ).
tt(l43_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_struct_0 C D) & (r1_struct_0 C E))  => (r1_struct_0 C (k6_algstr_0 B D E))) ) ) ) ) ) ) ) ) ) ).
tt(l43_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k13_glib_001 A (k2_helly A B C))) =>  ((k9_subset_1 (k6_glib_000 A) (k9_subset_1 (k6_glib_000 A) (k13_glib_001 A (k2_helly A B C)) (k13_glib_001 A (k2_helly A C D))) (k13_glib_001 A (k2_helly A D B))) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(l43_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (B = 2)  & (r2_hidden B (k4_finseq_1 A)))  =>  ((k1_recdef_1 (k13_idea_1 A) B) = (k1_recdef_1 A 3)) ) ) ) ) ) ).
tt(l43_jgraph_2,ax, ((v4_pre_topc a_0_5_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_5_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l43_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))))  => (r2_hidden (k4_tarski C (k1_jordan1a (k1_jordan8 A B))) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ).
tt(l43_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) )  =>  ( (B = C)  |  ( ((r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B)) &  (~  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) ) )  | (r1_jordan3 (k4_jordan3 A B C) B C)) ) ) ) ) ) ) ) ) ).
tt(l43_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  => (r1_tarski (k10_lopclset A) (k1_lopclset (k11_lopclset A)))) ) ).
tt(l43_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A) (k6_algstr_0 A B C)) = (k6_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A) B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A) C))) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A) (k1_group_1 A)) = (k1_group_1 A)) ) ) ) ).
tt(l43_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ( ((r2_hidden A (u2_modelc_3 B C)) & (v8_modelc_2 A))  =>  ((r8_modelc_2 D (k14_modelc_3 B C)) <=>  ((r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A))) | (r8_modelc_2 D (k14_modelc_3 B (k6_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((r2_hidden (k4_tarski F G) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D E)) <=>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E))))) )  &  (? [J:$i] :  ((m1_subset_1 J (k1_funct_1 (u3_msualg_1 A B) H)) &  (? [K:$i] :  ((m1_subset_1 K (k1_funct_1 (u3_msualg_1 A B) H)) &  ( ( (H = E)  &  (? [L:$i] :  ((m1_msualg_6 L A B) &  (I = (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) L H)) ) ) )  &  ((r2_hidden (k4_tarski J K) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C H)) &  ( (F = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E) I J))  &  (G = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) H) (k1_funct_1 (u3_msualg_1 A B) E) I K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_msualg_6 D A B) &  ((r2_pboole (u1_struct_0 A) C D) &  (! [E:$i] :  ((m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( ((v4_msualg_6 E A B) & (r2_pboole (u1_struct_0 A) C E))  => (r2_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ( ((r2_nattra_1 A B C D) & (v1_nattra_1 E A B C D))  => (r2_nattra_1 A B D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k7_euclid 3 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k1_euclid_8 (k7_real_1 A D) (k7_real_1 B E) (k7_real_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B C (k4_polynom7 A B D)) E) = (k8_group_1 B (k5_polynom2 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r3_orders_2 A C (k1_yellow_0 A B))) ) ) ) ) ) ) ).
tt(l43_prepower,ax, ((k2_real_1 1) = 1) ).
tt(l43_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v3_rinfsup2 A) & (v8_valued_0 A))  =>  ((v7_mesfunc5 A) &  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k2_rinfsup2 A)) ) ) ) ) ) ).
tt(l43_scmbsort,ax, (~  ((k4_scmfsa_2 2) = (k4_scmfsa_2 3)) ) ).
tt(l43_scmfsa10,ax, (~  ((k5_scmfsa_2 k6_numbers) = (k4_scmfsa_2 k6_numbers)) ) ).
tt(l43_scmisort,ax, (~ (r4_scmfsa7b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) ).
tt(l43_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos5 (k4_xcmplx_0 A)) = (k1_real_1 (k1_sin_cos5 A))) ) ) ).
tt(l43_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k12_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k9_binop_2 (k3_square_1 A) 1)) (k19_binop_2 1))) ) ) ) ).
tt(l43_sin_cos9,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))))).
tt(l43_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l43_topreal2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_struct_0 B) &  ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A)) )  => (v2_struct_0 A)) ) ) ) ) ) ) ).
tt(l43_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (r1_tarski (u1_struct_0 (k1_vectsp_5 A B C (k2_vectsp_5 A B D E))) (u1_struct_0 (k2_vectsp_5 A B (k1_vectsp_5 A B D C) (k1_vectsp_5 A B C E))))) ) ) ) ) ) ) ) ) ) ).
tt(l43_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C))) &  ((v22_waybel_0 D B (k6_yellow_1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C)))))) ) )  =>  ((r2_hidden D (k9_funct_2 (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 C)))) &  ((r1_tarski (k10_xtuple_0 (k10_funct_6 D)) (k9_funct_2 (u1_struct_0 B) (u1_struct_0 C))) &  ((k9_xtuple_0 (k10_funct_6 D)) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(l43_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)) B (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)))) => (v5_orders_3 B A (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ) ).
tt(l43_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_waybel_5 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_3_waybel_5 A B C))) ) ) ) ) ) ) ).
tt(l43_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_relat_1 (k2_tarski (k4_tarski A B) (k4_tarski B B)) (k1_tarski (k4_tarski B C))) = (k2_tarski (k4_tarski A C) (k4_tarski B C))) ) ) ) ).
tt(l43_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( ((u1_struct_0 C) = B)  => (v7_zmodul01 B A)) ) ) ) ) ) ) ).
tt(l44_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_1)) =>  ( ((k6_algstr_0 k3_algstr_1 B A) = (k6_algstr_0 k3_algstr_1 C A))  =>  ( (A = (k4_struct_0 k3_algstr_1))  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(l44_borsuk_7,ax, ((u1_struct_0 (k8_toprealb 3)) = (k3_topreal9 3 (k4_euclid_5 k6_numbers k6_numbers k6_numbers) 1)) ).
tt(l44_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))) =>  ((r2_hidden B (k6_c0sp2 A)) => (r2_hidden (k4_algstr_0 (k12_funcsdom (u1_struct_0 A)) B) (k6_c0sp2 A))) ) ) ) ) ).
tt(l44_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k5_card_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k5_card_1 A) A)))) )  & (v2_funct_1 B)) ) ) ) ).
tt(l44_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k13_coh_sp A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_coh_sp A)) =>  ( (B = C)  =>  (! [D:$i] :  ((m1_cat_1 D (k13_coh_sp A) B B) =>  ( (D = (k8_coh_sp A C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k13_coh_sp A))) =>  ( ( (~  ((k2_cat_1 (k13_coh_sp A) B E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k13_coh_sp A) B E) =>  ((k1_cat_1 (k13_coh_sp A) D F) = F) ) ) )  &  ( (~  ((k2_cat_1 (k13_coh_sp A) E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k13_coh_sp A) E B) =>  ((k1_cat_1 (k13_coh_sp A) F D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A (k6_cqc_lang A B) C)) (a_2_0_cqc_the1 A D))) ) ) ) ) ) ) ) ).
tt(l44_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 16) & (v3_card_1 C 16))  =>  ((v3_card_1 (k8_finseq_1 A B C) 32) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 B 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 B 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 B 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 B 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 9) = (k1_funct_1 B 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 10) = (k1_funct_1 B 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 11) = (k1_funct_1 B 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 12) = (k1_funct_1 B 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 13) = (k1_funct_1 B 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 14) = (k1_funct_1 B 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 15) = (k1_funct_1 B 15))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 16) = (k1_funct_1 B 16))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 17) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 18) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 19) = (k1_funct_1 C 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 20) = (k1_funct_1 C 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 21) = (k1_funct_1 C 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 22) = (k1_funct_1 C 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 23) = (k1_funct_1 C 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 24) = (k1_funct_1 C 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 25) = (k1_funct_1 C 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 26) = (k1_funct_1 C 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 27) = (k1_funct_1 C 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 28) = (k1_funct_1 C 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 29) = (k1_funct_1 C 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 30) = (k1_funct_1 C 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 31) = (k1_funct_1 C 15))  &  ((k1_funct_1 (k8_finseq_1 A B C) 32) = (k1_funct_1 C 16)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ).
tt(l44_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_fomodel2 F D A) & (v3_fomodel3 F D A E)) ) )  =>  ((k8_nat_1 (k9_funct_2 (k35_fomodel1 D) (k8_eqrel_1 A E)) (k8_fomodel2 D (k8_eqrel_1 A E) (k3_funct_2 A (k8_eqrel_1 A E) (k17_fomodel3 A E) B) (k23_fomodel3 D A E F)) C) = (k3_relat_1 (k8_nat_1 (k9_funct_2 (k35_fomodel1 D) A) (k8_fomodel2 D A B F) C) (k17_fomodel3 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k24_gfacirc1 A B C)))  &  (H = (k1_funct_1 F E)) )  =>  ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1)) = (k2_binarith G (k9_margrel1 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l44_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k3_fuzzy_1 A C) (k3_fuzzy_1 A B))) ) ) ) ) ) ) ).
tt(l44_fuzzy_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((k8_real_1 C (k1_square_1 A B)) = (k1_square_1 (k8_real_1 C A) (k8_real_1 C B))) ) ) ) ) ) ) ) ).
tt(l44_fvaluat1,ax, (! [A:$i] :  ((v1_fvaluat1 A) =>  (! [B:$i] :  ((v1_fvaluat1 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 k6_numbers (k3_xxreal_3 B A))) ) ) ) ) ).
tt(l44_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (B = (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D F)))  =>  ((k1_rlvect_1 A B G) = (k3_rlvect_1 A (k1_rlvect_1 A C (k8_real_1 G E)) (k1_rlvect_1 A D (k8_real_1 G F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k7_glib_000 A) = (k21_glib_000 A (k6_glib_000 A))) ) ) ).
tt(l44_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( ((k3_glib_001 A B) = (k4_glib_001 A (k6_glib_001 A B)))  &  ((k4_glib_001 A B) = (k3_glib_001 A (k6_glib_001 A B))) ) ) ) ) ) ).
tt(l44_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~ (r2_int_1 C B A)) ) ) ) ) ) ) ) ) ).
tt(l44_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k5_group_1 B (k1_nat_1 A 1) C) = (k6_algstr_0 B (k5_group_1 B A C) C))  &  ((k5_group_1 B (k1_nat_1 A 1) C) = (k6_algstr_0 B C (k5_group_1 B A C))) ) ) ) ) ) ) ) ).
tt(l44_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_struct_0 C D) => (r1_struct_0 C (k2_group_1 B D))) ) ) ) ) ) ) ) ).
tt(l44_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  (! [F:$i] :  ( ((v5_glib_001 F A) & (m3_glib_001 F A))  =>  ( ( (E = (k2_helly A B C))  &  (F = (k2_helly A B D)) )  =>  ((r1_tarski E F) |  ((r1_tarski F E) |  ((k9_subset_1 (k6_glib_000 A) (k9_subset_1 (k6_glib_000 A) (k13_glib_001 A E) (k13_glib_001 A (k2_helly A C D))) (k13_glib_001 A (k2_helly A D B))) = (k1_tarski (k1_funct_1 E (k3_finseq_1 (k1_helly E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( (B = 3)  & (r2_hidden B (k4_finseq_1 A)))  =>  ((k1_recdef_1 (k13_idea_1 A) B) = (k1_recdef_1 A 2)) ) ) ) ) ) ).
tt(l44_integra8,ax, ((k9_xtuple_0 k16_sin_cos) = k1_numbers) ).
tt(l44_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B)))  &  ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B))) ) ) ) ) ) ).
tt(l44_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ( ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A))) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A)) (k1_pre_topc (k15_euclid 2) (k9_jordan6 A)) (k4_topmetr (k1_real_1 1) 1)) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) ) )  &  ((v2_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A))) &  ((k2_relset_1 k1_numbers (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k9_jordan6 A))) = (k2_struct_0 (k4_topmetr (k1_real_1 1) 1))) ) ) ) ) ) ).
tt(l44_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k4_real_1 (k13_complex1 C (k13_newton 2 A)) (k9_real_1 (k1_jordan1a (k1_jordan8 B A)) 2)) = (k13_complex1 C 2)) ) ) ) ) ) ) ) ).
tt(l44_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_0_lfuzzy_1 A B C D E) = (a_5_1_lfuzzy_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_matrixr2,ax, ((v1_funct_1 (k1_finseq_2 k6_numbers)) &  ((v1_funct_2 (k1_finseq_2 k6_numbers) (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers)) &  ((v3_funct_2 (k1_finseq_2 k6_numbers) (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers)) & (m1_subset_1 (k1_finseq_2 k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers))))) ) ) ).
tt(l44_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v13_vectsp_1 C A B) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(l44_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_1 A) =>  (A = (k10_modelc_1 (k14_modelc_1 A))) ) ) ) ).
tt(l44_msaterm,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  =>  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B)) & (r2_hidden (k1_funct_1 B (k2_nat_1 A 1)) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(l44_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k3_graph_1 A D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k4_graph_1 A D)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l44_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v12_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l44_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  ( ( (B = C)  &  (D = E) )  =>  ((r2_nfcont_4 A B D) <=>  ((r2_hidden E (k1_relset_1 (u1_struct_0 (k4_real_ns1 A)) C)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 (k4_real_ns1 A)) F) (k1_relset_1 (u1_struct_0 (k4_real_ns1 A)) C)) &  ((v3_normsp_1 F (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) F) = E) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) F C)) &  ((k7_partfun1 k1_numbers C E) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r3_orders_2 A D C)) ) )  => (r3_orders_2 A (k1_yellow_0 A B) C)) ) ) ) ) ) ) ).
tt(l44_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v3_rinfsup2 A) & (v7_valued_0 A))  =>  ((v7_mesfunc5 A) &  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k1_rinfsup2 A)) ) ) ) ) ) ).
tt(l44_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k5_card_1 B) = (k23_binop_2 A 1))  => (v4_pre_topc (k3_convex1 (k15_euclid A) B) (k15_euclid A))) ) ) ) ) ).
tt(l44_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) =>  ((u1_struct_0 (k1_rmod_3 A B D (k2_rmod_3 A B C E))) = (u1_struct_0 (k2_rmod_3 A B (k1_rmod_3 A B C D) (k1_rmod_3 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_scmbsort,ax, (~  ((k4_scmfsa_2 2) = (k4_scmfsa_2 4)) ) ).
tt(l44_scmfsa10,ax, (~  ((k5_scmfsa_2 k6_numbers) = (k4_scmfsa_2 1)) ) ).
tt(l44_scmisort,ax, (~ (r4_scmfsa7b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) ).
tt(l44_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ((r2_hidden A a_0_1_scmpds_2) =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14) ) ) ) ).
tt(l44_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ((r1_xxreal_0 (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 A) 1)) 1) & (r1_xxreal_0 (k19_binop_2 1) (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 A) 1)))) ) ) ) ) ) ).
tt(l44_sin_cos9,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))))).
tt(l44_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l44_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_xboole_0 B (k1_seq_4 A)) = B) ) ) ) ) ) ).
tt(l44_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r1_tarski B (k1_relset_1 k1_numbers A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_taylor_1 A C B) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_tarski (k1_rcomp_1 D E) B) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A B) C) (k1_rcomp_1 D E))) & (r1_taylor_1 A (k2_nat_1 C 1) (k2_rcomp_1 D E))) )  =>  ((r1_xxreal_0 E D) |  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers F) = B)  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ((k1_seq_1 F G) = (k9_real_1 (k1_seq_1 A D) (k1_seq_1 (k3_series_1 (k6_taylor_1 A B G D)) C))) ) ) ) )  =>  ( ((k1_seq_1 F D) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 D E))) &  ((r2_fdiff_1 F (k2_rcomp_1 D E)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 F G) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A (k2_rcomp_1 D E)) (k2_nat_1 C 1)) G) (k2_newton (k9_real_1 D G) C)) (k3_newton C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_topreal2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (v3_tops_2 C A B)) )  =>  ((v2_struct_0 A) <=> (v2_struct_0 B)) ) ) ) ) ) ).
tt(l44_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k1_tops_1 A B))) ) ) ) ) ).
tt(l44_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_turing_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  (! [E:$i] :  ((m2_funct_2 E k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (G = D)  &  ((m1_subset_1 1 (u1_turing_1 A)) &  ( (B = (k4_domain_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) C D E))  &  ( ((k1_funct_1 (u3_turing_1 A) (k1_domain_1 (u2_turing_1 A) k5_numbers C 1)) = (k4_domain_1 (u2_turing_1 A) k5_numbers k5_numbers C 1 1))  &  (! [H:$i] :  ((v1_int_1 H) =>  ((r1_xxreal_0 G H) =>  ((r1_xxreal_0 (k2_nat_1 G F) H) |  ((k1_funct_1 E H) = 1) ) ) ) ) ) ) ) )  =>  ( (C = (u5_turing_1 A))  |  ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) F) = (k4_domain_1 (u2_turing_1 A) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) C (k2_nat_1 G F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l44_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v11_quantal1 B) =>  (! [C:$i] :  ((r2_hidden C (k2_relset_1 (u1_struct_0 A) B)) =>  ((k1_funct_1 B C) = C) ) ) ) ) ) ) ) ).
tt(l44_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D C))  =>  ((k5_waybel11 (k3_yellow_3 C A)) = (u1_pre_topc (k2_borsuk_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(l44_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_tarski (k2_tarski A B)) = (k2_xboole_0 A B)) ) ) ).
tt(l45_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  ((k6_algstr_0 k3_algstr_1 A (k4_struct_0 k3_algstr_1)) = (k4_struct_0 k3_algstr_1)) ) ) ).
tt(l45_analmetr,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_analmetr A B C)) ) ) ) ) ) ).
tt(l45_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A C D)) (k6_cqc_lang A (k7_cqc_lang A B D)))) (a_2_0_cqc_the1 A E))) ) ) ) ) ) ) ) ) ) ).
tt(l45_euclid_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  ( ((k6_euclid B (k9_euclid B C A)) = (k9_euclid B C (k1_real_1 A)))  &  ((k6_euclid B (k9_euclid B C A)) = (k9_euclid B (k6_euclid B C) A)) ) ) ) ) ) ) ) ).
tt(l45_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r2_euclidlp A B C) & (r3_euclidlp A B C)) ) ) ) ) ) ) ) ).
tt(l45_fib_num4,ax, (~ (r1_xxreal_0 (k3_xcmplx_0 2 (k7_square_1 5)) (k3_xcmplx_0 2 1))) ).
tt(l45_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_fomodel2 D B A) & (v3_fomodel3 D B A C)) ) )  => (r2_funct_2 (k35_fomodel1 B) (k8_eqrel_1 A C) (k10_fomodel2 B (k8_eqrel_1 A C) (k23_fomodel3 B A C D)) (k1_partfun1 (k35_fomodel1 B) A A (k8_eqrel_1 A C) (k10_fomodel2 B A D) (k17_fomodel3 A C)))) ) ) ) ) ) ) ) ).
tt(l45_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp)) = (k10_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 E D) k3_gfacirc1)) = (k10_margrel1 K (k9_margrel1 J)))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith G (k9_margrel1 H)) I)))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k10_xtuple_0 (k7_funct_6 A)) (k4_card_3 (k3_funct_6 A)))) ) ).
tt(l45_fuzzy_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((k8_real_1 C (k2_square_1 A B)) = (k2_square_1 (k8_real_1 C A) (k8_real_1 C B))) ) ) ) ) ) ) ) ).
tt(l45_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_analmetr A B C) &  ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G))) )  =>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k1_relset_1 k5_numbers (k6_glib_001 A B))) =>  ( ((k1_funct_1 (k6_glib_001 A B) C) = (k1_funct_1 B (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1)))  & (r2_hidden (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ).
tt(l45_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_int_1 A B C) =>  ( (C = k6_numbers)  | (r2_int_1 (k1_newton A D) (k1_newton B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(l45_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r3_pre_poly A B C) & (r3_pre_poly A C D))  => (r3_pre_poly A B D)) ) ) ) ) ) ) ) ) ).
tt(l45_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k5_group_1 C (k24_binop_2 A B) D) = (k5_group_1 C B (k5_group_1 C A D))) ) ) ) ) ) ) ) ) ).
tt(l45_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((r3_lattices (k5_substlat A B) (k4_lattices (k5_substlat A B) C (k2_lattice2 (u1_struct_0 (k5_substlat A B)) (k5_substlat A B) (k6_heyting2 A B C) (k6_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (u1_lattices (k5_substlat A B)) (k4_heyting2 A B) (k9_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k5_heyting2 A B) (k7_heyting2 A B C) D)))) D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_substlat A B))) =>  ((r3_lattices (k5_substlat A B) (k4_lattices (k5_substlat A B) C D) E) => (r3_lattices (k5_substlat A B) D (k2_lattice2 (u1_struct_0 (k5_substlat A B)) (k5_substlat A B) (k6_heyting2 A B C) (k6_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (u1_lattices (k5_substlat A B)) (k4_heyting2 A B) (k9_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k5_heyting2 A B) (k7_heyting2 A B C) E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_heyting3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ( (~  (A = (k1_tarski k1_xboole_0)) )  &  ((r2_hidden k1_xboole_0 A) &  (! [B:$i] :  (~  ((r2_hidden B A) &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(l45_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ( (B = 2)  |  ( (B = 3)  |  ((k1_recdef_1 (k13_idea_1 A) B) = (k1_recdef_1 A B)) ) ) ) ) ) ) ) ).
tt(l45_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k6_int_1 A C) = k6_numbers)  =>  ((r1_xxreal_0 C k6_numbers) |  ((k6_int_1 (k3_xcmplx_0 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l45_integra8,ax, ((k9_xtuple_0 k19_sin_cos) = k1_numbers) ).
tt(l45_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 A C F G))  =>  (! [H:$i] :  ((m1_nattra_1 H A B D E) =>  (! [I:$i] :  ((m1_nattra_1 I A C F G) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C)) (k14_funct_3 (u1_struct_0 A) (u4_struct_0 B) (u4_struct_0 C) H I) J) = (k10_cat_2 B C (k4_nattra_1 A B D E H J) (k4_nattra_1 A C F G I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))) (k5_square_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))))) ) ) ) ) ).
tt(l45_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ( ((v1_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A))) &  ((v1_funct_2 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) &  ((v5_pre_topc (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A)) (k1_pre_topc (k15_euclid 2) (k8_jordan6 A)) (k4_topmetr (k1_real_1 1) 1)) & (m1_subset_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) ) )  &  ((v2_funct_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A))) &  ((k2_relset_1 k1_numbers (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k8_jordan6 A))) = (k2_struct_0 (k4_topmetr (k1_real_1 1) 1))) ) ) ) ) ) ).
tt(l45_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k13_complex1 C (k13_newton 2 B)) (k13_complex1 C (k13_newton 2 A)))) ) ) ) ) ) ) ) ) ).
tt(l45_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k17_euclid B) = (k6_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_8_jordan5d D))  &  (A = (k6_seq_4 C)) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) 1 A)) (k18_euclid B))) ) ) ) ) ) ) ) ) ).
tt(l45_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ((k6_algstr_0 A (k1_lopban_3 A (k1_lopban_4 A B)) (k1_lopban_3 A (k1_lopban_4 A C))) = (k1_lopban_3 A (k1_lopban_4 A (k3_rlvect_1 A B C)))) ) ) ) ) ) ) ) ).
tt(l45_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) B A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 E) B C) =>  ( (~  (F = (k4_struct_0 E)) )  =>  ((k4_matrix15 E G H) = (k4_matrix15 E (k3_matrix11 D B A (u1_struct_0 E) G (k10_fvsum_1 (k1_matrix_1 G) E (k8_matrix_1 (u1_struct_0 E) G D) F)) (k3_matrix11 D B C (u1_struct_0 E) H (k10_fvsum_1 (k1_matrix_1 H) E (k8_matrix_1 (u1_struct_0 E) H D) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_matrlin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) & (r1_xxreal_0 (k3_finseq_1 A) k6_numbers)) ) ) ) ) ).
tt(l45_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v1_ringcat1 C B A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_algstr_0 B D)) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ).
tt(l45_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_modelc_1 A) =>  (A = (k8_modelc_1 (k15_modelc_1 A) (k16_modelc_1 A))) ) ) ) ).
tt(l45_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  =>  ((k1_modelc_3 A) = (k2_xboole_0 (k1_modelc_3 (k10_modelc_2 A)) (k1_tarski A))) ) ) ) ).
tt(l45_nagata_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k1_metric_1 A A B C C) = k6_numbers)  &  ( ((k1_metric_1 A A B C D) = (k1_metric_1 A A B D C))  & (r1_xxreal_0 (k1_metric_1 A A B C E) (k7_real_1 (k1_metric_1 A A B C D) (k1_metric_1 A A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D)))) ) ) ) ) ) ) ) ) ) ).
tt(l45_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(l45_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  => (v2_poset_1 (k8_poset_1 A B C) A B)) ) ) ) ) ) ).
tt(l45_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A D B) (k7_cqc_lang A D C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(l45_scmbsort,ax, (~  ((k4_scmfsa_2 2) = (k4_scmfsa_2 5)) ) ).
tt(l45_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B D A) & (r6_scmfsa7b B D A))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)) 2))) = (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)) 2))))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)) 2) E))  &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D) E)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) )  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D))) =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D) E)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D) E))) ) ) )  &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)) 1))) = (k5_card_1 B))  &  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D)) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 D)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k8_memstr_0 3 k1_scmfsa_2 D)) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_scmisort,ax, (~ (r4_scmfsa7b (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) ).
tt(l45_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ((r2_hidden A a_0_2_scmpds_2) =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 1) ) ) ) ).
tt(l45_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k12_binop_2 (k11_binop_2 2 A) (k9_binop_2 1 (k3_square_1 A))) k6_numbers)) ) ) ) ).
tt(l45_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l45_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) &  ((r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E)) &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ( ((k1_relset_1 k1_numbers F) = C)  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G C) =>  ((k1_seq_1 F G) = (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C G D)) A))) ) ) )  &  ( ((k1_seq_1 F D) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 D E))) &  ((r2_fdiff_1 F (k2_rcomp_1 D E)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 F G) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) G) (k2_newton (k9_real_1 D G) A)) (k3_newton A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k2_tops_1 A B)) = (k2_tops_1 A B)) ) ) ) ) ).
tt(l45_uniroots,ax,(r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k4_uniroots 1 k1_complfld) (k4_polynom5 k1_complfld (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld)) (k1_group_1 k1_complfld)))).
tt(l45_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k4_matrlin A B B C (k8_group_1 A D E)) (k4_matrlin A B B (k4_matrlin A B B C E) D))) ) ) ) ) ) ) ) ) ) ).
tt(l45_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) =>  ((u1_struct_0 (k1_vectsp_5 A B D (k2_vectsp_5 A B C E))) = (u1_struct_0 (k2_vectsp_5 A B (k1_vectsp_5 A B C D) (k1_vectsp_5 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_8 A) &  ((v2_waybel_8 B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_waybel_3 A F D) & (r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E (u1_struct_0 (k1_waybel_8 B))) =>  ((r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r2_hidden F (u1_struct_0 (k1_waybel_8 A))) &  ((r3_orders_2 A F D) & (r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l45_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D C))  =>  ((k5_waybel11 (k3_yellow_3 C A)) = (u1_pre_topc (k2_borsuk_1 D B))) ) ) ) ) ) )  => (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ).
tt(l45_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  (A = B) )  =>  ((k3_relat_1 (k2_tarski (k4_tarski C A) (k4_tarski D B)) (k2_tarski (k4_tarski A E) (k4_tarski B F))) = (k2_tarski (k4_tarski C E) (k4_tarski D F))) ) ) ) ) ) ) ) ).
tt(l46_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  ((k6_algstr_0 k3_algstr_1 (k4_struct_0 k3_algstr_1) A) = (k4_struct_0 k3_algstr_1)) ) ) ).
tt(l46_analmetr,ax, (? [A:$i] :  ((m1_subset_1 A (u1_struct_0 c1__analmetr)) &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 c1__analmetr)) & (r1_analmetr c1__analmetr A B)) ) ) ) ).
tt(l46_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((r2_hidden D (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A B))) &  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A C))) &  ((k1_funct_1 (k2_pua2mss1 A B) D) = (k1_funct_1 (k2_pua2mss1 A C) E)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_arytm_2,ax, (! [A:$i] :  (~  ((r2_hidden A k2_arytm_2) &  (A = k5_arytm_3) ) ) ) ).
tt(l46_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k7_real_1 (k9_real_1 (k5_square_1 A) A) 1) k6_numbers)) ) ) ).
tt(l46_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v2_rcomp_1 (k4_rcomp_1 k2_xxreal_0 A))) ) ).
tt(l46_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ( ((u1_struct_0 C) = B)  => (v6_clvect_1 B A)) ) ) ) ) ) ) ).
tt(l46_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) (k7_cqc_lang A C B)) (a_2_0_cqc_the1 A D))) ) ) ) ) ) ) ) ).
tt(l46_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 32) & (v3_card_1 C 16))  =>  ((v3_card_1 (k8_finseq_1 A B C) 48) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 B 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 B 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 B 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 B 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 9) = (k1_funct_1 B 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 10) = (k1_funct_1 B 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 11) = (k1_funct_1 B 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 12) = (k1_funct_1 B 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 13) = (k1_funct_1 B 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 14) = (k1_funct_1 B 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 15) = (k1_funct_1 B 15))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 16) = (k1_funct_1 B 16))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 17) = (k1_funct_1 B 17))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 18) = (k1_funct_1 B 18))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 19) = (k1_funct_1 B 19))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 20) = (k1_funct_1 B 20))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 21) = (k1_funct_1 B 21))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 22) = (k1_funct_1 B 22))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 23) = (k1_funct_1 B 23))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 24) = (k1_funct_1 B 24))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 25) = (k1_funct_1 B 25))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 26) = (k1_funct_1 B 26))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 27) = (k1_funct_1 B 27))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 28) = (k1_funct_1 B 28))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 29) = (k1_funct_1 B 29))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 30) = (k1_funct_1 B 30))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 31) = (k1_funct_1 B 31))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 32) = (k1_funct_1 B 32))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 33) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 34) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 35) = (k1_funct_1 C 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 36) = (k1_funct_1 C 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 37) = (k1_funct_1 C 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 38) = (k1_funct_1 C 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 39) = (k1_funct_1 C 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 40) = (k1_funct_1 C 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 41) = (k1_funct_1 C 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 42) = (k1_funct_1 C 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 43) = (k1_funct_1 C 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 44) = (k1_funct_1 C 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 45) = (k1_funct_1 C 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 46) = (k1_funct_1 C 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 47) = (k1_funct_1 C 15))  &  ((k1_funct_1 (k8_finseq_1 A B C) 48) = (k1_funct_1 C 16)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ( (~  (B = C) )  &  ((k12_euclid (k8_euclid A B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l46_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k16_sin_cos 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k16_sin_cos 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k16_sin_cos 2)) A) C) = (k8_real_1 2 (k1_seq_1 k19_sin_cos C))) ) ) ) ) ) ) ) ) ) ).
tt(l46_fib_num4,ax, (~ (r1_xxreal_0 (k4_xcmplx_0 2) (k4_xcmplx_0 (k3_xcmplx_0 2 (k7_square_1 5))))) ).
tt(l46_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  &  (C = D) )  =>  ( ((k3_filter_0 A C) = (k3_filter_0 B D))  &  ((k7_filter_2 A C) = (k7_filter_2 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (v12_fomodel1 (k1_funct_1 (k28_fomodel1 B) A) B)) ) ) ) ).
tt(l46_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v15_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_fomodel2 E B A) & (v3_fomodel3 E B A C)) ) )  =>  ( (~  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) D) = (k34_fomodel2 B)) )  =>  ((k14_fomodel2 B (k8_eqrel_1 A C) (k23_fomodel3 B A C E) D) = (k14_fomodel2 B A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1)) = (k2_binarith (k9_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I)) (k9_margrel1 K)))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k10_xtuple_0 B) = A)  &  ( ((k3_relat_1 B C) = (k4_relat_1 (k9_xtuple_0 D)))  &  ((k3_relat_1 C D) = (k4_relat_1 A)) ) )  =>  (D = B) ) ) ) ) ) ) ) ) ).
tt(l46_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k19_sin_cos) (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l46_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k2_nat_1 (k3_finseq_1 (k7_glib_001 A B C)) 1) = (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(l46_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B A (k2_group_1 B C)) = (k2_group_1 B (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(l46_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) => (m1_group_9 C A D)) ) ) ) ) ) ) ) ).
tt(l46_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((r3_lattices (k12_normform A) (k4_lattices (k12_normform A) B (k2_lattice2 (u1_struct_0 (k12_normform A)) (k12_normform A) (k10_heyting1 A B) (k6_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (u1_lattices (k12_normform A)) (k8_heyting1 A) (k9_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k9_heyting1 A) (k11_heyting1 A B) C)))) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ((r3_lattices (k12_normform A) (k4_lattices (k12_normform A) B C) D) => (r3_lattices (k12_normform A) C (k2_lattice2 (u1_struct_0 (k12_normform A)) (k12_normform A) (k10_heyting1 A B) (k6_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (u1_lattices (k12_normform A)) (k8_heyting1 A) (k9_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k9_heyting1 A) (k11_heyting1 A B) D))))) ) ) ) ) ) ) ) ) ).
tt(l46_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) => (v3_filter_0 (k5_substlat A B))) ) ) ).
tt(l46_hfdiff_1,ax,(r2_relset_1 k1_numbers k1_numbers (k1_taylor_1 1) (k6_partfun1 k1_numbers))).
tt(l46_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (B = (k9_int_3 A))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (~  ( ((k2_hurwitz B D) = C)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_int_7 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  ( ( (E = F)  &  (G = (k5_group_1 (k3_int_7 A) C F)) )  =>  ((k2_polynom4 B D E) = (k5_algstr_0 (k9_int_3 A) G (k1_group_1 (k9_int_3 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_integra8,ax, ((k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = k1_numbers) ).
tt(l46_jgraph_2,ax, ((v4_pre_topc a_0_4_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_4_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l46_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k2_xcmplx_0 D (k13_complex1 C (k13_newton 2 B))) (k2_xcmplx_0 D (k13_complex1 C (k13_newton 2 A))))) ) ) ) ) ) ) ) ) ).
tt(l46_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) ) ) ) )  =>  ( (B = C)  |  ( (B = (k1_funct_1 A 1))  |  ( ((r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B)) &  (~  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) ) )  | (r1_jordan3 (k4_jordan3 A B C) B C)) ) ) ) ) ) ) ) ) ) ).
tt(l46_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k17_euclid B) = (k6_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_8_jordan5d D))  &  (A = (k1_xxreal_2 C)) ) ) )  => (r1_xxreal_0 (k18_euclid B) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) 1 A)))) ) ) ) ) ) ) ) ) ).
tt(l46_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_1_lfuzzy_1 A B C D E) = (a_5_2_lfuzzy_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A B) (k8_cqc_lang A B (k6_cqc_lang A (k5_cqc_lang A)))) (k4_cqc_the1 A))) ) ) ) ).
tt(l46_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [E:$i] :  ((m1_matrix_1 E C A B) => (m1_matrix_1 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers (k3_finseq_2 C) D E) C A B)) ) ) ) ) ) ) ) ) ) ).
tt(l46_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r2_mesfun6c A B C D) &  ((k1_mesfun6c A B C D) = k6_numbers) )  =>  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  ( (E = (k1_relset_1 A D))  & (r1_mesfun6c A B D E)) ) ) )  | (r1_xxreal_0 (k17_complex1 (k1_mesfun6c A B C D)) (k1_mesfunc6 A B C (k55_valued_1 A k2_numbers D)))) ) ) ) ) ) ) ) ) ) ).
tt(l46_mesfunc5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) => (r2_hidden (k1_funct_1 B C) A)) ) )  => (m2_finseq_1 B A)) ) ) ) ).
tt(l46_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_mod_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_mod_2)) =>  ( (B = 1)  =>  ( ((k6_algstr_0 k18_mod_2 A B) = A)  &  ((k6_algstr_0 k18_mod_2 B A) = A) ) ) ) ) ) ) ).
tt(l46_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((v1_ringcat1 C B A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k5_algstr_0 B D E)) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_modelc_1 A) =>  (A = (k11_modelc_1 (k15_modelc_1 A) (k16_modelc_1 A))) ) ) ) ).
tt(l46_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  ((k1_modelc_3 A) = (k2_xboole_0 (k4_subset_1 k9_modelc_2 (k1_modelc_3 (k11_modelc_2 A)) (k1_modelc_3 (k12_modelc_2 A))) (k1_tarski A))) ) ) ) ).
tt(l46_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A E F) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_cat_1 G A D E) =>  (! [H:$i] :  ((m1_cat_1 H A E F) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k1_cat_1 A G H)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) H) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_relat_2 A B) => (v1_relat_2 (k2_wellord1 A B))) ) ) ) ).
tt(l46_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ((v12_o_ring_1 D C) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 B (k3_finseq_1 D))) )  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 C) D (k12_finseq_1 (u1_struct_0 C) (k1_algstr_0 C (k7_partfun1 (u1_struct_0 C) D A) (k7_partfun1 (u1_struct_0 C) D B)))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ( ((r2_hidden C (u1_struct_0 A)) & (r3_pcs_0 A B))  => (m1_subset_1 C (u1_struct_0 B))) ) ) ) ) ) ).
tt(l46_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden (k4_tarski (k3_termord A B C D) E) B) =>  ( (E = (k3_termord A B C D))  |  ((k3_polynom1 A C D E) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  => (m1_subset_1 (k8_poset_1 A B C) (u1_struct_0 (k6_poset_1 A B)))) ) ) ) ) ) ).
tt(l46_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B D) (k9_cqc_lang A C D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(l46_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k3_complex1 (k5_arytm_0 A B)) = A)  &  ((k4_complex1 (k5_arytm_0 A B)) = B) ) ) ) ) ) ).
tt(l46_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_seq_1 (k3_real_3 (k10_real_1 1 (k5_real_1 B (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) k6_numbers)))) A) = (k3_funct_2 k5_numbers k1_numbers (k3_real_3 B) (k1_nat_1 A 1)))  &  ((k1_seq_1 (k4_real_3 (k10_real_1 1 (k5_real_1 B (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) k6_numbers)))) A) = (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 1))) ) ) ) ) ) ).
tt(l46_scmbsort,ax, (~  ((k4_scmfsa_2 2) = (k4_scmfsa_2 6)) ) ).
tt(l46_scmisort,ax, ((v1_scmfsa7b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))) & (v2_scm_halt (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) ).
tt(l46_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ((r2_hidden A a_0_3_scmpds_2) &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 2) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 3) ) ) ) ) ) ) ).
tt(l46_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v5_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ((v6_ordinal1 B) &  ((v1_setfam_1 B) &  ((k5_card_1 B) = (k5_card_1 (k5_setfam_1 (u1_struct_0 A) B))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ((r1_xboole_0 C (k5_setfam_1 (u1_struct_0 A) B)) & (v1_rlaffin1 (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C) A))  => (m3_simplex0 (k4_subset_1 (u1_struct_0 A) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C)))) (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C)))) (k5_card_1 B))) ) ) ) ) ) ) ) ).
tt(l46_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_seq_1 k31_binop_2 A) = (k8_real_1 (k1_real_1 1) A)) ) ) ).
tt(l46_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k12_binop_2 (k11_binop_2 2 A) (k9_binop_2 1 (k3_square_1 A))) 1)) ) ) ).
tt(l46_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 A k7_complex1))) = (k2_xcmplx_0 (k1_seq_1 k19_sin_cos A) (k3_xcmplx_0 (k1_seq_1 k16_sin_cos A) k7_complex1))) ) ) ).
tt(l46_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l46_toprealb,ax, (~  (k9_toprealb = k10_toprealb) ) ).
tt(l46_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A (k2_tops_1 A (k2_tops_1 A B))) = k1_xboole_0) ) ) ) ) ).
tt(l46_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k4_matrlin A B B (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E D) C) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E (k4_matrlin A B B D C)))) ) ) ) ) ) ) ) ) ) ).
tt(l46_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_8 B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E (u1_struct_0 (k1_waybel_8 B))) =>  ((r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r2_hidden F (u1_struct_0 (k1_waybel_8 A))) &  ((r3_orders_2 A F D) & (r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_waybel_3 A F D) & (r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l46_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_waybel_4 A))) & (r2_lattice3 (k8_waybel_4 A) (u1_struct_0 (k8_waybel_4 A)) B)) ) ) ) ).
tt(l46_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_xcmplx_0 B A) k6_numbers)) ) ) ) ) ) ).
tt(l46_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_tarski A B))  <=>  (C = (k2_tarski (k4_tarski A (k1_funct_1 C A)) (k4_tarski B (k1_funct_1 C B)))) ) ) ) ) ) ).
tt(l46_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 C D)) <=>  ((r2_hidden A C) & (r2_hidden B D)) ) ) ) ) ) ).
tt(l47_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_4 C A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  (~ (r1_aff_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_afvect0 A B C) = D)  <=> (r2_analoaf A C B B D)) ) ) ) ) ) ) ) ) ).
tt(l47_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) ) )  =>  ( ((k1_funct_1 (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)) (k6_ami_wstd A B (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)))) = (k2_compos_1 B))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)) C) = (k2_compos_1 B))  & (r2_hidden C (k1_relset_1 (k1_tarski (k1_ami_wstd A B k6_numbers)) (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)))))  =>  (C = (k6_ami_wstd A B (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)))) ) ) ) ) ) ) ) ) ).
tt(l47_analmetr,ax, (? [A:$i] :  ((m1_subset_1 A (u1_struct_0 c1__analmetr)) &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 c1__analmetr)) & (r1_analmetr c1__analmetr A B)) ) ) ) ).
tt(l47_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ( ((r2_hidden C a_0_0_arytm_2) &  ((r2_hidden A C) & (r3_arytm_3 B A)) )  => (r2_hidden B C)) ) ) ) ) ) ).
tt(l47_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = D)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 C E) =>  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) ) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (v2_rcomp_1 (k3_rcomp_1 A k1_xxreal_0))) ) ).
tt(l47_borsuk_7,ax,(m1_subset_1 k3_numbers (k1_zfmisc_1 k1_numbers))).
tt(l47_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xxreal_0 B (k4_metric_1 A D E))) ) ) ) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) =>  ( (D = (a_2_2_compl_sp A C))  => (v1_pcomps_1 D (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r2_hidden B (a_2_0_cqc_the1 A D)) & (r2_hidden (k8_cqc_lang A B C) (a_2_0_cqc_the1 A D)))  => (r2_hidden C (a_2_0_cqc_the1 A D))) ) ) ) ) ) ) ) ) ).
tt(l47_csspace4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(l47_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) => (m2_subset_1 (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) (k4_algstr_0 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C)) (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))) ) ) ) ) ) ).
tt(l47_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden B (k2_euclid_4 A D E)) &  ((r2_hidden C (k2_euclid_4 A D E)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((k8_euclid A B C) = (k9_euclid A (k8_euclid A D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k1_funct_1 C D) = (k12_euclid (k5_algstr_0 (k15_euclid A) D B))) ) )  => (v5_pre_topc C (k15_euclid A) k3_topmetr)) ) ) ) ) ) ) ).
tt(l47_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ( (~ (r3_euclidlp A B C))  &  ( (~  (B = (k5_euclid A)) )  &  ( (~  (C = (k5_euclid A)) )  &  (~ (r2_euclidlp A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_fib_num4,ax, (~ (r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 2) 6) (k2_xcmplx_0 (k4_xcmplx_0 (k3_xcmplx_0 2 (k7_square_1 5))) 6))) ).
tt(l47_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k1_tarski (k4_tarski C D))) =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ).
tt(l47_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0)) (k35_fomodel1 C)) =>  (! [E:$i] :  ( ((v14_fomodel1 E k6_numbers C) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))))  =>  ((k1_funct_1 (k8_nat_1 (k9_funct_2 (k35_fomodel1 C) (k35_fomodel1 C)) (k8_fomodel2 C (k35_fomodel1 C) D (k7_fomodel3 C A)) (k1_nat_1 B 1)) E) = E) ) ) ) ) ) ) ) ) ) ).
tt(l47_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp)))  &  ( (H = (k1_funct_1 F (k4_tarski (k10_finseq_1 E D) k3_gfacirc1)))  &  (I = (k1_funct_1 F (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp))) ) )  =>  ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k33_gfacirc1 (k24_gfacirc1 A B C) E D)) = (k9_margrel1 (k1_binarith (k1_binarith G H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k4_card_3 (k3_funct_6 A)) (k10_xtuple_0 (k7_funct_6 A)))) ) ).
tt(l47_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k1_fvaluat1 (k2_relset_1 k7_numbers B)) (k2_relset_1 k7_numbers B))) ) ) ) ) ).
tt(l47_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 (k7_glib_001 A B C))) & (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ).
tt(l47_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_polynom1 A C))) =>  ( ( (D = F)  &  (E = G) )  =>  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (~  ((r1_rewrite1 (k3_polyred A B C H) D E) &  (! [I:$i] :  ((m2_ideal_1 I (k11_polynom1 A C) H) =>  (~  ( (F = (k3_rlvect_1 (k11_polynom1 A C) G (k4_rlvect_1 (k11_polynom1 A C) I)))  &  (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  (~  ((r2_hidden J (k4_finseq_1 I)) &  (! [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 K A C) &  ((v3_polynom7 K A C) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [L:$i] :  ( ((v1_funct_1 L) &  ((v1_funct_2 L (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 L A C) &  ((v1_polynom1 L (k15_pre_poly A) C) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (~  ((r2_hidden L H) &  ( ((k1_funct_1 I J) = (k10_polynom1 A C K L))  & (r1_termord A B (k3_termord A B C (k10_polynom1 A C K L)) (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k6_algstr_0 B C D) = (k6_algstr_0 B D C))  =>  ((k6_algstr_0 B C (k5_group_1 B A D)) = (k6_algstr_0 B (k5_group_1 B A D) C)) ) ) ) ) ) ) ) ) ) ).
tt(l47_heyting1,ax, (! [A:$i] : (v3_filter_0 (k12_normform A))) ).
tt(l47_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k1_funct_1 (k8_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) D) (k6_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(l47_integra8,ax, ((k9_xtuple_0 k24_sin_cos) = k1_numbers) ).
tt(l47_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k1_real_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k9_real_1 (k1_real_1 (k17_euclid A)) (k1_real_1 (k17_euclid B))))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(l47_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k6_xcmplx_0 D (k13_complex1 C (k13_newton 2 A))) (k6_xcmplx_0 D (k13_complex1 C (k13_newton 2 B))))) ) ) ) ) ) ) ) ) ).
tt(l47_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  (F = (a_4_6_jordan1 A B C D)) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ((k2_pre_topc (k15_euclid 2) F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k17_euclid B) = (k8_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_9_jordan5d D))  &  (A = (k6_seq_4 C)) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k3_finseq_1 (k2_goboard2 D)) A)) (k18_euclid B))) ) ) ) ) ) ) ) ) ).
tt(l47_lattice8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r2_hidden A (k2_finseq_1 4)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  (~  (A = 4) ) ) ) ) ) ) ) ) ).
tt(l47_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_2_lfuzzy_1 A B C D E) = (a_5_3_lfuzzy_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((v2_rlvect_1 (k17_lmod_7 A B C)) &  ((v3_rlvect_1 (k17_lmod_7 A B C)) &  ((v4_rlvect_1 (k17_lmod_7 A B C)) & (v13_algstr_0 (k17_lmod_7 A B C))) ) ) ) ) ) ) ) ) ).
tt(l47_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A (k5_cqc_lang A))) B) (k4_cqc_the1 A))) ) ) ) ).
tt(l47_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v6_struct_0 F))  &  ((v13_algstr_0 F) &  ((v33_algstr_0 F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 F) D A) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 F) D B) =>  ((r2_hidden C (k2_finseq_1 D)) =>  ( (E = C)  |  ((k4_matrix15 F H I) = (k4_matrix15 F (k3_matrix11 E D A (u1_struct_0 F) H (k4_fvsum_1 (k1_matrix_1 H) F (k8_matrix_1 (u1_struct_0 F) H E) (k10_fvsum_1 (k1_matrix_1 H) F (k8_matrix_1 (u1_struct_0 F) H C) G))) (k3_matrix11 E D B (u1_struct_0 F) I (k4_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I E) (k10_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I C) G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  ((r1_mesfunc2 A B E) &  ((k1_relset_1 A E) = (k1_relset_1 A D)) ) )  =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((r1_mesfunc2 A B (k3_mesfunc1 A D E)) &  (~  ((k1_relset_1 A (k3_mesfunc1 A D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ((r2_midsp_3 A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m2_finseq_2 H (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  ( ((k3_midsp_1 C E G) = (k3_midsp_1 C (k5_midsp_3 A (u1_struct_0 C) H B) F))  =>  ( ((k4_midsp_3 A C E (k6_midsp_3 A C H B (k3_midsp_1 C (k5_midsp_3 A (u1_struct_0 C) H B) F))) = (k3_midsp_1 C (k4_midsp_3 A C E H) (k4_midsp_3 A C E (k6_midsp_3 A C H B F))))  <=>  ((k9_midsp_2 C D E (k4_midsp_3 A C E (k6_midsp_3 A C H B G))) = (k1_algstr_0 (u1_midsp_2 C D) (k9_midsp_2 C D E (k4_midsp_3 A C E H)) (k9_midsp_2 C D E (k4_midsp_3 A C E (k6_midsp_3 A C H B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~  ( (~ (v3_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  (~ (v6_modelc_1 A)) ) ) )  & (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k14_modelc_1 A)))) ) ) ) ).
tt(l47_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_modelc_2 A) =>  ((k1_modelc_3 A) = (k1_tarski A)) ) ) ) ).
tt(l47_nagata_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) k1_numbers)))) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((k1_metric_1 B B (k5_nagata_1 (k2_zfmisc_1 B B) A C) D E) = (k3_xxreal_0 A (k1_metric_1 B B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 4001 A))  &  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 2 A))) ) ) ) ) ) ) ) ) ).
tt(l47_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A D C))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r8_relat_2 A B) => (v8_relat_2 (k2_wellord1 A B))) ) ) ) ).
tt(l47_ordinal2,ax, (1 = (k1_ordinal1 k1_xboole_0)) ).
tt(l47_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 B A) & (v12_o_ring_1 C A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(l47_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_polynom3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_polynom3 A))) =>  ( (C = (k5_struct_0 (k14_polynom3 A)))  =>  ( ((k8_group_1 (k14_polynom3 A) B C) = B)  &  ((k8_group_1 (k14_polynom3 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l47_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k3_termord A B C D) = (k16_pre_poly A))  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_termord A B C D) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(l47_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  =>  (! [D:$i] :  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_poset_1 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A D B) (k9_cqc_lang A D C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(l47_quaterni,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_arytm_0 (k3_complex1 A) (k4_complex1 A)) = A) ) ) ).
tt(l47_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B C) (k9_polynom3 A)) &  ( (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k9_polynom3 A)))  &  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) C (k9_polynom3 A))) ) ) ) ) ) ) ) ) ) ).
tt(l47_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=>  ((k3_rusub_1 A C B) = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(l47_scmbsort,ax, (~  ((k4_scmfsa_2 3) = (k4_scmfsa_2 4)) ) ).
tt(l47_scmisort,ax, ( (~ (v1_xboole_0 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))))  &  ((v1_relat_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) &  ((v4_relat_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))) k5_numbers) &  ((v5_relat_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))) (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) &  ((v1_finset_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) &  ((v1_afinsq_1 (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) &  ((v2_scm_halt (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) & (v1_scmfsa7b (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))))) ) ) ) ) ) ) ) ).
tt(l47_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ((r2_hidden A a_0_4_scmpds_2) &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 4) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 5) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 6) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 7) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 8) ) ) ) ) ) ) ) ) ) ).
tt(l47_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k2_scmpds_7 A B C D))) = (k2_nat_1 (k5_card_1 D) 4)) ) ) ) ) ) ) ) ) ).
tt(l47_seq_1,ax, ((k2_real_1 (k1_real_1 1)) = (k1_real_1 1)) ).
tt(l47_sin_cos2,ax, ((k1_relset_1 k1_numbers k31_binop_2) = k1_numbers) ).
tt(l47_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_square_1 (k1_seq_1 k4_sin_cos2 A)) = (k7_real_1 1 (k5_square_1 (k1_seq_1 k1_sin_cos2 A)))) ) ) ).
tt(l47_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 k6_numbers (k12_binop_2 (k10_binop_2 1 (k7_square_1 (k9_binop_2 1 (k3_square_1 A)))) A))) ) ) ) ).
tt(l47_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l47_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ( ((v13_vectsp_1 D B B) & (v1_mod_2 D A B B))  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k4_matrlin A B B (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E D) C) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (k4_matrlin A B B E C) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l47_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_algstr_0 A (k5_struct_0 A)) B) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(l47_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_8 A) &  ((v2_waybel_8 B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_6_waybel17 A B C D))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_5_waybel17 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(l47_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k1_yellow_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (v6_waybel_6 D A)) ) ) ) ) ) ) )  => (v1_waybel_5 A)) ) ) ).
tt(l48_analmetr,ax,(r1_analmetr c1__analmetr c2__analmetr c3__analmetr)).
tt(l48_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ( (~ (r1_arytm_2 B A))  &  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  (~  ((r2_hidden C k5_arytm_3) &  ( (~ (r1_arytm_2 B C))  &  (~ (r1_arytm_2 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k7_real_1 (k9_real_1 (k5_square_1 A) A) 1) (k5_square_1 A))) ) ) ).
tt(l48_borsuk_5,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (v3_rcomp_1 (k2_rcomp_1 A B))) ) ) ) ).
tt(l48_borsuk_7,ax, ((u1_struct_0 (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7))) = c15__borsuk_7) ).
tt(l48_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers A) = 1)  |  ((k1_afinsq_1 A) = 1) )  =>  ((k7_afinsq_2 A) = (k1_seq_1 A k6_numbers)) ) ) ) ).
tt(l48_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B)))) =>  (~  ( (! [D:$i] :  ((r2_hidden D C) => (v1_finset_1 (k1_xtuple_0 D))) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D A))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E A))  =>  ((r1_tarski D E) =>  (! [F:$i] :  ((r2_hidden (k4_tarski D F) C) => (r2_hidden (k4_tarski E F) C)) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D A))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski D F) C))  => (r2_hidden (k2_tarski E F) B)) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v8_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ( (C = (k6_cohsp_1 A B D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A B D E) = (k7_relat_1 C (k3_cohsp_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_hidden (k8_cqc_lang A (k11_cqc_lang A C B) B) (a_2_0_cqc_the1 A D))) ) ) ) ) ) ) ) ).
tt(l48_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 48) & (v3_card_1 C 8))  =>  ((v3_card_1 (k8_finseq_1 A B C) 56) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 B 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 B 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 B 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 B 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 9) = (k1_funct_1 B 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 10) = (k1_funct_1 B 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 11) = (k1_funct_1 B 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 12) = (k1_funct_1 B 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 13) = (k1_funct_1 B 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 14) = (k1_funct_1 B 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 15) = (k1_funct_1 B 15))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 16) = (k1_funct_1 B 16))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 17) = (k1_funct_1 B 17))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 18) = (k1_funct_1 B 18))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 19) = (k1_funct_1 B 19))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 20) = (k1_funct_1 B 20))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 21) = (k1_funct_1 B 21))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 22) = (k1_funct_1 B 22))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 23) = (k1_funct_1 B 23))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 24) = (k1_funct_1 B 24))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 25) = (k1_funct_1 B 25))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 26) = (k1_funct_1 B 26))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 27) = (k1_funct_1 B 27))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 28) = (k1_funct_1 B 28))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 29) = (k1_funct_1 B 29))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 30) = (k1_funct_1 B 30))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 31) = (k1_funct_1 B 31))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 32) = (k1_funct_1 B 32))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 33) = (k1_funct_1 B 33))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 34) = (k1_funct_1 B 34))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 35) = (k1_funct_1 B 35))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 36) = (k1_funct_1 B 36))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 37) = (k1_funct_1 B 37))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 38) = (k1_funct_1 B 38))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 39) = (k1_funct_1 B 39))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 40) = (k1_funct_1 B 40))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 41) = (k1_funct_1 B 41))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 42) = (k1_funct_1 B 42))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 43) = (k1_funct_1 B 43))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 44) = (k1_funct_1 B 44))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 45) = (k1_funct_1 B 45))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 46) = (k1_funct_1 B 46))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 47) = (k1_funct_1 B 47))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 48) = (k1_funct_1 B 48))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 49) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 50) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 51) = (k1_funct_1 C 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 52) = (k1_funct_1 C 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 53) = (k1_funct_1 C 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 54) = (k1_funct_1 C 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 55) = (k1_funct_1 C 7))  &  ((k1_funct_1 (k8_finseq_1 A B C) 56) = (k1_funct_1 C 8)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ((r2_hidden E (k2_euclid_4 A B C)) &  ((r1_rvsum_1 (k8_euclid A B C) (k8_euclid A D E)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F (k2_euclid_4 A B C)) => (r1_xxreal_0 (k12_euclid (k8_euclid A D E)) (k12_euclid (k8_euclid A D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k1_funct_1 C D) = (k12_euclid (k5_algstr_0 (k15_euclid A) D B))) ) )  & (v5_pre_topc C (k15_euclid A) k3_topmetr)) ) ) ) ) ) ) ).
tt(l48_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k19_sin_cos 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k19_sin_cos 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers k19_sin_cos 2)) A) C) = (k1_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos C)))) ) ) ) ) ) ) ) ) ) ).
tt(l48_fib_num4,ax, (~ (r1_xxreal_0 4 (k2_xcmplx_0 (k6_xcmplx_0 1 (k3_xcmplx_0 2 (k7_square_1 5))) 5))) ).
tt(l48_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_relset_1 k5_numbers k5_numbers (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k2_finseq_1 (k1_nat_1 A k6_numbers))) (k2_finseq_1 A)) (k14_finseq_1 (k2_finseq_1 A)))) ) ).
tt(l48_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0)) (k35_fomodel1 C)) =>  ((k5_relat_1 (k8_nat_1 (k9_funct_2 (k35_fomodel1 C) (k35_fomodel1 C)) (k8_fomodel2 C (k35_fomodel1 C) D (k7_fomodel3 C A)) (k1_nat_1 B 1)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))) (k39_fomodel1 C) B)) = (k3_fomodel2 (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))) (k39_fomodel1 C) B))) ) ) ) ) ) ) ) ).
tt(l48_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1)))  &  (H = (k1_funct_1 F D)) )  =>  ((k1_funct_1 (k6_circuit2 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F) (k36_gfacirc1 (k24_gfacirc1 A B C) E D)) = (k2_binarith G (k9_margrel1 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_funct_9,ax,(v1_funct_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) (k55_valued_1 k1_numbers k1_numbers k19_sin_cos)) (k10_real_1 k32_sin_cos 2))).
tt(l48_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (D = (k3_rlvect_1 A (k1_rlvect_1 A B (k2_geomtrap A B C D)) (k1_rlvect_1 A C (k3_geomtrap A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l48_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((r2_hidden C (k26_glib_000 A B)) <=>  ((r2_hidden C (k7_glib_000 A)) &  ((k1_funct_1 (k11_glib_000 A) C) = B) ) ) ) ) ) ) ) ).
tt(l48_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ( ((k3_glib_001 A (k7_glib_001 A B C)) = (k3_glib_001 A B))  &  ( ((k4_glib_001 A (k7_glib_001 A B C)) = (k4_glib_001 A C))  & (r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A C) (k7_glib_001 A B C))) ) ) ) ) ) ) ) ) ).
tt(l48_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( ((k6_algstr_0 C D E) = (k6_algstr_0 C E D))  =>  ((k6_algstr_0 C (k5_group_1 C A D) (k5_group_1 C B E)) = (k6_algstr_0 C (k5_group_1 C B E) (k5_group_1 C A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_integra8,ax, ((k9_xtuple_0 k1_sin_cos2) = k1_numbers) ).
tt(l48_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 C B)) D) (k3_intpro_1 (k3_intpro_1 C A) D)) k8_intpro_1)) ) ) ) ) ) ) ) ).
tt(l48_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 A C F G))  =>  (! [H:$i] :  ((m1_nattra_1 H A B D E) =>  (! [I:$i] :  ((m1_nattra_1 I A C F G) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) => (r2_hidden (k3_funct_2 (u1_struct_0 A) (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C)) (k14_funct_3 (u1_struct_0 A) (u4_struct_0 B) (u4_struct_0 C) H I) J) (k2_cat_1 (k8_cat_2 B C) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) J) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C E G) J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k1_real_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B)))) (k5_square_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))))) ) ) ) ) ).
tt(l48_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  (F = (a_4_7_jordan1 A B C D)) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ((k2_pre_topc (k15_euclid 2) F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k17_euclid B) = (k8_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_9_jordan5d D))  &  (A = (k1_xxreal_2 C)) ) ) )  => (r1_xxreal_0 (k18_euclid B) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k3_finseq_1 (k2_goboard2 D)) A)))) ) ) ) ) ) ) ) ) ).
tt(l48_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) & (r1_borsuk_6 A E F)) ) )  =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) G) (k2_relset_1 (u1_struct_0 A) H)) (k2_relset_1 (u1_struct_0 A) I)) (k2_relset_1 (u1_struct_0 A) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_lattice8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 4 A))  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  (~  (A = 3) ) ) ) ) ) ) ) ) ).
tt(l48_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ( ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = (a_7_0_lfuzzy_1 A B C D E F G))  &  (~  ((k2_relset_1 k1_numbers (k3_fuzzy_4 A B C D E F G)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ((k9_xtuple_0 (k10_matrlin A B C D E F)) = (k9_xtuple_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ( (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (u1_midsp_2 C D))) =>  ((k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B (k1_algstr_0 (u1_midsp_2 C D) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) E B) F))) = (k1_algstr_0 (u1_midsp_2 C D) (k10_midsp_3 A C D E) (k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B F)))) ) ) ) )  => (r2_midsp_3 A B C)) ) ) ) ) ) ) ) ) ).
tt(l48_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_mod_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_mod_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k18_mod_2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_enumset1 k6_numbers 1 2)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_enumset1 k6_numbers 1 2)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_enumset1 k6_numbers 1 2)) =>  ( ( (D = A)  &  ( (E = B)  &  (F = C) ) )  =>  ( ((k1_algstr_0 k18_mod_2 (k1_algstr_0 k18_mod_2 A B) C) = (k11_mod_2 (k11_mod_2 D E) F))  &  ( ((k1_algstr_0 k18_mod_2 A (k1_algstr_0 k18_mod_2 B C)) = (k11_mod_2 D (k11_mod_2 E F)))  &  ( ((k6_algstr_0 k18_mod_2 (k6_algstr_0 k18_mod_2 A B) C) = (k12_mod_2 (k12_mod_2 D E) F))  &  ((k6_algstr_0 k18_mod_2 A (k6_algstr_0 k18_mod_2 B C)) = (k12_mod_2 D (k12_mod_2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_mod_4 C A B) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(l48_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v4_modelc_1 A) | (v7_modelc_1 A))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k15_modelc_1 A))))  &  (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k16_modelc_1 A)))) ) ) ) ) ).
tt(l48_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (~ (r2_hidden k1_xboole_0 B)) ) ) ) ) ).
tt(l48_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A C D))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_relat_2 A B) => (v4_relat_2 (k2_wellord1 A B))) ) ) ) ).
tt(l48_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 C A) & (v1_o_ring_1 B A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) A)) ) ) ) ) ) ) ).
tt(l48_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_polyred A B C D E) <=>  (~  ( (~  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) D (k7_polynom1 A C)) &  (~  (E = (k7_polynom1 A C)) ) ) )  &  ( (~ (r2_termord A B (k3_termord A B C D) (k3_termord A B C E)))  &  (~  ( ((k3_termord A B C D) = (k3_termord A B C E))  & (r2_polyred A B C (k6_termord A B C D) (k6_termord A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((k3_rlsub_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(l48_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ((k3_rmod_2 A B (k4_struct_0 B) C) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(l48_scmbsort,ax, (~  ((k4_scmfsa_2 3) = (k4_scmfsa_2 5)) ) ).
tt(l48_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B (k1_scmfsa_m D) A) & (r6_scmfsa7b B (k1_scmfsa_m D) A))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 2))) = (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 2))))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 2) E))  &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) )  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))) =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E))) ) ) )  &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k5_card_1 B))  &  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_scmisort,ax, ((v1_scmfsa7b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))))))) & (v2_scm_halt (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))))) ).
tt(l48_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ((r2_hidden A a_0_5_scmpds_2) &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 9) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 10) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 11) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 12) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 13) ) ) ) ) ) ) ) ) ) ).
tt(l48_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers A k31_binop_2) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fdiff_1 A B) &  ((k1_fdiff_1 A B) = (k1_real_1 1)) ) ) ) ) ) ) ).
tt(l48_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k9_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) 1) = (k5_square_1 (k1_seq_1 k1_sin_cos2 A))) ) ) ).
tt(l48_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A 1) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 k6_numbers (k10_binop_2 1 (k3_square_1 A)))) ) ) ) ).
tt(l48_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k15_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 A k7_complex1)))) = (k11_comseq_3 (k3_sin_cos (k4_xcmplx_0 (k3_xcmplx_0 A k7_complex1))))) ) ) ).
tt(l48_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v1_topreal1 A) => (v1_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l48_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l48_stirl2_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (~  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_afinsq_1 B)) => (v1_finset_1 (k1_funct_1 B C))) ) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_afinsq_1 B)) & (r2_hidden D (k2_afinsq_1 B)))  =>  ( (C = D)  | (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k2_afinsq_1 C) = (k2_afinsq_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 C)) =>  ((k1_funct_1 C D) = (k1_card_1 (k1_funct_1 B D))) ) ) )  &  ((k1_card_1 (k3_tarski (k2_relset_1 A B))) = (k7_afinsq_2 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  ((r2_hidden C A) => (r2_hidden C B)) )  => (m1_subset_1 A (k1_zfmisc_1 B))) ) ) ).
tt(l48_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_borsuk_6 A B C) &  (! [D:$i] :  ( ((v1_partfun1 D (k1_topalg_1 A B C)) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C))))) ) )  =>  (~  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) D) <=>  ((r2_hidden E (k1_topalg_1 A B C)) &  ((r2_hidden F (k1_topalg_1 A B C)) &  (? [G:$i] :  ((m1_borsuk_2 G A B C) &  (? [H:$i] :  ((m1_borsuk_2 H A B C) &  ( (G = E)  &  ( (H = F)  & (r3_borsuk_2 A B C G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l48_topalg_5,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_toprealb 2 B A))) => (r2_group_6 k2_gr_cy_1 (k5_topalg_1 (k7_toprealb 2 B A) C))) ) ) ) ) ) ).
tt(l48_tops_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A C) &  (B = (k6_subset_1 C A)) )  => (r1_tarski A (k6_subset_1 C B))) ) ) ) ).
tt(l48_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E (k3_matrlin A B B C D)) (k3_matrlin A B B (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E C) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) E D)))) ) ) ) ) ) ) ) ) ) ).
tt(l48_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel_5 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_1 A) &  ((v3_waybel_3 A) & (v3_waybel_3 (k7_lattice3 A))) ) ) ) ).
tt(l48_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = D)  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A E) A A)) )  &  ((v10_waybel_0 B A) & (r3_waybel_9 A B C)) ) )  => (r2_lattice3 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) D)) ) ) ) ) ) ) ) ) ).
tt(l48_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(l49_analmetr,ax, ( ( (~ (v7_struct_0 (g1_analoaf (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr)) (u1_analoaf (k2_analmetr c1__analmetr c2__analmetr c3__analmetr)))))  &  ((v1_diraf (g1_analoaf (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr)) (u1_analoaf (k2_analmetr c1__analmetr c2__analmetr c3__analmetr)))) & (l1_analoaf (g1_analoaf (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr)) (u1_analoaf (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))))) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  ( ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B A B) =>  (A = B) )  &  ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B C C) &  ( ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B C D) =>  ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B D C) & (r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) C D A B)) )  &  ( (~  ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B E F) &  ((r2_analoaf (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B G H) &  ( (~ (r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) E F G H))  &  (~  (A = B) ) ) ) ) )  &  ( ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B E F) & (r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B E H))  => (r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (~  ( (~  (A = B) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (~  ((r2_analoaf (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B A D) & (r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B D C)) ) ) ) ) ) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr c1__analmetr c2__analmetr c3__analmetr))) &  ((r4_analmetr (k2_analmetr c1__analmetr c2__analmetr c3__analmetr) A B C D) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 B C))  => (r1_arytm_2 A C)) ) ) ) ) ) ) ).
tt(l49_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k5_square_1 A) (k8_real_1 2 (k7_real_1 (k9_real_1 (k5_square_1 A) A) 1)))) ) ) ).
tt(l49_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ((v11_bcialg_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(l49_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C)))  => (m2_finseq_1 (k1_xtuple_0 (k1_funct_1 C B)) (k3_cqc_lang A))) ) ) ) ) ) ) ).
tt(l49_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers A) = (k1_relset_1 k5_numbers B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_afinsq_1 A)) =>  ((k1_seq_1 A C) = (k1_seq_1 B (k7_nat_d (k1_afinsq_1 A) (k23_binop_2 1 C)))) ) ) ) )  =>  ((k7_afinsq_2 A) = (k7_afinsq_2 B)) ) ) ) ) ) ).
tt(l49_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r2_hidden (k8_cqc_lang A B C) (a_2_0_cqc_the1 A E)) =>  ((r2_hidden D (k24_qc_lang1 A B)) | (r2_hidden (k8_cqc_lang A B (k11_cqc_lang A D C)) (a_2_0_cqc_the1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_diff_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v1_funct_1 (k1_seqfunc k1_numbers k1_numbers A B)) &  ((v1_funct_2 (k1_seqfunc k1_numbers k1_numbers A B) k5_numbers k1_numbers) & (m1_subset_1 (k1_seqfunc k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ) ).
tt(l49_fib_num4,ax, (~ (r1_xxreal_0 4 (k2_xcmplx_0 (k6_xcmplx_0 (k1_pepin 1) (k3_xcmplx_0 (k3_xcmplx_0 2 1) (k7_square_1 5))) (k5_square_1 (k7_square_1 5))))) ).
tt(l49_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) => (r2_relset_1 k5_numbers k5_numbers (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k2_finseq_1 (k2_xcmplx_0 B A))) (k2_finseq_1 B)) (k14_finseq_1 (k2_finseq_1 B)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_relset_1 k5_numbers k5_numbers (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k2_finseq_1 (k1_nat_1 B (k1_nat_1 A 1)))) (k2_finseq_1 B)) (k14_finseq_1 (k2_finseq_1 B)))) ) ) ) ) ).
tt(l49_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k29_fomodel1 A) A)) ) ).
tt(l49_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (r2_funct_2 (k35_fomodel1 B) (k35_fomodel1 B) (k10_fomodel2 B (k35_fomodel1 B) (k7_fomodel3 B A)) (k3_fomodel2 (k35_fomodel1 B)))) ) ) ).
tt(l49_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) (k33_gfacirc1 (k24_gfacirc1 A B C) E D)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I) K) (k10_margrel1 K (k9_margrel1 J))) (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith G (k9_margrel1 H)) I)))))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) (k55_valued_1 k1_numbers k1_numbers k19_sin_cos)) (k8_real_1 (k10_real_1 k32_sin_cos 2) (k3_real_1 A 1)))) ) ).
tt(l49_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_analmetr A B C) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) )  =>  ( (E = (k2_geomtrap A B C D))  &  (F = (k3_geomtrap A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((r2_hidden C (k27_glib_000 A B)) <=>  ((r2_hidden C (k7_glib_000 A)) &  ((k1_funct_1 (k10_glib_000 A) C) = B) ) ) ) ) ) ) ) ).
tt(l49_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ( ((k1_funct_1 (k7_glib_001 A B C) D) = (k1_funct_1 B D))  & (r2_hidden D (k1_relset_1 k5_numbers (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(l49_groeb_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (k7_subset_1 (u1_struct_0 A) B (k1_tarski (k4_struct_0 A))))  =>  (! [D:$i] :  ((m1_ideal_1 D A B) =>  (! [E:$i] :  (~  ( (E = (k4_rlvect_1 A D))  &  (! [F:$i] :  ((m1_ideal_1 F A C) =>  (~  (E = (k4_rlvect_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k6_algstr_0 B C D) = (k6_algstr_0 B D C))  =>  ((k5_group_1 B A (k6_algstr_0 B C D)) = (k6_algstr_0 B (k5_group_1 B A C) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ) ).
tt(l49_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k4_real_ns1 A))) =>  ( ( (B = D)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  (~  ( (F = (k4_finseqop (k1_euclid A) k1_numbers B (k1_pdiff_1 E A)))  &  ((k1_seq_1 C E) = (k18_rvsum_1 F)) ) ) ) ) ) ) ) ) )  =>  (C = (k4_rlvect_1 (k4_real_ns1 A) D)) ) ) ) ) ) ) ) ) ) ).
tt(l49_integra8,ax, ((k9_xtuple_0 k4_sin_cos2) = k1_numbers) ).
tt(l49_jgraph_2,ax, ((v4_pre_topc a_0_6_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_6_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l49_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) =>  ((r1_xxreal_0 C D) | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(l49_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k18_euclid B) = (k9_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_10_jordan5d D))  &  (A = (k6_seq_4 C)) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A 1)) (k17_euclid B))) ) ) ) ) ) ) ) ) ).
tt(l49_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) G) (k2_relset_1 (u1_struct_0 A) H)) (k2_relset_1 (u1_struct_0 A) I)) (k2_relset_1 (u1_struct_0 A) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((k7_lfuzzy_0 (k2_zfmisc_1 A C) (k4_fuzzy_4 A B C D E) (k1_domain_1 A C F G)) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_7_0_lfuzzy_1 A B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_matrtop3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v13_vectsp_1 D (k15_euclid B) (k15_euclid B)) &  ((v1_topreal9 D B) &  ((v2_matrtop3 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) ) ) )  =>  ((v1_matrtop3 D A) =>  ((r2_hidden C A) |  ((k1_funct_1 D (k6_matrixr2 B C)) = (k6_matrixr2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l49_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_xxreal_2 A) => (v3_xxreal_2 (k4_measure6 A))) ) ) ).
tt(l49_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) =>  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  ( (E = (k1_relset_1 A D))  & (r1_mesfun6c A B D E)) ) ) )  |  ( ((k1_mesfun6c A B C D) = k6_numbers)  | (r1_xxreal_0 (k17_complex1 (k1_mesfun6c A B C D)) (k1_mesfunc6 A B C (k55_valued_1 A k2_numbers D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_enumset1 k6_numbers 1 2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_enumset1 k6_numbers 1 2)) =>  ( (D = k6_numbers)  =>  ( ((k11_mod_2 A (k10_mod_2 A)) = D)  &  ( ((k11_mod_2 A D) = A)  &  ((k11_mod_2 (k11_mod_2 A B) C) = (k11_mod_2 A (k11_mod_2 B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v2_mod_4 C B A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_algstr_0 B D)) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ).
tt(l49_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k12_finseq_1 k5_numbers k6_numbers) (k1_relset_1 (k2_trees_1 1) (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 1) (k1_domain_1 k5_numbers k5_numbers A B))))) ) ) ) ).
tt(l49_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k1_normsp_0 A B))) ) ) )  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l49_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r6_relat_2 A B) => (v6_relat_2 (k2_wellord1 A B))) ) ) ) ).
tt(l49_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 C A) & (v1_o_ring_1 B A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l49_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) =>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ( ((k6_rlvect_2 A C) = (k4_struct_0 A))  &  ((k3_rlaffin1 A C) = k6_numbers) )  =>  ((k3_rlvect_2 A C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(l49_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ).
tt(l49_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ).
tt(l49_scmbsort,ax, (~  ((k4_scmfsa_2 3) = (k4_scmfsa_2 6)) ) ).
tt(l49_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ((r2_hidden A (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))) =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = k6_numbers) ) ) ) ).
tt(l49_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) = (k8_real_1 (k1_real_1 1) (k1_seq_1 k24_sin_cos (k1_seq_1 B A)))) ) ) ) ) ) ) ).
tt(l49_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A 1) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 k6_numbers (k10_binop_2 4 (k11_binop_2 4 (k3_square_1 A))))) ) ) ) ).
tt(l49_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v1_topreal1 A) => (v1_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(l49_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l49_subset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r2_hidden A C) => (m1_subset_1 A B)) ) ) ) ) ).
tt(l49_termord,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v3_orders_1 C) => (r3_orders_1 C B)) ) ) ) ) ) ).
tt(l49_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ( ((v13_vectsp_1 E B B) & (v1_mod_2 E A B B))  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (k3_matrlin A B B C D) E) (k3_matrlin A B B (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) C E) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k3_vectsp_4 A B (k4_struct_0 B) C) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(l49_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v2_funct_2 (k2_waybel_1 A B C) (u1_struct_0 (k1_yellow_2 A B C)))) ) ) ) ) ) ).
tt(l49_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( ((v2_waybel_1 A) &  ((v3_waybel_3 A) & (v3_waybel_3 (k7_lattice3 A))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k1_yellow_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (v6_waybel_6 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l49_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = D)  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A E) A A)) )  & (r3_waybel_9 A B C)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_lattice3 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) E) => (r3_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_diraf A B C C B)) ) ) ) ) ) ).
tt(l4_algstr_2,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  ( ((k8_group_1 k2_vectsp_1 A B) = (k8_group_1 k2_vectsp_1 A C))  =>  ( (A = (k4_struct_0 k2_vectsp_1))  |  (B = C) ) ) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  ( ((k8_group_1 k2_vectsp_1 B A) = (k8_group_1 k2_vectsp_1 C A))  =>  ( (A = (k4_struct_0 k2_vectsp_1))  |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(l4_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  => (r2_hidden (k5_memstr_0 A B (k4_extpro_1 A B (k2_funct_7 E (k4_struct_0 B) D) (k2_funct_7 F D C))) (k1_amistd_1 A B D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(l4_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k1_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 E F)) (k1_rlvect_1 A C (k8_real_1 E G))) (k1_rlvect_1 A D (k8_real_1 E H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_arytm_2,ax,(r1_xboole_0 k5_arytm_3 a_0_1_arytm_2)).
tt(l4_axioms,ax,(r2_hidden k1_xboole_0 (k1_tarski k1_xboole_0))).
tt(l4_bcialg_4,ax, ((v3_bcialg_1 k2_bcialg_4) &  ((v4_bcialg_1 k2_bcialg_4) &  ((v5_bcialg_1 k2_bcialg_4) &  ((v7_bcialg_1 k2_bcialg_4) &  ((v8_bcialg_1 k2_bcialg_4) & (v2_bcialg_4 k2_bcialg_4)) ) ) ) ) ).
tt(l4_bhsp_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) A B)) = k6_numbers) ) ) ) )  & (r2_hidden (k4_struct_0 o_0_5_bhsp_1) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)))) ).
tt(l4_binom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B)))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A k5_numbers) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A k5_numbers) B)))) )  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k2_binop_1 A k5_numbers B E F k6_numbers) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k2_binop_1 A k5_numbers B E F (k2_nat_1 G 1)) = (k2_binop_1 B A B D (k2_binop_1 A k5_numbers B E F G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  ((r1_t_0topsp A B) => (r1_t_0topsp B A)) ) ) ) ) ).
tt(l4_borsuk_7,ax,(r2_hidden k6_numbers (k1_tarski k6_numbers))).
tt(l4_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k5_bvfunc_1 A C (k1_bvfunc_1 A D))) (k5_bvfunc_1 A D (k1_bvfunc_1 A B))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A C (k1_bvfunc_1 A B)) (k5_bvfunc_1 A D (k1_bvfunc_1 A C))) (k5_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(l4_bvfunc14,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  (B = C) )  =>  ((k1_funct_1 (k1_funct_4 (k1_funct_4 A (k16_funcop_1 B D)) (k16_funcop_1 C E)) B) = D) ) ) ) ) ) ) ) ).
tt(l4_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  => (v1_c0sp1 (k2_struct_0 A) A)) ) ).
tt(l4_calcul_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r1_calcul_1 A B) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l4_card_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( (~  (C = D) )  =>  ((r2_wellord2 (k10_ordinal2 A B) (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski C)) (k2_zfmisc_1 B (k1_tarski D)))) &  ((k1_card_1 (k10_ordinal2 A B)) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski C)) (k2_zfmisc_1 B (k1_tarski D))))) ) ) ) ) ) ) ) ) ).
tt(l4_card_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k3_xcmplx_0 (k2_newton 2 A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k3_xcmplx_0 (k2_newton 2 C) (k2_nat_1 (k4_nat_1 2 D) 1)))  => (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ) ).
tt(l4_collsp,ax,(r2_hidden 1 (k6_domain_1 k5_numbers 1))).
tt(l4_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k7_comseq_3 A) C)) &  ((k1_seq_1 (k8_comseq_3 A) C) = k6_numbers) ) ) )  =>  ((k1_seq_1 (k55_valued_1 k5_numbers k2_numbers (k10_comseq_3 A)) B) = (k1_seq_1 (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)) B)) ) ) ) ) ) ).
tt(l4_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_2 A) & (v1_comseq_2 B))  => (v1_comseq_2 (k2_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(l4_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  => (m2_finseq_1 A k1_numbers)) ) ).
tt(l4_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ( ((k1_seq_1 (k6_euclid 3 A) 1) = (k7_binop_2 (k1_seq_1 A 1)))  &  ( ((k1_seq_1 (k6_euclid 3 A) 2) = (k7_binop_2 (k1_seq_1 A 2)))  &  ((k1_seq_1 (k6_euclid 3 A) 3) = (k7_binop_2 (k1_seq_1 A 3))) ) ) ) ) ).
tt(l4_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos A) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos A)))  &  ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos A) (k1_real_1 1)))  &  (~  ((k10_real_1 (k1_seq_1 k16_sin_cos A) (k10_prepower (k9_real_1 1 (k1_seq_1 k19_sin_cos A)) (k10_real_1 1 2))) = (k10_prepower (k7_real_1 1 (k1_seq_1 k19_sin_cos A)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ).
tt(l4_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k8_real_1 2 (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 A 2)))) = (k7_real_1 1 (k1_seq_1 k19_sin_cos A))) ) ) ).
tt(l4_fib_fusc,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( ((k6_power 2 (k4_nat_1 2 A)) = (k2_xcmplx_0 1 (k5_power 2 A)))  &  ((k6_power 2 (k4_nat_1 2 A)) = (k2_xcmplx_0 (k5_power 2 A) 1)) ) ) ) ) ).
tt(l4_fib_num,ax, ((k2_nat_1 (k2_nat_1 k6_numbers 1) 1) = 2) ).
tt(l4_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ((v2_binop_1 C A) & (v1_binop_1 C A)) )  =>  ((k1_finsop_1 A B C) = (k7_setwiseo k5_numbers A C (k3_finsop_1 B) (k2_finsop_1 A (k8_funcop_1 A k5_numbers (k4_binop_1 A C)) B))) ) ) ) ) ) ) ) ).
tt(l4_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) & (m2_subset_1 B (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) C)))) ) ) ) ) ) ).
tt(l4_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) => (v7_pre_topc A)) ) ) ).
tt(l4_functor3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  (! [F:$i] :  ((m2_pboole F A D (k3_relat_1 C E)) => (r6_pboole A (k8_pboole F (k3_relat_1 C (k2_msualg_3 B E))) F)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 C B))  => (r2_funct_2 A k1_numbers B C)) ) ) ) ) ) ) ).
tt(l4_fvaluat1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_xcmplx_0 A B) = (k3_xxreal_3 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l4_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (B = D) )  =>  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 B C)) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ).
tt(l4_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_finset_1 C) =>  ( (C = (a_2_0_graph_2 A B))  =>  ((k5_card_1 C) = (k2_nat_1 B 1)) ) ) ) ) ) ) ) ).
tt(l4_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( ((k3_xboole_0 (k10_xtuple_0 C) (k10_xtuple_0 D)) = k1_xboole_0)  &  ((r2_hidden A (k9_xtuple_0 C)) &  ((r2_hidden B (k9_xtuple_0 D)) &  ((k1_funct_1 C A) = (k1_funct_1 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_polynom1 A C))) =>  ( ( (F = D)  &  (G = E) )  =>  ((k5_algstr_0 (k11_polynom1 A C) F G) = (k6_polynom1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r5_aff_1 A B C) &  ((r5_aff_1 A B D) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I D) &  ((r2_hidden J D) &  ((r2_analoaf A E G F H) & (r2_analoaf A E I F J)) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (B = D)  | (r2_analoaf A G I H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_int_1 A (k4_xcmplx_0 A)) & (r1_int_1 (k4_xcmplx_0 A) A)) ) ) ).
tt(l4_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) => (r2_hidden A k1_numbers)) ) ).
tt(l4_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k4_numbers)) => (r1_tarski (k1_integra2 B A) k4_numbers)) ) ) ) ).
tt(l4_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((v1_seq_2 (k2_partfun1 A k1_numbers B A)) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_integr15 E A B C) =>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden F (k4_finseq_1 C)) &  (~  ((r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 (k4_integra1 A B C) F)) &  (~ (r1_xxreal_0 (k1_seq_1 E F) (k9_real_1 (k1_seq_1 (k4_integra1 A B C) F) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) )  => (r1_tarski (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)) (k3_integra5 A B))) ) ) ) ) ) ) ) ) ).
tt(l4_integr1c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_numbers)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 k1_numbers)) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers D)) &  ((v3_rcomp_1 E) &  ((v3_rcomp_1 F) &  ((r1_tarski (k1_rcomp_1 A B) E) &  ((r1_tarski E F) &  ((r2_fdiff_1 C F) &  ((r2_fdiff_1 D F) & (r1_tarski (k2_relset_1 k2_numbers (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers C (k25_valued_1 k1_numbers k1_numbers D k7_complex1)) (k1_rcomp_1 A B))) (k1_relset_1 k2_numbers G))) ) ) ) ) ) ) ) )  =>  ((k2_integr1c A B C D E G) = (k2_integr1c A B C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_jordan1a,ax, ((k3_nat_d 1 2) = k6_numbers) ).
tt(l4_jordan1c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k8_real_1 2 (k6_real_1 A 4)))) ) ) ) ).
tt(l4_jordan1d,ax, ((k3_nat_d 2 2) = 1) ).
tt(l4_jordan21,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_xboole_0 A D) &  ((r1_xboole_0 B D) & (r1_xboole_0 C D)) )  => (r1_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D)) ) ) ) ) ).
tt(l4_jordan5b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  =>  ((r1_xxreal_0 k6_numbers (k9_real_1 1 A)) & (r1_xxreal_0 (k9_real_1 1 A) 1)) ) ) ) ).
tt(l4_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_lattice3 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 A))) => (r3_orders_2 (k3_lattice3 A) C B)) ) ) ) ) ) ).
tt(l4_lattice8,ax,(v1_abian 2)).
tt(l4_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (g3_lattices (k1_zfmisc_1 k1_xboole_0) A B))) =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(l4_lexbfs,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 C A) 1) (k2_xcmplx_0 (k6_xcmplx_0 C B) 1))) ) ) ) ) ) ) ) ).
tt(l4_limfunc2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) D)) =>  ((r1_tarski (k2_relset_1 k1_numbers A) (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r1_tarski (k2_relset_1 k1_numbers A) D) &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))  &  ((r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) D)) & (r1_tarski (k2_relset_1 k1_numbers A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_limfunc3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) D)) =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( ((k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 B)) &  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 C)) &  ((r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 B) D)) & (r1_tarski (k10_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_hidden C (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(l4_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 A k6_numbers) |  ((k4_power (k8_real_1 B C) A) = (k8_real_1 (k4_power B A) (k4_power C A))) ) ) ) ) ) ) ) ) ).
tt(l4_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (C = (k4_struct_0 B)) )  &  ((k1_laplace B (k4_group_1 B) C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(l4_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k1_mboolean A (k3_pboole A B C)) D) = (k1_zfmisc_1 (k3_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l4_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) => (r1_tarski (k4_member_1 A) (k4_member_1 B))) ) ) ) ) ).
tt(l4_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  ((k5_binop_1 1 k9_funct_5 A B) = (k5_binop_1 1 k9_funct_5 B A)) ) ) ) ) ).
tt(l4_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_metric_2 A B B)) ) ) ) ).
tt(l4_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_mod_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_mod_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_mod_4 A))) =>  ( ((k1_algstr_0 (k2_mod_4 A) (k1_algstr_0 (k2_mod_4 A) B C) D) = (k1_algstr_0 (k2_mod_4 A) B (k1_algstr_0 (k2_mod_4 A) C D)))  &  ((k1_algstr_0 (k2_mod_4 A) B (k4_struct_0 (k2_mod_4 A))) = B) ) ) ) ) ) ) ) ) ) ).
tt(l4_modelc_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k1_int_1 A) (k1_int_1 B))) ) ) ) ) ).
tt(l4_normsp_1,ax, ((k1_funct_1 c2__normsp_1 (k4_struct_0 o_0_5_normsp_1)) = k6_numbers) ).
tt(l4_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v3_metric_1 (u1_metric_1 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))) (u1_struct_0 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))))) ) ).
tt(l4_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k5_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ( ((k8_nat_1 k5_numbers C k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 B))  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers C (k2_nat_1 G 1)) = (k8_nat_1 k5_numbers D G))  &  ((k8_nat_1 k5_numbers D (k2_nat_1 G 1)) = (k4_nat_d (k8_nat_1 k5_numbers C G) (k8_nat_1 k5_numbers D G))) ) ) )  &  ( ((k8_nat_1 k5_numbers E k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers F k6_numbers) = (k1_int_2 B))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers E (k2_nat_1 G 1)) = (k8_nat_1 k5_numbers F G))  &  ((k8_nat_1 k5_numbers F (k2_nat_1 G 1)) = (k4_nat_d (k8_nat_1 k5_numbers E G) (k8_nat_1 k5_numbers F G))) ) ) ) ) ) ) ) )  =>  ((r2_funct_2 k5_numbers k5_numbers C E) & (r2_funct_2 k5_numbers k5_numbers D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_numbers,ax,(r1_tarski k2_arytm_2 k1_numbers)).
tt(l4_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((r1_xxreal_0 A (k3_finseq_1 C)) =>  ( (A = k6_numbers)  |  ((k7_partfun1 (u1_struct_0 B) (k8_finseq_1 (u1_struct_0 B) C D) A) = (k7_partfun1 (u1_struct_0 B) C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_ortsp_1,ax, (! [A:$i] :  ((m1_subset_1 A c1__ortsp_1) =>  (! [B:$i] :  ((m1_subset_1 B c1__ortsp_1) =>  ((k5_binop_1 c1__ortsp_1 c3__ortsp_1 A B) = c2__ortsp_1) ) ) ) ) ).
tt(l4_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( ((k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A D E)) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k8_group_1 A B F) (k8_group_1 A G E)) = (k4_struct_0 A)) )  =>  ( (B = (k4_struct_0 A))  |  ((k5_algstr_0 A (k8_group_1 A D F) (k8_group_1 A G C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ( ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)))) = (k4_struct_0 A))  &  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)))) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E))) (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)))) = (k4_struct_0 A)) ) )  <=>  (~  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( ((k8_group_1 A F (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C))) = (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)))  &  ( ((k8_group_1 A F (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C))) = (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E)))  &  ((k8_group_1 A F (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C))) = (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E))) ) ) ) ) )  &  (~  ( ((k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) = (k4_struct_0 A))  &  ( ((k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k2_nat_1 (k7_nat_d A 1) 1) = (k7_nat_d (k1_nat_1 A 1) 1)) ) ) ) ).
tt(l4_polyeq_2,ax, (3 = (k2_xcmplx_0 (k3_xcmplx_0 2 1) 1)) ).
tt(l4_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_xxreal_0 B (k8_real_1 C A))) ) ) ) ) )  => (r1_xxreal_0 B k6_numbers)) ) ) ) ) ).
tt(l4_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (~ (r1_pre_poly A B C))  <=> (r2_pre_poly A C B)) ) ) ) ) ) ) ).
tt(l4_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_lattice3 A (u1_struct_0 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_orders_2 A B C)) ) ) ) ) ) ) ).
tt(l4_pralg_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k4_card_3 A)) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(l4_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( (C = (k24_qc_lang1 A B))  <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)))))) )  &  ( (C = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D B))  &  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k3_qc_lang1 A))) =>  ( ( (E = (k12_qc_lang1 A))  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k1_subset_1 (k3_qc_lang1 A))) )  &  ( ((v2_qc_lang1 E A) =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k23_qc_lang1 A (k17_qc_lang1 A E))) )  &  ( ( ((v3_qc_lang1 E A) &  (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k18_qc_lang1 A E))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = F) )  &  ( ( ((v4_qc_lang1 E A) &  ( (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k19_qc_lang1 A E)))  &  (G = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k20_qc_lang1 A E))) ) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k4_subset_1 (k3_qc_lang1 A) F G)) )  &  ( ((v5_qc_lang1 E A) &  (F = (k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D (k22_qc_lang1 A E))) )  =>  ((k3_funct_2 (k9_qc_lang1 A) (k1_zfmisc_1 (k3_qc_lang1 A)) D E) = (k7_subset_1 (k3_qc_lang1 A) F (k1_tarski (k21_qc_lang1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 2 (k1_radix_1 A))) ) ) ).
tt(l4_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((k4_radix_1 C A C (k10_radix_1 A C (k4_nat_d B (k1_newton (k1_radix_1 A) C)))) = (k4_radix_1 C A C (k10_radix_1 A C B))) ) ) ) ) ) ) ) ).
tt(l4_rat_1,ax,(m1_subset_1 k6_numbers k2_arytm_2)).
tt(l4_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k1_lattices k3_real_lat A B) = (k1_lattices k3_real_lat B A)) ) ) ) ) ).
tt(l4_realset2,ax,(r2_hidden k6_numbers 2)).
tt(l4_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (v1_finset_1 (k1_funct_1 B C))) ) ) ) ) ) ) ).
tt(l4_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  ( (~ (r1_xxreal_0 B (k3_finseq_1 A)))  & (r1_xxreal_0 (k3_finseq_1 A) B)) )  &  ( (~  ( (~ (r1_xxreal_0 1 B))  & (r1_xxreal_0 B k6_numbers)) )  &  (~ (r2_hidden B (k4_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(l4_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_rlvect_3 A B) = (k1_rlvect_3 A (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))))) ) ) ) ) ).
tt(l4_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r2_hidden (k1_algstr_0 A C D) (k5_rusub_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(l4_rlvect_5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  ((k2_xboole_0 (k6_subset_1 A (k1_tarski B)) (k1_tarski B)) = A) ) ) ) ).
tt(l4_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v3_orders_2 A) & (v7_struct_0 A))  => (v1_orders_3 A)) ) ) ).
tt(l4_rsspace2,ax, ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 (k8_real_1 (k7_real_1 A B) (k7_real_1 A B)) (k7_real_1 (k8_real_1 (k8_real_1 2 A) A) (k8_real_1 (k8_real_1 2 B) B)))) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 (k8_real_1 A A) (k7_real_1 (k8_real_1 (k8_real_1 2 (k9_real_1 A B)) (k9_real_1 A B)) (k8_real_1 (k8_real_1 2 B) B)))) ) ) ) ) ).
tt(l4_rsspace3,ax, ( (~ (v2_struct_0 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))))  &  ((v13_algstr_0 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v2_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v3_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v4_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v5_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v6_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v7_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) &  ((v8_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3))) & (l1_rlvect_1 (g1_rlvect_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3)))) ) ) ) ) ) ) ) ) ).
tt(l4_rsspace4,ax,(m1_rlsub_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4)) k7_rsspace)).
tt(l4_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((r1_struct_0 (k1_rusub_1 A) B) <=>  (B = (k4_struct_0 A)) ) ) ) ) ).
tt(l4_scm_comp,ax, ((k7_dtconstr k1_scm_comp) = (k2_zfmisc_1 1 5)) ).
tt(l4_scmfsa_i,ax,(r1_tarski k2_scmfsa_i (k3_zfmisc_1 k5_numbers (k13_finseq_1 k5_numbers) (k10_xtuple_0 k2_scmfsa_i)))).
tt(l4_scm_halt,ax, ((k9_xtuple_0 (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1))) = (k2_xboole_0 (k4_scmfsa_m (k4_scmfsa_2 k6_numbers)) (k1_tarski (k4_struct_0 k1_scmfsa_2)))) ).
tt(l4_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((k9_xtuple_0 (k3_relat_1 k3_ami_2 (k1_scmring1 A))) = k1_ami_2) ) ) ).
tt(l4_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B C)))) ) ) ) )  &  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B C)))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A C))) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A C))) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B 1)))) ) ) ) ) ) ) ).
tt(l4_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (4 = (k13_newton 2 2))  &  ((k1_newton (k2_xcmplx_0 A B) 2) = (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k1_newton B 2))) ) ) ) ) ) ).
tt(l4_series_3,ax, ((k13_newton 3 3) = 27) ).
tt(l4_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)) = (k6_xcmplx_0 (k1_newton A 2) (k1_newton B 2))) ) ) ) ) ).
tt(l4_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_power (k13_complex1 A B) (k4_xcmplx_0 C)) = (k3_power (k13_complex1 B A) C)) ) ) ) ) ) ) ).
tt(l4_sin_cos9,ax,(r2_fdiff_1 k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos))).
tt(l4_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)))) &  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers))) &  (? [D:$i] :  ((m1_subset_1 D (k1_tarski k6_numbers)) &  (? [E:$i] :  ((m1_subset_1 E (k1_tarski k6_numbers)) &  ( (C = (k1_domain_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers) D E))  &  (E = c2__symsp_1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_tdgroup,ax,(v12_vectsp_1 k1_vectsp_1)).
tt(l4_topalg_2,ax, ((u1_struct_0 (k2_borsuk_1 (k15_euclid 1) k5_topmetr)) = (k2_zfmisc_1 (u1_struct_0 (k15_euclid 1)) (u1_struct_0 k5_topmetr))) ).
tt(l4_topalg_5,ax,(r2_hidden k6_numbers (k6_domain_1 k1_numbers k6_numbers))).
tt(l4_topreal2,ax, ((k17_euclid (k19_euclid k6_numbers k6_numbers)) = k6_numbers) ).
tt(l4_toprealb,ax, ((u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(l4_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A B C D) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ( (~ (r1_aff_1 A B C E))  &  ((r2_analoaf A E F B C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_aff_1 A E F G) &  ( (~  (E = G) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k10_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  (B = (k1_funct_1 A (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ).
tt(l4_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = D)  =>  (B = (k5_algstr_0 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(l4_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_waybel11 (k5_waybel_0 A B) A)) ) ) ) ).
tt(l4_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k7_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ( (C = (k3_tarski B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ((r2_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B D) => (r3_orders_2 (k2_yellow_1 (k7_waybel_0 A)) C D)) ) ) ) ) ) ) ) ) ) ).
tt(l4_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((v3_lattice3 A) & (v3_lattice3 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_waybel_0 C A B) =>  ((v5_orders_3 (k1_waybel34 A B C) B A) &  ((v5_waybel_1 (k1_waybel34 A B C) A B) & (v18_waybel_0 (k1_waybel34 A B C) B A)) ) ) ) ) ) ) ) ) ) ).
tt(l4_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_waybel_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A C)) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A D)) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(l4_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_relat_2 A) <=>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k1_relat_1 A)) &  ((r2_hidden C (k1_relat_1 A)) &  ( (~  (B = C) )  &  ( (~ (r2_hidden (k4_tarski B C) A))  &  (~ (r2_hidden (k4_tarski C B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 B (k2_xcmplx_0 A B)))  &  ( ((r1_xxreal_0 B (k2_xcmplx_0 A B)) => (r1_xxreal_0 k6_numbers A))  &  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 A B) B)) )  &  ( (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 A B) B))  & (r1_xxreal_0 A k6_numbers)) )  &  ( ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 (k6_xcmplx_0 B A) B))  &  ( ((r1_xxreal_0 (k6_xcmplx_0 B A) B) => (r1_xxreal_0 k6_numbers A))  &  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 B (k6_xcmplx_0 B A))) )  &  (~  ( (~ (r1_xxreal_0 B (k6_xcmplx_0 B A)))  & (r1_xxreal_0 A k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l4_xreal_0,ax,(r2_hidden k1_xboole_0 (k1_tarski k1_xboole_0))).
tt(l4_xreal_1,ax,(r2_hidden k1_xboole_0 (k1_tarski k1_xboole_0))).
tt(l4_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( ((k2_tarski A B) = (k2_tarski C D))  &  ( (~  (A = C) )  &  (~  (A = D) ) ) ) ) ) ) ) ) ).
tt(l4_zf_fund1,ax, ( ((k1_relset_1 k4_ordinal1 k2_zf_fund1) = k4_ordinal1)  &  ( ((k2_relset_1 k1_zf_lang k2_zf_fund1) = k1_zf_lang)  &  ((v2_funct_1 k2_zf_fund1) &  ((v2_funct_1 (k2_funct_1 k2_zf_fund1)) &  ( ((k9_xtuple_0 (k2_funct_1 k2_zf_fund1)) = k1_zf_lang)  &  ((k10_xtuple_0 (k2_funct_1 k2_zf_fund1)) = k4_ordinal1) ) ) ) ) ) ).
tt(l4_zf_fund2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (~  ((r2_hidden B (k3_card_3 A)) &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden B (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(l50_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_1)) =>  ((k6_algstr_0 k3_algstr_1 (k6_algstr_0 k3_algstr_1 A B) C) = (k6_algstr_0 k3_algstr_1 A (k6_algstr_0 k3_algstr_1 B C))) ) ) ) ) ) ) ).
tt(l50_anproj_2,ax, (? [A:$i] :  ( (~ (v1_xboole_0 A))  &  (? [B:$i] :  ((m1_subset_1 B A) &  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) &  ( (A = (k8_domain_1 A B C D))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k9_real_1 (k8_real_1 C (k6_power 2 (k7_real_1 1 A))) (k8_real_1 8 (k6_power 2 C))) (k8_real_1 8 (k6_power 2 C)))) ) ) ) ) ) ) ) ) ) ).
tt(l50_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ((r2_hidden A (k1_relat_1 B)) &  (! [C:$i] :  ( (~ (r2_hidden (k4_tarski A C) B))  &  (~ (r2_hidden (k4_tarski C A) B)) ) ) ) ) ) ) ) ).
tt(l50_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k1_normsp_0 A B))) ) ) )  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l50_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r2_hidden (k13_cqc_lang A B C) (k3_cqc_lang A)) &  ((r2_hidden (k13_cqc_lang A B D) (k3_cqc_lang A)) & (r2_hidden (k13_cqc_lang A B C) (a_2_0_cqc_the1 A E))) )  =>  ((r2_hidden C (k24_qc_lang1 A B)) | (r2_hidden (k13_cqc_lang A B D) (a_2_0_cqc_the1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v3_card_1 B 32) & (v3_card_1 C 32))  =>  ((v3_card_1 (k8_finseq_1 A B C) 64) &  ( ((k1_funct_1 (k8_finseq_1 A B C) 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 2) = (k1_funct_1 B 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 3) = (k1_funct_1 B 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 4) = (k1_funct_1 B 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 5) = (k1_funct_1 B 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 6) = (k1_funct_1 B 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 7) = (k1_funct_1 B 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 8) = (k1_funct_1 B 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 9) = (k1_funct_1 B 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 10) = (k1_funct_1 B 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 11) = (k1_funct_1 B 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 12) = (k1_funct_1 B 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 13) = (k1_funct_1 B 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 14) = (k1_funct_1 B 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 15) = (k1_funct_1 B 15))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 16) = (k1_funct_1 B 16))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 17) = (k1_funct_1 B 17))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 18) = (k1_funct_1 B 18))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 19) = (k1_funct_1 B 19))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 20) = (k1_funct_1 B 20))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 21) = (k1_funct_1 B 21))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 22) = (k1_funct_1 B 22))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 23) = (k1_funct_1 B 23))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 24) = (k1_funct_1 B 24))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 25) = (k1_funct_1 B 25))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 26) = (k1_funct_1 B 26))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 27) = (k1_funct_1 B 27))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 28) = (k1_funct_1 B 28))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 29) = (k1_funct_1 B 29))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 30) = (k1_funct_1 B 30))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 31) = (k1_funct_1 B 31))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 32) = (k1_funct_1 B 32))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 33) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 34) = (k1_funct_1 C 2))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 35) = (k1_funct_1 C 3))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 36) = (k1_funct_1 C 4))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 37) = (k1_funct_1 C 5))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 38) = (k1_funct_1 C 6))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 39) = (k1_funct_1 C 7))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 40) = (k1_funct_1 C 8))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 41) = (k1_funct_1 C 9))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 42) = (k1_funct_1 C 10))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 43) = (k1_funct_1 C 11))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 44) = (k1_funct_1 C 12))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 45) = (k1_funct_1 C 13))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 46) = (k1_funct_1 C 14))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 47) = (k1_funct_1 C 15))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 48) = (k1_funct_1 C 16))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 49) = (k1_funct_1 C 17))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 50) = (k1_funct_1 C 18))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 51) = (k1_funct_1 C 19))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 52) = (k1_funct_1 C 20))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 53) = (k1_funct_1 C 21))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 54) = (k1_funct_1 C 22))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 55) = (k1_funct_1 C 23))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 56) = (k1_funct_1 C 24))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 57) = (k1_funct_1 C 25))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 58) = (k1_funct_1 C 26))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 59) = (k1_funct_1 C 27))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 60) = (k1_funct_1 C 28))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 61) = (k1_funct_1 C 29))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 62) = (k1_funct_1 C 30))  &  ( ((k1_funct_1 (k8_finseq_1 A B C) 63) = (k1_funct_1 C 31))  &  ((k1_funct_1 (k8_finseq_1 A B C) 64) = (k1_funct_1 C 32)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k7_real_1 (k8_real_1 (k3_funct_2 k1_numbers k1_numbers C B) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D A) 1) B)) (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) 1) B) (k3_funct_2 k1_numbers k1_numbers D (k7_real_1 B A))))) ) ) ) ) ) ) ) ) ).
tt(l50_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  (~  ( (~  ((k2_cat_1 (k11_ens_1 A) B C) = k1_xboole_0) )  &  ((k1_funct_2 (k13_ens_1 A B) (k13_ens_1 A C)) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(l50_fib_num4,ax, (~ (r1_xxreal_0 (k1_pepin 2) (k3_square_1 (k6_xcmplx_0 1 (k7_square_1 5))))) ).
tt(l50_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_relset_1 k5_numbers k5_numbers (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k2_finseq_1 (k2_xcmplx_0 B A))) (k2_finseq_1 B)) (k14_finseq_1 (k2_finseq_1 B)))) ) ) ) ).
tt(l50_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k8_fomodel3 A B C k6_numbers) = (k3_fomodel2 (k1_tarski k1_xboole_0))) ) ) ) ) ) ) ).
tt(l50_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) (k36_gfacirc1 (k24_gfacirc1 A B C) E D)) = (k2_binarith (k2_binarith (k2_binarith (k2_binarith G (k9_margrel1 H)) I) (k9_margrel1 J)) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k1_fvaluat1 (k2_relset_1 k7_numbers B)) k1_numbers)) ) ) ) ) ).
tt(l50_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r1_analmetr A B C) =>  ( ((k2_geomtrap A B C (k3_rlvect_1 A D E)) = (k7_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)))  &  ( ((k3_geomtrap A B C (k3_rlvect_1 A D E)) = (k7_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E)))  &  ( ((k2_geomtrap A B C (k5_algstr_0 A D E)) = (k9_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)))  &  ( ((k3_geomtrap A B C (k5_algstr_0 A D E)) = (k9_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E)))  &  ( ((k2_geomtrap A B C (k1_rlvect_1 A D F)) = (k8_real_1 F (k2_geomtrap A B C D)))  &  ((k3_geomtrap A B C (k1_rlvect_1 A D F)) = (k8_real_1 F (k3_geomtrap A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  =>  ( ((k1_funct_1 (k7_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) D)) = (k1_funct_1 C (k2_nat_1 D 1)))  & (r2_hidden (k2_nat_1 (k3_finseq_1 B) D) (k1_relset_1 k5_numbers (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 B (k4_nat_1 A B))) ) ) ) ) ).
tt(l50_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B (k1_uniroots A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( ((k2_hurwitz A D) = C)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ( (E = G)  &  (F = (k5_group_1 B C G)) )  =>  ((k2_polynom4 A D E) = (k5_algstr_0 A F (k5_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_int_1 A B) =>  ((k6_int_1 B A) = k6_numbers) )  &  ( ((k6_int_1 B A) = k6_numbers)  =>  ( (A = k6_numbers)  | (r1_int_1 A B)) ) ) ) ) ) ) ).
tt(l50_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A k19_sin_cos) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos A))) ) ) ).
tt(l50_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B)))  &  ((k1_real_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k9_real_1 (k1_real_1 (k17_euclid A)) (k1_real_1 (k17_euclid B)))) ) ) ) ) ) ).
tt(l50_jgraph_4,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (k3_pcomps_1 (k14_euclid 2))) ).
tt(l50_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_real_1 D (k4_real_1 (k13_complex1 (k6_xcmplx_0 C D) (k13_newton 2 B)) (k9_real_1 (k3_finseq_1 (k1_jordan8 A B)) 2))) = (k2_xcmplx_0 C (k13_complex1 (k6_xcmplx_0 C D) (k13_newton 2 B)))) ) ) ) ) ) ) ) ) ).
tt(l50_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k17_finseq_1 B A (k6_finseq_1 B)) = (k6_finseq_1 B)) ) ) ) ) ).
tt(l50_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ( ((k18_euclid B) = (k7_pscomp_1 (k3_topreal1 2 D)))  &  ((r2_hidden B (k3_topreal1 2 D)) &  ( (C = (a_1_11_jordan5d D))  &  (A = (k6_seq_4 C)) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k1_matrix_1 (k2_goboard2 D)))) (k17_euclid B))) ) ) ) ) ) ) ) ) ).
tt(l50_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_borsuk_2 H A B C) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A D E) =>  (! [K:$i] :  ((m1_borsuk_2 K A E F) =>  (! [L:$i] :  ((m1_borsuk_2 L A F G) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) &  ((r1_borsuk_6 A E F) & (r1_borsuk_6 A F G)) ) ) )  =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B F G (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D H I) J) K) L)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) H) (k2_relset_1 (u1_struct_0 A) I)) (k2_relset_1 (u1_struct_0 A) J)) (k2_relset_1 (u1_struct_0 A) K)) (k2_relset_1 (u1_struct_0 A) L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_4_lfuzzy_1 A B C D E) = (a_5_6_lfuzzy_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_ideal_1 (k11_lpspace1 A B C) (k10_lpspace1 A B C)) & (v1_lpspace1 (k11_lpspace1 A B C) (k10_lpspace1 A B C))) ) ) ) ) ) ) ).
tt(l50_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A (k5_cqc_lang A))) (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ).
tt(l50_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 C))))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r2_hidden B (k2_finseq_1 A)) =>  ((k8_matrix_1 (u1_struct_0 C) (k1_matrix13 (u1_struct_0 C) D A (k5_card_1 (k2_finseq_1 (k1_matrix_1 D))) E (k5_matrix13 (k2_finseq_1 (k1_matrix_1 D)))) B) = (k8_matrix_1 (u1_struct_0 C) D (k1_funct_1 E B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (? [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E k1_numbers))  &  ((r1_xxreal_0 (k12_euclid (k1_funct_1 (k3_matrtop1 A B C) D)) (k11_binop_2 (k18_rvsum_1 E) (k12_euclid D))) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k12_euclid (k2_matrtop1 (k9_matrix_1 (u1_struct_0 k2_vectsp_1) C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_xxreal_2 A) => (v4_xxreal_2 (k4_measure6 A))) ) ) ).
tt(l50_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((v2_mod_4 C B A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k5_algstr_0 B D E)) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_nat_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k10_xtuple_0 (k9_nat_1 A B)) (k10_xtuple_0 A))) ) ) ) ).
tt(l50_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l50_ordinal6,ax,(r2_hidden k1_xboole_0 k4_ordinal1)).
tt(l50_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l50_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_int_1 B 1 A) =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 B 1) |  ((k4_nat_d B A) = 1) ) ) ) ) ) ) ) ).
tt(l50_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ( ((k3_termord A B C D) = (k3_termord A B C E))  & (r1_polyred A B C (k6_termord A B C D) (k6_termord A B C E)))  =>  ( (E = (k7_polynom1 A C))  | (r1_polyred A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  => (m1_subset_1 (k9_poset_1 A B) (u1_struct_0 (k6_poset_1 A B)))) ) ) ) ).
tt(l50_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  ( ((r2_hidden (k1_rcomp_1 A B) C) & (r1_xxreal_0 A B))  =>  ((r1_tarski (k2_relset_1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B))) C) &  ( ((k5_setfam_1 k1_numbers (k2_relset_1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)))) = (k1_rcomp_1 A B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 1 D) =>  ( (~  ((r1_xxreal_0 D (k3_finseq_1 (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)))) & (v1_xboole_0 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) D))) )  &  ( ((r1_xxreal_0 (k1_nat_1 D 1) (k3_finseq_1 (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)))) =>  ((r1_xxreal_0 (k5_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) D)) (k5_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) (k1_nat_1 D 1)))) &  ((r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) D)) (k4_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) (k1_nat_1 D 1)))) &  (~ (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) D)) (k5_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) (k1_nat_1 D 1))))) ) ) )  &  ((r1_xxreal_0 (k1_nat_1 D 2) (k3_finseq_1 (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)))) => (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) D)) (k5_seq_4 (k7_partfun1 (k1_zfmisc_1 k1_numbers) (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) (k1_nat_1 D 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ( ((k6_rlvect_2 A C) = (k4_struct_0 A))  &  ((k3_rlaffin1 A C) = k6_numbers) )  =>  ((k3_rlvect_2 A C) = k1_xboole_0) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (v1_rlvect_3 (k7_subset_1 (u1_struct_0 A) (k5_rusub_4 A B (k4_algstr_0 A C)) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) A)) ) ) ) ) ) ) ) ).
tt(l50_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( ((k1_rlsub_2 A B C) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ( ((k1_rusub_2 A B C) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_xboole_0 A) & (v1_finseq_1 A)) ) )  =>  ((k19_rvsum_1 A) = 1) ) ) ).
tt(l50_scmbsort,ax, (~  ((k4_scmfsa_2 4) = (k4_scmfsa_2 5)) ) ).
tt(l50_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) B A) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))) ) ) ) ) ).
tt(l50_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_4 B C) (k1_scmpds_6 A)) D)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)) ) ) ) ) ) ) ) ) ).
tt(l50_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((k1_seq_1 k24_sin_cos (k8_real_1 (k1_real_1 1) A)) = (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A)) ) ) ) ) ) ).
tt(l50_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) k6_numbers)) ) ) ) ) ).
tt(l50_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = B)  =>  ( ((k17_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 A k7_complex1)))) = 1)  &  ((r1_xxreal_0 (k18_complex1 (k1_seq_1 k16_sin_cos B)) 1) & (r1_xxreal_0 (k18_complex1 (k1_seq_1 k19_sin_cos B)) 1)) ) ) ) ) ) ) ).
tt(l50_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_algstr_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((k3_polynom1 A C (k9_polynom1 A C D E) (k11_pre_poly A (k3_termord A B C D) (k3_termord A B C E))) = (k6_algstr_0 C (k3_polynom1 A C D (k3_termord A B C D)) (k3_polynom1 A C E (k3_termord A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l50_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  ( (~ (v1_xboole_0 (k3_topalg_1 A B C)))  &  ((v1_partfun1 (k3_topalg_1 A B C) (k1_topalg_1 A B C)) &  ((v3_relat_2 (k3_topalg_1 A B C)) & (v8_relat_2 (k3_topalg_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(l50_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k3_matrlin A B B (k3_matrlin A B B C D) E) (k3_matrlin A B B C (k3_matrlin A B B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(l50_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~  ((k4_algstr_0 A (k5_struct_0 A)) = (k4_struct_0 A)) ) ) ) ).
tt(l50_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v5_orders_3 (k9_waybel_4 A) (k2_yellow_1 (k3_waybel_4 A)) (k8_waybel_4 A))) ) ).
tt(l50_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k1_xxreal_3 A C) (k1_xxreal_3 B C))) ) ) ) ) ) ) ).
tt(l51_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_1)) =>  ((k6_algstr_0 k3_algstr_1 A B) = (k6_algstr_0 k3_algstr_1 B A)) ) ) ) ) ).
tt(l51_arytm_2,ax, (k12_arytm_3 = 1) ).
tt(l51_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_connsp_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7))))))) )  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) B)) &  ( (~ (r1_xxreal_0 (k1_funct_1 B D) (k1_funct_1 B C)))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)))) =>  (~  ((r1_xboole_0 E F) &  ( (~  (E = (k1_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B))) )  &  ( (~  (F = (k1_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B))) )  &  ((v3_pre_topc E (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)) &  ((v3_pre_topc F (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)) &  ((k2_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)) = (k4_subset_1 (u1_struct_0 (k7_waybel18 A (k1_pre_topc k3_topmetr (k5_toprealb c15__borsuk_7)) B)) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l51_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_eqrel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A)))))  =>  (! [D:$i] :  (~  ((r2_hidden D (a_3_1_eqrel_1 A B C)) &  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (~  ((r2_hidden E C) &  (D = (k11_eqrel_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ( (B = D)  &  ( (C = E)  &  ((k2_euclid_4 A D E) = (k3_euclid_4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_fib_num4,ax, (~ (r1_xxreal_0 (k4_power 2 2) (k3_square_1 (k6_xcmplx_0 1 (k7_square_1 5))))) ).
tt(l51_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_fintopo6 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(l51_funct_9,ax,(v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) k32_sin_cos)).
tt(l51_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( ((k8_real_1 2 (k2_geomtrap A B C (k1_geomtrap A D E))) = (k7_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)))  &  ((k8_real_1 2 (k3_geomtrap A B C (k1_geomtrap A D E))) = (k7_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k5_numbers (k7_glib_001 A B C))) &  ( (~ (r2_hidden D (k1_relset_1 k5_numbers B)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) E))  &  (D = (k2_nat_1 (k3_finseq_1 B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1) (k4_nat_1 3 A)))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1) A))  &  (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1) (k4_nat_1 2 A))) ) ) ) ) ).
tt(l51_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B (k1_uniroots A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v8_struct_0 B) &  ( ((k6_group_1 B C) = E)  &  ((k5_group_1 B E D) = (k1_group_1 B)) ) )  =>  ((r1_xxreal_0 E k6_numbers) | (m1_subset_1 D (u1_struct_0 (k5_group_4 B (k6_domain_1 (u1_struct_0 B) C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) =>  (B = (k3_xcmplx_0 (k5_int_1 B A) A)) ) ) ) ) ) ).
tt(l51_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))) (k5_square_1 (k1_real_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B)))))) ) ) ) ) ).
tt(l51_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C 1) (k2_matrix_1 (k1_jordan8 A B))) =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C 1)) = (k9_real_1 (k9_pscomp_1 A) (k13_complex1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k13_newton 2 B)))) ) ) ) ) ) ) ) ).
tt(l51_jordan3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ( ((k3_finseq_6 A B C C) = (k12_finseq_1 A (k7_partfun1 A B C)))  &  ((k3_finseq_1 (k3_finseq_6 A B C C)) = 1) ) ) ) ) ) ) ) ) ).
tt(l51_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ( ((k18_euclid C) = (k9_pscomp_1 (k3_topreal1 2 A)))  &  ((r2_hidden C (k3_topreal1 2 A)) &  ( (D = (a_1_10_jordan5d A))  &  (B = (k1_xxreal_2 D)) ) ) )  => (r1_xxreal_0 (k17_euclid C) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1)))) ) ) ) ) ) ) ) ) ).
tt(l51_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_borsuk_2 H A B C) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A D E) =>  (! [K:$i] :  ((m1_borsuk_2 K A E F) =>  (! [L:$i] :  ((m1_borsuk_2 L A F G) =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B F G (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D H I) J) K) L)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) H) (k2_relset_1 (u1_struct_0 A) I)) (k2_relset_1 (u1_struct_0 A) J)) (k2_relset_1 (u1_struct_0 A) K)) (k2_relset_1 (u1_struct_0 A) L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_6_lfuzzy_1 A B C D E) = (a_5_8_lfuzzy_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l51_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  ( ((v2_o_ring_1 C B) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ( (k6_numbers = A)  | (v13_o_ring_1 (k7_partfun1 (u1_struct_0 B) C A) B)) ) ) ) ) ) ) ) ).
tt(l51_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (B = (k1_algstr_0 A C D))  <=>  (C = (k5_algstr_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(l51_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (? [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  & (r1_rusub_2 A C B)) ) ) ) ) ) ).
tt(l51_scmbsort,ax, (~  ((k4_scmfsa_2 4) = (k4_scmfsa_2 6)) ) ).
tt(l51_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r5_scmfsa7b C B A) <=> (r5_scmfsa7b C (k1_scmfsa_m B) A)) ) ) ) ) ) ) ) ).
tt(l51_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 4 1))) k6_numbers))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) B A) (k4_scmfsa_2 (k2_nat_1 3 1))) = (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 3 1)))) )  &  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 4 1))) k6_numbers) =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) B A) (k4_scmfsa_2 (k2_nat_1 3 1))) = (k2_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 3 1))) 1)) ) ) ) ) ) ) ).
tt(l51_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((r1_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A) &  ((r1_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A) &  ( ((k1_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A) = (k7_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos (k7_binop_2 A))))  &  ((k1_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A) = (k9_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos (k7_binop_2 A)))) ) ) ) ) ) ) ) ) ).
tt(l51_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) A) k6_numbers)) ) ) ) ) ).
tt(l51_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((v1_topreal1 A) => (v1_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(l51_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v2_topgen_1 B A))  =>  ((k2_topgen_1 A B) = B) ) ) ) ) ) ).
tt(l51_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k9_xtuple_0 B) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) A)))) ) ) ) ) ) ).
tt(l51_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k1_vectsp11 C (k4_matrlin B C C (k3_struct_0 C) D) A) (k4_matrlin B C C (k3_struct_0 C) (k1_laplace B (k4_group_1 B) D A)))) ) ) ) ) ) ) ) ).
tt(l51_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = D)  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A E) A A)) )  &  ((v11_waybel_0 B A) & (r3_waybel_9 A B C)) ) )  => (r1_lattice3 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) D)) ) ) ) ) ) ) ) ) ).
tt(l51_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k1_xxreal_3 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(l52_analmetr,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_analmetr A B C)) ) ) ) ) ) ).
tt(l52_arytm_2,ax, (k11_arytm_3 = k11_arytm_3) ).
tt(l52_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ( ((k5_card_1 C) = (k1_nat_1 B 1))  =>  ((k5_card_1 (k6_subset_1 C (k6_domain_1 (u1_struct_0 A) (k11_bagorder A C)))) = B) ) ) ) ) ) ) ) ).
tt(l52_borsuk_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) A)) ) ).
tt(l52_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k1_seq_1 D E))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(l52_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k5_square_1 (k17_complex1 A)) = (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) ) ) ).
tt(l52_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  => (r2_hidden (k1_binop_1 (k9_conlat_1 A) B C) (k2_relset_1 (k8_conlat_1 A) (k9_conlat_1 A)))) ) ) ) ) ) ).
tt(l52_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (a_2_0_cqc_the1 A B) (k1_cqc_the1 A B))) ) ) ) ).
tt(l52_fib_num4,ax, (~ (r1_xxreal_0 (k4_power 2 2) (k3_power (k6_xcmplx_0 1 (k7_square_1 5)) 2))) ).
tt(l52_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k14_finseq_1 (k2_finseq_1 A)) = (k1_finseq_2 A))  =>  ((k14_finseq_1 (k2_finseq_1 (k1_nat_1 A 1))) = (k1_finseq_2 (k1_nat_1 A 1))) ) ) ) ).
tt(l52_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_funct_1 (k1_funct_5 (k23_fomodel2 B A C))) &  ((v1_funct_2 (k1_funct_5 (k23_fomodel2 B A C)) (k16_fomodel2 B C) (k9_funct_2 (k25_fomodel2 B A) k6_margrel1)) & (m1_subset_1 (k1_funct_5 (k23_fomodel2 B A C)) (k1_zfmisc_1 (k2_zfmisc_1 (k16_fomodel2 B C) (k9_funct_2 (k25_fomodel2 B A) k6_margrel1))))) ) ) ) ) ) ) ) ).
tt(l52_funct_9,ax,(v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) k32_sin_cos)).
tt(l52_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k4_algstr_0 A B) (k4_algstr_0 A C)) = (k4_algstr_0 A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ).
tt(l52_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( ((k2_nat_1 (k3_finseq_1 (k8_glib_001 A B C D)) C) = (k2_nat_1 D 1))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k8_glib_001 A B C D)) E))  =>  ( ((k1_funct_1 (k8_glib_001 A B C D) (k2_nat_1 E 1)) = (k1_funct_1 B (k2_nat_1 C E)))  & (r2_hidden (k2_nat_1 C E) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l52_graph_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  (B = C) ) ) )  =>  ((k1_card_1 A) = 1) ) ) ) ).
tt(l52_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B (k4_nat_1 2 A)) =>  ((r1_xxreal_0 B A) |  ( (~  ( (~ (r1_xxreal_0 B (k4_nat_1 2 A)))  & (r1_xxreal_0 B (k4_nat_1 3 A))) )  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 3 A))) ) ) )  &  ( ( (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 3 A))) )  =>  ( (~  ( (~ (r1_xxreal_0 B (k4_nat_1 2 A)))  & (r1_xxreal_0 B (k4_nat_1 3 A))) )  &  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 2 A))) ) ) )  &  ((r1_xxreal_0 B (k4_nat_1 3 A)) =>  ((r1_xxreal_0 B (k4_nat_1 2 A)) |  ( (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 2 A))) )  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 3 A))) ) ) ) ) ) ) ) ) ) ).
tt(l52_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~  ( (A = k6_numbers)  &  (B = k6_numbers) ) )  => (r1_int_2 (k5_int_1 A (k3_int_2 A B)) (k5_int_1 B (k3_int_2 A B)))) ) ) ) ) ).
tt(l52_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 A C F G))  =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  (! [I:$i] :  ((m2_nattra_1 I A C F G) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A J K) = k1_xboole_0) )  =>  (! [L:$i] :  ((m1_cat_1 L A J K) =>  ((k5_cat_1 (k8_cat_2 B C) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) J) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) K) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C E G) K) (k9_cat_3 A J K (k8_cat_2 B C) (k8_isocat_2 A B C D F) L) (k4_nattra_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G) (k13_isocat_2 A B C D E F G H I) K)) = (k5_cat_1 (k8_cat_2 B C) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) J) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C E G) J) (k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C E G) K) (k4_nattra_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G) (k13_isocat_2 A B C D E F G H I) J) (k9_cat_3 A J K (k8_cat_2 B C) (k8_isocat_2 A B C E G) L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l52_jgraph_2,ax, ((v4_pre_topc a_0_7_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_7_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l52_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski 1 C) (k2_matrix_1 (k1_jordan8 A B))) =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) 1 C)) = (k9_real_1 (k6_pscomp_1 A) (k13_complex1 (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) (k13_newton 2 B)))) ) ) ) ) ) ) ) ).
tt(l52_jordan3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k3_finseq_6 A B k6_numbers k6_numbers) = (k17_finseq_1 A 1 B)) ) ) ) ) ).
tt(l52_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ( ((k18_euclid C) = (k7_pscomp_1 (k3_topreal1 2 A)))  &  ((r2_hidden C (k3_topreal1 2 A)) &  ( (D = (a_1_11_jordan5d A))  &  (B = (k1_xxreal_2 D)) ) ) )  => (r1_xxreal_0 (k17_euclid C) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A)))))) ) ) ) ) ) ) ) ) ).
tt(l52_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v2_lattice6 A) & (l3_lattices A)) ) ) )  => (v9_lattice6 (k5_lattice6 A) A)) ) ).
tt(l52_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((k1_relset_1 (k6_glib_000 A) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k9_lexbfs A))) = (k6_glib_000 A))  &  ((k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k9_lexbfs A)) B) = k1_xboole_0) ) ) ) ) ).
tt(l52_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((a_5_8_lfuzzy_1 A B C D E) = (k5_card_3 (k1_domain_1 A A D E) (a_3_1_lfuzzy_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l52_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k1_normsp_0 A B))) ) ) )  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l52_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A) =>  ((v3_matrtop3 (k3_matrtop1 A A B) A) =>  ((k12_matrix_3 A k2_vectsp_1 B) = (k5_struct_0 k2_vectsp_1)) ) ) ) ) ) ).
tt(l52_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(l52_poset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((m1_subset_1 A (u1_struct_0 (k6_poset_1 B B))) =>  ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_poset_1 A B B) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(l52_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v3_rlvect_1 (k19_quofield A)) &  ((v4_rlvect_1 (k19_quofield A)) & (v13_algstr_0 (k19_quofield A))) ) ) ) ).
tt(l52_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A))  =>  ((v5_ratfunc1 B A) =>  ((k12_ratfunc1 A B) = (k4_xxreal_0 (k2_hurwitz A (k4_ratfunc1 A B)) (k2_hurwitz A (k5_ratfunc1 A B)))) ) ) ) ) ) ).
tt(l52_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (? [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  & (r1_rlsub_2 A C B)) ) ) ) ) ) ).
tt(l52_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_funct_1 (k3_rltopsp1 A B))) ) ) ) ).
tt(l52_scmbsort,ax, (~  ((k4_scmfsa_2 5) = (k4_scmfsa_2 6)) ) ).
tt(l52_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A)) )  &  ( ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A))  =>  ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A)) ) ) ) ) ) ) ) ) ) ).
tt(l52_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (~  ( (~  (B = (k4_scmfsa_2 (k2_nat_1 3 1))) )  &  ( (~  (B = (k4_scmfsa_2 (k2_nat_1 1 1))) )  &  (~  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))) C A) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l52_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) => (v4_scmyciel (k6_subset_1 (k5_scmyciel (k3_tarski A)) (k1_scmyciel A)))) ) ).
tt(l52_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((r1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A) &  ((k1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A) = (k8_real_1 (k10_real_1 1 2) (k1_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A))) ) ) ) ) ) ) ).
tt(l52_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 k6_numbers (k3_sin_cos2 A))) ) ) ).
tt(l52_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ((k12_binop_2 (k11_binop_2 2 A) (k10_binop_2 (k3_square_1 A) 1)) = k6_numbers) ) ) ) ) ) ).
tt(l52_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 A 4) => (m1_subset_1 A (u2_turing_1 k16_turing_1))) ) ) ).
tt(l52_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k4_matrlin A B B C (k3_rlvect_1 A D E)) (k3_matrlin A B B (k4_matrlin A B B C D) (k4_matrlin A B B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(l52_waybel11,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v2_pre_topc A))  => (v2_pre_topc B)) ) ) ) ) ).
tt(l52_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v5_orders_3 (k3_waybel_1 A B C) (k1_yellow_2 A B C) B)) ) ) ) ) ) ).
tt(l52_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v5_orders_3 (k10_waybel_4 A) (k8_waybel_4 A) (k2_yellow_1 (k3_waybel_4 A)))) ) ).
tt(l52_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = D)  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A E) A A)) )  & (r3_waybel_9 A B C)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_lattice3 A (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) E) => (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l52_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 k6_numbers (k1_xxreal_3 A B))) ) ) ) ) ) ) ).
tt(l52_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_21_yellow_4 A B C) = (k6_domain_1 (u1_struct_0 A) (k11_lattice3 A B C))) ) ) ) ) ) ) ).
tt(l53_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_afvect0 A B))) =>  ((k1_algstr_0 (k5_afvect0 A B) C D) = (k1_algstr_0 (k5_afvect0 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(l53_analmetr,ax, (? [A:$i] :  ((m1_subset_1 A (u1_struct_0 c4__analmetr)) &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 c4__analmetr)) & (r1_analmetr c4__analmetr A B)) ) ) ) ).
tt(l53_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ( ((k5_arytm_2 A B) = A)  =>  ( (A = k11_arytm_3)  |  (B = k11_arytm_3) ) ) ) ) ) ) ).
tt(l53_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))) =>  ( ((r2_hidden B (k6_cc0sp2 A)) & (r2_hidden C (k6_cc0sp2 A)))  => (r2_hidden (k3_rlvect_1 (k8_cfuncdom (u1_struct_0 A)) B C) (k6_cc0sp2 A))) ) ) ) ) ) ) ).
tt(l53_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  => (r2_hidden (k1_binop_1 (k10_conlat_1 A) B C) (k2_relset_1 (k8_conlat_1 A) (k10_conlat_1 A)))) ) ) ) ) ) ).
tt(l53_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_finseq_1 A)) &  ((v1_descip_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k2_finseq_1 A))))) ) )  =>  ((k2_relset_1 (k2_finseq_1 A) B) = (k2_finseq_1 A)) ) ) ) ) ).
tt(l53_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlsub_1 B (k10_funcsdom (k2_finseq_1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C (u1_struct_0 B)) & (r2_hidden D (u1_struct_0 B)))  => (r2_hidden (k7_euclid A (k9_euclid A C E) D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l53_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k5_algstr_0 A (k3_rlvect_1 A B (k1_rlvect_1 A C E)) (k3_rlvect_1 A D (k1_rlvect_1 A C F))) = (k3_rlvect_1 A (k5_algstr_0 A B D) (k1_rlvect_1 A C (k9_real_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( ((k3_glib_001 A (k8_glib_001 A B C D)) = (k1_funct_1 B C))  &  ( ((k4_glib_001 A (k8_glib_001 A B C D)) = (k1_funct_1 B D))  & (r1_glib_001 A (k1_funct_1 B C) (k1_funct_1 B D) (k8_glib_001 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_rewrite1 E (k3_polyred A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 E)))  =>  ((r1_xxreal_0 (k3_finseq_1 E) 1) |  ((v1_funct_1 (k1_funct_1 E F)) &  ((v1_funct_2 (k1_funct_1 E F) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 (k1_funct_1 E F) (k15_pre_poly A) C) & (m1_subset_1 (k1_funct_1 E F) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B (k19_binop_2 A) C) = (k2_group_1 B (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(l53_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) &  ((r1_int_1 C B) & (r1_int_2 A C)) )  => (r1_int_1 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(l53_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k1_real_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k9_real_1 (k1_real_1 (k18_euclid A)) (k1_real_1 (k18_euclid B))))  &  ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B))) ) ) ) ) ) ).
tt(l53_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C (k3_finseq_1 (k1_jordan8 A B))) (k2_matrix_1 (k1_jordan8 A B))) =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k3_finseq_1 (k1_jordan8 A B)))) = (k7_real_1 (k7_pscomp_1 A) (k13_complex1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k13_newton 2 B)))) ) ) ) ) ) ) ) ).
tt(l53_jordan3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k3_finseq_6 A B C C) = (k6_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(l53_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xxreal_0 2 (k3_finseq_1 A))) ) ).
tt(l53_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v1_lattice6 A) & (l3_lattices A)) ) ) )  => (v8_lattice6 (k6_lattice6 A) A)) ) ).
tt(l53_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_5_3_lfuzzy_1 A B C D E)) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_5_4_lfuzzy_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l53_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 1 2 3)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 1 2 3) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 1 2 3) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v5_matrix_2 (k3_finseq_4 k5_numbers 1 2 3) 3) & (m1_subset_1 (k3_finseq_4 k5_numbers 1 2 3) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(l53_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k8_matrix13 B (k12_matrix_1 B A)) = A) ) ) ) ) ).
tt(l53_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_tarski D (k1_relset_1 A F)) &  ((r1_mesfunc1 A B F D) &  ( (D = k1_xboole_0)  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers E G))) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_mesfunc9 G H) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers E H) D))) ) )  &  ((v1_mesfunc9 G) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers F D)) = (k3_mesfunc9 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D A) =>  ((k1_seq_1 B D) = (k1_seq_1 C D)) ) ) )  =>  ((k6_series_1 B A) = (k6_series_1 C A)) ) ) ) ) ) ) ) ).
tt(l53_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v8_o_ring_1 B A) => (v12_o_ring_1 B A)) ) ) ) ) ).
tt(l53_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k6_afinsq_1 A B)) = (k2_tarski A B)) ) ) ).
tt(l53_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (m1_subset_1 B (u1_struct_0 (k6_poset_1 A A)))) ) ) ) ) ).
tt(l53_quaterni,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)) (k3_square_1 D)) = k6_numbers)  =>  ( (A = k6_numbers)  &  ( (B = k6_numbers)  &  ( (C = k6_numbers)  &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ( ((k6_rinfsup2 A) = (k5_rinfsup2 A))  &  ((k6_rinfsup2 A) = k1_supinf_1) )  =>  ((v10_mesfunc5 A) &  ( ((k2_mesfunc5 A) = (k6_rinfsup2 A))  &  ((k2_mesfunc5 A) = (k5_rinfsup2 A)) ) ) ) ) ) ).
tt(l53_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) = (k4_struct_0 A)) ) ) ).
tt(l53_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) => (r1_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(l53_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 1 (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 1 1)))) & (r1_xxreal_0 (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 1 1))) (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 2 1))))  &  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 5 1))) = (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 5 1))))  &  ( ((k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  (? [C:$i] :  ((v1_int_1 C) &  ( (C = (k1_funct_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)) (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 1 1)))))  &  ( ( (~ (r1_xxreal_0 (k6_xcmplx_0 C (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 5 1)))) k6_numbers))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 1 1))) = k6_numbers)  &  ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 3 1))) = (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 3 1)))) ) )  &  ((r1_xxreal_0 (k6_xcmplx_0 C (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 5 1)))) k6_numbers) =>  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 1 1))) = (k6_xcmplx_0 (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 1 1))) 1))  &  ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))) A B) (k4_scmfsa_2 (k2_nat_1 3 1))) = (k2_xcmplx_0 (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 3 1))) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmpds_4 (k1_scmpds_4 (k2_scmpds_4 A B) C) D) k6_numbers) = A) ) ) ) ) ) ) ) ) ).
tt(l53_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k3_tarski A) = (k3_tarski (k6_subset_1 (k5_scmyciel (k3_tarski A)) (k1_scmyciel A)))) ) ) ).
tt(l53_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((k1_seq_1 k1_sin_cos2 A) = (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A)) ) ) ) ) ) ).
tt(l53_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 k6_numbers (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k9_binop_2 1 (k3_square_1 A)))) A))) ) ) ) ).
tt(l53_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 A) & (v1_topreal1 B))  =>  ( ( (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) )  &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) )  | (v1_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ) ).
tt(l53_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_newton A 3) = (k24_binop_2 (k24_binop_2 A A) A)) ) ) ).
tt(l53_toprealb,ax, ((u1_struct_0 (k11_toprealb k9_toprealb)) = (k2_struct_0 (k11_toprealb k9_toprealb))) ).
tt(l53_turing_1,ax, ((r2_hidden k6_numbers (u1_turing_1 k16_turing_1)) & (r2_hidden 1 (u1_turing_1 k16_turing_1))) ).
tt(l53_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v6_waybel_0 C A) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) ) )  =>  ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v6_waybel_0 C B) &  ((v7_waybel_0 C) & (l1_waybel_0 C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l53_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v5_waybel_7 (k1_waybel_4 A) A) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A (k12_lattice3 A C D) B) &  ( (~ (r3_orders_2 A C B))  &  (~ (r3_orders_2 A D B)) ) ) ) ) ) ) )  &  (~ (v5_waybel_6 B A)) ) ) ) ) ) ) ) ).
tt(l53_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k2_xxreal_3 B) (k2_xxreal_3 A))) ) ) ) ) ).
tt(l53_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((a_4_1_yellow_4 A B C D) = (k7_domain_1 (u1_struct_0 A) (k11_lattice3 A B C) (k11_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(l54_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_afvect0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_afvect0 A B))) =>  ((k1_algstr_0 (k5_afvect0 A B) (k1_algstr_0 (k5_afvect0 A B) C D) E) = (k1_algstr_0 (k5_afvect0 A B) C (k1_algstr_0 (k5_afvect0 A B) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_analmetr,ax, (? [A:$i] :  ((m1_subset_1 A (u1_struct_0 c4__analmetr)) &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 c4__analmetr)) & (r1_analmetr c4__analmetr A B)) ) ) ) ).
tt(l54_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((k7_arytm_2 A B) = A)  =>  (B = k11_arytm_3) ) ) ) ) ) ).
tt(l54_borsuk_1,ax, ((k3_pcomps_1 k8_metric_1) = (g1_pre_topc (u1_struct_0 k8_metric_1) (k2_pcomps_1 k8_metric_1))) ).
tt(l54_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))) =>  ((r2_hidden C (k6_cc0sp2 A)) => (r2_hidden (k1_clvect_1 (k8_cfuncdom (u1_struct_0 A)) C B) (k6_cc0sp2 A))) ) ) ) ) ) ) ).
tt(l54_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((a_2_5_cgames_1 A B) = (a_2_6_cgames_1 A B))  &  ((a_2_7_cgames_1 A B) = (a_2_8_cgames_1 A B)) ) ) ) ) ) ).
tt(l54_clopban1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(l54_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 k2_numbers C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers C) C)))) )  =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (g1_clvect_1 C D E F))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ( (B = C)  &  ( (F = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers B)))  &  (H = I) ) )  =>  ((k1_clvect_1 (g1_clvect_1 C D E F) H G) = (k1_clvect_1 A I G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_fomodel3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  ((v1_funct_1 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 B)) (k3_finseq_2 (k1_fomodel1 B)) (k20_fomodel0 (k1_fomodel1 B) C D) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A))) &  ((v1_funct_2 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 B)) (k3_finseq_2 (k1_fomodel1 B)) (k20_fomodel0 (k1_fomodel1 B) C D) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A)) & (m1_subset_1 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 B)) (k3_finseq_2 (k1_fomodel1 B)) (k20_fomodel0 (k1_fomodel1 B) C D) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A)) (k1_zfmisc_1 (k2_zfmisc_1 (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A))))) ) ) ) ) ) ) ) ) ) ).
tt(l54_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 E (k3_finseq_1 B))) )  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k7_glib_001 A (k8_glib_001 A B C D) (k8_glib_001 A B D E)) (k8_glib_001 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_ideal_1 E (k11_polynom1 A C)) &  ((v2_ideal_1 E (k11_polynom1 A C)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (~  ((r2_hidden D E) &  ( (~  (D = (k7_polynom1 A C)) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r2_hidden F E) &  ( ((k5_termord A B C F) = (k1_polynom7 A C (k5_struct_0 C) (k3_termord A B C D)))  &  (~  (F = (k7_polynom1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ( (~ (r1_xxreal_0 1 A))  &  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(l54_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k1_real_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B)))) (k5_square_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))))) ) ) ) ) ).
tt(l54_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k5_pscomp_1)) &  ((v1_funct_2 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k5_pscomp_1) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k5_pscomp_1) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(l54_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden E (k10_metric_1 (k14_euclid 2) D (k7_real_1 (k12_euclid C) 1))) &  ( (B = F)  &  ( (A = E)  &  ( (D = (k4_struct_0 (k15_euclid 2)))  &  ((k12_euclid A) = (k12_euclid B)) ) ) ) )  => (r2_hidden B (k10_metric_1 (k14_euclid 2) D (k7_real_1 (k12_euclid C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski (k3_finseq_1 (k1_jordan8 A B)) C) (k2_matrix_1 (k1_jordan8 A B))) =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k3_finseq_1 (k1_jordan8 A B)) C)) = (k7_real_1 (k8_pscomp_1 A) (k13_complex1 (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) (k13_newton 2 B)))) ) ) ) ) ) ) ) ).
tt(l54_jordan3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_finseq_6 A B C D) = (k4_finseq_5 A (k3_finseq_6 A B D C))) ) ) ) ) ) ) ) ) ).
tt(l54_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k1_seq_1 D E))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(l54_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 2 3 1)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 2 3 1) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 2 3 1) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v5_matrix_2 (k3_finseq_4 k5_numbers 2 3 1) 3) & (m1_subset_1 (k3_finseq_4 k5_numbers 2 3 1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(l54_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_tarski D (k1_relset_1 A F)) &  ((v6_supinf_2 F) &  ((r1_mesfunc1 A B F D) &  ((v2_mesfunc9 E A) &  ((r1_seqfunc A k7_numbers E D) &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers E G)) & (v6_supinf_2 (k4_mesfunc5 A k7_numbers E G))) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) =>  ((v1_mesfunc9 (k3_mesfunc5 A E G)) &  ((k1_mesfunc9 F G) = (k3_mesfunc9 (k3_mesfunc5 A E G))) ) ) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_mesfunc9 G H) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers E H) D))) ) )  &  ((v1_mesfunc9 G) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers F D)) = (k3_mesfunc9 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 E A) =>  ( (E = B)  |  ((k1_seq_1 C E) = (k1_seq_1 D E)) ) ) ) )  & (r1_xxreal_0 B A))  =>  ((k9_real_1 (k6_series_1 C A) (k1_seq_1 C B)) = (k9_real_1 (k6_series_1 D A) (k1_seq_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(l54_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) (k3_oppcat_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(l54_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r6_relat_2 A B) & (r1_tarski C B))  => (r6_relat_2 A C)) ) ) ) ) ).
tt(l54_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(l54_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ( ((k6_rinfsup2 A) = (k5_rinfsup2 A))  &  ((k6_rinfsup2 A) = k2_supinf_1) )  =>  ((v10_mesfunc5 A) &  ( ((k2_mesfunc5 A) = (k6_rinfsup2 A))  &  ((k2_mesfunc5 A) = (k5_rinfsup2 A)) ) ) ) ) ) ).
tt(l54_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_struct_0 C B) <=>  ((k3_rlsub_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(l54_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) => (r1_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(l54_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k3_rltopsp1 A B) A A)) ) ) ) ).
tt(l54_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_finseq_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((k3_finseq_1 B) = k6_numbers)  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(l54_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 1 1))) = B)  & (r1_xxreal_0 (k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 1 1))) (k3_finseq_1 (k18_scmfsa_2 C (k5_scmfsa_2 k6_numbers)))))  =>  ( ((k18_scmfsa_2 C (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))) C A) (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 2 1))) = (k1_funct_1 (k1_scmfsa6b (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))) C A) (k4_scmfsa_2 (k2_nat_1 2 1))))  &  (~  ( (~  (B = k6_numbers) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (D = (k6_xcmplx_0 (k1_funct_1 (k1_scmfsa6b (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers)))))) C A) (k4_scmfsa_2 (k2_nat_1 3 1))) (k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 3 1)))))  &  ((r1_xxreal_0 D B) &  ( ((r1_xxreal_0 1 (k6_xcmplx_0 B D)) =>  ( (E = (k1_funct_1 (k18_scmfsa_2 C (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 B D)))  & (r1_xxreal_0 (k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 5 1))) E)) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 F (k6_xcmplx_0 B D)))  &  ( (~ (r1_xxreal_0 (k2_nat_1 B 1) F))  &  (! [G:$i] :  ((v1_int_1 G) =>  (~  ( (G = (k1_funct_1 (k18_scmfsa_2 C (k5_scmfsa_2 k6_numbers)) F))  & (r1_xxreal_0 G (k1_funct_1 C (k4_scmfsa_2 (k2_nat_1 5 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( (~  ( (~ (r2_hidden A (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))))  &  ( (~ (r2_hidden A a_0_1_scmpds_2))  &  ( (~ (r2_hidden A a_0_2_scmpds_2))  &  ( (~ (r2_hidden A a_0_3_scmpds_2))  &  (~ (r2_hidden A a_0_5_scmpds_2)) ) ) ) ) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = k6_numbers) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 1) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 2) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 3) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 9) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 10) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 11) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 12) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 13) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l54_scmpds_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_tarski (k61_valued_1 A 1) (k2_scmpds_7 B C D A))) ) ) ) ) ) ) ) ).
tt(l54_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  =>  ( (B = C)  |  ((r2_hidden (k2_tarski B C) (k1_scmyciel A)) <=>  (~ (r2_hidden (k2_tarski B C) (k1_scmyciel (k6_subset_1 (k5_scmyciel (k3_tarski A)) (k1_scmyciel A))))) ) ) ) ) ) ) ) ).
tt(l54_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers A k31_binop_2) => (r2_relset_1 k1_numbers k1_numbers k1_sin_cos2 (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A k24_sin_cos)) (k10_real_1 1 2)))) ) ) ).
tt(l54_toprealb,ax, ((u1_struct_0 (k11_toprealb k10_toprealb)) = (k2_struct_0 (k11_toprealb k10_toprealb))) ).
tt(l54_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k16_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)))) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (A = (k3_xtuple_0 B C D))  =>  ( (B = 4)  |  ((k9_turing_1 k16_turing_1 A) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 k16_turing_1) (u1_turing_1 k16_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k16_turing_1 A)) (k2_xcmplx_0 (k7_turing_1 k16_turing_1 A) (k6_turing_1 k16_turing_1 (k8_turing_1 k16_turing_1 A))) (k5_turing_1 k16_turing_1 (k3_mcart_1 (u2_turing_1 k16_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)) A) (k7_turing_1 k16_turing_1 A) (k2_mcart_1 (u2_turing_1 k16_turing_1) (u1_turing_1 k16_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k16_turing_1 A))))) ) ) ) ) ) ) ) ).
tt(l54_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  ((k6_yellow_6 A) = (k6_yellow_6 B)) ) ) ) ) ) ).
tt(l54_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 k6_numbers (k6_xcmplx_0 A B))) ) ) ) ) ) ).
tt(l55_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A B C) & (r5_aff_1 A C D))  => (r5_aff_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(l55_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~  ( (~  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k14_afproj A))) => (r1_incsp_1 (k14_afproj A) B C)) ) ) ) ) ) ) ) ).
tt(l55_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  ((k1_algstr_0 (k5_afvect0 A B) C (k4_struct_0 (k5_afvect0 A B))) = C) ) ) ) ) ) ) ).
tt(l55_analmetr,ax,(r1_analmetr c4__analmetr c5__analmetr c6__analmetr)).
tt(l55_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (~  ( (~  (A = k11_arytm_3) )  &  ((r1_tarski A B) &  ( (~  (A = B) )  &  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (~  ((k5_arytm_2 A C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_borsuk_7,ax,(m1_subset_1 k8_borsuk_7 (u1_struct_0 (k15_euclid 3)))).
tt(l55_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_algstr_0 (k9_c0sp2 A) B C) = (k3_rlvect_1 (k11_c0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))) =>  ((r2_hidden B (k6_cc0sp2 A)) => (r2_hidden (k4_algstr_0 (k8_cfuncdom (u1_struct_0 A)) B) (k6_cc0sp2 A))) ) ) ) ) ).
tt(l55_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ((m2_subset_1 (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers) (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) &  ((k1_funct_1 (k5_ec_pf_1 A B C) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers)) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ).
tt(l55_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_fintopo6 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(l55_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  ((v1_funct_1 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 A)) (k3_finseq_2 (k1_fomodel1 A)) (k20_fomodel0 (k1_fomodel1 A) B C) (k35_fomodel1 A))) &  ((v1_funct_2 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 A)) (k3_finseq_2 (k1_fomodel1 A)) (k20_fomodel0 (k1_fomodel1 A) B C) (k35_fomodel1 A)) (k35_fomodel1 A) (k35_fomodel1 A)) & (m1_subset_1 (k2_partfun1 (k3_finseq_2 (k1_fomodel1 A)) (k3_finseq_2 (k1_fomodel1 A)) (k20_fomodel0 (k1_fomodel1 A) B C) (k35_fomodel1 A)) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 A) (k35_fomodel1 A))))) ) ) ) ) ) ) ) ).
tt(l55_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l55_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A B 1 (k3_finseq_1 B)) B)) ) ) ) ).
tt(l55_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C D)) &  ((r2_hidden G (k2_polynom1 (k15_pre_poly A) C E)) &  ( (~  ( (F = (k3_termord A B C D))  &  (G = (k3_termord A B C E)) ) )  &  ((k11_pre_poly A (k3_termord A B C D) G) = (k11_pre_poly A (k3_termord A B C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B (k21_binop_2 A 1) C) = (k6_algstr_0 B (k5_group_1 B A C) (k5_group_1 B (k19_binop_2 1) C))) ) ) ) ) ) ) ).
tt(l55_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~ (v3_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) ) ) ).
tt(l55_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) => (m2_subset_1 (k2_wsierp_1 A) k1_numbers k5_numbers)) ) ).
tt(l55_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((r2_hidden B (k4_finseq_1 C)) & (r1_xxreal_0 A B)) )  =>  ((k3_finseq_1 (k2_finseq_6 C A B)) = (k7_real_1 (k9_real_1 B A) 1)) ) ) ) ) ) ) ) ).
tt(l55_jgraph_2,ax, ((v4_pre_topc a_0_8_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_8_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l55_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_funct_1 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k4_pscomp_1)) &  ((v1_funct_2 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k4_pscomp_1) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 (k3_relat_1 (k5_relat_1 (k2_funct_1 k1_jgraph_3) A) k4_pscomp_1) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) ) ) ) ).
tt(l55_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A))) ) )  => (r1_tarski (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(l55_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 3 1 2)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 3 1 2) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 3 1 2) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v5_matrix_2 (k3_finseq_4 k5_numbers 3 1 2) 3) & (m1_subset_1 (k3_finseq_4 k5_numbers 3 1 2) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(l55_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 A) => (v2_rcomp_1 (k4_measure6 A))) ) ) ).
tt(l55_mod_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden (u1_struct_0 k18_mod_2) A)) ) ).
tt(l55_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_ringcat1 C A B) => (v13_vectsp_1 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(l55_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)) &  ((v13_vectsp_1 E (k14_prvect_2 A) B) &  ((v1_lopban_1 E (k14_prvect_2 A) B) &  ((v2_lopban_1 E (k14_prvect_2 A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B))))) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) &  ( ((k4_finseq_1 G) = (k2_finseq_1 (k3_finseq_1 A)))  &  ( (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r2_hidden H (k2_finseq_1 (k3_finseq_1 A))) =>  ((k1_funct_1 G H) = (k17_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A H)) B (k6_ndiff_5 A B H C D) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H))) (k3_ndiff_5 A (k5_ndiff_5 A H)) F))) ) ) )  &  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) E F) = (k4_rlvect_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ( (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((r2_hidden D B) => (r2_hidden D C)) ) )  => (r1_tarski B C)) ) ) ) ) ) ).
tt(l55_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v9_o_ring_1 B A) => (v12_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l55_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_poset_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_poset_1 A A))) =>  ((r3_orders_2 (k6_poset_1 A A) B C) =>  ((r2_hidden B (k4_poset_1 A A)) &  ((r2_hidden C (k4_poset_1 A A)) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ( (B = D)  &  ( (C = E)  & (r1_yellow_2 (u1_struct_0 A) A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k19_quofield A)))  &  ((v5_group_1 (k19_quofield A)) & (l6_algstr_0 (k19_quofield A))) ) ) ) ).
tt(l55_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ( ((k6_rinfsup2 A) = (k5_rinfsup2 A))  & (r2_hidden (k6_rinfsup2 A) k1_numbers))  =>  ((v10_mesfunc5 A) &  ( ((k2_mesfunc5 A) = (k6_rinfsup2 A))  &  ((k2_mesfunc5 A) = (k5_rinfsup2 A)) ) ) ) ) ) ).
tt(l55_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v3_pre_topc B A) => (v3_pre_topc (k5_rusub_4 A B C) A)) ) ) ) ) ) ) ).
tt(l55_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_struct_0 D C) <=>  ((k3_rmod_2 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(l55_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( ((k1_rmod_3 A B C D) = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B)))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l55_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) B A) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1))  &  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) B A) (k5_scmfsa_2 k6_numbers)) = (k3_funct_7 k4_numbers (k3_funct_7 k4_numbers (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_int_2 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) (k7_partfun1 k4_numbers (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_int_2 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)))) (k1_int_2 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)) (k7_partfun1 k4_numbers (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_int_2 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))))))) ) ) ) ) ) ).
tt(l55_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 B) 1) (k1_funct_4 C (k10_compos_1 k1_scmpds_2 (k2_scmpds_4 A B))))) ) ) ) ) ) ).
tt(l55_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((v4_scmyciel B) =>  ( (B = (k6_subset_1 (k5_scmyciel (k3_tarski A)) (k1_scmyciel A)))  =>  ((k6_subset_1 (k5_scmyciel (k3_tarski B)) (k1_scmyciel B)) = A) ) ) ) ) ) ).
tt(l55_tmap_1,ax, (! [A:$i] :  ((v1_funct_1 k1_xboole_0) &  ((v1_funct_2 k1_xboole_0 A k1_xboole_0) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 A k1_xboole_0)))) ) ) ).
tt(l55_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E B)) ) )  =>  ( ( (D = E)  & (r1_waybel_0 A D C))  => (r1_waybel_0 B E C)) ) ) ) ) ) ) ) ) ) ).
tt(l55_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) <=> (r1_int_1 A (k1_int_2 B))) ) ) ) ) ).
tt(l56_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) B D) &  ((r1_incsp_1 (k13_afproj A) B E) &  ((r1_incsp_1 (k13_afproj A) C D) &  ((r1_incsp_1 (k13_afproj A) C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_rlvect_1 (k5_afvect0 A B)) &  ((v3_rlvect_1 (k5_afvect0 A B)) & (v4_rlvect_1 (k5_afvect0 A B))) ) ) ) ) ) ).
tt(l56_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) => (v2_funct_1 (k16_algstr_4 A B))) ) ) ).
tt(l56_analmetr,ax, ( ( (~ (v7_struct_0 (g1_analoaf (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)) (u1_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)))))  &  ((v1_diraf (g1_analoaf (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)) (u1_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)))) &  ((v2_diraf (g1_analoaf (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)) (u1_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)))) & (l1_analoaf (g1_analoaf (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr)) (u1_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  ( ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B A B) =>  (A = B) )  &  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B C C) &  ( ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B C D) =>  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B D C) & (r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) C D A B)) )  &  ( (~  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B E F) &  ((r2_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B G H) &  ( (~ (r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) E F G H))  &  (~  (A = B) ) ) ) ) )  &  (~  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B E F) &  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B G H) &  ( (~ (r2_analoaf (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) E F G H))  &  (~  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr c4__analmetr c5__analmetr c6__analmetr))) &  ((r4_analmetr (k2_analmetr c4__analmetr c5__analmetr c6__analmetr) A B C D) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((r1_arytm_2 A B) => (r1_tarski (k3_arytm_2 A) (k3_arytm_2 B))) ) ) ) ) ).
tt(l56_asympt_1,ax, ((k5_series_1 2 12) = 4096) ).
tt(l56_borsuk_7,ax,(m1_subset_1 k8_borsuk_7 (u1_struct_0 (k8_toprealb (k2_nat_1 2 1))))).
tt(l56_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 (u1_struct_0 A)))) =>  ( (C = D)  =>  ((k1_rlvect_1 (k9_c0sp2 A) C B) = (k1_rlvect_1 (k11_c0sp1 (u1_struct_0 A)) D B)) ) ) ) ) ) ) ) ) ) ).
tt(l56_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_wellord2 A B) =>  (A = B) ) ) ) ) ) ).
tt(l56_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = (k10_cgames_1 A))  &  (! [C:$i] :  ((v2_cgames_1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (g1_cgames_1 (a_2_1_cgames_1 B C) (a_2_2_cgames_1 B C))) ) ) ) )  =>  (! [C:$i] :  ((v2_cgames_1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k13_cgames_1 C)) ) ) ) ) ) ) ) ) ).
tt(l56_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_yellow_1 k1_xboole_0 A)))  &  ((v3_dickson (k5_yellow_1 k1_xboole_0 A)) &  ((v4_dickson (k5_yellow_1 k1_xboole_0 A)) & (v5_orders_2 (k5_yellow_1 k1_xboole_0 A))) ) ) ) ) ).
tt(l56_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((v2_euclid_4 B A) &  ((r2_hidden C B) & (r2_hidden D B)) )  =>  ( (C = D)  |  (B = (k4_euclid_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) (k21_fomodel2 B C (k23_fomodel2 B A C))) = (k2_zfmisc_1 (k16_fomodel2 B C) (k29_fomodel2 B A))) ) ) ) ) ) ) ).
tt(l56_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (? [E:$i] :  ( ((v4_fomodel2 E A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ( ((k32_fomodel2 A D) = (k32_fomodel2 A E))  &  ((k3_funct_2 (k3_finseq_2 (k15_fomodel1 A)) (k3_finseq_2 (k1_fomodel1 A)) (k20_fomodel0 (k1_fomodel1 A) B C) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k8_glib_001 A B C C) = (k12_finseq_1 (k6_glib_000 A) (k5_glib_001 A B C))) ) ) ) ) ) ) ) ).
tt(l56_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~  (A = (k19_binop_2 1)) )  & (r1_xxreal_0 (k19_binop_2 1) A)) ) ) ) ) ).
tt(l56_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k1_real_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k9_real_1 (k1_real_1 (k18_euclid A)) (k1_real_1 (k18_euclid B)))) ) ) ) ) ) ).
tt(l56_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( ((r2_hidden A (k4_finseq_1 D)) & (r2_hidden B (k4_finseq_1 D)))  => (r1_xxreal_0 1 (k3_finseq_1 (k3_finseq_6 C D A B)))) ) ) ) ) ) ) ) ) ).
tt(l56_jordan6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((v5_pre_topc A k17_borsuk_1 k3_topmetr) &  ( (~ (r1_xxreal_0 D (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr) A k18_borsuk_1)))  &  ( (~ (r1_xxreal_0 (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k3_topmetr) A k19_borsuk_1) D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 1 E))  &  ((k1_funct_1 A E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v3_matrtop3 B A) => (v4_matrix_6 (k3_matrtop3 A B) A k2_vectsp_1)) ) ) ) ) ).
tt(l56_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden (k1_relset_1 A D) B) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A D)) =>  ((k12_supinf_2 D F) = E) ) ) )  => (r1_mesfunc2 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  => (r2_modelc_1 A B C k6_numbers)) ) ) ) ) ) ).
tt(l56_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 C A) & (v9_o_ring_1 B A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l56_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k6_matrix_3 A (k4_matrix_3 A (k12_matrix_1 A (k4_nat_1 2 B)) (k4_polynom8 (k4_nat_1 2 B) A (k13_polynom3 A C D))) (k1_polynom8 A (k4_nat_1 2 B))) = (k6_matrix_3 A (k4_polynom8 (k4_nat_1 2 B) A (k13_polynom3 A C D)) (k1_polynom8 A (k4_nat_1 2 B)))) ) ) ) ) ) ) ) ) ) ).
tt(l56_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k10_poset_1 A)) &  ((v1_funct_2 (k10_poset_1 A) (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A)) &  ((v5_orders_3 (k10_poset_1 A) (k6_poset_1 A A) A) & (m1_subset_1 (k10_poset_1 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A))))) ) ) ) ) ).
tt(l56_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v4_vectsp_1 (k19_quofield A))) ) ).
tt(l56_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (v3_pre_topc (k7_rusub_4 A C B) A)) ) ) ) ) ) ).
tt(l56_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k3_rlvect_1 B D E))  <=>  (D = (k5_algstr_0 B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_scmisort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 3 1))) = A)  & (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) |  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k5_scmfsa_2 k6_numbers))) &  ( ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A))  &  ( ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A)) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) =>  ((r1_xxreal_0 D (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A)) |  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k5_scmfsa_2 k6_numbers)) D) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 D 1))) ) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))) =>  ((r1_xxreal_0 D (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) |  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k5_scmfsa_2 k6_numbers)) D) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) D)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) D) |  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))) B C) (k5_scmfsa_2 k6_numbers)) D) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  => (r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 C) 2) (k1_funct_4 D (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 (k4_scmpds_4 A B) C))))) ) ) ) ) ) ) ) ).
tt(l56_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_semi_af1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((r1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A) &  ((k1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A) = (k8_real_1 (k10_real_1 1 2) (k1_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) A))) ) ) ) ) ) ) ).
tt(l56_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_topalg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_topalg_1 A B))) =>  (! [E:$i] :  ((m1_borsuk_2 E A B B) =>  (! [F:$i] :  ((m1_borsuk_2 F A B B) =>  ( ( (C = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) E))  &  (D = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) F)) )  =>  ((k6_algstr_0 (k5_topalg_1 A B) C D) = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) (k1_borsuk_2 A B B B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_topalg_6 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_topalg_6 A)) =>  ((k1_funct_1 (k5_topalg_6 A (k8_finseq_1 (k1_topalg_6 A) B C)) (k3_finseq_1 B)) = (k1_funct_1 (k5_topalg_6 A B) (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(l56_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_struct_0 D C) <=>  ((k3_vectsp_4 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(l56_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k1_vectsp_5 A B C D) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( (C = D)  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = F)  & (r2_hidden E (k10_yellow_6 A C)))  => (r2_hidden F (k10_yellow_6 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l56_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_int_1 (k3_xcmplx_0 A B) B) = k6_numbers) ) ) ) ) ).
tt(l57_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k13_afproj A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) &  ((r1_incsp_1 (k13_afproj A) C B) &  ((r1_incsp_1 (k13_afproj A) D B) &  ((r1_incsp_1 (k13_afproj A) E B) &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v13_algstr_0 (k5_afvect0 A B))) ) ) ) ).
tt(l57_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ((k1_relset_1 (k11_algstr_4 A 1) (k16_algstr_4 A 1)) = A)  &  (! [B:$i] :  ((r2_hidden B A) =>  ((k1_funct_1 (k16_algstr_4 A 1) B) = (k4_tarski B 1)) ) ) ) ) ) ).
tt(l57_anproj_2,ax, (? [A:$i] :  ( (~ (v1_xboole_0 A))  &  (? [B:$i] :  ((m1_subset_1 B A) &  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) &  (? [E:$i] :  ((m1_subset_1 E A) &  ( (A = (k9_domain_1 A B C D E))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_asympt_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 3 A) & (r1_xxreal_0 (k3_square_1 A) (k2_nat_1 (k4_nat_1 2 A) 1))) ) ) ) ).
tt(l57_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k7_bcialg_1 A B)) =>  ((k1_bcialg_1 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(l57_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_finset_1 A) <=> (r2_hidden A k4_ordinal1)) ) ) ).
tt(l57_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k12_csspace A (k3_rlvect_1 A (k1_clvect_1 A D B) (k1_clvect_1 A E C)) (k3_rlvect_1 A (k1_clvect_1 A D B) (k1_clvect_1 A E C))) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 B (k15_complex1 B)) (k12_csspace A D D)) (k3_xcmplx_0 (k3_xcmplx_0 B (k15_complex1 C)) (k12_csspace A D E))) (k3_xcmplx_0 (k3_xcmplx_0 (k15_complex1 B) C) (k12_csspace A E D))) (k3_xcmplx_0 (k3_xcmplx_0 C (k15_complex1 C)) (k12_csspace A E E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_descip_1,ax, ((m1_subset_1 k6_numbers 16) &  ((m1_subset_1 1 16) &  ((m1_subset_1 2 16) &  ((m1_subset_1 3 16) &  ((m1_subset_1 4 16) &  ((m1_subset_1 5 16) &  ((m1_subset_1 6 16) &  ((m1_subset_1 7 16) &  ((m1_subset_1 8 16) &  ((m1_subset_1 9 16) &  ((m1_subset_1 10 16) &  ((m1_subset_1 11 16) &  ((m1_subset_1 12 16) &  ((m1_subset_1 13 16) &  ((m1_subset_1 14 16) & (m1_subset_1 15 16)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) => (m2_subset_1 (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers B C 1) (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A)))) ) ) ) ) ) ).
tt(l57_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_finset_1 (k8_euclid_7 A)) &  ((k1_card_1 (k8_euclid_7 A)) = A) ) ) ) ).
tt(l57_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  &  ( (C = E)  &  (D = F) ) )  =>  ((k5_filter_0 A C D) = (k5_filter_0 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) (k19_fomodel2 B C (k23_fomodel2 B A C))) = (k2_zfmisc_1 (k16_fomodel2 B C) (k28_fomodel2 B A))) ) ) ) ) ) ) ).
tt(l57_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k32_fomodel2 A D) = (k32_fomodel2 A (k24_fomodel3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(l57_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((k36_gfacirc1 A B C) = (k4_tarski D k3_twoscomp)) ) ) ) ) ) ).
tt(l57_funct_9,ax,(v1_funct_9 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k32_sin_cos)).
tt(l57_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) =>  ((v1_abian C) | (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A (k8_glib_001 A B 1 D) 1 C) (k8_glib_001 A B 1 C))) ) ) ) ) ) ) ) ) ) ).
tt(l57_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B (k20_binop_2 A 1) C) = (k6_algstr_0 B (k5_group_1 B A C) (k5_group_1 B 1 C))) ) ) ) ) ) ) ).
tt(l57_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) = (k7_real_1 (k5_square_1 (k17_euclid (k5_algstr_0 (k15_euclid 2) A B))) (k5_square_1 (k1_real_1 (k18_euclid (k5_algstr_0 (k15_euclid 2) A B)))))) ) ) ) ) ).
tt(l57_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k5_square_1 1) (k4_square_1 (k13_complex1 (k1_real_1 (k5_real_1 (k13_complex1 C (k12_euclid A)) B)) (k9_real_1 1 B)))))  & (r1_xxreal_0 (k1_real_1 k6_numbers) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 C (k12_euclid A)) B) (k9_real_1 1 B)))))))) ) ) ) ) ) ) ) ).
tt(l57_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (~  ((r2_hidden A (k4_finseq_1 D)) &  ((r2_hidden B (k4_finseq_1 D)) & (v1_xboole_0 (k3_finseq_6 C D A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  ((k1_partfun1 k5_numbers k5_numbers (k2_finseq_1 3) (k2_finseq_1 3) (k3_finseq_4 k5_numbers 1 2 3) A) = A) ) ) ).
tt(l57_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) =>  ((v2_matrixj1 (k4_matrixj1 B C) B) & (m2_finseq_1 (k4_matrixj1 B C) (k3_finseq_2 (k3_finseq_2 B)))) ) ) ) ) ) ) ).
tt(l57_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k1_xboole_0))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 E) k1_xboole_0))  &  (~  ((k11_ranknull A B C (k4_matrlin2 A B C D E F)) = (k6_xcmplx_0 (k3_finseq_1 D) (k8_matrix13 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_measure6 A B) = (a_2_0_measure6 A B)) ) ) ) ) ).
tt(l57_mod_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r2_hidden A B) => (r2_hidden C B)) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r2_hidden A B) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(l57_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_1 B) & (l2_modelc_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k18_modelc_1 (u3_modelc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 B))))) )  =>  ((r2_modelc_1 B C D (k2_nat_1 A 1)) => (r2_modelc_1 B C D A)) ) ) ) ) ) ) ) ) ).
tt(l57_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ((r1_xxreal_0 (k1_newton C B) (k4_nat_1 2 A)) &  ( ((k3_finseq_1 D) = (k4_nat_1 2 A))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k5_real_1 (k1_int_1 (k10_real_1 (k4_nat_1 2 A) (k1_newton C E))) (k8_real_1 2 (k1_int_1 (k10_real_1 A (k1_newton C E)))))) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_newton C (k2_nat_1 B 1)) (k4_nat_1 2 A)) | (r1_xxreal_0 (k18_rvsum_1 D) B)) ) ) ) ) ) ) ) ) ) ).
tt(l57_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l57_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) => (m1_subset_1 (k3_tarski (k4_orders_2 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(l57_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l57_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (! [E:$i] :  (~  ( (D = (a_3_1_poset_1 A B C))  &  ((r2_hidden E D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 G A A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ( (E = F)  &  ((r2_hidden G B) &  (F = (k1_funct_1 (k9_funct_7 G C) (k3_yellow_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l57_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k4_prepower A B))) ) ) ) ) ).
tt(l57_quaterni,ax, ((k6_quaterni 1 k6_numbers k6_numbers k6_numbers) = 1) ).
tt(l57_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k17_ringcat1 A))) =>  ( ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B))  =>  ( ((k3_graph_1 (k17_ringcat1 A) (k1_cat_1 (k17_ringcat1 A) B C)) = (k3_graph_1 (k17_ringcat1 A) B))  &  ((k4_graph_1 (k17_ringcat1 A) (k1_cat_1 (k17_ringcat1 A) B C)) = (k4_graph_1 (k17_ringcat1 A) C)) ) ) ) ) ) ) ) ) ).
tt(l57_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v4_pre_topc (k5_rusub_4 A B C) A)) ) ) ) ) ) ).
tt(l57_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) A B) (k4_scmfsa_2 (k2_nat_1 1 1))) = (k6_xcmplx_0 (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))) (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))))  &  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) A B) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))) (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) 1))  &  ( ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) A B) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) A B) (k4_scmfsa_2 (k2_nat_1 3 1))) = k6_numbers)  &  ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) A B) (k4_scmfsa_2 (k2_nat_1 5 1))) = (k7_partfun1 k4_numbers (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)) (k1_int_2 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))) (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) 1)))) ) ) ) ) ) ) ) ) ).
tt(l57_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers B k31_binop_2) =>  ((k1_seq_1 k4_sin_cos2 A) = (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos)) (k10_real_1 1 2)) A)) ) ) ) ) ) ).
tt(l57_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( (D = (k10_metric_1 A B C))  => (v3_pre_topc (k3_subset_1 (u1_struct_0 (k3_pcomps_1 A)) D) (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(l57_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ((k12_yellow_6 A) = (k12_yellow_6 B)) ) ) ) ) ) ).
tt(l57_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k6_int_1 A B) = (k6_int_1 C B))  =>  ((k6_int_1 (k6_xcmplx_0 A C) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l57_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 C D)) = (k7_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(l57_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (? [B:$i] :  ( ((v1_pre_topc B) &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((v1_tops_2 (u1_pre_topc A) B) &  ((v2_cantor_1 (u1_pre_topc A) B) & (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(l58_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) )  => (v5_relat_1 A k2_numbers)) ) ).
tt(l58_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) &  ((r1_incsp_1 (k13_afproj A) B D) & (r1_incsp_1 (k13_afproj A) C D)) ) ) ) ) ) ) ) ) ).
tt(l58_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 10 A) & (r1_xxreal_0 (k4_power 2 (k9_real_1 A 1)) (k5_square_1 (k4_nat_1 2 A)))) ) ) ) ).
tt(l58_borsuk_7,ax,(m1_subset_1 k9_borsuk_7 (u1_struct_0 (k15_euclid 3)))).
tt(l58_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v6_metric_1 A) => (v6_metric_1 (k3_compl_sp A B C)))  &  ( ((v8_metric_1 A) => (v8_metric_1 (k3_compl_sp A B C)))  &  ( ( ((v9_metric_1 A) &  ((v8_metric_1 A) & (v6_metric_1 A)) )  => (v9_metric_1 (k3_compl_sp A B C)))  &  ( ((v9_metric_1 A) &  ((v8_metric_1 A) &  ((v6_metric_1 A) & (v7_metric_1 A)) ) )  => (v7_metric_1 (k3_compl_sp A B C))) ) ) ) ) ) ) ) ) ).
tt(l58_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] : (r1_xboole_0 (k2_msafree2 (k37_gfacirc1 A B C)) (k3_msafree2 (k25_gfacirc1 D E F)))) ) ) ) ) ) ) ) ) ).
tt(l58_funct_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_funct_9 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k8_real_1 k32_sin_cos (k3_real_1 A 1)))) ) ).
tt(l58_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k4_glib_001 A B) = (k3_glib_001 A C)) ) )  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A (k7_glib_001 A B C) D E) (k8_glib_001 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l58_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) A))) ) ) ).
tt(l58_jgraph_2,ax, ((v4_pre_topc a_0_9_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_9_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(l58_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( ((r2_hidden A (k4_finseq_1 D)) & (r2_hidden B (k4_finseq_1 D)))  =>  ((k7_partfun1 C (k3_finseq_6 C D A B) 1) = (k7_partfun1 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(l58_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) B) &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) D) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B D) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B D) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c D (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) )  &  ( (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) C) &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) D) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c C (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c D (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) )  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(l58_lopban_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(l58_matrix13,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_setfam_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski A B) =>  ((k1_card_1 A) = (k5_card_1 (k8_relat_1 (k5_matrix13 B) A))) ) ) ) ) ).
tt(l58_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  ((k1_partfun1 (k2_finseq_1 3) (k2_finseq_1 3) k5_numbers k5_numbers A (k3_finseq_4 k5_numbers 1 2 3)) = A) ) ) ).
tt(l58_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ((k9_subset_1 A C (k15_mesfunc1 A D (k1_measure6 E))) = (k15_mesfunc1 A (k2_partfun1 A k7_numbers D C) (k1_measure6 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l58_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_1 B) & (l2_modelc_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k18_modelc_1 (u3_modelc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 B))))) )  =>  ((r1_modelc_1 B C D) => (r2_modelc_1 B C D A)) ) ) ) ) ) ) ) ) ).
tt(l58_mycielsk,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 A) = k5_numbers)  &  ( ((k1_funct_1 A k6_numbers) = (k5_mycielsk 2))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_mycielsk D (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 C)) 1)) =>  ( (D = (k1_funct_1 A C))  =>  ((k1_funct_1 A (k2_xcmplx_0 C 1)) = (k6_mycielsk (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 C)) 1) D)) ) ) ) ) )  &  ( ((k9_xtuple_0 B) = k5_numbers)  &  ( ((k1_funct_1 B k6_numbers) = (k5_mycielsk 2))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_mycielsk D (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 C)) 1)) =>  ( (D = (k1_funct_1 B C))  =>  ((k1_funct_1 B (k2_xcmplx_0 C 1)) = (k6_mycielsk (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 C)) 1) D)) ) ) ) ) ) ) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(l58_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ((r1_xxreal_0 3 A) =>  ( ( (~ (r1_xxreal_0 B (k4_nat_1 2 A)))  =>  ((k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B) = k6_numbers) )  &  ( ((r1_xxreal_0 B (k4_nat_1 2 A)) =>  ((r1_xxreal_0 B A) | (r1_xxreal_0 (k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B) 1)) )  &  ( ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 B (k10_real_1 (k4_nat_1 2 A) 3)) |  ((k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B) = k6_numbers) ) )  &  ( ((r1_xxreal_0 B (k10_real_1 (k4_nat_1 2 A) 3)) =>  ((r1_xxreal_0 B (k7_square_1 (k4_nat_1 2 A))) | (r1_xxreal_0 (k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B) 1)) )  &  ((r1_xxreal_0 B (k7_square_1 (k4_nat_1 2 A))) => (r1_xxreal_0 (k1_newton B (k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B)) (k4_nat_1 2 A))) ) ) ) ) ) ) ) ) ) ).
tt(l58_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k3_graph_1 A D)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k4_graph_1 A D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l58_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_relat_2 A B) => (r1_relat_2 (k2_relat_1 A) B)) ) ) ) ).
tt(l58_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  ((v6_orders_2 (k3_tarski (k4_orders_2 A B)) A) & (m1_subset_1 (k3_tarski (k4_orders_2 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(l58_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v10_o_ring_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ( (C = k6_numbers)  | (v13_o_ring_1 (k7_partfun1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ).
tt(l58_poset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 B B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 B B))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (E = (a_3_1_poset_1 B C D))  & (r2_hidden A E))  => (m1_subset_1 A (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(l58_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k17_ringcat1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k17_ringcat1 A))) =>  ( ( ((k3_graph_1 (k17_ringcat1 A) D) = (k4_graph_1 (k17_ringcat1 A) C))  &  ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B)) )  =>  ((k1_cat_1 (k17_ringcat1 A) (k1_cat_1 (k17_ringcat1 A) B C) D) = (k1_cat_1 (k17_ringcat1 A) B (k1_cat_1 (k17_ringcat1 A) C D))) ) ) ) ) ) ) ) ) ) ).
tt(l58_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) = (k6_xcmplx_0 (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))) 1))  =>  ((r2_classes1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) A B) (k5_scmfsa_2 k6_numbers))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( (E = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) A B) (k5_scmfsa_2 k6_numbers)) C))  &  (F = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 3 1)))) (k2_scmfsa_9 (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 5 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 4 1)) (k11_compos_1 k1_scmfsa_2 (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 1 1)))) (k6_scmfsa6a (k7_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))))))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 1 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers)))))) A B) (k5_scmfsa_2 k6_numbers)) D)) )  => (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l58_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 k6_numbers (k8_real_1 (k1_seq_1 (k3_series_1 A) B) (k1_seq_1 A (k2_nat_1 B 1))))) ) ) ) ) ).
tt(l58_sin_cos2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers A k31_binop_2) => (r2_relset_1 k1_numbers k1_numbers k4_sin_cos2 (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A k24_sin_cos)) (k10_real_1 1 2)))) ) ) ).
tt(l58_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~ (r2_hidden (k3_termord A B C D) (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)))) ) ) ) ) ) ) ) ) ).
tt(l58_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) => (r1_vectsp_5 A B D C)) ) ) ) ) ) ) ) ) ).
tt(l58_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(l58_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_hidden (k3_yellow_0 A) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ((r3_orders_2 A C E) & (r1_waybel_3 A E D)) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_tarski (u1_struct_0 (k1_waybel_8 A)) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r3_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l58_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((k6_int_1 B A) = k6_numbers)  =>  ( (A = k6_numbers)  | (r1_int_1 A B)) ) ) ) ) ) ).
tt(l58_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r2_xboole_0 B C))  => (r2_xboole_0 A C)) ) ) ) ).
tt(l58_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_xcmplx_0 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 B A)) ) ) ) ) ).
tt(l59_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  => (v5_relat_1 A k1_numbers)) ) ).
tt(l59_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k13_afproj A))) =>  (~  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) D B) & (r1_incsp_1 (k13_afproj A) D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_asympt_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 9 A) & (r1_xxreal_0 (k4_nat_1 2 (k5_series_1 A 6)) (k5_series_1 (k1_nat_1 A 1) 6))) ) ) ) ).
tt(l59_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B)))) =>  (~  ( (! [D:$i] :  ((r2_hidden D C) => (v1_finset_1 (k1_xtuple_0 D))) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E G) C))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E F) C))  =>  (D = E) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v9_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ( (C = (k8_cohsp_1 A B D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A B D E) = (k7_relat_1 C (k3_cohsp_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k3_finseq_1 (k8_glib_001 A B 1 C)) = C) ) ) ) ) ) ) ) ).
tt(l59_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v2_funct_1 B) &  ((v1_msscyc_1 B A) & (m2_graph_1 B A)) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_graph_2 A C B) & (r2_hidden D (k10_xtuple_0 C)))  => (v1_abian (k7_graph_3 A D (k10_xtuple_0 B)))) ) ) ) ) ) ) ) ) ).
tt(l59_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden B (k2_finseq_1 A)) &  ((r2_hidden C (k2_finseq_1 A)) &  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ((v1_finset_1 E) =>  (~  ( (E = (a_1_0_matrix11 A))  &  ( (D = (a_1_1_matrix11 A))  &  ( ((k3_xboole_0 E D) = k1_xboole_0)  &  ( ((k2_xboole_0 E D) = (k12_matrix_2 A))  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F E D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 E D)))) )  &  (? [G:$i] :  ((m1_matrix_2 G (k12_matrix_2 A)) &  ((v4_matrix_2 G (k11_matrix_2 (k12_matrix_2 A))) &  ( ((k1_funct_1 G B) = C)  &  ( ((k9_xtuple_0 F) = E)  &  ((v3_funct_2 F E D) &  (! [H:$i] :  ((m1_matrix_2 H (k12_matrix_2 A)) =>  ((r2_hidden H E) =>  ((k1_funct_1 F H) = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc1 A B (k2_partfun1 A k7_numbers E D) D) <=> (r1_mesfunc1 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_1 B) & (l2_modelc_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k18_modelc_1 (u3_modelc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k12_modelc_1 (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 B))))) )  =>  ( ((r2_modelc_1 B C D A) & (r2_modelc_1 B C E A))  =>  (! [F:$i] :  ( ((v1_modelc_1 F) & (m2_finseq_1 F k5_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 F) A) =>  ((k1_funct_1 D F) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r8_relat_2 A B) => (r8_relat_2 (k2_relat_1 A) B)) ) ) ) ).
tt(l59_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (D = (a_3_1_poset_1 A B C))  =>  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(l59_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m2_ringcat1 C (k9_ringcat1 A)) =>  ( (B = C)  =>  (! [D:$i] :  ((m1_cat_1 D (k17_ringcat1 A) B B) =>  ( (D = (k13_ringcat1 (k9_ringcat1 A) C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k17_ringcat1 A))) =>  ( ( (~  ((k2_cat_1 (k17_ringcat1 A) B E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k17_ringcat1 A) B E) =>  ((k1_cat_1 (k17_ringcat1 A) D F) = F) ) ) )  &  ( (~  ((k2_cat_1 (k17_ringcat1 A) E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k17_ringcat1 A) E B) =>  ((k1_cat_1 (k17_ringcat1 A) F D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B)) = B) ) ) ) ) ).
tt(l59_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k10_xtuple_0 A)) => (r1_tarski (k3_topreal1 2 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 A))) ) ) ) ) ).
tt(l59_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E (k2_polynom1 (k15_pre_poly A) C D)) =>  ( (E = (k3_termord A B C D))  | (r2_hidden E (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_trees_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  =>  ((r2_hidden (k2_nat_1 A 1) (k1_relset_1 k5_numbers B)) & (r2_hidden (k1_funct_1 B (k2_nat_1 A 1)) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(l59_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v1_finset_1 (k6_polynom5 A B)) &  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ( (C = (k1_card_1 (k6_polynom5 A B)))  &  (~ (r1_xxreal_0 (k1_algseq_1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(l59_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ( (D = E)  & (r2_lattice3 A C D))  => (r2_lattice3 B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r3_orders_2 A E D)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r1_waybel_3 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l59_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v5_orders_3 (k11_waybel_4 A B) A (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(l59_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( ( (~ (r1_xxreal_0 A 1))  =>  ( (~ (r1_xxreal_0 (k6_square_1 A) 1))  &  (~ (r1_xxreal_0 A (k6_square_1 A))) ) )  &  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( (~ (r1_xxreal_0 (k6_square_1 A) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k6_square_1 A)))  &  (~ (r1_xxreal_0 (k6_square_1 A) A)) ) ) ) ) ) ) ) ) ) ).
tt(l59_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 A (k7_xcmplx_0 B C)) = (k7_xcmplx_0 (k3_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(l5_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_diraf A B C D D) =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(l5_algstr_2,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  ((k8_group_1 k2_vectsp_1 A (k4_struct_0 k2_vectsp_1)) = (k4_struct_0 k2_vectsp_1)) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  ((k8_group_1 k2_vectsp_1 (k4_struct_0 k2_vectsp_1) A) = (k4_struct_0 k2_vectsp_1)) ) ) ) ).
tt(l5_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 A) =>  ( ((k3_compos_1 k1_ami_3 A k6_numbers) = (k2_ami_3 (k10_ami_3 2) (k10_ami_3 1)))  &  ( ((k3_compos_1 k1_ami_3 A 1) = (k6_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1)))  &  ( ((k3_compos_1 k1_ami_3 A 2) = (k2_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 2)))  &  ( ((k3_compos_1 k1_ami_3 A 3) = (k9_ami_3 k6_numbers (k10_ami_3 1)))  & (r1_compos_1 k1_ami_3 A 4)) ) ) ) ) ) ) ).
tt(l5_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (k8_struct_0 k1_ami_3)) =>  ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3))) ) ) ).
tt(l5_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (D = (k3_rlvect_1 A (k1_rlvect_1 A B (k2_geomtrap A B C D)) (k1_rlvect_1 A C (k3_geomtrap A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l5_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B C) D) (k3_rlvect_1 A (k3_rlvect_1 A E F) G)) = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B E) (k3_rlvect_1 A C F)) (k3_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_axioms,ax,(m1_subset_1 k6_numbers k2_arytm_2)).
tt(l5_bhsp_1,ax, ((k1_funct_1 c2__bhsp_1 (k1_domain_1 (u1_struct_0 o_0_5_bhsp_1) (u1_struct_0 o_0_5_bhsp_1) (k4_struct_0 o_0_5_bhsp_1) (k4_struct_0 o_0_5_bhsp_1))) = k6_numbers) ).
tt(l5_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 A (k13_complex1 1 2)) & (r1_xxreal_0 k6_numbers A))  => (r2_hidden A (u1_struct_0 k17_borsuk_1))) ) ) ).
tt(l5_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r2_hidden B D) &  ( (~  (B = C) )  &  ((v9_rltopsp1 (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C)) (k15_euclid A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  (~  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k2_tops_1 (k15_euclid A) D) (k4_topreal9 A B C))) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid A))) =>  ( ( (G = B)  & (r2_hidden F (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C))))  => (r1_xxreal_0 (k4_metric_1 (k14_euclid A) G F) (k4_metric_1 (k14_euclid A) G E))) ) ) ) )  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ( (~ (r1_xxreal_0 F k1_xboole_0))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid A))) =>  (~  ((r2_hidden G (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C))) &  (~ (r1_xxreal_0 F (k4_metric_1 (k14_euclid A) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ( (~  (A = B) )  &  ( (~  (C = A) )  &  (~  ((k1_funct_1 (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F)) A) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_calcul_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ((k1_funct_1 A C) = B) ) ) )  => (r1_calcul_1 A B)) ) ) ) ).
tt(l5_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A)) &  ((k1_card_1 (k2_zfmisc_1 A B)) = (k1_card_1 (k2_zfmisc_1 B A))) ) ) ) ).
tt(l5_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) =>  ((k5_relset_1 B (k1_tarski C) (k7_funcop_1 B C) A) = (k7_funcop_1 A C)) ) ) ) ) ) ) ) ).
tt(l5_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k9_finseq_1 A) = (k9_finseq_1 B))  =>  (A = B) ) ) ) ).
tt(l5_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_relset_1 k5_numbers k2_numbers B (k25_valued_1 k5_numbers k2_numbers A k7_complex1)) =>  ((v2_relat_1 A) <=> (v2_relat_1 B)) ) ) ) ) ) ).
tt(l5_closure3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k13_pre_poly B) = (a_2_0_closure3 A B)) ) ) ) ) ).
tt(l5_collsp,ax,(r1_tarski (k1_tarski (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1)) (k3_zfmisc_1 (k6_domain_1 k5_numbers 1) (k6_domain_1 k5_numbers 1) (k6_domain_1 k5_numbers 1)))).
tt(l5_comptrig,ax,(r2_hidden k32_sin_cos (k2_rcomp_1 k6_numbers 4))).
tt(l5_comseq_3,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) k5_numbers k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers k5_numbers k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ).
tt(l5_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) B) A) & (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) C) A)) ) ) ) ) ) ) ).
tt(l5_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  ((k11_comseq_3 (k2_comseq_2 k5_numbers A)) = (k15_complex1 (k11_comseq_3 A))) ) ) ) ).
tt(l5_csspace4,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 B) => (v1_comseq_2 (k25_valued_1 k5_numbers k2_numbers B A))) ) ) ) ) ).
tt(l5_fdiff_1,ax, ((v1_funct_1 (k8_funcop_1 k5_numbers k1_numbers k6_numbers)) &  ((v1_funct_2 (k8_funcop_1 k5_numbers k1_numbers k6_numbers) k1_numbers k1_numbers) & (m1_subset_1 (k8_funcop_1 k5_numbers k1_numbers k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ).
tt(l5_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k8_real_1 2 (k5_square_1 (k1_seq_1 k16_sin_cos (k10_real_1 A 2)))) = (k9_real_1 1 (k1_seq_1 k19_sin_cos A))) ) ) ).
tt(l5_fdiff_8,ax, ((k3_limfunc1 k6_numbers) = a_0_0_fdiff_8) ).
tt(l5_fib_fusc,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (A = (k4_nat_1 2 B))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k2_xcmplx_0 6 (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 B)) 1)) 1)) = (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 A)) 1)) 1)) ) ) ) ) ) ) ).
tt(l5_fib_num,ax, ((k1_pre_ff 2) = 1) ).
tt(l5_finseq_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k7_nat_d (k7_nat_d A B) 1) = (k7_nat_d (k7_nat_d A 1) B)) ) ) ) ) ).
tt(l5_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ( ((k3_finseq_1 B) = k6_numbers)  &  ((v1_setwiseo C A) &  ((v2_binop_1 C A) & (v1_binop_1 C A)) ) )  =>  ((k1_finsop_1 A B C) = (k7_setwiseo k5_numbers A C (k3_finsop_1 B) (k2_finsop_1 A (k8_funcop_1 A k5_numbers (k4_binop_1 A C)) B))) ) ) ) ) ) ) ) ).
tt(l5_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v5_relat_1 B A) & (v1_finseq_1 B))  => (m2_finseq_1 B A)) ) ) ) ).
tt(l5_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m3_fomodel2 C A B) => (r1_tarski (k37_fomodel1 A) (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(l5_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=> (v4_pre_topc (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) A)) ) ) ) ) ).
tt(l5_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((k12_gfacirc1 A B C) = (k4_tarski D k2_twoscomp)) ) ) ) ) ) ).
tt(l5_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  => (v1_funct_9 (k7_funcop_1 k1_numbers B) A)) ) ) ) ) ).
tt(l5_fvaluat1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k7_xcmplx_0 A B) = (k6_xxreal_3 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l5_goboard6,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (B = (k9_metric_1 A D C))  => (v3_pre_topc B (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(l5_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( (~  (C = D) )  &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~ (r6_polyred A B C D (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(l5_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) => (m2_subset_1 (k6_domain_1 (k7_normform A) B) (k5_finsub_1 (k7_normform A)) (k8_normform A))) ) ) ).
tt(l5_hurwitz,ax, ( ((k4_complex1 (k1_group_1 k1_complfld)) = k6_numbers)  &  ( ((k4_complex1 (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld))) = k6_numbers)  &  ((k4_complex1 (k4_struct_0 k1_complfld)) = k6_numbers) ) ) ).
tt(l5_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 B C))  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(l5_int_3,ax,(r2_hidden k6_numbers k4_numbers)).
tt(l5_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k4_numbers)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_hidden A (k1_integra2 B C)) <=>  (? [D:$i] :  ((v1_int_1 D) &  ((r2_hidden D B) &  (A = (k3_xcmplx_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k1_valued_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(l5_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr15 D A B C) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_seq_2 (k2_partfun1 A k1_numbers B A)) & (r2_hidden E (k4_finseq_1 C)))  => (r1_xxreal_0 (k1_seq_1 D E) (k1_seq_1 (k4_integra1 A B C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_integr1c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 k1_numbers)) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers D)) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers E)) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers F)) &  ((r2_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)) (k2_partfun1 k1_numbers k1_numbers E (k1_rcomp_1 A B))) &  ((r2_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers D (k1_rcomp_1 A B)) (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 A B))) &  ((v3_rcomp_1 G) &  ((r1_tarski (k1_rcomp_1 A B) G) &  ((r2_fdiff_1 C G) &  ((r2_fdiff_1 D G) &  ((r1_tarski (k2_relset_1 k2_numbers (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers C (k25_valued_1 k1_numbers k1_numbers D k7_complex1)) (k1_rcomp_1 A B))) (k1_relset_1 k2_numbers H)) &  ((r2_fdiff_1 E G) &  ((r2_fdiff_1 F G) & (r1_tarski (k2_relset_1 k2_numbers (k2_partfun1 k1_numbers k2_numbers (k2_valued_1 k1_numbers k1_numbers k2_numbers E (k25_valued_1 k1_numbers k1_numbers F k7_complex1)) (k1_rcomp_1 A B))) (k1_relset_1 k2_numbers H))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k2_integr1c A B C D G H) = (k2_integr1c A B E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_jordan19,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 A)))  => (r2_hidden (k4_tarski (k1_jordan1a A) B) (k2_matrix_1 A))) ) ) ) ) ).
tt(l5_jordan1d,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 B C) D) E)) <=>  (~  ( (~ (r2_hidden A B))  &  ( (~ (r2_hidden A C))  &  ( (~ (r2_hidden A D))  &  (~ (r2_hidden A E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_borsuk_2 (k15_euclid A))) ) ).
tt(l5_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) =>  (! [D:$i] :  ( (B = C)  =>  ( ((v1_yellow_8 D A B) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  <=>  ((v1_yellow_8 D (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) C) &  ((v1_tops_2 D (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  => (v4_lattice3 A)) ) ).
tt(l5_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g2_lattices (k1_zfmisc_1 k1_xboole_0) A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g2_lattices (k1_zfmisc_1 k1_xboole_0) A))) =>  (B = C) ) ) ) ) ) ) ).
tt(l5_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A D C)) E) (k8_cqc_lang A (k8_cqc_lang A D B) E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l5_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden A (k2_finseq_1 B)) &  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B B) =>  (~  ( ((k12_matrix_3 B k2_vectsp_1 C) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1)))  &  ( ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C A A) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ( ( (D = E)  =>  ( (D = A)  |  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C D D) = (k5_struct_0 k2_vectsp_1)) ) )  &  ( (~  (D = E) )  =>  ((k3_matrix_1 (u1_struct_0 k2_vectsp_1) C D E) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k1_mboolean A (k4_pboole A B C)) D) = (k1_zfmisc_1 (k4_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l5_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  (! [C:$i] :  ((m1_subset_1 C 1) => (r1_xxreal_0 (k5_binop_1 1 k9_funct_5 A C) (k2_xcmplx_0 (k5_binop_1 1 k9_funct_5 A B) (k5_binop_1 1 k9_funct_5 B C)))) ) ) ) ) ) ).
tt(l5_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_mod_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_mod_4 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ( ((k1_algstr_0 A B C) = (k1_algstr_0 (k2_mod_4 A) D E))  &  ( ((k6_algstr_0 A B C) = (k6_algstr_0 (k2_mod_4 A) E D))  &  ((k4_algstr_0 A B) = (k4_algstr_0 (k2_mod_4 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_modelc_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A (k5_real_1 B 1)) => (r1_xxreal_0 (k1_int_1 A) (k5_real_1 (k1_int_1 B) 1))) ) ) ) ) ).
tt(l5_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = 1) )  &  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~ (r1_nat_d B A)) ) ) ) ) ) ) ).
tt(l5_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers c2__normsp_1 (k1_rlvect_1 (k1_rlsub_1 o_0_5_normsp_1) A B)) = (k8_real_1 (k18_complex1 B) (k3_funct_2 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers c2__normsp_1 A))) ) ) ) ) ).
tt(l5_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v4_metric_1 (u1_metric_1 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))) (u1_struct_0 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))))) ) ).
tt(l5_orders_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A C) => (m1_subset_1 A (u1_struct_0 B))) ) ) ) ) ) ).
tt(l5_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((r1_xxreal_0 A (k3_finseq_1 C)) =>  ( (A = k6_numbers)  |  ((k7_partfun1 (u1_struct_0 B) (k8_finseq_1 (u1_struct_0 B) D C) (k2_nat_1 (k3_finseq_1 D) A)) = (k7_partfun1 (u1_struct_0 B) C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1))) &  (! [C:$i] :  ((r2_hidden C B) <=>  ((r2_hidden C (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1)) &  (? [D:$i] :  ((m1_subset_1 D c1__ortsp_1) &  (? [E:$i] :  ((m1_subset_1 E c1__ortsp_1) &  ( (C = (k1_domain_1 c1__ortsp_1 c1__ortsp_1 D E))  &  (E = c2__ortsp_1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A D E)) = (k4_struct_0 A))  =>  ((k5_algstr_0 A (k8_group_1 A E D) (k8_group_1 A C B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  ((k2_rfinseq k1_numbers A (k5_euclid B)) = (k5_euclid (k7_nat_d B A))) ) ) ) ) ) ).
tt(l5_polyeq_2,ax, (~ (v1_abian 3)) ).
tt(l5_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom7 C A B) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  &  ( (~  ((k3_polynom1 A B C D) = (k4_struct_0 B)) )  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r1_pre_poly A D E) =>  ((k3_polynom1 A B C E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)))  =>  ((v2_rlvect_1 A) & (v3_rlvect_1 A)) ) ) ) ).
tt(l5_qmax_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k12_prob_1 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k12_prob_1 k1_numbers)))) )  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden B k12_prob_1) =>  ( ((r2_hidden k6_numbers B) =>  ((k1_funct_1 A B) = 1) )  &  ( (~ (r2_hidden k6_numbers B))  =>  ((k1_funct_1 A B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(l5_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k4_radix_1 D C (k2_xcmplx_0 A 1) (k10_radix_1 C (k2_xcmplx_0 A 1) B)) = (k4_radix_1 D C A (k10_radix_1 C A (k4_nat_d B (k1_newton (k1_radix_1 C) A))))) ) ) ) ) ) ) ) ) ) ).
tt(l5_ramsey_1,ax, (! [A:$i] :  ((k3_group_10 A k6_numbers) = (k1_tarski k6_numbers)) ) ).
tt(l5_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_prob_2 E) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  ( ((r2_mesfunc6 A B C) &  ((v6_supinf_2 C) &  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B E)))  &  ( ((k4_finseq_1 E) = (k4_finseq_1 F))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 E)) =>  (! [I:$i] :  ((r2_hidden I (k1_funct_1 E H)) =>  ((k1_seq_1 C I) = (k1_seq_1 F H)) ) ) ) ) )  &  ( ((k4_finseq_1 G) = (k4_finseq_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k1_measure6 (k1_seq_1 F H)) (k12_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E D) H))) ) ) ) ) ) ) ) ) )  =>  ( ((k1_relset_1 A C) = k1_xboole_0)  |  ((k1_mesfunc6 A B D C) = (k4_extreal1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l5_rat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( (B = A)  =>  ((k2_arytm_1 c1__rat_1 B) = (k4_xcmplx_0 A)) ) ) ) ) ) ).
tt(l5_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_real_lat)) =>  ((k1_lattices k3_real_lat A (k1_lattices k3_real_lat B C)) = (k1_lattices k3_real_lat (k1_lattices k3_real_lat A B) C)) ) ) ) ) ) ) ).
tt(l5_realset2,ax, ((k1_funct_7 k6_numbers 2) = k6_numbers) ).
tt(l5_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ( ( ((k3_finseq_1 B) = (k5_card_1 A))  & (v1_rearran1 B))  =>  (! [C:$i] :  ((v1_finset_1 C) =>  ( (C = (k1_funct_1 B (k3_finseq_1 B)))  =>  (C = A) ) ) ) ) ) ) ) ) ).
tt(l5_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  => (r2_hidden (k1_nat_1 B 1) (k4_finseq_1 A))) ) ) ) ) ).
tt(l5_rfinseq,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( ((k5_card_1 (k9_xtuple_0 (k5_relat_1 B A))) = k6_numbers)  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~ (r2_classes1 (k5_relat_1 B A) C)) ) ) ) ) ) ) ) ) ).
tt(l5_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (m1_subset_1 (a_3_0_rltopsp1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(l5_rsspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(l5_rsspace4,ax, ((v2_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v3_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v4_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v13_algstr_0 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v5_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v6_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) &  ((v7_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4))) & (v8_rlvect_1 (g1_rlvect_1 k1_rsspace4 (k10_rsspace k7_rsspace k1_rsspace4) (k8_rsspace k7_rsspace k1_rsspace4) (k9_rsspace k7_rsspace k1_rsspace4)))) ) ) ) ) ) ) ).
tt(l5_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  => (m2_finseq_1 A k2_numbers)) ) ).
tt(l5_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ((k5_extpro_1 2 k1_ami_3 A C (k2_nat_1 B 1)) = (k2_extpro_1 2 k1_ami_3 (k3_extpro_1 2 k1_ami_3 A (k5_extpro_1 2 k1_ami_3 A C B)) (k5_extpro_1 2 k1_ami_3 A C B))) ) ) ) ) ) ) ).
tt(l5_scmfsa6c,ax,(v7_amistd_1 (k11_compos_1 k1_scmfsa_2 (k2_compos_1 k1_scmfsa_2)) 3 k1_scmfsa_2)).
tt(l5_scmfsa7b,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ((k1_ordinal4 (k1_ordinal4 (k1_ordinal4 A B) C) D) = (k1_ordinal4 A (k1_ordinal4 (k1_ordinal4 B C) D))) ) ) ) ) ) ) ) ) ).
tt(l5_scmpds_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  => (m1_subset_1 (k6_xcmplx_0 A 2) k5_numbers)) ) ) ).
tt(l5_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B C)) (k8_nat_1 k1_numbers A B))) ) ) ) )  &  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B C)) (k8_nat_1 k1_numbers A B))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k8_nat_1 k1_numbers A C) (k8_nat_1 k1_numbers A B))) ) ) ) ) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k8_nat_1 k1_numbers A C) (k8_nat_1 k1_numbers A B))) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 B 1)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ) ).
tt(l5_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k2_xcmplx_0 A 1) 3) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 3 (k1_newton A 2))) (k3_xcmplx_0 3 A)) 1)) ) ) ).
tt(l5_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k4_xcmplx_0 A) 3) = (k4_xcmplx_0 (k1_newton A 3))) ) ) ).
tt(l5_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_newton (k6_xcmplx_0 A B) 2) = (k2_xcmplx_0 (k6_xcmplx_0 (k1_newton A 2) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k1_newton B 2))) ) ) ) ) ).
tt(l5_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  => (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 B C) (k3_square_1 (k2_xcmplx_0 A D))) (k3_xcmplx_0 (k2_xcmplx_0 (k3_square_1 (k6_square_1 (k3_xcmplx_0 A B))) (k3_square_1 (k6_square_1 (k3_xcmplx_0 C D)))) (k2_xcmplx_0 (k3_square_1 (k6_square_1 (k3_xcmplx_0 A C))) (k3_square_1 (k6_square_1 (k3_xcmplx_0 B D))))))) ) ) ) ) ) ) ) ).
tt(l5_sincos10,ax,(r1_tarski (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) (k2_rcomp_1 (k1_real_1 k32_sin_cos) k6_numbers))).
tt(l5_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) = (k6_binop_2 (k4_binop_2 (k15_sin_cos A) (k15_sin_cos (k1_binop_2 A))) 2)) ) ) ).
tt(l5_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  (A = k6_numbers) )  =>  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  &  (~  ((k9_sin_cos2 A) = k6_numbers) ) ) ) ) ) ).
tt(l5_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) =>  ((k1_fdiff_1 k29_sin_cos A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos A)))) ) ) ) ).
tt(l5_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)))) =>  ((v2_rlvect_1 (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C)) &  ((v3_rlvect_1 (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C)) &  ((v4_rlvect_1 (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C)) & (v13_algstr_0 (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C))) ) ) ) ) ) ) ) ) ).
tt(l5_taylor_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_prepower (k25_sin_cos B) A) = (k25_sin_cos (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(l5_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((r2_hidden C k5_numbers) => (m1_subset_1 (k1_funct_1 B C) (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(l5_topalg_2,ax, ((u1_struct_0 (k2_borsuk_1 k3_topmetr k5_topmetr)) = (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k5_topmetr))) ).
tt(l5_topalg_5,ax, ((u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) = (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))) ).
tt(l5_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v1_card_1 (k3_tarski (a_1_0_topgen_2 A))) &  (! [B:$i] :  ((v1_card_1 B) =>  ( (B = (k3_tarski (a_1_0_topgen_2 A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_ordinal1 (k1_topgen_2 A C) B)) )  &  (! [C:$i] :  ((v1_card_1 C) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_ordinal1 (k1_topgen_2 A D) C)) )  => (r1_ordinal1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l5_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k1_rltopsp1 (k15_euclid A) C D)) => (r1_tarski (k1_rltopsp1 (k15_euclid A) C B) (k1_rltopsp1 (k15_euclid A) C D))) ) ) ) ) ) ) ) ) ).
tt(l5_topreal2,ax, ((k18_euclid (k19_euclid k6_numbers k6_numbers)) = k6_numbers) ).
tt(l5_toprealb,ax,(r1_xxreal_0 (k9_real_1 1 k6_numbers) 1)).
tt(l5_trees_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((r1_tarski A B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(l5_trees_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  =>  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B)) & (r2_hidden (k1_funct_1 B (k2_nat_1 A 1)) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(l5_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (B = (k5_algstr_0 A C D))  =>  ((k3_rlvect_1 A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(l5_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k5_waybel_0 A B)) ) ) ) ) ).
tt(l5_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((v3_lattice3 A) & (v3_lattice3 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v18_waybel_0 C A B) =>  ((v5_orders_3 (k2_waybel34 B A C) B A) &  ((v4_waybel_1 (k2_waybel34 B A C) B A) & (v17_waybel_0 (k2_waybel34 B A C) B A)) ) ) ) ) ) ) ) ) ) ).
tt(l5_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A C)) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A D)) => (r1_tarski C D)) ) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(l5_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_waybel_0 A B) = (a_2_0_waybel_9 A B)) ) ) ) ) ).
tt(l5_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 C B))  =>  ((r1_xxreal_0 C (k2_xcmplx_0 A B)) & (r1_xxreal_0 (k6_xcmplx_0 C A) B)) ) ) ) ) ) ) ) ).
tt(l5_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B A))  =>  (A = B) ) ) ) ) ) ).
tt(l5_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k2_xcmplx_0 A C) (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l5_yellow11,ax,(r1_tarski (k6_subset_1 3 2) (k6_subset_1 3 1))).
tt(l60_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k13_afproj A))) => (r1_incsp_1 (k13_afproj A) B C)) ) ) ) ) ) ) ).
tt(l60_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) => (r1_tarski (k6_arytm_2 A (k6_arytm_2 B C)) (k6_arytm_2 (k6_arytm_2 A B) C))) ) ) ) ) ) ).
tt(l60_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 30 A) & (r1_xxreal_0 (k5_series_1 2 A) (k5_series_1 A 6))) ) ) ) ).
tt(l60_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k18_seq_4 (k3_finseq_1 A) (k17_seq_4 (k3_finseq_1 A))) = (k17_seq_4 (k3_finseq_1 A))) ) ) ).
tt(l60_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) A C))) ) ) )  =>  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A D)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D B))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A D)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski C B) => (r1_tarski (k9_funct_7 C A) (k9_funct_7 B A))) ) ) ) ) ) ) ).
tt(l60_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden (k4_tarski A B) (k9_xtuple_0 D)) &  ( (E = (k1_funct_1 (k1_funct_5 D) A))  & (r2_hidden C (k9_xtuple_0 E))) )  => (r2_hidden (k4_tarski A C) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(l60_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k16_sin_cos B) A) (k8_real_1 2 k32_sin_cos))) ) ) ) ).
tt(l60_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden D (k1_relset_1 k5_numbers (k8_glib_001 A B 1 C))) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k1_funct_1 (k8_glib_001 A B 1 C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(l60_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_graph_2 A (k12_finseq_1 (u1_struct_0 A) B) k1_xboole_0)) ) ) ) ).
tt(l60_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B A (k2_group_1 B C)) = (k2_group_1 B (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(l60_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 C k1_complfld) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) A (k13_polynom3 k1_complfld B C)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ( ((r1_polynom5 k1_complfld B D) | (r1_polynom5 k1_complfld C D))  => (r1_polynom5 k1_complfld A D)) ) ) ) ) ) ) ) ) ) ).
tt(l60_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_0_jordan1 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(l60_matrix_9,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k13_matrix_2 3))) =>  (~  ( ((k4_nat_d (k3_finseq_1 A) 2) = k6_numbers)  &  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 3)) =>  (~  ( ((k1_funct_1 A B) = C)  & (v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 3)))) ) ) ) ) ) ) )  &  ( (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 1 2 3)) )  &  ( (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 2 3 1)) )  &  (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ) ) ) ) ) ) ).
tt(l60_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ( (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( (F = (k1_relset_1 A D))  & (r1_mesfunc1 A B D F)) ) )  &  ( (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( (F = (k1_relset_1 A E))  & (r1_mesfunc1 A B E F)) ) )  &  ( ((k1_relset_1 A D) = (k1_relset_1 A E))  &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A (k3_mesfunc1 A D E)))  & (r1_mesfunc1 A B (k3_mesfunc1 A D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  & (r2_modelc_1 A B D C)) ) ) ) ) ) ) ) ).
tt(l60_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_relat_2 A B) => (r4_relat_2 (k2_relat_1 A) B)) ) ) ) ).
tt(l60_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ((v12_o_ring_1 D C) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 B (k3_finseq_1 D))) )  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 C) D (k12_finseq_1 (u1_struct_0 C) (k6_algstr_0 C (k7_partfun1 (u1_struct_0 C) D A) (k7_partfun1 (u1_struct_0 C) D B)))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r1_yellow_2 (u1_struct_0 A) A C D))  &  (~ (r1_yellow_2 (u1_struct_0 A) A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  => (v5_lattices A)) ) ).
tt(l60_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( (~  ( (~ (r2_hidden A (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))))  &  ( (~ (r2_hidden A a_0_1_scmpds_2))  &  ( (~ (r2_hidden A a_0_2_scmpds_2))  &  ( (~ (r2_hidden A a_0_3_scmpds_2))  &  (~ (r2_hidden A a_0_4_scmpds_2)) ) ) ) ) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = k6_numbers) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 1) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 2) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 3) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 4) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 5) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 6) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 7) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 8) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 k6_numbers (k8_real_1 (k1_seq_1 (k3_series_1 A) B) (k1_seq_1 A (k2_nat_1 B 1))))) ) ) ) ) ).
tt(l60_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos2 k4_sin_cos2) A) &  ((k1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos2 k4_sin_cos2) A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)))) ) ) ) ).
tt(l60_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k10_xtuple_0 A)) => (r1_tarski (k3_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 A))) ) ) ) ) ).
tt(l60_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l60_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)) = (k7_subset_1 (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) C D) (k1_tarski (k3_termord A B C D)))) ) ) ) ) ) ) ) ) ).
tt(l60_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 A 4) => (m1_subset_1 A (u2_turing_1 k18_turing_1))) ) ) ).
tt(l60_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ( (D = E)  & (r1_lattice3 A C D))  => (r1_lattice3 B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l60_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r1_tarski (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k11_waybel_4 A C) B) (k5_waybel_0 A B))) ) ) ) ) ) ).
tt(l61_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k6_arytm_2 A (k6_arytm_2 B C)) = (k6_arytm_2 (k6_arytm_2 A B) C)) ) ) ) ) ) ) ).
tt(l61_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 9))  & (r1_xxreal_0 (k4_power 2 A) (k5_square_1 (k8_real_1 2 A)))) ) ) ) ).
tt(l61_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A A)) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C))) ) ) )  =>  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A D)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D A))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B D)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ).
tt(l61_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((v2_fintopo6 B A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) B) C) &  ( ((k1_funct_1 B 1) = D)  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = E)  &  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  (~  ((v2_fintopo6 F A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) F) C) &  ( ((k1_funct_1 F 1) = D)  &  ( ((k1_funct_1 F (k3_finseq_1 F)) = E)  &  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  ( ((v2_fintopo6 G A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) G) C) &  ( ((k1_funct_1 G 1) = D)  &  ((k1_funct_1 G (k3_finseq_1 G)) = E) ) ) )  => (r1_xxreal_0 (k3_finseq_1 F) (k3_finseq_1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) => (r8_relat_2 (k18_finseq_1 A) (k1_relat_1 A))) ) ).
tt(l61_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  ((r2_hidden C (k7_subset_1 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k25_fomodel2 B A) (k25_fomodel2 B k6_numbers))) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((v3_fomodel2 C B (k1_nat_1 D 1)) &  ( (~ (v3_fomodel2 C B D))  & (r1_xxreal_0 (k1_nat_1 D 1) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v15_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  ((v15_fomodel1 (k26_fomodel3 A B D C) A) & (m2_subset_1 (k26_fomodel3 A B D C) (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ) ).
tt(l61_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k19_sin_cos B) A) (k8_real_1 2 k32_sin_cos))) ) ) ) ).
tt(l61_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k2_nat_1 (k3_finseq_1 (k9_glib_001 A B C D)) D) = (k2_nat_1 (k3_finseq_1 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(l61_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_1_jordan1 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(l61_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ((k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) = (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 (k3_ranknull A B C E)) (u1_struct_0 D) E (k7_matrlin2 A C D (k3_ranknull A B C E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_xxreal_2 A) => (v4_xxreal_2 (k2_measure6 A B))) ) ) ) ) ).
tt(l61_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r2_modelc_1 A B C D)) )  => (r1_modelc_1 A B C)) ) ) ) ) ) ) ).
tt(l61_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_mssubfam (k1_mssubfam A B) A B) &  ((v2_mssubfam (k1_mssubfam A B) A B) &  ((v3_mssubfam (k1_mssubfam A B) A B) &  ((v4_mssubfam (k1_mssubfam A B) A B) &  ((v5_mssubfam (k1_mssubfam A B) A B) & (v6_mssubfam (k1_mssubfam A B) A B)) ) ) ) ) ) ) ) ).
tt(l61_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r6_relat_2 A B) => (r6_relat_2 (k2_relat_1 A) B)) ) ) ) ).
tt(l61_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 C A) & (v1_o_ring_1 B A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) (k12_finseq_1 (u1_struct_0 A) (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l61_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (D = (a_3_1_poset_1 A B C))  =>  ( (~ (v1_xboole_0 D))  &  ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(l61_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  (! [E:$i] :  ((v1_quaterni E) =>  ( (E = (k7_quaterni (k7_quaterni (k7_quaterni A B) C) D))  =>  ( ((k17_quaterni E) = (k7_real_1 (k7_real_1 (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k17_quaterni C)) (k17_quaterni D)))  &  ( ((k18_quaterni E) = (k7_real_1 (k7_real_1 (k7_real_1 (k18_quaterni A) (k18_quaterni B)) (k18_quaterni C)) (k18_quaterni D)))  &  ( ((k19_quaterni E) = (k7_real_1 (k7_real_1 (k7_real_1 (k19_quaterni A) (k19_quaterni B)) (k19_quaterni C)) (k19_quaterni D)))  &  ((k20_quaterni E) = (k7_real_1 (k7_real_1 (k7_real_1 (k20_quaterni A) (k20_quaterni B)) (k20_quaterni C)) (k20_quaterni D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k4_rlaffin1 A B))) ) ) ) ).
tt(l61_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  => (v5_robbins1 A)) ) ).
tt(l61_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k2_scmbsort A) =>  ( ((k3_compos_1 k1_scmfsa_2 A k6_numbers) = (k6_scmfsa_2 (k4_scmfsa_2 2) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 1) = (k11_scmfsa_2 2))  &  ( ((k3_compos_1 k1_scmfsa_2 A 2) = (k6_scmfsa_2 (k4_scmfsa_2 3) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 3) = (k11_scmfsa_2 4))  &  ( ((k3_compos_1 k1_scmfsa_2 A 4) = (k6_scmfsa_2 (k4_scmfsa_2 4) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 5) = (k11_scmfsa_2 6))  &  ( ((k3_compos_1 k1_scmfsa_2 A 6) = (k6_scmfsa_2 (k4_scmfsa_2 5) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 7) = (k11_scmfsa_2 8))  &  ( ((k3_compos_1 k1_scmfsa_2 A 8) = (k6_scmfsa_2 (k4_scmfsa_2 6) (k4_scmfsa_2 k6_numbers)))  &  ( ((k3_compos_1 k1_scmfsa_2 A 9) = (k11_scmfsa_2 10))  &  ( ((k3_compos_1 k1_scmfsa_2 A 10) = (k16_scmfsa_2 (k4_scmfsa_2 1) (k5_scmfsa_2 k6_numbers)))  &  ((k3_compos_1 k1_scmfsa_2 A 11) = (k11_scmfsa_2 12)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l61_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers (k10_funcop_1 k2_numbers k2_numbers k29_binop_2 A (k6_partfun1 k2_numbers)) B) = (k5_binop_2 A B)) ) ) ) ) ).
tt(l61_sincos10,ax, ((k2_funct_1 k1_sincos10) = (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l61_sin_cos2,ax,(r2_relset_1 k1_numbers k1_numbers k7_sin_cos2 (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos2 k4_sin_cos2))).
tt(l61_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l61_toprealb,ax, ((k1_relset_1 (u1_struct_0 k2_topalg_2) k12_toprealb) = k1_numbers) ).
tt(l61_turing_1,ax, ((r2_hidden k6_numbers (u1_turing_1 k18_turing_1)) & (r2_hidden 1 (u1_turing_1 k18_turing_1))) ).
tt(l61_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((k1_yellow_0 A C) = (k1_yellow_0 B C)) ) ) ) ) ) ) ).
tt(l62_asympt_1,ax, (? [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 (k9_real_1 (k7_square_1 B) (k6_power 2 B)) 1)) ) ) ) ) ) ).
tt(l62_fib_num4,ax, ((k13_complex1 (k7_square_1 5) (k3_xcmplx_0 (k6_xcmplx_0 (k7_square_1 5) 5) k1_fib_num)) = (k10_complex1 (k13_complex1 1 2))) ).
tt(l62_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) => (r1_tarski (k1_relat_1 (k18_finseq_1 A)) (k1_relat_1 A))) ) ).
tt(l62_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  (~  ((v3_fomodel2 C B (k1_nat_1 A 1)) &  ( (~ (v3_fomodel2 C B A))  &  ( (! [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  (! [E:$i] :  ( ((v3_fomodel2 E B A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  (C = (k30_fomodel2 B (k31_fomodel2 B D) E)) ) ) ) ) )  &  (! [D:$i] :  ( ((v3_fomodel2 D B A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v3_fomodel2 E B A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  (C = (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l62_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v15_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)) =>  ( ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) (k27_fomodel3 A B D C)) = (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) C))  &  ((k34_fomodel1 A (k27_fomodel3 A B D C)) = (k3_relat_1 (k34_fomodel1 A C) (k10_fomodel2 A (k35_fomodel1 A) (k37_fomodel2 A (k35_fomodel1 A) (k7_fomodel3 A k1_xboole_0) B D)))) ) ) ) ) ) ) ) ) ) ).
tt(l62_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k16_sin_cos B) A) (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 C 1)))) ) ) ) ) ) ).
tt(l62_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  (! [F:$i] :  ((r1_glib_001 A E F B) => (r1_glib_001 A E F (k9_glib_001 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l62_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A B C) = (k8_group_1 A C B)) ) ) ) ) ) ) ).
tt(l62_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_2_jordan1 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(l62_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l62_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [D:$i] :  ((r2_hidden D C) => (r2_hidden (k1_funct_1 B D) (k7_relset_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(l62_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ( (C = (k7_quaterni A B))  =>  ( ((k17_quaterni C) = (k7_real_1 (k17_quaterni A) (k17_quaterni B)))  &  ( ((k18_quaterni C) = (k7_real_1 (k18_quaterni A) (k18_quaterni B)))  &  ( ((k19_quaterni C) = (k7_real_1 (k19_quaterni A) (k19_quaterni B)))  &  ((k20_quaterni C) = (k7_real_1 (k20_quaterni A) (k20_quaterni B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l62_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (B = (k4_rlaffin1 A B)) ) ) ) ) ).
tt(l62_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k3_rusub_1 A C B)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 B E) &  (D = (k3_rlvect_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l62_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k2_scmbsort B) =>  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 1) (k4_struct_0 k1_scmfsa_2)) = 1)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 1) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 1) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 2) (k4_struct_0 k1_scmfsa_2)) = 2)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 2) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 2) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 3) (k4_struct_0 k1_scmfsa_2)) = 3)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 3) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 3) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 4) (k4_struct_0 k1_scmfsa_2)) = 4)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 4) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 4) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 5) (k4_struct_0 k1_scmfsa_2)) = 5)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 5) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 5) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 6) (k4_struct_0 k1_scmfsa_2)) = 6)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 6) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 6) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 7) (k4_struct_0 k1_scmfsa_2)) = 7)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 7) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 7) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 8) (k4_struct_0 k1_scmfsa_2)) = 8)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 8) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 8) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 9) (k4_struct_0 k1_scmfsa_2)) = 9)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 9) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 9) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 10) (k4_struct_0 k1_scmfsa_2)) = 10)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 10) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 10) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_struct_0 k1_scmfsa_2)) = 11)  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 1)) = (k3_finseq_1 (k18_scmfsa_2 A (k5_scmfsa_2 k6_numbers))))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 2)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 3)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 4)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 5)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers)))  &  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B A 11) (k4_scmfsa_2 6)) = (k1_funct_1 A (k4_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l62_sincos10,ax, ((k2_funct_1 k2_sincos10) = (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) ).
tt(l62_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l62_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B 1)) ) )  => (r1_xxreal_0 (k3_xcmplx_0 (k2_xcmplx_0 1 (k3_square_1 A)) (k3_square_1 B)) (k2_xcmplx_0 1 (k3_square_1 B)))) ) ) ) ) ).
tt(l62_topalg_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_mfold_2 A))) =>  (! [C:$i] :  ((m1_borsuk_2 C (k4_mfold_2 A) B B) =>  ( (~  ((k2_relset_1 (u1_struct_0 (k4_mfold_2 A)) C) = (u1_struct_0 (k4_mfold_2 A))) )  => (v3_topalg_6 C (k4_mfold_2 A) B)) ) ) ) ) ) ) ).
tt(l62_topgen_1,ax, (k3_numbers = (k6_subset_1 k1_numbers k1_borsuk_5)) ).
tt(l62_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)))) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (A = (k3_xtuple_0 B C D))  =>  ( (B = 4)  |  ((k9_turing_1 k18_turing_1 A) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 k18_turing_1) (u1_turing_1 k18_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k18_turing_1 A)) (k2_xcmplx_0 (k7_turing_1 k18_turing_1 A) (k6_turing_1 k18_turing_1 (k8_turing_1 k18_turing_1 A))) (k5_turing_1 k18_turing_1 (k3_mcart_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) A) (k7_turing_1 k18_turing_1 A) (k2_mcart_1 (u2_turing_1 k18_turing_1) (u1_turing_1 k18_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k18_turing_1 A))))) ) ) ) ) ) ) ) ).
tt(l62_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((k2_yellow_0 A C) = (k2_yellow_0 B C)) ) ) ) ) ) ) ).
tt(l62_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k7_xcmplx_0 (k3_xcmplx_0 B A) A)) ) ) ) ) ) ).
tt(l63_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B I) &  ((r2_hidden B J) &  ((r2_hidden B K) &  ((r2_hidden C I) &  ((r2_hidden F I) &  ((r2_hidden D J) &  ((r2_hidden G J) &  ((r2_hidden E K) &  ((r2_hidden H K) &  ((v1_aff_1 I A) &  ((v1_aff_1 J A) &  ((v1_aff_1 K A) &  ((r2_analoaf A C D F G) & (r2_analoaf A C E F H)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_aff_4 A I J K) |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (I = J)  |  ( (I = K)  | (r2_analoaf A D E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_4 D A) &  ((r1_tarski B D) &  ((r1_tarski C D) &  ( (H = (k4_tarski B 1))  &  ( (I = (k4_tarski C 1))  &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) G I) &  ((r1_incsp_1 (k13_afproj A) F J) &  ((r1_incsp_1 (k13_afproj A) G J) &  ( (J = (k4_tarski E 1))  & (v1_aff_1 E A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (F = G)  | (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ( ((k8_arytm_2 A B) = k11_arytm_3)  &  ( (~  (A = k11_arytm_3) )  &  (~  (B = k11_arytm_3) ) ) ) ) ) ) ) ) ).
tt(l63_asympt_1,ax, ((k9_newton 5) = 120) ).
tt(l63_dickson,ax,(v16_waybel_0 k11_dickson)).
tt(l63_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  => (m3_cat_2 (k11_ens_1 B) (k11_ens_1 A))) ) ) ) ).
tt(l63_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) => (r1_relat_2 (k18_finseq_1 A) (k1_relat_1 A))) ) ).
tt(l63_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ((v4_fomodel1 D C) & (m1_subset_1 D (k1_fomodel1 C)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel2 E C B)) )  =>  (! [F:$i] :  ((m2_subset_1 F (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0)) (k35_fomodel1 C)) => (r2_funct_2 (k35_fomodel1 C) B (k1_partfun1 (k35_fomodel1 C) (k35_fomodel1 C) (k35_fomodel1 C) B (k10_fomodel2 C (k35_fomodel1 C) (k37_fomodel2 C (k35_fomodel1 C) (k7_fomodel3 C A) D F)) (k10_fomodel2 C B E)) (k10_fomodel2 C B (k5_fomodel2 E D (k3_funct_2 (k35_fomodel1 C) B (k10_fomodel2 C B E) F))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (A = k1_xboole_0) )  &  (~ (r2_wellord2 (k4_card_3 (k9_funct_6 A B)) (k1_funct_2 A (k4_card_3 B)))) ) ) ) ) ) ) ).
tt(l63_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (J = (k8_real_1 (k9_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k3_rlvect_1 A D E)) (k8_real_1 2 (k4_geomtrap A B C (k5_algstr_0 A D E) F))) (k2_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A D E)))))  &  ( (K = (k8_real_1 (k9_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k3_rlvect_1 A D E)) (k8_real_1 2 (k4_geomtrap A B C (k5_algstr_0 A D E) G))) (k2_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A D E)))))  &  ( (H = (k3_rlvect_1 A F (k1_rlvect_1 A (k5_algstr_0 A D E) J)))  &  (I = (k3_rlvect_1 A G (k1_rlvect_1 A (k5_algstr_0 A D E) K))) ) ) )  =>  ( ((k5_algstr_0 A I H) = (k3_rlvect_1 A (k5_algstr_0 A G F) (k1_rlvect_1 A (k5_algstr_0 A D E) (k9_real_1 K J))))  &  ((k9_real_1 K J) = (k8_real_1 (k8_real_1 (k1_real_1 2) (k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A G F))) (k2_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_xxreal_0 (k3_finseq_1 (k9_glib_001 A B C D)) (k3_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(l63_jgraph_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k8_real_1 (k5_real_1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 1) (k3_square_1 A)) (k3_square_1 B)) => (r1_xxreal_0 (k8_real_1 (k5_real_1 (k3_square_1 A) 1) (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B))) k6_numbers)) ) ) ) ) ).
tt(l63_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_4_jordan1 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(l63_lattice5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 5 A))  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  (~  (A = 4) ) ) ) ) ) ) ) ) ) ).
tt(l63_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v3_xxreal_2 A) => (v3_xxreal_2 (k2_measure6 A B))) ) ) ) ) ).
tt(l63_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ( (D = (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers)))  &  ((v2_mesfunc9 E A) &  ((v1_mesfunc8 E A k7_numbers) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers E F)) & (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E F) D)) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F D) => (v1_mesfunc9 (k3_mesfunc5 A E F))) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_mesfunc9 F G) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers E G) D))) ) )  &  ((v1_mesfunc9 F) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k7_mesfunc8 A (k4_mesfunc9 A E)) D)) = (k3_mesfunc9 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  (~  ((r2_hidden B (k10_normform A C D)) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B) & (r2_hidden E (k10_normform A (k9_normform A C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) (k4_cat_1 (k2_oppcat_1 A) D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k4_oppcat_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(l63_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  ( ((v4_o_ring_1 C B) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ( (k6_numbers = A)  | (v13_o_ring_1 (k7_partfun1 (u1_struct_0 B) C A) B)) ) ) ) ) ) ) ) ).
tt(l63_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( (C = (k1_funct_1 (k10_poset_1 A) B))  &  (D = (k1_funct_1 (k9_funct_7 B E) (k3_yellow_0 A))) )  => (r3_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k7_quaterni A B) = (k6_quaterni (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k7_real_1 (k18_quaterni A) (k18_quaterni B)) (k7_real_1 (k19_quaterni A) (k19_quaterni B)) (k7_real_1 (k20_quaterni A) (k20_quaterni B)))) ) ) ) ) ).
tt(l63_scmbsort,ax, (~ (r4_scmfsa7b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) (k4_scmfsa_2 (k2_nat_1 1 1)))) ).
tt(l63_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k3_tarski (k7_scmyciel A B))) => (r2_hidden C B)) ) ) ) ) ).
tt(l63_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k1_seq_1 B E) = (k5_square_1 (k7_real_1 (k1_seq_1 C E) (k1_seq_1 D E)))) ) )  => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 B) A))) ) ) ) ) ) ) ) ) ).
tt(l63_sincos10,ax, ((k2_funct_1 k3_sincos10) = (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) ).
tt(l63_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden B (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))) => (r2_hidden (k3_real_1 B (k8_real_1 2 k32_sin_cos)) (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1))) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))))) ) ) ) ) ) ) ) ) ).
tt(l63_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l63_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k3_polynom1 A C (k6_termord A B C D) (k3_termord A B C D)) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(l63_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_tex_4 A B) = (k2_tex_4 A C))  =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(l63_topalg_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_mfold_2 A))) =>  (! [C:$i] :  ((m1_borsuk_2 C (k4_mfold_2 A) B B) =>  (~  ((r1_xxreal_0 2 A) &  ( ((k2_relset_1 (u1_struct_0 (k4_mfold_2 A)) C) = (u1_struct_0 (k4_mfold_2 A)))  &  (! [D:$i] :  ((m1_borsuk_2 D (k4_mfold_2 A) B B) =>  (~  ((r3_borsuk_2 (k4_mfold_2 A) B B D C) &  (~  ((k2_relset_1 (u1_struct_0 (k4_mfold_2 A)) D) = (u1_struct_0 (k4_mfold_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l63_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v1_waybel_0 C A))  => (v1_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(l63_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v22_waybel_0 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(l64_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_4 D A) &  ((r1_tarski B D) &  ((r1_tarski C D) &  ( (H = (k4_tarski B 1))  &  ( (I = (k4_tarski C 1))  &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) G I) &  ((r1_incsp_1 (k13_afproj A) F J) &  ((r1_incsp_1 (k13_afproj A) G J) &  ( (J = (k4_tarski (k6_afproj A E) 2))  & (v1_aff_4 E A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (F = G)  |  ((r1_aff_4 A E D) & (r1_aff_4 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ((k6_arytm_2 A (k5_arytm_2 B C)) = (k5_arytm_2 (k6_arytm_2 A B) (k6_arytm_2 A C))) ) ) ) ) ) ) ).
tt(l64_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 10 A) & (r1_xxreal_0 (k10_real_1 1 (k4_power 2 (k9_real_1 A 9))) (k10_real_1 (k5_series_1 2 (k4_nat_1 2 A)) (k9_newton A)))) ) ) ) ).
tt(l64_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A)) ) ).
tt(l64_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A B C) => (r7_cqc_the3 A (k6_cqc_lang A B) (k6_cqc_lang A C))) ) ) ) ) ) ) ).
tt(l64_dickson,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (v2_struct_0 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))))  &  ((v4_dickson (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) &  ((v3_dickson (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) & (v5_orders_2 (k5_yellow_1 A (k7_funcop_1 A k11_dickson)))) ) ) ) ) ).
tt(l64_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) 1)) ).
tt(l64_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k1_relat_1 (k18_finseq_1 A)) = (k1_relat_1 A)) ) ) ).
tt(l64_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (~  ( (~ (v15_fomodel1 B A))  &  ((k32_fomodel2 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(l64_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k9_glib_001 A B C C) B)) ) ) ) ) ) ).
tt(l64_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k9_real_1 A B) A)) ) ) ) ).
tt(l64_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  ((r2_incsp_1 A C B) &  (~ (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_jgraph_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k5_real_1 (k3_square_1 A) 1) = k6_numbers)  &  ( (~  (A = 1) )  &  (~  (A = (k1_real_1 1)) ) ) ) ) ) ) ).
tt(l64_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l64_lattice5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r2_hidden A (k2_finseq_1 5)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  (~  (A = 5) ) ) ) ) ) ) ) ) ) ).
tt(l64_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  ( (~  (D = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) &  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H C) =>  (! [I:$i] :  ((m1_subset_1 I D) =>  (~  (E = (k6_xtuple_0 F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(l64_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  =>  (! [C:$i] :  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v6_orders_2 E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ( (E = (a_3_1_poset_1 A B D))  &  ((r2_hidden C (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) F E)) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 G A A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((r2_hidden G B) &  (C = (k1_funct_1 F (k1_funct_1 (k9_funct_7 G D) (k3_yellow_0 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ( (C = (k10_quaterni A B))  =>  ( ((k17_quaterni C) = (k9_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))))  &  ( ((k18_quaterni C) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k17_quaterni B))) (k8_real_1 (k19_quaterni A) (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k19_quaterni B))))  &  ( ((k19_quaterni C) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k17_quaterni B))) (k8_real_1 (k20_quaterni A) (k18_quaterni B))) (k8_real_1 (k18_quaterni A) (k20_quaterni B))))  &  ((k20_quaterni C) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k17_quaterni B))) (k8_real_1 (k18_quaterni A) (k19_quaterni B))) (k8_real_1 (k19_quaterni A) (k18_quaterni B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_rlsub_1 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(l64_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_rusub_1 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(l64_scmbsort,ax, ((v1_scmfsa7b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))))) & (v2_scm_halt (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))))) ).
tt(l64_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden C B) & (r2_hidden C (k3_tarski A)))  => (r2_hidden C (k3_tarski (k7_scmyciel A B)))) ) ) ) ) ).
tt(l64_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  => (r1_tarski (k7_relset_1 B A D C) A)) ) ) ) ) ) ).
tt(l64_sincos10,ax, ((k2_funct_1 k4_sincos10) = (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l64_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden B (k8_subset_1 k1_numbers (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) k1_numbers)) => (r2_hidden (k3_real_1 B (k8_real_1 2 k32_sin_cos)) (k8_subset_1 k1_numbers (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1))) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 A 1)))) k1_numbers))) ) ) ) ) ) ) ) ) ).
tt(l64_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l64_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( (~  (E = (k3_termord A B C D)) )  =>  ((k3_polynom1 A C (k6_termord A B C D) E) = (k3_polynom1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_waybel_3 A C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  => (r1_waybel_3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l64_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 B C) = (k7_xcmplx_0 (k3_xcmplx_0 B A) (k3_xcmplx_0 C A))) ) ) ) ) ) ) ) ).
tt(l65_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v2_collsp (k5_anproj_1 A))) ) ).
tt(l65_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 3 A) => (r1_xxreal_0 (k9_real_1 A 1) (k8_real_1 2 (k9_real_1 A 2)))) ) ) ).
tt(l65_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (B = (k1_tarski (k4_struct_0 A)))  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) => (r2_hidden (k2_bcialg_1 A C) (k1_tarski (k4_struct_0 A)))) ) ) ) ) ) ) ).
tt(l65_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers C) = (k5_card_1 B))  &  ( ((k21_binop_2 (k13_newton (k5_card_1 B) (k5_card_1 A)) (k7_afinsq_2 C)) = (k1_card_1 (a_2_1_card_fin A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k22_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k6_newton (k23_binop_2 D 1) (k5_card_1 B))) (k1_newton (k21_binop_2 (k21_binop_2 (k5_card_1 B) D) 1) (k5_card_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l65_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A (k6_cqc_lang A B) (k6_cqc_lang A C)) => (r7_cqc_the3 A B C)) ) ) ) ) ) ) ).
tt(l65_fib_num4,ax, ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k6_xcmplx_0 1 1)))  &  (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ) ).
tt(l65_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_filter_0 A C D) B) =>  ((r2_hidden (k4_filter_0 A C (k3_lattices A D E)) B) &  ((r2_hidden (k4_filter_0 A C (k3_lattices A E D)) B) &  ((r2_hidden (k4_filter_0 A (k4_lattices A C E) D) B) & (r2_hidden (k4_filter_0 A (k4_lattices A E C) D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l65_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k9_funct_7 A k1_xboole_0) (k18_finseq_1 A))) ) ).
tt(l65_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  (~  ((v4_fomodel2 B A) &  ( (~ (v15_fomodel1 B A))  &  ( (~ (r2_hidden (k1_funct_1 B 1) (k16_fomodel1 A)))  &  (~  ((k1_funct_1 B 1) = (k1_fomodel2 A)) ) ) ) ) ) ) ) ) ) ).
tt(l65_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v13_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k33_fomodel1 A (k24_fomodel3 A B C D)) = (k3_relat_1 (k33_fomodel1 A D) (k20_fomodel0 (k1_fomodel1 A) B C))) ) ) ) ) ) ) ) ) ).
tt(l65_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k19_sin_cos B) A) (k8_real_1 (k8_real_1 2 k32_sin_cos) (k3_real_1 C 1)))) ) ) ) ) ) ).
tt(l65_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k4_glib_001 A (k8_glib_001 A B 1 C)) = (k3_glib_001 A (k8_glib_001 A B D (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ).
tt(l65_graphsp,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 A) F) |  ((k1_seq_1 A (k9_real_1 (k3_finseq_1 A) F)) = (k1_seq_1 C (k2_nat_1 (k7_partfun1 k5_numbers A (k7_real_1 (k9_real_1 (k3_finseq_1 A) F) 1)) E))) ) ) ) )  &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 B) F) |  ((k1_seq_1 B (k9_real_1 (k3_finseq_1 B) F)) = (k1_seq_1 C (k2_nat_1 (k7_partfun1 k5_numbers B (k7_real_1 (k9_real_1 (k3_finseq_1 B) F) 1)) E))) ) ) ) )  &  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)) &  ((k1_seq_1 A (k3_finseq_1 A)) = (k1_seq_1 B (k3_finseq_1 B))) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 A) F) |  ((k1_seq_1 A (k9_real_1 (k3_finseq_1 A) F)) = (k1_seq_1 B (k9_real_1 (k3_finseq_1 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l65_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) B) k6_hilbert1)) ) ) ) ) ) ).
tt(l65_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  => (r1_ordinal1 (k1_ordinal1 k1_xboole_0) (k7_lattice5 A B C))) ) ) ) ) ) ).
tt(l65_modelc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_1 B) & (l2_modelc_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k18_modelc_1 (u3_modelc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 B))))) )  => (r2_hidden (k21_modelc_1 B C A) (k23_modelc_1 B C))) ) ) ) ) ) ).
tt(l65_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) => (v12_o_ring_1 (k12_finseq_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(l65_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r3_polyred A B C D E F G) & (r2_hidden G (k2_polynom1 (k15_pre_poly A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l65_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_orders_2 B (k6_poset_1 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A A))))) )  => (r3_orders_2 A (k3_funct_2 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A) (k10_poset_1 A) (k1_yellow_0 (k6_poset_1 A A) B)) (k1_yellow_0 A (k7_relset_1 (u1_struct_0 (k6_poset_1 A A)) (u1_struct_0 A) (k10_poset_1 A) B)))) ) ) ) ).
tt(l65_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k7_quaterni (k7_quaterni (k7_quaterni A B) C) D) = (k6_quaterni (k7_real_1 (k7_real_1 (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k17_quaterni C)) (k17_quaterni D)) (k7_real_1 (k7_real_1 (k7_real_1 (k18_quaterni A) (k18_quaterni B)) (k18_quaterni C)) (k18_quaterni D)) (k7_real_1 (k7_real_1 (k7_real_1 (k19_quaterni A) (k19_quaterni B)) (k19_quaterni C)) (k19_quaterni D)) (k7_real_1 (k7_real_1 (k7_real_1 (k20_quaterni A) (k20_quaterni B)) (k20_quaterni C)) (k20_quaterni D)))) ) ) ) ) ) ) ) ) ).
tt(l65_scmbsort,ax, (~ (r4_scmfsa7b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) ).
tt(l65_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers)) ) )  & (r1_xxreal_0 (k2_power (k2_nat_1 A 1) (k1_seq_1 (k1_series_3 B) A)) k6_numbers)) ) ) ) ) ) ).
tt(l65_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden B (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))) => (r2_hidden (k5_real_1 B (k8_real_1 2 k32_sin_cos)) (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) (k5_real_1 A 1))) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) (k5_real_1 A 1)))))) ) ) ) ) ) ) ) ) ).
tt(l65_sin_cos,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = (k7_real_1 (k8_real_1 2 B) 1)) ) ) ) ) ).
tt(l65_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l65_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B A))  => (r1_xxreal_0 (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))) (k3_xcmplx_0 A (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))))) ) ) ) ) ).
tt(l65_stirl2_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  (~  ((r2_hidden B A) & (r1_xxreal_0 (k5_card_1 A) (k5_card_1 (k6_subset_1 A (k1_tarski B))))) ) ) ) ) ).
tt(l65_toprealb,ax, ((k1_funct_1 k12_toprealb (k10_real_1 1 2)) = (k19_euclid (k1_real_1 1) k6_numbers)) ).
tt(l65_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( (C = D)  =>  ((k1_waybel11 A C) = (k1_waybel11 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l65_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k3_xcmplx_0 B A) (k3_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ).
tt(l66_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A H I) &  ((r5_aff_1 A H J) &  ((r2_hidden B H) &  ((r2_hidden C H) &  ((r2_hidden D I) &  ((r2_hidden E I) &  ((r2_hidden F J) &  ((r2_hidden G J) &  ((v1_aff_1 H A) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) ) ) ) ) ) ) ) )  =>  ((r2_aff_4 A H I J) |  ( (H = I)  |  ( (H = J)  | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l66_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) B G) &  ((r1_incsp_1 (k13_afproj A) C G) &  ((r1_incsp_1 (k13_afproj A) D H) &  ((r1_incsp_1 (k13_afproj A) E H) &  ((r1_incsp_1 (k13_afproj A) F G) &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) B I) &  ((r1_incsp_1 (k13_afproj A) D I) &  ((r1_incsp_1 (k13_afproj A) C J) &  ((r1_incsp_1 (k13_afproj A) E J) &  ( (~ (r1_incsp_1 (k13_afproj A) F I))  &  ( (~ (r1_incsp_1 (k13_afproj A) F J))  &  ( (~  (G = H) )  &  ((m1_subset_1 F (u1_struct_0 A)) &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) K I) & (r1_incsp_1 (k13_afproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l66_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v3_collsp (k5_anproj_1 A))) ) ).
tt(l66_arytm_2,ax,(r2_hidden k12_arytm_3 k5_arytm_3)).
tt(l66_asympt_1,ax, ((k5_series_1 5 5) = 3125) ).
tt(l66_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_bcialg_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ( ((u1_struct_0 C) = (k2_relset_1 (u1_struct_0 A) D))  =>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v2_bcialg_6 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l66_fib_num4,ax, (~ (r1_xxreal_0 (k7_square_1 5) 2)) ).
tt(l66_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k9_funct_7 B (k2_xcmplx_0 A 1)) (k18_finseq_1 B))) ) ) ) ).
tt(l66_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (v12_fomodel1 (k25_fomodel2 B A) B)) ) ) ) ).
tt(l66_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v15_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k34_fomodel1 A (k24_fomodel3 A B C D)) = (k3_relat_1 (k34_fomodel1 A D) (k20_fomodel0 (k1_fomodel1 A) B C))) ) ) ) ) ) ) ) ) ).
tt(l66_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  (! [F:$i] :  ( ( (~ (v1_abian F))  & (m1_subset_1 F k5_numbers))  =>  ( ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k3_finseq_1 B)) &  ((k1_funct_1 B E) = (k1_funct_1 B F)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 E)) =>  ((k1_funct_1 (k9_glib_001 A B E F) G) = (k1_funct_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l66_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_graph_3 A (k10_xtuple_0 B))) =>  ((k10_xtuple_0 (k10_graph_3 A C B)) = (k10_xtuple_0 B)) ) ) ) ) ) ) ) ).
tt(l66_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 B A) => (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k2_fdiff_1 B A) A) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 2))) ) ) ) ) ).
tt(l66_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 A B) C)) (k4_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l66_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A k24_sin_cos) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers k24_sin_cos A))) ) ) ).
tt(l66_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( (B = (k6_newton A (k4_nat_1 2 A)))  & (r1_xxreal_0 3 A))  =>  (B = (k4_nat_1 (k4_nat_1 (k3_wsierp_1 (k14_finseq_1 (a_2_4_nat_4 A B))) (k3_wsierp_1 (k14_finseq_1 (a_2_5_nat_4 A B)))) (k3_wsierp_1 (k14_finseq_1 (a_2_6_nat_4 A B))))) ) ) ) ) ) ).
tt(l66_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 (k2_oppcat_1 B) (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(l66_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 C A) & (v5_o_ring_1 B A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) B)) (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l66_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k10_quaterni A B) = (k6_quaterni (k9_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k17_quaterni B))) (k8_real_1 (k19_quaterni A) (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k19_quaterni B))) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k17_quaterni B))) (k8_real_1 (k20_quaterni A) (k18_quaterni B))) (k8_real_1 (k18_quaterni A) (k20_quaterni B))) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k17_quaterni B))) (k8_real_1 (k18_quaterni A) (k19_quaterni B))) (k8_real_1 (k19_quaterni A) (k18_quaterni B))))) ) ) ) ) ).
tt(l66_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  ( ((v2_robbins2 A) & (v3_robbins2 A))  =>  ((v4_lattices A) &  ((v6_robbins1 A) & (v5_lattices A)) ) ) ) ) ).
tt(l66_scmbsort,ax, (~ (r4_scmfsa7b (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))))) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)))) ).
tt(l66_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((r1_tarski B (k3_tarski A)) =>  ((k3_tarski (k7_scmyciel A B)) = B) ) ) ) ) ).
tt(l66_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers))  & (r1_xxreal_0 (k1_seq_1 B (k5_real_1 C 1)) (k1_seq_1 B C))) ) )  => (r1_xxreal_0 k6_numbers (k13_complex1 (k9_real_1 (k1_seq_1 B (k2_nat_1 A 1)) (k13_complex1 (k1_seq_1 (k3_series_1 B) A) (k2_nat_1 A 1))) (k2_nat_1 A 2)))) ) ) ) ) ).
tt(l66_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 2 (k7_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos (k7_binop_2 A))))) ) ).
tt(l66_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden B (k8_subset_1 k1_numbers (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) k1_numbers)) => (r2_hidden (k5_real_1 B (k8_real_1 2 k32_sin_cos)) (k8_subset_1 k1_numbers (k1_rcomp_1 (k3_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) (k5_real_1 A 1))) (k3_real_1 D (k8_real_1 (k8_real_1 2 k32_sin_cos) (k5_real_1 A 1)))) k1_numbers))) ) ) ) ) ) ) ) ) ).
tt(l66_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers c1__sin_cos A) = (k7_real_1 (k8_real_1 2 A) 1)) ) ) ).
tt(l66_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l66_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k3_xcmplx_0 A (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))) (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))))) ) ) ) ) ).
tt(l66_topgen_1,ax,(m1_subset_1 k3_numbers (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))).
tt(l66_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E B)) ) )  =>  ( (D = E)  =>  (! [F:$i] :  ((m3_yellow_6 F (u1_struct_0 D) A) =>  (! [G:$i] :  ((m3_yellow_6 G (u1_struct_0 E) B) =>  ( (F = G)  =>  ((k8_yellow_6 A D F) = (k8_yellow_6 B E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l66_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_orders_2 A (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C)) B)) ) ) ) ) ) ).
tt(l66_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B C))  => (r1_xxreal_0 (k7_xcmplx_0 B A) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ).
tt(l67_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) B G) &  ((r1_incsp_1 (k13_afproj A) C G) &  ((r1_incsp_1 (k13_afproj A) D H) &  ((r1_incsp_1 (k13_afproj A) E H) &  ((r1_incsp_1 (k13_afproj A) F G) &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) B I) &  ((r1_incsp_1 (k13_afproj A) D I) &  ((r1_incsp_1 (k13_afproj A) C J) &  ((r1_incsp_1 (k13_afproj A) E J) &  ( (~ (r1_incsp_1 (k13_afproj A) F I))  &  ( (~ (r1_incsp_1 (k13_afproj A) F J))  &  ( (~  (G = H) )  &  ( (~ (m1_subset_1 F (u1_struct_0 A)))  &  ((m1_subset_1 B (u1_struct_0 A)) &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) K I) & (r1_incsp_1 (k13_afproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_arytm_2,ax,(m1_subset_1 k12_arytm_3 k2_arytm_2)).
tt(l67_asympt_1,ax, ((k5_series_1 4 4) = 256) ).
tt(l67_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A (k3_lattices A B C) (k3_boolealg A B C)) (k4_lattices A B C))) ) ) ) ) ) ).
tt(l67_fib_num4,ax, (~ (r1_xxreal_0 (k4_xcmplx_0 2) (k4_xcmplx_0 (k7_square_1 5)))) ).
tt(l67_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k4_filter_0 A C D) B) & (r2_hidden (k4_filter_0 A E D) B))  => (r2_hidden (k4_filter_0 A (k3_lattices A C E) D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k9_funct_7 B A) (k18_finseq_1 B))) ) ) ) ).
tt(l67_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (r1_tarski (k1_funct_1 (k39_fomodel1 B) A) (k3_finseq_2 (k5_fomodel1 B)))) ) ) ) ).
tt(l67_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k33_fomodel2 A) A)) ) ).
tt(l67_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ( ((v4_fomodel1 E D) & (m1_subset_1 E (k1_fomodel1 D)))  =>  (! [F:$i] :  ( ((v4_fomodel1 F D) & (m1_subset_1 F (k1_fomodel1 D)))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_fomodel2 G D A)) )  =>  ((k2_partfun1 (k35_fomodel1 D) A (k10_fomodel2 D A (k5_fomodel2 G E B)) (k9_subset_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0)) (k2_fomodel0 (k1_fomodel1 D) (k6_subset_1 (k1_fomodel1 D) (k6_domain_1 (k1_fomodel1 D) F))) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k39_fomodel1 D) C))) = (k2_partfun1 (k3_finseq_2 (k1_fomodel1 D)) A (k1_partfun1 (k3_finseq_2 (k1_fomodel1 D)) (k3_finseq_2 (k1_fomodel1 D)) (k35_fomodel1 D) A (k20_fomodel0 (k1_fomodel1 D) E F) (k10_fomodel2 D A (k5_fomodel2 G F B))) (k9_subset_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0)) (k2_fomodel0 (k1_fomodel1 D) (k6_subset_1 (k1_fomodel1 D) (k6_domain_1 (k1_fomodel1 D) F))) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k39_fomodel1 D) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 C E) & (r1_xxreal_0 E (k3_finseq_1 (k9_glib_001 A B C D))))  =>  ( ((k1_funct_1 (k9_glib_001 A B C D) E) = (k1_funct_1 B (k2_xcmplx_0 (k6_xcmplx_0 E C) D)))  &  ((m1_subset_1 (k2_xcmplx_0 (k6_xcmplx_0 E C) D) k5_numbers) & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 E C) D) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_graph_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k1_rvsum_1 A)) => (r1_xxreal_0 k6_numbers B)) ) )  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) ) ) ) ).
tt(l67_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k25_grcat_1 A))) =>  ( ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B))  =>  ( ((k3_graph_1 (k25_grcat_1 A) (k1_cat_1 (k25_grcat_1 A) B C)) = (k3_graph_1 (k25_grcat_1 A) B))  &  ((k4_graph_1 (k25_grcat_1 A) (k1_cat_1 (k25_grcat_1 A) B C)) = (k4_graph_1 (k25_grcat_1 A) C)) ) ) ) ) ) ) ) ) ).
tt(l67_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l67_measure6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 B) => (v2_rcomp_1 (k2_measure6 B A))) ) ) ) ) ).
tt(l67_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  (~  ((r1_tarski B C) &  ( (~  (B = C) )  &  (! [D:$i] :  (~  ((r2_hidden D C) & (r1_tarski B (k7_subset_1 (k13_modelc_2 A) C (k1_tarski D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( (B = (k6_newton A (k4_nat_1 2 A)))  & (r1_xxreal_0 3 A))  => (r1_xxreal_0 (k3_wsierp_1 (k14_finseq_1 (a_2_4_nat_4 A B))) (k4_power (k4_nat_1 2 A) (k7_square_1 (k4_nat_1 2 A))))) ) ) ) ) ).
tt(l67_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l67_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k17_quaterni (k10_quaterni A B)) = (k9_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))))  &  ( ((k18_quaterni (k10_quaterni A B)) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k17_quaterni B))) (k8_real_1 (k19_quaterni A) (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k19_quaterni B))))  &  ( ((k19_quaterni (k10_quaterni A B)) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k17_quaterni B))) (k8_real_1 (k20_quaterni A) (k18_quaterni B))) (k8_real_1 (k18_quaterni A) (k20_quaterni B))))  &  ((k20_quaterni (k10_quaterni A B)) = (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k17_quaterni B))) (k8_real_1 (k18_quaterni A) (k19_quaterni B))) (k8_real_1 (k19_quaterni A) (k18_quaterni B)))) ) ) ) ) ) ) ) ).
tt(l67_scmbsort,ax, ((v1_scmfsa7b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))))))) & (v2_scm_halt (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))))))) ).
tt(l67_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r2_hidden (k2_tarski C D) A)) )  => (r2_hidden (k2_tarski C D) (k7_scmyciel A B))) ) ) ) ) ) ).
tt(l67_sin_cos,ax, ((v1_funct_1 c1__sin_cos) &  ((v1_funct_2 c1__sin_cos k5_numbers k5_numbers) &  ((v5_valued_0 c1__sin_cos) & (m1_subset_1 c1__sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ).
tt(l67_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ((v4_topreal1 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2))))  =>  (! [F:$i] :  ( ((v4_topreal1 F) & (m2_finseq_1 F (u1_struct_0 (k15_euclid 2))))  =>  (~  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E 1))  &  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) F 1))  &  ( (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k3_finseq_1 E)))  &  ( (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) F (k3_finseq_1 F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 E) (k3_topreal1 2 F)) = (k2_tarski B C))  &  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 E) (k3_topreal1 2 F)))  &  ( (~  (D = B) )  &  ((r2_hidden D (k10_xtuple_0 E)) &  (! [G:$i] :  ( ((v4_topreal1 G) & (m2_finseq_1 G (u1_struct_0 (k15_euclid 2))))  =>  (! [H:$i] :  ( ((v4_topreal1 H) & (m2_finseq_1 H (u1_struct_0 (k15_euclid 2))))  =>  (~  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) G 1))  &  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) H 1))  &  ( (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) G (k3_finseq_1 G)))  &  ( (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) H (k3_finseq_1 H)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 G) (k3_topreal1 2 H)) = (k2_tarski B D))  &  (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 G) (k3_topreal1 2 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B A))  => (r1_xxreal_0 (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))) (k3_xcmplx_0 A (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))))) ) ) ) ) ).
tt(l67_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k5_card_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k5_card_1 B))))) )  =>  (~  ((r2_hidden A B) &  ((v3_funct_2 C B (k5_card_1 B)) &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden D (k1_relset_1 B C)) &  ((r2_hidden E (k1_relset_1 B C)) &  ( (~ (r1_xxreal_0 E D))  & (r1_xxreal_0 (k2_stirl2_1 B (k5_card_1 B) C E) (k2_stirl2_1 B (k5_card_1 B) C D))) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r2_hidden E B) &  (~  ( ( (~ (r1_xxreal_0 A E))  =>  ((k1_funct_1 D E) = (k1_funct_1 (k2_funct_1 C) (k23_binop_2 (k2_stirl2_1 B (k5_card_1 B) C E) 1))) )  &  ( ( (E = A)  =>  ((k1_funct_1 D E) = (k1_funct_1 (k2_funct_1 C) k6_numbers)) )  &  ( (~ (r1_xxreal_0 E A))  =>  ((k1_funct_1 D E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v5_transgeo D A) =>  ((r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C) |  ((r2_analoaf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C)) & (r2_analoaf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k4_uproots (u1_struct_0 A) (k8_uproots A (k13_polynom3 A B C))) = (k2_nat_1 (k4_uproots (u1_struct_0 A) (k8_uproots A B)) (k4_uproots (u1_struct_0 A) (k8_uproots A C)))) ) ) ) ) ) ) ).
tt(l67_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E B)) ) )  =>  ( (D = E)  =>  (! [F:$i] :  ((m3_yellow_6 F (u1_struct_0 D) A) => (m3_yellow_6 F (u1_struct_0 E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l67_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_xcmplx_0 (k3_xcmplx_0 A (k5_xcmplx_0 B))) = (k3_xcmplx_0 (k5_xcmplx_0 A) B)) ) ) ) ) ).
tt(l67_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(l68_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) B G) &  ((r1_incsp_1 (k13_afproj A) C G) &  ((r1_incsp_1 (k13_afproj A) D H) &  ((r1_incsp_1 (k13_afproj A) E H) &  ((r1_incsp_1 (k13_afproj A) F G) &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) B I) &  ((r1_incsp_1 (k13_afproj A) D I) &  ((r1_incsp_1 (k13_afproj A) C J) &  ((r1_incsp_1 (k13_afproj A) E J) &  ( (~ (r1_incsp_1 (k13_afproj A) F I))  &  ( (~ (r1_incsp_1 (k13_afproj A) F J))  &  ( (~  (G = H) )  &  ( (~ (m1_subset_1 F (u1_struct_0 A)))  &  ( (~  ( (~ (m1_subset_1 B (u1_struct_0 A)))  &  ( (~ (m1_subset_1 C (u1_struct_0 A)))  &  ( (~ (m1_subset_1 D (u1_struct_0 A)))  &  (~ (m1_subset_1 E (u1_struct_0 A))) ) ) ) )  &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) K I) & (r1_incsp_1 (k13_afproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (~  ((r1_collsp (k5_anproj_1 A) B C D) &  ((r1_collsp (k5_anproj_1 A) B C E) &  ((r1_collsp (k5_anproj_1 A) C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) =>  (~  ((r1_collsp (k5_anproj_1 A) B D G) & (r1_collsp (k5_anproj_1 A) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_arytm_2,ax, (! [A:$i] :  (~  ((r2_hidden A a_0_0_arytm_2) &  ( (~  (A = k11_arytm_3) )  &  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (~  ((r2_hidden B A) &  (~  (B = k11_arytm_3) ) ) ) ) ) ) ) ) ) ).
tt(l68_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k10_real_1 (k10_real_1 A B) (k10_real_1 C D)) = (k8_real_1 (k10_real_1 A C) (k10_real_1 D B))) ) ) ) ) ) ) ) ) ).
tt(l68_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_algstr_0 (k9_cc0sp2 A) B C) = (k3_rlvect_1 (k7_cc0sp1 (u1_struct_0 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_classes2,ax,(v4_ordinal1 k4_ordinal1)).
tt(l68_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  ( ( ((k2_xtuple_0 B) = (k2_xtuple_0 C))  &  ( ((k21_coh_sp A B) = (k21_coh_sp A C))  &  ((k22_coh_sp A B) = (k22_coh_sp A C)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(l68_fib_num4,ax, (~ (r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 2) 5) (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) 5))) ).
tt(l68_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_lattices (k1_lattice2 A) (k1_filter_2 A B)) = (k7_lattices A B)) ) ) ) ) ).
tt(l68_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 B) (k10_xtuple_0 C)) (k9_xtuple_0 D)) &  (A = (k3_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) )  =>  ((k9_xtuple_0 (k3_funcop_1 D B C)) = (k2_finseq_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(l68_finseq_4,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( ((k5_card_1 A) = (k5_card_1 B))  &  ((k10_xtuple_0 C) = B) )  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(l68_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k10_xtuple_0 D) (k9_xtuple_0 D)) &  ((r2_hidden A (k9_xtuple_0 D)) &  ( ((k1_funct_1 C k1_xboole_0) = A)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 B E))  =>  ((k1_funct_1 C (k2_xcmplx_0 E 1)) = (k1_funct_1 D (k1_funct_1 C E))) ) ) ) ) ) )  =>  ((k1_funct_1 C B) = (k1_funct_1 (k9_funct_7 D B) A)) ) ) ) ) ) ) ) ) ).
tt(l68_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ((v4_fomodel1 D C) & (m1_subset_1 D (k1_fomodel1 C)))  =>  (! [E:$i] :  ( ((v4_fomodel1 E C) & (m1_subset_1 E (k1_fomodel1 C)))  =>  (! [F:$i] :  ( ((v15_fomodel1 F C) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_fomodel2 G C A)) )  =>  ((v5_relat_1 F (k6_subset_1 (k1_fomodel1 C) (k6_domain_1 (k1_fomodel1 C) D))) =>  ((k14_fomodel2 C A (k5_fomodel2 G E B) F) = (k14_fomodel2 C A (k5_fomodel2 G D B) (k24_fomodel3 C E D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k3_finseq_1 (k9_glib_001 A B C D)) = (k6_xcmplx_0 (k2_nat_1 (k3_finseq_1 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(l68_graph_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( (C = (k8_finseq_1 k1_numbers A B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k1_rvsum_1 C)) => (r1_xxreal_0 k6_numbers D)) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A D))) ) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m2_grcat_1 C (k17_grcat_1 A)) =>  ( (B = C)  =>  (! [D:$i] :  ((m1_cat_1 D (k25_grcat_1 A) B B) =>  ( (D = (k21_grcat_1 (k17_grcat_1 A) C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k25_grcat_1 A))) =>  ( ( (~  ((k2_cat_1 (k25_grcat_1 A) B E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k25_grcat_1 A) B E) =>  ((k1_cat_1 (k25_grcat_1 A) D F) = F) ) ) )  &  ( (~  ((k2_cat_1 (k25_grcat_1 A) E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k25_grcat_1 A) E B) =>  ((k1_cat_1 (k25_grcat_1 A) F D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l68_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 A C)) k6_hilbert1)) ) ) ) ) ) ).
tt(l68_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((k4_finseq_1 (k3_fvsum_1 A B C)) = (k3_finsub_1 (k1_zfmisc_1 k5_numbers) (k4_finseq_1 B) (k4_finseq_1 C))) ) ) ) ) ) ) ).
tt(l68_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ( (~  (k17_modal_1 = (k10_modal_1 A)) )  &  ( (~  (k17_modal_1 = (k11_modal_1 A)) )  &  (~  (k17_modal_1 = (k12_modal_1 A B)) ) ) ) ) ) ) ) ).
tt(l68_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) => (r2_hidden (k6_algstr_0 A C D) B)) ) ) )  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v15_algstr_0 C) & (m2_monoid_0 C A)) )  =>  (~  ((u1_struct_0 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(l68_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) (k4_cat_1 (k2_oppcat_1 A) D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k4_oppcat_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(l68_ordinal5,ax,(r2_hidden k6_numbers 1)).
tt(l68_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  ( ((v6_o_ring_1 C B) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ( (k6_numbers = A)  | (v13_o_ring_1 (k7_partfun1 (u1_struct_0 B) C A) B)) ) ) ) ) ) ) ) ).
tt(l68_scmpds_2,ax, ((k8_struct_0 k1_scmpds_2) = k2_ami_2) ).
tt(l68_sin_cos,ax, ((v1_funct_1 c1__sin_cos) &  ((v1_funct_2 c1__sin_cos k5_numbers k5_numbers) &  ((v5_valued_0 c1__sin_cos) & (m1_subset_1 c1__sin_cos (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ).
tt(l68_topgen_1,ax,(m1_subset_1 k1_borsuk_5 (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))).
tt(l68_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo D A) & (r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C))  =>  ( (B = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))  | (r2_analoaf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ) ).
tt(l68_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 A 3) => (m1_subset_1 A (u2_turing_1 k20_turing_1))) ) ) ).
tt(l68_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  => (r1_tarski (k2_waybel11 A) (k2_waybel11 B))) ) ) ) ) ).
tt(l68_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k7_xcmplx_0 A 2))) ) ) ) ).
tt(l69_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k13_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k13_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k13_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k13_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) B G) &  ((r1_incsp_1 (k13_afproj A) C G) &  ((r1_incsp_1 (k13_afproj A) D H) &  ((r1_incsp_1 (k13_afproj A) E H) &  ((r1_incsp_1 (k13_afproj A) F G) &  ((r1_incsp_1 (k13_afproj A) F H) &  ((r1_incsp_1 (k13_afproj A) B I) &  ((r1_incsp_1 (k13_afproj A) D I) &  ((r1_incsp_1 (k13_afproj A) C J) &  ((r1_incsp_1 (k13_afproj A) E J) &  ( (~ (r1_incsp_1 (k13_afproj A) F I))  &  ( (~ (r1_incsp_1 (k13_afproj A) F J))  &  ( (~  (G = H) )  &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) K I) & (r1_incsp_1 (k13_afproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (~  ( (~ (r1_collsp (k5_anproj_1 A) B C D))  &  ((r1_collsp (k5_anproj_1 A) B C E) &  ((r1_collsp (k5_anproj_1 A) C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) =>  (~  ((r1_collsp (k5_anproj_1 A) B D G) & (r1_collsp (k5_anproj_1 A) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (~  ( (~  (A = k11_arytm_3) )  &  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (~  ((k6_arytm_2 A B) = (k3_arytm_2 c3__arytm_2)) ) ) ) ) ) ) ) ).
tt(l69_asympt_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k6_square_1 A) = (k3_power A (k10_real_1 1 2))) ) ) ) ).
tt(l69_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) => (r1_tarski (a_4_0_bcialg_1 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(l69_card_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ((v1_finset_1 B) =>  ( ( ((k5_card_1 B) = A)  &  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r1_tarski C D))  &  (~ (r1_tarski D C)) ) ) ) ) ) ) )  =>  ( (B = k1_xboole_0)  | (r2_hidden (k3_tarski B) B)) ) ) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ( ((k5_card_1 B) = (k2_nat_1 A 1))  &  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r1_tarski C D))  &  (~ (r1_tarski D C)) ) ) ) ) ) ) )  =>  ( (B = k1_xboole_0)  | (r2_hidden (k3_tarski B) B)) ) ) ) ) ) ) ).
tt(l69_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ( ((k1_relset_1 A C) = A)  &  ((v2_funct_1 C) &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k4_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers D) = (k5_card_1 A))  &  ( ((k21_binop_2 (k9_newton (k5_card_1 A)) (k7_afinsq_2 D)) = (k1_card_1 (a_3_3_card_fin A B C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 D E) = (k12_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) E) (k9_newton (k5_card_1 A))) (k9_newton (k23_binop_2 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A)))) =>  ( (C = D)  =>  ((k1_clvect_1 (k9_cc0sp2 A) C B) = (k1_clvect_1 (k7_cc0sp1 (u1_struct_0 A)) D B)) ) ) ) ) ) ) ) ) ) ).
tt(l69_fib_num4,ax, (~ (r1_xxreal_0 3 (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) (k5_square_1 (k7_square_1 5))))) ).
tt(l69_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k4_filter_0 A C D) B) & (r2_hidden (k4_filter_0 A C E) B))  => (r2_hidden (k4_filter_0 A C (k4_lattices A D E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k36_gfacirc1 A B C)))  &  ( (H = (k1_funct_1 F D))  &  (I = (k1_funct_1 F E)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1)) = (k10_margrel1 G (k9_margrel1 I)))  &  ( ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 E D) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 I) H))  &  ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) = (k10_margrel1 H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_glib_001 A B) = (k1_funct_1 B C))  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k9_glib_001 A B 1 C) (k8_glib_001 A B C (k3_finseq_1 B)))) ) ) ) ) ) ) ).
tt(l69_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (m1_group_2 B (k8_group_4 A B C))) ) ) ) ) ) ).
tt(l69_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  ((m1_group_9 D A C) <=>  ((k17_group_9 A B D C) = D) ) ) ) ) ) ) ) ) ).
tt(l69_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) B) (k4_hilbert1 (k4_hilbert1 A C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l69_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (A = (k2_xcmplx_0 C (k3_xcmplx_0 D k7_complex1)))  &  (B = (k2_xcmplx_0 E (k3_xcmplx_0 F k7_complex1))) )  =>  ((k6_xcmplx_0 (k5_square_1 (k17_complex1 (k8_complex1 A (k15_complex1 B)))) (k5_square_1 (k17_complex1 (k11_complex1 A B)))) = (k3_xcmplx_0 (k3_xcmplx_0 4 C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos2 A))) ) ).
tt(l69_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k4_member_1 (k8_member_1 A B)) = (k8_member_1 (k4_member_1 A) (k4_member_1 B))) ) ) ) ) ).
tt(l69_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(l69_modal_1,ax,(m1_subset_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) k4_modal_1)).
tt(l69_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(l69_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ( ((k17_quaterni A) = B)  &  ( ((k18_quaterni A) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ((k20_quaterni A) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l69_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 5 1))) k6_numbers))  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)) B A) (k5_scmfsa_2 k6_numbers)) = (k2_funct_7 (k2_funct_7 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_complex1 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) (k7_partfun1 k4_numbers (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_complex1 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 3 1)))))) (k18_complex1 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 3 1)))) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 4 1))))) )  &  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 5 1))) k6_numbers) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)) B A) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ).
tt(l69_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k1_newton B (k4_nat_1 2 A)) = (k1_newton (k1_newton B A) 2))  &  ( ((k2_newton (k1_real_1 1) (k4_nat_1 2 A)) = 1)  &  ((k2_newton (k1_real_1 1) (k2_nat_1 (k4_nat_1 2 A) 1)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l69_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_funct_1 k12_toprealb A) = (k19_euclid (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) k6_numbers) k19_sin_cos) A) (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) k6_numbers) k16_sin_cos) A))) ) ) ).
tt(l69_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo D A) & (r1_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C))  =>  ( (B = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))  | (r2_analoaf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ) ).
tt(l69_turing_1,ax, ((r2_hidden k6_numbers (u1_turing_1 k20_turing_1)) & (r2_hidden 1 (u1_turing_1 k20_turing_1))) ).
tt(l69_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k2_waybel11 A) = (k2_waybel11 B)) ) ) ) ) ) ).
tt(l6_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_diraf A B C F G) & (r2_diraf A D E F G))  => (r2_diraf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_extpro_1 A))) =>  ((k5_xtuple_0 B) = k6_numbers) ) ) ) ) ).
tt(l6_ami_wstd,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_extpro_1 C B)) ) )  => (r1_ami_wstd B C A A)) ) ) ) ) ) ).
tt(l6_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_analmetr A B C) &  ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G))) )  =>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_analmetr A B C) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) )  =>  ( (E = (k2_geomtrap A B C D))  &  (F = (k3_geomtrap A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) => (v8_comput_1 (k1_aofa_000 A A (k4_finseq_2 C A) B) C)) ) ) ) ) ) ).
tt(l6_arytm_2,ax,(r1_tarski (k2_xboole_0 k5_arytm_3 k1_arytm_2) (k2_xboole_0 k5_arytm_3 a_0_0_arytm_2))).
tt(l6_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~  (C = 1) )  &  (~  ((k4_power A B) = (k4_power C (k8_real_1 B (k6_power C A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r4_alg_1 A A B) =>  ((v1_funct_1 (k2_funct_1 B)) &  ((v1_funct_2 (k2_funct_1 B) (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 (k2_funct_1 B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(l6_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) A B)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) B A))) ) ) ) ) ).
tt(l6_boole,ax, (! [A:$i] :  ((v1_xboole_0 A) =>  (A = k1_xboole_0) ) ) ).
tt(l6_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A (k13_complex1 1 2)))  => (r2_hidden (k2_xcmplx_0 A (k13_complex1 1 2)) (u1_struct_0 k17_borsuk_1))) ) ) ).
tt(l6_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( (G = (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F)))  =>  ((k10_xtuple_0 G) = (k1_enumset1 (k1_funct_1 G A) (k1_funct_1 G B) (k1_funct_1 G C))) ) ) ) ) ) ) ) ) ) ).
tt(l6_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A k6_margrel1) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) H) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) H) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_card_4,ax, (! [A:$i] :  (~  ((r2_hidden A (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (A = (k1_domain_1 k5_numbers k5_numbers B C)) ) ) ) ) ) ) ) ) ).
tt(l6_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_catalan2 (k8_funcop_1 k5_numbers A k6_numbers))) ) ).
tt(l6_cfdiff_1,ax, ((v1_funct_1 (k8_funcop_1 k2_numbers k5_numbers k5_complex1)) &  ((v1_funct_2 (k8_funcop_1 k2_numbers k5_numbers k5_complex1) k5_numbers k2_numbers) & (m1_subset_1 (k8_funcop_1 k2_numbers k5_numbers k5_complex1) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ).
tt(l6_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_relset_1 k5_numbers k2_numbers B (k25_valued_1 k5_numbers k2_numbers A k7_complex1)) =>  ( ( ((v1_cfdiff_1 A k6_numbers) & (v2_relat_1 A))  =>  ((v1_cfdiff_1 B k6_numbers) & (v2_relat_1 B)) )  &  ( ((v1_cfdiff_1 B k6_numbers) & (v2_relat_1 B))  =>  ((v1_cfdiff_1 A k6_numbers) & (v2_relat_1 A)) ) ) ) ) ) ) ) ).
tt(l6_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_hidden C (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(l6_collsp,ax, (~ (v1_xboole_0 (k6_domain_1 k5_numbers 1))) ).
tt(l6_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k3_complex1 (k5_arytm_0 A B)) = A)  &  ((k4_complex1 (k5_arytm_0 A B)) = B) ) ) ) ) ) ).
tt(l6_comptrig,ax, (~ (r1_xxreal_0 k32_sin_cos k6_numbers)) ).
tt(l6_comseq_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers c1__comseq_3 A) = k6_numbers) ) ) ).
tt(l6_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski (a_2_0_convex3 A B) B) => (v1_convex1 B A)) ) ) ) ) ).
tt(l6_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k7_cqc_lang A B C) A) =>  ((v2_cqc_the1 B A) & (v2_cqc_the1 C A)) ) ) ) ) ) ) ) ).
tt(l6_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_3 A) => (r1_xxreal_0 (k17_complex1 (k11_comseq_3 A)) (k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)))) ) ) ).
tt(l6_csspace4,ax,(m1_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4)) k7_csspace)).
tt(l6_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C))) =>  ((r2_hidden (k4_tarski A B) D) =>  ((r2_hidden A C) & (r2_hidden B C)) ) ) ) ) ) ) ).
tt(l6_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k7_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 2 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k8_euclid 3 A B) = (k1_euclid_8 (k10_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k10_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k10_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(l6_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  => (m2_finseq_2 A k1_numbers (k1_euclid (k3_finseq_1 A)))) ) ).
tt(l6_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k6_xcmplx_0 1 A) B) &  ((r1_xxreal_0 B (k6_xcmplx_0 A 1)) & (r1_int_1 A B)) )  =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(l6_fib_fusc,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k6_xcmplx_0 (k4_nat_1 6 A) 4) k6_numbers)) ) ) ) ).
tt(l6_fib_num,ax, ((k2_nat_1 (k2_nat_1 1 1) 1) = 3) ).
tt(l6_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k1_funct_2 B C)) => (r1_tarski (k3_tarski A) (k2_zfmisc_1 B C))) ) ) ) ).
tt(l6_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_fomodel2 C A B) => (r1_tarski (k37_fomodel1 A) (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(l6_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_unialg_2 B A) => (r1_tarski (k6_unialg_2 A) B)) ) ) ) ) ).
tt(l6_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] : (r1_xboole_0 (k2_msafree2 (k13_gfacirc1 A B C)) (k3_msafree2 (k13_gfacirc1 D E F)))) ) ) ) ) ) ) ) ) ).
tt(l6_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_hidden C (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(l6_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v2_connsp_1 (k2_pre_topc (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k4_connsp_3 (k15_euclid 2) (k2_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) &  ( ((k4_connsp_3 (k15_euclid 2) (k2_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) = (k2_goboard9 A))  & (v3_connsp_1 (k4_connsp_3 (k15_euclid 2) (k2_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))))) ) ) ) ).
tt(l6_graph_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_funct_1 B A) = (k1_funct_1 (k7_finseq_1 B C) A)) ) ) ) ) ) ) ) ).
tt(l6_graphsp,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_funct_1 B A) = (k1_funct_1 (k7_finseq_1 B C) A)) ) ) ) ) ) ) ) ).
tt(l6_hilbert1,ax, (! [A:$i] :  (~  ((v5_hilbert1 A) & (v1_xboole_0 A)) ) ) ).
tt(l6_holder_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ).
tt(l6_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) <=> (r1_int_1 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(l6_int_3,ax, (k6_numbers = (k4_struct_0 k1_int_3)) ).
tt(l6_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k45_valued_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(l6_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (~  ((r1_tarski (k1_polynom2 k10_newton A) (k1_polynom2 k10_newton B)) &  ( ((k5_relat_1 A (k1_polynom2 k10_newton A)) = (k5_relat_1 B (k1_polynom2 k10_newton A)))  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ( ((k1_polynom2 k10_newton C) = (k7_subset_1 k10_newton (k1_polynom2 k10_newton B) (k1_polynom2 k10_newton A)))  &  ((r1_xboole_0 (k1_polynom2 k10_newton A) (k1_polynom2 k10_newton C)) &  ( ((k5_relat_1 C (k1_polynom2 k10_newton C)) = (k5_relat_1 B (k1_polynom2 k10_newton C)))  & (r8_pboole k10_newton (k11_pre_poly k10_newton A C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_integra1 A)) =>  ( ((k3_integra1 A) = k6_numbers)  =>  ((v1_integra1 B A) &  ((k10_integra1 A B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l6_jordan19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k4_tarski C (k1_matrix_1 (k1_jordan8 A B))) (k2_matrix_1 (k1_jordan8 A B))) =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k1_matrix_1 (k1_jordan8 A B)))) = (k7_real_1 (k9_pscomp_1 A) (k8_real_1 (k10_real_1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k13_newton 2 B)) (k5_real_1 (k1_matrix_1 (k1_jordan8 A B)) 2)))) ) ) ) ) ) ) ) ).
tt(l6_jordan1d,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_tarski (k2_enumset1 A B C D)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D)) ) ) ) ) ).
tt(l6_jordan1h,ax,(r1_relat_2 k1_jordan1h k1_numbers)).
tt(l6_jordan22,ax, ((k1_relset_1 (u1_struct_0 (k15_euclid 2)) k5_pscomp_1) = (u1_struct_0 (k15_euclid 2))) ).
tt(l6_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k2_complex2 B A) = (k2_complex2 B (k7_real_1 A (k8_real_1 (k8_real_1 2 k32_sin_cos) C)))) ) ) ) ) ) ) ).
tt(l6_lattices,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 k1_xboole_0) (k1_zfmisc_1 k1_xboole_0)) (k1_zfmisc_1 k1_xboole_0))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_lattices (k1_zfmisc_1 k1_xboole_0) A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_lattices (k1_zfmisc_1 k1_xboole_0) A))) =>  (B = C) ) ) ) ) ) ) ).
tt(l6_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (1 = A)  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space (k1_series_1 k1_numbers B C) A)) D) (k10_real_1 1 A)) (k7_real_1 (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space B A)) D) (k10_real_1 1 A)) (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space C A)) D) (k10_real_1 1 A))))) ) ) ) ) ) ) ) ) ).
tt(l6_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A C D)) (k8_cqc_lang A (k8_cqc_lang A E C) (k8_cqc_lang A B (k8_cqc_lang A E D)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l6_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) B A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) B A) =>  (! [H:$i] :  ((m2_finseq_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ( ((r2_hidden I (k2_finseq_1 B)) &  ((r2_hidden J (k2_finseq_1 (k1_matrix_1 F))) &  ( (H = (k8_matrix_1 (u1_struct_0 C) F E))  &  (G = (k3_matrix11 E B A (u1_struct_0 C) F (k9_fvsum_1 C H D))) ) ) )  =>  ( ( (I = E)  =>  ((k3_matrix_1 (u1_struct_0 C) G I J) = (k8_group_1 C D (k3_matrix_1 (u1_struct_0 C) F E J))) )  &  ( (~  (I = E) )  =>  ((k3_matrix_1 (u1_struct_0 C) G I J) = (k3_matrix_1 (u1_struct_0 C) F I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k1_mboolean A (k5_pboole A B C)) D) = (k1_zfmisc_1 (k5_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D)))) ) ) ) ) ) ) ) ).
tt(l6_mesfunc7,ax,(r3_binop_1 k7_numbers k8_mesfunc1 k1_mesfunc7)).
tt(l6_metrizts,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((r2_borsuk_3 A B) => (r1_ordinal1 (k2_waybel23 B) (k2_waybel23 A))) ) ) ) ) ).
tt(l6_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m2_finseq_2 E C (k4_finseq_2 A C)) =>  ((r2_hidden B (k2_finseq_1 A)) =>  ((k1_funct_1 (k1_midsp_3 C A E B D) B) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (A = k6_numbers)  | (r1_xxreal_0 1 A)) ) ) ).
tt(l6_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( (~  ((r2_hidden C (k6_dtconstr (k5_msafree A B))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  (~  (C = (k4_tarski E D)) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  ( (C = (k4_tarski E D))  => (r2_hidden C (k6_dtconstr (k5_msafree A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1))) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers c2__normsp_1 (k3_rlvect_1 (k1_rlsub_1 o_0_5_normsp_1) A B)) (k7_real_1 (k3_funct_2 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers c2__normsp_1 A) (k3_funct_2 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) k1_numbers c2__normsp_1 B)))) ) ) ) ).
tt(l6_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v5_metric_1 (u1_metric_1 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))) (u1_struct_0 (g1_metric_1 (u1_struct_0 A) (k1_normsp_2 A))))) ) ).
tt(l6_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ( ((k8_nat_1 k5_numbers C k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k5_numbers D E))  &  ((k8_nat_1 k5_numbers D (k2_nat_1 E 1)) = (k4_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E))) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  ((k8_nat_1 k5_numbers D E) = k6_numbers) )  =>  ((k6_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E)) = (k6_nat_d (k8_nat_1 k5_numbers C (k2_nat_1 E 1)) (k8_nat_1 k5_numbers D (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k1_relat_1 B) = A) ) ) ) ).
tt(l6_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1))) =>  ((v2_rlvect_1 (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C)) &  ((v3_rlvect_1 (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C)) &  ((v4_rlvect_1 (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C)) & (v13_algstr_0 (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C))) ) ) ) ) ) ) ) ) ).
tt(l6_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( ((k5_algstr_0 A (k8_group_1 A C D) (k8_group_1 A E B)) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k8_group_1 A C F) (k8_group_1 A G B)) = (k4_struct_0 A)) )  =>  ( (B = (k4_struct_0 A))  |  ((k5_algstr_0 A (k8_group_1 A E F) (k8_group_1 A G D)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A B))  =>  ((k2_rfinseq k1_numbers A (k5_euclid B)) = (k5_euclid (k7_nat_d B A))) ) ) ) ) ) ).
tt(l6_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) => (r1_tarski (k2_petri_2 A B) (k9_setfam_1 (k4_partfun1 C A)))) ) ) ) ) ).
tt(l6_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 D (k2_xboole_0 (k1_tarski C) B)) => (r3_orders_1 D B)) ) ) ) ) ) ) ) ).
tt(l6_polynom7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k15_pre_poly k1_xboole_0) (u1_struct_0 A)) &  ((v1_polynom1 B (k15_pre_poly k1_xboole_0) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly k1_xboole_0) (u1_struct_0 A))))) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_funct_2 (k15_pre_poly k1_xboole_0) (u1_struct_0 A) (k6_domain_1 (k15_pre_poly k1_xboole_0) (k16_pre_poly k1_xboole_0)) (u1_struct_0 A) B (k8_funcop_1 (u1_struct_0 A) (k6_domain_1 (k15_pre_poly k1_xboole_0) (k16_pre_poly k1_xboole_0)) C))) ) ) ) ) ) ).
tt(l6_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k3_finseq_1 B) = (k2_xcmplx_0 D 1))  &  (C = (k2_partfun1 k5_numbers (u1_struct_0 A) B (k2_finseq_1 D))) )  =>  ((k4_rlvect_1 A B) = (k3_rlvect_1 A (k4_rlvect_1 A C) (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ).
tt(l6_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A B D F) &  ( (~  (B = E) )  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((r3_binop_1 (u1_struct_0 A) (k4_struct_0 A) (u1_algstr_0 A)) => (v4_rlvect_1 A)) ) ) ).
tt(l6_qmax_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden A k12_prob_1) =>  ( ((r2_hidden k6_numbers A) =>  ((k1_funct_1 c2__qmax_1 A) = 1) )  &  ( (~ (r2_hidden k6_numbers A))  =>  ((k1_funct_1 c2__qmax_1 A) = k6_numbers) ) ) ) ) ) ).
tt(l6_quaterni,ax,(r2_zfmisc_1 k6_numbers 1 2 3)).
tt(l6_ramsey_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((k5_card_1 B) = A)  =>  ((k3_group_10 B A) = (k1_tarski B)) ) ) ) ) ) ).
tt(l6_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ((r2_mesfunc6 A B C) &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  (~  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_seq_1 C G) = (k1_seq_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_rat_1,ax, (! [A:$i] :  (~  ((r2_hidden A k3_numbers) &  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k7_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ).
tt(l6_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k1_lattices k3_real_lat (k2_lattices k3_real_lat A B) B) = B) ) ) ) ) ).
tt(l6_realset2,ax, ((k1_funct_7 1 2) = 1) ).
tt(l6_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (? [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) &  ( ((k3_finseq_1 B) = (k5_card_1 A))  &  ((v2_rearran1 B) & (v1_rearran1 B)) ) ) ) ) ) ).
tt(l6_reloc,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  (~ (v2_compos_1 B k1_ami_3)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 C) & (v4_extpro_1 C 2 k1_ami_3 B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 E (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski C D) & (r1_tarski (k9_memstr_0 2 k1_ami_3 C A) E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ((r1_tarski B F) & (r1_tarski (k6_compos_1 k1_ami_3 B A) G))  =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 F D H)) A) = (k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 G E H)))  &  ( ((k5_compos_0 (u1_compos_1 k1_ami_3) (k3_extpro_1 2 k1_ami_3 F (k5_extpro_1 2 k1_ami_3 F D H)) A) = (k3_extpro_1 2 k1_ami_3 G (k5_extpro_1 2 k1_ami_3 G E H)))  &  ( ((k5_relat_1 (k5_extpro_1 2 k1_ami_3 F D H) (k9_xtuple_0 (k6_memstr_0 2 k1_ami_3 C))) = (k5_relat_1 (k5_extpro_1 2 k1_ami_3 G E H) (k9_xtuple_0 (k6_memstr_0 2 k1_ami_3 C))))  &  ((k6_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 F (k1_funct_4 D (k6_memstr_0 2 k1_ami_3 E)) H)) = (k6_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 G E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_rfinseq,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ( ((k5_card_1 (k9_xtuple_0 (k5_relat_1 C B))) = A)  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~ (r2_classes1 (k5_relat_1 C B) D)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ( ((k5_card_1 (k9_xtuple_0 (k5_relat_1 C B))) = (k3_real_1 A 1))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~ (r2_classes1 (k5_relat_1 C B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  => (v1_ringcat1 (k3_struct_0 A) A A)) ) ).
tt(l6_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_subset_1 (u1_struct_0 A) (k5_rusub_4 A B D) (k5_rusub_4 A C D)) = (k5_rusub_4 A (k7_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(l6_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k1_rlsub_2 A B C) = (k1_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(l6_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k1_rmod_3 A B C D) = (k1_rmod_3 A B D C)) ) ) ) ) ) ) ) ) ).
tt(l6_roughs_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_orders_3 A) => (v1_roughs_1 A)) ) ) ).
tt(l6_rsspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k9_real_1 (k1_seq_1 B D) A) (k9_real_1 (k1_seq_1 B D) A))) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k8_real_1 (k9_real_1 (k2_seq_2 B) A) (k9_real_1 (k2_seq_2 B) A))) ) ) ) ) ) ) ) ) ) ).
tt(l6_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k1_rusub_2 A B C) = (k1_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(l6_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_ami_3)))  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D B)) = C)  =>  ( ( (~  ((k3_compos_1 k1_ami_3 A C) = (k2_ami_3 E F)) )  &  ( (~  ((k3_compos_1 k1_ami_3 A C) = (k3_ami_3 E F)) )  &  ( (~  ((k3_compos_1 k1_ami_3 A C) = (k4_ami_3 E F)) )  &  ( (~  ((k3_compos_1 k1_ami_3 A C) = (k5_ami_3 E F)) )  &  (~  ( (~  (E = F) )  &  ((k3_compos_1 k1_ami_3 A C) = (k6_ami_3 E F)) ) ) ) ) ) )  |  ( ((k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) = (k2_extpro_1 2 k1_ami_3 (k3_compos_1 k1_ami_3 A C) (k5_extpro_1 2 k1_ami_3 A D B)))  &  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = (k2_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_scmfsa6c,ax,(v1_scmfsa6b (k11_compos_1 k1_scmfsa_2 (k2_compos_1 k1_scmfsa_2)))).
tt(l6_scmfsa7b,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 B 3 k1_scmfsa_2 A)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 (k2_scmfsa_7 D E)) F))  =>  ((k1_funct_1 (k2_scmfsa_7 D E) F) = (k3_compos_1 k1_scmfsa_2 C (k2_nat_1 A F))) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 F (k1_afinsq_1 (k2_scmfsa_7 D E))) =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 C B F)) = (k2_nat_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ((k1_funct_1 B (k1_scmp_gcd 3)) = C) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 1)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 1)) (k1_funct_1 B (k1_scmp_gcd C))))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 2)) = (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 2)) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 3)) = (k2_nat_1 C 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 D 3))  =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1)) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd D)) = (k1_funct_1 B (k1_scmp_gcd D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_xcmplx_0 (k3_xcmplx_0 (k4_nat_1 A (k2_nat_1 (k4_nat_1 2 A) 1)) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton A 2)) (k4_nat_1 3 A)) 1)) (k4_nat_1 (k13_newton (k2_nat_1 A 1) 3) 30)) = (k3_xcmplx_0 (k4_nat_1 (k2_nat_1 A 2) (k2_nat_1 (k4_nat_1 2 (k2_nat_1 A 1)) 1)) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton (k2_nat_1 A 1) 2)) (k4_nat_1 3 (k2_nat_1 A 1))) 1))) ) ) ).
tt(l6_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_newton (k2_xcmplx_0 A B) 3) = (k7_real_1 (k7_real_1 (k3_real_1 (k1_newton A 3) (k8_real_1 (k8_real_1 3 (k3_square_1 A)) B)) (k8_real_1 (k8_real_1 3 A) (k3_square_1 B))) (k1_newton B 3))) ) ) ) ) ).
tt(l6_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (B = 1) )  =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k7_xcmplx_0 (k3_xcmplx_0 B (k6_xcmplx_0 1 (k1_newton B A))) (k1_newton (k6_xcmplx_0 1 B) 2)) (k7_xcmplx_0 (k3_xcmplx_0 A (k1_newton B (k2_nat_1 A 1))) (k6_xcmplx_0 1 B))) (k3_xcmplx_0 A (k1_newton B (k2_nat_1 A 1)))) (k1_newton B (k2_nat_1 A 1))) = (k6_xcmplx_0 (k7_xcmplx_0 (k3_xcmplx_0 B (k6_xcmplx_0 1 (k1_newton B (k2_nat_1 A 1)))) (k1_newton (k6_xcmplx_0 1 B) 2)) (k7_xcmplx_0 (k3_xcmplx_0 (k2_nat_1 A 1) (k1_newton B (k2_nat_1 A 2))) (k6_xcmplx_0 1 B)))) ) ) ) ) ) ).
tt(l6_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_square_1 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 (k3_xcmplx_0 2 B) C)) (k3_xcmplx_0 (k3_xcmplx_0 2 C) A))) ) ) ) ) ) ) ).
tt(l6_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v1_scmfsa7b B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k1_funct_1 D (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r6_scmfsa7b B D A) &  ((r6_scmfsa7b C (k1_scmfsa6b B D A) A) &  ((r5_scmfsa7b B D A) &  ((r5_scmfsa7b C (k1_scmfsa6b B D A) A) &  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) D) & (r1_tarski (k3_scmfsa6a B C) A)) ) ) ) ) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k5_card_1 B))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D)))))  &  ((r1_tarski (k6_compos_1 k1_scmfsa_2 C (k5_card_1 B)) A) &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1)) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r1_extpro_1 3 k1_scmfsa_2 A D) &  ( ((k8_extpro_1 3 k1_scmfsa_2 A D) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A B) C) (k1_scmfsa_m (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D)))))  &  ((v1_scmfsa7b C) =>  ((k1_funct_1 (k6_extpro_1 3 k1_scmfsa_2 A D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) = (k6_binop_2 (k3_binop_2 (k15_sin_cos A) (k15_sin_cos (k1_binop_2 A))) 2)) ) ) ).
tt(l6_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k6_xcmplx_0 A B) = k6_numbers) )  &  ((k3_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2))) = k6_numbers) ) ) ) ) ) ) ).
tt(l6_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (k2_rcomp_1 k6_numbers k32_sin_cos)) =>  ((k1_fdiff_1 k30_sin_cos A) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos A))))) ) ) ) ).
tt(l6_sprect_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ((k2_goboard9 A) = (k3_goboard9 A)) ) ) ) ) ).
tt(l6_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_tarski k6_numbers)) =>  ((k2_binop_1 (u1_struct_0 A) (k1_tarski k6_numbers) (k1_tarski k6_numbers) B C D) = c2__symsp_1) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_symsp_1 D A)) ) ) ) )  =>  ( (D = (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C))  =>  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) & (v11_vectsp_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E C) & (r2_hidden E D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(l6_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_xtuple_0 (k2_partfun1 k1_numbers k1_numbers B A)) = A) ) ) ) ) ).
tt(l6_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k1_relat_1 B)) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_topalg_2,ax, ((k9_xtuple_0 (k3_struct_0 k5_topmetr)) = (u1_struct_0 k5_topmetr)) ).
tt(l6_topalg_5,ax, ((m1_subset_1 k6_numbers (u1_struct_0 k5_topmetr)) & (m1_subset_1 1 (u1_struct_0 k5_topmetr))) ).
tt(l6_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v7_ordinal1 (k1_xxreal_3 (k2_topdim_1 A B) 1))) ) ) ) ).
tt(l6_topgen_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  & (r1_tarski (u1_pre_topc A) (u1_pre_topc B))) ) ) ) ) ) ).
tt(l6_topreal2,ax, ((k17_euclid (k19_euclid k6_numbers 1)) = k6_numbers) ).
tt(l6_toprealb,ax,(r1_xxreal_0 (k9_real_1 (k10_real_1 3 2) (k10_real_1 1 2)) 1)).
tt(l6_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_funct_2 A A (k1_transgeo A C B) (k1_transgeo A D B)) => (r2_funct_2 A A C D)) ) ) ) ) ) ) ) ) ).
tt(l6_trees_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) A))  => (r2_hidden (k1_funct_1 C (k2_nat_1 A 1)) B)) ) ) ) ) ) ).
tt(l6_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v4_pre_topc (k5_waybel_0 A B) A)) ) ) ) ).
tt(l6_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D)))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( (E = F)  => (r1_tarski (a_3_2_waybel33 A C E) (a_3_2_waybel33 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_wellset1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_tarski A B) <=>  (? [C:$i] :  ( (! [D:$i] :  (~  ((r2_hidden D A) &  (! [E:$i] :  (~  ((r2_hidden E B) & (r2_hidden (k4_tarski D E) C)) ) ) ) ) )  &  ( (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  (~  ((r2_hidden E A) & (r2_hidden (k4_tarski E D) C)) ) ) ) ) )  &  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski F G) C))  =>  ( (D = F)  <=>  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( ((r1_xxreal_0 k6_numbers A) &  (~ (r1_xxreal_0 B C)) )  |  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 C B)) )  =>  ( (~ (r1_xxreal_0 (k2_xcmplx_0 A B) C))  &  (~ (r1_xxreal_0 B (k6_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ).
tt(l6_xcmplx_0,ax, (k6_numbers = (k5_arytm_0 k6_numbers k6_numbers)) ).
tt(l6_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k2_xcmplx_0 A C) (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l6_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k2_xcmplx_0 A C) (k2_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(l6_xxreal_0,ax, (~  (k1_xxreal_0 = (k4_tarski k6_numbers k6_numbers)) ) ).
tt(l6_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_funct_1 A D))) =>  ( ((r2_hidden B (k4_card_3 A)) & (r2_hidden (k2_funct_7 B C E) (k8_relat_1 (k12_card_3 A D) F)))  =>  ( (C = D)  | (r2_hidden B (k8_relat_1 (k12_card_3 A D) F))) ) ) ) ) ) ) ) ) ) ) ).
tt(l6_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v7_waybel_0 A) <=> (v7_waybel_0 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(l6_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model A)) & (r1_zf_model B C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang A (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  =>  ((r2_hidden D (k4_zf_lang1 A)) |  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model (k6_zf_lang1 A (k2_zf_lang k6_numbers) D))) &  ((r1_zf_model B C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang (k6_zf_lang1 A (k2_zf_lang k6_numbers) D) (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) & (r2_funct_2 B B (k1_zfmodel1 A B C) (k1_zfmodel1 (k6_zf_lang1 A (k2_zf_lang k6_numbers) D) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (r1_aff_1 A B C D))  &  ((r2_analoaf A B C E F) &  ((r2_hidden B G) &  ((r2_hidden C G) &  ((r2_hidden D G) &  ((v1_aff_4 G A) &  ((r2_hidden E G) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_analoaf A B D E H) & (r2_analoaf A C D F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v2_anproj_2 (k5_anproj_1 A))) ) ).
tt(l70_asympt_1,ax, (? [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 (k9_real_1 B (k8_real_1 (k7_square_1 B) (k6_power 2 B))) (k10_real_1 B 2))) ) ) ) ) ) ).
tt(l70_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k7_bcialg_6 A B C D)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) & (r2_hidden E (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ( (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski C B)) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  | (r2_hidden (k3_tarski A) A)) ) ) ) ).
tt(l70_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k2_comput_1 k5_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_comput_1 k5_numbers))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k2_comput_1 k5_numbers)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_comput_1 k5_numbers))))) )  =>  ( ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F H))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H)))) (k9_xtuple_0 B))) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 H 1)) = (k1_funct_4 (k8_nat_1 (k2_comput_1 k5_numbers) F H) (k16_funcop_1 (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D (k2_nat_1 H 1)) (k1_funct_1 B (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H)))))))) )  &  ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F H))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D H)))) (k9_xtuple_0 B))) ) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 H 1)) = (k8_nat_1 (k2_comput_1 k5_numbers) F H)) ) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) G H))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) G H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H)))) (k9_xtuple_0 B))) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) G (k2_nat_1 H 1)) = (k1_funct_4 (k8_nat_1 (k2_comput_1 k5_numbers) G H) (k16_funcop_1 (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D (k2_nat_1 H 1)) (k1_funct_1 B (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) G H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H)))))))) )  &  ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) G H))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) G H) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D H)))) (k9_xtuple_0 B))) ) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) G (k2_nat_1 H 1)) = (k8_nat_1 (k2_comput_1 k5_numbers) G H)) ) ) ) ) )  =>  ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1))) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = (k8_funcop_1 k5_numbers (k1_tarski (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D k6_numbers)) (k1_recdef_1 A (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))))) ) ) )  |  ( ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) & (r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1))) (k1_relset_1 (k3_finseq_2 k5_numbers) A))) )  &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = k1_xboole_0) ) )  |  ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E))) &  ((r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E)) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) G k6_numbers) = (k8_funcop_1 k5_numbers (k1_tarski (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E) D k6_numbers)) (k1_recdef_1 A (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E))))) ) ) )  |  ( ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E))) & (r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E)) (k1_relset_1 (k3_finseq_2 k5_numbers) A))) )  &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) G k6_numbers) = k1_xboole_0) ) )  | (r2_funct_2 k5_numbers (k2_comput_1 k5_numbers) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 3 5) (k13_complex1 (k3_xcmplx_0 (k7_square_1 5) (k6_xcmplx_0 (k7_square_1 5) 1)) 5))) ).
tt(l70_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((r1_tarski (k10_xtuple_0 C) (k9_xtuple_0 C)) &  ((r2_hidden A (k9_xtuple_0 C)) &  ( ((k1_funct_1 D 1) = A)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 (k2_xcmplx_0 B 1) E) |  ((k1_funct_1 D (k2_xcmplx_0 E 1)) = (k1_funct_1 C (k1_funct_1 D E))) ) ) ) ) ) ) )  =>  ((k1_funct_1 D (k2_xcmplx_0 B 1)) = (k1_funct_1 (k9_funct_7 C B) A)) ) ) ) ) ) ) ) ) ).
tt(l70_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_relset_1 (k4_finseq_2 2 A) k6_margrel1 (k2_fomodel2 A) (k6_domain_1 k5_numbers 1)) = (k7_relset_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A) (k11_monoid_0 A) (k3_fomodel2 (k4_finseq_2 1 A)))) ) ) ).
tt(l70_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_fomodel4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_fomodel4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ((r2_hidden (k1_domain_1 (k1_zfmisc_1 (k1_fomodel4 A)) (k1_fomodel4 A) B C) D) => (r2_hidden C (k3_funct_2 (k1_zfmisc_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k21_fomodel4 A D) B))) ) ) ) ) ) ) ) ) ).
tt(l70_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k36_gfacirc1 A B C)))  &  (H = (k1_funct_1 F E)) )  =>  ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1)) = (k2_binarith G (k9_margrel1 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k3_glib_001 A (k9_glib_001 A B C D)) = (k3_glib_001 A B))  &  ((k4_glib_001 A (k9_glib_001 A B C D)) = (k4_glib_001 A B)) ) ) ) ) ) ) ) ) ) ).
tt(l70_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) => (m1_group_2 (k8_group_4 A (k8_group_4 A B C) D) (k8_group_4 A B (k8_group_4 A C D)))) ) ) ) ) ) ) ) ).
tt(l70_hfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k3_rfunct_1 k1_numbers k1_numbers A A) = (k8_funcop_1 k5_numbers (k4_xboole_0 (k1_relset_1 k1_numbers A) (k8_relset_1 k1_numbers k1_numbers A (k1_tarski k6_numbers))) 1)) ) ) ).
tt(l70_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 A C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l70_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (A = (k2_xcmplx_0 C (k3_xcmplx_0 D k7_complex1)))  &  (B = (k2_xcmplx_0 E (k3_xcmplx_0 F k7_complex1))) )  =>  ((r1_xxreal_0 k6_numbers E) |  ( (~  ( (~ (r1_xxreal_0 k6_numbers C))  & (r1_xxreal_0 (k17_complex1 (k8_complex1 A (k15_complex1 B))) (k17_complex1 (k11_complex1 A B)))) )  &  ( (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 (k17_complex1 (k11_complex1 A B)) (k17_complex1 (k8_complex1 A (k15_complex1 B))))) )  &  ( (C = k6_numbers)  =>  ((k17_complex1 (k11_complex1 A B)) = (k17_complex1 (k8_complex1 A (k15_complex1 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A k1_sin_cos2) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos2 A))) ) ) ).
tt(l70_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k2_finseq_1 (k5_card_1 C))) &  ( (~  ((k12_matrix_3 (k5_card_1 C) A (k7_matrix13 (u1_struct_0 A) B C D)) = (k4_struct_0 A)) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 (k5_card_1 C))) &  (~  ((k12_matrix_3 (k7_nat_d (k5_card_1 C) 1) A (k2_laplace E F (k5_card_1 C) A (k7_matrix13 (u1_struct_0 A) B C D))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_algstr_0 B D)) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(l70_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) =>  (~  (k17_modal_1 = (k16_modal_1 A)) ) ) ) ).
tt(l70_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k4_pepin A) 1)) ) ) ).
tt(l70_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 B) =>  ((k1_seq_1 (k3_rinfsup1 B) A) = (k1_seq_1 B A)) ) ) ) ) ) ).
tt(l70_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)) B A) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) ) ) ) ) ).
tt(l70_simplex0,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) & (l1_pre_topc B)) )  =>  (~  ((r1_xxreal_0 (k2_xxreal_3 1) A) &  ((r1_xxreal_0 A (k6_simplex0 B)) &  (! [C:$i] :  ( ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((k1_card_1 C) = (k1_xxreal_3 A 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) = (k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) 1)) ) ) ).
tt(l70_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k16_substut1 A) (k9_qc_lang1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k16_substut1 A) (k9_qc_lang1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k16_substut1 A) (k9_qc_lang1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k16_substut1 A) (k9_qc_lang1 A))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) =>  ( ((v2_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B D) = (k5_cqc_lang A)) )  &  ( ((v4_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B D) = (k10_qc_lang1 A (k16_qc_lang1 A (k18_substut1 A D)) (k3_substut1 A (k26_substut1 A D) (k19_substut1 A D)))) )  &  ( ((v5_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B D) = (k13_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B (k27_substut1 A D)))) )  &  ( ((v6_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B D) = (k14_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B (k28_substut1 A D)) (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B (k29_substut1 A D)))) )  &  ((v7_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B D) = (k36_substut1 A D (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B (k31_substut1 A D)))) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) =>  ( ((v2_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C D) = (k5_cqc_lang A)) )  &  ( ((v4_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C D) = (k10_qc_lang1 A (k16_qc_lang1 A (k18_substut1 A D)) (k3_substut1 A (k26_substut1 A D) (k19_substut1 A D)))) )  &  ( ((v5_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C D) = (k13_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C (k27_substut1 A D)))) )  &  ( ((v6_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C D) = (k14_qc_lang1 A (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C (k28_substut1 A D)) (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C (k29_substut1 A D)))) )  &  ((v7_substut1 D A) =>  ((k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C D) = (k36_substut1 A D (k3_funct_2 (k16_substut1 A) (k9_qc_lang1 A) C (k31_substut1 A D)))) ) ) ) ) ) ) ) )  => (r2_funct_2 (k16_substut1 A) (k9_qc_lang1 A) B C)) ) ) ) ) ) ) ).
tt(l70_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc B k17_borsuk_1 (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C k17_borsuk_1 (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) )  => (v5_pre_topc (k7_topalg_1 A B C) (k2_borsuk_1 k17_borsuk_1 k17_borsuk_1) (k15_euclid A))) ) ) ) ) ) ).
tt(l70_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo D A) & (r1_diraf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B)))  =>  ( (B = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))  |  ( (C = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))  | (r2_analoaf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l70_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k20_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)))) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (A = (k3_xtuple_0 B C D))  =>  ( (B = 3)  |  ((k9_turing_1 k20_turing_1 A) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 k20_turing_1) (u1_turing_1 k20_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k20_turing_1 A)) (k2_xcmplx_0 (k7_turing_1 k20_turing_1 A) (k6_turing_1 k20_turing_1 (k8_turing_1 k20_turing_1 A))) (k5_turing_1 k20_turing_1 (k3_mcart_1 (u2_turing_1 k20_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)) A) (k7_turing_1 k20_turing_1 A) (k2_mcart_1 (u2_turing_1 k20_turing_1) (u1_turing_1 k20_turing_1) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 k20_turing_1 A))))) ) ) ) ) ) ) ) ).
tt(l70_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k5_waybel11 A) = (k5_waybel11 B)) ) ) ) ) ) ).
tt(l70_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k5_xcmplx_0 A) = (k5_xcmplx_0 B))  =>  (A = B) ) ) ) ) ) ).
tt(l71_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_anproj_2 A) => (v4_collsp (k5_anproj_1 A))) ) ) ).
tt(l71_arytm_2,ax, (! [A:$i] :  ((m2_subset_1 A (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 k5_arytm_3) k1_arytm_2) =>  ( (A = a_0_2_arytm_2)  =>  ((k6_arytm_2 A B) = B) ) ) ) ) ) ).
tt(l71_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k4_power (k7_real_1 1 (k10_real_1 1 (k2_nat_1 B 1))) (k2_nat_1 B 1))) ) )  => (v7_valued_0 A)) ) ) ).
tt(l71_bcialg_4,ax, ((v5_bcialg_4 k2_bcialg_4) &  ((v6_bcialg_4 k2_bcialg_4) &  ((v7_bcialg_4 k2_bcialg_4) &  ((v5_bcialg_1 k2_bcialg_4) & (v2_bcialg_4 k2_bcialg_4)) ) ) ) ).
tt(l71_borsuk_5,ax,(r1_tarski (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k3_borsuk_5 2 4) (k1_seq_4 4)) (k1_seq_4 5)) (k2_rcomp_1 1 k1_xxreal_0))).
tt(l71_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((k7_enumset1 A B C D E F G H I) = (k2_xboole_0 (k2_enumset1 A B C D) (k3_enumset1 E F G H I))) ) ) ) ) ) ) ) ) ) ).
tt(l71_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v8_clvect_1 (k9_cc0sp2 A))) ) ).
tt(l71_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k2_comput_1 k5_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_comput_1 k5_numbers))))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F G))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G)))) (k9_xtuple_0 B))) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 G 1)) = (k1_funct_4 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k16_funcop_1 (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D (k2_nat_1 G 1)) (k1_funct_1 B (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G)))))))) )  &  ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F G))) & (r2_hidden (k8_finseq_1 k5_numbers (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G) (k12_finseq_1 k5_numbers (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F G) (k3_funct_7 k5_numbers (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D G)))) (k9_xtuple_0 B))) ) )  =>  ((k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 G 1)) = (k8_nat_1 (k2_comput_1 k5_numbers) F G)) ) ) ) )  =>  ( ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) &  ((r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1))) (k1_relset_1 (k3_finseq_2 k5_numbers) A)) &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = (k8_funcop_1 k5_numbers (k1_tarski (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) D k6_numbers)) (k1_recdef_1 A (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))))) ) ) )  |  ( ( (~  ((r2_hidden D (k4_finseq_1 (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)))) & (r2_hidden (k2_finseq_3 D (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1))) (k1_relset_1 (k3_finseq_2 k5_numbers) A))) )  &  (~  ((k8_nat_1 (k2_comput_1 k5_numbers) F k6_numbers) = k1_xboole_0) ) )  |  ( ((k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F (k2_nat_1 E 1)) (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E)) = (k1_recdef_1 (k8_nat_1 (k2_comput_1 k5_numbers) F E) (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D E)))  &  (~ (r2_hidden (k1_midsp_3 k5_numbers (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 E 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k8_nat_1 (k2_comput_1 k5_numbers) F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k27_descip_1 (k25_descip_1 A)) = A) ) ) ).
tt(l71_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 6 10) (k3_xcmplx_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k13_complex1 (k7_square_1 5) 5)))) ).
tt(l71_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k9_filter_0 A B) D)) <=> (r2_hidden (k7_filter_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(l71_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k2_zfmisc_1 (k1_tarski A) (k10_xtuple_0 B)) (k9_xtuple_0 C)) =>  ((k9_xtuple_0 (k5_funcop_1 C A B)) = (k4_finseq_1 B)) ) ) ) ) ) ) ).
tt(l71_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ((r2_hidden A (k18_finseq_1 B)) &  ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~ (r2_hidden A (k9_funct_7 B C))) ) ) ) ) ) ) ) ) ).
tt(l71_fomodel1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fomodel1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) & (v1_funct_1 B)) )  =>  ( ((k2_fomodel1 (k40_fomodel1 B A)) = (k2_xboole_0 (k8_relat_1 (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) (k15_fomodel1 A))) (k6_domain_1 k5_numbers k6_numbers)) (k2_fomodel1 A)))  &  ((k5_relset_1 (k6_subset_1 (u1_struct_0 (k40_fomodel1 B A)) (k1_tarski (u3_struct_0 (k40_fomodel1 B A)))) k4_numbers (u1_fomodel1 (k40_fomodel1 B A)) (k9_fomodel1 A)) = (k5_relset_1 (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A))) k4_numbers (u1_fomodel1 A) (k9_fomodel1 A))) ) ) ) ) ) ).
tt(l71_fomodel3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_funct_2 F (k33_fomodel2 B) (k33_fomodel2 B) (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B))) =>  ((v4_fomodel2 (k28_fomodel3 B C D A F E) B) & (m2_subset_1 (k28_fomodel3 B C D A F E) (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v2_fomodel4 B A) =>  (! [C:$i] :  ((v1_fomodel4 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ((r2_hidden (k4_tarski B C) D) => (v4_fomodel4 C 1 A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k21_fomodel4 A D)) B)) ) ) ) ) ) ) ) ) ).
tt(l71_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1)) = (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) (k9_margrel1 K)))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 E D) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 K) J))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) = (k10_margrel1 J (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I))))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k5_numbers (k9_glib_001 A B C D))) &  ( (~ (r2_hidden E (k2_finseq_1 C)))  &  (~  ((r1_xxreal_0 C E) & (r1_xxreal_0 E (k3_finseq_1 (k9_glib_001 A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_hfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((k8_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A (k20_valued_1 k1_numbers k1_numbers k1_numbers A A)) (k1_tarski k6_numbers)) = (k8_relset_1 k1_numbers k1_numbers A (k1_tarski k6_numbers))) ) ) ).
tt(l71_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 B A) C)) k6_hilbert1)) ) ) ) ) ) ).
tt(l71_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k5_algstr_0 B D E)) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~ (r1_nat_d (k1_newton B 2) (k6_moebius1 A))) ) ) ) ) ).
tt(l71_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  (~  ((r2_hidden B (k10_normform A C D)) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E D) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 (k2_oppcat_1 B) (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(l71_orders_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r6_relat_2 C A) & (r1_tarski B A))  => (r6_relat_2 C B)) ) ) ) ) ).
tt(l71_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_nat_d (k7_nat_d (k4_pepin A) 1) 2) = k6_numbers) ) ) ).
tt(l71_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))) & (r1_xxreal_0 2 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1))  &  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers))) &  ( ( ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  |  ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1))) )  &  ( ( ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  |  ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))))) )  &  ( ( ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)))  |  ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1))) )  &  ( (! [C:$i] :  ((r2_hidden C (k4_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))) =>  ( (C = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1))  |  ( (C = (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))))  |  ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) C) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) C)) ) ) ) )  &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ( (C = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) 1)))  &  ( (D = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2))) B A) (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  ((k4_finseq_1 B) = (k2_finseq_1 A)) ) ) ) ) ).
tt(l71_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_borsuk_2 D (k15_euclid A) B C) =>  (! [E:$i] :  ((m1_borsuk_2 E (k15_euclid A) B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k7_topalg_1 A D E) F k6_numbers) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)) D F))  &  ( ((k1_binop_1 (k7_topalg_1 A D E) F 1) = (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)) E F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k17_borsuk_1)) =>  ( ((k1_binop_1 (k7_topalg_1 A D E) k6_numbers G) = B)  &  ((k1_binop_1 (k7_topalg_1 A D E) 1 G) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A) (u1_struct_0 (k1_pre_topc k2_topalg_2 A)) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 A)) (u1_struct_0 (k8_toprealb 2)))))) ) ) ) ).
tt(l71_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo D A) & (r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C))  =>  ( (B = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))  | (r2_analoaf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ) ).
tt(l71_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_turing_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  (! [E:$i] :  ((m2_funct_2 E k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ( (G = D)  &  ((m1_subset_1 k6_numbers (u1_turing_1 A)) &  ( (B = (k4_domain_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) C D E))  &  ( ((k1_funct_1 (u3_turing_1 A) (k1_domain_1 (u2_turing_1 A) k5_numbers C 1)) = (k4_domain_1 (u2_turing_1 A) k5_numbers k5_numbers C k6_numbers 1))  &  ( (~  (C = (u5_turing_1 A)) )  &  ( (! [H:$i] :  ((v1_int_1 H) =>  ((r1_xxreal_0 G H) =>  ((r1_xxreal_0 (k2_nat_1 G F) H) |  ((k1_funct_1 E H) = 1) ) ) ) )  &  (! [H:$i] :  ((m2_funct_2 H k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (~  ( ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) F) = (k4_domain_1 (u2_turing_1 A) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) C (k2_nat_1 G F) H))  &  ( (! [I:$i] :  ((v1_int_1 I) =>  ((r1_xxreal_0 G I) =>  ((r1_xxreal_0 (k2_nat_1 G F) I) |  ((k1_funct_1 H I) = k6_numbers) ) ) ) )  &  (! [I:$i] :  ((v1_int_1 I) =>  ( (~  ((r1_xxreal_0 G I) &  (~ (r1_xxreal_0 (k2_nat_1 G F) I)) ) )  =>  ((k1_funct_1 H I) = (k1_funct_1 E I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l71_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v3_lattice3 A))  => (v3_lattice3 B)) ) ) ) ) ).
tt(l71_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v6_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(l72_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k4_power (k10_real_1 (k2_nat_1 A 1) A) A) (k4_power (k10_real_1 (k2_nat_1 A 2) (k2_nat_1 A 1)) (k2_nat_1 A 1)))) ) ) ).
tt(l72_borsuk_5,ax,(r1_tarski (k2_rcomp_1 1 k1_xxreal_0) (k3_rcomp_1 1 k1_xxreal_0))).
tt(l72_cat_4,ax, (! [A:$i] :  (! [B:$i] : (v2_cat_1 (k23_cat_4 A B))) ) ).
tt(l72_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers))))) )  =>  ( (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  ((k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F G) = (k6_comput_1 A B D G)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) => (r1_tarski (k1_relset_1 (k3_finseq_2 k5_numbers) (k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D G))) (k1_relset_1 (k3_finseq_2 k5_numbers) (k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 G H)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k25_descip_1 (k27_descip_1 A)) = A) ) ) ).
tt(l72_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 6 10) (k3_xcmplx_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k13_complex1 (k7_square_1 5) (k5_square_1 (k7_square_1 5)))))) ).
tt(l72_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  ((k18_finseq_1 A) = (k3_tarski (a_1_0_fomodel0 A))) ) ) ) ).
tt(l72_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((v2_fomodel4 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 B)) (k1_fomodel4 B)))) =>  ((r2_hidden A (k1_funct_1 (k21_fomodel4 B D) C)) <=>  ((r2_hidden A (k1_fomodel4 B)) & (r2_hidden (k4_tarski C A) D)) ) ) ) ) ) ) ) ) ).
tt(l72_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1)) = (k2_binarith (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) (k9_margrel1 K)))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k10_glib_001 A B C) = (k7_finseq_1 B (k10_finseq_1 C D))) ) ) ) ) ) ) ) ).
tt(l72_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 C A) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l72_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_normsp_0 B (k1_rlvect_1 B C (k8_binop_2 A))) = (k12_binop_2 (k1_normsp_0 B C) (k18_complex1 A))) ) ) ) ) ) ) ).
tt(l72_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan9 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden A (k2_finseq_1 (k5_card_1 D))) &  ( (~  ((k12_matrix_3 (k5_card_1 D) B (k7_matrix13 (u1_struct_0 B) C D E)) = (k4_struct_0 B)) )  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden G (k2_finseq_1 (k5_card_1 D))) &  (~  ((k12_matrix_3 (k7_nat_d (k5_card_1 D) 1) B (k2_laplace G A (k5_card_1 D) B (k7_matrix13 (u1_struct_0 B) C D E))) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) C D) E) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k12_matrix_2 A)) (k1_matrix_9 A B C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(l72_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v1_moebius1 (k6_moebius1 A))) ) ) ).
tt(l72_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k9_normform A (k5_setwiseo (k7_normform A) (k10_normform A B C) C)) = (k9_normform A C)) ) ) ) ) ) ).
tt(l72_orders_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r2_wellord1 C A) & (r1_tarski B A))  => (r2_wellord1 C B)) ) ) ) ) ).
tt(l72_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A B) C) =>  ((k17_complex1 (k10_binop_2 (k1_seq_1 (k1_pdiff_7 A B D) F) (k1_seq_1 (k1_pdiff_7 A B E) F))) = (k12_euclid (k8_euclid 1 (k1_pdiff_6 A 1 (k8_pdiff_1 A 1 C D) F) (k1_pdiff_6 A 1 (k8_pdiff_1 A 1 C E) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k7_nat_d (k4_pepin A) 1) k6_numbers)) ) ) ).
tt(l72_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_rlvect_3 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))) = (k1_rlvect_3 A B)) ) ) ) ) ).
tt(l72_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (~  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 1 1)))) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 1 1)))))  &  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) &  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 1 1)))) C) &  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B A) (k5_scmfsa_2 k6_numbers)) C) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v1_topreal4 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l72_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k21_pscomp_1 (k3_topreal1 2 A))) ) ) ) )  =>  ( ((k20_pscomp_1 (k3_topreal1 2 A)) = (k11_pscomp_1 (k3_topreal1 2 A)))  |  ( ((k21_pscomp_1 (k3_topreal1 2 A)) = (k12_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ).
tt(l72_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((r1_xxreal_0 k6_numbers (k10_real_1 (k6_sin_cos6 A) (k8_real_1 2 k32_sin_cos))) & (r1_xxreal_0 (k10_real_1 (k6_sin_cos6 A) (k8_real_1 2 k32_sin_cos)) (k10_real_1 1 2))) ) ) ) ).
tt(l72_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v3_waybel_3 A))  => (v3_waybel_3 B)) ) ) ) ) ).
tt(l72_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k5_zmodul01 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(l73_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_anproj_2 A) => (v3_anproj_2 (k5_anproj_1 A))) ) ) ).
tt(l73_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) =>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  ( ( (A = C)  &  (B = D) )  =>  ((k10_ordinal2 A B) = (k9_arytm_3 C D)) ) ) ) ) ) ) ) ) ) ).
tt(l73_borsuk_5,ax, ((k9_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 1) (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 2) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) = (k2_rcomp_1 k2_xxreal_0 1)) ).
tt(l73_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_comseq_2 (k55_valued_1 A k2_numbers B)) <=> (v1_comseq_2 B)) ) ) ) ) ).
tt(l73_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers))))) )  =>  ( (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers)) =>  ((k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F G) = (k6_comput_1 A B D G)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ( (~ (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D G)))))  & (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D G) (k1_relset_1 (k3_finseq_2 k5_numbers) (k3_funct_2 (k4_finseq_2 (k2_nat_1 (k19_margrel1 A) 1) k5_numbers) (k2_comput_1 k5_numbers) F (k8_comput_1 (k2_nat_1 (k19_margrel1 A) 1) C D (k2_nat_1 G H)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l73_descip_1,ax,(r2_funct_2 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k1_partfun1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) k26_descip_1 k28_descip_1) (k6_partfun1 (k4_finseq_2 64 k6_margrel1)))).
tt(l73_fib_num4,ax, ( (~ (r1_xxreal_0 (k13_complex1 6 10) (k3_xcmplx_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k13_complex1 (k3_xcmplx_0 1 (k7_square_1 5)) (k3_xcmplx_0 (k7_square_1 5) (k7_square_1 5))))))  &  (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ) ).
tt(l73_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 C)) (k1_fomodel4 C)))) =>  ((r2_hidden A (k1_funct_1 (k21_fomodel4 C D) B)) <=>  ((r2_hidden A (k1_fomodel4 C)) & (r2_hidden (k4_tarski B A) D)) ) ) ) ) ) ) ) ).
tt(l73_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1)))  &  ( (H = (k1_funct_1 F (k4_tarski (k10_finseq_1 E D) k3_twoscomp)))  &  (I = (k1_funct_1 F (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp))) ) )  =>  ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k21_gfacirc1 (k36_gfacirc1 A B C) E D)) = (k1_binarith (k1_binarith G H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l73_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ( ((k3_glib_001 A (k10_glib_001 A B C)) = (k3_glib_001 A B))  &  ( ((k4_glib_001 A (k10_glib_001 A B C)) = D)  & (r1_glib_001 A (k3_glib_001 A B) D (k10_glib_001 A B C))) ) ) ) ) ) ) ) ) ).
tt(l73_group_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((m2_subset_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1) k1_numbers k5_numbers) &  ((r1_xxreal_0 1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1)) & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 A) B) 1) (k3_finseq_1 A))) ) ) ) ) ) ) ).
tt(l73_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 C B) A)) k6_hilbert1)) ) ) ) ) ) ).
tt(l73_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k4_sin_cos2 A))) ) ).
tt(l73_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan9 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l73_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k6_grcat_1 C D) (k3_rlvect_1 C E F)) = (k3_rlvect_1 D (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k6_grcat_1 C D) E) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k6_grcat_1 C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l73_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) D) = (k5_oppcat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k6_oppcat_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(l73_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((k2_relat_1 (k2_wellord1 A B)) = (k2_wellord1 (k2_relat_1 A) B)) ) ) ) ).
tt(l73_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_nat_d (k4_pepin A) (k2_newton 2 (k2_newton 2 A))) = 1) ) ) ).
tt(l73_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k1_numbers))  => (v2_funct_1 (k4_rltopsp1 A B))) ) ) ) ).
tt(l73_scmbsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ( (A = (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 1 1))))  & (r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) |  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B C) (k5_scmfsa_2 k6_numbers))) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) D))  & (r1_xxreal_0 1 D))  |  ( (~ (r1_xxreal_0 D (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))))  & (r2_hidden D (k4_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))))) )  =>  ((k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) D) = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B C) (k5_scmfsa_2 k6_numbers)) D)) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) D) &  ((r1_xxreal_0 D (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) &  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (E = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B C) (k5_scmfsa_2 k6_numbers)) (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A)))  &  ( (F = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B C) (k5_scmfsa_2 k6_numbers)) D))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) D) &  ((r1_xxreal_0 D (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1))) A) E) &  ((r1_xxreal_0 E (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 2 1)))) &  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))) B C) (k5_scmfsa_2 k6_numbers)) D) = (k1_funct_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l73_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k24_pscomp_1 (k3_topreal1 2 A)) (k13_pscomp_1 (k3_topreal1 2 A))) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 (k3_topreal1 2 A)) (k20_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(l74_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (B = (a_2_5_armstrng A C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden (k6_armstrng A D E) B) <=>  (! [F:$i] :  ( ((r2_hidden F C) & (r1_tarski D F))  => (r1_tarski E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (~  ( (~ (r3_arytm_3 (k9_arytm_3 B C) A))  &  ( (~  (B = k11_arytm_3) )  &  ( (~  (C = k11_arytm_3) )  &  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  (! [E:$i] :  ((m1_subset_1 E k5_arytm_3) =>  (~  ( (A = (k9_arytm_3 D E))  &  ( (~ (r3_arytm_3 B D))  &  (~ (r3_arytm_3 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_borsuk_5,ax, ((k9_subset_1 k1_numbers (k2_rcomp_1 1 k1_xxreal_0) (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 2) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 1 2) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) ).
tt(l74_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 D) &  ((v4_valued_0 D) & (v2_margrel1 D)) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 C) 1) k5_numbers)) =>  ((r2_hidden A (k4_finseq_1 E)) =>  ( ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) => (r2_hidden (k2_finseq_3 A E) (k1_relset_1 (k3_finseq_2 k5_numbers) C)))  &  ( ((r2_hidden (k2_finseq_3 A E) (k1_relset_1 (k3_finseq_2 k5_numbers) C)) => (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))))  &  ( ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) =>  ((k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A k6_numbers)) = (k1_recdef_1 C (k2_finseq_3 A E))) )  &  ( ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) =>  ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) & (r2_hidden (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))) (k1_relset_1 (k3_finseq_2 k5_numbers) D))) )  &  ( ( ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) & (r2_hidden (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))) (k1_relset_1 (k3_finseq_2 k5_numbers) D)))  => (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))))  &  ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) =>  ((k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1))) = (k1_recdef_1 D (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_descip_1,ax,(r2_funct_2 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k1_partfun1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) k28_descip_1 k26_descip_1) (k6_partfun1 (k4_finseq_2 64 k6_margrel1)))).
tt(l74_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 6 10) (k3_xcmplx_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k13_complex1 1 (k7_square_1 5))))) ).
tt(l74_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 B) (k1_tarski A)) (k9_xtuple_0 C)) =>  ((k9_xtuple_0 (k4_funcop_1 C B A)) = (k4_finseq_1 B)) ) ) ) ) ) ) ).
tt(l74_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( ( ((k32_fomodel2 B C) = (k1_nat_1 A 1))  & (v5_fomodel2 C B))  => (r2_hidden C (k28_fomodel2 B A))) ) ) ) ) ) ) ).
tt(l74_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1)))  &  (H = (k1_funct_1 F D)) )  =>  ((k1_funct_1 (k6_circuit2 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F) (k24_gfacirc1 (k36_gfacirc1 A B C) E D)) = (k2_binarith G (k9_margrel1 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k11_fvsum_1 A (k2_finseq_4 (u1_struct_0 A) B C) (k2_finseq_4 (u1_struct_0 A) D E)) = (k2_finseq_4 (u1_struct_0 A) (k6_algstr_0 A B D) (k6_algstr_0 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k3_finseq_1 (k10_glib_001 A B C)) = (k2_nat_1 (k3_finseq_1 B) 2)) ) ) ) ) ) ) ) ).
tt(l74_group_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 C)) =>  ((k1_funct_1 D G) = (k1_funct_1 F (k1_funct_1 C G))) ) ) )  &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_group_4 A (k4_group_4 A E C))) = (k3_group_4 B (k4_group_4 B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 A (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(l74_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  &  ((r1_tarski (k2_rcomp_1 B C) (k1_relset_1 k1_numbers E)) &  (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F (k2_rcomp_1 B C)) =>  ((k1_funct_1 E F) = (k6_integr18 (k4_real_ns1 A) D B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A k4_sin_cos2) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers k4_sin_cos2 A))) ) ) ).
tt(l74_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) B) k8_intpro_1)) ) ) ) ) ) ).
tt(l74_jgraph_5,ax, ((k17_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = (k1_real_1 1)) ).
tt(l74_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan9 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k3_finseq_1 (k1_jordan8 B A)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 E A) &  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_funct_2 (k2_finseq_1 E) (k2_finseq_1 A)) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_2 (k2_finseq_1 E) (k2_finseq_1 A)) (u1_struct_0 B))))) )  =>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_finseq_1 E) (k2_finseq_1 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 E) (k2_finseq_1 A))))) )  &  (? [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) &  ( (H = (k1_funct_4 (k4_matrix_6 A B C D) (k5_relat_1 (k3_relat_1 (k1_funct_4 (k1_finseq_2 A) G) D) (k2_finseq_1 E))))  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden I (k2_finseq_1 E)) =>  ((k1_funct_1 H I) = (k1_funct_1 D (k1_funct_1 G I))) )  &  ( (~ (r2_hidden I (k2_finseq_1 E)))  =>  ((k1_funct_1 H I) = (k1_funct_1 (k4_matrix_6 A B C D) I)) ) ) ) )  &  (! [I:$i] :  ((m2_finseq_1 I (u1_struct_0 B)) =>  (~  ( ((k3_finseq_1 I) = E)  &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  (! [K:$i] :  ((v7_ordinal1 K) =>  ( ((r2_hidden K (k2_finseq_1 E)) &  (J = (k1_funct_1 G K)) )  =>  ((k1_funct_1 I K) = (k3_matrix_1 (u1_struct_0 B) C K J)) ) ) ) ) )  &  ((k1_funct_1 F G) = (k8_group_1 B (k1_finsop_1 (u1_struct_0 B) I (u2_algstr_0 B)) (k12_matrix_3 A B H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_mesfunc6 A B D) &  ((r2_mesfunc6 A B E) &  ((k1_relset_1 A E) = (k1_relset_1 A D)) ) )  =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((r2_mesfunc6 A B (k3_valued_1 A k1_numbers k1_numbers D E)) &  (~  ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E A) &  ((v9_vectsp_1 E A) &  ((v10_vectsp_1 E A) &  ((v11_vectsp_1 E A) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E A)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) (k6_grcat_1 D E) (k4_vectsp_1 B D F G)) = (k4_vectsp_1 A E (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C F) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) (k6_grcat_1 D E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden A (k1_modelc_3 B)) => (r1_xxreal_0 (k18_modelc_3 B (k19_modelc_3 B A)) (k9_real_1 (k3_finseq_1 A) 1))) ) ) ) ) ).
tt(l74_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k2_wellord1 A k1_xboole_0) = k1_xboole_0) ) ) ).
tt(l74_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) => (r2_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B E) C) (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B E) D)) (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B E) (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l74_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_abian (k4_pepin A))) ) ) ).
tt(l74_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r4_polyred A B C D F E) =>  ( (~  (D = (k7_polynom1 A C)) )  &  (~  (F = (k7_polynom1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l74_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) B A) (k4_scmfsa_2 (k2_nat_1 1 1))) = (k6_xcmplx_0 (k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) 1))  &  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) B A) (k4_scmfsa_2 (k2_nat_1 2 1))) = (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))))  &  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) B A) (k5_scmfsa_2 k6_numbers)) = (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ).
tt(l74_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k1_scmpds_4 (k4_scmpds_4 A B) C)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ).
tt(l74_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) ) )  =>  ( ((k20_pscomp_1 (k3_topreal1 2 A)) = (k11_pscomp_1 (k3_topreal1 2 A)))  |  ( ((k24_pscomp_1 (k3_topreal1 2 A)) = (k13_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k13_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k13_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ).
tt(l74_toprealb,ax,(v2_funct_1 (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k3_rcomp_1 k6_numbers 1)))).
tt(l74_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C A) &  ( (C = (u1_struct_0 B))  &  ( (D = E)  & (v3_tops_1 D A)) ) )  => (v3_tops_1 E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l75_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ((r2_hidden A k5_arytm_3) &  ((r2_hidden B k5_arytm_3) &  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  (~  ( (A = C)  &  ( (B = D)  &  ((k7_arytm_2 A B) = (k9_arytm_3 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l75_classes2,ax, ( ((k16_classes2 k1_xboole_0) = k13_classes2)  &  ( (! [A:$i] :  ((v3_ordinal1 A) =>  ((k16_classes2 (k1_ordinal1 A)) = (k1_classes1 (k16_classes2 A))) ) )  &  (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) & (v1_funct_1 B)) )  =>  ( ((v4_ordinal1 A) &  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k16_classes2 C)) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ((k16_classes2 A) = (k15_classes2 (k3_card_3 B))) ) ) ) ) ) ) ) ) ).
tt(l75_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 6 10) (k13_complex1 (k6_xcmplx_0 (k7_square_1 5) 1) (k7_square_1 5)))) ).
tt(l75_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A B) C)) (k32_fomodel2 A C))) ) ) ) ) ) ) ).
tt(l75_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) (k21_gfacirc1 (k36_gfacirc1 A B C) E D)) = (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) (k9_margrel1 K)) (k10_margrel1 (k9_margrel1 K) J)) (k10_margrel1 J (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)))))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l75_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ( ((k1_funct_1 (k10_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) 1)) = C)  &  ( ((k1_funct_1 (k10_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) 2)) = D)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 (k10_glib_001 A B C) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l75_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 A (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(l75_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 A B) C)) (k4_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l75_jgraph_5,ax, ((k18_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = k6_numbers) ).
tt(l75_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden A (k1_modelc_3 B)) => (r1_xxreal_0 (k18_modelc_3 B (k20_modelc_3 B A)) (k9_real_1 (k3_finseq_1 A) 1))) ) ) ) ) ).
tt(l75_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v2_o_ring_1 C A) & (v1_o_ring_1 B A))  => (v2_o_ring_1 (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l75_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ( ((k4_finseq_1 C) = (k4_finseq_1 B))  &  ( ((k10_xtuple_0 C) = (k9_xtuple_0 (k12_pnproc_1 B A)))  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k1_funct_1 C D) = (k2_nat_1 A D)) ) ) )  & (v2_funct_1 C)) ) ) ) ) ) ) ) ) ).
tt(l75_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_relat_2 (k17_pre_poly A) (k15_pre_poly A))) ) ).
tt(l75_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k1_numbers))  => (v5_pre_topc (k4_rltopsp1 A B) A A)) ) ) ) ).
tt(l75_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) = (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers))))  =>  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))))) B A) (k5_scmfsa_2 k6_numbers))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( (E = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))))) B A) (k5_scmfsa_2 k6_numbers)) C))  &  (F = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 k6_numbers 1)) (k3_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 (k2_nat_1 k6_numbers 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 1 1)) (k4_scmfsa_2 k6_numbers))) (k16_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k2_scmfsa8c (k4_scmfsa_2 (k2_nat_1 1 1)) (k3_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 3 1)) (k4_scmfsa_2 (k2_nat_1 2 1))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 2 1)) (k4_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 4 1)))) (k2_scmfsa8b (k4_scmfsa_2 (k2_nat_1 5 1)) (k5_scmfsa6a (k6_scmfsa6a (k14_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers)) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 5 1)) (k4_scmfsa_2 (k2_nat_1 2 1)) (k5_scmfsa_2 k6_numbers))) (k15_scmfsa_2 (k4_scmfsa_2 (k2_nat_1 4 1)) (k4_scmfsa_2 (k2_nat_1 3 1)) (k5_scmfsa_2 k6_numbers))) (k4_compos_1 k1_scmfsa_2)))))) B A) (k5_scmfsa_2 k6_numbers)) D)) )  => (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l76_card_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_finset_1 (k4_classes1 A)) => (v1_finset_1 (k4_classes1 (k1_nat_1 A 1)))) ) ) ).
tt(l76_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ((k5_clvect_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(l76_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D)))) =>  ( (~  (A = (k4_tarski (k10_finseq_1 B C) D)) )  =>  ( ((k11_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) (k6_circuit2 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E) (k9_facirc_1 B C A D)) = (k1_funct_1 D (k10_finseq_1 (k1_funct_1 E (k4_tarski (k10_finseq_1 B C) D)) (k1_funct_1 E A))))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E) (k4_tarski (k10_finseq_1 B C) D)) = (k1_funct_1 D (k10_finseq_1 (k1_funct_1 E B) (k1_funct_1 E C))))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E) B) = (k1_funct_1 E B))  &  ( ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E) C) = (k1_funct_1 E C))  &  ((k1_funct_1 (k6_circuit2 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E) A) = (k1_funct_1 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l76_fib_num4,ax,(r1_xxreal_0 (k6_square_1 (k4_square_1 (k13_complex1 3 2))) (k7_square_1 5))).
tt(l76_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( ((k32_fomodel2 B C) = (k1_nat_1 A 1))  =>  ((v5_fomodel2 C B) | (r2_hidden C (k35_fomodel2 B A))) ) ) ) ) ) ) ) ).
tt(l76_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  => (r2_hidden (k34_fomodel3 A B C) (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A)))) ) ) ) ) ) ).
tt(l76_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) (k24_gfacirc1 (k36_gfacirc1 A B C) E D)) = (k9_margrel1 (k2_binarith (k2_binarith (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) J) (k9_margrel1 K))))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l76_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_glib_001 A D E B) & (r1_glib_000 A E F C))  => (r1_glib_001 A D F (k10_glib_001 A B C))) ) ) ) ) ) ) ) ) ).
tt(l76_goboard6,ax, ((k7_real_1 (k10_real_1 1 2) (k10_real_1 1 2)) = 1) ).
tt(l76_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_xboole_0 C) =>  ((k18_group_9 A B C) = (k4_group_9 A B)) ) ) ) ) ) ) ).
tt(l76_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l76_jgraph_5,ax, ( ((k17_euclid (k19_euclid 1 k6_numbers)) = 1)  &  ((k18_euclid (k19_euclid 1 k6_numbers)) = k6_numbers) ) ).
tt(l76_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_nat_d A B) =>  ((v1_moebius1 A) | (r1_nat_d A (k6_moebius1 B))) ) ) ) ) ) ).
tt(l76_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k1_lattices (k12_normform A) B C) = (k1_lattices (k12_normform A) C B)) ) ) ) ) ) ).
tt(l76_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v3_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l76_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r4_relat_2 (k17_pre_poly A) (k15_pre_poly A))) ) ).
tt(l76_quatern3,ax, (k4_quatern2 = (k5_arytm_0 k6_numbers 1)) ).
tt(l76_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k6_quaterni A B C D) = (k7_quaterni (k7_quaterni (k23_quaterni A (k25_quaterni B k1_xcmplx_0)) (k25_quaterni C k11_quaterni)) (k25_quaterni D k12_quaterni))) ) ) ) ) ) ) ) ) ).
tt(l76_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k1_scmpds_4 (k4_scmpds_4 A B) C))) & (r2_hidden 1 (k9_xtuple_0 (k1_scmpds_4 (k4_scmpds_4 A B) C)))) ) ) ) ) ) ) ).
tt(l77_card_2,ax, (1 = (k5_card_1 1)) ).
tt(l77_fib_num4,ax,(r1_xxreal_0 (k13_complex1 3 2) (k7_square_1 5))).
tt(l77_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ((v1_abian C) & (m1_subset_1 C k5_numbers))  =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((r2_hidden (k3_nat_d C 2) (k1_relset_1 k5_numbers (k12_glib_001 A B))) &  ((k1_funct_1 B C) = (k1_funct_1 (k12_glib_001 A B) (k3_nat_d C 2))) ) ) ) ) ) ) ) ) ).
tt(l77_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  ((k2_group_9 A B D (k4_matrix_2 A C)) = (k3_funct_2 A (k1_funct_2 B B) D C)) ) ) ) ) ) ) ) ).
tt(l77_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 (k4_hilbert1 C B) A)) k6_hilbert1)) ) ) ) ) ) ).
tt(l77_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 A C)) k8_intpro_1)) ) ) ) ) ) ).
tt(l77_jgraph_5,ax, ((k17_euclid (k19_euclid k6_numbers (k1_real_1 1))) = k6_numbers) ).
tt(l77_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ((k1_lattices (k12_normform A) B (k1_lattices (k12_normform A) C D)) = (k1_lattices (k12_normform A) (k1_lattices (k12_normform A) B C) D)) ) ) ) ) ) ) ) ).
tt(l77_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v6_o_ring_1 C A) & (v5_o_ring_1 B A))  => (v6_o_ring_1 (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l77_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r8_relat_2 (k17_pre_poly A) (k15_pre_poly A))) ) ).
tt(l77_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k26_quaterni A B) = (k26_quaterni (k26_quaterni (k23_quaterni (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k25_quaterni (k7_real_1 (k18_quaterni A) (k18_quaterni B)) k1_xcmplx_0)) (k25_quaterni (k7_real_1 (k19_quaterni A) (k19_quaterni B)) k11_quaterni)) (k25_quaterni (k7_real_1 (k20_quaterni A) (k20_quaterni B)) k12_quaterni))) ) ) ) ) ).
tt(l77_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 B) =>  ((k1_seq_1 (k4_rinfsup1 B) A) = (k1_seq_1 B A)) ) ) ) ) ) ).
tt(l77_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k18_seq_4 A (k17_seq_4 A)) = (k17_seq_4 A)) ) ) ).
tt(l77_sincos10,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)))) = (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))) ).
tt(l77_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k8_nat_1 k2_numbers (k3_sin_cos B) 1) = B)  &  ( ((k8_nat_1 k2_numbers (k3_sin_cos B) k6_numbers) = k6_complex1)  &  ((k17_complex1 (k1_newton B A)) = (k2_newton (k17_complex1 B) A)) ) ) ) ) ) ) ).
tt(l77_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l78_card_2,ax, (2 = (k5_card_1 2)) ).
tt(l78_classes2,ax, (1 = (k1_ordinal1 k6_numbers)) ).
tt(l78_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 B) (k2_ens_1 (k16_ens_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (k2_ens_1 (k16_ens_1 B)))))) )  =>  ((r1_tarski (k16_ens_1 B) A) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A)))))) ) ) ) ) ) ) ) ) ).
tt(l78_fib_num4,ax,(r1_xxreal_0 (k3_xcmplx_0 (k13_complex1 3 2) 2) (k3_xcmplx_0 (k7_square_1 5) 2))).
tt(l78_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C)) (k32_fomodel2 A B)))  &  (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C)) (k32_fomodel2 A C))) ) ) ) ) ) ) ) ).
tt(l78_fomodel3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_funct_2 F (k33_fomodel2 B) (k33_fomodel2 B) (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B))) =>  ((k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D F) (k1_nat_1 A 1)) E) = (k29_fomodel3 B C D A (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D F) A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l78_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (r1_tarski (k2_relset_1 A B) (k1_relset_1 A B))) ) ) ).
tt(l78_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k8_group_1 A (k11_algstr_0 A B) (k8_group_1 A B C)) = C) ) ) ) ) ) ) ) ).
tt(l78_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r1_analmetr A B C) & (r2_analoaf (k7_geomtrap A B C) D E E F))  =>  ( (D = E)  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l78_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k1_relset_1 k5_numbers (k12_glib_001 A B))) <=> (r2_hidden (k4_nat_1 2 C) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ).
tt(l78_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  => (m1_group_2 (k8_group_5 A B C) (k8_group_5 A C B))) ) ) ) ) ) ).
tt(l78_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k1_funct_2 B B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r2_funct_2 B B (k2_group_9 A B E (k8_finseq_1 A D (k4_matrix_2 A C))) (k1_partfun1 B B B B (k2_group_9 A B E (k4_matrix_2 A C)) (k2_group_9 A B E D)))) ) ) ) ) ) ) ) ) ).
tt(l78_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 (k4_hilbert1 B A) C)) k6_hilbert1)) ) ) ) ) ) ).
tt(l78_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) B) (k4_intpro_1 (k4_intpro_1 A C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l78_jgraph_5,ax, ((k18_euclid (k19_euclid k6_numbers (k1_real_1 1))) = (k1_real_1 1)) ).
tt(l78_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  (~  ( ((k7_real_1 (k10_real_1 1 F) (k10_real_1 1 G)) = 1)  &  ((r2_hidden D (k1_lpspace2 A B C F)) &  ((r2_hidden E (k1_lpspace2 A B C F)) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers D))))  &  ( (I = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers E))))  &  ( (J = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers D E)))))  & (r1_xxreal_0 (k4_power J (k10_real_1 1 F)) (k7_real_1 (k4_power H (k10_real_1 1 F)) (k4_power I (k10_real_1 1 F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l78_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (~  ((r1_tarski C (k4_finseq_1 B)) &  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ( (D = (k1_partfun1 k5_numbers k5_numbers k5_numbers (u1_struct_0 A) (k14_finseq_1 C) B))  &  ( (E = (k1_partfun1 k5_numbers k5_numbers k5_numbers (u1_struct_0 A) (k14_finseq_1 (k7_subset_1 k5_numbers (k4_finseq_1 B) C)) B))  &  ((k4_rlvect_1 A B) = (k3_rlvect_1 A (k4_rlvect_1 A D) (k4_rlvect_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l78_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k1_binop_1 (u2_lattices (k12_normform A)) (k1_binop_1 (u1_lattices (k12_normform A)) B C) C) = C) ) ) ) ) ) ).
tt(l78_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((r2_hidden k4_ordinal1 A) =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 A) k6_numbers)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 A) k6_numbers) (k2_ordinal1 A) (k2_ordinal1 A)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 A) k6_numbers)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 A) k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ) ) ).
tt(l78_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v7_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l78_pepin,ax, ((k13_newton 3 2) = 9) ).
tt(l78_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r3_orders_1 (k17_pre_poly A) (k15_pre_poly A))) ) ).
tt(l78_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmpds_4 (k4_scmpds_4 A B) C) k6_numbers) = A)  &  ((k1_funct_1 (k1_scmpds_4 (k4_scmpds_4 A B) C) 1) = B) ) ) ) ) ) ) ) ).
tt(l78_sincos10,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos))) = (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)) ).
tt(l78_sin_cos6,ax, ((k2_funct_1 k1_sin_cos6) = (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(l78_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k11_comseq_3 (k3_sin_cos A)) = (k4_series_1 (k4_sin_cos A))) ) ) ).
tt(l78_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l78_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 1 (k4_xcmplx_0 A)) (k2_rcomp_1 (k2_xcmplx_0 B A) (k3_real_1 (k2_xcmplx_0 B A) 1)))) = (k2_rcomp_1 B (k3_real_1 B 1))) ) ) ) ) ).
tt(l78_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_struct_0 C B) <=>  ((k5_zmodul01 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(l79_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) &  ((v1_aff_4 C A) & (r1_aff_4 A B C)) )  =>  ( (B = C)  |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C B) = (k1_bcialg_1 A B C)) ) ) ) )  => (v13_bcialg_1 A)) ) ) ).
tt(l79_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k2_finseq_1 A)) => (m1_subset_1 (k6_xcmplx_0 B 1) (u1_struct_0 (k9_int_3 A)))) ) ) ) ) ).
tt(l79_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_ens_1 A))) =>  ( (E = (k2_cat_1 B C D))  =>  ((k3_funct_2 (u4_struct_0 B) (k2_ens_1 (k16_ens_1 B)) (k19_ens_1 B C) (k4_cat_1 B D)) = (k4_cat_1 (k11_ens_1 A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_fib_num4,ax,(r1_xxreal_0 (k13_complex1 3 4) (k13_complex1 (k3_xcmplx_0 2 (k7_square_1 5)) (k3_xcmplx_0 2 2)))).
tt(l79_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_finseq_3 (k9_finseq_1 A) B) = (k9_finseq_1 A))  <=>  (~ (r2_hidden A B)) ) ) ) ).
tt(l79_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ((k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) B) C)) = (k1_nat_1 (k4_xxreal_0 (k32_fomodel2 A B) (k32_fomodel2 A C)) 1)) ) ) ) ) ) ) ).
tt(l79_fomodel3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_funct_2 F (k33_fomodel2 B) (k33_fomodel2 B) (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B))) =>  ( ((k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D F) (k2_xcmplx_0 (k32_fomodel2 B E) A)) E) = (k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D F) (k32_fomodel2 B E)) E))  &  ( ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) E) = C)  =>  ((k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D (k36_fomodel3 B C D)) (k32_fomodel2 B E)) E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_funct_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))))))) )  =>  ( ((r2_relset_1 (k1_relat_1 A) (k1_relat_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) C k6_numbers) (k6_partfun1 (k1_relat_1 A))) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) C (k1_nat_1 E 1)) = (k3_relat_1 A (k1_funct_1 C E))) ) )  &  ((r2_relset_1 (k1_relat_1 A) (k1_relat_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) D k6_numbers) (k6_partfun1 (k1_relat_1 A))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) D (k1_nat_1 E 1)) = (k3_relat_1 A (k1_funct_1 D E))) ) ) ) ) )  => (r2_funct_2 k5_numbers (k9_setfam_1 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A))) C D)) ) ) ) ) ) ) ) ) ).
tt(l79_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k8_group_1 A B (k8_group_1 A (k11_algstr_0 A B) C)) = C) ) ) ) ) ) ) ) ).
tt(l79_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k7_geomtrap A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r1_analmetr A B C) &  ((r2_analoaf (k7_geomtrap A B C) D E F G) & (r2_analoaf (k7_geomtrap A B C) D E H I)) )  =>  ( (D = E)  | (r2_analoaf (k7_geomtrap A B C) F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (? [C:$i] :  ( ((v1_abian C) & (m1_subset_1 C k5_numbers))  &  ( (C = (k6_xcmplx_0 (k3_finseq_1 B) 1))  &  ((k3_finseq_1 (k12_glib_001 A B)) = (k3_nat_d C 2)) ) ) ) ) ) ) ) ).
tt(l79_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k1_funct_2 B B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r2_funct_2 B B (k2_group_9 A B E (k8_finseq_1 A (k4_matrix_2 A C) D)) (k1_partfun1 B B B B (k2_group_9 A B E D) (k2_group_9 A B E (k4_matrix_2 A C))))) ) ) ) ) ) ) ) ) ).
tt(l79_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 (k4_hilbert1 B C) A)) k6_hilbert1)) ) ) ) ) ) ).
tt(l79_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 A C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l79_jgraph_5,ax, ((k17_euclid (k19_euclid k6_numbers 1)) = k6_numbers) ).
tt(l79_lattice3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) A)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 (k1_zfmisc_1 A) A B (k6_domain_1 A C)) = C) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k3_funct_2 (k1_zfmisc_1 A) A B (k7_relset_1 (k9_setfam_1 A) A B C)) = (k3_funct_2 (k1_zfmisc_1 A) A B (k5_setfam_1 A C))) ) )  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) & (l3_lattices C)) ) )  =>  (~  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k15_lattice3 C D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_modelc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_partfun1 B A) =>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r2_hidden D A) & (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(l79_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k1_lattices (k12_normform A) (k2_lattices (k12_normform A) B C) C) = C) ) ) ) ) ) ).
tt(l79_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden k4_ordinal1 B) &  ((r2_hidden A B) &  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) A)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) A) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) A)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) (k1_ordinal1 A))) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) (k1_ordinal1 A)) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) (k1_ordinal1 A))) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) (k1_ordinal1 A)) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) ) ) ).
tt(l79_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v10_o_ring_1 C A) & (v9_o_ring_1 B A))  => (v10_o_ring_1 (k8_finseq_1 (u1_struct_0 A) C (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C)) B))) A)) ) ) ) ) ) ) ).
tt(l79_pepin,ax, ((k13_newton 3 4) = 81) ).
tt(l79_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k27_quaterni A B) = (k26_quaterni (k26_quaterni (k23_quaterni (k9_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))) (k25_quaterni (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k17_quaterni B))) (k8_real_1 (k19_quaterni A) (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k19_quaterni B))) k1_xcmplx_0)) (k25_quaterni (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k17_quaterni B))) (k8_real_1 (k20_quaterni A) (k18_quaterni B))) (k8_real_1 (k18_quaterni A) (k20_quaterni B))) k11_quaterni)) (k25_quaterni (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k17_quaterni B))) (k8_real_1 (k18_quaterni A) (k19_quaterni B))) (k8_real_1 (k19_quaterni A) (k18_quaterni B))) k12_quaterni))) ) ) ) ) ).
tt(l79_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ( ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k8_memstr_0 3 k1_scmfsa_2 B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B)))) = (k11_scmfsa_2 k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B))) &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k8_memstr_0 3 k1_scmfsa_2 B) D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l79_sincos10,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))))) = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))) ).
tt(l79_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l79_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  ((k16_qc_lang1 A (k4_cqc_lang B A C D)) = C) ) ) ) ) ) ) ) ) ).
tt(l79_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_tex_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (D = E)  => (r1_tarski (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) E)) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_diraf A B D D C)) ) ) ) ) ) ) ) ).
tt(l7_algstr_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  ((k1_algstr_0 k3_algstr_0 A (k4_struct_0 k3_algstr_0)) = A) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  ((k1_algstr_0 k3_algstr_0 (k4_struct_0 k3_algstr_0) A) = A) ) ) ) ).
tt(l7_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_extpro_1 A)))) =>  ((k3_compos_0 (u1_compos_1 (k1_extpro_1 A)) B) = (k1_tarski k6_numbers)) ) ) ) ) ).
tt(l7_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r1_analmetr A B C) =>  ( ((k2_geomtrap A B C (k3_rlvect_1 A D E)) = (k7_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)))  &  ( ((k3_geomtrap A B C (k3_rlvect_1 A D E)) = (k7_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E)))  &  ( ((k2_geomtrap A B C (k5_algstr_0 A D E)) = (k9_real_1 (k2_geomtrap A B C D) (k2_geomtrap A B C E)))  &  ( ((k3_geomtrap A B C (k5_algstr_0 A D E)) = (k9_real_1 (k3_geomtrap A B C D) (k3_geomtrap A B C E)))  &  ( ((k2_geomtrap A B C (k1_rlvect_1 A D F)) = (k8_real_1 F (k2_geomtrap A B C D)))  &  ((k3_geomtrap A B C (k1_rlvect_1 A D F)) = (k8_real_1 F (k3_geomtrap A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((k1_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J)) F) = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 F G)) (k1_rlvect_1 A C (k8_real_1 F H))) (k1_rlvect_1 A D (k8_real_1 F I))) (k1_rlvect_1 A E (k8_real_1 F J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_arytm_2,ax,(r1_tarski k2_arytm_2 (k2_xboole_0 k5_arytm_3 a_0_0_arytm_2))).
tt(l7_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k3_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1) A B) C)) = (k7_real_1 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) A C)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) B C)))) ) ) ) ) ) ) ).
tt(l7_collsp,ax,(m1_collsp (k1_tarski (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1)) c2__collsp)).
tt(l7_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_arytm_0 (k3_complex1 A) (k4_complex1 A)) = A) ) ) ).
tt(l7_comptrig,ax, (~ (r1_xxreal_0 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k10_real_1 k32_sin_cos 2)) (k7_real_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l7_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_rlvect_2 D A C) =>  ( ((v2_convex1 D A) & (r1_tarski C B))  => (r2_hidden (k6_rlvect_2 A D) B)) ) ) ) ) ) ) ) ) ).
tt(l7_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_convex1 C A) & (m2_rlvect_2 C A B))  =>  (~  ((r1_xxreal_0 2 (k5_card_1 (k3_rlvect_2 A C))) &  (! [D:$i] :  ( ((v2_convex1 D A) & (m2_rlvect_2 D A B))  =>  (! [E:$i] :  ( ((v2_convex1 E A) & (m2_rlvect_2 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 1 F))  &  ((r1_rlvect_2 A C (k7_rlvect_2 A (k8_rlvect_2 A F D) (k8_rlvect_2 A (k9_real_1 1 F) E))) &  ( ((k5_card_1 (k3_rlvect_2 A D)) = 1)  &  ((k5_card_1 (k3_rlvect_2 A E)) = (k5_real_1 (k5_card_1 (k3_rlvect_2 A C)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A B D) A))  => (v2_cqc_the1 (k8_cqc_lang A B (k7_cqc_lang A C D)) A)) ) ) ) ) ) ) ) ) ).
tt(l7_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_3 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k7_comseq_3 A) B)) &  ((k1_seq_1 (k8_comseq_3 A) B) = k6_numbers) ) ) ) )  =>  ((k17_complex1 (k11_comseq_3 A)) = (k4_series_1 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ) ).
tt(l7_csspace4,ax, ((v2_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v3_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v4_rlvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v13_algstr_0 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v2_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v3_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) &  ((v4_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4))) & (v5_clvect_1 (g1_clvect_1 k1_csspace4 (k10_csspace k7_csspace k1_csspace4) (k8_csspace k7_csspace k1_csspace4) (k9_csspace k7_csspace k1_csspace4)))) ) ) ) ) ) ) ).
tt(l7_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_endalg A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_endalg A))) =>  ( (C = (k6_partfun1 (u1_struct_0 A)))  =>  ( ((k6_algstr_0 (k3_endalg A) B C) = B)  &  ((k6_algstr_0 (k3_endalg A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l7_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k7_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 4 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (B = (k2_nat_1 (k1_nat_1 A 1) C)) ) ) ) ) ) ) ) ) ) ).
tt(l7_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k23_rvsum_1 A B) = (k9_binop_2 (k9_binop_2 (k11_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k11_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2))) (k11_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(l7_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos A) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos A)))  &  ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos A) (k1_real_1 1)))  &  (~  ((k10_real_1 (k1_seq_1 k16_sin_cos A) (k10_prepower (k7_real_1 1 (k1_seq_1 k19_sin_cos A)) (k10_real_1 1 2))) = (k10_prepower (k9_real_1 1 (k1_seq_1 k19_sin_cos A)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ).
tt(l7_fib_fusc,ax, (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 1)) ) ).
tt(l7_fib_num4,ax, ((k3_xcmplx_0 k1_fib_num k2_fib_num) = (k4_xcmplx_0 1)) ).
tt(l7_fib_num,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 A (k1_pre_ff (k1_nat_1 A 1)))) ) ).
tt(l7_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) =>  ((k1_finsop_1 A (k6_finseq_1 A) B) = (k4_binop_1 A B)) ) ) ) ) ) ).
tt(l7_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_fomodel0 B A) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k3_xboole_0 (k9_xtuple_0 B) A)) &  ((r2_hidden D (k3_xboole_0 (k9_xtuple_0 B) A)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(l7_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m2_funct_2 D (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_fomodel4 B))) =>  (! [F:$i] :  ((v2_fomodel4 F B) =>  ( ((k1_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B C)) = (k9_setfam_1 (k1_fomodel4 B)))  &  ((r1_tarski (k10_xtuple_0 (k2_fomodel4 B C)) (k1_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B C))) &  ( ((v1_funct_1 (k9_funct_7 (k2_fomodel4 B C) A)) &  ((v1_funct_2 (k9_funct_7 (k2_fomodel4 B C) A) (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) & (m1_subset_1 (k9_funct_7 (k2_fomodel4 B C) A) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B)))))) )  &  ( ((k9_xtuple_0 (k9_funct_7 (k2_fomodel4 B C) A)) = (k9_setfam_1 (k1_fomodel4 B)))  &  ( ((k2_xboole_0 (k1_relset_1 (k9_setfam_1 (k1_fomodel4 B)) (k2_fomodel4 B C)) (k10_xtuple_0 (k2_fomodel4 B C))) = (k9_setfam_1 (k1_fomodel4 B)))  &  ((r2_hidden E (k1_relset_1 (k9_setfam_1 (k1_fomodel4 B)) D)) & (r2_hidden F (k9_xtuple_0 (k9_funct_7 D A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (B = k1_xboole_0)  &  ((k6_unialg_2 A) = k1_xboole_0) ) )  =>  ((m1_freealg B A) <=>  ((u1_struct_0 (k7_unialg_2 A B)) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(l7_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (r2_hidden B (k1_glib_002 A B))) ) ) ) ).
tt(l7_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((k1_funct_1 (k5_finseq_2 k5_numbers A B) C) = B) ) ) ) ) ) ) ) ).
tt(l7_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v2_connsp_1 (k2_pre_topc (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k4_connsp_3 (k15_euclid 2) (k3_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) &  ( ((k4_connsp_3 (k15_euclid 2) (k3_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) = (k3_goboard9 A))  & (v3_connsp_1 (k4_connsp_3 (k15_euclid 2) (k3_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))))) ) ) ) ).
tt(l7_graph_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_funct_1 B A) = (k1_funct_1 (k7_finseq_1 C B) (k2_nat_1 (k3_finseq_1 C) A))) ) ) ) ) ) ) ) ).
tt(l7_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ((k1_funct_1 C A) = (k1_funct_1 (k7_finseq_1 B C) (k2_nat_1 (k3_finseq_1 B) A))) ) ) ) ) ) ) ) ).
tt(l7_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_group_4 A (k4_group_4 A (k6_finseq_1 k4_numbers) (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 (k6_finseq_1 k4_numbers)) B))) = (k5_group_1 A (k1_gr_cy_1 (k6_finseq_1 k4_numbers)) B)) ) ) ) ) ).
tt(l7_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k1_tarski (k4_tarski C D))) =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ).
tt(l7_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v1_funct_1 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B)))) &  ((v1_funct_2 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B))) A (k1_funct_2 B B)) & (m1_subset_1 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B))) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) ) ) ) ).
tt(l7_holder_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ).
tt(l7_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) & (r1_aff_1 A B C E))  =>  ( (B = C)  |  ( (B = D)  |  ( ( (~  ( (~ (r1_aff_1 A B C F))  &  ((r1_aff_1 A B F E) & (r2_analoaf A C F D E)) ) )  &  (~  ((r1_aff_1 A B C F) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G D H) &  ((r2_analoaf A G F H E) & (r1_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) )  | (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_int_1,ax, (! [A:$i] :  ((r2_hidden A k4_numbers) => (r2_hidden A k1_numbers)) ) ).
tt(l7_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) <=> (r1_int_1 (k4_xcmplx_0 A) B)) ) ) ) ) ).
tt(l7_int_3,ax, ((k1_group_1 k1_int_3) = 1) ).
tt(l7_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k18_valued_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(l7_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  (~  ((r1_tarski B (k1_polynom2 k10_newton A)) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k10_newton) &  ((v1_funct_1 C) &  ((v1_partfun1 C k10_newton) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k10_newton) &  ((v1_funct_1 D) &  ((v1_partfun1 D k10_newton) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (~  ( ((k1_polynom2 k10_newton C) = (k7_subset_1 k10_newton (k1_polynom2 k10_newton A) B))  &  ( ((k1_polynom2 k10_newton D) = B)  &  ((r1_xboole_0 (k1_polynom2 k10_newton C) (k1_polynom2 k10_newton D)) &  ( ((k5_relat_1 C (k1_polynom2 k10_newton C)) = (k5_relat_1 A (k1_polynom2 k10_newton C)))  &  ( ((k5_relat_1 D (k1_polynom2 k10_newton D)) = (k5_relat_1 A (k1_polynom2 k10_newton D)))  & (r8_pboole k10_newton (k11_pre_poly k10_newton C D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_integra1 A)) =>  ( ((k3_integra1 A) = k6_numbers)  =>  ((v2_integra1 B A) &  ((k11_integra1 A B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l7_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k9_xtuple_0 B)) =>  ((v1_funct_1 (k1_integra5 B A)) &  ((v1_funct_2 (k1_integra5 B A) A k1_numbers) & (m1_subset_1 (k1_integra5 B A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ) ) ).
tt(l7_jordan1c,ax, ((k3_pcomps_1 (k14_euclid 2)) = (g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2)))) ).
tt(l7_jordan1h,ax,(r4_relat_2 k1_jordan1h k1_numbers)).
tt(l7_jordan22,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 1 (k3_finseq_1 (k1_jordan8 A B)))) ) ) ) ).
tt(l7_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_int_1 B) => (r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) (k1_jordan24 (k7_real_1 A (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))) ) ) ) ).
tt(l7_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_rcomp_1 A) => (r2_hidden A (k2_pcomps_1 k8_metric_1))) ) ) ).
tt(l7_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k1_relset_1 k1_numbers C)) & (r1_xxreal_0 D (k1_seq_1 C F))) ) ) ) ) ) ) ) ) ) )  &  ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  & (r1_tarski (k2_relset_1 k1_numbers B) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k3_limfunc1 A)))) ) )  => (v2_limfunc1 (k8_funct_2 k5_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(l7_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A B D) E) (k8_cqc_lang A (k8_cqc_lang A C D) E))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(l7_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k2_finseq_1 A)))  =>  ( ((k2_xcmplx_0 B C) = (k2_xcmplx_0 A 1))  | (r2_hidden (k6_int_1 (k6_xcmplx_0 (k2_xcmplx_0 B C) 1) A) (k2_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(l7_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((k4_finseq_1 (k5_matrlin A B D C)) = (k9_subset_1 k5_numbers (k4_finseq_1 D) (k4_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(l7_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m2_measure8 (k7_funcop_1 k5_numbers A) A B)) ) ) ).
tt(l7_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  ((k2_memstr_0 A (k1_memstr_0 A)) = (k16_funcop_1 k6_numbers k5_numbers)) ) ) ).
tt(l7_metrizts,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v1_xboole_0 (k2_waybel23 A))) ) ).
tt(l7_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m2_finseq_2 E C (k4_finseq_2 A C)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k7_subset_1 k5_numbers (k4_finseq_1 E) (k1_tarski B))) =>  ((k1_funct_1 (k1_midsp_3 C A E B D) F) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_mod_4 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_mod_4 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_mod_4 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_mod_4 A))) =>  ( ( (B = F)  &  ( (C = G)  &  ( (D = H)  &  (E = I) ) ) )  =>  ( ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 (k2_mod_4 A) (k1_algstr_0 (k2_mod_4 A) F G) H))  &  ( ((k1_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 (k2_mod_4 A) F (k1_algstr_0 (k2_mod_4 A) G H)))  &  ( ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 (k2_mod_4 A) H (k6_algstr_0 (k2_mod_4 A) G F)))  &  ( ((k6_algstr_0 A B (k6_algstr_0 A C D)) = (k6_algstr_0 (k2_mod_4 A) (k6_algstr_0 (k2_mod_4 A) H G) F))  &  ( ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k6_algstr_0 (k2_mod_4 A) (k1_algstr_0 (k2_mod_4 A) G H) F))  &  ( ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k6_algstr_0 (k2_mod_4 A) F (k1_algstr_0 (k2_mod_4 A) G H)))  &  ((k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A D E)) = (k1_algstr_0 (k2_mod_4 A) (k6_algstr_0 (k2_mod_4 A) G F) (k6_algstr_0 (k2_mod_4 A) I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  => (r2_modelc_2 (k10_modelc_2 A) A)) ) ) ).
tt(l7_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ( (~  ((r2_hidden D (k6_dtconstr (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  (~  ((r2_hidden F (k1_funct_1 (u3_msualg_1 A B) E)) &  (D = (k4_tarski F E)) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 C E)) =>  (~  (D = (k4_tarski F E)) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (! [F:$i] :  ( ((r2_hidden F (k1_funct_1 (u3_msualg_1 A B) E)) &  (D = (k4_tarski F E)) )  => (r2_hidden D (k6_dtconstr (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))))) )  &  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 C E)) =>  ( (D = (k4_tarski F E))  => (r2_hidden D (k6_dtconstr (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_mssublat,ax,(m1_subset_1 k6_numbers (k1_tarski k6_numbers))).
tt(l7_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_finset_1 (k1_enumset1 A B C)) & (m1_subset_1 (k1_enumset1 A B C) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ) ) ).
tt(l7_net_1,ax,(v1_net_1 (g1_petri k1_xboole_0 k1_xboole_0 (k1_partit_2 k1_xboole_0 k1_xboole_0) (k1_partit_2 k1_xboole_0 k1_xboole_0)))).
tt(l7_normsp_1,ax, ( (~ (v2_struct_0 (g1_normsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_normsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_normsp_1)) c2__normsp_1)))  & (l1_normsp_1 (g1_normsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_normsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_normsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_normsp_1)) c2__normsp_1))) ).
tt(l7_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ( ((k8_nat_1 k5_numbers C k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k5_numbers D E))  &  ((k8_nat_1 k5_numbers D (k2_nat_1 E 1)) = (k4_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E))) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  ((k8_nat_1 k5_numbers D E) = k6_numbers) )  =>  ((k6_nat_d (k8_nat_1 k5_numbers C k6_numbers) (k8_nat_1 k5_numbers D k6_numbers)) = (k6_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D c1__ortsp_1) =>  ((k1_funct_1 B (k4_tarski C D)) = c2__ortsp_1) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_symsp_1 D A)) ) ) ) )  =>  ( (D = (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C))  =>  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) & (v11_vectsp_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k8_group_1 A (k8_group_1 A B C) (k8_group_1 A D E)) = (k8_group_1 A (k8_group_1 A (k8_group_1 A D B) C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_petri_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  =>  (~  ( (~ (r1_tarski D C))  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (~  ( ((k2_partfun1 B A G C) = E)  &  (~  ((k2_partfun1 B A G D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_newton A 2) = (k5_binop_2 A A)) ) ) ).
tt(l7_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v2_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ).
tt(l7_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  (~  ((r2_hidden C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C D) &  ((r2_hidden D B) &  ((r2_hidden C E) & (r2_hidden E B)) ) )  =>  (D = E) ) ) ) ) ) ) ) ).
tt(l7_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((r1_tarski (k2_zfmisc_1 (k1_tarski 4) (k1_qc_lang1 A)) (k2_qc_lang1 A)) &  ((r1_tarski (k2_zfmisc_1 (k1_tarski 5) (k1_qc_lang1 A)) (k2_qc_lang1 A)) & (r1_tarski (k2_zfmisc_1 (k1_tarski 6) k5_numbers) (k2_qc_lang1 A))) ) ) ) ).
tt(l7_qmax_1,ax, (! [A:$i] :  ((m1_prob_1 A k1_numbers k12_prob_1) => (r1_xxreal_0 k6_numbers (k3_funct_2 k12_prob_1 k1_numbers c2__qmax_1 A))) ) ).
tt(l7_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_mesfunc6 A B C) => (v5_xxreal_2 (k1_rvsum_1 C))) ) ) ) ) ) ) ).
tt(l7_rat_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (A = (k6_real_1 C B))  => (r2_hidden A k3_numbers)) ) ) ) ) ) ).
tt(l7_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k2_lattices k3_real_lat A B) = (k2_lattices k3_real_lat B A)) ) ) ) ) ).
tt(l7_realset2,ax, (~ (v1_zfmisc_1 2)) ).
tt(l7_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_domain_1 (u1_struct_0 A) (k1_algstr_0 A B C)) = (k5_rusub_4 A (k6_domain_1 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ).
tt(l7_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_rlaffin2 A B) (k3_convex1 A B))) ) ) ) ).
tt(l7_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 (k1_rlsub_2 A B C)))) ) ) ) ) ) ).
tt(l7_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (r1_tarski (u1_struct_0 C) (u1_struct_0 (k1_rmod_3 A B C D)))) ) ) ) ) ) ) ) ).
tt(l7_rsspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) & (v2_comseq_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 (k9_real_1 (k1_seq_1 B E) A) (k9_real_1 (k1_seq_1 B E) A)) (k1_seq_1 C E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k8_real_1 (k9_real_1 (k2_seq_2 B) A) (k9_real_1 (k2_seq_2 B) A)) (k2_seq_2 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 A B) = k6_numbers) ) )  =>  ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k56_valued_1 k5_numbers k1_numbers A))) = k6_numbers) ) ) ) ) ).
tt(l7_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 (k1_rusub_2 A B C)))) ) ) ) ) ) ).
tt(l7_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (~ (r1_extpro_1 3 k1_scmfsa_2 (k2_funct_7 B (k5_memstr_0 3 k1_scmfsa_2 A) (k11_scmfsa_2 (k5_memstr_0 3 k1_scmfsa_2 A))) A)) ) ) ) ) ).
tt(l7_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_tarski (k2_scmfsa_7 C D) B) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k1_afinsq_1 (k2_scmfsa_7 C D))) =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A E)) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  ( ((r1_xxreal_0 3 D) &  ((r1_scpisort E B D) &  ( ((k3_finseq_1 E) = C)  &  ( ((k1_funct_1 B (k1_scmp_gcd 1)) = k6_numbers)  &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = (k4_xcmplx_0 C))  &  ((k1_funct_1 B (k1_scmp_gcd 3)) = (k2_nat_1 D 1)) ) ) ) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_8 k2_scmp_gcd 2 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1))) (k8_memstr_0 2 k1_scmpds_2 B) A) (k1_scmp_gcd 1)) = (k1_gr_cy_1 E))  &  ((r1_scmpds_6 (k1_scmpds_8 k2_scmp_gcd 2 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1))) B A) & (r2_scmpds_6 (k1_scmpds_8 k2_scmp_gcd 2 (k3_scmpds_4 (k4_scmpds_4 (k12_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 3) 1 k6_numbers) (k11_scmpds_2 k2_scmp_gcd 2 1)) (k11_scmpds_2 k2_scmp_gcd 3 1))) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_newton (k2_xcmplx_0 A 1) 4) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 4 (k1_newton A 3))) (k3_xcmplx_0 6 (k1_newton A 2))) (k3_xcmplx_0 4 A)) 1))  &  ((k1_newton (k2_xcmplx_0 A 1) 5) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 5) (k3_xcmplx_0 5 (k1_newton A 4))) (k3_xcmplx_0 10 (k1_newton A 3))) (k3_xcmplx_0 10 (k1_newton A 2))) (k3_xcmplx_0 5 A)) 1)) ) ) ) ).
tt(l7_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)) = (k3_xcmplx_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B)))) ) ) ) ) ).
tt(l7_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k7_xcmplx_0 1 (k2_xcmplx_0 (k3_prepower 2 (k2_nat_1 A 2)) (k3_prepower 2 (k2_nat_1 A 1)))) = (k6_xcmplx_0 (k3_prepower 2 (k2_nat_1 A 2)) (k3_prepower 2 (k2_nat_1 A 1)))) ) ) ).
tt(l7_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 1 (k18_complex1 A)))  & (r1_xxreal_0 1 (k3_square_1 A))) ) ) ) ).
tt(l7_sincos10,ax,(r1_tarski (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k2_rcomp_1 k6_numbers k32_sin_cos))).
tt(l7_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k5_binop_2 (k15_sin_cos A) (k15_sin_cos (k1_binop_2 A))) = 1) ) ) ).
tt(l7_sin_cos6,ax, ((k1_rcomp_1 (k7_real_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers)) (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers))) = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) ).
tt(l7_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k2_xcmplx_0 A B) = k6_numbers) )  &  ((k3_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2))) = k6_numbers) ) ) ) ) ) ) ).
tt(l7_sprect_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ((k2_goboard9 A) = (k3_goboard9 A)) ) ) ) ) ).
tt(l7_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_tarski k6_numbers)) (k1_tarski k6_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers)))) =>  ( (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k2_zfmisc_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers))) &  (? [E:$i] :  ((m1_subset_1 E (k1_tarski k6_numbers)) &  (? [F:$i] :  ((m1_subset_1 F (k1_tarski k6_numbers)) &  ( (D = (k1_domain_1 (k1_tarski k6_numbers) (k1_tarski k6_numbers) E F))  &  (F = c2__symsp_1) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_symsp_1 D A)) ) ) ) )  =>  ( (D = (g1_symsp_1 A (k1_tarski k6_numbers) c3__symsp_1 c2__symsp_1 B C))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (~  ( (~  (E = (k4_struct_0 D)) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) => (r1_orders_2 D F E)) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 D E F) => (r1_orders_2 D (k4_vectsp_1 A D G E) F)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r1_orders_2 D F E) & (r1_orders_2 D G E))  => (r1_orders_2 D (k3_rlvect_1 D F G) E)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (~  ( (~ (r1_orders_2 D F E))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~ (r1_orders_2 D (k5_algstr_0 D G (k4_vectsp_1 A D H F)) E)) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r1_orders_2 D E (k3_rlvect_1 D F G)) & (r1_orders_2 D F (k3_rlvect_1 D G E)))  => (r1_orders_2 D G (k3_rlvect_1 D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_taylor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_prepower (k25_sin_cos B) A) = (k25_sin_cos (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(l7_topalg_5,ax, ((k2_struct_0 k5_topmetr) = (u1_struct_0 k5_topmetr)) ).
tt(l7_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 B)))))) )  =>  (~  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((v1_topdim_1 (k8_nat_1 (k9_setfam_1 (u1_struct_0 B)) C D) B) &  ((r1_xxreal_0 (k2_topdim_1 B (k8_nat_1 (k9_setfam_1 (u1_struct_0 B)) C D)) A) & (v5_topgen_4 (k8_nat_1 (k9_setfam_1 (u1_struct_0 B)) C D) B)) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  (~  ((v2_tops_2 D B) &  ((v2_topdim_1 D B) &  ((r1_xxreal_0 (k3_topdim_1 B D) A) &  ((v4_card_3 D) &  ((k1_prob_1 (u1_struct_0 B) C) = (k5_setfam_1 (u1_struct_0 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_topreal2,ax, ((k18_euclid (k19_euclid k6_numbers 1)) = 1) ).
tt(l7_toprealb,ax, (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 1) (k10_real_1 k32_sin_cos 2))) ).
tt(l7_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_funct_2 A A (k1_transgeo A C B) (k1_transgeo A C D)) => (r2_funct_2 A A B D)) ) ) ) ) ) ) ) ) ).
tt(l7_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) =>  ((r1_aff_1 A B C D) |  ( (D = E)  |  ( (~ (r1_aff_1 A D E B))  &  ( (~ (r1_aff_1 A C B E))  &  (~ (r1_aff_1 A E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v1_pre_topc (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) & (m1_pre_topc (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) A)) ) ) ) ) ).
tt(l7_tsp_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_tdlat_3 A) & (l1_pre_topc A)) )  =>  (~ (v6_pre_topc A)) ) ) ).
tt(l7_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_tarski (u1_struct_0 C) (u1_struct_0 (k1_vectsp_5 A B C D)))) ) ) ) ) ) ) ) ).
tt(l7_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v25_waybel_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D)))  => (r1_tarski (a_2_1_waybel33 A C) (a_2_1_waybel33 B D))) ) ) ) ) ) ) ) ) ) ).
tt(l7_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_waybel_0 A B) = (a_2_2_waybel_9 A B)) ) ) ) ) ).
tt(l7_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = (k4_nat_1 2 B)) )  &  (~  (A = (k2_nat_1 (k4_nat_1 2 B) 1)) ) ) ) ) ) ) ) ).
tt(l7_xcmplx_0,ax,(m1_subset_1 1 k1_numbers)).
tt(l7_xreal_0,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  => (r1_xxreal_0 A C)) ) ) ) ) ) ) ).
tt(l7_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l7_xxreal_0,ax, (~ (r2_hidden k1_xxreal_0 k2_arytm_2)) ).
tt(l7_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_orders_2 A) <=> (v4_orders_2 (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(l7_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((r1_zf_model B C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang A (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) =>  ((r2_hidden (k2_zf_lang 4) (k2_zf_model A)) |  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k7_relset_1 B B (k1_zfmodel1 A B C) D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(l7_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((v2_zf_lang A) =>  ((k4_zf_model A B) = (a_2_2_zf_model A B)) )  &  ( ((v3_zf_lang A) =>  ((k4_zf_model A B) = (a_2_3_zf_model A B)) )  &  ( ((v4_zf_lang A) =>  ((k4_zf_model A B) = (k6_subset_1 (k3_zf_model B) (k3_tarski (k1_tarski (k4_zf_model (k20_zf_lang A) B))))) )  &  ( ((v5_zf_lang A) =>  (! [C:$i] :  (! [D:$i] :  ( ( (C = (k4_zf_model (k21_zf_lang A) B))  &  (D = (k4_zf_model (k22_zf_lang A) B)) )  =>  ((k4_zf_model A B) = (k3_xboole_0 (k3_tarski (k1_tarski C)) (k3_tarski (k1_tarski D)))) ) ) ) )  &  ((v6_zf_lang A) =>  ((k4_zf_model A B) = (a_2_4_zf_model A B)) ) ) ) ) ) ) ) ) ) ).
tt(l80_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v4_anproj_2 (k5_anproj_1 A))) ) ).
tt(l80_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k10_real_1 (k6_newton A (k2_nat_1 B 1)) (k2_nat_1 B 1)) (k6_newton A B))) ) ) ) ) ).
tt(l80_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A B) = B) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A C B)) ) ) ) ) ) ) ) ).
tt(l80_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_cqc_the1 B A) <=> (r2_hidden B (k4_cqc_the1 A))) ) ) ) ) ).
tt(l80_descip_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) => (r1_xxreal_0 (k3_xcmplx_0 A B) A)) ) ) ) ).
tt(l80_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (~  ( ((k9_xtuple_0 F) = (k2_finseq_1 A))  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k9_xtuple_0 F)) =>  ((k1_funct_1 F G) = (a_4_2_ec_pf_1 A B C G)) ) ) )  &  ((v1_prob_2 F) &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k9_xtuple_0 F)) => (v1_finset_1 (k1_funct_1 F G))) ) )  &  ((k3_card_3 F) = (a_3_1_ec_pf_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_ens_1 A))) =>  ( (E = (k2_cat_1 B C D))  =>  ((k3_funct_2 (u4_struct_0 B) (k2_ens_1 (k16_ens_1 B)) (k20_ens_1 B D) (k4_cat_1 B C)) = (k4_cat_1 (k11_ens_1 A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 B C A D)) ) ) ) ) ).
tt(l80_fib_num4,ax, ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k7_square_1 5) 1) (k6_xcmplx_0 1 1)))  &  (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ) ).
tt(l80_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_finseq_3 (k9_finseq_1 A) B) = k1_xboole_0)  <=> (r2_hidden A B)) ) ) ).
tt(l80_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k9_fomodel0 A B) = (k1_funct_4 (k7_funcop_1 B k1_xboole_0) (k1_margrel1 k5_numbers (k3_xboole_0 A B) 1))) ) ) ).
tt(l80_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden C (k16_fomodel2 A B)) =>  ((k9_xtuple_0 C) = (k37_fomodel1 A)) ) ) ) ) ) ) ) ).
tt(l80_fomodel3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v13_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((v3_fomodel2 E B A) =>  ((k37_fomodel3 B C D E) = (k1_funct_1 (k8_nat_1 (k9_funct_2 (k33_fomodel2 B) (k33_fomodel2 B)) (k32_fomodel3 B C D (k36_fomodel3 B C D)) A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) =>  ((k1_funct_4 B A) = B) ) ) ) ) ) ).
tt(l80_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  ((r2_analoaf (k7_geomtrap A B C) D E F G) =>  ((r2_analoaf (k7_geomtrap A B C) F G D E) & (r2_analoaf (k7_geomtrap A B C) E D G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_relset_1 k5_numbers (k7_glib_000 A) (k12_glib_001 A (k8_glib_001 A B 1 C)) (k12_glib_001 A B))) ) ) ) ) ) ).
tt(l80_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k1_funct_2 B B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r2_funct_2 B B (k2_group_9 A B E (k8_finseq_1 A C D)) (k1_partfun1 B B B B (k2_group_9 A B E D) (k2_group_9 A B E C)))) ) ) ) ) ) ) ) ) ).
tt(l80_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 (k4_hilbert1 A C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(l80_integra8,ax, ((k9_xtuple_0 (k2_fdiff_1 k1_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1))) = (k2_rcomp_1 (k1_real_1 1) 1)) ).
tt(l80_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 B A) C)) k8_intpro_1)) ) ) ) ) ) ).
tt(l80_jgraph_5,ax, ((k18_euclid (k19_euclid k6_numbers 1)) = 1) ).
tt(l80_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_lpspace2 D) & (m1_subset_1 D k1_numbers))  =>  ((v4_normsp_0 (k12_lpspace2 A B C D)) &  ((v3_normsp_0 (k12_lpspace2 A B C D)) &  ((v2_normsp_1 (k12_lpspace2 A B C D)) &  ((v5_rlvect_1 (k12_lpspace2 A B C D)) &  ((v6_rlvect_1 (k12_lpspace2 A B C D)) &  ((v7_rlvect_1 (k12_lpspace2 A B C D)) &  ((v8_rlvect_1 (k12_lpspace2 A B C D)) &  ((v2_rlvect_1 (k12_lpspace2 A B C D)) &  ((v3_rlvect_1 (k12_lpspace2 A B C D)) &  ((v4_rlvect_1 (k12_lpspace2 A B C D)) & (v13_algstr_0 (k12_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_9 B (k7_matrix15 B (k12_matrix_1 B A))) = k1_xboole_0) ) ) ) ) ).
tt(l80_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ((k2_matrix13 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) (k5_matrixj1 (u1_struct_0 A) D E))) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) (k5_matrixj1 (u1_struct_0 A) D E))) A (k13_matrixj1 (u1_struct_0 A) C (k5_matrixj1 (u1_struct_0 A) D E)) B) = (k13_matrixj1 (u1_struct_0 A) (k8_group_1 A B C) (k5_matrixj1 (u1_struct_0 A) (k6_matrix_3 A D B) (k6_matrix_3 A E B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l80_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k5_member_1 (k9_member_1 A B)) = (k9_member_1 (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(l80_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ((v3_mesfunc5 A) &  ( (~ (r2_hidden (k8_supinf_2 (k17_supinf_2 A)) k1_numbers))  &  (~  ((k8_supinf_2 (k17_supinf_2 A)) = k1_supinf_1) ) ) ) ) ) ) ).
tt(l80_modelc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r2_hidden D A) & (r2_hidden (k4_tarski C D) B)) ) ) ) ) )  => (v1_partfun1 B A)) ) ) ) ).
tt(l80_newton,ax, ((k11_newton 2) = k1_xboole_0) ).
tt(l80_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k2_lattices (k12_normform A) B C) = (k2_lattices (k12_normform A) C B)) ) ) ) ) ) ).
tt(l80_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 B) (u4_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C))))) )  => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k9_oppcat_1 A C (k1_partfun1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E)) (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) (k9_oppcat_1 A B D) E))) ) ) ) ) ) ) ) ) ) ).
tt(l80_ordinal6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden A B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) C)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) C) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) C)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) A)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) A) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) A)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) ) ) ).
tt(l80_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v11_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l80_pepin,ax, ((k13_newton 3 8) = 6561) ).
tt(l80_prepower,ax, (! [A:$i] :  ( ((v5_relat_1 A k3_numbers) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((v2_comseq_2 A) & (r1_xxreal_0 1 B))  => (v2_comseq_2 (k8_prepower B A))) ) ) ) ) ).
tt(l80_sincos10,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)))) = (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))) ).
tt(l81_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v5_anproj_2 (k5_anproj_1 A))) ) ).
tt(l81_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski B)))) =>  (~  ( (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E G) C))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) )  &  ( (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E F) C))  =>  (D = E) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v10_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ( (C = (k11_cohsp_1 A B D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A B D E) = (k7_relat_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l81_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k28_coh_sp A))) =>  (! [C:$i] :  ((m1_subset_1 C (k16_coh_sp A)) =>  ( (B = C)  =>  (! [D:$i] :  ((m1_cat_1 D (k28_coh_sp A) B B) =>  ( (D = (k23_coh_sp A C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k28_coh_sp A))) =>  ( ( (~  ((k2_cat_1 (k28_coh_sp A) B E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k28_coh_sp A) B E) =>  ((k1_cat_1 (k28_coh_sp A) D F) = F) ) ) )  &  ( (~  ((k2_cat_1 (k28_coh_sp A) E B) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_cat_1 F (k28_coh_sp A) E B) =>  ((k1_cat_1 (k28_coh_sp A) F D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l81_fib_num4,ax, ( (~ (r1_xxreal_0 (k2_xcmplx_0 k6_numbers (k7_square_1 5)) (k2_xcmplx_0 (k4_xcmplx_0 1) (k7_square_1 5))))  &  (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ) ).
tt(l81_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k1_finseq_3 (k7_finseq_1 A k1_xboole_0) B) = (k7_finseq_1 (k1_finseq_3 A B) (k1_finseq_3 k1_xboole_0 B))) ) ) ) ).
tt(l81_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k9_fomodel0 A B) = (k1_funct_4 (k7_funcop_1 (k6_subset_1 B A) k1_xboole_0) (k1_margrel1 k5_numbers (k3_xboole_0 A B) 1))) ) ) ).
tt(l81_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) =>  ((v3_fomodel2 C B A) =>  ((k1_funct_1 (k24_fomodel2 B D A E) C) = (k1_funct_1 (k23_fomodel2 B A D) (k1_domain_1 (k16_fomodel2 B D) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l81_funct_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ((k3_relat_1 (k6_partfun1 (k1_relat_1 A)) A) = A)  &  ((k3_relat_1 A (k6_partfun1 (k1_relat_1 A))) = A) ) ) ) ).
tt(l81_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (~  ((r1_analmetr A B C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  ( (~ (r2_analoaf (k7_geomtrap A B C) D E F G))  &  (~ (r2_analoaf (k7_geomtrap A B C) D E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l81_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k12_glib_001 A (k10_glib_001 A B C)) = (k7_finseq_1 (k12_glib_001 A B) (k9_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(l81_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  => (v1_finset_1 (k7_graph_5 A))) ) ).
tt(l81_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 B) A) 1))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1) (k2_nat_1 (k4_nat_1 2 B) A)))  &  (~ (r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 B) A) A)) ) ) ) ) ) ) ) ).
tt(l81_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k1_funct_2 B B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  ((r1_group_9 A B E D) => (r1_tarski (k7_relset_1 B B (k2_group_9 A B E C) D) D)) ) ) ) ) ) ) ) ) ).
tt(l81_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 A (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(l81_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 C A) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l81_jgraph_5,ax, ( ((k12_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = 1)  &  ( ((k12_euclid (k19_euclid 1 k6_numbers)) = 1)  &  ( ((k12_euclid (k19_euclid k6_numbers (k1_real_1 1))) = 1)  &  ((k12_euclid (k19_euclid k6_numbers 1)) = 1) ) ) ) ).
tt(l81_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (~ (v1_xboole_0 (k7_relat_1 B (k1_tarski C)))) ) ) ) ) ) ) ).
tt(l81_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ((k2_lattices (k12_normform A) B (k2_lattices (k12_normform A) C D)) = (k2_lattices (k12_normform A) (k2_lattices (k12_normform A) B C) D)) ) ) ) ) ) ) ) ).
tt(l81_o_ring_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ((v12_o_ring_1 D C) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 B (k3_finseq_1 D))) )  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 C) D (k12_finseq_1 (u1_struct_0 C) (k1_algstr_0 C (k7_partfun1 (u1_struct_0 C) D A) (k7_partfun1 (u1_struct_0 C) D B)))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l81_pepin,ax, ((k13_newton 3 16) = (k4_nat_1 6561 6561)) ).
tt(l81_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k26_quaterni A k21_quaterni) = A) ) ) ).
tt(l81_sincos10,ax, ( ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) = (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))  &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) =>  ((k1_seq_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) A) = (k1_seq_1 k1_fdiff_9 A)) ) ) ) ) ).
tt(l81_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l81_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l82_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_anproj_2 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (v6_anproj_2 (k5_anproj_1 A))) ) ).
tt(l82_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k6_power 2 (k9_newton B))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k6_series_1 k2_asympt_1 B)) ) ) ) ) ) ).
tt(l82_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r1_struct_0 C B) <=>  ((k5_clvect_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(l82_descip_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A 16 (k2_finseq_1 16)) &  ((v1_descip_1 A 16) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 16 (k2_finseq_1 16))))) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J B) =>  (! [K:$i] :  ((m1_subset_1 K B) =>  (! [L:$i] :  ((m1_subset_1 L B) =>  (! [M:$i] :  ((m1_subset_1 M B) =>  (! [N:$i] :  ((m1_subset_1 N B) =>  (! [O:$i] :  ((m1_subset_1 O B) =>  (! [P:$i] :  ((m1_subset_1 P B) =>  (! [Q:$i] :  ((m1_subset_1 Q B) =>  (! [R:$i] :  ((m1_subset_1 R B) =>  (! [S:$i] :  ((m2_finseq_2 S B (k4_finseq_2 16 B)) =>  ( ( ((k1_funct_1 S 1) = C)  &  ( ((k1_funct_1 S 2) = D)  &  ( ((k1_funct_1 S 3) = E)  &  ( ((k1_funct_1 S 4) = F)  &  ( ((k1_funct_1 S 5) = G)  &  ( ((k1_funct_1 S 6) = H)  &  ( ((k1_funct_1 S 7) = I)  &  ( ((k1_funct_1 S 8) = J)  &  ( ((k1_funct_1 S 9) = K)  &  ( ((k1_funct_1 S 10) = L)  &  ( ((k1_funct_1 S 11) = M)  &  ( ((k1_funct_1 S 12) = N)  &  ( ((k1_funct_1 S 13) = O)  &  ( ((k1_funct_1 S 14) = P)  &  ( ((k1_funct_1 S 15) = Q)  &  ((k1_funct_1 S 16) = R) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) k6_numbers) = C)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 1) = D)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 2) = E)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 3) = F)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 4) = G)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 5) = H)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 6) = I)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 7) = J)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 8) = K)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 9) = L)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 10) = M)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 11) = N)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 12) = O)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 13) = P)  &  ( ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 14) = Q)  &  ((k1_funct_1 (k1_partfun1 16 (k2_finseq_1 16) k5_numbers B A S) 15) = R) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_fib_num4,ax, ( (~ (r1_xxreal_0 (k13_complex1 (k7_square_1 5) (k7_square_1 5)) (k13_complex1 (k6_xcmplx_0 (k7_square_1 5) 1) (k7_square_1 5))))  &  (~ (r1_xxreal_0 (k7_square_1 5) k6_numbers)) ) ).
tt(l82_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((k1_finseq_3 (k7_finseq_1 A (k9_finseq_1 B)) C) = (k7_finseq_1 (k1_finseq_3 A C) (k1_finseq_3 (k9_finseq_1 B) C))) ) ) ) ) ).
tt(l82_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden C (k10_xtuple_0 D)) =>  ((r1_xxreal_0 (k4_finseq_4 D C) A) |  ((k1_nat_1 A (k4_finseq_4 (k2_rfinseq B A D) C)) = (k4_finseq_4 D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k9_fomodel0 A B) = (k2_xboole_0 (k7_funcop_1 (k6_subset_1 B A) k1_xboole_0) (k1_margrel1 k5_numbers (k3_xboole_0 A B) 1))) ) ) ).
tt(l82_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v4_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 B C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  ( ( ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) G) = (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k16_fomodel2 B C) (k25_fomodel2 B A)))  & (v3_fomodel2 E B A))  =>  ( ((k18_fomodel2 B C F G (k30_fomodel2 B (k31_fomodel2 B D) E)) = 1)  <=>  (? [H:$i] :  ((m1_subset_1 H C) &  ((k1_binop_1 G (k37_fomodel2 B C F D H) E) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 C B)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 D) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 D B)) =>  ( ( ((k5_relat_1 E A) = (k5_relat_1 F A))  &  ((k2_partfun1 (k6_subset_1 (u1_struct_0 C) (k1_tarski (u3_struct_0 C))) k4_numbers (u1_fomodel1 C) A) = (k2_partfun1 (k6_subset_1 (u1_struct_0 D) (k1_tarski (u3_struct_0 D))) k4_numbers (u1_fomodel1 D) A)) )  => (r1_relset_1 (k35_fomodel1 C) B (k2_partfun1 (k35_fomodel1 C) B (k10_fomodel2 C B E) (k3_finseq_2 A)) (k2_partfun1 (k35_fomodel1 D) B (k10_fomodel2 D B F) (k3_finseq_2 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k4_struct_0 A) (a_2_2_fvaluat1 A B))) ) ) ) ) ).
tt(l82_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k7_geomtrap A B C))) =>  (~  ((r1_analmetr A B C) &  ((r2_analoaf (k7_geomtrap A B C) D E F G) &  ((r2_analoaf (k7_geomtrap A B C) D E F H) &  ( (~  (D = E) )  &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k13_glib_001 A B)) <=>  (? [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(l82_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  => (v1_finset_1 (k6_graph_5 A B))) ) ) ) ).
tt(l82_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ( (~ (r1_xxreal_0 (k2_nat_1 B A) 1))  &  ((r1_xxreal_0 (k2_nat_1 B A) (k4_nat_1 2 B)) &  (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1) (k2_nat_1 B A))) ) ) ) ) ) ) ) ).
tt(l82_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (~ (v1_xboole_0 D))  =>  ((r2_hidden E (k1_group_9 A B C D)) <=>  (? [F:$i] :  ((m2_finseq_1 F A) &  (? [G:$i] :  ((m1_subset_1 G D) &  ((k1_funct_1 (k2_group_9 A B C F) G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 C B) A)) k8_intpro_1)) ) ) ) ) ) ).
tt(l82_jgraph_5,ax,(r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1))).
tt(l82_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v2_normsp_1 (k20_lpspace1 A B C)) &  ((v5_rlvect_1 (k20_lpspace1 A B C)) &  ((v6_rlvect_1 (k20_lpspace1 A B C)) &  ((v7_rlvect_1 (k20_lpspace1 A B C)) &  ((v8_rlvect_1 (k20_lpspace1 A B C)) &  ((v2_rlvect_1 (k20_lpspace1 A B C)) &  ((v3_rlvect_1 (k20_lpspace1 A B C)) &  ((v4_rlvect_1 (k20_lpspace1 A B C)) & (v13_algstr_0 (k20_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ( ((k3_funct_2 k5_numbers A D k6_numbers) = C)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden (k4_tarski (k3_funct_2 k5_numbers A D E) (k3_funct_2 k5_numbers A D (k2_nat_1 E 1))) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(l82_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k1_binop_1 (u1_lattices (k12_normform A)) B (k1_binop_1 (u2_lattices (k12_normform A)) C D)) = (k1_binop_1 (u2_lattices (k12_normform A)) (k1_binop_1 (u1_lattices (k12_normform A)) B C) (k1_binop_1 (u1_lattices (k12_normform A)) B D))) ) ) ) ) ) ) ) ).
tt(l82_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v3_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l82_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_nat_d (k4_pepin 1) (k2_nat_1 (k13_newton 3 (k2_nat_1 (k4_nat_1 4 A) 2)) 1))) ) ).
tt(l82_prepower,ax, (! [A:$i] :  ( ((v5_relat_1 A k3_numbers) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v5_relat_1 B k3_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ( ((k2_seq_2 A) = (k2_seq_2 B))  & (r1_xxreal_0 1 C)) ) )  =>  ((k2_seq_2 (k8_prepower C A)) = (k2_seq_2 (k8_prepower C B))) ) ) ) ) ) ) ) ).
tt(l82_quaterni,ax, ( ((k25_quaterni k6_numbers k1_xcmplx_0) = k6_numbers)  &  ( ((k25_quaterni k6_numbers k11_quaterni) = k6_numbers)  &  ((k25_quaterni k6_numbers k12_quaterni) = k6_numbers) ) ) ).
tt(l82_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 A)) =>  ( ((k15_seq_4 A B C) = (k15_seq_4 A D C))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(l82_sincos10,ax, ( ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) = (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))  &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) =>  ((k1_seq_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) A) = (k1_seq_1 k1_fdiff_9 A)) ) ) ) ) ).
tt(l82_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k20_pscomp_1 (k3_topreal1 2 A)) (k11_pscomp_1 (k3_topreal1 2 A))) (k1_rltopsp1 (k15_euclid 2) (k12_pscomp_1 (k3_topreal1 2 A)) (k22_pscomp_1 (k3_topreal1 2 A)))) = k1_xboole_0) ) ) ).
tt(l82_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l83_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 4 A) => (r1_xxreal_0 (k4_nat_1 2 A) (k8_real_1 A (k6_power 2 A)))) ) ) ).
tt(l83_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) => (r2_hidden (k4_borsuk_1 k5_topmetr k5_topmetr A B) (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) ) ) ) ).
tt(l83_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k4_xcmplx_0 A)) = (k17_complex1 A)) ) ) ).
tt(l83_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  (~  ( ((k3_complex1 (k1_complex2 (k11_complex1 A B) (k11_complex1 C B))) = k6_numbers)  <=>  ( ((k4_complex2 A B C) = (k13_complex1 k32_sin_cos 2))  |  ((k4_complex2 A B C) = (k4_real_1 (k13_complex1 3 2) k32_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_fib_num4,ax, (~ (r1_xxreal_0 1 (k13_complex1 (k6_xcmplx_0 (k7_square_1 5) 1) (k7_square_1 5)))) ).
tt(l83_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((k1_finseq_3 (k7_finseq_1 C A) D) = (k7_finseq_1 (k1_finseq_3 C D) (k1_finseq_3 A D))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((k1_finseq_3 (k7_finseq_1 C (k7_finseq_1 A (k9_finseq_1 B))) D) = (k7_finseq_1 (k1_finseq_3 C D) (k1_finseq_3 (k7_finseq_1 A (k9_finseq_1 B)) D))) ) ) ) ) ) ) ) ).
tt(l83_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ( ((k26_fomodel2 A B E (k30_fomodel2 A (k31_fomodel2 A C) D)) = k8_margrel1)  <=>  (? [F:$i] :  ((m1_subset_1 F B) &  ((k26_fomodel2 A B (k37_fomodel2 A B E C F) D) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((k48_gfacirc1 A B C) = (k4_tarski D k4_twoscomp)) ) ) ) ) ) ).
tt(l83_funct_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  ((k9_funct_7 A k6_numbers) = (k6_partfun1 (k9_xtuple_0 A))) ) ) ) ).
tt(l83_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  ((k9_geomtrap (k7_geomtrap A B C) D E) = (k9_geomtrap (k7_geomtrap A B C) E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k14_glib_001 A B)) <=>  (? [D:$i] :  ( ((v1_abian D) & (m1_subset_1 D k5_numbers))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v1_finset_1 (k4_graph_5 A B C))) ) ) ) ) ) ).
tt(l83_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 C B)) )  =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 2 B) (k4_nat_1 B A)) C) 1))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 2 B) (k4_nat_1 B A)) C) A))  &  (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1) (k2_nat_1 (k2_nat_1 (k4_nat_1 2 B) (k4_nat_1 B A)) C))) ) ) ) ) ) ) ) ) ) ).
tt(l83_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 A (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(l83_jgraph_5,ax,(r2_hidden 1 (k1_rcomp_1 k6_numbers 1))).
tt(l83_lpspace2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k5_numbers) &  ((v5_valued_0 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ( ((v1_rsspace3 B A) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_seq_1 D F) = (k1_normsp_0 A (k5_algstr_0 A C (k1_normsp_1 A B (k1_recdef_1 E F))))) ) )  &  ((v2_comseq_2 D) &  ((k2_seq_2 D) = k6_numbers) ) ) )  =>  ((v3_normsp_1 B A) &  ( ((k6_normsp_1 A B) = C)  &  ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 C))))  =>  (~  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 D) (k10_xtuple_0 E)) (k2_matrix_1 F)) &  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  =>  (A = k6_numbers) )  &  (! [G:$i] :  ( ((v1_finset_1 G) &  ((v1_setfam_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers))) )  =>  (! [H:$i] :  ( ((v1_finset_1 H) &  ((v1_setfam_1 H) & (m1_subset_1 H (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( (G = (k10_xtuple_0 D))  &  (H = (k10_xtuple_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l83_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k2_lattices (k12_normform A) B (k1_lattices (k12_normform A) B C)) = B) ) ) ) ) ) ).
tt(l83_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v12_o_ring_1 B A) & (v12_o_ring_1 C A))  => (v12_o_ring_1 (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B C) (k12_finseq_1 (u1_struct_0 A) (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B)) (k7_partfun1 (u1_struct_0 A) C (k3_finseq_1 C))))) A)) ) ) ) ) ) ) ).
tt(l83_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (B = (k4_relat_1 A))  => (v1_partfun1 B A)) ) ) ) ).
tt(l83_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 B)) & (r1_tarski (k1_rvsum_1 B) C)) )  => (r2_hidden (k7_partfun1 k5_numbers B A) C)) ) ) ) ) ) ).
tt(l83_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (A = 1)  => (r2_int_1 (k13_newton 3 (k3_nat_d (k7_nat_d (k4_pepin A) 1) 2)) (k4_xcmplx_0 1) (k4_pepin A))) ) ) ).
tt(l83_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (v9_rltopsp1 (k1_convex1 A B C) A)) ) ) ) ) ) ).
tt(l83_sincos10,ax, ( ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) = (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))  &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) =>  ((k1_seq_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) A) = (k1_seq_1 k2_fdiff_9 A)) ) ) ) ) ).
tt(l83_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l84_borsuk_7,ax, ((v1_funct_1 k16_sin_cos) &  ((v1_funct_2 k16_sin_cos (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 k16_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) ) ).
tt(l84_card_3,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v2_card_3 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B A) =>  ((k9_xtuple_0 B) = (k9_card_3 A)) ) ) ) ) ) ).
tt(l84_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A k6_numbers) =>  ((k17_complex1 A) = (k4_xcmplx_0 A)) ) ) ) ).
tt(l84_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v16_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_exchsort C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 C)) =>  ( ((r2_hidden D E) &  (A = (k7_exchsort B C D E)) )  =>  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k9_xtuple_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (k9_xtuple_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (k9_xtuple_0 C)) =>  ( ((r2_hidden F H) &  ((r2_hidden G I) &  ((k1_binop_1 A F H) = (k1_binop_1 A G I)) ) )  =>  ( (F = G)  &  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l84_fib_num4,ax, (~ (r1_xxreal_0 (k6_square_1 (k1_pepin 3)) (k7_square_1 5))) ).
tt(l84_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((k1_finseq_3 (k7_finseq_1 B A) C) = (k7_finseq_1 (k1_finseq_3 B C) (k1_finseq_3 A C))) ) ) ) ) ) ).
tt(l84_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B D) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) k6_margrel1))))  =>  ( ( ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B D) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) G) = (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) (k16_fomodel2 B D) (k25_fomodel2 B A)))  & (v3_fomodel2 E B A))  =>  ( ((k20_fomodel2 B D G F (k30_fomodel2 B (k30_fomodel2 B (k31_fomodel2 B (k1_fomodel2 B)) E) C)) = 1)  <=>  ( ((k1_binop_1 G F E) = k6_numbers)  &  ((k1_binop_1 G F C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l84_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ((v15_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 C A)) =>  (~  ( ((k5_relat_1 E (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 D) (k37_fomodel1 B))) = (k5_relat_1 F (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 D) (k37_fomodel1 B))))  &  ( ((k2_partfun1 (k6_subset_1 (u1_struct_0 B) (k1_tarski (u3_struct_0 B))) k4_numbers (u1_fomodel1 B) (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 D) (k37_fomodel1 B))) = (k2_partfun1 (k6_subset_1 (u1_struct_0 C) (k1_tarski (u3_struct_0 C))) k4_numbers (u1_fomodel1 C) (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 D) (k37_fomodel1 B))))  &  ( ((k34_fomodel2 B) = (k34_fomodel2 C))  &  (! [G:$i] :  ( ((v15_fomodel1 G C) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))))  =>  (~  ( (G = D)  &  ((k14_fomodel2 C A F G) = (k14_fomodel2 B A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l84_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] : (r1_xboole_0 (k2_msafree2 (k49_gfacirc1 A B C)) (k3_msafree2 (k49_gfacirc1 D E F)))) ) ) ) ) ) ) ) ) ).
tt(l84_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_funct_1 (k13_funcop_1 A B C)) &  ((v1_funct_2 (k13_funcop_1 A B C) (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C)) & (m1_subset_1 (k13_funcop_1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) (k1_tarski C))))) ) ) ) ) ).
tt(l84_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  ((k9_geomtrap (k7_geomtrap A B C) D D) = D) ) ) ) ) ) ) ) ) ).
tt(l84_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (~  ((r2_hidden C (k14_glib_001 A B)) &  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (! [F:$i] :  ( ( (~ (v1_abian F))  & (m1_subset_1 F k5_numbers))  =>  (~  ((r1_xxreal_0 (k2_nat_1 F 2) (k3_finseq_1 B)) &  ( (D = (k1_funct_1 B F))  &  ( (C = (k1_funct_1 B (k2_nat_1 F 1)))  &  ( (E = (k1_funct_1 B (k2_nat_1 F 2)))  & (r1_glib_000 A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l84_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (v1_finset_1 (k5_graph_5 B C D A))) ) ) ) ) ) ) ).
tt(l84_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B)) ) )  =>  ((r1_xxreal_0 (k2_nat_1 (k4_nat_1 3 B) 1) (k2_nat_1 (k2_nat_1 (k4_nat_1 2 B) (k4_nat_1 B A)) C)) & (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k4_nat_1 2 B) (k4_nat_1 B A)) C) (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)))) ) ) ) ) ) ) ) ).
tt(l84_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 A (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(l84_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) (k4_cat_1 (k2_oppcat_1 A) D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l84_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v13_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l84_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( (B = (k4_relat_1 A))  =>  ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v4_relat_2 B) & (v8_relat_2 B)) ) ) ) ) ) ) ).
tt(l84_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_nat_d (k4_pepin 2) (k2_nat_1 (k13_newton 3 (k2_nat_1 (k4_nat_1 16 A) 8)) 1))) ) ).
tt(l84_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattices A B C) <=>  ( ((k3_lattices A B C) = (k6_lattices A))  &  ((k4_lattices A B C) = (k5_lattices A)) ) ) ) ) ) ) ) ) ).
tt(l84_sincos10,ax, ( ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) = (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))  &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) =>  ((k1_seq_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) A) = (k1_seq_1 k2_fdiff_9 A)) ) ) ) ) ).
tt(l84_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l84_toprealb,ax, ( ( (~ (v1_xboole_0 (k3_rcomp_1 (k1_real_1 1) 1)))  & (m1_subset_1 (k3_rcomp_1 (k1_real_1 1) 1) (k1_zfmisc_1 k1_numbers)))  &  ( (~ (v1_xboole_0 (k4_rcomp_1 k6_numbers k32_sin_cos)))  & (m1_subset_1 (k4_rcomp_1 k6_numbers k32_sin_cos) (k1_zfmisc_1 k1_numbers))) ) ).
tt(l85_borsuk_7,ax, ((v1_funct_1 k19_sin_cos) &  ((v1_funct_2 k19_sin_cos (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 k19_sin_cos (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) ) ).
tt(l85_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_square_1 (k3_square_1 A)) = (k17_complex1 A)) ) ) ).
tt(l85_fib_num4,ax, (~ (r1_xxreal_0 3 (k7_square_1 5))) ).
tt(l85_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ( ((k26_fomodel2 A B E (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D)) = k8_margrel1)  <=>  ( ((k26_fomodel2 A B E C) = k7_margrel1)  &  ((k26_fomodel2 A B E D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l85_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  ((k9_geomtrap (k7_geomtrap A B C) (k9_geomtrap (k7_geomtrap A B C) D E) (k9_geomtrap (k7_geomtrap A B C) F G)) = (k9_geomtrap (k7_geomtrap A B C) (k9_geomtrap (k7_geomtrap A B C) D F) (k9_geomtrap (k7_geomtrap A B C) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l85_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C (k14_glib_001 A B)) & (r1_glib_000 A D E C))  =>  ((r2_hidden D (k13_glib_001 A B)) & (r2_hidden E (k13_glib_001 A B))) ) ) ) ) ) ) ) ) ).
tt(l85_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))))  &  ((v10_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) & (l3_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A)))) )  &  ( ( (~ (v2_struct_0 (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))))  &  ((v10_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) &  ((v13_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) & (l3_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A)))) ) )  &  ( (~ (v2_struct_0 (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))))  &  ((v10_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) &  ((v14_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A))) & (l3_lattices (g3_lattices (k1_group_3 A) (k9_group_4 A) (k10_group_4 A)))) ) ) ) ) ) ) ).
tt(l85_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_oppcat_1 A))) =>  ( ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k3_graph_1 (k2_oppcat_1 A) D)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k4_graph_1 (k2_oppcat_1 A) D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l85_partfun1,ax, (! [A:$i] : (m1_subset_1 (k4_relat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ).
tt(l85_pepin,ax, ((k4_nat_d (k13_newton 3 1) (k4_pepin 3)) = 3) ).
tt(l85_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A C B) = B) ) )  =>  (B = (k5_lattices A)) ) ) ) ) ) ).
tt(l85_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k24_sin_cos (k2_xcmplx_0 A B)) = (k8_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ).
tt(l85_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c25__toprealb))) = (k5_toprealb c25__toprealb)) ).
tt(l85_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_8 A) =>  ( ((v6_waybel23 (u1_struct_0 (k1_waybel_8 A)) A) & (m1_waybel23 (u1_struct_0 (k1_waybel_8 A)) A))  &  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (r1_tarski (u1_struct_0 (k1_waybel_8 A)) B)) ) ) ) ) ) ).
tt(l86_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v1_anproj_2 A)) ) ) ).
tt(l86_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 A (k2_int_1 (k10_real_1 A 2)))) ) ) ) ).
tt(l86_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_funct_1 k12_borsuk_7 A) = (k4_euclid_5 (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) c1__borsuk_7) k19_sin_cos) A) (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) k6_numbers) k16_sin_cos) A) k6_numbers)) ) ) ).
tt(l86_card_2,ax,(v4_ordinal1 k4_ordinal1)).
tt(l86_classes1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (k10_xtuple_0 A)))  =>  ((k10_relat_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(l86_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 C B A D)) ) ) ) ) ).
tt(l86_fib_num4,ax, (~ (r1_xxreal_0 (k4_xcmplx_0 (k7_square_1 5)) (k4_xcmplx_0 3))) ).
tt(l86_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_partfun1 B A)) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k10_xtuple_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k10_xtuple_0 B))))) )  &  ((r1_relset_1 A (k10_xtuple_0 B) C B) &  ((k1_relset_1 A C) = A) ) ) ) ) ) ) ).
tt(l86_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A C B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A C B))) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A C B))) &  ((k9_geomtrap (k7_geomtrap A C B) F D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l86_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) => (r1_xxreal_0 (k17_glib_001 A B C) C)) ) ) ) ) ) ) ).
tt(l86_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = (u1_struct_0 (k5_group_4 B D)))  =>  ((k18_group_9 A B D) = (k18_group_9 A B C)) ) ) ) ) ) ) ) ) ).
tt(l86_ideal_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k1_tarski A) (k2_tarski A B))) ) ).
tt(l86_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 (k4_intpro_1 C B) A)) k8_intpro_1)) ) ) ) ) ) ).
tt(l86_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( (~  ((k3_funct_2 A k6_margrel1 (k31_modelc_1 A C) B) = k8_margrel1) )  =>  ((k3_funct_2 A k6_margrel1 (k31_modelc_1 A C) B) = k7_margrel1) ) ) ) ) ) ) ).
tt(l86_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k11_newton A) = (a_1_1_newton A)) ) ) ).
tt(l86_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v7_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l86_pepin,ax, ((k4_nat_d (k13_newton 3 2) (k4_pepin 3)) = 9) ).
tt(l86_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k28_quaterni A) = (k26_quaterni (k26_quaterni (k23_quaterni (k1_real_1 (k17_quaterni A)) (k25_quaterni (k1_real_1 (k18_quaterni A)) k1_xcmplx_0)) (k25_quaterni (k1_real_1 (k19_quaterni A)) k11_quaterni)) (k25_quaterni (k1_real_1 (k20_quaterni A)) k12_quaterni))) ) ) ).
tt(l86_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((v1_finset_1 E) =>  ( ( (E = (k1_relset_1 A (k2_partfun1 A k1_numbers B D)))  &  ((v1_finset_1 (k1_relset_1 A (k2_partfun1 A k1_numbers B C))) &  ((r1_tarski D C) &  ( (k6_numbers = (k5_card_1 E))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden F (k1_relset_1 A (k2_partfun1 A k1_numbers B D))) & (r2_hidden G (k1_relset_1 A (k2_partfun1 A k1_numbers B (k6_subset_1 C D)))))  => (r1_xxreal_0 (k1_seq_1 B G) (k1_seq_1 B F))) ) ) ) ) ) ) ) )  =>  ((k20_rfunct_3 A B C) = (k8_finseq_1 k1_numbers (k20_rfunct_3 A B D) (k20_rfunct_3 A B (k6_subset_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l86_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A C B) = B) ) )  =>  (B = (k6_lattices A)) ) ) ) ) ) ).
tt(l86_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l86_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) = (k5_toprealb c26__toprealb)) ).
tt(l87_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_collsp (k5_anproj_1 A)) & (v3_anproj_2 (k5_anproj_1 A))) ) ) ) ).
tt(l87_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( (~  ((k4_complex2 A B C) = k6_numbers) )  =>  ((k4_complex2 C B A) = (k9_real_1 (k8_real_1 2 k32_sin_cos) (k4_complex2 A B C))) ) ) ) ) ) ) ) ).
tt(l87_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 B A)) => (r2_hidden (k1_midsp_3 A B E C D) (k4_finseq_2 B A))) ) ) ) ) ) ) ) ) ) ) ).
tt(l87_fib_num4,ax, (~ (r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) 3) (k2_xcmplx_0 (k4_xcmplx_0 3) 3))) ).
tt(l87_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 3)) & (r2_hidden 2 (k2_finseq_1 3))) ).
tt(l87_fomodel0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski (k9_xtuple_0 B) (k9_xtuple_0 A)) & (r1_tarski A B))  =>  (A = B) ) ) ) ) ) ).
tt(l87_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ((r1_tarski (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B)) C) => (v1_partfun1 (k6_fomodel4 B C A) (k35_fomodel1 B))) ) ) ) ) ) ).
tt(l87_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((k9_geomtrap (k7_geomtrap A B C) D E) = (k9_geomtrap (k7_geomtrap A B C) D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l87_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) => (r1_xxreal_0 C (k19_glib_001 A B C))) ) ) ) ) ) ) ).
tt(l87_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_graph_1 D) &  ((v6_graph_1 D) & (l1_graph_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 D) k8_graph_5) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 D) k8_graph_5)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ((r6_graphsp B D A E) &  ( (F = 1)  &  ((r1_xxreal_0 1 A) &  (C = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) 1) B)) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (~  ( (~  (G = F) )  &  ( (G = H)  &  ( (~  ((k1_seq_1 C (k2_nat_1 A H)) = (k1_real_1 1)) )  &  (! [I:$i] :  ((m2_finseq_1 I k5_numbers) =>  (! [J:$i] :  ( ((v7_graph_1 J D) & (m2_graph_1 J D))  =>  (~  ((r4_graphsp I C H A) &  ( (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 K) =>  ((r1_xxreal_0 (k3_finseq_1 I) K) | (r2_hidden (k1_seq_1 I K) (k14_graphsp C A))) ) ) )  &  ((r5_graphsp D J I) &  ((r8_graph_5 D F G J (k14_graphsp C A) E) &  ( ((k10_graph_5 D J E) = (k1_seq_1 C (k2_nat_1 (k4_nat_1 2 A) H)))  &  ( (~ (r2_hidden G (k14_graphsp C A)))  => (r9_graph_5 D J (k14_graphsp C A) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ( ((k1_seq_1 C (k2_nat_1 A H)) = (k1_real_1 1))  &  ((r1_xxreal_0 1 H) &  ((r1_xxreal_0 H A) & (r2_hidden G (k14_graphsp C A))) ) )  =>  ((k1_seq_1 B (k2_nat_1 (k2_nat_1 (k4_nat_1 2 A) (k4_nat_1 A G)) H)) = (k1_real_1 1)) ) ) ) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r2_hidden G (k14_graphsp C A)) &  ((k1_seq_1 C (k2_nat_1 A G)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l87_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 (k4_intpro_1 B A) C)) k8_intpro_1)) ) ) ) ) ) ).
tt(l87_measure6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v5_measure6 B A) => (v6_measure6 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(l87_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 (k2_oppcat_1 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l87_pepin,ax, ((k4_nat_d (k13_newton 3 4) (k4_pepin 3)) = 81) ).
tt(l87_rfunct_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_finset_1 F) =>  ( ( (F = (k1_relset_1 B (k2_partfun1 B k1_numbers C E)))  &  ((v1_finset_1 (k1_relset_1 B (k2_partfun1 B k1_numbers C D))) &  ((r1_tarski E D) &  ( (A = (k5_card_1 F))  &  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  ( ((r2_hidden G (k1_relset_1 B (k2_partfun1 B k1_numbers C E))) & (r2_hidden H (k1_relset_1 B (k2_partfun1 B k1_numbers C (k6_subset_1 D E)))))  => (r1_xxreal_0 (k1_seq_1 C H) (k1_seq_1 C G))) ) ) ) ) ) ) ) )  =>  ((k20_rfunct_3 B C D) = (k8_finseq_1 k1_numbers (k20_rfunct_3 B C E) (k20_rfunct_3 B C (k6_subset_1 D E)))) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_finset_1 F) =>  ( ( (F = (k1_relset_1 B (k2_partfun1 B k1_numbers C E)))  &  ((v1_finset_1 (k1_relset_1 B (k2_partfun1 B k1_numbers C D))) &  ((r1_tarski E D) &  ( ((k2_nat_1 A 1) = (k5_card_1 F))  &  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  ( ((r2_hidden G (k1_relset_1 B (k2_partfun1 B k1_numbers C E))) & (r2_hidden H (k1_relset_1 B (k2_partfun1 B k1_numbers C (k6_subset_1 D E)))))  => (r1_xxreal_0 (k1_seq_1 C H) (k1_seq_1 C G))) ) ) ) ) ) ) ) )  =>  ((k20_rfunct_3 B C D) = (k8_finseq_1 k1_numbers (k20_rfunct_3 B C E) (k20_rfunct_3 B C (k6_subset_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l87_sin_cos,ax, ((k1_seq_1 k24_sin_cos k6_numbers) = 1) ).
tt(l87_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k20_pscomp_1 (k3_topreal1 2 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(l87_toprealb,ax, ((u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) = (k5_toprealb (k2_rcomp_1 k6_numbers 1))) ).
tt(l87_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ( (? [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  &  (! [C:$i] :  ( ((v6_waybel23 C A) & (m1_waybel23 C A))  => (r1_tarski B C)) ) ) )  => (v2_waybel_8 A)) ) ) ).
tt(l88_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k5_square_1 A) (k2_nat_1 A 1))) ) ) ) ).
tt(l88_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A B)) = B) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = B) ) ) ) ) ) ) ) ).
tt(l88_fib_num4,ax, (~ (r1_xxreal_0 (k4_xcmplx_0 1) (k4_xcmplx_0 (k7_square_1 5)))) ).
tt(l88_finseq_1,ax,(r2_hidden 3 (k2_finseq_1 3))).
tt(l88_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v4_relat_1 D A))  =>  ( ((v1_partfun1 D A) &  ((v4_relat_1 B A) &  ((v1_funct_1 (k3_relat_1 (k3_relat_1 (k3_relat_1 C D) (k2_relat_1 D)) B)) & (r1_tarski (k10_xtuple_0 C) (k9_xtuple_0 B))) ) )  =>  ((k3_relat_1 (k3_relat_1 (k3_relat_1 C D) (k2_relat_1 D)) B) = (k3_relat_1 C B)) ) ) ) ) ) ) ) ) ).
tt(l88_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r1_tarski (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k26_fomodel4 B)) C) & (v10_fomodel4 A B C))  => (v3_relat_2 (k6_fomodel4 B C A))) ) ) ) ) ) ).
tt(l88_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r1_analmetr A B C) & (r2_analoaf (k7_geomtrap A B C) D E F G))  => (r2_analoaf (k7_geomtrap A B C) D E (k9_geomtrap (k7_geomtrap A B C) D F) (k9_geomtrap (k7_geomtrap A B C) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l88_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v2_glib_001 B A) <=>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  => (r2_glib_000 A (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 2)) (k1_funct_1 B (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(l88_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ( (D = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) E))  &  ( (F = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) E))  &  ((r2_hidden C (k14_graphsp D A)) &  ((k3_finseq_1 E) = (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1)) ) ) )  =>  ( ((k7_graphsp D A) = k1_xboole_0)  |  ((k1_seq_1 F (k2_nat_1 A C)) = (k1_seq_1 D (k2_nat_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l88_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_integra5 A k16_sin_cos) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos A))) ) ) ).
tt(l88_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 (k4_intpro_1 B C) A)) k8_intpro_1)) ) ) ) ) ) ).
tt(l88_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( ( ((k1_matrix_1 C) = (k1_matrix_1 D))  & (r2_hidden A (k4_finseq_1 C)))  =>  ((k8_matrix_1 (u1_struct_0 B) (k3_matrix_3 B C D) A) = (k3_fvsum_1 B (k8_matrix_1 (u1_struct_0 B) C A) (k8_matrix_1 (u1_struct_0 B) D A))) ) ) ) ) ) ) ) ) ) ).
tt(l88_measure6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v6_measure6 B A) => (v5_measure6 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(l88_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( ( (! [D:$i] :  ((r2_hidden D (k30_modelc_1 A)) =>  ((k1_funct_1 B D) = (k32_modelc_1 A D)) ) )  &  (! [D:$i] :  ((r2_hidden D (k30_modelc_1 A)) =>  ((k1_funct_1 C D) = (k32_modelc_1 A D)) ) ) )  => (r2_funct_2 (k30_modelc_1 A) (k30_modelc_1 A) B C)) ) ) ) ) ) ) ).
tt(l88_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) (k3_graph_1 A D)) = (k3_graph_1 (k2_oppcat_1 B) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) (k4_graph_1 A D)) = (k4_graph_1 (k2_oppcat_1 B) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l88_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v11_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l88_pepin,ax, ((k4_nat_d (k13_newton 3 8) (k4_pepin 3)) = 136) ).
tt(l88_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k29_quaterni A B) = (k26_quaterni (k26_quaterni (k23_quaterni (k9_real_1 (k17_quaterni A) (k17_quaterni B)) (k25_quaterni (k9_real_1 (k18_quaterni A) (k18_quaterni B)) k1_xcmplx_0)) (k25_quaterni (k9_real_1 (k19_quaterni A) (k19_quaterni B)) k11_quaterni)) (k25_quaterni (k9_real_1 (k20_quaterni A) (k20_quaterni B)) k12_quaterni))) ) ) ) ) ).
tt(l88_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(l88_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers)) = (u1_struct_0 k2_topalg_2)) ).
tt(l88_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_3 A k6_numbers) = k6_numbers) ) ) ).
tt(l89_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) =>  (~  ( (~ (r1_collsp (k5_anproj_1 A) G D C))  &  ((r1_collsp (k5_anproj_1 A) D C B) &  ((r1_collsp (k5_anproj_1 A) G E D) &  ((r1_collsp (k5_anproj_1 A) G F C) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_anproj_1 A))) =>  (~  ((r1_collsp (k5_anproj_1 A) E F H) & (r1_collsp (k5_anproj_1 A) G B H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l89_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k9_real_1 (k5_series_1 2 (k2_nat_1 A 1)) (k5_series_1 2 A)) 1)) ) ) ) ).
tt(l89_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = B) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(l89_fib_num4,ax, (~ (r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 1) 3) (k2_xcmplx_0 (k4_xcmplx_0 (k7_square_1 5)) 3))) ).
tt(l89_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 4)) & (r2_hidden 2 (k2_finseq_1 4))) ).
tt(l89_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r1_tarski (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k22_fomodel4 B)) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k25_fomodel4 B))) C) & (v10_fomodel4 A B C))  => (v8_relat_2 (k6_fomodel4 B C A))) ) ) ) ) ) ).
tt(l89_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  (~  ((r1_analmetr A B C) &  ((r2_analoaf (k7_geomtrap A B C) D E F G) &  ( (~ (r2_analoaf (k7_geomtrap A B C) D E (k9_geomtrap (k7_geomtrap A B C) D G) (k9_geomtrap (k7_geomtrap A B C) E F)))  &  (~ (r2_analoaf (k7_geomtrap A B C) D E (k9_geomtrap (k7_geomtrap A B C) E F) (k9_geomtrap (k7_geomtrap A B C) D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l89_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v2_glib_001 B A) &  ((r1_glib_001 A C E B) & (r2_glib_000 A E F D)) )  =>  ((v2_glib_001 (k10_glib_001 A B D) A) & (r1_glib_001 A C F (k10_glib_001 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(l89_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [G:$i] :  ((m2_finseq_1 G k5_numbers) =>  ( ( (D = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) E))  &  ( (F = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) E))  &  ( ((k3_finseq_1 E) = (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1))  &  ((r4_graphsp G D C A) &  ( ((k1_seq_1 D (k2_nat_1 A C)) = (k1_seq_1 F (k2_nat_1 A C)))  &  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 H) =>  ((r1_xxreal_0 (k3_finseq_1 G) H) | (r2_hidden (k1_seq_1 G H) (k14_graphsp D A))) ) ) ) ) ) ) ) )  =>  ( ((k7_graphsp D A) = k1_xboole_0)  | (r4_graphsp G F C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l89_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 (k4_intpro_1 A C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(l89_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ( ( (~ (v3_xxreal_0 E))  & (v1_xreal_0 E))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B D) &  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_brouwer 2 C E)))) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_brouwer 2 C E)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 C E)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)))))) )  =>  (~  ((v5_pre_topc F (k2_brouwer 2 C E) (k1_pre_topc (k15_euclid 2) D)) &  ((k2_partfun1 (u1_struct_0 (k2_brouwer 2 C E)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)) F D) = (k6_partfun1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l89_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v11_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l89_pepin,ax, ((k4_nat_d (k13_newton 3 16) (k4_pepin 3)) = (k4_nat_1 83 3)) ).
tt(l89_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_finseq_1 D)) )  =>  ( ((r1_tarski C A) & (r1_tarski D B))  => (r1_tarski (k9_xtuple_0 (k2_xboole_0 C (k12_pnproc_1 D (k3_finseq_1 A)))) (k4_finseq_1 (k7_finseq_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(l89_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_polynom1 A C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k11_polynom1 A C))) =>  ( ( (E = G)  &  ( (F = H)  & (r5_polyred A B C E F D)) )  => (r11_polyred (k11_polynom1 A C) (k7_ideal_1 (k11_polynom1 A C) D) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l89_toprealb,ax, ((k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers) (k5_toprealb c26__toprealb))) = (k5_toprealb c26__toprealb)) ).
tt(l89_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k4_xxreal_3 A B) = k6_numbers)  =>  ((v1_xreal_0 A) |  (B = k6_numbers) ) ) ) ) ) ) ).
tt(l8_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_diraf A F B F C) & (r2_diraf A F D F E))  =>  ( (B = C)  |  ( (D = E)  | (r2_diraf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_0)) &  ((k1_algstr_0 k3_algstr_0 A C) = B) ) ) ) ) ) ) ).
tt(l8_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  ((k1_algstr_3 k3_algstr_3 A (k5_struct_0 k3_algstr_3) (k4_struct_0 k3_algstr_3)) = A) ) ) ).
tt(l8_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(l8_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ((k1_rlvect_1 A B D) = (k1_rlvect_1 A C (k1_real_1 E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B C) D) E) (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A F G) H) I)) = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B F) (k3_rlvect_1 A C G)) (k3_rlvect_1 A D H)) (k3_rlvect_1 A E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_arithm,ax, ((k5_xcmplx_0 1) = 1) ).
tt(l8_arytm_0,ax, (! [A:$i] :  (! [B:$i] :  (~  (1 = (k4_tarski A B)) ) ) ) ).
tt(l8_arytm_2,ax, (k2_arytm_2 = (k2_xboole_0 k5_arytm_3 (k7_subset_1 a_0_0_arytm_2 (k6_subset_1 a_0_0_arytm_2 (k1_tarski k5_arytm_3)) a_0_1_arytm_2))) ).
tt(l8_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A)) =>  ( ((k1_relset_1 (u1_struct_0 A) B) = (k2_relset_1 (u1_struct_0 A) B))  &  ((k1_relset_1 (u1_struct_0 A) B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(l8_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_4 A B C) B) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A D B) C) => (r1_bcialg_1 A D (k1_bcialg_4 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(l8_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1) A C) B)) = (k8_real_1 C (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1))) k1_numbers c2__bhsp_1 (k1_domain_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) A B)))) ) ) ) ) ) ) ).
tt(l8_brouwer2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (r1_xxreal_0 A k1_xboole_0))  =>  (! [B:$i] :  ( ((v1_convex1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ((v2_compts_1 B (k15_euclid A)) &  ((r2_hidden (k5_euclid A) (k1_tops_1 (k15_euclid A) B)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid A) B)) (u1_struct_0 (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)) (u1_struct_0 (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1)))))) )  =>  (~  ((v3_tops_2 C (k1_pre_topc (k15_euclid A) B) (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1)) &  ((k7_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)) (u1_struct_0 (k2_brouwer A (k4_struct_0 (k15_euclid A)) 1)) C (k2_tops_1 (k15_euclid A) B)) = (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 1))) =>  ( ( (C = (k12_finseq_1 k1_numbers A))  &  (D = (k12_finseq_1 k1_numbers B)) )  =>  ( ((k3_rlvect_1 (k4_real_ns1 1) C D) = (k12_finseq_1 k1_numbers (k7_real_1 A B)))  &  ((k5_algstr_0 (k4_real_ns1 1) C D) = (k12_finseq_1 k1_numbers (k9_real_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k2_numbers))))  =>  ((r2_hidden A (k8_relset_1 C k2_numbers D B)) <=>  ((r2_hidden A (k1_relset_1 C D)) & (r2_hidden (k7_partfun1 k2_numbers D A) B)) ) ) ) ) ) ) ) ).
tt(l8_collsp,ax, ( (~ (v2_struct_0 (g1_collsp c2__collsp c3__collsp)))  & (l1_collsp (g1_collsp c2__collsp c3__collsp))) ).
tt(l8_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  => (m2_finseq_1 A k2_numbers)) ) ).
tt(l8_compos_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)))) =>  ((k3_compos_0 (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) A) = (k6_domain_1 k5_numbers k6_numbers)) ) ) ).
tt(l8_comptrig,ax, (~ (r1_xxreal_0 (k7_real_1 k32_sin_cos k32_sin_cos) (k7_real_1 k6_numbers k32_sin_cos))) ).
tt(l8_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_rlvect_2 D A C) =>  ( ((v2_convex1 D A) & (r1_tarski C B))  => (r2_hidden (k6_rlvect_2 A D) B)) ) ) ) )  => (v1_convex1 B A)) ) ) ) ) ).
tt(l8_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_convex1 B A) => (r1_tarski (a_2_0_convex3 A B) B)) ) ) ) ) ).
tt(l8_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_convfun1 A k4_convfun1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (C = (k1_domain_1 (u1_struct_0 A) k1_numbers B E))  =>  ((k1_rlvect_1 (k3_convfun1 A k4_convfun1) C D) = (k1_domain_1 (u1_struct_0 A) k1_numbers (k1_rlvect_1 A B D) (k11_binop_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A D E) A))  => (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A B D) (k9_cqc_lang A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k7_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k2_comseq_2 k5_numbers A))) B)) &  ((k1_seq_1 (k8_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k2_comseq_2 k5_numbers A))) B) = k6_numbers) ) ) ) ) ) ).
tt(l8_csspace3,ax, ( (~ (v2_struct_0 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))))  &  ((v13_algstr_0 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v2_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v3_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v4_rlvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v2_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v3_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v4_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) &  ((v5_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3))) & (l1_clvect_1 (g1_clvect_1 k1_csspace3 (k10_csspace k7_csspace k1_csspace3) (k8_csspace k7_csspace k1_csspace3) (k9_csspace k7_csspace k1_csspace3)))) ) ) ) ) ) ) ) ) ).
tt(l8_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k9_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 4 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k9_euclid 3 (k1_euclid_8 B C D) A) = (k1_euclid_8 (k11_binop_2 A B) (k11_binop_2 A C) (k11_binop_2 A D))) ) ) ) ) ) ) ) ) ).
tt(l8_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers A))  =>  ((k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos)) = A) ) ) ) ).
tt(l8_fib_fusc,ax, (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 2)) ) ).
tt(l8_fib_num4,ax, ((k13_complex1 k2_fib_num k1_fib_num) = (k13_complex1 (k6_xcmplx_0 (k7_square_1 5) 3) 2)) ).
tt(l8_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r1_xxreal_0 (k1_pre_ff A) (k1_pre_ff (k2_nat_1 A 1)))) ) ).
tt(l8_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k12_finseq_1 A B) C) = B) ) ) ) ) ) ) ).
tt(l8_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((r1_tarski B C) & (v1_fomodel0 D C))  => (v1_fomodel0 D B)) ) ) ) ) ) ) ).
tt(l8_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r3_xboole_0 (k2_fsm_1 A B D (k6_finseq_1 A)) (k2_fsm_1 A B D C))) ) ) ) ) ) ) ) ).
tt(l8_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k1_glib_002 A B)) & (r1_glib_000 A D E C))  => (r2_hidden E (k1_glib_002 A B))) ) ) ) ) ) ) ) ).
tt(l8_gobrd11,ax, ((u1_struct_0 (k15_euclid 2)) = (k1_euclid 2)) ).
tt(l8_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k2_nat_1 C 1)) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( ((k2_nat_1 (k3_finseq_1 (k1_graph_2 A B C)) B) = (k2_nat_1 C 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_graph_2 A B C)) D))  =>  ((k1_funct_1 (k1_graph_2 A B C) (k2_nat_1 D 1)) = (k1_funct_1 A (k2_nat_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ( ((k3_group_4 A (k4_group_4 A C (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 C) B))) = (k5_group_1 A (k1_gr_cy_1 C) B))  =>  ((k3_group_4 A (k4_group_4 A (k8_finseq_1 k4_numbers C (k12_finseq_1 k4_numbers D)) (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 (k8_finseq_1 k4_numbers C (k12_finseq_1 k4_numbers D))) B))) = (k5_group_1 A (k1_gr_cy_1 (k8_finseq_1 k4_numbers C (k12_finseq_1 k4_numbers D))) B)) ) ) ) ) ) ) ) ) ) ).
tt(l8_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_group_9 C A))  &  ((v2_group_9 C A) &  ((v3_group_9 C A) &  ((v2_group_1 C) &  ((v3_group_1 C) &  (B = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(l8_holder_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((k1_seq_1 (k3_series_1 A) B) = k6_numbers)  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) =>  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(l8_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_aff_1 A B C D) =>  ( (B = C)  |  ( (B = D)  |  ( ( (~  ( (~ (r1_aff_1 A B C E))  &  ((r1_aff_1 A B E F) & (r2_analoaf A C E D F)) ) )  &  (~  ((r1_aff_1 A B C E) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G D H) &  ((r2_analoaf A G E H F) & (r1_aff_1 A B C F)) ) ) ) ) ) ) ) ) ) )  |  ( (~  (B = D) )  &  ( (~  (B = C) )  &  ((r1_aff_1 A B D C) &  ( ( (~ (r1_aff_1 A B D F))  &  ((r1_aff_1 A B F E) & (r2_analoaf A D F C E)) )  |  ((r1_aff_1 A B D F) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B D G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A D G C H) &  ((r2_analoaf A G F H E) & (r1_aff_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_int_1 A k6_numbers) &  ((r1_int_1 1 A) & (r1_int_1 (k4_xcmplx_0 1) A)) ) ) ) ).
tt(l8_integr19,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r1_tarski C (k1_relset_1 A D)) =>  ((v1_funct_1 (k2_partfun1 A B D C)) &  ((v1_funct_2 (k2_partfun1 A B D C) C B) & (m1_subset_1 (k2_partfun1 A B D C) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_intpro_1,ax, (! [A:$i] :  (~  ((v7_intpro_1 A) & (v1_xboole_0 A)) ) ) ).
tt(l8_jordan1,ax, ((u1_struct_0 (k15_euclid 2)) = (k1_euclid 2)) ).
tt(l8_jordan1c,ax, ((g1_pre_topc (u1_struct_0 (k15_euclid 2)) (u1_pre_topc (k15_euclid 2))) = (g1_pre_topc (u1_struct_0 (k14_euclid 2)) (k2_pcomps_1 (k14_euclid 2)))) ).
tt(l8_jordan1h,ax,(r8_relat_2 k1_jordan1h k1_numbers)).
tt(l8_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden A (k2_pcomps_1 k8_metric_1)) => (v3_rcomp_1 A)) ) ) ).
tt(l8_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k17_borsuk_1)) => (m1_subset_1 A k1_numbers)) ) ).
tt(l8_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  => (v1_wellfnd1 (k7_lattice3 (k3_lattice3 A)))) ) ).
tt(l8_lp_space,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( (1 = C)  &  ((v1_series_1 (k1_lp_space A C)) & (v1_series_1 (k1_lp_space B C))) )  =>  ((v1_series_1 (k1_lp_space (k1_series_1 k1_numbers A B) C)) & (r1_xxreal_0 (k4_power (k4_series_1 (k1_lp_space (k1_series_1 k1_numbers A B) C)) (k10_real_1 1 C)) (k7_real_1 (k4_power (k4_series_1 (k1_lp_space A C)) (k10_real_1 1 C)) (k4_power (k4_series_1 (k1_lp_space B C)) (k10_real_1 1 C))))) ) ) ) ) ) ) ) ).
tt(l8_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A C D) E)) (k8_cqc_lang A (k8_cqc_lang A C F) (k8_cqc_lang A B (k8_cqc_lang A (k8_cqc_lang A F D) E)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) ) ) ) ) ) ) ) ).
tt(l8_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k4_tarski B C) (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))) =>  ( ((k2_xcmplx_0 B C) = (k2_xcmplx_0 A 1))  | (r2_hidden (k6_int_1 (k6_xcmplx_0 (k2_xcmplx_0 B C) 1) A) (k2_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(l8_matrix_7,ax, (~  ((k10_finseq_1 1 2) = (k10_finseq_1 2 1)) ) ).
tt(l8_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_finseq_1 (k3_fvsum_1 A B C)) = (k9_subset_1 k5_numbers (k4_finseq_1 B) (k4_finseq_1 C))) ) ) ) ) ) ) ).
tt(l8_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 (k2_nat_1 A 2) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k2_nat_1 A 2) (u1_struct_0 B)) (u1_struct_0 B))))) )  => (v2_midsp_1 (g1_midsp_3 (k2_nat_1 A 2) (u1_struct_0 B) (u1_midsp_1 B) C))) ) ) ) ) ) ).
tt(l8_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  ((r2_modelc_2 (k11_modelc_2 A) A) & (r2_modelc_2 (k12_modelc_2 A) A)) ) ) ) ).
tt(l8_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v4_msualg_1 (k2_msafree1 A) A) & (v1_msafree1 (k2_msafree1 A) A)) ) ) ).
tt(l8_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k5_msafree A B)) (k7_dtconstr (k5_msafree A B))) <=> (r2_hidden C (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ).
tt(l8_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v1_msscyc_1 B A) & (r1_graph_2 A C B))  =>  ((k1_funct_1 C 1) = (k1_funct_1 C (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(l8_msualg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v2_margrel1 B) &  ((v3_margrel1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) )  =>  ((k9_xtuple_0 B) = (k4_finseq_2 (k19_margrel1 B) A)) ) ) ) ) ).
tt(l8_nagata_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) =>  ((v2_seq_2 B) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~ (v1_xboole_0 (k7_relset_1 A k1_numbers (k2_nagata_2 A B D) C)))  & (v3_xxreal_2 (k7_relset_1 A k1_numbers (k2_nagata_2 A B D) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((v1_finset_1 (k2_enumset1 A B C D)) & (m1_subset_1 (k2_enumset1 A B C D) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ) ) ) ) ).
tt(l8_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c3__normsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c3__normsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((k1_normsp_0 c3__normsp_1 A) = k6_numbers)  =>  (A = (k4_struct_0 c3__normsp_1)) )  &  ( ( (A = (k4_struct_0 c3__normsp_1))  =>  ((k1_normsp_0 c3__normsp_1 A) = k6_numbers) )  &  ( ((k1_normsp_0 c3__normsp_1 (k1_rlvect_1 c3__normsp_1 A C)) = (k8_real_1 (k18_complex1 C) (k1_normsp_0 c3__normsp_1 A)))  & (r1_xxreal_0 (k1_normsp_0 c3__normsp_1 (k1_algstr_0 c3__normsp_1 A B)) (k7_real_1 (k1_normsp_0 c3__normsp_1 A) (k1_normsp_0 c3__normsp_1 B)))) ) ) ) ) ) ) ) ) ).
tt(l8_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ( ((k8_nat_1 k5_numbers C k6_numbers) = (k1_int_2 A))  &  ( ((k8_nat_1 k5_numbers D k6_numbers) = (k1_int_2 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 k5_numbers C (k2_nat_1 E 1)) = (k8_nat_1 k5_numbers D E))  &  ((k8_nat_1 k5_numbers D (k2_nat_1 E 1)) = (k4_nat_d (k8_nat_1 k5_numbers C E) (k8_nat_1 k5_numbers D E))) ) ) ) ) )  =>  ( (~ (v1_xboole_0 (a_1_0_ntalgo_1 D)))  & (m1_subset_1 (a_1_0_ntalgo_1 D) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ) ) ) ) ) ).
tt(l8_numbers,ax,(r1_tarski k5_arytm_3 k3_numbers)).
tt(l8_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) c1__ortsp_1) c1__ortsp_1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1))) =>  ( (! [D:$i] :  ((r2_hidden D C) <=>  ((r2_hidden D (k2_zfmisc_1 c1__ortsp_1 c1__ortsp_1)) &  (? [E:$i] :  ((m1_subset_1 E c1__ortsp_1) &  (? [F:$i] :  ((m1_subset_1 F c1__ortsp_1) &  ( (D = (k1_domain_1 c1__ortsp_1 c1__ortsp_1 E F))  &  (F = c2__ortsp_1) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_symsp_1 D A)) ) ) ) )  =>  ( (D = (g1_symsp_1 A c1__ortsp_1 c3__ortsp_1 c2__ortsp_1 B C))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (~  ( (~  (E = (k4_struct_0 D)) )  &  ( (~  (F = (k4_struct_0 D)) )  &  ( (~  (G = (k4_struct_0 D)) )  &  ( (~  (H = (k4_struct_0 D)) )  &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (~  ( (~ (r1_orders_2 D I E))  &  ( (~ (r1_orders_2 D I F))  &  ( (~ (r1_orders_2 D I G))  &  (~ (r1_orders_2 D I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_orders_2 D E F) => (r1_orders_2 D (k4_vectsp_1 A D G E) F)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r1_orders_2 D F E) & (r1_orders_2 D G E))  => (r1_orders_2 D (k3_rlvect_1 D F G) E)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (~  ( (~ (r1_orders_2 D F E))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~ (r1_orders_2 D (k5_algstr_0 D G (k4_vectsp_1 A D H F)) E)) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r1_orders_2 D E (k5_algstr_0 D F G)) & (r1_orders_2 D F (k5_algstr_0 D G E)))  => (r1_orders_2 D G (k5_algstr_0 D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A D E)) = (k4_struct_0 A))  =>  ((k5_algstr_0 A (k8_group_1 A (k8_group_1 A (k8_group_1 A B F) G) C) (k8_group_1 A (k8_group_1 A (k8_group_1 A D F) G) E)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k1_algstr_0 A C B) (k1_algstr_0 A D B)) = (k5_algstr_0 A C D)) ) ) ) ) ) ) ) ) ).
tt(l8_petri_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  =>  (~  ( (~  (C = D) )  &  ((r1_tarski D C) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (~  ( ((k2_partfun1 B A G D) = F)  &  (~  ((k2_partfun1 B A G C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A C))  |  ((r1_xxreal_0 (k2_nat_1 C 1) A) & (r1_xxreal_0 A (k2_nat_1 C B))) )  =>  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 C B))) ) ) ) ) ) ) ) ).
tt(l8_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_polyalg1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_polyalg1 A))) =>  ( (C = (k10_polynom3 A))  =>  ( ((k6_algstr_0 (k1_polyalg1 A) B C) = B)  &  ((k6_algstr_0 (k1_polyalg1 A) C B) = B) ) ) ) ) ) ) ) ) ).
tt(l8_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_abian (u1_struct_0 A) B k6_numbers) C) = C) ) ) ) ) ) ) ).
tt(l8_qmax_1,ax, ((k1_funct_1 c2__qmax_1 k1_numbers) = 1) ).
tt(l8_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((r2_zfmisc_1 A B C D) => (r1_tarski (k2_enumset1 E F G H) (k10_xtuple_0 (k2_quaterni A B C D E F G H)))) ) ) ) ) ) ) ) ) ).
tt(l8_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v5_xxreal_2 (k1_rvsum_1 D)) =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C (k1_relset_1 A D))) |  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  ( (E = (k1_relset_1 A D))  & (r1_mesfunc6 A B D E)) ) ) )  | (r3_mesfunc6 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_rat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (A = (k7_xcmplx_0 B C))  => (r2_hidden A k3_numbers)) ) ) ) ) ) ).
tt(l8_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_real_lat)) =>  ((k2_lattices k3_real_lat A (k2_lattices k3_real_lat B C)) = (k2_lattices k3_real_lat (k2_lattices k3_real_lat A B) C)) ) ) ) ) ) ) ).
tt(l8_realset2,ax,(m1_subset_1 (k1_funct_7 k6_numbers 2) c4__realset2)).
tt(l8_rfunct_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) =>  ((k17_finseq_1 B A C) = C) ) ) ) ) ) ) ) ).
tt(l8_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) =>  ((k1_rlsub_2 A B C) = C) ) ) ) ) ) ) ) ).
tt(l8_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) =>  ((k1_rmod_3 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(l8_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k56_valued_1 k5_numbers k1_numbers A))) = k6_numbers) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(l8_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) =>  ((k1_rusub_2 A B C) = C) ) ) ) ) ) ) ) ).
tt(l8_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_funct_1 (k5_funcop_1 k35_binop_2 A (k6_partfun1 k1_numbers)) B) = (k11_binop_2 A B)) ) ) ) ) ).
tt(l8_scm_comp,ax, ((m2_subset_1 (k4_tarski k6_numbers k6_numbers) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 1) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 2) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 3) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) & (m2_subset_1 (k4_tarski k6_numbers 4) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp))) ) ) ) ).
tt(l8_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ((r1_tarski (k4_scmfsa_7 C D) B) => (r1_extpro_1 3 k1_scmfsa_2 B A)) ) ) ) ) ) ) ) ) ).
tt(l8_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( (~ (r2_hidden A (k1_tarski (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))))  &  ( (~ (r2_hidden A a_0_1_scmpds_2))  &  ( (~ (r2_hidden A a_0_2_scmpds_2))  &  ( (~ (r2_hidden A a_0_3_scmpds_2))  &  ( (~ (r2_hidden A a_0_4_scmpds_2))  &  (~ (r2_hidden A a_0_5_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(l8_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  ( ((r1_xxreal_0 3 D) &  ((r1_scpisort E B D) &  ((k3_finseq_1 E) = C) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scpinvar C D) B A) (k1_scmp_gcd 1)) = (k1_gr_cy_1 E))  & (r2_scmpds_6 (k1_scpinvar C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_series_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) & (v1_valued_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_partfun1 B k5_numbers) & (v1_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) &  ((v1_partfun1 C k5_numbers) & (v1_valued_0 C)) ) ) )  =>  ( (A = (k1_valued_1 B C))  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_funct_1 A D) = (k2_xcmplx_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(l8_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k3_square_1 A) (k3_xcmplx_0 B C)) => (r1_xxreal_0 (k18_complex1 A) (k6_square_1 (k3_xcmplx_0 B C)))) ) ) ) ) ) ) ).
tt(l8_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  & (r1_xxreal_0 1 (k18_complex1 A))) ) ) ) ).
tt(l8_sin_cos6,ax, ((k1_rcomp_1 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers)) (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers))) = (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) ).
tt(l8_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 k6_numbers (k10_binop_2 (k3_square_1 A) 1))) ) ) ).
tt(l8_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k5_square_1 (k3_sin_cos2 A)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k6_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 2 A)) 1)))  &  ((k5_square_1 (k6_sin_cos2 A)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 2 A)) 1))) ) ) ) ).
tt(l8_tex_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) <=> (m1_subset_1 A (k1_zfmisc_1 B))) ) ) ).
tt(l8_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 B)) &  ((v5_pre_topc C k5_topmetr B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 B)) &  ((v5_pre_topc D k5_topmetr B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 B))))) ) )  => (v5_pre_topc (k1_topalg_2 A B C D) (k2_borsuk_1 k5_topmetr k5_topmetr) B)) ) ) ) ) ) ) ) ).
tt(l8_topalg_5,ax, ((k1_pre_topc k5_topmetr (k2_struct_0 k5_topmetr)) = k5_topmetr) ).
tt(l8_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_topdim_1 B A) & (r2_hidden B (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) (k5_card_1 B)))) ) ) ) ) ).
tt(l8_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ((v5_waybel23 B) =>  ( ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) &  ((v2_tops_2 C B) &  ((m1_setfam_1 C (u1_struct_0 B)) &  ((v4_card_3 C) &  ((v2_topdim_1 C B) & (r1_xxreal_0 (k3_topdim_1 B C) A)) ) ) ) ) )  =>  ((v3_topdim_1 B) & (r1_xxreal_0 (k4_topdim_1 B) A)) )  &  (~  ((v3_topdim_1 B) &  ((r1_xxreal_0 (k4_topdim_1 B) A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k2_struct_0 B) = (k4_subset_1 (u1_struct_0 B) C D))  &  ((r1_xboole_0 C D) &  ((r1_xxreal_0 (k2_topdim_1 B C) (k3_xxreal_3 A 1)) & (r1_xxreal_0 (k2_topdim_1 B D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_topgen_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v4_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  & (r1_tarski (u1_pre_topc A) (u1_pre_topc B))) ) ) ) ) ) ).
tt(l8_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k1_group_2 A B) (k1_group_2 A C))) ) ) ) ) ) ) ).
tt(l8_topmetr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v6_metric_1 (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A))) &  ((v7_metric_1 (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A))) &  ((v8_metric_1 (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A))) &  ((v9_metric_1 (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A))) & (l1_metric_1 (g1_metric_1 (u1_struct_0 A) (u1_metric_1 A)))) ) ) ) ) ) ).
tt(l8_topreal2,ax, ((k17_euclid (k19_euclid 1 k6_numbers)) = 1) ).
tt(l8_toprealb,ax, (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 1 k32_sin_cos))) ).
tt(l8_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 (k7_setfam_1 (u1_struct_0 A) B)) => (v1_finset_1 B)) ) ) ) ) ).
tt(l8_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) & (r2_analoaf A B D C E))  =>  ((r1_aff_1 A B C D) |  ( (~ (r1_aff_1 A D E B))  &  ( (~ (r1_aff_1 A C B E))  &  (~ (r1_aff_1 A E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(l8_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) => (v1_group_1 A)) ) ) ).
tt(l8_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) =>  ((k1_vectsp_5 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(l8_xcmplx_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((k1_arytm_0 A B) = k6_numbers)  &  ((k1_arytm_0 A C) = k6_numbers) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(l8_xreal_0,ax,(m1_subset_1 k6_numbers k2_arytm_2)).
tt(l8_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 C D) & (r1_xxreal_0 (k2_xcmplx_0 B D) (k2_xcmplx_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(l8_xxreal_0,ax, (~ (r2_hidden k2_xxreal_0 k2_arytm_2)) ).
tt(l8_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (~  ( (~ (r2_hidden B (k4_zf_lang1 A)))  &  ( (~  (C = (k2_zf_lang k6_numbers)) )  &  ( (~  (B = (k2_zf_lang k6_numbers)) )  &  ( (~  (B = (k2_zf_lang 4)) )  &  (~  ((r2_hidden (k2_zf_lang 4) (k2_zf_model A)) <=> (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model (k13_zf_lang (k2_zf_lang 3) (k7_zf_lang (k5_zf_lang (k2_zf_lang 3) C) (k6_zf_lang1 (k6_zf_lang1 A (k2_zf_lang k6_numbers) B) (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l90_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r2_hidden (k9_real_1 (k5_series_1 2 A) 1) k6_asympt_1)) ) ) ) ).
tt(l90_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k1_real_1 (k17_complex1 A)) A) & (r1_xxreal_0 A (k17_complex1 A))) ) ) ).
tt(l90_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((v2_convex4 B A) =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (C = E)  &  ( (D = F)  &  ((r1_xxreal_0 k1_xboole_0 E) & (r1_xxreal_0 k1_xboole_0 F)) ) ) ) ) ) ) )  | (r1_tarski (k7_rusub_4 A (k19_convex4 A B C) (k19_convex4 A B D)) (k19_convex4 A B (k2_xcmplx_0 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(l90_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden D (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k8_cqc_lang A B C)) (k8_cqc_lang A B (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ) ).
tt(l90_descip_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D (k4_finseq_2 A k6_margrel1) (k4_finseq_2 C (k4_finseq_2 A k6_margrel1))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k4_finseq_2 B k6_margrel1) (k4_finseq_2 A k6_margrel1)) (k4_finseq_2 B k6_margrel1)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B k6_margrel1) (k4_finseq_2 A k6_margrel1)) (k4_finseq_2 B k6_margrel1))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1)) &  ((v3_funct_2 F (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1))))) ) )  =>  (! [G:$i] :  ((m2_finseq_2 G k6_margrel1 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1)) =>  (? [H:$i] :  ((m2_finseq_2 H k6_margrel1 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1)) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers (k4_finseq_2 B k6_margrel1)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 B k6_margrel1))))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers (k4_finseq_2 B k6_margrel1)) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 B k6_margrel1))))) )  &  ( ((k14_descip_1 B k6_margrel1 I k6_numbers) = (k4_descip_1 k6_margrel1 B (k3_funct_2 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) F G)))  &  ( ((k14_descip_1 B k6_margrel1 J k6_numbers) = (k5_descip_1 k6_margrel1 B (k3_funct_2 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) F G)))  &  ( (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers K) & (r1_xxreal_0 K (k6_xcmplx_0 C 1)))  =>  ( ((k14_descip_1 B k6_margrel1 I (k2_nat_1 K 1)) = (k14_descip_1 B k6_margrel1 J K))  &  ((k14_descip_1 B k6_margrel1 J (k2_nat_1 K 1)) = (k12_descip_1 B (k14_descip_1 B k6_margrel1 I K) (k2_binop_1 (k4_finseq_2 B k6_margrel1) (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1) E (k14_descip_1 B k6_margrel1 J K) (k7_partfun1 (k4_finseq_2 A k6_margrel1) D (k2_nat_1 K 1))))) ) ) ) )  &  (H = (k1_funct_1 (k2_funct_2 (k4_finseq_2 (k4_nat_1 2 B) k6_margrel1) F) (k9_binarith B B k6_margrel1 (k14_descip_1 B k6_margrel1 J C) (k14_descip_1 B k6_margrel1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l90_fib_num4,ax, (~ (r1_xxreal_0 (k13_complex1 2 2) (k13_complex1 (k6_xcmplx_0 3 (k7_square_1 5)) 2))) ).
tt(l90_finseq_1,ax, ((r2_hidden 3 (k2_finseq_1 4)) & (r2_hidden 4 (k2_finseq_1 4))) ).
tt(l90_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((r1_tarski (k7_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k22_fomodel4 B) (k25_fomodel4 B)) C) &  ((r1_tarski (k7_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B) (k26_fomodel4 B)) C) & (v10_fomodel4 A B C)) )  =>  ((v1_partfun1 (k6_fomodel4 B C A) (k35_fomodel1 B)) &  ((v3_relat_2 (k6_fomodel4 B C A)) &  ((v8_relat_2 (k6_fomodel4 B C A)) & (m1_subset_1 (k6_fomodel4 B C A) (k1_zfmisc_1 (k2_zfmisc_1 (k35_fomodel1 B) (k35_fomodel1 B))))) ) ) ) ) ) ) ) ) ).
tt(l90_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k7_geomtrap A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k7_geomtrap A B C))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k7_geomtrap A B C))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k7_geomtrap A B C))) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r2_analoaf (k7_geomtrap A B C) D E F G) &  ( ((k9_geomtrap (k7_geomtrap A B C) D H) = I)  &  ( ((k9_geomtrap (k7_geomtrap A B C) E J) = I)  &  ( ((k9_geomtrap (k7_geomtrap A B C) F K) = I)  &  ((k9_geomtrap (k7_geomtrap A B C) G L) = I) ) ) ) )  => (r2_analoaf (k7_geomtrap A B C) H J K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l90_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v2_glib_001 B A) => (v2_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(l90_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [H:$i] :  ((m2_finseq_1 H k5_numbers) =>  ( ( (E = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) F))  &  ( (G = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) F))  &  ( ((k3_finseq_1 F) = (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)) 1))  &  ((r4_graphsp H E C A) &  ( (C = (k1_seq_1 G (k2_nat_1 A D)))  &  ( ((k1_seq_1 E (k2_nat_1 A C)) = (k1_seq_1 G (k2_nat_1 A C)))  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 I) =>  ((r1_xxreal_0 (k3_finseq_1 H) I) | (r2_hidden (k1_seq_1 H I) (k14_graphsp E A))) ) ) ) ) ) ) ) ) )  =>  ( ((k7_graphsp E A) = k1_xboole_0)  |  ( (C = D)  |  ((r2_hidden D (k14_graphsp E A)) | (r4_graphsp (k8_finseq_1 k5_numbers H (k12_finseq_1 k5_numbers D)) G D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l90_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 A (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(l90_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ((v1_topreal2 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) D))))) =>  (! [I:$i] :  ( ((v2_xxreal_0 I) & (v1_xreal_0 I))  =>  ( ((r1_topreal1 (k15_euclid 2) A B E) &  ((r1_tarski E D) &  ((r1_tarski D (k1_topreal9 2 C I)) &  ((r2_hidden C H) &  ((r1_tarski (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) F) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) F)) E) & (r1_tarski F (k1_topreal9 2 C I))) ) ) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) E))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) E)))))) )  =>  (~  ((v5_pre_topc J (k2_brouwer 2 C I) (k1_pre_topc (k15_euclid 2) E)) &  ( ((k2_partfun1 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) E)) J E) = (k6_partfun1 E))  &  ( (H = F)  &  ((v3_connsp_1 H (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) D))) &  ( (G = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal9 2 C I) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) C)))  &  (! [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G))) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)))))) )  =>  (~  ((v5_pre_topc K (k2_brouwer 2 C I) (k1_pre_topc (k15_euclid 2) G)) &  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 (k2_brouwer 2 C I))) =>  ( ((r2_hidden L (k2_pre_topc (k15_euclid 2) F)) =>  ((k3_funct_2 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)) K L) = (k3_funct_2 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) E)) J L)) )  &  ((r2_hidden L (k3_subset_1 (u1_struct_0 (k15_euclid 2)) F)) =>  ((k3_funct_2 (u1_struct_0 (k2_brouwer 2 C I)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)) K L) = L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l90_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) (k4_cat_1 (k2_oppcat_1 A) D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l90_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v11_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l90_pepin,ax, ((k4_nat_d (k13_newton 3 32) (k4_pepin 3)) = 64) ).
tt(l90_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((r1_tarski B A) => (r1_xboole_0 B (k12_pnproc_1 C (k3_finseq_1 A)))) ) ) ) ) ) ) ).
tt(l90_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 k6_numbers (k9_prepower A B))) ) ) ) ) ).
tt(l90_toprealb,ax,(r1_tarski (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers) (k5_toprealb c26__toprealb))) (k2_rcomp_1 k6_numbers 1))).
tt(l90_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k7_xcmplx_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 C D)) = (k7_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ) ).
tt(l90_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (A = k6_numbers)  =>  ((k4_xxreal_3 A (k4_xxreal_3 B C)) = (k4_xxreal_3 (k4_xxreal_3 A B) C)) ) ) ) ) ) ) ) ).
tt(l91_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 5)) & (r2_hidden 2 (k2_finseq_1 5))) ).
tt(l91_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  ((k3_group_4 A (k6_finseq_1 (u1_struct_0 A))) = (k5_struct_0 A)) ) ) ).
tt(l91_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_geomtrap A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k7_geomtrap A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k7_geomtrap A B C))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k7_geomtrap A B C))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k7_geomtrap A B C))) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 (k7_geomtrap A B C))) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r1_analmetr A B C) &  ((r2_analoaf (k7_geomtrap A B C) D E F G) &  ((r2_analoaf (k7_geomtrap A B C) D E H I) &  ((r2_analoaf (k7_geomtrap A B C) D E J K) &  ((r2_analoaf (k7_geomtrap A B C) D E L M) & (r2_analoaf (k7_geomtrap A B C) F H J L)) ) ) ) )  =>  ( (D = E)  | (r2_analoaf (k7_geomtrap A B C) G I K M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (~ (v3_glib_001 B A))  <=> (r1_xxreal_0 3 (k3_finseq_1 B))) ) ) ) ) ).
tt(l91_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_graph_1 F) &  ((v6_graph_1 F) & (l1_graph_1 F)) ) )  =>  (! [G:$i] :  ( ((v7_graph_1 G F) & (m2_graph_1 G F))  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u4_struct_0 F) k8_graph_5) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 F) k8_graph_5)))) )  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 F)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 F)) =>  (~  ((r6_graphsp D F A H) &  ((r5_graph_5 F H) &  ( (I = B)  &  ( (~  (J = I) )  &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ((r8_graph_5 F J I G C H) &  ( (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  (! [L:$i] :  ((m2_subset_1 L k1_numbers k5_numbers) =>  ( ( ((k1_seq_1 E (k2_nat_1 A L)) = (k1_real_1 1))  &  ((r1_xxreal_0 1 L) &  ((r1_xxreal_0 L A) & (r2_hidden K C)) ) )  =>  ((k1_seq_1 D (k2_nat_1 (k2_nat_1 (k4_nat_1 2 A) (k4_nat_1 A K)) L)) = (k1_real_1 1)) ) ) ) ) )  &  ((k1_seq_1 E (k2_nat_1 A B)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((r2_group_6 (k5_group_6 B (k9_group_6 B A C)) (k10_group_6 B A C)) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_group_6 B (k9_group_6 B A C))) (u1_struct_0 (k10_group_6 B A C))) &  ((v1_group_6 D (k5_group_6 B (k9_group_6 B A C)) (k10_group_6 B A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_group_6 B (k9_group_6 B A C))) (u1_struct_0 (k10_group_6 B A C)))))) ) )  &  ((v3_funct_2 D (u1_struct_0 (k5_group_6 B (k9_group_6 B A C))) (u1_struct_0 (k10_group_6 B A C))) & (r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k10_group_6 B A C)) C (k1_partfun1 (u1_struct_0 B) (u1_struct_0 (k5_group_6 B (k9_group_6 B A C))) (u1_struct_0 (k5_group_6 B (k9_group_6 B A C))) (u1_struct_0 (k10_group_6 B A C)) (k8_group_6 B (k9_group_6 B A C)) D))) ) ) ) ) ) ) ) ) ) ).
tt(l91_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B))))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B))))) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~  (E = F) )  =>  (! [H:$i] :  ( ((v2_xxreal_0 H) & (v1_xreal_0 H))  =>  ( ((r1_tarski G B) &  ((r1_tarski B (k1_topreal9 2 A H)) &  ((r2_hidden A F) & (r1_tarski (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) C) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) C)) G)) ) )  =>  ((r1_xboole_0 (k1_topreal9 2 A H) C) |  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)))))) )  =>  (~  ((v5_pre_topc I (k2_brouwer 2 A H) (k1_pre_topc (k15_euclid 2) G)) &  ( ((k2_partfun1 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)) I G) = (k6_partfun1 G))  &  ( (E = C)  &  ((v3_connsp_1 E (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B))) &  ((v3_connsp_1 F (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) B))) &  ( (D = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal9 2 A H) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) A)))  &  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)))))) )  =>  (~  ((v5_pre_topc J (k2_brouwer 2 A H) (k1_pre_topc (k15_euclid 2) D)) &  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k2_brouwer 2 A H))) =>  ( ((r2_hidden K (k2_pre_topc (k15_euclid 2) C)) =>  ((k3_funct_2 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)) J K) = K) )  &  ((r2_hidden K (k3_subset_1 (u1_struct_0 (k15_euclid 2)) C)) =>  ((k3_funct_2 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)) J K) = (k3_funct_2 (u1_struct_0 (k2_brouwer 2 A H)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) G)) I K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_hidden D (k9_lpspace1 A B C)) =>  ((r3_mesfunc6 A B C D) &  (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( ((k1_funct_1 C (k3_subset_1 A E)) = k6_numbers)  &  ( (E = (k1_relset_1 A D))  & (r1_mesfunc6 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  ((v6_supinf_2 D) &  ((r1_mesfunc2 A B E) &  ( ((k1_relset_1 A E) = (k1_relset_1 A D))  &  ((v6_supinf_2 E) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A D)) => (r1_xxreal_0 (k12_supinf_2 E F) (k12_supinf_2 D F))) ) ) ) ) ) )  =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((r1_mesfunc2 A B (k4_mesfunc1 A D E)) &  ( (~  ((k1_relset_1 A (k4_mesfunc1 A D E)) = k1_xboole_0) )  &  ((v6_supinf_2 (k4_mesfunc1 A D E)) &  ((k1_mesfunc3 A B C D) = (k3_supinf_2 (k1_mesfunc3 A B C (k4_mesfunc1 A D E)) (k1_mesfunc3 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_oppcat_1 A))) =>  ( ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k3_graph_1 (k2_oppcat_1 A) D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k4_graph_1 (k2_oppcat_1 A) D)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l91_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v11_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l91_pepin,ax, ((k4_nat_d (k13_newton 3 64) (k4_pepin 3)) = 241) ).
tt(l91_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((r1_tarski C B) => (r1_tarski (k9_xtuple_0 (k12_pnproc_1 C A)) (k9_xtuple_0 (k12_pnproc_1 B A)))) ) ) ) ) ) ) ).
tt(l91_polyred,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_polynom1 A C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_polynom1 A C))) =>  ((r2_hidden F D) =>  ( (F = (k7_polynom1 A C))  |  ( (G = (k7_polynom1 A C))  | (r2_rewrite1 (k3_polyred A B C D) E (k3_rlvect_1 (k11_polynom1 A C) E (k8_group_1 (k11_polynom1 A C) G F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l91_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k9_prepower A B) = k6_numbers) ) ) ) ) ) ) ).
tt(l91_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_convex1 (k2_pre_topc A B) A)) ) ) ) ).
tt(l91_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) B) = k6_numbers)  =>  ((k2_extpro_1 2 k1_scmpds_2 B A) = A) ) ) ) ) ) ).
tt(l91_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_pre_topc B C)) ) ) ) ) ) ) ).
tt(l91_toprealb,ax, ((v1_funct_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers) (k5_toprealb c26__toprealb))) &  ((v1_funct_2 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers) (k5_toprealb c26__toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) & (m1_subset_1 (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers) (k5_toprealb c26__toprealb)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) ) ).
tt(l91_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k3_xcmplx_0 B C) (k3_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(l91_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (A = k6_numbers)  =>  ((k4_xxreal_3 B (k4_xxreal_3 A C)) = (k4_xxreal_3 (k4_xxreal_3 B A) C)) ) ) ) ) ) ) ) ).
tt(l92_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k4_complex1 A) = k6_numbers)  =>  ((r1_xxreal_0 (k3_complex1 A) k6_numbers) |  ((r1_xxreal_0 (k1_comptrig B) k6_numbers) |  ((r1_xxreal_0 k32_sin_cos (k1_comptrig B)) |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k4_complex2 A k5_complex1 B) (k4_complex2 k5_complex1 B A)) (k4_complex2 B A k5_complex1)) = k32_sin_cos)  &  ( (~ (r1_xxreal_0 (k4_complex2 k5_complex1 B A) k6_numbers))  &  (~ (r1_xxreal_0 (k4_complex2 B A k5_complex1) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(l92_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_ens_1 A))) =>  ( (E = (k2_cat_1 B C D))  =>  ((k3_funct_2 (u4_struct_0 (k8_cat_2 B B)) (k2_ens_1 (k16_ens_1 B)) (k22_ens_1 B) (k10_cat_2 B B (k4_cat_1 B C) (k4_cat_1 B D))) = (k4_cat_1 (k11_ens_1 A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l92_finseq_1,ax, ((r2_hidden 3 (k2_finseq_1 5)) & (r2_hidden 4 (k2_finseq_1 5))) ).
tt(l92_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v5_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v3_card_1 C (k1_int_2 (k19_fomodel1 A B))) & (m2_subset_1 C (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  =>  (! [D:$i] :  ( ((v3_card_1 D (k1_int_2 (k19_fomodel1 A B))) & (m2_subset_1 D (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  =>  ((v8_fomodel1 B A) => (v3_fomodel4 (k4_lang1 (k1_zfmisc_1 (k33_fomodel2 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_domain_1 (k1_zfmisc_1 (k33_fomodel2 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k36_fomodel4 A (k1_int_2 (k19_fomodel1 A B)) C D) (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k34_fomodel2 A)) (k1_fomodel3 A B C)) (k1_fomodel3 A B D)))) A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k27_fomodel4 A)) k1_xboole_0)) ) ) ) ) ) ) ) ) ).
tt(l92_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (? [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A (k4_vectsp_2 A)))  &  ((u1_struct_0 C) = B) ) ) ) ) ) ) ).
tt(l92_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (~  ( (~ (v3_glib_001 B A))  &  ((k3_finseq_1 B) = 1) ) )  &  (~  ( (~  ((k3_finseq_1 B) = 1) )  & (v3_glib_001 B A)) ) ) ) ) ) ) ).
tt(l92_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_graph_1 F) &  ((v6_graph_1 F) & (l1_graph_1 F)) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u4_struct_0 F) k8_graph_5) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 F) k8_graph_5)))) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 F)) =>  ( ((r6_graphsp C F A G) &  ( (H = 1)  &  ((r1_xxreal_0 1 A) &  ( (D = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C))  &  ( (E = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) C))  &  ((r2_hidden 1 (k14_graphsp D A)) &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 F)) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  (~  ( (~  (I = H) )  &  ( (I = J)  &  ( (~  ((k1_seq_1 D (k2_nat_1 A J)) = (k1_real_1 1)) )  &  (! [K:$i] :  ((m2_finseq_1 K k5_numbers) =>  (! [L:$i] :  ( ((v7_graph_1 L F) & (m2_graph_1 L F))  =>  (~  ((r4_graphsp K D J A) &  ( (! [M:$i] :  ((m2_subset_1 M k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 M) =>  ((r1_xxreal_0 (k3_finseq_1 K) M) | (r2_hidden (k1_seq_1 K M) (k14_graphsp D A))) ) ) )  &  ((r5_graphsp F L K) &  ((r8_graph_5 F H I L (k14_graphsp D A) G) &  ( ((k10_graph_5 F L G) = (k1_seq_1 D (k2_nat_1 (k4_nat_1 2 A) J)))  &  ( (~ (r2_hidden I (k14_graphsp D A)))  => (r9_graph_5 F L (k14_graphsp D A) H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( ((k1_seq_1 D (k2_nat_1 A J)) = (k1_real_1 1))  &  ((r1_xxreal_0 1 J) &  ((r1_xxreal_0 J A) & (r2_hidden I (k14_graphsp D A))) ) )  =>  ((k1_seq_1 C (k2_nat_1 (k2_nat_1 (k4_nat_1 2 A) (k4_nat_1 A I)) J)) = (k1_real_1 1)) ) ) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (~  ((r2_hidden I (k14_graphsp D A)) &  ((k1_seq_1 D (k2_nat_1 A I)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k7_graphsp D A) = k1_xboole_0)  |  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 F)) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  (~  ( (~  (I = H) )  &  ( (I = J)  &  ( (~  ((k1_seq_1 E (k2_nat_1 A J)) = (k1_real_1 1)) )  &  (! [K:$i] :  ((m2_finseq_1 K k5_numbers) =>  (! [L:$i] :  ( ((v7_graph_1 L F) & (m2_graph_1 L F))  =>  (~  ((r4_graphsp K E J A) &  ( (! [M:$i] :  ((m2_subset_1 M k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 M) =>  ((r1_xxreal_0 (k3_finseq_1 K) M) | (r2_hidden (k1_seq_1 K M) (k14_graphsp E A))) ) ) )  &  ((r5_graphsp F L K) &  ((r8_graph_5 F H I L (k14_graphsp E A) G) &  ( ((k10_graph_5 F L G) = (k1_seq_1 E (k2_nat_1 (k4_nat_1 2 A) J)))  &  ( (~ (r2_hidden I (k14_graphsp E A)))  => (r9_graph_5 F L (k14_graphsp E A) H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( ((k1_seq_1 E (k2_nat_1 A J)) = (k1_real_1 1))  &  ((r1_xxreal_0 1 J) &  ((r1_xxreal_0 J A) & (r2_hidden I (k14_graphsp E A))) ) )  =>  ((k1_seq_1 C (k2_nat_1 (k2_nat_1 (k4_nat_1 2 A) (k4_nat_1 A I)) J)) = (k1_real_1 1)) ) ) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (~  ((r2_hidden I (k14_graphsp E A)) &  ((k1_seq_1 E (k2_nat_1 A I)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l92_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  ( ( (C = B)  & (v3_connsp_1 C (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))  =>  ((v1_xboole_0 (k1_jordan2c 2 A)) |  (A = (k2_tops_1 (k15_euclid 2) B)) ) ) ) ) ) ) ) ) ).
tt(l92_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ((r2_hidden D (k1_lpspace2 A B C E)) => (r3_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l92_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( ( (! [E:$i] :  ((r2_hidden E (k30_modelc_1 A)) =>  ((k1_funct_1 C E) = (k35_modelc_1 A B E)) ) )  &  (! [E:$i] :  ((r2_hidden E (k30_modelc_1 A)) =>  ((k1_funct_1 D E) = (k35_modelc_1 A B E)) ) ) )  => (r2_funct_2 (k30_modelc_1 A) (k30_modelc_1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(l92_pepin,ax, ((k4_nat_d (k13_newton 3 128) (k4_pepin 3)) = 256) ).
tt(l92_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_convex1 (k1_tops_1 A B) A)) ) ) ) ).
tt(l92_toprealb,ax, ((k6_toprealb (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers)) = (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers)) ).
tt(l92_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (v1_xreal_0 A))  =>  ((k4_xxreal_3 B (k4_xxreal_3 A C)) = (k4_xxreal_3 (k4_xxreal_3 B A) C)) ) ) ) ) ) ) ) ).
tt(l93_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((k7_enumset1 A B C D E F G H I) = (k2_xboole_0 (k2_enumset1 A B C D) (k3_enumset1 E F G H I))) ) ) ) ) ) ) ) ) ) ).
tt(l93_finseq_1,ax,(r2_hidden 5 (k2_finseq_1 5))).
tt(l93_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v7_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v3_card_1 C (k1_int_2 (k19_fomodel1 A B))) & (m2_subset_1 C (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  =>  (! [D:$i] :  ( ((v3_card_1 D (k1_int_2 (k19_fomodel1 A B))) & (m2_subset_1 D (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  => (v3_fomodel4 (k1_tarski (k4_tarski (k2_xboole_0 (k36_fomodel4 A (k1_int_2 (k19_fomodel1 A B)) C D) (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k1_fomodel3 A B C))) (k1_fomodel3 A B D))) A (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))) (k28_fomodel4 A)) k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(l93_funct_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((k9_funct_7 (k9_funct_7 C A) B) = (k9_funct_7 C (k4_nat_1 A B)))  =>  ((k9_funct_7 (k9_funct_7 C A) (k2_nat_1 B 1)) = (k9_funct_7 C (k4_nat_1 A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(l93_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) & (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B (k1_glib_001 A C))) ) ) ) ) ) ) ).
tt(l93_jordan,ax, ((k17_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = (k1_real_1 1)) ).
tt(l93_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( ((k1_funct_1 C (k3_subset_1 A E)) = k6_numbers)  &  ( (E = (k1_relset_1 A D))  & (r1_mesfunc6 A B D E)) ) ) )  => (r1_tarski (k5_lpspace2 A B C D 1) (k13_lpspace1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(l93_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) (k4_cat_1 A D)) = (k4_cat_1 (k2_oppcat_1 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(l93_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_wellord1 A B) & (r1_tarski C B))  => (r2_wellord1 A C)) ) ) ) ) ).
tt(l93_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l93_pepin,ax, ((k4_nat_d (k13_newton 3 1) (k4_pepin 4)) = 3) ).
tt(l93_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_rltopsp1 (k2_pre_topc A B) A)) ) ) ) ).
tt(l93_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers)) = k1_numbers) ).
tt(l93_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (v1_xreal_0 A))  =>  ((k4_xxreal_3 A (k4_xxreal_3 B C)) = (k4_xxreal_3 (k4_xxreal_3 A B) C)) ) ) ) ) ) ) ) ).
tt(l94_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k9_newton A) 1)) ) ) ) ).
tt(l94_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A B E) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D B)))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B E) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A E C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l94_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 6)) & (r2_hidden 2 (k2_finseq_1 6))) ).
tt(l94_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  (! [F:$i] :  ( ((v5_fomodel1 F D) & (m1_subset_1 F (k1_fomodel1 D)))  =>  (~  ((v10_fomodel4 A D E) &  ((r2_hidden (k4_tarski B C) (k9_fomodel3 (k35_fomodel1 D) (k6_fomodel4 D E A) (k1_int_2 (k19_fomodel1 D F)))) &  (! [G:$i] :  ( ((v3_card_1 G (k1_int_2 (k19_fomodel1 D F))) & (m2_subset_1 G (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0)) (k35_fomodel1 D))))  =>  (! [H:$i] :  ( ((v3_card_1 H (k1_int_2 (k19_fomodel1 D F))) & (m2_subset_1 H (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 D)) (k1_tarski k1_xboole_0)) (k35_fomodel1 D))))  =>  (~  ( (G = B)  &  ( (H = C)  & (r1_tarski (k36_fomodel4 D (k1_int_2 (k19_fomodel1 D F)) G H) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l94_geomtrap,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  ( ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B B C) =>  ( (A = B)  &  (B = C) ) )  &  ( ( ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B E F) & (r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B G H))  =>  ( (A = B)  | (r2_analoaf (k8_geomtrap o_0_3_geomtrap) E F G H)) )  &  ( ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B C D) =>  ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) C D A B) & (r2_analoaf (k8_geomtrap o_0_3_geomtrap) B A D C)) )  &  ( (~  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k8_geomtrap o_0_3_geomtrap))) =>  ( (~ (r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B C K))  &  (~ (r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B K C)) ) ) ) )  &  (~  ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B C I) &  ((r2_analoaf (k8_geomtrap o_0_3_geomtrap) A B C J) &  ( (~  (A = B) )  &  (~  (I = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l94_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=>  (! [C:$i] :  ( ((v1_abian C) & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_abian D) & (m1_subset_1 D k5_numbers))  =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l94_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) => (m1_group_9 C A (k19_group_9 A B C D))) ) ) ) ) ) ) ).
tt(l94_jordan,ax, ((k17_euclid (k19_euclid 1 k6_numbers)) = 1) ).
tt(l94_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r1_tarski (k13_lpspace1 A B C D) (k5_lpspace2 A B C D 1))) ) ) ) ) ) ) ) ).
tt(l94_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (C = (k4_struct_0 B)) )  &  ((k1_laplace B (k4_group_1 B) C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(l94_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) (k3_graph_1 A D)) = (k4_graph_1 (k2_oppcat_1 B) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) (k4_graph_1 A D)) = (k3_graph_1 (k2_oppcat_1 B) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(l94_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l94_pepin,ax, ((k4_nat_d (k13_newton 3 2) (k4_pepin 4)) = 9) ).
tt(l94_toprealb,ax, ((k2_relset_1 k1_numbers (k1_fcont_1 (k10_real_1 1 (k8_real_1 2 k32_sin_cos)) k6_numbers)) = k1_numbers) ).
tt(l94_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k18_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( (A = (k4_domain_1 k5_numbers k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) k6_numbers C B))  & (r2_turing_1 (k2_finseq_4 k5_numbers C D) k18_turing_1 B))  =>  ((v2_turing_1 A k18_turing_1) &  ( ((k2_mcart_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) (k11_turing_1 k18_turing_1 A)) = C)  & (r2_turing_1 (k2_finseq_4 k5_numbers C k6_numbers) k18_turing_1 (k3_mcart_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) (k11_turing_1 k18_turing_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l95_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k9_newton B) (k9_newton A))) ) ) ) ) ).
tt(l95_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k2_bcialg_1 A C) (k1_bcialg_1 A (k4_struct_0 A) B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(l95_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ( ((k4_complex1 A) = k6_numbers)  &  ((k1_comptrig B) = k32_sin_cos) )  =>  ((r1_xxreal_0 (k3_complex1 A) k6_numbers) |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k4_complex2 A k6_numbers B) (k4_complex2 k6_numbers B A)) (k4_complex2 B A k6_numbers)) = k32_sin_cos)  &  ( (k6_numbers = (k4_complex2 k6_numbers B A))  &  (k6_numbers = (k4_complex2 B A k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(l95_finseq_1,ax, ((r2_hidden 3 (k2_finseq_1 6)) & (r2_hidden 4 (k2_finseq_1 6))) ).
tt(l95_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ( ((v5_fomodel1 D B) & (m1_subset_1 D (k1_fomodel1 B)))  =>  ( ((r1_tarski (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k27_fomodel4 B)) C) &  ((v10_fomodel4 A B C) & (v8_fomodel1 D B)) )  => (v2_fomodel3 (k4_fomodel3 B D A) B (k35_fomodel1 B) D (k6_fomodel4 B C A))) ) ) ) ) ) ) ) ).
tt(l95_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k48_gfacirc1 A B C)))  &  ( (H = (k1_funct_1 F D))  &  (I = (k1_funct_1 F E)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 G) (k9_margrel1 I)))  &  ( ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 E D) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 I) (k9_margrel1 H)))  &  ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 H) (k9_margrel1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l95_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=> (v4_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(l95_jordan,ax, ((k18_euclid (k19_euclid (k1_real_1 1) k6_numbers)) = k6_numbers) ).
tt(l95_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( ((k1_funct_1 C (k3_subset_1 A E)) = k6_numbers)  &  ( (E = (k1_relset_1 A D))  & (r1_mesfunc6 A B D E)) ) ) )  =>  ((k5_lpspace2 A B C D 1) = (k13_lpspace1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(l95_newton,ax,(r1_xxreal_0 (k1_nat_1 k6_numbers 1) (k2_newton 2 k6_numbers))).
tt(l95_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l95_pepin,ax, ((k4_nat_d (k13_newton 3 4) (k4_pepin 4)) = 81) ).
tt(l95_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v9_rltopsp1 (k2_pre_topc A B) A)) ) ) ) ).
tt(l95_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_complex1 (k3_xcmplx_0 (k3_xcmplx_0 A k7_complex1) B)) = (k1_real_1 (k8_real_1 A (k4_complex1 B))))  &  ( ((k4_complex1 (k3_xcmplx_0 (k3_xcmplx_0 A k7_complex1) B)) = (k8_real_1 A (k3_complex1 B)))  &  ( ((k3_complex1 (k3_xcmplx_0 A B)) = (k8_real_1 A (k3_complex1 B)))  &  ((k4_complex1 (k3_xcmplx_0 A B)) = (k8_real_1 A (k4_complex1 B))) ) ) ) ) ) ) ) ).
tt(l95_toprealb,ax, ((k1_pre_topc k2_topalg_2 (k2_struct_0 k2_topalg_2)) = k2_topalg_2) ).
tt(l96_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k9_newton B) A) &  ( (~ (r1_xxreal_0 (k9_newton (k2_nat_1 B 1)) A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k9_newton C) A) =>  ((r1_xxreal_0 (k9_newton (k2_nat_1 C 1)) A) |  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l96_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(l96_finseq_1,ax, ((r2_hidden 5 (k2_finseq_1 6)) & (r2_hidden 6 (k2_finseq_1 6))) ).
tt(l96_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ( ((v7_fomodel1 E D) & (m1_subset_1 E (k1_fomodel1 D)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  ( ((r1_tarski (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k28_fomodel4 D)) F) &  ((v10_fomodel4 A D F) &  ((r2_hidden (k4_tarski B C) (k9_fomodel3 (k35_fomodel1 D) (k6_fomodel4 D F A) (k1_int_2 (k19_fomodel1 D E)))) & (r2_hidden (k1_funct_1 (k2_fomodel3 D E) B) A)) ) )  => (r2_hidden (k1_funct_1 (k2_fomodel3 D E) C) A)) ) ) ) ) ) ) ) ) ) ).
tt(l96_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k48_gfacirc1 A B C)))  &  (H = (k1_funct_1 F E)) )  =>  ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp)) = (k2_binarith G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l96_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v4_glib_001 B A) => (v4_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(l96_jordan,ax, ((k18_euclid (k19_euclid 1 k6_numbers)) = k6_numbers) ).
tt(l96_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k30_modelc_1 A) (k30_modelc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A))))) )  =>  ( ( (! [E:$i] :  ((r2_hidden E (k30_modelc_1 A)) =>  ((k1_funct_1 C E) = (k38_modelc_1 A B E)) ) )  &  (! [E:$i] :  ((r2_hidden E (k30_modelc_1 A)) =>  ((k1_funct_1 D E) = (k38_modelc_1 A B E)) ) ) )  => (r2_funct_2 (k30_modelc_1 A) (k30_modelc_1 A) C D)) ) ) ) ) ) ) ) ) ).
tt(l96_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 (k1_nat_1 A 1) (k2_newton 2 A)) => (r1_xxreal_0 (k1_nat_1 (k1_nat_1 A 1) 1) (k2_newton 2 (k1_nat_1 A 1)))) ) ) ).
tt(l96_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l96_pepin,ax, ((k4_nat_d (k13_newton 3 8) (k4_pepin 4)) = 6561) ).
tt(l96_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ( ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (~ (r1_xxreal_0 E (k18_complex1 F)))  => (r1_tarski (k1_convex1 A C F) B)) ) )  &  (D = (a_3_31_rltopsp1 A C E)) )  =>  ((m1_connsp_2 (k5_setfam_1 (u1_struct_0 A) D) A (k4_struct_0 A)) &  ((v3_rltopsp1 (k5_setfam_1 (u1_struct_0 A) D) A) & (r1_tarski (k5_setfam_1 (u1_struct_0 A) D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l96_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( ((k3_complex1 (k13_complex1 B (k3_xcmplx_0 A k7_complex1))) = (k10_real_1 (k4_complex1 B) A))  &  ( ((k4_complex1 (k13_complex1 B (k3_xcmplx_0 A k7_complex1))) = (k1_real_1 (k10_real_1 (k3_complex1 B) A)))  &  ((k17_complex1 (k13_complex1 B A)) = (k10_real_1 (k17_complex1 B) A)) ) ) ) ) ) ) ) ).
tt(l96_toprealb,ax, ((v1_funct_1 c28__toprealb) &  ((v1_funct_2 c28__toprealb (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1))))) &  ((v5_pre_topc c28__toprealb (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb)) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) & (m1_subset_1 c28__toprealb (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb c26__toprealb))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))))))) ) ) ).
tt(l96_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 A (k7_xcmplx_0 1 B)) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(l97_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = (k1_bcialg_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l97_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  => (r1_tarski (k13_cohsp_1 (k13_cohsp_1 A)) A)) ) ).
tt(l97_finseq_1,ax, ((r2_hidden 1 (k2_finseq_1 7)) & (r2_hidden 2 (k2_finseq_1 7))) ).
tt(l97_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((k3_finseq_1 B) = A)  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  (! [E:$i] :  ((v1_finset_1 E) =>  (~  ( (E = (a_3_0_finseq_3 B C D))  &  ( (~ (r2_hidden (k1_funct_1 B D) C))  &  (~  ((k1_funct_1 (k1_finseq_3 B C) (k6_xcmplx_0 D (k5_card_1 E))) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  (! [E:$i] :  ((v1_finset_1 E) =>  (~  ( (E = (a_3_0_finseq_3 B C D))  &  ( (~ (r2_hidden (k1_funct_1 B D) C))  &  (~  ((k1_funct_1 (k1_finseq_3 B C) (k6_xcmplx_0 D (k5_card_1 E))) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l97_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ( (C = D)  =>  ((k18_fomodel0 B D A (k12_finseq_1 B C)) = (k9_finseq_1 A)) )  &  ( (~  (C = D) )  =>  ((k18_fomodel0 B D A (k12_finseq_1 B C)) = (k12_finseq_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(l97_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ( ((v7_fomodel1 E D) & (m1_subset_1 E (k1_fomodel1 D)))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  ( ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k24_fomodel4 D)) F) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k24_fomodel4 D)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k26_fomodel4 D)) F) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k26_fomodel4 D)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) F (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k28_fomodel4 D))) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))) (k28_fomodel4 D)))  &  ((v10_fomodel4 A D F) & (r2_hidden (k4_tarski B C) (k9_fomodel3 (k35_fomodel1 D) (k6_fomodel4 D F A) (k1_int_2 (k19_fomodel1 D E))))) ) ) )  =>  ((r2_hidden (k1_funct_1 (k2_fomodel3 D E) B) A) <=> (r2_hidden (k1_funct_1 (k2_fomodel3 D E) C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l97_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp)) = (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)) (k9_margrel1 K)))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 E D) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 K) (k9_margrel1 J)))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I))))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l97_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ((v4_glib_001 B A) & (r2_hidden C (k28_glib_000 A (k4_glib_001 A B))))  =>  ((r2_hidden C (k14_glib_001 A B)) | (v4_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(l97_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_2 C B) <=>  ((g3_algstr_0 (u1_struct_0 (k10_group_2 A C B)) (u2_algstr_0 (k10_group_2 A C B))) = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ).
tt(l97_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  ((k1_lattices (k21_interva1 A) B C) = (k1_lattices (k21_interva1 A) C B)) ) ) ) ) ) ) ).
tt(l97_jordan,ax, ((k17_euclid (k19_euclid k6_numbers 3)) = k6_numbers) ).
tt(l97_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 C) (k4_finseq_2 A (u1_struct_0 C))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 A (u1_struct_0 C))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  ((k4_rlvect_1 C (k11_fvsum_1 C (k8_finseq_1 (u1_struct_0 C) D F) (k8_finseq_1 (u1_struct_0 C) E G))) = (k3_rlvect_1 C (k4_rlvect_1 C (k11_fvsum_1 C D E)) (k4_rlvect_1 C (k11_fvsum_1 C F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l97_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l97_pepin,ax, ((k4_nat_d (k13_newton 3 16) (k4_pepin 4)) = (k2_nat_1 (k4_nat_1 164 332) 1)) ).
tt(l97_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))) (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))))).
tt(l97_toprealb,ax, ((k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1)) = k1_numbers) ).
tt(l97_xboole_1,ax, (! [A:$i] :  (! [B:$i] : (r1_xboole_0 (k3_xboole_0 A B) (k5_xboole_0 A B))) ) ).
tt(l97_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k7_xcmplx_0 1 A) (k7_xcmplx_0 B C)) = (k7_xcmplx_0 B (k3_xcmplx_0 C A))) ) ) ) ) ) ) ).
tt(l98_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 3 A) & (r1_xxreal_0 (k9_newton A) A)) ) ) ) ).
tt(l98_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A C D)) = (k1_bcialg_1 A (k1_bcialg_1 A D C) (k2_bcialg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(l98_facirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l98_finseq_1,ax, ((r2_hidden 3 (k2_finseq_1 7)) & (r2_hidden 4 (k2_finseq_1 7))) ).
tt(l98_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((k3_finseq_1 B) = A)  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  (! [E:$i] :  ((v1_finset_1 E) =>  (~  ( (E = (a_3_0_finseq_3 B C D))  &  ( (~ (r2_hidden (k1_funct_1 B D) C))  &  (~  ((k1_funct_1 (k1_finseq_3 B C) (k6_xcmplx_0 D (k5_card_1 E))) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l98_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E B) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ((k19_fomodel0 B A C (k7_finseq_1 D E)) = (k1_monoid_0 B (k19_fomodel0 B A C D) (k19_fomodel0 B A C E))) ) ) ) ) ) ) ) ) ) ).
tt(l98_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  ( ((k32_fomodel2 B C) = (k1_nat_1 A 1))  &  ( (~ (v5_fomodel2 C B))  &  (! [D:$i] :  ( ((v3_fomodel2 D B A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  ((k41_fomodel2 B C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l98_fomodel4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( ((r2_hidden C B) => (r2_hidden D B))  &  ( ((r2_hidden D B) => (r2_hidden C B))  &  (~ (r2_hidden (k1_domain_1 k6_margrel1 k6_margrel1 (k3_funct_2 A k6_margrel1 (k9_fomodel0 B A) C) (k3_funct_2 A k6_margrel1 (k9_fomodel0 B A) D)) (k3_fomodel2 k6_margrel1))) ) ) ) ) ) ) ) ) ) ) ).
tt(l98_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp)) = (k2_binarith (k9_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I))) K))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 3) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l98_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_diraf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_diraf A))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_diraf A))) & (r2_analoaf (k2_diraf A) B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(l98_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((r1_xxreal_0 (k3_finseq_1 B) 3) => (v4_glib_001 B A)) ) ) ) ) ).
tt(l98_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k21_interva1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_interva1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k21_interva1 A))) =>  ((k1_lattices (k21_interva1 A) B (k1_lattices (k21_interva1 A) C D)) = (k1_lattices (k21_interva1 A) (k1_lattices (k21_interva1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(l98_jordan,ax, ((k18_euclid (k19_euclid k6_numbers 3)) = 3) ).
tt(l98_ordinal6,ax, ((k13_ordinal6 1 k6_numbers) = (k3_ordinal5 k6_numbers)) ).
tt(l98_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(l98_pepin,ax, ((k4_nat_d (k13_newton 3 32) (k4_pepin 4)) = (k4_nat_1 123 503)) ).
tt(l98_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)) (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)))).
tt(l98_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((u1_struct_0 (k1_pre_topc A B)) = B) ) ) ) ) ).
tt(l98_toprealb,ax, ((k1_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k6_toprealb (k1_fcont_1 (k1_real_1 1) 1)) (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) = (k2_rcomp_1 k6_numbers 1)) ).
tt(l98_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k5_xboole_0 A B) = (k4_xboole_0 (k2_xboole_0 A B) (k3_xboole_0 A B))) ) ) ).
tt(l99_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A C B) = (k1_bcialg_1 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(l99_finseq_1,ax, ((r2_hidden 5 (k2_finseq_1 7)) & (r2_hidden 6 (k2_finseq_1 7))) ).
tt(l99_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((v3_fomodel2 C B (k1_nat_1 A 1)) =>  ((v15_fomodel1 C B) |  ((v5_fomodel2 C B) |  ( ((v3_fomodel2 (k40_fomodel2 B C) B A) & (m2_subset_1 (k40_fomodel2 B C) (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  &  ((v3_fomodel2 (k41_fomodel2 B C) B A) & (m2_subset_1 (k41_fomodel2 B C) (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ) ) ) ).
tt(l99_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v7_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B)) D) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k24_fomodel4 B)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k26_fomodel4 B)) D) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k26_fomodel4 B)))  &  ( ((k9_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) D (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k28_fomodel4 B))) = (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k28_fomodel4 B)))  & (v10_fomodel4 A B D)) ) )  => (v2_fomodel3 (k4_fomodel3 B C A) B (k35_fomodel1 B) C (k6_fomodel4 B D A))) ) ) ) ) ) ) ) ).
tt(l99_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp)))  &  ( (H = (k1_funct_1 F (k4_tarski (k10_finseq_1 E D) k4_twoscomp)))  &  (I = (k1_funct_1 F (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp))) ) )  =>  ((k1_funct_1 (k6_circuit2 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F) (k45_gfacirc1 (k48_gfacirc1 A B C) E D)) = (k9_margrel1 (k1_binarith (k1_binarith G H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l99_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_diraf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_diraf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_diraf A))) =>  ((r2_analoaf (k2_diraf A) B C D E) => (r2_analoaf (k2_diraf A) D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(l99_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A B D C) => (v5_glib_001 (k2_glib_001 A B D C) A)) ) ) ) ) ) ).
tt(l99_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k18_interva1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k18_interva1 A)) =>  ((k1_binop_1 (u2_lattices (k21_interva1 A)) (k1_binop_1 (u1_lattices (k21_interva1 A)) B C) C) = C) ) ) ) ) ) ) ).
tt(l99_jordan,ax, ((k17_euclid (k19_euclid k6_numbers (k1_real_1 3))) = k6_numbers) ).
tt(l99_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k30_modelc_1 A) (k30_modelc_1 A)) (k30_modelc_1 A))))) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 A)) & (r2_hidden E (k30_modelc_1 A)))  =>  ((k1_binop_1 B D E) = (k40_modelc_1 A D E)) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k30_modelc_1 A)) & (r2_hidden E (k30_modelc_1 A)))  =>  ((k1_binop_1 C D E) = (k40_modelc_1 A D E)) ) ) ) )  => (r8_binop_1 (k30_modelc_1 A) (k30_modelc_1 A) (k30_modelc_1 A) B C)) ) ) ) ) ) ) ).
tt(l99_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( ((k13_ordinal6 1 A) = (k3_ordinal5 A))  =>  ((k13_ordinal6 1 (k1_ordinal1 A)) = (k3_ordinal5 (k1_ordinal1 A))) ) ) ) ).
tt(l99_pepin,ax, ((k4_nat_d (k13_newton 3 64) (k4_pepin 4)) = (k2_nat_1 (k4_nat_1 14 1367) 1)) ).
tt(l99_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))) (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))))).
tt(l99_toprealb,ax,(r1_tarski (k2_relset_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k2_partfun1 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k1_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_relset_1 k1_numbers (k1_fcont_1 (k1_real_1 1) 1))))) (k6_toprealb (k1_fcont_1 (k1_real_1 1) 1)) (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (k2_rcomp_1 k6_numbers 1))).
tt(l99_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r2_hidden (k4_xxreal_3 A B) k1_numbers) &  ( (~  ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers)) )  &  (~  ((k4_xxreal_3 A B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l9_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r5_aff_1 A E F) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ((r2_hidden D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_hidden G F) & (r2_analoaf A B D C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = D) )  & (r2_diraf A B C C D)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (E = F) )  &  ((r2_diraf A B C E F) &  ((r2_diraf A B E E C) & (r2_diraf A B F F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_0)) &  ((k1_algstr_0 k3_algstr_0 C A) = B) ) ) ) ) ) ) ).
tt(l9_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  ((k1_algstr_3 k3_algstr_3 (k5_struct_0 k3_algstr_3) A (k4_struct_0 k3_algstr_3)) = A) ) ) ).
tt(l9_ami_2,ax,(r2_hidden k5_numbers k1_ami_2)).
tt(l9_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 C (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = 1)  =>  ((k5_memstr_0 A (k4_amistd_1 A) (k2_extpro_1 A (k4_amistd_1 A) B C)) = (k1_ordinal1 (k5_memstr_0 A (k4_amistd_1 A) C))) ) ) ) ) ) ) ) ).
tt(l9_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  |  (B = (k3_rlvect_1 A (k1_rlvect_1 A C (k1_real_1 (k8_real_1 (k2_real_1 E) F))) (k1_rlvect_1 A D (k1_real_1 (k8_real_1 (k2_real_1 E) G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k1_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 E F)) (k1_rlvect_1 A C (k8_real_1 E G))) (k1_rlvect_1 A D (k8_real_1 E H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_arytm_2,ax,(r1_tarski (k7_subset_1 (k1_zfmisc_1 k5_arytm_3) k1_arytm_2 a_0_1_arytm_2) k2_arytm_2)).
tt(l9_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) C) = (k10_real_1 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) ) ) ) ) ).
tt(l9_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_4 A B C) B) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A D B) C) => (r1_bcialg_1 A D (k1_bcialg_4 A B C))) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) ) ) ).
tt(l9_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( ((k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A A) = k6_numbers)  =>  (A = (k4_struct_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1))) )  &  ( ( (A = (k4_struct_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1)))  =>  ((k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A A) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A A)) &  ( ((k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A B) = (k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) B A))  &  ( ((k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) (k1_algstr_0 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A B) C) = (k7_real_1 (k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A C) (k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) B C)))  &  ((k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) (k1_rlvect_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A D) B) = (k8_real_1 D (k1_bhsp_1 (g1_bhsp_1 (u1_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (k4_struct_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_algstr_0 (k1_rlsub_1 o_0_5_bhsp_1)) (u1_rlvect_1 (k1_rlsub_1 o_0_5_bhsp_1)) c2__bhsp_1) A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_borsuk_2,ax, ((r2_hidden k6_numbers (k1_rcomp_1 k6_numbers 1)) & (r2_hidden 1 (k1_rcomp_1 k6_numbers 1))) ).
tt(l9_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C E)) (k5_bvfunc_1 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A D E))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A D B) (k9_bvfunc_1 A E C)) (k5_bvfunc_1 A D E)) (k1_bvfunc_1 A (k2_bvfunc_1 A B C))))) ) ) ) ) ) ) ) ) ) ).
tt(l9_cfdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 2)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid 2)) =>  ( ( (E = (k10_finseq_1 A B))  &  (F = (k10_finseq_1 C D)) )  =>  ( ((k7_euclid 2 E F) = (k10_finseq_1 (k7_real_1 A C) (k7_real_1 B D)))  &  ((k8_euclid 2 E F) = (k10_finseq_1 (k9_real_1 A C) (k9_real_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_collsp,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 c4__collsp)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 c4__collsp)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 c4__collsp)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 c4__collsp)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 c4__collsp)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 c4__collsp)) =>  ( ( (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  (~  (B = C) ) ) ) )  => (r2_hidden (k4_domain_1 (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) A B C) (u1_collsp c4__collsp)))  &  ( ((r2_hidden (k4_domain_1 (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) A B D) (u1_collsp c4__collsp)) &  ((r2_hidden (k4_domain_1 (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) A B E) (u1_collsp c4__collsp)) & (r2_hidden (k4_domain_1 (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) A B F) (u1_collsp c4__collsp))) )  =>  ( (A = B)  | (r2_hidden (k4_domain_1 (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) (u1_struct_0 c4__collsp) D E F) (u1_collsp c4__collsp))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) & (v2_compos_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((r2_hidden C (k4_finseq_1 (k5_xtuple_0 B))) => (r1_tarski (k1_funct_1 (k10_card_3 (k3_compos_0 A (k2_compos_0 A B))) C) k5_numbers)) ) ) ) ) ) ).
tt(l9_comptrig,ax, (~ (r1_xxreal_0 (k7_real_1 k32_sin_cos (k10_real_1 k32_sin_cos 2)) (k7_real_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(l9_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_convex1 A B 1) = B) ) ) ) ) ).
tt(l9_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_convfun1 A k4_convfun1))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_convfun1 A k4_convfun1))) =>  ( ( (F = (k1_domain_1 (u1_struct_0 A) k1_numbers B D))  &  (G = (k1_domain_1 (u1_struct_0 A) k1_numbers C E)) )  =>  ((k1_algstr_0 (k3_convfun1 A k4_convfun1) F G) = (k1_domain_1 (u1_struct_0 A) k1_numbers (k1_algstr_0 A B C) (k9_binop_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A D E) A))  => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B D) (k7_cqc_lang A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  & (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace A)) (k55_valued_1 k5_numbers k2_numbers (k2_csspace A))))) ) ) ).
tt(l9_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) )  =>  ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A))) = k6_numbers) ) ) ) ) ).
tt(l9_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k9_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 6 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 A (k6_euclid 3 B)) = (k1_euclid_8 (k10_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k10_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k10_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(l9_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ( (~  (B = C) )  &  ((k12_euclid (k8_euclid A B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(l9_fib_fusc,ax, (~  ((k10_ami_3 k6_numbers) = (k10_ami_3 3)) ) ).
tt(l9_fib_num4,ax, ((k13_complex1 k1_fib_num k2_fib_num) = (k13_complex1 (k6_xcmplx_0 (k4_xcmplx_0 3) (k7_square_1 5)) 2)) ).
tt(l9_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k1_pre_ff B) (k1_pre_ff A))) ) ) ) ) ).
tt(l9_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) =>  ((k1_finsop_1 A (k8_finseq_1 A C (k12_finseq_1 A B)) D) = (k5_binop_1 A D (k1_finsop_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(l9_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xboole_0 (k4_finseq_2 C A) (k4_finseq_2 D B)))  =>  (C = D) ) ) ) ) ) ) ) ).
tt(l9_fomodel3,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ((k8_fomodel3 B C D A) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ) ) ) ) ) ) ) ) ).
tt(l9_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_frechet A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( ((k9_xtuple_0 D) = k5_numbers)  &  ( ((k10_xtuple_0 D) = C)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k1_funct_1 D F) (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_fsm_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ((k7_finseq_1 (k2_finseq_3 (k3_finseq_1 A) A) B) = (k7_finseq_1 A (k2_finseq_3 1 B))) ) ) ) ) ) ) ) ).
tt(l9_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k1_glib_002 A C)) =>  ((k1_glib_002 A B) = (k1_glib_002 A C)) ) ) ) ) ) ) ) ).
tt(l9_goboard6,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))) =>  ( (B = C)  =>  ((k1_tops_1 A B) = (k1_tops_1 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) C)) ) ) ) ) ) ) ) ).
tt(l9_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( (B = (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A))  =>  ((k2_goboard2 B) = (k2_goboard2 A)) ) ) ) ) ) ).
tt(l9_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_group_7 A B C)) (u1_struct_0 (k2_group_12 A B C))) &  ((v1_group_6 D (k1_group_7 A B C) (k2_group_12 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_group_7 A B C)) (u1_struct_0 (k2_group_12 A B C)))))) ) )  &  ((v3_funct_2 D (u1_struct_0 (k1_group_7 A B C)) (u1_struct_0 (k2_group_12 A B C))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_group_7 A B C))) =>  ((k3_funct_2 (u1_struct_0 (k1_group_7 A B C)) (u1_struct_0 (k2_group_12 A B C)) D E) = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))))  => (v1_finset_1 (k1_heyting2 A B C))) ) ) ) ) ).
tt(l9_holder_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) =>  ((k1_seq_1 A C) = k6_numbers) ) ) )  =>  ((k1_seq_1 (k3_series_1 A) B) = k6_numbers) ) ) ) ) ) ).
tt(l9_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (D = B)  =>  ( (B = C)  |  ( ( (~  ( (~ (r1_aff_1 A B C D))  &  ((r1_aff_1 A B D E) & (r2_analoaf A C D F E)) ) )  &  (~  ((r1_aff_1 A B C D) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (~ (r1_aff_1 A B C G))  &  ((r1_aff_1 A B G H) &  ((r2_analoaf A C G F H) &  ((r2_analoaf A G D H E) & (r1_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) )  |  (E = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A C))  => (r1_int_1 A (k6_int_1 B C))) ) ) ) ) ) ) ).
tt(l9_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A C))  => (r1_int_1 A (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(l9_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 A k1_numbers)) ) ).
tt(l9_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (m1_subset_1 (a_1_1_jordan1 A) (k1_zfmisc_1 (k1_euclid 2)))) ) ).
tt(l9_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid 2))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k3_real_1 B 1) (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k3_real_1 D 1) (k1_matrix_1 (k1_jordan8 A C))) &  ( (E = G)  & (r2_hidden E (k3_goboard5 (k1_jordan8 A C) B D))) ) ) ) )  =>  ((r1_xxreal_0 F k6_numbers) |  ((r1_xxreal_0 (k6_real_1 F 4) (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A C) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A C) 1 2))) |  ((r1_xxreal_0 (k6_real_1 F 4) (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A C) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A C) 2 1))) | (r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k9_metric_1 (k14_euclid 2) G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_jordan1d,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 k6_numbers (k9_real_1 (k8_real_1 2 A) 2))) ) ) ).
tt(l9_jordan1h,ax,(r6_relat_2 k1_jordan1h k1_numbers)).
tt(l9_jordan_a,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((g1_pre_topc (u1_struct_0 (k2_borsuk_1 A B)) (u1_pre_topc (k2_borsuk_1 A B))) = (k2_borsuk_1 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ).
tt(l9_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) D) (k8_cqc_lang A B D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(l9_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_mathmorp A C (k6_domain_1 (u1_struct_0 A) B)) = (k1_mathmorp A B (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(l9_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ( (~ (v6_struct_0 G))  &  ((v13_algstr_0 G) &  ((v33_algstr_0 G) &  ((v3_group_1 G) &  ((v5_group_1 G) &  ((v2_rlvect_1 G) &  ((v3_rlvect_1 G) &  ((v4_rlvect_1 G) &  ((v4_vectsp_1 G) &  ((v5_vectsp_1 G) & (l6_algstr_0 G)) ) ) ) ) ) ) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 G)) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 G) C A) =>  (! [J:$i] :  ((m1_matrix_1 J (u1_struct_0 G) C A) =>  (! [K:$i] :  ((m2_finseq_1 K (u1_struct_0 G)) =>  (! [L:$i] :  ((m2_finseq_1 L (u1_struct_0 G)) =>  ( ((r2_hidden B (k2_finseq_1 C)) &  ((r2_hidden D (k2_finseq_1 (k1_matrix_1 I))) &  ((r2_hidden E (k4_finseq_1 I)) &  ( (K = (k8_matrix_1 (u1_struct_0 G) I F))  &  ( (L = (k8_matrix_1 (u1_struct_0 G) I E))  &  (J = (k3_matrix11 F C A (u1_struct_0 G) I (k3_fvsum_1 G (k9_fvsum_1 G L H) K))) ) ) ) ) )  =>  ( ( (B = F)  =>  ((k3_matrix_1 (u1_struct_0 G) J B D) = (k1_algstr_0 G (k8_group_1 G H (k3_matrix_1 (u1_struct_0 G) I E D)) (k3_matrix_1 (u1_struct_0 G) I F D))) )  &  ( (~  (B = F) )  =>  ((k3_matrix_1 (u1_struct_0 G) J B D) = (k3_matrix_1 (u1_struct_0 G) I B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((k4_finseq_1 (k3_fvsum_1 B C D)) = (k9_subset_1 k5_numbers (k4_finseq_1 C) (k4_finseq_1 D))) ) ) ) ) ) ) ) ) ).
tt(l9_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_modelc_2 A B) => (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 (k13_modelc_2 B)))) ) ) ) ) ).
tt(l9_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) &  ((v2_dtconstr A) & (l1_lang1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((m2_subset_1 B (u1_struct_0 A) (k6_dtconstr A)) | (m2_subset_1 B (u1_struct_0 A) (k7_dtconstr A)))  &  (~  ((m2_subset_1 B (u1_struct_0 A) (k6_dtconstr A)) & (m2_subset_1 B (u1_struct_0 A) (k7_dtconstr A))) ) ) ) ) ) ) ).
tt(l9_numbers,ax,(r1_tarski k5_numbers k4_numbers)).
tt(l9_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r1_ordinal2 B A) &  ((k9_xtuple_0 A) = k1_xboole_0) ) ) ) ) ) ) ).
tt(l9_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k8_group_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) = (k3_rlvect_1 A (k8_group_1 A B D) (k3_rlvect_1 A (k4_algstr_0 A (k8_group_1 A B E)) (k4_algstr_0 A (k8_group_1 A C (k5_algstr_0 A D E)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) = (k5_algstr_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(l9_pdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 1)) =>  ( ((k12_finseq_1 k1_numbers A) = B)  =>  ((k17_complex1 A) = (k12_euclid B)) ) ) ) ) ) ).
tt(l9_petri_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  =>  (~  ( (~  (C = D) )  &  ((a_4_2_petri_2 A B C E) = (a_4_2_petri_2 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_projdes1 A B C D E) => (r1_projdes1 A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_qmax_1,ax, (! [A:$i] :  ((m1_prob_1 A k1_numbers k12_prob_1) =>  (! [B:$i] :  ((m1_prob_1 B k1_numbers k12_prob_1) =>  ((r1_xboole_0 A B) =>  ((k3_funct_2 k12_prob_1 k1_numbers c2__qmax_1 (k6_prob_1 k1_numbers k12_prob_1 A B)) = (k7_real_1 (k3_funct_2 k12_prob_1 k1_numbers c2__qmax_1 A) (k3_funct_2 k12_prob_1 k1_numbers c2__qmax_1 B))) ) ) ) ) ) ).
tt(l9_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_mesfunc6 A B D) & (r2_hidden (k1_relset_1 A D) B))  =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C (k1_relset_1 A D))) | (r3_mesfunc6 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (v3_xxreal_2 (k10_prob_1 A))) ) ) ).
tt(l9_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k2_lattices k3_real_lat A (k1_lattices k3_real_lat A B)) = A) ) ) ) ) ).
tt(l9_realset2,ax, ((k9_xtuple_0 (k13_funcop_1 1 1 k6_numbers)) = (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 1))) ).
tt(l9_rfinseq,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) =>  ((k17_finseq_1 B A C) = C) ) ) ) ) ) ) ) ).
tt(l9_rfunct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (k10_xtuple_0 A)))  =>  ((k8_relat_1 A (k1_tarski B)) = k1_xboole_0) ) ) ) ) ).
tt(l9_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (? [C:$i] :  ( ((v1_partfun1 C (u1_struct_0 A)) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  ((r2_hidden D (u1_struct_0 A)) &  ((r2_hidden E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (F = D)  &  ( (G = E)  & (r2_hidden (k5_algstr_0 A F G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B D) => (m1_rusub_1 (k2_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(l9_scmfsa6c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v1_scmfsa6b A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m (k1_scmfsa6b A B C))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b A B C))) ) ) ) ) ) ) ).
tt(l9_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 k1_scmpds_2 (k1_scmpds_8 A B C))) = (k2_nat_1 (k5_card_1 C) 3)) ) ) ) ) ) ) ).
tt(l9_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( ((k6_xcmplx_0 1 (k13_complex1 1 (k2_nat_1 A 2))) = (k13_complex1 (k2_nat_1 A 1) (k2_nat_1 A 2)))  &  ((k13_complex1 1 (k9_newton (k2_nat_1 A 1))) = (k13_complex1 (k2_nat_1 A 2) (k4_nat_1 (k9_newton (k2_nat_1 A 1)) (k2_nat_1 A 2)))) ) ) ) ).
tt(l9_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_square_1 A)) (k6_square_1 (k3_xcmplx_0 B C))) 2) (k3_square_1 B)) (k6_square_1 (k3_xcmplx_0 A C))) 2) (k3_square_1 C)) (k6_square_1 (k3_xcmplx_0 A B))) = (k1_newton (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 A) B) C) 3)) ) ) ) ) ) ) ).
tt(l9_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((r2_hidden C A) => (m1_subset_1 (k2_xboole_0 B (k1_tarski C)) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(l9_simplex2,ax,(r2_hidden k1_xboole_0 k1_numbers)).
tt(l9_sin_cos6,ax, ((k1_rcomp_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers) (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) k6_numbers))) = (k1_rcomp_1 k6_numbers k32_sin_cos)) ).
tt(l9_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k3_sin_cos2 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k3_sin_cos2 A)))  &  ( ((k6_sin_cos2 (k4_xcmplx_0 A)) = (k6_sin_cos2 A))  &  ( ((k9_sin_cos2 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k9_sin_cos2 A)))  &  ( ((k1_sin_cos5 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k1_sin_cos5 A)))  &  ( ((k2_sin_cos5 (k4_xcmplx_0 A)) = (k2_sin_cos5 A))  &  ((k3_sin_cos5 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k3_sin_cos5 A))) ) ) ) ) ) ) ) ).
tt(l9_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_borsuk_2 E B C D) =>  (! [F:$i] :  ((m1_borsuk_2 F B C D) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 (k1_topalg_2 A B E F) G k6_numbers) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) E G))  &  ( ((k1_binop_1 (k1_topalg_2 A B E F) G 1) = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) F G))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 (k1_topalg_2 A B E F) k6_numbers H) = C)  &  ((k1_binop_1 (k1_topalg_2 A B E F) 1 H) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_topalg_5,ax,(r1_xxreal_0 (k9_real_1 1 k6_numbers) 1)).
tt(l9_topreal2,ax, ((k18_euclid (k19_euclid 1 k6_numbers)) = k6_numbers) ).
tt(l9_toprealb,ax, (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) ).
tt(l9_uniform1,ax, ((k4_topmetr k6_numbers 1) = (k3_pcomps_1 (k2_topmetr k6_numbers 1))) ).
tt(l9_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_vectsp_4 F A C) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  ((r1_funct_2 (u1_struct_0 E) (u1_struct_0 F) (u1_struct_0 E) (u1_struct_0 C) G (k8_matrlin2 A B C E D)) =>  ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 F)) &  ((v13_vectsp_1 G E F) &  ((v1_mod_2 G A E F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(l9_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) =>  ((k5_struct_0 A) = (k1_group_1 A)) ) ) ) ).
tt(l9_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) => (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(l9_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (v8_relat_2 B)) ) ) ) ).
tt(l9_xreal_0,ax, (~ (r2_hidden k6_numbers (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ).
tt(l9_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 B A) B)) ) ) ) ) ) ).
tt(l9_xxreal_0,ax, (~ (r2_hidden k1_xxreal_0 (k2_zfmisc_1 (k1_tarski k6_numbers) k2_arytm_2))) ).
tt(l9_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_2 (k1_tarski A)) = A) ) ) ).
tt(l9_yellow_6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  ( (D = F)  &  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (r1_orders_2 A C D)) ) )  => (r1_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(projectivity_k10_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  =>  ((k10_euclid A (k10_euclid A B)) = (k10_euclid A B)) ) ) ).
tt(projectivity_k13_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k13_seq_4 (k13_seq_4 A)) = (k13_seq_4 A)) ) ) ).
tt(projectivity_k16_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k16_complex1 (k16_complex1 A)) = (k16_complex1 A)) ) ) ).
tt(projectivity_k17_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k17_complex1 A)) = (k17_complex1 A)) ) ) ).
tt(projectivity_k18_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k18_complex1 (k18_complex1 A)) = (k18_complex1 A)) ) ) ).
tt(projectivity_k1_abcmiz_1,ax, (! [A:$i] :  ((k1_abcmiz_1 (k1_abcmiz_1 A)) = (k1_abcmiz_1 A)) ) ).
tt(projectivity_k1_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_absvalue (k1_absvalue A)) = (k1_absvalue A)) ) ) ).
tt(projectivity_k1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k1_afinsq_1 (k1_afinsq_1 A)) = (k1_afinsq_1 A)) ) ) ).
tt(projectivity_k1_card_1,ax, (! [A:$i] :  ((k1_card_1 (k1_card_1 A)) = (k1_card_1 A)) ) ).
tt(projectivity_k1_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_int_1 (k1_int_1 A)) = (k1_int_1 A)) ) ) ).
tt(projectivity_k1_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_int_2 (k1_int_2 A)) = (k1_int_2 A)) ) ) ).
tt(projectivity_k1_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ((k1_scmfsa_m (k1_scmfsa_m A)) = (k1_scmfsa_m A)) ) ) ).
tt(projectivity_k1_tdlat_2,ax, (! [A:$i,B:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ((k1_tdlat_2 A (k1_tdlat_2 A B)) = (k1_tdlat_2 A B)) ) ) ).
tt(projectivity_k1_tops_1,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_tops_1 A (k1_tops_1 A B)) = (k1_tops_1 A B)) ) ) ).
tt(projectivity_k21_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  =>  ((k21_seq_4 A (k21_seq_4 A B)) = (k21_seq_4 A B)) ) ) ).
tt(projectivity_k2_absvalue,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k2_absvalue (k2_absvalue A)) = (k2_absvalue A)) ) ) ).
tt(projectivity_k2_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_int_1 (k2_int_1 A)) = (k2_int_1 A)) ) ) ).
tt(projectivity_k2_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  ((k2_int_3 (k2_int_3 A)) = (k2_int_3 A)) ) ) ).
tt(projectivity_k2_pre_topc,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_pre_topc A (k2_pre_topc A B)) = (k2_pre_topc A B)) ) ) ).
tt(projectivity_k3_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k3_euclid (k3_euclid A)) = (k3_euclid A)) ) ) ).
tt(projectivity_k3_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k3_extreal1 (k3_extreal1 A)) = (k3_extreal1 A)) ) ) ).
tt(projectivity_k3_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_finseq_1 (k3_finseq_1 A)) = (k3_finseq_1 A)) ) ) ).
tt(projectivity_k54_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k54_valued_1 (k54_valued_1 A)) = (k54_valued_1 A)) ) ) ).
tt(projectivity_k55_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k55_valued_1 A B (k55_valued_1 A B C)) = (k55_valued_1 A B C)) ) ) ).
tt(projectivity_k56_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k56_valued_1 A B (k56_valued_1 A B C)) = (k56_valued_1 A B C)) ) ) ).
tt(projectivity_k5_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k5_card_1 (k5_card_1 A)) = (k5_card_1 A)) ) ) ).
tt(projectivity_k5_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((k5_rfinseq2 (k5_rfinseq2 A)) = (k5_rfinseq2 A)) ) ) ).
tt(projectivity_k5_seqfunc,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ((k5_seqfunc A (k5_seqfunc A B)) = (k5_seqfunc A B)) ) ) ).
tt(projectivity_k6_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k6_measure6 (k6_measure6 A)) = (k6_measure6 A)) ) ) ).
tt(projectivity_k6_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ((l1_memstr_0 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((k6_memstr_0 A B (k6_memstr_0 A B C)) = (k6_memstr_0 A B C)) ) ) ).
tt(projectivity_k6_rfinseq2,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((k6_rfinseq2 (k6_rfinseq2 A)) = (k6_rfinseq2 A)) ) ) ).
tt(projectivity_k7_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k7_group_2 (k7_group_2 A)) = (k7_group_2 A)) ) ) ).
tt(projectivity_k7_random_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_random_1 C A B)) )  =>  ((k7_random_1 A B (k7_random_1 A B C)) = (k7_random_1 A B C)) ) ) ).
tt(projectivity_k8_memstr_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) ) )  =>  ((k8_memstr_0 A B (k8_memstr_0 A B C)) = (k8_memstr_0 A B C)) ) ) ).
tt(rd10_xtuple_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((k5_xtuple_0 (k6_xtuple_0 A B C D)) = C) ) ).
tt(rd11_xtuple_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((k2_xtuple_0 (k6_xtuple_0 A B C D)) = D) ) ).
tt(rd12_xtuple_0,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  ((k6_xtuple_0 (k7_xtuple_0 A) (k8_xtuple_0 A) (k5_xtuple_0 A) (k2_xtuple_0 A)) = A) ) ) ).
tt(rd1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k1_ordinal4 A k1_xboole_0) = A) ) ) ).
tt(rd1_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_cat_1 C A B B)) )  =>  ((k5_cat_1 A B B B (k4_cat_1 A B) C) = C) ) ) ).
tt(rd1_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((k5_compos_1 A B k6_numbers) = B) ) ) ).
tt(rd1_extpro_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) ) ) ) )  =>  ((k5_extpro_1 A B C D k6_numbers) = D) ) ) ).
tt(rd1_funct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) &  ((v3_binop_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) ) )  & (m1_subset_1 C A))  =>  ((k5_binop_1 A B C C) = C) ) ) ).
tt(rd1_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_xboole_0 B)) ) )  =>  ((k1_funct_4 B A) = A) ) ) ).
tt(rd1_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k1_lattices A B B) = B) ) ) ).
tt(rd1_relat_1,ax, (! [A:$i] :  ((k9_xtuple_0 (k4_relat_1 A)) = A) ) ).
tt(rd1_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) & (v1_funct_1 A)) )  =>  ((k61_valued_1 A k6_numbers) = A) ) ) ).
tt(rd1_xtuple_0,ax, (! [A:$i,B:$i] :  ((k1_xtuple_0 (k4_tarski A B)) = A) ) ).
tt(rd2_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k1_ordinal4 k1_xboole_0 A) = A) ) ) ).
tt(rd2_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_cat_1 C A B B)) )  =>  ((k5_cat_1 A B B B C (k4_cat_1 A B)) = C) ) ) ).
tt(rd2_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) & (v7_ordinal1 B))  =>  ((k5_compos_1 A (k4_compos_1 A) B) = (k4_compos_1 A)) ) ) ).
tt(rd2_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_xboole_0 B)) ) )  =>  ((k1_funct_4 A B) = A) ) ) ).
tt(rd2_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_lattices A B B) = B) ) ) ).
tt(rd2_relat_1,ax, (! [A:$i] :  ((k10_xtuple_0 (k4_relat_1 A)) = A) ) ).
tt(rd2_xtuple_0,ax, (! [A:$i,B:$i] :  ((k2_xtuple_0 (k4_tarski A B)) = B) ) ).
tt(rd3_cat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k3_graph_1 A (k4_cat_1 A B)) = B) ) ) ).
tt(rd3_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) ) )  =>  ((k8_compos_1 A B (k4_compos_1 A)) = B) ) ) ).
tt(rd3_funct_4,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((k1_funct_4 (k1_funct_4 A B) B) = (k1_funct_4 A B)) ) ) ).
tt(rd3_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k3_lattices A (k5_lattices A) B) = B) ) ) ).
tt(rd3_relat_1,ax, (! [A:$i] :  ((k2_relat_1 (k4_relat_1 A)) = (k4_relat_1 A)) ) ).
tt(rd3_xtuple_0,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  ((k4_tarski (k1_xtuple_0 A) (k2_xtuple_0 A)) = A) ) ) ).
tt(rd4_cat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_graph_1 A (k4_cat_1 A B)) = B) ) ) ).
tt(rd4_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) ) )  =>  ((k8_compos_1 A (k4_compos_1 A) B) = B) ) ) ).
tt(rd4_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_lattices A (k5_lattices A) B) = (k5_lattices A)) ) ) ).
tt(rd4_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k5_relat_1 A (k9_xtuple_0 A)) = A) ) ) ).
tt(rd4_xtuple_0,ax, (! [A:$i,B:$i,C:$i] :  ((k4_xtuple_0 (k3_xtuple_0 A B C)) = A) ) ).
tt(rd5_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((k6_compos_1 A B k6_numbers) = B) ) ) ).
tt(rd5_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_lattices A (k6_lattices A) B) = B) ) ) ).
tt(rd5_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) =>  ((k5_relat_1 (k5_relat_1 A B) B) = (k5_relat_1 A B)) ) ) ).
tt(rd5_xtuple_0,ax, (! [A:$i,B:$i,C:$i] :  ((k5_xtuple_0 (k3_xtuple_0 A B C)) = B) ) ).
tt(rd6_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k63_valued_1 (k10_compos_1 A B)) = B) ) ) ).
tt(rd6_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k3_lattices A (k6_lattices A) B) = (k6_lattices A)) ) ) ).
tt(rd6_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k6_relat_1 (k10_xtuple_0 A) A) = A) ) ) ).
tt(rd6_xtuple_0,ax, (! [A:$i,B:$i,C:$i] :  ((k2_xtuple_0 (k3_xtuple_0 A B C)) = C) ) ).
tt(rd7_lattices,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k7_lattices A (k7_lattices A B)) = B) ) ) ).
tt(rd7_relat_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 B) =>  ((k6_relat_1 A (k6_relat_1 A B)) = (k6_relat_1 A B)) ) ) ).
tt(rd7_xtuple_0,ax, (! [A:$i] :  ((v2_xtuple_0 A) =>  ((k3_xtuple_0 (k4_xtuple_0 A) (k5_xtuple_0 A) (k2_xtuple_0 A)) = A) ) ) ).
tt(rd8_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((k5_relat_1 B A) = B) ) ) ).
tt(rd8_xtuple_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((k7_xtuple_0 (k6_xtuple_0 A B C D)) = A) ) ).
tt(rd9_relat_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  ((k6_relat_1 A B) = B) ) ) ).
tt(rd9_xtuple_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((k8_xtuple_0 (k6_xtuple_0 A B C D)) = B) ) ).
tt(redefinition_k10_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((k10_aofa_i00 A B C) = (k2_aofa_i00 B C)) ) ) ).
tt(redefinition_k10_binarith,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k10_binarith A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k10_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k10_binop_2 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k10_bspace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k10_bspace A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k10_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k10_bvfunc_1 A B C) = (k8_bvfunc_1 B C)) ) ) ).
tt(redefinition_k10_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m1_subset_1 C (u4_struct_0 A)) & (m1_subset_1 D (u4_struct_0 B))) ) )  =>  ((k10_cat_2 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k10_catalg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k10_catalg_1 A B C D) = (k7_catalg_1 B C D)) ) ) ).
tt(redefinition_k10_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k9_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k10_clopban1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k10_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k10_complex1 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k10_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k10_comseq_3 A) = (k2_series_1 A)) ) ) ).
tt(redefinition_k10_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k10_cqc_lang A B C) = (k4_qc_lang2 A B C)) ) ) ).
tt(redefinition_k10_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) & (v7_ordinal1 C)) )  =>  ((k10_descip_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k10_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  =>  ((k10_domain_1 A B C D E F) = (k3_enumset1 B C D E F)) ) ) ).
tt(redefinition_k10_dtconstr,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k7_dtconstr k5_dtconstr)) & (m1_subset_1 B (k4_dtconstr k5_dtconstr)))  =>  ((k10_dtconstr A B) = (k5_trees_4 A B)) ) ) ).
tt(redefinition_k10_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  =>  ((k10_euclid A B) = (k54_valued_1 B)) ) ) ).
tt(redefinition_k10_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((k10_filter_0 A B) = (k8_filter_0 A B)) ) ) ).
tt(redefinition_k10_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  =>  ((k10_finseq_4 A B C D E F) = (k8_finseq_4 B C D E F)) ) ) ).
tt(redefinition_k10_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) &  ((v1_xboole_0 C) & (v7_ordinal1 C)) ) )  =>  ((k10_fomodel3 A B C) = (k9_fomodel3 A B C)) ) ) ).
tt(redefinition_k10_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((k10_funcop_1 A B C D E) = (k5_funcop_1 C D E)) ) ) ).
tt(redefinition_k10_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((k10_funct_2 A B C D) = (k7_partfun1 B C D)) ) ) ).
tt(redefinition_k10_funct_3,ax, (! [A:$i,B:$i] :  ((k10_funct_3 A B) = (k8_funct_3 A B)) ) ).
tt(redefinition_k10_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 C))  &  ((m1_funct_2 D B C) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A D)))) )  & (m1_subset_1 F A)) ) ) )  =>  ((k10_funct_5 A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k10_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k10_fvsum_1 A B C D) = (k9_fvsum_1 B C D)) ) ) ).
tt(redefinition_k10_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) & (m1_subset_1 G k5_numbers)) ) ) ) ) )  =>  ((k10_genealg1 A B C D E F G) = (k4_genealg1 A B C D E F G)) ) ) ).
tt(redefinition_k10_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k10_glib_000 A) = (k8_glib_000 A)) ) ) ).
tt(redefinition_k10_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((k10_group_2 A B C) = (k9_group_2 A B C)) ) ) ).
tt(redefinition_k10_laplace,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((k10_laplace A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k10_margrel1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k10_margrel1 A B) = (k4_xboolean A B)) ) ) ).
tt(redefinition_k10_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  =>  ((k10_matrixj1 A B) = (k8_matrixj1 A B)) ) ) ).
tt(redefinition_k10_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((m1_subset_1 F (k1_zfmisc_1 B)) &  ((m1_subset_1 G (k1_zfmisc_1 C)) & (m1_subset_1 H (k1_zfmisc_1 D))) ) )  =>  ((k10_mcart_1 A B C D E F G H) = (k4_zfmisc_1 E F G H)) ) ) ).
tt(redefinition_k10_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_measure8 C A B) &  ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) )  =>  ((k10_measure8 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k10_mesfunc9,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers)))))) )  & (v7_ordinal1 C)) )  =>  ((k10_mesfunc9 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k10_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (u1_struct_0 (k9_monoid_1 A B))) & (m1_subset_1 D B)) ) )  =>  ((k10_monoid_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k10_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C)) )  =>  ((k10_nat_1 A B C) = (k9_nat_1 B C)) ) ) ).
tt(redefinition_k10_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  & (m1_subset_1 C (u1_struct_0 (k8_pcs_0 A B)))) )  =>  ((k10_pcs_0 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k10_petri,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k10_petri A B C) = (k2_relat_1 C)) ) ) ).
tt(redefinition_k10_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((k10_polynom1 A B C D) = (k9_polynom1 A B C D)) ) ) ).
tt(redefinition_k10_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k10_pralg_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k10_pre_poly,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k3_finseq_2 A)) =>  ((k10_pre_poly A B) = (k1_card_3 B)) ) ) ).
tt(redefinition_k10_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k10_prepower A B) = (k9_prepower A B)) ) ) ).
tt(redefinition_k10_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m2_prvect_1 B A) & (m1_subset_1 C (k4_finseq_1 A))) )  =>  ((k10_prvect_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k10_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  & (m4_pua2mss1 B A))  =>  ((k10_pua2mss1 A B) = (k10_xtuple_0 B)) ) ) ).
tt(redefinition_k10_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  & (m1_subset_1 B (k1_quofield A)))  =>  ((k10_quofield A B) = (k6_quofield A B)) ) ) ).
tt(redefinition_k10_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k10_real_1 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k10_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  & (v1_xreal_0 B))  =>  ((k10_rvsum_1 A B) = (k24_valued_1 A B)) ) ) ).
tt(redefinition_k10_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  & (v1_xcmplx_0 C)) )  =>  ((k10_rvsum_2 A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k10_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  =>  ((k10_seq_4 A B) = (k45_valued_1 A B)) ) ) ).
tt(redefinition_k10_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k10_sincos10 A) = (k6_sincos10 A)) ) ) ).
tt(redefinition_k10_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_borsuk_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D))) ) ) )  =>  ((k10_topalg_4 A B C D E) = (k12_mcart_1 E)) ) ) ).
tt(redefinition_k10_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  =>  ((k10_toprealc A B C) = (k14_valued_2 B C)) ) ) ).
tt(redefinition_k10_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v1_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((k10_yellow_3 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k11_ami_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  & (v1_int_1 B))  =>  ((k11_ami_3 A B) = (k16_funcop_1 A B)) ) ) ).
tt(redefinition_k11_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  ((k11_aofa_000 A) = (k10_aofa_000 A)) ) ) ).
tt(redefinition_k11_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((k11_aofa_i00 A B C) = (k3_aofa_i00 B C)) ) ) ).
tt(redefinition_k11_arytm_3,ax, (k11_arytm_3 = k1_xboole_0) ).
tt(redefinition_k11_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k11_binop_2 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k11_card_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  & (m1_subset_1 B (k4_card_3 A)))  =>  ((k11_card_3 A B C) = (k5_relat_1 B C)) ) ) ).
tt(redefinition_k11_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D (k8_cat_2 A B) C) &  ((m1_subset_1 E (u4_struct_0 A)) & (m1_subset_1 F (u4_struct_0 B))) ) ) ) )  =>  ((k11_cat_2 A B C D E F) = (k1_binop_1 D E F)) ) ) ).
tt(redefinition_k11_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C k5_numbers)) )  =>  ((k11_chain_1 A B C) = (k5_chain_1 A B C)) ) ) ).
tt(redefinition_k11_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((k11_cohsp_1 A B C) = (k10_cohsp_1 C)) ) ) ).
tt(redefinition_k11_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  =>  ((k11_complex1 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k11_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k11_cqc_lang A B C) = (k15_qc_lang1 A B C)) ) ) ).
tt(redefinition_k11_cqc_sim1,ax, (! [A:$i] :  ((k11_cqc_sim1 A) = (k4_relat_1 A)) ) ).
tt(redefinition_k11_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) & (m1_subset_1 G A)) ) ) ) ) )  =>  ((k11_domain_1 A B C D E F G) = (k4_enumset1 B C D E F G)) ) ) ).
tt(redefinition_k11_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  =>  ((k11_euclid A B) = (k39_valued_1 B)) ) ) ).
tt(redefinition_k11_facirc_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msafree2 B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k11_facirc_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k11_filter_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  & (m2_nat_lat B A))  =>  ((k11_filter_2 A B) = (k1_lattice2 B)) ) ) ).
tt(redefinition_k11_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((k11_funcop_1 A B C D) = (k10_xtuple_0 D)) ) ) ).
tt(redefinition_k11_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((k11_funct_5 A B C D) = (k1_funct_5 D)) ) ) ).
tt(redefinition_k11_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) & (m1_subset_1 H k5_numbers)) ) ) ) ) ) )  =>  ((k11_genealg1 A B C D E F G H) = (k5_genealg1 A B C D E F G H)) ) ) ).
tt(redefinition_k11_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k11_glib_000 A) = (k9_glib_000 A)) ) ) ).
tt(redefinition_k11_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) &  ((v3_group_9 D A) & (l1_group_9 D A)) ) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v1_group_6 F C D) &  ((v7_group_9 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) ) )  =>  ((k11_group_9 A B C D E F) = (k3_relat_1 E F)) ) ) ).
tt(redefinition_k11_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_finseq_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) )  =>  ((k11_lang1 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k11_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  =>  ((k11_matrix_2 A) = (k10_matrix_2 A)) ) ) ).
tt(redefinition_k11_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  =>  ((k11_matrixj1 A B) = (k9_matrixj1 A B)) ) ) ).
tt(redefinition_k11_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) )  =>  ((k11_measure8 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k11_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ((k11_monoid_1 A B) = (k9_monoid_1 A B)) ) ) ).
tt(redefinition_k11_nat_3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k11_nat_3 A B) = (k10_nat_3 A B)) ) ) ).
tt(redefinition_k11_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k11_openlatt A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k11_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  & (m1_subset_1 C (u1_struct_0 (k8_pcs_0 A B)))) )  =>  ((k11_pcs_0 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k11_pdiff_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B k5_numbers) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (m1_subset_1 D (k1_euclid A))) ) )  =>  ((k11_pdiff_1 A B C D) = (k10_pdiff_1 A B C D)) ) ) ).
tt(redefinition_k11_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_valued_0 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_valued_0 C)) ) ) ) )  =>  ((k11_pre_poly A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k11_prvect_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  & (m2_prvect_1 B A))  =>  ((k11_prvect_1 A B) = (k7_funct_6 B)) ) ) ).
tt(redefinition_k11_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ((k11_prvect_2 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k11_quaterni,ax, (k11_quaterni = k4_quaterni) ).
tt(redefinition_k11_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  & (m1_subset_1 B (k10_ringcat1 A)))  =>  ((k11_ringcat1 A B) = (k1_ringcat1 B)) ) ) ).
tt(redefinition_k11_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (v1_xreal_0 C)) )  =>  ((k11_rvsum_1 A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k11_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  =>  ((k11_rvsum_2 A B) = (k18_valued_1 A B)) ) ) ).
tt(redefinition_k11_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k11_seq_4 A) = (k30_valued_1 A)) ) ) ).
tt(redefinition_k11_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k11_sincos10 A) = (k7_sincos10 A)) ) ) ).
tt(redefinition_k11_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k11_toprealc A B C) = (k18_valued_1 B C)) ) ) ).
tt(redefinition_k12_abcmiz_a,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((v2_abcmiz_1 B A) &  ((v4_abcmiz_a B A) & (m2_abcmiz_1 B A (k12_abcmiz_1 A))) ) )  =>  ((k12_abcmiz_a A B) = (k29_abcmiz_1 A B)) ) ) ).
tt(redefinition_k12_ami_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ((k12_ami_3 A B C D) = (k4_funct_4 A B C D)) ) ) ).
tt(redefinition_k12_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((k12_aofa_i00 A B C) = (k4_aofa_i00 B C)) ) ) ).
tt(redefinition_k12_arytm_3,ax, (k12_arytm_3 = k1_arytm_3) ).
tt(redefinition_k12_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k12_binop_2 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k12_cgames_1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 B (k2_cgames_1 A)))  =>  ((k12_cgames_1 A B) = (k10_cgames_1 B)) ) ) ).
tt(redefinition_k12_complex1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k12_complex1 A) = (k5_xcmplx_0 A)) ) ) ).
tt(redefinition_k12_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k12_cqc_lang A B C) = (k5_qc_lang2 A B C)) ) ) ).
tt(redefinition_k12_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_subset_1 B (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 C (k4_finseq_2 A k6_margrel1))) )  =>  ((k12_descip_1 A B C) = (k4_bvfunc_1 B C)) ) ) ).
tt(redefinition_k12_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k4_partfun1 k1_numbers k1_numbers)) &  ((v1_diff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) )  & (m1_subset_1 B k5_numbers))  =>  ((k12_diff_1 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k12_finseq_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k12_finseq_1 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k12_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_fomodel2 D A B C)) )  &  ((v10_fomodel1 E A) & (m1_subset_1 E (k1_fomodel1 A))) ) ) ) )  =>  ((k12_fomodel2 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k12_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  & (v1_relat_1 E)) ) ) )  =>  ((k12_fomodel3 A B C D E) = (k11_fomodel3 A B C D E)) ) ) ).
tt(redefinition_k12_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ((k12_freealg A B) = (k8_freealg A B)) ) ) ).
tt(redefinition_k12_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((k12_funcop_1 A B C D) = (k1_funcop_1 D)) ) ) ).
tt(redefinition_k12_funct_3,ax, (! [A:$i] :  ((k12_funct_3 A) = (k11_funct_3 A)) ) ).
tt(redefinition_k12_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((k12_funct_5 A B C D) = (k3_funct_5 D)) ) ) ).
tt(redefinition_k12_funct_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k12_funct_7 A B C) = (k11_funct_7 B C)) ) ) ).
tt(redefinition_k12_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ((k12_functor0 A) = (k11_functor0 A)) ) ) ).
tt(redefinition_k12_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  =>  ((k12_fvsum_1 A B C D) = (k11_fvsum_1 B C D)) ) ) ).
tt(redefinition_k12_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) &  ((m1_subset_1 F k5_numbers) &  ((m1_subset_1 G k5_numbers) &  ((m1_subset_1 H k5_numbers) & (m1_subset_1 I k5_numbers)) ) ) ) ) ) ) )  =>  ((k12_genealg1 A B C D E F G H I) = (k6_genealg1 A B C D E F G H I)) ) ) ).
tt(redefinition_k12_graphsp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k8_graph_5)))) ) ) ) )  =>  ((k12_graphsp A B C D) = (k11_graphsp A B C D)) ) ) ).
tt(redefinition_k12_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k12_ideal_1 A B C) = (k11_ideal_1 A B C)) ) ) ).
tt(redefinition_k12_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k12_lattice3 A B C) = (k11_lattice3 A B C)) ) ) ).
tt(redefinition_k12_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  =>  ((k12_lattice5 A B C D E) = (k11_lattice5 A B C D E)) ) ) ).
tt(redefinition_k12_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k11_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k12_lopban_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k12_margrel1,ax, (! [A:$i] :  ((k12_margrel1 A) = (k11_margrel1 A)) ) ).
tt(redefinition_k12_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v16_monoid_0 A) &  ((v17_monoid_0 A) & (l3_algstr_0 A)) ) ) ) ) )  =>  ((k12_monoid_1 A B) = (k9_monoid_1 A B)) ) ) ).
tt(redefinition_k12_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ((m1_subset_1 B (k9_openlatt A)) & (m1_subset_1 C (k9_openlatt A))) )  =>  ((k12_openlatt A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k12_polynom3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k12_polynom3 A) = (k5_finseq_1 A)) ) ) ).
tt(redefinition_k12_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v4_funct_1 A) &  (~ (v1_xboole_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k12_prvect_1 A B C D) = (k1_binop_1 B C D)) ) ) ).
tt(redefinition_k12_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  &  ((m3_pua2mss1 B A) & (m1_subset_1 C (u4_struct_0 (k11_pua2mss1 A B)))) )  =>  ((k12_pua2mss1 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k12_quaterni,ax, (k12_quaterni = k5_quaterni) ).
tt(redefinition_k12_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (v1_xreal_0 D)) ) )  =>  ((k12_rfunct_3 A B C D) = (k24_valued_1 C D)) ) ) ).
tt(redefinition_k12_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  & (m1_subset_1 B (k10_ringcat1 A)))  =>  ((k12_ringcat1 A B) = (k2_ringcat1 B)) ) ) ).
tt(redefinition_k12_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k12_rvsum_1 A) = (k39_valued_1 A)) ) ) ).
tt(redefinition_k12_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  =>  ((k12_rvsum_2 A B C) = (k18_valued_1 B C)) ) ) ).
tt(redefinition_k12_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (v1_xcmplx_0 B))  =>  ((k12_seq_4 A B) = (k24_valued_1 A B)) ) ) ).
tt(redefinition_k12_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k12_sincos10 A) = (k8_sincos10 A)) ) ) ).
tt(redefinition_k12_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k3_qc_lang1 A)) & (m1_subset_1 D B)) ) )  =>  ((k12_sublemma A B C D) = (k16_funcop_1 C D)) ) ) ).
tt(redefinition_k12_supinf_2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((k12_supinf_2 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k12_toprealc,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  =>  ((k12_toprealc A B) = (k39_valued_1 B)) ) ) ).
tt(redefinition_k12_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v13_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((k12_yellow_3 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k13_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) )  =>  ((k13_aofa_i00 A B C) = (k5_aofa_i00 B C)) ) ) ).
tt(redefinition_k13_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k13_binop_2 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k13_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  =>  ((k13_cat_5 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k13_complex1,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k13_complex1 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k13_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  &  ((m1_subset_1 C (k4_finseq_2 B (k4_finseq_2 A k6_margrel1))) & (m1_subset_1 D (k2_finseq_1 B))) ) )  =>  ((k13_descip_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k13_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) &  ((m1_subset_1 F A) &  ((m1_subset_1 G A) &  ((m1_subset_1 H A) & (m1_subset_1 I A)) ) ) ) ) ) ) )  =>  ((k13_domain_1 A B C D E F G H I) = (k6_enumset1 B C D E F G H I)) ) ) ).
tt(redefinition_k13_fomodel1,ax, (! [A:$i,B:$i] :  ( ((l4_struct_0 A) & (m1_subset_1 B (k6_subset_1 (u1_struct_0 A) (k1_tarski (u3_struct_0 A)))))  =>  ((k13_fomodel1 A B) = (k12_fomodel1 A B)) ) ) ).
tt(redefinition_k13_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (v7_ordinal1 C)) )  =>  ((k13_fomodel3 A B C) = (k9_fomodel3 A B C)) ) ) ).
tt(redefinition_k13_funct_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) )  =>  ((k13_funct_5 A B C D) = (k2_funct_5 D)) ) ) ).
tt(redefinition_k13_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k13_ideal_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k13_lang1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k13_lang1 A B) = (k18_finseq_1 B)) ) ) ).
tt(redefinition_k13_lattice3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k13_lattice3 A B C) = (k10_lattice3 A B C)) ) ) ).
tt(redefinition_k13_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m2_lexbfs B A) & (v7_ordinal1 C)) )  =>  ((k13_lexbfs A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k13_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k13_lopclset A) = (k8_lopclset A)) ) ) ).
tt(redefinition_k13_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k13_matrixj1 A B C) = (k12_matrixj1 A B C)) ) ) ).
tt(redefinition_k13_newton,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k13_newton A B) = (k1_newton A B)) ) ) ).
tt(redefinition_k13_ordinal6,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v3_ordinal1 B))  =>  ((k13_ordinal6 A B) = (k12_ordinal6 A B)) ) ) ).
tt(redefinition_k13_osalg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((k13_osalg_2 A B) = (k12_osalg_2 A B)) ) ) ).
tt(redefinition_k13_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k13_polynom3 A B C) = (k11_polynom3 A B C)) ) ) ).
tt(redefinition_k13_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v1_funct_1 D) &  ((v1_funct_2 D B (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k9_setfam_1 C))))) ) )  =>  ((k13_prob_1 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k13_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  &  ((m3_pua2mss1 B A) & (m1_subset_1 C (u4_struct_0 (k11_pua2mss1 A B)))) )  =>  ((k13_pua2mss1 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k13_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k4_finseq_2 A k1_numbers)))  =>  ((k13_rvsum_1 A B) = (k39_valued_1 B)) ) ) ).
tt(redefinition_k13_seq_4,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k13_seq_4 A) = (k54_valued_1 A)) ) ) ).
tt(redefinition_k13_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k13_toprealc A B C) = (k50_valued_1 B C)) ) ) ).
tt(redefinition_k13_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v12_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) )  =>  ((k13_yellow_3 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k14_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k5_abcmiz_a) =>  ((k14_abcmiz_a A) = (k13_abcmiz_a A)) ) ) ).
tt(redefinition_k14_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  & (m1_subset_1 C (k8_afinsq_1 A)))  =>  ((k14_afinsq_1 A B C) = (k1_ordinal4 B C)) ) ) ).
tt(redefinition_k14_binop_2,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k14_binop_2 A) = (k5_xcmplx_0 A)) ) ) ).
tt(redefinition_k14_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k14_borsuk_7 A) = (k13_borsuk_7 A)) ) ) ).
tt(redefinition_k14_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  =>  ((k14_cat_5 A B C) = (k13_mcart_1 C)) ) ) ).
tt(redefinition_k14_descip_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_finseq_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_finseq_2 A B))))) )  & (v7_ordinal1 D)) ) )  =>  ((k14_descip_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k14_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k2_zfmisc_1 A B) C))) ) )  =>  ((k14_domain_1 A B C D) = (k13_mcart_1 D)) ) ) ).
tt(redefinition_k14_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k14_fomodel2 A B C D) = (k13_fomodel2 A B C D)) ) ) ).
tt(redefinition_k14_funct_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) )  =>  ((k14_funct_3 A B C D E) = (k13_funct_3 D E)) ) ) ).
tt(redefinition_k14_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k14_funct_7 A B C D) = (k13_funct_7 B C D)) ) ) ).
tt(redefinition_k14_grcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  ((m1_grcat_1 D B C) & (m1_grcat_1 E A B)) ) ) )  =>  ((k14_grcat_1 A B C D E) = (k13_grcat_1 D E)) ) ) ).
tt(redefinition_k14_lexbfs,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m2_lexbfs B A))  =>  ((k14_lexbfs A B) = (k40_glib_000 B)) ) ) ).
tt(redefinition_k14_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  =>  ((k14_matrixj1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k14_monoid_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))))  =>  ((k14_monoid_1 A B) = (k10_xtuple_0 B)) ) ) ).
tt(redefinition_k14_pralg_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ((m1_pralg_1 C A B) & (m1_subset_1 D A)) ) )  =>  ((k14_pralg_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k14_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k14_rvsum_1 A B) = (k18_valued_1 A B)) ) ) ).
tt(redefinition_k14_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  =>  ((k14_sublemma A B C D) = (k1_funct_4 C D)) ) ) ).
tt(redefinition_k14_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 D)) )  =>  ((k14_toprealc A B C D) = (k2_funct_7 B C D)) ) ) ).
tt(redefinition_k14_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k14_valued_1 A B C D) = (k13_valued_1 C D)) ) ) ).
tt(redefinition_k15_afinsq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_subset_1 C (k8_afinsq_1 A)))  =>  ((k15_afinsq_1 A B C) = (k1_ordinal4 B C)) ) ) ).
tt(redefinition_k15_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) )  =>  ((k15_aofa_i00 A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k15_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k15_binop_2 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k15_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  &  ((v2_borsuk_1 C B) & (m1_borsuk_1 C B)) ) )  =>  ((k15_borsuk_1 A B C) = (k13_borsuk_1 A B C)) ) ) ).
tt(redefinition_k15_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_eqrel_1 C A)) )  =>  ((k15_bvfunc_1 A B C) = (k11_eqrel_1 A B C)) ) ) ).
tt(redefinition_k15_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k11_cat_5 A B)))) )  =>  ((k15_cat_5 A B C) = (k14_mcart_1 C)) ) ) ).
tt(redefinition_k15_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k15_clopban1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k15_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_complex1 A) = (k14_complex1 A)) ) ) ).
tt(redefinition_k15_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k15_csspace A B C) = (k14_csspace A B C)) ) ) ).
tt(redefinition_k15_descip_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A 64 16) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 64 16)))) )  =>  ((k15_descip_1 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k15_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k2_zfmisc_1 A B) C))) ) )  =>  ((k15_domain_1 A B C D) = (k14_mcart_1 D)) ) ) ).
tt(redefinition_k15_fomodel1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fomodel1 A))  =>  ((k15_fomodel1 A) = (k1_fomodel1 A)) ) ) ).
tt(redefinition_k15_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D A) & (m1_subset_1 E A))  =>  ((k15_funcop_1 A B C D E) = (k14_funcop_1 B C D E)) ) ) ).
tt(redefinition_k15_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 E B))  =>  ((k15_funct_7 A B C D E) = (k2_funct_7 C D E)) ) ) ).
tt(redefinition_k15_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k15_glib_000 A) = (k14_glib_000 A)) ) ) ).
tt(redefinition_k15_glib_004,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ((m3_glib_004 B A) & (v7_ordinal1 C)) )  =>  ((k15_glib_004 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k15_ideal_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l6_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k15_ideal_1 A B C) = (k14_ideal_1 A B C)) ) ) ).
tt(redefinition_k15_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  & (m1_lattice5 D A B C)) ) )  =>  ((k15_lattice5 A B C D) = (k14_lattice5 A B C D)) ) ) ).
tt(redefinition_k15_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((k15_margrel1 A B) = (k13_margrel1 B)) ) ) ).
tt(redefinition_k15_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v2_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k15_matrixj1 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k15_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  =>  ((k15_mesfunc1 A B C) = (k11_mesfunc1 B C)) ) ) ).
tt(redefinition_k15_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k15_mmlquery A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k15_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))) & (m1_subset_1 C A)) )  =>  ((k15_monoid_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k15_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k15_pcs_0 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k15_pre_poly,ax, (! [A:$i] :  ((k15_pre_poly A) = (k14_pre_poly A)) ) ).
tt(redefinition_k15_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  =>  ((k15_rvsum_1 A B C) = (k18_valued_1 B C)) ) ) ).
tt(redefinition_k15_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k14_seq_4 A))) )  =>  ((k15_seq_4 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k15_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_sin_cos A) = (k14_sin_cos A)) ) ) ).
tt(redefinition_k15_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k15_valued_1 A B C D) = (k13_valued_1 C D)) ) ) ).
tt(redefinition_k16_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) ) ) )  =>  ((k16_aofa_i00 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k16_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k16_binop_2 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k16_borsuk_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  &  ((v2_borsuk_1 C B) & (m1_borsuk_1 C B)) ) )  =>  ((k16_borsuk_1 A B C) = (k11_borsuk_1 B C)) ) ) ).
tt(redefinition_k16_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E A C)) ) ) )  =>  ((k16_cat_2 A B C D E) = (k13_funct_3 D E)) ) ) ).
tt(redefinition_k16_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  =>  ((k16_cat_5 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k16_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k16_csspace A B C) = (k2_normsp_1 A B C)) ) ) ).
tt(redefinition_k16_descip_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  & (m1_subset_1 B A))  =>  ((k16_descip_1 A B) = (k1_ordinal1 B)) ) ) ).
tt(redefinition_k16_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) ) )  =>  ((k16_domain_1 A B C D) = (k15_mcart_1 D)) ) ) ).
tt(redefinition_k16_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k16_euclid A) = (k4_euclid A)) ) ) ).
tt(redefinition_k16_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k16_fomodel1 A) = (k2_fomodel1 A)) ) ) ).
tt(redefinition_k16_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  (~ (v1_xboole_0 B)) )  =>  ((k16_fomodel2 A B) = (k15_fomodel2 A B)) ) ) ).
tt(redefinition_k16_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v1_fomodel3 E C D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) )  =>  ((k16_fomodel3 A B C D E) = (k11_fomodel3 A B C D E)) ) ) ).
tt(redefinition_k16_funct_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) )  =>  ((k16_funct_3 A B C D E F) = (k15_funct_3 E F)) ) ) ).
tt(redefinition_k16_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k16_margrel1 A B C) = (k14_margrel1 B C)) ) ) ).
tt(redefinition_k16_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_matrix_1 C A B B)) )  =>  ((k16_matrixj1 A B C) = (k5_finseq_1 C)) ) ) ).
tt(redefinition_k16_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  =>  ((k16_mesfunc1 A B C) = (k12_mesfunc1 B C)) ) ) ).
tt(redefinition_k16_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k16_mmlquery A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k16_monoid_1,ax, (! [A:$i,B:$i] :  ((k16_monoid_1 A B) = (k4_funct_3 A B)) ) ).
tt(redefinition_k16_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((k16_openlatt A) = (k8_openlatt A)) ) ) ).
tt(redefinition_k16_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((k16_pralg_1 A B C) = (k15_pralg_1 B C)) ) ) ).
tt(redefinition_k16_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k16_valued_2 A B C) = (k15_valued_2 C)) ) ) ).
tt(redefinition_k17_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k17_binop_2 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k17_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  &  ((m2_cat_1 E A C) & (m2_cat_1 F B D)) ) ) ) )  =>  ((k17_cat_2 A B C D E F) = (k15_funct_3 E F)) ) ) ).
tt(redefinition_k17_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  =>  ((k17_cat_5 A B C) = (k13_mcart_1 C)) ) ) ).
tt(redefinition_k17_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  ((k17_coh_sp A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k17_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 A) = (k16_complex1 A)) ) ) ).
tt(redefinition_k17_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) ) )  =>  ((k17_domain_1 A B C D) = (k16_mcart_1 D)) ) ) ).
tt(redefinition_k17_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  =>  ((k17_finseq_1 A B C) = (k16_finseq_1 B C)) ) ) ).
tt(redefinition_k17_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  =>  ((k17_fomodel1 A) = (k10_fomodel1 A)) ) ) ).
tt(redefinition_k17_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m1_finseq_1 A k5_numbers)) )  & (v1_freealg B))  =>  ((k17_freealg A B) = (k16_freealg A B)) ) ) ).
tt(redefinition_k17_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ((k17_funcop_1 A B C) = (k13_funcop_1 A B C)) ) ).
tt(redefinition_k17_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k17_glib_000 A) = (k16_glib_000 A)) ) ) ).
tt(redefinition_k17_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  ((k17_lexbfs A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k17_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k17_lopban_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k17_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k4_partfun1 (k3_finseq_2 A) A)))  =>  ((k17_margrel1 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k17_matrixj1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((m1_matrix_1 D A B B) & (m1_matrix_1 E A C C)) ) ) )  =>  ((k17_matrixj1 A B C D E) = (k10_finseq_1 D E)) ) ) ).
tt(redefinition_k17_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  =>  ((k17_mesfunc1 A B C) = (k13_mesfunc1 B C)) ) ) ).
tt(redefinition_k17_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k17_mmlquery A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k17_monoid_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k17_monoid_1 A B) = (k2_funcop_1 A B)) ) ) ).
tt(redefinition_k17_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) =>  ((k17_quatern2 A) = (k30_quaterni A)) ) ) ).
tt(redefinition_k17_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k17_quaterni A) = (k13_quaterni A)) ) ) ).
tt(redefinition_k17_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k17_rvsum_1 A) = (k16_rvsum_1 A)) ) ) ).
tt(redefinition_k17_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k17_seq_4 A) = (k16_seq_4 A)) ) ) ).
tt(redefinition_k17_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((k17_supinf_2 A) = (k10_xtuple_0 A)) ) ) ).
tt(redefinition_k17_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k17_valued_2 A B C) = (k15_valued_2 C)) ) ) ).
tt(redefinition_k18_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ((m1_subset_1 E (k9_funct_2 (k9_funct_2 A B) C)) &  ((v1_funct_1 F) &  ((v1_funct_2 F A D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A D)))) ) ) ) ) ) )  =>  ((k18_aofa_i00 A B C D E F) = (k17_aofa_i00 D E F)) ) ) ).
tt(redefinition_k18_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_rat_1 A) & (v1_rat_1 B))  =>  ((k18_binop_2 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k18_cat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u4_struct_0 (k12_cat_5 A B)))) )  =>  ((k18_cat_5 A B C) = (k14_mcart_1 C)) ) ) ).
tt(redefinition_k18_coh_sp,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  ((k18_coh_sp A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k18_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k18_complex1 A) = (k16_complex1 A)) ) ) ).
tt(redefinition_k18_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  ((k18_fomodel0 A B C D) = (k17_fomodel0 B C D)) ) ) ).
tt(redefinition_k18_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l1_fomodel1 A))  =>  ((k18_fomodel1 A) = (k7_fomodel1 A)) ) ) ).
tt(redefinition_k18_funcop_1,ax, (! [A:$i,B:$i] :  ((k18_funcop_1 A B) = (k16_funcop_1 A B)) ) ).
tt(redefinition_k18_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k18_matrixj1 A B C) = (k16_finseq_1 B C)) ) ) ).
tt(redefinition_k18_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  =>  ((k18_mesfunc1 A B C) = (k14_mesfunc1 B C)) ) ) ).
tt(redefinition_k18_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ((k18_openlatt A) = (k8_openlatt A)) ) ) ).
tt(redefinition_k18_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k18_quaterni A) = (k14_quaterni A)) ) ) ).
tt(redefinition_k18_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((k18_rvsum_1 A) = (k16_rvsum_1 A)) ) ) ).
tt(redefinition_k18_scmfsa_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  & (m1_scmfsa_2 B))  =>  ((k18_scmfsa_2 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k18_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  =>  ((k18_seq_4 A B) = (k30_valued_1 B)) ) ) ).
tt(redefinition_k18_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k18_sin_cos A) = (k17_sin_cos A)) ) ) ).
tt(redefinition_k18_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  =>  ((k18_substut1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k18_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B))))) )  =>  ((k18_toprealc A B C) = (k2_toprealc C)) ) ) ).
tt(redefinition_k19_binop_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k19_binop_2 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k19_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k19_bvfunc_1 A B) = (k8_xboolean A B)) ) ) ).
tt(redefinition_k19_euclid,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k19_euclid A B) = (k10_finseq_1 A B)) ) ) ).
tt(redefinition_k19_fomodel0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 C A) &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) ) )  =>  ((k19_fomodel0 A B C D) = (k17_fomodel0 B C D)) ) ) ).
tt(redefinition_k19_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ((k19_fomodel3 A B C) = (k18_fomodel3 A B C)) ) ) ).
tt(redefinition_k19_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  & (m1_subset_1 B (k18_grcat_1 A)))  =>  ((k19_grcat_1 A B) = (k7_grcat_1 B)) ) ) ).
tt(redefinition_k19_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_margrel1 A)) )  =>  ((k19_margrel1 A) = (k18_margrel1 A)) ) ) ).
tt(redefinition_k19_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k19_matrixj1 A B C) = (k1_rfinseq B C)) ) ) ).
tt(redefinition_k19_mesfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  & (v1_xxreal_0 C))  =>  ((k19_mesfunc1 A B C) = (k10_relat_1 B C)) ) ) ).
tt(redefinition_k19_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k19_mmlquery A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k19_pre_poly,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) &  ((v2_pre_poly B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((k19_pre_poly A B) = (k13_pre_poly B)) ) ) ).
tt(redefinition_k19_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k19_quaterni A) = (k15_quaterni A)) ) ) ).
tt(redefinition_k19_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C (k14_seq_4 A))) )  =>  ((k19_seq_4 A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k19_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  =>  ((k19_substut1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k19_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k19_valued_1 A B C D E) = (k18_valued_1 D E)) ) ) ).
tt(redefinition_k1_abian,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (m1_subset_1 C k5_numbers))  =>  ((k1_abian A B C) = (k9_funct_7 B C)) ) ) ).
tt(redefinition_k1_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k1_afinsq_1 A) = (k1_card_1 A)) ) ) ).
tt(redefinition_k1_amistd_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_subset_1 E (k4_memstr_0 A B D))) ) ) )  =>  ((k1_amistd_4 A B C D E) = (k2_funct_7 C D E)) ) ) ).
tt(redefinition_k1_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((m1_finseq_2 C A) & (m1_subset_1 D B)) )  =>  ((k1_aofa_000 A B C D) = (k2_funcop_1 C D)) ) ) ).
tt(redefinition_k1_arrow,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B)))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  & (m1_subset_1 E A)) ) ) )  =>  ((k1_arrow A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k1_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  ((k1_asympt_0 A B) = (k1_valued_1 A B)) ) ) ).
tt(redefinition_k1_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k1_binarith A B) = (k5_xboolean A B)) ) ) ).
tt(redefinition_k1_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_binop_2 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k1_bor_cant,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_xxreal_0 B) &  ((v1_xxreal_0 C) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) )  =>  ((k1_bor_cant A B C D E) = (k5_xxreal_0 B C D E)) ) ) ).
tt(redefinition_k1_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 B)) &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (m1_connsp_2 E B C)) ) ) )  =>  ((k1_borsuk_1 A B C D E) = (k8_relat_1 D E)) ) ) ).
tt(redefinition_k1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((k1_bvfunc_1 A B) = (k13_margrel1 B)) ) ) ).
tt(redefinition_k1_bvfunc_2,ax, (! [A:$i] :  ((k1_bvfunc_2 A) = (k1_partit1 A)) ) ).
tt(redefinition_k1_card_fil,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_card_fil B A))  =>  ((k1_card_fil A B) = (k7_setfam_1 A B)) ) ) ).
tt(redefinition_k1_cat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((k1_cat_3 A B C) = (k16_funcop_1 B C)) ) ) ).
tt(redefinition_k1_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_5 A) & (l1_cat_1 A)) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k1_cat_5 A B) = (k13_mcart_1 B)) ) ) ).
tt(redefinition_k1_catalan2,ax, (! [A:$i,B:$i] :  ( ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((k1_catalan2 A B) = (k1_ordinal4 A B)) ) ) ).
tt(redefinition_k1_chain_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k1_chain_1 A B) = (k1_zfmisc_1 B)) ) ) ).
tt(redefinition_k1_circcomb,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v4_relat_1 E D) &  ((v1_funct_1 E) & (v1_partfun1 E D)) ) ) )  &  ( ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v4_relat_1 F D) &  ((v1_funct_1 F) & (v1_partfun1 F D)) ) ) )  &  ((m2_pboole G A B C) & (m2_pboole H D E F)) ) ) ) )  =>  ((k1_circcomb A B C D E F G H) = (k1_funct_4 G H)) ) ) ).
tt(redefinition_k1_circuit2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_msafree2 D A B)) ) )  =>  ((k1_circuit2 A B C D) = (k1_funct_4 C D)) ) ) ).
tt(redefinition_k1_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  =>  ((k1_classes2 A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k1_clopban2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_clopban1 B A A) &  ((v2_clopban1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_clopban1 C A A) &  ((v2_clopban1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((k1_clopban2 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k1_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ((m2_pboole D A B C) & (m1_pboole E A B)) ) )  =>  ((k1_closure1 A B C D E) = (k15_pralg_1 D E)) ) ) ).
tt(redefinition_k1_closure3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ((k1_closure3 A B) = (k13_pre_poly B)) ) ) ).
tt(redefinition_k1_convex4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k9_funct_2 (u1_struct_0 A) k2_numbers)))  =>  ((k1_convex4 A B) = (k13_pre_poly B)) ) ) ).
tt(redefinition_k1_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 B A))) )  =>  ((k1_descip_1 A B C) = (k3_finseq_5 C)) ) ) ).
tt(redefinition_k1_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 B A) =>  ((k1_dist_1 A B C) = (k10_relat_1 B C)) ) ) ).
tt(redefinition_k1_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D B)) ) )  =>  ((k1_domain_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k1_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_trees_3 B A) & (m1_finseq_1 C B)) )  =>  ((k1_dtconstr A B C) = (k14_trees_3 C)) ) ) ).
tt(redefinition_k1_dynkin,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 A)) &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 A))) ) )  =>  ((k1_dynkin A B C D) = (k13_funct_7 B C D)) ) ) ).
tt(redefinition_k1_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_ec_pf_1 A) = (k7_struct_0 A)) ) ) ).
tt(redefinition_k1_euclid_7,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k1_euclid_7 A B C) = (k13_funct_3 B C)) ) ) ).
tt(redefinition_k1_euclid_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  =>  ((k1_euclid_8 A B C) = (k11_finseq_1 A B C)) ) ) ).
tt(redefinition_k1_euler_2,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k1_euler_2 A B) = (k24_valued_1 A B)) ) ) ).
tt(redefinition_k1_extreal1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_extreal1 A B) = (k4_xxreal_3 A B)) ) ) ).
tt(redefinition_k1_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_extreal2 A B) = (k4_xxreal_0 A B)) ) ) ).
tt(redefinition_k1_finance1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k1_finance1 A B) = (k2_xxreal_1 A B)) ) ) ).
tt(redefinition_k1_finseq_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (m1_subset_1 D A)) ) )  =>  ((k1_finseq_7 A B C D) = (k2_funct_7 B C D)) ) ) ).
tt(redefinition_k1_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k1_finseq_8 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k1_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_finseq_1 E A) & (m1_finseq_1 F B)) ) ) ) )  =>  ((k1_finseqop A B C D E F) = (k3_funcop_1 D E F)) ) ) ).
tt(redefinition_k1_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k1_finsub_1 A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k1_fintopo5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k1_fintopo5 A B C D) = (k9_relat_1 C D)) ) ) ).
tt(redefinition_k1_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k3_catalan2 A)) & (m1_subset_1 C (k3_catalan2 A)))  =>  ((k1_flang_1 A B C) = (k1_ordinal4 B C)) ) ) ).
tt(redefinition_k1_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k1_fomodel2 A) = (k8_fomodel1 A)) ) ) ).
tt(redefinition_k1_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B)) (k9_funct_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A B)) (k9_funct_2 A B))))) )  &  ((m1_subset_1 D (k9_funct_2 A B)) & (m1_subset_1 E (k9_funct_2 A B))) ) )  =>  ((k1_funcsdom A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k1_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ((k1_functor0 A B C D) = (k2_funct_4 D)) ) ) ).
tt(redefinition_k1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ((v15_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((k1_functor3 A B C D E) = (k13_functor0 A B C D E)) ) ) ).
tt(redefinition_k1_fuzzy_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) )  =>  ((k1_fuzzy_4 A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k1_glib_003,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ((k1_glib_003 A B C) = (k15_finseq_1 C)) ) ) ).
tt(redefinition_k1_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m1_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((k1_goboard9 A) = (k3_finseq_5 A)) ) ) ).
tt(redefinition_k1_graph_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((k1_graph_3 A B) = (k5_graph_2 A B)) ) ) ).
tt(redefinition_k1_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 A k1_numbers) & (m1_subset_1 C k1_numbers))  =>  ((k1_graphsp A B C) = (k2_funct_7 A B C)) ) ) ).
tt(redefinition_k1_gr_cy_1,ax, (! [A:$i] :  ((m1_finseq_1 A k4_numbers) =>  ((k1_gr_cy_1 A) = (k16_rvsum_1 A)) ) ) ).
tt(redefinition_k1_grnilp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) & (m1_group_2 C A)) )  =>  ((k1_grnilp_1 A B C) = (k8_group_5 A B C)) ) ) ).
tt(redefinition_k1_groeb_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) )  =>  ((k1_groeb_1 A B C) = (k1_tarski C)) ) ) ).
tt(redefinition_k1_groeb_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) ) ) )  =>  ((k1_groeb_3 A B C D) = (k2_tarski C D)) ) ) ).
tt(redefinition_k1_group_10,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) )  & (m1_subset_1 D (u1_struct_0 A))) )  =>  ((k1_group_10 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_group_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((k1_group_4 A B C) = (k1_finseq_3 B C)) ) ) ).
tt(redefinition_k1_group_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_group_7 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k1_group_7 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_index_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k1_index_1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k1_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_int_2 A) = (k16_complex1 A)) ) ) ).
tt(redefinition_k1_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k1_integr16 A) = (k3_comseq_3 A)) ) ) ).
tt(redefinition_k1_integra2,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  =>  ((k1_integra2 A B) = (k23_member_1 A B)) ) ) ).
tt(redefinition_k1_integra5,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k1_integra5 A B) = (k5_relat_1 A B)) ) ) ).
tt(redefinition_k1_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) )  =>  ((k1_isocat_2 A B C D) = (k2_funct_5 D)) ) ) ).
tt(redefinition_k1_jordan2b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_jordan2b A) = (k5_finseq_1 A)) ) ) ).
tt(redefinition_k1_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  =>  ((k1_jordan A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k1_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_kurato_0 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k1_laplace,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k5_numbers) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v7_ordinal1 D)) ) )  =>  ((k1_laplace A B C D) = (k1_binop_1 B C D)) ) ) ).
tt(redefinition_k1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k1_lfuzzy_1 A B C) = (k1_fuzzy_1 A B C)) ) ) ).
tt(redefinition_k1_lmod_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k1_lmod_7 A B) = (k3_vectsp_5 A B)) ) ) ).
tt(redefinition_k1_lopban_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_lopban_1 B A A) &  ((v2_lopban_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_lopban_1 C A A) &  ((v2_lopban_1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((k1_lopban_2 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k1_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((k1_margrel1 A B C) = (k2_funcop_1 B C)) ) ) ).
tt(redefinition_k1_matrix15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((m1_matrix_1 E A B C) & (m1_matrix_1 F A B D)) ) ) ) )  =>  ((k1_matrix15 A B C D E F) = (k8_pre_poly E F)) ) ) ).
tt(redefinition_k1_matrix_6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  & (m1_matrix_1 C (u1_struct_0 B) A A)) )  =>  ((k1_matrix_6 A B C) = (k2_matrix_3 B C)) ) ) ).
tt(redefinition_k1_matrix_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k1_matrix_7 A B C D) = (k6_matrix_3 B C D)) ) ) ).
tt(redefinition_k1_matrixr2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  =>  ((k1_matrixr2 A B C) = (k6_matrixr1 B C)) ) ) ).
tt(redefinition_k1_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_finseq_1 E (u1_struct_0 B)) & (m1_matrlin F A C)) ) ) ) )  =>  ((k1_matrlin2 A B C D E F) = (k10_matrlin A B C D E F)) ) ) ).
tt(redefinition_k1_matrlin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((k1_matrlin A B C) = (k2_finseq_3 B C)) ) ) ).
tt(redefinition_k1_matrprob,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k3_finseq_2 A)) & (v7_ordinal1 C))  =>  ((k1_matrprob A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  =>  ((k1_mcart_1 A B C D) = (k4_xtuple_0 D)) ) ) ).
tt(redefinition_k1_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k1_measure1 A B C D) = (k2_xboole_0 C D)) ) ) ).
tt(redefinition_k1_measure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  =>  ((k1_measure2 A B C) = (k1_setfam_1 C)) ) ) ).
tt(redefinition_k1_measure3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  ((k1_measure3 A B C) = (k10_xtuple_0 C)) ) ) ).
tt(redefinition_k1_measure5,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k1_measure5 A B) = (k4_xxreal_1 A B)) ) ) ).
tt(redefinition_k1_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m2_measure8 C A B) & (v7_ordinal1 D)) )  =>  ((k1_measure8 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_member_1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k1_member_1 A) = (k2_xxreal_3 A)) ) ) ).
tt(redefinition_k1_mesfunc9,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_valued_0 A)) )  =>  ((k1_mesfunc9 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k1_metric_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers))))  &  ((m1_subset_1 D A) & (m1_subset_1 E B)) )  =>  ((k1_metric_1 A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k1_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C (k4_finseq_2 B A)) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E A)) ) ) )  =>  ((k1_midsp_3 A B C D E) = (k2_funct_7 C D E)) ) ) ).
tt(redefinition_k1_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C A))  =>  ((k1_mmlquery A B C) = (k9_relat_1 B C)) ) ) ).
tt(redefinition_k1_mod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((k1_mod_4 A B C D) = (k2_funct_4 D)) ) ) ).
tt(redefinition_k1_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  =>  ((k1_modelc_3 A) = (k13_modelc_2 A)) ) ) ).
tt(redefinition_k1_monoid_0,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k1_monoid_0 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k1_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k1_mssubfam A B) = (k1_mboolean A B)) ) ) ).
tt(redefinition_k1_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m2_pboole D A B C) & (m1_subset_1 E A)) ) ) )  =>  ((k1_msualg_3 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k1_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m1_msualg_4 D A B C) & (m1_subset_1 E A)) ) ) )  =>  ((k1_msualg_4 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k1_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A B B) & (m2_pboole D A B B)) )  =>  ((k1_msualg_6 A B C D) = (k8_pboole C D)) ) ) ).
tt(redefinition_k1_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  & (m1_subset_1 C k5_numbers)) )  =>  ((k1_nagata_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  =>  ((k1_nat_1 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k1_nat_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((k1_nat_5 A B C) = (k5_relat_1 B C)) ) ) ).
tt(redefinition_k1_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k1_nat_d A B) = (k5_int_1 A B)) ) ) ).
tt(redefinition_k1_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k1_zfmisc_1 A))) )  =>  ((k1_nattra_1 A B C D) = (k5_relat_1 C D)) ) ) ).
tt(redefinition_k1_ndiff_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  &  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) & (m1_subset_1 C (k4_finseq_1 A))) )  =>  ((k1_ndiff_5 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_normsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  =>  ((k1_normsp_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_oppcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) )  =>  ((k1_oppcat_1 A B C D) = (k2_funct_4 D)) ) ) ).
tt(redefinition_k1_partfun1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) )  =>  ((k1_partfun1 A B C D E F) = (k3_relat_1 E F)) ) ) ).
tt(redefinition_k1_partfun2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((k1_partfun2 A B) = (k4_relat_1 B)) ) ) ).
tt(redefinition_k1_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k1_pcs_0 A B C) = (k1_relat_1 C)) ) ) ).
tt(redefinition_k1_pdiff_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  & (m1_subset_1 D (k1_euclid A))) ) )  =>  ((k1_pdiff_6 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_pencil_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v11_pencil_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k1_pencil_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_pepin,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_pepin A) = (k3_square_1 A)) ) ) ).
tt(redefinition_k1_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k1_polyeq_3 A) = (k3_square_1 A)) ) ) ).
tt(redefinition_k1_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  =>  ((k1_polyform A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k1_polynom2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((k1_polynom2 A B) = (k13_pre_poly B)) ) ) ).
tt(redefinition_k1_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_finseq_1 C A)) )  =>  ((k1_polynom3 A B C) = (k2_finseq_3 B C)) ) ) ).
tt(redefinition_k1_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k2_zfmisc_1 A B))) )  =>  ((k1_pralg_1 A B C) = (k11_mcart_1 C)) ) ) ).
tt(redefinition_k1_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k3_finseq_2 A)) & (m1_subset_1 C (k3_finseq_2 A)))  =>  ((k1_pre_poly A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k1_prob_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_prob_1 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k1_prob_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  & (m1_subset_1 D k5_numbers)) )  =>  ((k1_prob_2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_prob_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  & (m1_subset_1 D k5_numbers)) )  =>  ((k1_prob_4 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D (k4_finseq_2 B A)) & (m1_subset_1 E (k4_finseq_2 B A))) ) ) )  =>  ((k1_prvect_1 A B C D E) = (k3_funcop_1 C D E)) ) ) ).
tt(redefinition_k1_prvect_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m1_prvect_2 C A B) & (m1_subset_1 D (k4_finseq_1 A))) )  =>  ((k1_prvect_2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k4_partfun1 (k3_finseq_2 A) A)))  =>  ((k1_pua2mss1 A B) = (k10_xtuple_0 B)) ) ) ).
tt(redefinition_k1_quatern2,ax, (k1_quatern2 = k21_quaterni) ).
tt(redefinition_k1_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_random_1 A) = (k1_zfmisc_1 A)) ) ) ).
tt(redefinition_k1_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k1_rcomp_1 A B) = (k1_xxreal_1 A B)) ) ) ).
tt(redefinition_k1_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_real_1 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k1_rearran1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (m1_subset_1 D k1_numbers)) ) )  =>  ((k1_rearran1 A B C D) = (k24_valued_1 C D)) ) ) ).
tt(redefinition_k1_recdef_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v4_valued_0 A)) )  =>  ((k1_recdef_1 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k1_relset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  ((k1_relset_1 A B) = (k9_xtuple_0 B)) ) ) ).
tt(redefinition_k1_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k1_relset_2 A B C D) = (k9_relat_1 C D)) ) ) ).
tt(redefinition_k1_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k1_zfmisc_1 A)) & (v7_ordinal1 C))  =>  ((k1_roughs_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k1_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v3_valued_0 A))  =>  ((k1_rvsum_1 A) = (k10_xtuple_0 A)) ) ) ).
tt(redefinition_k1_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_valued_0 A))  =>  ((k1_rvsum_2 A) = (k10_xtuple_0 A)) ) ) ).
tt(redefinition_k1_scmfsa_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  & (v1_int_1 B))  =>  ((k1_scmfsa_3 A B) = (k16_funcop_1 A B)) ) ) ).
tt(redefinition_k1_scm_inst,ax, (k1_scm_inst = k1_xboole_0) ).
tt(redefinition_k1_scmpds_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  & (v1_int_1 B))  =>  ((k1_scmpds_3 A B) = (k16_funcop_1 A B)) ) ) ).
tt(redefinition_k1_scmpds_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) ) )  =>  ((k1_scmpds_4 A B) = (k1_ordinal4 A B)) ) ) ).
tt(redefinition_k1_scmpds_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  &  ((v1_int_1 C) & (v1_int_1 D)) ) )  =>  ((k1_scmpds_9 A B C D) = (k4_funct_4 A B C D)) ) ) ).
tt(redefinition_k1_seq_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  ((k1_seq_1 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k1_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_seq_4 A) = (k1_tarski A)) ) ) ).
tt(redefinition_k1_seqfunc,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  & (v7_ordinal1 D))  =>  ((k1_seqfunc A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_series_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_membered A) & (v7_membered A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  ((k1_series_1 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k1_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k1_square_1 A B) = (k3_xxreal_0 A B)) ) ) ).
tt(redefinition_k1_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k1_stacks_1 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k1_stirl2_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k1_stirl2_1 A B C D) = (k8_relat_1 C D)) ) ) ).
tt(redefinition_k1_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_valuat_1 A B)) &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) )  =>  ((k1_sublemma A B C D) = (k1_funct_4 C D)) ) ) ).
tt(redefinition_k1_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k1_substut1 A))) )  =>  ((k1_substut2 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k1_supinf_1,ax, (k1_supinf_1 = k1_xxreal_0) ).
tt(redefinition_k1_supinf_2,ax, (k1_supinf_2 = k1_xboole_0) ).
tt(redefinition_k1_toler_1,ax, (! [A:$i,B:$i] :  ((v1_relat_1 A) =>  ((k1_toler_1 A B) = (k2_wellord1 A B)) ) ) ).
tt(redefinition_k1_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_borsuk_2 E A C D) &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) )  =>  ((k1_topalg_3 A B C D E F) = (k3_relat_1 E F)) ) ) ).
tt(redefinition_k1_topgen_3,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 B)))) =>  ((k1_topgen_3 A B C) = (k10_xtuple_0 C)) ) ) ).
tt(redefinition_k1_transgeo,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k1_transgeo A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k1_twoscomp,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) ) )  &  ( ((v4_msafree2 B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) )  &  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k1_twoscomp A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k1_unialg_3 A) = (k9_unialg_2 A)) ) ) ).
tt(redefinition_k1_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  & (m1_subset_1 D k5_numbers)) ) )  =>  ((k1_urysohn3 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_valued_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C)) )  =>  ((k1_valued_0 A B C) = (k9_nat_1 B C)) ) ) ).
tt(redefinition_k1_waybel10,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((k1_waybel10 A B) = (k7_lattice3 B)) ) ) ).
tt(redefinition_k1_waybel_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  ((k1_waybel_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k1_waybel20,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ((l1_orders_2 C) &  ((l1_orders_2 D) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((k1_waybel20 A B C D E F) = (k15_funct_3 E F)) ) ) ).
tt(redefinition_k1_waybel23,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))  =>  ((k1_waybel23 A B) = (k3_tarski B)) ) ) ).
tt(redefinition_k1_waybel27,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) & (m1_subset_1 D A)) ) )  =>  ((k1_waybel27 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((m2_pboole D A C (k7_funcop_1 A B)) & (m1_subset_1 E A)) ) ) )  =>  ((k1_waybel_5 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k1_waybel_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  & (m1_subset_1 D k5_numbers)) ) )  =>  ((k1_waybel_6 A B C D) = (k9_funct_7 C D)) ) ) ).
tt(redefinition_k1_wsierp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  &  ((m1_finseq_1 C B) & (m1_finseq_1 D B)) ) )  =>  ((k1_wsierp_1 A B C D) = (k7_finseq_1 C D)) ) ) ).
tt(redefinition_k1_yellow12,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k1_yellow12 A B C D) = (k1_binop_1 B C D)) ) ) ).
tt(redefinition_k1_yellow14,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) & (m1_subset_1 D A)) ) )  =>  ((k1_yellow14 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k1_yellow16,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_yellow_1 A B))))) ) )  =>  ((k1_yellow16 A B C D) = (k5_card_3 C D)) ) ) ).
tt(redefinition_k1_yellow_1,ax, (! [A:$i] :  ((k1_yellow_1 A) = (k1_wellord2 A)) ) ).
tt(redefinition_k1_zf_fund1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k1_zf_fund1 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k20_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k20_binop_2 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k20_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k20_bvfunc_1 A B) = (k9_xboolean A B)) ) ) ).
tt(redefinition_k20_glib_001,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_glib_001 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  =>  ((k20_glib_001 A B C D) = (k9_glib_001 A B C D)) ) ) ).
tt(redefinition_k20_grcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  & (m1_subset_1 B (k18_grcat_1 A)))  =>  ((k20_grcat_1 A B) = (k8_grcat_1 B)) ) ) ).
tt(redefinition_k20_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v2_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k20_matrixj1 A B C) = (k12_matrixj1 A B C)) ) ) ).
tt(redefinition_k20_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k20_mmlquery A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k20_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k20_quaterni A) = (k16_quaterni A)) ) ) ).
tt(redefinition_k20_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k20_rvsum_1 A) = (k19_rvsum_1 A)) ) ) ).
tt(redefinition_k20_seq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k14_seq_4 A)) & (m1_subset_1 C k2_numbers)) )  =>  ((k20_seq_4 A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k20_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k20_valued_1 A B C D E) = (k18_valued_1 D E)) ) ) ).
tt(redefinition_k21_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k4_abcmiz_1 k5_numbers)) =>  ((k21_abcmiz_1 A) = (k1_xtuple_0 A)) ) ) ).
tt(redefinition_k21_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k9_funct_2 A B)) & (m1_subset_1 D A)) ) )  =>  ((k21_aofa_i00 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k21_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k21_binop_2 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k21_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k21_bvfunc_1 A B) = (k7_xboolean A B)) ) ) ).
tt(redefinition_k21_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k21_euclid A) = (k20_euclid A)) ) ) ).
tt(redefinition_k21_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  &  ( ((v1_partfun1 D B) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v2_fomodel3 E A B C D) & (m1_fomodel2 E A B C)) ) ) ) )  =>  ((k21_fomodel3 A B C D E) = (k20_fomodel3 A B C D E)) ) ) ).
tt(redefinition_k21_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k21_mmlquery A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k21_rvsum_1,ax, (! [A:$i] :  ((m1_finseq_1 A k1_numbers) =>  ((k21_rvsum_1 A) = (k19_rvsum_1 A)) ) ) ).
tt(redefinition_k21_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k14_seq_4 A)))  =>  ((k21_seq_4 A B) = (k54_valued_1 B)) ) ) ).
tt(redefinition_k21_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k21_sin_cos A) = (k20_sin_cos A)) ) ) ).
tt(redefinition_k22_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k4_abcmiz_1 k5_numbers)) =>  ((k22_abcmiz_1 A) = (k2_xtuple_0 A)) ) ) ).
tt(redefinition_k22_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k22_binop_2 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k22_matrixj1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v2_matrixj1 B (u1_struct_0 A)) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) )  =>  ((k22_matrixj1 A B) = (k21_matrixj1 A B)) ) ) ).
tt(redefinition_k22_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k22_mmlquery A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k22_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  ((k22_substut1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k22_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v5_membered B) &  ((v5_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k22_valued_1 A B C D E) = (k18_valued_1 D E)) ) ) ).
tt(redefinition_k22_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k22_valued_2 A B C) = (k21_valued_2 C)) ) ) ).
tt(redefinition_k23_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((k23_abcmiz_1 A) = (k1_xtuple_0 A)) ) ) ).
tt(redefinition_k23_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k23_binop_2 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k23_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_partfun1 C B) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_fomodel2 D A B) & (v3_fomodel3 D A B C)) ) ) ) ) )  =>  ((k23_fomodel3 A B C D) = (k22_fomodel3 A B C D)) ) ) ).
tt(redefinition_k23_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m3_lexbfs B A) & (v7_ordinal1 C)) )  =>  ((k23_lexbfs A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k23_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ((k23_monoid_1 A) = (k22_monoid_1 A)) ) ) ).
tt(redefinition_k23_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k23_rvsum_1 A B) = (k22_rvsum_1 A B)) ) ) ).
tt(redefinition_k23_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  ((k23_substut1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k24_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ((k24_abcmiz_1 A) = (k2_xtuple_0 A)) ) ) ).
tt(redefinition_k24_binop_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k24_binop_2 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k24_fomodel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((k24_fomodel1 A B C) = (k23_fomodel1 A B C)) ) ) ).
tt(redefinition_k24_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 C (k1_fomodel1 A)) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((k24_fomodel3 A B C D) = (k17_fomodel0 B C D)) ) ) ).
tt(redefinition_k24_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_glib_000 B A))  =>  ((k24_glib_000 A B) = (k6_glib_000 B)) ) ) ).
tt(redefinition_k24_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k21_turing_1 A B))) )  =>  ((k24_turing_1 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k25_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k25_cat_4 A B C) = (k21_cat_4 A B C)) ) ) ).
tt(redefinition_k25_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v7_ordinal1 B) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((k25_fomodel3 A B C) = (k13_fomodel0 B C)) ) ) ).
tt(redefinition_k25_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  & (m1_glib_000 B A))  =>  ((k25_glib_000 A B) = (k7_glib_000 B)) ) ) ).
tt(redefinition_k25_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k16_substut1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((k25_substut1 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k25_turing_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_turing_1 A) &  ((l1_turing_1 B) & (m1_subset_1 C (k21_turing_1 A B))) )  =>  ((k25_turing_1 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k25_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k25_valued_1 A B C D) = (k24_valued_1 C D)) ) ) ).
tt(redefinition_k26_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k26_cat_4 A B C) = (k22_cat_4 A B C)) ) ) ).
tt(redefinition_k26_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k26_fomodel1 A) = (k11_fomodel1 A)) ) ) ).
tt(redefinition_k26_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k26_quaterni A B) = (k7_quaterni A B)) ) ) ).
tt(redefinition_k26_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k26_sin_cos A) = (k25_sin_cos A)) ) ) ).
tt(redefinition_k26_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k26_valued_1 A B C D) = (k24_valued_1 C D)) ) ) ).
tt(redefinition_k26_valued_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_valued_2 B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k26_valued_2 A B C) = (k25_valued_2 C)) ) ) ).
tt(redefinition_k27_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k27_cat_4 A B C) = (k21_cat_4 A B C)) ) ) ).
tt(redefinition_k27_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((m1_subset_1 C (k35_fomodel1 A)) &  ((v15_fomodel1 D A) & (m1_subset_1 D (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k27_fomodel3 A B C D) = (k26_fomodel3 A B C D)) ) ) ).
tt(redefinition_k27_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k27_quaterni A B) = (k10_quaterni A B)) ) ) ).
tt(redefinition_k28_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k28_cat_4 A B C) = (k22_cat_4 A B C)) ) ) ).
tt(redefinition_k28_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k28_fomodel1 A) = (k25_fomodel1 A)) ) ) ).
tt(redefinition_k28_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k28_quaterni A) = (k8_quaterni A)) ) ) ).
tt(redefinition_k29_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (v1_int_1 F)) ) ) ) )  =>  ((k29_aofa_i00 A B C D E F) = (k7_valued_1 E F)) ) ) ).
tt(redefinition_k29_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k29_fomodel1 A) = (k27_fomodel1 A)) ) ) ).
tt(redefinition_k29_fomodel3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ( ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  &  ((v7_ordinal1 D) &  ((m1_subset_1 E (k9_funct_2 (k33_fomodel2 A) (k33_fomodel2 A))) &  ((v4_fomodel2 F A) & (m1_subset_1 F (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) ) ) )  =>  ((k29_fomodel3 A B C D E F) = (k28_fomodel3 A B C D E F)) ) ) ).
tt(redefinition_k29_modelc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  & (v7_ordinal1 C))  =>  ((k29_modelc_1 A B C) = (k9_funct_7 B C)) ) ) ).
tt(redefinition_k29_quaterni,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k29_quaterni A B) = (k9_quaterni A B)) ) ) ).
tt(redefinition_k2_absvalue,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k2_absvalue A) = (k1_absvalue A)) ) ) ).
tt(redefinition_k2_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_aff_1 A B C) = (k1_aff_1 A B C)) ) ) ).
tt(redefinition_k2_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((k2_afinsq_1 A) = (k9_xtuple_0 A)) ) ) ).
tt(redefinition_k2_algstr_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k8_afinsq_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) A)))) )  &  ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) )  =>  ((k2_algstr_4 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_ami_2,ax, (k2_ami_2 = k2_scm_inst) ).
tt(redefinition_k2_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v2_xxreal_0 B) & (m1_subset_1 B k1_numbers)) )  =>  ((k2_asympt_0 A B) = (k24_valued_1 A B)) ) ) ).
tt(redefinition_k2_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_bhsp_1 A B C) = (k1_bhsp_1 A B C)) ) ) ).
tt(redefinition_k2_binarith,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_margrel1) & (m1_subset_1 B k6_margrel1))  =>  ((k2_binarith A B) = (k10_xboolean A B)) ) ) ).
tt(redefinition_k2_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F B)) ) ) )  =>  ((k2_binop_1 A B C D E F) = (k1_binop_1 D E F)) ) ) ).
tt(redefinition_k2_binop_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_binop_2 A) = (k5_xcmplx_0 A)) ) ) ).
tt(redefinition_k2_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) & (v1_xreal_0 B))  =>  ((k2_borsuk_7 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k2_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k2_bvfunc_1 A B C) = (k14_margrel1 B C)) ) ) ).
tt(redefinition_k2_calcul_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k2_calcul_2 A B) = (k1_calcul_2 A B)) ) ) ).
tt(redefinition_k2_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_5 A) & (l1_cat_1 A)) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k2_cat_5 A B) = (k14_mcart_1 B)) ) ) ).
tt(redefinition_k2_chain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) & (m1_subset_1 C (k2_finseq_1 A))) )  =>  ((k2_chain_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  =>  ((k2_classes2 A B) = (k1_zfmisc_1 B)) ) ) ).
tt(redefinition_k2_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) & (m1_pboole D A (k5_mssubfam A B))) )  =>  ((k2_closure1 A B C D) = (k15_pralg_1 C D)) ) ) ).
tt(redefinition_k2_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k2_closure2 A B) = (k1_closure2 A B)) ) ) ).
tt(redefinition_k2_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k2_complfld A) = (k14_complex1 A)) ) ) ).
tt(redefinition_k2_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  =>  ((k2_complsp2 A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k2_compos_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  & (m1_subset_1 B A))  =>  ((k2_compos_0 A B) = (k4_xtuple_0 B)) ) ) ).
tt(redefinition_k2_comseq_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) ) )  =>  ((k2_comseq_2 A B) = (k1_comseq_2 B)) ) ) ).
tt(redefinition_k2_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v7_ordinal1 B))  =>  ((k2_comseq_3 A B) = (k1_newton A B)) ) ) ).
tt(redefinition_k2_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k5_qc_lang1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((k2_cqc_lang A B C) = (k16_funcop_1 B C)) ) ) ).
tt(redefinition_k2_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  =>  ((k2_descip_1 A B C) = (k16_finseq_1 B C)) ) ) ).
tt(redefinition_k2_diff_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  & (v1_xreal_0 B))  =>  ((k2_diff_1 A B) = (k1_diff_1 A B)) ) ) ).
tt(redefinition_k2_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  =>  ((k2_domain_1 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k2_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 C (k2_zfmisc_1 A B)) =>  ((k2_dtconstr A B C) = (k11_mcart_1 C)) ) ) ).
tt(redefinition_k2_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  & (m1_subset_1 B (k1_ec_pf_2 A)))  =>  ((k2_ec_pf_2 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k2_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k2_eqrel_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k2_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k2_euclid_4 A B C) = (k1_euclid_4 A B C)) ) ) ).
tt(redefinition_k2_extreal1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k2_extreal1 A B) = (k6_xxreal_3 A B)) ) ) ).
tt(redefinition_k2_extreal2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k2_extreal2 A B) = (k3_xxreal_0 A B)) ) ) ).
tt(redefinition_k2_fib_num3,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k2_fib_num3 A B) = (k4_tarski A B)) ) ) ).
tt(redefinition_k2_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_finseq_1 A) = (k1_finseq_1 A)) ) ) ).
tt(redefinition_k2_finseq_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k2_finseq_4 A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k2_finseq_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  =>  ((k2_finseq_7 A B C D) = (k10_funct_7 B C D)) ) ) ).
tt(redefinition_k2_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_finseq_1 E A) & (m1_subset_1 F B)) ) ) ) )  =>  ((k2_finseqop A B C D E F) = (k4_funcop_1 D E F)) ) ) ).
tt(redefinition_k2_finsop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (m1_finseq_1 C A)) )  =>  ((k2_finsop_1 A B C) = (k1_funct_4 B C)) ) ) ).
tt(redefinition_k2_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k2_finsub_1 A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k2_flang_1,ax, (! [A:$i] :  ((k2_flang_1 A) = (k4_afinsq_1 A)) ) ).
tt(redefinition_k2_fomodel0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_fomodel0 A B) = (k13_finseq_1 B)) ) ) ).
tt(redefinition_k2_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C D) (k9_funct_2 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C D) (k9_funct_2 A B))))) )  & (m1_subset_1 F (k2_zfmisc_1 C D))) ) ) ) )  =>  ((k2_funcsdom A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k2_funct_2,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k2_funct_2 A B) = (k2_funct_1 B)) ) ) ).
tt(redefinition_k2_funct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k2_funct_3 A B C) = (k1_funct_3 C)) ) ) ).
tt(redefinition_k2_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  &  ((v16_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((k2_functor3 A B C D E) = (k13_functor0 A B C D E)) ) ) ).
tt(redefinition_k2_fuzzy_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) k1_numbers)))) ) ) ) )  =>  ((k2_fuzzy_4 A B C) = (k2_funct_4 C)) ) ) ).
tt(redefinition_k2_graph_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  =>  ((k2_graph_2 A B C D) = (k1_graph_2 B C D)) ) ) ).
tt(redefinition_k2_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_group_2 B A) &  ((v1_group_3 C A) & (m1_group_2 C A)) ) )  =>  ((k2_group_6 A B C) = (k9_group_2 A B C)) ) ) ).
tt(redefinition_k2_groupp_1,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((k2_groupp_1 A B) = (k1_groupp_1 A B)) ) ) ).
tt(redefinition_k2_henmodel,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k6_qc_lang1 A)) &  ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C (k7_qc_lang1 A B)) & (m1_finseq_1 C (k2_qc_lang1 A))) ) ) )  =>  ((k2_henmodel A B C) = (k10_qc_lang1 A B C)) ) ) ).
tt(redefinition_k2_heyting1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k7_normform A)) =>  ((k2_heyting1 A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k2_index_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k2_index_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  ((k2_int_3 A) = (k16_complex1 A)) ) ) ).
tt(redefinition_k2_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  &  ((m2_integr15 D A B C) & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((k2_integr15 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k2_integr16,ax, (! [A:$i] :  ((m1_finseq_1 A k2_numbers) =>  ((k2_integr16 A) = (k4_comseq_3 A)) ) ) ).
tt(redefinition_k2_integr18,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  &  ((m2_integr18 E A B C D) & (m1_subset_1 F k5_numbers)) ) ) ) )  =>  ((k2_integr18 A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k2_integra2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  & (m1_subset_1 C k5_numbers)) )  =>  ((k2_integra2 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k2_interva1 A B C) = (k1_interva1 A B C)) ) ) ).
tt(redefinition_k2_jordan1h,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k3_finseq_2 A)))  =>  ((k2_jordan1h A B) = (k16_matrix_1 B)) ) ) ).
tt(redefinition_k2_jordan,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  & (m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B)))) )  =>  ((k2_jordan A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k2_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  &  ((m1_kolmog01 D A B C) & (m1_subset_1 E (k1_zfmisc_1 A))) ) )  =>  ((k2_kolmog01 A B C D E) = (k5_relat_1 D E)) ) ) ).
tt(redefinition_k2_kurato_0,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k2_kurato_0 A B) = (k4_funct_6 B)) ) ) ).
tt(redefinition_k2_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k2_lattice3 A) = (k8_filter_1 A)) ) ) ).
tt(redefinition_k2_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k2_lfuzzy_0 A B C) = (k4_xxreal_0 B C)) ) ) ).
tt(redefinition_k2_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k2_lfuzzy_1 A B C) = (k2_fuzzy_1 A B C)) ) ) ).
tt(redefinition_k2_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k2_lopclset A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k2_lpspace1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k3_rfunct_3 A B) (k3_rfunct_3 A B)) (k3_rfunct_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_rfunct_3 A B) (k3_rfunct_3 A B)) (k3_rfunct_3 A B))))) )  &  ((m1_subset_1 D (k3_rfunct_3 A B)) & (m1_subset_1 E (k3_rfunct_3 A B))) ) ) )  =>  ((k2_lpspace1 A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k2_matrix10,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_matrix_1 B k1_numbers A A))  =>  ((k2_matrix10 A B) = (k4_matrixr1 B)) ) ) ).
tt(redefinition_k2_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) & (m1_subset_1 E (u1_struct_0 C))) ) ) )  =>  ((k2_matrix13 A B C D E) = (k6_matrix_3 C D E)) ) ) ).
tt(redefinition_k2_matrix14,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  & (m1_subset_1 B k5_numbers))  =>  ((k2_matrix14 A B) = (k1_matrix14 A B)) ) ) ).
tt(redefinition_k2_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) & (m1_subset_1 D A)) ) )  =>  ((k2_matrix_2 A B C D) = (k1_matrix_2 B C D)) ) ) ).
tt(redefinition_k2_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((k2_matrix_6 A B C D) = (k3_matrix_3 B C D)) ) ) ).
tt(redefinition_k2_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A)))) )  =>  ((k2_matrixj1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (v7_ordinal1 C)) )  =>  ((k2_matrixj2 A B C) = (k1_matrixj2 A B C)) ) ) ).
tt(redefinition_k2_matrixr2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_matrix_1 B k1_numbers A A))  =>  ((k2_matrixr2 A B) = (k1_matrixr1 B)) ) ) ).
tt(redefinition_k2_matrlin,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((k2_matrlin A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k2_matrprob,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_matrprob A) = (k5_finseq_1 A)) ) ) ).
tt(redefinition_k2_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  =>  ((k2_mcart_1 A B C D) = (k5_xtuple_0 D)) ) ) ).
tt(redefinition_k2_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k2_measure1 A B C D) = (k3_xboole_0 C D)) ) ) ).
tt(redefinition_k2_measure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  =>  ((k2_measure2 A B C) = (k3_tarski C)) ) ) ).
tt(redefinition_k2_measure4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_measure2 C A B))  =>  ((k2_measure4 A B C) = (k3_tarski C)) ) ) ).
tt(redefinition_k2_measure6,ax, (! [A:$i,B:$i] :  ( ((v3_membered A) & (v1_xreal_0 B))  =>  ((k2_measure6 A B) = (k17_member_1 A B)) ) ) ).
tt(redefinition_k2_measure7,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) &  ((m1_measure7 B A) & (m1_subset_1 C k5_numbers)) )  =>  ((k2_measure7 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_member_1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k2_member_1 A) = (k5_xxreal_3 A)) ) ) ).
tt(redefinition_k2_midsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((k2_midsp_3 A B C) = (k5_finseq_1 C)) ) ) ).
tt(redefinition_k2_mmlquery,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k2_mmlquery A B C) = (k7_relat_1 B C)) ) ) ).
tt(redefinition_k2_morph_01,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k2_morph_01 A B C) = (k6_rusub_4 A B C)) ) ) ).
tt(redefinition_k2_msaterm,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((k2_msaterm A B C) = (k6_msafree A B C)) ) ) ).
tt(redefinition_k2_mssubfam,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m3_pboole C A (k1_mboolean A B)) & (m1_subset_1 D A)) ) )  =>  ((k2_mssubfam A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k2_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k2_msualg_4 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k2_msualg_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) &  ((m1_msualg_6 C A B) & (m1_msualg_6 D A B)) ) )  =>  ((k2_msualg_6 A B C D) = (k8_pboole C D)) ) ) ).
tt(redefinition_k2_multop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_zfmisc_1 A B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  &  ((m1_subset_1 F A) &  ((m1_subset_1 G B) & (m1_subset_1 H C)) ) ) ) ) ) )  =>  ((k2_multop_1 A B C D E F G H) = (k1_multop_1 E F G H)) ) ) ).
tt(redefinition_k2_nagata_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) ) )  =>  ((k2_nagata_1 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k2_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k2_nat_1 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k2_nat_3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k1_numbers) & (v7_ordinal1 B))  =>  ((k2_nat_3 A B) = (k1_nat_3 A B)) ) ) ).
tt(redefinition_k2_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k2_nat_d A B) = (k6_int_1 A B)) ) ) ).
tt(redefinition_k2_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  &  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 A A C C) C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 B B D D) D)))) ) ) ) ) )  =>  ((k2_nattra_1 A B C D E F) = (k3_funct_4 E F)) ) ) ).
tt(redefinition_k2_newton,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v7_ordinal1 B))  =>  ((k2_newton A B) = (k1_newton A B)) ) ) ).
tt(redefinition_k2_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k2_openlatt A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k2_partfun1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k2_partfun1 A B C D) = (k5_relat_1 C D)) ) ) ).
tt(redefinition_k2_partfun2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k2_partfun2 A B C) = (k2_funct_1 C)) ) ) ).
tt(redefinition_k2_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k2_partfun3 A B C) = (k1_partfun3 C)) ) ) ).
tt(redefinition_k2_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((k2_pcs_0 A B C D E F) = (k2_xboole_0 E F)) ) ) ).
tt(redefinition_k2_pencil_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k2_pencil_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_pencil_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_pre_topc A))) )  =>  ((k2_pencil_2 A B C) = (k7_relat_1 B C)) ) ) ).
tt(redefinition_k2_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_petri A)))  =>  ((k2_petri A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k2_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((k2_pnproc_1 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k2_polyeq_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k2_numbers)) ) )  =>  ((k2_polyeq_3 A B C D) = (k3_polyeq_1 A B C D)) ) ) ).
tt(redefinition_k2_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v7_ordinal1 B))  =>  ((k2_polyform A B) = (k1_newton A B)) ) ) ).
tt(redefinition_k2_polynom2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  =>  ((k2_polynom2 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k2_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k2_polynom3 A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k2_power,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k1_numbers))  =>  ((k2_power A B) = (k1_power A B)) ) ) ).
tt(redefinition_k2_pralg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_finseq_1 C (k2_zfmisc_1 A B))) )  =>  ((k2_pralg_1 A B C) = (k12_mcart_1 C)) ) ) ).
tt(redefinition_k2_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((k2_pralg_2 A) = (k7_funct_6 A)) ) ) ).
tt(redefinition_k2_pre_ff,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k3_finseq_2 k5_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 k5_numbers))))) )  & (m1_subset_1 B k5_numbers))  =>  ((k2_pre_ff A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k2_pre_poly,ax, (! [A:$i] :  ((k2_pre_poly A) = (k6_finseq_1 A)) ) ).
tt(redefinition_k2_quatern2,ax, (k2_quatern2 = k22_quaterni) ).
tt(redefinition_k2_quatern3,ax, (! [A:$i] :  ((m1_subset_1 A k1_quaterni) =>  ((k2_quatern3 A) = (k1_quatern3 A)) ) ) ).
tt(redefinition_k2_quin_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) & (m1_subset_1 C k1_numbers)) )  =>  ((k2_quin_1 A B C) = (k1_quin_1 A B C)) ) ) ).
tt(redefinition_k2_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k2_ranknull A B C D) = (k7_relat_1 C D)) ) ) ).
tt(redefinition_k2_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  =>  ((k2_rcomp_1 A B) = (k4_xxreal_1 A B)) ) ) ).
tt(redefinition_k2_real_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k2_real_1 A) = (k5_xcmplx_0 A)) ) ) ).
tt(redefinition_k2_relset_1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  ((k2_relset_1 A B) = (k10_xtuple_0 B)) ) ) ).
tt(redefinition_k2_rfinseq,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  =>  ((k2_rfinseq A B C) = (k1_rfinseq B C)) ) ) ).
tt(redefinition_k2_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((k2_robbins3 A) = (k8_filter_1 A)) ) ) ).
tt(redefinition_k2_roughs_1,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k1_zfmisc_1 A)) =>  ((k2_roughs_1 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k2_scm_comp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A (k7_dtconstr k1_scm_comp)) &  ((m1_subset_1 B (k4_dtconstr k1_scm_comp)) & (m1_subset_1 C (k4_dtconstr k1_scm_comp))) )  =>  ((k2_scm_comp A B C) = (k6_trees_4 A B C)) ) ) ).
tt(redefinition_k2_scmfsa_1,ax, (k2_scmfsa_1 = k2_scm_inst) ).
tt(redefinition_k2_scmfsa_2,ax, (k2_scmfsa_2 = k2_scm_inst) ).
tt(redefinition_k2_scmpds_i,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_scm_inst) & (v1_int_1 B))  =>  ((k2_scmpds_i A B) = (k10_finseq_1 A B)) ) ) ).
tt(redefinition_k2_scmring2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 B (u1_struct_0 (k1_scmring2 A)))) ) ) )  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A)))) ) )  =>  ((k2_scmring2 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_scpinvar,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) ) )  =>  ((k2_scpinvar A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k2_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k2_seq_2 A) = (k1_seq_2 A)) ) ) ).
tt(redefinition_k2_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k2_setlim_1 A B) = (k1_setlim_1 B)) ) ) ).
tt(redefinition_k2_setwiseo,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k2_setwiseo A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k2_setwop_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_setwop_2 A) = (k1_finseq_1 A)) ) ) ).
tt(redefinition_k2_simplex0,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k2_simplex0 A B) = (k1_simplex0 B)) ) ) ).
tt(redefinition_k2_simplex2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v1_simplex2 B A) & (l1_pre_topc B)) ) ) )  =>  ((k2_simplex2 A B) = (k1_simplex2 A B)) ) ) ).
tt(redefinition_k2_square_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k2_square_1 A B) = (k4_xxreal_0 A B)) ) ) ).
tt(redefinition_k2_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 B) & (m1_finseq_1 C A))  =>  ((k2_stacks_1 A B C) = (k2_finseq_3 B C)) ) ) ).
tt(redefinition_k2_stirl2_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k2_stirl2_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k2_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  =>  ((k2_sublemma A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k2_substlat,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_substlat A B)) & (m1_subset_1 D (k1_substlat A B)))  =>  ((k2_substlat A B C D) = (k2_xboole_0 C D)) ) ) ).
tt(redefinition_k2_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k1_substut1 A))) )  =>  ((k2_substut2 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k2_supinf_1,ax, (k2_supinf_1 = k2_xxreal_0) ).
tt(redefinition_k2_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k2_supinf_2 A) = (k2_xxreal_3 A)) ) ) ).
tt(redefinition_k2_tbsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  & (m1_subset_1 C k5_numbers)) )  =>  ((k2_tbsp_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_toler_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k2_toler_1 A B C) = (k2_wellord1 B C)) ) ) ).
tt(redefinition_k2_topalg_2,ax, (k2_topalg_2 = k3_topmetr) ).
tt(redefinition_k2_topalg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A C C) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) )  =>  ((k2_topalg_3 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k2_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) ) ) )  =>  ((k2_topalg_4 A B C D E) = (k13_funct_3 D E)) ) ) ).
tt(redefinition_k2_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_topalg_5 A) = (k1_topalg_5 A)) ) ) ).
tt(redefinition_k2_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k2_topgen_4 A B C) = (k3_setfam_1 B C)) ) ) ).
tt(redefinition_k2_topreal7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k2_topreal7 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k2_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k2_trees_4 A B) = (k1_trees_4 B)) ) ) ).
tt(redefinition_k2_trees_a,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  & (m1_subset_1 B A))  =>  ((k2_trees_a A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k2_turing_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C A) & (m1_subset_1 D B)) ) )  =>  ((k2_turing_1 A B C D) = (k16_funcop_1 C D)) ) ) ).
tt(redefinition_k2_valuat_1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  (~ (v1_xboole_0 B)) )  =>  ((k2_valuat_1 A B) = (k1_valuat_1 A B)) ) ) ).
tt(redefinition_k2_valued_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) )  =>  ((k2_valued_0 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k2_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k2_valued_1 A B C D E) = (k1_valued_1 D E)) ) ) ).
tt(redefinition_k2_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((k2_vectmetr A) = (k1_vectmetr A)) ) ) ).
tt(redefinition_k2_vectsp_8,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  ((k2_vectsp_8 A B) = (k3_vectsp_5 A B)) ) ) ).
tt(redefinition_k2_waybel26,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_waybel26 A B))))) ) )  =>  ((k2_waybel26 A B C D) = (k5_card_3 C D)) ) ) ).
tt(redefinition_k2_waybel28,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_waybel28 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) )  =>  ((k2_waybel28 A B C) = (k1_waybel28 A B C)) ) ) ).
tt(redefinition_k2_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (m2_pboole D A C (k7_funcop_1 A B)))  =>  ((k2_waybel_5 A B C D) = (k7_funct_6 D)) ) ) ).
tt(redefinition_k2_waybel_6,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  & (m1_subset_1 E B)) ) ) )  =>  ((k2_waybel_6 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k2_wsierp_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) =>  ((k2_wsierp_1 A) = (k16_rvsum_1 A)) ) ) ).
tt(redefinition_k2_yellow14,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A B)))) & (m1_subset_1 D A)) ) )  =>  ((k2_yellow14 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k2_yellow16,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  ((k2_yellow16 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k2_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((k2_yellow_3 A B C D E F) = (k1_yellow_3 E F)) ) ) ).
tt(redefinition_k2_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k2_yellow_4 A B C) = (k1_yellow_4 A B C)) ) ) ).
tt(redefinition_k2_yellow_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  & (m1_subset_1 D A)) ) )  =>  ((k2_yellow_6 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k2_zf_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  &  ((m1_subset_1 C k1_zf_lang) & (m1_subset_1 D A)) ) )  =>  ((k2_zf_lang1 A B C D) = (k2_funct_7 B C D)) ) ) ).
tt(redefinition_k2_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((k2_zf_model A) = (k1_zf_model A)) ) ) ).
tt(redefinition_k2_zfrefle1,ax, (k2_zfrefle1 = k1_zfrefle1) ).
tt(redefinition_k2_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  &  ((v3_ordinal1 C) & (m1_subset_1 C B)) ) )  =>  ((k2_zf_refle A B C) = (k1_zf_refle A B C)) ) ) ).
tt(redefinition_k30_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) )  =>  ((k30_fomodel2 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k31_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (v1_int_1 F)) ) ) ) )  =>  ((k31_aofa_i00 A B C D E F) = (k24_valued_1 E F)) ) ) ).
tt(redefinition_k31_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_fomodel1 A)))  =>  ((k31_fomodel2 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k31_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k31_quaterni A) = (k30_quaterni A)) ) ) ).
tt(redefinition_k31_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k31_valued_1 A B C) = (k30_valued_1 C)) ) ) ).
tt(redefinition_k31_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k31_valued_2 A B C D) = (k30_valued_2 B C D)) ) ) ).
tt(redefinition_k32_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k32_abcmiz_1 A) = (k15_abcmiz_1 A)) ) ) ).
tt(redefinition_k32_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k32_aofa_i00 A B C D E F) = (k45_valued_1 E F)) ) ) ).
tt(redefinition_k32_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k32_fomodel1 A) = (k31_fomodel1 A)) ) ) ).
tt(redefinition_k32_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((k32_glib_000 A B) = (k30_glib_000 A B)) ) ) ).
tt(redefinition_k32_sin_cos,ax, (k32_sin_cos = k31_sin_cos) ).
tt(redefinition_k32_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k32_valued_1 A B C) = (k30_valued_1 C)) ) ) ).
tt(redefinition_k32_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k32_valued_2 A B C D) = (k30_valued_2 B C D)) ) ) ).
tt(redefinition_k33_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((k33_abcmiz_1 A) = (k16_abcmiz_1 A)) ) ) ).
tt(redefinition_k33_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k33_aofa_i00 A B C D E F) = (k1_valued_1 E F)) ) ) ).
tt(redefinition_k33_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k33_fomodel2 A) = (k27_fomodel2 A)) ) ) ).
tt(redefinition_k33_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((k33_glib_000 A B) = (k31_glib_000 A B)) ) ) ).
tt(redefinition_k33_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))))  =>  ((k33_substut1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k34_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k34_aofa_i00 A B C D E F) = (k18_valued_1 E F)) ) ) ).
tt(redefinition_k34_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k34_fomodel2 A) = (k7_fomodel1 A)) ) ) ).
tt(redefinition_k34_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A))))  =>  ((k34_substut1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k34_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v5_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k34_valued_1 A B C) = (k30_valued_1 C)) ) ) ).
tt(redefinition_k35_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k35_aofa_i00 A B C D E F) = (k2_aofa_i00 E F)) ) ) ).
tt(redefinition_k35_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k35_fomodel1 A) = (k27_fomodel1 A)) ) ) ).
tt(redefinition_k35_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  ((k35_fomodel2 A B) = (k29_fomodel2 A B)) ) ) ).
tt(redefinition_k35_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  & (m1_subset_1 B (k6_glib_000 A)))  =>  ((k35_glib_000 A B) = (k34_glib_000 A B)) ) ) ).
tt(redefinition_k36_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k36_aofa_i00 A B C D E F) = (k3_aofa_i00 E F)) ) ) ).
tt(redefinition_k36_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (v7_ordinal1 B))  =>  ((k36_fomodel2 A B) = (k28_fomodel2 A B)) ) ) ).
tt(redefinition_k36_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  &  ((v13_fomodel1 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((k36_fomodel3 A B C) = (k34_fomodel3 A B C)) ) ) ).
tt(redefinition_k36_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  &  ( ((v3_card_1 C B) & (m1_subset_1 C (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))))  &  ((v3_card_1 D B) & (m1_subset_1 D (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A)))) ) ) )  =>  ((k36_fomodel4 A B C D) = (k35_fomodel4 A B C D)) ) ) ).
tt(redefinition_k36_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k36_valued_1 A B C) = (k35_valued_1 C)) ) ) ).
tt(redefinition_k37_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k37_aofa_i00 A B C D E F) = (k4_aofa_i00 E F)) ) ) ).
tt(redefinition_k37_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k37_fomodel1 A) = (k9_fomodel1 A)) ) ) ).
tt(redefinition_k37_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k16_fomodel2 A B)) &  ( ((v4_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A)))  & (m1_subset_1 E B)) ) ) )  =>  ((k37_fomodel2 A B C D E) = (k5_fomodel2 C D E)) ) ) ).
tt(redefinition_k37_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k37_valued_1 A B C) = (k35_valued_1 C)) ) ) ).
tt(redefinition_k37_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k37_valued_2 A B C D) = (k36_valued_2 B C D)) ) ) ).
tt(redefinition_k38_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) &  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  &  ((m3_aofa_i00 E A B C D) & (m3_aofa_i00 F A B C D)) ) ) ) )  =>  ((k38_aofa_i00 A B C D E F) = (k5_aofa_i00 E F)) ) ) ).
tt(redefinition_k38_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k38_valued_2 A B C D) = (k36_valued_2 B C D)) ) ) ).
tt(redefinition_k39_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k39_fomodel1 A) = (k25_fomodel1 A)) ) ) ).
tt(redefinition_k39_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( ((v12_fomodel4 B k6_numbers A) &  ((v12_fomodel4 B 1 A) & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  & (v10_fomodel4 C A B)) )  =>  ((k39_fomodel4 A B C) = (k38_fomodel4 A B C)) ) ) ).
tt(redefinition_k39_substut1,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  =>  ((k39_substut1 A B) = (k37_substut1 A B)) ) ) ).
tt(redefinition_k3_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  ((k3_abcmiz_1 A) = (k1_xtuple_0 A)) ) ) ).
tt(redefinition_k3_ami_wstd,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_setfam_1 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  & (v7_ordinal1 C)) )  =>  ((k3_ami_wstd A B C) = (k2_ami_wstd A B C)) ) ) ).
tt(redefinition_k3_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k9_funct_2 A B)) & (m1_subset_1 D (k9_funct_2 A B))) ) )  =>  ((k3_aofa_000 A B C D E) = (k2_aofa_000 C D E)) ) ) ).
tt(redefinition_k3_asympt_0,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ( (~ (v3_xxreal_0 B))  & (m1_subset_1 B k1_numbers)) )  =>  ((k3_asympt_0 A B) = (k7_valued_1 A B)) ) ) ).
tt(redefinition_k3_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  =>  ((k3_binop_1 A B C D) = (k1_binop_1 B C D)) ) ) ).
tt(redefinition_k3_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k3_binop_2 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k3_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_boolealg A B C) = (k2_boolealg A B C)) ) ) ).
tt(redefinition_k3_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((k3_borsuk_1 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k3_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) )  =>  ((k3_borsuk_2 A B C D E F) = (k15_funct_3 E F)) ) ) ).
tt(redefinition_k3_borsuk_7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) & (v1_xreal_0 B))  =>  ((k3_borsuk_7 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k3_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k3_bvfunc26 A B C) = (k1_bvfunc26 B C)) ) ) ).
tt(redefinition_k3_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m1_cat_2 D B C) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A D)))) )  & (m1_subset_1 F A)) ) ) ) )  =>  ((k3_cat_2 A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k3_catalan2,ax, (! [A:$i] :  ((k3_catalan2 A) = (k8_afinsq_1 A)) ) ).
tt(redefinition_k3_catalg_1,ax, (! [A:$i] :  ((k3_catalg_1 A) = (k2_catalg_1 A)) ) ).
tt(redefinition_k3_cgames_1,ax, (k3_cgames_1 = k1_cgames_1) ).
tt(redefinition_k3_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m3_chord B A) & (m1_subset_1 C (k6_glib_000 A))) )  =>  ((k3_chord A B C) = (k4_finseq_4 B C)) ) ) ).
tt(redefinition_k3_classes1,ax, (! [A:$i,B:$i] :  ((v3_ordinal1 B) =>  ((k3_classes1 A B) = (k2_classes1 A B)) ) ) ).
tt(redefinition_k3_classes2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  & (m1_subset_1 B A))  =>  ((k3_classes2 A B) = (k3_tarski B)) ) ) ).
tt(redefinition_k3_closure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) & (m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B))) )  =>  ((k3_closure1 A B C D) = (k8_pboole C D)) ) ) ).
tt(redefinition_k3_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k3_closure3 A B C D) = (k2_xboole_0 C D)) ) ) ).
tt(redefinition_k3_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  & (m1_subset_1 B A))  =>  ((k3_cohsp_1 A B) = (k5_finsub_1 B)) ) ) ).
tt(redefinition_k3_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) &  ((m2_cat_1 E B C) & (m1_subset_1 F (k2_commacat A B C D E))) ) ) ) )  =>  ((k3_commacat A B C D E F) = (k13_mcart_1 F)) ) ) ).
tt(redefinition_k3_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_complex1 A) = (k1_complex1 A)) ) ) ).
tt(redefinition_k3_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  =>  ((k3_complsp2 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k3_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  & (v7_ordinal1 C)) )  =>  ((k3_compos_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k3_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  =>  ((k3_descip_1 A B C) = (k1_rfinseq B C)) ) ) ).
tt(redefinition_k3_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  =>  ((k3_domain_1 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k3_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ((m1_finseq_1 C (k2_zfmisc_1 A B)) =>  ((k3_dtconstr A B C) = (k12_mcart_1 C)) ) ) ).
tt(redefinition_k3_ec_pf_2,ax, (! [A:$i,B:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  & (m1_subset_1 B (k1_ec_pf_2 A)))  =>  ((k3_ec_pf_2 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k3_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k3_eqrel_1 A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k3_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k3_euclid A) = (k54_valued_1 A)) ) ) ).
tt(redefinition_k3_finance1,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k3_finance1 A B) = (k18_valued_1 A B)) ) ) ).
tt(redefinition_k3_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_finseq_1 A) = (k1_card_1 A)) ) ) ).
tt(redefinition_k3_finseq_2,ax, (! [A:$i] :  ((k3_finseq_2 A) = (k13_finseq_1 A)) ) ).
tt(redefinition_k3_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k3_finseq_4 A B C D) = (k11_finseq_1 B C D)) ) ) ).
tt(redefinition_k3_finseq_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) ) )  =>  ((k3_finseq_6 A B C D) = (k2_finseq_6 B C D)) ) ) ).
tt(redefinition_k3_finseq_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((v7_ordinal1 C) & (v7_ordinal1 D)) )  =>  ((k3_finseq_8 A B C D) = (k2_finseq_8 B C D)) ) ) ).
tt(redefinition_k3_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((m1_subset_1 E A) & (m1_finseq_1 F B)) ) ) ) )  =>  ((k3_finseqop A B C D E F) = (k5_funcop_1 D E F)) ) ) ).
tt(redefinition_k3_finsop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_finsop_1 A) = (k9_xtuple_0 A)) ) ) ).
tt(redefinition_k3_finsub_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k3_finsub_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k3_flang_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k3_flang_1 A B) = (k3_afinsq_1 B)) ) ) ).
tt(redefinition_k3_fomodel2,ax, (! [A:$i] :  ((k3_fomodel2 A) = (k4_relat_1 A)) ) ).
tt(redefinition_k3_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((k3_funcsdom A B C D E) = (k3_funcop_1 C D E)) ) ) ).
tt(redefinition_k3_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D A)) )  =>  ((k3_funct_2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k3_funct_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 B A) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D A)) )  =>  ((k3_funct_7 A B C D) = (k2_funct_7 B C D)) ) ) ).
tt(redefinition_k3_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  &  ((v16_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((k3_functor3 A B C D E) = (k13_functor0 A B C D E)) ) ) ).
tt(redefinition_k3_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k3_graph_1 A B) = (k1_graph_1 A B)) ) ) ).
tt(redefinition_k3_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_funct_2 A A)) & (m1_subset_1 C (k1_funct_2 A A)))  =>  ((k3_graphsp A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k3_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k3_group_2 A B C) = (k2_group_2 A B C)) ) ) ).
tt(redefinition_k3_group_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v1_group_3 B A) & (m1_group_2 B A))  & (m1_group_2 C A)) )  =>  ((k3_group_6 A B C) = (k9_group_2 A B C)) ) ) ).
tt(redefinition_k3_idea_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k6_margrel1))  &  ((v3_card_1 C A) & (m1_finseq_1 C k6_margrel1)) ) )  =>  ((k3_idea_1 A B C) = (k2_idea_1 A B C)) ) ) ).
tt(redefinition_k3_int_5,ax, (! [A:$i,B:$i] :  ( ((v1_finset_1 A) & (m1_finseq_1 B (k1_zfmisc_1 A)))  =>  ((k3_int_5 A B) = (k1_card_3 B)) ) ) ).
tt(redefinition_k3_jgraph_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((k3_jgraph_1 A B) = (k2_jgraph_1 B)) ) ) ).
tt(redefinition_k3_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k3_jordan10 A) = (k1_jordan10 A)) ) ) ).
tt(redefinition_k3_kolmog01,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) &  ( (~ (v1_xboole_0 C))  &  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D C) &  ((v4_prob_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C)))) ) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B (k9_setfam_1 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k9_setfam_1 D))))) ) ) ) )  =>  ((k3_kolmog01 A B C D E) = (k3_card_3 E)) ) ) ).
tt(redefinition_k3_lattice5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((l1_struct_0 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((k3_lattice5 A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_lattices A B C) = (k1_lattices A B C)) ) ) ).
tt(redefinition_k3_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_lfuzzy_0 A B C) = (k3_xxreal_0 B C)) ) ) ).
tt(redefinition_k3_lfuzzy_1,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k3_lfuzzy_1 A B) = (k4_funct_3 A B)) ) ) ).
tt(redefinition_k3_lopclset,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_lopclset A)) & (m1_subset_1 C (k1_lopclset A))) )  =>  ((k3_lopclset A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k3_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  =>  ((k3_matrix10 A B C) = (k3_matrixr1 B C)) ) ) ).
tt(redefinition_k3_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_matrix13 A) = (k1_tarski A)) ) ) ).
tt(redefinition_k3_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((k3_matrix_6 A B C D) = (k1_matrix_4 B C D)) ) ) ).
tt(redefinition_k3_matrix_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k12_matrix_2 A)))  =>  ((k3_matrix_7 A B) = (k2_funct_1 B)) ) ) ).
tt(redefinition_k3_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrixj1 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k3_matrixj1 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k3_matrixj2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrixj2 B A) & (m1_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  &  ((v1_matrixj2 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) ) )  =>  ((k3_matrixj2 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k3_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k3_zfmisc_1 A B C))) ) )  =>  ((k3_mcart_1 A B C D) = (k2_xtuple_0 D)) ) ) ).
tt(redefinition_k3_measure1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k3_measure1 A B C D) = (k4_xboole_0 C D)) ) ) ).
tt(redefinition_k3_measure8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((m4_measure8 D A B C) & (v7_ordinal1 E)) ) )  =>  ((k3_measure8 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k3_member_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k3_member_1 A B) = (k4_xxreal_3 A B)) ) ) ).
tt(redefinition_k3_mesfunc2,ax, (! [A:$i,B:$i] :  ((k3_mesfunc2 A B) = (k4_funct_3 A B)) ) ).
tt(redefinition_k3_metric_1,ax, (k3_metric_1 = k7_funct_5) ).
tt(redefinition_k3_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_midsp_1 A B C) = (k1_midsp_1 A B C)) ) ) ).
tt(redefinition_k3_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E (k4_finseq_2 C (u1_struct_0 B))) & (m1_subset_1 F (k4_finseq_2 D (u1_struct_0 B)))) ) ) ) )  =>  ((k3_midsp_3 A B C D E F) = (k7_finseq_1 E F)) ) ) ).
tt(redefinition_k3_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ((k3_modcat_1 A B) = (k2_modcat_1 A B)) ) ) ).
tt(redefinition_k3_monoid_0,ax, (k3_monoid_0 = k2_gr_cy_1) ).
tt(redefinition_k3_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) )  =>  ((k3_monoid_1 A B C D E F G) = (k3_funcop_1 E F G)) ) ) ).
tt(redefinition_k3_msafree,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k3_msafree A B) = (k2_card_3 B)) ) ) ).
tt(redefinition_k3_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k1_msaterm A B)) & (m1_subset_1 D (k9_xtuple_0 C))) ) )  =>  ((k3_msaterm A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k3_msualg_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  &  ((m2_pboole E A B C) & (m2_pboole F A C D)) ) ) )  =>  ((k3_msualg_3 A B C D E F) = (k8_pboole E F)) ) ) ).
tt(redefinition_k3_msualg_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 A B))))) ) )  =>  ((k3_msualg_8 A B C D) = (k5_card_3 C D)) ) ) ).
tt(redefinition_k3_nagata_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((k3_nagata_1 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k3_nat_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B k5_numbers))  =>  ((k3_nat_1 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k3_nat_3,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k3_nat_3 A B) = (k1_nat_3 A B)) ) ) ).
tt(redefinition_k3_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k3_nat_d A B) = (k5_int_1 A B)) ) ) ).
tt(redefinition_k3_normsp_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_normsp_0 B))  &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ((k3_normsp_0 A B C) = (k2_normsp_0 B C)) ) ) ).
tt(redefinition_k3_openlatt,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (k1_openlatt A)) & (m1_subset_1 C (k1_openlatt A))) )  =>  ((k3_openlatt A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k3_partfun2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k3_partfun2 A B C D) = (k6_relat_1 C D)) ) ) ).
tt(redefinition_k3_partfun3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k3_partfun3 A B) = (k1_partfun3 B)) ) ) ).
tt(redefinition_k3_pencil_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  & (m1_subset_1 C (u1_pre_topc A))) )  =>  ((k3_pencil_2 A B C) = (k8_relat_1 B C)) ) ) ).
tt(redefinition_k3_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u1_petri A)))  =>  ((k3_petri A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k3_polyform,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k3_polyform A) = (k5_finseq_1 A)) ) ) ).
tt(redefinition_k3_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) ) ) )  =>  ((k3_polynom1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k3_polynom3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D (k4_finseq_2 B A)) & (m1_subset_1 E (k4_finseq_2 C A))) ) ) )  =>  ((k3_polynom3 A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k3_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k3_pre_poly A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k3_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k3_prepower A B) = (k2_prepower A B)) ) ) ).
tt(redefinition_k3_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 A)))  =>  ((k3_prvect_2 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k3_pscomp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k3_pscomp_1 A B C) = (k5_relat_1 B C)) ) ) ).
tt(redefinition_k3_pua2mss1,ax, (! [A:$i,B:$i] :  ((m2_pua2mss1 B A) =>  ((k3_pua2mss1 A B) = (k10_xtuple_0 B)) ) ) ).
tt(redefinition_k3_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k3_quatern2 A) = (k32_quaterni A)) ) ) ).
tt(redefinition_k3_quaterni,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 F A) &  ((m1_subset_1 G A) &  ((m1_subset_1 H A) & (m1_subset_1 I A)) ) ) )  =>  ((k3_quaterni A B C D E F G H I) = (k2_quaterni B C D E F G H I)) ) ) ).
tt(redefinition_k3_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_radix_1 A) = (k2_radix_1 A)) ) ) ).
tt(redefinition_k3_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_radix_3 A) = (k1_radix_3 A)) ) ) ).
tt(redefinition_k3_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  =>  ((k3_random_1 A B C D) = (k1_valued_1 C D)) ) ) ).
tt(redefinition_k3_ratfunc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ( (~ (v1_ratfunc1 C A))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) )  =>  ((k3_ratfunc1 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k3_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xxreal_0 B))  =>  ((k3_rcomp_1 A B) = (k2_xxreal_1 A B)) ) ) ).
tt(redefinition_k3_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k3_real_1 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k3_relset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k3_relset_1 A B C) = (k2_relat_1 C)) ) ) ).
tt(redefinition_k3_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k8_afinsq_1 A)) & (v7_ordinal1 C))  =>  ((k3_rewrite2 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k3_rfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k3_rfunct_1 A B C D) = (k1_rfunct_1 C D)) ) ) ).
tt(redefinition_k3_rfunct_3,ax, (! [A:$i,B:$i] :  ((k3_rfunct_3 A B) = (k4_partfun1 A B)) ) ).
tt(redefinition_k3_rlvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_rlvect_1 A) & (l1_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_rlvect_1 A B C) = (k1_algstr_0 A B C)) ) ) ).
tt(redefinition_k3_rlvect_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  & (m1_subset_1 B (k9_funct_2 (u1_struct_0 A) k1_numbers)))  =>  ((k3_rlvect_2 A B) = (k13_pre_poly B)) ) ) ).
tt(redefinition_k3_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  =>  ((k3_rvsum_2 A B) = (k1_valued_1 A B)) ) ) ).
tt(redefinition_k3_scm_comp,ax, (! [A:$i] :  ((m1_subset_1 A (k6_dtconstr k1_scm_comp)) =>  ((k3_scm_comp A) = (k1_trees_4 A)) ) ) ).
tt(redefinition_k3_scmfsa_1,ax, (k3_scmfsa_1 = k1_scmfsa_i) ).
tt(redefinition_k3_scmpds_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_ami_2) & (v1_int_1 B))  =>  ((k3_scmpds_1 A B) = (k10_finseq_1 A B)) ) ) ).
tt(redefinition_k3_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k3_series_1 A) = (k2_series_1 A)) ) ) ).
tt(redefinition_k3_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k3_setwiseo A B C) = (k2_tarski B C)) ) ) ).
tt(redefinition_k3_sin_cos2,ax, (! [A:$i] :  ((k3_sin_cos2 A) = (k2_sin_cos2 A)) ) ).
tt(redefinition_k3_sin_cos6,ax, (! [A:$i] :  ((k3_sin_cos6 A) = (k2_sin_cos6 A)) ) ).
tt(redefinition_k3_substut2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_qc_lang1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((k3_substut2 A B C) = (k16_funcop_1 B C)) ) ) ).
tt(redefinition_k3_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k3_supinf_2 A B) = (k1_xxreal_3 A B)) ) ) ).
tt(redefinition_k3_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) )  =>  ((k3_topalg_4 A B C D) = (k11_mcart_1 D)) ) ) ).
tt(redefinition_k3_topgen_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_topgen_2 B A))  =>  ((k3_topgen_2 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k3_topgen_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k3_topgen_4 A B C) = (k2_setfam_1 B C)) ) ) ).
tt(redefinition_k3_topreal7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  & (m1_subset_1 C (u1_struct_0 (k1_topreal7 A B)))) )  =>  ((k3_topreal7 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k3_toprealb,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k3_toprealb A B) = (k1_toprealb A B)) ) ) ).
tt(redefinition_k3_trees_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  & (m1_subset_1 C (k9_xtuple_0 B))) )  =>  ((k3_trees_2 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k3_turing_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_turing_1 A) = (k1_ordinal1 A)) ) ) ).
tt(redefinition_k3_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k3_valued_1 A B C D E) = (k1_valued_1 D E)) ) ) ).
tt(redefinition_k3_vfunct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((k3_vfunct_2 A B C D) = (k1_vfunct_1 A B C D)) ) ) ).
tt(redefinition_k3_waybel27,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  &  ((m1_subset_1 C (u1_struct_0 (k2_waybel27 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k3_waybel27 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k3_waybel_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k3_waybel_3 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k3_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  &  ((m2_pboole D A C (k7_funcop_1 A B)) &  ((m2_pboole E (k4_card_3 (k2_funct_6 D)) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) A) (k7_funcop_1 (k4_card_3 (k2_funct_6 D)) B)) & (m1_subset_1 F (k4_card_3 (k2_funct_6 D)))) ) ) ) )  =>  ((k3_waybel_5 A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k3_wsierp_1,ax, (! [A:$i] :  ((m1_finseq_1 A k5_numbers) =>  ((k3_wsierp_1 A) = (k19_rvsum_1 A)) ) ) ).
tt(redefinition_k3_yellow20,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) ) )  =>  ((k3_yellow20 A B) = (k10_functor0 A B)) ) ) ).
tt(redefinition_k3_yellow21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k3_yellow21 A B) = (k1_yellow21 B)) ) ) ).
tt(redefinition_k3_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k3_yellow_5 A B C) = (k2_yellow_5 A B C)) ) ) ).
tt(redefinition_k3_zf_lang,ax, (! [A:$i] :  ((m1_subset_1 A k1_zf_lang) =>  ((k3_zf_lang A) = (k5_finseq_1 A)) ) ) ).
tt(redefinition_k3_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k3_zf_refle A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k40_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))))  &  ((v9_abcmiz_1 C A) & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) ) )  =>  ((k40_abcmiz_1 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k40_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v13_fomodel4 B A) & (v13_fomodel4 C A)) )  =>  ((k40_fomodel4 A B C) = (k13_fomodel0 B C)) ) ) ).
tt(redefinition_k41_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  =>  ((k41_abcmiz_1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k41_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  ((k41_fomodel4 A B C) = (k13_fomodel0 B C)) ) ) ).
tt(redefinition_k41_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k41_valued_1 A B C) = (k39_valued_1 C)) ) ) ).
tt(redefinition_k42_abcmiz_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  & (m3_abcmiz_1 B A))  =>  ((k42_abcmiz_1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k42_fomodel2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v15_fomodel1 B A))  &  ((v4_fomodel2 B A) &  ( (~ (v5_fomodel2 B A))  & (m1_subset_1 B (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) ) )  =>  ((k42_fomodel2 A B) = (k41_fomodel2 A B)) ) ) ).
tt(redefinition_k42_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k42_valued_2 A B C D) = (k41_valued_2 B C D)) ) ) ).
tt(redefinition_k43_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) &  ((v4_funct_1 C) & (m1_subset_1 D (k43_fomodel2 A))) ) )  =>  ((k43_fomodel4 A B C D) = (k42_fomodel4 A B C D)) ) ) ).
tt(redefinition_k43_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k43_valued_2 A B C D) = (k41_valued_2 B C D)) ) ) ).
tt(redefinition_k46_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k46_valued_1 A B C D E) = (k45_valued_1 D E)) ) ) ).
tt(redefinition_k47_fomodel4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) & (m1_subset_1 D (k33_fomodel2 B))) )  =>  ((k47_fomodel4 A B C D) = (k46_fomodel4 A B C D)) ) ) ).
tt(redefinition_k47_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k47_valued_1 A B C D E) = (k45_valued_1 D E)) ) ) ).
tt(redefinition_k48_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k48_valued_2 A B C D) = (k47_valued_2 B C D)) ) ) ).
tt(redefinition_k49_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k49_valued_2 A B C D) = (k47_valued_2 B C D)) ) ) ).
tt(redefinition_k4_altcat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_zfmisc_1 A A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k2_zfmisc_1 A A))) ) )  &  ((m2_pboole C (k3_zfmisc_1 A A A) (k3_altcat_1 A B B) (k2_altcat_1 A B)) &  ((m1_subset_1 D A) &  ((m1_subset_1 E A) & (m1_subset_1 F A)) ) ) ) )  =>  ((k4_altcat_1 A B C D E F) = (k1_multop_1 C D E F)) ) ) ).
tt(redefinition_k4_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D (k9_funct_2 A B)) & (m1_subset_1 E (k9_funct_2 B C))) ) ) )  =>  ((k4_aofa_000 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k4_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k4_binop_2 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k4_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k4_borsuk_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k4_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k4_bvfunc26 A B C) = (k2_bvfunc26 B C)) ) ) ).
tt(redefinition_k4_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_eqrel_1 B A))  =>  ((k4_bvfunc_2 A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k4_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_card_1 A) = (k1_ordinal1 A)) ) ) ).
tt(redefinition_k4_cat_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ((k4_cat_2 A B) = (k2_cat_2 A B)) ) ) ).
tt(redefinition_k4_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m3_chord B A) & (v7_ordinal1 C)) )  =>  ((k4_chord A B C) = (k1_chord B C)) ) ) ).
tt(redefinition_k4_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((k4_circcmb3 A B C D) = (k5_circcomb C D)) ) ) ).
tt(redefinition_k4_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k3_clopban1 A B))) & (m1_subset_1 D A)) ) )  =>  ((k4_clopban1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_closure3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  ((k4_closure3 A B C D) = (k3_xboole_0 C D)) ) ) ).
tt(redefinition_k4_cohsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v3_cohsp_1 A))  &  ((v1_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  ((k4_cohsp_1 A B) = (k3_tarski B)) ) ) ).
tt(redefinition_k4_commacat,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A C) &  ((m2_cat_1 E B C) & (m1_subset_1 F (k2_commacat A B C D E))) ) ) ) )  =>  ((k4_commacat A B C D E F) = (k14_mcart_1 F)) ) ) ).
tt(redefinition_k4_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k4_complex1 A) = (k2_complex1 A)) ) ) ).
tt(redefinition_k4_complsp2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (v1_xcmplx_0 C)) )  =>  ((k4_complsp2 A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k4_cqc_lang,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_qc_lang1 B) &  ((m1_subset_1 C (k8_qc_lang1 B A)) &  ((v5_relat_1 D (k3_qc_lang1 B)) &  ((v3_card_1 D A) & (m1_finseq_1 D (k2_qc_lang1 B))) ) ) ) )  =>  ((k4_cqc_lang A B C D) = (k10_qc_lang1 B C D)) ) ) ).
tt(redefinition_k4_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 (k4_nat_1 2 B) A))) )  =>  ((k4_descip_1 A B C) = (k16_finseq_1 B C)) ) ) ).
tt(redefinition_k4_dickson,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k4_dickson A B) = (k3_dickson B)) ) ) ).
tt(redefinition_k4_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((m1_subset_1 D A) &  ((m1_subset_1 E B) & (m1_subset_1 F C)) ) ) ) )  =>  ((k4_domain_1 A B C D E F) = (k3_xtuple_0 D E F)) ) ) ).
tt(redefinition_k4_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k4_eqrel_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k4_euclid_4,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((k4_euclid_4 A B C) = (k3_euclid_4 A B C)) ) ) ).
tt(redefinition_k4_euclid_5,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_xreal_0 A) &  ((v1_xreal_0 B) & (v1_xreal_0 C)) )  =>  ((k4_euclid_5 A B C) = (k11_finseq_1 A B C)) ) ) ).
tt(redefinition_k4_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k4_finseq_1 A) = (k9_xtuple_0 A)) ) ) ).
tt(redefinition_k4_finseq_5,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B A) =>  ((k4_finseq_5 A B) = (k3_finseq_5 B)) ) ) ).
tt(redefinition_k4_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_finseq_1 C A) &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((k4_finseqop A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k4_flang_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k3_catalan2 A)) =>  ((k4_flang_1 A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k4_fomodel2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  &  ((v9_fomodel1 D A) & (m1_subset_1 D (k1_fomodel1 A))) ) ) )  =>  ((k4_fomodel2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_fomodel3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v10_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A))) )  =>  ((k4_fomodel3 A B C) = (k3_fomodel3 A B C)) ) ) ).
tt(redefinition_k4_funcsdom,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((k4_funcsdom A B C D E) = (k5_funcop_1 C D E)) ) ) ).
tt(redefinition_k4_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((k4_funct_2 A B C D) = (k11_mcart_1 D)) ) ) ).
tt(redefinition_k4_functor2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((v15_functor0 C A B) & (m2_functor0 C A B)) ) )  =>  ((k4_functor2 A B C) = (k1_functor2 A B C)) ) ) ).
tt(redefinition_k4_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  &  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  &  ((v15_functor0 E B C) & (m2_functor0 E B C)) ) ) ) )  =>  ((k4_functor3 A B C D E) = (k13_functor0 A B C D E)) ) ) ).
tt(redefinition_k4_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  =>  ((k4_fvsum_1 A B C D) = (k3_fvsum_1 B C D)) ) ) ).
tt(redefinition_k4_glib_005,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  &  ((m2_glib_005 C A B) & (v7_ordinal1 D)) ) )  =>  ((k4_glib_005 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k4_graph_1 A B) = (k2_graph_1 A B)) ) ) ).
tt(redefinition_k4_graph_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k4_graph_2 A B C) = (k3_graph_2 B C)) ) ) ).
tt(redefinition_k4_graphsp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_funct_2 A A)) & (m1_subset_1 C A))  =>  ((k4_graphsp A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_group_7,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_group_7 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k4_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m1_ideal_1 D A B) & (m1_ideal_1 E A C)) ) ) )  =>  ((k4_ideal_1 A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k4_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_int_1 A) = (k3_int_1 A)) ) ) ).
tt(redefinition_k4_integr16,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  &  ((m2_integr16 D A B C) & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((k4_integr16 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k4_jgraph_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((k4_jgraph_1 A B) = (k2_jgraph_1 B)) ) ) ).
tt(redefinition_k4_jordan10,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k4_jordan10 A) = (k2_jordan10 A)) ) ) ).
tt(redefinition_k4_jordan1k,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  &  ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ) )  =>  ((k4_jordan1k A B C) = (k1_jordan1k A B C)) ) ) ).
tt(redefinition_k4_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 C (k2_zfmisc_1 A B))) )  =>  ((k4_lang1 A B C) = (k1_tarski C)) ) ) ).
tt(redefinition_k4_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_lattices A B C) = (k2_lattices A B C)) ) ) ).
tt(redefinition_k4_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_matrix_1 B k1_numbers A A) & (m1_matrix_1 C k1_numbers A A)) )  =>  ((k4_matrix10 A B C) = (k5_matrixr1 B C)) ) ) ).
tt(redefinition_k4_matrix11,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  & (m1_matrix_1 E C A B)) ) ) )  =>  ((k4_matrix11 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k4_matrix13,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k4_matrix13 A B) = (k2_tarski A B)) ) ) ).
tt(redefinition_k4_matrix_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k4_matrix_2 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k4_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((k4_matrix_6 A B C D) = (k4_matrix_3 B C D)) ) ) ).
tt(redefinition_k4_matrixj1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A))) )  =>  ((k4_matrixj1 A B) = (k5_finseq_1 B)) ) ) ).
tt(redefinition_k4_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  =>  ((k4_mcart_1 A B C D E) = (k7_xtuple_0 E)) ) ) ).
tt(redefinition_k4_measure1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  ((k4_measure1 A B C) = (k10_xtuple_0 C)) ) ) ).
tt(redefinition_k4_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k4_measure6 A) = (k5_member_1 A)) ) ) ).
tt(redefinition_k4_measure7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  &  ((m2_measure7 B A) & (m1_subset_1 C k5_numbers)) )  =>  ((k4_measure7 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_mesfunc5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k3_rfunct_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_rfunct_3 A B))))) )  & (v7_ordinal1 D))  =>  ((k4_mesfunc5 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_mesfunc7,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (v7_ordinal1 B))  =>  ((k4_mesfunc7 A B) = (k3_mesfunc7 A B)) ) ) ).
tt(redefinition_k4_metric_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v8_metric_1 A) & (l1_metric_1 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_metric_1 A B C) = (k2_metric_1 A B C)) ) ) ).
tt(redefinition_k4_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C A)) )  =>  ((k4_monoid_1 A B C) = (k2_finseq_2 B C)) ) ) ).
tt(redefinition_k4_mssubfam,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m3_pboole C A (k1_mboolean A B)))  =>  ((k4_mssubfam A B C) = (k3_mssubfam A B C)) ) ) ).
tt(redefinition_k4_multop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_zfmisc_1 A B C D) E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 A B C D) E)))) )  &  ((m1_subset_1 G A) &  ((m1_subset_1 H B) &  ((m1_subset_1 I C) & (m1_subset_1 J D)) ) ) ) ) ) ) ) )  =>  ((k4_multop_1 A B C D E F G H I J) = (k3_multop_1 F G H I J)) ) ) ).
tt(redefinition_k4_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (v7_ordinal1 B))  =>  ((k4_nat_1 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k4_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k4_nat_d A B) = (k6_int_1 A B)) ) ) ).
tt(redefinition_k4_normsp_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_normsp_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k4_normsp_0 A B) = (k2_normsp_0 A B)) ) ) ).
tt(redefinition_k4_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k4_ordinal4 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_ordinal6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v3_ordinal1 B) &  ((v1_funct_1 C) &  ((v1_funct_2 C B (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k2_ordinal1 A))))) ) ) )  =>  ((k4_ordinal6 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_partfun2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D B)) ) )  =>  ((k4_partfun2 A B C D) = (k2_funcop_1 C D)) ) ) ).
tt(redefinition_k4_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u2_petri A)))  =>  ((k4_petri A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k4_pnproc_1,ax, (! [A:$i,B:$i] :  ((m1_pnproc_1 B A) =>  ((k4_pnproc_1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k4_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k1_numbers)) ) )  =>  ((k4_polyeq_1 A B C D) = (k3_polyeq_1 A B C D)) ) ) ).
tt(redefinition_k4_polyform,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((k4_polyform A B) = (k10_finseq_1 A B)) ) ) ).
tt(redefinition_k4_polynom3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) &  ((m1_subset_1 C k5_numbers) &  ((m1_finseq_1 D (k4_finseq_2 B A)) & (m1_finseq_1 E (k4_finseq_2 C A))) ) ) )  =>  ((k4_polynom3 A B C D E) = (k8_pre_poly D E)) ) ) ).
tt(redefinition_k4_power,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k4_power A B) = (k3_power A B)) ) ) ).
tt(redefinition_k4_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k4_pre_poly A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k4_prob_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B (k9_setfam_1 A)) & (v7_ordinal1 C))  =>  ((k4_prob_3 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_pua2mss1,ax, (! [A:$i,B:$i] :  ((m1_eqrel_1 B A) =>  ((k4_pua2mss1 A B) = (k4_relat_1 B)) ) ) ).
tt(redefinition_k4_quatern2,ax, (k4_quatern2 = k1_xcmplx_0) ).
tt(redefinition_k4_quatern3,ax, (! [A:$i] :  ((m1_subset_1 A k1_quaterni) =>  ((k4_quatern3 A) = (k3_quatern3 A)) ) ) ).
tt(redefinition_k4_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  =>  ((k4_quofield A B C) = (k2_quofield A B C)) ) ) ).
tt(redefinition_k4_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_radix_3 A) = (k2_radix_3 A)) ) ) ).
tt(redefinition_k4_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  =>  ((k4_random_1 A B C D) = (k45_valued_1 C D)) ) ) ).
tt(redefinition_k4_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  & (m1_ratfunc1 B A))  =>  ((k4_ratfunc1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k4_rcomp_1,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xreal_0 B))  =>  ((k4_rcomp_1 A B) = (k3_xxreal_1 A B)) ) ) ).
tt(redefinition_k4_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k4_real_1 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k4_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((k4_relset_1 A B C D E F) = (k3_relat_1 E F)) ) ) ).
tt(redefinition_k4_relset_2,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((k4_relset_2 A B C) = (k3_relset_2 B C)) ) ) ).
tt(redefinition_k4_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_finseq_1 C (k8_afinsq_1 A)))  =>  ((k4_rewrite2 A B C) = (k1_rewrite2 B C)) ) ) ).
tt(redefinition_k4_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D B)) ) )  =>  ((k4_rfunct_3 A B C D) = (k2_funcop_1 C D)) ) ) ).
tt(redefinition_k4_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) & (l1_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_robbins3 A B C) = (k2_lattices A B C)) ) ) ).
tt(redefinition_k4_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k4_rvsum_1 A B) = (k1_valued_1 A B)) ) ) ).
tt(redefinition_k4_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  =>  ((k4_rvsum_2 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k4_scmfsa_m,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((k4_scmfsa_m A) = (k1_tarski A)) ) ) ).
tt(redefinition_k4_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k4_seq_4 A) = (k2_seq_4 A)) ) ) ).
tt(redefinition_k4_setlim_1,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k4_setlim_1 A B) = (k3_setlim_1 B)) ) ) ).
tt(redefinition_k4_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k4_setwiseo A B C D) = (k1_enumset1 B C D)) ) ) ).
tt(redefinition_k4_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k4_square_1 A) = (k3_square_1 A)) ) ) ).
tt(redefinition_k4_stacks_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k1_zfmisc_1 A)) &  ((m1_subset_1 D (k1_zfmisc_1 B)) &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) )  =>  ((k4_stacks_1 A B C D E F) = (k1_funct_4 E F)) ) ) ).
tt(redefinition_k4_sublemma,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_qc_lang1 B) &  ((m1_subset_1 C (k8_qc_lang1 B A)) &  ( ((v5_relat_1 D (k3_qc_lang1 B)) &  ((v3_card_1 D A) & (m1_finseq_1 D (k2_qc_lang1 B))) )  & (m1_subset_1 E (k1_substut1 B))) ) ) )  =>  ((k4_sublemma A B C D E) = (k17_substut1 B C D E)) ) ) ).
tt(redefinition_k4_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k4_subset_1 A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k4_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k7_numbers) & (m1_subset_1 B k7_numbers))  =>  ((k4_supinf_2 A B) = (k3_xxreal_3 A B)) ) ) ).
tt(redefinition_k4_tex_4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_tex_4 A B) = (k2_tex_4 A B)) ) ) ).
tt(redefinition_k4_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) )  =>  ((k4_topalg_4 A B C D) = (k12_mcart_1 D)) ) ) ).
tt(redefinition_k4_topgen_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_topgen_2 B A) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k4_topgen_2 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k4_topgrp_1 A) = (k3_struct_0 A)) ) ) ).
tt(redefinition_k4_topreal7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  & (m1_subset_1 C (u1_struct_0 (k1_topreal7 A B)))) )  =>  ((k4_topreal7 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_k4_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (u1_struct_0 (k15_euclid A))))  =>  ((k4_toprealc A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_turing_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_finseq_1 B k5_numbers))  =>  ((k4_turing_1 A B) = (k16_finseq_1 A B)) ) ) ).
tt(redefinition_k4_uproots,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((k4_uproots A B) = (k3_uproots A B)) ) ) ).
tt(redefinition_k4_urysohn1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v2_pre_topc A) & (l1_pre_topc A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_zfmisc_1 (u1_struct_0 A)))))) )  & (m1_subset_1 D B)) ) )  =>  ((k4_urysohn1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_urysohn3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v2_pre_topc B) & (l1_pre_topc B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k9_setfam_1 (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k9_setfam_1 (u1_struct_0 B)))))) )  & (m1_subset_1 D A)) ) )  =>  ((k4_urysohn3 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C k5_numbers) &  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D C) & (m1_finseq_1 D (k2_qc_lang1 A))) )  & (m1_subset_1 E (k2_valuat_1 A B))) ) ) )  =>  ((k4_valuat_1 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k4_waybel18,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  & (m1_subset_1 C A)) )  =>  ((k4_waybel18 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_waybel35,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_struct_0 A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((k4_waybel35 A B C D) = (k3_waybel35 B C D)) ) ) ).
tt(redefinition_k4_waybel_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) & (m1_subset_1 D A)) ) )  =>  ((k4_waybel_3 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k4_wsierp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_finseq_1 C A)) )  =>  ((k4_wsierp_1 A B C) = (k2_finseq_3 B C)) ) ) ).
tt(redefinition_k4_yellow_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k4_yellow_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k4_yellow20,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  ((k4_yellow20 A B C D) = (k14_functor0 A B C D)) ) ) ).
tt(redefinition_k4_yellow21,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v3_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k4_yellow21 A B) = (k1_yellow21 B)) ) ) ).
tt(redefinition_k4_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((k4_yellow_3 A B C) = (k9_xtuple_0 C)) ) ) ).
tt(redefinition_k4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k4_yellow_4 A B C) = (k3_yellow_4 A B C)) ) ) ).
tt(redefinition_k4_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  =>  ((k4_zf_lang1 A) = (k3_zf_lang1 A)) ) ) ).
tt(redefinition_k4_zf_refle,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) ) )  =>  ((k4_zf_refle A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k51_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((k51_abcmiz_1 A) = (k1_lang1 A)) ) ) ).
tt(redefinition_k51_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v1_membered B) &  ((v1_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k51_valued_1 A B C D E) = (k50_valued_1 D E)) ) ) ).
tt(redefinition_k52_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((k52_abcmiz_1 A) = (k2_lang1 A)) ) ) ).
tt(redefinition_k52_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_membered B) &  ((v3_membered C) &  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) )  =>  ((k52_valued_1 A B C D E) = (k50_valued_1 D E)) ) ) ).
tt(redefinition_k52_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((k52_valued_2 A B C D) = (k51_valued_2 B C D)) ) ) ).
tt(redefinition_k53_abcmiz_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D A) & (m1_subset_1 E A))  =>  ((k53_abcmiz_1 A B C D E) = (k2_matrix_7 B C D E)) ) ) ).
tt(redefinition_k53_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((k53_valued_2 A B C D) = (k51_valued_2 B C D)) ) ) ).
tt(redefinition_k55_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k55_valued_1 A B C) = (k54_valued_1 C)) ) ) ).
tt(redefinition_k56_valued_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k56_valued_1 A B C) = (k54_valued_1 C)) ) ) ).
tt(redefinition_k58_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_finseq_1 C (k34_abcmiz_1 A))) )  =>  ((k58_abcmiz_1 A B C) = (k57_abcmiz_1 A B C)) ) ) ).
tt(redefinition_k58_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((k58_valued_2 A B C D) = (k57_valued_2 B C D)) ) ) ).
tt(redefinition_k59_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k14_abcmiz_1 A))) )  =>  ((k59_abcmiz_1 A B C) = (k56_abcmiz_1 A B C)) ) ) ).
tt(redefinition_k59_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((k59_valued_2 A B C D) = (k57_valued_2 B C D)) ) ) ).
tt(redefinition_k5_abcmiz_a,ax, (k5_abcmiz_a = k17_abcmiz_1) ).
tt(redefinition_k5_afinsq_1,ax, (! [A:$i] :  ((k5_afinsq_1 A) = (k3_afinsq_1 A)) ) ).
tt(redefinition_k5_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 C A) & (m1_subset_1 D A)) )  =>  ((k5_binop_1 A B C D) = (k1_binop_1 B C D)) ) ) ).
tt(redefinition_k5_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k5_binop_2 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k5_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m1_connsp_2 E A C) & (m1_connsp_2 F B D)) ) ) ) )  =>  ((k5_borsuk_1 A B C D E F) = (k2_zfmisc_1 E F)) ) ) ).
tt(redefinition_k5_borsuk_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  & (v1_xreal_0 C))  =>  ((k5_borsuk_7 A B C) = (k13_valued_1 B C)) ) ) ).
tt(redefinition_k5_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k5_bvfunc_1 A B C) = (k3_bvfunc_1 B C)) ) ) ).
tt(redefinition_k5_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k5_bvfunc26 A B C) = (k1_bvfunc26 B C)) ) ) ).
tt(redefinition_k5_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k5_card_1 A) = (k1_card_1 A)) ) ) ).
tt(redefinition_k5_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k5_cat_5 A B) = (k13_mcart_1 B)) ) ) ).
tt(redefinition_k5_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  &  ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) ) ) ) )  =>  ((k5_circcmb3 A B C D) = (k7_circcomb A B C D)) ) ) ).
tt(redefinition_k5_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k5_classes2 A B C) = (k2_tarski B C)) ) ) ).
tt(redefinition_k5_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))))  =>  ((k5_closure2 A B C) = (k4_closure2 A B C)) ) ) ).
tt(redefinition_k5_complex1,ax, (k5_complex1 = k1_xboole_0) ).
tt(redefinition_k5_complsp2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B (k4_finseq_2 A k2_numbers)))  =>  ((k5_complsp2 A B) = (k30_valued_1 B)) ) ) ).
tt(redefinition_k5_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((k5_comseq_3 A B) = (k3_comseq_3 B)) ) ) ).
tt(redefinition_k5_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  =>  ((k5_convex4 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k5_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k5_cqc_lang A) = (k12_qc_lang1 A)) ) ) ).
tt(redefinition_k5_cqc_sim1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B k5_numbers) &  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m1_finseq_1 C (k2_qc_lang1 A))) )  & (m1_subset_1 D (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)))) ) )  =>  ((k5_cqc_sim1 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k5_descip_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  & (m1_subset_1 C (k4_finseq_2 (k4_nat_1 2 B) A))) )  =>  ((k5_descip_1 A B C) = (k1_rfinseq B C)) ) ) ).
tt(redefinition_k5_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ((m1_subset_1 E A) &  ((m1_subset_1 F B) &  ((m1_subset_1 G C) & (m1_subset_1 H D)) ) ) ) ) ) )  =>  ((k5_domain_1 A B C D E F G H) = (k6_xtuple_0 E F G H)) ) ) ).
tt(redefinition_k5_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_euclid A) = (k4_euclid A)) ) ) ).
tt(redefinition_k5_exchsort,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((k5_exchsort A B C D E) = (k10_funct_7 C D E)) ) ) ).
tt(redefinition_k5_finseq_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C A)) )  =>  ((k5_finseq_2 A B C) = (k2_finseq_2 B C)) ) ) ).
tt(redefinition_k5_flang_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  & (v7_ordinal1 C))  =>  ((k5_flang_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k5_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) )  =>  ((k5_funct_2 A B C D) = (k12_mcart_1 D)) ) ) ).
tt(redefinition_k5_funct_3,ax, (! [A:$i,B:$i] :  ((k5_funct_3 A B) = (k4_funct_3 A B)) ) ).
tt(redefinition_k5_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 D A) & (m1_subset_1 E A)) )  =>  ((k5_funct_4 A B C D E) = (k4_funct_4 B C D E)) ) ) ).
tt(redefinition_k5_funct_5,ax, (k5_funct_5 = k1_xboole_0) ).
tt(redefinition_k5_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((k5_functor0 A B C D E) = (k4_functor0 A B C D E)) ) ) ).
tt(redefinition_k5_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k5_glib_002 A) = (k4_glib_002 A)) ) ) ).
tt(redefinition_k5_glib_004,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k3_rfunct_3 A B) C)))  =>  ((k5_glib_004 A B C D) = (k1_xtuple_0 D)) ) ) ).
tt(redefinition_k5_groeb_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v3_ordinal1 A) &  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)))))  &  ((m2_ideal_1 D (k11_polynom1 A B) C) & (m2_ideal_1 E (k11_polynom1 A B) C)) ) ) )  =>  ((k5_groeb_2 A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k5_group_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k5_group_7 A B C D) = (k10_finseq_1 C D)) ) ) ).
tt(redefinition_k5_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m2_ideal_1 D A B) & (m2_ideal_1 E A C)) ) ) )  =>  ((k5_ideal_1 A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k5_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  =>  ((k5_index_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k5_integr15,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  &  ((m4_integr15 E A B C D) & (m1_subset_1 F k5_numbers)) ) ) ) )  =>  ((k5_integr15 A B C D E F) = (k1_funct_1 E F)) ) ) ).
tt(redefinition_k5_knaster,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v3_ordinal1 D)) ) )  =>  ((k5_knaster A B C D) = (k3_knaster A B C D)) ) ) ).
tt(redefinition_k5_lang1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  =>  ((k5_lang1 A B C D) = (k2_tarski C D)) ) ) ).
tt(redefinition_k5_lexbfs,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  &  ((m1_lexbfs B A) & (v7_ordinal1 C)) )  =>  ((k5_lexbfs A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k5_matrix10,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B k1_numbers) & (m1_matrix_1 C k1_numbers A A)) )  =>  ((k5_matrix10 A B C) = (k7_matrixr1 B C)) ) ) ).
tt(redefinition_k5_matrix13,ax, (! [A:$i] :  ( ((v1_finset_1 A) &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  =>  ((k5_matrix13 A) = (k14_finseq_1 A)) ) ) ).
tt(redefinition_k5_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( (~ (v1_xboole_0 B))  & (m1_matrix_1 C B A A)) )  =>  ((k5_matrix_1 A B C) = (k4_matrix_1 B C)) ) ) ).
tt(redefinition_k5_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) & (m1_subset_1 C (k4_finseq_2 B A))) )  =>  ((k5_matrix_2 A B C) = (k5_finseq_1 C)) ) ) ).
tt(redefinition_k5_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 E (u1_struct_0 D) A B) & (m1_matrix_1 F (u1_struct_0 D) (k1_matrix_1 E) C)) ) ) ) )  =>  ((k5_matrix_3 A B C D E F) = (k4_matrix_3 D E F)) ) ) ).
tt(redefinition_k5_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((k5_matrixj1 A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k5_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 D (u1_struct_0 C) A B) &  ((v1_matrix_1 E) & (m1_finseq_1 E (k3_finseq_2 (u1_struct_0 C)))) ) ) ) )  =>  ((k5_matrlin2 A B C D E) = (k3_matrix_3 C D E)) ) ) ).
tt(redefinition_k5_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  =>  ((k5_mcart_1 A B C D E) = (k8_xtuple_0 E)) ) ) ).
tt(redefinition_k5_mesfunc9,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) (k4_partfun1 C k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k4_partfun1 C k7_numbers))))) )  &  ((m1_subset_1 E A) & (m1_subset_1 F B)) ) ) ) )  =>  ((k5_mesfunc9 A B C D E F) = (k1_binop_1 D E F)) ) ) ).
tt(redefinition_k5_midsp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  & (m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))  =>  ((k5_midsp_1 A B) = (k4_midsp_1 A B)) ) ) ).
tt(redefinition_k5_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k4_finseq_2 (k2_nat_1 A 1) B)) & (m1_midsp_3 D A)) ) )  =>  ((k5_midsp_3 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k5_modal_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  & (m1_subset_1 B A))  =>  ((k5_modal_1 A B) = (k8_trees_2 A B)) ) ) ).
tt(redefinition_k5_monoid_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((k5_monoid_1 A B C) = (k2_funcop_1 B C)) ) ) ).
tt(redefinition_k5_mssubfam,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k5_mssubfam A B) = (k1_mboolean A B)) ) ) ).
tt(redefinition_k5_msualg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u4_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u4_struct_0 A))) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u4_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u4_struct_0 A))) ) )  &  ((m2_pboole D (u4_struct_0 A) B C) & (m1_subset_1 E (u4_struct_0 A))) ) ) )  =>  ((k5_msualg_4 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k5_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k5_nat_d A B) = (k2_int_2 A B)) ) ) ).
tt(redefinition_k5_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k5_newton A B) = (k4_newton A B)) ) ) ).
tt(redefinition_k5_numbers,ax, (k5_numbers = k4_ordinal1) ).
tt(redefinition_k5_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) )  =>  ((k5_ordinal4 A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k5_partfun3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((k5_partfun3 A B C) = (k1_rfunct_1 B C)) ) ) ).
tt(redefinition_k5_petri,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  & (m1_subset_1 B (u2_petri A)))  =>  ((k5_petri A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k5_pnproc_1,ax, (! [A:$i,B:$i] :  ((m1_pnproc_1 B A) =>  ((k5_pnproc_1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k5_polyform,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_int_1 A) &  ((v1_int_1 B) & (v1_int_1 C)) )  =>  ((k5_polyform A B C) = (k11_finseq_1 A B C)) ) ) ).
tt(redefinition_k5_polynom1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((k5_polynom1 A B C D) = (k4_polynom1 A B C D)) ) ) ).
tt(redefinition_k5_pralg_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  &  ((m1_pralg_2 C A B) & (m1_subset_1 D A)) ) )  =>  ((k5_pralg_2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k5_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_int_1 B))  =>  ((k5_prepower A B) = (k4_prepower A B)) ) ) ).
tt(redefinition_k5_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k5_prob_1 A B C D) = (k3_xboole_0 C D)) ) ) ).
tt(redefinition_k5_prob_3,ax, (! [A:$i,B:$i] :  ((m1_finseq_1 B (k9_setfam_1 A)) =>  ((k5_prob_3 A B) = (k3_card_3 B)) ) ) ).
tt(redefinition_k5_prvect_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  & (m1_subset_1 B (k4_finseq_1 (k4_prvect_2 A))))  =>  ((k5_prvect_2 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k5_quofield,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  &  ((m1_subset_1 B (k1_quofield A)) & (m1_subset_1 C (k1_quofield A))) )  =>  ((k5_quofield A B C) = (k3_quofield A B C)) ) ) ).
tt(redefinition_k5_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_subset_1 D k1_numbers)) ) )  =>  ((k5_random_1 A B C D) = (k24_valued_1 C D)) ) ) ).
tt(redefinition_k5_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_6 C A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((k5_ranknull A B C D) = (k7_relat_1 C D)) ) ) ).
tt(redefinition_k5_ratfunc1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  & (m1_ratfunc1 B A))  =>  ((k5_ratfunc1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k5_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k5_real_1 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k5_real_ns1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_euclid A))))) )  & (v7_ordinal1 C)) )  =>  ((k5_real_ns1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k5_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k5_relset_1 A B C D) = (k5_relat_1 C D)) ) ) ).
tt(redefinition_k5_rewrite2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k8_afinsq_1 A)) & (m1_finseq_1 C (k8_afinsq_1 A)))  =>  ((k5_rewrite2 A B C) = (k2_rewrite2 B C)) ) ) ).
tt(redefinition_k5_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  =>  ((k5_rfunct_3 A B C D) = (k1_valued_1 C D)) ) ) ).
tt(redefinition_k5_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k5_ringcat1 A) = (k4_ringcat1 A)) ) ) ).
tt(redefinition_k5_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_robbins1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k5_robbins1 A B C) = (k1_lattices A B C)) ) ) ).
tt(redefinition_k5_robbins3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) & (l2_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k5_robbins3 A B C) = (k1_lattices A B C)) ) ) ).
tt(redefinition_k5_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  =>  ((k5_rvsum_1 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k5_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k5_rvsum_2 A) = (k30_valued_1 A)) ) ) ).
tt(redefinition_k5_scmfsa_m,ax, (! [A:$i,B:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ((k5_scmfsa_m A B) = (k2_tarski A B)) ) ) ).
tt(redefinition_k5_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) & (m1_subset_1 C k2_ami_2)) )  =>  ((k5_scmring1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k5_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((k5_seq_4 A) = (k3_seq_4 A)) ) ) ).
tt(redefinition_k5_series_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k5_series_1 A B) = (k3_power A B)) ) ) ).
tt(redefinition_k5_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k5_setfam_1 A B) = (k3_tarski B)) ) ) ).
tt(redefinition_k5_setlim_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((k5_setlim_1 A B C) = (k1_setlim_1 C)) ) ) ).
tt(redefinition_k5_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  =>  ((k5_setwiseo A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k5_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k5_sin_cos9 A) = (k3_sin_cos9 A)) ) ) ).
tt(redefinition_k5_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k5_square_1 A) = (k3_square_1 A)) ) ) ).
tt(redefinition_k5_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k38_substut1 A)))  =>  ((k5_sublemma A B) = (k20_substut1 A B)) ) ) ).
tt(redefinition_k5_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k5_subset_1 A B C) = (k5_xboole_0 B C)) ) ) ).
tt(redefinition_k5_substut2,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k16_substut1 A)))  =>  ((k5_substut2 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k5_supinf_2,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  ((k5_supinf_2 A B) = (k8_member_1 A B)) ) ) ).
tt(redefinition_k5_topmetr,ax, (k5_topmetr = k17_borsuk_1) ).
tt(redefinition_k5_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  & (m1_subset_1 E (u1_struct_0 (k2_borsuk_1 A B)))) ) ) )  =>  ((k5_toprealc A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k5_waybel18,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A B))) & (m1_subset_1 D A)) ) )  =>  ((k5_waybel18 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k5_waybel_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  &  ((m1_subset_1 C A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B))))) ) )  =>  ((k5_waybel_3 A B C D) = (k5_card_3 C D)) ) ) ).
tt(redefinition_k5_waybel_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  & (m1_subset_1 C (u1_struct_0 B))) )  =>  ((k5_waybel_9 A B C) = (k4_waybel_9 A B C)) ) ) ).
tt(redefinition_k5_wsierp_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  &  ((v7_ordinal1 C) & (m1_finseq_1 D B)) ) )  =>  ((k5_wsierp_1 A B C D) = (k2_finseq_3 C D)) ) ) ).
tt(redefinition_k5_yellow20,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  &  ((v16_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  ((k5_yellow20 A B C D) = (k14_functor0 A B C D)) ) ) ).
tt(redefinition_k5_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((k5_yellow_3 A B C) = (k10_xtuple_0 C)) ) ) ).
tt(redefinition_k5_zf_model,ax, (! [A:$i,B:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  (~ (v1_xboole_0 B)) )  =>  ((k5_zf_model A B) = (k4_zf_model A B)) ) ) ).
tt(redefinition_k5_zf_refle,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) )  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k5_zf_refle A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k60_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) )  =>  ((k60_abcmiz_1 A B C) = (k56_abcmiz_1 A B C)) ) ) ).
tt(redefinition_k61_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  &  ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A))) ) )  =>  ((k61_abcmiz_1 A B C) = (k56_abcmiz_1 A B C)) ) ) ).
tt(redefinition_k62_abcmiz_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  & (m1_abcmiz_1 C A (k12_abcmiz_1 A))) )  =>  ((k62_abcmiz_1 A B C) = (k56_abcmiz_1 A B C)) ) ) ).
tt(redefinition_k63_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((k63_valued_2 A B C D) = (k62_valued_2 B C D)) ) ) ).
tt(redefinition_k64_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((k64_valued_2 A B C D) = (k62_valued_2 B C D)) ) ) ).
tt(redefinition_k69_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) ) ) )  =>  ((k69_valued_2 A B C D) = (k68_valued_2 B C D)) ) ) ).
tt(redefinition_k6_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((k6_armstrng A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k6_bcialg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  ((m1_subset_1 B (k5_bcialg_1 A)) & (m1_subset_1 C (k5_bcialg_1 A))) )  =>  ((k6_bcialg_1 A B C) = (k1_bcialg_1 A B C)) ) ) ).
tt(redefinition_k6_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k6_bhsp_1 A B C) = (k2_normsp_1 A B C)) ) ) ).
tt(redefinition_k6_bilinear,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k6_bilinear A B C D E) = (k2_bilinear A B C D E)) ) ) ).
tt(redefinition_k6_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xcmplx_0 A) & (v1_xcmplx_0 B))  =>  ((k6_binop_2 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k6_borsuk_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((m1_subset_1 D (u1_struct_0 B)) &  ((m2_connsp_2 E A C) & (m1_connsp_2 F B D)) ) ) ) )  =>  ((k6_borsuk_1 A B C D E F) = (k2_zfmisc_1 E F)) ) ) ).
tt(redefinition_k6_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k6_bvfunc_1 A B C) = (k4_bvfunc_1 B C)) ) ) ).
tt(redefinition_k6_bvfunc26,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k6_bvfunc26 A B C) = (k2_bvfunc26 B C)) ) ) ).
tt(redefinition_k6_calcul_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C A)) )  =>  ((k6_calcul_2 A B C) = (k2_finseq_2 B C)) ) ) ).
tt(redefinition_k6_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) ) ) ) )  =>  ((k6_cat_2 A B C D E F) = (k15_funct_3 E F)) ) ) ).
tt(redefinition_k6_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k6_cat_5 A B) = (k14_mcart_1 B)) ) ) ).
tt(redefinition_k6_circcmb3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_circcmb3 B A) & (m1_circcmb3 C A)) )  =>  ((k6_circcmb3 A B C) = (k2_circcomb B C)) ) ) ).
tt(redefinition_k6_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k6_classes2 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k6_closure2,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k6_closure2 A B) = (k1_closure2 A B)) ) ) ).
tt(redefinition_k6_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((k6_cohsp_1 A B C) = (k5_cohsp_1 C)) ) ) ).
tt(redefinition_k6_comseq_3,ax, (! [A:$i,B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((k6_comseq_3 A B) = (k4_comseq_3 B)) ) ) ).
tt(redefinition_k6_cqc_lang,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k3_cqc_lang A)))  =>  ((k6_cqc_lang A B) = (k13_qc_lang1 A B)) ) ) ).
tt(redefinition_k6_domain_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k6_domain_1 A B) = (k1_tarski B)) ) ) ).
tt(redefinition_k6_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) & (l1_lang1 A)) )  =>  ((k6_dtconstr A) = (k1_lang1 A)) ) ) ).
tt(redefinition_k6_eqrel_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k6_eqrel_1 A B C D) = (k9_relat_1 C D)) ) ) ).
tt(redefinition_k6_euclid_7,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k6_euclid_7 A B) = (k6_matrixr2 A B)) ) ) ).
tt(redefinition_k6_euclid,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k1_euclid A)))  =>  ((k6_euclid A B) = (k30_valued_1 B)) ) ) ).
tt(redefinition_k6_filter_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) )  =>  ((k6_filter_1 A B C D) = (k3_funct_4 C D)) ) ) ).
tt(redefinition_k6_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  & (m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))))  =>  ((k6_fomodel4 A B C) = (k5_fomodel4 A B C)) ) ) ).
tt(redefinition_k6_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) )  =>  ((k6_funcop_1 A B C D E) = (k3_funcop_1 C D E)) ) ) ).
tt(redefinition_k6_funct_3,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k6_funct_3 A B) = (k4_relat_1 B)) ) ) ).
tt(redefinition_k6_fvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  & (m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B)))) )  =>  ((k6_fvsum_1 A B C) = (k5_fvsum_1 B C)) ) ) ).
tt(redefinition_k6_graphsp,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) & (m1_subset_1 B (k3_finseq_2 k1_numbers)))  =>  ((k6_graphsp A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k6_group_7,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) & (m1_subset_1 F (u1_struct_0 C))) ) ) ) )  =>  ((k6_group_7 A B C D E F) = (k11_finseq_1 D E F)) ) ) ).
tt(redefinition_k6_ideal_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((m3_ideal_1 D A B) & (m3_ideal_1 E A C)) ) ) )  =>  ((k6_ideal_1 A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k6_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_partfun1 D B) & (v1_funcop_1 D)) ) ) ) )  =>  ((k6_index_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k6_knaster,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (v3_ordinal1 D)) ) )  =>  ((k6_knaster A B C D) = (k4_knaster A B C D)) ) ) ).
tt(redefinition_k6_lattice3,ax, (! [A:$i,B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k6_lattice3 A B) = (k2_relat_1 B)) ) ) ).
tt(redefinition_k6_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  &  ((m1_lattice5 D A B C) & (v3_ordinal1 E)) ) ) )  =>  ((k6_lattice8 A B C D E) = (k5_lattice8 A B C D E)) ) ) ).
tt(redefinition_k6_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k5_lopban_1 A B))) & (m1_subset_1 D A)) ) )  =>  ((k6_lopban_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k6_matrix15,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  & (m1_finseq_1 C (u1_struct_0 A))) )  =>  ((k6_matrix15 A B C) = (k5_matrix15 A B C)) ) ) ).
tt(redefinition_k6_matrix_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((k6_matrix_2 A B C D E) = (k3_matrix_2 B C D E)) ) ) ).
tt(redefinition_k6_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k6_matrixj1 A B C) = (k16_finseq_1 B C)) ) ) ).
tt(redefinition_k6_matrixj2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_matrixj2 C A B) & (m1_matrixj2 D A B)) ) )  =>  ((k6_matrixj2 A B C D) = (k7_finseq_1 C D)) ) ) ).
tt(redefinition_k6_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v13_vectsp_1 F C D) &  ((v1_mod_2 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) ) ) ) ) ) )  =>  ((k6_matrlin2 A B C D E F) = (k3_relat_1 E F)) ) ) ).
tt(redefinition_k6_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  =>  ((k6_mcart_1 A B C D E) = (k5_xtuple_0 E)) ) ) ).
tt(redefinition_k6_midsp_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  &  ((m1_subset_1 C (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E (u1_struct_0 B))) ) ) )  =>  ((k6_midsp_3 A B C D E) = (k2_funct_7 C D E)) ) ) ).
tt(redefinition_k6_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ((m1_subset_1 F B) &  ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) )  =>  ((k6_monoid_1 A B C D E F G) = (k5_funcop_1 E F G)) ) ) ).
tt(redefinition_k6_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k7_dtconstr (k5_msafree A B))) & (m1_msaterm D A B C)) ) )  =>  ((k6_msaterm A B C D) = (k4_trees_4 C D)) ) ) ).
tt(redefinition_k6_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k6_nat_1 A B) = (k3_xxreal_0 A B)) ) ) ).
tt(redefinition_k6_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k6_nat_d A B) = (k3_int_2 A B)) ) ) ).
tt(redefinition_k6_nattra_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m2_cat_1 C A B)) )  =>  ((k6_nattra_1 A B C) = (k3_nattra_1 A B C)) ) ) ).
tt(redefinition_k6_newton,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k6_newton A B) = (k4_newton A B)) ) ) ).
tt(redefinition_k6_numbers,ax, (k6_numbers = k1_xboole_0) ).
tt(redefinition_k6_ordinal4,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((v3_ordinal1 B) & (m1_subset_1 B A)) )  =>  ((k6_ordinal4 A B) = (k1_ordinal1 B)) ) ) ).
tt(redefinition_k6_partfun1,ax, (! [A:$i] :  ((k6_partfun1 A) = (k4_relat_1 A)) ) ).
tt(redefinition_k6_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v7_pcs_0 B)) ) ) )  & (m1_subset_1 C A)) )  =>  ((k6_pcs_0 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k6_pdiff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B k5_numbers) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k6_pdiff_1 A B C) = (k5_pdiff_1 B C)) ) ) ).
tt(redefinition_k6_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) & (m1_subset_1 D k1_numbers)) ) )  =>  ((k6_polyeq_1 A B C D) = (k5_polyeq_1 A B C D)) ) ) ).
tt(redefinition_k6_polyform,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k4_numbers) & (m1_finseq_1 B k4_numbers))  =>  ((k6_polyform A B) = (k7_finseq_1 A B)) ) ) ).
tt(redefinition_k6_power,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (m1_subset_1 B k1_numbers))  =>  ((k6_power A B) = (k5_power A B)) ) ) ).
tt(redefinition_k6_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  &  ((m1_finseq_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k6_prelamb A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k6_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k6_prob_1 A B C D) = (k2_xboole_0 C D)) ) ) ).
tt(redefinition_k6_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  =>  ((k6_qmax_1 A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k6_quatern2,ax, (! [A:$i,B:$i] :  ( ((v1_quaterni A) & (v1_quaterni B))  =>  ((k6_quatern2 A B) = (k5_quatern2 A B)) ) ) ).
tt(redefinition_k6_random_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_random_1 C A B) & (m1_random_1 D A B)) ) )  =>  ((k6_random_1 A B C D) = (k18_valued_1 C D)) ) ) ).
tt(redefinition_k6_real_1,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (m1_subset_1 B k1_numbers))  =>  ((k6_real_1 A B) = (k7_xcmplx_0 A B)) ) ) ).
tt(redefinition_k6_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k6_relset_1 A B C D) = (k6_relat_1 C D)) ) ) ).
tt(redefinition_k6_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k6_relset_2 A B C D) = (k5_relset_2 A B C D)) ) ) ).
tt(redefinition_k6_rewrite2,ax, (! [A:$i] :  ((k6_rewrite2 A) = (k4_relat_1 A)) ) ).
tt(redefinition_k6_rfunct_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k6_rfunct_1 A B C) = (k4_rfunct_1 C)) ) ) ).
tt(redefinition_k6_robbins1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (l2_robbins1 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k6_robbins1 A B C) = (k4_robbins1 A B C)) ) ) ).
tt(redefinition_k6_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k6_rvsum_1 A) = (k30_valued_1 A)) ) ) ).
tt(redefinition_k6_rvsum_2,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) &  ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers)) )  =>  ((k6_rvsum_2 A B) = (k30_valued_1 B)) ) ) ).
tt(redefinition_k6_scmfsa_m,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) ) )  =>  ((k6_scmfsa_m A B C) = (k1_enumset1 A B C)) ) ) ).
tt(redefinition_k6_scmring1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B k2_ami_2) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k6_scmring1 A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k6_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v6_membered A))  =>  ((k6_seq_4 A) = (k2_xxreal_2 A)) ) ) ).
tt(redefinition_k6_setfam_1,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k6_setfam_1 A B) = (k1_setfam_1 B)) ) ) ).
tt(redefinition_k6_setlim_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) )  =>  ((k6_setlim_1 A B C) = (k3_setlim_1 C)) ) ) ).
tt(redefinition_k6_setwiseo,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A)))  =>  ((k6_setwiseo A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k6_sin_cos2,ax, (! [A:$i] :  ((k6_sin_cos2 A) = (k5_sin_cos2 A)) ) ).
tt(redefinition_k6_sin_cos6,ax, (! [A:$i] :  ((k6_sin_cos6 A) = (k5_sin_cos6 A)) ) ).
tt(redefinition_k6_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k6_sin_cos9 A) = (k4_sin_cos9 A)) ) ) ).
tt(redefinition_k6_subset_1,ax, (! [A:$i,B:$i] :  ((k6_subset_1 A B) = (k4_xboole_0 A B)) ) ).
tt(redefinition_k6_substut1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) & (m1_subset_1 B (k1_substut1 A)))  =>  ((k6_substut1 A B C) = (k5_relat_1 B C)) ) ) ).
tt(redefinition_k6_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k7_numbers)) =>  ((k6_supinf_2 A) = (k4_member_1 A)) ) ) ).
tt(redefinition_k6_topalg_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k6_topalg_5 A) = (k5_topalg_5 A)) ) ) ).
tt(redefinition_k6_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k6_topgrp_1 A B) = (k1_topgrp_1 A B)) ) ) ).
tt(redefinition_k6_toprealc,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  &  ((m1_subset_1 E (u1_struct_0 A)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  =>  ((k6_toprealc A B C D E F) = (k1_binop_1 D E F)) ) ) ).
tt(redefinition_k6_trees_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  =>  ((k6_trees_2 A B) = (k4_trees_2 B)) ) ) ).
tt(redefinition_k6_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((k6_trees_3 A B) = (k7_funct_3 A B)) ) ) ).
tt(redefinition_k6_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_valuat_1 A B) k6_margrel1))))) )  & (m1_subset_1 D (k3_cqc_lang A))) ) )  =>  ((k6_valuat_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k6_vfunct_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) )  =>  ((k6_vfunct_1 A B C D) = (k1_vfunct_1 A B C D)) ) ) ).
tt(redefinition_k6_waybel35,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((k6_waybel35 A B C) = (k5_waybel35 A B C)) ) ) ).
tt(redefinition_k6_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) ) ) )  =>  ((k6_waybel_5 A B C D) = (k1_funct_5 D)) ) ) ).
tt(redefinition_k6_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((l1_orders_2 A) &  ((l1_orders_2 B) &  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((k6_yellow_3 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k6_zf_lang1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_zf_lang A) & (m1_finseq_1 A k5_numbers))  &  ((m1_subset_1 B k1_zf_lang) & (m1_subset_1 C k1_zf_lang)) )  =>  ((k6_zf_lang1 A B C) = (k5_zf_lang1 A B C)) ) ) ).
tt(redefinition_k70_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_valued_2 B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) ) ) )  =>  ((k70_valued_2 A B C D) = (k68_valued_2 B C D)) ) ) ).
tt(redefinition_k73_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k73_valued_2 A B C D E F) = (k72_valued_2 C D E F)) ) ) ).
tt(redefinition_k74_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k74_valued_2 A B C D E F) = (k72_valued_2 C D E F)) ) ) ).
tt(redefinition_k79_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k79_valued_2 A B C D E F) = (k78_valued_2 C D E F)) ) ) ).
tt(redefinition_k7_abcmiz_a,ax, (k7_abcmiz_a = k19_abcmiz_1) ).
tt(redefinition_k7_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  & (v1_int_1 C)) )  =>  ((k7_aofa_i00 A B C) = (k7_valued_1 B C)) ) ) ).
tt(redefinition_k7_binom,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k7_binom A B) = (k4_newton A B)) ) ) ).
tt(redefinition_k7_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_binop_2 A) = (k4_xcmplx_0 A)) ) ) ).
tt(redefinition_k7_borsuk_7,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A (u1_struct_0 k3_topmetr)) &  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) &  ((m1_borsuk_2 C k3_topmetr A B) & (v1_xreal_0 D)) ) )  =>  ((k7_borsuk_7 A B C D) = (k13_valued_1 C D)) ) ) ).
tt(redefinition_k7_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_card_1 A) = (k6_card_1 A)) ) ) ).
tt(redefinition_k7_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) )  =>  ((k7_cat_2 A B C D) = (k3_funct_4 C D)) ) ) ).
tt(redefinition_k7_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k7_cat_4 A B C) = (k3_cat_4 A B C)) ) ) ).
tt(redefinition_k7_chain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  &  ((m1_chain_1 B A) &  ((m1_subset_1 C k5_numbers) &  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 A B C))) & (m1_subset_1 E (k1_zfmisc_1 (k4_chain_1 A B C)))) ) ) )  =>  ((k7_chain_1 A B C D E) = (k5_xboole_0 D E)) ) ) ).
tt(redefinition_k7_circcmb3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  &  ((m1_circcmb3 B A) &  ((m1_circcmb3 C A) &  ((m2_circcmb3 D A B) & (m2_circcmb3 E A C)) ) ) )  =>  ((k7_circcmb3 A B C D E) = (k3_circcomb B C D E)) ) ) ).
tt(redefinition_k7_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k7_classes2 A B C) = (k2_xboole_0 B C)) ) ) ).
tt(redefinition_k7_clopban1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k6_clopban1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k7_clopban1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k7_closure2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  & (m1_subset_1 D (k6_closure2 A B))) )  =>  ((k7_closure2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k7_complex1,ax, (k7_complex1 = k1_xcmplx_0) ).
tt(redefinition_k7_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k7_comseq_3 A) = (k3_comseq_3 A)) ) ) ).
tt(redefinition_k7_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k7_cqc_lang A B C) = (k14_qc_lang1 A B C)) ) ) ).
tt(redefinition_k7_domain_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k7_domain_1 A B C) = (k2_tarski B C)) ) ) ).
tt(redefinition_k7_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) & (l1_lang1 A)) )  =>  ((k7_dtconstr A) = (k2_lang1 A)) ) ) ).
tt(redefinition_k7_dynkin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_dynkin B A) & (m1_subset_1 C B)) )  =>  ((k7_dynkin A B C) = (k6_dynkin A B C)) ) ) ).
tt(redefinition_k7_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k7_euclid A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k7_finseqop,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ((k7_finseqop A B C D) = (k6_finseqop B C D)) ) ) ).
tt(redefinition_k7_fomodel3,ax, (! [A:$i,B:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k7_fomodel3 A B) = (k5_fomodel3 A B)) ) ) ).
tt(redefinition_k7_fomodel4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ((v1_xboole_0 B) &  ((v4_fomodel2 C A) & (m1_subset_1 C (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)))) ) )  =>  ((k7_fomodel4 A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k7_funcop_1,ax, (! [A:$i,B:$i] :  ((k7_funcop_1 A B) = (k2_funcop_1 A B)) ) ).
tt(redefinition_k7_funct_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_funct_4 A B C D) = (k1_funct_4 C D)) ) ) ).
tt(redefinition_k7_functor0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  &  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  &  ((m1_subset_1 D (u1_struct_0 A)) & (m1_subset_1 E (u1_struct_0 A))) ) ) )  =>  ((k7_functor0 A B C D E) = (k4_functor0 A B C D E)) ) ) ).
tt(redefinition_k7_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) & (m1_subset_1 D k5_numbers)) ) )  =>  ((k7_genealg1 A B C D) = (k1_genealg1 A B C D)) ) ) ).
tt(redefinition_k7_group_1,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_struct_0 A))  =>  ((k7_group_1 A) = (k7_struct_0 A)) ) ) ).
tt(redefinition_k7_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_index_1 B)) ) ) )  &  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_index_1 C)) ) ) )  &  ((m2_index_1 D A B C) & (m1_subset_1 E A)) ) ) )  =>  ((k7_index_1 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k7_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k7_interva1 A B) = (k1_setfam_1 B)) ) ) ).
tt(redefinition_k7_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 D (k2_zfmisc_1 (k3_rfunct_3 A B) C)))  =>  ((k7_lexbfs A B C D) = (k1_xtuple_0 D)) ) ) ).
tt(redefinition_k7_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  & (m1_subset_1 C A)) )  =>  ((k7_lfuzzy_0 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k7_margrel1,ax, (k7_margrel1 = k1_xboolean) ).
tt(redefinition_k7_matrixj1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v1_matrixj1 C A) & (m1_finseq_1 C (k3_finseq_2 (k3_finseq_2 A)))) ) )  =>  ((k7_matrixj1 A B C) = (k1_rfinseq B C)) ) ) ).
tt(redefinition_k7_matrixj2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((v7_ordinal1 C) & (m1_matrixj2 D A B)) ) )  =>  ((k7_matrixj2 A B C D) = (k16_finseq_1 C D)) ) ) ).
tt(redefinition_k7_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 D A B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) )  =>  ((k7_matrlin2 A B C D E) = (k2_matrlin2 D E)) ) ) ).
tt(redefinition_k7_matrlin,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 A))) ) )  =>  ((k7_matrlin A B C) = (k8_pre_poly B C)) ) ) ).
tt(redefinition_k7_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 E (k4_zfmisc_1 A B C D))) ) ) )  =>  ((k7_mcart_1 A B C D E) = (k2_xtuple_0 E)) ) ) ).
tt(redefinition_k7_measure6,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_membered B) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_measure6 A B C) = (k35_valued_1 C)) ) ) ).
tt(redefinition_k7_modal_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k6_modal_1) & (m1_subset_1 B (k9_xtuple_0 A)))  =>  ((k7_modal_1 A B) = (k5_trees_2 A B)) ) ) ).
tt(redefinition_k7_monoid_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 G C)) ) ) ) )  =>  ((k7_monoid_1 A B C D E F G) = (k4_funcop_1 E F G)) ) ) ).
tt(redefinition_k7_nat_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((k7_nat_1 A B) = (k4_xxreal_0 A B)) ) ) ).
tt(redefinition_k7_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((k7_nat_d A B) = (k1_xreal_0 A B)) ) ) ).
tt(redefinition_k7_ordinal4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  &  ((v3_ordinal1 C) & (m1_subset_1 C A)) ) )  =>  ((k7_ordinal4 A B C) = (k10_ordinal2 B C)) ) ) ).
tt(redefinition_k7_prepower,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_rat_1 B))  =>  ((k7_prepower A B) = (k6_prepower A B)) ) ) ).
tt(redefinition_k7_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_subset_1 C B) & (m1_subset_1 D B)) )  =>  ((k7_prob_1 A B C D) = (k4_xboole_0 C D)) ) ) ).
tt(redefinition_k7_prvect_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ((m1_subset_1 D A) & (m1_subset_1 E (k4_finseq_2 B A))) ) ) )  =>  ((k7_prvect_1 A B C D E) = (k5_funcop_1 C D E)) ) ) ).
tt(redefinition_k7_qmax_1,ax, (! [A:$i,B:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  & (m1_subset_1 B (k5_qmax_1 A)))  =>  ((k7_qmax_1 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k7_random_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m1_random_1 C A B)) )  =>  ((k7_random_1 A B C) = (k54_valued_1 C)) ) ) ).
tt(redefinition_k7_ranknull,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((k7_ranknull A B C D) = (k8_relat_1 C D)) ) ) ).
tt(redefinition_k7_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k7_real_1 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k7_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k7_relset_1 A B C D) = (k7_relat_1 C D)) ) ) ).
tt(redefinition_k7_relset_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((k7_relset_2 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k7_rfunct_1,ax, (! [A:$i,B:$i] :  ((k7_rfunct_1 A B) = (k4_funct_3 A B)) ) ).
tt(redefinition_k7_rfunct_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered B) &  ((m1_subset_1 C (k3_rfunct_3 A B)) & (m1_subset_1 D (k3_rfunct_3 A B))) ) )  =>  ((k7_rfunct_3 A B C D) = (k18_valued_1 C D)) ) ) ).
tt(redefinition_k7_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  =>  ((k7_rlvect_2 A B C) = (k1_valued_1 B C)) ) ) ).
tt(redefinition_k7_rusub_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k7_rusub_4 A B C) = (k6_rusub_4 A B C)) ) ) ).
tt(redefinition_k7_rvsum_1,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (m1_subset_1 B (k4_finseq_2 A k1_numbers)))  =>  ((k7_rvsum_1 A B) = (k30_valued_1 B)) ) ) ).
tt(redefinition_k7_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) ) )  =>  ((k7_rvsum_2 A B) = (k45_valued_1 A B)) ) ) ).
tt(redefinition_k7_scmfsa_m,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  &  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  &  ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k7_scmfsa_m A B C D) = (k2_enumset1 A B C D)) ) ) ).
tt(redefinition_k7_scmringi,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B k2_scm_inst) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k7_scmringi A B C) = (k10_finseq_1 B C)) ) ) ).
tt(redefinition_k7_square_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k7_square_1 A) = (k6_square_1 A)) ) ) ).
tt(redefinition_k7_sublemma,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k38_substut1 A)) & (m1_subset_1 C (k3_qc_lang1 A))) )  =>  ((k7_sublemma A B C) = (k4_tarski B C)) ) ) ).
tt(redefinition_k7_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k7_subset_1 A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k7_supinf_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((k7_supinf_2 A) = (k2_xxreal_2 A)) ) ) ).
tt(redefinition_k7_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) &  ((m1_subset_1 F (u1_struct_0 B)) & (m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) )  =>  ((k7_topalg_4 A B C D E F G) = (k11_mcart_1 G)) ) ) ).
tt(redefinition_k7_topgrp_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  & (m1_subset_1 B (u1_struct_0 A)))  =>  ((k7_topgrp_1 A B) = (k2_topgrp_1 A B)) ) ) ).
tt(redefinition_k7_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  =>  ((k7_toprealc A B C) = (k7_valued_1 B C)) ) ) ).
tt(redefinition_k7_trees_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((k7_trees_3 A B) = (k8_funct_3 A B)) ) ) ).
tt(redefinition_k7_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B (k5_trees_3 A)))  =>  ((k7_trees_4 A B) = (k2_funct_6 B)) ) ) ).
tt(redefinition_k7_valuat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_qc_lang1 A) &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C k5_numbers) &  ((m1_valuat_1 D A B) & (m1_subset_1 E (k8_qc_lang1 A C))) ) ) )  =>  ((k7_valuat_1 A B C D E) = (k1_funct_1 D E)) ) ) ).
tt(redefinition_k7_waybel_5,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_waybel_5 A B C D) = (k2_funcop_1 C D)) ) ) ).
tt(redefinition_k7_yellow_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k7_yellow_3 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k7_yellow_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((l1_struct_0 B) &  ((m3_yellow_6 C A B) & (m1_subset_1 D A)) ) )  =>  ((k7_yellow_6 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k80_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k80_valued_2 A B C D E F) = (k78_valued_2 C D E F)) ) ) ).
tt(redefinition_k84_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k84_valued_2 A B C D E F) = (k83_valued_2 C D E F)) ) ) ).
tt(redefinition_k85_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k85_valued_2 A B C D E F) = (k83_valued_2 C D E F)) ) ) ).
tt(redefinition_k89_aofa_i00,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_card_3 A))  &  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) &  ((v3_aofa_000 B) &  ((v4_aofa_000 B) &  ((v5_aofa_000 B) &  ((v6_aofa_000 B) &  ((v2_aofa_i00 B) & (l1_unialg_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) &  ( ((v1_aofa_i00 D B A C) & (m1_aofa_000 D B (k9_funct_2 A k4_numbers) C))  &  ((m1_subset_1 E (k9_funct_2 A k4_numbers)) & (m1_subset_1 F (u1_struct_0 B))) ) ) ) )  =>  ((k89_aofa_i00 A B C D E F) = (k1_binop_1 D E F)) ) ) ).
tt(redefinition_k8_aofa_000,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k9_funct_2 A A)) & (m1_subset_1 D (k9_funct_2 A A))) )  =>  ((k8_aofa_000 A B C D) = (k7_aofa_000 B C D)) ) ) ).
tt(redefinition_k8_binop_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k8_binop_2 A) = (k5_xcmplx_0 A)) ) ) ).
tt(redefinition_k8_cat_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k8_cat_4 A B C) = (k4_cat_4 A B C)) ) ) ).
tt(redefinition_k8_cat_5,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  & (m1_subset_1 B (u4_struct_0 A)))  =>  ((k8_cat_5 A B) = (k2_xtuple_0 B)) ) ) ).
tt(redefinition_k8_catalg_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B A))  =>  ((k8_catalg_1 A B) = (k5_catalg_1 B)) ) ) ).
tt(redefinition_k8_closure2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) )  =>  ((k8_closure2 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k8_cohsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((k8_cohsp_1 A B C) = (k7_cohsp_1 C)) ) ) ).
tt(redefinition_k8_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  =>  ((k8_complex1 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k8_compos_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_compos_1 A) &  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) ) ) )  =>  ((k8_compos_1 A B C) = (k7_compos_1 A B C)) ) ) ).
tt(redefinition_k8_comput_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k5_numbers)) &  ((m1_subset_1 C k5_numbers) & (m1_subset_1 D k5_numbers)) ) )  =>  ((k8_comput_1 A B C D) = (k2_funct_7 B C D)) ) ) ).
tt(redefinition_k8_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k8_comseq_3 A) = (k4_comseq_3 A)) ) ) ).
tt(redefinition_k8_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k8_conlat_1 A) = (k7_conlat_1 A)) ) ) ).
tt(redefinition_k8_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k8_cqc_lang A B C) = (k2_qc_lang2 A B C)) ) ) ).
tt(redefinition_k8_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_cqc_lang A) (k9_funct_2 (k2_zfmisc_1 (k1_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k3_cqc_lang A)))))) )  & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k8_cqc_sim1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k8_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) & (m1_subset_1 D A)) ) )  =>  ((k8_domain_1 A B C D) = (k1_enumset1 B C D)) ) ) ).
tt(redefinition_k8_dtconstr,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) & (l1_lang1 A)) )  & (m1_subset_1 B (k6_dtconstr A)))  =>  ((k8_dtconstr A B) = (k1_trees_4 B)) ) ) ).
tt(redefinition_k8_eqrel_1,ax, (! [A:$i,B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k8_eqrel_1 A B) = (k7_eqrel_1 A B)) ) ) ).
tt(redefinition_k8_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((k8_euclid A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k8_finseq_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_finseq_1 B A) & (m1_finseq_1 C A))  =>  ((k8_finseq_1 A B C) = (k7_finseq_1 B C)) ) ) ).
tt(redefinition_k8_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_fomodel0 A) = (k7_fomodel0 A)) ) ) ).
tt(redefinition_k8_funcop_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 C A))  =>  ((k8_funcop_1 A B C) = (k2_funcop_1 B C)) ) ) ).
tt(redefinition_k8_funct_5,ax, (k8_funct_5 = k6_funct_5) ).
tt(redefinition_k8_fvsum_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 A k5_numbers) &  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  &  ((m1_subset_1 C (k4_finseq_2 A (u1_struct_0 B))) & (m1_subset_1 D (k4_finseq_2 A (u1_struct_0 B)))) ) )  =>  ((k8_fvsum_1 A B C D) = (k7_fvsum_1 B C D)) ) ) ).
tt(redefinition_k8_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) & (m1_subset_1 E k5_numbers)) ) ) )  =>  ((k8_genealg1 A B C D E) = (k2_genealg1 A B C D E)) ) ) ).
tt(redefinition_k8_graph_5,ax, (k8_graph_5 = k2_arytm_2) ).
tt(redefinition_k8_group_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((k8_group_1 A B C) = (k6_algstr_0 A B C)) ) ) ).
tt(redefinition_k8_index_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m3_index_1 E A B C D)) ) ) )  =>  ((k8_index_1 A B C D E) = (k2_xtuple_0 E)) ) ) ).
tt(redefinition_k8_interva1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k8_interva1 A B) = (k3_tarski B)) ) ) ).
tt(redefinition_k8_isocat_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E A C)) ) ) )  =>  ((k8_isocat_2 A B C D E) = (k13_funct_3 D E)) ) ) ).
tt(redefinition_k8_lexbfs,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 D (k2_zfmisc_1 A (k9_funct_2 C B)))) )  =>  ((k8_lexbfs A B C D) = (k2_xtuple_0 D)) ) ) ).
tt(redefinition_k8_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((m1_subset_1 D A) & (m1_subset_1 E B)) ) ) )  =>  ((k8_lfuzzy_0 A B C D E) = (k1_binop_1 C D E)) ) ) ).
tt(redefinition_k8_lpspace1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B k1_numbers))  =>  ((k8_lpspace1 A B) = (k2_funcop_1 A B)) ) ) ).
tt(redefinition_k8_margrel1,ax, (k8_margrel1 = k2_xboolean) ).
tt(redefinition_k8_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  =>  ((k8_matrix_1 A B C) = (k6_matrix_1 A B C)) ) ) ).
tt(redefinition_k8_matrix_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v1_matrix_1 C) & (m1_finseq_1 C (k3_finseq_2 (u1_struct_0 A)))) ) )  =>  ((k8_matrix_2 A B C) = (k2_finseq_3 B C)) ) ) ).
tt(redefinition_k8_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ((m1_subset_1 C (k5_finsub_1 A)) & (m1_subset_1 D (k5_finsub_1 B))) ) )  =>  ((k8_matrix_3 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k8_matrixc1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k2_numbers)) & (m1_subset_1 C (k4_finseq_2 A k2_numbers))) )  =>  ((k8_matrixc1 A B C) = (k5_matrixc1 B C)) ) ) ).
tt(redefinition_k8_matrlin2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  ((m1_vectsp_4 D A B) &  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) )  =>  ((k8_matrlin2 A B C D E) = (k2_matrlin2 D E)) ) ) ).
tt(redefinition_k8_matrlin,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) &  ((v7_ordinal1 D) &  ((m1_matrix_1 E A B D) & (m1_matrix_1 F A C D)) ) ) ) )  =>  ((k8_matrlin A B C D E F) = (k7_finseq_1 E F)) ) ) ).
tt(redefinition_k8_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 A)) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ((k8_mcart_1 A B C D) = (k2_zfmisc_1 C D)) ) ) ).
tt(redefinition_k8_msaterm,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  &  ((m1_subset_1 C (k1_msaterm A B)) & (m1_subset_1 D (k9_xtuple_0 C))) ) )  =>  ((k8_msaterm A B C D) = (k5_trees_2 C D)) ) ) ).
tt(redefinition_k8_nat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v7_ordinal1 C))  =>  ((k8_nat_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k8_nat_3,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((k8_nat_3 A B) = (k7_nat_3 A B)) ) ) ).
tt(redefinition_k8_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k8_ordinal3 A B) = (k10_ordinal2 A B)) ) ) ).
tt(redefinition_k8_polyeq_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((m1_subset_1 A k1_numbers) &  ((m1_subset_1 B k1_numbers) &  ((m1_subset_1 C k1_numbers) &  ((m1_subset_1 D k1_numbers) & (m1_subset_1 E k1_numbers)) ) ) )  =>  ((k8_polyeq_1 A B C D E) = (k7_polyeq_1 A B C D E)) ) ) ).
tt(redefinition_k8_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k8_polynom3 A B C) = (k2_normsp_1 A B C)) ) ) ).
tt(redefinition_k8_power,ax, (k8_power = k7_power) ).
tt(redefinition_k8_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) ) )  =>  ((k8_prelamb A B C) = (k3_relat_1 B C)) ) ) ).
tt(redefinition_k8_prob_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) ) ) )  =>  ((k8_prob_1 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k8_prob_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_finseq_1 C B) & (v7_ordinal1 D)) )  =>  ((k8_prob_3 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k8_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  (~ (v1_xboole_0 A)) ) ) )  &  ((m1_subset_1 B (k4_card_3 A)) & (m1_subset_1 C (k9_xtuple_0 A))) )  =>  ((k8_prvect_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k8_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_quatern2 A) = (k7_quatern2 A)) ) ) ).
tt(redefinition_k8_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k8_real_1 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k8_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k8_relset_1 A B C D) = (k8_relat_1 C D)) ) ) ).
tt(redefinition_k8_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((k8_rvsum_1 A B) = (k45_valued_1 A B)) ) ) ).
tt(redefinition_k8_rvsum_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ( ((v3_card_1 B A) & (m1_finseq_1 B k2_numbers))  &  ((v3_card_1 C A) & (m1_finseq_1 C k2_numbers)) ) )  =>  ((k8_rvsum_2 A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k8_setwiseo,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  & (m1_subset_1 D (k5_finsub_1 A))) ) )  =>  ((k8_setwiseo A B C D) = (k7_relat_1 C D)) ) ) ).
tt(redefinition_k8_sublemma,ax, (! [A:$i,B:$i] :  ( ((m1_qc_lang1 A) &  ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A)))) )  =>  ((k8_sublemma A B) = (k1_xtuple_0 B)) ) ) ).
tt(redefinition_k8_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k8_subset_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k8_supinf_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((k8_supinf_2 A) = (k1_xxreal_2 A)) ) ) ).
tt(redefinition_k8_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 A)) &  ((m1_subset_1 E (u1_struct_0 B)) &  ((m1_subset_1 F (u1_struct_0 B)) & (m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) )  =>  ((k8_topalg_4 A B C D E F G) = (k12_mcart_1 G)) ) ) ).
tt(redefinition_k8_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  ((k8_topgrp_1 A) = (k3_group_1 A)) ) ) ).
tt(redefinition_k8_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  =>  ((k8_toprealc A B C) = (k13_valued_1 B C)) ) ) ).
tt(redefinition_k8_trees_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_finseq_1 C (k5_trees_3 A))) )  =>  ((k8_trees_4 A B C) = (k4_trees_4 B C)) ) ) ).
tt(redefinition_k8_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v1_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xcmplx_0 D)) )  =>  ((k8_valued_1 A B C D) = (k7_valued_1 C D)) ) ) ).
tt(redefinition_k8_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  & (m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B)))) )  =>  ((k8_yellow_3 A B C) = (k1_xtuple_0 C)) ) ) ).
tt(redefinition_k90_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v1_valued_2 C) &  ((v1_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k90_valued_2 A B C D E F) = (k89_valued_2 C D E F)) ) ) ).
tt(redefinition_k91_valued_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((v3_valued_2 C) &  ((v3_valued_2 D) &  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  &  ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) )  =>  ((k91_valued_2 A B C D E F) = (k89_valued_2 C D E F)) ) ) ).
tt(redefinition_k9_aofa_i00,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k4_numbers)))) )  & (v1_int_1 C)) )  =>  ((k9_aofa_i00 A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k9_binarith,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ((v7_ordinal1 A) &  ((v7_ordinal1 B) &  ( (~ (v1_xboole_0 C))  &  ( ((v3_card_1 D A) & (m1_finseq_1 D C))  &  ((v3_card_1 E B) & (m1_finseq_1 E C)) ) ) ) )  =>  ((k9_binarith A B C D E) = (k7_finseq_1 D E)) ) ) ).
tt(redefinition_k9_binop_2,ax, (! [A:$i,B:$i] :  ( ((v1_xreal_0 A) & (v1_xreal_0 B))  =>  ((k9_binop_2 A B) = (k2_xcmplx_0 A B)) ) ) ).
tt(redefinition_k9_bspace,ax, (! [A:$i] :  ((k9_bspace A) = (k8_bspace A)) ) ).
tt(redefinition_k9_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  =>  ((k9_bvfunc_1 A B C) = (k7_bvfunc_1 B C)) ) ) ).
tt(redefinition_k9_cat_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  &  ((m2_cat_1 D A B) & (m2_cat_1 E B C)) ) ) )  =>  ((k9_cat_1 A B C D E) = (k3_relat_1 D E)) ) ) ).
tt(redefinition_k9_cat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k9_cat_2 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k9_catalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k9_catalg_1 A B C) = (k6_catalg_1 B C)) ) ) ).
tt(redefinition_k9_classes2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  &  ((m1_subset_1 B A) & (m1_subset_1 C A)) )  =>  ((k9_classes2 A B C) = (k4_xboole_0 B C)) ) ) ).
tt(redefinition_k9_complex1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k2_numbers) & (m1_subset_1 B k2_numbers))  =>  ((k9_complex1 A B) = (k3_xcmplx_0 A B)) ) ) ).
tt(redefinition_k9_compos_1,ax, (! [A:$i,B:$i] :  ( ((l1_compos_1 A) & (m1_subset_1 B (u1_compos_1 A)))  =>  ((k9_compos_1 A B) = (k3_afinsq_1 B)) ) ) ).
tt(redefinition_k9_comseq_3,ax, (! [A:$i,B:$i] :  ( ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k9_comseq_3 A B) = (k3_relat_1 A B)) ) ) ).
tt(redefinition_k9_cqc_lang,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((k9_cqc_lang A B C) = (k3_qc_lang2 A B C)) ) ) ).
tt(redefinition_k9_domain_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((k9_domain_1 A B C D E) = (k2_enumset1 B C D E)) ) ) ).
tt(redefinition_k9_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_dtconstr A) &  ((v3_dtconstr A) & (l1_lang1 A)) ) )  &  ((m1_subset_1 B (k7_dtconstr A)) & (m2_dtconstr C A B)) )  =>  ((k9_dtconstr A B C) = (k4_trees_4 B C)) ) ) ).
tt(redefinition_k9_ec_pf_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  &  ((m1_subset_1 B (k1_ec_pf_2 A)) &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))))) )  & (m1_subset_1 D (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))) ) )  =>  ((k9_ec_pf_2 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k9_eqrel_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  & (m1_subset_1 C A)) )  =>  ((k9_eqrel_1 A B C) = (k9_relat_1 B C)) ) ) ).
tt(redefinition_k9_euclid,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k1_euclid A)) & (v1_xreal_0 C)) )  =>  ((k9_euclid A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k9_filter_0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((k9_filter_0 A B) = (k8_filter_0 A B)) ) ) ).
tt(redefinition_k9_filter_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k9_filter_1 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k9_finseq_1,ax, (! [A:$i] :  ((k9_finseq_1 A) = (k5_finseq_1 A)) ) ).
tt(redefinition_k9_finseq_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((m1_subset_1 C A) &  ((m1_subset_1 D A) & (m1_subset_1 E A)) ) ) )  =>  ((k9_finseq_4 A B C D E) = (k7_finseq_4 B C D E)) ) ) ).
tt(redefinition_k9_fomodel0,ax, (! [A:$i,B:$i] :  ((k9_fomodel0 A B) = (k4_funct_3 A B)) ) ).
tt(redefinition_k9_freealg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 A k5_numbers))  &  ( (~ (v1_xboole_0 B))  & (v1_freealg B)) )  =>  ((k9_freealg A B) = (k8_freealg A B)) ) ) ).
tt(redefinition_k9_funcop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (m1_subset_1 E A)) ) )  =>  ((k9_funcop_1 A B C D E) = (k4_funcop_1 C D E)) ) ) ).
tt(redefinition_k9_funct_2,ax, (! [A:$i,B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k9_funct_2 A B) = (k1_funct_2 A B)) ) ) ).
tt(redefinition_k9_funct_3,ax, (! [A:$i,B:$i] :  ((k9_funct_3 A B) = (k7_funct_3 A B)) ) ).
tt(redefinition_k9_funct_5,ax, (k9_funct_5 = k7_funct_5) ).
tt(redefinition_k9_functor3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ((v15_functor0 C A B) & (m2_functor0 C A B)) ) )  =>  ((k9_functor3 A B C) = (k1_functor2 A B C)) ) ) ).
tt(redefinition_k9_genealg1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  &  ((m1_genealg1 B A) &  ((m1_genealg1 C A) &  ((m1_subset_1 D k5_numbers) &  ((m1_subset_1 E k5_numbers) & (m1_subset_1 F k5_numbers)) ) ) ) )  =>  ((k9_genealg1 A B C D E F) = (k3_genealg1 A B C D E F)) ) ) ).
tt(redefinition_k9_glib_003,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  & (m3_glib_001 B A))  =>  ((k9_glib_003 A B) = (k8_glib_003 A B)) ) ) ).
tt(redefinition_k9_glib_004,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  &  ((m2_glib_004 B A) & (v7_ordinal1 C)) )  =>  ((k9_glib_004 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k9_lattice8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  & (m1_lattice5 D A B C)) ) )  =>  ((k9_lattice8 A B C D) = (k8_lattice8 A B C D)) ) ) ).
tt(redefinition_k9_lfuzzy_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) & (m1_subset_1 C A)) )  =>  ((k9_lfuzzy_0 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k9_lopban_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 C (u1_struct_0 (k8_lopban_1 A B))) & (m1_subset_1 D (u1_struct_0 A))) ) )  =>  ((k9_lopban_1 A B C D) = (k1_funct_1 C D)) ) ) ).
tt(redefinition_k9_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k9_lopclset A) = (k8_lopclset A)) ) ) ).
tt(redefinition_k9_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  ((k9_margrel1 A) = (k3_xboolean A)) ) ) ).
tt(redefinition_k9_matrix13,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ((v7_ordinal1 B) &  ((v7_ordinal1 C) & (m1_matrix_1 D (u1_struct_0 A) B C)) ) )  =>  ((k9_matrix13 A B C D) = (k10_xtuple_0 D)) ) ) ).
tt(redefinition_k9_matrix_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_matrix_1 B) & (m1_finseq_1 B (k3_finseq_2 A)))  & (v7_ordinal1 C)) )  =>  ((k9_matrix_1 A B C) = (k7_matrix_1 A B C)) ) ) ).
tt(redefinition_k9_matrix_3,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) )  =>  ((k9_matrix_3 A B C D E F) = (k6_finseqop D E F)) ) ) ).
tt(redefinition_k9_matrix_5,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k9_matrix_5 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k9_mcart_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ((m1_subset_1 D (k1_zfmisc_1 A)) &  ((m1_subset_1 E (k1_zfmisc_1 B)) & (m1_subset_1 F (k1_zfmisc_1 C))) )  =>  ((k9_mcart_1 A B C D E F) = (k3_zfmisc_1 D E F)) ) ) ).
tt(redefinition_k9_measure8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) )  =>  ((k9_measure8 A B C) = (k6_measure8 A B C)) ) ) ).
tt(redefinition_k9_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k9_newton A) = (k3_newton A)) ) ) ).
tt(redefinition_k9_ordinal3,ax, (! [A:$i,B:$i] :  ( ( ((v3_ordinal1 A) & (v7_ordinal1 A))  &  ((v3_ordinal1 B) & (v7_ordinal1 B)) )  =>  ((k9_ordinal3 A B) = (k11_ordinal2 A B)) ) ) ).
tt(redefinition_k9_osafree,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((k9_osafree A B C) = (k3_osafree A B C)) ) ) ).
tt(redefinition_k9_pcs_0,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pcs_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_pcs_0 B))  &  ((m1_subset_1 C (u1_struct_0 A)) & (m1_subset_1 D (u1_struct_0 B))) ) )  =>  ((k9_pcs_0 A B C D) = (k4_tarski C D)) ) ) ).
tt(redefinition_k9_pre_poly,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v1_xboole_0 C))  & (m1_finseq_2 C A))  &  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ((k9_pre_poly A B C D E) = (k7_partfun1 C D E)) ) ) ).
tt(redefinition_k9_prob_3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  &  ((m1_finseq_1 C B) & (m2_prob_1 D A B)) ) )  =>  ((k9_prob_3 A B C D) = (k3_relat_1 C D)) ) ) ).
tt(redefinition_k9_prvect_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  &  ((m1_prvect_1 B A) & (m1_subset_1 C (k4_finseq_1 A))) )  =>  ((k9_prvect_1 A B C) = (k1_funct_1 B C)) ) ) ).
tt(redefinition_k9_real_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k1_numbers) & (v1_xreal_0 B))  =>  ((k9_real_1 A B) = (k6_xcmplx_0 A B)) ) ) ).
tt(redefinition_k9_rvsum_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (k4_finseq_2 A k1_numbers)) & (m1_subset_1 C (k4_finseq_2 A k1_numbers))) )  =>  ((k9_rvsum_1 A B C) = (k45_valued_1 B C)) ) ) ).
tt(redefinition_k9_rvsum_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  & (v1_xcmplx_0 B))  =>  ((k9_rvsum_2 A B) = (k24_valued_1 A B)) ) ) ).
tt(redefinition_k9_scmfsa_1,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) & (m1_subset_1 B k3_scmfsa_1))  =>  ((k9_scmfsa_1 A B) = (k1_funct_1 A B)) ) ) ).
tt(redefinition_k9_seq_4,ax, (! [A:$i,B:$i] :  ( ((m1_finseq_1 A k2_numbers) & (m1_finseq_1 B k2_numbers))  =>  ((k9_seq_4 A B) = (k1_valued_1 A B)) ) ) ).
tt(redefinition_k9_setfam_1,ax, (! [A:$i] :  ((k9_setfam_1 A) = (k1_zfmisc_1 A)) ) ).
tt(redefinition_k9_simplex0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_matroid0 B) & (m1_simplex0 B A))  & (v1_int_1 C))  =>  ((k9_simplex0 A B C) = (k8_simplex0 A B C)) ) ) ).
tt(redefinition_k9_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k9_sincos10 A) = (k5_sincos10 A)) ) ) ).
tt(redefinition_k9_sin_cos2,ax, (! [A:$i] :  ((k9_sin_cos2 A) = (k8_sin_cos2 A)) ) ).
tt(redefinition_k9_subset_1,ax, (! [A:$i,B:$i,C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k9_subset_1 A B C) = (k3_xboole_0 B C)) ) ) ).
tt(redefinition_k9_supinf_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  &  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) )  =>  ((k9_supinf_2 A B C) = (k10_xtuple_0 C)) ) ) ).
tt(redefinition_k9_topalg_4,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_subset_1 D (u1_struct_0 B)) & (m1_borsuk_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D))) ) ) )  =>  ((k9_topalg_4 A B C D E) = (k11_mcart_1 E)) ) ) ).
tt(redefinition_k9_toprealc,ax, (! [A:$i,B:$i,C:$i] :  ( ((v7_ordinal1 A) &  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) & (v1_xreal_0 C)) )  =>  ((k9_toprealc A B C) = (k24_valued_1 B C)) ) ) ).
tt(redefinition_k9_valued_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v3_membered B) &  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  & (v1_xreal_0 D)) )  =>  ((k9_valued_1 A B C D) = (k7_valued_1 C D)) ) ) ).
tt(redefinition_k9_yellow_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  & (m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B)))) )  =>  ((k9_yellow_3 A B C) = (k2_xtuple_0 C)) ) ) ).
tt(redefinition_m1_armstrng,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  (! [C:$i] :  ((m1_armstrng C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_autalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_autalg_1 A B B)))) )  =>  (! [D:$i] :  ((m1_autalg_1 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  (! [B:$i] :  ((m1_bintree2 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m1_bvfunc_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m1_bvfunc_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_bvfunc_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_eqrel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_bvfunc_2 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_card_lar,ax, (! [A:$i,B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_card_lar C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_cat_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_cat_5 A))  =>  (! [B:$i] :  ((m1_cat_5 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m1_closure2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  (! [D:$i] :  ((m1_closure2 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_complfld,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A (u1_struct_0 k1_complfld)) &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers)) )  =>  (! [C:$i] :  ((m1_complfld C A B) <=> (m1_comptrig C A B)) ) ) ) ).
tt(redefinition_m1_comput_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v1_xboole_0 C))  & (m1_rfunct_3 C A B))  &  ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 C))) ) ) )  =>  (! [E:$i] :  ((m1_comput_1 E A B C D) <=> (m1_subset_1 E D)) ) ) ) ).
tt(redefinition_m1_dtconstr,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_trees_3 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B))) ) )  =>  (! [D:$i] :  ((m1_dtconstr D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_glib_004,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k3_glib_004 A)))) )  =>  (! [C:$i] :  ((m1_glib_004 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_graph_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v1_xboole_0 B))  & (m1_finseq_2 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B))) )  =>  (! [D:$i] :  ((m1_graph_3 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_graph_5,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k3_finseq_2 A))))  =>  (! [C:$i] :  ((m1_graph_5 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_group_6 C A B) <=> (m1_group_2 C B)) ) ) ) ).
tt(redefinition_m1_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_incproj B A) <=> (m2_collsp B A)) ) ) ) ).
tt(redefinition_m1_matrix_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_matrix_2 A))  =>  (! [B:$i] :  ((m1_matrix_2 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m1_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ((m1_orders_3 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m1_osalg_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  & (m1_subset_1 B (k7_osalg_1 A)))  =>  (! [C:$i] :  ((m1_osalg_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_partit_2,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A)))) )  =>  (! [C:$i] :  ((m1_partit_2 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_petri,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_petri D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_pre_poly,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k5_finsub_1 A))))  =>  (! [C:$i] :  ((m1_pre_poly C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_prob_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m1_prob_3,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_3 C A B) <=> (m1_finseq_1 C B)) ) ) ) ).
tt(redefinition_m1_pua2mss1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k4_partfun1 A B)))) ) )  =>  (! [D:$i] :  ((m1_pua2mss1 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m1_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m1_trees_4,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_trees_4 C A B) <=> (m1_finseq_1 C B)) ) ) ) ).
tt(redefinition_m2_cat_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  & (m1_cat_2 C A B)) )  =>  (! [D:$i] :  ((m2_cat_2 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m2_conlat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  & (m1_conlat_1 B A))  =>  (! [C:$i] :  ((m2_conlat_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) <=> (m1_finseq_1 B A)) ) ) ).
tt(redefinition_m2_finseq_2,ax, (! [A:$i,B:$i] :  ((m1_finseq_2 B A) =>  (! [C:$i] :  ((m2_finseq_2 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_fomodel2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v10_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A))) ) )  =>  (! [D:$i] :  ((m2_fomodel2 D A B C) <=> (m1_fomodel2 D A B C)) ) ) ) ).
tt(redefinition_m2_funct_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_funct_2 C A B))  =>  (! [D:$i] :  ((m2_funct_2 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m2_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) <=> (m1_graph_1 B A)) ) ) ) ).
tt(redefinition_m2_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ((m2_grcat_1 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m2_lmod_7,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  & (m1_lmod_7 C A B)) )  =>  (! [D:$i] :  ((m2_lmod_7 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m2_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m1_modcat_1 B A))  =>  (! [C:$i] :  ((m2_modcat_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_prob_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  & (m2_prob_1 C A B)) )  =>  (! [D:$i] :  ((m2_prob_4 D A B C) <=> (m1_prob_4 D A B C)) ) ) ) ).
tt(redefinition_m2_rfunct_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_rfunct_3 C A B))  =>  (! [D:$i] :  ((m2_rfunct_3 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m2_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ((m2_ringcat1 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m2_rlaffin3,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_rlaffin3 C A B) <=> (m1_rlaffin3 C B)) ) ) ) ).
tt(redefinition_m2_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m2_subset_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_trees_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m2_trees_3 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_unialg_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  & (m1_unialg_3 B A)) )  =>  (! [C:$i] :  ((m2_unialg_3 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m2_valued_0,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) )  =>  (! [C:$i] :  ((m2_valued_0 C A B) <=> (m1_valued_0 C B)) ) ) ) ).
tt(redefinition_m2_vectsp_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  &  ( (~ (v1_xboole_0 C))  & (m1_vectsp_8 C A B)) ) )  =>  (! [D:$i] :  ((m2_vectsp_8 D A B C) <=> (m1_subset_1 D C)) ) ) ) ).
tt(redefinition_m3_conlat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  &  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A))))) )  =>  (! [C:$i] :  ((m3_conlat_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m3_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_grcat_1 A))  =>  (! [B:$i] :  ((m3_grcat_1 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m3_msalimit,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_msalimit A))  =>  (! [B:$i] :  ((m3_msalimit B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m3_pnproc_1,ax, (! [A:$i,B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m3_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v5_ringcat1 A))  =>  (! [B:$i] :  ((m3_ringcat1 B A) <=> (m1_subset_1 B A)) ) ) ) ).
tt(redefinition_m3_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) <=> (m2_topgrp_1 B A)) ) ) ) ).
tt(redefinition_m3_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m3_trees_3 B A) <=> (m2_trees_1 B A)) ) ) ) ).
tt(redefinition_m4_modcat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  & (m3_modcat_1 B A))  =>  (! [C:$i] :  ((m4_modcat_1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m5_bcialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  & (m2_bcialg_1 B A))  =>  (! [C:$i] :  ((m5_bcialg_2 C A B) <=> (m4_bcialg_2 C A B)) ) ) ) ).
tt(redefinition_m5_margrel1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  & (m4_margrel1 B A))  =>  (! [C:$i] :  ((m5_margrel1 C A B) <=> (m1_subset_1 C B)) ) ) ) ).
tt(redefinition_m5_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m2_monoid_0 B A))  =>  (! [C:$i] :  ((m5_monoid_0 C A B) <=> (m2_monoid_0 C B)) ) ) ) ).
tt(redefinition_m6_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m3_monoid_0 B A))  =>  (! [C:$i] :  ((m6_monoid_0 C A B) <=> (m2_monoid_0 C B)) ) ) ) ).
tt(redefinition_m7_monoid_0,ax, (! [A:$i,B:$i] :  ( ((l3_algstr_0 A) & (m3_monoid_0 B A))  =>  (! [C:$i] :  ((m7_monoid_0 C A B) <=> (m3_monoid_0 C B)) ) ) ) ).
tt(redefinition_r10_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r10_analmetr A B C) <=> (r7_analmetr A B C)) ) ) ).
tt(redefinition_r1_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_boolealg A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_borsuk_3,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) <=> (r1_t_0topsp A B)) ) ) ).
tt(redefinition_r1_borsuk_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_borsuk_6 A B C) <=> (r1_borsuk_2 A B C)) ) ) ).
tt(redefinition_r1_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  =>  ((r1_convex4 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_exchsort,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_exchsort A B C) <=> (r2_orders_2 A B C)) ) ) ).
tt(redefinition_r1_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((r1_filter_2 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) )  =>  ((r1_funct_2 A B C D E F) <=>  (E = F) ) ) ) ).
tt(redefinition_r1_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  =>  ((r1_group_2 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_heyting1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A))) )  =>  ((r1_heyting1 A B C) <=> (r1_tarski B C)) ) ) ).
tt(redefinition_r1_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  =>  ((r1_interva1 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_lattice7,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r1_lattice7 A B C) <=> (r1_tarski B C)) ) ) ).
tt(redefinition_r1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) )  =>  ((r1_lfuzzy_1 A B C D) <=> (r1_fuzzy_1 C D)) ) ) ).
tt(redefinition_r1_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k3_margrel1 A)) & (m1_subset_1 C (k3_margrel1 A))) )  =>  ((r1_margrel1 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_mfold_2,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  ((r1_mfold_2 A B) <=> (r1_t_0topsp A B)) ) ) ).
tt(redefinition_r1_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  =>  ((r1_nat_d A B) <=> (r1_int_1 A B)) ) ) ).
tt(redefinition_r1_ordinal1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  =>  ((r1_ordinal1 A B) <=> (r1_tarski A B)) ) ) ).
tt(redefinition_r1_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((r1_pnproc_1 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_relset_1 A B C D) <=> (r1_tarski C D)) ) ) ).
tt(redefinition_r1_revrot_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_finseq_1 B A))  =>  ((r1_revrot_1 A B C) <=> (r2_finseq_4 B C)) ) ) ).
tt(redefinition_r1_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  =>  ((r1_rlvect_2 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r1_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_4 C A B) & (m1_rmod_4 D A B)) ) )  =>  ((r1_rmod_4 A B C D) <=>  (C = D) ) ) ) ).
tt(redefinition_r1_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((r1_subset_1 A B) <=> (r1_xboole_0 A B)) ) ) ).
tt(redefinition_r1_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_vectsp_6 C A B) & (m1_vectsp_6 D A B)) ) )  =>  ((r1_vectsp_6 A B C D) <=>  (C = D) ) ) ) ).
tt(redefinition_r1_yellow10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_yellow10 A B C) <=> (r6_waybel_1 A B C)) ) ) ).
tt(redefinition_r2_abian,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B A) &  ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r2_abian A B C) <=> (r1_abian B C)) ) ) ).
tt(redefinition_r2_altcat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  =>  ((r2_altcat_2 A B C D) <=> (r1_altcat_2 C D)) ) ) ).
tt(redefinition_r2_bhsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((r2_bhsp_3 A B C) <=> (r1_bhsp_3 A B C)) ) ) ).
tt(redefinition_r2_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_borsuk_2 A B C) <=> (r1_borsuk_2 A B C)) ) ) ).
tt(redefinition_r2_borsuk_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v2_struct_0 B))  & (l1_pre_topc B)) )  =>  ((r2_borsuk_3 A B) <=> (r1_t_0topsp A B)) ) ) ).
tt(redefinition_r2_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((r2_clvect_2 A B C) <=> (r1_clvect_2 A B C)) ) ) ).
tt(redefinition_r2_compos_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  =>  ((r2_compos_2 A B) <=> (r1_compos_2 A B)) ) ) ).
tt(redefinition_r2_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((r2_euclidlp A B C) <=> (r1_euclidlp A B C)) ) ) ).
tt(redefinition_r2_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((r2_funct_2 A B C D) <=>  (C = D) ) ) ) ).
tt(redefinition_r2_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  =>  ((r2_fuzzy_1 A B C) <=> (r1_fuzzy_1 B C)) ) ) ).
tt(redefinition_r2_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l4_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_gcd_1 A B C) <=> (r1_gcd_1 A B C)) ) ) ).
tt(redefinition_r2_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_group_3 A B C) <=> (r1_group_3 A B C)) ) ) ).
tt(redefinition_r2_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ((r2_group_6 A B) <=> (r1_group_6 A B)) ) ) ).
tt(redefinition_r2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m2_interva1 B A) & (m2_interva1 C A)) )  =>  ((r2_interva1 A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r2_metric_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_metric_2 A B C) <=> (r1_metric_2 A B C)) ) ) ).
tt(redefinition_r2_necklace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ((r2_necklace A B) <=> (r1_necklace A B)) ) ) ).
tt(redefinition_r2_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_pcs_0 A) & (l1_pcs_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_pcs_0 A B C) <=> (r1_pcs_0 A B C)) ) ) ).
tt(redefinition_r2_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r2_relset_1 A B C D) <=>  (C = D) ) ) ) ).
tt(redefinition_r2_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((r2_subset_1 A B) <=> (r1_xboole_0 A B)) ) ) ).
tt(redefinition_r2_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v7_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A)))  &  ((v7_topalg_6 C A) & (m1_subset_1 C (k1_topalg_6 A))) ) )  =>  ((r2_topalg_6 A B C) <=> (r1_topalg_6 A B C)) ) ) ).
tt(redefinition_r2_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_tsep_2 A B C) <=> (r1_tsep_2 A B C)) ) ) ).
tt(redefinition_r2_wellord2,ax, (! [A:$i,B:$i] :  ((r2_wellord2 A B) <=> (r2_tarski A B)) ) ).
tt(redefinition_r2_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_yellow_5 A B C) <=> (r1_yellow_5 A B C)) ) ) ).
tt(redefinition_r3_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_boolealg A B C) <=> (r2_boolealg A B C)) ) ) ).
tt(redefinition_r3_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  =>  ((r3_finseq_8 A B C) <=> (r1_tarski B C)) ) ) ).
tt(redefinition_r3_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  =>  ((r3_group_9 A B C) <=> (r2_group_9 A B C)) ) ) ).
tt(redefinition_r3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_lattices A B C) <=> (r1_lattices A B C)) ) ) ).
tt(redefinition_r3_metric_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) & (l1_metric_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_metric_2 A B C) <=> (r1_metric_2 A B C)) ) ) ).
tt(redefinition_r3_orders_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_orders_2 A B C) <=> (r1_orders_2 A B C)) ) ) ).
tt(redefinition_r3_osalg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) ) ) )  =>  ((r3_osalg_3 A B C) <=> (r1_osalg_3 A B C)) ) ) ).
tt(redefinition_r3_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((r3_pboole A B C) <=> (r1_pboole A B C)) ) ) ).
tt(redefinition_r3_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r3_yellow_4 A B C) <=> (r1_yellow_4 A B C)) ) ) ).
tt(redefinition_r4_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r4_boolealg A B C) <=> (r2_boolealg A B C)) ) ) ).
tt(redefinition_r4_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  =>  ((r4_borsuk_2 A B C D E) <=> (r3_borsuk_2 A B C D E)) ) ) ).
tt(redefinition_r4_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r4_gcd_1 A B C) <=> (r3_gcd_1 A B C)) ) ) ).
tt(redefinition_r4_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r4_group_3 A B C) <=> (r3_group_3 A B C)) ) ) ).
tt(redefinition_r4_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ((r4_tsep_2 A B C) <=> (r3_tsep_2 A B C)) ) ) ).
tt(redefinition_r4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r4_yellow_4 A B C) <=> (r2_yellow_4 A B C)) ) ) ).
tt(redefinition_r5_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r5_aff_1 A B C) <=> (r3_aff_1 A B C)) ) ) ).
tt(redefinition_r5_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) ) )  =>  ((r5_pua2mss1 A B) <=> (r4_pua2mss1 A B)) ) ) ).
tt(redefinition_r6_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  =>  ((r6_group_3 A B C) <=> (r5_group_3 A B C)) ) ) ).
tt(redefinition_r6_msualg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (l3_msualg_1 C A)) )  =>  ((r6_msualg_3 A B C) <=> (r5_msualg_3 A B C)) ) ) ).
tt(redefinition_r6_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((r6_pboole A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r7_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r7_gcd_1 A B C) <=> (r6_gcd_1 A B C)) ) ) ).
tt(redefinition_r8_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) )  =>  ((r8_binop_1 A B C D E) <=>  (D = E) ) ) ) ).
tt(redefinition_r8_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((r8_pboole A B C) <=>  (B = C) ) ) ) ).
tt(redefinition_r9_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r9_analmetr A B C) <=> (r8_analmetr A B C)) ) ) ).
tt(reflexivity_r1_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  => (r1_abcmiz_a A B B)) ) ).
tt(reflexivity_r1_altcat_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  => (r1_altcat_2 A A)) ) ).
tt(reflexivity_r1_anproj_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_anproj_1 A B B)) ) ).
tt(reflexivity_r1_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_boolealg A B B)) ) ).
tt(reflexivity_r1_borsuk_3,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  => (r1_borsuk_3 A A)) ) ).
tt(reflexivity_r1_borsuk_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_borsuk_6 A B B)) ) ).
tt(reflexivity_r1_bvfunc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) ) )  => (r1_bvfunc_1 A B B)) ) ).
tt(reflexivity_r1_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_cat_1 A B B)) ) ).
tt(reflexivity_r1_circcomb,ax, (! [A:$i,B:$i] :  ( ((l1_msualg_1 A) & (l1_msualg_1 B))  => (r1_circcomb A A)) ) ).
tt(reflexivity_r1_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  => (r1_convex4 A B B)) ) ).
tt(reflexivity_r1_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (r1_dist_1 A B B)) ) ).
tt(reflexivity_r1_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (k3_ec_pf_1 (k9_int_3 A))) & (m1_subset_1 C (k3_ec_pf_1 (k9_int_3 A)))) )  => (r1_ec_pf_1 A B B)) ) ).
tt(reflexivity_r1_endalg,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  &  ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l4_algstr_0 B)) ) )  => (r1_endalg A A)) ) ).
tt(reflexivity_r1_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  => (r1_filter_1 A A)) ) ).
tt(reflexivity_r1_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A))) )  => (r1_filter_2 A B B)) ) ).
tt(reflexivity_r1_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) )  => (r1_funct_2 A B C D E E)) ) ).
tt(reflexivity_r1_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  => (r1_functor0 A A)) ) ).
tt(reflexivity_r1_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ((m2_functor0 C A B) & (m2_functor0 D A B)) ) )  => (r1_functor2 A B C C)) ) ).
tt(reflexivity_r1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  => (r1_functor3 A B C C)) ) ).
tt(reflexivity_r1_fuzzy_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) ) )  => (r1_fuzzy_1 A A)) ) ).
tt(reflexivity_r1_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  => (r1_group_2 A B B)) ) ).
tt(reflexivity_r1_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  => (r1_group_6 A A)) ) ).
tt(reflexivity_r1_heyting1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k5_finsub_1 A)) & (m1_subset_1 C (k5_finsub_1 A))) )  => (r1_heyting1 A B B)) ) ).
tt(reflexivity_r1_int_1,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  => (r1_int_1 A A)) ) ).
tt(reflexivity_r1_integra1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  => (r1_integra1 A A)) ) ).
tt(reflexivity_r1_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  => (r1_interva1 A B B)) ) ).
tt(reflexivity_r1_isocat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (r1_isocat_1 A A)) ) ).
tt(reflexivity_r1_lattice7,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r1_lattice7 A B B)) ) ).
tt(reflexivity_r1_lfuzzy_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  &  ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) ) ) ) )  => (r1_lfuzzy_1 A B C C)) ) ).
tt(reflexivity_r1_lmod_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) ) )  => (r1_lmod_6 A B B)) ) ).
tt(reflexivity_r1_lopban_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_lopban_4 A B B)) ) ).
tt(reflexivity_r1_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k3_margrel1 A)) & (m1_subset_1 C (k3_margrel1 A))) )  => (r1_margrel1 A B B)) ) ).
tt(reflexivity_r1_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (r1_matrix_6 A B C C)) ) ).
tt(reflexivity_r1_matrix_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (r1_matrix_8 A B C C)) ) ).
tt(reflexivity_r1_msuhom_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  => (r1_msuhom_1 A A)) ) ).
tt(reflexivity_r1_nat_d,ax, (! [A:$i,B:$i] :  ( ((v7_ordinal1 A) & (v7_ordinal1 B))  => (r1_nat_d A A)) ) ).
tt(reflexivity_r1_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  => (r1_nattra_1 A B C C)) ) ).
tt(reflexivity_r1_normform,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  &  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  &  ((m1_subset_1 C (k2_zfmisc_1 A B)) & (m1_subset_1 D (k2_zfmisc_1 A B))) ) )  => (r1_normform A B C C)) ) ).
tt(reflexivity_r1_ordinal1,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (r1_ordinal1 A A)) ) ).
tt(reflexivity_r1_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  => (r1_osalg_1 A B B)) ) ).
tt(reflexivity_r1_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r1_osalg_4 A B B)) ) ).
tt(reflexivity_r1_partfun1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  => (r1_partfun1 A A)) ) ).
tt(reflexivity_r1_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  => (r1_pnproc_1 A B B)) ) ).
tt(reflexivity_r1_pzfmisc1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  => (r1_pzfmisc1 A B B)) ) ).
tt(reflexivity_r1_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_relset_1 A B C C)) ) ).
tt(reflexivity_r1_ringcat1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  => (r1_ringcat1 A A)) ) ).
tt(reflexivity_r1_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  => (r1_rlvect_2 A B B)) ) ).
tt(reflexivity_r1_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_4 C A B) & (m1_rmod_4 D A B)) ) )  => (r1_rmod_4 A B C C)) ) ).
tt(reflexivity_r1_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r1_roughs_1 A B B)) ) ).
tt(reflexivity_r1_setfam_1,ax, (! [A:$i,B:$i] : (r1_setfam_1 A A)) ).
tt(reflexivity_r1_tarski,ax, (! [A:$i,B:$i] : (r1_tarski A A)) ).
tt(reflexivity_r1_unialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) )  => (r1_unialg_2 A A)) ) ).
tt(reflexivity_r1_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_vectsp_6 C A B) & (m1_vectsp_6 D A B)) ) )  => (r1_vectsp_6 A B C C)) ) ).
tt(reflexivity_r1_xxreal_0,ax, (! [A:$i,B:$i] :  ( ((v1_xxreal_0 A) & (v1_xxreal_0 B))  => (r1_xxreal_0 A A)) ) ).
tt(reflexivity_r1_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) ) )  => (r1_yellow18 A A)) ) ).
tt(reflexivity_r2_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A)))) )  => (r2_abcmiz_a A B B)) ) ).
tt(reflexivity_r2_altcat_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  &  ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) ) )  => (r2_altcat_2 A B C C)) ) ).
tt(reflexivity_r2_altcat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r2_altcat_3 A B B)) ) ).
tt(reflexivity_r2_arytm_3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (r2_arytm_3 A A)) ) ).
tt(reflexivity_r2_bhsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (r2_bhsp_3 A B B)) ) ).
tt(reflexivity_r2_borsuk_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r2_borsuk_2 A B B)) ) ).
tt(reflexivity_r2_borsuk_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v2_struct_0 B))  & (l1_pre_topc B)) )  => (r2_borsuk_3 A A)) ) ).
tt(reflexivity_r2_circtrm1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  => (r2_circtrm1 A A)) ) ).
tt(reflexivity_r2_classes1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  => (r2_classes1 A A)) ) ).
tt(reflexivity_r2_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  => (r2_clvect_2 A B B)) ) ).
tt(reflexivity_r2_compos_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) )  => (r2_compos_2 A A)) ) ).
tt(reflexivity_r2_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (r2_cqc_sim1 A B B)) ) ).
tt(reflexivity_r2_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (r2_funct_2 A B C C)) ) ).
tt(reflexivity_r2_functor2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  => (r2_functor2 A B C C)) ) ).
tt(reflexivity_r2_fuzzy_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  &  ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) )  => (r2_fuzzy_1 A B B)) ) ).
tt(reflexivity_r2_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l4_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r2_gcd_1 A B B)) ) ).
tt(reflexivity_r2_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r2_group_3 A B B)) ) ).
tt(reflexivity_r2_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  => (r2_group_6 A A)) ) ).
tt(reflexivity_r2_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  => (r2_group_9 A B B)) ) ).
tt(reflexivity_r2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m2_interva1 B A) & (m2_interva1 C A)) )  => (r2_interva1 A B B)) ) ).
tt(reflexivity_r2_isocat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  => (r2_isocat_1 A A)) ) ).
tt(reflexivity_r2_matrix_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  => (r2_matrix_8 A B C C)) ) ).
tt(reflexivity_r2_metric_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r2_metric_2 A B B)) ) ).
tt(reflexivity_r2_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) )  => (r2_midsp_1 A B B)) ) ).
tt(reflexivity_r2_modelc_2,ax, (! [A:$i,B:$i] :  ( ( ((v1_modelc_2 A) & (m1_finseq_1 A k5_numbers))  &  ((v1_modelc_2 B) & (m1_finseq_1 B k5_numbers)) )  => (r2_modelc_2 A A)) ) ).
tt(reflexivity_r2_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  => (r2_nattra_1 A B C C)) ) ).
tt(reflexivity_r2_necklace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  => (r2_necklace B B)) ) ).
tt(reflexivity_r2_ordinal2,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  => (r2_ordinal2 A A)) ) ).
tt(reflexivity_r2_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (k3_finseq_2 (u1_struct_0 A))) & (m1_subset_1 C (k3_finseq_2 (u1_struct_0 A)))) )  => (r2_osalg_1 A B B)) ) ).
tt(reflexivity_r2_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  => (r2_pboole A B B)) ) ).
tt(reflexivity_r2_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  => (r2_pnproc_1 A B B)) ) ).
tt(reflexivity_r2_polynom3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k4_finseq_2 A k5_numbers)) & (m1_subset_1 C (k4_finseq_2 A k5_numbers))) )  => (r2_polynom3 A B B)) ) ).
tt(reflexivity_r2_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ((v3_ordinal1 A) &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) ) )  => (r2_pre_poly A B B)) ) ).
tt(reflexivity_r2_qc_lang2,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k9_qc_lang1 A)) & (m1_subset_1 C (k9_qc_lang1 A))) )  => (r2_qc_lang2 A B B)) ) ).
tt(reflexivity_r2_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  => (r2_relset_1 A B C C)) ) ).
tt(reflexivity_r2_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_roughs_1 A B B)) ) ).
tt(reflexivity_r2_setfam_1,ax, (! [A:$i,B:$i] : (r2_setfam_1 B B)) ).
tt(reflexivity_r2_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  => (r2_stacks_1 A B B)) ) ).
tt(reflexivity_r2_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v7_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A)))  &  ((v7_topalg_6 C A) & (m1_subset_1 C (k1_topalg_6 A))) ) )  => (r2_topalg_6 A B B)) ) ).
tt(reflexivity_r2_wellord2,ax, (! [A:$i,B:$i] : (r2_wellord2 A A)) ).
tt(reflexivity_r2_zfrefle1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (r2_zfrefle1 A A)) ) ).
tt(reflexivity_r3_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m3_abcmiz_1 B A) & (m3_abcmiz_1 C A)) )  => (r3_abcmiz_a A B B)) ) ).
tt(reflexivity_r3_armstrng,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 B (k4_armstrng A)) & (m1_subset_1 C (k4_armstrng A)))  => (r3_armstrng A B B)) ) ).
tt(reflexivity_r3_finseq_8,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  => (r3_finseq_8 A B B)) ) ).
tt(reflexivity_r3_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  => (r3_group_9 A B B)) ) ).
tt(reflexivity_r3_lattices,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r3_lattices A B B)) ) ).
tt(reflexivity_r3_nattra_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  &  ((m2_cat_1 C A B) & (m2_cat_1 D A B)) ) )  => (r3_nattra_1 A B C C)) ) ).
tt(reflexivity_r3_necklace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  => (r3_necklace A A)) ) ).
tt(reflexivity_r3_orders_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r3_orders_2 A B B)) ) ).
tt(reflexivity_r3_pcs_0,ax, (! [A:$i,B:$i] :  ( ((l2_pcs_0 A) & (l2_pcs_0 B))  => (r3_pcs_0 A A)) ) ).
tt(reflexivity_r3_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r3_prelamb A B B)) ) ).
tt(reflexivity_r3_pre_poly,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) ) )  => (r3_pre_poly A B B)) ) ).
tt(reflexivity_r3_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  &  ((m1_subset_1 B (k5_qmax_1 A)) & (m1_subset_1 C (k5_qmax_1 A))) )  => (r3_qmax_1 A B B)) ) ).
tt(reflexivity_r3_roughs_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r3_roughs_1 A B B)) ) ).
tt(reflexivity_r3_xboole_0,ax, (! [A:$i,B:$i] : (r3_xboole_0 A A)) ).
tt(reflexivity_r3_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r3_yellow_4 A B B)) ) ).
tt(reflexivity_r3_zfrefle1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  => (r3_zfrefle1 A A)) ) ).
tt(reflexivity_r4_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  => (r4_borsuk_2 A B C D D)) ) ).
tt(reflexivity_r4_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A)))) )  => (r4_cqc_the3 A B B)) ) ).
tt(reflexivity_r4_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B)) ) ) )  => (r4_fsm_1 A B C C)) ) ).
tt(reflexivity_r4_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  => (r4_gcd_1 A B B)) ) ).
tt(reflexivity_r4_graph_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_graph_1 B)) )  => (r4_graph_1 A A)) ) ).
tt(reflexivity_r4_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r4_group_3 A B B)) ) ).
tt(reflexivity_r4_group_9,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( ((v8_group_9 C A B) & (m1_finseq_1 C (k6_group_9 A B)))  &  ((v8_group_9 D A B) & (m1_finseq_1 D (k6_group_9 A B))) ) )  => (r4_group_9 A B C C)) ) ).
tt(reflexivity_r4_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  &  ((m1_subset_1 B (k5_qmax_1 A)) & (m1_subset_1 C (k5_qmax_1 A))) )  => (r4_qmax_1 A B B)) ) ).
tt(reflexivity_r4_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) ) )  => (r4_stacks_1 A A)) ) ).
tt(reflexivity_r4_yellow_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r4_yellow_4 A C C)) ) ).
tt(reflexivity_r5_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  => (r5_abcmiz_a A B B)) ) ).
tt(reflexivity_r5_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (r5_cqc_the3 A B B)) ) ).
tt(reflexivity_r5_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ((m1_subset_1 D (u1_struct_0 C)) & (m1_subset_1 E (u1_struct_0 C))) ) ) )  => (r5_fsm_1 A B C D D)) ) ).
tt(reflexivity_r5_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) ) )  => (r5_glib_000 A A)) ) ).
tt(reflexivity_r5_pua2mss1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) ) )  => (r5_pua2mss1 A A)) ) ).
tt(reflexivity_r5_waybel_1,ax, (! [A:$i,B:$i] :  ( ((l1_orders_2 A) & (l1_orders_2 B))  => (r5_waybel_1 A A)) ) ).
tt(reflexivity_r6_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  => (r6_abcmiz_a A B B)) ) ).
tt(reflexivity_r6_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) ) )  => (r6_glib_000 A A)) ) ).
tt(reflexivity_r6_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  => (r6_group_3 A B B)) ) ).
tt(reflexivity_r6_msualg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  &  ((l3_msualg_1 B A) & (l3_msualg_1 C A)) )  => (r6_msualg_3 A B B)) ) ).
tt(reflexivity_r6_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  => (r6_osalg_1 A B B)) ) ).
tt(reflexivity_r6_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  => (r6_pboole A B B)) ) ).
tt(reflexivity_r7_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  => (r7_cqc_the3 A B B)) ) ).
tt(reflexivity_r7_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B)) ) ) )  => (r7_fsm_1 A B C C)) ) ).
tt(reflexivity_r7_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  => (r7_pboole A B B)) ) ).
tt(reflexivity_r8_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) )  => (r8_binop_1 A B C D D)) ) ).
tt(reflexivity_r8_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  => (r8_pboole A B B)) ) ).
tt(symmetry_r10_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r10_analmetr A B C) => (r10_analmetr A C B)) ) ) ).
tt(symmetry_r10_rewrite1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  =>  ((r10_rewrite1 A B) => (r10_rewrite1 B A)) ) ) ).
tt(symmetry_r11_rewrite1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  =>  ((r11_rewrite1 A B) => (r11_rewrite1 B A)) ) ) ).
tt(symmetry_r12_rewrite1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  =>  ((r12_rewrite1 A B) => (r12_rewrite1 B A)) ) ) ).
tt(symmetry_r1_afvect0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_afvect0 A B C) => (r1_afvect0 A C B)) ) ) ).
tt(symmetry_r1_anproj_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_anproj_1 A B C) => (r1_anproj_1 A C B)) ) ) ).
tt(symmetry_r1_arytm_3,ax, (! [A:$i,B:$i] :  ( ((v3_ordinal1 A) & (v3_ordinal1 B))  =>  ((r1_arytm_3 A B) => (r1_arytm_3 B A)) ) ) ).
tt(symmetry_r1_bhsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_bhsp_1 A B C) => (r1_bhsp_1 A C B)) ) ) ).
tt(symmetry_r1_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_boolealg A B C) => (r1_boolealg A C B)) ) ) ).
tt(symmetry_r1_borsuk_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_borsuk_6 A B C) => (r1_borsuk_6 A C B)) ) ) ).
tt(symmetry_r1_cat_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_cat_1 A B C) => (r1_cat_1 A C B)) ) ) ).
tt(symmetry_r1_chord,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((m1_subset_1 B (k6_glib_000 A)) & (m1_subset_1 C (k6_glib_000 A))) )  =>  ((r1_chord A B C) => (r1_chord A C B)) ) ) ).
tt(symmetry_r1_circcomb,ax, (! [A:$i,B:$i] :  ( ((l1_msualg_1 A) & (l1_msualg_1 B))  =>  ((r1_circcomb A B) => (r1_circcomb B A)) ) ) ).
tt(symmetry_r1_connsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r1_connsp_1 A B C) => (r1_connsp_1 A C B)) ) ) ).
tt(symmetry_r1_convex4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_convex4 B A) & (m1_convex4 C A)) )  =>  ((r1_convex4 A B C) => (r1_convex4 A C B)) ) ) ).
tt(symmetry_r1_csspace,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_csspace A B C) => (r1_csspace A C B)) ) ) ).
tt(symmetry_r1_dist_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((m1_finseq_1 B A) & (m1_finseq_1 C A)) )  =>  ((r1_dist_1 A B C) => (r1_dist_1 A C B)) ) ) ).
tt(symmetry_r1_ec_pf_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v7_ordinal1 A) & (v1_int_2 A))  &  ((m1_subset_1 B (k3_ec_pf_1 (k9_int_3 A))) & (m1_subset_1 C (k3_ec_pf_1 (k9_int_3 A)))) )  =>  ((r1_ec_pf_1 A B C) => (r1_ec_pf_1 A C B)) ) ) ).
tt(symmetry_r1_filter_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) )  =>  ((r1_filter_1 A B) => (r1_filter_1 B A)) ) ) ).
tt(symmetry_r1_filter_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((r1_filter_2 A B C) => (r1_filter_2 A C B)) ) ) ).
tt(symmetry_r1_fintopo4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r1_fintopo4 A B C) => (r1_fintopo4 A C B)) ) ) ).
tt(symmetry_r1_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 D))  &  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) )  =>  ((r1_funct_2 A B C D E F) => (r1_funct_2 A B C D F E)) ) ) ).
tt(symmetry_r1_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r1_functor0 A B) => (r1_functor0 B A)) ) ) ).
tt(symmetry_r1_functor3,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  &  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  &  ((v15_functor0 D A B) & (m2_functor0 D A B)) ) ) )  =>  ((r1_functor3 A B C D) => (r1_functor3 A B D C)) ) ) ).
tt(symmetry_r1_gobrd10,ax, (! [A:$i,B:$i] :  ( ((m1_subset_1 A k5_numbers) & (m1_subset_1 B k5_numbers))  =>  ((r1_gobrd10 A B) => (r1_gobrd10 B A)) ) ) ).
tt(symmetry_r1_group_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  =>  ((r1_group_2 A B C) => (r1_group_2 A C B)) ) ) ).
tt(symmetry_r1_int_2,ax, (! [A:$i,B:$i] :  ( ((v1_int_1 A) & (v1_int_1 B))  =>  ((r1_int_2 A B) => (r1_int_2 B A)) ) ) ).
tt(symmetry_r1_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  &  ( (~ (v1_xboole_0 C))  & (m1_interva1 C A)) ) )  =>  ((r1_interva1 A B C) => (r1_interva1 A C B)) ) ) ).
tt(symmetry_r1_isocat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ((r1_isocat_1 A B) => (r1_isocat_1 B A)) ) ) ).
tt(symmetry_r1_lopban_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_lopban_4 A B C) => (r1_lopban_4 A C B)) ) ) ).
tt(symmetry_r1_margrel1,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((m1_subset_1 B (k3_margrel1 A)) & (m1_subset_1 C (k3_margrel1 A))) )  =>  ((r1_margrel1 A B C) => (r1_margrel1 A C B)) ) ) ).
tt(symmetry_r1_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((r1_matrix_6 A B C D) => (r1_matrix_6 A B D C)) ) ) ).
tt(symmetry_r1_matrix_8,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((r1_matrix_8 A B C D) => (r1_matrix_8 A B D C)) ) ) ).
tt(symmetry_r1_mfold_2,ax, (! [A:$i,B:$i] :  ( ((l1_pre_topc A) & (l1_pre_topc B))  =>  ((r1_mfold_2 A B) => (r1_mfold_2 B A)) ) ) ).
tt(symmetry_r1_osalg_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((r1_osalg_1 A B C) => (r1_osalg_1 A C B)) ) ) ).
tt(symmetry_r1_osalg_4,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_osalg_4 A B C) => (r1_osalg_4 A C B)) ) ) ).
tt(symmetry_r1_partfun1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) & (v1_funct_1 A))  &  ((v1_relat_1 B) & (v1_funct_1 B)) )  =>  ((r1_partfun1 A B) => (r1_partfun1 B A)) ) ) ).
tt(symmetry_r1_pnproc_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((r1_pnproc_1 A B C) => (r1_pnproc_1 A C B)) ) ) ).
tt(symmetry_r1_rlvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  &  ((m1_rlvect_2 B A) & (m1_rlvect_2 C A)) )  =>  ((r1_rlvect_2 A B C) => (r1_rlvect_2 A C B)) ) ) ).
tt(symmetry_r1_rmod_4,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  &  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  &  ((m1_rmod_4 C A B) & (m1_rmod_4 D A B)) ) )  =>  ((r1_rmod_4 A B C D) => (r1_rmod_4 A B D C)) ) ) ).
tt(symmetry_r1_rpr_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((v1_finset_1 A) &  ((m1_subset_1 B (k1_zfmisc_1 A)) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  ((r1_rpr_1 A B C) => (r1_rpr_1 A C B)) ) ) ).
tt(symmetry_r1_rvsum_1,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) ) )  =>  ((r1_rvsum_1 A B) => (r1_rvsum_1 B A)) ) ) ).
tt(symmetry_r1_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((r1_subset_1 A B) => (r1_subset_1 B A)) ) ) ).
tt(symmetry_r1_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( ((v7_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A)))  &  ((v7_topalg_6 C A) & (m1_subset_1 C (k1_topalg_6 A))) ) )  =>  ((r1_topalg_6 A B C) => (r1_topalg_6 A C B)) ) ) ).
tt(symmetry_r1_tsep_1,ax, (! [A:$i,B:$i] :  ( ((l1_struct_0 A) & (l1_struct_0 B))  =>  ((r1_tsep_1 A B) => (r1_tsep_1 B A)) ) ) ).
tt(symmetry_r1_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_struct_0 A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r1_tsep_2 A B C) => (r1_tsep_2 A C B)) ) ) ).
tt(symmetry_r1_unialg_2,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) )  =>  ((r1_unialg_2 A B) => (r1_unialg_2 B A)) ) ) ).
tt(symmetry_r1_vectsp_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  &  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  &  ((m1_vectsp_6 C A B) & (m1_vectsp_6 D A B)) ) )  =>  ((r1_vectsp_6 A B C D) => (r1_vectsp_6 A B D C)) ) ) ).
tt(symmetry_r1_xboole_0,ax, (! [A:$i,B:$i] :  ((r1_xboole_0 A B) => (r1_xboole_0 B A)) ) ).
tt(symmetry_r1_yellow10,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r1_yellow10 A B C) => (r1_yellow10 A C B)) ) ) ).
tt(symmetry_r1_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) ) )  =>  ((r1_yellow18 A B) => (r1_yellow18 B A)) ) ) ).
tt(symmetry_r1_yellow20,ax, (! [A:$i,B:$i] :  ( ((l2_altcat_1 A) & (l2_altcat_1 B))  =>  ((r1_yellow20 A B) => (r1_yellow20 B A)) ) ) ).
tt(symmetry_r2_altcat_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_altcat_3 A B C) => (r2_altcat_3 A C B)) ) ) ).
tt(symmetry_r2_bhsp_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((r2_bhsp_3 A B C) => (r2_bhsp_3 A C B)) ) ) ).
tt(symmetry_r2_borsuk_3,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ( (~ (v2_struct_0 B))  & (l1_pre_topc B)) )  =>  ((r2_borsuk_3 A B) => (r2_borsuk_3 B A)) ) ) ).
tt(symmetry_r2_circtrm1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  &  ( (~ (v2_struct_0 B))  & (l1_msualg_1 B)) )  =>  ((r2_circtrm1 A B) => (r2_circtrm1 B A)) ) ) ).
tt(symmetry_r2_classes1,ax, (! [A:$i,B:$i] :  ( ((v1_relat_1 A) & (v1_relat_1 B))  =>  ((r2_classes1 A B) => (r2_classes1 B A)) ) ) ).
tt(symmetry_r2_clvect_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  &  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((r2_clvect_2 A B C) => (r2_clvect_2 A C B)) ) ) ).
tt(symmetry_r2_cqc_sim1,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((r2_cqc_sim1 A B C) => (r2_cqc_sim1 A C B)) ) ) ).
tt(symmetry_r2_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((r2_euclidlp A B C) => (r2_euclidlp A C B)) ) ) ).
tt(symmetry_r2_funct_2,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((r2_funct_2 A B C D) => (r2_funct_2 A B D C)) ) ) ).
tt(symmetry_r2_functor0,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_functor0 A B) => (r2_functor0 B A)) ) ) ).
tt(symmetry_r2_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_group_3 A B C) => (r2_group_3 A C B)) ) ) ).
tt(symmetry_r2_group_6,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ((r2_group_6 A B) => (r2_group_6 B A)) ) ) ).
tt(symmetry_r2_interva1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  &  ((m2_interva1 B A) & (m2_interva1 C A)) )  =>  ((r2_interva1 A B C) => (r2_interva1 A C B)) ) ) ).
tt(symmetry_r2_isocat_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ((r2_isocat_1 A B) => (r2_isocat_1 B A)) ) ) ).
tt(symmetry_r2_jordan12,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_finseq_1 B (u1_struct_0 (k15_euclid A))) & (m1_finseq_1 C (u1_struct_0 (k15_euclid A)))) )  =>  ((r2_jordan12 A B C) => (r2_jordan12 A C B)) ) ) ).
tt(symmetry_r2_matrix_6,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((v7_ordinal1 A) &  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  ((m1_matrix_1 C (u1_struct_0 B) A A) & (m1_matrix_1 D (u1_struct_0 B) A A)) ) )  =>  ((r2_matrix_6 A B C D) => (r2_matrix_6 A B D C)) ) ) ).
tt(symmetry_r2_midsp_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  &  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) )  =>  ((r2_midsp_1 A B C) => (r2_midsp_1 A C B)) ) ) ).
tt(symmetry_r2_pcs_0,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v6_pcs_0 A) & (l1_pcs_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_pcs_0 A B C) => (r2_pcs_0 A C B)) ) ) ).
tt(symmetry_r2_quofield,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  &  ( (~ (v2_struct_0 B))  & (l6_algstr_0 B)) )  =>  ((r2_quofield A B) => (r2_quofield B A)) ) ) ).
tt(symmetry_r2_relset_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r2_relset_1 A B C D) => (r2_relset_1 A B D C)) ) ) ).
tt(symmetry_r2_stacks_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  &  ((m1_subset_1 B (u4_struct_0 A)) & (m1_subset_1 C (u4_struct_0 A))) )  =>  ((r2_stacks_1 A B C) => (r2_stacks_1 A C B)) ) ) ).
tt(symmetry_r2_subset_1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((r2_subset_1 A B) => (r2_subset_1 B A)) ) ) ).
tt(symmetry_r2_topalg_6,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ((v7_topalg_6 B A) & (m1_subset_1 B (k1_topalg_6 A)))  &  ((v7_topalg_6 C A) & (m1_subset_1 C (k1_topalg_6 A))) ) )  =>  ((r2_topalg_6 A B C) => (r2_topalg_6 A C B)) ) ) ).
tt(symmetry_r2_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_tsep_1 A B C) => (r2_tsep_1 A C B)) ) ) ).
tt(symmetry_r2_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_tsep_2 A B C) => (r2_tsep_2 A C B)) ) ) ).
tt(symmetry_r2_wellord2,ax, (! [A:$i,B:$i] :  ((r2_wellord2 A B) => (r2_wellord2 B A)) ) ).
tt(symmetry_r2_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  &  ( (~ (v2_struct_0 B))  & (l2_altcat_1 B)) )  =>  ((r2_yellow18 A B) => (r2_yellow18 B A)) ) ) ).
tt(symmetry_r2_yellow_5,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r2_yellow_5 A B C) => (r2_yellow_5 A C B)) ) ) ).
tt(symmetry_r2_zfrefle1,ax, (! [A:$i,B:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) )  =>  ((r2_zfrefle1 A B) => (r2_zfrefle1 B A)) ) ) ).
tt(symmetry_r3_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_boolealg A B C) => (r3_boolealg A C B)) ) ) ).
tt(symmetry_r3_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  =>  ((r3_borsuk_2 A B C D E) => (r3_borsuk_2 A B C E D)) ) ) ).
tt(symmetry_r3_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((r3_euclidlp A B C) => (r3_euclidlp A C B)) ) ) ).
tt(symmetry_r3_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_gcd_1 A B C) => (r3_gcd_1 A C B)) ) ) ).
tt(symmetry_r3_group_9,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  &  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  =>  ((r3_group_9 A B C) => (r3_group_9 A C B)) ) ) ).
tt(symmetry_r3_metric_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) & (l1_metric_1 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_metric_2 A B C) => (r3_metric_2 A C B)) ) ) ).
tt(symmetry_r3_necklace,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  &  ( (~ (v2_struct_0 B))  & (l1_orders_2 B)) )  =>  ((r3_necklace A B) => (r3_necklace B A)) ) ) ).
tt(symmetry_r3_osalg_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  &  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  &  ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) ) ) )  =>  ((r3_osalg_3 A B C) => (r3_osalg_3 A C B)) ) ) ).
tt(symmetry_r3_prelamb,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r3_prelamb A B C) => (r3_prelamb A C B)) ) ) ).
tt(symmetry_r3_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_pre_topc B A) & (m1_pre_topc C A)) )  =>  ((r3_tsep_1 A B C) => (r3_tsep_1 A C B)) ) ) ).
tt(symmetry_r3_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((m1_pre_topc B A) & (m1_pre_topc C A)) )  =>  ((r3_tsep_2 A B C) => (r3_tsep_2 A C B)) ) ) ).
tt(symmetry_r3_xboole_0,ax, (! [A:$i,B:$i] :  ((r3_xboole_0 A B) => (r3_xboole_0 B A)) ) ).
tt(symmetry_r3_yellow18,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) ) )  =>  ((r3_yellow18 A B) => (r3_yellow18 B A)) ) ) ).
tt(symmetry_r4_boolealg,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r4_boolealg A B C) => (r4_boolealg A C B)) ) ) ).
tt(symmetry_r4_borsuk_2,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) &  ((m1_subset_1 C (u1_struct_0 A)) &  ((m1_borsuk_2 D A B C) & (m1_borsuk_2 E A B C)) ) ) )  =>  ((r4_borsuk_2 A B C D E) => (r4_borsuk_2 A B C E D)) ) ) ).
tt(symmetry_r4_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A)))) )  =>  ((r4_cqc_the3 A B C) => (r4_cqc_the3 A C B)) ) ) ).
tt(symmetry_r4_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclid A)) & (m1_subset_1 C (k1_euclid A))) )  =>  ((r4_euclidlp A B C) => (r4_euclidlp A C B)) ) ) ).
tt(symmetry_r4_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B)) ) ) )  =>  ((r4_fsm_1 A B C D) => (r4_fsm_1 A B D C)) ) ) ).
tt(symmetry_r4_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r4_gcd_1 A B C) => (r4_gcd_1 A C B)) ) ) ).
tt(symmetry_r4_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r4_group_3 A B C) => (r4_group_3 A C B)) ) ) ).
tt(symmetry_r4_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((r4_pboole A B C) => (r4_pboole A C B)) ) ) ).
tt(symmetry_r4_qmax_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v2_qmax_1 A) & (l1_qmax_1 A))  &  ((m1_subset_1 B (k5_qmax_1 A)) & (m1_subset_1 C (k5_qmax_1 A))) )  =>  ((r4_qmax_1 A B C) => (r4_qmax_1 A C B)) ) ) ).
tt(symmetry_r4_stacks_1,ax, (! [A:$i,B:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) ) )  =>  ((r4_stacks_1 A B) => (r4_stacks_1 B A)) ) ) ).
tt(symmetry_r4_tsep_1,ax, (! [A:$i,B:$i,C:$i] :  ( ((l1_pre_topc A) &  ((m1_pre_topc B A) & (m1_pre_topc C A)) )  =>  ((r4_tsep_1 A B C) => (r4_tsep_1 A C B)) ) ) ).
tt(symmetry_r4_tsep_2,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ( (~ (v2_struct_0 C))  & (m1_pre_topc C A)) ) )  =>  ((r4_tsep_2 A B C) => (r4_tsep_2 A C B)) ) ) ).
tt(symmetry_r5_abcmiz_a,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  &  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) & (m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))))) )  =>  ((r5_abcmiz_a A B C) => (r5_abcmiz_a A C B)) ) ) ).
tt(symmetry_r5_aff_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r5_aff_1 A B C) => (r5_aff_1 A C B)) ) ) ).
tt(symmetry_r5_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((r5_cqc_the3 A B C) => (r5_cqc_the3 A C B)) ) ) ).
tt(symmetry_r5_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclidlp A)) & (m1_subset_1 C (k1_euclidlp A))) )  =>  ((r5_euclidlp A B C) => (r5_euclidlp A C B)) ) ) ).
tt(symmetry_r5_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ((m1_subset_1 D (u1_struct_0 C)) & (m1_subset_1 E (u1_struct_0 C))) ) ) )  =>  ((r5_fsm_1 A B C D E) => (r5_fsm_1 A B C E D)) ) ) ).
tt(symmetry_r5_glib_000,ax, (! [A:$i,B:$i] :  ( ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) ) )  =>  ((r5_glib_000 A B) => (r5_glib_000 B A)) ) ) ).
tt(symmetry_r5_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((r5_pboole A B C) => (r5_pboole A C B)) ) ) ).
tt(symmetry_r6_euclidlp,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_subset_1 A k5_numbers) &  ((m1_subset_1 B (k1_euclidlp A)) & (m1_subset_1 C (k1_euclidlp A))) )  =>  ((r6_euclidlp A B C) => (r6_euclidlp A C B)) ) ) ).
tt(symmetry_r6_group_3,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  &  ( ((v15_algstr_0 B) & (m1_group_2 B A))  &  ((v15_algstr_0 C) & (m1_group_2 C A)) ) )  =>  ((r6_group_3 A B C) => (r6_group_3 A C B)) ) ) ).
tt(symmetry_r6_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((r6_pboole A B C) => (r6_pboole A C B)) ) ) ).
tt(symmetry_r7_cqc_the3,ax, (! [A:$i,B:$i,C:$i] :  ( ((m1_qc_lang1 A) &  ((m1_subset_1 B (k3_cqc_lang A)) & (m1_subset_1 C (k3_cqc_lang A))) )  =>  ((r7_cqc_the3 A B C) => (r7_cqc_the3 A C B)) ) ) ).
tt(symmetry_r7_fsm_1,ax, (! [A:$i,B:$i,C:$i,D:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  &  ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B)) ) ) )  =>  ((r7_fsm_1 A B C D) => (r7_fsm_1 A B D C)) ) ) ).
tt(symmetry_r7_gcd_1,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  &  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) )  =>  ((r7_gcd_1 A B C) => (r7_gcd_1 A C B)) ) ) ).
tt(symmetry_r8_binop_1,ax, (! [A:$i,B:$i,C:$i,D:$i,E:$i] :  ( ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) ) )  =>  ((r8_binop_1 A B C D E) => (r8_binop_1 A B C E D)) ) ) ).
tt(symmetry_r8_pboole,ax, (! [A:$i,B:$i,C:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  &  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) )  =>  ((r8_pboole A B C) => (r8_pboole A C B)) ) ) ).
tt(symmetry_r9_analmetr,ax, (! [A:$i,B:$i,C:$i] :  ( ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r9_analmetr A B C) => (r9_analmetr A C B)) ) ) ).
tt(t100_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((k46_abcmiz_1 A (k37_abcmiz_1 A B)) = (k46_abcmiz_1 A B)) ) ) ) ) ).
tt(t100_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 D)) =>  (! [F:$i] :  ((m1_subset_1 F D) =>  (! [G:$i] :  ((m1_aofa_000 G A D E) =>  ( ((v3_freealg A) &  ((r2_hidden (k4_tarski F (k16_aofa_000 A B C)) (k21_aofa_000 A D E G)) & (r2_hidden (k2_binop_1 D (u1_struct_0 A) D G F B) E)) )  => (r2_hidden (k4_tarski (k2_binop_1 D (u1_struct_0 A) D G F B) C) (k21_aofa_000 A D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_card_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v4_card_3 A) & (v4_card_3 B))  => (v4_card_3 (k5_xboole_0 A B))) ) ) ).
tt(t100_card_3,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v2_card_3 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B A) =>  ((k9_xtuple_0 B) = (k9_xtuple_0 (k10_card_3 A))) ) ) ) ) ) ).
tt(t100_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~ (r1_chord A B C))  &  (? [D:$i] :  ((m2_chord D A B C) &  ((v4_chord D A B C) &  (? [E:$i] :  ((m2_glib_000 E A (k6_subset_1 (k6_glib_000 A) D) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) D))) &  (? [F:$i] :  ((m1_subset_1 F (k6_glib_000 E)) &  ( (B = F)  &  (! [G:$i] :  ((m1_subset_1 G (k6_glib_000 A)) =>  (~  ((r2_hidden G (k1_glib_002 E F)) &  (! [H:$i] :  ((m1_subset_1 H (k6_glib_000 A)) =>  ((r2_hidden H D) => (r1_chord A G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  ( (? [E:$i] :  ((m2_clvect_1 E A D) &  ((r2_hidden B E) & (r2_hidden C E)) ) )  <=> (r1_struct_0 D (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t100_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_fdiff_1 A G) &  ((r1_fdiff_1 B G) &  ((r1_fdiff_1 C G) &  ((r1_fdiff_1 D G) &  ((r1_fdiff_1 E G) & (r1_fdiff_1 F G)) ) ) ) )  =>  ((k8_euclid_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers A D) (k20_valued_1 k1_numbers k1_numbers k1_numbers B E) (k20_valued_1 k1_numbers k1_numbers k1_numbers C F) G) = (k7_euclid 3 (k1_euclid_8 (k11_binop_2 (k1_seq_1 D G) (k1_fdiff_1 A G)) (k11_binop_2 (k1_seq_1 E G) (k1_fdiff_1 B G)) (k11_binop_2 (k1_seq_1 F G) (k1_fdiff_1 C G))) (k1_euclid_8 (k11_binop_2 (k1_seq_1 A G) (k1_fdiff_1 D G)) (k11_binop_2 (k1_seq_1 B G) (k1_fdiff_1 E G)) (k11_binop_2 (k1_seq_1 C G) (k1_fdiff_1 F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ( (~ (r2_hidden B C))  &  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r2_hidden B D) &  ((r1_tarski C D) & (v1_euclidlp D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 2) & (m2_finseq_1 B A))  =>  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) &  (B = (k10_finseq_1 C D)) ) ) ) ) ) ) ) ) ).
tt(t100_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v2_funct_1 A) &  ( ((k10_xtuple_0 A) = (k1_enumset1 B C D))  & (v2_funct_1 (k11_finseq_1 B C D))) )  =>  ((k3_finseq_1 A) = 3) ) ) ) ) ) ) ).
tt(t100_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  &  ((v1_finseq_6 B A) & (m2_finseq_1 B A)) )  =>  ((k10_xtuple_0 (k2_rfinseq A 1 B)) = (k10_xtuple_0 B)) ) ) ) ) ).
tt(t100_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((r2_hidden (k2_flang_1 A) B) & (r2_hidden (k2_flang_1 A) C))  =>  ((r1_tarski (k2_flang_2 A B) (k6_flang_1 A B C)) & (r1_tarski (k2_flang_2 A B) (k6_flang_1 A C B))) ) ) ) ) ) ) ).
tt(t100_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((k3_relat_1 (k5_relat_1 A C) (k5_relat_1 B D)) = (k5_relat_1 (k3_relat_1 A B) (k3_xboole_0 C (k8_relat_1 A D)))) ) ) ) ) ) ) ).
tt(t100_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((k3_subset_1 A (k8_relset_1 A B C D)) = (k8_relset_1 A B C (k3_subset_1 B D))) ) ) ) ) ) ) ) ).
tt(t100_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (B = C) )  & (r2_hidden B (k10_xtuple_0 (k6_funct_4 A B C)))) ) ) ) ) ) ).
tt(t100_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] : (r1_tarski (k10_xtuple_0 (k2_funct_7 A B C)) (k2_xboole_0 (k10_xtuple_0 A) (k1_tarski C)))) ) ) ) ).
tt(t100_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) C) k4_gfacirc1) (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (u1_struct_0 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (u1_struct_0 (k37_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) k29_twoscomp) (u1_struct_0 (k37_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k14_glib_001 A B)) <=>  (? [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  &  ((k1_funct_1 B (k2_nat_1 D 1)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t100_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k11_group_2 A D (k12_group_2 A C B)) = (k12_group_2 A C (k11_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t100_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_group_3 A (k6_domain_1 (u1_struct_0 A) B)) = (a_2_2_group_3 A B)) ) ) ) ) ).
tt(t100_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  ( (~  (D = C) )  &  ((v9_group_9 D A B) &  ((r4_group_9 A B D C) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden (k1_nat_1 E 1) (k4_finseq_1 C)) &  ((r2_hidden (k1_nat_1 E 1) (k4_finseq_1 D)) &  ((r2_hidden F (k4_finseq_1 D)) &  ( (~ (r1_xxreal_0 F (k1_nat_1 E 1)))  &  ( ((k1_funct_1 C E) = (k1_funct_1 D E))  &  ( (~  ((k1_funct_1 C (k1_nat_1 E 1)) = (k1_funct_1 D (k1_nat_1 E 1))) )  &  ((k1_funct_1 C (k1_nat_1 E 1)) = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k24_sin_cos)) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k24_sin_cos (k4_seq_4 A))) (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k24_sin_cos (k5_seq_4 A)))))) ) ) ).
tt(t100_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) B) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  (~  ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  & (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid D)) &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 (k18_euclid B) H) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((k17_euclid A) = (k18_euclid B))  &  ( ((k1_real_1 (k18_euclid A)) = (k17_euclid B))  &  (A = (k1_rlvect_1 (k15_euclid 2) B C)) ) )  =>  ( ((k17_euclid A) = k6_numbers)  &  ( ((k18_euclid A) = k6_numbers)  &  (A = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ).
tt(t100_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((v3_limfunc1 B) &  ( ((k4_limfunc1 A) = (k4_limfunc1 B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E D))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 D))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k3_limfunc1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 D))))  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 D))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k3_limfunc1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 D)))) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k3_limfunc1 D))) =>  ((r1_xxreal_0 (k1_seq_1 A E) (k1_seq_1 C E)) & (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((v3_limfunc1 C) &  ((k4_limfunc1 C) = (k4_limfunc1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t100_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) &  ((v2_matrix_1 B A) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 C C) (k2_matrix_1 B)) => (v2_matrix_1 (k6_matrix13 (u1_struct_0 A) B C C) A)) ) ) ) ) ) ) ).
tt(t100_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k13_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k5_binop_2 A C) (k5_binop_2 A D) (k5_binop_2 B C) (k5_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t100_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( (E = (k1_relset_1 A D))  & (r1_mesfunc1 A B D E)) ) )  =>  ((r1_mesfunc5 A B C D) <=> (r1_mesfunc5 A B C (k10_mesfunc1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t100_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r3_mesfunc6 A B C D) & (r3_mesfunc6 A B C E))  => (r3_mesfunc6 A B C (k3_valued_1 A k1_numbers k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r13_ncfcont1 A B C E) & (r13_ncfcont1 A B D F))  => (r13_ncfcont1 A B (k3_xboole_0 C D) (k3_vfunct_2 (u1_struct_0 A) B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r4_pboole A B C) & (r2_pboole A B D))  => (r4_pboole A D C)) ) ) ) ) ) ) ) ).
tt(t100_prepower,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k5_prepower k6_numbers A) = k6_numbers) ) ) ) ).
tt(t100_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) => (r1_tarski (k6_relat_1 A C) (k6_relat_1 B C))) ) ) ) ) ).
tt(t100_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E D))  =>  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 D E)))))  =>  ((r4_rewrite3 C D E A (k2_flang_1 C) B) <=>  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_rvsum_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_rvsum_1 (k11_finseq_1 A B C)) = (k5_binop_2 (k5_binop_2 A B) C)) ) ) ) ) ) ) ).
tt(t100_scmfsa_2,ax, ((k8_struct_0 k1_scmfsa_2) = (k4_subset_1 (u1_struct_0 k1_scmfsa_2) k2_scmfsa_2 k3_scmfsa_2)) ).
tt(t100_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F))) |  ((k6_scmpds_4 (k4_scmpds_6 E F C D) B A) = (k1_funct_4 (k6_scmpds_4 C B A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden (k2_tarski (k4_tarski B (k3_tarski A)) C) (k12_scmyciel A)) &  (B = C) ) ) ) ) ) ) ).
tt(t100_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r4_semi_af1 A B C D E F) &  ((r4_semi_af1 A B C G H F) & (r4_semi_af1 A D E I J F)) )  => (r2_analoaf A G I H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) => (r1_xxreal_0 (k10_binop_2 (k22_seq_4 B) (k22_seq_4 C)) (k22_seq_4 (k15_seq_4 A B C)))) ) ) ) ) ) ).
tt(t100_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A D C)) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A D D) B)) (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A (k5_sheffer1 A D D) B)))) ) ) ) ) ) ) ) ) ).
tt(t100_sincos10,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k4_sincos10 (k1_rcomp_1 1 (k7_square_1 2)))) = (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))) ).
tt(t100_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( (~ (r1_xxreal_0 (k6_sin_cos6 A) k6_numbers))  &  (~ (r1_xxreal_0 k32_sin_cos (k6_sin_cos6 A))) ) ) ) ) ) ) ) ).
tt(t100_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k2_sin_cos9) (k10_real_1 1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = (k8_real_1 2 C))  &  ( (~ (r1_xxreal_0 (k1_seq_1 B C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 B C))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k2_sin_cos9) (k10_real_1 1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k2_sin_cos9) (k10_real_1 1 2)) A) C) = (k1_real_1 (k10_real_1 1 (k7_real_1 1 (k5_square_1 (k8_real_1 2 C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t100_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k8_tdlat_1 A)))) =>  ( (C = B)  =>  ((k15_lattice3 (k8_tdlat_1 A) C) = (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ) ) ).
tt(t100_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ((u1_struct_0 C) = B)  =>  ((v1_funct_1 (k2_tmap_1 A (k6_tmap_1 A B) (k7_tmap_1 A B) C)) &  ((v1_funct_2 (k2_tmap_1 A (k6_tmap_1 A B) (k7_tmap_1 A B) C) (u1_struct_0 C) (u1_struct_0 (k6_tmap_1 A B))) &  ((v5_pre_topc (k2_tmap_1 A (k6_tmap_1 A B) (k7_tmap_1 A B) C) C (k6_tmap_1 A B)) & (m1_subset_1 (k2_tmap_1 A (k6_tmap_1 A B) (k7_tmap_1 A B) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k6_tmap_1 A B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t100_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 A B) = (k5_xboole_0 A (k3_xboole_0 A B))) ) ) ).
tt(t100_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k10_xboolean A (k5_xboolean A B)) = (k11_xboolean B A)) ) ) ) ) ).
tt(t100_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 A (k7_xcmplx_0 1 B)) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t100_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k7_xcmplx_0 A C) (k7_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t100_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 A C) & (r1_tarski (k1_xxreal_1 A C) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t100_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((v1_xreal_0 A) =>  ((k4_xxreal_3 A (k3_xxreal_3 B C)) = (k3_xxreal_3 (k4_xxreal_3 A B) (k4_xxreal_3 A C))) ) ) ) ) ) ) ) ).
tt(t100_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k12_zf_lang A B) (k11_zf_lang B A))) & (r2_zf_model C (k11_zf_lang (k12_zf_lang A B) (k11_zf_lang B A)))) ) ) ) ) ) ) ) ) ).
tt(t100_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 C D)) = (k3_xboole_0 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) ) ) ) ) ).
tt(t100_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((k6_zmodul01 A (k3_zmodul01 A) (k4_zmodul01 A)) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ).
tt(t101_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  ((k1_abcmiz_1 (k48_abcmiz_1 A B)) = (k48_abcmiz_1 A B)) ) ) ) ) ).
tt(t101_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  ( ((v15_aofa_000 F A) & (m1_subset_1 F (u1_struct_0 A)))  =>  (! [G:$i] :  ( ((v15_aofa_000 G A) & (m1_subset_1 G (u1_struct_0 A)))  =>  ((r4_aofa_000 A (k13_aofa_000 A G F) B (k2_binop_1 B (u1_struct_0 A) B E D F) C E) => (r2_hidden (k4_tarski D (k16_aofa_000 A F G)) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_card_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (~  ( (~ (v1_finset_1 (k9_xtuple_0 A)))  &  ((v1_finset_1 (k10_xtuple_0 A)) &  (! [B:$i] :  (~  ((r2_hidden B (k10_xtuple_0 A)) &  (~ (v1_finset_1 (k8_relat_1 A (k1_tarski B)))) ) ) ) ) ) ) ) ) ).
tt(t101_card_3,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C (k9_xtuple_0 (k10_card_3 A))))  => (r2_hidden (k1_funct_1 B C) (k1_funct_1 (k10_card_3 A) C))) ) ) ) ) ) ).
tt(t101_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~ (r1_chord A B C))  &  (? [D:$i] :  ((m2_chord D A B C) &  ((v4_chord D A B C) &  (? [E:$i] :  ((m2_glib_000 E A (k6_subset_1 (k6_glib_000 A) D) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) D))) &  (? [F:$i] :  ((m1_subset_1 F (k6_glib_000 E)) &  ( (B = F)  &  (? [G:$i] :  ((m1_subset_1 G (k6_glib_000 A)) &  (? [H:$i] :  ((m1_subset_1 H (k6_glib_000 A)) &  ((r2_hidden G D) &  ((r2_hidden H D) &  (! [I:$i] :  ((m1_subset_1 I (k6_glib_000 A)) =>  (~  ((r2_hidden I (k1_glib_002 E F)) &  ((r1_chord A I G) & (r1_chord A I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  (! [D:$i] :  ((m2_clvect_1 D A C) =>  (! [E:$i] :  ((m2_clvect_1 E A C) =>  ( ((r2_hidden B D) & (r2_hidden B E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_fdiff_1 A G) &  ((r1_fdiff_1 B G) &  ((r1_fdiff_1 C G) &  ((r1_fdiff_1 D (k1_seq_1 A G)) &  ((r1_fdiff_1 E (k1_seq_1 B G)) & (r1_fdiff_1 F (k1_seq_1 C G))) ) ) ) )  =>  ((k8_euclid_8 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A D) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B E) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C F) G) = (k1_euclid_8 (k11_binop_2 (k1_fdiff_1 D (k1_seq_1 A G)) (k1_fdiff_1 A G)) (k11_binop_2 (k1_fdiff_1 E (k1_seq_1 B G)) (k1_fdiff_1 B G)) (k11_binop_2 (k1_fdiff_1 F (k1_seq_1 C G)) (k1_fdiff_1 C G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((r2_hidden B D) &  ((r1_tarski C D) & (v1_euclid_4 C A)) )  =>  ((r2_hidden B C) | (v1_euclidlp D A)) ) ) ) ) ) ) ) ) ) ).
tt(t101_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r2_hidden (k10_finseq_1 B C) (k4_finseq_2 2 A))) ) ) ) ) ) ).
tt(t101_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v2_funct_1 A) &  ((k10_xtuple_0 A) = (k1_enumset1 B C D)) )  =>  ( (B = C)  |  ( (C = D)  |  ( (B = D)  |  ((k3_finseq_1 A) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t101_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) => (r1_tarski (k10_xtuple_0 (k2_rfinseq A 1 C)) (k10_xtuple_0 (k1_finseq_6 A C B)))) ) ) ) ) ) ).
tt(t101_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k6_flang_1 A B (k2_flang_2 A C))) & (r1_tarski B (k6_flang_1 A (k2_flang_2 A C) B))) ) ) ) ) ) ).
tt(t101_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski C (k9_xtuple_0 (k3_relat_1 A B))) <=>  ((r1_tarski C (k9_xtuple_0 A)) & (r1_tarski (k7_relat_1 A C) (k9_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t101_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A D)))) )  =>  ( ((r1_tarski B A) & (r1_tarski (k7_relset_1 A D E B) C))  =>  ((v1_funct_1 (k2_partfun1 A D E B)) &  ((v1_funct_2 (k2_partfun1 A D E B) B C) & (m1_subset_1 (k2_partfun1 A D E B) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t101_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r2_hidden C (k10_xtuple_0 (k6_funct_4 A B C)))) ) ) ) ) ).
tt(t101_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] : (r1_tarski (k10_xtuple_0 A) (k2_xboole_0 (k10_xtuple_0 (k2_funct_7 A B C)) (k1_tarski (k1_funct_1 A B))))) ) ) ) ).
tt(t101_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k3_msafree2 (k37_gfacirc1 A B C))) &  ((r2_hidden (k36_gfacirc1 A B C) (k3_msafree2 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k3_msafree2 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k3_msafree2 (k37_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k3_msafree2 (k37_gfacirc1 A B C))) & (r2_hidden (k33_gfacirc1 A B C) (k3_msafree2 (k37_gfacirc1 A B C)))) ) ) ) ) ) ) ) ).
tt(t101_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k2_relset_1 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B) = (k2_xboole_0 (k13_glib_001 A B) (k14_glib_001 A B))) ) ) ) ) ).
tt(t101_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_2 A (k12_group_2 A C (k8_group_2 A D)) B) = (k12_group_2 A C (k12_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t101_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v8_struct_0 A) => (v1_finset_1 (k8_group_3 A B))) ) ) ) ) ).
tt(t101_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (! [E:$i] :  ( ((v8_group_9 E A B) & (m2_finseq_1 E (k6_group_9 A B)))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden F (k4_finseq_1 E)) &  ((r2_hidden G (k4_finseq_1 E)) &  ((r1_xxreal_0 F G) &  ( (C = (k1_funct_1 E F))  &  (D = (k1_funct_1 E G)) ) ) ) )  => (m1_group_9 D A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k5_seq_4 A)))) ) ) ).
tt(t101_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k7_jgraph_4 A)) & (v5_pre_topc B (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t101_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid D)) &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (v2_tops_1 (k1_rltopsp1 (k15_euclid 2) A B) (k15_euclid 2))) ) ) ) ).
tt(t101_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((v3_limfunc1 B) &  ((k4_limfunc1 A) = (k4_limfunc1 B)) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_tarski (k3_limfunc1 D) (k9_subset_1 k1_numbers (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)) (k1_relset_1 k1_numbers C))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k3_limfunc1 D)) =>  ((r1_xxreal_0 (k1_seq_1 A E) (k1_seq_1 C E)) & (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((v3_limfunc1 C) &  ((k4_limfunc1 C) = (k4_limfunc1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t101_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) &  ((v2_matrix_1 B A) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( (C = (a_2_1_matrix13 A B))  =>  ((k8_matrix13 A B) = (k1_card_1 C)) ) ) ) ) ) ) ).
tt(t101_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k14_member_1 A B) = (a_2_6_member_1 A B)) ) ) ) ) ).
tt(t101_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc5 A B C D) => (r1_xxreal_0 (k3_extreal1 (k7_mesfunc5 A B C D)) (k7_mesfunc5 A B C (k10_mesfunc1 A D)))) ) ) ) ) ) ) ) ) ).
tt(t101_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ((r3_mesfunc6 A B C D) &  ((r3_mesfunc6 A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k1_mesfunc6 A B C (k3_valued_1 A k1_numbers k1_numbers D E)) = (k3_supinf_2 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D F)) (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r14_ncfcont1 A B C E) & (r14_ncfcont1 A B D F))  => (r14_ncfcont1 A B (k3_xboole_0 C D) (k6_vfunct_1 (u1_struct_0 A) B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) &  ((r2_pboole A D E) & (r4_pboole A B D)) )  => (r4_pboole A C E)) ) ) ) ) ) ) ) ) ) ).
tt(t101_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski B C) => (r1_tarski (k6_relat_1 A B) (k6_relat_1 A C))) ) ) ) ) ) ).
tt(t101_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ((r4_rewrite3 C E F A (k3_flang_1 C D) B) =>  ((r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))) | (r2_rewrite3 C E F A (k3_flang_1 C D) B (k2_flang_1 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k4_finseq_2 k6_numbers k1_numbers)) =>  ((k21_rvsum_1 A) = 1) ) ) ).
tt(t101_scmfsa_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = B) )  &  ((k4_scmfsa_2 A) = (k4_scmfsa_2 B)) ) ) ) ) ) ) ).
tt(t101_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F))) &  ((r1_scmpds_6 D B A) & (r2_scmpds_6 D B A)) )  =>  ((k6_scmpds_4 (k4_scmpds_6 E F C D) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden C (k3_tarski A)) & (r2_hidden (k2_tarski (k4_tarski B (k3_tarski A)) C) (k12_scmyciel A)))  => (r2_hidden (k2_tarski B C) A)) ) ) ) ) ).
tt(t101_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_semi_af1 A B C D) & (r5_semi_af1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t101_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) => (r1_xxreal_0 (k10_binop_2 (k22_seq_4 B) (k22_seq_4 C)) (k22_seq_4 (k19_seq_4 A B C)))) ) ) ) ) ) ).
tt(t101_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B B) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C C) C) B)) ) ) ) ) ) ) ).
tt(t101_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k7_square_1 2)) &  ((k9_sincos10 A) = k6_numbers) ) )  =>  (A = 1) )  &  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k7_square_1 2)) &  ((k9_sincos10 A) = (k10_real_1 k32_sin_cos 4)) ) )  =>  (A = (k7_square_1 2)) ) ) ) ) ).
tt(t101_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k6_sin_cos6 A) = (k9_real_1 k32_sin_cos (k6_sin_cos6 (k4_xcmplx_0 A)))) ) ) ) ).
tt(t101_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 B D) = 1) ) ) )  &  (C = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) D) = (k8_real_1 2 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k8_tdlat_1 A)))) =>  ( (C = B)  =>  ( ( (~  (C = k1_xboole_0) )  =>  ((k16_lattice3 (k8_tdlat_1 A) C) = (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)))) )  &  ( (C = k1_xboole_0)  =>  ((k16_lattice3 (k8_tdlat_1 A) C) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((v1_funct_1 (k7_tmap_1 A B)) &  ((v1_funct_2 (k7_tmap_1 A B) (u1_struct_0 A) (u1_struct_0 (k6_tmap_1 A B))) &  ((v5_pre_topc (k7_tmap_1 A B) A (k6_tmap_1 A B)) & (m1_subset_1 (k7_tmap_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k6_tmap_1 A B)))))) ) ) ) ) ) ) ) ).
tt(t101_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k5_xboole_0 A B) = (k4_xboole_0 (k2_xboole_0 A B) (k3_xboole_0 A B))) ) ) ).
tt(t101_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ((k4_xboolean A B) = k2_xboolean)  =>  ( (A = k2_xboolean)  &  (B = k2_xboolean) ) ) ) ) ) ) ).
tt(t101_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k7_xcmplx_0 A B) C) = (k3_xcmplx_0 (k3_xcmplx_0 (k7_xcmplx_0 1 B) C) A)) ) ) ) ) ) ) ).
tt(t101_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t101_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k4_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t101_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k4_xxreal_3 B C) (k4_xxreal_3 A C))) ) ) ) ) ) ) ).
tt(t101_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  => (r2_zf_model D (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang (k11_zf_lang B C) (k11_zf_lang A C))))) ) ) ) ) ) ) ) ).
tt(t101_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  =>  ((k3_xboole_0 (k2_zfmisc_1 A D) (k2_zfmisc_1 B C)) = (k2_zfmisc_1 A C)) ) ) ) ) ) ).
tt(t101_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k6_zmodul01 A (k4_zmodul01 A) B) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ) ) ).
tt(t102_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ( ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A)))  =>  ((k47_abcmiz_1 A (k43_abcmiz_1 A B C)) = (k4_subset_1 k2_abcmiz_1 (k45_abcmiz_1 A C) (k47_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(t102_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) &  ((v3_freealg C) &  ((v3_aofa_000 C) &  ((v4_aofa_000 C) &  ((v5_aofa_000 C) &  ((v6_aofa_000 C) &  ((v12_aofa_000 C) & (l1_unialg_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_aofa_000 D C A B) =>  (! [E:$i] :  ((m1_aofa_000 E C A B) =>  ((r2_relset_1 (k2_zfmisc_1 A (u1_struct_0 C)) A (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A D (k2_zfmisc_1 A (k18_aofa_000 C))) (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A E (k2_zfmisc_1 A (k18_aofa_000 C)))) => (r2_relset_1 A (u1_struct_0 C) (k21_aofa_000 C A B D) (k21_aofa_000 C A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_card_3,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v2_card_3 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C (k9_xtuple_0 B)))  => (r2_hidden (k1_funct_1 B C) (k1_funct_1 (k10_card_3 A) C))) ) ) ) ) ) ).
tt(t102_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v6_chord A)) ) ) ) ) ) )  =>  (~  ( (~ (v2_chord A))  &  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~ (r1_chord A B C))  &  ((v3_chord B A) & (v3_chord C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_normsp_0 A (k4_struct_0 A)) = k6_numbers) ) ) ).
tt(t102_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_fdiff_1 A G) &  ((r1_fdiff_1 B G) &  ((r1_fdiff_1 C G) &  ((r1_fdiff_1 D G) &  ((r1_fdiff_1 E G) & (r1_fdiff_1 F G)) ) ) ) )  =>  ( ((k1_seq_1 D G) = k6_numbers)  |  ( ((k1_seq_1 E G) = k6_numbers)  |  ( ((k1_seq_1 F G) = k6_numbers)  |  ((k8_euclid_8 (k3_rfunct_1 k1_numbers k1_numbers A D) (k3_rfunct_1 k1_numbers k1_numbers B E) (k3_rfunct_1 k1_numbers k1_numbers C F) G) = (k1_euclid_8 (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 A G) (k1_seq_1 D G)) (k11_binop_2 (k1_fdiff_1 D G) (k1_seq_1 A G))) (k5_square_1 (k1_seq_1 D G))) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B G) (k1_seq_1 E G)) (k11_binop_2 (k1_fdiff_1 E G) (k1_seq_1 B G))) (k5_square_1 (k1_seq_1 E G))) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C G) (k1_seq_1 F G)) (k11_binop_2 (k1_fdiff_1 F G) (k1_seq_1 C G))) (k5_square_1 (k1_seq_1 F G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((v1_euclid_4 C A) &  ((r2_hidden B D) &  ((r1_tarski C D) &  ((r2_hidden B E) & (r1_tarski C E)) ) ) )  =>  ((r2_hidden B C) |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_finseq_2 3 A) = (a_1_2_finseq_2 A)) ) ) ).
tt(t102_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (~  ( (C = (k1_funct_1 B 1))  & (r2_relset_1 k5_numbers A B (k8_finseq_1 A (k12_finseq_1 A C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 D) (k10_xtuple_0 (k1_finseq_5 A D C)))) =>  ((k1_finseq_6 A (k1_finseq_6 A D C) B) = (k1_finseq_6 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t102_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((r1_tarski B (k2_flang_2 A C)) & (r1_tarski D (k2_flang_2 A C)))  => (r1_tarski (k6_flang_1 A B D) (k1_flang_2 A C k6_numbers 2))) ) ) ) ) ) ) ) ).
tt(t102_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) => (r2_hidden (k1_funct_1 B C) A)) ) ) ) ) ).
tt(t102_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ((r1_tarski D E) => (r1_tarski (k6_funct_2 A B C D) (k6_funct_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k6_funct_4 A B B) = A) ) ) ) ).
tt(t102_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (r2_hidden C (k10_xtuple_0 (k2_funct_7 A B C)))) ) ) ) ) ).
tt(t102_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_gfacirc1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (~  ((r2_hidden A (k2_msafree2 (k37_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k37_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k37_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k14_glib_001 A (k7_glib_001 A B C)) = (k4_subset_1 (k7_glib_000 A) (k14_glib_001 A B) (k14_glib_001 A C))) ) ) ) ) ) ) ) ).
tt(t102_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k11_group_2 A C B) = (k12_group_2 A C B)) ) ) ) ) ) ) ) ).
tt(t102_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r5_group_3 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r1_group_2 A C (k6_group_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t102_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  ((r2_hidden C (k10_xtuple_0 (k20_group_9 A B D))) =>  ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v2_group_9 C A) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos))) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) (k5_seq_4 A)))) ) ) ).
tt(t102_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (v2_funct_1 (k7_jgraph_4 A))) ) ) ) ) ) ).
tt(t102_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_jordan2c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v2_tops_1 (k3_topreal1 2 A) (k15_euclid 2))) ) ).
tt(t102_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((v6_limfunc1 B) &  ( ((k5_limfunc1 A) = (k5_limfunc1 B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 D E))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 D))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k10_prob_1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 D))))  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 D))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k10_prob_1 D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 D)))) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k10_prob_1 D))) =>  ((r1_xxreal_0 (k1_seq_1 A E) (k1_seq_1 C E)) & (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((v6_limfunc1 C) &  ((k5_limfunc1 C) = (k5_limfunc1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t102_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_prvect_1 B A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_prvect_1 B A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_prvect_1 B A))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [H:$i] :  ((m2_finseq_2 H (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [I:$i] :  ((m2_finseq_2 I (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((u1_struct_0 (k6_prvect_1 B A)) = (k4_finseq_2 A (u1_struct_0 B)))  &  ( ((k4_struct_0 (k6_prvect_1 B A)) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)))  &  ( ( ( (G = D)  &  (H = E) )  =>  ((k3_fvsum_1 B G H) = (k1_algstr_0 (k6_prvect_1 B A) D E)) )  &  ( (I = F)  =>  ((k9_fvsum_1 B I C) = (k4_vectsp_1 B (k6_prvect_1 B A) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k6_xxreal_3 C D) (k14_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t102_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( ((k1_relset_1 A D) = (k1_relset_1 A E))  &  ((r1_mesfunc5 A B C E) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A D)) => (r1_xxreal_0 (k3_extreal1 (k12_supinf_2 D F)) (k12_supinf_2 E F))) ) ) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  & (r1_mesfunc1 A B D F)) ) ) )  |  ((r1_mesfunc5 A B C D) & (r1_xxreal_0 (k7_mesfunc5 A B C (k10_mesfunc1 A D)) (k7_mesfunc5 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r3_mesfunc6 A B C D) =>  ((r3_mesfunc6 A B C (k26_valued_1 A k1_numbers D E)) &  ((k1_mesfunc6 A B C (k26_valued_1 A k1_numbers D E)) = (k1_extreal1 (k1_measure6 E) (k1_mesfunc6 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r15_ncfcont1 B A C E) & (r15_ncfcont1 B A D F))  => (r15_ncfcont1 B A (k3_xboole_0 C D) (k3_vfunct_2 (u1_struct_0 B) A E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r4_pboole A B (k3_pboole A C D)) =>  ((r4_pboole A B C) & (r4_pboole A B D)) ) ) ) ) ) ) ) ) ).
tt(t102_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((r1_tarski C D) & (r1_tarski A B))  => (r1_tarski (k6_relat_1 A C) (k6_relat_1 B D))) ) ) ) ) ) ) ).
tt(t102_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ( ((v2_rewrite3 G E F) &  ((r4_rewrite3 E F G A B C) & (r4_rewrite3 E F G A B D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k19_rvsum_1 (k5_finseq_2 k5_numbers A 1)) = 1) ) ) ).
tt(t102_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r2_hidden B (k1_relset_1 (u1_struct_0 k1_scmfsa_2) (k7_memstr_0 3 k1_scmfsa_2 A)))) ) ) ) ) ).
tt(t102_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k4_scmpds_6 E F C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k2_tarski B C) (k1_scmyciel A)) => (r2_hidden (k2_tarski (k4_tarski B (k3_tarski A)) C) (k12_scmyciel A))) ) ) ) ) ).
tt(t102_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ( ((k22_seq_4 (k19_seq_4 A B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t102_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A (k5_sheffer1 A B B) C)) = C) ) ) ) ) ) ) ).
tt(t102_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) &  ((r1_xxreal_0 A (k1_real_1 1)) &  ((k10_sincos10 A) = (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) ) )  =>  (A = (k1_real_1 (k7_square_1 2))) )  &  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) &  ((r1_xxreal_0 A (k1_real_1 1)) &  ((k10_sincos10 A) = k32_sin_cos) ) )  =>  (A = (k1_real_1 1)) ) ) ) ) ).
tt(t102_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((k2_xcmplx_0 (k3_square_1 B) (k3_square_1 A)) = 1) )  =>  ((k18_sin_cos (k6_sin_cos6 B)) = A) ) ) ) ) ) ).
tt(t102_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2)))) &  ( (C = (k1_taylor_1 2))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 B D) = 1) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2)) A) D) = (k10_real_1 D (k7_real_1 1 (k5_square_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_tdlat_1 A)))) =>  ( (C = B)  =>  ( ( (~  (C = k1_xboole_0) )  =>  ((k16_lattice3 (k4_tdlat_1 A) C) = (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)))) )  &  ( (C = k1_xboole_0)  =>  ((k16_lattice3 (k4_tdlat_1 A) C) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ( ((u1_struct_0 (k8_tmap_1 A B)) = (u1_struct_0 A))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((u1_pre_topc (k8_tmap_1 A B)) = (k5_tmap_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t102_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 A (k5_xboole_0 B C)) = (k2_xboole_0 (k4_xboole_0 A (k2_xboole_0 B C)) (k3_xboole_0 (k3_xboole_0 A B) C))) ) ) ) ).
tt(t102_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k4_xboolean A (k3_xboolean A))) = k2_xboolean) ) ) ).
tt(t102_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k7_xcmplx_0 1 A) (k7_xcmplx_0 1 B)) = (k7_xcmplx_0 1 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t102_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k3_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 k6_numbers C))  &  ( (~  (C = k2_xxreal_0) )  & (r1_xxreal_0 (k4_xxreal_3 A C) (k4_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t102_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ( ((r1_zf_model D E (k11_zf_lang A B)) & (r1_zf_model D E (k11_zf_lang B C)))  => (r1_zf_model D E (k11_zf_lang A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t102_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k2_zfmisc_1 (k4_xboole_0 A B) C) = (k4_xboole_0 (k2_zfmisc_1 A C) (k2_zfmisc_1 B C)))  &  ((k2_zfmisc_1 C (k4_xboole_0 A B)) = (k4_xboole_0 (k2_zfmisc_1 C A) (k2_zfmisc_1 C B))) ) ) ) ) ).
tt(t102_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  =>  ((k6_zmodul01 A (k4_zmodul01 A) (k4_zmodul01 A)) = A) ) ) ).
tt(t103_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ( ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A)))  =>  ((k48_abcmiz_1 A (k43_abcmiz_1 A B C)) = (k4_subset_1 k2_abcmiz_1 (k46_abcmiz_1 A C) (k48_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(t103_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) &  ((v3_freealg C) &  ((v3_aofa_000 C) &  ((v4_aofa_000 C) &  ((v5_aofa_000 C) &  ((v6_aofa_000 C) &  ((v12_aofa_000 C) & (l1_unialg_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_aofa_000 D C A B) =>  (! [E:$i] :  ((m1_aofa_000 E C A B) =>  ((r2_relset_1 (k2_zfmisc_1 A (u1_struct_0 C)) A (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A D (k2_zfmisc_1 A (k18_aofa_000 C))) (k2_partfun1 (k2_zfmisc_1 A (u1_struct_0 C)) A E (k2_zfmisc_1 A (k18_aofa_000 C)))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r2_hidden (k4_tarski F G) (k21_aofa_000 C A B D)) =>  ((k2_binop_1 A (u1_struct_0 C) A D F G) = (k2_binop_1 A (u1_struct_0 C) A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v5_funct_1 C B)) ) )  => (r2_hidden C (k8_card_3 B))) ) ) ) ) ).
tt(t103_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) & (v3_chord B A)) ) ) ) ).
tt(t103_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_normsp_0 A (k4_algstr_0 A B)) = (k1_normsp_0 A B)) ) ) ) ) ).
tt(t103_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_fdiff_1 A D) &  ((r1_fdiff_1 B D) & (r1_fdiff_1 C D)) )  =>  ( ((k1_seq_1 A D) = k6_numbers)  |  ( ((k1_seq_1 B D) = k6_numbers)  |  ( ((k1_seq_1 C D) = k6_numbers)  |  ((k8_euclid_8 (k6_rfunct_1 k1_numbers k1_numbers A) (k6_rfunct_1 k1_numbers k1_numbers B) (k6_rfunct_1 k1_numbers k1_numbers C) D) = (k6_euclid 3 (k1_euclid_8 (k12_binop_2 (k1_fdiff_1 A D) (k5_square_1 (k1_seq_1 A D))) (k12_binop_2 (k1_fdiff_1 B D) (k5_square_1 (k1_seq_1 B D))) (k12_binop_2 (k1_fdiff_1 C D) (k5_square_1 (k1_seq_1 C D)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((v1_euclid_4 B A) &  ((v1_euclid_4 C A) &  ((r7_euclidlp A B C) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r1_tarski B D) &  ((r1_tarski C D) & (v1_euclidlp D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 3) & (m2_finseq_1 B A))  =>  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) &  (? [E:$i] :  ((m1_subset_1 E A) &  (B = (k11_finseq_1 C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r2_hidden A (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 C) B) (k1_nat_1 A 1)) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t103_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 D) (k10_xtuple_0 (k2_finseq_5 A D C)))) =>  ( ((k4_finseq_4 D B) = 1)  |  ((k1_finseq_6 A (k1_finseq_6 A D C) B) = (k1_finseq_6 A D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_xxreal_0 C k6_numbers) | (r1_tarski (k2_flang_2 A B) (k7_flang_1 A B C))) ) ) ) ) ) ) ).
tt(t103_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v5_funct_1 A B) &  ((k9_xtuple_0 A) = (k9_xtuple_0 B)) )  => (v2_relat_1 B)) ) ) ) ) ).
tt(t103_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski D E) => (r1_tarski (k7_funct_2 A B C D) (k7_funct_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden B (k10_xtuple_0 A)))  =>  ((k6_funct_4 A B C) = A) ) ) ) ) ) ).
tt(t103_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k10_xtuple_0 (k10_funct_7 A B C)) = (k10_xtuple_0 A)) ) ) ) ) ).
tt(t103_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_gfacirc1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k37_gfacirc1 A B C) (k38_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k37_gfacirc1 A B C) (k38_gfacirc1 A B C) D 2) (k36_gfacirc1 A B C)) = (k2_binarith (k2_binarith (k9_margrel1 E) F) (k9_margrel1 G)))  &  ((k1_funct_1 (k5_facirc_1 (k37_gfacirc1 A B C) (k38_gfacirc1 A B C) D 2) (k33_gfacirc1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F (k9_margrel1 G))) (k10_margrel1 (k9_margrel1 G) (k9_margrel1 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (~  ((r2_hidden C (k14_glib_001 A B)) &  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (! [F:$i] :  ( ( (~ (v1_abian F))  & (m1_subset_1 F k5_numbers))  =>  (~  ((r1_xxreal_0 (k2_nat_1 F 2) (k3_finseq_1 B)) &  ( (D = (k1_funct_1 B F))  &  ( (C = (k1_funct_1 B (k2_nat_1 F 1)))  &  ( (E = (k1_funct_1 B (k2_nat_1 F 2)))  & (r1_glib_000 A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r2_hidden A (k13_group_2 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B C E))  & (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r5_group_3 A B B)) ) ) ) ).
tt(t103_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 (k20_group_9 A B C))) &  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_group_1 E) &  ((v3_group_1 E) &  ((v3_group_9 E A) & (l1_group_9 E A)) ) ) )  =>  ( (E = (k1_funct_1 (k20_group_9 A B C) D))  => (v7_struct_0 E)) ) ) )  =>  ((r2_hidden D (k4_finseq_1 C)) &  ((r2_hidden (k1_nat_1 D 1) (k4_finseq_1 C)) &  ((k1_funct_1 C D) = (k1_funct_1 C (k1_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( ((v1_funct_1 (k7_jgraph_4 A)) &  ((v1_funct_2 (k7_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k7_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A)) = (u1_struct_0 (k15_euclid 2))) ) ) ) ) ) ) ) ).
tt(t103_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ( (D = C)  & (r2_hidden E (k9_metric_1 (k14_euclid A) C B)))  =>  ( (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid A) D E))))  &  (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((v6_limfunc1 B) &  ((k5_limfunc1 A) = (k5_limfunc1 B)) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_tarski (k10_prob_1 D) (k9_subset_1 k1_numbers (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)) (k1_relset_1 k1_numbers C))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k10_prob_1 D)) =>  ((r1_xxreal_0 (k1_seq_1 A E) (k1_seq_1 C E)) & (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((v6_limfunc1 C) &  ((k5_limfunc1 C) = (k5_limfunc1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t103_matrix13,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) C B) =>  ((r2_hidden A (k9_matrix13 D C B E)) <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden F (k2_finseq_1 C)) &  (A = (k8_matrix_1 (u1_struct_0 D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  (! [D:$i] :  ((v2_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k14_member_1 A C) (k14_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t103_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden (k1_relset_1 A D) B) &  ((r1_xxreal_0 k6_numbers E) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A D)) =>  ((k12_supinf_2 D F) = E) ) ) ) )  =>  ( ((k1_relset_1 A D) = k1_xboole_0)  |  ((k1_mesfunc3 A B C D) = (k4_xxreal_3 E (k12_supinf_2 C (k1_relset_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r3_mesfunc6 A B C D) &  ((r3_mesfunc6 A B C E) & (r1_tarski F (k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers D E)))) )  =>  ((r3_mesfunc6 A B C (k3_valued_1 A k1_numbers k1_numbers D E)) &  ((k2_mesfunc6 A B C (k3_valued_1 A k1_numbers k1_numbers D E) F) = (k3_supinf_2 (k2_mesfunc6 A B C D F) (k2_mesfunc6 A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r13_ncfcont1 A B C E) & (r13_ncfcont1 A B D F))  => (r13_ncfcont1 A B (k3_xboole_0 C D) (k2_vfunct_1 (u1_struct_0 A) B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r4_pboole A B C) & (r2_pboole A B D))  => (r4_pboole A B (k3_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t103_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k6_relat_1 (k2_xboole_0 A B) C) = (k2_xboole_0 (k6_relat_1 A C) (k6_relat_1 B C))) ) ) ) ) ).
tt(t103_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  ((r2_hidden F (k3_rewrite3 C D E A B)) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) &  ((r2_hidden G B) & (r4_rewrite3 C D E G A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ( (? [B:$i] :  ((v7_ordinal1 B) &  ((r2_hidden B (k4_finseq_1 A)) &  ((k1_funct_1 A B) = k6_numbers) ) ) )  <=>  ((k19_rvsum_1 A) = k6_numbers) ) ) ) ).
tt(t103_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (~ (r2_hidden B (k1_relset_1 (u1_struct_0 k1_scmfsa_2) (k7_memstr_0 3 k1_scmfsa_2 A)))) ) ) ) ) ).
tt(t103_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) G))))  =>  ((k1_funct_1 (k6_scmpds_4 (k4_scmpds_6 E G C D) B A) F) = (k1_funct_1 (k6_scmpds_4 C B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) &  ((r2_hidden C (k3_tarski A)) & (r2_hidden (k2_tarski B C) (k12_scmyciel A))) )  => (r2_hidden (k2_tarski B C) A)) ) ) ) ) ).
tt(t103_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r5_semi_af1 A B C) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t103_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k22_seq_4 (k19_seq_4 A B C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t103_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A (k5_sheffer1 A B B) B))) = (k5_sheffer1 A (k5_sheffer1 A B B) B)) ) ) ) ) ) ) ).
tt(t103_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) &  ((r1_xxreal_0 A (k1_real_1 1)) &  ((k11_sincos10 A) = (k1_real_1 (k10_real_1 k32_sin_cos 2))) ) )  =>  (A = (k1_real_1 1)) )  &  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) &  ((r1_xxreal_0 A (k1_real_1 1)) &  ((k11_sincos10 A) = (k1_real_1 (k10_real_1 k32_sin_cos 4))) ) )  =>  (A = (k1_real_1 (k7_square_1 2))) ) ) ) ) ).
tt(t103_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) &  ((k2_xcmplx_0 (k3_square_1 B) (k3_square_1 A)) = 1) )  =>  ((k18_sin_cos (k6_sin_cos6 B)) = (k4_xcmplx_0 A)) ) ) ) ) ) ).
tt(t103_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (C = (k1_taylor_1 2))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 B D) = 1) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))) A) D) = (k1_seq_1 k1_sin_cos9 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((u1_struct_0 (k12_tdlat_1 A)) = (k9_tdlat_1 A)) ) ) ).
tt(t103_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_pre_topc C (k8_tmap_1 A B)) =>  ( ((u1_struct_0 C) = (u1_struct_0 B))  =>  ((v1_tsep_1 C (k8_tmap_1 A B)) & (m1_pre_topc C (k8_tmap_1 A B))) ) ) ) ) ) ) ) ).
tt(t103_xboole_1,ax, (! [A:$i] :  (! [B:$i] : (r1_xboole_0 (k3_xboole_0 A B) (k5_xboole_0 A B))) ) ).
tt(t103_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k6_xboolean A A) = k2_xboolean) ) ) ).
tt(t103_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k7_xcmplx_0 1 A) (k7_xcmplx_0 B C)) = (k7_xcmplx_0 B (k3_xcmplx_0 C A))) ) ) ) ) ) ) ).
tt(t103_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 k6_numbers B) | (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k2_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t103_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 k6_numbers C) | (r1_xxreal_0 (k6_xxreal_3 B C) (k6_xxreal_3 A C))) ) ) ) ) ) ) ) ).
tt(t103_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ((r2_zf_model D (k11_zf_lang A B)) & (r2_zf_model D (k11_zf_lang B C)))  => (r2_zf_model D (k11_zf_lang A C))) ) ) ) ) ) ) ) ) ).
tt(t103_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_xboole_0 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) = (k2_xboole_0 (k2_zfmisc_1 (k4_xboole_0 A C) B) (k2_zfmisc_1 A (k4_xboole_0 B D)))) ) ) ) ) ).
tt(t103_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ((k7_zmodul01 A B B) = B) ) ) ) ) ).
tt(t104_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v9_abcmiz_1 B A) & (m1_abcmiz_1 B A (k12_abcmiz_1 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))))  =>  ((k47_abcmiz_1 A (k40_abcmiz_1 A C B)) = (k2_xboole_0 (k3_tarski (a_2_5_abcmiz_1 A C)) (k45_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(t104_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ( ((v15_aofa_000 E A) & (m1_subset_1 E (u1_struct_0 A)))  => (r5_aofa_000 A B C E D)) ) ) ) ) ) ) ) ) ) ).
tt(t104_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v5_funct_1 C B)) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 B)) & (r1_tarski C D)) ) ) ) ) ) ) ).
tt(t104_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) =>  ((k3_finseq_1 B) = (k5_card_1 (k6_glib_000 A))) ) ) ) ) ).
tt(t104_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ).
tt(t104_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_fdiff_1 B E) &  ((r1_fdiff_1 C E) & (r1_fdiff_1 D E)) )  =>  ((k8_euclid_8 (k26_valued_1 k1_numbers k1_numbers B A) (k26_valued_1 k1_numbers k1_numbers C A) (k26_valued_1 k1_numbers k1_numbers D A) E) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k11_binop_2 A (k1_fdiff_1 B E))) (k9_euclid 3 k3_euclid_8 (k11_binop_2 A (k1_fdiff_1 C E)))) (k9_euclid 3 k4_euclid_8 (k11_binop_2 A (k1_fdiff_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((v1_euclid_4 B A) &  ((v1_euclid_4 C A) &  ( (~  (B = C) )  &  ( (~ (r1_xboole_0 B C))  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r1_tarski B D) &  ((r1_tarski C D) & (v1_euclidlp D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_hidden (k11_finseq_1 B C D) (k4_finseq_2 3 A))) ) ) ) ) ) ) ) ).
tt(t104_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~  ((r2_hidden A (k1_relset_1 k5_numbers B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k3_finseq_1 B) = (k1_nat_1 C 1))  &  ((k3_finseq_1 (k2_finseq_3 A B)) = C) ) ) ) ) ) )  &  ( (~ (r2_hidden A (k1_relset_1 k5_numbers B)))  =>  ((k2_finseq_3 A B) = B) ) ) ) ) ) ) ).
tt(t104_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((r2_hidden B (k10_xtuple_0 (k2_rfinseq A 1 D))) & (r2_finseq_4 D B))  =>  ((k1_finseq_6 A (k1_finseq_6 A D C) B) = (k1_finseq_6 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t104_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k2_flang_2 A B) (k7_flang_1 A B C)) = (k6_flang_1 A (k7_flang_1 A B C) (k2_flang_2 A B))) ) ) ) ) ) ).
tt(t104_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v5_funct_1 k1_xboole_0 A)) ) ).
tt(t104_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ((m1_setfam_1 (k7_funct_2 A B C (k6_funct_2 A B C D)) E) => (m1_setfam_1 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] : (r1_tarski (k10_xtuple_0 (k6_funct_4 A B C)) (k2_xboole_0 (k6_subset_1 (k10_xtuple_0 A) (k1_tarski B)) (k1_tarski C)))) ) ) ) ).
tt(t104_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r1_funct_7 A B D) => (r1_funct_7 (k1_funct_4 A C) (k1_funct_4 B C) D)) ) ) ) ) ) ) ) ).
tt(t104_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_gfacirc1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k37_gfacirc1 A B C) (k38_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k37_gfacirc1 A B C) (k38_gfacirc1 A B C) D 2) (k37_gfacirc1 A B C) (k38_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k14_glib_001 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k1_relset_1 k5_numbers (k12_glib_001 A B))) &  ((k1_funct_1 (k12_glib_001 A B) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t104_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r2_hidden A (k14_group_2 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B E C))  & (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r5_group_3 A B C) => (r5_group_3 A C B)) ) ) ) ) ) ) ).
tt(t104_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  ((r2_hidden (k1_nat_1 E 1) (k4_finseq_1 C)) &  ( ((k1_funct_1 C E) = (k1_funct_1 C (k1_nat_1 E 1)))  &  (D = (k2_finseq_3 E C)) ) ) )  =>  ((k20_group_9 A B D) = (k2_finseq_3 E (k20_group_9 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r2_hidden B D) &  ((v3_pre_topc D (k15_euclid 2)) &  ((r1_tarski D C) & (r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ((r2_hidden C (k3_topreal1 2 (k1_sprect_1 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D (k2_jordan2c 2 (k3_topreal1 2 (k1_sprect_1 A)))) &  (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) & (v3_limfunc1 B))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 C))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) )  &  (~  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 C)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 C))) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) ) ) ) )  | (r1_xxreal_0 (k4_limfunc1 A) (k4_limfunc1 B))) ) ) ) ) ) ).
tt(t104_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 B A)))))  =>  (? [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) (k5_card_1 C) A) &  ((v2_funct_1 D) &  ((k9_matrix13 B (k5_card_1 C) A D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t104_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k14_member_1 (k2_xboole_0 A B) C) = (k2_xboole_0 (k14_member_1 A C) (k14_member_1 B C))) ) ) ) ) ) ) ).
tt(t104_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden (k1_relset_1 A D) B) &  ((r1_xxreal_0 k6_numbers E) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A D)) =>  ((k12_supinf_2 D F) = E) ) ) ) )  =>  ((k5_mesfunc5 A B C D) = (k1_extreal1 (k1_measure6 E) (k12_supinf_2 C (k1_relset_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ((r3_mesfunc6 A B C D) =>  ((r3_mesfunc6 A B C (k2_partfun1 A k1_numbers D F)) &  ((k2_mesfunc6 A B C (k26_valued_1 A k1_numbers D E) F) = (k1_extreal1 (k1_measure6 E) (k2_mesfunc6 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r14_ncfcont1 A B C E) & (r14_ncfcont1 A B D F))  => (r14_ncfcont1 A B (k3_xboole_0 C D) (k2_vfunct_1 (u1_struct_0 A) B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r4_pboole A B (k4_pboole A C D)) => (r4_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t104_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k6_relat_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k6_relat_1 A C) (k6_relat_1 B C))) ) ) ) ) ).
tt(t104_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (~ (r2_hidden (k2_flang_1 A) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))))  =>  ((k3_rewrite3 A B C (k2_flang_1 A) D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t104_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k19_rvsum_1 (k2_finseq_2 (k23_binop_2 A B) C)) = (k11_binop_2 (k19_rvsum_1 (k2_finseq_2 A C)) (k19_rvsum_1 (k2_finseq_2 B C)))) ) ) ) ) ) ) ).
tt(t104_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k5_memstr_0 3 k1_scmfsa_2 A) = (k5_memstr_0 3 k1_scmfsa_2 B))  &  ( (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  &  (! [C:$i] :  ((m1_scmfsa_2 C) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 A C) (k18_scmfsa_2 B C))) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t104_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) G))) =>  ((k1_funct_1 (k6_scmpds_4 (k4_scmpds_6 E G C D) (k8_memstr_0 2 k1_scmpds_2 B) A) F) = (k1_funct_1 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 B) A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (A = (k7_scmyciel (k12_scmyciel A) (k3_tarski A))) ) ) ).
tt(t104_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r5_semi_af1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  & (r5_semi_af1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ((k22_seq_4 (k19_seq_4 A B C)) = (k22_seq_4 (k19_seq_4 A C B))) ) ) ) ) ) ) ).
tt(t104_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C C) C) = (k5_sheffer1 A (k5_sheffer1 A B B) B)) ) ) ) ) ) ) ).
tt(t104_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k7_square_1 2)) &  ((k12_sincos10 A) = (k10_real_1 k32_sin_cos 4)) ) )  =>  (A = (k7_square_1 2)) )  &  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k7_square_1 2)) &  ((k12_sincos10 A) = (k10_real_1 k32_sin_cos 2)) ) )  =>  (A = 1) ) ) ) ) ).
tt(t104_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k18_sin_cos (k6_sin_cos6 A)) = (k7_square_1 (k9_real_1 1 (k3_square_1 A)))) ) ) ) ).
tt(t104_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k2_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (C = (k1_taylor_1 2))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 B D) = 1) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k2_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k2_sin_cos9) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2))) A) D) = (k1_seq_1 k2_sin_cos9 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_tdlat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_tdlat_1 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ( ( (B = D)  &  (C = E) )  =>  ( ((k1_lattices (k12_tdlat_1 A) B C) = (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) D E))))  &  ((k2_lattices (k12_tdlat_1 A) B C) = (k9_subset_1 (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  <=>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k8_tmap_1 A B)) ) ) ) ) ) ).
tt(t104_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~ (r2_xboole_0 A B))  &  ( (~  (A = B) )  &  (~ (r2_xboole_0 B A)) ) ) )  <=> (r3_xboole_0 A B)) ) ) ).
tt(t104_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k6_xboolean B A)) = k2_xboolean) ) ) ) ) ).
tt(t104_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k7_xcmplx_0 (k7_xcmplx_0 A B) C) = (k3_xcmplx_0 (k7_xcmplx_0 1 B) (k7_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(t104_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 k6_numbers B) | (r1_xxreal_0 (k7_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 A C) & (r1_tarski (k1_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 k6_numbers C))  &  ( (~  (C = k2_xxreal_0) )  & (r1_xxreal_0 (k6_xxreal_3 A C) (k6_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t104_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang B C)) (k11_zf_lang A C))) & (r2_zf_model D (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang B C)) (k11_zf_lang A C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t104_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_xboole_0 A B) | (r1_xboole_0 C D))  => (r1_xboole_0 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) ) ) ) ) ).
tt(t104_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((k7_zmodul01 A B (k7_zmodul01 A C D)) = (k7_zmodul01 A (k7_zmodul01 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t105_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v9_abcmiz_1 B A) & (m1_abcmiz_1 B A (k12_abcmiz_1 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))))  =>  ((k48_abcmiz_1 A (k40_abcmiz_1 A C B)) = (k2_xboole_0 (k3_tarski (a_2_6_abcmiz_1 A C)) (k46_abcmiz_1 A B))) ) ) ) ) ) ) ).
tt(t105_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r5_aofa_000 A B C E D) <=> (r6_aofa_000 A B C E D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_card_3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((r4_wellord1 A B) & (v1_finset_1 A))  => (v1_finset_1 B)) ) ) ) ) ).
tt(t105_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) => (r1_xxreal_0 1 (k3_finseq_1 B))) ) ) ) ).
tt(t105_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k1_normsp_0 A B))) ) ) ) ).
tt(t105_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_fdiff_1 B H) &  ((r1_fdiff_1 C H) &  ((r1_fdiff_1 D H) &  ((r1_fdiff_1 E H) &  ((r1_fdiff_1 F H) & (r1_fdiff_1 G H)) ) ) ) )  =>  ((k8_euclid_8 (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B E) A) (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C F) A) (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D G) A) H) = (k7_euclid 3 (k9_euclid 3 (k8_euclid_8 B C D H) A) (k9_euclid 3 (k8_euclid_8 E F G H) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((v1_euclid_4 B A) &  ((v1_euclid_4 C A) &  ((r1_tarski B D) &  ((r1_tarski C D) &  ((r1_tarski B E) & (r1_tarski C E)) ) ) ) )  =>  ( (B = C)  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k4_finseq_2 (k2_xcmplx_0 A B) C) = (a_3_0_finseq_2 A B C)) ) ) ) ) ) ) ).
tt(t105_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) => (m2_finseq_1 (k2_finseq_3 A C) B)) ) ) ) ) ) ).
tt(t105_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((v1_finseq_6 D A) & (r2_finseq_4 D B))  =>  ((k1_finseq_6 A (k1_finseq_6 A D C) B) = (k1_finseq_6 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t105_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k2_flang_2 A B) (k8_flang_1 A C))) ) ) ) ) ) ).
tt(t105_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_funct_1 B A)) )  => (r1_tarski (k9_xtuple_0 B) (k9_xtuple_0 A))) ) ) ) ).
tt(t105_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((m1_setfam_1 D E) => (m1_setfam_1 (k6_funct_2 A B C (k7_funct_2 A B C D)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( (~  ((k1_funct_1 B A) = C) )  =>  ((k1_funct_1 (k6_funct_4 B C D) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t105_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r1_funct_7 A B D) => (r1_funct_7 (k1_funct_4 C A) (k1_funct_4 C B) D)) ) ) ) ) ) ) ) ).
tt(t105_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k41_gfacirc1 A B C)) = (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))) ) ) ) ).
tt(t105_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C (k14_glib_001 A B)) & (r1_glib_000 A D E C))  =>  ((r2_hidden D (k13_glib_001 A B)) & (r2_hidden E (k13_glib_001 A B))) ) ) ) ) ) ) ) ) ).
tt(t105_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k13_group_2 A D (k6_algstr_0 A B C)) = (k4_group_2 A B (k13_group_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t105_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( ((r6_group_3 A C D) & (r5_group_3 A D B))  => (r5_group_3 A C B)) ) ) ) ) ) ) ) ) ).
tt(t105_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( (D = (k20_group_9 A B C))  &  ((r2_hidden E (k4_finseq_1 D)) &  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_group_1 F) &  ((v3_group_1 F) &  ((v3_group_9 F A) & (l1_group_9 F A)) ) ) )  =>  ( (F = (k1_funct_1 D E))  => (v7_struct_0 F)) ) ) ) )  =>  ( ((v8_group_9 (k2_finseq_3 E C) A B) & (m2_finseq_1 (k2_finseq_3 E C) (k6_group_9 A B)))  &  (! [F:$i] :  ( ((v8_group_9 F A B) & (m2_finseq_1 F (k6_group_9 A B)))  =>  ( (F = (k2_finseq_3 E C))  =>  ((k20_group_9 A B F) = (k2_finseq_3 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k7_jgraph_4 A)) & (v3_tops_2 B (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t105_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_jordan2c,ax, ((k1_euclid k6_numbers) = (k1_seq_4 (k4_struct_0 (k15_euclid k6_numbers)))) ).
tt(t105_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) & (v6_limfunc1 B))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 C))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) )  &  (~  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 C)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 C))) => (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 B D))) ) ) ) ) ) ) )  | (r1_xxreal_0 (k5_limfunc1 A) (k5_limfunc1 B))) ) ) ) ) ) ).
tt(t105_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  ( ((k8_matrix13 C D) = B)  => (v2_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t105_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) => (r1_tarski (k14_member_1 (k3_xboole_0 A B) C) (k3_xboole_0 (k14_member_1 A C) (k14_member_1 B C)))) ) ) ) ) ) ).
tt(t105_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc5 A B C D) =>  ((r2_hidden (k8_relset_1 A k7_numbers D (k1_tarski k1_supinf_1)) B) &  ((r2_hidden (k8_relset_1 A k7_numbers D (k1_tarski k2_supinf_1)) B) &  ( ((k12_supinf_2 C (k8_relset_1 A k7_numbers D (k1_tarski k1_supinf_1))) = k6_numbers)  &  ( ((k12_supinf_2 C (k8_relset_1 A k7_numbers D (k1_tarski k2_supinf_1))) = k6_numbers)  &  ((r2_hidden (k4_subset_1 A (k8_relset_1 A k7_numbers D (k1_tarski k1_supinf_1)) (k8_relset_1 A k7_numbers D (k1_tarski k2_supinf_1))) B) &  ((k12_supinf_2 C (k4_subset_1 A (k8_relset_1 A k7_numbers D (k1_tarski k1_supinf_1)) (k8_relset_1 A k7_numbers D (k1_tarski k2_supinf_1)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r15_ncfcont1 B A C E) & (r15_ncfcont1 B A D F))  => (r15_ncfcont1 B A (k3_xboole_0 C D) (k2_vfunct_1 (u1_struct_0 B) A E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ( (~ (r4_pboole A B C))  & (r4_pboole A (k3_pboole A D B) (k3_pboole A D C))) ) ) ) ) ) ) ) ) ).
tt(t105_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k6_relat_1 (k6_subset_1 A B) C) = (k6_subset_1 (k6_relat_1 A C) (k6_relat_1 B C))) ) ) ) ) ).
tt(t105_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F D))  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G E))  =>  ( ( ((u1_struct_0 F) = (u1_struct_0 G))  &  ((u1_rewrite3 D F) = (u1_rewrite3 E G)) )  =>  ((k3_rewrite3 C D F A B) = (k3_rewrite3 C E G A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k19_rvsum_1 (k2_finseq_2 (k24_binop_2 A B) C)) = (k19_rvsum_1 (k2_finseq_2 B (k19_rvsum_1 (k2_finseq_2 A C))))) ) ) ) ) ) ) ).
tt(t105_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k9_scmpds_6 A B C)) = (k2_nat_1 (k5_card_1 C) 1)) ) ) ) ) ) ) ).
tt(t105_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v4_scmyciel B) &  ((v5_scmyciel B) & (m1_subset_1 B (k1_zfmisc_1 (k12_scmyciel A)))) ) )  =>  ((r1_xxreal_0 3 (k2_scmyciel B)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_tarski B)) =>  (~  (C = (k3_tarski A)) ) ) ) ) ) ) ) ) ).
tt(t105_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  &  ((r1_semi_af1 A B C E) &  ((r5_semi_af1 A B C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~ (r4_semi_af1 A C E D F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 A)) => (r1_xxreal_0 (k22_seq_4 (k19_seq_4 A B C)) (k9_binop_2 (k22_seq_4 (k19_seq_4 A B D)) (k22_seq_4 (k19_seq_4 A D C))))) ) ) ) ) ) ) ) ).
tt(t105_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A B (k5_sheffer1 A C C))) = B) ) ) ) ) ) ) ).
tt(t105_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_square_1 2)))  =>  ((r1_xxreal_0 k6_numbers (k9_sincos10 A)) & (r1_xxreal_0 (k9_sincos10 A) (k10_real_1 k32_sin_cos 4))) ) ) ) ).
tt(t105_sin_cos6,ax,(v6_valued_0 (k5_relset_1 k1_numbers k1_numbers k4_sin_cos6 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t105_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k10_real_1 D A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)) B) D) = (k7_real_1 (k1_seq_1 k1_sin_cos9 (k10_real_1 D A)) (k10_real_1 D (k8_real_1 A (k7_real_1 1 (k5_square_1 (k10_real_1 D A))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((k5_lattices (k12_tdlat_1 A)) = (k1_struct_0 A))  &  ((k6_lattices (k12_tdlat_1 A)) = (k2_struct_0 A)) ) ) ) ).
tt(t105_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  => (r1_funct_2 (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B)) (u1_struct_0 A) (u1_struct_0 A) (k9_tmap_1 A B) (k3_struct_0 A))) ) ) ) ).
tt(t105_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_xboole_0 A B) &  ((k4_xboole_0 B A) = k1_xboole_0) ) ) ) ) ).
tt(t105_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k6_xboolean (k6_xboolean A B) B)) = k2_xboolean) ) ) ) ) ).
tt(t105_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k7_xcmplx_0 (k7_xcmplx_0 A B) C) = (k3_xcmplx_0 (k7_xcmplx_0 1 C) (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t105_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k4_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t105_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_3 (k6_xxreal_3 A 2) (k6_xxreal_3 A 2)) = A) ) ) ).
tt(t105_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang A (k11_zf_lang B A))) & (r2_zf_model C (k11_zf_lang A (k11_zf_lang B A)))) ) ) ) ) ) ) ) ) ).
tt(t105_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 (k1_tarski C) D)) <=>  ( (A = C)  & (r2_hidden B D)) ) ) ) ) ) ).
tt(t105_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (m1_zmodul01 (k7_zmodul01 A B C) B)) ) ) ) ) ) ).
tt(t106_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v9_abcmiz_1 B A) & (m1_abcmiz_1 B A (k12_abcmiz_1 A)))  =>  ((k47_abcmiz_1 A (k40_abcmiz_1 A (k1_subset_1 (k38_abcmiz_1 A)) B)) = (k45_abcmiz_1 A B)) ) ) ) ) ).
tt(t106_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r5_aofa_000 A B C E D) =>  (! [F:$i] : (r6_aofa_000 A B C E D F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_card_3,ax, ((k10_card_3 (k1_tarski k1_xboole_0)) = k1_xboole_0) ).
tt(t106_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) & (v2_glib_000 B)) ) ) ) )  =>  (! [C:$i] :  ((m3_chord C A) =>  ((r5_glib_000 A B) => (m3_chord C B)) ) ) ) ) ) ) ).
tt(t106_clvect_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (r1_xxreal_0 (k1_normsp_0 C (k3_rlvect_1 C (k1_clvect_1 C D A) (k1_clvect_1 C E B))) (k7_real_1 (k8_real_1 (k17_complex1 A) (k1_normsp_0 C D)) (k8_real_1 (k17_complex1 B) (k1_normsp_0 C E))))) ) ) ) ) ) ) ) ) ) ).
tt(t106_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_fdiff_1 B H) &  ((r1_fdiff_1 C H) &  ((r1_fdiff_1 D H) &  ((r1_fdiff_1 E H) &  ((r1_fdiff_1 F H) & (r1_fdiff_1 G H)) ) ) ) )  =>  ((k8_euclid_8 (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B E) A) (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C F) A) (k26_valued_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers D G) A) H) = (k8_euclid 3 (k9_euclid 3 (k8_euclid_8 B C D H) A) (k9_euclid 3 (k8_euclid_8 E F G H) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r5_euclidlp A B C) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r1_tarski B D) &  ((r1_tarski C D) & (v1_euclidlp D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A B)) & (m2_finseq_1 D C))  =>  (? [E:$i] :  ((m2_finseq_2 E C (k4_finseq_2 A C)) &  (? [F:$i] :  ((m2_finseq_2 F C (k4_finseq_2 B C)) &  (D = (k8_finseq_1 C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k10_xtuple_0 (k2_finseq_3 A B)) (k10_xtuple_0 B))) ) ) ) ).
tt(t106_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v1_finseq_6 C A) & (r2_finseq_4 C B))  =>  ((k4_finseq_5 A (k1_finseq_6 A C B)) = (k1_finseq_6 A (k4_finseq_5 A C) B)) ) ) ) ) ) ) ) ).
tt(t106_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k8_flang_1 A C)) =>  ((k8_flang_1 A C) = (k8_flang_1 A (k4_subset_1 (k8_afinsq_1 A) C (k2_flang_2 A B)))) ) ) ) ) ) ) ).
tt(t106_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  ((r2_hidden B (k9_xtuple_0 C)) => (m1_subset_1 (k1_funct_1 C B) A)) ) ) ) ) ).
tt(t106_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) => (r1_tarski (k5_setfam_1 B (k7_funct_2 A B C (k6_funct_2 A B C D))) (k5_setfam_1 B D))) ) ) ) ) ) ) ) ).
tt(t106_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden A (k9_xtuple_0 B)) &  ((k1_funct_1 B A) = C) )  =>  ((k1_funct_1 (k6_funct_4 B C D) A) = D) ) ) ) ) ) ) ).
tt(t106_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k1_funct_4 A C) = (k1_funct_4 B C))  <=> (r1_funct_7 A B (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t106_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k43_gfacirc1 A B C)) = (k2_xboole_0 (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) (k1_tarski (k45_gfacirc1 A B C)))) ) ) ) ).
tt(t106_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k14_glib_001 A (k8_glib_001 A B C D)) (k14_glib_001 A B))) ) ) ) ) ) ) ) ).
tt(t106_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k5_group_2 A C (k13_group_2 A D B)) = (k4_group_2 A B (k14_group_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t106_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  ((r2_hidden A (k9_group_3 B C)) =>  ((v15_algstr_0 A) & (m1_group_2 A B)) ) ) ) ) ) ) ).
tt(t106_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  ( (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 F (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  &  ((r6_group_9 A B C F) &  (E = (k1_funct_1 (k2_funct_2 (k4_finseq_1 B) F) D)) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_1 (k2_finseq_3 D B)) (k4_finseq_1 (k2_finseq_3 D B))) &  ((v3_funct_2 F (k4_finseq_1 (k2_finseq_3 D B)) (k4_finseq_1 (k2_finseq_3 D B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 (k2_finseq_3 D B)) (k4_finseq_1 (k2_finseq_3 D B)))))) ) )  =>  (~ (r6_group_9 A (k2_finseq_3 D B) (k2_finseq_3 E C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 (k17_euclid B) k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 (k17_euclid C) k6_numbers))  & (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) => (v9_rltopsp1 (k1_jordan2c A B) (k15_euclid A))) ) ) ) ) ).
tt(t106_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) )  =>  ( ( (~ (v4_limfunc1 A))  &  (~ (v5_limfunc1 A)) )  |  ((v3_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A)) &  ((k4_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A)) = k6_numbers) ) ) ) ) ) ).
tt(t106_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_vectsp_6 F D (k6_prvect_1 D B)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 D) A B) =>  ( ((r2_hidden C (k2_finseq_1 (k3_finseq_1 G))) &  (E = (k1_funct_1 F (k1_funct_1 G C))) )  =>  ((k8_matrix_1 (u1_struct_0 D) (k10_matrix13 D B (k3_vectsp_6 D (k6_prvect_1 D B) (k11_matrix13 D A B G) F)) C) = (k10_fvsum_1 (k1_matrix_1 G) D (k8_matrix_1 (u1_struct_0 D) G C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k14_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k14_member_1 A B) (k14_member_1 A C))) ) ) ) ) ) ) ).
tt(t106_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  ((v6_supinf_2 D) & (v6_supinf_2 E)) ) )  => (r1_mesfunc5 A B C (k3_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_ncfcont1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r13_ncfcont1 B C D E) => (r13_ncfcont1 B C D (k2_vfunct_2 (u1_struct_0 B) C E A))) ) ) ) ) ) ) ) ) ) ).
tt(t106_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r4_pboole A B (k4_pboole A C D)) => (r4_pboole A C (k4_pboole A B D))) ) ) ) ) ) ) ) ).
tt(t106_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k6_relat_1 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t106_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k21_rvsum_1 (k5_finseq_2 k1_numbers A (k11_binop_2 B C))) = (k11_binop_2 (k19_rvsum_1 (k2_finseq_2 A B)) (k19_rvsum_1 (k2_finseq_2 A C)))) ) ) ) ) ) ) ).
tt(t106_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r2_hidden k6_numbers (k9_xtuple_0 (k9_scmpds_6 A B C)))) ) ) ) ) ) ).
tt(t106_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ( ((k8_scmyciel A) = k6_numbers)  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v4_scmyciel B) &  ((v5_scmyciel B) & (m1_subset_1 B (k1_zfmisc_1 (k12_scmyciel A)))) ) )  => (r1_xxreal_0 (k2_scmyciel B) 1)) ) ) ) ) ).
tt(t106_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (B = k1_xboole_0)  => (v1_seq_4 B A)) ) ) ) ) ).
tt(t106_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A B B)) (k5_sheffer1 A B C)) = C) ) ) ) ) ) ) ).
tt(t106_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) & (r1_xxreal_0 A (k1_real_1 1)))  =>  ((r1_xxreal_0 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) (k10_sincos10 A)) & (r1_xxreal_0 (k10_sincos10 A) k32_sin_cos)) ) ) ) ).
tt(t106_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k4_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1)) &  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ((k1_fdiff_1 k4_sin_cos6 A) = (k1_real_1 (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k3_square_1 A)))))) ) ) ) ) ) ) ) ).
tt(t106_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k10_real_1 D A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)) B) D) = (k9_real_1 (k1_seq_1 k2_sin_cos9 (k10_real_1 D A)) (k10_real_1 D (k8_real_1 A (k7_real_1 1 (k5_square_1 (k10_real_1 D A))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_tdlat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_tdlat_1 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_lattices (k12_tdlat_1 A) B C) <=> (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r1_tsep_1 B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (r1_tmap_1 C (k8_tmap_1 A B) (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t106_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k4_xboole_0 B C)) =>  ((r1_tarski A B) & (r1_xboole_0 A C)) ) ) ) ) ).
tt(t106_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A B) (k6_xboolean (k6_xboolean B C) (k6_xboolean A C))) = k2_xboolean) ) ) ) ) ) ) ).
tt(t106_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_xcmplx_0 A (k7_xcmplx_0 1 A)) = 1) ) ) ) ).
tt(t106_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k3_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k2_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k11_zf_lang (k11_zf_lang A (k11_zf_lang B C)) (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang A C)))) & (r2_zf_model D (k11_zf_lang (k11_zf_lang A (k11_zf_lang B C)) (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t106_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 C (k1_tarski D))) <=>  ((r2_hidden A C) &  (B = D) ) ) ) ) ) ) ).
tt(t106_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ((m1_zmodul01 C B) <=>  ((k7_zmodul01 A C B) = C) ) ) ) ) ) ) ) ).
tt(t107_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((v4_abcmiz_1 B A (k28_abcmiz_1 A)) <=>  ((k45_abcmiz_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t107_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ( ((v15_aofa_000 E A) & (m1_subset_1 E (u1_struct_0 A)))  =>  (! [F:$i] : (r6_aofa_000 A B C E D F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_funct_1 C B) & (v1_partfun1 C A)) ) ) )  => (r2_hidden C (k4_card_3 B))) ) ) ) ) ).
tt(t107_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (~  ((r1_xxreal_0 C (k3_finseq_1 B)) & (v1_xboole_0 (k4_chord A B C))) ) ) ) ) ) ) ) ).
tt(t107_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t107_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_fdiff_1 B H) &  ((r1_fdiff_1 C H) &  ((r1_fdiff_1 D H) &  ((r1_fdiff_1 E H) &  ((r1_fdiff_1 F H) & (r1_fdiff_1 G H)) ) ) ) )  =>  ((k8_euclid_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers B A) E) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A) F) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers D A) G) H) = (k7_euclid 3 (k9_euclid 3 (k1_euclid_8 (k11_binop_2 (k1_seq_1 E H) (k1_fdiff_1 B H)) (k11_binop_2 (k1_seq_1 F H) (k1_fdiff_1 C H)) (k11_binop_2 (k1_seq_1 G H) (k1_fdiff_1 D H))) A) (k9_euclid 3 (k1_euclid_8 (k11_binop_2 (k1_seq_1 B H) (k1_fdiff_1 E H)) (k11_binop_2 (k1_seq_1 C H) (k1_fdiff_1 F H)) (k11_binop_2 (k1_seq_1 D H) (k1_fdiff_1 G H))) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r6_euclidlp A B C) &  ( (~ (r1_xboole_0 B C))  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((v1_euclidlp D A) &  ((r1_tarski B D) & (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D C))  =>  (! [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E C))  =>  ((v3_card_1 (k8_finseq_1 C D E) (k2_xcmplx_0 A B)) & (m2_finseq_1 (k8_finseq_1 C D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( (A = (k1_nat_1 B 1))  & (r2_hidden C (k2_finseq_1 A)))  =>  ((k3_finseq_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k2_finseq_1 A) (k1_tarski C)))) = B) ) ) ) ) ) ) ) ).
tt(t107_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zfmisc_1 B) & (m2_finseq_1 B A))  =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k12_finseq_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t107_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k6_flang_1 A (k2_flang_2 A B) (k8_flang_1 A B)) = (k6_flang_1 A (k8_flang_1 A B) (k2_flang_2 A B))) ) ) ) ).
tt(t107_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r1_tarski B (k9_xtuple_0 A)))  =>  ((k7_relat_1 (k2_funct_1 A) (k7_relat_1 A B)) = B) ) ) ) ) ).
tt(t107_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski (k5_setfam_1 A D) (k5_setfam_1 A (k6_funct_2 A B C (k7_funct_2 A B C D))))) ) ) ) ) ) ) ) ).
tt(t107_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden B (k9_xtuple_0 A)))  => (r1_tarski A (k1_funct_4 A (k16_funcop_1 B C)))) ) ) ) ) ).
tt(t107_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((k1_funct_1 D A) = (k1_funct_1 D B))  =>  ((k1_funct_1 D C) = (k1_funct_1 (k3_relat_1 (k2_funct_7 (k6_partfun1 (k9_xtuple_0 D)) A B) D) C)) ) ) ) ) ) ) ).
tt(t107_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k43_gfacirc1 A B C)))) ) ) ).
tt(t107_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k14_glib_001 A B) = (k14_glib_001 A (k6_glib_001 A B))) ) ) ) ) ).
tt(t107_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k5_group_2 A C (k14_group_2 A D B)) = (k14_group_2 A D (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t107_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r2_hidden B (k9_group_3 A C)) <=> (r6_group_3 A B C)) ) ) ) ) ) ) ).
tt(t107_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (! [E:$i] :  ( ((v8_group_9 E A C) & (m2_finseq_1 E (k6_group_9 A C)))  =>  ( ((v1_xboole_0 D) & (v1_xboole_0 E))  => (r5_group_9 A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t107_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) k6_numbers))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  &  (~  ( (~ (r1_xxreal_0 (k17_euclid C) k6_numbers))  &  (~ (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_jordan2c,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 C A) &  ((v3_connsp_1 D A) &  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  & (r1_xboole_0 D B)) ) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) )  =>  ( ( (~ (v7_limfunc1 A))  &  (~ (v8_limfunc1 A)) )  |  ((v6_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A)) &  ((k5_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A)) = k6_numbers) ) ) ) ) ) ).
tt(t107_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E D (k6_prvect_1 D C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) A C) =>  ( ((v2_funct_1 F) &  ((r1_tarski (k1_vectsp_6 D (k6_prvect_1 D C) E) (k9_matrix13 D A C F)) & (r2_hidden B (k2_finseq_1 C))) )  =>  ((k1_funct_1 (k4_vectsp_6 D (k6_prvect_1 D C) E) B) = (k4_rlvect_1 D (k9_matrix_1 (u1_struct_0 D) (k10_matrix13 D C (k3_vectsp_6 D (k6_prvect_1 D C) (k11_matrix13 D A C F) E)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) => (r1_tarski (k14_member_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k14_member_1 A B) (k14_member_1 A C)))) ) ) ) ) ) ).
tt(t107_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) & (r1_mesfunc5 A B C E))  => (r2_hidden (k1_relset_1 A (k3_mesfunc1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_ncfcont1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r14_ncfcont1 B C D E) => (r14_ncfcont1 B C D (k4_vfunct_1 (u1_struct_0 B) C E A))) ) ) ) ) ) ) ) ) ) ).
tt(t107_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ( (~ (r5_pboole A B C))  &  ((r2_pboole A C D) & (r5_pboole A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t107_relat_1,ax, (! [A:$i] :  ((k6_relat_1 A k1_xboole_0) = k1_xboole_0) ) ).
tt(t107_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k21_rvsum_1 (k15_rvsum_1 A B C)) = (k11_binop_2 (k21_rvsum_1 B) (k21_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t107_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_funct_1 (k9_scmpds_6 A B C) k6_numbers) = (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 1))) ) ) ) ) ) ) ).
tt(t107_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((k3_tarski A) = (k1_tarski B))  =>  ((k12_scmyciel A) = (k3_enumset1 k1_xboole_0 (k1_tarski B) (k1_tarski (k4_tarski B (k3_tarski A))) (k1_tarski (k3_tarski A)) (k2_tarski (k4_tarski B (k3_tarski A)) (k3_tarski A)))) ) ) ) ) ).
tt(t107_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (B = (k14_seq_4 A))  => (v1_seq_4 B A)) ) ) ) ) ).
tt(t107_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A C (k5_sheffer1 A B B))) = C) ) ) ) ) ) ) ).
tt(t107_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) & (r1_xxreal_0 A (k1_real_1 1)))  =>  ((r1_xxreal_0 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k11_sincos10 A)) & (r1_xxreal_0 (k11_sincos10 A) (k1_real_1 (k10_real_1 k32_sin_cos 4)))) ) ) ) ).
tt(t107_sin_cos6,ax,(v1_fcont_1 (k5_relset_1 k1_numbers k1_numbers k4_sin_cos6 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t107_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ( (D = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2)))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 E F) = (k10_real_1 F A)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) F) = (k10_real_1 (k8_real_1 2 F) (k5_square_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k12_tdlat_1 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_tdlat_1 A))) &  ((r4_lattice3 (k12_tdlat_1 A) C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_tdlat_1 A))) =>  ((r4_lattice3 (k12_tdlat_1 A) D B) => (r1_lattices (k12_tdlat_1 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t107_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_tmap_1 B (k8_tmap_1 A B) (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) B) C)) ) ) ) ) ) ).
tt(t107_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k5_xboole_0 B C)) <=>  ((r1_tarski A (k2_xboole_0 B C)) & (r1_xboole_0 A (k3_xboole_0 B C))) ) ) ) ) ).
tt(t107_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A B) (k6_xboolean (k6_xboolean C A) (k6_xboolean C B))) = k2_xboolean) ) ) ) ) ) ) ).
tt(t107_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k3_xcmplx_0 (k3_xcmplx_0 B A) (k7_xcmplx_0 1 A))) ) ) ) ) ) ).
tt(t107_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k3_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k3_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t107_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k7_zf_lang A B) A)) & (r2_zf_model C (k11_zf_lang (k7_zf_lang A B) A))) ) ) ) ) ) ) ) ) ).
tt(t107_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = k1_xboole_0) )  =>  ( (~  ((k2_zfmisc_1 (k1_tarski B) A) = k1_xboole_0) )  &  (~  ((k2_zfmisc_1 A (k1_tarski B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t107_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k7_zmodul01 A (k3_zmodul01 A) B) = (k3_zmodul01 A)) ) ) ) ) ).
tt(t108_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_abcmiz_1 B A (k28_abcmiz_1 A)) &  ((v9_abcmiz_1 B A) & (m1_abcmiz_1 B A (k12_abcmiz_1 A))) )  => (v10_abcmiz_1 (k40_abcmiz_1 A (k1_subset_1 (k38_abcmiz_1 A)) B) A)) ) ) ) ).
tt(t108_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r7_aofa_000 A B C E D B)) ) ) ) ) ) ) ) ) ) ).
tt(t108_card_3,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v2_card_3 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B A) =>  ((k9_xtuple_0 B) = (k9_card_3 A)) ) ) ) ) ) ).
tt(t108_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v4_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (? [C:$i] :  ((m3_chord C A) &  ( (C = (k12_finseq_1 (k6_glib_000 A) B))  & (v7_chord C A)) ) ) ) ) ) ) ).
tt(t108_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k5_algstr_0 A C B))) ) ) ) ) ) ) ).
tt(t108_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_fdiff_1 B H) &  ((r1_fdiff_1 C H) &  ((r1_fdiff_1 D H) &  ((r1_fdiff_1 E (k1_seq_1 B H)) &  ((r1_fdiff_1 F (k1_seq_1 C H)) & (r1_fdiff_1 G (k1_seq_1 D H))) ) ) ) )  =>  ((k8_euclid_8 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers E A)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers F A)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k26_valued_1 k1_numbers k1_numbers G A)) H) = (k9_euclid 3 (k1_euclid_8 (k11_binop_2 (k1_fdiff_1 E (k1_seq_1 B H)) (k1_fdiff_1 B H)) (k11_binop_2 (k1_fdiff_1 F (k1_seq_1 C H)) (k1_fdiff_1 C H)) (k11_binop_2 (k1_fdiff_1 G (k1_seq_1 D H)) (k1_fdiff_1 D H))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((r1_tarski C F) &  ((r1_tarski D F) &  ((r1_tarski E F) &  ((r2_hidden B C) &  ((r2_hidden B D) &  ((r2_hidden B E) &  ((r6_euclidlp A C E) & (r6_euclidlp A D E)) ) ) ) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_finseq_2 A) = (k3_tarski (a_1_3_finseq_2 A))) ) ) ).
tt(t108_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (D = (k1_nat_1 C 1))  &  ((r2_hidden B (k2_finseq_1 D)) & (r2_hidden A (k2_finseq_1 C))) )  =>  ( ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 B A) |  ((k1_funct_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k2_finseq_1 D) (k1_tarski B))) A) = A) ) )  &  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 A C))  =>  ((k1_funct_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k2_finseq_1 D) (k1_tarski B))) A) = (k1_nat_1 A 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (~ (r1_xxreal_0 A (k3_finseq_1 B)))  &  ( ((r1_xxreal_0 A (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) | (r1_xxreal_0 A (k3_finseq_1 (k7_finseq_1 B C))))  &  (~  ((k1_funct_1 (k7_finseq_1 B C) A) = (k1_funct_1 C (k5_real_1 A (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k6_flang_1 A (k2_flang_2 A B) (k8_flang_1 A B)) = (k8_flang_1 A B)) ) ) ) ).
tt(t108_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A B) & (r2_hidden A (k9_xtuple_0 C)))  => (r2_hidden (k1_funct_1 C A) (k7_relat_1 C B))) ) ) ) ) ).
tt(t108_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A))))  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r1_tarski (k2_relset_1 C D) (k1_relset_1 C E)) =>  ( (B = k1_xboole_0)  |  ((k1_funct_1 (k8_funct_2 B A C D E) F) = (k1_funct_1 E (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ((v1_funct_1 (k1_funct_4 C (k16_funcop_1 D E))) & (m1_subset_1 (k1_funct_4 C (k16_funcop_1 D E)) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ).
tt(t108_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) =>  ((r2_hidden B (k9_xtuple_0 C)) &  ((k1_funct_1 C A) = (k1_funct_1 C B)) ) )  =>  (C = (k3_relat_1 (k2_funct_7 (k6_partfun1 (k9_xtuple_0 C)) A B) C)) ) ) ) ) ) ).
tt(t108_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  ((k2_msafree2 (k41_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t108_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) <=>  ((k14_glib_001 A (k2_glib_001 A C D B)) = (k1_tarski B)) ) ) ) ) ) ) ).
tt(t108_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r2_hidden B (k13_group_2 A C B)) & (r2_hidden B (k14_group_2 A C B))) ) ) ) ) ) ) ).
tt(t108_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  => (r2_hidden (k6_group_3 A C B) (k9_group_3 A C))) ) ) ) ) ) ).
tt(t108_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (! [E:$i] :  ( ((v8_group_9 E A C) & (m2_finseq_1 E (k6_group_9 A C)))  =>  (~  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~  ((r5_group_9 A B C D E) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_1 (k20_group_9 A B D)) (k4_finseq_1 (k20_group_9 A B D))) &  ((v3_funct_2 F (k4_finseq_1 (k20_group_9 A B D)) (k4_finseq_1 (k20_group_9 A B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 (k20_group_9 A B D)) (k4_finseq_1 (k20_group_9 A B D)))))) ) )  & (r6_group_9 A (k20_group_9 A B D) (k20_group_9 A C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) & (r1_xxreal_0 A (k13_complex1 (k18_euclid C) (k12_euclid C))))  =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 (k17_euclid B) k6_numbers) |  ((r1_xxreal_0 (k17_euclid C) k6_numbers) |  ((r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v9_rltopsp1 A (k15_euclid 2)) & (v1_jordan1 A))  => (r1_jordan2c 2 A (k1_jordan2c 2 A))) ) ) ).
tt(t108_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ( ((k4_limfunc1 A) = k6_numbers)  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B))) &  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) ) )  | (v4_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t108_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B A) =>  (~  ((v2_funct_1 D) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 B)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (~  ((k8_matrix_1 (u1_struct_0 C) E F) = (k10_fvsum_1 (k1_matrix_1 D) C (k8_matrix_1 (u1_struct_0 C) D F) G)) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m2_vectsp_6 F C (k6_prvect_1 C A) (k9_matrix13 C B A D)) =>  (~  ((k3_vectsp_6 C (k6_prvect_1 C A) (k11_matrix13 C B A D) F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k14_member_1 (k12_member_1 A B) C) = (k12_member_1 A (k14_member_1 B C))) ) ) ) ) ) ) ).
tt(t108_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) & (r1_mesfunc5 A B C E))  => (r1_mesfunc5 A B C (k3_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_ncfcont1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r15_ncfcont1 C B D E) => (r15_ncfcont1 C B D (k2_vfunct_2 (u1_struct_0 C) B E A))) ) ) ) ) ) ) ) ) ) ).
tt(t108_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r5_pboole A B (k4_pboole A C B))) ) ) ) ) ).
tt(t108_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k6_relat_1 A (k3_relat_1 B C)) = (k3_relat_1 B (k6_relat_1 A C))) ) ) ) ) ) ).
tt(t108_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k21_rvsum_1 (k11_rvsum_1 A C B)) = (k11_binop_2 (k19_rvsum_1 (k2_finseq_2 A B)) (k21_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t108_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((r1_scmpds_6 (k9_scmpds_6 D E C) B A) & (r2_scmpds_6 (k9_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ( ((k8_scmyciel A) = 1)  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v4_scmyciel B) &  ((v5_scmyciel B) & (m1_subset_1 B (k1_zfmisc_1 (k12_scmyciel A)))) ) )  => (r1_xxreal_0 (k2_scmyciel B) 2)) ) ) ) ) ).
tt(t108_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k14_seq_4 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ((r2_hidden C B) => (v1_seq_4 C A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (C = (k3_tarski B))  => (v1_seq_4 C A)) ) ) ) ) ) ) ) ).
tt(t108_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A B B)) (k5_sheffer1 A C (k5_sheffer1 A B B))) (k5_sheffer1 A B C))) = (k5_sheffer1 A B C)) ) ) ) ) ) ) ).
tt(t108_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_square_1 2)))  =>  ((r1_xxreal_0 (k10_real_1 k32_sin_cos 4) (k12_sincos10 A)) & (r1_xxreal_0 (k12_sincos10 A) (k10_real_1 k32_sin_cos 2))) ) ) ) ).
tt(t108_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k7_real_1 (k3_sin_cos6 A) (k6_sin_cos6 A)) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t108_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k10_real_1 A 2)))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ( (D = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2)))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 E F) = (k10_real_1 F A)) ) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k10_real_1 A 2)) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k10_real_1 A 2)) B) F) = (k10_real_1 F (k8_real_1 A (k7_real_1 1 (k5_square_1 (k10_real_1 F A)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v4_lattice3 (k12_tdlat_1 A))) ) ).
tt(t108_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r1_tsep_1 B C) =>  ((v1_funct_1 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) C)) &  ((v1_funct_2 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) C) (u1_struct_0 C) (u1_struct_0 (k8_tmap_1 A B))) &  ((v5_pre_topc (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) C) C (k8_tmap_1 A B)) & (m1_subset_1 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k8_tmap_1 A B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t108_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k3_xboole_0 A C) B)) ) ) ) ).
tt(t108_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean (k6_xboolean A (k6_xboolean A B)) (k6_xboolean A B)) = k2_xboolean) ) ) ) ) ).
tt(t108_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k3_xcmplx_0 B (k3_xcmplx_0 (k7_xcmplx_0 1 A) A))) ) ) ) ) ) ).
tt(t108_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k3_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) & (r1_tarski (k1_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t108_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k7_zf_lang A B) B)) & (r2_zf_model C (k11_zf_lang (k7_zf_lang A B) B))) ) ) ) ) ) ) ) ) ).
tt(t108_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  =>  ((r1_xboole_0 (k2_zfmisc_1 (k1_tarski A) C) (k2_zfmisc_1 (k1_tarski B) D)) & (r1_xboole_0 (k2_zfmisc_1 C (k1_tarski A)) (k2_zfmisc_1 D (k1_tarski B)))) ) ) ) ) ) ).
tt(t108_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((k7_zmodul01 A (k3_zmodul01 A) (k4_zmodul01 A)) = (k3_zmodul01 A)) ) ) ).
tt(t109_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k49_abcmiz_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k49_abcmiz_1)) =>  ((r3_orders_2 k49_abcmiz_1 A B) <=> (r1_tarski B A)) ) ) ) ) ).
tt(t109_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r7_aofa_000 A B C F D E) & (r7_aofa_000 A B C G D E))  => (r7_aofa_000 A B C (k13_aofa_000 A F G) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_funct_1 B))  =>  ( (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C B) => (r2_hidden A (k9_xtuple_0 C))) ) )  => (r2_hidden A (k9_card_3 B))) ) ) ) ).
tt(t109_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_chord B A) =>  ((v7_chord B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ( ((r1_chord A C D) & (r1_chord A C E))  =>  ( (D = E)  |  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r2_hidden F (k4_finseq_1 B)) &  ((r2_hidden G (k4_finseq_1 B)) &  ((r2_hidden H (k4_finseq_1 B)) &  ( ((k1_funct_1 B F) = C)  &  ( ((k1_funct_1 B G) = D)  &  ((k1_funct_1 B H) = E) ) ) ) ) )  =>  ((r1_xxreal_0 G F) |  ((r1_xxreal_0 H F) | (r1_chord A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k9_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)) (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t109_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_fdiff_1 B H) &  ((r1_fdiff_1 C H) &  ((r1_fdiff_1 D H) &  ((r1_fdiff_1 E H) &  ((r1_fdiff_1 F H) & (r1_fdiff_1 G H)) ) ) ) )  =>  ( ((k1_seq_1 E H) = k6_numbers)  |  ( ((k1_seq_1 F H) = k6_numbers)  |  ( ((k1_seq_1 G H) = k6_numbers)  |  ((k8_euclid_8 (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers B A) E) (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A) F) (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers D A) G) H) = (k9_euclid 3 (k1_euclid_8 (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B H) (k1_seq_1 E H)) (k11_binop_2 (k1_fdiff_1 E H) (k1_seq_1 B H))) (k5_square_1 (k1_seq_1 E H))) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C H) (k1_seq_1 F H)) (k11_binop_2 (k1_fdiff_1 F H) (k1_seq_1 C H))) (k5_square_1 (k1_seq_1 F H))) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 D H) (k1_seq_1 G H)) (k11_binop_2 (k1_fdiff_1 G H) (k1_seq_1 D H))) (k5_square_1 (k1_seq_1 G H)))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r7_euclidlp A B C) &  ((r6_euclidlp A B C) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t109_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D C))  => (m2_finseq_2 D B (k4_finseq_2 A B))) ) ) ) ) ) ) ) ).
tt(t109_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ((k3_finseq_1 C) = (k1_nat_1 A 1))  & (r2_hidden B (k1_relset_1 k5_numbers C)))  =>  ((k3_finseq_1 (k2_finseq_3 B C)) = A) ) ) ) ) ) ) ) ).
tt(t109_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) =>  ( ((k1_funct_1 (k7_finseq_1 C (k9_finseq_1 B)) 1) = (k1_funct_1 C 1))  &  ( ((k1_funct_1 (k7_finseq_1 C (k9_finseq_1 B)) 1) = (k7_partfun1 A C 1))  &  ( ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 B) C) (k2_nat_1 (k3_finseq_1 C) 1)) = (k1_funct_1 C (k3_finseq_1 C)))  &  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 B) C) (k2_nat_1 (k3_finseq_1 C) 1)) = (k7_partfun1 A C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t109_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k7_flang_1 A (k2_flang_2 A B) C) (k8_flang_1 A B))) ) ) ) ) ).
tt(t109_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( (~  (A = k1_xboole_0) )  &  ((r1_tarski A (k9_xtuple_0 B)) &  ((k7_relat_1 B A) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t109_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A))))  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r1_tarski (k2_relset_1 C D) (k1_relset_1 C E)) =>  ( (B = k1_xboole_0)  |  ((k1_funct_1 (k8_funct_2 B A C D E) F) = (k7_partfun1 A E (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 (k7_funcop_1 B C) (k16_funcop_1 B A))) = (k1_ordinal1 B)) ) ) ) ).
tt(t109_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_4 A (k16_funcop_1 B (k1_funct_1 A B))) = A) ) ) ) ) ).
tt(t109_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  ((k2_msafree2 (k43_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t109_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (r1_tarski (k14_glib_001 A B) (k21_glib_000 A (k13_glib_001 A B)))) ) ) ) ).
tt(t109_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((k13_group_2 A B (k1_group_1 A)) = (k8_group_2 A B))  &  ((k14_group_2 A B (k1_group_1 A)) = (k8_group_2 A B)) ) ) ) ) ) ).
tt(t109_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r2_hidden B (k9_group_3 A B))) ) ) ) ).
tt(t109_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ((r4_group_9 A B C D) &  ((v10_group_9 D A B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 (k20_group_9 A B C))) &  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_group_1 F) &  ((v3_group_1 F) &  ((v3_group_9 F A) & (l1_group_9 F A)) ) ) )  =>  ( (F = (k1_funct_1 (k20_group_9 A B C) E))  => (v7_struct_0 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) k6_numbers))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 (k17_euclid C) k6_numbers))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid C) (k12_euclid C))))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ((r2_hidden C (k3_topreal1 2 (k1_sprect_1 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D (k1_jordan2c 2 (k3_topreal1 2 (k1_sprect_1 A)))) &  (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ( ((k4_limfunc1 A) = k6_numbers)  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B))) &  (~ (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) ) )  | (v5_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t109_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  ((v2_funct_1 D) =>  ( ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k2_finseq_1 B)) &  ((k8_matrix_1 (u1_struct_0 C) D E) = (k5_finseq_2 (u1_struct_0 C) A (k4_struct_0 C))) ) ) ) )  &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B A) =>  ( ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 B)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (~  ((k8_matrix_1 (u1_struct_0 C) E F) = (k10_fvsum_1 (k1_matrix_1 D) C (k8_matrix_1 (u1_struct_0 C) D F) G)) ) ) ) ) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k4_rlvect_1 C (k9_matrix_1 (u1_struct_0 C) E F)) = (k4_struct_0 C)) ) ) ) )  =>  (E = (k1_matrix_3 C B A)) ) ) ) )  <=> (v1_vectsp_7 (k9_matrix13 C B A D) C (k6_prvect_1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t109_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k12_member_1 (k14_member_1 A B) C) = (k14_member_1 (k12_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t109_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k7_mesfunc5 A B C (k3_mesfunc1 A D E)) = (k3_supinf_2 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r13_ncfcont1 A B C D) =>  ((r13_ncfcont1 A B C (k5_vfunct_1 (u1_struct_0 A) B D)) & (r17_ncfcont1 A C (k3_normsp_0 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t109_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r5_pboole A (k3_pboole A B C) (k4_pboole A B C))) ) ) ) ) ).
tt(t109_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k5_relat_1 (k6_relat_1 A C) B) = (k6_relat_1 A (k5_relat_1 C B))) ) ) ) ) ).
tt(t109_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k21_rvsum_1 (k13_rvsum_1 A B)) = (k5_square_1 (k21_rvsum_1 B))) ) ) ) ) ).
tt(t109_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) =>  ((r1_scmpds_6 (k9_scmpds_6 D E C) B A) & (r2_scmpds_6 (k9_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ((r1_xxreal_0 2 (k8_scmyciel A)) =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v4_scmyciel B) &  ((v5_scmyciel B) & (m1_subset_1 B (k1_zfmisc_1 (k12_scmyciel A)))) ) )  => (r1_xxreal_0 (k2_scmyciel B) (k8_scmyciel A))) ) ) ) ) ).
tt(t109_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( ((v1_seq_4 B A) & (v1_seq_4 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (D = (k9_subset_1 (k14_seq_4 A) B C))  => (v1_seq_4 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t109_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A B B)) (k5_sheffer1 A C B)) = C) ) ) ) ) ) ) ).
tt(t109_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 (k7_square_1 2) A))  &  (~  ( (~ (r1_xxreal_0 (k9_sincos10 A) k6_numbers))  &  (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 4) (k9_sincos10 A))) ) ) ) ) ) ) ) ).
tt(t109_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k9_real_1 (k6_sin_cos6 (k4_xcmplx_0 A)) (k3_sin_cos6 A)) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t109_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 C F) = (k10_real_1 F A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C F))) ) ) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 D F) = 1) ) ) )  &  ( (E = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 C F) = (k10_real_1 F A)) ) ) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))) B) F) = (k1_seq_1 k1_sin_cos9 (k10_real_1 F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v3_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k12_tdlat_1 A)))) =>  ( (C = B)  =>  ((k15_lattice3 (k12_tdlat_1 A) C) = (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ).
tt(t109_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((v1_funct_1 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) B)) &  ((v1_funct_2 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) B) (u1_struct_0 B) (u1_struct_0 (k8_tmap_1 A B))) &  ((v5_pre_topc (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) B) B (k8_tmap_1 A B)) & (m1_subset_1 (k2_tmap_1 A (k8_tmap_1 A B) (k9_tmap_1 A B) B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k8_tmap_1 A B)))))) ) ) ) ) ) ) ).
tt(t109_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k4_xboole_0 A C) B)) ) ) ) ).
tt(t109_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A (k6_xboolean B C)) (k6_xboolean (k6_xboolean A B) (k6_xboolean A C))) = k2_xboolean) ) ) ) ) ) ) ).
tt(t109_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k3_xcmplx_0 (k3_xcmplx_0 B (k7_xcmplx_0 1 A)) A)) ) ) ) ) ) ).
tt(t109_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k3_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) & (r1_tarski (k1_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t109_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k7_zf_lang A B) (k7_zf_lang B A))) & (r2_zf_model C (k11_zf_lang (k7_zf_lang A B) (k7_zf_lang B A)))) ) ) ) ) ) ) ) ) ).
tt(t109_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k2_zfmisc_1 (k2_tarski A B) C) = (k2_xboole_0 (k2_zfmisc_1 (k1_tarski A) C) (k2_zfmisc_1 (k1_tarski B) C)))  &  ((k2_zfmisc_1 C (k2_tarski A B)) = (k2_xboole_0 (k2_zfmisc_1 C (k1_tarski A)) (k2_zfmisc_1 C (k1_tarski B)))) ) ) ) ) ).
tt(t109_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ((k7_zmodul01 A (k4_zmodul01 A) B) = B) ) ) ) ) ).
tt(t10_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l2_abcmiz_0 A)) ) ) )  =>  ((v9_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (r1_tarski (k2_abcmiz_0 A C) (k2_abcmiz_0 A B))) ) ) ) ) ) ) ) ).
tt(t10_abcmiz_1,ax, (! [A:$i] :  ((k1_abcmiz_1 (k3_tarski A)) = (k3_tarski (a_1_0_abcmiz_1 A))) ) ).
tt(t10_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) )  => (r1_subset_1 k2_abcmiz_1 (u4_struct_0 A))) ) ).
tt(t10_abian,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k3_funct_2 B B (k1_abian B C (k2_nat_1 A 1)) D) = (k3_funct_2 B B C (k3_funct_2 B B (k1_abian B C A) D))) ) ) ) ) ) ) ) ) ).
tt(t10_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 (k13_complex1 A B) k6_numbers))  =>  ((k6_square_1 (k13_complex1 A B)) = (k13_complex1 (k7_square_1 (k18_complex1 A)) (k7_square_1 (k18_complex1 B)))) ) ) ) ) ) ).
tt(t10_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C D) & (r1_aff_1 A B C E))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_aff_2 A) <=>  ((v2_aff_2 A) & (v13_aff_2 A)) ) ) ) ).
tt(t10_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_3 A) => (v6_aff_3 A)) ) ) ).
tt(t10_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B F) &  ((r2_hidden C G) &  ((r2_hidden D G) &  (B = E) ) ) )  =>  ( ( (~ (r5_aff_1 A F G))  &  (~ (r5_aff_1 A G F)) )  |  ( (F = G)  |  ( ( (~ (r2_analoaf A B C E D))  &  (~ (r2_analoaf A C B D E)) )  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A)) =>  ((v1_relat_1 (k3_relat_1 B A)) &  ((v5_ordinal1 (k3_relat_1 B A)) &  ((v1_funct_1 (k3_relat_1 B A)) & (v1_finset_1 (k3_relat_1 B A))) ) ) ) ) ) ) ) ).
tt(t10_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((k2_afinsq_2 A k6_numbers) = A) ) ) ).
tt(t10_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 B A) =>  (! [C:$i] :  ((r2_hidden C (k6_afproj A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (C = D)  &  ((v1_aff_4 D A) & (r1_aff_4 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_afvect01 A B C) & (r2_analoaf A B C C D))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t10_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A F G C B) & (r2_analoaf A F H E D)) )  =>  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((r4_alg_1 A B C) &  (D = (k2_funct_1 C)) )  => (r4_alg_1 B A D)) ) ) ) ) ) ) ) ) ).
tt(t10_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (~  ( ((k1_algseq_1 B C) = (k1_nat_1 A 1))  &  ((k1_funct_1 C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t10_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 B) = A)  =>  ((k1_algspec1 A B) = B) ) ) ) ) ).
tt(t10_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_algstr_0)) =>  ((k6_algstr_0 k8_algstr_0 A B) = (k5_struct_0 k8_algstr_0)) ) ) ) ) ).
tt(t10_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k1_algstr_0 A C B)) ) ) ) )  &  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k5_struct_0 A) B) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = (k6_algstr_0 A D B))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_algstr_4 B A) <=> (r1_tarski (k2_group_2 A B B) B)) ) ) ) ) ).
tt(t10_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_binop_1 (k17_funcop_1 A B C) A B) = C) ) ) ) ).
tt(t10_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tarski (k8_mcart_1 (u4_struct_0 A) (u4_struct_0 A) (k2_cat_1 A C D) (k2_cat_1 A B C)) (k9_xtuple_0 (u1_cat_1 A)))) ) ) ) ) ) ) ) ).
tt(t10_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  ((v5_altcat_3 E A B C) &  ((v5_altcat_3 F A C D) &  (~ (v5_altcat_3 (k5_altcat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_altcat_3 B A) & (r2_altcat_3 A C B))  => (v7_altcat_3 C A)) ) ) ) ) ) ) ).
tt(t10_ami_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_ami_2 k2_ami_2) =>  ((k5_card_3 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) = k4_numbers) ) ) ).
tt(t10_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = B) )  &  ((k10_ami_3 A) = (k10_ami_3 B)) ) ) ) ) ) ) ).
tt(t10_ami_4,ax,(r2_extpro_1 2 k1_ami_3 k1_ami_4 (k7_memstr_0 2 k1_ami_3 k6_numbers) k2_ami_4)).
tt(t10_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 3)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k4_ami_3 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  ( (A = 7)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_ami_3) A))) = (k1_tarski 1)) ) ) ) ).
tt(t10_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 (k4_amistd_1 A))) =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) C) = 1)  =>  ((k1_amistd_1 A (k4_amistd_1 A) B C) = (k1_tarski (k1_ordinal1 B))) ) ) ) ) ) ) ) ).
tt(t10_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C A) &  ((v3_memstr_0 C A) & (l1_extpro_1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A C)) & (v1_partfun1 D (u1_struct_0 C))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 C)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 C)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 C)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ((r1_tarski E F) &  ((r1_tarski E G) &  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B H))  => (r2_hidden (k5_memstr_0 A C (k5_extpro_1 A C G D H)) (k2_afinsq_1 E))) ) ) ) )  =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r1_xxreal_0 H B) => (r8_pboole (u1_struct_0 C) (k5_extpro_1 A C F D H) (k5_extpro_1 A C G D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) <=> (v1_xboole_0 (k2_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t10_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  (~ (v2_compos_1 D B)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 E))  & (v1_finset_1 E)) ) ) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 E)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ( ((r1_tarski E F) & (v4_extpro_1 (k9_memstr_0 A B E C) A B (k6_compos_1 B D C)))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 B)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ((r1_tarski D G) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 B) (k5_extpro_1 A B G F H) (k10_memstr_0 A B (k5_extpro_1 A B (k1_funct_4 G (k6_compos_1 B D C)) (k1_funct_4 F (k9_memstr_0 A B E C)) H) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  => (v1_ami_wstd B A)) ) ) ) ).
tt(t10_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r2_analmetr A D E B C) & (r2_analmetr A D F B C)) )  =>  ((r2_analmetr A D (k3_rlvect_1 A E F) B C) & (r2_analmetr A D (k5_algstr_0 A E F) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analoaf A B C C B) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t10_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k2_analort A B C (k3_rlvect_1 A D E)) = (k3_rlvect_1 A (k2_analort A B C D) (k2_analort A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  (D = (k4_struct_0 A)) ) ) ) )  => (r2_anproj_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t10_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (? [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) &  ( ((k3_funct_2 A k1_numbers C B) = 1)  &  (! [D:$i] :  ((r2_hidden D A) =>  ( (D = B)  |  ((k1_funct_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~ (r1_tarski (k5_aofa_000 A C) D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ((k1_funct_1 (k7_aofa_000 A D B) C) = (k1_funct_1 (k9_funct_7 A E) C))  &  ( (~ (r2_hidden (k1_funct_1 (k9_funct_7 A E) C) D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  => (r2_hidden (k1_funct_1 (k9_funct_7 A F) C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) &  ((v1_funct_2 B (k1_card_1 A) A) &  ((v2_funct_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_card_1 A) A)))) ) ) )  => (r2_hidden (k1_funct_1 B k6_numbers) A)) ) ) ) ).
tt(t10_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_armstrng A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_armstrng A))) =>  ((r2_hidden (k4_tarski B C) (k5_armstrng A)) <=> (r2_armstrng A B C)) ) ) ) ) ) ) ).
tt(t10_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k2_arrow A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (k2_arrow A)) =>  (~  ( (~ (r1_arrow F C B))  &  ( (~ (r1_arrow F D B))  &  ( (~  ( (~ (r1_arrow F D C))  & (r1_arrow E D C)) )  &  ( (~  ( (~ (r1_arrow E D C))  & (r1_arrow F D C)) )  &  ( (~  ( (~ (r1_arrow F C D))  & (r1_arrow E C D)) )  &  (~  ( (~ (r1_arrow E C D))  & (r1_arrow F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k5_arytm_0 A B) = (k5_arytm_0 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r1_arytm_2 A B) &  ((k1_arytm_1 B A) = k11_arytm_3) )  =>  (A = B) ) ) ) ) ) ).
tt(t10_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( (~  ((k7_arytm_2 A C) = B) )  &  (~  ((k7_arytm_2 B C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t10_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( ((r2_hidden k1_xboole_0 B) & (r2_arytm_3 A B))  => (r1_ordinal1 A B)) ) ) ) ) ).
tt(t10_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (r2_hidden A (k6_asympt_0 A))) ) ).
tt(t10_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k7_real_1 (k9_real_1 (k4_nat_1 3 (k5_series_1 10 6)) (k4_nat_1 (k4_nat_1 18 (k5_series_1 10 3)) B)) (k8_real_1 27 (k5_square_1 B)))) ) )  => (r2_hidden A (k6_asympt_0 (k3_asympt_1 2)))) ) ) ).
tt(t10_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r1_pzfmisc1 A B C) & (r1_pzfmisc1 A C D))  => (r1_pzfmisc1 A B D)) ) ) ) ) ) ) ) ).
tt(t10_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_autgroup A))) =>  ( (B = C)  =>  ((k2_funct_1 B) = (k2_group_1 (k3_autgroup A) C)) ) ) ) ) ) ) ) ).
tt(t10_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v1_wellfnd1 A) &  ((v1_bagorder B A) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ((v7_ordinal1 D) &  ((r1_xxreal_0 C D) &  (~  ((k8_nat_1 (u1_struct_0 A) B C) = (k8_nat_1 (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) (k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))))) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t10_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k1_bcialg_2 A (k1_bcialg_2 A B C D) C E) = (k1_bcialg_2 A B C (k2_nat_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))) = (k1_bcialg_1 A B C))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A (k1_bcialg_1 A B C) B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t10_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_4 A (k1_bcialg_4 A B C) D) = (k1_bcialg_4 A B (k1_bcialg_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t10_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_bcialg_5 A B C D (k2_nat_1 E 1)) = (k1_bcialg_1 A (k1_bcialg_5 A B C D E) (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_bcialg_6 A C (k2_bcialg_1 A B)) = (k3_bcialg_6 A (k19_binop_2 C) B)) ) ) ) ) ) ) ).
tt(t10_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((m2_bcialg_1 (k5_bcialg_1 A) A) =>  ((v12_bcialg_1 (k5_bcialg_1 A) A) & (m2_bcialg_1 (k5_bcialg_1 A) A)) ) ) ) ).
tt(t10_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k4_algstr_0 A B) (k4_algstr_0 A C)) = (k2_bhsp_1 A B C)) ) ) ) ) ) ) ).
tt(t10_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 C) & (r2_hidden B (k10_xtuple_0 C)))  =>  ((k1_bhsp_2 A C) = B) ) ) ) ) ) ) ) ).
tt(t10_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r1_bhsp_3 A B B)) ) ) ) ).
tt(t10_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v3_bhsp_3 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k3_bhsp_1 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) E) (k1_normsp_1 A (k1_bhsp_4 A B) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r1_tarski C (k9_xtuple_0 D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski C (k9_xtuple_0 E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k1_funct_1 E F) = (k1_funct_1 (u1_bhsp_1 A) (k4_tarski B (k1_funct_1 D F)))) ) ) ) )  =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  ( ((v2_funct_1 F) &  ((k10_xtuple_0 F) = C) )  =>  ((k1_funct_1 (u1_bhsp_1 A) (k4_tarski B (k1_finsop_1 (u1_struct_0 A) (k4_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) D F) (u1_algstr_0 A)))) = (k1_finsop_1 k1_numbers (k4_bhsp_5 k1_numbers (u1_struct_0 A) E F) k33_binop_2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v3_bhsp_3 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_bhsp_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 D))  &  ((r1_tarski D B) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 E))  &  ((r1_tarski E B) &  ((r1_xboole_0 D E) & (r1_xxreal_0 C (k3_bhsp_1 A (k1_bhsp_6 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k1_bilinear A B C) D) (k7_hahnban1 A C))) ) ) ) ) ) ) ) ).
tt(t10_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))) = (k21_binop_2 (k6_binarith A B) (k15_funcop_1 k5_numbers C k7_margrel1 k6_numbers (k5_series_1 2 A)))) ) ) ) ) ) ) ).
tt(t10_binari_3,ax, ((k1_binari_2 1) = (k10_binarith k6_margrel1 k8_margrel1)) ).
tt(t10_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k23_binop_2 B C) (k21_binop_2 (k5_series_1 2 A) 1)) =>  ((k8_binarith A (k1_binari_3 A B) (k1_binari_3 A C)) = k7_margrel1) ) ) ) ) ) ) ) ).
tt(t10_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k5_xboolean A k8_margrel1) = k8_margrel1) ) ) ).
tt(t10_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_binom A B (k2_xcmplx_0 C D)) = (k6_algstr_0 A (k2_binom A B C) (k2_binom A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r3_binop_1 A C B) & (r3_binop_1 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t10_binop_2,ax, ((k4_binop_1 k5_numbers k48_binop_2) = 1) ).
tt(t10_bintree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) &  ((v2_dtconstr A) &  ((v3_bintree1 A) & (l1_lang1 A)) ) ) )  =>  (! [B:$i] :  ((m1_trees_4 B (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lang1 A C (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) B)) =>  ((m2_subset_1 C (u1_struct_0 A) (k7_dtconstr A)) &  ( ((k4_finseq_1 B) = (k2_tarski 1 2))  &  ((r2_hidden 1 (k4_finseq_1 B)) &  ((r2_hidden 2 (k4_finseq_1 B)) &  (? [D:$i] :  ((m1_dtconstr D (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) &  (? [E:$i] :  ((m1_dtconstr E (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) &  ( ((k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) B) = (k4_pre_poly (u1_struct_0 A) (k1_bintree1 (u1_struct_0 A) D) (k1_bintree1 (u1_struct_0 A) E)))  &  ( (D = (k1_funct_1 B 1))  &  ( (E = (k1_funct_1 B 2))  &  ( ((k8_trees_4 (u1_struct_0 A) C B) = (k6_trees_4 C D E))  &  ((r2_hidden D (k2_relset_1 (k5_trees_3 (u1_struct_0 A)) B)) & (r2_hidden E (k2_relset_1 (k5_trees_3 (u1_struct_0 A)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (A = (k3_finseq_2 (k7_domain_1 k5_numbers k6_numbers 1)))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden (k5_euclid B) (k2_trees_2 A B))) ) ) ) ) ).
tt(t10_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A B C) &  ((r3_lattices A B D) & (r1_boolealg A (k4_lattices A C D) (k5_lattices A))) )  => (r1_boolealg A B (k5_lattices A))) ) ) ) ) ) ) ) ) ).
tt(t10_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_boolmark A B C) <=> (r2_boolmark A B (k12_finseq_1 (u4_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t10_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_bor_cant A B C D) =>  ((k3_funct_2 B k1_numbers C (k1_prob_2 A B (k1_prob_3 A (k2_prob_1 A D)) E)) = (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B (k2_prob_1 A D) C)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k4_borsuk_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 C D)))) =>  ((v3_pre_topc G (k2_borsuk_1 C D)) => (v3_pre_topc (k8_relset_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 C D)) (k3_borsuk_2 A C B D E F) G) (k2_borsuk_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v3_pre_topc C (k2_borsuk_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  (! [D:$i] :  (~  ((r1_tarski (k2_zfmisc_1 (k1_tarski D) (u1_struct_0 B)) C) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) & (v1_partfun1 E (u1_struct_0 B))) ) )  =>  (? [F:$i] :  ((r2_hidden F (u1_struct_0 B)) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_funct_1 E F) = (k1_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 B)) G H))  &  ((r2_hidden (k4_tarski D F) (k3_borsuk_1 A B G H)) &  ((v3_pre_topc G A) &  ((v3_pre_topc H B) & (r1_tarski (k3_borsuk_1 A B G H) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_rcomp_1 B C))  =>  ((r1_xxreal_0 C B) | (r1_tarski (k1_rcomp_1 B C) (u1_struct_0 k5_topmetr))) ) ) ) ) ) ) ) ).
tt(t10_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r1_xxreal_0 D E) &  ( (A = (k3_rcomp_1 C D))  &  (B = (k4_rcomp_1 E F)) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) | (r1_connsp_1 k3_topmetr A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_0_borsuk_6)  &  (B = a_0_1_borsuk_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 1 k6_numbers (k10_real_1 1 2) (k10_real_1 1 2)) A) = B) ) ) ) ) ) ).
tt(t10_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( ((k20_sin_cos A) = (k20_sin_cos B))  &  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (A = (k3_real_1 B (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) )  &  (~  (A = (k3_real_1 (k4_xcmplx_0 B) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_brouwer,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C (k2_brouwer 2 B A)))  =>  (~  ( (C = (k7_toprealb 2 B A))  & (r1_borsuk_1 (k2_brouwer 2 B A) C)) ) ) ) ) ) ) ) ).
tt(t10_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_bspace A B) = (k4_struct_0 k2_bspace))  <=>  (~ (r2_hidden B A)) ) ) ) ).
tt(t10_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A D E)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B (k2_bvfunc_1 A (k2_bvfunc_1 A C D) E)) (k9_bvfunc_1 A C (k2_bvfunc_1 A D E))) (k9_bvfunc_1 A D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  ( (B = (k2_enumset1 C D E F))  =>  ( (C = F)  |  ( (D = F)  |  ( (E = F)  |  ((k5_bvfunc_2 A F B) = (k2_partit1 A (k2_partit1 A C E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k12_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t10_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k6_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t10_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k2_bvfunc_1 A C D)) (k5_bvfunc26 A (k2_bvfunc_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t10_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k11_bvfunc_1 A) B D) (k11_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t10_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k5_bvfunc_1 A C D) B E) (k5_bvfunc_1 A (k7_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) <=>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C B) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t10_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k1_bvfunc_1 A C)) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A B) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t10_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k2_bvfunc_1 A C (k1_bvfunc_1 A C))) (k1_bvfunc_1 A B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t10_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k9_bvfunc_1 A B C)) (k2_bvfunc_1 A B C))) ) ) ) ) ) ).
tt(t10_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B C) (k2_bvfunc_1 A B (k5_bvfunc_1 A (k1_bvfunc_1 A B) C)))) ) ) ) ) ) ).
tt(t10_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t10_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m2_c0sp1 (k7_c0sp1 A) (k12_funcsdom A))) ) ).
tt(t10_c0sp2,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_funcsdom B) & (l1_funcsdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((g1_funcsdom (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u3_struct_0 A) (u2_struct_0 A)) = B)  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_funcsdom A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_calcul_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 (k7_finseq_1 B (k9_finseq_1 A)))) & (r2_hidden (k3_finseq_1 (k7_finseq_1 B (k9_finseq_1 A))) (k1_relset_1 k5_numbers (k7_finseq_1 B (k9_finseq_1 A))))) ) ) ) ).
tt(t10_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k3_finseq_1 (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)))) = (k3_finseq_1 C)) ) ) ) ) ) ) ).
tt(t10_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (a_2_0_cantor_1 A B))  =>  ((k8_setfam_1 A C) = (k8_setfam_1 A (k5_setfam_1 (k9_setfam_1 A) B))) ) ) ) ) ) ) ).
tt(t10_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((v2_funct_1 C) &  ( ((k9_xtuple_0 C) = A)  & (r1_tarski (k10_xtuple_0 C) B)) ) ) ) ) ) ) ).
tt(t10_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  (! [D:$i] :  ( (~  (C = D) )  =>  ((r2_wellord2 (k1_card_2 A B) (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski C)) (k2_zfmisc_1 B (k1_tarski D)))) &  ((k1_card_2 A B) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski C)) (k2_zfmisc_1 B (k1_tarski D))))) ) ) ) ) ) ) ) ) ).
tt(t10_card_3,ax, ((k4_card_3 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t10_card_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v4_card_3 A) => (v4_card_3 (k4_finseq_2 B A))) ) ) ) ) ).
tt(t10_card_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ((v2_ordinal2 A) & (v2_ordinal2 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t10_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  (! [C:$i] :  ((m2_card_fil C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D B) & (r2_hidden D (k1_card_fil A B))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D C) & (r2_hidden D (k7_setfam_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cardfin2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k5_card_1 (k2_cardfin2 A)) = (k1_cardfin2 (k12_binop_2 (k3_newton (k5_card_1 A)) k8_power))) ) ) ).
tt(t10_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 D (k5_card_1 C)))  => (v1_xboole_0 (k1_card_fin C D A B))) ) ) ) ) ) ) ).
tt(t10_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  ((v2_card_lar (k2_subset_1 A) A) & (v1_card_lar (k2_subset_1 A) A)) ) ) ).
tt(t10_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_cat_1 G B C D) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k2_cat_1 B C D) = k1_xboole_0)  | (m1_cat_1 G A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  => (r1_funct_2 A (u4_struct_0 (k2_oppcat_1 (k2_oppcat_1 B))) A (u4_struct_0 B) (k4_cat_3 (k2_oppcat_1 B) A (k4_cat_3 B A C)) C)) ) ) ) ) ).
tt(t10_cat_4,ax, (! [A:$i] :  (! [B:$i] : (v3_cat_4 (k5_cat_4 A B))) ) ).
tt(t10_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ( ( ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B)))  & (v3_cat_5 A))  => (v3_cat_5 B)) ) ) ) ) ).
tt(t10_catalan1,ax, ((k1_catalan1 k6_numbers) = k6_numbers) ).
tt(t10_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ((v1_catalan2 C) & (r1_xxreal_0 A (k21_binop_2 (k23_binop_2 B (k1_afinsq_1 C)) (k24_binop_2 2 (k7_afinsq_2 C)))))  => (v1_catalan2 (k1_catalan2 (k1_catalan2 (k8_funcop_1 k5_numbers B k6_numbers) C) (k8_funcop_1 k5_numbers A 1)))) ) ) ) ) ) ) ).
tt(t10_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_catalg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden (k5_catalg_1 C) (u4_struct_0 B)) &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden (k6_catalg_1 C D) (u1_struct_0 B)) &  (! [E:$i] :  ((m1_subset_1 E A) => (r2_hidden (k7_catalg_1 C D E) (u4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cayley,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) => (v1_group_6 (k3_cayley A B C) (k2_cayley A) (k2_cayley B))) ) ) ) ) ) ) ).
tt(t10_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k2_numbers B A)) => (v4_xxreal_2 (k5_cc0sp1 A B))) ) ) ) ) ).
tt(t10_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cc0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k2_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k3_rlvect_1 (k3_cc0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers G H) = (k8_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers E H) (k3_funct_2 (u1_struct_0 A) k2_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_tarski (k2_relset_1 k2_numbers A) (k1_relset_1 k2_numbers (k2_cfunct_1 k2_numbers B))) => (v2_relat_1 (k8_funct_2 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(t10_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  ((v6_cfdiff_1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~ (r1_tarski (a_2_0_cfdiff_1 B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers (k1_cfuncdom A) (k4_cfuncdom A) B) B)) ) ) ) ).
tt(t10_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k8_relset_1 A k1_numbers (k55_valued_1 A k2_numbers B) (k1_tarski k6_numbers)) = (k8_relset_1 A k2_numbers B (k1_tarski k6_numbers)))  &  ((k8_relset_1 A k2_numbers (k31_valued_1 A k2_numbers B) (k1_tarski k6_numbers)) = (k8_relset_1 A k2_numbers B (k1_tarski k6_numbers))) ) ) ) ) ) ).
tt(t10_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v2_cgames_1 C) =>  ( ((r2_hidden C (k2_cgames_1 B)) & (r2_hidden A (k8_cgames_1 C)))  => (r2_hidden A (k2_cgames_1 B))) ) ) ) ) ) ).
tt(t10_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_abian A))  =>  ((r1_xxreal_0 A 1) =>  (A = k6_numbers) ) ) ) ).
tt(t10_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A D))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 C F))) =>  ( (G = (k5_relat_1 H (u1_struct_0 A)))  =>  ((k6_circuit2 A D G) = (k5_relat_1 (k6_circuit2 C F H) (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  ((r2_circcomb A B D E) =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( (F = (k3_circcomb A B D E))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( ( (H = (k5_relat_1 G (u1_struct_0 A)))  & (v1_circcmb3 H A D))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (I = (k5_relat_1 (k5_facirc_1 C F G (k2_circcmb3 A D H)) (u1_struct_0 B)))  & (v1_circcmb3 I B E))  =>  ((k2_circcmb3 C F G) = (k2_nat_1 (k2_circcmb3 A D H) (k2_circcmb3 B E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) & (l1_msualg_1 B)) )  => (v8_struct_0 (k2_circcomb A B))) ) ) ) ).
tt(t10_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_circled1 A B) (k2_circled1 A C))) ) ) ) ) ) ) ).
tt(t10_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((k1_circtrm1 A B (k4_subset_1 (k1_msaterm A B) C D)) = (k2_circcomb (k1_circtrm1 A B C) (k1_circtrm1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_circuit1 A B C) = 1)  <=> (r2_hidden C (k4_subset_1 (u1_struct_0 A) (k2_msafree2 A) (k1_msafree2 A)))) ) ) ) ) ) ) ).
tt(t10_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ((r2_hidden C (k2_msafree2 A)) =>  ((k5_circuit2 A B C D) = (k1_funct_1 D C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A (k3_classes1 B (k1_ordinal1 C))) <=>  (~  ( (~  ((r1_tarski A (k3_classes1 B C)) & (r2_hidden A (k1_classes1 B))) )  &  (! [D:$i] :  (~  ((r2_hidden D (k3_classes1 B C)) &  ((r1_tarski A D) |  (A = (k9_setfam_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_classes2,ax, (! [A:$i] :  ((k2_ordinal1 (k1_classes1 A)) = (k1_card_1 (k1_classes1 A))) ) ).
tt(t10_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))))  &  ((v13_algstr_0 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v2_rlvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v3_rlvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v4_rlvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v2_clvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v3_clvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v4_clvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) &  ((v5_clvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B))) & (l1_clvect_1 (g1_clvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k2_clopban1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  ((k3_clopban2 A B (k2_clopban2 A C D)) = (k2_clopban2 A (k3_clopban2 A B C) (k3_clopban2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k1_valued_0 (u1_struct_0 A) C D))) ) )  | (v9_clvect_1 C A)) ) ) ) ) ) ) ) ).
tt(t10_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A (k1_bhsp_4 A C) B)) (k1_seq_1 (k3_series_1 (k4_normsp_0 A C)) B))) ) ) ) ) ) ).
tt(t10_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_pboole C A B) =>  (! [D:$i] :  ((m1_pboole D A B) =>  ((m1_pboole (k2_pboole A C D) A B) => (r6_pboole A (k16_pralg_1 A (k2_msualg_3 A B) (k2_pboole A C D)) (k2_pboole A (k1_closure1 A B B (k2_msualg_3 A B) C) (k1_closure1 A B B (k2_msualg_3 A B) D)))) ) ) ) ) ) ) ) ).
tt(t10_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_closure2 C A B (k2_closure2 A B)) =>  (! [D:$i] :  ((m1_closure2 D A B (k2_closure2 A B)) => (r2_hidden (k2_pboole A C D) (k2_closure2 A B))) ) ) ) ) ) ) ).
tt(t10_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) => (r6_pboole A (k2_closure3 A B (k3_closure3 A B C D)) (k2_pboole A (k2_closure3 A B C) (k2_closure3 A B D)))) ) ) ) ) ) ) ).
tt(t10_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k1_clvect_1 A B (k6_xcmplx_0 C D)) = (k5_algstr_0 A (k1_clvect_1 A B C) (k1_clvect_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 C) & (r2_hidden B (k10_xtuple_0 C)))  =>  ((k1_clvect_2 A C) = B) ) ) ) ) ) ) ) ).
tt(t10_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) &  ((v4_clvect_2 A) & (l1_csspace A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k13_csspace A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) E) (k1_normsp_1 A (k1_bhsp_4 A B) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cohsp_1,ax, (! [A:$i] :  (! [B:$i] : (v1_cohsp_1 (k1_enumset1 A B (k2_xboole_0 A B)))) ) ).
tt(t10_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ((r2_hidden (k3_tarski A) A) =>  (A = (k9_setfam_1 (k3_tarski A))) ) ) ) ).
tt(t10_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k1_collsp A B C)) & (r2_hidden C (k1_collsp A B C))) ) ) ) ) ) ) ).
tt(t10_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k1_combgras A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k1_combgras A B))) =>  ((r1_incsp_1 (k1_combgras A B) C D) <=> (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_complex1 (k3_xcmplx_0 A k7_complex1)) = k6_numbers) ) ) ).
tt(t10_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k17_sin_cos A) = k6_numbers)  &  ((k20_sin_cos A) = k6_numbers) ) ) ) ) ).
tt(t10_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k4_algstr_0 k1_complfld A) = (k8_group_1 k1_complfld (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld)) A)) ) ) ).
tt(t10_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k45_valued_1 A B) = (k1_valued_1 A (k30_valued_1 B))) ) ) ) ) ) ).
tt(t10_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v4_tbsp_1 A) <=>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) &  ((v7_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) ) ) )  =>  (~  ((v2_prob_1 B) &  ( ((k2_seq_2 (k1_compl_sp A B)) = k6_numbers)  & (v1_xboole_0 (k2_kurato_0 (u1_struct_0 A) B))) ) ) ) ) ) ) ) ).
tt(t10_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C A) &  ((k2_compos_0 A C) = B) ) ) ) ) ) ) ).
tt(t10_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k5_card_1 (k1_compos_2 A B C)) = (k2_xcmplx_0 (k5_card_1 C) 1)) ) ) ) ) ) ) ).
tt(t10_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))) => (r1_xxreal_0 (k1_seq_1 k16_sin_cos A) k6_numbers)) ) ) ).
tt(t10_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_compts_1 B A) & (v2_compts_1 C A))  => (v2_compts_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t10_comput_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_finseq_2 B A) => (r1_tarski B (k3_finseq_2 A))) ) ) ).
tt(t10_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k2_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B) (k19_valued_1 k5_numbers k2_numbers k2_numbers A C)))) ) ) ) ) ) ).
tt(t10_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A C) = B) ) )  =>  ((k3_comseq_2 A) = B) ) ) ) ) ) ).
tt(t10_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ((k3_comseq_2 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) = k5_complex1) ) )  =>  ((k3_comseq_2 A) = (k3_comseq_2 B)) ) ) ) ) ) ).
tt(t10_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ((r1_tarski C (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) <=> (r1_relset_1 (u1_struct_0 A) (u4_struct_0 A) (k8_mcart_1 (u1_struct_0 A) (u4_struct_0 A) B C) (u1_conlat_1 A))) ) ) ) ) ) ) ).
tt(t10_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k16_lattice3 (k11_conlat_1 A) (a_2_5_conlat_2 A B)) = B) ) ) ) ) ).
tt(t10_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_2 A) <=> (v6_conmetr1 A)) ) ) ).
tt(t10_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v4_conmetr A) => (v7_conmetr A)) ) ) ).
tt(t10_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_connsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ( (~  (B = (k1_struct_0 A)) )  &  ( (~  (C = (k1_struct_0 A)) )  &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_pre_topc A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((m1_connsp_2 E A F) &  ( (D = E)  &  (C = F) ) )  => (m1_connsp_2 D (k1_pre_topc A B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 B A) &  ((v2_connsp_1 C A) & (r1_tarski C B)) )  =>  ( (C = k1_xboole_0)  |  (B = (k1_connsp_3 A C)) ) ) ) ) ) ) ) ) ).
tt(t10_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = k1_xboole_0)  => (v1_convex1 B A)) ) ) ) ) ).
tt(t10_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k3_rusub_4 A (k1_rlsub_2 A B C)) = (k7_rusub_4 A (k3_rusub_4 A B) (k3_rusub_4 A C))) ) ) ) ) ) ) ).
tt(t10_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ((k3_convex4 A (k3_finseq_4 (u1_struct_0 A) B C D) E) = (k3_finseq_4 (u1_struct_0 A) (k1_clvect_1 A B (k3_funct_2 (u1_struct_0 A) k2_numbers E B)) (k1_clvect_1 A C (k3_funct_2 (u1_struct_0 A) k2_numbers E C)) (k1_clvect_1 A D (k3_funct_2 (u1_struct_0 A) k2_numbers E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (m2_subset_1 (k2_qc_lang2 A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ).
tt(t10_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_qc_lang2 A B (k6_cqc_lang A B))) ) ) ) ).
tt(t10_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A C D) (k7_cqc_lang A D C)) (k1_cqc_the1 A B))) ) ) ) ) ) ) ) ).
tt(t10_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A (k6_qc_lang2 A C D B))))  &  (~ (r2_hidden D (k24_qc_lang1 A (k6_qc_lang2 A C D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r2_cqc_the3 A C (k6_domain_1 (k3_cqc_lang A) B)) <=> (r3_cqc_the1 A C B)) ) ) ) ) ) ) ).
tt(t10_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_3 A) => (r1_xxreal_0 (k17_complex1 (k11_comseq_3 A)) (k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)))) ) ) ).
tt(t10_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_csspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_csspace4 A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) &  ((v1_csspace4 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_csspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (E = C)  &  (F = D) )  =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( (D = (k1_clvect_1 (k5_csspace4 A B) C G))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A (u1_struct_0 B) F H) = (k1_clvect_1 B (k3_funct_2 A (u1_struct_0 B) E H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  ((k1_clvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) A k6_complex1) = A) ) ) ).
tt(t10_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_decomp_1 A) (k14_decomp_1 A)) = (u1_pre_topc A)) ) ) ).
tt(t10_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A (k8_descip_1 A B C) D) = (k8_descip_1 A B (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v3_dickson A) & (v16_waybel_0 A))  => (r3_orders_1 (k2_dickson A) (k8_eqrel_1 (u1_struct_0 A) (k1_dickson A)))) ) ) ).
tt(t10_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers F B) (k26_valued_1 k1_numbers k1_numbers G C)) D) (k2_nat_1 A 1)) E) = (k7_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 F D) (k2_nat_1 A 1)) E)) (k8_real_1 C (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 G D) (k2_nat_1 A 1)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k1_numbers k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k11_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers G A) (k26_valued_1 k1_numbers k1_numbers H B)) C D E F) = (k7_real_1 (k8_real_1 A (k11_diff_1 G C D E F)) (k8_real_1 B (k11_diff_1 H C D E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers F B) (k26_valued_1 k1_numbers k1_numbers G C)) D) (k2_nat_1 A 1)) E) = (k9_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 F D) (k2_nat_1 A 1)) E)) (k8_real_1 C (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 G D) (k2_nat_1 A 1)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k2_fdiff_9)) & (r2_hidden B (k1_relset_1 k1_numbers k2_fdiff_9)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_fdiff_9) A B) = (k13_complex1 (k8_real_1 4 (k8_real_1 (k18_sin_cos (k7_real_1 B A)) (k18_sin_cos (k9_real_1 B A)))) (k8_real_1 (k5_square_1 (k9_real_1 (k21_sin_cos (k7_real_1 A B)) (k21_sin_cos (k9_real_1 A B)))) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t10_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 C (k5_card_1 B)) &  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_dilworth D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_tarski D B) &  ((k5_card_1 D) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_diraf A B B C) & (r1_diraf A B C C)) ) ) ) ) ) ) ).
tt(t10_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v4_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_dirort A B C F G) & (r2_analoaf A B C D E))  =>  ( (B = C)  | (r2_analoaf A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_dist_1 A B C) <=>  ((k4_dist_1 A B) = (k4_dist_1 A C)) ) ) ) ) ) ) ) ).
tt(t10_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  ((r2_hidden A (k4_zfmisc_1 B C D E)) <=>  (? [F:$i] :  ((m1_subset_1 F B) &  (? [G:$i] :  ((m1_subset_1 G C) &  (? [H:$i] :  ((m1_subset_1 H D) &  (? [I:$i] :  ((m1_subset_1 I E) &  (A = (k6_xtuple_0 F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_dtconstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dtconstr A) &  ((v2_dtconstr A) & (l1_lang1 A)) ) )  =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k7_dtconstr A)) =>  (~  ( ((k1_funct_1 B k1_xboole_0) = C)  &  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (~  ( (B = (k8_trees_4 (u1_struct_0 A) C D))  & (r1_lang1 A C (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k9_subset_1 A C (k1_prob_1 A B)) = (k1_prob_1 A (k2_dynkin A B C))) ) ) ) ) ) ) ).
tt(t10_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v36_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v36_algstr_0 B) & (m1_ec_pf_1 B A))  =>  ( ((k1_ec_pf_1 A) = (k7_struct_0 B))  =>  (B = A) ) ) ) ) ) ).
tt(t10_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) = (k8_group_1 A (k8_group_1 A (k8_group_1 A E C) D) B))  &  ((k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) = (k8_group_1 A (k8_group_1 A (k8_group_1 A B E) D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_endalg A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_endalg A B))) =>  (! [E:$i] :  ((m1_autalg_1 E (u1_struct_0 A) (u3_msualg_1 A B) (k4_endalg A B)) =>  (! [F:$i] :  ((m1_autalg_1 F (u1_struct_0 A) (u3_msualg_1 A B) (k4_endalg A B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 (k6_endalg A B) C D) = (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (u3_msualg_1 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski (k4_tarski C D) B) (k2_ens_1 A)) =>  ( ( (D = k1_xboole_0)  =>  (C = k1_xboole_0) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B C D) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((v4_partfun3 B) & (r1_xxreal_0 k6_numbers A))  => (v4_partfun3 (k10_rvsum_1 B A))) ) ) ) ) ).
tt(t10_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_enumset1 A B C D E) = (k2_xboole_0 (k2_enumset1 A B C D) (k1_tarski E))) ) ) ) ) ) ).
tt(t10_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k4_eqrel_1 A (k6_partfun1 A) B) (k6_partfun1 A))) ) ) ).
tt(t10_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((r1_pzfmisc1 A B C) => (r6_pboole A (k1_equation A C D) B)) ) ) ) ) ) ) ) ).
tt(t10_e_siec,ax, (! [A:$i] :  (! [B:$i] :  ((v2_e_siec (g1_e_siec (k2_xboole_0 A B) (k4_relat_1 A) (k4_relat_1 A))) &  ((v3_e_siec (g1_e_siec (k2_xboole_0 A B) (k4_relat_1 A) (k4_relat_1 A))) & (l1_e_siec (g1_e_siec (k2_xboole_0 A B) (k4_relat_1 A) (k4_relat_1 A)))) ) ) ) ).
tt(t10_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k23_rvsum_1 (k5_euclid (k3_finseq_1 A)) A) = k6_numbers) ) ) ).
tt(t10_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k19_euclid (k3_complex1 (k4_xcmplx_0 A)) (k4_complex1 (k4_xcmplx_0 A))) = (k19_euclid (k1_real_1 (k3_complex1 A)) (k1_real_1 (k4_complex1 A)))) ) ) ).
tt(t10_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r2_hidden B (k2_euclid_4 A C D)) & (r2_hidden E (k2_euclid_4 A C D)))  => (r1_tarski (k2_euclid_4 A B E) (k2_euclid_4 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k4_algstr_0 (k15_euclid 3) A) = (k4_euclid_5 (k1_real_1 (k1_euclid_5 A)) (k1_real_1 (k2_euclid_5 A)) (k1_real_1 (k3_euclid_5 A)))) ) ) ).
tt(t10_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (A = B)  |  ((k4_euclid_3 D B C) = (k4_euclid_3 D B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 D)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 D))) ) )  =>  ( ((k1_funct_1 (k2_finseq_7 C D A B) A) = (k1_funct_1 D B))  &  ((k1_funct_1 (k2_finseq_7 C D A B) B) = (k1_funct_1 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euclid_8,ax, ((k23_rvsum_1 k2_euclid_8 k2_euclid_8) = 1) ).
tt(t10_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ((r2_hidden C (k9_metric_1 (k14_euclid A) D B)) =>  (! [E:$i] :  ( (~ (r1_xxreal_0 B (k18_complex1 (k1_funct_1 (k8_rvsum_1 C D) E))))  &  (~ (r1_xxreal_0 B (k18_complex1 (k6_xcmplx_0 (k1_funct_1 C E) (k1_funct_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k12_euclid (k6_rvsum_1 A)) = (k12_euclid A)) ) ) ).
tt(t10_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  (~  ( ((k8_euclid B C D) = (k9_euclid B E A))  &  ( (~  (C = D) )  &  (A = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_euclmetr A) <=> (v2_conmetr A)) ) ) ).
tt(t10_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  ((k2_xcmplx_0 (k3_xcmplx_0 D A) (k3_xcmplx_0 E B)) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_euler_2,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ((r2_classes1 A B) =>  ((k3_wsierp_1 A) = (k3_wsierp_1 B)) ) ) ) ) ) ).
tt(t10_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_exchsort B A) & (v1_exchsort B))  <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ( ((k9_xtuple_0 B) = (k6_subset_1 C A))  & (r1_ordinal1 A C)) ) ) ) ) ) ) ) ).
tt(t10_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (r8_pboole (u1_struct_0 A) (k3_funct_6 (k15_msafree A B)) B)) ) ) ) ).
tt(t10_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) & (v1_funct_1 D)) ) )  =>  ((r1_tarski (k16_funcop_1 C (k2_compos_1 B)) D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v5_memstr_0 E A B C)) ) ) )  => (v5_extpro_1 E A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_extreal1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k7_numbers) =>  (~  ( (~ (r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)))  &  ( (~ (r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers B)))  &  (~  ((k4_extreal1 (k8_finseq_1 k7_numbers A B)) = (k3_supinf_2 (k4_extreal1 A) (k4_extreal1 B))) ) ) ) ) ) ) ) ) ).
tt(t10_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (~ (r1_xxreal_0 B (k3_extreal1 A)))  =>  ( (~ (r1_xxreal_0 A (k2_supinf_2 B)))  &  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t10_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k1_funct_1 (k6_circuit2 A B C) (k2_msualg_1 A D)) = (k1_funct_1 (k5_msualg_1 A D B) (k3_relat_1 (k1_msualg_1 A D) C))) ) ) ) ) ) ) ) ) ).
tt(t10_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ((k3_facirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k3_facirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ( ((k4_facirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k4_facirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ((k5_facirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k5_facirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fcont_1 B A) =>  ( ((k1_seq_1 B A) = k6_numbers)  | (r1_fcont_1 (k6_rfunct_1 k1_numbers k1_numbers B) A)) ) ) ) ) ) ).
tt(t10_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t10_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A)) (k7_relset_1 k1_numbers k1_numbers B A)))) ) ) ) ).
tt(t10_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos B)) (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ) ).
tt(t10_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k1_sin_cos9 B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k1_sin_cos9 B))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k7_real_1 1 (k5_square_1 B)) (k7_real_1 1 (k5_square_1 (k1_seq_1 k1_sin_cos9 B))))))) ) ) ) ) ) ) ) ).
tt(t10_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 B A) => (v3_rcomp_1 A)) ) ) ) ) ).
tt(t10_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ( (~  ((k1_seq_1 C A) = B) )  &  ((r1_fdiff_1 C A) &  (! [D:$i] :  ((m1_rcomp_1 D A) =>  (~  ((r1_tarski D (k1_relset_1 k1_numbers C)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E D) &  ((k1_seq_1 C E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r4_fdiff_3 A C) & (r4_fdiff_3 B C))  =>  ((r4_fdiff_3 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k1_fdiff_3 C (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k1_fdiff_3 C A) (k1_fdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 A B))))) &  ( (D = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ( ((k1_seq_1 E F) = (k7_real_1 F B))  &  (~ (r1_xxreal_0 (k1_seq_1 E F) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 A B))) C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 A B))) C) F) = (k10_real_1 (k9_real_1 F A) (k7_real_1 F B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))))) &  ((r1_xxreal_0 1 A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 A D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))) B) D) = (k8_real_1 (k8_real_1 A (k5_prepower (k1_seq_1 k16_sin_cos D) (k9_real_1 A 1))) (k1_seq_1 k16_sin_cos (k8_real_1 (k7_real_1 A 1) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C B) k3_taylor_1)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 B D) = D)  &  ( (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers))  &  ( ((k1_seq_1 C D) = (k9_real_1 D 1))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C B) k3_taylor_1)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C B) k3_taylor_1)) A) D) = (k10_real_1 1 (k8_real_1 (k5_square_1 D) (k9_real_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)))) & (r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)) B) C) = (k10_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 k1_sin_cos6 C) (k5_real_1 A 1))) (k7_square_1 (k9_real_1 1 (k5_square_1 C))))) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k29_sin_cos))) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k29_sin_cos) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k29_sin_cos) D) G) = (k10_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G)) (k5_square_1 (k1_seq_1 k19_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k1_fdiff_9))) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k1_fdiff_9) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k1_fdiff_9) D) G) = (k10_real_1 (k8_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G)) (k1_seq_1 k16_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G))))) (k5_square_1 (k1_seq_1 k19_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k9_xtuple_0 (k4_relat_1 (u4_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k9_xtuple_0 (k4_relat_1 (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k10_xtuple_0 (k4_relat_1 (u1_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) (k10_xtuple_0 (k4_relat_1 (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k9_xtuple_0 (k4_relat_1 (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))) &  ((r1_xboole_0 (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k9_xtuple_0 (k4_relat_1 (u1_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k10_xtuple_0 (k4_relat_1 (u4_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))) &  ((r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k10_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))) & (r1_xboole_0 (k9_xtuple_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) (k10_xtuple_0 (k4_relat_1 (u4_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_xreal_0 B))  =>  ((k3_xcmplx_0 (k3_power B A) (k3_power B (k4_xcmplx_0 A))) = 1) ) ) ) ) ).
tt(t10_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_xcmplx_0 (k3_power k2_fib_num A) (k3_power k2_fib_num (k1_nat_1 A 1))) = (k3_power k2_fib_num (k1_nat_1 A 2))) ) ) ).
tt(t10_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B A) =>  ((v1_abian B) | (r1_xxreal_0 (k3_power k2_fib_num B) (k3_power k2_fib_num A))) ) ) ) ) ) ).
tt(t10_fib_num,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k1_seq_1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) C) = (k13_complex1 (k1_seq_1 A C) (k1_seq_1 B C)))  &  ((k1_seq_1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) C) = (k3_xcmplx_0 (k1_seq_1 A C) (k5_xcmplx_0 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ).
tt(t10_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( (E = (k11_finseq_1 A B C))  =>  ((r2_hidden A D) &  ((r2_hidden B D) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ).
tt(t10_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden B D) =>  ((r2_hidden (k3_lattices A B C) D) & (r2_hidden (k3_lattices A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t10_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  (! [D:$i] :  ((m2_filter_1 D A B) =>  ((r5_binop_1 A C D) => (r5_binop_1 (k8_eqrel_1 A B) (k3_filter_1 A B C) (k3_filter_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v14_lattices B) & (l3_lattices B)) ) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  ((k6_lattices A) = (k6_lattices B)) ) ) ) ) ) ).
tt(t10_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_finance1 A k1_numbers B k12_prob_1 (k7_funcop_1 A C))) ) ) ) ) ) ).
tt(t10_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_finseq_1 A) = (k7_subset_1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k1_tarski (k1_nat_1 A 1)))) ) ) ).
tt(t10_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k10_xtuple_0 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((k1_funct_1 B C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t10_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden (k2_xcmplx_0 A B) (k2_finseq_1 A)) =>  (B = k6_numbers) ) ) ) ) ) ).
tt(t10_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  ((k9_relat_1 A (k1_finseq_4 A B)) = (k1_tarski B)) ) ) ) ) ).
tt(t10_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B)) &  (C = (k5_relat_1 B (k2_finseq_1 A))) )  =>  ((k5_relat_1 B (k2_finseq_1 (k1_nat_1 A 1))) = (k7_finseq_1 C (k9_finseq_1 (k1_funct_1 B (k1_nat_1 A 1))))) ) ) ) ) ) ) ) ).
tt(t10_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski A (k7_finseq_1 A B))) ) ) ) ).
tt(t10_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( (D = E)  |  ((k7_partfun1 A (k1_finseq_7 A B E C) D) = (k7_partfun1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) => (r1_xxreal_0 (k3_finseq_1 (k4_finseq_8 A B C)) (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t10_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B C) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [H:$i] :  ( ((v3_card_1 H F) & (m2_finseq_1 H B))  =>  (! [I:$i] :  ( ((v3_card_1 I F) & (m2_finseq_1 I C))  => (r2_relset_1 k5_numbers A (k1_finseqop B C A G (k8_finseq_1 B H (k12_finseq_1 B D)) (k8_finseq_1 C I (k12_finseq_1 C E))) (k8_finseq_1 A (k1_finseqop B C A G H I) (k12_finseq_1 A (k2_binop_1 B C A G D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_finset_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_finset_1 (k9_xtuple_0 A)) <=> (v1_finset_1 A)) ) ) ).
tt(t10_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) =>  ((k1_finsop_1 A (k6_finseq_1 A) B) = (k4_binop_1 A B)) ) ) ) ) ) ).
tt(t10_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k5_finsub_1 A) (k5_finsub_1 B))) ) ) ).
tt(t10_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k8_fin_topo A C)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_fintopo2 A B D) = k8_margrel1)  =>  ((k1_fintopo2 A B D C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k8_fin_topo A B) (k8_fin_topo A C)) = (k8_fin_topo A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t10_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_fin_topo A) =>  ((r1_fintopo4 A B C) <=> (r1_xboole_0 (k9_fin_topo A B) C)) ) ) ) ) ) ) ) ).
tt(t10_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_fintopo4 C)) (u1_struct_0 (k2_fintopo4 C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_fintopo4 C)) (u1_struct_0 (k2_fintopo4 C)))))) )  =>  (~  ((r2_fintopo4 (k2_fintopo4 C) (k2_fintopo4 C) D A) &  ( (B = (k2_int_1 (k13_complex1 A 2)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_fintopo4 C))) =>  (~ (r2_hidden (k3_funct_2 (u1_struct_0 (k2_fintopo4 C)) (u1_struct_0 (k2_fintopo4 C)) D E) (k10_fintopo3 (k2_fintopo4 C) B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_fintopo6 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t10_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k11_fin_topo A C)) <=>  ((r2_hidden B C) &  (~ (r1_xboole_0 (k7_subset_1 (u1_struct_0 A) (k1_fin_topo A B) (k6_domain_1 (u1_struct_0 A) B)) C)) ) ) ) ) ) ) ) ) ).
tt(t10_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_catalan2 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( ((k1_afinsq_1 B) = (k2_xcmplx_0 C D))  &  (! [E:$i] :  ((m1_subset_1 E (k3_catalan2 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_catalan2 A)) =>  (~  ( ((k1_afinsq_1 E) = C)  &  ( ((k1_afinsq_1 F) = D)  &  (B = (k1_flang_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( ((k7_flang_1 B C D) = (k1_tarski A))  &  ((k7_flang_1 B C E) = (k1_tarski A)) )  =>  ( (D = E)  |  (A = (k2_flang_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) (k1_flang_3 A B C)) <=>  ( (C = k6_numbers)  | (r2_hidden (k2_flang_1 A) B)) ) ) ) ) ) ) ).
tt(t10_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_xboole_0 B) =>  ((k4_finseq_2 B A) = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t10_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k6_subset_1 (k5_fomodel1 A) (k16_fomodel1 A)) = (k3_fomodel1 A)) ) ) ).
tt(t10_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  => (v12_fomodel1 (k32_fomodel1 A) A)) ) ).
tt(t10_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel1 C B) & (m1_subset_1 C (k1_fomodel1 B)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ((m2_subset_1 E (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k35_fomodel1 B)) =>  ( ((k32_fomodel2 B (k37_fomodel3 B C E D)) = (k32_fomodel2 B D))  &  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  ((k26_fomodel2 B A F (k37_fomodel3 B C E D)) = (k26_fomodel2 B A (k37_fomodel2 B A F C (k3_funct_2 (k35_fomodel1 B) A (k10_fomodel2 B A F) E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((v2_fomodel4 D B) =>  (~  ((v3_fomodel4 (k1_tarski A) B C D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (v4_fomodel4 A E B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r1_frechet A B C))  &  (! [D:$i] :  ((m2_valued_0 D (u1_struct_0 A) B) =>  (? [E:$i] :  ((m2_valued_0 E (u1_struct_0 A) D) & (r1_frechet A E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_frechet,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k5_numbers)  => (v4_pre_topc A k3_topmetr)) ) ) ).
tt(t10_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v2_relat_1 A))  & (m2_finseq_1 A k5_numbers)) )  =>  (! [B:$i] :  ((v1_freealg B) => (v2_freealg (k17_freealg A B) (k15_freealg A B))) ) ) ) ).
tt(t10_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D B)) )  =>  ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((k4_fscirc_2 (k2_nat_1 B 1) A C D) = (k1_fscirc_1 (k1_funct_1 C (k2_nat_1 B 1)) (k1_funct_1 D (k2_nat_1 B 1)) (k3_fscirc_2 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_fsm_1 D A B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ((k1_funct_1 (k5_fsm_1 A B D E C) 1) = (k3_funct_2 (u1_struct_0 D) B (u4_fsm_1 A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  => (v2_fsm_2 (u2_fsm_1 A B) A B)) ) ) ) ).
tt(t10_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ( ((r2_hidden B (k9_flang_1 A)) & (r2_hidden C (k9_flang_1 A)))  =>  ( (B = C)  |  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( (~  ((k1_flang_1 A B D) = C) )  &  (~  ((k1_flang_1 A D B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E)))) => (v1_circuit2 (k5_facirc_1 (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E) F 4) (k1_ftacell1 A B C D E) (k2_ftacell1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_funcop_1,ax, (! [A:$i] :  ( ((k9_xtuple_0 (k2_funcop_1 k1_xboole_0 A)) = k1_xboole_0)  &  ((k10_xtuple_0 (k2_funcop_1 k1_xboole_0 A)) = k1_xboole_0) ) ) ).
tt(t10_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k8_funcsdom A) B) B)) ) ) ).
tt(t10_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) <=>  ((r2_hidden D (k9_xtuple_0 A)) & (r2_hidden (k1_funct_1 A D) (k9_xtuple_0 B))) ) )  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k1_funct_1 B (k1_funct_1 A D))) ) ) )  =>  (C = (k3_relat_1 A B)) ) ) ) ) ) ) ) ).
tt(t10_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  (~  ((r2_hidden E A) &  (D = (k1_funct_1 C E)) ) ) ) ) ) )  =>  ((k2_relset_1 B C) = B) ) ) ) ) ) ).
tt(t10_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k7_relat_1 (k1_funct_3 B) A) (k1_zfmisc_1 (k10_xtuple_0 B)))) ) ) ).
tt(t10_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 (k1_funct_4 A B))) & (r1_tarski (k9_xtuple_0 B) (k9_xtuple_0 (k1_funct_4 A B)))) ) ) ) ) ).
tt(t10_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k9_xtuple_0 (k2_zfmisc_1 A B)) A) & (r1_tarski (k10_xtuple_0 (k2_zfmisc_1 A B)) B)) ) ) ).
tt(t10_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_funct_2 (k2_zfmisc_1 A B) C)) =>  ( ((k2_zfmisc_1 A B) = k1_xboole_0)  |  ((r2_hidden (k1_funct_5 D) (k1_funct_2 A (k1_funct_2 B C))) & (r2_hidden (k3_funct_5 D) (k1_funct_2 B (k1_funct_2 A C)))) ) ) ) ) ) ) ) ).
tt(t10_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k3_relat_1 A (k1_funct_4 B C)) = (k1_funct_4 (k3_relat_1 A B) (k3_relat_1 A C))) ) ) ) ) ) ) ).
tt(t10_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r2_funct_8 A k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t10_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) => (v1_funct_9 (k54_valued_1 B) A)) ) ) ) ) ).
tt(t10_functor0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) & (v2_funct_1 B))  =>  ((k2_funct_1 (k2_funct_4 (k15_funct_3 A B))) = (k2_funct_4 (k2_funct_1 (k15_funct_3 B A)))) ) ) ) ) ) ).
tt(t10_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  ( ((v19_functor0 D A B) & (v19_functor0 E B C))  => (v19_functor0 (k13_functor0 A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  ( ((r2_functor2 A B C D) & (r2_functor2 A B D E))  =>  (! [F:$i] :  ((m2_functor2 F A B C D) =>  (! [G:$i] :  ((m2_functor2 G A B D E) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k2_functor2 A B C E (k3_functor2 A B C D E F G) H) = (k5_altcat_1 B (k3_functor0 A B C H) (k3_functor0 A B D H) (k3_functor0 A B E H) (k2_functor2 A B C D F H) (k2_functor2 A B D E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  ( ((r1_functor2 A B D E) & (r1_functor2 B C F G))  => (r1_functor2 A C (k1_functor3 A B C D F) (k1_functor3 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A B (k1_fuzzy_2 A C B)) (k2_fuzzy_1 A B C))) ) ) ) ) ) ).
tt(t10_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r1_fuzzy_1 C D) => (r1_fuzzy_1 (k2_fuzzy_4 B A C) (k2_fuzzy_4 B A D))) ) ) ) ) ) ) ) ) ).
tt(t10_fvaluat1,ax, (! [A:$i] :  ((v1_fvaluat1 A) =>  (! [B:$i] :  ((v1_fvaluat1 B) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xxreal_0 (k1_xxreal_3 A 1) B)) ) ) ) ) ).
tt(t10_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) )  => (r6_binop_1 (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A))) ) ).
tt(t10_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 (k5_gate_1 A B)))  <=>  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B)) )  &  (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 A)) ) ) ) ) ) ).
tt(t10_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_gcd_1 A B (k5_struct_0 A)) = B) ) ) ) ) ).
tt(t10_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_genealg1 D C) =>  (! [E:$i] :  ((m1_genealg1 E C) =>  ((r1_xxreal_0 (k3_finseq_1 D) A) =>  ((k8_genealg1 C D E B A) = (k7_genealg1 C D E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_rlvect_1 A (k5_algstr_0 A (k1_geomtrap A B C) B) 2) = (k5_algstr_0 A C B))  &  ((k1_rlvect_1 A (k5_algstr_0 A C (k1_geomtrap A B C)) 2) = (k5_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(t10_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k5_gfacirc1 A B C)) = (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) ) ) ) ).
tt(t10_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((k4_gfacirc2 (k1_nat_1 B 1) A C D) = (k12_gfacirc1 (k1_funct_1 C (k1_nat_1 B 1)) (k1_funct_1 D (k1_nat_1 B 1)) (k3_gfacirc2 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r2_hidden C k5_glib_000))  =>  ( ((k6_glib_000 A) = (k6_glib_000 (k13_glib_000 A C B)))  &  ( ((k7_glib_000 A) = (k7_glib_000 (k13_glib_000 A C B)))  &  ( ((k10_glib_000 A) = (k8_glib_000 (k13_glib_000 A C B)))  &  ( ((k11_glib_000 A) = (k9_glib_000 (k13_glib_000 A C B)))  &  ((v1_relat_1 (k13_glib_000 A C B)) &  ((v4_relat_1 (k13_glib_000 A C B) k5_numbers) &  ((v1_funct_1 (k13_glib_000 A C B)) &  ((v1_finset_1 (k13_glib_000 A C B)) & (v1_glib_000 (k13_glib_000 A C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  => (r2_hidden (k1_funct_1 B (k2_nat_1 C 1)) (k28_glib_000 A (k5_glib_001 A B C)))) ) ) ) ) ) ) ).
tt(t10_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ( ((r2_hidden B (k1_glib_002 A E)) & (r1_glib_000 A B D C))  => (r2_hidden D (k1_glib_002 A E))) ) ) ) ) ) ) ) ).
tt(t10_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) & (v1_glib_003 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m1_glib_000 C A)) )  =>  ( ((r5_glib_000 A B) &  ((k5_glib_003 A) = (k5_glib_003 B)) )  =>  ((v1_glib_003 C) &  ((v4_glib_003 C B) & (m1_glib_000 C B)) ) ) ) ) ) ) ) ) ).
tt(t10_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski B)))) )  =>  ((r2_hidden B (k7_glib_000 A)) =>  ((k4_glib_004 A) = (k2_xcmplx_0 (k4_glib_004 C) (k1_seq_1 (k5_glib_003 A) B))) ) ) ) ) ) ) ).
tt(t10_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) => (r2_hidden C (k1_relset_1 (k6_glib_000 A) (k6_glib_005 A B C)))) ) ) ) ) ) ).
tt(t10_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 C))) &  ((k1_matrix_1 C) = (k2_nat_1 B 1)) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((k1_matrix_1 (k3_goboard1 C A)) = B) ) ) ) ) ) ) ) ) ).
tt(t10_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = k1_xboole_0) )  &  ((k2_goboard1 A) = k1_xboole_0) ) ) ) ) ).
tt(t10_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_matrix_1 B))) )  =>  ((v3_relat_1 B) |  ((k1_goboard5 B k6_numbers) = (a_2_9_goboard5 A B)) ) ) ) ) ) ) ).
tt(t10_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ( (E = (k19_euclid A B))  & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 D C) | (r2_hidden (k19_euclid A (k9_real_1 B C)) (k9_metric_1 (k14_euclid 2) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_goboard7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((v1_sppol_1 (k2_topreal1 2 A B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k2_topreal1 2 A B)) =>  ((k18_euclid D) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k1_matrix_1 (k2_goboard2 A)))) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k1_matrix_1 (k2_goboard2 A))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k7_nat_d (k1_matrix_1 (k2_goboard2 A)) 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k1_matrix_1 (k2_goboard2 A))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k7_nat_d (k1_matrix_1 (k2_goboard2 A)) 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k7_nat_d (k1_matrix_1 (k2_goboard2 A)) 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid k6_numbers 1))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t10_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ((k2_nat_1 B C) = (k3_finseq_1 A)) ) )  =>  ((k5_goboard5 (k1_goboard9 A) B) = (k4_goboard5 A C)) ) ) ) ) ) ) ) ).
tt(t10_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (B = (a_1_5_gobrd11 A))  &  (C = (a_1_6_gobrd11 A)) )  =>  (B = (k3_subset_1 (u1_struct_0 (k15_euclid 2)) C)) ) ) ) ) ) ) ) ).
tt(t10_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_goboard9 A))) ) ) ).
tt(t10_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 D) (k16_matrix_1 E)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 E)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k3_finseq_1 E) C)) ) ) ) )  =>  (A = (k3_finseq_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k1_jordan8 D C))) & (r2_hidden (k4_tarski (k2_nat_1 A 1) B) (k2_matrix_1 (k1_jordan8 D C))))  =>  ((k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D C) (k2_nat_1 A 1) B)) = (k10_real_1 (k9_real_1 (k8_pscomp_1 D) (k6_pscomp_1 D)) (k13_newton 2 C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( ((v1_henmodel D A) & (m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [E:$i] :  ((m1_henmodel E A D) =>  ((r1_valuat_1 A (k1_henmodel A) (k12_cqc_lang A C B) E (k3_henmodel A)) <=>  (? [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) & (r1_valuat_1 A (k1_henmodel A) (k4_substut2 A B C F) E (k3_henmodel A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ((r1_graph_1 A B C) => (r1_graph_1 A C B)) ) ) ) ) ) ) ).
tt(t10_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k7_finseq_1 (k7_finseq_1 (k1_graph_2 A 1 B) (k1_graph_2 A (k2_nat_1 B 1) C)) (k1_graph_2 A (k2_nat_1 C 1) (k3_finseq_1 A))) = A) ) ) ) ) ) ) ) ).
tt(t10_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v2_funct_1 C) &  ((v1_msscyc_1 C A) & (m2_graph_1 C A)) )  =>  (~  ((r2_hidden B (k4_finseq_1 C)) &  (! [D:$i] :  ( ((v2_funct_1 D) &  ((v1_msscyc_1 D A) & (m2_graph_1 D A)) )  =>  (~  ( ((k1_funct_1 D 1) = (k1_funct_1 C B))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  &  ((k10_xtuple_0 D) = (k10_xtuple_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ( ((r3_graph_4 A B D) & (r3_graph_4 A C D))  =>  ( (D = k1_xboole_0)  |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ((m2_graph_1 (k7_finseq_1 A B) C) =>  ((m2_graph_1 A C) & (m2_graph_1 B C)) ) ) ) ) ) ) ) ).
tt(t10_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (u4_struct_0 A)) &  ((r2_hidden E (u4_struct_0 A)) &  ((r1_graph_4 A B C D) & (r1_graph_4 A B C E)) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ).
tt(t10_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_grcat_1 C) & (l1_grcat_1 C))  =>  ( ( ((k7_grcat_1 C) = A)  &  ( ((k8_grcat_1 C) = B)  & (v13_vectsp_1 (k9_grcat_1 C) (k7_grcat_1 C) (k8_grcat_1 C))) )  =>  ((v1_grcat_1 C) & (m1_grcat_1 C A B)) ) ) ) ) ) ) ) ).
tt(t10_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k2_group_1 B (k5_group_1 B A C)) = (k5_group_1 B (k21_binop_2 (k7_group_1 B) (k4_nat_d A (k7_group_1 B))) C)) ) ) ) ) ) ) ).
tt(t10_gr_cy_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ( ((k7_group_1 (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C A D)))) = (k7_group_1 (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C B D)))))  & (r1_struct_0 (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C A D))) (k5_group_1 C B D)))  => (r1_group_2 C (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C A D))) (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C B D))))) ) ) ) ) ) ) ) ) ).
tt(t10_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  (? [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v2_gr_cy_3 B)) )  &  (A = (k2_nat_1 (k4_nat_1 2 B) 1)) ) ) ) ) ).
tt(t10_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski A B) & (v2_funct_1 B))  => (v2_funct_1 A)) ) ) ) ) ).
tt(t10_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_6 B A C) => (r1_tarski (k5_group_5 A C B) (k8_group_2 A C))) ) ) ) ) ) ) ).
tt(t10_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (v9_rewrite1 (k3_polyred A B C (k1_groeb_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t10_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r3_pre_poly A (k2_groeb_2 A B D) (k2_groeb_2 A C D)) => (r3_pre_poly A B (k2_groeb_2 A C D))) ) ) ) ) ) ) ) ).
tt(t10_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_2 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom7 D A B) &  ((v3_polynom7 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) ) )  =>  ((k5_card_1 (k2_polynom1 (k15_pre_poly A) B C)) = (k5_card_1 (k2_polynom1 (k15_pre_poly A) B (k9_polynom1 A B D C)))) ) ) ) ) ) ) ) ) ).
tt(t10_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (? [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  & (r3_group_10 B A C)) ) ) ) ) ) ).
tt(t10_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((u1_struct_0 B) = (k7_group_4 A C D))  =>  ((k2_group_2 A (k13_group_2 A C E) (k13_group_2 A D F)) = (k13_group_2 A B (k6_algstr_0 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_group_12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_finseq_1 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k2_finseq_1 A)) &  ((v1_group_7 B) &  ((v2_group_7 B (k2_finseq_1 A)) & (v3_group_7 B (k2_finseq_1 A))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) =>  ( ( ((k3_finseq_1 D) = A)  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k2_group_12 (k2_finseq_1 A) B F) (k1_funct_1 D F))) )  &  ( (C = (k3_group_4 (k2_group_7 (k2_finseq_1 A) B) D))  &  ( ((k3_finseq_1 E) = A)  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k2_group_12 (k2_finseq_1 A) B F) (k1_funct_1 E F))) )  &  (C = (k3_group_4 (k2_group_7 (k2_finseq_1 A) B) E)) ) ) ) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_group_1 A B) = (k1_group_1 A))  =>  (B = (k1_group_1 A)) ) ) ) ) ) ).
tt(t10_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_group_1 A) =>  ((k2_group_2 A (k2_group_2 A B C) D) = (k2_group_2 A B (k2_group_2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_2 A (k13_group_2 A D B) C) = (k4_group_2 A B (k12_group_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t10_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_4 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t10_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_group_5 A (k6_finseq_1 (u1_struct_0 A)) B) = k1_xboole_0) ) ) ) ) ).
tt(t10_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v7_struct_0 (k6_group_2 A))) ) ).
tt(t10_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) & (v1_group_7 (k9_finseq_1 A))) ) ) ) ) ) ).
tt(t10_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v4_group_1 B A))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k5_group_1 A C B) = (k5_group_1 A (k6_int_1 C (k6_group_1 A B)) B)) ) ) ) ) ) ) ) ).
tt(t10_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  => (m1_group_9 B A B)) ) ) ).
tt(t10_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ( ((m1_group_6 B A (k10_group_5 A)) & (v1_gr_cy_1 (k5_group_6 A B)))  => (v5_group_1 A)) ) ) ) ) ).
tt(t10_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ((v15_algstr_0 (k2_grsolv_1 A B C D)) & (m1_group_6 (k2_grsolv_1 A B C D) B (k10_group_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t10_hahnban1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k3_complex1 (k3_rlvect_1 k1_complfld A B)) = (k7_real_1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k3_rlvect_1 k1_complfld A B)) = (k7_real_1 (k4_complex1 A) (k4_complex1 B))) ) ) ) ) ) ).
tt(t10_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k1_rlvect_3 B (k6_domain_1 (u1_struct_0 B) D)) = (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k1_funct_1 B C)) & (r2_hidden E (k1_funct_1 B C)))  =>  ( (D = E)  |  ((k4_subset_1 (k1_funct_1 B C) (k6_subset_1 (k1_funct_1 B C) (k1_tarski D)) (k6_subset_1 (k1_funct_1 B C) (k1_tarski E))) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_hausdorf,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))))  =>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  &  ( (A = B)  &  ((k3_weierstr A) = (k5_seq_4 B)) ) ) ) ) ) ).
tt(t10_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_xxreal_0 (k3_finseq_1 (k8_glib_001 A B C D)) (k3_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t10_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_henmodel A B (k6_cqc_lang A C)) <=>  (~ (v1_henmodel (k4_subset_1 (k3_cqc_lang A) B (k6_domain_1 (k3_cqc_lang A) C)) A)) ) ) ) ) ) ) ) ).
tt(t10_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k4_complex1 A) = k6_numbers)  =>  ( ((k3_complex1 (k8_group_1 k1_complfld A B)) = (k8_real_1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k8_group_1 k1_complfld A B)) = (k8_real_1 (k3_complex1 A) (k4_complex1 B))) ) ) ) ) ) ) ).
tt(t10_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A D F E) &  ( (~  (F = D) )  &  ( (~  (E = B) )  & (r1_collsp A F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (B = (k2_lattice2 (k7_normform A) (k12_normform A) (k3_heyting1 A B) (k4_heyting1 A))) ) ) ) ).
tt(t10_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( (C = k1_xboole_0)  =>  ((k2_heyting2 A B C) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ).
tt(t10_heyting3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A C))) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k4_partfun1 B D))) =>  ( ((r1_tarski A B) &  ((r1_tarski C D) &  (E = F) ) )  =>  ((k3_substlat A C E) = (k3_substlat B D F)) ) ) ) ) ) ) ) ) ) ).
tt(t10_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A B) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos B) 3) A) = (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) A)) ) ) ) ) ) ).
tt(t10_hilbasis,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k2_hilbasis A B) = (k2_hilbasis A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t10_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r1_tarski A B) => (r1_tarski (k5_hilbert1 A) (k5_hilbert1 B))) ) ) ) ) ).
tt(t10_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (r1_xxreal_0 1 (k3_finseq_1 A))) ) ).
tt(t10_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k4_funct_4 A B C D) = (k4_funct_4 A B E F))  =>  ( (A = B)  |  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ).
tt(t10_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k4_power (k1_seq_1 B D) A)) ) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k4_power (k2_seq_2 B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k5_vfunct_1 k5_numbers A B)) B)) ) ) ) ).
tt(t10_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_binari_3 A k6_numbers) = (k1_idea_1 A)) ) ) ).
tt(t10_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v1_ideal_1 (u1_struct_0 A) A) &  ((v2_ideal_1 (u1_struct_0 A) A) &  ((v3_ideal_1 (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t10_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ((r1_collsp A E F G) <=>  (? [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k3_incproj A))) &  ((r1_incsp_1 (k3_incproj A) B H) &  ((r1_incsp_1 (k3_incproj A) C H) & (r1_incsp_1 (k3_incproj A) D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((r4_incsp_1 A (k4_subset_1 (u1_incsp_1 A) C D) B) <=>  ((r4_incsp_1 A C B) & (r4_incsp_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t10_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u2_graph_1 A) (u1_graph_1 A) (k1_oppcat_1 (u4_struct_0 A) (u4_struct_0 A) (u4_struct_0 A) (u1_cat_1 A)) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k2_cat_1 A C D)))  =>  (! [E:$i] :  ((m1_cat_1 E A C D) => (m2_cat_1 (k7_index_1 (u4_struct_0 A) (k3_relat_1 (u2_graph_1 A) (k1_xtuple_0 B)) (k3_relat_1 (u1_graph_1 A) (k1_xtuple_0 B)) (k8_index_1 (u1_struct_0 A) (u4_struct_0 A) (u2_graph_1 A) (u1_graph_1 A) B) E) (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) D) (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) & (r1_tarski (u4_struct_0 B) (u4_struct_0 A))) ) ) ) ) ).
tt(t10_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((k3_xcmplx_0 A B) = (k1_real_1 1))  <=>  ( ( (A = (k1_real_1 1))  &  (B = 1) )  |  ( (A = 1)  &  (B = (k1_real_1 1)) ) ) ) ) ) ) ) ).
tt(t10_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_int_1 A B) => (r1_int_1 A (k4_xcmplx_0 B)))  &  ( ((r1_int_1 A (k4_xcmplx_0 B)) => (r1_int_1 A B))  &  ( ((r1_int_1 A B) => (r1_int_1 (k4_xcmplx_0 A) B))  &  ( ((r1_int_1 (k4_xcmplx_0 A) B) => (r1_int_1 A B))  &  ( ((r1_int_1 A B) => (r1_int_1 (k4_xcmplx_0 A) (k4_xcmplx_0 B)))  &  ( ((r1_int_1 (k4_xcmplx_0 A) (k4_xcmplx_0 B)) => (r1_int_1 A B))  &  ( ((r1_int_1 A (k4_xcmplx_0 B)) => (r1_int_1 (k4_xcmplx_0 A) B))  &  ((r1_int_1 (k4_xcmplx_0 A) B) => (r1_int_1 A (k4_xcmplx_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_int_3,ax, ((v6_struct_0 (k9_int_3 1)) &  ( ( (~ (v2_struct_0 (k9_int_3 1)))  &  ((v13_algstr_0 (k9_int_3 1)) &  ((v3_group_1 (k9_int_3 1)) &  ((v2_rlvect_1 (k9_int_3 1)) &  ((v3_rlvect_1 (k9_int_3 1)) &  ((v4_rlvect_1 (k9_int_3 1)) &  ((v4_vectsp_1 (k9_int_3 1)) &  ((v5_vectsp_1 (k9_int_3 1)) & (l6_algstr_0 (k9_int_3 1))) ) ) ) ) ) ) )  &  ((v33_algstr_0 (k9_int_3 1)) &  ((v1_group_1 (k9_int_3 1)) &  ((v5_vectsp_1 (k9_int_3 1)) & (v5_group_1 (k9_int_3 1))) ) ) ) ) ).
tt(t10_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_int_1 A B C) => (r2_int_1 (k3_xcmplx_0 A D) (k3_xcmplx_0 B D) (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t10_int_5,ax,(r1_int_5 1 2)).
tt(t10_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k3_xcmplx_0 C (k1_funct_1 A B)) = (k19_rvsum_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_int_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((k1_polynom2 A (k5_nat_3 A B C)) = (k9_subset_1 A (k1_polynom2 A B) (k1_polynom2 A C))) ) ) ) ) ) ).
tt(t10_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_tarski (k1_limfunc1 C) (k1_relset_1 k1_numbers A)) &  ((r1_tarski (k1_limfunc1 C) (k1_relset_1 k1_numbers B)) &  ((r4_integr10 A C) & (r4_integr10 B C)) ) )  =>  ((r4_integr10 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k4_integr10 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) = (k7_real_1 (k4_integr10 A C) (k4_integr10 B C))) ) ) ) ) ) ) ) ) ).
tt(t10_integr11,ax, ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k4_sin_cos2) k1_sin_cos2) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k4_sin_cos2) k1_sin_cos2) k1_numbers) A) = (k8_real_1 A (k1_seq_1 k1_sin_cos2 A))) ) ) ) ).
tt(t10_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos) k16_sin_cos))) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t10_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k24_sin_cos)) &  ((r1_tarski C (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) (k10_real_1 1 2)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t10_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) A) B) = (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t10_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 B) =>  ((v3_integra1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [E:$i] :  ((m2_integr15 E A B D) =>  ( ((v2_comseq_2 (k2_integra3 A D)) &  ((k2_seq_2 (k2_integra3 A D)) = k6_numbers) )  =>  ((v2_comseq_2 (k3_integr15 A B D E)) &  ((k2_seq_2 (k3_integr15 A B D E)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr16 D A B C) =>  (! [E:$i] :  ((m1_integr15 E A (k6_comseq_3 A B) C) =>  ( (E = (k2_integr16 D))  =>  ((k4_complex1 (k3_integr16 A B C D)) = (k1_integr15 A (k6_comseq_3 A B) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_integr18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ( ( (D = F)  &  (E = G) )  =>  ((k6_vfunct_1 B C F G) = (k6_vfunct_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_integr15 A (k3_integra5 B E) F) &  ((r1_integr15 A (k3_integra5 B E) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B E)) A) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B E)) A) &  ((r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers F)) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers G))) ) ) ) ) ) ) )  =>  ((r1_integr15 A (k3_integra5 C D) (k7_integr15 A k1_numbers F G)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) (k7_integr15 A k1_numbers F G) (k3_integra5 C D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r1_tarski (k1_rvsum_1 (k3_valued_1 A k1_numbers k1_numbers B C)) (k9_member_1 (k1_rvsum_1 B) (k1_rvsum_1 C)))) ) ) ) ) ) ).
tt(t10_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v4_xxreal_2 B) & (r1_xxreal_0 A k6_numbers))  => (v3_xxreal_2 (k1_integra2 B A))) ) ) ) ) ).
tt(t10_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k2_integra1 B C (k3_finseq_1 C))) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r1_integra1 C D) &  ( ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 C) (k1_seq_4 A)))  & (v1_comseq_2 (k2_partfun1 B k1_numbers E B))) ) ) )  => (r1_xxreal_0 (k9_real_1 (k18_rvsum_1 (k5_integra1 B E D)) (k18_rvsum_1 (k5_integra1 B E C))) (k8_real_1 (k9_real_1 (k4_seq_4 (k1_rvsum_1 E)) (k5_seq_4 (k1_rvsum_1 E))) (k1_integra3 B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) =>  ((v1_integra1 B A) & (v2_integra1 B A)) ) ) ) ) ) ).
tt(t10_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)))  => (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t10_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 D)) &  ((r1_integra5 (k3_integra5 A B) D) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B)))) ) )  =>  ((k4_integra5 A B (k26_valued_1 k1_numbers k1_numbers D C)) = (k4_real_1 C (k4_integra5 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) C) &  ((r2_fdiff_1 D C) &  ((r1_integra5 (k3_integra5 A B) (k2_fdiff_1 D C)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 D C) (k3_integra5 A B)))) ) ) )  =>  ((k1_seq_1 D B) = (k7_real_1 (k4_integra5 A B (k2_fdiff_1 D C)) (k1_seq_1 D A))) ) ) ) ) ) ) ) ) ).
tt(t10_integra8,ax, ((k3_sin_cos6 (k10_real_1 (k7_square_1 2) 2)) = (k10_real_1 k32_sin_cos 4)) ).
tt(t10_integra9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k19_sin_cos) A) B) = (k9_real_1 (k1_seq_1 k19_sin_cos B) (k8_real_1 B (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ).
tt(t10_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_interva1 (k1_tarski B) A)) ) ) ) ).
tt(t10_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ( ((r2_hidden B (k7_intpro_1 A)) & (r2_hidden (k3_intpro_1 B C) (k7_intpro_1 A)))  => (r2_hidden C (k7_intpro_1 A))) ) ) ) ) ) ) ).
tt(t10_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_seq_1 (k2_irrat_1 k6_numbers) A) = 1) ) ) ).
tt(t10_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) => (v12_cat_1 (k1_isocat_1 A B C) B A)) ) ) ) ) ) ) ).
tt(t10_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k8_cat_1 B C (k12_cat_2 A B C D E) F) = (k8_cat_1 (k8_cat_2 A B) C D (k9_cat_2 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ((r1_tarski (k1_tops_1 A (k2_pre_topc A B)) B) & (r1_tarski B (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ) ).
tt(t10_jct_misc,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  => (r1_xxreal_0 k6_numbers (k1_jct_misc A B))) ) ) ) ).
tt(t10_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_jgraph_1 A B C) => (r1_tarski (k2_relset_1 (u4_struct_0 (k1_jgraph_1 A)) (k4_jgraph_1 A C)) (k2_relset_1 (u4_struct_0 (k1_jgraph_1 A)) (k4_jgraph_1 A B)))) ) ) ) ) ) ) ).
tt(t10_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) E) &  ((v3_pre_topc E B) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D F) &  ((v3_pre_topc F A) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = k6_numbers) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k6_real_1 G (k7_square_1 (k7_real_1 1 (k3_square_1 (k7_xcmplx_0 F G)))))) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (~  (E = k6_numbers) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C F) = k6_numbers) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B G) = H)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C G) = I) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) F G) = (k4_real_1 I (k7_square_1 (k18_complex1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 H I) D) E))))))) ) ) ) ) ) ) )  & (v5_pre_topc F A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_algstr_0 (k15_euclid A) (k4_struct_0 (k15_euclid A))) = (k4_struct_0 (k15_euclid A))) ) ) ).
tt(t10_jgraph_6,ax, ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 (k19_euclid (k1_real_1 1) k6_numbers)) = (k19_euclid (k1_real_1 1) k6_numbers)) ).
tt(t10_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k17_euclid A) = D)  &  ( ((k17_euclid B) = D)  &  ((r1_xxreal_0 E (k18_euclid B)) & (r1_xxreal_0 (k18_euclid A) F)) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) | (r1_jordan6 (k1_sppol_2 C D E F) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_subset_1 B (k2_goboard9 (k1_jordan9 B A)))) ) ) ) ).
tt(t10_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_jordan1h B A) & (r1_xboole_0 (k3_goboard5 (k1_jordan8 B A) (k7_nat_d (k3_jordan1h B A) 1) (k7_nat_d (k3_jordan11 B A) 1)) B)) ) ) ) ) ) ).
tt(t10_jordan12,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) => (v1_finset_1 (k3_setfam_1 (a_1_0_jordan12 A) (a_1_0_jordan12 B)))) ) ) ) ).
tt(t10_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_xboole_0 A (k3_goboard9 (k1_jordan13 A B)))) ) ) ) ) ).
tt(t10_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) D E A) &  ((r1_topreal1 (k15_euclid 2) D E B) &  ((r1_topreal1 (k15_euclid 2) D E C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k2_tarski D E))  &  ((r1_tarski A (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C)) &  ( (~  (A = B) )  &  (~  (A = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan17 A B C D E) => (r1_jordan17 A C D E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k5_topreal1 A))) = (k17_euclid A)) ) ) ).
tt(t10_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k9_pscomp_1 B) (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t10_jordan1a,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_tarski B (k6_jordan6 A)) => (v2_sppol_1 B)) ) ) ) ) ).
tt(t10_jordan1b,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (r1_sprect_2 A (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ).
tt(t10_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((r2_hidden B (k1_jordan2c 2 C)) &  ( (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k17_euclid B) (k6_pscomp_1 C)) (k9_real_1 (k8_pscomp_1 C) (k6_pscomp_1 C))) (k13_newton 2 A)) 2)))  & (r1_xxreal_0 D 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k23_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t10_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_nat_1 (k3_finseq_1 (k1_jordan1e A B)) (k3_finseq_1 (k2_jordan1e A B))) = (k2_nat_1 (k3_finseq_1 (k1_jordan9 A B)) 1)) ) ) ) ) ).
tt(t10_jordan1f,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) (k1_jordan8 A B))) ) ) ) ).
tt(t10_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k25_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) )  & (r1_xxreal_0 (k17_euclid (k24_pscomp_1 (k3_topreal1 2 A))) (k17_euclid (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t10_jordan1h,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (r2_relset_1 k5_numbers k1_numbers (k1_goboard1 A) (k1_partfun1 k5_numbers (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_numbers A k4_pscomp_1))) ) ).
tt(t10_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_xxreal_0 (k17_euclid B) (k8_pscomp_1 (k3_topreal1 2 A))))  => (r2_hidden B (k2_goboard9 A))) ) ) ) ) ).
tt(t10_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k2_jordan1e B A))) & (r2_hidden (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ).
tt(t10_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E C) => (r1_xxreal_0 A (k4_metric_1 B D E))) ) )  => (r1_xxreal_0 A (k1_funct_1 (k6_weierstr B C) D))) ) ) ) ) ) ) ) ) ).
tt(t10_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ( (~ (r1_xxreal_0 (k17_euclid C) E))  &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  ( (~ (r3_jordan20 A B C D E))  &  ( (~ (r4_jordan20 A B C D E))  &  (~ (r6_jordan20 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (r1_xboole_0 (k2_jordan2c 2 A) A)) ) ).
tt(t10_jordan22,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~  ( (~ (r1_xxreal_0 B C))  &  ((r2_hidden (k1_domain_1 k5_numbers k5_numbers A D) (k2_matrix_1 (k1_jordan8 E C))) &  ((r2_hidden (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 A 1) D) (k2_matrix_1 (k1_jordan8 E C))) & (r1_xxreal_0 (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E C) A D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E C) (k2_nat_1 A 1) D)) (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) A D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) (k2_nat_1 A 1) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v3_jordan23 A) => (v3_jordan23 (k3_finseq_5 A))) ) ) ).
tt(t10_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 D A) => (v2_connsp_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k18_rvsum_1 (k3_funct_7 k1_numbers (k5_euclid B) A C)) = C) ) ) ) ) ) ) ) ).
tt(t10_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k12_euclid (k1_jordan2b A)) = (k18_complex1 A)) ) ) ).
tt(t10_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k2_topreal1 2 A 1)) =>  ((k1_jordan3 A B) = 1) ) ) ) ) ) ).
tt(t10_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B))) )  =>  ((k1_funct_1 (k3_finseq_6 A B C D) (k3_finseq_1 (k3_finseq_6 A B C D))) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden C (k2_pcomps_1 (k2_topmetr A B))) =>  ((r1_xxreal_0 B A) |  ((r2_hidden A C) |  ((r2_hidden B C) | (v3_rcomp_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (B = C)  | (r2_jordan3 B C B A)) ) ) ) ) ) ) ) ).
tt(t10_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r2_hidden D A))  =>  ((r1_jordan5c A B C B D) & (r1_jordan5c A B C D C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 A)) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k2_goboard2 A))) &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_topreal1 (k15_euclid A) C D B) => (v2_connsp_1 B (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t10_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) &  ((r1_jordan6 A B C) & (r1_jordan6 A C D)) )  =>  ( ( (B = C)  &  (B = (k18_pscomp_1 A)) )  |  ( ( (C = D)  &  (C = (k18_pscomp_1 A)) )  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A B C) (k1_jordan7 A C D)) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_jordan8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 4 (k3_finseq_1 (k1_jordan8 A B)))) ) ) ) ).
tt(t10_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C))) )  =>  ((v1_convex1 (k1_tops_1 (k15_euclid 2) (k3_gobrd13 C B A)) (k15_euclid 2)) & (v1_convex1 (k1_tops_1 (k15_euclid 2) (k2_gobrd13 C B A)) (k15_euclid 2))) ) ) ) ) ) ) ) ).
tt(t10_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A (k22_pscomp_1 A) B) =>  ((k1_jordan7 A B (k18_pscomp_1 A)) = (k5_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) B (k18_pscomp_1 A))) ) ) ) ) ) ).
tt(t10_jordan,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xboole_0 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_topreal1 (k1_jordan21 A)) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan21 A))) A)) ) ).
tt(t10_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (~  ((v2_funct_1 C) &  ((v2_funct_1 D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~ (v3_funct_2 E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  &  ((v2_finsub_1 D) &  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 B)))  &  ((v2_finsub_1 E) &  (! [F:$i] :  ((m1_prob_1 F A B) =>  (! [G:$i] :  ((m1_prob_1 G A B) =>  ( ((r2_hidden F D) & (r2_hidden G E))  => (r1_prob_2 A B C F G)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  (! [G:$i] :  ((m1_prob_1 G A B) =>  ( ((r2_hidden F (k9_prob_1 A D)) & (r2_hidden G (k9_prob_1 A E)))  => (r1_prob_2 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k9_subset_1 A (k3_funct_2 k5_numbers (k9_setfam_1 A) B E) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E))) ) )  =>  ((k3_kurato_0 A D) = (k9_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t10_kurato_1,ax, ((k2_pre_topc k3_topmetr k6_kurato_1) = (k4_subset_1 k1_numbers (k1_seq_4 1) (k3_rcomp_1 2 k1_xxreal_0))) ).
tt(t10_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid A))) =>  (~  ( (~ (r1_xboole_0 (k9_metric_1 (k14_euclid A) E B) (k9_metric_1 (k14_euclid A) G D)))  &  ( (~ (r1_xboole_0 (k9_metric_1 (k14_euclid A) G D) (k9_metric_1 (k14_euclid A) F C)))  & (r1_xxreal_0 (k3_real_1 (k2_xcmplx_0 B C) (k8_real_1 2 D)) (k4_metric_1 (k14_euclid A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lang1,ax, (! [A:$i] :  ((k1_lang1 (k6_lang1 A)) = k1_xboole_0) ) ).
tt(t10_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden B (k2_finseq_1 (k1_nat_1 A 1))) &  ((r1_xxreal_0 2 A) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_sgraph1 (k2_finseq_1 A)) (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 1)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_sgraph1 (k2_finseq_1 A)) (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 1))))))) )  =>  (~  ( ((k10_xtuple_0 D) = (k6_subset_1 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 1))) (a_2_1_laplace A B)))  &  ((v2_funct_1 D) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k2_tarski E F) (k2_sgraph1 (k2_finseq_1 A))) =>  ((r1_xxreal_0 F E) |  ( (~  ( (~ (r1_xxreal_0 B F))  &  ( (~ (r1_xxreal_0 B E))  &  (~  ((k1_funct_1 D (k2_tarski E F)) = (k2_tarski E F)) ) ) ) )  &  ( ((r1_xxreal_0 B F) =>  ((r1_xxreal_0 B E) |  ((k1_funct_1 D (k2_tarski E F)) = (k2_tarski E (k1_nat_1 F 1))) ) )  &  ( ((r1_xxreal_0 B F) & (r1_xxreal_0 B E))  =>  ((k1_funct_1 D (k2_tarski E F)) = (k2_tarski (k1_nat_1 E 1) (k1_nat_1 F 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 (k5_group_4 A D))))) ) ) ) ) ) ) ) ).
tt(t10_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (u1_struct_0 A)) => (m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B)))) ) ) ) ) ) ).
tt(t10_lattice2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 A)) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) =>  ((k1_funct_1 C F) = (k1_funct_1 D F)) ) ) )  =>  ((k7_funct_4 A B D (k2_partfun1 A B C E)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lattice3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_lattice3 A) <=> (v2_lattice3 (k7_lattice3 A))) ) ) ).
tt(t10_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_lattice4 A (k2_setwiseo (u1_struct_0 A) B)) = B) ) ) ) ) ).
tt(t10_lattice5,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_lattice5 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_lattice5 A))) =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k13_lattice3 (k1_lattice5 A) B C) = (k5_eqrel_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ( ((k3_lattice6 A (k6_lattices A)) = (k6_lattices A))  & (v2_waybel_6 (k4_lattice3 A (k6_lattices A)) (k3_lattice3 A))) ) ) ).
tt(t10_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k3_lattice7 A)) <=>  ( (~  (B = (k3_yellow_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (B = (k13_lattice3 A C D))  &  ( (~  (B = C) )  &  (~  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v2_lattice5 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (v2_lattice5 (k2_lattice8 A B C D) (k1_lattice8 A) B)) ) ) ) ) ) ) ) ) ).
tt(t10_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_lattices A (k3_lattices A (k4_lattices A B C) (k4_lattices A C D)) (k4_lattices A D B)) = (k4_lattices A (k4_lattices A (k3_lattices A B C) (k3_lattices A C D)) (k3_lattices A D B))) ) ) ) ) ) )  => (v11_lattices A)) ) ) ).
tt(t10_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k5_numbers) &  ((v2_lexbfs A) & (v3_lexbfs A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 (k39_glib_000 A) B) & (r1_xxreal_0 B C))  =>  ((k1_funct_1 A C) = (k1_funct_1 A B)) ) ) ) ) ) ) ) ).
tt(t10_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) )  => (v2_lattice3 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t10_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( ((v2_lfuzzy_1 B A) & (v2_lfuzzy_1 C A))  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k2_fuzzy_4 A A (k2_lfuzzy_1 (k2_zfmisc_1 A A) B C)) (k2_lfuzzy_1 (k2_zfmisc_1 A A) B C))) ) ) ) ) ) ) ).
tt(t10_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (? [D:$i] :  ((m1_rcomp_1 D C) &  ((r1_tarski D (k1_relset_1 k1_numbers A)) &  ((r1_tarski D (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 A D) &  ((r2_fdiff_1 B D) &  ((r1_tarski (k7_subset_1 k1_numbers D (k1_tarski C)) (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers A B))) &  ((r1_tarski D (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D)))) &  ( ((k1_seq_1 A C) = k6_numbers)  &  ( ((k1_seq_1 B C) = k6_numbers)  & (r1_fcont_1 (k3_rfunct_1 k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D)) C)) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) &  ((k1_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) = (k10_real_1 (k1_fdiff_1 A C) (k1_fdiff_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t10_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) & (v1_limfunc1 B))  => (v1_limfunc1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t10_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_limfunc2 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k1_relset_1 k1_numbers B)) & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 B F) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_limfunc3 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A E)) k6_numbers))  &  ( (~ (r1_xxreal_0 D (k18_complex1 (k9_real_1 A E))))  &  ((r2_hidden E (k9_xtuple_0 B)) & (r1_xxreal_0 (k1_seq_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v8_limfunc1 A) &  ((v8_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  => (v8_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t10_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((k1_lmod_5 A B (k1_subset_1 (u1_struct_0 B))) = (k1_vectsp_4 A B)) ) ) ) ) ).
tt(t10_lmod_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_4 D B C) =>  ((r2_hidden A (k2_lmod_6 B C D (k2_struct_0 D))) <=> (r1_struct_0 D A)) ) ) ) ) ) ) ) ).
tt(t10_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden C (k3_vectsp_4 A B D E)) <=> (r1_struct_0 E (k5_algstr_0 B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))))  &  ((v13_algstr_0 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v2_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v3_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v4_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v5_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v6_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v7_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) &  ((v8_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B))) & (l1_rlvect_1 (g1_rlvect_1 (k9_funct_2 A (u1_struct_0 B)) (k4_lopban_1 A B) (k2_lopban_1 A B) (k3_lopban_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  ((k3_lopban_2 A B (k2_lopban_2 A C D)) = (k2_lopban_2 A (k3_lopban_2 A B C) (k3_lopban_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k1_valued_0 (u1_struct_0 A) C D))) ) )  | (v3_normsp_1 C A)) ) ) ) ) ) ) ) ).
tt(t10_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r1_xxreal_0 (k1_normsp_0 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A C) B)) (k8_nat_1 k1_numbers (k3_series_1 (k4_normsp_0 A C)) B))) ) ) ) ) ) ).
tt(t10_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (B = C)  =>  ((k2_pre_topc (k3_normsp_2 A) B) = (k2_pre_topc (k4_normsp_2 A) C)) ) ) ) ) ) ) ) ).
tt(t10_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_lopclset A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_lopclset A))) =>  ((k3_lattices (k6_lopclset A) B C) = (k2_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t10_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) B C) (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) C B))) ) ) ) ) ) ).
tt(t10_lpspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) =>  ((r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 A) B) (k1_seq_1 (k3_series_1 A) C))) (k9_real_1 (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B) (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) C))) & (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 A) B) (k1_seq_1 (k3_series_1 A) C))) (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B))) ) ) ) ) ) ) ) ).
tt(t10_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  ( ((u1_struct_0 B) = (k2_lp_space A))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) <=>  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (v1_series_1 (k1_lp_space (k2_rsspace C) A))) ) )  &  ( ((k4_struct_0 B) = k6_rsspace)  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (C = (k2_rsspace C)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_algstr_0 B C D) = (k1_series_1 k1_numbers (k2_rsspace C) (k2_rsspace D))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_rlvect_1 B D C) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace D) C)) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k4_algstr_0 B C) = (k32_valued_1 k5_numbers k1_numbers (k2_rsspace C)))  & (r2_funct_2 k5_numbers k1_numbers (k2_rsspace (k4_algstr_0 B C)) (k32_valued_1 k5_numbers k1_numbers (k2_rsspace C)))) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_algstr_0 B C D) = (k47_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace C) (k2_rsspace D))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v1_series_1 (k1_lp_space (k2_rsspace C) A))) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_normsp_0 B C) = (k4_power (k4_series_1 (k1_lp_space (k2_rsspace C) A)) (k10_real_1 1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k6_ltlaxio1 A))) = 1)  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 B D) A)) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t10_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A B C)) (k8_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t10_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  ((r1_tarski (k3_mathmorp A D C) (k3_mathmorp A D B)) & (r1_tarski (k6_rusub_4 A D B) (k6_rusub_4 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v4_matrix10 B) & (v1_matrix10 C))  => (v1_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t10_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ( (~ (v6_struct_0 G))  &  ((v13_algstr_0 G) &  ((v33_algstr_0 G) &  ((v3_group_1 G) &  ((v5_group_1 G) &  ((v2_rlvect_1 G) &  ((v3_rlvect_1 G) &  ((v4_rlvect_1 G) &  ((v4_vectsp_1 G) &  ((v5_vectsp_1 G) & (l6_algstr_0 G)) ) ) ) ) ) ) ) ) ) )  =>  ( ((r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) D (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) C B)) &  ((v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) &  ((k1_funct_1 C E) = F) ) )  =>  ((r1_xxreal_0 F E) |  ( ((k1_group_1 G) = (k4_algstr_0 G (k1_group_1 G)))  |  ( (~  ((k1_funct_1 (k1_matrix11 A G B) (k2_tarski E F)) = (k1_funct_1 (k1_matrix11 A G D) (k2_tarski E F))) )  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k2_finseq_1 (k1_nat_1 A 2))) =>  ( (E = H)  |  ( (F = H)  |  ( (~  ( (~  ((k1_funct_1 (k1_matrix11 A G B) (k2_tarski E H)) = (k1_funct_1 (k1_matrix11 A G D) (k2_tarski E H))) )  &  ((k1_funct_1 (k1_matrix11 A G B) (k2_tarski F H)) = (k1_funct_1 (k1_matrix11 A G D) (k2_tarski F H))) ) )  &  (~  ( (~  ((k1_funct_1 (k1_matrix11 A G B) (k2_tarski F H)) = (k1_funct_1 (k1_matrix11 A G D) (k2_tarski F H))) )  &  ((k1_funct_1 (k1_matrix11 A G B) (k2_tarski E H)) = (k1_funct_1 (k1_matrix11 A G D) (k2_tarski E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) A B) =>  ((k1_matrix12 A B E F C D) = (k1_matrix12 A B E F D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_card_1 (k2_sgraph1 (k2_finseq_1 A))) = (k6_newton 2 A)) ) ) ).
tt(t10_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k13_fvsum_1 A B (k9_fvsum_1 A C D)) = (k8_group_1 A D (k13_fvsum_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 C E) (k2_matrix_1 B)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden F (k7_subset_1 k5_numbers (k4_finseq_1 B) C)) &  ((r2_hidden G (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 B)) D)) &  ( (~  ((k3_matrix_1 (u1_struct_0 A) B F G) = (k4_struct_0 A)) )  &  ((r1_tarski D E) &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers (u1_struct_0 A) (k5_matrix13 E) (k8_matrix_1 (u1_struct_0 A) B F)) = (k5_finseq_2 (u1_struct_0 A) (k5_card_1 E) (k4_struct_0 A)))  & (r1_xxreal_0 (k8_matrix13 A B) (k8_matrix13 A (k6_matrix13 (u1_struct_0 A) B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v1_matrix16 F (u1_struct_0 B)) &  ((v1_matrix16 G (u1_struct_0 B)) & (v1_matrix16 H (u1_struct_0 B))) )  => (v1_matrix16 (k2_matrix_6 A B (k2_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v5_matrix17 B (u1_struct_0 A)) &  ((v5_matrix17 C (u1_struct_0 A)) &  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) )  => (v5_matrix17 (k3_fvsum_1 A B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t10_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) => (m1_matrix_1 (k5_finseq_2 (k4_finseq_2 B C) A (k5_finseq_2 C B D)) C A B)) ) ) ) ) ) ) ) ).
tt(t10_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  =>  ( ((k3_finseq_1 (k4_matrix_1 A B)) = (k1_matrix_1 B))  &  ((k1_matrix_1 (k4_matrix_1 A B)) = (k3_finseq_1 B)) ) ) ) ) ) ) ).
tt(t10_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k12_matrix_1 B A))) =>  ( (C = D)  |  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) D) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_4 A C B) = C) ) )  =>  (B = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ) ) ) ).
tt(t10_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k7_matrix_5 1 A) = A) ) ) ).
tt(t10_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k5_matrix_1 A (u1_struct_0 B) (k12_matrix_1 B A)) = (k12_matrix_1 B A)) ) ) ) ) ).
tt(t10_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k13_matrix_2 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k13_matrix_2 2))) =>  (~  ( (? [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 2)) &  ( (C = A)  & (v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 2)))) ) )  &  ( (? [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 2)) &  ( (C = B)  & (v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 2)))) ) )  &  (~  ((k6_algstr_0 (k13_matrix_2 2) A B) = (k10_finseq_1 1 2)) ) ) ) ) ) ) ) ) ).
tt(t10_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (v1_matrix_8 C A B))  =>  (C = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t10_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 2)) =>  ( (F = (k3_finseq_5 (k1_finseq_2 2)))  =>  ((k10_matrix_3 2 A (k6_matrix_2 (u1_struct_0 A) B C D E) F) = (k2_finseq_4 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 C)) =>  ((k3_matrix_1 k2_numbers (k4_matrix_5 C) A B) = (k1_binop_2 (k3_matrix_1 k2_numbers C A B))) ) ) ) ) ) ) ) ).
tt(t10_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ((r2_hidden A (k4_finseq_1 C)) & (r2_hidden B (k2_finseq_1 (k7_partfun1 k5_numbers C A))))  =>  ((r2_hidden (k1_nat_1 B (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d A 1) C))) (k2_finseq_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers A C)))) &  ((k1_matrixj1 C (k1_nat_1 B (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d A 1) C)))) = A) ) ) ) ) ) ) ) ) ).
tt(t10_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_matrixj2 k1_xboole_0 A B)) ) ) ) ).
tt(t10_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k8_rvsum_1 A B) = (k5_euclid (k3_finseq_1 A))) )  =>  (A = B) ) ) ) ) ) ).
tt(t10_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers (k4_matrixr1 A) B C) = (k1_real_1 (k3_matrix_1 k1_numbers A B C))) ) ) ) ) ) ) ) ).
tt(t10_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  =>  ((k4_rlvect_1 B (k3_fvsum_1 B C D)) = (k3_rlvect_1 B (k4_rlvect_1 B C) (k4_rlvect_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k9_xtuple_0 D)) =>  ((k1_funct_1 E F) = (k4_vectsp_1 A B (k7_partfun1 (u1_struct_0 A) D F) C)) ) ) ) )  =>  ((k4_rlvect_1 B E) = (k4_vectsp_1 A B (k4_rlvect_1 A D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matroid0,ax, (! [A:$i] :  ((v4_taxonom2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_matroid0 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( (! [D:$i] :  ((r2_hidden D B) => (r2_hidden D (k1_funct_1 C D))) )  =>  ((v3_pre_topc B (k2_matroid0 A)) <=> (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(t10_matrprob,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  (! [E:$i] :  ((m2_finseq_1 E A) =>  (~  ( ((k1_funct_1 B D) = E)  &  ((k3_finseq_1 E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_matrtop1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v2_finseq_1 C) & (v1_valued_0 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_xtuple_0 B) (k9_xtuple_0 B)) &  ((v3_funct_2 D (k9_xtuple_0 B) (k9_xtuple_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (k9_xtuple_0 B))))) ) )  =>  ( (C = (k3_relat_1 D B))  =>  ((k16_rvsum_1 (k15_finseq_1 (k5_relat_1 B A))) = (k16_rvsum_1 (k15_finseq_1 (k5_relat_1 C (k8_relat_1 D A))))) ) ) ) ) ) ) ) ) ).
tt(t10_matrtop2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) => (m1_rlvect_2 (k2_partfun1 (u1_struct_0 A) k1_numbers C (u1_struct_0 B)) B)) ) ) ) ) ) ).
tt(t10_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 B B (k1_matrtop3 B A)) C) = (k2_funct_7 C A (k1_real_1 (k1_seq_1 C A)))) ) ) ) ) ) ) ) ).
tt(t10_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_comseq_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k6_normsp_1 A (k2_ndiff_1 A B C)) = (k1_rlvect_1 A B (k2_seq_2 C))) ) ) ) ) ) ) ).
tt(t10_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k1_mboolean A (k4_pboole A B C)) (k2_pboole A (k7_funcop_1 A (k1_tarski k1_xboole_0)) (k4_pboole A (k1_mboolean A B) (k1_mboolean A C))))) ) ) ) ) ).
tt(t10_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_zfmisc_1 B C)) =>  ((r2_hidden (k1_xtuple_0 A) B) & (r2_hidden (k2_xtuple_0 A) C)) ) ) ) ) ).
tt(t10_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) => (r1_xxreal_0 (k12_supinf_2 C (k1_measure1 A B D E)) (k3_supinf_2 (k12_supinf_2 C D) (k12_supinf_2 C E)))) ) ) ) ) ) ) ) ) ).
tt(t10_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B D (k2_nat_1 F 1)) = (k1_measure1 A B (k8_nat_1 B C (k2_nat_1 F 1)) (k8_nat_1 B D F))) ) )  &  ( ((k8_nat_1 B E k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B E (k2_nat_1 F 1)) = (k3_measure1 A B (k8_nat_1 B C (k2_nat_1 F 1)) (k8_nat_1 B D F))) ) ) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 G F))  => (r1_xboole_0 (k8_nat_1 B E F) (k8_nat_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = k1_xboole_0)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 F 1)) = (k3_measure1 A B (k8_nat_1 B E k6_numbers) (k8_nat_1 B E F)))  & (r1_tarski (k8_nat_1 B E (k2_nat_1 F 1)) (k8_nat_1 B E F))) ) ) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k8_nat_1 B E k6_numbers))) |  ((k8_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C))) = (k4_supinf_2 (k12_supinf_2 C (k8_nat_1 B E k6_numbers)) (k7_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_measure4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_measure4 D A) =>  ( ((r2_hidden B (k1_measure4 A D)) & (r2_hidden C (k1_measure4 A D)))  => (r2_hidden (k6_subset_1 B C) (k1_measure4 A D))) ) ) ) ) ) ).
tt(t10_measure5,ax, ((k2_measure5 k1_xboole_0) = k1_supinf_2) ).
tt(t10_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 B C) &  (A = (k1_xxreal_1 B C)) ) ) )  =>  (B = (k7_supinf_2 A)) ) ) ) ) ) ).
tt(t10_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k5_numbers)))) )  =>  ((v2_funct_1 C) => (r1_xxreal_0 (k19_supinf_2 (k1_measure7 B (k1_partfun1 B k5_numbers k5_numbers k7_numbers C A))) (k19_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t10_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  => (v6_supinf_2 (k6_measure8 A B C))) ) ) ) ) ).
tt(t10_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_member_1 (k2_tarski A B)) = (k2_tarski (k2_xxreal_3 A) (k2_xxreal_3 B))) ) ) ) ) ).
tt(t10_membered,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_membered A))  =>  (? [B:$i] :  ((v1_rat_1 B) & (r2_hidden B A)) ) ) ) ).
tt(t10_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v4_memstr_0 C A B)) ) ) )  =>  (~ (r2_hidden (k4_struct_0 B) (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t10_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_euclid_6 (k4_struct_0 (k15_euclid 2)) A B) = (k12_binop_2 (k10_binop_2 (k11_binop_2 (k17_euclid A) (k18_euclid B)) (k11_binop_2 (k17_euclid B) (k18_euclid A))) 2)) ) ) ) ) ).
tt(t10_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ((r2_hidden C k1_numbers) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k12_supinf_2 A D) = (k3_supinf_2 C (k12_supinf_2 B D))) ) ) )  =>  ( ((k6_rinfsup2 A) = (k3_supinf_2 C (k6_rinfsup2 B)))  &  ((k5_rinfsup2 A) = (k3_supinf_2 C (k5_rinfsup2 B))) ) ) ) ) ) ) ) ) ).
tt(t10_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C D) & (r1_mesfun6c A B C E))  => (r1_mesfun6c A B C (k6_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers (k5_mesfun7c A B) C) (k3_mesfun7c A (k10_nat_1 (k4_partfun1 A k1_numbers) B C)))) ) ) ) ) ) ).
tt(t10_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_relset_1 A (k4_mesfunc5 A k1_numbers (k2_mesfun9c A B) C)) = (k1_setfam_1 (a_3_0_mesfun9c A B C))) ) ) ) ) ) ) ).
tt(t10_mesfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k6_xcmplx_0 B A) (k10_real_1 1 (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(t10_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v3_valued_0 B) => (v3_valued_0 (k6_mesfunc1 A B C))) ) ) ) ) ) ) ).
tt(t10_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ( ((k4_finseq_1 A) = (k4_finseq_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k12_supinf_2 B D) = (k1_extreal1 C (k12_supinf_2 A D))) ) ) ) )  =>  ( ( (~ (v1_xreal_0 C))  &  ( (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden D (k4_finseq_1 A)) & (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 A D))) ) )  &  (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden D (k4_finseq_1 A)) & (r1_xxreal_0 (k12_supinf_2 A D) k1_supinf_2)) ) ) ) )  |  ((k4_extreal1 B) = (k1_extreal1 C (k4_extreal1 A))) ) ) ) ) ) ) ) ) ).
tt(t10_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [C:$i] :  (~  ((r2_hidden C (k1_relset_1 A B)) & (r1_xxreal_0 (k12_supinf_2 B C) k2_supinf_1)) ) )  <=> (v3_mesfunc5 B)) ) ) ) ) ).
tt(t10_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_funct_1 D G) = (k3_xboole_0 B (k12_mesfunc1 E (k9_real_1 F (k13_complex1 1 (k1_nat_1 G 1)))))) ) )  =>  ((k3_xboole_0 B (k11_mesfunc1 E F)) = (k5_setfam_1 A (k4_measure1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_mesfunc7,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_mesfunc7 A (k1_nat_1 B 1)) = (k1_extreal1 (k4_mesfunc7 A B) A)) ) ) ) ) ).
tt(t10_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) => (r2_funct_2 k5_numbers k7_numbers (k3_mesfunc5 A (k4_mesfunc8 A B) C) (k4_rinfsup2 (k3_mesfunc5 A B C)))) ) ) ) ) ) ) ).
tt(t10_mesfunc9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((v10_mesfunc5 A) &  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 B (k12_supinf_2 A C))) ) )  => (r1_xxreal_0 B (k2_mesfunc5 A))) ) ) ) ) ).
tt(t10_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_xxreal_0 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 A B) (k7_real_1 (k1_metric_1 k1_numbers k1_numbers k7_metric_1 A C) (k1_metric_1 k1_numbers k1_numbers k7_metric_1 C B)))) ) ) ) ) ) ).
tt(t10_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k1_metric_2 A B)) & (r2_hidden D (k1_metric_2 A B)))  =>  ((k4_metric_1 A C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t10_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ( ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) C D) = k6_numbers)  <=>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t10_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v2_tbsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r1_metric_6 A B C)) ) ) ) ) ) ) ) ) ).
tt(t10_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ( ((v5_topgen_4 C A) &  (D = (k9_subset_1 (u1_struct_0 A) C B)) )  => (v5_topgen_4 D (k1_pre_topc A B))) ) ) ) ) ) ) ) ) ).
tt(t10_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_mfold_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  => (r1_metrizts (k15_euclid A) (k15_euclid A) B (k2_struct_0 (k15_euclid A)))) ) ) ) ).
tt(t10_mfold_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((v8_pre_topc A) & (r1_mfold_2 A B))  => (v8_pre_topc B)) ) ) ) ) ).
tt(t10_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_midsp_1 A B B C C)) ) ) ) ) ) ).
tt(t10_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A D E)) = (k3_rlvect_1 A (k3_rlvect_1 A B D) (k3_rlvect_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_midsp_3 F A) =>  ( (F = B)  =>  ((k1_funct_1 (k1_midsp_3 (u1_struct_0 C) (k2_nat_1 A 1) E B D) F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B C) =>  ( (E = k6_numbers)  | (r1_tarski (k10_mmlquery A B D E) (k4_mmlquery A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_mod_2 B A) &  ((v3_mod_2 B A) & (l1_mod_2 B A)) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  &  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  &  ( ((v2_mod_2 B A) & (m1_mod_2 B A C D))  &  ( (B = (g1_mod_2 A C D E))  &  ((v13_vectsp_1 E C D) & (v1_mod_2 E A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (m1_vectsp_4 (k1_mod_3 A B C) A (k1_mod_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t10_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  => (r8_binop_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k5_mod_4 A B)) (u1_struct_0 (k5_mod_4 A B)) (u1_vectsp_1 (k2_mod_4 A) (k5_mod_4 A B)) (k6_mod_4 A B (u1_vectsp_2 A B)))) ) ) ) ).
tt(t10_modal_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) )  => (r2_hidden A (k4_partfun1 (k3_finseq_2 k5_numbers) (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers)))) ) ).
tt(t10_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ((m4_modcat_1 C A (k4_modcat_1 A B)) =>  (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  ( ((k2_mod_2 A C) = (k3_mod_2 A D))  => (r2_hidden (k8_mod_2 A C D) (k4_modcat_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t10_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_modelc_1 C) & (l2_modelc_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k18_modelc_1 (u3_modelc_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 C))))) )  =>  ((k24_modelc_1 C D (k13_modelc_1 A B)) = (k28_modelc_1 C (k24_modelc_1 C D A) (k24_modelc_1 C D B))) ) ) ) ) ) ) ) ) ).
tt(t10_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  =>  ( ((k3_finseq_1 A) = (k2_nat_1 1 (k3_finseq_1 (k10_modelc_2 A))))  &  (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k10_modelc_2 A)))) ) ) ) ) ).
tt(t10_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  ((r2_hidden B C) =>  ((k18_modelc_3 A (k7_subset_1 (k13_modelc_2 A) C (k1_tarski B))) = (k9_real_1 (k18_modelc_3 A C) (k3_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t10_moebius1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ((r1_nat_d (k1_newton B 2) A) => (r1_nat_d B A)) ) ) ) ) ).
tt(t10_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v13_monoid_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( ((k6_algstr_0 A B D) = C)  &  ((k6_algstr_0 A E B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v1_setwiseo C B) =>  ( ((k4_binop_1 (k9_funct_2 A B) (k8_monoid_1 B B B C A)) = (k5_monoid_1 B A (k4_binop_1 B C)))  & (v1_setwiseo (k8_monoid_1 B B B C A) (k9_funct_2 A B))) ) ) ) ) ) ) ).
tt(t10_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A B (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t10_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v6_trees_3 D)) ) )  =>  ((r2_hidden (k4_trees_4 (k4_tarski C (u1_struct_0 A)) D) (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) (k2_msualg_1 A C))) =>  ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_msafree3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (u1_struct_0 A)) =>  ((k1_funct_1 (k2_msafree3 A (k1_trees_4 (k4_tarski C B))) B) = (k1_tarski C)) )  &  (! [D:$i] :  ( (~  ( (D = B)  & (r2_hidden B (u1_struct_0 A))) )  =>  ((k1_funct_1 (k2_msafree3 A (k1_trees_4 (k4_tarski C B))) D) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t10_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k4_dtconstr (k5_msafree A B))) =>  ((r1_lang1 (k5_msafree A B) (k6_msafree A B C) (k1_dtconstr (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) D)) <=> (r2_hidden D (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k8_msafree A B))) C))) ) ) ) ) ) ) ) ) ).
tt(t10_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~  ( ((k1_funct_1 C k1_xboole_0) = (k4_tarski D (u1_struct_0 A)))  &  (! [E:$i] :  ((m1_msaterm E A B (k2_msaterm A B D)) =>  (~  (C = (k4_trees_4 (k4_tarski D (u1_struct_0 A)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  ((k3_finseq_1 (k7_graph_2 A B)) = (k2_nat_1 (k3_finseq_1 B) 1)) ) ) ) ) ).
tt(t10_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (B = (k2_tarski C D))  =>  ((k8_setfam_1 A B) = (k9_subset_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t10_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_unialg_2 A B) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 (k6_msualg_1 B)) (u3_msualg_1 (k6_msualg_1 B) (k9_msualg_1 B))) =>  ( (C = (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)))  => (v3_msualg_2 C (k6_msualg_1 B) (k9_msualg_1 B))) ) ) ) ) ) ) ) ).
tt(t10_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 (k1_unialg_1 A)) (k3_finseq_2 (k1_tarski k6_numbers))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 (k1_unialg_1 A)) (k3_finseq_2 (k1_tarski k6_numbers)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_tarski k6_numbers)) =>  ( (B = (k1_partfun1 k5_numbers k5_numbers k5_numbers (k3_finseq_2 (k1_tarski k6_numbers)) (k1_unialg_1 A) (k7_finseq_2 k6_numbers)))  =>  ((k6_msualg_1 A) = (g1_msualg_1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) B (k1_margrel1 (k1_tarski k6_numbers) (k4_finseq_1 (k1_unialg_1 A)) C))) ) ) ) ) ) ) ) ).
tt(t10_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) => (m3_pboole (k2_msualg_2 A B) (u1_struct_0 A) (u3_msualg_1 A C))) ) ) ) ) ) ).
tt(t10_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ( ((r1_msualg_3 A B C E) & (r1_msualg_3 A C D F))  => (r1_msualg_3 A B D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  (! [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  =>  ((r8_pboole A E (k3_pboole A C D)) => (r8_pboole A (k4_msualg_5 A B C E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_msualg_6 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k3_msualg_1 A B D)) =>  ((v1_funct_1 (k4_msualg_6 A B C D E)) &  ((v1_funct_2 (k4_msualg_6 A B C D E) (k1_funct_1 (u3_msualg_1 A D) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) C)) (k1_funct_1 (u3_msualg_1 A D) (k2_msualg_1 A B))) & (m1_subset_1 (k4_msualg_6 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A D) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) C)) (k1_funct_1 (u3_msualg_1 A D) (k2_msualg_1 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A (k6_pboole A B B)))) =>  ( (D = C)  =>  ((v1_xboole_0 C) |  (! [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  =>  (! [F:$i] :  ( ((v1_msualg_4 F A B) & (m1_msualg_4 F A B B))  =>  ( ((r8_pboole A E (k4_mssubfam A (k6_pboole A B B) (k5_closure2 A (k6_pboole A B B) D))) &  (F = (k16_lattice3 (k5_msualg_5 A B) C)) )  => (r8_pboole A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msualg_8,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_msualg_5 C)))) =>  ( ((r2_hidden A C) & (r2_hidden B C))  =>  ((r2_hidden (k4_tarski A B) (k15_lattice3 (k2_msualg_5 C) D)) <=>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ((r1_xxreal_0 1 (k3_finseq_1 E)) &  ( (A = (k1_funct_1 E 1))  &  ( (B = (k1_funct_1 E (k3_finseq_1 E)))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 E) F) | (r2_hidden (k4_tarski (k1_funct_1 E F) (k1_funct_1 E (k2_nat_1 F 1))) (k3_tarski D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A (k1_pzfmisc1 A B) C) => (v1_msualg_3 D)) ) ) ) ) ) ) ).
tt(t10_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  ((k6_msualg_1 A) = (k6_msualg_1 B)) ) ) ) ) ) ).
tt(t10_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_dilworth (k1_mycielsk (u1_struct_0 A) B C) (k5_yellow_0 A C)) & (m1_eqrel_1 (k1_mycielsk (u1_struct_0 A) B C) (u1_struct_0 (k5_yellow_0 A C)))) ) ) ) ) ) ) ).
tt(t10_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_nagata_1 B A) =>  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B))) ) ) ) ) ) ).
tt(t10_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( ((r1_pcomps_1 (u1_struct_0 A) B) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_pre_topc A C) = (a_3_0_nagata_2 A B C)) ) ) )  => (v3_pcomps_1 A)) ) ) ) ) ).
tt(t10_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (B = (k2_xcmplx_0 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((k3_power 2 B) = (k3_xcmplx_0 (k3_power 2 A) (k3_power 2 (k7_nat_d B A)))) ) ) ) ) ) ).
tt(t10_nat_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k2_nat_3 A 1) = A) ) ) ).
tt(t10_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k6_nat_d B C) = 1)  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ((k6_nat_d (k1_newton B A) C) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t10_nat_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  ( ( ((k2_xboole_0 A B) = (k4_finseq_1 C))  &  ((r1_xboole_0 A B) &  ((r2_relset_1 k5_numbers k1_numbers D (k1_partfun1 k5_numbers k5_numbers k5_numbers k1_numbers (k14_finseq_1 A) C)) & (r2_relset_1 k5_numbers k1_numbers E (k1_partfun1 k5_numbers k5_numbers k5_numbers k1_numbers (k14_finseq_1 B) C))) ) )  =>  ((k18_rvsum_1 C) = (k9_binop_2 (k18_rvsum_1 D) (k18_rvsum_1 E))) ) ) ) ) ) ) ) ) ) ).
tt(t10_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d A (k2_xcmplx_0 B C)))  => (r1_nat_d A C)) ) ) ) ) ) ) ).
tt(t10_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_nat_lat)) =>  ( ((k1_binop_1 k1_nat_lat A (k1_binop_1 k1_nat_lat B C)) = (k1_binop_1 k1_nat_lat (k1_binop_1 k1_nat_lat B A) C))  &  ( ((k1_binop_1 k1_nat_lat A (k1_binop_1 k1_nat_lat B C)) = (k1_binop_1 k1_nat_lat (k1_binop_1 k1_nat_lat A C) B))  &  ( ((k1_binop_1 k1_nat_lat A (k1_binop_1 k1_nat_lat B C)) = (k1_binop_1 k1_nat_lat (k1_binop_1 k1_nat_lat C B) A))  &  ((k1_binop_1 k1_nat_lat A (k1_binop_1 k1_nat_lat B C)) = (k1_binop_1 k1_nat_lat (k1_binop_1 k1_nat_lat C A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t10_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_1 A) &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_cat_1 B) & (m3_cat_2 B A))  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((u4_struct_0 B) = (u4_struct_0 A)) )  =>  (B = A) ) ) ) ) ) ).
tt(t10_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r3_ncfcont1 B A C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden G (k1_relset_1 (u1_struct_0 B) C)) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B G D))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) C G) (k7_partfun1 (u1_struct_0 A) C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ((r1_ncfcont2 A C D E) => (r1_ncfcont2 A C D (k2_vfunct_2 (u1_struct_0 C) D E B))) ) ) ) ) ) ) ) ) ) ).
tt(t10_ndiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_normsp_1 B (k1_ndiff_1 B C D) A) (k1_ndiff_1 B (k5_normsp_1 B C A) D))) ) ) ) ) ) ) ) ).
tt(t10_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k7_partfun1 (u1_struct_0 B) D (k4_struct_0 A)) = (k4_struct_0 B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v2_ndiff_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((k7_partfun1 (u1_struct_0 C) E (k4_struct_0 B)) = (k4_struct_0 C))  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v2_ndiff_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r2_ndiff_3 A C B) <=>  ((r1_tarski B (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) => (r1_ndiff_3 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ((r1_ndiff_4 B C A) =>  ((r1_ndiff_4 B (k2_nfcont_4 B k1_numbers C) A) &  ((k1_ndiff_4 B (k2_nfcont_4 B k1_numbers C) A) = (k6_euclid B (k1_ndiff_4 B C A))) ) ) ) ) ) ) ) ) ).
tt(t10_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ((u1_struct_0 (k14_prvect_2 A)) = (k4_card_3 (k4_prvect_2 A))) ) ) ).
tt(t10_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((l1_orders_2 C) =>  ((r1_xboole_0 (u1_struct_0 B) (u1_struct_0 C)) =>  ( ( (~  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k1_neckla_2 B C)) )  &  (~  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k2_neckla_2 B C)) ) )  |  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_necklace,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( ( (A = B)  =>  (C = D) )  &  ( ( (C = D)  =>  (A = B) )  &  (~  ((k2_funct_1 (k4_funct_4 A B C D)) = (k4_funct_4 C D A B)) ) ) ) ) ) ) ) ) ).
tt(t10_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) => (r1_tarski (k3_net_1 A B) (k2_net_1 A))) ) ) ) ).
tt(t10_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_newton 1 A) = 1) ) ) ).
tt(t10_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_nfcont_1 B A C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  (! [E:$i] :  ((m1_nfcont_1 E A (k7_partfun1 (u1_struct_0 A) C D)) =>  (? [F:$i] :  ((m1_nfcont_1 F B D) & (r1_tarski (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_nfcont_1 D B) & (r3_nfcont_1 B A C D))  => (r1_nfcont_2 D B A C)) ) ) ) ) ) ) ) ) ).
tt(t10_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_nfcont_3 A B C) <=>  ((r2_hidden C (k1_relset_1 k1_numbers B)) &  (! [D:$i] :  ((m1_nfcont_1 D A (k7_partfun1 (u1_struct_0 A) B C)) =>  (? [E:$i] :  ((m1_rcomp_1 E C) & (r1_tarski (k7_relset_1 k1_numbers (u1_struct_0 A) B E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k2_vfunct_1 B (k4_real_ns1 A) C D) = (k8_integr15 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((r1_normform A B C (k1_normform A B C D)) & (r1_normform A B D (k1_normform A B C D))) ) ) ) ) ) ) ) ) ).
tt(t10_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A (k5_algstr_0 A B D)) (k1_normsp_0 A (k5_algstr_0 A D C))))) ) ) ) ) ) ) ) ).
tt(t10_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v6_waybel_3 A) => (v2_yellow_8 A)) ) ) ).
tt(t10_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  ( ( (A = (k6_int_1 B C))  & (r1_int_2 B C))  =>  ( (C = k6_numbers)  | (r1_int_2 A C)) ) ) ) ) ) ) ) ).
tt(t10_numbers,ax,(r2_xboole_0 k5_numbers k2_numbers)).
tt(t10_numeral1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_nat_d 5 A) <=> (r1_nat_d 5 (k1_recdef_1 (k2_numeral1 A 10) k6_numbers))) ) ) ).
tt(t10_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden B (k7_openlatt A)) <=>  ( (~  (B = (u1_struct_0 A)) )  & (v2_filter_0 B A)) ) ) ) ) ) ).
tt(t10_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v2_necklace A) => (v3_necklace A)) ) ) ).
tt(t10_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( ((k3_graph_1 (k2_oppcat_1 A) (k7_oppcat_1 A B C D)) = (k4_graph_1 A D))  &  ((k4_graph_1 (k2_oppcat_1 A) (k7_oppcat_1 A B C D)) = (k3_graph_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_orders_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r8_relat_2 C A) & (r1_tarski B A))  => (r8_relat_2 C B)) ) ) ) ) ).
tt(t10_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C B) =>  ((v6_orders_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(t10_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ((m1_orders_3 B A) =>  (! [C:$i] :  ((m1_orders_3 C A) => (r1_tarski (k1_orders_3 B C) (k1_ens_1 (k2_orders_3 A)))) ) ) ) ) ) ).
tt(t10_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_ordinal1 C) =>  ( ((r2_hidden A B) & (r2_hidden B C))  => (r2_hidden A C)) ) ) ) ) ).
tt(t10_ordinal2,ax, (! [A:$i] : (r1_tarski (k3_ordinal1 A) A)) ).
tt(t10_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k2_ordinal2 (k1_tarski A)) = A) ) ) ).
tt(t10_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((v2_ordinal2 A) & (r2_hidden B (k9_xtuple_0 A)))  => (r1_ordinal1 B (k1_funct_1 A B))) ) ) ) ) ).
tt(t10_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((r2_hidden 1 A) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k12_ordinal2 A C)) ) ) ) )  => (v2_ordinal2 B)) ) ) ) ) ).
tt(t10_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ((k10_xtuple_0 (k1_ordinal4 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t10_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) =>  ( ( (~ (v3_o_ring_1 C A))  &  ( (~ (v5_o_ring_1 C A))  &  ( (~ (v7_o_ring_1 C A))  &  ( (~ (v9_o_ring_1 C A))  &  ( (~ (v11_o_ring_1 C A))  &  (~ (v13_o_ring_1 C A)) ) ) ) ) )  | (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ) ).
tt(t10_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (C = (k4_struct_0 B)) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_orders_2 B C C)) ) ) ) ) ) ) ) ) ).
tt(t10_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k1_funct_1 B C)) =>  ((m1_dtconstr (k1_trees_4 (k4_tarski E C)) (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) &  ( (! [F:$i] :  (~  ((k4_tarski F (u1_struct_0 A)) = (k1_funct_1 (k1_trees_4 (k4_tarski E C)) k1_xboole_0)) ) )  &  ( ((r2_hidden (k1_trees_4 (k4_tarski E C)) (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) D)) => (r3_orders_2 A C D))  &  ((r3_orders_2 A C D) => (r2_hidden (k1_trees_4 (k4_tarski E C)) (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((v8_osalg_1 A) &  ( ((k1_msualg_1 A B) = k1_xboole_0)  &  ((r1_osalg_1 A B C) &  ((k1_msualg_1 A C) = k1_xboole_0) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t10_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  => (r2_pboole (u1_struct_0 A) (k2_msualg_2 A B) (k3_osalg_2 A B))) ) ) ) ).
tt(t10_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v12_osalg_1 D A) & (l3_msualg_1 D A)) )  =>  ( ((r3_osalg_3 A B C) & (r3_osalg_3 A C D))  => (r3_osalg_3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t10_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_orders_2 A D E) => (r1_tarski (k6_osalg_4 A B C D) (k6_osalg_4 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ( ((k5_algstr_0 A B C) = (k1_rlvect_1 A (k5_algstr_0 A E B) G))  &  ((r1_geomtrap A B D B F) & (r1_geomtrap A C D E F)) )  =>  ( (G = k6_numbers)  |  ((r1_geomtrap A B C B D) |  ( (F = (k3_rlvect_1 A E (k1_rlvect_1 A (k5_algstr_0 A D C) (k2_real_1 (k1_real_1 G)))))  &  ( (F = (k3_rlvect_1 A B (k1_rlvect_1 A (k5_algstr_0 A D B) (k2_real_1 (k1_real_1 G)))))  &  ((k5_algstr_0 A D C) = (k1_rlvect_1 A (k5_algstr_0 A F E) (k1_real_1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 (k9_parsp_1 A)) = (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) ) ) ).
tt(t10_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_parsp_2 A B C D) =>  ((r1_parsp_2 A B D C) &  ((r1_parsp_2 A D C B) &  ((r1_parsp_2 A C B D) &  ((r1_parsp_2 A C D B) & (r1_parsp_2 A D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k5_relset_1 A B D C)) & (m1_subset_1 (k5_relset_1 A B D C) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) ) ) ) ) ) ).
tt(t10_partfun2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ( ((v2_funct_1 E) &  ((r2_hidden A (k1_relset_1 C E)) &  ((r2_hidden B (k1_relset_1 C E)) &  ((k7_partfun1 D E A) = (k7_partfun1 D E B)) ) ) )  =>  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t10_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_partit1 A B C) =>  ( (C = A)  | (r1_partit1 A B (k3_subset_1 A C))) ) ) ) ) ) ) ) ).
tt(t10_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A (k4_relset_1 A A A A B C) (k4_relset_1 A A A A C B)) =>  ((v1_partfun1 (k4_relset_1 A A A A B C) A) &  ((v3_relat_2 (k4_relset_1 A A A A B C)) &  ((v8_relat_2 (k4_relset_1 A A A A B C)) & (m1_subset_1 (k4_relset_1 A A A A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_diraf A B D C E) &  ((r2_diraf A B D F G) &  ((r1_diraf A B C F) & (r3_diraf A D E G)) ) )  =>  ((r3_diraf A B C D) | (r1_diraf A D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r1_pboole A B C) & (r1_pboole A B D))  => (r4_pboole A C D)) ) ) ) ) ) ) ) ).
tt(t10_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 B) => (v1_pcomps_1 B A)) ) ) ) ) ).
tt(t10_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_pcs_0 A B))) =>  ((r1_orders_2 (k17_pcs_0 A B) C D) <=>  (? [E:$i] :  (? [F:$i] :  ((l2_pcs_0 F) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 F)) &  ((r2_hidden E A) &  ( (F = (k1_funct_1 B E))  &  ( (G = C)  &  ( (H = D)  & (r1_orders_2 F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = (k2_pdiff_1 B))  &  ( (C = (k12_finseq_1 k1_numbers D))  & (r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 1) A C)) )  =>  ((k1_funct_1 (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 1) A C) (k12_finseq_1 k5_numbers 1)) = (k12_finseq_1 k1_numbers (k1_fdiff_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_1 2 2 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  &  (? [E:$i] :  ((m1_rcomp_1 E D) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 A B))) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v3_fdiff_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v2_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H E) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 A B) H) (k1_seq_1 (k1_pdiff_2 2 2 A B) D)) = (k7_real_1 (k1_seq_1 F (k9_real_1 H D)) (k1_seq_1 G (k9_real_1 H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r2_pdiff_3 B A) <=> (r3_pdiff_1 2 2 (k1_pdiff_3 1 2 B) A)) ) ) ) ) ).
tt(t10_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (~  ( (D = (k11_finseq_1 A B C))  &  ((r3_pdiff_1 3 1 E D) &  (! [F:$i] :  ((m1_rcomp_1 F A) =>  (~  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 E D))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 E D) I) (k1_seq_1 (k1_pdiff_2 3 1 E D) A)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I A)) (k1_seq_1 H (k9_real_1 I A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r1_pdiff_5 E D))  =>  ((k1_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 E) D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) => (m1_subset_1 (k8_pdiff_1 A B C D) (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B))))) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k1_finseq_7 k1_numbers (k5_euclid A) D (k11_binop_2 C B)) = (k10_rvsum_1 (k1_finseq_7 k1_numbers (k5_euclid A) D B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 (k1_pdiff_1 D A) (k7_euclid A B C)) = (k9_binop_2 (k1_seq_1 (k1_pdiff_1 D A) B) (k1_seq_1 (k1_pdiff_1 D A) C))) ) ) ) ) ) ) ) ) ).
tt(t10_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( (B = C)  =>  ((v1_pdiff_7 B A) <=> (v3_nfcont_1 C (k4_real_ns1 A))) ) ) ) ) ) ) ) ).
tt(t10_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  (! [D:$i] : (v16_pencil_1 (k2_funct_7 (k1_pzfmisc1 A B) C D) A)) ) ) ) ) ) ).
tt(t10_pencil_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_pencil_1 B A) & (v2_pencil_1 B A))  => (r1_pencil_2 A B B)) ) ) ) ) ).
tt(t10_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v11_pencil_1 B) & (v14_pencil_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v13_pencil_1 C))  &  ((v16_pencil_1 C A) & (m3_pboole C A (k12_pralg_1 A B))) )  =>  ((m1_pencil_2 (k4_card_3 C) A B) =>  ((k1_funct_1 C (k3_pencil_1 A C)) = (k2_struct_0 (k1_pencil_1 A B (k3_pencil_1 A C)))) ) ) ) ) ) ) ) ).
tt(t10_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k1_vectsp_9 A B) C))  & (v1_xboole_0 (k4_pencil_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t10_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_int_1 (k2_xcmplx_0 (k3_xcmplx_0 B A) 1) A) = (k4_nat_d 1 A)) ) ) ) ) ).
tt(t10_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ((k7_petri A (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ).
tt(t10_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k6_relat_1 A B) (k5_relat_1 B (k8_relat_1 B A)))) ) ) ).
tt(t10_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_algstr_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k11_polynom3 A C D) B) (k11_polynom3 A (k3_polynom5 A C B) D))) ) ) ) ) ) ) ) ).
tt(t10_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ((k3_polyeq_1 k6_numbers k6_numbers A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t10_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  (! [J:$i] :  ((v1_xreal_0 J) =>  ( (! [K:$i] :  ((v1_xreal_0 K) =>  ((k1_polyeq_2 A B C D E K) = (k2_polyeq_2 A G H I J K)) ) )  =>  ( (A = k6_numbers)  |  ((k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k1_newton F 4)) (k3_xcmplx_0 B (k1_newton F 3))) (k3_xcmplx_0 C (k3_square_1 F))) (k3_xcmplx_0 D F)) E) A) = (k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_square_1 F) (k3_square_1 F)) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 G H) I) (k3_xcmplx_0 (k3_square_1 F) F))) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 G I) (k3_xcmplx_0 H I)) (k3_xcmplx_0 G H)) (k3_square_1 F))) (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 G H) I) F)) (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 F G) (k6_xcmplx_0 F H)) (k6_xcmplx_0 F I)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k2_quin_1 A B C)) &  ( ((k7_polyeq_1 A B C k6_numbers D) = k6_numbers)  &  ( (~  (D = (k12_binop_2 (k9_binop_2 (k7_binop_2 B) (k7_square_1 (k2_quin_1 A B C))) (k11_binop_2 2 A))) )  &  ( (~  (D = (k12_binop_2 (k10_binop_2 (k7_binop_2 B) (k7_square_1 (k2_quin_1 A B C))) (k11_binop_2 2 A))) )  &  ( (~  (D = (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A)))) )  &  (~  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 B A)))  &  ((v1_abian D) &  ((r1_xxreal_0 1 D) &  ( ((k4_polyeq_1 A B k6_numbers (k2_newton C D)) = k6_numbers)  &  ( (~  (C = k6_numbers) )  &  ( (~  (C = (k1_power D (k4_xcmplx_0 (k7_xcmplx_0 B A)))) )  &  (~  (C = (k4_xcmplx_0 (k1_power D (k4_xcmplx_0 (k7_xcmplx_0 B A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k1_newton B 2) = A)  <=>  ( (B = (k1_polyeq_5 2 A))  |  (B = (k4_xcmplx_0 (k1_polyeq_5 2 A))) ) ) ) ) ) ) ).
tt(t10_polyform,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_int_1 (k1_newton (k4_xcmplx_0 1) A))) ) ).
tt(t10_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((k9_fvsum_1 A (k8_finseq_1 (u1_struct_0 A) C D) B) = (k8_finseq_1 (u1_struct_0 A) (k9_fvsum_1 A C B) (k9_fvsum_1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t10_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (r2_hidden C B))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ( (D = (k2_xboole_0 (k1_tarski C) B))  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v1_relat_2 E) &  ((v4_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 E D) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r2_hidden F (k4_finseq_1 (k7_pre_poly A D E))) &  ((k7_partfun1 A (k7_pre_poly A D E) F) = C) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 F G) & (r1_xxreal_0 G (k3_finseq_1 (k7_pre_poly A B E))))  =>  ((k7_partfun1 A (k7_pre_poly A D E) (k2_nat_1 G 1)) = (k7_partfun1 A (k7_pre_poly A B E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k6_polynom3 1 A) = (k2_matrlin k5_numbers (k3_pre_poly k5_numbers A))) ) ) ).
tt(t10_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k8_group_1 A (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) (k1_normsp_1 A C (k7_nat_d (k1_algseq_1 A C) 1))) = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k11_polynom3 A B C)) = (k6_xcmplx_0 (k2_nat_1 (k1_algseq_1 A B) (k1_algseq_1 A C)) 1)) ) ) ) ) ) ) ) ).
tt(t10_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k1_polynom5 (k2_polynom3 (u1_struct_0 k1_complfld) A B)) = (k2_polynom3 k1_numbers (k17_complex1 A) (k17_complex1 B))) ) ) ) ) ).
tt(t10_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k10_ordinal2 A B)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (k10_ordinal2 A B)) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly A) (k15_pre_poly A)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_pre_poly B) (k15_pre_poly B)) =>  (~  ((r3_pre_poly (k10_ordinal2 A B) C (k1_polynom6 A B D E)) &  (! [F:$i] :  ((m2_subset_1 F (k14_pre_poly A) (k15_pre_poly A)) =>  (! [G:$i] :  ((m2_subset_1 G (k14_pre_poly B) (k15_pre_poly B)) =>  (~  ((r3_pre_poly A F D) &  ((r3_pre_poly B G E) & (r6_pboole (k10_ordinal2 A B) C (k1_polynom6 A B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ( (~ (v9_struct_0 C B))  & (m1_subset_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((k2_polynom7 A B (k1_polynom7 A B C D)) = D) ) ) ) ) ) ) ) ).
tt(t10_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k3_polynom5 A D C) B) (k3_polynom5 A D (k6_algstr_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t10_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B (k5_polynom7 A B C D) (k5_polynom7 A B C E)) (k5_polynom7 A B C (k1_algstr_0 B D E)))) ) ) ) ) ) ) ) ) ).
tt(t10_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_poset_1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r1_yellow_2 (u1_struct_0 A) A B C) => (r3_orders_2 A (k3_poset_1 A B) (k3_poset_1 A C))) ) ) ) ) ) ) ).
tt(t10_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (v1_abian B))  =>  ((k1_power B A) = (k4_xcmplx_0 (k1_power B (k4_xcmplx_0 A)))) ) ) ) ) ) ).
tt(t10_pralg_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ( (~  (A = k1_xboole_0) )  =>  ( (~ (v2_struct_0 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A))))  &  ((v1_unialg_1 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A))) &  ((v2_unialg_1 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A))) &  ((v3_unialg_1 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A))) &  ((v4_unialg_1 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A))) & (l1_unialg_1 (g1_unialg_1 (k1_tarski k1_xboole_0) (k8_pralg_1 A)))) ) ) ) ) ) ) ) ).
tt(t10_pralg_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k9_xtuple_0 (k2_pralg_2 (k12_pralg_2 A B C D)))) =>  ( ((k9_xtuple_0 E) = A)  &  ( (! [F:$i] :  ((m1_subset_1 F A) => (r2_hidden (k1_funct_1 E F) (k3_msualg_1 B D (k5_pralg_2 A B C F)))) )  & (r1_tarski (k10_xtuple_0 E) (k9_funct_2 (k9_xtuple_0 (k1_msualg_1 B D)) (k7_pralg_2 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k1_msualg_1 B D) = k1_xboole_0)  &  ( ((k9_xtuple_0 E) = A)  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_funct_1 E F) = (k1_pralg_3 B (k5_pralg_2 A B C F) D)) ) ) ) )  =>  (E = (k1_pralg_3 B (k14_pralg_2 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pre_circ,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C A) =>  ((k5_trees_1 A C B) = (k2_xboole_0 (a_2_1_pre_circ A C) (a_3_0_pre_circ A B C))) ) ) ) ) ) ) ).
tt(t10_pre_ff,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k5_power A B) (k5_power A C))) ) ) ) ) ) ) ) ) ).
tt(t10_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (~  ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 7)  &  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 B)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m2_finseq_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( (D = (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))  &  ( (E = (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)))  &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k6_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) G F) H) J))  &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B D)) = (k6_prelamb A F I))  &  ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B E)) = (k6_prelamb A (k8_finseq_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) G (k12_finseq_1 (u1_struct_0 A) I)) H) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 C B) => (v2_funct_1 (k7_pre_poly A B C))) ) ) ) ) ) ).
tt(t10_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k1_newton B C) (k1_newton A C))) ) ) ) ) ) ) ) ) ) ).
tt(t10_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((l1_pre_topc C) =>  (! [D:$i] :  ((l1_pre_topc D) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D)))  & (m1_pre_topc C A)) )  => (m1_pre_topc D B)) ) ) ) ) ) ) ) ) ).
tt(t10_prgcor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) |  ((k1_prgcor_1 A B) = (k5_int_1 A B)) ) ) ) ) ) ) ).
tt(t10_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((r1_tarski (k2_tarski k1_xboole_0 A) B) & (r1_tarski B (k9_setfam_1 A))) ) ) ) ).
tt(t10_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ((m2_prob_1 C A B) <=>  ( (! [D:$i] :  ((m1_prob_1 D A B) => (r1_xxreal_0 k6_numbers (k1_seq_1 C D))) )  &  ( ((k1_seq_1 C A) = 1)  &  ( (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ((r1_xboole_0 D E) =>  ((k1_seq_1 C (k6_prob_1 A B D E)) = (k7_real_1 (k1_seq_1 C D) (k1_seq_1 C E))) ) ) ) ) )  &  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 D) =>  ((v2_comseq_2 (k8_prob_1 A B D C)) &  ((k2_seq_2 (k8_prob_1 A B D C)) = (k1_seq_1 C (k1_prob_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (v2_prob_1 (k1_prob_3 A B))) ) ) ).
tt(t10_prob_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k7_numbers A B) & (v1_seq_2 A))  =>  ((k1_rinfsup1 A) = (k1_xxreal_2 (k2_relset_1 k7_numbers B))) ) ) ) ) ) ).
tt(t10_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k9_cqc_lang A B C)) (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t10_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) &  ((r1_projdes1 A E F G B) & (r1_projdes1 A E F G C)) )  =>  ( (B = C)  | (r1_projdes1 A E F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((v1_projpl_1 A) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) &  ( (~  (B = C) )  &  ( (~ (r1_incsp_1 A D E))  & (r4_projpl_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A B F) &  ((r1_incsp_1 A B G) &  ( (~  (F = G) )  &  ((r1_incsp_1 A C F) &  ( (~  (B = C) )  &  ((r1_incsp_1 A D G) &  ((r1_incsp_1 A E G) &  ( (~  (D = E) )  &  ((r1_incsp_1 A C H) &  ((r1_incsp_1 A D H) &  ((r1_incsp_1 A E I) &  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ( (~ (r1_incsp_1 A B C))  =>  ((k1_projred1 A C C B) = (k6_partfun1 (k1_projred2 A C))) ) ) ) ) ) ) ) ).
tt(t10_prvect_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m2_finseq_2 F B (k4_finseq_2 A B)) =>  (! [G:$i] :  ((m2_finseq_2 G B (k4_finseq_2 A B)) =>  ((r6_binop_1 B C D) =>  ((k3_finseqop B B B C E (k1_prvect_1 B A D F G)) = (k1_finseqop B B B D (k3_finseqop B B B C E F) (k3_finseqop B B B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A B))) =>  ( ( (D = C)  &  (E = (k1_funct_1 D B)) )  => (r1_xxreal_0 (k1_normsp_0 (k11_prvect_2 A B) E) (k1_normsp_0 (k14_prvect_2 A) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_rlvect_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_prvect_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E))  =>  ((k4_algstr_0 (k5_prvect_3 A B) C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_algstr_0 A D) (k4_algstr_0 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ((v1_pscomp_1 C B) => (v1_pscomp_1 (k9_valued_1 (u1_struct_0 B) k1_numbers C A) B)) ) ) ) ) ) ) ).
tt(t10_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (m1_eqrel_1 (a_3_0_pua2mss1 A B C) (k4_finseq_2 B A))) ) ) ) ) ) ).
tt(t10_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_int_2 A B) &  ((v1_abian A) & (v1_abian B)) ) ) ) ) ) ) ).
tt(t10_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k2_pzfmisc1 A B C))) ) ) ) ) ).
tt(t10_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) => (r1_xxreal_0 1 (k3_finseq_1 (k11_qc_lang1 A B)))) ) ) ) ).
tt(t10_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k3_qc_lang2 A B C) = (k3_qc_lang2 A D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k14_qc_lang1 A B C)) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k24_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t10_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_hidden B (k10_xtuple_0 (k2_qc_lang4 A C))) <=> (r2_qc_lang2 A B C)) ) ) ) ) ) ) ).
tt(t10_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k5_qmax_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k5_qmax_1 A))) =>  ( ((r2_hidden B (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) & (r2_hidden C (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_qmax_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_qmax_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_qmax_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_qmax_1 A)) =>  ( ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F C) &  ((r2_hidden G C) & (r3_qmax_1 A D F)) ) ) )  => (r3_qmax_1 A E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v14_quantal1 B A) =>  ((v15_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k15_lattice3 A C)) = (k15_lattice3 A (a_3_5_quantal1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t10_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k3_quatern2 A) k6_numbers)) ) ) ) ).
tt(t10_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ( ((k18_quaterni A) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ((k20_quaterni A) = k6_numbers) ) )  =>  (A = (k17_quaterni A)) ) ) ) ).
tt(t10_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~ (r2_hidden (k3_quaterni k1_numbers k6_numbers 1 2 3 A B C D) k2_numbers)) ) ) ) ) ) ) ) ) ).
tt(t10_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) )  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t10_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((k9_quofield A (k10_quofield A B) (k10_quofield A C)) = (k10_quofield A (k5_quofield A B C))) ) ) ) ) ) ) ).
tt(t10_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k2_radix_1 A) (k2_radix_1 (k2_xcmplx_0 A 1)))) ) ).
tt(t10_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k1_nat_1 B 1)) & (m2_finseq_1 C (k3_radix_1 A)))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k3_radix_1 A)))  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 B)) =>  ((k1_seq_1 C E) = (k1_seq_1 D E)) ) ) )  =>  ((k2_xcmplx_0 (k8_radix_1 B A D) (k3_xcmplx_0 (k1_newton (k1_radix_1 A) B) (k4_radix_1 (k1_nat_1 B 1) A (k1_nat_1 B 1) C))) = (k8_radix_1 (k1_nat_1 B 1) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k1_radix_3 A) k4_numbers)) ) ).
tt(t10_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k11_radix_1 (k1_radix_1 A)) = 1) ) ) ) ).
tt(t10_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 2 B))  =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (~ (r1_xxreal_0 (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_5 (k2_xcmplx_0 A 2) A B))) (k8_radix_1 (k2_xcmplx_0 A 2) B (k4_radix_6 A B C)))) ) ) ) ) ) ) ) ).
tt(t10_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ((r1_xxreal_0 A (k5_card_1 B)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (~  ((k5_card_1 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t10_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_random_1 A) k7_numbers) &  ((v10_valued_0 B) &  ((v6_supinf_2 B) &  ((v4_measure1 B A (k1_random_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_random_1 A) k7_numbers)))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D k7_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k12_supinf_2 D F) = (k1_extreal1 (k1_measure6 (k1_seq_1 C (k1_funct_1 E F))) (k12_supinf_2 B (k1_tarski (k1_funct_1 E F))))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 B A)) |  ((k1_mesfunc6 A (k1_random_1 A) B C) = (k4_extreal1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((v2_funct_1 D) &  ((k2_relset_1 A D) = C) )  =>  ((k5_bhsp_5 k1_numbers A k33_binop_2 C B) = (k18_rvsum_1 (k4_bhsp_5 k1_numbers A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t10_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 (k1_ranknull A B C D) E) <=>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D E) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (~ (r1_xxreal_0 (k1_rat_1 A) k6_numbers)) ) ) ).
tt(t10_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_hurwitz A (k13_polynom3 A B C) (k3_hurwitz A D 1)) &  ( (~ (r1_hurwitz A B (k3_hurwitz A D 1)))  &  (~ (r1_hurwitz A C (k3_hurwitz A D 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_rcomp_1 A) => (v5_xxreal_2 A)) ) ) ).
tt(t10_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_seq_4 (k10_prob_1 A)) = A) ) ) ).
tt(t10_real_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [B:$i] :  ((r2_hidden B k5_numbers) => (v7_ordinal1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t10_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k4_real_lat A) (k1_funcsdom A k1_numbers (k4_real_lat A) B C) D) (k1_funcsdom A k1_numbers (k4_real_lat A) B (k1_funcsdom A k1_numbers (k4_real_lat A) C D)))) ) ) ) ) ) ) ) ).
tt(t10_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid (k23_binop_2 A 1))) =>  ((k5_square_1 (k12_euclid B)) = (k9_binop_2 (k5_square_1 (k12_euclid (k17_finseq_1 k1_numbers A B))) (k5_square_1 (k1_seq_1 B (k23_binop_2 A 1))))) ) ) ) ) ).
tt(t10_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((m1_subset_1 (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) B C) (u1_struct_0 A)) &  ((m1_subset_1 (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C) (u1_struct_0 A)) & (m1_subset_1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) B) (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t10_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B C) D) = (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B D) (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t10_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_rearran1 C) &  ((v2_rearran1 C) & (m2_finseq_1 C (k1_zfmisc_1 B))) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k9_real_1 (k3_finseq_1 C) 1)) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~  ( ((k6_subset_1 (k1_funct_1 C (k2_nat_1 A 1)) (k1_funct_1 C A)) = (k1_tarski D))  &  ( ((k1_funct_1 C (k2_nat_1 A 1)) = (k2_xboole_0 (k1_funct_1 C A) (k1_tarski D)))  &  ((k6_subset_1 (k1_funct_1 C (k2_nat_1 A 1)) (k1_tarski D)) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_recdef_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( ((k4_xtuple_0 A) = (k4_xtuple_0 B))  &  ( ((k5_xtuple_0 A) = (k5_xtuple_0 B))  &  ( ((k2_xtuple_0 A) = (k2_xtuple_0 B))  &  ((r2_hidden B (k3_zfmisc_1 C D E)) & (r2_hidden A (k3_zfmisc_1 C D E))) ) ) )  =>  (A = B) ) ) ) ) ) ) ).
tt(t10_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((v1_relat_1 E) =>  ( (E = (k2_tarski (k4_tarski A B) (k4_tarski C D)))  =>  ( ((k9_xtuple_0 E) = (k2_tarski A C))  &  ((k10_xtuple_0 E) = (k2_tarski B D)) ) ) ) ) ) ) ) ) ).
tt(t10_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  (~ (r2_hidden (k4_tarski E D) C)) ) ) ) )  <=>  ((k2_relset_1 B C) = B) ) ) ) ) ) ).
tt(t10_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k9_relat_1 (k2_xboole_0 B C) A) = (k2_xboole_0 (k9_relat_1 B A) (k9_relat_1 C A))) ) ) ) ) ) ).
tt(t10_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) &  ((r1_xxreal_0 (k4_finseq_4 D C) A) & (r1_xxreal_0 A (k3_finseq_1 D))) )  =>  ((k7_partfun1 B D A) = (k7_partfun1 B (k1_finseq_6 B D C) (k7_nat_d (k2_nat_1 A 1) (k4_finseq_4 D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) =>  (! [C:$i] :  ((m1_rewrite1 C A) => (m1_rewrite1 C B)) ) ) ) ) ) ) ).
tt(t10_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r1_rewrite2 A B C D) => (r2_rewrite2 A B C D)) ) ) ) ) ) ) ) ).
tt(t10_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( (B = (k1_flang_1 A C D))  =>  ( (C = (k2_flang_1 A))  |  ( (D = (k2_flang_1 A))  |  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) (k1_afinsq_1 C)))  &  (~ (r1_xxreal_0 (k1_afinsq_1 B) (k1_afinsq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ( ((k4_rfinseq2 (k10_rvsum_1 A B)) = (k8_real_1 B (k4_rfinseq2 A)))  &  ((k2_rfinseq2 (k10_rvsum_1 A B)) = (k2_rfinseq2 A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_real_1 C 2))  &  ((k1_seq_1 A (k3_real_1 C 1)) = B) )  =>  ((k3_rfinseq (k17_finseq_1 k1_numbers (k3_real_1 C 1) A)) = (k8_finseq_1 k1_numbers (k17_finseq_1 k1_numbers C (k3_rfinseq A)) (k12_finseq_1 k1_numbers B))) ) ) ) ) ) ) ) ).
tt(t10_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k18_valued_1 (k1_valued_1 A B) C) = (k1_valued_1 (k18_valued_1 A C) (k18_valued_1 B C))) ) ) ) ) ) ) ).
tt(t10_rfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A B)) =>  ((r2_relset_1 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A C B)) (k8_funct_2 k5_numbers k1_numbers A C (k56_valued_1 A k1_numbers B))) & (r2_relset_1 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A C B)) (k8_funct_2 k5_numbers k1_numbers A C (k32_valued_1 A k1_numbers B)))) ) ) ) ) ) ) ) ).
tt(t10_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers C))  =>  ((k8_relset_1 A k1_numbers (k56_valued_1 A k1_numbers B) (k1_tarski C)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t10_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_rfunct_4 A B) & (r1_tarski C B))  => (r1_rfunct_4 A C)) ) ) ) ) ).
tt(t10_rinfsup1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 A (k1_seq_1 B C))) )  <=>  ((v2_seq_2 B) & (r1_xxreal_0 A (k2_rinfsup1 B))) ) ) ) ) ) ).
tt(t10_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers A B) & (v1_comseq_2 B))  =>  ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers (k3_rinfsup2 A) (k3_rinfsup1 B)) &  ((k6_rinfsup2 A) = (k6_rinfsup1 B)) ) ) ) ) ) ) ).
tt(t10_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k8_eqrel_1 (u1_struct_0 A) (k1_ring_1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))) = (k10_xtuple_0 (k11_setwiseo (u1_struct_0 A)))) ) ) ).
tt(t10_ringcat1,ax, (! [A:$i] :  ( ((v2_ringcat1 A) &  ((v3_ringcat1 A) & (l1_ringcat1 A)) )  =>  (! [B:$i] :  ( ((v2_ringcat1 B) &  ((v3_ringcat1 B) & (l1_ringcat1 B)) )  =>  (! [C:$i] :  ( ((v2_ringcat1 C) &  ((v3_ringcat1 C) & (l1_ringcat1 C)) )  =>  ( ( ((k1_ringcat1 C) = (k2_ringcat1 B))  &  ((k1_ringcat1 B) = (k2_ringcat1 A)) )  =>  ((k6_ringcat1 C (k6_ringcat1 B A)) = (k6_ringcat1 (k6_ringcat1 C B) A)) ) ) ) ) ) ) ) ).
tt(t10_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k1_convex1 C D (k8_real_1 A B)) = (k1_convex1 C (k1_convex1 C D B) A)) ) ) ) ) ) ) ) ) ).
tt(t10_rlaffin2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_hidden A (k1_rlaffin2 B C)) &  (! [D:$i] :  ((m2_rlvect_2 D B C) =>  (~  ((v2_convex1 D B) &  (A = (k6_rlvect_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rlaffin3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 B)))))  =>  (! [E:$i] :  ((k7_relset_1 C (u1_struct_0 B) (k4_vfunct_1 C B D A) E) = (k1_convex1 B (k7_relset_1 C (u1_struct_0 B) D E) A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t10_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( ((k1_rlsub_2 A (k1_rlsub_1 A) (k2_rlsub_1 A)) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  &  ((k1_rlsub_2 A (k2_rlsub_1 A) (k1_rlsub_1 A)) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ).
tt(t10_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k6_rusub_4 A B D) (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t10_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ( (A = k6_numbers)  |  (C = (k4_struct_0 B)) )  =>  ((k1_rlvect_1 B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t10_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  ((k2_rlvect_2 A (k7_domain_1 (u1_struct_0 A) B C)) = (k3_rlvect_1 A B C)) ) ) ) ) ) ) ) ).
tt(t10_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) =>  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_rlvect_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k3_rlsub_1 B C (k1_rlvect_3 B (k6_domain_1 (u1_struct_0 B) D)))) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (A = (k3_rlvect_1 B C (k1_rlvect_1 B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((r1_tarski (k3_rlvect_2 A C) (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rlvect_2 D B) =>  ( (D = (k2_partfun1 (u1_struct_0 A) k1_numbers C (u1_struct_0 B)))  =>  ( ((k3_rlvect_2 A C) = (k3_rlvect_2 B D))  &  ((k6_rlvect_2 A C) = (k6_rlvect_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rlvect_x,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden C (k2_rlvect_x B D)) => (r2_hidden (k1_rlvect_1 B C A) (k2_rlvect_x B D))) ) ) ) ) ) ) ) ) ).
tt(t10_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (m1_subset_1 D (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t10_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ( ((k1_rmod_3 A B (k1_rmod_2 A B) (k2_rmod_2 A B)) = B)  &  ((k1_rmod_3 A B (k2_rmod_2 A B) (k1_rmod_2 A B)) = B) ) ) ) ) ) ).
tt(t10_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k4_subset_1 (u1_struct_0 B) C D)) = (k5_algstr_0 B (k3_rlvect_1 B (k1_rmod_4 A B C) (k1_rmod_4 A B D)) (k1_rmod_4 A B (k9_subset_1 (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t10_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_robbins1 A B) = (k3_robbins1 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t10_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A B (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A C D)) (k3_robbins1 A (k1_lattices A C B)))))) = (k3_robbins1 A (k1_lattices A C B))) ) ) ) ) ) ) ) ) ).
tt(t10_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v6_lattices A))  => (v6_lattices B)) ) ) ) ) ).
tt(t10_robbins4,ax,(r1_tarski (u1_struct_0 k2_robbins4) (k1_zfmisc_1 3))).
tt(t10_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 C D))) ) ) ) ) )  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) ) ) ) ) ) ) ).
tt(t10_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (~  ((r2_hidden C (k4_roughs_1 A B)) & (r1_xboole_0 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) C) B)) ) ) ) ) ) ) ).
tt(t10_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ( ((v3_card_1 C 1) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (~ (r1_tarski C B)) ) ) ) ) ) ) ) ) ).
tt(t10_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k5_rsspace4 A B)) = (k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ).
tt(t10_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  ((k1_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) A 1) = A) ) ) ).
tt(t10_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = D)  &  (F = C) )  =>  ((k5_algstr_0 B E F) = (k5_algstr_0 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rusub_2 A (k1_rusub_1 A) (k2_rusub_1 A)) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)))  &  ((k1_rusub_2 A (k2_rusub_1 A) (k1_rusub_1 A)) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ).
tt(t10_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (m1_rusub_1 (k1_rusub_3 A (k9_subset_1 (u1_struct_0 A) B C)) (k2_rusub_2 A (k1_rusub_3 A B) (k1_rusub_3 A C)))) ) ) ) ) ) ).
tt(t10_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_rusub_4 A) = (k1_rusub_4 (k2_rusub_1 A))) ) ) ).
tt(t10_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r1_tarski (k7_rusub_4 A B (k6_domain_1 (u1_struct_0 A) D)) (k7_rusub_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t10_rvsum_1,ax,(r7_binop_1 k1_numbers k31_binop_2 k33_binop_2)).
tt(t10_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k5_rvsum_2 (k3_rvsum_2 A B)) = (k3_rvsum_2 (k5_rvsum_2 A) (k5_rvsum_2 B))) ) ) ) ) ).
tt(t10_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D B)) = C)  &  ((k3_compos_1 k1_ami_3 A C) = (k8_ami_3 F E)) )  =>  ( ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) E) = k6_numbers)  =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = F) )  &  ( ( (~  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) E) = k6_numbers) )  =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = (k2_nat_1 C 1)) )  &  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) G) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ( ( (~  (B = (k14_scmfsa_2 D E C)) )  &  (~  (B = (k15_scmfsa_2 D E C)) ) )  | (r2_hidden C (k4_sf_mastr A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k17_scm_comp (k2_scm_comp A B C)) = (k7_nat_1 (k17_scm_comp B) (k17_scm_comp C))) ) ) ) ) ) ) ).
tt(t10_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k6_scmfsa_2 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t10_scmfsa_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_scmfsa_1 k2_scmfsa_1) =>  ((k1_funct_1 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1) A) = k4_numbers) ) ) ).
tt(t10_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3))) ) ) ).
tt(t10_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmfsa_2)))  =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k10_scmfsa_2 H I))  & (r2_hidden I (k9_xtuple_0 B)))  =>  ((k6_int_1 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) I)) = (k6_int_1 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H) (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmfsa6c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa6c C D) A B) C) = (k1_funct_1 A D))  &  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa6c C D) A B) D) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  & (r3_scmfsa7b (k10_scmfsa_2 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t10_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_scmfsa7b A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (v1_scmfsa7b (k6_compos_1 k1_scmfsa_2 A B))) ) ) ) ).
tt(t10_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_scmfsa6c C) &  ((v2_scmfsa6c C) & (m1_subset_1 C (u1_compos_1 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa6a C D) B A) E) = (k18_scmfsa_2 (k1_scmfsa6b D (k2_extpro_1 3 k1_scmfsa_2 C (k1_scmfsa_m B)) A) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k4_sf_mastr (k2_scmfsa8b A B C)) = (k1_finsub_1 (k1_zfmisc_1 k3_scmfsa_2) (k4_sf_mastr B) (k4_sf_mastr C))) ) ) ) ) ) ) ).
tt(t10_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k2_afinsq_1 (k1_scmfsa_9 A B))) &  ((r2_hidden 1 (k2_afinsq_1 (k1_scmfsa_9 A B))) &  ((r2_hidden k6_numbers (k2_afinsq_1 (k2_scmfsa_9 A B))) & (r2_hidden 1 (k2_afinsq_1 (k2_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t10_scmfsa_m,ax,(r2_hidden (k4_scmfsa_2 k6_numbers) (k9_xtuple_0 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))).
tt(t10_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) A) &  ((r1_tarski C B) & (r1_extpro_1 3 k1_scmfsa_2 B A)) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 B A)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 B A E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (r1_xxreal_0 (k2_compos_0 k3_scm_inst A) 8)) ) ).
tt(t10_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_scm_halt C D A) &  ((r2_scm_halt C D A) &  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k1_scmfsa_m D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m D))))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m D) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m D)))) 4)) ) )  =>  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k1_scmfsa_m D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m D))))) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 C) 4))) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmpds_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r2_hidden A (k3_enumset1 4 5 6 7 8)) => (r2_hidden (k3_xtuple_0 A k1_xboole_0 (k11_finseq_1 B C D)) k1_scmpds_i)) ) ) ) ) ) ) ) ).
tt(t10_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((k1_ordinal1 (k5_memstr_0 2 k1_scmpds_2 A)) = (k17_scmpds_2 A 1)) ) ) ).
tt(t10_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ((k4_scmpds_4 A B) = (k2_scmpds_4 A (k9_compos_1 k1_scmpds_2 B))) ) ) ) ) ).
tt(t10_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_scmpds_6 D C A) &  ((r2_scmpds_6 D C A) &  ((r1_tarski (k10_compos_1 k1_scmpds_2 D) A) & (r1_tarski (k10_compos_1 k1_scmpds_2 D) B)) ) )  =>  ( ((k8_extpro_1 2 k1_scmpds_2 A C) = (k8_extpro_1 2 k1_scmpds_2 B C))  &  ((k6_extpro_1 2 k1_scmpds_2 A C) = (k6_extpro_1 2 k1_scmpds_2 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k6_scmpds_4 (k1_scmpds_8 D F C) B A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k1_amistd_1 2 k1_scmpds_2 C (k12_scmpds_2 A B D E)) = (k1_tarski (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmp_gcd,ax, ( ((k1_funct_1 k4_scmp_gcd k6_numbers) = (k5_scmpds_2 k2_scmp_gcd k6_numbers))  &  ( ((k1_funct_1 k4_scmp_gcd 1) = (k5_scmpds_2 k3_scmp_gcd 7))  &  ( ((k1_funct_1 k4_scmp_gcd 2) = (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i))  &  ( ((k1_funct_1 k4_scmp_gcd 3) = (k3_scmpds_2 2))  &  ( ((k1_funct_1 k4_scmp_gcd 4) = (k2_compos_1 k1_scmpds_2))  &  ( ((k1_funct_1 k4_scmp_gcd 5) = (k8_scmpds_2 k3_scmp_gcd 3 9))  &  ( ((k1_funct_1 k4_scmp_gcd 6) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 6 3))  &  ( ((k1_funct_1 k4_scmp_gcd 7) = (k15_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 3))  &  ( ((k1_funct_1 k4_scmp_gcd 8) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 7 3))  &  ( ((k1_funct_1 k4_scmp_gcd 9) = (k16_scmpds_2 k3_scmp_gcd k2_scmp_gcd (k2_nat_1 4 k14_scmpds_i) 1))  &  ( ((k1_funct_1 k4_scmp_gcd 10) = (k11_scmpds_2 k2_scmp_gcd 1 4))  &  ( ((k1_funct_1 k4_scmp_gcd 11) = (k6_scmpds_2 k3_scmp_gcd k15_scmpds_i))  &  ( ((k1_funct_1 k4_scmp_gcd 12) = (k3_scmpds_2 (k4_xcmplx_0 7)))  &  ( ((k1_funct_1 k4_scmp_gcd 13) = (k16_scmpds_2 k3_scmp_gcd k3_scmp_gcd 2 6))  &  ((k1_funct_1 k4_scmp_gcd 14) = (k4_scmpds_2 k3_scmp_gcd)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (k4_scmring1 A B C D) k5_numbers) = (k1_funct_1 B k5_numbers)) ) ) ) ) ) ) ) ) ).
tt(t10_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 B (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 (k1_scmring2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_scmringi A)) =>  ( (D = C)  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  ( (E = B)  =>  ((k2_extpro_1 2 (k1_scmring2 A) C B) = (k7_scmring1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) (k8_scmring2 A B)) = 6) ) ) ) ) ).
tt(t10_scmring4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 B))))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 B))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 E (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 F (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 I) &  ((v1_finset_1 I) &  (~ (v2_compos_1 I (k1_scmring2 B))) ) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 (k1_scmring2 B))) &  ( (~ (v1_xboole_0 J))  &  ((v1_finset_1 J) & (v4_extpro_1 J 2 (k1_scmring2 B) I)) ) ) ) ) )  =>  ( ((r1_tarski J E) &  ((r1_tarski J F) &  ((r1_tarski I G) &  ((r1_tarski I H) &  ( ((k3_extpro_1 2 (k1_scmring2 B) G (k5_extpro_1 2 (k1_scmring2 B) G E A)) = (k6_scmring2 B C D))  & (r2_hidden C (k9_xtuple_0 J))) ) ) ) )  =>  ((k6_algstr_0 B (k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) G E A) C) (k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) G E A) D)) = (k6_algstr_0 B (k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) H F A) C) (k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) H F A) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k3_xtuple_0 6 (k12_finseq_1 k5_numbers B) k1_xboole_0) (k1_scmringi A))) ) ) ) ).
tt(t10_scmyciel,ax, (! [A:$i] :  ((k1_card_1 (a_1_0_scmyciel A)) = (k1_card_1 A)) ) ).
tt(t10_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k4_scpinvar A B C))) & (r2_hidden 1 (k9_xtuple_0 (k4_scpinvar A B C)))) ) ) ) ) ) ) ).
tt(t10_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_scmpds_4 D) &  ((v1_scmpds_5 D) & (m1_subset_1 D (u1_compos_1 k1_scmpds_2))) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_scmpds_6 (k3_scmpds_4 C D) B A) & (r2_scmpds_6 (k3_scmpds_4 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ((r1_xxreal_0 (k2_nat_1 D 1) C) & (r1_xxreal_0 7 D)) ) )  =>  ((r1_scmpds_6 k1_scpqsort B A) & (r2_scmpds_6 k1_scpqsort B A)) ) ) ) ) ) ) ) ) ) ).
tt(t10_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~ (r2_analoaf A B C D E))  =>  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers A (k32_valued_1 k5_numbers k1_numbers B)) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 A C) = (k1_real_1 (k1_seq_1 B C))) ) ) ) ) ) ) ) ).
tt(t10_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  ((k2_seq_2 (k32_valued_1 k5_numbers k1_numbers A)) = (k1_real_1 (k2_seq_2 A))) ) ) ) ).
tt(t10_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_seq_4 (k1_seq_4 A)) = (k4_seq_4 (k1_seq_4 A))) ) ) ).
tt(t10_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k2_seqfunc A D (k8_real_1 B C)) (k2_seqfunc A (k2_seqfunc A D C) B))) ) ) ) ) ) ) ) ).
tt(t10_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A k6_numbers) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ) ).
tt(t10_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 B) =>  ((v1_series_1 (k26_valued_1 k5_numbers k1_numbers B A)) &  ((k4_series_1 (k26_valued_1 k5_numbers k1_numbers B A)) = (k4_real_1 A (k4_series_1 B))) ) ) ) ) ) ) ).
tt(t10_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 1 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 2)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 1 4) (k13_complex1 1 (k4_nat_1 (k4_nat_1 2 (k2_nat_1 B 1)) (k2_nat_1 B 2))))) ) ) ) ) ) ).
tt(t10_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 B C)) (k3_xcmplx_0 A C)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)))) ) ) ) ) ) ).
tt(t10_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 C D) = (k1_newton B D)) ) )  =>  ( (B = 1)  |  ((k1_seq_1 (k3_series_1 C) A) = (k7_xcmplx_0 (k6_xcmplx_0 1 (k1_newton B (k2_nat_1 A 1))) (k6_xcmplx_0 1 B))) ) ) ) ) ) ) ) ) ).
tt(t10_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k13_complex1 2 (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B))) (k13_complex1 (k2_xcmplx_0 A B) 2))) ) ) ) ).
tt(t10_setfam_1,ax, (! [A:$i] :  ((k1_setfam_1 (k1_tarski A)) = A) ) ).
tt(t10_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C D) = B) ) )  =>  ((k1_kurato_0 A C) = B) ) ) ) ) ) ) ).
tt(t10_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k7_subset_1 A (k1_prob_1 A B) (k1_prob_1 A C)) (k1_prob_1 A (k3_setlim_2 A B C)))) ) ) ) ) ).
tt(t10_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F C) => (r2_hidden (k3_funct_2 A B E F) D)) ) )  => (r1_tarski (k7_relset_1 A B E C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t10_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 D B) &  ((v2_binop_1 D B) & (v1_setwiseo D B)) )  =>  ((k5_binop_1 B D (k7_setwiseo A B D C E) (k7_setwiseo A B D C F)) = (k7_setwiseo A B D C (k6_funcop_1 B A D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A)) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m (k1_scmfsa6b C B A))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b C B A))) ) ) ) ) ) ) ) ).
tt(t10_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) k6_numbers) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ).
tt(t10_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) k6_numbers) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ( ((k15_scmfsa_2 B A E) = (k15_scmfsa_2 D C F))  =>  ( (A = C)  &  ( (B = D)  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k2_tarski B C) (k2_sgraph1 A)) =>  ((r2_hidden B A) &  ((r2_hidden C A) &  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t10_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) )  => (v8_lattices A)) ) ).
tt(t10_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A C B)) B) B)) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t10_simplex0,ax, (! [A:$i] :  ( ((v6_ordinal1 A) & (v1_finset_1 A))  =>  ((v1_setfam_1 A) => (r1_ordinal1 (k5_card_1 A) (k1_card_1 (k3_tarski A)))) ) ) ).
tt(t10_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_simplex1 C A B) =>  ((k3_simplex1 A B) = (k3_simplex1 A C)) ) ) ) ) ) ) ).
tt(t10_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_simplex2 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))) = (k3_tbsp_1 A B)) ) ) ) ) ).
tt(t10_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t10_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 k16_sin_cos A) = (k1_seq_1 k16_sin_cos (k7_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A))) ) ) ) ) ).
tt(t10_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) = (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k1_binop_2 A))) ) ) ).
tt(t10_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  (~  ((k2_sin_cos4 (k6_xcmplx_0 A B)) = (k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_sin_cos4 A) (k2_sin_cos4 B)) 1) (k6_xcmplx_0 (k2_sin_cos4 B) (k2_sin_cos4 A)))) ) ) ) ) ) ) ) ) ).
tt(t10_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k17_sin_cos A) = k6_numbers) )  =>  ((k2_sin_cos4 (k8_real_1 2 A)) = (k10_real_1 (k9_real_1 (k5_square_1 (k2_sin_cos4 A)) 1) (k8_real_1 2 (k2_sin_cos4 A)))) ) ) ) ).
tt(t10_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_seq_1 k19_sin_cos A) = (k1_seq_1 k19_sin_cos (k3_real_1 A (k8_real_1 (k8_real_1 2 k32_sin_cos) B)))) ) ) ) ) ).
tt(t10_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k9_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 A 1) 2)) (k7_square_1 (k12_binop_2 (k10_binop_2 A 1) 2))) k6_numbers)) ) ) ) ).
tt(t10_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  =>  ( ((k2_xcmplx_0 (k1_sin_cos5 A) (k9_sin_cos2 B)) = (k7_xcmplx_0 (k6_sin_cos2 (k2_xcmplx_0 A B)) (k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B))))  &  ((k6_xcmplx_0 (k1_sin_cos5 A) (k9_sin_cos2 B)) = (k7_xcmplx_0 (k6_sin_cos2 (k6_xcmplx_0 A B)) (k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)))) ) ) ) ) ) ) ).
tt(t10_sin_cos9,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)))).
tt(t10_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k8_nat_1 k2_numbers (k3_sin_cos A) k6_numbers) = 1)  &  ((k8_nat_1 k2_numbers (k8_sin_cos k6_numbers A B) k6_numbers) = 1) ) ) ) ) ) ).
tt(t10_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_sppol_1 A B (k6_domain_1 (u1_struct_0 (k15_euclid A)) B))) ) ) ) ).
tt(t10_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k2_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B) (k1_nat_1 C 1)) = (k2_topreal1 2 A (k1_nat_1 C (k4_finseq_4 A B)))) ) ) ) ) ) ) ) ).
tt(t10_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_tarski A B) & (v2_sppol_1 B))  => (v2_sppol_1 A)) ) ) ) ) ).
tt(t10_sprect_2,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) &  ((k18_euclid B) = (k7_pscomp_1 A)) )  => (r2_hidden B (k15_pscomp_1 A))) ) ) ) ) ).
tt(t10_sprect_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) & (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) B C)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t10_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k10_xtuple_0 A)) &  ((r2_hidden C (k10_xtuple_0 A)) &  ((r2_hidden D (k10_xtuple_0 A)) &  ( (~ (r1_xxreal_0 (k4_finseq_4 A C) (k4_finseq_4 A B)))  &  ( (~ (r1_xxreal_0 (k4_finseq_4 A D) (k4_finseq_4 A C)))  & (r1_xxreal_0 (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A C) B) (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  ((k6_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) = k6_numbers) )  =>  ((k7_xcmplx_0 1 (k2_xcmplx_0 A B)) = (k7_xcmplx_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 (k3_square_1 A) (k3_square_1 B)))) ) ) ) ) ) ).
tt(t10_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k9_stacks_1 A B) = k1_xboole_0)  => (r1_stacks_1 A B)) ) ) ) ) ).
tt(t10_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A B) =>  ((r1_xxreal_0 A (k21_binop_2 B 1)) & (m1_subset_1 (k21_binop_2 B 1) k5_numbers)) ) ) ) ) ) ).
tt(t10_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((v5_relat_1 (k3_substut1 A C D) (k3_qc_lang1 A)) &  ((v3_card_1 (k3_substut1 A C D) B) & (m2_finseq_1 (k3_substut1 A C D) (k2_qc_lang1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t10_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k4_subset_1 A B (k3_subset_1 A B)) = (k2_subset_1 A)) ) ) ) ).
tt(t10_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((v1_finset_1 D) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  (~  ((r1_tarski E D) & (r2_hidden E (k3_substlat A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (B = (k1_domain_1 (k9_qc_lang1 A) (k1_substut1 A) (k18_substut1 A B) (k19_substut1 A B))) ) ) ) ) ).
tt(t10_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ( ( ((k19_substut1 A E) = (k14_sublemma A (k3_qc_lang1 A) (k2_substut1 A (k7_substut1 A C (k11_cqc_lang A C B) D)) (k12_sublemma A (k3_qc_lang1 A) C (k35_substut1 A (k1_substut2 A (k11_cqc_lang A C B) D)))))  &  ((k2_sublemma A E) = B) )  =>  ((v3_substut1 (k7_sublemma A E C) A) &  (? [F:$i] :  ((m2_subset_1 F (k16_substut1 A) (k38_substut1 A)) &  (F = (k1_substut2 A (k11_cqc_lang A C B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  ( ((v4_xxreal_2 A) & (v4_xxreal_2 B))  => (r1_xxreal_0 (k8_supinf_2 (k5_supinf_2 A B)) (k3_supinf_2 (k8_supinf_2 A) (k8_supinf_2 B)))) ) ) ) ) ).
tt(t10_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 B)) )  &  ( (~  (D = (k4_struct_0 B)) )  &  ( (~  (E = (k4_struct_0 B)) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B F C))  &  ( (~ (r1_orders_2 B F D))  &  (~ (r1_orders_2 B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r1_xboole_0 A B) & (r1_tarski C (k2_xboole_0 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A))))  => (r1_tarski (k5_relat_1 C A) (k2_zfmisc_1 A B))) ) ) ) ) ).
tt(t10_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_t_0topsp B)) (u1_struct_0 (k3_t_0topsp A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_t_0topsp B)) (u1_struct_0 (k3_t_0topsp A)))))) )  &  ((v3_tops_2 C (k3_t_0topsp B) (k3_t_0topsp A)) & (r2_classes1 (k4_t_0topsp A) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 (k3_t_0topsp B)) (u1_struct_0 (k3_t_0topsp B)) (u1_struct_0 (k3_t_0topsp A)) (k4_t_0topsp B) C))) ) )  => (r1_t_0topsp A B)) ) ) ) ) ).
tt(t10_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relset_1 A A B C) => (r1_relset_1 A A (k13_lang1 A B) (k13_lang1 A C))) ) ) ) ) ) ) ).
tt(t10_taxonom2,ax, (! [A:$i] : (v4_taxonom2 (k1_tarski A))) ).
tt(t10_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k9_prepower (k1_seq_1 k24_sin_cos 1) A) = (k1_seq_1 k24_sin_cos A))  &  ( ((k3_power (k1_seq_1 k24_sin_cos 1) A) = (k1_seq_1 k24_sin_cos A))  &  ( ((k3_power k8_power A) = (k1_seq_1 k24_sin_cos A))  &  ((k9_prepower k8_power A) = (k1_seq_1 k24_sin_cos A)) ) ) ) ) ) ).
tt(t10_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_taylor_1 k24_sin_cos B A)) ) ) ) ).
tt(t10_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~  (B = k1_xboole_0) )  &  ((v6_tbsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E B) => (r1_xxreal_0 (k2_metric_1 A D E) C)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((v8_metric_1 A) & (v9_metric_1 A))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E B) => (r1_xxreal_0 (k2_metric_1 A D E) C)) ) ) ) ) ) ) ) )  | (v6_tbsp_1 B A)) ) ) ) ) ) ) ).
tt(t10_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r1_tdgroup A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t10_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A C)) C)))) (k4_subset_1 (u1_struct_0 A) B (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A C)) C))) = (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t10_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k1_pcomps_1 A (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_pcomps_1 A B) (k1_pcomps_1 A C)))) ) ) ) ) ) ).
tt(t10_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v1_tdlat_3 A) & (v2_tdlat_3 A))  =>  ((k9_setfam_1 (u1_struct_0 A)) = (k2_tarski k1_xboole_0 (u1_struct_0 A))) ) ) ) ).
tt(t10_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r3_pre_poly A C D) => (r1_termord A B C D)) ) ) ) ) ) ) ) ) ).
tt(t10_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~  (B = (u1_struct_0 A)) )  =>  ((k1_tops_1 A B) = k1_xboole_0) )  &  ( (B = (u1_struct_0 A))  =>  ((k1_tops_1 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t10_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (~  ( ((u1_struct_0 B) = (u1_struct_0 A))  & (v1_tex_2 B A)) ) ) ) ) ) ).
tt(t10_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tops_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t10_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_tex_4 (k1_tex_4 A B) A)) ) ) ) ).
tt(t10_tietze,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r1_seqfunc A k1_numbers C B) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (v1_xreal_0 E))  =>  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_tietze (k47_valued_1 A k1_numbers k1_numbers (k1_seqfunc A k1_numbers C F) (k1_seqfunc A k1_numbers C (k1_nat_1 F 1))) (k3_xcmplx_0 D (k3_power E F)) B)) )  =>  ((r1_xxreal_0 1 E) |  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r1_xxreal_0 (k9_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers C k6_numbers) F) (k6_real_1 D (k9_real_1 1 E))) (k1_seq_1 (k11_seqfunc A C B) F)) & (r1_xxreal_0 (k1_seq_1 (k11_seqfunc A C B) F) (k7_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers C k6_numbers) F) (k6_real_1 D (k9_real_1 1 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((m1_pre_topc B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) &  (E = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v3_relat_2 D) => (v3_relat_2 (k1_toler_1 D C))) ) ) ) ) ) ).
tt(t10_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  => (r1_xxreal_0 (k12_euclid (k9_euclid B C A)) (k12_euclid C))) ) ) ) ) ) ) ).
tt(t10_topalg_2,ax,(v2_topalg_2 k5_topmetr)).
tt(t10_topalg_3,ax, (! [A:$i] :  ((m1_pre_topc A (k15_euclid 2)) =>  ( ((v1_topreal2 (u1_struct_0 A)) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_borsuk_2 A)) ) ) ).
tt(t10_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 B C))) &  ((v5_pre_topc D A (k2_borsuk_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 B C)))))) ) )  => (v5_pre_topc (k4_topalg_4 B C A D) A C)) ) ) ) ) ) ) ) ).
tt(t10_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_tops_2 E A B) & (r3_connsp_1 B D C))  => (r3_connsp_1 A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) E D) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_xxreal_0 2 C) &  ( (D = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_tarski B)))  & (r1_mfold_2 (k15_euclid C) A)) )  => (v1_borsuk_2 (k1_pre_topc A D))) ) ) ) ) ) ) ) ) ).
tt(t10_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ( ((k3_topdim_1 A B) = (k1_real_1 1))  & (v2_topdim_1 B A))  <=> (r1_tarski B (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_struct_0 A)))) ) ) ) ) ).
tt(t10_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k2_tops_1 (k2_borsuk_1 A B) (k3_borsuk_1 A B C D)) = (k4_subset_1 (u1_struct_0 (k2_borsuk_1 A B)) (k3_borsuk_1 A B (k2_tops_1 A C) (k2_pre_topc B D)) (k3_borsuk_1 A B (k2_pre_topc A C) (k2_tops_1 B D)))) ) ) ) ) ) ) ) ) ).
tt(t10_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_tops_1 A B)) <=>  (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) =>  ( (~ (r1_xboole_0 B E))  &  (~  ((k7_subset_1 (u1_struct_0 A) E B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  (~  ((r2_hidden E D) & (r1_xboole_0 E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topgen_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_tops_1 A C) = (k1_tops_1 B D)) ) ) ) ) ) )  =>  ((u1_pre_topc A) = (u1_pre_topc B)) ) ) ) ) ) ).
tt(t10_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((v7_topgen_1 A) <=> (r1_ordinal1 (k1_card_1 (k2_struct_0 A)) k4_ordinal1)) ) ) ).
tt(t10_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v4_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_pre_topc A C) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 B)) &  ((v5_pre_topc F (k1_pre_topc A D) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 B))))) ) )  =>  ((r1_partfun1 E F) =>  ((v1_funct_1 (k1_funct_4 E F)) &  ((v1_funct_2 (k1_funct_4 E F) (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) (u1_struct_0 B)) &  ((v5_pre_topc (k1_funct_4 E F) (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D)) B) & (m1_subset_1 (k1_funct_4 E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_group_1 A) B) = (k1_group_2 A B)) ) ) ) ) ).
tt(t10_topmetr3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k2_topmetr A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k2_topmetr A B)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 (k2_topmetr A B)) k5_numbers k1_numbers D C) &  ((r1_xxreal_0 A B) & (v8_valued_0 C)) )  => (v2_tbsp_1 D (k2_topmetr A B))) ) ) ) ) ) ) ) ) ).
tt(t10_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((u1_struct_0 (k2_topmetr A B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(t10_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) C D B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) B (k1_rltopsp1 (k15_euclid A) D E)) = (k1_tarski D)) )  => (r1_topreal1 (k15_euclid A) C E (k4_subset_1 (u1_struct_0 (k15_euclid A)) B (k1_rltopsp1 (k15_euclid A) D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topreal3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((a_3_1_topreal3 A B C) = (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C))) ) ) ) ) ) ) ) ).
tt(t10_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden A (k9_metric_1 (k14_euclid 2) D C)) &  ((r2_hidden B (k9_metric_1 (k14_euclid 2) D C)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal4 E A B) & (r1_tarski E (k9_metric_1 (k14_euclid 2) D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_topreal5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr))))) )  =>  ( (A = k4_pscomp_1)  => (v5_pre_topc A (k15_euclid 2) k3_topmetr)) ) ) ).
tt(t10_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) =>  ( (A = k6_numbers)  |  ((k2_newton A (k7_nat_d C B)) = (k10_real_1 (k2_newton A C) (k2_newton A B))) ) ) ) ) ) ) ) ) ).
tt(t10_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k12_rvsum_1 (k8_finseq_1 k1_numbers A B)) = (k8_finseq_1 k1_numbers (k12_rvsum_1 A) (k12_rvsum_1 B))) ) ) ) ) ).
tt(t10_topreal8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k3_graph_2 A B)))) ) ) ) ).
tt(t10_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C (k1_topreal9 A (k4_struct_0 (k15_euclid A)) B)) & (r1_xxreal_0 B (k12_euclid C))) ) ) ) ) ) ) ) ).
tt(t10_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 (k1_pre_topc B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 (k1_pre_topc B D)))))) )  =>  ( ( (F = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) E C))  &  ((v2_funct_2 F (u1_struct_0 (k1_pre_topc B D))) &  ((v1_t_0topsp E A B) & (v2_funct_1 E)) ) )  => (v1_t_0topsp F (k1_pre_topc A C) (k1_pre_topc B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) => (m1_pre_topc (k7_toprealb 2 (k4_struct_0 (k15_euclid 2)) A) (k1_topreala (k4_xcmplx_0 A) A (k4_xcmplx_0 A) A))) ) ).
tt(t10_toprealc,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k39_valued_1 (k14_valued_2 B A)) = (k14_valued_2 (k39_valued_1 B) (k3_square_1 A))) ) ) ) ) ).
tt(t10_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k1_toprns_1 A (k1_toprns_1 A B C) D) = (k1_toprns_1 A B (k1_toprns_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t10_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_pre_topc C A))  => (v3_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t10_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) <=> (v2_tops_2 (k7_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t10_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_tops_1 B A) &  (B = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t10_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  ((v1_t_0topsp B A k3_topmetr) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (~ (r1_tarski (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) E) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) E)) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_funct_2 A A (k2_transgeo A B (k6_partfun1 A)) B)) ) ) ) ).
tt(t10_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v11_aff_2 A) &  ((v7_transgeo B A) & (v7_transgeo C A)) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_transgeo (u1_struct_0 A) C B) (k1_transgeo (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t10_treal_1,ax,(r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k3_treal_1 k6_numbers 1 (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1)) (k3_struct_0 (k4_topmetr k6_numbers 1)))).
tt(t10_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~  ( (~ (r2_xboole_0 k1_xboole_0 A))  &  (k1_xboole_0 = A) ) )  => (r2_xboole_0 B (k7_finseq_1 B A))) ) ) ) ) ).
tt(t10_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) => (m4_trees_1 (k1_trees_2 A B) A)) ) ) ) ).
tt(t10_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_trees_3 A) & (v3_trees_3 B))  => (v3_trees_3 (k5_xboole_0 A B))) ) ) ).
tt(t10_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v6_trees_3 B)) ) )  =>  ((k9_xtuple_0 (k4_trees_4 A B)) = (k11_trees_3 (k2_funct_6 B))) ) ) ) ).
tt(t10_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((r2_hidden A (k3_trees_9 B)) <=>  (? [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) &  (A = (k5_trees_2 B C)) ) ) ) ) ) ) ).
tt(t10_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m4_trees_1 C (k9_xtuple_0 A)) =>  ( (~  (C = k1_xboole_0) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D (k9_xtuple_0 (k3_trees_a A C B))) &  ( (? [E:$i] :  ((m2_finseq_1 E k5_numbers) &  ((r2_hidden E C) &  (~  ( (~ (r1_tarski E D))  &  ((k1_funct_1 (k3_trees_a A C B) D) = (k1_funct_1 A D)) ) ) ) ) )  &  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (~  ((r2_hidden E C) &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (D = (k8_finseq_1 k5_numbers E F))  &  ((k1_funct_1 (k3_trees_a A C B) D) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) & (m1_pre_topc C A)) )  &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(t10_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A (k2_pre_topc A B) (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B))) &  ((r2_tsep_2 A (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) (k1_tops_1 A B)) &  ((r2_tsep_2 A (k1_tops_1 A B) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))) & (r2_tsep_2 A (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B)) (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(t10_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tex_4 B A) &  ( (~ (v1_zfmisc_1 B))  & (v1_tsp_1 B A)) ) ) ) ) ) ) ).
tt(t10_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v1_tsp_2 B A)) ) ) ) ).
tt(t10_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((l1_turing_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C)))) =>  ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) (k2_nat_1 A B)) = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) B)) ) ) ) ) ) ) ) ) ).
tt(t10_twoscomp,ax, ( ((k1_funct_1 k8_twoscomp (k10_finseq_1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k8_twoscomp (k10_finseq_1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k8_twoscomp (k10_finseq_1 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k8_twoscomp (k10_finseq_1 1 1)) = 1)  &  ( ((k1_funct_1 k9_twoscomp (k10_finseq_1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k9_twoscomp (k10_finseq_1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k9_twoscomp (k10_finseq_1 1 k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k9_twoscomp (k10_finseq_1 1 1)) = 1)  &  ( ((k1_funct_1 k10_twoscomp (k10_finseq_1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k10_twoscomp (k10_finseq_1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k10_twoscomp (k10_finseq_1 1 k6_numbers)) = 1)  &  ((k1_funct_1 k10_twoscomp (k10_finseq_1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ( ( ((v1_unialg_1 A) & (m1_unialg_2 A B))  &  ((v1_unialg_1 B) & (m1_unialg_2 B A)) )  =>  (A = B) ) ) ) ) ) ).
tt(t10_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  => (r1_tarski (k6_unialg_2 A) (k1_funct_1 (k3_unialg_3 A) B))) ) ) ) ).
tt(t10_uniform1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_topmetr k6_numbers 1)) (u1_struct_0 (k14_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_topmetr k6_numbers 1)) (u1_struct_0 (k14_euclid A)))))) ) ) ) ) ) ).
tt(t10_uniroots,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A))) = (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) (k4_nat_d B A)) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) (k4_nat_d B A)) A)))) ) ) ) ) ).
tt(t10_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xboole_0 B C) =>  ((k2_uproots A (k4_subset_1 A B C) D) = (k11_pre_poly A (k2_uproots A B D) (k2_uproots A C D))) ) ) ) ) ) ) ) ) ).
tt(t10_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  ( (B = (k6_real_1 (k6_urysohn1 A B) (k13_newton 2 A)))  & (r1_xxreal_0 (k6_urysohn1 A B) (k13_newton 2 A))) ) ) ) ) ).
tt(t10_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v3_measure5 A) =>  ((r1_xxreal_0 k6_numbers B) | (v4_measure5 (k1_integra2 A B))) ) ) ) ) ) ).
tt(t10_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k3_urysohn1 (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k3_urysohn1 (k9_setfam_1 (u1_struct_0 A)))))) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F k3_urysohn1) =>  ( ((r2_hidden F (k10_prob_1 k6_numbers)) =>  ((k1_funct_1 E F) = k1_xboole_0) )  &  ( ((r2_hidden F (k3_limfunc1 1)) =>  ((k1_funct_1 E F) = (u1_struct_0 A)) )  &  ((r2_hidden F k2_urysohn1) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden F (k1_urysohn1 G)) =>  ((k1_funct_1 E F) = (k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E (k6_cqc_lang A D)) C) = (k9_margrel1 (k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E D) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v5_relat_1 A k3_numbers) <=>  (! [B:$i] : (v1_rat_1 (k1_funct_1 A B))) ) ) ) ).
tt(t10_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((k1_funct_1 (k35_valued_1 A) B) = (k5_xcmplx_0 (k1_funct_1 A B))) ) ) ) ).
tt(t10_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k7_valued_1 B A)) = (k13_valued_1 (k30_valued_1 B) A)) ) ) ) ) ).
tt(t10_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_group_1 (k5_vectmetr A)) = (k3_struct_0 (k4_vectmetr A))) ) ) ).
tt(t10_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 D E) =>  ((k4_vectsp_5 A B E C D) = (k1_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_struct_0 B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_vectsp11 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_vectsp11 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((m1_vectsp11 E A B C) & (m1_vectsp11 F A B D))  =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((m2_vectsp11 G A B C E) &  ((m2_vectsp11 G A B D F) &  (~  (G = (k4_struct_0 B)) ) ) ) ) ) )  |  ((v1_vectsp11 (k3_matrlin A B B C D) A B) &  ((m1_vectsp11 (k3_rlvect_1 A E F) A B (k3_matrlin A B B C D)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((m2_vectsp11 G A B C E) & (m2_vectsp11 G A B D F))  => (m2_vectsp11 G A B (k3_matrlin A B B C D) (k3_rlvect_1 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_algstr_0 A B) (k4_algstr_0 A C)) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t10_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k1_group_1 A))  =>  ( (C = (k11_algstr_0 A B))  &  (B = (k11_algstr_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (m1_subset_1 D (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t10_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( ((k1_vectsp_5 A B (k1_vectsp_4 A B) (k2_vectsp_4 A B)) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)))  &  ((k1_vectsp_5 A B (k2_vectsp_4 A B) (k1_vectsp_4 A B)) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ).
tt(t10_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k3_vectsp_6 A B (k12_finseq_1 (u1_struct_0 B) C) D) = (k12_finseq_1 (u1_struct_0 B) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C))) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_vectsp_7 A B C) = (k1_vectsp_4 A B))  &  ( (~  (C = k1_xboole_0) )  &  (~  (C = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((v1_vectsp_4 D A C) & (r1_struct_0 (k1_vectsp_7 A C D) B))  =>  ((v1_xboole_0 D) | (r2_hidden B D)) ) ) ) ) ) ) ) ) ).
tt(t10_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_7 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 (k1_vectsp_7 A B C) D)) ) ) ) ) ) ) ) ).
tt(t10_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B (k3_vfunct_1 A B E C) D) (k3_vfunct_1 A B E (k4_vfunct_1 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B (k1_vfunct_2 A B E C) D) (k1_vfunct_2 A B E (k2_vfunct_2 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((r2_waybel_0 A B C) <=>  (~ (r1_waybel_0 A B (k6_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t10_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_waybel10 A))) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t10_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) ) ) ) ).
tt(t10_waybel12,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_yellow_4 A B (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)))) ) ) ) ).
tt(t10_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  => (v2_waybel_8 (k2_yellow_1 (k7_waybel_0 A)))) ) ).
tt(t10_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ((k6_waybel_0 A (k3_yellow_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t10_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((r5_waybel_1 A B) &  ((v1_yellow_0 A) & (v3_waybel_8 A)) )  => (v3_waybel_8 B)) ) ) ) ) ).
tt(t10_waybel16,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))))))  =>  ((r2_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B) &  ((k2_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B) = (k1_setfam_1 B)) ) ) ) ) ).
tt(t10_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_waybel11 A (k4_waybel17 A B)) = (k1_yellow_0 A B)) ) ) ) ) ).
tt(t10_waybel18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) => (v5_pre_topc (k8_waybel18 A B C) A (k7_waybel18 A B C))) ) ) ) ) ) ) ).
tt(t10_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D B) &  ((r2_hidden (k2_yellow_0 A C) D) & (r1_xboole_0 C D)) ) ) ) )  => (r2_hidden (k2_yellow_0 A C) (k2_pre_topc A C))) ) ) ) ) ) ) ).
tt(t10_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) <=>  ((v5_orders_3 C A B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r3_waybel_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_waybel_0 B E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v21_waybel_0 E A C) & (v21_waybel_0 F B D))  => (v21_waybel_0 (k1_waybel20 A B C D E F) (k3_yellow_3 A B) (k3_yellow_3 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) )  => (v22_waybel_0 (k1_yellow_9 A B) B A)) ) ) ) ).
tt(t10_waybel22,ax, (! [A:$i] :  ((k1_card_1 (k1_waybel22 A)) = (k1_card_1 A)) ) ).
tt(t10_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_waybel_0 A (k6_waybel_0 A B)) = (k6_waybel_0 A B)) ) ) ) ) ).
tt(t10_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v5_orders_3 D (k3_yellow_3 A B) C) =>  ((v5_orders_3 (k1_waybel24 A B C D E) B C) & (v5_orders_3 (k2_waybel24 A B C D F) A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((v2_waybel18 B) & (r1_waybel18 A B))  => (v2_waybel18 A)) ) ) ) ) ).
tt(t10_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  => (v5_orders_3 (k4_waybel26 A B C D) (k1_waybel26 C A) (k1_waybel26 B A))) ) ) ) ) ) ) ) ).
tt(t10_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v11_quantal1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 B B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 B B C)))))) )  =>  ((k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 B B C)) (u1_struct_0 B) (u1_struct_0 B) D C) = D) ) ) ) ) ) ) ) ) ).
tt(t10_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ((r2_hidden B (k6_yellow_6 A)) => (r2_hidden (k1_waybel28 A B C) (k6_yellow_6 A))) ) ) ) ) ) ) ).
tt(t10_waybel29,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_waybel_9 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_waybel_9 D))  =>  ( ((g1_waybel_9 (u1_struct_0 C) (u1_orders_2 C) (u1_pre_topc C)) = (g1_waybel_9 (u1_struct_0 D) (u1_orders_2 D) (u1_pre_topc D)))  =>  ((k3_waybel24 A C) = (k3_waybel24 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k3_yellow_3 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((k1_yellow_0 A (a_2_1_waybel_2 A B)) = (k1_yellow_0 A (k3_tarski (a_2_3_waybel_2 A B)))) ) ) ) ) ).
tt(t10_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  => (r1_tarski (k5_waybel11 A) (k2_waybel19 A))) ) ).
tt(t10_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C A)) )  =>  (! [D:$i] :  ( ((v1_tops_2 D C) &  ((v1_cantor_1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) )  =>  ((v1_tops_2 (a_3_0_waybel31 A C D) B) &  ((v1_cantor_1 (a_3_0_waybel31 A C D) B) & (m1_subset_1 (a_3_0_waybel31 A C D) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (u1_pre_topc (k13_yellow_6 A (k2_waybel11 A)))) <=>  ((v1_waybel11 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ).
tt(t10_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel33 B) & (m1_yellow_9 B A))  =>  ((k4_waybel28 A) = (u1_pre_topc B)) ) ) ) ) ).
tt(t10_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k2_waybel34 A B (k1_waybel34 A B C)) C)) ) ) ) ) ) ).
tt(t10_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_waybel35 C A B))  =>  ((v2_waybel35 C A B) => (v3_lattice3 (k5_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t10_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_lattice3 A (k2_waybel_3 A B) B)) ) ) ) ).
tt(t10_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v5_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((v5_waybel_4 (k9_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B C) A) & (m1_subset_1 (k9_subset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t10_waybel_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A C (k7_funcop_1 A B)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k1_relset_1 (k4_card_3 (k2_funct_6 D)) (k2_pralg_2 D))) =>  ((v1_funct_1 (k1_funct_1 (k2_pralg_2 D) E)) &  ((v1_funct_2 (k1_funct_1 (k2_pralg_2 D) E) A B) & (m1_subset_1 (k1_funct_1 (k2_pralg_2 D) E) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  => (v2_waybel_6 (k4_yellow_0 A) A)) ) ).
tt(t10_waybel_7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v12_waybel_0 B (k3_yellow_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) )  =>  ((v1_waybel_0 B (k3_yellow_1 A)) <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_tarski C B) => (r2_hidden (k5_setfam_1 A C) B)) ) ) ) ) ) ) ).
tt(t10_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k2_waybel_8 A C) = (k2_waybel_8 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ( (~ (v2_struct_0 (k3_waybel_2 A B C)))  &  ((v4_orders_2 (k3_waybel_2 A B C)) &  ((v7_waybel_0 (k3_waybel_2 A B C)) & (l1_waybel_0 (k3_waybel_2 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(t10_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k7_group_3 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_group_3 A B)) =>  ( (~  (C = D) )  => (r1_xboole_0 (k8_relset_1 (u1_struct_0 A) (k7_group_3 A B) (k2_weddwitt A B) (k1_tarski C)) (k8_relset_1 (u1_struct_0 A) (k7_group_3 A B) (k2_weddwitt A B) (k1_tarski D)))) ) ) ) ) ) ) ) ) ).
tt(t10_weierstr,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v2_compts_1 B (k15_euclid 2)) & (v5_pre_topc A (k15_euclid 2) k3_topmetr))  => (v2_compts_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) A B) k3_topmetr)) ) ) ) ) ).
tt(t10_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_wellfnd1 A) <=>  (! [B:$i] :  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tarski (k1_wellord1 (u1_orders_2 A) C) B) => (r2_hidden C B)) ) )  => (r1_tarski (u1_struct_0 A) B)) ) ) ) ) ).
tt(t10_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_wellord1 B A) = (k5_relat_1 (k6_relat_1 A B) A)) ) ) ) ).
tt(t10_wellord2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r4_wellord1 (k1_wellord2 A) (k1_wellord2 B)) =>  (A = B) ) ) ) ) ) ).
tt(t10_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_int_2 B C) => (r1_int_2 (k1_newton B A) C)) ) ) ) ) ) ) ).
tt(t10_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski A (k2_xboole_0 C B))) ) ) ) ).
tt(t10_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k5_xboolean (k5_xboolean (k4_xboolean A B) (k4_xboolean B C)) (k4_xboolean C A)) = (k4_xboolean (k4_xboolean (k5_xboolean A B) (k5_xboolean B C)) (k5_xboolean C A))) ) ) ) ) ) ) ).
tt(t10_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C D)) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 A D)) (k3_xcmplx_0 B C)) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t10_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) <=> (r1_xxreal_0 (k6_xcmplx_0 C B) (k6_xcmplx_0 C A))) ) ) ) ) ) ) ).
tt(t10_xregular,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden A B) &  ((r2_hidden B C) &  ((r2_hidden C D) &  ((r2_hidden D E) &  ((r2_hidden E F) & (r2_hidden F A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k11_xtuple_0 A) (k11_xtuple_0 B))) ) ) ).
tt(t10_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r2_hidden A k1_numbers) &  ((r1_xxreal_0 A B) &  ( (~ (r2_hidden B k1_numbers))  &  (~  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ).
tt(t10_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden A (k2_xxreal_1 B C)) &  ( (~  ((r2_hidden A (k3_xxreal_1 B C)) &  (~  (A = C) ) ) )  &  (~  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t10_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k1_xxreal_2 (k2_xboole_0 A B)) = (k4_xxreal_0 (k1_xxreal_2 A) (k1_xxreal_2 B))) ) ) ) ) ).
tt(t10_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k2_xxreal_3 A) = (k2_xxreal_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t10_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((r1_lattice3 A B D) & (r1_lattice3 A C D))  => (r1_lattice3 A (k2_xboole_0 B C) D))  &  ( ((r2_lattice3 A B D) & (r2_lattice3 A C D))  => (r2_lattice3 A (k2_xboole_0 B C) D)) ) ) ) ) ) ) ) ).
tt(t10_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_yellow_3 A B))) =>  ((r2_lattice3 (k3_yellow_3 A B) (k7_domain_1 (u1_struct_0 (k3_yellow_3 A B)) D E) C) <=>  ((r2_lattice3 A (k7_domain_1 (u1_struct_0 A) (k8_yellow_3 A B D) (k8_yellow_3 A B E)) (k8_yellow_3 A B C)) & (r2_lattice3 B (k7_domain_1 (u1_struct_0 B) (k9_yellow_3 A B D) (k9_yellow_3 A B E)) (k9_yellow_3 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~  ( (? [B:$i] :  ( ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  & (r5_waybel_1 k2_yellow11 B)) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  &  ( ((k12_lattice3 A B C) = B)  &  ( ((k12_lattice3 A B D) = B)  &  ( ((k12_lattice3 A B E) = B)  &  ( ((k12_lattice3 A C F) = C)  &  ( ((k12_lattice3 A D F) = D)  &  ( ((k12_lattice3 A E F) = E)  &  ( ((k12_lattice3 A C D) = B)  &  ( ((k12_lattice3 A C E) = B)  &  ( ((k12_lattice3 A D E) = B)  &  ( ((k13_lattice3 A C D) = F)  &  ( ((k13_lattice3 A C E) = F)  &  ((k13_lattice3 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  &  ( ((k12_lattice3 A B C) = B)  &  ( ((k12_lattice3 A B D) = B)  &  ( ((k12_lattice3 A B E) = B)  &  ( ((k12_lattice3 A C F) = C)  &  ( ((k12_lattice3 A D F) = D)  &  ( ((k12_lattice3 A E F) = E)  &  ( ((k12_lattice3 A C D) = B)  &  ( ((k12_lattice3 A C E) = B)  &  ( ((k12_lattice3 A D E) = B)  &  ( ((k13_lattice3 A C D) = F)  &  ( ((k13_lattice3 A C E) = F)  &  ((k13_lattice3 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (~ (r5_waybel_1 k2_yellow11 B)) ) ) ) ) ) ) ) ).
tt(t10_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (C = E)  &  (D = F) ) )  =>  ((k13_lattice3 A C D) = (k10_lattice3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow13,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r5_waybel_1 A (k2_yellow_1 (k7_waybel_0 A)))) ) ).
tt(t10_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) => (v23_waybel_0 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t10_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k6_margrel1) =>  ( ( ((k1_funct_1 C 1) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k12_finseq_1 (k1_zfmisc_1 A) B) C) 1) = B) )  &  ( ((k1_funct_1 C 1) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k12_finseq_1 (k1_zfmisc_1 A) B) C) 1) = (k6_subset_1 A B)) ) ) ) ) ) ) ) ).
tt(t10_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_yellow16 A B C) =>  ((k10_xtuple_0 C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t10_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k2_struct_0 (k4_waybel18 A B C))) = (k2_struct_0 (k3_waybel18 A B))) ) ) ) ) ) ) ).
tt(t10_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k8_altcat_1 A C) = (k8_altcat_1 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((r2_hidden C (k2_yellow19 A B)) <=>  ((r1_waybel_0 A B C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t10_yellow_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) <=> (r1_tarski B C)) ) ) ) )  => (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (k1_yellow_1 (u1_struct_0 A)))) ) ) ).
tt(t10_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) <=>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden F (k9_xtuple_0 (k1_funct_1 (u2_altcat_1 A) (k3_xtuple_0 C D E)))) & (r2_hidden F (k9_xtuple_0 (k1_funct_1 (u2_altcat_1 B) (k3_xtuple_0 C D E)))))  =>  ((k1_funct_1 (k1_funct_1 (u2_altcat_1 A) (k3_xtuple_0 C D E)) F) = (k1_funct_1 (k1_funct_1 (u2_altcat_1 B) (k3_xtuple_0 C D E)) F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_wellord1 (u1_orders_2 A)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_orders_2 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v1_waybel_3 D A) &  ((r3_orders_2 A C D) & (r3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_yellow_2 A B C))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow_3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((r2_hidden C (k1_yellow_3 A B)) <=>  ((r2_hidden (k4_tarski (k1_xtuple_0 (k1_xtuple_0 C)) (k1_xtuple_0 (k2_xtuple_0 C))) A) &  ((r2_hidden (k4_tarski (k2_xtuple_0 (k1_xtuple_0 C)) (k2_xtuple_0 (k2_xtuple_0 C))) B) &  ( (? [D:$i] :  (? [E:$i] :  (C = (k4_tarski D E)) ) )  &  ( (? [D:$i] :  (? [E:$i] :  ((k1_xtuple_0 C) = (k4_tarski D E)) ) )  &  (? [D:$i] :  (? [E:$i] :  ((k2_xtuple_0 C) = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  => (r2_hidden (k10_lattice3 A D E) (k1_yellow_4 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A C B) =>  ((k12_lattice3 A B C) = C) ) ) ) ) ) ) ) ).
tt(t10_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  (! [C:$i] :  ((m1_yellow_6 C A B) => (r1_tarski (u1_struct_0 C) (u1_struct_0 B))) ) ) ) ) ) ).
tt(t10_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((r1_yellow_0 A B) <=> (r2_yellow_0 (k7_lattice3 A) B)) ) ) ) ).
tt(t10_yellow_8,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_pre_topc C A)) ) ) ) ) ) ) ).
tt(t10_yellow_9,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v1_tops_2 (k1_tarski (u1_struct_0 A)) A) &  ((v1_cantor_1 (k1_tarski (u1_struct_0 A)) A) & (m1_subset_1 (k1_tarski (u1_struct_0 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  ( ((v1_tops_2 k1_xboole_0 A) &  ((v2_cantor_1 k1_xboole_0 A) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  ((v1_tops_2 (k1_tarski k1_xboole_0) A) &  ((v2_cantor_1 (k1_tarski k1_xboole_0) A) & (m1_subset_1 (k1_tarski k1_xboole_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t10_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_funct_1 B C) = (k7_relat_1 B C)) ) ) )  => (v1_ordinal1 (k10_xtuple_0 B))) ) ) ) ) ).
tt(t10_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k4_ordinal1)))  =>  ( ((v8_zf_fund1 D A) &  ((r2_hidden B (k9_funct_2 E k4_ordinal1)) & (r2_hidden C D)) )  => (r2_hidden (a_3_4_zf_fund1 A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k10_zf_lang A B) = (k11_zf_lang (k6_zf_lang A) B)) ) ) ) ) ).
tt(t10_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~ (v7_zf_lang A))  &  ( (~ (v4_zf_lang A))  &  ( (~ (v5_zf_lang A))  &  (~ (v6_zf_lang A)) ) ) ) ) ) ) ).
tt(t10_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_xboole_0 (k1_tarski A) (k1_tarski B)) &  (A = B) ) ) ) ) ).
tt(t10_zfmodel1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D B) =>  ((r2_hidden A (k2_zf_model B)) | (r1_zf_model C D (k8_zf_lang A B))) ) ) ) ) ) ) ) ) ) ).
tt(t10_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ((r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) =>  ((r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model B)) |  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k3_funct_2 A A (k1_zfmodel1 B A C) D) = E)  <=> (r1_zf_model A (k2_zf_lang1 A (k2_zf_lang1 A C (k2_zf_lang 3) D) (k2_zf_lang 4) E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t10_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((v5_zf_lang A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( ((r2_hidden C (k5_zf_model (k21_zf_lang A) B)) & (r2_hidden C (k5_zf_model (k22_zf_lang A) B)))  <=> (r2_hidden C (k5_zf_model A B))) ) ) ) ) ) ) ) ).
tt(t10_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((v1_zf_model A) &  ((r2_zfrefle1 A B) & (v1_ordinal1 B)) )  => (v1_zf_model B)) ) ) ) ) ).
tt(t10_zf_refle,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  => (v3_ordinal1 (k3_card_3 A))) ) ).
tt(t10_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((v6_zmodul01 B) &  ((k1_zmodul01 B C A) = (k1_zmodul01 B D A)) )  =>  ( (A = k6_numbers)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k49_abcmiz_1)) <=>  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_abcmiz_1)))  &  ((k1_abcmiz_1 A) = A) ) ) ) ).
tt(t110_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C E D) & (r5_aofa_000 A B C F D))  => (r5_aofa_000 A B C (k13_aofa_000 A E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) &  ((v2_glib_000 B) & (v6_chord B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_chord C A) & (m3_chord C A))  =>  ((r5_glib_000 A B) =>  ((v7_chord C B) & (m3_chord C B)) ) ) ) ) ) ) ) ).
tt(t110_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C))) (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t110_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_fdiff_1 B E) &  ((r1_fdiff_1 C E) & (r1_fdiff_1 D E)) )  =>  ( ((k1_seq_1 B E) = k6_numbers)  |  ( ((k1_seq_1 C E) = k6_numbers)  |  ( ((k1_seq_1 D E) = k6_numbers)  |  ( (A = k6_numbers)  |  ((k8_euclid_8 (k6_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers B A)) (k6_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A)) (k6_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers D A)) E) = (k6_euclid 3 (k9_euclid 3 (k1_euclid_8 (k12_binop_2 (k1_fdiff_1 B E) (k5_square_1 (k1_seq_1 B E))) (k12_binop_2 (k1_fdiff_1 C E) (k5_square_1 (k1_seq_1 C E))) (k12_binop_2 (k1_fdiff_1 D E) (k5_square_1 (k1_seq_1 D E)))) (k12_binop_2 1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((r1_tarski C F) &  ((r1_tarski D F) &  ((r6_euclidlp A C D) &  ((r2_hidden B F) &  ((r5_euclidlp A E D) & (r2_hidden B E)) ) ) ) )  =>  ((r1_tarski E F) & (r6_euclidlp A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ((k4_finseq_2 A D) = (k4_finseq_2 B C))  =>  (A = B) ) ) ) ) ) ) ) ) ).
tt(t110_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_funct_1 (k2_finseq_3 B C) A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t110_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k3_finseq_1 A) = 1)  =>  ((k3_finseq_5 A) = A) ) ) ) ).
tt(t110_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k2_flang_2 A (k7_flang_1 A B C)) (k8_flang_1 A B))) ) ) ) ) ).
tt(t110_funct_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k3_tarski A))  =>  ( ((k9_xtuple_0 B) = (k3_tarski (a_1_0_funct_1 A)))  &  ((k10_xtuple_0 B) = (k3_tarski (a_1_1_funct_1 A))) ) ) ) ) ) ) ).
tt(t110_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((r1_tarski (k2_relset_1 C D) (k1_relset_1 C E)) => (r2_funct_2 B A (k1_partfun1 B B B A F (k8_funct_2 B A C D E)) (k8_funct_2 B A C (k1_partfun1 B B B C F D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 (k1_funct_4 (k7_funcop_1 B C) (k16_funcop_1 B A)) (k16_funcop_1 (k1_ordinal1 B) A))) = (k1_ordinal1 (k1_ordinal1 B))) ) ) ) ).
tt(t110_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_funct_1 (k2_funct_7 (k2_funct_7 B C (k1_funct_1 B D)) D (k1_funct_1 B C))) &  ((v1_funct_2 (k2_funct_7 (k2_funct_7 B C (k1_funct_1 B D)) D (k1_funct_1 B C)) A A) &  ((v3_funct_2 (k2_funct_7 (k2_funct_7 B C (k1_funct_1 B D)) D (k1_funct_1 B C)) A A) & (m1_subset_1 (k2_funct_7 (k2_funct_7 B C (k1_funct_1 B D)) D (k1_funct_1 B C)) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ) ).
tt(t110_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k43_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t110_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ((k14_glib_001 A C) = (k14_glib_001 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t110_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k14_group_2 A (k6_group_2 A) B) = (k6_domain_1 (u1_struct_0 A) B))  &  ((k13_group_2 A (k6_group_2 A) B) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ) ).
tt(t110_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r2_hidden B (k9_group_3 A C)) => (r2_hidden C (k9_group_3 A B))) ) ) ) ) ) ) ).
tt(t110_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  =>  ((v10_group_9 C A B) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 (k20_group_9 A B C))) =>  ( (~ (v2_struct_0 (k1_funct_1 (k20_group_9 A B C) D)))  &  ((v2_group_1 (k1_funct_1 (k20_group_9 A B C) D)) &  ((v3_group_1 (k1_funct_1 (k20_group_9 A B C) D)) &  ((v2_group_9 (k1_funct_1 (k20_group_9 A B C) D) A) &  ((v3_group_9 (k1_funct_1 (k20_group_9 A B C) D) A) &  ((v6_group_9 (k1_funct_1 (k20_group_9 A B C) D) A) & (l1_group_9 (k1_funct_1 (k20_group_9 A B C) D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 (k17_euclid B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k17_euclid C) k6_numbers))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_xxreal_0 G (k18_euclid D)) &  ((r1_xxreal_0 (k18_euclid D) H) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  =>  ((r1_xxreal_0 (k6_pscomp_1 (k3_topreal1 2 A)) (k17_euclid B)) | (r2_hidden B (k2_goboard9 A))) ) ) ) ) ) ).
tt(t110_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ( ((k5_limfunc1 A) = k6_numbers)  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B))) &  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) ) )  | (v7_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t110_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  ( ((k8_matrix13 C D) = B)  => (v1_vectsp_7 (k9_matrix13 C B A D) C (k6_prvect_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t110_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k14_member_1 (k14_member_1 A B) C) = (k14_member_1 A (k12_member_1 B C))) ) ) ) ) ) ) ).
tt(t110_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_mesfunc5 A B C D) =>  ((r1_mesfunc5 A B C (k6_mesfunc1 A D E)) &  ((k7_mesfunc5 A B C (k6_mesfunc1 A D E)) = (k1_extreal1 (k1_measure6 E) (k7_mesfunc5 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r14_ncfcont1 A B C D) =>  ((r14_ncfcont1 A B C (k5_vfunct_1 (u1_struct_0 A) B D)) & (r17_ncfcont1 A C (k3_normsp_0 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t110_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r5_pboole A (k3_pboole A B C) (k5_pboole A B C))) ) ) ) ) ).
tt(t110_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k7_relat_1 C B)) <=>  (? [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) &  ((r2_hidden (k4_tarski D A) C) & (r2_hidden D B)) ) ) ) ) ) ) ) ).
tt(t110_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k20_rvsum_1 A) = (k1_finsop_1 k2_numbers A k29_binop_2)) ) ) ).
tt(t110_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((k6_scmpds_4 (k9_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ((r1_xxreal_0 2 (k8_scmyciel A)) =>  ((k8_scmyciel (k12_scmyciel A)) = (k8_scmyciel A)) ) ) ) ).
tt(t110_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 A)) =>  ((r2_hidden C (k23_seq_4 A D B)) <=>  (~ (r1_xxreal_0 B (k22_seq_4 (k19_seq_4 A D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t110_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E E) E) D) (k5_sheffer1 A (k5_sheffer1 A C C) D)) = (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A B B)) (k5_sheffer1 A B (k5_sheffer1 A B B))) C)) (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A B B)) (k5_sheffer1 A B (k5_sheffer1 A B B))) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 (k7_square_1 2))))  &  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  &  (~  ( (~ (r1_xxreal_0 (k10_sincos10 A) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))  &  (~ (r1_xxreal_0 k32_sin_cos (k10_sincos10 A))) ) ) ) ) ) ) ) ).
tt(t110_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k9_real_1 (k6_sin_cos6 A) (k3_sin_cos6 (k4_xcmplx_0 A))) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t110_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 C F) = (k10_real_1 F A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C F))) ) ) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 D F) = 1) ) ) )  &  ( (E = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 C F) = (k10_real_1 F A)) ) ) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) k3_taylor_1) (k10_real_1 A 2))) B) F) = (k1_seq_1 k2_sin_cos9 (k10_real_1 F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v3_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k12_tdlat_1 A)))) =>  ( (C = B)  =>  ( ( (~  (C = k1_xboole_0) )  =>  ((k16_lattice3 (k12_tdlat_1 A) C) = (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B))) )  &  ( (C = k1_xboole_0)  =>  ((k16_lattice3 (k12_tdlat_1 A) C) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  <=>  ((v1_funct_1 (k9_tmap_1 A B)) &  ((v1_funct_2 (k9_tmap_1 A B) (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B))) &  ((v5_pre_topc (k9_tmap_1 A B) A (k8_tmap_1 A B)) & (m1_subset_1 (k9_tmap_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k8_tmap_1 A B)))))) ) ) ) ) ) ) ) ).
tt(t110_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r1_tarski C B))  => (r1_tarski (k5_xboole_0 A C) B)) ) ) ) ).
tt(t110_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A (k6_xboolean B C)) (k6_xboolean B (k6_xboolean A C))) = k2_xboolean) ) ) ) ) ) ) ).
tt(t110_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k7_xcmplx_0 B (k3_xcmplx_0 A (k7_xcmplx_0 1 A)))) ) ) ) ) ) ).
tt(t110_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 D B) (k3_xcmplx_0 C A)))  & (r1_xxreal_0 (k7_xcmplx_0 D A) (k3_xcmplx_0 C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k2_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t110_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((r1_zf_model B C (k11_zf_lang A (k7_zf_lang A A))) & (r2_zf_model B (k11_zf_lang A (k7_zf_lang A A)))) ) ) ) ) ) ) ).
tt(t110_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k2_zfmisc_1 A B) = (k2_zfmisc_1 C D))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ).
tt(t110_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  =>  ((k7_zmodul01 A (k4_zmodul01 A) (k4_zmodul01 A)) = A) ) ) ).
tt(t111_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k49_abcmiz_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k49_abcmiz_1)) =>  ( ((k13_lattice3 k49_abcmiz_1 A B) = (k3_xboole_0 A B))  &  ((k12_lattice3 k49_abcmiz_1 A B) = (k2_xboole_0 A B)) ) ) ) ) ) ).
tt(t111_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r6_aofa_000 A B C F D E) &  ((r6_aofa_000 A B C G D E) & (r7_aofa_000 A B C F D E)) )  => (r6_aofa_000 A B C (k13_aofa_000 A F G) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ( (? [B:$i] :  ((m3_chord B A) & (v7_chord B A)) )  => (v6_chord A)) ) ) ).
tt(t111_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A (k5_algstr_0 A B D)) (k1_normsp_0 A (k5_algstr_0 A D C))))) ) ) ) ) ) ) ) ).
tt(t111_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_fdiff_1 A G) &  ((r1_fdiff_1 B G) &  ((r1_fdiff_1 C G) &  ((r1_fdiff_1 D G) &  ((r1_fdiff_1 E G) & (r1_fdiff_1 F G)) ) ) ) )  =>  ((k8_euclid_8 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B F) (k20_valued_1 k1_numbers k1_numbers k1_numbers C E)) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k20_valued_1 k1_numbers k1_numbers k1_numbers A F)) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A E) (k20_valued_1 k1_numbers k1_numbers k1_numbers B D)) G) = (k7_euclid 3 (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_seq_1 B G) (k1_fdiff_1 F G)) (k11_binop_2 (k1_seq_1 C G) (k1_fdiff_1 E G))) (k10_binop_2 (k11_binop_2 (k1_seq_1 C G) (k1_fdiff_1 D G)) (k11_binop_2 (k1_seq_1 A G) (k1_fdiff_1 F G))) (k10_binop_2 (k11_binop_2 (k1_seq_1 A G) (k1_fdiff_1 E G)) (k11_binop_2 (k1_seq_1 B G) (k1_fdiff_1 D G)))) (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B G) (k1_seq_1 F G)) (k11_binop_2 (k1_fdiff_1 C G) (k1_seq_1 E G))) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C G) (k1_seq_1 D G)) (k11_binop_2 (k1_fdiff_1 A G) (k1_seq_1 F G))) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 A G) (k1_seq_1 E G)) (k11_binop_2 (k1_fdiff_1 B G) (k1_seq_1 D G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  ( ((r1_tarski B E) &  ((r1_tarski C E) &  ((r1_tarski D E) &  ((r6_euclidlp A B C) & (r6_euclidlp A B D)) ) ) )  => (r5_euclidlp A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_2 (k1_finseq_2 A) k5_numbers (k4_finseq_2 A k5_numbers))) ) ).
tt(t111_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k3_finseq_1 D) = (k1_nat_1 A 1))  &  ((r2_hidden B (k1_relset_1 k5_numbers D)) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C A)) ) )  =>  ((k1_funct_1 (k2_finseq_3 B D) C) = (k1_funct_1 D (k1_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ).
tt(t111_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_finseq_1 (k2_rfinseq A C B)) = (k7_nat_d (k3_finseq_1 B) C)) ) ) ) ) ) ) ).
tt(t111_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k2_flang_2 A B) (k1_flang_2 A B C D)) = (k6_flang_1 A (k1_flang_2 A B C D) (k2_flang_2 A B))) ) ) ) ) ) ) ) ).
tt(t111_funct_1,ax, (! [A:$i] :  (~  ( (! [B:$i] :  (~  ((r2_hidden B A) &  (B = k1_xboole_0) ) ) )  &  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden (k1_funct_1 B C) C)) ) ) ) ) ) ) ) ) ).
tt(t111_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_1 C) <=>  (? [D:$i] :  ((m1_subset_1 D B) &  ((k2_relset_1 B C) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(t111_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k1_funct_4 (k5_relat_1 A B) A) = A) ) ) ) ).
tt(t111_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_xtuple_0 A) (k9_xtuple_0 A)) &  ((v3_funct_2 D (k9_xtuple_0 A) (k9_xtuple_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 A) (k9_xtuple_0 A))))) ) )  =>  (~  ((k2_funct_7 (k2_funct_7 A B (k1_funct_1 A C)) C (k1_funct_1 A B)) = (k3_relat_1 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k43_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k43_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k43_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (u1_struct_0 (k43_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (u1_struct_0 (k43_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (u1_struct_0 (k43_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) k29_twoscomp) (u1_struct_0 (k43_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t111_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k14_glib_001 A (k10_glib_001 A B C)) = (k2_xboole_0 (k14_glib_001 A B) (k1_tarski C))) ) ) ) ) ) ) ) ).
tt(t111_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k13_group_2 A (k7_group_2 A) B) = (u1_struct_0 A))  &  ((k14_group_2 A (k7_group_2 A) B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t111_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( ((k9_group_3 A B) = (k9_group_3 A C))  <=>  (~ (r1_xboole_0 (k9_group_3 A B) (k9_group_3 A C))) ) ) ) ) ) ) ) ).
tt(t111_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k6_xcmplx_0 (k3_finseq_1 C) 1)))  =>  ( ((v2_group_9 (k1_funct_1 C D) A) & (m1_group_9 (k1_funct_1 C D) A B))  &  ((v2_group_9 (k1_funct_1 C (k1_nat_1 D 1)) A) & (m1_group_9 (k1_funct_1 C (k1_nat_1 D 1)) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t111_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k13_complex1 (k18_euclid B) (k12_euclid B)) = A)  =>  ((r1_xxreal_0 (k17_euclid B) k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 (k17_euclid C) k6_numbers))  &  ((k18_euclid C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_xxreal_0 G (k18_euclid D)) &  ((r1_xxreal_0 (k18_euclid D) H) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  =>  ((r1_xxreal_0 (k17_euclid B) (k8_pscomp_1 (k3_topreal1 2 A))) | (r2_hidden B (k2_goboard9 A))) ) ) ) ) ) ).
tt(t111_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ( ((k5_limfunc1 A) = k6_numbers)  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  (~  ((k1_seq_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B))) &  (~ (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) ) )  | (v8_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t111_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_matrix_1 C B) & (m1_matrix_1 C (u1_struct_0 B) A A))  =>  ( ((k8_matrix13 B C) = A)  => (m1_vectsp_7 (k9_matrix13 B A A C) B (k6_prvect_1 B A))) ) ) ) ) ) ) ).
tt(t111_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k14_member_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k6_xxreal_3 A B))) ) ) ) ) ).
tt(t111_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) & (r1_tarski F (k1_relset_1 A (k3_mesfunc1 A D E)))) )  =>  ((r1_mesfunc5 A B C (k3_mesfunc1 A D E)) &  ((k8_mesfunc5 A B C (k3_mesfunc1 A D E) F) = (k3_supinf_2 (k8_mesfunc5 A B C D F) (k8_mesfunc5 A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r15_ncfcont1 B A C D) =>  ((r15_ncfcont1 B A C (k5_vfunct_1 (u1_struct_0 B) A D)) & (r6_nfcont_1 B C (k3_normsp_0 (u1_struct_0 B) A D))) ) ) ) ) ) ) ) ) ).
tt(t111_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r5_pboole A B C) => (r6_pboole A (k3_pboole A B C) (k1_pboole A))) ) ) ) ) ) ).
tt(t111_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k7_relat_1 B A) (k10_xtuple_0 B))) ) ) ).
tt(t111_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k20_rvsum_1 (k5_finseq_2 k2_numbers (k23_binop_2 A B) C)) = (k5_binop_2 (k20_rvsum_1 (k5_finseq_2 k2_numbers A C)) (k20_rvsum_1 (k5_finseq_2 k2_numbers B C)))) ) ) ) ) ) ) ).
tt(t111_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) =>  ((k6_scmpds_4 (k9_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  =>  (? [B:$i] :  ( ((v10_scmyciel B (k12_scmyciel A)) & (m1_eqrel_1 B (k3_tarski (k12_scmyciel A))))  &  ((k1_card_1 B) = (k2_nat_1 1 (k10_scmyciel A))) ) ) ) ) ).
tt(t111_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r2_hidden C (k23_seq_4 A C B))) ) ) ) ) ) ) ).
tt(t111_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A (k5_sheffer1 A C C) B)) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A D D)) (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A D D)) (k5_sheffer1 A D (k5_sheffer1 A D D))) C)))) ) ) ) ) ) ) ) ) ).
tt(t111_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 (k7_square_1 2))))  &  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  &  (~  ( (~ (r1_xxreal_0 (k11_sincos10 A) (k1_real_1 (k10_real_1 k32_sin_cos 2))))  &  (~ (r1_xxreal_0 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k11_sincos10 A))) ) ) ) ) ) ) ) ).
tt(t111_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B))) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) A) B) = (k1_real_1 (k10_real_1 1 (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ) ).
tt(t111_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v3_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_tdlat_1 A)))) =>  ( (C = B)  =>  ((k15_lattice3 (k4_tdlat_1 A) C) = (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ).
tt(t111_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_tsep_1 A C D))) =>  ( ( (H = F)  &  (H = G) )  =>  ((r1_tmap_1 (k1_tsep_1 A C D) B E H) <=>  ((r1_tmap_1 C B (k3_tmap_1 A B (k1_tsep_1 A C D) C E) F) & (r1_tmap_1 D B (k3_tmap_1 A B (k1_tsep_1 A C D) D E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 C B)) = (k3_xboole_0 (k4_xboole_0 A C) B)) ) ) ) ).
tt(t111_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean (k6_xboolean A B) C) (k6_xboolean B C)) = k2_xboolean) ) ) ) ) ) ) ).
tt(t111_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((k7_xcmplx_0 1 (k3_xcmplx_0 A B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t111_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 D B) (k3_xcmplx_0 C A)))  & (r1_xxreal_0 (k7_xcmplx_0 D A) (k3_xcmplx_0 C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k3_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang (k11_zf_lang A C) (k11_zf_lang A (k7_zf_lang B C))))) & (r2_zf_model D (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang (k11_zf_lang A C) (k11_zf_lang A (k7_zf_lang B C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t111_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A (k2_zfmisc_1 A B)) | (r1_tarski A (k2_zfmisc_1 B A)))  =>  (A = k1_xboole_0) ) ) ) ).
tt(t111_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (m1_zmodul01 (k7_zmodul01 A B C) (k6_zmodul01 A B C))) ) ) ) ) ) ).
tt(t112_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k49_abcmiz_1))))  =>  ((r1_yellow_0 k49_abcmiz_1 A) &  ((k1_yellow_0 k49_abcmiz_1 A) = (k1_setfam_1 A)) ) ) ) ).
tt(t112_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C E D) &  ((r5_aofa_000 A B C F D) & (r5_aofa_000 A B C G D)) )  => (r5_aofa_000 A B C (k14_aofa_000 A E F G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t112_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ( ((r1_fdiff_1 A J) &  ((r1_fdiff_1 B J) &  ((r1_fdiff_1 C J) &  ((r1_fdiff_1 D J) &  ((r1_fdiff_1 E J) &  ((r1_fdiff_1 F J) &  ((r1_fdiff_1 G J) &  ((r1_fdiff_1 H J) & (r1_fdiff_1 I J)) ) ) ) ) ) ) )  =>  ((k8_euclid_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers G (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B F) (k20_valued_1 k1_numbers k1_numbers k1_numbers C E))) (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k20_valued_1 k1_numbers k1_numbers k1_numbers A F))) (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A E) (k20_valued_1 k1_numbers k1_numbers k1_numbers B D))) J) = (k7_euclid 3 (k7_euclid 3 (k1_euclid_8 (k11_binop_2 (k1_fdiff_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 E J)))) (k11_binop_2 (k1_fdiff_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 F J)))) (k11_binop_2 (k1_fdiff_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 D J))))) (k1_euclid_8 (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 E J)))) (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 F J)))) (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 D J)))))) (k1_euclid_8 (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 E J)))) (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 F J)))) (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 D J))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r1_tarski B F) &  ((r1_tarski C F) &  ((r1_tarski D F) &  ((r5_euclidlp A B C) &  ((r5_euclidlp A C D) &  ( (~  (B = C) )  &  ( (~ (r1_xboole_0 E B))  &  ( (~ (r1_xboole_0 E C))  & (r1_xboole_0 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) => (m2_finseq_2 (k2_finseq_2 A C) B (k4_finseq_2 A B))) ) ) ) ) ) ).
tt(t112_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_xxreal_0 A B) =>  ((k1_funct_1 (k16_finseq_1 B C) A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t112_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k17_finseq_1 A (k7_nat_d D C) (k2_rfinseq A C B)) = (k2_rfinseq A C (k17_finseq_1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t112_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k2_flang_2 A B) (k7_flang_1 A B C)) = (k1_flang_2 A B C (k2_xcmplx_0 C 1))) ) ) ) ) ) ).
tt(t112_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_hidden (k3_funct_2 A B D C) (k2_relset_1 B D))) ) ) ) ) ) ) ) ).
tt(t112_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ( ((k9_xtuple_0 C) = (k1_tarski A))  &  ((k10_xtuple_0 C) = (k1_tarski B)) )  =>  (C = (k16_funcop_1 A B)) ) ) ) ) ) ).
tt(t112_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k9_xtuple_0 A) = (k9_xtuple_0 (k1_funct_4 A (k16_funcop_1 B C)))) ) ) ) ) ) ).
tt(t112_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k3_msafree2 (k43_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k3_msafree2 (k43_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k3_msafree2 (k43_gfacirc1 A B C))) & (r2_hidden (k45_gfacirc1 A B C) (k3_msafree2 (k43_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t112_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k3_finseq_1 B) = (k2_nat_1 (k4_nat_1 2 (k15_glib_001 A B)) 1)) ) ) ) ) ).
tt(t112_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k13_group_2 A C B) = (k14_group_2 A C B)) ) ) ) ) ) ) ) ).
tt(t112_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v8_struct_0 A) => (v1_finset_1 (k9_group_3 A B))) ) ) ) ) ).
tt(t112_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (! [E:$i] :  ( ((v8_group_9 E A B) & (m2_finseq_1 E (k6_group_9 A B)))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F (k6_xcmplx_0 (k3_finseq_1 E) 1)) &  ( (C = (k1_funct_1 E F))  &  (D = (k1_funct_1 E (k1_nat_1 F 1))) ) ) )  =>  ((v4_group_9 D A C) & (m1_group_9 D A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_struct_0 (k15_euclid 2)) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) (k4_struct_0 (k15_euclid 2)))) ) ) ).
tt(t112_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  =>  ((r1_xxreal_0 (k9_pscomp_1 (k3_topreal1 2 A)) (k18_euclid B)) | (r2_hidden B (k2_goboard9 A))) ) ) ) ) ) ).
tt(t112_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((k4_limfunc1 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B))) & (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) )  | (v4_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t112_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_9 B (k6_prvect_1 B A)) = A) ) ) ) ) ).
tt(t112_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k14_member_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k6_xxreal_3 A B) (k6_xxreal_3 A C))) ) ) ) ) ) ) ).
tt(t112_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ((r1_mesfunc5 A B C D) =>  ((r1_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) &  ((k8_mesfunc5 A B C (k6_mesfunc1 A D E) F) = (k1_extreal1 (k1_measure6 E) (k8_mesfunc5 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C)))  => (r13_ncfcont1 A B C D)) ) ) ) ) ) ) ) ).
tt(t112_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (~  ( (~  (B = (k1_pboole A)) )  & (r5_pboole A B B)) ) ) ) ) ).
tt(t112_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k7_relat_1 B A) = (k7_relat_1 B (k3_xboole_0 (k9_xtuple_0 B) A))) ) ) ) ).
tt(t112_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k20_rvsum_1 (k5_finseq_2 k2_numbers (k24_binop_2 A B) C)) = (k20_rvsum_1 (k5_finseq_2 k2_numbers B (k20_rvsum_1 (k5_finseq_2 k2_numbers A C))))) ) ) ) ) ) ) ).
tt(t112_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k9_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k2_nat_1 (k5_card_1 C) 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v11_scmyciel A))  =>  ((k10_scmyciel (k12_scmyciel A)) = (k2_nat_1 1 (k10_scmyciel A))) ) ) ).
tt(t112_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) => (v1_seq_4 (k23_seq_4 A C B) A)) ) ) ) ) ) ).
tt(t112_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B D) (k5_sheffer1 A B (k5_sheffer1 A D (k5_sheffer1 A C (k5_sheffer1 A C C))))) = B) ) ) ) ) ) ) ) ) ).
tt(t112_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 (k7_square_1 2) A))  &  (~  ( (~ (r1_xxreal_0 (k12_sincos10 A) (k10_real_1 k32_sin_cos 4)))  &  (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 2) (k12_sincos10 A))) ) ) ) ) ) ) ) ).
tt(t112_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B))) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9) A) B) = (k10_real_1 1 (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t112_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_tsep_1 A D E))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  ( ( (F = G)  &  (F = H) )  =>  ((r1_tmap_1 (k1_tsep_1 A D E) B (k2_tmap_1 A B C (k1_tsep_1 A D E)) F) <=>  ((r1_tmap_1 D B (k2_tmap_1 A B C D) G) & (r1_tmap_1 E B (k2_tmap_1 A B C E) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 C B)) = (k3_xboole_0 (k5_xboole_0 A C) B)) ) ) ) ).
tt(t112_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k6_xboolean (k6_xboolean k2_xboolean A) A) = k2_xboolean) ) ) ).
tt(t112_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_xcmplx_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 B A)) = 1) ) ) ) ) ) ) ) ) ).
tt(t112_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k7_xcmplx_0 C B)))  & (r1_xxreal_0 (k3_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_tarski (k4_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t112_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang A (k10_zf_lang A B))) & (r2_zf_model C (k11_zf_lang A (k10_zf_lang A B)))) ) ) ) ) ) ) ) ) ).
tt(t112_zfmisc_1,ax, (! [A:$i] :  (? [B:$i] :  ((r2_hidden A B) &  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r1_tarski D C))  => (r2_hidden D B)) ) )  &  ( (! [C:$i] :  ((r2_hidden C B) => (r2_hidden (k1_zfmisc_1 C) B)) )  &  (! [C:$i] :  (~  ((r1_tarski C B) &  ( (~ (r2_tarski C B))  &  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ).
tt(t112_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ((k6_zmodul01 A (k7_zmodul01 A B C) C) = C) ) ) ) ) ) ) ).
tt(t113_abcmiz_1,ax, ((k4_yellow_0 k49_abcmiz_1) = k1_xboole_0) ).
tt(t113_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r6_aofa_000 A B C F D E) &  ((r6_aofa_000 A B C G D E) &  ((r6_aofa_000 A B C H D E) & (r7_aofa_000 A B C F D E)) ) )  => (r6_aofa_000 A B C (k14_aofa_000 A F G H) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) & (v9_clvect_1 C A))  => (v9_clvect_1 (k2_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t113_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ( ((r1_fdiff_1 A J) &  ((r1_fdiff_1 B J) &  ((r1_fdiff_1 C J) &  ((r1_fdiff_1 D J) &  ((r1_fdiff_1 E J) &  ((r1_fdiff_1 F J) &  ((r1_fdiff_1 G J) &  ((r1_fdiff_1 H J) & (r1_fdiff_1 I J)) ) ) ) ) ) ) )  =>  ((k8_euclid_8 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H B) F) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I C) E)) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I C) D) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers G A) F)) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers G A) E) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H B) D)) J) = (k7_euclid 3 (k7_euclid 3 (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 H J) (k1_seq_1 B J)) (k1_fdiff_1 F J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 I J) (k1_seq_1 C J)) (k1_fdiff_1 E J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 I J) (k1_seq_1 C J)) (k1_fdiff_1 D J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 G J) (k1_seq_1 A J)) (k1_fdiff_1 F J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 G J) (k1_seq_1 A J)) (k1_fdiff_1 E J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 H J) (k1_seq_1 B J)) (k1_fdiff_1 D J)))) (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 H J) (k1_fdiff_1 B J)) (k1_seq_1 F J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 I J) (k1_fdiff_1 C J)) (k1_seq_1 E J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 I J) (k1_fdiff_1 C J)) (k1_seq_1 D J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 G J) (k1_fdiff_1 A J)) (k1_seq_1 F J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_seq_1 G J) (k1_fdiff_1 A J)) (k1_seq_1 E J)) (k11_binop_2 (k11_binop_2 (k1_seq_1 H J) (k1_fdiff_1 B J)) (k1_seq_1 D J))))) (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_fdiff_1 H J) (k1_seq_1 B J)) (k1_seq_1 F J)) (k11_binop_2 (k11_binop_2 (k1_fdiff_1 I J) (k1_seq_1 C J)) (k1_seq_1 E J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_fdiff_1 I J) (k1_seq_1 C J)) (k1_seq_1 D J)) (k11_binop_2 (k11_binop_2 (k1_fdiff_1 G J) (k1_seq_1 A J)) (k1_seq_1 F J))) (k10_binop_2 (k11_binop_2 (k11_binop_2 (k1_fdiff_1 G J) (k1_seq_1 A J)) (k1_seq_1 E J)) (k11_binop_2 (k11_binop_2 (k1_fdiff_1 H J) (k1_seq_1 B J)) (k1_seq_1 D J)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((r7_euclidlp A B C) &  ((v1_euclid_4 B A) &  ((v1_euclid_4 C A) & (r1_xboole_0 B C)) ) )  => (r5_euclidlp A B C)) ) ) ) ) ) ) ).
tt(t113_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  => (m2_finseq_2 (k1_partfun1 k5_numbers B B C D E) C (k4_finseq_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t113_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) =>  ((k16_finseq_1 (k3_finseq_1 A) B) = A) ) ) ) ) ) ).
tt(t113_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ((k4_finseq_5 A (k3_finseq_6 A B C D)) = (k3_finseq_6 A (k4_finseq_5 A B) (k2_nat_1 (k7_nat_d (k3_finseq_1 B) D) 1) (k2_nat_1 (k7_nat_d (k3_finseq_1 B) C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t113_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_2 A (k2_flang_2 A B) C D) (k8_flang_1 A B))) ) ) ) ) ) ) ).
tt(t113_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (~  ((r2_hidden A (k2_relset_1 C D)) &  (! [E:$i] :  ((m1_subset_1 E B) =>  (~  (A = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 B C)) B) = C) ) ) ) ) ).
tt(t113_funct_7,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  (B = (k3_funct_7 k4_numbers (k3_funct_7 k4_numbers A C (k7_partfun1 k4_numbers A D)) D (k7_partfun1 k4_numbers A C))) ) ) ) )  =>  ( ((k1_funct_1 A C) = (k1_funct_1 B D))  &  ( ((k1_funct_1 A D) = (k1_funct_1 B C))  &  ( (! [E:$i] :  ((r2_hidden E (k4_finseq_1 A)) =>  ( (E = C)  |  ( (E = D)  |  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) ) )  & (r2_classes1 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  ((r2_hidden A (k2_msafree2 (k43_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k43_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k43_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t113_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  <=>  ((k15_glib_001 A B) = (k15_glib_001 A C)) ) ) ) ) ) ) ) ).
tt(t113_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_struct_0 C B) <=>  ((k13_group_2 A C B) = (k8_group_2 A C)) ) ) ) ) ) ) ) ).
tt(t113_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r5_group_3 A C B) <=> (r4_group_3 A (k8_group_2 A C) (k8_group_2 A B))) ) ) ) ) ) ) ).
tt(t113_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  => (r5_group_9 A B B C C)) ) ) ) ) ).
tt(t113_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 B (k13_complex1 (k17_euclid A) (k12_euclid A))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))) (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))))))) ) )  &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 B) A) = A) ) ) ) ) ) ) ).
tt(t113_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid B)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_jordan2c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  =>  ((r1_xxreal_0 (k18_euclid B) (k7_pscomp_1 (k3_topreal1 2 A))) | (r2_hidden B (k2_goboard9 A))) ) ) ) ) ) ).
tt(t113_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((k4_limfunc1 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B))) & (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) )  | (v5_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t113_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 B)) =>  ((k3_matrix_1 (u1_struct_0 C) D G E) = F) ) ) )  =>  ((v2_funct_1 D) <=> (v2_funct_1 (k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 (k3_finseq_1 D)) (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 D)) (k3_matrix13 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k14_member_1 (k2_tarski A B) (k1_tarski C)) = (k2_tarski (k6_xxreal_3 A C) (k6_xxreal_3 B C))) ) ) ) ) ) ) ).
tt(t113_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C)))  => (r14_ncfcont1 A B C D)) ) ) ) ) ) ) ) ).
tt(t113_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) &  ((r2_pboole A B D) & (r5_pboole A C D)) )  => (r6_pboole A B (k1_pboole A))) ) ) ) ) ) ) ) ).
tt(t113_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k7_relat_1 A (k9_xtuple_0 A)) = (k10_xtuple_0 A)) ) ) ).
tt(t113_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k20_rvsum_1 (k5_finseq_2 k2_numbers A (k5_binop_2 B C))) = (k5_binop_2 (k20_rvsum_1 (k5_finseq_2 k2_numbers A B)) (k20_rvsum_1 (k5_finseq_2 k2_numbers A C)))) ) ) ) ) ) ) ).
tt(t113_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))))  =>  ((k1_funct_1 (k6_scmpds_4 (k9_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k1_funct_1 (k13_scmyciel A) k6_numbers) = A) ) ) ).
tt(t113_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) )  =>  ( (A = k1_xboole_0)  | (r1_xxreal_0 B (k5_seq_4 A))) ) ) ) ) ) ).
tt(t113_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D (k5_sheffer1 A C (k5_sheffer1 A C C)))) (k5_sheffer1 A B D)) = B) ) ) ) ) ) ) ) ) ).
tt(t113_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_square_1 2)))  =>  ( ((k1_seq_1 k16_sin_cos (k9_sincos10 A)) = (k10_real_1 (k7_square_1 (k9_real_1 (k5_square_1 A) 1)) A))  &  ((k1_seq_1 k19_sin_cos (k9_sincos10 A)) = (k10_real_1 1 A)) ) ) ) ) ).
tt(t113_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos9))) &  ( (E = (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ( (~ (r1_xxreal_0 (k1_seq_1 E H) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 E H))) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ((k1_seq_1 F H) = (k7_real_1 B (k8_real_1 C H))) ) ) )  &  (G = (k1_taylor_1 2)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)) k1_sin_cos9) D) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)) k1_sin_cos9) D) H) = (k10_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) H)) (k7_real_1 1 (k5_square_1 (k7_real_1 (k7_real_1 B (k8_real_1 C H)) (k8_real_1 A (k5_square_1 H))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( (A = (k1_tsep_1 A D E))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  ( ( (F = G)  &  (F = H) )  =>  ((r1_tmap_1 A B C F) <=>  ((r1_tmap_1 D B (k2_tmap_1 A B C D) G) & (r1_tmap_1 E B (k2_tmap_1 A B C E) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D) = (k2_xboole_0 A (k2_xboole_0 (k2_xboole_0 B C) D))) ) ) ) ) ).
tt(t113_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ( ((k6_xboolean A B) = k2_xboolean)  =>  ((k6_xboolean (k6_xboolean B C) (k6_xboolean A C)) = k2_xboolean) ) ) ) ) ) ) ) ).
tt(t113_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 (k7_xcmplx_0 B A) C) = (k7_xcmplx_0 (k2_xcmplx_0 B (k3_xcmplx_0 A C)) A)) ) ) ) ) ) ) ) ).
tt(t113_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k7_xcmplx_0 C B)))  & (r1_xxreal_0 (k3_xcmplx_0 D B) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k4_xxreal_1 C B) (k1_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t113_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang A (k10_zf_lang B A))) & (r2_zf_model C (k11_zf_lang A (k10_zf_lang B A)))) ) ) ) ) ) ) ) ) ).
tt(t113_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden A (k2_zfmisc_1 B C)) & (r2_hidden A (k2_zfmisc_1 D E)))  => (r2_hidden A (k2_zfmisc_1 (k3_xboole_0 B D) (k3_xboole_0 C E)))) ) ) ) ) ) ).
tt(t113_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ((k7_zmodul01 A C (k6_zmodul01 A C B)) = C) ) ) ) ) ) ) ).
tt(t114_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v13_abcmiz_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k1_funct_1 B C) = k1_xboole_0)  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~  ((k2_msualg_1 A D) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C F E) &  ((r5_aofa_000 A B C G E) & (r4_aofa_000 A (k13_aofa_000 A G F) B (k2_binop_1 B (u1_struct_0 A) B E D F) C E)) )  => (r2_hidden (k4_tarski D (k16_aofa_000 A F G)) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) & (v9_clvect_1 C A))  => (v9_clvect_1 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t114_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ( ((v1_funct_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ( ((r1_fdiff_1 A J) &  ((r1_fdiff_1 B J) &  ((r1_fdiff_1 C J) &  ((r1_fdiff_1 D J) &  ((r1_fdiff_1 E J) &  ((r1_fdiff_1 F J) &  ((r1_fdiff_1 G J) &  ((r1_fdiff_1 H J) & (r1_fdiff_1 I J)) ) ) ) ) ) ) )  =>  ((k8_euclid_8 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A E) (k20_valued_1 k1_numbers k1_numbers k1_numbers B D))) (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k20_valued_1 k1_numbers k1_numbers k1_numbers A F)))) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers I (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B F) (k20_valued_1 k1_numbers k1_numbers k1_numbers C E))) (k20_valued_1 k1_numbers k1_numbers k1_numbers G (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A E) (k20_valued_1 k1_numbers k1_numbers k1_numbers B D)))) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers G (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k20_valued_1 k1_numbers k1_numbers k1_numbers A F))) (k20_valued_1 k1_numbers k1_numbers k1_numbers H (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B F) (k20_valued_1 k1_numbers k1_numbers k1_numbers C E)))) J) = (k7_euclid 3 (k7_euclid 3 (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 D J)))) (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 F J))))) (k10_binop_2 (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 E J)))) (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 D J))))) (k10_binop_2 (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_fdiff_1 F J)))) (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_fdiff_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_fdiff_1 E J)))))) (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 D J)))) (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 F J))))) (k10_binop_2 (k11_binop_2 (k1_seq_1 I J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 E J)))) (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 D J))))) (k10_binop_2 (k11_binop_2 (k1_seq_1 G J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_fdiff_1 A J) (k1_seq_1 F J)))) (k11_binop_2 (k1_seq_1 H J) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_fdiff_1 C J) (k1_seq_1 E J))))))) (k1_euclid_8 (k10_binop_2 (k11_binop_2 (k1_fdiff_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 D J)))) (k11_binop_2 (k1_fdiff_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 F J))))) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 I J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 E J)))) (k11_binop_2 (k1_fdiff_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 E J)) (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 D J))))) (k10_binop_2 (k11_binop_2 (k1_fdiff_1 G J) (k10_binop_2 (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 D J)) (k11_binop_2 (k1_seq_1 A J) (k1_seq_1 F J)))) (k11_binop_2 (k1_fdiff_1 H J) (k10_binop_2 (k11_binop_2 (k1_seq_1 B J) (k1_seq_1 F J)) (k11_binop_2 (k1_seq_1 C J) (k1_seq_1 E J)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_euclid A)) (k5_euclidlp A)) =>  (~  ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D F) &  ((r2_hidden E F) &  ((r3_euclidlp A (k8_euclid A C B) (k8_euclid A E D)) & (r1_xboole_0 (k2_euclid_4 A B C) (k2_euclid_4 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  ( ((k10_xtuple_0 D) = (k2_finseq_1 A))  => (m2_finseq_2 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers B D C) B (k4_finseq_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t114_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_funct_1 (k8_finseq_1 k5_numbers (k14_finseq_1 (k8_relat_1 B A)) (k14_finseq_1 (k8_relat_1 B (k6_subset_1 (k10_xtuple_0 B) A))))) &  ((v1_funct_2 (k8_finseq_1 k5_numbers (k14_finseq_1 (k8_relat_1 B A)) (k14_finseq_1 (k8_relat_1 B (k6_subset_1 (k10_xtuple_0 B) A)))) (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 (k8_finseq_1 k5_numbers (k14_finseq_1 (k8_relat_1 B A)) (k14_finseq_1 (k8_relat_1 B (k6_subset_1 (k10_xtuple_0 B) A)))) (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 (k8_finseq_1 k5_numbers (k14_finseq_1 (k8_relat_1 B A)) (k14_finseq_1 (k8_relat_1 B (k6_subset_1 (k10_xtuple_0 B) A)))) (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) ) ) ) ) ).
tt(t114_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C B) (k3_finseq_1 D)))  =>  ((k1_funct_1 (k2_rfinseq A B D) C) = (k1_funct_1 D (k2_nat_1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(t114_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k2_flang_2 A (k1_flang_2 A B C D)) (k8_flang_1 A B))) ) ) ) ) ) ) ).
tt(t114_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (r2_hidden (k3_funct_2 B C D E) A)) )  => (r1_tarski (k2_relset_1 C D) A)) ) ) ) ) ) ) ) ).
tt(t114_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k1_funct_4 (k1_funct_4 C (k16_funcop_1 D A)) (k16_funcop_1 D B)) = (k1_funct_4 C (k16_funcop_1 D B))) ) ) ) ) ) ).
tt(t114_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (~  ( (~  (B = D) )  &  ( (~  (B = F) )  &  (~  ((k1_funct_1 (k1_funct_4 (k1_funct_4 (k1_funct_4 A (k16_funcop_1 B C)) (k16_funcop_1 D E)) (k16_funcop_1 F G)) B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k43_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t114_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ((k15_glib_001 A C) = (k15_glib_001 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t114_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((k13_group_2 A D B) = (k13_group_2 A D C))  <=> (r1_struct_0 D (k6_algstr_0 A (k2_group_1 A C) B))) ) ) ) ) ) ) ) ) ).
tt(t114_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_group_3 (k6_group_2 A) A) & (v1_group_3 (k7_group_2 A) A)) ) ) ).
tt(t114_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  ((r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 D)) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  (~ (r1_xxreal_0 (k3_finseq_1 D) 1)) )  | (r4_group_9 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t114_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))) (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))))))) ) ) ) ) ) ) ).
tt(t114_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid D)) &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 (k18_euclid C) H) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_jordan2c,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_connsp_1 A B C) => (v2_connsp_1 C A)) ) ) ) ) ) ) ).
tt(t114_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((k5_limfunc1 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B))) & (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) )  | (v7_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t114_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v2_funct_1 D) &  ((v1_vectsp_7 (k9_matrix13 C B A D) C (k6_prvect_1 C A)) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 B)) =>  ((k3_matrix_1 (u1_struct_0 C) D F E) = (k4_struct_0 C)) ) ) ) ) )  => (v1_vectsp_7 (k9_matrix13 C (k5_card_1 (k2_finseq_1 (k3_finseq_1 D))) (k5_card_1 (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 D)) (k3_matrix13 E))) (k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 (k3_finseq_1 D)) (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 D)) (k3_matrix13 E)))) C (k6_prvect_1 C (k5_card_1 (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 D)) (k3_matrix13 E)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k14_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k6_xxreal_3 A C) (k6_xxreal_3 A D) (k6_xxreal_3 B C) (k6_xxreal_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t114_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) D C)))  => (r15_ncfcont1 B A C D)) ) ) ) ) ) ) ) ).
tt(t114_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r6_pboole A (k2_pboole A B C) (k2_pboole A D E)) &  ((r5_pboole A D B) & (r5_pboole A E C)) )  =>  ((r6_pboole A D C) & (r6_pboole A E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k7_relat_1 B A) (k7_relat_1 B (k9_xtuple_0 B)))) ) ) ).
tt(t114_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k3_finseq_1 (k6_rvsum_1 A)) = (k3_finseq_1 A)) ) ) ).
tt(t114_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k1_funct_1 (k6_scmpds_4 (k9_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (v4_scmyciel (k1_funct_1 (k13_scmyciel A) B))) ) ) ) ).
tt(t114_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~  (C = k1_xboole_0) )  => (r1_xxreal_0 k6_numbers (k24_seq_4 A B C))) ) ) ) ) ) ) ).
tt(t114_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) D) C) (k5_sheffer1 A (k5_sheffer1 A B B) C)) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) B)) (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) B)))) ) ) ) ) ) ) ) ) ).
tt(t114_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) & (r1_xxreal_0 A (k1_real_1 1)))  =>  ( ((k1_seq_1 k16_sin_cos (k10_sincos10 A)) = (k1_real_1 (k10_real_1 (k7_square_1 (k9_real_1 (k5_square_1 A) 1)) A)))  &  ((k1_seq_1 k19_sin_cos (k10_sincos10 A)) = (k10_real_1 1 A)) ) ) ) ) ).
tt(t114_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k2_sin_cos9))) &  ( (E = (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ( (~ (r1_xxreal_0 (k1_seq_1 E H) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 E H))) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ((k1_seq_1 F H) = (k7_real_1 B (k8_real_1 C H))) ) ) )  &  (G = (k1_taylor_1 2)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)) k2_sin_cos9) D) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers F (k26_valued_1 k1_numbers k1_numbers G A)) k2_sin_cos9) D) H) = (k1_real_1 (k10_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) H)) (k7_real_1 1 (k5_square_1 (k7_real_1 (k7_real_1 B (k8_real_1 C H)) (k8_real_1 A (k5_square_1 H)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((r4_tsep_1 A C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_tsep_1 A C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) C E) C B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) D E) D B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_xboole_0 A D) &  ((r1_xboole_0 B D) & (r1_xboole_0 C D)) )  => (r1_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D)) ) ) ) ) ).
tt(t114_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ((k6_xboolean A (k6_xboolean A B)) = k2_xboolean)  =>  ((k6_xboolean A B) = k2_xboolean) ) ) ) ) ) ).
tt(t114_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 B C) = (k3_xcmplx_0 A (k2_xcmplx_0 (k7_xcmplx_0 B A) (k7_xcmplx_0 C A)))) ) ) ) ) ) ) ) ).
tt(t114_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 D B) (k3_xcmplx_0 C A)))  & (r1_xxreal_0 (k3_xcmplx_0 C B) (k7_xcmplx_0 D A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k2_xxreal_1 C B) (k1_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t114_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k10_zf_lang A B) (k10_zf_lang B A))) & (r2_zf_model C (k11_zf_lang (k10_zf_lang A B) (k10_zf_lang B A)))) ) ) ) ) ) ) ) ) ).
tt(t114_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_tarski (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) =>  ( ((k2_zfmisc_1 A B) = k1_xboole_0)  |  ((r1_tarski A C) & (r1_tarski B D)) ) ) ) ) ) ) ).
tt(t114_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) => (m1_zmodul01 (k6_zmodul01 A (k7_zmodul01 A B C) (k7_zmodul01 A C D)) (k7_zmodul01 A C (k6_zmodul01 A B D)))) ) ) ) ) ) ) ) ).
tt(t115_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_lang1 B))  =>  ((r1_relset_1 (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_lang1 A) (u1_lang1 B)) =>  ((r1_tarski (k52_abcmiz_1 A) (k52_abcmiz_1 B)) &  ((r1_tarski (k9_subset_1 (u1_struct_0 B) (u1_struct_0 A) (k51_abcmiz_1 B)) (k51_abcmiz_1 A)) &  ((r1_tarski (k51_abcmiz_1 A) (k51_abcmiz_1 B)) => (r1_tarski (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t115_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r6_aofa_000 A B C G E F) &  ((r6_aofa_000 A B C H E F) &  ((r7_aofa_000 A B C G E F) &  ((r7_aofa_000 A B C H E F) &  ((r4_aofa_000 A (k13_aofa_000 A H G) B (k2_binop_1 B (u1_struct_0 A) B E D G) C E) & (r2_hidden D F)) ) ) ) )  => (r2_hidden (k4_tarski D (k16_aofa_000 A G H)) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 C A) => (v9_clvect_1 (k4_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t115_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ((v3_card_1 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers B D C) A) & (m2_finseq_1 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers B D C) B)) ) ) ) ) ) ) ) ) ).
tt(t115_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k10_xtuple_0 A))) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers A)) &  ((v3_funct_2 C (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers A))))) ) )  &  ((k7_finseq_1 (k1_finseq_3 A (k3_subset_1 (k10_xtuple_0 A) B)) (k1_finseq_3 A B)) = (k3_relat_1 C A)) ) ) ) ) ) ) ).
tt(t115_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C)))  =>  ((k1_funct_1 (k4_finseq_5 A C) B) = (k1_funct_1 C (k7_real_1 (k9_real_1 (k3_finseq_1 C) B) 1))) ) ) ) ) ) ) ) ).
tt(t115_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_2 A B) = (k2_flang_2 A (k7_subset_1 (k8_afinsq_1 A) B (k4_flang_1 A (k2_flang_1 A))))) ) ) ) ).
tt(t115_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((v1_partfun1 E A) =>  ((k3_funct_2 B C (k8_funct_2 B C A D E) F) = (k1_funct_1 E (k3_funct_2 B A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k1_funct_4 (k1_funct_4 (k1_funct_4 C A) B) A) = (k1_funct_4 (k1_funct_4 C A) B)) ) ) ) ) ) ) ) ).
tt(t115_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden D B) =>  ((v1_funct_1 (k2_funct_7 E C D)) &  ((v1_funct_2 (k2_funct_7 E C D) A B) & (m1_subset_1 (k2_funct_7 E C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t115_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 E) (k9_margrel1 F)))  &  ( ((k1_funct_1 (k6_circuit2 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 F) (k9_margrel1 G)))  &  ((k1_funct_1 (k6_circuit2 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 G) (k9_margrel1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((r1_xxreal_0 (k16_glib_001 A B (k1_funct_1 B C)) C) & (r1_xxreal_0 C (k18_glib_001 A B (k1_funct_1 B C)))) ) ) ) ) ) ) ) ).
tt(t115_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((k13_group_2 A D B) = (k13_group_2 A D C))  <=>  (~ (r1_xboole_0 (k13_group_2 A D B) (k13_group_2 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t115_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  => (v1_group_3 (k10_group_2 A B C) A)) ) ) ) ) ) ).
tt(t115_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  ( ((r5_group_9 A B B C D) & (v10_group_9 C A B))  => (v10_group_9 D A B)) ) ) ) ) ) ) ) ).
tt(t115_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 B))  &  (~  ( ( ((r1_xxreal_0 B (k13_complex1 (k17_euclid A) (k12_euclid A))) & (r1_xxreal_0 (k18_euclid A) k6_numbers))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))) (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))))))) ) )  &  ( ((r1_xxreal_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) & (r1_xxreal_0 (k18_euclid A) k6_numbers))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))) (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid D)) &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 (k18_euclid C) H) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_jordan2c A B C) => (v2_connsp_1 C (k15_euclid A))) ) ) ) ) ) ) ).
tt(t115_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((k5_limfunc1 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B))) & (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) )  | (v8_limfunc1 (k6_rfunct_1 k1_numbers k1_numbers A))) ) ) ) ).
tt(t115_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))))  =>  ((v1_vectsp_7 D A C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((r2_hidden E D) & (r2_hidden F D))  =>  ( (E = F)  | (v1_vectsp_7 (k4_subset_1 (u1_struct_0 C) (k7_subset_1 (u1_struct_0 C) D (k6_domain_1 (u1_struct_0 C) E)) (k6_domain_1 (u1_struct_0 C) (k3_rlvect_1 C E (k4_vectsp_1 A C B F)))) A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k15_member_1 A B) = (a_2_7_member_1 A B)) ) ) ) ) ).
tt(t115_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r13_ncfcont1 A A B (k1_partfun2 (u1_struct_0 A) B))) ) ) ) ).
tt(t115_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r5_pboole A B C) => (r6_pboole A (k4_pboole A B C) B)) ) ) ) ) ) ).
tt(t115_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k10_xtuple_0 (k5_relat_1 B A)) = (k7_relat_1 B A)) ) ) ) ).
tt(t115_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k4_rvsum_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t115_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k10_scmpds_6 A B C)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ).
tt(t115_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((v4_scmyciel B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 (k13_scmyciel A) (k1_nat_1 C 1)) = (k12_scmyciel (k1_funct_1 (k13_scmyciel A) C))) ) ) ) ) ) ) ).
tt(t115_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~  (D = k1_xboole_0) )  => (r1_xxreal_0 (k24_seq_4 A (k15_seq_4 A B C) D) (k9_binop_2 (k24_seq_4 A B D) (k22_seq_4 C)))) ) ) ) ) ) ) ) ) ).
tt(t115_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) (k5_sheffer1 A (k5_sheffer1 A D B) (k5_sheffer1 A (k5_sheffer1 A C C) B))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A C C)) (k5_sheffer1 A D B)) (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t115_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 (k7_square_1 2)) A) & (r1_xxreal_0 A (k1_real_1 1)))  =>  ( ((k1_seq_1 k16_sin_cos (k11_sincos10 A)) = (k10_real_1 1 A))  &  ((k1_seq_1 k19_sin_cos (k11_sincos10 A)) = (k1_real_1 (k10_real_1 (k7_square_1 (k9_real_1 (k5_square_1 A) 1)) A))) ) ) ) ) ).
tt(t115_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 1 (k1_seq_1 k24_sin_cos B))) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t115_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_tsep_1 A C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) C E) C B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) D E) D B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_xboole_1,ax, (! [A:$i] :  (~ (r2_xboole_0 A k1_xboole_0)) ) ).
tt(t115_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ( ((k6_xboolean A (k6_xboolean B C)) = k2_xboolean)  =>  ((k6_xboolean (k6_xboolean A B) (k6_xboolean A C)) = k2_xboolean) ) ) ) ) ) ) ) ).
tt(t115_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 B C) = (k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 B A) (k3_xcmplx_0 C A)) A)) ) ) ) ) ) ) ) ).
tt(t115_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 D B) (k3_xcmplx_0 C A)))  & (r1_xxreal_0 (k3_xcmplx_0 C B) (k7_xcmplx_0 D A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k3_xxreal_1 C B) (k1_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t115_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((r1_zf_model B C (k11_zf_lang A (k10_zf_lang A A))) & (r2_zf_model B (k11_zf_lang A (k10_zf_lang A A)))) ) ) ) ) ) ) ).
tt(t115_zfmisc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) | (r1_tarski (k2_zfmisc_1 B A) (k2_zfmisc_1 D C)))  => (r1_tarski B D)) ) ) ) ) ) ).
tt(t115_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((m1_zmodul01 B C) =>  ((k7_zmodul01 A C (k6_zmodul01 A B D)) = (k6_zmodul01 A (k7_zmodul01 A B C) (k7_zmodul01 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t116_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_lang1 B))  =>  ( ((r1_tarski (k51_abcmiz_1 A) (k51_abcmiz_1 B)) & (r1_relset_1 (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_lang1 A) (u1_lang1 B)))  => (r1_tarski (k4_dtconstr A) (k4_dtconstr B))) ) ) ) ) ).
tt(t116_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_aofa_000 E A B C) =>  (! [F:$i] :  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C G E) &  ((r6_aofa_000 A B C H E F) &  ((r7_aofa_000 A B C G E F) &  ( (! [I:$i] :  ((m1_subset_1 I B) =>  ( ((r2_hidden I F) & (r2_hidden (k2_binop_1 B (u1_struct_0 A) B E (k2_binop_1 B (u1_struct_0 A) B E I H) G) C))  => (r2_hidden (k2_binop_1 B (u1_struct_0 A) B E I H) F)) ) )  &  ((r4_aofa_000 A (k13_aofa_000 A H G) B (k2_binop_1 B (u1_struct_0 A) B E D G) C E) & (r2_hidden D F)) ) ) ) )  => (r2_hidden (k4_tarski D (k16_aofa_000 A G H)) (k21_aofa_000 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_clvect_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v9_clvect_1 C B) => (v9_clvect_1 (k6_clvect_1 B C A) B)) ) ) ) ) ) ) ).
tt(t116_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((k1_funct_1 (k8_finseq_1 B C (k12_finseq_1 B D)) (k1_nat_1 A 1)) = D) ) ) ) ) ) ) ) ) ).
tt(t116_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k15_finseq_1 A) = A) ) ) ) ).
tt(t116_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((k3_finseq_6 A B 1 C) = (k17_finseq_1 A C B)) ) ) ) ) ) ) ) ).
tt(t116_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k2_flang_2 A C)) => (r1_tarski (k2_flang_2 A B) (k2_flang_2 A C))) ) ) ) ) ) ).
tt(t116_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((v1_partfun1 E A) =>  ((k3_funct_2 B C (k8_funct_2 B C A D E) F) = (k7_partfun1 C E (k3_funct_2 B A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) & (r1_tarski A (k1_funct_4 C B)))  => (r1_tarski A C)) ) ) ) ) ) ) ).
tt(t116_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski (k10_xtuple_0 B) A) =>  ((k6_funct_4 B C D) = (k3_relat_1 B (k2_funct_7 (k6_partfun1 A) C D))) ) ) ) ) ) ) ).
tt(t116_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k4_twoscomp)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k4_twoscomp)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 C A) k4_twoscomp))) ) )  =>  ((k1_twoscomp (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) (k6_circuit2 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D) (k45_gfacirc1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith E F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  (! [E:$i] :  ( (C = D)  =>  ( ((k16_glib_001 A C E) = (k16_glib_001 B D E))  &  ((k18_glib_001 A C E) = (k18_glib_001 B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_tarski (k13_group_2 A D (k6_algstr_0 A B C)) (k2_group_2 A (k13_group_2 A D B) (k13_group_2 A D C)))) ) ) ) ) ) ) ) ).
tt(t116_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  => (v1_group_3 B A)) ) ) ) ) ).
tt(t116_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) 1))  &  (~ (r4_group_9 A B (k21_group_9 A B C D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k9_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k18_euclid D) k6_numbers) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t116_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_jordan2c A B C) => (v2_connsp_1 C (k15_euclid A))) ) ) ) ) ) ) ).
tt(t116_matrix13,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r1_struct_0 (k1_vectsp_7 B C (k7_domain_1 (u1_struct_0 C) D E)) A) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (A = (k3_rlvect_1 C (k4_vectsp_1 B C F D) (k4_vectsp_1 B C G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k6_binop_2 C D) (k15_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t116_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r13_ncfcont1 A B C D) => (r7_ncfcont1 A B D C)) ) ) ) ) ) ) ) ).
tt(t116_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r5_pboole A B C) => (r6_pboole A (k4_pboole A (k2_pboole A B C) C) B)) ) ) ) ) ) ).
tt(t116_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k8_rvsum_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t116_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k10_scmpds_6 A B C))) & (r2_hidden 1 (k9_xtuple_0 (k10_scmpds_6 A B C)))) ) ) ) ) ) ) ).
tt(t116_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_scmyciel (k1_funct_1 (k13_scmyciel A) B)) = (k6_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_newton 2 B) (k2_scmyciel A)) (k2_newton 2 B)) 1)) ) ) ) ) ).
tt(t116_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ((r2_hidden B C) =>  ((k24_seq_4 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t116_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) (k5_sheffer1 A (k5_sheffer1 A D B) (k5_sheffer1 A (k5_sheffer1 A C C) B))) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D B)) (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t116_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_square_1 2)))  =>  ( ((k1_seq_1 k16_sin_cos (k12_sincos10 A)) = (k10_real_1 1 A))  &  ((k1_seq_1 k19_sin_cos (k12_sincos10 A)) = (k10_real_1 (k7_square_1 (k9_real_1 (k5_square_1 A) 1)) A)) ) ) ) ) ).
tt(t116_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 1 (k1_seq_1 k24_sin_cos B))) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k24_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t116_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_tsep_1 A C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) C E) C B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E)) &  ((v1_funct_2 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k3_tmap_1 A B (k1_tsep_1 A C D) D E) D B) & (m1_subset_1 (k3_tmap_1 A B (k1_tsep_1 A C D) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 A (k3_xboole_0 B C)) = (k3_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(t116_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ( ((k6_xboolean A B) = k2_xboolean)  &  ((k6_xboolean B A) = k2_xboolean) )  =>  (A = B) ) ) ) ) ) ).
tt(t116_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k2_xcmplx_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B)) = (k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) (k3_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k7_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 C A) (k3_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 C B) & (r1_tarski (k1_xxreal_1 C B) (k1_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang (k11_zf_lang C B) (k11_zf_lang (k10_zf_lang A C) B)))) & (r2_zf_model D (k11_zf_lang (k11_zf_lang A B) (k11_zf_lang (k11_zf_lang C B) (k11_zf_lang (k10_zf_lang A C) B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t116_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k2_xboole_0 (k4_xboole_0 B (k1_tarski A)) (k1_tarski A)) = B) ) ) ) ).
tt(t116_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) => (m1_zmodul01 (k6_zmodul01 A B (k7_zmodul01 A C D)) (k7_zmodul01 A (k6_zmodul01 A C B) (k6_zmodul01 A B D)))) ) ) ) ) ) ) ) ).
tt(t117_abcmiz_1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  ( ((r2_pboole (u1_struct_0 A) B C) & (v13_abcmiz_1 B A))  => (v13_abcmiz_1 C A)) ) ) ) ) ) ) ).
tt(t117_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C E D) &  ((r5_aofa_000 A B C F D) &  (! [G:$i] :  ((m1_subset_1 G B) => (r4_aofa_000 A (k13_aofa_000 A F E) B G C D)) ) ) )  => (r5_aofa_000 A B C (k16_aofa_000 A E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) => (v2_comseq_2 (k4_normsp_0 A B))) ) ) ) ) ).
tt(t117_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C (k1_nat_1 A 1)) & (m2_finseq_1 C B))  =>  (? [D:$i] :  ((m2_finseq_2 D B (k4_finseq_2 A B)) &  (? [E:$i] :  ((m1_subset_1 E B) &  (C = (k8_finseq_1 B D (k12_finseq_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_finseq_3,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) => (m2_finseq_1 A k1_numbers)) ) ).
tt(t117_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k3_finseq_6 A B C (k3_finseq_1 B)) = (k2_rfinseq A (k7_nat_d C 1) B)) ) ) ) ) ) ) ) ).
tt(t117_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k2_flang_2 A C)) =>  ((k2_flang_2 A C) = (k2_flang_2 A (k4_subset_1 (k8_afinsq_1 A) C B))) ) ) ) ) ) ) ).
tt(t117_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r1_tarski (k2_relset_1 B E) (k1_relset_1 B (k2_partfun1 B C F D))) => (r2_funct_2 A C (k8_funct_2 A C B E (k2_partfun1 B C F D)) (k8_funct_2 A C B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) & (r1_tarski A C))  => (r1_tarski A (k1_funct_4 C B))) ) ) ) ) ) ) ).
tt(t117_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((k6_funct_4 (k1_funct_4 A B) C D) = (k1_funct_4 (k6_funct_4 A C D) (k6_funct_4 B C D))) ) ) ) ) ) ) ).
tt(t117_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_twoscomp (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) (k5_facirc_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D 2) (k45_gfacirc1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) (k9_margrel1 F)) (k10_margrel1 (k9_margrel1 F) (k9_margrel1 G))) (k10_margrel1 (k9_margrel1 G) (k9_margrel1 E)))))  &  ( ((k1_funct_1 (k5_facirc_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 E) (k9_margrel1 F)))  &  ( ((k1_funct_1 (k5_facirc_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 F) (k9_margrel1 G)))  &  ((k1_funct_1 (k5_facirc_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) = (k10_margrel1 (k9_margrel1 G) (k9_margrel1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((r1_xxreal_0 (k17_glib_001 A B C) C) & (r1_xxreal_0 C (k19_glib_001 A B C))) ) ) ) ) ) ) ) ).
tt(t117_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_tarski (k8_group_2 A C) (k2_group_2 A (k13_group_2 A C B) (k13_group_2 A C (k2_group_1 A B)))) & (r1_tarski (k8_group_2 A C) (k2_group_2 A (k13_group_2 A C (k2_group_1 A B)) (k13_group_2 A C B)))) ) ) ) ) ) ) ).
tt(t117_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_group_2 A B C) = (k14_group_2 A B C)) ) ) ) ) ) ) ) ).
tt(t117_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) 1))  &  (~ (r5_group_9 A B B (k21_group_9 A B C D) (k21_group_9 A B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k7_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k18_euclid D) k6_numbers) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t117_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r3_connsp_1 (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B) C) => (r1_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t117_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B A) =>  ( ((v1_vectsp_7 (k9_matrix13 C B A E) C (k6_prvect_1 C A)) & (v2_funct_1 E))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k3_finseq_1 E))) =>  ( (F = G)  |  ((v2_funct_1 (k3_matrix11 F B A (u1_struct_0 C) E (k4_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E F) (k10_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E G) D)))) & (v1_vectsp_7 (k9_matrix13 C B A (k3_matrix11 F B A (u1_struct_0 C) E (k4_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E F) (k10_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E G) D)))) C (k6_prvect_1 C A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  (! [D:$i] :  ((v1_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k15_member_1 A C) (k15_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t117_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r14_ncfcont1 A B C D) => (r8_ncfcont1 A B D C)) ) ) ) ) ) ) ) ).
tt(t117_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k4_pboole A B C) B) => (r5_pboole A B C)) ) ) ) ) ) ).
tt(t117_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k3_finseq_1 (k10_rvsum_1 B A)) = (k3_finseq_1 B)) ) ) ) ) ).
tt(t117_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k10_scmpds_6 A B C) k6_numbers) = (k9_scmpds_2 A B 2))  &  ((k1_funct_1 (k10_scmpds_6 A B C) 1) = (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 1))) ) ) ) ) ) ) ) ).
tt(t117_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_scmyciel (k1_funct_1 (k13_scmyciel A) B)) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_newton 3 B) (k3_scmyciel A)) (k3_xcmplx_0 (k6_xcmplx_0 (k2_newton 3 B) (k2_newton 2 B)) (k2_scmyciel A))) (k3_stirl2_1 (k1_nat_1 B 1) 3))) ) ) ) ) ).
tt(t117_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  (~  ( (~ (r2_hidden B C))  &  ( (~  (C = k1_xboole_0) )  &  ((v2_seq_4 C A) & (r1_xxreal_0 (k24_seq_4 A B C) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t117_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A (k5_sheffer1 A D D) C)) (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) D)) (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) D)))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C)) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t117_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 (k7_square_1 2) A))  &  (~  ((k1_seq_1 k2_fdiff_9 (k9_sincos10 A)) = (k10_real_1 A (k7_square_1 (k9_real_1 (k5_square_1 A) 1)))) ) ) ) ) ) ) ).
tt(t117_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k3_taylor_1 B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k3_taylor_1 B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) A) B) = (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t117_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((r4_tsep_1 A C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 (k2_tmap_1 A B E (k1_tsep_1 A C D))) &  ((v1_funct_2 (k2_tmap_1 A B E (k1_tsep_1 A C D)) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B E (k1_tsep_1 A C D)) (k1_tsep_1 A C D) B) & (m1_subset_1 (k2_tmap_1 A B E (k1_tsep_1 A C D)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B E C)) &  ((v1_funct_2 (k2_tmap_1 A B E C) (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B E C) C B) & (m1_subset_1 (k2_tmap_1 A B E C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B E D)) &  ((v1_funct_2 (k2_tmap_1 A B E D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B E D) D B) & (m1_subset_1 (k2_tmap_1 A B E D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski C B) =>  ((k4_xboole_0 A C) = (k2_xboole_0 (k4_xboole_0 A B) (k3_xboole_0 A (k4_xboole_0 B C)))) ) ) ) ) ).
tt(t117_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ( ( ((k6_xboolean A B) = k2_xboolean)  &  ((k6_xboolean B C) = k2_xboolean) )  =>  ((k6_xboolean A C) = k2_xboolean) ) ) ) ) ) ) ) ).
tt(t117_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 A B) = (k3_xcmplx_0 A (k2_xcmplx_0 1 (k7_xcmplx_0 B A)))) ) ) ) ) ) ).
tt(t117_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D A) (k7_xcmplx_0 C B)))  & (r1_xxreal_0 (k7_xcmplx_0 C A) (k3_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k4_xxreal_1 C B) (k2_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang C B)) (k11_zf_lang (k10_zf_lang A C) B))) & (r2_zf_model D (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang C B)) (k11_zf_lang (k10_zf_lang A C) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t117_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden A B))  =>  ((k4_xboole_0 (k2_xboole_0 B (k1_tarski A)) (k1_tarski A)) = B) ) ) ) ).
tt(t117_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((m1_zmodul01 B C) =>  ((k6_zmodul01 A C (k7_zmodul01 A B D)) = (k7_zmodul01 A (k6_zmodul01 A B C) (k6_zmodul01 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t118_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r1_tarski (k3_card_3 (k3_msafree A B)) (k3_card_3 (k3_msafree A C)))) ) ) ) ) ) ).
tt(t118_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_aofa_000 D A B C) =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r5_aofa_000 A B C F D) &  ((r6_aofa_000 A B C G D E) &  ((r7_aofa_000 A B C F D E) &  ( (! [H:$i] :  ((m1_subset_1 H B) =>  ( ((r2_hidden H E) & (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D (k2_binop_1 B (u1_struct_0 A) B D H G) F) C))  => (r2_hidden (k2_binop_1 B (u1_struct_0 A) B D H G) E)) ) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ((r2_hidden (k2_binop_1 B (u1_struct_0 A) B D H F) E) => (r4_aofa_000 A (k13_aofa_000 A G F) B (k2_binop_1 B (u1_struct_0 A) B D H F) C D)) ) ) ) ) ) )  => (r6_aofa_000 A B C (k16_aofa_000 A F G) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 C A) &  ((k7_clvect_1 A C) = B) )  =>  ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A C B))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A C B))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t118_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  ((k3_relat_1 (k1_finseq_2 A) C) = C) ) ) ) ) ) ) ).
tt(t118_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A)))  <=> (r2_xboole_0 (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers B))) ) ) ) ) ).
tt(t118_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ( ((k1_funct_1 (k3_finseq_6 A B C D) 1) = (k1_funct_1 B C))  &  ( ((r1_xxreal_0 C D) =>  ( ((k3_finseq_1 (k3_finseq_6 A B C D)) = (k2_nat_1 (k7_nat_d D C) 1))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 (k3_finseq_6 A B C D))))  =>  ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k7_nat_d (k2_nat_1 E C) 1))) ) ) ) ) )  &  ( (~ (r1_xxreal_0 C D))  =>  ( ((k3_finseq_1 (k3_finseq_6 A B C D)) = (k2_nat_1 (k7_nat_d C D) 1))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 (k3_finseq_6 A B C D))))  =>  ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k2_nat_1 (k7_nat_d C E) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( ((r1_tarski (k2_relset_1 B F) (k1_relset_1 B (k2_partfun1 B C G D))) & (r1_tarski D E))  => (r2_funct_2 A C (k8_funct_2 A C B F (k2_partfun1 B C G D)) (k8_funct_2 A C B F (k2_partfun1 B C G E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k1_funct_4 (k1_funct_4 C A) B) = (k1_funct_4 (k1_funct_4 C B) A)) ) ) ) ) ) ) ) ).
tt(t118_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((k9_xtuple_0 (k11_funct_7 A B)) = k5_numbers) ) ) ).
tt(t118_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k43_gfacirc1 A B C) (k44_gfacirc1 A B C) D 2) (k43_gfacirc1 A B C) (k44_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t118_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_glib_001 B A) <=>  ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t118_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k13_group_2 A C (k5_group_1 A 2 B)) (k2_group_2 A (k13_group_2 A C B) (k13_group_2 A C B)))) ) ) ) ) ) ).
tt(t118_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k13_group_2 A B C) (k14_group_2 A B C))) ) ) ) ) ) ) ).
tt(t118_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  (? [E:$i] :  ( ((v8_group_9 E A B) & (m2_finseq_1 E (k6_group_9 A B)))  &  (? [F:$i] :  ( ((v8_group_9 F A B) & (m2_finseq_1 F (k6_group_9 A B)))  &  ((r4_group_9 A B E C) &  ((r4_group_9 A B F D) & (r5_group_9 A B B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k9_real_1 1 A)))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k18_euclid D) k6_numbers) &  ((r1_xxreal_0 A (k13_complex1 (k17_euclid D) (k12_euclid D))) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t118_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r2_jordan2c A D C) & (r1_jordan2c A D B))  => (r1_xboole_0 C B)) ) ) ) ) ) ) ) ) ).
tt(t118_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  ((r1_tarski D (k2_finseq_1 A)) => (r1_tarski (k9_matrix13 C (k5_card_1 D) (k5_card_1 (k2_finseq_1 B)) (k6_matrix13 (u1_struct_0 C) E D (k2_finseq_1 B))) (k9_matrix13 C A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k15_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k15_member_1 A B) (k15_member_1 A C))) ) ) ) ) ) ) ).
tt(t118_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r15_ncfcont1 B A C D) => (r9_ncfcont1 B A D C)) ) ) ) ) ) ) ) ).
tt(t118_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r5_pboole A (k4_pboole A B C) (k4_pboole A C B))) ) ) ) ) ).
tt(t118_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((k7_relat_1 B A) = k1_xboole_0)  <=> (r1_xboole_0 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t118_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k14_rvsum_1 (k4_rvsum_1 A B) C) = (k4_rvsum_1 (k14_rvsum_1 A C) (k14_rvsum_1 B C))) ) ) ) ) ) ) ) ).
tt(t118_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((r1_scmpds_6 (k10_scmpds_6 D E C) B A) & (r2_scmpds_6 (k10_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k8_scmyciel (k1_funct_1 (k13_scmyciel (k5_scmyciel 2)) A)) = 2)  &  ((k10_scmyciel (k1_funct_1 (k13_scmyciel (k5_scmyciel 2)) A)) = (k1_nat_1 A 2)) ) ) ) ).
tt(t118_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~  (D = k1_xboole_0) )  => (r1_xxreal_0 (k24_seq_4 A B D) (k9_binop_2 (k22_seq_4 (k19_seq_4 A B C)) (k24_seq_4 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t118_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D C)) (k5_sheffer1 A C (k5_sheffer1 A D C))) (k5_sheffer1 A B (k5_sheffer1 A B B))) = (k5_sheffer1 A (k5_sheffer1 A D D) C)) ) ) ) ) ) ) ) ) ).
tt(t118_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 (k7_square_1 2))))  &  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  &  (~  ((k1_seq_1 k2_fdiff_9 (k10_sincos10 A)) = (k1_real_1 (k10_real_1 A (k7_square_1 (k9_real_1 (k5_square_1 A) 1))))) ) ) ) ) ) ) ).
tt(t118_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k3_taylor_1 B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k3_taylor_1 B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 (k1_seq_1 k3_taylor_1 B))))))) ) ) ) ) ) ) ) ).
tt(t118_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v1_borsuk_1 E A) & (m1_pre_topc E A)) )  =>  ( ((v1_funct_1 (k2_tmap_1 A B C (k1_tsep_1 A D E))) &  ((v1_funct_2 (k2_tmap_1 A B C (k1_tsep_1 A D E)) (u1_struct_0 (k1_tsep_1 A D E)) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C (k1_tsep_1 A D E)) (k1_tsep_1 A D E) B) & (m1_subset_1 (k2_tmap_1 A B C (k1_tsep_1 A D E)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A D E)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C D) D B) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B C E)) &  ((v1_funct_2 (k2_tmap_1 A B C E) (u1_struct_0 E) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C E) E B) & (m1_subset_1 (k2_tmap_1 A B C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k6_xboolean (k6_xboolean (k3_xboolean A) A) A) = k2_xboolean) ) ) ).
tt(t118_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 (k7_xcmplx_0 A (k3_xcmplx_0 2 B)) (k7_xcmplx_0 A (k3_xcmplx_0 2 B))) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(t118_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 A C))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 B C) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ) ).
tt(t118_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k3_xxreal_1 C B) (k2_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k11_zf_lang A (k6_zf_lang B)) (k11_zf_lang B (k6_zf_lang A)))) & (r2_zf_model C (k11_zf_lang (k11_zf_lang A (k6_zf_lang B)) (k11_zf_lang B (k6_zf_lang A))))) ) ) ) ) ) ) ) ) ).
tt(t118_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_tarski D (k1_enumset1 A B C)) <=>  (~  ( (~  (D = k1_xboole_0) )  &  ( (~  (D = (k1_tarski A)) )  &  ( (~  (D = (k1_tarski B)) )  &  ( (~  (D = (k1_tarski C)) )  &  ( (~  (D = (k2_tarski A B)) )  &  ( (~  (D = (k2_tarski B C)) )  &  ( (~  (D = (k2_tarski A C)) )  &  (~  (D = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t118_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ( ((v1_zmodul01 B) & (m1_zmodul01 B C))  =>  ((k6_zmodul01 A B (k7_zmodul01 A D C)) = (k7_zmodul01 A (k6_zmodul01 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t119_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  ((r2_pboole (u1_struct_0 A) B C) => (r1_tarski (u1_struct_0 (k5_msafree A B)) (u1_struct_0 (k5_msafree A C)))) ) ) ) ) ) ) ).
tt(t119_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) & (v9_clvect_1 C A))  =>  ((k7_clvect_1 A (k2_normsp_1 A B C)) = (k3_rlvect_1 A (k7_clvect_1 A B) (k7_clvect_1 A C))) ) ) ) ) ) ) ) ).
tt(t119_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D B))  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t119_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (~  (B = k6_numbers) )  &  (A = k1_xboole_0) )  <=>  ((k4_finseq_2 B A) = k1_xboole_0) ) ) ) ) ).
tt(t119_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k10_xtuple_0 (k3_finseq_6 A B C D)) (k10_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(t119_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A (k2_zfmisc_1 B C) D E) = (k4_tarski (k3_funct_2 A B (k4_funct_2 A B C D) E) (k3_funct_2 A C (k5_funct_2 A B C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k6_subset_1 (k1_funct_4 A B) B) = A) ) ) ) ) ) ).
tt(t119_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((k1_funct_1 (k11_funct_7 A B) k6_numbers) = A) ) ) ).
tt(t119_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k46_gfacirc1 A B C)) = (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) (k1_tarski (k48_gfacirc1 A B C)))) ) ) ) ).
tt(t119_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_glib_001 B A) <=>  (? [C:$i] : (r1_glib_001 A C C B)) ) ) ) ) ) ).
tt(t119_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_struct_0 C B) <=>  ((k14_group_2 A C B) = (k8_group_2 A C)) ) ) ) ) ) ) ) ).
tt(t119_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k14_group_2 A B C) (k13_group_2 A B C))) ) ) ) ) ) ) ).
tt(t119_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v8_group_9 C A B) & (m2_finseq_1 C (k6_group_9 A B)))  =>  (! [D:$i] :  ( ((v8_group_9 D A B) & (m2_finseq_1 D (k6_group_9 A B)))  =>  ( ((v10_group_9 C A B) & (v10_group_9 D A B))  => (r5_group_9 A B B C D)) ) ) ) ) ) ) ) ).
tt(t119_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k7_real_1 1 A)))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k18_euclid D) k6_numbers) &  ((r1_xxreal_0 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t119_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v9_rltopsp1 D (k15_euclid A)) &  ((r2_jordan2c A D B) & (r2_jordan2c A D C)) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  ( ((r1_tarski D (k2_finseq_1 A)) & (v1_vectsp_7 (k9_matrix13 C A B E) C (k6_prvect_1 C B)))  => (v1_vectsp_7 (k9_matrix13 C (k5_card_1 D) (k5_card_1 (k2_finseq_1 B)) (k6_matrix13 (u1_struct_0 C) E D (k2_finseq_1 B))) C (k6_prvect_1 C (k5_card_1 (k2_finseq_1 B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) => (r1_tarski (k15_member_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k15_member_1 A B) (k15_member_1 A C)))) ) ) ) ) ) ).
tt(t119_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r16_ncfcont1 A B C) => (r10_ncfcont1 A C B)) ) ) ) ) ) ).
tt(t119_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r7_pboole A B C)) ) ) ) ) ) ).
tt(t119_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ( (~  (A = k1_xboole_0) )  &  ((r1_tarski A (k9_xtuple_0 B)) &  ((k7_relat_1 B A) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t119_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (r1_xxreal_0 k6_numbers (k23_rvsum_1 A A))) ) ).
tt(t119_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))))  =>  ((r1_scmpds_6 (k10_scmpds_6 D E C) B A) & (r2_scmpds_6 (k10_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ((v1_finset_1 B) & (v4_scmyciel B))  &  ( ((k8_scmyciel B) = 2)  &  (~ (r1_xxreal_0 (k10_scmyciel B) A)) ) ) ) ) ) ).
tt(t119_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  ((r2_hidden C (k25_seq_4 A D B)) <=>  (~ (r1_xxreal_0 B (k24_seq_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t119_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C B)) = (k5_sheffer1 A (k5_sheffer1 A C C) B)) ) ) ) ) ) ) ).
tt(t119_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 (k7_square_1 2))))  &  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  &  (~  ((k1_seq_1 k1_fdiff_9 (k11_sincos10 A)) = (k1_real_1 (k10_real_1 A (k7_square_1 (k9_real_1 (k5_square_1 A) 1))))) ) ) ) ) ) ) ).
tt(t119_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k1_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t119_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v1_tsep_1 E A) & (m1_pre_topc E A)) )  =>  ( ((v1_funct_1 (k2_tmap_1 A B C (k1_tsep_1 A D E))) &  ((v1_funct_2 (k2_tmap_1 A B C (k1_tsep_1 A D E)) (u1_struct_0 (k1_tsep_1 A D E)) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C (k1_tsep_1 A D E)) (k1_tsep_1 A D E) B) & (m1_subset_1 (k2_tmap_1 A B C (k1_tsep_1 A D E)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A D E)) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C D) D B) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B C E)) &  ((v1_funct_2 (k2_tmap_1 A B C E) (u1_struct_0 E) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C E) E B) & (m1_subset_1 (k2_tmap_1 A B C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ((k3_xboolean A) = k2_xboolean)  =>  ((k6_xboolean A B) = k2_xboolean) ) ) ) ) ) ).
tt(t119_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k7_xcmplx_0 A (k3_xcmplx_0 3 B)) (k7_xcmplx_0 A (k3_xcmplx_0 3 B))) (k7_xcmplx_0 A (k3_xcmplx_0 3 B))) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(t119_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 C B))  =>  ((r1_xxreal_0 k6_numbers B) | (r1_xxreal_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 A C))) ) ) ) ) ) ) ) ).
tt(t119_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k2_xxreal_1 C B) (k2_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t119_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k6_zf_lang A) (k11_zf_lang A B))) & (r2_zf_model C (k11_zf_lang (k6_zf_lang A) (k11_zf_lang A B)))) ) ) ) ) ) ) ) ) ).
tt(t119_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_tarski A (k2_zfmisc_1 C D)) & (r1_tarski B (k2_zfmisc_1 E F)))  => (r1_tarski (k2_xboole_0 A B) (k2_zfmisc_1 (k2_xboole_0 C E) (k2_xboole_0 D F)))) ) ) ) ) ) ) ).
tt(t119_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ( ((k6_zmodul01 A B C) = C)  <=>  ((k7_zmodul01 A B C) = B) ) ) ) ) ) ) ) ).
tt(t11_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((l2_abcmiz_0 B) =>  ( ((g2_abcmiz_0 (u1_struct_0 A) (u1_abcmiz_0 A) (u1_orders_2 A) (u2_abcmiz_0 A) (u3_abcmiz_0 A)) = (g2_abcmiz_0 (u1_struct_0 B) (u1_abcmiz_0 B) (u1_orders_2 B) (u2_abcmiz_0 B) (u3_abcmiz_0 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_abcmiz_0 B)) =>  ( (C = D)  =>  ((k3_abcmiz_0 A C) = (k3_abcmiz_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ((k1_abcmiz_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k1_abcmiz_1 A) (k1_abcmiz_1 B))) ) ) ).
tt(t11_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  (~  ( (B = (k35_abcmiz_1 C A))  &  ((k1_funct_1 B k1_xboole_0) = (k4_tarski C k8_abcmiz_1)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (~  ( ((k1_funct_1 B k1_xboole_0) = (k4_tarski C (u1_struct_0 A)))  &  (~  ( (~ (r2_hidden C k20_abcmiz_1))  &  ( (~  (C = k9_abcmiz_1) )  &  (~  (C = k10_abcmiz_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_abian,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) <=>  (? [B:$i] :  ((v1_int_1 B) &  (A = (k3_xcmplx_0 2 B)) ) ) ) ) ) ).
tt(t11_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B)) =>  ((k18_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k18_complex1 A) (k18_complex1 B))) ) ) ) ) ) ).
tt(t11_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_aff_1 A D E B) &  ((r1_aff_1 A D E C) & (r1_aff_1 A B C F)) )  =>  ( (B = C)  | (r1_aff_1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_2 A) => (v4_aff_2 A)) ) ) ).
tt(t11_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden B D) &  ((r2_hidden C D) & (v1_aff_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) A))  =>  ((k2_afinsq_1 (k5_relat_1 B A)) = A) ) ) ) ) ) ).
tt(t11_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) )  =>  ((k2_afinsq_2 (k1_ordinal4 B C) (k23_binop_2 (k1_afinsq_1 B) A)) = (k2_afinsq_2 C A)) ) ) ) ) ) ) ).
tt(t11_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) & (v1_aff_1 C A))  =>  ( ((k5_afproj A B) = (k5_afproj A C))  <=> (r5_aff_1 A B C)) ) ) ) ) ) ) ) ).
tt(t11_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_afvect01 A B C) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t11_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A F G H I) &  ((r2_analoaf A C J F G) & (r2_analoaf A E K H I)) ) )  => (r2_analoaf A B J D K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((r4_alg_1 A B D) & (r4_alg_1 B C E))  => (r4_alg_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  ( (A = (k1_algseq_1 B C))  <=>  ((k7_card_1 A) = (k2_algseq_1 B C)) ) ) ) ) ) ) ) ).
tt(t11_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r6_pboole A (k1_algspec1 A (k1_algspec1 A B)) (k1_algspec1 A B))) ) ) ).
tt(t11_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v21_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_algstr_1 A) & (l4_algstr_0 A)) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k1_algstr_0 A C B)) ) ) ) )  &  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v2_algstr_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_group_6 C A B) =>  ((v2_algstr_4 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B) & (m1_subset_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_altcat_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((v4_funct_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (k2_zfmisc_1 A B)) & (v7_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ((k1_binop_1 C D E) = (k3_relat_1 E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tarski (k7_relat_1 (u1_cat_1 A) (k8_mcart_1 (u4_struct_0 A) (u4_struct_0 A) (k2_cat_1 A C D) (k2_cat_1 A B C))) (k2_cat_1 A B D))) ) ) ) ) ) ) ) ).
tt(t11_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  ((v4_altcat_3 (k5_altcat_1 A B C D E F) A B D) &  (~ (v4_altcat_3 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v6_altcat_3 B A) & (r2_altcat_3 A B C))  => (v6_altcat_3 C A)) ) ) ) ) ) ) ).
tt(t11_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_funct_1 (k6_ami_2 A B) k5_numbers) = B) ) ) ) ) ).
tt(t11_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  ((k4_memstr_0 2 k1_ami_3 A) = k4_numbers) ) ) ).
tt(t11_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 4)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k5_ami_3 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  ( (A = 8)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_ami_3) A))) = (k1_tarski 1)) ) ) ) ).
tt(t11_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_amistd_1 A (k4_amistd_1 A) B) = (k2_tarski B (k1_ordinal1 B))) ) ) ) ) ).
tt(t11_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r8_pboole (u1_struct_0 B) D (k4_extpro_1 A B D C)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 B) (k5_extpro_1 A B C D E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_4 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v1_xboole_0 (k3_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t11_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 D))  & (v1_finset_1 D)) ) ) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((v4_extpro_1 D A B C) <=> (v4_extpro_1 (k9_memstr_0 A B D E) A B (k6_compos_1 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k4_ami_wstd A B C k6_numbers) = C) ) ) ) ) ) ) ).
tt(t11_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_analmetr A D D B C))  =>  (D = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analoaf A B C D E) & (r1_analoaf A B C F G))  =>  ( (B = C)  | (r1_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k2_analort A B C (k5_algstr_0 A D E)) = (k5_algstr_0 A (k2_analort A B C D) (k2_analort A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~ (r1_anproj_1 A B C))  &  ( (~ (r1_anproj_1 A D B))  &  (~ (r1_anproj_1 A C D)) ) ) )  => (r2_anproj_1 A D B C)) ) ) ) ) ) ) ) ) ).
tt(t11_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ( ((k3_funct_2 A k1_numbers B E) = 1)  &  ( (! [H:$i] :  ((r2_hidden H A) =>  ( (H = E)  |  ((k1_funct_1 B H) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers C F) = 1)  &  ( (! [H:$i] :  ((r2_hidden H A) =>  ( (H = F)  |  ((k1_funct_1 C H) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers D G) = 1)  &  (! [H:$i] :  ((r2_hidden H A) =>  ( (H = G)  |  ((k1_funct_1 D H) = k6_numbers) ) ) ) ) ) ) ) )  =>  ( (E = F)  |  ( (E = G)  |  ( (F = G)  |  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) H B)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I C))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J D))) (k8_funcsdom A)) =>  ( (H = k6_numbers)  &  ( (I = k6_numbers)  &  (J = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ( ((k3_relat_1 A B) = B)  & (r2_hidden C D)) ) )  =>  ((k1_funct_1 (k7_aofa_000 A D B) C) = (k1_funct_1 (k7_aofa_000 A D B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(t11_aofa_i00,ax, (! [A:$i] :  ((v4_card_3 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) &  ((v1_funct_2 B A (k1_card_1 A)) &  ((v2_funct_2 B (k1_card_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) )  => (r1_tarski (k2_relset_1 (k1_card_1 A) B) k5_numbers)) ) ) ) ).
tt(t11_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k4_armstrng A)) =>  (! [C:$i] :  ((m1_subset_1 C (k4_armstrng A)) =>  ( ((r3_armstrng A C B) & (r3_armstrng A B C))  =>  (B = C) ) ) ) ) ) ) ).
tt(t11_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k2_arrow A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (k2_arrow A)) =>  (~  ( (~ (r1_arrow F B C))  &  ( (~ (r1_arrow F B D))  &  ( (~  ( (~ (r1_arrow F D C))  & (r1_arrow E D C)) )  &  ( (~  ( (~ (r1_arrow E D C))  & (r1_arrow F D C)) )  &  ( (~  ( (~ (r1_arrow F C D))  & (r1_arrow E C D)) )  &  (~  ( (~ (r1_arrow E C D))  & (r1_arrow F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = k6_numbers)  =>  ((k1_arytm_0 A B) = A) ) ) ) ) ) ).
tt(t11_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) => (r1_arytm_2 (k1_arytm_1 A B) A)) ) ) ) ).
tt(t11_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((k7_arytm_2 A B) = (k7_arytm_2 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t11_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  ( ((r2_arytm_3 A B) & (r2_arytm_3 A (k8_ordinal3 B C)))  => (r2_arytm_3 A C)) ) ) ) ) ) ) ).
tt(t11_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden A (k6_asympt_0 B)) => (r1_tarski (k6_asympt_0 A) (k6_asympt_0 B))) ) ) ) ) ).
tt(t11_asympt_1,ax,(r2_hidden (k3_asympt_1 2) (k6_asympt_0 (k3_asympt_1 3)))).
tt(t11_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k1_tarski A)) &  ((v1_funct_1 B) & (v1_partfun1 B (k1_tarski A))) ) )  =>  (B = (k16_funcop_1 A (k1_funct_1 B A))) ) ) ) ).
tt(t11_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r1_tarski (k4_autgroup A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(t11_bagorder,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( ( (C = (k1_tarski B))  & (r3_orders_1 D C))  =>  ((k7_pre_poly A C D) = (k9_finseq_1 B)) ) ) ) ) ) ) ) ) ).
tt(t11_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  <=>  ((v7_bcialg_1 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B D)) (k1_bcialg_1 A D C)) = (k4_struct_0 A))  &  ((k1_bcialg_1 A B (k4_struct_0 A)) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k1_bcialg_2 A (k1_bcialg_2 A B C E) D F) = (k1_bcialg_2 A (k1_bcialg_2 A B D F) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A B D) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B))) = (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_4 A (k1_bcialg_4 A B C) D) = (k1_bcialg_4 A (k1_bcialg_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t11_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_bcialg_1 A (k1_bcialg_5 A B C (k2_nat_1 D 1) (k2_nat_1 D 1)) (k1_bcialg_5 A C B D (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ).
tt(t11_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_bcialg_1 A)) & (r1_xxreal_0 1 C))  =>  ((k3_bcialg_6 A C B) = B) ) ) ) ) ) ) ) ).
tt(t11_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  ( ((k9_subset_1 (u1_struct_0 A) B C) = (k1_tarski (k4_struct_0 A)))  <=>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) C) =>  ((k1_bcialg_1 A D E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k5_algstr_0 A B C) D) = (k9_real_1 (k2_bhsp_1 A B D) (k2_bhsp_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t11_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 C) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((k1_normsp_1 A C D) = B) ) ) )  |  ((k1_bhsp_2 A C) = B) ) ) ) ) ) ) ) ) ).
tt(t11_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_bhsp_3 A B C) => (r1_bhsp_3 A C B)) ) ) ) ) ) ) ).
tt(t11_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) => (v2_bhsp_3 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(t11_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m2_bhsp_5 C A))  =>  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski C (k9_xtuple_0 D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = (k5_square_1 (k2_bhsp_1 A B E))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((r1_tarski C (k9_xtuple_0 E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k1_funct_1 E F) = (k1_rlvect_1 A F (k2_bhsp_1 A B F))) ) ) ) )  =>  ((k2_bhsp_1 A B (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) C E)) = (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k1_bilinear A B C) D) (k7_hahnban1 A B))) ) ) ) ) ) ) ) ).
tt(t11_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k21_binop_2 (k20_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k7_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) (k15_funcop_1 k5_numbers (k4_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) (k15_funcop_1 k5_numbers (k5_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) = (k20_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D))) (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k6_binarith A (k1_binari_2 A)) = 1) ) ) ).
tt(t11_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k23_binop_2 B C) (k21_binop_2 (k5_series_1 2 A) 1)) =>  ((k6_binarith A (k7_binarith A (k1_binari_3 A B) (k1_binari_3 A C))) = (k23_binop_2 B C)) ) ) ) ) ) ) ) ).
tt(t11_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k5_xboolean (k5_xboolean A B) C) = (k5_xboolean A (k5_xboolean B C))) ) ) ) ) ) ) ).
tt(t11_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_binom A (k2_binom A B C) D) = (k2_binom A B (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t11_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r6_binop_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k3_binop_1 A B D (k3_binop_1 A C E F)) = (k3_binop_1 A C (k3_binop_1 A B D E) (k3_binop_1 A B D F)))  &  ((k3_binop_1 A B (k3_binop_1 A C D E) F) = (k3_binop_1 A C (k3_binop_1 A B D F) (k3_binop_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (A = (k3_finseq_2 (k7_domain_1 k5_numbers k6_numbers 1)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 B k6_margrel1)) => (r2_hidden C (k2_trees_2 A B))) ) ) ) ) ) ) ).
tt(t11_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k3_lattices A B C) (k5_lattices A)) <=>  ((r1_boolealg A B (k5_lattices A)) & (r1_boolealg A C (k5_lattices A))) ) ) ) ) ) ) ) ).
tt(t11_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) k6_margrel1 (k2_boolmark A B C) (k3_boolmark A B (k12_finseq_1 (u4_struct_0 A) C)))) ) ) ) ) ) ).
tt(t11_bor_cant,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A B) (k7_bor_cant A B)) & (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A B) (k9_bor_cant A B))) ) ) ) ).
tt(t11_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((r1_tarski C D) => (r1_tarski (k7_borsuk_1 A B C) (k7_borsuk_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v3_pre_topc C (k2_borsuk_1 B A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A)))))  =>  (! [D:$i] :  (~  ((r1_tarski (k2_zfmisc_1 (k2_struct_0 B) (k1_tarski D)) C) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden D E) & (r1_tarski E (a_3_0_borsuk_3 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_borsuk_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = B) )  =>  ((k6_measure6 (k4_rcomp_1 A B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(t11_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A C) & (r1_xxreal_0 C B))  =>  ((k4_subset_1 k1_numbers (k1_rcomp_1 A B) (k3_rcomp_1 C k1_xxreal_0)) = (k3_rcomp_1 A k1_xxreal_0)) ) ) ) ) ) ) ) ).
tt(t11_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_2_borsuk_6)  &  (B = a_0_3_borsuk_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 1 k6_numbers (k10_real_1 1 2) (k10_real_1 1 2)) A) = B) ) ) ) ) ) ).
tt(t11_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( ((k17_sin_cos A) = (k17_sin_cos B))  &  ( ((k20_sin_cos A) = (k20_sin_cos B))  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k3_real_1 B (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_brouwer,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_brouwer B C A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k2_brouwer B C A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k2_brouwer B C A)))))) )  =>  ((m1_subset_1 D (u1_struct_0 (k7_toprealb B C A))) =>  ((r2_abian (u1_struct_0 (k2_brouwer B C A)) D E) |  ((k3_funct_2 (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k7_toprealb B C A)) (k5_brouwer B A C E) D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ((k3_bspace A B) = (k4_struct_0 k2_bspace)) )  <=>  ((k3_bspace A B) = (k5_struct_0 k2_bspace)) ) ) ) ).
tt(t11_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C E)) (k5_bvfunc_1 A B C)) (k5_bvfunc_1 A D E))) ) ) ) ) ) ) ) ) ) ).
tt(t11_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k6_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k9_xtuple_0 (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F))) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t11_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k2_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t11_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k6_bvfunc_1 A C D)) (k6_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t11_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc_1 A C D)) (k2_bvfunc_1 A (k1_bvfunc_1 A (k2_bvfunc_1 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B D))))) ) ) ) ) ) ) ) ).
tt(t11_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r1_bvfunc_1 A (k6_bvfunc_2 A C B D) C)) ) ) ) ) ) ) ) ).
tt(t11_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k5_bvfunc_1 A C D) B E) (k5_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t11_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k1_bvfunc_1 A B) B) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t11_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A B D)) (k5_bvfunc_1 A B (k2_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t11_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k1_bvfunc_1 A C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t11_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k5_bvfunc_1 A B (k2_bvfunc_1 A (k1_bvfunc_1 A B) C)))) ) ) ) ) ) ).
tt(t11_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t11_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_c0sp1 A)))  &  ((v13_algstr_0 (k7_c0sp1 A)) &  ((v2_rlvect_1 (k7_c0sp1 A)) &  ((v3_rlvect_1 (k7_c0sp1 A)) &  ((v4_rlvect_1 (k7_c0sp1 A)) &  ((v5_rlvect_1 (k7_c0sp1 A)) &  ((v6_rlvect_1 (k7_c0sp1 A)) &  ((v7_rlvect_1 (k7_c0sp1 A)) &  ((v8_rlvect_1 (k7_c0sp1 A)) & (l1_rlvect_1 (k7_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  ((k1_binop_1 (k5_c0sp1 (k12_funcsdom (u1_struct_0 A)) (k2_c0sp2 A)) 1 B) = B) ) ) ) ) ).
tt(t11_calcul_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_finseq_1 (k14_finseq_1 (k4_subset_1 k5_numbers (k2_finseq_1 B) (k6_domain_1 k5_numbers (k2_nat_1 B A))))) = (k2_nat_1 B 1)) ) ) ) ) ) ).
tt(t11_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k1_relset_1 k5_numbers (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)))) = (k1_relset_1 k5_numbers C)) ) ) ) ) ) ) ).
tt(t11_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k2_cantor_1 A B) = (k2_cantor_1 A (k2_cantor_1 A B))) ) ) ) ).
tt(t11_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_ordinal1 (k1_card_1 A) (k1_card_1 B))) ) ) ).
tt(t11_card_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_wellord2 (k11_ordinal2 A B) (k2_zfmisc_1 A B)) &  ((k1_card_1 (k11_ordinal2 A B)) = (k1_card_1 (k2_zfmisc_1 A B))) ) ) ) ) ) ).
tt(t11_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((k1_funct_2 A B) = (k4_card_3 (k7_funcop_1 A B))) ) ) ).
tt(t11_card_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v4_card_3 (k9_xtuple_0 A)) &  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (v4_card_3 (k1_funct_1 A B))) ) )  => (v4_card_3 (k3_card_3 A))) ) ) ).
tt(t11_card_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((v2_ordinal2 A) => (v2_funct_1 A)) ) ) ).
tt(t11_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_card_fil B A) => (r2_hidden k1_xboole_0 B)) ) ) ) ).
tt(t11_cardfin2,ax, ((k2_cardfin2 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t11_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  ( (~  (A = B) )  =>  ((k5_card_1 (k1_card_fin C k6_numbers A B)) = 1) ) ) ) ) ) ).
tt(t11_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((r2_hidden B A) &  ((v2_card_lar C A) & (v1_card_lar C A)) )  =>  ((v2_card_lar (k7_subset_1 A C B) A) & (v1_card_lar (k7_subset_1 A C B) A)) ) ) ) ) ) ) ) ).
tt(t11_cat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cat_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k3_cat_1 A B))) => (r2_hidden E (k2_cat_1 (k3_cat_1 A B) C D))) ) ) ) ) ) ) ) ).
tt(t11_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ( (C = E)  &  ( (D = F)  &  ((k3_graph_1 B D) = (k4_graph_1 B C)) ) )  =>  ((k1_cat_1 B C D) = (k1_cat_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k2_oppcat_1 B))) => (r2_funct_2 A (u4_struct_0 B) (k5_cat_3 B A (k8_funcop_1 (u4_struct_0 (k2_oppcat_1 B)) A C)) (k8_funcop_1 (u4_struct_0 B) A (k6_oppcat_1 B C)))) ) ) ) ) ).
tt(t11_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  => (v10_cat_1 (k1_cat_4 A) A)) ) ).
tt(t11_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (v3_cat_5 (k3_cat_1 A (k4_tarski (k4_tarski A A) (k10_cat_1 A))))) ) ).
tt(t11_catalan1,ax, ((k1_catalan1 1) = 1) ).
tt(t11_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((v1_catalan2 B) &  ((k24_binop_2 2 (k7_afinsq_2 (k5_relat_1 B A))) = A) )  =>  ((r1_xxreal_0 A (k1_afinsq_1 B)) &  ((k1_afinsq_1 (k5_relat_1 B A)) = A) ) ) ) ) ) ) ).
tt(t11_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k5_catalg_1 A) = (k5_catalg_1 B))  =>  (A = B) ) ) ) ).
tt(t11_cayley,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) => (v2_funct_1 (k3_cayley A B C))) ) ) ) ) ) ) ).
tt(t11_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k2_numbers B A)) <=> (v4_xxreal_2 (k5_cc0sp1 A B))) ) ) ) ) ).
tt(t11_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cc0sp2 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( ( (D = B)  &  (E = C) )  =>  ( (C = (k1_clvect_1 (k3_cc0sp2 A) B F))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers E G) = (k3_xcmplx_0 F (k3_funct_2 (u1_struct_0 A) k2_numbers D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_tarski (k2_relset_1 k2_numbers A) (k1_relset_1 k2_numbers (k2_cfunct_1 k2_numbers B))) => (r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A (k2_cfunct_1 k2_numbers B)) (k36_valued_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ) ).
tt(t11_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  ( (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_cfdiff_1 C B) =>  (~ (r1_tarski C A)) ) ) ) ) ) )  => (v6_cfdiff_1 A)) ) ) ).
tt(t11_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers (k1_cfuncdom A) B (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) (k10_complex1 k6_complex1) B))) (k4_cfuncdom A))) ) ) ) ).
tt(t11_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((k1_relset_1 A (k2_cfunct_1 A (k2_cfunct_1 A B))) = (k1_relset_1 A (k2_partfun1 A k2_numbers B (k1_relset_1 A (k2_cfunct_1 A B))))) ) ) ) ) ).
tt(t11_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v2_cgames_1 C) =>  ((r2_hidden C (k2_cgames_1 B)) =>  ( ( (~ (r2_hidden A (k6_cgames_1 C)))  &  (~ (r2_hidden A (k7_cgames_1 C))) )  | (r2_hidden A (k2_cgames_1 B))) ) ) ) ) ) ) ).
tt(t11_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t11_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_abian A))  =>  (~  ((r1_xxreal_0 A 3) &  ( (~  (A = k6_numbers) )  &  (~  (A = 2) ) ) ) ) ) ) ).
tt(t11_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k3_msafree2 A) (k2_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A D))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) =>  ( ( (G = (k5_relat_1 I (u1_struct_0 A)))  &  ( (H = (k5_relat_1 I (u1_struct_0 B)))  &  ((v1_circuit2 G A D) & (v1_circuit2 H B E)) ) )  => (v1_circuit2 I C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( ( (H = (k5_relat_1 G (u1_struct_0 A)))  & (v1_circcmb3 H A D))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (I = (k5_relat_1 (k5_facirc_1 C F G (k2_circcmb3 A D H)) (u1_struct_0 B)))  & (v1_circcmb3 I B E))  =>  ((k5_relat_1 (k1_circcmb3 C F G) (u1_struct_0 A)) = (k1_circcmb3 A D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_circcomb A B) =>  ( ((k3_msafree2 (k2_circcomb A B)) = (k2_xboole_0 (k3_msafree2 A) (k3_msafree2 B)))  & (r1_tarski (k2_msafree2 (k2_circcomb A B)) (k2_xboole_0 (k2_msafree2 A) (k2_msafree2 B)))) ) ) ) ) ) ).
tt(t11_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k2_circled1 A B))) ) ) ) ).
tt(t11_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ((r2_hidden D (k2_msafree2 (k1_circtrm1 A B C))) <=>  ((r2_hidden D (k9_trees_9 C)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (k1_funct_1 B E)) &  (D = (k1_trees_4 (k4_tarski F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finseq_1 G) & (v6_trees_3 G)) ) )  =>  ( ((r2_hidden C (k7_subset_1 (u1_struct_0 A) (k3_msafree2 A) (k1_msafree2 A))) &  ( ((k5_card_1 E) = (k4_circuit1 A B C))  &  ( (E = (k4_trees_4 (k4_tarski (k4_msafree2 A C) (u1_struct_0 A)) G))  & (r2_hidden F (k10_xtuple_0 G))) ) )  =>  ((k5_card_1 F) = (k4_circuit1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ((r2_hidden C (k1_msafree2 A)) =>  ((k5_circuit2 A B C D) = (k1_funct_1 (k1_circuit1 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r1_tarski A B) & (r2_hidden B (k3_classes1 C D)))  => (r2_hidden A (k3_classes1 C (k1_ordinal1 D)))) ) ) ) ) ) ).
tt(t11_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_classes1 A) & (r2_hidden B A))  => (r2_hidden (k1_card_1 B) A)) ) ) ).
tt(t11_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_clopban1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_clopban1 A B))) =>  ( (E = (k3_rlvect_1 (k3_clopban1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k4_clopban1 A B E F) = (k3_rlvect_1 B (k4_clopban1 A B C F) (k4_clopban1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k4_clopban2 A (k3_clopban2 A C B) (k3_xcmplx_0 D E)) = (k3_clopban2 A (k4_clopban2 A C E) (k4_clopban2 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k1_valued_0 (u1_struct_0 A) C D))) ) )  |  ((k7_clvect_1 A C) = (k7_clvect_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t11_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E B) =>  ((k1_normsp_1 A C E) = (k1_normsp_1 A D E)) ) ) )  =>  ((k1_normsp_1 A (k1_bhsp_4 A C) B) = (k1_normsp_1 A (k1_bhsp_4 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_pboole C A (k5_mssubfam A B)) =>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D A) &  ((r2_hidden E (k1_funct_1 (k2_closure1 A B (k2_msualg_3 A (k5_mssubfam A B)) C) D)) &  (! [F:$i] :  ( ((v2_finset_1 F) & (m1_pboole F A (k5_mssubfam A B)))  =>  (~  ((r2_pboole A F C) & (r2_hidden E (k1_funct_1 (k2_closure1 A B (k2_msualg_3 A (k5_mssubfam A B)) F) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m1_closure2 D A C (k2_closure2 A C)) => (r2_hidden (k4_pboole A D B) (k2_closure2 A C))) ) ) ) ) ) ) ).
tt(t11_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  ((r1_tarski C D) => (r2_pboole A (k2_closure3 A B C) (k2_closure3 A B D))) ) ) ) ) ) ) ) ).
tt(t11_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k1_clvect_1 A B D) = (k1_clvect_1 A C D))  =>  ( (D = k6_numbers)  |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A C D) = B) ) ) )  |  ((k1_clvect_2 A C) = B) ) ) ) ) ) ) ) ) ).
tt(t11_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) => (v3_clvect_2 (k1_bhsp_4 A B) A)) ) ) ) ) ).
tt(t11_cohsp_1,ax, (! [A:$i] :  (! [B:$i] : (v2_cohsp_1 (k1_enumset1 A B (k3_xboole_0 A B)))) ) ).
tt(t11_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ( (A = (k9_setfam_1 (k3_tarski A)))  => (r2_relset_1 (k3_tarski A) (k3_tarski A) (k1_coh_sp A) (k1_eqrel_1 (k3_tarski A)))) ) ) ).
tt(t11_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C D) <=> (r2_hidden D (k1_collsp A B C))) ) ) ) ) ) ) ) ) ).
tt(t11_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) | (v4_incproj (k1_combgras A B))) ) ) ) ) ) ).
tt(t11_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_complex1 (k3_xcmplx_0 A k7_complex1)) = A) ) ) ).
tt(t11_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ( ((k17_sin_cos A) = (k17_sin_cos B))  &  ((k20_sin_cos A) = (k20_sin_cos B)) ) ) )  =>  ((r1_xxreal_0 (k8_real_1 2 k32_sin_cos) A) |  ((r1_xxreal_0 (k8_real_1 2 k32_sin_cos) B) |  (A = B) ) ) ) ) ) ) ) ).
tt(t11_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k5_algstr_0 k1_complfld A (k4_algstr_0 k1_complfld B)) = (k3_rlvect_1 k1_complfld A B)) ) ) ) ) ).
tt(t11_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k4_finseq_2 A k2_numbers)) =>  ((k4_complsp2 A B (k19_binop_2 1)) = (k11_seq_4 B)) ) ) ) ) ).
tt(t11_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  =>  ((v2_prob_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) B))  => (v3_finset_1 C)) ) ) ) ) ) ) ) ).
tt(t11_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) & (v2_compos_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k5_xtuple_0 B) = k1_xboole_0)  =>  ((k3_compos_0 A (k2_compos_0 A B)) = (k6_domain_1 k5_numbers k6_numbers)) ) ) ) ) ) ).
tt(t11_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k5_card_1 (k2_compos_2 A C B)) = (k2_xcmplx_0 (k5_card_1 C) 1)) ) ) ) ) ) ) ).
tt(t11_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden A (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) & (r1_xxreal_0 (k1_seq_1 k19_sin_cos A) k6_numbers)) ) ) ) ).
tt(t11_compts_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v8_pre_topc A) &  ((v2_compts_1 B A) & (v2_compts_1 C A)) )  => (v2_compts_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t11_comput_1,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v1_comput_1 A))  <=>  ((v1_relat_1 (k3_tarski A)) & (v1_funct_1 (k3_tarski A))) ) ) ).
tt(t11_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers A) (k25_valued_1 k5_numbers k2_numbers A (k10_complex1 k6_complex1)))) ) ).
tt(t11_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k2_comseq_3 A k6_numbers) = k6_complex1) ) ) ).
tt(t11_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ((r1_tarski B (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) C)) <=> (r1_tarski C (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B))) ) ) ) ) ) ) ).
tt(t11_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ( (~ (v5_conlat_1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k4_conlat_2 A) B) A))  &  ((v7_conlat_1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k4_conlat_2 A) B) A) & (l2_conlat_1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k4_conlat_2 A) B) A)) )  &  ( (~ (v5_conlat_1 (k3_funct_2 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k5_conlat_2 A) C) A))  &  ((v7_conlat_1 (k3_funct_2 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k5_conlat_2 A) C) A) & (l2_conlat_1 (k3_funct_2 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k5_conlat_2 A) C) A)) ) ) ) ) ) ) ) ) ).
tt(t11_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_aff_2 A) <=> (v4_conmetr1 A)) ) ) ).
tt(t11_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_conaffm A) => (v5_conmetr A)) ) ) ).
tt(t11_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_connsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ( (~  (B = (k1_struct_0 A)) )  &  ( (~  (C = (k1_struct_0 A)) )  &  ((v3_pre_topc B A) &  ((v3_pre_topc C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 B A) & (r1_tarski B C))  => (r3_connsp_1 A C B)) ) ) ) ) ) ) ).
tt(t11_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) =>  ( (B = k1_xboole_0)  |  ((k1_connsp_3 A (k1_connsp_3 A B)) = (k1_connsp_3 A B)) ) ) ) ) ) ) ).
tt(t11_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((v1_convex1 B A) & (v1_convex1 C A))  => (v1_convex1 (k7_rusub_4 A (k1_convex1 A B D) (k1_convex1 A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k3_rusub_4 A (k2_rlsub_2 A B C)) = (k9_subset_1 (u1_struct_0 A) (k3_rusub_4 A B) (k3_rusub_4 A C))) ) ) ) ) ) ) ).
tt(t11_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  ((k4_convex4 A (k2_convex4 A)) = (k4_struct_0 A)) ) ) ).
tt(t11_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (m2_subset_1 (k3_qc_lang2 A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ).
tt(t11_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_qc_lang2 A B (k7_cqc_lang A B C)) & (r2_qc_lang2 A C (k7_cqc_lang A B C))) ) ) ) ) ) ) ).
tt(t11_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden C (k1_cqc_the1 A B)) & (r2_hidden (k8_cqc_lang A C D) (k1_cqc_the1 A B)))  => (r2_hidden D (k1_cqc_the1 A B))) ) ) ) ) ) ) ) ) ).
tt(t11_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A (k7_qc_lang2 A C D B))))  &  (~ (r2_hidden D (k24_qc_lang1 A (k7_qc_lang2 A C D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_cqc_the3 A (k6_domain_1 (k3_cqc_lang A) B) (k6_domain_1 (k3_cqc_lang A) C)) <=> (r1_cqc_the3 A B C)) ) ) ) ) ) ) ).
tt(t11_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_3 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k7_comseq_3 A) B)) &  ((k1_seq_1 (k8_comseq_3 A) B) = k6_numbers) ) ) ) )  =>  ((k17_complex1 (k11_comseq_3 A)) = (k4_series_1 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ) ).
tt(t11_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k5_csspace4 A B)) = (k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ).
tt(t11_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ((v1_xboole_0 B) | (m1_clvect_1 (g1_clvect_1 B (k10_csspace A B) (k8_csspace A B) (k9_csspace A B)) A)) ) ) ) ) ) ).
tt(t11_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k8_decomp_1 A) (k15_decomp_1 A)) = (k6_decomp_1 A)) ) ) ).
tt(t11_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A B k6_numbers) = B) ) ) ) ) ) ).
tt(t11_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_dickson A) B) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t11_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) 1) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers C B))) ) ) ) ) ) ) ).
tt(t11_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_diff_2 (k26_valued_1 k1_numbers k1_numbers G A) B C D E F) = (k8_real_1 A (k1_diff_2 G B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 B A) 1) (k4_diff_1 B A))) ) ) ) ).
tt(t11_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k2_fdiff_9)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k2_fdiff_9)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_fdiff_9) B) A) = (k10_complex1 (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k7_real_1 (k8_real_1 2 A) B))) (k18_sin_cos B)) (k5_square_1 (k9_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B)))))) ) ) ) ) ) ).
tt(t11_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_waybel_4 A B C) & (r1_orders_2 A C D))  =>  ((v1_dilworth (k2_xboole_0 B (k1_tarski D)) A) & (m1_subset_1 (k2_xboole_0 B (k1_tarski D)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_diraf A B C D) & (r1_diraf A B D E))  => (r1_diraf A C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v2_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C E F) & (r2_dirort A E F D G))  =>  ( (E = F)  | (r2_analoaf A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden C (k5_dist_1 A B)) =>  ((k4_dist_1 A B) = (k4_dist_1 A C)) ) ) ) ) ) ) ) ).
tt(t11_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  ( (! [F:$i] :  ((r2_hidden F A) <=>  (? [G:$i] :  ((m1_subset_1 G B) &  (? [H:$i] :  ((m1_subset_1 H C) &  (? [I:$i] :  ((m1_subset_1 I D) &  (? [J:$i] :  ((m1_subset_1 J E) &  (F = (k6_xtuple_0 G H I J)) ) ) ) ) ) ) ) ) ) )  =>  (A = (k4_zfmisc_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_dtconstr,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr)) =>  (A = (k8_nat_1 (k4_dtconstr k5_dtconstr) k14_dtconstr (k3_funct_2 (k4_dtconstr k5_dtconstr) k5_numbers k12_dtconstr A))) ) ) ).
tt(t11_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_dynkin (k9_setfam_1 A) A)) ) ).
tt(t11_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (k6_numbers = (k4_struct_0 (k9_int_3 A))) ) ) ).
tt(t11_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) = (k8_group_1 A B (k8_group_1 A (k8_group_1 A C D) E)))  &  ((k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) F) = (k8_group_1 A B (k8_group_1 A (k8_group_1 A (k8_group_1 A C D) E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) = (k1_group_1 (k6_endalg A B))) ) ) ) ) ).
tt(t11_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k2_xtuple_0 (k5_ens_1 A B)) = (k6_partfun1 B))  &  ( ((k3_ens_1 A (k5_ens_1 A B)) = B)  &  ((k4_ens_1 A (k5_ens_1 A B)) = B) ) ) ) ) ) ) ).
tt(t11_entropy1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ((r1_entropy1 C A) =>  ( (B = A)  |  ((k1_seq_1 C B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t11_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k1_tarski A) (k3_enumset1 B C D E F))) ) ) ) ) ) ) ).
tt(t11_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A A)))) =>  ( (! [C:$i] :  ((r2_hidden C B) =>  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) )  =>  ( (B = k1_xboole_0)  |  ((v3_relat_2 (k6_setfam_1 (k2_zfmisc_1 A A) B)) &  ((v8_relat_2 (k6_setfam_1 (k2_zfmisc_1 A A) B)) &  ((v1_partfun1 (k6_setfam_1 (k2_zfmisc_1 A A) B) A) & (m1_subset_1 (k6_setfam_1 (k2_zfmisc_1 A A) B) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ).
tt(t11_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  ((r2_pboole A B (k3_funct_6 C)) => (r6_pboole A (k9_pboole A (k1_equation A B C) C) B)) ) ) ) ) ) ).
tt(t11_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k4_xboole_0 (u1_e_siec A) (k4_relat_1 (k9_xtuple_0 (u1_e_siec A)))) = (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))  &  ( ((k4_xboole_0 (u2_e_siec A) (k4_relat_1 (k9_xtuple_0 (u2_e_siec A)))) = (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))))  &  ( ((k4_xboole_0 (u1_e_siec A) (k4_relat_1 (k10_xtuple_0 (u1_e_siec A)))) = (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))  &  ((k4_xboole_0 (u2_e_siec A) (k4_relat_1 (k10_xtuple_0 (u2_e_siec A)))) = (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t11_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k5_square_1 (k12_euclid (k4_rvsum_1 A B))) = (k9_binop_2 (k9_binop_2 (k5_square_1 (k12_euclid A)) (k11_binop_2 2 (k23_rvsum_1 B A))) (k5_square_1 (k12_euclid B)))) ) ) ) ) ) ).
tt(t11_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_euclid_3 (k4_xcmplx_0 A)) = (k4_algstr_0 (k15_euclid 2) (k1_euclid_3 A))) ) ) ).
tt(t11_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r2_hidden B (k2_euclid_4 A C D)) & (r2_hidden E (k2_euclid_4 A C D)))  =>  ( (B = E)  | (r1_tarski (k2_euclid_4 A C D) (k2_euclid_4 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_algstr_0 (k15_euclid 3) (k4_euclid_5 A B C)) = (k4_euclid_5 (k1_real_1 A) (k1_real_1 B) (k1_real_1 C))) ) ) ) ) ) ) ).
tt(t11_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((k4_euclid_3 A B C) = k32_sin_cos)  => (r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C))) ) ) ) ) ) ) ).
tt(t11_euclid_7,ax, ((v1_funct_1 k1_xboole_0) &  ((v1_funct_2 k1_xboole_0 k1_xboole_0 k1_xboole_0) &  ((v3_funct_2 k1_xboole_0 k1_xboole_0 k1_xboole_0) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 k1_xboole_0)))) ) ) ).
tt(t11_euclid_8,ax, ((k23_rvsum_1 k3_euclid_8 k3_euclid_8) = 1) ).
tt(t11_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r2_hidden C (k4_euclid_9 A C B))) ) ) ) ) ) ) ).
tt(t11_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ((k12_euclid (k10_rvsum_1 B A)) = (k8_real_1 (k18_complex1 A) (k12_euclid B))) ) ) ) ) ).
tt(t11_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid C)) =>  ( ((k9_euclid C D (k9_real_1 A B)) = (k7_euclid C (k9_euclid C D A) (k9_euclid C D (k1_real_1 B))))  &  ( ((k9_euclid C D (k9_real_1 A B)) = (k7_euclid C (k9_euclid C D A) (k6_euclid C (k9_euclid C D B))))  &  ((k9_euclid C D (k9_real_1 A B)) = (k8_euclid C (k9_euclid C D A) (k9_euclid C D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v3_euclmetr A) <=> (v1_conaffm A)) ) ) ).
tt(t11_euler_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ((k1_card_1 A) = (k1_card_1 B)) ) ) ) ) ) ) ).
tt(t11_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ( (~  (A = k1_xboole_0) )  =>  ((k4_nat_d (k3_wsierp_1 (k2_euler_2 B A)) A) = (k4_nat_d (k3_wsierp_1 B) A)) ) ) ) ) ) ).
tt(t11_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v3_exchsort B A) &  ( (~ (v1_xboole_0 B))  & (v1_exchsort B)) )  <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ( ((k9_xtuple_0 B) = (k6_subset_1 A C))  & (r2_hidden C A)) ) ) ) ) ) ) ) ).
tt(t11_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  (! [G:$i] :  ( ((v2_relat_1 G) & (m3_pboole G A C))  =>  ((r2_pboole A (k3_funct_6 E) G) =>  ((k8_pboole E (k1_msafree A C D G F)) = (k3_msualg_3 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) & (v1_funct_1 D)) ) )  =>  ((r1_tarski (k16_funcop_1 C (k2_compos_1 B)) D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v5_memstr_0 E A B C)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ((r1_tarski E F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k5_extpro_1 A B D F G) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_extreal1,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k7_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 A) (k4_finseq_1 A)) &  ((v3_funct_2 C (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) ) )  =>  ( (B = (k1_partfun1 (k4_finseq_1 A) (k4_finseq_1 A) k5_numbers k7_numbers C A))  =>  ((r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)) |  ((k4_extreal1 A) = (k4_extreal1 B)) ) ) ) ) ) ) ) ) ).
tt(t11_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~ (r1_xxreal_0 B (k2_supinf_2 A)))  &  ( (~ (r1_xxreal_0 A B))  &  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (~ (r1_xxreal_0 A (k3_extreal1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t11_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((k5_facirc_1 A B C k6_numbers) = C) ) ) ) ) ) ) ).
tt(t11_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((k3_facirc_2 (k2_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k2_circcomb (k3_facirc_2 A B C) (k19_facirc_1 D E (k5_facirc_2 A B C))))  &  ( ((k4_facirc_2 (k2_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k3_circcomb (k3_facirc_2 A B C) (k19_facirc_1 D E (k5_facirc_2 A B C)) (k4_facirc_2 A B C) (k20_facirc_1 D E (k5_facirc_2 A B C))))  &  ((k5_facirc_2 (k2_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k17_facirc_1 D E (k5_facirc_2 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers B)) &  ((r1_fcont_1 C A) & (r1_fcont_1 B A)) )  =>  ( ((k1_seq_1 C A) = k6_numbers)  | (r1_fcont_1 (k3_rfunct_1 k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t11_fcont_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski B (k1_relset_1 k1_numbers A)) &  ((v1_rcomp_1 B) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) )  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t11_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((k7_relset_1 k1_numbers k1_numbers B A) = (k10_prob_1 C)) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t11_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos) A) B) = (k9_real_1 (k1_real_1 (k1_seq_1 k19_sin_cos B)) (k10_real_1 (k1_seq_1 k19_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t11_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_sin_cos9))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k2_sin_cos9 B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k2_sin_cos9 B))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_sin_cos9) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k7_real_1 1 (k5_square_1 B)) (k7_real_1 1 (k5_square_1 (k1_seq_1 k2_sin_cos9 B))))))) ) ) ) ) ) ) ) ).
tt(t11_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((k2_relset_1 k1_numbers B) = (k1_tarski C)) ) ) )  |  ((r2_fdiff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 B A) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 B A) <=>  ( (? [C:$i] :  ((m1_rcomp_1 C A) & (r1_tarski C (k1_relset_1 k1_numbers B))) )  &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski A))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers B)))  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers D B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r4_fdiff_3 A C) & (r4_fdiff_3 B C))  =>  ((r4_fdiff_3 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k1_fdiff_3 C (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k9_real_1 (k1_fdiff_3 C A) (k1_fdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B))))) &  ( (D = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ( ((k1_seq_1 E F) = (k9_real_1 F A))  &  (~ (r1_xxreal_0 (k1_seq_1 E F) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B))) C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B))) C) F) = (k10_real_1 (k9_real_1 F B) (k9_real_1 F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))))) &  ((r1_xxreal_0 1 A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 A D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A))) B) D) = (k8_real_1 (k8_real_1 A (k5_prepower (k1_seq_1 k16_sin_cos D) (k9_real_1 A 1))) (k1_seq_1 k19_sin_cos (k8_real_1 (k7_real_1 A 1) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 D (k6_power k8_power A))) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) B) D) = (k8_real_1 (k10_prepower A D) (k6_power k8_power A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A)))) & (r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A)) B) C) = (k1_real_1 (k10_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 k4_sin_cos6 C) (k5_real_1 A 1))) (k7_square_1 (k9_real_1 1 (k5_square_1 C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k30_sin_cos))) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k30_sin_cos) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k30_sin_cos) D) G) = (k1_real_1 (k10_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G)) (k5_square_1 (k1_seq_1 k16_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k2_fdiff_9))) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k2_fdiff_9) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k2_fdiff_9) D) G) = (k1_real_1 (k10_real_1 (k8_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G)) (k1_seq_1 k19_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G))))) (k5_square_1 (k1_seq_1 k16_sin_cos (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k5_square_1 G)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) = k1_xboole_0)  &  ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t11_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_power (k4_xcmplx_0 1) (k4_xcmplx_0 A)) = (k3_power (k4_xcmplx_0 1) A)) ) ) ).
tt(t11_fib_num3,ax, ( ((k1_fib_num3 k6_numbers) = 2)  &  ( ((k1_fib_num3 1) = 1)  &  (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_fib_num3 (k2_nat_1 (k1_nat_1 A 1) 1)) = (k2_nat_1 (k1_fib_num3 A) (k1_fib_num3 (k1_nat_1 A 1)))) ) ) ) ) ).
tt(t11_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v1_abian A) &  ((v1_abian B) & (r1_xxreal_0 B A)) )  => (r1_xxreal_0 (k3_power k2_fib_num A) (k3_power k2_fib_num B))) ) ) ) ) ).
tt(t11_fib_num,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k1_pre_ff (k2_nat_1 B 1)) (k1_pre_ff B))) ) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k1_fib_num) ) ) ) ) ).
tt(t11_filerec1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( (C = (k9_finseq_1 A))  =>  ((k17_finseq_1 B 1 C) = (k9_finseq_1 A)) ) ) ) ) ) ) ).
tt(t11_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  => (r2_hidden (k6_lattices A) B)) ) ) ) ) ).
tt(t11_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  (! [D:$i] :  ((m2_filter_1 D A B) =>  ((r6_binop_1 A C D) => (r6_binop_1 (k8_eqrel_1 A B) (k3_filter_1 A B C) (k3_filter_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v15_lattices B) &  ((v16_lattices B) & (l3_lattices B)) ) ) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  ( (D = F)  & (r2_lattices A C D)) )  => (r2_lattices B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_finance1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_finance1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k4_finance1 C A B) = (k9_binop_2 (k1_seq_1 A k6_numbers) (k5_finance1 C A B))) ) ) ) ) ) ) ) ).
tt(t11_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (~  ( (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski (k9_xtuple_0 A) (k2_finseq_1 B))) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~ (r1_tarski A B)) ) ) ) ) ) ) ).
tt(t11_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r2_hidden A (k4_finseq_1 C)) => (r2_hidden (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t11_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  => (r2_hidden (k1_nat_1 A 1) (k2_finseq_1 B))) ) ) ) ) ).
tt(t11_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  ((k8_relat_1 A (k1_tarski B)) = (k1_tarski (k1_finseq_4 A B))) ) ) ) ) ).
tt(t11_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v2_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k4_finseq_4 B (k1_funct_1 B A)) = A) ) ) ) ) ) ).
tt(t11_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r1_tarski C (k4_finseq_1 A)) =>  ((k5_relat_1 (k7_finseq_1 A B) C) = (k5_relat_1 A C)) ) ) ) ) ) ) ).
tt(t11_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 F (k3_finseq_1 B)))  =>  ((r1_xxreal_0 F E) |  ((k1_finseq_7 A (k1_finseq_7 A B F C) E D) = (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k17_finseq_1 A (k7_nat_d E 1) B) (k12_finseq_1 A D)) (k17_finseq_1 A (k7_nat_d (k7_nat_d F E) 1) (k2_rfinseq A E B))) (k12_finseq_1 A C)) (k2_rfinseq A F B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k5_finseq_8 A B C) = (k1_finseq_8 A (k17_finseq_1 A (k7_nat_d (k3_finseq_1 B) (k3_finseq_1 (k4_finseq_8 A B C))) B) C)) ) ) ) ) ) ) ).
tt(t11_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G D) & (m2_finseq_1 G B))  =>  (! [H:$i] :  ( ((v3_card_1 H D) & (m2_finseq_1 H C))  =>  (! [I:$i] :  ( ((v3_card_1 I E) & (m2_finseq_1 I B))  =>  (! [J:$i] :  ( ((v3_card_1 J E) & (m2_finseq_1 J C))  => (r2_relset_1 k5_numbers A (k1_finseqop B C A F (k8_finseq_1 B G I) (k8_finseq_1 C H J)) (k8_finseq_1 A (k1_finseqop B C A F G H) (k1_finseqop B C A F I J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_finset_1,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  ( (~  (A = k1_xboole_0) )  &  ((v6_ordinal1 A) &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  ((r2_hidden C A) => (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k12_finseq_1 A B) C) = B) ) ) ) ) ) ) ).
tt(t11_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((k5_finsub_1 (k3_xboole_0 A B)) = (k3_xboole_0 (k5_finsub_1 A) (k5_finsub_1 B))) ) ) ).
tt(t11_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k9_fin_topo A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_fintopo2 A B D C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(t11_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) (k12_fin_topo A B) (k12_fin_topo A C)) = (k12_fin_topo A (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t11_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_fin_topo A) =>  ((r1_fintopo4 A B C) <=> (r1_xboole_0 B (k9_fin_topo A C))) ) ) ) ) ) ) ) ).
tt(t11_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  => (v3_orders_2 (k3_fintopo5 A B))) ) ) ) ).
tt(t11_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fin_topo B A) <=> (v2_fin_topo (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t11_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k12_fin_topo A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D C) & (r2_hidden B (k1_fin_topo A D))) ) ) ) ) ) ) ) ) ) ).
tt(t11_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_catalan2 A)) =>  ( ((k1_flang_1 A B B) = B)  =>  (B = k1_xboole_0) ) ) ) ) ).
tt(t11_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_flang_1 A (k7_flang_1 A B C) D) = (k7_flang_1 A (k7_flang_1 A B D) C)) ) ) ) ) ) ) ) ).
tt(t11_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_flang_3 A B C) = (k8_flang_1 A B))  <=>  ((r2_hidden (k2_flang_1 A) B) |  (C = k6_numbers) ) ) ) ) ) ) ) ).
tt(t11_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_finseq_2 B A) = (k1_funct_2 (k2_finseq_1 B) A)) ) ) ) ).
tt(t11_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((k7_subset_1 (k15_fomodel1 A) (k17_fomodel1 A) (k4_fomodel1 A)) = (k5_fomodel1 A)) ) ) ).
tt(t11_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) (k21_fomodel2 B C (k23_fomodel2 B A C))) = (k2_zfmisc_1 (k16_fomodel2 B C) (k29_fomodel2 B A))) ) ) ) ) ) ) ).
tt(t11_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 C B)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 D) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 D B)) =>  ( ( ((k5_relat_1 E A) = (k5_relat_1 F A))  &  ((k2_partfun1 (k6_subset_1 (u1_struct_0 C) (k1_tarski (u3_struct_0 C))) k4_numbers (u1_fomodel1 C) A) = (k2_partfun1 (k6_subset_1 (u1_struct_0 D) (k1_tarski (u3_struct_0 D))) k4_numbers (u1_fomodel1 D) A)) )  =>  ((k2_partfun1 (k35_fomodel1 C) B (k10_fomodel2 C B E) (k3_finseq_2 A)) = (k2_partfun1 (k35_fomodel1 D) B (k10_fomodel2 D B F) (k3_finseq_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 D)) (k9_setfam_1 (k1_fomodel4 D))))) =>  ( ((r1_tarski E F) & (v4_fomodel4 B A D E C))  =>  ( ( (~ (v6_fomodel4 F D))  &  (~ (v6_fomodel4 E D)) )  | (v4_fomodel4 B A D F C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) E (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C)) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_frechet A D)) (k2_frechet B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_pcomps_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (B = C)  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_frechet A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_frechet A B))))) )  =>  (~  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (k1_frechet A B) D E) = (k9_metric_1 A C (k10_real_1 1 (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (v1_relat_1 (k3_msafree2 (k1_fscirc_2 A B C)))) ) ) ) ) ) ).
tt(t11_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ((r1_fsm_1 A E C F G) =>  ((k4_fsm_1 A B E F (k8_finseq_1 A C D)) = (k8_finseq_1 B (k4_fsm_1 A B E F C) (k4_fsm_1 A B E G D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (~  ((v1_fsm_2 C A) &  ((r1_fsm_2 A C D B) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (? [F:$i] :  ((m2_finseq_1 F A) &  ((r1_xxreal_0 E (k2_nat_1 (k3_finseq_1 F) 1)) &  ( ((k1_funct_1 F 1) = B)  &  (~  ( (D = (k1_funct_1 (k2_fsm_1 A C (u2_fsm_1 A C) F) E))  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m2_subset_1 G k1_numbers k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 E G))  &  ((k1_funct_1 (k2_fsm_1 A C (u2_fsm_1 A C) F) G) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l1_rewrite3 B (k9_flang_1 A)) =>  ( ((v1_relat_1 (u1_rewrite3 (k9_flang_1 A) B)) & (v1_funct_1 (u1_rewrite3 (k9_flang_1 A) B)))  => (v2_rewrite3 B A (k9_flang_1 A))) ) ) ) ) ).
tt(t11_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_msafree2 (k7_ftacell1 A B C D E)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k24_gfacirc1 A B C)) (k2_enumset1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k21_gfacirc1 A B C))) (k2_tarski (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1) (k36_gfacirc1 (k24_gfacirc1 A B C) E D))) (k2_enumset1 (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp) (k4_tarski (k10_finseq_1 E D) k3_gfacirc1) (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp) (k33_gfacirc1 (k24_gfacirc1 A B C) E D)))) ) ) ) ) ) ).
tt(t11_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) )  =>  (A = (k2_funcop_1 (k9_xtuple_0 A) B)) ) ) ) ) ).
tt(t11_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) B (k3_funct_2 (k2_zfmisc_1 k1_numbers (k9_funct_2 A k1_numbers)) (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) (k1_real_1 1) B))) (k8_funcsdom A))) ) ) ).
tt(t11_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k3_relat_1 C B))) <=>  ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden (k1_funct_1 C A) (k9_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t11_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ((r2_hidden C (k2_relset_1 B D)) &  (! [E:$i] :  (~  ((r2_hidden E A) &  ((k1_funct_1 D E) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k8_relat_1 (k1_funct_3 B) A) (k1_zfmisc_1 (k9_xtuple_0 B)))) ) ) ).
tt(t11_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (~ (r2_hidden A (k9_xtuple_0 B)))  =>  ((k1_funct_1 (k1_funct_4 C B) A) = (k1_funct_1 C A)) ) ) ) ) ) ) ).
tt(t11_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_zfmisc_1 B C)) =>  ((r1_tarski (k9_xtuple_0 A) B) & (r1_tarski (k10_xtuple_0 A) C)) ) ) ) ) ).
tt(t11_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_funct_2 A (k1_funct_2 B C))) =>  ((r2_hidden (k2_funct_5 D) (k1_funct_2 (k2_zfmisc_1 A B) C)) & (r2_hidden (k4_funct_5 D) (k1_funct_2 (k2_zfmisc_1 B A) C))) ) ) ) ) ) ) ).
tt(t11_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_xboole_0 (k10_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k3_relat_1 A (k1_funct_4 C B)) = (k3_relat_1 A C)) ) ) ) ) ) ) ) ).
tt(t11_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r1_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t11_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) => (v1_funct_9 (k35_valued_1 B) A)) ) ) ) ) ).
tt(t11_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) => (r1_relset_1 B B (k6_partfun1 B) (k7_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 A)))) ) ) ) ) ).
tt(t11_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  ( ((v20_functor0 D A B) & (v20_functor0 E B C))  => (v20_functor0 (k13_functor0 A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  =>  (! [G:$i] :  ((m2_functor2 G A B C D) =>  (! [H:$i] :  ((m2_functor2 H A B D E) =>  ( ((r2_functor2 A B C D) &  ((r2_functor2 A B D E) & (r2_functor2 A B E F)) )  =>  (! [I:$i] :  ((m2_functor2 I A B E F) => (r8_pboole (u1_struct_0 A) (k5_functor2 A B C D F G (k5_functor2 A B D E F H I)) (k5_functor2 A B C E F (k5_functor2 A B C D E G H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D C B) & (m2_functor0 D C B))  =>  (! [E:$i] :  ( ((v15_functor0 E C B) & (m2_functor0 E C B))  =>  (! [F:$i] :  ( ((v15_functor0 F B A) & (m2_functor0 F B A))  =>  (! [G:$i] :  ((m1_functor2 G C B D E) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((r1_functor2 C B D E) =>  ((k2_functor2 C A (k1_functor3 C B A D F) (k1_functor3 C B A E F) (k5_functor3 C B A D E G F) H) = (k6_functor0 B A F (k3_functor0 C B D H) (k3_functor0 C B E H) (k2_functor2 C B D E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k2_fuzzy_1 A B C)) (k1_fuzzy_1 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C))) & (r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k1_fuzzy_1 A B C)) (k2_fuzzy_1 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C)))) ) ) ) ) ) ) ).
tt(t11_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A B (k1_fuzzy_2 A C D)) (k2_fuzzy_1 A (k1_fuzzy_2 A B C) (k1_fuzzy_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t11_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 B A) k1_numbers (k2_fuzzy_4 B A (k1_fuzzy_2 (k2_zfmisc_1 A B) C D)) (k1_fuzzy_2 (k2_zfmisc_1 B A) (k2_fuzzy_4 B A C) (k2_fuzzy_4 B A D)))) ) ) ) ) ) ) ) ).
tt(t11_fvaluat1,ax, (! [A:$i] :  ((v1_fvaluat1 A) =>  (~ (r1_xxreal_0 A k2_xxreal_0)) ) ) ).
tt(t11_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k2_fvsum_1 A) B C) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t11_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 (k5_gate_1 A B)))  <=> (v1_xboole_0 (k4_gate_1 A B))) ) ) ).
tt(t11_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (D = (k4_struct_0 A)) )  =>  ( ( ((r2_gcd_1 A D (k8_group_1 A B C)) & (r2_gcd_1 A D B))  =>  ((k1_gcd_1 A (k8_group_1 A B C) D) = (k8_group_1 A (k1_gcd_1 A B D) C)) )  &  ( ((r2_gcd_1 A D (k8_group_1 A B C)) & (r2_gcd_1 A D C))  =>  ((k1_gcd_1 A (k8_group_1 A B C) D) = (k8_group_1 A B (k1_gcd_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_genealg1 D C) =>  (! [E:$i] :  ((m1_genealg1 E C) =>  ( ((r1_xxreal_0 (k3_finseq_1 D) A) & (r1_xxreal_0 (k3_finseq_1 D) B))  =>  ((k8_genealg1 C D E A B) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_analoaf A B (k1_geomtrap A B C) (k1_geomtrap A B C) C)) ) ) ) ) ) ).
tt(t11_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k7_gfacirc1 A B C)) = (k2_xboole_0 (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) (k1_tarski (k9_gfacirc1 A B C)))) ) ) ) ).
tt(t11_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (v1_relat_1 (k3_msafree2 (k1_gfacirc2 A B C)))) ) ) ) ) ) ).
tt(t11_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((k6_glib_000 (k13_glib_000 A k1_glib_000 B)) = B)  &  ( ((k7_glib_000 (k13_glib_000 A k2_glib_000 B)) = B)  &  ( ((k8_glib_000 (k13_glib_000 A k3_glib_000 B)) = B)  &  ((k9_glib_000 (k13_glib_000 A k4_glib_000 B)) = B) ) ) ) ) ) ) ).
tt(t11_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((r1_xxreal_0 C 1) | (r2_hidden (k1_funct_1 B (k6_xcmplx_0 C 1)) (k28_glib_000 A (k5_glib_001 A B C)))) ) ) ) ) ) ) ) ).
tt(t11_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k21_glib_000 A (k1_glib_002 A B)) = (k20_glib_000 A (k1_glib_002 A B))) ) ) ) ) ).
tt(t11_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m1_glib_000 B A)) )  =>  (! [C:$i] :  ((r2_hidden C (k25_glib_000 A B)) =>  ((k1_funct_1 (k5_glib_003 B) C) = (k1_funct_1 (k5_glib_003 A) C)) ) ) ) ) ) ) ).
tt(t11_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k21_glib_000 A B))) =>  (! [D:$i] :  ( ((v1_glib_003 D) &  ((v4_glib_003 D A) & (m2_glib_000 D A B C)) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_glib_003 F) &  ((v4_glib_003 F A) & (m2_glib_000 F A B (k2_xboole_0 C (k1_tarski E)))) )  =>  ((r2_hidden E (k21_glib_000 A B)) =>  ((r2_hidden E C) |  ((k2_xcmplx_0 (k4_glib_004 D) (k1_seq_1 (k5_glib_003 A) E)) = (k4_glib_004 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k6_glib_000 A))) =>  ( ((r1_glib_005 A B C D) & (r2_hidden C E))  =>  ((r2_hidden D E) |  ((k1_glib_005 A B C D) = (k6_xcmplx_0 (k3_uproots (k23_glib_000 A E (k6_subset_1 (k6_glib_000 A) E)) (k5_relat_1 B (k23_glib_000 A E (k6_subset_1 (k6_glib_000 A) E)))) (k3_uproots (k23_glib_000 A (k6_subset_1 (k6_glib_000 A) E) E) (k5_relat_1 B (k23_glib_000 A (k6_subset_1 (k6_glib_000 A) E) E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 B))) =>  ((r1_xxreal_0 (k1_matrix_1 B) 1) |  ((k1_matrix_1 B) = (k2_nat_1 (k1_matrix_1 (k3_goboard1 B A)) 1)) ) ) ) ) ) ) ).
tt(t11_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((v1_topreal1 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski F G) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B F G))  &  ( (~  (D = F) )  &  (~  (G = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) |  ((k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B))) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((v2_sppol_1 (k2_topreal1 2 A B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k2_topreal1 2 A B)) =>  ((k17_euclid D) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 D (k1_matrix_1 (k2_goboard2 A))) &  ((k3_goboard5 (k2_goboard2 A) C D) = (k5_goboard5 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (B = (a_1_7_gobrd11 A))  &  (C = (a_1_8_gobrd11 A)) )  =>  (B = (k3_subset_1 (u1_struct_0 (k15_euclid 2)) C)) ) ) ) ) ) ) ) ).
tt(t11_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 D) (k16_matrix_1 E)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 E)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C 1)) ) ) ) )  =>  (B = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_gobrd14,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 B (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 2))))  &  (~ (r1_xxreal_0 C (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 2 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r1_valuat_1 A D (k6_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B))) E F) <=> (r1_valuat_1 A D (k11_cqc_lang A C B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  => (r1_graph_1 A A A)) ) ).
tt(t11_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_tarski (k10_xtuple_0 (k1_graph_2 A B C)) (k10_xtuple_0 A))) ) ) ) ) ) ).
tt(t11_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = (k1_funct_1 (u1_graph_1 A) B))  &  (D = (k1_funct_1 (u2_graph_1 A) B)) )  => (r1_graph_2 A (k2_finseq_4 (u1_struct_0 A) D C) (k9_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t11_graph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v7_graph_1 E B) & (m2_graph_1 E B))  =>  (! [F:$i] :  ( ((v7_graph_1 F B) & (m2_graph_1 F B))  =>  ( ((r3_graph_4 B C E) &  ( (F = (k2_partfun1 k5_numbers (u4_struct_0 B) E (k2_finseq_1 A)))  &  (D = (k2_partfun1 k5_numbers (u1_struct_0 B) C (k2_finseq_1 (k2_nat_1 A 1)))) ) )  => (r3_graph_4 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((v7_graph_1 (k7_finseq_1 A B) C) & (m2_graph_1 (k7_finseq_1 A B) C))  =>  ( ((v7_graph_1 A C) & (m2_graph_1 A C))  &  ((v7_graph_1 B C) & (m2_graph_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t11_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( ((u1_struct_0 A) = (k2_xboole_0 B C))  &  ((r2_hidden D B) &  ((r2_hidden E C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden F B) & (r2_hidden G C))  =>  (! [H:$i] :  (~  ((r2_hidden H (u4_struct_0 A)) & (r1_graph_4 A F G H)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v7_graph_1 F A) & (m2_graph_1 F A))  =>  (~ (r1_graph_5 A F D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v13_vectsp_1 C A B) =>  ((v1_grcat_1 (g1_grcat_1 A B C)) & (m1_grcat_1 (g1_grcat_1 A B C) A B)) ) ) ) ) ) ) ) ).
tt(t11_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 (k7_group_1 A) 1))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_group_1 A)) ) ) ) ) ) ) ).
tt(t11_gr_cy_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v2_group_1 D) &  ((v3_group_1 D) & (l3_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_group_2 E D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( ((k7_group_1 D) = A)  &  ( (D = (k5_group_4 D (k6_domain_1 (u1_struct_0 D) F)))  &  ( ((k7_group_1 E) = B)  &  (E = (k5_group_4 D (k6_domain_1 (u1_struct_0 D) (k5_group_1 D C F)))) ) ) )  => (r1_nat_d A (k3_xcmplx_0 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  (? [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v2_gr_cy_3 B)) )  &  ((k1_euler_1 A) = (k4_nat_1 2 B)) ) ) ) ) ).
tt(t11_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k3_xboole_0 B C))) =>  ((k1_funct_1 (k3_xboole_0 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t11_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_6 B A C) => (m1_group_6 (k1_grnilp_1 A C B) A C)) ) ) ) ) ) ) ).
tt(t11_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((r2_hidden E D) &  ((k7_ideal_1 (k11_polynom1 A C) D) = (k7_ideal_1 (k11_polynom1 A C) (k1_groeb_1 A C E))) ) ) )  => (v9_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(t11_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k15_pre_poly A))))  =>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  &  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E C) => (r1_termord A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_termord A B C (k7_polynom1 A C)) (k7_polynom1 A C))) ) ) ) ) ) ).
tt(t11_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ((r1_nat_d B (k7_group_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_group_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t11_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k5_group_2 A (k2_group_1 A C) (k13_group_2 A B C)) (k8_group_2 A B))) ) ) ) ) ) ).
tt(t11_group_12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_finseq_1 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k2_finseq_1 A)) &  ((v1_group_7 B) &  ((v2_group_7 B (k2_finseq_1 A)) & (v3_group_7 B (k2_finseq_1 A))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) =>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) &  ( ((k3_finseq_1 D) = A)  &  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k2_group_12 (k2_finseq_1 A) B E) (k1_funct_1 D E))) )  &  (C = (k3_group_4 (k2_group_7 (k2_finseq_1 A) B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_group_2 A (k2_group_2 A B C)) = (k2_group_2 A (k1_group_2 A C) (k1_group_2 A B))) ) ) ) ) ) ) ).
tt(t11_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k5_group_2 A B (k11_group_2 A D C)) = (k2_group_2 A C (k14_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t11_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_group_4 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k6_algstr_0 A (k6_algstr_0 A B C) D))  &  ((k3_group_4 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t11_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_group_5 A (k12_finseq_1 (u1_struct_0 A) B) C) = (k12_finseq_1 (u1_struct_0 A) (k2_group_3 A B C))) ) ) ) ) ) ) ).
tt(t11_group_6,ax, ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ( ((k7_group_1 A) = 1)  & (v8_struct_0 A)) ) )  &  (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ( ((k7_group_1 A) = 1)  => (v7_struct_0 A)) ) ) ) ).
tt(t11_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_group_7 (k9_finseq_1 A)) & (v2_group_7 (k9_finseq_1 A) (k1_tarski 1))) ) ) ) ) ) ) ).
tt(t11_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v4_group_1 B A))  => (v8_struct_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t11_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) &  ((v3_group_9 D A) & (l1_group_9 D A)) ) ) )  =>  ( ((m1_group_9 B A C) & (m1_group_9 C A D))  => (m1_group_9 B A D)) ) ) ) ) ) ) ) ).
tt(t11_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ( ( (B = (k10_group_5 A))  & (v1_gr_cy_1 (k5_group_6 A B)))  => (v5_group_1 A)) ) ) ) ) ).
tt(t11_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((r1_group_2 B (k2_grsolv_1 A B C (k6_group_2 A)) (k6_group_2 B)) &  ((k2_grsolv_1 A B C (k7_group_2 A)) = (k7_group_2 (k10_group_6 A B C))) ) ) ) ) ) ) ) ).
tt(t11_hahnban1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k3_complex1 (k8_group_1 k1_complfld A B)) = (k9_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))))  &  ((k4_complex1 (k8_group_1 k1_complfld A B)) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B)) (k8_real_1 (k3_complex1 B) (k4_complex1 A)))) ) ) ) ) ) ).
tt(t11_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( (~ (r1_struct_0 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (E = C) )  => (r1_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k1_funct_1 B C)))  =>  ((k5_card_1 (k1_funct_1 (k2_hallmar1 A B C D) C)) = (k6_xcmplx_0 (k5_card_1 (k1_funct_1 B C)) 1)) ) ) ) ) ) ) ) ) ).
tt(t11_hausdorf,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))))  =>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  &  ( (A = B)  &  ((k2_weierstr A) = (k4_seq_4 B)) ) ) ) ) ) ).
tt(t11_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (v3_glib_001 (k8_glib_001 A B C D) A))  & (v3_glib_001 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (k3_cqc_lang A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k3_cqc_lang A)))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden D (k1_relset_1 k5_numbers B)) & (r2_hidden C (k1_relset_1 k5_numbers B)))  =>  ((r1_xxreal_0 D C) |  ((v1_henmodel (k3_funct_2 k5_numbers (k9_setfam_1 (k3_cqc_lang A)) B C) A) & (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (k3_cqc_lang A)) B C) (k3_funct_2 k5_numbers (k9_setfam_1 (k3_cqc_lang A)) B D))) ) ) ) ) ) )  => (v1_henmodel (k5_setfam_1 (k3_cqc_lang A) (k2_relset_1 (k9_setfam_1 (k3_cqc_lang A)) B)) A)) ) ) ) ) ).
tt(t11_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ( ((k4_complex1 A) = k6_numbers)  &  ((k4_complex1 B) = k6_numbers) )  =>  ((k4_complex1 (k8_group_1 k1_complfld A B)) = k6_numbers) ) ) ) ) ) ).
tt(t11_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A D E F) &  ( (~  (E = F) )  & (r1_collsp A C B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden C (k6_heyting1 A B)) &  (! [D:$i] :  ((m2_funct_2 D (k7_normform A) (k1_heyting1 A) (k9_funct_2 (k7_normform A) (k1_heyting1 A))) =>  (~  ( (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((r2_hidden E B) => (r2_hidden (k3_funct_2 (k7_normform A) (k1_heyting1 A) D E) (k5_setwiseo A (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) E) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) E)))) ) )  &  (C = (k4_tarski (a_3_0_heyting1 A B D) (a_3_1_heyting1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( (C = (k1_tarski k1_xboole_0))  =>  ((k2_heyting2 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t11_heyting3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  =>  ((u2_lattices (k5_substlat A C)) = (k1_realset1 (u2_lattices (k5_substlat B D)) (u1_struct_0 (k5_substlat A C)))) ) ) ) ) ) ).
tt(t11_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A C) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos C) B) A) = (k1_seq_1 k16_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 B k32_sin_cos) 2)))) ) ) ) ) ) ) ) ).
tt(t11_hilbasis,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v4_vectsp_1 C) & (l6_algstr_0 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  ((k3_polynom2 A (k2_hilbasis A B) C D) = (k3_funct_2 A (u1_struct_0 C) D B)) ) ) ) ) ) ) ) ) ).
tt(t11_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  ((k5_hilbert1 (k5_hilbert1 A)) = (k5_hilbert1 A)) ) ) ).
tt(t11_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ( ((k1_funct_1 A 1) = 1)  => (v2_hilbert2 A)) ) ) ).
tt(t11_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden C E) & (r2_hidden D F))  =>  ( (A = B)  | (r2_hidden (k4_funct_4 A B C D) (k4_card_3 (k4_funct_4 A B E F)))) ) ) ) ) ) ) ) ).
tt(t11_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_series_1 B) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k4_power (k1_seq_1 (k3_series_1 B) D) A)) ) ) ) )  =>  ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = (k4_power (k4_series_1 B) A))  &  ((v7_valued_0 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 C D) (k4_power (k4_series_1 B) A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k8_polynom3 A B C)) (k8_polynom3 A (k5_vfunct_1 k5_numbers A B) (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ).
tt(t11_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 B A) =>  ((k4_idea_1 B A (k6_idea_1 B A)) = k6_numbers) ) ) ) ) ) ).
tt(t11_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v1_ideal_1 (u1_struct_0 A) A) &  ((v2_ideal_1 (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t11_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k3_incproj A))) => (r1_incsp_1 (k3_incproj A) B C)) ) ) ) ) ) ) ).
tt(t11_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((r5_incsp_1 A (k4_subset_1 (u1_incsp_1 A) C D) B) <=>  ((r5_incsp_1 A C B) & (r5_incsp_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ((m4_index_1 D (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  ((r1_funct_2 (u4_struct_0 A) (u4_struct_0 C) (u4_struct_0 A) (u4_struct_0 D) (k9_index_1 A B C) (k9_index_1 A B D)) & (r1_funct_2 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (k7_cat_1 A C (k9_index_1 A B C)) (k7_cat_1 A D (k9_index_1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t11_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  ((r1_tarski (u2_msualg_1 B) (u2_msualg_1 A)) & (r1_tarski (u1_msualg_1 B) (u1_msualg_1 A))) ) ) ) ) ).
tt(t11_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (r2_int_1 A A B)) ) ) ) ).
tt(t11_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_int_1 A B) &  ((r1_int_1 B A) &  ( (~  (A = B) )  &  (~  (A = (k4_xcmplx_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ( (~ (v6_struct_0 (k9_int_3 A)))  &  ( (~ (v2_struct_0 (k9_int_3 A)))  &  ((v13_algstr_0 (k9_int_3 A)) &  ((v3_group_1 (k9_int_3 A)) &  ((v5_group_1 (k9_int_3 A)) &  ((v2_rlvect_1 (k9_int_3 A)) &  ((v3_rlvect_1 (k9_int_3 A)) &  ((v4_rlvect_1 (k9_int_3 A)) &  ((v4_vectsp_1 (k9_int_3 A)) &  ((v5_vectsp_1 (k9_int_3 A)) & (l6_algstr_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r2_int_1 A B C) => (r2_int_1 (k3_xcmplx_0 A D) (k3_xcmplx_0 B D) C)) ) ) ) ) ) ) ) ) ).
tt(t11_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_int_5 A C) & (r2_int_1 A B C))  => (r1_int_5 B C)) ) ) ) ) ) ) ).
tt(t11_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ( (C = B)  |  ( ((k1_funct_1 A C) = k6_numbers)  | (v1_int_1 (k7_xcmplx_0 (k19_rvsum_1 A) (k3_xcmplx_0 (k1_funct_1 A B) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ).
tt(t11_int_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ( (C = (k3_int_2 A B))  =>  ((k1_polynom2 k10_newton (k13_nat_3 C)) = (k9_subset_1 k10_newton (k1_polynom2 k10_newton (k13_nat_3 A)) (k1_polynom2 k10_newton (k13_nat_3 B)))) ) ) ) ) ) ) ) ).
tt(t11_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_tarski (k1_limfunc1 B) (k1_relset_1 k1_numbers A)) & (r4_integr10 A B))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r4_integr10 (k26_valued_1 k1_numbers k1_numbers A C) B) &  ((k4_integr10 (k26_valued_1 k1_numbers k1_numbers A C) B) = (k8_real_1 C (k4_integr10 A B))) ) ) ) ) ) ) ) ) ).
tt(t11_integr11,ax, ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k1_sin_cos2) k4_sin_cos2) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k1_sin_cos2) k4_sin_cos2) k1_numbers) A) = (k8_real_1 A (k1_seq_1 k4_sin_cos2 A))) ) ) ) ).
tt(t11_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D C) & (r1_xxreal_0 D k6_numbers)) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos) (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C))))) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t11_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t11_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9)) A) B) = (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t11_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [E:$i] :  ((m4_integr15 E A B C D) =>  ( ((v1_integr15 C A B) &  ((v2_integr15 C A B) &  ((v2_comseq_2 (k2_integra3 B D)) &  ((k2_seq_2 (k2_integra3 B D)) = k6_numbers) ) ) )  =>  ((v3_normsp_1 (k6_integr15 A B C D E) (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) (k6_integr15 A B C D E)) = (k10_integr15 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((v1_comseq_2 A) <=>  ((v1_comseq_2 (k5_comseq_3 k1_numbers A)) & (v1_comseq_2 (k6_comseq_3 k1_numbers A))) ) ) ) ).
tt(t11_integr18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ( ( (D = F)  &  (E = G) )  =>  ((k2_vfunct_1 B C F G) = (k2_vfunct_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_integr15 A (k3_integra5 B E) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B E)) A) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers G))) ) ) ) )  =>  ((r1_integr15 A (k3_integra5 C D) (k9_integr15 A F k1_numbers G)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) (k9_integr15 A F k1_numbers G) (k3_integra5 C D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) => (v3_xxreal_2 (k1_rvsum_1 B))) ) ) ) ) ).
tt(t11_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v3_xxreal_2 B) & (r1_xxreal_0 k6_numbers A))  => (v3_xxreal_2 (k1_integra2 B A))) ) ) ) ) ).
tt(t11_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k2_integra1 B C (k3_finseq_1 C))) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r1_integra1 C D) &  ( ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 C) (k1_seq_4 A)))  & (v1_comseq_2 (k2_partfun1 B k1_numbers E B))) ) ) )  => (r1_xxreal_0 (k9_real_1 (k18_rvsum_1 (k4_integra1 B E C)) (k18_rvsum_1 (k4_integra1 B E D))) (k8_real_1 (k9_real_1 (k4_seq_4 (k1_rvsum_1 E)) (k5_seq_4 (k1_rvsum_1 E))) (k1_integra3 B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  &  ((v2_comseq_2 (k2_integra3 A B)) &  ((k2_seq_2 (k2_integra3 A B)) = k6_numbers) ) ) ) ) ) ).
tt(t11_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)))  => (r1_integra5 A B)) ) ) ) ) ).
tt(t11_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ((r1_tarski A (k9_xtuple_0 C)) &  ((r1_integra5 A B) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((r1_integra5 A C) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((r1_integra5 A (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) &  ((r1_integra5 A (k47_valued_1 k1_numbers k1_numbers k1_numbers B C)) &  ( ((k2_integra5 A (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k7_real_1 (k2_integra5 A B) (k2_integra5 A C)))  &  ((k2_integra5 A (k47_valued_1 k1_numbers k1_numbers k1_numbers B C)) = (k9_real_1 (k2_integra5 A B) (k2_integra5 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra7 A B C) => (r1_tarski A (k1_relset_1 k1_numbers B))) ) ) ) ) ) ).
tt(t11_integra8,ax, ((k3_sin_cos6 (k1_real_1 (k10_real_1 (k7_square_1 2) 2))) = (k1_real_1 (k10_real_1 k32_sin_cos 4))) ).
tt(t11_integra9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k19_sin_cos)) A) B) = (k1_real_1 (k8_real_1 B (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ).
tt(t11_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  ((r1_tarski C D) &  (B = (k2_interva1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_intpro_1)) =>  ( ((v8_intpro_1 A) & (r1_tarski B A))  => (r1_tarski (k7_intpro_1 B) A)) ) ) ) ) ).
tt(t11_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k9_complex1 (k13_complex1 1 (k2_nat_1 A 1)) (k13_complex1 1 (k9_newton A))) = (k13_complex1 1 (k9_newton (k2_nat_1 A 1)))) ) ) ).
tt(t11_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) =>  ((k2_funct_1 (k7_cat_1 A B C)) = (k7_cat_1 B A (k1_isocat_1 A B C))) ) ) ) ) ) ) ) ).
tt(t11_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  ((k2_cat_1 B E F) = k1_xboole_0) ) )  <=>  (~  ((k2_cat_1 (k8_cat_2 A B) (k9_cat_2 A B C E) (k9_cat_2 A B D F)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v6_tops_1 (k2_struct_0 A) A) & (v5_tops_1 (k2_struct_0 A) A)) ) ) ).
tt(t11_jct_misc,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (~  ((r1_subset_1 A B) & (r1_xxreal_0 (k1_jct_misc A B) k6_numbers)) ) ) ) ) ) ).
tt(t11_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_jgraph_1 A B C) =>  ( ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B)))  | (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(t11_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v3_pre_topc B (k15_euclid 2)) &  ((r2_hidden A B) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (a_2_0_jgraph_2 A C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k17_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid C) (k17_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t11_jgraph_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k1_relset_1 (u1_struct_0 (k15_euclid A)) (k1_jgraph_4 A)) = (u1_struct_0 (k15_euclid A)))  &  ((k1_relset_1 (u1_struct_0 (k15_euclid A)) (k1_jgraph_4 A)) = (k1_euclid A)) ) ) ) ).
tt(t11_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (~  ( (G = k6_numbers)  &  ( (H = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (~  (C = D) )  &  ( (~  (E = F) )  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G)) = C)  &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G)) F) &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H)) = D)  &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H)) F) &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G)) = E)  &  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G)) D) &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H)) = F)  &  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H)) D) &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  ( (~  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) C))  &  ( (~ (r1_xxreal_0 D (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I))))  &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) E))  &  (~ (r1_xxreal_0 F (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)))) ) ) ) )  &  (~  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) C))  &  ( (~ (r1_xxreal_0 D (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I))))  &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) E))  &  (~ (r1_xxreal_0 F (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)))) ) ) ) ) ) ) )  & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jgraph_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_0_jgraph_6)  =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 (k19_euclid (k1_real_1 1) k6_numbers)) = (k18_pscomp_1 A)) ) ) ) ).
tt(t11_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k17_euclid A) = D)  &  ( ((k18_euclid B) = E)  &  ((r1_xxreal_0 E (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) F) & (r1_xxreal_0 (k17_euclid B) D)) ) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 (k17_euclid B) C) | (r1_jordan6 (k1_sppol_2 C D E F) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_tarski B (k3_goboard9 (k1_jordan9 B A)))) ) ) ) ).
tt(t11_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan1h B A) => (r1_xboole_0 (k3_goboard5 (k1_jordan8 B A) (k7_nat_d (k3_jordan1h B A) 1) (k3_jordan11 B A)) B)) ) ) ) ) ).
tt(t11_jordan12,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_jordan12 2 A B) => (v1_finset_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)))) ) ) ) ) ).
tt(t11_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski A (k2_goboard9 (k1_jordan13 A B)))) ) ) ) ) ).
tt(t11_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k2_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F G) &  ((r1_xxreal_0 G E) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) D E B) &  ((r1_topreal1 (k15_euclid 2) D E C) &  ((r1_tarski B A) & (r1_tarski C A)) ) )  =>  ( (B = C)  |  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = A)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k2_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan17 A B C D E) => (r1_jordan17 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) & (r1_tarski (k4_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ) ).
tt(t11_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k6_pscomp_1 B) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t11_jordan1a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( ((k17_euclid A) = (k17_euclid B))  & (r2_hidden C (k1_rcomp_1 (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B))))  => (r2_hidden (k19_euclid (k17_euclid A) C) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ).
tt(t11_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_0_jordan1 A))  => (v1_convex1 B (k15_euclid 2))) ) ) ) ) ).
tt(t11_jordan1b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (r1_xxreal_0 1 (k1_jordan1a A))) ) ).
tt(t11_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r2_hidden B (k1_jordan2c 2 C)) &  (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k17_euclid B) (k6_pscomp_1 C)) (k9_real_1 (k8_pscomp_1 C) (k6_pscomp_1 C))) (k13_newton 2 A)) 2))) )  => (r1_xxreal_0 (k3_real_1 D 1) (k3_finseq_1 (k1_jordan8 C A)))) ) ) ) ) ) ) ) ) ).
tt(t11_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k22_pscomp_1 B) (k2_gobrd13 (k1_jordan9 B A) (k1_jordan8 B A) C))) ) ) ) ) ) ) ) ).
tt(t11_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) = (k4_graph_2 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) (k2_jordan1e A B))) ) ) ) ) ).
tt(t11_jordan1f,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) &  ((r2_hidden (k4_tarski F G) (k2_matrix_1 A)) &  ( (B = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A F G)) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 F D)) (k18_complex1 (k6_xcmplx_0 G E))) = 1) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) &  (B = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E)) ) ) ) ) ) )  | (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) C) A)) ) ) ) ) ) ) ) ).
tt(t11_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k25_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) )  &  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ).
tt(t11_jordan1h,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (r2_relset_1 k5_numbers k1_numbers (k2_goboard1 A) (k1_partfun1 k5_numbers (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_numbers A k5_pscomp_1))) ) ).
tt(t11_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_xxreal_0 (k9_pscomp_1 (k3_topreal1 2 A)) (k18_euclid B)))  => (r2_hidden B (k2_goboard9 A))) ) ) ) ) ).
tt(t11_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k23_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k2_jordan1e B A))) & (r2_hidden (k23_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ).
tt(t11_jordan1k,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  => (r1_xxreal_0 k6_numbers (k7_weierstr A B C))) ) ) ) ) ) ).
tt(t11_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (k3_rcomp_1 k6_numbers B))  => (v3_pre_topc A k5_topmetr)) ) ) ) ) ).
tt(t11_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ( (B = D)  |  ( (C = E)  |  ( (~ (r2_hidden B (k5_jordan6 A B C D E)))  &  (~ (r2_hidden C (k5_jordan6 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan22,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) 2 1)) (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) 2 1)))) ) ) ) ) ) ) ) ).
tt(t11_jordan23,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_jordan23 B) =>  (! [C:$i] :  ((m1_subset_1 C A) => (v1_jordan23 (k1_finseq_6 A B C))) ) ) ) ) ) ) ).
tt(t11_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 D A) => (v3_connsp_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden D (k2_finseq_1 A)) &  (B = C) )  =>  ((r1_xxreal_0 (k7_partfun1 k1_numbers C D) (k12_euclid B)) & (r1_xxreal_0 (k5_square_1 (k7_partfun1 k1_numbers C D)) (k5_square_1 (k12_euclid B)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) <=>  ((v6_tbsp_1 B (k14_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_euclid A))))) ) ) ) ) ) ).
tt(t11_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 2 (k3_finseq_1 A)) =>  ((k1_jordan3 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) = 1) ) ) ) ) ) ).
tt(t11_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ((k1_funct_1 (k3_finseq_6 A B C D) (k3_finseq_1 (k3_finseq_6 A B C D))) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan5a,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_tarski A (k1_rcomp_1 B C)) =>  ( (~ (r2_hidden B A))  &  (~ (r2_hidden C A)) ) ) ) ) ) ) ) ) ).
tt(t11_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (B = C)  | (r2_jordan3 B C A C)) ) ) ) ) ) ) ) ).
tt(t11_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) => (r1_jordan5c A B C B C)) ) ) ) ) ) ) ).
tt(t11_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((r1_xxreal_0 (k9_pscomp_1 (k3_topreal1 2 A)) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B))) & (r1_xxreal_0 (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) (k7_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t11_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t11_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r1_jordan6 A B C))  =>  ( (B = (k18_pscomp_1 A))  |  ( (C = (k18_pscomp_1 A))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A B C) (k1_jordan7 A C (k18_pscomp_1 A))) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))))  =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) 2 A)) = (k6_pscomp_1 C)) ) ) ) ) ) ) ) ).
tt(t11_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C))) )  =>  ( ((k2_pre_topc (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k3_gobrd13 C B A))) = (k3_gobrd13 C B A))  &  ((k2_pre_topc (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k2_gobrd13 C B A))) = (k2_gobrd13 C B A)) ) ) ) ) ) ) ) ) ).
tt(t11_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan6 A B C) & (r1_jordan6 A (k22_pscomp_1 A) B))  =>  ((k1_jordan7 A B C) = (k5_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) B C)) ) ) ) ) ) ) ) ).
tt(t11_jordan,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xboole_0 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k6_topreal1 (k2_jordan21 A)) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan21 A))) A)) ) ).
tt(t11_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) => (r2_tarski A B)) ) ) ) ) ) ) ).
tt(t11_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D B A C) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  ((k9_prob_1 A (k7_kolmog01 A C B E D)) = (k4_kolmog01 B A C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k4_subset_1 A (k3_funct_2 k5_numbers (k9_setfam_1 A) B E) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E))) ) )  =>  ((k4_kurato_0 A D) = (k4_subset_1 A (k4_kurato_0 A B) (k4_kurato_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t11_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr k6_kurato_1)) = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 1) (k2_rcomp_1 1 2))) ).
tt(t11_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((m2_connsp_2 E (k2_borsuk_1 A B) (k3_borsuk_1 A B (k6_domain_1 (u1_struct_0 A) C) (k6_domain_1 (u1_struct_0 B) D))) <=> (m1_connsp_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lang1,ax, (! [A:$i] :  ((k3_lang1 (k6_lang1 A)) = (k1_tarski k1_xboole_0)) ) ).
tt(t11_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 2 A))  =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) &  (B = (k1_finseq_2 A)) ) ) ) ) ) ) ).
tt(t11_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (F = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D)))  =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E (u1_struct_0 (k8_group_4 A C D))) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E (u1_struct_0 (k5_group_4 A F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B)))) ) ) ) ) ) ).
tt(t11_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((v1_binop_1 (u2_lattices A) (u1_struct_0 A)) &  ((v2_binop_1 (u2_lattices A) (u1_struct_0 A)) &  ((v1_binop_1 (u1_lattices A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_lattices A) (u1_struct_0 A)) &  ((r1_lattice2 (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) & (r1_lattice2 (u1_struct_0 A) (u1_lattices A) (u2_lattices A))) ) ) ) )  => (v10_lattices A)) ) ) ).
tt(t11_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_lattice3 (k3_lattice3 A)) & (v2_lattice3 (k3_lattice3 A))) ) ) ).
tt(t11_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v11_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  ((v2_funct_2 C (u1_struct_0 A)) => (v11_lattices A)) ) ) ) ) ) ) ).
tt(t11_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v1_relat_1 D) =>  (! [E:$i] :  ((v1_relat_1 E) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_finseq_1 F A))  =>  ( ((r1_relat_2 D A) &  ((r1_relat_2 E A) &  (F = (k2_finseq_2 C B)) ) )  => (r1_lattice5 A F B B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ( ((k4_lattice6 A (k5_lattices A)) = (k5_lattices A))  & (v3_waybel_6 (k4_lattice3 A (k5_lattices A)) (k3_lattice3 A))) ) ) ).
tt(t11_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((r2_hidden B (k3_lattice7 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_orders_2 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_orders_2 A D B) => (r3_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v1_lattice5 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (v1_lattice5 (k2_lattice8 A B C D) (k1_lattice8 A) B)) ) ) ) ) ) ) ) ) ).
tt(t11_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_lattices A B (k4_lattices A C D)) = (k4_lattices A (k3_lattices A B C) (k3_lattices A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k39_glib_000 B) C))  =>  ((r2_hidden (k6_lexbfs A B C) (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B (k1_nat_1 C 1)))) &  ((k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B (k1_nat_1 C 1))) = (k2_xboole_0 (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C)) (k1_tarski (k6_lexbfs A B C)))) ) ) ) ) ) ) ) ) ).
tt(t11_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k4_waybel_3 A B (k11_lattice3 (k5_yellow_1 A B) C D) E) = (k11_lattice3 (k3_waybel_3 A B E) (k4_waybel_3 A B C E) (k4_waybel_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( ((v3_lfuzzy_1 B A) & (v3_lfuzzy_1 C A))  => (r1_fuzzy_1 (k4_fuzzy_4 A A A (k1_lfuzzy_1 (k2_zfmisc_1 A A) B C) (k1_lfuzzy_1 (k2_zfmisc_1 A A) B C)) (k1_lfuzzy_1 (k2_zfmisc_1 A A) B C))) ) ) ) ) ) ) ).
tt(t11_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) & (v2_limfunc1 B))  => (v2_limfunc1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t11_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r5_limfunc2 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  &  ((r2_hidden E (k1_relset_1 k1_numbers B)) & (r1_xxreal_0 (k1_seq_1 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r3_limfunc3 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A E)) k6_numbers))  &  ( (~ (r1_xxreal_0 D (k18_complex1 (k9_real_1 A E))))  &  ((r2_hidden E (k9_xtuple_0 B)) & (r1_xxreal_0 C (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  ((v4_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t11_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_lmod_5 A B C) = (k1_vectsp_4 A B))  &  ( (~  (C = k1_xboole_0) )  &  (~  (C = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (r1_tarski C (k2_struct_0 (k1_mod_3 A B C)))) ) ) ) ) ) ).
tt(t11_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k3_vectsp_4 A B C E) = (k3_vectsp_4 A B D E))  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_lopban_1 A B))) =>  ( (E = (k3_rlvect_1 (k5_lopban_1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k6_lopban_1 A B E F) = (k3_rlvect_1 B (k6_lopban_1 A B C F) (k6_lopban_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k4_lopban_2 A (k3_lopban_2 A C B) (k8_real_1 D E)) = (k3_lopban_2 A (k4_lopban_2 A C E) (k4_lopban_2 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k1_valued_0 (u1_struct_0 A) C D))) ) )  |  ((k6_normsp_1 A C) = (k6_normsp_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t11_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E B) =>  ((k8_nat_1 (u1_struct_0 A) C E) = (k8_nat_1 (u1_struct_0 A) D E)) ) ) )  =>  ((k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A C) B) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_lopban_5 A (k4_struct_0 A) C) = (k1_convex1 A (k1_lopban_5 A (k4_struct_0 A) C) (k1_real_1 1))) ) ) ) ) ) ) ).
tt(t11_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_lopclset A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_lopclset A))) =>  ((k4_lattices (k6_lopclset A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t11_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) B (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) C D)) (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) B C) D))) ) ) ) ) ) ) ) ).
tt(t11_lpspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v2_xxreal_0 C) & (m1_subset_1 C k1_numbers))  =>  ( ((v2_comseq_2 A) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 B D) = (k4_power (k17_complex1 (k9_real_1 (k2_seq_2 A) (k1_seq_1 A D))) C)) ) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t11_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = k6_numbers) ) )  =>  ((v1_series_1 (k1_lp_space B A)) &  ((k4_power (k4_series_1 (k1_lp_space B A)) (k10_real_1 1 A)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t11_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k7_ltlaxio1 A))) = 1)  <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 B D) A)) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t11_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A C D)) (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t11_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ( (A = k7_margrel1)  =>  ((k3_xboolean A) = k8_margrel1) )  &  ( ( ((k3_xboolean A) = k8_margrel1)  =>  (A = k7_margrel1) )  &  ( ( (A = k8_margrel1)  =>  ((k3_xboolean A) = k7_margrel1) )  &  ( ((k3_xboolean A) = k7_margrel1)  =>  (A = k8_margrel1) ) ) ) ) ) ) ).
tt(t11_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden (k4_struct_0 A) B) =>  ((r1_tarski (k3_mathmorp A C B) C) & (r1_tarski C (k6_rusub_4 A C B))) ) ) ) ) ) ) ) ).
tt(t11_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v1_matrix10 B) &  ((v2_matrix10 C) & (r1_matrix10 (k1_matrix10 C) (k1_matrix10 B))) )  => (v1_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t11_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  ( ((k2_matrix11 A B C) = (k1_group_1 B))  |  ((k2_matrix11 A B C) = (k4_algstr_0 B (k1_group_1 B))) ) ) ) ) ) ) ) ).
tt(t11_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) A B) =>  ( ((r2_hidden C (k4_finseq_1 F)) & (r2_hidden D (k4_finseq_1 F)))  =>  ((k1_matrix12 A B E (k1_matrix12 A B E F C D) C D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( (B = (k3_finseq_5 (k1_finseq_2 A)))  =>  ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) <=>  ((k4_nat_d (k6_newton 2 A) 2) = k6_numbers) ) ) ) ) ) ) ).
tt(t11_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 D)) )  =>  ((k13_fvsum_1 A B (k3_fvsum_1 A C D)) = (k1_algstr_0 A (k13_fvsum_1 A B C) (k13_fvsum_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k7_subset_1 k5_numbers (k4_finseq_1 B) C)) =>  ((k8_matrix_1 (u1_struct_0 A) B D) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 B) (k4_struct_0 A))) ) ) ) )  =>  ((k8_matrix13 A B) = (k8_matrix13 A (k6_matrix13 (u1_struct_0 A) B C (k2_finseq_1 (k1_matrix_1 B))))) ) ) ) ) ) ) ) ).
tt(t11_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix16 C (u1_struct_0 B)) => (v1_matrix16 (k1_matrix_6 A B C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t11_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((v5_matrix17 B (u1_struct_0 A)) & (v5_matrix17 C (u1_struct_0 A))) )  =>  ((k1_matrix17 (u1_struct_0 A) (k3_fvsum_1 A B C)) = (k3_matrix_3 A (k1_matrix17 (u1_struct_0 A) B) (k1_matrix17 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t11_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (m1_matrix_1 (k9_finseq_1 B) A 1 (k3_finseq_1 B))) ) ) ) ).
tt(t11_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( ((k4_matrix_1 A B) = (k4_matrix_1 A C))  =>  ((r1_xxreal_0 (k1_matrix_1 B) k6_numbers) |  ((r1_xxreal_0 (k1_matrix_1 C) k6_numbers) |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t11_matrix_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  ((k4_rlvect_1 B (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = (k4_struct_0 B)) ) ) ) ) ).
tt(t11_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k1_matrix_4 A B (k1_matrix_4 A C C))) ) ) ) ) ) ) ) ).
tt(t11_matrix_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ((k6_matrix_3 A (k6_matrix_3 A D C) B) = (k6_matrix_3 A D (k8_group_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t11_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_matrix_6 B A (k5_matrix_1 B (u1_struct_0 A) (k12_matrix_1 A B))) = (k12_matrix_1 A B)) ) ) ) ) ).
tt(t11_matrix_7,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k13_matrix_2 2))) =>  ( ( ((k4_nat_d (k3_finseq_1 A) 2) = k6_numbers)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 2)) =>  (~  ( ((k1_funct_1 A B) = C)  & (v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 2)))) ) ) ) ) ) ) ) )  =>  ((k3_group_4 (k13_matrix_2 2) A) = (k10_finseq_1 1 2)) ) ) ) ).
tt(t11_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) &  ((v1_matrix_8 D A B) & (r1_matrix_6 A B C D)) )  => (v1_matrix_8 (k4_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t11_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_finsop_1 (u1_struct_0 A) (k2_finseq_4 (u1_struct_0 A) B C) (u2_algstr_0 A)) = (k8_group_1 A B C)) ) ) ) ) ) ) ).
tt(t11_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k7_matrix_5 (k19_binop_2 1) A) = (k4_matrix_5 A)) ) ) ).
tt(t11_matrixj1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((k2_wsierp_1 (k17_finseq_1 k5_numbers B A)) = (k2_wsierp_1 (k17_finseq_1 k5_numbers C A))) ) )  =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((k1_funct_1 A B) = k1_xboole_0) )  |  ( ((r2_hidden C (k4_finseq_1 A)) &  ((k1_funct_1 A C) = k1_xboole_0) )  |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t11_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_matrixj2 (k16_matrixj1 (u1_struct_0 B) A (k2_matrixj2 B C A)) B C)) ) ) ) ) ) ).
tt(t11_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k8_rvsum_1 (k8_rvsum_1 A B) C) = (k8_rvsum_1 A (k4_rvsum_1 B C))) ) ) ) ) ) ) ) ).
tt(t11_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((k7_matrixr1 (k8_real_1 A B) C) = (k7_matrixr1 A (k7_matrixr1 B C))) ) ) ) ) ) ) ).
tt(t11_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ((k4_rlvect_1 C (k5_matrlin A C (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 D) B) D)) = (k4_vectsp_1 A C B (k4_rlvect_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t11_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k7_partfun1 (u1_struct_0 A) B C) = (k4_struct_0 A)) ) ) )  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t11_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_matroid0 A B)))) =>  ((v3_pre_topc C (k3_matroid0 A B)) <=>  ((v1_vectsp_7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t11_matrprob,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  ( (? [C:$i] :  ((v7_ordinal1 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k3_finseq_1 (k1_matrprob A B D)) = C) ) ) ) ) )  <=>  ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A))) ) ) ) ) ).
tt(t11_matrtop1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k23_binop_2 E D) A) <=> (r2_hidden E B)) ) )  =>  ((k5_relat_1 (k12_pnproc_1 C D) A) = (k12_pnproc_1 (k5_relat_1 C B) D)) ) ) ) ) ) ) ) ).
tt(t11_matrtop2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_vectsp_4 C k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B)) =>  (! [D:$i] :  ((m1_rlsub_1 D (k15_euclid B)) =>  ( ((k2_struct_0 C) = (k2_struct_0 D))  =>  ((m1_vectsp_6 A k2_vectsp_1 C) <=> (m1_rlvect_2 A D)) ) ) ) ) ) ) ) ) ).
tt(t11_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (v1_matrtop3 (k3_matrtop1 B B (k1_matrtop3 B A)) (k3_matrix13 A))) ) ) ) ) ).
tt(t11_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v1_mazurulm D A B) & (v1_mazurulm E B C))  => (v1_mazurulm (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B (k4_pboole A C D)) <=>  ((r2_pboole A B C) & (r5_pboole A B D)) ) ) ) ) ) ) ) ) ).
tt(t11_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden (k1_xtuple_0 A) B) & (r2_hidden (k2_xtuple_0 A) C))  =>  ( (! [D:$i] :  (! [E:$i] :  (~  (A = (k4_tarski D E)) ) ) )  | (r2_hidden A (k2_zfmisc_1 B C))) ) ) ) ) ).
tt(t11_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((r2_hidden k1_xboole_0 B) &  ((r2_hidden A B) &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  ((r2_hidden (k6_subset_1 A D) B) &  ((r2_hidden (k2_xboole_0 D E) B) & (r2_hidden (k3_xboole_0 D E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_measure2 D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (D = (k4_measure1 A B E))  => (r1_xxreal_0 (k3_funct_2 B k7_numbers C (k2_measure2 A B D)) (k19_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = k1_xboole_0)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 F 1)) = (k3_measure1 A B (k8_nat_1 B E k6_numbers) (k8_nat_1 B E F)))  & (r1_tarski (k8_nat_1 B E (k2_nat_1 F 1)) (k8_nat_1 B E F))) ) ) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k8_nat_1 B E k6_numbers))) |  ((k7_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C))) = (k4_supinf_2 (k12_supinf_2 C (k8_nat_1 B E k6_numbers)) (k8_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B E F) = (k2_measure1 A B D (k8_nat_1 B C F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ( ((v6_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v6_xxreal_2 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C D) &  ( (D = (k1_xxreal_1 A B))  & (r1_xxreal_0 B A)) )  =>  ( ((k2_measure5 C) = k1_supinf_2)  &  ((k2_measure5 D) = k1_supinf_2) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 B C) &  (A = (k2_xxreal_1 B C)) ) ) )  =>  (B = (k7_supinf_2 A)) ) ) ) ) ) ).
tt(t11_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k5_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k5_numbers)))) )  =>  ( ((v2_funct_1 D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E C) =>  ((k12_supinf_2 A E) = (k12_supinf_2 (k1_partfun1 C k5_numbers k5_numbers k7_numbers D B) E)) )  &  ( (~ (r2_hidden E C))  =>  ((k12_supinf_2 A E) = k1_supinf_2) ) ) ) ) )  => (r1_xxreal_0 (k19_supinf_2 A) (k19_supinf_2 B))) ) ) ) ) ) ) ) ) ) ).
tt(t11_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k1_mesfunc9 (k6_measure8 A B C) k1_xboole_0) = k6_numbers) ) ) ) ) ) ).
tt(t11_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r2_hidden B A) <=> (r2_hidden (k1_binop_2 B) (k5_member_1 A))) ) ) ) ) ).
tt(t11_membered,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v5_membered A))  =>  (? [B:$i] :  ((v1_int_1 B) & (r2_hidden B A)) ) ) ) ).
tt(t11_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v4_memstr_0 D A B)) ) ) )  =>  ((k5_memstr_0 A B (k1_funct_4 C D)) = (k5_memstr_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(t11_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((k1_euclid_6 (k3_rlvect_1 (k15_euclid 2) A B) C D) = (k10_binop_2 (k9_binop_2 (k1_euclid_6 A C D) (k1_euclid_6 B C D)) (k1_euclid_6 (k4_struct_0 (k15_euclid 2)) C D))) ) ) ) ) ) ) ) ) ).
tt(t11_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)))  &  ((v1_mesfunc8 B A k7_numbers) &  ( ((k8_relset_1 A k7_numbers D (k6_domain_1 k7_numbers k1_supinf_1)) = k1_xboole_0)  &  ( ((k8_relset_1 A k7_numbers D (k6_domain_1 k7_numbers k2_supinf_1)) = k1_xboole_0)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers B E) (k3_mesfunc1 A D (k4_mesfunc5 A k7_numbers C E)))) ) ) ) ) )  =>  ((r2_relset_1 A k7_numbers (k5_mesfunc8 A B) (k3_mesfunc1 A D (k5_mesfunc8 A C))) & (r2_relset_1 A k7_numbers (k6_mesfunc8 A B) (k3_mesfunc1 A D (k6_mesfunc8 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C E) & (r1_mesfun6c A B D E))  => (r1_mesfun6c A B (k2_valued_1 A k2_numbers k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) => (r2_funct_2 k5_numbers k7_numbers (k3_mesfunc5 A (k5_mesfun7c A B) C) (k4_rinfsup2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C))))) ) ) ) ) ) ) ).
tt(t11_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_mesfunc8 B A k1_numbers) =>  ((k1_relset_1 A (k4_mesfunc5 A k1_numbers (k2_mesfun9c A B) C)) = (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) ) ) ) ) ) ) ) ).
tt(t11_mesfunc1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k5_real_1 A (k10_real_1 1 (k2_nat_1 C 1))) B)) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t11_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( ((v3_valued_0 C) &  ((v3_valued_0 D) &  ((r1_mesfunc1 A B C E) &  ((r1_mesfunc1 A B D E) & (r1_tarski E (k1_relset_1 A D))) ) ) )  => (r1_mesfunc1 A B (k4_mesfunc1 A C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) => (m2_finseq_1 A k7_numbers)) ) ).
tt(t11_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [C:$i] :  (~  ((r2_hidden C (k1_relset_1 A B)) & (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 B C))) ) )  <=> (v4_mesfunc5 B)) ) ) ) ) ).
tt(t11_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_funct_1 D G) = (k3_xboole_0 B (k14_mesfunc1 E (k7_real_1 F (k13_complex1 1 (k1_nat_1 G 1)))))) ) )  =>  ((k3_xboole_0 B (k13_mesfunc1 E F)) = (k5_setfam_1 A (k4_measure1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mesfunc7,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (A = B)  =>  ((k4_mesfunc7 A C) = (k1_newton B C)) ) ) ) ) ) ) ) ).
tt(t11_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k5_mesfunc8 A B))) =>  ( ((k12_supinf_2 (k5_mesfunc8 A B) C) = (k1_rinfsup2 (k3_rinfsup2 (k3_mesfunc5 A B C))))  &  ( ((k12_supinf_2 (k5_mesfunc8 A B) C) = (k1_rinfsup2 (k3_mesfunc5 A (k3_mesfunc8 A B) C)))  &  ((k12_supinf_2 (k5_mesfunc8 A B) C) = (k12_supinf_2 (k2_mesfunc8 A (k3_mesfunc8 A B)) C)) ) ) ) ) )  & (r2_relset_1 A k7_numbers (k5_mesfunc8 A B) (k2_mesfunc8 A (k3_mesfunc8 A B)))) ) ) ) ) ).
tt(t11_mesfunc9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v10_mesfunc5 A) &  ((v10_mesfunc5 B) &  ((v6_supinf_2 A) &  ((v6_supinf_2 B) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k12_supinf_2 C D) = (k3_supinf_2 (k12_supinf_2 A D) (k12_supinf_2 B D))) ) ) ) ) ) )  =>  ((v6_supinf_2 C) &  ((v10_mesfunc5 C) &  ((k2_mesfunc5 C) = (k3_supinf_2 (k2_mesfunc5 A) (k2_mesfunc5 B))) ) ) ) ) ) ) ) ) ) ).
tt(t11_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k9_metric_1 B C A)) <=>  ( (~ (v2_struct_0 B))  &  (~ (r1_xxreal_0 A (k2_metric_1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_metric_2 A B C) <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t11_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) C D) = (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(t11_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) =>  ((k1_tbsp_1 A C) = B) ) ) ) ) ) ) ) ).
tt(t11_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ( ((v6_topgen_4 C A) &  (D = (k9_subset_1 (u1_struct_0 A) C B)) )  => (v6_topgen_4 D (k1_pre_topc A B))) ) ) ) ) ) ) ) ) ).
tt(t11_mfold_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A C) =>  (! [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r1_metrizts A B D E) &  (! [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [G:$i] :  ( ((v3_pre_topc G B) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r1_tarski F D) &  ((r2_hidden C F) & (r1_metrizts A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((v2_mfold_1 B A) & (r1_mfold_2 B C))  => (v2_mfold_1 C A)) ) ) ) ) ) ) ).
tt(t11_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_midsp_1 A B C D E) => (r1_midsp_1 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_midsp_2 A (k3_rlvect_1 A B C)) = (k3_rlvect_1 A (k1_midsp_2 A B) (k1_midsp_2 A C))) ) ) ) ) ) ) ).
tt(t11_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_midsp_3 C A) =>  ((r2_midsp_3 A C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  ( (G = (k6_midsp_3 A B F C E))  =>  ((k4_midsp_3 A B D (k6_midsp_3 A B F C (k3_midsp_1 B D E))) = (k3_midsp_1 B D (k4_midsp_3 A B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k12_mmlquery A B C (k1_nat_1 D 1)) = (k14_mmlquery A B C D)) ) ) ) ) ) ) ) ).
tt(t11_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_mod_2 B A) & (l1_mod_2 B A))  =>  (! [C:$i] :  ( ((v3_mod_2 C A) & (l1_mod_2 C A))  =>  (~  ( ((k2_mod_2 A B) = (k3_mod_2 A C))  &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E A) &  ((v9_vectsp_1 E A) &  ((v10_vectsp_1 E A) &  ((v11_vectsp_1 E A) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E A)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v8_vectsp_1 F A) &  ((v9_vectsp_1 F A) &  ((v10_vectsp_1 F A) &  ((v11_vectsp_1 F A) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l1_vectsp_1 F A)) ) ) ) ) ) ) ) )  =>  (~  ((m1_mod_2 B A E F) & (m1_mod_2 C A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((k1_mod_3 A B C) = B)  & (r1_tarski C D))  =>  ((k1_mod_3 A B D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t11_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_mod_4 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_mod_4 A B))) =>  ( ( (D = E)  &  (F = G) )  =>  ((k2_binop_1 (u1_struct_0 (k3_mod_4 A B)) (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k3_mod_4 A B)) (k4_mod_4 A B C) G E) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  (! [D:$i] :  ((m1_trees_1 D A) =>  ( ((k5_trees_1 A D B) = (k5_trees_1 A D C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t11_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_modcat_1 B A) =>  (! [C:$i] :  ((m4_modcat_1 C A (k4_modcat_1 A B)) =>  (! [D:$i] :  ((m4_modcat_1 D A (k4_modcat_1 A B)) =>  ((r2_hidden (k4_tarski C D) (k1_relset_1 (k2_zfmisc_1 (k4_modcat_1 A B) (k4_modcat_1 A B)) (k10_modcat_1 A B))) <=>  ((k2_mod_2 A C) = (k3_mod_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r2_hidden E D) =>  ((r3_modelc_1 A B D C E) <=> (r2_hidden E (k3_funct_2 A (k1_zfmisc_1 D) (k46_modelc_1 A D) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  ( ((k3_finseq_1 A) = (k2_nat_1 (k2_nat_1 1 (k3_finseq_1 (k11_modelc_2 A))) (k3_finseq_1 (k12_modelc_2 A))))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k11_modelc_2 A))))  &  (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 (k12_modelc_2 A)))) ) ) ) ) ) ).
tt(t11_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k13_modelc_2 A))) =>  ( (D = (k2_xboole_0 C (k1_tarski B)))  =>  ((r2_hidden B C) |  ((k18_modelc_3 A D) = (k7_real_1 (k18_modelc_3 A C) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_moebius1,ax, (! [A:$i] :  ( ((v1_int_2 A) & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (~  ((r1_int_2 B C) &  ((r1_nat_d (k13_newton A 2) (k4_nat_1 B C)) &  ( (~ (r1_nat_d (k13_newton A 2) B))  &  (~ (r1_nat_d (k13_newton A 2) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v14_monoid_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v3_binop_1 C B) => (v3_binop_1 (k8_monoid_1 B B B C A) (k9_funct_2 A B))) ) ) ) ) ) ).
tt(t11_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_morph_01 A (k2_morph_01 A B C) D) = (k2_morph_01 A B (k2_morph_01 A C D))) ) ) ) ) ) ) ) ) ).
tt(t11_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v6_trees_3 D)) ) )  =>  ((r2_hidden (k4_trees_4 (k4_tarski C (u1_struct_0 A)) D) (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) (k2_msualg_1 A C))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers (k1_msualg_1 A C))) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) (k1_funct_1 (k1_msualg_1 A C) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_msafree3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((l1_msualg_1 C) =>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v6_trees_3 E)) ) )  =>  ((r2_hidden A (k1_funct_1 (k2_msafree3 C (k4_trees_4 (k4_tarski B (u1_struct_0 C)) E)) D)) <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v3_trees_2 F)) )  &  ((r2_hidden F (k10_xtuple_0 E)) & (r2_hidden A (k1_funct_1 (k2_msafree3 C F) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k3_tarski (k10_xtuple_0 (k8_msafree A B))) = (k4_dtconstr (k5_msafree A B))) ) ) ) ) ).
tt(t11_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_hidden C (k7_msafree A B D))) ) ) ) ) ) ) ) ).
tt(t11_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ( ((k1_funct_1 (k7_graph_2 A B) C) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B C)))  &  ((k1_funct_1 (k7_graph_2 A B) (k2_nat_1 C 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t11_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B C) => (m1_pboole B A C)) ) ) ) ) ) ).
tt(t11_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_unialg_2 A B) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 (k6_msualg_1 B)) (u3_msualg_1 (k6_msualg_1 B) (k9_msualg_1 B))) =>  ( (C = (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)))  =>  ((u4_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) = (k4_msualg_2 (k6_msualg_1 B) (k9_msualg_1 B) C)) ) ) ) ) ) ) ) ) ).
tt(t11_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msualg_2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  =>  ((v2_relat_1 (k2_msualg_2 A B)) & (m3_pboole (k2_msualg_2 A B) (u1_struct_0 A) (u3_msualg_1 A C))) ) ) ) ) ) ) ).
tt(t11_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ( ((r2_msualg_3 A B C E) & (r2_msualg_3 A C D F))  => (r2_msualg_3 A B D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  ((v1_msualg_4 (k3_pboole A C D) A B) & (m1_msualg_4 (k3_pboole A C D) A B B)) ) ) ) ) ) ) ) ) ).
tt(t11_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_msualg_6 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_msualg_6 A B C D E) =>  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_1 (u3_msualg_1 A D) B) (k1_funct_1 (u3_msualg_1 A D) C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A D) B) (k1_funct_1 (u3_msualg_1 A D) C))))) )  &  ( (~  ((k1_funct_1 (u3_msualg_1 A D) B) = k1_xboole_0) )  &  (~  ((k1_funct_1 (u3_msualg_1 A D) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k3_lattices A C D) = (k3_lattices B E F))  &  ((k4_lattices A C D) = (k4_lattices B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  ((v2_msualg_4 (k16_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) A B) &  ((v3_msualg_4 (k16_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) A B) & (m1_msualg_4 (k16_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ).
tt(t11_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v1_msualg_3 (k15_msafree A B))) ) ) ) ).
tt(t11_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_unialg_2 A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k6_msualg_1 A))) => (r1_funct_2 (k1_funct_1 (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (k2_msualg_1 (k6_msualg_1 A) D)) (k1_funct_1 (u3_msualg_1 (k6_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B))) (k2_msualg_1 (k6_msualg_1 A) D)) (u1_struct_0 A) (u1_struct_0 B) (k1_msualg_3 (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B))) (k2_msuhom_1 A B C) (k2_msualg_1 (k6_msualg_1 A) D)) C)) ) ) ) ) ) ) ) ) ).
tt(t11_mycielsk,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  => (r1_xxreal_0 (k1_dilworth A) (k5_card_1 (u1_struct_0 A)))) ) ).
tt(t11_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_nagata_1 B A) => (v1_pcomps_1 B A)) ) ) ) ) ).
tt(t11_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers))))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r2_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (k1_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers B C) D) & (r1_nagata_1 (u1_struct_0 A) D)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) => (v1_series_1 (k10_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B C))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers C D) = (k4_series_1 (k10_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B D))) ) )  => (r1_nagata_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(t11_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 A (k2_xcmplx_0 A B))) ) ) ) ).
tt(t11_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) => (r1_nat_d (k3_power 2 A) (k3_power 2 B))) ) ) ) ) ).
tt(t11_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_3 (k2_pre_poly k1_numbers) A) = (k2_pre_poly k1_numbers)) ) ) ).
tt(t11_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d (k1_newton A (k4_nat_1 2 B)) C) = (k4_nat_d (k4_nat_1 (k4_nat_d (k1_newton A B) C) (k4_nat_d (k1_newton A B) C)) C)) ) ) ) ) ) ) ).
tt(t11_nat_5,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ((r2_relset_1 k5_numbers k1_numbers B (k1_partfun1 k5_numbers k5_numbers k5_numbers k1_numbers (k14_finseq_1 A) C)) &  ((r1_tarski (k7_subset_1 k5_numbers (k4_finseq_1 C) (k8_relset_1 k5_numbers k1_numbers C (k6_domain_1 k5_numbers k6_numbers))) A) & (r1_tarski A (k4_finseq_1 C))) )  =>  ((k18_rvsum_1 C) = (k18_rvsum_1 B)) ) ) ) ) ) ) ).
tt(t11_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d A C))  => (r1_nat_d A (k4_nat_d B C))) ) ) ) ) ) ) ).
tt(t11_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ( ((k1_binop_1 k1_nat_lat A (k1_binop_1 k2_nat_lat A B)) = A)  &  ( ((k1_binop_1 k1_nat_lat (k1_binop_1 k2_nat_lat B A) A) = A)  &  ( ((k1_binop_1 k1_nat_lat A (k1_binop_1 k2_nat_lat B A)) = A)  &  ((k1_binop_1 k1_nat_lat (k1_binop_1 k2_nat_lat A B) A) = A) ) ) ) ) ) ) ) ).
tt(t11_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D C A) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( (~  ((k2_cat_1 C F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_cat_1 H C F G) =>  ((k9_cat_3 C F G B (k9_cat_1 C A B D E) H) = (k9_cat_3 A (k8_cat_1 C A D F) (k8_cat_1 C A D G) B E (k9_cat_3 C F G A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k1_relset_1 (u1_struct_0 A) B)) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A F C))))  & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers B F) (k7_partfun1 k1_numbers B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C)))))  =>  ((r2_ncfcont2 A C D E) => (r2_ncfcont2 A C D (k4_vfunct_1 (u1_struct_0 D) C E B))) ) ) ) ) ) ) ) ) ) ).
tt(t11_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_ndiff_1 A B (k47_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k3_normsp_1 A (k1_ndiff_1 A B C) (k1_ndiff_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t11_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k7_partfun1 (u1_struct_0 B) D (k4_struct_0 A)) = (k4_struct_0 B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v2_ndiff_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((k7_partfun1 (u1_struct_0 C) E (k4_struct_0 B)) = (k4_struct_0 C))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 F A B) &  ((v1_lopban_1 F A B) &  ((v2_lopban_1 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E)) &  ((v2_ndiff_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r2_ndiff_3 A C B) => (v3_rcomp_1 B)) ) ) ) ) ) ) ).
tt(t11_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r1_ndiff_4 B C A) & (r1_ndiff_4 B D A))  =>  ((r1_ndiff_4 B (k7_integr15 B k1_numbers C D) A) &  ((k1_ndiff_4 B (k7_integr15 B k1_numbers C D) A) = (k7_euclid B (k1_ndiff_4 B C A) (k1_ndiff_4 B D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden C (u1_struct_0 (k11_prvect_2 A B))) & (r2_hidden D (k4_card_3 (k4_prvect_2 A))))  => (r2_hidden (k2_funct_7 D B C) (u1_struct_0 (k14_prvect_2 A)))) ) ) ) ) ) ) ) ).
tt(t11_neckla_3,ax, ((u1_orders_2 (k3_necklace (k4_necklace 4))) = (k11_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers 2) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers 3) (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers) (k1_domain_1 k5_numbers k5_numbers 1 3) (k1_domain_1 k5_numbers k5_numbers 3 1))) ).
tt(t11_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden B C) =>  ((r1_xxreal_0 B A) | (r2_hidden A C)) ) ) ) ) ) ) ) ).
tt(t11_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) => (r1_tarski (k4_net_1 A B) (k2_net_1 A))) ) ) ) ).
tt(t11_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_newton k6_numbers A) = k6_numbers) ) ) ) ).
tt(t11_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) =>  ( (! [E:$i] :  ((m1_nfcont_1 E B D) =>  (~  ((k9_subset_1 (u1_struct_0 B) (k1_relset_1 (u1_struct_0 B) C) E) = (k1_tarski D)) ) ) )  | (r1_nfcont_1 B A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski D (k1_relset_1 (u1_struct_0 B) C)) &  ((v1_nfcont_1 D B) & (r1_nfcont_2 D B A C)) )  => (v1_nfcont_1 (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t11_nfcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ( (? [D:$i] :  ((m1_rcomp_1 D A) &  ((k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) D) = (k1_tarski A)) ) )  => (r1_nfcont_3 B C A)) ) ) ) ) ) ) ).
tt(t11_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_nfcont_4 A C B) <=>  ((r2_hidden B (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid A))) =>  (~  ( (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((a_4_0_nfcont_4 A B C E) = D) ) ) )  &  (! [E:$i] :  ((m1_rcomp_1 E B) =>  (? [F:$i] :  ((v1_xreal_0 F) &  ((r2_hidden F (k1_relset_1 k1_numbers C)) &  ((r2_hidden F E) &  (~ (r2_hidden (k7_partfun1 (k1_euclid A) C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ( (C = (k1_normform A B C D))  => (r1_normform A B D C)) ) ) ) ) ) ) ) ) ).
tt(t11_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t11_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  => (v4_frechet (k3_normsp_2 A))) ) ).
tt(t11_ntalgo_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (k2_zfmisc_1 k4_numbers k4_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) &  ((k1_funct_1 C D) = k6_numbers) ) ) ) )  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) =>  ( ((k1_xtuple_0 (k1_funct_1 A D)) = (k1_funct_1 B D))  &  ((k2_xtuple_0 (k1_funct_1 A D)) = (k1_funct_1 C D)) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) & (r2_hidden E (k2_finseq_1 (k3_finseq_1 A))))  =>  ( (D = E)  | (r1_int_2 (k1_funct_1 C D) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) =>  ((k6_int_1 (k4_ntalgo_1 A) (k1_funct_1 C D)) = (k6_int_1 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_numbers,ax,(r1_tarski k1_numbers k2_numbers)).
tt(t11_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k1_funct_1 (k8_openlatt A) C)) <=>  ((r2_hidden B (k7_openlatt A)) & (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(t11_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_oposet_1 A) => (v3_oposet_1 A)) ) ) ).
tt(t11_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_oppcat_1 A))) =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) B C) =>  ( ((k3_graph_1 A (k6_oppcat_1 A D)) = (k4_graph_1 (k2_oppcat_1 A) D))  &  ((k4_graph_1 A (k6_oppcat_1 A D)) = (k3_graph_1 (k2_oppcat_1 A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_orders_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r7_relat_2 C A) & (r1_tarski B A))  => (r7_relat_2 C B)) ) ) ) ) ).
tt(t11_orders_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (? [D:$i] :  ( ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden B D) & (r2_hidden C D)) ) )  &  ( (~ (r1_orders_2 A B C))  &  (~ (r1_orders_2 A C B)) ) ) )  &  (~  ( ((r1_orders_2 A B C) | (r1_orders_2 A C B))  &  (! [D:$i] :  ( ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden B D) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_orders_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) => (r1_tarski (k1_orders_3 A B) (k1_funct_2 (u1_struct_0 A) (u1_struct_0 B)))) ) ) ) ).
tt(t11_ordinal1,ax, (! [A:$i] :  ((v1_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_xboole_0 A B) => (r2_hidden A B)) ) ) ) ) ).
tt(t11_ordinal2,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k3_ordinal1 A) (k3_ordinal1 B))) ) ) ).
tt(t11_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r1_tarski B A) => (v3_ordinal1 (k1_setfam_1 B))) ) ) ) ).
tt(t11_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v2_ordinal2 A) => (v3_ordinal1 (k8_relat_1 A B))) ) ) ) ) ).
tt(t11_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((r2_hidden k6_numbers A) & (v4_ordinal1 B))  =>  ((v1_xboole_0 B) |  ((r2_hidden C (k12_ordinal2 A B)) <=>  (? [D:$i] :  ((v3_ordinal1 D) &  ((r2_hidden D B) & (r2_hidden C (k12_ordinal2 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=> (r1_ordinal1 (k3_ordinal5 A) (k3_ordinal5 B))) ) ) ) ) ).
tt(t11_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t11_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  => (r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B (k1_ortsp_1 A B D C E) C)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k1_funct_1 C k1_xboole_0) = (k4_tarski D (u1_struct_0 A)))  =>  ( (? [E:$i] :  ((m2_dtconstr E (k2_osafree A B) (k9_osafree A B D)) &  ( (C = (k9_dtconstr (k2_osafree A B) (k9_osafree A B D) E))  &  ((r1_lang1 (k2_osafree A B) (k9_osafree A B D) (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) E)) &  ((r2_hidden E (k3_msualg_1 A D (k8_osafree A B))) &  (C = (k1_funct_1 (k5_msualg_1 A D (k8_osafree A B)) E)) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  (~  (C = (k1_trees_4 (k4_tarski F E))) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) E)) <=> (r3_orders_2 A (k2_msualg_1 A D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  ((v10_osalg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (~  ((r2_osalg_1 A C (k1_msualg_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~ (r5_osalg_1 A B D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((r2_pboole (u1_struct_0 A) (k2_msualg_2 A B) C) => (r2_pboole (u1_struct_0 A) (k3_osalg_2 A B) C)) ) ) ) ) ) ) ).
tt(t11_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((v1_osalg_3 D A) & (r1_msualg_3 A B C D))  => (v12_osalg_1 (k6_msualg_3 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t11_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_osalg_4 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r3_orders_2 A D B) & (r3_orders_2 A D C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_orders_2 A B D) & (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  => (v6_papdesaf B)) ) ) ) ) ).
tt(t11_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) => (r2_hidden (k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C D E) (k6_parsp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t11_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_2 A B C D))  &  ((r1_parsp_1 A B C E F) &  ((r1_parsp_1 A B D E G) &  ( (~  (E = F) )  &  ( (~  (E = G) )  & (r1_parsp_2 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k5_relset_1 A B D C)) & (m1_subset_1 (k5_relset_1 A B D C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ).
tt(t11_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ((r2_relset_1 B A D (k2_partfun2 A B C)) <=>  ( ((k1_relset_1 B D) = (k2_relset_1 B C))  &  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ( ((r2_hidden E (k2_relset_1 B C)) &  (F = (k7_partfun1 A D E)) )  =>  ((r2_hidden F (k1_relset_1 A C)) &  (E = (k7_partfun1 B C F)) ) )  &  ( ((r2_hidden F (k1_relset_1 A C)) &  (E = (k7_partfun1 B C F)) )  =>  ((r2_hidden E (k2_relset_1 B C)) &  (F = (k7_partfun1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((r2_hidden D E) & (r2_partit1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A B C) => (r1_bvfunc_1 A (k1_bvfunc_1 A C) (k1_bvfunc_1 A B))) ) ) ) ) ) ) ).
tt(t11_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v3_pasch A)) ) ).
tt(t11_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((r4_pboole A B C) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r1_pboole A D B) & (r1_pboole A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pcomps_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (v2_tops_2 (k1_pcomps_1 A B) A)) ) ) ) ).
tt(t11_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_pcs_0 A B))) =>  ((r1_orders_2 (k17_pcs_0 A B) C D) <=>  (? [E:$i] :  ((m1_subset_1 E A) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_pcs_0 A B E))) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_pcs_0 A B E))) &  ( (F = C)  &  ( (G = D)  & (r1_orders_2 (k15_pcs_0 A B E) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_pdiff_1 B A) = (k3_relat_1 (k1_pdiff_1 B A) (k2_funct_1 (k1_pdiff_1 1 1)))) ) ) ) ) ).
tt(t11_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (D = (k10_finseq_1 A B))  & (r3_pdiff_1 2 1 E D))  =>  ( (C = (k11_pdiff_1 2 1 E D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (D = (k10_finseq_1 F G))  &  (? [H:$i] :  ((m1_rcomp_1 H F) &  ((r1_tarski H (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 E D))) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v3_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v2_fdiff_1 J) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 I 1))  &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ((r2_hidden K H) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 1 E D) K) (k1_seq_1 (k1_pdiff_2 2 1 E D) F)) = (k7_real_1 (k1_seq_1 I (k9_real_1 K F)) (k1_seq_1 J (k9_real_1 K F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r3_pdiff_3 B A) <=> (r3_pdiff_1 2 1 (k1_pdiff_3 2 2 B) A)) ) ) ) ) ).
tt(t11_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (~  ( (D = (k11_finseq_1 A B C))  &  ((r3_pdiff_1 3 2 E D) &  (! [F:$i] :  ((m1_rcomp_1 F B) =>  (~  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 E D))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 E D) I) (k1_seq_1 (k1_pdiff_2 3 2 E D) B)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I B)) (k1_seq_1 H (k9_real_1 I B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r2_pdiff_5 E D))  =>  ((k2_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 E) D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  ((v1_pdiff_6 C B A) =>  ((k3_funct_2 (k1_euclid A) (k1_euclid B) C (k5_euclid A)) = (k5_euclid B)) ) ) ) ) ) ) ) ).
tt(t11_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ( (~  (B = k6_numbers) )  &  ((k1_finseq_7 k1_numbers (k5_euclid A) C B) = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D A) (k5_algstr_0 (k4_real_ns1 A) B C)) = (k5_algstr_0 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D A) B) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D A) C))) ) ) ) ) ) ) ) ) ).
tt(t11_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ((k12_euclid (k3_funct_2 k1_numbers (k1_euclid B) (k6_pdiff_1 B A (k5_euclid B)) C)) = (k17_complex1 C)) ) ) ) ) ) ) ) ).
tt(t11_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v2_pralg_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_pboole C A (k12_pralg_1 A B)) => (m3_pboole (k1_pzfmisc1 A C) A (k12_pralg_1 A B))) ) ) ) ) ) ).
tt(t11_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  ( ((v1_pencil_1 C (k5_pencil_1 A B)) &  ((v2_pencil_1 C (k5_pencil_1 A B)) &  ((v1_pencil_1 D (k5_pencil_1 A B)) &  ((v2_pencil_1 D (k5_pencil_1 A B)) & (r1_pencil_2 (k5_pencil_1 A B) C D)) ) ) )  =>  ((v1_zfmisc_1 C) |  ((v1_zfmisc_1 D) |  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  ( ( (C = (k4_card_3 E))  &  (D = (k4_card_3 F)) )  =>  ( ((k3_pencil_1 A E) = (k3_pencil_1 A F))  &  (! [G:$i] :  ( (~  (G = (k3_pencil_1 A E)) )  =>  ((k1_funct_1 E G) = (k1_funct_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v11_pencil_1 B) & (v14_pencil_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v13_pencil_1 C))  &  ((v16_pencil_1 C A) & (m3_pboole C A (k12_pralg_1 A B))) )  =>  (! [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  =>  ( ((m1_pencil_2 (k4_card_3 C) A B) &  ((m1_pencil_2 (k4_card_3 D) A B) &  ((k3_pencil_1 A C) = (k3_pencil_1 A D)) ) )  =>  ((r2_subset_1 (k4_card_3 C) (k4_card_3 D)) | (r8_pboole A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_vectsp_4 F A B) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ( ((k1_nat_1 (k1_vectsp_9 A C) 1) = G)  &  ( ((k1_vectsp_9 A D) = (k1_nat_1 G 1))  &  ((r2_hidden E (k3_pencil_4 A B C D G)) & (r2_hidden F (k3_pencil_4 A B C D G))) ) )  =>  ( (E = F)  |  ( ((k2_vectsp_5 A B E F) = (k2_vectsp_4 A C))  &  ((k1_vectsp_5 A B E F) = (k2_vectsp_4 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k4_nat_d (k3_xcmplx_0 B C) A) = (k4_nat_d C A))  & (r1_int_2 C A))  =>  ((r1_xxreal_0 A 1) |  ((k4_nat_d B A) = 1) ) ) ) ) ) ) ) ) ).
tt(t11_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ((k8_petri A (k1_subset_1 (u4_struct_0 A))) = k1_xboole_0) ) ) ).
tt(t11_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k6_relat_1 A B) = (k5_relat_1 B (k8_relat_1 B A))) ) ) ) ).
tt(t11_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) => (m1_polyalg1 B A B)) ) ) ) ).
tt(t11_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (! [F:$i] :  ((v1_xreal_0 F) =>  ((k3_polyeq_1 C D E F) = (k5_polyeq_1 C F A B)) ) )  =>  ( (C = k6_numbers)  |  ( ((k7_xcmplx_0 D C) = (k4_xcmplx_0 (k2_xcmplx_0 A B)))  &  ((k7_xcmplx_0 E C) = (k3_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  (! [J:$i] :  ((v1_xreal_0 J) =>  ( (! [K:$i] :  ((v1_xreal_0 K) =>  ((k1_polyeq_2 A B C D E K) = (k2_polyeq_2 A G H I J K)) ) )  =>  ( (A = k6_numbers)  |  ((k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k1_newton F 4)) (k3_xcmplx_0 B (k1_newton F 3))) (k3_xcmplx_0 C (k3_square_1 F))) (k3_xcmplx_0 D F)) E) A) = (k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_newton F 4) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 G H) I) J) (k1_newton F 3))) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 G H) (k3_xcmplx_0 G I)) (k3_xcmplx_0 G J)) (k2_xcmplx_0 (k3_xcmplx_0 H I) (k3_xcmplx_0 H J))) (k3_xcmplx_0 I J)) (k3_square_1 F))) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 G H) I) (k3_xcmplx_0 (k3_xcmplx_0 G H) J)) (k3_xcmplx_0 (k3_xcmplx_0 G I) J)) (k3_xcmplx_0 (k3_xcmplx_0 H I) J)) F)) (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 G H) I) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k2_quin_1 A B C)))  &  ( ((k7_polyeq_1 A B C k6_numbers D) = k6_numbers)  &  ( (~  (D = (k3_binop_2 (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A))) (k5_binop_2 (k12_binop_2 (k7_square_1 (k7_binop_2 (k2_quin_1 A B C))) (k11_binop_2 2 A)) k7_complex1))) )  &  ( (~  (D = (k3_binop_2 (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A))) (k5_binop_2 (k7_binop_2 (k12_binop_2 (k7_square_1 (k7_binop_2 (k2_quin_1 A B C))) (k11_binop_2 2 A))) k7_complex1))) )  &  (~  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k2_xcmplx_0 (k2_newton A 3) (k2_newton B 3)) = (k3_xcmplx_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 (k6_xcmplx_0 (k5_square_1 A) (k3_xcmplx_0 A B)) (k5_square_1 B))))  &  ((k2_xcmplx_0 (k2_newton A 5) (k2_newton B 5)) = (k3_xcmplx_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k2_newton A 4) (k3_xcmplx_0 (k2_newton A 3) B)) (k3_xcmplx_0 (k2_newton A 2) (k2_newton B 2))) (k3_xcmplx_0 A (k2_newton B 3))) (k2_newton B 4)))) ) ) ) ) ) ).
tt(t11_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( (B = (k4_xcmplx_0 (k2_xcmplx_0 C D)))  &  (E = (k3_xcmplx_0 C D)) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k3_xcmplx_0 B A)) E) = k6_numbers)  <=>  ( (A = C)  |  (A = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polyform,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (r1_xxreal_0 (k3_finseq_1 (k7_finseq_1 A B)) (k3_finseq_1 (k7_finseq_1 A (k7_finseq_1 B C))))) ) ) ) ) ) ).
tt(t11_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((k1_polynom1 A (k8_finseq_1 (u1_struct_0 A) C D) B) = (k8_finseq_1 (u1_struct_0 A) (k1_polynom1 A C B) (k1_polynom1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t11_polynom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (r2_hidden C B))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ( (D = (k2_xboole_0 (k1_tarski C) B))  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v1_relat_2 E) &  ((v4_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 E D) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r2_hidden (k2_nat_1 F 1) (k4_finseq_1 (k7_pre_poly A D E))) &  ((k7_partfun1 A (k7_pre_poly A D E) (k2_nat_1 F 1)) = C) )  =>  ((k7_pre_poly A D E) = (k5_finseq_5 A (k7_pre_poly A B E) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k6_polynom3 2 C) A) = (k2_polynom3 k5_numbers D (k7_nat_d C D)))  &  ((k1_funct_1 (k6_polynom3 2 C) B) = (k2_polynom3 k5_numbers E (k7_nat_d C E))) )  =>  ( (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 E D)) )  &  (~  ( (~ (r1_xxreal_0 E D))  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_polynom4 A B) (k15_funct_7 k5_numbers (u1_struct_0 A) (k9_polynom3 A) (k7_nat_d (k1_algseq_1 A B) 1) (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1))))) ) ) ) ).
tt(t11_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ((k1_polynom5 (k3_finseq_4 (u1_struct_0 k1_complfld) A B C)) = (k3_finseq_4 k1_numbers (k17_complex1 A) (k17_complex1 B) (k17_complex1 C))) ) ) ) ) ) ) ).
tt(t11_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly A) (k15_pre_poly A)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_pre_poly B) (k15_pre_poly B)) =>  (! [F:$i] :  ((m2_subset_1 F (k14_pre_poly B) (k15_pre_poly B)) =>  ((r1_pre_poly (k10_ordinal2 A B) (k1_polynom6 A B C E) (k1_polynom6 A B D F)) <=>  ((r1_pre_poly A C D) |  ((r6_pboole A C D) & (r1_pre_poly B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k1_polynom7 A B (k3_polynom7 A B C) (k2_polynom7 A B C)) C)) ) ) ) ) ).
tt(t11_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_xxreal_0 (k1_algseq_1 A (k2_polynom8 A B C)) (k6_nat_1 (k1_algseq_1 A B) (k1_algseq_1 A C)))) ) ) ) ) ) ).
tt(t11_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l5_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_polynom7 A B C (k6_algstr_0 B D E)) (k5_polynom7 A B (k5_polynom7 A B C E) D))) ) ) ) ) ) ) ) ) ).
tt(t11_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C (k6_poset_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_poset_1 A B))))) )  =>  ((r1_yellow_0 (k6_poset_1 A B) C) &  ((k8_poset_1 A B C) = (k1_yellow_0 (k6_poset_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t11_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~  ( (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B)) ) )  & (v1_abian C)) )  =>  ((k1_power C (k3_xcmplx_0 A B)) = (k3_xcmplx_0 (k1_power C A) (k1_power C B))) ) ) ) ) ) ) ) ).
tt(t11_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_pralg_1 C A B) =>  ((v4_pralg_1 C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k19_margrel1 (k14_pralg_1 A B C D)) = (k19_margrel1 (k14_pralg_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pralg_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( ((k9_xtuple_0 (k2_funct_6 (k12_pralg_2 A B C D))) = A)  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 (k2_funct_6 (k12_pralg_2 A B C D)) E) = (k3_msualg_1 B D (k5_pralg_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pralg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 A D B)) =>  ( ( (E = k1_xboole_0)  &  ((k1_msualg_1 A D) = k1_xboole_0) )  =>  ( ((k3_msualg_1 A D B) = k1_xboole_0)  |  ( ((k3_msualg_1 A D C) = k1_xboole_0)  |  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((k5_msualg_3 A B C D F E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pre_circ,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D (k5_trees_1 A C B)) &  ((r1_tarski C D) &  (! [E:$i] :  ((m1_trees_1 E B) =>  (~  (D = (k8_finseq_1 k5_numbers C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k2_xcmplx_0 (k1_int_1 (k6_power 2 (k4_nat_1 2 A))) 1) = (k1_int_1 (k6_power 2 (k2_nat_1 (k4_nat_1 2 A) 1)))) ) ) ) ) ).
tt(t11_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (~  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = k6_numbers) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 1) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 2) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 3) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 4) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 5) )  &  ( (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 6) )  &  (~  ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 7) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r3_orders_1 C B) =>  ((k3_finseq_1 (k7_pre_poly A B C)) = (k5_card_1 B)) ) ) ) ) ) ) ).
tt(t11_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 1 (k1_newton A B))) ) ) ) ) ).
tt(t11_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t11_prgcor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ( ( (B = k6_numbers)  &  ( (C = A)  &  (D = B) ) )  =>  ( ((k5_int_1 A B) = k6_numbers)  &  ((k3_nat_d C D) = k6_numbers) ) )  &  ( ( ((r1_xxreal_0 k6_numbers A) &  ( (C = A)  &  (D = B) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((k5_int_1 A B) = (k3_nat_d C D)) ) )  &  ( ( ((r1_xxreal_0 k6_numbers A) &  ( (C = A)  &  (D = (k4_xcmplx_0 B)) ) )  =>  ((r1_xxreal_0 k6_numbers B) |  ( ( ((k4_nat_1 D (k3_nat_d C D)) = C)  =>  ((k5_int_1 A B) = (k4_xcmplx_0 (k3_nat_d C D))) )  &  ( (~  ((k4_nat_1 D (k3_nat_d C D)) = C) )  =>  ((k5_int_1 A B) = (k6_xcmplx_0 (k4_xcmplx_0 (k3_nat_d C D)) 1)) ) ) ) )  &  ( ( ( (C = (k4_xcmplx_0 A))  &  (D = B) )  =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 B k6_numbers) |  ( ( ((k4_nat_1 D (k3_nat_d C D)) = C)  =>  ((k5_int_1 A B) = (k4_xcmplx_0 (k3_nat_d C D))) )  &  ( (~  ((k4_nat_1 D (k3_nat_d C D)) = C) )  =>  ((k5_int_1 A B) = (k6_xcmplx_0 (k4_xcmplx_0 (k3_nat_d C D)) 1)) ) ) ) ) )  &  ( ( (C = (k4_xcmplx_0 A))  &  (D = (k4_xcmplx_0 B)) )  =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 k6_numbers B) |  ((k5_int_1 A B) = (k3_nat_d C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (m1_subset_1 (k3_tarski (k10_xtuple_0 B)) (k1_zfmisc_1 A))) ) ) ).
tt(t11_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ((k1_seq_1 F (k6_prob_1 A B (k6_prob_1 A B C D) E)) = (k7_real_1 (k9_real_1 (k7_real_1 (k7_real_1 (k1_seq_1 F C) (k1_seq_1 F D)) (k1_seq_1 F E)) (k7_real_1 (k7_real_1 (k1_seq_1 F (k5_prob_1 A B C D)) (k1_seq_1 F (k5_prob_1 A B D E))) (k1_seq_1 F (k5_prob_1 A B C E)))) (k1_seq_1 F (k5_prob_1 A B (k5_prob_1 A B C D) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (v3_prob_1 (k2_prob_3 A B))) ) ) ).
tt(t11_prob_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k7_numbers A B) & (v2_seq_2 A))  =>  ((k2_rinfsup1 A) = (k2_xxreal_2 (k2_relset_1 k7_numbers B))) ) ) ) ) ) ).
tt(t11_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B B) B) (k4_cqc_the1 A))) ) ) ) ).
tt(t11_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_projdes1 A B C D E) &  ((r1_projdes1 A B C D F) &  ((r1_projdes1 A B C D G) &  ((r1_projdes1 A B C D H) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r1_collsp A E F I) & (r1_collsp A G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r4_projpl_1 A B C D) =>  ((r4_projpl_1 A B D C) &  ((r4_projpl_1 A C B D) &  ((r4_projpl_1 A C D B) &  ((r4_projpl_1 A D B C) & (r4_projpl_1 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E) =>  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B D C) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C B D) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D B) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D B C) E) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D C B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) => (m1_projred2 (k6_partfun1 (k1_projred2 A B)) A)) ) ) ) ).
tt(t11_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m1_prvect_1 B A) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C)) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(t11_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_prvect_2 A B))) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (k4_prvect_2 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (k4_prvect_2 A))) =>  ( ( (E = (k1_funct_1 G B))  &  ( (G = C)  &  ( (F = (k1_funct_1 H B))  &  (H = D) ) ) )  => (r1_xxreal_0 (k1_normsp_0 (k11_prvect_2 A B) (k5_algstr_0 (k11_prvect_2 A B) F E)) (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))))))) )  &  ((v2_funct_1 B) &  ((v2_funct_2 B (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A)))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B C) = (k12_finseq_1 (u1_struct_0 A) C)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B (k3_rlvect_1 A C D)) = (k3_rlvect_1 (k10_prvect_2 (k9_finseq_1 A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B D))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B (k1_rlvect_1 A C D)) = (k1_rlvect_1 (k10_prvect_2 (k9_finseq_1 A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B C) D)) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k10_prvect_2 (k9_finseq_1 A))) B (k4_struct_0 A)) = (k4_struct_0 (k10_prvect_2 (k9_finseq_1 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_pscomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) =>  ((r2_hidden k6_numbers (k2_relset_1 k1_numbers B)) | (v1_pscomp_1 (k7_measure6 (u1_struct_0 A) k1_numbers B) A)) ) ) ) ) ) ).
tt(t11_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r1_tarski B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (m1_eqrel_1 (a_3_1_pua2mss1 A B C) B)) ) ) ) ) ) ).
tt(t11_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( ((k2_nat_1 (k1_pepin A) (k1_pepin B)) = (k1_pepin C))  &  ((r1_int_2 A B) &  ( (~ (v1_abian A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 D E) &  ( (A = (k6_xcmplx_0 (k1_pepin E) (k1_pepin D)))  &  ( (B = (k4_nat_1 (k4_nat_1 2 D) E))  &  (C = (k2_nat_1 (k1_pepin E) (k1_pepin D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k2_pzfmisc1 A B B) (k1_pzfmisc1 A B))) ) ) ).
tt(t11_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ((k7_qc_lang1 A C) = B) ) ) ) ) ) ) ).
tt(t11_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k2_qc_lang2 A B C) = (k2_qc_lang2 A D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v5_qc_lang1 B A) =>  ((k24_qc_lang1 A B) = (k7_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A (k22_qc_lang1 A B)) (k1_tarski (k21_qc_lang1 A B)))) ) ) ) ) ) ).
tt(t11_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k10_xtuple_0 (k2_qc_lang4 A B)) = (k15_qc_lang2 A B)) ) ) ) ) ).
tt(t11_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  ((r3_qmax_1 A B C) <=> (r2_hidden (k1_domain_1 (k1_zfmisc_1 (k5_qmax_1 A)) (k1_zfmisc_1 (k5_qmax_1 A)) (k6_eqrel_1 (k5_qmax_1 A) (k5_qmax_1 A) (k9_qmax_1 A) B) (k6_eqrel_1 (k5_qmax_1 A) (k5_qmax_1 A) (k9_qmax_1 A) C)) (k10_qmax_1 A))) ) ) ) ) ) ) ).
tt(t11_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k6_algstr_0 A B C) D) <=> (r3_lattices A C (k2_quantal1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_quatern2,ax, (k1_quatern2 = (k6_quaterni k6_numbers k6_numbers k6_numbers k6_numbers)) ).
tt(t11_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k5_square_1 (k3_quatern2 A)) = (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A)))) ) ) ).
tt(t11_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  ( ((r2_zfmisc_1 A B C D) &  ((k2_quaterni A B C D E F G H) = (k2_quaterni A B C D I J K L)) )  =>  ( (E = I)  &  ( (F = J)  &  ( (G = K)  &  (H = L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) )  =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t11_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k8_quofield A B (k8_quofield A C D)) = (k8_quofield A (k8_quofield A B C) D))  &  ((k8_quofield A B C) = (k8_quofield A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_radix_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_radix_1 B)) => (v1_int_1 A)) ) ) ) ).
tt(t11_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C (k3_radix_1 A)))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k3_radix_1 A)))  =>  ((r1_xxreal_0 2 A) =>  ((k2_xcmplx_0 (k8_radix_1 B A (k14_radix_1 B A C D)) (k3_xcmplx_0 (k11_radix_1 (k2_xcmplx_0 (k4_radix_1 B A B C) (k4_radix_1 B A B D))) (k1_newton (k1_radix_1 A) B))) = (k2_xcmplx_0 (k8_radix_1 B A C) (k8_radix_1 B A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k4_radix_3 C)))  =>  ((r2_hidden A (k2_finseq_1 B)) => (m2_subset_1 (k1_funct_1 D A) k4_numbers (k4_radix_3 C))) ) ) ) ) ) ) ) ) ).
tt(t11_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k12_radix_1 (k1_radix_1 A) A) = k6_numbers) ) ) ) ).
tt(t11_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 2 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  ((k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k10_radix_1 B (k2_xcmplx_0 A 2) k6_numbers))) = (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_5 (k2_xcmplx_0 A 2) A B)))) ) ) ) ) ) ) ) ).
tt(t11_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k1_nat_1 B 1) (k6_newton A (k2_xcmplx_0 B A)))) ) ) ) ) ).
tt(t11_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_random_1 A) k7_numbers) &  ((v10_valued_0 B) &  ((v6_supinf_2 B) &  ((v4_measure1 B A (k1_random_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_random_1 A) k7_numbers)))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 B A)))  &  (! [D:$i] :  ((m2_finseq_1 D k7_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  (~  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k12_supinf_2 D F) = (k1_extreal1 (k1_measure6 (k1_seq_1 C (k1_funct_1 E F))) (k12_supinf_2 B (k1_tarski (k1_funct_1 E F))))) ) ) )  &  ((k1_mesfunc6 A (k1_random_1 A) B C) = (k4_extreal1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 A))) )  =>  (! [G:$i] :  ((m2_finseq_1 G A) =>  ( ((v2_funct_1 G) &  ((k2_relset_1 A G) = F) )  =>  (! [H:$i] :  ((m2_finseq_1 H B) =>  (! [I:$i] :  ((m2_finseq_1 I (k2_zfmisc_1 A B)) =>  (! [J:$i] :  ( ( (~ (v1_xboole_0 J))  &  ((v1_finset_1 J) & (m1_subset_1 J (k1_zfmisc_1 B))) )  =>  (! [K:$i] :  ( ((v1_finset_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v2_funct_1 H) &  ( ((k2_relset_1 B H) = J)  &  ((v2_funct_1 I) &  ((r2_relset_1 A B (k2_relset_1 (k2_zfmisc_1 A B) I) K) &  ( (K = (k2_zfmisc_1 F J))  &  (! [L:$i] :  (! [M:$i] :  ( ((r2_hidden L F) & (r2_hidden M J))  =>  ((k1_binop_1 E L M) = (k11_binop_2 (k1_seq_1 C L) (k1_seq_1 D M))) ) ) ) ) ) ) ) )  =>  ((k18_rvsum_1 (k4_bhsp_5 k1_numbers (k2_zfmisc_1 A B) E I)) = (k11_binop_2 (k18_rvsum_1 (k4_bhsp_5 k1_numbers A C G)) (k18_rvsum_1 (k4_bhsp_5 k1_numbers B D H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  => (r1_struct_0 (k1_ranknull A C B D) (k4_struct_0 C))) ) ) ) ) ) ) ) ).
tt(t11_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (r1_xxreal_0 1 (k1_rat_1 A))) ) ).
tt(t11_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_polynom3 A))) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k1_funct_1 B C) = (k3_hurwitz A D 1)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (C = (k3_group_4 (k14_polynom3 A) B))  &  (C = (k9_polynom3 A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ((v5_xxreal_2 A) & (v2_rcomp_1 A))  => (v1_rcomp_1 A)) ) ) ).
tt(t11_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_seq_4 (k2_limfunc1 A)) = A) ) ) ).
tt(t11_real_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  <=>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ) ).
tt(t11_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) (k1_funcsdom A k1_numbers (k5_real_lat A) B C) D) (k1_funcsdom A k1_numbers (k5_real_lat A) B (k1_funcsdom A k1_numbers (k5_real_lat A) C D)))) ) ) ) ) ) ) ) ).
tt(t11_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_euclid A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_euclid A))))) )  =>  ( ( (C = B)  & (r1_funct_2 k5_numbers (k1_euclid A) k5_numbers (u1_struct_0 (k4_real_ns1 A)) E D))  =>  ( ((v3_normsp_1 D (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) D) = B) )  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden F (k2_finseq_1 A)) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((k1_seq_1 G H) = (k1_seq_1 (k5_real_ns1 A E H) F))  &  ((v2_comseq_2 G) &  ((k1_seq_1 C F) = (k2_seq_2 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k8_group_1 A B (k5_algstr_0 A C D)) = (k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) C B))) ) ) ) ) ) ) ).
tt(t11_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) =>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) & (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t11_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((k1_relset_1 B (k3_relset_1 A B C)) = (k2_relset_1 B C))  &  ((k2_relset_1 A (k3_relset_1 A B C)) = (k1_relset_1 A C)) ) ) ) ) ) ).
tt(t11_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k9_relat_1 (k3_xboole_0 B C) A) = (k3_xboole_0 (k9_relat_1 B A) (k9_relat_1 C A))) ) ) ) ) ) ).
tt(t11_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k7_partfun1 A (k1_finseq_6 A C B) (k3_finseq_1 (k2_finseq_5 A C B))) = (k7_partfun1 A C (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t11_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k6_numbers))  &  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = C)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k2_nat_1 E 1) (k4_finseq_1 D)))  => (r2_hidden (k4_tarski (k1_funct_1 D E) (k1_funct_1 D (k2_nat_1 E 1))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (~  ((r2_rewrite2 A B C C) &  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (~  ( (C = (k1_flang_1 A (k1_flang_1 A D F) E))  & (r1_rewrite2 A B F F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((k1_flang_1 A B C) = (k1_flang_1 A D E))  =>  ( ( (~  ((k1_afinsq_1 B) = (k1_afinsq_1 D)) )  &  (~  ((k1_afinsq_1 C) = (k1_afinsq_1 E)) ) )  |  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ( ((k3_rfinseq2 (k6_rvsum_1 A)) = (k1_real_1 (k4_rfinseq2 A)))  &  ((k1_rfinseq2 (k6_rvsum_1 A)) = (k2_rfinseq2 A)) ) ) ) ) ).
tt(t11_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_real_1 D 2))  &  ( ((k1_seq_1 A (k3_real_1 D 1)) = B)  &  ((k1_seq_1 A (k3_real_1 D 2)) = C) ) )  =>  ((k3_rfinseq A) = (k8_finseq_1 k1_numbers (k17_finseq_1 k1_numbers D (k3_rfinseq A)) (k2_finseq_4 k1_numbers (k9_real_1 B C) C))) ) ) ) ) ) ) ) ) ) ).
tt(t11_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k18_valued_1 A (k1_valued_1 B C)) = (k1_valued_1 (k18_valued_1 A B) (k18_valued_1 A C))) ) ) ) ) ) ) ).
tt(t11_rfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A (k6_rfunct_1 A k1_numbers B))) => (v2_relat_1 (k8_funct_2 k5_numbers k1_numbers A C B))) ) ) ) ) ) ) ).
tt(t11_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~  (E = k6_numbers) )  =>  ((r2_classes1 C D) <=> (r2_classes1 (k26_valued_1 A k1_numbers C E) (k26_valued_1 B k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((r1_rfunct_4 B C) <=> (r1_rfunct_4 (k15_valued_1 k1_numbers k1_numbers B A) C)) ) ) ) ) ) ).
tt(t11_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) <=> (v2_seq_2 (k32_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t11_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v3_rinfsup2 A) =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ).
tt(t11_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_ring_1 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t11_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( ((k1_ringcat1 (k5_ringcat1 A)) = A)  &  ( ((k2_ringcat1 (k5_ringcat1 A)) = A)  &  ( (! [B:$i] :  ( ((v2_ringcat1 B) &  ((v3_ringcat1 B) & (l1_ringcat1 B)) )  =>  ( ((k2_ringcat1 B) = A)  =>  ((k6_ringcat1 (k5_ringcat1 A) B) = B) ) ) )  &  (! [B:$i] :  ( ((v2_ringcat1 B) &  ((v3_ringcat1 B) & (l1_ringcat1 B)) )  =>  ( ((k1_ringcat1 B) = A)  =>  ((k6_ringcat1 B (k5_ringcat1 A)) = B) ) ) ) ) ) ) ) ) ).
tt(t11_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_convex1 A B 1) = B) ) ) ) ) ).
tt(t11_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ((v2_convex1 C A) & (r2_hidden (k6_rlvect_2 A C) (k1_rlaffin2 A B)))  =>  ((k3_rlvect_2 A C) = B) ) ) ) ) ) ) ) ).
tt(t11_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_hidden (k5_euclid A) B) =>  ((k4_rlaffin1 (k15_euclid A) B) = (k2_struct_0 (k1_rlvect_3 (k15_euclid A) B))) ) ) ) ) ) ).
tt(t11_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t11_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ( ((k1_rlsub_2 A (k2_rlsub_1 A) B) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  &  ((k1_rlsub_2 A B (k2_rlsub_1 A)) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ).
tt(t11_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B D) & (r1_tarski C E))  => (r1_tarski (k6_rusub_4 A B C) (k6_rusub_4 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( ((k1_rlvect_1 B C A) = (k4_struct_0 B))  &  ( (~  (A = k6_numbers) )  &  (~  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (B = D) )  &  (~  ((k2_rlvect_2 A (k8_domain_1 (u1_struct_0 A) B C D)) = (k3_rlvect_1 A (k3_rlvect_1 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B (k4_struct_0 A)) A))  &  (~ (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) (k4_struct_0 A) B) A)) ) ) ) ) ) ).
tt(t11_rlvect_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_struct_0 (k1_rlvect_3 B (k7_domain_1 (u1_struct_0 B) C D)) A) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (A = (k3_rlvect_1 B (k1_rlvect_1 B C E) (k1_rlvect_1 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  (? [D:$i] :  ((m1_rlvect_2 D A) &  ( ((k3_rlvect_2 B C) = (k3_rlvect_2 A D))  &  ((k6_rlvect_2 B C) = (k6_rlvect_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t11_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r2_hidden (k4_struct_0 A) (k2_rlvect_x A B))) ) ) ) ).
tt(t11_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ((k4_struct_0 C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t11_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ( ((k1_rmod_3 A B (k2_rmod_2 A B) C) = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B)))  &  ((k1_rmod_3 A B C (k2_rmod_2 A B)) = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B))) ) ) ) ) ) ) ) ).
tt(t11_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k9_subset_1 (u1_struct_0 B) C D)) = (k5_algstr_0 B (k3_rlvect_1 B (k1_rmod_4 A B C) (k1_rmod_4 A B D)) (k1_rmod_4 A B (k4_subset_1 (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t11_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A C (k3_robbins1 A C)))) = B) ) ) ) ) ) ) ).
tt(t11_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) D)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C)))) C)) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t11_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v5_lattices A))  => (v5_lattices B)) ) ) ) ) ).
tt(t11_robbins4,ax, (! [A:$i] :  ((r2_hidden A (u1_struct_0 k2_robbins4)) => (r1_tarski A (k1_enumset1 k6_numbers 1 2))) ) ).
tt(t11_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k2_rcomp_1 A B)) => (r1_xxreal_0 k6_numbers (k1_fdiff_1 C D))) ) ) ) )  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) ) ) ) ) ) ) ).
tt(t11_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) C) B))  => (r2_hidden C (k4_roughs_1 A B))) ) ) ) ) ) ) ).
tt(t11_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((r1_tarski B (k4_subset_1 A C (k3_subset_1 A C))) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski B (k3_subset_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t11_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_rsspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  => (v4_xxreal_2 (k7_rsspace4 A B C))) ) ) ) ) ) ).
tt(t11_rsspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  ((v1_xboole_0 B) | (m1_rlsub_1 (g1_rlvect_1 B (k10_rsspace A B) (k8_rsspace A B) (k9_rsspace A B)) A)) ) ) ) ) ) ).
tt(t11_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (r1_struct_0 B (k4_struct_0 A))) ) ) ) ).
tt(t11_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ( ((k1_rusub_2 A (k2_rusub_1 A) B) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)))  &  ((k1_rusub_2 A B (k2_rusub_1 A)) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ).
tt(t11_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B C) &  ((v1_rlvect_3 C A) &  ((k1_rusub_3 A C) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ( ((k1_rusub_4 A) = (k1_rusub_4 B))  <=>  ((k2_rusub_1 A) = (k2_rusub_1 B)) ) ) ) ) ) ).
tt(t11_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r1_tarski (k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) D)) (k1_rusub_5 A B C))) ) ) ) ) ) ) ) ) ).
tt(t11_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 B k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 B k1_numbers)) =>  ((k1_seq_1 (k5_rvsum_1 B C D) A) = (k9_binop_2 (k1_seq_1 C A) (k1_seq_1 D A))) ) ) ) ) ) ) ) ).
tt(t11_rvsum_2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C k2_numbers))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D k2_numbers))  =>  ((k1_funct_1 (k8_rvsum_2 B C D) A) = (k4_binop_2 (k1_funct_1 C A) (k1_funct_1 D A))) ) ) ) ) ) ) ) ).
tt(t11_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D B)) = C)  &  ((k3_compos_1 k1_ami_3 A C) = (k9_ami_3 F E)) )  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) E) k6_numbers))  =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = F) )  &  ( ((r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) E) k6_numbers) =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = (k2_nat_1 C 1)) )  &  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) G) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ( ( (~  (B = (k16_scmfsa_2 D C)) )  &  (~  (B = (k17_scmfsa_2 D C)) ) )  | (r2_hidden D (k2_sf_mastr A))) ) ) ) ) ) ) ) ) ) ).
tt(t11_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k17_scm_comp A)) =>  ((k1_funct_1 B (k10_ami_3 D)) = (k1_funct_1 C (k10_ami_3 D))) ) ) )  =>  ((k12_scm_comp B A) = (k12_scm_comp C A)) ) ) ) ) ) ) ) ).
tt(t11_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k7_scmfsa_2 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t11_scmfsa_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_scmfsa_1 k3_scmfsa_1) =>  ((k1_funct_1 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1) A) = (k3_finseq_2 k4_numbers)) ) ) ).
tt(t11_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((k4_memstr_0 3 k1_scmfsa_2 A) = k4_numbers) ) ) ).
tt(t11_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k12_scmfsa_2 I H))  =>  ( (I = (k1_ordinal1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G))))  |  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) = k6_numbers)  <=>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v7_amistd_1 C 3 k1_scmfsa_2) & (v1_scmfsa6b C)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa6b C A B) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ).
tt(t11_scmfsa6c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k4_sf_mastr (k1_scmfsa6c A B)) = k1_xboole_0) ) ) ) ) ).
tt(t11_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r3_scmfsa7b (k11_scmfsa_2 B) A)) ) ) ) ) ).
tt(t11_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  &  ( (~ (r4_scmfsa7b B C))  & (r4_scmfsa7b (k1_funct_4 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t11_scmfsa8b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k1_scmfsa8b C A B)) = (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 4)) ) ) ) ) ) ) ).
tt(t11_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k1_scmfsa_9 A B)) = (k1_finsub_1 (k1_zfmisc_1 k2_scmfsa_2) (k4_scmfsa_m A) (k2_sf_mastr B))) ) ) ) ) ).
tt(t11_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa_9 A B) k6_numbers) = (k12_scmfsa_2 4 A))  &  ( ((k1_funct_1 (k1_scmfsa_9 A B) 1) = (k11_scmfsa_2 2))  &  ( ((k1_funct_1 (k2_scmfsa_9 A B) k6_numbers) = (k13_scmfsa_2 4 A))  &  ((k1_funct_1 (k2_scmfsa_9 A B) 1) = (k11_scmfsa_2 2)) ) ) ) ) ) ) ) ).
tt(t11_scmfsa_m,ax, ((k9_xtuple_0 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) = (k7_domain_1 (u1_struct_0 k1_scmfsa_2) (k4_scmfsa_2 k6_numbers) (k4_struct_0 k1_scmfsa_2))) ).
tt(t11_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scm_halt C)) ) ) ) ) ) )  =>  ( ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) &  ((r1_tarski (k2_scmfsa6a C) B) & (r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) A)) )  =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) 1))) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t11_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) |  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k1_scmfsa_m B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3))) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3)) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k1_scmfsa_m B) E)) (k9_xtuple_0 (k2_scmfsa_9 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r2_hidden A (k3_enumset1 9 10 11 12 13)) => (r2_hidden (k3_xtuple_0 A k1_xboole_0 (k7_finseq_4 B C D E)) k1_scmpds_i)) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k16_scmpds_2 J K H I))  &  ((r2_hidden J (k9_xtuple_0 D)) & (r2_hidden (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) J) H) (k9_xtuple_0 D))) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) K) I)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) K) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmpds_4 (k1_scmpds_4 B C) A) = (k1_scmpds_4 B (k3_scmpds_4 C A))) ) ) ) ) ) ) ).
tt(t11_scmpds_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 D (k10_compos_1 k1_scmpds_2 (k2_scmpds_4 A C))) (k8_memstr_0 2 k1_scmpds_2 B)) = A) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r1_scmpds_6 E C A) &  ((r2_scmpds_6 E C A) &  ((k6_memstr_0 2 k1_scmpds_2 C) = (k6_memstr_0 2 k1_scmpds_2 D)) ) )  =>  ( ((k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 E)) (k8_memstr_0 2 k1_scmpds_2 C)) = (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 E)) (k8_memstr_0 2 k1_scmpds_2 D)))  &  ((k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 E)) (k8_memstr_0 2 k1_scmpds_2 C)) = (k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 E)) (k8_memstr_0 2 k1_scmpds_2 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k1_scmpds_8 D E C) B A)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k1_amistd_1 2 k1_scmpds_2 C (k13_scmpds_2 A B D E)) = (k1_tarski (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k4_scmp_gcd A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A B 4)) = 5)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B 4) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B 4) k3_scmp_gcd) = 7)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B 4) (k1_scmp_gcd (k2_nat_1 7 k15_scmpds_i))) = 2)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B 4) (k1_scmp_gcd 9)) = (k1_funct_1 B (k1_scmp_gcd 9)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B 4) (k1_scmp_gcd 10)) = (k1_funct_1 B (k1_scmp_gcd 10))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (k4_scmring1 A B C D) C) = D) ) ) ) ) ) ) ) ) ).
tt(t11_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k3_scmring2 A B C) D) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) D)))  &  ( ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k3_scmring2 A B C) D) B) = (k2_scmring2 A D C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 A))))  =>  ( (~  (E = B) )  =>  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k3_scmring2 A B C) D) E) = (k2_scmring2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) (k9_scmring2 A C B)) = 7) ) ) ) ) ) ) ).
tt(t11_scmring4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 B))))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 E (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 F (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 I) &  ((v1_finset_1 I) &  (~ (v2_compos_1 I (k1_scmring2 B))) ) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 (k1_scmring2 B))) &  ( (~ (v1_xboole_0 J))  &  ((v1_finset_1 J) & (v4_extpro_1 J 2 (k1_scmring2 B) I)) ) ) ) ) )  =>  ( ((r1_tarski J E) &  ((r1_tarski J F) &  ((r1_tarski I G) &  ((r1_tarski I H) &  ((k3_extpro_1 2 (k1_scmring2 B) G (k5_extpro_1 2 (k1_scmring2 B) G E A)) = (k9_scmring2 B D C)) ) ) ) )  =>  ( (D = (k1_ordinal1 (k5_memstr_0 2 (k1_scmring2 B) (k5_extpro_1 2 (k1_scmring2 B) G E A))))  |  ( ((k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) G E A) C) = (k4_struct_0 B))  <=>  ((k2_scmring2 B (k5_extpro_1 2 (k1_scmring2 B) H F A) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_hidden (k3_xtuple_0 7 (k12_finseq_1 k5_numbers C) (k12_finseq_1 k2_scm_inst B)) (k1_scmringi A))) ) ) ) ) ) ).
tt(t11_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden B (k1_scmyciel A)) &  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (C = D) )  &  ((r2_hidden C (k3_tarski A)) &  ((r2_hidden D (k3_tarski A)) &  (B = (k2_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k4_scpinvar A B C) k6_numbers) = (k7_scmpds_2 A B 2))  &  ( ((k1_funct_1 (k4_scpinvar A B C) 1) = (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))  &  ((k1_funct_1 (k4_scpinvar A B C) (k2_nat_1 (k5_card_1 C) 2)) = (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ).
tt(t11_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 B F) H) (k1_funct_1 B E)) &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 J F) H) (k1_funct_1 J E)) &  ((k1_funct_1 J D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) G)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) D) = (k1_funct_1 J D))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) (k2_scmpds_2 (k1_funct_1 B D) G)) = (k6_xcmplx_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) G)) I))  &  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) & (r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) F) H) (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) E))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 I k6_numbers) |  ((r1_scmpds_6 (k2_scmpds_7 D G I C) B A) & (r2_scmpds_6 (k2_scmpds_7 D G I C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k4_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k4_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ((r1_xxreal_0 (k2_nat_1 D 1) C) &  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 4)) (k2_nat_1 D E)) &  ((r1_xxreal_0 7 D) &  ((r1_scpisort F B D) &  ( ((k3_finseq_1 F) = E)  &  ((r1_scpisort G (k6_scmpds_4 k1_scpqsort B A) D) &  ((k3_finseq_1 G) = E) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) (k1_funct_1 B (k1_scmp_gcd 2))) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd 1)) = (k1_funct_1 B (k1_scmp_gcd 1)))  &  ((r2_classes1 F G) &  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ( (H = (k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd 4)))  &  ((r1_xxreal_0 C H) &  ((r1_xxreal_0 H (k1_funct_1 B (k1_scmp_gcd 4))) &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 C I) =>  ((r1_xxreal_0 H I) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd I)) (k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd H)))) ) ) )  &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 I (k1_funct_1 B (k1_scmp_gcd 4))) =>  ((r1_xxreal_0 I H) | (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd H)) (k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd I)))) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 D 1) I) =>  ( ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd 2)) I) & (r1_xxreal_0 I (k1_funct_1 B (k1_scmp_gcd 4))))  |  ((k1_funct_1 (k6_scmpds_4 k1_scpqsort B A) (k1_scmp_gcd I)) = (k1_funct_1 B (k1_scmp_gcd I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A C E C D) & (r2_analoaf A E B E D)) )  => (r2_analoaf A B C B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A B) (k3_valued_1 k5_numbers k1_numbers k1_numbers A (k32_valued_1 k5_numbers k1_numbers B)))) ) ) ) ).
tt(t11_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  => (v2_comseq_2 (k47_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t11_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v5_xxreal_2 A) =>  ((v1_xboole_0 A) | (r1_xxreal_0 (k5_seq_4 A) (k4_seq_4 A))) ) ) ) ).
tt(t11_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k2_seqfunc A B 1) B)) ) ) ) ).
tt(t11_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A k6_numbers) (k8_nat_1 k1_numbers A B))) ) ) ) ) ).
tt(t11_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers B C) = (k3_funct_2 k5_numbers k1_numbers A k6_numbers)) ) )  => (r2_funct_2 k5_numbers k1_numbers (k3_series_1 (k1_valued_0 k1_numbers A 1)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers (k3_series_1 A) 1) B))) ) ) ) ) ).
tt(t11_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 1 (k4_nat_1 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 2)) (k2_nat_1 B 3)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 1 18) (k13_complex1 1 (k4_nat_1 (k4_nat_1 (k4_nat_1 3 (k2_nat_1 B 1)) (k2_nat_1 B 2)) (k2_nat_1 B 3))))) ) ) ) ) ) ).
tt(t11_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_xxreal_0 (k8_real_1 3 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 B C)) (k3_xcmplx_0 A C))) (k3_square_1 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)))) ) ) ) ) ) ).
tt(t11_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k1_newton (k7_xcmplx_0 1 A) C)) ) )  =>  ( (A = 1)  |  ( (A = k6_numbers)  |  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 (k3_series_1 B) C) = (k7_xcmplx_0 (k6_xcmplx_0 (k1_newton (k7_xcmplx_0 1 A) C) A) (k6_xcmplx_0 1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t11_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k6_square_1 (k3_xcmplx_0 A B)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)))) ) ) ) ).
tt(t11_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((k1_setfam_1 (k2_tarski A B)) = (k3_xboole_0 A B)) ) ) ).
tt(t11_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C D) = B) ) )  =>  ((k3_prob_1 A C) = B) ) ) ) ) ) ) ).
tt(t11_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k5_subset_1 A (k1_prob_1 A B) (k1_prob_1 A C)) (k1_prob_1 A (k4_setlim_2 A B C)))) ) ) ) ) ).
tt(t11_setwiseo,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ((r1_tarski C B) => (m1_subset_1 C (k5_finsub_1 A))) ) ) ) ) ).
tt(t11_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 D B) &  ((v2_binop_1 D B) &  ((v1_setwiseo D B) &  ((v1_finseqop D B) & (r8_binop_1 B B B E (k7_finseqop B D (k6_partfun1 B) (k5_finseqop B D)))) ) ) )  =>  ((k5_binop_1 B E (k7_setwiseo A B D C F) (k7_setwiseo A B D C G)) = (k7_setwiseo A B D C (k6_funcop_1 B A E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b C (k1_scmfsa_m B) A)) )  =>  ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a C D) B A) E) = (k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa6b C B A)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( (~  ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C)) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) k6_numbers) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) k6_numbers) B) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ( ((k16_scmfsa_2 A C) = (k16_scmfsa_2 B D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sgraph1,ax, ((k2_sgraph1 k1_xboole_0) = k1_xboole_0) ).
tt(t11_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  => (v9_lattices A)) ) ).
tt(t11_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C B)) = B) ) ) ) ) ) ) ).
tt(t11_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v6_ordinal1 A) => (v6_ordinal1 (k2_xboole_0 A (k1_tarski (k2_xboole_0 (k3_tarski A) B))))) ) ) ).
tt(t11_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) => (m1_simplex1 B A B)) ) ) ) ).
tt(t11_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v3_pre_topc C (k4_simplex1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_simplex1 A B)))))  =>  (! [D:$i] :  ( ((v6_ordinal1 D) &  ((v1_finset_1 D) &  ((v5_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ( (C = (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) D))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden E C) &  ((r2_hidden F C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ((r2_hidden G (k4_simplex0 (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k5_setfam_1 (u1_struct_0 A) D)))))) &  ((r2_hidden H (k4_simplex0 (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k5_setfam_1 (u1_struct_0 A) D)))))) &  ( ((k5_algstr_0 A E F) = (k1_rlvect_1 A (k5_algstr_0 A G H) I))  &  ((r1_xxreal_0 k1_xboole_0 I) & (r1_xxreal_0 I (k13_complex1 (k5_real_1 (k5_card_1 (k5_setfam_1 (u1_struct_0 A) D)) 1) (k5_card_1 (k5_setfam_1 (u1_struct_0 A) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t11_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 k19_sin_cos A) = (k1_seq_1 k19_sin_cos (k7_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A))) ) ) ) ) ).
tt(t11_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A B)) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B)))) ) ) ) ) ).
tt(t11_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  ( (~  ((k20_sin_cos C) = k6_numbers) )  &  (~  ((k17_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) (k20_sin_cos C)) (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) (k1_sin_cos4 C)) (k3_xcmplx_0 (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) (k1_sin_cos4 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k20_sin_cos A) = k6_numbers) )  =>  ((k5_square_1 (k4_sin_cos4 A)) = (k7_real_1 1 (k5_square_1 (k1_sin_cos4 A)))) ) ) ) ).
tt(t11_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k8_real_1 (k8_real_1 2 k32_sin_cos) B)))  &  ( (~ (r1_xxreal_0 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 (k17_sin_cos A) k6_numbers)) ) ) ) ) ) ) ).
tt(t11_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  =>  ( (~ (r1_xxreal_0 (k9_binop_2 A 1) k6_numbers))  &  (~ (r1_xxreal_0 (k10_binop_2 1 A) k6_numbers)) ) ) ) ) ).
tt(t11_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k6_xcmplx_0 (k6_sin_cos2 (k2_xcmplx_0 A B)) (k6_sin_cos2 (k6_xcmplx_0 A B)))))  &  ( ((k3_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k2_xcmplx_0 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k3_sin_cos2 (k6_xcmplx_0 A B)))))  &  ( ((k3_xcmplx_0 (k6_sin_cos2 A) (k3_sin_cos2 B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k6_xcmplx_0 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k3_sin_cos2 (k6_xcmplx_0 A B)))))  &  ((k3_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k2_xcmplx_0 (k6_sin_cos2 (k2_xcmplx_0 A B)) (k6_sin_cos2 (k6_xcmplx_0 A B))))) ) ) ) ) ) ) ) ).
tt(t11_sin_cos9,ax, ((k2_relset_1 k1_numbers k1_sin_cos9) = (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) ).
tt(t11_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) =>  ((k8_nat_1 k2_numbers (k10_sin_cos (k2_nat_1 D 1) A B) C) = (k8_complex1 (k8_nat_1 k2_numbers (k10_sin_cos D A B) C) (k8_nat_1 k2_numbers (k9_sin_cos (k2_nat_1 D 1) A B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t11_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_sppol_1 A B (k1_rltopsp1 (k15_euclid A) B C))) ) ) ) ) ) ).
tt(t11_sppol_2,ax, ((k3_topreal1 2 (k6_finseq_1 (u1_struct_0 (k15_euclid 2)))) = k1_xboole_0) ).
tt(t11_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k20_pscomp_1 A) A) & (r2_hidden (k21_pscomp_1 A) A)) ) ) ).
tt(t11_sprect_2,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) &  ((k18_euclid B) = (k9_pscomp_1 A)) )  => (r2_hidden B (k17_pscomp_1 A))) ) ) ) ) ).
tt(t11_sprect_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) &  ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) D C)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) D C)) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t11_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k10_xtuple_0 A)) &  ((r2_hidden C (k10_xtuple_0 A)) &  ((r2_hidden D (k10_xtuple_0 A)) &  ( (~ (r1_xxreal_0 (k4_finseq_4 A C) (k4_finseq_4 A B)))  &  ( (~ (r1_xxreal_0 (k4_finseq_4 A D) (k4_finseq_4 A C)))  & (r1_xxreal_0 (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A D) C) (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A D) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  ((k6_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) = k6_numbers) )  =>  ((k7_xcmplx_0 1 (k6_xcmplx_0 A B)) = (k7_xcmplx_0 (k2_xcmplx_0 A B) (k6_xcmplx_0 (k3_square_1 A) (k3_square_1 B)))) ) ) ) ) ) ).
tt(t11_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k8_stacks_1 A))) =>  ((k9_stacks_1 (k8_stacks_1 A) B) = B) ) ) ) ) ).
tt(t11_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_nat_1 A) = k6_numbers) ) ) ).
tt(t11_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ( (~ (r2_hidden B (k9_xtuple_0 (k19_substut1 A E))))  =>  ((k3_funct_2 (k3_qc_lang1 A) C (k1_sublemma A C D (k3_sublemma A E C D)) B) = (k3_funct_2 (k3_qc_lang1 A) C D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k4_subset_1 A B (k2_subset_1 A)) = (k2_subset_1 A)) ) ) ) ).
tt(t11_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k3_substlat A B C) = C) ) ) ) ) ).
tt(t11_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v4_substut1 B A) => (v2_qc_lang1 (k18_substut1 A B) A)) ) ) ) ) ).
tt(t11_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (? [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A E) = B)  &  ((k19_substut1 A E) = D) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (? [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A E) = (k11_cqc_lang A C B))  &  ((k19_substut1 A E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  ( ((v3_xxreal_2 A) & (v3_xxreal_2 B))  => (r1_xxreal_0 (k3_supinf_2 (k7_supinf_2 A) (k7_supinf_2 B)) (k7_supinf_2 (k5_supinf_2 A B)))) ) ) ) ) ).
tt(t11_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_orders_2 B (k5_algstr_0 B C D) E) & (r1_orders_2 B (k5_algstr_0 B C F) E))  => (r1_orders_2 B (k5_algstr_0 B D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) => (r1_tarski (k2_relat_1 A) (k2_relat_1 B))) ) ) ) ) ).
tt(t11_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_borsuk_1 A A D E) (k1_t_0topsp A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_setfam_1 (k10_eqrel_1 A) (k1_tarski A))) ) ).
tt(t11_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (B = k1_xboole_0)  => (v5_taxonom2 B A)) ) ) ) ).
tt(t11_taylor_1,ax, (~ (r1_xxreal_0 k8_power 2)) ).
tt(t11_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) =>  ((r1_xxreal_0 F k6_numbers) |  ((r1_xxreal_0 1 F) | (r1_xxreal_0 (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D))) (k10_real_1 (k8_real_1 B (k2_newton C D)) (k3_newton D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((v6_metric_1 A) =>  ((r1_xxreal_0 C k6_numbers) | (r2_hidden B (k9_metric_1 A B C))) ) ) ) ) ) ) ) ).
tt(t11_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_tdgroup A B C D E) & (r1_tdgroup A B F D G))  => (r1_tdgroup A C F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A B)) B) C))) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A B)) B) C)) = (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t11_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_pcomps_1 A B) (k1_pcomps_1 A C)) (k1_pcomps_1 A (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)))) ) ) ) ) ) ).
tt(t11_tdlat_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((r2_hidden k1_xboole_0 (u1_pre_topc A)) &  ((r2_hidden (u1_struct_0 A) (u1_pre_topc A)) &  ((k9_setfam_1 (u1_struct_0 A)) = (k2_tarski k1_xboole_0 (u1_struct_0 A))) ) )  =>  ((v1_tdlat_3 A) & (v2_tdlat_3 A)) ) ) ) ).
tt(t11_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r6_pboole A (k1_termord A B C D) C) | (r6_pboole A (k1_termord A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t11_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 B))  =>  ((k2_pre_topc A B) = (u1_struct_0 A)) ) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t11_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v1_tex_2 B A))  & (m1_pre_topc B A))  =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) ) ) ) ) ).
tt(t11_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v1_tops_1 D B) <=> (v1_tops_1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_domain_1 (u1_struct_0 A) B) = (k6_setfam_1 (u1_struct_0 A) (k1_tex_4 A B))) ) ) ) ) ).
tt(t11_tietze,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r1_seqfunc A k1_numbers C B) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (v1_xreal_0 E))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_tietze (k45_valued_1 (k1_seqfunc A k1_numbers C G) F) (k3_xcmplx_0 D (k3_power E G)) B)) )  =>  ((r1_xxreal_0 1 E) |  ((r2_seqfunc A C B) &  ((k11_seqfunc A C B) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_tsep_1 A B C))) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  (E = D) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  ((r1_tarski A B) =>  ((v1_relat_2 (k1_toler_1 C A)) &  ((v3_relat_2 (k1_toler_1 C A)) &  ((v1_partfun1 (k1_toler_1 C A) A) & (m1_subset_1 (k1_toler_1 C A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ).
tt(t11_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k17_borsuk_1)) => (r1_xxreal_0 (k12_euclid (k9_euclid A B C)) (k12_euclid B))) ) ) ) ) ) ).
tt(t11_topalg_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v1_borsuk_2 (k4_topmetr A B))) ) ) ) ) ).
tt(t11_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (B = (k1_tarski (u1_struct_0 A)))  &  ((m1_setfam_1 B (u1_struct_0 A)) & (v1_tops_2 B A)) ) ) ) ) ) ).
tt(t11_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) => (r1_borsuk_6 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ( (C = D)  & (v2_connsp_2 C A))  => (v2_connsp_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t11_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_topalg_6 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  (! [D:$i] :  ((m1_borsuk_2 D A B B) => (r3_borsuk_2 A B B C D)) ) ) ) ) ) ) ) ) ).
tt(t11_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( ((v2_topdim_1 B A) & (r1_xxreal_0 (k3_topdim_1 A B) C))  =>  ((r1_xxreal_0 (k1_real_1 1) C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D B) =>  ((v1_topdim_1 D A) & (r1_xxreal_0 (k2_topdim_1 A D) C)) ) ) ) ) )  &  ( ((r1_xxreal_0 (k1_real_1 1) C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D B) =>  ((v1_topdim_1 D A) & (r1_xxreal_0 (k2_topdim_1 A D) C)) ) ) ) )  =>  ((v2_topdim_1 B A) & (r1_xxreal_0 (k3_topdim_1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t11_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v4_pre_topc C B) &  ((v4_pre_topc D B) & (r1_xboole_0 C D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r1_xxreal_0 (k2_topdim_1 B E) A) &  ((v5_waybel23 (k1_pre_topc B E)) &  ((v3_topdim_1 (k1_pre_topc B E)) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_metrizts B C D F) & (r1_xxreal_0 (k2_topdim_1 B (k9_subset_1 (u1_struct_0 B) F E)) (k3_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_tops_1 A B)) <=>  (? [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) =>  ( (~ (r1_xboole_0 B E))  &  (~  ((k7_subset_1 (u1_struct_0 A) E B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (? [C:$i] :  ( ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  &  ((r1_tarski C B) &  ( ((k5_setfam_1 (u1_struct_0 A) C) = (k5_setfam_1 (u1_struct_0 A) B))  & (r1_ordinal1 (k1_card_1 C) (k2_waybel23 A))) ) ) ) ) ) ) ) ).
tt(t11_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v3_pre_topc (k3_rcomp_1 A B) k2_topgen_3) & (m1_subset_1 (k3_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ) ) ).
tt(t11_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((v7_topgen_1 A) <=> (v1_orders_4 A)) ) ) ).
tt(t11_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v4_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_pre_topc A C) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 B)) &  ((v5_pre_topc F (k1_pre_topc A D) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k1_funct_4 E F)) &  ((v1_funct_2 (k1_funct_4 E F) (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) (u1_struct_0 B)) &  ((v5_pre_topc (k1_funct_4 E F) (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D)) B) & (m1_subset_1 (k1_funct_4 E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_group_1 A) B) = (k1_group_2 A B)) ) ) ) ) ).
tt(t11_topmetr3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ((v4_xxreal_2 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v7_valued_0 B) &  ((v2_comseq_2 B) &  ((r1_tarski (k2_relset_1 k1_numbers B) A) &  ((k2_seq_2 B) = (k4_seq_4 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topmetr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_metric_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_metric_1)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = A)  &  (D = B) )  =>  ((k4_metric_1 k8_metric_1 A B) = (k18_complex1 (k6_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t11_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) D C B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) E D) B) = (k1_tarski D)) )  => (r1_topreal1 (k15_euclid A) E C (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) E D) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))) =>  ((k17_euclid A) = B) ) ) ) ) ) ) ) ) ) ).
tt(t11_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) = (k18_euclid A))  &  ((v4_topreal1 B) &  ((r2_hidden A (k2_topreal1 2 B 1)) &  (C = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k17_euclid A)) 2) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) A)) ) ) )  =>  ( (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  |  ((v4_topreal1 C) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = A)  &  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) &  ((r1_tarski (k3_topreal1 2 C) (k3_topreal1 2 B)) &  ((k3_topreal1 2 C) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 1 B)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_topreal5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr))))) )  =>  ( (A = k5_pscomp_1)  => (v5_pre_topc A (k15_euclid 2) k3_topmetr)) ) ) ).
tt(t11_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k12_rvsum_1 (k2_finseq_4 k1_numbers A B)) = (k2_finseq_4 k1_numbers (k5_square_1 A) (k5_square_1 B))) ) ) ) ) ).
tt(t11_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k3_euclid (k8_finseq_1 k1_numbers A B)) = (k8_finseq_1 k1_numbers (k3_euclid A) (k3_euclid B))) ) ) ) ) ).
tt(t11_topreal8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_zfmisc_1 C))  & (m2_finseq_1 C A))  =>  ( ((k7_partfun1 A C (k3_finseq_1 C)) = (k7_partfun1 A B 1))  => (v1_finseq_6 (k4_graph_2 A B C) A)) ) ) ) ) ) ) ).
tt(t11_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden C (k2_topreal9 A (k4_struct_0 (k15_euclid A)) B)) => (r1_xxreal_0 (k12_euclid C) B)) ) ) ) ) ) ) ).
tt(t11_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v1_t_0topsp D A B) & (v1_t_0topsp E B C))  => (v1_t_0topsp (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_toprealb,ax, (! [A:$i] :  ( ((v1_toprealb A) & (m1_pre_topc A (k15_euclid 2)))  =>  (! [B:$i] :  ( ((v1_toprealb B) & (m1_pre_topc B (k15_euclid 2)))  => (r2_borsuk_3 A B)) ) ) ) ).
tt(t11_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k12_euclid (k8_rvsum_1 (k2_finseq_2 A B) (k2_finseq_2 A C))) = (k3_xcmplx_0 (k6_square_1 A) (k18_complex1 (k6_xcmplx_0 B C)))) ) ) ) ) ) ) ).
tt(t11_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k3_toprns_1 A B) = (k2_toprns_1 (k1_real_1 1) A B)) ) ) ) ) ).
tt(t11_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_pre_topc C A))  => (v3_pre_topc (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t11_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B C) & (v1_tops_2 C A))  => (v1_tops_2 B A)) ) ) ) ) ) ) ).
tt(t11_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_tops_1 B A) & (r1_tarski C B))  => (v2_tops_1 C A)) ) ) ) ) ) ) ).
tt(t11_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k3_topmetr) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A))))) )  =>  ((v1_t_0topsp B k3_topmetr A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_topmetr)) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 A) B C) E) & (r1_tarski E (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A) B (k2_rcomp_1 (k6_xcmplx_0 C D) (k2_xcmplx_0 C D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k3_funct_2 A A C B) = B)  =>  ((k3_funct_2 A A (k2_transgeo A C D) (k3_funct_2 A A D B)) = (k3_funct_2 A A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t11_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v7_transgeo C A) &  ((v7_transgeo D A) & (r2_analoaf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C B) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B))) )  => (r2_analoaf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C B) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_transgeo (u1_struct_0 A) D C) B))) ) ) ) ) ) ) ) ) ).
tt(t11_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_topmetr A B))) =>  ((k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 A B C D) E) = (k2_xcmplx_0 (k3_xcmplx_0 (k13_complex1 (k6_xcmplx_0 D C) (k6_xcmplx_0 B A)) E) (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 B C) (k3_xcmplx_0 A D)) (k6_xcmplx_0 B A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_trees_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden A (k1_trees_1 B)) =>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) ) ) ) ).
tt(t11_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m4_trees_1 B A) =>  (! [C:$i] :  ((m1_trees_2 C A) =>  (? [D:$i] :  ((m1_trees_1 D A) & (r1_tarski (k9_subset_1 A B C) (k1_tarski D))) ) ) ) ) ) ) ) ).
tt(t11_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v3_trees_3 A) =>  ((v3_trees_3 (k3_xboole_0 A B)) &  ((v3_trees_3 (k3_xboole_0 B A)) & (v3_trees_3 (k6_subset_1 A B))) ) ) ) ) ).
tt(t11_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v6_trees_3 C)) ) )  =>  ((r2_hidden A (k9_xtuple_0 (k4_trees_4 B C))) <=>  (~  ( (~  (A = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_trees_2 E)) )  =>  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 E)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  &  ( (E = (k1_funct_1 C (k2_nat_1 D 1)))  &  (A = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  => (r2_hidden A (k3_trees_9 A))) ) ).
tt(t11_trees_a,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D (k9_xtuple_0 (k7_trees_2 B A C))) &  ( (~  ( (~ (r1_tarski A D))  &  ((k1_funct_1 (k7_trees_2 B A C) D) = (k1_funct_1 B D)) ) )  &  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (~  ((r2_hidden E (k9_xtuple_0 C)) &  ( (D = (k8_finseq_1 k5_numbers A E))  &  ((k1_funct_1 (k7_trees_2 B A C) D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ( ((v1_borsuk_1 B A) & (m1_pre_topc B A))  <=> (v4_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t11_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v3_pre_topc B A) <=> (v4_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t11_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_tsp_1 B A)) ) ) ) ).
tt(t11_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v1_tsp_2 C A) <=> (v2_tsp_2 B A)) ) ) ) ) ) ) ) ).
tt(t11_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((l1_turing_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C)))) =>  ( ((r1_xxreal_0 A B) &  ((k9_turing_1 C (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) )  =>  ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) B) = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t11_twoscomp,ax, ( ((k1_funct_1 k14_twoscomp (k10_finseq_1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k14_twoscomp (k10_finseq_1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k14_twoscomp (k10_finseq_1 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k14_twoscomp (k10_finseq_1 1 1)) = k6_numbers)  &  ( ((k1_funct_1 k15_twoscomp (k10_finseq_1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k15_twoscomp (k10_finseq_1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k15_twoscomp (k10_finseq_1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k15_twoscomp (k10_finseq_1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t11_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_unialg_2 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_unialg_2 B C)) ) ) ) ) ) ) ).
tt(t11_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k6_unialg_2 A)) => (r2_hidden C (u1_struct_0 B))) ) ) ) ) ) ).
tt(t11_uniform1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k18_complex1 (k6_xcmplx_0 A B)) = (k18_complex1 (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t11_uniroots,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_group_1 k1_complfld (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A))) (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C) A)))) = (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) (k4_nat_d (k23_binop_2 B C) A)) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) (k4_nat_d (k23_binop_2 B C) A)) A)))) ) ) ) ) ) ) ).
tt(t11_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( (B = (k16_pre_poly A))  =>  ((k3_uproots A B) = k6_numbers) ) ) ) ) ).
tt(t11_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  ( (~ (r1_xxreal_0 B (k10_real_1 (k5_real_1 (k6_urysohn1 A B) 1) (k13_newton 2 A))))  &  (~ (r1_xxreal_0 (k10_real_1 (k2_nat_1 (k6_urysohn1 A B) 1) (k13_newton 2 A)) B)) ) ) ) ) ) ).
tt(t11_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_measure5 A) =>  ((r1_xxreal_0 B k6_numbers) | (v4_measure5 (k1_integra2 A B))) ) ) ) ) ) ).
tt(t11_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (F = (k1_funct_1 (k3_urysohn3 A B C D) E))  & (r2_hidden E k3_urysohn1))  => (v3_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E (k7_cqc_lang A C D)) (k16_margrel1 (k2_valuat_1 A B) (k8_valuat_1 A B E C) (k8_valuat_1 A B E D)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v5_relat_1 A k4_numbers) <=>  (! [B:$i] : (v1_int_1 (k1_funct_1 A B))) ) ) ) ).
tt(t11_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ( ((k9_xtuple_0 (k39_valued_1 A)) = (k9_xtuple_0 A))  &  (! [B:$i] :  ((k1_funct_1 (k39_valued_1 A) B) = (k3_square_1 (k1_funct_1 A B))) ) ) ) ) ).
tt(t11_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k13_valued_1 B A)) = (k7_valued_1 (k30_valued_1 B) A)) ) ) ) ) ).
tt(t11_vectmetr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_vectmetr A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_vectmetr A)) (u1_struct_0 (k4_vectmetr A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_vectmetr A)) (u1_struct_0 (k4_vectmetr A)))))) )  =>  ( (B = C)  =>  ((k2_group_1 (k5_vectmetr A) B) = (k2_tops_2 (u1_struct_0 (k4_vectmetr A)) (u1_struct_0 (k4_vectmetr A)) C)) ) ) ) ) ) ) ) ).
tt(t11_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 D E) => (m1_subset_1 E (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v1_vectsp11 (k3_struct_0 B) A B) &  ((m1_vectsp11 (k1_group_1 A) A B (k3_struct_0 B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m2_vectsp11 C A B (k3_struct_0 B) (k1_group_1 A))) ) ) ) ) ) ) ) ).
tt(t11_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_algstr_0 A C D)) = (k5_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ).
tt(t11_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  ((k6_algstr_0 A (k11_algstr_0 A B) (k11_algstr_0 A C)) = (k11_algstr_0 A (k6_algstr_0 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k4_struct_0 C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t11_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( ((k1_vectsp_5 A B (k2_vectsp_4 A B) C) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)))  &  ((k1_vectsp_5 A B C (k2_vectsp_4 A B)) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ) ) ).
tt(t11_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k3_vectsp_6 A B (k2_finseq_4 (u1_struct_0 B) C D) E) = (k2_finseq_4 (u1_struct_0 B) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (C = (u1_struct_0 D))  =>  ((k1_vectsp_7 A B C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t11_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((m1_lattice4 C A B) <=>  ((m4_vectsp_8 C A B) & (m3_vectsp_8 C A B)) ) ) ) ) ) ) ) ).
tt(t11_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((v1_vectsp_7 D A C) =>  ((v1_vectsp_7 D A B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k3_vfunct_1 A B (k47_valued_1 A k1_numbers k1_numbers D E) C) (k2_vfunct_1 A B (k3_vfunct_1 A B D C) (k3_vfunct_1 A B E C)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k1_vfunct_2 A B (k46_valued_1 A k2_numbers k2_numbers D E) C) (k2_vfunct_1 A B (k1_vfunct_2 A B D C) (k1_vfunct_2 A B E C)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v10_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B D E) => (r1_orders_2 A (k2_waybel_0 A B C) (k2_waybel_0 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel10,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_yellow_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_yellow_1 A B))) =>  ( ( (E = C)  &  (F = D) )  =>  ((r1_orders_2 (k6_yellow_1 A B) E F) <=> (r1_yellow_2 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v4_pre_topc (k5_waybel_0 A B) A)) ) ) ) ).
tt(t11_waybel12,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_yellow_4 A B (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) = (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) ) ) ) ) ).
tt(t11_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ((v1_waybel_3 B (k2_yellow_1 (k7_waybel_0 A))) <=>  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) &  ((v14_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t11_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ((k5_waybel_0 A (k4_yellow_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t11_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v22_waybel_0 D A B) & (v22_waybel_0 E B C))  => (v22_waybel_0 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k9_setfam_1 A)))  &  ((v2_waybel_0 (k9_setfam_1 A) (k3_yellow_1 A)) &  ((v13_waybel_0 (k9_setfam_1 A) (k3_yellow_1 A)) & (m1_subset_1 (k9_setfam_1 A) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) ) ) ) ).
tt(t11_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_waybel11 A D)) (k1_waybel11 B (k6_waybel_9 A B C D)))) )  => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t11_waybel18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v2_waybel18 A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 (k8_waybel18 A B C) A (k7_waybel18 A B C)) => (r1_waybel18 A B)) ) ) ) ) ) ) ) ).
tt(t11_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v1_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) => (v21_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(t11_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) <=>  ((v5_orders_3 D B A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_waybel_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D (k5_waybel_0 A E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v5_orders_2 C) & (l1_orders_2 C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v5_orders_2 D) & (l1_orders_2 D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v18_waybel_0 E A C) & (v18_waybel_0 F B D))  => (v18_waybel_0 (k1_waybel20 A B C D E F) (k3_yellow_3 A B) (k3_yellow_3 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v3_waybel_0 B A) & (m1_yellow_0 B A)) ) )  => (v21_waybel_0 (k1_yellow_9 A B) B A)) ) ) ) ).
tt(t11_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 A)) &  ((v13_waybel_0 B (k3_yellow_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) ) )  =>  (B = (k1_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) (a_2_0_waybel22 A B))) ) ) ) ).
tt(t11_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  => (r1_tarski (k3_waybel_0 B D) (k3_waybel_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t11_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) & (l1_orders_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v5_waybel_0 D (k3_yellow_3 A B) C) =>  ((v5_waybel_0 (k1_waybel24 A B C D E) B C) & (v5_waybel_0 (k2_waybel24 A B C D F) A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((m1_pre_topc A B) => (r1_waybel18 A B)) ) ) ) ) ).
tt(t11_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v5_pre_topc C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ((v11_quantal1 C) => (v11_quantal1 (k4_waybel26 A B B C))) ) ) ) ) ) ) ).
tt(t11_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  ((m1_yellow_0 B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((v5_orders_3 D A B) & (r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 C) D E))  => (v5_orders_3 E A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ( ((g1_waybel_0 A (u1_struct_0 B) (u1_orders_2 B) (u1_waybel_0 A B)) = (g1_waybel_0 A (u1_struct_0 C) (u1_orders_2 C) (u1_waybel_0 A C)))  => (m2_yellow_6 C A B)) ) ) ) ) ) ) ).
tt(t11_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v24_waybel_0 (k2_yellow16 A B C))) )  => (v24_waybel_0 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t11_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  ((v24_waybel_0 (k3_yellow_3 A B)) =>  ((v24_waybel_0 A) & (v24_waybel_0 B)) ) ) ) ) ) ).
tt(t11_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k2_waybel19 A) = (k2_waybel19 B)) ) ) ) ) ) ).
tt(t11_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v8_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k2_waybel_8 A B))) ) ) ) ) ).
tt(t11_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ( ((u1_pre_topc B) = (k5_waybel11 A))  => (v4_waybel11 B)) ) ) ) ) ).
tt(t11_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((k1_waybel11 A B) = (k1_yellow_0 A (a_2_0_waybel33 A B))) ) ) ) ) ).
tt(t11_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v18_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k1_waybel34 B A (k2_waybel34 B A C)) C)) ) ) ) ) ) ).
tt(t11_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ((v2_waybel35 C A B) => (r2_hidden (k3_yellow_0 A) C)) ) ) ) ) ) ) ).
tt(t11_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_tarski (k1_waybel_3 A B) (k5_waybel_0 A B)) & (r1_tarski (k2_waybel_3 A B) (k6_waybel_0 A B))) ) ) ) ) ).
tt(t11_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))))))  =>  ((v5_waybel_4 (k1_setfam_1 B) A) & (m1_subset_1 (k1_setfam_1 B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(t11_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) )  =>  ( ( ((k9_xtuple_0 B) = (k9_xtuple_0 C))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k4_yellow_2 A (k1_funct_1 B D)) = (k4_yellow_2 A (k1_funct_1 C D))) ) ) )  => (r1_funct_2 (k9_xtuple_0 B) (u1_struct_0 A) (k9_xtuple_0 C) (u1_struct_0 A) (k4_waybel_5 A B) (k4_waybel_5 A C))) ) ) ) ) ) ) ).
tt(t11_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_waybel_6 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (B = (k2_yellow_0 A C))  => (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(t11_waybel_7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v13_waybel_0 B (k3_yellow_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) )  =>  ((v2_waybel_0 B (k3_yellow_1 A)) <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_tarski C B) => (r2_hidden (k8_setfam_1 A C) B)) ) ) ) ) ) ) ).
tt(t11_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (~  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (~ (v2_struct_0 A))  & (v2_struct_0 B)) ) ) ) ) ) ) ).
tt(t11_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((g1_orders_2 (u1_struct_0 (k7_lattice3 A)) (u1_orders_2 (k7_lattice3 A))) = (g1_orders_2 (u1_struct_0 (k3_waybel_9 A)) (u1_orders_2 (k3_waybel_9 A)))) ) ) ).
tt(t11_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_eqrel_1 (a_2_1_weddwitt A B) (u1_struct_0 A))) ) ) ) ).
tt(t11_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((v2_compts_1 A k3_topmetr) => (v5_xxreal_2 (k1_weierstr A))) ) ) ).
tt(t11_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_wellfnd1 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B)))) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B)))) )  & (r1_wellfnd1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t11_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_wellord1 B A) = (k6_relat_1 A (k5_relat_1 B A))) ) ) ) ).
tt(t11_wellord2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r4_wellord1 A (k1_wellord2 B)) & (r4_wellord1 A (k1_wellord2 C)))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t11_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_int_2 C D) => (r1_int_2 (k1_newton C A) (k1_newton D B))) ) ) ) ) ) ) ) ) ).
tt(t11_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_xboole_0 A B) C) => (r1_tarski A C)) ) ) ) ).
tt(t11_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k5_xboolean (k3_xboolean A) B)) = (k4_xboolean A B)) ) ) ) ) ).
tt(t11_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 2 A) = (k2_xcmplx_0 A A)) ) ) ).
tt(t11_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A (k6_xcmplx_0 B C)) => (r1_xxreal_0 C (k6_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t11_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k12_xtuple_0 A) (k12_xtuple_0 B))) ) ) ).
tt(t11_xxreal_0,ax, (~ (r2_hidden k2_xxreal_0 k1_numbers)) ).
tt(t11_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden A (k3_xxreal_1 B C)) &  ( (~  ((r2_hidden A (k2_xxreal_1 B C)) &  (~  (A = B) ) ) )  &  (~  (A = C) ) ) ) ) ) ) ) ) ) ).
tt(t11_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_2 (k1_tarski A)) = A) ) ) ).
tt(t11_xxreal_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((k1_xxreal_3 A B) = (k1_xxreal_3 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t11_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_lattice3 A B C) & (r1_orders_2 A C D))  => (r2_lattice3 A B D)) ) ) ) ) ) ) ) ).
tt(t11_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r2_yellow_0 (k3_yellow_3 A B) (k7_domain_1 (u1_struct_0 (k3_yellow_3 A B)) C D)) <=>  ((r2_yellow_0 A (k7_domain_1 (u1_struct_0 A) (k8_yellow_3 A B C) (k8_yellow_3 A B D))) & (r2_yellow_0 B (k7_domain_1 (u1_struct_0 B) (k9_yellow_3 A B C) (k9_yellow_3 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_yellow11 A) <=>  (! [B:$i] :  ( ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (~ (r5_waybel_1 k1_yellow11 B)) ) ) ) ) ) ).
tt(t11_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (C = E)  &  (D = F) ) )  =>  ((k4_yellow_4 A C D) = (k3_yellow_4 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_waybel_0 A A (k4_waybel_1 A B) C)) ) ) ) ) ) ).
tt(t11_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v2_lattice3 A))  => (v2_lattice3 B)) ) ) ) ) ).
tt(t11_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k6_margrel1) =>  ((k3_finseq_1 (k1_yellow15 A (k2_finseq_4 (k1_zfmisc_1 A) B C) D)) = 2) ) ) ) ) ) ) ) ).
tt(t11_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_yellow16 A B C) =>  ((k10_xtuple_0 C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t11_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel18 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_waybel18 A B))) => (r2_hidden (k2_funct_7 E C D) (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski D)))) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (l2_altcat_1 B)) )  =>  ( ((r2_yellow18 A B) & (v11_altcat_1 A))  => (v11_altcat_1 B)) ) ) ) ) ).
tt(t11_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_9 A B C) <=> (r1_waybel_7 A (k2_yellow19 A B) C)) ) ) ) ) ) ) ).
tt(t11_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k2_xboole_0 B C) A)) ) )  => (v1_lattice3 (k2_yellow_1 A))) ) ) ).
tt(t11_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (l2_altcat_1 B)) )  =>  ((r1_yellow20 A B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  ( (~  ((k1_altcat_1 B F G) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 B G H) = k1_xboole_0) )  &  ( (F = C)  &  ( (G = D)  &  ( (H = E)  &  (? [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A C D)) &  (? [J:$i] :  ((m1_subset_1 J (k1_altcat_1 B F G)) &  ( (J = I)  &  (? [K:$i] :  ((m1_subset_1 K (k1_altcat_1 A D E)) &  (? [L:$i] :  ((m1_subset_1 L (k1_altcat_1 B G H)) &  ( (L = K)  &  (~  ((k5_altcat_1 A C D E I K) = (k5_altcat_1 B F G H J L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_wellord1 (u1_orders_2 A)) => (v2_waybel_8 A)) ) ) ).
tt(t11_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v5_orders_3 (k3_struct_0 A) A A)) ) ).
tt(t11_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_orders_2 A C D) & (r1_orders_2 B E F))  <=> (r1_orders_2 (k3_yellow_3 A B) (k7_yellow_3 A B C E) (k7_yellow_3 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_yellow_4 A B (k2_yellow_4 A B C))) ) ) ) ) ) ).
tt(t11_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_waybel_1 A B C) <=>  (C = (k7_waybel_1 A B)) ) ) ) ) ) ) ) ).
tt(t11_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_waybel_0 B A) =>  (! [C:$i] :  ((m1_yellow_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (D = F)  &  ( (E = G)  & (r1_orders_2 C F G)) )  => (r1_orders_2 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((r1_yellow_0 (k7_lattice3 A) B) <=> (r2_yellow_0 A B)) ) ) ) ).
tt(t11_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A C) = (k3_tarski (a_3_1_yellow_8 A B C))) ) ) ) ) ) ) ).
tt(t11_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k1_tarski B))  =>  ( ((k2_cantor_1 A C) = (k2_tarski B A))  &  ((k1_cantor_1 A C) = (k2_tarski B k1_xboole_0)) ) ) ) ) ) ) ).
tt(t11_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_zf_model A k6_zf_model) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t11_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ((m1_subset_1 E k4_ordinal1) =>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 k4_ordinal1)))  =>  ( ((v8_zf_fund1 D A) &  ((r2_hidden E F) &  ((r2_hidden B D) &  ((r2_hidden C D) & (r1_tarski C (k1_funct_2 F B))) ) ) )  => (r2_hidden (a_5_0_zf_fund1 A B C E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v6_zf_lang (k14_zf_lang B C A)) &  ( ((k23_zf_lang (k14_zf_lang B C A)) = B)  &  ((k24_zf_lang (k14_zf_lang B C A)) = (k8_zf_lang C A)) ) ) ) ) ) ) ) ) ).
tt(t11_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_zf_lang A) =>  ((k3_finseq_1 A) = 3) ) ) ) ).
tt(t11_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  => (r1_xboole_0 (k1_tarski A) (k1_tarski B))) ) ) ).
tt(t11_zfmodel1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ( ((r1_xboole_0 (k2_tarski A B) (k2_zf_model C)) & (r1_zf_model D E C))  => (r1_zf_model D E (k14_zf_lang A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t11_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_tarski (k2_zf_model B) (k2_tarski (k2_zf_lang 3) (k2_zf_lang 4))) & (r2_zf_model A (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  => (r2_funct_2 A A (k1_zfmodel1 B A C) (k2_zfmodel1 B A))) ) ) ) ) ) ) ).
tt(t11_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((v6_zf_lang A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( ((r2_hidden C (k5_zf_model (k24_zf_lang A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ( (~  ((k3_funct_2 k1_zf_lang B D E) = (k3_funct_2 k1_zf_lang B C E)) )  =>  ((k23_zf_lang A) = E) ) ) )  => (r2_hidden D (k5_zf_model (k24_zf_lang A) B))) ) ) )  <=> (r2_hidden C (k5_zf_model A B))) ) ) ) ) ) ) ) ).
tt(t11_zfrefle1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden (k9_xtuple_0 A) B) & (r1_tarski (k10_xtuple_0 A) B))  => (r2_hidden (k10_xtuple_0 A) B)) ) ) ) ) ).
tt(t11_zf_refle,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  => (v3_ordinal1 (k3_card_3 (k6_relat_1 A B)))) ) ) ).
tt(t11_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_zmodul01 C) &  ((v3_zmodul01 C) &  ((v4_zmodul01 C) &  ((v5_zmodul01 C) & (l1_zmodul01 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((v6_zmodul01 C) &  ((k1_zmodul01 C D A) = (k1_zmodul01 C D B)) )  =>  ( (D = (k4_struct_0 C))  |  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v13_abcmiz_1 B A) =>  ( ((k52_abcmiz_1 (k5_msafree A B)) = (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))  &  ((k51_abcmiz_1 (k5_msafree A B)) = (k3_card_3 (k3_msafree (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t120_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) & (v9_clvect_1 C A))  =>  ((k7_clvect_1 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k7_clvect_1 A B) (k7_clvect_1 A C))) ) ) ) ) ) ) ) ).
tt(t120_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F A) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ( ((v3_card_1 G A) & (m2_finseq_1 G C))  => (m2_finseq_2 (k3_funcop_1 E F G) D (k4_finseq_2 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((k1_relset_1 k5_numbers (k4_finseqop A B C D)) = (k1_relset_1 k5_numbers C))  &  ( ((k3_finseq_1 (k4_finseqop A B C D)) = (k3_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers (k4_finseqop A B C D))) =>  ((k1_funct_1 (k4_finseqop A B C D) E) = (k1_funct_1 D (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k3_finseq_6 A B 1 (k3_finseq_1 B)) = B) ) ) ) ) ) ).
tt(t120_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) )  =>  ((r1_partfun1 E F) =>  ((v1_funct_1 (k9_subset_1 (k2_zfmisc_1 C D) E F)) &  ((v1_funct_2 (k9_subset_1 (k2_zfmisc_1 C D) E F) (k3_xboole_0 A C) (k3_xboole_0 B D)) & (m1_subset_1 (k9_subset_1 (k2_zfmisc_1 C D) E F) (k1_zfmisc_1 (k2_zfmisc_1 (k3_xboole_0 A C) (k3_xboole_0 B D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k6_subset_1 A B) = A) ) ) ) ) ) ).
tt(t120_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_funct_1 (k11_funct_7 A B) C) = B) ) ) ) ) ) ).
tt(t120_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k46_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k46_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k46_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k46_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k14_twoscomp) C) k14_twoscomp) (u1_struct_0 (k46_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t120_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_glib_001 B A) <=> (v1_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(t120_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((k14_group_2 A D B) = (k14_group_2 A D C))  <=> (r1_struct_0 D (k6_algstr_0 A C (k2_group_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t120_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k11_group_2 A B C) = (k12_group_2 A B C)) ) ) ) ) ) ) ) ).
tt(t120_group_9,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (A = (k6_relat_1 (k10_xtuple_0 A) B))  <=>  ((k2_relat_1 A) = (k5_relat_1 (k2_relat_1 B) (k9_xtuple_0 (k2_relat_1 A)))) ) ) ) ) ) ).
tt(t120_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (C = a_0_3_jgraph_4)  &  (B = (a_1_12_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 G (k18_euclid D)) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v9_rltopsp1 (k7_topreal1 A) (k15_euclid 2))) ) ) ).
tt(t120_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  ( ((r1_tarski D (k2_finseq_1 A)) & (v2_funct_1 E))  => (v2_funct_1 (k6_matrix13 (u1_struct_0 C) E D (k2_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k15_member_1 A (k5_member_1 B)) = (k5_member_1 (k15_member_1 A B))) ) ) ) ) ).
tt(t120_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ((r17_ncfcont1 A B C) => (r11_ncfcont1 A C B)) ) ) ) ) ) ).
tt(t120_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r7_pboole A B C) & (r7_pboole A C D))  => (r7_pboole A B D)) ) ) ) ) ) ) ) ).
tt(t120_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k7_relat_1 C (k2_xboole_0 A B)) = (k2_xboole_0 (k7_relat_1 C A) (k7_relat_1 C B))) ) ) ) ) ).
tt(t120_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k23_rvsum_1 (k4_rvsum_1 A B) C) = (k9_binop_2 (k23_rvsum_1 A C) (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ).
tt(t120_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((k6_scmpds_4 (k10_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ((v1_finset_1 B) & (v4_scmyciel B))  &  ( ((k11_scmyciel B) = 2)  &  (~ (r1_xxreal_0 (k9_scmyciel B) A)) ) ) ) ) ) ).
tt(t120_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  ((r2_hidden C D) =>  ((r1_xxreal_0 B k6_numbers) | (r2_hidden C (k25_seq_4 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t120_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A (k5_sheffer1 A C C) B)) = (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C B))) ) ) ) ) ) ) ).
tt(t120_sincos10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 (k7_square_1 2) A))  &  (~  ((k1_seq_1 k1_fdiff_9 (k12_sincos10 A)) = (k10_real_1 A (k7_square_1 (k9_real_1 (k5_square_1 A) 1)))) ) ) ) ) ) ) ).
tt(t120_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t120_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ( (A = (k1_tsep_1 A D E))  & (r4_tsep_1 A D E))  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C D) D B) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B C E)) &  ((v1_funct_2 (k2_tmap_1 A B C E) (u1_struct_0 E) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C E) E B) & (m1_subset_1 (k2_tmap_1 A B C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ( ((k6_xboolean A B) = k2_xboolean)  &  ((k6_xboolean A (k3_xboolean B)) = k2_xboolean) )  =>  ((k3_xboolean A) = k2_xboolean) ) ) ) ) ) ).
tt(t120_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 C B)) = (k7_xcmplx_0 (k6_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t120_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 A C))) ) ) ) ) ) ) ) ).
tt(t120_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k4_xxreal_1 C B) (k3_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t120_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang A (k6_zf_lang B))) (k6_zf_lang A))) & (r2_zf_model C (k11_zf_lang (k7_zf_lang (k11_zf_lang A B) (k11_zf_lang A (k6_zf_lang B))) (k6_zf_lang A)))) ) ) ) ) ) ) ) ) ).
tt(t120_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~ (r2_hidden A C))  &  ( (~ (r2_hidden B C))  &  (~  (C = (k4_xboole_0 C (k2_tarski A B))) ) ) ) ) ) ) ) ).
tt(t120_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  (! [D:$i] :  ( ((v1_zmodul01 D) & (m1_zmodul01 D A))  =>  ((m1_zmodul01 B C) => (m1_zmodul01 (k6_zmodul01 A B D) (k6_zmodul01 A C D))) ) ) ) ) ) ) ) ) ).
tt(t121_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  ( ((r2_pboole (u1_struct_0 A) B C) & (v13_abcmiz_1 B A))  =>  ((r1_tarski (k51_abcmiz_1 (k5_msafree A B)) (k51_abcmiz_1 (k5_msafree A C))) &  ((r1_relset_1 (u1_struct_0 (k5_msafree A B)) (k3_finseq_2 (u1_struct_0 (k5_msafree A B))) (u1_lang1 (k5_msafree A B)) (u1_lang1 (k5_msafree A C))) & (r1_tarski (k4_dtconstr (k5_msafree A B)) (k4_dtconstr (k5_msafree A C)))) ) ) ) ) ) ) ) ) ).
tt(t121_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 C A) =>  ((k7_clvect_1 A (k4_normsp_1 A C B)) = (k5_algstr_0 A (k7_clvect_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t121_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G A) & (m2_finseq_1 G C))  => (m2_finseq_2 (k5_funcop_1 F E G) D (k4_finseq_2 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_relset_1 (k3_finseq_2 A) (k3_finseq_2 A) (k3_finseq_3 A (k6_partfun1 A)) (k6_partfun1 (k3_finseq_2 A)))) ) ).
tt(t121_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k3_finseq_6 A B (k3_finseq_1 B) 1) = (k4_finseq_5 A B)) ) ) ) ) ) ).
tt(t121_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (m1_funct_2 (k1_tarski C) A B)) ) ) ) ).
tt(t121_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k1_funct_4 (k6_subset_1 C A) B) = (k6_subset_1 (k1_funct_4 C B) A)) ) ) ) ) ) ) ) ).
tt(t121_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k13_funct_7 A B C)) = k5_numbers) ) ) ) ).
tt(t121_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k46_gfacirc1 A B C))) & (r2_hidden (k48_gfacirc1 A B C) (k3_msafree2 (k46_gfacirc1 A B C)))) ) ) ) ).
tt(t121_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ( (C = D)  & (v1_glib_001 C A))  => (v1_glib_001 D B)) ) ) ) ) ) ) ) ) ).
tt(t121_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((k14_group_2 A D B) = (k14_group_2 A D C))  <=>  (~ (r1_xboole_0 (k14_group_2 A D B) (k14_group_2 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t121_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_group_2 B (k6_group_3 A B C))) ) ) ) ) ) ) ).
tt(t121_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k3_relat_1 B (k5_relat_1 C A)) = (k3_relat_1 (k6_relat_1 A B) C)) ) ) ) ) ) ).
tt(t121_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (C = a_0_3_jgraph_4)  &  (B = (a_1_13_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 G (k18_euclid D)) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v9_rltopsp1 (k5_topreal1 A) (k15_euclid 2))) ) ) ).
tt(t121_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  ( ((v1_vectsp_7 (k9_matrix13 C A B D) C (k6_prvect_1 C B)) & (v2_funct_1 D))  <=>  ((k8_matrix13 C D) = A) ) ) ) ) ) ) ) ) ) ).
tt(t121_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k15_member_1 (k5_member_1 A) B) = (k5_member_1 (k15_member_1 A B))) ) ) ) ) ).
tt(t121_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r18_ncfcont1 A B C) => (r12_ncfcont1 A C B)) ) ) ) ) ) ).
tt(t121_pboole,ax,(r1_pboole k1_xboole_0 (k1_pboole k1_xboole_0) (k1_pboole k1_xboole_0))).
tt(t121_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k7_relat_1 C (k3_xboole_0 A B)) (k3_xboole_0 (k7_relat_1 C A) (k7_relat_1 C B)))) ) ) ) ).
tt(t121_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k23_rvsum_1 (k10_rvsum_1 A C) B) = (k11_binop_2 C (k23_rvsum_1 A B))) ) ) ) ) ) ) ) ).
tt(t121_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))))  =>  ((k6_scmpds_4 (k10_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_tarski C (k25_seq_4 A C B))) ) ) ) ) ) ) ).
tt(t121_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C B))) ) ) ) ) ) ) ).
tt(t121_sincos10,ax,(r2_fdiff_1 k1_sincos10 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t121_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_partfun2 k1_numbers A)))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_partfun2 k1_numbers A)) A) B) = (k1_real_1 (k10_real_1 (k5_square_1 B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t121_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v1_borsuk_1 E A) & (m1_pre_topc E A)) )  =>  ( (A = (k1_tsep_1 A D E))  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C D) D B) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B C E)) &  ((v1_funct_2 (k2_tmap_1 A B C E) (u1_struct_0 E) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C E) E B) & (m1_subset_1 (k2_tmap_1 A B C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A B) (k6_xboolean (k3_xboolean (k4_xboolean B C)) (k3_xboolean (k4_xboolean A C)))) = k2_xboolean) ) ) ) ) ) ) ).
tt(t121_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k6_xcmplx_0 A (k7_xcmplx_0 A 2)) = (k7_xcmplx_0 A 2)) ) ) ).
tt(t121_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 C B))  =>  ((r1_xxreal_0 k6_numbers B) | (r1_xxreal_0 (k7_xcmplx_0 A C) (k7_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t121_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 C B) & (r1_tarski (k1_xxreal_1 C B) (k3_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t121_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((r2_zf_model C (k11_zf_lang A B)) & (r2_zf_model C A))  => (r2_zf_model C B)) ) ) ) ) ) ) ).
tt(t121_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~ (r2_hidden A C))  &  ( (~ (r2_hidden B C))  &  (~  (C = (k4_xboole_0 (k2_xboole_0 C (k2_tarski A B)) (k2_tarski A B))) ) ) ) ) ) ) ) ).
tt(t121_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( (~  ( (? [D:$i] :  ((m1_zmodul01 D A) &  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) )  &  ( (~ (m1_zmodul01 B C))  &  (~ (m1_zmodul01 C B)) ) ) )  &  (~  ( ((m1_zmodul01 B C) | (m1_zmodul01 C B))  &  (! [D:$i] :  ((m1_zmodul01 D A) =>  (~  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k51_abcmiz_1 (k5_msafree A (k28_abcmiz_1 A)))) <=>  (? [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) &  (B = (k1_domain_1 k2_abcmiz_1 (u1_struct_0 A) C (k14_abcmiz_1 A))) ) ) ) ) ) ) ).
tt(t122_clvect_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v9_clvect_1 C B) =>  ((k7_clvect_1 B (k6_clvect_1 B C A)) = (k1_clvect_1 B (k7_clvect_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t122_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G A) & (m2_finseq_1 G B))  => (m2_finseq_2 (k4_funcop_1 F G E) D (k4_finseq_2 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k8_eqrel_1 A B)) =>  (? [D:$i] :  ((m2_finseq_1 D A) & (r1_finseq_3 A B C D)) ) ) ) ) ) ) ) ).
tt(t122_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) & (r1_xxreal_0 1 E)) ) )  =>  ( ( (~ (r1_xxreal_0 E (k2_nat_1 (k7_nat_d D C) 1)))  &  ( (~ (r1_xxreal_0 E (k3_real_1 (k6_xcmplx_0 D C) 1)))  &  (~ (r1_xxreal_0 E (k9_real_1 (k2_nat_1 D 1) C))) ) )  |  ( ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k7_nat_d (k2_nat_1 E C) 1)))  &  ( ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k2_nat_1 (k7_nat_d E 1) C)))  &  ( ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k9_real_1 (k2_nat_1 E C) 1)))  &  ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k7_real_1 (k5_real_1 E 1) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (m1_funct_2 (k1_funct_2 A B) A B)) ) ) ).
tt(t122_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski A C) &  ((r1_tarski B D) & (r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 D))) )  => (r1_tarski (k1_funct_4 A B) (k1_funct_4 C D))) ) ) ) ) ) ) ) ) ).
tt(t122_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_funct_1 (k13_funct_7 A B C) k6_numbers) = A) ) ) ) ).
tt(t122_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  ((r2_hidden A (k2_msafree2 (k46_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k46_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k46_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t122_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v2_glib_001 B A) <=>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  => (r2_glib_000 A (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 2)) (k1_funct_1 B (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(t122_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_tarski (k5_group_2 A C (k14_group_2 A D B)) (k2_group_2 A (k14_group_2 A D B) (k14_group_2 A D C)))) ) ) ) ) ) ) ) ).
tt(t122_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_group_2 (k6_group_3 A B C) B)) ) ) ) ) ) ) ).
tt(t122_group_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k2_finseq_1 A)) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)) & (r1_tarski (k7_relset_1 k1_numbers k1_numbers C B) (k7_subset_1 k1_numbers k5_numbers (k1_tarski k6_numbers)))) ) )  =>  ((k14_finseq_1 (k7_relset_1 k1_numbers k1_numbers C B)) = (k1_partfun1 k5_numbers k5_numbers k1_numbers k1_numbers (k14_finseq_1 B) C)) ) ) ) ) ) ) ).
tt(t122_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_14_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t122_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v9_rltopsp1 (k4_topreal1 A) (k15_euclid 2))) ) ) ).
tt(t122_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 C A)))) =>  (~  ((r1_tarski E (k9_matrix13 C B A D)) &  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (~  ((r1_tarski F (k2_finseq_1 B)) &  ( ((k9_matrix13 C (k5_card_1 F) (k5_card_1 (k2_finseq_1 A)) (k6_matrix13 (u1_struct_0 C) D F (k2_finseq_1 A))) = E)  & (v2_funct_1 (k6_matrix13 (u1_struct_0 C) D F (k2_finseq_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) => (r1_tarski (k15_member_1 (k9_member_1 A B) C) (k9_member_1 (k15_member_1 A C) (k15_member_1 B C)))) ) ) ) ) ) ).
tt(t122_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ((k2_relset_1 (u1_struct_0 B) C) = (k1_tarski D)) ) )  => (r7_ncfcont1 A B C (k1_relset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t122_pboole,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) & (v1_partfun1 A k1_xboole_0)) ) )  =>  (A = k1_xboole_0) ) ) ).
tt(t122_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k6_subset_1 (k7_relat_1 C A) (k7_relat_1 C B)) (k7_relat_1 C (k6_subset_1 A B)))) ) ) ) ).
tt(t122_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k23_rvsum_1 (k6_rvsum_1 A) B) = (k7_binop_2 (k23_rvsum_1 A B))) ) ) ) ) ) ).
tt(t122_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k10_scmpds_6 D E C) B A)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~  (C = k1_xboole_0) )  => (v1_seq_4 (k25_seq_4 A C B) A)) ) ) ) ) ) ) ).
tt(t122_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) B) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C C)) (k5_sheffer1 A B (k5_sheffer1 A C C))) (k5_sheffer1 A C B))) ) ) ) ) ) ) ).
tt(t122_sincos10,ax,(r2_fdiff_1 k2_sincos10 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t122_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_sin_cos9) (k1_partfun2 k1_numbers A)))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_sin_cos9) (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_sin_cos9) (k1_partfun2 k1_numbers A)) A) B) = (k1_real_1 (k10_real_1 (k5_square_1 B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t122_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v1_tsep_1 E A) & (m1_pre_topc E A)) )  =>  ( (A = (k1_tsep_1 A D E))  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  <=>  ( ((v1_funct_1 (k2_tmap_1 A B C D)) &  ((v1_funct_2 (k2_tmap_1 A B C D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C D) D B) & (m1_subset_1 (k2_tmap_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A B C E)) &  ((v1_funct_2 (k2_tmap_1 A B C E) (u1_struct_0 E) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B C E) E B) & (m1_subset_1 (k2_tmap_1 A B C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k6_xboolean A B)) = k2_xboolean) ) ) ) ) ).
tt(t122_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k7_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) C) D) = (k6_xcmplx_0 (k6_xcmplx_0 (k7_xcmplx_0 A D) (k7_xcmplx_0 B D)) (k7_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t122_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k5_xcmplx_0 A) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k5_xcmplx_0 A) k6_numbers))  & (r1_xxreal_0 A k6_numbers)) ) ) ) ) ).
tt(t122_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k2_xxreal_1 C B) (k3_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t122_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k6_zf_lang (k7_zf_lang A B)) (k10_zf_lang (k6_zf_lang A) (k6_zf_lang B)))) & (r2_zf_model C (k11_zf_lang (k6_zf_lang (k7_zf_lang A B)) (k10_zf_lang (k6_zf_lang A) (k6_zf_lang B))))) ) ) ) ) ) ) ) ) ).
tt(t122_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_zfmisc_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k4_tarski A C) (k4_tarski A D) (k4_tarski B C) (k4_tarski B D))) ) ) ) ) ).
tt(t122_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  => (r2_hidden A (k8_zmodul01 A))) ) ).
tt(t123_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k52_abcmiz_1 (k5_msafree A (k28_abcmiz_1 A)))) <=>  (~  ( (~  (B = (k4_tarski (k33_abcmiz_1 A) (u1_struct_0 A))) )  &  ( (~  (B = (k4_tarski (k32_abcmiz_1 A) (u1_struct_0 A))) )  &  (! [C:$i] :  ( ((v2_abcmiz_1 C A) & (m1_subset_1 C (u4_struct_0 A)))  =>  (~  (B = (k4_tarski C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_clvect_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k2_numbers B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers B) B)))) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v2_clvect_1 F) &  ((v3_clvect_1 F) &  ((v4_clvect_1 F) &  ((v5_clvect_1 F) & (l1_clvect_1 F)) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 F))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 F)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (g1_clvect_1 B C D E))) =>  ( ( (G = B)  &  ( (E = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 F)) (u1_struct_0 F) (u1_clvect_1 F) (k2_zfmisc_1 k2_numbers G)))  &  (I = H) ) )  =>  ((k1_clvect_1 (g1_clvect_1 B C D E) I A) = (k1_clvect_1 F H A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((k2_finseq_2 (k2_xcmplx_0 A B) C) = (k7_finseq_1 (k2_finseq_2 A C) (k2_finseq_2 B C))) ) ) ) ) ) ).
tt(t123_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k4_card_3 (k9_finseq_1 B))) <=>  (? [C:$i] :  ((r2_hidden C B) &  (A = (k9_finseq_1 C)) ) ) ) ) ) ).
tt(t123_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D C) & (r1_xxreal_0 C (k3_finseq_1 B))) )  =>  ((k1_funct_1 (k3_finseq_6 A B 1 C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t123_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  ((k9_xtuple_0 (k3_relat_1 C B)) = (k9_xtuple_0 C)) ) ) ) ) ) ) ).
tt(t123_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A B) => (r1_tarski (k1_funct_4 A C) (k1_funct_4 B C))) ) ) ) ) ) ) ).
tt(t123_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_funct_1 (k13_funct_7 A B C) 1) = B) ) ) ) ).
tt(t123_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) = (k2_binarith E F))  &  ( ((k1_funct_1 (k6_circuit2 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D) A) = E)  &  ( ((k1_funct_1 (k6_circuit2 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D) B) = F)  &  ((k1_funct_1 (k6_circuit2 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v2_glib_001 B A) &  ((r1_glib_001 A C D B) & (r2_glib_000 A D F E)) )  =>  ((v2_glib_001 (k10_glib_001 A B E) A) & (r1_glib_001 A C F (k10_glib_001 A B E))) ) ) ) ) ) ) ) ) ) ).
tt(t123_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_tarski (k8_group_2 A C) (k2_group_2 A (k14_group_2 A C B) (k14_group_2 A C (k2_group_1 A B)))) & (r1_tarski (k8_group_2 A C) (k2_group_2 A (k14_group_2 A C (k2_group_1 A B)) (k14_group_2 A C B)))) ) ) ) ) ) ) ).
tt(t123_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  ((k9_group_3 A B) = (k1_tarski B)) ) ) ) ) ) ).
tt(t123_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_tarski A (k2_finseq_1 (k1_nat_1 C 1))) &  ((r2_hidden B (k2_finseq_1 (k1_nat_1 C 1))) &  ( (~ (r2_hidden B A))  &  (! [D:$i] :  (~  ( ((k14_finseq_1 D) = (k3_relat_1 (k14_finseq_1 A) (k2_funct_1 (k14_finseq_1 (k7_subset_1 k5_numbers (k2_finseq_1 (k1_nat_1 C 1)) (k1_tarski B))))))  & (r1_tarski D (k2_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_15_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t123_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~ (v9_rltopsp1 (k6_topreal1 A) (k15_euclid 2))) ) ) ).
tt(t123_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k8_matrix13 C D) = E)  <=>  ( (? [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 C B)))))  &  ((v1_vectsp_7 F C (k6_prvect_1 C B)) &  ((r1_tarski F (k9_matrix13 C A B D)) &  ((k5_card_1 F) = E) ) ) ) )  &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 C B)))))  =>  ( ((v1_vectsp_7 F C (k6_prvect_1 C B)) & (r1_tarski F (k9_matrix13 C A B D)))  => (r1_xxreal_0 (k5_card_1 F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) => (r1_tarski (k15_member_1 (k11_member_1 A B) C) (k11_member_1 (k15_member_1 A C) (k15_member_1 B C)))) ) ) ) ) ) ).
tt(t123_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ((k2_relset_1 (u1_struct_0 B) C) = (k1_tarski D)) ) )  => (r8_ncfcont1 A B C (k1_relset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t123_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((r4_pboole A B C) & (r5_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t123_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) => (r1_tarski (k7_relat_1 C A) (k7_relat_1 C B))) ) ) ) ) ).
tt(t123_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k23_rvsum_1 (k6_rvsum_1 A) (k6_rvsum_1 B)) = (k23_rvsum_1 A B)) ) ) ) ) ) ).
tt(t123_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k1_funct_1 (k6_scmpds_4 (k10_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  ((k9_member_1 A B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t123_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) (k5_sheffer1 A (k5_sheffer1 A D B) (k5_sheffer1 A (k5_sheffer1 A C C) B))) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D B)) B)) ) ) ) ) ) ) ) ) ).
tt(t123_sincos10,ax,(r2_fdiff_1 k3_sincos10 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t123_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k1_sin_cos9 B)) (k10_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t123_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r3_tsep_1 A B C) <=>  ((r1_tsep_1 B C) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D))))) )  =>  ( ( ((v1_funct_1 (k3_tmap_1 A D (k1_tsep_1 A B C) B E)) &  ((v1_funct_2 (k3_tmap_1 A D (k1_tsep_1 A B C) B E) (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc (k3_tmap_1 A D (k1_tsep_1 A B C) B E) B D) & (m1_subset_1 (k3_tmap_1 A D (k1_tsep_1 A B C) B E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  &  ((v1_funct_1 (k3_tmap_1 A D (k1_tsep_1 A B C) C E)) &  ((v1_funct_2 (k3_tmap_1 A D (k1_tsep_1 A B C) C E) (u1_struct_0 C) (u1_struct_0 D)) &  ((v5_pre_topc (k3_tmap_1 A D (k1_tsep_1 A B C) C E) C D) & (m1_subset_1 (k3_tmap_1 A D (k1_tsep_1 A B C) C E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) )  =>  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D)) &  ((v5_pre_topc E (k1_tsep_1 A B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k5_xboolean A B)) = k2_xboolean) ) ) ) ) ).
tt(t123_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k7_xcmplx_0 C A) = (k7_xcmplx_0 D B))  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  |  ( (A = B)  |  ((k7_xcmplx_0 C A) = (k7_xcmplx_0 (k6_xcmplx_0 C D) (k6_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 k6_numbers (k5_xcmplx_0 A))) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k5_xcmplx_0 A)))  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(t123_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k3_xxreal_1 C B) (k3_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t123_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k10_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k6_zf_lang (k7_zf_lang A B)))) & (r2_zf_model C (k11_zf_lang (k10_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k6_zf_lang (k7_zf_lang A B))))) ) ) ) ) ) ) ) ) ).
tt(t123_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((k4_xboole_0 (k2_xboole_0 C (k1_tarski A)) (k1_tarski B)) = (k2_xboole_0 (k4_xboole_0 C (k1_tarski B)) (k1_tarski A))) ) ) ) ) ).
tt(t123_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_zmodul01 A B C) => (m3_zmodul01 C A B)) ) ) ) ) ) ) ).
tt(t124_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v13_abcmiz_1 B A)) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) => (m1_dtconstr C (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))))) (k1_msaterm A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))))) ) ) ) ) ) ).
tt(t124_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  =>  ((k4_finseq_1 C) = (k2_finseq_1 A)) ) ) ) ) ) ) ).
tt(t124_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k4_card_3 (k10_finseq_1 B C))) <=>  (? [D:$i] :  (? [E:$i] :  ((r2_hidden D B) &  ((r2_hidden E C) &  (A = (k10_finseq_1 D E)) ) ) ) ) ) ) ) ) ).
tt(t124_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B))) )  => (r1_xxreal_0 (k3_finseq_1 (k3_finseq_6 A B C D)) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ).
tt(t124_funct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A B C) = C) ) )  => (r2_funct_2 A A B (k6_partfun1 A))) ) ) ) ) ).
tt(t124_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A B) & (r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 C)))  => (r1_tarski A (k1_funct_4 B C))) ) ) ) ) ) ) ).
tt(t124_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 D 1))  =>  ((k1_funct_1 (k13_funct_7 A B C) D) = C) ) ) ) ) ) ) ).
tt(t124_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k14_twoscomp)))  &  ( (F = (k1_funct_1 D A))  &  ( (G = (k1_funct_1 D B))  &  (H = (k1_funct_1 D C)) ) ) )  =>  ((k1_twoscomp (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) (k6_circuit2 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D) (k48_gfacirc1 A B C)) = (k2_binarith E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v2_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (v2_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t124_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k14_group_2 A C (k5_group_1 A 2 B)) (k2_group_2 A (k14_group_2 A C B) (k14_group_2 A C B)))) ) ) ) ) ) ).
tt(t124_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) => (r1_tarski (k7_group_3 A C) (k8_group_2 A B))) ) ) ) ) ) ) ) ).
tt(t124_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  (B = (k2_finseq_3 (k1_nat_1 D 1) (k5_finseq_5 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t124_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_3_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_jordan2c 2 A))) ) ).
tt(t124_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k15_member_1 (k13_member_1 A B) C) = (k13_member_1 A (k15_member_1 B C))) ) ) ) ) ) ) ).
tt(t124_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k2_relset_1 (u1_struct_0 A) C) = (k1_tarski D)) ) )  => (r9_ncfcont1 B A C (k1_relset_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(t124_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (~ (r3_pboole A B (k1_pboole A))) ) ) ) ) ).
tt(t124_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski B C) => (r1_tarski (k7_relat_1 B A) (k7_relat_1 C A))) ) ) ) ) ) ).
tt(t124_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k23_rvsum_1 (k8_rvsum_1 A B) C) = (k10_binop_2 (k23_rvsum_1 A C) (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ).
tt(t124_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))))  =>  ((k1_funct_1 (k6_scmpds_4 (k10_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ((v3_xxreal_2 A) & (v3_xxreal_2 B))  => (v3_xxreal_2 (k9_member_1 A B))) ) ) ) ) ).
tt(t124_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A D D)) (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A D D)) (k5_sheffer1 A D (k5_sheffer1 A D D))) C))) = B) ) ) ) ) ) ) ) ) ).
tt(t124_sincos10,ax,(r2_fdiff_1 k4_sincos10 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t124_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) A) B) = (k9_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k2_sin_cos9 B)) (k10_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t124_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r3_tsep_1 A B C) <=>  ((r1_tsep_1 B C) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  ( ( ((v1_funct_1 (k2_tmap_1 A D E B)) &  ((v1_funct_2 (k2_tmap_1 A D E B) (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc (k2_tmap_1 A D E B) B D) & (m1_subset_1 (k2_tmap_1 A D E B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A D E C)) &  ((v1_funct_2 (k2_tmap_1 A D E C) (u1_struct_0 C) (u1_struct_0 D)) &  ((v5_pre_topc (k2_tmap_1 A D E C) C D) & (m1_subset_1 (k2_tmap_1 A D E C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) )  =>  ((v1_funct_1 (k2_tmap_1 A D E (k1_tsep_1 A B C))) &  ((v1_funct_2 (k2_tmap_1 A D E (k1_tsep_1 A B C)) (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D)) &  ((v5_pre_topc (k2_tmap_1 A D E (k1_tsep_1 A B C)) (k1_tsep_1 A B C) D) & (m1_subset_1 (k2_tmap_1 A D E (k1_tsep_1 A B C)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean (k3_xboolean A) (k6_xboolean (k6_xboolean A B) B)) = k2_xboolean) ) ) ) ) ).
tt(t124_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k7_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 A B) C) D) = (k6_xcmplx_0 (k2_xcmplx_0 (k7_xcmplx_0 A D) (k7_xcmplx_0 B D)) (k7_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t124_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k5_xcmplx_0 B) (k5_xcmplx_0 A))) ) ) ) ) ) ) ).
tt(t124_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C B) & (r1_tarski (k1_xxreal_1 C B) (k4_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t124_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k6_zf_lang (k10_zf_lang A B)) (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)))) & (r2_zf_model C (k11_zf_lang (k6_zf_lang (k10_zf_lang A B)) (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B))))) ) ) ) ) ) ) ) ) ).
tt(t124_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) &  ( ((k3_xboole_0 B C) = (k1_tarski D))  & (r2_hidden D A)) )  =>  ((k3_xboole_0 A C) = (k1_tarski D)) ) ) ) ) ) ).
tt(t124_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  ((r1_zmodul01 A C B) & (r1_zmodul01 A B C)) ) ) ) ) ) ) ).
tt(t125_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v13_abcmiz_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))))) (k1_msaterm A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))) =>  ((r2_hidden C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) => (r2_hidden C (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) (k7_msaterm A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))) C)))) ) ) ) ) ) ) ).
tt(t125_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A)))  =>  ((k3_relat_1 (k10_finseq_1 B C) A) = (k10_finseq_1 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ).
tt(t125_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k4_card_3 (k11_finseq_1 B C D))) <=>  (? [E:$i] :  (? [F:$i] :  (? [G:$i] :  ((r2_hidden E B) &  ((r2_hidden F C) &  ((r2_hidden G D) &  (A = (k11_finseq_1 E F G)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k17_finseq_1 A (k2_nat_1 C 1) (k8_finseq_1 A (k12_finseq_1 A D) B)) = (k8_finseq_1 A (k12_finseq_1 A D) (k17_finseq_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t125_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_tarski A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_tarski A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B)))) )  =>  ( ((k1_funct_1 C A) = (k1_funct_1 D A))  => (r2_funct_2 (k1_tarski A) B C D)) ) ) ) ) ) ) ).
tt(t125_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_partfun1 A B) &  ((r1_partfun1 B C) & (r1_partfun1 C A)) )  => (r1_partfun1 (k1_funct_4 A B) C)) ) ) ) ) ) ) ).
tt(t125_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k13_funct_7 A B C) = (k2_funct_7 (k11_funct_7 A C) 1 B)) ) ) ) ).
tt(t125_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_twoscomp (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) (k48_gfacirc1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ( ((k1_funct_1 (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) = (k2_binarith E F))  &  ( ((k1_funct_1 (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) A) = E)  &  ( ((k1_funct_1 (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) B) = F)  &  ((k1_funct_1 (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (~ (v3_glib_001 B A))  <=> (r1_xxreal_0 3 (k3_finseq_1 B))) ) ) ) ) ).
tt(t125_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k13_group_2 A (k10_group_2 A C D) B) = (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k13_group_2 A C B) (k13_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t125_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((k2_group_2 A (k8_group_2 A B) (k8_group_2 A C)) = (k2_group_2 A (k8_group_2 A C) (k8_group_2 A B))) ) ) ) ) ) ) ).
tt(t125_group_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 C)) =>  ((k1_funct_1 D G) = (k1_funct_1 F (k1_funct_1 C G))) ) ) )  &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_group_4 A (k4_group_4 A E C))) = (k3_group_4 B (k4_group_4 B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_2_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xboole_0 B A) =>  ((v9_rltopsp1 B (k15_euclid 2)) | (r1_tarski B (k2_jordan2c 2 A))) ) ) ) ) ) ).
tt(t125_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k13_member_1 (k15_member_1 A B) C) = (k15_member_1 (k13_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t125_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C)))  => (r7_ncfcont1 A B D C)) ) ) ) ) ) ) ) ).
tt(t125_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r3_pboole A B C) &  ((r3_pboole A B D) &  ((k3_pboole A C D) = (k1_pboole A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((r1_tarski C D) & (r1_tarski A B))  => (r1_tarski (k7_relat_1 C A) (k7_relat_1 D B))) ) ) ) ) ) ) ).
tt(t125_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_valued_0 E) & (v1_finseq_1 E)) ) )  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) )  =>  ((k23_rvsum_1 (k4_rvsum_1 (k10_rvsum_1 C A) (k10_rvsum_1 D B)) E) = (k9_binop_2 (k11_binop_2 A (k23_rvsum_1 C E)) (k11_binop_2 B (k23_rvsum_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmpds_6 C B A) <=> (r1_scmpds_6 C (k8_memstr_0 2 k1_scmpds_2 B) A)) ) ) ) ) ) ) ).
tt(t125_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ((v3_xxreal_2 A) & (v3_xxreal_2 B))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ((k3_seq_4 (k9_member_1 A B)) = (k9_binop_2 (k5_seq_4 A) (k5_seq_4 B))) ) ) ) ) ) ) ) ).
tt(t125_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C)) C) = (k5_sheffer1 A C (k5_sheffer1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t125_sincos10,ax,(v3_rcomp_1 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t125_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) D) = (k1_real_1 (k10_real_1 (k5_square_1 (k8_real_1 A D)) (k7_real_1 1 (k5_square_1 (k8_real_1 A D)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (A = (k1_tsep_1 A B C))  =>  ((r3_tsep_1 A B C) <=>  ((r1_tsep_1 B C) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  ( ( ((v1_funct_1 (k2_tmap_1 A D E B)) &  ((v1_funct_2 (k2_tmap_1 A D E B) (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc (k2_tmap_1 A D E B) B D) & (m1_subset_1 (k2_tmap_1 A D E B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  &  ((v1_funct_1 (k2_tmap_1 A D E C)) &  ((v1_funct_2 (k2_tmap_1 A D E C) (u1_struct_0 C) (u1_struct_0 D)) &  ((v5_pre_topc (k2_tmap_1 A D E C) C D) & (m1_subset_1 (k2_tmap_1 A D E C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) )  =>  ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) &  ((v5_pre_topc E A D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k7_xboolean A A) = k2_xboolean) ) ) ).
tt(t125_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) C) D) = (k2_xcmplx_0 (k6_xcmplx_0 (k7_xcmplx_0 A D) (k7_xcmplx_0 B D)) (k7_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t125_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k5_xcmplx_0 A)))  &  ( (~ (r1_xxreal_0 (k5_xcmplx_0 B) k6_numbers))  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t125_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k2_xxreal_1 C B) (k4_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t125_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C D (k11_zf_lang (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k6_zf_lang (k10_zf_lang A B)))) & (r2_zf_model C (k11_zf_lang (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k6_zf_lang (k10_zf_lang A B))))) ) ) ) ) ) ) ) ) ).
tt(t125_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski (k3_xboole_0 A B) (k1_tarski D)) &  ((r2_hidden D C) & (r1_xboole_0 C B)) )  => (r1_xboole_0 (k2_xboole_0 A C) B)) ) ) ) ) ).
tt(t125_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  ((k6_zmodul01 A B C) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ) ) ) ) ).
tt(t126_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_lang1 A B C) => (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t126_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden D (k9_xtuple_0 A))) )  =>  ((k3_relat_1 (k11_finseq_1 B C D) A) = (k11_finseq_1 (k1_funct_1 A B) (k1_funct_1 A C) (k1_funct_1 A D))) ) ) ) ) ) ) ).
tt(t126_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_card_3 (k9_finseq_1 A)) = (k4_finseq_2 1 A)) ) ) ).
tt(t126_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((r1_xxreal_0 D C) |  ((k3_finseq_6 A B C D) = (k7_finseq_1 (k9_finseq_1 (k1_funct_1 B C)) (k3_finseq_6 A B (k2_nat_1 C 1) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k11_funct_7 A B)) = (k2_tarski A B)) ) ) ).
tt(t126_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ((k1_twoscomp (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) (k5_facirc_1 (k46_gfacirc1 A B C) (k47_gfacirc1 A B C) D 2) (k48_gfacirc1 A B C)) = (k9_margrel1 (k2_binarith (k2_binarith (k9_margrel1 E) (k9_margrel1 F)) (k9_margrel1 G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (~  ( (~ (v3_glib_001 B A))  &  ((k3_finseq_1 B) = 1) ) )  &  (~  ( (~  ((k3_finseq_1 B) = 1) )  & (v3_glib_001 B A)) ) ) ) ) ) ) ).
tt(t126_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k14_group_2 A (k10_group_2 A C D) B) = (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k14_group_2 A C B) (k14_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t126_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (? [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  &  ((u1_struct_0 D) = (k2_group_2 A (k8_group_2 A B) (k8_group_2 A C))) ) ) ) ) ) ) ) ) ).
tt(t126_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_3_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xboole_0 (k7_topreal1 B) A) => (r1_tarski (k7_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ).
tt(t126_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k15_member_1 (k15_member_1 A B) C) = (k15_member_1 A (k13_member_1 B C))) ) ) ) ) ) ) ).
tt(t126_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C)))  => (r8_ncfcont1 A B D C)) ) ) ) ) ) ) ) ).
tt(t126_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (~ (r4_pboole A B (k1_pboole A))) ) ) ) ) ).
tt(t126_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k7_relat_1 (k3_relat_1 B C) A) = (k7_relat_1 C (k7_relat_1 B A))) ) ) ) ) ) ).
tt(t126_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) & (v1_finseq_1 D)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((k23_rvsum_1 (k4_rvsum_1 A B) (k4_rvsum_1 C D)) = (k9_binop_2 (k9_binop_2 (k9_binop_2 (k23_rvsum_1 A C) (k23_rvsum_1 A D)) (k23_rvsum_1 B C)) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t126_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_scmpds_6 C B A) <=> (r2_scmpds_6 C (k8_memstr_0 2 k1_scmpds_2 B) A)) ) ) ) ) ) ) ).
tt(t126_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ((v3_xxreal_2 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D B) & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  | (r1_xxreal_0 (k5_seq_4 B) (k5_seq_4 A))) ) ) ) ) ) ).
tt(t126_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C B) B)) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t126_sincos10,ax,(v3_rcomp_1 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t126_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_sin_cos9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) D) = (k1_real_1 (k10_real_1 (k5_square_1 (k8_real_1 A D)) (k7_real_1 1 (k5_square_1 (k8_real_1 A D)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) E (k10_tmap_1 A B C D (k3_tmap_1 A B (k1_tsep_1 A C D) C E) (k3_tmap_1 A B (k1_tsep_1 A C D) D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t126_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k7_xboolean (k7_xboolean (k7_xboolean (k7_xboolean A B) C) A) (k7_xboolean B C)) = k2_xboolean) ) ) ) ) ) ) ).
tt(t126_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k6_xcmplx_0 (k7_xcmplx_0 B A) C) = (k7_xcmplx_0 (k6_xcmplx_0 B (k3_xcmplx_0 C A)) A)) ) ) ) ) ) ) ) ).
tt(t126_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 k6_numbers A))  =>  (k6_numbers = (k3_xcmplx_0 A B)) ) ) ) ) ) ).
tt(t126_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k3_xxreal_1 C B) (k4_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t126_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  => (r2_zf_model C (k11_zf_lang (k8_zf_lang B A) A))) ) ) ) ) ) ).
tt(t126_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  => (r1_xboole_0 C D)) ) )  => (r1_xboole_0 (k3_tarski A) (k3_tarski B))) ) ) ).
tt(t126_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  ((k7_zmodul01 A B C) = (k3_zmodul01 A)) ) ) ) ) ) ) ).
tt(t127_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_msafree A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_msafree A C))) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k5_msafree A B))) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k5_msafree A C))) =>  ( ( (D = E)  &  ( (F = G)  & (r1_lang1 (k5_msafree A B) D F)) )  => (r1_lang1 (k5_msafree A C) E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t127_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k10_finseq_1 A B)) = (k2_tarski A B)) ) ) ).
tt(t127_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k4_card_3 (k10_finseq_1 A B)) = (a_2_0_finseq_3 A B)) ) ) ) ) ).
tt(t127_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k10_xtuple_0 (k13_funct_7 A B C)) = (k1_enumset1 A B C)) ) ) ) ).
tt(t127_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k49_gfacirc1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) (k1_tarski (k48_gfacirc1 A B C))) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp))) (k1_tarski (k45_gfacirc1 A B C)))) ) ) ) ).
tt(t127_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (~  ( (~  ((k3_glib_001 A B) = (k4_glib_001 A B)) )  & (v3_glib_001 B A)) ) ) ) ) ) ).
tt(t127_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (? [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  &  ((u1_struct_0 D) = (k5_group_2 A (k2_group_1 A B) (k13_group_2 A C B))) ) ) ) ) ) ) ) ) ).
tt(t127_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((k15_group_2 A B) = (k16_group_2 A B)) ) ) ) ) ).
tt(t127_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_2_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t127_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t127_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xboole_0 (k5_topreal1 B) A) => (r1_tarski (k5_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ).
tt(t127_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k15_member_1 A (k15_member_1 B C)) = (k15_member_1 (k13_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t127_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) D C)))  => (r9_ncfcont1 B A D C)) ) ) ) ) ) ) ) ).
tt(t127_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((r6_pboole A (k3_pboole A B C) (k1_pboole A)) & (r4_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t127_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k10_xtuple_0 (k3_relat_1 A B)) = (k7_relat_1 B (k10_xtuple_0 A))) ) ) ) ) ).
tt(t127_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) & (v1_finseq_1 D)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((k23_rvsum_1 (k8_rvsum_1 A B) (k8_rvsum_1 C D)) = (k9_binop_2 (k10_binop_2 (k10_binop_2 (k23_rvsum_1 A C) (k23_rvsum_1 A D)) (k23_rvsum_1 B C)) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t127_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  (~ (r1_xxreal_0 k6_numbers (k26_seq_4 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t127_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (C = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) D) C) (k5_sheffer1 A (k5_sheffer1 A B B) C))) ) ) ) ) ) ) ) ) ).
tt(t127_sincos10,ax,(v3_rcomp_1 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t127_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k1_sin_cos9 B) B) (k10_real_1 (k1_seq_1 k3_taylor_1 B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t127_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (A = (k1_tsep_1 A C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) E (k10_tmap_1 A B C D (k2_tmap_1 A B E C) (k2_tmap_1 A B E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t127_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ( ( ((k7_xboolean A B) = k2_xboolean)  &  ((k7_xboolean B C) = k2_xboolean) )  =>  ((k7_xboolean A C) = k2_xboolean) ) ) ) ) ) ) ) ).
tt(t127_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k6_xcmplx_0 B (k7_xcmplx_0 C A)) = (k7_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 B A) C) A)) ) ) ) ) ) ) ) ).
tt(t127_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t127_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_tarski (k4_xxreal_1 C B) (k4_xxreal_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t127_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  => (r2_zf_model C (k11_zf_lang A (k13_zf_lang B A)))) ) ) ) ) ) ).
tt(t127_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~ (r2_hidden A (k2_zfmisc_1 A B))) ) ) ).
tt(t127_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_zmodul01 A B C) => (r1_zmodul01 A C B)) ) ) ) ) ) ) ).
tt(t128_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v13_abcmiz_1 B A)) ) ) )  =>  ((k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) = (k4_dtconstr (k5_msafree A B))) ) ) ) ) ).
tt(t128_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k10_xtuple_0 (k11_finseq_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ).
tt(t128_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_card_3 (k10_finseq_1 A A)) = (k4_finseq_2 2 A)) ) ) ).
tt(t128_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((k1_funct_1 (k2_funct_7 C D E) D) = E) ) ) ) ) ) ) ) ) ) ).
tt(t128_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k49_gfacirc1 A B C)))) ) ) ).
tt(t128_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) & (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B (k1_glib_001 A C))) ) ) ) ) ) ) ).
tt(t128_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r2_wellord2 (k13_group_2 A D B) (k13_group_2 A D C))) ) ) ) ) ) ) ) ).
tt(t128_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_finset_1 (k15_group_2 A B)) &  ((k18_group_2 A B) = 2) )  =>  ((v1_group_3 B A) & (m1_group_2 B A)) ) ) ) ) ) ).
tt(t128_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B)) = (k12_euclid B)) ) ) ) ) ).
tt(t128_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 G (k18_euclid D)) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t128_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xboole_0 (k6_topreal1 B) A) => (r1_tarski (k6_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ).
tt(t128_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_member_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k6_binop_2 A B))) ) ) ) ) ).
tt(t128_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) =>  ((k7_partfun1 (u1_struct_0 A) B C) = C) ) ) )  => (r7_ncfcont1 A A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t128_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (~  ((r4_pboole A B B) &  (B = (k1_pboole A)) ) ) ) ) ) ) ).
tt(t128_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k7_relat_1 (k5_relat_1 C A) B) (k7_relat_1 C B))) ) ) ) ).
tt(t128_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k23_rvsum_1 (k4_rvsum_1 A B) (k4_rvsum_1 A B)) = (k9_binop_2 (k9_binop_2 (k23_rvsum_1 A A) (k11_binop_2 2 (k23_rvsum_1 A B))) (k23_rvsum_1 B B))) ) ) ) ) ) ).
tt(t128_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ((k26_seq_4 A B C) = (k26_seq_4 A C B)) ) ) ) ) ) ) ).
tt(t128_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) B)) (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C C) B))) = C) ) ) ) ) ) ) ).
tt(t128_sincos10,ax,(v3_rcomp_1 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t128_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) A) B) = (k9_real_1 (k10_real_1 (k1_seq_1 k2_sin_cos9 B) B) (k10_real_1 (k1_seq_1 k3_taylor_1 B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t128_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) C (k10_tmap_1 A B C D E F)) E) & (r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) D (k10_tmap_1 A B C D E F)) F))  <=> (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t128_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  (! [D:$i] :  ((v1_xboolean D) =>  ( ( ((k7_xboolean A B) = k2_xboolean)  &  ((k7_xboolean C D) = k2_xboolean) )  =>  ((k7_xboolean (k7_xboolean A C) (k7_xboolean B D)) = k2_xboolean) ) ) ) ) ) ) ) ) ) ).
tt(t128_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k6_xcmplx_0 B C) = (k3_xcmplx_0 A (k6_xcmplx_0 (k7_xcmplx_0 B A) (k7_xcmplx_0 C A)))) ) ) ) ) ) ) ) ).
tt(t128_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t128_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xxreal_1 A B) = (k2_xboole_0 (k4_xxreal_1 A B) (k2_tarski A B))) ) ) ) ) ) ).
tt(t128_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( (~ (r2_hidden C (k2_zf_model A)))  => (r2_zf_model D (k11_zf_lang (k8_zf_lang C (k11_zf_lang A B)) (k11_zf_lang A (k8_zf_lang C B))))) ) ) ) ) ) ) ) ) ).
tt(t128_zfmisc_1,ax, (! [A:$i] : (r2_hidden (k4_tarski A (k1_tarski A)) (k2_zfmisc_1 (k1_tarski A) (k4_tarski A (k1_tarski A))))) ).
tt(t128_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) => (m3_zmodul01 B A C)) ) ) ) ) ) ).
tt(t129_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))))))) )  =>  ((m4_abcmiz_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D)) => (r2_hidden (k1_funct_1 C E) (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t129_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_tarski A C) &  ((r1_tarski B C) &  ((k3_finseq_1 A) = (k3_finseq_1 B)) ) )  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t129_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k4_card_3 (k11_finseq_1 A B C)) = (a_3_1_finseq_3 A B C)) ) ) ) ) ) ) ).
tt(t129_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~  ((k3_funct_2 A B C F) = (k3_funct_2 A B D F)) )  =>  (F = E) ) ) )  => (r2_funct_2 A B C (k15_funct_7 A B D E (k3_funct_2 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t129_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  ((k2_msafree2 (k49_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t129_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) <=> (v3_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(t129_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r2_wellord2 (k13_group_2 A D B) (k14_group_2 A D C))) ) ) ) ) ) ) ) ).
tt(t129_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_struct_0 (k10_group_3 B C) A) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ( (A = D)  &  ((k4_group_3 B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t129_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_3_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k9_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t129_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid D)))  &  ((r1_xxreal_0 G (k18_euclid D)) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t129_jordan2c,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xboole_0 (k4_topreal1 B) A) => (r1_tarski (k4_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ).
tt(t129_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k15_member_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k6_binop_2 A B) (k6_binop_2 A C))) ) ) ) ) ) ) ).
tt(t129_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun2 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) B))) => (r7_ncfcont1 A A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t129_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v3_relat_1 B) <=> (r6_pboole A B (k1_pboole A))) ) ) ) ).
tt(t129_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) =>  ((k7_relat_1 (k5_relat_1 A C) B) = (k7_relat_1 A B)) ) ) ) ) ) ).
tt(t129_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k23_rvsum_1 (k8_rvsum_1 A B) (k8_rvsum_1 A B)) = (k9_binop_2 (k10_binop_2 (k23_rvsum_1 A A) (k11_binop_2 2 (k23_rvsum_1 A B))) (k23_rvsum_1 B B))) ) ) ) ) ) ).
tt(t129_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k14_seq_4 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ( (~  (D = k1_xboole_0) )  &  (~ (r1_xxreal_0 (k26_seq_4 A C D) (k9_binop_2 (k24_seq_4 A B C) (k24_seq_4 A B D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t129_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C)) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A (k5_sheffer1 A D D) C)) C)) ) ) ) ) ) ) ) ) ).
tt(t129_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_sincos10 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))))).
tt(t129_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k1_seq_1 k1_sin_cos9 B) (k5_square_1 B))) (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ) ).
tt(t129_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ((r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)) =>  ( ((m1_pre_topc C D) => (r1_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (u1_struct_0 D) (u1_struct_0 B) (k10_tmap_1 A B C D E F) F))  &  ( ((r1_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (u1_struct_0 D) (u1_struct_0 B) (k10_tmap_1 A B C D E F) F) => (m1_pre_topc C D))  &  ( ((m1_pre_topc D C) => (r1_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 B) (k10_tmap_1 A B C D E F) E))  &  ((r1_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 B) (k10_tmap_1 A B C D E F) E) => (m1_pre_topc D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t129_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k7_xboolean A (k3_xboolean A))) = k2_xboolean) ) ) ).
tt(t129_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k6_xcmplx_0 B C) = (k7_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 B A) (k3_xcmplx_0 C A)) A)) ) ) ) ) ) ) ) ).
tt(t129_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t129_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xxreal_1 A B) = (k2_xboole_0 (k2_xxreal_1 A B) (k1_tarski B))) ) ) ) ) ) ).
tt(t129_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((r2_zf_model D (k11_zf_lang A B)) =>  ((r2_hidden C (k2_zf_model A)) | (r2_zf_model D (k11_zf_lang A (k8_zf_lang C B)))) ) ) ) ) ) ) ) ) ) ).
tt(t129_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k2_zfmisc_1 B A)) &  (! [C:$i] :  (~  ((r2_hidden C B) &  (A = (k4_tarski C (k1_tarski C))) ) ) ) ) ) ) ) ).
tt(t129_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((r1_zmodul01 A (k3_zmodul01 A) (k4_zmodul01 A)) & (r1_zmodul01 A (k4_zmodul01 A) (k3_zmodul01 A))) ) ) ).
tt(t12_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  ((k3_abcmiz_0 A B) = (a_2_0_abcmiz_0 A B)) ) ) ) ) ).
tt(t12_abcmiz_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B A) =>  ((k1_abcmiz_1 B) = B) ) )  =>  ((k1_abcmiz_1 (k1_setfam_1 A)) = (k1_setfam_1 A)) ) ) ) ).
tt(t12_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k1_funct_1 B k1_xboole_0) = (k4_tarski C (u1_struct_0 A)))  => (m1_abcmiz_1 B A (k2_msualg_1 A C))) ) ) ) ) ) ) ).
tt(t12_abian,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_abian A)) )  => (r1_xxreal_0 1 A)) ) ).
tt(t12_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k18_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k18_complex1 A) (k18_complex1 B)))  => (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t12_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_aff_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t12_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) => (v7_aff_2 A)) ) ) ).
tt(t12_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(t12_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) ) ) ) ).
tt(t12_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((k2_afinsq_2 (k1_ordinal4 A B) (k1_afinsq_1 A)) = B) ) ) ) ) ).
tt(t12_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) & (v1_aff_1 C A))  =>  ( ((k5_afproj A B) = (k5_afproj A C))  <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ).
tt(t12_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) & (r2_analoaf A B F G E))  => (r2_analoaf A C F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r5_alg_1 A A)) ) ).
tt(t12_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( ((k1_algseq_1 A B) = (k1_algseq_1 A C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) D))  =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(t12_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r6_pboole A (k1_algspec1 A (k1_funct_4 (k6_partfun1 A) B)) (k1_algspec1 A B))) ) ) ).
tt(t12_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v21_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_algstr_1 A) & (l4_algstr_0 A)) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k1_algstr_0 A C B)) ) ) ) )  &  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B C) = (k5_struct_0 A)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v2_algstr_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_group_6 C B A) =>  ((v2_algstr_4 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) C D) B) & (m1_subset_1 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k10_xtuple_0 (k6_altcat_1 (k1_funct_2 A B) (k1_funct_2 B C))) (k1_funct_2 A C))) ) ) ).
tt(t12_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k4_cat_1 A B) (k1_binop_1 (k2_altcat_2 A) B B))) ) ) ) ).
tt(t12_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  ((v5_altcat_3 (k5_altcat_1 A B C D E F) A B D) &  (~ (v5_altcat_3 F A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v6_altcat_3 B A) & (v7_altcat_3 C A))  =>  ( ((k1_altcat_1 A C B) = k1_xboole_0)  |  ((v6_altcat_3 C A) & (v7_altcat_3 B A)) ) ) ) ) ) ) ) ) ).
tt(t12_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  ((k1_funct_1 (k6_ami_2 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ).
tt(t12_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k10_ami_3 A) = B) ) ) ) ) ) ).
tt(t12_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 5)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k6_ami_3 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_ami_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_ami_3) (k2_compos_0 (u1_compos_1 k1_ami_3) (k7_ami_3 A)))) 1) = k5_numbers) ) ) ).
tt(t12_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 B)) =>  ((v4_amistd_1 D A B) =>  ((k1_amistd_1 A B C D) = (k1_tarski (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t12_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v1_xboole_0 (k4_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t12_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) &  ((v5_amistd_5 B A) &  ((v6_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v4_extpro_1 D A B C)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) =>  ((v5_extpro_1 D A B C) <=> (v5_extpro_1 (k9_memstr_0 A B D E) A B (k6_compos_1 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v2_ami_wstd C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k4_ami_wstd B C D A) = (k4_ami_wstd B C E A))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r2_analmetr A D (k5_algstr_0 A E F) B C) & (r2_analmetr A E (k5_algstr_0 A F D) B C)) )  => (r2_analmetr A F (k5_algstr_0 A D E) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analoaf A B C D E) =>  ((r1_analoaf A C B E D) & (r1_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_analmetr A B C) =>  ((k2_analort A B C (k1_rlvect_1 A D E)) = (k1_rlvect_1 A (k2_analort A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_anproj_1 A B C D))  =>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  ( (~ (v9_struct_0 D A))  &  ( (~ (r1_anproj_1 A B C))  &  ( (~ (r1_anproj_1 A C D))  &  (~ (r1_anproj_1 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [E:$i] :  ((m2_funct_2 E A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) H E)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I F))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J G))) (k8_funcsdom A)) &  (~  ( (H = k6_numbers)  &  ( (I = k6_numbers)  &  (J = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) & (r2_hidden C (k9_xtuple_0 A)))  =>  ((r2_hidden C D) |  ((k1_funct_1 (k7_aofa_000 A D B) C) = C) ) ) ) ) ) ) ) ) ).
tt(t12_aofa_i00,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_power k6_numbers (k2_xcmplx_0 A B)) = (k3_xcmplx_0 (k3_power k6_numbers A) (k3_power k6_numbers B))) ) ) ) ) ).
tt(t12_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k4_armstrng A)) =>  (! [C:$i] :  ((m1_subset_1 C (k4_armstrng A)) =>  (! [D:$i] :  ((m1_subset_1 D (k4_armstrng A)) =>  ( ((r3_armstrng A C B) & (r3_armstrng A D C))  => (r3_armstrng A D B)) ) ) ) ) ) ) ) ).
tt(t12_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_subset_1 D (k2_arrow A) (k3_arrow A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_arrow A) (k3_arrow A)) =>  ( (~  ( (~  ( (~ (r1_arrow D C B))  & (r1_arrow E C B)) )  &  ( (~  ( (~ (r1_arrow E C B))  & (r1_arrow D C B)) )  &  ( (~  ( (~ (r1_arrow D B C))  & (r1_arrow E B C)) )  &  ( (~  ( (~ (r1_arrow E B C))  & (r1_arrow D B C)) )  &  (~  ( (~  ( (~ (r1_arrow D C B))  & (r1_arrow E C B)) )  &  (~  ( (~ (r1_arrow E C B))  & (r1_arrow D C B)) ) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (r1_arrow D C B))  & (r1_arrow E C B)) )  &  ( (~  ( (~ (r1_arrow E C B))  & (r1_arrow D C B)) )  &  (~  ( (~  ( (~ (r1_arrow D C B))  & (r1_arrow E C B)) )  &  ( (~  ( (~ (r1_arrow E C B))  & (r1_arrow D C B)) )  &  ( (~  ( (~ (r1_arrow D B C))  & (r1_arrow E B C)) )  &  (~  ( (~ (r1_arrow E B C))  & (r1_arrow D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = k6_numbers)  =>  ((k2_arytm_0 A B) = k6_numbers) ) ) ) ) ) ).
tt(t12_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 A C))  =>  ((k7_arytm_2 B (k1_arytm_1 C A)) = (k7_arytm_2 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ).
tt(t12_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((k8_arytm_2 A (k8_arytm_2 B C)) = (k8_arytm_2 (k8_arytm_2 A B) C)) ) ) ) ) ) ) ).
tt(t12_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  => (r2_arytm_3 (k2_arytm_3 A B) (k9_ordinal3 A B))) ) ) ) ).
tt(t12_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k6_asympt_0 B)) & (r2_hidden B (k6_asympt_0 C)))  => (r2_hidden A (k6_asympt_0 C))) ) ) ) ) ) ) ).
tt(t12_asympt_1,ax, (~ (r2_hidden (k3_asympt_1 2) (k7_asympt_0 (k3_asympt_1 3)))) ).
tt(t12_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ( ((v1_msualg_3 D) & (v2_msualg_3 D A B C))  =>  ((v1_msualg_3 (k4_msualg_3 A B C D)) & (v2_msualg_3 (k4_msualg_3 A B C D) A C B)) ) ) ) ) ) ) ) ) ).
tt(t12_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) => (m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A))) ) ) ) ).
tt(t12_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  ( ( (D = (k2_polynom2 A (k7_pre_poly A (k1_polynom2 A B) (k1_yellow_1 A)) B))  &  (E = (k2_polynom2 A (k7_pre_poly A (k1_finsub_1 (k1_zfmisc_1 A) (k1_polynom2 A B) C) (k1_yellow_1 A)) B)) )  =>  ((k2_wsierp_1 D) = (k2_wsierp_1 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B C (k1_bcialg_1 B C D)) = (k1_bcialg_1 B D (k1_bcialg_1 B D C))) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t12_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_bcialg_1 A (k2_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B C))) = (k1_bcialg_2 A (k4_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(t12_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (v2_bcialg_3 B A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t12_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A B (k1_bcialg_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t12_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_bcialg_1 A (k1_bcialg_5 A B C D (k2_nat_1 D 1)) (k1_bcialg_5 A C B D D))) ) ) ) ) ) ) ) ).
tt(t12_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden B (k4_bcialg_1 A)) =>  ((k3_bcialg_6 A (k19_binop_2 C) B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t12_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v13_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) => (v12_bcialg_1 B A)) ) ) ) ).
tt(t12_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_bhsp_1 A B (k5_algstr_0 A C D)) = (k9_real_1 (k2_bhsp_1 A B C) (k2_bhsp_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r1_xxreal_0 D E) &  (~  ((k1_normsp_1 A C E) = (k1_normsp_1 A B E)) ) ) ) ) ) )  |  ((k1_bhsp_2 A B) = (k1_bhsp_2 A C)) ) ) ) ) ) ) ) ) ).
tt(t12_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r2_bhsp_3 A B C) & (r2_bhsp_3 A C D))  => (r2_bhsp_3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t12_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C D) = (k1_normsp_1 A B k6_numbers)) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k1_valued_0 (u1_struct_0 A) B 1)) (k3_normsp_1 A (k1_valued_0 (u1_struct_0 A) (k1_bhsp_4 A B) 1) C))) ) ) ) ) ) ) ).
tt(t12_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m2_bhsp_5 C A))  =>  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((r1_tarski C (k9_xtuple_0 D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = (k1_rlvect_1 A E (k2_bhsp_1 A B E))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski C (k9_xtuple_0 E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k1_funct_1 E F) = (k5_square_1 (k2_bhsp_1 A B F))) ) ) ) )  =>  ((k2_bhsp_1 A (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) C D) (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) C D)) = (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k2_bilinear A B C D E) F) (k3_hahnban1 A B (k8_bilinear A B C D F) (k8_bilinear A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k3_binari_2 (k1_nat_1 A 1) (k7_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) = (k20_binop_2 (k21_binop_2 (k20_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D))) (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) (k15_funcop_1 k5_numbers (k4_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) (k15_funcop_1 k5_numbers (k5_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_binari_3,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( (~  ( ((k1_binarith A B) = k8_margrel1)  &  ( (~  (A = k8_margrel1) )  &  (~  (B = k8_margrel1) ) ) ) )  &  ( ( ( (A = k8_margrel1)  |  (B = k8_margrel1) )  =>  ((k1_binarith A B) = k8_margrel1) )  &  ( ( ((k1_binarith A B) = k7_margrel1)  =>  ( (A = k7_margrel1)  &  (B = k7_margrel1) ) )  &  ( ( (A = k7_margrel1)  &  (B = k7_margrel1) )  =>  ((k1_binarith A B) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(t12_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( ((k7_partfun1 k6_margrel1 B A) = k8_margrel1)  => (r1_xxreal_0 (k5_series_1 2 (k7_nat_d A 1)) (k6_binarith A B))) ) ) ) ) ).
tt(t12_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k5_xboolean A A) = A) ) ) ).
tt(t12_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_binom A B k6_numbers) = (k4_struct_0 A))  &  ((k6_binom A B k6_numbers) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t12_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 C A) =>  ((r6_binop_1 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A C D (k3_binop_1 A B E F)) = (k3_binop_1 A B (k3_binop_1 A C D E) (k3_binop_1 A C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  => (r1_tarski (k2_finseq_1 (k5_series_1 2 B)) (k10_xtuple_0 (k1_bintree2 A B)))) ) ) ) ).
tt(t12_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A B C) & (r1_boolealg A (k4_lattices A C D) (k5_lattices A)))  => (r1_boolealg A (k4_lattices A B D) (k5_lattices A))) ) ) ) ) ) ) ) ) ).
tt(t12_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v4_petri B A) <=>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  ( ((k7_relat_1 C B) = (k6_domain_1 k6_margrel1 k7_margrel1))  =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 A)) =>  ((r2_boolmark A C D) =>  ((k7_relat_1 (k3_boolmark A C D) B) = (k6_domain_1 k6_margrel1 k7_margrel1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) (k6_setlim_1 A B C) (k7_bor_cant A C)) & (r2_funct_2 k5_numbers (k9_setfam_1 A) (k5_setlim_1 A B C) (k9_bor_cant A C))) ) ) ) ) ) ) ).
tt(t12_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 (k2_borsuk_1 A B)) (k7_borsuk_1 A B C)) C)) ) ) ) ) ) ).
tt(t12_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r2_borsuk_2 A B C) => (r3_borsuk_2 A B C D D)) ) ) ) ) ) ) ) ) ).
tt(t12_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v3_pre_topc C (k2_borsuk_1 B A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A)))))  => (r2_hidden (a_3_0_borsuk_3 A B C) (u1_pre_topc A))) ) ) ) ) ) ).
tt(t12_borsuk_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = B) )  =>  ((k6_measure6 (k3_rcomp_1 A B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(t12_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A C) & (r1_xxreal_0 C B))  =>  ((k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 C) (k1_rcomp_1 A B)) = (k4_rcomp_1 k2_xxreal_0 B)) ) ) ) ) ) ) ) ).
tt(t12_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_4_borsuk_6)  &  (B = a_0_5_borsuk_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 1 k6_numbers (k10_real_1 1 2) (k1_real_1 (k10_real_1 1 2))) A) = B) ) ) ) ) ) ).
tt(t12_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ( ((k17_complex1 B) = (k17_complex1 C))  &  ((k1_comptrig B) = (k7_real_1 (k1_comptrig C) (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t12_brouwer,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k2_brouwer B C A))) &  ((v5_pre_topc D (k2_brouwer B C A) (k2_brouwer B C A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k2_brouwer B C A)))))) ) )  =>  ( (~ (v2_abian D))  =>  ((k2_partfun1 (u1_struct_0 (k2_brouwer B C A)) (u1_struct_0 (k7_toprealb B C A)) (k5_brouwer B A C D) (k3_topreal9 B C A)) = (k3_struct_0 (k7_toprealb B C A))) ) ) ) ) ) ) ) ) ) ).
tt(t12_bspace,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k3_bspace A B) = (k3_bspace A C))  <=>  ((r2_hidden B A) <=> (r2_hidden C A)) ) ) ) ) ).
tt(t12_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A (k2_bvfunc_1 A B C) (k1_bvfunc_1 A D)) B) D) (k1_bvfunc_1 A C))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t12_bvfunc14,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  (B = C) )  =>  ((k1_funct_1 (k1_funct_4 (k1_funct_4 A (k16_funcop_1 B D)) (k16_funcop_1 C E)) B) = D) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k5_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k1_bvfunc_1 A (k6_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t12_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k6_bvfunc_1 A C D)) (k10_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r1_bvfunc_1 A C (k7_bvfunc_2 A C B D))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A (k2_bvfunc_1 A C D)) (k1_bvfunc_1 A (k2_bvfunc_1 A B D)))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A B D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t12_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B C) (k1_bvfunc_1 A (k10_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t12_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t12_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_c0sp1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_c0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_c0sp1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k3_rlvect_1 (k7_c0sp1 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_seq_1 G H) = (k7_real_1 (k1_seq_1 E H) (k1_seq_1 F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k1_c0sp2 A k6_numbers) = (k4_struct_0 (k5_c0sp2 A))) ) ) ).
tt(t12_calcul_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_relset_1 k5_numbers (k14_finseq_1 (k4_subset_1 k5_numbers (k2_finseq_1 B) (k6_domain_1 k5_numbers (k2_nat_1 B A))))) = (k2_finseq_1 (k2_nat_1 B 1))) ) ) ) ) ) ).
tt(t12_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k2_relset_1 k5_numbers (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)))) = (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t12_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k2_cantor_1 A B)) & (r2_hidden D (k2_cantor_1 A B)))  => (r2_hidden (k3_xboole_0 C D) (k2_cantor_1 A B))) ) ) ) ) ) ).
tt(t12_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( ((k9_xtuple_0 C) = B)  & (r1_tarski A (k10_xtuple_0 C))) ) ) ) ) ) ).
tt(t12_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((r2_wellord2 A B) & (r2_wellord2 C D))  =>  ( (E = F)  |  ( (G = H)  |  ((r2_wellord2 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski E)) (k2_zfmisc_1 C (k1_tarski F))) (k2_xboole_0 (k2_zfmisc_1 B (k1_tarski G)) (k2_zfmisc_1 D (k1_tarski H)))) &  ((k1_card_1 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski E)) (k2_zfmisc_1 C (k1_tarski F)))) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 B (k1_tarski G)) (k2_zfmisc_1 D (k1_tarski H))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ( ((k4_card_3 B) = k1_xboole_0)  |  ((k5_card_3 A (k4_card_3 B)) = (k1_funct_1 B A)) ) ) ) ) ) ).
tt(t12_card_4,ax, (! [A:$i] :  ( ((v4_card_3 A) &  (! [B:$i] :  ((r2_hidden B A) => (v4_card_3 B)) ) )  => (v4_card_3 (k3_tarski A))) ) ).
tt(t12_card_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((k5_relat_1 (k1_ordinal4 A B) (k9_xtuple_0 A)) = A) ) ) ) ) ).
tt(t12_card_fil,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))))  =>  ((r1_card_fil B A C) => (r2_card_fil B A (k7_setfam_1 B C))) ) ) ) ) ) ) ).
tt(t12_cardfin2,ax, (! [A:$i] :  ((k2_cardfin2 (k1_tarski A)) = k1_xboole_0) ) ).
tt(t12_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  ((k5_card_1 (k1_card_fin C (k5_card_1 C) A B)) = 1) ) ) ) ) ).
tt(t12_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) =>  ((v2_card_lar (k6_subset_1 A B) A) & (v1_card_lar (k6_subset_1 A B) A)) ) ) ) ) ) ).
tt(t12_cat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cat_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k3_cat_1 A B))) => (m1_cat_1 E (k3_cat_1 A B) C D)) ) ) ) ) ) ) ) ).
tt(t12_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m3_cat_2 A A)) ) ).
tt(t12_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( (~  (A = B) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_oppcat_1 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k2_oppcat_1 C))) => (r2_funct_2 (k2_tarski A B) (u4_struct_0 C) (k5_cat_3 C (k2_tarski A B) (k5_funct_4 (u4_struct_0 (k2_oppcat_1 C)) A B D E)) (k5_funct_4 (u4_struct_0 C) A B (k6_oppcat_1 C D) (k6_oppcat_1 C E)))) ) ) ) ) ) ) ) ) ).
tt(t12_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_cat_1 C A B (k1_cat_4 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B (k1_cat_4 A)) =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t12_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_catalan1,ax, ((k1_catalan1 2) = 1) ).
tt(t12_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ((v1_catalan2 B) &  ( ((k24_binop_2 2 (k7_afinsq_2 (k5_relat_1 B A))) = A)  &  (B = (k1_catalan2 (k5_relat_1 B A) C)) ) )  => (v1_catalan2 C)) ) ) ) ) ) ) ).
tt(t12_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k6_catalg_1 A C) = (k6_catalg_1 B D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ).
tt(t12_cayley,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) => (v2_funct_2 (k3_cayley A B C) (u1_struct_0 (k2_cayley B)))) ) ) ) ) ) ) ).
tt(t12_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k2_numbers B A)) => (r2_funct_2 A k2_numbers (k4_cc0sp1 A B) B)) ) ) ) ) ).
tt(t12_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cc0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cc0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k2_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k8_group_1 (k3_cc0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers G H) = (k9_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers E H) (k3_funct_2 (u1_struct_0 A) k2_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r1_tarski (k2_relset_1 k2_numbers A) (k1_relset_1 k2_numbers B)) => (r2_relset_1 k5_numbers k1_numbers (k7_comseq_3 (k9_comseq_3 C (k8_funct_2 k5_numbers k2_numbers k2_numbers A B))) (k7_comseq_3 (k8_funct_2 k5_numbers k2_numbers k2_numbers (k9_comseq_3 C A) B)))) ) ) ) ) ) ) ).
tt(t12_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  ((v6_cfdiff_1 A) <=>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_cfdiff_1 C B) =>  (~ (r1_tarski C A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) k6_complex1 B)) B)) ) ) ) ).
tt(t12_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( (~  (C = k6_numbers) )  =>  ((k8_relset_1 A k2_numbers (k25_valued_1 A k2_numbers B C) (k1_tarski k6_numbers)) = (k8_relset_1 A k2_numbers B (k1_tarski k6_numbers))) ) ) ) ) ) ) ) ).
tt(t12_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden B (k2_cgames_1 A)) <=> (r1_ordinal1 (k9_cgames_1 B) A)) ) ) ) ) ).
tt(t12_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t12_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_abian A))  =>  (~  ((r1_xxreal_0 A 5) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 2) )  &  (~  (A = 4) ) ) ) ) ) ) ) ).
tt(t12_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A D))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) =>  ( ( (G = (k5_relat_1 I (u1_struct_0 A)))  &  ( (H = (k5_relat_1 I (u1_struct_0 B)))  &  ((v1_circuit2 G A D) & (v1_circuit2 H B E)) ) )  => (v1_circuit2 I C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D C) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 C B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C B) B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k5_circcomb E D) (k7_circcomb C B E D)))) => (m2_finseq_2 (k3_relat_1 D F) B (k4_finseq_2 C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r2_hidden C (k2_msafree2 (k2_circcomb A B))) => (r2_hidden C (k2_msafree2 B))) ) ) ) ) ) ) ).
tt(t12_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_rltopsp1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k2_circled1 A B) C)) ) ) ) ) ) ) ).
tt(t12_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_msaterm C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k1_circtrm1 A B C))) =>  (D = (k4_trees_4 (k1_funct_1 D k1_xboole_0) (k1_msualg_1 (k1_circtrm1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t12_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (~  ((r2_hidden C (k7_subset_1 (u1_struct_0 A) (k3_msafree2 A) (k1_msafree2 A))) &  ( ((k5_card_1 D) = (k4_circuit1 A B C))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v6_trees_3 E)) ) )  =>  (~  (D = (k4_trees_4 (k4_tarski (k4_msafree2 A C) (u1_struct_0 A)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ((r1_tarski D C) => (r1_tarski D (k6_circuit2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t12_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A (k3_classes1 B C)) => (r2_hidden (k9_setfam_1 A) (k3_classes1 B (k1_ordinal1 C)))) ) ) ) ) ).
tt(t12_classes2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k1_classes1 B)) => (r2_hidden (k1_card_1 A) (k1_classes1 B))) ) ) ).
tt(t12_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_clopban1 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (D = (k1_clvect_1 (k3_clopban1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k4_clopban1 A B D F) = (k1_clvect_1 B (k4_clopban1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k6_clopban1 A A)) (k8_clopban1 A A)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k4_clopban2 A (k3_clopban2 A C B) D) = (k3_clopban2 A C (k4_clopban2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v9_clvect_1 B A)) ) ) ) ) ).
tt(t12_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A B D)) (k1_seq_1 C D))) )  &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = k6_numbers) ) )  =>  ((v9_clvect_1 B A) &  ((k7_clvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t12_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_closure1 (k2_msualg_3 A (k5_mssubfam A B)) A B) & (m2_pboole (k2_msualg_3 A (k5_mssubfam A B)) A (k5_mssubfam A B) (k5_mssubfam A B))) ) ) ) ).
tt(t12_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_closure2 C A B (k2_closure2 A B)) =>  (! [D:$i] :  ((m1_closure2 D A B (k2_closure2 A B)) => (r2_hidden (k5_pboole A C D) (k2_closure2 A B))) ) ) ) ) ) ) ).
tt(t12_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) => (r2_pboole A (k2_closure3 A B (k4_closure3 A B C D)) (k3_pboole A (k2_closure3 A B C) (k2_closure3 A B D)))) ) ) ) ) ) ) ).
tt(t12_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k1_clvect_1 A B C) = (k1_clvect_1 A B D))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  (~  ((k1_normsp_1 A C E) = (k1_normsp_1 A B E)) ) ) ) ) ) )  |  ((k1_clvect_2 A B) = (k1_clvect_2 A C)) ) ) ) ) ) ) ) ) ).
tt(t12_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A B D) = (k1_normsp_1 A C k6_numbers)) ) )  =>  ((k1_bhsp_4 A (k1_valued_0 (u1_struct_0 A) C 1)) = (k3_normsp_1 A (k1_valued_0 (u1_struct_0 A) (k1_bhsp_4 A C) 1) B)) ) ) ) ) ) ) ) ).
tt(t12_cohsp_1,ax, (! [A:$i] :  ((v1_cohsp_1 (k5_finsub_1 A)) & (v2_cohsp_1 (k5_finsub_1 A))) ) ).
tt(t12_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k1_coh_sp (k2_coh_sp A B)) = B) ) ) ) ).
tt(t12_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k1_combgras A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k1_combgras A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k1_combgras A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k1_combgras A B))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k1_combgras A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 (k1_combgras A B))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k1_combgras A B))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k1_combgras A B))) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 (k1_combgras A B))) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 (k1_combgras A B))) =>  (~  ((r1_incsp_1 (k1_combgras A B) C I) &  ((r1_incsp_1 (k1_combgras A B) D I) &  ((r1_incsp_1 (k1_combgras A B) E J) &  ((r1_incsp_1 (k1_combgras A B) F J) &  ((r1_incsp_1 (k1_combgras A B) G I) &  ((r1_incsp_1 (k1_combgras A B) G J) &  ((r1_incsp_1 (k1_combgras A B) C K) &  ((r1_incsp_1 (k1_combgras A B) E K) &  ((r1_incsp_1 (k1_combgras A B) D L) &  ((r1_incsp_1 (k1_combgras A B) F L) &  ( (~ (r1_incsp_1 (k1_combgras A B) G K))  &  ( (~ (r1_incsp_1 (k1_combgras A B) G L))  &  ( (~  (I = J) )  &  ( (~  (K = L) )  &  (! [M:$i] :  ((m1_subset_1 M (u1_incsp_1 (k1_combgras A B))) =>  (~  ((r1_incsp_1 (k1_combgras A B) M K) &  ((r1_incsp_1 (k1_combgras A B) M L) &  (M = (k2_xboole_0 (k3_xboole_0 C D) (k3_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k3_complex1 (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1))) = A)  &  ((k4_complex1 (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1))) = B) ) ) ) ) ) ).
tt(t12_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (A = (k2_xcmplx_0 (k8_real_1 (k17_complex1 A) (k21_sin_cos (k1_comptrig A))) (k3_xcmplx_0 (k8_real_1 (k17_complex1 A) (k18_sin_cos (k1_comptrig A))) k7_complex1))) ) ) ).
tt(t12_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (A = (k5_algstr_0 k1_complfld (k3_rlvect_1 k1_complfld A B) B)) ) ) ) ) ).
tt(t12_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k12_seq_4 A (k19_binop_2 1)) = (k11_seq_4 A)) ) ) ).
tt(t12_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) =>  ( (C = (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) B))  =>  ( ((v6_compl_sp B A) => (v1_tops_2 C (k3_pcomps_1 A)))  &  ((v7_compl_sp B A) => (v2_tops_2 C (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(t12_compos_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_compos_0 B) &  ((v2_compos_0 B) &  ((v3_compos_0 B) & (v5_compos_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ( ((k5_compos_0 B C A) = (k6_compos_0 B))  =>  (C = (k6_compos_0 B)) ) ) ) ) ) ) ) ).
tt(t12_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  ((k5_card_1 (k3_compos_2 A B C)) = 3) ) ) ) ) ) ) ).
tt(t12_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) => (r1_xxreal_0 k6_numbers (k1_seq_1 k19_sin_cos A))) ) ) ).
tt(t12_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v8_pre_topc A) & (v1_compts_1 A))  => (v9_pre_topc A)) ) ) ).
tt(t12_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_funct_1 A) & (v1_comput_1 A)) )  =>  ((k9_xtuple_0 (k3_tarski A)) = (k3_tarski (a_1_0_comput_1 A))) ) ) ).
tt(t12_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k19_valued_1 k5_numbers k2_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A) C))) ) ) ) ) ) ).
tt(t12_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers A)) = (k15_complex1 (k3_comseq_2 A))) ) ) ) ).
tt(t12_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (r1_xxreal_0 (k17_complex1 A) (k7_real_1 (k18_complex1 (k3_complex1 A)) (k18_complex1 (k4_complex1 A))))) ) ).
tt(t12_conlat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_waybel_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (C = (k1_waybel_1 A B D E))  =>  ((v3_conlat_1 C A B) <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r3_orders_2 A F (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E G)) <=> (r3_orders_2 B G (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((v8_lattice6 (k2_relset_1 (u1_struct_0 (k11_conlat_1 A)) (k4_conlat_2 A)) (k11_conlat_1 A)) & (v9_lattice6 (k2_relset_1 (u1_struct_0 (k11_conlat_1 A)) (k5_conlat_2 A)) (k11_conlat_1 A))) ) ) ).
tt(t12_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v6_conmetr1 A) => (v5_conmetr1 A)) ) ) ).
tt(t12_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( ((v7_conmetr A) & (v5_conmetr A))  => (v6_conmetr A)) ) ) ).
tt(t12_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_connsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (k1_struct_0 A)) )  &  ( (~  (B = (k2_struct_0 A)) )  & (r1_xboole_0 (k2_pre_topc A B) (k2_pre_topc A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)))) ) ) ) ) ) ) ) ).
tt(t12_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  => (r1_tarski (k1_connsp_1 B D) (k1_connsp_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t12_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((v2_connsp_1 C A) & (r1_tarski B C)) )  =>  ( (B = k1_xboole_0)  |  ((k1_connsp_3 A B) = (k1_connsp_3 A C)) ) ) ) ) ) ) ) ) ).
tt(t12_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_tarski (k1_convex1 A B (k7_real_1 C D)) (k6_rusub_4 A (k1_convex1 A B C) (k1_convex1 A B D)))) ) ) ) ) ) ) ) ).
tt(t12_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_convex1 B A) & (m1_rlvect_2 B A))  =>  (! [C:$i] :  ( ((v2_convex1 C A) & (m1_rlvect_2 C A))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 (k8_real_1 D E) k6_numbers))  =>  ((k3_rlvect_2 A (k7_rlvect_2 A (k8_rlvect_2 A D B) (k8_rlvect_2 A E C))) = (k4_subset_1 (u1_struct_0 A) (k3_rlvect_2 A (k8_rlvect_2 A D B)) (k3_rlvect_2 A (k8_rlvect_2 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = k1_xboole_0) )  =>  ((v6_clvect_1 B A) <=>  (! [C:$i] :  ((m2_convex4 C A B) => (r2_hidden (k4_convex4 A C) B)) ) ) ) ) ) ) ) ).
tt(t12_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (m2_subset_1 (k4_qc_lang2 A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ).
tt(t12_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_qc_lang2 A B (k11_cqc_lang A C B))) ) ) ) ) ) ).
tt(t12_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_hidden (k8_cqc_lang A (k11_cqc_lang A D C) C) (k1_cqc_the1 A B))) ) ) ) ) ) ) ) ).
tt(t12_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k13_cqc_lang A (k2_qc_lang2 A B C) D) = (k2_qc_lang2 A (k13_cqc_lang A B D) (k13_cqc_lang A C D))) ) ) ) ) ) ) ) ) ).
tt(t12_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r1_tarski B C) => (r2_cqc_the3 A C B)) ) ) ) ) ) ) ).
tt(t12_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k7_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k2_comseq_2 k5_numbers A))) B)) &  ((k1_seq_1 (k8_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k2_comseq_2 k5_numbers A))) B) = k6_numbers) ) ) ) ) ) ).
tt(t12_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_csspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  => (v4_xxreal_2 (k7_csspace4 A B C))) ) ) ) ) ) ).
tt(t12_csspace,ax, ((v6_clvect_1 k11_csspace k7_csspace) &  (~ (v1_xboole_0 k11_csspace)) ) ).
tt(t12_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k7_decomp_1 A) (k16_decomp_1 A)) = (k6_decomp_1 A)) ) ) ).
tt(t12_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A B (k3_finseq_1 B)) = B) ) ) ) ) ) ).
tt(t12_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( (A = (k3_dickson A))  <=> (v5_relat_2 A)) ) ) ).
tt(t12_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 B A) C)) &  ((v1_funct_2 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 B A) C) k1_numbers k1_numbers) & (m1_subset_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 B A) C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t12_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_diff_2 (k3_valued_1 k1_numbers k1_numbers k1_numbers F G) A B C D E) = (k7_real_1 (k1_diff_2 F A B C D E) (k1_diff_2 G A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 E C) A) C) B) D) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 E C) (k2_nat_1 A B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k2_fdiff_9)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k2_fdiff_9)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_fdiff_9) B) A) = (k10_complex1 (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k9_real_1 (k8_real_1 2 A) B))) (k18_sin_cos B)) (k5_square_1 (k9_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B)))))) ) ) ) ) ) ).
tt(t12_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r5_waybel_4 A B C) & (r1_orders_2 A D C))  =>  ((v1_dilworth (k2_xboole_0 B (k1_tarski D)) A) & (m1_subset_1 (k2_xboole_0 B (k1_tarski D)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_diraf A D B C) & (r1_diraf A B C E))  =>  ( (B = C)  | (r1_diraf A D C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v2_dirort A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_dirort A B C D E) & (r2_dirort A D E F G))  =>  ( (D = E)  | (r2_dirort A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k1_funct_1 (k7_dist_1 A) (k5_dist_1 A B)) = (k4_dist_1 A B)) ) ) ) ) ).
tt(t12_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  ( (A = (k4_zfmisc_1 B C D E))  <=>  (! [F:$i] :  ((r2_hidden F A) <=>  (? [G:$i] :  ((m1_subset_1 G B) &  (? [H:$i] :  ((m1_subset_1 H C) &  (? [I:$i] :  ((m1_subset_1 I D) &  (? [J:$i] :  ((m1_subset_1 J E) &  (F = (k6_xtuple_0 G H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (A = (k3_funct_2 (k4_dtconstr k5_dtconstr) k5_numbers k12_dtconstr (k8_nat_1 (k4_dtconstr k5_dtconstr) k14_dtconstr A))) ) ) ).
tt(t12_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (! [C:$i] :  ((r2_hidden C A) => (m1_dynkin C B)) )  => (m1_dynkin (k1_setfam_1 A) B)) ) ) ) ) ).
tt(t12_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (1 = (k5_struct_0 (k9_int_3 A))) ) ) ).
tt(t12_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) F) G) = (k8_group_1 A B (k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A C D) E) F) G)))  &  ((k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A (k8_group_1 A B C) D) E) F) G) = (k8_group_1 A (k8_group_1 A (k8_group_1 A B (k8_group_1 A (k8_group_1 A C D) E)) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) => (m2_pboole (k16_funcop_1 k6_numbers B) (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) ) ) ) ).
tt(t12_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  ( ((k3_ens_1 A B) = (k4_ens_1 A C))  =>  ( ((k2_xtuple_0 (k6_ens_1 A C B)) = (k3_relat_1 (k2_xtuple_0 C) (k2_xtuple_0 B)))  &  ( ((k3_ens_1 A (k6_ens_1 A C B)) = (k3_ens_1 A C))  &  ((k4_ens_1 A (k6_ens_1 A C B)) = (k4_ens_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t12_entropy1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  & (r1_entropy1 B A))  =>  ((r1_entropy1 (k14_rvsum_1 B C) A) &  ((k1_seq_1 (k14_rvsum_1 B C) A) = (k8_real_1 (k1_seq_1 B A) (k1_seq_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t12_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k2_tarski A B) (k2_enumset1 C D E F))) ) ) ) ) ) ) ).
tt(t12_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (? [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  ((r1_relset_1 A A B C) &  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_relset_1 A A B D) => (r1_relset_1 A A C D)) ) ) ) ) ) ) ) ) ).
tt(t12_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k9_pboole A C B) (k3_funct_6 B))) ) ) ) ) ).
tt(t12_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((k1_sysrel (u1_e_siec A)) = (k1_sysrel (u2_e_siec A))) ) ) ).
tt(t12_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k5_square_1 (k12_euclid (k8_rvsum_1 A B))) = (k9_binop_2 (k10_binop_2 (k5_square_1 (k12_euclid A)) (k11_binop_2 2 (k23_rvsum_1 B A))) (k5_square_1 (k12_euclid B)))) ) ) ) ) ) ).
tt(t12_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k2_xcmplx_0 (k17_euclid (k4_algstr_0 (k15_euclid 2) A)) (k3_xcmplx_0 (k18_euclid (k4_algstr_0 (k15_euclid 2) A)) k7_complex1)) = (k2_xcmplx_0 (k1_real_1 (k17_euclid A)) (k3_xcmplx_0 (k1_real_1 (k18_euclid A)) k7_complex1))) ) ) ).
tt(t12_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ((v1_euclid_4 B A) &  ((v1_euclid_4 C A) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~  (D = E) )  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k5_algstr_0 (k15_euclid 3) A B) = (k4_euclid_5 (k9_real_1 (k1_euclid_5 A) (k1_euclid_5 B)) (k9_real_1 (k2_euclid_5 A) (k2_euclid_5 B)) (k9_real_1 (k3_euclid_5 A) (k3_euclid_5 B)))) ) ) ) ) ).
tt(t12_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B D)) &  ( (~  (C = D) )  &  ( (~  (A = B) )  &  ( (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) B D)))  &  (~ (r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_euclid_7,ax, ((v1_funct_1 (k12_finseq_1 k5_numbers 1)) &  ((v1_funct_2 (k12_finseq_1 k5_numbers 1) (k6_domain_1 k5_numbers 1) (k6_domain_1 k5_numbers 1)) &  ((v3_funct_2 (k12_finseq_1 k5_numbers 1) (k6_domain_1 k5_numbers 1) (k6_domain_1 k5_numbers 1)) & (m1_subset_1 (k12_finseq_1 k5_numbers 1) (k1_zfmisc_1 (k2_zfmisc_1 (k6_domain_1 k5_numbers 1) (k6_domain_1 k5_numbers 1))))) ) ) ).
tt(t12_euclid_8,ax, ((k23_rvsum_1 k4_euclid_8 k4_euclid_8) = 1) ).
tt(t12_euclid_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid k6_numbers))) =>  ((k4_euclid_9 k6_numbers B A) = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t12_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k7_euclid A B C)) (k7_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t12_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  ( ((k9_euclid B (k8_euclid B C D) A) = (k7_euclid B (k9_euclid B C A) (k6_euclid B (k9_euclid B D A))))  &  ( ((k9_euclid B (k8_euclid B C D) A) = (k7_euclid B (k9_euclid B C A) (k9_euclid B D (k1_real_1 A))))  &  ((k9_euclid B (k8_euclid B C D) A) = (k8_euclid B (k9_euclid B C A) (k9_euclid B D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_euclmetr A) <=> (v5_conmetr A)) ) ) ).
tt(t12_euler_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k6_int_1 (k2_xcmplx_0 A (k3_xcmplx_0 B C)) C) = (k6_int_1 A C)) ) ) ) ) ) ) ).
tt(t12_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k4_nat_d (k3_xcmplx_0 A C) B) = (k4_nat_d C B))  & (r1_int_2 B C))  =>  ( (A = k1_xboole_0)  |  ((r1_xxreal_0 B 1) |  ((k4_nat_d A B) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t12_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v2_exchsort A (k2_ordinal2 (k9_xtuple_0 A)))) ) ).
tt(t12_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((v2_msualg_3 D A B C) <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) ) )  =>  (! [F:$i] :  ((m2_pboole F A C E) =>  (! [G:$i] :  ((m2_pboole G A C E) =>  ((r6_pboole A (k3_msualg_3 A B C E D F) (k3_msualg_3 A B C E D G)) => (r6_pboole A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) & (v1_funct_1 D)) ) )  =>  ((r1_tarski (k16_funcop_1 C (k2_compos_1 B)) D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v5_memstr_0 E A B C)) ) ) )  => (v4_extpro_1 E A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( ((r1_xxreal_0 (k2_supinf_2 A) B) & (r1_xxreal_0 B A))  <=> (r1_xxreal_0 (k3_extreal1 B) A)) ) ) ) ) ).
tt(t12_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_facirc_1 A B C (k1_nat_1 D 1)) = (k6_circuit2 A B (k5_facirc_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t12_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((k3_facirc_2 (k2_nat_1 A 1) B C) = (k2_circcomb (k3_facirc_2 A B C) (k19_facirc_1 (k1_funct_1 B (k2_nat_1 A 1)) (k1_funct_1 C (k2_nat_1 A 1)) (k5_facirc_2 A B C))))  &  ( ((k4_facirc_2 (k2_nat_1 A 1) B C) = (k3_circcomb (k3_facirc_2 A B C) (k19_facirc_1 (k1_funct_1 B (k2_nat_1 A 1)) (k1_funct_1 C (k2_nat_1 A 1)) (k5_facirc_2 A B C)) (k4_facirc_2 A B C) (k20_facirc_1 (k1_funct_1 B (k2_nat_1 A 1)) (k1_funct_1 C (k2_nat_1 A 1)) (k5_facirc_2 A B C))))  &  ((k5_facirc_2 (k2_nat_1 A 1) B C) = (k17_facirc_1 (k1_funct_1 B (k2_nat_1 A 1)) (k1_funct_1 C (k2_nat_1 A 1)) (k5_facirc_2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t12_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C B))) &  ((r1_fcont_1 C A) & (r1_fcont_1 B (k1_seq_1 C A))) )  => (r1_fcont_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C B) A)) ) ) ) ) ) ) ).
tt(t12_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  ((v1_rcomp_1 A) & (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers B A))) )  => (v1_rcomp_1 (k7_relset_1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t12_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((k7_relset_1 k1_numbers k1_numbers B A) = (k3_limfunc1 C)) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t12_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos) A) B) = (k7_real_1 (k1_seq_1 k16_sin_cos B) (k10_real_1 (k1_seq_1 k16_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t12_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_sin_cos9))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k2_sin_cos9 B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k2_sin_cos9 B))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_sin_cos9) A) B) = (k10_real_1 1 (k8_real_1 (k7_real_1 1 (k5_square_1 B)) (k7_real_1 1 (k5_square_1 (k1_seq_1 k2_sin_cos9 B)))))) ) ) ) ) ) ) ) ).
tt(t12_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_rcomp_1 C B) =>  ( ((r1_fdiff_1 A B) & (r1_tarski C (k1_relset_1 k1_numbers A)))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski B))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) &  ((k1_fdiff_1 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((r1_fdiff_1 C A) &  ((k1_fdiff_1 C A) = B) )  =>  ( (? [D:$i] :  ((m1_rcomp_1 D A) & (r1_tarski D (k1_relset_1 k1_numbers C))) )  &  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski A))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers C)))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) C) (k8_funct_2 k5_numbers k1_numbers k1_numbers E C)))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) C) (k8_funct_2 k5_numbers k1_numbers k1_numbers E C)))) = B) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski A))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers C)))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) C) (k8_funct_2 k5_numbers k1_numbers k1_numbers E C)))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) C) (k8_funct_2 k5_numbers k1_numbers k1_numbers E C)))) = B) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_rcomp_1 D A) =>  (~ (r1_tarski D (k1_relset_1 k1_numbers C))) ) )  |  ((r1_fdiff_1 C A) &  ((k1_fdiff_1 C A) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r4_fdiff_3 A C) & (r4_fdiff_3 B C))  =>  ((r4_fdiff_3 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k1_fdiff_3 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k8_real_1 (k1_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k1_fdiff_3 C B) (k1_seq_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)))) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G))) ) ) )  &  (F = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) D) G) = (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))))) &  ((r1_xxreal_0 1 A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 A D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))) B) D) = (k1_real_1 (k8_real_1 (k8_real_1 A (k5_prepower (k1_seq_1 k19_sin_cos D) (k9_real_1 A 1))) (k1_seq_1 k16_sin_cos (k8_real_1 (k7_real_1 A 1) D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) D) (k10_real_1 1 (k6_power k8_power A))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k8_real_1 E (k6_power k8_power A)))  &  ((k1_seq_1 D E) = (k9_real_1 E (k10_real_1 1 (k6_power k8_power A)))) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) D) (k10_real_1 1 (k6_power k8_power A))) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) D) (k10_real_1 1 (k6_power k8_power A))) B) E) = (k8_real_1 E (k10_prepower A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) A) B) = (k10_real_1 (k1_seq_1 k1_sin_cos6 B) (k7_square_1 (k9_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t12_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t12_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t12_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) = (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))  &  ( ((k3_relat_1 (k4_relat_1 (u4_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))  &  ( ((k3_relat_1 (k4_relat_1 (u4_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k4_relat_1 (u1_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k4_relat_1 (u1_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))  &  ( ((k3_relat_1 (k4_relat_1 (u4_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_relat_1 (u4_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_relat_1 (u1_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_relat_1 (u1_struct_0 A)) (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A))) = k1_xboole_0)  &  ( ((k3_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = k1_xboole_0)  &  ((k3_relat_1 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_nat_d B C) & (r1_nat_d B A))  => (r1_nat_d B (k2_nat_1 (k4_nat_1 C D) (k3_nat_1 A E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_fib_num3 (k1_nat_1 A 2)) = (k2_nat_1 (k1_fib_num3 A) (k1_fib_num3 (k1_nat_1 A 1)))) ) ) ).
tt(t12_fib_num4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k1_fib_num3 B) (k1_fib_num3 A))) ) ) ) ) ).
tt(t12_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( (D = (k10_finseq_1 A B))  =>  ((k2_rfinseq C 1 D) = (k9_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t12_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ( (~ (v1_xboole_0 (k6_domain_1 (u1_struct_0 A) (k6_lattices A))))  &  ((v19_lattices (k6_domain_1 (u1_struct_0 A) (k6_lattices A)) A) &  ((v20_lattices (k6_domain_1 (u1_struct_0 A) (k6_lattices A)) A) & (m1_subset_1 (k6_domain_1 (u1_struct_0 A) (k6_lattices A)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t12_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  (! [D:$i] :  ((m2_filter_1 D A B) =>  ((r1_lattice2 A C D) => (r1_lattice2 (k8_eqrel_1 A B) (k3_filter_1 A B C) (k3_filter_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k7_lattices A C) = (k7_lattices B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k6_finance1 A k1_numbers B k12_prob_1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k6_finance1 A k1_numbers B k12_prob_1))))) )  =>  ((r2_funct_2 A k1_numbers (k9_finance1 k6_numbers A k1_numbers B k12_prob_1 (k6_finance1 A k1_numbers B k12_prob_1) F) (k8_funcop_1 k1_numbers A (k9_binop_2 1 D))) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k11_finance1 C E A B (k6_finance1 A k1_numbers B k12_prob_1) F G) = (k9_binop_2 (k11_binop_2 (k9_binop_2 1 D) (k1_seq_1 E k6_numbers)) (k12_finance1 C E A B (k6_finance1 A k1_numbers B k12_prob_1) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (A = (k4_tarski C (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t12_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) => (r2_hidden (k1_funct_1 A C) B)) ) )  => (m2_finseq_1 A B)) ) ) ) ).
tt(t12_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((r1_xxreal_0 A C) | (r2_hidden (k6_xcmplx_0 A C) (k2_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t12_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r2_hidden B (k10_xtuple_0 A)))  =>  ((k1_funct_1 (k2_funct_1 A) B) = (k1_finseq_4 A B)) ) ) ) ) ).
tt(t12_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ( ((k4_finseq_1 B) = (k4_finseq_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k7_partfun1 A B D) = (k7_partfun1 A C D)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t12_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k10_xtuple_0 A)) =>  ((k5_finseq_4 (k7_finseq_1 A B) C) = (k5_finseq_4 A C)) ) ) ) ) ) ) ).
tt(t12_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_finseq_7 A (k12_finseq_1 A B) 1 C) = (k12_finseq_1 A C)) ) ) ) ) ) ) ).
tt(t12_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k5_finseq_8 A B C) = (k1_finseq_8 A (k1_finseq_8 A (k6_finseq_8 A B C) (k4_finseq_8 A B C)) (k7_finseq_8 A B C)))  &  ((k5_finseq_8 A B C) = (k1_finseq_8 A (k6_finseq_8 A B C) (k1_finseq_8 A (k4_finseq_8 A B C) (k7_finseq_8 A B C)))) ) ) ) ) ) ) ) ).
tt(t12_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A C) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) B)))) )  =>  (! [G:$i] :  ((m2_finseq_1 G C) => (r2_relset_1 k5_numbers B (k3_finseqop A C B F D (k8_finseq_1 C G (k12_finseq_1 C E))) (k8_finseq_1 B (k3_finseqop A C B F D G) (k12_finseq_1 B (k2_binop_1 A C B F D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_finset_1,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  ( (~  (A = k1_xboole_0) )  &  ((v6_ordinal1 A) &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  ((r2_hidden C A) => (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ).
tt(t12_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k2_finseq_4 A B C) D) = (k5_binop_1 A D B C)) ) ) ) ) ) ) ) ) ).
tt(t12_finsub_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k2_xboole_0 (k5_finsub_1 A) (k5_finsub_1 B)) (k5_finsub_1 (k2_xboole_0 A B)))) ) ).
tt(t12_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_fintopo2 A B C) = k8_margrel1)  <=> (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t12_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k1_fintopo3 A B) (k1_fintopo3 A C)) = (k1_fintopo3 A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t12_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_fin_topo A) =>  ((v4_fin_topo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_fintopo4 A C D) &  ( (~  (C = B) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  => (v1_fin_topo (k3_fintopo5 A B))) ) ) ) ).
tt(t12_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_fin_topo B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tarski (k1_fin_topo A C) B) => (r2_hidden C B)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r1_tarski (k1_fin_topo A C) B)) ) ) ) ) ) ) ) ) ).
tt(t12_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_fin_topo A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fin_topo A B) = (k12_fin_topo A B)) ) ) ) ) ) ).
tt(t12_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k6_flang_1 A B C) = k1_xboole_0)  <=>  ( (B = k1_xboole_0)  |  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t12_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k7_flang_1 A B C) (k7_flang_1 A B D)) = (k6_flang_1 A (k7_flang_1 A B D) (k7_flang_1 A B C))) ) ) ) ) ) ) ) ).
tt(t12_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_flang_1 A B) = (k4_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B k6_numbers C) (k1_flang_3 A B (k2_xcmplx_0 C 1)))) ) ) ) ) ) ).
tt(t12_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k4_finseq_2 C B)) => (m2_finseq_1 A B)) ) ) ) ) ).
tt(t12_fomodel1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  ((m2_subset_1 A (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) <=>  ( (~ (v1_xboole_0 A))  & (m2_finseq_2 A (k15_fomodel1 B) (k3_finseq_2 (k15_fomodel1 B)))) ) ) ) ) ).
tt(t12_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k1_relset_1 (k8_mcart_1 (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k3_finseq_2 (k1_fomodel1 B)) (k16_fomodel2 B C) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0))) (k19_fomodel2 B C (k23_fomodel2 B A C))) = (k2_zfmisc_1 (k16_fomodel2 B C) (k28_fomodel2 B A))) ) ) ) ) ) ) ).
tt(t12_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  ( ( ((k1_fomodel2 B) = (k1_fomodel2 C))  &  ( ((k34_fomodel2 B) = (k34_fomodel2 C))  &  ((k2_partfun1 (k6_subset_1 (u1_struct_0 B) (k1_tarski (u3_struct_0 B))) k4_numbers (u1_fomodel1 B) (k37_fomodel1 B)) = (k2_partfun1 (k6_subset_1 (u1_struct_0 C) (k1_tarski (u3_struct_0 C))) k4_numbers (u1_fomodel1 C) (k37_fomodel1 B))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 C A)) =>  (! [F:$i] :  ( ((v4_fomodel2 F B) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (~  ( ((k5_relat_1 D (k37_fomodel1 B)) = (k5_relat_1 E (k37_fomodel1 B)))  &  (! [G:$i] :  ( ((v4_fomodel2 G C) & (m2_subset_1 G (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))))  =>  (~  ( (G = F)  &  ((k26_fomodel2 C A E G) = (k26_fomodel2 B A D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ((v8_fomodel4 A C D B) =>  ((v4_fomodel2 A C) & (m2_subset_1 A (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ).
tt(t12_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_frechet A) =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) E (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C)) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_frechet A D)) (k2_frechet B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_frechet,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k10_xtuple_0 (k1_funct_4 A B)) = (k2_xboole_0 (k7_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 B))) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t12_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k3_fscirc_1 A B C)) = (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) ) ) ) ).
tt(t12_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l2_fsm_1 F A B))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 F)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 F)) =>  (~  ((r1_fsm_1 A E C G H) &  ((r1_fsm_1 A F C I J) &  ( (~  ((k4_fsm_1 A B E H D) = (k4_fsm_1 A B F J D)) )  &  ((k4_fsm_1 A B E G (k8_finseq_1 A C D)) = (k4_fsm_1 A B F I (k8_finseq_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E C)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E D))) ) ) ) ) ) )  => (v1_fsm_2 B A)) ) ) ) ) ).
tt(t12_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ((r3_rewrite3 C (k9_flang_1 C) (k1_fsm_3 C E F) A (k3_flang_1 C D) B (k2_flang_1 C)) => (r2_rewrite3 C (k9_flang_1 C) (k1_fsm_3 C E F) A (k3_flang_1 C D) B (k2_flang_1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (v1_relat_1 (k3_msafree2 (k7_ftacell1 A B C D E)))) ) ) ) ) ).
tt(t12_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_relat_1 (k2_funcop_1 A B) C) = (k2_funcop_1 (k3_xboole_0 A C) B)) ) ) ) ).
tt(t12_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  ((k2_binop_1 k1_numbers (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers) (k7_funcsdom A) 1 B) = B) ) ) ) ).
tt(t12_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k3_relat_1 C B))) =>  ((k1_funct_1 (k3_relat_1 C B) A) = (k1_funct_1 B (k1_funct_1 C A))) ) ) ) ) ) ) ).
tt(t12_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) )  => (r2_relset_1 A B C D)) ) ) ) ) ) ) ).
tt(t12_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (r1_tarski (k8_relat_1 (k1_funct_3 D) B) (k1_zfmisc_1 A))) ) ) ) ) ) ).
tt(t12_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k1_funct_4 B C))) <=>  ((r2_hidden A (k9_xtuple_0 B)) | (r2_hidden A (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t12_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((k9_xtuple_0 (k1_tarski (k4_tarski A B))) = (k1_tarski A))  &  ((k10_xtuple_0 (k1_tarski (k4_tarski A B))) = (k1_tarski B)) ) ) ) ).
tt(t12_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r1_tarski (k9_xtuple_0 F) (k2_zfmisc_1 D E)) =>  ( ( (~ (r2_hidden (k1_funct_5 F) (k1_funct_2 A (k1_funct_2 B C))))  &  (~ (r2_hidden (k3_funct_5 F) (k1_funct_2 B (k1_funct_2 A C)))) )  | (r2_hidden F (k1_funct_2 (k2_zfmisc_1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t12_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (r1_xboole_0 A (k10_xtuple_0 (k1_funct_4 (k6_partfun1 B) (k7_funcop_1 A C)))))  => (r2_hidden C A)) ) ) ) ).
tt(t12_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r2_funct_8 A k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t12_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) => (v1_funct_9 (k39_valued_1 B) A)) ) ) ) ) ).
tt(t12_functor0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k3_relat_1 C (k8_pboole A B)) = (k8_pboole (k3_relat_1 C A) (k3_relat_1 C B))) ) ) ) ) ) ) ).
tt(t12_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  ( ((v21_functor0 D A B) & (v21_functor0 E B C))  => (v21_functor0 (k13_functor0 A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D C A) & (m2_functor0 D C A))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  =>  (! [G:$i] :  ((m1_functor2 G A B E F) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((r1_functor2 A B E F) =>  ((k2_functor2 C B (k1_functor3 C A B D E) (k1_functor3 C A B D F) (k6_functor3 C A B E F D G) H) = (k2_functor2 A B E F G (k3_functor0 C A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_relat_1 (k7_rfunct_1 k1_xboole_0 A) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k7_rfunct_1 k1_xboole_0 A)) &  ((v1_funct_2 (k7_rfunct_1 k1_xboole_0 A) A k1_numbers) & (m1_subset_1 (k7_rfunct_1 k1_xboole_0 A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(t12_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k1_fuzzy_1 A B C) (k1_fuzzy_2 A B (k1_fuzzy_2 A B C)))) ) ) ) ) ) ).
tt(t12_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 B A) k1_numbers (k2_fuzzy_4 B A (k6_fuzzy_1 (k2_zfmisc_1 A B) C D)) (k6_fuzzy_1 (k2_zfmisc_1 B A) (k2_fuzzy_4 B A C) (k2_fuzzy_4 B A D)))) ) ) ) ) ) ) ) ).
tt(t12_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ((k6_algstr_0 A (k4_algstr_0 A (k5_struct_0 A)) (k4_algstr_0 A (k5_struct_0 A))) = (k5_struct_0 A)) ) ) ).
tt(t12_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r7_binop_1 (u1_struct_0 A) (k1_fvsum_1 A B) (u1_algstr_0 A))) ) ) ) ).
tt(t12_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~ (v1_xboole_0 (k6_gate_1 A B)))  &  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) )  & (v1_xboole_0 (k6_gate_1 A B))) ) ) ) ) ).
tt(t12_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_gcd_1 A D B) &  ((r2_gcd_1 A D C) & (r2_gcd_1 A D (k3_rlvect_1 A B C))) )  =>  ( (D = (k4_struct_0 A))  |  ((k3_rlvect_1 A (k1_gcd_1 A B D) (k1_gcd_1 A C D)) = (k1_gcd_1 A (k3_rlvect_1 A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_genealg1 C B) =>  (! [D:$i] :  ((m1_genealg1 D B) =>  ((k8_genealg1 B C D A A) = C) ) ) ) ) ) ) ) ) ).
tt(t12_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analoaf A B C B (k1_geomtrap A B C)) & (r1_analoaf A B C (k1_geomtrap A B C) C)) ) ) ) ) ) ) ).
tt(t12_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k7_gfacirc1 A B C)))) ) ) ).
tt(t12_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_facirc_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k2_msafree2 (k1_gfacirc2 (k1_nat_1 C 1) A B)) = (k2_xboole_0 (k2_msafree2 (k1_gfacirc2 C A B)) (k7_subset_1 (u1_struct_0 (k13_gfacirc1 (k1_funct_1 A (k1_nat_1 C 1)) (k1_funct_1 B (k1_nat_1 C 1)) (k3_gfacirc2 C A B))) (k2_msafree2 (k13_gfacirc1 (k1_funct_1 A (k1_nat_1 C 1)) (k1_funct_1 B (k1_nat_1 C 1)) (k3_gfacirc2 C A B))) (k1_tarski (k3_gfacirc2 C A B)))))  &  ((v1_relat_1 (k3_msafree2 (k1_gfacirc2 C A B))) &  (~ (v1_facirc_1 (k2_msafree2 (k1_gfacirc2 C A B)))) ) ) ) ) ) ) ) ) ).
tt(t12_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~  (D = E) )  =>  ((r2_hidden D (k1_relset_1 k5_numbers (k13_glib_000 (k13_glib_000 A D B) E C))) &  ((r2_hidden E (k1_relset_1 k5_numbers (k13_glib_000 (k13_glib_000 A D B) E C))) &  ( ((k1_funct_1 (k13_glib_000 (k13_glib_000 A D B) E C) D) = B)  &  ((k1_funct_1 (k13_glib_000 (k13_glib_000 A D B) E C) E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) &  ((r2_hidden (k2_nat_1 C 1) (k1_relset_1 k5_numbers B)) & (r2_hidden (k2_nat_1 C 2) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ) ).
tt(t12_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k1_glib_002 A C)) =>  ((k1_glib_002 A B) = (k1_glib_002 A C)) ) ) ) ) ) ) ) ).
tt(t12_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) =>  ((k8_glib_003 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t12_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_glib_001 B A) &  ((v5_glib_001 B A) & (m3_glib_001 B A)) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_glib_004 A B C D) => (r2_glib_004 A (k8_glib_001 A B E F) (k3_glib_001 A (k8_glib_001 A B E F)) (k4_glib_001 A (k8_glib_001 A B E F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k6_glib_000 A))) =>  ( ((r1_glib_005 A B C D) & (r2_hidden C E))  =>  ((r2_hidden D E) | (r1_xxreal_0 (k1_glib_005 A B C D) (k3_uproots (k23_glib_000 A E (k6_subset_1 (k6_glib_000 A) E)) (k5_relat_1 (k5_glib_003 A) (k23_glib_000 A E (k6_subset_1 (k6_glib_000 A) E)))))) ) ) ) ) ) ) ) ) ) ).
tt(t12_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) &  ((r2_hidden B (k4_finseq_1 D)) & (r2_hidden C (k2_finseq_1 (k1_matrix_1 (k3_goboard1 D A))))) )  =>  ((r1_xxreal_0 (k1_matrix_1 D) 1) |  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 D A) B C) = (k1_funct_1 (k2_finseq_3 A (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) D B)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) )  &  ((v1_topreal1 A) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ((r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1))) ) ) ) ) )  &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ( ((k3_topreal1 2 A) = (k3_topreal1 2 C))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))  & (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_goboard5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k2_goboard2 A))) &  ((r2_hidden (k4_tarski E F) (k2_matrix_1 (k2_goboard2 A))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) E F)) ) ) )  =>  ((k7_real_1 (k18_complex1 (k6_xcmplx_0 C E)) (k18_complex1 (k6_xcmplx_0 D F))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k1_goboard5 A k6_numbers)) = (a_1_0_goboard6 A)) ) ) ).
tt(t12_goboard7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v1_topreal1 A) &  ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A)))) )  => (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t12_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_goboard9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_matrix_1 B)) => (v1_convex1 (k1_tops_1 (k15_euclid 2) (k2_goboard5 B A)) (k15_euclid 2))) ) ) ) ) ).
tt(t12_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (a_1_1_gobrd11 B))  => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ).
tt(t12_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 D) (k16_matrix_1 E)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 E)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C (k1_matrix_1 E))) ) ) ) )  =>  (B = (k1_matrix_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))))) =>  (~  ((v3_connsp_1 B (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) &  ( (~  (B = (k3_goboard9 A)) )  &  (~  (B = (k2_goboard9 A)) ) ) ) ) ) ) ) ) ).
tt(t12_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r1_henmodel A B (k6_cqc_lang A (k12_cqc_lang A D (k6_cqc_lang A C)))) <=> (r1_henmodel A B (k11_cqc_lang A D C))) ) ) ) ) ) ) ) ) ).
tt(t12_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( (? [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  &  ((r4_graph_1 A C) & (r4_graph_1 B C)) ) )  =>  ((k5_graph_1 A B) = (k5_graph_1 B A)) ) ) ) ) ) ).
tt(t12_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( ((k1_funct_1 (k1_graph_2 A B C) 1) = (k1_funct_1 A B))  &  ((k1_funct_1 (k1_graph_2 A B C) (k3_finseq_1 (k1_graph_2 A B C))) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t12_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((r2_hidden D (u4_struct_0 A)) &  ((r1_graph_2 A C B) &  ((k1_funct_1 C (k3_finseq_1 C)) = (k1_funct_1 (u1_graph_1 A) D)) ) )  =>  ((m1_graph_1 (k7_finseq_1 B (k9_finseq_1 D)) A) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ( (E = (k3_graph_2 C (k10_finseq_1 (k1_funct_1 (u1_graph_1 A) D) (k1_funct_1 (u2_graph_1 A) D))))  &  ((r1_graph_2 A E (k7_finseq_1 B (k9_finseq_1 D))) &  ( ((k1_funct_1 E 1) = (k1_funct_1 C 1))  &  ((k1_funct_1 E (k3_finseq_1 E)) = (k1_funct_1 (u2_graph_1 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_graph_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_graph_1 D))  =>  (! [E:$i] :  ( ((v7_graph_1 E D) & (m2_graph_1 E D))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C (k3_finseq_1 E)) &  (A = (k2_graph_2 (u4_struct_0 D) E B C)) ) ) )  =>  ((v7_graph_1 A D) & (m2_graph_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  ( ((k1_funct_1 (u2_graph_1 A) (k1_funct_1 B (k3_finseq_1 B))) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 C 1)))  =>  ((v7_graph_1 (k8_finseq_1 (u4_struct_0 A) B C) A) & (m2_graph_1 (k8_finseq_1 (u4_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t12_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((u1_struct_0 A) = (k2_xboole_0 C D))  &  ((r2_hidden E C) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_hidden G C) & (r2_hidden H D))  =>  (! [I:$i] :  (~  ((r2_hidden I (u4_struct_0 A)) & (r1_graph_4 A G H I)) ) ) ) ) ) ) )  & (r1_graph_5 A B E F)) ) )  => (r2_graph_5 A E F B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_grcat_1 C A B) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ( ((g1_grcat_1 (u1_grcat_1 C) (u2_grcat_1 C) (u3_grcat_1 C)) = (g1_grcat_1 A B D))  & (v13_vectsp_1 D A B)) ) ) ) ) ) ) ) ) ).
tt(t12_gr_cy_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ( ((k7_group_1 B) = A)  & (v1_int_2 A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C B))  =>  ((r1_group_2 B C (k6_group_2 B)) |  (C = B) ) ) ) ) ) ) ) ) ).
tt(t12_gr_cy_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v15_algstr_0 C) &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ( (C = (k5_group_4 C (k6_domain_1 (u1_struct_0 C) D)))  &  ((k7_group_1 C) = A) )  =>  ( (C = (k5_group_4 C (k6_domain_1 (u1_struct_0 C) (k5_group_1 C B D))))  <=>  ((k6_nat_d B A) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v1_gr_cy_3 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (A = B) )  &  ( (C = (k3_xcmplx_0 A B))  &  (! [D:$i] :  ( ((v7_ordinal1 D) &  ((v1_int_2 D) & (v2_gr_cy_3 D)) )  =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  ((v1_int_2 E) & (v2_gr_cy_3 E)) )  =>  (~  ((k1_euler_1 C) = (k4_nat_1 (k4_nat_1 4 D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v2_funct_1 A) => (v2_funct_1 (k3_xboole_0 A B))) ) ) ) ) ).
tt(t12_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_6 B A C) => (m1_group_6 (k1_grnilp_1 A B C) A C)) ) ) ) ) ) ) ).
tt(t12_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((v9_rewrite1 (k3_polyred A B C D)) => (v7_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(t12_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_vectsp_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  => (r8_pboole (k15_pre_poly A) (k1_polyred A E B (k4_polynom1 A B C D)) (k4_polynom1 A B (k1_polyred A E B C) (k1_polyred A E B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k6_polynom1 A B C D) (k7_polynom1 A B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) C D)) ) ) ) ) ) ) ) ) ).
tt(t12_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (! [C:$i] :  ((m1_group_2 C A) =>  (~  ((v2_group_10 C B) &  (! [D:$i] :  ((m1_group_2 D A) =>  (~  ((r3_group_10 B A D) & (m1_group_2 C D)) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((r3_group_10 B A C) & (r3_group_10 B A D))  => (r5_group_3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_group_11 A B C)) => (r1_tarski (k13_group_2 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t12_group_12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_finseq_1 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (k2_finseq_1 A)) &  ((v1_group_7 C) &  ((v2_group_7 C (k2_finseq_1 A)) & (v3_group_7 C (k2_finseq_1 A))) ) ) ) ) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers (k2_finseq_1 A)) => (m1_group_2 (k1_group_7 (k2_finseq_1 A) C D) B)) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  ( ((k3_finseq_1 E) = A)  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k1_group_7 (k2_finseq_1 A) C F) (k1_funct_1 E F))) )  &  (D = (k3_group_4 B E)) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = A)  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k1_group_7 (k2_finseq_1 A) C F) (k1_funct_1 D F))) )  &  ( ((k3_finseq_1 E) = A)  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k1_group_7 (k2_finseq_1 A) C F) (k1_funct_1 E F))) )  &  ((k3_group_4 B D) = (k3_group_4 B E)) ) ) ) )  =>  (D = E) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 B)) &  ((v1_group_6 D (k2_group_7 (k2_finseq_1 A) C) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 B))))) ) )  =>  (~  ((v3_funct_2 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C))) =>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) &  ( ((k3_finseq_1 F) = A)  &  ( (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k1_group_7 (k2_finseq_1 A) C G) (k1_funct_1 F G))) )  &  ( (F = E)  &  ((k3_funct_2 (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 B) D E) = (k3_group_4 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k1_group_1 A))  =>  ( (B = (k2_group_1 A C))  &  (C = (k2_group_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t12_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_group_2 A B (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) C D)) = (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_group_2 A B C) (k2_group_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_2 A (k14_group_2 A D B) C) = (k12_group_2 A D (k4_group_2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t12_group_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_group_4 B (k5_finseq_2 (u1_struct_0 B) A C)) = (k5_group_1 B A C)) ) ) ) ) ) ) ).
tt(t12_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_group_5 A (k2_finseq_4 (u1_struct_0 A) B C) D) = (k2_finseq_4 (u1_struct_0 A) (k2_group_3 A B D) (k2_group_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t12_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  ((k6_group_2 A) = A) ) ) ).
tt(t12_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_group_7 (k9_finseq_1 A)) & (v3_group_7 (k9_finseq_1 A) (k1_tarski 1))) ) ) ) ) ) ) ).
tt(t12_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_group_1 B A) => (v4_group_1 (k2_group_1 A B) A)) ) ) ) ) ).
tt(t12_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) => (m1_group_9 C A D)) ) ) ) ) ) ) ) ).
tt(t12_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (~  ( (~  ((k7_group_1 B) = (k7_group_1 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) ) ) ) ) ) ) ) ).
tt(t12_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ((m1_group_6 D A E) => (m1_group_6 (k2_grsolv_1 A B C D) B (k2_grsolv_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k3_hahnban1 A B C D) (k3_hahnban1 A B D C))) ) ) ) ) ) ) ) ).
tt(t12_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_struct_0 C B) |  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) D E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 E) (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) (k4_struct_0 E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ((k1_hallmar1 A (k2_hallmar1 A B C D) (k6_subset_1 E (k1_tarski C))) = (k1_hallmar1 A B (k6_subset_1 E (k1_tarski C)))) ) ) ) ) ) ) ) ) ).
tt(t12_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( (D = (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B))  => (v3_xxreal_2 D)) ) ) ) ) ) ) ) ) ).
tt(t12_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (~  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((r1_xxreal_0 E (k3_finseq_1 (k8_glib_001 A B C D))) &  (! [F:$i] :  ( ((v7_ordinal1 F) &  (~ (v1_abian F)) )  =>  (~  ( ((k1_funct_1 (k8_glib_001 A B C D) E) = (k1_funct_1 B F))  &  ( (F = (k6_xcmplx_0 (k2_xcmplx_0 C E) 1))  & (r1_xxreal_0 F (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (~ (v1_henmodel B A))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (~ (r6_calcul_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( ((k4_complex1 A) = k6_numbers)  =>  (A = (k2_complfld A)) ) ) ) ).
tt(t12_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A D F E) &  ( (~  (E = F) )  &  ( (~  (C = E) )  & (r1_collsp A E C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_heyting1,ax, (! [A:$i] : (m2_subset_1 (k4_tarski k1_xboole_0 k1_xboole_0) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))) ).
tt(t12_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k3_substlat A B (k4_substlat A B C (k2_heyting2 A B C))) = (k5_lattices (k5_substlat A B))) ) ) ) ) ) ).
tt(t12_heyting3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_heyting3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_heyting3 A B))) =>  ((r3_orders_2 (k1_heyting3 A B) C D) <=>  (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A B) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos B) 2) A) = (k1_real_1 (k1_seq_1 k19_sin_cos A))) ) ) ) ) ) ).
tt(t12_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v1_group_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k3_polynom1 A B (k3_hilbasis A C B) (k2_hilbasis A C)) = (k1_group_1 B))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (~  (D = (k2_hilbasis A C)) )  =>  ((k3_polynom1 A B (k3_hilbasis A C B) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t12_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  ((v6_hilbert1 A) <=>  ((k5_hilbert1 A) = A) ) ) ) ).
tt(t12_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ( ((k1_funct_1 A 1) = 2)  => (v1_hilbert2 A)) ) ) ).
tt(t12_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B 2 A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 2 A)))) )  =>  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) & (r1_funct_2 2 A (k2_tarski k6_numbers 1) A B (k5_funct_4 A k6_numbers 1 C D))) ) ) ) ) ) ) ) ).
tt(t12_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k7_real_1 (k10_real_1 1 A) (k10_real_1 1 B)) = 1)  =>  ((r1_xxreal_0 A 1) |  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((k1_seq_1 E H) = (k4_power (k18_complex1 (k1_seq_1 C H)) A))  &  ( ((k1_seq_1 F H) = (k4_power (k18_complex1 (k1_seq_1 D H)) B))  &  ((k1_seq_1 G H) = (k18_complex1 (k8_real_1 (k1_seq_1 C H) (k1_seq_1 D H)))) ) ) ) )  &  ((v1_series_1 E) & (v1_series_1 F)) )  =>  ((v1_series_1 G) & (r1_xxreal_0 (k4_series_1 G) (k8_real_1 (k4_power (k4_series_1 E) (k10_real_1 1 A)) (k4_power (k4_series_1 F) (k10_real_1 1 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k11_polynom3 A B C)) (k11_polynom3 A (k5_vfunct_1 k5_numbers A B) C)) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k11_polynom3 A B C)) (k11_polynom3 A B (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ) ).
tt(t12_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k4_idea_1 C A B) = (k4_idea_1 C B A)) ) ) ) ) ) ) ).
tt(t12_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v1_ideal_1 (u1_struct_0 A) A) &  ((v3_ideal_1 (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t12_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k3_incproj A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  ( (~  (E = C) )  &  ((r1_incsp_1 (k3_incproj A) C B) &  ((r1_incsp_1 (k3_incproj A) D B) & (r1_incsp_1 (k3_incproj A) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((r1_tarski B C) & (v3_incsp_1 C A))  => (v3_incsp_1 B A)) ) ) ) ) ) ) ).
tt(t12_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  ((k7_cat_1 A C (k9_index_1 A B C)) = (k1_xtuple_0 B)) ) ) ) ) ) ) ).
tt(t12_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  ( ((u1_msualg_1 B) = (k2_partfun1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_msualg_1 A) (u4_struct_0 B)))  &  ((u2_msualg_1 B) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_msualg_1 A) (u4_struct_0 B))) ) ) ) ) ) ).
tt(t12_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r2_int_1 A k6_numbers A) & (r2_int_1 k6_numbers A A)) ) ) ).
tt(t12_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_int_1 A k6_numbers) &  ((r1_int_1 1 A) & (r1_int_1 (k4_xcmplx_0 1) A)) ) ) ) ).
tt(t12_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ( ( (~ (v2_struct_0 (k9_int_3 A)))  &  ( (~ (v6_struct_0 (k9_int_3 A)))  &  ((v13_algstr_0 (k9_int_3 A)) &  ((v33_algstr_0 (k9_int_3 A)) &  ((v3_group_1 (k9_int_3 A)) &  ((v5_group_1 (k9_int_3 A)) &  ((v2_rlvect_1 (k9_int_3 A)) &  ((v3_rlvect_1 (k9_int_3 A)) &  ((v4_rlvect_1 (k9_int_3 A)) &  ((v4_vectsp_1 (k9_int_3 A)) &  ((v5_vectsp_1 (k9_int_3 A)) & (l6_algstr_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) )  <=>  ((v7_ordinal1 A) & (v1_int_2 A)) ) ) ) ) ).
tt(t12_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (k6_numbers = (k6_int_1 k6_numbers A)) ) ) ).
tt(t12_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) =>  ((k3_int_2 A B) = (k1_int_2 A)) ) ) ) ) ) ).
tt(t12_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( (~  (C = B) )  &  ( (~  ((k1_funct_1 A C) = k6_numbers) )  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k3_xcmplx_0 D (k1_funct_1 A B)) = (k7_xcmplx_0 (k19_rvsum_1 A) (k1_funct_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((v1_int_7 A) &  ((v1_int_7 B) & (r1_xboole_0 (k1_polynom2 k10_newton A) (k1_polynom2 k10_newton B))) )  => (r1_int_2 (k8_nat_3 k10_newton A) (k8_nat_3 k10_newton B))) ) ) ) ) ).
tt(t12_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers A)) &  ((r1_integra5 (k3_integra5 B C) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 B C)))) )  =>  ((r1_xxreal_0 C B) |  ((k1_integr10 A B C) = (k4_integra5 B C A)) ) ) ) ) ) ) ) ) ).
tt(t12_integr11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~  ((k8_real_1 A (k7_real_1 C 1)) = k6_numbers) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A B) (k1_taylor_1 (k7_real_1 C 1))) (k10_real_1 1 (k8_real_1 A (k7_real_1 C 1)))) k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A B) (k1_taylor_1 (k7_real_1 C 1))) (k10_real_1 1 (k8_real_1 A (k7_real_1 C 1)))) k1_numbers) D) = (k5_prepower (k7_real_1 (k8_real_1 A D) B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D C) & (r1_xxreal_0 D k6_numbers)) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C))))) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t12_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t12_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) A) B) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k1_seq_1 k19_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t12_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ((v1_integr15 C A B) =>  ((v2_integr15 C A B) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_integra1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [F:$i] :  ((m4_integr15 F A B C E) =>  ( ((v2_comseq_2 (k2_integra3 B E)) &  ((k2_seq_2 (k2_integra3 B E)) = k6_numbers) )  =>  ((v3_normsp_1 (k6_integr15 A B C E F) (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) (k6_integr15 A B C E F)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( (B = C)  =>  ( ((k5_comseq_3 k1_numbers B) = (k5_comseq_3 A C))  &  ((k6_comseq_3 k1_numbers B) = (k6_comseq_3 A C)) ) ) ) ) ) ) ) ) ).
tt(t12_integr18,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( (E = F)  =>  ((k4_vfunct_1 C D F A) = (k4_vfunct_1 B D E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_integr15 A (k3_integra5 B E) F) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B E)) A) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers F))) ) ) ) )  =>  ((r1_integr15 A (k3_integra5 C D) (k2_nfcont_4 A k1_numbers F)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) (k2_nfcont_4 A k1_numbers F) (k3_integra5 C D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v3_xxreal_2 (k1_rvsum_1 B)) => (v2_seq_2 (k2_partfun1 A k1_numbers B A))) ) ) ) ) ).
tt(t12_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v3_xxreal_2 B) & (r1_xxreal_0 A k6_numbers))  => (v4_xxreal_2 (k1_integra2 B A))) ) ) ) ) ).
tt(t12_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  (! [E:$i] :  ((m1_integra1 E D) =>  (~  ((r2_hidden B (k4_finseq_1 E)) &  ((r2_hidden C (k4_finseq_1 E)) &  ((r1_xxreal_0 B C) &  ( (~ (r1_xxreal_0 (k1_seq_1 (k3_finseq_6 k1_numbers E B C) 1) A))  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v2_measure5 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (A = (k5_seq_4 F))  &  ( ((k4_seq_4 F) = (k1_seq_1 (k3_finseq_6 k1_numbers E B C) (k3_finseq_1 (k3_finseq_6 k1_numbers E B C))))  & (m1_integra1 (k3_finseq_6 k1_numbers E B C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) =>  ((v3_integra1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  ( ((v2_comseq_2 (k2_integra3 A C)) &  ((k2_seq_2 (k2_integra3 A C)) = k6_numbers) )  =>  ((k9_real_1 (k2_seq_2 (k3_integra2 A B C)) (k2_seq_2 (k4_integra2 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t12_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_integra1 D A) =>  ( ((r1_tarski A B) &  ((r2_fdiff_1 C B) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 C B) A))) )  =>  ((r1_xxreal_0 (k7_integra1 A (k1_integra5 (k2_fdiff_1 C B) A) D) (k9_real_1 (k1_seq_1 C (k4_seq_4 A)) (k1_seq_1 C (k5_seq_4 A)))) & (r1_xxreal_0 (k9_real_1 (k1_seq_1 C (k4_seq_4 A)) (k1_seq_1 C (k5_seq_4 A))) (k6_integra1 A (k1_integra5 (k2_fdiff_1 C B) A) D))) ) ) ) ) ) ) ) ) ).
tt(t12_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 C)) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 D)) &  ((r1_integra5 (k3_integra5 A B) C) &  ((r1_integra5 (k3_integra5 A B) D) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k3_integra5 A B))) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B)))) ) ) ) ) )  =>  ( ((k4_integra5 A B (k3_valued_1 k1_numbers k1_numbers k1_numbers C D)) = (k7_real_1 (k4_integra5 A B C) (k4_integra5 A B D)))  &  ((k4_integra5 A B (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) = (k9_real_1 (k4_integra5 A B C) (k4_integra5 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_integra7 A B C) & (r1_integra7 A D E))  =>  ((r1_integra7 A (k3_valued_1 k1_numbers k1_numbers k1_numbers B D) (k3_valued_1 k1_numbers k1_numbers k1_numbers C E)) & (r1_integra7 A (k47_valued_1 k1_numbers k1_numbers k1_numbers B D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 k6_numbers (k21_sin_cos (k10_real_1 A 2))) =>  ((k21_sin_cos (k10_real_1 A 2)) = (k7_square_1 (k10_real_1 (k7_real_1 1 (k21_sin_cos A)) 2))) ) ) ) ).
tt(t12_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) k16_sin_cos)) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t12_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r1_tarski B C) & (r1_tarski D E))  =>  ((k3_setfam_1 (k2_interva1 A B C) (k2_interva1 A D E)) = (a_5_0_interva1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (r1_tarski A (k7_intpro_1 A))) ) ).
tt(t12_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((v2_comseq_2 (k2_irrat_1 A)) &  ( ((k2_seq_2 (k2_irrat_1 A)) = (k13_complex1 1 (k9_newton A)))  &  ((k2_seq_2 (k2_irrat_1 A)) = (k1_seq_1 k5_irrat_1 A)) ) ) ) ) ).
tt(t12_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  ((v12_cat_1 C A B) => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k1_isocat_1 B A (k1_isocat_1 A B C)) C)) ) ) ) ) ) ) ).
tt(t12_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~  ((k2_cat_1 (k8_cat_2 A B) (k9_cat_2 A B C E) (k9_cat_2 A B D F)) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 B)) =>  ((m1_cat_1 (k10_cat_2 A B G H) (k8_cat_2 A B) (k9_cat_2 A B C E) (k9_cat_2 A B D F)) <=>  ((m1_cat_1 G A C D) & (m1_cat_1 H B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k1_tops_1 A (k2_pre_topc A (k1_struct_0 A))) = (k1_struct_0 A)) ) ) ).
tt(t12_jct_misc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_xboole_0 C D) &  ((r1_tarski C (k1_rcomp_1 A B)) & (r1_tarski D (k1_rcomp_1 A B))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_zfmisc_1 k1_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k1_numbers))))) )  =>  (~  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((v6_xxreal_2 (k8_nat_1 (k1_zfmisc_1 k1_numbers) E F)) &  ( (~ (r1_xboole_0 (k8_nat_1 (k1_zfmisc_1 k1_numbers) E F) C))  &  (~ (r1_xboole_0 (k8_nat_1 (k1_zfmisc_1 k1_numbers) E F) D)) ) ) ) )  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((r2_hidden F (k1_rcomp_1 A B)) &  ( (~ (r2_hidden F (k4_subset_1 k1_numbers C D)))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r2_hidden F (k8_nat_1 (k1_zfmisc_1 k1_numbers) E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v3_topreal1 A) => (v1_goboard5 A)) ) ) ).
tt(t12_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k1_pre_topc B D)) (u1_struct_0 (k1_pre_topc C E))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc B D)) (u1_struct_0 (k1_pre_topc C E)))))) )  =>  (~  ((v5_pre_topc F A B) &  ((v5_pre_topc G (k1_pre_topc B D) (k1_pre_topc C E)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 B) F) D) &  ( (~  (D = k1_xboole_0) )  &  ( (~  (E = k1_xboole_0) )  &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((v5_pre_topc H A C) &  (H = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k1_pre_topc B D)) (u1_struct_0 (k1_pre_topc C E)) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k18_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid C) (k17_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t12_jgraph_4,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v5_pre_topc (k1_jgraph_4 A) (k15_euclid A) k3_topmetr)) ) ).
tt(t12_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( ((k1_funct_1 B k6_numbers) = (k1_funct_1 A 1))  &  ( ((k1_funct_1 B 1) = (k1_funct_1 A k6_numbers))  &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) = (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))  &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) & (v2_funct_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jgraph_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)))))) )  =>  (~  ((v5_pre_topc C A (k15_euclid B)) &  ((v5_pre_topc D A (k15_euclid B)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)))))) )  =>  (~  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)) E F) = (k3_rlvect_1 (k15_euclid B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)) C F) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)) D F))) ) )  & (v5_pre_topc E A (k15_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k18_euclid A) = E)  &  ( ((k18_euclid B) = E)  & (r1_xxreal_0 (k17_euclid A) D)) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 (k17_euclid B) C) |  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) | (r1_jordan6 (k1_sppol_2 C D E F) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_tarski B (k1_jordan2c 2 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ).
tt(t12_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r2_subset_1 (k2_jordan2c 2 A) (k2_jordan2c 2 B))) ) ) ) ) ).
tt(t12_jordan12,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_jordan12 2 A B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (v1_finset_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k2_topreal1 2 B C)))) ) ) ) ) ) ) ).
tt(t12_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski A (k2_jordan2c 2 (k3_topreal1 2 (k1_jordan13 A B))))) ) ) ) ) ).
tt(t12_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k2_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) C D A) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) = (k2_tarski E F))  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan17 A B C D E) => (r1_jordan17 A E B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) & (r1_tarski (k6_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ) ).
tt(t12_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan1a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( ((k18_euclid A) = (k18_euclid B))  & (r2_hidden C (k1_rcomp_1 (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B))))  => (r2_hidden (k19_euclid C (k18_euclid A)) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ).
tt(t12_jordan1b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) => (r1_xxreal_0 (k1_jordan1a A) (k3_finseq_1 A))) ) ) ).
tt(t12_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r2_hidden B (k1_jordan2c 2 C)) &  (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k18_euclid B) (k9_pscomp_1 C)) (k9_real_1 (k7_pscomp_1 C) (k9_pscomp_1 C))) (k13_newton 2 A)) 2))) )  =>  ( (~ (r1_xxreal_0 D 1))  & (r1_xxreal_0 (k3_real_1 D 1) (k1_matrix_1 (k1_jordan8 C A)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k22_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t12_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_topreal1 2 (k1_jordan9 A B)) = (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) (k2_jordan1e A B)))) ) ) ) ) ).
tt(t12_jordan1f,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e A B) (k1_jordan8 A B))) ) ) ) ).
tt(t12_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k19_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) )  & (r1_xxreal_0 (k18_euclid (k19_pscomp_1 (k3_topreal1 2 A))) (k18_euclid (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t12_jordan1h,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 B))) => (r1_tarski (k2_relset_1 A (k9_matrix_1 A B C)) (k2_jordan1h A B))) ) ) ) ) ) ) ).
tt(t12_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_xxreal_0 (k18_euclid B) (k7_pscomp_1 (k3_topreal1 2 A))))  => (r2_hidden B (k2_goboard9 A))) ) ) ) ) ).
tt(t12_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k2_jordan1e B A))) & (r2_hidden (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ).
tt(t12_jordan1k,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ((v2_compts_1 C (k3_pcomps_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( (~ (r1_xboole_0 B C))  =>  ((k7_weierstr A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t12_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (k4_rcomp_1 B 1))  => (v3_pre_topc A k5_topmetr)) ) ) ) ) ).
tt(t12_jordan21,ax, (! [A:$i] :  ( ((v1_jordan21 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (v1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) ) ) ).
tt(t12_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 E B))  &  ( (~ (r1_xxreal_0 C (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) 1 2))))  &  (~ (r1_xxreal_0 D (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) 2 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan23,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((v2_jordan23 B) & (v1_finseq_6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (v2_jordan23 (k1_finseq_6 A B C))) ) ) ) ) ) ) ).
tt(t12_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))))))) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ( (C = (a_3_0_jordan2b A B D))  & (r2_hidden D (k2_finseq_1 A)))  => (v3_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t12_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v9_rltopsp1 C (k15_euclid A)) & (r1_tarski B C))  => (v9_rltopsp1 B (k15_euclid A))) ) ) ) ) ) ) ).
tt(t12_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v4_topreal1 A) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  (B = (k1_funct_1 A C)) ) )  =>  ((r1_xxreal_0 C 1) |  ((k2_nat_1 (k1_jordan3 A B) 1) = C) ) ) ) ) ) ) ) ) ).
tt(t12_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k2_nat_1 (k7_nat_d C D) 1))) ) ) )  =>  ((k1_funct_1 (k3_finseq_6 A B C D) E) = (k1_funct_1 B (k2_nat_1 (k7_nat_d C E) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_topmetr A B)))) =>  ( ( (D = C)  & (v3_rcomp_1 C))  => (r2_hidden D (k2_pcomps_1 (k2_topmetr A B)))) ) ) ) ) ) ) ) ) ).
tt(t12_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_jordan3 A B C D) & (r2_jordan3 A B D E))  =>  ( (A = B)  | (r2_jordan3 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) &  ((r1_jordan5c A B C D E) & (r1_jordan5c A B C E D)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((r1_xxreal_0 (k6_pscomp_1 (k3_topreal1 2 A)) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B))) & (r1_xxreal_0 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) (k8_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t12_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D A) &  ((k17_euclid D) = (k10_real_1 (k7_real_1 (k17_euclid B) (k17_euclid C)) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r1_jordan6 A B C))  =>  ( (B = C)  |  ( (B = (k18_pscomp_1 A))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A C (k18_pscomp_1 A)) (k1_jordan7 A (k18_pscomp_1 A) B)) = (k1_tarski (k18_pscomp_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))))  =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) (k7_nat_d (k3_finseq_1 (k1_jordan8 C B)) 1) A)) = (k8_pscomp_1 C)) ) ) ) ) ) ) ) ).
tt(t12_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v1_sppol_1 (k2_topreal1 2 C A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k2_topreal1 2 C A)) =>  ((k18_euclid E) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan6 A B (k22_pscomp_1 A)) & (r1_jordan6 A (k22_pscomp_1 A) C))  =>  ((k1_jordan7 A B C) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_jordan6 (k8_jordan6 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B) (k3_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) C))) ) ) ) ) ) ) ) ).
tt(t12_jordan,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_topreal1 (k1_jordan21 A)) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan21 A))) (k2_jordan2c 2 A))) ) ).
tt(t12_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v2_funct_1 C) & (v2_funct_1 D))  => (r2_tarski A B)) ) ) ) ) ) ) ) ) ).
tt(t12_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D B C) =>  (! [E:$i] :  ((m1_kolmog01 E A B C) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 A)))  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 A)))  =>  ( ((r2_kolmog01 B C D A E) & (r1_subset_1 F G))  =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 B)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 B)) =>  ( ((r2_hidden H (k7_kolmog01 B C A F E)) & (r2_hidden I (k7_kolmog01 B C A G E)))  =>  ((k1_funct_1 D (k3_finsub_1 (k1_zfmisc_1 B) H I)) = (k3_xcmplx_0 (k1_funct_1 D H) (k1_funct_1 D I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k4_subset_1 A (k3_funct_2 k5_numbers (k9_setfam_1 A) B E) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E))) ) )  => (r1_tarski (k4_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C)) (k3_kurato_0 A D))) ) ) ) ) ) ) ) ).
tt(t12_kurato_1,ax, ((k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr k6_kurato_1))) = (k4_rcomp_1 k2_xxreal_0 2)) ).
tt(t12_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m2_valued_0 C (k9_setfam_1 (u1_struct_0 A)) B) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_1 B E) = D) ) ) )  => (r2_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C B)) ) ) ) ) ) ) ) ) ).
tt(t12_lang1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k1_lang1 (k7_lang1 A B)) = (k1_tarski B)) ) ) ) ).
tt(t12_laplace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k5_finsub_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k5_finsub_1 B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 B) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  ( ( (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 B)) =>  ((r1_xboole_0 G H) =>  ((k5_binop_1 C F (k3_funct_2 (k5_finsub_1 B) C E G) (k3_funct_2 (k5_finsub_1 B) C E H)) = (k3_funct_2 (k5_finsub_1 B) C E (k1_finsub_1 (k5_finsub_1 B) G H))) ) ) ) ) )  &  ((v1_binop_1 F C) &  ((v2_binop_1 F C) &  ((v1_setwiseo F C) &  ((k1_funct_1 E k1_xboole_0) = (k4_binop_1 C F)) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 A)) =>  ( (! [H:$i] :  (! [I:$i] :  ( ((r2_hidden H G) & (r2_hidden I G))  =>  ((r1_xboole_0 (k1_funct_1 D H) (k1_funct_1 D I)) |  (H = I) ) ) ) )  =>  ( ((k7_setwiseo A C F G (k1_partfun1 A (k5_finsub_1 B) (k5_finsub_1 B) C D E)) = (k7_setwiseo (k5_finsub_1 B) C F (k8_setwiseo A (k5_finsub_1 B) D G) E))  &  ( ((k7_setwiseo (k5_finsub_1 B) C F (k8_setwiseo A (k5_finsub_1 B) D G) E) = (k1_funct_1 E (k3_tarski (k8_setwiseo A (k5_finsub_1 B) D G))))  & (m1_subset_1 (k3_tarski (k8_setwiseo A (k5_finsub_1 B) D G)) (k5_finsub_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k1_tarski (k1_group_1 A)))  => (r1_group_2 A (k5_group_4 A B) (k6_group_2 A))) ) ) ) ) ).
tt(t12_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((r2_hidden C (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t12_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((u1_struct_0 A) = (u1_struct_0 (k1_lattice2 A)))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k1_lattice2 A)) (u1_struct_0 (k1_lattice2 A))) (u1_struct_0 (k1_lattice2 A)) (u2_lattices A) (u1_lattices (k1_lattice2 A))) & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k1_lattice2 A)) (u1_struct_0 (k1_lattice2 A))) (u1_struct_0 (k1_lattice2 A)) (u1_lattices A) (u2_lattices (k1_lattice2 A)))) ) ) ) ).
tt(t12_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_lattice3 A) =>  ((v1_lattice3 A) & (v2_lattice3 A)) ) ) ) ).
tt(t12_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v13_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  ((v2_funct_2 C (u1_struct_0 A)) =>  ((v13_lattices A) & (r3_lattice4 B A C)) ) ) ) ) ) ) ) ).
tt(t12_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_relat_1 D) =>  (! [E:$i] :  ((v1_relat_1 E) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 F G) &  ((r1_relat_2 D A) &  ((r1_relat_2 E A) &  ( (? [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  &  ( ((k3_finseq_1 H) = F)  & (r1_lattice5 A H B C D E)) ) )  &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  =>  (~  ( ((k3_finseq_1 H) = G)  & (r1_lattice5 A H B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_lattice6 B A) =>  ((r1_lattice6 A (k3_lattice6 A B) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice6 A C B) =>  (C = (k3_lattice6 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t12_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k3_lattice7 A))) = B) ) ) ) ) ).
tt(t12_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v1_yellow11 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ( ((v1_lattice5 C A B) & (v3_lattice5 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) =>  ((r3_orders_2 B (k3_lattice5 A B C (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k13_lattice3 B (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))) => (v3_lattice5 (k2_lattice8 A B C D) (k1_lattice8 A) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k4_lattices A B C) = (k4_lattices A B D))  &  ((k3_lattices A B C) = (k3_lattices A B D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t12_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k39_glib_000 B) C))  =>  ((k1_recdef_1 (k5_lexbfs A B (k1_nat_1 C 1)) (k6_lexbfs A B C)) = (k7_nat_d (k39_glib_000 B) C)) ) ) ) ) ) ) ) ).
tt(t12_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k4_waybel_3 A B (k10_lattice3 (k5_yellow_1 A B) C D) E) = (k10_lattice3 (k3_waybel_3 A B E) (k4_waybel_3 A B C E) (k4_waybel_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) => (v1_lfuzzy_1 (k3_lfuzzy_1 B (k2_zfmisc_1 A A)) A)) ) ) ) ) ).
tt(t12_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) & (v1_seq_2 B))  => (v2_limfunc1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t12_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r6_limfunc2 B A) <=>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  &  ((r2_hidden E (k1_relset_1 k1_numbers B)) & (r1_xxreal_0 C (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_limfunc3 B A) <=>  ((r2_limfunc2 B A) & (r5_limfunc2 B A)) ) ) ) ) ) ).
tt(t12_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  ((v5_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r3_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t12_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (C = (u1_struct_0 D))  =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  ((k1_lmod_5 A B C) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  ((v1_vectsp_4 C A B) =>  ( (C = k1_xboole_0)  | (r2_hidden (k4_vectsp_6 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k7_lmod_7 A B C)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k8_lmod_7 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (D = (k1_rlvect_1 (k5_lopban_1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k6_lopban_1 A B D F) = (k1_rlvect_1 B (k6_lopban_1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 (k8_lopban_1 A A)) (k10_lopban_1 A A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k4_lopban_2 A (k3_lopban_2 A C B) D) = (k3_lopban_2 A C (k4_lopban_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v3_normsp_1 B A)) ) ) ) ) ).
tt(t12_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_normsp_0 A (k8_nat_1 (u1_struct_0 A) B D)) (k8_nat_1 k1_numbers C D))) )  &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = k6_numbers) ) )  =>  ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t12_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (D = (k1_lopban_5 A B C))  => (v1_convex1 D (k4_normsp_2 A))) ) ) ) ) ) ) ) ) ).
tt(t12_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((u1_struct_0 (k6_lopclset A)) = (k1_lopclset A)) ) ) ).
tt(t12_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B C) (k2_lpspace1 A k1_numbers (k3_lpspace1 A) C B))) ) ) ) ) ) ).
tt(t12_lpspace2,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (r2_relset_1 B k1_numbers (k2_mesfun6c A B (k8_lpspace1 B k6_numbers)) (k8_lpspace1 B k6_numbers))) ) ) ) ).
tt(t12_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_series_1 (k1_lp_space B A)) &  ((k4_power (k4_series_1 (k1_lp_space B A)) (k10_real_1 1 A)) = k6_numbers) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_seq_1 B C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t12_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k8_ltlaxio1 A B))) = 1)  <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C E) B)) = 1)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (~ (r1_xxreal_0 E F))  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C F) A)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k5_cqc_lang A)) B) (k4_cqc_the1 A))) ) ) ) ).
tt(t12_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ( ((k4_xboolean A B) = k8_margrel1)  =>  ( (A = k8_margrel1)  &  (B = k8_margrel1) ) )  &  ( ( ( (A = k8_margrel1)  &  (B = k8_margrel1) )  =>  ((k4_xboolean A B) = k8_margrel1) )  &  ( (~  ( ((k4_xboolean A B) = k7_margrel1)  &  ( (~  (A = k7_margrel1) )  &  (~  (B = k7_margrel1) ) ) ) )  &  ( ( (A = k7_margrel1)  |  (B = k7_margrel1) )  =>  ((k4_xboolean A B) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(t12_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = (k6_rusub_4 A C B)) ) ) ) ) ) ) ).
tt(t12_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v1_matrix10 B) & (v2_matrix10 C))  => (v1_matrix10 (k4_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t12_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  ( (C = (k1_finseq_2 (k1_nat_1 A 2)))  =>  ((k2_matrix11 A B C) = (k1_group_1 B)) ) ) ) ) ) ) ) ).
tt(t12_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ((v1_matrix_6 (k1_matrix12 B B D (k12_matrix_1 D B) A C) B D) &  ((k5_matrix_6 B D (k1_matrix12 B B D (k12_matrix_1 D B) A C)) = (k1_matrix12 B B D (k12_matrix_1 D B) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ( ( (D = (k3_finseq_5 (k1_finseq_2 A)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 A)) &  ((r2_hidden F (k2_finseq_1 A)) & (r1_xxreal_0 (k2_xcmplx_0 E F) A)) )  =>  ((k3_matrix_1 (u1_struct_0 B) C E F) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((v1_matrix_2 (k4_matrix11 A A (u1_struct_0 B) D C) A B) & (m1_matrix_1 (k4_matrix11 A A (u1_struct_0 B) D C) (u1_struct_0 B) A A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) )  =>  ((k13_fvsum_1 A (k8_finseq_1 (u1_struct_0 A) B D) (k8_finseq_1 (u1_struct_0 A) C E)) = (k1_algstr_0 A (k13_fvsum_1 A B C) (k13_fvsum_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski C (k2_finseq_1 (k1_matrix_1 B))) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 B)) C)) =>  ((k9_matrix_1 (u1_struct_0 A) B D) = (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 B) (k4_struct_0 A))) ) ) ) )  =>  ((k8_matrix13 A B) = (k8_matrix13 A (k6_matrix13 (u1_struct_0 A) B (k2_finseq_1 (k3_finseq_1 B)) C))) ) ) ) ) ) ) ) ).
tt(t12_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix16 C (u1_struct_0 B)) & (v1_matrix16 D (u1_struct_0 B)))  => (v1_matrix16 (k3_matrix_6 A B C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t12_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v5_matrix17 C (u1_struct_0 A)) => (v5_matrix17 (k9_fvsum_1 A C B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t12_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ( ((k3_finseq_1 C) = A)  &  ((k3_finseq_1 D) = A) )  => (m1_matrix_1 (k10_finseq_1 C D) B 2 A)) ) ) ) ) ) ) ) ) ).
tt(t12_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (~  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_matrix_1 C) k6_numbers))  &  (~  ( (B = C)  <=>  ( ((k4_matrix_1 A B) = (k4_matrix_1 A C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ( (D = C)  |  ((k1_funct_1 B D) = (k4_struct_0 A)) ) ) ) ) )  =>  ((k4_rlvect_1 A B) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(t12_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k2_matrix_3 A (k3_matrix_3 A B C)) = (k3_matrix_3 A (k2_matrix_3 A B) (k2_matrix_3 A C))) ) ) ) ) ) ) ) ).
tt(t12_matrix_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ((k6_matrix_3 A D (k3_rlvect_1 A B C)) = (k3_matrix_3 A (k6_matrix_3 A D B) (k6_matrix_3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t12_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) D) (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 A) 2 2) =>  ((k12_matrix_3 2 A B) = (k5_algstr_0 A (k8_group_1 A (k3_matrix_1 (u1_struct_0 A) B 1 1) (k3_matrix_1 (u1_struct_0 A) B 2 2)) (k8_group_1 A (k3_matrix_1 (u1_struct_0 A) B 1 2) (k3_matrix_1 (u1_struct_0 A) B 2 1)))) ) ) ) ) ).
tt(t12_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) &  ((v1_matrix_8 D A B) & (r1_matrix_6 A B C D)) )  => (v1_matrix_8 (k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) (k5_matrix_1 A (u1_struct_0 B) D)) A B)) ) ) ) ) ) ) ) ) ).
tt(t12_matrix_9,ax, ((v1_funct_1 (k2_finseq_4 k5_numbers 2 1)) &  ((v1_funct_2 (k2_finseq_4 k5_numbers 2 1) (k2_finseq_1 2) (k2_finseq_1 2)) &  ((v3_funct_2 (k2_finseq_4 k5_numbers 2 1) (k2_finseq_1 2) (k2_finseq_1 2)) &  ( (~ (v5_matrix_2 (k2_finseq_4 k5_numbers 2 1) 2))  & (m1_subset_1 (k2_finseq_4 k5_numbers 2 1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 2) (k2_finseq_1 2))))) ) ) ) ).
tt(t12_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k1_matrixc1 (k4_matrix_5 A)) = (k4_matrix_5 (k1_matrixc1 A))) ) ) ).
tt(t12_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_matrixj1 k1_xboole_0 A) & (m2_finseq_1 k1_xboole_0 (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(t12_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_matrixj2 D A B) => (m1_matrixj2 (k25_matrixj1 A D (k24_matrixj1 A (k23_matrixj1 A (k10_matrixj1 (u1_struct_0 A) D)) (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 D) C))) A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ).
tt(t12_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k4_rvsum_1 A (k8_rvsum_1 B C)) = (k8_rvsum_1 (k4_rvsum_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t12_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((k7_matrixr1 (k7_real_1 A B) C) = (k3_matrixr1 (k7_matrixr1 A C) (k7_matrixr1 B C))) ) ) ) ) ) ) ).
tt(t12_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 B (k5_matrlin A B D (k5_finseq_2 (u1_struct_0 B) (k3_finseq_1 D) C))) = (k4_vectsp_1 A B (k4_rlvect_1 A D) C)) ) ) ) ) ) ) ) ) ).
tt(t12_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((k9_xtuple_0 D) = (k9_xtuple_0 C))  =>  ((k9_xtuple_0 (k5_matrlin A B D C)) = (k9_xtuple_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((r1_tarski D C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((r1_struct_0 (k1_vectsp_7 A B C) E) &  ( (~ (r1_struct_0 (k1_vectsp_7 A B D) E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r2_hidden F (k7_subset_1 (u1_struct_0 B) C D)) & (r1_struct_0 (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) F)) (k6_domain_1 (u1_struct_0 B) E))) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_matrix_1 C)) ) )  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 C)) <=>  ((r2_hidden A (k2_finseq_1 (k3_finseq_1 C))) & (r2_hidden B (k2_finseq_1 (k1_matrix_1 C)))) ) ) ) ) ) ) ) ).
tt(t12_matrtop1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k5_numbers)) &  ( ((k15_finseq_1 (k5_relat_1 (k7_finseq_1 B C) A)) = (k7_finseq_1 (k15_finseq_1 (k5_relat_1 B A)) (k15_finseq_1 (k5_relat_1 C D))))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 E k6_numbers))  =>  ((r2_hidden E D) <=> (r2_hidden (k23_binop_2 E (k3_finseq_1 B)) (k9_subset_1 k5_numbers A (k4_finseq_1 (k7_finseq_1 B C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_vectsp_4 B k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C (k15_euclid A)) =>  (! [D:$i] :  ((m1_vectsp_6 D k2_vectsp_1 B) =>  (! [E:$i] :  ((m1_rlvect_2 E C) =>  ((r1_funct_2 (u1_struct_0 B) (u1_struct_0 k2_vectsp_1) (u1_struct_0 C) k1_numbers D E) =>  ( ((k1_vectsp_6 k2_vectsp_1 B D) = (k3_rlvect_2 C E))  &  ((k4_vectsp_6 k2_vectsp_1 B D) = (k6_rlvect_2 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( (C = (k20_sin_cos A))  &  (D = (k17_sin_cos A)) )  =>  ((k12_matrix_3 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 k2_vectsp_1) (k17_matrixj1 (u1_struct_0 k2_vectsp_1) 2 B (k6_matrix_2 (u1_struct_0 k2_vectsp_1) C D (k4_algstr_0 k2_vectsp_1 D) C) (k12_matrix_1 k2_vectsp_1 B)))) k2_vectsp_1 (k20_matrixj1 (u1_struct_0 k2_vectsp_1) (k4_struct_0 k2_vectsp_1) (k17_matrixj1 (u1_struct_0 k2_vectsp_1) 2 B (k6_matrix_2 (u1_struct_0 k2_vectsp_1) C D (k4_algstr_0 k2_vectsp_1 D) C) (k12_matrix_1 k2_vectsp_1 B)))) = (k5_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ).
tt(t12_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v1_mazurulm C A B))  => (v1_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t12_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k2_pboole A (k1_mboolean A (k4_pboole A B C)) (k1_mboolean A (k4_pboole A C B))) (k1_mboolean A (k5_pboole A B C)))) ) ) ) ) ).
tt(t12_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_zfmisc_1 (k1_tarski B) C)) =>  ( ((k1_xtuple_0 A) = B)  & (r2_hidden (k2_xtuple_0 A) C)) ) ) ) ) ).
tt(t12_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_measure1 E A B C) =>  ((r1_tarski D E) => (m1_measure1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_measure2 C A B) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  (C = (k4_measure1 A B D)) ) ) ) ) ) ) ) ).
tt(t12_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_tarski (k8_nat_1 B D (k2_nat_1 E 1)) (k8_nat_1 B D E))) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k8_nat_1 B D k6_numbers))) |  ((k12_supinf_2 C (k1_measure2 A B (k1_measure3 A B D))) = (k7_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  ( (~ (v1_xboole_0 (k1_measure4 A B)))  &  ((v1_prob_1 (k1_measure4 A B) A) &  ((v4_prob_1 (k1_measure4 A B) A) & (m1_subset_1 (k1_measure4 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ).
tt(t12_measure5,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k2_measure5 A) (k2_measure5 B))) ) ) ) ) ).
tt(t12_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 C B) &  (A = (k1_measure5 C B)) ) ) )  =>  (B = (k8_supinf_2 A)) ) ) ) ) ) ).
tt(t12_measure7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_measure7 B A) => (v6_supinf_2 (k3_measure7 A B))) ) ) ) ).
tt(t12_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r1_tarski D E) => (r1_xxreal_0 (k1_mesfunc9 (k6_measure8 A B C) D) (k1_mesfunc9 (k6_measure8 A B C) E))) ) ) ) ) ) ) ) ) ) ).
tt(t12_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r2_hidden (k1_binop_2 B) A) <=> (r2_hidden B (k5_member_1 A))) ) ) ) ) ).
tt(t12_membered,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v6_membered A))  =>  (? [B:$i] :  ((v7_ordinal1 B) & (r2_hidden B A)) ) ) ) ).
tt(t12_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  => (r1_tarski (k6_memstr_0 A B C) C)) ) ) ) ) ) ).
tt(t12_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) => (r2_hidden A (k4_euclid_4 2 B C))) ) ) ) ) ) ) ).
tt(t12_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc5 A B C D) & (r1_mesfunc5 A B C E))  => (r1_mesfunc5 A B C (k4_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C E) &  ((r1_mesfun6c A B D E) & (r1_tarski E (k1_relset_1 A D))) )  => (r1_mesfun6c A B (k46_valued_1 A k2_numbers k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k6_mesfun7c A B))) =>  ((k12_supinf_2 (k6_mesfun7c A B) C) = (k6_rinfsup2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ) ).
tt(t12_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_mesfunc8 B A k1_numbers) &  ((r1_tarski E (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) & (r2_hidden D E)) )  =>  ((k1_seq_1 (k3_series_1 (k10_seqfunc A B D)) C) = (k1_seq_1 (k10_seqfunc A (k2_mesfun9c A B) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mesfunc1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r1_xxreal_0 A (k1_measure6 B))) ) )  =>  (A = k1_supinf_1) ) ) ) ).
tt(t12_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k1_mesfunc2 A B) C))) ) ) ) ) ) ).
tt(t12_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B C) &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (~ (r1_mesfunc3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 B) => (v3_mesfunc5 B)) ) ) ) ) ).
tt(t12_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc6 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k8_subset_1 A D (k11_mesfunc1 C E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mesfunc7,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k4_mesfunc7 A B))) ) ) ) ) ).
tt(t12_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k6_mesfunc8 A B))) =>  ( ((k12_supinf_2 (k6_mesfunc8 A B) C) = (k2_rinfsup2 (k4_rinfsup2 (k3_mesfunc5 A B C))))  &  ( ((k12_supinf_2 (k6_mesfunc8 A B) C) = (k2_rinfsup2 (k3_mesfunc5 A (k4_mesfunc8 A B) C)))  &  ((k12_supinf_2 (k6_mesfunc8 A B) C) = (k12_supinf_2 (k1_mesfunc8 A (k4_mesfunc8 A B)) C)) ) ) ) ) )  & (r2_relset_1 A k7_numbers (k6_mesfunc8 A B) (k1_mesfunc8 A (k4_mesfunc8 A B)))) ) ) ) ) ).
tt(t12_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ( (! [F:$i] :  ((v7_ordinal1 F) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers B F) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers C F) E))) )  & (r2_hidden D E))  =>  ( ((v8_mesfunc5 (k3_mesfunc5 A C D)) => (v8_mesfunc5 (k3_mesfunc5 A B D)))  &  ( ((v9_mesfunc5 (k3_mesfunc5 A C D)) => (v9_mesfunc5 (k3_mesfunc5 A B D)))  &  ( ((v7_mesfunc5 (k3_mesfunc5 A C D)) => (v7_mesfunc5 (k3_mesfunc5 A B D)))  &  ((v10_mesfunc5 (k3_mesfunc5 A C D)) => (v10_mesfunc5 (k3_mesfunc5 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k10_metric_1 B C A)) <=>  ( (~ (v2_struct_0 B))  & (r1_xxreal_0 (k2_metric_1 B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_metric_2 A B)) <=>  (C = B) ) ) ) ) ) ) ) ).
tt(t12_metric_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 k6_numbers D)) ) )  => (r1_xxreal_0 (k6_square_1 (k2_xcmplx_0 (k3_square_1 (k2_xcmplx_0 A C)) (k3_square_1 (k2_xcmplx_0 B D)))) (k2_xcmplx_0 (k6_square_1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B))) (k6_square_1 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 D)))))) ) ) ) ) ) ) ) ) ).
tt(t12_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) <=>  ((v2_tbsp_1 C A) &  ((k1_tbsp_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(t12_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v7_pre_topc A) & (v2_tex_2 B A))  =>  ((v3_pre_topc B (k1_pre_topc A (k2_pre_topc A B))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A (k2_pre_topc A B)))))) ) ) ) ) ) ).
tt(t12_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v2_mfold_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_connsp_2 D B C) &  (? [E:$i] :  ( ((v1_mfold_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  & (r1_metrizts B (k15_euclid A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((v3_mfold_1 B A) & (r1_mfold_2 B C))  => (v3_mfold_1 C A)) ) ) ) ) ) ) ).
tt(t12_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_midsp_1 A B B C D) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t12_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_midsp_2 A (k4_algstr_0 A B)) = (k4_algstr_0 A (k1_midsp_2 A B))) ) ) ) ) ).
tt(t12_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 B 2))) )  =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (u1_midsp_2 C D))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 B 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  ((r2_hidden A (k2_finseq_1 (k2_nat_1 B 1))) =>  ( ((k1_funct_1 (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 B 1) F A E) A) = E)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k7_subset_1 k5_numbers (k4_finseq_1 F) (k1_tarski A))) =>  ((k1_funct_1 (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 B 1) F A E) G) = (k1_funct_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k11_mmlquery A B C D) = (k13_mmlquery A B C (k1_nat_1 D 1))) ) ) ) ) ) ) ) ).
tt(t12_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_mod_2 E A B C) =>  (! [F:$i] :  ((m1_mod_2 F A D B) =>  ((v2_mod_2 (k8_mod_2 A E F) A) & (m1_mod_2 (k8_mod_2 A E F) A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k1_mod_3 A B (k4_subset_1 (u1_struct_0 B) C D)) = (k1_vectsp_5 A B (k1_mod_3 A B C) (k1_mod_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_vectsp_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ( ( (B = (k2_mod_4 A))  &  ( (D = (k3_mod_4 A C))  &  ( (E = F)  &  (G = H) ) ) )  =>  ((k5_vectsp_2 B D F H) = (k4_vectsp_1 A C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_modal_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v3_trees_2 D)) ) )  =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 B)) =>  ( ((k7_trees_2 B E C) = (k7_trees_2 B E D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_modcat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k11_modcat_1 A B))) =>  ((r2_hidden (k4_tarski D C) (k1_relset_1 (k2_zfmisc_1 (u4_struct_0 (k11_modcat_1 A B)) (u4_struct_0 (k11_modcat_1 A B))) (u1_cat_1 (k11_modcat_1 A B)))) <=>  ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k3_robbins1 (k48_modelc_1 A B D) E)) <=>  (~ (r3_modelc_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((k1_funct_1 (k3_modelc_2 A) 1) = k6_numbers)  &  ( ((k1_funct_1 (k4_modelc_2 A B) 1) = 1)  &  ( ((k1_funct_1 (k5_modelc_2 A B) 1) = 2)  &  ( ((k1_funct_1 (k6_modelc_2 A) 1) = 3)  &  ( ((k1_funct_1 (k7_modelc_2 A B) 1) = 4)  &  ((k1_funct_1 (k8_modelc_2 A B) 1) = 5) ) ) ) ) ) ) ) ) ) ).
tt(t12_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k13_modelc_2 A))) =>  ( (C = (k2_xboole_0 D (k1_tarski B)))  => (r1_xxreal_0 (k18_modelc_3 A C) (k7_real_1 (k18_modelc_3 A D) (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t12_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_partfun1 B k5_numbers) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((k13_pre_poly B) = (k1_tarski A))  =>  ((k3_uproots k5_numbers B) = (k1_seq_1 B A)) ) ) ) ) ) ).
tt(t12_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v15_monoid_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = (k6_algstr_0 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v5_monoid_0 C B) => (v5_monoid_0 (k8_monoid_1 B B B C A) (k9_funct_2 A B))) ) ) ) ) ) ).
tt(t12_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_morph_01 A (k5_setfam_1 (u1_struct_0 A) B) C) = (k3_tarski (a_3_5_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t12_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  (~  ( ((k1_funct_1 E k1_xboole_0) = (k4_tarski D (u1_struct_0 A)))  &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  (~  ( ((k3_finseq_1 F) = (k3_finseq_1 (k1_msualg_1 A D)))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k1_relset_1 k5_numbers F)) => (r2_hidden (k1_funct_1 F G) (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) (k1_funct_1 (k1_msualg_1 A D) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_msafree3,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_funct_1 B C)) =>  ((k1_funct_1 (k3_msafree3 A B (k1_trees_4 (k4_tarski D C))) C) = (k1_tarski D)) )  &  (! [E:$i] :  ( (~  ( (E = C)  & (r2_hidden D (k1_funct_1 B C))) )  =>  ((k1_funct_1 (k3_msafree3 A B (k1_trees_4 (k4_tarski D C))) E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t12_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (C = D) )  => (r1_subset_1 (k1_funct_1 (k8_msafree A B) C) (k1_funct_1 (k8_msafree A B) D))) ) ) ) ) ) ) ) ) ).
tt(t12_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k7_msafree A B C) (k1_msaterm A B))) ) ) ) ) ) ).
tt(t12_msscyc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  & (v1_finseq_1 C)) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k3_finseq_1 C)) & (v1_xboole_0 (k1_graph_2 C A B))) ) ) ) ) ) ) ) ) ) ).
tt(t12_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ((m1_pboole B A C) => (r1_pboole A B C)) ) ) ) ) ) ).
tt(t12_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_unialg_2 A B) => (m1_msualg_2 (k9_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B))) ) ) ) ) ).
tt(t12_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msualg_2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (m1_msualg_2 D A B))  => (v2_relat_1 (k3_pboole (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)))) ) ) ) ) ) ) ) ).
tt(t12_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ( ((r3_msualg_3 A B C E) & (r3_msualg_3 A C D F))  => (r3_msualg_3 A B D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) & (v1_finseq_1 H)) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v1_funct_1 I) & (v1_finseq_1 I)) )  =>  ((r2_hidden (k4_tarski F G) (k3_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) (k2_nat_1 (k3_finseq_1 H) 1))) (k2_msualg_4 A B D (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) (k2_nat_1 (k3_finseq_1 H) 1))) (k2_msualg_4 A B E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) (k2_nat_1 (k3_finseq_1 H) 1))))) =>  (! [J:$i] :  ((m1_subset_1 J (k3_msualg_1 A C B)) =>  (! [K:$i] :  ((m1_subset_1 K (k3_msualg_1 A C B)) =>  ( ( (J = (k7_finseq_1 (k7_finseq_1 H (k9_finseq_1 F)) I))  &  (K = (k7_finseq_1 (k7_finseq_1 H (k9_finseq_1 G)) I)) )  => (r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) J) (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) K)) (k3_eqrel_1 (k1_funct_1 (u3_msualg_1 A B) (k2_msualg_1 A C)) (k2_msualg_4 A B D (k2_msualg_1 A C)) (k2_msualg_4 A B E (k2_msualg_1 A C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_msualg_6 A B C D E) => (r2_hidden (k4_tarski B C) (k3_msualg_6 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ((r3_lattice3 A D C) <=> (r3_lattice3 B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))) =>  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((k1_msualg_8 A B C) = C) ) ) ) ) ) ) ) ).
tt(t12_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) ) )  =>  (? [C:$i] :  ((m2_pboole C A (k7_funcop_1 A k5_numbers) B) & (v2_msualg_3 C A (k7_funcop_1 A k5_numbers) B)) ) ) ) ) ).
tt(t12_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k6_msualg_1 A))) =>  ((k5_msualg_1 (k6_msualg_1 A) B (k9_msualg_1 A)) = (k1_funct_1 (u1_unialg_1 A) B)) ) ) ) ) ).
tt(t12_mycielsk,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  => (r1_xxreal_0 (k2_dilworth A) (k5_card_1 (u1_struct_0 A)))) ) ).
tt(t12_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ((v2_nagata_1 B A) => (v3_nagata_1 B A)) ) ) ) ) ).
tt(t12_nagata_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D B) => (r1_xxreal_0 (k8_nat_1 k1_numbers C D) A)) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D B) => (r1_xxreal_0 (k8_nat_1 k1_numbers (k3_series_1 C) D) (k8_real_1 A (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t12_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( ((k3_nat_d B A) = k6_numbers)  & (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(t12_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_nat_3 (k3_pre_poly k1_numbers B) A) = (k3_pre_poly k1_numbers (k2_newton B A))) ) ) ) ) ).
tt(t12_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  ( (~ (v1_int_2 A))  &  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_nat_d B A) &  ( (~ (r1_xxreal_0 B 1))  &  (~ (r1_xxreal_0 A B)) ) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_nat_d B A) &  ( (~ (r1_xxreal_0 B 1))  &  (~ (r1_xxreal_0 A B)) ) ) ) ) ) ) )  & (v1_int_2 A)) ) ) ) ) ).
tt(t12_nat_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (A = (k1_finseq_3 B (k6_domain_1 k5_numbers k6_numbers)))  =>  ((k18_rvsum_1 B) = (k18_rvsum_1 A)) ) ) ) ) ) ).
tt(t12_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k4_nat_d A 2) = k6_numbers)  |  ((k4_nat_d A 2) = 1) ) ) ) ).
tt(t12_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ( ((k1_binop_1 k2_nat_lat A (k1_binop_1 k1_nat_lat A B)) = A)  &  ( ((k1_binop_1 k2_nat_lat (k1_binop_1 k1_nat_lat B A) A) = A)  &  ( ((k1_binop_1 k2_nat_lat A (k1_binop_1 k1_nat_lat B A)) = A)  &  ((k1_binop_1 k2_nat_lat (k1_binop_1 k1_nat_lat A B) A) = A) ) ) ) ) ) ) ) ).
tt(t12_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_cat_1 G A E F) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C G) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) D G)) ) ) ) ) ) ) )  => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)) ) ) ) ) ) ) ) ) ).
tt(t12_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r4_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k1_relset_1 (u1_struct_0 A) B)) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A F C))))  & (r1_xxreal_0 D (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers B F) (k7_partfun1 k2_numbers B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ((r3_ncfcont2 A C D E) => (r3_ncfcont2 A C D (k2_vfunct_2 (u1_struct_0 C) D E B))) ) ) ) ) ) ) ) ) ) ).
tt(t12_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_ndiff_1 A (k3_normsp_1 A C D) B) (k3_normsp_1 A (k1_ndiff_1 A C B) (k1_ndiff_1 A D B)))) ) ) ) ) ) ) ) ).
tt(t12_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k7_partfun1 (u1_struct_0 B) D (k4_struct_0 A)) = (k4_struct_0 B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v2_ndiff_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((k7_partfun1 (u1_struct_0 C) E (k4_struct_0 B)) = (k4_struct_0 C))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 F A B) &  ((v1_lopban_1 F A B) &  ((v2_lopban_1 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 G B C) &  ((v1_lopban_1 G B C) &  ((v2_lopban_1 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  ((v1_funct_1 (k6_vfunct_1 (u1_struct_0 A) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D G) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E))) &  ((v2_ndiff_1 (k6_vfunct_1 (u1_struct_0 A) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D G) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E)) A C) & (m1_subset_1 (k6_vfunct_1 (u1_struct_0 A) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D G) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k6_vfunct_1 (u1_struct_0 A) B F D) E)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k2_relset_1 (u1_struct_0 A) C) = (k1_tarski D)) ) ) )  |  ((r2_ndiff_3 A C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k7_partfun1 (u1_struct_0 A) (k2_ndiff_3 A C B) D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r1_ndiff_4 B C A) & (r1_ndiff_4 B D A))  =>  ((r1_ndiff_4 B (k8_integr15 B k1_numbers C D) A) &  ((k1_ndiff_4 B (k8_integr15 B k1_numbers C D) A) = (k8_euclid B (k1_ndiff_4 B C A) (k1_ndiff_4 B D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k4_prvect_2 A))) =>  ( ( (B = E)  &  (C = F) )  =>  ( ((k3_rlvect_1 (k14_prvect_2 A) B C) = D)  <=>  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k4_finseq_1 A)) =>  ((k1_ndiff_5 A D G) = (k3_rlvect_1 (k3_prvect_2 A G) (k1_ndiff_5 A E G) (k1_ndiff_5 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) => (r1_xboole_0 (u1_orders_2 A) (u1_orders_2 (k3_necklace A)))) ) ).
tt(t12_necklace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  ( ((r2_necklace B A) & (r2_necklace C B))  => (r2_necklace C A)) ) ) ) ) ) ) ).
tt(t12_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) => (r1_tarski (k4_net_1 A B) (k2_net_1 A))) ) ) ) ).
tt(t12_newton,ax, ((k3_newton k6_numbers) = 1) ).
tt(t12_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k9_subset_1 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) C) (k1_relset_1 (u1_struct_0 A) D))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k6_vfunct_1 (u1_struct_0 A) B C D)) (k2_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k2_vfunct_1 (u1_struct_0 A) B C D)) (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  ((v1_nfcont_1 C A) &  ((r2_nfcont_2 C A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( ((k7_partfun1 k1_numbers B D) = (k4_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C)))  &  ((k7_partfun1 k1_numbers B E) = (k5_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_nfcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ( ((r2_hidden A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D))) &  ((r1_nfcont_3 B C A) & (r1_nfcont_3 B D A)) )  =>  ((r1_nfcont_3 B (k6_vfunct_1 k1_numbers B C D) A) & (r1_nfcont_3 B (k2_vfunct_1 k1_numbers B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_nfcont_4 A C B) <=>  ((r2_hidden B (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid A))) =>  (~  ( (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((a_4_0_nfcont_4 A B C E) = D) ) ) )  &  (! [E:$i] :  ((m1_rcomp_1 E B) =>  (~ (r1_tarski (k7_relset_1 k1_numbers (k1_euclid A) C E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((r1_normform A B C D) =>  ((r1_normform A B (k1_normform A B E C) (k1_normform A B E D)) & (r1_normform A B (k1_normform A B C E) (k1_normform A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_normsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 B)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [D:$i] :  ((r2_hidden D k5_numbers) => (m1_subset_1 (k1_funct_1 A D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(t12_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_normsp_2 A))) =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_normsp_2 A)) B C) &  (D = E) )  =>  ((r1_frechet (k3_normsp_2 A) C E) <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B H) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C k4_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_finseq_1 D k4_numbers))  =>  ( ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 (k3_finseq_1 C))) & (r2_hidden F (k2_finseq_1 (k3_finseq_1 C))))  =>  ( (E = F)  | (r1_int_2 (k1_funct_1 C E) (k1_funct_1 C F))) ) ) ) ) )  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 (k3_finseq_1 C))) =>  ((k6_int_1 A (k1_funct_1 C E)) = (k6_int_1 B (k1_funct_1 C E))) ) ) )  &  ((k1_funct_1 D 1) = 1) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F E))  =>  ((k1_funct_1 D (k1_nat_1 F 1)) = (k3_xcmplx_0 (k1_funct_1 D F) (k1_funct_1 C F))) ) ) ) ) )  =>  ((k6_int_1 A (k1_funct_1 D (k2_nat_1 E 1))) = (k6_int_1 B (k1_funct_1 D (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_numbers,ax,(r1_tarski k3_numbers k1_numbers)).
tt(t12_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k1_funct_1 (k8_openlatt A) B)) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ( (D = C)  &  ( (~  (D = (u1_struct_0 A)) )  &  ((v2_filter_0 D A) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  ((v8_oposet_1 A) => (v3_necklace A)) ) ) ).
tt(t12_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( ((k3_oppcat_1 A (k3_graph_1 A D)) = (k4_graph_1 (k2_oppcat_1 A) (k7_oppcat_1 A B C D)))  &  ((k3_oppcat_1 A (k4_graph_1 A D)) = (k3_graph_1 (k2_oppcat_1 A) (k7_oppcat_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k1_relat_1 B) = A) ) ) ) ).
tt(t12_orders_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ( ((v6_orders_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden B D) & (r2_hidden C D)) ) )  <=>  ((r2_orders_2 A B C) <=>  (~ (r1_orders_2 A C B)) ) ) ) ) ) ) ) ) ).
tt(t12_orders_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_orders_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_orders_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_orders_3 A))) =>  (! [D:$i] :  ((m1_orders_3 D A) =>  (! [E:$i] :  ((m1_orders_3 E A) =>  ( ( (B = D)  &  (C = E) )  => (r1_tarski (k1_altcat_1 (k4_orders_3 A) B C) (k9_funct_2 (u1_struct_0 D) (u1_struct_0 E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ordinal1,ax, (! [A:$i] :  ((v1_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r1_tarski A B) & (r2_hidden B C))  => (r2_hidden A C)) ) ) ) ) ) ) ).
tt(t12_ordinal2,ax, (! [A:$i] : (r1_tarski (k3_ordinal1 A) (k2_ordinal1 A))) ).
tt(t12_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k2_xboole_0 A B) = A)  |  ((k2_xboole_0 A B) = B) ) ) ) ) ) ).
tt(t12_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ((v2_ordinal2 A) =>  ((v1_relat_1 (k3_relat_1 A B)) &  ((v5_ordinal1 (k3_relat_1 A B)) &  ((v1_funct_1 (k3_relat_1 A B)) & (v1_ordinal2 (k3_relat_1 A B))) ) ) ) ) ) ) ) ).
tt(t12_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden k6_numbers A) & (r2_hidden (k12_ordinal2 A B) (k12_ordinal2 A C)))  => (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t12_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) <=> (r2_hidden (k3_ordinal5 A) (k3_ordinal5 B))) ) ) ) ) ).
tt(t12_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t12_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_ortsp_1 A B D C (k4_vectsp_1 A B F E)) = (k8_group_1 A F (k1_ortsp_1 A B D C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_osafree A B))) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r1_lang1 (k2_osafree A B) C (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) D)) =>  ((r2_hidden C (k7_dtconstr (k2_osafree A B))) &  ((r2_hidden (k8_trees_4 (u1_struct_0 (k2_osafree A B)) C D) (k4_dtconstr (k2_osafree A B))) &  (? [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) &  ( (C = (k4_tarski E (u1_struct_0 A)))  &  ((r2_hidden D (k3_msualg_1 A E (k8_osafree A B))) &  ( ((k8_trees_4 (u1_struct_0 (k2_osafree A B)) C D) = (k1_funct_1 (k5_msualg_1 A E (k8_osafree A B)) D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden (k8_trees_4 (u1_struct_0 (k2_osafree A B)) C D) (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) F)) <=> (r3_orders_2 A (k2_msualg_1 A E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  ((v6_osalg_1 A) => (v10_osalg_1 A)) ) ) ).
tt(t12_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r8_pboole (u1_struct_0 A) (k3_osalg_2 A B) (k2_osalg_2 A (k2_msualg_2 A B)))) ) ) ) ) ) ).
tt(t12_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((v1_osalg_3 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ((r6_osalg_1 A E F) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A E B)) =>  (! [H:$i] :  ((m1_subset_1 H (k3_msualg_1 A F B)) =>  ( (G = H)  =>  ((k5_msualg_3 A B C E D G) = (k5_msualg_3 A B C F D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ( ((k8_osalg_4 A B C D E) = (k8_osalg_4 A B C D F))  <=> (r2_hidden (k4_tarski E F) (k2_msualg_4 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  =>  ((v6_papdesaf B) & (v5_papdesaf B)) ) ) ) ) ) ).
tt(t12_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) =>  ((r1_parsp_1 (k9_parsp_1 A) B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [H:$i] :  ((m1_subset_1 H (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  ( ((k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C D E) = (k5_domain_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) F G H I))  &  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I)) (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)))) = (k4_struct_0 A))  &  ( ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I))) (k8_group_1 A (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)))) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I))) (k8_group_1 A (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I)) (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) )  => (r1_parsp_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t12_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k6_relset_1 A B C D)) & (m1_subset_1 (k6_relset_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) ).
tt(t12_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden C (k1_relset_1 A D)) =>  ( (C = (k7_partfun1 A (k2_partfun2 A B D) (k7_partfun1 B D C)))  &  (C = (k7_partfun1 A (k1_partfun1 A B B A D (k2_partfun2 A B D)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  ((r2_hidden C D) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ).
tt(t12_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r1_bvfunc_1 A B C) => (r1_bvfunc_1 A (k6_bvfunc_2 A B D E) (k6_bvfunc_2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_analoaf A C B B E) &  ((r2_analoaf A D B B F) & (r2_diraf A C D E F)) )  =>  ((r3_diraf A B C D) | (r2_analoaf A C D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A B (k4_pboole A C D)) => (r1_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t12_pcomps_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = k1_xboole_0)  =>  ((k1_pcomps_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t12_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_pcs_0 A B))) =>  ((r1_pcs_0 (k17_pcs_0 A B) C D) <=>  (? [E:$i] :  (? [F:$i] :  ((l2_pcs_0 F) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 F)) &  ((r2_hidden E A) &  ( (F = (k1_funct_1 B E))  &  ( (G = C)  &  ( (H = D)  & (r1_pcs_0 F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (C = D)  => (r1_funct_2 (k1_euclid 1) (k1_euclid A) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 (k1_euclid 1) k1_numbers k1_numbers (k1_euclid A) (k1_pdiff_1 1 1) (k6_pdiff_1 A B D)) (k7_pdiff_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (D = (k10_finseq_1 A B))  & (r3_pdiff_1 2 2 E D))  =>  ( (C = (k11_pdiff_1 2 2 E D))  <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( (D = (k10_finseq_1 F G))  &  (? [H:$i] :  ((m1_rcomp_1 H G) &  ((r1_tarski H (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 E D))) &  (? [I:$i] :  ( ((v1_funct_1 I) &  ((v3_fdiff_1 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [J:$i] :  ( ((v1_funct_1 J) &  ((v2_fdiff_1 J) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (C = (k1_seq_1 I 1))  &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ((r2_hidden K H) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 2 2 E D) K) (k1_seq_1 (k1_pdiff_2 2 2 E D) G)) = (k7_real_1 (k1_seq_1 I (k9_real_1 K G)) (k1_seq_1 J (k9_real_1 K G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r4_pdiff_3 B A) <=> (r3_pdiff_1 2 2 (k1_pdiff_3 2 2 B) A)) ) ) ) ) ).
tt(t12_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (~  ( (D = (k11_finseq_1 A B C))  &  ((r3_pdiff_1 3 3 E D) &  (! [F:$i] :  ((m1_rcomp_1 F C) =>  (~  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 E D))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 E D) I) (k1_seq_1 (k1_pdiff_2 3 3 E D) C)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I C)) (k1_seq_1 H (k9_real_1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r3_pdiff_5 E D))  =>  ((k3_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 E) D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) )  =>  ((r1_funct_2 (k1_euclid A) (k1_euclid B) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C D) =>  ((v1_pdiff_6 C B A) <=> (v13_vectsp_1 D (k4_real_ns1 A) (k4_real_ns1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  (C = (k1_seq_1 (k1_pdiff_1 E A) D)) ) )  =>  ( ((k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_finseq_7 k1_numbers D E B) D) = (k1_finseq_7 k1_numbers (k5_euclid A) E (k10_binop_2 B C)))  &  ((k47_valued_1 k5_numbers k1_numbers k1_numbers D (k1_finseq_7 k1_numbers D E B)) = (k1_finseq_7 k1_numbers (k5_euclid A) E (k10_binop_2 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 (k1_pdiff_1 D A) (k8_euclid A B C)) = (k10_binop_2 (k1_seq_1 (k1_pdiff_1 D A) B) (k1_seq_1 (k1_pdiff_1 D A) C))) ) ) ) ) ) ) ) ) ).
tt(t12_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (C = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A B C) (k1_seq_1 (k1_pdiff_1 B A) C))) ) ) ) ) ) ) ).
tt(t12_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~  (C = (k3_pencil_1 A B)) )  => (v3_card_1 (k1_funct_1 B C) 1)) ) ) ) ) ) ) ).
tt(t12_pencil_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) => (v3_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t12_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v13_pencil_1 C))  &  ((v16_pencil_1 C A) & (m3_pboole C A (k12_pralg_1 A B))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_pre_topc (k2_pencil_1 A B (k3_pencil_1 A C)))) => (m1_subset_1 (k4_card_3 (k2_funct_7 C (k3_pencil_1 A C) D)) (u1_pre_topc (k5_pencil_1 A B)))) ) ) ) ) ) ) ) ).
tt(t12_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  (C = (k4_struct_0 B)) )  =>  ((k1_vectsp_9 A (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) = 1) ) ) ) ) ) ) ) ).
tt(t12_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d (k1_newton A B) C) = (k4_nat_d (k1_newton (k4_nat_d A C) B) C)) ) ) ) ) ) ) ).
tt(t12_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ((k9_petri A (k1_subset_1 (u4_struct_0 A))) = k1_xboole_0) ) ) ).
tt(t12_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r2_pnproc_1 A (k1_pnproc_1 A) B)) ) ) ).
tt(t12_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) =>  (! [C:$i] :  ((l1_polyalg1 C A) =>  (! [D:$i] :  ((l1_polyalg1 D A) =>  ( ((m1_polyalg1 B A C) & (m1_polyalg1 C A D))  => (m1_polyalg1 B A D)) ) ) ) ) ) ) ) ) ).
tt(t12_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( (! [I:$i] :  ((v1_xreal_0 I) =>  ((k7_polyeq_1 A B C D I) = (k7_polyeq_1 E F G H I)) ) )  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  ( (! [J:$i] :  ((v1_xreal_0 J) =>  ((k1_polyeq_2 A B C D E J) = (k2_polyeq_2 A F G H I J)) ) )  =>  ( (A = k6_numbers)  |  ( ((k13_complex1 B A) = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 F G) H) I)))  &  ( ((k13_complex1 C A) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 F G) (k3_xcmplx_0 F H)) (k3_xcmplx_0 F I)) (k2_xcmplx_0 (k3_xcmplx_0 G H) (k3_xcmplx_0 G I))) (k3_xcmplx_0 H I)))  &  ( ((k13_complex1 D A) = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 F G) H) (k3_xcmplx_0 (k3_xcmplx_0 F G) I)) (k3_xcmplx_0 (k3_xcmplx_0 F H) I)) (k3_xcmplx_0 (k3_xcmplx_0 G H) I))))  &  ((k13_complex1 E A) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 F G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( ((k5_square_1 A) = B)  &  ( (~  (A = (k7_square_1 B)) )  &  (~  (A = (k7_binop_2 (k7_square_1 B))) ) ) ) ) ) ) ) ) ).
tt(t12_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k6_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 3 (k5_square_1 A)))) &  ( ((k8_polyeq_1 A B B A C) = k6_numbers)  &  ( (~  (C = (k4_xcmplx_0 1)) )  &  ( (~  (C = (k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) (k6_square_1 (k6_xcmplx_0 (k6_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 3 (k5_square_1 A))))) (k3_xcmplx_0 2 A))) )  &  (~  (C = (k7_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) (k6_square_1 (k6_xcmplx_0 (k6_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 3 (k5_square_1 A))))) (k3_xcmplx_0 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( (~  (B = k6_numbers) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 B (k1_newton A 2)) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  ( (A = (k8_complex1 (k10_complex1 (k13_complex1 C (k3_xcmplx_0 2 B))) (k13_complex1 (k1_polyeq_5 2 (k1_quin_1 D C B)) (k3_xcmplx_0 2 B))))  |  (A = (k11_complex1 (k10_complex1 (k13_complex1 C (k3_xcmplx_0 2 B))) (k13_complex1 (k1_polyeq_5 2 (k1_quin_1 D C B)) (k3_xcmplx_0 2 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_polyform,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k2_xcmplx_0 A 2) 1)) ) ) ).
tt(t12_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k9_fvsum_1 A C B)) = (k6_algstr_0 A B (k4_rlvect_1 A C))) ) ) ) ) ) ) ).
tt(t12_polynom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((k13_pre_poly B) = k1_xboole_0)  =>  (B = (k16_pre_poly A)) ) ) ) ) ).
tt(t12_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k6_polynom3 2 B) A) = (k2_polynom3 k5_numbers C (k7_nat_d B C)))  &  ((k1_funct_1 (k6_polynom3 2 B) (k2_nat_1 A 1)) = (k2_polynom3 k5_numbers D (k7_nat_d B D))) )  =>  (D = (k2_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ).
tt(t12_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_algseq_1 A B) = k6_numbers)  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_polynom4 A B) (k9_polynom3 A))) ) ) ) ) ).
tt(t12_polynom5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 k1_complfld)) =>  ((k1_polynom5 (k8_finseq_1 (u1_struct_0 k1_complfld) A B)) = (k8_finseq_1 k1_numbers (k1_polynom5 A) (k1_polynom5 B))) ) ) ) ) ).
tt(t12_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_finseq_2 (k15_pre_poly (k10_ordinal2 A B)))) =>  ( ( ((k4_finseq_1 E) = (k4_finseq_1 (k20_pre_poly A C)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 (k20_pre_poly A C))) &  (! [G:$i] :  ((m2_subset_1 G (k14_pre_poly A) (k15_pre_poly A)) =>  (! [H:$i] :  ((m2_finseq_1 H (k15_pre_poly (k10_ordinal2 A B))) =>  (~  ( (H = (k9_pre_poly (k15_pre_poly (k10_ordinal2 A B)) k5_numbers (k3_finseq_2 (k15_pre_poly (k10_ordinal2 A B))) E F))  &  ((r6_pboole A (k7_partfun1 (k15_pre_poly A) (k20_pre_poly A C) F) G) &  ( ((k3_finseq_1 H) = (k3_finseq_1 (k20_pre_poly B D)))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ((r2_hidden I (k4_finseq_1 H)) &  (! [J:$i] :  ((m2_subset_1 J (k14_pre_poly B) (k15_pre_poly B)) =>  (~  ((r6_pboole B (k7_partfun1 (k15_pre_poly B) (k20_pre_poly B D) I) J) & (r6_pboole (k10_ordinal2 A B) (k7_partfun1 (k15_pre_poly (k10_ordinal2 A B)) H I) (k1_polynom6 A B G J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k20_pre_poly (k10_ordinal2 A B) (k1_polynom6 A B C D)) = (k5_pre_poly (k15_pre_poly (k10_ordinal2 A B)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v3_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B C D) = (k6_algstr_0 B (k3_polynom7 A B C) (k3_polynom2 A (k2_polynom7 A B C) B D))) ) ) ) ) ) ) ) ) ).
tt(t12_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_algseq_1 A B) = (k1_algseq_1 A C))  =>  ((k1_algseq_1 A (k2_polynom8 A B C)) = (k1_algseq_1 A B)) ) ) ) ) ) ) ) ).
tt(t12_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_polynom7 A B (k9_polynom1 A B C D) E) (k9_polynom1 A B C (k5_polynom7 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_poset_1 A B))) =>  ( (C = (k9_poset_1 A B))  => (r1_lattice3 (k6_poset_1 A B) (u1_struct_0 (k6_poset_1 A B)) C)) ) ) ) ) ) ) ).
tt(t12_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 1 B))  |  ( (~  (A = k6_numbers) )  &  (~ (v1_abian B)) ) )  =>  ((k2_power B (k10_real_1 1 A)) = (k10_real_1 1 (k1_power B A))) ) ) ) ) ) ).
tt(t12_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  ((r8_pboole (u1_struct_0 B) (u3_msualg_1 B (k14_pralg_2 A B C)) (k10_pralg_2 A B C)) & (r8_pboole (u4_struct_0 B) (u4_msualg_1 B (k14_pralg_2 A B C)) (k13_pralg_2 A B C))) ) ) ) ) ) ).
tt(t12_pralg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) => (r2_hidden F (k4_card_3 (k2_funct_6 (k3_relat_1 (k1_msualg_1 A B) E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)) =>  ((k4_trees_1 (k11_trees_3 A) (k12_finseq_1 k5_numbers B)) = (k1_funct_1 A (k2_nat_1 B 1))) ) ) ) ) ) ).
tt(t12_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k1_int_1 (k6_power 2 (k2_nat_1 (k4_nat_1 2 A) 1))) (k2_xcmplx_0 (k1_int_1 (k6_power 2 (k4_nat_1 2 A))) 1))) ) ) ).
tt(t12_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A B C)) (k12_finseq_1 (u1_struct_0 A) C)) B) & (r2_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) C) (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A C B))) B)) ) ) ) ) ) ) ).
tt(t12_pre_poly,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  =>  ((k3_finseq_1 (k2_finseq_3 (k1_nat_1 A 1) B)) = A) ) ) ) ) ) ).
tt(t12_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 A (k1_newton A B))) ) ) ) ) ).
tt(t12_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (k1_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t12_prgcor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_prgcor_1 A B) = (k5_int_1 A B)) ) ) ) ) ).
tt(t12_prob_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r2_hidden B (k1_prob_1 A C)) <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) & (r2_hidden B (k8_nat_1 (k9_setfam_1 A) C D))) ) ) ) ) ) ) ).
tt(t12_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((k1_seq_1 E (k7_prob_1 A B C (k5_prob_1 A B C D))) = (k9_real_1 (k1_seq_1 E C) (k1_seq_1 E (k5_prob_1 A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((r2_hidden C (k1_funct_1 (k1_prob_3 B D) A)) <=>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 E A) => (r2_hidden C (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t12_prob_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k7_numbers A B) &  ((v4_partfun3 A) & (v1_series_1 A)) )  =>  ((k4_series_1 A) = (k19_supinf_2 B)) ) ) ) ) ) ).
tt(t12_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k9_cqc_lang A B B)) (k4_cqc_the1 A))) ) ) ) ).
tt(t12_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_projdes1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (r4_projpl_1 A B C D))  =>  ( (~ (r4_projpl_1 A B D C))  &  ( (~ (r4_projpl_1 A C B D))  &  ( (~ (r4_projpl_1 A C D B))  &  ( (~ (r4_projpl_1 A D B C))  &  (~ (r4_projpl_1 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  (! [S:$i] :  ((m1_subset_1 S (u2_incsp_1 A)) =>  (! [T:$i] :  ((m1_subset_1 T (u2_incsp_1 A)) =>  (~  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B F E) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B H G) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H F K) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H I D) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F J D) Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) K E G) R) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C I G) S) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C J E) T) &  ((r1_zfmisc_1 L M N) &  ( (~  (B = H) )  &  ( (~  (B = C) )  &  ( (~  (B = E) )  &  ( (~  (F = E) )  &  (! [U:$i] :  ((m1_subset_1 U (u2_incsp_1 A)) =>  (~ (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) I J K) U)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B C))  &  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A B E))  &  (~  ((k3_relat_1 (k1_projred1 A C E B) (k1_projred1 A E D B)) = (k1_projred1 A C D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m2_prvect_1 B A) <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k1_funct_1 A C) (k1_funct_1 A C)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 A C) (k1_funct_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(t12_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k14_prvect_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k14_prvect_2 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  ( ( (C = D)  &  ((v3_normsp_1 B (k14_prvect_2 A)) &  ((k6_normsp_1 (k14_prvect_2 A) B) = C) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 A)) =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 (k11_prvect_2 A E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k11_prvect_2 A E)))))) )  &  ((v3_normsp_1 F (k11_prvect_2 A E)) &  ( ((k1_funct_1 D E) = (k6_normsp_1 (k11_prvect_2 A E) F))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m1_subset_1 H (k4_card_3 (k4_prvect_2 A))) &  ( (H = (k1_normsp_1 (k14_prvect_2 A) B G))  &  ((k1_normsp_1 (k11_prvect_2 A E) F G) = (k1_funct_1 H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 C D E) = (k10_finseq_1 D E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_3 A B))) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C (k3_rlvect_1 (k5_prvect_3 A B) D E)) = (k3_rlvect_1 (k10_prvect_2 (k10_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C D) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C (k1_rlvect_1 (k5_prvect_3 A B) D E)) = (k1_rlvect_1 (k10_prvect_2 (k10_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C D) E)) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) C (k4_struct_0 (k5_prvect_3 A B))) = (k4_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pscomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ( ((v1_pscomp_1 B A) & (v1_measure6 C))  => (v1_tops_2 (k7_relset_1 (k9_setfam_1 k1_numbers) (k9_setfam_1 (u1_struct_0 A)) (k3_measure6 (u1_struct_0 A) k1_numbers B) C) A)) ) ) ) ) ) ) ).
tt(t12_pua2mss1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ((m1_eqrel_1 B (k9_xtuple_0 A)) => (m1_eqrel_1 (a_2_1_pua2mss1 A B) A)) ) ) ) ).
tt(t12_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ( (A = (k6_xcmplx_0 (k1_pepin B) (k1_pepin C)))  &  ( (D = (k4_nat_1 (k4_nat_1 2 C) B))  &  (E = (k2_nat_1 (k1_pepin B) (k1_pepin C))) ) )  =>  ((k2_nat_1 (k1_pepin A) (k1_pepin D)) = (k1_pepin E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t12_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ( ( ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = k6_numbers)  =>  (B = (k12_qc_lang1 A)) )  &  ( ( ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 1)  => (v3_qc_lang1 B A))  &  ( ( ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 2)  => (v4_qc_lang1 B A))  &  ( ( ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 3)  => (v5_qc_lang1 B A))  &  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) & (m2_subset_1 (k1_funct_1 (k11_qc_lang1 A B) 1) (k6_qc_lang1 A) (k8_qc_lang1 A C))) )  => (v2_qc_lang1 B A)) ) ) ) ) ) ) ) ) ).
tt(t12_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k4_qc_lang2 A B C) = (k4_qc_lang2 A D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k15_qc_lang1 A B C)) = (k7_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A C) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t12_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((r2_hidden C (k1_trees_2 (k9_xtuple_0 (k2_qc_lang4 A B)) D)) => (r1_qc_lang2 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t12_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k5_qmax_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k5_qmax_1 A))) =>  ( ((r2_hidden B (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) & (r2_hidden C (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_qmax_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_qmax_1 A)) =>  ( ((r2_hidden D B) &  ((r2_hidden E B) & (r2_hidden (k8_qmax_1 A D) C)) )  => (r2_hidden (k8_qmax_1 A E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k6_algstr_0 A B C) D) <=> (r3_lattices A B (k1_quantal1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t12_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k27_quaterni k1_quatern2 A) = k6_numbers) ) ) ).
tt(t12_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k5_square_1 (k3_quatern2 A)) = (k3_quatern2 (k27_quaterni A (k31_quaterni A)))) ) ) ).
tt(t12_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((k6_quaterni A B C D) = (k6_quaterni E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (~ (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) ) )  &  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 k6_numbers (k1_quin_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t12_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k8_quofield A B (k11_quofield A)) = B)  &  ((k8_quofield A (k11_quofield A) B) = B) ) ) ) ) ) ).
tt(t12_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k2_radix_1 A) k4_numbers)) ) ).
tt(t12_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (C = D)  =>  ((k2_radix_2 A B C) = (k7_radix_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_radix_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 1) (k5_radix_3 A B)) & (r1_xxreal_0 (k5_radix_3 A B) 1)) ) ) ) ) ).
tt(t12_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k4_radix_1 E B A C) = (k4_radix_1 E B A D)) ) ) )  =>  ((k8_radix_1 A B C) = (k8_radix_1 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 2 B))  =>  ((k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k10_radix_1 B (k2_xcmplx_0 A 2) k6_numbers))) = (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k4_radix_5 (k2_xcmplx_0 A 2) A B)))) ) ) ) ) ) ) ) ).
tt(t12_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 (k1_nat_1 A 1) (k6_newton A (k2_xcmplx_0 B A)))) ) ) ) ) ).
tt(t12_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_seq_1 D F) = (k8_real_1 (k1_seq_1 C (k1_funct_1 E F)) (k1_seq_1 B (k1_tarski (k1_funct_1 E F))))) ) ) ) ) ) ) )  =>  ((k1_mesfunc6 A (k1_random_1 A) (k2_prob_4 A (k1_random_1 A) B) C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 A))) )  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 B))) )  =>  (! [H:$i] :  ( ((v1_finset_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ( (H = (k2_zfmisc_1 F G))  &  (! [I:$i] :  (! [J:$i] :  ( ((r2_hidden I F) & (r2_hidden J G))  =>  ((k1_binop_1 E I J) = (k11_binop_2 (k1_seq_1 C I) (k1_seq_1 D J))) ) ) ) )  =>  ((k5_bhsp_5 k1_numbers (k2_zfmisc_1 A B) k33_binop_2 H E) = (k11_binop_2 (k5_bhsp_5 k1_numbers A k33_binop_2 F C) (k5_bhsp_5 k1_numbers B k33_binop_2 G D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) => (m1_subset_1 (k2_ranknull C B D E) (k1_zfmisc_1 (u1_struct_0 (k3_ranknull A C B D))))) ) ) ) ) ) ) ) ) ) ).
tt(t12_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (~ (r1_xxreal_0 (k2_real_1 (k1_rat_1 A)) k6_numbers)) ) ) ).
tt(t12_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_polynom3 A))) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k1_funct_1 B C) = (k3_hurwitz A D 1)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (C = (k3_group_4 (k14_polynom3 A) B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k2_polynom4 A C D) = (k4_struct_0 A))  <=>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r2_hidden E (k4_finseq_1 B)) &  ((k1_funct_1 B E) = (k3_hurwitz A D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ((v2_rcomp_1 A) & (v4_xxreal_2 A))  =>  ( (A = k1_xboole_0)  | (r2_hidden (k4_seq_4 A) A)) ) ) ) ).
tt(t12_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_seq_4 (k3_limfunc1 A)) = A) ) ) ).
tt(t12_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_funct_2 k5_numbers k5_numbers (k2_real_3 A B) 1) = (k3_nat_d B (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) k6_numbers))) ) ) ) ) ).
tt(t12_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k4_real_lat A) B (k1_funcsdom A k1_numbers (k5_real_lat A) B C)) B)) ) ) ) ) ) ).
tt(t12_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ((v1_rsspace3 B (k4_real_ns1 A)) => (v3_normsp_1 B (k4_real_ns1 A))) ) ) ) ) ).
tt(t12_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k8_group_1 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A (k8_group_1 A B D) (k8_group_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t12_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) B) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) B C))) ) ) ) ) ) ) ).
tt(t12_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k3_finseq_1 (k3_rfinseq (k20_rfunct_3 A C A))) = (k3_finseq_1 (k15_rfunct_3 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t12_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k10_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t12_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_2 A) =>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 (k2_relat_1 A)))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 (k2_relat_1 A))) ) ) ) ) ).
tt(t12_relset_1,ax, (! [A:$i] :  (! [B:$i] : (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(t12_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k9_relat_1 (k6_subset_1 B C) A) = (k6_subset_1 (k9_relat_1 B A) (k9_relat_1 C A))) ) ) ) ) ) ).
tt(t12_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) & (r1_xxreal_0 A (k3_finseq_1 D)))  =>  ((r1_xxreal_0 A (k3_finseq_1 (k2_finseq_5 B D C))) |  ((k7_partfun1 B (k1_finseq_6 B D C) A) = (k7_partfun1 B D (k7_nat_d (k2_nat_1 A (k4_finseq_4 D C)) (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] : (r1_rewrite1 A B B)) ) ) ).
tt(t12_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r2_rewrite2 A B C D) =>  ((r2_rewrite2 A B (k1_flang_1 A E C) (k1_flang_1 A E D)) & (r2_rewrite2 A B (k1_flang_1 A C E) (k1_flang_1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (~  ( ((k1_flang_1 A B C) = (k1_flang_1 A D E))  &  ( ((r1_xxreal_0 (k1_afinsq_1 B) (k1_afinsq_1 D)) | (r1_xxreal_0 (k1_afinsq_1 E) (k1_afinsq_1 C)))  &  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (~  ( ((k1_flang_1 A B F) = D)  &  (C = (k1_flang_1 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ( ((k4_rfinseq2 (k6_rvsum_1 A)) = (k1_real_1 (k3_rfinseq2 A)))  &  ((k2_rfinseq2 (k6_rvsum_1 A)) = (k1_rfinseq2 A)) ) ) ) ) ).
tt(t12_rfinseq,ax, ((k3_rfinseq (k6_finseq_1 k1_numbers)) = (k6_finseq_1 k1_numbers)) ).
tt(t12_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k18_valued_1 A B) C) = (k18_valued_1 (k24_valued_1 A C) B)) ) ) ) ) ) ) ).
tt(t12_rfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A (k6_rfunct_1 A k1_numbers B))) => (r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A C (k6_rfunct_1 A k1_numbers B)) (k37_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A C B)))) ) ) ) ) ) ) ).
tt(t12_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_classes1 C D) <=> (r2_classes1 (k32_valued_1 A k1_numbers C) (k32_valued_1 B k1_numbers D))) ) ) ) ) ) ) ) ) ).
tt(t12_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_rfunct_4 B C) <=> (r1_rfunct_4 (k26_valued_1 k1_numbers k1_numbers B A) C)) ) ) ) ) ) ) ).
tt(t12_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) <=> (v1_seq_2 (k32_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t12_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers A B) =>  ((v2_rinfsup2 A) <=> (v1_seq_2 B)) ) ) ) ) ) ).
tt(t12_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_subset_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) C) (u1_struct_0 (k2_ring_1 A B)))) ) ) ) ) ) ).
tt(t12_ringcat1,ax, (! [A:$i] :  ( ((v2_ringcat1 A) &  ((v3_ringcat1 A) & (l1_ringcat1 A)) )  =>  ( (~ (v1_xboole_0 (k1_tarski A)))  & (v5_ringcat1 (k1_tarski A))) ) ) ).
tt(t12_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_convex1 A B k6_numbers) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))) ) ) ) ).
tt(t12_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ((v2_convex1 C A) &  ((k3_rlvect_2 A C) = B) )  => (r2_hidden (k6_rlvect_2 A C) (k1_rlaffin2 A B))) ) ) ) ) ) ) ).
tt(t12_rlaffin3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((k1_card_1 C) = (k1_card_1 (k1_convex1 B C A)))  <=>  (~  ( (A = k1_xboole_0)  &  (~ (v1_zfmisc_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k4_struct_0 B) = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t12_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k1_rlsub_2 A (k2_rlsub_1 A) (k2_rlsub_1 A)) = A) ) ) ).
tt(t12_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden (k4_struct_0 A) C) => (r1_tarski B (k6_rusub_4 A B C))) ) ) ) ) ) ) ).
tt(t12_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  ((k4_algstr_0 A (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ).
tt(t12_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 C B) =>  ((k2_rlvect_2 A (k4_subset_1 (u1_struct_0 A) C B)) = (k3_rlvect_1 A (k2_rlvect_2 A C) (k2_rlvect_2 A B))) ) ) ) ) ) ) ) ).
tt(t12_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) =>  ( (B = C)  |  ( (~  (C = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  (B = (k1_rlvect_1 A C D)) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  (B = (k1_rlvect_1 A C D)) ) ) )  =>  ( (C = (k4_struct_0 A))  |  ( (~  (B = C) )  & (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) B C)) B) & (r1_struct_0 (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) B C)) C)) ) ) ) ) ) ) ).
tt(t12_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (~  ((r1_tarski (k3_rlvect_2 A C) (u1_struct_0 B)) &  (! [D:$i] :  ((m1_rlvect_2 D B) =>  (~  ( ((k3_rlvect_2 B D) = (k3_rlvect_2 A C))  &  ((k6_rlvect_2 B D) = (k6_rlvect_2 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A C) => (r2_hidden A (k2_rlvect_x B C))) ) ) ) ) ) ).
tt(t12_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k4_struct_0 C) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(t12_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((k1_rmod_3 A B (k2_rmod_2 A B) (k2_rmod_2 A B)) = B) ) ) ) ) ).
tt(t12_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k7_subset_1 (u1_struct_0 B) C D)) = (k5_algstr_0 B (k1_rmod_4 A B (k4_subset_1 (u1_struct_0 B) C D)) (k1_rmod_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t12_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A B B) = B) ) ) ) ) ).
tt(t12_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A B (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A C D)) (k3_robbins1 A (k1_lattices A D B)))))) = (k3_robbins1 A (k1_lattices A D B))) ) ) ) ) ) ) ) ) ).
tt(t12_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v7_lattices A))  => (v7_lattices B)) ) ) ) ) ).
tt(t12_robbins4,ax, ((k3_lattice3 (g3_lattices (u1_struct_0 k2_robbins4) (u2_lattices k2_robbins4) (u1_lattices k2_robbins4))) = k1_robbins4) ).
tt(t12_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k2_rcomp_1 A B)) => (r1_xxreal_0 (k1_fdiff_1 C D) k6_numbers)) ) ) ) )  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) ) ) ) ) ) ) ).
tt(t12_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_roughs_1 A B) B)) ) ) ) ).
tt(t12_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v3_card_1 C 1) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ( (B = C)  | (r1_subset_1 B C)) ) ) ) ) ) ) ).
tt(t12_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v1_rsspace4 C A B) <=> (v4_xxreal_2 (k7_rsspace4 A B C))) ) ) ) ) ) ) ).
tt(t12_rsspace,ax,(m1_rlsub_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace)) k7_rsspace)).
tt(t12_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t12_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_rusub_2 A (k2_rusub_1 A) (k2_rusub_1 A)) = A) ) ) ).
tt(t12_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rusub_3 A B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) &  ((v1_rlvect_3 C A) &  ((k1_rusub_3 A C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rusub_4 A) = k6_numbers)  <=>  ((k2_rusub_1 A) = (k1_rusub_1 A)) ) ) ) ).
tt(t12_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r2_hidden (k4_struct_0 A) (k1_rusub_5 A B B))) ) ) ) ).
tt(t12_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k4_rvsum_1 (k6_finseq_1 k1_numbers) A) = (k6_finseq_1 k1_numbers)) ) ) ).
tt(t12_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ( ((k7_rvsum_2 (k6_finseq_1 k2_numbers) A) = (k6_finseq_1 k2_numbers))  &  ((k7_rvsum_2 A (k6_finseq_1 k2_numbers)) = (k6_finseq_1 k2_numbers)) ) ) ) ).
tt(t12_scm_1,ax, ( ((k4_xtuple_0 (k2_compos_1 k1_ami_3)) = k6_numbers)  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_xtuple_0 (k2_ami_3 A B)) = 1) ) ) ) )  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_xtuple_0 (k3_ami_3 A B)) = 2) ) ) ) )  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_xtuple_0 (k4_ami_3 A B)) = 3) ) ) ) )  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_xtuple_0 (k5_ami_3 A B)) = 4) ) ) ) )  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  ((k4_xtuple_0 (k6_ami_3 A B)) = 5) ) ) ) )  &  ( (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k4_xtuple_0 (k7_ami_3 A)) = 6) ) )  &  ( (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_xtuple_0 (k8_ami_3 B A)) = 7) ) ) ) )  &  (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_xtuple_0 (k9_ami_3 B A)) = 8) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ( ( (~  (B = (k16_scmfsa_2 D C)) )  &  (~  (B = (k17_scmfsa_2 D C)) ) )  | (r2_hidden C (k4_sf_mastr A))) ) ) ) ) ) ) ) ) ) ).
tt(t12_scm_comp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_tarski (k61_valued_1 (k15_scm_comp B C) D) A) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) &  ((v1_partfun1 E (u1_struct_0 k1_ami_3)) & (v5_memstr_0 E 2 k1_ami_3 D)) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 C (k17_scm_comp B)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 G (u1_struct_0 k1_ami_3))) ) ) )  =>  (~  ( (G = (k5_extpro_1 2 k1_ami_3 A E (k2_nat_1 F 1)))  &  ( ((k2_nat_1 F 1) = (k1_afinsq_1 (k15_scm_comp B C)))  &  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A E F)) = (k2_nat_1 D F))  &  ( ((k5_memstr_0 2 k1_ami_3 G) = (k2_nat_1 D (k2_nat_1 F 1)))  &  ( ((k1_funct_1 G (k10_ami_3 C)) = (k12_scm_comp E B))  &  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C H))  =>  ((k1_funct_1 E (k10_ami_3 H)) = (k1_funct_1 G (k10_ami_3 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k8_scmfsa_2 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t12_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k4_memstr_0 3 k1_scmfsa_2 A) = (k3_finseq_2 k4_numbers)) ) ) ).
tt(t12_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k13_scmfsa_2 I H))  =>  ( (I = (k1_ordinal1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G))))  |  ( (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v6_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ( ((r1_tarski B D) & (r1_extpro_1 3 k1_scmfsa_2 D A))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 D A)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 D A E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 D (k3_scmfsa6a B C)) A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r3_scmfsa7b (k12_scmfsa_2 C B) A)) ) ) ) ) ) ) ).
tt(t12_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_scmfsa7b A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_scmfsa7b B)) ) ) ) )  => (v1_scmfsa7b (k1_funct_4 A B))) ) ) ) ).
tt(t12_scmfsa8b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k2_scmfsa8b C A B)) = (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 4)) ) ) ) ) ) ) ).
tt(t12_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((r2_hidden (k2_compos_0 (u1_compos_1 k1_scmfsa_2) B) (k2_enumset1 k6_numbers 6 7 8)) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 B A)) = (k6_memstr_0 3 k1_scmfsa_2 A)) ) ) ) ) ) ).
tt(t12_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k1_scmfsa_9 A B)) = (k4_sf_mastr B)) ) ) ) ) ).
tt(t12_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 6 C))  => (r2_hidden C (k2_afinsq_1 (k1_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t12_scmfsa_m,ax, ((k1_funct_1 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) (k4_scmfsa_2 k6_numbers)) = 1) ).
tt(t12_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scm_halt C)) ) ) ) ) ) )  =>  ( ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) &  ((r1_tarski (k2_scmfsa6a C) B) & (r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) A)) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) 1)))) ) ) ) ) ) ) ) ).
tt(t12_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3)) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k1_scmfsa_m B) E)) (k9_xtuple_0 (k2_scmfsa_9 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k3_scmpds_2 A)) = 14) ) ) ).
tt(t12_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k12_scmpds_2 J K H I))  &  ((r2_hidden J (k9_xtuple_0 D)) & (r2_hidden (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) J) H) (k9_xtuple_0 D))) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) K) I)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) K) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_scmpds_4 (k3_scmpds_4 B A) C) = (k1_scmpds_4 B (k2_scmpds_4 A C))) ) ) ) ) ) ) ).
tt(t12_scmpds_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B)))) ) ) ) ).
tt(t12_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_scmpds_2 A) = B)  =>  ((k17_scmpds_2 A C) = (k2_nat_1 B C)) ) ) ) ) ) ) ) ).
tt(t12_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r1_scmpds_6 E C A) &  ((r2_scmpds_6 E C A) &  ((r1_tarski (k10_compos_1 k1_scmpds_2 E) A) & (r1_tarski (k10_compos_1 k1_scmpds_2 E) B)) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((k5_extpro_1 2 k1_scmpds_2 A C F) = D) ) ) )  |  ((k6_extpro_1 2 k1_scmpds_2 A C) = (k6_extpro_1 2 k1_scmpds_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_8 D F C) B A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k1_amistd_1 2 k1_scmpds_2 C (k14_scmpds_2 A B D E)) = (k1_tarski (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (~  ((r1_tarski k4_scmp_gcd A) &  ( ((k5_memstr_0 2 k1_scmpds_2 B) = 5)  &  ( (~ (r1_xxreal_0 (k1_funct_1 B k3_scmp_gcd) k6_numbers))  &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))) &  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3)) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2))) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A B C)) = (k4_scmpds_2 k3_scmp_gcd))  &  ( ((k1_funct_1 B k3_scmp_gcd) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) k3_scmp_gcd))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) = (k3_int_2 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 D (k2_xcmplx_0 (k1_funct_1 B k3_scmp_gcd) 1)) =>  ((r1_xxreal_0 D 1) |  ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) (k1_scmp_gcd D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_ami_2 k2_ami_2) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_subset_1 E k1_ami_2 k2_ami_2) =>  ( (~  (E = C) )  =>  ((k1_funct_1 (k4_scmring1 A B C D) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k4_scmring2 A B C) D) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) D)))  &  ( ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k4_scmring2 A B C) D) B) = (k1_algstr_0 A (k2_scmring2 A D B) (k2_scmring2 A D C)))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 A))))  =>  ( (~  (E = B) )  =>  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k4_scmring2 A B C) D) E) = (k2_scmring2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = k6_numbers)  =>  (B = (k2_compos_1 (k1_scmring2 A))) ) ) ) ) ) ).
tt(t12_scmring4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 C (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 B))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 B)))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  (~ (v2_compos_1 E (k1_scmring2 B))) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 (k1_scmring2 B))) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 (k1_scmring2 B))) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (v4_extpro_1 F 2 (k1_scmring2 B) E)) ) ) ) ) )  =>  ( ((r1_tarski F C) & (r1_tarski (k9_memstr_0 2 (k1_scmring2 B) F A) D))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 (k1_scmring2 B))) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ((r1_tarski E G) & (r1_tarski (k6_compos_1 (k1_scmring2 B) E A) H))  =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 2 (k1_scmring2 B) (k5_extpro_1 2 (k1_scmring2 B) G C I)) A) = (k5_memstr_0 2 (k1_scmring2 B) (k5_extpro_1 2 (k1_scmring2 B) H D I)))  &  ( ((k5_compos_0 (u1_compos_1 (k1_scmring2 B)) (k3_extpro_1 2 (k1_scmring2 B) G (k5_extpro_1 2 (k1_scmring2 B) G C I)) A) = (k3_extpro_1 2 (k1_scmring2 B) H (k5_extpro_1 2 (k1_scmring2 B) H D I)))  &  ( ((k5_relat_1 (k5_extpro_1 2 (k1_scmring2 B) G C I) (k9_xtuple_0 (k6_memstr_0 2 (k1_scmring2 B) F))) = (k5_relat_1 (k5_extpro_1 2 (k1_scmring2 B) H D I) (k9_xtuple_0 (k6_memstr_0 2 (k1_scmring2 B) F))))  &  ((k6_memstr_0 2 (k1_scmring2 B) (k5_extpro_1 2 (k1_scmring2 B) G (k1_funct_4 C (k6_memstr_0 2 (k1_scmring2 B) D)) I)) = (k6_memstr_0 2 (k1_scmring2 B) (k5_extpro_1 2 (k1_scmring2 B) H D I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k2_tarski B C) A) =>  ( (B = C)  | (r2_hidden (k2_tarski B C) (k1_scmyciel A))) ) ) ) ) ).
tt(t12_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  =>  ((r1_scmpds_6 (k4_scpinvar D E C) B A) & (r2_scmpds_6 (k4_scpinvar D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 B F) H) (k1_funct_1 B E)) &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 J F) H) (k1_funct_1 J E)) &  ((k1_funct_1 J D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) G)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) D) = (k1_funct_1 J D))  &  ( ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) (k2_scmpds_2 (k1_funct_1 B D) G)) = (k6_xcmplx_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) G)) I))  &  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) & (r1_xxreal_0 (k2_xcmplx_0 (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) F) H) (k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) J K) E))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 I k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) G)) k6_numbers) |  ((k6_scmpds_4 (k2_scmpds_7 D G I C) B A) = (k6_scmpds_4 (k2_scmpds_7 D G I C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D G (k4_xcmplx_0 I))) B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_scpqsort,ax, ((v2_compos_1 k1_scpqsort k1_scmpds_2) & (v3_scmpds_4 k1_scpqsort)) ).
tt(t12_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C B D))  &  ( (~  (E = F) )  &  ((r2_analoaf A E F E B) &  ((r2_analoaf A E F E C) & (r2_analoaf A E F E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers A (k56_valued_1 k5_numbers k1_numbers B)) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 A C) = (k18_complex1 (k1_seq_1 B C))) ) ) ) ) ) ) ) ).
tt(t12_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  =>  ((k2_seq_2 (k47_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k9_real_1 (k2_seq_2 A) (k2_seq_2 B))) ) ) ) ) ) ).
tt(t12_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v5_xxreal_2 A) =>  ((v1_xboole_0 A) |  ( (~  ( (? [B:$i] :  ((v1_xreal_0 B) &  (? [C:$i] :  ((v1_xreal_0 C) &  ((r2_hidden B A) &  ((r2_hidden C A) &  (~  (C = B) ) ) ) ) ) ) )  & (r1_xxreal_0 (k4_seq_4 A) (k5_seq_4 A))) )  &  (~  ( (~ (r1_xxreal_0 (k4_seq_4 A) (k5_seq_4 A)))  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  (~  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A k6_numbers))) ) ) ) ) ).
tt(t12_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (v1_series_1 (k1_valued_0 k1_numbers A B))) ) ) ) ) ).
tt(t12_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 2)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 (k4_nat_1 2 B) 1)) 6)) ) ) ) ) ) ).
tt(t12_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k8_real_1 (k8_real_1 (k8_real_1 3 A) B) C) (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)) (k1_newton C 3)))) ) ) ) ) ) ).
tt(t12_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k2_nat_1 (k2_nat_1 (k13_newton 10 C) (k4_nat_1 2 C)) 1)) ) )  =>  ((k1_seq_1 (k3_series_1 B) A) = (k2_xcmplx_0 (k6_xcmplx_0 (k7_xcmplx_0 (k13_newton 10 (k2_nat_1 A 1)) 9) (k7_xcmplx_0 1 9)) (k13_newton (k2_nat_1 A 1) 2))) ) ) ) ) ) ).
tt(t12_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k13_complex1 2 (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B))) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)))) ) ) ) ).
tt(t12_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_setfam_1 A B)) ) ) ).
tt(t12_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_funct_1 B) =>  ((k1_kurato_0 A B) = (k3_prob_1 A B)) ) ) ) ) ).
tt(t12_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A (k1_setlim_2 A B C)) = (k9_subset_1 A (k3_prob_1 A B) (k3_prob_1 A C))) ) ) ) ) ) ).
tt(t12_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t12_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 F B) &  ((v2_binop_1 F B) &  ((v1_setwiseo F B) &  ( (D = (k4_binop_1 B F))  &  ((r6_binop_1 B G F) &  ((k5_binop_1 B G E D) = D) ) ) ) ) )  =>  ((k5_binop_1 B G E (k7_setwiseo A B F C H)) = (k7_setwiseo A B F C (k10_funcop_1 B A G E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b C (k1_scmfsa_m B) A)) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a C D) B A) E) = (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa6b C B A)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r5_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k1_funct_4 B (k1_sfmastr2 C D))) & (r6_scmfsa7b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k1_funct_4 B (k1_sfmastr2 C D)))) )  =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) (k2_nat_1 E 1)) (k4_scmfsa_2 k6_numbers)) = 1)  &  ( (~ (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) k6_numbers))  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) (k2_nat_1 E 1)) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) = (k6_xcmplx_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( (~  (B = C) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) k6_numbers) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ( ((k17_scmfsa_2 A C) = (k17_scmfsa_2 B D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k2_sgraph1 A) (k2_sgraph1 B))) ) ) ).
tt(t12_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  => (v14_lattices A)) ) ).
tt(t12_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B B))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ).
tt(t12_simplex0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v1_setfam_1 B) &  ((v6_ordinal1 B) &  ((r2_hidden A B) &  ( ((k1_card_1 A) = (k1_card_1 B))  &  (! [C:$i] :  (~  ((r2_hidden C B) &  ( (~  ((k1_card_1 C) = 1) )  &  (! [D:$i] :  (~  ((r2_hidden D C) & (r2_hidden (k6_subset_1 C (k1_tarski D)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) => (m1_simplex1 (k5_simplex0 (u1_struct_0 B) (u1_pre_topc B)) A B)) ) ) ) ).
tt(t12_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m2_rlaffin3 D (k15_euclid A) C) =>  ( (~ (v1_xboole_0 (k7_subset_1 k5_numbers (k4_finseq_1 D) B)))  =>  ((k3_convex1 (k15_euclid A) (k7_relset_1 k5_numbers (u1_struct_0 (k15_euclid A)) D B)) = (k1_setfam_1 (a_4_0_simplex2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t12_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t12_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 k24_sin_cos (k9_binop_2 A B)) = (k8_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ).
tt(t12_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k4_binop_2 A B)) = (k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B)))) ) ) ) ) ).
tt(t12_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  ( (~  ((k20_sin_cos C) = k6_numbers) )  &  (~  ((k20_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) (k20_sin_cos C)) (k6_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 1 (k3_xcmplx_0 (k1_sin_cos4 B) (k1_sin_cos4 C))) (k3_xcmplx_0 (k1_sin_cos4 C) (k1_sin_cos4 A))) (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_sin_cos4 A) = (k10_real_1 1 (k1_sin_cos4 A))) ) ) ).
tt(t12_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 k6_numbers (k17_sin_cos A))) ) ) ) ) ) ) ).
tt(t12_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  (A = 1) )  & (r1_xxreal_0 (k5_square_1 (k10_binop_2 1 A)) k6_numbers)) ) ) ) ).
tt(t12_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k5_square_1 (k3_sin_cos2 A)) (k5_square_1 (k6_sin_cos2 B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k3_sin_cos2 (k6_xcmplx_0 A B))) 1)) ) ) ) ) ).
tt(t12_sin_cos9,ax, ((k2_relset_1 k1_numbers k2_sin_cos9) = (k2_rcomp_1 k6_numbers k32_sin_cos)) ).
tt(t12_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k10_comseq_3 (k10_sin_cos (k2_nat_1 C 1) A B)) C) = (k8_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k10_sin_cos C A B)) C) (k8_nat_1 k2_numbers (k10_comseq_3 (k9_sin_cos (k2_nat_1 C 1) A B)) C))) ) ) ) ) ) ) ).
tt(t12_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_sppol_1 A B (k1_rltopsp1 (k15_euclid A) C B))) ) ) ) ) ) ).
tt(t12_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k3_topreal1 2 (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) A)) = k1_xboole_0) ) ) ).
tt(t12_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k25_pscomp_1 A) A) & (r2_hidden (k24_pscomp_1 A) A)) ) ) ).
tt(t12_sprect_2,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) &  ((k17_euclid B) = (k6_pscomp_1 A)) )  => (r2_hidden B (k14_pscomp_1 A))) ) ) ) ) ).
tt(t12_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_matrix_1 D)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 D))) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C A)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C B)))) ) ) ) ) ) ) ) ) ).
tt(t12_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  ((r2_hidden C (k10_xtuple_0 A)) &  ((r2_hidden D (k10_xtuple_0 A)) & (r1_xxreal_0 (k4_finseq_4 A B) (k4_finseq_4 A C))) ) )  =>  ((r1_xxreal_0 (k4_finseq_4 A D) (k4_finseq_4 A C)) | (r1_xxreal_0 (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A D) B) (k4_finseq_4 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A D) C))) ) ) ) ) ) ) ) ) ) ).
tt(t12_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  (k6_numbers = A) )  & (r1_xxreal_0 (k3_square_1 A) k6_numbers)) ) ) ) ).
tt(t12_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  ((k9_stacks_1 A C) = B) ) ) ) ) ) ) ).
tt(t12_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ((r1_tarski B A) => (r1_xxreal_0 (k5_nat_1 B) (k21_binop_2 A 1))) ) ) ) ) ).
tt(t12_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ((r2_hidden B (k9_xtuple_0 (k19_substut1 A E))) =>  ((k3_funct_2 (k3_qc_lang1 A) C (k1_sublemma A C D (k3_sublemma A E C D)) B) = (k1_funct_1 (k3_sublemma A E C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski B C) <=> (r1_tarski (k3_subset_1 A C) (k3_subset_1 A B))) ) ) ) ) ) ).
tt(t12_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) => (r1_tarski (k3_substlat A B (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) C D)) (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) (k3_substlat A B C) D))) ) ) ) ) ) ).
tt(t12_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (~  ( (~ (v2_substut1 B A))  &  ( (~ (v4_substut1 B A))  &  ( (~ (v5_substut1 B A))  &  ( (~ (v6_substut1 B A))  &  (~ (v7_substut1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (? [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A D) = B)  &  ((k19_substut1 A D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t12_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((m1_xxreal_2 B A) <=> (m2_xxreal_2 (k2_supinf_2 B) (k6_supinf_2 A))) ) ) ) ) ).
tt(t12_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B F C)) D) & (r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B G C)) D))  =>  ((r1_orders_2 B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_sysrel,ax, (! [A:$i] :  ((k3_relat_1 (k4_relat_1 A) (k4_relat_1 A)) = (k4_relat_1 A)) ) ).
tt(t12_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_t_0topsp A) D)) = (k1_tarski (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t12_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_taxonom1 (k1_tarski (k1_tarski A)) A)) ) ).
tt(t12_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v4_taxonom2 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (! [D:$i] :  ((r2_hidden D C) =>  ((r1_xboole_0 B D) &  (~  (A = k1_xboole_0) ) ) ) )  =>  ( ((v4_taxonom2 (k2_xboole_0 C (k1_tarski B))) & (m1_subset_1 (k2_xboole_0 C (k1_tarski B)) (k1_zfmisc_1 (k1_zfmisc_1 A))))  &  (~  ( (~  (B = k1_xboole_0) )  &  ((k3_tarski (k2_xboole_0 C (k1_tarski B))) = (k5_setfam_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t12_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k5_power k8_power (k25_sin_cos A)) = A) ) ) ).
tt(t12_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k10_real_1 (k8_real_1 A (k2_newton B E)) (k3_newton E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 C k6_numbers) =>  ((k9_metric_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t12_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r1_tdgroup A B D D C)) ) ) ) ) ) ) ) ).
tt(t12_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A C)) C)))) (k9_subset_1 (u1_struct_0 A) B (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A C)) C))) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t12_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)) (k2_pre_topc A C)) & (r1_tarski (k2_pre_topc A C) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ) ) ) ) ).
tt(t12_tdlat_3,ax, (! [A:$i] :  ( ((v1_tdlat_3 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r2_hidden (k6_subset_1 (u1_struct_0 A) B) (u1_pre_topc A))) ) ) ) ).
tt(t12_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r6_pboole A (k2_termord A B C D) C) | (r6_pboole A (k2_termord A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t12_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = (u1_struct_0 A)) )  =>  ((k1_tops_1 A B) = k1_xboole_0) ) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t12_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v1_tdlat_3 A))  => (v1_tdlat_3 B)) ) ) ) ) ).
tt(t12_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tex_3 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((m1_pre_topc B C) => (v1_tex_3 C A)) ) ) ) ) ) ) ).
tt(t12_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k6_domain_1 (u1_struct_0 A) B) (k5_setfam_1 (u1_struct_0 A) (k1_tex_4 A B)))) ) ) ) ).
tt(t12_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden G (u1_struct_0 C)) =>  ((k1_funct_1 (k10_tmap_1 A B C D E F) G) = (k1_funct_1 E G)) )  &  ((r2_hidden G (u1_struct_0 D)) =>  ((k1_funct_1 (k10_tmap_1 A B C D E F) G) = (k1_funct_1 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tsep_1 A B C))) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (E = D) ) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) &  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (m1_toler_1 k1_xboole_0 A B)) ) ) ).
tt(t12_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k14_euclid C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k14_euclid C))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid C))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid C))) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 (k15_euclid C))) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k15_euclid C))) =>  (~  ( (D = J)  &  ( (E = K)  &  ( (F = L)  &  ( (G = M)  &  ( (H = (k3_rlvect_1 (k15_euclid C) J L))  &  ( (I = (k3_rlvect_1 (k15_euclid C) K M))  &  ( (~ (r1_xxreal_0 A (k4_metric_1 (k14_euclid C) D E)))  &  ( (~ (r1_xxreal_0 B (k4_metric_1 (k14_euclid C) F G)))  & (r1_xxreal_0 (k2_xcmplx_0 A B) (k4_metric_1 (k14_euclid C) H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) => (r4_borsuk_2 A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t12_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v4_taxonom2 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v2_connsp_1 C A) &  ((r2_hidden D B) & (m1_setfam_1 B C)) )  =>  ((r1_xboole_0 D C) | (r1_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t12_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) => (r1_borsuk_6 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v1_connsp_2 A))  => (v1_connsp_2 B)) ) ) ) ) ).
tt(t12_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_topalg_6 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) &  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ((k6_eqrel_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C) (k3_topalg_1 A B C) D) = (k6_eqrel_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C) (k3_topalg_1 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_topdim_1 B A) & (r1_tarski C B))  =>  ((v2_topdim_1 C A) & (r1_xxreal_0 (k3_topdim_1 A C) (k3_topdim_1 A B))) ) ) ) ) ) ) ) ).
tt(t12_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ( ((v3_topdim_1 B) &  ((v5_waybel23 B) & (r1_xxreal_0 (k4_topdim_1 B) A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v4_pre_topc C B) &  ((v4_pre_topc D B) &  ((r1_xboole_0 C D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_metrizts B C D E) & (r1_xxreal_0 (k2_topdim_1 B E) (k3_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k9_subset_1 (u1_struct_0 A) B C)) (k4_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k2_tops_1 A C)) (k9_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_pre_topc A C))))) ) ) ) ) ) ).
tt(t12_topgen_2,ax, (! [A:$i] :  ((k1_card_1 (k10_eqrel_1 A)) = (k1_card_1 A)) ) ).
tt(t12_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v3_pre_topc (k2_rcomp_1 A B) k2_topgen_3) & (m1_subset_1 (k2_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ) ) ).
tt(t12_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_topgen_4 B A) => (r2_hidden k1_xboole_0 B)) ) ) ) ).
tt(t12_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v3_pre_topc C A) &  ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B)) &  ((v5_pre_topc D (k1_pre_topc A C) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A (k3_subset_1 (u1_struct_0 A) C))) (u1_struct_0 B)) &  ((v5_pre_topc E (k1_pre_topc A (k3_subset_1 (u1_struct_0 A) C)) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A (k3_subset_1 (u1_struct_0 A) C))) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k1_funct_4 D E)) &  ((v1_funct_2 (k1_funct_4 D E) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_funct_4 D E) A B) & (m1_subset_1 (k1_funct_4 D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v2_funct_1 (k3_group_1 A))) ) ).
tt(t12_topmetr3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ((v3_xxreal_2 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v8_valued_0 B) &  ((v2_comseq_2 B) &  ((r1_tarski (k2_relset_1 k1_numbers B) A) &  ((k2_seq_2 B) = (k5_seq_4 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topmetr,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( ((u1_struct_0 A) = (u1_struct_0 (k3_pcomps_1 A)))  &  ((u1_pre_topc (k3_pcomps_1 A)) = (k2_pcomps_1 A)) ) ) ) ).
tt(t12_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) B C) (k1_rltopsp1 (k15_euclid A) C D)) = (k1_tarski C))  =>  ( ( (B = C)  &  (C = D) )  | (r1_topreal1 (k15_euclid A) B D (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) B C) (k1_rltopsp1 (k15_euclid A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid D C))) =>  ((k18_euclid A) = C) ) ) ) ) ) ) ) ) ) ).
tt(t12_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) = (k17_euclid A))  &  ((v4_topreal1 B) &  ((r2_hidden A (k2_topreal1 2 B 1)) &  (C = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k10_real_1 (k7_real_1 (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k18_euclid A)) 2)) A)) ) ) )  =>  ( (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  |  ((v4_topreal1 C) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = A)  &  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) &  ((r1_tarski (k3_topreal1 2 C) (k3_topreal1 2 B)) &  ((k3_topreal1 2 C) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 1 B)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~  ((v5_pre_topc B k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc C k5_topmetr k3_topmetr) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (u1_struct_0 k5_topmetr)) &  (E = (k1_funct_1 B D)) )  =>  ((k17_euclid E) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ((r2_hidden B (k4_finseq_1 (k3_euclid C))) &  (A = (k1_seq_1 C B)) )  =>  ((k1_seq_1 (k3_euclid C) B) = (k18_complex1 A)) ) ) ) ) ) ) ) ).
tt(t12_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k12_rvsum_1 (k4_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D))) = (k8_finseq_1 k1_numbers (k12_rvsum_1 (k4_rvsum_1 A B)) (k12_rvsum_1 (k4_rvsum_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_topreal8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_finseq_1 D A))  =>  ( ( ((k7_partfun1 A C (k3_finseq_1 C)) = (k7_partfun1 A D 1))  &  ((r1_goboard1 A C B) & (r1_goboard1 A D B)) )  => (r1_goboard1 A (k4_graph_2 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t12_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden C (k3_topreal9 A (k4_struct_0 (k15_euclid A)) B)) =>  ((k12_euclid C) = B) ) ) ) ) ) ) ) ).
tt(t12_topreala,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_tsep_1 C B) & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ( (D = E)  & (v1_t_0topsp E A C))  => (v1_t_0topsp D A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((m1_subset_1 B (u1_struct_0 (k8_toprealb A))) =>  ((k12_euclid B) = 1) ) ) ) ) ) ).
tt(t12_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k39_valued_1 (k2_funct_7 (k5_euclid B) A C)) = (k2_funct_7 (k5_euclid B) A (k3_square_1 C))) ) ) ) ) ) ).
tt(t12_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k2_toprns_1 B A (k1_toprns_1 A C D)) = (k1_toprns_1 A (k2_toprns_1 B A C) (k2_toprns_1 B A D))) ) ) ) ) ) ) ) ) ).
tt(t12_tops_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden C D) & (r1_xboole_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B C) & (v2_tops_2 C A))  => (v2_tops_2 B A)) ) ) ) ) ) ) ).
tt(t12_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski (k3_subset_1 (u1_struct_0 A) B) C) & (v4_pre_topc C A))  =>  (C = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t12_tops_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  ((v1_t_0topsp A k3_topmetr k3_topmetr) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (? [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  & (r1_tarski (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A B) D) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A B) D)) (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A (k2_rcomp_1 (k6_xcmplx_0 B C) (k2_xcmplx_0 B C))))) ) ) ) ) ) ) ) ) ).
tt(t12_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ((r1_relat_2 B (k2_zfmisc_1 A A)) => (r1_transgeo A (k6_partfun1 A) B)) ) ) ) ) ).
tt(t12_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v1_translac A) &  ((v11_aff_2 A) &  ((v7_transgeo B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v7_transgeo C A) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_transgeo (u1_struct_0 A) C C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr k6_numbers 1))) => (v5_pre_topc (k4_treal_1 A B C D) (k4_topmetr A B) (k4_topmetr k6_numbers 1))) ) ) ) ) ) ) ) ) ).
tt(t12_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden A (k1_trees_1 B)) <=> (r2_xboole_0 A B)) ) ) ) ) ).
tt(t12_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers C)) (k1_trees_2 A B)) <=> (r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers C)) A)) ) ) ) ) ) ) ).
tt(t12_trees_3,ax, (! [A:$i] :  ((v1_trees_3 (k1_tarski A)) <=>  ( (~ (v1_xboole_0 A))  & (v1_trees_1 A)) ) ) ).
tt(t12_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v6_trees_3 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_trees_2 D)) )  =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 D)) =>  ( (D = (k1_funct_1 B (k2_nat_1 C 1)))  =>  ((r1_xxreal_0 (k3_finseq_1 B) C) |  ((k1_funct_1 (k4_trees_4 A B) (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) E)) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ( ((v1_finset_1 A) &  ((k3_trees_9 A) = (k3_trees_9 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t12_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m4_trees_1 C (k9_xtuple_0 A)) =>  ( (~  (C = k1_xboole_0) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden D (k9_xtuple_0 (k3_trees_a A C B))) & (r2_hidden D (a_2_2_trees_a A C)))  =>  ((k1_funct_1 (k3_trees_a A C B) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_borsuk_1 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v4_pre_topc D B) <=> (v4_pre_topc C A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v4_pre_topc B A) <=> (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t12_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_tsp_1 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t12_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tsp_2 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) & (m1_pre_topc C A)) )  =>  (~  ((v2_tsp_2 C A) &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((l1_turing_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C)))) =>  ( ((r1_xxreal_0 A B) &  ((k1_mcart_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C)) (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) = (u5_turing_1 C)) )  =>  ((k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) B) = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 C) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 C))) (k10_turing_1 C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t12_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 A B C)) = (k10_margrel1 (k10_margrel1 A B) C))  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 A B C)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 A) B) C))  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 A B C)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B)) C))  &  ((k1_funct_1 k20_twoscomp (k11_finseq_1 A B C)) = (k10_margrel1 (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B)) (k9_margrel1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t12_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t12_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_unialg_3 A))))  =>  ( (~ (v1_xboole_0 (k6_setfam_1 (u1_struct_0 A) (k7_relset_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)) (k3_unialg_3 A) B))))  & (m1_subset_1 (k6_setfam_1 (u1_struct_0 A) (k7_relset_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)) (k3_unialg_3 A) B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t12_uniform1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden A (k1_rcomp_1 C D)) & (r2_hidden B (k1_rcomp_1 C D)))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 A B)) (k9_real_1 D C))) ) ) ) ) ) ) ) ) ).
tt(t12_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k24_binop_2 C D)) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t12_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((k3_uproots A B) = k6_numbers)  =>  (B = (k16_pre_poly A)) ) ) ) ) ).
tt(t12_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  (~ (r1_xxreal_0 (k10_real_1 (k2_nat_1 (k6_urysohn1 A B) 1) (k13_newton 2 A)) (k10_real_1 (k5_real_1 (k6_urysohn1 A B) 1) (k13_newton 2 A)))) ) ) ) ) ).
tt(t12_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_measure5 A) =>  ((r1_xxreal_0 k6_numbers B) | (v3_measure5 (k1_integra2 A B))) ) ) ) ) ) ).
tt(t12_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden E k3_urysohn1) & (r2_hidden F k3_urysohn1))  =>  ((r1_xxreal_0 F E) |  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (G = (k1_funct_1 (k3_urysohn3 A B C D) E))  => (r1_tarski (k2_pre_topc A G) (k1_funct_1 (k3_urysohn3 A B C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F (k7_cqc_lang A D E)) C) = (k10_margrel1 (k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F D) C) (k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F E) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_valued_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_valued_0 A) <=>  (! [B:$i] : (v7_ordinal1 (k1_funct_1 A B))) ) ) ) ).
tt(t12_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k9_xtuple_0 (k45_valued_1 A B)) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) ) ) ) ) ).
tt(t12_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k7_valued_1 (k7_valued_1 C A) B) = (k7_valued_1 C (k2_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t12_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_vectsp_4 F A E) =>  (! [G:$i] :  ((m1_vectsp_4 G A E) =>  ( ( (F = C)  &  (G = D) )  =>  ((k1_vectsp_5 A E F G) = (k1_vectsp_5 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp11 C A B (k3_struct_0 B)) =>  (C = (k1_group_1 A)) ) ) ) ) ) ) ).
tt(t12_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k8_group_1 A B C) = (k4_struct_0 A))  <=>  ( (B = (k4_struct_0 A))  |  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k6_algstr_0 A B C) = (k4_struct_0 A))  &  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k4_struct_0 C) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_5 A B (k2_vectsp_4 A B) (k2_vectsp_4 A B)) = B) ) ) ) ) ).
tt(t12_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k3_vectsp_6 A B (k3_finseq_4 (u1_struct_0 B) C D E) F) = (k3_finseq_4 (u1_struct_0 B) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F C) C) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F D) D) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F E) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = (u1_struct_0 B))  =>  ((k1_vectsp_7 A B C) = B) ) ) ) ) ) ) ) ).
tt(t12_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v13_vectsp_1 D B C) & (v1_mod_2 D A B C))  => (m4_vectsp_8 (k6_vectsp_8 A B C D) (k1_vectsp_8 A B) (k1_vectsp_8 A C))) ) ) ) ) ) ) ) ) ).
tt(t12_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_vectsp_7 D A B) & (r1_tarski D (u1_struct_0 C)))  =>  ((v1_vectsp_7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B (k3_vfunct_1 A B E C) (k3_vfunct_1 A B E D)) (k3_vfunct_1 A B E (k2_vfunct_1 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B (k1_vfunct_2 A B E C) (k1_vfunct_2 A B E D)) (k1_vfunct_2 A B E (k2_vfunct_1 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((v11_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B D E) => (r1_orders_2 A (k2_waybel_0 A B E) (k2_waybel_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_waybel10 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_waybel10 A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((r3_orders_2 (k2_waybel10 A) D E) <=> (r1_yellow_2 (u1_struct_0 A) A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A)) ) ) ) ).
tt(t12_waybel12,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_yellow_4 A B (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))) (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A)))) ) ) ) ).
tt(t12_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ((v1_waybel_3 B (k2_yellow_1 (k7_waybel_0 A))) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k5_waybel_0 A C)) ) ) ) ) ) ) ) ).
tt(t12_waybel14,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k2_yellow_4 A (k2_waybel_3 A B) (k2_waybel_3 A C)) (k6_waybel_0 A (k13_lattice3 A B C)))) ) ) ) ) ) ).
tt(t12_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_yellow_2 A B C)))) =>  ((k7_relset_1 (u1_struct_0 (k1_yellow_2 A B C)) (u1_struct_0 B) (k3_waybel_1 A B C) D) = D) ) ) ) ) ) ) ) ) ).
tt(t12_waybel16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k1_tarski A)))  &  ((v2_waybel_0 (k1_tarski A) (k3_yellow_1 A)) &  ((v13_waybel_0 (k1_tarski A) (k3_yellow_1 A)) & (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) ) ) ) ).
tt(t12_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_0_waybel17 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel18,ax, (! [A:$i] :  ( ((v4_waybel11 A) & (m1_yellow_9 A (k3_yellow_1 1)))  =>  ((u1_pre_topc A) = (u1_pre_topc k9_waybel18)) ) ) ).
tt(t12_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v1_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v5_pre_topc C A B) &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_waybel_0 A B C D)) ) )  => (v17_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(t12_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_waybel_1 C A B) => (v17_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(t12_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v22_waybel_0 E A C) & (v22_waybel_0 F B D))  => (v22_waybel_0 (k1_waybel20 A B C D E F) (k3_yellow_3 A B) (k3_yellow_3 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel21,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((l1_orders_2 C) =>  (! [D:$i] :  ((m1_yellow_0 D A) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C))) )  =>  ((m1_yellow_0 C B) &  ((v4_yellow_0 D A) =>  ((v4_yellow_0 C B) & (m1_yellow_0 C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) )  => (v5_orders_3 (k2_waybel22 A B C) (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B)) ) ) ) ) ).
tt(t12_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  => (r1_tarski (k4_waybel_0 B D) (k4_waybel_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t12_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v5_orders_3 (k1_waybel24 A B C D E) B C) & (v5_orders_3 (k2_waybel24 A B C D F) A C)) ) ) ) )  => (v5_orders_3 D (k3_yellow_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t12_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  => (v2_waybel18 B)) ) ) ) ).
tt(t12_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_waybel26 A B)))) =>  ((k2_waybel26 A C E (k7_relset_1 (u1_struct_0 (k1_waybel26 A B)) (u1_struct_0 (k1_waybel26 A C)) (k3_waybel26 A B C D) F)) = (k7_relset_1 (u1_struct_0 B) (u1_struct_0 C) D (k2_waybel26 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  ( ((v4_yellow_0 B C) & (m1_yellow_0 B C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((v5_orders_3 E A C) & (r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 C) D E))  => (v5_orders_3 D A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_waybel28 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  => (m2_yellow_6 (k1_waybel28 A B C) A B)) ) ) ) ) ) ).
tt(t12_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v24_waybel_0 (k2_yellow16 A B C)) & (v1_yellow_0 (k2_yellow16 A B C))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  ((r1_waybel_3 (k5_yellow_1 A B) C D) <=>  ( (! [E:$i] :  ((m1_subset_1 E A) => (r1_waybel_3 (k3_waybel_3 A B E) (k4_waybel_3 A B C E) (k4_waybel_3 A B D E))) )  &  (? [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 A)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~ (r2_hidden F E))  =>  ((k4_waybel_3 A B C F) = (k3_yellow_0 (k2_yellow16 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k3_yellow_3 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((k1_yellow_0 (k3_yellow_3 A A) B) = (k7_yellow_3 A A (k1_yellow_0 A (k4_yellow_3 A A B)) (k1_yellow_0 A (k5_yellow_3 A A B)))) ) ) ) ) ).
tt(t12_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k2_waybel19 A)) <=> (v3_pre_topc B A)) ) ) ) ) ).
tt(t12_waybel31,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (v3_waybel_8 A)) ) ).
tt(t12_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  ((k5_waybel11 A) = (u1_pre_topc B)) ) ) ) ) ).
tt(t12_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow19 A (k2_struct_0 A) B))) =>  ( ((k2_xtuple_0 D) = C)  =>  ((k2_yellow_0 A C) = (k1_waybel_9 A (k5_waybel_9 A (k3_yellow19 A (k2_struct_0 A) B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden D (k1_binop_1 (u1_altcat_1 A) B C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (E = B)  &  ( (F = C)  &  ((r2_hidden D (k1_altcat_1 A E F)) & (m1_subset_1 D (k1_altcat_1 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_waybel35 C A B) &  ((r4_waybel_1 A D C) & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D (k4_yellow_0 A)) B)) )  =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_yellow_0 A) (k4_yellow_0 A)) B) &  (D = (k4_yellow_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  ((r1_tarski (k1_waybel_3 A B) (k1_waybel_3 A C)) & (r1_tarski (k2_waybel_3 A C) (k2_waybel_3 A B))) ) ) ) ) ) ) ) ).
tt(t12_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r1_tarski (k5_waybel_4 A B C) (k5_waybel_0 A B))) ) ) ) ) ) ).
tt(t12_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) )  =>  ( ( ((k9_xtuple_0 B) = (k9_xtuple_0 C))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k5_yellow_2 A (k1_funct_1 B D)) = (k5_yellow_2 A (k1_funct_1 C D))) ) ) )  => (r1_funct_2 (k9_xtuple_0 B) (u1_struct_0 A) (k9_xtuple_0 C) (u1_struct_0 A) (k5_waybel_5 A B) (k5_waybel_5 A C))) ) ) ) ) ) ) ).
tt(t12_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B))))  &  ((v2_waybel_0 (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)) A) &  ((v13_waybel_0 (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)) A) & (m1_subset_1 (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v2_waybel_6 B A)) ) ) ) ) ).
tt(t12_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_waybel_7 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r2_hidden (k2_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v3_orders_2 A))  => (v3_orders_2 B)) ) ) ) ) ).
tt(t12_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((u1_struct_0 (k4_waybel_9 A B C)) = (a_3_0_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(t12_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_card_1 (a_2_2_weddwitt A B)) = (k5_card_1 (k7_group_3 A B))) ) ) ) ) ).
tt(t12_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((v2_compts_1 A k3_topmetr) => (v2_rcomp_1 (k1_weierstr A))) ) ) ).
tt(t12_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( (~ (v1_zfmisc_1 B))  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B)))) )  =>  ( ((r1_wellfnd1 A B C D) & (r1_wellfnd1 A B C E))  => (r2_funct_2 (u1_struct_0 A) B D E)) ) ) ) ) ) )  => (v1_wellfnd1 A)) ) ) ) ) ).
tt(t12_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k1_relat_1 (k2_wellord1 C B))) =>  ((r2_hidden A (k1_relat_1 C)) & (r2_hidden A B)) ) ) ) ) ) ).
tt(t12_wellord2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (~  ((v2_wellord1 A) &  ( (! [B:$i] :  (~  ((r2_hidden B (k1_relat_1 A)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~ (r4_wellord1 (k2_wellord1 A (k1_wellord1 A B)) (k1_wellord2 C))) ) ) ) ) )  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~ (r4_wellord1 A (k1_wellord2 B))) ) ) ) ) ) ) ) ).
tt(t12_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((k3_int_2 C D) = 1)  =>  ( ((k3_int_2 C (k1_newton D A)) = 1)  &  ((k3_int_2 (k1_newton C B) (k1_newton D A)) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  ((k2_xboole_0 A B) = B) ) ) ) ).
tt(t12_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k4_xboolean (k3_xboolean A) B)) = (k5_xboolean A B)) ) ) ) ) ).
tt(t12_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 3 A) = (k2_xcmplx_0 (k2_xcmplx_0 A A) A)) ) ) ).
tt(t12_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) C) => (r1_xxreal_0 (k6_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t12_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k11_xtuple_0 B)) &  (! [C:$i] :  (! [D:$i] :  (~ (r2_hidden (k3_xtuple_0 A C D) B)) ) ) ) ) ) ) ).
tt(t12_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (~  ((r2_hidden A k1_numbers) & (r1_xxreal_0 A k2_xxreal_0)) ) ) ) ).
tt(t12_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k3_xxreal_1 B C)) =>  ((r2_hidden A (k1_xxreal_1 B C)) &  (~  (A = B) ) ) ) ) ) ) ) ) ).
tt(t12_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_0 A B) = (k1_xxreal_2 (k2_tarski A B))) ) ) ) ) ).
tt(t12_xxreal_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((k3_xxreal_3 A B) = (k3_xxreal_3 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t12_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_lattice3 A B C) & (r1_orders_2 A D C))  => (r1_lattice3 A B D)) ) ) ) ) ) ) ) ).
tt(t12_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_yellow_0 (k3_yellow_3 A B) (k7_domain_1 (u1_struct_0 (k3_yellow_3 A B)) C D)) <=>  ((r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) (k8_yellow_3 A B C) (k8_yellow_3 A B D))) & (r1_yellow_0 B (k7_domain_1 (u1_struct_0 B) (k9_yellow_3 A B C) (k9_yellow_3 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_yellow11 A) =>  ((v2_waybel_1 A) <=>  (! [B:$i] :  ( ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (~ (r5_waybel_1 k2_yellow11 B)) ) ) ) ) ) ) ).
tt(t12_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (C = E)  &  (D = F) ) )  =>  ((k2_yellow_4 A C D) = (k1_yellow_4 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v19_waybel_0 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(t12_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v1_lattice3 A))  => (v1_lattice3 B)) ) ) ) ) ).
tt(t12_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k6_margrel1) =>  ( ( ((k1_funct_1 D 1) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k2_finseq_4 (k1_zfmisc_1 A) B C) D) 1) = B) )  &  ( ( ((k1_funct_1 D 1) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k2_finseq_4 (k1_zfmisc_1 A) B C) D) 1) = (k6_subset_1 A B)) )  &  ( ( ((k1_funct_1 D 2) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k2_finseq_4 (k1_zfmisc_1 A) B C) D) 2) = C) )  &  ( ((k1_funct_1 D 2) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k2_finseq_4 (k1_zfmisc_1 A) B C) D) 2) = (k6_subset_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_yellow16 A B C) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v11_quantal1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel18 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B D)))) =>  ( (~  (F = (k2_struct_0 (k4_waybel18 A B D))) )  =>  ((r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski E)) (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B D)) (k6_waybel18 A B D) F)) <=>  ( (C = D)  & (r2_hidden E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (l2_altcat_1 B)) )  =>  ( ((r2_yellow18 A B) & (v12_altcat_1 A))  => (v12_altcat_1 B)) ) ) ) ) ).
tt(t12_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k10_yellow_6 A B)) <=> (r2_waybel_7 A (k2_yellow19 A B) C)) ) ) ) ) ) ) ).
tt(t12_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k3_xboole_0 B C) A)) ) )  => (v2_lattice3 (k2_yellow_1 A))) ) ) ).
tt(t12_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v9_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) &  ((v2_yellow18 B) & (l2_altcat_1 B)) ) ) ) ) )  => (r1_yellow20 A B)) ) ) ) ).
tt(t12_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r1_tarski (u1_struct_0 (k6_yellow21 A)) (k2_yellow21 A))) ) ).
tt(t12_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v5_orders_3 D A B) & (v5_orders_3 E B C))  => (v5_orders_3 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_orders_2 (k3_yellow_3 A B) C D) <=>  ((r1_orders_2 A (k8_yellow_3 A B C) (k8_yellow_3 A B D)) & (r1_orders_2 B (k9_yellow_3 A B C) (k9_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r2_yellow_4 A B (k2_yellow_4 A B C))) ) ) ) ) ) ).
tt(t12_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A B D) => (r1_orders_2 A (k1_yellow_5 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t12_yellow_6,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_yellow_6 C A B) & (m1_yellow_6 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (D = F)  &  ( (E = G)  & (r1_orders_2 B D E)) )  => (r1_orders_2 C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((r1_yellow_0 A B) | (r2_yellow_0 (k7_lattice3 A) B))  =>  ((k1_yellow_0 A B) = (k2_yellow_0 (k7_lattice3 A) B)) ) ) ) ) ).
tt(t12_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) =>  ((v3_pre_topc D A) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (B = (k2_xboole_0 C (k1_tarski A)))  |  (C = (k7_subset_1 (k1_zfmisc_1 A) B (k1_tarski A))) )  =>  ((k8_setfam_1 A B) = (k8_setfam_1 A C)) ) ) ) ) ) ) ).
tt(t12_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ((r2_zf_model A k6_zf_model) &  (! [B:$i] :  (~  ((v1_ordinal1 B) & (r2_zf_colla A B)) ) ) ) ) ) ) ).
tt(t12_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ((m1_subset_1 E k4_ordinal1) =>  ( ((v8_zf_fund1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  => (r2_hidden (a_4_0_zf_fund1 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v11_zf_lang (k15_zf_lang B C A)) &  ( ((k23_zf_lang (k15_zf_lang B C A)) = B)  &  ((k24_zf_lang (k15_zf_lang B C A)) = (k13_zf_lang C A)) ) ) ) ) ) ) ) ) ).
tt(t12_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~ (v7_zf_lang A))  &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~ (r1_xxreal_0 (k2_nat_1 (k3_finseq_1 B) 1) (k3_finseq_1 A))) ) ) ) ) ) ) ).
tt(t12_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_xboole_0 (k1_tarski A) (k1_tarski B)) = (k1_tarski A))  =>  (A = B) ) ) ) ).
tt(t12_zfmodel1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang E)))) )  =>  ( ((r1_xboole_0 (k1_enumset1 A B C) (k2_zf_model D)) & (r1_zf_model E F D))  => (r1_zf_model E F (k16_zf_lang A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ( (~ (r2_hidden A (k4_zf_lang1 D)))  =>  ((r1_zf_model C E (k6_zf_lang1 D B A)) <=> (r1_zf_model C (k2_zf_lang1 C E B (k3_funct_2 k1_zf_lang C E A)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t12_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((r1_zf_model A B (k4_zf_lang C D)) <=>  ((k3_funct_2 k1_zf_lang A B C) = (k3_funct_2 k1_zf_lang A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t12_zfrefle1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_tarski A B) |  ((k1_card_1 A) = (k1_card_1 B)) )  =>  ((r2_tarski (k1_zfmisc_1 A) (k1_zfmisc_1 B)) &  ((k1_card_1 (k1_zfmisc_1 A)) = (k1_card_1 (k1_zfmisc_1 B))) ) ) ) ) ).
tt(t12_zf_refle,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k2_ordinal1 (k4_classes1 A)) = A) ) ) ).
tt(t12_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  (F = (k1_funct_1 D E)) )  =>  ((k1_funct_1 C E) = (k1_zmodul01 B F A)) ) ) ) ) ) )  =>  ((k4_rlvect_1 B C) = (k1_zmodul01 B (k4_rlvect_1 B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t130_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m4_abcmiz_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D)) =>  ((m2_finseq_1 (k1_partfun1 k5_numbers (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) E C) (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D)) &  ((k5_card_1 (k1_partfun1 k5_numbers (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))) E C)) = (k3_finseq_1 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  (B = (k8_finseq_1 A (k12_finseq_1 A D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_finseq_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_card_3 (k11_finseq_1 A A A)) = (k4_finseq_2 3 A)) ) ) ).
tt(t130_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) )  => (r1_funct_7 B (k1_funct_4 B C) A)) ) ) ) ) ).
tt(t130_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k49_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t130_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((v3_glib_001 B A) => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k7_glib_001 A C B) C)) ) ) ) ) ) ) ).
tt(t130_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r2_wellord2 (k14_group_2 A D B) (k14_group_2 A D C))) ) ) ) ) ) ) ) ).
tt(t130_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_card_1 (k8_group_3 A B)) = (k17_group_2 A (k10_group_3 A B))) ) ) ) ) ).
tt(t130_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_2_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k9_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t130_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( (C = (k5_euclid A))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( ( (F = D)  &  ((k1_rlvect_1 (k15_euclid A) F B) = E) )  =>  ((k8_real_1 B (k4_metric_1 (k14_euclid A) C D)) = (k4_metric_1 (k14_euclid A) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k15_member_1 (k2_tarski A B) (k1_tarski C)) = (k2_tarski (k6_binop_2 A C) (k6_binop_2 B C))) ) ) ) ) ) ) ).
tt(t130_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) & (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_partfun2 (u1_struct_0 A) C)))  => (r7_ncfcont1 A A B C)) ) ) ) ) ) ) ).
tt(t130_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v3_relat_1 B) & (r2_pboole A C B))  => (v3_relat_1 C)) ) ) ) ) ) ).
tt(t130_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k3_xboole_0 (k9_xtuple_0 B) A) (k7_relat_1 (k2_relat_1 B) (k7_relat_1 B A)))) ) ) ).
tt(t130_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k5_rvsum_1 A B C) D) = (k9_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t130_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (~ (r1_xboole_0 B C))  =>  ((k26_seq_4 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t130_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C)) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D D) C) (k5_sheffer1 A B C))) = (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A B B)))) ) ) ) ) ) ) ) ) ).
tt(t130_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_sincos10 (k7_relset_1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))))).
tt(t130_sin_cos9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k1_seq_1 k2_sin_cos9 B) (k5_square_1 B))) (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ) ).
tt(t130_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)))  => (r1_funct_2 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (u1_struct_0 (k1_tsep_1 A D C)) (u1_struct_0 B) (k10_tmap_1 A B C D E F) (k10_tmap_1 A B D C F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  (! [D:$i] :  ((v1_xboolean D) =>  ( ( ((k7_xboolean A B) = k2_xboolean)  &  ((k7_xboolean C D) = k2_xboolean) )  =>  ((k7_xboolean (k4_xboolean A C) (k4_xboolean B D)) = k2_xboolean) ) ) ) ) ) ) ) ) ) ).
tt(t130_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k6_xcmplx_0 (k7_xcmplx_0 C A) (k7_xcmplx_0 D B)) = (k7_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 C B) (k3_xcmplx_0 D A)) (k3_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t130_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t130_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xxreal_1 A B) = (k2_xboole_0 (k1_tarski A) (k3_xxreal_1 A B))) ) ) ) ) ) ).
tt(t130_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( (~ (r2_hidden C (k2_zf_model A)))  => (r2_zf_model D (k11_zf_lang (k8_zf_lang C (k11_zf_lang B A)) (k11_zf_lang (k13_zf_lang C B) A)))) ) ) ) ) ) ) ) ) ).
tt(t130_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A B) & (v1_zfmisc_1 B))  => (v1_zfmisc_1 A)) ) ) ).
tt(t130_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ((m3_zmodul01 (k3_zmodul01 A) A (k4_zmodul01 A)) & (m3_zmodul01 (k4_zmodul01 A) A (k3_zmodul01 A))) ) ) ).
tt(t131_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)) =>  ( ((k1_relset_1 k2_abcmiz_1 (k54_abcmiz_1 A B)) = B)  &  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  ((r2_hidden C B) =>  ((k1_funct_1 (k54_abcmiz_1 A B) C) = (k35_abcmiz_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t131_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C B))  <=> (r2_hidden C (k4_finseq_2 A B))) ) ) ) ) ) ).
tt(t131_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((k4_card_3 (k2_finseq_2 A B)) = (k4_finseq_2 A B)) ) ) ) ).
tt(t131_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) )  => (r1_funct_7 B C A)) ) ) ) ) ).
tt(t131_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k49_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t131_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((v3_glib_001 (k8_glib_001 A B C D) A) <=>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r2_wellord2 (k8_group_2 A C) (k13_group_2 A C B)) & (r2_wellord2 (k8_group_2 A C) (k14_group_2 A C B))) ) ) ) ) ) ) ).
tt(t131_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((v1_finset_1 (k8_group_3 A B)) | (v1_finset_1 (k15_group_2 A (k10_group_3 A B))))  &  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (k8_group_3 A B))  &  ((k5_card_1 C) = (k18_group_2 A (k10_group_3 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) B) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  (~  ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  & (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid C)))  &  ((r1_xxreal_0 G (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_xxreal_0 (k17_euclid D) F) &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (D = (k5_euclid A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (E = (k9_metric_1 (k14_euclid A) D C))  =>  ((k1_convex1 (k15_euclid A) E B) = (k9_metric_1 (k14_euclid A) D (k8_real_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k15_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k6_binop_2 A C) (k6_binop_2 A D) (k6_binop_2 B C) (k6_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t131_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F B) =>  ((k7_partfun1 (u1_struct_0 A) C F) = (k3_rlvect_1 A (k1_clvect_1 A F D) E)) ) ) ) )  => (r7_ncfcont1 A A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t131_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) & (r2_pboole A B C))  => (v2_relat_1 C)) ) ) ) ) ) ).
tt(t131_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k8_relat_1 C B)) <=>  (? [D:$i] :  ((r2_hidden D (k10_xtuple_0 C)) &  ((r2_hidden (k4_tarski A D) C) & (r2_hidden D B)) ) ) ) ) ) ) ) ).
tt(t131_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k23_rvsum_1 (k11_rvsum_1 A B D) C) = (k11_binop_2 D (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t131_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ((r2_hidden B (k27_seq_4 A)) <=> (v1_seq_4 B A)) ) ) ) ) ).
tt(t131_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A C B)) C) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t131_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k3_sincos10 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))))).
tt(t131_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 E) (u1_struct_0 B)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) )  =>  (~  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) F) (k3_tmap_1 A B D (k2_tsep_1 A C D) G)))  &  ( ((r1_tsep_1 C E) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C E)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C E) F) (k3_tmap_1 A B E (k2_tsep_1 A C E) H)))  &  ( ((r1_tsep_1 D E) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A D E)) (u1_struct_0 B) (k3_tmap_1 A B D (k2_tsep_1 A D E) G) (k3_tmap_1 A B E (k2_tsep_1 A D E) H)))  &  (~ (r1_funct_2 (u1_struct_0 (k1_tsep_1 A (k1_tsep_1 A C D) E)) (u1_struct_0 B) (u1_struct_0 (k1_tsep_1 A C (k1_tsep_1 A D E))) (u1_struct_0 B) (k10_tmap_1 A B (k1_tsep_1 A C D) E (k10_tmap_1 A B C D F G) H) (k10_tmap_1 A B C (k1_tsep_1 A D E) F (k10_tmap_1 A B D E G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t131_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  (! [D:$i] :  ((v1_xboolean D) =>  ( ( ((k7_xboolean A B) = k2_xboolean)  &  ((k7_xboolean C D) = k2_xboolean) )  =>  ((k7_xboolean (k5_xboolean A C) (k5_xboolean B D)) = k2_xboolean) ) ) ) ) ) ) ) ) ) ).
tt(t131_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k6_xcmplx_0 A B) = (k3_xcmplx_0 A (k6_xcmplx_0 1 (k7_xcmplx_0 B A)))) ) ) ) ) ) ).
tt(t131_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(t131_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_xxreal_1 A B) = (k2_xboole_0 (k1_tarski A) (k4_xxreal_1 A B))) ) ) ) ) ) ).
tt(t131_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((r2_zf_model D (k11_zf_lang B A)) =>  ((r2_hidden C (k2_zf_model A)) | (r2_zf_model D (k11_zf_lang (k13_zf_lang C B) A))) ) ) ) ) ) ) ) ) ) ).
tt(t131_zfmisc_1,ax, (! [A:$i] :  (~  ( (~ (v1_xboole_0 A))  &  ((v1_zfmisc_1 A) &  (! [B:$i] :  (~  (A = (k1_tarski B)) ) ) ) ) ) ) ).
tt(t131_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m2_zmodul01 D A B) =>  (! [E:$i] :  ((m2_zmodul01 E A C) =>  ( (~ (r1_xboole_0 D E))  => (m2_zmodul01 (k9_subset_1 (u1_struct_0 A) D E) A (k7_zmodul01 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t132_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  ( (~ (r2_hidden C (k1_relset_1 k2_abcmiz_1 B)))  =>  ((k56_abcmiz_1 A B (k35_abcmiz_1 C A)) = (k35_abcmiz_1 C A)) ) ) ) ) ) ) ) ).
tt(t132_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C (k4_finseq_2 B A)) <=>  ( ((k3_finseq_1 C) = B)  & (r1_tarski (k10_xtuple_0 C) A)) ) ) ) ) ) ) ).
tt(t132_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k2_funct_6 (k9_finseq_1 A)) = (k9_finseq_1 (k9_xtuple_0 A)))  &  ((k3_funct_6 (k9_finseq_1 A)) = (k9_finseq_1 (k10_xtuple_0 A))) ) ) ) ).
tt(t132_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  => (r1_funct_7 (k1_funct_4 D B) (k1_funct_4 D C) A)) ) ) ) ) ) ) ).
tt(t132_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k14_twoscomp) C) k14_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) k29_twoscomp) (u1_struct_0 (k49_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t132_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (~  ((r1_glib_000 A (k4_glib_001 A B) D C) & (v3_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ).
tt(t132_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ((k7_struct_0 C) = (k1_card_1 (k13_group_2 A C B)))  &  ((k7_struct_0 C) = (k1_card_1 (k14_group_2 A C B))) ) ) ) ) ) ) ) ).
tt(t132_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_card_1 (k7_group_3 A B)) = (k17_group_2 A (k10_group_3 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t132_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (v5_pre_topc (k9_jgraph_4 A) (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ).
tt(t132_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k17_euclid C) F) &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t132_jordan2c,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 C k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( (E = (k5_euclid A))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (F = (k9_metric_1 (k14_euclid A) E B))  => (r1_tarski (k1_convex1 (k15_euclid A) F C) (k1_convex1 (k15_euclid A) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t132_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k1_xxreal_3 C B) (k16_member_1 A C))) ) ) ) ) ) ) ).
tt(t132_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) =>  ((k7_partfun1 k1_numbers B C) = (k1_normsp_0 A C)) ) ) )  => (r11_ncfcont1 A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t132_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) & (r7_pboole A B C))  => (r2_pboole A B C)) ) ) ) ) ) ).
tt(t132_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k8_relat_1 B A) (k9_xtuple_0 B))) ) ) ).
tt(t132_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k7_rvsum_1 A B) C) = (k7_binop_2 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t132_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k14_seq_4 A))) =>  ((v2_seq_4 B A) <=> (v1_seq_4 (k3_subset_1 (k14_seq_4 A) B) A)) ) ) ) ) ).
tt(t132_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A C B)) = C) ) ) ) ) ) ) ).
tt(t132_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k4_sincos10 (k7_relset_1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))))).
tt(t132_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ( ((r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)) & (r4_tsep_1 A C D))  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t132_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ((k7_xboolean A B) = k2_xboolean)  <=>  ( ((k6_xboolean A B) = k2_xboolean)  &  ((k6_xboolean B A) = k2_xboolean) ) ) ) ) ) ) ).
tt(t132_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  (B = (k7_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) C) C) A)) ) ) ) ) ) ) ) ).
tt(t132_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t132_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k3_xxreal_1 A B) = (k2_xboole_0 (k4_xxreal_1 A B) (k1_tarski B))) ) ) ) ) ) ).
tt(t132_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((r2_zf_model D (k11_zf_lang A (k8_zf_lang C B))) => (r2_zf_model D (k11_zf_lang A B))) ) ) ) ) ) ) ) ) ).
tt(t132_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_zfmisc_1 B) =>  ((r2_hidden A B) =>  (B = (k1_tarski A)) ) ) ) ) ).
tt(t132_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_zmodul01 A B C) <=>  (! [D:$i] :  ((m2_zmodul01 D A B) =>  (! [E:$i] :  ((m2_zmodul01 E A C) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k9_subset_1 (u1_struct_0 A) D E) = (k6_domain_1 (u1_struct_0 A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t133_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  ((r2_hidden C (k1_relset_1 k2_abcmiz_1 B)) =>  ((k56_abcmiz_1 A B (k35_abcmiz_1 C A)) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(t133_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden C (k4_finseq_2 B A)) <=>  ((k3_finseq_1 C) = B) ) ) ) ) ) ) ).
tt(t133_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k2_funct_6 (k10_finseq_1 A B)) = (k10_finseq_1 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  ((k3_funct_6 (k10_finseq_1 A B)) = (k10_finseq_1 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t133_funct_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) & (v1_funct_1 B)) )  =>  ((k1_card_1 (k61_valued_1 B A)) = (k1_card_1 B)) ) ) ) ) ).
tt(t133_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k49_gfacirc1 A B C))) &  ((r2_hidden (k48_gfacirc1 A B C) (k3_msafree2 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k3_msafree2 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k3_msafree2 (k49_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k3_msafree2 (k49_gfacirc1 A B C))) & (r2_hidden (k45_gfacirc1 A B C) (k3_msafree2 (k49_gfacirc1 A B C)))) ) ) ) ) ) ) ) ).
tt(t133_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (~  ( (~ (v3_glib_001 B A))  &  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (~  ( (C = (k6_xcmplx_0 (k3_finseq_1 B) 2))  & (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k10_glib_001 A (k8_glib_001 A B 1 C) (k1_funct_1 B (k2_nat_1 C 1))) B)) ) ) ) ) ) ) ) ) ) ).
tt(t133_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v8_struct_0 C) & (m1_group_2 C A))  =>  (? [D:$i] :  ((v1_finset_1 D) &  (? [E:$i] :  ((v1_finset_1 E) &  ( (D = (k13_group_2 A C B))  &  ( (E = (k14_group_2 A C B))  &  ( ((k7_group_1 C) = (k5_card_1 D))  &  ((k7_group_1 C) = (k5_card_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t133_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( ((v1_finset_1 (k7_group_3 A B)) | (v1_finset_1 (k15_group_2 A (k10_group_3 A (k6_domain_1 (u1_struct_0 A) B)))))  &  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (k7_group_3 A B))  &  ((k5_card_1 C) = (k18_group_2 A (k10_group_3 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t133_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (v2_funct_1 (k9_jgraph_4 A))) ) ) ) ) ) ).
tt(t133_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k17_euclid C) F) &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t133_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k16_member_1 A B) = (a_2_8_member_1 A B)) ) ) ) ) ).
tt(t133_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) =>  ((k7_partfun1 k1_numbers C D) = (k1_normsp_0 A D)) ) ) ) )  => (r11_ncfcont1 A C B)) ) ) ) ) ) ).
tt(t133_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) & (r7_pboole A B C))  => (v2_relat_1 C)) ) ) ) ) ) ).
tt(t133_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k8_relat_1 B A) = (k8_relat_1 B (k3_xboole_0 (k10_xtuple_0 B) A))) ) ) ) ).
tt(t133_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k7_rvsum_1 A B) (k7_rvsum_1 A C)) = (k23_rvsum_1 B C)) ) ) ) ) ) ) ).
tt(t133_seq_4,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~  (A = k1_xboole_0) )  =>  ((v4_xxreal_2 A) &  ((r2_hidden (k4_seq_4 A) A) &  ((v3_xxreal_2 A) & (r2_hidden (k5_seq_4 A) A)) ) ) ) ) ) ).
tt(t133_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A B B)) = B) ) ) ) ) ) ) ).
tt(t133_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((r1_tsep_1 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((r4_tsep_1 A C D) =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t133_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  (! [D:$i] :  ((v1_xboolean D) =>  ( ( ((k7_xboolean A B) = k2_xboolean)  &  ((k7_xboolean C D) = k2_xboolean) )  =>  ((k7_xboolean (k6_xboolean A C) (k6_xboolean B D)) = k2_xboolean) ) ) ) ) ) ) ) ) ) ).
tt(t133_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k4_xcmplx_0 A) = (k4_xcmplx_0 B))  =>  (A = B) ) ) ) ) ) ).
tt(t133_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B)))  &  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (~ (r1_xxreal_0 k6_numbers B)) ) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t133_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A B) (k2_tarski A B)) = (k4_xxreal_1 A B)) ) ) ) ) ) ).
tt(t133_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((r2_zf_model D (k11_zf_lang (k13_zf_lang C A) B)) => (r2_zf_model D (k11_zf_lang A B))) ) ) ) ) ) ) ) ) ).
tt(t133_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden A D) &  ((r2_hidden B D) & (r2_hidden C D)) )  => (r1_tarski (k1_enumset1 A B C) D)) ) ) ) ) ).
tt(t133_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( ((k6_zmodul01 A B C) = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t134_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_trees_4 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k1_msualg_1 A B)))  =>  ((k56_abcmiz_1 A D (k36_abcmiz_1 A B C)) = (k36_abcmiz_1 A B (k58_abcmiz_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t134_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k4_finseq_2 B A) (k3_finseq_2 A))) ) ) ).
tt(t134_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k2_funct_6 (k11_finseq_1 A B C)) = (k11_finseq_1 (k9_xtuple_0 A) (k9_xtuple_0 B) (k9_xtuple_0 C)))  &  ((k3_funct_6 (k11_finseq_1 A B C)) = (k11_finseq_1 (k10_xtuple_0 A) (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ) ).
tt(t134_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = (k9_xtuple_0 D))  &  ((r1_tarski (k9_xtuple_0 C) (k2_xboole_0 A B)) &  ((k5_relat_1 C B) = (k5_relat_1 D B)) ) )  => (r1_funct_7 C D A)) ) ) ) ) ) ) ).
tt(t134_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  ((r2_hidden A (k2_msafree2 (k49_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k49_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k49_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t134_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r1_tarski (k14_glib_001 A B) (k14_glib_001 A C)) =>  ((v3_glib_001 B A) | (r1_tarski (k13_glib_001 A B) (k13_glib_001 A C))) ) ) ) ) ) ) ) ).
tt(t134_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v8_struct_0 A) =>  ((v1_finset_1 (k16_group_2 A B)) & (v1_finset_1 (k15_group_2 A B))) ) ) ) ) ) ).
tt(t134_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C B))  =>  ((r1_struct_0 (k11_group_3 B C) A) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ( (A = D)  & (r1_group_2 B (k6_group_3 B C D) C)) ) ) ) ) ) ) ) ) ).
tt(t134_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( ((v1_funct_1 (k9_jgraph_4 A)) &  ((v1_funct_2 (k9_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k9_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A)) = (u1_struct_0 (k15_euclid 2))) ) ) ) ) ) ) ) ).
tt(t134_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 (k17_euclid B) F) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t134_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k16_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k1_xxreal_3 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t134_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (r1_pboole A C B)) ) ) ) ) ).
tt(t134_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k8_relat_1 A (k10_xtuple_0 A)) = (k9_xtuple_0 A)) ) ) ).
tt(t134_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k9_rvsum_1 A B C) D) = (k10_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t134_seq_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k1_nat_1 A 1) (k3_finseq_1 B)))  =>  ((r2_hidden A (k4_finseq_1 B)) & (r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B))) )  &  ( ((r2_hidden A (k4_finseq_1 B)) & (r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B)))  =>  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k1_nat_1 A 1) (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(t134_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A C (k5_sheffer1 A C C))) (k5_sheffer1 A D B)) = D) ) ) ) ) ) ) ) ) ).
tt(t134_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  ( (~ (r1_tsep_1 C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)) =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t134_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k9_xboolean A (k3_xboolean A))) = k2_xboolean) ) ) ).
tt(t134_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k4_xcmplx_0 A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t134_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 (k3_xcmplx_0 A B) k6_numbers))  &  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (~ (r1_xxreal_0 B k6_numbers)) ) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  (~ (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ) ) ) ) ).
tt(t134_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A B) (k1_tarski A)) = (k3_xxreal_1 A B)) ) ) ) ) ) ).
tt(t134_zf_lang1,ax,(r1_tarski k9_zf_lang (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))).
tt(t134_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski A B) C) =>  ((r2_hidden A (k3_tarski (k3_tarski C))) & (r2_hidden B (k3_tarski (k3_tarski C)))) ) ) ) ) ).
tt(t134_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_zmodul01 A B C) &  ( ((k3_rlvect_1 A D E) = (k3_rlvect_1 A F G))  &  ((r1_struct_0 B D) &  ((r1_struct_0 B F) &  ((r1_struct_0 C E) & (r1_struct_0 C G)) ) ) ) )  =>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k56_abcmiz_1 A C (k30_abcmiz_1 A (k32_abcmiz_1 A) B)) = (k30_abcmiz_1 A (k32_abcmiz_1 A) (k56_abcmiz_1 A C B))) ) ) ) ) ) ) ).
tt(t135_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k4_finseq_2 1 A)) <=>  (? [C:$i] :  ((r2_hidden C A) &  (B = (k9_finseq_1 C)) ) ) ) ) ) ).
tt(t135_finseq_3,ax, (! [A:$i] :  ( ((k3_card_3 (k9_finseq_1 A)) = A)  &  ((k4_funct_6 (k9_finseq_1 A)) = A) ) ) ).
tt(t135_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = (k9_xtuple_0 D))  &  ((r1_tarski A (k9_xtuple_0 C)) &  ((r1_xboole_0 B A) & (r1_funct_7 C D B)) ) )  =>  ((k5_relat_1 C A) = (k5_relat_1 D A)) ) ) ) ) ) ) ) ).
tt(t135_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k49_gfacirc1 A B C) (k50_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k49_gfacirc1 A B C) (k50_gfacirc1 A B C) D 2) (k48_gfacirc1 A B C)) = (k9_margrel1 (k2_binarith (k2_binarith (k9_margrel1 E) (k9_margrel1 F)) (k9_margrel1 G))))  &  ((k1_funct_1 (k5_facirc_1 (k49_gfacirc1 A B C) (k50_gfacirc1 A B C) D 2) (k45_gfacirc1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) (k9_margrel1 F)) (k10_margrel1 (k9_margrel1 F) (k9_margrel1 G))) (k10_margrel1 (k9_margrel1 G) (k9_margrel1 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (~ (v3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ((r2_hidden C (k13_glib_001 A B)) & (v10_glib_000 C A)) ) ) ) ) ) ) ) ) ).
tt(t135_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((r2_hidden (k8_group_2 A B) (k15_group_2 A B)) & (r2_hidden (k8_group_2 A B) (k16_group_2 A B))) ) ) ) ) ).
tt(t135_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ((k1_card_1 (k9_group_3 A B)) = (k17_group_2 A (k11_group_3 A B))) ) ) ) ) ).
tt(t135_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r2_hidden B D) &  ((v3_pre_topc D (k15_euclid 2)) &  ((r1_tarski D C) & (r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = F)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 (k17_euclid B) F) &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_tarski (k16_member_1 A C) (k16_member_1 B C)) => (r1_tarski A B)) ) ) ) ) ) ) ).
tt(t135_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D C) <=> (r1_pboole A D B)) ) )  => (r6_pboole A C B)) ) ) ) ) ) ).
tt(t135_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k8_relat_1 B A) (k8_relat_1 B (k10_xtuple_0 B)))) ) ) ).
tt(t135_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k5_rvsum_1 A (k11_rvsum_1 A D B) (k11_rvsum_1 A E C)) F) = (k9_binop_2 (k11_binop_2 B (k23_rvsum_1 D F)) (k11_binop_2 C (k23_rvsum_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_seq_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k1_nat_1 A 2) (k3_finseq_1 B)))  =>  ((r2_hidden A (k4_finseq_1 B)) &  ((r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B)) & (r2_hidden (k1_nat_1 A 2) (k4_finseq_1 B))) ) )  &  ( ((r2_hidden A (k4_finseq_1 B)) &  ((r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B)) & (r2_hidden (k1_nat_1 A 2) (k4_finseq_1 B))) )  =>  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k1_nat_1 A 2) (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(t135_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C B) (k5_sheffer1 A C C)) = C) ) ) ) ) ) ) ).
tt(t135_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  ( (~ (r1_tsep_1 C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)) =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t135_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k8_xboolean A (k3_xboolean A)) = k2_xboolean) ) ) ).
tt(t135_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k2_xcmplx_0 A (k4_xcmplx_0 B)) = k6_numbers)  =>  (A = B) ) ) ) ) ) ).
tt(t135_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B))) ) ) ) ) ).
tt(t135_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A B) (k1_tarski B)) = (k2_xxreal_1 A B)) ) ) ) ) ) ).
tt(t135_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  (~  (A = 4) ) ) ) ) ) ) ) ).
tt(t135_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r1_tarski C (k2_xboole_0 A (k1_tarski B))) &  ( (~ (r2_hidden B C))  &  (~ (r1_tarski C A)) ) ) ) ) ) ) ).
tt(t135_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( (A = (k6_zmodul01 A B C))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( ((k3_rlvect_1 A E F) = (k3_rlvect_1 A G H))  &  ((r1_struct_0 B E) &  ((r1_struct_0 B G) &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  (~  ( (E = G)  &  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  | (r1_zmodul01 A B C)) ) ) ) ) ) ) ) ).
tt(t136_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k12_abcmiz_1 A)) =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k56_abcmiz_1 A D (k31_abcmiz_1 A (k33_abcmiz_1 A) C B)) = (k31_abcmiz_1 A (k33_abcmiz_1 A) (k56_abcmiz_1 A D C) (k56_abcmiz_1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t136_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k9_finseq_1 B) (k4_finseq_2 1 A)) => (r2_hidden B A)) ) ) ).
tt(t136_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_card_3 (k10_finseq_1 A B)) = (k2_xboole_0 A B))  &  ((k4_funct_6 (k10_finseq_1 A B)) = (k3_xboole_0 A B)) ) ) ) ).
tt(t136_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r1_tarski A (k2_xboole_0 B C)) &  ((k5_relat_1 D C) = (k5_relat_1 E C)) )  => (r1_funct_7 D E B)) ) ) ) ) ) ) ) ).
tt(t136_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k4_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k4_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k49_gfacirc1 A B C) (k50_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k49_gfacirc1 A B C) (k50_gfacirc1 A B C) D 2) (k49_gfacirc1 A B C) (k50_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t136_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) <=>  ((k14_glib_001 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t136_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (r2_wellord2 (k15_group_2 A B) (k16_group_2 A B))) ) ) ) ).
tt(t136_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (~  ( ((v1_finset_1 (k9_group_3 A B)) | (v1_finset_1 (k15_group_2 A (k11_group_3 A B))))  &  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (k9_group_3 A B))  &  ((k5_card_1 C) = (k18_group_2 A (k11_group_3 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t136_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k9_jgraph_4 A)) & (v3_tops_2 B (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t136_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = G)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k17_euclid A) F) &  ( (~ (r1_xxreal_0 (k17_euclid A) (k17_euclid B)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t136_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k16_member_1 A C) = (k16_member_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t136_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E D) <=>  ((r1_pboole A E B) & (r1_pboole A E C)) ) ) )  => (r6_pboole A D (k3_pboole A B C))) ) ) ) ) ) ) ) ).
tt(t136_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k5_rvsum_1 A B C) (k5_rvsum_1 A D E)) = (k9_binop_2 (k9_binop_2 (k9_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t136_seq_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k7_partfun1 A (k8_finseq_1 A B C) (k2_nat_1 D (k3_finseq_1 B))) = (k7_partfun1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t136_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A D C) (k5_sheffer1 A D (k5_sheffer1 A B (k5_sheffer1 A B B)))) = D) ) ) ) ) ) ) ) ) ).
tt(t136_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  ((r1_tsep_1 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t136_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k8_xboolean A B)) = k2_xboolean) ) ) ) ) ).
tt(t136_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k2_xcmplx_0 (k2_xcmplx_0 A B) (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t136_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B))) ) ) ) ) ).
tt(t136_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 A B) (k1_tarski A)) = (k4_xxreal_1 A B)) ) ) ) ) ) ).
tt(t136_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (~ (r2_hidden A (k3_enumset1 k6_numbers 1 2 3 4))) ) ) ).
tt(t136_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_xboole_0 C (k1_tarski B))) <=>  ((r2_hidden A C) |  (A = B) ) ) ) ) ) ).
tt(t136_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_zmodul01 A B C) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D C B))) ) ) ) ) ) ) ) ) ) ).
tt(t137_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k2_abcmiz_1)) =>  ((k56_abcmiz_1 A (k54_abcmiz_1 A C) B) = B) ) ) ) ) ) ) ).
tt(t137_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k4_finseq_2 2 A)) <=>  (? [C:$i] :  (? [D:$i] :  ((r2_hidden C A) &  ((r2_hidden D A) &  (B = (k10_finseq_1 C D)) ) ) ) ) ) ) ) ).
tt(t137_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k3_card_3 (k11_finseq_1 A B C)) = (k2_xboole_0 (k2_xboole_0 A B) C))  &  ((k4_funct_6 (k11_finseq_1 A B C)) = (k3_xboole_0 (k3_xboole_0 A B) C)) ) ) ) ) ).
tt(t137_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  ( ((r1_tarski A B) &  ((r1_xboole_0 C A) & (r1_funct_7 D E C)) )  =>  ((k5_relat_1 D A) = (k5_relat_1 E A)) ) ) ) ) ) ) ) ) ).
tt(t137_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ( (C = D)  & (v3_glib_001 C A))  => (v3_glib_001 D B)) ) ) ) ) ) ) ) ) ).
tt(t137_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((k5_setfam_1 (u1_struct_0 A) (k15_group_2 A B)) = (u1_struct_0 A))  &  ((k5_setfam_1 (u1_struct_0 A) (k16_group_2 A B)) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t137_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=>  ((k11_group_3 A B) = A) ) ) ) ) ) ).
tt(t137_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  & (r1_xxreal_0 k6_numbers (k17_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t137_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k18_euclid A) = G)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k17_euclid A) F) &  ( (~ (r1_xxreal_0 (k17_euclid A) (k17_euclid B)))  &  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid C)))  &  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  &  ( (~ (r1_xxreal_0 (k17_euclid D) E))  &  ((r1_topreal1 (k15_euclid 2) A C I) &  ((r1_topreal1 (k15_euclid 2) B D J) &  ((r1_tarski I (k2_jgraph_6 E F G H)) &  ((r1_tarski J (k2_jgraph_6 E F G H)) & (r1_xboole_0 I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t137_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k16_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k16_member_1 A C) (k16_member_1 B C))) ) ) ) ) ) ) ).
tt(t137_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (~ (r2_hidden k1_xboole_0 (k10_xtuple_0 B))) ) ) ) ).
tt(t137_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k9_rvsum_1 A B C) (k9_rvsum_1 A D E)) = (k9_binop_2 (k10_binop_2 (k10_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t137_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v5_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ).
tt(t137_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D) (k5_sheffer1 A (k5_sheffer1 A C C) D)) (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A F C)) (k5_sheffer1 A D (k5_sheffer1 A F C)))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A B (k5_sheffer1 A B B))) (k5_sheffer1 A D (k5_sheffer1 A F C))) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A F C) (k5_sheffer1 A F C)) (k5_sheffer1 A D (k5_sheffer1 A F C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t137_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  ((r1_tsep_1 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) (k1_tsep_1 A C D) B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t137_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A (k9_xboolean A B)) = k2_xboolean) ) ) ) ) ).
tt(t137_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k2_xcmplx_0 A (k2_xcmplx_0 B (k4_xcmplx_0 B)))) ) ) ) ) ).
tt(t137_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(t137_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A B) (k1_tarski B)) = (k4_xxreal_1 A B)) ) ) ) ) ) ).
tt(t137_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((r2_hidden B (k3_zf_lang1 A)) =>  ( (~  (B = k6_numbers) )  &  ( (~  (B = 1) )  &  ( (~  (B = 2) )  &  ( (~  (B = 3) )  &  (~  (B = 4) ) ) ) ) ) ) ) ) ) ).
tt(t137_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_xboole_0 C (k1_tarski A)) B) <=>  ((r2_hidden A B) & (r1_tarski C B)) ) ) ) ) ).
tt(t137_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_zmodul01 A B C) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D C B))) ) ) ) ) ) ) ) ) ) ).
tt(t138_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)) => (r2_relset_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k55_abcmiz_1 A (k54_abcmiz_1 A B)) (k6_partfun1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))) ) ) ) ).
tt(t138_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k10_finseq_1 B C) (k4_finseq_2 2 A)) =>  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) ).
tt(t138_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ( ((k5_funct_6 (k9_finseq_1 B) 1 A) = (k1_funct_1 B A))  &  ( ((k5_funct_6 (k10_finseq_1 B C) 1 A) = (k1_funct_1 B A))  &  ((k5_funct_6 (k11_finseq_1 B C D) 1 A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski A B) =>  ((r2_hidden C (k9_xtuple_0 A)) | (r1_tarski A (k2_funct_7 B C D))) ) ) ) ) ) ) ) ).
tt(t138_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=>  (! [C:$i] :  ( ((v1_abian C) & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_abian D) & (m1_subset_1 D k5_numbers))  =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k15_group_2 A (k6_group_2 A)) = (a_1_0_group_2 A)) ) ) ).
tt(t138_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k11_group_3 A (k6_group_2 A)) = A) ) ) ).
tt(t138_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  (~ (r1_xxreal_0 k6_numbers (k17_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xxreal_0 C) => (r1_tarski (k6_subset_1 (k16_member_1 A C) (k16_member_1 B C)) (k16_member_1 (k6_subset_1 A B) C))) ) ) ) ) ) ).
tt(t138_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k10_xtuple_0 B)) =>  (? [D:$i] :  ((r2_hidden D A) &  (C = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ).
tt(t138_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((k8_relat_1 B A) = k1_xboole_0)  <=> (r1_xboole_0 (k10_xtuple_0 B) A)) ) ) ) ).
tt(t138_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k5_rvsum_1 A B C) (k5_rvsum_1 A B C)) = (k9_binop_2 (k9_binop_2 (k23_rvsum_1 B B) (k11_binop_2 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t138_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v5_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( (~  (B = C) )  &  ((k1_seq_1 A B) = (k1_seq_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C) (k5_sheffer1 A (k5_sheffer1 A B B) C)) (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A E B)) (k5_sheffer1 A C (k5_sheffer1 A E B)))) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E B) (k5_sheffer1 A E B)) (k5_sheffer1 A C (k5_sheffer1 A E B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r3_tsep_1 A B C) <=>  ((r1_tsep_1 B C) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 D)) &  ((v5_pre_topc E B D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v5_pre_topc F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) )  =>  ((v1_funct_1 (k10_tmap_1 A D B C E F)) &  ((v1_funct_2 (k10_tmap_1 A D B C E F) (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D)) &  ((v5_pre_topc (k10_tmap_1 A D B C E F) (k1_tsep_1 A B C) D) & (m1_subset_1 (k10_tmap_1 A D B C E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k4_xboolean A (k3_xboolean A)) = k1_xboolean) ) ) ).
tt(t138_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) A) B)) ) ) ) ) ).
tt(t138_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(t138_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~  ((k3_xboole_0 (k3_xxreal_1 A B) (k2_xxreal_1 B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t138_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k4_zf_lang A B)) = (k2_tarski A B)) ) ) ) ) ).
tt(t138_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r1_tarski A B) &  ((r1_tarski B (k2_xboole_0 A (k1_tarski C))) &  ( (~  ((k2_xboole_0 A (k1_tarski C)) = B) )  &  (~  (A = B) ) ) ) ) ) ) ) ) ).
tt(t138_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ( ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) = D)  &  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) )  =>  (E = (k9_zmodul01 A D B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t139_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ( ((v1_xboole_0 C) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) )  =>  ((k56_abcmiz_1 A C B) = B) ) ) ) ) ) ) ).
tt(t139_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k4_finseq_2 3 A)) <=>  (? [C:$i] :  (? [D:$i] :  (? [E:$i] :  ((r2_hidden C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  (B = (k11_finseq_1 C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t139_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ( ((k5_funct_6 (k10_finseq_1 C B) 2 A) = (k1_funct_1 B A))  &  ((k5_funct_6 (k11_finseq_1 C B D) 2 A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t139_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  (! [F:$i] :  ((k1_funct_4 B (k4_funct_4 C D E F)) = (k2_funct_7 (k2_funct_7 B C E) D F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t139_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((r1_xxreal_0 (k3_finseq_1 B) 3) => (v4_glib_001 B A)) ) ) ) ) ).
tt(t139_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k16_group_2 A (k6_group_2 A)) = (a_1_0_group_2 A)) ) ) ).
tt(t139_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k11_group_3 A (k7_group_2 A)) = A) ) ) ).
tt(t139_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))) & (r1_xxreal_0 A (k13_complex1 (k17_euclid C) (k12_euclid C))))  =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  ((r1_xxreal_0 k6_numbers (k18_euclid C)) |  ((r1_xxreal_0 (k13_complex1 (k17_euclid C) (k12_euclid C)) (k13_complex1 (k17_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k17_euclid E) (k12_euclid E)) (k13_complex1 (k17_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t139_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k16_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k16_member_1 A C) (k16_member_1 B C))) ) ) ) ) ) ) ).
tt(t139_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((r2_hidden C A) => (m1_subset_1 (k1_funct_1 B C) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t139_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ( (~  (A = k1_xboole_0) )  &  ((r1_tarski A (k10_xtuple_0 B)) &  ((k8_relat_1 B A) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t139_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k23_rvsum_1 (k9_rvsum_1 A B C) (k9_rvsum_1 A B C)) = (k9_binop_2 (k10_binop_2 (k23_rvsum_1 B B) (k11_binop_2 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t139_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v5_valued_0 A) & (r2_relset_1 k5_numbers k1_numbers B (k2_partfun1 k5_numbers k1_numbers A (k2_finseq_1 C))))  => (v5_valued_0 B)) ) ) ) ) ) ) ).
tt(t139_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C) (k5_sheffer1 A (k5_sheffer1 A B B) C)) (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A E B)) (k5_sheffer1 A C (k5_sheffer1 A E B)))) = (k5_sheffer1 A C (k5_sheffer1 A E B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t139_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (A = (k1_tsep_1 A C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ( ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) C (k10_tmap_1 A B C D E F)) E) &  ((r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) D (k10_tmap_1 A B C D E F)) F) & (r4_tsep_1 A C D)) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) A B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t139_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k4_xboolean A A) = k1_xboolean)  =>  (A = k1_xboolean) ) ) ) ).
tt(t139_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k2_xcmplx_0 A B)) = (k2_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t139_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t139_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k3_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 C D)) = (k2_xxreal_1 (k4_xxreal_0 A C) (k3_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t139_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k5_zf_lang A B)) = (k2_tarski A B)) ) ) ) ) ).
tt(t139_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C))) = D) ) ) ) ) ) ) ) ) ).
tt(t13_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r2_hidden C (k2_abcmiz_0 A B)) <=> (r2_hidden B (k3_abcmiz_0 A C))) ) ) ) ) ) ) ).
tt(t13_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ((k1_abcmiz_1 (k3_xboole_0 (k1_abcmiz_1 A) (k1_abcmiz_1 B))) = (k3_xboole_0 (k1_abcmiz_1 A) (k1_abcmiz_1 B))) ) ) ).
tt(t13_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ( ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k9_abcmiz_1)  => (m1_abcmiz_1 B A (k12_abcmiz_1 A)))  &  ( ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k10_abcmiz_1)  => (m1_abcmiz_1 B A (k13_abcmiz_1 A))) ) ) ) ) ) ).
tt(t13_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k13_complex1 (k18_complex1 (k2_xcmplx_0 A B)) (k7_real_1 1 (k18_complex1 (k2_xcmplx_0 A B)))) (k8_complex1 (k13_complex1 (k18_complex1 A) (k7_real_1 1 (k18_complex1 A))) (k13_complex1 (k18_complex1 B) (k7_real_1 1 (k18_complex1 B)))))) ) ) ) ).
tt(t13_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_aff_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v8_aff_2 A) => (v12_aff_2 A)) ) ) ).
tt(t13_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_aff_1 B A))  =>  ((k1_aff_4 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t13_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_relat_1 (k7_funcop_1 A B)) &  ((v5_ordinal1 (k7_funcop_1 A B)) &  ((v1_funct_1 (k7_funcop_1 A B)) & (v1_finset_1 (k7_funcop_1 A B))) ) ) ) ) ) ).
tt(t13_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((k1_ordinal4 (k5_relat_1 B A) (k2_afinsq_2 B A)) = B) ) ) ) ) ).
tt(t13_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) & (v1_aff_4 C A))  =>  ( ((k6_afproj A B) = (k6_afproj A C))  <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ).
tt(t13_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  &  (~ (r1_afvect0 A B C)) ) ) ) ) ) ) ) ).
tt(t13_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r5_alg_1 A B) => (r5_alg_1 B A)) ) ) ) ) ).
tt(t13_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ( (~  ((u1_struct_0 A) = (k1_tarski (k4_struct_0 A))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  &  ((k1_algseq_1 A C) = B) ) ) ) ) ) ) ) ).
tt(t13_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski B (k6_partfun1 A)) => (r6_pboole A (k1_algspec1 A B) (k6_partfun1 A))) ) ) ) ).
tt(t13_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v21_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_algstr_1 A) & (l4_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k9_algstr_0 A B) B) = (k5_struct_0 A))  &  ((k6_algstr_0 A B (k9_algstr_0 A B)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t13_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v1_group_6 C B A) & (v1_group_6 D B A))  =>  ((v2_algstr_4 (a_4_0_algstr_4 A B C D) B) & (m1_subset_1 (a_4_0_algstr_4 A B C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_altcat_1,ax, (! [A:$i] : (r8_pboole (k2_zfmisc_1 (k1_tarski (k4_relat_1 A)) (k1_tarski (k4_relat_1 A))) (k6_altcat_1 (k1_tarski (k4_relat_1 A)) (k1_tarski (k4_relat_1 A))) (k17_funcop_1 (k4_relat_1 A) (k4_relat_1 A) (k4_relat_1 A)))) ).
tt(t13_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((k1_binop_1 (k4_altcat_1 (u1_struct_0 A) (k2_altcat_2 A) (k3_altcat_2 A) B C D) F E) = (k5_cat_1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_altcat_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_altcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_altcat_1 A))) =>  ( (~  ((k1_altcat_1 (k7_altcat_1 A) B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 (k7_altcat_1 A) B C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( (E = D)  =>  ((v4_altcat_3 D (k7_altcat_1 A) B C) <=> (v2_funct_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k8_functor0 A B C D D (k8_altcat_1 A D)) = (k8_altcat_1 B (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t13_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 (k6_ami_2 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ).
tt(t13_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  ((k4_struct_0 k1_ami_3) = (k10_ami_3 A)) )  &  (~  ((k4_struct_0 k1_ami_3) = A) ) ) ) ) ).
tt(t13_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 6)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  (A = (k7_ami_3 B)) ) ) ) ) ) ) ) ).
tt(t13_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_ami_3) (k2_compos_0 (u1_compos_1 k1_ami_3) (k8_ami_3 B A)))) 1) = k5_numbers) ) ) ) ) ).
tt(t13_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (~  ( (~ (v1_xboole_0 (k2_amistd_1 A B C)))  & (v4_amistd_1 C A B)) ) ) ) ) ) ) ) ).
tt(t13_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v1_xboole_0 (k5_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t13_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) &  ((v5_amistd_5 B A) &  ((v6_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) &  ((v4_extpro_1 D A B C) & (v5_extpro_1 D A B C)) ) ) ) ) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k6_memstr_0 A B (k7_extpro_1 A B C D)) = (k6_memstr_0 A B (k7_extpro_1 A B (k6_compos_1 B C E) (k9_memstr_0 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v2_ami_wstd C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_nat_1 (k3_ami_wstd B C D) A) = (k3_ami_wstd B C (k4_ami_wstd B C D A))) ) ) ) ) ) ) ) ) ).
tt(t13_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ( (~  (D = (k4_struct_0 A)) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~ (r2_analmetr A (k5_algstr_0 A E (k1_rlvect_1 A D F)) D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analoaf A B C C D) => (r1_analoaf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(t13_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((k2_analort A B C D) = (k2_analort A B C E)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = (k4_struct_0 A))  => (r1_anproj_1 A B C)) ) ) ) ) ) ) ).
tt(t13_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ( (A = (k8_domain_1 A E F G))  &  ( ((k3_funct_2 A k1_numbers B E) = 1)  &  ( (! [H:$i] :  ((r2_hidden H A) =>  ( (H = E)  |  ((k1_funct_1 B H) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers C F) = 1)  &  ( (! [H:$i] :  ((r2_hidden H A) =>  ( (H = F)  |  ((k1_funct_1 C H) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers D G) = 1)  &  (! [H:$i] :  ((r2_hidden H A) =>  ( (H = G)  |  ((k1_funct_1 D H) = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (E = F)  |  ( (E = G)  |  ( (F = G)  |  (! [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) & (r2_funct_2 A k1_numbers H (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I B)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J C))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B k5_numbers))  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  &  ( ((u1_struct_0 C) = A)  &  ((k1_unialg_1 C) = B) ) ) ) ) ) ) ) ).
tt(t13_aofa_i00,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_power (k3_power A B) C) = (k3_power A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t13_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r3_armstrng A (k6_armstrng A B C) (k6_armstrng A D E)) <=>  ((r1_tarski B D) & (r1_tarski E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k2_arrow A) (k3_arrow A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_arrow A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ( (~ (r1_arrow B E D))  & (r1_arrow C E D)) ) ) ) ) )  <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (~  ( (~ (r1_arrow B E D))  & (r1_arrow C E D)) )  &  (~  ( (~ (r1_arrow C E D))  & (r1_arrow B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_arytm_0 A (k2_arytm_0 B C)) = (k2_arytm_0 (k2_arytm_0 A B) C)) ) ) ) ) ) ) ).
tt(t13_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k7_arytm_2 C (k1_arytm_1 B A)) = (k1_arytm_1 (k7_arytm_2 C B) A)) ) ) ) ) ) ) ) ).
tt(t13_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((k8_arytm_2 A (k7_arytm_2 B C)) = (k7_arytm_2 (k8_arytm_2 A B) (k8_arytm_2 A C))) ) ) ) ) ) ) ).
tt(t13_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( (~  (A = k1_xboole_0) )  => (r2_arytm_3 (k6_ordinal3 (k9_ordinal3 B A) (k2_arytm_3 B A)) B)) ) ) ) ) ).
tt(t13_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v2_xxreal_0 B) & (m1_subset_1 B k1_numbers))  =>  ((k6_asympt_0 A) = (k6_asympt_0 (k2_asympt_0 A B))) ) ) ) ) ).
tt(t13_asympt_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((r2_funct_2 k5_numbers k1_numbers A (k1_asympt_1 2 1 1)) & (r2_hidden (k1_asympt_1 2 1 k6_numbers) (k8_asympt_0 A))) ) ) ).
tt(t13_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ( ((v1_msualg_3 D) & (v2_msualg_3 D A B C))  => (r6_pboole A (k4_msualg_3 A C B (k4_msualg_3 A B C D)) D)) ) ) ) ) ) ) ) ).
tt(t13_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r1_tarski (k4_autgroup A) (k1_autgroup A))) ) ).
tt(t13_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((k3_bagorder A (k11_pre_poly A B C)) = (k2_xcmplx_0 (k3_bagorder A B) (k3_bagorder A C))) ) ) ) ) ) ) ).
tt(t13_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) D) = (k1_bcialg_1 B C D)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t13_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_bcialg_2 A (k4_struct_0 A) B (k2_nat_1 C D)) = (k1_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B C) (k2_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B D)))) ) ) ) ) ) ) ) ) ).
tt(t13_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  ((v4_bcialg_3 A) & (v5_bcialg_3 A)) ) ) ) ).
tt(t13_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A C (k1_bcialg_4 A B (k1_bcialg_1 A C B)))) ) ) ) ) ) ).
tt(t13_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((m1_bcialg_5 A B C D E) <=> (m1_bcialg_5 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) => (r2_hidden (k3_bcialg_6 A C B) (k5_bcialg_1 A))) ) ) ) ) ) ).
tt(t13_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v14_bcialg_1 A) => (v12_bcialg_1 B A)) ) ) ) ) ).
tt(t13_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) = (k7_real_1 (k9_real_1 (k9_real_1 (k2_bhsp_1 A B D) (k2_bhsp_1 A B E)) (k2_bhsp_1 A C D)) (k2_bhsp_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (v1_bhsp_2 C A))  =>  ((k1_bhsp_2 A (k2_normsp_1 A B C)) = (k3_rlvect_1 A (k1_bhsp_2 A B) (k1_bhsp_2 A C))) ) ) ) ) ) ) ) ).
tt(t13_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r2_bhsp_3 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k3_bhsp_1 A (k5_algstr_0 A (k1_normsp_1 A B F) (k1_normsp_1 A C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_bhsp_4 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t13_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m2_bhsp_5 C A))  =>  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski C (k9_xtuple_0 D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = (k5_square_1 (k2_bhsp_1 A B E))) ) ) ) )  => (r1_xxreal_0 (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 C D) (k5_square_1 (k3_bhsp_1 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k2_bilinear A B C D E) F) (k3_hahnban1 A C (k7_bilinear A B C D F) (k7_bilinear A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ((k6_binarith A (k3_binarith A B)) = (k21_binop_2 (k20_binop_2 (k19_binop_2 (k6_binarith A B)) (k5_series_1 2 A)) 1)) ) ) ) ) ).
tt(t13_binari_3,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k8_binarith 1 (k10_binarith k6_margrel1 A) (k10_binarith k6_margrel1 B)) = k8_margrel1)  <=>  ( (A = k8_margrel1)  &  (B = k8_margrel1) ) ) ) ) ) ) ).
tt(t13_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k23_binop_2 B C) (k21_binop_2 (k5_series_1 2 (k7_nat_d A 1)) 1)) =>  ((k7_partfun1 k6_margrel1 (k4_binarith A (k1_binari_3 A B) (k1_binari_3 A C)) A) = k7_margrel1) ) ) ) ) ) ) ) ).
tt(t13_binarith,ax, ((k2_binarith k8_margrel1 k7_margrel1) = k8_margrel1) ).
tt(t13_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_binom A B 1) = B) ) ) ) ) ).
tt(t13_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 C A) =>  ((r6_binop_1 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_binop_1 A C (k3_binop_1 A B D E) F) = (k3_binop_1 A B (k3_binop_1 A C D F) (k3_binop_1 A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  ((k1_funct_1 (k1_bintree2 A B) (k5_euclid B)) = 1) ) ) ) ) ).
tt(t13_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_boolealg A B C) & (r3_lattices A C D))  => (r3_boolealg A B D)) ) ) ) ) ) ) ) ) ).
tt(t13_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v2_comseq_2 (k3_series_1 (k8_prob_1 A B D C))) =>  ( ((k3_funct_2 B k1_numbers C (k8_bor_cant A B D)) = k6_numbers)  &  ( ((k2_seq_2 (k11_bor_cant A B C D)) = k6_numbers)  & (v2_comseq_2 (k11_bor_cant A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((v3_pre_topc C (k2_borsuk_1 A B)) =>  (C = (k5_setfam_1 (u1_struct_0 (k2_borsuk_1 A B)) (k7_borsuk_1 A B C))) ) ) ) ) ) ) ) ).
tt(t13_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc E k5_topmetr A) &  ( (B = (k1_funct_1 E k6_numbers))  &  ( (C = (k1_funct_1 E 1))  &  ((v5_pre_topc F k5_topmetr A) &  ( (C = (k1_funct_1 F k6_numbers))  &  ( (D = (k1_funct_1 F 1))  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc G k5_topmetr A) &  ( (B = (k1_funct_1 G k6_numbers))  &  ( (D = (k1_funct_1 G 1))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) G) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_borsuk_3 (k2_borsuk_1 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) B) B)) ) ) ) ) ) ).
tt(t13_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_rcomp_1 B C))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k5_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t13_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_metric_1)) =>  ((r2_hidden B (k2_pre_topc k3_topmetr A)) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xboole_0 (k9_metric_1 k8_metric_1 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t13_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_6_borsuk_6)  &  (B = a_0_7_borsuk_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 1 k6_numbers (k10_real_1 1 2) (k1_real_1 (k10_real_1 1 2))) A) = B) ) ) ) ) ) ).
tt(t13_borsuk_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k3_finseq_1 (k30_valued_1 A)) = (k3_finseq_1 A)) ) ) ).
tt(t13_brouwer,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A))) &  ((v5_pre_topc C (k2_brouwer 2 B A) (k2_brouwer 2 B A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A)))))) ) )  =>  ( (~ (v2_abian C))  => (v5_pre_topc (k5_brouwer 2 A B C) (k2_brouwer 2 B A) (k7_toprealb 2 B A))) ) ) ) ) ) ) ).
tt(t13_bspace,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k3_bspace A C) = (k3_bspace B C))  <=>  ((r2_hidden C A) <=> (r2_hidden C B)) ) ) ) ) ).
tt(t13_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k5_bvfunc_1 A (k5_bvfunc_1 A E F) G)) (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A E) (k1_bvfunc_1 A F)) D) (k5_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ( (~  (A = B) )  &  ( (~  (C = A) )  &  (~  ((k1_funct_1 (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F)) A) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k5_bvfunc_1 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t13_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B B) (k11_bvfunc_1 A))) ) ) ) ).
tt(t13_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc26 A C D)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k2_bvfunc_1 A C D))) & (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc26 A C D)) (k9_bvfunc_1 A B (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k5_bvfunc_1 A (k6_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)) (k6_bvfunc_2 A (k5_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A B D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A (k2_bvfunc_1 A B C) D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t13_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k12_bvfunc_1 A) B) B)) ) ) ) ).
tt(t13_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B C) (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))))) ) ) ) ) ) ).
tt(t13_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k5_bvfunc_1 A B D))) ) ) ) ) ) ) ) ).
tt(t13_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_c0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_c0sp1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ( (E = C)  &  (F = D) )  =>  ( (D = (k1_rlvect_1 (k7_c0sp1 A) C B))  <=>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k1_seq_1 F G) = (k8_real_1 B (k1_seq_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k5_c0sp2 A) B))) ) ) ) ).
tt(t13_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  => (r2_calcul_1 A B (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B) C) (k12_finseq_1 (k3_cqc_lang A) (k2_calcul_1 A B))))) ) ) ) ) ) ) ).
tt(t13_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r2_hidden B (k1_relset_1 k5_numbers (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 C) (k3_finseq_1 D))))) =>  ((k1_funct_1 (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 C) (k3_finseq_1 D))) B) = (k2_nat_1 (k3_finseq_1 C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C (k2_cantor_1 A B)) & (r1_tarski D (k2_cantor_1 A B)))  => (r1_tarski (k3_setfam_1 C D) (k2_cantor_1 A B))) ) ) ) ) ) ).
tt(t13_card_1,ax, (! [A:$i] :  (~ (r2_wellord2 A (k1_zfmisc_1 A))) ) ).
tt(t13_card_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k1_card_1 (k10_ordinal2 A B)) = (k1_card_2 (k1_card_1 A) (k1_card_1 B))) ) ) ) ) ).
tt(t13_card_3,ax, (! [A:$i] :  ((k5_card_3 A k1_xboole_0) = k1_xboole_0) ) ).
tt(t13_card_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v4_card_3 A) => (v4_card_3 (k3_finseq_2 A))) ) ) ).
tt(t13_card_5,ax, (! [A:$i] :  (! [B:$i] :  ((v1_card_1 B) =>  ( (~  (A = k1_xboole_0) )  => (r1_ordinal1 (k1_card_1 (a_2_0_card_5 A B)) (k2_card_2 B (k3_card_2 (k1_card_1 A) B)))) ) ) ) ).
tt(t13_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_card_fil C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D (k2_card_fil A C B)) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((r2_hidden E C) & (r1_tarski (k9_subset_1 A E B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_cardfin2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k22_binop_2 B (k7_afinsq_2 A)) = (k20_binop_2 (k7_afinsq_2 (k5_relat_1 (k24_valued_1 A B) (k7_nat_d (k1_afinsq_1 A) 1))) (k22_binop_2 B (k1_funct_1 A (k7_nat_d (k1_afinsq_1 A) 1))))) ) ) ) ) ).
tt(t13_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r2_hidden A D))  =>  ((k5_card_1 (k1_card_fin D E B C)) = (k1_card_1 (a_5_0_card_fin A B C D E))) ) ) ) ) ) ) ) ) ).
tt(t13_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((v3_card_lar B A) & (r1_tarski B C))  => (v3_card_lar C A)) ) ) ) ) ) ) ).
tt(t13_cat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cat_1 A B))) =>  (~  ((k2_cat_1 (k3_cat_1 A B) C D) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t13_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) => (m2_cat_1 (k10_cat_1 B) B A)) ) ) ) ).
tt(t13_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  => (r2_funct_2 A (u4_struct_0 B) (k5_cat_3 B A (k4_cat_3 B A C)) C)) ) ) ) ) ).
tt(t13_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k2_cat_1 A B (k1_cat_4 A)) = k1_xboole_0) ) ) ) ) ) ).
tt(t13_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_graph_1 A B) = (k1_cat_5 A B))  &  ((k4_graph_1 A B) = (k2_cat_5 A B)) ) ) ) ) ) ).
tt(t13_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_int_1 (k1_catalan1 A))) ) ).
tt(t13_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ((v1_catalan2 C) &  ( ((k24_binop_2 2 (k7_afinsq_2 (k5_relat_1 C A))) = A)  &  (A = (k23_binop_2 B 1)) ) )  =>  ((k5_relat_1 C A) = (k1_catalan2 (k5_relat_1 C B) (k8_funcop_1 k5_numbers 1 1))) ) ) ) ) ) ) ) ).
tt(t13_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k7_catalg_1 A C E) = (k7_catalg_1 B D F))  =>  ( (A = B)  &  ( (C = D)  &  (E = F) ) ) ) ) ) ) ) ) ) ).
tt(t13_cayley,ax, (! [A:$i] :  (! [B:$i] :  ((r2_tarski A B) => (r2_group_6 (k2_cayley A) (k2_cayley B))) ) ) ).
tt(t13_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k2_numbers B A)) =>  ((k1_seq_1 (k6_cc0sp1 A) B) = (k4_seq_4 (k5_cc0sp1 A B))) ) ) ) ) ) ).
tt(t13_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_struct_0 (k3_cc0sp2 A)) = (k1_cc0sp2 A k5_complex1)) ) ) ).
tt(t13_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r1_tarski (k2_relset_1 k2_numbers A) (k1_relset_1 k2_numbers B)) => (r2_relset_1 k5_numbers k1_numbers (k8_comseq_3 (k9_comseq_3 C (k8_funct_2 k5_numbers k2_numbers k2_numbers A B))) (k8_comseq_3 (k8_funct_2 k5_numbers k2_numbers k2_numbers (k9_comseq_3 C A) B)))) ) ) ) ) ) ) ).
tt(t13_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (a_2_2_cfdiff_1 B C))  => (v6_cfdiff_1 A)) ) ) ) ) ) ) ).
tt(t13_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k1_funct_1 (k3_cfuncdom A) (k4_tarski C (k1_funct_1 (k3_cfuncdom A) (k4_tarski D B)))) = (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) (k5_binop_2 C D) B))) ) ) ) ) ) ) ) ) ).
tt(t13_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C) D) (k2_valued_1 A k2_numbers k2_numbers B (k2_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t13_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden (k9_cgames_1 B) A) <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ((r2_hidden C A) & (r2_hidden B (k2_cgames_1 C))) ) ) ) ) ) ) ) ).
tt(t13_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 D B))  &  (~ (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_abian A))  =>  (~  ((r1_xxreal_0 A 7) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 2) )  &  ( (~  (A = 4) )  &  (~  (A = 6) ) ) ) ) ) ) ) ) ).
tt(t13_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( (H = (k5_relat_1 G (u1_struct_0 A)))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((k5_relat_1 (k5_facirc_1 C F G I) (u1_struct_0 A)) = (k5_facirc_1 A D H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k10_xtuple_0 (k7_finseq_4 A B C D)) = (k2_enumset1 A B C D)) ) ) ) ) ).
tt(t13_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_circcomb A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_msafree2 (k2_circcomb A B))) => (r2_hidden C (k2_msafree2 A))) ) ) ) ) ) ) ) ).
tt(t13_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_circled1 A B) = B) ) ) ) ) ).
tt(t13_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m3_msaterm D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k1_circtrm1 A B D))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k1_funct_1 E k1_xboole_0) = (k4_tarski F (u1_struct_0 A)))  =>  ((k3_relat_1 (k1_msualg_1 (k1_circtrm1 A B D) E) (k4_circtrm1 A B D C)) = (k3_relat_1 (k1_msualg_1 A F) (u3_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (~  ((r2_hidden C (k7_subset_1 (u1_struct_0 A) (k3_msafree2 A) (k1_msafree2 A))) &  ( ((k5_card_1 D) = (k4_circuit1 A B C))  &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (~  ((k1_funct_1 D k1_xboole_0) = (k4_tarski E (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_xxreal_0 (k6_circuit1 A B F) E) =>  ((k1_funct_1 C F) = (k5_circuit2 A B F D)) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_xxreal_0 (k6_circuit1 A B F) (k2_nat_1 E 1)) =>  ((k1_funct_1 (k6_circuit2 A B C) F) = (k5_circuit2 A B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ((v4_ordinal1 C) =>  ( (C = k1_xboole_0)  |  ((r2_hidden B (k3_classes1 A C)) <=>  (? [D:$i] :  ((v3_ordinal1 D) &  ((r2_hidden D C) & (r2_hidden B (k3_classes1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_classes1 A) & (r2_hidden B (k1_card_1 A)))  => (r2_hidden B A)) ) ) ).
tt(t13_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  => (v6_clvect_1 (k5_clopban1 A B) (k3_clopban1 (u1_struct_0 A) B))) ) ) ) ).
tt(t13_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_clopban2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_clopban2 A))) =>  ( ((k1_algstr_0 (k7_clopban2 A) B C) = (k1_algstr_0 (k7_clopban2 A) C B))  &  ( ((k1_algstr_0 (k7_clopban2 A) (k1_algstr_0 (k7_clopban2 A) B C) D) = (k1_algstr_0 (k7_clopban2 A) B (k1_algstr_0 (k7_clopban2 A) C D)))  &  ( ((k1_algstr_0 (k7_clopban2 A) B (k4_struct_0 (k7_clopban2 A))) = B)  &  ((v10_algstr_0 B (k7_clopban2 A)) &  ( ((k6_algstr_0 (k7_clopban2 A) (k6_algstr_0 (k7_clopban2 A) B C) D) = (k6_algstr_0 (k7_clopban2 A) B (k6_algstr_0 (k7_clopban2 A) C D)))  &  ( ((k6_algstr_0 (k7_clopban2 A) B (k5_struct_0 (k7_clopban2 A))) = B)  &  ( ((k6_algstr_0 (k7_clopban2 A) (k5_struct_0 (k7_clopban2 A)) B) = B)  &  ( ((k6_algstr_0 (k7_clopban2 A) B (k1_algstr_0 (k7_clopban2 A) C D)) = (k1_algstr_0 (k7_clopban2 A) (k6_algstr_0 (k7_clopban2 A) B C) (k6_algstr_0 (k7_clopban2 A) B D)))  &  ((k6_algstr_0 (k7_clopban2 A) (k1_algstr_0 (k7_clopban2 A) C D) B) = (k1_algstr_0 (k7_clopban2 A) (k6_algstr_0 (k7_clopban2 A) C B) (k6_algstr_0 (k7_clopban2 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) )  => (v2_clopban3 B A)) ) ) ) ) ).
tt(t13_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k1_normsp_1 A (k1_clopban4 A B) (k2_nat_1 C 1)) = (k6_algstr_0 A (k1_clvect_1 A B (k13_complex1 k6_complex1 (k2_nat_1 C 1))) (k1_normsp_1 A (k1_clopban4 A B) C)))  &  ( ((k1_normsp_1 A (k1_clopban4 A B) k6_numbers) = (k5_struct_0 A))  & (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A (k1_clopban4 A B) C)) (k1_seq_1 (k4_sin_cos (k1_normsp_0 A B)) C))) ) ) ) ) ) ) ) ).
tt(t13_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v2_closure1 (k2_msualg_3 A (k5_mssubfam A B)) A B) & (m2_pboole (k2_msualg_3 A (k5_mssubfam A B)) A (k5_mssubfam A B) (k5_mssubfam A B))) ) ) ) ).
tt(t13_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))))  =>  ((k9_xtuple_0 (k3_closure2 C)) = A) ) ) ) ) ) ).
tt(t13_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( (! [D:$i] :  ((r2_hidden D C) => (m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_closure2 A B))) =>  ( ( (E = (a_3_0_closure3 A B C))  &  (D = (k3_tarski C)) )  => (r6_pboole A (k2_closure3 A B E) (k2_closure3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  (F = (k1_funct_1 D E)) )  =>  ((k1_funct_1 C E) = (k1_clvect_1 A F B)) ) ) ) ) ) )  =>  ((k4_rlvect_1 A C) = (k1_clvect_1 A (k4_rlvect_1 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 B A) & (v1_clvect_2 C A))  =>  ((k1_clvect_2 A (k16_csspace A B C)) = (k3_rlvect_1 A (k1_clvect_2 A B) (k1_clvect_2 A C))) ) ) ) ) ) ) ) ).
tt(t13_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_clvect_3 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t13_cohsp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (~  ((v1_cohsp_1 A) &  ((r1_tarski B (k3_tarski A)) &  ((v1_finset_1 B) &  (! [C:$i] :  (~  ((r2_hidden C A) & (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ((k2_coh_sp (k3_tarski A) (k1_coh_sp A)) = A) ) ) ).
tt(t13_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = C)  =>  ((k1_collsp A B C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t13_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) | (v9_incproj (k1_combgras A B))) ) ) ) ) ) ).
tt(t13_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_xcmplx_0 (k3_complex1 A) (k3_xcmplx_0 (k4_complex1 A) k7_complex1)) = A) ) ) ).
tt(t13_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ( ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig A)))  =>  ((k1_comptrig (k4_xcmplx_0 A)) = (k7_real_1 (k1_comptrig A) k32_sin_cos)) )  &  ((r1_xxreal_0 k32_sin_cos (k1_comptrig A)) =>  ((k1_comptrig (k4_xcmplx_0 A)) = (k9_real_1 (k1_comptrig A) k32_sin_cos)) ) ) ) ) ) ).
tt(t13_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (A = (k3_rlvect_1 k1_complfld (k5_algstr_0 k1_complfld A B) B)) ) ) ) ) ).
tt(t13_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k9_matrix_5 (k11_seq_4 B) A) = (k1_binop_2 (k9_matrix_5 B A))) ) ) ) ) ).
tt(t13_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) C) B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((v2_prob_1 D) &  ( ((v3_finset_1 B) => (v2_relat_1 D))  &  ( ((v1_tops_2 B A) => (v4_compl_sp D A))  &  ( ((v2_tops_2 B A) => (v5_compl_sp D A))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) D E) = (k1_setfam_1 (a_3_1_compl_sp A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  ((k5_card_1 (k2_compos_2 A (k3_compos_2 A B C) D)) = 4) ) ) ) ) ) ) ) ) ).
tt(t13_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden A (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) & (r1_xxreal_0 k6_numbers (k1_seq_1 k19_sin_cos A))) ) ) ) ).
tt(t13_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v8_pre_topc A) & (v1_compts_1 A))  => (v10_pre_topc A)) ) ) ).
tt(t13_comput_1,ax, (! [A:$i] :  ( ((v4_funct_1 A) & (v1_comput_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B A) =>  ((r1_tarski (k9_xtuple_0 B) (k9_xtuple_0 (k3_tarski A))) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 (k3_tarski A) C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t13_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k19_valued_1 k5_numbers k2_numbers k2_numbers B (k25_valued_1 k5_numbers k2_numbers C A)))) ) ) ) ) ) ).
tt(t13_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((r1_xxreal_0 (k18_complex1 (k3_complex1 A)) (k17_complex1 A)) & (r1_xxreal_0 (k18_complex1 (k4_complex1 A)) (k17_complex1 A))) ) ) ).
tt(t13_conlat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_waybel_1 C A B) =>  ((v3_conlat_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (C = (k1_waybel_1 A B D E))  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) D E) D)) & (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) E (k1_partfun1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) E D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_conlat_1 A B C) <=> (r3_lattices (k11_conlat_1 A) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k4_conlat_2 A) B) (k3_funct_2 (u4_struct_0 A) (u1_struct_0 (k11_conlat_1 A)) (k5_conlat_2 A) C))) ) ) ) ) ) ) ).
tt(t13_conmetr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v3_conmetr1 (k3_analmetr A)) <=> (v6_conmetr A)) ) ) ).
tt(t13_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( ((v1_conmetr A) & (v1_conaffm A))  => (v2_conmetr A)) ) ) ).
tt(t13_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_connsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc B A) &  ((v4_pre_topc B A) &  ( (~  (B = (k1_struct_0 A)) )  &  (~  (B = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_connsp_2 A B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m1_connsp_2 C A B) &  ((r3_connsp_1 A C D) & (r2_hidden B D)) )  => (m1_connsp_2 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((v2_connsp_1 C A) & (r1_tarski B C)) )  =>  ( (B = k1_xboole_0)  | (r1_tarski C (k1_connsp_3 A B))) ) ) ) ) ) ) ) ).
tt(t13_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 k6_numbers D) & (v1_convex1 B A)) )  =>  ((k7_rusub_4 A (k1_convex1 A B C) (k1_convex1 A B D)) = (k1_convex1 A B (k7_real_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_convex2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_classes1 A B) =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) &  ((r2_hidden D (k9_xtuple_0 A)) &  ( (~  (C = D) )  &  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden E (k9_xtuple_0 B)) &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  (E = F) )  &  ( ((k1_funct_1 A C) = (k1_funct_1 B E))  &  ((k1_funct_1 A D) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_convex4 B A (k1_subset_1 (u1_struct_0 A))) =>  ((k4_convex4 A B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t13_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((m2_subset_1 (k15_qc_lang1 A B C) (k9_qc_lang1 A) (k3_cqc_lang A)) <=> (m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ) ).
tt(t13_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r2_hidden (k1_funct_1 C D) (k3_qc_lang1 A))) ) ) ) ) ) ) ) ) ).
tt(t13_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r2_hidden (k8_cqc_lang A C D) (k1_cqc_the1 A B)) =>  ((r2_hidden E (k24_qc_lang1 A C)) | (r2_hidden (k8_cqc_lang A C (k11_cqc_lang A E D)) (k1_cqc_the1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k13_cqc_lang A (k3_qc_lang2 A B C) D) = (k3_qc_lang2 A (k13_cqc_lang A B D) (k13_cqc_lang A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r2_cqc_the3 A B (k4_cqc_the1 A))) ) ) ) ).
tt(t13_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_3 A) &  ((k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)) = k6_numbers) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) ) ) ) ) ).
tt(t13_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((v1_csspace4 C A B) <=> (v4_xxreal_2 (k7_csspace4 A B C))) ) ) ) ) ) ) ).
tt(t13_csspace,ax,(m1_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace)) k7_csspace)).
tt(t13_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_decomp_1 A) (k17_decomp_1 A)) = (k6_decomp_1 A)) ) ) ).
tt(t13_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A B (k4_xcmplx_0 (k3_finseq_1 B))) = B) ) ) ) ) ) ).
tt(t13_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_relat_2 A) => (v8_relat_2 (k3_dickson A))) ) ) ).
tt(t13_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v3_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C B) (k2_nat_1 A 1)) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t13_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k1_numbers k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k1_numbers k1_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_diff_2 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers H A) (k26_valued_1 k1_numbers k1_numbers I B)) C D E F G) = (k7_real_1 (k8_real_1 A (k1_diff_2 H C D E F G)) (k8_real_1 B (k1_diff_2 I C D E F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers E B) F) C) (k2_nat_1 A 1)) D) = (k7_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E C) (k2_nat_1 A 1)) D)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 F C) (k2_nat_1 A 1)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k2_fdiff_9)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k2_fdiff_9)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_fdiff_9) B) A) = (k10_complex1 (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k8_real_1 2 A))) (k18_sin_cos B)) (k5_square_1 (k9_real_1 (k21_sin_cos (k8_real_1 2 A)) (k21_sin_cos B)))))) ) ) ) ) ) ).
tt(t13_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v2_dilworth (k7_domain_1 (u1_struct_0 A) B C) A) & (m1_subset_1 (k7_domain_1 (u1_struct_0 A) B C) (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (B = C)  |  ( (~ (r1_orders_2 A B C))  &  (~ (r1_orders_2 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_diraf A B C D) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_dirort D) & (l1_analoaf D)) )  =>  ( ((r1_analmetr A B C) &  (D = (k5_analort A B C)) )  =>  ((v5_dirort D) &  ((v4_dirort D) &  ((v3_dirort D) & (v2_dirort D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k2_finseq_1 (k5_card_1 A))) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( ((k1_funct_1 (k9_dist_1 A B) C) = (k2_dist_1 A B D))  &  (D = (k1_funct_1 (k1_uproots A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k4_zfmisc_1 B C D E)) =>  ( (A = (k4_mcart_1 B C D E F))  <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H C) =>  (! [I:$i] :  ((m1_subset_1 I D) =>  (! [J:$i] :  ((m1_subset_1 J E) =>  ( (F = (k5_domain_1 B C D E G H I J))  =>  (A = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_dtconstr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A (u1_struct_0 k5_dtconstr)) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) )  =>  ((r2_hidden A (k4_dtconstr k5_dtconstr)) =>  ((k15_dtconstr k5_dtconstr A) = (k3_pre_poly k5_numbers k6_numbers)) ) ) ) ).
tt(t13_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin D A) &  ((v2_finsub_1 D) &  ((r2_hidden B D) & (r2_hidden C D)) ) )  => (r2_hidden (k7_subset_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t13_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (? [C:$i] :  ((v7_ordinal1 C) &  (B = (k4_nat_d C A)) ) ) ) ) ) ) ).
tt(t13_ec_pf_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_binom B (k8_group_1 B (k8_group_1 B C D) E) A) = (k8_group_1 B (k8_group_1 B (k2_binom B C A) (k2_binom B D A)) (k2_binom B E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  ((v1_funct_1 (k6_partfun1 (u1_struct_0 A))) &  ((v1_funct_2 (k6_partfun1 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A)) &  ((v6_group_1 (k6_partfun1 (u1_struct_0 A)) A A) &  ((v1_group_6 (k6_partfun1 (u1_struct_0 A)) A A) & (m1_subset_1 (k6_partfun1 (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t13_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_ens_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ( ( ((k3_ens_1 A B) = (k4_ens_1 A C))  &  ((k3_ens_1 A D) = (k4_ens_1 A B)) )  =>  ((k6_ens_1 A (k6_ens_1 A C B) D) = (k6_ens_1 A C (k6_ens_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_entropy1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r1_entropy1 B A) =>  ((k18_rvsum_1 B) = (k1_seq_1 B A)) ) ) ) ) ) ).
tt(t13_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k1_enumset1 A B C) (k1_enumset1 D E F))) ) ) ) ) ) ) ).
tt(t13_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k5_eqrel_1 A (k5_eqrel_1 A B C) D) (k5_eqrel_1 A B (k5_eqrel_1 A C D)))) ) ) ) ) ) ) ).
tt(t13_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  => (r6_pboole A (k9_pboole A (k2_funct_6 B) B) (k3_funct_6 B))) ) ) ).
tt(t13_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k10_xtuple_0 (u1_e_siec A)) = (k10_xtuple_0 (k1_sysrel (u1_e_siec A))))  &  ( ((k10_xtuple_0 (u1_e_siec A)) = (k9_xtuple_0 (k1_sysrel (u1_e_siec A))))  &  ( ((k10_xtuple_0 (u2_e_siec A)) = (k10_xtuple_0 (k1_sysrel (u2_e_siec A))))  &  ( ((k10_xtuple_0 (u2_e_siec A)) = (k9_xtuple_0 (k1_sysrel (u2_e_siec A))))  &  ((k10_xtuple_0 (u1_e_siec A)) = (k10_xtuple_0 (u2_e_siec A))) ) ) ) ) ) ) ).
tt(t13_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k9_binop_2 (k5_square_1 (k12_euclid (k4_rvsum_1 A B))) (k5_square_1 (k12_euclid (k8_rvsum_1 A B)))) = (k11_binop_2 2 (k9_binop_2 (k5_square_1 (k12_euclid A)) (k5_square_1 (k12_euclid B))))) ) ) ) ) ) ).
tt(t13_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k2_euclid_3 (k4_algstr_0 (k15_euclid 2) A)) = (k10_complex1 (k2_euclid_3 A))) ) ) ).
tt(t13_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (~  ((v1_euclid_4 B A) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k5_algstr_0 (k15_euclid 3) (k4_euclid_5 A B C) (k4_euclid_5 D E F)) = (k4_euclid_5 (k9_real_1 A D) (k9_real_1 B E) (k9_real_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  ((k7_real_1 (k4_euclid_3 B A D) (k4_euclid_3 D A C)) = k32_sin_cos) )  &  (~  ((k7_real_1 (k4_euclid_3 B A D) (k4_euclid_3 D A C)) = (k8_real_1 3 k32_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_euclid_7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v2_funct_1 A) <=> (v2_funct_1 (k6_rfinseq2 A))) ) ) ).
tt(t13_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k23_rvsum_1 A (k1_euclid_8 k6_numbers k6_numbers k6_numbers)) = k6_numbers) ) ) ).
tt(t13_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ((r1_xxreal_0 B C) => (r1_tarski (k4_euclid_9 A D B) (k4_euclid_9 A D C))) ) ) ) ) ) ) ) ) ).
tt(t13_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k8_euclid A B C)) (k7_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t13_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  ((k9_euclid D E (k9_real_1 (k9_real_1 A B) C)) = (k8_euclid D (k8_euclid D (k9_euclid D E A) (k9_euclid D E B)) (k9_euclid D E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v6_euclmetr A) <=> (v8_conmetr A)) ) ) ).
tt(t13_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A (k3_xcmplx_0 B C)) & (r1_int_2 B A))  => (r1_nat_d A C)) ) ) ) ) ) ) ).
tt(t13_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ((k2_euler_2 (k2_euler_2 B A) A) = (k2_euler_2 B A)) ) ) ) ) ).
tt(t13_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_exchsort A (k3_ordinal2 (k9_xtuple_0 A)))) ) ).
tt(t13_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((v2_relat_1 B) =>  ((v1_msualg_3 D) <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  (! [F:$i] :  ((m2_pboole F A E B) =>  (! [G:$i] :  ((m2_pboole G A E B) =>  ( ((k8_pboole F D) = (k8_pboole G D))  => (r6_pboole A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  => (r2_extpro_1 A B C D k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(t13_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) => (r1_xxreal_0 (k3_extreal1 (k3_supinf_2 A B)) (k3_supinf_2 (k3_extreal1 A) (k3_extreal1 B)))) ) ) ) ).
tt(t13_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k5_facirc_1 A B C (k2_xcmplx_0 D E)) = (k5_facirc_1 A B (k5_facirc_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  => (r1_tarski (k3_msafree2 (k3_facirc_2 A C D)) (k3_msafree2 (k3_facirc_2 B C D)))) ) ) ) ) ) ) ) ) ).
tt(t13_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) A) &  ((v2_comseq_2 C) & (r2_hidden (k2_seq_2 C) A)) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C B)) &  ((k1_seq_1 B (k2_seq_2 C)) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C B))) ) ) ) ) ) ) ) ) ) ).
tt(t13_fcont_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski B (k1_relset_1 k1_numbers A)) &  ((v1_rcomp_1 B) &  ((v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers A B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( ((k1_seq_1 A C) = (k4_seq_4 (k7_relset_1 k1_numbers k1_numbers A B)))  &  ((k1_seq_1 A D) = (k5_seq_4 (k7_relset_1 k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((k7_relset_1 k1_numbers k1_numbers B A) = (k1_limfunc1 C)) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t13_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k30_sin_cos) A) B) = (k9_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k30_sin_cos B)) (k10_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t13_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k16_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k16_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k1_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t13_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 B A) & (r1_fdiff_1 C A))  =>  ((r1_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k7_real_1 (k1_fdiff_1 B A) (k1_fdiff_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 B A) & (r1_fdiff_1 C (k1_seq_1 B A)))  =>  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k8_real_1 (k1_fdiff_1 C (k1_seq_1 B A)) (k1_fdiff_1 B A))) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r4_fdiff_3 A C) & (r4_fdiff_3 B C))  =>  ( ((k1_seq_1 B C) = k6_numbers)  |  ((r4_fdiff_3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) &  ((k1_fdiff_3 C (k3_rfunct_1 k1_numbers k1_numbers A B)) = (k10_real_1 (k9_real_1 (k8_real_1 (k1_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k1_fdiff_3 C B) (k1_seq_1 A C))) (k5_square_1 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski D (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k3_taylor_1))) &  ( (F = (k1_taylor_1 2))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ( ((k1_seq_1 E G) = (k7_real_1 B (k8_real_1 C G)))  &  (~ (r1_xxreal_0 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) G) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k3_taylor_1) D) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G D) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F A)) k3_taylor_1) D) G) = (k10_real_1 (k7_real_1 C (k8_real_1 (k8_real_1 2 A) G)) (k7_real_1 (k7_real_1 B (k8_real_1 C G)) (k8_real_1 A (k2_newton G 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))))) &  ((r1_xxreal_0 1 A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 A D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A))) B) D) = (k8_real_1 (k8_real_1 A (k5_prepower (k1_seq_1 k19_sin_cos D) (k9_real_1 A 1))) (k1_seq_1 k19_sin_cos (k8_real_1 (k7_real_1 A 1) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k7_real_1 1 (k6_power k8_power A)))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 D (k6_power k8_power A))) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = (k10_real_1 1 k8_power))  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k7_real_1 1 (k6_power k8_power A)))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k7_real_1 1 (k6_power k8_power A)))) B) D) = (k8_real_1 (k10_prepower A D) (k1_seq_1 k24_sin_cos D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k4_sin_cos6 B) (k7_square_1 (k9_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t13_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t13_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t13_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (k2_net_1 A))) &  ((r1_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (k2_net_1 A))) &  ((r1_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (k2_net_1 A))) & (r1_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (k2_net_1 A)))) ) ) ) ) ).
tt(t13_fib_num2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  => (r1_tarski (k10_xtuple_0 (k15_finseq_1 A)) (k10_xtuple_0 A))) ) ).
tt(t13_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_1 (k1_fib_num3 (k1_nat_1 A 1)) (k1_fib_num3 (k1_nat_1 A 2))) = (k1_fib_num3 (k1_nat_1 A 3))) ) ) ).
tt(t13_fib_num4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (r1_xxreal_0 (k3_power k1_fib_num A) (k3_power k2_fib_num A))) ) ) ).
tt(t13_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( (E = (k11_finseq_1 A B C))  =>  ((k17_finseq_1 D 1 E) = (k9_finseq_1 A)) ) ) ) ) ) ) ) ) ).
tt(t13_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k6_domain_1 (u1_struct_0 A) B)))  &  ((v19_lattices (k6_domain_1 (u1_struct_0 A) B) A) &  ((v20_lattices (k6_domain_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_domain_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v14_lattices A)) ) ) ) ) ).
tt(t13_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m2_filter_1 (u2_lattices A) (u1_struct_0 A) (k9_filter_0 A B))) ) ) ) ).
tt(t13_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  <=> (r2_hidden (k4_lattices A C D) B)) ) ) ) )  =>  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t13_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (~ (r1_xxreal_0 D (k19_binop_2 1)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [F:$i] :  ((m1_finance1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k6_finance1 A k1_numbers B k12_prob_1)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k6_finance1 A k1_numbers B k12_prob_1))))) )  =>  ((r2_funct_2 A k1_numbers (k9_finance1 k6_numbers A k1_numbers B k12_prob_1 (k6_finance1 A k1_numbers B k12_prob_1) G) (k8_funcop_1 k1_numbers A (k9_binop_2 1 D))) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r1_xxreal_0 (k4_finance1 C E F) k6_numbers) => (r1_xxreal_0 (k11_finance1 C E A B (k6_finance1 A k1_numbers B k12_prob_1) G H) (k10_binop_2 (k12_finance1 C E A B (k6_finance1 A k1_numbers B k12_prob_1) G H) (k11_binop_2 (k9_binop_2 1 D) (k5_finance1 C E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k4_finseq_1 A) = (k4_finseq_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t13_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (m2_finseq_1 (k10_finseq_1 B C) A)) ) ) ) ) ) ).
tt(t13_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden (k6_xcmplx_0 A B) (k2_finseq_1 A)) <=>  (~ (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t13_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_finseq_4 A B) =>  ((k1_finseq_4 A (k1_funct_1 A B)) = B) ) ) ) ) ).
tt(t13_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((k7_partfun1 A B D) = (k7_partfun1 A C D)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t13_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_tarski A B) => (r1_tarski (k7_finseq_1 C A) (k7_finseq_1 C B))) ) ) ) ) ) ) ).
tt(t13_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_finseq_7 A (k2_finseq_4 A B C) 1 D) = (k2_finseq_4 A D C)) ) ) ) ) ) ) ) ) ).
tt(t13_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((k5_finseq_8 A B B) = B)  &  ( ((k4_finseq_8 A B B) = B)  &  ( ((k6_finseq_8 A B B) = k1_xboole_0)  &  ((k7_finseq_8 A B B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t13_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A C) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) B)))) )  =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  (! [G:$i] :  ((m2_finseq_1 G C) => (r2_relset_1 k5_numbers B (k3_finseqop A C B E D (k8_finseq_1 C F G)) (k8_finseq_1 B (k3_finseqop A C B E D F) (k3_finseqop A C B E D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_finset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((v1_finset_1 A) &  ((r1_tarski A (k2_zfmisc_1 B C)) &  (! [D:$i] :  (! [E:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D B) &  ((v1_finset_1 E) &  ((r1_tarski E C) & (r1_tarski A (k2_zfmisc_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 D A) =>  ((k1_finsop_1 A (k2_finseq_4 A B C) D) = (k1_finsop_1 A (k2_finseq_4 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_finsub_1,ax, (! [A:$i] : (r1_tarski (k5_finsub_1 A) (k1_zfmisc_1 A))) ).
tt(t13_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k6_fin_topo A C)) <=>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( ((k1_fintopo2 A B D C) = k8_margrel1)  &  ((k2_fintopo2 A B E C) = k8_margrel1) ) ) ) ) )  &  ((k4_fintopo2 A B C) = k8_margrel1) ) ) ) ) ) ) ) ) ).
tt(t13_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_fintopo3 A B (k2_nat_1 C 1)) = (k9_fin_topo A (k3_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t13_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_fin_topo A) =>  ((v4_fin_topo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ( (~  ((k7_subset_1 (u1_struct_0 A) B C) = k1_xboole_0) )  &  ((r1_tarski C B) & (r1_xboole_0 (k9_fin_topo A C) (k7_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_fintopo5 A 1)) (u1_struct_0 (k2_fintopo4 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_fintopo5 A 1)) (u1_struct_0 (k2_fintopo4 A)))))) )  & (v1_fintopo5 B (k3_fintopo5 A 1) (k2_fintopo4 A))) ) ) ) ).
tt(t13_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_fintopo6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k9_fin_topo B D) = (k9_subset_1 (u1_struct_0 B) (k9_fin_topo A C) (k2_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(t13_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k9_fin_topo A B))) ) ) ) ).
tt(t13_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k6_flang_1 A B (k4_flang_1 A (k2_flang_1 A))) = B)  &  ((k6_flang_1 A (k4_flang_1 A (k2_flang_1 A)) B) = B) ) ) ) ) ).
tt(t13_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_tarski C (k6_flang_1 A C (k7_flang_1 A B D))) & (r1_tarski C (k6_flang_1 A (k7_flang_1 A B D) C))) ) ) ) ) ) ) ) ) ).
tt(t13_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B C) => (r1_tarski (k1_flang_3 A B D) (k1_flang_3 A C D))) ) ) ) ) ) ) ) ).
tt(t13_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((k1_funct_1 (k5_fomodel0 A C) (k12_finseq_1 A B)) = B)  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_finseq_1 D A))  =>  ((k1_funct_1 (k5_fomodel0 A C) (k1_monoid_0 A D (k12_finseq_1 A B))) = (k1_binop_1 C (k1_funct_1 (k5_fomodel0 A C) D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_fomodel1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  ((m2_subset_1 A (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) <=>  ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (k15_fomodel1 B))) ) ) ) ) ).
tt(t13_fomodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_relset_1 (k4_finseq_2 2 A) k6_margrel1 (k2_fomodel2 A) (k6_domain_1 k5_numbers 1)) = (a_1_1_fomodel2 A)) ) ) ).
tt(t13_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 B A)) =>  ( ((k5_relat_1 D (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 C) (k37_fomodel1 B))) = (k5_relat_1 E (k9_subset_1 (k15_fomodel1 B) (k10_xtuple_0 C) (k37_fomodel1 B))))  =>  ((k26_fomodel2 B A D C) = (k26_fomodel2 B A E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  ( ((v14_fomodel4 A B D) &  ((v6_fomodel4 D B) &  ((r2_hidden (k23_fomodel4 B) D) & (r2_hidden (k33_fomodel4 B) D)) ) )  => (v8_fomodel4 (k38_fomodel2 B C) B D A)) ) ) ) ) ) ) ) ).
tt(t13_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) & (r2_hidden D (k2_frechet A C)))  => (r2_hidden D (k2_pre_topc A B))) ) ) ) ) ) ) ) ) ).
tt(t13_frechet,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski B A) =>  ((k7_relset_1 A A (k6_partfun1 A) B) = B) ) ) ) ).
tt(t13_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k3_twoscomp)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k2_twoscomp)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) ) )  =>  ((k11_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (~  ((k2_msafree2 (k3_fscirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t13_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l3_fsm_1 C A B)) )  =>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) )  & (r3_fsm_1 A B D C)) ) ) ) ) ) ) ) ).
tt(t13_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( ( (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  (E = (u2_fsm_1 A B)) )  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E C)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E D))) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A D C)) = (u2_fsm_1 A B)) ) ) ) ) ) )  => (v1_fsm_2 B A)) ) ) ) ) ).
tt(t13_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E D))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 E))) =>  ( ((k1_afinsq_1 C) = 1)  =>  ( (A = (k3_rewrite3 B D E C F))  <=> (r4_rewrite3 B (k9_flang_1 B) (k1_fsm_3 B D E) F C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (~  ((k2_msafree2 (k7_ftacell1 A B C D E)) = (k3_enumset1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k9_xtuple_0 (k2_funcop_1 A B)) = A)  & (r1_tarski (k10_xtuple_0 (k2_funcop_1 A B)) (k1_tarski B))) ) ) ).
tt(t13_funcsdom,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  ((k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) A (k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) B D)) = (k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k8_real_1 A B) D)) ) ) ) ) ) ) ) ).
tt(t13_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k1_funct_1 (k3_relat_1 B C) A) = (k1_funct_1 C (k1_funct_1 B A))) ) ) ) ) ) ) ).
tt(t13_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( (~  ( (B = k1_xboole_0)  &  ( (~  (C = k1_xboole_0) )  &  (~  (A = k1_xboole_0) ) ) ) )  => (v1_funct_2 (k4_relset_1 A B B C D E) A C)) ) ) ) ) ) ) ) ).
tt(t13_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k3_tarski (k7_relat_1 (k1_funct_3 B) A)) (k7_relat_1 B (k3_tarski A)))) ) ) ).
tt(t13_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k1_funct_1 (k1_funct_4 C B) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t13_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k9_xtuple_0 (k2_tarski (k4_tarski A B) (k4_tarski C D))) = (k2_tarski A C))  &  ((k10_xtuple_0 (k2_tarski (k4_tarski A B) (k4_tarski C D))) = (k2_tarski B D)) ) ) ) ) ) ).
tt(t13_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r1_tarski (k10_xtuple_0 F) (k4_partfun1 D E)) &  ((k9_xtuple_0 F) = A) )  =>  ( ( (~ (r2_hidden (k2_funct_5 F) (k1_funct_2 (k2_zfmisc_1 A B) C)))  &  (~ (r2_hidden (k4_funct_5 F) (k1_funct_2 (k2_zfmisc_1 B A) C))) )  | (r2_hidden F (k1_funct_2 A (k1_funct_2 B C)))) ) ) ) ) ) ) ) ) ).
tt(t13_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = B) )  & (r2_hidden A (k10_xtuple_0 (k1_funct_4 (k6_partfun1 C) (k16_funcop_1 A B))))) ) ) ) ) ).
tt(t13_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r1_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t13_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k1_funct_1 B (k6_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ).
tt(t13_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ((v2_funct_2 (k1_functor0 A B C D) C) => (v2_funct_2 D C)) ) ) ) ) ) ).
tt(t13_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (m1_altcat_2 C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_altcat_2 D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_altcat_2 E C))  =>  ( (D = E)  =>  (! [F:$i] :  ((l2_functor0 F A B) =>  ((k14_functor0 A B D F) = (k14_functor0 C B E (k14_functor0 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G C A) & (m2_functor0 G C A))  =>  (! [H:$i] :  ((m1_functor2 H B C D E) =>  (! [I:$i] :  ((m1_functor2 I B C E F) =>  ( ((r1_functor2 B C D E) & (r1_functor2 B C E F))  => (r8_pboole (u1_struct_0 B) (k5_functor3 B C A D F (k3_functor2 B C D E F H I) G) (k3_functor2 B A (k1_functor3 B C A D G) (k1_functor3 B C A E G) (k1_functor3 B C A F G) (k5_functor3 B C A D E H G) (k5_functor3 B C A E F I G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r1_tarski (k10_xtuple_0 D) (k1_rcomp_1 B C)) & (r1_xxreal_0 B C))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  ((r1_xxreal_0 B (k1_seq_1 D E)) & (r1_xxreal_0 (k1_seq_1 D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k1_fuzzy_2 A B C) (k1_fuzzy_2 A (k2_fuzzy_1 A B C) C))) ) ) ) ) ) ).
tt(t13_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A C) k1_numbers (k4_fuzzy_4 A B C D (k2_fuzzy_1 (k2_zfmisc_1 B C) E F)) (k2_fuzzy_1 (k2_zfmisc_1 A C) (k4_fuzzy_4 A B C D E) (k4_fuzzy_4 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_fvaluat1 A B 1) = B) ) ) ) ) ).
tt(t13_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_algstr_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r1_finseqop (u1_struct_0 A) (k5_vectsp_1 A) (u1_algstr_0 A))) ) ).
tt(t13_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 (k7_gate_1 A B)))  <=>  ((v1_xboole_0 A) & (v1_xboole_0 B)) ) ) ) ).
tt(t13_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_gcd_1 A D B) & (r2_gcd_1 A D C))  =>  ( (D = (k4_struct_0 A))  |  ( ((k1_gcd_1 A B D) = (k1_gcd_1 A C D))  <=>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_genealg1 D C) =>  (! [E:$i] :  ((m1_genealg1 E C) =>  ((k8_genealg1 C D E A B) = (k8_genealg1 C D E B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analoaf A B C C D) => (r1_analoaf A (k1_geomtrap A B C) C C (k1_geomtrap A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  ((k2_msafree2 (k5_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t13_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  ((k2_msafree2 (k1_gfacirc2 A B C)) = (k2_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t13_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) =>  ((r2_hidden C (k6_glib_000 A)) & (r2_hidden D (k6_glib_000 A))) ) ) ) ) ) ) ).
tt(t13_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ( ((k3_finseq_1 (k1_glib_001 A B)) = 1)  &  ( ((k1_funct_1 (k1_glib_001 A B) 1) = B)  &  ( ((k3_glib_001 A (k1_glib_001 A B)) = B)  &  ( ((k4_glib_001 A (k1_glib_001 A B)) = B)  & (r1_glib_001 A B B (k1_glib_001 A B))) ) ) ) ) ) ) ) ).
tt(t13_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r2_hidden B (k13_glib_001 A C)) => (r1_tarski (k13_glib_001 A C) (k1_glib_002 A B))) ) ) ) ) ) ) ).
tt(t13_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k3_finseq_1 (k8_glib_003 A B)) = (k15_glib_001 A B)) ) ) ) ) ).
tt(t13_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_glib_001 B A) &  ((v5_glib_001 B A) & (m3_glib_001 B A)) )  =>  (! [C:$i] :  ( ((v2_glib_001 C A) &  ((v5_glib_001 C A) & (m3_glib_001 C A)) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_glib_004 A B D E) & (r2_glib_004 A C D E))  =>  ((k10_glib_003 A B) = (k10_glib_003 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (~  ( (~ (v3_glib_001 C A))  &  ((r5_glib_005 A B C) & (r1_xxreal_0 (k9_glib_005 A B C) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t13_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) &  ( ((k1_matrix_1 D) = (k2_nat_1 B 1))  & (r1_xxreal_0 1 C)) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 A C) |  ( ((k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 D A) C) = (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) D C))  &  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 (k3_goboard1 D A)))) & (r2_hidden C (k2_finseq_1 (k1_matrix_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ( ((k3_finseq_1 (k2_goboard2 A)) = (k5_card_1 (k10_xtuple_0 (k1_goboard1 A))))  &  ((k1_matrix_1 (k2_goboard2 A)) = (k5_card_1 (k10_xtuple_0 (k2_goboard1 A)))) ) ) ) ).
tt(t13_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 C) &  ((v5_goboard1 C) & (r1_xxreal_0 1 B)) )  =>  ((v3_relat_1 C) |  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k1_goboard5 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t13_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k1_goboard5 A (k3_finseq_1 A))) = (a_1_1_goboard6 A)) ) ) ).
tt(t13_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 2)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(t13_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_goboard9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 A (k3_finseq_1 B)) => (v1_convex1 (k1_tops_1 (k15_euclid 2) (k1_goboard5 B A)) (k15_euclid 2))) ) ) ) ) ).
tt(t13_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (a_1_3_gobrd11 B))  => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ).
tt(t13_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 E) (k16_matrix_1 F)) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 E) A) |  ((r1_xxreal_0 (k3_finseq_1 F) C) | (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F (k2_nat_1 C 1) D)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 A 1) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  &  ((r1_xboole_0 B C) &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))))) =>  ( ( (D = B)  &  (E = C) )  =>  ((v3_connsp_1 D (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) & (v3_connsp_1 E (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))))) ) ) ) ) )  &  ( (~  ( (B = (k3_goboard9 A))  &  (C = (k2_goboard9 A)) ) )  &  (~  ( (B = (k2_goboard9 A))  &  (C = (k3_goboard9 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k7_cqc_sim1 A (k12_cqc_lang A C B)) = (k2_nat_1 (k7_cqc_sim1 A B) 1)) ) ) ) ) ) ) ).
tt(t13_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( (? [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_graph_1 D))  &  ((r4_graph_1 A D) &  ((r4_graph_1 B D) & (r4_graph_1 C D)) ) ) )  =>  ((k5_graph_1 (k5_graph_1 A B) C) = (k5_graph_1 A (k5_graph_1 B C))) ) ) ) ) ) ) ) ).
tt(t13_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~  (A = k1_xboole_0) )  =>  ((k2_nat_1 (k3_finseq_1 (k3_graph_2 B A)) 1) = (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t13_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((r2_hidden D (u4_struct_0 A)) &  ((r1_graph_2 A C B) &  ((k1_funct_1 C (k3_finseq_1 C)) = (k1_funct_1 (u2_graph_1 A) D)) ) )  =>  ((m1_graph_1 (k7_finseq_1 B (k9_finseq_1 D)) A) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ( (E = (k3_graph_2 C (k10_finseq_1 (k1_funct_1 (u2_graph_1 A) D) (k1_funct_1 (u1_graph_1 A) D))))  &  ((r1_graph_2 A E (k7_finseq_1 B (k9_finseq_1 D))) &  ( ((k1_funct_1 E 1) = (k1_funct_1 C 1))  &  ((k1_funct_1 E (k3_finseq_1 E)) = (k1_funct_1 (u1_graph_1 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_graph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v7_graph_1 F C) & (m2_graph_1 F C))  =>  (! [G:$i] :  ( ((v7_graph_1 G C) & (m2_graph_1 G C))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k3_finseq_1 F)) &  ( (G = (k2_graph_2 (u4_struct_0 C) F A B))  &  ((r3_graph_4 C D F) &  (E = (k2_graph_2 (u1_struct_0 C) D A (k2_nat_1 B 1))) ) ) ) ) )  => (r3_graph_4 C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v7_graph_1 k1_xboole_0 A) &  ((v1_graph_4 k1_xboole_0 A) & (m2_graph_1 k1_xboole_0 A)) ) ) ) ).
tt(t13_graphsp,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_graph_1 C) & (l1_graph_1 C)) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m2_graph_1 D C))  =>  (! [E:$i] :  ( ((v7_graph_1 E C) & (m2_graph_1 E C))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ( ((r5_graph_5 C A) &  ((r8_graph_5 C F G D B A) &  ((r8_graph_5 C F H E B A) &  ( (! [I:$i] :  (~  ((r2_hidden I (u4_struct_0 C)) & (r1_graph_4 C G H I)) ) )  & (r9_graph_5 C D B F A)) ) ) )  =>  ( (F = G)  |  ( (F = H)  | (r8_graph_5 C F H E (k2_xboole_0 B (k1_tarski G)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_grcat_1 C) & (m1_grcat_1 C A B))  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (C = (g1_grcat_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t13_gr_cy_1,ax, ((k1_group_1 k2_gr_cy_1) = k6_numbers) ).
tt(t13_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (A = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) C)))  & (r1_struct_0 B C))  =>  ((g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)) = (g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B))) ) ) ) ) ) ) ) ).
tt(t13_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  (? [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v2_gr_cy_3 B)) )  &  ((k7_group_1 (k3_int_7 A)) = (k4_nat_1 2 B)) ) ) ) ) ).
tt(t13_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((v1_relat_1 (k2_xboole_0 A B)) & (v1_funct_1 (k2_xboole_0 A B))) ) ) ) ) ) ).
tt(t13_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_6 (k1_grnilp_1 A B (k7_group_2 A)) A C) => (m1_group_6 (k1_grnilp_1 A (k10_group_2 A B D) D) A (k10_group_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((v7_rewrite1 (k3_polyred A B C D)) => (v4_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(t13_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  => (r8_pboole (k15_pre_poly A) (k1_polyred A D B (k5_vfunct_1 (k15_pre_poly A) B C)) (k5_vfunct_1 (k15_pre_poly A) B (k1_polyred A D B C)))) ) ) ) ) ) ) ) ).
tt(t13_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_vfunct_1 (k15_pre_poly A) B (k7_polynom1 A B)) (k7_polynom1 A B))) ) ) ).
tt(t13_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ((k4_nat_d (k5_card_1 (k15_group_10 A B)) B) = 1)  & (r1_nat_d (k5_card_1 (k15_group_10 A B)) (k7_group_1 A))) ) ) ) ) ).
tt(t13_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski (k13_group_2 A C D) B) => (r2_hidden D (k1_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t13_group_12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k2_finseq_1 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k2_finseq_1 A)) &  ((v1_group_7 B) &  ((v2_group_7 B (k2_finseq_1 A)) &  ((v3_group_7 B (k2_finseq_1 A)) & (v4_group_7 B (k2_finseq_1 A))) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_finseq_1 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (k2_finseq_1 A)) &  ((v1_group_7 C) &  ((v2_group_7 C (k2_finseq_1 A)) &  ((v3_group_7 C (k2_finseq_1 A)) & (v4_group_7 C (k2_finseq_1 A))) ) ) ) ) ) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers (k2_finseq_1 A)) =>  ((k1_group_7 (k2_finseq_1 A) C D) = (k2_group_12 (k2_finseq_1 A) B D)) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) &  ((v1_group_6 D (k2_group_7 (k2_finseq_1 A) C) (k2_group_7 (k2_finseq_1 A) B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B)))))) ) )  =>  (~  ((v3_funct_2 D (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C))) =>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B))) &  ( ((k3_finseq_1 F) = A)  &  ( (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 A)) => (r1_struct_0 (k1_group_7 (k2_finseq_1 A) C G) (k1_funct_1 F G))) )  &  ( (F = E)  &  ((k3_funct_2 (u1_struct_0 (k2_group_7 (k2_finseq_1 A) C)) (u1_struct_0 (k2_group_7 (k2_finseq_1 A) B)) D E) = (k3_group_4 (k2_group_7 (k2_finseq_1 A) B) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = D)  <=>  (C = (k6_algstr_0 A (k2_group_1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_group_2 A (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) D) = (k1_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_group_2 A B D) (k2_group_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k11_group_2 A D (k14_group_2 A C B)) = (k12_group_2 A C (k13_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t13_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k3_group_4 A (k1_group_4 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) (k1_group_1 A)))) = (k3_group_4 A B)) ) ) ) ) ).
tt(t13_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_group_5 A (k3_finseq_4 (u1_struct_0 A) B C D) E) = (k3_finseq_4 (u1_struct_0 A) (k2_group_3 A B E) (k2_group_3 A C E) (k2_group_3 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  (~  ((r2_hidden B (k15_group_2 A C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (B = (k13_group_2 A C D))  &  (B = (k14_group_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_group_7 (k9_finseq_1 A)) & (v4_group_7 (k9_finseq_1 A) (k1_tarski 1))) ) ) ) ) ) ) ).
tt(t13_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_group_1 B A) <=>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k5_group_1 A C B) = (k1_group_1 A))  =>  (C = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t13_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) => (r1_struct_0 D E)) ) )  => (m1_group_9 C A D)) ) ) ) ) ) ) ) ).
tt(t13_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (v1_groupp_1 (k1_group_1 A) B A)) ) ) ) ).
tt(t13_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k13_group_2 B (k2_grsolv_1 A B C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k13_group_2 A D E)))  &  ((k14_group_2 B (k2_grsolv_1 A B C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k14_group_2 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k3_hahnban1 A B (k3_hahnban1 A B C D) E) (k3_hahnban1 A B C (k3_hahnban1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_struct_0 C B) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  ((r1_struct_0 C F) =>  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) (u1_struct_0 A) F (k4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ( (~ (r2_hidden C E))  =>  ((k1_hallmar1 A B E) = (k1_hallmar1 A (k2_hallmar1 A B C D) E)) ) ) ) ) ) ) ) ) ) ).
tt(t13_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A B) C) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r1_tarski B C) => (r1_tarski (k13_glib_001 A B) (k13_glib_001 A C))) ) ) ) ) ) ) ).
tt(t13_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (v1_henmodel (k6_domain_1 (k3_cqc_lang A) (k5_cqc_lang A)) A)) ) ).
tt(t13_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k8_group_1 k1_complfld A (k2_complfld A)) = (k5_square_1 (k17_complex1 A))) ) ) ).
tt(t13_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A D F B) &  ( (~  (B = E) )  &  ( (~  (B = F) )  & (r1_collsp A E B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ( (B = k1_xboole_0)  =>  ((k6_heyting1 A B) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ) ) ) ) ).
tt(t13_heyting2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( (C = k1_xboole_0)  =>  ((k3_substlat A B (k2_heyting2 A B C)) = (k6_lattices (k5_substlat A B))) ) ) ) ) ) ) ) ).
tt(t13_heyting3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  =>  ((v4_yellow_0 (k1_heyting3 A C) (k1_heyting3 B D)) & (m1_yellow_0 (k1_heyting3 A C) (k1_heyting3 B D))) ) ) ) ) ) ).
tt(t13_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A B) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos B) 3) A) = (k1_seq_1 k16_sin_cos A)) ) ) ) ) ) ).
tt(t13_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_1 C) &  ((v4_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) )  =>  ((k2_polynom1 (k15_pre_poly A) C (k3_hilbasis A B C)) = (k6_domain_1 (k15_pre_poly A) (k2_hilbasis A B))) ) ) ) ) ) ).
tt(t13_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  ((v6_hilbert1 A) => (r1_tarski k6_hilbert1 A)) ) ) ).
tt(t13_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( ((k1_funct_1 B 1) = (k2_nat_1 3 A))  => (v3_hilbert2 B)) ) ) ) ) ).
tt(t13_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  =>  ((k3_relat_1 (k4_funct_4 A B B A) (k4_funct_4 A B C D)) = (k4_funct_4 A B D C)) ) ) ) ) ) ).
tt(t13_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A 1))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((k1_seq_1 D G) = (k4_power (k18_complex1 (k1_seq_1 B G)) A))  &  ( ((k1_seq_1 E G) = (k4_power (k18_complex1 (k1_seq_1 C G)) A))  &  ((k1_seq_1 F G) = (k4_power (k18_complex1 (k7_real_1 (k1_seq_1 B G) (k1_seq_1 C G))) A)) ) ) ) )  &  ((v1_series_1 D) & (v1_series_1 E)) )  =>  ((v1_series_1 F) & (r1_xxreal_0 (k4_power (k4_series_1 F) (k10_real_1 1 A)) (k7_real_1 (k4_power (k4_series_1 D) (k10_real_1 1 A)) (k4_power (k4_series_1 E) (k10_real_1 1 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k14_polynom3 A))) =>  ( (B = (k4_rlvect_1 (k14_polynom3 A) C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_normsp_1 A B D) = (k4_rlvect_1 A (k1_hurwitz A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 B A) =>  ((k4_idea_1 B k6_numbers A) = A) ) ) ) ) ) ).
tt(t13_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t13_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k3_incproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k3_incproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k3_incproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k3_incproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k3_incproj A))) =>  (~  ((r1_incsp_1 (k3_incproj A) B G) &  ((r1_incsp_1 (k3_incproj A) C G) &  ((r1_incsp_1 (k3_incproj A) D H) &  ((r1_incsp_1 (k3_incproj A) E H) &  ((r1_incsp_1 (k3_incproj A) F G) &  ((r1_incsp_1 (k3_incproj A) F H) &  ((r1_incsp_1 (k3_incproj A) B I) &  ((r1_incsp_1 (k3_incproj A) D I) &  ((r1_incsp_1 (k3_incproj A) C J) &  ((r1_incsp_1 (k3_incproj A) E J) &  ( (~ (r1_incsp_1 (k3_incproj A) F I))  &  ( (~ (r1_incsp_1 (k3_incproj A) F J))  &  ( (~  (G = H) )  &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k3_incproj A))) =>  (~  ((r1_incsp_1 (k3_incproj A) K I) & (r1_incsp_1 (k3_incproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_incsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((r1_tarski B C) & (v4_incsp_1 C A))  => (v4_incsp_1 B A)) ) ) ) ) ) ) ).
tt(t13_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k8_cat_1 A C (k9_index_1 A B C) D) = (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) D)) ) ) ) ) ) ) ) ) ).
tt(t13_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  ( ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ((r1_tarski (u1_msualg_1 B) (u1_msualg_1 A)) & (r1_tarski (u2_msualg_1 B) (u2_msualg_1 A))) )  => (m1_instalg1 B A)) ) ) ) ) ).
tt(t13_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (r2_int_1 A B 1)) ) ) ) ).
tt(t13_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (~  ( ((r1_int_1 A 1) | (r1_int_1 A (k4_xcmplx_0 1)))  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ).
tt(t13_int_3,ax, ((k5_struct_0 k1_int_3) = 1) ).
tt(t13_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ( (B = (k2_xcmplx_0 (k3_xcmplx_0 A C) D))  &  ((r1_xxreal_0 k6_numbers D) &  (~ (r1_xxreal_0 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((k6_int_1 B D) = (k6_int_1 C D))  =>  ((k6_int_1 (k1_newton B A) D) = (k6_int_1 (k1_newton C A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_int_1 (k1_int_2 A) A) & (r1_int_1 A (k1_int_2 A))) ) ) ).
tt(t13_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (~  ((v1_int_7 A) &  ((k8_nat_3 k10_newton A) = k6_numbers) ) ) ) ) ).
tt(t13_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers A)) &  ((r1_integra5 (k3_integra5 B C) A) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_integra5 B C)))) )  =>  ((r1_xxreal_0 C B) |  ((k2_integr10 A B C) = (k4_integra5 B C A)) ) ) ) ) ) ) ) ) ).
tt(t13_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) (k5_seq_4 A)))) ) ) ).
tt(t13_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos)))) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t13_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r2_relset_1 k1_numbers k1_numbers B (k1_taylor_1 2)) &  ((r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) B)) (k3_rfunct_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)))) &  ((r1_tarski D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k29_sin_cos))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9)) A) B) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k1_seq_1 k16_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t13_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k1_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ( ((k2_partfun1 k1_numbers (k1_euclid A) C B) = D)  =>  ((r1_integr15 A B C) <=> (v2_integr15 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 B) <=>  ((v1_comseq_2 (k5_comseq_3 A B)) & (v1_comseq_2 (k6_comseq_3 A B))) ) ) ) ) ) ).
tt(t13_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers D)) & (r1_integr18 A C D))  =>  ((r1_integr18 A C (k4_vfunct_1 k1_numbers A D B)) &  ((k5_integr18 A C (k4_vfunct_1 k1_numbers A D B)) = (k1_rlvect_1 A (k5_integr18 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_integr15 A (k3_integra5 B E) F) &  ((r1_integr15 A (k3_integra5 B E) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B E)) A) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B E)) A) &  ((r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers F)) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers G))) ) ) ) ) ) ) )  =>  ((r1_integr15 A (k3_integra5 C D) (k8_integr15 A k1_numbers F G)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers F G) (k3_integra5 C D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_seq_2 (k2_partfun1 A k1_numbers B A)) => (v4_xxreal_2 (k1_rvsum_1 B))) ) ) ) ) ).
tt(t13_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v4_xxreal_2 B) & (r1_xxreal_0 k6_numbers A))  =>  ((k4_seq_4 (k1_integra2 B A)) = (k8_real_1 A (k4_seq_4 B))) ) ) ) ) ) ).
tt(t13_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k2_integra1 B C (k3_finseq_1 C))) &  ((r1_integra1 C D) &  ( ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 C) (k1_seq_4 A)))  & (v1_comseq_2 (k2_partfun1 B k1_numbers E B))) ) )  =>  ( ((k3_integra1 B) = k6_numbers)  |  ((r1_xxreal_0 A (k5_seq_4 B)) | (r1_xxreal_0 (k9_real_1 (k18_rvsum_1 (k5_integra1 B E D)) (k18_rvsum_1 (k5_integra1 B E C))) (k8_real_1 (k9_real_1 (k4_seq_4 (k1_rvsum_1 E)) (k5_seq_4 (k1_rvsum_1 E))) (k1_integra3 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_partfun1 (k18_rfunct_3 A B) A) & (v1_partfun1 (k19_rfunct_3 A B) A)) ) ) ) ) ).
tt(t13_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r2_fdiff_1 C B) &  ((r1_integra5 A (k2_fdiff_1 C B)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 C B) A))) ) )  =>  ((k2_integra5 A (k2_fdiff_1 C B)) = (k9_real_1 (k1_seq_1 C (k4_seq_4 A)) (k1_seq_1 C (k5_seq_4 A)))) ) ) ) ) ) ) ).
tt(t13_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers B A)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C A)))  => (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A))) ) ) ) ) ) ) ).
tt(t13_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_integra7 B C D) => (r1_integra7 B (k26_valued_1 k1_numbers k1_numbers C A) (k26_valued_1 k1_numbers k1_numbers D A))) ) ) ) ) ) ) ) ).
tt(t13_integra8,ax, ((k21_sin_cos (k10_real_1 k32_sin_cos 4)) = (k10_real_1 (k7_square_1 2) 2)) ).
tt(t13_integra9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos)) A) B) = (k1_real_1 (k8_real_1 B (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ).
tt(t13_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r1_tarski B C) & (r1_tarski D E))  =>  ((k2_setfam_1 (k2_interva1 A B C) (k2_interva1 A D E)) = (a_5_1_interva1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_intpro_1)) =>  ((r1_tarski A B) => (r1_tarski (k7_intpro_1 A) (k7_intpro_1 B))) ) ) ) ) ).
tt(t13_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B A))  =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k1_irrat_1 A) B) k6_numbers))  & (r1_xxreal_0 (k1_seq_1 (k1_irrat_1 A) B) 1)) ) ) ) ) ) ).
tt(t13_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  ((v12_cat_1 C B A) =>  ((r2_funct_2 (u4_struct_0 A) (u4_struct_0 A) (k9_cat_1 A B A (k1_isocat_1 B A C) C) (k10_cat_1 A)) & (r2_funct_2 (u4_struct_0 B) (u4_struct_0 B) (k9_cat_1 B A B C (k1_isocat_1 B A C)) (k10_cat_1 B))) ) ) ) ) ) ) ) ).
tt(t13_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_nattra_1 (k8_cat_2 A B) C D E) =>  (! [F:$i] :  ((m2_nattra_1 F (k8_cat_2 A B) C D E) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_nattra_1 B C (k12_cat_2 A B C D G) (k12_cat_2 A B C E G)) & (m2_nattra_1 (k1_funct_1 (k1_funct_5 F) G) B C (k12_cat_2 A B C D G) (k12_cat_2 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) => (v5_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t13_jct_misc,ax, (! [A:$i] :  ( ((v4_pre_topc A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v9_rltopsp1 A (k15_euclid 2)) => (v2_rcomp_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A))) ) ) ).
tt(t13_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_goboard5 A) & (r1_xboole_0 (k2_topreal1 2 A 1) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 1))))  => (v3_topreal1 A)) ) ) ).
tt(t13_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k1_real_1 (k17_euclid A)) (k18_euclid A))) )  &  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k1_real_1 (k17_euclid A)))) )  &  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A))) )  &  (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) ) ) ) ) ) ) ) ).
tt(t13_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k18_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid C) (k18_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t13_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid A) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) =>  ((k1_funct_1 C D) = (k1_funct_1 (k1_jgraph_4 A) D)) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid A) B) k3_topmetr)) ) ) ) ) ) ) ).
tt(t13_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_0_jgraph_5)  &  ( (D = a_0_1_jgraph_5)  &  ( (E = a_0_2_jgraph_5)  &  ( (F = a_0_3_jgraph_5)  &  ( (G = a_0_4_jgraph_5)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) F) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) G) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jgraph_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc E A k3_topmetr) &  ((v5_pre_topc F A k3_topmetr) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)))))) )  =>  (~  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)) G H) = (k3_rlvect_1 (k15_euclid B) (k1_rlvect_1 (k15_euclid B) C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) E H)) (k1_rlvect_1 (k15_euclid B) D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) F H)))) ) )  & (v5_pre_topc G A (k15_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k18_euclid A) = F)  &  ( ((k17_euclid B) = D)  &  ((r1_xxreal_0 C (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) D) &  ((r1_xxreal_0 E (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) F)) ) ) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) | (r1_jordan6 (k1_sppol_2 C D E F) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_tarski (k2_jordan2c 2 (k3_topreal1 2 (k1_jordan9 B A))) (k2_jordan2c 2 B))) ) ) ) ).
tt(t13_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k2_jordan2c 2 A)) &  ((r2_hidden C (k1_jordan2c 2 A)) & (r1_xxreal_0 (k1_topreal6 2 B C) (k5_jordan1k 2 B A))) ) ) ) ) ) ) ) ) ).
tt(t13_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) B C) (k3_topreal1 2 A)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) D) &  ((r2_hidden B D) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski (k1_jordan2c 2 (k3_topreal1 2 (k1_jordan13 A B))) (k1_jordan2c 2 A))) ) ) ) ) ).
tt(t13_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) D E B) &  ((r1_topreal1 (k15_euclid 2) D E C) &  ((r1_tarski B A) &  ((r1_tarski C A) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k2_tarski D E)) ) ) ) )  =>  ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A B C D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A B F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) & (r1_tarski (k5_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ) ).
tt(t13_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan1a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden A (k6_jordan6 C)) & (r2_hidden B (k6_jordan6 C)))  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) A B) (k6_jordan6 C))) ) ) ) ) ) ) ).
tt(t13_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_1_jordan1 A))  => (v1_convex1 B (k15_euclid 2))) ) ) ) ) ).
tt(t13_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_xxreal_0 (k1_jordan1a A) (k3_finseq_1 A))) ) ).
tt(t13_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k17_euclid C) (k6_pscomp_1 A)) (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A))) (k13_newton 2 B)) 2)))  => (r1_xxreal_0 (k7_real_1 (k6_pscomp_1 A) (k8_real_1 (k10_real_1 (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) (k13_newton 2 B)) (k5_real_1 D 2))) (k17_euclid C))) ) ) ) ) ) ) ) ) ).
tt(t13_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k25_pscomp_1 B) (k2_gobrd13 (k1_jordan9 B A) (k1_jordan8 B A) C))) ) ) ) ) ) ) ) ).
tt(t13_jordan1e,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_topreal1 2 (k1_jordan9 A B)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan1e A B)) (k3_topreal1 2 (k2_jordan1e A B)))) ) ) ) ) ).
tt(t13_jordan1f,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_topreal2 B) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k17_euclid C) = (k13_complex1 (k2_xcmplx_0 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2))  &  ( ((k18_euclid C) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) (k1_jordan1a (k1_jordan8 B 1)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) (k1_jordan1a (k1_jordan8 B 1)) (k1_matrix_1 (k1_jordan8 B 1)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))))))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  (C = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k19_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) )  &  ((k18_pscomp_1 (k3_topreal1 2 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ).
tt(t13_jordan1h,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_tarski (k2_relset_1 A (k8_matrix_1 A B C)) (k2_jordan1h A B))) ) ) ) ) ) ) ).
tt(t13_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1) D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  & (r1_xxreal_0 (k1_matrix_1 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k25_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k2_jordan1e B A))) & (r2_hidden (k25_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ).
tt(t13_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r1_xxreal_0 A (k4_metric_1 B E F))) ) ) ) )  => (r1_xxreal_0 A (k7_weierstr B C D))) ) ) ) ) ) ) ) ) ).
tt(t13_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_xxreal_0 E 1) &  ( (B = (a_3_0_jordan20 A D E))  &  (C = (k3_rcomp_1 k6_numbers E)) ) )  =>  ((k7_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) D C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v2_rcomp_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2))))) &  ((v3_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2))))) & (v4_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) ) ) ) ).
tt(t13_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) (k3_finseq_1 (k1_jordan8 A B))))))) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k6_jordan6 (k13_complex1 (k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)))))) ) ) ) ) ) ).
tt(t13_jordan23,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((v3_jordan23 B) & (v1_finseq_6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (v3_jordan23 (k1_finseq_6 A B C))) ) ) ) ) ) ) ).
tt(t13_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))))))) )  =>  ( (E = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D))  => (v5_pre_topc E (k1_pre_topc A D) (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ( (C = (a_3_1_jordan2b A B D))  & (r2_hidden D (k2_finseq_1 A)))  => (v3_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t13_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_jordan2c A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))))) &  ( (D = C)  &  ((v3_connsp_1 D (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) &  ((v6_tbsp_1 D (k14_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_euclid A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((v3_topreal1 A) &  ((r2_hidden B (k2_topreal1 2 A C)) &  ( (~  (C = (k1_jordan3 A B)) )  &  (~  (C = (k2_nat_1 (k1_jordan3 A B) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E D) &  ((r1_xxreal_0 D (k3_finseq_1 C)) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 (k7_nat_d D E) 1))) ) ) )  =>  ( ((k1_funct_1 (k3_finseq_6 B C D E) A) = (k1_funct_1 (k3_finseq_6 B C E D) (k7_real_1 (k9_real_1 (k3_real_1 (k6_xcmplx_0 D E) 1) A) 1)))  &  ((k7_real_1 (k9_real_1 (k3_real_1 (k6_xcmplx_0 D E) 1) A) 1) = (k2_nat_1 (k7_nat_d (k2_nat_1 (k7_nat_d D E) 1) A) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_topmetr A B))) =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tmap_1 (k4_topmetr A B) (k4_topmetr C D) F G) &  ( ((k1_funct_1 F A) = C)  &  ( ((k1_funct_1 F B) = D)  &  ((v2_funct_1 F) &  ( (F = H)  &  (G = E) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (r1_fcont_1 (k2_partfun1 k1_numbers k1_numbers H (k1_rcomp_1 A B)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = B) )  =>  ((k1_rltopsp1 (k15_euclid 2) A B) = (a_2_0_jordan5b A B)) ) ) ) ) ) ).
tt(t13_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan5c A B C D E) & (r1_jordan5c A B C E F))  => (r1_jordan5c A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_0_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k14_pscomp_1 (k3_topreal1 2 A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k14_pscomp_1 (k3_topreal1 2 A)))))) ) ) ) ) ) ).
tt(t13_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) C D A) &  (B = (a_2_0_jordan6 C D)) )  =>  ( (~ (r1_xboole_0 A B))  & (v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) &  ((r1_jordan6 A B C) &  ((r1_jordan6 A C D) & (r1_jordan6 A D E)) ) )  =>  ( (B = C)  |  ( (C = D)  | (r1_xboole_0 (k1_jordan7 A B C) (k1_jordan7 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))))  =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) A 2)) = (k9_pscomp_1 C)) ) ) ) ) ) ) ) ).
tt(t13_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v2_sppol_1 (k2_topreal1 2 C A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k2_topreal1 2 C A)) =>  ((k17_euclid E) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B (k22_pscomp_1 A)) =>  ((k1_jordan7 A B (k18_pscomp_1 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_jordan6 (k8_jordan6 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B) (k3_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) (k18_pscomp_1 A)))) ) ) ) ) ) ).
tt(t13_jordan,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k6_topreal1 (k2_jordan21 A)) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan21 A))) (k2_jordan2c 2 A))) ) ).
tt(t13_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_knaster A B C k1_xboole_0) = C) ) ) ) ) ) ) ).
tt(t13_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D B A C) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  ( (~ (v1_xboole_0 (k7_kolmog01 A C B E D)))  & (m1_subset_1 (k7_kolmog01 A C B E D) (k1_zfmisc_1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) D E) = (k9_subset_1 A (k3_funct_2 k5_numbers (k9_setfam_1 A) B E) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E))) ) )  => (r1_tarski (k4_kurato_0 A D) (k9_subset_1 A (k4_kurato_0 A B) (k4_kurato_0 A C)))) ) ) ) ) ) ) ) ).
tt(t13_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr k6_kurato_1)))) = (k2_rcomp_1 2 k1_xxreal_0)) ).
tt(t13_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m2_valued_0 C (k9_setfam_1 (u1_struct_0 A)) B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r1_xxreal_0 D E) &  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C D) = (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_lang1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k3_lang1 (k7_lang1 A B)) = (k1_tarski (k9_finseq_1 B))) ) ) ) ).
tt(t13_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r2_hidden E (k2_finseq_1 A)))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden F (k2_finseq_1 (k7_nat_d A 1))) & (r2_hidden G (k2_finseq_1 (k7_nat_d A 1))))  =>  ( (~  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 E G))  &  (~  ((k3_matrix_1 (u1_struct_0 B) (k2_laplace D E A B C) F G) = (k3_matrix_1 (u1_struct_0 B) C F G)) ) ) ) )  &  ( ((r1_xxreal_0 E G) =>  ((r1_xxreal_0 D F) |  ((k3_matrix_1 (u1_struct_0 B) (k2_laplace D E A B C) F G) = (k3_matrix_1 (u1_struct_0 B) C F (k1_nat_1 G 1))) ) )  &  ( ((r1_xxreal_0 D F) =>  ((r1_xxreal_0 E G) |  ((k3_matrix_1 (u1_struct_0 B) (k2_laplace D E A B C) F G) = (k3_matrix_1 (u1_struct_0 B) C (k1_nat_1 F 1) G)) ) )  &  ( ((r1_xxreal_0 D F) & (r1_xxreal_0 E G))  =>  ((k3_matrix_1 (u1_struct_0 B) (k2_laplace D E A B C) F G) = (k3_matrix_1 (u1_struct_0 B) C (k1_nat_1 F 1) (k1_nat_1 G 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_struct_0 B C)) ) ) ) ) ) ) ).
tt(t13_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((r2_hidden C (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))) => (m1_subset_1 C (u1_struct_0 B))) ) ) ) ) ) ).
tt(t13_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_lattices A) & (l3_lattices A)) )  =>  ((k1_lattice2 (k1_lattice2 A)) = A) ) ) ).
tt(t13_lattice3,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_lattice3 A B C) = (k10_lattice3 A C B)) ) ) ) ) ) ) ).
tt(t13_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k2_lattice2 (u1_struct_0 A) A (k5_setwiseo (u1_struct_0 A) B (k2_setwiseo (u1_struct_0 A) C)) D) = (k3_lattices A (k2_lattice2 (u1_struct_0 A) A B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t13_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_yellow_0 B (k1_lattice5 A)) &  ((v6_yellow_0 B (k1_lattice5 A)) & (m1_yellow_0 B (k1_lattice5 A))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) &  ((r2_hidden (k4_tarski F G) (k5_eqrel_1 A D E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m2_finseq_1 H A))  =>  (~  ( ((k3_finseq_1 H) = (k2_nat_1 C 2))  & (r1_lattice5 A H F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (~  ((r2_hidden D (u1_struct_0 B)) &  (~  (D = (k6_partfun1 A)) ) ) ) ) )  | (r1_xxreal_0 (k2_lattice5 A B) C)) ) ) ) ) ) ) ) ).
tt(t13_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_lattice6 B A) =>  ((r1_lattice6 A B (k4_lattice6 A B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice6 A B C) =>  (C = (k4_lattice6 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A)))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A))))))))) )  &  ((v23_waybel_0 B A (k2_yellow_1 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A))))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A))))) B C) = (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A C) (k3_lattice7 A))) ) ) ) ) ) ) ) ).
tt(t13_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (r1_relset_1 (k2_zfmisc_1 A A) (u1_struct_0 B) C (k2_lattice8 A B C D))) ) ) ) ) ) ) ) ).
tt(t13_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_lattices A (k4_lattices A (k3_lattices A B C) (k3_lattices A C D)) (k3_lattices A D B)) = (k3_lattices A (k3_lattices A (k4_lattices A B C) (k4_lattices A C D)) (k4_lattices A D B))) ) ) ) ) ) ) ) ) ).
tt(t13_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 C (k39_glib_000 B)) =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) = C) ) ) ) ) ) ) ) ).
tt(t13_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) &  ((v9_waybel_1 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) ) )  =>  ((v3_lattice3 (k5_yellow_1 A B)) & (v9_waybel_1 (k5_yellow_1 A B))) ) ) ) ) ) ).
tt(t13_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v4_relat_2 B) => (v4_lfuzzy_1 (k3_lfuzzy_1 B (k2_zfmisc_1 A A)) A)) ) ) ) ) ).
tt(t13_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v1_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v1_limfunc1 (k26_valued_1 k5_numbers k1_numbers A B))) )  &  ( ((v1_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v2_limfunc1 (k26_valued_1 k5_numbers k1_numbers A B))) )  &  ( (B = k6_numbers)  =>  ( ((k2_relset_1 k1_numbers (k26_valued_1 k5_numbers k1_numbers A B)) = (k1_tarski k6_numbers))  & (v3_funct_1 (k26_valued_1 k5_numbers k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t13_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  ((r2_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r2_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t13_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r3_limfunc3 B A) <=>  ((r3_limfunc2 B A) & (r6_limfunc2 B A)) ) ) ) ) ) ).
tt(t13_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc2 B A) &  ((v7_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t13_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = (u1_struct_0 B))  =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  ((k1_lmod_5 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(t13_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r2_hidden (k4_struct_0 B) C) & (v1_vectsp_4 C A B))  =>  (C = (k2_struct_0 (k1_mod_3 A B C))) ) ) ) ) ) ) ) ).
tt(t13_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k8_lmod_7 A B E C) = (k8_lmod_7 A B E D))  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k5_lopban_1 A B)) = (k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ).
tt(t13_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lopban_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_lopban_2 A))) =>  ( ((k1_algstr_0 (k7_lopban_2 A) B C) = (k1_algstr_0 (k7_lopban_2 A) C B))  &  ( ((k1_algstr_0 (k7_lopban_2 A) (k1_algstr_0 (k7_lopban_2 A) B C) D) = (k1_algstr_0 (k7_lopban_2 A) B (k1_algstr_0 (k7_lopban_2 A) C D)))  &  ( ((k1_algstr_0 (k7_lopban_2 A) B (k4_struct_0 (k7_lopban_2 A))) = B)  &  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_lopban_2 A))) &  ((k1_algstr_0 (k7_lopban_2 A) B E) = (k4_struct_0 (k7_lopban_2 A))) ) )  &  ( ((k6_algstr_0 (k7_lopban_2 A) (k6_algstr_0 (k7_lopban_2 A) B C) D) = (k6_algstr_0 (k7_lopban_2 A) B (k6_algstr_0 (k7_lopban_2 A) C D)))  &  ( ((k6_algstr_0 (k7_lopban_2 A) B (k5_struct_0 (k7_lopban_2 A))) = B)  &  ( ((k6_algstr_0 (k7_lopban_2 A) (k5_struct_0 (k7_lopban_2 A)) B) = B)  &  ( ((k6_algstr_0 (k7_lopban_2 A) B (k1_algstr_0 (k7_lopban_2 A) C D)) = (k1_algstr_0 (k7_lopban_2 A) (k6_algstr_0 (k7_lopban_2 A) B C) (k6_algstr_0 (k7_lopban_2 A) B D)))  &  ((k6_algstr_0 (k7_lopban_2 A) (k1_algstr_0 (k7_lopban_2 A) C D) B) = (k1_algstr_0 (k7_lopban_2 A) (k6_algstr_0 (k7_lopban_2 A) C B) (k6_algstr_0 (k7_lopban_2 A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) )  => (v2_lopban_3 B A)) ) ) ) ) ).
tt(t13_lopban_4,ax, ( (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k8_real_1 (k3_newton (k7_nat_d A 1)) A) = (k3_newton A)) ) ) )  &  (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 B A) =>  ((k8_real_1 (k3_newton (k7_nat_d A B)) (k9_real_1 (k2_nat_1 A 1) B)) = (k3_newton (k7_nat_d (k2_nat_1 A 1) B))) ) ) ) ) ) ) ).
tt(t13_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 E A B) &  ((v1_lopban_1 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 B)))) =>  ( (F = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E (k1_lopban_5 A C D)))  => (v1_convex1 F (k4_normsp_2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_subset_1 (k2_struct_0 A) (u1_struct_0 (k6_lopclset A)))) ) ).
tt(t13_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B (k2_lpspace1 A k1_numbers (k3_lpspace1 A) C D)) (k2_lpspace1 A k1_numbers (k3_lpspace1 A) (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B C) D))) ) ) ) ) ) ) ) ).
tt(t13_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] : (r2_relset_1 A k1_numbers (k56_valued_1 A k1_numbers (k2_partfun1 A k1_numbers B C)) (k2_partfun1 A k1_numbers (k56_valued_1 A k1_numbers B) C))) ) ) ) ) ).
tt(t13_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_normsp_0 B C) = k6_numbers)  =>  (C = (k4_struct_0 B)) )  &  ( ( (C = (k4_struct_0 B))  =>  ((k1_normsp_0 B C) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_normsp_0 B C)) &  ((r1_xxreal_0 (k1_normsp_0 B (k1_algstr_0 B C D)) (k7_real_1 (k1_normsp_0 B C) (k1_normsp_0 B D))) &  ((k1_normsp_0 B (k1_rlvect_1 B C E)) = (k8_real_1 (k18_complex1 E) (k1_normsp_0 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k9_ltlaxio1 A B))) = 1)  <=>  (~  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C E) A)) = 1)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F E) =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C F) B)) = 1) ) ) ) ) ) ) )  &  (~  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 C E) B)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden B (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A C B) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t13_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k4_xboolean k7_margrel1 A) = k7_margrel1) ) ) ).
tt(t13_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_tarski (k1_mathmorp A D B) (k1_mathmorp A E C)) <=> (r1_tarski (k1_mathmorp A (k5_algstr_0 A D E) B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r1_matrix10 B C) => (v1_matrix10 (k4_matrix10 A C B))) ) ) ) ) ) ) ).
tt(t13_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 (k1_nat_1 A 2))) =>  ( ((r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) E (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) D C)) & (v4_matrix_2 D (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))))  =>  ((k2_matrix11 A B E) = (k4_algstr_0 B (k2_matrix11 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ( (C = A)  |  ((v1_matrix_6 (k3_matrix12 B B D (k12_matrix_1 D B) A C E) B D) &  ((k5_matrix_6 B D (k3_matrix12 B B D (k12_matrix_1 D B) A C E)) = (k3_matrix12 B B D (k12_matrix_1 D B) A C (k4_algstr_0 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ( ( (D = (k3_finseq_5 (k1_finseq_2 A)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 A)) & (r2_hidden F (k2_finseq_1 A)))  =>  ((r1_xxreal_0 (k2_xcmplx_0 E F) (k1_nat_1 A 1)) |  ((k3_matrix_1 (u1_struct_0 B) C E F) = (k4_struct_0 B)) ) ) ) ) ) ) )  =>  ((v2_matrix_2 (k4_matrix11 A A (u1_struct_0 B) D C) A B) & (m1_matrix_1 (k4_matrix11 A A (u1_struct_0 B) D C) (u1_struct_0 B) A A)) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k12_fvsum_1 A B C (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ) ) ).
tt(t13_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (m1_vectsp_4 (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) (k6_domain_1 (u1_struct_0 B) (k3_rlvect_1 B D (k4_vectsp_1 A B F E))))) A (k1_vectsp_7 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  ( ((v1_matrix16 E (u1_struct_0 B)) & (v1_matrix16 F (u1_struct_0 B)))  => (v1_matrix16 (k3_matrix_6 A B (k2_matrix13 A A B E C) (k2_matrix13 A A B F D)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v5_matrix17 C (u1_struct_0 A)) =>  ((k1_matrix17 (u1_struct_0 A) (k9_fvsum_1 A C B)) = (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k1_matrix17 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(t13_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (m1_matrix_1 k1_xboole_0 B k1_xboole_0 A)) ) ) ) ).
tt(t13_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  &  (~  ((k4_matrix_1 A (k4_matrix_1 A B)) = B) ) ) ) ) ) ) ) ) ).
tt(t13_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k3_finseq_1 (k11_fvsum_1 A B C)) = (k6_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t13_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k1_matrix_4 A B (k1_matrix_4 A B C)) = C) ) ) ) ) ) ) ) ).
tt(t13_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k3_matrix_5 A A) = (k7_matrix_5 2 A)) ) ) ).
tt(t13_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) =>  ((r1_xxreal_0 A k6_numbers) |  ((k5_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C)) = (k5_matrix_1 A (u1_struct_0 B) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t13_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_finseq_1 (k1_matrix_3 A B C)) = B)  &  ((k4_finseq_1 (k1_matrix_3 A B C)) = (k2_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t13_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) &  ((v1_matrix_8 D A B) & (v1_matrix_6 C A B)) )  => (v1_matrix_8 (k4_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t13_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k12_matrix_3 2 A (k6_matrix_2 (u1_struct_0 A) B C D E)) = (k5_algstr_0 A (k8_group_1 A B E) (k8_group_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ((k3_finseq_1 (k5_matrix_5 A B)) = (k3_finseq_1 A))  &  ((k1_matrix_1 (k5_matrix_5 A B)) = (k1_matrix_1 A)) ) ) ) ) ) ).
tt(t13_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  ( ((k2_wsierp_1 (k10_matrixj1 A B)) = k1_xboole_0)  =>  ((k2_wsierp_1 (k11_matrixj1 A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t13_matrixj2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ((v2_matrixj2 C A B) <=>  (? [D:$i] :  ((v7_ordinal1 D) & (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C D) (k6_grcat_1 B B))) ) ) ) ) ) ) ) ) ).
tt(t13_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k8_rvsum_1 A (k8_rvsum_1 B C)) = (k4_rvsum_1 (k8_rvsum_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t13_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((k7_matrixr1 (k9_real_1 A B) C) = (k5_matrixr1 (k7_matrixr1 A C) (k7_matrixr1 B C))) ) ) ) ) ) ) ).
tt(t13_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ((k4_rlvect_1 C (k5_matrlin A C (k9_fvsum_1 A E B) D)) = (k4_vectsp_1 A C B (k4_rlvect_1 C (k5_matrlin A C E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((k3_finseq_1 C) = k6_numbers)  =>  ((k4_rlvect_1 B (k6_matrlin B C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t13_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~ (r2_hidden D (u1_struct_0 (k1_vectsp_7 A B C))))  => (v1_vectsp_7 (k4_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) <=>  ((r2_hidden A (k4_finseq_1 D)) & (r2_hidden B (k4_finseq_1 (k1_matrprob C D A)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrtop1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  & (r1_xxreal_0 (k3_finseq_1 D) (k3_finseq_1 E)))  =>  ((k15_finseq_1 (k5_relat_1 (k7_finseq_1 C E) (k8_relat_1 (k7_finseq_1 B D) A))) = (k7_finseq_1 (k15_finseq_1 (k5_relat_1 C (k8_relat_1 B A))) (k15_finseq_1 (k5_relat_1 E (k8_relat_1 D A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  => (m1_matrlin C k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k9_matrix13 k2_vectsp_1 B A C)))) ) ) ) ) ) ) ).
tt(t13_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k12_matrix_3 D k2_vectsp_1 (k2_matrtop3 D A B C)) = (k5_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v3_mazurulm D A B) & (v3_mazurulm E B C))  => (v3_mazurulm (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B (k5_pboole A C D)) <=>  ((r2_pboole A B (k2_pboole A C D)) & (r5_pboole A B (k3_pboole A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_zfmisc_1 B (k1_tarski C))) =>  ((r2_hidden (k1_xtuple_0 A) B) &  ((k2_xtuple_0 A) = C) ) ) ) ) ) ).
tt(t13_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_measure1 D A B C) =>  (! [E:$i] :  ((m1_measure1 E A B C) =>  ((m1_measure1 (k1_measure1 A B D E) A B C) &  ((m1_measure1 (k2_measure1 A B D E) A B C) & (m1_measure1 (k3_measure1 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_measure2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k1_funct_1 B k6_numbers) = k1_xboole_0)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k1_funct_1 B (k2_nat_1 C 1)) = (k6_subset_1 (k1_funct_1 A k6_numbers) (k1_funct_1 A C)))  & (r1_tarski (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 A C))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_tarski (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t13_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  => (r1_xxreal_0 (k19_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)) (k12_supinf_2 C (k2_measure2 A B (k1_measure3 A B D))))) ) ) ) ) ) ) ).
tt(t13_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  ((v1_funct_1 (k3_measure4 A B)) &  ((v1_funct_2 (k3_measure4 A B) (k1_measure4 A B) k7_numbers) &  ((v10_valued_0 (k3_measure4 A B)) &  ((v6_supinf_2 (k3_measure4 A B)) &  ((v2_measure1 (k3_measure4 A B) A (k1_measure4 A B)) & (m1_subset_1 (k3_measure4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_measure4 A B) k7_numbers)))) ) ) ) ) ) ) ) ).
tt(t13_measure5,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r1_xxreal_0 k1_supinf_2 (k2_measure5 A))) ) ).
tt(t13_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 C B) &  (A = (k3_xxreal_1 C B)) ) ) )  =>  (B = (k8_supinf_2 A)) ) ) ) ) ) ).
tt(t13_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ((m2_measure7 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k7_measure7 A B) C))) ) ) ) ) ) ).
tt(t13_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_xxreal_0 (k1_mesfunc9 (k6_measure8 A B C) (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) D))) (k19_supinf_2 (k1_partfun1 k5_numbers (k9_setfam_1 A) (k9_setfam_1 A) k7_numbers D (k6_measure8 A B C))))) ) ) ) ) ) ) ).
tt(t13_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((r1_tarski A B) <=> (r1_tarski (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(t13_membered,ax, (! [A:$i] :  ((v1_membered A) =>  ( (! [B:$i] :  ((v1_xcmplx_0 B) => (r2_hidden B A)) )  =>  (A = k2_numbers) ) ) ) ).
tt(t13_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  ((k9_xtuple_0 C) = (k4_subset_1 (u1_struct_0 B) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) (k8_struct_0 B))) ) ) ) ) ) ) ).
tt(t13_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = B) )  =>  ((r1_euclid_6 C A B) <=> (r2_hidden C (k4_euclid_4 2 A B))) ) ) ) ) ) ) ) ).
tt(t13_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  (! [F:$i] :  ((m1_subset_1 F B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k7_mesfunc5 A B C (k4_mesfunc1 A D E)) = (k3_supinf_2 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k7_mesfunc1 A E) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_tarski B (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers C D))) =>  ( ((k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers (k2_partfun1 A k2_numbers C B) (k2_partfun1 A k2_numbers D B))) = B)  & (r2_relset_1 A k2_numbers (k2_partfun1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers C D) B) (k2_valued_1 A k2_numbers k2_numbers (k2_partfun1 A k2_numbers C B) (k2_partfun1 A k2_numbers D B)))) ) ) ) ) ) ) ) ) ).
tt(t13_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k7_mesfun7c A B))) =>  ((k12_supinf_2 (k7_mesfun7c A B) C) = (k5_rinfsup2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ) ).
tt(t13_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_mesfunc8 B A k1_numbers) &  ((r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) & (r2_hidden C D)) )  =>  ((v2_comseq_2 (k3_series_1 (k10_seqfunc A B C))) <=> (v2_comseq_2 (k10_seqfunc A (k2_mesfun9c A B) C))) ) ) ) ) ) ) ) ) ).
tt(t13_mesfunc1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r1_xxreal_0 (k1_measure6 B) A)) ) )  =>  (A = k2_supinf_1) ) ) ) ).
tt(t13_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k2_mesfunc2 A B) C))) ) ) ) ) ) ).
tt(t13_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_prob_2 C) & (m2_finseq_1 C B))  =>  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  ( ((k3_tarski (k2_relset_1 B C)) = (k3_tarski (k2_relset_1 B D)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ( (~  ((k1_funct_1 D E) = k1_xboole_0) )  &  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden F (k4_finseq_1 C)) &  ((k1_funct_1 C F) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v2_mesfunc5 B) => (v4_mesfunc5 B)) ) ) ) ) ).
tt(t13_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski D (k1_relset_1 A C)) =>  ((r1_mesfunc6 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k8_subset_1 A D (k14_mesfunc1 C E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mesfunc7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k4_mesfunc7 k1_supinf_1 A) = k1_supinf_1) ) ) ) ).
tt(t13_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) =>  ((v10_mesfunc5 (k3_mesfunc5 A B C)) <=>  ((k12_supinf_2 (k6_mesfunc8 A B) C) = (k12_supinf_2 (k5_mesfunc8 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t13_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (D = (k1_relset_1 A E))  &  ((r1_mesfunc1 A B E D) & (v6_supinf_2 E)) )  =>  ( ((k12_supinf_2 C (k9_subset_1 A D (k19_mesfunc1 A E k1_supinf_1))) = k6_numbers)  |  ((k7_mesfunc5 A B C E) = k1_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k11_metric_1 B C A)) <=>  ( (~ (v2_struct_0 B))  &  ((k2_metric_1 B C D) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_metric_2 A B) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t13_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) => (r1_xxreal_0 (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) C E) (k7_real_1 (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) C D) (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k10_metric_3 A B) D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v2_tbsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_metric_6 A B C) &  ((k1_tbsp_1 A B) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_metrizts,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  (~  ((v1_tops_2 C B) &  ((m1_setfam_1 C (u1_struct_0 B)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  (~  ((r1_tarski D C) &  ((m1_setfam_1 D (u1_struct_0 B)) & (r1_ordinal1 (k1_card_1 D) A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v4_pre_topc C B) & (v2_tex_2 C B))  => (r1_ordinal1 (k1_card_1 C) A)) ) ) ) ) ) ) ) ).
tt(t13_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v2_mfold_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_connsp_2 D B C) & (r1_metrizts B (k15_euclid A) D (k2_struct_0 (k15_euclid A)))) ) ) ) ) ) ) ) ) ).
tt(t13_mfold_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 (k14_rvsum_1 A B))) =>  ( ((k1_seq_1 (k14_rvsum_1 A B) C) = (k11_binop_2 (k7_partfun1 k1_numbers A C) (k7_partfun1 k1_numbers B C)))  &  ((k7_partfun1 k1_numbers (k14_rvsum_1 A B) C) = (k11_binop_2 (k7_partfun1 k1_numbers A C) (k7_partfun1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t13_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_midsp_1 A B C D D) =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t13_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B))))) )  =>  ( ((r1_midsp_2 (u1_struct_0 A) B C) & (v1_midsp_2 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((k1_midsp_1 A D E) = (k1_midsp_1 A F G))  <=>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C D G) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_midsp_1 C) & (l1_midsp_3 C (k2_nat_1 A 2))) )  =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (u1_midsp_2 C D))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  ( (! [G:$i] :  ((m1_midsp_3 G A) =>  ( (G = B)  =>  ((k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) F B E) G) = E) ) ) )  &  (! [G:$i] :  ((m1_midsp_3 G A) =>  (! [H:$i] :  ((m1_midsp_3 H A) =>  ( (~  (G = H) )  =>  ((k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) F H E) G) = (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 F G) &  ((r1_tarski B C) & (r1_relset_1 A A D E)) )  => (r1_tarski (k12_mmlquery A B D G) (k12_mmlquery A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_mod_2 E A B C) =>  (! [F:$i] :  ((m1_mod_2 F A D B) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ( (E = (g1_mod_2 A B C G))  &  (F = (g1_mod_2 A D B H)) )  =>  ( ((k9_mod_2 A D B C E F) = (g1_mod_2 A D C (k1_partfun1 (u1_struct_0 D) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) H G)))  &  ((k8_mod_2 A E F) = (g1_mod_2 A D C (k1_partfun1 (u1_struct_0 D) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (m1_vectsp_4 (k1_mod_3 A B (k9_subset_1 (u1_struct_0 B) C D)) A (k2_vectsp_5 A B (k1_mod_3 A B C) (k1_mod_3 A B D)))) ) ) ) ) ) ) ) ).
tt(t13_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_vectsp_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ( ( (D = (k3_mod_4 A C))  &  ( (E = G)  &  (F = H) ) )  =>  ((k1_algstr_0 D G H) = (k1_algstr_0 C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) =>  (! [D:$i] :  ((m1_trees_1 D (k5_trees_1 A C B)) =>  (! [E:$i] :  ((m1_trees_1 E A) =>  ( ( (D = E)  & (r2_xboole_0 E C))  =>  ((k1_trees_2 (k5_trees_1 A C B) D) = (k1_trees_2 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k2_lattices (k48_modelc_1 A B D) E F)) <=>  ((r3_modelc_1 A B D C E) & (r3_modelc_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_modelc_2 A (k3_modelc_2 B)) <=>  (A = B) ) ) ) ) ) ).
tt(t13_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((k18_modelc_3 A (k7_modelc_3 A)) = k6_numbers) ) ) ).
tt(t13_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ((r1_nat_d B A) =>  ((a_2_0_moebius1 A B) = (a_2_1_moebius1 A B)) ) ) ) ) ) ).
tt(t13_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v16_monoid_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  |  ((k6_algstr_0 A C B) = (k6_algstr_0 A D B)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v8_monoid_0 C B) => (v8_monoid_0 (k8_monoid_1 B B B C A) (k9_funct_2 A B))) ) ) ) ) ) ).
tt(t13_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_morph_01 A C (k5_setfam_1 (u1_struct_0 A) B)) = (k3_tarski (a_3_6_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t13_msafree3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((l1_msualg_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 C))) ) )  =>  (! [E:$i] :  ((r2_hidden E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  ((r2_hidden A (k1_funct_1 (k3_msafree3 C D (k4_trees_4 (k4_tarski B (u1_struct_0 C)) F)) E)) <=>  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v3_trees_2 G)) )  &  ((r2_hidden G (k10_xtuple_0 F)) & (r2_hidden A (k1_funct_1 (k3_msafree3 C D G) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_msafree A B C) = (a_3_1_msafree A B C)) ) ) ) ) ) ) ).
tt(t13_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k1_msaterm A B) = (k3_card_3 (k8_msafree A B))) ) ) ) ) ).
tt(t13_msscyc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_graph_1 C)) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m1_graph_1 D C))  =>  (! [E:$i] :  ( ((v7_graph_1 E C) & (m1_graph_1 E C))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k3_finseq_1 D)) &  (E = (k1_graph_2 D A B)) ) ) )  =>  ((k7_graph_2 C E) = (k2_graph_2 (u1_struct_0 C) (k7_graph_2 C D) A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) & (v1_funcop_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A B) &  (D = (k1_funct_1 C A)) )  =>  ((k1_funct_1 (k3_funct_6 C) A) = (k10_xtuple_0 D)) ) ) ) ) ) ) ) ).
tt(t13_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_msualg_2 (k9_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) => (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ).
tt(t13_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r2_hidden D (k5_msualg_2 A B C)) <=>  ((v3_msualg_2 D A B) &  ((r2_pboole (u1_struct_0 A) (k2_msualg_2 A B) D) & (r2_pboole (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r4_msualg_3 A B C D) <=>  ((r1_msualg_3 A B C D) &  ((v2_msualg_3 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) & (v1_msualg_3 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [F:$i] :  ( ((v2_msualg_4 F A B) & (m1_msualg_4 F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r8_pboole (u1_struct_0 A) F (k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) D E)) =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v1_funct_1 J) & (v1_finseq_1 J)) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v1_funct_1 K) & (v1_finseq_1 K)) )  =>  (! [L:$i] :  ( ((v1_relat_1 L) &  ((v1_funct_1 L) & (v1_finseq_1 L)) )  =>  ( ( ((k3_finseq_1 J) = I)  &  ( ((k3_finseq_1 J) = (k3_finseq_1 K))  &  ( (! [M:$i] :  ((m1_subset_1 M k5_numbers) =>  ((r2_hidden M (k4_finseq_1 J)) => (r2_hidden (k4_tarski (k1_funct_1 J M) (k1_funct_1 K M)) (k2_msualg_4 A B F (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) M)))) ) )  &  ((r2_hidden (k4_tarski (k1_funct_1 (k5_msualg_1 A C B) (k7_finseq_1 (k7_finseq_1 J (k9_finseq_1 G)) L)) (k1_funct_1 (k5_msualg_1 A C B) (k7_finseq_1 (k7_finseq_1 K (k9_finseq_1 G)) L))) (k2_msualg_4 A B F (k2_msualg_1 A C))) & (r2_hidden (k4_tarski G H) (k2_msualg_4 A B F (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) (k2_nat_1 I 1))))) ) ) )  =>  (! [M:$i] :  ((m1_subset_1 M (k3_msualg_1 A C B)) =>  ( (M = (k7_finseq_1 (k7_finseq_1 J (k9_finseq_1 G)) L))  => (r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) M) (k1_funct_1 (k5_msualg_1 A C B) (k7_finseq_1 (k7_finseq_1 K (k9_finseq_1 H)) L))) (k2_msualg_4 A B F (k2_msualg_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (~  ((r2_hidden (k4_tarski B C) (k3_msualg_6 A)) &  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (~ (r1_msualg_6 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ((r4_lattice3 A D C) <=> (r4_lattice3 B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B))))) => (r8_pboole (u1_struct_0 A) (k1_msualg_8 A B (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C)) (k2_msualg_8 A B C))) ) ) ) ) ) ).
tt(t13_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  ( (! [E:$i] :  ((k1_funct_1 (k12_card_3 (u3_msualg_1 A B) E) C) = (k1_funct_1 (k12_card_3 (u3_msualg_1 A B) E) D)) )  => (r8_pboole (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(t13_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k6_msualg_1 A))) => (m5_margrel1 (k5_msualg_1 (k6_msualg_1 A) B (k9_msualg_1 A)) (u1_struct_0 A) (k1_unialg_2 A))) ) ) ) ).
tt(t13_mycielsk,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  => (r1_xxreal_0 (k2_mycielsk A) (k5_card_1 (u1_struct_0 A)))) ) ).
tt(t13_nagata_1,ax, (! [A:$i] :  ( (~ (v4_card_3 A))  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k1_compts_1 (k2_zfmisc_1 A A)))))) &  ((v1_pcomps_1 B (k1_compts_1 (k2_zfmisc_1 A A))) &  (~ (v4_nagata_1 B (k1_compts_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(t13_nagata_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 A) B)) (k8_nat_1 k1_numbers (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B))) ) ) ) ).
tt(t13_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k1_nat_1 B 1) A))  <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t13_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 1 (k3_nat_d B A))) ) ) ) ) ) ).
tt(t13_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ((k2_nat_3 (k8_finseq_1 k1_numbers C (k3_pre_poly k1_numbers B)) A) = (k8_finseq_1 k1_numbers (k2_nat_3 C A) (k2_nat_3 (k3_pre_poly k1_numbers B) A))) ) ) ) ) ) ) ).
tt(t13_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_nat_d A B) &  ( (~ (r1_xxreal_0 A 1))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_nat_d C B) &  ((r1_xxreal_0 C A) & (v1_int_2 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_nat_5,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) => (m2_finseq_1 A k1_numbers)) ) ).
tt(t13_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_nat_d (k3_xcmplx_0 A B) A) = k6_numbers) ) ) ) ) ).
tt(t13_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k1_lattices k10_nat_lat A B) = (k5_nat_d (k11_nat_lat A) (k11_nat_lat B))) ) ) ) ) ).
tt(t13_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k2_cat_1 B D E) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 B E F) = k1_xboole_0) )  &  (~  (! [G:$i] :  ((m1_cat_1 G B D E) =>  (! [H:$i] :  ((m1_cat_1 H B E F) =>  ((k9_cat_3 B D F A C (k5_cat_1 B D E F G H)) = (k5_cat_1 A (k8_cat_1 B A C D) (k8_cat_1 B A C E) (k8_cat_1 B A C F) (k9_cat_3 B D E A C G) (k9_cat_3 B E F A C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_ncfcont1 A B C) <=>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k1_relset_1 (u1_struct_0 A) B)) &  ( (~ (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A F C))))  & (r1_xxreal_0 D (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers B F) (k7_partfun1 k2_numbers B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_ncfcont2 A B C D) => (r1_ncfcont2 A B C (k5_vfunct_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ).
tt(t13_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_comseq_2 B) & (v3_normsp_1 C A))  => (v3_normsp_1 (k1_ndiff_1 A C B) A)) ) ) ) ) ) ) ).
tt(t13_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v7_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r1_ndiff_1 A B E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D)))))  =>  ((r1_ndiff_1 B D F (k7_partfun1 (u1_struct_0 B) E C)) =>  ((r1_ndiff_1 A D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 D) E F) C) &  ((k3_ndiff_1 A D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 D) E F) C) = (k2_ndiff_2 A B D (k3_ndiff_1 A B E C) (k3_ndiff_1 B D F (k7_partfun1 (u1_struct_0 B) E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_rcomp_1 D C) =>  ( ((r1_ndiff_3 A B C) & (r1_tarski D (k1_relset_1 k1_numbers B)))  =>  (! [E:$i] :  ( ((v2_relat_1 E) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) &  ((v1_fdiff_1 E k6_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v3_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers F) = (k1_tarski C))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers E F)) D))  =>  ((v3_normsp_1 (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers E F) B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers F B)) (k37_valued_1 k5_numbers k1_numbers E)) A) &  ((k1_ndiff_3 A B C) = (k6_normsp_1 A (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers E F) B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers F B)) (k37_valued_1 k5_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers D)) & (r2_ndiff_4 B D C))  =>  ((r2_ndiff_4 B (k9_integr15 B A k1_numbers D) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_funct_1 (k2_ndiff_4 B (k9_integr15 B A k1_numbers D) C) E) = (k9_euclid B (k1_ndiff_4 B D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  ( (B = E)  =>  ( ((k1_rlvect_1 (k14_prvect_2 A) B C) = D)  <=>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k4_finseq_1 A)) =>  ((k1_ndiff_5 A D F) = (k1_rlvect_1 (k3_prvect_2 A F) (k1_ndiff_5 A E F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) => (r1_xboole_0 (k6_partfun1 (u1_struct_0 A)) (u1_orders_2 (k3_necklace A)))) ) ).
tt(t13_necklace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  ( ((r3_necklace A B) & (r3_necklace B C))  => (r3_necklace A C)) ) ) ) ) ) ) ).
tt(t13_net_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_net_1 B) & (l1_petri B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_net_1 B)) =>  ((r2_hidden C (u4_struct_0 B)) =>  ((r2_hidden A (k3_net_1 B C)) <=> (r1_net_1 B C A)) ) ) ) ) ) ) ).
tt(t13_newton,ax, ((k3_newton 1) = 1) ).
tt(t13_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k4_vfunct_1 (u1_struct_0 A) B C E)) (k5_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))  => (r1_nfcont_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t13_nfcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ((r1_nfcont_3 C D B) => (r1_nfcont_3 C (k4_vfunct_1 k1_numbers C D A) B)) ) ) ) ) ) ) ) ) ).
tt(t13_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( (? [D:$i] :  ((m1_rcomp_1 D B) &  ((k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) D) = (k1_tarski B)) ) )  => (r1_nfcont_4 A C B)) ) ) ) ) ) ) ).
tt(t13_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ((k1_normform A B (k3_normform A B C D) D) = (k1_normform A B C D)) ) ) ) ) ) ) ) ) ).
tt(t13_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  &  ((k10_xtuple_0 C) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ) ) ).
tt(t13_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_normsp_2 A)) B C) =>  ((v2_frechet C (k3_normsp_2 A)) <=> (v3_normsp_1 B A)) ) ) ) ) ) ) ) ).
tt(t13_ntalgo_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  ( ((k3_finseq_1 A) = 1)  =>  ((k19_rvsum_1 A) = (k1_funct_1 A 1)) ) ) ) ).
tt(t13_numbers,ax,(r1_tarski k3_numbers k2_numbers)).
tt(t13_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k9_openlatt A)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k1_funct_1 (k8_openlatt A) C)) ) ) ) ) ) ) ).
tt(t13_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_oposet_1 A) & (l2_qmax_1 A)) )  =>  ((v5_orders_2 A) => (v6_oposet_1 A)) ) ) ).
tt(t13_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_oppcat_1 A))) =>  ( (~  ((k2_cat_1 (k2_oppcat_1 A) B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) B C) =>  ( ((k4_oppcat_1 A (k3_graph_1 (k2_oppcat_1 A) D)) = (k4_graph_1 A (k6_oppcat_1 A D)))  &  ((k4_oppcat_1 A (k4_graph_1 (k2_oppcat_1 A) D)) = (k3_graph_1 A (k6_oppcat_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) =>  ( ((k1_relset_1 A B) = A)  &  ((k1_relat_1 B) = A) ) ) ) ) ) ).
tt(t13_orders_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_wellord1 (u1_orders_2 A) B) =>  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t13_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) => (v3_ordinal1 A)) ) ) ) ).
tt(t13_ordinal2,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v3_ordinal1 B)) )  => (v3_ordinal1 (k1_setfam_1 A))) ) ).
tt(t13_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k3_xboole_0 A B) = A)  |  ((k3_xboole_0 A B) = B) ) ) ) ) ) ).
tt(t13_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (~  ((v2_ordinal2 A) &  ((v2_ordinal2 B) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  (~  ( (C = (k3_relat_1 B A))  & (v2_ordinal2 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal5 A k6_numbers) = 1) ) ) ).
tt(t13_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((v2_ordinal5 B) => (v2_ordinal5 (k5_relat_1 B A))) ) ) ) ) ).
tt(t13_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t13_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_ortsp_1 A B D C (k3_rlvect_1 B E F)) = (k3_rlvect_1 A (k1_ortsp_1 A B D C E) (k1_ortsp_1 A B D C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((r2_hidden D (k3_msualg_1 A C (k8_osafree A B))) <=>  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) & (r1_lang1 (k2_osafree A B) (k9_osafree A B C) (k14_trees_3 D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( ((r3_osalg_1 A C B E) & (r3_osalg_1 A C D E))  =>  (B = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  => (m2_osalg_2 (k3_osalg_2 A B) A C)) ) ) ) ) ) ).
tt(t13_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((v1_osalg_3 D A) & (r1_msualg_3 A B C D))  =>  ((v12_osalg_1 (k6_msualg_3 A B C D) A) &  ((v12_osalg_1 (k6_msualg_3 A B C D) A) &  ((v13_osalg_1 (k6_msualg_3 A B C D) A) & (l3_msualg_1 (k6_msualg_3 A B C D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_osalg_4 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r3_orders_2 A D E) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ( (G = F)  =>  ((k8_osalg_4 A B C D F) = (k8_osalg_4 A B C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  => (v2_aff_2 (k2_diraf B))) ) ) ) ) ).
tt(t13_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) => (r1_parsp_1 (k9_parsp_1 A) B C C B)) ) ) ) ) ) ).
tt(t13_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) &  ((r1_parsp_2 A B C E) & (r1_parsp_2 A B C F)) )  =>  ( (B = C)  | (r1_parsp_2 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k6_relset_1 A B C D)) & (m1_subset_1 (k6_relset_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ).
tt(t13_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden C (k2_relset_1 B D)) =>  ( (C = (k7_partfun1 B D (k7_partfun1 A (k2_partfun2 A B D) C)))  &  (C = (k7_partfun1 B (k1_partfun1 B A A B (k2_partfun2 A B D) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ((k2_partit1 A B B) = B) ) ) ) ) ).
tt(t13_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r1_bvfunc_1 A B C) => (r1_bvfunc_1 A (k7_bvfunc_2 A B D E) (k7_bvfunc_2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B E) &  ((r2_analoaf A B D B F) & (r2_diraf A C D E F)) )  =>  ((r3_diraf A B C D) | (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A C D))  => (r2_pboole A B D)) ) ) ) ) ) ) ) ).
tt(t13_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))  =>  ((k1_pcomps_1 A C) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_pre_topc A B))) ) ) ) ) ) ) ) ).
tt(t13_pcs_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v16_pcs_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_pcs_0 A B))) =>  ((r1_pcs_0 (k17_pcs_0 A B) C D) <=>  (? [E:$i] :  ((m1_subset_1 E A) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_pcs_0 A B E))) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_pcs_0 A B E))) &  ( (F = C)  &  ( (G = D)  & (r1_pcs_0 (k15_pcs_0 A B E) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( ( (C = (k3_pdiff_1 A D))  &  (E = F) )  =>  ((k2_pdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B F) D)) = (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k7_pdiff_1 A B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r3_pdiff_1 2 1 D C))  =>  ((k11_pdiff_1 2 1 D C) = (k1_fdiff_1 (k1_pdiff_2 2 1 D C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r1_pdiff_3 B A) =>  ((k2_pdiff_3 B A) = (k11_pdiff_1 2 1 (k1_pdiff_3 1 2 B) A)) ) ) ) ) ) ).
tt(t13_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 1 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F C) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 A B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 A B) I) (k1_seq_1 (k1_pdiff_2 3 1 A B) C)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I C)) (k1_seq_1 H (k9_real_1 I C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r4_pdiff_5 E D))  =>  ((k4_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 E) D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) )  =>  ((r1_funct_2 (k1_euclid A) (k1_euclid B) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C D) =>  ((v2_pdiff_6 C B A) <=> (v1_lopban_1 D (k4_real_ns1 A) (k4_real_ns1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D (k5_euclid A)) (k9_binop_2 B C)) = (k7_euclid A (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D (k5_euclid A)) B) (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D (k5_euclid A)) C))) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  ( ( (E = (k3_relat_1 C (k4_pdiff_1 D B)))  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B)) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) E) (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((r1_pdiff_6 C B A D) => (v1_pdiff_7 C A)) ) ) ) ) ) ) ) ) ).
tt(t13_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((r1_ordinal1 2 (k1_card_1 (k4_card_3 B))) <=>  ((v2_relat_1 B) &  (~ (v13_pencil_1 B)) ) ) ) ) ) ) ).
tt(t13_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) &  ((v1_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A A) & (m1_subset_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t13_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_pencil_1 A B C))) =>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  ( (~  (C = (k3_pencil_1 A E)) )  =>  ( (~ (v13_pencil_1 (k2_funct_7 E C (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B C)) D))))  &  ((v16_pencil_1 (k2_funct_7 E C (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B C)) D)) A) & (m3_pboole (k2_funct_7 E C (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B C)) D)) A (k12_pralg_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~ (r1_struct_0 C D))  =>  ((k1_vectsp_9 A (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) D)))) = (k1_nat_1 (k1_vectsp_9 A C) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t13_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k4_nat_d (k3_square_1 A) (k1_nat_1 A 1)) = 1) ) ) ) ).
tt(t13_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ((k11_petri (k11_petri A)) = (g1_petri (u1_struct_0 A) (u4_struct_0 A) (u1_petri A) (u2_petri A))) ) ) ).
tt(t13_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A C D))  => (r2_pnproc_1 A B D)) ) ) ) ) ) ) ) ).
tt(t13_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) =>  (! [C:$i] :  ((l1_polyalg1 C A) =>  ( ((m1_polyalg1 B A C) & (m1_polyalg1 C A B))  =>  ((g1_polyalg1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_algstr_0 B) (u2_struct_0 B) (u3_struct_0 B) (u1_vectsp_1 A B)) = (g1_polyalg1 A (u1_struct_0 C) (u1_algstr_0 C) (u2_algstr_0 C) (u2_struct_0 C) (u3_struct_0 C) (u1_vectsp_1 A C))) ) ) ) ) ) ) ) ).
tt(t13_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( (! [H:$i] :  ((v1_xreal_0 H) =>  ((k7_polyeq_1 A B C D H) = (k9_polyeq_1 A H E F G)) ) )  =>  ( (A = k6_numbers)  |  ( ((k7_xcmplx_0 B A) = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 E F) G)))  &  ( ((k7_xcmplx_0 C A) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 E F) (k3_xcmplx_0 F G)) (k3_xcmplx_0 E G)))  &  ((k7_xcmplx_0 D A) = (k4_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 E F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((k2_xcmplx_0 (k1_newton D 4) (k1_newton A 4)) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 B A) D) (k2_xcmplx_0 (k3_square_1 D) (k3_square_1 A)))) ) )  =>  ( (A = k6_numbers)  |  ((k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k1_newton C 4) (k3_xcmplx_0 B (k1_newton C 3))) (k3_xcmplx_0 B C)) 1) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t13_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ( ( ((k4_complex1 D) = k6_numbers)  &  ((k7_polyeq_1 A k6_numbers B C D) = k6_numbers) )  =>  ( (A = k6_numbers)  |  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( ((k3_complex1 D) = (k9_binop_2 E F))  &  ( ((k9_binop_2 (k11_binop_2 (k11_binop_2 3 F) E) (k12_binop_2 B A)) = k6_numbers)  &  ( (~  (D = (k9_binop_2 (k2_power 3 (k9_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))) (k2_power 3 (k10_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))))) )  &  ( (~  (D = (k9_binop_2 (k2_power 3 (k9_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))) (k2_power 3 (k9_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))))) )  &  (~  (D = (k9_binop_2 (k2_power 3 (k10_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))) (k2_power 3 (k10_binop_2 (k7_binop_2 (k12_binop_2 C (k11_binop_2 2 A))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 C) (k11_binop_2 4 (k5_square_1 A))) (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_polyeq_4 A B C C B A D) = k6_numbers)  =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 5 (k5_square_1 A))) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)) k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (E = (k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) (k6_square_1 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 5 (k5_square_1 A))) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)))) (k3_xcmplx_0 2 A)))  &  ( (F = (k7_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) (k6_square_1 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k5_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 5 (k5_square_1 A))) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)))) (k3_xcmplx_0 2 A)))  &  ( (~  (D = (k4_xcmplx_0 1)) )  &  ( (~  (D = (k7_xcmplx_0 (k2_xcmplx_0 E (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 E) 1))) 2)) )  &  ( (~  (D = (k7_xcmplx_0 (k2_xcmplx_0 F (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 F) 1))) 2)) )  &  ( (~  (D = (k7_xcmplx_0 (k6_xcmplx_0 E (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 E) 1))) 2)) )  &  (~  (D = (k7_xcmplx_0 (k6_xcmplx_0 F (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 F) 1))) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( ( (A = (k6_xcmplx_0 E (k13_complex1 B 3)))  &  ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 C) (k1_newton B 2)) 9))  &  (G = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 B) C) (k3_xcmplx_0 2 (k1_newton B 3))) (k3_xcmplx_0 27 D)) 54)) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  ((k6_xcmplx_0 (k2_xcmplx_0 (k1_newton E 3) (k3_xcmplx_0 (k3_xcmplx_0 3 F) E)) (k3_xcmplx_0 2 G)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polyform,ax, ((k2_polyform (k4_xcmplx_0 1) 2) = 1) ).
tt(t13_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k1_polynom1 A C B)) = (k6_algstr_0 A (k4_rlvect_1 A C) B)) ) ) ) ) ) ) ).
tt(t13_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r3_orders_1 (k1_yellow_1 A) (k1_polynom2 A B))) ) ) ) ).
tt(t13_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_funct_1 (k6_polynom3 2 A) 1) = (k2_polynom3 k5_numbers k6_numbers A)) ) ) ).
tt(t13_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_polynom4 A (k9_polynom3 A)) (k9_polynom3 A))) ) ).
tt(t13_polynom5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k1_polynom5 (k8_finseq_1 (u1_struct_0 k1_complfld) A (k12_finseq_1 (u1_struct_0 k1_complfld) B))) = (k8_finseq_1 k1_numbers (k1_polynom5 A) (k12_finseq_1 k1_numbers (k17_complex1 B))))  &  ((k1_polynom5 (k8_finseq_1 (u1_struct_0 k1_complfld) (k12_finseq_1 (u1_struct_0 k1_complfld) B) A)) = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers (k17_complex1 B)) (k1_polynom5 A))) ) ) ) ) ) ).
tt(t13_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly A) (k15_pre_poly A)) =>  (! [E:$i] :  ((m2_subset_1 E (k14_pre_poly A) (k15_pre_poly A)) =>  (! [F:$i] :  ((m2_subset_1 F (k14_pre_poly B) (k15_pre_poly B)) =>  (! [G:$i] :  ((m2_subset_1 G (k14_pre_poly B) (k15_pre_poly B)) =>  (! [H:$i] :  ((m2_subset_1 H (k14_pre_poly B) (k15_pre_poly B)) =>  ( ((r6_pboole A E (k12_pre_poly A D C)) & (r6_pboole B H (k12_pre_poly B G F)))  => (r6_pboole (k10_ordinal2 A B) (k12_pre_poly (k10_ordinal2 A B) (k1_polynom6 A B D G) (k1_polynom6 A B C F)) (k1_polynom6 A B E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k1_polynom7 A B C D) E) = (k6_algstr_0 B C (k3_polynom2 A D B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_polynom8 A B k6_numbers) = (k5_struct_0 A)) ) ) ) ) ).
tt(t13_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_struct_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 D))))) )  =>  ((k3_polynom1 A D (k1_polyred A B D E) (k11_pre_poly A C B)) = (k3_polynom1 A D E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 1 C)) )  |  ( (~  (B = k6_numbers) )  &  (~ (v1_abian C)) ) )  =>  ((k1_power C (k13_complex1 A B)) = (k13_complex1 (k1_power C A) (k1_power C B))) ) ) ) ) ) ) ) ).
tt(t13_pralg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  (! [G:$i] :  ((r2_hidden G (k1_relset_1 k5_numbers (k1_msualg_1 A B))) =>  ((k1_funct_1 (k5_msualg_3 A C D B E F) G) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D) E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) G)) (k1_funct_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v6_trees_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)) => (r2_hidden (k12_finseq_1 k5_numbers B) (k11_trees_3 (k2_funct_6 A)))) ) ) ) ) ).
tt(t13_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_int_1 (k6_power 2 (k4_nat_1 2 A))) = (k1_int_1 (k6_power 2 (k2_nat_1 (k4_nat_1 2 A) 1)))) ) ) ) ).
tt(t13_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) (k2_prelamb A C (k1_prelamb A B C))) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) (k1_prelamb A (k2_prelamb A C B) C))) ) ) ) ) ) ) ).
tt(t13_pre_poly,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  =>  (B = (k7_finseq_1 (k2_finseq_3 (k3_finseq_1 B) B) (k9_finseq_1 (k1_funct_1 B (k3_finseq_1 B))))) ) ) ) ) ) ).
tt(t13_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ((r1_xxreal_0 2 B) & (r1_xxreal_0 (k1_newton A B) A)) ) ) ) ) ) ) ).
tt(t13_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v4_pre_topc C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v4_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 B) D (k2_struct_0 B)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_prob_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r2_hidden B (k3_prob_1 A C)) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_hidden B (k8_nat_1 (k9_setfam_1 A) C D))) ) ) ) ) ) ) ).
tt(t13_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_xxreal_0 (k1_seq_1 E (k5_prob_1 A B C D)) (k1_seq_1 E D)) & (r1_xxreal_0 (k1_seq_1 E (k5_prob_1 A B C D)) (k1_seq_1 E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((r2_hidden C (k1_funct_1 (k2_prob_3 B D) A)) <=>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r1_xxreal_0 E A) & (r2_hidden C (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t13_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B (k6_cqc_lang A B)) C) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t13_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_projdes1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((r5_projpl_1 A B C D E) =>  ((r5_projpl_1 A B D C E) &  ((r5_projpl_1 A C B D E) &  ((r5_projpl_1 A C D B E) &  ((r5_projpl_1 A D B C E) &  ((r5_projpl_1 A D C B E) &  ((r5_projpl_1 A B C E D) &  ((r5_projpl_1 A B D E C) &  ((r5_projpl_1 A C B E D) &  ((r5_projpl_1 A C D E B) &  ((r5_projpl_1 A D B E C) &  ((r5_projpl_1 A D C E B) &  ((r5_projpl_1 A B E C D) &  ((r5_projpl_1 A B E D C) &  ((r5_projpl_1 A C E B D) &  ((r5_projpl_1 A C E D B) &  ((r5_projpl_1 A D E B C) &  ((r5_projpl_1 A D E C B) &  ((r5_projpl_1 A E B C D) &  ((r5_projpl_1 A E B D C) &  ((r5_projpl_1 A E C B D) &  ((r5_projpl_1 A E C D B) &  ((r5_projpl_1 A E D B C) & (r5_projpl_1 A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  ((r1_incsp_1 A C B) &  ((r1_incsp_1 A D B) &  ((r1_incsp_1 A E B) &  ((r1_incsp_1 A F B) & (r2_zfmisc_1 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  ((r1_incsp_1 A C B) &  ((r1_incsp_1 A D B) &  ((r1_incsp_1 A E B) &  ((r1_incsp_1 A F B) & (r2_zfmisc_1 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A B E))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A C F))  &  ((r1_projred2 A D E F) &  ( (~  (D = F) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A G D))  &  ( (~ (r1_incsp_1 A G F))  &  ((k3_relat_1 (k1_projred1 A D E B) (k1_projred1 A E F C)) = (k1_projred1 A D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_card_3 A) (k4_card_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 A) (k4_card_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (k4_card_3 A)) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 A)) =>  ((k8_prvect_1 A (k3_funct_2 (k4_card_3 A) (k4_card_3 A) B D) E) = (k8_prvect_1 A (k3_funct_2 (k4_card_3 A) (k4_card_3 A) C D) E)) ) ) ) )  => (r2_funct_2 (k4_card_3 A) (k4_card_3 A) B C)) ) ) ) ) ) ) ).
tt(t13_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k14_prvect_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k14_prvect_2 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  ( ( (C = D)  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 A)) =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 (k11_prvect_2 A E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k11_prvect_2 A E)))))) )  &  ((v3_normsp_1 F (k11_prvect_2 A E)) &  ( ((k1_funct_1 D E) = (k6_normsp_1 (k11_prvect_2 A E) F))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m1_subset_1 H (k4_card_3 (k4_prvect_2 A))) &  ( (H = (k1_normsp_1 (k14_prvect_2 A) B G))  &  ((k1_normsp_1 (k11_prvect_2 A E) F G) = (k1_funct_1 H E)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_normsp_1 B (k14_prvect_2 A)) &  ((k6_normsp_1 (k14_prvect_2 A) B) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_prvect_2 B)) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k10_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k10_prvect_2 B))) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( (D = F)  &  ( (E = G)  &  ((k1_binop_1 C D E) = (k7_finseq_1 F G)) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)))) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C (k3_rlvect_1 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)) D E)) = (k3_rlvect_1 (k10_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C D) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C (k1_rlvect_1 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)) D E)) = (k1_rlvect_1 (k10_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C D) E)) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B))) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A B))) C (k4_struct_0 (k5_prvect_3 (k10_prvect_2 A) (k10_prvect_2 B)))) = (k4_struct_0 (k10_prvect_2 (k7_finseq_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_pscomp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ( ((v1_pscomp_1 B A) & (v2_measure6 C))  => (v2_tops_2 (k7_relset_1 (k9_setfam_1 k1_numbers) (k9_setfam_1 (u1_struct_0 A)) (k3_measure6 (u1_struct_0 A) k1_numbers B) C) A)) ) ) ) ) ) ) ).
tt(t13_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k10_eqrel_1 A)) =>  (? [C:$i] :  ((m2_finseq_1 C A) &  ((k4_card_3 B) = (k1_tarski C)) ) ) ) ) ) ).
tt(t13_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 2))  &  (! [B:$i] :  ((m1_pythtrip B) =>  (~  ( (~ (v2_pythtrip B))  & (r2_hidden A B)) ) ) ) ) ) ) ) ).
tt(t13_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t13_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((k11_qc_lang1 A B) = (k7_finseq_1 (k11_qc_lang1 A C) D))  =>  ((k11_qc_lang1 A B) = (k11_qc_lang1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k5_qc_lang2 A B D) = (k5_qc_lang2 A C E))  =>  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v1_qc_lang2 B A) =>  ((k24_qc_lang1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A (k10_qc_lang2 A B)) (k24_qc_lang1 A (k11_qc_lang2 A B)))) ) ) ) ) ) ).
tt(t13_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((r1_tarski C D) => (r2_qc_lang2 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D) (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t13_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k5_qmax_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k5_qmax_1 A))) =>  ( ((r2_hidden B (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))) & (r2_hidden C (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_qmax_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_qmax_1 A)) =>  ( ((r2_hidden (k8_qmax_1 A D) C) &  ((r2_hidden (k8_qmax_1 A E) C) & (r2_hidden D B)) )  => (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A C D) =>  ((r3_lattices A (k1_quantal1 A D B) (k1_quantal1 A C B)) & (r3_lattices A (k2_quantal1 A D B) (k2_quantal1 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t13_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k27_quaterni A k1_quatern2) = k6_numbers) ) ) ).
tt(t13_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k5_square_1 (k3_quatern2 A)) = (k17_quaterni (k27_quaterni A (k31_quaterni A)))) ) ) ).
tt(t13_quaterni,ax, ((k10_quaterni k1_xcmplx_0 k1_xcmplx_0) = (k1_real_1 1)) ).
tt(t13_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (~ (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) ) )  &  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 k6_numbers (k1_quin_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t13_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k9_quofield A B (k9_quofield A C D)) = (k9_quofield A (k9_quofield A B C) D))  &  ((k9_quofield A B C) = (k9_quofield A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_radix_1 B)) =>  ((r1_xxreal_0 A (k6_xcmplx_0 (k1_radix_1 B) 1)) & (r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 B)) 1) A)) ) ) ) ) ) ).
tt(t13_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (C = D)  =>  ((k3_radix_2 A B C) = (k8_radix_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 2 A) & (r2_hidden B (k3_radix_1 A)))  =>  ((r1_xxreal_0 (k4_xcmplx_0 (k1_radix_1 (k7_nat_d A 1))) (k6_radix_3 B A)) & (r1_xxreal_0 (k6_radix_3 B A) (k6_xcmplx_0 (k1_radix_1 (k7_nat_d A 1)) 1))) ) ) ) ) ) ).
tt(t13_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k2_finseq_1 A)) => (r1_xxreal_0 (k4_radix_1 E B A D) (k4_radix_1 E B A C))) ) )  => (r1_xxreal_0 (k8_radix_1 A B D) (k8_radix_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t13_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 2 B))  =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (~ (r1_xxreal_0 (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_5 (k2_xcmplx_0 A 2) A B))) (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)))) ) ) ) ) ) ) ) ).
tt(t13_ramsey_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) D) =>  ( ((r2_hidden B E) &  ((k3_funct_2 A D (k13_eqrel_1 A D) B) = (k3_funct_2 A D (k13_eqrel_1 A D) C)) )  => (r2_hidden C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  (? [E:$i] :  ((m2_finseq_1 E A) &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_seq_1 D F) = (k8_real_1 (k1_seq_1 C (k1_funct_1 E F)) (k1_seq_1 B (k1_tarski (k1_funct_1 E F))))) ) ) )  &  ((k1_mesfunc6 A (k1_random_1 A) (k2_prob_4 A (k1_random_1 A) B) C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ( (! [D:$i] :  ((r2_hidden D C) => (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) )  => (r1_xxreal_0 k6_numbers (k5_bhsp_5 k1_numbers A k33_binop_2 C B))) ) ) ) ) ) ) ).
tt(t13_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 (k3_ranknull A C B D) E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) &  (E = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (r1_xxreal_0 (k2_real_1 (k1_rat_1 A)) 1)) ) ).
tt(t13_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) => (r1_polynom5 A (k5_vfunct_1 k5_numbers A B) C)) ) ) ) ) ) ) ).
tt(t13_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ((v2_rcomp_1 A) & (v3_xxreal_2 A))  =>  ( (A = k1_xboole_0)  | (r2_hidden (k5_seq_4 A) A)) ) ) ) ).
tt(t13_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( ((r2_hidden (k5_seq_4 A) A) & (r2_hidden (k4_seq_4 A) A))  =>  (A = (k1_rcomp_1 (k5_seq_4 A) (k4_seq_4 A))) ) ) ) ).
tt(t13_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) 1) = (k4_nat_d B (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) k6_numbers))) ) ) ) ) ).
tt(t13_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k4_real_lat A) (k1_funcsdom A k1_numbers (k5_real_lat A) B C) B) B)) ) ) ) ) ) ).
tt(t13_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_real_ns1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_real_ns1 A))) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k3_rlvect_1 (k4_real_ns1 A) C D) = (k3_rlvect_1 (k7_real_ns1 A) E F))  &  ( ((k4_algstr_0 (k4_real_ns1 A) C) = (k4_algstr_0 (k7_real_ns1 A) E))  &  ((k1_rlvect_1 (k4_real_ns1 A) C B) = (k1_rlvect_1 (k7_real_ns1 A) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_group_1 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t13_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B C) = (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) D E))  <=>  ((k3_rlvect_1 A B E) = (k3_rlvect_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k1_relset_1 B (k3_rearran1 A B D C)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t13_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k10_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t13_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_relat_2 A) <=>  (A = (k2_relat_1 A)) ) ) ) ).
tt(t13_relset_1,ax, (! [A:$i] : (r1_tarski (k4_relat_1 A) (k2_zfmisc_1 A A))) ).
tt(t13_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k7_relat_1 (k3_xboole_0 B C) (k10_eqrel_1 A)) (k3_xboole_0 (k7_relat_1 B (k10_eqrel_1 A)) (k7_relat_1 C (k10_eqrel_1 A))))) ) ) ) ) ).
tt(t13_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) & (r1_xxreal_0 A (k4_finseq_4 D C)))  =>  ((r1_xxreal_0 A 1) |  ((k7_partfun1 B D A) = (k7_partfun1 B (k1_finseq_6 B D C) (k7_nat_d (k2_nat_1 A (k3_finseq_1 D)) (k4_finseq_4 D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rewrite1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_rewrite1 k1_xboole_0 A B) =>  (A = B) ) ) ) ).
tt(t13_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ((r2_rewrite2 A B C D) => (r2_rewrite2 A B (k1_flang_1 A (k1_flang_1 A E C) F) (k1_flang_1 A (k1_flang_1 A E D) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (~  ( ((k1_flang_1 A B C) = (k1_flang_1 A D E))  &  ( (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (~  ( ((k1_flang_1 A B F) = D)  &  (C = (k1_flang_1 A F E)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (~  ( ((k1_flang_1 A D F) = B)  &  (E = (k1_flang_1 A F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  =>  ((r1_xxreal_0 (k3_rfinseq2 (k2_rfinseq k1_numbers B A)) (k3_rfinseq2 A)) & (r1_xxreal_0 (k4_rfinseq2 A) (k4_rfinseq2 (k2_rfinseq k1_numbers B A)))) ) ) ) ) ) ).
tt(t13_rfinseq,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_rfinseq (k12_finseq_1 k1_numbers A)) = (k12_finseq_1 k1_numbers A)) ) ) ).
tt(t13_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k18_valued_1 A B) C) = (k18_valued_1 A (k24_valued_1 B C))) ) ) ) ) ) ) ).
tt(t13_rfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( ((v1_partfun1 B A) & (v1_partfun1 C A))  =>  ((r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D (k3_valued_1 A k1_numbers k1_numbers B C)) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D B) (k8_funct_2 k5_numbers k1_numbers A D C))) &  ((r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D (k47_valued_1 A k1_numbers k1_numbers B C)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D B) (k8_funct_2 k5_numbers k1_numbers A D C))) & (r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D (k20_valued_1 A k1_numbers k1_numbers B C)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers A D B) (k8_funct_2 k5_numbers k1_numbers A D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_classes1 C D) => (r2_classes1 (k56_valued_1 A k1_numbers C) (k56_valued_1 B k1_numbers D))) ) ) ) ) ) ) ) ) ).
tt(t13_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((r1_rfunct_4 A C) & (r1_rfunct_4 B C))  => (r1_rfunct_4 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C)) ) ) ) ) ) ).
tt(t13_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) =>  ((k1_rinfsup1 A) = (k1_real_1 (k2_rinfsup1 (k32_valued_1 k5_numbers k1_numbers A)))) ) ) ) ).
tt(t13_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers A B) =>  ((v1_rinfsup2 A) <=> (v2_seq_2 B)) ) ) ) ) ) ).
tt(t13_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_ring_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_ring_1 A B))) =>  ( ( (E = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) C))  &  (F = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) D)) )  =>  ((k1_algstr_0 (k2_ring_1 A B) E F) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k3_rlvect_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_ringcat1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  ((m4_ringcat1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) => (m1_ringcat1 D B C)) ) ) ) ) ) ) ) ) ).
tt(t13_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((k4_finseqop (u1_struct_0 A) k1_numbers D (k7_rlvect_2 A B C)) = (k4_rvsum_1 (k4_finseqop (u1_struct_0 A) k1_numbers D B) (k4_finseqop (u1_struct_0 A) k1_numbers D C))) ) ) ) ) ) ) ) ) ).
tt(t13_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 (k1_rlaffin2 A B)))  => (v1_finset_1 B)) ) ) ) ) ).
tt(t13_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_rlaffin3 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (m2_rlaffin3 (k3_fvsum_1 A C (k5_finseq_2 (u1_struct_0 A) (k5_card_1 B) D)) A (k5_rusub_4 A B D))) ) ) ) ) ) ) ) ).
tt(t13_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k3_rlvect_1 D E F) = (k3_rlvect_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ((k2_rlsub_2 A B B) = B) ) ) ) ) ).
tt(t13_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_convex1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) B) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ).
tt(t13_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_algstr_0 A B (k4_struct_0 A)) = B) ) ) ) ) ).
tt(t13_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k4_subset_1 (u1_struct_0 A) C B)) = (k5_algstr_0 A (k3_rlvect_1 A (k2_rlvect_2 A C) (k2_rlvect_2 A B)) (k2_rlvect_2 A (k9_subset_1 (u1_struct_0 A) C B)))) ) ) ) ) ) ) ).
tt(t13_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~  (B = C) )  & (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A))  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rlvect_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden A (k3_rlsub_1 B C (k1_rlvect_3 B (k7_domain_1 (u1_struct_0 B) D E)))) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B C (k1_rlvect_1 B D F)) (k1_rlvect_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 (k1_rlvect_3 A B) C)) ) ) ) ) ) ).
tt(t13_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_rlvect_x A B) (k2_rlvect_x A C))) ) ) ) ) ) ) ).
tt(t13_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( ( (F = C)  &  (G = D) )  =>  ((k3_rlvect_1 E F G) = (k3_rlvect_1 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ((k2_rmod_3 A B C C) = C) ) ) ) ) ) ) ).
tt(t13_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k7_subset_1 (u1_struct_0 B) C D)) = (k5_algstr_0 B (k1_rmod_4 A B C) (k1_rmod_4 A B (k9_subset_1 (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t13_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A B (k7_robbins1 A)) = B) ) ) ) ) ).
tt(t13_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A D B)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A C) (k3_robbins1 A (k1_lattices A E C)))))))) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v9_lattices A))  => (v9_lattices B)) ) ) ) ) ).
tt(t13_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_robbins4)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_robbins4)) =>  ( ( (A = C)  &  (B = D) )  =>  ((r3_orders_2 k1_robbins4 A B) <=> (r3_lattices k2_robbins4 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k4_roughs_1 A B))) ) ) ) ).
tt(t13_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r1_xboole_0 (k9_subset_1 A B C) (k9_subset_1 A B (k3_subset_1 A C)))) ) ) ) ) ) ).
tt(t13_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_rsspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  => (r2_funct_2 A (u1_struct_0 B) (k6_rsspace4 A B C) C)) ) ) ) ) ) ).
tt(t13_rsspace,ax, ( (~ (v2_struct_0 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))))  &  ((v13_algstr_0 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v2_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v3_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v4_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v5_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v6_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v7_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) &  ((v8_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace))) & (l1_rlvect_1 (g1_rlvect_1 k11_rsspace (k10_rsspace k7_rsspace k11_rsspace) (k8_rsspace k7_rsspace k11_rsspace) (k9_rsspace k7_rsspace k11_rsspace)))) ) ) ) ) ) ) ) ) ).
tt(t13_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (r1_struct_0 A (k4_struct_0 B))) ) ) ) ).
tt(t13_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ((k2_rusub_2 A B B) = B) ) ) ) ) ).
tt(t13_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_rusub_3 C A) =>  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t13_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rusub_4 A) = 1)  <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~  (B = (k4_struct_0 A)) )  &  ((k2_rusub_1 A) = (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t13_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_rusub_4 B A) & (r2_hidden C B))  => (r1_tarski (k7_rusub_4 A B (k6_domain_1 (u1_struct_0 A) C)) B)) ) ) ) ) ) ) ).
tt(t13_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_rvsum_1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k1_numbers (k9_binop_2 A B))) ) ) ) ) ).
tt(t13_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_rvsum_2 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k2_numbers (k4_binop_2 A B))) ) ) ) ) ).
tt(t13_scm_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 E (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ( ((k1_funct_1 E (k10_ami_3 k6_numbers)) = A)  &  ( ((k1_funct_1 E (k10_ami_3 1)) = B)  &  ( ((k1_funct_1 E (k10_ami_3 2)) = C)  &  ((k1_funct_1 E (k10_ami_3 3)) = D) ) ) )  => (m1_scm_1 E (k16_afinsq_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  (~  ((r1_tarski (k9_xtuple_0 A) (k4_subset_1 (u1_struct_0 k1_scmfsa_2) k2_scmfsa_2 k3_scmfsa_2)) &  ((r2_hidden C (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 A) (k4_sf_mastr B)) (k2_sf_mastr B))) &  ( (~  ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  &  (~ (m1_scmfsa_2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_scm_comp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_tarski (k61_valued_1 (k1_ordinal4 (k15_scm_comp B C) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) D) A) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_ami_3)) &  ((v1_partfun1 E (u1_struct_0 k1_ami_3)) & (v5_memstr_0 E 2 k1_ami_3 D)) ) ) ) )  =>  ( (~ (r1_xxreal_0 C (k17_scm_comp B)))  =>  ((r1_extpro_1 2 k1_ami_3 A E) &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A E) (k10_ami_3 C)) = (k12_scm_comp E B))  &  ((k8_extpro_1 2 k1_ami_3 A E) = (k1_afinsq_1 (k15_scm_comp B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k9_scmfsa_2 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t13_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmfsa_2)))  =>  (! [J:$i] :  ((m1_scmfsa_2 J) =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k14_scmfsa_2 H I J))  & (r2_hidden H (k9_xtuple_0 B)))  =>  (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k5_numbers) =>  ( ( (K = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) I)))  &  (L = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) I))) )  =>  ((k7_partfun1 k4_numbers (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G) J) K) = (k7_partfun1 k4_numbers (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G) J) L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v6_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) & (r1_tarski (k2_scmfsa6a C) B))  =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) 1))) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t13_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r3_scmfsa7b (k13_scmfsa_2 C B) A)) ) ) ) ) ) ) ).
tt(t13_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  & (r4_scmfsa7b (k1_scmfsa6a A B) C)) ) ) ) ) ) ) ) ).
tt(t13_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A)) )  =>  ((r5_scmfsa7b (k1_scmfsa8b E C D) B A) & (r6_scmfsa7b (k1_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  => (r1_scmfsa9a A B C D)) ) ) ) ) ) ) ) ).
tt(t13_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 6 C))  => (r2_hidden (k2_nat_1 (k5_card_1 B) C) (k2_afinsq_1 (k1_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t13_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  => (r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) (k1_scmfsa_m A))) ) ).
tt(t13_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) A) & (r1_tarski C B))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 B A)) &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) A D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) |  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k1_scmfsa_m B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3))) = k6_numbers)  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k1_scmfsa_m B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k4_scmpds_2 A)) = 1) ) ) ).
tt(t13_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k13_scmpds_2 J K H I))  &  ((r2_hidden J (k9_xtuple_0 D)) & (r2_hidden (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) J) H) (k9_xtuple_0 D))) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) K) I)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) K) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmpds_4 (k3_scmpds_4 C A) B) = (k1_scmpds_4 C (k4_scmpds_4 A B))) ) ) ) ) ) ) ).
tt(t13_scmpds_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_ordinal1 (k9_xtuple_0 (k10_compos_1 k1_scmpds_2 A)) (k9_xtuple_0 (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B))))) ) ) ) ).
tt(t13_scmpds_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 B) (k5_card_1 A)) (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B)))) ) ) ) ).
tt(t13_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((r2_scmpds_6 C B A) =>  ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) D) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 B) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 B))) D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  =>  ( ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_recdef_1 G H) = k6_numbers)  => (r1_xxreal_0 k6_numbers (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))) ) )  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E))) |  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ( (~ (r1_xxreal_0 (k1_recdef_1 G H) (k1_recdef_1 G (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C H I)))))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 (k6_scmpds_4 C H I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k1_scmpds_8 D E C) B A) & (r2_scmpds_6 (k1_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k1_amistd_1 2 k1_scmpds_2 C (k15_scmpds_2 A B D E)) = (k1_tarski (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (~  ((r1_tarski k4_scmp_gcd A) &  ( ((k5_memstr_0 2 k1_scmpds_2 B) = 5)  &  ( (~ (r1_xxreal_0 (k1_funct_1 B k3_scmp_gcd) k6_numbers))  &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2))) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A B C)) = (k4_scmpds_2 k3_scmp_gcd))  &  ( ((k1_funct_1 B k3_scmp_gcd) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) k3_scmp_gcd))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) = (k3_int_2 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 2)) (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B k3_scmp_gcd) 3))))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 D (k2_xcmplx_0 (k1_funct_1 B k3_scmp_gcd) 1)) =>  ((r1_xxreal_0 D 1) |  ((k1_funct_1 B (k1_scmp_gcd D)) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A B C) (k1_scmp_gcd D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k5_scmring2 A B C) D) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) D)))  &  ( ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k5_scmring2 A B C) D) B) = (k5_algstr_0 A (k2_scmring2 A D B) (k2_scmring2 A D C)))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 A))))  =>  ( (~  (E = B) )  =>  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k5_scmring2 A B C) D) E) = (k2_scmring2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 1)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 A))))  =>  (~  (B = (k3_scmring2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k2_tarski B C) (k1_scmyciel A)) =>  ( (~  (B = C) )  &  ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A))) ) ) ) ) ) ).
tt(t13_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers)  =>  ((k6_scmpds_4 (k4_scpinvar D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 G (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 G 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ((k1_funct_1 G D) = (k1_funct_1 B D))  =>  ( ((k1_funct_1 (k6_scmpds_4 C G H) D) = (k1_funct_1 G D))  &  ( ((k1_funct_1 (k6_scmpds_4 C G H) (k2_scmpds_2 (k1_funct_1 B D) E)) = (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E)))  &  ((r1_scmpds_6 C G H) & (r2_scmpds_6 C G H)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ((r1_xxreal_0 F k6_numbers) |  ( (D = (k2_scmpds_2 (k1_funct_1 B D) E))  |  ((r1_scmpds_6 (k2_scmpds_7 D E F C) B A) & (r2_scmpds_6 (k2_scmpds_7 D E F C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_scpqsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k5_card_1 (k2_scpqsort A B)) = 57) ) ) ) ) ).
tt(t13_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t13_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A B) C) (k3_valued_1 k5_numbers k1_numbers k1_numbers A (k3_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t13_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) => (v1_comseq_2 A)) ) ) ).
tt(t13_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) => (v2_comseq_2 (k56_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t13_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k8_seqfunc A (k3_seqfunc A B) (k3_seqfunc A C)) (k3_seqfunc A (k8_seqfunc A B C)))) ) ) ) ) ) ).
tt(t13_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (m2_subset_1 (k8_nat_1 k1_numbers A B) k1_numbers k5_numbers)) ) ) ) ) ).
tt(t13_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) & (v1_series_1 (k1_valued_0 k1_numbers A B))) )  => (v1_series_1 A)) ) ) ).
tt(t13_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 1)) (k13_newton B 2))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 1)) B) (k2_nat_1 B 1)) 2)) ) ) ) ) ) ).
tt(t13_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 A B) C) (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)) (k1_newton C 3)) 3))) ) ) ) ) ) ).
tt(t13_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 2 C) 1) (k1_newton (k7_xcmplx_0 1 2) C))) ) )  =>  ((k1_seq_1 (k3_series_1 B) A) = (k6_xcmplx_0 (k2_nat_1 (k13_newton A 2) 1) (k1_newton (k7_xcmplx_0 1 2) A))) ) ) ) ) ) ).
tt(t13_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k18_complex1 A)))  &  ( (~ (r1_xxreal_0 1 (k18_complex1 B)))  &  (~ (r1_xxreal_0 (k18_complex1 (k13_complex1 (k2_xcmplx_0 A B) (k2_xcmplx_0 1 (k3_xcmplx_0 A B)))) 1)) ) ) ) ) ) ) ) ).
tt(t13_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_setfam_1 A B) => (r1_tarski (k3_tarski A) (k3_tarski B))) ) ) ).
tt(t13_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_tarski (a_3_3_setlim_1 A C D)) = B) ) ) ) ) ) ) ) ) ).
tt(t13_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k4_subset_1 A (k3_prob_1 A B) (k3_prob_1 A C)) (k3_prob_1 A (k2_setlim_2 A B C)))) ) ) ) ) ).
tt(t13_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  ( ((k7_relset_1 B A C D) = k1_xboole_0)  =>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t13_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 F B) &  ((v2_binop_1 F B) &  ((v1_setwiseo F B) &  ( (D = (k4_binop_1 B F))  &  ((r6_binop_1 B G F) &  ((k5_binop_1 B G D E) = D) ) ) ) ) )  =>  ((k5_binop_1 B G (k7_setwiseo A B F C H) E) = (k7_setwiseo A B F C (k9_funcop_1 B A G H E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2)))  =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b C (k1_scmfsa_m B) A)) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa6b C B A)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( (~  ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C)) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) k6_numbers) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( (~  (B = C) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B D C E A) k6_numbers) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_sf_mastr,ax, ((k1_sf_mastr (k2_compos_1 k1_scmfsa_2)) = k1_xboole_0) ).
tt(t13_sgraph1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k2_sgraph1 A))) ) ).
tt(t13_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  => (v1_sheffer1 A)) ) ).
tt(t13_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B C)) C) = (k5_sheffer1 A B C)) ) ) ) ) ) ) ).
tt(t13_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ((v1_finset_1 B) &  ((v1_setfam_1 B) &  ((v6_ordinal1 B) &  ((r2_hidden A B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ((r1_tarski B C) &  ((v1_setfam_1 C) &  ((v6_ordinal1 C) &  ( ((k1_card_1 A) = (k1_card_1 C))  &  (! [D:$i] :  (~  ((r2_hidden D C) &  ( (~  ((k1_card_1 D) = 1) )  &  (! [E:$i] :  (~  ((r2_hidden E D) & (r2_hidden (k6_subset_1 D (k1_tarski E)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matroid0 B) & (m1_simplex0 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( (C = (k2_cohsp_1 (u1_pre_topc B)))  => (m1_simplex1 (k5_simplex0 (u1_struct_0 B) C) A B)) ) ) ) ) ) ) ).
tt(t13_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ( ((v6_tbsp_1 C (k14_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))))  =>  ( (C = B)  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ((r2_hidden D (k3_convex1 (k15_euclid A) B)) => (r1_tarski (k3_convex1 (k15_euclid A) B) (k10_metric_1 (k14_euclid A) D (k3_tbsp_1 (k14_euclid A) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t13_sin_cos2,ax, ((k1_seq_1 k24_sin_cos k6_numbers) = 1) ).
tt(t13_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k4_binop_2 A B)) = (k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B)))) ) ) ) ) ).
tt(t13_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  ( (~  ((k20_sin_cos C) = k6_numbers) )  &  (~  ((k1_sin_cos4 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k7_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) (k1_sin_cos4 C)) (k3_xcmplx_0 (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) (k1_sin_cos4 C))) (k6_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 1 (k3_xcmplx_0 (k1_sin_cos4 B) (k1_sin_cos4 C))) (k3_xcmplx_0 (k1_sin_cos4 C) (k1_sin_cos4 A))) (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  (~  ( ((k4_sin_cos4 (k8_real_1 2 A)) = (k10_real_1 (k5_square_1 (k4_sin_cos4 A)) (k9_real_1 1 (k5_square_1 (k1_sin_cos4 A)))))  &  ((k4_sin_cos4 (k8_real_1 2 A)) = (k10_real_1 (k7_real_1 (k2_sin_cos4 A) (k1_sin_cos4 A)) (k9_real_1 (k2_sin_cos4 A) (k1_sin_cos4 A)))) ) ) ) ) ) ) ) ).
tt(t13_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ( (~ (r1_xxreal_0 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 (k20_sin_cos A) k6_numbers)) ) ) ) ) ) ) ).
tt(t13_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  => (r1_xxreal_0 k6_numbers (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k10_binop_2 1 (k3_square_1 A))))) ) ) ).
tt(t13_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k6_xcmplx_0 (k3_square_1 (k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B))) (k3_square_1 (k6_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)))) = (k3_xcmplx_0 4 (k5_square_1 (k3_sin_cos2 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)))))  &  ((k6_xcmplx_0 (k3_square_1 (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) (k3_square_1 (k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)))) = (k3_xcmplx_0 4 (k5_square_1 (k6_sin_cos2 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2))))) ) ) ) ) ) ).
tt(t13_sin_cos9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) =>  ((k1_seq_1 k29_sin_cos A) = (k1_sin_cos4 A)) ) ) ) ).
tt(t13_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k3_sin_cos A) C) = (k8_nat_1 k2_numbers (k9_sin_cos C A B) C)) ) ) ) ) ) ) ).
tt(t13_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_sppol_1 A B (k1_rltopsp1 (k15_euclid A) C D)) &  ( (~  (B = C) )  &  (~  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k2_topreal1 2 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k18_pscomp_1 A) A) & (r2_hidden (k19_pscomp_1 A) A)) ) ) ).
tt(t13_sprect_2,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) &  ((k17_euclid B) = (k8_pscomp_1 A)) )  => (r2_hidden B (k16_pscomp_1 A))) ) ) ) ) ).
tt(t13_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 D)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 D))) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D B A)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C A)))) ) ) ) ) ) ) ) ) ).
tt(t13_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t13_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 A (k3_square_1 A))) ) ) ) ) ).
tt(t13_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r2_stacks_1 A B C) & (r2_stacks_1 A C D))  => (r2_stacks_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t13_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  (~  ((r1_tarski B A) &  ( (~  (B = (k1_seq_4 (k21_binop_2 A 1))) )  & (r1_xxreal_0 (k21_binop_2 A 1) (k5_nat_1 B))) ) ) ) ) ) ) ).
tt(t13_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [F:$i] :  ( ((v5_relat_1 F (k3_qc_lang1 A)) &  ((v3_card_1 F B) & (m2_finseq_1 F (k2_qc_lang1 A))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_substut1 A)) => (r2_relset_1 k5_numbers C (k4_valuat_1 A C B F (k1_sublemma A C D (k3_sublemma A (k4_sublemma B A E F G) C D))) (k4_valuat_1 A C B (k3_substut1 A F G) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k7_subset_1 A B C) = (k9_subset_1 A B (k3_subset_1 A C))) ) ) ) ) ) ).
tt(t13_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) (k3_substlat A B C) D)) = (k3_substlat A B (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) C D))) ) ) ) ) ) ) ).
tt(t13_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  => (v6_substut1 (k21_substut1 A B C) A)) ) ) ) ) ) ) ).
tt(t13_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k4_substut2 A (k5_cqc_lang A) B C) = (k5_cqc_lang A)) ) ) ) ) ) ) ).
tt(t13_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((m2_xxreal_2 B A) <=> (m1_xxreal_2 (k2_supinf_2 B) (k6_supinf_2 A))) ) ) ) ) ).
tt(t13_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  => (r1_orders_2 B C C)) ) ) ) ) ) ) ).
tt(t13_sysrel,ax, (! [A:$i] :  ((k4_relat_1 (k1_tarski A)) = (k1_tarski (k4_tarski A A))) ) ).
tt(t13_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_t_0topsp A)) (u1_struct_0 B)) &  ((v5_pre_topc D (k3_t_0topsp A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_t_0topsp A)) (u1_struct_0 B))))) ) )  & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A)) (u1_struct_0 (k3_t_0topsp A)) (u1_struct_0 B) (k4_t_0topsp A) D))) ) ) ) ) ) ) ) ).
tt(t13_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_taxonom1 (k1_tarski (k10_eqrel_1 A)) A)) ) ).
tt(t13_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_taxonom2 B A))  =>  (~  ((v7_taxonom2 B A) &  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (~ (r1_tarski C B)) ) ) ) ) ) ) ) ).
tt(t13_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_power k8_power (k1_seq_1 k24_sin_cos A)) = A) ) ) ).
tt(t13_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C D) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 1 F))  & (r1_xxreal_0 B (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tbsp_1 B A) & (v6_tbsp_1 C A))  => (v6_tbsp_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t13_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_tdgroup A B C C D) & (r1_tdgroup A B E E D))  =>  (C = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) B) C))) (k9_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) B) C)) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t13_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) B) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ).
tt(t13_tdlat_3,ax, (! [A:$i] :  ( ((v2_tdlat_3 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (u1_pre_topc A)) => (r2_hidden (k6_subset_1 (u1_struct_0 A) B) (u1_pre_topc A))) ) ) ) ) ).
tt(t13_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r1_termord A B (k1_termord A B C D) C) & (r1_termord A B (k1_termord A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t13_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~  (B = k1_xboole_0) )  => (v1_tops_1 B A))  &  ( (~  (B = (u1_struct_0 A)) )  => (v2_tops_1 B A)) ) ) ) ) ) ).
tt(t13_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v2_tdlat_3 A))  => (v2_tdlat_3 B)) ) ) ) ) ).
tt(t13_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((m1_pre_topc B C) =>  ((v1_tex_3 B C) & (m1_pre_topc B C)) ) ) ) ) ) ) ) ).
tt(t13_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_tex_4 (k5_setfam_1 (u1_struct_0 A) (k1_tex_4 A B)) A)) ) ) ) ).
tt(t13_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)))  => (r1_tarski (k2_relset_1 (u1_struct_0 B) (k10_tmap_1 A B C D E F)) (k4_subset_1 (u1_struct_0 B) (k2_relset_1 (u1_struct_0 B) E) (k2_relset_1 (u1_struct_0 B) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_tsep_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 C))) =>  (~  ((v4_pre_topc E B) &  ((r2_hidden D E) &  ((v4_pre_topc F C) &  ((r2_hidden D F) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)))) =>  (~  ((v4_pre_topc G (k1_tsep_1 A B C)) &  ((r2_hidden D G) & (r1_tarski G (k2_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((v1_toler_1 k1_xboole_0 A B) & (m1_toler_1 k1_xboole_0 A B))  =>  (B = k1_xboole_0) ) ) ) ) ).
tt(t13_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid C))) =>  (~  ( (D = H)  &  ( (E = I)  &  ( (F = (k1_rlvect_1 (k15_euclid C) H A))  &  ( (G = (k1_rlvect_1 (k15_euclid C) I A))  &  ( (~ (r1_xxreal_0 B (k4_metric_1 (k14_euclid C) D E)))  &  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k8_real_1 (k18_complex1 A) B) (k4_metric_1 (k14_euclid C) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  ((u1_struct_0 (k5_topalg_1 A B)) = (k1_tarski (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) C))) ) ) ) ) ) ) ).
tt(t13_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((g1_pre_topc (u1_struct_0 (k2_borsuk_1 A B)) (u1_pre_topc (k2_borsuk_1 A B))) = (k2_borsuk_1 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ).
tt(t13_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) => (m1_borsuk_2 (k3_topalg_4 A B k5_topmetr G) A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) <=> (v2_connsp_2 (k2_struct_0 A) A)) ) ) ).
tt(t13_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((r1_mfold_2 A B) & (v1_topalg_6 A))  => (v1_topalg_6 B)) ) ) ) ) ).
tt(t13_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((v2_topdim_1 B A) &  ((v2_topdim_1 C A) &  ((r1_xxreal_0 (k3_topdim_1 A B) D) & (r1_xxreal_0 (k3_topdim_1 A C) D)) ) )  => (r1_xxreal_0 (k3_topdim_1 A (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) D)) ) ) ) ) ) ) ) ) ).
tt(t13_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v5_waybel23 (k1_pre_topc B C)) =>  ( ((v1_topdim_1 C B) & (r1_xxreal_0 (k2_topdim_1 B C) A))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden D E) &  (! [F:$i] :  ( ((v3_pre_topc F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden D F) &  ((r1_tarski F E) &  ((v1_topdim_1 (k9_subset_1 (u1_struct_0 B) C (k2_tops_1 B F)) B) & (r1_xxreal_0 (k2_topdim_1 B (k9_subset_1 (u1_struct_0 B) C (k2_tops_1 B F))) (k3_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k2_tops_1 A B)) (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t13_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  =>  ( ((v1_tops_2 (k10_eqrel_1 (u1_struct_0 A)) A) &  ((v1_cantor_1 (k10_eqrel_1 (u1_struct_0 A)) A) & (m1_subset_1 (k10_eqrel_1 (u1_struct_0 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (r1_tarski (k10_eqrel_1 (u1_struct_0 A)) B)) ) ) ) ) ).
tt(t13_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v3_pre_topc (k10_prob_1 A) k2_topgen_3) & (m1_subset_1 (k10_prob_1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t13_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  <=>  ((v1_prob_1 B A) & (v3_topgen_4 B A)) ) ) ) ) ).
tt(t13_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r2_hidden B (k1_topreal9 A B C))) ) ) ) ) ) ).
tt(t13_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k2_relset_1 (u1_struct_0 A) (k3_group_1 A)) = (u1_struct_0 A)) ) ) ).
tt(t13_topmetr3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers E) &  ((r1_xxreal_0 F 1) &  ((r1_xxreal_0 E F) &  ((r2_hidden (k1_funct_1 B E) C) &  ((r2_hidden (k1_funct_1 B F) D) &  ((v4_pre_topc C (k3_pcomps_1 A)) &  ((v4_pre_topc D (k3_pcomps_1 A)) &  ((v5_pre_topc B k5_topmetr (k3_pcomps_1 A)) &  ( ((k4_subset_1 (u1_struct_0 (k3_pcomps_1 A)) C D) = (u1_struct_0 A))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_xxreal_0 E G) &  ((r1_xxreal_0 G F) & (r2_hidden (k1_funct_1 B G) (k9_subset_1 (u1_struct_0 (k3_pcomps_1 A)) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_topmetr B A))  => (m1_pre_topc (k3_pcomps_1 B) (k3_pcomps_1 A))) ) ) ) ).
tt(t13_topreal1,ax, ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) = a_0_0_topreal1)  &  ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)) = a_0_1_topreal1)  &  ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)) = a_0_2_topreal1)  &  ((k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)) = a_0_3_topreal1) ) ) ) ).
tt(t13_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid A) = (k18_euclid B))  =>  ( ((k17_euclid A) = (k17_euclid B))  | (r2_hidden (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid A) (k17_euclid B)) 2) (k18_euclid A)) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ).
tt(t13_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v4_topreal1 B) &  ((r2_hidden D (k4_finseq_1 B)) &  ((r2_hidden (k2_nat_1 D 1) (k4_finseq_1 B)) &  ((r2_hidden A (k2_topreal1 2 B D)) &  (C = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) D B) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) ) )  =>  ((r1_xxreal_0 D 1) |  ( (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B D))  |  ((v4_topreal1 C) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = A)  &  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) &  ((r1_tarski (k3_topreal1 2 C) (k3_topreal1 2 B)) &  ((k3_topreal1 2 C) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) D B)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B D) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~  ((v5_pre_topc B k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc C k5_topmetr k3_topmetr) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (u1_struct_0 k5_topmetr)) &  (E = (k1_funct_1 B D)) )  =>  ((k18_euclid E) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_euclid (k2_finseq_4 k1_numbers A B)) = (k2_finseq_4 k1_numbers (k18_complex1 A) (k18_complex1 B))) ) ) ) ) ).
tt(t13_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k3_euclid (k4_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D))) = (k8_finseq_1 k1_numbers (k3_euclid (k4_rvsum_1 A B)) (k3_euclid (k4_rvsum_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 1 A) =>  ((k2_graph_2 B C (k2_nat_1 A 1) (k3_finseq_1 C)) = (k2_rfinseq B A C)) ) ) ) ) ) ) ).
tt(t13_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = D)  =>  ((k9_metric_1 (k14_euclid A) D B) = (k1_topreal9 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t13_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_funct_1 C) & (v2_funct_2 C (u1_struct_0 B)))  =>  ((v5_pre_topc C A B) <=> (v1_t_0topsp (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ) ).
tt(t13_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) 1)) ) ) ) ) ) ).
tt(t13_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k12_euclid (k2_funct_7 (k5_euclid B) A C)) = (k18_complex1 C)) ) ) ) ) ) ) ).
tt(t13_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k2_toprns_1 (k8_real_1 B C) A D) = (k2_toprns_1 B A (k2_toprns_1 C A D))) ) ) ) ) ) ) ) ) ).
tt(t13_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (r1_tarski (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A C)) (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t13_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_tops_2 C A))  => (v1_tops_2 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t13_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v3_pre_topc C A) & (r1_xboole_0 (k3_subset_1 (u1_struct_0 A) B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ((v1_t_0topsp B (k15_euclid A) k3_topmetr) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  & (r1_tarski (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B C) E) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B C) E)) (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B (k1_topreal9 A C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ((r3_relat_2 C (k2_zfmisc_1 A A)) & (r1_transgeo A B C))  => (r1_transgeo A (k2_funct_2 A B) C)) ) ) ) ) ) ) ).
tt(t13_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v1_translac A) &  ((v7_transgeo B A) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_transgeo (u1_struct_0 A) B B) (k6_partfun1 (u1_struct_0 A)))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t13_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr k6_numbers 1))) =>  ( ((k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 A B C D) (k1_treal_1 A B)) = C)  &  ((k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 A B C D) (k2_treal_1 A B)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ((r2_hidden A (k1_trees_1 B)) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t13_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( (B = k1_xboole_0)  =>  ((k2_trees_2 A 1) = (k1_trees_2 A B)) ) ) ) ) ) ).
tt(t13_trees_3,ax, (! [A:$i] :  ((v2_trees_3 (k1_tarski A)) <=>  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) ) ) ) ).
tt(t13_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((k9_xtuple_0 (k5_trees_4 A B)) = (k12_trees_3 (k9_xtuple_0 B))) ) ) ) ).
tt(t13_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) => (r1_tarski (k3_trees_9 (k5_trees_2 A B)) (k3_trees_9 A))) ) ) ) ).
tt(t13_trees_a,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r2_hidden D (k9_xtuple_0 (k7_trees_2 B A C))) & (r2_hidden D (a_2_3_trees_a A B)))  =>  ((k1_funct_1 (k7_trees_2 B A C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_borsuk_1 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_borsuk_1 C B) & (m1_pre_topc C B))  =>  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ).
tt(t13_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B C) & (r2_tsep_2 A D E))  => (r2_tsep_2 A (k9_subset_1 (u1_struct_0 A) B D) (k4_subset_1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v1_tsp_1 C A) <=> (v6_pre_topc B)) ) ) ) ) ) ) ) ).
tt(t13_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_pre_topc B) & (m1_pre_topc B A)) )  =>  (? [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  &  ((m1_pre_topc B C) & (v2_tsp_2 C A)) ) ) ) ) ) ) ).
tt(t13_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (~  ((v2_turing_1 B A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) C)) = (u5_turing_1 A))  &  ( ((k11_turing_1 A B) = (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ((k1_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k8_nat_1 (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A))) (k10_turing_1 A B) D)) = (u5_turing_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k21_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 A B) C)))  &  ( ((k1_funct_1 k22_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 A) B) C)))  &  ( ((k1_funct_1 k23_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B)) C)))  &  ((k1_funct_1 k24_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k10_margrel1 (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B)) (k9_margrel1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_unialg_2 A B) => (r1_unialg_2 A B)) ) ) ) ) ).
tt(t13_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  ((u1_struct_0 (k12_unialg_2 A)) = (k1_unialg_3 A)) ) ) ).
tt(t13_uniform1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ((v5_pre_topc C k5_topmetr (k15_euclid A)) &  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  (~  ( ((k1_funct_1 F 1) = k6_numbers)  &  ( ((k1_funct_1 F (k3_finseq_1 F)) = 1)  &  ((r1_xxreal_0 5 (k3_finseq_1 F)) &  ((r1_tarski (k2_relset_1 k1_numbers F) (u1_struct_0 k5_topmetr)) &  ((v5_valued_0 F) &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (~  ((r1_xxreal_0 1 G) &  ( (~ (r1_xxreal_0 (k3_finseq_1 F) G))  &  ( (H = (k1_rcomp_1 (k7_partfun1 k1_numbers F G) (k7_partfun1 k1_numbers F (k2_nat_1 G 1))))  &  ( (I = (k7_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)) C H))  & (r1_xxreal_0 B (k3_tbsp_1 (k14_euclid A) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_uniroots,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((v1_int_1 B) => (v1_int_1 (k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) B A))) ) ) ) ) ).
tt(t13_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ( (B = (k13_pre_poly C))  &  ((k4_uproots A C) = (k5_card_1 B)) )  <=>  (C = (k2_uproots A B 1)) ) ) ) ) ) ) ).
tt(t13_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 (k2_nat_1 A 1))) =>  ( (~ (r2_hidden B (k1_urysohn1 A)))  =>  ((r2_hidden (k10_real_1 (k5_real_1 (k6_urysohn1 (k2_nat_1 A 1) B) 1) (k13_newton 2 (k2_nat_1 A 1))) (k1_urysohn1 A)) & (r2_hidden (k10_real_1 (k2_nat_1 (k6_urysohn1 (k2_nat_1 A 1) B) 1) (k13_newton 2 (k2_nat_1 A 1))) (k1_urysohn1 A))) ) ) ) ) ) ).
tt(t13_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (C = (k1_integra2 A B))  &  (A = (k1_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) )  =>  ( (C = (k1_xxreal_1 (k7_supinf_2 C) (k8_supinf_2 C)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (D = (k7_supinf_2 A))  &  (E = (k8_supinf_2 A)) )  =>  ( ((k7_supinf_2 C) = (k8_real_1 B D))  &  ((k8_supinf_2 C) = (k8_real_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_tarski (k5_urysohn3 A B C D E) k2_urysohn1)) ) ) ) ) ) ) ) ) ) ).
tt(t13_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E (k11_cqc_lang A C D)) (k3_valuat_1 A B C (k8_valuat_1 A B E D)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_funct_1 A) & (v1_valued_0 A)) ) ) )  =>  (? [B:$i] :  ((v1_xcmplx_0 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t13_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 (k45_valued_1 A B))) =>  ((k1_funct_1 (k45_valued_1 A B) C) = (k6_xcmplx_0 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ) ).
tt(t13_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k13_valued_1 (k7_valued_1 C A) B) = (k7_valued_1 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t13_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( (D = E)  =>  ((k1_vectsp_7 A C (k6_domain_1 (u1_struct_0 C) E)) = (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  ( (~ (v7_struct_0 (k1_ranknull A B B C)))  =>  ((v1_vectsp11 C A B) & (m1_vectsp11 (k4_struct_0 A) A B C)) ) ) ) ) ) ) ) ).
tt(t13_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A (k6_algstr_0 A B D) (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ((k11_algstr_0 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t13_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( ( (F = C)  &  (G = D) )  =>  ((k3_rlvect_1 E F G) = (k3_rlvect_1 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ((k2_vectsp_5 A B C C) = C) ) ) ) ) ) ) ).
tt(t13_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k3_vectsp_6 A B (k8_finseq_1 (u1_struct_0 B) C D) E) = (k8_finseq_1 (u1_struct_0 B) (k3_vectsp_6 A B C E) (k3_vectsp_6 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (m1_vectsp_4 (k1_vectsp_7 A B C) A (k1_vectsp_7 A B D))) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v2_funct_1 D) &  ((v13_vectsp_1 D B C) & (v1_mod_2 D A B C)) )  => (m1_lattice4 (k6_vectsp_8 A B C D) (k1_vectsp_8 A B) (k1_vectsp_8 A C))) ) ) ) ) ) ) ) ) ).
tt(t13_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_7 D A C) =>  (? [E:$i] :  ((m1_vectsp_7 E A B) & (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ).
tt(t13_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r2_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B (k6_vfunct_1 A B C D) E) (k6_vfunct_1 A B (k4_vfunct_1 A B C E) (k4_vfunct_1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B (k3_vfunct_2 A B C D) E) (k3_vfunct_2 A B (k2_vfunct_2 A B C E) (k2_vfunct_2 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t13_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ( ((k3_waybel_0 A C) = (k3_waybel_0 B D))  &  ((k4_waybel_0 A C) = (k4_waybel_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ( ((v4_yellow_0 C A) & (m1_yellow_0 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_yellow_0 B C)) ) ) ) ) ) ) ).
tt(t13_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (r2_hidden B C))  => (m2_connsp_2 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A C)) ) ) ) ) ) ) ).
tt(t13_waybel12,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_yellow_4 A B (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))) = (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))) ) ) ) ) ).
tt(t13_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k1_waybel_8 (k2_yellow_1 (k7_waybel_0 A))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel_8 (k2_yellow_1 (k7_waybel_0 A)))))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_waybel_8 (k2_yellow_1 (k7_waybel_0 A)))) B C) = (k5_waybel_0 A C)) ) )  => (v23_waybel_0 B A (k1_waybel_8 (k2_yellow_1 (k7_waybel_0 A))))) ) ) ) ) ).
tt(t13_waybel14,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k4_yellow_4 A (k1_waybel_3 A B) (k1_waybel_3 A C)) (k5_waybel_0 A (k12_lattice3 A B C)))) ) ) ) ) ) ).
tt(t13_waybel15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k3_yellow_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k3_yellow_1 A)))))) )  =>  ( ((v11_quantal1 B) & (v22_waybel_0 B (k3_yellow_1 A) (k3_yellow_1 A)))  => (v22_waybel_0 (k3_waybel_1 (k3_yellow_1 A) (k3_yellow_1 A) B) (k1_yellow_2 (k3_yellow_1 A) (k3_yellow_1 A) B) (k3_yellow_1 A))) ) ) ) ).
tt(t13_waybel16,ax, (! [A:$i] : (v2_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))))) ).
tt(t13_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_1_waybel17 A B C D))) ) )  => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t13_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_tops_2 (a_1_0_waybel18 A) (k3_waybel18 A (k7_funcop_1 A k9_waybel18))) &  ((v2_cantor_1 (a_1_0_waybel18 A) (k3_waybel18 A (k7_funcop_1 A k9_waybel18))) & (m1_subset_1 (a_1_0_waybel18 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A k9_waybel18))))))) ) ) ) ).
tt(t13_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k6_waybel_0 A B)) ) ) ) ) ).
tt(t13_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v5_waybel_1 C A B) => (v18_waybel_0 C B A)) ) ) ) ) ) ) ).
tt(t13_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ( ((r1_tarski B (k6_partfun1 (u1_struct_0 A))) & (r2_yellow_0 (k3_yellow_3 A A) B))  => (r2_hidden (k2_yellow_0 (k3_yellow_3 A A) B) (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t13_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_yellow_0 A A) &  ((v7_yellow_0 A A) &  ((v8_yellow_0 A A) & (m1_yellow_0 A A)) ) ) ) ) ).
tt(t13_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) )  =>  ((k3_funct_2 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B) (k2_waybel22 A B C) (k4_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))))) = (k4_yellow_0 B)) ) ) ) ) ) ).
tt(t13_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  => (r1_tarski (k5_waybel_0 B D) (k5_waybel_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t13_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v5_waybel_0 (k1_waybel24 A B C D E) B C) & (v5_waybel_0 (k2_waybel24 A B C D F) A C)) ) ) ) )  => (v5_waybel_0 D (k3_yellow_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t13_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ((k1_waybel25 A) = (k1_waybel25 B)) ) ) ) ) ) ).
tt(t13_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) &  ((v6_pre_topc C) &  ((v1_waybel25 C) & (l1_pre_topc C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  => (v22_waybel_0 (k3_waybel26 A B C D) (k1_waybel26 A B) (k1_waybel26 A C))) ) ) ) ) ) ) ) ).
tt(t13_waybel27,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ((k8_relset_1 A (k2_tarski k1_xboole_0 1) (k5_funct_3 B A) (k1_tarski 1)) = B)  &  ((k8_relset_1 A (k2_tarski k1_xboole_0 1) (k5_funct_3 B A) (k1_tarski k6_numbers)) = (k6_subset_1 A B)) ) ) ) ) ).
tt(t13_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden B (k6_yellow_6 A)) &  ( (C = (k1_waybel11 A B))  &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ((r2_hidden D (k6_yellow_6 A)) => (r1_orders_2 A (k1_waybel_9 A D) C)) ) ) ) )  =>  ( (C = (k1_waybel11 A B))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_waybel28 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  => (r1_orders_2 A (k1_waybel_9 A (k2_waybel28 A B D)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t13_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C A))  =>  ((u1_pre_topc B) = (u1_pre_topc C)) ) ) ) ) ) ) ).
tt(t13_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k3_waybel_0 A C)) (k3_waybel_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ).
tt(t13_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel11 B A) => (v3_waybel11 (k4_waybel_0 A B) A)) ) ) ) ) ).
tt(t13_waybel31,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ( ((k5_card_1 B) = (k1_waybel31 A))  <=>  (B = (u1_struct_0 (k1_waybel_8 A))) ) ) ) ) ) ).
tt(t13_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) ) ) ) ).
tt(t13_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  ((k1_waybel33 A (k2_struct_0 A) B) = (k1_waybel11 A (k3_yellow19 A (k2_struct_0 A) B))) ) ) ) ) ).
tt(t13_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((m1_subset_1 B (u1_struct_0 (k4_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (r2_hidden (u1_struct_0 B) A)) ) ) ) ) ) ) ).
tt(t13_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((r1_waybel35 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden (k4_tarski D E) C) &  ( (~  (D = E) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F B) &  ((r2_hidden (k4_tarski D F) C) &  ((r2_hidden (k4_tarski F E) C) & (r2_orders_2 A D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A B C) => (r1_waybel_3 A B C)) ) ) ) ) ) ) ).
tt(t13_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k5_waybel_4 A D B)) <=> (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ).
tt(t13_waybel_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) )  =>  ( (~  ((r2_hidden A (k2_relset_1 (u1_struct_0 B) (k4_waybel_5 B C))) &  (! [D:$i] :  (~  ((r2_hidden D (k9_xtuple_0 C)) &  (A = (k4_yellow_2 B (k1_funct_1 C D))) ) ) ) ) )  &  ( ( (? [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) &  (A = (k4_yellow_2 B (k1_funct_1 C D))) ) )  => (r2_hidden A (k2_relset_1 (u1_struct_0 B) (k4_waybel_5 B C))))  &  ( (~  ((r2_hidden A (k2_relset_1 (u1_struct_0 B) (k5_waybel_5 B C))) &  (! [D:$i] :  (~  ((r2_hidden D (k9_xtuple_0 C)) &  (A = (k5_yellow_2 B (k1_funct_1 C D))) ) ) ) ) )  &  ( (? [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) &  (A = (k5_yellow_2 B (k1_funct_1 C D))) ) )  => (r2_hidden A (k2_relset_1 (u1_struct_0 B) (k5_waybel_5 B C)))) ) ) ) ) ) ) ) ) ).
tt(t13_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_waybel_4 A (k3_subset_1 (u1_struct_0 A) C) B) => (v2_waybel_6 B A)) ) ) ) ) ) ) ).
tt(t13_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) &  ((v1_waybel_7 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C B) &  ((v12_waybel_0 C B) &  ((v1_waybel_7 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v4_orders_2 A))  => (v4_orders_2 B)) ) ) ) ) ).
tt(t13_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_tarski (u1_struct_0 (k4_waybel_9 A B C)) (u1_struct_0 B))) ) ) ) ) ) ).
tt(t13_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_group_1 A) = (k4_nat_1 (k5_card_1 (k7_group_3 A B)) (k7_group_1 (k1_weddwitt A B)))) ) ) ) ) ).
tt(t13_weierstr,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ((v2_compts_1 A k3_topmetr) => (v1_rcomp_1 (k1_weierstr A))) ) ) ).
tt(t13_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_wellfnd1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k3_rfunct_3 (u1_struct_0 A) B)) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) B)))) )  =>  ( ((r1_wellfnd1 A B C D) & (r1_wellfnd1 A B C E))  => (r2_funct_2 (u1_struct_0 A) B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k1_relat_1 (k2_wellord1 B A)) (k1_relat_1 B)) & (r1_tarski (k1_relat_1 (k2_wellord1 B A)) A)) ) ) ) ).
tt(t13_wellord2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (~  ((v2_wellord1 A) &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~ (r4_wellord1 A (k1_wellord2 B))) ) ) ) ) ) ) ).
tt(t13_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 (k1_int_2 A) B) <=> (r1_int_1 A B)) ) ) ) ) ).
tt(t13_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k2_xboole_0 A C) (k2_xboole_0 B D))) ) ) ) ) ).
tt(t13_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k6_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t13_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 4 A) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A A) A) A)) ) ) ).
tt(t13_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k6_xcmplx_0 A D) (k6_xcmplx_0 B C))) ) ) ) ) ) ) ) ) ).
tt(t13_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k3_xtuple_0 A B C) D) => (r2_hidden A (k11_xtuple_0 D))) ) ) ) ) ).
tt(t13_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r2_hidden A k1_numbers) &  ((r1_xxreal_0 B A) &  ( (~ (r2_hidden B k1_numbers))  &  (~  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ) ).
tt(t13_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k2_xxreal_1 B C)) =>  ((r2_hidden A (k1_xxreal_1 B C)) &  (~  (A = C) ) ) ) ) ) ) ) ) ).
tt(t13_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_2 (k1_tarski A)) = A) ) ) ).
tt(t13_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( (~  (A = k1_xxreal_0) )  =>  ( ((k3_xxreal_3 k1_xxreal_0 A) = k1_xxreal_0)  &  ((k3_xxreal_3 A k1_xxreal_0) = k2_xxreal_0) ) ) ) ) ).
tt(t13_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ( ((v1_yellow_0 A) => (v1_yellow_0 B))  &  ((v2_yellow_0 A) => (v2_yellow_0 B)) ) ) ) ) ) ) ).
tt(t13_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ( ((k8_yellow_3 A B (k12_lattice3 (k3_yellow_3 A B) C D)) = (k12_lattice3 A (k8_yellow_3 A B C) (k8_yellow_3 A B D)))  &  ((k9_yellow_3 A B (k12_lattice3 (k3_yellow_3 A B) C D)) = (k12_lattice3 B (k9_yellow_3 A B C) (k9_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_yellow11 A B C) = (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k5_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t13_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  (C = D) )  =>  ( ((k1_waybel_3 A C) = (k1_waybel_3 B D))  &  ((k2_waybel_3 A C) = (k2_waybel_3 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_yellow_8 (k1_tarski (u1_struct_0 A)) A B) &  ((v1_tops_2 (k1_tarski (u1_struct_0 A)) A) & (m1_subset_1 (k1_tarski (u1_struct_0 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t13_yellow14,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v3_yellow_0 A)) ) ) ).
tt(t13_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E k6_margrel1) =>  ((k3_finseq_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E)) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r1_yellow16 B A C) =>  ((k1_yellow_2 A A C) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B))) ) ) ) ) ) ) ) ).
tt(t13_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel18 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B D)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_waybel18 A B))) =>  ( (~  (C = D) )  =>  ((r2_hidden G (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B D)) (k6_waybel18 A B D) F)) <=> (r2_hidden (k2_funct_7 G C E) (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B D)) (k6_waybel18 A B D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_altcat_1 C))  =>  ((r2_yellow18 A B) =>  ((r2_yellow18 A C) <=>  ((g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B)) = (g2_altcat_1 (u1_struct_0 C) (u1_altcat_1 C) (u2_altcat_1 C))) ) ) ) ) ) ) ) ) ).
tt(t13_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) )  =>  ((k7_subset_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A))) B (k1_tarski k1_xboole_0)) = (k2_yellow19 A (k3_yellow19 A (k2_struct_0 A) B))) ) ) ) ) ).
tt(t13_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_hidden k1_xboole_0 A) =>  ((k3_yellow_0 (k2_yellow_1 A)) = k1_xboole_0) ) ) ) ).
tt(t13_yellow20,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k1_yellow20 B C) = (k3_pboole A B C)) ) ) ) ) ) ).
tt(t13_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_yellow21 A))) <=>  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  & (r2_hidden B (k2_yellow21 A))) ) ) ) ) ).
tt(t13_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v5_orders_3 C A B) & (r1_lattice3 A D E))  => (r1_lattice3 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k1_binop_1 D F G) = (k1_binop_1 E F G)) ) ) ) )  => (r2_funct_2 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k2_yellow_4 A B B))) ) ) ) ).
tt(t13_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A B C) => (r1_orders_2 A (k1_yellow_5 A B D) (k1_yellow_5 A C D))) ) ) ) ) ) ) ) ) ).
tt(t13_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_yellow_6 B (k3_yellow_6 A B C)) = C) ) ) ) ) ) ) ).
tt(t13_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((r2_yellow_0 A B) | (r1_yellow_0 (k7_lattice3 A) B))  =>  ((k2_yellow_0 A B) = (k1_yellow_0 (k7_lattice3 A) B)) ) ) ) ) ).
tt(t13_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B D) &  ((v3_pre_topc D A) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E C) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (B = (k2_xboole_0 C (k1_tarski A)))  |  (C = (k7_subset_1 (k1_zfmisc_1 A) B (k1_tarski A))) )  =>  ((k2_cantor_1 A B) = (k2_cantor_1 A C)) ) ) ) ) ) ) ).
tt(t13_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v8_zf_fund1 B A) &  ((v1_finset_1 C) &  (! [D:$i] :  ((r2_hidden D C) => (r2_hidden D B)) ) ) )  => (r2_hidden C B)) ) ) ) ) ) ).
tt(t13_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k16_zf_lang B C D A) = (k8_zf_lang B (k8_zf_lang C (k8_zf_lang D A))))  &  ((k16_zf_lang B C D A) = (k14_zf_lang B C (k8_zf_lang D A))) ) ) ) ) ) ) ) ) ) ).
tt(t13_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  => (r1_xxreal_0 3 (k3_finseq_1 A))) ) ).
tt(t13_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_xboole_0 (k1_tarski A) (k2_tarski A B)) = (k1_tarski A)) ) ) ).
tt(t13_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ( (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (~  ( (~  ((k3_funct_2 k1_zf_lang A C E) = (k3_funct_2 k1_zf_lang A D E)) )  & (r2_hidden E (k2_zf_model B))) ) ) )  & (r1_zf_model A C B))  => (r1_zf_model A D B)) ) ) ) ) ) ) ) ) ).
tt(t13_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C E D) =>  ((r2_hidden A (k4_zf_lang1 D)) | (r1_zf_model C (k2_zf_lang1 C E A (k3_funct_2 k1_zf_lang C E B)) (k6_zf_lang1 D B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((r1_zf_model A B (k5_zf_lang C D)) <=> (r2_hidden (k3_funct_2 k1_zf_lang A B C) (k3_funct_2 k1_zf_lang A B D))) ) ) ) ) ) ) ) ) ).
tt(t13_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k9_funct_2 (k2_ordinal1 A) (k2_ordinal1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k9_funct_2 (k2_ordinal1 A) (k2_ordinal1 A)))))) )  =>  (~  ((r2_hidden (k1_card_1 B) (k1_card_1 A)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 D) &  ((v3_ordinal2 D) &  ( ((k4_ordinal4 A D (k2_ordinal4 A)) = (k2_ordinal4 A))  &  ( (! [E:$i] :  ( ((v3_ordinal1 E) & (m1_subset_1 E A))  =>  ((k4_ordinal4 A D (k6_ordinal4 A E)) = (k3_ordinal2 (k2_xboole_0 (k1_classes2 A (k4_ordinal4 A D E)) (k7_relat_1 (k13_funct_5 B (k2_ordinal1 A) (k2_ordinal1 A) C) (k2_zfmisc_1 B (k1_classes2 A (k6_ordinal4 A E))))))) ) )  &  (! [E:$i] :  ( ((v3_ordinal1 E) & (m1_subset_1 E A))  =>  ((v4_ordinal1 E) =>  ( (E = (k2_ordinal4 A))  |  ((k4_ordinal4 A D E) = (k4_ordinal2 (k5_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t13_zf_refle,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ((k5_relat_1 B (k4_classes1 A)) = (k5_relat_1 B A)) ) ) ) ) ).
tt(t13_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_zmodul01 A (k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t140_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) &  ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) )  => (r2_relset_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k55_abcmiz_1 A B) (k6_partfun1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))) ) ) ) ).
tt(t140_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k11_finseq_1 B C D) (k4_finseq_2 3 A)) =>  ((r2_hidden B A) &  ((r2_hidden C A) & (r2_hidden D A)) ) ) ) ) ) ) ).
tt(t140_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k5_funct_6 (k11_finseq_1 C D B) 3 A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ) ).
tt(t140_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=> (v4_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(t140_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((k15_group_2 A B) = (a_1_0_group_2 A))  => (r1_group_2 A B (k6_group_2 A))) ) ) ) ) ).
tt(t140_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k17_euclid C) (k12_euclid C))))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k17_euclid C) (k12_euclid C)) (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k17_euclid E) (k12_euclid E)) (k13_complex1 (k17_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t140_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k16_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k16_member_1 A C) (k16_member_1 B C))) ) ) ) ) ) ) ).
tt(t140_pboole,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) )  =>  ((k8_pboole A (k8_pboole B C)) = (k8_pboole (k8_pboole A B) C)) ) ) ) ) ) ) ).
tt(t140_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k8_relat_1 C (k2_xboole_0 A B)) = (k2_xboole_0 (k8_relat_1 C A) (k8_relat_1 C B))) ) ) ) ) ).
tt(t140_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) => (r1_xxreal_0 (k23_rvsum_1 B C) (k9_binop_2 (k23_rvsum_1 B B) (k23_rvsum_1 C C)))) ) ) ) ) ) ).
tt(t140_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (? [B:$i] :  ((m2_finseq_1 B k1_numbers) &  ( ((k1_rvsum_1 B) = (k1_rvsum_1 A))  &  ( ((k3_finseq_1 B) = (k5_card_1 (k1_rvsum_1 A)))  & (v5_valued_0 B)) ) ) ) ) ) ).
tt(t140_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D) (k5_sheffer1 A (k5_sheffer1 A B B) D)) (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A F B)) (k5_sheffer1 A D (k5_sheffer1 A F B)))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C (k5_sheffer1 A C C))) (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D)) (k5_sheffer1 A (k5_sheffer1 A D D) (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t140_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ( ( (A = (k1_tsep_1 A C D))  &  ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) C (k10_tmap_1 A B C D E F)) E) & (r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) D (k10_tmap_1 A B C D E F)) F)) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) A B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t140_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (~  ( ((k4_xboolean A B) = k1_xboolean)  &  ( (~  (A = k1_xboolean) )  &  (~  (B = k1_xboolean) ) ) ) ) ) ) ) ) ).
tt(t140_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B)) = (k2_xcmplx_0 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t140_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t140_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k3_xboole_0 (k1_xxreal_1 A B) (k1_xxreal_1 C D)) = (k1_xxreal_1 (k4_xxreal_0 A C) (k3_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t140_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((k3_zf_lang1 (k6_zf_lang A)) = (k3_zf_lang1 A)) ) ) ).
tt(t140_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C))) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)))) ) ) ) ) ) ) ) ) ).
tt(t141_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k60_abcmiz_1 A C (k37_abcmiz_1 A B)) = (k37_abcmiz_1 A (k60_abcmiz_1 A C B))) ) ) ) ) ) ) ).
tt(t141_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k4_finseq_2 A C)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t141_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 (k6_funct_6 (k9_finseq_1 A))) = (k9_xtuple_0 A))  &  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 (k6_funct_6 (k9_finseq_1 A)) B) = (k9_finseq_1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t141_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (v4_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t141_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((k16_group_2 A B) = (a_1_0_group_2 A))  => (r1_group_2 A B (k6_group_2 A))) ) ) ) ) ).
tt(t141_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k17_euclid C) (k12_euclid C)) (k13_complex1 (k17_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k17_euclid E) (k12_euclid E)) (k13_complex1 (k17_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t141_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k3_binop_2 C B) (k17_member_1 A C))) ) ) ) ) ) ) ).
tt(t141_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v5_funct_1 C B)) ) )  =>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v5_funct_1 D B) & (v1_partfun1 D A)) ) ) )  & (r1_tarski C D)) ) ) ) ) ) ) ).
tt(t141_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k8_relat_1 C (k3_xboole_0 A B)) (k3_xboole_0 (k8_relat_1 C A) (k8_relat_1 C B)))) ) ) ) ).
tt(t141_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((r1_rvsum_1 C D) => (r1_rvsum_1 (k11_rvsum_1 A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t141_seq_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_rvsum_1 A) = (k1_rvsum_1 B))  &  ((v5_valued_0 A) & (v5_valued_0 B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t141_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k5_sheffer1 A D (k5_sheffer1 A F B)) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) (k5_sheffer1 A C (k5_sheffer1 A C C))) (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D)) (k5_sheffer1 A (k5_sheffer1 A D D) (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A E (k5_sheffer1 A E E))) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t141_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) &  ((v5_pre_topc E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ( ( (A = (k1_tsep_1 A C D))  &  ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) C (k10_tmap_1 A B C D E F)) E) & (r2_funct_2 (u1_struct_0 D) (u1_struct_0 B) (k3_tmap_1 A B (k1_tsep_1 A C D) D (k10_tmap_1 A B C D E F)) F)) )  =>  ((v1_funct_1 (k10_tmap_1 A B C D E F)) &  ((v1_funct_2 (k10_tmap_1 A B C D E F) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k10_tmap_1 A B C D E F) A B) & (m1_subset_1 (k10_tmap_1 A B C D E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t141_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k6_xboolean A A)) = k1_xboolean) ) ) ).
tt(t141_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 A B) = (k4_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 B)))) ) ) ) ) ).
tt(t141_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t141_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k3_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 C D)) = (k3_xxreal_1 (k4_xxreal_0 A C) (k3_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t141_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k3_zf_lang1 (k7_zf_lang A B)) = (k2_xboole_0 (k3_zf_lang1 A) (k3_zf_lang1 B))) ) ) ) ) ).
tt(t141_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t142_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) &  ((v15_abcmiz_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v15_abcmiz_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  &  (! [D:$i] :  ((m1_subset_1 D k2_abcmiz_1) =>  (! [E:$i] :  ((m1_subset_1 E k2_abcmiz_1) =>  ( ( ((r2_hidden D (k1_relset_1 k2_abcmiz_1 B)) &  ((k1_funct_1 B D) = (k35_abcmiz_1 E A)) )  =>  ((r2_hidden E (k1_relset_1 k2_abcmiz_1 C)) &  ((k1_funct_1 C E) = (k35_abcmiz_1 D A)) ) )  &  ( ((r2_hidden E (k1_relset_1 k2_abcmiz_1 C)) &  ((k1_funct_1 C E) = (k35_abcmiz_1 D A)) )  =>  ((r2_hidden D (k1_relset_1 k2_abcmiz_1 B)) &  ((k1_funct_1 B D) = (k35_abcmiz_1 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t142_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k4_finseq_2 B A) (k3_finseq_2 A))) ) ) ) ).
tt(t142_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 (k6_funct_6 (k10_finseq_1 A B))) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))  &  (! [C:$i] :  ((r2_hidden C (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 (k6_funct_6 (k10_finseq_1 A B)) C) = (k10_finseq_1 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(t142_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((r2_hidden C (k28_glib_000 A (k4_glib_001 A B))) =>  ((r2_hidden C (k14_glib_001 A B)) | (v4_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(t142_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ((k15_group_2 A (k7_group_2 A)) = (k1_tarski (u1_struct_0 A)))  &  ((k16_group_2 A (k7_group_2 A)) = (k1_tarski (u1_struct_0 A))) ) ) ) ).
tt(t142_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k13_complex1 (k17_euclid B) (k12_euclid B)) = A)  =>  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  ((k17_euclid C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t142_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k17_member_1 A B) = (a_2_9_member_1 A B)) ) ) ) ) ).
tt(t142_pboole,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((k5_relat_1 (k1_funct_4 D (k5_relat_1 C B)) B) = (k5_relat_1 C B)) ) ) ) ) ) ) ).
tt(t142_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k6_subset_1 (k8_relat_1 C A) (k8_relat_1 C B)) (k8_relat_1 C (k6_subset_1 A B)))) ) ) ) ).
tt(t142_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k16_rvsum_1 (k7_finseq_4 A B C D)) = (k9_binop_2 (k9_binop_2 (k9_binop_2 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t142_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k5_seq_4 (k4_subset_1 k1_numbers A B)) = (k1_square_1 (k5_seq_4 A) (k5_seq_4 B))) ) ) ) ) ).
tt(t142_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A C (k5_sheffer1 A E B)) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t142_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k7_xboolean A (k3_xboolean A)) = k1_xboolean) ) ) ).
tt(t142_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k6_xcmplx_0 A B)) = (k6_xcmplx_0 B A)) ) ) ) ) ).
tt(t142_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 k6_numbers (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t142_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k3_xboole_0 (k4_xxreal_1 A B) (k4_xxreal_1 C D)) = (k4_xxreal_1 (k4_xxreal_0 A C) (k3_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t142_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k8_zf_lang B A)) = (k2_xboole_0 (k3_zf_lang1 A) (k1_tarski B))) ) ) ) ) ).
tt(t142_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_zmodul01 B A) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ((m3_zmodul01 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D B C)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k9_zmodul01 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t143_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) &  ((v15_abcmiz_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v15_abcmiz_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A))))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k2_abcmiz_1) =>  (! [E:$i] :  ((m1_subset_1 E k2_abcmiz_1) =>  ( ((r2_hidden D (k1_relset_1 k2_abcmiz_1 B)) &  ((k1_funct_1 B D) = (k35_abcmiz_1 E A)) )  =>  ((r2_hidden E (k1_relset_1 k2_abcmiz_1 C)) &  ((k1_funct_1 C E) = (k35_abcmiz_1 D A)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r1_tarski (k45_abcmiz_1 A D) (k1_relset_1 k2_abcmiz_1 B)) =>  ((k56_abcmiz_1 A C (k56_abcmiz_1 A B D)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t143_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k2_finseq_2 B A) = (k2_finseq_2 C A))  =>  (B = C) ) ) ) ) ) ) ).
tt(t143_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 (k7_funct_6 (k9_finseq_1 A))) = (k4_card_3 (k9_finseq_1 (k9_xtuple_0 A))))  &  ( ((k10_xtuple_0 (k7_funct_6 (k9_finseq_1 A))) = (k4_card_3 (k9_finseq_1 (k10_xtuple_0 A))))  &  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 (k7_funct_6 (k9_finseq_1 A)) (k9_finseq_1 B)) = (k9_finseq_1 (k1_funct_1 A B))) ) ) ) ) ) ) ).
tt(t143_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ((r2_hidden C (k13_glib_001 A B)) &  ((v11_glib_000 C A) &  ( (~  (C = (k3_glib_001 A B)) )  &  (~  (C = (k4_glib_001 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t143_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((k15_group_2 A B) = (k1_tarski (u1_struct_0 A)))  =>  (B = A) ) ) ) ) ) ).
tt(t143_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_struct_0 (k15_euclid 2)) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) (k4_struct_0 (k15_euclid 2)))) ) ) ).
tt(t143_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k17_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k3_binop_2 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t143_pboole,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 C D) = (k7_partfun1 B C D)) ) ) ) ) ) ) ) ) ).
tt(t143_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) => (r1_tarski (k8_relat_1 C A) (k8_relat_1 C B))) ) ) ) ) ).
tt(t143_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 (k12_rvsum_1 A)))  &  ((k4_finseq_1 A) = (k4_finseq_1 (k12_rvsum_1 A))) ) ) ) ).
tt(t143_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k4_seq_4 (k4_subset_1 k1_numbers A B)) = (k2_square_1 (k4_seq_4 A) (k4_seq_4 B))) ) ) ) ) ).
tt(t143_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A C (k5_sheffer1 A E B)) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t143_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k3_xboolean (k7_xboolean A A)) = k1_xboolean) ) ) ).
tt(t143_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 (k4_xcmplx_0 A) B) = (k6_xcmplx_0 (k4_xcmplx_0 B) A)) ) ) ) ) ).
tt(t143_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B)))  &  ( (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  (~ (r1_xxreal_0 A k6_numbers)) ) )  &  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 k6_numbers A)) ) ) ) ) ) ) ) ) ) ).
tt(t143_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k1_xxreal_1 A C) (k1_xxreal_1 B D)) = (k1_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t143_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k3_zf_lang1 (k10_zf_lang A B)) = (k2_xboole_0 (k3_zf_lang1 A) (k3_zf_lang1 B))) ) ) ) ) ).
tt(t143_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))))  &  ((v10_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))) & (l3_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ) ) ).
tt(t144_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [D:$i] :  ( ((v8_abcmiz_1 D A) & (m1_abcmiz_1 D A (k13_abcmiz_1 A)))  =>  ( (C = (k6_domain_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) D))  =>  ((k63_abcmiz_1 A B C) = (k6_domain_1 (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k61_abcmiz_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t144_finseq_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((k3_relat_1 (k2_finseq_2 A B) (k16_funcop_1 B C)) = (k2_finseq_2 A C)) ) ) ) ) ).
tt(t144_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 (k7_funct_6 (k10_finseq_1 A B))) = (k4_card_3 (k10_finseq_1 (k9_xtuple_0 A) (k9_xtuple_0 B))))  &  ( ((k10_xtuple_0 (k7_funct_6 (k10_finseq_1 A B))) = (k4_card_3 (k10_finseq_1 (k10_xtuple_0 A) (k10_xtuple_0 B))))  &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden D (k9_xtuple_0 B)))  =>  ((k1_funct_1 (k7_funct_6 (k10_finseq_1 A B)) (k10_finseq_1 C D)) = (k10_finseq_1 (k1_funct_1 A C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t144_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  => (r1_xxreal_0 (k3_finseq_1 (k12_glib_001 A B)) (k17_glib_000 A))) ) ) ) ).
tt(t144_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((k16_group_2 A B) = (k1_tarski (u1_struct_0 A)))  =>  (B = A) ) ) ) ) ) ).
tt(t144_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski A B) <=> (r1_tarski (k17_member_1 A C) (k17_member_1 B C))) ) ) ) ) ) ) ).
tt(t144_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k5_relat_1 (k1_funct_4 B C) A) = C) ) ) ) ) ) ).
tt(t144_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski B C) => (r1_tarski (k8_relat_1 B A) (k8_relat_1 C A))) ) ) ) ) ) ).
tt(t144_rvsum_1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k12_rvsum_1 (k8_finseq_1 k1_numbers A B)) = (k8_finseq_1 k1_numbers (k12_rvsum_1 A) (k12_rvsum_1 B))) ) ) ) ) ).
tt(t144_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) )  => (r1_xxreal_0 (k4_seq_4 A) B)) ) ) ) ) ).
tt(t144_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A F E))) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A F (k5_sheffer1 A B (k5_sheffer1 A B B))) D) (k5_sheffer1 A (k5_sheffer1 A E E) D))) = (k5_sheffer1 A D (k5_sheffer1 A F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t144_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k9_xboolean A B)) = k1_xboolean) ) ) ) ) ).
tt(t144_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_xcmplx_0 (k4_xcmplx_0 A) B))) ) ) ) ) ).
tt(t144_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers))  &  ( (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 A k6_numbers)) ) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  (~ (r1_xxreal_0 k6_numbers A)) ) ) ) ) ) ) ) ) ) ).
tt(t144_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k2_xxreal_1 A C) (k1_xxreal_1 B D)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t144_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k3_zf_lang1 (k11_zf_lang A B)) = (k2_xboole_0 (k3_zf_lang1 A) (k3_zf_lang1 B))) ) ) ) ) ).
tt(t144_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  => (v13_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ).
tt(t145_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  ((k63_abcmiz_1 A B (k4_subset_1 (k38_abcmiz_1 A) C D)) = (k4_subset_1 (k38_abcmiz_1 A) (k63_abcmiz_1 A B C) (k63_abcmiz_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t145_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k1_tarski C)) &  ((v1_funct_1 D) & (v1_partfun1 D (k1_tarski C))) ) )  =>  ( (D = (k16_funcop_1 C A))  =>  ((k1_funct_1 (k3_relat_1 (k7_finseq_2 C) (k6_finseq_2 (k1_tarski C) D)) B) = (k9_funct_2 (k2_finseq_1 B) A)) ) ) ) ) ) ) ) ) ).
tt(t145_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 B)) & (r2_hidden A (k9_xtuple_0 C)))  =>  (! [D:$i] :  (! [E:$i] :  ( ((k1_funct_1 (k13_funct_3 B C) A) = (k4_tarski D E))  <=>  ((k1_funct_1 (k6_funct_6 (k10_finseq_1 B C)) A) = (k10_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ).
tt(t145_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((r1_xxreal_0 (k3_finseq_1 B) 3) => (v5_glib_001 B A)) ) ) ) ) ).
tt(t145_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((k17_group_2 A B) = (k1_card_1 (k15_group_2 A B)))  &  ((k17_group_2 A B) = (k1_card_1 (k16_group_2 A B))) ) ) ) ) ) ).
tt(t145_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k17_member_1 A C) = (k17_member_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t145_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v5_relat_1 C B) & (v1_funct_1 C)) ) )  =>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  & (r1_tarski C D)) ) ) ) ) ) ) ).
tt(t145_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((r1_tarski C D) & (r1_tarski A B))  => (r1_tarski (k8_relat_1 C A) (k8_relat_1 D B))) ) ) ) ) ) ) ).
tt(t145_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 A k1_numbers)) ) ).
tt(t145_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C)) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) (k5_sheffer1 A (k5_sheffer1 A D B) (k5_sheffer1 A (k5_sheffer1 A C C) B))) = (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) ) ) ) ) ) ) ) ) ).
tt(t145_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k6_xboolean A B)) = k1_xboolean) ) ) ) ) ).
tt(t145_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C) = (k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) C) B)) ) ) ) ) ) ) ).
tt(t145_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 (k2_xcmplx_0 B 1) A)) ) ) ) ) ) ).
tt(t145_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 C D) |  ((k3_xboole_0 (k2_xxreal_1 A C) (k1_xxreal_1 B D)) = (k1_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t145_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k3_zf_lang1 (k12_zf_lang A B)) = (k2_xboole_0 (k3_zf_lang1 A) (k3_zf_lang1 B))) ) ) ) ) ).
tt(t145_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  => (v14_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ).
tt(t146_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  ((r1_tarski C D) => (r1_tarski (k63_abcmiz_1 A B C) (k63_abcmiz_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t146_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_tarski (k61_valued_1 B C) A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 A (k2_nat_1 C D)) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t146_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 D)))  =>  (! [E:$i] :  (! [F:$i] :  ( ((k1_binop_1 (k15_funct_3 C D) A B) = (k4_tarski E F))  <=>  ((k1_funct_1 (k7_funct_6 (k10_finseq_1 C D)) (k10_finseq_1 A B)) = (k10_finseq_1 E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t146_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) )  => (v5_glib_001 B A)) ) ) ) ) ).
tt(t146_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v1_finset_1 (k15_group_2 A B)) =>  ( (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (k15_group_2 A B))  &  ((k18_group_2 A B) = (k5_card_1 C)) ) ) )  &  (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (k16_group_2 A B))  &  ((k18_group_2 A B) = (k5_card_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t146_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k17_member_1 A k6_numbers) = A) ) ) ).
tt(t146_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A C B))  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t146_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k8_relat_1 (k3_relat_1 B C) A) = (k8_relat_1 B (k8_relat_1 C A))) ) ) ) ) ) ).
tt(t146_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D C)) C) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A D D) B))) ) ) ) ) ) ) ) ) ).
tt(t146_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k8_xboolean A B)) = k1_xboolean) ) ) ) ) ).
tt(t146_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C) = (k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) C) A)) ) ) ) ) ) ) ).
tt(t146_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 A (k6_xcmplx_0 A 1))) ) ) ).
tt(t146_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k3_xboole_0 (k3_xxreal_1 A C) (k1_xxreal_1 B D)) = (k1_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t146_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k13_zf_lang B A)) = (k2_xboole_0 (k3_zf_lang1 A) (k1_tarski B))) ) ) ) ) ).
tt(t146_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))))  &  ((v10_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))) &  ((v15_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A))) & (l3_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ) ) ) ).
tt(t147_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m3_abcmiz_1 C A) =>  ( ((k41_abcmiz_1 A (k64_abcmiz_1 A B C)) = (k63_abcmiz_1 A B (k41_abcmiz_1 A C)))  &  ((k42_abcmiz_1 A (k64_abcmiz_1 A B C)) = (k62_abcmiz_1 A B (k42_abcmiz_1 A C))) ) ) ) ) ) ) ) ).
tt(t147_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((k8_funct_6 (k9_finseq_1 A) B) = (k9_finseq_1 (k1_funct_2 A B))) ) ) ).
tt(t147_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  ( (~ (v1_glib_001 B A))  =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t147_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k7_group_1 A) = (k4_nat_1 (k7_group_1 B) (k18_group_2 A B))) ) ) ) ) ).
tt(t147_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k17_member_1 A (k3_binop_2 B C)) = (k17_member_1 (k17_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t147_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k9_xtuple_0 (k3_relat_1 A B)) = (k8_relat_1 A (k9_xtuple_0 B))) ) ) ) ) ).
tt(t147_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) C) = (k5_sheffer1 A C (k5_sheffer1 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t147_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k10_xboolean A A) = k1_xboolean) ) ) ).
tt(t147_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C) = (k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 C) B) A)) ) ) ) ) ) ) ).
tt(t147_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 B (k6_xcmplx_0 A 1))) ) ) ) ) ) ).
tt(t147_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 D C))  =>  ((k3_xboole_0 (k3_xxreal_1 A C) (k1_xxreal_1 B D)) = (k3_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t147_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k14_zf_lang B C A)) = (k2_xboole_0 (k3_zf_lang1 A) (k2_tarski B C))) ) ) ) ) ) ) ).
tt(t147_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  => (v12_lattices (g3_lattices (k8_zmodul01 A) (k10_zmodul01 A) (k11_zmodul01 A)))) ) ).
tt(t148_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [C:$i] :  ((m3_abcmiz_1 C A) =>  (! [D:$i] :  ( ((v8_abcmiz_1 D A) & (m1_abcmiz_1 D A (k13_abcmiz_1 A)))  =>  ((k64_abcmiz_1 A B (k43_abcmiz_1 A C D)) = (k43_abcmiz_1 A (k64_abcmiz_1 A B C) (k61_abcmiz_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t148_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k8_funct_6 (k10_finseq_1 A B) C) = (k10_finseq_1 (k1_funct_2 A C) (k1_funct_2 B C))) ) ) ) ).
tt(t148_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_glib_001 B A) <=> (v5_glib_001 (k6_glib_001 A B) A)) ) ) ) ) ).
tt(t148_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (r1_nat_d (k7_group_1 B) (k7_group_1 A))) ) ) ) ).
tt(t148_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k17_member_1 (k9_member_1 A B) C) = (k9_member_1 (k17_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t148_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k3_xboole_0 (k10_xtuple_0 B) A) (k8_relat_1 (k2_relat_1 B) (k8_relat_1 B A)))) ) ) ).
tt(t148_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A C (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D D) C))) = (k5_sheffer1 A C (k5_sheffer1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t148_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 A C)) = (k4_xcmplx_0 (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t148_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 1)))  & (r1_xxreal_0 (k2_xcmplx_0 1 A) k6_numbers)) ) ) ) ).
tt(t148_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k3_xboole_0 (k4_xxreal_1 A C) (k1_xxreal_1 B D)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t148_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k15_zf_lang B C A)) = (k2_xboole_0 (k3_zf_lang1 A) (k2_tarski B C))) ) ) ) ) ) ) ).
tt(t148_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  (! [D:$i] :  ( ((v1_zmodul01 D) & (m1_zmodul01 D A))  =>  ((m1_zmodul01 B C) => (m1_zmodul01 (k7_zmodul01 A B D) (k7_zmodul01 A C D))) ) ) ) ) ) ) ) ) ).
tt(t149_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k56_abcmiz_1 A D (k56_abcmiz_1 A C B)) = (k56_abcmiz_1 A (k65_abcmiz_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t149_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((k9_funct_6 A (k9_finseq_1 B)) = (k9_finseq_1 (k1_funct_2 A B))) ) ) ).
tt(t149_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (v5_glib_001 (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t149_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D C) =>  ( (B = D)  =>  ((k18_group_2 A B) = (k4_nat_1 (k18_group_2 C D) (k18_group_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t149_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k17_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k17_member_1 A C) (k17_member_1 B C))) ) ) ) ) ) ) ).
tt(t149_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_relat_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t149_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A E B)) (k5_sheffer1 A C (k5_sheffer1 A E B))) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C) (k5_sheffer1 A (k5_sheffer1 A B B) C))) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t149_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k6_xcmplx_0 k6_numbers A) = (k4_xcmplx_0 A)) ) ) ).
tt(t149_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k6_xcmplx_0 1 A) k6_numbers)) ) ) ) ).
tt(t149_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 C D) |  ((k3_xboole_0 (k4_xxreal_1 A C) (k1_xxreal_1 B D)) = (k3_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t149_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k16_zf_lang B C D A)) = (k2_xboole_0 (k3_zf_lang1 A) (k1_enumset1 B C D))) ) ) ) ) ) ) ) ) ).
tt(t149_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_zmodul01 A))) ) ) ) ) ) ).
tt(t14_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r1_tarski C (k2_abcmiz_0 A B)) <=> (r2_hidden B (k4_abcmiz_0 A C))) ) ) ) ) ) ) ).
tt(t14_abcmiz_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ( ( ((k1_funct_1 A k6_numbers) = a_0_0_abcmiz_1)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_funct_1 A (k1_nat_1 B 1)) = (a_2_0_abcmiz_1 A B)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(t14_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k2_abcmiz_1) &  ( ((k2_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k8_abcmiz_1)  & (m1_abcmiz_1 B A (k14_abcmiz_1 A))) )  |  ( ((k2_xtuple_0 (k1_funct_1 B k1_xboole_0)) = (u1_struct_0 A))  &  (~  ( (~  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) & (r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) (u4_struct_0 A))) )  &  ( (~  ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k9_abcmiz_1) )  &  (~  ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k10_abcmiz_1) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k1_absvalue A) = 1)  & (r1_xxreal_0 A k6_numbers)) ) ) ) ).
tt(t14_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_aff_1 A B D E) & (r2_analoaf A C D C E))  =>  ((r1_aff_1 A B C D) |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_2 A) => (v11_aff_2 A)) ) ) ).
tt(t14_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 B A) => (r1_tarski C (k1_aff_4 A B C))) ) ) ) ) ) ) ).
tt(t14_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C B) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  &  ((k1_afinsq_1 C) = A) ) ) ) ) ) ) ).
tt(t14_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 B C))  =>  ((k3_afinsq_2 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t14_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((r2_hidden B (k7_afproj A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k5_afproj A C))  & (v1_aff_1 C A)) ) ) ) ) ) ) ).
tt(t14_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_afvect0 A B C) &  ((r1_afvect0 A B D) &  ( (~  (C = D) )  &  (~ (r1_afvect0 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  ( ((r5_alg_1 A B) & (r5_alg_1 B C))  => (r5_alg_1 A C)) ) ) ) ) ) ) ).
tt(t14_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_algseq_1 A (k4_struct_0 A))) <=>  ((k1_algseq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t14_algspec1,ax, (! [A:$i] : (r6_pboole A (k1_algspec1 A k1_xboole_0) (k6_partfun1 A))) ).
tt(t14_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  (B = (k11_binop_2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_xboole_0 B) <=> (v2_struct_0 (k9_algstr_4 A B))) ) ) ) ) ).
tt(t14_altcat_1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((v4_funct_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ((k6_altcat_1 C D) = (k5_relat_1 (k6_altcat_1 A B) (k8_mcart_1 B A D C))) ) ) ) ) ) ) ) ) ).
tt(t14_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (v3_altcat_1 (k3_altcat_2 A) (u1_struct_0 A) (k2_altcat_2 A))) ) ).
tt(t14_altcat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_altcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_altcat_1 A))) =>  ( (~  ((k1_altcat_1 (k7_altcat_1 A) B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 (k7_altcat_1 A) B C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( (E = D)  =>  ((v5_altcat_3 D (k7_altcat_1 A) B C) <=> (v2_funct_2 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  ((v18_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v2_funct_2 (k7_functor0 A B C E D) (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_funct_1 (k7_ami_2 A B C) k5_numbers) = (k1_funct_1 A k5_numbers)) ) ) ) ) ) ) ).
tt(t14_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 A B) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 B))) ) )  & (v2_extpro_1 A 2 k1_ami_3)) ) ) ) ).
tt(t14_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 7)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k8_ami_3 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_ami_3) (k2_compos_0 (u1_compos_1 k1_ami_3) (k9_ami_3 B A)))) 1) = k5_numbers) ) ) ) ) ).
tt(t14_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((v5_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r2_hidden (k5_memstr_0 A B D) (k1_relset_1 k5_numbers C)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B C D E)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (~  ((v4_amistd_1 C A B) & (r2_hidden (k4_struct_0 B) (k3_amistd_4 A B C))) ) ) ) ) ) ) ) ).
tt(t14_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) &  ((v5_amistd_5 B A) &  ((v6_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v6_memstr_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k11_memstr_0 A B) (k11_memstr_0 A B))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  (~ (v2_compos_1 E B)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) &  ((v4_extpro_1 F A B E) & (v5_extpro_1 F A B E)) ) ) ) ) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 F)) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_extpro_1 A B E F C) <=> (r2_extpro_1 A B (k6_compos_1 B E G) (k9_memstr_0 A B F G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k5_ami_wstd A B C) = (k1_ami_wstd A B (k2_nat_1 (k3_ami_wstd A B C) 1))) ) ) ) ) ) ) ).
tt(t14_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( ((r1_analoaf A B C D E) | (r1_analoaf A B C E D))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( ((k1_rlvect_1 A (k5_algstr_0 A C B) F) = (k1_rlvect_1 A (k5_algstr_0 A E D) G))  &  (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) )  &  (~  ( (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( ((k1_rlvect_1 A (k5_algstr_0 A C B) F) = (k1_rlvect_1 A (k5_algstr_0 A E D) G))  &  (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) )  &  ( (~ (r1_analoaf A B C D E))  &  (~ (r1_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_analoaf A B C B D) &  ( (~ (r1_analoaf A B C C D))  &  (~ (r1_analoaf A B D D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k2_analort A B C (k2_analort A B C D)) = (k4_algstr_0 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_anproj_1 A B C D) &  ((r2_anproj_1 A B C E) & (r2_anproj_1 A B C F)) )  =>  ((r1_anproj_1 A B C) |  ((v9_struct_0 B A) |  ((v9_struct_0 C A) | (r2_anproj_1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (A = (k8_domain_1 A B C D))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [E:$i] :  ((m2_funct_2 E A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (~ (r2_funct_2 A k1_numbers H (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I E)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J F))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  &  ( ((u1_struct_0 B) = k5_numbers)  &  ( ((k1_unialg_1 B) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  (D = (k1_recdef_1 A C)) )  =>  ((k1_funct_1 (u1_unialg_1 B) C) = (k7_funcop_1 (k4_finseq_2 D k5_numbers) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (r2_funct_2 (k9_funct_2 A k4_numbers) k4_numbers (k22_aofa_i00 A B) (k23_aofa_i00 A (k24_aofa_i00 A B)))) ) ) ) ).
tt(t14_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k7_armstrng A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k4_armstrng A)) &  (? [D:$i] :  ((m1_subset_1 D (k4_armstrng A)) &  ( (B = (k4_tarski C D))  & (r3_armstrng A D C)) ) ) ) ) ) ) ) ).
tt(t14_arrow,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_funct_2 B (k2_arrow A)) (k2_arrow A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B (k2_arrow A)) (k2_arrow A))))) )  =>  (~  ( (! [D:$i] :  ((m2_funct_2 D B (k2_arrow A) (k9_funct_2 B (k2_arrow A))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ( (! [G:$i] :  ((m1_subset_1 G B) =>  (~ (r1_arrow (k3_funct_2 B (k2_arrow A) D G) F E)) ) )  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C D) F E)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_funct_2 D B (k2_arrow A) (k9_funct_2 B (k2_arrow A))) =>  (! [E:$i] :  ((m2_funct_2 E B (k2_arrow A) (k9_funct_2 B (k2_arrow A))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  ( (~ (r1_arrow (k3_funct_2 B (k2_arrow A) D H) G F))  & (r1_arrow (k3_funct_2 B (k2_arrow A) E H) G F)) )  &  ( (~  ( (~ (r1_arrow (k3_funct_2 B (k2_arrow A) E H) G F))  & (r1_arrow (k3_funct_2 B (k2_arrow A) D H) G F)) )  &  ( (~  ( (~ (r1_arrow (k3_funct_2 B (k2_arrow A) D H) F G))  & (r1_arrow (k3_funct_2 B (k2_arrow A) E H) F G)) )  &  (~  ( (~ (r1_arrow (k3_funct_2 B (k2_arrow A) E H) F G))  & (r1_arrow (k3_funct_2 B (k2_arrow A) D H) F G)) ) ) ) ) ) )  =>  ( (~  ( (~ (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C D) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C E) G F)) )  &  (~  ( (~ (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C E) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C D) G F)) ) ) ) ) ) ) ) ) ) ) )  &  ((r1_xxreal_0 3 (k5_card_1 A)) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (? [E:$i] :  ((m2_funct_2 E B (k2_arrow A) (k9_funct_2 B (k2_arrow A))) &  (? [F:$i] :  ((m1_subset_1 F A) &  (? [G:$i] :  ((m1_subset_1 G A) &  ( (~ (r1_arrow (k3_funct_2 B (k2_arrow A) E D) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k2_arrow A)) (k2_arrow A) C E) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_arytm_0 A (k1_arytm_0 B C)) = (k1_arytm_0 (k2_arytm_0 A B) (k2_arytm_0 A C))) ) ) ) ) ) ) ).
tt(t14_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 C A))  =>  ((k7_arytm_2 (k1_arytm_1 B A) C) = (k1_arytm_1 B (k1_arytm_1 A C))) ) ) ) ) ) ) ) ).
tt(t14_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (~  ( (~  (A = k11_arytm_3) )  &  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ((k8_arytm_2 A B) = k12_arytm_3) ) ) ) ) ) ) ) ).
tt(t14_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( ((k3_arytm_3 A k1_xboole_0) = A)  &  ((k2_arytm_3 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t14_asympt_0,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden B (k6_asympt_0 C)) => (r2_hidden B (k6_asympt_0 (k3_asympt_0 C A)))) ) ) ) ) ) ) ).
tt(t14_asympt_1,ax, (~ (r2_hidden (k5_asympt_1 k6_numbers) (k8_asympt_0 (k5_asympt_1 1)))) ).
tt(t14_autalg_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  ( ((v1_msualg_3 A) & (v1_msualg_3 B))  => (v1_msualg_3 (k8_pboole A B))) ) ) ) ) ).
tt(t14_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  ((k1_binop_1 (k2_autgroup A) B C) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B)) ) ) ) ) ) ) ).
tt(t14_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A C B) =>  ((k3_bagorder A (k12_pre_poly A B C)) = (k6_xcmplx_0 (k3_bagorder A B) (k3_bagorder A C))) ) ) ) ) ) ) ) ).
tt(t14_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B C (k1_bcialg_1 B D C)) = C) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t14_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B (k2_nat_1 C D))) = (k1_bcialg_1 A (k2_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B C)) (k1_bcialg_2 A (k4_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t14_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v4_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) )  &  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v5_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t14_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_4 A B D) (k1_bcialg_4 A C D)) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t14_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_bcialg_5 E A B C D) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (m1_bcialg_5 E (k2_nat_1 A F) B C (k2_nat_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_bcialg_1 A (k3_bcialg_6 A (k23_binop_2 C 1) B)) = (k1_bcialg_1 A (k2_bcialg_1 A (k3_bcialg_6 A C B)) B)) ) ) ) ) ) ) ).
tt(t14_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_bciideal B A) => (m2_bcialg_1 B A)) ) ) ) ) ).
tt(t14_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k4_struct_0 A) B) = k6_numbers) ) ) ) ) ).
tt(t14_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (v1_bhsp_2 C A))  =>  ((k1_bhsp_2 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k1_bhsp_2 A B) (k1_bhsp_2 A C))) ) ) ) ) ) ) ) ).
tt(t14_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) =>  ((k1_normsp_1 A B E) = (k1_normsp_1 A C E)) ) ) ) ) )  => (r2_bhsp_3 A B C)) ) ) ) ) ) ) ).
tt(t14_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) & (v1_bhsp_4 (k1_valued_0 (u1_struct_0 A) B C) A)) )  => (v1_bhsp_4 B A)) ) ) ) ) ).
tt(t14_bhsp_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v1_setwiseo C A)) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  ((r1_xboole_0 D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((r1_tarski D (k9_xtuple_0 F)) & (r1_tarski E (k9_xtuple_0 F)))  =>  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 B)))  =>  ( (G = (k2_xboole_0 D E))  =>  ((k5_bhsp_5 A B C G F) = (k5_binop_1 A C (k5_bhsp_5 A B C D F) (k5_bhsp_5 A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k3_bilinear A B C D E) F) (k6_hahnban1 A B E (k8_bilinear A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k2_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))) = (k9_binarith A 1 k6_margrel1 (k2_binari_2 A B) (k10_binarith k6_margrel1 (k2_binarith (k9_margrel1 C) (k8_binarith A (k3_binarith A B) (k1_binari_2 A)))))) ) ) ) ) ) ) ).
tt(t14_binari_3,ax, ((k3_binarith 1 (k10_binarith k6_margrel1 k7_margrel1)) = (k10_binarith k6_margrel1 k8_margrel1)) ).
tt(t14_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((r1_xxreal_0 (k23_binop_2 A B) (k21_binop_2 (k5_series_1 2 (k7_nat_d C 1)) 1)) =>  ((k3_binari_2 C (k7_binarith C (k1_binari_3 C A) (k1_binari_3 C B))) = (k23_binop_2 A B)) ) ) ) ) ) ) ) ).
tt(t14_binarith,ax, (! [A:$i] :  ( ((v3_card_1 A 1) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k12_finseq_1 k6_margrel1 k7_margrel1))  |  (A = (k12_finseq_1 k6_margrel1 k8_margrel1)) ) ) ) ).
tt(t14_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_binom A B 1) = B) ) ) ) ) ).
tt(t14_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 C A) =>  ((r6_binop_1 A C B) <=> (r4_binop_1 A C B)) ) ) ) ) ) ) ) ).
tt(t14_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 B k6_margrel1)) =>  ( (C = (k5_euclid B))  =>  ((k1_funct_1 (k1_bintree2 A B) (k3_binarith B C)) = (k5_series_1 2 B)) ) ) ) ) ) ) ) ).
tt(t14_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_boolealg A B (k4_lattices A C D)) =>  ((r3_boolealg A B C) & (r3_boolealg A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ( (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 C))))) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ( (~  ( (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) & (r2_hidden F (k3_funct_2 k5_numbers (k9_setfam_1 C) (k1_valued_0 (k9_setfam_1 C) D E) G))) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 E G) & (r2_hidden F (k3_funct_2 k5_numbers (k9_setfam_1 C) D G))) ) ) ) ) )  &  (~  ( (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) &  ((r1_xxreal_0 E G) & (r2_hidden F (k3_funct_2 k5_numbers (k9_setfam_1 C) D G))) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~ (r2_hidden F (k3_funct_2 k5_numbers (k9_setfam_1 C) (k1_valued_0 (k9_setfam_1 C) D E) G))) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 C))))) )  =>  (! [E:$i] :  ((r2_hidden E (k3_prob_1 C (k7_bor_cant C D))) <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) &  ((r1_xxreal_0 F G) & (r2_hidden E (k3_funct_2 k5_numbers (k9_setfam_1 C) D G))) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((r2_hidden D (k2_prob_2 A B (k7_bor_cant A C))) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r2_hidden D (k1_prob_2 A B C F))) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 C))))) )  =>  (! [E:$i] :  ((r2_hidden E (k1_prob_1 C (k9_bor_cant C D))) <=>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 F G) => (r2_hidden E (k3_funct_2 k5_numbers (k9_setfam_1 C) D G))) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((r2_hidden D (k1_prob_1 A (k9_bor_cant A C))) <=>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) => (r2_hidden D (k1_prob_2 A B C F))) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_prob_1 A (k9_bor_cant A (k2_prob_1 A C)))) <=>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 E F) & (r2_hidden D (k1_prob_2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((k1_tops_1 (k2_borsuk_1 A B) C) = (k5_setfam_1 (u1_struct_0 (k2_borsuk_1 A B)) (k7_borsuk_1 A B C))) ) ) ) ) ) ) ).
tt(t14_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) =>  ( ((v5_pre_topc E k5_topmetr A) &  ((v5_pre_topc F k5_topmetr A) &  ( ((k1_funct_1 E k6_numbers) = B)  &  ( ((k1_funct_1 E 1) = C)  &  ( ((k1_funct_1 F k6_numbers) = C)  &  ((k1_funct_1 F 1) = D) ) ) ) ) )  =>  ((v5_pre_topc (k1_borsuk_2 A B C D E F) k5_topmetr A) &  ( ((k1_funct_1 (k1_borsuk_2 A B C D E F) k6_numbers) = B)  &  ((k1_funct_1 (k1_borsuk_2 A B C D E F) 1) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((r2_borsuk_3 A B) & (v1_compts_1 A))  => (v1_compts_1 B)) ) ) ) ) ).
tt(t14_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_rcomp_1 B C))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k5_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t14_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_metric_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k8_metric_1)) =>  ((r1_xxreal_0 A B) =>  ((k4_metric_1 k8_metric_1 A B) = (k6_xcmplx_0 B A)) ) ) ) ) ) ).
tt(t14_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((v3_topmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_xreal_0 B)) ) ) ) ) ).
tt(t14_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_euclid A (k5_euclid A)) = (k5_euclid A)) ) ) ).
tt(t14_brouwer,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A))) &  ((v5_pre_topc C (k2_brouwer 2 B A) (k2_brouwer 2 B A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A)))))) ) )  => (v2_abian C)) ) ) ) ) ) ).
tt(t14_bspace,ax, (! [A:$i] :  ((k3_bspace k1_xboole_0 A) = (k4_struct_0 k2_bspace)) ) ).
tt(t14_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A D B)) (k5_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t14_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( (G = (k1_funct_4 (k1_funct_4 (k16_funcop_1 A D) (k16_funcop_1 B E)) (k16_funcop_1 C F)))  =>  ((k10_xtuple_0 G) = (k1_enumset1 (k1_funct_1 G A) (k1_funct_1 G B) (k1_funct_1 G C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k2_bvfunc_1 A B C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t14_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k1_bvfunc_1 A B)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t14_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k6_bvfunc26 A C D)) (k5_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) C) D)) & (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k6_bvfunc26 A C D)) (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A B D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k5_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t14_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k11_bvfunc_1 A)) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t14_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k12_bvfunc_1 A)) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t14_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A D E)) (k5_bvfunc_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_c0sp1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_c0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_c0sp1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k8_group_1 (k7_c0sp1 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_seq_1 G H) = (k8_real_1 (k1_seq_1 E H) (k1_seq_1 F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  ( (B = (k4_struct_0 (k5_c0sp2 A)))  =>  (k6_numbers = (k1_normsp_0 (k5_c0sp2 A) B)) ) ) ) ) ) ).
tt(t14_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r2_hidden 1 (k1_relset_1 k5_numbers (k10_finseq_1 B C))) &  ((r2_hidden 2 (k1_relset_1 k5_numbers (k10_finseq_1 B C))) &  ( ((k1_funct_1 (k7_finseq_1 D (k10_finseq_1 B C)) (k2_nat_1 (k3_finseq_1 D) 1)) = B)  &  ((k1_funct_1 (k7_finseq_1 D (k10_finseq_1 B C)) (k2_nat_1 (k3_finseq_1 D) 2)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t14_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) => (r1_tarski (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)) (k1_relset_1 k5_numbers (k8_finseq_1 (k3_cqc_lang A) B C)))) ) ) ) ) ) ).
tt(t14_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_cantor_1 A B) (k2_cantor_1 A C))) ) ) ) ) ) ).
tt(t14_card_1,ax, (! [A:$i] : (r2_hidden (k1_card_1 A) (k1_card_1 (k1_zfmisc_1 A)))) ).
tt(t14_card_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k1_card_1 (k11_ordinal2 A B)) = (k2_card_2 (k1_card_1 A) (k1_card_1 B))) ) ) ) ) ).
tt(t14_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k5_card_3 A (k1_tarski B)) = (k1_tarski (k1_funct_1 B A))) ) ) ) ).
tt(t14_card_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_ordinal1 k4_ordinal1 (k1_card_1 (k3_finseq_2 A)))) ) ).
tt(t14_card_5,ax, (! [A:$i] :  ((v1_card_1 A) => (r2_hidden A (k3_card_2 2 A))) ) ).
tt(t14_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_card_fil C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D C) & (r1_xboole_0 D B)) ) ) )  =>  ((r2_hidden B (k2_card_fil A C B)) &  ((m1_card_fil (k2_card_fil A C B) A) & (r1_tarski C (k2_card_fil A C B))) ) ) ) ) ) ) ) ) ).
tt(t14_cardfin2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((k1_afinsq_1 B) = (k23_binop_2 (k1_afinsq_1 A) 1))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k5_relat_1 B (k1_afinsq_1 A)) = (k24_valued_1 A C))  =>  ((k7_afinsq_2 B) = (k20_binop_2 (k22_binop_2 C (k7_afinsq_2 A)) (k1_funct_1 B (k1_afinsq_1 A)))) ) ) ) ) ) ) ) ) ).
tt(t14_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~ (r2_hidden A D))  &  ( (~  (B = C) )  &  (~  ((k5_card_1 (k1_card_fin D E B C)) = (k1_card_1 (a_5_1_card_fin A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r4_card_lar A B) &  ((r1_tarski B C) & (r1_tarski C A)) )  => (r4_card_lar A C)) ) ) ) ) ).
tt(t14_cat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cat_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_cat_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_cat_1 A B))) =>  (! [G:$i] :  ((m1_cat_1 G (k3_cat_1 A B) C D) =>  (! [H:$i] :  ((m1_cat_1 H (k3_cat_1 A B) E F) =>  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_cat_1 B A (k5_cat_2 A B)) C) = C) ) ) ) ) ) ) ).
tt(t14_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  ( (~  (A = B) )  => (r2_funct_2 (k2_tarski A B) (u4_struct_0 C) (k6_cat_3 C (k2_tarski A B) (k5_funct_4 (u4_struct_0 C) A B D E) F) (k5_funct_4 (u4_struct_0 C) A B (k1_cat_1 C F D) (k1_cat_1 C F E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_cat_4 A B) = (k10_cat_3 A B (k1_cat_4 A))) ) ) ) ) ).
tt(t14_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u4_struct_0 A) = (u4_struct_0 B)) )  =>  ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B))) ) ) ) ) ) ).
tt(t14_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_catalan1 (k1_nat_1 A 1)) = (k10_real_1 (k9_newton (k4_nat_1 2 A)) (k4_nat_1 (k9_newton A) (k9_newton (k1_nat_1 A 1))))) ) ) ).
tt(t14_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (~  ( (A = (k5_nat_1 (a_1_0_catalan2 B)))  &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((v1_catalan2 B) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k5_relat_1 B A) = (k1_catalan2 (k1_catalan2 (k8_funcop_1 k5_numbers 1 k6_numbers) C) (k8_funcop_1 k5_numbers 1 1)))  & (v1_catalan2 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_catalg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ((m1_subset_1 D A) &  (? [E:$i] :  ((m1_subset_1 E A) &  (C = (k9_catalg_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_cayley,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r1_group_6 A (k10_group_6 A (k2_cayley (u1_struct_0 A)) (k4_cayley A)))) ) ).
tt(t14_cc0sp1,ax, (! [A:$i] :  ((l1_clopban2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v2_cfuncdom B) & (l1_cfuncdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((g1_cfuncdom (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_clvect_1 A) (u3_struct_0 A) (u2_struct_0 A)) = B)  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k1_group_1 (k3_cc0sp2 A)) = (k1_cc0sp2 A k6_complex1)) ) ) ).
tt(t14_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((v1_partfun1 B k2_numbers) & (v1_partfun1 C k2_numbers))  =>  ((r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A (k2_valued_1 k2_numbers k2_numbers k2_numbers B C)) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A B) (k8_funct_2 k5_numbers k2_numbers k2_numbers A C))) &  ((r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A (k46_valued_1 k2_numbers k2_numbers k2_numbers B C)) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A B) (k8_funct_2 k5_numbers k2_numbers k2_numbers A C))) & (r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A (k19_valued_1 k2_numbers k2_numbers k2_numbers B C)) (k19_valued_1 k5_numbers k2_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers A B) (k8_funct_2 k5_numbers k2_numbers k2_numbers A C)))) ) ) ) ) ) ) ) ) ).
tt(t14_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (a_2_3_cfdiff_1 B C))  => (v5_cfdiff_1 A)) ) ) ) ) ) ) ).
tt(t14_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k1_binop_1 (k1_cfuncdom A) (k1_funct_1 (k3_cfuncdom A) (k4_tarski C B)) (k1_funct_1 (k3_cfuncdom A) (k4_tarski D B))) = (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) (k3_binop_2 C D) B))) ) ) ) ) ) ) ) ) ).
tt(t14_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) D) (k19_valued_1 A k2_numbers k2_numbers B (k19_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t14_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k8_cgames_1 B)) => (r2_hidden (k9_cgames_1 A) (k9_cgames_1 B))) ) ) ) ) ).
tt(t14_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t14_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( ((v2_funct_1 A) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((k4_finseq_4 A (k1_funct_1 A B)) = B) ) ) ) ) ) ).
tt(t14_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 B) (k3_msafree2 A)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  ( (H = (k5_relat_1 G (u1_struct_0 B)))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((k5_relat_1 (k5_facirc_1 C F G I) (u1_struct_0 B)) = (k5_facirc_1 B E H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k10_xtuple_0 (k8_finseq_4 A B C D E)) = (k3_enumset1 A B C D E)) ) ) ) ) ) ).
tt(t14_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_circcomb A B))) =>  ( (C = D)  =>  ( ((k1_msualg_1 (k2_circcomb A B) D) = (k1_msualg_1 B C))  &  ((k2_msualg_1 (k2_circcomb A B) D) = (k2_msualg_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k2_circled1 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t14_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_circtrm1 A B D))) =>  ((k1_funct_1 (u3_msualg_1 (k1_circtrm1 A B D) (k6_circtrm1 A B D C)) E) = (k2_circtrm1 A B D E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C (k3_msafree2 A)) &  ((r2_hidden D (k2_relset_1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A C)))) & (r1_xxreal_0 (k4_circuit1 A B C) (k4_circuit1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  ((v3_funct_1 (k10_funct_6 C)) =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ((m1_msafree2 E A B) =>  ( (E = (k1_funct_1 (k10_funct_6 C) k6_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) => (r1_tarski E (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((v4_ordinal1 D) & (r2_hidden A (k3_classes1 B D)))  =>  ( (D = k1_xboole_0)  |  ( ( (~ (r1_tarski C A))  &  (~  (C = (k9_setfam_1 A)) ) )  | (r2_hidden C (k3_classes1 B D))) ) ) ) ) ) ) ) ).
tt(t14_classes2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k1_card_1 (k1_classes1 B))) => (r2_hidden A (k1_classes1 B))) ) ) ).
tt(t14_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  => (m1_clvect_1 (g1_clvect_1 (k5_clopban1 A B) (k10_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k8_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B)) (k9_csspace (k3_clopban1 (u1_struct_0 A) B) (k5_clopban1 A B))) (k3_clopban1 (u1_struct_0 A) B))) ) ) ) ).
tt(t14_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_clopban2 A)))  &  ((v13_algstr_0 (k7_clopban2 A)) &  ((v2_rlvect_1 (k7_clopban2 A)) &  ((v3_rlvect_1 (k7_clopban2 A)) &  ((v4_rlvect_1 (k7_clopban2 A)) &  ((v3_group_1 (k7_clopban2 A)) &  ((v4_vectsp_1 (k7_clopban2 A)) &  ((v5_vectsp_1 (k7_clopban2 A)) & (l6_algstr_0 (k7_clopban2 A))) ) ) ) ) ) ) ) ) ) ).
tt(t14_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clopban3 B A) =>  ((v9_clvect_1 B A) &  ((k7_clvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t14_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_normsp_1 A (k4_lopban_4 A C) B) = (k1_normsp_1 A C (k7_nat_d B 1))) ) ) ) ) ) ) ) ).
tt(t14_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v3_closure1 (k2_msualg_3 A (k5_mssubfam A B)) A B) & (m2_pboole (k2_msualg_3 A (k5_mssubfam A B)) A (k5_mssubfam A B) (k5_mssubfam A B))) ) ) ) ).
tt(t14_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k4_closure2 A B C) D) = (a_4_0_closure2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t14_closure3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v4_closure2 (k6_msualg_2 A B) (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_subset_1 (k6_msualg_2 A B) (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B))))) ) ) ) ) ).
tt(t14_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_clvect_1 A (k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t14_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 B A) & (v1_clvect_2 C A))  =>  ((k1_clvect_2 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k1_clvect_2 A B) (k1_clvect_2 A C))) ) ) ) ) ) ) ) ).
tt(t14_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) & (v1_clvect_3 (k1_valued_0 (u1_struct_0 A) B C) A)) )  => (v1_clvect_3 B A)) ) ) ) ) ).
tt(t14_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ((v1_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  => (r2_hidden (k3_tarski B) A)) ) ) ) ).
tt(t14_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_hidden B (k2_coh_sp A C)) <=> (m1_toler_1 B A C)) ) ) ) ) ).
tt(t14_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m2_collsp B A) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (C = D) )  &  ((r2_hidden C B) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((r1_xxreal_0 2 A) & (r1_ordinal1 (k2_nat_1 A 2) (k1_card_1 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ( ((v3_combgras C A B) | (v4_combgras C A B))  => (v2_combgras C (k1_combgras A B))) ) ) ) ) ) ) ) ).
tt(t14_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k4_complex1 A) = k6_numbers)  &  ((k4_complex1 B) = k6_numbers) )  =>  ( ((k3_complex1 (k3_xcmplx_0 A B)) = (k8_real_1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k3_xcmplx_0 A B)) = k6_numbers) ) ) ) ) ) ) ).
tt(t14_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k1_comptrig A) = k6_numbers) ) ) ) ).
tt(t14_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k11_algstr_0 k1_complfld A) = (k11_algstr_0 k1_complfld B))  =>  ( (A = (k4_struct_0 k1_complfld))  |  ( (B = (k4_struct_0 k1_complfld))  |  (A = B) ) ) ) ) ) ) ) ).
tt(t14_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k4_finseq_2 A k2_numbers)) =>  ( (C = (k9_matrix_5 D B))  =>  ((k9_matrix_5 (k5_complsp2 A D) B) = (k1_binop_2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v4_tbsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))) =>  (~  ((v2_tops_2 B (k3_pcomps_1 A)) &  ((v3_finset_1 B) &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D B) &  ((v6_tbsp_1 D A) &  (~ (r1_xxreal_0 C (k3_tbsp_1 A D))) ) ) ) ) ) ) ) ) )  & (v1_xboole_0 (k6_setfam_1 (u1_struct_0 (k3_pcomps_1 A)) B))) ) ) ) ) ) ) ) ) ).
tt(t14_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  ((k5_card_1 (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E)) = 5) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) => (r1_xxreal_0 (k1_seq_1 k19_sin_cos A) k6_numbers)) ) ) ).
tt(t14_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_compts_1 A) &  ((v5_pre_topc C A B) &  ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B)) ) )  => (v1_compts_1 B)) ) ) ) ) ) ) ).
tt(t14_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_funct_1 A) & (v1_comput_1 A)) )  =>  ((k10_xtuple_0 (k3_tarski A)) = (k3_tarski (a_1_1_comput_1 A))) ) ) ).
tt(t14_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A B) C) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A C) (k19_valued_1 k5_numbers k2_numbers k2_numbers B C)))) ) ) ) ) ) ).
tt(t14_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k8_complex1 (k3_comseq_2 A) (k3_comseq_2 B))) ) ) ) ) ).
tt(t14_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers k1_numbers (k7_comseq_3 A) (k7_comseq_3 B)) & (r2_funct_2 k5_numbers k1_numbers (k8_comseq_3 A) (k8_comseq_3 B)))  => (r2_funct_2 k5_numbers k2_numbers A B)) ) ) ) ) ).
tt(t14_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  => (v3_conlat_1 (k1_waybel_1 (k3_yellow_1 (u1_struct_0 A)) (k3_yellow_1 (u4_struct_0 A)) (k3_conlat_1 A) (k4_conlat_1 A)) (k3_yellow_1 (u1_struct_0 A)) (k3_yellow_1 (u4_struct_0 A)))) ) ).
tt(t14_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_conlat_1 B))  & (l1_conlat_1 B))  =>  ((r1_filter_1 (k11_conlat_1 B) A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u1_struct_0 A))))) )  &  ((v8_lattice6 (k2_relset_1 (u1_struct_0 A) C) A) &  ((v9_lattice6 (k2_relset_1 (u1_struct_0 A) D) A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ((r1_conlat_1 B E F) <=> (r3_lattices A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) (k3_funct_2 (u4_struct_0 B) (u1_struct_0 A) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_conmetr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_conmetr A) <=> (v7_aff_2 (k3_analmetr A))) ) ) ).
tt(t14_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( ((v3_conmetr A) & (v4_conmetr A))  => (v1_conmetr A)) ) ) ).
tt(t14_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v5_pre_topc C A B) &  ( ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_struct_0 A)) = (k2_struct_0 B))  & (v1_connsp_1 A)) )  => (v1_connsp_1 B)) ) ) ) ) ) ) ).
tt(t14_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_connsp_2 A B) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc C A) &  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_pre_topc A C))) =>  (~  ( (D = B)  & (r2_hidden B (k1_tops_1 (k1_pre_topc A C) (k1_connsp_1 (k1_pre_topc A C) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) & (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B C) A))  =>  ( (B = k1_xboole_0)  | (r1_tarski (k4_subset_1 (u1_struct_0 A) B C) (k1_connsp_3 A B))) ) ) ) ) ) ) ) ).
tt(t14_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((v1_convex1 B A) &  ((v1_convex1 C A) & (v1_convex1 D A)) )  => (v1_convex1 (k7_rusub_4 A (k7_rusub_4 A (k1_convex1 A B E) (k1_convex1 A C F)) (k1_convex1 A D G)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C (k3_rlvect_2 A B)) &  (! [D:$i] :  ((m1_rlvect_2 D A) =>  (~  ((k3_rlvect_2 A D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_convex4 C A (k6_domain_1 (u1_struct_0 A) B)) =>  ((k4_convex4 A C) = (k1_clvect_1 A B (k3_funct_2 (u1_struct_0 A) k2_numbers C B))) ) ) ) ) ) ) ).
tt(t14_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (m2_subset_1 (k5_qc_lang2 A B C) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ).
tt(t14_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k7_cqc_sim1 A (k5_cqc_lang A)) = k6_numbers) ) ) ).
tt(t14_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((r2_hidden (k13_cqc_lang A C D) (k3_cqc_lang A)) &  ((r2_hidden (k13_cqc_lang A C E) (k3_cqc_lang A)) & (r2_hidden (k13_cqc_lang A C D) (k1_cqc_the1 A B))) )  =>  ((r2_hidden D (k24_qc_lang1 A C)) | (r2_hidden (k13_cqc_lang A C E) (k1_cqc_the1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = D) )  =>  ((k13_cqc_lang A (k12_cqc_lang A C B) D) = (k5_qc_lang2 A C (k13_cqc_lang A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r2_cqc_the3 A (k1_subset_1 (k3_cqc_lang A)) (k4_cqc_the1 A))) ) ).
tt(t14_csspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers A) (k55_valued_1 k5_numbers k2_numbers (k2_comseq_2 k5_numbers A)))) ) ).
tt(t14_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_csspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  => (r2_funct_2 A (u1_struct_0 B) (k6_csspace4 A B C) C)) ) ) ) ) ) ).
tt(t14_csspace,ax, ( (~ (v2_struct_0 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))))  &  ((v13_algstr_0 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v2_rlvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v3_rlvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v4_rlvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v2_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v3_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v4_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) &  ((v5_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace))) & (l1_clvect_1 (g1_clvect_1 k11_csspace (k10_csspace k7_csspace k11_csspace) (k8_csspace k7_csspace k11_csspace) (k9_csspace k7_csspace k11_csspace)))) ) ) ) ) ) ) ) ) ).
tt(t14_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k9_decomp_1 A) (k18_decomp_1 A)) = (k8_decomp_1 A)) ) ) ).
tt(t14_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_finseq_2 D A (k4_finseq_2 B A)) => (m2_finseq_2 (k8_descip_1 A D C) A (k4_finseq_2 B A))) ) ) ) ) ) ) ) ).
tt(t14_dickson,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((v4_relat_2 A) =>  ((r2_hidden (k4_tarski B C) (k3_dickson A)) <=>  ((r2_hidden (k4_tarski B C) A) &  (~  (B = C) ) ) ) ) ) ) ) ) ).
tt(t14_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k26_valued_1 k1_numbers k1_numbers E B) C) (k2_nat_1 A 1)) D) = (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 E C) (k2_nat_1 A 1)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k1_numbers k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k2_diff_2 (k26_valued_1 k1_numbers k1_numbers H A) B C D E F G) = (k8_real_1 A (k2_diff_2 H B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F B)) C) (k2_nat_1 A 1)) D) = (k7_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E C) (k2_nat_1 A 1)) D) (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 F C) (k2_nat_1 A 1)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k1_fdiff_9)) & (r2_hidden B (k1_relset_1 k1_numbers k1_fdiff_9)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_fdiff_9) A B) = (k13_complex1 (k8_real_1 4 (k8_real_1 (k18_sin_cos (k7_real_1 A B)) (k18_sin_cos (k9_real_1 A B)))) (k8_real_1 (k5_square_1 (k7_real_1 (k21_sin_cos (k7_real_1 A B)) (k21_sin_cos (k9_real_1 A B)))) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t14_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 A B C))  &  ( (~ (r1_orders_2 A C B))  &  (~  ((v2_dilworth (k7_domain_1 (u1_struct_0 A) B C) A) & (m1_subset_1 (k7_domain_1 (u1_struct_0 A) B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_diraf A B C D) & (r1_diraf A C B D))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t14_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_dirort D) & (l1_analoaf D)) )  =>  ( ((r1_analmetr A B C) &  (D = (k6_analort A B C)) )  =>  ((v6_dirort D) &  ((v4_dirort D) &  ((v3_dirort D) & (v2_dirort D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k9_dist_1 A B) = (k10_rvsum_1 (k4_dist_1 A B) (k3_finseq_1 B))) ) ) ) ) ).
tt(t14_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k4_zfmisc_1 B C D E)) =>  ( (A = (k5_mcart_1 B C D E F))  <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H C) =>  (! [I:$i] :  ((m1_subset_1 I D) =>  (! [J:$i] :  ((m1_subset_1 J E) =>  ( (F = (k5_domain_1 B C D E G H I J))  =>  (A = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_dtconstr)) =>  ((k18_dtconstr k5_dtconstr A) = (k6_domain_1 (k3_finseq_2 k5_numbers) (k3_pre_poly k5_numbers k6_numbers))) ) ) ).
tt(t14_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin D A) &  ((v2_finsub_1 D) &  ((r2_hidden B D) & (r2_hidden C D)) ) )  => (r2_hidden (k4_subset_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t14_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (m1_subset_1 (k6_int_1 A B) (u1_struct_0 (k9_int_3 B)))) ) ) ) ).
tt(t14_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_group_1 A B (k3_rlvect_1 A (k3_rlvect_1 A C D) E)) = (k3_rlvect_1 A (k3_rlvect_1 A (k8_group_1 A B C) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k5_algstr_0 A (k3_rlvect_1 A C D) E)) = (k5_algstr_0 A (k3_rlvect_1 A (k8_group_1 A B C) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k3_rlvect_1 A (k5_algstr_0 A C D) E)) = (k3_rlvect_1 A (k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k5_algstr_0 A (k5_algstr_0 A C D) E)) = (k5_algstr_0 A (k5_algstr_0 A (k8_group_1 A B C) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k3_rlvect_1 A (k3_rlvect_1 A (k4_algstr_0 A C) D) E)) = (k3_rlvect_1 A (k3_rlvect_1 A (k4_algstr_0 A (k8_group_1 A B C)) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k5_algstr_0 A (k3_rlvect_1 A (k4_algstr_0 A C) D) E)) = (k5_algstr_0 A (k3_rlvect_1 A (k4_algstr_0 A (k8_group_1 A B C)) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ( ((k8_group_1 A B (k3_rlvect_1 A (k5_algstr_0 A (k4_algstr_0 A C) D) E)) = (k3_rlvect_1 A (k5_algstr_0 A (k4_algstr_0 A (k8_group_1 A B C)) (k8_group_1 A B D)) (k8_group_1 A B E)))  &  ((k8_group_1 A B (k5_algstr_0 A (k5_algstr_0 A (k4_algstr_0 A C) D) E)) = (k5_algstr_0 A (k5_algstr_0 A (k4_algstr_0 A (k8_group_1 A B C)) (k8_group_1 A B D)) (k8_group_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = (k1_endalg A))  &  (! [C:$i] :  ((r2_hidden C (k1_endalg A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_endalg A)) (u1_struct_0 (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A)))) &  ((v6_group_1 B (k3_endalg A) (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))) &  ((v1_group_6 B (k3_endalg A) (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_endalg A)) (u1_struct_0 (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))))))) ) ) ) ) ) ) ) ) ).
tt(t14_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  ( ((k6_ens_1 A (k5_ens_1 A (k3_ens_1 A B)) B) = B)  &  ((k6_ens_1 A B (k5_ens_1 A (k4_ens_1 A B))) = B) ) ) ) ) ) ).
tt(t14_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v4_partfun3 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((k1_seq_1 A B) = (k18_rvsum_1 A)) )  => (r1_entropy1 A B)) ) ) ) ) ) ).
tt(t14_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k2_enumset1 A B C D) (k2_tarski E F))) ) ) ) ) ) ) ).
tt(t14_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k5_eqrel_1 A B B) B)) ) ) ).
tt(t14_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  => (r6_pboole A (k1_equation A (k3_funct_6 B) B) (k2_funct_6 B))) ) ) ).
tt(t14_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k9_xtuple_0 (u1_e_siec A)) (u1_struct_0 A)) &  ((r1_tarski (k10_xtuple_0 (u1_e_siec A)) (u1_struct_0 A)) &  ((r1_tarski (k9_xtuple_0 (u2_e_siec A)) (u1_struct_0 A)) & (r1_tarski (k10_xtuple_0 (u2_e_siec A)) (u1_struct_0 A))) ) ) ) ) ).
tt(t14_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k10_binop_2 (k5_square_1 (k12_euclid (k4_rvsum_1 A B))) (k5_square_1 (k12_euclid (k8_rvsum_1 A B)))) = (k11_binop_2 4 (k23_rvsum_1 A B))) ) ) ) ) ) ).
tt(t14_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_euclid_3 (k6_xcmplx_0 A B)) = (k5_algstr_0 (k15_euclid 2) (k1_euclid_3 A) (k1_euclid_3 B))) ) ) ) ) ).
tt(t14_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (~  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ( (~  (B = D) )  & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 3))) =>  ( (D = (k4_euclid_5 A B C))  =>  ( ((k1_euclid_5 D) = A)  &  ( ((k2_euclid_5 D) = B)  &  ((k3_euclid_5 D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (A = B)  |  ( (A = C)  |  ( ( (~  ((k4_euclid_3 D A B) = (k10_real_1 k32_sin_cos 2)) )  &  (~  ((k4_euclid_3 D A B) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) )  |  ((k4_euclid_3 B A D) = (k4_euclid_3 D A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclid_7,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (~  ((v2_funct_1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 A) (k4_finseq_1 A)) &  ((v3_funct_2 B (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (~  ( (C = (k1_partfun1 (k4_finseq_1 A) (k4_finseq_1 A) k5_numbers k5_numbers B A))  &  ((v5_valued_0 C) &  ( ((k4_finseq_1 A) = (k4_finseq_1 C))  &  ((k2_relset_1 k5_numbers A) = (k2_relset_1 k5_numbers C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ((r2_hidden C (k4_euclid_9 A D B)) =>  ( ( (A = k6_numbers)  & (r1_xxreal_0 B k6_numbers))  |  (! [E:$i] :  ( (~ (r1_xxreal_0 B (k18_complex1 (k1_funct_1 (k8_rvsum_1 C D) E))))  &  (~ (r1_xxreal_0 B (k18_complex1 (k6_xcmplx_0 (k1_funct_1 C E) (k1_funct_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k9_real_1 (k12_euclid B) (k12_euclid C)) (k12_euclid (k7_euclid A B C)))) ) ) ) ) ) ).
tt(t14_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid D)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid D)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid D)) =>  ((k8_euclid D E (k7_euclid D (k7_euclid D (k9_euclid D F A) (k9_euclid D G B)) (k9_euclid D H C))) = (k7_euclid D E (k7_euclid D (k7_euclid D (k9_euclid D F (k1_real_1 A)) (k9_euclid D G (k1_real_1 B))) (k9_euclid D H (k1_real_1 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v7_euclmetr A) => (v3_euclmetr A)) ) ) ).
tt(t14_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_int_2 A B) & (r1_int_2 C B))  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (r1_int_2 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t14_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ((k2_euler_2 (k1_euler_2 (k2_euler_2 C B) A) B) = (k2_euler_2 (k1_euler_2 C A) B)) ) ) ) ) ) ) ).
tt(t14_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v3_exchsort C A) & (r2_hidden B (k9_xtuple_0 C)))  => (r2_hidden B A)) ) ) ) ) ) ) ).
tt(t14_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A C)) (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A C)) (u3_msualg_1 A B)) =>  ( ((r1_msualg_3 A (k11_msafree A C) B D) &  ((r1_msualg_3 A (k11_msafree A C) B E) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A C)) (u3_msualg_1 A B) (k13_msafree A C) D) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A C)) (u3_msualg_1 A B) (k13_msafree A C) E))) )  => (r8_pboole (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  =>  ((m1_extpro_1 D A B C) <=> (r2_extpro_1 A B C D (k16_funcop_1 k1_xboole_0 (k7_extpro_1 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t14_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (~  ( (~ (r1_xxreal_0 A k2_supinf_1))  &  ( (~ (r1_xxreal_0 k1_supinf_1 A))  &  ( (~  (A = k6_numbers) )  &  (~  ((k1_extreal1 (k3_extreal1 A) (k3_extreal1 (k2_extreal1 k8_mesfunc1 A))) = k8_mesfunc1) ) ) ) ) ) ) ) ).
tt(t14_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((k5_facirc_1 A B C 1) = (k6_circuit2 A B C)) ) ) ) ) ) ) ).
tt(t14_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k3_msafree2 (k3_facirc_2 (k2_nat_1 A 1) B C)) = (k2_xboole_0 (k3_msafree2 (k3_facirc_2 A B C)) (k3_msafree2 (k19_facirc_1 (k1_funct_1 B (k2_nat_1 A 1)) (k1_funct_1 C (k2_nat_1 A 1)) (k5_facirc_2 A B C))))) ) ) ) ) ) ) ).
tt(t14_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden C A) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((r2_hidden F A) &  ( (~ (r1_xxreal_0 E (k18_complex1 (k6_xcmplx_0 F C))))  & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 B F) (k1_seq_1 B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers B A)))  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t14_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((k7_relset_1 k1_numbers k1_numbers B A) = (k2_limfunc1 C)) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t14_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k29_sin_cos) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t14_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k16_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k16_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t14_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 B A) & (r1_fdiff_1 C A))  =>  ((r1_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k9_real_1 (k1_fdiff_1 B A) (k1_fdiff_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 C A) & (r1_fdiff_1 B A))  =>  ( ((k1_seq_1 B A) = k6_numbers)  |  ((r1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C B) A) &  ((k1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C B) A) = (k10_real_1 (k9_real_1 (k8_real_1 (k1_fdiff_1 C A) (k1_seq_1 B A)) (k8_real_1 (k1_fdiff_1 B A) (k1_seq_1 C A))) (k5_square_1 (k1_seq_1 B A)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_fdiff_3 A B) =>  ( ((k1_seq_1 A B) = k6_numbers)  |  ((r4_fdiff_3 (k6_rfunct_1 k1_numbers k1_numbers A) B) &  ((k1_fdiff_3 B (k6_rfunct_1 k1_numbers k1_numbers A)) = (k1_real_1 (k10_real_1 (k1_fdiff_3 B A) (k5_square_1 (k1_seq_1 A B))))) ) ) ) ) ) ) ) ).
tt(t14_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~  ((k1_seq_1 C D) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers C) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers C) B) D) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k7_real_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos) A) B) = (k9_real_1 (k8_real_1 (k10_real_1 1 B) (k1_seq_1 k19_sin_cos B)) (k8_real_1 (k10_real_1 1 (k5_square_1 B)) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = (k1_real_1 C)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) C) = (k1_real_1 (k26_sin_cos (k1_real_1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ( ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D E) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D E))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6) C) E) = (k10_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 (k7_real_1 (k8_real_1 A E) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) A) B) = (k10_real_1 1 (k8_real_1 B (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t14_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B)) (k8_real_1 B (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t14_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))  &  ( ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))  &  ((k4_xboole_0 (k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k4_relat_1 (u4_struct_0 A))) (k4_relat_1 (k2_net_1 A))) = (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t14_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~  (C = k6_numbers) )  &  ((r1_xxreal_0 (k2_nat_1 C A) B) & (r1_xxreal_0 B A)) ) ) ) ) ) ) ) ) ).
tt(t14_fib_num3,ax, ((k1_fib_num3 2) = 3) ).
tt(t14_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k3_power k2_fib_num A) (k10_complex1 (k13_complex1 1 2)))) ) ) ) ).
tt(t14_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( (E = (k11_finseq_1 A B C))  =>  ((k17_finseq_1 D 2 E) = (k10_finseq_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t14_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v19_lattices (u1_struct_0 A) A) &  ((v20_lattices (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t14_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m2_filter_1 (u1_lattices A) (u1_struct_0 A) (k9_filter_0 A B))) ) ) ) ).
tt(t14_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  <=> (r2_hidden (k3_lattices A C D) B)) ) ) ) )  =>  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t14_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (~ (r1_xxreal_0 D (k19_binop_2 1)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [F:$i] :  ((m1_finance1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k6_finance1 A k1_numbers B k12_prob_1)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k6_finance1 A k1_numbers B k12_prob_1))))) )  =>  ( ((r2_funct_2 A k1_numbers (k9_finance1 k6_numbers A k1_numbers B k12_prob_1 (k6_finance1 A k1_numbers B k12_prob_1) G) (k8_funcop_1 k1_numbers A (k9_binop_2 1 D))) & (r1_xxreal_0 (k4_finance1 C E F) k6_numbers))  =>  ((r1_tarski (a_5_1_finance1 A B C E G) (a_7_0_finance1 A B C D E F G)) & (r1_tarski (a_5_2_finance1 A B C E G) (a_7_1_finance1 A B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t14_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (m2_finseq_1 (k11_finseq_1 B C D) A)) ) ) ) ) ) ) ) ).
tt(t14_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xboole_0 (k2_finseq_1 A) (k1_tarski (k1_nat_1 A 1)))) ) ).
tt(t14_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_finseq_4 A B) => (r1_finseq_4 A (k1_finseq_4 A B))) ) ) ) ).
tt(t14_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((k3_finseq_1 B) = 1)  =>  (B = (k12_finseq_1 A (k7_partfun1 A B 1))) ) ) ) ) ) ).
tt(t14_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_relat_1 (k7_finseq_1 A B) (k2_finseq_1 (k2_nat_1 (k3_finseq_1 A) C))) = (k7_finseq_1 A (k5_relat_1 B (k2_finseq_1 C)))) ) ) ) ) ) ) ).
tt(t14_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_finseq_7 A (k2_finseq_4 A B C) 2 D) = (k2_finseq_4 A B D)) ) ) ) ) ) ) ) ) ).
tt(t14_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k4_finseq_8 A (k1_finseq_8 A B C) C) = C)  &  ((k4_finseq_8 A B (k1_finseq_8 A B C)) = B) ) ) ) ) ) ) ) ).
tt(t14_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C A) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  =>  (! [G:$i] :  ((m2_finseq_1 G C) => (r2_relset_1 k5_numbers B (k2_finseqop C A B F (k8_finseq_1 C G (k12_finseq_1 C D)) E) (k8_finseq_1 B (k2_finseqop C A B F G E) (k12_finseq_1 B (k2_binop_1 C A B F D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_finset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((v1_finset_1 A) &  ((r1_tarski A (k2_zfmisc_1 B C)) &  (! [D:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D B) & (r1_tarski A (k2_zfmisc_1 D C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k3_finseq_4 A B C D) E) = (k5_binop_1 A E (k5_binop_1 A E B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_finsub_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k5_finsub_1 A) = (k1_zfmisc_1 A)) ) ) ).
tt(t14_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k7_fin_topo A C)) <=>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( ((k1_fintopo2 A B D C) = k8_margrel1)  &  ((k2_fintopo2 A B E C) = k8_margrel1) ) ) ) ) )  &  ((k4_fintopo2 A B C) = k7_margrel1) ) ) ) ) ) ) ) ) ).
tt(t14_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_fintopo3 A B k6_numbers) = B) ) ) ) ) ).
tt(t14_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r2_fintopo4 A B D k6_numbers) => (r2_fintopo4 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t14_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  => (v3_orders_2 (k5_fintopo5 A B))) ) ) ) ).
tt(t14_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_fintopo6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (E = C)  &  ( (F = D)  & (r1_fintopo4 B E F)) )  => (r1_fintopo4 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k9_fin_topo A B) (k9_fin_topo A C))) ) ) ) ) ) ) ).
tt(t14_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k6_flang_1 A B C) = (k4_flang_1 A (k2_flang_1 A)))  <=>  ( (B = (k4_flang_1 A (k2_flang_1 A)))  &  (C = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ) ) ) ) ).
tt(t14_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_tarski B (k7_flang_1 A C E)) & (r1_tarski D (k7_flang_1 A C F)))  => (r1_tarski (k6_flang_1 A B D) (k7_flang_1 A C (k2_xcmplx_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden A C) &  ( (~  (A = (k2_flang_1 B)) )  &  ((k1_flang_3 B C D) = (k4_flang_1 B (k2_flang_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t14_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_2 B (k3_finseq_2 A) (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k3_funct_2 (k3_finseq_2 (k3_finseq_2 A)) (k3_finseq_2 A) (k8_fomodel0 A) B) = (k1_funct_1 (k5_fomodel0 (k3_finseq_2 A) (k11_monoid_0 A)) B)) ) ) ) ) ).
tt(t14_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ((v1_funct_1 (k28_fomodel1 A)) &  ((v1_funct_2 (k28_fomodel1 A) k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 A)))) & (m1_subset_1 (k28_fomodel1 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 A))))))) ) ) ) ).
tt(t14_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v15_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  ( ( (~  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) C) = (k34_fomodel2 A)) )  =>  ((k14_fomodel2 A B D C) = (k1_funct_1 (k1_funct_1 D (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) C)) (k3_relat_1 (k34_fomodel1 A C) (k10_fomodel2 A B D)))) )  &  ( ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) C) = (k34_fomodel2 A))  =>  ((k14_fomodel2 A B D C) = (k1_funct_1 (k2_fomodel2 B) (k3_relat_1 (k34_fomodel1 A C) (k10_fomodel2 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ( (~ (v6_struct_0 D))  &  ((v11_fomodel1 D) & (l1_fomodel1 D)) )  =>  (! [E:$i] :  ( ((v4_fomodel1 E D) & (m1_subset_1 E (k1_fomodel1 D)))  =>  (! [F:$i] :  ((m2_subset_1 F (k9_funct_2 (k37_fomodel1 D) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 D B)) =>  ((v10_fomodel2 A B D F) =>  ((v7_fomodel2 E A D) | (v10_fomodel2 A B D (k37_fomodel2 D B F E C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [C:$i] :  ( ((v12_fomodel4 C k6_numbers A) &  ((v12_fomodel4 C 1 A) & (m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))))) )  =>  (! [D:$i] :  ((v10_fomodel4 D A C) =>  ( ((r2_hidden (k23_fomodel4 A) C) &  ((r2_hidden (k29_fomodel4 A) C) &  ((r2_hidden (k31_fomodel4 A) C) &  ((r2_hidden (k32_fomodel4 A) C) &  ((r2_hidden (k33_fomodel4 A) C) &  ((v6_fomodel2 D A) & (v15_fomodel4 D A)) ) ) ) ) )  =>  ( ((k26_fomodel2 A (k8_eqrel_1 (k35_fomodel1 A) (k6_fomodel4 A C D)) (k39_fomodel4 A C D) B) = 1)  <=> (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_frechet2 A B) (k2_pre_topc A B))) ) ) ) ).
tt(t14_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B C))) = (k2_xboole_0 A B)) ) ) ) ).
tt(t14_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D B)) )  =>  ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k4_fscirc_1 A B C)) = (k2_xboole_0 (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) (k1_tarski (k6_fscirc_1 A B C)))) ) ) ) ).
tt(t14_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l3_fsm_1 D A B)) )  & (r3_fsm_1 A B C D)) ) ) ) ) ) ) ) ).
tt(t14_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( ((v3_fsm_2 B A) & (v1_fsm_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  (E = (u2_fsm_1 A B)) )  =>  ((k1_funct_1 (k2_fsm_1 A B E (k12_finseq_1 A C)) 2) = (k1_funct_1 (k2_fsm_1 A B E (k12_finseq_1 A D)) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_3 C A B))  =>  ((u1_struct_0 (k2_fsm_3 A B C)) = (k1_zfmisc_1 (u1_struct_0 C))) ) ) ) ) ) ) ).
tt(t14_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden B (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden C (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden D (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden E (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k24_gfacirc1 A B C) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k21_gfacirc1 A B C) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k36_gfacirc1 (k24_gfacirc1 A B C) E D) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k3_gfacirc1) (u1_struct_0 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp) (u1_struct_0 (k7_ftacell1 A B C D E))) & (r2_hidden (k33_gfacirc1 (k24_gfacirc1 A B C) E D) (u1_struct_0 (k7_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B C) =>  ((k8_relat_1 (k2_funcop_1 A B) C) = A) ) ) ) ) ).
tt(t14_funcsdom,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  ((k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) A D) (k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) B D)) = (k2_binop_1 k1_numbers (k9_funct_2 C k1_numbers) (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k7_real_1 A B) D)) ) ) ) ) ) ) ) ).
tt(t14_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k10_xtuple_0 (k3_relat_1 C B))) => (r2_hidden A (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t14_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( ((k2_relset_1 B D) = B)  &  ((k2_relset_1 C E) = C) )  =>  ( (C = k1_xboole_0)  |  ((k2_relset_1 C (k1_partfun1 A B B C D E)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t14_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A (k1_zfmisc_1 (k9_xtuple_0 B))) =>  ((k7_relat_1 B (k3_tarski A)) = (k3_tarski (k7_relat_1 (k1_funct_3 B) A))) ) ) ) ) ).
tt(t14_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k1_funct_4 (k1_funct_4 A B) C) = (k1_funct_4 A (k1_funct_4 B C))) ) ) ) ) ) ) ).
tt(t14_funct_5,ax, (! [A:$i] :  ( (! [B:$i] :  (! [C:$i] :  (~ (r2_hidden (k4_tarski B C) A)) ) )  =>  ( ((k9_xtuple_0 A) = k1_xboole_0)  &  ((k10_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(t14_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k4_partfun1 (k2_zfmisc_1 A B) C)) =>  ((r2_hidden (k1_funct_5 D) (k4_partfun1 A (k4_partfun1 B C))) & (r2_hidden (k3_funct_5 D) (k4_partfun1 B (k4_partfun1 A C)))) ) ) ) ) ) ) ).
tt(t14_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_xboole_0 A (k1_tarski B)))  =>  (C = (k1_funct_4 (k5_relat_1 C A) (k16_funcop_1 B (k1_funct_1 C B)))) ) ) ) ) ) ).
tt(t14_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_8 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 B k1_numbers k1_numbers C) => (r2_funct_8 B k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A))) ) ) ) ) ) ) ).
tt(t14_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) => (v1_funct_9 B (k4_xcmplx_0 A))) ) ) ) ) ).
tt(t14_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r1_relset_1 B B (k7_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 A)) (k6_partfun1 B))) ) ) ) ) ).
tt(t14_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  ((v2_altcat_2 B A) <=> (v18_functor0 (k10_functor0 A B) B A)) ) ) ) ) ).
tt(t14_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ((m1_functor2 H B C E F) =>  (! [I:$i] :  ((m1_functor2 I B C F G) =>  ( ((r1_functor2 B C E F) & (r1_functor2 B C F G))  => (r8_pboole (u1_struct_0 A) (k6_functor3 A B C E G D (k3_functor2 B C E F G H I)) (k3_functor2 A C (k1_functor3 A B C D E) (k1_functor3 A B C D F) (k1_functor3 A B C D G) (k6_functor3 A B C E F D H) (k6_functor3 A B C F G D I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k4_fuzzy_1 A) B)) ) ) ) ).
tt(t14_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A B (k2_fuzzy_1 A C D)) (k1_fuzzy_1 A (k1_fuzzy_2 A B C) (k1_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t14_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A C) k1_numbers (k4_fuzzy_4 A B C (k2_fuzzy_1 (k2_zfmisc_1 A B) D E) F) (k2_fuzzy_1 (k2_zfmisc_1 A C) (k4_fuzzy_4 A B C D F) (k4_fuzzy_4 A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_fvaluat1 A B 2) = (k14_ideal_1 A B B)) ) ) ) ) ).
tt(t14_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_algstr_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (v1_finseqop (u1_algstr_0 A) (u1_struct_0 A))) ) ).
tt(t14_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 (k8_gate_1 A B C)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t14_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_gcd_1 A C B) & (r2_gcd_1 A E D))  =>  ( (C = (k4_struct_0 A))  |  ( (E = (k4_struct_0 A))  |  ((k8_group_1 A (k1_gcd_1 A B C) (k1_gcd_1 A D E)) = (k1_gcd_1 A (k8_group_1 A B D) (k8_group_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) => (m1_genealg1 (k3_genealg1 D E F A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analoaf A B C D E) => (r1_analoaf A B C (k1_geomtrap A B D) (k1_geomtrap A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  ((k2_msafree2 (k7_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t14_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k1_gfacirc2 A B C) (k2_gfacirc2 A B C)))) => (v1_circuit2 (k5_facirc_1 (k1_gfacirc2 A B C) (k2_gfacirc2 A B C) D (k2_nat_1 1 (k4_nat_1 2 A))) (k1_gfacirc2 A B C) (k2_gfacirc2 A B C))) ) ) ) ) ) ) ) ).
tt(t14_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) => (r1_glib_000 A D C B)) ) ) ) ) ) ).
tt(t14_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) =>  ((k3_finseq_1 (k2_glib_001 A C D B)) = 3) ) ) ) ) ) ) ).
tt(t14_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( (C = D)  => (r1_tarski (k1_glib_002 B D) (k1_glib_002 A C))) ) ) ) ) ) ) ) ) ).
tt(t14_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A B C D) =>  ((k8_glib_003 A (k2_glib_001 A B C D)) = (k9_finseq_1 (k1_funct_1 (k5_glib_003 A) D))) ) ) ) ) ) ) ).
tt(t14_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_glib_001 B A) &  ((v5_glib_001 B A) & (m3_glib_001 B A)) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_glib_004 A B C D) =>  ((k1_glib_004 A C D) = (k10_glib_003 A B)) ) ) ) ) ) ) ) ).
tt(t14_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  ( ((r1_glib_005 A B C D) &  ((r1_glib_001 A C D E) & (r5_glib_005 A B E)) )  =>  ( (C = D)  | (r1_glib_005 A (k10_glib_005 A B E) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) &  ( ((k1_matrix_1 D) = (k2_nat_1 B 1))  &  ((r1_xxreal_0 A C) & (r1_xxreal_0 C B)) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  ( ((k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 D A) C) = (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)))  &  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 (k3_goboard1 D A)))) & (r2_hidden (k2_nat_1 C 1) (k2_finseq_1 (k1_matrix_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_goboard2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 C) &  ((v5_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 1 B)) ) ) )  =>  ((v3_relat_1 C) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k1_goboard5 C A))) ) ) ) ) ) ) ) ) ).
tt(t14_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k1_goboard5 B A)) = (a_2_0_goboard6 A B)) ) ) ) ) ) ) ).
tt(t14_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 2) B))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B))) ) ) ) ) ) ) ) ).
tt(t14_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C)) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) C)) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) C)) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_goboard9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 B (k1_matrix_1 C)) &  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t14_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (a_1_7_gobrd11 B))  => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ).
tt(t14_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k7_nat_d A 1) B) (k16_matrix_1 F)) &  ((r1_xxreal_0 A (k3_finseq_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 E)) &  ((r1_xxreal_0 C (k3_finseq_1 F)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 C 1) | (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k7_nat_d A 1) B)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F (k7_nat_d C 1) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_subset_1 (k2_goboard9 A) (k3_goboard9 A))) ) ).
tt(t14_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k4_substut2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t14_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (m2_graph_1 k1_xboole_0 A)) ) ).
tt(t14_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k1_funct_1 (k3_graph_2 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t14_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_graph_2 A C B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  ( (~  ( ((k1_funct_1 C D) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D)))  &  ((k1_funct_1 C (k2_nat_1 D 1)) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B D))) ) )  &  (~  ( ((k1_funct_1 C D) = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 B D)))  &  ((k1_funct_1 C (k2_nat_1 D 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  (! [E:$i] :  ( ((v7_graph_1 E A) & (m2_graph_1 E A))  =>  ( ((r3_graph_4 A B D) &  ((r3_graph_4 A C E) &  ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 C 1)) ) )  =>  ((v7_graph_1 (k8_finseq_1 (u4_struct_0 A) D E) A) & (m2_graph_1 (k8_finseq_1 (u4_struct_0 A) D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((v7_graph_1 (k7_finseq_1 A B) C) &  ((v1_graph_4 (k7_finseq_1 A B) C) & (m2_graph_1 (k7_finseq_1 A B) C)) )  =>  ( ((v7_graph_1 A C) &  ((v1_graph_4 A C) & (m2_graph_1 A C)) )  &  ((v7_graph_1 B C) &  ((v1_graph_4 B C) & (m2_graph_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_graph_1 B) &  ((v6_graph_1 B) & (l1_graph_1 B)) ) )  =>  (! [C:$i] :  ( ((v7_graph_1 C B) & (m2_graph_1 C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 B) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) k8_graph_5)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_hidden A (u4_struct_0 B)) &  ( (C = (k9_finseq_1 A))  & (r1_graph_4 B E F A)) )  => (r8_graph_5 B E F C (k1_tarski E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_grcat_1,ax, (! [A:$i] :  ( ((v2_grcat_1 A) & (l1_grcat_1 A))  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  & (m1_grcat_1 A B C)) ) ) ) ) ) ).
tt(t14_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((k1_group_1 (k4_gr_cy_1 A)) = k6_numbers) ) ) ).
tt(t14_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (A = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)))  =>  ((v8_struct_0 A) <=>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ( (~  (C = D) )  &  ((k5_group_1 A C B) = (k5_group_1 A D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k7_group_1 A) = (k3_xcmplx_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( ((k6_group_1 A D) = B)  &  ((v15_algstr_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) D))) & (m1_group_2 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A B) & (r1_tarski C B))  =>  ((v1_relat_1 (k2_xboole_0 A C)) & (v1_funct_1 (k2_xboole_0 A C))) ) ) ) ) ) ) ) ).
tt(t14_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (m1_group_6 (k1_grnilp_1 A B C) A (k1_grnilp_1 A B (k7_group_2 A)))) ) ) ) ) ) ).
tt(t14_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((v4_rewrite1 (k3_polyred A B C D)) => (v8_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(t14_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_algstr_0 B) &  ((v1_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r8_pboole (k15_pre_poly A) (k1_polyred A D B (k5_polynom7 A B C E)) (k5_polynom7 A B (k1_polyred A D B C) E))) ) ) ) ) ) ) ) ) ) ).
tt(t14_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k6_polynom1 A B (k7_polynom1 A B) C) (k5_vfunct_1 (k15_pre_poly A) B C))) ) ) ) ) ).
tt(t14_group_10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k1_card_1 (a_2_2_group_10 A B)) = (k1_card_1 B)) ) ) ) ) ).
tt(t14_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k2_group_11 A B C)) & (r1_xboole_0 (k13_group_2 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = D)  <=>  (B = (k6_algstr_0 A D (k2_group_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_group_2 A B (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) C D)) (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_group_2 A B C) (k2_group_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t14_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r2_hidden A (k1_group_3 A))) ) ).
tt(t14_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k1_funct_1 C (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) D) 1)) = (k2_group_1 A (k7_partfun1 (u1_struct_0 A) B D))) ) ) ) )  =>  ((k3_group_4 A B) = (k2_group_1 A (k3_group_4 A C))) ) ) ) ) ) ) ) ).
tt(t14_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k3_group_4 A (k1_group_5 A C B)) = (k2_group_3 A (k3_group_4 A C) B)) ) ) ) ) ) ) ).
tt(t14_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ((r2_hidden (k13_group_2 A C B) (k15_group_2 A C)) & (r2_hidden (k14_group_2 A C B) (k15_group_2 A C))) ) ) ) ) ) ) ).
tt(t14_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_group_7 (k9_finseq_1 A)) &  ((v2_group_7 (k9_finseq_1 A) (k1_tarski 1)) & (v3_group_7 (k9_finseq_1 A) (k1_tarski 1))) ) ) ) ) ) ) ) ).
tt(t14_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_group_1 A)) ) ) )  =>  ( (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( (B = A)  | (r1_group_2 A B (k6_group_2 A))) ) )  <=>  ((v1_gr_cy_1 A) &  ((v8_struct_0 A) &  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  ( ((k7_struct_0 A) = B)  & (v1_int_2 B)) ) ) ) ) ) ) ) ) ).
tt(t14_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t14_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_ordinal1 D) & (v1_int_2 D))  =>  ((v1_groupp_1 (k2_group_3 A B C) D A) => (v1_groupp_1 B D A)) ) ) ) ) ) ) ) ) ).
tt(t14_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_group_2 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E)) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_group_2 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_hahnban1 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t14_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k4_rlsub_2 A B C D) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C (k4_finseq_1 (k2_hallmar1 A B C D))) & (r2_hidden C E))  =>  ((k1_hallmar1 A (k2_hallmar1 A B C D) E) = (k2_xboole_0 (k1_hallmar1 A B (k6_subset_1 E (k1_tarski C))) (k6_subset_1 (k1_funct_1 B C) (k1_tarski D)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E B) => (r1_xxreal_0 C (k4_metric_1 A D E))) ) )  => (r1_xxreal_0 C (k1_funct_1 (k6_weierstr A B) D))) ) ) ) ) ) ) ) ) ).
tt(t14_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r1_tarski B C) => (r1_tarski (k14_glib_001 A B) (k14_glib_001 A C))) ) ) ) ) ) ) ).
tt(t14_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  ((k4_valuat_1 A (k1_henmodel A) B C (k3_henmodel A)) = C) ) ) ) ) ) ) ).
tt(t14_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( ((r1_xxreal_0 k6_numbers (k3_complex1 A)) &  ((k4_complex1 A) = k6_numbers) )  =>  ((k17_complex1 A) = (k3_complex1 A)) ) ) ) ).
tt(t14_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_collsp A D E F) &  ((r1_collsp A D E G) &  ((r1_collsp A B C F) & (r1_collsp A B C G)) ) )  =>  ( (B = C)  |  ( (D = E)  |  ((r1_collsp A B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ( ( (B = k1_xboole_0)  &  (C = k1_xboole_0) )  =>  ((k7_heyting1 A B C) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ) ) ) ) ) ) ).
tt(t14_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k4_partfun1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (~  ( (E = (k1_tarski D))  &  ( ((k4_substlat A B C E) = k1_xboole_0)  &  (! [F:$i] :  ((v1_finset_1 F) =>  (~  ((r2_hidden F (k2_heyting2 A B C)) & (r1_tarski F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 A) 1) B) (k3_heyting3 A B))) ) ) ) ).
tt(t14_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A C) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos C) B) A) = (k1_seq_1 k19_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 B k32_sin_cos) 2)))) ) ) ) ) ) ) ) ).
tt(t14_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((r2_funct_2 (k15_pre_poly B) (u1_struct_0 A) (k3_hilbasis B C A) (k3_hilbasis B D A)) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t14_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (r2_hidden (k3_hilbert1 A A) k6_hilbert1)) ) ).
tt(t14_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ( ((k1_funct_1 A 1) = k6_numbers)  =>  (A = k2_hilbert1) ) ) ) ).
tt(t14_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden C (k9_xtuple_0 E)) & (r2_hidden D (k9_xtuple_0 E)))  =>  ( (A = B)  |  ((k3_relat_1 (k4_funct_4 A B C D) E) = (k4_funct_4 A B (k1_funct_1 E C) (k1_funct_1 E D))) ) ) ) ) ) ) ) ) ).
tt(t14_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k3_polynom5 A B D) C) (k3_polynom5 A B (k6_algstr_0 A C D)))) ) ) ) ) ) ) ) ).
tt(t14_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k4_idea_1 C (k4_idea_1 C A B) D) = (k4_idea_1 C A (k4_idea_1 C B D))) ) ) ) ) ) ) ) ) ).
tt(t14_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t14_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_collsp A B C F) & (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k3_incproj A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) &  ((r1_incsp_1 (k3_incproj A) D B) & (r1_incsp_1 (k3_incproj A) D C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((r4_incsp_1 A D B) & (r3_incsp_1 A B C))  => (r5_incsp_1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t14_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  ((m3_cat_2 (k10_index_1 A B) C) <=> (m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B)) ) ) ) ) ) ) ).
tt(t14_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  ( ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) &  ( ((u1_msualg_1 B) = (k2_partfun1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_msualg_1 A) (u4_struct_0 B)))  &  ((u2_msualg_1 B) = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_msualg_1 A) (u4_struct_0 B))) ) )  => (m1_instalg1 B A)) ) ) ) ) ).
tt(t14_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) => (r2_int_1 B A C)) ) ) ) ) ) ) ).
tt(t14_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( ( (A = 1)  |  (A = (k4_xcmplx_0 1)) )  =>  ((r1_int_1 A 1) & (r1_int_1 A (k4_xcmplx_0 1))) ) ) ) ).
tt(t14_int_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k5_struct_0 (k9_int_3 A)) = 1) ) ) ) ).
tt(t14_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) =>  ((k3_int_2 A C) = (k3_int_2 B C)) ) ) ) ) ) ) ) ).
tt(t14_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ( ( ((k3_int_2 A C) = 1)  &  ((k6_int_1 (k6_xcmplx_0 (k1_pepin B) A) C) = k6_numbers) )  => (r1_int_2 B C)) ) ) ) ) ) ) ).
tt(t14_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_int_2 A B) = (k3_int_2 A (k1_int_2 B))) ) ) ) ) ).
tt(t14_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  ((v1_int_7 A) =>  ( ((k8_nat_3 k10_newton A) = 1)  <=>  ((k1_polynom2 k10_newton A) = k1_xboole_0) ) ) ) ) ).
tt(t14_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers A) = (k2_limfunc1 k6_numbers))  &  ( ((k1_relset_1 k1_numbers B) = (k2_limfunc1 k6_numbers))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 k6_numbers)) => (r3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers A (k6_integr10 C)) k6_numbers)) ) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 k6_numbers)) => (r3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k6_integr10 C)) k6_numbers)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 k6_numbers)) => (r3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) (k6_integr10 C)) k6_numbers)) ) )  & (r2_relset_1 k1_numbers k1_numbers (k7_integr10 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k7_integr10 A) (k7_integr10 B)))) ) ) ) ) ) ).
tt(t14_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers k32_sin_cos))  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t14_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos)))) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t14_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) C)) (k3_rfunct_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)))) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_taylor_1 2)) &  ((r1_tarski D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k30_sin_cos))) &  ( (D = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k1_seq_1 k19_sin_cos B) (k10_real_1 (k1_seq_1 k19_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t14_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k1_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ( ((k2_partfun1 k1_numbers (k1_euclid A) C B) = D)  =>  ((k11_integr15 A B C) = (k10_integr15 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ((m2_integr16 D A B C) =>  ( ((v1_comseq_2 B) &  ((v1_integr16 B A) &  ((v2_comseq_2 (k2_integra3 A C)) &  ((k2_seq_2 (k2_integra3 A C)) = k6_numbers) ) ) )  =>  ((v2_comseq_2 (k5_integr16 A B C D)) &  ((k3_comseq_2 (k5_integr16 A B C D)) = (k6_integr16 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_integr18 A B C) &  ((r1_integr18 A B D) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) & (r1_tarski B (k1_relset_1 k1_numbers D))) ) )  =>  ((r1_integr18 A B (k6_vfunct_1 k1_numbers A C D)) &  ((k5_integr18 A B (k6_vfunct_1 k1_numbers A C D)) = (k3_rlvect_1 A (k5_integr18 A B C) (k5_integr18 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_integr19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_euclid B))))) )  =>  ((v1_integr15 C B A) <=> (v1_comseq_2 (k1_nfcont_4 B A C))) ) ) ) ) ) ) ).
tt(t14_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v4_xxreal_2 (k1_rvsum_1 B)) => (v1_seq_2 (k2_partfun1 A k1_numbers B A))) ) ) ) ) ).
tt(t14_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v4_xxreal_2 B) & (r1_xxreal_0 A k6_numbers))  =>  ((k5_seq_4 (k1_integra2 B A)) = (k8_real_1 A (k4_seq_4 B))) ) ) ) ) ) ).
tt(t14_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k2_integra1 B C (k3_finseq_1 C))) &  ((r1_integra1 C D) &  ( ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 C) (k1_seq_4 A)))  & (v1_comseq_2 (k2_partfun1 B k1_numbers E B))) ) )  =>  ( ((k3_integra1 B) = k6_numbers)  |  ((r1_xxreal_0 A (k5_seq_4 B)) | (r1_xxreal_0 (k9_real_1 (k18_rvsum_1 (k4_integra1 B E C)) (k18_rvsum_1 (k4_integra1 B E D))) (k8_real_1 (k9_real_1 (k4_seq_4 (k1_rvsum_1 E)) (k5_seq_4 (k1_rvsum_1 E))) (k1_integra3 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_seq_2 (k2_partfun1 A k1_numbers C B)) => (v1_seq_2 (k2_partfun1 A k1_numbers (k18_rfunct_3 A C) B))) ) ) ) ) ) ).
tt(t14_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) & (r1_tarski A (k1_relset_1 k1_numbers B)))  => (v5_xxreal_2 (k1_rvsum_1 (k2_partfun1 k1_numbers k1_numbers B A)))) ) ) ) ) ).
tt(t14_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ((r1_tarski A (k9_xtuple_0 C)) &  ((r1_integra5 A B) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((r1_integra5 A C) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  => (r1_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t14_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_integra7 A B C) & (r1_integra7 A D E))  => (r1_integra7 A (k20_valued_1 k1_numbers k1_numbers k1_numbers B D) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k20_valued_1 k1_numbers k1_numbers k1_numbers B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_integra8,ax, ((k21_sin_cos (k10_real_1 (k8_real_1 3 k32_sin_cos) 4)) = (k1_real_1 (k10_real_1 (k7_square_1 2) 2))) ).
tt(t14_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) k19_sin_cos)) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k16_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k16_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t14_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ((r2_hidden C B) <=>  ((r1_tarski (k5_interva1 A B) C) & (r1_tarski C (k6_interva1 A B))) ) ) ) ) ) ) ).
tt(t14_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((k7_intpro_1 (k7_intpro_1 A)) = (k7_intpro_1 A)) ) ) ).
tt(t14_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k2_irrat_1 B) A)) &  ((r1_xxreal_0 (k1_seq_1 (k2_irrat_1 B) A) (k13_complex1 1 (k9_newton B))) &  ((r1_xxreal_0 (k1_seq_1 (k2_irrat_1 B) A) (k1_seq_1 k5_irrat_1 B)) &  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k3_irrat_1 A) B)) &  ((r1_xxreal_0 (k1_seq_1 (k3_irrat_1 A) B) (k13_complex1 1 (k9_newton B))) & (r1_xxreal_0 (k1_seq_1 (k3_irrat_1 A) B) (k1_seq_1 k5_irrat_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t14_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  ( ((v12_cat_1 D A B) & (v12_cat_1 E B C))  => (v12_cat_1 (k9_cat_1 A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 B)) =>  ( ((r2_hidden G (k2_cat_1 A C D)) & (r2_hidden H (k2_cat_1 B E F)))  => (r2_hidden (k10_cat_2 A B G H) (k2_cat_1 (k8_cat_2 A B) (k9_cat_2 A B C E) (k9_cat_2 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) => (v6_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t14_jct_misc,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) => (v5_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A))) ) ) ).
tt(t14_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jgraph_1 A 2) & (v1_graph_4 (k4_jgraph_1 (u1_struct_0 (k15_euclid 2)) A) (k1_jgraph_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_goboard5 A)) ) ) ).
tt(t14_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  =>  ( ( ( ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A)))  |  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  =>  ((k1_funct_1 k1_jgraph_2 A) = (k19_euclid (k10_real_1 (k10_real_1 (k17_euclid A) (k18_euclid A)) (k18_euclid A)) (k10_real_1 1 (k18_euclid A)))) )  &  (~  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A))) )  &  ( (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  &  (~  ((k1_funct_1 k1_jgraph_2 A) = (k19_euclid (k10_real_1 1 (k17_euclid A)) (k10_real_1 (k10_real_1 (k18_euclid A) (k17_euclid A)) (k17_euclid A)))) ) ) ) ) ) ) ) ) ).
tt(t14_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k17_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid C) (k18_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t14_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (D = (k10_metric_1 (k14_euclid A) B C))  =>  ((v9_rltopsp1 D (k15_euclid A)) & (v4_pre_topc D (k15_euclid A))) ) ) ) ) ) ) ) ) ) ).
tt(t14_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_5_jgraph_5)  &  ( (D = a_0_1_jgraph_5)  &  ( (E = a_0_2_jgraph_5)  &  ( (F = a_0_3_jgraph_5)  &  ( (G = a_0_4_jgraph_5)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) G) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jgraph_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_1_jgraph_6)  &  ( (D = a_0_2_jgraph_6)  &  ( (E = a_0_3_jgraph_6)  &  ( (F = a_0_4_jgraph_6)  &  ( (G = a_0_5_jgraph_6)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) F) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) G) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = E)  &  ( ((k17_euclid D) = E)  &  ((r1_xxreal_0 G (k18_euclid A)) & (r1_xxreal_0 (k18_euclid D) H)) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) |  ((r1_xxreal_0 (k18_euclid D) (k18_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan10,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k5_setfam_1 (u1_struct_0 (k15_euclid 2)) (k3_jordan10 A)) = (k2_jordan2c 2 A)) ) ) ).
tt(t14_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r2_hidden B (k1_jordan2c 2 A)))  => (r1_xxreal_0 (k5_jordan1k 2 B A) (k5_jordan1k 2 B (k1_jordan2c 2 A)))) ) ) ) ) ).
tt(t14_jordan12,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( (~  ( (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C)) D) &  ((r2_hidden A D) & (r2_hidden B D)) ) ) )  &  ( (~  ((r2_hidden A (k3_goboard9 C)) & (r2_hidden B (k3_goboard9 C))) )  &  (~  ((r2_hidden A (k2_goboard9 C)) & (r2_hidden B (k2_goboard9 C))) ) ) ) )  &  (~  ( ( ((r2_hidden A (k3_goboard9 C)) & (r2_hidden B (k3_goboard9 C)))  |  ((r2_hidden A (k2_goboard9 C)) & (r2_hidden B (k2_goboard9 C))) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C)) D) &  ((r2_hidden A D) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski (k2_jordan2c 2 A) (k2_jordan2c 2 (k3_topreal1 2 (k1_jordan13 A B))))) ) ) ) ) ).
tt(t14_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k2_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F G) &  ((r1_xxreal_0 G E) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_tarski B A) &  ((r1_tarski C A) &  ((r1_topreal1 (k15_euclid 2) D E B) & (r1_topreal1 (k15_euclid 2) D E C)) ) )  =>  ( (B = C)  |  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal1 (k15_euclid 2) D E F) &  ((r1_tarski F A) &  ( (~  (F = B) )  &  (~  (F = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A B C D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A B F C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) & (r1_tarski (k7_topreal1 B) (k2_jordan2c 2 A))) ) ) ) ) ) ).
tt(t14_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan1a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xboole_0 A B))  & (r1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A) (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B))) ) ) ) ) ) ).
tt(t14_jordan1b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 A)) & (r1_xxreal_0 (k1_jordan1a A) 1)) ) ) ) ).
tt(t14_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k17_euclid C) (k6_pscomp_1 A)) (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A))) (k13_newton 2 B)) 2)))  & (r1_xxreal_0 (k7_real_1 (k6_pscomp_1 A) (k8_real_1 (k10_real_1 (k9_real_1 (k8_pscomp_1 A) (k6_pscomp_1 A)) (k13_newton 2 B)) (k5_real_1 D 1))) (k17_euclid C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k25_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t14_jordan1e,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k18_pscomp_1 A) = (k23_pscomp_1 A)) ) ) ) ).
tt(t14_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k23_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) )  & (r1_xxreal_0 (k18_euclid (k22_pscomp_1 (k3_topreal1 2 A))) (k18_euclid (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t14_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_xxreal_0 (k3_finseq_1 A) (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A))))) ) ).
tt(t14_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k2_nat_1 D 1)))  & (r1_xxreal_0 (k3_finseq_1 B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k2_jordan1e B A))) & (r2_hidden (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ).
tt(t14_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r3_connsp_1 (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) C) B) &  ( (~ (r1_jordan2c A C B))  &  (~ (r2_jordan2c A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers E) &  ( (B = (a_3_1_jordan20 A D E))  &  (C = (k4_rcomp_1 E 1)) ) )  =>  ((k7_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) D C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k10_jordan6 A) A)) ) ).
tt(t14_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) (k3_finseq_1 (k1_jordan8 A B))))))) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k6_jordan6 (k13_complex1 (k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)))))) ) ) ) ) ) ).
tt(t14_jordan23,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_jordan23 B) <=>  ((v2_funct_1 (k2_rfinseq A 1 B)) & (v2_funct_1 (k17_finseq_1 A (k7_nat_d (k3_finseq_1 B) 1) B))) ) ) ) ) ) ).
tt(t14_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))))))) )  =>  ( (E = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D))  => (v3_tops_2 E (k1_pre_topc A D) (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ( (B = (a_4_0_jordan2b A C D E))  & (r2_hidden E (k2_finseq_1 A)))  => (v3_pre_topc B (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_jordan2c A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))))) &  ( (D = C)  &  ((v3_connsp_1 D (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) &  (~  ((v6_tbsp_1 D (k14_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_euclid A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k2_topreal1 2 A C))) ) )  =>  ( (B = (k1_funct_1 A C))  |  (C = (k1_jordan3 A B)) ) ) ) ) ) ) ) ) ).
tt(t14_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 (k7_nat_d E D) 1))) ) ) )  =>  ( ((k1_funct_1 (k3_finseq_6 B C D E) A) = (k1_funct_1 (k3_finseq_6 B C E D) (k7_real_1 (k9_real_1 (k3_real_1 (k6_xcmplx_0 E D) 1) A) 1)))  &  ((k7_real_1 (k9_real_1 (k3_real_1 (k6_xcmplx_0 E D) 1) A) 1) = (k2_nat_1 (k7_nat_d (k2_nat_1 (k7_nat_d E D) 1) A) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_pre_topc E (k4_topmetr A B) (k4_topmetr C D)) &  ((v2_funct_1 E) &  ( (E = F)  &  ( ((k1_funct_1 E A) = C)  &  ((k1_funct_1 E B) = D) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F (k1_rcomp_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_topreal1 (k15_euclid A) C D B) => (r1_topreal1 (k15_euclid A) D C B)) ) ) ) ) ) ) ) ) ).
tt(t14_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( (~  (D = E) )  &  ( (~  ((r1_jordan5c A B C D E) &  (~ (r1_jordan5c A B C E D)) ) )  &  (~  ((r1_jordan5c A B C E D) &  (~ (r1_jordan5c A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_1_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k16_pscomp_1 (k3_topreal1 2 A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k16_pscomp_1 (k3_topreal1 2 A)))))) ) ) ) ) ) ).
tt(t14_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) C D A) &  (B = (a_2_1_jordan6 C D)) )  =>  ( (~ (r1_xboole_0 A B))  & (v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) &  ((r1_jordan6 A B C) & (r1_jordan6 A C D)) )  =>  ( (B = (k18_pscomp_1 A))  |  ( (C = D)  | (r1_xboole_0 (k1_jordan7 A B C) (k1_jordan7 A D (k18_pscomp_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))))  =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) A (k7_nat_d (k3_finseq_1 (k1_jordan8 C B)) 1))) = (k7_pscomp_1 C)) ) ) ) ) ) ) ) ).
tt(t14_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((v1_topreal1 D) &  ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 B (k1_matrix_1 C))) ) )  => (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k3_topreal1 2 D))) ) ) ) ) ) ) ) ) ).
tt(t14_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k4_jordan6 (k8_jordan6 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B) = (k5_jordan6 (k8_jordan6 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B (k22_pscomp_1 A))) ) ) ) ) ).
tt(t14_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_jordan2c 2 B A) => (r1_xboole_0 (k2_jordan2c 2 B) A)) ) ) ) ) ).
tt(t14_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_knaster A B C k1_xboole_0) = C) ) ) ) ) ) ) ).
tt(t14_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D B C) =>  (! [E:$i] :  ((m1_kolmog01 E A B C) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 A)))  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 A)))  =>  ( ((r2_kolmog01 B C D A E) & (r1_subset_1 F G))  =>  (! [H:$i] :  ((m1_prob_1 H B C) =>  (! [I:$i] :  ((m1_prob_1 I B C) =>  ( ((r2_hidden H (k4_kolmog01 A B C E F)) & (r2_hidden I (k4_kolmog01 A B C E G)))  =>  ((k3_funct_2 C k1_numbers D (k5_prob_1 B C H I)) = (k3_xcmplx_0 (k3_funct_2 C k1_numbers D H) (k3_funct_2 C k1_numbers D I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) )  =>  ((k4_kurato_0 A B) = C) ) ) ) ) ) ) ).
tt(t14_kurato_1,ax, ((k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr k6_kurato_1))))) = (k3_rcomp_1 2 k1_xxreal_0)) ).
tt(t14_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = D)  =>  ((r2_hidden C (k1_kurato_2 (k15_euclid A) B)) <=>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ( (~ (r1_xxreal_0 G F))  & (r1_xboole_0 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))) B G) (k9_metric_1 (k14_euclid A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_lang1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k1_lang1 (k8_lang1 A B)) = (k1_tarski B)) ) ) ) ).
tt(t14_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r2_hidden E (k2_finseq_1 A)))  =>  ((k5_matrix_1 (k7_nat_d A 1) (u1_struct_0 B) (k2_laplace D E A B C)) = (k2_laplace E D A B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r2_hidden (k1_group_1 A) (k1_funct_1 (k1_latsubgr A) B))) ) ) ) ).
tt(t14_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B))) =>  ( ((r2_hidden C (u1_struct_0 A)) &  ((r2_hidden D (u1_struct_0 B)) & (r1_latsum_1 A B)) )  =>  ((r1_orders_2 (k1_latsum_1 A B) C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_latsum_1 A B))) &  ((r2_hidden E (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))) &  ((r1_orders_2 (k1_latsum_1 A B) C E) & (r1_orders_2 (k1_latsum_1 A B) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A B C) = C) ) )  =>  (B = (k5_lattices A)) ) ) ) ) ) ).
tt(t14_lattice3,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v4_orders_2 A) =>  ((k10_lattice3 A (k10_lattice3 A B C) D) = (k10_lattice3 A B (k10_lattice3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattice4 A (k5_setwiseo (u1_struct_0 A) B (k2_setwiseo (u1_struct_0 A) C))) = (k3_lattices A (k1_lattice4 A B) C)) ) ) ) ) ) ) ).
tt(t14_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  => (v19_waybel_0 (k4_lattice5 A B C) B (k1_lattice5 A))) ) ) ) ) ) ).
tt(t14_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v1_lattice6 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_lattice6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice6 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice6 A D B) =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (r5_waybel_1 A (k2_yellow_1 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A)))))) ) ).
tt(t14_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_lattice8 A k1_xboole_0) = A) ) ) ).
tt(t14_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattices A (k5_lattices A) B) = B) ) ) ) ) ).
tt(t14_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_relset_1 k5_numbers (k5_lexbfs A B C)) = (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 (k39_glib_000 B)) (k2_finseq_1 (k7_nat_d (k39_glib_000 B) C)))) ) ) ) ) ) ) ).
tt(t14_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((u1_struct_0 (k4_lfuzzy_0 A)) = (k9_funct_2 A (k1_rcomp_1 k6_numbers 1))) ) ) ).
tt(t14_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v3_relat_2 B) => (v2_lfuzzy_1 (k3_lfuzzy_1 B (k2_zfmisc_1 A A)) A)) ) ) ) ) ).
tt(t14_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v2_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v2_limfunc1 (k26_valued_1 k5_numbers k1_numbers A B))) )  &  ( ((v2_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v1_limfunc1 (k26_valued_1 k5_numbers k1_numbers A B))) )  &  ( (B = k6_numbers)  =>  ( ((k2_relset_1 k1_numbers (k26_valued_1 k5_numbers k1_numbers A B)) = (k1_tarski k6_numbers))  & (v3_funct_1 (k26_valued_1 k5_numbers k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t14_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc2 B A) &  ((r3_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r3_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t14_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  ((r2_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_limfunc3 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t14_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc2 B A) &  ((v8_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r3_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t14_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (m1_vectsp_4 (k1_lmod_5 A B C) A (k1_lmod_5 A B D))) ) ) ) ) ) ) ) ) ).
tt(t14_lmod_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 B C D) =>  ( ((r1_struct_0 C A) => (r1_struct_0 D A))  &  ((m1_subset_1 A (u1_struct_0 C)) => (m1_subset_1 A (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (m1_subset_1 (k8_lmod_7 A B D C) (u1_struct_0 (k13_lmod_7 A B D)))) ) ) ) ) ) ) ) ).
tt(t14_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  => (v1_rlsub_1 (k7_lopban_1 A B) (k5_lopban_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t14_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k7_lopban_2 A)))  &  ((v13_algstr_0 (k7_lopban_2 A)) &  ((v2_rlvect_1 (k7_lopban_2 A)) &  ((v3_rlvect_1 (k7_lopban_2 A)) &  ((v4_rlvect_1 (k7_lopban_2 A)) &  ((v3_group_1 (k7_lopban_2 A)) &  ((v4_vectsp_1 (k7_lopban_2 A)) &  ((v5_vectsp_1 (k7_lopban_2 A)) & (l6_algstr_0 (k7_lopban_2 A))) ) ) ) ) ) ) ) ) ) ).
tt(t14_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_lopban_3 B A) =>  ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t14_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) (k2_nat_1 C 1)) = (k6_algstr_0 A (k1_rlvect_1 A B (k10_real_1 1 (k2_nat_1 C 1))) (k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) C)))  &  ( ((k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) k6_numbers) = (k5_struct_0 A))  & (r1_xxreal_0 (k1_normsp_0 A (k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) C)) (k8_nat_1 k1_numbers (k4_sin_cos (k1_normsp_0 A B)) C))) ) ) ) ) ) ) ) ).
tt(t14_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k1_lopban_5 A B C) (k1_lopban_5 A B D))) ) ) ) ) ) ) ) ) ).
tt(t14_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_subset_1 (k1_struct_0 A) (u1_struct_0 (k6_lopclset A)))) ) ).
tt(t14_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k3_lpspace1 A) (k6_lpspace1 A) B) B)) ) ) ) ).
tt(t14_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v6_supinf_2 B) => (r2_relset_1 A k1_numbers (k56_valued_1 A k1_numbers B) B)) ) ) ) ) ).
tt(t14_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  ((v4_normsp_0 B) &  ((v3_normsp_0 B) & (v2_normsp_1 B)) ) ) ) ) ) ) ) ).
tt(t14_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k1_ltlaxio1 (k2_ltlaxio1 A)))) = (k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k2_ltlaxio1 (k1_ltlaxio1 A))))) ) ) ) ) ) ) ).
tt(t14_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden B (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t14_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k4_xboolean k8_margrel1 A) = A) ) ) ).
tt(t14_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_mathmorp A (k1_mathmorp A D B) C) = (k1_mathmorp A D (k3_mathmorp A B C))) ) ) ) ) ) ) ) ) ).
tt(t14_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ((v1_matrix10 C) =>  ((r1_xxreal_0 A k6_numbers) | (v1_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ) ).
tt(t14_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  ((v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) =>  ((k2_matrix11 A B C) = (k4_algstr_0 B (k1_group_1 B))) ) ) ) ) ) ) ) ).
tt(t14_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((r2_hidden A (k4_finseq_1 (k12_matrix_1 C B))) =>  ( (D = (k4_struct_0 C))  |  ((v1_matrix_6 (k2_matrix12 B B C (k12_matrix_1 C B) A D) B C) &  ((k5_matrix_6 B C (k2_matrix12 B B C (k12_matrix_1 C B) A D)) = (k2_matrix12 B B C (k12_matrix_1 C B) A (k11_algstr_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  ( (D = (k3_finseq_5 (k1_finseq_2 A)))  =>  ( ( (? [E:$i] :  ((v7_ordinal1 E) &  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden E (k2_finseq_1 A)) &  ((r2_hidden F (k2_finseq_1 A)) &  ((r1_xxreal_0 (k2_xcmplx_0 E F) A) &  (~  ((k3_matrix_1 (u1_struct_0 B) C E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) )  &  (? [E:$i] :  ((v7_ordinal1 E) &  (? [F:$i] :  ((v7_ordinal1 F) &  ((r2_hidden E (k2_finseq_1 A)) &  ((r2_hidden F (k2_finseq_1 A)) &  ( (~ (r1_xxreal_0 (k2_xcmplx_0 E F) (k1_nat_1 A 1)))  &  (~  ((k3_matrix_1 (u1_struct_0 B) C E F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) )  |  ((k12_matrix_3 A B C) = (k14_matrix_2 B A (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B C D) (u2_algstr_0 B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k12_matrix_1 A k6_numbers) = (k11_matrix_1 A k6_numbers))  &  ((k12_matrix_1 A k6_numbers) = k1_xboole_0) ) ) ) ).
tt(t14_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( ( (D = E)  &  ( (F = (k4_algstr_0 A (k1_group_1 A)))  &  (~  (D = (k4_struct_0 B)) ) ) )  |  ((k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) (k6_domain_1 (u1_struct_0 B) (k3_rlvect_1 B D (k4_vectsp_1 A B F E))))) = (k1_vectsp_7 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v1_matrix16 F (u1_struct_0 B)) &  ((v1_matrix16 G (u1_struct_0 B)) & (v1_matrix16 H (u1_struct_0 B))) )  => (v1_matrix16 (k3_matrix_6 A B (k2_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((v5_matrix17 D (u1_struct_0 A)) =>  ((k2_matrix_6 (k3_finseq_1 D) A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix17 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix17 (u1_struct_0 A) D) C)) = (k1_matrix17 (u1_struct_0 A) (k9_fvsum_1 A D (k3_rlvect_1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_matrix_1 (k9_finseq_1 k1_xboole_0) A 1 k1_xboole_0)) ) ).
tt(t14_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k8_matrix_1 A B C) = (k9_matrix_1 A (k4_matrix_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t14_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k1_funct_1 B D) = (k5_struct_0 A))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( (E = D)  |  ((k1_funct_1 B E) = (k4_struct_0 A)) ) ) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 (k11_fvsum_1 A B C))) =>  ( ( (D = E)  =>  ((k1_funct_1 (k11_fvsum_1 A B C) E) = (k1_funct_1 C D)) )  &  ( (~  (D = E) )  =>  ((k1_funct_1 (k11_fvsum_1 A B C) E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k1_matrix_4 A B D) = (k1_matrix_4 A C D)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k3_matrix_5 (k3_matrix_5 A A) A) = (k7_matrix_5 3 A)) ) ) ).
tt(t14_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) B B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) B B) =>  ( ((r2_matrix_6 B A E C) & (r2_matrix_6 B A F D))  => (r2_matrix_6 B A (k4_matrix_6 B A E F) (k4_matrix_6 B A D C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k2_finseq_1 B)) => (r2_hidden (k1_funct_1 C D) (k2_finseq_1 B))) ) ) ) ) ) ) ) ) ).
tt(t14_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) & (v4_matrix_6 C A B))  => (v2_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t14_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k2_matrix_9 2 A (k6_matrix_2 (u1_struct_0 A) B C D E)) = (k1_algstr_0 A (k8_group_1 A B E) (k8_group_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  & (r2_hidden (k4_tarski A B) (k2_matrix_1 C))) )  =>  ((k3_matrix_1 k2_numbers (k5_matrix_5 C D) A B) = (k4_binop_2 (k3_matrix_1 k2_numbers C A B) (k3_matrix_1 k2_numbers D A B))) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k10_matrixj1 A (k3_matrixj1 A B C)) = (k8_finseq_1 k5_numbers (k10_matrixj1 A B) (k10_matrixj1 A C))) ) ) ) ) ) ) ).
tt(t14_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  ((v1_funct_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D)) &  ((v1_funct_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A)))) &  ((v13_vectsp_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (k1_ranknull B C C (k1_vectsp11 C D A)) (k1_ranknull B C C (k1_vectsp11 C D A))) &  ((v1_mod_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) B (k1_ranknull B C C (k1_vectsp11 C D A)) (k1_ranknull B C C (k1_vectsp11 C D A))) &  ((v2_matrixj2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) B (k1_ranknull B C C (k1_vectsp11 C D A))) & (m1_subset_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (A = (k8_rvsum_1 (k4_rvsum_1 A B) B)) ) ) ) ) ) ).
tt(t14_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) k6_numbers))  &  (~  ((k4_matrix_3 B (k1_matrix_3 B A (k3_finseq_1 C)) C) = (k1_matrix_3 B A (k1_matrix_1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 E)) =>  ( (D = F)  =>  ((k5_matrlin A B C D) = (k5_matrlin A E C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) (k1_nat_1 A 1) k6_numbers) =>  ((k4_rlvect_1 C (k6_matrlin C D)) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(t14_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v4_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) &  ((v3_pre_topc C A) &  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski C D) & (r1_matroid0 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) =>  ((k3_matrix_1 C D A B) = (k1_funct_1 (k1_matrprob C D A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrtop1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D B C) => (m1_matrix_1 (k1_finseq_3 E A) D (k7_nat_d B (k5_card_1 (k8_relat_1 E A))) C)) ) ) ) ) ) ) ) ) ).
tt(t14_matrtop2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m2_vectsp_6 F A B E) =>  ((v2_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D E)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k4_vectsp_6 A B F)) = (k4_vectsp_6 A C (k8_ranknull A B C F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 C D) & (r2_hidden E (k2_finseq_1 D))) )  =>  ((r1_xxreal_0 C B) |  ( (E = B)  |  ( (E = C)  |  ((k13_fvsum_1 k2_vectsp_1 (k1_matrtop1 F) (k9_matrix_1 (u1_struct_0 k2_vectsp_1) (k2_matrtop3 D A B C) E)) = (k1_seq_1 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v3_mazurulm C A B))  => (v3_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t14_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) | (r2_pboole A D C))  => (r2_pboole A (k3_pboole A B D) C)) ) ) ) ) ) ) ) ).
tt(t14_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_zfmisc_1 (k1_tarski B) (k1_tarski C))) =>  ( ((k1_xtuple_0 A) = B)  &  ((k2_xtuple_0 A) = C) ) ) ) ) ) ).
tt(t14_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_measure1 E A B C) =>  ( ((k12_supinf_2 C (k1_measure1 A B D E)) = (k12_supinf_2 C D))  &  ( ((k12_supinf_2 C (k2_measure1 A B D E)) = k1_supinf_2)  &  ((k12_supinf_2 C (k3_measure1 A B D E)) = (k12_supinf_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_measure2 D A B) =>  ( (! [E:$i] :  ((r2_hidden E D) => (m2_measure1 E A B C)) )  => (m2_measure1 (k2_measure2 A B D) A B C)) ) ) ) ) ) ) ) ).
tt(t14_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ( (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  => (r1_xxreal_0 (k12_supinf_2 C (k2_measure2 A B (k1_measure3 A B D))) (k19_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  ((v1_funct_1 (k3_measure4 A B)) &  ((v1_funct_2 (k3_measure4 A B) (k1_measure4 A B) k7_numbers) &  ((v10_valued_0 (k3_measure4 A B)) &  ((v6_supinf_2 (k3_measure4 A B)) &  ((v4_measure1 (k3_measure4 A B) A (k1_measure4 A B)) & (m1_subset_1 (k3_measure4 A B) (k1_zfmisc_1 (k2_zfmisc_1 (k1_measure4 A B) k7_numbers)))) ) ) ) ) ) ) ) ).
tt(t14_measure5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ( (~ (v1_xboole_0 A))  & (v2_measure5 A))  <=>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r1_xxreal_0 B C) &  (A = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t14_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 C B) &  (A = (k1_xxreal_1 C B)) ) ) )  =>  (B = (k8_supinf_2 A)) ) ) ) ) ) ).
tt(t14_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))))) )  =>  ( ((v2_funct_1 A) &  ((k11_funcop_1 k5_numbers k5_numbers k5_numbers A) = (k2_zfmisc_1 k5_numbers k5_numbers)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [E:$i] :  ((m2_measure7 E D) => (r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 (k3_measure7 (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) D)) (k11_measure7 D E A))) B) (k12_supinf_2 (k18_supinf_2 (k7_measure7 D E)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  => (m1_measure4 (k6_measure8 A B C) A)) ) ) ) ) ).
tt(t14_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ( ((k5_member_1 A) = (k5_member_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t14_membered,ax, (! [A:$i] :  ((v2_membered A) =>  ( (! [B:$i] :  ((v1_xxreal_0 B) => (r2_hidden B A)) )  =>  (A = k7_numbers) ) ) ) ).
tt(t14_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k9_subset_1 (u1_struct_0 B) (k9_xtuple_0 C) (k8_struct_0 B)) = (k9_xtuple_0 (k6_memstr_0 A B C))) ) ) ) ) ) ) ).
tt(t14_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_euclid_6 A B C))  &  ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 E)) (k1_rlvect_1 (k15_euclid 2) C E)))  &  (A = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k12_supinf_2 A C) = (k2_supinf_2 (k12_supinf_2 B C))) ) )  =>  ( ((k6_rinfsup2 B) = (k2_supinf_2 (k5_rinfsup2 A)))  &  ((k5_rinfsup2 B) = (k2_supinf_2 (k6_rinfsup2 A))) ) ) ) ) ) ) ).
tt(t14_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C D) &  (E = (k9_subset_1 A (k1_relset_1 A C) D)) )  => (r1_mesfun6c A B (k2_partfun1 A k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k8_mesfun7c A B))) =>  ((k12_supinf_2 (k8_mesfun7c A B) C) = (k2_mesfunc5 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ) ).
tt(t14_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((v1_mesfunc8 B A k1_numbers) &  ((r1_tarski (k1_relset_1 A C) (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) &  ((r2_hidden D (k1_relset_1 A C)) &  ((k1_seq_1 C D) = (k4_series_1 (k10_seqfunc A B D))) ) ) )  =>  ((k1_seq_1 C D) = (k2_seq_2 (k10_seqfunc A (k2_mesfun9c A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((r1_tarski C (k9_xtuple_0 B)) =>  ((k9_subset_1 A C (k18_mesfunc1 A B D)) = (k6_subset_1 C (k9_subset_1 A C (k15_mesfunc1 A B D)))) ) ) ) ) ) ) ) ).
tt(t14_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  => (r2_relset_1 A k7_numbers (k2_mesfunc2 A B) (k1_mesfunc2 A (k7_mesfunc1 A B)))) ) ) ) ).
tt(t14_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B C) &  ( (! [D:$i] :  ((r2_hidden D (k1_relset_1 A C)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 C D))) )  &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (~  ((r1_mesfunc3 A B C D E) &  ( ((k12_supinf_2 E 1) = k1_supinf_2)  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 2 F) & (r2_hidden F (k4_finseq_1 E)))  =>  ( (~ (r1_xxreal_0 (k12_supinf_2 E F) k1_supinf_2))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc2 A B C) =>  ((v4_mesfunc5 C) & (v3_mesfunc5 C)) ) ) ) ) ) ) ) ).
tt(t14_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc6 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k8_subset_1 A D (k12_mesfunc1 C E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfunc7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 B) C) =>  ( ((r1_tarski E (k1_relset_1 B D)) & (r1_mesfunc1 B C D E))  => (r1_mesfunc1 B C (k5_mesfunc7 A B (k10_mesfunc1 B D)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k1_relset_1 A (k7_mesfunc8 A B))) & (v10_mesfunc5 (k3_mesfunc5 A B C)))  =>  ( ((k12_supinf_2 (k7_mesfunc8 A B) C) = (k12_supinf_2 (k6_mesfunc8 A B) C))  &  ((k12_supinf_2 (k7_mesfunc8 A B) C) = (k12_supinf_2 (k5_mesfunc8 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t14_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((k7_mesfunc5 A B C (k3_mesfunc2 D A)) = (k12_supinf_2 C D))  &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k3_mesfunc2 D A) D)) = (k12_supinf_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_tarski (k9_metric_1 B C A) (k10_metric_1 B C A))) ) ) ) ) ) ).
tt(t14_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_metric_2 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(t14_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ( ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) D E) = k6_numbers)  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) <=>  ((v2_comseq_2 (k2_metric_6 A C B)) &  ((k2_seq_2 (k2_metric_6 A C B)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t14_metrizts,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v4_pre_topc C B) & (v2_tex_2 C B))  => (r1_ordinal1 (k1_card_1 C) A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v2_tex_2 C B) => (r1_ordinal1 (k1_card_1 C) A)) ) ) ) ) ) ) ) ).
tt(t14_mfold_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k14_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D)) = (k8_finseq_1 k1_numbers (k14_rvsum_1 A B) (k14_rvsum_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_midsp_1 A B C B C)) ) ) ) ) ) ).
tt(t14_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((r1_midsp_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ( ( ((k2_binop_1 A A (u1_struct_0 B) C D E) = (k2_binop_1 A A (u1_struct_0 B) C E G))  &  ((k2_binop_1 A A (u1_struct_0 B) C D F) = (k2_binop_1 A A (u1_struct_0 B) C F H)) )  =>  ((k2_binop_1 A A (u1_struct_0 B) C G H) = (k1_midsp_2 B (k2_binop_1 A A (u1_struct_0 B) C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  ( (! [F:$i] :  ((m1_midsp_3 F A) =>  ((k5_midsp_3 A (u1_struct_0 (u1_midsp_2 B C)) D F) = (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 B C)) E F)) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 F G) &  ((r1_tarski B C) & (r1_relset_1 A A D E)) )  => (r1_tarski (k14_mmlquery A B D G) (k14_mmlquery A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_mod_2 B A) &  ((v3_mod_2 B A) & (l1_mod_2 B A)) )  =>  (! [C:$i] :  ( ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) )  =>  (~  ( ((k2_mod_2 A C) = (k3_mod_2 A B))  &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E A) &  ((v9_vectsp_1 E A) &  ((v10_vectsp_1 E A) &  ((v11_vectsp_1 E A) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E A)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v8_vectsp_1 F A) &  ((v9_vectsp_1 F A) &  ((v10_vectsp_1 F A) &  ((v11_vectsp_1 F A) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l1_vectsp_1 F A)) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  (~  ( (B = (g1_mod_2 A D E G))  &  ( (C = (g1_mod_2 A E F H))  &  ((k8_mod_2 A C B) = (g1_mod_2 A D F (k1_partfun1 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 F) G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (v2_mod_3 (k1_vectsp_4 A B) A)) ) ) ) ).
tt(t14_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_mod_4 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_mod_4 A B))) =>  ( ( (D = E)  &  (F = G) )  =>  ((k2_binop_1 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k5_mod_4 A B)) (u1_struct_0 (k5_mod_4 A B)) (k6_mod_4 A B C) E G) = (k2_binop_1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) =>  (! [D:$i] :  ((m1_trees_1 D (k5_trees_1 A C B)) =>  (! [E:$i] :  ((m1_trees_1 E A) =>  ( (D = E)  =>  ((r3_xboole_0 C E) |  ((k1_trees_2 (k5_trees_1 A C B) D) = (k1_trees_2 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k25_modelc_1 (k48_modelc_1 A B D) E)) <=>  (? [F:$i] :  ((m1_modelc_1 F A B) &  ( ((k3_funct_2 k5_numbers A F k6_numbers) = C)  & (r3_modelc_1 A B D (k3_funct_2 k5_numbers A F 1) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_modelc_2 A (k6_modelc_2 B)) <=>  (A = B) ) ) ) ) ) ).
tt(t14_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  ( (C = (k1_tarski B))  =>  ((k18_modelc_3 A C) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t14_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) & (r1_tarski (k1_polynom2 k10_newton (k13_nat_3 A)) (k2_finseq_1 B))) ) ) ) ).
tt(t14_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v17_monoid_0 A) <=>  ((v1_setwiseo (u2_algstr_0 A) (u1_struct_0 A)) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)))  =>  ( (B = C)  &  (C = (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v9_monoid_0 C B) => (v9_monoid_0 (k8_monoid_1 B B B C A) (k9_funct_2 A B))) ) ) ) ) ) ).
tt(t14_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k2_morph_01 A (k6_setfam_1 (u1_struct_0 A) B) C) (k1_setfam_1 (a_3_5_morph_01 A B C)))) ) ) ) ) ) ).
tt(t14_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) => (r2_pboole (u1_struct_0 A) (k2_msafree3 A C) B)) ) ) ) ) ) ).
tt(t14_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v2_relat_1 (k13_msafree A B))) ) ) ) ).
tt(t14_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  ( (C = (k1_trees_4 (k4_tarski E D)))  =>  ((k7_msaterm A B C) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  ((k1_funct_1 (k7_graph_2 A B) (k2_nat_1 (k3_finseq_1 B) 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B (k3_finseq_1 B)))) ) ) ) ) ).
tt(t14_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) & (v1_funcop_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A B) &  (D = (k1_funct_1 C A)) )  =>  ((k1_funct_1 (k2_funct_6 C) A) = (k9_xtuple_0 D)) ) ) ) ) ) ) ) ).
tt(t14_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_msualg_2 (k9_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( (C = (u1_struct_0 A))  => (v1_unialg_2 C B)) ) ) ) ) ) ) ) ).
tt(t14_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r2_hidden C (k6_msualg_2 A B)) <=> (v3_msualg_2 C A B)) ) ) ) ) ) ) ).
tt(t14_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) =>  ( ((r4_msualg_3 A B C D) & (r8_pboole (u1_struct_0 A) E (k4_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D)))  => (r4_msualg_3 A C B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [F:$i] :  ( ((v2_msualg_4 F A B) & (m1_msualg_4 F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r8_pboole (u1_struct_0 A) F (k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) D E)) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A C B)) =>  (! [H:$i] :  ((m1_subset_1 H (k3_msualg_1 A C B)) =>  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k9_xtuple_0 G)) => (r2_hidden (k4_tarski (k1_funct_1 G I) (k1_funct_1 H I)) (k2_msualg_4 A B F (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) I)))) ) )  => (r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) G) (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) H)) (k2_msualg_4 A B F (k2_msualg_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_msualg_6 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rewrite1 E (k3_msualg_6 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v1_funcop_1 F)) ) )  =>  ( ( ((k3_finseq_1 E) = (k2_nat_1 (k3_finseq_1 F) 1))  &  ( (C = (k1_funct_1 E 1))  &  ( (D = (k1_funct_1 E (k3_finseq_1 E)))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r2_hidden G (k4_finseq_1 F)) &  ( (H = (k1_funct_1 F G))  &  ( (I = (k1_funct_1 E G))  &  (J = (k1_funct_1 E (k2_nat_1 G 1))) ) ) )  => (r1_msualg_6 A I J B H)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((v1_funct_1 (k4_funct_7 (k1_funct_1 (u3_msualg_1 A B) C) F)) &  ((v1_funct_2 (k4_funct_7 (k1_funct_1 (u3_msualg_1 A B) C) F) (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D)) & (m1_subset_1 (k4_funct_7 (k1_funct_1 (u3_msualg_1 A B) C) F) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D))))) )  &  ( (~  (F = k1_xboole_0) )  =>  ( (~  ((k1_funct_1 (u3_msualg_1 A B) C) = k1_xboole_0) )  &  (~  ((k1_funct_1 (u3_msualg_1 A B) D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v1_msualg_7 B A) => (v4_lattice3 B)) ) ) ) ) ).
tt(t14_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [F:$i] :  ( ((v2_msualg_4 F A B) &  ((v3_msualg_4 F A B) & (m1_msualg_4 F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ( ( (E = (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C))  &  (F = (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) D)) )  =>  ((k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) E F) = (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) (k4_subset_1 (u1_struct_0 (k6_msualg_5 A B)) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_pralg_2 D B A) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k9_pralg_2 B A C D))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k9_pralg_2 B A C D))) =>  ( (! [G:$i] :  ((m1_subset_1 G B) =>  ((k1_funct_1 (k12_card_3 (k9_pralg_2 B A C D) G) E) = (k1_funct_1 (k12_card_3 (k9_pralg_2 B A C D) G) F)) ) )  => (r8_pboole B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k6_msualg_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_msualg_1 (k6_msualg_1 A) B (k9_msualg_1 A))) => (m2_finseq_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t14_mycielsk,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  => (r1_xxreal_0 (k3_mycielsk A) (k5_card_1 (u1_struct_0 A)))) ) ).
tt(t14_nagata_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r2_hidden (k7_subset_1 (u1_struct_0 B) (k2_struct_0 B) (k10_metric_1 B C A)) (k2_pcomps_1 B))) ) ) ) ) ) ).
tt(t14_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 (u1_struct_0 A) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (u1_struct_0 A) k1_numbers))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  &  ((r2_relset_1 (u1_struct_0 A) k1_numbers (k1_seqfunc (u1_struct_0 A) k1_numbers B C) D) &  ((v1_pscomp_1 D A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers D E))) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v1_series_1 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k8_nat_1 k1_numbers (k10_seqfunc (u1_struct_0 A) B E) D) (k8_nat_1 k1_numbers C D))) ) ) ) ) ) ) )  |  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers C D) = (k4_series_1 (k10_seqfunc (u1_struct_0 A) B D))) ) )  => (v1_pscomp_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t14_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 1 A))  =>  (A = k6_numbers) ) ) ) ).
tt(t14_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_nat_d (k2_xcmplx_0 B A) A) = (k2_nat_1 (k3_nat_d B A) 1)) ) ) ) ) ) ).
tt(t14_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k21_rvsum_1 (k2_nat_3 B (k23_binop_2 A 1))) = (k11_binop_2 (k21_rvsum_1 (k2_nat_3 B A)) (k21_rvsum_1 B))) ) ) ) ) ).
tt(t14_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 A) <=>  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ((r1_xxreal_0 (k4_nat_1 B B) A) &  ((v1_int_2 B) & (r1_nat_d B A)) ) ) ) ) ) ) ) ) ) ).
tt(t14_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k3_moebius1 A)) &  ((r2_hidden D (k3_moebius1 B)) & (r1_int_2 A B)) )  => (r1_int_2 C D)) ) ) ) ) ) ) ) ) ).
tt(t14_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k4_nat_d 1 A) = 1) ) ) ) ).
tt(t14_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k10_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k10_nat_lat)) =>  ((k2_lattices k10_nat_lat A B) = (k6_nat_d (k11_nat_lat A) (k11_nat_lat B))) ) ) ) ) ).
tt(t14_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k9_cat_3 A D D B C (k4_cat_1 A D)) = (k4_cat_1 B E))  =>  ((k8_cat_1 A B C D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_ncfcont1 E B (k7_partfun1 (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_ncfcont1 F A D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden G (k1_relset_1 (u1_struct_0 A) C)) & (r2_hidden G F))  => (r2_hidden (k7_partfun1 (u1_struct_0 B) C G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r2_ncfcont2 A B C D) => (r2_ncfcont2 A B C (k5_vfunct_1 (u1_struct_0 C) B D))) ) ) ) ) ) ) ) ).
tt(t14_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_comseq_2 B) & (v3_normsp_1 C A))  =>  ((k6_normsp_1 A (k1_ndiff_1 A C B)) = (k1_rlvect_1 A (k6_normsp_1 A C) (k2_seq_2 B))) ) ) ) ) ) ) ) ).
tt(t14_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_ndiff_3 A C B) & (r1_ndiff_3 A D B))  =>  ((r1_ndiff_3 A (k6_vfunct_1 k1_numbers A C D) B) &  ((k1_ndiff_3 A (k6_vfunct_1 k1_numbers A C D) B) = (k3_rlvect_1 A (k1_ndiff_3 A C B) (k1_ndiff_3 A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) & (r2_ndiff_4 A C B))  =>  ((r2_ndiff_4 A (k2_nfcont_4 A k1_numbers C) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_funct_1 (k2_ndiff_4 A (k2_nfcont_4 A k1_numbers C) B) D) = (k6_euclid A (k1_ndiff_4 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) =>  ( ((k4_struct_0 (k14_prvect_2 A)) = B)  <=>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ((k1_ndiff_5 A B C) = (k4_struct_0 (k11_prvect_2 A C))) ) ) ) ) ) ) ) ).
tt(t14_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) = (k2_xboole_0 (k3_eqrel_1 (u1_struct_0 A) (k6_partfun1 (u1_struct_0 A)) (u1_orders_2 A)) (u1_orders_2 (k3_necklace A)))) ) ) ).
tt(t14_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_necklace A) => (r1_xboole_0 (u1_orders_2 A) (k3_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A)))) ) ) ).
tt(t14_net_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_net_1 B) & (l1_petri B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_net_1 B)) =>  ((r2_hidden C (u4_struct_0 B)) =>  ((r2_hidden A (k4_net_1 B C)) <=> (r2_net_1 B C A)) ) ) ) ) ) ) ).
tt(t14_newton,ax, ((k3_newton 2) = 2) ).
tt(t14_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) =>  ((r2_funct_2 k5_numbers k1_numbers (k4_normsp_0 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D (k3_normsp_0 (u1_struct_0 A) B C))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_vfunct_1 k5_numbers B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k5_vfunct_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_nfcont_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_nfcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers C)) & (r1_nfcont_3 B C A))  =>  ((r1_fcont_1 (k3_normsp_0 k1_numbers B C) A) & (r1_nfcont_3 B (k5_vfunct_1 k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t14_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r2_hidden B (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D))) &  ((r1_nfcont_4 A C B) & (r1_nfcont_4 A D B)) )  => (r1_nfcont_4 A (k7_integr15 A k1_numbers C D) B)) ) ) ) ) ) ) ) ) ).
tt(t14_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((r1_normform A B (k3_normform A B C D) E) => (r1_normform A B C (k1_normform A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k10_xtuple_0 B) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_normsp_2 A)) B C) & (v2_frechet C (k3_normsp_2 A)))  =>  ( ((k2_frechet (k3_normsp_2 A) C) = (k6_domain_1 (u1_struct_0 A) (k6_normsp_1 A B)))  &  ((k2_frechet2 (k3_normsp_2 A) C) = (k6_normsp_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t14_ntalgo_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B k4_numbers))  &  ( ((k3_finseq_1 B) = (k2_nat_1 (k3_finseq_1 A) 1))  &  ( ((k1_funct_1 B 1) = 1)  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k1_funct_1 B (k1_nat_1 C 1)) = (k3_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 A C))) ) ) )  &  ((k19_rvsum_1 A) = (k1_funct_1 B (k2_nat_1 (k3_finseq_1 A) 1))) ) ) ) ) ) ) ) ).
tt(t14_numbers,ax,(r1_tarski k4_numbers k3_numbers)).
tt(t14_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (k8_openlatt A) (k3_lattices A B C)) = (k2_xboole_0 (k1_funct_1 (k8_openlatt A) B) (k1_funct_1 (k8_openlatt A) C))) ) ) ) ) ) ) ).
tt(t14_oposet_1,ax,(v9_oposet_1 (u1_robbins1 k1_oposet_1) k1_oposet_1)).
tt(t14_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( ((k1_relset_1 A B) = A)  &  ((k2_relset_1 A B) = A) ) ) ) ) ).
tt(t14_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k1_orders_2 A (k1_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t14_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~ (r2_hidden A B))  &  ( (~  (A = B) )  &  (~ (r2_hidden B A)) ) ) ) ) ) ) ) ).
tt(t14_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden A B) => (r1_ordinal1 (k2_ordinal2 B) A)) ) ) ) ).
tt(t14_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_hidden A 1) =>  (A = k1_xboole_0) ) ) ) ).
tt(t14_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_ordinal2 D)) ) )  =>  ( ((v2_ordinal2 C) &  ((r1_ordinal2 B D) &  ( ((k3_ordinal2 (k10_xtuple_0 C)) = (k9_xtuple_0 D))  &  (A = (k3_relat_1 C D)) ) ) )  => (r1_ordinal2 B A)) ) ) ) ) ) ) ) ) ).
tt(t14_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k1_ordinal5 A (k1_ordinal1 B)) = (k12_ordinal2 A (k1_ordinal5 A B))) ) ) ) ) ).
tt(t14_ordinal6,ax, ((k1_ordinal6 k1_xboole_0) = k6_numbers) ).
tt(t14_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t14_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (F = (k4_struct_0 A)) )  &  (~  ((k1_ortsp_1 A B D (k4_vectsp_1 A B F C) E) = (k8_group_1 A (k11_algstr_0 A F) (k1_ortsp_1 A B D C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k8_osafree A B)))) <=> (m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ) ) ) ) ).
tt(t14_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_osalg_1 A C (k1_msualg_1 A B)) => (r5_osalg_1 A B (k2_osalg_1 A B C) C)) ) ) ) ) ) ) ).
tt(t14_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msualg_2 A) &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (m1_msualg_2 C A B)) )  =>  ((v2_relat_1 (k3_osalg_2 A B)) & (m2_osalg_2 (k3_osalg_2 A B) A C)) ) ) ) ) ) ) ).
tt(t14_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  => (v13_osalg_1 C A)) ) ) ) ) ) ).
tt(t14_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_osalg_4 D A C)) )  =>  (! [E:$i] :  (~  ((r2_hidden E (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k7_osalg_4 A C D))) B)) &  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  (~  (E = (k9_osalg_4 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  => (v4_aff_2 (k2_diraf B))) ) ) ) ) ).
tt(t14_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) => (r1_parsp_1 (k9_parsp_1 A) B C D D)) ) ) ) ) ) ) ) ).
tt(t14_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_parsp_2 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_funct_1 (k5_relat_1 (k6_relat_1 A C) B)) & (m1_subset_1 (k5_relat_1 (k6_relat_1 A C) B) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ).
tt(t14_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ( ((v2_funct_1 C) &  ( ((k1_relset_1 A C) = (k2_relset_1 A D))  &  ( ((k2_relset_1 B C) = (k1_relset_1 B D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ( ((r2_hidden E (k1_relset_1 A C)) & (r2_hidden F (k1_relset_1 B D)))  =>  ( ((k7_partfun1 B C E) = F)  <=>  ((k7_partfun1 A D F) = E) ) ) ) ) ) ) ) ) )  =>  (D = (k2_funct_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((k2_partit1 A (k2_partit1 A B C) D) = (k2_partit1 A B (k2_partit1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t14_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ((v2_bvfunc_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  ( ((r1_tarski C B) & (r1_tarski D B))  => (r2_relset_1 A A (k4_relset_1 A A A A (k4_partit1 A (k2_bvfunc_2 A C)) (k4_partit1 A (k2_bvfunc_2 A D))) (k4_relset_1 A A A A (k4_partit1 A (k2_bvfunc_2 A D)) (k4_partit1 A (k2_bvfunc_2 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_diraf A B C D E) & (r2_diraf A B D C E))  =>  ((r3_diraf A B C D) |  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A B (k2_pboole A B C))) ) ) ) ) ).
tt(t14_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B C) => (r1_tarski (k1_pcomps_1 A B) (k1_pcomps_1 A C))) ) ) ) ) ) ) ).
tt(t14_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ( ((u1_struct_0 (k18_pcs_0 A B)) = (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u1_orders_2 (k18_pcs_0 A B)) = (k2_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 A) (u1_orders_2 B)))  &  ((u1_pcs_0 (k18_pcs_0 A B)) = (k2_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_pcs_0 A) (u1_pcs_0 B))) ) ) ) ) ) ) ).
tt(t14_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( ( (C = (k3_pdiff_1 A D))  &  (E = F) )  =>  ((r2_pdiff_1 1 A B C E) <=> (r3_pdiff_1 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r3_pdiff_1 2 2 D C))  =>  ((k11_pdiff_1 2 2 D C) = (k1_fdiff_1 (k1_pdiff_2 2 2 D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r2_pdiff_3 B A) =>  ((k3_pdiff_3 B A) = (k11_pdiff_1 2 2 (k1_pdiff_3 1 2 B) A)) ) ) ) ) ) ).
tt(t14_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 2 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F D) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 A B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 A B) I) (k1_seq_1 (k1_pdiff_2 3 2 A B) D)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I D)) (k1_seq_1 H (k9_real_1 I D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r5_pdiff_5 E D))  =>  ((k5_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 E) D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 C B A) &  ((v2_pdiff_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) )  <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 C (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v1_lopban_1 C (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) (k3_rlvect_1 (k4_real_ns1 1) B C)) = (k3_rlvect_1 (k4_real_ns1 A) (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) B) (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (E = (k3_relat_1 C (k4_pdiff_1 G B)))  &  ( (F = (k3_relat_1 D (k4_pdiff_1 G B)))  &  ((r1_xxreal_0 1 G) & (r1_xxreal_0 G B)) ) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) E F)) (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((v1_pdiff_7 C A) =>  ((r1_pdiff_6 C B A D) <=>  ((r1_tarski C (k1_relset_1 (k1_euclid A) D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E C) => (r1_pdiff_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_pencil_1 A B))) =>  ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) ) ) ) ) ) ) ).
tt(t14_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_zfmisc_1 C))  & (v1_zfmisc_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t14_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B C)))) =>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  => (m1_subset_1 (k4_card_3 (k2_funct_7 E C D)) (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((v1_vectsp_7 (k7_domain_1 (u1_struct_0 B) D E) A B) &  ((k2_vectsp_5 A B C (k1_vectsp_7 A B (k7_domain_1 (u1_struct_0 B) D E))) = (k1_vectsp_4 A B)) )  =>  ( (D = E)  |  ((k1_vectsp_9 A (k1_vectsp_5 A B C (k1_vectsp_7 A B (k7_domain_1 (u1_struct_0 B) D E)))) = (k1_nat_1 (k1_vectsp_9 A C) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d C B) = A)  =>  ((r1_xxreal_0 B (k3_square_1 A)) |  ((k4_nat_d (k3_square_1 C) B) = (k3_square_1 A)) ) ) ) ) ) ) ) ) ).
tt(t14_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 (k11_petri A)))  &  ( ((u4_struct_0 A) = (u4_struct_0 (k11_petri A)))  &  ( ((k10_petri (u1_struct_0 A) (u4_struct_0 A) (u1_petri A)) = (u2_petri (k11_petri A)))  &  ((k10_petri (u4_struct_0 A) (u1_struct_0 A) (u2_petri A)) = (u1_petri (k11_petri A))) ) ) ) ) ) ).
tt(t14_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r1_pnproc_1 A (k2_pnproc_1 A B (k1_pnproc_1 A)) B)) ) ) ).
tt(t14_polyalg1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_polyalg1 B A) =>  (! [C:$i] :  ((l1_polyalg1 C A) =>  ( ((g1_polyalg1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_algstr_0 B) (u2_struct_0 B) (u3_struct_0 B) (u1_vectsp_1 A B)) = (g1_polyalg1 A (u1_struct_0 C) (u1_algstr_0 C) (u2_algstr_0 C) (u2_struct_0 C) (u3_struct_0 C) (u1_vectsp_1 A C)))  => (m1_polyalg1 B A C)) ) ) ) ) ) ) ).
tt(t14_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_newton (k2_xcmplx_0 A B) 3) = (k7_real_1 (k3_real_1 (k1_newton A 3) (k7_real_1 (k8_real_1 (k8_real_1 3 B) (k3_square_1 A)) (k8_real_1 (k8_real_1 3 (k3_square_1 B)) A))) (k1_newton B 3))) ) ) ) ) ).
tt(t14_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ( ((k7_polyeq_1 A k6_numbers B C D) = k6_numbers)  =>  ( (A = k6_numbers)  |  ( ((k4_complex1 D) = k6_numbers)  |  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( ((k3_complex1 D) = (k9_binop_2 E F))  &  ( ((k9_binop_2 (k11_binop_2 (k11_binop_2 3 F) E) (k12_binop_2 B (k11_binop_2 4 A))) = k6_numbers)  &  ( (~  (D = (k3_binop_2 (k9_binop_2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3))))) (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k9_binop_2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3))))) (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) )  &  ( (~  (D = (k4_binop_2 (k9_binop_2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3))))) (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k9_binop_2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3))))) (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) )  &  ( (~  (D = (k3_binop_2 (k11_binop_2 2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k11_binop_2 2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) )  &  ( (~  (D = (k4_binop_2 (k11_binop_2 2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k11_binop_2 2 (k2_power 3 (k9_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) )  &  ( (~  (D = (k3_binop_2 (k11_binop_2 2 (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k11_binop_2 2 (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) )  &  (~  (D = (k4_binop_2 (k11_binop_2 2 (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))) (k5_binop_2 (k7_square_1 (k9_binop_2 (k11_binop_2 3 (k5_square_1 (k11_binop_2 2 (k2_power 3 (k10_binop_2 (k12_binop_2 C (k11_binop_2 16 A)) (k7_square_1 (k9_binop_2 (k5_square_1 (k12_binop_2 C (k11_binop_2 16 A))) (k2_newton (k12_binop_2 B (k11_binop_2 12 A)) 3)))))))) (k12_binop_2 B A))) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( ((k2_xcmplx_0 A B) = C)  &  ( ((k3_xcmplx_0 A B) = D)  &  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D))) &  ( (~  ( (A = (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))  &  (B = (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)) ) )  &  (~  ( (A = (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))  &  (B = (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( ( (B = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 C D) G)))  &  ( (E = (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 C D) (k3_xcmplx_0 C G)) (k3_xcmplx_0 D G)))  &  (F = (k4_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 C D) G))) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 E A)) F) = k6_numbers)  <=>  (~  ( (~  (A = C) )  &  ( (~  (A = D) )  &  (~  (A = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_polyform,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_polyform (k4_xcmplx_0 1) A) = (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 A 2))) ) ) ).
tt(t14_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))) =>  ((k4_rlvect_1 A (k5_pre_poly (u1_struct_0 A) B)) = (k4_rlvect_1 A (k6_matrlin A B))) ) ) ) ) ).
tt(t14_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k3_polynom2 A (k16_pre_poly A) B C) = (k5_struct_0 B)) ) ) ) ) ) ) ).
tt(t14_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 (k2_nat_1 A 1))) =>  ((k1_funct_1 (k6_polynom3 2 A) B) = (k2_polynom3 k5_numbers (k7_nat_d B 1) (k7_nat_d (k2_nat_1 A 1) B))) ) ) ) ) ) ).
tt(t14_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_polynom4 A (k10_polynom3 A)) (k10_polynom3 A))) ) ).
tt(t14_polynom5,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) => (r1_xxreal_0 (k17_complex1 (k4_rlvect_1 k1_complfld A)) (k18_rvsum_1 (k1_polynom5 A)))) ) ).
tt(t14_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_finseq_2 (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B))))) =>  ( ( ((k4_finseq_1 E) = (k4_finseq_1 (k21_pre_poly A C)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 (k21_pre_poly A C))) &  (! [G:$i] :  ((m2_subset_1 G (k14_pre_poly A) (k15_pre_poly A)) =>  (! [H:$i] :  ((m2_subset_1 H (k14_pre_poly A) (k15_pre_poly A)) =>  (! [I:$i] :  ((m2_finseq_1 I (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B)))) =>  (~  ( (I = (k9_pre_poly (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B))) k5_numbers (k3_finseq_2 (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B)))) E F))  &  ( ((k9_pre_poly (k15_pre_poly A) k5_numbers (k4_finseq_2 2 (k15_pre_poly A)) (k21_pre_poly A C) F) = (k2_polynom3 (k15_pre_poly A) G H))  &  ( ((k3_finseq_1 I) = (k3_finseq_1 (k21_pre_poly B D)))  &  (! [J:$i] :  ((v7_ordinal1 J) =>  (~  ((r2_hidden J (k4_finseq_1 I)) &  (! [K:$i] :  ((m2_subset_1 K (k14_pre_poly B) (k15_pre_poly B)) =>  (! [L:$i] :  ((m2_subset_1 L (k14_pre_poly B) (k15_pre_poly B)) =>  (~  ( ((k9_pre_poly (k15_pre_poly B) k5_numbers (k4_finseq_2 2 (k15_pre_poly B)) (k21_pre_poly B D) J) = (k2_polynom3 (k15_pre_poly B) K L))  &  ((k9_pre_poly (k15_pre_poly (k10_ordinal2 A B)) k5_numbers (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B))) I J) = (k2_polynom3 (k15_pre_poly (k10_ordinal2 A B)) (k1_polynom6 A B G K) (k1_polynom6 A B H L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k21_pre_poly (k10_ordinal2 A B) (k1_polynom6 A B C D)) = (k5_pre_poly (k4_finseq_2 2 (k15_pre_poly (k10_ordinal2 A B))) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  <=>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) C (k7_polynom1 A B)) |  ((k2_polynom1 (k15_pre_poly A) B C) = (k6_domain_1 (k15_pre_poly A) (k16_pre_poly A))) ) ) ) ) ) ) ) ).
tt(t14_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_polynom8 A B 1) = B) ) ) ) ) ).
tt(t14_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k1_polyred A D B C)) (a_4_0_polyred A B C D))) ) ) ) ) ) ) ) ).
tt(t14_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 1 C)) )  |  ( (~ (v1_abian B))  &  (~ (v1_abian C)) ) )  =>  ((k1_power B (k1_power C A)) = (k1_power (k4_nat_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t14_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) => (r2_hidden E (k1_funct_2 (k1_relset_1 k5_numbers (k1_msualg_1 B D)) (k1_funct_2 A (k3_tarski (a_3_1_pralg_3 A B C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ( (D = (k2_nat_1 C 1))  |  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_trees_1 D))  =>  ( ((k1_funct_1 B (k2_nat_1 C 1)) = D)  =>  ((k11_trees_3 B) = (k5_trees_1 (k11_trees_3 A) (k12_finseq_1 k5_numbers C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k2_xcmplx_0 (k1_int_1 (k5_power 2 A)) 1) = (k1_int_1 (k6_power 2 (k2_nat_1 (k4_nat_1 2 A) 1)))) ) ) ) ).
tt(t14_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A B C)) (k2_prelamb A (k2_prelamb A B D) (k2_prelamb A C D)))) ) ) ) ) ) ) ) ).
tt(t14_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t14_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k1_newton A B) A)) ) ) ) ) ) ).
tt(t14_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v4_pre_topc C A)) ) )  => (v4_pre_topc (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t14_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k3_prob_1 A (k12_funct_7 (k1_zfmisc_1 A) B C)) = (k9_subset_1 A B C)) ) ) ) ) ) ).
tt(t14_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ( (C = (k3_subset_1 A D))  =>  ((k1_seq_1 F E) = (k7_real_1 (k1_seq_1 F (k5_prob_1 A B E D)) (k1_seq_1 F (k5_prob_1 A B E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A (k1_prob_3 A B)) = (k3_prob_1 A B)) ) ) ) ).
tt(t14_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ( ((k1_funct_1 C A) = (k1_measure6 1))  => (m2_prob_1 C A B)) ) ) ) ) ) ) ).
tt(t14_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k9_cqc_lang A (k6_cqc_lang A B) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t14_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ( (~  (B = E) )  &  ( (~  (C = E) )  &  (~  (E = D) ) ) ) ) ) ) )  => (r1_projdes1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  ( ((v1_projpl_1 A) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) F) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) G) &  ((r1_projpl_1 A B C G) & (r1_projpl_1 A D E F)) ) ) )  =>  ( (B = C)  |  ( (D = E)  | (r5_projpl_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v8_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) &  (? [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) &  (? [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) &  (? [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) &  (? [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) &  (? [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) &  (? [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) &  (? [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) &  (? [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) &  ( (~ (r1_incsp_1 A C M))  &  ( (~ (r1_incsp_1 A D M))  &  ( (~ (r1_incsp_1 A B L))  &  ( (~ (r1_incsp_1 A E L))  &  ( (~ (r1_incsp_1 A B N))  &  ( (~ (r1_incsp_1 A D N))  &  ( (~ (r1_incsp_1 A C O))  &  ( (~ (r1_incsp_1 A E O))  &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F B E) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F C D) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G C E) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G B D) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H B C) I) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) H D E) J) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) F G) K) &  (~ (r1_incsp_1 A H K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A D I) &  ((r1_incsp_1 A D K) &  ((r1_incsp_1 A D L) &  ((r1_incsp_1 A B M) &  ((r1_incsp_1 A C M) &  ((r1_incsp_1 A E K) &  ((r1_incsp_1 A E J) &  ((r1_incsp_1 A B N) &  ((r1_incsp_1 A E N) &  ((r1_incsp_1 A F I) &  ((r1_incsp_1 A F N) &  ((r1_incsp_1 A G M) &  ((r1_incsp_1 A G O) &  ((r1_incsp_1 A F O) &  ((r1_incsp_1 A H O) &  ((r1_incsp_1 A E P) &  ((r1_incsp_1 A C P) &  ((r1_incsp_1 A H P) & (r1_incsp_1 A H L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_incsp_1 A B I) |  ((r1_incsp_1 A C J) |  ((r1_incsp_1 A B K) |  ((r1_incsp_1 A C K) |  ((r1_projred2 A I J K) |  ((r1_incsp_1 A C L) |  ( (I = L)  |  ((r1_projred2 A J K M) |  ( (G = B)  |  ((r1_incsp_1 A G I) |  ((r1_incsp_1 A G L) |  ((k3_relat_1 (k1_projred1 A I K B) (k1_projred1 A K J C)) = (k3_relat_1 (k1_projred1 A I L G) (k1_projred1 A L J C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_prvect_1 B A) =>  ( ((k2_funct_6 B) = A)  & (r1_tarski (k4_card_3 (k3_funct_6 B)) (k4_card_3 A))) ) ) ) ) ).
tt(t14_prvect_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) => (v3_lopban_1 (k11_prvect_2 A B))) )  => (v3_lopban_1 (k14_prvect_2 A))) ) ) ).
tt(t14_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k10_finseq_1 D E)) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k10_finseq_1 E G))  &  (D = (k10_finseq_1 F H)) )  =>  ((k3_rlvect_1 (k10_prvect_2 (k10_finseq_1 A B)) C D) = (k10_finseq_1 (k3_rlvect_1 A E F) (k3_rlvect_1 B G H))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k4_struct_0 (k10_prvect_2 (k10_finseq_1 A B))) = (k10_finseq_1 (k4_struct_0 A) (k4_struct_0 B)))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k10_finseq_1 D E))  =>  ((k4_algstr_0 (k10_prvect_2 (k10_finseq_1 A B)) C) = (k10_finseq_1 (k4_algstr_0 A D) (k4_algstr_0 B E))) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( (C = (k10_finseq_1 D E))  =>  ((k1_rlvect_1 (k10_prvect_2 (k10_finseq_1 A B)) C F) = (k10_finseq_1 (k1_rlvect_1 A D F) (k1_rlvect_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) => (v5_measure6 B (u1_struct_0 A))) ) )  <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) => (v6_measure6 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(t14_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) )  =>  ( ( ((k3_card_3 B) = A)  &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k9_xtuple_0 B)) & (r2_hidden D (k9_xtuple_0 B)))  =>  ( (C = D)  | (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) )  => (m2_pua2mss1 B A)) ) ) ) ).
tt(t14_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_pythtrip B) =>  (~  ( (~ (v2_pythtrip B))  &  ((v3_pythtrip B) & (r2_hidden (k4_nat_1 4 A) B)) ) ) ) ) ) ) ) ) ).
tt(t14_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A C D)) =>  ((r6_pboole A B C) & (r6_pboole A B D)) ) ) ) ) ) ) ) ) ).
tt(t14_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (~  ((v3_qc_lang1 B A) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A B)) (k3_finseq_1 (k11_qc_lang1 A (k18_qc_lang1 A B))))) ) ) ) ) ) ).
tt(t14_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( ((k6_qc_lang2 A B C D) = (k15_qc_lang1 A B (k15_qc_lang1 A C D)))  &  ((k7_qc_lang2 A B C D) = (k5_qc_lang2 A B (k5_qc_lang2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k3_qc_lang2 A B C)) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k24_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t14_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (~  ((r2_xboole_0 C D) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) (k3_finseq_1 (k11_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  => (r2_qmax_1 (g2_qmax_1 (k8_eqrel_1 (k5_qmax_1 A) (k9_qmax_1 A)) (k10_qmax_1 A) (k11_qmax_1 A)))) ) ).
tt(t14_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = (k1_quantal1 A (k1_quantal1 A D B) B)) ) )  => (v14_quantal1 C A)) ) ) ) ) ) ) ).
tt(t14_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k27_quaterni A k2_quatern2) = A) ) ) ).
tt(t14_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_real_1 2 (k17_quaterni A)) = (k17_quaterni (k26_quaterni A (k31_quaterni A)))) ) ) ).
tt(t14_quaterni,ax, ((k10_quaterni k11_quaterni k11_quaterni) = (k1_real_1 1)) ).
tt(t14_quin_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) = k6_numbers)  =>  ( (A = k6_numbers)  |  ((k6_xcmplx_0 (k3_square_1 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 A) D) B)) (k1_quin_1 A B C)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k9_quofield A B (k12_quofield A)) = B)  &  ((k9_quofield A (k12_quofield A) B) = B) ) ) ) ) ) ).
tt(t14_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden k6_numbers (k2_radix_1 A))) ) ).
tt(t14_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_radix_2 C B A) = (k10_radix_1 C B A)) ) ) ) ) ) ) ).
tt(t14_radix_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 2 B) => (r2_hidden (k5_radix_3 A B) (k3_radix_3 B))) ) ) ) ) ).
tt(t14_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 2 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E (k3_radix_1 B)))  =>  (! [F:$i] :  ( ((v3_card_1 F A) & (m2_finseq_1 F (k3_radix_1 B)))  =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden G (k2_finseq_1 A)) &  ( (~  ( ((k4_radix_1 G B A C) = (k4_radix_1 G B A E))  &  ((k4_radix_1 G B A D) = (k4_radix_1 G B A F)) ) )  &  (~  ( ((k4_radix_1 G B A D) = (k4_radix_1 G B A E))  &  ((k4_radix_1 G B A C) = (k4_radix_1 G B A F)) ) ) ) ) ) ) )  =>  ((k2_xcmplx_0 (k8_radix_1 A B E) (k8_radix_1 A B F)) = (k2_xcmplx_0 (k8_radix_1 A B C) (k8_radix_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 2 B) &  ((r1_radix_6 A B C) &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B D)) (k3_xcmplx_0 E C)) (k4_xcmplx_0 C)))  &  (~ (r1_xxreal_0 C (k6_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k4_radix_6 A B D)) (k3_xcmplx_0 E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_group_10 C A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 C A) B)))) )  =>  (~  ( (~  (B = k6_numbers) )  &  ( (~ (v1_finset_1 C))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (~  ( (~ (v1_finset_1 E))  & (v3_funct_1 (k2_partfun1 (k3_group_10 C A) B D (k3_group_10 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ((v2_prob_1 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B C) = (k3_funct_2 k5_numbers (k9_setfam_1 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ( ((r1_tarski C D) &  (! [E:$i] :  ((r2_hidden E D) => (r1_xxreal_0 k6_numbers (k1_seq_1 B E))) ) )  => (r1_xxreal_0 (k5_bhsp_5 k1_numbers A k33_binop_2 C B) (k5_bhsp_5 k1_numbers A k33_binop_2 D B))) ) ) ) ) ) ) ) ) ).
tt(t14_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_ranknull A B C D))) =>  ((k1_funct_1 D E) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k2_rat_1 A) = k6_numbers)  <=>  (A = k6_numbers) ) ) ) ).
tt(t14_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v2_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ratfunc1 A B C D) => (r1_polynom5 A (k8_polynom3 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t14_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v1_rcomp_1 A) =>  ( (A = k1_xboole_0)  |  ((r2_hidden (k4_seq_4 A) A) & (r2_hidden (k5_seq_4 A) A)) ) ) ) ) ).
tt(t14_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden (k5_seq_4 A) A))  => (r1_tarski A (k4_rcomp_1 (k5_seq_4 A) (k4_seq_4 A)))) ) ) ).
tt(t14_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 A B) &  ((k1_seq_1 (k1_real_3 C D) A) = k6_numbers) )  =>  ((k1_seq_1 (k1_real_3 C D) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t14_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k4_real_lat A) (k1_funcsdom A k1_numbers (k5_real_lat A) B C) C) C)) ) ) ) ) ) ).
tt(t14_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_real_ns1 A))) =>  ( (B = C)  =>  ((k5_square_1 (k1_normsp_0 (k4_real_ns1 A) B)) = (k2_bhsp_1 (k7_real_ns1 A) C C)) ) ) ) ) ) ) ) ).
tt(t14_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_group_1 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t14_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) (k4_struct_0 A) B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 A) B)) ) ) ) ) ).
tt(t14_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 A)) & (m2_finseq_1 E (k1_zfmisc_1 A))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ( ((r2_hidden C (k1_funct_1 E 1)) =>  ((k17_rfunct_3 A (k16_rfunct_3 A (k15_rfunct_3 A E) (k3_rfinseq (k20_rfunct_3 B D B))) C) = (k3_rfinseq (k20_rfunct_3 B D B))) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r2_hidden C (k6_subset_1 (k1_funct_1 E (k2_nat_1 F 1)) (k1_funct_1 E F))))  =>  ((r1_xxreal_0 (k3_finseq_1 E) F) |  ((k17_rfunct_3 A (k16_rfunct_3 A (k15_rfunct_3 A E) (k3_rfinseq (k20_rfunct_3 B D B))) C) = (k8_finseq_1 k1_numbers (k5_finseq_2 k1_numbers F k6_numbers) (k3_rfinseq (k2_rfinseq k1_numbers F (k20_rfunct_3 B D B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k6_subset_1 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k10_xtuple_0 (k6_subset_1 A B)))) ) ) ) ).
tt(t14_relset_1,ax, (! [A:$i] : (m1_subset_1 (k4_relat_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ).
tt(t14_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k7_relat_1 C (k5_setfam_1 A B)) = (k3_tarski (a_3_0_relset_2 A B C))) ) ) ) ) ) ).
tt(t14_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k3_finseq_1 (k1_finseq_6 A C B)) = (k3_finseq_1 C)) ) ) ) ) ) ) ).
tt(t14_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) =>  ((r2_hidden B (k1_relat_1 A)) |  (B = C) ) ) ) ) ) ) ).
tt(t14_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r1_rewrite2 A B C D) =>  ((r2_rewrite2 A B (k1_flang_1 A E C) (k1_flang_1 A E D)) & (r2_rewrite2 A B (k1_flang_1 A C E) (k1_flang_1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((l1_rewrite3 C B) =>  ( ((k9_xtuple_0 (u1_rewrite3 B C)) = k1_xboole_0)  => (v2_rewrite3 C A B)) ) ) ) ) ) ) ).
tt(t14_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_classes1 A B) =>  ((k3_rfinseq2 A) = (k3_rfinseq2 B)) ) ) ) ) ) ).
tt(t14_rfinseq,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_rfinseq (k2_finseq_4 k1_numbers A B)) = (k2_finseq_4 k1_numbers (k9_real_1 A B) B)) ) ) ) ) ).
tt(t14_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k18_valued_1 (k45_valued_1 A B) C) = (k45_valued_1 (k18_valued_1 A C) (k18_valued_1 B C))) ) ) ) ) ) ) ).
tt(t14_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ((v1_partfun1 C B) => (r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers B D (k26_valued_1 B k1_numbers C A)) (k26_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers B D C) A))) ) ) ) ) ) ) ) ) ).
tt(t14_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_binop_1 (k13_rfunct_3 A) (k3_rfunct_3 A k1_numbers))) ) ).
tt(t14_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((r1_rfunct_4 A C) & (r2_rfunct_3 B C))  => (r1_rfunct_4 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C)) ) ) ) ) ) ).
tt(t14_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) =>  ((k2_rinfsup1 A) = (k1_real_1 (k1_rinfsup1 (k32_valued_1 k5_numbers k1_numbers A)))) ) ) ) ).
tt(t14_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers A B) & (v2_comseq_2 B))  =>  ((v7_mesfunc5 A) &  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k2_seq_2 B)) ) ) ) ) ) ) ) ).
tt(t14_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_ring_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_ring_1 A B))) =>  ( ( (E = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) C))  &  (F = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) D)) )  =>  ((k6_algstr_0 (k2_ring_1 A B) E F) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_ringcat1 C A B) => (m4_ringcat1 (k1_tarski C) A B)) ) ) ) ) ) ).
tt(t14_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((k4_finseqop (u1_struct_0 B) k1_numbers D (k8_rlvect_2 B A C)) = (k10_rvsum_1 (k4_finseqop (u1_struct_0 B) k1_numbers D C) A)) ) ) ) ) ) ) ) ) ).
tt(t14_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_rlaffin1 F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((r2_hidden C F) &  ((r2_hidden D (k1_rlaffin2 B F)) &  ((r2_hidden E (k3_convex1 B (k7_subset_1 (u1_struct_0 B) F (k6_domain_1 (u1_struct_0 B) C)))) &  ((k3_rlvect_1 B (k1_rlvect_1 B C A) (k1_rlvect_1 B E (k9_real_1 1 A))) = D) ) ) )  => (r2_hidden E (k1_rlaffin2 B (k7_subset_1 (u1_struct_0 B) F (k6_domain_1 (u1_struct_0 B) C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rlaffin3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m2_rlaffin3 D B C) =>  ((m2_rlaffin3 (k4_vfunct_1 k5_numbers B D A) B (k1_convex1 B C A)) <=>  (~  ( (A = k1_xboole_0)  &  (~ (v1_zfmisc_1 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (E = B)  =>  ((k1_rlvect_1 D E C) = (k1_rlvect_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k2_rlsub_2 A B C) = (k2_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(t14_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  =>  ((r2_hidden (k4_struct_0 A) (k1_convex1 A B C)) => (r2_hidden (k4_struct_0 A) B)) ) ) ) ) ) ) ).
tt(t14_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_algstr_0 A (k4_struct_0 A) B) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(t14_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k9_subset_1 (u1_struct_0 A) C B)) = (k5_algstr_0 A (k3_rlvect_1 A (k2_rlvect_2 A C) (k2_rlvect_2 A B)) (k2_rlvect_2 A (k4_subset_1 (u1_struct_0 A) C B)))) ) ) ) ) ) ) ).
tt(t14_rlvect_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_struct_0 (k1_rlvect_3 B C) A) <=>  (? [D:$i] :  ((m2_rlvect_2 D B C) &  (A = (k6_rlvect_2 B D)) ) ) ) ) ) ) ) ) ).
tt(t14_rlvect_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 (k1_rlvect_3 B (k8_domain_1 (u1_struct_0 B) C D E)) A) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B (k1_rlvect_1 B C F) (k1_rlvect_1 B D G)) (k1_rlvect_1 B E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rlvect_3 C B) =>  ((v1_rlvect_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(t14_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_rlvect_x A (k4_subset_1 (u1_struct_0 A) B C)) = (k7_rusub_4 A (k2_rlvect_x A B) (k2_rlvect_x A C))) ) ) ) ) ) ) ).
tt(t14_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rmod_2 E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  ( (F = D)  =>  ((k5_vectsp_2 A E B F) = (k5_vectsp_2 A C B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k2_rmod_3 A B C D) = (k2_rmod_3 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t14_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k5_subset_1 (u1_struct_0 B) C D)) = (k5_algstr_0 B (k1_rmod_4 A B (k4_subset_1 (u1_struct_0 B) C D)) (k1_rmod_4 A B (k9_subset_1 (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t14_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_robbins1 A B (k6_lattices A)) = B) ) ) ) ) ).
tt(t14_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A B C)) = (k3_robbins1 A (k1_lattices A C B))) ) ) ) ) ) ) ).
tt(t14_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v8_lattices A))  => (v8_lattices B)) ) ) ) ) ).
tt(t14_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_robbins4)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_robbins4)) =>  ( ( (A = C)  &  (B = D) )  =>  ( ((k13_lattice3 k1_robbins4 A B) = (k3_lattices k2_robbins4 C D))  &  ((k12_lattice3 k1_robbins4 A B) = (k4_lattices k2_robbins4 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_roughs_1 A B) (k4_roughs_1 A B))) ) ) ) ).
tt(t14_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((k1_rpr_1 A B) = (k10_real_1 1 (k5_card_1 A))) ) ) ) ) ).
tt(t14_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_rsspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ((k1_seq_1 (k8_rsspace4 A B) C) = (k4_seq_4 (k7_rsspace4 A B C))) ) ) ) ) ) ) ).
tt(t14_rsspace,ax, ( ((u1_struct_0 k7_rsspace) = k1_rsspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_rsspace)) <=>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_rsspace)) =>  (A = (k2_rsspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_rsspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k7_rsspace)) =>  ((k3_rlvect_1 k7_rsspace A B) = (k1_series_1 k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k7_rsspace)) =>  ((k1_rlvect_1 k7_rsspace B A) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace B) A)) ) ) ) ) ) ) ) ) ).
tt(t14_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_struct_0 B C) & (r1_struct_0 B D))  => (r1_struct_0 B (k3_rlvect_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t14_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k2_rusub_2 A B C) = (k2_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(t14_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rusub_3 A B) = A)  &  (! [C:$i] :  ((m1_rusub_3 C A) =>  (~ (r1_tarski C B)) ) ) ) ) ) ) ) ) ).
tt(t14_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rusub_4 A) = 2)  <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  &  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) &  ((k2_rusub_1 A) = (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_rusub_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ((v3_rusub_4 C A) &  ((v3_rusub_4 D A) &  ((r1_rusub_5 A B C) & (r1_rusub_5 A B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t14_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k4_rvsum_1 (k2_finseq_2 A B) (k2_finseq_2 A C)) = (k5_finseq_2 k1_numbers A (k9_binop_2 B C))) ) ) ) ) ) ) ).
tt(t14_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k7_rvsum_2 (k2_finseq_2 A B) (k2_finseq_2 A C)) = (k5_finseq_2 k2_numbers A (k4_binop_2 B C))) ) ) ) ) ) ) ).
tt(t14_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k5_afinsq_1 (k2_compos_1 k1_ami_3)) A) =>  (! [B:$i] :  ( ((v5_memstr_0 B 2 k1_ami_3 k6_numbers) & (m1_scm_1 B (k6_finseq_1 k4_numbers)))  =>  ((r1_extpro_1 2 k1_ami_3 A B) &  ( ((k8_extpro_1 2 k1_ami_3 A B) = k6_numbers)  &  ((k6_extpro_1 2 k1_ami_3 A B) = B) ) ) ) ) ) ) ) ).
tt(t14_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_finset_1 E)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 G (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 H (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_xxreal_0 D C) &  ((r1_tarski F A) &  ((r1_tarski F B) &  ((r1_tarski (k9_xtuple_0 E) (k4_subset_1 (u1_struct_0 k1_scmfsa_2) k2_scmfsa_2 k3_scmfsa_2)) &  ( (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ((r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A G I)) (k9_xtuple_0 F)) & (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B H I)) (k9_xtuple_0 F))) ) )  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A G D) (k4_struct_0 k1_scmfsa_2)) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B H D) (k4_struct_0 k1_scmfsa_2)))  &  ((k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 A G D) (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 E) (k4_sf_mastr F)) (k2_sf_mastr F))) = (k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 B H D) (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 E) (k4_sf_mastr F)) (k2_sf_mastr F)))) ) ) ) ) ) )  =>  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A G C) (k4_struct_0 k1_scmfsa_2)) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B H C) (k4_struct_0 k1_scmfsa_2)))  &  ((k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 A G C) (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 E) (k4_sf_mastr F)) (k2_sf_mastr F))) = (k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 B H C) (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 E) (k4_sf_mastr F)) (k2_sf_mastr F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k10_scmfsa_2 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t14_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmfsa_2)))  =>  (! [J:$i] :  ((m1_scmfsa_2 J) =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k15_scmfsa_2 H I J))  & (r2_hidden J (k9_xtuple_0 B)))  =>  (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k5_numbers) =>  ( ( (K = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) I)))  &  (L = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) I))) )  =>  ((k2_funct_7 (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G) J) K (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H)) = (k2_funct_7 (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G) J) L (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v6_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) & (r1_tarski (k2_scmfsa6a C) B))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B A (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) 1)))) ) ) ) ) ) ) ) ).
tt(t14_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~  ( (~  (A = B) )  & (r3_scmfsa7b (k14_scmfsa_2 B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k2_afinsq_1 A)) =>  ((k1_funct_1 (k3_scmfsa6a A B) C) = (k1_funct_1 (k2_scmfsa6a A) C)) ) ) ) ) ) ) ).
tt(t14_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k4_compos_1 k1_scmfsa_2) B A) (k1_scmfsa_m B))) ) ) ) ).
tt(t14_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_scmfsa9a A B C D) & (r2_scmfsa9a A B C D))  =>  ((r6_scmfsa7b (k1_scmfsa_9 C D) B A) & (r5_scmfsa7b (k1_scmfsa_9 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa_9 A B) (k2_nat_1 (k5_card_1 B) 5)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ).
tt(t14_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~ (r2_hidden (k2_scmfsa_m A) A)) ) ) ).
tt(t14_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scm_halt C)) ) ) ) ) ) )  =>  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A))) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_scmfsa_m A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r8_pboole (u1_struct_0 k1_scmfsa_2) E (k1_scmfsa_m B)) &  ( (F = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) 3))  &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) E F)) = k6_numbers)  &  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) E F) G) = (k1_funct_1 (k1_scmfsa6b C B A) G)) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) E F) G) = (k18_scmfsa_2 (k1_scmfsa6b C B A) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k5_scmpds_2 B A)) = 2) ) ) ) ) ).
tt(t14_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k14_scmpds_2 J K H I))  &  ((r2_hidden J (k9_xtuple_0 D)) & (r2_hidden (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) J) H) (k9_xtuple_0 D))) )  =>  ((k3_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) J) H)) (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) K) I))) = (k3_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) J) H)) (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) K) I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_scmpds_4 (k2_scmpds_4 A B) C) = (k2_scmpds_4 A (k1_scmpds_4 B C))) ) ) ) ) ) ) ).
tt(t14_scmpds_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_4 (k10_compos_1 k1_scmpds_2 A) (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B))) = (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B))) ) ) ) ) ).
tt(t14_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) D) = (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 B) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 B))) D)) ) ) ) ) ) ) ) ) ).
tt(t14_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  =>  ( ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_recdef_1 G H) = k6_numbers)  => (r1_xxreal_0 k6_numbers (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))) ) )  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E))) |  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  ( (~ (r1_xxreal_0 (k1_recdef_1 G H) (k1_recdef_1 G (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C H I)))))  &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 (k6_scmpds_4 C H I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((k6_scmpds_4 (k1_scmpds_8 D E C) B A) = (k6_scmpds_4 (k1_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k1_amistd_1 2 k1_scmpds_2 B (k7_scmpds_2 A C D)) = (k2_tarski (k1_ordinal1 B) (k1_int_2 (k2_xcmplx_0 D B)))) ) ) ) ) ) ) ) ) ).
tt(t14_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ((r1_tarski k4_scmp_gcd A) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ( ((k1_funct_1 B (k1_scmp_gcd 9)) = C)  &  ( ((k1_funct_1 B (k1_scmp_gcd 10)) = D)  &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 k6_numbers D)) ) )  =>  ((k1_funct_1 (k6_extpro_1 2 k1_scmpds_2 A B) (k1_scmp_gcd 9)) = (k3_int_2 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k6_scmring2 A B C) D) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) D)))  &  ( ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k6_scmring2 A B C) D) B) = (k6_algstr_0 A (k2_scmring2 A D B) (k2_scmring2 A D C)))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 A))))  =>  ( (~  (E = B) )  =>  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k6_scmring2 A B C) D) E) = (k2_scmring2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 2)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 A))))  =>  (~  (B = (k4_scmring2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k1_scmyciel A) (k1_scmyciel B))) ) ) ).
tt(t14_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k4_scpinvar D E C) (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k2_nat_1 (k5_card_1 C) 3)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_scpisort,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_card_1 (k1_scpisort A B)) = 23) ) ) ) ) ).
tt(t14_scpqsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 7 A) => (v2_scmpds_4 (k2_scpqsort B A))) ) ) ) ) ).
tt(t14_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_analoaf A B C B D))  =>  ( (~ (r2_analoaf A B C D B))  &  ( (~ (r2_analoaf A C B B D))  &  ( (~ (r2_analoaf A C B D B))  &  ( (~ (r2_analoaf A B D B C))  &  ( (~ (r2_analoaf A B D C B))  &  ( (~ (r2_analoaf A D B B C))  &  ( (~ (r2_analoaf A D B C B))  &  ( (~ (r2_analoaf A C B C D))  &  ( (~ (r2_analoaf A C B D C))  &  ( (~ (r2_analoaf A B C C D))  &  ( (~ (r2_analoaf A B C D C))  &  ( (~ (r2_analoaf A C D C B))  &  ( (~ (r2_analoaf A C D B C))  &  ( (~ (r2_analoaf A D C B C))  &  ( (~ (r2_analoaf A D C C B))  &  ( (~ (r2_analoaf A D C D B))  &  ( (~ (r2_analoaf A D C B D))  &  ( (~ (r2_analoaf A C D D B))  &  ( (~ (r2_analoaf A C D B D))  &  ( (~ (r2_analoaf A D B D C))  &  ( (~ (r2_analoaf A D B C D))  &  ( (~ (r2_analoaf A B D C D))  &  (~ (r2_analoaf A B D D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B) C) (k20_valued_1 k5_numbers k1_numbers k1_numbers A (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t14_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t14_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  ((k2_seq_2 (k56_valued_1 k5_numbers k1_numbers A)) = (k18_complex1 (k2_seq_2 A))) ) ) ) ).
tt(t14_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (~  (B = k6_numbers) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k3_seqfunc A (k2_seqfunc A C B)) (k2_seqfunc A (k3_seqfunc A C) (k2_real_1 B)))) ) ) ) ) ) ) ).
tt(t14_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 B (k8_nat_1 k5_numbers A B))) ) ) ) ).
tt(t14_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A C) (k3_funct_2 k5_numbers k1_numbers B C))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) C) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 B) C))) ) ) ) ) ) ) ).
tt(t14_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k1_newton (k6_xcmplx_0 (k4_nat_1 2 B) 1) 2))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 B (k6_xcmplx_0 (k4_nat_1 4 (k13_newton B 2)) 1)) 3)) ) ) ) ) ) ) ).
tt(t14_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k8_complex1 (k8_complex1 (k13_complex1 B A) (k13_complex1 C B)) (k13_complex1 A C)) (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton (k13_complex1 A B) 3) (k1_newton (k13_complex1 B C) 3)) (k1_newton (k13_complex1 C A) 3)))) ) ) ) ) ) ).
tt(t14_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k3_xcmplx_0 C (k1_newton (k7_xcmplx_0 1 2) C))) ) )  =>  ((k1_seq_1 (k3_series_1 B) A) = (k6_xcmplx_0 2 (k3_xcmplx_0 (k2_nat_1 2 A) (k1_newton (k7_xcmplx_0 1 2) A)))) ) ) ) ) ) ).
tt(t14_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k13_complex1 (k18_complex1 (k2_xcmplx_0 A B)) (k2_xcmplx_0 1 (k18_complex1 (k2_xcmplx_0 A B)))) (k8_complex1 (k13_complex1 (k18_complex1 A) (k2_xcmplx_0 1 (k18_complex1 A))) (k13_complex1 (k18_complex1 B) (k2_xcmplx_0 1 (k18_complex1 B)))))) ) ) ) ).
tt(t14_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_setfam_1 B A) =>  ( (A = k1_xboole_0)  | (r1_tarski (k1_setfam_1 B) (k1_setfam_1 A))) ) ) ) ).
tt(t14_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_setfam_1 (a_3_3_setlim_1 A C D)) = B) ) ) ) ) ) ) ) ) ).
tt(t14_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k3_prob_1 A (k3_setlim_2 A B C)) (k7_subset_1 A (k3_prob_1 A B) (k3_prob_1 A C)))) ) ) ) ) ).
tt(t14_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) <=> (r3_binop_1 A (k4_binop_1 A B) B)) ) ) ) ) ).
tt(t14_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) &  ((v2_binop_1 E B) &  ((v1_setwiseo E B) &  ((v1_finseqop E B) & (r6_binop_1 B F E)) ) ) )  =>  ((k5_binop_1 B F D (k7_setwiseo A B E C G)) = (k7_setwiseo A B E C (k10_funcop_1 B A F D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) &  ((v1_sfmastr1 D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A) & (r5_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A)) )  =>  ((k1_funct_1 (k1_scmfsa6b (k4_scmfsa6a D C) B A) E) = (k1_funct_1 (k1_scmfsa6b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ((k18_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A E C) k6_numbers) D) = (k18_scmfsa_2 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ((r2_hidden C (k2_sf_mastr F)) =>  ( (B = C)  |  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B D E F A) k6_numbers) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( (~  ( (~  (C = (k6_scmfsa_2 A B)) )  &  ( (~  (C = (k7_scmfsa_2 A B)) )  &  ( (~  (C = (k8_scmfsa_2 A B)) )  &  ( (~  (C = (k9_scmfsa_2 A B)) )  &  (~  (C = (k10_scmfsa_2 A B)) ) ) ) ) ) )  =>  ((k1_sf_mastr C) = (k5_scmfsa_m A B)) ) ) ) ) ) ) ) ).
tt(t14_sgraph1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (~ (v1_xboole_0 (k2_sgraph1 A))) ) ) ).
tt(t14_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  => (v13_lattices A)) ) ).
tt(t14_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C B) B)) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t14_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) <=> (r1_tarski B (u1_pre_topc A))) ) ) ) ) ).
tt(t14_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_simplex1 C A B) =>  (! [D:$i] :  ((m1_simplex1 D A C) => (m1_simplex1 D A B)) ) ) ) ) ) ) ) ).
tt(t14_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) <=> (v9_rltopsp1 (k3_convex1 (k15_euclid A) B) (k15_euclid A))) ) ) ) ) ).
tt(t14_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t14_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k9_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) (k5_square_1 (k1_seq_1 k1_sin_cos2 A))) = 1)  &  ((k9_real_1 (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 A)) (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 A))) = 1) ) ) ) ).
tt(t14_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A B)) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B)))) ) ) ) ) ).
tt(t14_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  ( (~  ((k17_sin_cos C) = k6_numbers) )  &  (~  ((k2_sin_cos4 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k7_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k2_sin_cos4 A) (k2_sin_cos4 B)) (k2_sin_cos4 C)) (k2_sin_cos4 A)) (k2_sin_cos4 B)) (k2_sin_cos4 C)) (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_sin_cos4 B) (k2_sin_cos4 C)) (k3_xcmplx_0 (k2_sin_cos4 C) (k2_sin_cos4 A))) (k3_xcmplx_0 (k2_sin_cos4 A) (k2_sin_cos4 B))) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k17_sin_cos A) = k6_numbers) )  =>  ((k5_square_1 (k3_sin_cos4 A)) = (k7_real_1 1 (k5_square_1 (k2_sin_cos4 A)))) ) ) ) ).
tt(t14_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 k6_numbers (k20_sin_cos A))) ) ) ) ) ) ) ).
tt(t14_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  & (r1_xxreal_0 1 (k5_square_1 (k12_binop_2 (k11_binop_2 2 A) (k9_binop_2 1 (k3_square_1 A)))))) ) ) ) ).
tt(t14_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B))) = (k3_xcmplx_0 (k9_sin_cos2 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k1_sin_cos5 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)))) ) ) ) ) ).
tt(t14_sin_cos9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k2_rcomp_1 k6_numbers k32_sin_cos)) =>  ((k1_seq_1 k30_sin_cos A) = (k2_sin_cos4 A)) ) ) ) ).
tt(t14_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos (k8_complex1 A B))) C) = (k8_nat_1 k2_numbers (k10_comseq_3 (k10_sin_cos C A B)) C)) ) ) ) ) ) ) ).
tt(t14_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  ((k17_euclid A) = (k17_euclid B)) )  &  ( (~  ((k18_euclid A) = (k18_euclid B)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (~  ((k17_euclid C) = (k17_euclid A)) )  &  ( (~  ((k17_euclid C) = (k17_euclid B)) )  &  ( (~  ((k18_euclid C) = (k18_euclid A)) )  &  (~  ((k18_euclid C) = (k18_euclid B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k23_pscomp_1 A) A) & (r2_hidden (k22_pscomp_1 A) A)) ) ) ).
tt(t14_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 B (k3_finseq_1 C))) )  =>  ((k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B)) = (k3_tarski (a_3_0_sprect_2 A B C))) ) ) ) ) ) ) ) ).
tt(t14_sprect_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)) (k3_topreal1 2 (k1_sprect_1 A)))) ) ).
tt(t14_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t14_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k3_square_1 A) A)) ) ) ) ).
tt(t14_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((r2_stacks_1 A B C) & (r1_stacks_1 A B))  => (r1_stacks_1 A C)) ) ) ) ) ) ) ).
tt(t14_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  ((r1_tarski B A) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k5_nat_1 B) (k21_binop_2 A 1))) ) ) ) ) ) ).
tt(t14_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) =>  ((k2_sublemma A (k4_sublemma B A C D E)) = (k4_cqc_lang B A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k3_subset_1 A (k7_subset_1 A B C)) = (k4_subset_1 A (k3_subset_1 A B) C)) ) ) ) ) ) ).
tt(t14_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A B))) =>  ((r1_tarski C D) => (r1_tarski (k4_substlat A B C E) (k4_substlat A B D E))) ) ) ) ) ) ) ) ) ).
tt(t14_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) => (v7_substut1 (k24_substut1 A B C) A)) ) ) ) ) ) ) ).
tt(t14_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [F:$i] :  ( ((v5_relat_1 F (k3_qc_lang1 A)) &  ((v3_card_1 F B) & (m2_finseq_1 F (k2_qc_lang1 A))) )  =>  ( ((k4_substut2 A (k4_cqc_lang B A E F) C D) = (k4_cqc_lang B A E (k3_substut1 A F (k3_substut2 A C D))))  &  ((k7_cqc_sim1 A (k4_cqc_lang B A E F)) = (k7_cqc_sim1 A (k4_substut2 A (k4_cqc_lang B A E F) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  ((k7_supinf_2 (k6_supinf_2 A)) = (k2_supinf_2 (k8_supinf_2 A))) ) ) ).
tt(t14_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  => (r1_orders_2 B (k5_algstr_0 B E (k4_vectsp_1 A B (k1_symsp_1 A B D C E) C)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_relat_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k4_relat_1 A) (k4_relat_1 B)))  &  ( ((k4_relat_1 (k3_xboole_0 A B)) = (k3_xboole_0 (k4_relat_1 A) (k4_relat_1 B)))  &  ((k4_relat_1 (k6_subset_1 A B)) = (k6_subset_1 (k4_relat_1 A) (k4_relat_1 B))) ) ) ) ) ).
tt(t14_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  ( (B = (k2_tarski (k1_tarski A) (k10_eqrel_1 A)))  => (m1_taxonom1 B A)) ) ) ) ) ).
tt(t14_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_taxonom2 B A))  =>  (! [C:$i] :  ( ((v4_taxonom2 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski C B) &  (! [D:$i] :  ( ((v4_taxonom2 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski D B) & (r1_tarski (k5_setfam_1 A C) (k5_setfam_1 A D)))  =>  (C = D) ) ) ) )  => (m1_eqrel_1 C A)) ) ) ) ) ) ).
tt(t14_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k25_sin_cos (k5_power k8_power A)) = A) ) ) ) ).
tt(t14_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C D) &  (? [E:$i] :  ((v1_xreal_0 E) &  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) & (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k1_seq_1 k24_sin_cos E) (k1_seq_1 (k3_series_1 (k1_taylor_2 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A) E)) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tbsp_1 B A) & (r1_tarski C B))  => (v6_tbsp_1 C A)) ) ) ) ) ) ) ).
tt(t14_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_tdgroup A B C D E) => (r1_tdgroup A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v4_tops_1 (k1_struct_0 A) A)) ) ).
tt(t14_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k2_pre_topc A (k6_setfam_1 (u1_struct_0 A) B)) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ).
tt(t14_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( ((k9_setfam_1 (u1_struct_0 A)) = (k2_tarski k1_xboole_0 (u1_struct_0 A)))  =>  ((v1_tdlat_3 A) & (v2_tdlat_3 A)) ) ) ) ).
tt(t14_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r1_termord A B C (k2_termord A B C D)) & (r1_termord A B D (k2_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(t14_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = k1_xboole_0) )  => (v1_tops_1 B A)) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t14_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v3_tdlat_3 A))  => (v3_tdlat_3 B)) ) ) ) ) ).
tt(t14_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tex_3 C B) & (m1_pre_topc C B)) )  =>  ( (~ (v2_struct_0 C))  &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t14_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v3_tex_4 C A)) )  => (v3_tex_4 D B)) ) ) ) ) ) ) ) ) ).
tt(t14_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ( ((r1_tsep_1 C D) | (r2_funct_2 (u1_struct_0 (k2_tsep_1 A C D)) (u1_struct_0 B) (k3_tmap_1 A B C (k2_tsep_1 A C D) E) (k3_tmap_1 A B D (k2_tsep_1 A C D) F)))  =>  ( (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k7_relset_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (k10_tmap_1 A B C D E F) G) = (k7_relset_1 (u1_struct_0 C) (u1_struct_0 B) E G)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 D))) =>  ((k7_relset_1 (u1_struct_0 (k1_tsep_1 A C D)) (u1_struct_0 B) (k10_tmap_1 A B C D E F) G) = (k7_relset_1 (u1_struct_0 D) (u1_struct_0 B) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_tsep_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 C))) =>  (~  ((v3_pre_topc E B) &  ((r2_hidden D E) &  ((v3_pre_topc F C) &  ((r2_hidden D F) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)))) =>  (~  ((v3_pre_topc G (k1_tsep_1 A B C)) &  ((r2_hidden D G) & (r1_tarski G (k2_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_toler_1,ax, ((v1_relat_2 k1_xboole_0) &  ((v3_relat_2 k1_xboole_0) &  ((v1_partfun1 k1_xboole_0 k1_xboole_0) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 k1_xboole_0)))) ) ) ).
tt(t14_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid E))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid E))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k14_euclid E))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k14_euclid E))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k14_euclid E))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k14_euclid E))) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 (k15_euclid E))) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k15_euclid E))) =>  (! [N:$i] :  ((m1_subset_1 N (u1_struct_0 (k15_euclid E))) =>  (! [O:$i] :  ((m1_subset_1 O (u1_struct_0 (k15_euclid E))) =>  (~  ( (F = L)  &  ( (G = M)  &  ( (H = N)  &  ( (I = O)  &  ( (J = (k3_rlvect_1 (k15_euclid E) (k1_rlvect_1 (k15_euclid E) L A) (k1_rlvect_1 (k15_euclid E) N B)))  &  ( (K = (k3_rlvect_1 (k15_euclid E) (k1_rlvect_1 (k15_euclid E) M A) (k1_rlvect_1 (k15_euclid E) O B)))  &  ( (~ (r1_xxreal_0 C (k4_metric_1 (k14_euclid E) F G)))  &  ( (~ (r1_xxreal_0 D (k4_metric_1 (k14_euclid E) H I)))  &  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  & (r1_xxreal_0 (k7_real_1 (k8_real_1 (k18_complex1 A) C) (k8_real_1 (k18_complex1 B) D)) (k4_metric_1 (k14_euclid E) J K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topalg_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr A B))) =>  (! [E:$i] :  ((m1_borsuk_2 E (k4_topmetr A B) C D) =>  (! [F:$i] :  ((m1_borsuk_2 F (k4_topmetr A B) C D) => (r3_borsuk_2 (k4_topmetr A B) C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k2_pre_topc (k2_borsuk_1 A B) (k3_borsuk_1 A B C D)) = (k3_borsuk_1 A B (k2_pre_topc A C) (k2_pre_topc B D))) ) ) ) ) ) ) ) ) ).
tt(t14_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) => (m1_borsuk_2 (k4_topalg_4 A B k5_topmetr G) B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  ((v1_connsp_2 A) => (v1_connsp_2 B)) ) ) ) ) ).
tt(t14_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((r1_mfold_2 A B) & (v2_topalg_6 A))  => (v2_topalg_6 B)) ) ) ) ) ).
tt(t14_topdim_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_topdim_1 (k1_compts_1 A)) = k6_numbers) ) ) ).
tt(t14_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v5_waybel23 (k1_pre_topc B C)) =>  ( ((v1_topdim_1 C B) & (r1_xxreal_0 (k2_topdim_1 B C) A))  <=>  (? [D:$i] :  ( ((v1_tops_2 D B) &  ((v1_cantor_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E D) =>  ((v1_topdim_1 (k9_subset_1 (u1_struct_0 B) C (k2_tops_1 B E)) B) & (r1_xxreal_0 (k2_topdim_1 B (k9_subset_1 (u1_struct_0 B) C (k2_tops_1 B E))) (k3_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc B A))  <=>  ((k2_tops_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t14_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  =>  ((k2_waybel23 A) = (k1_card_1 (u1_struct_0 A))) ) ) ).
tt(t14_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v3_pre_topc (k3_limfunc1 A) k2_topgen_3) & (m1_subset_1 (k3_limfunc1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t14_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ( ((v2_topgen_4 B A) & (v1_prob_1 B (u1_struct_0 A)))  =>  ((v1_topgen_4 B A) & (v1_prob_1 B (u1_struct_0 A))) )  &  ( ((v1_topgen_4 B A) & (v1_prob_1 B (u1_struct_0 A)))  =>  ((v2_topgen_4 B A) & (v1_prob_1 B (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t14_topgen_5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k10_finseq_1 A B) k1_topgen_5) <=>  ((r2_hidden A k1_numbers) &  (B = k6_numbers) ) ) ) ) ).
tt(t14_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_funct_2 (u1_struct_0 A) (k3_group_1 A)) (k3_group_1 A))) ) ).
tt(t14_topmetr3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((r1_topreal1 (k15_euclid A) B C D) &  ((r1_topreal1 (k15_euclid A) C B E) & (r1_tarski E D)) )  =>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v9_metric_1 B) & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))) =>  ( (D = (k9_metric_1 B C A))  => (v3_pre_topc D (k3_pcomps_1 B))) ) ) ) ) ) ) ) ) ).
tt(t14_topreal1,ax, (k1_topreal1 = a_0_4_topreal1) ).
tt(t14_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid A) = (k17_euclid B))  =>  ( ((k18_euclid A) = (k18_euclid B))  | (r2_hidden (k19_euclid (k17_euclid A) (k10_real_1 (k7_real_1 (k18_euclid A) (k18_euclid B)) 2)) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ).
tt(t14_topreal4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ( ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)))  &  (B = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) 2) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  |  ((v4_topreal1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))  &  ((r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)) &  ((r1_tarski (k3_topreal1 2 B) (k3_topreal1 2 A)) &  ( ((k3_topreal1 2 B) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 1 A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))))  &  ((k3_topreal1 2 B) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 2 A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_topreal2 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ((r2_hidden C A) &  (~  ((k18_euclid C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t14_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k7_real_1 (k18_complex1 (k6_xcmplx_0 B A)) (k18_complex1 (k6_xcmplx_0 D C))) = (k2_xcmplx_0 (k6_xcmplx_0 B A) (k6_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k12_rvsum_1 (k8_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D))) = (k8_finseq_1 k1_numbers (k12_rvsum_1 (k8_rvsum_1 A B)) (k12_rvsum_1 (k8_rvsum_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t14_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 A (k3_finseq_1 C)) =>  ((k2_graph_2 B C 1 A) = (k17_finseq_1 B A C)) ) ) ) ) ) ) ).
tt(t14_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = D)  =>  ((k10_metric_1 (k14_euclid A) D B) = (k2_topreal9 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_funct_1 C) & (v2_funct_2 C (u1_struct_0 B)))  =>  ((v1_t_0topsp C A B) <=> (v5_pre_topc (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ) ).
tt(t14_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) &  ((k17_euclid A) = 1) )  =>  ((k18_euclid A) = k6_numbers) ) ) ) ).
tt(t14_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_funct_7 (k16_euclid B) A k6_numbers) = (k16_euclid B)) ) ) ) ).
tt(t14_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k2_toprns_1 B A (k4_toprns_1 A C D)) = (k4_toprns_1 A (k2_toprns_1 B A C) (k2_toprns_1 B A D))) ) ) ) ) ) ) ) ) ).
tt(t14_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A C))) = (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t14_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) => (v1_tops_2 (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t14_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) =>  ((k1_tops_1 A C) = (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ) ).
tt(t14_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_t_0topsp B k3_topmetr (k15_euclid A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_topmetr)) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  & (r1_tarski (k1_topreal9 A (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)) B C) E) (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)) B (k2_rcomp_1 (k6_xcmplx_0 C D) (k2_xcmplx_0 C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ((r8_relat_2 D (k2_zfmisc_1 A A)) &  ((r1_transgeo A B D) & (r1_transgeo A C D)) )  => (r1_transgeo A (k1_transgeo A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t14_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v11_aff_2 A) &  ((v1_translac A) &  ((v7_transgeo B A) &  ((v7_transgeo C A) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D (k1_transgeo (u1_struct_0 A) B B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D (k1_transgeo (u1_struct_0 A) C C))) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ).
tt(t14_treal_1,ax,(r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 k6_numbers 1 (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1)) (k3_struct_0 (k4_topmetr k6_numbers 1)))).
tt(t14_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden (k7_finseq_1 B C) (k1_trees_1 A)) => (r2_hidden B (k1_trees_1 A))) ) ) ) ) ) ) ).
tt(t14_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (A = (k3_tarski (a_1_0_trees_2 A))) ) ) ).
tt(t14_trees_3,ax, (! [A:$i] :  ((v3_trees_3 (k1_tarski A)) <=>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) ) ) ).
tt(t14_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((k9_xtuple_0 (k6_trees_4 A B C)) = (k13_trees_3 (k9_xtuple_0 B) (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t14_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((r2_hidden A (k6_trees_9 B)) <=>  (? [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) &  (A = (k4_tarski C (k5_trees_2 B C))) ) ) ) ) ) ) ).
tt(t14_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m4_trees_1 C (k9_xtuple_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D (k9_xtuple_0 (k3_trees_a A C B))) &  ((r2_hidden D (a_3_1_trees_a A B C)) &  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 A)) =>  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 B)) =>  (~  ( (D = (k8_finseq_1 k5_numbers E F))  &  ((r2_hidden E C) &  ((k1_funct_1 (k3_trees_a A C B) D) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) =>  ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B C) & (m1_pre_topc B C)) ) ) ) ) ) ) ) ) ).
tt(t14_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B C) & (r2_tsep_2 A D E))  => (r2_tsep_2 A (k4_subset_1 (u1_struct_0 A) B D) (k9_subset_1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_pre_topc C) & (m1_pre_topc C A)) )  =>  ((m1_pre_topc B C) => (v6_pre_topc B)) ) ) ) ) ) ) ).
tt(t14_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tsp_2 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = C)  =>  ((v3_pre_topc D B) <=>  ((v3_pre_topc (k3_tex_4 A C) A) &  (D = (k8_subset_1 (u1_struct_0 A) (k3_tex_4 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_turing_1,ax, ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers k6_numbers 1))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 3 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 k6_numbers (k1_real_1 1)))  &  ( ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 4 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 1 (k1_real_1 1)))  &  ((k1_funct_1 k13_turing_1 (k1_domain_1 k5_numbers k5_numbers 4 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 5 k6_numbers k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t14_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 A B C)) = (k1_binarith (k1_binarith A B) C))  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 A B C)) = (k1_binarith (k1_binarith (k9_margrel1 A) B) C))  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 A B C)) = (k1_binarith (k1_binarith (k9_margrel1 A) (k9_margrel1 B)) C))  &  ((k1_funct_1 k28_twoscomp (k11_finseq_1 A B C)) = (k1_binarith (k1_binarith (k9_margrel1 A) (k9_margrel1 B)) (k9_margrel1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t14_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v2_struct_0 (g1_unialg_1 B (k3_unialg_2 A B))))  &  ((v1_unialg_1 (g1_unialg_1 B (k3_unialg_2 A B))) &  ((v2_unialg_1 (g1_unialg_1 B (k3_unialg_2 A B))) &  ((v3_unialg_1 (g1_unialg_1 B (k3_unialg_2 A B))) &  ((v4_unialg_1 (g1_unialg_1 B (k3_unialg_2 A B))) & (l1_unialg_1 (g1_unialg_1 B (k3_unialg_2 A B)))) ) ) ) ) ) ) ) ) ).
tt(t14_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_unialg_3 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (k6_setfam_1 (u1_struct_0 A) (k7_relset_1 (k1_unialg_3 A) (k9_setfam_1 (u1_struct_0 A)) (k3_unialg_3 A) B)))  => (v1_unialg_2 C A)) ) ) ) ) ) ) ).
tt(t14_uniform1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ((v5_pre_topc C k5_topmetr (k15_euclid A)) &  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  (~  ( ((k1_funct_1 F 1) = 1)  &  ( ((k1_funct_1 F (k3_finseq_1 F)) = k6_numbers)  &  ((r1_xxreal_0 5 (k3_finseq_1 F)) &  ((r1_tarski (k2_relset_1 k1_numbers F) (u1_struct_0 k5_topmetr)) &  ((v2_uniform1 F) &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (~  ((r1_xxreal_0 1 G) &  ( (~ (r1_xxreal_0 (k3_finseq_1 F) G))  &  ( (H = (k1_rcomp_1 (k7_partfun1 k1_numbers F (k2_nat_1 G 1)) (k7_partfun1 k1_numbers F G)))  &  ( (I = (k7_relset_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)) C H))  & (r1_xxreal_0 B (k3_tbsp_1 (k14_euclid A) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_uniroots,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (v1_int_1 (k1_funct_1 A B))) ) )  => (v1_int_1 (k4_rlvect_1 k1_complfld A))) ) ) ).
tt(t14_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ((r1_tarski (k13_pre_poly C) B) &  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (~  ( (D = (k3_relat_1 (k1_uproots B) C))  &  ((k3_uproots A C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers (k1_urysohn1 A)) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k6_urysohn1 A C) (k6_urysohn1 A B))) ) ) ) ) ) ) ) ).
tt(t14_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (C = (k1_integra2 A B))  &  (A = (k3_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) )  =>  ( (C = (k3_xxreal_1 (k7_supinf_2 C) (k8_supinf_2 C)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (D = (k7_supinf_2 A))  &  (E = (k8_supinf_2 A)) )  =>  ( ((k7_supinf_2 C) = (k8_real_1 B D))  &  ((k8_supinf_2 C) = (k8_real_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 k7_numbers)))  =>  ( (F = (k5_urysohn3 A B C D E))  =>  (! [G:$i] :  ((m1_subset_1 G k7_numbers) =>  ( (G = 1)  =>  ((r1_xxreal_0 k1_supinf_2 (k8_supinf_2 F)) & (r1_xxreal_0 (k8_supinf_2 F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E (k7_cqc_lang A D (k6_cqc_lang A D))) C) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_funct_1 A) & (v2_valued_0 A)) ) ) )  =>  (? [B:$i] :  ((v1_xxreal_0 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t14_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 C) = (k9_xtuple_0 (k45_valued_1 A B)))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((k1_funct_1 C D) = (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) )  =>  (C = (k45_valued_1 A B)) ) ) ) ) ) ) ) ).
tt(t14_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k7_valued_1 (k13_valued_1 C A) B) = (k13_valued_1 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t14_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( (~ (r1_struct_0 D C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (F = D) )  => (r1_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v1_vectsp11 C A B) & (m1_vectsp11 D A B C))  <=>  (~ (v7_struct_0 (k1_ranknull A B B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) (k4_algstr_0 A D)))))) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k4_vectsp_1 A C (k4_struct_0 A) D) = (k4_struct_0 C))  &  ( ((k4_vectsp_1 A C (k4_algstr_0 A (k5_struct_0 A)) D) = (k4_algstr_0 C D))  &  ((k4_vectsp_1 A C B (k4_struct_0 C)) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k11_algstr_0 A (k11_algstr_0 A B)) = B) ) ) ) ) ) ).
tt(t14_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  ( (F = D)  =>  ((k4_vectsp_1 A E C F) = (k4_vectsp_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((k2_vectsp_5 A B C (k2_vectsp_5 A B D E)) = (k2_vectsp_5 A B (k2_vectsp_5 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  =>  ( ( (~  (C = k1_xboole_0) )  & (v1_vectsp_4 C A B))  <=>  (! [D:$i] :  ((m2_vectsp_6 D A B C) => (r2_hidden (k4_vectsp_6 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((k1_vectsp_7 A B C) = B)  & (r1_tarski C D))  =>  ((k1_vectsp_7 A B D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (v2_funct_1 D)) )  => (v2_funct_1 (k6_vectsp_8 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t14_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (E = (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)))  & (r1_struct_0 (k1_vectsp_7 A B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r2_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B C (k8_real_1 D E)) (k4_vfunct_1 A B (k4_vfunct_1 A B C E) D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B C (k9_complex1 D E)) (k2_vfunct_2 A B (k2_vfunct_2 A B C E) D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_waybel_0 A B) = (a_2_0_waybel_0 A B)) ) ) ) ) ).
tt(t14_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r1_yellow_2 (u1_struct_0 A) A B C) <=> (m1_yellow_0 (k1_yellow_2 A A C) (k1_yellow_2 A A B))) ) ) ) ) ) ) ).
tt(t14_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (B = (k6_setfam_1 (u1_struct_0 A) C))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) => (m2_connsp_2 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A)) B) = B) ) ) ) ) ).
tt(t14_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  => (v3_waybel_8 (k2_yellow_1 (k7_waybel_0 A)))) ) ).
tt(t14_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_orders_2 A B (k13_lattice3 A C D)) &  ( (~ (r3_orders_2 A B C))  &  (~ (r3_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) =>  ((v3_orders_2 (k1_yellow_2 A A B)) &  ((v4_orders_2 (k1_yellow_2 A A B)) &  ((v5_orders_2 (k1_yellow_2 A A B)) &  ((v1_lattice3 (k1_yellow_2 A A B)) &  ((v2_lattice3 (k1_yellow_2 A A B)) &  ((v3_waybel_3 (k1_yellow_2 A A B)) & (l1_orders_2 (k1_yellow_2 A A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel16,ax, (! [A:$i] : (v1_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))))) ).
tt(t14_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_2_waybel17 A B C D))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_waybel_3 A F D) & (r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1)))))))) )  &  ((v23_waybel_0 B (k3_yellow_1 A) (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1)))) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_funct_1 B C) = (k5_funct_3 C A)) ) ) ) ) ) ) ) ).
tt(t14_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_subset_1 (u1_struct_0 (k3_yellow_3 A B)) (k6_waybel_0 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) = (k2_xboole_0 (k2_zfmisc_1 (k3_subset_1 (u1_struct_0 A) (k6_waybel_0 A C)) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 B) (k6_waybel_0 B D))))) ) ) ) ) ) ) ) ) ).
tt(t14_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ((v3_lattice3 A) &  ((v17_waybel_0 C A B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r3_waybel_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_waybel_0 B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ( ((r1_tarski B (k6_partfun1 (u1_struct_0 A))) & (r1_yellow_0 (k3_yellow_3 A A) B))  => (r2_hidden (k1_yellow_0 (k3_yellow_3 A A) B) (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t14_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v5_yellow_0 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  => (r2_hidden (k2_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t14_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) )  =>  ((k2_partfun1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B) (k2_waybel22 A B C) (k1_waybel22 A)) = C) ) ) ) ) ) ).
tt(t14_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  => (r1_tarski (k6_waybel_0 B D) (k6_waybel_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t14_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 C) (k2_waybel24 A B C D E) F) = (k7_relset_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D (k6_yellow_3 A B F (k6_domain_1 (u1_struct_0 B) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((g1_orders_2 (u1_struct_0 (k1_waybel25 (k3_waybel18 A (k7_funcop_1 A B)))) (u1_orders_2 (k1_waybel25 (k3_waybel18 A (k7_funcop_1 A B))))) = (g1_orders_2 (u1_struct_0 (k5_yellow_1 A (k7_funcop_1 A (k1_waybel25 B)))) (u1_orders_2 (k5_yellow_1 A (k7_funcop_1 A (k1_waybel25 B)))))) ) ) ) ) ).
tt(t14_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_waybel26 C A)))) =>  ((k2_waybel26 B A E (k7_relset_1 (u1_struct_0 (k1_waybel26 C A)) (u1_struct_0 (k1_waybel26 B A)) (k4_waybel26 A B C D) F)) = (k2_waybel26 C A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_yellow_1 A B))) =>  ((r1_orders_2 (k6_yellow_1 A B) C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_orders_2 B (k1_waybel27 A B C E) (k1_waybel27 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (C = (k1_waybel11 A B))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v1_waybel28 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  => (r1_orders_2 A (k1_waybel_9 A (k2_waybel28 A B D)) C)) ) )  =>  (! [D:$i] :  ((m2_yellow_6 D A B) =>  (C = (k1_waybel11 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_waybel_9 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_waybel_9 B)) ) ) )  =>  ( ( ((g1_waybel_9 (u1_struct_0 A) (u1_orders_2 A) (u1_pre_topc A)) = (g1_waybel_9 (u1_struct_0 B) (u1_orders_2 B) (u1_pre_topc B)))  & (v4_waybel11 A))  => (v4_waybel11 B)) ) ) ) ) ).
tt(t14_waybel_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k4_waybel_0 A C)) (k4_waybel_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ).
tt(t14_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C (k2_waybel19 A)) => (r2_hidden (k4_waybel_0 A C) (k5_waybel11 B))) ) ) ) ) ) ) ).
tt(t14_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_waybel31 A (k1_struct_0 A) B) = (k2_waybel_3 A B)) ) ) ) ) ).
tt(t14_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v13_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( (~ (r2_hidden C D))  => (m2_connsp_2 (k3_subset_1 (u1_struct_0 B) (k5_waybel_0 B C)) B D)) ) ) ) ) ) ) ) ) ).
tt(t14_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  => (r2_hidden (k3_yellow19 A (k2_struct_0 A) B) (k6_yellow_6 A))) ) ) ) ).
tt(t14_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k4_waybel34 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k4_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k4_waybel34 A) C))) &  ((v17_waybel_0 D (k4_yellow21 (k4_waybel34 A) B) (k4_yellow21 (k4_waybel34 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k4_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k4_waybel34 A) C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel35,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ( ((v2_waybel35 C A B) & (v8_waybel_4 B A))  => (r1_waybel35 A C B)) ) ) ) ) ) ) ).
tt(t14_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) =>  ((v1_waybel_3 B A) | (r2_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t14_waybel_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k6_waybel_4 B D C)) <=> (r2_hidden (k4_tarski D A) C)) ) ) ) ) ) ) ) ).
tt(t14_waybel_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D C) &  ((v1_funct_1 D) & (v1_partfun1 D C)) ) )  =>  (! [E:$i] :  ((m2_pboole E C D (k7_funcop_1 C (u1_struct_0 B))) =>  ( (~  ((r2_hidden A (k2_relset_1 (u1_struct_0 B) (k4_waybel_5 B E))) &  (! [F:$i] :  ((m1_subset_1 F C) =>  (~  (A = (k4_yellow_2 B (k1_waybel_5 C (u1_struct_0 B) D E F))) ) ) ) ) )  &  ( ( (? [F:$i] :  ((m1_subset_1 F C) &  (A = (k4_yellow_2 B (k1_waybel_5 C (u1_struct_0 B) D E F))) ) )  => (r2_hidden A (k2_relset_1 (u1_struct_0 B) (k4_waybel_5 B E))))  &  ( (~  ((r2_hidden A (k2_relset_1 (u1_struct_0 B) (k5_waybel_5 B E))) &  (! [F:$i] :  ((m1_subset_1 F C) =>  (~  (A = (k5_yellow_2 B (k1_waybel_5 C (u1_struct_0 B) D E F))) ) ) ) ) )  &  ( (? [F:$i] :  ((m1_subset_1 F C) &  (A = (k5_yellow_2 B (k1_waybel_5 C (u1_struct_0 B) D E F))) ) )  => (r2_hidden A (k2_relset_1 (u1_struct_0 B) (k5_waybel_5 B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A C B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v2_waybel_6 D A) &  ((r3_orders_2 A B D) &  (~ (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v2_waybel_7 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r2_hidden (k1_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_waybel_8,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v5_orders_2 A))  => (v5_orders_2 B)) ) ) ) ) ).
tt(t14_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v2_yellow_6 (k4_waybel_9 A B C) A B) & (m1_yellow_6 (k4_waybel_9 A B C) A B)) ) ) ) ) ) ) ).
tt(t14_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_weddwitt A)) =>  ( ((v2_funct_1 B) &  ((k2_relset_1 (k3_weddwitt A) B) = (k3_weddwitt A)) )  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_seq_1 C D) = (k1_card_1 (k1_funct_1 B D))) ) ) ) )  =>  ((k7_group_1 A) = (k2_wsierp_1 C)) ) ) ) ) ) ) ) ) ).
tt(t14_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C A) &  ((v5_pre_topc B A k3_topmetr) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = (k2_weierstr (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_wellfnd1 A) <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~ (v3_wellfnd1 B A)) ) ) ) ) ) ).
tt(t14_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k1_wellord1 (k2_wellord1 C A) B) (k1_wellord1 C B))) ) ) ) ).
tt(t14_wellord2,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski A B) => (r1_ordinal1 (k2_wellord2 (k1_wellord2 A)) B)) ) ) ) ).
tt(t14_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_nat_d A B) => (r1_nat_d (k1_newton A C) (k1_newton B C))) ) ) ) ) ) ) ).
tt(t14_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) &  ((r1_tarski C B) &  (! [D:$i] :  ( ((r1_tarski A D) & (r1_tarski C D))  => (r1_tarski B D)) ) ) )  =>  (B = (k2_xboole_0 A C)) ) ) ) ) ).
tt(t14_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k6_xboolean A B)) = (k4_xboolean A B)) ) ) ) ) ).
tt(t14_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k6_xcmplx_0 A A) = k6_numbers) ) ) ).
tt(t14_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 C D) & (r1_xxreal_0 (k6_xcmplx_0 B C) (k6_xcmplx_0 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k12_xtuple_0 B)) &  (! [C:$i] :  (! [D:$i] :  (~ (r2_hidden (k3_xtuple_0 C A D) B)) ) ) ) ) ) ) ).
tt(t14_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (~  ( (~ (r2_hidden A k1_numbers))  &  ( (~  (A = k1_xxreal_0) )  &  (~  (A = k2_xxreal_0) ) ) ) ) ) ) ).
tt(t14_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k4_xxreal_1 B C)) =>  ((r2_hidden A (k2_xxreal_1 B C)) &  (~  (A = B) ) ) ) ) ) ) ) ) ).
tt(t14_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k2_xxreal_2 (k2_tarski A B)) = (k3_xxreal_0 A B)) ) ) ) ) ).
tt(t14_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( (~  (A = k2_xxreal_0) )  =>  ( ((k3_xxreal_3 k2_xxreal_0 A) = k2_xxreal_0)  &  ((k3_xxreal_3 A k2_xxreal_0) = k1_xxreal_0) ) ) ) ) ).
tt(t14_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ((r1_yellow_0 A C) => (r1_yellow_0 B C))  &  ((r2_yellow_0 A C) => (r2_yellow_0 B C)) ) ) ) ) ) ) ) ).
tt(t14_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ( ((k8_yellow_3 A B (k13_lattice3 (k3_yellow_3 A B) C D)) = (k13_lattice3 A (k8_yellow_3 A B C) (k8_yellow_3 A B D)))  &  ((k9_yellow_3 A B (k13_lattice3 (k3_yellow_3 A B) C D)) = (k13_lattice3 B (k9_yellow_3 A B C) (k9_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t14_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_yellow11 A) => (r5_waybel_1 (k5_yellow_0 A (k3_yellow11 A C (k13_lattice3 A B C))) (k5_yellow_0 A (k3_yellow11 A (k12_lattice3 A B C) B)))) ) ) ) ) ) ) ).
tt(t14_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  => (v2_waybel_2 B)) ) ) ) ) ).
tt(t14_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_yellow_8 C A B) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (C = (k1_tarski (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t14_yellow14,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((r5_waybel_1 A B) & (v1_yellow_0 A))  => (v1_yellow_0 B)) ) ) ) ) ).
tt(t14_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E k6_margrel1) =>  ( ( ((k1_funct_1 E 1) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 1) = B) )  &  ( ( ((k1_funct_1 E 1) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 1) = (k6_subset_1 A B)) )  &  ( ( ((k1_funct_1 E 2) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 2) = C) )  &  ( ( ((k1_funct_1 E 2) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 2) = (k6_subset_1 A C)) )  &  ( ( ((k1_funct_1 E 3) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 3) = D) )  &  ( ((k1_funct_1 E 3) = k7_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A (k3_finseq_4 (k1_zfmisc_1 A) B C D) E) 3) = (k6_subset_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r1_yellow16 B A C) =>  ((v22_waybel_0 C A A) & (v6_waybel_1 C A)) ) ) ) ) ) ) ) ).
tt(t14_yellow17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 B A) &  ((r1_tarski (k2_struct_0 A) (k3_tarski B)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((r1_tarski (k2_struct_0 A) (k3_tarski C)) & (v1_finset_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  ((k2_functor3 B A B (k2_yellow18 B A) (k2_yellow18 A B)) = (k12_functor0 B)) ) ) ) ) ) ).
tt(t14_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (B = (k2_yellow19 A (k3_yellow19 A (k2_struct_0 A) B))) ) ) ) ) ).
tt(t14_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_hidden (k3_tarski A) A) =>  ((k4_yellow_0 (k2_yellow_1 A)) = (k3_tarski A)) ) ) ) ).
tt(t14_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  ((v1_relat_1 (k1_yellow20 C D)) &  ((v4_relat_1 (k1_yellow20 C D) (k3_xboole_0 A B)) &  ((v1_funct_1 (k1_yellow20 C D)) & (v1_partfun1 (k1_yellow20 C D) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t14_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r2_hidden (u1_struct_0 B) A) =>  ((m1_subset_1 B (u1_struct_0 (k6_yellow21 A))) <=>  ((v1_orders_2 B) & (v3_lattice3 B)) ) ) ) ) ) ) ).
tt(t14_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v5_orders_3 C A B) & (r2_lattice3 A D E))  => (r2_lattice3 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_yellow_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( (~ (v2_struct_0 (k3_yellow_3 A B)))  =>  ( (~ (v2_struct_0 A))  &  (~ (v2_struct_0 B)) ) ) ) ) ) ) ).
tt(t14_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_yellow_4 A (k2_yellow_4 A B C) D) = (k2_yellow_4 A B (k2_yellow_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t14_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A (k1_yellow_5 A B C) D) & (r3_orders_2 A (k1_yellow_5 A C B) D))  => (r3_orders_2 A (k3_yellow_5 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t14_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  => (m2_yellow_6 B A B)) ) ) ) ).
tt(t14_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v2_lattice3 A))  => (v2_lattice3 B)) ) ) ) ) ).
tt(t14_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B (u1_pre_topc A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  & (r1_tarski D B)) ) ) ) )  =>  ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t14_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden A B) =>  (! [C:$i] :  ((r2_hidden C (k2_cantor_1 A B)) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  &  ((r1_tarski D B) &  (C = (k8_setfam_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t14_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k4_ordinal1)))  =>  ( ((v8_zf_fund1 C A) &  ((r1_tarski D C) & (r2_hidden B (k1_funct_2 E D))) )  => (r2_hidden B C)) ) ) ) ) ) ) ) ) ) ).
tt(t14_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k14_zf_lang C D A) = (k14_zf_lang E F B))  =>  ( (C = E)  &  ( (D = F)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k3_finseq_1 A) = 3)  => (v7_zf_lang A)) ) ) ).
tt(t14_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) (k1_tarski B)) = (k1_tarski A))  <=>  (~  (A = B) ) ) ) ) ).
tt(t14_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_zfmodel1 B A) => (r2_zfmodel1 B A)) ) ) ) ) ).
tt(t14_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  ((r1_zf_model C E (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang D (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) =>  ((r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model D)) |  ((r2_hidden A (k4_zf_lang1 D)) |  ((r2_hidden B (k2_zf_model D)) |  ( (A = (k2_zf_lang k6_numbers))  |  ( (A = (k2_zf_lang 3))  |  ( (A = (k2_zf_lang 4))  |  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model (k6_zf_lang1 D B A))))  &  ((r1_zf_model C (k2_zf_lang1 C E A (k3_funct_2 k1_zf_lang C E B)) (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang (k6_zf_lang1 D B A) (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) & (r2_funct_2 C C (k1_zfmodel1 D C E) (k1_zfmodel1 (k6_zf_lang1 D B A) C (k2_zf_lang1 C E A (k3_funct_2 k1_zf_lang C E B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t14_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_zf_model A B C) <=>  (~ (r1_zf_model A B (k6_zf_lang C))) ) ) ) ) ) ) ) ).
tt(t14_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ((v2_ordinal2 B) => (v2_ordinal2 (k1_ordinal3 A B))) ) ) ) ) ).
tt(t14_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  ( ((k2_zf_refle C A B) = (k3_card_3 (k5_relset_1 (k2_ordinal1 A) (k2_ordinal1 A) C B)))  &  ((k2_zf_refle (k5_relset_1 (k2_ordinal1 A) (k2_ordinal1 A) C B) A B) = (k3_card_3 (k5_relset_1 (k2_ordinal1 A) (k2_ordinal1 A) C B))) ) ) ) ) ) ) ) ).
tt(t14_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_zmodul01 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) C D)) B) = (k3_rlvect_1 A (k1_zmodul01 A C B) (k1_zmodul01 A D B))) ) ) ) ) ) ) ) ) ).
tt(t150_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k63_abcmiz_1 A D (k63_abcmiz_1 A C B)) = (k63_abcmiz_1 A (k65_abcmiz_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t150_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_funct_6 A (k10_finseq_1 B C)) = (k10_finseq_1 (k1_funct_2 A B) (k1_funct_2 A C))) ) ) ) ).
tt(t150_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_glib_000 A (k4_glib_001 A B) D C) &  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 E 1))  &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B E) = D) ) ) ) ) ) )  =>  ((r2_hidden C (k14_glib_001 A B)) |  ( ( (~ (v3_glib_001 B A))  & (v1_glib_001 B A))  | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(t150_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k18_group_2 A (k7_group_2 A)) = 1) ) ) ).
tt(t150_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k17_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k17_member_1 A C) (k17_member_1 B C))) ) ) ) ) ) ) ).
tt(t150_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( ((k5_relat_1 A C) = (k5_relat_1 B C))  &  ((k5_relat_1 A D) = (k5_relat_1 B D)) )  =>  ((k5_relat_1 A (k2_xboole_0 C D)) = (k5_relat_1 B (k2_xboole_0 C D))) ) ) ) ) ) ) ) ).
tt(t150_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A C (k5_sheffer1 A E B)) = (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t150_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 A B) = (k6_xcmplx_0 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t150_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 B 1) &  ((k3_xcmplx_0 A B) = 1) ) ) )  =>  (A = 1) ) ) ) ) ) ).
tt(t150_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k2_xxreal_1 A C) (k2_xxreal_1 B D)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t150_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((k3_zf_lang1 (k17_zf_lang B C D A)) = (k2_xboole_0 (k3_zf_lang1 A) (k1_enumset1 B C D))) ) ) ) ) ) ) ) ) ).
tt(t150_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_zmodul01 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(t151_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((k64_abcmiz_1 A D (k64_abcmiz_1 A C B)) = (k64_abcmiz_1 A (k65_abcmiz_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t151_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( ((k10_xtuple_0 C) = (k2_tarski A B))  &  ( ((k3_finseq_1 C) = 2)  &  ( (~  ( ((k1_funct_1 C 1) = A)  &  ((k1_funct_1 C 2) = B) ) )  &  (~  ( ((k1_funct_1 C 1) = B)  &  ((k1_funct_1 C 2) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t151_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((r2_hidden D (k13_glib_001 A B)) |  ( ( (~ (v3_glib_001 B A))  & (v1_glib_001 B A))  | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(t151_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_finset_1 (k15_group_2 A B)) &  ((k18_group_2 A B) = 1) )  =>  (B = A) ) ) ) ) ) ).
tt(t151_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k17_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k17_member_1 A C) (k17_member_1 B C))) ) ) ) ) ) ) ).
tt(t151_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r1_tarski (k9_xtuple_0 C) A) & (r1_tarski C B))  => (r1_tarski C (k5_relat_1 B A))) ) ) ) ) ) ).
tt(t151_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A E C)) = (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t151_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k6_xcmplx_0 A (k2_xcmplx_0 B (k4_xcmplx_0 B)))) ) ) ) ) ).
tt(t151_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 A (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t151_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 D C))  =>  ((k3_xboole_0 (k2_xxreal_1 A C) (k2_xxreal_1 B D)) = (k2_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t151_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  => (r1_tarski (k2_zf_model A) (k3_zf_lang1 A))) ) ).
tt(t151_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (C = D)  =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C B) = (k5_binom A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t152_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_tarski A (k2_finseq_1 B)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k1_relset_1 k5_numbers (k14_finseq_1 A))) &  (D = (k1_funct_1 (k14_finseq_1 A) C)) )  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t152_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k16_glib_001 A B (k1_funct_1 B C)) = (k18_glib_001 A B (k1_funct_1 B C))) ) ) )  => (v5_glib_001 B A)) ) ) ) ) ).
tt(t152_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k17_group_2 A (k6_group_2 A)) = (k7_struct_0 A)) ) ) ).
tt(t152_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k3_xxreal_3 C B) (k18_member_1 A C))) ) ) ) ) ) ) ).
tt(t152_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_xboole_0 B (k9_xtuple_0 A)) =>  ((k5_relat_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(t152_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A D C)) = (k5_sheffer1 A B (k5_sheffer1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t152_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k6_xcmplx_0 A B) = (k2_xcmplx_0 C (k4_xcmplx_0 B)))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t152_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B 1))  => (r1_xxreal_0 A (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t152_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k3_xboole_0 (k3_xxreal_1 A C) (k2_xxreal_1 B D)) = (k1_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t152_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k5_zf_lang1 (k4_zf_lang A B) C D) = (k4_zf_lang E F))  <=>  (~  ( (~  ( (~  (A = C) )  &  ( (~  (B = C) )  &  ( (E = A)  &  (F = B) ) ) ) )  &  ( (~  ( (A = C)  &  ( (~  (B = C) )  &  ( (E = D)  &  (F = B) ) ) ) )  &  ( (~  ( (~  (A = C) )  &  ( (B = C)  &  ( (E = A)  &  (F = D) ) ) ) )  &  (~  ( (A = C)  &  ( (B = C)  &  ( (E = D)  &  (F = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t152_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  ( (C = k6_numbers)  =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t153_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k19_glib_001 A B C) = C) ) ) )  => (v5_glib_001 B A)) ) ) ) ) ).
tt(t153_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k18_group_2 A (k6_group_2 A)) = (k7_group_1 A)) ) ) ).
tt(t153_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k18_member_1 A B) = (a_2_10_member_1 A B)) ) ) ) ) ).
tt(t153_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C D) &  ((k5_relat_1 A D) = (k5_relat_1 B D)) )  =>  ((k5_relat_1 A C) = (k5_relat_1 B C)) ) ) ) ) ) ) ) ).
tt(t153_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A D C) B) = (k5_sheffer1 A B (k5_sheffer1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t153_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k6_xcmplx_0 A B) = (k2_xcmplx_0 A (k4_xcmplx_0 C)))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t153_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B 1))  => (r1_xxreal_0 (k3_xcmplx_0 A B) A)) ) ) ) ) ).
tt(t153_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 D C))  =>  ((k3_xboole_0 (k3_xxreal_1 A C) (k2_xxreal_1 B D)) = (k4_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t153_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (? [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) &  (? [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) &  ((k5_zf_lang1 (k4_zf_lang A B) C D) = (k4_zf_lang E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t153_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t154_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  => (r1_xxreal_0 (k3_finseq_1 (k11_glib_001 A B)) (k2_nat_1 (k15_glib_000 A) 1))) ) ) ) ).
tt(t154_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((k18_group_2 A B) = (k7_group_1 A))  => (r1_group_2 A B (k6_group_2 A))) ) ) ) ) ).
tt(t154_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k18_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k3_xxreal_3 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t154_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k5_relat_1 A (k9_xtuple_0 B)) = (k5_relat_1 A (k9_xtuple_0 (k5_relat_1 B (k9_xtuple_0 A))))) ) ) ) ) ).
tt(t154_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A D C) B) D) = (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A C C) B))) ) ) ) ) ) ) ) ) ).
tt(t154_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k2_xcmplx_0 A B) C) = (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 C) A) B)) ) ) ) ) ) ) ).
tt(t154_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 (k3_xcmplx_0 A B) A)) ) ) ) ) ).
tt(t154_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k3_xboole_0 (k4_xxreal_1 A C) (k2_xxreal_1 B D)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t154_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k5_zf_lang1 (k5_zf_lang A B) C D) = (k5_zf_lang E F))  <=>  (~  ( (~  ( (~  (A = C) )  &  ( (~  (B = C) )  &  ( (E = A)  &  (F = B) ) ) ) )  &  ( (~  ( (A = C)  &  ( (~  (B = C) )  &  ( (E = D)  &  (F = B) ) ) ) )  &  ( (~  ( (~  (A = C) )  &  ( (B = C)  &  ( (E = A)  &  (F = D) ) ) ) )  &  (~  ( (A = C)  &  ( (B = C)  &  ( (E = D)  &  (F = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t154_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t155_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v6_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((r2_hidden D (k13_glib_001 A B)) | (v6_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ).
tt(t155_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( ((v1_finset_1 (k15_group_2 A B)) &  ((k17_group_2 A B) = (k7_struct_0 A)) )  =>  ((v8_struct_0 A) & (r1_group_2 A B (k6_group_2 A))) ) ) ) ) ) ).
tt(t155_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_tarski (k18_member_1 A C) (k18_member_1 B C)) => (r1_tarski A B)) ) ) ) ) ) ) ).
tt(t155_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ( (~ (v3_relat_1 (k5_relat_1 B A)))  & (v3_relat_1 B)) ) ) ) ) ).
tt(t155_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A C E) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A E B) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D)))) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t155_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k6_xcmplx_0 A B) C) = (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) C) A)) ) ) ) ) ) ) ).
tt(t155_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B 1))  & (r1_xxreal_0 (k3_xcmplx_0 A B) A)) ) ) ) ) ) ) ).
tt(t155_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 D C))  =>  ((k3_xboole_0 (k4_xxreal_1 A C) (k2_xxreal_1 B D)) = (k4_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t155_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (? [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) &  (? [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) &  ((k5_zf_lang1 (k5_zf_lang A B) C D) = (k5_zf_lang E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t155_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  ( (C = 1)  =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C B) = B) ) ) ) ) ) ) ) ).
tt(t156_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_glib_000 A C C B) => (v8_glib_001 (k2_glib_001 A C C B) A)) ) ) ) ) ).
tt(t156_group_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_finset_1 D) =>  (~  ( (D = C)  &  ( ((k5_card_1 D) = A)  &  (! [E:$i] :  ((r2_hidden E B) =>  ( (C = E)  |  ((r2_wellord2 C E) & (r1_xboole_0 C E)) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (k3_tarski B))  &  ((k5_card_1 C) = (k3_nat_1 A (k5_card_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t156_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k18_member_1 A C) = (k18_member_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t156_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k9_xtuple_0 (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) A))) = (k6_subset_1 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t156_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B D) = (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A D C) (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t156_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A (k6_xcmplx_0 (k4_xcmplx_0 B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t156_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 1 B))  & (r1_xxreal_0 (k3_xcmplx_0 A B) A)) ) ) ) ) ) ) ).
tt(t156_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k3_xxreal_1 A C) (k3_xxreal_1 B D)) = (k3_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t156_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k6_zf_lang A) = (k5_zf_lang1 (k6_zf_lang B) C D))  <=>  (A = (k5_zf_lang1 B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t156_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C D) &  (E = (k6_xcmplx_0 D C)) )  =>  ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) E B) = (k5_algstr_0 A (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) D B) (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t157_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r1_glib_000 A D E C) &  ((r2_hidden C (k14_glib_001 A B)) &  ((v8_glib_001 B A) &  (! [F:$i] :  ((m3_glib_001 F A) =>  (~  ((r1_glib_001 A D E F) &  (~ (r2_hidden C (k14_glib_001 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t157_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k18_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k18_member_1 A C) (k18_member_1 B C))) ) ) ) ) ) ) ).
tt(t157_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k5_relat_1 B A) = (k5_relat_1 B (k3_xboole_0 (k9_xtuple_0 B) A))) ) ) ) ).
tt(t157_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C E) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D)))) B) C)) = (k5_sheffer1 A (k5_sheffer1 A C E) (k5_sheffer1 A C (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t157_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) C) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) C) A)) ) ) ) ) ) ) ).
tt(t157_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 B))  & (r1_xxreal_0 A (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t157_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 D C))  =>  ((k3_xboole_0 (k3_xxreal_1 A C) (k3_xxreal_1 B D)) = (k3_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t157_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) => (r2_hidden (k5_zf_lang1 A B C) k9_zf_lang)) ) ) ) ) ) ).
tt(t157_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k4_algstr_0 A (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) C B)) = (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) C (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t158_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (m4_glib_001 B A B)) ) ) ) ).
tt(t158_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k18_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k18_member_1 A C) (k18_member_1 B C))) ) ) ) ) ) ) ).
tt(t158_relat_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k9_xtuple_0 (k2_zfmisc_1 A B)) A)) ) ).
tt(t158_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B E) (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D))) (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D)))) C))) = (k5_sheffer1 A (k5_sheffer1 A B E) (k5_sheffer1 A B (k5_sheffer1 A E (k5_sheffer1 A D (k5_sheffer1 A D D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t158_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) C) = (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 C) A) B)) ) ) ) ) ) ) ).
tt(t158_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B 1))  & (r1_xxreal_0 A (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t158_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k4_xxreal_1 A C) (k3_xxreal_1 B D)) = (k4_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t158_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k7_zf_lang A B) = (k6_zf_lang1 (k7_zf_lang C D) E F))  <=>  ( (A = (k6_zf_lang1 C E F))  &  (B = (k6_zf_lang1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t158_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ((r2_hidden C k5_numbers) =>  ((r2_hidden D k5_numbers) |  ((k1_binop_1 (k12_zmodul01 A) (k2_xcmplx_0 C D) B) = (k3_rlvect_1 A (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C B) (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t159_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) =>  (! [D:$i] :  ((m4_glib_001 D A C) => (m4_glib_001 D A B)) ) ) ) ) ) ) ) ).
tt(t159_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k18_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k18_member_1 A C) (k18_member_1 B C))) ) ) ) ) ) ) ).
tt(t159_relat_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k2_zfmisc_1 A B)) B)) ) ).
tt(t159_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A C E) (k5_sheffer1 A C (k5_sheffer1 A E D))) = (k5_sheffer1 A (k5_sheffer1 A C E) (k5_sheffer1 A C (k5_sheffer1 A E (k5_sheffer1 A B (k5_sheffer1 A B B)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t159_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) C) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 C) B) A)) ) ) ) ) ) ) ).
tt(t159_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 1 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t159_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 C D) |  ((k3_xboole_0 (k4_xxreal_1 A C) (k3_xxreal_1 B D)) = (k3_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t159_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ( (~  (C = D) )  =>  ( ((k8_zf_lang C A) = (k6_zf_lang1 (k8_zf_lang C B) D E))  <=>  (A = (k6_zf_lang1 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t159_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ((k1_binop_1 (k12_zmodul01 A) (k2_xcmplx_0 C D) B) = (k3_rlvect_1 A (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C B) (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B))) ) ) ) ) ) ) ) ) ).
tt(t15_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_abcmiz_0 A B) = (a_2_1_abcmiz_0 A B)) ) ) ) ) ).
tt(t15_abcmiz_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  ( ( ((k1_funct_1 A k6_numbers) = a_0_0_abcmiz_1)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_funct_1 A (k1_nat_1 B 1)) = (a_2_0_abcmiz_1 A B)) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)))  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) & (r1_tarski B (k1_funct_1 A C))) ) ) ) ) ) ) ).
tt(t15_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) => (r2_hidden B (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))) (k1_xtuple_0 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)))))) ) ) ) ) ).
tt(t15_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k1_absvalue A) = (k1_real_1 1))  & (r1_xxreal_0 k6_numbers A)) ) ) ) ).
tt(t15_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k2_aff_1 A B C)) & (r2_hidden C (k2_aff_1 A B C))) ) ) ) ) ) ) ).
tt(t15_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v11_aff_2 A) => (v13_aff_2 A)) ) ) ).
tt(t15_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r5_aff_1 A B C) =>  ((k1_aff_4 A B C) = C) ) ) ) ) ) ) ) ).
tt(t15_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ( ((k1_afinsq_1 A) = k6_numbers)  <=>  (A = k1_xboole_0) ) ) ) ).
tt(t15_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C (k1_afinsq_1 A)))  =>  ((k3_afinsq_2 A B C) = (k5_relat_1 (k2_afinsq_2 A (k7_nat_d B 1)) (k7_nat_d (k23_binop_2 C 1) B))) ) ) ) ) ) ) ) ).
tt(t15_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((r2_hidden B (k8_afproj A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k6_afproj A C))  & (v1_aff_4 C A)) ) ) ) ) ) ) ).
tt(t15_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_afvect0 A B C) & (r2_analoaf A B C D E))  => (r1_afvect0 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 (k1_alg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t15_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_algseq_1 A (k4_struct_0 A))) <=>  ((k2_algseq_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t15_algspec1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A (k9_xtuple_0 B)) =>  ((k1_algspec1 A B) = (k5_relat_1 B A)) ) ) ) ) ).
tt(t15_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  (B = (k11_binop_2 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_group_6 C A B) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 (k9_algstr_4 A D))) = (u1_struct_0 (k9_algstr_4 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_funct_1 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D)) &  ((v1_funct_2 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D) (k2_zfmisc_1 (k1_altcat_1 A C D) (k1_altcat_1 A B C)) (k1_altcat_1 A B D)) & (m1_subset_1 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_altcat_1 A C D) (k1_altcat_1 A B C)) (k1_altcat_1 A B D))))) ) ) ) ) ) ) ) ) ) ).
tt(t15_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v5_altcat_1 (k3_altcat_2 A) (u1_struct_0 A) (k2_altcat_2 A)) & (v4_altcat_1 (k3_altcat_2 A) (u1_struct_0 A) (k2_altcat_2 A))) ) ) ).
tt(t15_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v1_altcat_3 D A B C) &  (~ (v5_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  ((v17_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v2_funct_1 (k7_functor0 A B C E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_funct_1 (k7_ami_2 A B C) B) = C) ) ) ) ) ) ) ).
tt(t15_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  ( (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))  => (v2_extpro_1 A 2 k1_ami_3)) ) ) ).
tt(t15_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 8)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k9_ami_3 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_amistd_1 2 k1_ami_3 A (k7_ami_3 B)) = (k1_tarski B)) ) ) ) ) ).
tt(t15_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ((v5_amistd_1 C A B) & (r2_hidden k6_numbers (k1_relset_1 k5_numbers C)))  => (v6_amistd_1 C A B)) ) ) ) ) ) ) ).
tt(t15_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ( (~  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k1_funct_1 (k2_extpro_1 A B C D) (k4_struct_0 B)) = (k5_memstr_0 A B D)) ) ) )  => (r2_hidden (k4_struct_0 B) (k2_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t15_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v3_amistd_5 B A) &  ((v4_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ((v1_finset_1 D) & (v4_extpro_1 D A B C)) ) ) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) => (r2_hidden (k5_memstr_0 A B D) (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(t15_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  (C = (k5_ami_wstd A B C)) ) ) ) ) ) ) ) ).
tt(t15_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (k1_diraf (u1_struct_0 A) (k1_analoaf A))) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ( ((k1_rlvect_1 A (k5_algstr_0 A C B) F) = (k1_rlvect_1 A (k5_algstr_0 A E D) G))  &  (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k5_algstr_0 A D E))  => (r1_analoaf A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k2_analort A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r2_anproj_1 A B C D))  &  ((r2_anproj_1 A B C E) &  ((r2_anproj_1 A C D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_anproj_1 A B D G) &  ((r2_anproj_1 A E F G) &  (~ (v9_struct_0 G A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (A = (k8_domain_1 A B C D))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [E:$i] :  ((m2_funct_2 E A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (~  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) H E)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I F))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J G))) (k8_funcsdom A)) =>  ( (H = k6_numbers)  &  ( (I = k6_numbers)  &  (J = k6_numbers) ) ) ) ) ) ) ) ) )  &  (! [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) & (r2_funct_2 A k1_numbers H (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) I E)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J F))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  (C = (k1_recdef_1 A B)) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 C D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C D) D)))) )  =>  (? [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_unialg_1 F) &  ((v3_unialg_1 F) &  ((v4_unialg_1 F) & (l1_unialg_1 F)) ) ) )  &  ( ((u1_struct_0 F) = D)  &  ( ((k1_unialg_1 F) = A)  &  ((k1_funct_1 (u1_unialg_1 F) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) )  =>  ((r2_funct_2 (k9_funct_2 A k4_numbers) k4_numbers (k16_aofa_i00 (k9_funct_2 A k4_numbers) B (k25_aofa_i00 A k6_numbers)) B) & (r2_funct_2 (k9_funct_2 A k4_numbers) k4_numbers (k22_valued_1 (k9_funct_2 A k4_numbers) k4_numbers k4_numbers B (k25_aofa_i00 A 1)) B)) ) ) ) ) ).
tt(t15_armstrng,ax, (! [A:$i] :  ((k1_relset_1 (k4_armstrng A) (k7_armstrng A)) = (k8_mcart_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k9_setfam_1 A) (k9_setfam_1 A))) ) ).
tt(t15_arrow,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_funct_2 B (k3_arrow A)) (k2_arrow A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B (k3_arrow A)) (k2_arrow A))))) )  =>  (~  ( (! [D:$i] :  ((m2_funct_2 D B (k3_arrow A) (k9_funct_2 B (k3_arrow A))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ( (! [G:$i] :  ((m1_subset_1 G B) =>  (~ (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) D G) F E)) ) )  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C D) F E)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m2_funct_2 D B (k3_arrow A) (k9_funct_2 B (k3_arrow A))) =>  (! [E:$i] :  ((m2_funct_2 E B (k3_arrow A) (k9_funct_2 B (k3_arrow A))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  ( (~ (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) D H) G F))  & (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) E H) G F)) )  &  (~  ( (~ (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) E H) G F))  & (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) D H) G F)) ) ) ) )  =>  ( (~  ( (~ (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C D) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C E) G F)) )  &  (~  ( (~ (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C E) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C D) G F)) ) ) ) ) ) ) ) ) ) ) )  &  ((r1_xxreal_0 3 (k5_card_1 A)) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~  (! [E:$i] :  ((m2_funct_2 E B (k3_arrow A) (k9_funct_2 B (k3_arrow A))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( (~  ( (~ (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) E D) G F))  & (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C E) G F)) )  &  (~  ( (~ (r1_arrow (k3_funct_2 (k9_funct_2 B (k3_arrow A)) (k2_arrow A) C E) G F))  & (r1_arrow (k1_arrow B (k2_arrow A) (k3_arrow A) E D) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_arytm_0 (k3_arytm_0 A) B) = (k3_arytm_0 (k2_arytm_0 A B))) ) ) ) ) ).
tt(t15_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 A C))  =>  ((k7_arytm_2 (k1_arytm_1 C A) B) = (k7_arytm_2 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ).
tt(t15_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( (A = k12_arytm_3)  =>  ((k8_arytm_2 A B) = B) ) ) ) ) ) ).
tt(t15_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( ((k3_arytm_3 A B) = k1_xboole_0)  =>  (A = k1_xboole_0) ) ) ) ) ) ).
tt(t15_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((r1_xxreal_0 (k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) k6_numbers) |  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ) ).
tt(t15_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_hidden A (k6_asympt_0 (k3_asympt_1 1))) => (r2_hidden (k20_valued_1 k5_numbers k1_numbers k1_numbers A A) (k6_asympt_0 (k3_asympt_1 2)))) ) ) ).
tt(t15_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  ( ((v2_msualg_3 E A B C) & (v2_msualg_3 F A C D))  => (v2_msualg_3 (k3_msualg_3 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (m2_funct_2 (k6_partfun1 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A))) ) ).
tt(t15_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((k3_bagorder A B) = k6_numbers)  <=>  (B = (k16_pre_poly A)) ) ) ) ) ) ).
tt(t15_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) D) = (k1_bcialg_1 B (k1_bcialg_1 B C E) (k1_bcialg_1 B D E))) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t15_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) (k1_bcialg_2 A (k4_struct_0 A) B C) D)) = (k1_bcialg_2 A (k4_struct_0 A) B (k4_nat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t15_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v5_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (v4_bcialg_3 A)) ) ) ).
tt(t15_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A B C) D) <=> (r1_bcialg_1 A B (k1_bcialg_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_bcialg_5 E A B C D) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (m1_bcialg_5 E A (k2_nat_1 B F) (k2_nat_1 C F) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_bcialg_6 A D (k6_bcialg_1 A B C)) = (k1_bcialg_1 A (k3_bcialg_6 A D B) (k3_bcialg_6 A D C))) ) ) ) ) ) ) ) ) ).
tt(t15_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m1_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bhsp_1 A B (k4_struct_0 A)) = k6_numbers) ) ) ) ) ).
tt(t15_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 C A) =>  ((k1_bhsp_2 A (k5_normsp_1 A C B)) = (k1_rlvect_1 A (k1_bhsp_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t15_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_3 B A) & (r2_bhsp_3 A B C))  => (v1_bhsp_3 C A)) ) ) ) ) ) ) ).
tt(t15_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_bhsp_4 A B k6_numbers) = (k1_normsp_1 A B k6_numbers)) ) ) ) ) ).
tt(t15_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k3_bilinear A B C D E) F) (k6_hahnban1 A C E (k7_bilinear A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k20_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k2_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C)))) (k15_funcop_1 k5_numbers (k4_binari_2 (k23_binop_2 A 1) (k3_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))) (k1_binari_2 (k23_binop_2 A 1))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) = (k19_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))))) ) ) ) ) ) ) ).
tt(t15_binari_3,ax, ((k3_binarith 1 (k10_binarith k6_margrel1 k8_margrel1)) = (k10_binarith k6_margrel1 k7_margrel1)) ).
tt(t15_binari_4,ax, (! [A:$i] :  ( ((v3_card_1 A 1) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k12_finseq_1 k6_margrel1 k8_margrel1))  =>  ((k3_binari_2 1 A) = (k19_binop_2 1)) ) ) ) ).
tt(t15_binarith,ax, (! [A:$i] :  ( ((v3_card_1 A 1) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k12_finseq_1 k6_margrel1 k7_margrel1))  =>  ((k6_binarith 1 A) = k6_numbers) ) ) ) ).
tt(t15_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k5_binom A B (k2_nat_1 C D)) = (k1_algstr_0 A (k5_binom A B C) (k5_binom A B D))) ) ) ) ) ) ) ) ) ).
tt(t15_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 C A) =>  ((r6_binop_1 A C B) <=> (r5_binop_1 A C B)) ) ) ) ) ) ) ) ).
tt(t15_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  ((k1_funct_1 (k2_bintree2 A B) 1) = (k5_euclid B)) ) ) ) ) ).
tt(t15_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_boolealg A B (k1_boolealg A C D)) => (r3_boolealg A B C)) ) ) ) ) ) ) ) ) ).
tt(t15_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ( ((k4_kurato_0 A D) = (k8_bor_cant A B D))  &  ( ((k3_kurato_0 A D) = (k10_bor_cant A B D))  &  ( ((k10_bor_cant A B (k2_prob_1 A D)) = (k3_subset_1 A (k8_bor_cant A B D)))  &  ( ((k7_real_1 (k3_funct_2 B k1_numbers C (k10_bor_cant A B (k2_prob_1 A D))) (k3_funct_2 B k1_numbers C (k8_bor_cant A B D))) = 1)  &  ((k2_xcmplx_0 (k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) (k1_funct_1 C (k4_kurato_0 A D))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  ( (! [E:$i] :  ((r2_hidden E D) =>  ((r1_tarski E C) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))) &  (E = (k3_borsuk_1 A B F G)) ) ) ) ) ) ) )  => (r1_tarski (k3_borsuk_1 A B (k5_setfam_1 (u1_struct_0 A) (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) D)) (k6_setfam_1 (u1_struct_0 B) (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) D))) C)) ) ) ) ) ) ) ) ) ).
tt(t15_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  &  ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = C)  &  ((k1_funct_1 D 1) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_pre_topc C A) => (m1_pre_topc (k2_borsuk_1 B C) (k2_borsuk_1 B A))) ) ) ) ) ) ).
tt(t15_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_rcomp_1 B C))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k5_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t15_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k3_numbers)  =>  ((k2_pre_topc k3_topmetr A) = (u1_struct_0 k3_topmetr)) ) ) ) ).
tt(t15_borsuk_6,ax, ((v4_pre_topc a_0_0_borsuk_6 (k15_euclid 2)) & (m1_subset_1 a_0_0_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(t15_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (~  ( (~  (B = (k5_euclid A)) )  &  ((k30_valued_1 B) = (k5_euclid A)) ) ) ) ) ) ) ).
tt(t15_brouwer,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A))) &  ((v5_pre_topc C (k2_brouwer 2 B A) (k2_brouwer 2 B A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A)))))) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_brouwer 2 B A))) &  ((k3_funct_2 (u1_struct_0 (k2_brouwer 2 B A)) (u1_struct_0 (k2_brouwer 2 B A)) C D) = D) ) ) ) ) ) ) ) ) ).
tt(t15_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_bspace (k5_subset_1 A B C) D) = (k3_rlvect_1 k2_bspace (k3_bspace B D) (k3_bspace C D))) ) ) ) ) ) ) ) ).
tt(t15_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A D B)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t15_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (F = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 C H) (k16_funcop_1 D I)) (k16_funcop_1 E J)) (k16_funcop_1 B G)))  =>  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (C = D)  |  ( (C = E)  |  ( (D = E)  |  ( ((k1_funct_1 F C) = H)  &  ( ((k1_funct_1 F D) = I)  &  ((k1_funct_1 F E) = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ( ((r1_bvfunc_1 A B C) & (r1_bvfunc_1 A C B))  => (r2_funct_2 A k6_margrel1 B C))  &  ( ((r1_bvfunc_1 A B C) & (r1_bvfunc_1 A C D))  => (r1_bvfunc_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C B)) (k9_bvfunc_1 A C B))) ) ) ) ) ) ).
tt(t15_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k10_bvfunc_1 A C D)) (k9_bvfunc_1 A B (k6_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t15_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k2_bvfunc_1 A B C) D E) (k2_bvfunc_1 A (k7_bvfunc_2 A B D E) (k7_bvfunc_2 A C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k10_bvfunc_1 A B D) (k10_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C (k9_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t15_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t15_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k11_bvfunc_1 A) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t15_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k11_bvfunc_1 A)) B)) ) ) ) ).
tt(t15_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k5_bvfunc_1 A B D))) ) ) ) ) ) ) ) ).
tt(t15_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_struct_0 (k7_c0sp1 A)) = (k8_funcop_1 k5_numbers A k6_numbers)) ) ) ).
tt(t15_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k3_rlvect_1 (k5_c0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers G H) = (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers E H) (k3_funct_2 (u1_struct_0 A) k1_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((r1_calcul_1 (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B)) => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B))) ) ) ) ) ).
tt(t15_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k1_relset_1 k5_numbers (k5_relset_1 k5_numbers (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) B C) (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)))) = (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t15_cantor_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (v2_pre_topc (g1_pre_topc A (k1_cantor_1 A (k2_cantor_1 A B))))) ) ) ) ).
tt(t15_card_1,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k2_card_1 A))) ).
tt(t15_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski k6_numbers)) (k2_zfmisc_1 B (k1_tarski 1))) (k2_xboole_0 (k2_zfmisc_1 B (k1_tarski k6_numbers)) (k2_zfmisc_1 A (k1_tarski 1)))) &  ((k1_card_1 (k2_xboole_0 (k2_zfmisc_1 A (k1_tarski k6_numbers)) (k2_zfmisc_1 B (k1_tarski 1)))) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 B (k1_tarski k6_numbers)) (k2_zfmisc_1 A (k1_tarski 1))))) ) ) ) ).
tt(t15_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k5_card_3 A (k2_tarski B C)) = (k2_tarski (k1_funct_1 B A) (k1_funct_1 C A))) ) ) ) ) ) ).
tt(t15_card_4,ax, (! [A:$i] :  ((v1_card_1 A) =>  ( (~ (v1_finset_1 A))  =>  ((k2_card_2 A A) = A) ) ) ) ).
tt(t15_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (? [B:$i] :  ((v3_ordinal1 B) &  (A = (k3_card_1 B)) ) ) ) ) ).
tt(t15_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r2_hidden B (k3_card_fil A)) <=> (m1_card_fil B A)) ) ) ) ).
tt(t15_cardfin2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k8_nat_1 k4_numbers k3_cardfin2 (k5_card_1 A)) = (k5_card_1 (k2_cardfin2 A))) ) ) ).
tt(t15_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~  (A = B) )  &  ( (~ (r2_hidden C D))  &  (~  ((k5_card_1 (k1_card_fin (k2_xboole_0 D (k1_tarski C)) (k23_binop_2 E 1) A B)) = (k23_binop_2 (k5_card_1 (k1_card_fin D (k23_binop_2 E 1) A B)) (k5_card_1 (k1_card_fin D E A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v3_card_lar B A) => (v1_card_lar B A)) ) ) ) ) ).
tt(t15_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A B) = (k4_graph_1 A C))  <=> (r2_hidden (k4_tarski B C) (k9_xtuple_0 (u1_cat_1 A)))) ) ) ) ) ) ) ).
tt(t15_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k8_cat_1 B A (k5_cat_2 A B) C) = C) ) ) ) ) ) ) ).
tt(t15_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  ( (~  (A = B) )  => (r2_funct_2 (k2_tarski A B) (u4_struct_0 C) (k7_cat_3 C (k2_tarski A B) (k5_funct_4 (u4_struct_0 C) A B E F) D) (k5_funct_4 (u4_struct_0 C) A B (k1_cat_1 C E D) (k1_cat_1 C F D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k6_cat_4 A B)) = B)  &  ((k4_graph_1 A (k6_cat_4 A B)) = (k1_cat_4 A)) ) ) ) ) ) ).
tt(t15_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  ((r1_tarski (u4_struct_0 A) (u4_struct_0 B)) => (m3_cat_2 A B)) ) ) ) ) ).
tt(t15_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k1_catalan1 (k1_nat_1 A 1)) (k1_catalan1 A))) ) ) ) ).
tt(t15_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (~  ((r1_tarski (k2_relset_1 k5_numbers A) (k7_domain_1 k5_numbers k6_numbers 1)) &  ( (~ (v1_catalan2 A))  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( ((k23_binop_2 (k24_binop_2 2 B) 1) = (k5_nat_1 (a_1_1_catalan2 A)))  &  ((r1_xxreal_0 (k23_binop_2 (k24_binop_2 2 B) 1) (k1_relset_1 k5_numbers A)) &  ( (B = (k7_afinsq_2 (k5_relat_1 A (k24_binop_2 2 B))))  &  ((k1_recdef_1 A (k24_binop_2 2 B)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k3_catalg_1 A))) =>  ( ( ((k1_xtuple_0 B) = 1)  &  ((k3_finseq_1 (k2_xtuple_0 B)) = 1) )  |  ( ((k1_xtuple_0 B) = 2)  &  ((k3_finseq_1 (k2_xtuple_0 B)) = 3) ) ) ) ) ) ) ).
tt(t15_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_cc0sp1 A)))  &  ((v13_algstr_0 (k7_cc0sp1 A)) &  ((v2_rlvect_1 (k7_cc0sp1 A)) &  ((v3_rlvect_1 (k7_cc0sp1 A)) &  ((v4_rlvect_1 (k7_cc0sp1 A)) &  ((v3_group_1 (k7_cc0sp1 A)) &  ((v5_group_1 (k7_cc0sp1 A)) &  ((v1_vectsp_1 (k7_cc0sp1 A)) &  ((v3_vectsp_1 (k7_cc0sp1 A)) &  ((v2_clvect_1 (k7_cc0sp1 A)) &  ((v3_clvect_1 (k7_cc0sp1 A)) &  ((v4_clvect_1 (k7_cc0sp1 A)) &  ((v2_cfuncdom (k7_cc0sp1 A)) & (l1_cfuncdom (k7_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_cc0sp1 B A) =>  (! [C:$i] :  ((m1_cc0sp1 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_cc0sp1 B C)) ) ) ) ) ) ) ).
tt(t15_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v1_partfun1 C k2_numbers) => (r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers B (k25_valued_1 k2_numbers k2_numbers C A)) (k25_valued_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers B C) A))) ) ) ) ) ) ) ).
tt(t15_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v6_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  ((r2_cfdiff_1 A B) <=>  ((r1_tarski B (k1_relset_1 k2_numbers A)) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r2_hidden C B) => (r1_cfdiff_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t15_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers (k2_cfuncdom A) B (k1_funcsdom A k2_numbers (k1_cfuncdom A) C D)) (k1_funcsdom A k2_numbers (k1_cfuncdom A) (k1_funcsdom A k2_numbers (k2_cfuncdom A) B C) (k1_funcsdom A k2_numbers (k2_cfuncdom A) B D)))) ) ) ) ) ) ) ) ).
tt(t15_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C) D) (k2_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B D) (k19_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t15_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ( ((r2_hidden A (k6_cgames_1 B)) | (r2_hidden A (k7_cgames_1 B)))  => (r2_hidden (k9_cgames_1 A) (k9_cgames_1 B))) ) ) ) ) ).
tt(t15_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((r1_xxreal_0 C D) & (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_chord,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k10_xtuple_0 A))))  =>  (? [C:$i] :  ((r2_hidden C B) &  (! [D:$i] :  ((r2_hidden D B) => (r1_xxreal_0 (k4_finseq_4 A C) (k4_finseq_4 A D))) ) ) ) ) ) ) ) ).
tt(t15_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( ( (H = (k5_relat_1 G (u1_struct_0 A)))  & (v1_circuit2 H A D))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( (I = (k5_relat_1 G (u1_struct_0 B)))  =>  ((k5_relat_1 (k6_circuit2 C F G) (u1_struct_0 B)) = (k6_circuit2 B E I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (A = (k5_circcomb C B))  =>  ((k3_circcmb3 A) = (k4_tarski B C)) ) ) ) ) ) ) ).
tt(t15_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k3_msafree2 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( (D = E)  =>  ((r2_hidden E (k3_msafree2 C)) &  ((k4_msafree2 C E) = (k4_msafree2 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_convex1 A (k2_circled1 A B) C) = (k2_circled1 A (k1_convex1 A B C))) ) ) ) ) ) ) ).
tt(t15_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v4_msafree2 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m3_msaterm D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k1_circtrm1 A B D))) =>  ((k5_msualg_1 (k1_circtrm1 A B D) E (k6_circtrm1 A B D C)) = (k3_circtrm1 A B D E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r1_xxreal_0 (k4_circuit1 A B C) k6_numbers)) ) ) ) ) ) ) ).
tt(t15_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((v3_funct_1 (k10_funct_6 C)) & (v1_circuit2 (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) E) A B))  =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 E F) => (r8_pboole (u1_struct_0 A) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) E) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) => (r1_tarski (k3_classes1 A B) (k3_classes1 A (k1_ordinal1 B)))) ) ) ).
tt(t15_classes2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A (k1_card_1 B)))  => (r2_hidden A B)) ) ) ) ).
tt(t15_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_clopban1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_clopban1 A B))) =>  ( (E = (k3_rlvect_1 (k6_clopban1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k7_clopban1 A B E F) = (k3_rlvect_1 B (k7_clopban1 A B C F) (k7_clopban1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_clopban2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_clopban2 A))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( ((k1_algstr_0 (k8_clopban2 A) B C) = (k1_algstr_0 (k8_clopban2 A) C B))  &  ( ((k1_algstr_0 (k8_clopban2 A) (k1_algstr_0 (k8_clopban2 A) B C) D) = (k1_algstr_0 (k8_clopban2 A) B (k1_algstr_0 (k8_clopban2 A) C D)))  &  ( ((k1_algstr_0 (k8_clopban2 A) B (k4_struct_0 (k8_clopban2 A))) = B)  &  ((v10_algstr_0 B (k8_clopban2 A)) &  ( ((k6_algstr_0 (k8_clopban2 A) (k6_algstr_0 (k8_clopban2 A) B C) D) = (k6_algstr_0 (k8_clopban2 A) B (k6_algstr_0 (k8_clopban2 A) C D)))  &  ( ((k6_algstr_0 (k8_clopban2 A) B (k5_struct_0 (k8_clopban2 A))) = B)  &  ( ((k6_algstr_0 (k8_clopban2 A) (k5_struct_0 (k8_clopban2 A)) B) = B)  &  ( ((k6_algstr_0 (k8_clopban2 A) B (k1_algstr_0 (k8_clopban2 A) C D)) = (k1_algstr_0 (k8_clopban2 A) (k6_algstr_0 (k8_clopban2 A) B C) (k6_algstr_0 (k8_clopban2 A) B D)))  &  ( ((k6_algstr_0 (k8_clopban2 A) (k1_algstr_0 (k8_clopban2 A) C D) B) = (k1_algstr_0 (k8_clopban2 A) (k6_algstr_0 (k8_clopban2 A) C B) (k6_algstr_0 (k8_clopban2 A) D B)))  &  ( ((k1_clvect_1 (k8_clopban2 A) (k6_algstr_0 (k8_clopban2 A) B C) E) = (k6_algstr_0 (k8_clopban2 A) (k1_clvect_1 (k8_clopban2 A) B E) C))  &  ( ((k1_clvect_1 (k8_clopban2 A) (k1_algstr_0 (k8_clopban2 A) B C) E) = (k1_algstr_0 (k8_clopban2 A) (k1_clvect_1 (k8_clopban2 A) B E) (k1_clvect_1 (k8_clopban2 A) C E)))  &  ( ((k1_clvect_1 (k8_clopban2 A) B (k2_xcmplx_0 E F)) = (k1_algstr_0 (k8_clopban2 A) (k1_clvect_1 (k8_clopban2 A) B E) (k1_clvect_1 (k8_clopban2 A) B F)))  &  ( ((k1_clvect_1 (k8_clopban2 A) B (k3_xcmplx_0 E F)) = (k1_clvect_1 (k8_clopban2 A) (k1_clvect_1 (k8_clopban2 A) B F) E))  &  ((k1_clvect_1 (k8_clopban2 A) (k6_algstr_0 (k8_clopban2 A) B C) (k3_xcmplx_0 E F)) = (k6_algstr_0 (k8_clopban2 A) (k1_clvect_1 (k8_clopban2 A) B E) (k1_clvect_1 (k8_clopban2 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k2_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t15_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_normsp_1 A (k1_bhsp_4 A C) B) = (k3_rlvect_1 A (k1_normsp_1 A (k1_bhsp_4 A (k4_lopban_4 A C)) B) (k1_normsp_1 A C B))) ) ) ) ) ) ) ).
tt(t15_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v4_closure1 (k2_msualg_3 A (k5_mssubfam A B)) A B) & (m2_pboole (k2_msualg_3 A (k5_mssubfam A B)) A (k5_mssubfam A B) (k5_mssubfam A B))) ) ) ) ).
tt(t15_closure2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k9_xtuple_0 (k3_closure2 (k1_tarski A))) = (k9_xtuple_0 A)) ) ) ).
tt(t15_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k1_clvect_1 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) D) = (k3_rlvect_1 A (k1_clvect_1 A B D) (k1_clvect_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 C A) =>  ((k1_clvect_2 A (k6_clvect_1 A C B)) = (k1_clvect_1 A (k1_clvect_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t15_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k2_clvect_3 A B k6_numbers) = (k1_normsp_1 A B k6_numbers)) ) ) ) ) ).
tt(t15_cohsp_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r1_cohsp_1 A A) =>  ((v1_cohsp_1 A) & (v2_cohsp_1 A)) ) ) ) ).
tt(t15_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k2_coh_sp A B) = (k3_toler_1 A B)) ) ) ) ).
tt(t15_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m2_collsp D A) =>  (~  ((r2_hidden B D) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((r1_xxreal_0 2 A) & (r1_ordinal1 (k2_nat_1 A 2) (k1_card_1 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  (~  ((v2_combgras C (k1_combgras A B)) &  ( (~ (v3_combgras C A B))  &  (~ (v4_combgras C A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k3_complex1 A) = k6_numbers)  &  ((k3_complex1 B) = k6_numbers) )  =>  ( ((k3_complex1 (k3_xcmplx_0 A B)) = (k1_real_1 (k8_real_1 (k4_complex1 A) (k4_complex1 B))))  &  ((k4_complex1 (k3_xcmplx_0 A B)) = k6_numbers) ) ) ) ) ) ) ).
tt(t15_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k1_comptrig A) = k6_numbers)  <=>  (A = (k17_complex1 A)) ) ) ) ).
tt(t15_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( ( ((k8_group_1 k1_complfld B A) = (k5_struct_0 k1_complfld))  |  ((k8_group_1 k1_complfld A B) = (k5_struct_0 k1_complfld)) )  &  (~  (B = (k11_algstr_0 k1_complfld A)) ) ) ) ) ) ) ) ) ).
tt(t15_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_finseq_1 (k12_seq_4 A B)) = (k4_finseq_1 A)) ) ) ) ) ).
tt(t15_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_topmetr A B)))) =>  ( (C = D)  =>  ((v6_tbsp_1 D (k1_topmetr A B)) <=> (v6_tbsp_1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k5_card_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F)) = 6) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r2_hidden A (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))) & (r1_xxreal_0 (k1_seq_1 k19_sin_cos A) k6_numbers)) ) ) ) ).
tt(t15_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((v5_pre_topc D A C) &  ( ((k2_relset_1 (u1_struct_0 C) D) = (k2_struct_0 C))  & (v2_compts_1 B A)) )  => (v2_compts_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 C) D B) C)) ) ) ) ) ) ) ) ) ).
tt(t15_comput_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_comput_1 C) & (m1_rfunct_3 C A B)) )  =>  ((v1_funct_1 (k3_tarski C)) & (m1_subset_1 (k3_tarski C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(t15_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B) (k19_valued_1 k5_numbers k2_numbers k2_numbers A C)) (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)))) ) ) ) ) ) ).
tt(t15_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k1_series_1 k1_numbers (k7_comseq_3 A) (k7_comseq_3 B)) (k7_comseq_3 (k1_series_1 k2_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k1_series_1 k1_numbers (k8_comseq_3 A) (k8_comseq_3 B)) (k8_comseq_3 (k1_series_1 k2_numbers A B)))) ) ) ) ) ).
tt(t15_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k4_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u4_struct_0 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) C))) ) ) ) ) ) ) ).
tt(t15_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  => (r1_filter_1 (k11_conlat_1 (k6_conlat_2 A)) A)) ) ).
tt(t15_conmetr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v11_aff_2 (k3_analmetr A)) <=> (v8_conmetr A)) ) ) ).
tt(t15_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v3_conaffm A) => (v1_conmetr A)) ) ) ).
tt(t15_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_connsp_1 A C D) &  ( (~  (C = (k1_struct_0 A)) )  &  (~  (D = (k1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) => (v3_pre_topc B A)) ) ) ) ) ) ).
tt(t15_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v2_connsp_1 B A) & (r2_hidden C B))  =>  ((k1_connsp_1 A C) = (k1_connsp_3 A B)) ) ) ) ) ) ) ) ).
tt(t15_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_convex1 C A)) ) )  => (v1_convex1 (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t15_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m2_convex4 D A (k7_domain_1 (u1_struct_0 A) B C)) =>  ((k4_convex4 A D) = (k3_rlvect_1 A (k1_clvect_1 A B (k3_funct_2 (u1_struct_0 A) k2_numbers D B)) (k1_clvect_1 A C (k3_funct_2 (u1_struct_0 A) k2_numbers D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k13_cqc_lang A (k5_cqc_lang A) B) = (k5_cqc_lang A)) ) ) ) ) ).
tt(t15_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ((k7_cqc_sim1 A (k4_cqc_lang B A D C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t15_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (v1_cqc_the1 (k1_cqc_the1 A B) A)) ) ) ) ).
tt(t15_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A B (k12_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t15_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the3 A B) <=> (r2_cqc_the3 A (k1_subset_1 (k3_cqc_lang A)) B)) ) ) ) ) ).
tt(t15_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)))) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) &  ((v1_csspace4 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ((k1_seq_1 (k8_csspace4 A B) C) = (k4_seq_4 (k7_csspace4 A B C))) ) ) ) ) ) ) ).
tt(t15_csspace,ax, ( ((u1_struct_0 k7_csspace) = k1_csspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_csspace)) <=>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_csspace)) <=>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_csspace)) =>  (A = (k2_csspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k7_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k7_csspace)) =>  ((k3_rlvect_1 k7_csspace A B) = (k1_series_1 k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) )  &  (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k7_csspace)) =>  ((k1_clvect_1 k7_csspace B A) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_decomp_1 A) (k19_decomp_1 A)) = (k8_decomp_1 A)) ) ) ).
tt(t15_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A B (k4_xcmplx_0 1)) = (k7_descip_1 B)) ) ) ) ) ) ).
tt(t15_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_wellfnd1 A) => (v1_wellfnd1 (k5_dickson A))) ) ) ).
tt(t15_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) B) (k2_nat_1 A 1)) C) = (k7_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) (k2_nat_1 A 1)) C) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 E B) (k2_nat_1 A 1)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k1_numbers k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k2_diff_2 (k3_valued_1 k1_numbers k1_numbers k1_numbers G H) A B C D E F) = (k7_real_1 (k2_diff_2 G A B C D E F) (k2_diff_2 H A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers F B) (k26_valued_1 k1_numbers k1_numbers G C)) D) (k2_nat_1 A 1)) E) = (k9_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 F D) (k2_nat_1 A 1)) E)) (k8_real_1 C (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 G D) (k2_nat_1 A 1)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k1_fdiff_9)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k1_fdiff_9)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_fdiff_9) B) A) = (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k7_real_1 (k8_real_1 2 A) B))) (k18_sin_cos B)) (k5_square_1 (k7_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B))))) ) ) ) ) ) ).
tt(t15_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D C) &  ((r2_hidden E C) &  ((r2_hidden D B) & (r2_hidden E B)) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ).
tt(t15_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r1_diraf A B C D) &  ((r1_diraf A B C E) &  ( (~ (r1_diraf A C D E))  &  (~ (r1_diraf A C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v4_dirort A) => (v3_dirort A)) ) ) ).
tt(t15_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k16_rvsum_1 (k9_dist_1 A B)) = (k11_binop_2 (k3_finseq_1 B) (k18_rvsum_1 (k4_dist_1 A B)))) ) ) ) ) ).
tt(t15_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k4_zfmisc_1 B C D E)) =>  ( (A = (k6_mcart_1 B C D E F))  <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H C) =>  (! [I:$i] :  ((m1_subset_1 I D) =>  (! [J:$i] :  ((m1_subset_1 J E) =>  ( (F = (k5_domain_1 B C D E G H I J))  =>  (A = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_dtconstr,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr)) =>  ((k16_dtconstr k5_dtconstr A) = (k8_finseq_1 k5_numbers (k5_finseq_2 k5_numbers (k6_trees_1 (k9_xtuple_0 A)) 1) (k3_pre_poly k5_numbers k6_numbers))) ) ) ).
tt(t15_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin B A) & (v2_finsub_1 B))  =>  (! [C:$i] :  ((v1_finset_1 C) =>  ((r1_tarski C B) => (r2_hidden (k3_tarski C) B)) ) ) ) ) ) ) ) ).
tt(t15_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  (E = (k6_int_1 B C)) )  =>  ((k3_rlvect_1 (k9_int_3 C) D E) = (k6_int_1 (k2_xcmplx_0 A B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A (k3_rlvect_1 A B C) (k5_algstr_0 A B C)) = (k5_algstr_0 A (k2_binom A B 2) (k2_binom A C 2))) ) ) ) ) ) ) ).
tt(t15_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_endalg A)) (u1_struct_0 (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A)))) &  ((v6_group_1 B (k3_endalg A) (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))) &  ((v1_group_6 B (k3_endalg A) (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_endalg A)) (u1_struct_0 (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))))))) ) ) )  =>  ( (! [C:$i] :  ((r2_hidden C (k1_endalg A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) )  => (v3_funct_2 B (u1_struct_0 (k3_endalg A)) (u1_struct_0 (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A))))) ) ) ) ) ).
tt(t15_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = k1_xboole_0)  =>  (B = k1_xboole_0) )  => (r2_hidden (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 B C)) (k1_domain_1 A A B C) D) (k7_ens_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t15_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((k1_seq_1 A B) = 1) )  => (r1_entropy1 A B)) ) ) ) ) ).
tt(t15_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k3_enumset1 A B C D E) (k1_tarski F))) ) ) ) ) ) ) ).
tt(t15_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k5_eqrel_1 A B C) (k5_eqrel_1 A C B))) ) ) ) ) ).
tt(t15_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k9_pboole A B (k2_msualg_3 A B)) B)) ) ) ).
tt(t15_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (u1_e_siec A) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ((k3_relat_1 (u2_e_siec A) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0) ) ) ) ).
tt(t15_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  => (r1_xxreal_0 (k18_complex1 (k23_rvsum_1 A B)) (k11_binop_2 (k12_euclid A) (k12_euclid B)))) ) ) ) ) ).
tt(t15_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k2_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)) = (k11_complex1 (k2_euclid_3 A) (k2_euclid_3 B))) ) ) ) ) ).
tt(t15_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ((k12_euclid B) = (k7_square_1 (k23_rvsum_1 B B))) ) ) ) ) ).
tt(t15_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k5_euclid_5 (k4_euclid_5 A B C) (k4_euclid_5 D E F)) = (k4_euclid_5 (k9_real_1 (k8_real_1 B F) (k8_real_1 C E)) (k9_real_1 (k8_real_1 C D) (k8_real_1 A F)) (k9_real_1 (k8_real_1 A E) (k8_real_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) D E)))  =>  ( (A = B)  |  ( (A = D)  |  ( (A = C)  |  ( (A = E)  |  ((k4_euclid_3 B A D) = (k4_euclid_3 C A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_euclid_7,ax, (! [A:$i] :  ((v1_euclid_7 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) )  =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (B = C)  | (r1_rvsum_1 B C)) ) ) ) ) ) ) ) ).
tt(t15_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (~  ( (~  (A = k6_numbers) )  &  ((r2_hidden C (k4_euclid_9 A D B)) & (r1_xxreal_0 (k3_xcmplx_0 A (k3_square_1 B)) (k18_rvsum_1 (k12_rvsum_1 (k8_rvsum_1 C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k9_real_1 (k12_euclid B) (k12_euclid C)) (k12_euclid (k8_euclid A B C)))) ) ) ) ) ) ).
tt(t15_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid D)) =>  ((k8_euclid D E (k9_euclid D F (k7_real_1 (k7_real_1 A B) C))) = (k7_euclid D (k7_euclid D (k7_euclid D E (k9_euclid D F (k1_real_1 A))) (k9_euclid D F (k1_real_1 B))) (k9_euclid D F (k1_real_1 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( ((v1_euclmetr A) & (v3_euclmetr A))  => (v2_euclmetr A)) ) ) ).
tt(t15_euler_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k3_int_2 (k3_xcmplx_0 B A) (k3_xcmplx_0 B C)) = (k3_xcmplx_0 B (k3_int_2 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ((k2_euler_2 (k1_wsierp_1 k1_numbers k5_numbers B C) A) = (k1_wsierp_1 k1_numbers k5_numbers (k2_euler_2 B A) (k2_euler_2 C A))) ) ) ) ) ) ) ).
tt(t15_exchsort,ax, ( ((k1_exchsort k1_xboole_0) = k1_xboole_0)  &  ( ((k2_exchsort k1_xboole_0) = k1_xboole_0)  &  ((k3_exchsort k1_xboole_0) = k1_xboole_0) ) ) ).
tt(t15_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r2_msualg_3 A B C D) =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A E)) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A E)) =>  ((r8_pboole (u1_struct_0 A) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A E) D F) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A E) D G)) => (r8_pboole (u1_struct_0 A) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  (~ (v2_compos_1 C B)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_finset_1 D)) ) ) )  =>  ((m1_extpro_1 D A B C) <=> (r2_extpro_1 A B C D (k16_funcop_1 k1_xboole_0 k1_xboole_0))) ) ) ) ) ) ) ) ) ).
tt(t15_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( ( (A = k1_supinf_1)  |  (A = k2_supinf_1) )  =>  ((k1_extreal1 (k3_extreal1 A) (k3_extreal1 (k2_extreal1 k8_mesfunc1 A))) = k6_numbers) ) ) ) ).
tt(t15_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((k5_facirc_1 A B C 2) = (k6_circuit2 A B (k6_circuit2 A B C))) ) ) ) ) ) ) ).
tt(t15_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((k6_facirc_2 (k2_nat_1 B 1) A C D) = (k12_facirc_1 (k1_funct_1 C (k2_nat_1 B 1)) (k1_funct_1 D (k2_nat_1 B 1)) (k5_facirc_2 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t15_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) <=> (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A) A))) ) ) ) ).
tt(t15_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k4_subset_1 k1_numbers (k1_rcomp_1 (k1_seq_1 C A) (k1_seq_1 C B)) (k1_rcomp_1 (k1_seq_1 C B) (k1_seq_1 C A)))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k1_rcomp_1 A B)) &  (D = (k1_seq_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((k7_relset_1 k1_numbers k1_numbers B A) = (k2_rcomp_1 C D)) ) ) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t15_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k9_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t15_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k19_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k19_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k1_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t15_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 C A) =>  ((r1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C B) A) &  ((k1_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C B) A) = (k8_real_1 B (k1_fdiff_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 B A) =>  ( ((k1_seq_1 B A) = k6_numbers)  |  ((r1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k1_real_1 (k10_real_1 (k1_fdiff_1 B A) (k5_square_1 (k1_seq_1 B A))))) ) ) ) ) ) ) ) ).
tt(t15_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((r3_fdiff_3 A B) &  ((k2_fdiff_3 B A) = C) )  =>  ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k1_rcomp_1 B (k7_real_1 B D)) (k1_relset_1 k1_numbers A))) ) )  &  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers A)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 D F) k6_numbers)) ) ) ) )  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) = C) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers A)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 D F) k6_numbers)) ) ) ) )  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) = C) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k1_rcomp_1 B (k7_real_1 B D)) (k1_relset_1 k1_numbers A))) ) ) )  |  ((r3_fdiff_3 A B) &  ((k2_fdiff_3 B A) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~  ((k1_seq_1 C D) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1)) B) D) = (k10_real_1 1 (k5_square_1 (k7_real_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) A) B) = (k9_real_1 (k1_real_1 (k8_real_1 (k10_real_1 1 B) (k1_seq_1 k16_sin_cos B))) (k8_real_1 (k10_real_1 1 (k5_square_1 B)) (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 B D) = (k9_real_1 (k1_real_1 D) 1))  &  ((k1_seq_1 C D) = (k1_real_1 D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) A) D) = (k10_real_1 D (k26_sin_cos D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ( ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D E) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D E))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6) C) E) = (k1_real_1 (k10_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 (k7_real_1 (k8_real_1 A E) B))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 B (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B))))))) ) ) ) ) ) ) ) ).
tt(t15_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 B)) (k8_real_1 B (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B))))))) ) ) ) ) ) ) ) ).
tt(t15_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k2_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u4_struct_0 A)))  &  ((k2_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = (k5_relat_1 (k2_relat_1 (k1_net_1 A)) (u1_struct_0 A))) ) ) ) ).
tt(t15_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  &  (~  ((v1_relat_1 (k2_tarski (k4_tarski A C) (k4_tarski B D))) &  ((v1_funct_1 (k2_tarski (k4_tarski A C) (k4_tarski B D))) & (v2_finseq_1 (k2_tarski (k4_tarski A C) (k4_tarski B D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fib_num3,ax, ((k1_fib_num3 3) = 4) ).
tt(t15_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 2))  => (r1_xxreal_0 (k10_complex1 (k13_complex1 1 (k7_square_1 5))) (k3_power k2_fib_num A))) ) ) ).
tt(t15_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( (E = (k11_finseq_1 A B C))  =>  ((k2_rfinseq D 1 E) = (k10_finseq_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t15_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k2_filter_0 A C)) <=> (r3_lattices A C B)) ) ) ) ) ) ) ).
tt(t15_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_lattices (k4_filter_1 A B) (k5_filter_1 A B C) (k5_filter_1 A B D)) = (k5_filter_1 A B (k3_lattices A C D)))  &  ((k4_lattices (k4_filter_1 A B) (k5_filter_1 A B C) (k5_filter_1 A B D)) = (k5_filter_1 A B (k4_lattices A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t15_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v1_xboole_0 C))  &  ((v19_lattices C B) &  ((v20_lattices C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((r1_finance1 A k1_numbers B k12_prob_1 C) =>  ((r1_mesfunc6 A B C (k4_prob_1 A B)) & (m1_random_1 C A B)) ) ) ) ) ) ) ) ).
tt(t15_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_relat_1 (k5_relat_1 B (k2_finseq_1 A))) &  ((v1_funct_1 (k5_relat_1 B (k2_finseq_1 A))) & (v1_finseq_1 (k5_relat_1 B (k2_finseq_1 A)))) ) ) ) ) ) ).
tt(t15_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden A (k4_finseq_1 B)) => (r2_hidden A (k4_finseq_1 (k7_finseq_1 B C)))) ) ) ) ) ) ) ).
tt(t15_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_subset_1 k5_numbers (k2_finseq_1 (k1_nat_1 A 1)) (k2_finseq_1 A)) = (k1_tarski (k1_nat_1 A 1))) ) ) ).
tt(t15_finseq_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 C)))  =>  ((k7_partfun1 B C A) = (k1_funct_1 C A)) ) ) ) ) ) ) ).
tt(t15_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k7_partfun1 A (k8_finseq_1 A (k12_finseq_1 A B) C) 1) = B) ) ) ) ) ) ) ).
tt(t15_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k6_subset_1 (k10_xtuple_0 A) (k10_xtuple_0 B))) =>  ((k5_finseq_4 (k7_finseq_1 B A) C) = (k7_finseq_1 B (k5_finseq_4 A C))) ) ) ) ) ) ) ).
tt(t15_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_finseq_7 A (k3_finseq_4 A B C D) 1 E) = (k3_finseq_4 A E C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k3_finseq_1 (k5_finseq_8 A B C)) = (k6_xcmplx_0 (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C)) (k3_finseq_1 (k4_finseq_8 A B C))))  &  ( ((k3_finseq_1 (k5_finseq_8 A B C)) = (k7_nat_d (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C)) (k3_finseq_1 (k4_finseq_8 A B C))))  &  ((k3_finseq_1 (k5_finseq_8 A B C)) = (k2_nat_1 (k3_finseq_1 B) (k7_nat_d (k3_finseq_1 C) (k3_finseq_1 (k4_finseq_8 A B C))))) ) ) ) ) ) ) ) ) ).
tt(t15_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  (! [G:$i] :  ((m2_finseq_1 G C) => (r2_relset_1 k5_numbers B (k2_finseqop C A B E (k8_finseq_1 C F G) D) (k8_finseq_1 B (k2_finseqop C A B E F D) (k2_finseqop C A B E G D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_finset_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~ (v1_finset_1 A))  & (r2_hidden A (k2_zfmisc_1 B A))) ) ) ) ).
tt(t15_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 E A) =>  ((k1_finsop_1 A (k3_finseq_4 A B C D) E) = (k1_finsop_1 A (k3_finseq_4 A C B D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_finsub_1,ax, ((k5_finsub_1 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t15_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_fintopo2 A B C) = k8_margrel1)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t15_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_fintopo3 A B 1) = (k9_fin_topo A B)) ) ) ) ) ).
tt(t15_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r2_fintopo4 A B E C) & (r1_xxreal_0 C D))  => (r2_fintopo4 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  => (v1_fin_topo (k5_fintopo5 A B))) ) ) ) ).
tt(t15_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_fintopo6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = E)  &  ( (D = F)  &  ((r1_tarski (k4_subset_1 (u1_struct_0 A) C D) (k2_struct_0 B)) & (r1_fintopo4 A C D)) ) )  => (r1_fintopo4 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_fin_topo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 (u1_struct_0 A))) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k6_numbers))  &  ( ((k7_partfun1 (k9_setfam_1 (u1_struct_0 A)) D 1) = (k6_domain_1 (u1_struct_0 A) C))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  (~  ((k7_partfun1 (k9_setfam_1 (u1_struct_0 A)) D (k2_nat_1 E 1)) = (k9_subset_1 (u1_struct_0 A) (k9_fin_topo A (k7_partfun1 (k9_setfam_1 (u1_struct_0 A)) D E)) B)) ) ) ) ) ) )  & (r1_tarski B (k7_partfun1 (k9_setfam_1 (u1_struct_0 A)) D (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r2_hidden (k2_flang_1 A) (k6_flang_1 A B C)) <=>  ((r2_hidden (k2_flang_1 A) B) & (r2_hidden (k2_flang_1 A) C)) ) ) ) ) ) ) ).
tt(t15_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (~  ((r2_hidden A C) &  ( (~  (A = (k2_flang_1 B)) )  &  ((k8_flang_1 B C) = (k4_flang_1 B (k2_flang_1 B))) ) ) ) ) ) ) ) ).
tt(t15_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_flang_3 A B C) = (k4_flang_1 A (k2_flang_1 A)))  <=>  ( (B = (k4_flang_1 A (k2_flang_1 A)))  |  ( (C = k6_numbers)  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t15_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_2 B A (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_finseq_2 C A (k3_finseq_2 A)) =>  ((k1_funct_1 (k8_fomodel0 A) (k10_finseq_1 B C)) = (k1_monoid_0 A B C)) ) ) ) ) ) ) ).
tt(t15_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  (~  ( (~  (B = (k8_fomodel1 A)) )  &  ( (~  (B = (k18_fomodel1 A)) )  &  (~ (r2_hidden B (k37_fomodel1 A))) ) ) ) ) ) ) ) ).
tt(t15_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  =>  (! [D:$i] :  ( ((v15_fomodel1 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) D) = (k34_fomodel2 A))  =>  ( ((k14_fomodel2 A B C D) = 1)  <=>  ((k1_funct_1 (k10_fomodel2 A B C) (k1_funct_1 (k34_fomodel1 A D) 1)) = (k1_funct_1 (k10_fomodel2 A B C) (k1_funct_1 (k34_fomodel1 A D) 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( ((v4_fomodel1 D C) & (m1_subset_1 D (k1_fomodel1 C)))  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [F:$i] :  ( ((v3_fomodel3 F C A E) & (m2_subset_1 F (k9_funct_2 (k37_fomodel1 C) (k3_rfunct_3 (k3_finseq_2 A) (k2_xboole_0 A k6_margrel1))) (k16_fomodel2 C A)))  =>  ((k37_fomodel2 C (k8_eqrel_1 A E) (k23_fomodel3 C A E F) D (k3_funct_2 A (k8_eqrel_1 A E) (k17_fomodel3 A E) B)) = (k22_fomodel3 C A E (k37_fomodel2 C A F D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((v14_fomodel4 D B C) => (v14_fomodel4 A B C)) ) ) ) ) ) ) ) ).
tt(t15_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_valued_0 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_frechet A B D) => (r1_frechet A C D)) ) ) ) ) ) ) ) ) ).
tt(t15_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (B = k1_xboole_0) )  =>  ((k10_xtuple_0 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B C))) = (k2_xboole_0 (k6_subset_1 A B) (k1_tarski C))) ) ) ) ) ).
tt(t15_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (~  ((k2_msafree2 (k4_fscirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t15_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  ( ((r4_fsm_1 A B C D) & (r4_fsm_1 A B D E))  => (r4_fsm_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( ((v3_fsm_2 B A) & (v1_fsm_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  (E = (u2_fsm_1 A B)) )  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E C)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_fsm_3 D A C))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  ((r2_hidden B (k3_fsm_3 A C D E)) <=>  (~ (r1_xboole_0 E (k3_rewrite3 A C D B (u1_fsm_3 A C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k24_gfacirc1 A B C) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k21_gfacirc1 A B C) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k4_gfacirc1) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k36_gfacirc1 (k24_gfacirc1 A B C) E D) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k24_gfacirc1 A B C) E) k3_twoscomp) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k3_gfacirc1) (k3_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp) (k3_msafree2 (k7_ftacell1 A B C D E))) & (r2_hidden (k33_gfacirc1 (k24_gfacirc1 A B C) E D) (k3_msafree2 (k7_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  ((k8_relat_1 (k2_funcop_1 A B) (k1_tarski B)) = A) ) ) ).
tt(t15_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k6_funcsdom A) B (k1_funcsdom A k1_numbers (k5_funcsdom A) C D)) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k6_funcsdom A) B C) (k1_funcsdom A k1_numbers (k6_funcsdom A) B D)))) ) ) ) ) ) ) ).
tt(t15_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 (k3_relat_1 B A)) = (k9_xtuple_0 B))  => (r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A))) ) ) ) ) ).
tt(t15_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden C A) =>  ( (B = k1_xboole_0)  |  ((k1_funct_1 (k3_relat_1 D E) C) = (k1_funct_1 E (k1_funct_1 D C))) ) ) ) ) ) ) ) ) ) ).
tt(t15_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((r1_tarski B (k1_zfmisc_1 A)) =>  ((k7_relat_1 D (k3_tarski B)) = (k3_tarski (k7_relat_1 (k1_funct_3 D) B))) ) ) ) ) ) ) ) ).
tt(t15_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_partfun1 B C) & (r2_hidden A (k9_xtuple_0 B)))  =>  ((k1_funct_1 (k1_funct_4 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t15_funct_5,ax, (! [A:$i] :  ( ( ((k9_xtuple_0 A) = k1_xboole_0)  |  ((k10_xtuple_0 A) = k1_xboole_0) )  =>  (! [B:$i] :  (! [C:$i] :  (~ (r2_hidden (k4_tarski B C) A)) ) ) ) ) ).
tt(t15_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k4_partfun1 A (k4_partfun1 B C))) =>  ((r2_hidden (k2_funct_5 D) (k4_partfun1 (k2_zfmisc_1 A B) C)) & (r2_hidden (k4_funct_5 D) (k4_partfun1 (k2_zfmisc_1 B A) C))) ) ) ) ) ) ) ).
tt(t15_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k1_funct_4 (k1_funct_4 A (k7_funcop_1 B C)) (k7_funcop_1 B D)) = (k1_funct_4 A (k7_funcop_1 B D))) ) ) ) ) ) ).
tt(t15_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_8 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 B k1_numbers k1_numbers C) => (r1_funct_8 B k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A))) ) ) ) ) ) ) ).
tt(t15_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 C A) & (v1_funct_9 C B))  =>  ( ((k2_xcmplx_0 A B) = k6_numbers)  | (v1_funct_9 C (k2_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t15_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (k2_zfmisc_1 B B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B))))) )  =>  ((r6_pboole (k2_zfmisc_1 A A) D (k7_funcop_1 (k2_zfmisc_1 A A) (k4_tarski C C))) =>  ((v1_functor0 D A B) & (v2_functor0 D A B)) ) ) ) ) ) ) ) ) ).
tt(t15_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  ((v18_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v2_funct_2 (k5_functor0 A B C D E) (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) )  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G C D) & (m2_functor0 G C D))  =>  (! [H:$i] :  ( ((v15_functor0 H C D) & (m2_functor0 H C D))  =>  (! [I:$i] :  ((m1_functor2 I C D G H) =>  ((r1_functor2 C D G H) => (r8_pboole (u1_struct_0 A) (k6_functor3 A B D (k1_functor3 B C D F G) (k1_functor3 B C D F H) E (k6_functor3 B C D G H F I)) (k6_functor3 A C D G H (k1_functor3 A B C E F) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 B (k5_fuzzy_1 A))) ) ) ) ).
tt(t15_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A B (k1_fuzzy_1 A C D)) (k2_fuzzy_1 A (k1_fuzzy_2 A B C) (k1_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t15_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  => (r1_fuzzy_1 (k4_fuzzy_4 A B C D (k1_fuzzy_1 (k2_zfmisc_1 B C) E F)) (k1_fuzzy_1 (k2_zfmisc_1 A C) (k4_fuzzy_4 A B C D E) (k4_fuzzy_4 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_fvaluat1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_group_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_realset2 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k3_fvaluat1 C D (k2_xcmplx_0 A B)) = (k8_group_1 C (k3_fvaluat1 C D A) (k3_fvaluat1 C D B))) ) ) ) ) ) ) ) ) ).
tt(t15_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_algstr_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_finseqop (u1_struct_0 A) (u1_algstr_0 A)) (k5_vectsp_1 A))) ) ).
tt(t15_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (~ (v1_xboole_0 (k9_gate_1 A B C)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) ) )  & (v1_xboole_0 (k9_gate_1 A B C))) ) ) ) ) ) ).
tt(t15_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_gcd_1 A (k8_group_1 A B C) (k8_group_1 A B D)) =>  ( (B = (k4_struct_0 A))  | (r2_gcd_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((k9_genealg1 D E F k6_numbers A B) = (k8_genealg1 D F E A B))  &  ( ((k9_genealg1 D E F C k6_numbers B) = (k8_genealg1 D F E C B))  &  ((k9_genealg1 D E F C A k6_numbers) = (k8_genealg1 D F E C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) => (r2_geomtrap A B C D D E E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k7_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t15_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  =>  ( ( ((k1_funct_1 C k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 D k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_msualg_1 G))  =>  (! [H:$i] :  ( ((v4_msualg_1 H G) & (l3_msualg_1 H G))  =>  (! [I:$i] :  ( ( (G = (k1_funct_1 C F))  &  ( (H = (k1_funct_1 D F))  &  (I = (k1_funct_1 E F)) ) )  =>  ( ((k1_funct_1 C (k1_nat_1 F 1)) = (k2_circcomb G (k25_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ( ((k1_funct_1 D (k1_nat_1 F 1)) = (k3_circcomb G (k25_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I) H (k26_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ((k1_funct_1 E (k1_nat_1 F 1)) = (k21_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((k5_gfacirc2 F A B) = (k1_funct_1 C F))  &  ( ((k6_gfacirc2 F A B) = (k1_funct_1 D F))  &  ((k7_gfacirc2 F A B) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ((r1_glib_000 A C D B) &  ((r1_glib_000 A E F B) &  ( (~  ( (C = E)  &  (D = F) ) )  &  (~  ( (C = F)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) =>  ( ((k3_glib_001 A (k2_glib_001 A C D B)) = C)  &  ( ((k4_glib_001 A (k2_glib_001 A C D B)) = D)  & (r1_glib_001 A C D (k2_glib_001 A C D B))) ) ) ) ) ) ) ) ).
tt(t15_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  ((k1_glib_002 A B) = (k6_glib_000 A)) ) )  => (v1_glib_002 A)) ) ) ).
tt(t15_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k8_glib_003 A (k6_glib_001 A B)) = (k3_finseq_5 (k8_glib_003 A B))) ) ) ) ) ).
tt(t15_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))) =>  ( ( ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) = (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B))))  =>  ((k6_glib_004 A B) = k1_xboole_0) )  &  ( ( ((k6_glib_004 A B) = k1_xboole_0)  =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) = (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B)))) )  &  ( (~  ( ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) = (k2_nat_1 (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B))) 1))  &  ((k6_glib_004 A B) = k1_xboole_0) ) )  &  ( (~  ((k6_glib_004 A B) = k1_xboole_0) )  =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) = (k2_nat_1 (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B))) 1)) ) ) ) ) ) ) ) ) ).
tt(t15_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  ( ((r1_glib_001 A C D E) & (r5_glib_005 A B E))  =>  ( (C = D)  |  ((k2_xcmplx_0 (k1_glib_005 A B C D) (k9_glib_005 A B E)) = (k1_glib_005 A (k10_glib_005 A B E) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 E))) &  ( ((k1_matrix_1 E) = (k2_nat_1 B 1))  &  ((r2_hidden C (k4_finseq_1 E)) & (r1_xxreal_0 1 D)) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 A D) |  ( ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 E A) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C D))  & (r2_hidden D (k2_finseq_1 (k1_matrix_1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_goboard2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 (k1_seq_1 (k1_goboard1 B) A) (k1_seq_1 (k1_goboard1 B) C))) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) 1)))) ) ) ) ) ).
tt(t15_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 C) &  ((v4_goboard1 C) & (r1_xxreal_0 1 B)) )  =>  ((v3_relat_1 C) |  ((r1_xxreal_0 (k1_matrix_1 C) A) |  ((r1_xxreal_0 (k3_finseq_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B (k2_nat_1 A 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) (k2_nat_1 A 1))) (k2_goboard5 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t15_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k2_goboard5 A k6_numbers)) = (a_1_2_goboard6 A)) ) ) ).
tt(t15_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(t15_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_tops_1 (k15_euclid 2) (k5_goboard5 A B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t15_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (a_1_5_gobrd11 B))  => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ).
tt(t15_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A (k2_nat_1 B 1)) (k16_matrix_1 F)) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 F)) &  ((r1_xxreal_0 1 D) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 E) B) |  ((r1_xxreal_0 (k1_matrix_1 F) D) | (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C (k2_nat_1 D 1))) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A (k2_nat_1 B 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_goboard9 A)) (k2_goboard9 A)) = (u1_struct_0 (k15_euclid 2))) ) ) ).
tt(t15_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [C:$i] :  ((m1_henmodel C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ( ((k7_cqc_sim1 A D) = 1)  &  ((v1_goedelcp B A) & (v2_goedelcp B A)) )  =>  ((r1_valuat_1 A (k1_henmodel A) D C (k3_henmodel A)) <=> (r1_henmodel A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_graph_1 B) & (m3_graph_1 B A))  =>  (! [C:$i] :  ( ((v1_graph_1 C) & (m3_graph_1 C A))  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 C))  &  ((u4_struct_0 B) = (u4_struct_0 C)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t15_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k1_funct_1 (k3_graph_2 B A) (k2_nat_1 (k3_finseq_1 B) C)) = (k1_funct_1 A (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ).
tt(t15_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((r1_graph_2 A C B) & (r2_hidden D (k10_xtuple_0 B)))  =>  ((r2_hidden (k1_funct_1 (u2_graph_1 A) D) (k10_xtuple_0 C)) & (r2_hidden (k1_funct_1 (u1_graph_1 A) D) (k10_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(t15_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v7_graph_1 E A) & (m2_graph_1 E A))  =>  (! [F:$i] :  ( ((v7_graph_1 F A) & (m2_graph_1 F A))  =>  (! [G:$i] :  ( ((v7_graph_1 G A) & (m2_graph_1 G A))  =>  ( ((r3_graph_4 A B E) &  ((r3_graph_4 A C F) &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 C 1))  &  ( (G = (k8_finseq_1 (u4_struct_0 A) E F))  &  (D = (k4_graph_2 (u1_struct_0 A) B C)) ) ) ) )  => (r3_graph_4 A D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 B) = 1)  =>  ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) ) ) ) ) ) ) ).
tt(t15_graphsp,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_graph_1 C) &  ((v6_graph_1 C) & (l1_graph_1 C)) ) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m2_graph_1 D C))  =>  (! [E:$i] :  ( ((v7_graph_1 E C) & (m2_graph_1 E C))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u4_struct_0 C) k8_graph_5) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 C) k8_graph_5)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  ( ((r2_hidden A (u4_struct_0 C)) &  ((r8_graph_5 C G H D B F) &  ( (E = (k7_finseq_1 D (k9_finseq_1 A)))  &  ((r1_graph_4 C H I A) &  ((r2_hidden G B) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 C)) =>  ((r2_hidden J B) =>  (! [K:$i] :  (~  ((r2_hidden K (u4_struct_0 C)) & (r1_graph_4 C J I K)) ) ) ) ) ) ) ) ) ) )  =>  ( (G = I)  | (r8_graph_5 C G I E (k2_xboole_0 B (k1_tarski H)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_grcat_1,ax, (! [A:$i] :  ( ((v1_grcat_1 A) &  ((v2_grcat_1 A) & (l1_grcat_1 A)) )  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  &  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_grcat_1 A B C) &  ( (A = (g1_grcat_1 B C D))  & (v13_vectsp_1 D B C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_gr_cy_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_gr_cy_1)) =>  ((k2_group_1 k2_gr_cy_1 A) = (k19_binop_2 A)) ) ) ).
tt(t15_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) )  => (r2_group_6 (k4_gr_cy_1 (k7_group_1 A)) A)) ) ).
tt(t15_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  (? [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v2_gr_cy_3 B)) )  &  (? [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C (k3_int_7 A)))  &  (? [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D (k3_int_7 A)))  &  (? [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E (k3_int_7 A)))  &  (? [F:$i] :  ( ((v15_algstr_0 F) & (m1_group_2 F (k3_int_7 A)))  &  ( ((k7_group_1 C) = 1)  &  ( ((k7_group_1 D) = 2)  &  ( ((k7_group_1 E) = B)  &  ( ((k7_group_1 F) = (k4_nat_1 2 B))  &  (! [G:$i] :  ( ((v15_algstr_0 G) & (m1_group_2 G (k3_int_7 A)))  =>  (~  ( (~ (r1_group_2 (k3_int_7 A) G C))  &  ( (~ (r1_group_2 (k3_int_7 A) G D))  &  ( (~ (r1_group_2 (k3_int_7 A) G E))  &  (~ (r1_group_2 (k3_int_7 A) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 B)) &  (C = (k2_xboole_0 D B)) )  =>  ((k1_funct_1 C A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ) ).
tt(t15_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((v1_group_3 B A) & (m1_group_2 B A))  <=> (m1_group_6 (k1_grnilp_1 A B (k7_group_2 A)) A B)) ) ) ) ) ).
tt(t15_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((v8_rewrite1 (k3_polyred A B C D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r1_rewrite1 (k3_polyred A B C D) E (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r8_pboole (k15_pre_poly A) (k5_polynom7 A B (k4_polynom1 A B C D) E) (k4_polynom1 A B (k5_polynom7 A B C E) (k5_polynom7 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_polynom1 A C D (k6_termord A B C D)) (k5_termord A B C D))) ) ) ) ) ) ) ) ).
tt(t15_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v7_ordinal1 D) & (v1_int_2 D))  =>  (~  ( (A = (k3_xcmplx_0 (k1_newton D C) B))  &  ( (~ (r1_nat_d D B))  &  ((k4_nat_d (k6_newton (k1_newton D C) A) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k13_group_2 A C D) B))  => (r2_hidden D (k2_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t15_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) ).
tt(t15_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_group_2 A (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) D) (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_group_2 A B D) (k2_group_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t15_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v8_struct_0 A) => (v1_finset_1 (k1_group_3 A))) ) ) ).
tt(t15_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ( (C = (k1_partfun1 (k4_finseq_1 B) (k4_finseq_1 B) k5_numbers (u1_struct_0 A) D B))  =>  ((k3_group_4 A B) = (k3_group_4 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ((k4_group_4 A D (k1_group_5 A C B)) = (k1_group_5 A (k4_group_4 A D C) B)) ) ) ) ) ) ) ) ) ).
tt(t15_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ((r2_hidden B (k15_group_2 A C)) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t15_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v1_relat_1 (k9_finseq_1 A)) &  ((v4_relat_1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_funct_1 (k9_finseq_1 A)) &  ((v1_partfun1 (k9_finseq_1 A) (k1_tarski 1)) &  ((v1_group_7 (k9_finseq_1 A)) &  ((v2_group_7 (k9_finseq_1 A) (k1_tarski 1)) &  ((v3_group_7 (k9_finseq_1 A) (k1_tarski 1)) & (v4_group_7 (k9_finseq_1 A) (k1_tarski 1))) ) ) ) ) ) ) ) ) ).
tt(t15_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D (k5_group_2 A C (k4_group_2 A B E))) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (D = (k6_algstr_0 A (k6_algstr_0 A B F) C))  & (r2_hidden F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((k4_group_9 A B) = (k4_group_9 A C)) ) ) ) ) ) ).
tt(t15_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((v2_group_10 C A) & (r1_struct_0 C D))  => (v1_groupp_1 D A B)) ) ) ) ) ) ) ) ) ).
tt(t15_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ( ((v15_algstr_0 D) &  ((v1_group_3 D E) & (m1_group_6 D A E)) )  =>  ((v15_algstr_0 (k2_grsolv_1 A B C D)) &  ((v1_group_3 (k2_grsolv_1 A B C D) (k2_grsolv_1 A B C E)) & (m1_group_6 (k2_grsolv_1 A B C D) B (k2_grsolv_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k3_hahnban1 A B C (k7_hahnban1 A B)) C)) ) ) ) ) ) ).
tt(t15_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_struct_0 C B) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) G (k1_rlvect_1 A B H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  ((v1_hallmar1 B A) => (v2_relat_1 B)) ) ) ) ) ).
tt(t15_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A B) C) (k7_real_1 (k4_metric_1 A C D) (k1_funct_1 (k6_weierstr A B) D)))) ) ) ) ) ) ) ) ).
tt(t15_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) => (r1_tarski B (k7_glib_001 A B C))) ) ) ) ) ) ).
tt(t15_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) B (k12_finseq_1 (k3_cqc_lang A) (k5_cqc_lang A))))) ) ) ) ).
tt(t15_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k7_real_1 (k3_complex1 A) (k3_complex1 (k2_complfld A))) = (k8_real_1 2 (k3_complex1 A))) ) ) ).
tt(t15_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ((r1_collsp A B D F) &  ( (~  (B = E) )  &  ( (~  (B = F) )  & (r1_collsp A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_heyting1,ax, (! [A:$i] :  ((m2_subset_1 A (k2_zfmisc_1 (k5_finsub_1 k1_xboole_0) (k5_finsub_1 k1_xboole_0)) (k7_normform k1_xboole_0)) =>  (A = (k4_tarski k1_xboole_0 k1_xboole_0)) ) ) ).
tt(t15_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  (~  ((r2_hidden E (k3_heyting2 A B C D)) &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  (~  ( (E = (k3_tarski (a_5_1_heyting2 A B C D F)))  &  ((k1_relset_1 C F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xboole_0 (k3_heyting3 A B) (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 A) 3) B)))) ) ) ) ).
tt(t15_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 C A B) & (r1_taylor_1 D A B))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) A) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C B) A) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 D B) A)))) ) ) ) ) ) ) ) ) ).
tt(t15_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_polynom3 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (B = C)  =>  ((k4_algstr_0 (k14_polynom3 A) B) = (k5_vfunct_1 k5_numbers A C)) ) ) ) ) ) ) ) ).
tt(t15_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r2_hidden A k6_hilbert1) => (r2_hidden (k3_hilbert1 B A) k6_hilbert1)) ) ) ) ) ).
tt(t15_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k4_hilbert1 A B)) (k3_finseq_1 A)))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k4_hilbert1 A B)) (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t15_hilbert3,ax, ((v1_funct_1 (k5_funct_4 k5_numbers k6_numbers 1 1 k6_numbers)) &  ((v1_funct_2 (k5_funct_4 k5_numbers k6_numbers 1 1 k6_numbers) 2 2) &  ((v3_funct_2 (k5_funct_4 k5_numbers k6_numbers 1 1 k6_numbers) 2 2) & (m1_subset_1 (k5_funct_4 k5_numbers k6_numbers 1 1 k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 2 2)))) ) ) ).
tt(t15_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k3_polynom5 A B C)) (k3_polynom5 A B (k4_algstr_0 A C)))) ) ) ) ) ) ).
tt(t15_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_idea_1 C (k4_idea_1 C A B))) ) ) ) ) ) ).
tt(t15_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t15_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_collsp A B C F) & (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k3_incproj A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) &  ((r1_incsp_1 (k3_incproj A) D B) & (r1_incsp_1 (k3_incproj A) D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) => (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B B C) A)) ) ) ) ) ) ).
tt(t15_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((m5_index_1 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) & (m5_index_1 (k6_index_1 (u1_struct_0 A) (u4_struct_0 A) (k7_funcop_1 (u1_struct_0 A) B) (k7_funcop_1 (u4_struct_0 A) (k10_cat_1 B))) (u1_struct_0 A) (u4_struct_0 A) (u2_graph_1 A) (u1_graph_1 A) (k1_oppcat_1 (u4_struct_0 A) (u4_struct_0 A) (u4_struct_0 A) (u1_cat_1 A)) (k7_isocat_1 A))) ) ) ) ) ).
tt(t15_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  => (m1_instalg1 A A)) ) ).
tt(t15_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r2_int_1 A B C) & (r2_int_1 B D C))  => (r2_int_1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t15_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) <=> (r1_int_1 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t15_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((r1_int_2 A B) &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 A D) C) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~ (r1_xxreal_0 B 2))  &  ( ((k3_int_2 A B) = 1)  &  ((r1_int_5 A B) &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( ((k6_int_1 (k6_xcmplx_0 (k1_pepin C) A) B) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 (k1_pepin D) A) B) = k6_numbers)  &  (~ (r2_int_1 C D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_2 A B) =>  ((k2_int_2 A B) = (k1_int_2 (k3_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t15_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k10_newton) &  ((v1_funct_1 B) &  ((v1_partfun1 B k10_newton) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((v1_int_7 A) &  ((v1_int_7 B) &  ((k8_nat_3 k10_newton A) = (k8_nat_3 k10_newton B)) ) )  => (r8_pboole k10_newton A B)) ) ) ) ) ).
tt(t15_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( ((k1_relset_1 k1_numbers A) = (k2_limfunc1 k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 k6_numbers)) => (r3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers A (k6_integr10 C)) k6_numbers)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 k6_numbers)) => (r3_integr10 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers A B) (k6_integr10 C)) k6_numbers)) ) )  & (r2_relset_1 k1_numbers k1_numbers (k7_integr10 (k26_valued_1 k1_numbers k1_numbers A B)) (k26_valued_1 k1_numbers k1_numbers (k7_integr10 A) B))) ) ) ) ) ) ).
tt(t15_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k8_real_1 2 k32_sin_cos)))  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)) = k32_sin_cos) ) ) ) ).
tt(t15_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B G) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1))) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k12_binop_2 H A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E H) (k19_binop_2 1)))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 E H)))  &  ((k1_seq_1 C H) = 1) ) ) ) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2))) &  ( (G = (k1_relset_1 k1_numbers F))  & (r2_relset_1 k1_numbers k1_numbers F (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos9))) ) ) ) )  =>  ( (A = k6_numbers)  |  ((k2_integra5 B F) = (k10_binop_2 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k12_binop_2 A 2))) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k12_binop_2 A 2))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k1_partfun2 k1_numbers C)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t15_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k1_seq_1 k16_sin_cos (k10_real_1 1 D)) (k8_real_1 (k5_square_1 D) (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t15_integr15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_euclid B)))))  =>  ((r2_relset_1 A k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers (k7_integr15 B A D E) (k1_pdiff_1 C B)) (k3_valued_1 A k1_numbers k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers D (k1_pdiff_1 C B)) (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers E (k1_pdiff_1 C B)))) & (r2_relset_1 A k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers (k8_integr15 B A D E) (k1_pdiff_1 C B)) (k47_valued_1 A k1_numbers k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers D (k1_pdiff_1 C B)) (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers E (k1_pdiff_1 C B))))) ) ) ) ) ) ) ) ) ) ).
tt(t15_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ((v1_comseq_2 B) =>  ((v1_integr16 B A) <=>  (? [C:$i] :  ((m1_subset_1 C k2_numbers) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_integra1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [E:$i] :  ((m2_integr16 E A B D) =>  ( ((v2_comseq_2 (k2_integra3 A D)) &  ((k2_seq_2 (k2_integra3 A D)) = k6_numbers) )  =>  ((v2_comseq_2 (k5_integr16 A B D E)) &  ((k3_comseq_2 (k5_integr16 A B D E)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_integr18 A B C) &  ((r1_integr18 A B D) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) & (r1_tarski B (k1_relset_1 k1_numbers D))) ) )  =>  ((r1_integr18 A B (k2_vfunct_1 k1_numbers A C D)) &  ((k5_integr18 A B (k2_vfunct_1 k1_numbers A C D)) = (k5_algstr_0 A (k5_integr18 A B C) (k5_integr18 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v3_integr15 C A) & (r1_tarski B (k1_relset_1 k1_numbers C)))  => (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) C B) A)) ) ) ) ) ) ) ).
tt(t15_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (v5_xxreal_2 (k1_rvsum_1 B))) ) ) ) ) ).
tt(t15_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v3_xxreal_2 B) & (r1_xxreal_0 k6_numbers A))  =>  ((k5_seq_4 (k1_integra2 B A)) = (k8_real_1 A (k5_seq_4 B))) ) ) ) ) ) ).
tt(t15_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  (! [E:$i] :  ((m1_integra1 E D) =>  (! [F:$i] :  ((m1_integra1 F D) =>  (~  ((r2_hidden B (k4_finseq_1 E)) &  ((r2_hidden C (k4_finseq_1 E)) &  ((r1_xxreal_0 B C) &  ((r1_integra1 E F) &  ( (~ (r1_xxreal_0 (k1_seq_1 (k3_finseq_6 k1_numbers F (k13_integra1 D E F B) (k13_integra1 D E F C)) 1) A))  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v2_measure5 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers))) )  =>  (! [H:$i] :  ((m1_integra1 H G) =>  (! [I:$i] :  ((m1_integra1 I G) =>  (~  ( (A = (k5_seq_4 G))  &  ( ((k4_seq_4 G) = (k1_seq_1 I (k3_finseq_1 I)))  &  ( ((k4_seq_4 G) = (k1_seq_1 H (k3_finseq_1 H)))  &  ((r1_integra1 H I) &  ( (H = (k3_finseq_6 k1_numbers E B C))  &  (I = (k3_finseq_6 k1_numbers F (k13_integra1 D E F B) (k13_integra1 D E F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (v2_seq_2 (k2_partfun1 A k1_numbers (k18_rfunct_3 A C) B))) ) ) ) ) ).
tt(t15_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) & (r1_tarski A (k1_relset_1 k1_numbers B)))  =>  ( ((k5_seq_4 (k1_rvsum_1 (k2_partfun1 k1_numbers k1_numbers B A))) = (k1_seq_1 B (k5_seq_4 A)))  &  ((k4_seq_4 (k1_rvsum_1 (k2_partfun1 k1_numbers k1_numbers B A))) = (k1_seq_1 B (k4_seq_4 A))) ) ) ) ) ) ) ).
tt(t15_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_integra1 A) k6_numbers))  &  (! [C:$i] :  ((m1_integra1 C A) =>  (~  ( ((k3_finseq_1 C) = B)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_seq_1 C D) = (k7_real_1 (k5_seq_4 A) (k8_real_1 (k10_real_1 (k3_integra1 A) B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( (! [F:$i] :  (~  ((r2_hidden F A) &  ((k1_seq_1 B F) = k6_numbers) ) ) )  &  ((r1_integra7 A C D) & (r1_integra7 A B E)) )  => (r1_integra7 A (k3_rfunct_1 k1_numbers k1_numbers C B) (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D B) (k20_valued_1 k1_numbers k1_numbers k1_numbers C E)) (k20_valued_1 k1_numbers k1_numbers k1_numbers B B)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_integra8,ax, ((k6_sin_cos6 (k10_real_1 (k7_square_1 2) 2)) = (k10_real_1 k32_sin_cos 4)) ).
tt(t15_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) =>  ((k2_integra5 A (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k19_sin_cos))) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t15_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (B = (k2_interva1 A (k5_interva1 A B) (k6_interva1 A B))) ) ) ) ) ).
tt(t15_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v8_intpro_1 A) <=>  ((k7_intpro_1 A) = A) ) ) ) ).
tt(t15_irrat_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 (k1_valued_0 k1_numbers A 1)) =>  ((v1_series_1 A) &  ((k4_series_1 A) = (k2_xcmplx_0 (k1_seq_1 A k6_numbers) (k4_series_1 (k1_valued_0 k1_numbers A 1)))) ) ) ) ) ).
tt(t15_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( ((r1_isocat_1 A B) & (r1_isocat_1 B C))  => (r1_isocat_1 A C)) ) ) ) ) ) ) ).
tt(t15_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_cat_1 G A E F) =>  ((r2_nattra_1 B C (k12_cat_2 A B C D E) (k12_cat_2 A B C D F)) & (m2_nattra_1 (k1_partfun1 (u1_struct_0 B) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) (k7_isocat_1 B) (k3_isocat_2 A B C D G)) B C (k12_cat_2 A B C D E) (k12_cat_2 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 (k1_tops_1 A (k2_pre_topc A B)) A) & (v5_tops_1 (k2_pre_topc A (k1_tops_1 A B)) A)) ) ) ) ) ).
tt(t15_jct_misc,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_rcomp_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A))) ) ).
tt(t15_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jgraph_1 A 2) & (v1_graph_4 (k4_jgraph_1 (u1_struct_0 (k15_euclid 2)) A) (k1_jgraph_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((k1_funct_1 A 1) = (k1_funct_1 A (k3_finseq_1 A)))  | (v3_topreal1 A)) ) ) ) ).
tt(t15_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( (B = a_0_0_jgraph_2)  => (r1_tarski (k2_relset_1 (k8_struct_0 (k15_euclid 2)) (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 B)) (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)))) ) ) ) ) ).
tt(t15_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_0_jgraph_3) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t15_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (k10_metric_1 (k14_euclid 2) A B))  => (v2_compts_1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t15_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_5_jgraph_5)  &  ( (D = a_0_1_jgraph_5)  &  ( (E = a_0_2_jgraph_5)  &  ( (F = a_0_3_jgraph_5)  &  ( (G = a_0_4_jgraph_5)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) F) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) G) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jgraph_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_1_jgraph_6)  &  ( (D = a_0_2_jgraph_6)  &  ( (E = a_0_3_jgraph_6)  &  ( (F = a_0_4_jgraph_6)  &  ( (G = a_0_5_jgraph_6)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) G) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = E)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid C) H) &  ((r1_xxreal_0 E (k17_euclid D)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan10,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_tarski A (k6_setfam_1 (u1_struct_0 (k15_euclid 2)) (k4_jordan10 A)))) ) ).
tt(t15_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_tarski A (k1_jordan2c 2 B)) & (r1_tarski B (k1_jordan2c 2 A))) ) ) ) ) ) ).
tt(t15_jordan12,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r2_hidden A (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C))) &  ((r2_hidden B (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C))) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C)) D) &  ((r2_hidden A D) & (r2_hidden B D)) ) ) ) ) ) )  <=>  ( ((r2_hidden A (k2_goboard9 C)) & (r2_hidden B (k3_goboard9 C)))  |  ((r2_hidden A (k3_goboard9 C)) & (r2_hidden B (k2_goboard9 C))) ) ) ) ) ) ) ).
tt(t15_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski (k3_goboard9 (k1_jordan13 A B)) (k1_jordan2c 2 A))) ) ) ) ) ).
tt(t15_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) B) &  ((r1_tarski B A) &  ( (~  (B = (k9_jordan6 A)) )  &  (~  (B = (k8_jordan6 A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A D B C E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A D B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan18,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) C D B) &  ((r1_tarski B A) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) C D E) &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B E) = A)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B E) = (k2_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan1a,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_xboole_0 B C) &  ((r1_tarski B (k6_jordan6 A)) & (r1_tarski C (k6_jordan6 A))) )  => (r1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B) (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 C))) ) ) ) ) ) ) ).
tt(t15_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_2_jordan1 A))  => (v1_convex1 B (k15_euclid 2))) ) ) ) ) ).
tt(t15_jordan1b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~  ((r1_xxreal_0 3 (k3_finseq_1 A)) & (r1_xxreal_0 (k3_finseq_1 A) (k1_jordan1a A))) ) ) ) ).
tt(t15_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k18_euclid C) (k9_pscomp_1 A)) (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A))) (k13_newton 2 B)) 2)))  => (r1_xxreal_0 (k7_real_1 (k9_pscomp_1 A) (k8_real_1 (k10_real_1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k13_newton 2 B)) (k5_real_1 D 2))) (k18_euclid C))) ) ) ) ) ) ) ) ) ).
tt(t15_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k24_pscomp_1 B) (k2_gobrd13 (k1_jordan9 B A) (k1_jordan8 B A) C))) ) ) ) ) ) ) ) ).
tt(t15_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 3 (k3_finseq_1 (k1_jordan1e A B))) & (r1_xxreal_0 3 (k3_finseq_1 (k2_jordan1e A B)))) ) ) ) ) ).
tt(t15_jordan1g,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (~  ( ( ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k23_pscomp_1 (k3_topreal1 2 A))) ) )  |  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) )  &  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ).
tt(t15_jordan1h,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v2_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  => (r1_xxreal_0 (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A))) (k3_finseq_1 A))) ) ).
tt(t15_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1) D))  & (r1_xxreal_0 D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k20_pscomp_1 B) A))  =>  ((k20_pscomp_1 A) = (k20_pscomp_1 B)) ) ) ) ) ) ).
tt(t15_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k1_jordan2c A (k1_struct_0 (k15_euclid A))) = (k1_struct_0 (k15_euclid A))) ) ) ) ).
tt(t15_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 D 1) &  ((v3_tops_2 C k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  (B = (a_3_0_jordan20 A C D)) ) )  => (v3_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ) ).
tt(t15_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k18_euclid (k10_jordan6 A)) = (k18_euclid (k11_jordan6 A))) ) ) ) ).
tt(t15_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k19_euclid (k13_complex1 (k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2) (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) (k3_finseq_1 (k1_jordan8 A B))))))))) ) ) ) ) ) ).
tt(t15_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (v2_jordan23 A))  =>  ((k4_jordan3 A B B) = (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)) ) ) ) ) ) ).
tt(t15_jordan24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_connsp_1 A E D) => (r3_connsp_1 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) D F) = (k7_partfun1 k1_numbers F E)) ) )  =>  ((k8_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) D (a_2_0_jordan2b B C)) = (a_4_0_jordan2b A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_jordan2c A B C) => (r1_tarski C (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) ) ) ) ) ) ) ).
tt(t15_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan3 A B C) => (r1_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) C B)) ) ) ) ) ) ) ).
tt(t15_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ( ((k3_finseq_6 A B C C) = (k12_finseq_1 A (k7_partfun1 A B C)))  &  ((k3_finseq_1 (k3_finseq_6 A B C C)) = 1) ) ) ) ) ) ) ) ) ).
tt(t15_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  ( ((v5_pre_topc E (k4_topmetr A B) (k4_topmetr C D)) &  ((v2_funct_1 E) &  ( ((k1_funct_1 E A) = C)  &  ((k1_funct_1 E B) = D) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_topmetr A B))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_topmetr A B))) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (~  ( (F = H)  &  ( (G = I)  &  ( (~ (r1_xxreal_0 I H))  &  ( (J = (k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) E F))  &  ( (K = (k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) E G))  & (r1_xxreal_0 K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v4_topreal1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)) &  (C = (k2_topreal1 2 B A)) ) ) )  => (r1_topreal1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) C)) ) ) ) ) ) ) ).
tt(t15_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) B) (k15_euclid 2)) &  ((r2_hidden C (k3_topreal1 2 A)) & (r2_hidden C B)) ) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) C)) ) ) ) ) ) ) ).
tt(t15_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_2_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k15_pscomp_1 (k3_topreal1 2 A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k15_pscomp_1 (k3_topreal1 2 A)))))) ) ) ) ) ) ).
tt(t15_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((r2_hidden (k1_jordan6 A B C) A) & (r2_hidden (k2_jordan6 A B C) A)) ) ) ) ) ) ) ) ).
tt(t15_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ((v3_tops_2 C k5_topmetr (k1_pre_topc (k15_euclid A) B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ( (C = D)  &  ((v5_pre_topc D k5_topmetr (k15_euclid A)) & (v2_funct_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_jordan8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) => (r1_xboole_0 (k3_goboard5 (k1_jordan8 A C) B (k3_finseq_1 (k1_jordan8 A C))) A)) ) ) ) ) ) ) ).
tt(t15_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v1_topreal1 C) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C))) ) )  =>  ((r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_gobrd13 C B A)) (k3_topreal1 2 C)) & (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k2_gobrd13 C B A)) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ).
tt(t15_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) B) = (k5_jordan6 (k9_jordan6 A) (k22_pscomp_1 A) (k18_pscomp_1 A) (k22_pscomp_1 A) B)) ) ) ) ) ).
tt(t15_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r2_jordan2c 2 B A) => (r1_xboole_0 (k1_jordan2c 2 B) A)) ) ) ) ) ).
tt(t15_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ((k3_knaster A B C (k1_ordinal1 D)) = (k1_funct_1 B (k3_knaster A B C D))) ) ) ) ) ) ) ) ) ).
tt(t15_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m1_kolmog01 D A B C) =>  ( (~ (v1_xboole_0 (k6_kolmog01 A B C D)))  &  ((v1_prob_1 (k6_kolmog01 A B C D) B) &  ((v4_prob_1 (k6_kolmog01 A B C D) B) & (m1_subset_1 (k6_kolmog01 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) )  =>  ((k3_kurato_0 A B) = C) ) ) ) ) ) ) ).
tt(t15_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr k6_kurato_1)))))) = (k2_rcomp_1 k2_xxreal_0 2)) ).
tt(t15_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((k2_pre_topc A (k1_kurato_2 A B)) = (k1_kurato_2 A B)) ) ) ) ) ).
tt(t15_lang1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k3_lang1 (k8_lang1 A B)) = (k3_finseq_2 (k1_tarski B))) ) ) ) ).
tt(t15_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 A)) & (r2_hidden F (k2_finseq_1 A)))  =>  ((k2_laplace E F A B C) = (k2_laplace E F A B (k3_matrix11 E A A (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (~  ((k1_funct_1 (k1_latsubgr A) B) = k1_xboole_0) ) ) ) ) ) ).
tt(t15_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  ( (D = F)  &  ((r1_latsum_1 A B) &  ((v4_orders_2 A) & (v4_orders_2 B)) ) ) )  =>  ((r1_orders_2 A C D) <=> (r1_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (u2_lattices A) B C) = C) ) )  =>  (B = (k5_lattices A)) ) ) ) ) ) ).
tt(t15_lattice3,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k11_lattice3 A B C) = (k11_lattice3 A C B)) ) ) ) ) ) ) ).
tt(t15_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((k3_lattices A (k1_lattice4 A B) (k1_lattice4 A C)) = (k1_lattice4 A (k5_setwiseo (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t15_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  ((v2_funct_2 C (u1_struct_0 B)) => (v2_funct_1 (k4_lattice5 A B C))) ) ) ) ) ) ) ).
tt(t15_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v2_lattice6 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_lattice6 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice6 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice6 A B D) =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (m2_lattice7 (k4_lattice7 (k5_yellow_0 A (k3_lattice7 A))))) ) ).
tt(t15_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k3_lattice8 A (k1_ordinal1 B)) = (k1_lattice8 (k3_lattice8 A B))) ) ) ) ) ).
tt(t15_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattices A (k5_lattices A) B) = (k5_lattices A)) ) ) ) ) ).
tt(t15_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((r1_xxreal_0 (k1_recdef_1 (k5_lexbfs A B C) D) (k39_glib_000 B)) &  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) => (r1_xxreal_0 1 (k1_recdef_1 (k5_lexbfs A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t15_lfuzzy_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v9_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A (k1_yellow_0 A B) C) = (k1_yellow_0 A (a_3_0_lfuzzy_0 A B C))) ) ) ) ) ) ) ).
tt(t15_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v8_relat_2 B) => (v3_lfuzzy_1 (k3_lfuzzy_1 B (k2_zfmisc_1 A A)) A)) ) ) ) ) ).
tt(t15_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) => (v2_limfunc1 (k32_valued_1 k5_numbers k1_numbers A)))  &  ((v2_limfunc1 A) => (v1_limfunc1 (k32_valued_1 k5_numbers k1_numbers A))) ) ) ) ).
tt(t15_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  ((r5_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r5_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r5_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t15_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc3 B A) &  ((r3_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r3_limfunc3 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t15_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  ((v4_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r5_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t15_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((k1_lmod_5 A B C) = B)  & (r1_tarski C D))  =>  ((k1_lmod_5 A B D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t15_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 D)) =>  ((r1_lmod_6 A C D) =>  ( ((k4_struct_0 C) = (k4_struct_0 D))  &  ( ( ( (E = H)  &  (F = I) )  =>  ((k1_algstr_0 C E F) = (k1_algstr_0 D H I)) )  &  ( ( (G = J)  =>  ((k4_vectsp_1 A C B G) = (k4_vectsp_1 A D B J)) )  &  ( ( (G = J)  =>  ((k4_algstr_0 D J) = (k4_algstr_0 C G)) )  &  ( ( ( (E = H)  &  (F = I) )  =>  ((k5_algstr_0 C E F) = (k5_algstr_0 D H I)) )  &  ((r1_struct_0 C (k4_struct_0 D)) &  ((r1_struct_0 D (k4_struct_0 C)) &  ( ( ((r1_struct_0 C H) & (r1_struct_0 C I))  => (r1_struct_0 C (k1_algstr_0 D H I)))  &  ( ((r1_struct_0 C J) => (r1_struct_0 C (k4_vectsp_1 A D B J)))  &  ( ((r1_struct_0 C J) => (r1_struct_0 C (k4_algstr_0 D J)))  &  ( ((r1_struct_0 C H) & (r1_struct_0 C I))  => (r1_struct_0 C (k5_algstr_0 D H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k13_lmod_7 A B C))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k14_lmod_7 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  => (m1_rlsub_1 (g1_rlvect_1 (k7_lopban_1 A B) (k10_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k8_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B)) (k9_rsspace (k5_lopban_1 (u1_struct_0 A) B) (k7_lopban_1 A B))) (k5_lopban_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t15_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_lopban_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_lopban_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((k1_algstr_0 (k8_lopban_2 A) B C) = (k1_algstr_0 (k8_lopban_2 A) C B))  &  ( ((k1_algstr_0 (k8_lopban_2 A) (k1_algstr_0 (k8_lopban_2 A) B C) D) = (k1_algstr_0 (k8_lopban_2 A) B (k1_algstr_0 (k8_lopban_2 A) C D)))  &  ( ((k1_algstr_0 (k8_lopban_2 A) B (k4_struct_0 (k8_lopban_2 A))) = B)  &  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k8_lopban_2 A))) &  ((k1_algstr_0 (k8_lopban_2 A) B G) = (k4_struct_0 (k8_lopban_2 A))) ) )  &  ( ((k6_algstr_0 (k8_lopban_2 A) (k6_algstr_0 (k8_lopban_2 A) B C) D) = (k6_algstr_0 (k8_lopban_2 A) B (k6_algstr_0 (k8_lopban_2 A) C D)))  &  ( ((k6_algstr_0 (k8_lopban_2 A) B (k5_struct_0 (k8_lopban_2 A))) = B)  &  ( ((k6_algstr_0 (k8_lopban_2 A) (k5_struct_0 (k8_lopban_2 A)) B) = B)  &  ( ((k6_algstr_0 (k8_lopban_2 A) B (k1_algstr_0 (k8_lopban_2 A) C D)) = (k1_algstr_0 (k8_lopban_2 A) (k6_algstr_0 (k8_lopban_2 A) B C) (k6_algstr_0 (k8_lopban_2 A) B D)))  &  ( ((k6_algstr_0 (k8_lopban_2 A) (k1_algstr_0 (k8_lopban_2 A) C D) B) = (k1_algstr_0 (k8_lopban_2 A) (k6_algstr_0 (k8_lopban_2 A) C B) (k6_algstr_0 (k8_lopban_2 A) D B)))  &  ( ((k1_rlvect_1 (k8_lopban_2 A) (k6_algstr_0 (k8_lopban_2 A) B C) E) = (k6_algstr_0 (k8_lopban_2 A) (k1_rlvect_1 (k8_lopban_2 A) B E) C))  &  ( ((k1_rlvect_1 (k8_lopban_2 A) (k1_algstr_0 (k8_lopban_2 A) B C) E) = (k1_algstr_0 (k8_lopban_2 A) (k1_rlvect_1 (k8_lopban_2 A) B E) (k1_rlvect_1 (k8_lopban_2 A) C E)))  &  ( ((k1_rlvect_1 (k8_lopban_2 A) B (k7_real_1 E F)) = (k1_algstr_0 (k8_lopban_2 A) (k1_rlvect_1 (k8_lopban_2 A) B E) (k1_rlvect_1 (k8_lopban_2 A) B F)))  &  ( ((k1_rlvect_1 (k8_lopban_2 A) B (k8_real_1 E F)) = (k1_rlvect_1 (k8_lopban_2 A) (k1_rlvect_1 (k8_lopban_2 A) B F) E))  &  ((k1_rlvect_1 (k8_lopban_2 A) (k6_algstr_0 (k8_lopban_2 A) B C) (k8_real_1 E F)) = (k6_algstr_0 (k8_lopban_2 A) (k1_rlvect_1 (k8_lopban_2 A) B E) (k1_rlvect_1 (k8_lopban_2 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k2_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t15_lopban_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k8_nat_1 (u1_struct_0 B) (k4_lopban_4 B C) A) = (k8_nat_1 (u1_struct_0 B) C (k7_nat_d A 1))) ) ) ) ) ) ) ) ).
tt(t15_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 B)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 B)))) =>  ( ( (G = (k1_lopban_5 B (k4_struct_0 B) D))  &  ( (F = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_lopban_5 A (k4_struct_0 A) 1)))  & (r1_tarski G (k2_pre_topc (k4_normsp_2 B) F))) )  =>  ((r1_xxreal_0 D k6_numbers) | (r1_tarski G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lopclset,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) ) )  =>  ((r2_hidden A (k7_lopclset B)) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C B) &  ((v20_lattices C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  &  ( (C = A)  & (v1_filter_0 C B)) ) ) ) ) ) ) ).
tt(t15_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) (k5_lpspace1 A) B) B)) ) ) ) ).
tt(t15_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( (A = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  (k6_numbers = (k1_seq_1 D E)) ) ) ) )  =>  ((r3_mesfunc6 A B C D) &  ((k1_mesfunc6 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_normsp_1 B))  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k3_hilbert1 (k1_ltlaxio1 (k2_ltlaxio1 A)) (k2_ltlaxio1 (k1_ltlaxio1 A))))) = 1) ) ) ) ) ) ) ).
tt(t15_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A C (k8_cqc_lang A B D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t15_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k4_xboolean A A) = k7_margrel1)  =>  (A = k7_margrel1) ) ) ) ).
tt(t15_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_rusub_4 A (k1_mathmorp A D B) C) = (k1_mathmorp A D (k6_rusub_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t15_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ((v2_matrix10 C) =>  ((r1_xxreal_0 k6_numbers A) | (v1_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ) ).
tt(t15_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k13_matrix_2 (k1_nat_1 A 2)))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  ( ( (D = (k3_group_4 (k13_matrix_2 (k1_nat_1 A 2)) C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 (k1_nat_1 A 2))) =>  (~  ( ((k1_funct_1 C E) = F)  & (v4_matrix_2 F (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2))))) ) ) ) ) ) ) ) )  =>  ( ( ((k4_nat_d (k3_finseq_1 C) 2) = k1_xboole_0)  =>  ((k2_matrix11 A B D) = (k1_group_1 B)) )  &  ( ((k4_nat_d (k3_finseq_1 C) 2) = 1)  =>  ((k2_matrix11 A B D) = (k4_algstr_0 B (k1_group_1 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) C D) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) C D) =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 F))) &  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 F))) &  (G = (k4_matrix_1 (u1_struct_0 E) F)) ) )  =>  ((r1_xxreal_0 C k6_numbers) |  ((r1_xxreal_0 D k6_numbers) |  ((k4_matrix_1 (u1_struct_0 E) (k1_matrix12 C D E G A B)) = (k4_matrix12 C D E F A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_matrix_2 D A B) & (m1_matrix_1 D (u1_struct_0 B) A A))  =>  (! [E:$i] :  ( ((v1_matrix_2 E A B) & (m1_matrix_1 E (u1_struct_0 B) A A))  =>  ( (C = (k4_matrix_6 A B D E))  =>  ( ((v1_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A))  &  ((k13_matrix_3 A B C) = (k11_fvsum_1 B (k13_matrix_3 A B D) (k13_matrix_3 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 A) k6_numbers k6_numbers) =>  ( (B = k1_xboole_0)  &  ( (B = (k12_matrix_1 A k6_numbers))  &  (B = (k11_matrix_1 A k6_numbers)) ) ) ) ) ) ) ).
tt(t15_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D A C) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ((k8_matrix_1 D (k1_matrix15 D A B C E F) G) = (k8_finseq_1 D (k8_matrix_1 D E G) (k8_matrix_1 D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v1_matrix16 F (u1_struct_0 B)) &  ((v1_matrix16 G (u1_struct_0 B)) & (v1_matrix16 H (u1_struct_0 B))) )  => (v1_matrix16 (k3_matrix_6 A B (k3_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((v5_matrix17 C (u1_struct_0 A)) &  ((v5_matrix17 D (u1_struct_0 A)) &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k1_matrix17 (u1_struct_0 A) C) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix17 (u1_struct_0 A) D) B)) = (k1_matrix17 (u1_struct_0 A) (k9_fvsum_1 A (k3_fvsum_1 A C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m1_matrix_1 (k9_finseq_1 (k12_finseq_1 A B)) A 1 1)) ) ) ) ).
tt(t15_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 B))) =>  ((k8_matrix_1 A (k4_matrix_1 A B) C) = (k9_matrix_1 A B C)) ) ) ) ) ) ) ) ).
tt(t15_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k12_matrix_1 B A))) =>  ( ( (C = D)  =>  ((k1_funct_1 (k8_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) C) D) = (k5_struct_0 B)) )  &  ( (~  (C = D) )  =>  ((k1_funct_1 (k8_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) C) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k1_matrix_4 A D B) = (k1_matrix_4 A D C)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrix_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_matrix_5 (k8_matrix_5 A B)) = (k1_matrix_3 k1_complfld A B)) ) ) ) ) ).
tt(t15_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ((r2_matrix_6 B A D C) => (r1_matrix_6 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t15_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k12_matrix_3 B A (k1_matrix_3 A B B)) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t15_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((k4_matrix_6 A B C D) = (k12_matrix_1 B A))  => (v1_matrix_8 (k4_matrix_6 A B D C) A B)) ) ) ) ) ) ) ) ) ).
tt(t15_matrix_9,ax, ((k3_finseq_5 (k1_finseq_2 3)) = (k3_finseq_4 k5_numbers 3 2 1)) ).
tt(t15_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 A) = (k1_matrix_1 B)) )  =>  ((k1_matrixc1 (k5_matrix_5 A B)) = (k5_matrix_5 (k1_matrixc1 A) (k1_matrixc1 B))) ) ) ) ) ) ).
tt(t15_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k10_matrixj1 A (k4_matrixj1 A B)) = (k4_matrix_2 k5_numbers (k3_finseq_1 B))) ) ) ) ) ).
tt(t15_matrixj2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ( ((k9_matrixj2 A B C) = k1_xboole_0)  <=>  ((k2_struct_0 B) = (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t15_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (A = (k4_rvsum_1 (k8_rvsum_1 A B) B)) ) ) ) ) ) ).
tt(t15_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k3_finseq_1 B) = (k1_matrix_1 C))  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_3 A (k2_matrix_3 A C) B) = (k2_matrix_3 A (k4_matrix_3 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 D)) =>  ( (C = E)  =>  ((k4_rlvect_1 B C) = (k4_rlvect_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrlin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k2_matrlin A (k3_pre_poly A B)) = (k4_matrix_1 A (k2_matrlin A (k3_pre_poly A B)))) ) ) ) ) ).
tt(t15_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  & (r1_matroid0 A C B)) ) ) ) ) ) ).
tt(t15_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) <=>  ((r2_hidden A (k4_finseq_1 (k9_matrix_1 C D B))) & (r2_hidden B (k4_finseq_1 (k8_matrix_1 C D A)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k1_matrix_1 E))) =>  ((k9_matrix_1 D (k4_matrix11 A B D C E) F) = (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers D C (k9_matrix_1 D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) B A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_finseq_1 B))) =>  (~  ((v2_funct_1 (k2_partfun1 k5_numbers (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) D E)) &  ( ((k2_relset_1 (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) (k2_partfun1 k5_numbers (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) D E)) = (k9_matrix13 k2_vectsp_1 B A D))  &  (! [F:$i] :  ((m2_vectsp_6 F k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k9_matrix13 k2_vectsp_1 B A D)) =>  (~  ( ((k4_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) F) = (k1_funct_1 (k3_matrtop1 B A D) C))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G E) =>  ((k1_funct_1 F (k8_matrix_1 (u1_struct_0 k2_vectsp_1) D G)) = (k16_rvsum_1 (k15_finseq_1 (k5_relat_1 C (k8_relset_1 k5_numbers (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) D (k1_tarski (k8_matrix_1 (u1_struct_0 k2_vectsp_1) D G))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k13_fvsum_1 k2_vectsp_1 (k1_matrtop1 E) (k9_matrix_1 (u1_struct_0 k2_vectsp_1) (k2_matrtop3 D A B C) B)) = (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k20_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k4_xcmplx_0 (k17_sin_cos A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v2_mazurulm D A B) & (v2_mazurulm E B C))  => (v2_mazurulm (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k4_pboole A B D) C)) ) ) ) ) ) ) ) ).
tt(t15_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_zfmisc_1 (k2_tarski B C) D)) =>  ( ( ((k1_xtuple_0 A) = B)  |  ((k1_xtuple_0 A) = C) )  & (r2_hidden (k2_xtuple_0 A) D)) ) ) ) ) ) ).
tt(t15_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ((k2_relset_1 (k9_setfam_1 A) C) = (k1_tarski B)) ) ) ) ) ) ).
tt(t15_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_measure2 D A B) =>  ( (? [E:$i] :  ((r2_hidden E D) & (m2_measure1 E A B C)) )  => (m2_measure1 (k1_measure2 A B D) A B C)) ) ) ) ) ) ) ) ).
tt(t15_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k2_measure3 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_measure3 A B C))))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r2_hidden (k8_nat_1 B E F) (k3_measure3 A B C (k8_nat_1 (k2_measure3 A B C) D F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((k12_supinf_2 B C) = k1_supinf_2)  => (r2_hidden C (k1_measure4 A B))) ) ) ) ) ) ).
tt(t15_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k7_numbers) &  ((r1_xxreal_0 C B) &  (A = (k2_xxreal_1 C B)) ) ) )  =>  (B = (k8_supinf_2 A)) ) ) ) ) ) ).
tt(t15_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 k1_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 k1_numbers))))) )  =>  (! [B:$i] :  ((m2_measure7 B A) => (r1_xxreal_0 (k7_supinf_2 (k8_measure7 (k5_setfam_1 k1_numbers (k2_relset_1 (k9_setfam_1 k1_numbers) A)))) (k19_supinf_2 (k7_measure7 A B)))) ) ) ) ).
tt(t15_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_measure8 C A B) => (m2_measure8 (k2_prob_3 A C) A B)) ) ) ) ) ).
tt(t15_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k5_member_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(t15_membered,ax, (! [A:$i] :  ((v3_membered A) =>  ( (! [B:$i] :  ((v1_xreal_0 B) => (r2_hidden B A)) )  =>  (A = k1_numbers) ) ) ) ).
tt(t15_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k7_memstr_0 A B C)))) ) ) ) ) ) ).
tt(t15_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_euclid_6 A B C))  =>  ( (~ (r1_euclid_6 A C B))  &  ( (~ (r1_euclid_6 B A C))  &  ( (~ (r1_euclid_6 B C A))  &  ( (~ (r1_euclid_6 C A B))  &  (~ (r1_euclid_6 C B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)))  &  ((v1_mesfunc8 B A k7_numbers) &  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers B D) (k7_mesfunc1 A (k4_mesfunc5 A k7_numbers C D)))) ) ) )  =>  ((r2_relset_1 A k7_numbers (k5_mesfunc8 A B) (k7_mesfunc1 A (k6_mesfunc8 A C))) & (r2_relset_1 A k7_numbers (k6_mesfunc8 A B) (k7_mesfunc1 A (k5_mesfunc8 A C)))) ) ) ) ) ) ) ) ).
tt(t15_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r2_hidden (k1_relset_1 A C) B) & (r2_hidden (k1_relset_1 A D) B))  => (r2_hidden (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers C D)) B)) ) ) ) ) ) ) ) ) ).
tt(t15_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k1_relset_1 A (k8_mesfun7c A B))) & (v2_comseq_2 (k10_seqfunc A B C)))  =>  ( ((k12_supinf_2 (k8_mesfun7c A B) C) = (k12_supinf_2 (k7_mesfun7c A B) C))  &  ((k12_supinf_2 (k8_mesfun7c A B) C) = (k12_supinf_2 (k6_mesfun7c A B) C)) ) ) ) ) ) ) ) ) ).
tt(t15_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r2_mesfunc6 A B (k4_mesfunc5 A k1_numbers C E))) )  => (r2_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k2_mesfun9c A C) D))) ) ) ) ) ) ) ) ) ).
tt(t15_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((r1_tarski C (k9_xtuple_0 B)) =>  ((k9_subset_1 A C (k17_mesfunc1 A B D)) = (k6_subset_1 C (k9_subset_1 A C (k16_mesfunc1 A B D)))) ) ) ) ) ) ) ) ).
tt(t15_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (r1_xxreal_0 (k12_supinf_2 (k1_mesfunc2 A B) C) k1_supinf_2))  =>  ((k12_supinf_2 (k2_mesfunc2 A B) C) = k1_supinf_2) ) ) ) ) ) ) ) ).
tt(t15_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ((r1_mesfunc3 A B C D E) &  ((r2_hidden F (k1_relset_1 A C)) &  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  (~  ( ((k4_finseq_1 G) = (k4_finseq_1 E))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k12_supinf_2 E H) (k12_supinf_2 (k3_mesfunc2 (k1_funct_1 D H) A) F))) ) ) )  &  ((k12_supinf_2 C F) = (k4_extreal1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 C) => (v6_supinf_2 (k2_partfun1 A k7_numbers C B))) ) ) ) ) ) ).
tt(t15_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski D (k1_relset_1 A C)) =>  ((r1_mesfunc6 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k8_subset_1 A D (k13_mesfunc1 C E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)) = E)  &  ((v3_valued_0 C) &  ((v3_valued_0 D) &  ((r1_mesfunc1 A B C E) & (r1_mesfunc1 A B D E)) ) ) )  => (r1_mesfunc1 A B (k5_mesfunc1 A C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k4_mesfunc5 A k7_numbers C F) (k1_measure6 E)))) ) )  =>  ((k3_tarski (k2_relset_1 B D)) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k2_mesfunc8 A C) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 A E)) &  ((r1_tarski D (k1_relset_1 A F)) &  ((r1_mesfunc1 A B E D) &  ((r1_mesfunc1 A B F D) &  ((v6_supinf_2 E) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) => (r1_xxreal_0 (k12_supinf_2 E G) (k12_supinf_2 F G))) ) ) ) ) ) ) )  => (r1_xxreal_0 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E D)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers F D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_tarski (k11_metric_1 B C A) (k10_metric_1 B C A))) ) ) ) ) ) ).
tt(t15_metric_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  ((r2_hidden A (k2_metric_2 B)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  (A = (k1_metric_2 B C)) ) ) ) ) ) ) ).
tt(t15_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) D E) = (k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  => (r2_metric_6 A (k9_metric_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_metrizts,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v2_tex_2 C B) => (r1_ordinal1 (k1_card_1 C) A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ((v1_tops_2 C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xboole_0 D E)) ) ) ) ) ) )  =>  ((r2_hidden k1_xboole_0 C) | (r1_ordinal1 (k1_card_1 C) A)) ) ) ) ) ) ) ) ) ).
tt(t15_mfold_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k23_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D)) = (k9_binop_2 (k23_rvsum_1 A B) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t15_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r1_midsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t15_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_midsp_1 A))) <=> (m1_midsp_1 B A)) )  &  ( ((k4_struct_0 (k15_midsp_1 A)) = (k6_midsp_1 A))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_midsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_midsp_1 A))) =>  (! [D:$i] :  ((m1_midsp_1 D A) =>  (! [E:$i] :  ((m1_midsp_1 E A) =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k15_midsp_1 A) B C) = (k7_midsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v4_midsp_2 E B) & (l1_midsp_2 E B))  =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B E)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B E)))) =>  ( ((k8_midsp_3 A B E C D) = F)  <=>  ((k7_midsp_3 A B E C F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 F G) &  ((r1_tarski B C) & (r1_relset_1 A A D E)) )  => (r1_tarski (k11_mmlquery A B E F) (k11_mmlquery A C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_mod_2 B A) &  ((v3_mod_2 B A) & (l1_mod_2 B A)) )  =>  (! [C:$i] :  ( ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) )  =>  ( ((k2_mod_2 A C) = (k3_mod_2 A B))  =>  ( ((k2_mod_2 A (k8_mod_2 A C B)) = (k2_mod_2 A B))  &  ((k3_mod_2 A (k8_mod_2 A C B)) = (k3_mod_2 A C)) ) ) ) ) ) ) ) ) ).
tt(t15_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v1_lmod_5 (k6_domain_1 (u1_struct_0 B) C) A B) <=>  (~  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t15_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_vectsp_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ( ( (C = (k5_mod_4 B D))  &  ( (E = F)  &  (G = H) ) )  =>  ((k5_vectsp_2 B D F H) = (k4_vectsp_1 A C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) =>  (! [D:$i] :  ((m1_trees_1 D (k5_trees_1 A C B)) =>  (! [E:$i] :  ((m1_trees_1 E B) =>  ( (D = (k8_finseq_1 k5_numbers C E))  => (r2_wellord2 (k1_trees_2 (k5_trees_1 A C B) D) (k1_trees_2 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_modcat_1 A B))) =>  (! [D:$i] :  ((m4_modcat_1 D B (k4_modcat_1 B (k3_modcat_1 A B))) =>  ( (C = D)  =>  ( ((k3_graph_1 (k11_modcat_1 A B) C) = (k2_mod_2 B D))  &  ((k4_graph_1 (k11_modcat_1 A B) C) = (k3_mod_2 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k26_modelc_1 (k48_modelc_1 A B D) E)) <=>  (? [F:$i] :  ((m1_modelc_1 F A B) &  ( ((k3_funct_2 k5_numbers A F k6_numbers) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) => (r3_modelc_1 A B D (k3_funct_2 k5_numbers A F G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_modelc_2 A (k4_modelc_2 B C)) <=>  ( (A = B)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t15_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  ((r1_tarski B C) => (r1_xxreal_0 (k18_modelc_3 A B) (k18_modelc_3 A C))) ) ) ) ) ) ) ).
tt(t15_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (~ (r2_hidden B (k1_polynom2 k10_newton (k13_nat_3 A))))  =>  ((k11_nat_3 A B) = k6_numbers) ) ) ) ) ) ).
tt(t15_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v3_group_1 A) =>  ((v13_monoid_0 A) <=>  ((v1_group_1 A) & (v1_finseqop (u2_algstr_0 A) (u1_struct_0 A))) ) ) ) ) ).
tt(t15_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((r1_lattice2 B C D) => (r1_lattice2 (k9_funct_2 A B) (k8_monoid_1 B B B C A) (k8_monoid_1 B B B D A))) ) ) ) ) ) ) ) ).
tt(t15_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k2_morph_01 A C (k6_setfam_1 (u1_struct_0 A) B)) (k1_setfam_1 (a_3_6_morph_01 A B C)))) ) ) ) ) ) ).
tt(t15_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) => (r8_pboole (u1_struct_0 A) (k4_msafree3 A B C) (k3_msafree3 A B C))) ) ) ) ) ) ).
tt(t15_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k3_tarski (k10_xtuple_0 (k13_msafree A B))) = (a_2_0_msafree A B)) ) ) ) ) ).
tt(t15_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((r2_hidden F (k1_funct_1 (u3_msualg_1 A C) E)) &  (D = (k1_trees_4 (k4_tarski F E))) )  =>  ((k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B) D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v7_graph_1 C A) & (m1_graph_1 C A)) )  =>  ( ((k1_funct_1 (k7_graph_2 A B) (k2_nat_1 (k3_finseq_1 B) 1)) = (k1_funct_1 (k7_graph_2 A C) 1))  <=>  ( (~ (v1_xboole_0 (k7_finseq_1 B C)))  &  ((v7_graph_1 (k7_finseq_1 B C) A) & (m1_graph_1 (k7_finseq_1 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t15_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  ((v1_relat_1 (k8_pboole B C)) &  ((v4_relat_1 (k8_pboole B C) A) &  ((v1_funct_1 (k8_pboole B C)) &  ((v1_partfun1 (k8_pboole B C) A) & (v1_funcop_1 (k8_pboole B C))) ) ) ) ) ) ) ) ) ).
tt(t15_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_msualg_2 (k9_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( (C = (u1_struct_0 A))  =>  ((u1_unialg_1 A) = (k3_unialg_2 B C)) ) ) ) ) ) ) ) ) ).
tt(t15_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) => (r2_pboole (u1_struct_0 A) (k2_pboole (u1_struct_0 A) (k2_msualg_2 A B) C) (k9_msualg_2 A B C))) ) ) ) ) ) ).
tt(t15_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ( ((r4_msualg_3 A B C E) & (r4_msualg_3 A C D F))  => (r4_msualg_3 A B D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v2_msualg_4 (k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) C D) A B) &  ((v3_msualg_4 (k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) C D) A B) & (m1_msualg_4 (k4_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B) C D) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t15_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) C D) =>  (! [E:$i] :  ((m1_rewrite1 E (k3_msualg_6 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v1_funcop_1 F)) ) )  =>  ( ( ((k3_finseq_1 E) = (k2_nat_1 (k3_finseq_1 F) 1))  &  ( (C = (k1_funct_1 E 1))  &  ( (D = (k1_funct_1 E (k3_finseq_1 E)))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r2_hidden G (k4_finseq_1 F)) &  ( (H = (k1_funct_1 F G))  &  ( (I = (k1_funct_1 E G))  &  (J = (k1_funct_1 E (k2_nat_1 G 1))) ) ) )  => (r1_msualg_6 A I J B H)) ) ) ) ) ) ) ) ) ) ) )  => (m2_msualg_6 (k4_funct_7 (k1_funct_1 (u3_msualg_1 A B) C) F) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v2_msualg_7 B A) => (v4_lattice3 B)) ) ) ) ) ).
tt(t15_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  ((k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) = (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) (a_3_2_msualg_8 A B C))) ) ) ) ) ) ) ).
tt(t15_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (m1_msualg_2 D A B))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ((r1_msualg_3 A C D E) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) E F) => (r1_msualg_3 A C B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_unialg_2 A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k6_msualg_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 (k6_msualg_1 A) D (k9_msualg_1 A))) =>  ((k5_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) D (k2_msuhom_1 A B C) E) = (k3_relat_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_mycielsk,ax, (! [A:$i] :  ( ((v3_dilworth A) &  ((v1_mycielsk A) & (l1_orders_2 A)) )  => (r1_xxreal_0 (k1_dilworth A) (k2_mycielsk A))) ) ).
tt(t15_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_pcomps_1 A) =>  ((v9_pre_topc A) & (v7_pre_topc A)) ) ) ) ).
tt(t15_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers))))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r2_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (k1_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers C D) E) &  ((r1_nagata_1 (u1_struct_0 A) E) &  ( (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) => (r1_xxreal_0 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers E F) B)) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers E F) => (v1_pscomp_1 F (k2_borsuk_1 A A))) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers D E) = (k4_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k1_prepower (k10_real_1 1 2)) (k10_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) C E)))) ) )  =>  ((r1_nagata_1 (u1_struct_0 A) D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers D E) => (v1_pscomp_1 E (k2_borsuk_1 A A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k3_xcmplx_0 A B) = 1)  =>  (A = 1) ) ) ) ) ) ).
tt(t15_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A)) ) )  =>  ((k3_nat_d (k7_nat_d B C) A) = (k6_xcmplx_0 (k3_nat_d B A) 1)) ) ) ) ) ) ) ) ).
tt(t15_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k21_rvsum_1 (k2_nat_3 B A)) = (k2_newton (k21_rvsum_1 B) A)) ) ) ) ) ).
tt(t15_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k4_nat_d (k1_newton A C) B) = 1)  &  ((r1_xxreal_0 1 C) & (v1_int_2 B)) )  => (r1_int_2 A B)) ) ) ) ) ) ) ).
tt(t15_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden C (k3_moebius1 A)) &  ((r2_hidden D (k3_moebius1 B)) &  ((r2_hidden E (k3_moebius1 A)) &  ((r2_hidden F (k3_moebius1 B)) &  ((r1_int_2 A B) &  ((k24_binop_2 C D) = (k24_binop_2 E F)) ) ) ) ) )  =>  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k4_nat_d A B) = k6_numbers)  &  (C = (k6_xcmplx_0 A (k3_xcmplx_0 D B))) )  =>  ((k4_nat_d C B) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t15_nat_lat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (m2_nat_lat A A)) ) ).
tt(t15_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k9_cat_3 B D D A C (k4_cat_1 B D)) = (k4_cat_1 A (k8_cat_1 B A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_nfcont_1 E B (k7_partfun1 (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_ncfcont1 F A D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden G (k1_relset_1 (u1_struct_0 A) C)) & (r2_hidden G F))  => (r2_hidden (k7_partfun1 (u1_struct_0 B) C G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_ncfcont2 A B C D) => (r3_ncfcont2 A B C (k5_vfunct_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ).
tt(t15_ndiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k1_valued_0 (u1_struct_0 B) (k2_normsp_1 B C D) A) (k2_normsp_1 B (k1_valued_0 (u1_struct_0 B) C A) (k1_valued_0 (u1_struct_0 B) D A)))) ) ) ) ) ) ) ) ).
tt(t15_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_ndiff_3 A C B) & (r1_ndiff_3 A D B))  =>  ((r1_ndiff_3 A (k2_vfunct_1 k1_numbers A C D) B) &  ((k1_ndiff_3 A (k2_vfunct_1 k1_numbers A C D) B) = (k5_algstr_0 A (k1_ndiff_3 A C B) (k1_ndiff_3 A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k7_integr15 A k1_numbers C D))) &  ((r2_ndiff_4 A C B) & (r2_ndiff_4 A D B)) )  =>  ((r2_ndiff_4 A (k7_integr15 A k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_funct_1 (k2_ndiff_4 A (k7_integr15 A k1_numbers C D) B) E) = (k7_euclid A (k1_ndiff_4 A C E) (k1_ndiff_4 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k4_prvect_2 A))) =>  ( ( (B = E)  &  (C = F) )  =>  ( ((k5_algstr_0 (k14_prvect_2 A) B C) = D)  <=>  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k4_finseq_1 A)) =>  ((k1_ndiff_5 A D G) = (k5_algstr_0 (k3_prvect_2 A G) (k1_ndiff_5 A E G) (k1_ndiff_5 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_neckla_3,ax, (! [A:$i] :  ( ((v1_orders_2 A) &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  ((v7_struct_0 A) =>  ((k3_necklace A) = A) ) ) ) ).
tt(t15_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v2_necklace (k1_necklace A))) ) ).
tt(t15_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (~  ( (~  ((k2_net_1 A) = k1_xboole_0) )  &  ( (~  ((k5_net_1 A B) = (k1_tarski B)) )  &  (~  ((k5_net_1 A B) = (k3_net_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t15_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_newton (k1_nat_1 A 1)) = (k8_real_1 (k3_newton A) (k1_nat_1 A 1))) ) ) ).
tt(t15_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_nfcont_1 B A C E) & (r1_nfcont_1 B A D E))  =>  ((r1_nfcont_1 B A (k6_vfunct_1 (u1_struct_0 B) A C D) E) & (r1_nfcont_1 B A (k2_vfunct_1 (u1_struct_0 B) A C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_nfcont_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((v1_funct_1 (k1_abian (u1_struct_0 A) B C)) &  ((v1_funct_2 (k1_abian (u1_struct_0 A) B C) (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_nfcont_2 (k1_abian (u1_struct_0 A) B C) A) & (m1_subset_1 (k1_abian (u1_struct_0 A) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_nfcont_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E))) &  ((r1_nfcont_3 B D A) & (r1_nfcont_1 B C E (k7_partfun1 (u1_struct_0 B) D A))) )  => (r1_nfcont_3 C (k1_partfun1 k1_numbers (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r2_hidden B (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D))) &  ((r1_nfcont_4 A C B) & (r1_nfcont_4 A D B)) )  => (r1_nfcont_4 A (k8_integr15 A k1_numbers C D) B)) ) ) ) ) ) ) ) ) ).
tt(t15_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((r1_normform A B C (k1_normform A B D E)) => (r1_normform A B (k3_normform A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k10_xtuple_0 B) = (k6_domain_1 (u1_struct_0 A) C)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ).
tt(t15_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  ( (B = C)  =>  ((v2_nfcont_1 B A) <=> (v4_pre_topc C (k3_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t15_ntalgo_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (k2_zfmisc_1 k4_numbers k4_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B k4_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C k4_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k4_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 A))) &  ((k1_funct_1 C F) = k6_numbers) ) ) ) )  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 A))) =>  ( ((k1_xtuple_0 (k1_funct_1 A F)) = (k1_funct_1 B F))  &  ((k2_xtuple_0 (k1_funct_1 A F)) = (k1_funct_1 C F)) ) ) ) )  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r2_hidden F (k2_finseq_1 (k3_finseq_1 A))) & (r2_hidden G (k2_finseq_1 (k3_finseq_1 A))))  =>  ( (F = G)  | (r1_int_2 (k1_funct_1 C F) (k1_funct_1 C G))) ) ) ) ) )  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 A))) =>  ((k6_int_1 D (k1_funct_1 C F)) = (k6_int_1 (k1_funct_1 B F) (k1_funct_1 C F))) ) ) )  &  (E = (k19_rvsum_1 C)) ) ) ) ) ) )  =>  ((k6_int_1 (k4_ntalgo_1 A) E) = (k6_int_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_numbers,ax,(r1_tarski k4_numbers k1_numbers)).
tt(t15_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (k8_openlatt A) (k4_lattices A B C)) = (k3_xboole_0 (k1_funct_1 (k8_openlatt A) B) (k1_funct_1 (k8_openlatt A) C))) ) ) ) ) ) ) ).
tt(t15_oposet_1,ax,(v11_oposet_1 k1_oposet_1)).
tt(t15_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_oppcat_1 A))) =>  (! [D:$i] :  ((m1_cat_1 D (k2_oppcat_1 A) B C) =>  ( (~  ((k2_cat_1 (k2_oppcat_1 A) B C) = k1_xboole_0) )  => (m1_cat_1 (k6_oppcat_1 A D) A (k4_oppcat_1 A C) (k4_oppcat_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t15_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((k1_relat_1 B) = A) ) ) ) ).
tt(t15_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k1_orders_2 A (k2_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t15_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) => (r3_xboole_0 A B)) ) ) ) ).
tt(t15_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C B) => (r1_ordinal1 A C)) ) )  =>  ( ((k2_ordinal1 B) = k1_xboole_0)  | (r1_ordinal1 A (k2_ordinal2 B))) ) ) ) ) ).
tt(t15_ordinal3,ax, (1 = (k1_tarski k1_xboole_0)) ).
tt(t15_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v2_ordinal2 A) => (v2_ordinal2 (k5_relat_1 A B))) ) ) ) ) ).
tt(t15_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k1_ordinal5 B D)) ) ) ) )  =>  ((k1_ordinal5 B A) = (k8_ordinal2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal6 (k1_tarski A)) = 1) ) ) ).
tt(t15_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t15_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (F = (k4_struct_0 A)) )  &  (~  ((k1_ortsp_1 A B (k4_vectsp_1 A B F D) C E) = (k1_ortsp_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) C)) => (m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ) ) ) ) ) ) ).
tt(t15_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((v2_relat_1 (k3_osalg_1 A B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) => (r1_tarski (k1_funct_1 (k3_osalg_1 A B) C) (k1_funct_1 (k3_osalg_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t15_osalg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A B) <=> (r2_hidden C (k4_card_3 (k1_mboolean A B)))) ) ) ) ) ).
tt(t15_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A B C D) &  ((v1_osalg_3 D A) &  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D))) =>  (~  ((r8_pboole (u1_struct_0 A) D E) &  ((v1_osalg_3 E A) & (r2_msualg_3 A B (k6_msualg_3 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  ((r2_msualg_3 A B (k16_osalg_4 A B C) (k18_osalg_4 A B C)) & (v1_osalg_3 (k18_osalg_4 A B C) A)) ) ) ) ) ) ) ).
tt(t15_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v4_aff_2 A) => (v7_aff_2 A)) ) ) ).
tt(t15_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_parsp_1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_parsp_1 A))) =>  (~  ((r1_parsp_1 (k9_parsp_1 A) B C D E) &  ((r1_parsp_1 (k9_parsp_1 A) B C F G) &  ( (~ (r1_parsp_1 (k9_parsp_1 A) D E F G))  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) & (r1_parsp_2 A B C E))  => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (~  ((r2_hidden C (k7_relat_1 D A)) &  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ((r2_hidden E (k1_relset_1 A D)) &  (C = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((r2_relset_1 C B D (k2_partfun1 C B E A)) <=>  ( ((k1_relset_1 C D) = (k8_subset_1 C (k1_relset_1 C E) A))  &  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F (k1_relset_1 C D)) =>  ((k7_partfun1 B D F) = (k7_partfun1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r1_setfam_1 (k2_partit1 A B C) B)) ) ) ) ) ) ).
tt(t15_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_diraf A B C D) &  ((r2_analoaf A C E D F) & (r2_analoaf A B E B F)) )  =>  ((r3_diraf A B F D) |  ( (B = C)  | (r1_diraf A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k3_pboole A B C) B)) ) ) ) ) ).
tt(t15_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_pcomps_1 A (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) = (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_pcomps_1 A B) (k1_pcomps_1 A C))) ) ) ) ) ) ) ).
tt(t15_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  ((k18_pcs_0 A B) = (g2_pcs_0 (k2_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k2_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 A) (u1_orders_2 B)) (k2_pcs_0 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_pcs_0 A) (u1_pcs_0 B)))) ) ) ) ) ).
tt(t15_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( ( (C = (k3_pdiff_1 A D))  &  ( (E = F)  & (r2_pdiff_1 1 A B C E)) )  =>  ((k1_funct_1 (k9_pdiff_1 A 1 B C E) (k12_finseq_1 k5_numbers 1)) = (k12_finseq_1 k1_numbers (k11_pdiff_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_euclid 2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r1_pdiff_2 B A) =>  ((r1_tarski A (k1_relset_1 (k1_euclid 2) B)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  ((r2_hidden C A) => (r3_pdiff_1 2 1 B C)) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r3_pdiff_3 B A) =>  ((k4_pdiff_3 B A) = (k11_pdiff_1 2 1 (k1_pdiff_3 2 2 B) A)) ) ) ) ) ) ).
tt(t15_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 3 A B) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k11_finseq_1 C D E))  &  (? [F:$i] :  ((m1_rcomp_1 F E) &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 A B))) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v3_fdiff_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v2_fdiff_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden I F) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 A B) I) (k1_seq_1 (k1_pdiff_2 3 3 A B) E)) = (k7_real_1 (k1_seq_1 G (k9_real_1 I E)) (k1_seq_1 H (k9_real_1 I E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r6_pdiff_5 E D))  =>  ((k6_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 E) D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (~  ( ((k3_finseq_1 B) = (k2_nat_1 (k3_finseq_1 C) 1))  &  ( ((k17_finseq_1 (k1_euclid A) (k3_finseq_1 C) B) = C)  &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ( (D = (k1_funct_1 B (k3_finseq_1 B)))  &  ((k5_euclid_7 A B) = (k7_euclid A (k5_euclid_7 A C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D (k5_euclid A)) (k11_binop_2 C B)) = (k9_euclid A (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D (k5_euclid A)) B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_pdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  => (r1_xxreal_0 (k18_complex1 (k1_seq_1 C D)) A)) ) )  => (r1_xxreal_0 (k12_euclid C) (k11_binop_2 B A))) ) ) ) ) ) ) ).
tt(t15_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ( ((r1_pdiff_6 C B A D) & (r1_pdiff_6 C B A E))  =>  ((r1_pdiff_6 C B A (k7_integr15 B (k1_euclid A) D E)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) (k1_euclid B)) (k1_pdiff_9 A B C (k7_integr15 B (k1_euclid A) D E)) F) = (k7_integr15 B (k1_euclid A) (k8_pdiff_1 A B D F) (k8_pdiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  (~  ( (~  (! [C:$i] :  ((m1_subset_1 C A) => (v3_pencil_1 (k1_pencil_1 A B C))) ) )  & (v3_pencil_1 (k5_pencil_1 A B))) ) ) ) ) ) ).
tt(t15_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_zfmisc_1 C))  & (v1_zfmisc_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t15_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (v3_card_1 (k1_funct_1 (k1_pzfmisc1 A B) C) 1)) ) ) ) ) ) ).
tt(t15_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((m1_vectsp_4 C A D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( ((k1_nat_1 (k1_vectsp_9 A C) 1) = E)  &  ((k1_vectsp_9 A D) = (k1_nat_1 E 1)) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_struct_0 D F) =>  ((r1_struct_0 C F) | (r2_hidden (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) F))) (k3_pencil_4 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v1_int_2 A) &  ((k4_nat_d B A) = (k4_xcmplx_0 1)) )  =>  ((k4_nat_d (k3_square_1 B) A) = 1) ) ) ) ) ) ).
tt(t15_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_petri (k11_petri A) (k12_petri A B)) = (k6_petri A B)) ) ) ) ) ).
tt(t15_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r2_pnproc_1 A B (k2_pnproc_1 A B C))) ) ) ) ) ).
tt(t15_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_polyalg1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (D = F)  &  (E = G) )  =>  ((k1_algstr_0 B D E) = (k1_algstr_0 C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k7_polyeq_1 A B C D E) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  (! [J:$i] :  ((v1_xreal_0 J) =>  ( ( (J = (k3_real_1 E (k6_real_1 B (k8_real_1 3 A))))  &  ( (I = (k1_real_1 (k6_real_1 B (k8_real_1 3 A))))  &  ( (F = (k7_xcmplx_0 B A))  &  ( (G = (k7_xcmplx_0 C A))  &  (H = (k7_xcmplx_0 D A)) ) ) ) )  =>  ((k7_real_1 (k3_real_1 (k1_newton J 3) (k7_real_1 (k8_real_1 (k7_real_1 (k8_real_1 3 I) F) (k3_square_1 J)) (k8_real_1 (k7_real_1 (k7_real_1 (k8_real_1 3 (k3_square_1 I)) (k8_real_1 2 (k3_xcmplx_0 F I))) G) J))) (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton I 3) (k3_xcmplx_0 F (k3_square_1 I))) (k2_xcmplx_0 (k3_xcmplx_0 G I) H))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ( ((k7_polyeq_1 A B C D E) = k6_numbers)  &  ((k4_complex1 E) = k6_numbers) )  =>  ( (A = k6_numbers)  |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (H = (k9_binop_2 (k3_complex1 E) (k12_binop_2 B (k11_binop_2 3 A))))  &  ( ((k3_complex1 E) = (k10_binop_2 (k9_binop_2 F G) (k12_binop_2 B (k11_binop_2 3 A))))  &  ( ((k9_binop_2 (k11_binop_2 (k11_binop_2 3 F) G) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 3 (k5_square_1 A)))) = k6_numbers)  &  ( (~  (E = (k3_binop_2 (k10_binop_2 (k9_binop_2 (k2_power 3 (k9_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3))))) (k2_power 3 (k10_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3)))))) (k12_binop_2 B (k11_binop_2 3 A))) (k5_binop_2 k6_numbers k7_complex1))) )  &  ( (~  (E = (k3_binop_2 (k10_binop_2 (k9_binop_2 (k2_power 3 (k9_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3))))) (k2_power 3 (k9_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3)))))) (k12_binop_2 B (k11_binop_2 3 A))) (k5_binop_2 k6_numbers k7_complex1))) )  &  (~  (E = (k3_binop_2 (k10_binop_2 (k9_binop_2 (k2_power 3 (k10_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3))))) (k2_power 3 (k10_binop_2 (k10_binop_2 (k7_binop_2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 6 (k5_square_1 A)))) (k7_square_1 (k9_binop_2 (k12_binop_2 (k5_square_1 (k9_binop_2 (k11_binop_2 2 (k2_newton (k12_binop_2 B (k11_binop_2 3 A)) 3)) (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) D) (k11_binop_2 B C)) (k11_binop_2 3 (k5_square_1 A))))) 4) (k2_newton (k12_binop_2 (k10_binop_2 (k11_binop_2 (k11_binop_2 3 A) C) (k5_square_1 B)) (k11_binop_2 9 (k5_square_1 A))) 3)))))) (k12_binop_2 B (k11_binop_2 3 A))) (k5_binop_2 k6_numbers k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k2_newton A E) (k2_newton B E)) = C)  &  ( ((k3_xcmplx_0 (k2_newton A E) (k2_newton B E)) = D)  &  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D))) &  ( (~ (v1_abian E))  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) )  &  (~  ( (A = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((v1_xcmplx_0 H) =>  (! [I:$i] :  ((v1_xcmplx_0 I) =>  ( ( (G = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) 9))  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 D)) 54))  &  ( (I = (k1_polyeq_5 2 (k2_xcmplx_0 (k1_newton G 3) (k1_newton H 2))))  &  ( (E = (k1_polyeq_5 3 (k2_xcmplx_0 H I)))  &  (F = (k10_complex1 (k13_complex1 G E))) ) ) ) )  =>  ( (G = k6_numbers)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 C (k1_newton A 2))) (k3_xcmplx_0 B A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k6_xcmplx_0 (k2_xcmplx_0 E F) (k13_complex1 C 3))) )  &  ( (~  (A = (k8_complex1 (k11_complex1 (k10_complex1 (k13_complex1 (k2_xcmplx_0 E F) 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 E F) (k1_polyeq_5 2 3)) k7_complex1) 2))) )  &  (~  (A = (k11_complex1 (k11_complex1 (k10_complex1 (k13_complex1 (k2_xcmplx_0 E F) 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 E F) (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polyform,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k1_funct_1 C D) = (k2_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 B D))) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) D) |  ((k1_funct_1 B D) = (k4_xcmplx_0 (k1_funct_1 A (k2_xcmplx_0 D 1)))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k16_rvsum_1 C) = (k2_xcmplx_0 (k1_funct_1 A 1) (k1_funct_1 B (k3_finseq_1 C)))) ) ) ) ) ) ) ) ) ).
tt(t15_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((k3_polynom1 A B (k4_polynom1 A B C D) E) = (k1_algstr_0 B (k3_polynom1 A B C E) (k3_polynom1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t15_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((k1_polynom2 A D) = (k1_tarski C))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k3_polynom2 A D B E) = (k1_binop_1 (k4_group_1 B) (k1_funct_1 E C) (k1_recdef_1 D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (k4_finseq_2 3 k5_numbers)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_1 E) (k4_finseq_1 E)) &  ((v3_funct_2 F (k4_finseq_1 E) (k4_finseq_1 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 E) (k4_finseq_1 E))))) ) )  =>  (! [G:$i] :  ((m2_finseq_1 G (k4_finseq_2 3 k5_numbers)) =>  ( (G = (k1_partfun1 (k4_finseq_1 E) (k4_finseq_1 E) k5_numbers (k4_finseq_2 3 k5_numbers) F E))  =>  ((k7_polynom3 A B C D G) = (k1_partfun1 (k4_finseq_1 E) (k4_finseq_1 E) k5_numbers (u1_struct_0 A) F (k7_polynom3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k1_algseq_1 A (k1_polynom4 A B)) = (k1_algseq_1 A B)) ) ) ) ) ).
tt(t15_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A B k6_numbers) (k10_polynom3 A))) ) ) ) ).
tt(t15_polynom6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  => (r2_quofield (k11_polynom1 A (k11_polynom1 B C)) (k11_polynom1 (k10_ordinal2 A B) C))) ) ) ) ) ) ).
tt(t15_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( ((k2_polynom1 (k15_pre_poly A) B C) = k1_xboole_0)  |  ((k2_polynom1 (k15_pre_poly A) B C) = (k6_domain_1 (k15_pre_poly A) (k16_pre_poly A))) ) ) ) ) ) ) ).
tt(t15_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_polynom8 A B (k4_xcmplx_0 1)) = (k11_algstr_0 A B)) ) ) ) ) ).
tt(t15_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((k3_termord A B C (k1_polyred A E C D)) = (k11_pre_poly A E (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 1 C)) )  |  ( (~ (v1_abian B))  &  (~ (v1_abian C)) ) )  =>  ((k3_xcmplx_0 (k1_power B A) (k1_power C A)) = (k1_power (k4_nat_1 B C) (k1_newton A (k2_nat_1 B C)))) ) ) ) ) ) ) ) ).
tt(t15_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  (! [F:$i] :  ((r2_hidden F (k1_relset_1 k5_numbers (k1_msualg_1 B D))) => (r2_hidden (k1_funct_1 E F) (k4_card_3 (k9_pralg_2 A B (k7_partfun1 (u1_struct_0 B) (k1_msualg_1 B D) F) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v6_trees_3 E)) ) )  =>  (~  ((r2_hidden (k12_finseq_1 k5_numbers D) (k9_xtuple_0 A)) &  ( (A = (k4_trees_4 C E))  &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  (~  ( ((k7_trees_2 A (k12_finseq_1 k5_numbers D) B) = (k4_trees_4 C F))  &  ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  ( ((k1_funct_1 F (k2_nat_1 D 1)) = B)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k4_finseq_1 E)) =>  ( (G = (k2_nat_1 D 1))  |  ((k1_funct_1 F G) = (k1_funct_1 E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pre_ff,ax, ( ((k3_pre_ff k6_numbers) = k6_numbers)  &  ( ((k3_pre_ff 1) = 1)  &  (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k3_pre_ff (k4_nat_1 2 A)) = (k3_pre_ff A))  &  ((k3_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1)) = (k2_nat_1 (k3_pre_ff A) (k3_pre_ff (k1_nat_1 A 1)))) ) ) ) ) ) ).
tt(t15_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A B C)) (k1_prelamb A (k1_prelamb A D B) (k1_prelamb A D C)))) ) ) ) ) ) ) ) ).
tt(t15_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  (! [D:$i] :  ((r1_tarski D C) => (r2_hidden D (k4_partfun1 A B))) ) ) ) ) ) ).
tt(t15_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ((r1_xxreal_0 2 B) & (r1_xxreal_0 A (k1_newton A B))) ) ) ) ) ) ) ) ).
tt(t15_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc D A) & (r1_tarski B D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  <=>  ((r1_tarski B (k9_setfam_1 A)) &  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r1_tarski (k10_xtuple_0 C) B) => (r2_hidden (k3_prob_1 A C) B)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) => (r2_hidden (k3_subset_1 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t15_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) => (r1_xxreal_0 (k9_real_1 (k7_real_1 (k1_seq_1 E C) (k1_seq_1 E D)) 1) (k1_seq_1 E (k5_prob_1 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_kurato_0 A (k2_prob_3 A B)) = (k1_kurato_0 A B)) ) ) ) ).
tt(t15_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_3 A B) B)) ) ) ) ).
tt(t15_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) (k6_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A C)))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t15_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_projdes1 A B C D E))  &  ((r1_collsp A E B F) &  ( (~  (B = F) )  & (r1_projdes1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (~  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~ (r5_projpl_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v8_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) &  ((r1_incsp_1 A B C) &  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A B E) &  ((r1_incsp_1 A B F) & (r2_zfmisc_1 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E F) K) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F G H) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E H I) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C H) O) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E J) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B F I) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C I J) Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F J D) R) & (r1_incsp_1 A D O)) ) ) ) ) ) ) )  =>  ((r1_incsp_1 A B K) |  ((r1_incsp_1 A B L) |  ((r1_incsp_1 A C M) |  ((r1_incsp_1 A C L) |  ((r1_incsp_1 A C N) |  ((r1_projred2 A K M L) |  ( (B = C)  |  ( (C = D)  |  ( (K = N)  |  ((k3_relat_1 (k1_projred1 A K L B) (k1_projred1 A L M C)) = (k3_relat_1 (k1_projred1 A K N D) (k1_projred1 A N M C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_prvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 A)) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 A)) =>  ((k8_prvect_1 A (k3_funct_2 (k4_card_3 A) (k4_card_3 A) (k11_prvect_1 A B) C) D) = (k3_funct_2 (k1_funct_1 A D) (k1_funct_1 A D) (k10_prvect_1 A B D) (k8_prvect_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 C D E) = (k10_finseq_1 D E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_prvect_3 A B))) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C (k3_rlvect_1 (k7_prvect_3 A B) D E)) = (k3_rlvect_1 (k14_prvect_2 (k10_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C D) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C (k1_rlvect_1 (k7_prvect_3 A B) D E)) = (k1_rlvect_1 (k14_prvect_2 (k10_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C D) E)) ) ) ) )  &  ( ((k4_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) = (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C (k4_struct_0 (k7_prvect_3 A B))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  ((k1_normsp_0 (k14_prvect_2 (k10_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) C D)) = (k1_normsp_0 (k7_prvect_3 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) => (v1_comseq_2 B)) ) )  <=>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) => (v5_measure6 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(t15_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_eqrel_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((r1_tarski C (k2_relset_1 C D)) & (v2_funct_1 D))  => (m2_pua2mss1 D B)) ) ) ) ) ) ) ) ) ).
tt(t15_pythtrip,ax, ( (~ (v2_pythtrip (k8_domain_1 k5_numbers 3 4 5)))  &  ((v3_pythtrip (k8_domain_1 k5_numbers 3 4 5)) & (m1_pythtrip (k8_domain_1 k5_numbers 3 4 5))) ) ).
tt(t15_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A C D)) => (r6_pboole A C D)) ) ) ) ) ) ) ) ).
tt(t15_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A B)) (k3_finseq_1 (k11_qc_lang1 A (k19_qc_lang1 A B)))))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A B)) (k3_finseq_1 (k11_qc_lang1 A (k20_qc_lang1 A B))))) ) ) ) ) ) ) ).
tt(t15_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k6_qc_lang2 A D F B) = (k6_qc_lang2 A E G C))  =>  ( (D = E)  &  ( (F = G)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang2 B A) =>  ((k24_qc_lang1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A (k12_qc_lang2 A B)) (k24_qc_lang1 A (k11_qc_lang2 A B)))) ) ) ) ) ) ).
tt(t15_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (~  ((r2_xboole_0 C D) &  ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D) = (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v18_quantal1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k6_algstr_0 A C D) B) => (r3_lattices A (k6_algstr_0 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t15_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k27_quaterni k2_quatern2 A) = A) ) ) ).
tt(t15_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((m1_subset_1 A k1_numbers) =>  ((k31_quaterni (k27_quaterni A B)) = (k27_quaterni (k31_quaterni A) (k31_quaterni B))) ) ) ) ) ) ).
tt(t15_quaterni,ax, ((k10_quaterni k12_quaterni k12_quaterni) = (k1_real_1 1)) ).
tt(t15_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_quin_1 A B C)) &  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) = k6_numbers)  &  ( (~  (D = (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))) )  &  (~  (D = (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k9_quofield A (k8_quofield A B C) D) = (k8_quofield A (k9_quofield A B D) (k9_quofield A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ((r2_hidden A (k2_finseq_1 B)) => (m2_subset_1 (k1_funct_1 D A) k4_numbers (k3_radix_1 C))) ) ) ) ) ) ) ) ) ).
tt(t15_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_radix_1 A B C) =>  (B = (k3_radix_2 A C (k5_radix_2 C A B))) ) ) ) ) ) ) ) ) ).
tt(t15_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 2 A) & (r2_hidden B (k3_radix_1 A)))  => (r2_hidden (k2_xcmplx_0 (k6_radix_3 B A) (k5_radix_3 C A)) (k4_radix_3 A))) ) ) ) ) ) ) ).
tt(t15_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 2 B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k3_radix_1 B)))  =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E (k3_radix_1 B)))  =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 A)) &  ( (~  ( ((k4_radix_1 F B A C) = (k4_radix_1 F B A E))  &  ((k4_radix_1 F B A D) = k6_numbers) ) )  &  (~  ( ((k4_radix_1 F B A D) = (k4_radix_1 F B A E))  &  ((k4_radix_1 F B A C) = k6_numbers) ) ) ) ) ) ) )  =>  ((k2_xcmplx_0 (k8_radix_1 A B E) (k8_radix_1 A B (k10_radix_1 B A k6_numbers))) = (k2_xcmplx_0 (k8_radix_1 A B C) (k8_radix_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 B)))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 2 B) &  ((r1_radix_6 A B C) &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B D)) (k3_xcmplx_0 E C)) (k4_xcmplx_0 C)))  &  (~ (r1_xxreal_0 C (k6_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B D)) (k3_xcmplx_0 E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_finset_1 C))  =>  (! [D:$i] :  ((m1_eqrel_1 D (k3_group_10 C A)) =>  (~  ( ((k1_card_1 D) = B)  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (~  ( (~ (v1_finset_1 E))  & (r1_ramsey_1 C A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ((v2_prob_1 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k3_prob_1 A B) = (k3_funct_2 k5_numbers (k9_setfam_1 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (? [E:$i] :  ((m2_finseq_1 E k1_numbers) &  (? [F:$i] :  ((m2_finseq_1 F C) &  ( ((k3_finseq_1 E) = (k5_card_1 C))  &  ((v2_funct_1 F) &  ( ((k2_relset_1 C F) = C)  &  ( ((k3_finseq_1 F) = (k5_card_1 C))  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 E)) =>  ((k1_seq_1 E G) = (k11_binop_2 (k1_seq_1 D (k1_funct_1 F G)) (k1_seq_1 B (k1_tarski (k1_funct_1 F G))))) ) ) )  &  ((k1_mesfunc6 A (k1_random_1 A) (k2_prob_4 A (k1_random_1 A) B) (k2_partfun1 A k1_numbers D C)) = (k18_rvsum_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  ((v2_funct_1 D) =>  ((k1_ranknull A C B D) = (k1_vectsp_4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (A = (k6_real_1 (k2_rat_1 A) (k1_rat_1 A)))  &  ( (A = (k4_real_1 (k2_rat_1 A) (k2_real_1 (k1_rat_1 A))))  &  (A = (k8_real_1 (k2_real_1 (k1_rat_1 A)) (k2_rat_1 A))) ) ) ) ) ).
tt(t15_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ratfunc1 A B C D) => (r1_polynom5 A (k5_vfunct_1 k5_numbers A (k8_polynom3 A B C)) D)) ) ) ) ) ) ) ) ) ).
tt(t15_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (~  ((v1_rcomp_1 A) &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_tarski (k1_rcomp_1 B C) A)) ) ) ) )  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  (A = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r2_hidden (k4_seq_4 A) A) =>  ((r2_hidden (k5_seq_4 A) A) |  (A = (k4_rcomp_1 (k5_seq_4 A) (k4_seq_4 A))) ) ) ) ) ).
tt(t15_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 (k1_seq_1 (k1_real_3 C D) A) (k1_seq_1 (k1_real_3 C D) B)) &  (~  ((k1_seq_1 (k1_real_3 C D) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k4_real_lat A) B (k1_funcsdom A k1_numbers (k5_real_lat A) C B)) B)) ) ) ) ) ) ).
tt(t15_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  <=>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k7_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k7_real_ns1 A)))))) ) ) ) ) ) ).
tt(t15_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k8_group_1 A B C)) = (k8_group_1 A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t15_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B (k4_struct_0 A)) = B) ) ) ) ) ).
tt(t15_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 A)) & (m2_finseq_1 E (k1_zfmisc_1 A))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ( ((r2_hidden C (k1_funct_1 E 1)) =>  ((k1_seq_1 (k3_rearran1 B A E D) C) = (k1_seq_1 (k20_rfunct_3 B D B) 1)) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r2_hidden C (k6_subset_1 (k1_funct_1 E (k2_nat_1 F 1)) (k1_funct_1 E F))))  =>  ((r1_xxreal_0 (k3_finseq_1 E) F) |  ((k1_seq_1 (k3_rearran1 B A E D) C) = (k1_seq_1 (k20_rfunct_3 B D B) (k2_nat_1 F 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden (k4_tarski A B) C) =>  ((r2_hidden A (k1_relat_1 C)) & (r2_hidden B (k1_relat_1 C))) ) ) ) ) ) ).
tt(t15_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski (k4_relat_1 C) D) =>  ((r1_tarski C (k1_relset_1 A D)) & (r1_tarski C (k2_relset_1 B D))) ) ) ) ) ) ) ).
tt(t15_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (B = (k3_tarski (a_2_0_relset_2 A B))) ) ) ) ) ).
tt(t15_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k4_finseq_1 (k1_finseq_6 A C B)) = (k4_finseq_1 C)) ) ) ) ) ) ) ).
tt(t15_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) A) => (r1_rewrite1 A B C)) ) ) ) ) ).
tt(t15_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ((r1_rewrite2 A B C D) => (r2_rewrite2 A B (k1_flang_1 A (k1_flang_1 A E C) F) (k1_flang_1 A (k1_flang_1 A E D) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((l1_rewrite3 E A) =>  ((r1_rewrite3 A E B C D) =>  ((r1_struct_0 E B) &  ((r2_hidden C A) &  ((r1_struct_0 E D) &  ((r2_hidden B (k9_xtuple_0 (k9_xtuple_0 (u1_rewrite3 A E)))) &  ((r2_hidden C (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 A E)))) & (r2_hidden D (k10_xtuple_0 (u1_rewrite3 A E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_classes1 A B) =>  ((k4_rfinseq2 A) = (k4_rfinseq2 B)) ) ) ) ) ) ).
tt(t15_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_rfinseq k1_numbers B (k3_rfinseq A)) = (k3_rfinseq (k2_rfinseq k1_numbers B A))) ) ) ) ) ).
tt(t15_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k45_valued_1 (k18_valued_1 A B) (k18_valued_1 A C)) = (k18_valued_1 A (k45_valued_1 B C))) ) ) ) ) ) ) ).
tt(t15_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ((r1_tarski (k2_relset_1 B D) (k1_relset_1 B (k2_partfun1 B k1_numbers C A))) => (r2_relset_1 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers B D (k2_partfun1 B k1_numbers C A))) (k8_funct_2 k5_numbers k1_numbers B D (k2_partfun1 B k1_numbers (k56_valued_1 B k1_numbers C) A)))) ) ) ) ) ) ) ) ).
tt(t15_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v2_binop_1 (k13_rfunct_3 A) (k3_rfunct_3 A k1_numbers))) ) ).
tt(t15_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((r1_rfunct_4 C E) & (r1_rfunct_4 D E))  =>  ( ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 k6_numbers B)) )  &  (~  ((r1_xxreal_0 k6_numbers A) &  (~ (r1_xxreal_0 B k6_numbers)) ) ) )  | (r1_rfunct_4 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A) (k26_valued_1 k1_numbers k1_numbers D B)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (v2_seq_2 B))  => (r1_xxreal_0 (k7_real_1 (k2_rinfsup1 A) (k2_rinfsup1 B)) (k2_rinfsup1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ).
tt(t15_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k7_numbers k5_numbers k1_numbers A B) & (v7_mesfunc5 A))  =>  ((v2_comseq_2 B) &  ((k2_mesfunc5 A) = (k2_seq_2 B)) ) ) ) ) ) ) ).
tt(t15_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) (k5_struct_0 A)) = (k5_struct_0 (k2_ring_1 A B))) ) ) ) ) ).
tt(t15_ringcat1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_ringcat1 A B) & (r2_ringcat1 A C))  =>  (B = C) ) ) ) ) ).
tt(t15_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  ((r1_tarski B C) &  ( ((k1_rlvect_3 A C) = A)  &  (! [D:$i] :  ( ((v1_rlvect_3 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski B D) &  ((r1_tarski D C) &  ((k1_rlvect_3 A D) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (? [D:$i] :  ((m2_rlvect_2 D B C) &  ( ((k6_rlvect_2 B D) = (k1_rlvect_1 B (k2_rlvect_2 B C) A))  &  ( ((k3_rlaffin1 B D) = (k8_real_1 A (k5_card_1 C)))  &  (D = (k1_funct_4 (k4_rlvect_2 B) (k8_funcop_1 k1_numbers C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  ( ((k8_matrix13 k2_vectsp_1 C) = A)  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [E:$i] :  ((m2_rlaffin3 E (k15_euclid A) D) => (m2_rlaffin3 (k4_finseqop (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) E (k3_matrtop1 A B C)) (k15_euclid B) (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B C) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (D = B)  =>  ((k4_algstr_0 A B) = (k4_algstr_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((k2_rlsub_2 A B (k2_rlsub_2 A C D)) = (k2_rlsub_2 A (k2_rlsub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t15_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k1_numbers))  =>  ((k9_subset_1 (u1_struct_0 A) (k1_convex1 A B D) (k1_convex1 A C D)) = (k1_convex1 A (k9_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t15_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_algstr_0 A B B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t15_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k7_subset_1 (u1_struct_0 A) C B)) = (k5_algstr_0 A (k2_rlvect_2 A (k4_subset_1 (u1_struct_0 A) C B)) (k2_rlvect_2 A B))) ) ) ) ) ) ) ).
tt(t15_rlvect_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A C) => (r1_struct_0 (k1_rlvect_3 B C) A)) ) ) ) ) ) ).
tt(t15_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rlvect_3 A (k8_domain_1 (u1_struct_0 A) B C D)) B) &  ((r1_struct_0 (k1_rlvect_3 A (k8_domain_1 (u1_struct_0 A) B C D)) C) & (r1_struct_0 (k1_rlvect_3 A (k8_domain_1 (u1_struct_0 A) B C D)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_rlvect_3 C A) & (r1_tarski C (u1_struct_0 B)))  =>  ((v1_rlvect_3 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t15_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_rlvect_x A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k2_rlvect_x A B) (k2_rlvect_x A C)))) ) ) ) ) ) ).
tt(t15_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (E = C)  =>  ((k4_algstr_0 B C) = (k4_algstr_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((k2_rmod_3 A B C (k2_rmod_3 A B D E)) = (k2_rmod_3 A B (k2_rmod_3 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((k1_rmod_4 A B (k5_subset_1 (u1_struct_0 B) C D)) = (k3_rlvect_1 B (k1_rmod_4 A B (k7_subset_1 (u1_struct_0 B) C D)) (k1_rmod_4 A B (k7_subset_1 (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ).
tt(t15_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_robbins1 A B (k3_robbins1 A B)) = (k7_robbins1 A)) ) ) ) ) ).
tt(t15_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A C D)))) D)) = (k3_robbins1 A (k1_lattices A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  & (v10_lattices A))  => (v10_lattices B)) ) ) ) ) ).
tt(t15_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  ( ( (A = (k6_subset_1 3 1))  &  (B = 2) )  =>  ( ((k13_lattice3 k1_robbins4 A B) = 3)  &  ((k12_lattice3 k1_robbins4 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t15_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v4_roughs_1 B A))  <=>  ((k3_roughs_1 A B) = B) ) ) ) ) ) ).
tt(t15_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k1_rpr_1 A (k2_subset_1 A)) = 1) ) ) ).
tt(t15_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B)) = (k4_struct_0 (k9_rsspace4 A B))) ) ) ) ) ).
tt(t15_rsspace,ax, (! [A:$i] :  ((l1_rlvect_1 A) =>  ( ( (~ (v2_struct_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))))  &  ((v13_algstr_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v2_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v3_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v4_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v5_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v6_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v7_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v8_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) & (l1_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_struct_0 B C) => (r1_struct_0 B (k1_rlvect_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t15_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((k2_rusub_2 A B (k2_rusub_2 A C D)) = (k2_rusub_2 A (k2_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t15_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_rusub_3 C A) =>  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t15_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k2_nat_1 (k1_rusub_4 (k1_rusub_2 A B C)) (k1_rusub_4 (k2_rusub_2 A B C))) = (k2_nat_1 (k1_rusub_4 B) (k1_rusub_4 C))) ) ) ) ) ) ) ).
tt(t15_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_struct_0 A) (k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(t15_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k4_rvsum_1 A (k4_rvsum_1 B C)) = (k4_rvsum_1 (k4_rvsum_1 A B) C)) ) ) ) ) ) ) ).
tt(t15_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  ((k8_rvsum_2 A B (k5_finseq_2 k2_numbers A k5_complex1)) = B) ) ) ) ) ).
tt(t15_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k2_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 k6_numbers)) = C)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ( (~  (E = (k10_ami_3 k6_numbers)) )  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 F (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 G (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_xxreal_0 D C) &  ((r1_tarski E A) &  ((r1_tarski E B) &  ( (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A F H)) (k9_xtuple_0 E)) & (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B G H)) (k9_xtuple_0 E))) ) )  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A F D) (k4_struct_0 k1_scmfsa_2)) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B G D) (k4_struct_0 k1_scmfsa_2)))  &  ((k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 A F D) (k2_xboole_0 (k4_sf_mastr E) (k2_sf_mastr E))) = (k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 B G D) (k2_xboole_0 (k4_sf_mastr E) (k2_sf_mastr E)))) ) ) ) ) )  =>  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A F C) (k4_struct_0 k1_scmfsa_2)) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 B G C) (k4_struct_0 k1_scmfsa_2)))  &  ((k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 A F C) (k2_xboole_0 (k4_sf_mastr E) (k2_sf_mastr E))) = (k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 B G C) (k2_xboole_0 (k4_sf_mastr E) (k2_sf_mastr E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k12_scmfsa_2 A B)) = (k12_finseq_1 k5_numbers A)) ) ) ) ) ).
tt(t15_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ((r1_xxreal_0 (k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) 8) => (m1_subset_1 A (u1_compos_1 k1_ami_3))) ) ) ).
tt(t15_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ((m1_scmfsa_2 I) =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k16_scmfsa_2 H I))  & (r2_hidden H (k9_xtuple_0 B)))  =>  ((k3_finseq_1 (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G) I)) = (k3_finseq_1 (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ( ((k1_funct_1 A C) = (k2_compos_1 k1_scmfsa_2))  |  ((k1_funct_1 (k3_scmfsa6a A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( ((r1_tarski C B) & (r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) A))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 B A)) &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) A D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~ (r3_scmfsa7b (k15_scmfsa_2 B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa8a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k5_card_1 (k1_scmfsa8a A)) = 1) ) ) ).
tt(t15_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b D B A) & (r6_scmfsa7b D B A))  =>  ( ((k1_funct_1 B E) = k6_numbers)  |  ((r5_scmfsa7b (k1_scmfsa8b E C D) B A) & (r6_scmfsa7b (k1_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r5_scmfsa7b C B A) => (r2_hidden k6_numbers (k2_afinsq_1 C))) ) ) ) ) ) ) ).
tt(t15_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((r2_scmfsa9a A B C D) =>  ((r6_scmfsa7b (k1_scmfsa_9 C D) B A) & (r5_scmfsa7b (k1_scmfsa_9 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa_9 A B) 3) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 B) 5))) ) ) ) ) ).
tt(t15_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)))  =>  ( ((k2_scmfsa_m C) = (k4_scmfsa_2 A))  =>  ((r2_hidden (k4_scmfsa_2 B) C) | (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ).
tt(t15_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scm_halt B) & (v3_scm_halt B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) D) & (r1_tarski (k3_scmfsa6a B C) A))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k5_card_1 B))  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_funct_4 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D)) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)))))  &  ((r1_tarski (k6_compos_1 k1_scmfsa_2 C (k5_card_1 B)) A) &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A D (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1)) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r1_extpro_1 3 k1_scmfsa_2 A D) &  ( ((k8_extpro_1 3 k1_scmfsa_2 A D) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A B) C) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A B) D) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1))))))  &  ((v1_scmfsa6b C) =>  ((k1_funct_1 (k6_extpro_1 3 k1_scmfsa_2 A D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort A B C E) (k2_nat_1 D 1)) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort A B C E) D) B C E) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k6_scmpds_2 B A)) = 3) ) ) ) ) ).
tt(t15_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  (! [J:$i] :  ((v1_int_1 J) =>  (! [K:$i] :  ((v1_int_1 K) =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k7_scmpds_2 I J K))  &  ( (H = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A E G)))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 H K))) )  =>  ( (K = 1)  |  ( ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) I) J)) = k6_numbers)  <=>  ((k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) I) J)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmpds_4 (k2_scmpds_4 A C) B) = (k2_scmpds_4 A (k3_scmpds_4 C B))) ) ) ) ) ) ) ).
tt(t15_scmpds_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((k1_funct_1 (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_1 B A)) ) ) ) ) ).
tt(t15_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 k1_scmpds_2)) &  ((v1_scmpds_5 C) & (m1_subset_1 C (u1_compos_1 k1_scmpds_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_4 C D) B A) E) = (k1_funct_1 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 C B)) A) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 C) A) &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 A B) D) | (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A B D)) (k2_afinsq_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 G (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 G 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ( (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 G I) = (k1_funct_1 B I)) ) ) )  &  ((k1_funct_1 G D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E))) |  ( ((k1_funct_1 (k6_scmpds_4 C G H) D) = (k1_funct_1 G D))  &  ( (~ (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C G H) (k2_scmpds_2 (k1_funct_1 B D) E)) (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E))))  &  ((r1_scmpds_6 C G H) &  ((r2_scmpds_6 C G H) &  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 (k6_scmpds_4 C G H) I) = (k1_funct_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k1_scmpds_8 D E C) B A) & (r2_scmpds_6 (k1_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k1_amistd_1 2 k1_scmpds_2 B (k8_scmpds_2 A C D)) = (k2_tarski (k1_ordinal1 B) (k1_int_2 (k2_xcmplx_0 D B)))) ) ) ) ) ) ) ) ) ).
tt(t15_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 C B) &  (A = (k4_funct_4 (k1_scmp_gcd 9) (k1_scmp_gcd 10) B C)) ) )  => (v4_extpro_1 (k8_memstr_0 2 k1_scmpds_2 A) 2 k1_scmpds_2 k4_scmp_gcd)) ) ) ) ) ) ) ).
tt(t15_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k8_scmring2 A C) D) (k4_struct_0 (k1_scmring2 A))) = C)  &  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k8_scmring2 A C) D) B) = (k2_scmring2 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 3)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 A))))  =>  (~  (B = (k5_scmring2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k1_card_1 (a_1_1_scmyciel A)) = (k4_nat_1 2 (k5_card_1 (k1_scmyciel A)))) ) ) ).
tt(t15_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers)  =>  ((k1_funct_1 (k6_scmpds_4 (k4_scpinvar D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_scpisort,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 7 A) => (v2_scmpds_4 (k1_scpisort B A))) ) ) ) ) ).
tt(t15_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 7 C) &  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k4_numbers) =>  (~  ( ((k3_finseq_1 E) = D)  &  ((r1_scpisort E B C) &  ( ((k3_finseq_1 F) = D)  &  ((r1_scpisort F (k6_scmpds_4 (k2_scpqsort D C) B A) C) &  ((r2_classes1 E F) & (r3_graph_2 F 1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  ((r2_analoaf A B C F G) &  ((r2_analoaf A D E H I) &  ( (~  (F = G) )  &  ( (~  (H = I) )  & (r2_analoaf A F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A B) C) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A C) (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t15_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  =>  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k8_real_1 (k2_seq_2 A) (k2_seq_2 B))) ) ) ) ) ) ).
tt(t15_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 (k56_valued_1 k5_numbers k1_numbers A)) &  ((k2_seq_2 (k56_valued_1 k5_numbers k1_numbers A)) = k6_numbers) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) ) ) ) ).
tt(t15_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k3_seqfunc A (k5_seqfunc A B)) (k5_seqfunc A (k3_seqfunc A B)))) ) ) ) ).
tt(t15_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers B C) A) = (k3_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers B A) (k1_valued_0 k1_numbers C A))) ) ) ) ) ) ) ).
tt(t15_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_series_1 A) = (k7_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) B) (k4_series_1 (k1_valued_0 k1_numbers A (k2_nat_1 B 1))))) ) ) ) ) ) ).
tt(t15_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 3)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k4_nat_1 (k13_newton B 2) (k13_newton (k2_nat_1 B 1) 2)) 4)) ) ) ) ) ) ).
tt(t15_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k8_real_1 3 (k1_power 3 (k3_xcmplx_0 (k3_xcmplx_0 A B) C))) (k2_xcmplx_0 (k2_xcmplx_0 A B) C))) ) ) ) ) ) ).
tt(t15_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k1_newton (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 2) B) (k13_newton 2 B)) 2)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 (k7_xcmplx_0 (k1_newton (k7_xcmplx_0 1 4) B) 3)) (k7_xcmplx_0 (k13_newton 4 (k2_nat_1 B 1)) 3)) (k4_nat_1 2 B)) 3)) ) ) ) ) ) ).
tt(t15_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~ (r1_xxreal_0 (k8_complex1 (k8_complex1 (k8_complex1 (k13_complex1 A (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) (k13_complex1 B (k2_xcmplx_0 (k2_xcmplx_0 A B) D))) (k13_complex1 D (k2_xcmplx_0 (k2_xcmplx_0 B D) C))) (k13_complex1 C (k2_xcmplx_0 (k2_xcmplx_0 A D) C))) 1)) ) ) ) ) ) ) ) ) ).
tt(t15_setfam_1,ax, (! [A:$i] : (r1_setfam_1 k1_xboole_0 A)) ).
tt(t15_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 C) = k5_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k1_setfam_1 (a_3_3_setlim_1 A B D))) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) ) ) ) ).
tt(t15_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k9_setlim_2 A C B) = (k2_setlim_2 A (k7_setlim_2 A C B) (k8_setlim_2 A C B))) ) ) ) ) ) ).
tt(t15_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k5_binop_1 A B (k4_binop_1 A B) C) = C)  &  ((k5_binop_1 A B C (k4_binop_1 A B)) = C) ) ) ) ) ) ) ) ) ).
tt(t15_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) &  ((v2_binop_1 E B) &  ((v1_setwiseo E B) &  ((v1_finseqop E B) & (r6_binop_1 B F E)) ) ) )  =>  ((k5_binop_1 B F (k7_setwiseo A B E C G) D) = (k7_setwiseo A B E C (k9_funcop_1 B A F G D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) &  ((v1_sfmastr1 D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2))) )  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A) & (r5_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A)) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa6a D C) B A) E) = (k18_scmfsa_2 (k1_scmfsa6b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((v7_amistd_1 D 3 k1_scmfsa_2) => (r1_sfmastr2 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t15_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ((k18_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D F A) k6_numbers) E) = (k18_scmfsa_2 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_sf_mastr,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_sf_mastr (k11_scmfsa_2 A)) = k1_xboole_0) ) ) ).
tt(t15_sgraph1,ax, (! [A:$i] :  ((k2_sgraph1 (k1_tarski A)) = k1_xboole_0) ) ).
tt(t15_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  => (v2_sheffer1 A)) ) ).
tt(t15_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B (k5_sheffer1 A D C))) = B) ) ) ) ) ) ) ) ) ).
tt(t15_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_xboole_0 (k4_simplex0 A)) <=> (v4_simplex0 A)) ) ) ).
tt(t15_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) &  ( (~ (v5_simplex0 B))  & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ( ((v3_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( (~ (v1_xboole_0 D))  => (r2_hidden (k1_funct_1 C D) (k3_convex1 A (k1_simplex1 A B D)))) ) )  => (m1_simplex1 (k10_simplex0 (u1_struct_0 A) B C) A B)) ) ) ) ) ) ) ) ).
tt(t15_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ( ((v6_tbsp_1 C (k14_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))))  =>  (! [D:$i] :  ( ((v6_tbsp_1 D (k14_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))))  =>  ( ( (D = (k3_convex1 (k15_euclid A) B))  &  (C = B) )  =>  ((k3_tbsp_1 (k14_euclid A) C) = (k3_tbsp_1 (k14_euclid A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t15_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k1_seq_1 k4_sin_cos2 A) = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 k4_sin_cos2 A) k6_numbers))  &  ((k1_seq_1 k4_sin_cos2 k6_numbers) = 1) ) ) ) ) ).
tt(t15_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k5_binop_2 k7_complex1 A)) = (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A))) ) ) ).
tt(t15_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k20_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)) (k17_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2))))) ) ) ) ) ).
tt(t15_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  (~  ( ((k3_sin_cos4 (k8_real_1 2 A)) = (k10_real_1 (k8_real_1 (k4_sin_cos4 A) (k3_sin_cos4 A)) 2))  &  ((k3_sin_cos4 (k8_real_1 2 A)) = (k10_real_1 (k7_real_1 (k1_sin_cos4 A) (k2_sin_cos4 A)) 2)) ) ) ) ) ) ) ) ).
tt(t15_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 (k20_sin_cos A) k6_numbers)) ) ) ) ) ) ) ).
tt(t15_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 1 A) (k10_binop_2 1 A)) k6_numbers)) ) ) ) ) ).
tt(t15_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) (k6_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k3_xcmplx_0 (k1_sin_cos5 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k1_sin_cos5 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)))) ) ) ) ) ).
tt(t15_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k19_sin_cos A) = k6_numbers) )  =>  ((k1_seq_1 k29_sin_cos A) = (k1_sin_cos4 A)) ) ) ) ).
tt(t15_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k11_complex1 (k9_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos A)) C) (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos B)) C)) (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos (k8_complex1 A B))) C)) = (k8_nat_1 k2_numbers (k10_comseq_3 (k12_sin_cos A B C)) C)) ) ) ) ) ) ) ).
tt(t15_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid A) = (k18_euclid B))  <=> (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ).
tt(t15_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1))))) )  => (r2_hidden B (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t15_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v2_sppol_1 A) <=>  ((k6_pscomp_1 A) = (k8_pscomp_1 A)) ) ) ) ).
tt(t15_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_finseq_1 (k1_goboard1 A)) = (k4_finseq_1 A)) ) ) ).
tt(t15_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r2_hidden (k20_pscomp_1 A) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(t15_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t15_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k3_square_1 A) (k3_square_1 B))) ) ) ) ) ).
tt(t15_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((r1_stacks_1 A B) & (r1_stacks_1 A C))  => (r2_stacks_1 A B C)) ) ) ) ) ) ) ).
tt(t15_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (A = k6_numbers)  &  (B = k6_numbers) )  =>  ((v2_funct_2 C B) & (v1_stirl2_1 C A B)) ) ) ) ) ) ) ) ).
tt(t15_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [F:$i] :  ( ((v5_relat_1 F (k3_qc_lang1 A)) &  ((v3_card_1 F B) & (m2_finseq_1 F (k2_qc_lang1 A))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_substut1 A)) =>  (! [H:$i] :  ((m2_funct_2 H (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r1_valuat_1 A C (k39_substut1 A (k4_sublemma B A E F G)) D H) <=> (r1_sublemma A (k4_sublemma B A E F G) C (k1_sublemma A C H (k3_sublemma A (k4_sublemma B A E F G) C H)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k3_subset_1 A (k5_subset_1 A B C)) = (k4_subset_1 A (k9_subset_1 A B C) (k9_subset_1 A (k3_subset_1 A B) (k3_subset_1 A C)))) ) ) ) ) ) ).
tt(t15_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  (~  ((r2_hidden E (k4_substlat A B C D)) &  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden F C) &  ((r2_hidden G D) &  (E = (k2_xboole_0 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k20_substut1 A B) = (k20_substut1 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t15_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) =>  ((k7_cqc_sim1 A (k4_cqc_lang B A C D)) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A (k4_cqc_lang B A C D) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  ((k8_supinf_2 (k6_supinf_2 A)) = (k2_supinf_2 (k7_supinf_2 A))) ) ) ).
tt(t15_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_symsp_1 A B D C (k4_vectsp_1 A B F E)) = (k8_group_1 A F (k1_symsp_1 A B D C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k4_relat_1 A) (k4_relat_1 B))) ) ) ).
tt(t15_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  ( (B = (k2_tarski (k1_tarski A) (k10_eqrel_1 A)))  => (m2_taxonom1 B A)) ) ) ) ) ).
tt(t15_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v5_taxonom2 B A) & (m1_taxonom2 B A)) )  =>  ((v6_taxonom2 B A) =>  ((r2_hidden k1_xboole_0 B) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v4_taxonom2 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r2_hidden C D) &  ((r1_tarski D B) &  (! [E:$i] :  ( ((v4_taxonom2 E) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r2_hidden C E) &  ((r1_tarski E B) & (r1_tarski (k5_setfam_1 A D) (k5_setfam_1 A E))) )  =>  ((k5_setfam_1 A D) = (k5_setfam_1 A E)) ) ) ) ) )  => (m1_eqrel_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t15_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_seq_1 k24_sin_cos (k5_power k8_power A)) = A) ) ) ) ).
tt(t15_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (v2_series_1 (k4_sin_cos A))) ) ).
tt(t15_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k6_domain_1 (u1_struct_0 A) B))  => (v6_tbsp_1 C A)) ) ) ) ) ) ) ).
tt(t15_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  ((r2_analoaf (k2_tdgroup A) B C D D) =>  (B = C) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_tdgroup A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_tdgroup A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_tdgroup A))) =>  ( ((r2_analoaf (k2_tdgroup A) B C F G) & (r2_analoaf (k2_tdgroup A) D E F G))  => (r2_analoaf (k2_tdgroup A) B C D E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_tdgroup A))) & (r2_analoaf (k2_tdgroup A) B C D E)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_tdgroup A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_tdgroup A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_tdgroup A))) =>  ( ((r2_analoaf (k2_tdgroup A) B C E F) & (r2_analoaf (k2_tdgroup A) B D E G))  => (r2_analoaf (k2_tdgroup A) C D F G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) & (r2_analoaf (k2_tdgroup A) B D D C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_tdgroup A))) =>  ( ((r2_analoaf (k2_tdgroup A) B C C D) & (r2_analoaf (k2_tdgroup A) B E E D))  =>  (C = E) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_tdgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_tdgroup A))) =>  ((r2_analoaf (k2_tdgroup A) B C D E) => (r2_analoaf (k2_tdgroup A) B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v4_tops_1 (k2_struct_0 A) A)) ) ).
tt(t15_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)) (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t15_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v3_pre_topc B A)) ) ) ) ) ).
tt(t15_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r6_pboole A (k1_termord A B C D) (k1_termord A B D C)) & (r6_pboole A (k2_termord A B C D) (k2_termord A B D C))) ) ) ) ) ) ) ) ) ).
tt(t15_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = (u1_struct_0 A)) )  => (v2_tops_1 B A)) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t15_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_tex_2 (k1_tex_2 A B) A) <=> (v1_subset_1 (k6_domain_1 (u1_struct_0 A) B) (u1_struct_0 A))) ) ) ) ) ).
tt(t15_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ( ((v1_tex_3 B A) & (m1_pre_topc B A))  <=>  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t15_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v3_tex_4 B A)) ) ) ) ) ).
tt(t15_tietze,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  ( ((r1_tarski C D) & (r1_tietze D A B))  => (r1_tietze C A B)) ) ) ) ) ) ) ) ).
tt(t15_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_tsep_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ( (E = D)  &  (F = D) )  =>  (! [G:$i] :  ((m1_connsp_2 G B E) =>  (! [H:$i] :  ((m1_connsp_2 H C F) =>  (? [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k1_tsep_1 A B C)))) &  ((v3_pre_topc I (k1_tsep_1 A B C)) &  ((r2_hidden D I) & (r1_tarski I (k2_xboole_0 G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) => (m1_toler_1 (k2_tarski C D) A B)) ) ) ) ) ) ).
tt(t15_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k15_euclid B)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 (k15_euclid B)))))) )  =>  ( ((v5_pre_topc D C (k15_euclid B)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 (k15_euclid B)) E F) = (k1_rlvect_1 (k15_euclid B) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 (k15_euclid B)) D F) A)) ) ) )  => (v5_pre_topc E C (k15_euclid B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topalg_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_topmetr A B))) =>  (! [D:$i] :  ((m1_borsuk_2 D (k4_topmetr A B) C C) =>  ((u1_struct_0 (k5_topalg_1 (k4_topmetr A B) C)) = (k1_tarski (k6_eqrel_1 (k2_topalg_1 (k4_topmetr A B) C) (k2_topalg_1 (k4_topmetr A B) C) (k4_topalg_1 (k4_topmetr A B) C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t15_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v4_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  => (v4_pre_topc (k3_borsuk_1 A B C D) (k2_borsuk_1 A B))) ) ) ) ) ) ) ) ).
tt(t15_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_borsuk_6 A C D) & (r1_borsuk_6 B E F))  => (r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((r2_borsuk_3 A B) & (v1_connsp_2 A))  => (v1_connsp_2 B)) ) ) ) ) ).
tt(t15_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topalg_6 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  (! [D:$i] :  ((m1_borsuk_2 D A B B) => (r3_borsuk_2 A B B C D)) ) ) ) ) ) ) ) ).
tt(t15_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C E) &  ((r1_tarski E D) &  ((v1_topdim_1 (k2_tops_1 A E) A) & (r1_xxreal_0 (k2_topdim_1 A (k2_tops_1 A E)) (k5_real_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v3_topdim_1 A)) ) ) ).
tt(t15_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v5_waybel23 A) &  ((v3_topdim_1 A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v5_waybel23 B) &  ((v3_topdim_1 B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) ) ) )  =>  ( (~  ((v2_struct_0 A) & (v2_struct_0 B)) )  => (r1_xxreal_0 (k4_topdim_1 (k2_borsuk_1 A B)) (k1_xxreal_3 (k4_topdim_1 A) (k4_topdim_1 B)))) ) ) ) ) ).
tt(t15_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r1_topgen_1 A B C) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t15_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topgen_2 A) & (l1_pre_topc A)) ) )  =>  (? [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_pre_topc A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_pre_topc A))))) )  &  ( (B = (k2_relset_1 (u1_pre_topc A) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k3_funct_2 (u1_struct_0 A) (u1_pre_topc A) C D)) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden D E) => (r1_tarski (k3_funct_2 (u1_struct_0 A) (u1_pre_topc A) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v3_pre_topc (k2_limfunc1 A) k2_topgen_3) & (m1_subset_1 (k2_limfunc1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t15_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_prob_1 B A) =>  (B = (k7_setfam_1 A B)) ) ) ) ) ).
tt(t15_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden (k19_euclid A B) k1_topgen_5) <=>  (B = k6_numbers) ) ) ) ) ) ).
tt(t15_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 A) (k2_zfmisc_1 B C)) = (k2_group_2 A B C)) ) ) ) ) ) ) ).
tt(t15_topmetr3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((v1_topreal2 A) &  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) B) &  ((r1_tarski B A) &  ( (~  (B = (k8_jordan6 A)) )  &  (~  (B = (k9_jordan6 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v3_pre_topc B (k3_pcomps_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k9_metric_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreal1,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1))) = (k1_tarski (k19_euclid k6_numbers 1))) ).
tt(t15_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (D = (k11_finseq_1 A B C))  =>  ( (E = k6_numbers)  |  ((r1_xxreal_0 F (k1_nat_1 E 1)) |  ((k2_topreal1 2 D F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreal4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ( ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)))  &  (B = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k10_real_1 (k7_real_1 (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  |  ((v4_topreal1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))  &  ((r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)) &  ((r1_tarski (k3_topreal1 2 B) (k3_topreal1 2 A)) &  ( ((k3_topreal1 2 B) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 1 A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))))  &  ((k3_topreal1 2 B) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 2 A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_topreal2 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ((r2_hidden C A) &  (~  ((k17_euclid C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r2_hidden A (k2_rcomp_1 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)))) ) ) ) ) ).
tt(t15_topreal7,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k3_euclid (k8_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D))) = (k8_finseq_1 k1_numbers (k3_euclid (k8_rvsum_1 A B)) (k3_euclid (k8_rvsum_1 C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreal8,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C B))  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((k4_finseq_4 C A) = (k3_finseq_1 C))  =>  ((k5_finseq_4 (k8_finseq_1 B C D) A) = (k2_graph_2 B C 1 (k7_nat_d (k3_finseq_1 C) 1))) ) ) ) ) ) ) ) ) ).
tt(t15_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = D)  =>  ((k11_metric_1 (k14_euclid A) D B) = (k3_topreal9 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t15_topreala,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((r1_t_0topsp A B) <=> (r1_t_0topsp (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ).
tt(t15_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) &  ((k17_euclid A) = (k1_real_1 1)) )  =>  ((k18_euclid A) = k6_numbers) ) ) ) ).
tt(t15_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) )  =>  ((k14_rvsum_1 D (k2_funct_7 (k16_euclid B) A C)) = (k2_funct_7 (k16_euclid B) A (k3_xcmplx_0 (k1_funct_1 D A) C))) ) ) ) ) ) ) ) ).
tt(t15_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k4_toprns_1 A B (k1_toprns_1 A C D)) = (k4_toprns_1 A (k4_toprns_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t15_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k1_tops_1 A (k2_struct_0 A)) = (k2_struct_0 A)) ) ) ).
tt(t15_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) => (v1_tops_2 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t15_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) => (v2_tops_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t15_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ((v5_pre_topc C A (k3_pcomps_1 B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  =>  (~  ( (E = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C D))  &  (! [G:$i] :  ( ((v3_pre_topc G A) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden D G) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C G) (k9_metric_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  ( ((r2_hidden (k4_tarski (k4_tarski G H) (k4_tarski E F)) D) & (r2_hidden (k4_tarski (k4_tarski E F) (k4_tarski I J)) D))  =>  ( (E = F)  | (r2_hidden (k4_tarski (k4_tarski G H) (k4_tarski I J)) D)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) => (r2_hidden (k4_tarski (k4_tarski E E) (k4_tarski F G)) D)) ) ) ) ) )  &  ((r1_transgeo A B D) & (r1_transgeo A C D)) ) )  => (r1_transgeo A (k1_transgeo A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t15_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((r2_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) (k3_struct_0 (k4_topmetr A B)) (k1_partfun1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1)) (k3_treal_1 A B (k1_treal_1 A B) (k2_treal_1 A B)))) & (r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k3_struct_0 (k4_topmetr k6_numbers 1)) (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k3_treal_1 A B (k1_treal_1 A B) (k2_treal_1 A B)) (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1))))) ) ) ) ) ) ).
tt(t15_trees_1,ax, ((k1_trees_1 k1_xboole_0) = k1_xboole_0) ).
tt(t15_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (A = (k3_tarski (a_1_1_trees_2 A))) ) ) ).
tt(t15_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_trees_3 (k2_tarski A B)) <=>  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(t15_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v6_trees_3 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) & (v6_trees_3 D)) ) )  =>  ( ((k4_trees_4 A C) = (k4_trees_4 B D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ).
tt(t15_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  => (r2_hidden (k4_tarski k1_xboole_0 A) (k6_trees_9 A))) ) ).
tt(t15_trees_a,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_trees_2 C)) )  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D (k9_xtuple_0 (k7_trees_2 B A C))) &  ((r2_hidden D (a_2_4_trees_a A C)) &  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 C)) =>  (~  ( (D = (k8_finseq_1 k5_numbers A E))  &  ((k1_funct_1 (k7_trees_2 B A C) D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_pre_topc B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B D) & (r2_tsep_2 A C E))  =>  ((r2_tsep_1 A B C) <=> (r2_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_pre_topc B) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  => (v6_pre_topc (k2_tsep_1 A B C))) ) ) ) ) ) ) ).
tt(t15_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tsp_2 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) <=>  ( (C = (k3_tex_4 A C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) &  ((v3_pre_topc D B) &  (D = (k8_subset_1 (u1_struct_0 A) C (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_turing_1 (k2_finseq_4 k5_numbers C D) A B) => (r1_turing_1 A B C (k2_nat_1 (k2_nat_1 C D) 2))) ) ) ) ) ) ) ) ) ).
tt(t15_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k29_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith A B) C)))  &  ( ((k1_funct_1 k30_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 A) B) C)))  &  ( ((k1_funct_1 k31_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 A) (k9_margrel1 B)) C)))  &  ((k1_funct_1 k32_twoscomp (k11_finseq_1 A B C)) = (k9_margrel1 (k1_binarith (k1_binarith (k9_margrel1 A) (k9_margrel1 B)) (k9_margrel1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) => (m1_subset_1 (k6_unialg_2 A) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ).
tt(t15_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_unialg_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_unialg_2 A))) =>  (! [D:$i] :  ( ((v1_unialg_1 D) & (m1_unialg_2 D A))  =>  (! [E:$i] :  ( ((v1_unialg_1 E) & (m1_unialg_2 E A))  =>  ( ( (B = D)  &  (C = E) )  =>  ((r3_lattices (k12_unialg_2 A) B C) <=> (r1_tarski (u1_struct_0 D) (u1_struct_0 E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k2_xboole_0 (u1_struct_0 (k1_uniroots A)) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))) ) ) ).
tt(t15_uproots,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v3_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (B = (k11_pre_poly A C D))  =>  ((k3_uproots A B) = (k2_xcmplx_0 (k3_uproots A C) (k3_uproots A D))) ) ) ) ) ) ) ) ) ).
tt(t15_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers (k1_urysohn1 A)) =>  ( (~ (r1_xxreal_0 C B))  =>  ((r1_xxreal_0 B (k10_real_1 (k5_real_1 (k6_urysohn1 A C) 1) (k13_newton 2 A))) & (r1_xxreal_0 (k10_real_1 (k2_nat_1 (k6_urysohn1 A B) 1) (k13_newton 2 A)) C)) ) ) ) ) ) ) ) ).
tt(t15_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (C = (k1_integra2 A B))  &  (A = (k1_measure5 (k7_supinf_2 A) (k8_supinf_2 A))) )  =>  ( (C = (k1_measure5 (k7_supinf_2 C) (k8_supinf_2 C)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (D = (k7_supinf_2 A))  &  (E = (k8_supinf_2 A)) )  =>  ( ((k7_supinf_2 C) = (k8_real_1 B D))  &  ((k8_supinf_2 C) = (k8_real_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k3_urysohn1) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 E (k1_seq_1 (k6_urysohn3 A B C D) F)))  => (r2_hidden F (k4_urysohn3 k3_urysohn1 A (k3_urysohn3 A B C D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E (k6_cqc_lang A (k7_cqc_lang A D (k6_cqc_lang A D)))) C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_funct_1 A) & (v3_valued_0 A)) ) ) )  =>  (? [B:$i] :  ((v1_xreal_0 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t15_valued_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_funct_1 (k46_valued_1 A B C D E) F) = (k6_xcmplx_0 (k1_funct_1 D F) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k13_valued_1 (k13_valued_1 C A) B) = (k13_valued_1 C (k2_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t15_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (D = F) )  =>  ((r1_struct_0 D C) |  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) E F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 F) (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) (k4_struct_0 F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A C) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 F C C) &  ((v1_mod_2 F A C C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  ( ((v1_vectsp11 F A C) & (m1_vectsp11 B A C F))  <=>  ((k12_matrix_3 (k3_finseq_1 D) A (k3_matrlin2 A C C (k3_matrlin A C C F (k4_matrlin A C C (k3_struct_0 C) (k4_algstr_0 A B))) D E)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k4_vectsp_1 A C B D) = (k4_struct_0 C))  <=>  ( (B = (k4_struct_0 A))  |  (D = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k1_vectsp_2 A (k1_group_1 A) B) = (k11_algstr_0 A B))  &  ((k1_vectsp_2 A (k1_group_1 A) (k11_algstr_0 A B)) = B) ) ) ) ) ) ) ).
tt(t15_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (E = C)  =>  ((k4_algstr_0 B C) = (k4_algstr_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((m1_vectsp_4 (k2_vectsp_5 A B C D) A C) & (m1_vectsp_4 (k2_vectsp_5 A B C D) A D)) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((k4_vectsp_6 A B (k2_vectsp_6 A B)) = (k4_struct_0 B)) ) ) ) ) ).
tt(t15_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) C D)) = (k1_vectsp_5 A B (k1_vectsp_7 A B C) (k1_vectsp_7 A B D))) ) ) ) ) ) ) ) ) ).
tt(t15_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (r2_funct_2 (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A B)) (k6_vectsp_8 A B B (k6_partfun1 (u1_struct_0 B))) (k6_partfun1 (u1_struct_0 (k1_vectsp_8 A B))))) ) ) ) ).
tt(t15_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_7 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((r1_xboole_0 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (E = (k4_subset_1 (u1_struct_0 B) C D))  & (v1_vectsp_7 E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r2_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B (k2_vfunct_1 A B C D) E) (k2_vfunct_1 A B (k4_vfunct_1 A B C E) (k4_vfunct_1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B (k2_vfunct_1 A B C D) E) (k2_vfunct_1 A B (k2_vfunct_2 A B C E) (k2_vfunct_2 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_waybel_0 A B) = (a_2_1_waybel_0 A B)) ) ) ) ) ).
tt(t15_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_waybel10 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel10 A))) =>  ( (D = B)  =>  ((r1_orders_2 (k3_waybel10 A) C D) <=> (m1_yellow_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((v13_waybel_0 B A) & (v3_waybel11 B A)) ) ) ) ) ) ).
tt(t15_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)) B) = B) ) ) ) ) ).
tt(t15_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_orders_2 (k1_waybel_8 A)) &  ((v4_orders_2 (k1_waybel_8 A)) &  ((v5_orders_2 (k1_waybel_8 A)) &  ((v1_lattice3 (k1_waybel_8 A)) &  ((v1_yellow_0 (k1_waybel_8 A)) & (l1_orders_2 (k1_waybel_8 A))) ) ) ) ) ) ) ).
tt(t15_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k5_waybel_0 A (k2_yellow_0 A B)) = (k1_setfam_1 (a_2_0_waybel14 A B))) ) ) ) ) ).
tt(t15_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v6_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) =>  ((v3_orders_2 (k1_yellow_2 A A B)) &  ((v4_orders_2 (k1_yellow_2 A A B)) &  ((v5_orders_2 (k1_yellow_2 A A B)) &  ((v1_lattice3 (k1_yellow_2 A A B)) &  ((v2_lattice3 (k1_yellow_2 A A B)) &  ((v3_waybel_3 (k1_yellow_2 A A B)) & (l1_orders_2 (k1_yellow_2 A A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel16,ax, (! [A:$i] :  ((k4_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) = (k9_setfam_1 A)) ) ).
tt(t15_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) =>  ( ( (~  ((r1_yellow_0 A C) & (r1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) )  &  (~  ((v3_lattice3 A) &  ((v5_orders_2 A) &  ((v3_lattice3 B) & (v5_orders_2 B)) ) ) ) )  | (r1_orders_2 B (k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k1_yellow_0 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1)))))  =>  ((u1_pre_topc B) = (u1_pre_topc (k3_waybel18 A (k7_funcop_1 A k9_waybel18)))) ) ) ) ) ).
tt(t15_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v1_waybel19 C) & (m1_yellow_9 C A)) )  =>  (! [D:$i] :  ( ((v2_pre_topc D) &  ((v1_waybel19 D) & (m1_yellow_9 D B)) )  =>  ((k1_waybel19 (k3_yellow_3 A B)) = (u1_pre_topc (k2_borsuk_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t15_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (~  ((v3_lattice3 B) &  ((v18_waybel_0 C B A) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 A B D C) A B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_waybel_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E) (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) C (k5_waybel_0 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v3_orders_2 A))  => (v3_orders_2 B)) ) ) ) ) ).
tt(t15_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v6_yellow_0 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  => (r2_hidden (k1_yellow_0 A C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t15_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_waybel22 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_waybel22 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_waybel16 D (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) B) =>  ( ((k2_partfun1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B) D (k1_waybel22 A)) = C)  => (r2_funct_2 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) (u1_struct_0 B) D (k2_waybel22 A B C))) ) ) ) ) ) ) ) ).
tt(t15_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D))) )  => (r2_hidden (k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k7_relset_1 (u1_struct_0 B) (u1_struct_0 C) (k1_waybel24 A B C D E) F) = (k7_relset_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D (k6_yellow_3 A B (k6_domain_1 (u1_struct_0 A) E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((k1_waybel25 A) = (g1_waybel_9 (u1_struct_0 A) (u1_orders_2 A) (u1_pre_topc A))) ) ) ).
tt(t15_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) &  ((v6_pre_topc C) &  ((v1_waybel25 C) & (l1_pre_topc C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (v22_waybel_0 (k4_waybel26 C A B D) (k1_waybel26 B C) (k1_waybel26 A C))) ) ) ) ) ) ) ) ).
tt(t15_waybel27,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  ( ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  =>  ((k6_yellow_1 A B) = (k6_yellow_1 A C)) ) ) ) ) ) ) ).
tt(t15_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k6_yellow_6 A)) =>  ((r2_hidden (k4_tarski B C) (k3_waybel28 A)) <=>  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ((r2_hidden D (k6_yellow_6 A)) =>  (C = (k1_waybel11 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  ((k1_waybel29 A) = (g1_waybel_9 (u1_struct_0 A) (u1_orders_2 A) (u1_pre_topc A))) ) ) ).
tt(t15_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C)) = (k12_lattice3 A B (k1_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t15_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v3_pre_topc C A))  => (v3_pre_topc (k4_waybel_0 B D) B)) ) ) ) ) ) ) ) ) ).
tt(t15_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k4_waybel_0 A B)) =>  ((k2_waybel31 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t15_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v13_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) &  ( (C = (k6_setfam_1 (u1_struct_0 B) D))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E D) => (m2_connsp_2 E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow19 A (k2_struct_0 A) B)) (u1_struct_0 (k3_yellow19 A (k2_struct_0 A) B))) &  ((v1_waybel28 C (k3_yellow19 A (k2_struct_0 A) B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow19 A (k2_struct_0 A) B)) (u1_struct_0 (k3_yellow19 A (k2_struct_0 A) B)))))) ) )  => (r1_orders_2 A (k1_waybel_9 A (k2_waybel28 A (k3_yellow19 A (k2_struct_0 A) B) C)) (k1_waybel33 A (k2_struct_0 A) B))) ) ) ) ) ) ).
tt(t15_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((m1_subset_1 B (u1_struct_0 (k5_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (r2_hidden (u1_struct_0 B) A)) ) ) ) ) ) ) ).
tt(t15_waybel35,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k3_waybel35 A B D)) <=>  ((r2_hidden (k4_tarski C D) A) & (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t15_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  => (v1_waybel_3 (k3_yellow_0 A) A)) ) ).
tt(t15_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (u1_orders_2 A)) =>  ((k5_waybel_4 A C B) = (k5_waybel_0 A C)) ) ) ) ) ) ) ) ).
tt(t15_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_funcop_1 C)) )  =>  ( (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_relset_1 (k4_card_3 (k2_funct_6 C)) (k2_pralg_2 C))) => (r3_orders_2 A (k5_yellow_2 A (k1_funct_1 (k2_pralg_2 C) D)) B)) ) )  => (r3_orders_2 A (k4_yellow_2 A (k5_waybel_5 A (k2_pralg_2 C))) B)) ) ) ) ) ) ) ).
tt(t15_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  (C = (k2_yellow_0 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) &  ((v2_waybel_7 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C B) &  ((v13_waybel_0 C B) &  ((v2_waybel_7 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v24_waybel_0 A))  => (v24_waybel_0 B)) ) ) ) ) ).
tt(t15_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel_9 A B C))) =>  ( (D = E)  =>  ((k2_waybel_0 A B D) = (k2_waybel_0 A (k4_waybel_9 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v1_matrlin B A) &  ( (C = (k1_vectsp_9 A B))  &  (D = (k5_card_1 (u1_struct_0 A))) ) )  =>  ((k1_card_1 (u1_struct_0 B)) = (k1_newton D C)) ) ) ) ) ) ) ) ) ) ).
tt(t15_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C A) &  ((v5_pre_topc B A k3_topmetr) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = (k3_weierstr (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v1_relat_2 B) => (v1_relat_2 (k2_wellord1 B A))) ) ) ) ).
tt(t15_wellord2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_wellord2 A B) & (r2_wellord2 B C))  => (r2_wellord2 A C)) ) ) ) ).
tt(t15_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_nat_d A 1) =>  (A = 1) ) ) ) ).
tt(t15_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k2_xboole_0 A B) = k1_xboole_0)  =>  (A = k1_xboole_0) ) ) ) ).
tt(t15_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k4_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t15_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k6_xcmplx_0 A B) = k6_numbers)  =>  (A = B) ) ) ) ) ) ).
tt(t15_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k6_xcmplx_0 B C) (k6_xcmplx_0 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k3_xtuple_0 A B C) D) => (r2_hidden B (k12_xtuple_0 D))) ) ) ) ) ).
tt(t15_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k3_xxreal_0 A B) = A)  |  ((k3_xxreal_0 A B) = B) ) ) ) ) ) ).
tt(t15_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k4_xxreal_1 B C)) =>  ((r2_hidden A (k3_xxreal_1 B C)) &  (~  (A = C) ) ) ) ) ) ) ) ) ).
tt(t15_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) &  (~ (v1_xboole_0 A)) )  =>  ((v3_xxreal_2 A) => (r2_hidden (k2_xxreal_2 A) k1_numbers)) ) ) ).
tt(t15_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_3 A k6_numbers) = A) ) ) ).
tt(t15_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((r1_yellow_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k7_yellow_3 A B (k12_lattice3 A C D) (k12_lattice3 B E F)) = (k12_lattice3 (k3_yellow_3 A B) (k7_yellow_3 A B C E) (k7_yellow_3 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  => (v3_waybel_3 B)) ) ) ) ) ).
tt(t15_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_yellow_8 (a_3_0_yellow13 A B C) A C) &  ((v1_tops_2 (a_3_0_yellow13 A B C) A) & (m1_subset_1 (a_3_0_yellow13 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t15_yellow14,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((r5_waybel_1 A B) & (v2_yellow_0 A))  => (v2_yellow_0 B)) ) ) ) ) ).
tt(t15_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) => (m1_subset_1 (a_2_0_yellow15 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ).
tt(t15_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) <=>  ((v5_orders_3 C A B) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_orders_3 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C) (k3_struct_0 B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_yellow17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_compts_1 A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (~  ((r1_tarski (k2_struct_0 A) (k3_tarski C)) &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 C)))  =>  (~ (r1_tarski (k2_struct_0 A) (k3_tarski D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) => (v21_functor0 (k2_yellow18 A B) A B)) ) ) ) ) ).
tt(t15_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden C B) <=> (r1_waybel_0 A (k3_yellow19 A (k2_struct_0 A) B) C)) ) ) ) ) ) ) ).
tt(t15_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_yellow_0 (k2_yellow_1 A)) => (r2_hidden (k3_tarski A) A)) ) ) ).
tt(t15_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  ( (E = (k1_yellow20 C D))  => (r2_altcat_2 B A E C)) ) ) ) ) ) ) ) ) ).
tt(t15_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_yellow21 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_yellow21 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k6_yellow21 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k6_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k6_yellow21 A) C))) &  ((v22_waybel_0 D (k4_yellow21 (k6_yellow21 A) B) (k4_yellow21 (k6_yellow21 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k6_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k6_yellow21 A) C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v5_orders_3 C A B) => (v1_waybel_0 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t15_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((v3_orders_2 (k3_yellow_3 A B)) =>  ((v3_orders_2 A) & (v3_orders_2 B)) ) ) ) ) ) ).
tt(t15_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) = (a_3_1_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(t15_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_yellow_5 A B B) <=>  (~  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ).
tt(t15_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  ( ((m2_yellow_6 B A C) & (m2_yellow_6 C A D))  => (m2_yellow_6 B A D)) ) ) ) ) ) ) ) ) ).
tt(t15_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v1_lattice3 A))  => (v1_lattice3 B)) ) ) ) ) ).
tt(t15_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v2_yellow_8 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v4_card_3 B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v3_tops_1 C A)) ) ) )  => (v2_tops_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ) ).
tt(t15_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k1_cantor_1 A (k1_cantor_1 A B)) = (k1_cantor_1 A B)) ) ) ) ).
tt(t15_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k4_ordinal1)))  =>  (! [F:$i] :  ((m1_subset_1 F k4_ordinal1) =>  ( ((v8_zf_fund1 D A) &  ((r2_hidden B D) &  ((r1_tarski B D) & (r2_hidden C (k1_funct_2 E B))) ) )  => (r2_hidden (a_4_1_zf_fund1 A B C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  (! [H:$i] :  ((m2_subset_1 H k5_numbers k1_zf_lang) =>  ( ((k16_zf_lang C D E A) = (k16_zf_lang F G H B))  =>  ( (C = F)  &  ( (D = G)  &  ( (E = H)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ( ((k1_funct_1 (k4_zf_lang A B) 1) = k6_numbers)  &  ((k1_funct_1 (k5_zf_lang A B) 1) = 1) ) ) ) ) ) ).
tt(t15_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) (k1_tarski B)) = k1_xboole_0)  =>  (A = B) ) ) ) ).
tt(t15_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ( (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) => (r2_zf_model A (k11_zf_model B))) ) )  <=>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) & (r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  =>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_hidden (k7_relset_1 A A (k1_zfmodel1 B A C) D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t15_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( (~ (r2_hidden A (k4_zf_lang1 D)))  =>  ((r2_zf_model C (k6_zf_lang1 D B A)) <=> (r2_zf_model C D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r1_zf_model A B (k7_zf_lang C D)) <=>  ((r1_zf_model A B C) & (r1_zf_model A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t15_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ((k5_relat_1 (k1_ordinal3 A C) B) = (k1_ordinal3 A (k5_relat_1 C B))) ) ) ) ) ) ) ).
tt(t15_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v5_relat_1 C A) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_zf_refle C A)) ) ) ) )  => (r2_hidden B (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t15_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_zmodul01 A (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C D E)) B) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_zmodul01 A C B) (k1_zmodul01 A D B)) (k1_zmodul01 A E B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t160_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  (! [E:$i] :  ((m4_glib_001 B A C) =>  ((r1_glib_001 A D E B) <=> (r1_glib_001 A D E C)) ) ) ) ) ) ) ) ) ) ).
tt(t160_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k4_binop_2 C B) (k19_member_1 A C))) ) ) ) ) ) ) ).
tt(t160_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ( ((k9_xtuple_0 (k2_zfmisc_1 A B)) = A)  &  ((k10_xtuple_0 (k2_zfmisc_1 A B)) = B) ) ) ) ) ) ) ) ).
tt(t160_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B D) (k5_sheffer1 A B (k5_sheffer1 A D C))) = B) ) ) ) ) ) ) ) ) ).
tt(t160_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k2_xcmplx_0 A B)) = (k6_xcmplx_0 (k4_xcmplx_0 B) A)) ) ) ) ) ).
tt(t160_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 B 1)) )  => (r1_xxreal_0 (k3_xcmplx_0 A B) 1)) ) ) ) ) ).
tt(t160_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k3_xboole_0 (k4_xxreal_1 A C) (k4_xxreal_1 B D)) = (k4_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t160_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k8_zf_lang C A) = (k6_zf_lang1 (k8_zf_lang D B) D C))  <=>  (A = (k6_zf_lang1 B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t160_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) D (k3_rlvect_1 A B C)) = (k3_rlvect_1 A (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) D B) (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) D C))) ) ) ) ) ) ) ) ) ).
tt(t161_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) =>  ( ((k3_glib_001 A B) = (k3_glib_001 A C))  &  ((k4_glib_001 A B) = (k4_glib_001 A C)) ) ) ) ) ) ) ) ) ).
tt(t161_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k19_member_1 A B) = (a_2_11_member_1 A B)) ) ) ) ) ).
tt(t161_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ((k9_xtuple_0 A) = k1_xboole_0)  &  ((k9_xtuple_0 B) = k1_xboole_0) )  =>  (A = B) ) ) ) ) ) ).
tt(t161_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l1_sheffer1 A)) ) ) )  => (v1_sheffer2 A)) ) ).
tt(t161_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k6_xcmplx_0 A B)) = (k2_xcmplx_0 (k4_xcmplx_0 A) B)) ) ) ) ) ).
tt(t161_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k3_xcmplx_0 A B) 1)) ) ) ) ) ) ) ).
tt(t161_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) => (r1_tarski (k2_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 C D)) (k2_xxreal_1 (k3_xxreal_0 A C) (k4_xxreal_0 B D)))) ) ) ) ) ) ) ) ).
tt(t161_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k10_zf_lang A B) = (k6_zf_lang1 (k10_zf_lang C D) E F))  <=>  ( (A = (k6_zf_lang1 C E F))  &  (B = (k6_zf_lang1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t161_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ((k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D (k3_rlvect_1 A B C)) = (k3_rlvect_1 A (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B) (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t162_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t162_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k19_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k4_binop_2 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t162_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ((k10_xtuple_0 A) = k1_xboole_0)  &  ((k10_xtuple_0 B) = k1_xboole_0) )  =>  (A = B) ) ) ) ) ) ).
tt(t162_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B)) = (k6_xcmplx_0 A B)) ) ) ) ) ).
tt(t162_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 1 A))  &  ((r1_xxreal_0 B 1) & (r1_xxreal_0 1 (k3_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t162_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 C D)))  =>  ((k2_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 C D)) = (k2_xxreal_1 (k3_xxreal_0 A C) (k4_xxreal_0 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t162_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k11_zf_lang A B) = (k6_zf_lang1 (k11_zf_lang C D) E F))  <=>  ( (A = (k6_zf_lang1 C E F))  &  (B = (k6_zf_lang1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t162_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) (k4_nat_1 C D) B) = (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) C (k2_binop_1 k5_numbers (u1_struct_0 A) (u1_struct_0 A) (k3_binom A) D B))) ) ) ) ) ) ) ) ) ).
tt(t163_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) =>  ((r1_tarski (k14_glib_001 A B) (k14_glib_001 A C)) & (r1_tarski (k13_glib_001 A B) (k13_glib_001 A C))) ) ) ) ) ) ) ) ).
tt(t163_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski A B) <=> (r1_tarski (k19_member_1 A C) (k19_member_1 B C))) ) ) ) ) ) ) ).
tt(t163_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  =>  ((k9_xtuple_0 (k3_relat_1 C A)) = (k9_xtuple_0 (k3_relat_1 C B))) ) ) ) ) ) ) ) ).
tt(t163_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 A B) = (k4_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B))) ) ) ) ) ).
tt(t163_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A (k4_xcmplx_0 1)) & (r1_xxreal_0 B (k4_xcmplx_0 1)))  => (r1_xxreal_0 1 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t163_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) => (r1_tarski (k2_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 C D)) (k3_xxreal_1 (k3_xxreal_0 A C) (k4_xxreal_0 B D)))) ) ) ) ) ) ) ) ).
tt(t163_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k12_zf_lang A B) = (k6_zf_lang1 (k12_zf_lang C D) E F))  <=>  ( (A = (k6_zf_lang1 C E F))  &  (B = (k6_zf_lang1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t163_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k4_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k4_numbers) =>  ((k1_binop_1 (k12_zmodul01 A) (k3_xcmplx_0 C D) B) = (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) C (k2_binop_1 k4_numbers (u1_struct_0 A) (u1_struct_0 A) (k12_zmodul01 A) D B))) ) ) ) ) ) ) ) ) ).
tt(t164_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (~  ((r1_xxreal_0 D (k3_finseq_1 B)) &  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  (~  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k1_funct_1 B D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t164_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k19_member_1 A C) = (k19_member_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t164_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  =>  ((k10_xtuple_0 (k3_relat_1 A C)) = (k10_xtuple_0 (k3_relat_1 B C))) ) ) ) ) ) ) ) ).
tt(t164_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C) = (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 C) B) A)) ) ) ) ) ) ) ).
tt(t164_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 1) A))  &  ((r1_xxreal_0 B (k4_xcmplx_0 1)) & (r1_xxreal_0 (k3_xcmplx_0 A B) 1)) ) ) ) ) ) ) ).
tt(t164_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 C D)))  =>  ((k2_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 C D)) = (k3_xxreal_1 (k3_xxreal_0 A C) (k4_xxreal_0 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t164_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ( (~  (C = D) )  =>  ( ((k13_zf_lang C A) = (k6_zf_lang1 (k13_zf_lang C B) D E))  <=>  (A = (k6_zf_lang1 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t164_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))))  &  ((v13_algstr_0 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v2_rlvect_1 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v3_rlvect_1 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v4_rlvect_1 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v2_zmodul01 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v3_zmodul01 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v4_zmodul01 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) &  ((v5_zmodul01 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A))) & (l1_zmodul01 (g1_zmodul01 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (k12_zmodul01 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t165_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((m4_glib_001 B A C) =>  (! [D:$i] :  ( ((v1_abian D) & (m1_subset_1 D k5_numbers))  =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  (! [E:$i] :  ( ((v1_abian E) & (m1_subset_1 E k5_numbers))  =>  (~  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k1_funct_1 B D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t165_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k19_member_1 A C) (k19_member_1 B C))) ) ) ) ) ) ) ).
tt(t165_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 (k5_relat_1 C A))) =>  ((k3_relat_1 B (k5_relat_1 C A)) = (k3_relat_1 B C)) ) ) ) ) ) ) ).
tt(t165_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 C) A) B)) ) ) ) ) ) ) ).
tt(t165_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) &  ((r1_xxreal_0 (k4_xcmplx_0 1) A) & (r1_xxreal_0 (k4_xcmplx_0 1) B)) )  => (r1_xxreal_0 (k3_xcmplx_0 A B) 1)) ) ) ) ) ).
tt(t165_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k2_xboole_0 (k1_xxreal_1 A B) (k1_xxreal_1 B C)) = (k1_xxreal_1 A C)) ) ) ) ) ) ) ) ).
tt(t165_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k13_zf_lang C A) = (k6_zf_lang1 (k13_zf_lang D B) D C))  <=>  (A = (k6_zf_lang1 B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t166_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  =>  (~  ( (~ (v3_glib_001 B A))  &  (! [C:$i] :  ( ((v5_glib_001 C A) & (m4_glib_001 C A B))  => (v3_glib_001 C A)) ) ) ) ) ) ) ) ).
tt(t166_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k19_member_1 A C) (k19_member_1 B C))) ) ) ) ) ) ) ).
tt(t166_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((k5_relat_1 B A) = (k5_relat_1 C A))  =>  ((k7_relat_1 B A) = (k7_relat_1 C A)) ) ) ) ) ) ) ).
tt(t166_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C)) ) ) ) ) ) ) ).
tt(t166_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 1)))  &  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 1 (k3_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t166_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k2_xboole_0 (k2_xxreal_1 A B) (k1_xxreal_1 B C)) = (k1_xxreal_1 A C)) ) ) ) ) ) ) ) ).
tt(t166_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v2_zf_lang A) <=> (v2_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t167_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C B) => (m3_glib_001 C A)) ) ) ) ) ) ).
tt(t167_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k19_member_1 A C) (k19_member_1 B C))) ) ) ) ) ) ) ).
tt(t167_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B A))  =>  (! [C:$i] :  ((r2_hidden C (k10_xtuple_0 B)) => (r2_hidden C A)) ) ) ) ) ).
tt(t167_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C)) ) ) ) ) ) ) ).
tt(t167_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C 1))  => (r1_xxreal_0 A (k3_xcmplx_0 B C))) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t167_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k2_xboole_0 (k1_xxreal_1 A B) (k3_xxreal_1 B C)) = (k1_xxreal_1 A C)) ) ) ) ) ) ) ) ).
tt(t167_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v3_zf_lang A) <=> (v3_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t168_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((v3_glib_001 C A) & (r2_hidden (k3_glib_001 A C) (k24_glib_000 A B)))  => (m3_glib_001 C B)) ) ) ) ) ) ) ).
tt(t168_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k3_xxreal_3 B C) (k20_member_1 A C))) ) ) ) ) ) ) ).
tt(t168_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A B) =>  ((k9_relat_1 (k2_zfmisc_1 B C) A) = C) ) ) ) ) ).
tt(t168_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) C)) = (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C)) ) ) ) ) ) ) ).
tt(t168_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_xxreal_0 (k3_xcmplx_0 A C) B)) ) ) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t168_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k2_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 B C)) = (k2_xxreal_1 A C)) ) ) ) ) ) ) ) ).
tt(t168_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v4_zf_lang A) <=> (v4_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t169_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((r1_tarski (k14_glib_001 A C) (k25_glib_000 A B)) =>  ((v3_glib_001 C A) | (m3_glib_001 C B)) ) ) ) ) ) ) ) ).
tt(t169_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k20_member_1 A B) = (a_2_12_member_1 A B)) ) ) ) ) ).
tt(t169_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden (k4_tarski A B) C) <=> (r2_hidden B (k9_relat_1 C A))) ) ) ) ) ).
tt(t169_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C)) ) ) ) ) ) ) ).
tt(t169_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_xxreal_0 A (k3_xcmplx_0 C B))) ) ) ) ) )  => (r1_xxreal_0 A k6_numbers)) ) ) ) ) ).
tt(t169_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C B) |  ((k2_xboole_0 (k1_xxreal_1 A B) (k4_xxreal_1 B C)) = (k2_xxreal_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t169_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v5_zf_lang A) <=> (v5_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t16_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_abcmiz_0 A))  =>  ((k4_abcmiz_0 A (k1_subset_1 (u1_abcmiz_0 A))) = (u1_struct_0 A)) ) ) ).
tt(t16_abcmiz_1,ax,(r1_tarski a_0_0_abcmiz_1 k2_abcmiz_1)).
tt(t16_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( (~ (r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k2_abcmiz_1))  <=> (m1_subset_1 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) (u4_struct_0 A))) ) ) ) ) ).
tt(t16_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_absvalue A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t16_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden B (k2_aff_1 A C D)) & (r2_hidden E (k2_aff_1 A C D)))  =>  ( (B = E)  | (r1_tarski (k2_aff_1 A B E) (k2_aff_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r5_aff_1 A B C) =>  ((k1_aff_4 A B D) = (k1_aff_4 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t16_afinsq_1,ax, (! [A:$i] :  ((v1_relat_1 k1_xboole_0) &  ((v5_relat_1 k1_xboole_0 A) &  ((v5_ordinal1 k1_xboole_0) &  ((v1_funct_1 k1_xboole_0) & (v1_finset_1 k1_xboole_0)) ) ) ) ) ).
tt(t16_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((k3_afinsq_2 B 1 A) = (k5_relat_1 B A)) ) ) ) ) ).
tt(t16_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (r1_subset_1 (u1_struct_0 A) (k7_afproj A))) ) ).
tt(t16_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_afvect0 A B C D) => (r2_afvect0 A D C B)) ) ) ) ) ) ) ) ) ).
tt(t16_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_unialg_1 B) &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  ((r3_alg_1 A B C) <=>  ((k1_alg_1 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(t16_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ((k1_funct_1 (k3_algseq_1 B (k4_struct_0 B)) A) = (k4_struct_0 B)) ) ) ) ) ).
tt(t16_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_algspec1 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t16_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ((v7_algstr_1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = (k6_algstr_0 A D B))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_algstr_4,ax, (! [A:$i] :  ((k11_algstr_4 A k6_numbers) = k1_xboole_0) ) ).
tt(t16_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A B D) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  (? [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  &  (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( (E = G)  &  ( (F = H)  &  (~  ((k5_altcat_1 A B C D E F) = (k3_relat_1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (v11_altcat_1 (k4_altcat_2 A))) ) ).
tt(t16_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v2_altcat_3 D A B C) &  (~ (v4_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B (k3_functor0 A B C D) (k3_functor0 A B C E))) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ((v18_functor0 C A B) &  ((v8_functor0 C A B) &  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  (~  (F = (k6_functor0 A B C D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_ami_2 k2_ami_2) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_ami_2 k2_ami_2) =>  ( (~  (D = B) )  =>  ((k1_funct_1 (k7_ami_2 A B C) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t16_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k2_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(t16_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 A C) = (k1_funct_1 (k1_funct_4 A (k7_memstr_0 2 k1_ami_3 B)) C)) ) ) ) ) ) ) ).
tt(t16_ami_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_amistd_1 2 k1_ami_3 (k7_ami_3 A)) = (k1_tarski A)) ) ) ).
tt(t16_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) ) )  => (v5_amistd_1 (k16_funcop_1 k6_numbers (k2_compos_1 B)) A B)) ) ) ) ).
tt(t16_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) => (r2_hidden (k4_struct_0 B) (k2_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t16_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k5_ami_wstd A B C) = (k5_ami_wstd A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t16_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 (k2_diraf (k2_analoaf A))) = (u1_struct_0 A)) ) ) ).
tt(t16_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (B = (k5_algstr_0 A (k3_rlvect_1 A C D) E))  =>  ((r1_analoaf A E C D B) & (r1_analoaf A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r1_analoaf A D E F G))  => (r1_analoaf A (k2_analort A B C D) (k2_analort A B C E) (k2_analort A B C F) (k2_analort A B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r1_anproj_1 A B C))  &  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 F A))  &  ((r2_anproj_1 A D E F) &  ( (~ (r1_anproj_1 A D F))  &  (~ (r1_anproj_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_anproj_2,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  (~  ((r2_hidden B (k4_dtconstr A)) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C (k1_lang1 A)) &  (B = (k2_trees_4 (u1_struct_0 A) C)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 A)) (k4_dtconstr A)) =>  (~  ((r1_lang1 A C (k1_dtconstr (u1_struct_0 A) (k5_trees_3 (u1_struct_0 A)) D)) &  (B = (k8_trees_4 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_aofa_i00,ax, (! [A:$i] :  ((m4_aofa_i00 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 k5_numbers k4_numbers) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 k5_numbers k4_numbers) k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_funct_2 k5_numbers k4_numbers) k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 k5_numbers k4_numbers) k4_numbers)))) )  => (r2_aofa_i00 (k7_freealg k19_aofa_000 k26_aofa_i00) k5_numbers (k1_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k6_numbers k6_numbers) A B C)) ) ) ) ) ) ).
tt(t16_armstrng,ax, (! [A:$i] :  ((k2_relset_1 (k4_armstrng A) (k7_armstrng A)) = (k8_mcart_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k9_setfam_1 A) (k9_setfam_1 A))) ) ).
tt(t16_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r2_hidden (k2_arytm_0 A A) k2_arytm_2)) ) ).
tt(t16_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) => (r1_arytm_2 (k1_arytm_1 C B) (k1_arytm_1 C A))) ) ) ) ) ) ) ).
tt(t16_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r2_hidden A k4_ordinal1) & (r2_hidden B k4_ordinal1))  => (r2_hidden (k7_arytm_2 B A) k4_ordinal1)) ) ) ) ) ).
tt(t16_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( ((k3_arytm_3 A A) = A)  &  ((k2_arytm_3 A A) = A) ) ) ) ).
tt(t16_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers) )  =>  ((r2_hidden A (k6_asympt_0 B)) &  (~ (r2_hidden B (k6_asympt_0 A))) ) ) ) ) ) ) ).
tt(t16_asympt_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((r2_funct_2 k5_numbers k1_numbers A (k1_asympt_1 2 1 k6_numbers)) &  ((r2_hidden (k2_asympt_0 (k3_asympt_1 1) 2) (k6_asympt_0 (k3_asympt_1 1))) &  (~ (r2_hidden (k1_asympt_1 2 2 k6_numbers) (k6_asympt_0 A))) ) ) ) ) ).
tt(t16_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  ( ((v1_msualg_3 E) &  ((v2_msualg_3 E A B C) &  ((v1_msualg_3 F) & (v2_msualg_3 F A C D)) ) )  => (r6_pboole A (k4_msualg_3 A B D (k3_msualg_3 A B C D E F)) (k3_msualg_3 A D C B (k4_msualg_3 A C D F) (k4_msualg_3 A B C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) => (m2_funct_2 (k2_funct_1 B) (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A))) ) ) ) ).
tt(t16_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_bagorder C A B (k16_pre_poly C)) = (k16_pre_poly (k7_nat_d B A))) ) ) ) ) ) ) ).
tt(t16_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B D C)) = (k1_bcialg_1 B C D)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t16_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k1_bcialg_2 A (k4_struct_0 A) B C) = (k4_struct_0 A))  =>  ((k1_bcialg_2 A (k4_struct_0 A) B (k4_nat_1 C D)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t16_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ).
tt(t16_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_4 A (k1_bcialg_1 A B D) (k1_bcialg_1 A D C)))) ) ) ) ) ) ) ) ).
tt(t16_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((v8_bcialg_1 A) & (m1_bcialg_5 A B C D E))  <=>  ((v8_bcialg_1 A) & (m1_bcialg_5 A D E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_bcialg_6 A (k19_binop_2 D) (k6_bcialg_1 A B C)) = (k1_bcialg_1 A (k3_bcialg_6 A (k19_binop_2 D) B) (k3_bcialg_6 A (k19_binop_2 D) C))) ) ) ) ) ) ) ) ) ).
tt(t16_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m1_bciideal B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A (k4_struct_0 A) C)) B)) ) ) ) ) ) ) ).
tt(t16_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A B C)) = (k7_real_1 (k7_real_1 (k2_bhsp_1 A B B) (k8_real_1 2 (k2_bhsp_1 A B C))) (k2_bhsp_1 A C C))) ) ) ) ) ) ) ).
tt(t16_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) =>  ((k1_bhsp_2 A (k5_vfunct_1 k5_numbers A B)) = (k4_algstr_0 A (k1_bhsp_2 A B))) ) ) ) ) ) ).
tt(t16_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (r2_bhsp_3 A B C))  => (v1_bhsp_2 C A)) ) ) ) ) ) ) ).
tt(t16_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_bhsp_4 A B 1) = (k3_rlvect_1 A (k3_bhsp_4 A B k6_numbers) (k1_normsp_1 A B 1))) ) ) ) ) ).
tt(t16_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k4_bilinear A B C D) E) (k4_hahnban1 A B (k8_bilinear A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k2_binari_2 (k1_nat_1 A 1) (k2_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C)))) = (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))) ) ) ) ) ) ) ).
tt(t16_binari_3,ax, ((k7_binarith 1 (k10_binarith k6_margrel1 k7_margrel1) (k10_binarith k6_margrel1 k7_margrel1)) = (k10_binarith k6_margrel1 k7_margrel1)) ).
tt(t16_binari_4,ax, (! [A:$i] :  ( ((v3_card_1 A 1) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k12_finseq_1 k6_margrel1 k7_margrel1))  =>  ((k3_binari_2 1 A) = k6_numbers) ) ) ) ).
tt(t16_binarith,ax, (! [A:$i] :  ( ((v3_card_1 A 1) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k12_finseq_1 k6_margrel1 k8_margrel1))  =>  ((k6_binarith 1 A) = 1) ) ) ) ).
tt(t16_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k6_binom A B (k2_nat_1 C D)) = (k1_algstr_0 A (k6_binom A B C) (k6_binom A B D))) ) ) ) ) ) ) ) ) ).
tt(t16_binop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 C A) =>  ((r5_binop_1 A C B) <=> (r4_binop_1 A C B)) ) ) ) ) ) ) ) ).
tt(t16_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 B k6_margrel1)) =>  ( (C = (k5_euclid B))  =>  ((k1_funct_1 (k2_bintree2 A B) (k5_series_1 2 B)) = (k3_binarith B C)) ) ) ) ) ) ) ) ).
tt(t16_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r4_boolealg A B (k5_lattices A))) ) ) ) ) ).
tt(t16_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ( ((v2_comseq_2 (k3_series_1 (k8_prob_1 A B D C))) =>  ( ((k1_funct_1 C (k4_kurato_0 A D)) = k6_numbers)  &  ((k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) = 1) ) )  &  ( ((r1_bor_cant A B C D) & (v1_limfunc1 (k3_series_1 (k8_prob_1 A B D C))))  =>  ( ((k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) = k6_numbers)  &  ((k1_funct_1 C (k4_kurato_0 A D)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  (! [D:$i] :  (~  ((r2_hidden D (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) C)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  (~  ((r2_hidden E C) &  (D = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 A) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A)))) =>  ( (D = (k3_borsuk_1 B A (k2_struct_0 B) (k6_domain_1 (u1_struct_0 A) C)))  => (v2_compts_1 D (k2_borsuk_1 B A))) ) ) ) ) ) ) ) ) ).
tt(t16_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 B C) &  (A = (k1_rcomp_1 B C)) )  =>  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 C 1)) ) ) ) ) ) ) ) ).
tt(t16_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_rcomp_1 B C))  =>  ( (B = C)  |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t16_borsuk_6,ax, ((v4_pre_topc a_0_2_borsuk_6 (k15_euclid 2)) & (m1_subset_1 a_0_2_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(t16_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k12_rvsum_1 (k11_finseq_1 A B C)) = (k11_finseq_1 (k3_square_1 A) (k3_square_1 B) (k3_square_1 C))) ) ) ) ) ) ) ).
tt(t16_bspace,ax, (! [A:$i] :  (! [B:$i] :  ( (A = B)  <=>  (! [C:$i] :  ((k3_bspace A C) = (k3_bspace B C)) ) ) ) ) ).
tt(t16_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A D B)) (k1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D))) (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) D) (k2_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) D)) (k2_bvfunc_1 A (k2_bvfunc_1 A B C) (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t16_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( (E = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B G) (k16_funcop_1 C H)) (k16_funcop_1 D I)) (k16_funcop_1 A F)))  =>  ((k9_xtuple_0 E) = (k2_enumset1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) <=> (r1_bvfunc_1 A B C)) ) ) ) ) ) ) ).
tt(t16_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))) (k5_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) (k2_bvfunc_1 A B (k1_bvfunc_1 A C))))) ) ) ) ) ) ).
tt(t16_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k2_bvfunc_1 A B C)) (k5_bvfunc26 A B C))) ) ) ) ) ) ).
tt(t16_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k6_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k7_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)) (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k10_bvfunc_1 A B C) D E) (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A B C) D E) (k6_bvfunc_2 A (k9_bvfunc_1 A C B) D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k9_bvfunc_1 A B C) D) (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t16_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k12_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t16_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B C) (k6_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t16_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) D)) (k5_bvfunc_1 A C D))) ) ) ) ) ) ) ) ).
tt(t16_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_group_1 (k7_c0sp1 A)) = (k8_funcop_1 k5_numbers A 1)) ) ) ).
tt(t16_c0sp2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_c0sp2 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ( ( (E = C)  &  (F = D) )  =>  ( (D = (k1_rlvect_1 (k5_c0sp2 B) C A))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) k1_numbers F G) = (k8_real_1 A (k3_funct_2 (u1_struct_0 B) k1_numbers E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k1_calcul_1 (k3_cqc_lang A) C)) &  ( ((k2_calcul_1 A B) = (k2_calcul_1 A C))  & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B))) )  => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C) (k2_calcul_1 A C))) ) ) ) ) ) ) ).
tt(t16_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k15_finseq_1 (k5_relset_1 k5_numbers (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) B C) (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C)))) = (k4_relset_1 k5_numbers k5_numbers k5_numbers (k3_cqc_lang A) (k14_finseq_1 (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C))) (k8_finseq_1 (k3_cqc_lang A) B C))) ) ) ) ) ) ) ).
tt(t16_cantor_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_tops_2 B (g1_pre_topc A (k1_cantor_1 A B))) &  ((v1_cantor_1 B (g1_pre_topc A (k1_cantor_1 A B))) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc A (k1_cantor_1 A B))))))) ) ) ) ) ) ).
tt(t16_card_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_card_1 A) = (k1_card_1 B))  =>  ((k2_card_1 A) = (k2_card_1 B)) ) ) ) ).
tt(t16_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_wellord2 (k2_xboole_0 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) (k2_xboole_0 (k2_zfmisc_1 B A) (k2_zfmisc_1 D C))) &  ((k1_card_1 (k2_xboole_0 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D))) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 B A) (k2_zfmisc_1 D C)))) ) ) ) ) ) ).
tt(t16_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_card_3 C (k2_xboole_0 A B)) = (k2_xboole_0 (k5_card_3 C A) (k5_card_3 C B))) ) ) ) ).
tt(t16_card_4,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((r2_hidden k6_numbers B) =>  ((v1_finset_1 A) |  ( ( (~ (r1_ordinal1 B A))  &  (~ (r2_hidden B A)) )  |  ( ((k2_card_2 A B) = A)  &  ((k2_card_2 B A) = A) ) ) ) ) ) ) ) ) ).
tt(t16_card_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( (~  (B = k6_numbers) )  &  ( (~  (B = 1) )  &  ( (~  (B = 2) )  &  ( (~  (B = (k5_card_1 A)) )  &  ((r2_hidden (k5_card_1 A) B) & (r1_ordinal1 k4_ordinal1 B)) ) ) ) ) ) ) ) ) ).
tt(t16_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k3_card_fil A))))  =>  ((v6_ordinal1 B) => (m1_card_fil (k3_tarski B) A)) ) ) ) ) ).
tt(t16_cardfin2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_xxreal_0 (k5_card_1 A) (k5_card_1 B)) =>  ((k5_card_1 (k4_cardfin2 A B)) = (k10_binop_2 (k13_newton (k5_card_1 B) (k5_card_1 A)) (k12_binop_2 (k3_newton (k5_card_1 B)) (k3_newton (k7_nat_d (k5_card_1 B) (k5_card_1 A)))))) ) ) ) ) ) ).
tt(t16_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  (A = B) )  =>  ((k5_card_1 (k1_card_fin C D A B)) = (k6_newton D (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(t16_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r1_tarski (k8_subset_1 A D B) C) => (r1_tarski (k9_subset_1 A B (k2_card_lar A D)) (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ).
tt(t16_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A B) = (k4_graph_1 A C))  =>  ((k1_cat_1 A C B) = (k1_binop_1 (u1_cat_1 A) B C)) ) ) ) ) ) ) ) ).
tt(t16_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) => (v14_cat_1 (k5_cat_2 A B) B A)) ) ) ) ).
tt(t16_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A D) (k8_funcop_1 (u1_struct_0 B) A (k4_graph_1 B C))) =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A (k6_cat_3 B A D C)) (k8_funcop_1 (u1_struct_0 B) A (k3_graph_1 B C))) & (r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A (k6_cat_3 B A D C)) (k3_cat_3 B A D))) ) ) ) ) ) ) ) ) ).
tt(t16_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_cat_1 A B (k1_cat_4 A)) = (k1_tarski (k6_cat_4 A B))) ) ) ) ) ).
tt(t16_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_cat_5 B) = B) ) ) ) ) ).
tt(t16_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 (k1_catalan1 A) (k1_catalan1 (k1_nat_1 A 1)))) ) ).
tt(t16_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k5_relat_1 A (k23_binop_2 (k24_binop_2 2 C) (k1_afinsq_1 B))) = (k1_catalan2 (k1_catalan2 (k8_funcop_1 k5_numbers C k6_numbers) B) (k8_funcop_1 k5_numbers C 1)))  &  ((v1_catalan2 B) &  ((k24_binop_2 2 (k7_afinsq_2 B)) = (k1_afinsq_1 B)) ) )  =>  ((r1_xxreal_0 C k6_numbers) |  ((k5_nat_1 (a_1_0_catalan2 A)) = (k23_binop_2 (k24_binop_2 2 C) (k1_afinsq_1 B))) ) ) ) ) ) ) ) ) ).
tt(t16_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k3_catalg_1 A))) =>  (~  ( ( ((k1_xtuple_0 B) = 1)  |  ((k3_finseq_1 (k2_xtuple_0 B)) = 1) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k8_catalg_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cc0sp1 A))) =>  ((k1_binop_1 (k1_cc0sp1 (k8_cfuncdom A) (k2_cc0sp1 A)) k6_complex1 B) = B) ) ) ) ) ).
tt(t16_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  => (m1_cc0sp1 (k3_cc0sp2 A) (k3_cc0sp1 (u1_struct_0 A)))) ) ).
tt(t16_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_tarski (k2_relset_1 k2_numbers B) (k1_relset_1 k2_numbers (k5_relset_1 k2_numbers k2_numbers C A))) &  ((k8_relset_1 k2_numbers k2_numbers C (k1_tarski k6_numbers)) = k1_xboole_0) )  => (r2_relset_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers B (k5_relset_1 k2_numbers k2_numbers (k2_cfunct_1 k2_numbers C) A)) (k36_valued_1 k5_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers B (k5_relset_1 k2_numbers k2_numbers C A))))) ) ) ) ) ) ).
tt(t16_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfdiff_1 B A) => (v6_cfdiff_1 A)) ) ) ) ) ).
tt(t16_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers (k2_cfuncdom A) (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) D B)) C) (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) D (k1_funcsdom A k2_numbers (k2_cfuncdom A) B C))))) ) ) ) ) ) ) ) ).
tt(t16_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers B (k2_valued_1 A k2_numbers k2_numbers C D)) (k2_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) (k19_valued_1 A k2_numbers k2_numbers B D)))) ) ) ) ) ) ) ) ).
tt(t16_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (~ (r2_hidden A (k8_cgames_1 A))) ) ) ).
tt(t16_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers B C) A) <=>  ((r2_hidden B A) &  ((r2_hidden C A) &  ( ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 D B))  &  (~ (r1_xxreal_0 C D)) ) ) ) ) ) )  |  ( (~ (r1_xxreal_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((r1_xxreal_0 D B) & (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  ((r2_hidden C (k4_finseq_1 A)) & (v2_funct_1 A)) )  =>  ((r2_hidden B (k1_chord A C)) <=> (r1_xxreal_0 C (k4_finseq_4 A B))) ) ) ) ) ) ) ).
tt(t16_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( ( (H = (k5_relat_1 G (u1_struct_0 A)))  & (v1_circuit2 H A D))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (I = (k5_relat_1 G (u1_struct_0 B)))  & (v1_circuit2 I B E))  => (v1_circuit2 G C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  ((k3_msafree2 A) = (k1_tarski (k3_circcmb3 A))) ) ) ).
tt(t16_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_circcomb A B) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_circcomb A B))) =>  ( (C = D)  =>  ( ((k1_msualg_1 (k2_circcomb A B) D) = (k1_msualg_1 A C))  &  ((k2_msualg_1 (k2_circcomb A B) D) = (k2_msualg_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (~  ((v1_circled1 B A) &  ((k3_rlvect_2 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t16_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v4_msafree2 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m3_msaterm D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k1_circtrm1 A B D))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k1_funct_1 E k1_xboole_0) = (k4_tarski F (u1_struct_0 A)))  => (r1_funct_2 (k3_msualg_1 (k1_circtrm1 A B D) E (k6_circtrm1 A B D C)) (k4_msualg_1 (k1_circtrm1 A B D) E (k6_circtrm1 A B D C)) (k3_msualg_1 A F C) (k4_msualg_1 A F C) (k5_msualg_1 (k1_circtrm1 A B D) E (k6_circtrm1 A B D C)) (k5_msualg_1 A F C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_finseq_1 E) & (v6_trees_3 E)) ) )  =>  ( ((r2_hidden C (k3_msafree2 A)) &  ( (D = (k4_trees_4 (k4_tarski (k4_msafree2 A C) (u1_struct_0 A)) E))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden F (k1_relset_1 k5_numbers E)) &  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A C)) F))) =>  (~  ( (G = (k1_funct_1 E F))  &  ((k5_card_1 G) = (k4_circuit1 A B (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A C)) F))) ) ) ) ) ) ) ) ) ) )  =>  ((k5_card_1 D) = (k4_circuit1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  ((v3_funct_1 (k10_funct_6 C)) =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ((m1_msafree2 E A B) =>  ( (E = (k1_funct_1 (k10_funct_6 C) k6_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_xxreal_0 (k6_circuit1 A B G) F) =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) F) G) = (k5_circuit2 A B G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 B C) => (r1_tarski (k3_classes1 A B) (k3_classes1 A C))) ) ) ) ) ) ).
tt(t16_classes2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((r2_hidden A (k1_card_1 (k1_classes1 B))) => (r2_hidden A (k1_classes1 B))) ) ) ) ).
tt(t16_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_clopban1 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (D = (k1_clvect_1 (k6_clopban1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k7_clopban1 A B D F) = (k1_clvect_1 B (k7_clopban1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_clopban2 A)))  &  ((v13_algstr_0 (k8_clopban2 A)) &  ((v2_rlvect_1 (k8_clopban2 A)) &  ((v3_rlvect_1 (k8_clopban2 A)) &  ((v4_rlvect_1 (k8_clopban2 A)) &  ((v2_clvect_1 (k8_clopban2 A)) &  ((v3_clvect_1 (k8_clopban2 A)) &  ((v4_clvect_1 (k8_clopban2 A)) &  ((v3_group_1 (k8_clopban2 A)) &  ((v1_vectsp_1 (k8_clopban2 A)) &  ((v3_vectsp_1 (k8_clopban2 A)) &  ((v2_cfuncdom (k8_clopban2 A)) & (l1_cfuncdom (k8_clopban2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k3_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t16_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k6_clopban3 A (k3_rlvect_1 A C D) B) = (k1_normsp_1 A (k1_bhsp_4 A (k2_clopban4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t16_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  ( ((r6_pboole A D B) & (v1_closure1 C A B))  => (r6_pboole A D (k2_closure1 A B C D))) ) ) ) ) ) ) ) ).
tt(t16_closure2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k9_xtuple_0 (k3_closure2 (k2_tarski A B))) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) ) ) ) ) ).
tt(t16_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k1_clvect_1 A (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D)) E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_clvect_1 A B E) (k1_clvect_1 A C E)) (k1_clvect_1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) =>  ((k1_clvect_2 A (k5_vfunct_1 k5_numbers A B)) = (k4_algstr_0 A (k1_clvect_2 A B))) ) ) ) ) ) ).
tt(t16_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k2_clvect_3 A B 1) = (k3_rlvect_1 A (k2_clvect_3 A B k6_numbers) (k1_normsp_1 A B 1))) ) ) ) ) ).
tt(t16_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_cohsp_1 A B C) <=>  ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden (k3_xboole_0 B C) A) & (r2_hidden (k2_xboole_0 B C) A)) ) ) ) ) ) ) ).
tt(t16_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k3_coh_sp A)) =>  ((r2_hidden (k2_tarski B C) D) =>  ((r2_hidden B (k3_tarski D)) & (r2_hidden C (k3_tarski D))) ) ) ) ) ) ) ).
tt(t16_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_collsp E A) =>  ( ((r2_hidden B E) &  ((r2_hidden C E) & (r2_hidden D E)) )  => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((l1_combgras D A B) =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((k2_combgras A B C E) = (k2_combgras A B D E)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((k3_combgras A B C E) = (k3_combgras A B D E)) ) ) )  =>  ((g1_combgras A B (u1_combgras A B C) (u2_combgras A B C)) = (g1_combgras A B (u1_combgras A B D) (u2_combgras A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k3_xcmplx_0 A A)) = (k9_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))))  &  ((k4_complex1 (k3_xcmplx_0 A A)) = (k8_real_1 2 (k8_real_1 (k3_complex1 A) (k4_complex1 A)))) ) ) ) ).
tt(t16_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig A)))  <=> (r1_xxreal_0 k32_sin_cos (k1_comptrig (k4_xcmplx_0 A)))) ) ) ) ).
tt(t16_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( ( ((k8_group_1 k1_complfld B A) = C)  |  ((k8_group_1 k1_complfld A B) = C) )  &  (~  ( (B = (k8_group_1 k1_complfld C (k11_algstr_0 k1_complfld A)))  &  (B = (k8_group_1 k1_complfld (k11_algstr_0 k1_complfld A) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k9_matrix_5 (k12_seq_4 A C) B) = (k5_binop_2 C (k9_matrix_5 A B))) ) ) ) ) ) ) ).
tt(t16_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_topmetr A B)))) =>  ( ( (C = D)  & (v6_tbsp_1 C A))  => (r1_xxreal_0 (k3_tbsp_1 (k1_topmetr A B) D) (k3_tbsp_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t16_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((k5_compos_1 A B k6_numbers) = B) ) ) ) ) ).
tt(t16_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k5_card_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G)) = 7) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))) => (r1_xxreal_0 k6_numbers (k1_seq_1 k19_sin_cos A))) ) ) ).
tt(t16_compts_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_compts_1 A) &  ((v8_pre_topc B) &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v5_pre_topc C A B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc D A) => (v4_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t16_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski (k9_xtuple_0 C) (k4_finseq_2 A B)) => (v2_margrel1 C)) ) ) ) ) ) ) ).
tt(t16_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A) (k25_valued_1 k5_numbers k2_numbers C A)))) ) ) ) ) ) ).
tt(t16_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k8_complex1 (k15_complex1 (k3_comseq_2 A)) (k15_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t16_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers (k7_comseq_3 A)) (k7_comseq_3 (k31_valued_1 k5_numbers k2_numbers A))) & (r2_funct_2 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers (k8_comseq_3 A)) (k8_comseq_3 (k31_valued_1 k5_numbers k2_numbers A)))) ) ) ).
tt(t16_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k4_subset_1 (u4_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) C))) ) ) ) ) ) ) ).
tt(t16_conlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v4_lattice3 A) <=>  (? [B:$i] :  ( ( (~ (v1_conlat_1 B))  & (l1_conlat_1 B))  & (r1_filter_1 (k11_conlat_1 B) A)) ) ) ) ) ).
tt(t16_conmetr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v2_conmetr A) <=> (v2_aff_2 (k3_analmetr A))) ) ) ).
tt(t16_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_connsp_1 B A) &  ((r1_tarski B (k4_subset_1 (u1_struct_0 A) C D)) &  ((r1_connsp_1 A C D) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_connsp_2 A B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v3_pre_topc C A) & (r2_hidden B C))  => (r2_connsp_2 A C B)) ) ) ) ) ) ) ) ).
tt(t16_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) & (v2_connsp_1 C A))  =>  ((r1_xboole_0 B C) |  ((r1_tarski (k4_subset_1 (u1_struct_0 A) B C) (k1_connsp_3 A B)) &  ((r1_tarski (k4_subset_1 (u1_struct_0 A) B C) (k1_connsp_3 A C)) &  ((r1_tarski B (k1_connsp_3 A C)) & (r1_tarski C (k1_connsp_3 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_rusub_4 B A) => (v1_convex1 B A)) ) ) ) ) ).
tt(t16_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ( ((k1_convex4 A B) = k1_xboole_0)  =>  ((k4_convex4 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t16_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v2_qc_lang1 C A) =>  ((k13_cqc_lang A C B) = (k10_qc_lang1 A (k16_qc_lang1 A C) (k1_cqc_lang A (k17_qc_lang1 A C) (k2_cqc_lang A (k3_qc_lang3 A k6_numbers) B)))) ) ) ) ) ) ) ) ).
tt(t16_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k7_cqc_sim1 A (k6_cqc_lang A B)) = (k7_cqc_sim1 A B)) ) ) ) ) ).
tt(t16_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((v1_cqc_the1 B A) & (r1_tarski C B))  => (r1_tarski (k1_cqc_the1 A C) B)) ) ) ) ) ) ) ).
tt(t16_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 B A) => (v2_cqc_the1 (k12_cqc_lang A C B) A)) ) ) ) ) ) ) ).
tt(t16_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r3_cqc_the3 A (k4_cqc_the1 A))) ) ).
tt(t16_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v2_comseq_2 B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A))) (k1_seq_1 B E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A))) (k2_seq_2 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_funcop_1 (u1_struct_0 B) A (k4_struct_0 B)) = (k4_struct_0 (k9_csspace4 A B))) ) ) ) ) ).
tt(t16_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  ((k12_csspace A (k4_struct_0 A) (k4_struct_0 A)) = k6_numbers) ) ) ).
tt(t16_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_decomp_1 A) (k15_decomp_1 A)) = (k7_decomp_1 A)) ) ) ).
tt(t16_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k8_descip_1 A B 1) = (k6_descip_1 B)) ) ) ) ) ) ).
tt(t16_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v1_wellfnd1 (k5_dickson A)) & (v5_orders_2 A))  => (v1_wellfnd1 A)) ) ) ).
tt(t16_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers D E) B) (k2_nat_1 A 1)) C) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) (k2_nat_1 A 1)) C) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 E B) (k2_nat_1 A 1)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k1_numbers k1_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k1_numbers k1_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k2_diff_2 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers I A) (k26_valued_1 k1_numbers k1_numbers J B)) C D E F G H) = (k7_real_1 (k8_real_1 A (k2_diff_2 I C D E F G H)) (k8_real_1 B (k2_diff_2 J C D E F G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 B A) 1) (k5_diff_1 B A))) ) ) ) ).
tt(t16_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k1_fdiff_9)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k1_fdiff_9)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_fdiff_9) B) A) = (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k9_real_1 (k8_real_1 2 A) B))) (k18_sin_cos B)) (k5_square_1 (k7_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B))))) ) ) ) ) ) ).
tt(t16_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t16_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r1_diraf A B C D) &  ((r1_diraf A B C E) &  ( (~ (r1_diraf A B D E))  &  (~ (r1_diraf A B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v4_dirort A) => (v2_dirort A)) ) ) ).
tt(t16_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( ((k1_funct_1 (k9_dist_1 A B) D) = (k2_dist_1 A B (k1_funct_1 B C)))  &  ((k1_funct_1 B C) = (k1_funct_1 (k1_uproots A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k4_zfmisc_1 B C D E)) =>  ( (A = (k7_mcart_1 B C D E F))  <=>  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H C) =>  (! [I:$i] :  ((m1_subset_1 I D) =>  (! [J:$i] :  ((m1_subset_1 J E) =>  ( (F = (k5_domain_1 B C D E G H I J))  =>  (A = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_dtconstr)) =>  ( ( (A = k6_numbers)  =>  ((k19_dtconstr k5_dtconstr A) = (k6_domain_1 (k3_finseq_2 k5_numbers) (k3_pre_poly k5_numbers k6_numbers))) )  &  ( (A = 1)  =>  ((k19_dtconstr k5_dtconstr A) = a_0_0_dtconstr) ) ) ) ) ).
tt(t16_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin B A) & (v2_finsub_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r1_tarski (k10_xtuple_0 C) B) => (r1_tarski (k10_xtuple_0 (k4_dynkin A C)) B)) ) ) ) ) ) ) ) ).
tt(t16_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 B))) =>  ( (C = (k6_int_1 A B))  =>  ((k4_algstr_0 (k9_int_3 B) C) = (k6_int_1 (k6_xcmplx_0 B A) B)) ) ) ) ) ) ) ) ).
tt(t16_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A (k5_algstr_0 A (k2_binom A B 2) (k8_group_1 A B C)) (k2_binom A C 2))) = (k3_rlvect_1 A (k2_binom A B 3) (k2_binom A C 3))) ) ) ) ) ) ) ).
tt(t16_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r1_endalg (k3_endalg A) (k6_endalg (k6_msualg_1 A) (k9_msualg_1 A)))) ) ).
tt(t16_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ((r2_hidden D (k7_ens_1 A B C)) =>  (D = (k4_tarski (k1_domain_1 A A B C) (k2_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v1_matrprob (k5_finseq_2 k1_numbers A (k10_real_1 1 A))) & (m2_finseq_1 (k5_finseq_2 k1_numbers A (k10_real_1 1 A)) k1_numbers)) ) ) ).
tt(t16_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k1_tarski A) (k4_enumset1 B C D E F G))) ) ) ) ) ) ) ) ).
tt(t16_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k4_eqrel_1 A B (k5_eqrel_1 A B C)) B)) ) ) ) ) ).
tt(t16_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k1_equation A B (k2_msualg_3 A B)) B)) ) ) ).
tt(t16_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ((k3_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0) ) ) ) ) ) ).
tt(t16_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  => (r1_xxreal_0 (k12_euclid (k4_rvsum_1 A B)) (k9_binop_2 (k12_euclid A) (k12_euclid B)))) ) ) ) ) ).
tt(t16_euclid_3,ax, ((k1_euclid_3 k5_complex1) = (k4_struct_0 (k15_euclid 2))) ).
tt(t16_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ( ((k23_rvsum_1 B B) = k6_numbers)  <=>  ((k12_euclid B) = k6_numbers) ) ) ) ) ) ).
tt(t16_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ( ((k5_euclid_5 (k1_rlvect_1 (k15_euclid 3) B A) C) = (k1_rlvect_1 (k15_euclid 3) (k5_euclid_5 B C) A))  &  ((k5_euclid_5 (k1_rlvect_1 (k15_euclid 3) B A) C) = (k5_euclid_5 B (k1_rlvect_1 (k15_euclid 3) C A))) ) ) ) ) ) ) ) ).
tt(t16_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)))  =>  ( (B = C)  |  ((k4_euclid_3 A B C) = (k4_euclid_3 B C A)) ) ) ) ) ) ) ) ) ).
tt(t16_euclid_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ( ((k12_euclid A) = 1)  => (v2_euclid_7 (k1_tarski A))) ) ) ).
tt(t16_euclid_8,ax, ((k5_euclid_8 k2_euclid_8 k3_euclid_8) = k4_euclid_8) ).
tt(t16_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (~  ( (~  (A = k6_numbers) )  &  ((r2_hidden C (k4_euclid_9 A D B)) & (r1_xxreal_0 (k3_xcmplx_0 B (k6_square_1 A)) (k4_metric_1 (k14_euclid A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ( ((k12_euclid (k8_euclid A B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t16_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((k7_euclid A (k7_euclid A B C) (k7_euclid A D E)) = (k7_euclid A (k7_euclid A B D) (k7_euclid A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r4_analmetr A B C B D) &  ((r4_analmetr A B E B F) &  ((r4_analmetr A B E B G) &  ((r4_analmetr A C E D F) & (r4_analmetr A C E D G)) ) ) )  =>  ((r5_analmetr A B C E) |  ( (B = D)  |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (A = k6_numbers) )  =>  ((k3_int_2 (k2_xcmplx_0 A (k3_xcmplx_0 C B)) B) = (k3_int_2 A B)) ) ) ) ) ) ) ) ).
tt(t16_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_trees_4 D k1_numbers k5_numbers) =>  ((k2_euler_2 (k1_euler_2 (k1_wsierp_1 k1_numbers k5_numbers C D) A) B) = (k1_wsierp_1 k1_numbers k5_numbers (k2_euler_2 (k1_euler_2 C A) B) (k2_euler_2 (k1_euler_2 D A) B))) ) ) ) ) ) ) ) ) ).
tt(t16_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k2_exchsort A) = (k3_ordinal2 (k9_xtuple_0 A))) ) ) ).
tt(t16_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  ((r3_msualg_3 A B C D) <=>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A E) (u3_msualg_1 A B)) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A E) (u3_msualg_1 A B)) =>  ( ((r1_msualg_3 A E B F) &  ((r1_msualg_3 A E B G) & (r8_pboole (u1_struct_0 A) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A E) (u3_msualg_1 A B) (u3_msualg_1 A C) F D) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A E) (u3_msualg_1 A B) (u3_msualg_1 A C) G D))) )  => (r8_pboole (u1_struct_0 A) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) & (r1_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((k3_extreal1 (k2_extreal1 k8_mesfunc1 A)) = (k2_extreal1 k8_mesfunc1 (k3_extreal1 A))) ) ) ) ).
tt(t16_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_facirc_1 A B C (k1_nat_1 D 1)) = (k5_facirc_1 A B (k6_circuit2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t16_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (v1_relat_1 (k3_msafree2 (k3_facirc_2 A B C)))) ) ) ) ) ) ).
tt(t16_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_tarski B A))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) ) ).
tt(t16_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k1_rcomp_1 (k5_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k4_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k1_rcomp_1 A B)) &  (D = (k1_seq_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  ((v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((k7_relset_1 k1_numbers k1_numbers B A) = k1_numbers) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t16_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos B) B) (k8_real_1 (k1_seq_1 k3_taylor_1 B) (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t16_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k19_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k19_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t16_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_fdiff_1 B A) & (r1_fdiff_1 C A))  =>  ((r1_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k7_real_1 (k8_real_1 (k1_seq_1 C A) (k1_fdiff_1 B A)) (k8_real_1 (k1_seq_1 B A) (k1_fdiff_1 C A)))) ) ) ) ) ) ) ) ) ).
tt(t16_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 B A) =>  ((r2_fdiff_1 (k2_partfun1 k1_numbers k1_numbers B A) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 B A) (k2_fdiff_1 (k2_partfun1 k1_numbers k1_numbers B A) A))) ) ) ) ) ) ).
tt(t16_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r3_fdiff_3 A C) & (r3_fdiff_3 B C))  =>  ((r3_fdiff_3 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k2_fdiff_3 C (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k2_fdiff_3 C A) (k2_fdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t16_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k9_real_1 A D))  &  (~  ((k1_seq_1 C D) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers C) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers C) B) D) = (k10_real_1 1 (k5_square_1 (k9_real_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))))) =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))) A) B) = (k7_real_1 (k1_seq_1 k19_sin_cos B) (k8_real_1 (k10_real_1 1 2) (k10_prepower B (k1_real_1 (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ).
tt(t16_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k1_real_1 (k8_real_1 D (k6_power k8_power A)))) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) B) D) = (k8_real_1 (k10_prepower A (k1_real_1 D)) (k6_power k8_power A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6) A) B) = (k7_real_1 (k1_seq_1 k1_sin_cos6 B) (k10_real_1 B (k7_square_1 (k9_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t16_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t16_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k1_fdiff_9 B)) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t16_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) = (k1_net_1 A))  &  ( ((k2_xboole_0 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)) (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) = (k1_net_1 A))  &  ( ((k2_xboole_0 (k2_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A))) (k2_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A)))) = (k2_relat_1 (k1_net_1 A)))  &  ((k2_xboole_0 (k2_relat_1 (k5_relat_1 (k1_net_1 A) (u4_struct_0 A))) (k2_relat_1 (k5_relat_1 (k1_net_1 A) (u1_struct_0 A)))) = (k2_relat_1 (k1_net_1 A))) ) ) ) ) ) ).
tt(t16_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v2_finseq_1 E)) )  =>  ( (E = (k2_tarski (k4_tarski A C) (k4_tarski B D)))  =>  ((r1_xxreal_0 B A) |  ((k15_finseq_1 E) = (k10_finseq_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fib_num3,ax, ((k1_fib_num3 4) = 7) ).
tt(t16_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 (k3_power k2_fib_num A) (k13_complex1 1 (k7_square_1 5)))) ) ) ).
tt(t16_filerec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( (E = (k11_finseq_1 A B C))  =>  ((k2_rfinseq D 2 E) = (k9_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(t16_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k2_filter_0 A B)) &  ((r2_hidden (k3_lattices A B C) (k2_filter_0 A B)) & (r2_hidden (k3_lattices A C B) (k2_filter_0 A B))) ) ) ) ) ) ) ) ).
tt(t16_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices (k4_filter_1 A B) (k5_filter_1 A B C) (k5_filter_1 A B D)) <=> (r2_hidden (k4_filter_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t16_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v1_xboole_0 C))  &  ((v18_lattices C B) &  ((v21_lattices C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_finance1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (r1_tarski (k6_finance1 A k1_numbers B k12_prob_1) (k3_random_2 A B))) ) ) ) ).
tt(t16_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A)) =>  ((v1_relat_1 (k3_relat_1 B A)) &  ((v1_funct_1 (k3_relat_1 B A)) & (v1_finseq_1 (k3_relat_1 B A))) ) ) ) ) ) ) ).
tt(t16_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_finseq_1 (k7_finseq_1 B (k9_finseq_1 A))) = (k2_nat_1 (k3_finseq_1 B) 1)) ) ) ) ).
tt(t16_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((k2_finseq_1 A) = (k2_finseq_1 (k1_nat_1 A 1))) ) ) ) ).
tt(t16_finseq_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k7_partfun1 A (k12_finseq_1 A B) 1) = B) ) ) ) ) ).
tt(t16_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k3_finseq_1 (k16_finseq_1 B A)) (k3_finseq_1 A))) ) ) ) ).
tt(t16_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r2_finseq_4 (k7_finseq_1 A B) C) => (r2_hidden C (k5_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ) ) ).
tt(t16_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_finseq_7 A (k3_finseq_4 A B C D) 2 E) = (k3_finseq_4 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_xxreal_0 (k3_finseq_1 (k4_finseq_8 A B C)) (k3_finseq_1 B)) & (r1_xxreal_0 (k3_finseq_1 (k4_finseq_8 A B C)) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t16_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r2_relset_1 k5_numbers B (k4_finseqop A B (k5_finseq_2 A D C) E) (k5_finseq_2 B D (k3_funct_2 A B E C)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k5_finseq_2 A 1 B) C) = B) ) ) ) ) ) ) ).
tt(t16_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) => (v1_finset_1 B)) ) ) ).
tt(t16_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k10_fin_topo A C)) <=>  ( ((k4_fintopo2 A B C) = k8_margrel1)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( ((k1_fintopo2 A B D C) = k8_margrel1)  &  ((k5_fintopo2 A B D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_fintopo3 A B 2) = (k9_fin_topo A (k9_fin_topo A B))) ) ) ) ) ).
tt(t16_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r2_fintopo4 A B E k6_numbers) &  (D = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E C)) )  => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E (k9_fin_topo A C)) (k9_fin_topo B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fintopo5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k5_fintopo5 A 1)) (u1_struct_0 (k2_fintopo4 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_fintopo5 A 1)) (u1_struct_0 (k2_fintopo4 A)))))) )  & (v1_fintopo5 B (k5_fintopo5 A 1) (k2_fintopo4 A))) ) ) ) ).
tt(t16_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v4_fin_topo B A) <=> (v1_fintopo6 (k1_fintopo6 A B))) ) ) ) ) ).
tt(t16_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k8_fin_topo A (k3_subset_1 (u1_struct_0 A) B))) = (k9_fin_topo A B)) ) ) ) ) ).
tt(t16_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_tarski C (k6_flang_1 A C B)) & (r1_tarski C (k6_flang_1 A B C))) ) ) ) ) ) ) ).
tt(t16_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_xxreal_0 C k6_numbers) |  ((k8_flang_1 A (k7_flang_1 A B C)) = (k8_flang_1 A B)) ) ) ) ) ) ) ) ).
tt(t16_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_flang_3 A B (k2_xcmplx_0 C 1)) = (k6_flang_1 A (k1_flang_3 A B C) B)) ) ) ) ) ) ).
tt(t16_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((v5_relat_1 C A) & (v3_card_1 C B))  => (r2_hidden C (k4_finseq_2 B A))) ) ) ) ) ) ).
tt(t16_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v13_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( (~ (v14_fomodel1 B k6_numbers A))  =>  ((v6_fomodel1 (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B) A) &  (~  ((k33_fomodel1 A B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t16_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel2 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  => (r2_hidden B (k33_fomodel2 A))) ) ) ) ).
tt(t16_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A))))) =>  ( (! [C:$i] :  ((m2_funct_2 C (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 A)) (k9_setfam_1 (k1_fomodel4 A)))) =>  ((r2_hidden C B) => (v17_fomodel4 C A)) ) )  => (v16_fomodel4 B A)) ) ) ) ) ).
tt(t16_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_valued_0 C (u1_struct_0 A) B) => (r1_tarski (k2_frechet A B) (k2_frechet A C))) ) ) ) ) ) ).
tt(t16_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C A) =>  ((k8_relat_1 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B D)) (k6_subset_1 C (k1_tarski D))) = (k7_subset_1 C (k6_subset_1 C B) (k1_tarski D))) ) ) ) ) ) ).
tt(t16_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (~  ((k2_msafree2 (k8_fscirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((r5_fsm_1 A B C D E) & (r5_fsm_1 A B C E F))  => (r5_fsm_1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( ((v3_fsm_2 B A) & (v1_fsm_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A (u2_fsm_1 A B) D)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A (u2_fsm_1 A B) E))) )  &  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 B) A) (u1_struct_0 B) (u1_fsm_1 A B) (k1_domain_1 (u1_struct_0 B) A F C)) = (u2_fsm_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  ((u1_struct_0 (k4_fsm_3 A B C)) = (k1_zfmisc_1 (u1_struct_0 C))) ) ) ) ) ) ) ).
tt(t16_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (~  ((r2_hidden A (k2_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden B (k2_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden C (k2_msafree2 (k7_ftacell1 A B C D E))) &  ((r2_hidden D (k2_msafree2 (k7_ftacell1 A B C D E))) & (r2_hidden E (k2_msafree2 (k7_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden B C))  =>  ((k8_relat_1 (k2_funcop_1 A B) C) = k1_xboole_0) ) ) ) ) ).
tt(t16_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k1_funcsdom A k1_numbers (k6_funcsdom A) (k2_binop_1 k1_numbers (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers) (k7_funcsdom A) E B) C) = (k2_binop_1 k1_numbers (k9_funct_2 A k1_numbers) (k9_funct_2 A k1_numbers) (k7_funcsdom A) E (k1_funcsdom A k1_numbers (k6_funcsdom A) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski (k10_xtuple_0 B) A) &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = A)  &  ( ((k9_xtuple_0 D) = A)  &  ((k3_relat_1 B C) = (k3_relat_1 B D)) ) )  =>  (C = D) ) ) ) ) ) )  =>  (A = (k10_xtuple_0 B)) ) ) ) ) ).
tt(t16_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (~  (B = k1_xboole_0) )  =>  ( ((k2_relset_1 B C) = B)  <=>  (! [D:$i] :  ( (~  (D = k1_xboole_0) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B D)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) )  =>  ((r2_relset_1 A D (k1_partfun1 A B B D C E) (k1_partfun1 A B B D C F)) => (r2_relset_1 B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k3_tarski (k8_relat_1 (k1_funct_3 B) A)) (k8_relat_1 B (k3_tarski A)))) ) ) ).
tt(t16_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)) & (r2_hidden A (k9_xtuple_0 B)))  =>  ((k1_funct_1 (k1_funct_4 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t16_funct_5,ax, (! [A:$i] :  ( ((k9_xtuple_0 A) = k1_xboole_0)  <=>  ((k10_xtuple_0 A) = k1_xboole_0) ) ) ).
tt(t16_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r1_tarski (k9_xtuple_0 F) (k2_zfmisc_1 D E)) =>  ( ( (~ (r2_hidden (k1_funct_5 F) (k4_partfun1 A (k4_partfun1 B C))))  &  (~ (r2_hidden (k3_funct_5 F) (k4_partfun1 B (k4_partfun1 A C)))) )  | (r2_hidden F (k4_partfun1 (k2_zfmisc_1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t16_funct_7,ax, (~  (k4_numbers = (k3_finseq_2 k4_numbers)) ) ).
tt(t16_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 A k1_numbers k1_numbers B) => (r2_funct_8 A k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t16_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 C A) & (v1_funct_9 C B))  =>  ( ((k6_xcmplx_0 A B) = k6_numbers)  | (v1_funct_9 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t16_functor0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (k2_zfmisc_1 B B)) &  ((v1_functor0 C A B) &  ((v2_functor0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B))))) ) ) )  =>  (? [D:$i] :  ((m1_subset_1 D B) & (r8_pboole (k2_zfmisc_1 A A) C (k7_funcop_1 (k2_zfmisc_1 A A) (k4_tarski D D)))) ) ) ) ) ) ) ) ).
tt(t16_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  ((v17_functor0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (v2_funct_1 (k5_functor0 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) )  =>  (! [E:$i] :  ( ((v15_functor0 E A C) & (m2_functor0 E A C))  =>  (! [F:$i] :  ( ((v15_functor0 F C D) & (m2_functor0 F C D))  =>  (! [G:$i] :  ( ((v15_functor0 G C D) & (m2_functor0 G C D))  =>  (! [H:$i] :  ( ((v15_functor0 H D B) & (m2_functor0 H D B))  =>  (! [I:$i] :  ((m1_functor2 I C D F G) =>  ((r1_functor2 C D F G) => (r8_pboole (u1_struct_0 A) (k6_functor3 A C B (k1_functor3 C D B F H) (k1_functor3 C D B G H) E (k5_functor3 C D B F G I H)) (k5_functor3 A D B (k1_functor3 A C D E F) (k1_functor3 A C D E G) (k6_functor3 A C D F G E I) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_xxreal_0 (k1_seq_1 (k4_fuzzy_1 A) B) (k1_seq_1 C B)) & (r1_xxreal_0 (k1_seq_1 C B) (k1_seq_1 (k5_fuzzy_1 A) B))) ) ) ) ) ) ) ).
tt(t16_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A (k1_fuzzy_2 A B C) D) (k1_fuzzy_2 A B (k2_fuzzy_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t16_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  => (r1_fuzzy_1 (k4_fuzzy_4 A B C (k1_fuzzy_1 (k2_zfmisc_1 A B) D E) F) (k1_fuzzy_1 (k2_zfmisc_1 A C) (k4_fuzzy_4 A B C D F) (k4_fuzzy_4 A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_fvaluat1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_realset2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (C = (k4_struct_0 B)) )  &  ((k3_fvaluat1 B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t16_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r7_binop_1 (u1_struct_0 A) (k5_vectsp_1 A) (u1_algstr_0 A))) ) ).
tt(t16_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 A B C)))  &  ( (~  ( ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  |  ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) ) )  & (v1_xboole_0 C)) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B)) )  &  ( (~  ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) ) )  &  (~ (v1_xboole_0 C)) ) ) ) ) ) )  &  (~  ( ( ( ( ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B))  |  ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) ) )  & (v1_xboole_0 C))  |  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 B)) )  &  ( (~  ((v1_xboole_0 A) &  (~ (v1_xboole_0 B)) ) )  &  (~ (v1_xboole_0 C)) ) ) )  & (v1_xboole_0 (k10_gate_1 A B C))) ) ) ) ) ) ).
tt(t16_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r4_gcd_1 A B (k4_struct_0 A)) =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t16_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((k9_genealg1 D E F k6_numbers k6_numbers A) = (k7_genealg1 D E F A))  &  ( ((k9_genealg1 D E F B k6_numbers k6_numbers) = (k7_genealg1 D E F B))  &  ((k9_genealg1 D E F k6_numbers C k6_numbers) = (k7_genealg1 D E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) => (r2_geomtrap A B C D E D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k7_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k7_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k7_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (u1_struct_0 (k7_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (u1_struct_0 (k7_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k7_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp) (u1_struct_0 (k7_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t16_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k5_gfacirc2 k6_numbers A B) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k6_gfacirc2 k6_numbers A B) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ((k7_gfacirc2 k6_numbers A B) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1))) ) ) ) ) ) ) ).
tt(t16_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A C D B) <=>  ((r2_glib_000 A C D B) | (r2_glib_000 A D C B)) ) ) ) ) ) ) ).
tt(t16_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ( ((k3_glib_001 A C) = (k3_glib_001 B D))  &  ((k4_glib_001 A C) = (k4_glib_001 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k1_glib_002 A B) = (k6_glib_000 A)) ) ) ) ) ) ).
tt(t16_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k8_glib_003 A (k7_glib_001 A B C)) = (k7_finseq_1 (k8_glib_003 A B) (k8_glib_003 A C))) ) ) ) ) ) ) ) ).
tt(t16_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)))) =>  ((r1_tarski (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) B)) (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) & (r1_tarski (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) B) (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k7_glib_004 A B)))) ) ) ) ) ).
tt(t16_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~  (B = C) )  => (r1_glib_005 A (k1_funct_1 (k12_glib_005 A B C) D) B C)) ) ) ) ) ) ) ) ) ).
tt(t16_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 E))) &  ( ((k1_matrix_1 E) = (k2_nat_1 B 1))  &  ((r2_hidden C (k4_finseq_1 E)) &  ((r1_xxreal_0 A D) & (r1_xxreal_0 D B)) ) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  ( ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 E A) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C (k2_nat_1 D 1)))  & (r2_hidden (k2_nat_1 D 1) (k2_finseq_1 (k1_matrix_1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_goboard2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 (k1_seq_1 (k1_goboard1 B) C) (k1_seq_1 (k1_goboard1 B) A))) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) (k3_finseq_1 (k2_goboard2 B)))))) ) ) ) ) ).
tt(t16_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 C)) & (r1_xxreal_0 1 B)) ) ) )  =>  ((v3_relat_1 C) |  ((r1_xxreal_0 (k3_finseq_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) A)) (k2_goboard5 C A))) ) ) ) ) ) ) ) ) ).
tt(t16_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k2_goboard5 A (k1_matrix_1 A))) = (a_1_3_goboard6 A)) ) ) ).
tt(t16_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(t16_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k3_finseq_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 2))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 1) (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 D 2) (k2_nat_1 C 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((k1_tops_1 (k15_euclid 2) (k4_goboard5 A B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t16_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  => (v4_pre_topc (k2_goboard5 B A) (k15_euclid 2))) ) ) ) ).
tt(t16_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 E) (k16_matrix_1 F)) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 E)) &  ((r1_xxreal_0 B (k1_matrix_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 F)) &  ((r1_xxreal_0 D (k1_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 B 1) |  ((r1_xxreal_0 D 1) | (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A (k7_nat_d B 1))) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C (k7_nat_d D 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) <=>  ( (~ (r2_hidden B (k2_goboard9 A)))  &  (~ (r2_hidden B (k3_goboard9 A))) ) ) ) ) ) ) ).
tt(t16_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [C:$i] :  ((m1_henmodel C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 (k7_cqc_sim1 A E) D) &  ((v1_goedelcp B A) & (v2_goedelcp B A)) )  =>  ((r1_valuat_1 A (k1_henmodel A) E C (k3_henmodel A)) <=> (r1_henmodel A B E)) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 (k7_cqc_sim1 A E) (k2_nat_1 D 1)) &  ((v1_goedelcp B A) & (v2_goedelcp B A)) )  =>  ((r1_valuat_1 A (k1_henmodel A) E C (k3_henmodel A)) <=> (r1_henmodel A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_graph_1 B) & (l1_graph_1 B)) )  =>  ( ((r4_graph_1 A B) & (r4_graph_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t16_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 1))  =>  ((k1_funct_1 (k3_graph_2 B A) (k3_finseq_1 (k3_graph_2 B A))) = (k1_funct_1 A (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t16_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((k1_graph_3 A k1_xboole_0) = k1_xboole_0) ) ) ).
tt(t16_graph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ((v7_graph_1 C B) & (m2_graph_1 C B))  =>  ((v7_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B) & (m2_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B)) ) ) ) ) ) ) ).
tt(t16_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( ((k3_finseq_1 C) = 1)  &  ( ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 C 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B (k3_finseq_1 B))))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 (u2_graph_1 A) (k1_funct_1 B D)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 C 1))) ) ) ) ) ) ) ) )  =>  ( ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 B 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B (k3_finseq_1 B))))  |  ((v7_graph_1 (k8_finseq_1 (u4_struct_0 A) B C) A) &  ((v1_graph_4 (k8_finseq_1 (u4_struct_0 A) B C) A) & (m2_graph_1 (k8_finseq_1 (u4_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t16_graphsp,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_graph_1 C) &  ((v6_graph_1 C) & (l1_graph_1 C)) ) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m2_graph_1 D C))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 C) k8_graph_5) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 C) k8_graph_5)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( ((u1_struct_0 C) = (k2_xboole_0 A B))  &  ((r2_hidden F A) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  ( ((r2_hidden H A) & (r2_hidden I B))  =>  (! [J:$i] :  (~  ((r2_hidden J (u4_struct_0 C)) & (r1_graph_4 C H I J)) ) ) ) ) ) ) ) ) )  =>  ((r8_graph_5 C F G D A E) <=> (r7_graph_5 C F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_grcat_1,ax, (! [A:$i] :  ( ((v2_grcat_1 A) & (l1_grcat_1 A))  =>  (! [B:$i] :  ( ((v2_grcat_1 B) & (l1_grcat_1 B))  =>  (~  ( ((k7_grcat_1 A) = (k8_grcat_1 B))  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l2_algstr_0 E)) ) ) )  =>  (~  ((m1_grcat_1 A D E) & (m1_grcat_1 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_gr_cy_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (A = (k5_group_1 k2_gr_cy_1 A (k5_gr_cy_1 1))) ) ) ).
tt(t16_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  ( (~ (v8_struct_0 A))  => (r2_group_6 k2_gr_cy_1 A)) ) ) ).
tt(t16_gr_cy_3,ax, ((k1_gr_cy_3 k6_numbers) = k6_numbers) ).
tt(t16_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ((r2_hidden A (k9_xtuple_0 B)) &  ( (B = (k2_xboole_0 C D))  &  ( (~  ((k1_funct_1 B A) = (k1_funct_1 C A)) )  &  (~  ((k1_funct_1 B A) = (k1_funct_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((v15_algstr_0 (k1_funct_1 B C)) &  ((v1_group_3 (k1_funct_1 B C) A) & (m1_group_2 (k1_funct_1 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t16_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r1_rewrite1 (k3_polyred A B C D) E (k7_polynom1 A C))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r7_polyred A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r8_pboole (k15_pre_poly A) (k5_vfunct_1 (k15_pre_poly A) B (k4_polynom7 A B C)) (k4_polynom7 A B (k4_algstr_0 B C)))) ) ) ) ) ).
tt(t16_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A))) =>  ( ((k2_polynom1 (k15_pre_poly A) B (k2_groeb_3 A B C D)) = (k3_xboole_0 (k2_polynom1 (k15_pre_poly A) B C) D))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E (k2_polynom1 (k15_pre_poly A) B (k2_groeb_3 A B C D))) =>  ((k3_polynom1 A B (k2_groeb_3 A B C D) E) = (k3_polynom1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_group_10,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((k7_group_1 (k4_gr_cy_1 A)) = A) ) ) ).
tt(t16_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k1_group_11 A B C) B)) ) ) ) ) ) ).
tt(t16_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) ).
tt(t16_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k2_group_2 A (k1_subset_1 (u1_struct_0 A)) B) = k1_xboole_0)  &  ((k2_group_2 A B (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ) ) ) ).
tt(t16_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k2_group_3 A B C) = (k2_group_3 A D C))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t16_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ((v2_funct_1 B) &  ((v2_funct_1 C) &  ((k10_xtuple_0 B) = (k10_xtuple_0 C)) ) ) )  =>  ((k3_group_4 A B) = (k3_group_4 A C)) ) ) ) ) ) ) ) ).
tt(t16_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_5 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A B) (k2_group_1 A C)) B) C))  &  ( ((k2_group_5 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A B) (k6_algstr_0 A (k2_group_1 A C) B)) C))  &  ( ((k2_group_5 A B C) = (k6_algstr_0 A (k2_group_1 A B) (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A C) B) C)))  &  ( ((k2_group_5 A B C) = (k6_algstr_0 A (k2_group_1 A B) (k6_algstr_0 A (k2_group_1 A C) (k6_algstr_0 A B C))))  &  ((k2_group_5 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A B) (k2_group_1 A C)) (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  =>  ( ((r2_hidden B (k15_group_2 A D)) & (r2_hidden C (k15_group_2 A D)))  => (r2_hidden (k2_group_2 A B C) (k15_group_2 A D))) ) ) ) ) ) ) ) ) ).
tt(t16_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) & (v1_group_7 (k10_finseq_1 A B))) ) ) ) ) ) ) ) ).
tt(t16_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_card_1 B) = (k1_card_1 (k5_group_2 A C (k4_group_2 A (k2_group_1 A C) B)))) ) ) ) ) ) ) ).
tt(t16_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) => (m1_group_9 (k4_group_9 A B) A C)) ) ) ) ) ).
tt(t16_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (v2_group_10 (k6_group_2 A) B)) ) ) ) ).
tt(t16_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_grsolv_1 A) & (l3_algstr_0 A)) ) ) )  => (v1_grsolv_1 (k10_group_6 A B C))) ) ) ) ) ) ) ).
tt(t16_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k5_hahnban1 A B C C) (k7_hahnban1 A B))) ) ) ) ) ) ).
tt(t16_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_struct_0 C B) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) H (k1_rlvect_1 A B J)))  &  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) G E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) I (k1_rlvect_1 A B K))) )  =>  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k3_rlvect_1 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F G) E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) (k3_rlvect_1 C H I) (k1_rlvect_1 A B (k7_real_1 J K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (v1_hallmar1 B A))  => (r1_xxreal_0 1 (k5_card_1 (k1_funct_1 B C)))) ) ) ) ) ) ) ).
tt(t16_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (B = C)  =>  ((k1_pre_topc (k3_pcomps_1 A) B) = (k3_pcomps_1 (k1_topmetr A C))) ) ) ) ) ) ) ) ).
tt(t16_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((v3_glib_001 B A) &  ((k4_glib_001 A B) = (k3_glib_001 A C)) )  =>  ((k7_glib_001 A B C) = C) ) ) ) ) ) ) ) ).
tt(t16_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [C:$i] :  ((m1_henmodel C A B) =>  ((r1_valuat_1 A (k1_henmodel A) (k5_cqc_lang A) C (k3_henmodel A)) <=> (r1_henmodel A B (k5_cqc_lang A))) ) ) ) ) ) ) ).
tt(t16_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k1_hermitan A B)) B)) ) ) ) ).
tt(t16_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v6_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r1_collsp A D B C) &  ((r1_collsp A G E F) &  ((r1_collsp A D E H) &  ((r1_collsp A G B H) &  ((r1_collsp A D F I) &  ((r1_collsp A C G I) &  ((r1_collsp A B F J) & (r1_collsp A C E J)) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = C)  |  ( (E = F)  |  ( (G = E)  |  ( (G = F)  |  ((r1_collsp A D B G) | (r1_collsp A J I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_heyting1,ax, ((k7_normform k1_xboole_0) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ).
tt(t16_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  ( (C = k1_xboole_0)  =>  ((k3_heyting2 A B C C) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ).
tt(t16_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_heyting3 (k2_nat_1 A 1) B) = (k2_xboole_0 (k3_heyting3 A B) (k6_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 A) 3) B)))) ) ) ) ) ).
tt(t16_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 C A B) & (r1_taylor_1 D A B))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) B) A) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C B) A) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 D B) A)))) ) ) ) ) ) ) ) ) ).
tt(t16_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_polynom3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_polynom3 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k14_polynom3 A) B C) = (k3_normsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (r2_hidden (k3_hilbert1 A k2_hilbert1) k6_hilbert1)) ) ).
tt(t16_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k3_hilbert1 A B)) (k3_finseq_1 A)))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k3_hilbert1 A B)) (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t16_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ((k1_partfun1 (k2_zfmisc_1 C D) (k2_zfmisc_1 A B) (k2_zfmisc_1 A B) A (k16_funct_3 C D A B E F) (k9_funct_3 A B)) = (k1_partfun1 (k2_zfmisc_1 C D) C C A (k9_funct_3 C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k3_polynom5 A B C)) (k3_polynom5 A (k5_vfunct_1 k5_numbers A B) C))) ) ) ) ) ) ).
tt(t16_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_idea_1 B (k6_idea_1 B A))) ) ) ) ).
tt(t16_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t16_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ((r1_collsp A B D G) &  ((r1_collsp A C E H) & (r1_collsp A F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k3_incproj A))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k3_incproj A))) &  (? [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k3_incproj A))) &  ((r1_incsp_1 (k3_incproj A) B G) &  ((r1_incsp_1 (k3_incproj A) E G) &  ((r1_incsp_1 (k3_incproj A) F G) &  ((r1_incsp_1 (k3_incproj A) E C) & (r1_incsp_1 (k3_incproj A) F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B B C D) A)) ) ) ) ) ) ) ) ).
tt(t16_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m5_index_1 (k4_tarski (k7_cat_1 A B C) (k12_mcart_1 C)) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A))) ) ) ) ) ) ).
tt(t16_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  (! [C:$i] :  ((m1_instalg1 C B) => (m1_instalg1 C A)) ) ) ) ) ) ).
tt(t16_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r2_int_1 A B C) & (r2_int_1 D E C))  => (r2_int_1 (k2_xcmplx_0 A D) (k2_xcmplx_0 B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 A B) <=> (r1_int_1 (k1_int_2 A) (k1_int_2 B))) ) ) ) ) ).
tt(t16_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_int_2 B A) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B D) C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (~  ( ((k3_finseq_1 B) = (k3_nat_d (k7_nat_d A 1) 2))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k3_int_2 (k1_recdef_1 B C) A) = 1) ) ) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_int_5 (k1_recdef_1 B C) A)) ) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 B)) &  ( (~  (C = D) )  & (r2_int_1 (k1_recdef_1 B C) (k1_recdef_1 B D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k3_int_2 (k3_xcmplx_0 A B) (k3_xcmplx_0 A C)) = (k4_nat_1 (k1_int_2 A) (k3_int_2 B C))) ) ) ) ) ) ) ).
tt(t16_int_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k10_newton) &  ((v1_funct_1 A) &  ((v1_partfun1 A k10_newton) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( ((v1_int_7 A) &  (B = (k8_nat_3 k10_newton A)) )  => (r8_pboole k10_newton (k13_nat_3 B) A)) ) ) ) ) ).
tt(t16_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) (k5_seq_4 A)))) ) ) ).
tt(t16_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B G) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1))) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k12_binop_2 H A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E H) (k19_binop_2 1)))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 E H)))  &  ((k1_seq_1 C H) = 1) ) ) ) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2))) &  ( (G = (k1_relset_1 k1_numbers F))  & (r2_relset_1 k1_numbers k1_numbers F (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k2_sin_cos9))) ) ) ) )  =>  ( (A = k6_numbers)  |  ((k2_integra5 B F) = (k10_binop_2 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k2_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k12_binop_2 A 2))) (k4_seq_4 B)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k2_sin_cos9)) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k12_binop_2 A 2))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) (k1_partfun2 k1_numbers C)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t16_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 D)) (k8_real_1 (k5_square_1 D) (k5_square_1 (k1_seq_1 k16_sin_cos (k10_real_1 1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t16_integr15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_euclid B)))))  => (r2_relset_1 A k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers (k9_integr15 B D A E) (k1_pdiff_1 C B)) (k26_valued_1 A k1_numbers (k1_partfun1 A (k1_euclid B) (k1_euclid B) k1_numbers E (k1_pdiff_1 C B)) D))) ) ) ) ) ) ) ) ) ).
tt(t16_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( ((k2_partfun1 k1_numbers k2_numbers B A) = C)  =>  ((r1_integr16 A B) <=> (v1_integr16 C A)) ) ) ) ) ) ) ) ).
tt(t16_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (C = (k1_rcomp_1 D E))  =>  ((k5_integr18 A C B) = (k6_integr18 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k1_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ( ((v3_integr15 C A) &  (C = D) )  => (v1_integr15 D A B)) ) ) ) ) ) ) ) ) ).
tt(t16_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v3_funct_1 (k2_partfun1 A k1_numbers (k7_rfunct_1 A A) A))) ) ).
tt(t16_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v3_xxreal_2 B) & (r1_xxreal_0 A k6_numbers))  =>  ((k4_seq_4 (k1_integra2 B A)) = (k8_real_1 A (k5_seq_4 B))) ) ) ) ) ) ).
tt(t16_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  ((r2_hidden A (k1_rvsum_1 C)) =>  ((r1_xxreal_0 (k1_seq_1 C 1) A) & (r1_xxreal_0 A (k1_seq_1 C (k3_finseq_1 C)))) ) ) ) ) ) ) ) ).
tt(t16_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v2_seq_2 (k2_partfun1 A k1_numbers C B)) => (v1_seq_2 (k2_partfun1 A k1_numbers (k19_rfunct_3 A C) B))) ) ) ) ) ) ).
tt(t16_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)) & (r1_tarski A (k1_relset_1 k1_numbers B)))  => (r1_integra5 A B)) ) ) ) ) ).
tt(t16_integra6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~ (r1_xxreal_0 (k3_integra1 A) k6_numbers))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_integra1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (~  ((v2_comseq_2 (k2_integra3 A B)) &  ( ((k2_seq_2 (k2_integra3 A B)) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m1_integra1 D A) &  ((r1_integra4 A D (k2_nat_1 C 1)) &  ((k2_integra2 A B C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k3_integra5 A B))) &  ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers D)) &  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden E (k2_rcomp_1 A B)) =>  ((k1_seq_1 D E) = (k7_real_1 (k4_integra5 A E C) (k1_seq_1 D A))) ) ) ) ) ) ) )  => (r1_integra7 (k2_rcomp_1 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(t16_integra8,ax, ((k6_sin_cos6 (k1_real_1 (k10_real_1 (k7_square_1 2) 2))) = (k10_real_1 (k8_real_1 3 k32_sin_cos) 4)) ).
tt(t16_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) =>  ((k2_integra5 A (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k16_sin_cos))) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) k19_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) k19_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t16_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r1_tarski (k5_interva1 A B) (k6_interva1 A B))) ) ) ) ).
tt(t16_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v8_intpro_1 A) => (r1_tarski k8_intpro_1 A)) ) ) ).
tt(t16_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((k1_funct_1 (k2_rfinseq B 1 C) A) = (k1_funct_1 C (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ).
tt(t16_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] : (r1_isocat_1 (k8_cat_2 (k3_cat_1 B C) A) A)) ) ) ) ).
tt(t16_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) => (r2_nattra_1 B C (k12_cat_2 A B C D (k3_graph_1 A E)) (k12_cat_2 A B C D (k4_graph_1 A E)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) <=>  ((v1_isomichi B A) & (v3_pre_topc B A)) ) ) ) ) ) ).
tt(t16_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ( (? [E:$i] :  ( (~  (E = C) )  & (r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) B C) (k1_rltopsp1 (k15_euclid A) C D)))) )  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid A) C D)))  &  (~ (r2_hidden D (k1_rltopsp1 (k15_euclid A) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( (B = a_0_1_jgraph_2)  => (r1_tarski (k2_relset_1 (k8_struct_0 (k15_euclid 2)) (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 B)) (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)))) ) ) ) ) ).
tt(t16_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_1_jgraph_3) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t16_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 B (k13_complex1 (k18_euclid A) (k12_euclid A))) =>  ((r1_xxreal_0 k6_numbers (k17_euclid A)) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))))) (k8_real_1 (k12_euclid A) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))) ) )  &  ((r1_xxreal_0 k6_numbers (k17_euclid A)) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 B) A) = A) ) ) ) ) ) ) ).
tt(t16_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (C = a_0_5_jgraph_5)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( ((k1_funct_1 A k6_numbers) = (k19_euclid (k1_real_1 1) k6_numbers))  &  ( ((k1_funct_1 A 1) = (k19_euclid 1 k6_numbers))  &  ( ((k1_funct_1 B 1) = (k19_euclid k6_numbers 1))  &  ( ((k1_funct_1 B k6_numbers) = (k19_euclid k6_numbers (k1_real_1 1)))  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = a_0_0_jgraph_6)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) & (r1_jordan6 E C D)) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc G k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 G) &  ((v5_pre_topc H k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 H) &  ( (F = a_0_1_jgraph_6)  &  ( ((k1_funct_1 G k6_numbers) = C)  &  ( ((k1_funct_1 G 1) = A)  &  ( ((k1_funct_1 H k6_numbers) = B)  &  ( ((k1_funct_1 H 1) = D)  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H) F) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = E)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid C) H) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) H)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_xboole_0 (k1_jordan2c 2 B) (k2_goboard9 (k1_jordan9 B A)))) ) ) ) ).
tt(t16_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_tarski A (k1_jordan2c 2 B)) => (r1_tarski B (k2_jordan2c 2 A))) ) ) ) ) ).
tt(t16_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden B E) & (r2_hidden C E)) ) ) )  &  ( (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden B E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski (k2_jordan2c 2 A) (k2_goboard9 (k1_jordan13 A B)))) ) ) ) ) ).
tt(t16_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k2_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r1_jordan5c A B C D E) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = B)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 F G) = D)  &  ( ((k1_funct_1 F H) = E)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 H 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A D B C E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A B F C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k1_jordan18 B A)) = (k17_euclid B))  &  ((k17_euclid (k2_jordan18 B A)) = (k17_euclid B)) ) ) ) ) ) ).
tt(t16_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k2_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) ) )  => (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k1_matrix_1 C))))) ) ) ) ) ) ) ).
tt(t16_jordan1b,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_jordan1a (k1_jordan8 A B)) = (k2_nat_1 (k13_newton 2 (k7_nat_d B 1)) 2)) ) ) ) ) ).
tt(t16_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (D = (k1_int_1 (k7_real_1 (k8_real_1 (k10_real_1 (k9_real_1 (k18_euclid C) (k9_pscomp_1 A)) (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A))) (k13_newton 2 B)) 2)))  & (r1_xxreal_0 (k7_real_1 (k9_pscomp_1 A) (k8_real_1 (k10_real_1 (k9_real_1 (k7_pscomp_1 A) (k9_pscomp_1 A)) (k13_newton 2 B)) (k5_real_1 D 1))) (k18_euclid C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k24_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t16_jordan1e,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan1e A B)) (k3_topreal1 2 (k2_jordan1e A B))) = (k2_tarski (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ).
tt(t16_jordan1g,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C (k10_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 B)) & (r1_xxreal_0 (k4_finseq_4 B D) (k4_finseq_4 B C))) )  =>  ((k2_finseq_5 A (k1_finseq_5 A B C) D) = (k1_finseq_5 A (k2_finseq_5 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_finseq_1 A) = (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A)))) ) ) ).
tt(t16_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  & (r1_xxreal_0 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k21_pscomp_1 B) A))  =>  ((k21_pscomp_1 A) = (k21_pscomp_1 B)) ) ) ) ) ) ).
tt(t16_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_jordan2c A (k2_struct_0 (k15_euclid A))) = (k1_struct_0 (k15_euclid A))) ) ) ).
tt(t16_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers D) &  ((v3_tops_2 C k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  (B = (a_3_1_jordan20 A C D)) ) )  => (v3_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ) ).
tt(t16_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k10_jordan6 A) = (k11_jordan6 A)) ) ) ) ).
tt(t16_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k2_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k19_euclid (k13_complex1 (k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2) (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_jordan9 A B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) (k3_finseq_1 (k1_jordan8 A B))))))))) ) ) ) ) ) ).
tt(t16_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_funct_1 A) => (v2_jordan23 A)) ) ) ).
tt(t16_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m3_topgrp_1 B (k15_euclid 2)) =>  ((v1_jordan1 A) => (v1_jordan1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(t16_jordan2b,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))) =>  ( (F = (k9_metric_1 B E D))  =>  ((r1_xxreal_0 D k6_numbers) | (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C F) A)) ) ) ) ) ) ) )  => (v5_pre_topc C A (k3_pcomps_1 B))) ) ) ) ) ) ) ).
tt(t16_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_jordan2c A B C) => (r1_tarski C (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) ) ) ) ) ) ) ).
tt(t16_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k3_topreal1 2 A)) &  ( (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) C) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A C) 1) (k3_finseq_1 A))))  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k1_nat_1 D 1) (k3_finseq_1 B))) ) )  => (r1_tarski (k2_topreal1 2 B D) (k2_topreal1 2 A (k7_nat_d (k2_nat_1 (k1_jordan3 A C) D) 1)))) ) ) ) ) ) ) ) ) ).
tt(t16_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k3_finseq_6 A B k6_numbers k6_numbers) = (k17_finseq_1 A 1 B)) ) ) ) ) ).
tt(t16_jordan5a,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc A k5_topmetr k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) ) )  =>  ( ( ((k1_funct_1 A k6_numbers) = k6_numbers)  &  ((k1_funct_1 A 1) = 1) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (B = D)  &  ( (C = E)  &  ( (~ (r1_xxreal_0 E D))  &  ( (F = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A B))  &  ( (G = (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr) A C))  & (r1_xxreal_0 G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((v4_topreal1 A) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B (k3_finseq_1 A))))) ) )  =>  (B = 1) ) ) ) ) ) ).
tt(t16_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) B) (k15_euclid 2)) &  ((r2_hidden C (k3_topreal1 2 A)) & (r2_hidden C B)) ) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) C (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ).
tt(t16_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_3_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k17_pscomp_1 (k3_topreal1 2 A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k17_pscomp_1 (k3_topreal1 2 A)))))) ) ) ) ) ) ).
tt(t16_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ( (B = (k1_jordan6 A B C))  <=>  ((k17_euclid B) = (k17_euclid C)) ) ) ) ) ) ) ) ) ).
tt(t16_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ((v5_pre_topc C k5_topmetr (k15_euclid A)) &  ((v2_funct_1 C) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid A)) C) = B)  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ( (D = C)  & (v3_tops_2 D k5_topmetr (k1_pre_topc (k15_euclid A) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) => (r1_xboole_0 (k3_goboard5 (k1_jordan8 A C) (k3_finseq_1 (k1_jordan8 A C)) B) A)) ) ) ) ) ) ) ).
tt(t16_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ( ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))))  &  ( ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)))  &  ( ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)))  &  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) =>  ( (B = (k18_pscomp_1 A))  | (r1_topreal1 (k15_euclid 2) B (k18_pscomp_1 A) (k1_jordan7 A B (k18_pscomp_1 A)))) ) ) ) ) ) ).
tt(t16_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_xxreal_0 B) & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r2_hidden C (k1_topreal9 A C B))) ) ) ) ) ) ).
tt(t16_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ((k4_knaster A B C (k1_ordinal1 D)) = (k1_funct_1 B (k4_knaster A B C D))) ) ) ) ) ) ) ) ) ).
tt(t16_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A C) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) C) =>  (! [F:$i] :  ((m1_kolmog01 F B A C) =>  (~  ((r2_kolmog01 A C D B F) &  ((r2_hidden E (k6_kolmog01 B A C F)) &  ( (~  ((k3_funct_2 C k1_numbers D E) = k6_numbers) )  &  (~  ((k3_funct_2 C k1_numbers D E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C E) = (k5_subset_1 A D (k3_funct_2 k5_numbers (k9_setfam_1 A) B E))) ) )  => (r1_tarski (k5_subset_1 A D (k3_kurato_0 A B)) (k4_kurato_0 A C))) ) ) ) ) ) ) ) ).
tt(t16_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1) = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 1) (k4_rcomp_1 1 2)) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) ).
tt(t16_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ((m2_valued_0 B (k9_setfam_1 (u1_struct_0 A)) C) => (r1_tarski (k1_kurato_2 A C) (k1_kurato_2 A B))) ) ) ) ) ) ) ).
tt(t16_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_lang1 (k9_lang1 A)) = A) ) ) ).
tt(t16_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k1_matrix_1 E))) =>  ( ( ( (G = C)  &  ((k3_finseq_1 F) = (k3_finseq_1 E)) )  =>  ((k9_matrix_1 D (k3_laplace C A B D E F) G) = F) )  &  ( (~  (G = C) )  =>  ((k9_matrix_1 D (k3_laplace C A B D E F) G) = (k9_matrix_1 D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) & (r2_hidden D (k1_funct_1 (k1_latsubgr A) B)))  => (r2_hidden (k6_algstr_0 A C D) (k1_funct_1 (k1_latsubgr A) B))) ) ) ) ) ) ) ) ) ).
tt(t16_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k13_lattice3 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t16_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A B C) = C) ) )  =>  (B = (k6_lattices A)) ) ) ) ) ) ).
tt(t16_lattice3,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v4_orders_2 A) =>  ((k11_lattice3 A (k11_lattice3 A B C) D) = (k11_lattice3 A B (k11_lattice3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((k1_lattice4 A (k1_setwiseo (u1_struct_0 A))) = (k5_lattices A)) ) ) ).
tt(t16_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v2_lattice5 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (v2_lattice5 (k6_lattice5 A B C D) (k5_lattice5 A) B)) ) ) ) ) ) ) ) ) ).
tt(t16_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_lattice6 B A) => (v2_waybel_6 (k4_lattice3 A B) (k3_lattice3 A))) ) ) ) ) ).
tt(t16_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_1 A) <=>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_lattice7 B))  & (r5_waybel_1 A (k2_yellow_1 B))) ) ) ) ) ).
tt(t16_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) & (v1_funct_1 C)) )  =>  ( ((v4_ordinal1 B) &  ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k3_lattice8 A D)) ) ) ) ) )  =>  ( (B = k1_xboole_0)  |  ((k3_lattice8 A B) = (k3_tarski (k10_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(t16_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r3_lattices A (k5_lattices A) B)) ) ) ) ).
tt(t16_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (r1_xxreal_0 D (k7_nat_d (k39_glib_000 B) C)))  &  ((r1_xxreal_0 D (k39_glib_000 B)) &  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) &  ((k1_recdef_1 (k5_lexbfs A B C) E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 (k7_lfuzzy_0 A B D) (k7_lfuzzy_0 A C D))) )  <=> (r1_orders_2 (k4_lfuzzy_0 A) (k6_lfuzzy_0 A B) (k6_lfuzzy_0 A C))) ) ) ) ) ) ) ).
tt(t16_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_lfuzzy_1 (k4_fuzzy_2 A A) A) &  ((v4_lfuzzy_1 (k4_fuzzy_2 A A) A) & (v3_lfuzzy_1 (k4_fuzzy_2 A A) A)) ) ) ) ).
tt(t16_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (v2_limfunc1 B))  => (v1_limfunc1 (k47_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t16_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r6_limfunc2 B A) &  ((r6_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r6_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r5_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t16_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers C (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))))) ) ) )  | (r2_limfunc3 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t16_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  ((v5_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r6_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t16_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k1_lmod_5 A B (k4_subset_1 (u1_struct_0 B) C D)) = (k1_vectsp_5 A B (k1_lmod_5 A B C) (k1_lmod_5 A B D))) ) ) ) ) ) ) ) ) ).
tt(t16_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  ( ((r1_lmod_6 A B C) & (r1_lmod_6 A D C))  =>  ( ((k4_struct_0 B) = (k4_struct_0 D))  &  ((r1_struct_0 D (k4_struct_0 B)) &  ( ((r1_tarski (u1_struct_0 B) (u1_struct_0 D)) => (r1_lmod_6 A B D))  &  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r1_struct_0 B E) => (r1_struct_0 D E)) ) )  => (r1_lmod_6 A B D))  &  ( ( ( ((u1_struct_0 B) = (u1_struct_0 D))  &  ((v7_vectsp_1 B A) & (v7_vectsp_1 D A)) )  =>  (B = D) )  & (r1_lmod_6 A (k1_vectsp_4 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k14_lmod_7 A B E C) = (k14_lmod_7 A B E D))  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_lopban_1 A B))) =>  ( (E = (k3_rlvect_1 (k8_lopban_1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k9_lopban_1 A B E F) = (k3_rlvect_1 B (k9_lopban_1 A B C F) (k9_lopban_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k8_lopban_2 A)))  &  ((v13_algstr_0 (k8_lopban_2 A)) &  ((v2_rlvect_1 (k8_lopban_2 A)) &  ((v3_rlvect_1 (k8_lopban_2 A)) &  ((v4_rlvect_1 (k8_lopban_2 A)) &  ((v5_rlvect_1 (k8_lopban_2 A)) &  ((v6_rlvect_1 (k8_lopban_2 A)) &  ((v7_rlvect_1 (k8_lopban_2 A)) &  ((v2_funcsdom (k8_lopban_2 A)) &  ((v3_group_1 (k8_lopban_2 A)) &  ((v1_vectsp_1 (k8_lopban_2 A)) &  ((v3_vectsp_1 (k8_lopban_2 A)) & (l1_funcsdom (k8_lopban_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k3_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t16_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A C) B) = (k3_rlvect_1 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k4_lopban_4 A C)) B) (k8_nat_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ).
tt(t16_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v3_lopban_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)))))) )  =>  ( ((r1_funct_2 (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)) (u1_struct_0 A) (u1_struct_0 B) D C) & (v2_funct_2 D (u1_struct_0 (k4_normsp_2 B))))  => (v1_t_0topsp D (k4_normsp_2 A) (k4_normsp_2 B))) ) ) ) ) ) ) ) ) ).
tt(t16_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (a_2_0_lopclset A B) (k7_lopclset A))) ) ) ) ).
tt(t16_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) B (k2_binop_1 k1_numbers (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers) (k4_lpspace1 A) (k1_real_1 1) B)) (k2_partfun1 A k1_numbers (k5_lpspace1 A) (k1_relset_1 A B)))) ) ) ) ).
tt(t16_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((r1_xxreal_0 (k4_power (k18_complex1 (k7_real_1 A B)) C) (k4_power (k7_real_1 (k18_complex1 A) (k18_complex1 B)) C)) &  ((r1_xxreal_0 (k4_power (k7_real_1 (k18_complex1 A) (k18_complex1 B)) C) (k4_power (k8_real_1 2 (k4_xxreal_0 (k18_complex1 A) (k18_complex1 B))) C)) & (r1_xxreal_0 (k4_power (k18_complex1 (k7_real_1 A B)) C) (k4_power (k8_real_1 2 (k4_xxreal_0 (k18_complex1 A) (k18_complex1 B))) C))) ) ) ) ) ) ) ) ) ).
tt(t16_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (B = (g1_normsp_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A)) (k3_lp_space A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v1_rsspace3 C B) => (v3_normsp_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t16_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k3_hilbert1 (k2_ltlaxio1 (k1_ltlaxio1 A)) (k1_ltlaxio1 (k2_ltlaxio1 A))))) = 1) ) ) ) ) ) ) ).
tt(t16_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) & (r2_hidden C (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A B D) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t16_margrel1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k4_xboolean A (k4_xboolean B C)) = (k4_xboolean (k4_xboolean A B) C)) ) ) ) ) ) ) ).
tt(t16_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_mathmorp A D (k1_mathmorp A C B)) = (k1_mathmorp A (k3_rlvect_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t16_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_matrix10 B) => (v2_matrix10 (k2_matrix10 A B))) ) ) ) ) ).
tt(t16_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r2_hidden A (k2_finseq_1 C)) &  ((r2_hidden B (k2_finseq_1 C)) &  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 C)) =>  (~  ((v4_matrix_2 D (k11_matrix_2 (k12_matrix_2 C))) &  ((k1_funct_1 D A) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) B C) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 D) B C) =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 F))) &  (G = (k4_matrix_1 (u1_struct_0 D) F)) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ((k4_matrix_1 (u1_struct_0 D) (k2_matrix12 B C D G A E)) = (k5_matrix12 B C D F A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v2_matrix_2 D A B) & (m1_matrix_1 D (u1_struct_0 B) A A))  =>  (! [E:$i] :  ( ((v2_matrix_2 E A B) & (m1_matrix_1 E (u1_struct_0 B) A A))  =>  ( (C = (k4_matrix_6 A B D E))  =>  ( ((v2_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A))  &  ((k13_matrix_3 A B C) = (k11_fvsum_1 B (k13_matrix_3 A B D) (k13_matrix_3 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 A) k6_numbers k6_numbers) => (v1_matrix_6 B k6_numbers A)) ) ) ) ).
tt(t16_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D A C) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k1_matrix_1 E))) =>  ((k9_matrix_1 D (k1_matrix15 D A B C E F) G) = (k9_matrix_1 D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v1_matrix16 F (u1_struct_0 B)) &  ((v1_matrix16 G (u1_struct_0 B)) & (v1_matrix16 H (u1_struct_0 B))) )  => (v1_matrix16 (k2_matrix_6 A B (k3_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ((v5_matrix17 D (u1_struct_0 A)) &  ((v5_matrix17 E (u1_struct_0 A)) &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix17 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 E) (k3_finseq_1 E) A (k1_matrix17 (u1_struct_0 A) E) C)) = (k1_matrix17 (u1_struct_0 A) (k3_fvsum_1 A (k9_fvsum_1 A D B) (k9_fvsum_1 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_matrix_1 (k10_finseq_1 k1_xboole_0 k1_xboole_0) A 2 k1_xboole_0)) ) ).
tt(t16_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k8_matrix_1 A B C)) ) ) ) ) ) ) ) ).
tt(t16_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k12_matrix_1 B A))) =>  ( ( (C = D)  =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) D) C) = (k5_struct_0 B)) )  &  ( (~  (C = D) )  =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) D) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A B C) D) = (k1_matrix_4 A (k1_matrix_4 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  (A = (k3_matrix_5 A B)) ) )  =>  (B = (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ) ) ).
tt(t16_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) =>  ((v1_matrix_6 (k5_matrix_6 A B C) A B) &  ((k5_matrix_6 A B (k5_matrix_6 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t16_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k12_matrix_3 B A (k12_matrix_1 A B)) = (k1_group_1 A)) ) ) ) ) ) ).
tt(t16_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) & (v4_matrix_6 C A B))  =>  (C = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t16_matrix_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( (E = (k3_finseq_4 A B C D))  =>  ((k4_finseq_5 A E) = (k3_finseq_4 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k4_finseq_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k4_finseq_2 A k2_numbers)) =>  ((k12_seq_4 (k5_matrixc1 C D) B) = (k5_matrixc1 (k12_seq_4 C B) D)) ) ) ) ) ) ) ) ) ).
tt(t16_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ((k2_wsierp_1 (k10_matrixj1 A (k5_matrixj1 A B C))) = (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t16_matrixj2,ax, (! [A:$i] :  ((l6_algstr_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~ (r1_xxreal_0 (k9_matrixj2 A B C) E))  &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C E) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_finseq_1 (k9_fvsum_1 A B C)) = (k3_finseq_1 B)) ) ) ) ) ) ) ).
tt(t16_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_3 A (k1_matrix_4 A C D) B) = (k1_matrix_4 A (k4_matrix_3 A C B) (k4_matrix_3 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ((r2_hidden A (k4_finseq_1 D)) =>  ((k4_rlvect_1 C (k5_matrlin B C (k8_matrix_1 (u1_struct_0 B) (k12_matrix_1 B (k3_finseq_1 D)) A) D)) = (k7_partfun1 (u1_struct_0 C) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ((v13_vectsp_1 D B C) & (v1_mod_2 D A B C))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k4_rlvect_1 B E)) = (k4_rlvect_1 C (k4_finseqop (u1_struct_0 B) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) & (l1_pre_topc A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_matroid0 A C B) & (r1_matroid0 A D B))  =>  ((k5_card_1 C) = (k5_card_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ( (C = D)  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k8_matrix_1 A C E) = (k8_matrix_1 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (~  ( ((k8_matrix13 C D) = A)  &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) (k7_nat_d B A) B) =>  (~  ((k8_matrix13 C (k8_matrlin (u1_struct_0 C) A (k7_nat_d B A) B D E)) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  (~  ((v2_funct_1 D) &  (! [E:$i] :  ((m2_vectsp_6 E k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B D)) =>  (~  ( ((k4_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) E) = (k1_funct_1 (k3_matrtop1 A B D) C))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 C)) =>  ((k1_funct_1 E (k8_matrix_1 (u1_struct_0 k2_vectsp_1) D F)) = (k1_funct_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k13_fvsum_1 k2_vectsp_1 (k1_matrtop1 E) (k9_matrix_1 (u1_struct_0 k2_vectsp_1) (k2_matrtop3 D A B C) C)) = (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k17_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k20_sin_cos A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (v2_mazurulm C A B))  => (v2_mazurulm (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t16_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D C))  => (r2_pboole A (k5_pboole A B D) C)) ) ) ) ) ) ) ) ).
tt(t16_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_zfmisc_1 B (k2_tarski C D))) =>  ((r2_hidden (k1_xtuple_0 A) B) &  ( ((k2_xtuple_0 A) = C)  |  ((k2_xtuple_0 A) = D) ) ) ) ) ) ) ) ).
tt(t16_measure1,ax, (! [A:$i] :  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_tarski A))))) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 (k1_tarski A) B C) = A) ) ) ) ) ) ).
tt(t16_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_measure2 D A B) =>  ( (! [E:$i] :  ((r2_hidden E D) => (m2_measure1 E A B C)) )  => (m2_measure1 (k1_measure2 A B D) A B C)) ) ) ) ) ) ) ) ).
tt(t16_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k2_measure3 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_measure3 A B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k9_setfam_1 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k8_nat_1 (k9_setfam_1 A) F G) = (k6_subset_1 (k8_nat_1 (k2_measure3 A B C) D G) (k8_nat_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) => (r1_measure3 A (k1_measure4 A B) (k3_measure4 A B))) ) ) ).
tt(t16_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v1_measure5 A) =>  (A = (k1_measure5 (k7_supinf_2 A) (k8_supinf_2 A))) ) ) ) ).
tt(t16_measure7,ax,(m1_measure4 k10_measure7 k1_numbers)).
tt(t16_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_measure8 C A B) => (m2_measure8 (k3_prob_3 A C) A B)) ) ) ) ) ).
tt(t16_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k5_member_1 (k3_xboole_0 A B)) = (k3_xboole_0 (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(t16_membered,ax, (! [A:$i] :  ((v4_membered A) =>  ( (! [B:$i] :  ((v1_rat_1 B) => (r2_hidden B A)) )  =>  (A = k3_numbers) ) ) ) ).
tt(t16_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_memstr_0 A B (k1_funct_4 C (k7_memstr_0 A B D))) = D) ) ) ) ) ) ) ) ) ).
tt(t16_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 F)) (k1_rlvect_1 (k15_euclid 2) C F)))  &  (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) A G))) )  =>  ((r1_euclid_6 A B C) |  ( (G = 1)  |  ( (~  ( (~  ((k9_binop_2 (k10_binop_2 1 G) (k11_binop_2 F G)) = k6_numbers) )  & (r1_xboole_0 (k4_euclid_4 2 A D) (k4_euclid_4 2 B E))) )  &  (~  ( (~ (r1_xboole_0 (k4_euclid_4 2 A D) (k4_euclid_4 2 B E)))  &  ((k9_binop_2 (k10_binop_2 1 G) (k11_binop_2 F G)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (E = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc1 A C (k4_mesfunc5 A k7_numbers B G) E)) )  &  ((r1_mesfunc5 A C D F) &  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G E) => (r1_xxreal_0 (k12_supinf_2 (k10_mesfunc1 A (k4_mesfunc5 A k7_numbers B H)) G) (k12_supinf_2 F G))) ) ) ) ) ) ) ) )  =>  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc5 A C D (k10_mesfunc1 A (k4_mesfunc5 A k7_numbers B G)))) )  &  ((r1_mesfunc5 A C D (k10_mesfunc1 A (k5_mesfunc8 A B))) & (r1_mesfunc5 A C D (k10_mesfunc1 A (k6_mesfunc8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((k1_relset_1 A C) = D)  =>  ((r1_mesfun6c A B C E) <=> (r1_mesfun6c A B C (k5_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 D F) = (k8_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) (k13_mesfunc1 (k4_mesfunc5 A k1_numbers C F) E))) ) )  =>  ((k3_tarski (k2_relset_1 B D)) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) (k17_mesfunc1 A (k3_mesfun7c A C) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers D F) C)) )  => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k2_mesfun9c A D) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((r1_tarski C (k9_xtuple_0 B)) =>  ((k9_subset_1 A C (k16_mesfunc1 A B D)) = (k6_subset_1 C (k9_subset_1 A C (k17_mesfunc1 A B D)))) ) ) ) ) ) ) ) ).
tt(t16_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (r1_xxreal_0 (k12_supinf_2 (k2_mesfunc2 A B) C) k1_supinf_2))  =>  ((k12_supinf_2 (k1_mesfunc2 A B) C) = k1_supinf_2) ) ) ) ) ) ) ) ).
tt(t16_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (A = B)  =>  ((k4_extreal1 A) = (k18_rvsum_1 B)) ) ) ) ) ) ).
tt(t16_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) & (v3_mesfunc5 C))  =>  ((k1_relset_1 A (k3_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ).
tt(t16_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_tarski D E) & (r1_mesfunc6 A B C E))  => (r1_mesfunc6 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v5_xxreal_2 (k2_relset_1 k7_numbers B)) => (v3_valued_0 B)) ) ) ) ) ).
tt(t16_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k4_mesfunc5 A k7_numbers C F) (k1_measure6 E)))) ) )  =>  ((k1_setfam_1 (k2_relset_1 B D)) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k1_mesfunc8 A C) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mesfunc9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  ((v6_supinf_2 (k2_mesfunc9 A)) & (v7_valued_0 (k2_mesfunc9 A))) ) ) ) ).
tt(t16_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_subset_1 (u1_struct_0 B) (k11_metric_1 B C A) (k9_metric_1 B C A)) = (k10_metric_1 B C A)) ) ) ) ) ) ) ).
tt(t16_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k1_metric_2 A B) (k2_metric_2 A))) ) ) ) ).
tt(t16_metric_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) => (r1_xxreal_0 (k7_real_1 (k7_real_1 (k8_real_1 (k8_real_1 2 (k3_xcmplx_0 A D)) (k3_xcmplx_0 C B)) (k8_real_1 (k8_real_1 2 (k3_xcmplx_0 A F)) (k3_xcmplx_0 E C))) (k8_real_1 (k8_real_1 2 (k3_xcmplx_0 B F)) (k3_xcmplx_0 E D))) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 (k3_xcmplx_0 A D)) (k3_square_1 (k3_xcmplx_0 C B))) (k3_square_1 (k3_xcmplx_0 A F))) (k3_square_1 (k3_xcmplx_0 E C))) (k3_square_1 (k3_xcmplx_0 B F))) (k3_square_1 (k3_xcmplx_0 E D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  => (r2_metric_6 A (k9_metric_1 A B D) C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) & (r2_hidden D (k2_pcomps_1 A)))  => (r2_metric_6 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (r1_ordinal1 (k1_card_1 C) (k1_card_1 (k2_struct_0 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k1_seq_1 (k3_rlvect_1 (k15_euclid B) C D) A) = (k9_binop_2 (k1_seq_1 C A) (k1_seq_1 D A))) ) ) ) ) ) ) ) ) ) ).
tt(t16_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_midsp_1 A B C D E) & (r1_midsp_1 A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v12_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k4_algstr_0 A B))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t16_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v4_midsp_2 D B) & (l1_midsp_2 D B))  =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 B D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B D)))) =>  ((k8_midsp_3 A B D C (k7_midsp_3 A B D C E)) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 F G) &  ((r1_tarski B C) & (r1_relset_1 A A D E)) )  => (r1_tarski (k13_mmlquery A B E F) (k13_mmlquery A C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E A) &  ((v9_vectsp_1 E A) &  ((v10_vectsp_1 E A) &  ((v11_vectsp_1 E A) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E A)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v2_mod_2 F A) & (m1_mod_2 F A B C))  =>  (! [G:$i] :  ( ((v2_mod_2 G A) & (m1_mod_2 G A C D))  =>  (! [H:$i] :  ( ((v2_mod_2 H A) & (m1_mod_2 H A D E))  =>  ((k8_mod_2 A H (k8_mod_2 A G F)) = (k8_mod_2 A (k8_mod_2 A H G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((v1_lmod_5 (k7_domain_1 (u1_struct_0 B) C D) A B) =>  ( (C = D)  |  ( (~  (D = (k4_struct_0 B)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (C = (k4_vectsp_1 A B E D)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (C = (k4_vectsp_1 A B E D)) ) ) )  =>  ( (D = (k4_struct_0 B))  |  ( (~  (C = D) )  & (v1_lmod_5 (k7_domain_1 (u1_struct_0 B) C D) A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_vectsp_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ( ( (C = (k5_mod_4 B D))  &  ( (E = G)  &  (F = H) ) )  =>  ((k1_algstr_0 D G H) = (k1_algstr_0 C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((r2_hidden B A) =>  (! [C:$i] :  ((m1_trees_1 C A) =>  (! [D:$i] :  ((m1_trees_1 D (k4_trees_1 A B)) =>  ( (C = (k8_finseq_1 k5_numbers B D))  => (r2_wellord2 (k1_trees_2 A C) (k1_trees_2 (k4_trees_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_modcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_modcat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k11_modcat_1 A B))) =>  (! [E:$i] :  ((m4_modcat_1 E B (k4_modcat_1 B (k3_modcat_1 A B))) =>  (! [F:$i] :  ((m4_modcat_1 F B (k4_modcat_1 B (k3_modcat_1 A B))) =>  ( ( (C = E)  &  (D = F) )  =>  ( ( ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C))  =>  ((k2_mod_2 B F) = (k3_mod_2 B E)) )  &  ( ( ((k2_mod_2 B F) = (k3_mod_2 B E))  =>  ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C)) )  &  ( ( ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C))  => (r2_hidden (k4_tarski F E) (k1_relset_1 (k2_zfmisc_1 (k4_modcat_1 B (k3_modcat_1 A B)) (k4_modcat_1 B (k3_modcat_1 A B))) (k10_modcat_1 B (k3_modcat_1 A B)))))  &  ( ((r2_hidden (k4_tarski F E) (k1_relset_1 (k2_zfmisc_1 (k4_modcat_1 B (k3_modcat_1 A B)) (k4_modcat_1 B (k3_modcat_1 A B))) (k10_modcat_1 B (k3_modcat_1 A B)))) =>  ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C)) )  &  ( ( ((k3_graph_1 (k11_modcat_1 A B) D) = (k4_graph_1 (k11_modcat_1 A B) C))  =>  ((k1_cat_1 (k11_modcat_1 A B) C D) = (k8_mod_2 B F E)) )  &  ( ( ((k3_graph_1 (k11_modcat_1 A B) C) = (k3_graph_1 (k11_modcat_1 A B) D))  =>  ((k2_mod_2 B E) = (k2_mod_2 B F)) )  &  ( ( ((k2_mod_2 B E) = (k2_mod_2 B F))  =>  ((k3_graph_1 (k11_modcat_1 A B) C) = (k3_graph_1 (k11_modcat_1 A B) D)) )  &  ( ( ((k4_graph_1 (k11_modcat_1 A B) C) = (k4_graph_1 (k11_modcat_1 A B) D))  =>  ((k3_mod_2 B E) = (k3_mod_2 B F)) )  &  ( ((k3_mod_2 B E) = (k3_mod_2 B F))  =>  ((k4_graph_1 (k11_modcat_1 A B) C) = (k4_graph_1 (k11_modcat_1 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k27_modelc_1 (k48_modelc_1 A B D) E F)) <=>  (? [G:$i] :  ((m1_modelc_1 G A B) &  ( ((k3_funct_2 k5_numbers A G k6_numbers) = C)  &  (? [H:$i] :  ((m1_subset_1 H k5_numbers) &  ( (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ( (~ (r1_xxreal_0 H I))  => (r3_modelc_1 A B D (k3_funct_2 k5_numbers A G I) E)) ) )  & (r3_modelc_1 A B D (k3_funct_2 k5_numbers A G H) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_modelc_2 A (k5_modelc_2 B C)) <=>  ( (A = B)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t16_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  ( (~ (r1_xxreal_0 1 (k18_modelc_3 A B)))  =>  (B = (k7_modelc_3 A)) ) ) ) ) ) ).
tt(t16_moebius1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_tarski (k1_polynom2 k10_newton (k13_nat_3 B)) (k2_finseq_1 (k2_nat_1 A 1))) =>  ((r1_tarski (k1_polynom2 k10_newton (k13_nat_3 B)) (k2_finseq_1 A)) |  ((v7_ordinal1 (k2_nat_1 A 1)) & (v1_int_2 (k2_nat_1 A 1))) ) ) ) ) ) ) ).
tt(t16_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k5_struct_0 A) B) = B)  &  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) ) ) ) ) ) ).
tt(t16_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ( (~ (v1_xboole_0 G))  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B C) D) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) D)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 E F) G) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 E F) G)))) )  =>  ((r1_relset_1 (k2_zfmisc_1 B C) D H I) => (r1_relset_1 (k2_zfmisc_1 (k9_funct_2 A B) (k9_funct_2 A C)) (k9_funct_2 A D) (k8_monoid_1 B C D H A) (k8_monoid_1 E F G I A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C D) => (r1_tarski (k6_rusub_4 A B C) (k6_rusub_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t16_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 B))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden A (k1_funct_1 (k5_msafree3 B C D) E)) => (m1_dtconstr A (u1_struct_0 (k5_msafree B C)) (k5_trees_3 (u1_struct_0 (k5_msafree B C))) (k1_msaterm B C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v1_msafree (k13_msafree A B) A (k11_msafree A B))) ) ) ) ).
tt(t16_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 B E)) =>  ( (D = (k1_trees_4 (k4_tarski F E)))  =>  ((k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B) D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v7_graph_1 C A) & (m1_graph_1 C A)) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v7_graph_1 D A) & (m1_graph_1 D A)) )  =>  ( (B = (k7_finseq_1 C D))  =>  ( ((k1_funct_1 (k7_graph_2 A B) 1) = (k1_funct_1 (k7_graph_2 A C) 1))  &  ((k1_funct_1 (k7_graph_2 A B) (k2_nat_1 (k3_finseq_1 B) 1)) = (k1_funct_1 (k7_graph_2 A D) (k2_nat_1 (k3_finseq_1 D) 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_pboole C A B (k1_pboole A)) => (r6_pboole A C (k1_pboole A))) ) ) ) ) ).
tt(t16_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((m1_msualg_2 (k9_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) => (m1_unialg_2 A B)) ) ) ) ) ).
tt(t16_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((v2_relat_1 (k2_pboole (u1_struct_0 A) (k2_msualg_2 A B) C)) => (v2_relat_1 (k9_msualg_2 A B C))) ) ) ) ) ) ) ).
tt(t16_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((r4_msualg_3 A B B (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B))) & (r5_msualg_3 A B B)) ) ) ) ) ).
tt(t16_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((v2_msualg_4 (k3_pboole (u1_struct_0 A) C D) A B) &  ((v3_msualg_4 (k3_pboole (u1_struct_0 A) C D) A B) & (m1_msualg_4 (k3_pboole (u1_struct_0 A) C D) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t16_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m2_msualg_6 (k6_partfun1 (k1_funct_1 (u3_msualg_1 A B) C)) A B C C)) ) ) ) ) ) ).
tt(t16_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v1_msualg_7 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k16_lattice3 A C) = (k16_lattice3 B C)) ) ) ) ) ) ) ) ).
tt(t16_msualg_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_partfun1 D (k1_funct_1 B C)) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 B C) (k1_funct_1 B C))))) ) )  =>  (? [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  &  ((r2_relset_1 (k1_funct_1 B C) (k1_funct_1 B C) (k1_msualg_4 A B B E C) D) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~  (F = C) )  => (r2_relset_1 (k1_funct_1 B F) (k1_funct_1 B F) (k1_msualg_4 A B B E F) (k1_eqrel_1 (k1_funct_1 B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r3_msualg_3 A B C D) => (r6_msualg_3 A B (k6_msualg_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t16_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) => (r1_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C))) ) ) ) ) ) ) ).
tt(t16_mycielsk,ax, (! [A:$i] :  ( ((v4_dilworth A) &  ((v2_mycielsk A) & (l1_orders_2 A)) )  => (r1_xxreal_0 (k2_dilworth A) (k3_mycielsk A))) ) ).
tt(t16_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ((v3_pcomps_1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  (~ (v6_nagata_1 B A)) ) ) ) ) ) ) ).
tt(t16_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( ((r1_nagata_1 (u1_struct_0 A) B) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers B C) => (v1_pscomp_1 C (k2_borsuk_1 A A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k2_pre_topc A C)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k3_nagata_2 (u1_struct_0 A) B C) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k2_xcmplx_0 B A) B)) ) ) ) ) ) ).
tt(t16_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((k3_nat_d (k3_power 2 B) (k3_power 2 A)) = (k3_power 2 (k7_nat_d B A))) ) ) ) ) ) ).
tt(t16_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) & (v3_valued_0 C)) ) ) )  =>  ( (~  (A = k6_numbers) )  =>  ((k13_pre_poly C) = (k13_pre_poly (k4_nat_3 B C A))) ) ) ) ) ) ) ).
tt(t16_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  (~  ( (~  (B = k6_numbers) )  &  ( (C = (k1_newton A (k11_nat_3 B A)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (D = C)  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k3_moebius1 A)) & (r2_hidden D (k3_moebius1 B)))  => (r2_hidden (k24_binop_2 C D) (k3_moebius1 (k24_binop_2 A B)))) ) ) ) ) ) ) ) ) ).
tt(t16_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d B A) = k6_numbers)  =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 A C) |  ((k4_nat_d (k2_xcmplx_0 B C) A) = C) ) ) ) ) ) ) ) ) ) ).
tt(t16_nat_lat,ax,(m2_nat_lat k10_nat_lat k3_nat_lat)).
tt(t16_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((k9_cat_3 A B C A (k10_cat_1 A) D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t16_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r3_ncfcont1 B A C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  (! [E:$i] :  ((m1_ncfcont1 E A (k7_partfun1 (u1_struct_0 A) C D)) =>  (? [F:$i] :  ((m1_nfcont_1 F B D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((r2_hidden G (k1_relset_1 (u1_struct_0 B) C)) & (r2_hidden G F))  => (r2_hidden (k7_partfun1 (u1_struct_0 A) C G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_ncfcont2 A B C D) => (r5_ncfcont2 A B (k3_normsp_0 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ).
tt(t16_ndiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k1_valued_0 (u1_struct_0 B) (k3_normsp_1 B C D) A) (k3_normsp_1 B (k1_valued_0 (u1_struct_0 B) C A) (k1_valued_0 (u1_struct_0 B) D A)))) ) ) ) ) ) ) ) ).
tt(t16_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_ndiff_3 A C B) =>  ((r1_ndiff_3 A (k4_vfunct_1 k1_numbers A C D) B) &  ((k1_ndiff_3 A (k4_vfunct_1 k1_numbers A C D) B) = (k1_rlvect_1 A (k1_ndiff_3 A C B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k8_integr15 A k1_numbers C D))) &  ((r2_ndiff_4 A C B) & (r2_ndiff_4 A D B)) )  =>  ((r2_ndiff_4 A (k8_integr15 A k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_funct_1 (k2_ndiff_4 A (k8_integr15 A k1_numbers C D) B) E) = (k8_euclid A (k1_ndiff_4 A C E) (k1_ndiff_4 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k2_ndiff_5 A B C) (k1_rltopsp1 A B C))) ) ) ) ) ) ).
tt(t16_neckla_3,ax, (! [A:$i] :  ( ((v1_orders_2 A) &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  ((k3_necklace (k3_necklace A)) = A) ) ) ).
tt(t16_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_card_1 (u1_orders_2 (k1_necklace A))) = (k5_real_1 A 1)) ) ) ) ).
tt(t16_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  => (r1_tarski (k5_net_1 A B) (k2_net_1 A))) ) ) ) ) ).
tt(t16_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_subset_1 (k3_newton A) k1_numbers k5_numbers)) ) ).
tt(t16_nfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r1_nfcont_1 C B D E) => (r1_nfcont_1 C B (k4_vfunct_1 (u1_struct_0 C) B D A) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_nfcont_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 C (k18_complex1 (k3_xcmplx_0 B (k3_power A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) =>  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) C B) A) <=>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers D) B) &  ((v2_comseq_2 D) & (r2_hidden (k2_seq_2 D) B)) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C) A) &  ((k7_partfun1 (u1_struct_0 A) C (k2_seq_2 D)) = (k6_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_nfcont_4 A D C) => (r1_nfcont_4 A (k9_integr15 A B k1_numbers D) C)) ) ) ) ) ) ) ) ) ).
tt(t16_normform,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E D) => (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) (k3_funct_2 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) C E) (k6_normform B A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B (k2_nat_1 C 1))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B (k2_nat_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  ( (B = C)  =>  ((v3_nfcont_1 B A) <=> (v3_pre_topc C (k3_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t16_numbers,ax,(r1_tarski k4_numbers k2_numbers)).
tt(t16_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k10_openlatt A B)) <=>  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  & (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t16_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_qmax_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_oposet_1 A B) => (r1_oposet_1 A B)) ) ) ) ) ).
tt(t16_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((k5_oppcat_1 A (k1_cat_1 A E F)) = (k1_cat_1 (k2_oppcat_1 A) (k7_oppcat_1 A C D F) (k7_oppcat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_orders_1 A) => (v1_orders_1 (k2_relat_1 A))) ) ) ).
tt(t16_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k2_orders_2 A (k1_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t16_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) | (r2_hidden B A)) ) ) ) ) ).
tt(t16_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (r1_tarski B C))  => (r1_ordinal1 (k2_ordinal2 C) (k2_ordinal2 B))) ) ) ) ) ).
tt(t16_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~  ((r1_ordinal1 A 1) &  ( (~  (A = k1_xboole_0) )  &  (~  (A = 1) ) ) ) ) ) ) ).
tt(t16_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  ( ((v2_ordinal2 A) & (v4_ordinal1 (k9_xtuple_0 A)))  => (v4_ordinal1 (k4_ordinal2 A))) ) ) ).
tt(t16_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal5 A 1) = A) ) ) ).
tt(t16_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (A = B) )  =>  ((k1_ordinal6 (k2_tarski A B)) = 2) ) ) ) ) ) ).
tt(t16_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t16_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_orders_2 B E D) =>  ((r1_orders_2 B C D) |  ( ((k1_ortsp_1 A B D (k3_rlvect_1 B C E) F) = (k1_ortsp_1 A B D C F))  &  ((k1_ortsp_1 A B D C (k3_rlvect_1 B F E)) = (k1_ortsp_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k1_funct_1 B C)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ( (E = (k1_trees_4 (k4_tarski D C)))  =>  ((k10_osafree A B E) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (v11_osalg_1 (k3_osalg_1 A B) A)) ) ) ) ).
tt(t16_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r1_tarski (k5_osalg_2 A B C) (k5_msualg_2 A B C))) ) ) ) ) ) ).
tt(t16_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A B C D) &  ((v1_osalg_3 D A) &  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D))) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A (k6_msualg_3 A B C D)) (u3_msualg_1 A C)) =>  (~  ((r2_msualg_3 A B (k6_msualg_3 A B C D) E) &  ((r3_msualg_3 A (k6_msualg_3 A B C D) C F) &  ((r8_pboole (u1_struct_0 A) D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D)) (u3_msualg_1 A C) E F)) &  ((v1_osalg_3 E A) & (v1_osalg_3 F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r1_msualg_3 A B C D) & (v1_osalg_3 D A))  =>  ((v2_msualg_4 (k17_msualg_4 A B C D) A B) &  ((v3_msualg_4 (k17_msualg_4 A B C D) A B) & (m1_osalg_4 (k17_msualg_4 A B C D) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  => (v7_aff_2 (k2_diraf B))) ) ) ) ) ).
tt(t16_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  ((r1_parsp_1 (k9_parsp_1 A) B C B D) => (r1_parsp_1 (k9_parsp_1 A) C B C D)) ) ) ) ) ) ) ) ) ).
tt(t16_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_2 A B C D))  &  ((r1_parsp_1 A B C D E) & (r1_parsp_2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B))))  => (r1_tarski (k10_xtuple_0 C) (k1_tarski (k1_funct_1 C A)))) ) ) ) ).
tt(t16_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden D (k8_subset_1 B (k1_relset_1 B E) A)) =>  ((k7_partfun1 C (k2_partfun1 B C E A) D) = (k7_partfun1 C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r1_setfam_1 B (k3_partit1 A B C))) ) ) ) ) ) ).
tt(t16_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_diraf A B C D) &  ((r2_analoaf A E C F D) & (r2_analoaf A B E B F)) )  =>  ((r3_diraf A B D F) |  ( (B = E)  | (r1_diraf A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D C))  => (r2_pboole A (k2_pboole A B D) C)) ) ) ) ) ) ) ) ).
tt(t16_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 B) =>  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B))) ) ) ) ) ) ).
tt(t16_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k18_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k18_pcs_0 A B))) =>  ((r1_orders_2 (k18_pcs_0 A B) C D) <=>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (E = C)  &  ( (F = D)  & (r1_orders_2 A E F)) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (E = C)  &  ( (F = D)  & (r1_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 C))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid C)))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid B)) =>  ( ( (D = E)  &  (F = G) )  =>  ((r2_pdiff_1 C B A D F) <=> (r4_pdiff_1 B C A E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_euclid 2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r2_pdiff_2 B A) =>  ((r1_tarski A (k1_relset_1 (k1_euclid 2) B)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  ((r2_hidden C A) => (r3_pdiff_1 2 2 B C)) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r4_pdiff_3 B A) =>  ((k5_pdiff_3 B A) = (k11_pdiff_1 2 2 (k1_pdiff_3 2 2 B) A)) ) ) ) ) ) ).
tt(t16_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 1 F E))  =>  ( (D = (k11_pdiff_1 3 1 F E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J G) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 1 F E) M) (k1_seq_1 (k1_pdiff_2 3 1 F E) G)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M G)) (k1_seq_1 L (k9_real_1 M G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r7_pdiff_5 E D))  =>  ((k7_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 E) D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 C B A) &  ((v2_pdiff_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k1_euclid B)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_funct_1 E F) = (k1_funct_1 C (k1_funct_1 D F))) ) ) ) )  =>  ((k5_euclid_7 B E) = (k1_pdiff_6 A B C (k5_euclid_7 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) (k1_rlvect_1 (k4_real_ns1 1) B C)) = (k1_rlvect_1 (k4_real_ns1 A) (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_pdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 B))) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D B) C)) A)) ) )  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 B) C) (k11_binop_2 B A))) ) ) ) ) ) ) ).
tt(t16_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ( ((r1_pdiff_6 C B A D) & (r1_pdiff_6 C B A E))  =>  ((r1_pdiff_6 C B A (k8_integr15 B (k1_euclid A) D E)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) (k1_euclid B)) (k1_pdiff_9 A B C (k8_integr15 B (k1_euclid A) D E)) F) = (k8_integr15 B (k1_euclid A) (k8_pdiff_1 A B D F) (k8_pdiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (v4_pencil_1 (k1_pencil_1 A B C)))  &  (~  (! [D:$i] :  ((m1_subset_1 D A) => (v3_pencil_1 (k1_pencil_1 A B D))) ) ) ) ) )  & (v4_pencil_1 (k5_pencil_1 A B))) ) ) ) ) ) ).
tt(t16_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_pencil_1 C A) => (v2_pencil_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t16_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v15_pencil_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_pre_topc (k2_pencil_1 A C B))) =>  (! [E:$i] :  ((m1_pboole E A (k12_pralg_1 A C)) => (m1_subset_1 (k4_card_3 (k2_funct_7 (k1_pzfmisc1 A E) B D)) (u1_pre_topc (k5_pencil_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((m1_vectsp_4 C A D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ((k1_nat_1 (k1_vectsp_9 A C) 1) = E)  &  ( ((k1_vectsp_9 A D) = (k1_nat_1 E 1))  & (v1_zfmisc_1 (k3_pencil_4 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((v1_abian A) & (v1_abian (k1_nat_1 A 1))) ) ) ) ).
tt(t16_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_petri (k11_petri A) (k12_petri A B)) = (k7_petri A B)) ) ) ) ) ).
tt(t16_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r1_pnproc_1 A (k3_pnproc_1 A B (k1_pnproc_1 A)) B)) ) ) ).
tt(t16_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_polyalg1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (D = F)  &  (E = G) )  =>  ((k6_algstr_0 B D E) = (k6_algstr_0 C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k7_polyeq_1 A B C D E) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  (! [J:$i] :  ((v1_xreal_0 J) =>  ( ( (J = (k3_real_1 E (k6_real_1 B (k8_real_1 3 A))))  &  ( (I = (k1_real_1 (k6_real_1 B (k8_real_1 3 A))))  &  ( (F = (k7_xcmplx_0 B A))  &  ( (G = (k7_xcmplx_0 C A))  &  (H = (k7_xcmplx_0 D A)) ) ) ) )  =>  ((k7_real_1 (k7_real_1 (k3_real_1 (k1_newton J 3) (k8_real_1 k6_numbers (k3_square_1 J))) (k8_real_1 (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 A) C) (k3_square_1 B)) (k8_real_1 3 (k3_square_1 A))) J)) (k7_real_1 (k8_real_1 2 (k2_newton (k6_real_1 B (k8_real_1 3 A)) 3)) (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 A) D) (k3_xcmplx_0 B C)) (k8_real_1 3 (k3_square_1 A))))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k1_polyeq_1 A B C) = k6_numbers)  =>  ( (A = k6_numbers)  |  (C = (k1_binop_2 (k6_binop_2 B A))) ) ) ) ) ) ) ) ) ).
tt(t16_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k2_newton A E) (k2_newton B E)) = C)  &  ( ((k3_xcmplx_0 (k2_newton A E) (k2_newton B E)) = D)  &  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D))) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((v1_abian E) &  ((r1_xxreal_0 1 E) &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) )  &  ( (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))))  &  (B = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) )  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))) ) )  &  ( (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))) ) )  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) )  &  ( (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))))  &  (B = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))) ) )  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))) ) )  &  (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2))))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C (k6_square_1 (k6_xcmplx_0 (k5_square_1 C) (k3_xcmplx_0 4 D)))) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( ( (F = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 3 B) (k1_newton C 2)) 9))  &  ( (F = k6_numbers)  &  ( (G = (k13_complex1 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 C) B) (k3_xcmplx_0 2 (k1_newton C 3))) (k3_xcmplx_0 27 D)) 54))  &  (E = (k1_polyeq_5 3 (k3_xcmplx_0 2 G))) ) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 C (k1_newton A 2))) (k3_xcmplx_0 B A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k6_xcmplx_0 E (k13_complex1 C 3))) )  &  ( (~  (A = (k8_complex1 (k11_complex1 (k10_complex1 (k13_complex1 E 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 E (k1_polyeq_5 2 3)) k7_complex1) 2))) )  &  (~  (A = (k11_complex1 (k11_complex1 (k10_complex1 (k13_complex1 E 2)) (k13_complex1 C 3)) (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 E (k1_polyeq_5 2 3)) k7_complex1) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polyform,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k3_finseq_1 (k7_finseq_1 (k7_finseq_1 A B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_finseq_1 A) (k3_finseq_1 B)) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t16_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((k3_polynom1 A B E F) = (k1_algstr_0 B (k3_polynom1 A B C F) (k3_polynom1 A B D F))) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) E (k4_polynom1 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k3_polynom2 A (k11_pre_poly A C D) B E) = (k8_group_1 B (k3_polynom2 A C B E) (k3_polynom2 A D B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polynom3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k10_pre_poly A (k17_finseq_1 (k3_finseq_2 A) C B)) = (k17_finseq_1 k5_numbers C (k10_pre_poly A B))) ) ) ) ) ) ).
tt(t16_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) (k1_algseq_1 A C)))  &  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k2_normsp_1 A C (k1_polynom4 A B))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k1_algseq_1 A B) 1) D))  =>  ((k1_normsp_1 A C D) = (k1_normsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A B 1) B)) ) ) ) ).
tt(t16_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ( ((k2_polynom7 A B C) = (k16_pre_poly A))  &  ((k3_polynom7 A B C) = (k3_polynom1 A B C (k16_pre_poly A))) ) ) ) ) ) ) ).
tt(t16_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_polynom8 A (k5_struct_0 A) B) = (k5_struct_0 A)) ) ) ) ) ).
tt(t16_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k1_polyred A E C D))) => (r1_termord A B F (k11_pre_poly A E (k3_termord A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 A B) =>  ( ( (~  ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 C)) )  & (v1_abian C))  | (r1_xxreal_0 (k1_power C A) (k1_power C B))) ) ) ) ) ) ) ) ).
tt(t16_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((r2_hidden F (k1_relset_1 k5_numbers (k1_msualg_1 B D))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (G = (k1_funct_1 (k1_msualg_1 B D) F))  =>  (! [H:$i] :  ((m1_subset_1 H (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  ( (I = (k1_funct_1 H F))  => (r2_hidden (k1_funct_1 I E) (k1_funct_1 (u3_msualg_1 B (k5_pralg_2 A B C E)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pre_circ,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (~  ( (~  (B = k1_xboole_0) )  & (r1_xxreal_0 (k5_card_1 A) (k5_card_1 (k4_trees_1 A B)))) ) ) ) ) ) ).
tt(t16_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k4_nat_1 2 A) A)) ) ) ) ).
tt(t16_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) C) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A B D)) (k2_prelamb A C D)) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A D B)) (k1_prelamb A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_pre_poly,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_partfun1 A B) (k9_setfam_1 (k2_zfmisc_1 A B)))) ) ).
tt(t16_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  => (r1_xxreal_0 (k7_real_1 1 (k3_xcmplx_0 B A)) (k2_newton (k7_real_1 1 A) B))) ) ) ) ) ).
tt(t16_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v4_pre_topc D A) & (r1_tarski B D)) ) ) )  &  ((k2_pre_topc A B) = (k6_setfam_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(t16_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_prob_1 A B) &  ((v4_prob_1 A B) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v2_finsub_1 A) &  ((v1_prob_1 A B) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ) ).
tt(t16_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((k1_seq_1 D C) = (k9_real_1 1 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)))) ) ) ) ) ) ) ) ) ).
tt(t16_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((r2_hidden C (k1_funct_1 (k3_prob_3 B D) A)) <=>  ((r2_hidden C (k1_funct_1 D A)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (~ (r1_xxreal_0 A E))  & (r2_hidden C (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ( ((k1_prob_4 A (k9_setfam_1 A) (k3_prob_3 A B) k6_numbers) = (k1_prob_4 A (k9_setfam_1 A) B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_prob_4 A (k9_setfam_1 A) (k3_prob_3 A B) (k2_nat_1 C 1)) = (k3_measure1 A (k9_setfam_1 A) (k1_prob_4 A (k9_setfam_1 A) B (k2_nat_1 C 1)) (k1_prob_4 A (k9_setfam_1 A) B C))) ) ) ) ) ) ) ) ).
tt(t16_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A C))) (k7_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t16_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r1_projdes1 A B C D H) &  ((r1_projdes1 A B C D I) &  ((r1_projdes1 A B C D J) &  ((r1_projdes1 A E F G H) &  ((r1_projdes1 A E F G I) & (r1_projdes1 A E F G J)) ) ) ) )  =>  ((r1_collsp A B C D) |  ((r1_collsp A E F G) |  ((r1_projdes1 A B C D E) | (r1_collsp A H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ( (~  (B = C) )  =>  ((r1_incsp_1 A B (k1_projpl_1 A B C)) &  ((r1_incsp_1 A C (k1_projpl_1 A B C)) &  ( ((k1_projpl_1 A B C) = (k1_projpl_1 A C B))  &  ( ((r1_incsp_1 A B D) & (r1_incsp_1 A C D))  =>  (D = (k1_projpl_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v8_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) &  ((r1_incsp_1 A B F) &  ((r1_incsp_1 A C F) &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A E F) & (r2_zfmisc_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) I) &  ((r1_incsp_1 A F L) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D F) J) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C G) M) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D H) K) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B F E) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) G E H) O) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C F H) P)) ) ) ) ) ) )  =>  ((r1_incsp_1 A B I) |  ((r1_incsp_1 A B J) |  ((r1_incsp_1 A C J) |  ((r1_incsp_1 A C K) |  ((r1_projred2 A I L J) |  ((r1_projred2 A L J M) |  ( (I = K)  |  ( (K = J)  |  ( (B = C)  |  ( (~  (G = B) )  &  ( (~  (G = C) )  &  ( (~ (r1_incsp_1 A G I))  &  (~ (r1_incsp_1 A G K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_card_3 A) (k4_card_3 A)) (k4_card_3 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (k4_card_3 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 A)) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k4_finseq_1 A)) =>  ((k8_prvect_1 A (k12_prvect_1 (k4_card_3 A) B D E) F) = (k8_prvect_1 A (k12_prvect_1 (k4_card_3 A) C D E) F)) ) ) ) ) ) )  => (r8_binop_1 (k4_card_3 A) (k4_card_3 A) (k4_card_3 A) B C)) ) ) ) ) ) ) ).
tt(t16_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))))))) )  &  ((v2_funct_1 B) &  ((v2_funct_2 B (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A)))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B C) = (k12_finseq_1 (u1_struct_0 A) C)) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B (k3_rlvect_1 A C D)) = (k3_rlvect_1 (k14_prvect_2 (k9_finseq_1 A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B D))) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B (k1_rlvect_1 A C D)) = (k1_rlvect_1 (k14_prvect_2 (k9_finseq_1 A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B C) D)) ) ) ) )  &  ( ((k4_struct_0 (k14_prvect_2 (k9_finseq_1 A))) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B (k4_struct_0 A)))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 (k14_prvect_2 (k9_finseq_1 A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k14_prvect_2 (k9_finseq_1 A))) B C)) = (k1_normsp_0 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_compts_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  ((r1_tarski B C) => (r1_xxreal_0 (k1_pscomp_1 (k1_pre_topc A C) (k3_pscomp_1 A D C)) (k1_pscomp_1 (k1_pre_topc A B) (k3_pscomp_1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t16_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k8_pua2mss1 A B k6_numbers) B) & (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k8_pua2mss1 A B 1) (k7_pua2mss1 A B))) ) ) ) ) ).
tt(t16_pythtrip,ax, (~ (v1_finset_1 a_0_0_pythtrip)) ).
tt(t16_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A B C)) & (r2_pboole A (k1_pzfmisc1 A C) (k2_pzfmisc1 A B C))) ) ) ) ) ) ).
tt(t16_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (~  ((v5_qc_lang1 B A) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A B)) (k3_finseq_1 (k11_qc_lang1 A (k22_qc_lang1 A B))))) ) ) ) ) ) ).
tt(t16_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  ( ((k6_qc_lang2 A B C E) = (k15_qc_lang1 A D F))  =>  ( (B = D)  &  ((k15_qc_lang1 A C E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k2_qc_lang2 A B C)) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k24_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t16_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((r2_xboole_0 C D) => (r3_qc_lang2 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D) (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t16_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v18_quantal1 B A) =>  ((r3_lattices A C (k1_quantal1 A (k1_quantal1 A C B) B)) & (r3_lattices A C (k2_quantal1 A (k2_quantal1 A C B) B))) ) ) ) ) ) ) ) ).
tt(t16_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni (k27_quaterni A B) C) = (k27_quaterni A (k27_quaterni B C))) ) ) ) ) ) ) ).
tt(t16_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k31_quaterni (k27_quaterni A B)) = (k27_quaterni (k31_quaterni B) (k31_quaterni A))) ) ) ) ) ).
tt(t16_quaterni,ax, ((k10_quaterni k1_xcmplx_0 k11_quaterni) = k12_quaterni) ).
tt(t16_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 k6_numbers (k1_quin_1 A B C)) =>  ( (A = k6_numbers)  |  ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) = (k3_xcmplx_0 (k3_xcmplx_0 A (k6_xcmplx_0 D (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) (k6_xcmplx_0 D (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k9_quofield A B (k8_quofield A C D)) = (k8_quofield A (k9_quofield A B C) (k9_quofield A B D))) ) ) ) ) ) ) ) ) ).
tt(t16_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k3_radix_1 C)))  =>  ((r2_hidden A (k2_finseq_1 B)) => (m2_subset_1 (k4_radix_1 A C B D) k4_numbers (k3_radix_1 C))) ) ) ) ) ) ) ) ) ).
tt(t16_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_radix_1 A C E) =>  ((r1_xxreal_0 D k6_numbers) |  (! [F:$i] :  ( ((v3_card_1 F A) & (m2_finseq_1 F (k3_radix_1 E)))  =>  ( (F = (k10_radix_1 E A C))  =>  ((k1_seq_1 (k7_radix_2 B E D A F) A) = (k6_int_1 (k3_xcmplx_0 B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_radix_3 k6_numbers A) = k6_numbers) ) ) ).
tt(t16_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k2_xcmplx_0 (k4_radix_1 D C A (k4_radix_5 A B C)) (k4_radix_1 D C A (k2_radix_5 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (~  ((r1_xxreal_0 2 B) &  ( (~  ((r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B C)) & (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B C) (k8_radix_1 (k2_xcmplx_0 A 2) B (k4_radix_6 A B C)))) )  &  (~  ((r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B C)) &  (~ (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 2 A) &  ((r1_xxreal_0 2 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 C (k6_newton (k7_nat_d A 1) (k7_nat_d (k2_xcmplx_0 A B) 2))) &  ((r1_xxreal_0 2 C) &  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_group_10 D 2) (k2_finseq_1 2)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_group_10 D 2) (k2_finseq_1 2))))) )  =>  (~  ((r1_xxreal_0 C (k5_card_1 D)) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 D)) =>  ( (~  ((r1_xxreal_0 A (k5_card_1 F)) &  ((k10_xtuple_0 (k2_partfun1 (k3_group_10 D 2) (k2_finseq_1 2) E (k3_group_10 F 2))) = (k1_tarski 1)) ) )  &  (~  ((r1_xxreal_0 B (k5_card_1 F)) &  ((k10_xtuple_0 (k2_partfun1 (k3_group_10 D 2) (k2_finseq_1 2) E (k3_group_10 F 2))) = (k1_tarski 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ((v3_prob_1 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B C) = (k3_funct_2 k5_numbers (k9_setfam_1 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 A))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 B))) )  =>  ((k1_seq_1 (k2_random_2 A B C D) (k2_zfmisc_1 E F)) = (k11_binop_2 (k1_seq_1 C E) (k1_seq_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_9 A (k1_vectsp_4 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t16_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k1_rat_1 A) = (k7_xcmplx_0 (k2_rat_1 A) A)) ) ) ) ).
tt(t16_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ratfunc1 A B C D) => (r1_polynom5 A (k8_polynom3 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t16_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_rcomp_1 B A) => (r2_hidden A B)) ) ) ) ).
tt(t16_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden (k4_seq_4 A) A))  => (r1_tarski A (k3_rcomp_1 (k5_seq_4 A) (k4_seq_4 A)))) ) ) ).
tt(t16_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k3_funct_2 k5_numbers k5_numbers (k2_real_3 A B) (k1_nat_1 C 1)) = k6_numbers)  =>  ((k1_seq_1 (k1_real_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t16_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) B (k1_funcsdom A k1_numbers (k4_real_lat A) B C)) B)) ) ) ) ) ) ).
tt(t16_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k7_real_ns1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k7_real_ns1 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 (k4_real_ns1 A)) k5_numbers (u1_struct_0 (k7_real_ns1 A)) B C) =>  ( ((v3_normsp_1 B (k4_real_ns1 A)) =>  ((v1_bhsp_2 C (k7_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) B) = (k1_bhsp_2 (k7_real_ns1 A) C)) ) )  &  ((v1_bhsp_2 C (k7_real_ns1 A)) =>  ((v3_normsp_1 B (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) B) = (k1_bhsp_2 (k7_real_ns1 A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k8_group_1 A (k5_struct_0 A) (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ).
tt(t16_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = D)  <=>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) D B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t16_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k1_rvsum_1 (k3_rearran1 A B D C)) = (k1_rvsum_1 (k20_rfunct_3 A C A))) ) ) ) ) ) ) ) ) ) ).
tt(t16_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) => (r1_tarski (k1_relat_1 A) (k1_relat_1 B))) ) ) ) ) ).
tt(t16_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((r1_tarski (k4_relat_1 B) C) =>  ( (B = (k1_relset_1 B C))  & (r1_tarski B (k2_relset_1 A C))) ) ) ) ) ) ).
tt(t16_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_subset_1 (a_2_0_relset_2 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ).
tt(t16_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_finseq_6 B A) & (m2_finseq_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  &  ((k7_partfun1 A B D) = (k7_partfun1 A B 1)) ) ) ) ) )  =>  ((k1_finseq_6 A (k1_finseq_6 A B C) (k7_partfun1 A B 1)) = B) ) ) ) ) ) ) ) ).
tt(t16_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_rewrite1 A B C) & (r1_rewrite1 A C D))  => (r1_rewrite1 A B D)) ) ) ) ) ) ).
tt(t16_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( ( ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))))  & (r1_rewrite2 A B C D))  => (r1_rewrite2 A B D C)) ) ) ) ) ) ) ) ).
tt(t16_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((l1_rewrite3 F A) =>  (! [G:$i] :  ((l1_rewrite3 G B) =>  ( ( ((u1_rewrite3 A F) = (u1_rewrite3 B G))  & (r1_rewrite3 A F C D E))  => (r1_rewrite3 B G C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t16_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ( ((k3_finseq_1 A) = k6_numbers)  |  ((k3_finseq_1 A) = 1) )  => (v1_integra2 A)) ) ) ).
tt(t16_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~  ((k3_finseq_1 A) = k6_numbers) )  =>  ((k18_rvsum_1 (k3_rfinseq A)) = (k1_seq_1 A 1)) ) ) ) ).
tt(t16_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k1_valued_1 A B) C) = (k1_valued_1 (k24_valued_1 A C) (k24_valued_1 B C))) ) ) ) ) ) ) ).
tt(t16_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ((r1_tarski (k2_relset_1 B D) (k1_relset_1 B (k2_partfun1 B k1_numbers C A))) &  ((k8_relset_1 B k1_numbers C (k1_seq_4 k6_numbers)) = k1_xboole_0) )  => (r2_relset_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers B D (k2_partfun1 B k1_numbers (k6_rfunct_1 B k1_numbers C) A)) (k37_valued_1 k5_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers B D (k2_partfun1 B k1_numbers C A))))) ) ) ) ) ) ) ) ).
tt(t16_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r3_binop_1 (k3_rfunct_3 A k1_numbers) (k4_rfunct_3 A k1_numbers (k2_subset_1 A) k6_numbers) (k13_rfunct_3 A))) ) ).
tt(t16_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_rfunct_3 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r2_hidden E B)) )  =>  ((r1_xxreal_0 E C) |  ((r1_xxreal_0 D E) |  ((r1_xxreal_0 (k12_binop_2 (k10_binop_2 (k1_seq_1 A E) (k1_seq_1 A C)) (k10_binop_2 E C)) (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A C)) (k10_binop_2 D C))) & (r1_xxreal_0 (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A C)) (k10_binop_2 D C)) (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A E)) (k10_binop_2 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (v1_seq_2 B))  => (r1_xxreal_0 (k1_rinfsup1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k7_real_1 (k1_rinfsup1 A) (k1_rinfsup1 B)))) ) ) ) ) ).
tt(t16_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_mesfunc5 (k1_valued_0 k7_numbers B A)) =>  ((v7_mesfunc5 B) &  ((v10_mesfunc5 B) &  ((k2_mesfunc5 B) = (k2_mesfunc5 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ) ).
tt(t16_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v1_subset_1 B (u1_struct_0 A)) <=>  (~ (v6_struct_0 (k2_ring_1 A B))) ) ) ) ) ) ).
tt(t16_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (? [B:$i] :  ((r2_hidden B A) & (r2_ringcat1 B k18_mod_2)) ) ) ) ).
tt(t16_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlvect_2 A (k1_rlaffin1 A B C)) = (k5_rusub_4 A (k3_rlvect_2 A B) C)) ) ) ) ) ) ) ).
tt(t16_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 B))  => (r2_hidden (k1_funct_1 (k2_rlaffin2 A) B) (k3_convex1 A B))) ) ) ) ) ).
tt(t16_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m2_rlaffin3 D B C) =>  ((k3_finseq_1 (k1_rlaffin3 B C D A)) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t16_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k5_algstr_0 D E F) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((m1_rlsub_1 (k2_rlsub_2 A B C) B) & (m1_rlsub_1 (k2_rlsub_2 A B C) C)) ) ) ) ) ) ) ).
tt(t16_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C D) => (m1_connsp_2 D A B)) ) ) ) ) ) ) ) ) ).
tt(t16_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_algstr_0 A B) = (k1_rlvect_1 A B (k1_real_1 1))) ) ) ) ) ).
tt(t16_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k7_subset_1 (u1_struct_0 A) C B)) = (k5_algstr_0 A (k2_rlvect_2 A C) (k2_rlvect_2 A (k9_subset_1 (u1_struct_0 A) C B)))) ) ) ) ) ) ) ).
tt(t16_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k1_rlvect_3 A (k1_subset_1 (u1_struct_0 A))) = (k1_rlsub_1 A)) ) ) ).
tt(t16_rlvect_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r2_hidden A (k3_rlsub_1 B C (k1_rlvect_3 B (k8_domain_1 (u1_struct_0 B) D E F)))) <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B (k3_rlvect_1 B C (k1_rlvect_1 B D G)) (k1_rlvect_1 B E H)) (k1_rlvect_1 B F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_3 C B) =>  (? [D:$i] :  ((m1_rlvect_3 D A) & (r1_tarski C D)) ) ) ) ) ) ) ) ).
tt(t16_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r2_hidden A (k2_rlvect_x B (k6_domain_1 (u1_struct_0 B) C))) <=>  (? [D:$i] :  ((v1_int_1 D) &  (A = (k1_rlvect_1 B C D)) ) ) ) ) ) ) ) ) ).
tt(t16_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( ( (F = C)  &  (G = D) )  =>  ((k5_algstr_0 E F G) = (k5_algstr_0 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((m1_rmod_2 (k2_rmod_3 A B C D) A C) & (m1_rmod_2 (k2_rmod_3 A B C D) A D)) ) ) ) ) ) ) ) ) ).
tt(t16_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((r2_hidden C (k2_rmod_4 A B D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (C = E)  &  (~  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_robbins1 A B (k6_robbins1 A C D)) = (k6_robbins1 A (k6_robbins1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t16_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) D)))) D)) = (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t16_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_lattices B))  =>  ( ((g2_lattices (u1_struct_0 A) (u2_lattices A)) = (g2_lattices (u1_struct_0 B) (u2_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_lattices A C D) = (k1_lattices B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  ( ( (A = (k6_subset_1 3 2))  &  (B = 1) )  =>  ( ((k13_lattice3 k1_robbins4 A B) = 3)  &  ((k12_lattice3 k1_robbins4 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t16_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v4_roughs_1 B A))  <=>  ((k4_roughs_1 A B) = B) ) ) ) ) ) ).
tt(t16_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((k1_rpr_1 A (k9_subset_1 A B C)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t16_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) &  ((v1_rsspace4 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( (D = C)  =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 A (u1_struct_0 B) D E)) (k1_normsp_0 (k9_rsspace4 A B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = k6_numbers) ) )  =>  ((v1_series_1 A) &  ((k4_series_1 A) = k6_numbers) ) ) ) ) ).
tt(t16_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) => (r1_struct_0 B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t16_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((m1_rusub_1 (k2_rusub_2 A B C) B) & (m1_rusub_1 (k2_rusub_2 A B C) C)) ) ) ) ) ) ) ).
tt(t16_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (~  ((r1_tarski (k10_xtuple_0 D) (u1_struct_0 (k1_rusub_3 A C))) &  (! [E:$i] :  ((m2_rlvect_2 E A C) =>  (~  ((k4_rlvect_1 A (k5_rlvect_2 A D B)) = (k6_rlvect_2 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (r1_xxreal_0 (k9_real_1 (k2_nat_1 (k1_rusub_4 B) (k1_rusub_4 C)) (k1_rusub_4 A)) (k1_rusub_4 (k2_rusub_2 A B C)))) ) ) ) ) ) ).
tt(t16_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_rusub_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ( (D = (k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) C)))  &  ((r1_rusub_5 A B D) & (v3_rusub_4 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k5_rvsum_1 A B (k5_finseq_2 k1_numbers A k6_numbers)) = B) ) ) ) ) ).
tt(t16_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k5_rvsum_2 (k7_rvsum_2 A B)) = (k7_rvsum_2 B A)) ) ) ) ) ).
tt(t16_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k3_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 k6_numbers)) = (k2_xcmplx_0 B C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ( (~  (E = (k10_ami_3 k6_numbers)) )  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k2_sf_mastr (k1_scmfsa8b C A B)) = (k4_subset_1 k2_scmfsa_2 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr A)) (k2_sf_mastr B)))  &  ((k2_sf_mastr (k2_scmfsa8b C A B)) = (k4_subset_1 k2_scmfsa_2 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr A)) (k2_sf_mastr B))) ) ) ) ) ) ) ) ).
tt(t16_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_xtuple_0 (k13_scmfsa_2 A B)) = (k12_finseq_1 k5_numbers A)) ) ) ) ) ).
tt(t16_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) => (r1_xxreal_0 (k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) 12)) ) ).
tt(t16_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ((m1_scmfsa_2 I) =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k17_scmfsa_2 H I))  & (r2_hidden I (k9_xtuple_0 B)))  =>  (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  ( ( (J = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H)))  &  (K = (k1_int_2 (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H))) )  =>  ((k5_finseq_2 k5_numbers J k6_numbers) = (k5_finseq_2 k5_numbers K k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski (k2_scmfsa6a A) (k3_scmfsa6a A B))) ) ) ) ).
tt(t16_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v6_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (~  ( (~  (A = B) )  & (r3_scmfsa7b (k16_scmfsa_2 B C) A)) ) ) ) ) ) ) ) ).
tt(t16_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ( ( ((k1_funct_1 A B) = (k2_compos_1 k1_scmfsa_2))  =>  ((k1_funct_1 (k2_scmfsa6a A) B) = (k11_scmfsa_2 (k5_card_1 A))) )  &  ( (~  ((k1_funct_1 A B) = (k2_compos_1 k1_scmfsa_2)) )  =>  ((k1_funct_1 (k2_scmfsa6a A) B) = (k1_funct_1 A B)) ) ) ) ) ) ) ).
tt(t16_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m E) A) & (r6_scmfsa7b C (k1_scmfsa_m E) A))  =>  ( ((k1_funct_1 E D) = k6_numbers)  | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b D B C) E A) (k1_funct_4 (k1_scmfsa6b C E A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 C 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r5_scmfsa7b E C A) & (r1_tarski E A))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_tarski (k6_compos_1 k1_scmfsa_2 E F) B) &  ( ((k5_memstr_0 3 k1_scmfsa_2 D) = F)  &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C G)) F) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D G)))  &  ( ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k3_extpro_1 3 k1_scmfsa_2 A (k5_extpro_1 3 k1_scmfsa_2 A C G)) F) = (k3_extpro_1 3 k1_scmfsa_2 B (k5_extpro_1 3 k1_scmfsa_2 B D G)))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C G)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 D 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  ((r1_tarski (k1_scmfsa_9 B C) A) =>  ( ((k1_funct_1 D B) = k6_numbers)  |  ( ((k8_extpro_1 3 k1_scmfsa_2 A D) = 4)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D E)) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa_9 A B) 2) = (k11_scmfsa_2 3)) ) ) ) ) ).
tt(t16_scmfsa_m,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k3_scmfsa_2)))  =>  (~ (r2_hidden (k3_scmfsa_m A) A)) ) ) ).
tt(t16_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scm_halt C)) ) ) ) ) ) )  =>  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scm_halt D)) ) ) ) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) A) & (r1_tarski (k3_scmfsa6a C D) B))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_funct_4 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 B C) D) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1))) E) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 B C) D) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1))) E)) (k5_card_1 C)))) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) A (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) A) 1) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) (k2_nat_1 k6_numbers 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k1_scmfsa_m D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k2_scmfsa_9 C B)) B) (k1_scmfsa_m D)) 3)))) ) ) ) ) ) ) ) ).
tt(t16_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k7_scmpds_2 C A B)) = 4) ) ) ) ) ) ) ).
tt(t16_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  (! [J:$i] :  ((v1_int_1 J) =>  (! [K:$i] :  ((v1_int_1 K) =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k8_scmpds_2 I J K))  &  ( (H = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A E G)))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 H K))) )  =>  ( (K = 1)  |  ( (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) I) J)) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) I) J)) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) I) J)) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) I) J)) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_scmpds_4 (k4_scmpds_4 A B) C) = (k2_scmpds_4 A (k2_scmpds_4 B C))) ) ) ) ) ) ) ).
tt(t16_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scmpds_4 D)) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 D) A) & (r1_tarski (k10_compos_1 k1_scmpds_2 D) B))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k5_extpro_1 2 k1_scmpds_2 A C E) = (k5_extpro_1 2 k1_scmpds_2 B C E))  &  ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A C E)) = (k3_extpro_1 2 k1_scmpds_2 B (k5_extpro_1 2 k1_scmpds_2 B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k7_scmpds_2 A B C) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ).
tt(t16_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v3_scmpds_4 E)) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 E) B) &  ((r1_scmpds_6 E D B) & (r2_scmpds_6 E D B)) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_tarski (k61_valued_1 E F) C) &  ( ((k5_memstr_0 2 k1_scmpds_2 A) = F)  &  ((k6_memstr_0 2 k1_scmpds_2 D) = (k6_memstr_0 2 k1_scmpds_2 A)) ) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 B D) G))  =>  ( ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) F) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ( ((k3_extpro_1 2 k1_scmpds_2 B (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k3_extpro_1 2 k1_scmpds_2 C (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 G (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 G 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ( (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 G I) = (k1_funct_1 B I)) ) ) )  &  ((k1_funct_1 G D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E))) |  ( ((k1_funct_1 (k6_scmpds_4 C G H) D) = (k1_funct_1 G D))  &  ( (~ (r1_xxreal_0 (k1_funct_1 (k6_scmpds_4 C G H) (k2_scmpds_2 (k1_funct_1 B D) E)) (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E))))  &  ((r1_scmpds_6 C G H) &  ((r2_scmpds_6 C G H) &  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 (k6_scmpds_4 C G H) I) = (k1_funct_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((k6_scmpds_4 (k1_scmpds_8 D E C) B A) = (k6_scmpds_4 (k1_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k1_amistd_1 2 k1_scmpds_2 B (k9_scmpds_2 A C D)) = (k2_tarski (k1_ordinal1 B) (k1_int_2 (k2_xcmplx_0 D B)))) ) ) ) ) ) ) ) ) ).
tt(t16_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 E (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ( ((k2_scmring2 A E B) = (k4_struct_0 A))  =>  ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k9_scmring2 A D B) E) (k4_struct_0 (k1_scmring2 A))) = D) )  &  ( ( (~  ((k2_scmring2 A E B) = (k4_struct_0 A)) )  =>  ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k9_scmring2 A D B) E) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) E))) )  &  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k9_scmring2 A D B) E) C) = (k2_scmring2 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 4)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 A))))  =>  (~  (B = (k6_scmring2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k1_card_1 (a_1_2_scmyciel A)) = (k4_nat_1 2 (k5_card_1 (k1_scmyciel A)))) ) ) ).
tt(t16_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  ( ( ((k1_funct_1 B D) = H)  &  ( ((k1_funct_1 B (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 B E) (k1_funct_1 B F)))  &  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 I) &  ((v5_funct_1 I (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 I (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 I 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J k5_numbers) &  ((v5_relat_1 J (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 J) & (v1_partfun1 J k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 I D) = H)  &  ((k1_funct_1 I (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 I E) (k1_funct_1 I F))) )  =>  ((r1_xxreal_0 (k1_funct_1 I E) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 I F) k6_numbers) |  ( ((k1_funct_1 I E) = (k1_funct_1 I F))  |  ( ((k1_funct_1 (k6_scmpds_4 C I J) D) = H)  &  ((r1_scmpds_6 C I J) &  ((r2_scmpds_6 C I J) &  ( ( (~ (r1_xxreal_0 (k1_funct_1 I E) (k1_funct_1 I F)))  =>  ( ((k1_funct_1 (k6_scmpds_4 C I J) E) = (k6_xcmplx_0 (k1_funct_1 I E) (k1_funct_1 I F)))  &  ((k1_funct_1 (k6_scmpds_4 C I J) F) = (k1_funct_1 I F)) ) )  &  ( ((r1_xxreal_0 (k1_funct_1 I E) (k1_funct_1 I F)) =>  ( ((k1_funct_1 (k6_scmpds_4 C I J) F) = (k6_xcmplx_0 (k1_funct_1 I F) (k1_funct_1 I E)))  &  ((k1_funct_1 (k6_scmpds_4 C I J) E) = (k1_funct_1 I E)) ) )  &  ((k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 (k6_scmpds_4 C I J) E) (k1_funct_1 (k6_scmpds_4 C I J) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k5_card_1 C) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B F) k6_numbers) |  ((r1_scmpds_6 (k4_scpinvar D G C) B A) &  ((r2_scmpds_6 (k4_scpinvar D G C) B A) &  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) G)) = k6_numbers) )  =>  ((k6_scmpds_4 (k4_scpinvar D G C) B A) = (k6_scmpds_4 (k4_scpinvar D G C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 (k2_xcmplx_0 7 (k1_funct_1 B (k1_scmp_gcd 6))) (k1_funct_1 B (k1_scmp_gcd 4))) &  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( (F = (k1_funct_1 B (k1_scmp_gcd 6)))  &  ( (E = (k6_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd 4)) (k1_funct_1 B (k1_scmp_gcd 6))) 1))  &  ((r1_scpisort C B E) &  ((r1_scpisort D (k6_scmpds_4 (k2_scmpds_8 k2_scmp_gcd 6 (k1_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k13_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 k6_numbers)) (k3_scmpds_6 k2_scmp_gcd 5 (k3_scmpds_4 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 (k16_scmpds_2 k2_scmp_gcd (k1_scmp_gcd 4) 5 (k4_xcmplx_0 1)) (k16_scmpds_2 (k1_scmp_gcd 4) (k1_scmp_gcd 4) (k4_xcmplx_0 1) k6_numbers)) (k16_scmpds_2 (k1_scmp_gcd 4) k2_scmp_gcd k6_numbers 5)) (k11_scmpds_2 k2_scmp_gcd 4 (k4_xcmplx_0 1))) (k11_scmpds_2 k2_scmp_gcd 6 (k4_xcmplx_0 1))) (k9_compos_1 k1_scmpds_2 (k10_scmpds_2 k2_scmp_gcd 6 k6_numbers))))) B A) E) &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  & (r3_graph_2 C 1 F)) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) F) |  ((r2_classes1 C D) &  ((r3_graph_2 D 1 (k2_nat_1 F 1)) &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 G (k3_finseq_1 C)) =>  ((r1_xxreal_0 G (k2_nat_1 F 1)) |  ((k1_funct_1 C G) = (k1_funct_1 D G)) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k2_nat_1 F 1)) &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r1_xxreal_0 1 H) &  ((r1_xxreal_0 H (k2_nat_1 F 1)) &  ((k1_funct_1 D G) = (k1_funct_1 C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C B D))  &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B D E G) &  ((r2_analoaf A C D F G) &  ( (~  (E = F) )  & (r2_analoaf A E F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A (k3_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B) (k20_valued_1 k5_numbers k1_numbers k1_numbers A C)))) ) ) ) ) ) ).
tt(t16_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~  ((k2_seq_2 A) = k6_numbers) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k18_complex1 (k1_seq_1 A C)) (k10_real_1 (k18_complex1 (k2_seq_2 A)) 2))) ) ) ) ) ) ) ) ) ) ).
tt(t16_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((m2_valued_0 A k1_numbers B) & (v2_comseq_2 B))  => (v2_comseq_2 A)) ) ) ) ) ).
tt(t16_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k5_seqfunc A (k8_seqfunc A B C)) (k8_seqfunc A (k5_seqfunc A B) (k5_seqfunc A C)))) ) ) ) ) ) ).
tt(t16_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k32_valued_1 k5_numbers k1_numbers B) A) = (k32_valued_1 k5_numbers k1_numbers (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t16_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A B))) )  => (v7_valued_0 (k3_series_1 A))) ) ) ).
tt(t16_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k1_newton (k6_xcmplx_0 (k4_nat_1 2 B) 1) 3))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k3_xcmplx_0 (k13_newton B 2) (k6_xcmplx_0 (k4_nat_1 2 (k13_newton B 2)) 1))) ) ) ) ) ) ) ).
tt(t16_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k1_power 3 (k3_xcmplx_0 (k3_xcmplx_0 A B) C)) (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) 3))) ) ) ) ) ) ).
tt(t16_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k1_newton (k2_xcmplx_0 (k1_newton (k7_xcmplx_0 1 3) B) (k13_newton 3 B)) 2)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 (k7_xcmplx_0 (k1_newton (k7_xcmplx_0 1 9) B) 8)) (k7_xcmplx_0 (k13_newton 9 (k2_nat_1 B 1)) 8)) (k4_nat_1 2 B)) 3)) ) ) ) ) ) ).
tt(t16_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~ (r1_xxreal_0 2 (k8_complex1 (k8_complex1 (k8_complex1 (k13_complex1 A (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) (k13_complex1 B (k2_xcmplx_0 (k2_xcmplx_0 A B) D))) (k13_complex1 D (k2_xcmplx_0 (k2_xcmplx_0 B D) C))) (k13_complex1 C (k2_xcmplx_0 (k2_xcmplx_0 A D) C))))) ) ) ) ) ) ) ) ) ).
tt(t16_setfam_1,ax, (! [A:$i] :  ((r1_setfam_1 A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ).
tt(t16_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 C) = k5_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_funct_1 C D) = (k3_tarski (a_3_3_setlim_1 A B D))) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) ) ) ) ) ) ) ).
tt(t16_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k5_setlim_2 B D C) A) = (k5_setlim_2 B (k10_nat_1 (k9_setfam_1 B) D A) C)) ) ) ) ) ) ) ) ).
tt(t16_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v3_binop_1 C B) &  ((v1_binop_1 C B) & (v2_binop_1 C B)) )  =>  ( ( (D = k1_xboole_0)  &  (~ (v1_setwiseo C B)) )  |  (! [F:$i] :  ((m1_subset_1 F B) =>  ( (F = (k7_setwiseo A B C D E))  <=>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k5_finsub_1 A) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 A) B)))) )  &  ( (F = (k3_funct_2 (k5_finsub_1 A) B G D))  &  ( (! [H:$i] :  ((m1_subset_1 H B) =>  ((r3_binop_1 B H C) =>  ((k1_funct_1 G k1_xboole_0) = H) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_funct_1 G (k1_tarski H)) = (k3_funct_2 A B E H)) ) )  &  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 A)) =>  ((r1_tarski H D) =>  ( (H = k1_xboole_0)  |  (! [I:$i] :  ((m1_subset_1 I A) =>  ((r2_hidden I D) =>  ((k1_funct_1 G (k2_xboole_0 H (k1_tarski I))) = (k5_binop_1 B C (k3_funct_2 (k5_finsub_1 A) B G H) (k3_funct_2 A B E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H C B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  ( ((v1_binop_1 E C) &  ((v2_binop_1 E C) &  ((v1_setwiseo E C) &  ((v1_binop_1 G B) &  ((v2_binop_1 G B) &  ((v1_setwiseo G B) &  ( ((k3_funct_2 C B H (k4_binop_1 C E)) = (k4_binop_1 B G))  &  (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  ((k3_funct_2 C B H (k5_binop_1 C E I J)) = (k5_binop_1 B G (k3_funct_2 C B H I) (k3_funct_2 C B H J))) ) ) ) ) ) ) ) ) ) ) )  =>  ((k3_funct_2 C B H (k7_setwiseo A C E D F)) = (k7_setwiseo A B G D (k1_partfun1 A C C B F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_scmfsa6c D) &  ((v1_sfmastr1 D) & (m1_subset_1 D (u1_compos_1 k1_scmfsa_2))) )  =>  ( ((v7_amistd_1 C 3 k1_scmfsa_2) |  ((r6_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A) & (r5_scmfsa7b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A)) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k4_scmfsa6a D C) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b C (k2_extpro_1 3 k1_scmfsa_2 D (k1_scmfsa_m B)) A))) ) ) ) ) ) ) ) ) ) ).
tt(t16_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ((r1_sfmastr2 B A C D) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k1_funct_1 A C)) =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  (! [G:$i] :  ( ((v1_ami_2 G) &  ( (~ (v1_scmfsa_m G))  & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2))) )  =>  ( (G = (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a (k6_scmfsa_2 G D) (k8_scmfsa_2 G C)) (k7_scmfsa_2 G (k4_scmfsa_2 k6_numbers))) (k6_scmfsa_2 B C)) A F)) = (k6_memstr_0 3 k1_scmfsa_2 (k2_funct_7 (k2_funct_7 A G (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1)) B (k1_funct_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( ( (C = (k12_scmfsa_2 B A))  |  (C = (k13_scmfsa_2 B A)) )  =>  ((k1_sf_mastr C) = (k4_scmfsa_m A)) ) ) ) ) ) ) ) ).
tt(t16_sgraph1,ax, (! [A:$i] : (r2_hidden (g1_sgraph1 k1_xboole_0 (k1_subset_1 (k2_sgraph1 k1_xboole_0))) (k3_sgraph1 A))) ).
tt(t16_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) & (l3_lattices A)) ) ) ) ) ) )  => (v5_lattices A)) ) ).
tt(t16_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B D)) = B) ) ) ) ) ) ) ) ) ).
tt(t16_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k4_simplex0 A) = (k5_setfam_1 (u1_struct_0 A) (u1_pre_topc A))) ) ) ).
tt(t16_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) =>  ((k5_simplex1 k1_xboole_0 A B) = B) ) ) ) ) ) ).
tt(t16_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v4_matroid0 B) &  ((v2_simplex2 B A) & (m1_simplex0 B (u1_struct_0 (k15_euclid A)))) ) ) ) )  =>  ((r1_tarski (k3_simplex1 (k15_euclid A) B) (k2_struct_0 B)) => (r1_xxreal_0 (k3_simplex2 A (k4_simplex1 (k15_euclid A) B)) (k4_real_1 (k13_complex1 (k6_simplex0 B) (k3_real_1 (k6_simplex0 B) 1)) (k3_simplex2 A B)))) ) ) ) ) ).
tt(t16_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t16_sin_cos2,ax, ((k1_seq_1 k1_sin_cos2 k6_numbers) = k6_numbers) ).
tt(t16_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k5_binop_2 k7_complex1 A)) = (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) ) ) ).
tt(t16_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k20_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k17_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2))))) ) ) ) ) ).
tt(t16_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k18_sin_cos (k8_real_1 3 A)) = (k7_real_1 (k1_real_1 (k8_real_1 4 (k1_newton (k17_sin_cos A) 3))) (k8_real_1 3 (k17_sin_cos A)))) ) ) ).
tt(t16_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) & (r1_xxreal_0 A (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  => (r1_xxreal_0 k6_numbers (k17_sin_cos A))) ) ) ) ) ).
tt(t16_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 1 (k3_square_1 A))) ) ) ) ) ).
tt(t16_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k6_xcmplx_0 A B) = k6_numbers) )  =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) (k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)))) ) ) ) ) ) ).
tt(t16_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k16_sin_cos A) = k6_numbers) )  =>  ((k1_seq_1 k30_sin_cos A) = (k2_sin_cos4 A)) ) ) ) ).
tt(t16_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos A)) B)) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B)) &  ((r1_xxreal_0 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B) (k4_series_1 (k4_sin_cos (k17_complex1 A)))) & (r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k3_sin_cos A)) B)) (k4_series_1 (k4_sin_cos (k17_complex1 A))))) ) ) ) ) ) ).
tt(t16_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid A) = (k17_euclid B))  <=> (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ).
tt(t16_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1))) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t16_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v1_sppol_1 A) <=>  ((k9_pscomp_1 A) = (k7_pscomp_1 A)) ) ) ) ).
tt(t16_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_finseq_1 (k2_goboard1 A)) = (k4_finseq_1 A)) ) ) ).
tt(t16_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k3_topreal1 2 A)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = B)  |  ( ( (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) = (k17_euclid B)) )  &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) = (k18_euclid B)) ) )  | (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) B) A))) ) ) ) ) ) ) ).
tt(t16_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t16_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k3_square_1 B) (k3_square_1 A))) ) ) ) ) ) ) ).
tt(t16_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_stacks_1 A B C) => (r2_stacks_1 A (k7_stacks_1 A B D) (k7_stacks_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t16_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k5_nat_1 (k1_stirl2_1 B A D (k1_seq_4 C))) (k21_binop_2 B 1))) ) ) ) ) ) ) ) ) ).
tt(t16_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  ( ((k18_substut1 A (k20_substut1 A B)) = (k6_cqc_lang A (k2_sublemma A B)))  &  ((k19_substut1 A (k20_substut1 A B)) = (k19_substut1 A B)) ) ) ) ) ) ).
tt(t16_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski B (k3_subset_1 A C)) => (r1_tarski C (k3_subset_1 A B))) ) ) ) ) ) ).
tt(t16_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_partfun1 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_partfun1 A B)) =>  ( ((r2_hidden E C) &  ((r2_hidden F D) & (r1_partfun1 E F)) )  => (r2_hidden (k2_xboole_0 E F) (k4_substlat A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((k27_substut1 A (k20_substut1 A B)) = B) ) ) ) ) ).
tt(t16_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((k2_substut2 A (k6_cqc_lang A B) C) = (k5_sublemma A (k2_substut2 A B C))) ) ) ) ) ) ) ).
tt(t16_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (r1_tarski (k9_supinf_2 A (k5_supinf_2 B C) (k13_supinf_2 A B C D E)) (k5_supinf_2 (k9_supinf_2 A B D) (k9_supinf_2 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_symsp_1 A B D C (k3_rlvect_1 B E F)) = (k3_rlvect_1 A (k1_symsp_1 A B D C E) (k1_symsp_1 A B D C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((k6_subset_1 (k4_relat_1 (k6_subset_1 A B)) (k4_relat_1 A)) = k1_xboole_0) ) ) ).
tt(t16_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((v2_metric_1 B A) & (r1_xxreal_0 k6_numbers C))  => (r1_relat_2 (k1_taxonom1 A B C) A)) ) ) ) ) ) ) ).
tt(t16_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v5_taxonom2 B A) & (m1_taxonom2 B A)) )  =>  ((v6_taxonom2 B A) =>  ((r2_hidden k1_xboole_0 B) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v4_taxonom2 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r2_hidden C D) &  ((r1_tarski D B) &  (! [E:$i] :  ( ((v4_taxonom2 E) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r2_hidden C E) &  ((r1_tarski E B) & (r1_tarski D E)) )  =>  (D = E) ) ) ) ) )  => (m1_eqrel_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t16_taylor_1,ax, ((v2_funct_1 k24_sin_cos) &  ((r2_fdiff_1 k24_sin_cos k1_numbers) &  ((r2_fdiff_1 k24_sin_cos (k2_subset_1 k1_numbers)) &  ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_fdiff_1 k24_sin_cos A) = (k1_seq_1 k24_sin_cos A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~ (r1_xxreal_0 (k1_fdiff_1 k24_sin_cos A) k6_numbers)) ) )  &  ( ((k1_relset_1 k1_numbers k24_sin_cos) = (k2_subset_1 k1_numbers))  &  ( ((k1_relset_1 k1_numbers k24_sin_cos) = (k2_subset_1 k1_numbers))  &  ((k2_relset_1 k1_numbers k24_sin_cos) = (k3_limfunc1 k6_numbers)) ) ) ) ) ) ) ) ).
tt(t16_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r2_funct_2 k5_numbers k1_numbers (k1_taylor_2 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B) (k4_sin_cos B)) &  ((v2_series_1 (k1_taylor_2 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) &  ((k1_seq_1 k24_sin_cos B) = (k4_series_1 (k1_taylor_2 k24_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B))) ) ) ) ) ) ) ) ).
tt(t16_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_finset_1 B) => (v6_tbsp_1 B A)) ) ) ) ) ).
tt(t16_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) =>  (B = C) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A D E F G))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r2_analoaf A B C D E)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C E F) & (r2_analoaf A B D E G))  => (r2_analoaf A C D F G)) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_analoaf A B D D C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B C C D) & (r2_analoaf A B E E D))  =>  (C = E) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) ) ) ) ) ).
tt(t16_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) => (v4_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t16_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_tdlat_2 A B) = (a_2_1_tdlat_2 A B)) ) ) ) ) ).
tt(t16_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v4_pre_topc B A)) ) ) ) ) ).
tt(t16_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r6_pboole A (k1_termord A B C D) C) <=> (r6_pboole A (k2_termord A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t16_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k2_pre_topc A B) = B)  &  ((k1_tops_1 A B) = B) ) ) ) ) ) ).
tt(t16_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v1_tex_2 (k1_tex_2 A B) A) & (v7_struct_0 A)) ) ) ) ) ) ).
tt(t16_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v2_tex_3 B A) <=> (v1_tops_3 C A)) ) ) ) ) ) ) ) ).
tt(t16_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v1_tex_4 B A) & (v3_pre_topc B A))  => (v3_tex_4 B A)) ) ) ) ) ).
tt(t16_tietze,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  ( ( ((k5_relat_1 C B) = (k5_relat_1 D B))  & (r1_tietze C A B))  =>  ( ( (~ (r1_tarski B (k9_xtuple_0 C)))  &  (~ (r1_tarski (k9_xtuple_0 D) (k9_xtuple_0 C))) )  | (r1_tietze D A B)) ) ) ) ) ) ) ) ) ).
tt(t16_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_tsep_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ( (E = D)  &  (F = D) )  =>  (! [G:$i] :  ((m1_connsp_2 G B E) =>  (! [H:$i] :  ((m1_connsp_2 H C F) =>  (? [I:$i] :  ((m1_connsp_2 I (k1_tsep_1 A B C) D) & (r1_tarski I (k2_xboole_0 G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((r2_hidden C A) => (m1_toler_1 (k1_tarski C) A B)) ) ) ) ) ).
tt(t16_topalg_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 (k15_euclid C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 (k15_euclid C))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 (k15_euclid C))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)))))) )  =>  ( ((v5_pre_topc E D (k15_euclid C)) &  ((v5_pre_topc F D (k15_euclid C)) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)) G H) = (k3_rlvect_1 (k15_euclid C) (k1_rlvect_1 (k15_euclid C) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)) E H) A) (k1_rlvect_1 (k15_euclid C) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 (k15_euclid C)) F H) B))) ) ) ) )  => (v5_pre_topc G D (k15_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_borsuk_2 C k5_topmetr A B) =>  (! [D:$i] :  ((m1_borsuk_2 D k5_topmetr A B) => (r4_borsuk_2 k5_topmetr A B C D)) ) ) ) ) ) ) ) ).
tt(t16_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v2_connsp_1 C A) & (v2_connsp_1 D B))  => (v2_connsp_1 (k3_borsuk_1 A B C D) (k2_borsuk_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t16_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_borsuk_6 A C D) & (r1_borsuk_6 B E F))  =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  (! [H:$i] :  ((m1_borsuk_2 H B E F) => (m1_borsuk_2 (k2_topalg_4 A B k5_topmetr G H) (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (? [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_connsp_1 C A)) ) ) ) )  => (v1_connsp_2 A)) ) ) ).
tt(t16_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A C C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_topalg_6 D A C) => (v3_topalg_6 (k2_topalg_3 A B C D E) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topdim_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_topdim_1 B) & (l1_pre_topc B)) )  =>  ((r1_xxreal_0 (k4_topdim_1 B) A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v3_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden C E) &  ((r1_tarski E D) &  ((v1_topdim_1 (k2_tops_1 B E) B) & (r1_xxreal_0 (k2_topdim_1 B (k2_tops_1 B E)) (k5_real_1 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v5_waybel23 A) &  ((v3_topdim_1 A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v5_waybel23 B) &  ((v3_topdim_1 B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) ) ) )  =>  ( ((k4_topdim_1 A) = k6_numbers)  =>  ((k4_topdim_1 (k2_borsuk_1 B A)) = (k4_topdim_1 B)) ) ) ) ) ) ).
tt(t16_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (k2_topgen_1 A B)) <=> (r1_topgen_1 A B C)) ) ) ) ) ) ).
tt(t16_topgen_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_pre_topc A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_pre_topc A))))) )  =>  ( ( (B = (k2_relset_1 (u1_pre_topc A) D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k1_funct_1 D E)) &  (! [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden E F) => (r1_tarski (k1_funct_1 D E) F)) ) ) ) ) ) )  => (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t16_topgen_3,ax, ((k1_card_1 k4_numbers) = k4_ordinal1) ).
tt(t16_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((r1_tarski B C) & (v1_prob_1 C A))  => (r1_tarski (k7_setfam_1 A B) C)) ) ) ) ) ) ).
tt(t16_topgen_5,ax, ((k1_card_1 k1_topgen_5) = k3_topgen_3) ).
tt(t16_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k1_topgrp_1 A C) B) = (k4_group_2 A C B)) ) ) ) ) ) ) ).
tt(t16_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v2_topmetr A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_topmetr B A) &  ((m1_setfam_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (v1_finset_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topreal1,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1))) = (k1_tarski (k19_euclid 1 k6_numbers))) ).
tt(t16_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( (D = (k11_finseq_1 A B C))  =>  ((k3_topreal1 2 D) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_topreal4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_topreal1 A) &  ((r2_hidden C (k4_finseq_1 A)) &  (B = (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A)) ) )  =>  ((r1_xxreal_0 C 2) |  ((v4_topreal1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C))  &  ((r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) &  ((r1_tarski (k3_topreal1 2 B) (k3_topreal1 2 A)) &  ((k3_topreal1 2 B) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((v1_topreal2 A) & (r1_xxreal_0 (k7_pscomp_1 A) (k9_pscomp_1 A))) ) ) ) ).
tt(t16_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers B) => (r2_hidden A (k1_rcomp_1 (k6_xcmplx_0 A B) (k2_xcmplx_0 A B)))) ) ) ) ) ).
tt(t16_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 B) = A)  => (r2_hidden B (u1_struct_0 (k14_euclid A)))) ) ) ) ) ).
tt(t16_topreal8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C A))  =>  ( ((k4_finseq_4 B (k7_partfun1 A C 1)) = (k3_finseq_1 B))  =>  ((k2_finseq_5 A (k4_graph_2 A B C) (k7_partfun1 A C 1)) = C) ) ) ) ) ) ) ) ).
tt(t16_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_tarski (k1_topreal9 A C B) (k2_topreal9 A C B))) ) ) ) ) ) ).
tt(t16_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (v1_t_0topsp C A B)) ) )  => (v3_tops_2 C A B)) ) ) ) ) ) ) ).
tt(t16_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) &  ((k18_euclid A) = 1) )  =>  ((k17_euclid A) = k6_numbers) ) ) ) ).
tt(t16_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) )  =>  ((k23_rvsum_1 D (k2_funct_7 (k16_euclid B) A C)) = (k3_xcmplx_0 (k1_funct_1 D A) C)) ) ) ) ) ) ) ) ).
tt(t16_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k2_toprns_1 1 A B) = B) ) ) ) ) ).
tt(t16_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_tops_1 A B) B)) ) ) ) ).
tt(t16_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_tops_2 B A) & (v2_tops_2 C A))  => (v2_tops_2 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t16_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v1_tops_1 (k2_struct_0 A) A)) ) ).
tt(t16_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A))))) )  =>  ((v5_pre_topc C (k3_pcomps_1 B) A) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden (k1_funct_1 C D) E) &  (! [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  =>  (~ (r1_tarski (k7_relset_1 (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A) C (k9_metric_1 B D F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) => (r2_transgeo A (k6_partfun1 A) B)) ) ) ) ).
tt(t16_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((r2_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) (k3_struct_0 (k4_topmetr A B)) (k1_partfun1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k4_treal_1 A B (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) (k3_treal_1 A B (k2_treal_1 A B) (k1_treal_1 A B)))) & (r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k3_struct_0 (k4_topmetr k6_numbers 1)) (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k3_treal_1 A B (k2_treal_1 A B) (k1_treal_1 A B)) (k4_treal_1 A B (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1))))) ) ) ) ) ) ).
tt(t16_trees_1,ax, (! [A:$i] :  ((k1_trees_1 (k9_finseq_1 A)) = (k1_tarski k1_xboole_0)) ) ).
tt(t16_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_trees_2 B A) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (B = (k2_trees_2 A C)) ) ) ) ) ) ) ).
tt(t16_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v2_trees_3 (k2_tarski A B)) <=>  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) ) ) ) ) ).
tt(t16_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((k1_trees_4 A) = (k3_trees_4 B C))  =>  ( (A = B)  &  (C = k1_xboole_0) ) ) ) ) ) ) ).
tt(t16_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ( ((k6_trees_9 A) = (k6_trees_9 B))  =>  (A = B) ) ) ) ) ) ).
tt(t16_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  ((k3_trees_a A (k2_trees_a (k9_xtuple_0 A) C) B) = (k7_trees_2 A C B)) ) ) ) ) ) ) ).
tt(t16_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  <=> (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t16_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=> (r2_tsep_1 A (k3_subset_1 (u1_struct_0 A) B) (k3_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t16_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_pre_topc B) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_pre_topc C) & (m1_pre_topc C A)) )  =>  ( ((v1_tsep_1 B A) | (v1_tsep_1 C A))  => (v6_pre_topc (k1_tsep_1 A B C))) ) ) ) ) ) ) ).
tt(t16_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tsp_2 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = C)  =>  ((v4_pre_topc D B) <=>  ((v4_pre_topc (k3_tex_4 A C) A) &  (D = (k8_subset_1 (u1_struct_0 A) (k3_tex_4 A C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_turing_1 A B C (k2_nat_1 (k2_nat_1 C D) 2)) => (r2_turing_1 (k2_finseq_4 k5_numbers C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t16_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k32_twoscomp (k11_finseq_1 A B C)))  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k31_twoscomp (k11_finseq_1 C B A)))  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k30_twoscomp (k11_finseq_1 C B A)))  &  ((k1_funct_1 k20_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k29_twoscomp (k11_finseq_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t16_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  ( (~ (v1_xboole_0 (k6_unialg_2 A)))  & (m1_subset_1 (k6_unialg_2 A) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ).
tt(t16_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_unialg_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_unialg_2 A))) =>  (! [D:$i] :  ( ((v1_unialg_1 D) & (m1_unialg_2 D A))  =>  (! [E:$i] :  ( ((v1_unialg_1 E) & (m1_unialg_2 E A))  =>  ( ( (B = D)  &  (C = E) )  =>  ((r3_lattices (k12_unialg_2 A) B C) <=> (m1_unialg_2 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_uniroots A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_uniroots A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k1_uniroots A) D E) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ( (C = (k1_partfun1 (k4_finseq_1 B) (k4_finseq_1 B) k5_numbers (u1_struct_0 A) D B))  =>  ((k3_group_4 A C) = (k3_group_4 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t16_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers (k1_urysohn1 (k2_nat_1 A 1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers (k1_urysohn1 (k2_nat_1 A 1))) =>  (~  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r2_hidden B (k1_urysohn1 A)))  &  ( (~ (r2_hidden C (k1_urysohn1 A)))  &  (~ (r1_xxreal_0 (k10_real_1 (k2_nat_1 (k6_urysohn1 (k2_nat_1 A 1) B) 1) (k13_newton 2 (k2_nat_1 A 1))) (k10_real_1 (k5_real_1 (k6_urysohn1 (k2_nat_1 A 1) C) 1) (k13_newton 2 (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (C = (k1_integra2 A B))  &  (A = (k2_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) )  =>  ( (C = (k2_xxreal_1 (k7_supinf_2 C) (k8_supinf_2 C)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (D = (k7_supinf_2 A))  &  (E = (k8_supinf_2 A)) )  =>  ( ((k7_supinf_2 C) = (k8_real_1 B D))  &  ((k8_supinf_2 C) = (k8_real_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k4_subset_1 k1_numbers k2_urysohn1 (k3_limfunc1 1))) =>  ((r1_xxreal_0 E k6_numbers) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F (k1_funct_1 (k3_urysohn3 A B C D) E)) => (r1_xxreal_0 (k1_seq_1 (k6_urysohn3 A B C D) F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ( ((v5_relat_1 E (k3_qc_lang1 A)) &  ((v3_card_1 E B) & (m2_finseq_1 E (k2_qc_lang1 A))) )  =>  (! [F:$i] :  ((m1_valuat_1 F A C) =>  (! [G:$i] :  ((m2_subset_1 G (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ((r1_valuat_1 A C (k4_cqc_lang B A G E) F D) <=>  ((k3_funct_2 (k2_valuat_1 A C) k6_margrel1 (k5_valuat_1 A C B E (k7_valuat_1 A C B F G)) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v5_relat_1 A k3_numbers) &  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) )  =>  (? [B:$i] :  ((v1_rat_1 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t16_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k9_xtuple_0 (k50_valued_1 A B)) = (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) ) ) ) ) ).
tt(t16_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k24_valued_1 (k24_valued_1 C A) B) = (k24_valued_1 C (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t16_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (D = F) )  =>  ((r1_struct_0 D C) |  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  ((r1_struct_0 D G) =>  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) G F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) (u1_struct_0 B) G (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_polynom5 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  => (v1_vectsp11 C A B)) ) ) ) ) ) ).
tt(t16_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B C) = (k4_struct_0 A))  <=>  ((k4_algstr_0 A B) = C) ) ) ) ) ) ) ) ).
tt(t16_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k6_algstr_0 A B (k1_vectsp_2 A (k1_group_1 A) B)) = (k1_group_1 A))  &  ((k6_algstr_0 A (k1_vectsp_2 A (k1_group_1 A) B) B) = (k1_group_1 A)) ) ) ) ) ) ) ).
tt(t16_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( ( (F = C)  &  (G = D) )  =>  ((k5_algstr_0 E F G) = (k5_algstr_0 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ((m1_vectsp_4 D A C) =>  ((k2_vectsp_5 A B D C) = D) ) ) )  &  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k2_vectsp_5 A B D C) = D)  => (m1_vectsp_4 D A C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_vectsp_6 C A B (k1_subset_1 (u1_struct_0 B))) =>  ((k4_vectsp_6 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t16_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (m1_vectsp_4 (k1_vectsp_7 A B (k9_subset_1 (u1_struct_0 B) C D)) A (k2_vectsp_5 A B (k1_vectsp_7 A B C) (k1_vectsp_7 A B D)))) ) ) ) ) ) ) ) ).
tt(t16_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski D (u1_struct_0 C)) => (m1_vectsp_4 (k1_vectsp_7 A B D) A C)) ) ) ) ) ) ) ) ) ).
tt(t16_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) (k4_vfunct_1 A B (k2_vfunct_1 A B D C) (k1_real_1 1)))) ) ) ) ) ) ) ) ).
tt(t16_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) (k2_vfunct_2 A B (k2_vfunct_1 A B D C) (k10_complex1 k6_complex1)))) ) ) ) ) ) ) ) ).
tt(t16_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k3_waybel_0 A B)) & (r1_tarski B (k4_waybel_0 A B))) ) ) ) ) ).
tt(t16_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_waybel10 A))) <=>  ((v1_orders_2 B) &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) ) ) ) ) ) ) ).
tt(t16_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_waybel_9 A)) ) )  =>  ( ((u1_pre_topc A) = (a_1_0_waybel11 A))  => (v2_pre_topc A)) ) ) ).
tt(t16_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  ((r3_yellow_4 A B C) & (r4_yellow_4 A C B)) ) ) ) ) ) ) ) ).
tt(t16_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A)))))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A)))) B C) = (k2_waybel_8 A C)) ) )  => (v23_waybel_0 B A (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))))) ) ) ) ) ).
tt(t16_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k6_waybel_0 A (k1_yellow_0 A B)) = (k1_setfam_1 (a_2_1_waybel14 A B))) ) ) ) ) ).
tt(t16_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (? [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v3_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v17_waybel_0 C B A) & (v22_waybel_0 C B A)) ) ) ) ) ) ) ) ) ).
tt(t16_waybel16,ax, (! [A:$i] :  ((k3_yellow_0 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A)))) = (k1_tarski A)) ) ).
tt(t16_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) =>  ( ( (~  ((r1_yellow_0 A C) & (r1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) )  &  (~  ((v24_waybel_0 A) & (v24_waybel_0 B)) ) )  | (r3_orders_2 B (k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k1_yellow_0 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ( ((u1_pre_topc A) = (u1_pre_topc B))  & (v2_waybel18 A)) )  => (v2_waybel18 B)) ) ) ) ) ).
tt(t16_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) )  =>  ((k1_waybel19 (k3_yellow_3 A B)) = (u1_pre_topc (k2_borsuk_1 A B))) ) ) ) ) ).
tt(t16_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_lattice3 A) =>  ((v17_waybel_0 C A B) <=>  ((v5_orders_3 C A B) & (v4_waybel_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t16_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v4_orders_2 A))  => (v4_orders_2 B)) ) ) ) ) ).
tt(t16_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ( ((r2_hidden (k4_yellow_0 A) (u1_struct_0 B)) & (v3_waybel_0 B A))  => (v7_yellow_0 B A)) ) ) ) ) ).
tt(t16_waybel22,ax, (! [A:$i] : (r1_waybel22 (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))) (k1_waybel22 A))) ).
tt(t16_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D))) )  => (r2_hidden (k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v22_waybel_0 D (k3_yellow_3 A B) C) =>  ((v22_waybel_0 (k1_waybel24 A B C D E) B C) & (v22_waybel_0 (k2_waybel24 A B C D F) A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  ((g1_orders_2 (u1_struct_0 (k1_waybel25 B)) (u1_orders_2 (k1_waybel25 B))) = (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A))) ) ) ) ) ).
tt(t16_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  ((v4_yellow_0 (k1_waybel26 A C) (k1_waybel26 A B)) & (m1_yellow_0 (k1_waybel26 A C) (k1_waybel26 A B))) ) ) ) ) ) ) ).
tt(t16_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D))) )  =>  ((k1_waybel26 A C) = (k1_waybel26 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  ((v1_yellow_6 C A) &  ((k4_yellow_6 A B) = (k4_yellow_6 A C)) ) ) ) ) ) ) ) ).
tt(t16_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k1_waybel29 A) = (k1_waybel29 B)) ) ) ) ) ) ).
tt(t16_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_yellow_0 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C)) = (k13_lattice3 A B (k2_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t16_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_tops_2 E A) &  ((v1_yellow_8 E A D) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( (C = D)  =>  ((v1_tops_2 (a_3_1_waybel30 A D E) B) &  ((v1_yellow_8 (a_3_1_waybel30 A D E) B C) & (m1_subset_1 (a_3_1_waybel30 A D E) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) ) )  => (v1_finset_1 (k7_waybel_0 A))) ) ).
tt(t16_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((v13_waybel_0 B A) & (v3_waybel11 B A)) ) ) ) ) ) ).
tt(t16_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A (k3_yellow19 A (k2_struct_0 A) B)) =>  ((k1_waybel33 A (k2_struct_0 A) B) = (k1_waybel11 A C)) ) ) ) ) ) ) ).
tt(t16_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k5_waybel34 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k5_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k5_waybel34 A) C))) &  ((v18_waybel_0 D (k4_yellow21 (k5_waybel34 A) B) (k4_yellow21 (k5_waybel34 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k5_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k5_waybel34 A) C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_lattice3 A (k4_waybel35 A B C D) D)) ) ) ) ) ) ) ).
tt(t16_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r2_hidden (k1_yellow_0 A B) B)) ) ) ) ).
tt(t16_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v4_yellow_0 (k8_waybel_4 A) (k6_yellow_1 (u1_struct_0 A) (k2_yellow_1 (k7_waybel_0 A)))) & (m1_yellow_0 (k8_waybel_4 A) (k6_yellow_1 (u1_struct_0 A) (k2_yellow_1 (k7_waybel_0 A))))) ) ) ).
tt(t16_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) => (r1_orders_2 A (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D))) (k5_yellow_2 A (k4_waybel_5 A D)))) ) ) ) ) ) ) ) ).
tt(t16_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) => (r2_hidden (k2_yellow_0 A D) C)) ) )  =>  ((u1_struct_0 A) = C) ) ) ) ) ) ) ) ) ).
tt(t16_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) &  ((v1_waybel_7 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  <=>  ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k7_lattice3 A)) &  ((v13_waybel_0 B (k7_lattice3 A)) &  ((v2_waybel_7 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A))))) ) ) ) ) ) ) ) ).
tt(t16_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((v1_waybel_8 A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k2_waybel_8 A C)))  & (v1_waybel_0 (k2_waybel_8 A C) A)) ) ) ) )  => (v1_waybel_8 B)) ) ) ) ) ).
tt(t16_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel_9 A B C))) =>  ( (D = E)  =>  ((k2_waybel_0 A B D) = (k2_waybel_0 A (k4_waybel_9 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  => (r1_tarski (u1_struct_0 (k4_weddwitt A)) (u1_struct_0 A))) ) ).
tt(t16_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ).
tt(t16_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v6_relat_2 B) => (v6_relat_2 (k2_wellord1 B A))) ) ) ) ).
tt(t16_wellord2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_wellord1 B A) =>  ( ((k1_relat_1 (k2_wellord1 B A)) = A)  & (v2_wellord1 (k2_wellord1 B A))) ) ) ) ) ).
tt(t16_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) &  ((k3_int_2 B C) = 1) )  =>  ((k3_int_2 A C) = 1) ) ) ) ) ) ) ) ).
tt(t16_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 (k3_xboole_0 A B) C) = (k3_xboole_0 A (k3_xboole_0 B C))) ) ) ) ).
tt(t16_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k3_xboolean (k6_xboolean A B))) = (k4_xboolean A (k3_xboolean B))) ) ) ) ) ).
tt(t16_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k6_xcmplx_0 A B) = A)  =>  (B = k6_numbers) ) ) ) ) ) ).
tt(t16_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 C D)) => (r1_xxreal_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t16_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k13_xtuple_0 A) (k13_xtuple_0 B))) ) ) ).
tt(t16_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k4_xxreal_0 A B) = A)  |  ((k4_xxreal_0 A B) = B) ) ) ) ) ) ).
tt(t16_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k4_xxreal_1 B C)) =>  ((r2_hidden A (k1_xxreal_1 B C)) &  ( (~  (A = B) )  &  (~  (A = C) ) ) ) ) ) ) ) ) ) ).
tt(t16_xxreal_2,ax, (! [A:$i] :  ( ((v3_membered A) &  (~ (v1_xboole_0 A)) )  =>  ((v4_xxreal_2 A) => (r2_hidden (k1_xxreal_2 A) k1_numbers)) ) ) ).
tt(t16_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k1_xxreal_3 A B) = k1_xxreal_0)  &  ( (~  (A = k1_xxreal_0) )  &  (~  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(t16_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((r2_yellow_0 A B) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r1_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) => (r1_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k7_yellow_3 A B (k13_lattice3 A C D) (k13_lattice3 B E F)) = (k13_lattice3 (k3_yellow_3 A B) (k7_yellow_3 A B C E) (k7_yellow_3 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow12,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  (C = D) )  =>  ((k5_yellow_0 A C) = (k5_yellow_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v23_waybel_0 D A B) & (r1_yellow_0 A C))  => (r1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t16_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k2_yellow15 A B) = (k1_tarski A)) ) ) ) ).
tt(t16_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r5_waybel_1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_orders_3 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C) (k3_struct_0 B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  (~  ((r2_hidden C (k2_waybel18 A B)) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B D)))) =>  (~  ((v3_pre_topc E (k4_waybel18 A B D)) &  ((k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B D)) (k6_waybel18 A B D) E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) => (r2_functor0 A B)) ) ) ) ) ).
tt(t16_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_9 A (k3_yellow19 A (k2_struct_0 A) B) C) <=> (r1_waybel_7 A B C)) ) ) ) ) ) ) ).
tt(t16_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_yellow_0 (k2_yellow_1 A)) => (r2_hidden (k1_setfam_1 A) A)) ) ) ).
tt(t16_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F B) &  ((v1_funct_1 F) & (v1_partfun1 F B)) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (k3_xboole_0 A B)) &  ((v1_funct_1 G) & (v1_partfun1 G (k3_xboole_0 A B))) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (k3_xboole_0 A B)) &  ((v1_funct_1 H) & (v1_partfun1 H (k3_xboole_0 A B))) ) )  =>  ( ( (G = (k1_yellow20 C E))  &  (H = (k1_yellow20 D F)) )  =>  (! [I:$i] :  ((m2_pboole I A C D) =>  (! [J:$i] :  ((m2_pboole J B E F) =>  ( (! [K:$i] :  ( ((r2_hidden K (k1_relset_1 A I)) & (r2_hidden K (k1_relset_1 B J)))  => (r1_partfun1 (k1_funct_1 I K) (k1_funct_1 J K))) )  => (m2_pboole (k1_yellow20 I J) (k3_xboole_0 A B) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r2_hidden (u1_struct_0 B) A) =>  ((m1_subset_1 B (u1_struct_0 (k7_yellow21 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (v3_waybel_3 B)) ) ) ) ) ) ) ) ).
tt(t16_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v22_waybel_0 B A A) => (v5_orders_3 B A A)) ) ) ) ) ).
tt(t16_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v5_orders_2 (k3_yellow_3 A B)) =>  ((v5_orders_2 A) & (v5_orders_2 B)) ) ) ) ) ) ).
tt(t16_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_yellow_4 A B (k4_subset_1 (u1_struct_0 A) C D)) = (k4_subset_1 (u1_struct_0 A) (k1_yellow_4 A B C) (k1_yellow_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t16_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  ((v2_waybel_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k10_lattice3 A (k12_lattice3 A B C) (k12_lattice3 A B D)) = B)  => (r1_orders_2 A B (k10_lattice3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t16_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k2_waybel_0 A B C) = (k4_yellow_6 A B)) ) ) ) ) ) ) ).
tt(t16_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_lattice3 A) <=> (v1_lattice3 (k7_lattice3 A))) ) ) ).
tt(t16_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_8 A B C) =>  (B = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t16_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k1_cantor_1 A B) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t16_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ((m1_subset_1 F k4_ordinal1) =>  (! [G:$i] :  ( ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 k4_ordinal1)))  =>  ( ((v8_zf_fund1 E A) &  ((r2_hidden B E) &  ((r1_tarski B E) &  ((r2_hidden C (k1_funct_2 G B)) &  ((r1_tarski D (k1_funct_2 (k4_subset_1 k4_ordinal1 G (k6_domain_1 k4_ordinal1 F)) B)) & (r2_hidden D E)) ) ) ) )  =>  ((r2_hidden F G) | (r2_hidden (a_5_1_zf_fund1 A B C D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  ( ((k16_zf_lang C D E A) = (k14_zf_lang F G B))  =>  ( (C = F)  &  ( (D = G)  &  ((k8_zf_lang E A) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k1_funct_1 (k7_zf_lang A B) 1) = 3) ) ) ) ) ).
tt(t16_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 (k1_tarski A) (k2_tarski A B)) = k1_xboole_0) ) ) ).
tt(t16_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ( (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) => (r2_zf_model A (k11_zf_model B))) ) )  <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_zfmodel1 B A) =>  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden (k7_relat_1 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t16_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (~  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model C)))  &  ((r1_zf_model A D (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang C (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) &  (! [E:$i] :  ( ((v1_zf_lang E) & (m2_finseq_1 E k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (~  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B G))  &  ((r2_hidden (k2_zf_lang G) (k4_zf_lang1 E)) &  ( (~  (G = 3) )  &  (~  (G = 4) ) ) ) ) ) ) )  &  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model E)))  &  ((r1_zf_model A F (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang E (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) & (r2_funct_2 A A (k1_zfmodel1 C A D) (k1_zfmodel1 E A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((r1_zf_model A B (k8_zf_lang D C)) <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( (~  ((k3_funct_2 k1_zf_lang A E F) = (k3_funct_2 k1_zf_lang A B F)) )  =>  (D = F) ) ) )  => (r1_zf_model A E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t16_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ( ((v2_ordinal2 B) & (v3_ordinal2 B))  => (v3_ordinal2 (k1_ordinal3 A B))) ) ) ) ) ).
tt(t16_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v5_relat_1 C A) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_zf_refle C A)) ) ) ) )  => (r1_tarski (k5_zf_refle A C B) (k4_zf_refle A C))) ) ) ) ) ) ).
tt(t16_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_zmodul01 B C (k4_xcmplx_0 A)) = (k4_algstr_0 B (k1_zmodul01 B C A))) ) ) ) ) ) ) ).
tt(t170_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((r1_tarski (k13_glib_001 A C) (k24_glib_000 A B)) & (r1_tarski (k14_glib_001 A C) (k25_glib_000 A B)))  => (m3_glib_001 C B)) ) ) ) ) ) ) ).
tt(t170_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k20_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k3_xxreal_3 D B))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t170_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_hidden A (k9_xtuple_0 B)) <=>  (~  ((k9_relat_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t170_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C)) = (k6_xcmplx_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t170_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) &  ( ((k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 (k6_xcmplx_0 1 A) C)) = k6_numbers)  &  ( (~  ( (A = k6_numbers)  &  (C = k6_numbers) ) )  &  ( (~  ( (A = 1)  &  (B = k6_numbers) ) )  &  (~  ( (B = k6_numbers)  &  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t170_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k2_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 B C)) = (k3_xxreal_1 A C)) ) ) ) ) ) ) ) ).
tt(t170_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v6_zf_lang A) <=> (v6_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t171_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m2_glib_000 D A (k6_subset_1 (k6_glib_000 A) (k1_tarski C)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski C)))) =>  ( (~ (r2_hidden C (k13_glib_001 A B)))  => (m3_glib_001 B D)) ) ) ) ) ) ) ) ) ).
tt(t171_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k20_member_1 A B) = (k4_member_1 (k18_member_1 A B))) ) ) ) ) ).
tt(t171_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v4_relat_1 k1_xboole_0 A) & (v5_relat_1 k1_xboole_0 B)) ) ) ).
tt(t171_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) B) C)) = (k2_xcmplx_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t171_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B C))  => (r1_xxreal_0 B (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C)))) ) ) ) ) ) ) ).
tt(t171_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C B) |  ((k2_xboole_0 (k3_xxreal_1 A B) (k4_xxreal_1 B C)) = (k4_xxreal_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t171_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v4_zf_lang A) =>  ((k20_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k20_zf_lang A) B C)) ) ) ) ) ) ) ) ).
tt(t172_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((m2_glib_000 D A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski C))) =>  ( (~ (r2_hidden C (k14_glib_001 A B)))  => (m3_glib_001 B D)) ) ) ) ) ) ) ) ).
tt(t172_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k18_member_1 A B) = (k4_member_1 (k20_member_1 A B))) ) ) ) ) ).
tt(t172_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_xboole_0 A B) =>  ((k5_relat_1 (k5_relat_1 C A) B) = k1_xboole_0) ) ) ) ) ) ).
tt(t172_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C)) = (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t172_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 B C))  => (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C)) C)) ) ) ) ) ) ) ).
tt(t172_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~  ((k2_xboole_0 (k3_xxreal_1 A B) (k2_xxreal_1 B C)) = (k4_xxreal_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t172_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v5_zf_lang A) =>  ( ((k21_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k21_zf_lang A) B C))  &  ((k22_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k22_zf_lang A) B C)) ) ) ) ) ) ) ) ) ).
tt(t173_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r1_glib_000 B C D E) =>  ((k2_glib_001 A C D E) = (k2_glib_001 B C D E)) ) ) ) ) ) ) ) ) ).
tt(t173_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k20_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k20_member_1 A C) (k20_member_1 B C))) ) ) ) ) ) ) ).
tt(t173_relat_1,ax, (! [A:$i] :  ((k1_relat_1 (k1_tarski (k4_tarski A A))) = (k1_tarski A)) ) ).
tt(t173_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k4_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t173_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 B D)) ) )  => (r1_xxreal_0 B (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) C) (k3_xcmplx_0 A D)))) ) ) ) ) ) ) ) ) ).
tt(t173_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~  ((k2_xboole_0 (k4_xxreal_1 A B) (k2_xxreal_1 B C)) = (k4_xxreal_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t173_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v6_zf_lang A) =>  ( ((k24_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k24_zf_lang A) B C))  &  ( ( ((k23_zf_lang A) = B)  =>  ((k23_zf_lang (k6_zf_lang1 A B C)) = C) )  &  ( (~  ((k23_zf_lang A) = B) )  =>  ((k23_zf_lang (k6_zf_lang1 A B C)) = (k23_zf_lang A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t174_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  (! [E:$i] :  ( ( (C = D)  & (r2_hidden E (k28_glib_000 B (k4_glib_001 B D))))  =>  ((k10_glib_001 A C E) = (k10_glib_001 B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t174_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k20_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k20_member_1 A C) (k20_member_1 B C))) ) ) ) ) ) ) ).
tt(t174_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v4_relat_1 B A))  =>  (B = (k5_relat_1 B A)) ) ) ) ).
tt(t174_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k4_xcmplx_0 A) B) = (k4_xcmplx_0 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t174_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 D C)) ) )  => (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A D)) C)) ) ) ) ) ) ) ) ) ).
tt(t174_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B C)) )  =>  ((k2_xboole_0 (k1_xxreal_1 A C) (k1_xxreal_1 B D)) = (k1_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t174_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v8_zf_lang A) <=> (v8_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t175_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C B) =>  ( ((v1_glib_001 C B) =>  ((v1_glib_001 C A) & (m3_glib_001 C A)) )  &  ( ((v2_glib_001 C B) =>  ((v2_glib_001 C A) & (m3_glib_001 C A)) )  &  ( ((v3_glib_001 C B) =>  ((v3_glib_001 C A) & (m3_glib_001 C A)) )  &  ( ((v4_glib_001 C B) =>  ((v4_glib_001 C A) & (m3_glib_001 C A)) )  &  ( ((v5_glib_001 C B) =>  ((v5_glib_001 C A) & (m3_glib_001 C A)) )  &  ((v6_glib_001 C B) =>  ((v6_glib_001 C A) & (m3_glib_001 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t175_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k20_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k20_member_1 A C) (k20_member_1 B C))) ) ) ) ) ) ) ).
tt(t175_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v4_relat_1 C A))  =>  ((r1_tarski C B) => (r1_tarski C (k5_relat_1 B A))) ) ) ) ) ) ).
tt(t175_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k4_xcmplx_0 A) B) = (k3_xcmplx_0 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t175_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) &  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 D B))  & (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) C) (k3_xcmplx_0 A D)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t175_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k2_xboole_0 (k2_xxreal_1 A C) (k3_xxreal_1 B D)) = (k1_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t175_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v9_zf_lang A) <=> (v9_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t176_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ( ((v1_glib_001 C A) => (v1_glib_001 D B))  &  ( ((v1_glib_001 D B) => (v1_glib_001 C A))  &  ( ((v2_glib_001 C A) => (v2_glib_001 D B))  &  ( ((v2_glib_001 D B) => (v2_glib_001 C A))  &  ( ((v3_glib_001 C A) => (v3_glib_001 D B))  &  ( ((v3_glib_001 D B) => (v3_glib_001 C A))  &  ( ((v4_glib_001 C A) => (v4_glib_001 D B))  &  ( ((v4_glib_001 D B) => (v4_glib_001 C A))  &  ( ((v5_glib_001 C A) => (v5_glib_001 D B))  &  ( ((v5_glib_001 D B) => (v5_glib_001 C A))  &  ( ((v6_glib_001 C A) => (v6_glib_001 D B))  &  ((v6_glib_001 D B) => (v6_glib_001 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t176_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k4_binop_2 B C) (k21_member_1 A C))) ) ) ) ) ) ) ).
tt(t176_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski (k9_xtuple_0 C) A) =>  ((k6_subset_1 C (k5_relat_1 C B)) = (k5_relat_1 C (k6_subset_1 A B))) ) ) ) ) ) ).
tt(t176_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 B)) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t176_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) &  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 C D))  & (r1_xxreal_0 C (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t176_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 D C) |  ((k2_xboole_0 (k1_xxreal_1 A C) (k2_xxreal_1 B D)) = (k2_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t176_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v10_zf_lang A) => (v10_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t177_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ( ((r5_glib_000 A B) & (m1_glib_001 C A))  => (m1_glib_001 C B)) ) ) ) ) ) ).
tt(t177_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k21_member_1 A B) = (a_2_13_member_1 A B)) ) ) ) ) ).
tt(t177_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k9_xtuple_0 (k6_subset_1 B (k5_relat_1 B A))) = (k6_subset_1 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t177_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k3_xcmplx_0 A (k4_xcmplx_0 B))) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t177_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ((r1_xxreal_0 B C) &  ( (~ (r1_xxreal_0 D B))  & (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) C) (k3_xcmplx_0 A D)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t177_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 B A) |  ((k2_xboole_0 (k3_xxreal_1 A C) (k1_xxreal_1 B D)) = (k3_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t177_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v11_zf_lang A) <=> (v11_zf_lang (k6_zf_lang1 A B C))) ) ) ) ) ) ) ).
tt(t178_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ( ((r5_glib_000 A B) & (m2_glib_001 C A))  => (m2_glib_001 C B)) ) ) ) ) ) ).
tt(t178_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k21_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k4_binop_2 D B))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t178_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k6_subset_1 (k9_xtuple_0 B) (k9_xtuple_0 (k5_relat_1 B A))) = (k9_xtuple_0 (k6_subset_1 B (k5_relat_1 B A)))) ) ) ) ).
tt(t178_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k3_xcmplx_0 (k4_xcmplx_0 A) B)) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t178_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 D C) & (r1_xxreal_0 C (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t178_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((k2_xboole_0 (k3_xxreal_1 A C) (k2_xxreal_1 B D)) = (k4_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t178_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v8_zf_lang A) =>  ( ((k21_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k21_zf_lang A) B C))  &  ((k22_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k22_zf_lang A) B C)) ) ) ) ) ) ) ) ) ).
tt(t179_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ( ((r5_glib_000 A B) & (m3_glib_001 C A))  => (m3_glib_001 C B)) ) ) ) ) ) ).
tt(t179_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski A B) <=> (r1_tarski (k21_member_1 A C) (k21_member_1 B C))) ) ) ) ) ) ) ).
tt(t179_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) => (r1_xboole_0 A B)) ) ) ) ) ).
tt(t179_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 (k4_xcmplx_0 1) A) = (k4_xcmplx_0 A)) ) ) ).
tt(t179_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 B (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C)))) )  =>  ((r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C)) C) |  (A = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t179_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) &  ((r1_xxreal_0 B D) & (r1_xxreal_0 C D)) ) )  =>  ((k2_xboole_0 (k2_xboole_0 (k2_xxreal_1 A B) (k1_xxreal_1 B C)) (k3_xxreal_1 C D)) = (k1_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t179_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v9_zf_lang A) =>  ( ((k25_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k25_zf_lang A) B C))  &  ((k26_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k26_zf_lang A) B C)) ) ) ) ) ) ) ) ) ).
tt(t17_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((l2_abcmiz_0 B) =>  ( ( ((g2_abcmiz_0 (u1_struct_0 A) (u1_abcmiz_0 A) (u1_orders_2 A) (u2_abcmiz_0 A) (u3_abcmiz_0 A)) = (g2_abcmiz_0 (u1_struct_0 B) (u1_abcmiz_0 B) (u1_orders_2 B) (u2_abcmiz_0 B) (u3_abcmiz_0 B)))  & (v10_abcmiz_0 A))  => (v10_abcmiz_0 B)) ) ) ) ) ).
tt(t17_abcmiz_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_abcmiz_1)))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden (k4_tarski (k1_abcmiz_1 A) B) k2_abcmiz_1)) ) ) ) ).
tt(t17_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k2_abcmiz_1) &  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  (~  ( (C = (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)))  &  (B = (k35_abcmiz_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (A = (k8_real_1 (k18_complex1 A) (k1_absvalue A))) ) ) ).
tt(t17_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden B (k2_aff_1 A C D)) & (r2_hidden E (k2_aff_1 A C D)))  =>  ( (C = D)  | (r1_tarski (k2_aff_1 A C D) (k2_aff_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B G) &  ((r2_hidden C G) &  ((r2_hidden D G) &  ((r2_hidden B H) &  ((r2_hidden E H) &  ((r2_hidden F H) &  ( (~ (r2_hidden B I))  &  ( (~ (r2_hidden B J))  &  ( (~  (G = H) )  &  ((r2_hidden C I) &  ((r2_hidden E I) &  ((r2_hidden D J) &  ((r2_hidden F J) &  ((v1_aff_1 G A) &  ((v1_aff_1 H A) &  ((v1_aff_1 I A) &  ((v1_aff_1 J A) &  ( (~ (r5_aff_1 A I J))  &  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r2_hidden K I) & (r2_hidden K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((k1_afinsq_1 (k1_ordinal4 A B)) = (k2_nat_1 (k1_afinsq_1 A) (k1_afinsq_1 B))) ) ) ) ) ).
tt(t17_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((r1_xxreal_0 (k1_afinsq_1 B) A) =>  ((k3_afinsq_2 B 1 A) = B) ) ) ) ) ) ).
tt(t17_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  => (r1_xboole_0 (k1_afproj A) (k8_afproj A))) ) ) ).
tt(t17_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_afvect0 A B C C) <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t17_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) => (r1_alg_1 A (k4_alg_1 A B) (k5_alg_1 A B))) ) ) ) ).
tt(t17_algseq_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_algseq_1 A (k4_struct_0 A))) <=>  ((k10_xtuple_0 B) = (k1_tarski (k4_struct_0 A))) ) ) ) ) ) ).
tt(t17_algspec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A B) =>  ((k5_relat_1 (k1_algspec1 B C) A) = (k1_algspec1 A C)) ) ) ) ) ) ).
tt(t17_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v32_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v6_algstr_1 A) & (l5_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k6_algstr_0 A (k11_algstr_0 A B) B) = (k5_struct_0 A))  &  ((k6_algstr_0 A B (k11_algstr_0 A B)) = (k5_struct_0 A)) ) ) ) ) ) ) ).
tt(t17_algstr_4,ax, (! [A:$i] :  ((k11_algstr_4 A 1) = A) ) ).
tt(t17_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k9_xtuple_0 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D)) = (k2_zfmisc_1 (k1_altcat_1 A C D) (k1_altcat_1 A B C)))  & (r1_tarski (k10_xtuple_0 (k4_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A) B C D)) (k1_altcat_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t17_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (v12_altcat_1 (k4_altcat_2 A))) ) ).
tt(t17_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v3_altcat_3 D A B C) &  (~  ((v4_altcat_3 D A B C) & (v5_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C D))) =>  (~  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  ((v18_functor0 C A B) &  ((v8_functor0 C A B) &  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  (~  (F = (k8_functor0 A B C D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k3_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(t17_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k2_ami_3 H I))  & (r2_hidden H (k9_xtuple_0 B))) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_amistd_1 2 k1_ami_3 B (k8_ami_3 C A)) = (k2_tarski C (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t17_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_extpro_1 A))) => (v2_extpro_1 B A (k1_extpro_1 A))) ) ) ) ).
tt(t17_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ( (~  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k1_funct_1 (k2_extpro_1 A B C D) (k4_struct_0 B)) = (k5_memstr_0 A B D)) ) ) )  => (r2_hidden (k4_struct_0 B) (k4_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t17_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  ((k1_ami_wstd B (k4_amistd_1 B) A) = A) ) ) ) ) ).
tt(t17_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((u1_analoaf (k2_diraf (k2_analoaf A))) = (k1_diraf (u1_struct_0 A) (k1_analoaf A))) ) ) ).
tt(t17_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_analoaf A B C D E) &  ((r1_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r1_analoaf A D E F G))  => (r1_analoaf A (k1_analort A B C D) (k1_analort A B C E) (k1_analort A B C F) (k1_analort A B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_anproj_1 A B C D))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 E A))  &  ( (~ (v9_struct_0 F A))  &  ( (~ (r1_anproj_1 A E F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 G A))  &  (~ (r2_anproj_1 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  ( ( ((k3_funct_2 A k1_numbers B F) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = F)  |  ((k1_funct_1 B J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers C G) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = G)  |  ((k1_funct_1 C J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers D H) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = H)  |  ((k1_funct_1 D J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers E I) = 1)  &  (! [J:$i] :  ((r2_hidden J A) =>  ( (J = I)  |  ((k1_funct_1 E J) = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J B)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K C))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L D))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M E))) (k8_funcsdom A)) =>  ( (J = k6_numbers)  &  ( (K = k6_numbers)  &  ( (L = k6_numbers)  &  (M = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k7_freealg B A))) =>  ( ((k3_finseq_1 D) = (k1_recdef_1 B C))  =>  ((k1_funct_1 (k2_pua2mss1 (k7_freealg B A) (k1_funct_7 C (k4_finseq_1 (u1_unialg_1 (k7_freealg B A))))) D) = (k4_trees_4 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_aofa_i00,ax, (! [A:$i] :  ((m4_aofa_i00 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 k5_numbers k4_numbers) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 k5_numbers k4_numbers) k5_numbers)))) )  => (m2_aofa_i00 B (k7_freealg k19_aofa_000 k26_aofa_i00) k5_numbers (k1_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k6_numbers k6_numbers) A)) ) ) ) ).
tt(t17_armstrng,ax, (! [A:$i] :  ((k1_relat_1 (k7_armstrng A)) = (k8_mcart_1 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k9_setfam_1 A) (k9_setfam_1 A))) ) ).
tt(t17_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k1_arytm_0 (k2_arytm_0 A A) (k2_arytm_0 B B)) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t17_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) => (r1_arytm_2 (k1_arytm_1 A C) (k1_arytm_1 B C))) ) ) ) ) ) ) ).
tt(t17_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_arytm_2)) =>  ( ((r2_hidden k11_arytm_3 A) &  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r2_hidden B A) &  (C = k12_arytm_3) )  => (r2_hidden (k7_arytm_2 B C) A)) ) ) ) ) )  => (r1_tarski k4_ordinal1 A)) ) ) ).
tt(t17_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  ((k3_arytm_3 (k9_ordinal3 A B) (k9_ordinal3 C B)) = (k9_ordinal3 (k3_arytm_3 A C) B)) ) ) ) ) ) ) ).
tt(t17_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_limfunc1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ( (~ (r2_hidden A (k6_asympt_0 B)))  & (r2_hidden B (k6_asympt_0 A))) ) ) ) ) ) ).
tt(t17_asympt_1,ax, ( (~ (r1_xxreal_0 (k10_real_1 159 100) (k6_power 2 3)))  =>  ((r2_hidden (k3_asympt_1 (k6_power 2 3)) (k6_asympt_0 (k3_asympt_1 (k10_real_1 159 100)))) &  ( (~ (r2_hidden (k3_asympt_1 (k6_power 2 3)) (k7_asympt_0 (k3_asympt_1 (k10_real_1 159 100)))))  &  (~ (r2_hidden (k3_asympt_1 (k6_power 2 3)) (k8_asympt_0 (k3_asympt_1 (k10_real_1 159 100))))) ) ) ) ).
tt(t17_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m2_pboole E A C B) =>  ( ((v1_msualg_3 D) &  ((v2_msualg_3 D A B C) & (r6_pboole A (k3_msualg_3 A B C B D E) (k2_msualg_3 A B))) )  => (r6_pboole A E (k4_msualg_3 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) => (m2_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B) (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A))) ) ) ) ) ) ).
tt(t17_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_partfun1 D C) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E C) &  ((v1_funct_1 E) &  ((v1_partfun1 E C) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((k1_bagorder C A B (k11_pre_poly C D E)) = (k11_pre_poly (k7_nat_d B A) (k1_bagorder C A B D) (k1_bagorder C A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B D C))) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t17_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k1_bcialg_1 A B C) = B)  =>  ((k1_bcialg_2 A B C D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t17_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C (k1_bcialg_1 A C B))) = (k1_bcialg_1 A (k4_struct_0 A) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t17_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  => (r3_binop_1 (u1_struct_0 A) (k4_struct_0 A) (u1_bcialg_4 A))) ) ).
tt(t17_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E (k2_nat_1 A F) B C (k2_nat_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_bcialg_6 A C (k2_bcialg_1 A B)) = (k2_bcialg_1 A (k3_bcialg_6 A C B))) ) ) ) ) ) ) ).
tt(t17_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A (k4_struct_0 A) C)) B)) )  =>  ((v12_bcialg_1 B A) & (m2_bcialg_1 B A)) ) ) ) ) ) ).
tt(t17_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k3_rlvect_1 A B C) (k5_algstr_0 A B C)) = (k9_real_1 (k2_bhsp_1 A B B) (k2_bhsp_1 A C C))) ) ) ) ) ) ) ).
tt(t17_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 C A) =>  ((k1_bhsp_2 A (k5_bhsp_1 A C B)) = (k3_rlvect_1 A (k1_bhsp_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t17_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ( ((k1_bhsp_2 A C) = B)  & (r2_bhsp_3 A C D)) )  =>  ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_bhsp_4 A B 1) = (k3_rlvect_1 A (k1_normsp_1 A B k6_numbers) (k1_normsp_1 A B 1))) ) ) ) ) ).
tt(t17_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k4_bilinear A B C D) E) (k4_hahnban1 A C (k7_bilinear A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((k6_binari_2 A B C) = (k7_binarith A B (k2_binari_2 A C))) ) ) ) ) ) ) ).
tt(t17_binari_3,ax, ( ((k7_binarith 1 (k10_binarith k6_margrel1 k7_margrel1) (k10_binarith k6_margrel1 k8_margrel1)) = (k10_binarith k6_margrel1 k8_margrel1))  &  ((k7_binarith 1 (k10_binarith k6_margrel1 k8_margrel1) (k10_binarith k6_margrel1 k7_margrel1)) = (k10_binarith k6_margrel1 k8_margrel1)) ) ).
tt(t17_binari_4,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k5_xboolean k8_margrel1 A) = k8_margrel1) ) ) ).
tt(t17_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k7_partfun1 k6_margrel1 (k4_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) F) = (k7_partfun1 k6_margrel1 (k4_binarith A B C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k5_binom A B C) = (k6_binom A B C)) ) ) ) ) ) ) ).
tt(t17_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A B) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ( (C = k1_xboole_0)  | (r2_hidden (k1_binop_1 F D E) C)) ) ) ) ) ) ) ) ) ).
tt(t17_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k5_series_1 2 B))) =>  ((k1_funct_1 (k2_bintree2 A B) C) = (k4_finseq_5 k6_margrel1 (k1_binari_3 B (k7_nat_d C 1)))) ) ) ) ) ) ) ) ).
tt(t17_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r4_boolealg A B C))  &  ((r3_lattices A D C) & (r4_boolealg A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r1_bor_cant A B C D) =>  ((v2_comseq_2 (k3_series_1 (k8_prob_1 A B D C))) |  ( ((k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) = k6_numbers)  &  ((k1_funct_1 C (k4_kurato_0 A D)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  (! [D:$i] :  (~  ((r2_hidden D (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) C)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  (~  ((r2_hidden E C) &  (D = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (a_2_0_borsuk_3 A B))  =>  ((v1_tops_2 C A) & (m1_setfam_1 C (k2_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t17_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( (A = (k3_rcomp_1 C D))  &  (B = (k4_rcomp_1 D E)) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 E D) | (r1_connsp_1 k5_topmetr A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (v1_rat_1 A))  <=> (r2_hidden A k1_borsuk_5)) ) ) ).
tt(t17_borsuk_6,ax, ((v4_pre_topc a_0_6_borsuk_6 (k15_euclid 2)) & (m1_subset_1 a_0_6_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(t17_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k18_rvsum_1 (k12_rvsum_1 (k11_finseq_1 A B C))) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C))) ) ) ) ) ) ) ).
tt(t17_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k4_bspace A B (k5_subset_1 A C D)) = (k5_subset_1 A (k4_bspace A B C) (k4_bspace A B D))) ) ) ) ) ) ) ) ).
tt(t17_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A B (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t17_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( ( (B = (k2_enumset1 C D E F))  &  (G = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 D I) (k16_funcop_1 E J)) (k16_funcop_1 F K)) (k16_funcop_1 C H))) )  =>  ((k10_xtuple_0 G) = (k2_enumset1 (k1_funct_1 G C) (k1_funct_1 G D) (k1_funct_1 G E) (k1_funct_1 G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) <=> (r2_funct_2 A k6_margrel1 B C)) ) ) ) ) ) ) ).
tt(t17_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))) (k2_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) C) (k5_bvfunc_1 A B (k1_bvfunc_1 A C))))) ) ) ) ) ) ).
tt(t17_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc_1 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A (k2_bvfunc_1 A B C))))) ) ) ) ) ) ).
tt(t17_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A C (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A B C D) (k7_bvfunc_2 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C (k9_bvfunc_1 A (k9_bvfunc_1 A C B) B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t17_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t17_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k1_bvfunc_1 A B)) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t17_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_1 A B C)) (k6_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t17_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D (k1_bvfunc_1 A C))) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t17_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (v4_xxreal_2 (k9_c0sp1 A B))) ) ) ) ) ).
tt(t17_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k8_group_1 (k5_c0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers G H) = (k8_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers E H) (k3_funct_2 (u1_struct_0 A) k1_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 E) k6_numbers))  =>  ( ((r9_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E) B C D) & (r1_valuat_1 A B (k2_calcul_1 A E) C D))  <=> (r9_calcul_1 A E B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k1_relset_1 k5_numbers (k15_finseq_1 (k5_relset_1 k5_numbers (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) B C) (k2_calcul_2 (k3_finseq_1 B) (k3_finseq_1 C))))) = (k1_relset_1 k5_numbers C)) ) ) ) ) ) ) ).
tt(t17_cantor_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_pre_topc A) &  ((v2_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_pre_topc B) &  ((v2_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((v1_tops_2 C B) &  ((v2_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) )  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t17_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 A B) =>  ((k2_card_1 A) = (k2_card_1 B)) ) ) ) ).
tt(t17_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  =>  ((k1_card_2 (k1_card_1 C) (k1_card_1 D)) = (k1_card_1 (k2_xboole_0 (k2_zfmisc_1 C (k1_tarski A)) (k2_zfmisc_1 D (k1_tarski B))))) ) ) ) ) ) ).
tt(t17_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k5_card_3 C (k3_xboole_0 A B)) (k3_xboole_0 (k5_card_3 C A) (k5_card_3 C B)))) ) ) ).
tt(t17_card_4,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (~  ( (~ (v1_finset_1 A))  &  ( ((r1_ordinal1 B A) | (r2_hidden B A))  &  (~  ((r1_ordinal1 (k2_card_2 A B) A) & (r1_ordinal1 (k2_card_2 B A) A)) ) ) ) ) ) ) ) ) ).
tt(t17_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( ((r1_ordinal1 B A) | (r2_hidden B A))  =>  ( (~ (v1_finset_1 A))  & (v1_card_1 A)) ) ) ) ) ) ).
tt(t17_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  (? [C:$i] :  ((m1_card_fil C A) &  ((r1_tarski B C) & (v3_card_fil C A)) ) ) ) ) ) ) ).
tt(t17_cardfin2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (~  ( ((k5_card_1 A) = 23)  &  ( ((k5_card_1 B) = 365)  & (r1_xxreal_0 (k24_binop_2 2 (k5_card_1 (k4_cardfin2 A B))) (k5_card_1 (k9_funct_2 A B)))) ) ) ) ) ) ) ).
tt(t17_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((v1_finset_1 D) =>  ( (~  (A = B) )  => (r2_hidden (k1_funct_4 (k7_funcop_1 C B) (k7_funcop_1 D A)) (k1_card_fin (k2_xboole_0 D C) (k5_card_1 D) A B))) ) ) ) ) ) ) ).
tt(t17_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski C B) => (r1_tarski (k2_card_lar A C) (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t17_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A B))  =>  ( ((k3_graph_1 A (k1_cat_1 A B C)) = (k3_graph_1 A B))  &  ((k4_graph_1 A (k1_cat_1 A B C)) = (k4_graph_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t17_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ((v13_cat_1 (k5_cat_2 A B) B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k2_cat_1 B C D) = (k2_cat_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  ((r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A D) (k8_funcop_1 (u1_struct_0 B) A (k3_graph_1 B C))) =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A (k7_cat_3 B A D C)) (k2_cat_3 B A D)) & (r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A (k7_cat_3 B A D C)) (k8_funcop_1 (u1_struct_0 B) A (k4_graph_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t17_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k3_cat_4 A B C)) = (k2_cat_4 A B C))  &  ((k4_graph_1 A (k3_cat_4 A B C)) = B) ) ) ) ) ) ) ) ).
tt(t17_cat_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_cat_5 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~  ( (! [C:$i] :  ((m1_cat_5 C A) =>  (! [D:$i] :  ((m1_cat_5 D A) =>  (! [E:$i] :  ((m1_cat_5 E A) =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G D E) =>  ( ((r2_hidden F B) & (r2_hidden G B))  => (r2_hidden (k9_cat_1 C D E F G) B)) ) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_cat_5 C A) => (r2_hidden (k10_cat_1 C) B)) )  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  =>  (~  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_cat_5 D A) =>  (! [E:$i] :  ((m1_cat_5 E A) =>  (! [F:$i] :  ((m2_cat_1 F D E) =>  ((m1_subset_1 (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 D) (u4_struct_0 E))) (k1_domain_1 A A D E) F) (u4_struct_0 C)) <=> (r2_hidden F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 k6_numbers (k1_catalan1 A))) ) ).
tt(t17_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (~  ((v1_catalan2 A) &  ( ((a_1_0_catalan2 A) = k1_xboole_0)  &  ( (~ (r1_xxreal_0 (k1_afinsq_1 A) k6_numbers))  &  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (~  ( (A = (k1_catalan2 (k5_afinsq_1 k6_numbers) B))  & (v1_catalan2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k3_catalg_1 A))) =>  (~  ( ( ((k1_xtuple_0 B) = 2)  |  ((k3_finseq_1 (k2_xtuple_0 B)) = 3) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  (B = (k10_catalg_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_cc0sp1 A)))  &  ((v13_algstr_0 (k7_cc0sp1 A)) &  ((v2_rlvect_1 (k7_cc0sp1 A)) &  ((v3_rlvect_1 (k7_cc0sp1 A)) &  ((v4_rlvect_1 (k7_cc0sp1 A)) &  ((v2_clvect_1 (k7_cc0sp1 A)) &  ((v3_clvect_1 (k7_cc0sp1 A)) &  ((v4_clvect_1 (k7_cc0sp1 A)) &  ((v5_clvect_1 (k7_cc0sp1 A)) & (l1_clvect_1 (k7_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 (k5_cc0sp2 A)))  &  ((v13_algstr_0 (k5_cc0sp2 A)) &  ((v2_rlvect_1 (k5_cc0sp2 A)) &  ((v3_rlvect_1 (k5_cc0sp2 A)) &  ((v4_rlvect_1 (k5_cc0sp2 A)) &  ((v3_group_1 (k5_cc0sp2 A)) &  ((v5_group_1 (k5_cc0sp2 A)) &  ((v1_vectsp_1 (k5_cc0sp2 A)) &  ((v3_vectsp_1 (k5_cc0sp2 A)) &  ((v2_clvect_1 (k5_cc0sp2 A)) &  ((v3_clvect_1 (k5_cc0sp2 A)) &  ((v4_clvect_1 (k5_cc0sp2 A)) &  ((v2_cfuncdom (k5_cc0sp2 A)) & (l1_cfuncdom (k5_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((m2_valued_0 A k2_numbers B) & (v2_comseq_2 B))  => (v2_comseq_2 A)) ) ) ) ) ).
tt(t17_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v6_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  ((r1_tarski B (k1_relset_1 k2_numbers A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (~  ((k2_relset_1 k2_numbers A) = (k1_tarski C)) ) ) )  |  ((r2_cfdiff_1 A B) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r2_hidden C B) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 A B) C) = k5_complex1) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ((m2_funct_2 C B k2_numbers (k9_funct_2 B k2_numbers)) &  (? [D:$i] :  ((m2_funct_2 D B k2_numbers (k9_funct_2 B k2_numbers)) &  ( (! [E:$i] :  ((r2_hidden E B) =>  ( ( (E = A)  =>  ((k1_funct_1 C E) = k6_complex1) )  &  ( (~  (E = A) )  =>  ((k1_funct_1 C E) = k6_numbers) ) ) ) )  &  (! [E:$i] :  ((r2_hidden E B) =>  ( ( (E = A)  =>  ((k1_funct_1 D E) = k6_numbers) )  &  ( (~  (E = A) )  =>  ((k1_funct_1 D E) = k6_complex1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) D) (k19_valued_1 A k2_numbers k2_numbers (k25_valued_1 A k2_numbers B D) C))) ) ) ) ) ) ) ) ).
tt(t17_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k8_cgames_1 B)) =>  ((v2_cgames_1 A) & (l1_cgames_1 A)) ) ) ) ) ).
tt(t17_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (A = (k7_domain_1 k1_numbers B C))  =>  ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers D E) A) <=>  ( ( (D = B)  &  (E = C) )  |  ( (D = C)  &  (E = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (A = (k7_finseq_1 (k9_finseq_1 C) B))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  =>  ((k1_chord A (k1_nat_1 D 1)) = (k1_chord B D)) ) ) ) ) ) ) ) ) ).
tt(t17_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  ((v1_circuit2 G C F) =>  ( (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( (H = (k5_relat_1 G (u1_struct_0 A)))  => (v1_circuit2 H A D)) ) )  &  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  ( (H = (k5_relat_1 G (u1_struct_0 B)))  => (v1_circuit2 H B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msafree2 B A) &  ((v5_circcmb3 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 C D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 C D) D)))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v3_card_1 F C) & (v1_finseq_1 F)) ) )  =>  ( (B = (k7_circcomb C D E F))  =>  (A = (k5_circcomb E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  ( ((r1_circcomb A C) &  (B = (k2_circcomb A C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k3_msafree2 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ((r2_hidden E (k3_msafree2 B)) &  ((k4_msafree2 B E) = (k4_msafree2 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v1_circled1 B A) &  ((r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers B C) k6_numbers) & (r2_hidden C (k3_rlvect_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t17_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v4_msafree2 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_msaterm A B))))  => (v4_msafree2 (k6_circtrm1 A B D C) (k1_circtrm1 A B D))) ) ) ) ) ) ) ) ).
tt(t17_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k6_circuit1 A B C) (k7_circuit1 A B))) ) ) ) ) ) ).
tt(t17_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m1_msafree2 D A B) =>  ( ((v3_funct_1 (k10_funct_6 C)) &  (D = (k1_funct_1 (k10_funct_6 C) k6_numbers)) )  =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( (G = (k7_circuit1 A B))  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C E) G) F) = (k5_circuit2 A B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_classes1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) &  ((k3_classes1 A B) = (k3_classes1 A (k1_ordinal1 B))) ) ) ) ).
tt(t17_classes2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A B))  => (r1_tarski A B)) ) ) ) ).
tt(t17_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k6_clopban1 A B)) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(t17_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((k1_normsp_0 A B) = 1) ) ) ) ) ).
tt(t17_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clopban3 B A) & (v1_clopban3 C A))  =>  ((v1_clopban3 (k2_normsp_1 A B C) A) &  ((k1_clopban3 A (k2_normsp_1 A B C)) = (k3_rlvect_1 A (k1_clopban3 A B) (k1_clopban3 A C))) ) ) ) ) ) ) ) ) ).
tt(t17_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_clopban4 D A B C) (k6_clvect_1 A (k2_clopban4 D A B C) (k13_complex1 k6_complex1 (k3_newton D))))) ) ) ) ) ) ) ) ).
tt(t17_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((v1_closure1 C A B) &  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) => (r2_pboole A (k2_closure1 A B C D) D)) ) )  => (v3_closure1 C A B)) ) ) ) ) ) ).
tt(t17_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k1_funct_1 (k3_closure2 (k1_tarski B)) A) = (k1_tarski (k1_funct_1 B A))) ) ) ) ) ).
tt(t17_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B B)) = (k1_clvect_1 A B (k8_complex1 k6_complex1 k6_complex1))) ) ) ) ) ).
tt(t17_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 C A) =>  ((k1_clvect_2 A (k5_bhsp_1 A C B)) = (k3_rlvect_1 A (k1_clvect_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t17_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k2_clvect_3 A B 1) = (k3_rlvect_1 A (k1_normsp_1 A B k6_numbers) (k1_normsp_1 A B 1))) ) ) ) ) ).
tt(t17_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_cohsp_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden (k2_xboole_0 B C) (k9_xtuple_0 A))) )  =>  ((k1_funct_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ).
tt(t17_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k4_coh_sp B)) <=>  (? [C:$i] :  ((m1_subset_1 C (k3_coh_sp B)) &  (? [D:$i] :  ((m1_subset_1 D (k3_coh_sp B)) &  ( ( ((k3_tarski D) = k1_xboole_0)  =>  ((k3_tarski C) = k1_xboole_0) )  &  ((v1_funct_1 A) &  ((v1_funct_2 A (k3_tarski C) (k3_tarski D)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski C) (k3_tarski D))))) ) ) ) ) ) ) ) ) ) ).
tt(t17_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m2_collsp B A) =>  (! [C:$i] :  ((m2_collsp C A) =>  ((r1_tarski B C) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t17_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((l1_combgras D A B) =>  ( ( ((g1_combgras A B (u1_combgras A B C) (u2_combgras A B C)) = (g1_combgras A B (u1_combgras A B D) (u2_combgras A B D)))  & (v6_combgras C A B))  => (v6_combgras D A B)) ) ) ) ) ) ) ) ) ).
tt(t17_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k4_xcmplx_0 A)) = (k1_real_1 (k3_complex1 A)))  &  ((k4_complex1 (k4_xcmplx_0 A)) = (k1_real_1 (k4_complex1 A))) ) ) ) ).
tt(t17_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  ( (A = B)  &  ((k6_xcmplx_0 A B) = k6_numbers) ) )  =>  ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig (k6_xcmplx_0 A B))))  <=> (r1_xxreal_0 k32_sin_cos (k1_comptrig (k6_xcmplx_0 B A)))) ) ) ) ) ) ).
tt(t17_complfld,ax, ((k11_algstr_0 k1_complfld (k5_struct_0 k1_complfld)) = (k5_struct_0 k1_complfld)) ).
tt(t17_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_complsp2 (k12_seq_4 A B)) = (k12_seq_4 (k1_complsp2 A) (k15_complex1 B))) ) ) ) ) ).
tt(t17_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k1_topmetr A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k1_topmetr A B)))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t17_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((l1_compos_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 C)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ((k5_compos_1 C (k5_compos_1 C D A) B) = (k5_compos_1 C D (k2_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t17_compos_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (~ (r2_hidden (k62_valued_1 A) (k9_xtuple_0 (k63_valued_1 A)))) ) ) ).
tt(t17_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) A))  &  ( ((k17_sin_cos A) = k6_numbers)  &  ( (~  (A = k6_numbers) )  &  (~  (A = k32_sin_cos) ) ) ) ) ) ) ) ) ).
tt(t17_compts_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_compts_1 A) &  ((v8_pre_topc B) &  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) & (v5_pre_topc C A B)) ) ) ) )  => (v3_tops_2 C A B)) ) ) ) ) ) ) ).
tt(t17_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_comput_1 A)) ) ) )  =>  ((v1_funct_1 A) &  ((v3_margrel1 A k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 k5_numbers) k5_numbers)))) ) ) ) ).
tt(t17_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers C (k9_complex1 A B)) (k25_valued_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers C B) A))) ) ) ) ) ) ).
tt(t17_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k8_real_1 A (k3_complex1 B)) = (k3_complex1 (k3_xcmplx_0 A B)))  &  ((k8_real_1 A (k4_complex1 B)) = (k4_complex1 (k3_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t17_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k1_funct_1 (k1_conlat_1 A) k1_xboole_0) = (u4_struct_0 A)) ) ) ).
tt(t17_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  &  ((v2_conlat_1 A) & (l1_conlat_1 A)) )  =>  ((k7_conlat_2 (k7_conlat_2 A)) = A) ) ) ).
tt(t17_conmetr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v1_conaffm A) <=> (v4_aff_2 (k3_analmetr A))) ) ) ).
tt(t17_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) & (v2_connsp_1 C A))  =>  ((r1_connsp_1 A B C) | (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t17_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc B A) => (v2_connsp_2 B A)) ) ) ) ) ) ).
tt(t17_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) =>  ( (B = k1_xboole_0)  | (r1_tarski (k2_pre_topc A B) (k1_connsp_3 A B))) ) ) ) ) ) ).
tt(t17_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (a_3_1_convex1 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t17_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_convex4 A B) = (k6_domain_1 (u1_struct_0 A) C))  =>  ((k4_convex4 A B) = (k1_clvect_1 A C (k3_funct_2 (u1_struct_0 A) k2_numbers B C))) ) ) ) ) ) ) ) ).
tt(t17_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E (k2_qc_lang1 A)))  =>  ((k13_cqc_lang A (k10_qc_lang1 A D E) C) = (k10_qc_lang1 A D (k1_cqc_lang A E (k2_cqc_lang A (k3_qc_lang3 A k6_numbers) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k7_cqc_sim1 A (k7_cqc_lang A B C)) = (k2_nat_1 (k7_cqc_sim1 A B) (k7_cqc_sim1 A C))) ) ) ) ) ) ) ).
tt(t17_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski B (k1_cqc_the1 A B))) ) ) ) ).
tt(t17_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C B) (k12_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t17_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the3 A B) <=> (r1_tarski B (k4_cqc_the1 A))) ) ) ) ) ).
tt(t17_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A)))) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) &  ((v1_csspace4 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( (D = C)  =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 A (u1_struct_0 B) D E)) (k1_normsp_0 (k9_csspace4 A B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k12_csspace A B (k3_rlvect_1 A C D)) = (k2_xcmplx_0 (k12_csspace A B C) (k12_csspace A B D))) ) ) ) ) ) ) ) ) ).
tt(t17_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_decomp_1 A) (k20_decomp_1 A)) = (k9_decomp_1 A)) ) ) ).
tt(t17_descip_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  (! [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  ((k12_descip_1 A (k12_descip_1 A B C) C) = B) ) ) ) ) ) ) ).
tt(t17_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_dickson A))) =>  ((r4_waybel_4 B C (u1_orders_2 (k5_dickson A))) <=>  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden (k4_tarski D C) (u1_orders_2 A)))  => (r2_hidden (k4_tarski C D) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ).
tt(t17_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers F B) (k26_valued_1 k1_numbers k1_numbers G C)) D) (k2_nat_1 A 1)) E) = (k7_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 F D) (k2_nat_1 A 1)) E)) (k8_real_1 C (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 G D) (k2_nat_1 A 1)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_zfmisc_1 A B C) =>  ((k10_diff_1 D A B C) = (k7_real_1 (k7_real_1 (k10_real_1 (k3_funct_2 k1_numbers k1_numbers D A) (k8_real_1 (k9_real_1 A B) (k9_real_1 A C))) (k10_real_1 (k3_funct_2 k1_numbers k1_numbers D B) (k8_real_1 (k9_real_1 B A) (k9_real_1 B C)))) (k10_real_1 (k3_funct_2 k1_numbers k1_numbers D C) (k8_real_1 (k9_real_1 C A) (k9_real_1 C B))))) ) ) ) ) ) ) ) ) ) ).
tt(t17_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E C) A) C) B) D) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E C) (k2_nat_1 A B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k1_fdiff_9)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k1_fdiff_9)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_fdiff_9) B) A) = (k13_complex1 (k8_real_1 (k8_real_1 4 (k18_sin_cos (k8_real_1 2 A))) (k18_sin_cos B)) (k5_square_1 (k7_real_1 (k21_sin_cos (k8_real_1 2 A)) (k21_sin_cos B))))) ) ) ) ) ) ).
tt(t17_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 C (k5_card_1 B)) &  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v2_dilworth D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((k5_card_1 D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_diraf A B C D) &  ((r1_diraf A B E D) &  ( (~ (r1_diraf A B C E))  &  (~ (r1_diraf A B E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v2_dirort A) =>  ((v3_dirort A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C F G) & (r2_analoaf A D E F G))  =>  ( (F = G)  | (r2_dirort A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_dist_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( ((v1_prob_2 A) &  ( ((k9_xtuple_0 A) = (k4_finseq_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((v1_finset_1 (k1_funct_1 A C)) &  ((k1_funct_1 B C) = (k1_card_1 (k1_funct_1 A C))) ) ) ) ) ) )  =>  ((v1_finset_1 (k3_card_3 A)) &  ((k1_card_1 (k3_card_3 A)) = (k16_rvsum_1 B)) ) ) ) ) ) ) ).
tt(t17_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_zfmisc_1 A B C D)) =>  ( ( ((k4_mcart_1 A B C D E) = (k4_mcart_1 A B C D F))  &  ( ((k5_mcart_1 A B C D E) = (k5_mcart_1 A B C D F))  &  ( ((k6_mcart_1 A B C D E) = (k6_mcart_1 A B C D F))  &  ((k7_mcart_1 A B C D E) = (k7_mcart_1 A B C D F)) ) ) )  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_dtconstr,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k5_dtconstr) (k5_trees_3 (u1_struct_0 k5_dtconstr)) (k4_dtconstr k5_dtconstr)) =>  ((k17_dtconstr k5_dtconstr A) = (k8_finseq_1 k5_numbers (k3_pre_poly k5_numbers k6_numbers) (k5_finseq_2 k5_numbers (k6_trees_1 (k9_xtuple_0 A)) 1))) ) ) ).
tt(t17_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin B A) & (v2_finsub_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r1_tarski (k10_xtuple_0 C) B) => (r2_hidden (k3_tarski (k10_xtuple_0 C)) B)) ) ) ) ) ) ) ) ).
tt(t17_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  (E = (k6_int_1 B C)) )  =>  ((k5_algstr_0 (k9_int_3 C) D E) = (k6_int_1 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_group_1 A (k5_algstr_0 A B C) (k3_rlvect_1 A (k3_rlvect_1 A (k2_binom A B 2) (k8_group_1 A B C)) (k2_binom A C 2))) = (k5_algstr_0 A (k2_binom A B 3) (k2_binom A C 3))) ) ) ) ) ) ) ).
tt(t17_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_tarski (k7_ens_1 A B C) (k2_ens_1 A))) ) ) ) ) ) ).
tt(t17_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ( (A = k1_xboole_0)  =>  ((k5_matrprob A) = k6_numbers) ) ) ) ).
tt(t17_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k2_tarski A B) (k3_enumset1 C D E F G))) ) ) ) ) ) ) ) ).
tt(t17_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k5_eqrel_1 A B (k4_eqrel_1 A B C)) B)) ) ) ) ) ).
tt(t17_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (m1_msualg_2 B A (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)))) ) ) ) ).
tt(t17_e_siec,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v2_e_siec C) &  ((v3_e_siec C) & (l1_e_siec C)) )  =>  (~  ( ((r2_hidden (k4_tarski A B) (u1_e_siec C)) | (r2_hidden (k4_tarski A B) (u2_e_siec C)))  &  ( (~  (A = B) )  &  (~  ((r2_hidden A (k8_e_siec C)) & (r2_hidden B (k7_e_siec C))) ) ) ) ) ) ) ) ) ).
tt(t17_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B C) = (k11_binop_2 (k18_binop_2 1 4) (k10_binop_2 (k5_square_1 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C))) (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)))))) ) ) ) ) ) ) ).
tt(t17_euclid_3,ax, ((k2_euclid_3 (k4_struct_0 (k15_euclid 2))) = k5_complex1) ).
tt(t17_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ( ((k23_rvsum_1 B B) = k6_numbers)  <=>  (B = (k5_euclid A)) ) ) ) ) ) ).
tt(t17_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 A B) = (k4_algstr_0 (k15_euclid 3) (k5_euclid_5 B A))) ) ) ) ) ).
tt(t17_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) =>  ( (D = B)  |  ( ((k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) C D) (k5_algstr_0 (k15_euclid 2) B A)) = k6_numbers)  <=>  ((k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) C D) (k5_algstr_0 (k15_euclid 2) B D)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_euclid_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ( ((v2_euclid_7 A) &  ((k12_euclid B) = 1) )  => (v2_euclid_7 (k2_xboole_0 A (k1_tarski B)))) ) ) ) ).
tt(t17_euclid_8,ax, ((k5_euclid_8 k3_euclid_8 k4_euclid_8) = k2_euclid_8) ).
tt(t17_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  ( (~  (A = k6_numbers) )  => (r1_tarski (k4_euclid_9 A C (k13_complex1 B (k6_square_1 A))) (k9_metric_1 (k14_euclid A) C B))) ) ) ) ) ) ) ).
tt(t17_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k12_euclid (k8_euclid A B C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t17_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  ((k7_euclid A (k7_euclid A (k7_euclid A B C) D) (k7_euclid A (k7_euclid A E F) G)) = (k7_euclid A (k7_euclid A (k7_euclid A B E) (k7_euclid A C F)) (k7_euclid A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r5_analmetr A B C E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r4_analmetr A B E B F) & (r4_analmetr A C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_euler_1,ax, ((k1_euler_1 1) = 1) ).
tt(t17_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  (! [C:$i] :  ((v7_ordinal1 C) => (r1_int_2 (k1_newton A C) B)) ) ) ) ) ) ) ) ) ).
tt(t17_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v3_exchsort A (k2_exchsort A))) ) ).
tt(t17_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m3_pboole C (u1_struct_0 A) D) => (m1_msualg_2 (k12_msualg_2 A B C) A (k12_msualg_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t17_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_extpro_1 A B C D) =>  ( ((k6_extpro_1 A B C D) = (k5_extpro_1 A B C D E))  <=> (r1_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~  ( ( (A = k2_supinf_1)  |  (A = k1_supinf_1) )  &  ( (B = k2_supinf_1)  |  (B = k1_supinf_1) ) ) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_extreal1 (k2_extreal1 A B)) = (k2_extreal1 (k3_extreal1 A) (k3_extreal1 B))) ) ) ) ) ) ) ) ) ).
tt(t17_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((r1_facirc_1 A B C D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_facirc_1 A B (k5_facirc_1 A B C E) D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k14_facirc_1 A B C)) = (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1))) ) ) ) ).
tt(t17_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B (k1_seq_4 A)))) ) ) ) ).
tt(t17_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((v2_funct_1 C) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r1_xxreal_0 A B) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))) (k7_relset_1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos) A) B) = (k9_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) B) (k8_real_1 (k1_seq_1 k3_taylor_1 B) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k29_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k29_sin_cos) A) B) = (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k1_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (r2_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A) (k1_partfun2 k1_numbers A)))  =>  ((r2_fdiff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 B A) C) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t17_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) & (r2_fdiff_1 C A))  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) (k2_fdiff_1 C A)))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r3_fdiff_3 A C) & (r3_fdiff_3 B C))  =>  ((r3_fdiff_3 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k2_fdiff_3 C (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k9_real_1 (k2_fdiff_3 C A) (k2_fdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t17_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = (k5_square_1 A)) ) ) )  &  (D = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) E) = (k8_real_1 2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos)))) &  (B = (k1_taylor_1 2)) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos)) A) C) = (k9_real_1 (k8_real_1 (k8_real_1 2 C) (k1_seq_1 k16_sin_cos (k10_real_1 1 C))) (k1_seq_1 k19_sin_cos (k10_real_1 1 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) D) (k10_real_1 1 (k6_power k8_power A))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k1_real_1 (k8_real_1 E (k6_power k8_power A))))  &  ((k1_seq_1 D E) = (k7_real_1 E (k10_real_1 1 (k6_power k8_power A)))) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) D) (k10_real_1 1 (k6_power k8_power A))) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) D) (k10_real_1 1 (k6_power k8_power A))) B) E) = (k10_real_1 E (k10_prepower A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6) A) B) = (k9_real_1 (k1_seq_1 k4_sin_cos6 B) (k10_real_1 B (k7_square_1 (k9_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t17_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k2_fdiff_9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t17_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k8_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A))) & (r1_tarski (k7_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A)))) ) ) ).
tt(t17_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((r1_xxreal_0 1 A) =>  ((v1_relat_1 (k1_tarski (k4_tarski A B))) &  ((v1_funct_1 (k1_tarski (k4_tarski A B))) & (v2_finseq_1 (k1_tarski (k4_tarski A B)))) ) ) ) ) ) ).
tt(t17_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 A (k1_fib_num3 A))) ) ).
tt(t17_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 (k8_complex1 (k13_complex1 (k3_power k2_fib_num A) (k7_square_1 5)) (k13_complex1 1 2)) k6_numbers))  &  (~ (r1_xxreal_0 1 (k8_complex1 (k13_complex1 (k3_power k2_fib_num A) (k7_square_1 5)) (k13_complex1 1 2)))) ) ) ) ).
tt(t17_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((k3_finseq_1 B) = k6_numbers)  =>  ((k4_finseq_5 A B) = B) ) ) ) ) ) ).
tt(t17_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((k1_filter_0 A) = (k2_filter_0 A (k5_lattices A))) ) ) ) ).
tt(t17_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_filter_0 A (k4_lattices A B C) D) = (k4_filter_0 A B (k4_filter_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t17_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_lattice2 A))) =>  ( ((k2_filter_2 A (k1_filter_2 A B)) = B)  &  ((k1_filter_2 A (k2_filter_2 A C)) = C) ) ) ) ) ) ) ) ).
tt(t17_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) &  (C = (k5_relat_1 B (k2_finseq_1 A))) )  =>  ( ((k3_finseq_1 C) = A)  &  ((k4_finseq_1 C) = (k2_finseq_1 A)) ) ) ) ) ) ) ) ) ).
tt(t17_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((k7_finseq_1 C (k9_finseq_1 A)) = (k7_finseq_1 D (k9_finseq_1 B)))  =>  ( (C = D)  &  (A = B) ) ) ) ) ) ) ) ) ).
tt(t17_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k2_finseq_1 A) = (k2_finseq_1 (k2_xcmplx_0 A B)))  =>  (B = k6_numbers) ) ) ) ) ) ).
tt(t17_finseq_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k7_partfun1 A (k2_finseq_4 A B C) 1) = B)  &  ((k7_partfun1 A (k2_finseq_4 A B C) 2) = C) ) ) ) ) ) ) ) ).
tt(t17_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k3_finseq_1 (k16_finseq_1 B A)) B)) ) ) ) ).
tt(t17_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((r2_finseq_4 (k7_finseq_1 A B) C) & (r2_hidden C (k10_xtuple_0 A)))  => (r2_finseq_4 A C)) ) ) ) ) ) ).
tt(t17_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_finseq_7 A (k3_finseq_4 A B C D) 3 E) = (k3_finseq_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_finseq_8 A B) <=>  ((k3_finseq_1 (k4_finseq_8 A (k2_rfinseq A 1 B) B)) = k6_numbers) ) ) ) ) ) ).
tt(t17_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A B) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  => (r2_relset_1 k5_numbers C (k1_finseqop A B C G (k5_finseq_2 A F D) (k5_finseq_2 B F E)) (k5_finseq_2 C F (k2_binop_1 A B C G D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((k1_finsop_1 A (k5_finseq_2 A 2 B) C) = (k5_binop_1 A C B B)) ) ) ) ) ) ) ).
tt(t17_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) => (m1_subset_1 B (k1_zfmisc_1 A))) ) ) ).
tt(t17_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k11_fin_topo A C)) <=>  ( ((k4_fintopo2 A B C) = k8_margrel1)  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( ((k1_fintopo2 A B D C) = k8_margrel1)  &  ((k5_fintopo2 A B D) = k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_fintopo3 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 A) (k3_fintopo3 A B D) (k3_fintopo3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t17_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v4_fin_topo C A) &  ((r2_fintopo4 A B E k6_numbers) &  (D = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E C)) ) )  => (v4_fin_topo D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_fin_topo A) =>  ((v4_fin_topo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_xboole_0 C D) &  ((r1_fintopo4 A C D) &  ( (~  (C = (k1_struct_0 A)) )  &  (~  (D = (k1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k9_fin_topo A (k3_subset_1 (u1_struct_0 A) B))) = (k8_fin_topo A B)) ) ) ) ) ).
tt(t17_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k6_flang_1 A B D) (k6_flang_1 A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t17_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((k8_flang_1 A (k7_flang_1 A B C)) = (k7_flang_1 A (k8_flang_1 A B) C)) ) ) ) ) ) ) ).
tt(t17_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k8_flang_1 A B)) = (k1_flang_3 A B C)) ) ) ) ) ) ).
tt(t17_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 A)) =>  ((k18_finseq_1 A) = (k3_tarski (a_1_0_fomodel0 A))) ) ) ) ).
tt(t17_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v15_fomodel1 B A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( (~  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B) = (k18_fomodel1 A)) )  => (v5_relat_1 B (k37_fomodel1 A))) ) ) ) ) ).
tt(t17_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( ((k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D)) = (k2_nat_1 1 (k4_xxreal_0 (k32_fomodel2 A C) (k32_fomodel2 A D))))  &  ((k32_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A B) C)) = (k1_nat_1 (k32_fomodel2 A C) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t17_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((v4_funct_1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k43_fomodel2 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 C))))) )  =>  ( ((v6_fomodel4 D C) &  ((r2_hidden (k23_fomodel4 C) D) &  ((r2_hidden (k33_fomodel4 C) D) &  ((r2_hidden (k24_fomodel4 C) D) & (r2_hidden (k30_fomodel4 C) D)) ) ) )  =>  ((v1_finset_1 (k7_subset_1 (k15_fomodel1 C) (k16_fomodel1 C) (k21_fomodel0 (k9_subset_1 (k3_finseq_2 (k1_fomodel1 C)) E (k6_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k1_tarski k1_xboole_0)))))) |  ((v14_fomodel4 E C D) |  ((r1_tarski (k8_nat_1 (k9_setfam_1 (k2_xboole_0 E (k33_fomodel2 C))) (k44_fomodel4 E C D F) A) (k8_nat_1 (k9_setfam_1 (k2_xboole_0 E (k33_fomodel2 C))) (k44_fomodel4 E C D F) (k2_xcmplx_0 A B))) &  ( (~ (v1_finset_1 (k7_subset_1 (k15_fomodel1 C) (k16_fomodel1 C) (k21_fomodel0 (k9_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k8_nat_1 (k9_setfam_1 (k2_xboole_0 E (k33_fomodel2 C))) (k44_fomodel4 E C D F) B) (k6_subset_1 (k3_finseq_2 (k1_fomodel1 C)) (k1_tarski k1_xboole_0)))))))  &  (~ (v14_fomodel4 (k8_nat_1 (k9_setfam_1 (k2_xboole_0 E (k33_fomodel2 C))) (k44_fomodel4 E C D F) B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((k1_frechet2 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t17_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden C A))  =>  ((k8_relat_1 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B C)) (k1_tarski C)) = B) ) ) ) ) ).
tt(t17_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ((k11_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F G)) (k10_margrel1 (k9_margrel1 E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k8_fscirc_1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k1_facirc_1) (k9_facirc_1 A B C k1_facirc_1)) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) (k1_tarski (k6_fscirc_1 A B C)))) ) ) ) ).
tt(t17_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( (F = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A G C)))  =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((r2_hidden H (k2_finseq_1 (k2_nat_1 (k3_finseq_1 D) 1))) =>  ((k1_funct_1 (k2_fsm_1 A E G (k8_finseq_1 A (k12_finseq_1 A C) D)) (k2_nat_1 H 1)) = (k1_funct_1 (k2_fsm_1 A E F D) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_tarski D E) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_tarski D E) A)))) )  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m2_subset_1 G k1_numbers k5_numbers))  =>  ((r1_xxreal_0 G (k2_nat_1 (k3_finseq_1 C) 1)) =>  ((r1_xxreal_0 G 1) |  ((k1_funct_1 (k2_fsm_1 B (k1_fsm_2 B A D E F) (u2_fsm_1 B (k1_fsm_2 B A D E F)) C) G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_3 D A C))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  ((r2_hidden B (k5_fsm_3 A C D E)) <=>  (~ (r1_xboole_0 (k3_rewrite3 A C D B E) (u2_fsm_3 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  (I = (k1_funct_1 F C)) ) )  =>  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) (k9_ftacell1 A B C D E)) = (k1_binarith (k1_binarith (k10_margrel1 G (k9_margrel1 H)) (k10_margrel1 (k9_margrel1 H) I)) (k10_margrel1 I G)))  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) (k10_ftacell1 A B C D E)) = (k9_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k3_relat_1 (k2_funcop_1 B C) A) = (k2_funcop_1 B (k1_funct_1 A C))) ) ) ) ) ) ).
tt(t17_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ((m2_funct_2 C B k1_numbers (k9_funct_2 B k1_numbers)) &  (? [D:$i] :  ((m2_funct_2 D B k1_numbers (k9_funct_2 B k1_numbers)) &  ( (! [E:$i] :  ((r2_hidden E B) =>  ( ( (E = A)  =>  ((k1_funct_1 C E) = 1) )  &  ( (~  (E = A) )  =>  ((k1_funct_1 C E) = k6_numbers) ) ) ) )  &  (! [E:$i] :  ((r2_hidden E B) =>  ( ( (E = A)  =>  ((k1_funct_1 D E) = k6_numbers) )  &  ( (~  (E = A) )  =>  ((k1_funct_1 D E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k4_relat_1 A))  <=>  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((r2_hidden C A) =>  ((k1_funct_1 B C) = C) ) ) ) ) ) ) ) ).
tt(t17_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r2_relset_1 A B (k4_relset_1 A A A B (k6_partfun1 A) C) C) & (r2_relset_1 A B (k4_relset_1 A B B B C (k6_partfun1 B)) C)) ) ) ) ) ).
tt(t17_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A (k1_zfmisc_1 (k10_xtuple_0 B))) =>  ((k8_relat_1 B (k3_tarski A)) = (k3_tarski (k8_relat_1 (k1_funct_3 B) A))) ) ) ) ) ).
tt(t17_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k10_xtuple_0 (k1_funct_4 A B)) (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t17_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 (k9_xtuple_0 A)) = (k10_xtuple_0 (k9_xtuple_0 (k2_funct_4 A))))  &  ((k10_xtuple_0 (k9_xtuple_0 A)) = (k9_xtuple_0 (k9_xtuple_0 (k2_funct_4 A)))) ) ) ) ).
tt(t17_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r1_tarski (k10_xtuple_0 F) (k4_partfun1 D E)) & (r1_tarski (k9_xtuple_0 F) A))  =>  ( ( (~ (r2_hidden (k2_funct_5 F) (k4_partfun1 (k2_zfmisc_1 A B) C)))  &  (~ (r2_hidden (k4_funct_5 F) (k4_partfun1 (k2_zfmisc_1 B A) C))) )  | (r2_hidden F (k4_partfun1 A (k4_partfun1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t17_funct_7,ax, ((k3_finseq_2 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t17_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t17_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((r2_hidden (k2_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((r2_hidden (k6_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((k1_funct_1 B (k2_xcmplx_0 C A)) = (k1_funct_1 B (k6_xcmplx_0 C A))) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((v1_funct_9 B (k8_real_1 2 A)) & (v2_funct_9 B)) ) ) ) ) ) ) ).
tt(t17_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F B) &  ((v1_funct_1 F) & (v1_partfun1 F B)) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G C) &  ((v1_funct_1 G) & (v1_partfun1 G C)) ) )  =>  (! [H:$i] :  ((m1_functor0 H B C E F G) => (m1_functor0 (k3_relat_1 D H) A C (k1_partfun1 A B B C D E) (k3_relat_1 D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  ((k15_functor0 A A (k12_functor0 A)) = (k12_functor0 A)) ) ) ).
tt(t17_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) )  =>  (! [E:$i] :  ( ((v15_functor0 E C D) & (m2_functor0 E C D))  =>  (! [F:$i] :  ( ((v15_functor0 F C D) & (m2_functor0 F C D))  =>  (! [G:$i] :  ( ((v15_functor0 G D A) & (m2_functor0 G D A))  =>  (! [H:$i] :  ( ((v15_functor0 H A B) & (m2_functor0 H A B))  =>  (! [I:$i] :  ((m1_functor2 I C D E F) =>  ((r1_functor2 C D E F) => (r8_pboole (u1_struct_0 C) (k5_functor3 C D B E F I (k1_functor3 D A B G H)) (k5_functor3 C A B (k1_functor3 C D A E G) (k1_functor3 C D A F G) (k5_functor3 C D A E F I G) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 (k1_fuzzy_1 A B C) B) & (r1_fuzzy_1 B (k2_fuzzy_1 A B C))) ) ) ) ) ) ) ).
tt(t17_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k6_fuzzy_1 A B C) (k1_fuzzy_2 A (k2_fuzzy_1 A B C) (k1_fuzzy_1 A B C)))) ) ) ) ) ) ).
tt(t17_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 C A) k1_numbers (k2_fuzzy_4 C A (k4_fuzzy_4 A B C D E)) (k4_fuzzy_4 C B A (k2_fuzzy_4 C B E) (k2_fuzzy_4 B A D)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k3_funct_2 (u1_struct_0 A) k7_numbers B (k5_struct_0 A)) = k6_numbers) ) ) ) ) ) ).
tt(t17_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r2_hidden F (k4_finseq_1 (k3_fvsum_1 A B C))) &  ( (D = (k1_funct_1 B F))  &  (E = (k1_funct_1 C F)) ) )  =>  ((k1_funct_1 (k3_fvsum_1 A B C) F) = (k1_algstr_0 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 A B C)))  &  ( (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) )  &  ( (~  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  &  (~  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 A)) ) ) ) ) ) )  &  (~  ( (~  ( (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) )  &  ( (~  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) )  &  (~  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 A)) ) ) ) ) )  & (v1_xboole_0 (k11_gate_1 A B C))) ) ) ) ) ) ).
tt(t17_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k8_group_1 A B C) = B)  =>  ( (B = (k4_struct_0 A))  |  (C = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t17_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_genealg1 B A) =>  (! [C:$i] :  ((m1_genealg1 C A) =>  ((k9_genealg1 A B C k6_numbers k6_numbers k6_numbers) = C) ) ) ) ) ) ) ).
tt(t17_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_geomtrap A D E B C C B) =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k3_msafree2 (k7_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k3_msafree2 (k7_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k3_msafree2 (k7_gfacirc1 A B C))) & (r2_hidden (k9_gfacirc1 A B C) (k3_msafree2 (k7_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t17_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  =>  ( ((k5_gfacirc2 1 A B) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k25_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ( ((k6_gfacirc2 1 A B) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k25_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k26_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ((k7_gfacirc2 1 A B) = (k21_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)) ) ) ) ) ) ) ) ) ).
tt(t17_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r1_glib_000 A C D B) =>  ( ( (~  ((r2_hidden C E) & (r2_hidden D F)) )  &  (~  ((r2_hidden C F) & (r2_hidden D E)) ) )  | (r3_glib_000 A E F B)) ) ) ) ) ) ) ) ) ).
tt(t17_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_001 A C D B) <=>  ( ((k1_funct_1 B 1) = C)  &  ((k1_funct_1 B (k3_finseq_1 B)) = D) ) ) ) ) ) ) ) ) ).
tt(t17_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( ((r5_glib_000 A B) &  (C = D) )  =>  ((k1_glib_002 A C) = (k1_glib_002 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k28_glib_000 A (k4_glib_001 A B))) =>  ((k8_glib_003 A (k10_glib_001 A B C)) = (k7_finseq_1 (k8_glib_003 A B) (k9_finseq_1 (k1_funct_1 (k5_glib_003 A) C)))) ) ) ) ) ) ) ).
tt(t17_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k8_glib_004 A B))) = (k6_domain_1 (k6_glib_000 A) B)) ) ) ) ) ).
tt(t17_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( (~  (B = C) )  => (v13_glib_000 (k12_glib_005 A B C))) ) ) ) ) ) ) ).
tt(t17_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( ((k1_matrix_1 C) = (k2_nat_1 A 1))  & (r2_hidden B (k2_finseq_1 A)))  =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 C 1) B) = (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1)))  &  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 (k3_goboard1 C 1)))) & (r2_hidden (k2_nat_1 B 1) (k2_finseq_1 (k1_matrix_1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_goboard2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 (k1_seq_1 (k2_goboard1 B) A) (k1_seq_1 (k2_goboard1 B) C))) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) 1)))) ) ) ) ) ).
tt(t17_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k2_goboard5 C B))) ) ) ) ) ) ) ).
tt(t17_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k2_goboard5 B A)) = (a_2_1_goboard6 A B)) ) ) ) ) ) ) ).
tt(t17_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B))) ) ) ) ) ) ) ) ).
tt(t17_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 1))) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 1))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 1))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t17_goboard9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 B (k1_matrix_1 C)))  => (v1_convex1 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t17_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  => (v4_pre_topc (k1_goboard5 B A) (k15_euclid 2))) ) ) ) ).
tt(t17_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 E) (k16_matrix_1 F)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) )  => (r1_tarski (k3_goboard5 F C D) (k3_goboard5 E A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k2_goboard9 A)) <=>  ( (~ (r2_hidden B (k3_topreal1 2 A)))  &  (~ (r2_hidden B (k3_goboard9 A))) ) ) ) ) ) ) ).
tt(t17_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [C:$i] :  ((m1_henmodel C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v1_goedelcp B A) & (v2_goedelcp B A))  =>  ((r1_valuat_1 A (k1_henmodel A) D C (k3_henmodel A)) <=> (r1_henmodel A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((r4_graph_1 A B) & (r4_graph_1 B C))  => (r4_graph_1 A C)) ) ) ) ) ) ) ).
tt(t17_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k10_xtuple_0 (k3_graph_2 A B)) (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t17_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (u4_struct_0 A)) &  ((r2_hidden B C) & (v1_xboole_0 (k1_graph_3 A C))) ) ) ) ) ) ) ).
tt(t17_graph_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ((v7_graph_1 C B) &  ((v3_graph_2 C B) & (m2_graph_1 C B)) )  =>  ((v7_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B) &  ((v3_graph_2 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B) & (m2_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B)) ) ) ) ) ) ) ) ).
tt(t17_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  => (v2_funct_1 B)) ) ) ) ).
tt(t17_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ( (A = B)  |  ((k1_seq_1 (k2_graphsp A B C D) A) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_grcat_1 D B C) =>  (! [E:$i] :  ((m1_grcat_1 E A B) => (m1_grcat_1 (k13_grcat_1 D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t17_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((v1_int_1 D) &  (C = (k5_group_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v1_gr_cy_1 B) & (l3_algstr_0 B)) ) ) ) ) )  =>  ( ((k7_group_1 B) = (k7_group_1 A))  => (r2_group_6 B A)) ) ) ) ) ).
tt(t17_gr_cy_3,ax, ((k1_gr_cy_3 1) = 1) ).
tt(t17_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_funct_1 A) &  ((v2_funct_1 B) &  ( (C = (k2_xboole_0 A B))  & (r1_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) )  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(t17_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r1_tarski (k2_grnilp_1 A) (k1_group_3 A))) ) ).
tt(t17_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r7_polyred A B C E D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r10_polyred A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  =>  ( (E = F)  |  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 H A C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r8_pboole (k15_pre_poly A) (k5_termord A B C (k10_polynom1 A C G E)) (k5_termord A B C (k10_polynom1 A C H F))) => (r1_rewrite1 (k3_polyred A B C D) (k6_polynom1 A C (k10_polynom1 A C G E) (k10_polynom1 A C H F)) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) )  => (r1_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t17_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k15_pre_poly A))) => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k2_groeb_3 A B C D)) (k2_polynom1 (k15_pre_poly A) B C))) ) ) ) ) ) ) ).
tt(t17_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_card_1 B) = (k1_card_1 (k5_group_2 A C B))) ) ) ) ) ) ) ).
tt(t17_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski B (k2_group_11 A B C))) ) ) ) ) ) ).
tt(t17_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k6_algstr_0 A B C)) = (k6_algstr_0 A (k2_group_1 A C) (k2_group_1 A B))) ) ) ) ) ) ) ).
tt(t17_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = k1_xboole_0) )  =>  ( ((k2_group_2 A (k2_subset_1 (u1_struct_0 A)) B) = (u1_struct_0 A))  &  ((k2_group_2 A B (k2_subset_1 (u1_struct_0 A))) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t17_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_group_3 A (k1_group_1 A) B) = (k1_group_1 A)) ) ) ) ) ).
tt(t17_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_funct_1 B E) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) C E) (k7_partfun1 (u1_struct_0 A) D E))) ) ) ) ) ) )  =>  ((k3_group_4 A B) = (k6_algstr_0 A (k3_group_4 A C) (k3_group_4 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B C) = (k6_algstr_0 A (k2_group_1 A (k6_algstr_0 A C B)) (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t17_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((u1_struct_0 (k5_group_6 A B)) = (k15_group_2 A B)) ) ) ) ) ).
tt(t17_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_group_7 (k10_finseq_1 A B)) & (v2_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ) ) ) ) ) ) ) ).
tt(t17_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ((r2_hidden B (k11_group_2 A E (k14_group_2 A D C))) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (B = (k6_algstr_0 A (k6_algstr_0 A F C) G))  &  ((r1_struct_0 D F) & (r1_struct_0 E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (~  ( ((k2_group_2 B (k15_group_9 A B C) (k15_group_9 A B D)) = (k2_group_2 B (k15_group_9 A B D) (k15_group_9 A B C)))  &  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  (~  ((u1_struct_0 E) = (k2_group_2 B (k15_group_9 A B C) (k15_group_9 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v1_groupp_1 C A B)) )  => (v2_group_10 B A)) ) ) ) ) ).
tt(t17_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k6_hahnban1 A B C (k3_hahnban1 A B D E)) (k3_hahnban1 A B (k6_hahnban1 A B C D) (k6_hahnban1 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [E:$i] :  ((m1_rlsub_1 E (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_struct_0 C B) |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) G (k1_rlvect_1 A B I)))  =>  ((k4_rlsub_2 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k1_rlvect_1 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) F H) E (k1_rlvect_3 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) (k6_domain_1 (u1_struct_0 (k1_rlsub_2 A C (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)))) D))) = (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) (k1_rlvect_1 C G H) (k1_rlvect_1 A B (k8_real_1 H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k5_card_1 (k1_funct_1 B C)) = 1) ) ) )  &  ((v1_hallmar1 B A) &  (! [C:$i] :  (~ (r1_hallmar1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t17_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_topmetr A C)))) =>  ( ( (B = D)  & (v6_tbsp_1 D (k1_topmetr A C)))  => (v6_tbsp_1 B A)) ) ) ) ) ) ) ) ) ).
tt(t17_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v4_glib_001 C A) & (m3_glib_001 C A))  =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  & (r1_xboole_0 (k14_glib_001 A B) (k14_glib_001 A C)))  => (v4_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(t17_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ( ((v1_henmodel E A) & (m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [F:$i] :  ((m1_henmodel F A E) =>  ((r1_valuat_1 A (k1_henmodel A) (k4_cqc_lang B A C D) F (k3_henmodel A)) <=> (r1_henmodel A E (k4_cqc_lang B A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k7_hahnban1 k1_complfld A)) (k7_hahnban1 k1_complfld A))) ) ).
tt(t17_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v6_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A D F I) &  ((r1_collsp A C E I) &  ((r1_collsp A F H J) &  ((r1_collsp A E G J) &  ((r1_collsp A D H K) &  ((r1_collsp A C G K) &  ((r1_collsp A B D C) &  ((r1_collsp A B F E) & (r1_collsp A B H G)) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = C)  |  ( (B = E)  |  ( (F = E)  |  ( (B = G)  |  ( (H = G)  |  ((r1_collsp A B D F) |  ((r1_collsp A B D H) |  ((r1_collsp A B F H) | (r1_collsp A J K I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_heyting1,ax, (! [A:$i] : (m2_subset_1 (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0)) (k5_finsub_1 (k7_normform A)) (k8_normform A))) ).
tt(t17_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((r1_tarski D C) => (m1_subset_1 D (u1_struct_0 (k5_substlat A B)))) ) ) ) ) ) ) ).
tt(t17_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_xboole_0 (k3_heyting3 A B) (k3_heyting3 (k2_nat_1 A 1) B))) ) ) ) ).
tt(t17_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 D A C) &  ((r1_taylor_1 E A C) & (r1_xxreal_0 B A)) )  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) C) B) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 D C) B) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 E C) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_polynom3 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((r2_hidden C (k4_hilbasis A B)) & (r2_hidden D B))  =>  ((r2_hidden C B) & (r1_xxreal_0 (k1_algseq_1 A C) (k1_algseq_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 A A)) k6_hilbert1)) ) ) ) ).
tt(t17_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (A = (k7_finseq_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t17_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ((k1_partfun1 (k2_zfmisc_1 C D) (k2_zfmisc_1 A B) (k2_zfmisc_1 A B) B (k16_funct_3 C D A B E F) (k10_funct_3 A B)) = (k1_partfun1 (k2_zfmisc_1 C D) D D B (k10_funct_3 C D) F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A B (k1_algstr_0 A C D)) (k2_normsp_1 A (k3_polynom5 A B C) (k3_polynom5 A B D)))) ) ) ) ) ) ) ) ).
tt(t17_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 B A) =>  ((r1_xxreal_0 (k7_idea_1 B A) (k5_series_1 2 B)) &  (~ (r1_xxreal_0 (k7_idea_1 B A) k6_numbers)) ) ) ) ) ) ) ).
tt(t17_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r2_hidden (k5_binom A C D) B)) ) ) ) ) ) ) ) ).
tt(t17_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_collsp A B C D) &  ((r1_collsp A E F D) &  ((r1_collsp A B E G) &  ((r1_collsp A C F G) &  ((r1_collsp A B F H) &  ((r1_collsp A C E H) &  ((r1_collsp A G D H) &  ( (~ (r1_collsp A B C F))  &  ( (~ (r1_collsp A B C E))  &  ( (~ (r1_collsp A B E F))  &  (~ (r1_collsp A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k3_incproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k3_incproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 (k3_incproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k3_incproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k3_incproj A))) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 (k3_incproj A))) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 (k3_incproj A))) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 (k3_incproj A))) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 (k3_incproj A))) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 (k3_incproj A))) =>  (~  ( (~ (r1_incsp_1 (k3_incproj A) C I))  &  ( (~ (r1_incsp_1 (k3_incproj A) D I))  &  ( (~ (r1_incsp_1 (k3_incproj A) B J))  &  ( (~ (r1_incsp_1 (k3_incproj A) E J))  &  ( (~ (r1_incsp_1 (k3_incproj A) B K))  &  ( (~ (r1_incsp_1 (k3_incproj A) D K))  &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) F B E) I) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) F C D) J) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) G C E) K) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) G B D) L) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) H B C) M) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) H D E) N) &  ((r4_incsp_1 (k3_incproj A) (k7_domain_1 (u1_incsp_1 (k3_incproj A)) F G) O) & (r1_incsp_1 (k3_incproj A) H O)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m4_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (k13_index_1 A B C))) ) ) ) ) ) ).
tt(t17_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  ((m1_instalg1 A B) =>  ((g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A)) = (g1_msualg_1 (u1_struct_0 B) (u4_struct_0 B) (u1_msualg_1 B) (u2_msualg_1 B))) ) ) ) ) ) ).
tt(t17_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r2_int_1 A B C) & (r2_int_1 D E C))  => (r2_int_1 (k6_xcmplx_0 A D) (k6_xcmplx_0 B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (m1_subset_1 (k2_int_2 A B) k5_numbers)) ) ) ) ).
tt(t17_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_int_1 (k3_int_2 B A) C))  &  (? [D:$i] :  ((v1_int_1 D) &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B D) C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ( ((k3_int_2 A B) = 1)  & (r1_int_5 A B))  =>  ((r1_xxreal_0 B 2) |  ((k6_int_1 (k1_newton A (k3_nat_d (k7_nat_d B 1) 2)) B) = 1) ) ) ) ) ) ) ).
tt(t17_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_int_2 (k3_xcmplx_0 A B) A) = (k1_int_2 A)) ) ) ) ) ).
tt(t17_int_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( ((k2_int_2 A B) = (k4_nat_1 D C))  &  ( ((k3_int_2 D C) = 1)  &  ((r1_int_1 D A) &  ((r1_int_1 C B) &  ( (~  (D = k6_numbers) )  &  (~  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers k32_sin_cos))  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t17_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos9) (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k41_valued_1 k1_numbers k1_numbers D)) A)))) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 E G) = 1)  &  ( ((k1_seq_1 D G) = (k12_binop_2 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D G))) ) ) ) ) ) )  &  ( (F = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) )  =>  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos9)) (k4_seq_4 B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos9)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers C)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos))) &  ((r1_tarski C (k1_relset_1 k1_numbers k29_sin_cos)) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t17_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t17_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_integr15 A B C) &  ((r1_integr15 A B D) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) &  ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) D B) A)) ) ) ) )  =>  ((r1_integr15 A B (k7_integr15 A k1_numbers C D)) &  ((r1_integr15 A B (k8_integr15 A k1_numbers C D)) &  ( ((k11_integr15 A B (k7_integr15 A k1_numbers C D)) = (k7_euclid A (k11_integr15 A B C) (k11_integr15 A B D)))  &  ((k11_integr15 A B (k8_integr15 A k1_numbers C D)) = (k8_euclid A (k11_integr15 A B C) (k11_integr15 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( ((k2_partfun1 k1_numbers k2_numbers B A) = C)  =>  ((k7_integr16 A B) = (k6_integr16 A C)) ) ) ) ) ) ) ) ).
tt(t17_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ( ((k3_integra1 C) = k6_numbers)  & (r1_tarski C (k1_relset_1 k1_numbers B)))  =>  ((r1_integr18 A C B) &  ((k5_integr18 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t17_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k1_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  ( (C = D)  =>  ((k1_nfcont_4 A k1_numbers C) = (k1_nfcont_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((k1_rvsum_1 (k7_rfunct_1 B B)) = (k1_seq_4 1)) ) ) ) ) ).
tt(t17_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ((k1_rvsum_1 (k26_valued_1 B k1_numbers C A)) = (k1_integra2 (k1_rvsum_1 C) A)) ) ) ) ) ) ) ).
tt(t17_integra3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((v5_valued_0 A) &  ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ((r2_hidden D (k4_finseq_1 A)) &  ((r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A D)) & (r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 A C))) ) ) ) )  => (r2_hidden (k1_seq_1 A D) (k1_rvsum_1 (k3_finseq_6 k1_numbers A B C)))) ) ) ) ) ) ) ) ) ).
tt(t17_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (v2_seq_2 (k2_partfun1 A k1_numbers (k19_rfunct_3 A C) B))) ) ) ) ) ).
tt(t17_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers A)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B)) & (r1_tarski C B)) )  => (r1_integra5 C A)) ) ) ) ) ) ) ).
tt(t17_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) D) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 D)) & (r2_hidden C (k3_integra5 A B))) ) ) )  =>  ((r1_integra5 (k3_integra5 A C) D) &  ((r1_integra5 (k3_integra5 C B) D) &  ((k4_integra5 A B D) = (k7_real_1 (k4_integra5 A C D) (k4_integra5 C B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r2_hidden E (k2_rcomp_1 A B)) &  ((r2_hidden F (k2_rcomp_1 A B)) & (r1_integra7 (k2_rcomp_1 A B) D C)) ) ) )  =>  ((k1_seq_1 D E) = (k7_real_1 (k4_integra5 F E C) (k1_seq_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_integra8,ax, ((k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 1) = (k10_real_1 (k9_real_1 (k5_square_1 k8_power) 1) (k8_real_1 2 k8_power))) ).
tt(t17_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k24_sin_cos)) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_fcont_1 1 (k1_real_1 1))) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_fcont_1 1 (k1_real_1 1))) (k5_seq_4 A)))) ) ) ).
tt(t17_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k4_interva1 A B C) = (k2_interva1 A (k4_subset_1 A (k5_interva1 A B) (k5_interva1 A C)) (k4_subset_1 A (k6_interva1 A B) (k6_interva1 A C)))) ) ) ) ) ) ) ).
tt(t17_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) => (r2_hidden (k3_intpro_1 A A) k8_intpro_1)) ) ).
tt(t17_irrat_1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((k18_rvsum_1 A) = (k2_xcmplx_0 (k1_seq_1 A 1) (k18_rvsum_1 (k2_rfinseq k1_numbers 1 A)))) ) ) ) ).
tt(t17_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  => (r1_isocat_1 (k8_cat_2 A B) (k8_cat_2 B A))) ) ) ) ).
tt(t17_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k4_nattra_1 B C (k12_cat_2 A B C D (k3_graph_1 A E)) (k12_cat_2 A B C D (k4_graph_1 A E)) (k4_isocat_2 A B C D E) F) = (k11_cat_2 A B C D E (k4_cat_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) <=>  ((v2_isomichi B A) & (v4_pre_topc B A)) ) ) ) ) ) ).
tt(t17_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v3_topreal1 A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A 1) (k2_topreal1 2 A (k2_nat_1 1 1))) (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 1 1)))) & (r1_tarski (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 2)) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 1))) (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k7_nat_d (k3_finseq_1 A) 1))))) )  => (v2_topreal1 A)) ) ) ).
tt(t17_jgraph_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ( (A = a_0_0_jgraph_2)  &  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) B) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2)))) )  =>  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))  &  ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ) ).
tt(t17_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_0_jgraph_3) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t17_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) =>  ((r1_xxreal_0 k6_numbers (k17_euclid A)) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))))) (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))) ) ) ) ) ) ) ).
tt(t17_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = a_0_5_jgraph_5)  &  ( ((k12_euclid A) = 1)  &  ( ((k12_euclid B) = 1)  &  ( ((k12_euclid C) = 1)  &  ((k12_euclid D) = 1) ) ) ) )  =>  ( (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ((r1_tarski (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) E) &  ( ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A) = (k19_euclid (k1_real_1 1) k6_numbers))  &  ( ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B) = (k19_euclid k6_numbers 1))  &  ( ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C) = (k19_euclid 1 k6_numbers))  &  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D) = (k19_euclid k6_numbers (k1_real_1 1))) ) ) ) ) ) ) ) )  |  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc F k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 F) &  ((v5_pre_topc G k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 G) &  ( ((k1_funct_1 F k6_numbers) = A)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 G k6_numbers) = D)  &  ( ((k1_funct_1 G 1) = B)  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) E) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) E) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = a_0_0_jgraph_6)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) & (r1_jordan6 E C D)) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc G k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 G) &  ((v5_pre_topc H k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 H) &  ( (F = a_0_1_jgraph_6)  &  ( ((k1_funct_1 G k6_numbers) = C)  &  ( ((k1_funct_1 G 1) = A)  &  ( ((k1_funct_1 H k6_numbers) = D)  &  ( ((k1_funct_1 H 1) = B)  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H) F) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = E)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid C) H) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_tarski (k1_jordan2c 2 B) (k3_goboard9 (k1_jordan9 B A)))) ) ) ) ).
tt(t17_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_tarski (k3_topreal1 2 (k1_jordan9 B A)) (k2_jordan2c 2 B))) ) ) ) ).
tt(t17_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden B (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) &  ((r2_hidden C (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) &  ((r2_hidden D (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden B E) & (r2_hidden C E)) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) E) &  ((r2_hidden B E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_xboole_0 (k2_jordan2c 2 A) (k1_jordan2c 2 (k3_topreal1 2 (k1_jordan13 A B))))) ) ) ) ) ).
tt(t17_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k2_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F G) &  ((r1_xxreal_0 G E) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r1_jordan5c A B C D E) &  ( (~  (D = E) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = B)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 F G) = D)  &  ( ((k1_funct_1 F H) = E)  &  ((r1_xxreal_0 k6_numbers G) &  ( (~ (r1_xxreal_0 H G))  & (r1_xxreal_0 H 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A D E B C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A D B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k1_jordan2c 2 B)) =>  ((r2_hidden (k1_jordan18 A B) B) &  ((r2_hidden (k1_jordan18 A B) (k4_topreal1 A)) &  ((r2_hidden (k2_jordan18 A B) B) & (r2_hidden (k2_jordan18 A B) (k6_topreal1 A))) ) ) ) ) ) ) ) ).
tt(t17_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k2_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) ) )  => (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C) B)))) ) ) ) ) ) ) ).
tt(t17_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_3_jordan1 A))  => (v1_convex1 B (k15_euclid 2))) ) ) ) ) ).
tt(t17_jordan1b,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_tarski A (k3_goboard5 (k1_jordan8 A k6_numbers) 2 2))) ) ).
tt(t17_jordan1c,ax, (! [A:$i] :  ( ((v4_pre_topc A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k9_metric_1 (k14_euclid 2) B C) (k1_jordan2c 2 A))) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k18_pscomp_1 B) (k2_gobrd13 (k1_jordan9 B A) (k1_jordan8 B A) C))) ) ) ) ) ) ) ) ).
tt(t17_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_sprect_2 (k1_jordan9 B A) (k1_jordan1e B A))) ) ) ) ).
tt(t17_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) (k3_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))))) = (k2_tarski (k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ).
tt(t17_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v4_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_xxreal_0 (k1_matrix_1 A) (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A))))) ) ).
tt(t17_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1) D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E)) = (k7_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k23_pscomp_1 B) A))  =>  ((k23_pscomp_1 A) = (k23_pscomp_1 B)) ) ) ) ) ) ).
tt(t17_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k2_jordan2c A (k1_struct_0 (k15_euclid A))) = (k2_struct_0 (k15_euclid A))) ) ) ) ).
tt(t17_jordan20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( ((k9_subset_1 (u1_struct_0 A) B C) = k1_xboole_0)  &  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  &  ((r2_hidden D B) &  ((r2_hidden E C) &  ((v3_pre_topc B A) & (v3_pre_topc C A)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  =>  (~  ((v5_pre_topc F k5_topmetr A) &  ( ((k1_funct_1 F k6_numbers) = D)  &  ((k1_funct_1 F 1) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k6_pscomp_1 A) = (k6_pscomp_1 (k8_jordan6 A))) ) ) ).
tt(t17_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k18_euclid (k1_jordan21 (k3_topreal1 2 (k1_jordan9 A B)))) (k18_euclid (k1_jordan21 A)))) ) ) ) ) ).
tt(t17_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_jordan23 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ((k4_jordan3 A B C) = (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k4_jordan3 A C B))) ) ) ) ) ) ) ) ) ).
tt(t17_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k8_metric_1)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = A)  =>  ((k9_metric_1 k8_metric_1 A B) = (a_2_1_jordan2b B C)) ) ) ) ) ) ) ) ).
tt(t17_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden C (k3_topreal1 2 A)) &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) C) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A C) 1) (k3_finseq_1 A)))) ) )  =>  ( (C = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A C) 1)))  | (r1_jordan3 B C (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) ) ) ) ) ) ).
tt(t17_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k3_finseq_6 A B C C) = (k6_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(t17_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( ( (G = F)  &  ((v5_pre_topc E (k4_topmetr A B) (k4_topmetr C D)) &  ((v2_funct_1 E) &  ((v2_compts_1 G k3_topmetr) &  ( ((k1_funct_1 E A) = C)  &  ( ((k1_funct_1 E B) = D)  &  ((k7_relset_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) E F) = H) ) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((k1_funct_1 E (k5_seq_4 (k1_weierstr G))) = (k5_seq_4 (k1_weierstr H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  (B = (k1_funct_1 A (k3_finseq_1 A))) )  =>  ((k2_jordan3 A B) = (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)) ) ) ) ) ) ).
tt(t17_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan5c (k1_rltopsp1 (k15_euclid 2) C D) C D A B) =>  ( (C = D)  | (r2_jordan3 C D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_4_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k3_topreal1 2 A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t17_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ( (B = (k2_jordan6 A B C))  <=>  ((k18_euclid B) = (k18_euclid C)) ) ) ) ) ) ) ) ) ).
tt(t17_jordan7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc D k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 D) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) D) = A)  &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) => (r1_xboole_0 (k3_goboard5 (k1_jordan8 A C) B k6_numbers) A)) ) ) ) ) ) ) ).
tt(t17_jordan9,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 A))) ) )  =>  ((r2_hidden B (k3_goboard5 A C D)) <=>  ((r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D)) (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1) D))) &  ((r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D)) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C (k2_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B C) =>  ( (B = C)  | (r1_topreal1 (k15_euclid 2) B C (k1_jordan7 A B C))) ) ) ) ) ) ) ) ).
tt(t17_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (m1_subset_1 C (u1_struct_0 (k2_brouwer A C B)))) ) ) ) ) ) ).
tt(t17_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v5_ordinal1 E)) )  =>  ( ((v4_ordinal1 D) &  ( ((k9_xtuple_0 E) = D)  &  (! [F:$i] :  ((v3_ordinal1 F) =>  ((r2_hidden F D) =>  ((k1_funct_1 E F) = (k3_knaster A B C F)) ) ) ) ) )  =>  ( (D = k1_xboole_0)  |  ((k3_knaster A B C D) = (k15_lattice3 A (k10_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) C E) = (k5_subset_1 A D (k3_funct_2 k5_numbers (k9_setfam_1 A) B E))) ) )  => (r1_tarski (k5_subset_1 A D (k4_kurato_0 A B)) (k4_kurato_0 A C))) ) ) ) ) ) ) ) ).
tt(t17_kurato_1,ax, ((k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)) = (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 4) (k1_seq_4 5))) ).
tt(t17_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C D))) )  => (r1_tarski (k1_kurato_2 A B) (k1_kurato_2 A C))) ) ) ) ) ) ) ).
tt(t17_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k3_lang1 (k9_lang1 A)) = (k3_finseq_2 A)) ) ) ).
tt(t17_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  ( (~ (r2_hidden C (k2_finseq_1 (k1_matrix_1 E))))  =>  ((k3_laplace C A B D E F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) => (r2_hidden (k2_group_1 A C) (k1_funct_1 (k1_latsubgr A) B))) ) ) ) ) ) ) ).
tt(t17_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) A) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) & (r2_hidden C (u1_struct_0 B))) )  => (r2_hidden D (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t17_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (u1_lattices A) B C) = C) ) )  =>  (B = (k6_lattices A)) ) ) ) ) ) ).
tt(t17_lattice3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A (k12_lattice3 A B C) C) = C) ) ) ) ) ) ) ).
tt(t17_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden (k5_lattices A) B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((r1_tarski C B) => (r2_hidden (k1_lattice4 A C) B)) ) ) ) ) ) ) ) ).
tt(t17_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v1_lattice5 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (v1_lattice5 (k6_lattice5 A B C D) (k5_lattice5 A) B)) ) ) ) ) ) ) ) ) ).
tt(t17_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v1_lattice6 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k6_lattices A)) )  =>  ((v3_lattice6 B A) <=> (v2_waybel_6 (k4_lattice3 A B) (k3_lattice3 A))) ) ) ) ) ) ).
tt(t17_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) => (r1_tarski A (k3_lattice8 A B))) ) ) ) ).
tt(t17_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattices A (k6_lattices A) B) = B) ) ) ) ) ).
tt(t17_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) => (r1_relset_1 (k6_glib_000 A) k5_numbers (k5_lexbfs A B C) (k5_lexbfs A B D))) ) ) ) ) ) ) ) ) ).
tt(t17_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_lfuzzy_0 A))) =>  ((r1_orders_2 (k4_lfuzzy_0 A) B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 (k7_lfuzzy_0 A (k5_lfuzzy_0 A B) D) (k7_lfuzzy_0 A (k5_lfuzzy_0 A C) D))) ) ) ) ) ) ) ) ) ).
tt(t17_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_lfuzzy_1 (k5_fuzzy_2 A A) A) &  ((v3_lfuzzy_1 (k5_fuzzy_2 A A) A) & (v1_lfuzzy_1 (k5_fuzzy_2 A A) A)) ) ) ) ).
tt(t17_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (v1_limfunc1 B))  => (v2_limfunc1 (k47_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t17_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 (k9_real_1 A D) A)))) ) ) )  | (r2_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t17_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) => (r1_xxreal_0 E (k1_seq_1 C F))) ) ) ) ) ) ) ) ) )  | (r2_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t17_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r6_limfunc2 B A) &  ((v7_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r5_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t17_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (m1_vectsp_4 (k1_lmod_5 A B (k9_subset_1 (u1_struct_0 B) C D)) A (k2_vectsp_5 A B (k1_lmod_5 A B C) (k1_lmod_5 A B D)))) ) ) ) ) ) ) ) ).
tt(t17_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( ((r1_lmod_6 A B C) & (r1_lmod_6 A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t17_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k1_algstr_0 (k13_lmod_7 A B E) (k14_lmod_7 A B E C) (k14_lmod_7 A B E D)) = (k14_lmod_7 A B E (k3_rlvect_1 B C D)))  &  ((k4_struct_0 (k13_lmod_7 A B E)) = (k14_lmod_7 A B E (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (D = (k1_rlvect_1 (k8_lopban_1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k9_lopban_1 A B D F) = (k1_rlvect_1 B (k9_lopban_1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((k1_normsp_0 A B) = 1) ) ) ) ) ).
tt(t17_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_lopban_3 B A) & (v1_lopban_3 C A))  =>  ((v1_lopban_3 (k2_normsp_1 A B C) A) &  ((k1_lopban_3 A (k2_normsp_1 A B C)) = (k3_rlvect_1 A (k1_lopban_3 A B) (k1_lopban_3 A C))) ) ) ) ) ) ) ) ) ).
tt(t17_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k6_lopban_3 A (k3_rlvect_1 A C D) B) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k5_lopban_4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_lopclset,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r2_hidden A (k1_funct_1 (k8_lopclset B) C)) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D B) &  ((v20_lattices D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  &  ( (D = A)  &  ((v1_filter_0 D B) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  ((k2_binop_1 k1_numbers (k3_rfunct_3 A k1_numbers) (k3_rfunct_3 A k1_numbers) (k4_lpspace1 A) 1 B) = B) ) ) ) ) ).
tt(t17_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((r1_xxreal_0 C k6_numbers) | (r1_xxreal_0 (k3_power (k4_xxreal_0 A B) C) (k7_real_1 (k4_power A C) (k4_power B C)))) ) ) ) ) ) ) ) ).
tt(t17_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k3_hilbert1 (k2_ltlaxio1 (k3_hilbert1 A B)) (k3_hilbert1 (k2_ltlaxio1 A) (k2_ltlaxio1 B))))) = 1) ) ) ) ) ) ) ) ) ).
tt(t17_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) &  ((r2_hidden C (k4_cqc_the1 A)) & (r2_hidden B (k4_cqc_the1 A))) )  => (r2_hidden D (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t17_margrel1,ax, (! [A:$i] :  ( ( (~ (r2_hidden k7_margrel1 A))  =>  ((k12_margrel1 A) = k8_margrel1) )  &  ( (~  ( ((k12_margrel1 A) = k8_margrel1)  & (r2_hidden k7_margrel1 A)) )  &  ( ((r2_hidden k7_margrel1 A) =>  ((k12_margrel1 A) = k7_margrel1) )  &  ( ((k12_margrel1 A) = k7_margrel1)  => (r2_hidden k7_margrel1 A)) ) ) ) ) ).
tt(t17_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_mathmorp A B (k1_mathmorp A D C)) = (k1_mathmorp A (k4_algstr_0 A D) (k3_mathmorp A B C))) ) ) ) ) ) ) ) ) ).
tt(t17_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v2_matrix10 B) & (v2_matrix10 C))  => (v2_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t17_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 1))) =>  (~  ( (~  ((k1_funct_1 B (k1_nat_1 A 1)) = (k1_nat_1 A 1)) )  &  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 1))) =>  (~  ((v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 1)))) &  ( ((k1_funct_1 C (k1_funct_1 B (k1_nat_1 A 1))) = (k1_nat_1 A 1))  &  ((k1_funct_1 (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 1)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 1)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 1)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 1)))) B C) (k1_nat_1 A 1)) = (k1_nat_1 A 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) C D) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 E) C D) =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 G))) &  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 G))) &  (H = (k4_matrix_1 (u1_struct_0 E) G)) ) )  =>  ((r1_xxreal_0 C k6_numbers) |  ((r1_xxreal_0 D k6_numbers) |  ((k4_matrix_1 (u1_struct_0 E) (k3_matrix12 C D E H A B F)) = (k6_matrix12 C D E G A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 A)))  =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [H:$i] :  ((m2_finseq_2 H k5_numbers (k4_finseq_2 C k5_numbers)) =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 G) (k10_xtuple_0 H)) (k2_matrix_1 F)) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_matrix13 A F B C G H))) <=> (r2_hidden (k4_tarski (k1_funct_1 G D) (k1_funct_1 H E)) (k2_matrix_1 F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k4_matrix_6 A B (k4_matrix_6 A B C D) E) = (k4_matrix_6 A B C (k4_matrix_6 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D A C) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k1_matrix_1 F))) =>  ((k9_matrix_1 D (k1_matrix15 D A B C E F) (k2_nat_1 (k1_matrix_1 E) G)) = (k9_matrix_1 D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) =>  ((v3_matrix16 C B) =>  ((r1_xxreal_0 A k6_numbers) | (v1_matrix16 (k5_matrix_1 A B C) B)) ) ) ) ) ) ) ) ).
tt(t17_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v4_matrix17 C (u1_struct_0 B)) =>  ((k5_matrix_1 A (u1_struct_0 B) C) = C) ) ) ) ) ) ) ) ).
tt(t17_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (m1_matrix_1 (k9_finseq_1 (k10_finseq_1 B C)) A 1 2)) ) ) ) ) ) ).
tt(t17_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_matrix_2 B))  &  ((k11_matrix_2 B) = A) ) ) ) ) ).
tt(t17_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 C)) &  ( ((k1_funct_1 B D) = (k5_struct_0 A))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( (E = D)  |  ((k1_funct_1 B E) = (k4_struct_0 A)) ) ) ) ) ) ) )  =>  ((k4_rlvect_1 A (k11_fvsum_1 A B C)) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A B D) = (k1_matrix_4 A (k1_matrix_4 A B C) (k1_matrix_4 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k3_matrix_5 A B) = (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A))) ) )  =>  (B = (k4_matrix_5 A)) ) ) ) ) ) ).
tt(t17_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ( ((k4_matrix_6 A B C D) = (k1_matrix_3 B A A))  & (v1_matrix_6 C A B))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ( ((r1_xxreal_0 1 B) & (v2_matrix_1 C A))  =>  ((k12_matrix_3 B A C) = (k1_finsop_1 (u1_struct_0 A) (k13_matrix_3 B A C) (u2_algstr_0 A))) ) ) ) ) ) ) ) ).
tt(t17_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_6 C A B) => (v2_matrix_6 (k4_matrix_6 A B C (k5_matrix_1 A (u1_struct_0 B) C)) A B)) ) ) ) ) ) ) ).
tt(t17_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden (k7_finseq_1 B C) (k12_matrix_2 A)) => (r2_hidden (k7_finseq_1 B (k3_finseq_5 C)) (k12_matrix_2 A))) ) ) ) ) ) ) ).
tt(t17_matrixc1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((k1_matrixc1 (k7_matrixc1 B A)) = (k7_matrix_5 (k15_complex1 A) (k1_matrixc1 B))) ) ) ) ) ).
tt(t17_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_matrixj1 C B) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 B))))  =>  ((k10_matrixj1 B (k6_matrixj1 B A C)) = (k17_finseq_1 k5_numbers A (k10_matrixj1 B C))) ) ) ) ) ) ) ).
tt(t17_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ( ((v1_funct_1 (k7_matrlin2 A B B C D)) &  ((v1_funct_2 (k7_matrlin2 A B B C D) (u1_struct_0 C) (u1_struct_0 C)) & (m1_subset_1 (k7_matrlin2 A B B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) )  =>  ((v1_funct_1 (k7_matrlin2 A B B C D)) &  ((v1_funct_2 (k7_matrlin2 A B B C D) (u1_struct_0 C) (u1_struct_0 C)) &  ((v2_matrixj2 (k7_matrlin2 A B B C D) A C) & (m1_subset_1 (k7_matrlin2 A B B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( (A = B)  &  (C = D) )  =>  ((k10_rvsum_1 C A) = (k9_fvsum_1 k2_vectsp_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k3_finseq_1 C) = (k1_matrix_1 A)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k6_matrixr1 (k5_matrixr1 A B) C) = (k5_matrixr1 (k6_matrixr1 A C) (k6_matrixr1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k9_matrlin A B C (k3_rlvect_1 B D E)) = (k3_fvsum_1 A (k9_matrlin A B C D) (k9_matrlin A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 C)) =>  ( ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  ((v13_vectsp_1 D C B) & (v1_mod_2 D A C B)) )  =>  ((k4_finseqop (u1_struct_0 C) (u1_struct_0 B) (k5_matrlin A C E F) D) = (k5_matrlin A B E (k4_finseqop (u1_struct_0 C) (u1_struct_0 B) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski C B) => (r1_xxreal_0 (k5_card_1 C) (k4_matroid0 A B))) ) ) ) ) ) ) ).
tt(t17_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ( (C = D)  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k2_finseq_1 (k1_matrix_1 C))) =>  ((k9_matrix_1 A C E) = (k9_matrix_1 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (~  ( ((k8_matrix13 C D) = B)  &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A (k7_nat_d A B)) =>  (~  ((k8_matrix13 C (k1_matrix15 (u1_struct_0 C) A B (k7_nat_d A B) D E)) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  (! [E:$i] :  ((m1_matrlin E k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B D))) =>  ( (E = D)  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B D)))) =>  ( (F = (k1_funct_1 (k3_matrtop1 A B D) C))  =>  ((k9_matrlin k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B D)) E F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D E))  =>  ((r1_xxreal_0 D C) |  ((k4_matrix_6 E k2_vectsp_1 (k2_matrtop3 E A C D) (k2_matrtop3 E B C D)) = (k2_matrtop3 E (k2_xcmplx_0 A B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) (k1_mazurulm A B)) (k3_struct_0 A))) ) ) ) ).
tt(t17_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k6_pboole A B C) (k1_mboolean A (k1_mboolean A (k2_pboole A B C))))) ) ) ) ) ).
tt(t17_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_zfmisc_1 (k2_tarski B C) (k1_tarski D))) =>  ( ( ((k1_xtuple_0 A) = B)  |  ((k1_xtuple_0 A) = C) )  &  ((k2_xtuple_0 A) = D) ) ) ) ) ) ) ).
tt(t17_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( ((k2_relset_1 (k9_setfam_1 A) E) = (k1_enumset1 B C D))  &  ( ((k1_prob_2 A (k9_setfam_1 A) E k6_numbers) = B)  &  ( ((k1_prob_2 A (k9_setfam_1 A) E 1) = C)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 F 1))  =>  ((k1_prob_2 A (k9_setfam_1 A) E F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = k1_xboole_0)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B C k6_numbers) (k8_nat_1 B C E)))  & (r1_tarski (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B C E))) ) ) )  =>  ((v1_measure2 (k4_measure1 A B D) A B) & (m1_measure2 (k4_measure1 A B D) A B)) ) ) ) ) ) ) ) ) ).
tt(t17_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (m1_measure3 (k8_nat_1 (k9_setfam_1 A) D E) A B C)) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (~  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_tarski (k8_nat_1 (k9_setfam_1 A) D F) (k8_nat_1 B E F)) &  ((k12_supinf_2 C (k8_nat_1 B E F)) = k1_supinf_2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v2_measure5 A) =>  (A = (k1_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) ) ) ) ).
tt(t17_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m3_measure8 D A C B) =>  (~  ((r2_hidden C B) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) &  ((v1_prob_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  (~  ( (C = (k3_tarski (k2_relset_1 B E)))  &  (! [F:$i] :  ((v7_ordinal1 F) => (r1_tarski (k8_nat_1 B E F) (k1_measure8 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k5_member_1 (k6_subset_1 A B)) = (k6_subset_1 (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(t17_membered,ax, (! [A:$i] :  ((v5_membered A) =>  ( (! [B:$i] :  ((v1_int_1 B) => (r2_hidden B A)) )  =>  (A = k4_numbers) ) ) ) ).
tt(t17_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v5_memstr_0 D A B C)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) & (v5_funct_1 E (k2_memstr_0 A B))) ) )  =>  ((r1_tarski D E) => (v5_memstr_0 E A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (A = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) E H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) B I))) ) )  =>  ((k1_euclid_6 A D F) = (k11_binop_2 (k9_binop_2 (k11_binop_2 (k11_binop_2 (k10_binop_2 1 G) (k10_binop_2 1 H)) (k10_binop_2 1 I)) (k11_binop_2 (k11_binop_2 G H) I)) (k1_euclid_6 E B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (E = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc1 A C (k4_mesfunc5 A k7_numbers B G) E)) )  &  ((r1_mesfunc5 A C D F) &  ((v6_supinf_2 F) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G E) => (r1_xxreal_0 (k12_supinf_2 (k10_mesfunc1 A (k4_mesfunc5 A k7_numbers B H)) G) (k12_supinf_2 F G))) ) ) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k12_supinf_2 G H) = (k7_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B H))) ) )  &  ((r1_xxreal_0 (k7_mesfunc5 A C D (k5_mesfunc8 A B)) (k6_rinfsup2 G)) &  ((r1_xxreal_0 (k5_rinfsup2 G) (k7_mesfunc5 A C D (k6_mesfunc8 A B))) &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H E) => (v10_mesfunc5 (k3_mesfunc5 A B H))) ) )  =>  ((v10_mesfunc5 G) &  ((k2_mesfunc5 G) = (k7_mesfunc5 A C D (k7_mesfunc8 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C E) & (r1_tarski E (k1_relset_1 A C)))  => (r1_mesfun6c A B (k25_valued_1 A k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 D F) = (k8_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) (k14_mesfunc1 (k4_mesfunc5 A k1_numbers C F) E))) ) )  =>  ((k1_setfam_1 (k2_relset_1 B D)) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) (k18_mesfunc1 A (k2_mesfun7c A C) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((v1_mesfunc8 B A k1_numbers) => (v1_mesfunc8 (k2_mesfun9c A B) A k1_numbers)) ) ) ) ) ).
tt(t17_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((r1_tarski C (k9_xtuple_0 B)) =>  ((k9_subset_1 A C (k15_mesfunc1 A B D)) = (k6_subset_1 C (k9_subset_1 A C (k18_mesfunc1 A B D)))) ) ) ) ) ) ) ) ).
tt(t17_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((k1_relset_1 A B) = (k1_relset_1 A (k4_mesfunc1 A (k1_mesfunc2 A B) (k2_mesfunc2 A B))))  &  ((k1_relset_1 A B) = (k1_relset_1 A (k3_mesfunc1 A (k1_mesfunc2 A B) (k2_mesfunc2 A B)))) ) ) ) ) ) ).
tt(t17_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  ((r2_hidden k1_supinf_1 (k2_relset_1 k7_numbers A)) =>  ((r2_hidden k2_supinf_1 (k2_relset_1 k7_numbers A)) |  ((k4_extreal1 A) = k1_supinf_1) ) ) ) ) ).
tt(t17_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) & (v4_mesfunc5 C))  =>  ((k1_relset_1 A (k4_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ).
tt(t17_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc6 A B C D) & (r1_mesfunc6 A B C E))  => (r1_mesfunc6 A B C (k6_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 k7_numbers)))  =>  ( ( ((k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)) = F)  &  ( ((k2_relset_1 k7_numbers D) = G)  &  ((v3_valued_0 E) &  ((r1_mesfunc1 A B D F) &  ((v5_xxreal_2 (k2_relset_1 k7_numbers D)) & (r1_mesfunc5 A B C E)) ) ) ) )  =>  ((r1_mesfunc5 A B C (k2_partfun1 A k7_numbers (k5_mesfunc1 A D E) F)) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ((r1_xxreal_0 (k7_supinf_2 G) H) &  ((r1_xxreal_0 H (k8_supinf_2 G)) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k5_mesfunc1 A D (k10_mesfunc1 A E)) F)) = (k1_extreal1 (k1_measure6 H) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k10_mesfunc1 A E) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k4_mesfunc5 A k7_numbers C F) (k1_measure6 E)))) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) (k6_setlim_1 A B D) F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc8 A C) F) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mesfunc9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_mesfunc9 A B) k6_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_mesfunc9 (k2_mesfunc9 A) B) k6_numbers)) ) ) ) ) ) ).
tt(t17_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k9_metric_1 B C A) = (a_3_3_metric_1 A B C)) ) ) ) ) ) ) ).
tt(t17_metric_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  ((r2_hidden A (k2_metric_2 B)) <=> (m1_metric_2 A B)) ) ) ) ).
tt(t17_metric_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) => (r1_xxreal_0 (k3_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D)) (k3_xcmplx_0 E F))) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 E)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 D)) (k3_square_1 F))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) & (r2_hidden D (k2_pcomps_1 A)))  => (r2_metric_6 A D C)) ) )  => (r1_metric_6 A C B)) ) ) ) ) ) ) ).
tt(t17_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) => (r1_ordinal1 (k2_waybel23 A) (k2_card_2 k4_ordinal1 (k1_card_1 B)))) ) ) ) ) ).
tt(t17_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlvect_2 B (k10_funcsdom (k2_finseq_1 A))) <=> (m1_rlvect_2 B (k15_euclid A))) ) ) ) ).
tt(t17_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_midsp_1 A B C D E) & (r1_midsp_1 A B C F G))  => (r1_midsp_1 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v12_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_midsp_2 A B) = (k1_midsp_2 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t17_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v4_midsp_2 E B) & (l1_midsp_2 E B))  =>  ((k7_midsp_3 A B E C (k8_midsp_3 A B E C D)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_relset_1 A A D E) &  ((r1_tarski B C) & (r1_relset_1 A A F G)) )  => (r1_tarski (k7_mmlquery A F B E) (k7_mmlquery A G C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_mod_2 B A) &  ((v3_mod_2 B A) & (l1_mod_2 B A)) )  =>  (! [C:$i] :  ( ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) )  =>  (! [D:$i] :  ( ((v2_mod_2 D A) &  ((v3_mod_2 D A) & (l1_mod_2 D A)) )  =>  ( ( ((k2_mod_2 A D) = (k3_mod_2 A C))  &  ((k2_mod_2 A C) = (k3_mod_2 A B)) )  =>  ((k8_mod_2 A D (k8_mod_2 A C B)) = (k8_mod_2 A (k8_mod_2 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ( (~  (C = D) )  & (v1_lmod_5 (k7_domain_1 (u1_struct_0 B) C D) A B))  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k3_rlvect_1 B (k4_vectsp_1 A B E C) (k4_vectsp_1 A B F D)) = (k4_struct_0 B))  =>  ( (E = (k4_struct_0 A))  &  (F = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v36_algstr_0 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  ((k5_mod_4 (k2_mod_4 A) (k3_mod_4 A B)) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ).
tt(t17_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( ((k8_trees_2 A (k1_modal_1 A)) = k6_numbers)  =>  ( ((k5_card_1 A) = 1)  &  (A = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t17_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k28_modelc_1 (k48_modelc_1 A B D) E F)) <=>  ((r3_modelc_1 A B D C E) | (r3_modelc_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_modelc_2 A (k7_modelc_2 B C)) <=>  ( (A = B)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t17_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) => (r1_xxreal_0 k6_numbers (k18_modelc_3 A B))) ) ) ) ).
tt(t17_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  => (r1_xxreal_0 (k11_nat_3 A C) (k11_nat_3 B C))) )  => (r1_tarski (k1_polynom2 k10_newton (k13_nat_3 A)) (k1_polynom2 k10_newton (k13_nat_3 B)))) ) ) ) ) ).
tt(t17_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) =>  ((k5_struct_0 A) = (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ).
tt(t17_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  ( ((u1_struct_0 (k9_monoid_1 B A)) = (k9_funct_2 A (u1_struct_0 B)))  & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k9_monoid_1 B A)) (u1_struct_0 (k9_monoid_1 B A))) (u1_struct_0 (k9_monoid_1 B A)) (k2_zfmisc_1 (k9_funct_2 A (u1_struct_0 B)) (k9_funct_2 A (u1_struct_0 B))) (k9_funct_2 A (u1_struct_0 B)) (u2_algstr_0 (k9_monoid_1 B A)) (k8_monoid_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) (u2_algstr_0 B) A))) ) ) ) ).
tt(t17_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k2_morph_01 A (k5_rusub_4 A C B) D) = (k2_morph_01 A C (k5_rusub_4 A D B)))  &  ((k2_morph_01 A (k5_rusub_4 A C B) D) = (k5_rusub_4 A (k2_morph_01 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden D (k1_funct_1 (k5_msafree3 A B C) E)) =>  ( ((k7_msaterm A B D) = E)  & (r2_pboole (u1_struct_0 A) (k4_msafree3 A B D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v2_msafree (k11_msafree A B) A)) ) ) ) ).
tt(t17_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k1_funct_1 C k1_xboole_0) = (k4_tarski D (u1_struct_0 A)))  =>  ((k7_msaterm A B C) = (k2_msualg_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  ((v1_msscyc_1 B A) =>  ((k1_funct_1 (k7_graph_2 A B) 1) = (k1_funct_1 (k7_graph_2 A B) (k2_nat_1 (k3_finseq_1 B) 1))) ) ) ) ) ) ).
tt(t17_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) )  =>  ( ((r1_pzfmisc1 A B C) & (m2_pboole D A B C))  =>  ((r6_pboole A (k2_funct_6 D) B) & (r2_pboole A (k3_funct_6 D) C)) ) ) ) ) ) ) ) ) ).
tt(t17_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  => (m1_subset_1 (u1_struct_0 (k12_msualg_1 A C)) (k1_zfmisc_1 (u1_struct_0 (k12_msualg_1 A B))))) ) ) ) ) ) ).
tt(t17_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r2_hidden E (k5_msualg_2 A C D)) => (r1_tarski (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_msualg_2 A C D))) B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) E)) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  ((r6_msualg_3 A B C) => (r6_msualg_3 A C B)) ) ) ) ) ) ) ).
tt(t17_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((v2_msualg_4 (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) A B) &  ((v3_msualg_4 (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) A B) & (m1_msualg_4 (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ).
tt(t17_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_msualg_6 A C D B E) =>  ((r1_rewrite1 (k3_msualg_6 A) C D) & (m2_msualg_6 E A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v2_msualg_7 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k15_lattice3 A C) = (k15_lattice3 B C)) ) ) ) ) ) ) ) ).
tt(t17_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B))))) =>  (! [E:$i] :  ( ((v1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B)) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ( (E = (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) D))  =>  ((k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) E C) = (k15_lattice3 (k2_msualg_5 (k1_funct_1 (u3_msualg_1 A B) C)) (k3_msualg_8 (u1_struct_0 A) (u3_msualg_1 A B) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((v2_msualg_3 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A E C)) =>  (? [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A E B)) &  ((k5_msualg_3 A B C E D G) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_unialg_2 A B) =>  ((v1_relat_1 (k2_msuhom_1 A B C)) &  ((v4_relat_1 (k2_msuhom_1 A B C) (k1_tarski k6_numbers)) &  ((v1_funct_1 (k2_msuhom_1 A B C)) & (v1_partfun1 (k2_msuhom_1 A B C) (k1_tarski k6_numbers))) ) ) ) ) ) ) ) ) ) ).
tt(t17_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_necklace A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_necklace A))) =>  (~  ( (B = D)  &  ( (C = E)  &  ((r1_orders_2 A B C) & (r1_orders_2 (k3_necklace A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v3_pre_topc (k8_nat_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) )  => (v3_pre_topc (k1_prob_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t17_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v7_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r2_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (k1_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers C D) E) &  ((r1_nagata_1 (u1_struct_0 A) E) &  ( (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) => (r1_xxreal_0 (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers E F) B)) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers E F) => (v1_pscomp_1 F (k2_borsuk_1 A A))) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (r2_hidden D E))  &  ((v4_pre_topc E A) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r2_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (k1_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers C F) G) & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k3_nagata_2 (u1_struct_0 A) G E) D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  &  ((r1_pcomps_1 (u1_struct_0 A) D) &  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers D E) = (k4_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k1_prepower (k10_real_1 1 2)) (k10_seqfunc (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) C E)))) ) ) ) ) )  & (v3_pcomps_1 A)) ) ) ) ) ) ) ) ) ).
tt(t17_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ((v7_ordinal1 D) &  ( (B = (k2_xcmplx_0 (k3_xcmplx_0 A C) D))  &  (~ (r1_xxreal_0 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k4_nat_d (k3_power 2 A) 2) = k6_numbers) ) ) ) ).
tt(t17_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r1_tarski (k13_pre_poly (k5_nat_3 A B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ).
tt(t17_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((v1_int_2 B) & (r1_nat_d D (k4_nat_1 A (k13_newton B (k2_nat_1 C 1)))))  =>  ((r1_nat_d D (k4_nat_1 A (k13_newton B C))) | (r1_nat_d (k13_newton B (k2_nat_1 C 1)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ((r1_int_2 B C) =>  ((k6_nat_d A (k24_binop_2 B C)) = (k24_binop_2 (k6_nat_d A B) (k6_nat_d A C))) ) ) ) ) ) ) ) ).
tt(t17_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d A B) = k6_numbers)  =>  ((k4_nat_d (k2_xcmplx_0 A C) B) = (k4_nat_d C B)) ) ) ) ) ) ) ) ).
tt(t17_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k2_cat_1 A B C) (k2_cat_1 A D E)))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_ncfcont1 E B (k7_partfun1 (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_ncfcont1 F A D) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r2_ncfcont2 A B C D) => (r5_ncfcont2 A C (k3_normsp_0 (u1_struct_0 C) B D))) ) ) ) ) ) ) ) ).
tt(t17_ndiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v12_struct_0 C k5_numbers B) => (v12_struct_0 (k1_valued_0 (u1_struct_0 B) C A) k5_numbers B)) ) ) ) ) ) ) ).
tt(t17_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k6_vfunct_1 k1_numbers A C D))) &  ((r2_ndiff_3 A C B) & (r2_ndiff_3 A D B)) )  =>  ((r2_ndiff_3 A (k6_vfunct_1 k1_numbers A C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_funct_1 (k2_ndiff_3 A (k6_vfunct_1 k1_numbers A C D) B) E) = (k3_rlvect_1 A (k1_ndiff_3 A C E) (k1_ndiff_3 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) & (v3_funct_1 (k2_partfun1 k1_numbers (k1_euclid A) C B)))  =>  ((r2_ndiff_4 A C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_funct_1 (k2_ndiff_4 A C B) D) = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((v1_partfun1 B k1_numbers) =>  ((v1_ndiff_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (E = k6_numbers) )  &  ( (~ (r1_xxreal_0 D (k18_complex1 E)))  & (r1_xxreal_0 C (k12_binop_2 (k1_normsp_0 A (k7_partfun1 (u1_struct_0 A) B E)) (k18_complex1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r1_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) =>  ((k3_necklace (k1_neckla_2 A B)) = (k2_neckla_2 (k3_necklace A) (k3_necklace B))) ) ) ) ) ) ).
tt(t17_necklace,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r5_waybel_1 A B) =>  ((k1_card_1 (u1_orders_2 A)) = (k1_card_1 (u1_orders_2 B))) ) ) ) ) ) ).
tt(t17_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  => (r1_tarski (k5_net_1 A B) (k2_net_1 A))) ) ) ) ) ).
tt(t17_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k3_newton A) k6_numbers)) ) ) ).
tt(t17_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_nfcont_1 B A C D) =>  ((r2_nfcont_1 B (k3_normsp_0 (u1_struct_0 B) A C) D) & (r1_nfcont_1 B A (k5_vfunct_1 (u1_struct_0 B) A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ((r1_tarski A (k1_relset_1 k1_numbers C)) =>  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) C A) B) <=>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 F (k18_complex1 (k6_xcmplx_0 G D))))  & (r1_xxreal_0 E (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C G) (k7_partfun1 (u1_struct_0 B) C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r2_hidden B (k1_relset_1 k1_numbers C)) & (r1_nfcont_4 A C B))  => (r1_fcont_1 (k1_nfcont_4 A k1_numbers C) B)) ) ) ) ) ) ) ).
tt(t17_normform,ax, (! [A:$i] : (r3_binop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k1_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) (k1_setwiseo A) (k1_setwiseo A)) (k5_normform A))) ).
tt(t17_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B (k2_nat_1 C D))) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_normsp_2 A))) =>  ( ( (B = C)  &  (D = E) )  =>  ((m1_nfcont_1 B A D) <=> (m1_connsp_2 C (k3_normsp_2 A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_numbers,ax,(r1_tarski k5_numbers k4_numbers)).
tt(t17_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_openlatt A B) (k10_openlatt A C))) =>  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r2_hidden B D) &  (~ (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_oposet_1,ax,(v12_oposet_1 k1_oposet_1)).
tt(t17_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B)) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A D) (k3_oppcat_1 A C)) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((k5_oppcat_1 A (k1_cat_1 A E F)) = (k1_cat_1 (k2_oppcat_1 A) (k7_oppcat_1 A C D F) (k7_oppcat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_orders_1 A) => (v2_orders_1 (k2_relat_1 A))) ) ) ).
tt(t17_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((k2_orders_2 A (k2_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t17_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v3_ordinal1 (k1_ordinal1 A))) ) ).
tt(t17_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden A B) => (r2_hidden (k2_ordinal2 B) B)) ) ) ) ).
tt(t17_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden C D) =>  ( ( (~ (r1_ordinal1 A B))  &  (~ (r2_hidden A B)) )  | (r2_hidden (k10_ordinal2 A C) (k10_ordinal2 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ((v2_ordinal2 A) &  ((v3_ordinal2 A) &  ((v3_ordinal2 B) &  (C = (k3_relat_1 A B)) ) ) )  => (v3_ordinal2 C)) ) ) ) ) ) ) ).
tt(t17_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal5 1 A) = 1) ) ) ).
tt(t17_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal6 A) = A) ) ) ).
tt(t17_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t17_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_orders_2 B E C) & (r1_orders_2 B E F))  =>  ((r1_orders_2 B C D) |  ((k1_ortsp_1 A B (k3_rlvect_1 B D E) C F) = (k1_ortsp_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_msualg_1 A C (k8_osafree A B))) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ( (E = (k3_funct_2 (k3_msualg_1 A C (k8_osafree A B)) (k4_msualg_1 A C (k8_osafree A B)) (k5_msualg_1 A C (k8_osafree A B)) D))  =>  ((k10_osafree A B E) = (k2_msualg_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v12_osalg_1 B A) <=>  ((v1_relat_1 (u3_msualg_1 A B)) &  ((v4_relat_1 (u3_msualg_1 A B) (u1_struct_0 A)) &  ((v1_funct_1 (u3_msualg_1 A B)) &  ((v1_partfun1 (u3_msualg_1 A B) (u1_struct_0 A)) & (v11_osalg_1 (u3_msualg_1 A B) A)) ) ) ) ) ) ) ) ) ).
tt(t17_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r2_hidden (u3_msualg_1 A B) (k5_osalg_2 A B C))) ) ) ) ) ) ).
tt(t17_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  ((v13_osalg_1 B A) <=> (v13_osalg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A)) ) ) ) ) ).
tt(t17_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r1_msualg_3 A B C D) & (v1_osalg_3 D A))  =>  ((r3_msualg_3 A (k16_osalg_4 A B (k19_osalg_4 A B C D)) C (k21_osalg_4 A B C D)) & (v1_osalg_3 (k21_osalg_4 A B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t17_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  => (v11_aff_2 (k2_diraf B))) ) ) ) ) ).
tt(t17_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) &  ((r1_parsp_1 (k9_parsp_1 A) B C D E) & (r1_parsp_1 (k9_parsp_1 A) B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_2 A B C D))  &  ((r1_parsp_1 A B C D E) &  ( (~  (D = E) )  &  ((r1_parsp_2 A B C F) & (r1_parsp_2 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B))))  => (v2_funct_1 C)) ) ) ) ).
tt(t17_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( ((r2_hidden D (k1_relset_1 B E)) & (r2_hidden D A))  =>  ((k7_partfun1 C (k2_partfun1 B C E A) D) = (k7_partfun1 C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ((k3_partit1 A B B) = B) ) ) ) ) ).
tt(t17_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k6_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r3_diraf A B C D))  &  ((r2_analoaf A B D B E) &  ((r2_analoaf A D C E F) &  ( (~  (B = F) )  & (r1_diraf A C B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A B D))  => (r2_pboole A B (k3_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t17_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_setfam_1 B (k1_pcomps_1 A B))) ) ) ) ).
tt(t17_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k18_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k18_pcs_0 A B))) =>  ((r1_pcs_0 (k18_pcs_0 A B) C D) <=>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (E = C)  &  ( (F = D)  & (r1_pcs_0 A E F)) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (E = C)  &  ( (F = D)  & (r1_pcs_0 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 C))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid C)))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid B)) =>  ( ( (D = E)  &  ( (F = G)  & (r2_pdiff_1 C B A D F)) )  =>  ((k1_funct_1 (k9_pdiff_1 B C A D F) (k12_finseq_1 k5_numbers 1)) = (k12_pdiff_1 B C A E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 2) B)) =>  ( ((r3_pdiff_1 2 1 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 A B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 A B))))) &  ((k11_pdiff_1 2 1 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 2) B)) =>  ( ((r1_pdiff_3 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B))))) &  ((k2_pdiff_3 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 2 F E))  =>  ( (D = (k11_pdiff_1 3 2 F E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J H) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 2 F E) M) (k1_seq_1 (k1_pdiff_2 3 2 F E) H)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M H)) (k1_seq_1 L (k9_real_1 M H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r8_pdiff_5 E D))  =>  ((k8_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 E) D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ( (E = (k1_funct_1 B D))  &  ((k1_seq_1 C D) = (k12_euclid E)) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k5_euclid_7 A B)) (k18_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t17_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ( (~  (B = k6_numbers) )  &  ((k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A C (k5_euclid A)) B) = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  => (r1_xxreal_0 (k17_complex1 (k1_seq_1 (k1_pdiff_1 D B) C)) A)) ) )  => (r1_xxreal_0 (k12_euclid C) (k11_binop_2 B A))) ) ) ) ) ) ) ).
tt(t17_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_pdiff_6 C B A D) =>  ((r1_pdiff_6 C B A (k9_integr15 B E (k1_euclid A) D)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) (k1_euclid B)) (k1_pdiff_9 A B C (k9_integr15 B E (k1_euclid A) D)) F) = (k9_integr15 B E (k1_euclid A) (k8_pdiff_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v5_pencil_1 (k1_pencil_1 A B C)) &  (~  (! [D:$i] :  ((m1_subset_1 D A) => (v3_pencil_1 (k1_pencil_1 A B D))) ) ) ) ) )  => (v5_pencil_1 (k5_pencil_1 A B))) ) ) ) ) ).
tt(t17_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_pencil_1 C A) => (v2_pencil_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t17_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_pencil_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_pencil_1 A B))) =>  ( (~  (C = D) )  =>  ((r1_pencil_1 (k5_pencil_1 A B) C D) <=>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  (~  ( (E = C)  &  ( (F = D)  &  (! [G:$i] :  ((m1_subset_1 G A) =>  (~  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_pencil_1 A B G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_pencil_1 A B G))) =>  ( ( (H = (k1_funct_1 E G))  &  (I = (k1_funct_1 F G)) )  =>  ( (~  (H = I) )  & (r1_pencil_1 (k2_pencil_1 A B G) H I)) ) ) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H A) =>  ( (~  (H = G) )  =>  ((k1_funct_1 E H) = (k1_funct_1 F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k1_vectsp_9 A B) C))  & (v3_pencil_1 (k5_pencil_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t17_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ((v1_int_2 A) & (v1_abian A)) ) ) ) ) ).
tt(t17_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_petri B A) <=> (v6_petri (k12_petri A B) (k11_petri A))) ) ) ) ) ).
tt(t17_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A C D))  => (r2_pnproc_1 A (k3_pnproc_1 A D C) (k3_pnproc_1 A D B))) ) ) ) ) ) ) ) ).
tt(t17_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_polyalg1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( (E = F)  =>  ((k4_vectsp_1 A B D E) = (k4_vectsp_1 A C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k7_real_1 (k7_real_1 (k3_real_1 (k1_newton A 3) (k8_real_1 k6_numbers (k3_square_1 A))) (k8_real_1 (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 B) C) (k3_square_1 D)) (k8_real_1 3 (k3_square_1 B))) A)) (k7_real_1 (k8_real_1 2 (k2_newton (k6_real_1 D (k8_real_1 3 B)) 3)) (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 B) E) (k3_xcmplx_0 D C)) (k8_real_1 3 (k3_square_1 B))))) = k6_numbers)  =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( (F = (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 B) C) (k3_square_1 D)) (k8_real_1 3 (k3_square_1 B))))  &  (G = (k7_real_1 (k8_real_1 2 (k2_newton (k6_real_1 D (k8_real_1 3 B)) 3)) (k10_real_1 (k9_real_1 (k8_real_1 (k8_real_1 3 B) E) (k3_xcmplx_0 D C)) (k8_real_1 3 (k3_square_1 B))))) )  =>  ((k7_polyeq_1 1 k6_numbers F G A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  ( (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  ((k3_polyeq_1 A B C G) = (k3_polyeq_1 D E F G)) ) )  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k2_newton A E) (k2_newton B E)) = C)  &  ( ((k6_xcmplx_0 (k2_newton A E) (k2_newton B E)) = D)  &  ((v1_abian E) &  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k2_xcmplx_0 C D) k6_numbers))  &  ( (~ (r1_xxreal_0 (k6_xcmplx_0 C D) k6_numbers))  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C D) 2)))  &  (B = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C D) 2))) ) )  &  ( (~  ( (A = (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C D) 2)))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C D) 2)))) ) )  &  ( (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C D) 2))))  &  (B = (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C D) 2))) ) )  &  (~  ( (A = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k2_xcmplx_0 C D) 2))))  &  (B = (k4_xcmplx_0 (k1_power E (k7_xcmplx_0 (k6_xcmplx_0 C D) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_polyeq_5 A B C) (k3_polyeq_5 A B C)) (k4_polyeq_5 A B C)) = (k4_xcmplx_0 C)) ) ) ) ) ) ) ).
tt(t17_polyform,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k1_funct_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) B) C) 1) = A) ) ) ) ) ) ).
tt(t17_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((k3_polynom1 A B (k5_vfunct_1 (k15_pre_poly A) B C) D) = (k4_algstr_0 B (k3_polynom1 A B C D))) ) ) ) ) ) ) ) ).
tt(t17_polynom2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly B) (u1_struct_0 A)) &  ((v1_polynom1 C (k15_pre_poly B) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 A))))) ) )  =>  ( ((k2_polynom1 (k15_pre_poly B) A C) = k1_xboole_0)  => (r2_funct_2 (k15_pre_poly B) (u1_struct_0 A) C (k7_polynom1 B A))) ) ) ) ) ) ) ).
tt(t17_polynom3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ( (A = B)  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k17_finseq_1 k1_numbers C A) = (k17_finseq_1 k5_numbers C B)) ) ) ) ) ) ) ) ).
tt(t17_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_polynom4 A (k9_polynom3 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t17_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A B 2) (k13_polynom3 A B B))) ) ) ) ).
tt(t17_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) C (k4_polynom7 A B D))) ) ) ) ) ) ) ) ).
tt(t17_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_polynom8 A B (k2_nat_1 C 1)) = (k8_group_1 A (k3_polynom8 A B C) B))  &  ((k3_polynom8 A B (k2_nat_1 C 1)) = (k8_group_1 A B (k3_polynom8 A B C))) ) ) ) ) ) ) ) ).
tt(t17_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k1_polyred A (k16_pre_poly A) C D) D)) ) ) ) ) ) ) ) ).
tt(t17_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~  ( (~  ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 C)) )  & (v1_abian C)) )  & (r1_xxreal_0 (k1_power C B) (k1_power C A))) ) ) ) ) ) ) ) ) ).
tt(t17_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  ( (~  ((k1_msualg_1 B D) = k1_xboole_0) )  => (r2_hidden (k10_funct_6 E) (k4_card_3 (k2_funct_6 (k12_pralg_2 A B C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pre_circ,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C A) =>  ((k2_nat_1 (k5_card_1 (k5_trees_1 A C B)) (k5_card_1 (k4_trees_1 A C))) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ) ).
tt(t17_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k2_nat_1 (k4_nat_1 2 A) 1) A)) ) ) ).
tt(t17_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) C) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A D C)) (k2_prelamb A D B)) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k1_prelamb A C D)) (k1_prelamb A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k4_partfun1 A B))) ) ) ).
tt(t17_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (r1_xxreal_0 (k2_newton (k7_real_1 1 A) B) (k7_real_1 1 (k8_real_1 (k2_newton 3 B) A)))) ) ) ) ) ) ) ) ).
tt(t17_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k2_pre_topc B D) = (k9_subset_1 (u1_struct_0 B) (k2_pre_topc A C) (k2_struct_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(t17_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (r2_hidden (k1_prob_1 A C) B)) ) ) ) ) ).
tt(t17_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ( (~  ( (~ (r1_xxreal_0 1 (k1_seq_1 D C)))  & (r1_xxreal_0 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)) k6_numbers))  & (r1_xxreal_0 1 (k1_seq_1 D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k1_funct_1 (k3_prob_3 B C) A) (k1_funct_1 C A))) ) ) ) ) ).
tt(t17_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_prob_4 A (k9_setfam_1 A) B (k2_nat_1 C 1)) = (k1_measure1 A (k9_setfam_1 A) (k1_prob_4 A (k9_setfam_1 A) (k3_prob_3 A B) (k2_nat_1 C 1)) (k1_prob_4 A (k9_setfam_1 A) B C))) ) ) ) ) ) ) ).
tt(t17_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A B C)) (k9_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t17_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A D B C) &  ((r1_collsp A B E I) &  ((r1_collsp A C G I) &  ((r1_collsp A E F J) &  ((r1_collsp A G H J) &  ((r1_collsp A B F K) & (r1_collsp A C H K)) ) ) ) ) )  =>  ( (B = C)  |  ((r1_projdes1 A B E F D) |  ((r1_collsp A C G H) | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (~  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) => (r4_projpl_1 A B C D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) => (r1_incsp_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t17_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v8_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  ((r1_incsp_1 A C B) &  ((r1_incsp_1 A D B) &  ((r1_incsp_1 A E B) &  ((r1_incsp_1 A F B) & (r2_zfmisc_1 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) K) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E F G) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D G H) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C G) O) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D I) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B E H) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C H I) Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E I J) R) & (r1_incsp_1 A J O)) ) ) ) ) ) ) )  =>  ((r1_incsp_1 A B K) |  ((r1_incsp_1 A B L) |  ((r1_incsp_1 A C M) |  ((r1_incsp_1 A C L) |  ((r1_incsp_1 A C N) |  ((r1_projred2 A K M L) |  ( (B = C)  |  ( (K = N)  |  ( (~ (r1_incsp_1 A J K))  &  ( (~ (r1_incsp_1 A J N))  &  (~  (C = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  ( (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) => (v1_binop_1 (k9_prvect_1 A B C) (k1_funct_1 A C))) )  => (v1_binop_1 (k13_prvect_1 A B) (k4_card_3 A))) ) ) ) ) ).
tt(t17_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_prvect_2 B)) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 B))) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( (D = F)  &  ( (E = G)  &  ((k1_binop_1 C D E) = (k7_finseq_1 F G)) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)))) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k3_rlvect_1 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)) D E)) = (k3_rlvect_1 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k1_rlvect_1 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)) D E)) = (k1_rlvect_1 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D) E)) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k4_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)))) = (k4_struct_0 (k14_prvect_2 (k7_finseq_1 A B))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)))) =>  ((k1_normsp_0 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D)) = (k1_normsp_0 (k7_prvect_3 (k14_prvect_2 A) (k14_prvect_2 B)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_compts_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  ((r1_tarski B C) => (r1_xxreal_0 (k2_pscomp_1 (k1_pre_topc A B) (k3_pscomp_1 A D B)) (k2_pscomp_1 (k1_pre_topc A C) (k3_pscomp_1 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t17_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) => (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k8_pua2mss1 A C (k2_nat_1 B 1)) (k7_pua2mss1 A (k8_pua2mss1 A C B)))) ) ) ) ) ) ).
tt(t17_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pzfmisc1 A B)) | (r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pzfmisc1 A C)))  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t17_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ( (~  ((k1_xtuple_0 C) = k6_numbers) )  &  ( (~  ((k1_xtuple_0 C) = 1) )  &  ( (~  ((k1_xtuple_0 C) = 2) )  &  (~  ((k1_xtuple_0 C) = 3) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k7_qc_lang2 A D F B) = (k7_qc_lang2 A E G C))  =>  ( (D = E)  &  ( (F = G)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang2 B A) =>  ((k24_qc_lang1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A (k13_qc_lang2 A B)) (k24_qc_lang1 A (k14_qc_lang2 A B)))) ) ) ) ) ) ).
tt(t17_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) = B)  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t17_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v18_quantal1 B A) =>  ( ((k1_quantal1 A C B) = (k1_quantal1 A (k1_quantal1 A (k1_quantal1 A C B) B) B))  &  ((k2_quantal1 A C B) = (k2_quantal1 A (k2_quantal1 A (k2_quantal1 A C B) B) B)) ) ) ) ) ) ) ) ) ).
tt(t17_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni A (k26_quaterni B C)) = (k26_quaterni (k27_quaterni A B) (k27_quaterni A C))) ) ) ) ) ) ) ).
tt(t17_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k5_square_1 (k3_quatern2 (k27_quaterni A B))) = (k8_real_1 (k5_square_1 (k3_quatern2 A)) (k5_square_1 (k3_quatern2 B)))) ) ) ) ) ).
tt(t17_quaterni,ax, ((k10_quaterni k11_quaterni k12_quaterni) = k1_xcmplx_0) ).
tt(t17_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) ) ) ) ) ) ) ) ) ).
tt(t17_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k8_quofield A B (k13_quofield A B)) = (k11_quofield A))  &  ((k8_quofield A (k13_quofield A B) B) = (k11_quofield A)) ) ) ) ) ) ).
tt(t17_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m2_finseq_1 B k4_numbers))  =>  ( ((k7_partfun1 k4_numbers B 1) = A)  =>  (B = (k9_finseq_1 A)) ) ) ) ) ) ).
tt(t17_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_radix_1 A E C) =>  ((r1_xxreal_0 D k6_numbers) |  (! [F:$i] :  ( ((v3_card_1 F A) & (m2_finseq_1 F k5_numbers))  =>  ( (F = (k5_radix_2 C A E))  =>  ((k1_recdef_1 (k9_radix_2 C D B A F) A) = (k4_nat_d (k1_newton B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D (k3_radix_1 A)))  =>  ( ((r1_xxreal_0 2 A) & (r2_hidden B (k2_finseq_1 (k2_xcmplx_0 C 1))))  => (m2_subset_1 (k8_radix_3 B A C D) k4_numbers (k4_radix_3 A))) ) ) ) ) ) ) ) ) ).
tt(t17_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 C) =>  ((k2_xcmplx_0 (k8_radix_1 A C (k4_radix_5 A B C)) (k8_radix_1 A C (k2_radix_5 A B C))) = (k8_radix_1 A C (k10_radix_1 C A k6_numbers))) ) ) ) ) ) ) ) ) ).
tt(t17_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  ((r1_xxreal_0 2 B) =>  ((k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B (k8_radix_6 A B C))) = (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 2) B C) (k8_radix_1 (k2_xcmplx_0 A 2) B (k10_radix_1 B (k2_xcmplx_0 A 2) k6_numbers)))) ) ) ) ) ) ) ) ).
tt(t17_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((m1_eqrel_1 D (k3_group_10 C 2)) =>  (~  ((r1_xxreal_0 B (k5_card_1 C)) &  ( ((k5_card_1 D) = 2)  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 C)) =>  (~  ((r1_xxreal_0 A (k5_card_1 E)) & (r1_ramsey_1 C 2 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ((v3_prob_1 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ((v7_ordinal1 D) &  ((r1_xxreal_0 C D) &  (~  ((k1_prob_1 A B) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_random_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m2_prob_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_prob_1 D B (k1_random_1 B)) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E A) & (r2_hidden F B))  =>  ((k1_seq_1 (k2_random_2 A B C D) (k1_tarski (k4_tarski E F))) = (k11_binop_2 (k1_seq_1 C (k1_tarski E)) (k1_seq_1 D (k1_tarski F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D E) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D F))  => (r1_struct_0 (k1_ranknull A C B D) (k5_algstr_0 C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((v1_int_1 A) =>  ( ((k1_rat_1 A) = 1)  &  ((k2_rat_1 A) = A) ) ) ) ) ).
tt(t17_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((r1_hurwitz A C B) & (v1_polynom5 B A))  => (r2_ratfunc1 A B C)) ) ) ) ) ) ) ).
tt(t17_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_rcomp_1 B A) =>  (! [C:$i] :  ((m1_rcomp_1 C A) =>  (? [D:$i] :  ((m1_rcomp_1 D A) &  ((r1_tarski D B) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ).
tt(t17_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((r2_hidden (k5_seq_4 A) A) =>  ((r2_hidden (k4_seq_4 A) A) |  (A = (k3_rcomp_1 (k5_seq_4 A) (k4_seq_4 A))) ) ) ) ) ).
tt(t17_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 A B) &  ((k1_seq_1 (k2_real_3 C D) A) = k6_numbers) )  =>  ( (A = k6_numbers)  |  ((k1_seq_1 (k2_real_3 C D) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) B (k1_funcsdom A k1_numbers (k4_real_lat A) C B)) B)) ) ) ) ) ) ).
tt(t17_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k7_real_ns1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k7_real_ns1 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 (k4_real_ns1 A)) k5_numbers (u1_struct_0 (k7_real_ns1 A)) B C) & (v1_rsspace3 B (k4_real_ns1 A)))  => (v1_bhsp_3 C (k7_real_ns1 A))) ) ) ) ) ) ) ).
tt(t17_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k8_group_1 A (k4_struct_0 A) (k5_struct_0 A)) = (k4_struct_0 A)) ) ) ).
tt(t17_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = D)  <=>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) D C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t17_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  => (r2_classes1 (k3_rearran1 A B D C) (k20_rfunct_3 A C A))) ) ) ) ) ) ) ) ) ).
tt(t17_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((k1_relat_1 (k1_tarski (k4_tarski A B))) = (k2_tarski A B)) ) ) ).
tt(t17_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski (k4_relat_1 B) C) =>  ((r1_tarski B (k1_relset_1 A C)) &  (B = (k2_relset_1 B C)) ) ) ) ) ) ) ).
tt(t17_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k7_relset_1 A B D C) = (k3_tarski (a_4_0_relset_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t17_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_finseq_6 D B) & (m2_finseq_1 D B))  =>  ( ((r2_hidden C (k10_xtuple_0 D)) &  ((r1_xxreal_0 (k3_finseq_1 (k2_finseq_5 B D C)) A) & (r1_xxreal_0 A (k3_finseq_1 D))) )  =>  ((k7_partfun1 B (k1_finseq_6 B D C) A) = (k7_partfun1 B D (k7_nat_d (k2_nat_1 A (k4_finseq_4 D C)) (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_rewrite1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 B)) & (r1_xxreal_0 C D)) )  => (r1_rewrite1 A (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t17_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( ( ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))))  & (r2_rewrite2 A B C D))  => (r2_rewrite2 A B D C)) ) ) ) ) ) ) ) ).
tt(t17_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  ( ( ((v1_relat_1 (u1_rewrite3 F G)) & (v1_funct_1 (u1_rewrite3 F G)))  &  ((r1_rewrite3 F G A B C) & (r1_rewrite3 F G A B D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v1_integra2 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ((r1_xxreal_0 C B) | (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t17_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  =>  ((k18_rvsum_1 (k3_rfinseq (k2_rfinseq k1_numbers B A))) = (k1_seq_1 A (k3_real_1 B 1))) ) ) ) ) ) ).
tt(t17_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 A (k3_xcmplx_0 B C)) = (k24_valued_1 (k24_valued_1 A C) B)) ) ) ) ) ) ) ).
tt(t17_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_funct_1 B)) )  =>  ((k2_funct_1 (k5_relat_1 B A)) = (k5_relat_1 (k2_funct_1 B) (k7_relat_1 B A))) ) ) ) ).
tt(t17_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_binop_1 (k3_rfunct_3 A k1_numbers) (k13_rfunct_3 A)) = (k4_rfunct_3 A k1_numbers (k2_subset_1 A) k6_numbers)) ) ) ).
tt(t17_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r1_rfunct_4 A B) <=>  ((r1_tarski B (k9_xtuple_0 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r2_hidden E B)) )  =>  ((r1_xxreal_0 E C) |  ((r1_xxreal_0 D E) |  ( (~ (r1_xxreal_0 (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A C)) (k10_binop_2 D C)) (k12_binop_2 (k10_binop_2 (k1_seq_1 A E) (k1_seq_1 A C)) (k10_binop_2 E C))))  &  (~ (r1_xxreal_0 (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A E)) (k10_binop_2 D E)) (k12_binop_2 (k10_binop_2 (k1_seq_1 A D) (k1_seq_1 A C)) (k10_binop_2 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v4_partfun3 B) => (v4_partfun3 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t17_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 (k1_valued_0 k7_numbers B A)) =>  ((v10_mesfunc5 B) &  ((k2_mesfunc5 B) = (k2_mesfunc5 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ).
tt(t17_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v1_ring_1 B A) <=> (v1_vectsp_2 (k2_ring_1 A B))) ) ) ) ) ).
tt(t17_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden k18_mod_2 (k9_ringcat1 A))) ) ).
tt(t17_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_rlvect_2 A (k1_rlaffin1 A (k7_rlvect_2 A B C) D) (k7_rlvect_2 A (k1_rlaffin1 A B D) (k1_rlaffin1 A C D)))) ) ) ) ) ) ) ) ).
tt(t17_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 (k5_setfam_1 (u1_struct_0 A) B)) => (r1_tarski (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) (k3_convex1 A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t17_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_rlaffin1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [E:$i] :  ((m2_rlaffin3 E A D) =>  (! [F:$i] :  ((m2_rlaffin3 F A (k5_rusub_4 A D B)) =>  ( ((r2_hidden C (k4_rlaffin1 A D)) &  (F = (k3_fvsum_1 A E (k5_finseq_2 (u1_struct_0 A) (k5_card_1 D) B))) )  =>  ((k1_rlaffin3 A D E C) = (k1_rlaffin3 A (k5_rusub_4 A D B) F (k1_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (r1_struct_0 B (k4_struct_0 A))) ) ) ) ).
tt(t17_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ((m1_rlsub_1 C B) <=>  ((k2_rlsub_2 A C B) = C) ) ) ) ) ) ) ) ).
tt(t17_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_convex1 A B) = B) ) ) ) ) ).
tt(t17_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_algstr_0 A (k4_algstr_0 A B)) = B) ) ) ) ) ).
tt(t17_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k5_subset_1 (u1_struct_0 A) C B)) = (k5_algstr_0 A (k2_rlvect_2 A (k4_subset_1 (u1_struct_0 A) C B)) (k2_rlvect_2 A (k9_subset_1 (u1_struct_0 A) C B)))) ) ) ) ) ) ) ).
tt(t17_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rlvect_3 A B) = (k1_rlsub_1 A))  &  ( (~  (B = k1_xboole_0) )  &  (~  (B = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t17_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) =>  ( (B = C)  | (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B (k5_algstr_0 A C B)) A)) ) ) ) ) ) ) ) ).
tt(t17_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (D = (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C)))  & (r1_struct_0 (k1_rlvect_3 A D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k2_rlvect_x A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t17_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t17_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ( (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ((m1_rmod_2 D A C) =>  ((k2_rmod_3 A B D C) = D) ) ) )  &  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( ((k2_rmod_3 A B D C) = D)  => (m1_rmod_2 D A C)) ) ) ) ) ) ) ) ) ) ).
tt(t17_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ( ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) = (k4_struct_0 A))  <=>  (~ (r2_hidden C (k2_rmod_4 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A B C) = (k3_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)))) ) ) ) ) ) ) ).
tt(t17_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) B)) C)) = (k3_robbins1 A (k1_lattices A C C))) ) ) ) ) ) ) ).
tt(t17_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_lattices B))  =>  ( ((g1_lattices (u1_struct_0 A) (u1_lattices A)) = (g1_lattices (u1_struct_0 B) (u1_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k2_lattices A C D) = (k2_lattices B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  ( ( (A = (k6_subset_1 3 1))  &  (B = 1) )  =>  ( ((k13_lattice3 k1_robbins4 A B) = 3)  &  ((k12_lattice3 k1_robbins4 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t17_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k3_roughs_1 A B))  <=>  (B = (k4_roughs_1 A B)) ) ) ) ) ) ).
tt(t17_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_xxreal_0 (k1_rpr_1 A B) 1)) ) ) ) ).
tt(t17_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k9_rsspace4 A B) C))) ) ) ) ) ) ).
tt(t17_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  &  ((v1_series_1 A) &  ((k4_series_1 A) = k6_numbers) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t17_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_struct_0 B C) & (r1_struct_0 B D))  => (r1_struct_0 B (k5_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t17_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ((m1_rusub_1 C B) <=>  ((k2_rusub_2 A C B) = C) ) ) ) ) ) ) ) ).
tt(t17_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski (k3_rlvect_2 A B) (u1_struct_0 (k1_rusub_3 A C))) &  (! [D:$i] :  ((m2_rlvect_2 D A C) =>  (~  ((k6_rlvect_2 A B) = (k6_rlvect_2 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) =>  ((k1_rusub_4 A) = (k2_nat_1 (k1_rusub_4 B) (k1_rusub_4 C))) ) ) ) ) ) ) ) ).
tt(t17_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) D)) = (k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k1_seq_1 (k30_valued_1 B) A) = (k7_binop_2 (k1_seq_1 B A))) ) ) ) ).
tt(t17_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k5_rvsum_2 (k7_rvsum_2 A B)) = (k3_rvsum_2 (k5_rvsum_2 A) B)) ) ) ) ) ).
tt(t17_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k4_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 k6_numbers)) = (k6_xcmplx_0 B C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ( (~  (E = (k10_ami_3 k6_numbers)) )  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_sf_mastr (k1_scmfsa6a A B)) = (k2_sf_mastr A)) ) ) ) ) ).
tt(t17_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = k6_numbers)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k6_numbers)) ) ) ) ).
tt(t17_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B k3_scm_inst) => (m1_subset_1 (k11_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1) A k1_ami_2) (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2)))) ) ) ) ).
tt(t17_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) => (m1_subset_1 A (u1_compos_1 k1_scmfsa_2))) ) ).
tt(t17_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 (k3_scmfsa6a A B)))) ) ) ) ).
tt(t17_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 B 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa6b C)) ) ) ) ) ) )  =>  ( (~ (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) B))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) B E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C D)) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (~ (r3_scmfsa7b (k17_scmfsa_2 B C) A)) ) ) ) ) ) ) ).
tt(t17_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a A B C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_scmfsa8a A B C) D))  =>  ((r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) D)) (k2_afinsq_1 C)) &  (~  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v7_amistd_1 (k1_scmfsa8b E C D) 3 k1_scmfsa_2) &  ( ( ((k1_funct_1 B E) = k6_numbers)  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3)))))  &  ( (~  ((k1_funct_1 B E) = k6_numbers) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 C 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 D 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r5_scmfsa7b E C A) &  ((r1_tarski E A) &  ((r1_tarski E B) &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C F)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D F)))  &  ( ((k3_extpro_1 3 k1_scmfsa_2 A (k5_extpro_1 3 k1_scmfsa_2 A C F)) = (k3_extpro_1 3 k1_scmfsa_2 B (k5_extpro_1 3 k1_scmfsa_2 B D F)))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C F)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b D B A) &  ((r6_scmfsa7b D B A) &  ((k1_funct_1 B C) = k6_numbers) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B)) 3))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k5_card_1 B) 6) C))  => (r2_hidden C (k2_afinsq_1 (k1_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t17_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k3_scmfsa_2)))  =>  ( ((k3_scmfsa_m C) = (k5_scmfsa_2 A))  =>  ((r2_hidden (k5_scmfsa_2 B) C) | (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ).
tt(t17_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scm_halt C)) ) ) ) ) ) )  =>  ( (~ (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_scmfsa_m A) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k5_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E)) = k6_numbers)  &  ((r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k1_scmfsa_m D) F)) &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E) (k4_scmfsa_2 k6_numbers)) = 1) ) )  =>  ((r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E) (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E))) & (r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) (k2_nat_1 E 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k1_scmfsa_m D) (k2_nat_1 F (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k2_scmfsa_9 C B)) B) (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) E))) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k8_scmpds_2 C A B)) = 5) ) ) ) ) ) ) ).
tt(t17_scmpds_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C k1_scmpds_2)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_finset_1 D) & (v4_extpro_1 D 2 k1_scmpds_2 C)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 F (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_tarski D E) &  ((r1_tarski D F) &  ((r1_tarski C A) & (r1_tarski C B)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  (! [J:$i] :  ((v1_int_1 J) =>  (! [K:$i] :  ((v1_int_1 K) =>  ( ( ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A E G)) = (k9_scmpds_2 I J K))  &  ( (H = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A E G)))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 H K))) )  =>  ( (K = 1)  |  ( (~  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) I) J))))  & (r1_xxreal_0 k6_numbers (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) I) J)))) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 B F G) I) J))))  & (r1_xxreal_0 k6_numbers (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) (k2_scmpds_2 (k1_funct_1 (k5_extpro_1 2 k1_scmpds_2 A E G) I) J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmpds_2)) =>  ((k3_scmpds_4 (k4_scmpds_4 A B) C) = (k2_scmpds_4 A (k4_scmpds_4 B C))) ) ) ) ) ) ) ).
tt(t17_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scmpds_4 D)) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 D) A) & (r1_tarski (k10_compos_1 k1_scmpds_2 D) B))  =>  ( ((k8_extpro_1 2 k1_scmpds_2 A C) = (k8_extpro_1 2 k1_scmpds_2 B C))  &  ((k6_extpro_1 2 k1_scmpds_2 A C) = (k6_extpro_1 2 k1_scmpds_2 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k8_scmpds_2 A B C) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ).
tt(t17_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (~  ((r1_tarski (k10_compos_1 k1_scmpds_2 C) A) &  ((r2_scmpds_6 C B A) & (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 A B) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t17_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k2_scmpds_8 A B C)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ).
tt(t17_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  ((k2_amistd_1 2 k1_scmpds_2 (k4_scmpds_2 A)) = a_0_0_scmpds_9) ) ) ).
tt(t17_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) (k7_scmring2 A C B) D) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) D)))  &  ( ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k7_scmring2 A C B) D) C) = B)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 A))))  =>  ( (~  (E = C) )  =>  ((k2_scmring2 A (k2_extpro_1 2 (k1_scmring2 A) (k7_scmring2 A C B) D) E) = (k2_scmring2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 5)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  (B = (k7_scmring2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scmyciel,ax, (! [A:$i] :  ((v1_scmyciel A) =>  ((k1_scmyciel A) = k1_xboole_0) ) ) ).
tt(t17_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  ( ( ((k1_funct_1 B D) = H)  &  ( ((k1_funct_1 B (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 B E) (k1_funct_1 B F)))  &  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 I) &  ((v5_funct_1 I (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 I (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 I 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J k5_numbers) &  ((v5_relat_1 J (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 J) & (v1_partfun1 J k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 I D) = H)  &  ((k1_funct_1 I (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 I E) (k1_funct_1 I F))) )  =>  ((r1_xxreal_0 (k1_funct_1 I E) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 I F) k6_numbers) |  ( ((k1_funct_1 I E) = (k1_funct_1 I F))  |  ( ((k1_funct_1 (k6_scmpds_4 C I J) D) = H)  &  ((r1_scmpds_6 C I J) &  ((r2_scmpds_6 C I J) &  ( ( (~ (r1_xxreal_0 (k1_funct_1 I E) (k1_funct_1 I F)))  =>  ( ((k1_funct_1 (k6_scmpds_4 C I J) E) = (k6_xcmplx_0 (k1_funct_1 I E) (k1_funct_1 I F)))  &  ((k1_funct_1 (k6_scmpds_4 C I J) F) = (k1_funct_1 I F)) ) )  &  ( ((r1_xxreal_0 (k1_funct_1 I E) (k1_funct_1 I F)) =>  ( ((k1_funct_1 (k6_scmpds_4 C I J) F) = (k6_xcmplx_0 (k1_funct_1 I F) (k1_funct_1 I E)))  &  ((k1_funct_1 (k6_scmpds_4 C I J) E) = (k1_funct_1 I E)) ) )  &  ((k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 H G)) = (k6_xcmplx_0 (k1_funct_1 (k6_scmpds_4 C I J) E) (k1_funct_1 (k6_scmpds_4 C I J) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r1_xxreal_0 (k1_funct_1 B F) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 (k4_scpinvar D G C) B A) E) = (k3_int_2 (k1_funct_1 B E) (k1_funct_1 B F)))  &  ((k1_funct_1 (k6_scmpds_4 (k4_scpinvar D G C) B A) F) = (k3_int_2 (k1_funct_1 B E) (k1_funct_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 6 E) &  ( ((k3_finseq_1 C) = F)  &  ( ((k3_finseq_1 D) = F)  &  ((r1_scpisort C B E) & (r1_scpisort D (k6_scmpds_4 (k1_scpisort F (k2_nat_1 E 1)) B A) E)) ) ) )  =>  ((r2_classes1 C D) & (r3_graph_2 D 1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_analoaf A B D E F) & (r2_analoaf A C D E F))  =>  ((r2_analoaf A B C B D) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers A) (k26_valued_1 k5_numbers k1_numbers A (k1_real_1 1)))) ) ).
tt(t17_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) )  => (r1_xxreal_0 k6_numbers (k2_seq_2 A))) ) ) ).
tt(t17_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((m2_valued_0 A k1_numbers B) & (v2_comseq_2 B))  =>  ((k2_seq_2 A) = (k2_seq_2 B)) ) ) ) ) ) ).
tt(t17_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k5_seqfunc A (k9_seqfunc A C B)) (k9_seqfunc A (k5_seqfunc A C) (k5_seqfunc A B)))) ) ) ) ) ) ).
tt(t17_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers B C) A) = (k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers B A) (k1_valued_0 k1_numbers C A))) ) ) ) ) ) ) ).
tt(t17_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A B))) )  =>  ((v1_seq_2 (k3_series_1 A)) <=> (v1_series_1 A)) ) ) ) ).
tt(t17_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 4)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 (k4_nat_1 2 B) 1)) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton B 2)) (k4_nat_1 3 B)) 1)) 30)) ) ) ) ) ) ).
tt(t17_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 B C)) (k3_xcmplx_0 A C)) (k13_complex1 1 3))) ) ) ) ) ) ) ).
tt(t17_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 B (k13_newton 2 B))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 B (k13_newton 2 (k2_nat_1 B 1))) (k13_newton 2 (k2_nat_1 B 1))) 2)) ) ) ) ) ) ).
tt(t17_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 A B) C))  &  ( (~ (r1_xxreal_0 (k2_xcmplx_0 B C) A))  &  ( (~ (r1_xxreal_0 (k2_xcmplx_0 A C) B))  &  (~ (r1_xxreal_0 (k13_complex1 9 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) (k8_complex1 (k8_complex1 (k13_complex1 1 (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) (k13_complex1 1 (k6_xcmplx_0 (k2_xcmplx_0 B C) A))) (k13_complex1 1 (k6_xcmplx_0 (k2_xcmplx_0 C A) B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_setfam_1 A B) & (r1_setfam_1 B C))  => (r1_setfam_1 A C)) ) ) ) ).
tt(t17_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A B) k6_numbers) = (k3_prob_1 A B)) ) ) ) ).
tt(t17_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k6_setlim_2 B D C) A) = (k6_setlim_2 B (k10_nat_1 (k9_setfam_1 B) D A) C)) ) ) ) ) ) ) ) ).
tt(t17_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v1_binop_1 C A) & (v2_binop_1 C A))  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((k7_setwiseo B A C (k2_setwiseo B E) D) = (k3_funct_2 B A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 D B) &  ((v2_binop_1 D B) &  ((v1_setwiseo D B) &  ( ((k3_funct_2 B B E (k4_binop_1 B D)) = (k4_binop_1 B D))  & (r7_binop_1 B E D)) ) ) )  =>  ((k3_funct_2 B B E (k7_setwiseo A B D C F)) = (k7_setwiseo A B D C (k1_partfun1 A B B B F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ((r1_sfmastr2 B A C D) =>  ( ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C))  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k1_funct_1 A C)) =>  ((k2_xcmplx_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) E) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) &  ((v1_afinsq_1 F) & (v7_amistd_1 F 3 k1_scmfsa_2)) ) ) ) ) ) )  => (r1_sfmastr3 E B C D F A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ( ( (D = (k14_scmfsa_2 A B C))  |  (D = (k15_scmfsa_2 A B C)) )  =>  ((k1_sf_mastr D) = (k5_scmfsa_m B A)) ) ) ) ) ) ) ) ) ) ).
tt(t17_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k3_sgraph1 A)) <=>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  &  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_sgraph1 C))))  &  (B = (g1_sgraph1 C D)) ) ) ) ) ) ) ) ).
tt(t17_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) &  ((v7_robbins1 A) &  ((v3_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) )  => (v7_lattices A)) ) ).
tt(t17_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A D C))) = (k5_sheffer1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t17_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (r1_tarski B (k4_simplex0 A))) ) ) ) ) ).
tt(t17_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) =>  ((k5_simplex1 1 A B) = (k4_simplex1 A B)) ) ) ) ) ) ).
tt(t17_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v4_matroid0 C) &  ((v2_simplex2 C A) & (m1_simplex0 C (u1_struct_0 (k15_euclid A)))) ) ) ) )  =>  ((r1_tarski (k3_simplex1 (k15_euclid A) C) (k2_struct_0 C)) => (r1_xxreal_0 (k3_simplex2 A (k5_simplex1 B (k15_euclid A) C)) (k4_real_1 (k1_newton (k13_complex1 (k6_simplex0 C) (k3_real_1 (k6_simplex0 C) 1)) B) (k3_simplex2 A C)))) ) ) ) ) ) ) ).
tt(t17_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t17_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_seq_1 k7_sin_cos2 A) = (k10_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k4_sin_cos2 A))) ) ) ).
tt(t17_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 k7_complex1 A)) = (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A))) ) ) ).
tt(t17_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k20_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k20_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2))))) ) ) ) ) ).
tt(t17_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k21_sin_cos (k8_real_1 3 A)) = (k9_real_1 (k8_real_1 4 (k1_newton (k20_sin_cos A) 3)) (k8_real_1 3 (k20_sin_cos A)))) ) ) ).
tt(t17_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A) & (r1_xxreal_0 A (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  => (r1_xxreal_0 (k17_sin_cos A) k6_numbers)) ) ) ) ) ).
tt(t17_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k12_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) 1)) ) ) ) ) ).
tt(t17_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k2_xcmplx_0 A B) = k6_numbers) )  =>  ((k7_xcmplx_0 (k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B)) (k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)))) ) ) ) ) ) ).
tt(t17_sin_cos9,ax, ( ((k1_seq_1 k29_sin_cos (k1_real_1 (k10_real_1 k32_sin_cos 4))) = (k1_real_1 1))  &  ((k1_sin_cos4 (k1_real_1 (k10_real_1 k32_sin_cos 4))) = (k1_real_1 1)) ) ).
tt(t17_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (r1_xxreal_0 1 (k4_series_1 (k4_sin_cos (k17_complex1 A))))) ) ).
tt(t17_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)) &  ((k18_euclid A) = (k18_euclid D)) ) )  =>  ( ((k17_euclid A) = (k17_euclid D))  | (v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden B (k2_topreal1 2 A C)) => (r2_hidden B (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t17_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k11_pscomp_1 A) = (k12_pscomp_1 A))  => (v2_sppol_1 A)) ) ) ).
tt(t17_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)) &  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  (~  ( ((k17_euclid A) = (k17_euclid B))  &  ((k17_euclid C) = (k17_euclid B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) & (r2_hidden C (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B 1 A))))  =>  ((r1_xxreal_0 A 1) | (r1_jordan5c (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) C (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ) ) ).
tt(t17_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t17_square_1,ax, ((k7_square_1 k6_numbers) = k6_numbers) ).
tt(t17_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_stacks_1 A B C) =>  ((r1_stacks_1 A B) | (r2_stacks_1 A (k5_stacks_1 A B) (k5_stacks_1 A C))) ) ) ) ) ) ) ) ).
tt(t17_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) => (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t17_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ( (~ (r1_sublemma A E B (k1_sublemma A B D (k3_sublemma A E B D)) C))  <=> (r1_sublemma A (k5_sublemma A E) B (k1_sublemma A B D (k3_sublemma A E B D)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski (k3_subset_1 A B) C) => (r1_tarski (k3_subset_1 A C) B)) ) ) ) ) ) ).
tt(t17_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) => (r1_tarski (k3_substlat A B (k4_substlat A B C D)) (k4_substlat A B (k3_substlat A B C) D))) ) ) ) ) ) ).
tt(t17_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k16_substut1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k16_substut1 A)) =>  ( ( ((k19_substut1 A B) = (k19_substut1 A C))  &  ( ((k19_substut1 A D) = (k19_substut1 A E))  &  ((k21_substut1 A B C) = (k21_substut1 A D E)) ) )  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k6_cqc_lang A (k4_substut2 A B C D)) = (k6_cqc_lang A (k4_substut2 A B C D)))  &  ( ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k4_substut2 A B C D)))  =>  ((k7_cqc_sim1 A (k6_cqc_lang A B)) = (k7_cqc_sim1 A (k6_cqc_lang A (k4_substut2 A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (r1_xxreal_0 (k10_supinf_2 k7_numbers A (k5_supinf_2 B C) (k13_supinf_2 A B C D E)) (k3_supinf_2 (k10_supinf_2 k7_numbers A B D) (k10_supinf_2 k7_numbers A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (F = (k4_struct_0 A)) )  &  (~  ((k1_symsp_1 A B D (k4_vectsp_1 A B F C) E) = (k8_group_1 A (k11_algstr_0 A F) (k1_symsp_1 A B D C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r1_tarski A (k4_relat_1 (k9_xtuple_0 A))) =>  (A = (k4_relat_1 (k9_xtuple_0 A))) ) ) ) ).
tt(t17_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((v4_metric_1 B A) => (r3_relat_2 (k1_taxonom1 A B C) A)) ) ) ) ) ) ) ).
tt(t17_taxonom2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v5_taxonom2 B A) & (m1_taxonom2 B A)) )  =>  ((v6_taxonom2 B A) =>  ((r2_hidden k1_xboole_0 B) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (~  ((r2_hidden C D) & (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_taylor_1,ax, ((r2_fdiff_1 (k2_partfun2 k1_numbers k1_numbers k24_sin_cos) (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers k24_sin_cos))) &  (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers k24_sin_cos))) =>  ((k1_fdiff_1 (k2_partfun2 k1_numbers k1_numbers k24_sin_cos) A) = (k10_real_1 1 A)) ) ) ) ) ).
tt(t17_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((k2_fdiff_1 k16_sin_cos A) = (k2_partfun1 k1_numbers k1_numbers k19_sin_cos A))  &  ( ((k2_fdiff_1 k19_sin_cos A) = (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) A))  &  ( ((k9_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos A)) = A)  &  ((k9_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos A)) = A) ) ) ) ) ) ).
tt(t17_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_finset_1 B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v6_tbsp_1 C A)) ) ) )  => (v6_tbsp_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t17_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_tdgroup A)))  &  ((v2_tdgroup (k2_tdgroup A)) & (l1_analoaf (k2_tdgroup A))) ) ) ) ) ).
tt(t17_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_tops_1 B A) & (v4_tops_1 C A))  =>  ((v4_tops_1 (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) (k4_subset_1 (u1_struct_0 A) B C)) A) & (v4_tops_1 (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) B C)) A)) ) ) ) ) ) ) ) ).
tt(t17_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k1_tarski C))  => (v3_pre_topc B A)) ) ) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t17_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k4_termord A B C D) = (k4_struct_0 C))  <=> (r8_pboole (k15_pre_poly A) D (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(t17_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = B) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t17_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v13_struct_0 B 1) & (m1_pre_topc B A))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 (k1_tex_2 A C)) (u1_pre_topc (k1_tex_2 A C)))) ) ) ) ) ) ) ).
tt(t17_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tops_3 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v2_tex_3 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t17_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v1_tex_4 B A) & (v4_pre_topc B A))  => (v3_tex_4 B A)) ) ) ) ) ).
tt(t17_tietze,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v10_pre_topc B) =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc B C)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc D (k1_pre_topc B C) k3_topmetr) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc B C)) (u1_struct_0 k3_topmetr))))) ) )  =>  (~  ((r1_tietze D A C) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc E B k3_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) ) )  =>  (~  ((r1_tietze E (k6_real_1 A 3) (k1_relset_1 (u1_struct_0 B) E)) & (r1_tietze (k45_valued_1 D E) (k10_real_1 (k8_real_1 2 A) 3) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((m1_pre_topc B C) =>  ( (~ (r1_tsep_1 B C))  &  (~ (r1_tsep_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t17_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_toler_1 C A B) => (m1_toler_1 (k3_xboole_0 C D) A B)) ) ) ) ) ) ).
tt(t17_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 (k15_euclid A) k17_borsuk_1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) k17_borsuk_1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k17_borsuk_1)) =>  ((k1_binop_1 B C D) = (k1_rlvect_1 (k15_euclid A) C (k9_real_1 1 D))) ) ) ) )  => (v5_pre_topc B (k2_borsuk_1 (k15_euclid A) k17_borsuk_1) (k15_euclid A))) ) ) ) ) ).
tt(t17_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_borsuk_2 B k5_topmetr A A) =>  ((u1_struct_0 (k5_topalg_1 k5_topmetr A)) = (k1_tarski (k6_eqrel_1 (k2_topalg_1 k5_topmetr A) (k2_topalg_1 k5_topmetr A) (k4_topalg_1 k5_topmetr A) B))) ) ) ) ) ).
tt(t17_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 (k1_pre_topc A D) B)) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k1_pre_topc A D) B)) (u1_struct_0 C))))) )  =>  ( ( (F = (k2_partfun1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C) E (k2_zfmisc_1 D (u1_struct_0 B))))  & (v5_pre_topc E (k2_borsuk_1 A B) C))  => (v5_pre_topc F (k2_borsuk_1 (k1_pre_topc A D) B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_6 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  (! [J:$i] :  ((m1_borsuk_2 J A C D) =>  (! [K:$i] :  ((m1_borsuk_2 K A C D) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) J (k3_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) K (k3_topalg_4 A B k5_topmetr H)) & (r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) )  => (m1_borsuk_6 (k3_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) A C D J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v1_connsp_2 (k4_topmetr A B))) ) ) ) ) ).
tt(t17_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) => (v3_topalg_6 C A B)) ) ) )  => (v1_topalg_6 A)) ) ) ).
tt(t17_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_topdim_1 (k1_pre_topc A B)) = (k2_topdim_1 A B)) ) ) ) ) ).
tt(t17_topdim_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 1))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k9_finseq_1 B) = A)  =>  ((k10_metric_1 (k14_euclid 1) A C) = (a_2_0_topdim_2 B C)) ) ) ) ) ) ) ) ).
tt(t17_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_topgen_1 A B)) <=>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E (k9_subset_1 (u1_struct_0 A) B D)) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_topgen_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_pre_topc A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_pre_topc A))))) )  =>  ( ( (B = (k2_relset_1 (u1_pre_topc A) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_funct_1 C D)) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden D E) => (r1_tarski (k1_funct_1 C D) E)) ) ) ) ) ) )  =>  ((k2_waybel23 A) = (k1_card_1 B)) ) ) ) ) ) ) ) ).
tt(t17_topgen_3,ax, ((k1_card_1 k3_numbers) = k4_ordinal1) ).
tt(t17_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( ((v4_topgen_4 B A) & (v1_prob_1 B A))  =>  ((v3_topgen_4 B A) & (v1_prob_1 B A)) )  &  ( ((v3_topgen_4 B A) & (v1_prob_1 B A))  =>  ((v4_topgen_4 B A) & (v1_prob_1 B A)) ) ) ) ) ) ).
tt(t17_topgen_5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k10_finseq_1 A B) k2_topgen_5) <=>  ((r2_hidden A k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (B = C)  & (r1_xxreal_0 k6_numbers C)) ) ) ) ) ) ) ).
tt(t17_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k2_topgrp_1 A C) B) = (k5_group_2 A C B)) ) ) ) ) ) ) ).
tt(t17_topmetr,ax, ((u1_struct_0 k3_topmetr) = k1_numbers) ).
tt(t17_topreal1,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers))) = (k1_tarski (k19_euclid k6_numbers k6_numbers))) ).
tt(t17_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A))) & (r2_hidden (k2_nat_1 B 1) (k4_finseq_1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A))))  =>  ((k2_topreal1 2 A B) = (k2_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A) B)) ) ) ) ) ) ) ) ).
tt(t17_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~  (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) )  &  ((v4_topreal1 B) &  ((r2_hidden A (k2_topreal1 2 B C)) &  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((v4_topreal1 D) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D)) = A)  &  ((r1_topreal4 (k3_topreal1 2 D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) &  ((r1_tarski (k3_topreal1 2 D) (k3_topreal1 2 B)) &  ((k3_topreal1 2 D) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C B)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((v1_topreal2 A) & (r1_xxreal_0 (k8_pscomp_1 A) (k6_pscomp_1 A))) ) ) ) ).
tt(t17_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ( ((k5_seq_4 (k2_rcomp_1 A B)) = A)  &  ((k4_seq_4 (k2_rcomp_1 A B)) = B) ) ) ) ) ) ) ).
tt(t17_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 B) = A)  => (r2_hidden B (u1_struct_0 (k15_euclid A)))) ) ) ) ) ).
tt(t17_topreal8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C A))  =>  ( ((k4_finseq_4 B (k7_partfun1 A C 1)) = (k3_finseq_1 B))  =>  ((k1_finseq_5 A (k4_graph_2 A B C) (k7_partfun1 A C 1)) = B) ) ) ) ) ) ) ) ).
tt(t17_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_tarski (k3_topreal9 A C B) (k2_topreal9 A C B))) ) ) ) ) ) ).
tt(t17_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (B = (k7_funcop_1 k1_numbers A))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B k1_numbers))) ) ) ) ) ).
tt(t17_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) &  ((k18_euclid A) = (k1_real_1 1)) )  =>  ((k17_euclid A) = k6_numbers) ) ) ) ).
tt(t17_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_valued_0 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) )  =>  ((k45_valued_1 (k2_funct_7 D A C) D) = (k2_funct_7 (k5_euclid B) A (k6_xcmplx_0 C (k1_funct_1 D A)))) ) ) ) ) ) ) ) ) ).
tt(t17_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k3_toprns_1 A (k3_toprns_1 A B)) = B) ) ) ) ) ).
tt(t17_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k1_tops_1 A C)) = (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t17_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) => (v2_tops_2 (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t17_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_1 B A) &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t17_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ((v5_pre_topc C (k3_pcomps_1 A) (k3_pcomps_1 B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  =>  (~  ( (E = (k1_funct_1 C D))  &  (! [G:$i] :  ( ((v1_xreal_0 G) & (v2_xxreal_0 G))  =>  (~ (r1_tarski (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) C (k9_metric_1 A D G)) (k9_metric_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ((r2_transgeo A B C) => (r2_transgeo A (k2_funct_2 A B) C)) ) ) ) ) ) ) ).
tt(t17_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((v3_tops_2 (k3_treal_1 A B (k1_treal_1 A B) (k2_treal_1 A B)) (k4_topmetr k6_numbers 1) (k4_topmetr A B)) &  ((r2_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k2_tops_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k3_treal_1 A B (k1_treal_1 A B) (k2_treal_1 A B))) (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1))) &  ((v3_tops_2 (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1)) (k4_topmetr A B) (k4_topmetr k6_numbers 1)) & (r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k2_tops_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 A B (k1_treal_1 k6_numbers 1) (k2_treal_1 k6_numbers 1))) (k3_treal_1 A B (k1_treal_1 A B) (k2_treal_1 A B)))) ) ) ) ) ) ) ) ).
tt(t17_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) => (r1_tarski (k1_trees_1 A) (k1_trees_1 B))) ) ) ) ) ).
tt(t17_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (~  ((v1_trees_2 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m1_trees_1 C A) &  (! [D:$i] :  ((v1_finset_1 D) =>  (~  ( (D = (k1_trees_2 A C))  & (r1_xxreal_0 (k5_card_1 D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v3_trees_3 (k2_tarski A B)) <=>  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) ) ) ) ).
tt(t17_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ((k1_trees_4 A) = (k4_trees_4 B C))  & (v6_trees_3 C))  =>  ( (A = B)  &  (C = k1_xboole_0) ) ) ) ) ) ) ).
tt(t17_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((r2_hidden A (k7_trees_9 B C)) <=>  (? [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) &  ( (A = (k5_trees_2 B D))  &  (~  ((r2_hidden D (k3_trees_1 (k9_xtuple_0 B))) &  (~ (r2_hidden (k1_funct_1 B D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v3_pre_topc D B) <=> (v3_pre_topc C A)) ) ) ) ) ) ) ) ) ) ).
tt(t17_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B D) &  ((r2_tsep_2 A C E) & (r1_connsp_1 A B C)) )  => (r2_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_pre_topc B) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_pre_topc C) & (m1_pre_topc C A)) )  =>  ( ((v1_borsuk_1 B A) | (v1_borsuk_1 C A))  => (v6_pre_topc (k1_tsep_1 A B C))) ) ) ) ) ) ) ).
tt(t17_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tsp_2 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) <=>  ( (C = (k3_tex_4 A C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) &  ((v4_pre_topc D B) &  (D = (k8_subset_1 (u1_struct_0 A) C (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_turing_1 (k2_finseq_4 k5_numbers C D) A B) =>  ( ((k1_funct_1 B C) = k6_numbers)  &  ( ((k1_funct_1 B (k2_nat_1 (k2_nat_1 C D) 2)) = k6_numbers)  &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 C D) 2) E))  &  (~  ((k1_funct_1 B E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k24_twoscomp (k11_finseq_1 A B C)))  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k23_twoscomp (k11_finseq_1 C B A)))  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k22_twoscomp (k11_finseq_1 C B A)))  &  ((k1_funct_1 k28_twoscomp (k11_finseq_1 A B C)) = (k1_funct_1 k21_twoscomp (k11_finseq_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_unialg_2 C A) =>  (~ (r2_subset_1 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ).
tt(t17_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  => (v15_lattices (k12_unialg_2 A))) ) ).
tt(t17_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((k1_group_1 A) = (k1_group_1 (k1_uniroots A))) ) ) ).
tt(t17_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_uproots B A) <=>  (~ (r1_xxreal_0 (k1_algseq_1 A B) k6_numbers)) ) ) ) ) ) ).
tt(t17_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_connsp_2 D A C) =>  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v6_xxreal_2 (k1_integra2 A B)) & (m1_subset_1 (k1_integra2 A B) (k1_zfmisc_1 k1_numbers))) ) ) ) ) ).
tt(t17_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k3_urysohn1) =>  ( (~ (r1_xxreal_0 E k6_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_urysohn3 A B C D) F) E))  & (r2_hidden F (k4_urysohn3 k3_urysohn1 A (k3_urysohn3 A B C D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ((r1_valuat_1 A B (k6_cqc_lang A D) E C) <=>  (~ (r1_valuat_1 A B D E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v3_funct_1 A)) ) ) )  =>  (? [B:$i] :  ((v1_int_1 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t17_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((k1_funct_1 (k50_valued_1 A B) C) = (k13_complex1 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ).
tt(t17_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k1_valued_1 A B)) = (k45_valued_1 (k30_valued_1 A) B)) ) ) ) ) ).
tt(t17_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((k4_vectsp_5 A B C D E) = (k1_domain_1 (u1_struct_0 B) (u1_struct_0 B) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 D B B) &  ((v1_mod_2 D A B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v1_vectsp11 D A B) & (m1_vectsp11 E A B D))  =>  ((m2_vectsp11 C A B D E) <=> (r1_struct_0 (k1_ranknull A B B (k3_matrlin A B B D (k4_matrlin A B B (k3_struct_0 B) (k4_algstr_0 A E)))) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k4_algstr_0 A (k1_algstr_0 A C D)) = (k5_algstr_0 A (k4_algstr_0 A D) C))  &  ( ((k4_algstr_0 A (k1_algstr_0 A D (k4_algstr_0 A C))) = (k5_algstr_0 A C D))  &  ( ((k4_algstr_0 A (k5_algstr_0 A C D)) = (k1_algstr_0 A D (k4_algstr_0 A C)))  &  ( ((k4_algstr_0 A (k5_algstr_0 A (k4_algstr_0 A C) D)) = (k1_algstr_0 A D C))  &  ((k5_algstr_0 A B (k1_algstr_0 A D C)) = (k5_algstr_0 A (k5_algstr_0 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k1_vectsp_2 A B B) = (k1_group_1 A)) ) ) ) ) ) ).
tt(t17_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t17_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) => (m1_vectsp_4 (k2_vectsp_5 A B C E) A (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_vectsp_6 D A B (k6_domain_1 (u1_struct_0 B) C)) =>  ((k4_vectsp_6 A B D) = (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C)) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_vectsp_7 C A B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r1_tarski C D) &  ((v1_vectsp_7 D A B) &  ((k1_vectsp_7 A B D) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (D = E)  =>  ((k1_vectsp_7 A B D) = (k1_vectsp_7 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k6_vfunct_1 A B D E)) (k2_vfunct_1 A B (k2_vfunct_1 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t17_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k3_vfunct_2 A B D E)) (k2_vfunct_1 A B (k2_vfunct_1 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k5_waybel_0 A B)) <=> (r1_orders_2 A C B)) ) ) ) ) ) ) ).
tt(t17_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel10 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel10 A))) =>  ( (D = B)  =>  ((r3_orders_2 (k4_waybel10 A) C D) <=> (m1_yellow_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_waybel11 A B C) & (r1_waybel_0 A B (k5_waybel_0 A D)))  => (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(t17_waybel12,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A C D) => (r2_yellow_4 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) D) B))) ) ) ) ) ) ) ) ) ).
tt(t17_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k2_waybel_8 A B)))  &  ((v1_waybel_0 (k2_waybel_8 A B) (k1_waybel_8 A)) &  ((v12_waybel_0 (k2_waybel_8 A B) (k1_waybel_8 A)) &  ((v14_waybel_0 (k2_waybel_8 A B) (k1_waybel_8 A)) & (m1_subset_1 (k2_waybel_8 A B) (k1_zfmisc_1 (u1_struct_0 (k1_waybel_8 A))))) ) ) )  <=> (v1_waybel_3 B A)) ) ) ) ) ).
tt(t17_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_yellow_8 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( (C = (k3_subset_1 (u1_struct_0 A) B))  => (v5_waybel_6 C (k2_yellow_1 (u1_pre_topc A)))) ) ) ) ) ) ) ).
tt(t17_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (? [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) &  ((v2_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v17_waybel_0 C B A) & (v22_waybel_0 C B A)) ) ) ) ) ) ) ) ) ).
tt(t17_waybel16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 A)))))  =>  ((r1_yellow_0 (k2_yellow_1 A) B) => (r1_tarski (k3_tarski B) (k1_yellow_0 (k2_yellow_1 A) B))) ) ) ) ) ).
tt(t17_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 D A B) =>  ( ( (~  ((r2_yellow_0 A C) & (r2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) )  &  (~  ((v3_lattice3 A) &  ((v5_orders_2 A) &  ((v3_lattice3 B) & (v5_orders_2 B)) ) ) ) )  | (r1_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k2_yellow_0 A C)) (k2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1)))))  => (v2_waybel18 B)) ) ) ) ).
tt(t17_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v1_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((m1_yellow_9 B (k3_yellow_3 A A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (C = (k4_waybel_2 A))  => (v5_pre_topc C B A)) ) ) ) ) ) ) ) ).
tt(t17_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_lattice3 B) =>  ((v18_waybel_0 C B A) <=>  ((v5_orders_3 C B A) & (v5_waybel_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t17_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v5_orders_2 A))  => (v5_orders_2 B)) ) ) ) ) ).
tt(t17_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ( ((r2_hidden (k3_yellow_0 A) (u1_struct_0 B)) & (v4_waybel_0 B A))  => (v8_yellow_0 B A)) ) ) ) ) ).
tt(t17_waybel22,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_waybel22 A C) &  ((r1_waybel22 B D) &  ((k1_card_1 C) = (k1_card_1 D)) ) )  => (r5_waybel_1 A B)) ) ) ) ) ) ) ).
tt(t17_waybel23,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v5_orders_3 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v1_waybel_0 G (k3_yellow_3 A B)) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))))  =>  ( ((r1_yellow_0 C (k7_relset_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D G)) &  ((r2_hidden E (k4_yellow_3 A B G)) & (r2_hidden F (k5_yellow_3 A B G))) )  => (r3_orders_2 C (k3_funct_2 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D (k7_yellow_3 A B E F)) (k1_yellow_0 C (k7_relset_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C) D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((v4_yellow_0 (k1_waybel25 B) (k1_waybel25 A)) & (m1_yellow_0 (k1_waybel25 B) (k1_waybel25 A))) ) ) ) ) ).
tt(t17_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) =>  ((v4_waybel_0 (k1_waybel25 B) (k1_waybel25 A)) & (m1_yellow_0 (k1_waybel25 B) (k1_waybel25 A))) ) ) ) ) ) ) ) ).
tt(t17_waybel27,ax, (! [A:$i] :  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k6_yellow_1 A (k3_yellow_1 1)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)) (u1_struct_0 (k6_yellow_1 A (k3_yellow_1 1))))))) )  &  ((v23_waybel_0 B (k3_yellow_1 A) (k6_yellow_1 A (k3_yellow_1 1))) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_funct_1 B C) = (k5_funct_3 C A)) ) ) ) ) ) ) ).
tt(t17_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (v4_yellow_6 (k3_waybel28 A) A)) ) ).
tt(t17_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) <=> (v23_waybel_0 (k2_waybel29 A B C) (k1_waybel29 A) (k1_waybel29 B))) ) ) ) ) ) ) ).
tt(t17_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r4_waybel_0 A A (k4_waybel_1 A B) C)) ) ) ) ) ) ).
tt(t17_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_tops_1 A C) = (k1_tops_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~ (v8_struct_0 A))  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  (~ (v1_finset_1 B)) ) ) ) ) ) ).
tt(t17_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r3_orders_2 A C (k1_yellow_0 A B))) ) ) ) ) ) ) ).
tt(t17_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  (~  ((r2_waybel_0 A B C) &  (! [D:$i] :  ( ((v6_waybel_0 D A) & (m2_yellow_6 D A B))  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A D)) C) & (m1_yellow_6 D A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((u1_struct_0 (k4_waybel34 A)) = (u1_struct_0 (k5_waybel34 A))) ) ) ).
tt(t17_waybel35,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) => (r1_lattice7 A (k4_waybel35 A B C D) (k4_waybel35 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v8_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel_3 B A)) ) ) ) ) ).
tt(t17_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) => (r1_tarski (k5_waybel_4 A C B) (k5_waybel_4 A D B))) ) ) ) ) ) ) ) ) ).
tt(t17_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_waybel_3 A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_waybel_3 A D B) => (r3_orders_2 A D C)) ) ) )  => (r3_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t17_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ((r3_orders_2 A C E) &  (~ (r3_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) &  ((v2_waybel_7 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  <=>  ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k7_lattice3 A)) &  ((v12_waybel_0 B (k7_lattice3 A)) &  ((v1_waybel_7 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A))))) ) ) ) ) ) ) ) ).
tt(t17_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v2_waybel_8 A))  => (v2_waybel_8 B)) ) ) ) ) ).
tt(t17_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m2_yellow_6 (k4_waybel_9 A B C) A B)) ) ) ) ) ) ).
tt(t17_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_struct_0 (k4_weddwitt A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(t17_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A B) D) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v8_relat_2 B) => (v8_relat_2 (k2_wellord1 B A))) ) ) ) ).
tt(t17_wellord2,ax, (! [A:$i] :  (? [B:$i] :  ((v1_relat_1 B) & (r2_wellord1 B A)) ) ) ).
tt(t17_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~  (A = k6_numbers) )  =>  ((r1_int_1 A B) <=> (v1_int_1 (k7_xcmplx_0 B A))) ) ) ) ) ) ).
tt(t17_xboole_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k3_xboole_0 A B) A)) ) ).
tt(t17_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean (k3_xboolean A) (k6_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t17_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k6_xcmplx_0 A (k6_xcmplx_0 B B))) ) ) ) ) ).
tt(t17_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 C D)) => (r1_xxreal_0 (k6_xcmplx_0 D B) (k6_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ).
tt(t17_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k14_xtuple_0 A) (k14_xtuple_0 B))) ) ) ).
tt(t17_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_xxreal_0 (k3_xxreal_0 A B) A)) ) ) ) ).
tt(t17_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 A A) = (k1_tarski A)) ) ) ).
tt(t17_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m2_xxreal_2 A (k1_xxreal_1 A B))) ) ) ) ).
tt(t17_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k1_xxreal_3 A B) = k2_xxreal_0)  &  ( (~  (A = k2_xxreal_0) )  &  (~  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(t17_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((r1_yellow_0 A B) & (r2_yellow_0 A B)) ) ) ) ).
tt(t17_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v3_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v3_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_yellow10 (k3_yellow_3 A B) D C) <=>  ((r1_yellow10 A (k8_yellow_3 A B D) (k8_yellow_3 A B C)) & (r1_yellow10 B (k9_yellow_3 A B D) (k9_yellow_3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t17_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_yellow_0 C A) =>  (! [D:$i] :  ((m1_yellow_0 D B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (v5_yellow_0 C A)) )  => (v5_yellow_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t17_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) & (r1_xboole_0 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v23_waybel_0 D A B) & (r2_yellow_0 A C))  => (r2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t17_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((r1_tarski C B) => (r1_setfam_1 (k2_yellow15 A B) (k2_yellow15 A C))) ) ) ) ) ) ).
tt(t17_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r5_waybel_1 A B) =>  ((r4_yellow16 A B) & (r4_yellow16 B A)) ) ) ) ) ) ).
tt(t17_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel18 A B C))) =>  (! [E:$i] :  (~  ((r2_hidden E (k2_waybel18 A B)) &  ((r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski D)) E) &  ( (~  (E = (k2_struct_0 (k3_waybel18 A B))) )  &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B C)))) =>  (~  ( (~  (F = (k2_struct_0 (k4_waybel18 A B C))) )  &  ((r2_hidden D F) &  ((v3_pre_topc F (k4_waybel18 A B C)) &  (E = (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  ((r2_yellow18 A B) =>  ((r1_functor0 A C) <=> (r2_functor0 B C)) ) ) ) ) ) ) ) ).
tt(t17_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k10_yellow_6 A (k3_yellow19 A (k2_struct_0 A) B))) <=> (r2_waybel_7 A B C)) ) ) ) ) ) ) ).
tt(t17_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_1 A))) =>  ( ((k13_lattice3 (k3_yellow_1 A) B C) = (k2_xboole_0 B C))  &  ((k12_lattice3 (k3_yellow_1 A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t17_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A A))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k2_zfmisc_1 B B)) &  ((v1_funct_1 D) & (v1_partfun1 D (k2_zfmisc_1 B B))) ) )  =>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B))) &  ((v1_funct_1 E) & (v1_partfun1 E (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B)))) ) )  &  ( (E = (k1_yellow20 C D))  &  ((k1_yellow20 (k2_altcat_1 A C) (k2_altcat_1 B D)) = (k2_altcat_1 (k3_xboole_0 A B) E)) ) ) ) ) ) ) ) ) ) ).
tt(t17_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r2_hidden (u1_struct_0 B) A) =>  ((m1_subset_1 B (u1_struct_0 (k8_yellow21 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (v2_waybel_8 B)) ) ) ) ) ) ) ) ).
tt(t17_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v21_waybel_0 B A A) => (v5_orders_3 B A A)) ) ) ) ) ).
tt(t17_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v4_orders_2 (k3_yellow_3 A B)) =>  ((v4_orders_2 A) & (v4_orders_2 B)) ) ) ) ) ) ).
tt(t17_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) B (k2_yellow_4 A C D)) (k2_yellow_4 A (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) B D)))) ) ) ) ) ) ) ) ).
tt(t17_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k13_lattice3 A B (k12_lattice3 A C D)) = (k12_lattice3 A (k13_lattice3 A B C) (k13_lattice3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t17_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r1_waybel_0 A B C) &  ((r1_waybel_0 A B D) & (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t17_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_lattice3 A) <=> (v3_lattice3 (k7_lattice3 A))) ) ) ).
tt(t17_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_yellow_8 (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) A)) ) ) ) ).
tt(t17_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k2_cantor_1 A B) = (k1_tarski A)) ) ) ) ).
tt(t17_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ( ((v8_zf_fund1 C A) & (r2_hidden B C))  => (r2_hidden (a_2_1_zf_fund1 A B) C)) ) ) ) ) ) ) ).
tt(t17_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( ((k15_zf_lang C D A) = (k15_zf_lang E F B))  =>  ( (C = E)  &  ( (D = F)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k1_funct_1 (k8_zf_lang A B) 1) = 4) ) ) ) ) ).
tt(t17_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k4_xboole_0 (k2_tarski A B) (k1_tarski B)) = (k1_tarski A)) ) ) ) ).
tt(t17_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_zf_model A) =>  ((v1_ordinal1 A) &  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r2_hidden (k2_tarski B C) A)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B A) => (r2_hidden (k3_tarski B) A)) )  &  ( (? [B:$i] :  ((m1_subset_1 B A) &  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_xboole_0 C D) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B A) => (r2_hidden (k3_xboole_0 A (k1_zfmisc_1 B)) A)) )  &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) & (r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  =>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_hidden (k7_relset_1 A A (k1_zfmodel1 B A C) D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (~  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model B)))  &  ((r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) &  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (~  ((r1_tarski (k9_subset_1 k1_zf_lang (k2_zf_model B) (k2_zf_model D)) (k2_tarski (k2_zf_lang 3) (k2_zf_lang 4))) &  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model D)))  &  ((r1_zf_model A E (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang D (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) & (r2_funct_2 A A (k1_zfmodel1 B A C) (k1_zfmodel1 D A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t17_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r1_zf_model A B (k10_zf_lang C D)) <=>  ((r1_zf_model A B C) | (r1_zf_model A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t17_zfrefle1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ((r2_hidden A (k10_xtuple_0 B)) => (v3_ordinal1 A)) ) ) ) ).
tt(t17_zf_refle,ax,(r2_tarski k5_numbers k1_zf_lang)).
tt(t17_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 D E) = (k1_zmodul01 B (k7_partfun1 (u1_struct_0 B) C E) A)) ) ) ) )  =>  ((k4_rlvect_1 B D) = (k1_zmodul01 B (k4_rlvect_1 B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t180_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r5_glib_000 A B) =>  ((k2_glib_001 A C E D) = (k2_glib_001 B C E D)) ) ) ) ) ) ) ) ) ).
tt(t180_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k21_member_1 A C) = (k21_member_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t180_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) => (r1_xboole_0 A B)) ) ) ) ) ).
tt(t180_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 1)) = A) ) ) ).
tt(t180_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C)) B)) )  =>  ((r1_xxreal_0 C (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 A) B) (k3_xcmplx_0 A C))) |  (A = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t180_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 D B))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k2_xboole_0 (k2_xboole_0 (k3_xxreal_1 A B) (k4_xxreal_1 B C)) (k2_xxreal_1 C D)) = (k4_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t180_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v10_zf_lang A) =>  ( ((k27_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k27_zf_lang A) B C))  &  ((k28_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k28_zf_lang A) B C)) ) ) ) ) ) ) ) ) ).
tt(t181_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ((r5_glib_000 A B) &  (C = D) )  =>  ( ((v1_glib_001 C A) => (v1_glib_001 D B))  &  ( ((v1_glib_001 D B) => (v1_glib_001 C A))  &  ( ((v2_glib_001 C A) => (v2_glib_001 D B))  &  ( ((v2_glib_001 D B) => (v2_glib_001 C A))  &  ( ((v3_glib_001 C A) => (v3_glib_001 D B))  &  ( ((v3_glib_001 D B) => (v3_glib_001 C A))  &  ( ((v4_glib_001 C A) => (v4_glib_001 D B))  &  ( ((v4_glib_001 D B) => (v4_glib_001 C A))  &  ( ((v5_glib_001 C A) => (v5_glib_001 D B))  &  ( ((v5_glib_001 D B) => (v5_glib_001 C A))  &  ( ((v6_glib_001 C A) => (v6_glib_001 D B))  &  ((v6_glib_001 D B) => (v6_glib_001 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t181_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k21_member_1 A B) = (k5_member_1 (k19_member_1 A B))) ) ) ) ) ).
tt(t181_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) =>  ((k5_relat_1 (k6_subset_1 C (k5_relat_1 C B)) A) = k1_xboole_0) ) ) ) ) ) ).
tt(t181_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_xcmplx_0 B A) = (k4_xcmplx_0 A))  =>  ( (A = k6_numbers)  |  (B = (k4_xcmplx_0 1)) ) ) ) ) ) ) ).
tt(t181_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 1 (k7_xcmplx_0 B A))) ) ) ) ) ) ).
tt(t181_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C D)) )  =>  ((k2_xboole_0 (k2_xboole_0 (k1_xxreal_1 A B) (k4_xxreal_1 B C)) (k1_xxreal_1 C D)) = (k1_xxreal_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t181_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((v11_zf_lang A) =>  ( ((k24_zf_lang (k6_zf_lang1 A B C)) = (k6_zf_lang1 (k24_zf_lang A) B C))  &  ( ( ((k23_zf_lang A) = B)  =>  ((k23_zf_lang (k6_zf_lang1 A B C)) = C) )  &  ( (~  ((k23_zf_lang A) = B) )  =>  ((k23_zf_lang (k6_zf_lang1 A B C)) = (k23_zf_lang A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t182_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k19_member_1 A B) = (k5_member_1 (k21_member_1 A B))) ) ) ) ) ).
tt(t182_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v4_relat_1 C A))  => (v4_relat_1 C B)) ) ) ) ) ).
tt(t182_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( ((k3_xcmplx_0 A A) = 1)  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ).
tt(t182_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 1 (k7_xcmplx_0 B A))) ) ) ) ) ) ).
tt(t182_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A C) (k1_xxreal_1 A B)) = (k3_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t182_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ( (~ (r2_hidden B (k4_zf_lang1 A)))  =>  ((k6_zf_lang1 A B C) = A) ) ) ) ) ) ) ) ).
tt(t183_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k21_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k21_member_1 A C) (k21_member_1 B C))) ) ) ) ) ) ) ).
tt(t183_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v5_relat_1 C A))  => (v5_relat_1 C B)) ) ) ) ) ).
tt(t183_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_xcmplx_0 (k4_xcmplx_0 A) (k3_xcmplx_0 2 A)) = A) ) ) ).
tt(t183_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k7_xcmplx_0 A B) 1)) ) ) ) ) ).
tt(t183_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A C) (k1_xxreal_1 A B)) = (k4_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t183_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k6_zf_lang1 A B B) = A) ) ) ) ) ).
tt(t184_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k21_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k21_member_1 A C) (k21_member_1 B C))) ) ) ) ) ) ) ).
tt(t184_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) <=> (r1_tarski A (k5_relat_1 B (k9_xtuple_0 A)))) ) ) ) ) ).
tt(t184_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) C) = (k3_xcmplx_0 (k6_xcmplx_0 B A) (k4_xcmplx_0 C))) ) ) ) ) ) ) ).
tt(t184_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k7_xcmplx_0 B A) 1)) ) ) ) ) ).
tt(t184_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k1_xxreal_1 A C) (k2_xxreal_1 A B)) = (k1_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t184_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (~  ( (~  (B = C) )  & (r2_hidden B (k4_zf_lang1 (k6_zf_lang1 A B C)))) ) ) ) ) ) ) ) ).
tt(t185_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k21_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k21_member_1 A C) (k21_member_1 B C))) ) ) ) ) ) ) ).
tt(t185_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) & (v5_relat_1 C B)) )  => (r1_tarski C (k2_zfmisc_1 A B))) ) ) ) ).
tt(t185_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) C) = (k4_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 B A) C))) ) ) ) ) ) ) ).
tt(t185_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B A))  => (r1_xxreal_0 (k7_xcmplx_0 B A) 1)) ) ) ) ) ).
tt(t185_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 A C) (k2_xxreal_1 A B)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t185_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((r2_hidden B (k4_zf_lang1 A)) => (r2_hidden C (k4_zf_lang1 (k6_zf_lang1 A B C)))) ) ) ) ) ) ) ).
tt(t186_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k4_xxreal_3 C B) (k22_member_1 A C))) ) ) ) ) ) ) ).
tt(t186_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k6_relat_1 A B)) (k9_xtuple_0 B))) ) ) ).
tt(t186_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k6_xcmplx_0 A (k3_xcmplx_0 2 A)) = (k4_xcmplx_0 A)) ) ) ).
tt(t186_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k7_xcmplx_0 B A) 1)) ) ) ) ) ).
tt(t186_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A C) (k1_xxreal_1 A B)) = (k3_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t186_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( (~  (B = C) )  =>  ((k6_zf_lang1 (k6_zf_lang1 A B C) B D) = (k6_zf_lang1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t187_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k22_member_1 A B) = (a_2_14_member_1 A B)) ) ) ) ) ).
tt(t187_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 (k4_xcmplx_0 A) B)) ) ) ) ) ).
tt(t187_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k7_xcmplx_0 B A) 1)) ) ) ) ) ) ) ).
tt(t187_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 A C) (k3_xxreal_1 A B)) = (k4_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t187_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) => (r1_tarski (k4_zf_lang1 (k6_zf_lang1 A B C)) (k2_xboole_0 (k7_subset_1 k1_zf_lang (k4_zf_lang1 A) (k1_tarski B)) (k1_tarski C)))) ) ) ) ) ) ).
tt(t188_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k22_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k4_xxreal_3 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t188_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 A (k4_xcmplx_0 B)) = (k4_xcmplx_0 (k7_xcmplx_0 A B))) ) ) ) ) ).
tt(t188_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k7_xcmplx_0 B A) 1)) ) ) ) ) ) ) ).
tt(t188_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A C) (k4_xxreal_1 A B)) = (k1_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t189_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k22_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k22_member_1 A C) (k22_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t189_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k7_xcmplx_0 A (k4_xcmplx_0 B))) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(t189_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 1 (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t189_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 A C) (k4_xxreal_1 A B)) = (k2_xxreal_1 B C)) ) ) ) ) ) ) ) ).
tt(t18_abcmiz_0,ax, (! [A:$i] :  ( ((v8_abcmiz_0 A) & (l2_abcmiz_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) => (r1_xboole_0 (k3_abcmiz_0 A B) (k3_abcmiz_0 A (k1_abcmiz_0 A B)))) ) ) ) ).
tt(t18_abcmiz_1,ax, (k2_abcmiz_1 = a_0_1_abcmiz_1) ).
tt(t18_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k9_abcmiz_1)  &  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (~  (B = (k6_trees_4 (k4_tarski k9_abcmiz_1 3) C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_absvalue (k3_xcmplx_0 A B)) = (k3_xcmplx_0 (k1_absvalue A) (k1_absvalue B))) ) ) ) ) ).
tt(t18_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 D A) &  ((v1_aff_1 E A) &  ((r2_hidden B D) &  ((r2_hidden C D) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D G) &  ((r2_hidden E G) &  ((r2_hidden B H) &  ((r2_hidden D H) &  ((r2_hidden C I) &  ((r2_hidden E I) &  ( (~  (F = G) )  &  ((r5_aff_1 A F G) &  ((v1_aff_1 H A) &  ((v1_aff_1 I A) &  ( (~ (r5_aff_1 A H I))  &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ((r2_hidden J H) & (r2_hidden J I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ((r1_xxreal_0 (k1_afinsq_1 B) A) =>  ((r1_xxreal_0 (k2_nat_1 (k1_afinsq_1 B) (k1_afinsq_1 C)) A) |  ((k1_funct_1 (k1_ordinal4 B C) A) = (k1_funct_1 C (k6_xcmplx_0 A (k1_afinsq_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t18_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((k3_afinsq_2 B k6_numbers A) = (k3_afinsq_2 B 1 A)) ) ) ) ) ).
tt(t18_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((r2_hidden B (k2_zfmisc_1 (k1_afproj A) (k1_tarski 1))) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k4_tarski C 1))  & (v1_aff_1 C A)) ) ) ) ) ) ) ).
tt(t18_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_afvect0 A B C B) <=>  ( (B = C)  | (r1_afvect0 A B C)) ) ) ) ) ) ) ) ).
tt(t18_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_alg_1 B A) => (r3_alg_1 A (k4_alg_1 A B) (k5_alg_1 A B))) ) ) ) ).
tt(t18_algspec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r6_pboole (k2_xboole_0 A B) (k1_algspec1 (k2_xboole_0 A B) C) (k1_funct_4 (k1_algspec1 A C) (k1_algspec1 B C)))) ) ) ) ).
tt(t18_algstr_4,ax, (! [A:$i] :  ((k11_algstr_4 A 2) = (k2_zfmisc_1 (k2_zfmisc_1 A A) (k1_tarski 1))) ) ).
tt(t18_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k1_altcat_1 A B B) = k1_xboole_0) ) ) ) ) ) ).
tt(t18_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (v2_altcat_1 (k4_altcat_2 A))) ) ).
tt(t18_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  ((v1_altcat_3 E A B C) &  ((v1_altcat_3 F A C D) &  (~ (v1_altcat_3 (k5_altcat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v1_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v1_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k4_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(t18_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k3_ami_3 H I))  & (r2_hidden H (k9_xtuple_0 B))) )  =>  ((k2_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I)) = (k2_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_amistd_1 2 k1_ami_3 (k8_ami_3 B A)) = (k1_tarski B)) ) ) ) ) ).
tt(t18_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_extpro_1 A))) =>  ((k2_compos_0 (u1_compos_1 (k1_extpro_1 A)) B) = k6_numbers) ) ) ) ) ).
tt(t18_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_amistd_1 C A B) => (r2_hidden (k4_struct_0 B) (k4_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t18_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 C (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = 1)  =>  ((k5_memstr_0 A (k4_amistd_1 A) (k2_extpro_1 A (k4_amistd_1 A) B C)) = (k5_ami_wstd A (k4_amistd_1 A) (k5_memstr_0 A (k4_amistd_1 A) C))) ) ) ) ) ) ) ) ).
tt(t18_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  ( ( (F = B)  &  ( (G = C)  &  ( (H = D)  &  (I = E) ) ) )  =>  ((r2_analoaf (k2_diraf (k2_analoaf A)) F G H I) <=>  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  ( ((k1_rlvect_1 A (k5_algstr_0 A C B) J) = (k1_rlvect_1 A (k5_algstr_0 A E D) K))  &  (~  ( (J = k6_numbers)  &  (K = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r1_analoaf A C B B D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_analoaf A E B B F) & (r1_analoaf A E C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r1_analort A B C D E F G))  => (r1_analort A B C F G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_anproj_1 A B C D) &  ((r2_anproj_1 A E F D) &  ((r2_anproj_1 A B E G) &  ((r2_anproj_1 A C F G) &  ((r2_anproj_1 A B F H) &  ((r2_anproj_1 A C E H) &  ((r2_anproj_1 A G D H) &  ( (~ (v9_struct_0 G A))  &  ( (~ (v9_struct_0 D A))  &  ( (~ (v9_struct_0 H A))  &  ( (~ (r2_anproj_1 A B C F))  &  ( (~ (r2_anproj_1 A B C E))  &  ( (~ (r2_anproj_1 A B E F))  &  (~ (r2_anproj_1 A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [I:$i] :  ((m2_funct_2 I A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  (? [L:$i] :  ((m1_subset_1 L k1_numbers) &  (? [M:$i] :  ((m1_subset_1 M k1_numbers) &  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J F)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K G))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L H))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M I))) (k8_funcsdom A)) &  (~  ( (J = k6_numbers)  &  ( (K = k6_numbers)  &  ( (L = k6_numbers)  &  (M = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_aofa_000 A B k6_numbers) = B) ) ) ) ) ).
tt(t18_aofa_i00,ax, (! [A:$i] :  ((m4_aofa_i00 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_funct_2 k5_numbers k4_numbers) k4_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 k5_numbers k4_numbers) k4_numbers)))) )  => (m3_aofa_i00 B (k7_freealg k19_aofa_000 k26_aofa_i00) k5_numbers (k1_aofa_i00 (k9_funct_2 k5_numbers k4_numbers) k6_numbers k6_numbers) A)) ) ) ) ).
tt(t18_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v8_relat_2 B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r2_hidden (k6_armstrng A C D) B) & (r2_hidden (k6_armstrng A D E) B))  => (r2_hidden (k6_armstrng A C E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((k2_arytm_0 A B) = 1)  &  ((k2_arytm_0 A C) = 1) )  =>  ( (A = k6_numbers)  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t18_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ((k2_arytm_1 A A) = k11_arytm_3) ) ) ).
tt(t18_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ((r2_hidden A k4_ordinal1) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ((r2_hidden B A) <=>  ((r2_hidden B k4_ordinal1) &  ( (~  (B = A) )  & (r1_arytm_2 B A)) ) ) ) ) ) ) ) ).
tt(t18_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( (~  (A = k1_xboole_0) )  =>  ( (~  ((k3_arytm_3 B A) = k1_xboole_0) )  &  (~  ((k6_ordinal3 A (k3_arytm_3 B A)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t18_asympt_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden A (k7_asympt_0 B)) =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ) ) ).
tt(t18_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 A C) = (k6_int_1 C 2)) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k6_int_1 (k2_nat_1 C 1) 2)) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v2_asympt_0 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C A) &  ((r2_funct_2 k5_numbers k1_numbers D B) &  ( (~ (r2_hidden C (k6_asympt_0 D)))  &  (~ (r2_hidden D (k6_asympt_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) => (v2_relat_1 (k7_pboole A B C))) ) ) ) ) ) ).
tt(t18_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_autgroup A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_autgroup A))) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  (! [E:$i] :  ((m2_funct_2 E (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k5_autgroup A) B C) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bagorder,ax, (! [A:$i] :  ((k1_polynom2 A (k16_pre_poly A)) = k1_xboole_0) ) ).
tt(t18_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v6_bcialg_1 A) <=>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t18_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_bcialg_2 A (k4_struct_0 A) (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A (k1_bcialg_2 A (k4_struct_0 A) B D) (k1_bcialg_2 A (k4_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t18_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k7_bcialg_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_bcialg_1 A B)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C D)) = (k1_bcialg_1 A D (k1_bcialg_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t18_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  ((k4_binop_1 (u1_struct_0 A) (u1_bcialg_4 A)) = (k4_struct_0 A)) ) ) ).
tt(t18_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A (k2_nat_1 B F) (k2_nat_1 C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_bcialg_6 A C (k2_bcialg_1 A B)) = (k2_bcialg_1 A (k3_bcialg_6 A C B))) ) ) ) ) ) ) ).
tt(t18_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_bciideal B A) => (m2_bcialg_1 B A)) ) ) ) ) ).
tt(t18_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A B C)) = (k7_real_1 (k9_real_1 (k2_bhsp_1 A B B) (k8_real_1 2 (k2_bhsp_1 A B C))) (k2_bhsp_1 A C C))) ) ) ) ) ) ) ).
tt(t18_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 C A) =>  ((k1_bhsp_2 A (k4_normsp_1 A C B)) = (k5_algstr_0 A (k1_bhsp_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t18_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_bhsp_3 B A) & (v2_bhsp_3 C A))  => (v2_bhsp_3 (k6_bhsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t18_bhsp_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((k3_bhsp_4 B C (k2_nat_1 A 1)) = (k3_rlvect_1 B (k3_bhsp_4 B C A) (k1_normsp_1 B C (k2_nat_1 A 1)))) ) ) ) ) ) ) ).
tt(t18_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k5_bilinear A B C D E) F) (k5_hahnban1 A B (k8_bilinear A B C D F) (k8_bilinear A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k6_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) = (k9_binarith A 1 k6_margrel1 (k7_binarith A B (k2_binari_2 A C)) (k10_binarith k6_margrel1 (k2_binarith (k2_binarith (k2_binarith D (k9_margrel1 E)) (k8_binarith A (k3_binarith A C) (k1_binari_2 A))) (k8_binarith A B (k2_binari_2 A C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_binari_3,ax, ((k7_binarith 1 (k10_binarith k6_margrel1 k8_margrel1) (k10_binarith k6_margrel1 k8_margrel1)) = (k10_binarith k6_margrel1 k7_margrel1)) ).
tt(t18_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((r1_xxreal_0 k6_numbers (k21_binop_2 (k5_series_1 2 (k7_nat_d A 1)) 1)) & (r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d A 1))) k6_numbers)) ) ) ).
tt(t18_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k8_binarith A B C) = (k7_partfun1 k6_margrel1 (k4_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) (k1_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k5_binom A B C) = (k6_binom A B C)) ) ) ) ) ) ) ).
tt(t18_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C D) E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C D) E)))) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ((r2_hidden A C) & (r2_hidden B D))  =>  ( (E = k1_xboole_0)  |  ((k1_binop_1 (k3_relat_1 F G) A B) = (k1_funct_1 G (k1_binop_1 F A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_card_1 (k2_trees_2 A B)) = (k5_series_1 2 B)) ) ) ) ) ).
tt(t18_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((r4_boolealg A B C) & (r4_boolealg A B D)) )  & (r4_boolealg A B (k4_lattices A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t18_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r1_bor_cant A B C D) =>  ( ( ((k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) = k6_numbers)  |  ((k1_funct_1 C (k3_kurato_0 A (k2_prob_1 A D))) = 1) )  &  ( ((k1_funct_1 C (k4_kurato_0 A D)) = k6_numbers)  |  ((k1_funct_1 C (k4_kurato_0 A D)) = 1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((v3_pre_topc C (k2_borsuk_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (D = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 A) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) C))  => (v3_pre_topc D A))  &  ( (E = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) C))  => (v3_pre_topc E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) =>  ( ((m1_setfam_1 D (u1_struct_0 (k2_borsuk_1 B A))) &  ((v1_tops_2 D (k2_borsuk_1 B A)) &  (C = (a_3_1_borsuk_3 A B D)) ) )  =>  ((v1_tops_2 C A) & (m1_setfam_1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t18_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) => (m1_subset_1 (k1_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) ) ) ).
tt(t18_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~ (v1_rat_1 (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t18_borsuk_6,ax, ((v4_pre_topc a_0_4_borsuk_6 (k15_euclid 2)) & (m1_subset_1 a_0_4_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(t18_borsuk_7,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k39_valued_1 (k24_valued_1 B A)) = (k24_valued_1 (k39_valued_1 B) (k3_square_1 A))) ) ) ) ) ).
tt(t18_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k4_bspace A (k3_rlvect_1 k2_bspace B C) D) = (k5_subset_1 A (k4_bspace A B D) (k4_bspace A C D))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A (k5_bvfunc_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k2_enumset1 C D E F))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  & (r1_xboole_0 (k15_bvfunc_1 A H (k2_partit1 A (k2_partit1 A D E) F)) (k15_bvfunc_1 A G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k11_bvfunc_1 A) B) & (r1_bvfunc_1 A B (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t18_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k6_bvfunc_1 A C D)) (k6_bvfunc_1 A (k6_bvfunc_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k10_bvfunc_1 A B C)) (k9_bvfunc_1 A B (k6_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t18_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_2 A C B D)) (k7_bvfunc_2 A (k1_bvfunc_1 A C) B D))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) D))) ) ) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k6_bvfunc_2 A B D E) C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A D (k9_bvfunc_1 A C B)) (k9_bvfunc_1 A C (k9_bvfunc_1 A D B))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D B) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D C) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D (k2_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A D B) (k9_bvfunc_1 A D C)))) ) ) ) ) ) ) ) ).
tt(t18_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k2_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) C)))) ) ) ) ) ) ).
tt(t18_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A (k1_bvfunc_1 A B) D)) (k5_bvfunc_1 A C D))) ) ) ) ) ) ) ) ).
tt(t18_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) <=> (v4_xxreal_2 (k9_c0sp1 A B))) ) ) ) ) ).
tt(t18_c0sp2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_c0sp2 B))) =>  ( ( ((k1_normsp_0 (k5_c0sp2 B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k5_c0sp2 B))) )  &  ( ( (C = (k4_struct_0 (k5_c0sp2 B)))  =>  ((k1_normsp_0 (k5_c0sp2 B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k5_c0sp2 B) (k1_rlvect_1 (k5_c0sp2 B) C A)) = (k8_real_1 (k18_complex1 A) (k1_normsp_0 (k5_c0sp2 B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k5_c0sp2 B) (k3_rlvect_1 (k5_c0sp2 B) C D)) (k7_real_1 (k1_normsp_0 (k5_c0sp2 B) C) (k1_normsp_0 (k5_c0sp2 B) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B)) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C))) &  ( ((k6_cqc_lang A (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B))) = (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C)))  &  ( ((k2_calcul_1 A B) = (k2_calcul_1 A C))  &  ((r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B)) & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C) (k2_calcul_1 A C))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) 1) |  ((r1_xxreal_0 (k3_finseq_1 C) 1) | (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B)) (k2_calcul_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t18_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) => (r2_calcul_1 A B (k8_finseq_1 (k3_cqc_lang A) C B))) ) ) ) ) ) ).
tt(t18_cantor_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_tops_2 B (g1_pre_topc A (k1_cantor_1 A (k2_cantor_1 A B)))) &  ((v2_cantor_1 B (g1_pre_topc A (k1_cantor_1 A (k2_cantor_1 A B)))) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc A (k1_cantor_1 A (k2_cantor_1 A B)))))))) ) ) ) ) ) ).
tt(t18_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r2_hidden A (k2_card_1 A))) ) ).
tt(t18_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k1_card_2 A k6_numbers) = A) ) ) ).
tt(t18_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k6_subset_1 (k5_card_3 B A) (k5_card_3 B C)) (k5_card_3 B (k6_subset_1 A C)))) ) ) ).
tt(t18_card_4,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((r2_wellord2 (k2_zfmisc_1 A A) A) &  ((k1_card_1 (k2_zfmisc_1 A A)) = (k1_card_1 A)) ) ) ) ).
tt(t18_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( ((r1_ordinal1 B A) | (r2_hidden B A))  =>  ( ((k1_card_2 B A) = A)  &  ( ((k1_card_2 A B) = A)  &  ( ((k2_card_2 B A) = A)  &  ((k2_card_2 A B) = A) ) ) ) ) ) ) ) ) ).
tt(t18_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r2_hidden B (k4_card_fil A)) <=> (r2_hidden (k1_card_1 (k6_subset_1 A B)) (k1_card_1 A))) ) ) ) ) ).
tt(t18_cardfin2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (~  ( ((k5_card_1 A) = 23)  &  ( ((k5_card_1 B) = 365)  & (r1_xxreal_0 (k1_rpr_1 (k1_funct_2 A B) (k4_cardfin2 A B)) (k18_binop_2 1 2))) ) ) ) ) ) ) ).
tt(t18_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((v1_finset_1 D) =>  ((r1_xboole_0 C D) =>  ( (A = B)  | (r2_hidden (k1_funct_4 (k7_funcop_1 C A) (k7_funcop_1 D B)) (k1_card_fin (k2_xboole_0 C D) (k5_card_1 C) A B))) ) ) ) ) ) ) ) ).
tt(t18_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (v2_card_lar (k2_card_lar A B) A)) ) ) ) ).
tt(t18_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ( ((k3_graph_1 A D) = (k4_graph_1 A C))  &  ((k3_graph_1 A C) = (k4_graph_1 A B)) )  =>  ((k1_cat_1 A (k1_cat_1 A B C) D) = (k1_cat_1 A B (k1_cat_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t18_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ((v1_cat_2 B A) <=> (v13_cat_1 (k5_cat_2 A B) B A)) ) ) ) ) ).
tt(t18_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A C) (k3_cat_3 B A D)) =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A (k8_cat_3 B A C D)) (k2_cat_3 B A D)) & (r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A (k8_cat_3 B A C D)) (k3_cat_3 B A C))) ) ) ) ) ) ) ) ) ).
tt(t18_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k4_cat_4 A B C)) = (k2_cat_4 A B C))  &  ((k4_graph_1 A (k4_cat_4 A B C)) = C) ) ) ) ) ) ) ) ).
tt(t18_cat_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_cat_5 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_cat_1 C) &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v1_cat_1 D) &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) ) )  =>  ( ( ((u1_struct_0 C) = A)  &  ( (! [E:$i] :  ((m1_cat_5 E A) =>  (! [F:$i] :  ((m1_cat_5 F A) =>  (! [G:$i] :  ((m2_cat_1 G E F) =>  ((m1_subset_1 (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 E) (u4_struct_0 F))) (k1_domain_1 A A E F) G) (u4_struct_0 C)) <=> (r2_hidden G B)) ) ) ) ) ) )  &  ( ((u1_struct_0 D) = A)  &  (! [E:$i] :  ((m1_cat_5 E A) =>  (! [F:$i] :  ((m1_cat_5 F A) =>  (! [G:$i] :  ((m2_cat_1 G E F) =>  ((m1_subset_1 (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 E) (u4_struct_0 F))) (k1_domain_1 A A E F) G) (u4_struct_0 D)) <=> (r2_hidden G B)) ) ) ) ) ) ) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t18_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_catalan1 A) k5_numbers)) ) ).
tt(t18_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_catalan2 A) =>  ((v1_catalan2 (k1_catalan2 (k5_afinsq_1 k6_numbers) A)) &  ((a_1_2_catalan2 A) = k1_xboole_0) ) ) ) ) ).
tt(t18_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k1_msualg_1 (k3_catalg_1 A) (k8_catalg_1 A B)) = k1_xboole_0)  &  ((k2_msualg_1 (k3_catalg_1 A) (k8_catalg_1 A B)) = (k9_catalg_1 A B B)) ) ) ) ) ) ).
tt(t18_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_funcop_1 k5_numbers A k6_numbers) = (k4_struct_0 (k7_cc0sp1 A))) ) ) ).
tt(t18_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  ((k1_binop_1 (k1_cc0sp1 (k8_cfuncdom (u1_struct_0 A)) (k2_cc0sp2 A)) k6_complex1 B) = B) ) ) ) ) ).
tt(t18_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((m2_valued_0 A k2_numbers B) & (v2_comseq_2 B))  =>  ((k3_comseq_2 A) = (k3_comseq_2 B)) ) ) ) ) ) ).
tt(t18_cfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k1_valued_0 k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers B A) (k1_valued_0 k2_numbers C A)))) ) ) ) ) ) ).
tt(t18_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D C k2_numbers (k9_funct_2 C k2_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k2_numbers (k9_funct_2 C k2_numbers)) =>  ( ((r2_hidden A C) &  ((r2_hidden B C) &  ( (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 D F) = k6_complex1) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 D F) = k6_numbers) ) ) ) )  &  (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 E F) = k6_numbers) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 E F) = k6_complex1) ) ) ) ) ) ) )  =>  ( (A = B)  |  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  ((r2_funct_2 C k2_numbers (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) F D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G E))) (k4_cfuncdom C)) =>  ( (F = k5_complex1)  &  (G = k5_complex1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) D) (k19_valued_1 A k2_numbers k2_numbers B (k25_valued_1 A k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t18_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v2_cgames_1 B) =>  ( ((r2_hidden A (k6_cgames_1 B)) | (r2_hidden A (k7_cgames_1 B)))  =>  ((v2_cgames_1 A) & (l1_cgames_1 A)) ) ) ) ) ).
tt(t18_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~ (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ) ).
tt(t18_chord,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ( ((k3_finseq_1 (k15_finseq_1 C)) = (k3_finseq_1 B))  =>  ((k15_finseq_1 C) = B) ) ) ) ) ) ) ).
tt(t18_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A D))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) =>  ( ( (G = (k5_relat_1 I (u1_struct_0 A)))  &  ( (H = (k5_relat_1 I (u1_struct_0 B)))  & (v1_circuit2 G A D)) )  =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ((k5_relat_1 (k5_facirc_1 C F I J) (u1_struct_0 B)) = (k5_facirc_1 B E H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_circcmb3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb C D) (k7_circcomb A B C D)))) =>  ((k1_funct_1 (k6_circuit2 (k5_circcomb C D) (k7_circcomb A B C D) E) (k3_circcmb3 (k5_circcomb C D))) = (k1_funct_1 C (k3_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (r2_circcomb A A B B)) ) ) ) ).
tt(t18_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (~  ((v1_circled1 B A) &  (B = (k4_rlvect_2 A)) ) ) ) ) ) ) ).
tt(t18_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A B) =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  => (r2_circcomb (k1_circtrm1 A B C) (k1_circtrm1 A B D) (k6_circtrm1 A B C E) (k6_circtrm1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t18_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_circuit1 A B C) = k6_numbers)  <=>  ((r2_hidden C (k2_msafree2 A)) | (r2_hidden C (k1_msafree2 A))) ) ) ) ) ) ) ) ).
tt(t18_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  ((v3_funct_1 (k10_funct_6 C)) =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (E = (k7_circuit1 A B))  => (v1_circuit2 (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) E) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k3_classes1 A B) = (k3_classes1 A (k1_ordinal1 B)))  =>  ((k3_classes1 A B) = (k1_classes1 A)) ) ) ) ) ).
tt(t18_classes2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((r2_hidden A (k1_classes1 B)) => (r1_tarski A (k1_classes1 B))) ) ) ) ).
tt(t18_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) &  ((v1_funct_2 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) A B) &  ((v1_clopban1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) A B) & (m1_subset_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ).
tt(t18_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k13_clopban1 A A) (k6_partfun1 (u1_struct_0 A))) = 1) ) ) ).
tt(t18_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clopban3 B A) & (v1_clopban3 C A))  =>  ((v1_clopban3 (k3_normsp_1 A B C) A) &  ((k1_clopban3 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k1_clopban3 A B) (k1_clopban3 A C))) ) ) ) ) ) ) ) ) ).
tt(t18_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k1_clvect_1 A (k6_clopban3 A (k3_rlvect_1 A C D) B) (k13_complex1 k6_complex1 (k3_newton B))) = (k1_normsp_1 A (k1_bhsp_4 A (k3_clopban4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  ((v2_closure1 C A B) => (r2_pboole A (k16_pralg_1 A C (k3_pboole A D E)) (k3_pboole A (k2_closure1 A B C D) (k2_closure1 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_closure2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_closure2 B C))) =>  ( ((r2_hidden A B) &  (E = (k1_tarski D)) )  =>  ((k1_funct_1 (k4_closure2 B C E) A) = (k1_tarski (k1_funct_1 D A))) ) ) ) ) ) ) ) ) ) ).
tt(t18_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) (k4_algstr_0 A B) (k4_algstr_0 A B))) = (k1_clvect_1 A B (k10_complex1 (k8_complex1 k6_complex1 k6_complex1)))) ) ) ) ) ).
tt(t18_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 C A) =>  ((k1_clvect_2 A (k4_normsp_1 A C B)) = (k5_algstr_0 A (k1_clvect_2 A C) B)) ) ) ) ) ) ) ) ).
tt(t18_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k2_clvect_3 A B (k2_nat_1 C 1)) = (k3_rlvect_1 A (k2_clvect_3 A B C) (k1_normsp_1 A B (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t18_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_cohsp_1 A) =>  ((k1_funct_1 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t18_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (? [C:$i] :  ((m1_subset_1 C (k4_coh_sp A)) &  (? [D:$i] :  ((m1_subset_1 D (k3_coh_sp A)) &  (? [E:$i] :  ((m1_subset_1 E (k3_coh_sp A)) &  ( (B = (k4_tarski (k4_tarski D E) C))  &  ( ( ((k3_tarski E) = k1_xboole_0)  =>  ((k3_tarski D) = k1_xboole_0) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k3_tarski D) (k3_tarski E)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski D) (k3_tarski E))))) )  &  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k2_tarski F G) D) => (r2_hidden (k2_tarski (k1_funct_1 C F) (k1_funct_1 C G)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_collsp D A) =>  ( ((r2_hidden B D) & (r2_hidden C D))  =>  ( (B = C)  | (r1_tarski (k1_collsp A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t18_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 A))) =>  ((k4_combgras A B C D) = (a_4_0_combgras A B C D)) ) ) ) ) ) ) ) ) ).
tt(t18_complex1,ax, ((k9_complex1 k7_complex1 k7_complex1) = (k10_complex1 k6_complex1)) ).
tt(t18_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r2_hidden (k1_comptrig A) (k2_rcomp_1 k6_numbers k32_sin_cos)) <=>  (~ (r1_xxreal_0 (k4_complex1 A) k6_numbers)) ) ) ) ).
tt(t18_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k11_algstr_0 k1_complfld (k8_group_1 k1_complfld A B)) = (k8_group_1 k1_complfld (k11_algstr_0 k1_complfld A) (k11_algstr_0 k1_complfld B))) ) ) ) ) ) ) ) ) ).
tt(t18_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k4_finseq_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k4_finseq_2 A k2_numbers)) =>  ((k9_matrix_5 (k3_complsp2 A C D) B) = (k3_binop_2 (k9_matrix_5 C B) (k9_matrix_5 D B))) ) ) ) ) ) ) ) ) ).
tt(t18_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k1_topmetr A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k1_topmetr A B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 (k1_topmetr A B)) k5_numbers (u1_struct_0 A) C D) =>  ((v3_tbsp_1 D A) <=> (v3_tbsp_1 C (k1_topmetr A B))) ) ) ) ) ) ) ) ) ) ).
tt(t18_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  => (r1_xboole_0 (k2_afinsq_1 (k63_valued_1 B)) (k9_xtuple_0 (k6_compos_1 A C (k7_nat_d (k5_card_1 B) 1))))) ) ) ) ) ) ).
tt(t18_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v4_compos_1 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_compos_1 C A)) ) ) ) ) ) )  =>  ((r1_tarski (k63_valued_1 B) C) => (r1_tarski (k63_valued_1 B) (k63_valued_1 C))) ) ) ) ) ) ) ).
tt(t18_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) A))  &  ( ((k20_sin_cos A) = k6_numbers)  &  ( (~  (A = (k10_real_1 k32_sin_cos 2)) )  &  (~  (A = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) ) ) ) ) ) ).
tt(t18_compts_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_finset_1 (u1_struct_0 A)) => (v1_compts_1 A)) ) ) ).
tt(t18_comput_1,ax, ((k19_margrel1 k1_xboole_0) = k6_numbers) ).
tt(t18_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A) (k25_valued_1 k5_numbers k2_numbers C A)))) ) ) ) ) ) ).
tt(t18_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_comseq_2 (k25_valued_1 k5_numbers k2_numbers A B)) = (k3_xcmplx_0 B (k3_comseq_2 A))) ) ) ) ) ).
tt(t18_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k7_comseq_3 A) (k7_comseq_3 B)) (k7_comseq_3 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_comseq_3 A) (k8_comseq_3 B)) (k8_comseq_3 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ) ).
tt(t18_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ((k1_funct_1 (k2_conlat_1 A) k1_xboole_0) = (u1_struct_0 A)) ) ) ).
tt(t18_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B) = (k1_funct_1 (k2_conlat_1 (k7_conlat_2 A)) B)) ) ) ) ) ).
tt(t18_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((r1_tarski B C) & (r1_tarski C (k2_pre_topc A B))) )  => (v2_connsp_1 C A)) ) ) ) ) ) ) ).
tt(t18_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (r3_connsp_1 A B C))  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t18_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 B A) &  ((v2_connsp_1 C A) & (r1_xboole_0 B C)) )  =>  ( (C = k1_xboole_0)  | (r1_xboole_0 B (k1_connsp_3 A C))) ) ) ) ) ) ) ) ).
tt(t18_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (a_3_2_convex1 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t18_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_convex4 A B) = (k7_domain_1 (u1_struct_0 A) C D))  =>  ( (C = D)  |  ((k4_convex4 A B) = (k3_rlvect_1 A (k1_clvect_1 A C (k3_funct_2 (u1_struct_0 A) k2_numbers B C)) (k1_clvect_1 A D (k3_funct_2 (u1_struct_0 A) k2_numbers B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v3_qc_lang1 C A) =>  ((k13_cqc_lang A C B) = (k13_qc_lang1 A (k13_cqc_lang A (k18_qc_lang1 A C) B))) ) ) ) ) ) ) ) ).
tt(t18_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k7_cqc_sim1 A (k11_cqc_lang A C B)) = (k2_nat_1 (k7_cqc_sim1 A B) 1)) ) ) ) ) ) ) ).
tt(t18_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r1_tarski B C) => (r1_tarski (k1_cqc_the1 A B) (k1_cqc_the1 A C))) ) ) ) ) ) ) ).
tt(t18_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C B) (k12_cqc_lang A D B)) A)) ) ) ) ) ) ) ) ).
tt(t18_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r4_cqc_the3 A B C) <=>  ((r2_cqc_the3 A B C) & (r2_cqc_the3 A C B)) ) ) ) ) ) ) ) ).
tt(t18_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v2_comseq_2 B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A)) (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers C E) A))) (k1_seq_1 B E))) ) )  =>  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k7_real_1 (k8_real_1 (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A)) (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 C) A))) (k2_seq_2 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k9_csspace4 A B) C))) ) ) ) ) ) ).
tt(t18_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) & (l1_csspace B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k12_csspace B C (k1_clvect_1 B D A)) = (k3_xcmplx_0 (k15_complex1 A) (k12_csspace B C D))) ) ) ) ) ) ) ) ) ).
tt(t18_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_decomp_1 C A B) <=>  ((v6_decomp_1 C A B) & (v14_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t18_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 (k2_xcmplx_0 C D) (k3_finseq_1 B)) =>  ((k8_finseq_1 A (k17_finseq_1 A C B) (k17_finseq_1 A D (k2_rfinseq A C B))) = (k17_finseq_1 A (k2_xcmplx_0 C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v3_dickson A) &  ((v5_orders_2 B) &  ((v1_wellfnd1 (k5_dickson B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A D E) => (r1_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))  => (r2_hidden (k7_yellow_3 A A D E) (k1_dickson A))) ) ) ) ) ) ) ) )  => (v1_wellfnd1 (k5_dickson A))) ) ) ) ) ) ) ).
tt(t18_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) 1) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers C B) (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k1_real_1 A)) B))) ) ) ) ) ) ) ).
tt(t18_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r2_zfmisc_1 A B C D) =>  ( ((k11_diff_1 E A B C D) = (k11_diff_1 E B C D A))  &  ((k11_diff_1 E A B C D) = (k11_diff_1 E D C B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) A) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k7_real_1 C (k8_real_1 (k6_real_1 A 2) B))))  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) A) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k9_real_1 C (k8_real_1 (k6_real_1 A 2) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))) & (r2_hidden B (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_fdiff_9) A B) = (k13_complex1 (k13_complex1 (k8_real_1 4 (k8_real_1 (k21_sin_cos (k7_real_1 B A)) (k18_sin_cos (k9_real_1 B A)))) (k8_real_1 (k18_sin_cos (k8_real_1 2 A)) (k18_sin_cos (k8_real_1 2 B)))) (k9_real_1 A B))) ) ) ) ) ) ).
tt(t18_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_dilworth A) & (l1_orders_2 A)) )  =>  ( ((v2_dilworth (k2_struct_0 A) A) & (m1_subset_1 (k2_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_dilworth A) = 1) ) ) ) ).
tt(t18_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_diraf A B C D E) <=> (r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (k1_diraf (u1_struct_0 A) (u1_analoaf A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  ((v3_dirort A) =>  ( ( (~ (v5_dirort A))  &  (~ (v6_dirort A)) )  | (v4_dirort A)) ) ) ) ).
tt(t18_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  ((k16_rvsum_1 (k9_dist_1 A B)) = (k3_finseq_1 B)) ) ) ) ) ).
tt(t18_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (A = (a_1_0_domain_1 A)) ) ) ).
tt(t18_dtconstr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_dtconstr)) =>  ( ( (A = k6_numbers)  =>  ((k20_dtconstr k5_dtconstr A) = (k6_domain_1 (k3_finseq_2 k5_numbers) (k3_pre_poly k5_numbers k6_numbers))) )  &  ( (A = 1)  =>  ((k20_dtconstr k5_dtconstr A) = a_0_1_dtconstr) ) ) ) ) ).
tt(t18_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_dynkin B A) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_xboole_0 C D) => (r2_hidden (k4_subset_1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t18_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  (E = (k6_int_1 B C)) )  =>  ((k8_group_1 (k9_int_3 C) D E) = (k6_int_1 (k3_xcmplx_0 A B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ec_pf_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ( (E = (k6_int_1 B C))  &  (F = (k6_int_1 (k2_xcmplx_0 A B) C)) ) )  =>  ((k3_rlvect_1 (k9_int_3 C) (k8_group_1 (k9_int_3 C) D G) (k8_group_1 (k9_int_3 C) E G)) = (k8_group_1 (k9_int_3 C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k2_ens_1 A) = (k3_tarski (a_1_2_ens_1 A))) ) ) ).
tt(t18_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k4_finseq_1 (k1_matrprob A B C)) = (k2_finseq_1 (k1_matrix_1 B))) ) ) ) ) ) ) ) ).
tt(t18_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k1_enumset1 A B C) (k2_enumset1 D E F G))) ) ) ) ) ) ) ) ).
tt(t18_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k9_relat_1 C B)) <=> (r2_hidden (k4_tarski B A) C)) ) ) ) ) ).
tt(t18_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k3_msualg_1 A D C)) => (r2_hidden E (k3_msualg_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t18_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k2_zfmisc_1 (k8_e_siec A) (k7_e_siec A))) & (r1_tarski (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k2_zfmisc_1 (k8_e_siec A) (k7_e_siec A)))) ) ) ).
tt(t18_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k3_rlvect_1 (k15_euclid A) B C) D) = (k9_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t18_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k2_euclid_3 A) = k5_complex1)  =>  (A = (k4_struct_0 (k15_euclid 2))) ) ) ) ).
tt(t18_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 B (k5_euclid A)) = k6_numbers) ) ) ) ) ).
tt(t18_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 (k4_algstr_0 (k15_euclid 3) A) B) = (k5_euclid_5 A (k4_algstr_0 (k15_euclid 3) B))) ) ) ) ) ).
tt(t18_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) C B)))  & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) A C)))  =>  ( (D = B)  |  ( (D = A)  |  ( ( (~  ((k4_euclid_3 B D A) = (k10_real_1 k32_sin_cos 2)) )  &  (~  ((k4_euclid_3 B D A) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) )  |  ((k4_euclid_3 A B D) = (k4_euclid_3 D B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_euclid_7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_euclid k6_numbers))) =>  ((v5_euclid_7 A k6_numbers) =>  (A = k1_xboole_0) ) ) ) ).
tt(t18_euclid_8,ax, ((k5_euclid_8 k4_euclid_8 k2_euclid_8) = k3_euclid_8) ).
tt(t18_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  ( (~  (A = k6_numbers) )  => (r1_tarski (k4_euclid_9 A C B) (k9_metric_1 (k14_euclid A) C (k3_xcmplx_0 B (k6_square_1 A))))) ) ) ) ) ) ) ).
tt(t18_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k12_euclid (k8_euclid A B C)) = (k12_euclid (k8_euclid A C B))) ) ) ) ) ) ) ).
tt(t18_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((k8_euclid A (k7_euclid A B C) (k7_euclid A D E)) = (k7_euclid A (k8_euclid A B D) (k8_euclid A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_analmetr A B C) &  ( (~  ((k4_struct_0 A) = D) )  &  ( (~  ((k4_struct_0 A) = E) )  &  ((r2_analmetr A D E B C) &  ( (D = (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)))  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~  (H = k6_numbers) )  &  (E = (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 H G)) (k1_rlvect_1 A C (k1_real_1 (k8_real_1 H F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_euler_1,ax, ((k1_euler_1 2) = 1) ).
tt(t18_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) =>  ( (A = k1_xboole_0)  |  ((r1_xxreal_0 B 1) |  ((k4_nat_d (k1_newton A (k1_euler_1 B)) B) = 1) ) ) ) ) ) ) ) ).
tt(t18_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v1_xboole_0 B) => (v2_exchsort B A)) ) ) ) ).
tt(t18_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r8_pboole (u1_struct_0 A) D E) =>  ((k12_msualg_2 A B D) = (k12_msualg_2 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E))) =>  ((k6_extpro_1 A B C D) = (k5_extpro_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((k3_extreal1 A) = (k3_extreal1 (k2_supinf_2 A))) ) ) ).
tt(t18_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((r2_hidden D (k2_msafree2 A)) => (r1_facirc_1 A B C D)) ) ) ) ) ) ) ) ).
tt(t18_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  (~  ((k2_msafree2 (k14_facirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t18_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C))) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) )  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A))) ) ) ) ) ) ) ) ).
tt(t18_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((v2_funct_1 C) &  ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ( (~  ( ((k5_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) = (k1_seq_1 C A))  &  ((k4_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) = (k1_seq_1 C B)) ) )  &  (~  ( ((k5_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) = (k1_seq_1 C B))  &  ((k4_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) = (k1_seq_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) (k7_relset_1 k1_numbers k1_numbers B (k10_prob_1 A))))) ) ) ) ) ) ).
tt(t18_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k24_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k24_sin_cos) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos B) B) (k8_real_1 (k1_seq_1 k3_taylor_1 B) (k1_seq_1 k24_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t18_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k29_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k29_sin_cos) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k2_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t18_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r2_fdiff_1 B A) & (r2_fdiff_1 C A)) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) D) = (k7_real_1 (k1_fdiff_1 B D) (k1_fdiff_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) & (r2_fdiff_1 C A))  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) (k2_fdiff_1 C A)))) ) ) ) ) ) ) ) ).
tt(t18_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r3_fdiff_3 A C) & (r3_fdiff_3 B C))  =>  ((r3_fdiff_3 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) &  ((k2_fdiff_3 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k8_real_1 (k2_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k2_fdiff_3 C B) (k1_seq_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1))) &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) B) E) = (k10_real_1 (k8_real_1 2 E) (k7_real_1 (k5_square_1 A) (k2_newton E 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos)))) &  (B = (k1_taylor_1 2)) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos)) A) C) = (k7_real_1 (k8_real_1 (k8_real_1 2 C) (k1_seq_1 k19_sin_cos (k10_real_1 1 C))) (k1_seq_1 k16_sin_cos (k10_real_1 1 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k9_real_1 (k6_power k8_power A) 1))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 D (k6_power k8_power A))) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = k8_power)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k9_real_1 (k6_power k8_power A) 1))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos) k24_sin_cos) (k10_real_1 1 (k9_real_1 (k6_power k8_power A) 1))) B) D) = (k10_real_1 (k10_prepower A D) (k1_seq_1 k24_sin_cos D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_sin_cos6))) &  ((r1_tarski C (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_sin_cos6) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_sin_cos6) C) E) = (k7_real_1 (k8_real_1 A (k1_seq_1 k1_sin_cos6 E)) (k10_real_1 (k7_real_1 (k8_real_1 A E) B) (k7_square_1 (k9_real_1 1 (k5_square_1 E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1) A) B) = (k10_real_1 1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t18_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t18_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k9_xtuple_0 (k8_ff_siec A)) (k2_net_1 A)) &  ((r1_tarski (k10_xtuple_0 (k8_ff_siec A)) (k2_net_1 A)) &  ((r1_tarski (k9_xtuple_0 (k7_ff_siec A)) (k2_net_1 A)) & (r1_tarski (k10_xtuple_0 (k7_ff_siec A)) (k2_net_1 A))) ) ) ) ) ).
tt(t18_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ( (C = (k1_tarski (k4_tarski 1 B)))  =>  ((k12_pnproc_1 C A) = (k1_tarski (k4_tarski (k2_nat_1 1 A) B))) ) ) ) ) ) ) ).
tt(t18_fib_num3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  => (r1_xxreal_0 (k1_fib_num3 A) (k1_fib_num3 (k2_nat_1 A 1)))) ) ).
tt(t18_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_int_1 (k8_complex1 (k13_complex1 (k3_power k1_fib_num A) (k7_square_1 5)) (k13_complex1 1 2))) = (k1_pre_ff A)) ) ) ).
tt(t18_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k4_finseq_5 A (k2_rfinseq A C B)) = (k17_finseq_1 A (k7_nat_d (k3_finseq_1 B) C) (k4_finseq_5 A B))) ) ) ) ) ) ) ) ).
tt(t18_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v13_lattices A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r1_tarski B C) & (v1_filter_0 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v13_lattices A) =>  ( ( (~ (v2_struct_0 (k4_filter_1 A B)))  &  ((v10_lattices (k4_filter_1 A B)) &  ((v13_lattices (k4_filter_1 A B)) & (l3_lattices (k4_filter_1 A B))) ) )  &  ((k5_lattices (k4_filter_1 A B)) = (k5_filter_1 A B (k5_lattices A))) ) ) ) ) ) ) ).
tt(t18_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_lattice2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_lattice2 A))) =>  ( ((k4_lattices A B C) = (k3_lattices (k1_lattice2 A) (k1_filter_2 A B) (k1_filter_2 A C)))  &  ( ((k3_lattices A B C) = (k4_lattices (k1_lattice2 A) (k1_filter_2 A B) (k1_filter_2 A C)))  &  ( ((k4_lattices (k1_lattice2 A) D E) = (k3_lattices A (k2_filter_2 A D) (k2_filter_2 A E)))  &  ((k3_lattices (k1_lattice2 A) D E) = (k4_lattices A (k2_filter_2 A D) (k2_filter_2 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) => (m2_finseq_1 (k2_partfun1 k5_numbers B C (k2_finseq_1 A)) B)) ) ) ) ) ).
tt(t18_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  (~  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k2_finseq_1 A) (k2_finseq_1 (k2_xcmplx_0 A B)))) ) ) ) ).
tt(t18_finseq_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k7_partfun1 A (k3_finseq_4 A B C D) 1) = B)  &  ( ((k7_partfun1 A (k3_finseq_4 A B C D) 2) = C)  &  ((k7_partfun1 A (k3_finseq_4 A B C D) 3) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k4_finseq_1 (k16_finseq_1 B A)) (k4_finseq_1 A))) ) ) ) ).
tt(t18_finseq_6,ax, (! [A:$i] :  ((k4_finseq_4 (k9_finseq_1 A) A) = 1) ) ).
tt(t18_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_finseq_1 (k2_finseq_7 A B C D)) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ).
tt(t18_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 D E) & (r2_finseq_8 A B C E))  => (r2_finseq_8 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A B) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  => (r2_relset_1 k5_numbers C (k3_finseqop A B C G D (k5_finseq_2 B F E)) (k5_finseq_2 C F (k2_binop_1 A B C G D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((v2_binop_1 C A) =>  ( ( (~ (v1_setwiseo C A))  &  (~  ( (~  (D = k6_numbers) )  &  (~  (E = k6_numbers) ) ) ) )  |  ((k1_finsop_1 A (k5_finseq_2 A (k2_nat_1 D E) B) C) = (k5_binop_1 A C (k1_finsop_1 A (k5_finseq_2 A D B) C) (k1_finsop_1 A (k5_finseq_2 A E B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_finset_1 A) => (m1_subset_1 B (k5_finsub_1 A))) ) ) ) ).
tt(t18_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k12_fin_topo A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( ((k4_fintopo2 A D C) = k8_margrel1)  &  ((k3_fintopo2 A D B) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k5_fintopo3 A B (k2_nat_1 C 1)) = (k8_fin_topo A (k5_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t18_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v3_orders_2 (k2_fintopo4 A))) ) ) ).
tt(t18_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_orders_2 A) &  ((v1_fintopo6 A) &  ( (~  (B = k1_xboole_0) )  &  ( (~  ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0) )  &  ((k5_fin_topo A B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t18_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fin_topo A B) = (k9_subset_1 (u1_struct_0 A) (k9_fin_topo A B) (k9_fin_topo A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t18_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k6_flang_1 A (k6_flang_1 A B C) D) = (k6_flang_1 A B (k6_flang_1 A C D))) ) ) ) ) ) ) ) ).
tt(t18_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k6_flang_1 A B (k8_flang_1 A C))) & (r1_tarski B (k6_flang_1 A (k8_flang_1 A C) B))) ) ) ) ) ) ).
tt(t18_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k1_flang_3 A B D)) = (k1_flang_3 A B (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ).
tt(t18_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski C B) => (r1_tarski (k9_funct_7 C A) (k9_funct_7 B A))) ) ) ) ) ) ) ).
tt(t18_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( ((k32_fomodel2 B C) = (k1_nat_1 A 1))  =>  ( ((v5_fomodel2 C B) => (r2_hidden C (k36_fomodel2 B A)))  &  ( ((r2_hidden C (k36_fomodel2 B A)) => (v5_fomodel2 C B))  &  ( ( (~ (v5_fomodel2 C B))  => (r2_hidden C (k35_fomodel2 B A)))  &  (~  ((r2_hidden C (k35_fomodel2 B A)) & (v5_fomodel2 C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (! [D:$i] :  ((v4_funct_1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k43_fomodel2 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k43_fomodel2 B))))) )  =>  ( ((v6_fomodel4 C B) &  ((r2_hidden (k23_fomodel4 B) C) &  ((r2_hidden (k33_fomodel4 B) C) &  ((r2_hidden (k24_fomodel4 B) C) &  ((r2_hidden (k30_fomodel4 B) C) &  ((r1_tarski (k45_fomodel4 D B C E) A) &  ((k10_xtuple_0 E) = (k43_fomodel2 B)) ) ) ) ) ) )  =>  ((v1_finset_1 (k7_subset_1 (k15_fomodel1 B) (k16_fomodel1 B) (k21_fomodel0 (k9_subset_1 (k3_finseq_2 (k1_fomodel1 B)) D (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)))))) |  ((v14_fomodel4 A B C) | (v15_fomodel4 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k1_frechet2 A B))) ) ) ) ).
tt(t18_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C A) =>  ((r2_hidden D A) |  ((k8_relat_1 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B D)) (k2_xboole_0 C (k1_tarski D))) = (k2_xboole_0 C B)) ) ) ) ) ) ) ).
tt(t18_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_fscirc_1 A B C) (k7_fscirc_1 A B C))) ) ) ) ) ) ) ) ).
tt(t18_fscirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k1_xtuple_0 (k3_fscirc_2 C A B)) = k1_xboole_0)  &  ( ((k2_xtuple_0 (k3_fscirc_2 C A B)) = (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1))  &  ((k9_xtuple_0 (k2_xtuple_0 (k3_fscirc_2 C A B))) = (k4_finseq_2 k6_numbers k6_margrel1)) ) )  |  ( ((k1_card_1 (k1_xtuple_0 (k3_fscirc_2 C A B))) = 3)  &  ( ((k2_xtuple_0 (k3_fscirc_2 C A B)) = k4_facirc_1)  &  ((k9_xtuple_0 (k2_xtuple_0 (k3_fscirc_2 C A B))) = (k4_finseq_2 3 k6_margrel1)) ) ) ) ) ) ) ) ) ) ).
tt(t18_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( (F = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A G C)))  =>  ((k4_fsm_1 A B E G (k8_finseq_1 A (k12_finseq_1 A C) D)) = (k8_finseq_1 B (k12_finseq_1 B (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) B (u3_fsm_1 A B E) (k1_domain_1 (u1_struct_0 E) A G C))) (k4_fsm_1 A B E F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_2 D B A))  =>  (~  ((v1_fsm_2 D B) &  ((r2_fsm_2 B C D) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (~  ( (! [F:$i] :  ((m2_finseq_1 F B) =>  ( ((r1_xxreal_0 E (k2_nat_1 (k3_finseq_1 F) 1)) &  ((k1_funct_1 F 1) = C) )  => (r2_hidden (k1_funct_1 (k2_fsm_1 B D (u2_fsm_1 B D) F) E) (u1_fsm_2 B D))) ) )  &  (! [F:$i] :  ((m2_finseq_1 F B) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m2_subset_1 G k1_numbers k5_numbers))  =>  (~  ((r1_xxreal_0 G (k2_nat_1 (k3_finseq_1 F) 1)) &  ( ((k1_funct_1 F 1) = C)  &  ( (~ (r1_xxreal_0 E G))  & (r2_hidden (k1_funct_1 (k2_fsm_1 B D (u2_fsm_1 B D) F) G) (u1_fsm_2 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_3 D A C))  =>  ((r2_hidden B (k6_fsm_3 A C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) &  ((r2_hidden E (u1_fsm_3 A C D)) &  ((r2_hidden F (u2_fsm_3 A C D)) & (r4_rewrite3 A C D E B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) (k24_gfacirc1 A B C)) = (k9_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I)))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 2) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (B = k1_xboole_0) )  &  ((r2_hidden C (k9_xtuple_0 A)) &  ((k9_xtuple_0 (k3_relat_1 (k2_funcop_1 B C) A)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t18_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k1_numbers (k9_funct_2 C k1_numbers)) =>  ( ((r2_hidden A C) &  ((r2_hidden B C) &  ( (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 D F) = 1) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 D F) = k6_numbers) ) ) ) )  &  (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 E F) = k6_numbers) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 E F) = 1) ) ) ) ) ) ) )  =>  ( (A = B)  |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_funct_2 C k1_numbers (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) F D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G E))) (k8_funcsdom C)) =>  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k1_funct_1 (k4_relat_1 B) A) = A) ) ) ) ).
tt(t18_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((r2_relset_1 B B (k1_partfun1 B A A B D C) (k6_partfun1 B)) =>  ((k2_relset_1 B C) = B) ) ) ) ) ) ) ) ).
tt(t18_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k1_funct_3 (k3_relat_1 A B)) = (k3_relat_1 (k1_funct_3 A) (k1_funct_3 B))) ) ) ) ) ).
tt(t18_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k1_funct_4 B A)))) ) ) ) ).
tt(t18_funct_5,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 A))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 A)) ) ) ) ).
tt(t18_funct_6,ax, (! [A:$i] : (r1_tarski (k1_funct_6 A) A)) ).
tt(t18_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k9_finseq_1 A) (k3_finseq_2 B)) <=> (r2_hidden A B)) ) ) ).
tt(t18_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 A k1_numbers k1_numbers B) => (r2_funct_8 A k1_numbers k1_numbers (k37_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t18_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((r2_hidden (k2_xcmplx_0 D A) (k9_xtuple_0 C)) &  ((r2_hidden (k6_xcmplx_0 D A) (k9_xtuple_0 C)) &  ((r2_hidden (k2_xcmplx_0 D B) (k9_xtuple_0 C)) &  ((r2_hidden (k6_xcmplx_0 D B) (k9_xtuple_0 C)) &  ((k1_funct_1 C (k2_xcmplx_0 D A)) = (k1_funct_1 C (k6_xcmplx_0 D B))) ) ) ) ) ) ) )  =>  ( ((k2_xcmplx_0 A B) = k6_numbers)  |  ((v1_funct_9 C (k2_xcmplx_0 A B)) & (v2_funct_9 C)) ) ) ) ) ) ) ) ) ).
tt(t18_functor0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (~  ((k1_funct_1 D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 D E)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_funct_2 A B G (k8_funcop_1 B A E)) => (m1_functor0 (a_6_0_functor0 A B C D E F) A B G C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_altcat_2 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) &  ((v1_altcat_2 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ( ((v8_functor0 D B A) & (l2_functor0 D B A))  =>  ( ((g2_functor0 B A (u1_functor0 B A D) (u2_functor0 B A D)) = (k15_functor0 A B C))  =>  ((k13_functor0 B A B D C) = (k12_functor0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  => (r8_pboole (u1_struct_0 A) (k6_functor3 A B C E E D (k4_functor2 B C E)) (k4_functor2 A C (k1_functor3 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k2_fuzzy_1 A B (k5_fuzzy_1 A)) (k5_fuzzy_1 A)) &  ((r2_funct_2 A k1_numbers (k1_fuzzy_1 A B (k5_fuzzy_1 A)) B) &  ((r2_funct_2 A k1_numbers (k2_fuzzy_1 A B (k4_fuzzy_1 A)) B) & (r2_funct_2 A k1_numbers (k1_fuzzy_1 A B (k4_fuzzy_1 A)) (k4_fuzzy_1 A))) ) ) ) ) ) ) ).
tt(t18_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 (k1_fuzzy_2 A B C) D) & (r1_fuzzy_1 (k1_fuzzy_2 A C B) D))  => (r1_fuzzy_1 (k6_fuzzy_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t18_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  ( ((v5_relat_1 G (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [H:$i] :  (! [I:$i] :  ( ((r2_hidden H A) &  ((r2_hidden I C) &  (! [J:$i] :  ((r2_hidden J B) =>  ((r1_xxreal_0 (k1_seq_1 D (k4_tarski H J)) (k1_seq_1 E (k4_tarski H J))) & (r1_xxreal_0 (k1_seq_1 F (k4_tarski J I)) (k1_seq_1 G (k4_tarski J I)))) ) ) ) )  => (r1_xxreal_0 (k1_seq_1 (k4_fuzzy_4 A B C D F) (k4_tarski H I)) (k1_seq_1 (k4_fuzzy_4 A B C E G) (k4_tarski H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  (~  ((v3_fvaluat1 A) &  ( (~  (B = (k4_struct_0 A)) )  &  ((k3_funct_2 (u1_struct_0 A) k7_numbers C B) = k1_xxreal_0) ) ) ) ) ) ) ) ) ) ).
tt(t18_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 A (u1_struct_0 C))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 C) (k4_finseq_2 A (u1_struct_0 C))) =>  ( ((r2_hidden B (k2_finseq_1 A)) &  ( (D = (k1_funct_1 F B))  &  (E = (k1_funct_1 G B)) ) )  =>  ((k1_funct_1 (k4_fvsum_1 A C F G) B) = (k1_algstr_0 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (~ (v1_xboole_0 (k12_gate_1 A B C)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~ (v1_xboole_0 C)) ) ) )  & (v1_xboole_0 (k12_gate_1 A B C))) ) ) ) ) ) ).
tt(t18_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r4_gcd_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((v1_gcd_1 D A) &  ((k8_group_1 A B D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ((r1_xxreal_0 (k3_finseq_1 E) A) =>  ((k9_genealg1 D E F A B C) = (k8_genealg1 D E F B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_geomtrap A B C D E E F))  =>  ( (D = E)  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  ((r2_hidden A (k2_msafree2 (k7_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k7_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k7_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_gfacirc2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  =>  ( ((k5_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k25_gfacirc1 A B C)))  &  ( ((k6_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k25_gfacirc1 A B C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k26_gfacirc1 A B C)))  &  ((k7_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k21_gfacirc1 A B C)) ) ) ) ) ) ) ).
tt(t18_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v3_glib_000 A) <=>  (! [B:$i] :  (! [C:$i] :  (~ (r1_glib_000 A B B C)) ) ) ) ) ) ).
tt(t18_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_001 A C D B) =>  ((m1_subset_1 C (k6_glib_000 A)) & (m1_subset_1 D (k6_glib_000 A))) ) ) ) ) ) ) ) ).
tt(t18_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (r2_hidden B (k2_glib_002 A B))) ) ) ) ).
tt(t18_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_glib_003 A B))) &  ((k9_glib_003 A C) = (k1_glib_003 k1_numbers (k9_glib_003 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t18_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((r1_tarski (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C))) (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) D)))) & (r1_tarski (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)) (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_glib_005 A B C D) &  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  (~  ((r1_glib_001 A C D E) & (r5_glib_005 A B E)) ) ) ) )  => (r2_glib_005 A B C D)) ) ) ) ) ) ) ).
tt(t18_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( ((k1_matrix_1 D) = (k2_nat_1 A 1))  &  ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k4_finseq_1 D))) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 D 1) C B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C (k2_nat_1 B 1)))  & (r2_hidden 1 (k2_finseq_1 (k1_matrix_1 D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_goboard2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 (k1_seq_1 (k2_goboard1 B) C) (k1_seq_1 (k2_goboard1 B) A))) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) (k1_matrix_1 (k2_goboard2 B)))))) ) ) ) ) ).
tt(t18_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_goboard5 C A B))) ) ) ) ) ) ) ) ) ).
tt(t18_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers k6_numbers)) = (a_1_4_goboard6 A)) ) ) ).
tt(t18_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B))) ) ) ) ) ) ) ) ).
tt(t18_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 1))) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 2))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k2_nat_1 C 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t18_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v2_goboard1 A) =>  ((k1_goboard5 A k6_numbers) = (a_1_9_gobrd11 A)) ) ) ) ).
tt(t18_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 E) (k16_matrix_1 F)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) )  => (r1_tarski (k3_goboard5 F (k7_nat_d C 1) D) (k3_goboard5 E (k7_nat_d A 1) B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_goboard9 A)) <=>  ( (~ (r2_hidden B (k3_topreal1 2 A)))  &  (~ (r2_hidden B (k2_goboard9 A))) ) ) ) ) ) ) ).
tt(t18_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v4_card_3 A) => (v4_card_3 (k9_qc_lang1 A))) ) ) ).
tt(t18_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ((r1_graph_1 A B C) =>  ((r4_graph_1 B A) & (r4_graph_1 C A)) ) ) ) ) ) ) ) ).
tt(t18_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ((k10_xtuple_0 (k3_graph_2 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(t18_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ((v5_graph_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_graph_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ( (~ (v1_xboole_0 D))  &  ((r1_graph_2 A E D) &  ( ((k1_funct_1 E 1) = B)  &  ((k1_funct_1 E (k3_finseq_1 E)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) )  =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  ( (C = B)  => (v1_graph_4 C A)) ) ) ) ) ) ) ).
tt(t18_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) &  ((v1_graph_4 D A) & (m2_graph_1 D A)) )  =>  ( ( (D = (k8_finseq_1 (u4_struct_0 A) B C))  &  ((r1_xxreal_0 1 (k3_finseq_1 B)) & (r1_xxreal_0 1 (k3_finseq_1 C))) )  =>  ( ((k1_funct_1 (u1_graph_1 A) (k1_funct_1 D 1)) = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 D (k3_finseq_1 D))))  |  ( (~ (r2_hidden (k1_funct_1 (u1_graph_1 A) (k1_funct_1 D 1)) (k2_graph_5 A C)))  &  (~ (r2_hidden (k1_funct_1 (u2_graph_1 A) (k1_funct_1 D (k3_finseq_1 D))) (k2_graph_5 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  (~  ((k1_seq_1 (k2_graphsp B C D E) A) = (k1_seq_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_grcat_1 D B C) =>  (! [E:$i] :  ((m1_grcat_1 E A B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( (D = (g1_grcat_1 B C F))  &  (E = (g1_grcat_1 A B G)) )  =>  ((k14_grcat_1 A B C D E) = (g1_grcat_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v1_gr_cy_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((v7_ordinal1 D) &  (C = (k5_group_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_gr_cy_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v15_algstr_0 C) &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) ) )  =>  ( ( ((k7_group_1 B) = A)  &  ( ((k7_group_1 C) = A)  & (v1_int_2 A)) )  => (r2_group_6 B C)) ) ) ) ) ) ) ).
tt(t18_gr_cy_3,ax, ((k1_gr_cy_3 2) = 3) ).
tt(t18_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) => (m2_finseq_1 B (k1_group_3 A))) ) ) ) ).
tt(t18_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r10_polyred A B C E D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (~  ((r2_hidden E (k2_groeb_1 A B C (k7_ideal_1 (k11_polynom1 A C) D))) &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (~  ((r2_hidden F (k2_groeb_1 A B C D)) & (r3_pre_poly A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  => (r2_hidden (k3_groeb_2 A B C E F) (k7_ideal_1 (k11_polynom1 A C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k2_groeb_3 A B C (k2_polynom1 (k15_pre_poly A) B C)) C) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k2_groeb_3 A B C (k1_subset_1 (k15_pre_poly A))) (k7_polynom1 A B))) ) ) ) ) ) ).
tt(t18_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k1_group_11 A B C) (k2_group_11 A B C))) ) ) ) ) ) ).
tt(t18_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A C B))  <=>  ((k2_group_1 A (k6_algstr_0 A B C)) = (k6_algstr_0 A (k2_group_1 A B) (k2_group_1 A C))) ) ) ) ) ) ) ) ).
tt(t18_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_2 A (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) = (k6_domain_1 (u1_struct_0 A) (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t18_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_3 A B C) = (k1_group_1 A))  =>  (B = (k1_group_1 A)) ) ) ) ) ) ) ) ).
tt(t18_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_tarski (k10_xtuple_0 C) (k8_group_2 A B)) => (r1_struct_0 B (k3_group_4 A C))) ) ) ) ) ) ) ).
tt(t18_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_5 A B C) = (k6_algstr_0 A (k2_group_3 A (k2_group_1 A C) B) C))  &  ((k2_group_5 A B C) = (k6_algstr_0 A (k2_group_1 A B) (k2_group_3 A B C))) ) ) ) ) ) ) ) ).
tt(t18_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k5_group_6 A B)) (u1_struct_0 (k5_group_6 A B))) (u1_struct_0 (k5_group_6 A B)) (k2_zfmisc_1 (k15_group_2 A B) (k15_group_2 A B)) (k15_group_2 A B) (u2_algstr_0 (k5_group_6 A B)) (k4_group_6 A B))) ) ) ) ).
tt(t18_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_group_7 (k10_finseq_1 A B)) & (v3_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ) ) ) ) ) ) ) ).
tt(t18_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ( ((k11_group_2 A E (k14_group_2 A D B)) = (k11_group_2 A E (k14_group_2 A D C)))  |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k11_group_2 A E (k14_group_2 A D B))) & (r2_hidden F (k11_group_2 A E (k14_group_2 A D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ( (! [E:$i] :  ((m1_group_9 E A B) =>  ( (E = (k17_group_9 A B C D))  =>  ((u1_struct_0 E) = (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) ) )  &  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ( ((u1_struct_0 E) = (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D)))  =>  (E = (k17_group_9 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_group_3 C B) & (m1_group_2 C B))  =>  ( ((v2_group_10 C A) & (v2_group_10 (k5_group_6 B C) A))  => (v2_group_10 B A)) ) ) ) ) ) ) ).
tt(t18_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k6_hahnban1 A B (k1_algstr_0 A C D) E) (k3_hahnban1 A B (k6_hahnban1 A B C E) (k6_hahnban1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v3_hahnban B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_algstr_0 A C)) = (k1_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ).
tt(t18_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ( (? [C:$i] : (r1_hallmar1 A B C))  => (v1_hallmar1 B A)) ) ) ) ) ).
tt(t18_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( ( (C = B)  & (v2_compts_1 C (k3_pcomps_1 A)))  => (v6_tbsp_1 B A)) ) ) ) ) ) ) ).
tt(t18_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  &  ((r1_xboole_0 (k14_glib_001 A B) (k14_glib_001 A C)) & (r1_tarski (k9_subset_1 (k6_glib_000 A) (k13_glib_001 A B) (k13_glib_001 A C)) (k2_tarski (k3_glib_001 A B) (k4_glib_001 A B)))) )  =>  ((v1_glib_001 B A) |  ((v1_glib_001 C A) |  ( ((r2_hidden (k3_glib_001 A B) (k13_glib_001 A C)) &  (~  ((k3_glib_001 A B) = (k4_glib_001 A C)) ) )  | (v5_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k3_hahnban1 k1_complfld A B C)) (k3_hahnban1 k1_complfld A (k1_hermitan A B) (k1_hermitan A C)))) ) ) ) ) ) ).
tt(t18_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden D (k7_heyting1 A B C)) &  (! [E:$i] :  ((m2_funct_2 E (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k9_funct_2 (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) =>  (~  ((r1_tarski (k8_setwiseo (k7_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) E B) C) &  (D = (k6_normform (k7_normform A) A B (k6_funcop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A) (k5_heyting1 A) E (k6_funct_3 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k2_lattice2 (k4_partfun1 A B) (k5_substlat A B) C (k8_heyting2 A B)) = (k10_setwiseo (k4_partfun1 A B) (k4_partfun1 A B) C (k11_setwiseo (k4_partfun1 A B)))) ) ) ) ) ) ).
tt(t18_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r1_tarski (k2_heyting3 A B) (k3_heyting3 C B))) ) ) ) ) ) ) ).
tt(t18_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 D A C) &  ((r1_taylor_1 E A C) & (r1_xxreal_0 B A)) )  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers D E) C) B) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 D C) B) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 E C) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~  (C = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k5_hilbasis A B C)) = (k2_nat_1 B 1)) )  &  ( ( (C = (k4_struct_0 A))  =>  ((k1_algseq_1 A (k5_hilbasis A B C)) = k6_numbers) )  & (r1_xxreal_0 (k1_algseq_1 A (k5_hilbasis A B C)) (k2_nat_1 B 1))) ) ) ) ) ) ) ) ).
tt(t18_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 B B)) k6_hilbert1)) ) ) ) ).
tt(t18_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ( ((k7_finseq_1 A B) = (k7_finseq_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k15_pralg_1 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t18_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k2_normsp_1 A B C) D) (k2_normsp_1 A (k3_polynom5 A B D) (k3_polynom5 A C D)))) ) ) ) ) ) ) ) ).
tt(t18_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_idea_1 A B) &  ((r1_idea_1 A C) &  ((k7_idea_1 A B) = (k7_idea_1 A C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t18_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~  (D = k6_numbers) )  => (r2_hidden (k2_binom A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t18_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A C D K) &  ((r1_collsp A F G K) &  ((r1_collsp A D E I) &  ((r1_collsp A G H I) &  ((r1_collsp A C E J) &  ((r1_collsp A F H J) &  ((r1_collsp A B C F) &  ((r1_collsp A B D G) & (r1_collsp A B E H)) ) ) ) ) ) ) )  =>  ( (B = F)  |  ( (C = F)  |  ( (B = G)  |  ( (D = G)  |  ( (B = H)  |  ( (E = H)  |  ((r1_collsp A B C D) |  ((r1_collsp A B C E) |  ((r1_collsp A B D E) | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k3_incproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k3_incproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 (k3_incproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 (k3_incproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 (k3_incproj A))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k3_incproj A))) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 (k3_incproj A))) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 (k3_incproj A))) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 (k3_incproj A))) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 (k3_incproj A))) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 (k3_incproj A))) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 (k3_incproj A))) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 (k3_incproj A))) =>  (! [S:$i] :  ((m1_subset_1 S (u2_incsp_1 (k3_incproj A))) =>  (! [T:$i] :  ((m1_subset_1 T (u2_incsp_1 (k3_incproj A))) =>  (~  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) B C D) L) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) B F E) M) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) B H G) N) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) H F K) O) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) H I D) P) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) F J D) Q) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) K E G) R) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) C I G) S) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) C J E) T) &  ((r1_zfmisc_1 L M N) &  ( (~  (B = D) )  &  ( (~  (B = F) )  &  ( (~  (B = H) )  &  ( (~  (B = C) )  &  ( (~  (B = E) )  &  ( (~  (B = G) )  &  ( (~  (D = C) )  &  ( (~  (F = E) )  &  ( (~  (H = G) )  &  (! [U:$i] :  ((m1_subset_1 U (u2_incsp_1 (k3_incproj A))) =>  (~ (r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) I J K) U)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) &  ( (~ (r1_incsp_1 A D E))  & (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m4_index_1 D (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (k13_index_1 A B C)) => (r1_funct_2 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (u4_struct_0 D) C (k9_index_1 A (k13_index_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t18_instalg1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m1_instalg1 B A) =>  (! [C:$i] :  ((l1_msualg_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A C D E) => (r3_pua2mss1 B C (k5_relat_1 D (u1_struct_0 B)) (k5_relat_1 E (u4_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r2_int_1 A B C) & (r2_int_1 D E C))  => (r2_int_1 (k3_xcmplx_0 A D) (k3_xcmplx_0 B E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (r1_int_1 A (k2_int_2 A B))) ) ) ) ).
tt(t18_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_int_1 (k3_int_2 B A) C) &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B D) C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k3_int_2 B A) = 1)  =>  ((r1_xxreal_0 A 2) |  ((r1_int_5 B A) |  ((k4_nat_d (k1_newton B (k3_nat_d (k7_nat_d A 1) 2)) A) = (k6_xcmplx_0 A 1)) ) ) ) ) ) ) ) ).
tt(t18_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k3_int_2 A (k3_int_2 B C)) = (k3_int_2 (k3_int_2 A B) C)) ) ) ) ) ) ) ).
tt(t18_int_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k5_card_1 (k1_int_7 A)) = (k6_xcmplx_0 A 1)) ) ) ) ).
tt(t18_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k8_real_1 2 k32_sin_cos)))  =>  ((k2_integra5 A (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)) = k32_sin_cos) ) ) ) ).
tt(t18_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_sin_cos9) (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k41_valued_1 k1_numbers k1_numbers D)) A)))) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 E G) = 1)  &  ( ((k1_seq_1 D G) = (k12_binop_2 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D G))) ) ) ) ) ) )  &  ( (F = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) )  =>  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_sin_cos9)) (k4_seq_4 B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_sin_cos9)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k30_sin_cos (k1_partfun2 k1_numbers C)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) &  ((r1_tarski C (k1_relset_1 k1_numbers k30_sin_cos)) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t18_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t18_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers D)) &  ((r1_integr15 A C D) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) D C) A)) )  =>  ((r1_integr15 A C (k9_integr15 A B k1_numbers D)) &  ((k11_integr15 A C (k9_integr15 A B k1_numbers D)) = (k9_euclid A (k11_integr15 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integr16,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ((r2_relset_1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers (k25_valued_1 k1_numbers k2_numbers B A)) (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers B) (k3_complex1 A)) (k26_valued_1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers B) (k4_complex1 A)))) & (r2_relset_1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers (k25_valued_1 k1_numbers k2_numbers B A)) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers B) (k3_complex1 A)) (k26_valued_1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers B) (k4_complex1 A))))) ) ) ) ) ).
tt(t18_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (C = (k1_rcomp_1 E D))  & (r1_tarski C (k1_relset_1 k1_numbers B)))  =>  ((k4_algstr_0 A (k5_integr18 A C B)) = (k6_integr18 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) => (r2_relset_1 k1_numbers k1_numbers (k1_nfcont_4 A k1_numbers (k2_partfun1 k1_numbers (k1_euclid A) C B)) (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 A k1_numbers C) B))) ) ) ) ) ) ) ).
tt(t18_integra1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (r1_xboole_0 C (k1_relset_1 B (k7_rfunct_1 B B))))  =>  ((k1_rvsum_1 (k2_partfun1 B k1_numbers (k7_rfunct_1 B B) C)) = (k1_seq_4 1)) ) ) ) ) ) ) ).
tt(t18_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((k1_rvsum_1 (k26_valued_1 B k1_numbers (k2_partfun1 B k1_numbers D C) A)) = (k1_integra2 (k1_rvsum_1 (k2_partfun1 B k1_numbers D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t18_integra3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers D B)) & (r2_hidden A (k4_finseq_1 C)))  => (r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 (k2_partfun1 B k1_numbers D (k2_integra1 B C A)))) (k4_seq_4 (k1_rvsum_1 D)))) ) ) ) ) ) ) ) ) ).
tt(t18_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_seq_2 (k2_partfun1 A k1_numbers C A)) => (v4_xxreal_2 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B)))) ) ) ) ) ) ).
tt(t18_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  (! [E:$i] :  ( ((r1_tarski B E) &  ((r2_fdiff_1 A E) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 A E) B)) &  ( ((k5_seq_4 B) = (k5_seq_4 C))  &  ( ((k4_seq_4 C) = (k5_seq_4 D))  &  ((k4_seq_4 D) = (k4_seq_4 B)) ) ) ) ) )  =>  ((r1_tarski C B) &  ((r1_tarski D B) &  ((k2_integra5 B (k2_fdiff_1 A E)) = (k7_real_1 (k2_integra5 C (k2_fdiff_1 A E)) (k2_integra5 D (k2_fdiff_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A D) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A D))) & (r1_tarski (k3_integra5 A D) (k9_xtuple_0 E))) ) ) ) )  =>  ((r1_integra5 (k3_integra5 B C) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 B C))) & (r1_tarski (k3_integra5 B C) (k9_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) C) &  ((r1_integra7 C D E) &  ((r1_integra5 (k3_integra5 A B) E) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B)))) ) ) )  =>  ((k1_seq_1 D B) = (k7_real_1 (k4_integra5 A B E) (k1_seq_1 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_integra8,ax, ((k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 k6_numbers) = 1) ).
tt(t18_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k7_real_1 A 1)) (k10_real_1 1 (k7_real_1 A 1))) k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k7_real_1 A 1)) (k10_real_1 1 (k7_real_1 A 1))) k1_numbers) B) = (k5_prepower B A)) ) ) ) ) ) ).
tt(t18_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k3_interva1 A B C) = (k2_interva1 A (k9_subset_1 A (k5_interva1 A B) (k5_interva1 A C)) (k9_subset_1 A (k6_interva1 A B) (k6_interva1 A C)))) ) ) ) ) ) ) ).
tt(t18_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((r2_hidden A k8_intpro_1) => (r2_hidden (k3_intpro_1 B A) k8_intpro_1)) ) ) ) ) ).
tt(t18_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 C) = A)  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A D))  =>  ((k1_seq_1 B D) = (k1_seq_1 C (k2_nat_1 D 1))) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 A D) =>  ((k1_seq_1 B D) = k6_numbers) ) ) ) ) )  =>  ((v1_series_1 B) &  ((k4_series_1 B) = (k18_rvsum_1 C)) ) ) ) ) ) ) ) ) ).
tt(t18_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  => (r1_isocat_1 (k8_cat_2 (k8_cat_2 A B) C) (k8_cat_2 A (k8_cat_2 B C)))) ) ) ) ) ) ).
tt(t18_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 C) (k6_nattra_1 B C (k12_cat_2 A B C D E)) (k4_isocat_2 A B C D (k4_cat_1 A E)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v6_tops_1 C A) &  ((r1_tarski C B) & (r1_tarski B (k2_pre_topc A C))) ) ) ) ) ) ) ) ) ).
tt(t18_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_graph_4 (k4_jgraph_1 A B) (k1_jgraph_1 A)) =>  ( ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B)))  |  ((v2_funct_1 B) &  (~  ((k3_finseq_1 B) = 1) ) ) ) ) ) ) ) ) ).
tt(t18_jgraph_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ( (A = a_0_1_jgraph_2)  &  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) B) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2)))) )  =>  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))  &  ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ) ).
tt(t18_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_1_jgraph_3) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t18_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 B))  &  (~  ( ( ((r1_xxreal_0 B (k13_complex1 (k18_euclid A) (k12_euclid A))) & (r1_xxreal_0 (k17_euclid A) k6_numbers))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))))) (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))))) ) )  &  ( ((r1_xxreal_0 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) & (r1_xxreal_0 (k17_euclid A) k6_numbers))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))))) (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 (k18_euclid B) k6_numbers))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  & (r1_xxreal_0 (k18_euclid C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = a_0_0_jgraph_6)  & (r1_jordan17 E A B C D))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc G k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 G) &  ((v5_pre_topc H k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 H) &  ( (F = a_0_1_jgraph_6)  &  ( ((k1_funct_1 G k6_numbers) = A)  &  ( ((k1_funct_1 G 1) = C)  &  ( ((k1_funct_1 H k6_numbers) = B)  &  ( ((k1_funct_1 H 1) = D)  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H) F) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 E (k17_euclid C)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) (k17_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((r1_jordan2c 2 C B) => (r1_xboole_0 B (k3_topreal1 2 (k1_jordan9 C A)))) ) ) ) ) ) ) ).
tt(t18_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 A (k3_finseq_1 B)) => (v1_convex1 (k1_goboard5 B A) (k15_euclid 2))) ) ) ) ) ).
tt(t18_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_xboole_0 (k2_jordan2c 2 A) (k3_goboard9 (k1_jordan13 A B)))) ) ) ) ) ).
tt(t18_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k1_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_jordan5c A D E B C) & (v1_xboole_0 (k5_jordan6 A D E B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A D E B C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A E B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k1_jordan2c 2 B)) =>  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid (k2_jordan18 A B))))  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan18 A B)) (k18_euclid A))) ) ) ) ) ) ) ).
tt(t18_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 E))) ) ) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C A)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan1b,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (r1_tarski (k3_goboard5 (k1_jordan8 A k6_numbers) 2 2) (k1_jordan2c 2 A))) ) ) ).
tt(t18_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ( (~ (r1_xxreal_0 G (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) 1 2))))  &  ( (~ (r1_xxreal_0 G (k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) 2 1))))  &  ((r2_hidden E (k3_goboard5 (k1_jordan8 A B) C D)) &  ((r2_hidden F (k3_goboard5 (k1_jordan8 A B) C D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k3_real_1 C 1) (k3_finseq_1 (k1_jordan8 A B))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k3_real_1 D 1) (k1_matrix_1 (k1_jordan8 A B))) & (r1_xxreal_0 (k8_real_1 2 G) (k1_topreal6 2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k18_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t18_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_sprect_2 (k1_jordan9 B A) (k2_jordan1e B A))) ) ) ) ).
tt(t18_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k2_jordan1e B A) = (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t18_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v3_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_xxreal_0 (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A))) (k1_matrix_1 A))) ) ).
tt(t18_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k2_nat_1 D 1)))  &  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E)) = (k8_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k22_pscomp_1 B) A))  =>  ((k22_pscomp_1 A) = (k22_pscomp_1 B)) ) ) ) ) ) ).
tt(t18_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_jordan2c A (k2_struct_0 (k15_euclid A))) = (k1_struct_0 (k15_euclid A))) ) ) ).
tt(t18_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) C D A) &  ((r2_hidden E A) &  (B = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k1_tarski E))) ) )  =>  ( (E = C)  |  ( (E = D)  |  ( (~ (v2_connsp_1 B (k1_pre_topc (k15_euclid 2) A)))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)))))) )  =>  (~  ((v5_pre_topc F k5_topmetr (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ((k1_funct_1 F 1) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k8_pscomp_1 A) = (k8_pscomp_1 (k8_jordan6 A))) ) ) ).
tt(t18_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k18_euclid (k2_jordan21 A)) (k18_euclid (k2_jordan21 (k3_topreal1 2 (k1_jordan9 A B)))))) ) ) ) ) ).
tt(t18_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v3_jordan23 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  (B = (k1_funct_1 A C)) ) ) ) )  =>  ((r1_xxreal_0 C 1) |  ((k2_nat_1 (k1_jordan3 A B) 1) = C) ) ) ) ) ) ) ) ) ).
tt(t18_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k2_finseq_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B D) = (k7_partfun1 k1_numbers D C)) ) ) )  => (v5_pre_topc B (k15_euclid A) k3_topmetr)) ) ) ) ) ) ) ).
tt(t18_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k3_topreal1 2 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k1_nat_1 D 1) (k3_finseq_1 B)) &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k1_jordan3 A C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) C))) ) ) )  => (r1_tarski (k2_topreal1 2 B D) (k2_topreal1 2 A D))) ) ) ) ) ) ) ) ) ).
tt(t18_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_finseq_6 A B C D) = (k4_finseq_5 A (k3_finseq_6 A B D C))) ) ) ) ) ) ) ) ) ).
tt(t18_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))  =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( ( (H = F)  &  ( (I = G)  &  ((v5_pre_topc E (k4_topmetr A B) (k4_topmetr C D)) &  ((v2_funct_1 E) &  ((v2_compts_1 H k3_topmetr) &  ( ((k1_funct_1 E A) = C)  &  ( ((k1_funct_1 E B) = D)  &  ((k7_relset_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) E F) = G) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((k1_funct_1 E (k4_seq_4 (k1_weierstr H))) = (k4_seq_4 (k1_weierstr I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (v4_topreal1 A))  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ((k1_jordan3 (k2_jordan3 A B) B) = 1) ) ) ) ) ) ) ).
tt(t18_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) C D A) & (v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)))  =>  ((r1_xboole_0 A B) |  ( ((k1_jordan5c A B C D) = (k2_jordan5c A B D C))  &  ((k2_jordan5c A B C D) = (k1_jordan5c A B D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_5_jordan5d A))  =>  (B = (k7_relat_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k3_topreal1 2 A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t18_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r1_jordan5c A B C D E))  => (r1_jordan5c A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) &  ((v5_pre_topc F k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 F) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) = A)  &  ( ((k1_funct_1 F k6_numbers) = B)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 F G) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  ( ((k1_funct_1 F H) = E)  &  ((r1_xxreal_0 k6_numbers H) &  ((r1_xxreal_0 H 1) & (r1_xxreal_0 G H)) ) ) ) ) ) ) ) ) ) ) )  => (r1_jordan5c A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_jordan8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) => (r1_xboole_0 (k3_goboard5 (k1_jordan8 A C) k6_numbers B) A)) ) ) ) ) ) ) ).
tt(t18_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((k3_goboard5 C A B) = (a_3_0_jordan9 A B C)) ) ) ) ) ) ) ) ).
tt(t18_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (A = (k1_jordan7 A (k18_pscomp_1 A) (k18_pscomp_1 A))) ) ) ).
tt(t18_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_topreal9 C D A) (k1_topreal9 C D B))) ) ) ) ) ) ) ) ) ).
tt(t18_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v5_ordinal1 E)) )  =>  ( ((v4_ordinal1 D) &  ( ((k9_xtuple_0 E) = D)  &  (! [F:$i] :  ((v3_ordinal1 F) =>  ((r2_hidden F D) =>  ((k1_funct_1 E F) = (k4_knaster A B C F)) ) ) ) ) )  =>  ( (D = k1_xboole_0)  |  ((k4_knaster A B C D) = (k16_lattice3 A (k10_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_kurato_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k1_funct_1 A (k2_nat_1 B 1)) (k1_funct_1 A B))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(t18_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1))) = (k4_subset_1 k1_numbers (k2_rcomp_1 4 5) (k2_rcomp_1 5 k1_xxreal_0))) ).
tt(t18_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) D E) = (k4_subset_1 (u1_struct_0 A) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C E))) ) )  => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k1_kurato_2 A B) (k1_kurato_2 A C)) (k1_kurato_2 A D))) ) ) ) ) ) ) ) ) ).
tt(t18_lang1,ax, (! [A:$i] :  ((v1_relat_1 A) => (r1_tarski A (k18_finseq_1 A))) ) ).
tt(t18_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  ((k3_laplace C A B D E (k9_matrix_1 D E C)) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((u1_struct_0 (k10_group_2 A B C)) = (k3_xboole_0 (k1_funct_1 (k1_latsubgr A) B) (k1_funct_1 (k1_latsubgr A) C))) ) ) ) ) ) ) ).
tt(t18_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B))) =>  ( ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) A) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_orders_2 (k1_latsum_1 A B) C D) & (r2_hidden C (u1_struct_0 B))) )  => (r2_hidden D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t18_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_setwiseo (u2_lattices A) (u1_struct_0 A)) =>  ((k5_lattices A) = (k4_binop_1 (u1_struct_0 A) (u2_lattices A))) ) ) ) ).
tt(t18_lattice3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A B (k13_lattice3 A B C)) = B) ) ) ) ) ) ) ).
tt(t18_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v14_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  ((v2_funct_2 C (u1_struct_0 A)) =>  ((v14_lattices A) & (r2_lattice4 B A C)) ) ) ) ) ) ) ) ).
tt(t18_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ( ((v1_lattice5 C A B) & (v3_lattice5 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) =>  ((r3_orders_2 B (k3_lattice5 A B C (k4_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k5_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D)) (k13_lattice3 B (k6_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D) (k7_mcart_1 A A (u1_struct_0 B) (u1_struct_0 B) D))) => (v3_lattice5 (k6_lattice5 A B C D) (k5_lattice5 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_lattice6 B A) => (v3_waybel_6 (k4_lattice3 A B) (k3_lattice3 A))) ) ) ) ) ).
tt(t18_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  ((k5_lattice8 A B C D k1_xboole_0) = C) ) ) ) ) ) ) ) ) ).
tt(t18_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattices A (k6_lattices A) B) = (k6_lattices A)) ) ) ) ) ).
tt(t18_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) => (v2_funct_1 (k5_lexbfs A B C))) ) ) ) ) ) ).
tt(t18_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k2_fuzzy_1 A B C) = (k13_lattice3 (k4_lfuzzy_0 A) (k6_lfuzzy_0 A B) (k6_lfuzzy_0 A C))) ) ) ) ) ) ) ).
tt(t18_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (v2_lfuzzy_1 (k2_lfuzzy_1 (k2_zfmisc_1 A A) B (k2_fuzzy_4 A A B)) A)) ) ) ) ).
tt(t18_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) & (v2_comseq_2 B))  => (v1_limfunc1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t18_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A))) => (r1_xxreal_0 E (k1_seq_1 C F))) ) ) ) ) ) ) ) ) )  | (r2_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t18_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r2_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r2_limfunc3 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r3_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r3_limfunc3 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r3_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ((r3_limfunc3 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r2_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r6_limfunc2 B A) &  ((v8_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  => (r6_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t18_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  ( ((r1_lmod_6 A B C) & (r1_lmod_6 A C D))  => (r1_lmod_6 A B D)) ) ) ) ) ) ) ) ) ).
tt(t18_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (m1_subset_1 (k14_lmod_7 A B D C) (u1_struct_0 (k17_lmod_7 A B D)))) ) ) ) ) ) ) ) ).
tt(t18_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k8_lopban_1 A B)) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(t18_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_seq_1 (k15_lopban_1 A A) (k6_partfun1 (u1_struct_0 A))) = 1) ) ) ).
tt(t18_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_lopban_3 B A) & (v1_lopban_3 C A))  =>  ((v1_lopban_3 (k3_normsp_1 A B C) A) &  ((k1_lopban_3 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k1_lopban_3 A B) (k1_lopban_3 A C))) ) ) ) ) ) ) ) ) ).
tt(t18_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k6_lopban_4 D A B C) (k5_normsp_1 A (k5_lopban_4 D A B C) (k10_real_1 1 (k3_newton D))))) ) ) ) ) ) ) ) ).
tt(t18_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden C (k1_funct_1 (k8_lopclset A) B)) <=>  ((v1_filter_0 C A) & (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(t18_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_rfunct_3 D C k1_numbers (k3_rfunct_3 C k1_numbers)) =>  ((k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) A (k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) B D)) = (k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) (k8_real_1 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t18_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  => (r2_relset_1 A k1_numbers (k26_valued_1 A k1_numbers (k2_mesfun6c D A (k56_valued_1 A k1_numbers B)) (k4_power (k18_complex1 C) D)) (k2_mesfun6c D A (k56_valued_1 A k1_numbers (k26_valued_1 A k1_numbers B C))))) ) ) ) ) ) ) ) ) ).
tt(t18_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k3_hilbert1 (k6_ltlaxio1 A) (k4_ltlaxio1 A (k2_ltlaxio1 (k6_ltlaxio1 A)))))) = 1) ) ) ) ) ) ) ).
tt(t18_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A B C)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t18_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v1_funct_1 (k16_funcop_1 (k6_finseq_1 A) B)) &  ( (~ (v1_xboole_0 (k16_funcop_1 (k6_finseq_1 A) B)))  &  ((v2_margrel1 (k16_funcop_1 (k6_finseq_1 A) B)) &  ((v3_margrel1 (k16_funcop_1 (k6_finseq_1 A) B) A) & (m1_subset_1 (k16_funcop_1 (k6_finseq_1 A) B) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) ) ) ) ) ) ).
tt(t18_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_rusub_4 A B (k1_mathmorp A D C)) = (k1_mathmorp A D (k6_rusub_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t18_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r1_matrix10 B (k2_matrix10 A C)) => (v2_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t18_matrix11,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) &  ((v3_funct_2 C (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)))))) ) )  =>  (~  ( ((k1_funct_1 C B) = B)  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (~  ((k2_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) C A) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) B B) =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k4_matrix_6 B D E (k4_matrix12 B B D (k12_matrix_1 D B) A C)) = (k4_matrix12 B B D E A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  (~  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 E) (k10_xtuple_0 F)) (k2_matrix_1 D)) &  ( ( (B = k6_numbers)  =>  (C = k6_numbers) )  &  ( ( (C = k6_numbers)  =>  (B = k6_numbers) )  &  (~  ((k4_matrix_1 A (k1_matrix13 A D B C E F)) = (k1_matrix13 A (k4_matrix_1 A D) C B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ( ((v1_matrix_6 C A B) &  (D = (k5_matrix_6 A B C)) )  =>  ( ((k4_matrix_6 A B D C) = (k12_matrix_1 B A))  &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) ) )  &  ( ( ((k4_matrix_6 A B D C) = (k12_matrix_1 B A))  &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) )  =>  ((v1_matrix_6 C A B) &  (D = (k5_matrix_6 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_matrix_1 F E A B) =>  (! [G:$i] :  ((m1_matrix_1 G E A C) =>  (! [H:$i] :  ((m2_finseq_1 H E) =>  (! [I:$i] :  ((m2_finseq_1 I E) =>  ( ( ((k3_finseq_1 H) = (k1_matrix_1 F))  &  ((k3_finseq_1 I) = (k1_matrix_1 G)) )  =>  ((k3_matrix11 D A (k2_nat_1 (k1_matrix_1 F) (k1_matrix_1 G)) E (k1_matrix15 E A B C F G) (k8_finseq_1 E H I)) = (k1_matrix15 E A B C (k3_matrix11 D A B E F H) (k3_matrix11 D A C E G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m1_matrix_1 D B A A) =>  ((r2_matrix16 B D C) =>  ((r1_xxreal_0 A k6_numbers) |  (C = (k9_matrix_1 B D 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (m1_matrix_1 (k10_finseq_1 (k12_finseq_1 A B) (k12_finseq_1 A C)) A 2 1)) ) ) ) ) ) ).
tt(t18_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k11_matrix_2 (k12_matrix_2 A)) = A) ) ) ).
tt(t18_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k4_matrix_3 B (k12_matrix_1 B A) C) = C) ) ) ) ) ) ) ).
tt(t18_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A D B) (k1_matrix_4 A D C)) = (k1_matrix_4 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k5_matrix_5 B A) = B) ) )  =>  (A = (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ) ) ).
tt(t18_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ( (C = (k4_matrix_6 A B C D))  & (v1_matrix_6 C A B))  => (r1_matrix_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t18_matrix_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) => (m1_matrix_2 (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B) (k12_matrix_2 A))) ) ) ) ).
tt(t18_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_6 C A B) => (v2_matrix_6 (k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) C) A B)) ) ) ) ) ) ) ).
tt(t18_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden (k7_finseq_1 B C) (k12_matrix_2 A)) => (r2_hidden (k7_finseq_1 C B) (k12_matrix_2 A))) ) ) ) ) ) ) ).
tt(t18_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 (k5_matrixc1 A B))) =>  ((k9_matrix_5 (k5_matrixc1 A B) C) = (k5_binop_2 (k9_matrix_5 A C) (k9_matrix_5 B C))) ) ) ) ) ) ) ) ).
tt(t18_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k11_matrixj1 A (k3_matrixj1 A B C)) = (k8_finseq_1 k5_numbers (k11_matrixj1 A B) (k11_matrixj1 A C))) ) ) ) ) ) ) ).
tt(t18_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_4 D B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 E C C) &  ((v1_mod_2 E B C C) &  ((v2_matrixj2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A)))) &  ((v2_matrixj2 F B (k3_ranknull B C C (k1_vectsp11 C E A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))))))) ) )  =>  ( ((r1_funct_2 (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C E A))) (u1_struct_0 C) F (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C E A)) E)) & (r1_xxreal_0 A (k9_matrixj2 B C E)))  =>  ((k2_xcmplx_0 (k9_matrixj2 B (k3_ranknull B C C (k1_vectsp11 C E A)) F) A) = (k9_matrixj2 B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ((k2_matrix_1 (k6_matrix_3 A C B)) = (k2_matrix_1 C)) ) ) ) ) ) ) ).
tt(t18_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (~  ( (~ (r1_xxreal_0 (k1_matrix_1 C) k6_numbers))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) k6_numbers))  &  (~  ((k4_matrix_3 A C (k1_matrix_3 A (k1_matrix_1 C) B)) = (k1_matrix_3 A (k3_finseq_1 C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k9_matrlin A C D (k4_vectsp_1 A C B E)) = (k9_fvsum_1 A (k9_matrlin A C D E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  ((v13_vectsp_1 D C B) & (v1_mod_2 D A C B)) )  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D (k4_rlvect_1 C (k5_matrlin A C F E))) = (k4_rlvect_1 B (k5_matrlin A B F (k4_finseqop (u1_struct_0 C) (u1_struct_0 B) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski C B) &  ((k5_card_1 C) = (k4_matroid0 A B)) ) ) ) ) ) ) ) ).
tt(t18_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((k3_finseq_1 D) = B)  => (m1_matrix_1 (k2_finseq_2 C D) A C B)) ) ) ) ) ) ) ) ) ).
tt(t18_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D C) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) C B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ( (C = k6_numbers)  |  ((k1_funct_1 (k1_funct_1 (k3_matrtop1 C B E) D) A) = (k13_fvsum_1 k2_vectsp_1 (k1_matrtop1 D) (k9_matrix_1 (u1_struct_0 k2_vectsp_1) E A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  ((k2_relset_1 (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B C)) = (k2_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B) (k9_matrix13 k2_vectsp_1 A B C)))) ) ) ) ) ) ) ).
tt(t18_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 B A) |  ((k2_matrtop3 C k1_xboole_0 A B) = (k12_matrix_1 k2_vectsp_1 C)) ) ) ) ) ) ) ) ) ).
tt(t18_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) B) = B)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) C) = C)  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t18_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) <=> (r1_pboole A B (k1_mboolean A C))) ) ) ) ) ) ).
tt(t18_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k2_zfmisc_1 (k1_tarski B) (k2_tarski C D))) =>  ( ((k1_xtuple_0 A) = B)  &  ( ((k2_xtuple_0 A) = C)  |  ((k2_xtuple_0 A) = D) ) ) ) ) ) ) ) ).
tt(t18_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (v1_xboole_0 (k1_enumset1 B C k1_xboole_0)))  &  ((v4_card_3 (k1_enumset1 B C k1_xboole_0)) & (m1_subset_1 (k1_enumset1 B C k1_xboole_0) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ).
tt(t18_measure2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A (k2_nat_1 B 1)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(t18_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F B) &  (? [G:$i] :  ((m1_measure3 G A B C) &  (E = (k2_xboole_0 F G)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D A) &  ((v4_prob_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v3_measure5 A) =>  (A = (k2_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) ) ) ) ).
tt(t18_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_measure8 C A B) =>  (! [D:$i] :  ((r2_hidden D B) =>  ((k1_mesfunc9 C D) = (k1_mesfunc9 (k9_measure8 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t18_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k5_member_1 (k5_xboole_0 A B)) = (k5_xboole_0 (k5_member_1 A) (k5_member_1 B))) ) ) ) ) ).
tt(t18_membered,ax, (! [A:$i] :  ((v6_membered A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden B A)) )  =>  (A = k5_numbers) ) ) ) ).
tt(t18_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  ((k7_memstr_0 A B (k5_memstr_0 A B C)) = (k5_relat_1 C (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)))) ) ) ) ) ) ) ).
tt(t18_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) A H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) B I))) ) )  =>  ((r1_euclid_6 A B C) |  ( (G = 1)  |  ( (H = 1)  |  ( (I = 1)  |  ((r1_euclid_6 D E F) <=>  ((k11_binop_2 (k11_binop_2 (k12_binop_2 G (k10_binop_2 1 G)) (k12_binop_2 H (k10_binop_2 1 H))) (k12_binop_2 I (k10_binop_2 1 I))) = (k19_binop_2 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (~  ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers B F)) & (r1_mesfunc1 A C (k4_mesfunc5 A k7_numbers B F) E)) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r2_hidden F E) & (r1_xxreal_0 G H))  => (r1_xxreal_0 (k12_supinf_2 (k4_mesfunc5 A k7_numbers B H) F) (k12_supinf_2 (k4_mesfunc5 A k7_numbers B G) F))) ) ) ) ) ) )  &  ( (~ (r1_xxreal_0 k1_supinf_1 (k7_mesfunc5 A C D (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers B k6_numbers) E))))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k12_supinf_2 F G) = (k7_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B G))) ) )  &  ((v10_mesfunc5 F) &  ((k2_mesfunc5 F) = (k7_mesfunc5 A C D (k7_mesfunc8 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( (? [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) &  ((k1_relset_1 A C) = D) ) )  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_mesfun6c A B C E) => (r1_mesfun6c A B (k25_valued_1 A k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers C E) D)) ) )  => (r1_mesfunc1 A B (k7_mesfun7c A C) D)) ) ) ) ) ) ) ) ) ).
tt(t18_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers D k6_numbers)) = C)  &  ((v1_mesfunc8 D A k1_numbers) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k2_mesfun9c A D) E) C)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) => (v1_series_1 (k10_seqfunc A D E))) ) ) ) ) )  => (r1_mesfunc1 A B (k8_mesfun7c A (k2_mesfun9c A D)) C)) ) ) ) ) ) ) ) ) ).
tt(t18_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ((k9_subset_1 A C (k19_mesfunc1 A B D)) = (k9_subset_1 A (k9_subset_1 A C (k18_mesfunc1 A B D)) (k16_mesfunc1 A B D))) ) ) ) ) ) ) ).
tt(t18_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ( ((k12_supinf_2 (k1_mesfunc2 A B) C) = (k12_supinf_2 B C))  |  ((k12_supinf_2 (k1_mesfunc2 A B) C) = k1_supinf_2) )  &  ( ((k12_supinf_2 (k2_mesfunc2 A B) C) = (k2_supinf_2 (k12_supinf_2 B C)))  |  ((k12_supinf_2 (k2_mesfunc2 A B) C) = k1_supinf_2) ) ) ) ) ) ) ) ) ).
tt(t18_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ( (C = (k3_finseq_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k12_supinf_2 A D) = B) ) ) ) )  =>  ((k4_extreal1 A) = (k1_extreal1 C B)) ) ) ) ) ) ) ) ).
tt(t18_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k3_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k3_numbers B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  ( ((v3_mesfunc5 C) &  ((v3_mesfunc5 D) &  (! [H:$i] :  ((v1_rat_1 H) =>  ((k1_funct_1 E H) = (k9_subset_1 A (k9_subset_1 A G (k15_mesfunc1 A C (k1_measure6 H))) (k9_subset_1 A G (k15_mesfunc1 A D (k1_measure6 (k9_real_1 F H)))))) ) ) ) )  =>  ((k9_subset_1 A G (k15_mesfunc1 A (k3_mesfunc1 A C D) (k1_measure6 F))) = (k3_tarski (k2_relset_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc6 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r2_hidden (k8_subset_1 A (k8_subset_1 A D (k13_mesfunc1 C E)) (k11_mesfunc1 C F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] : (r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k10_mesfunc1 A B) C) (k10_mesfunc1 A (k2_partfun1 A k7_numbers B C)))) ) ) ) ) ).
tt(t18_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k4_mesfunc5 A k7_numbers C F) (k1_measure6 E)))) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) (k5_setlim_1 A B D) F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k4_mesfunc5 A k7_numbers (k3_mesfunc8 A C) F) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((v1_mesfunc8 B A k7_numbers) &  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers C E) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers B E) D))) ) )  => (v1_mesfunc8 C A k7_numbers)) ) ) ) ) ) ) ) ).
tt(t18_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k10_metric_1 B C A) = (a_3_4_metric_1 A B C)) ) ) ) ) ) ) ).
tt(t18_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k6_domain_1 (u1_struct_0 A) B) (k2_metric_2 A))) ) ) ) ).
tt(t18_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) => (r1_xxreal_0 (k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) D F) (k7_real_1 (k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) D E) (k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k13_metric_3 A B C) E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  => (r2_metric_6 A (k9_metric_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t18_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k2_waybel23 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 C A) &  ((m1_setfam_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski D C) &  ((m1_setfam_1 D (u1_struct_0 A)) & (r1_ordinal1 (k1_card_1 D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) k1_numbers)))) )  =>  ( ((r1_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) k1_numbers C E) &  (B = D) )  =>  ((k5_rlvect_2 (k15_euclid A) B C) = (k5_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_midsp_1 A B C D E) & (r1_midsp_1 A C F E G))  => (r1_midsp_1 A B F D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_midsp_2 A (k4_struct_0 A)) = (k4_struct_0 A))  &  ( ((k3_midsp_2 A (k3_rlvect_1 A B C)) = (k3_rlvect_1 A (k3_midsp_2 A B) (k3_midsp_2 A C)))  &  ( ( ((k3_midsp_2 A B) = (k3_midsp_2 A C))  =>  (B = C) )  &  ((k3_midsp_2 A (k1_midsp_2 A B)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t18_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [F:$i] :  ( ((v4_midsp_2 F B) & (l1_midsp_2 F B))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (u1_midsp_2 B F))) =>  (! [H:$i] :  ((m2_finseq_2 H (u1_struct_0 (u1_midsp_2 B F)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B F)))) =>  ( ( ((k8_midsp_3 A B F C E) = H)  &  ((k9_midsp_2 B F C D) = G) )  =>  ( ((k4_midsp_3 A B C E) = D)  <=>  ((k9_midsp_3 A B F C H) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_relset_1 A A D E) &  ((r1_tarski B C) & (r1_relset_1 A A F G)) )  => (r1_tarski (k9_mmlquery A F B E) (k9_mmlquery A G C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( ((k2_mod_2 A (k6_mod_2 A B)) = B)  &  ( ((k3_mod_2 A (k6_mod_2 A B)) = B)  &  ( (! [C:$i] :  ( ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) )  =>  ( ((k3_mod_2 A C) = B)  =>  ((k8_mod_2 A (k6_mod_2 A B) C) = C) ) ) )  &  (! [C:$i] :  ( ((v2_mod_2 C A) &  ((v3_mod_2 C A) & (l1_mod_2 C A)) )  =>  ( ((k2_mod_2 A C) = B)  =>  ((k8_mod_2 A C (k6_mod_2 A B)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_lmod_5 C A B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r1_tarski C D) & (v1_mod_3 D A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v36_algstr_0 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_2 B A))  =>  ((k3_mod_4 (k2_mod_4 A) (k5_mod_4 A B)) = (g1_vectsp_2 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_2 A B))) ) ) ) ) ).
tt(t18_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( ((k8_trees_2 A (k1_modal_1 A)) = 1)  =>  ((k1_trees_2 A (k1_modal_1 A)) = (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) (k12_finseq_1 k5_numbers k6_numbers))) ) ) ) ).
tt(t18_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k30_modelc_1 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E)))))) )  =>  ((v2_modelc_1 A) =>  ((r4_modelc_1 B C E F D A) <=> (r2_hidden (k1_funct_1 F A) (k3_funct_2 B (k1_zfmisc_1 E) (k46_modelc_1 B E) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_modelc_2 A (k8_modelc_2 B C)) <=>  ( (A = B)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t18_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k13_modelc_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k13_modelc_2 A))) =>  ( (B = (k4_subset_1 (k13_modelc_2 A) C D))  => (r1_xxreal_0 (k18_modelc_3 A B) (k7_real_1 (k18_modelc_3 A C) (k18_modelc_3 A D)))) ) ) ) ) ) ) ) ) ).
tt(t18_moebius1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (~  ((r1_tarski (k1_polynom2 k10_newton (k13_nat_3 B)) (k2_finseq_1 (k2_nat_1 A 1))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_tarski (k1_polynom2 k10_newton (k13_nat_3 C)) (k2_finseq_1 A)) &  ( (B = (k4_nat_1 C (k13_newton (k2_nat_1 A 1) D)))  &  (! [E:$i] :  ( ((v7_ordinal1 E) & (v1_int_2 E))  =>  ( ((r2_hidden E (k1_polynom2 k10_newton (k13_nat_3 C))) =>  ((k11_nat_3 C E) = (k11_nat_3 B E)) )  &  ( (~ (r2_hidden E (k1_polynom2 k10_newton (k13_nat_3 C))))  => (r1_xxreal_0 (k11_nat_3 C E) (k11_nat_3 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_monoid_0 B A) =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 B) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 B) (u2_algstr_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 B C D) = (k6_algstr_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  ((m1_subset_1 A (u1_struct_0 (k9_monoid_1 C B))) <=>  ((v1_funct_1 A) &  ((v1_funct_2 A B (u1_struct_0 C)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C))))) ) ) ) ) ) ) ).
tt(t18_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_morph_01 A (k6_setfam_1 (u1_struct_0 A) B) C) = (k1_setfam_1 (a_3_7_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t18_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 B))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden (k1_trees_4 (k4_tarski A E)) (k1_funct_1 (k5_msafree3 B C D) E)) <=>  ((r2_hidden A (k1_funct_1 D E)) & (r2_hidden A (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (? [C:$i] :  ( ((v3_msualg_1 C A) &  ((v4_msualg_1 C A) &  ((v2_msafree C A) & (l3_msualg_1 C A)) ) )  &  (? [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) & (r2_msualg_3 A C B D)) ) ) ) ) ) ) ) ).
tt(t18_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A C) D)) =>  ((k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B) (k4_msaterm A C B D E)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v7_graph_1 B A) & (m1_graph_1 B A)) )  =>  ((v1_msscyc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ( ((v7_graph_1 D A) & (m1_graph_1 D A))  &  ( ((k3_finseq_1 D) = C)  &  ( (~ (v1_xboole_0 (k7_finseq_1 D B)))  &  ((v7_graph_1 (k7_finseq_1 D B) A) & (m1_graph_1 (k7_finseq_1 D B) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r2_pboole A B C) & (v2_finset_1 C))  => (v2_finset_1 B)) ) ) ) ) ) ).
tt(t18_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k12_msualg_1 A B)))))  =>  ( (D = (u1_struct_0 (k12_msualg_1 A C)))  => (v1_unialg_2 D (k12_msualg_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t18_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r2_hidden E (k5_msualg_2 A C D)) => (r1_tarski (k10_xtuple_0 (k5_relat_1 (k5_msualg_1 A B C) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_msualg_2 A C D))) B))) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) E) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  ( ((r6_msualg_3 A B C) & (r6_msualg_3 A C D))  => (r6_msualg_3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t18_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((v2_msualg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) A B) &  ((v3_msualg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) A B) & (m1_msualg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ).
tt(t18_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_rewrite1 (k3_msualg_6 A) C D) & (r1_rewrite1 (k3_msualg_6 A) D E))  =>  (! [F:$i] :  ((m2_msualg_6 F A B C D) =>  (! [G:$i] :  ((m2_msualg_6 G A B D E) => (m2_msualg_6 (k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E) F G) A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v1_msualg_7 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k16_lattice3 A C) = (k16_lattice3 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  ((v2_msualg_4 (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) A B) &  ((v3_msualg_4 (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) A B) & (m1_msualg_4 (k15_lattice3 (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)) C) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ).
tt(t18_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_msualg_1 A C B)) => (r2_hidden (k3_funct_2 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) D) (k1_funct_1 (u3_msualg_1 A B) (k2_msualg_1 A C)))) ) ) ) ) ) ) ) ).
tt(t18_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_alg_1 A B C) => (r2_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C))) ) ) ) ) ) ) ).
tt(t18_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_necklace A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_necklace A))) =>  ( ( (B = D)  &  ( (C = E)  & (r2_hidden B (u1_struct_0 A))) )  =>  ( (B = C)  |  ((r1_orders_2 (k3_necklace A) D E) | (r1_orders_2 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_pre_topc B A) &  ((v3_pre_topc C A) &  ((r1_tarski B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski B (k1_prob_1 (u1_struct_0 A) D)) &  ((r1_tarski (k1_prob_1 (u1_struct_0 A) D) C) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_tarski (k2_pre_topc A (k8_nat_1 (k1_zfmisc_1 (u1_struct_0 A)) D E)) C) & (v3_pre_topc (k8_nat_1 (k1_zfmisc_1 (u1_struct_0 A)) D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v10_pre_topc A)) ) ) ).
tt(t18_nagata_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (~  ((v2_funct_1 B) &  ((v2_funct_1 C) &  ((r1_tarski (k2_relset_1 A C) (k2_relset_1 A B)) &  ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ( ((v1_setwiseo D A) |  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  (~ (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) )  &  (! [E:$i] :  ((m2_finseq_1 E A) =>  (~  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = (k7_subset_1 A (k2_relset_1 A B) (k2_relset_1 A C)))  &  ((k1_finsop_1 A B D) = (k5_binop_1 A D (k1_finsop_1 A C D) (k1_finsop_1 A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ( (A = (k2_xcmplx_0 (k3_xcmplx_0 B C) D))  &  (A = (k2_xcmplx_0 (k3_xcmplx_0 B E) F)) )  =>  ((r1_xxreal_0 B D) |  ((r1_xxreal_0 B F) |  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( ((k4_nat_d A 2) = k6_numbers)  <=>  ((k4_nat_d (k7_nat_d A 1) 2) = 1) ) ) ) ) ).
tt(t18_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r1_tarski (k13_pre_poly (k6_nat_3 A B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ).
tt(t18_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_nat_d A (k13_newton B C)) &  ((v1_int_2 B) & (v1_int_2 A)) )  =>  (B = A) ) ) ) ) ) ) ) ).
tt(t18_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  (~  ((r1_int_2 B C) &  ((r2_hidden A (k3_moebius1 (k24_binop_2 B C))) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden D (k3_moebius1 B)) &  ((r2_hidden E (k3_moebius1 C)) &  (A = (k24_binop_2 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_nat_d (k3_xcmplx_0 A B) A) = B) ) ) ) ) ) ).
tt(t18_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r1_nattra_1 A B C D) & (r1_nattra_1 A B D E))  => (r1_nattra_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_ncfcont1 A B C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_nfcont_1 E B (k7_partfun1 (u1_struct_0 B) C D)) =>  (? [F:$i] :  ((m1_ncfcont1 F A D) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_ncfcont2 A B C D) => (r2_nfcont_2 A B (k3_normsp_0 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ).
tt(t18_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) =>  ((v3_normsp_1 B A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k6_normsp_1 A B) = (k1_normsp_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t18_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k2_vfunct_1 k1_numbers A C D))) &  ((r2_ndiff_3 A C B) & (r2_ndiff_3 A D B)) )  =>  ((r2_ndiff_3 A (k2_vfunct_1 k1_numbers A C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_funct_1 (k2_ndiff_3 A (k2_vfunct_1 k1_numbers A C D) B) E) = (k5_algstr_0 A (k1_ndiff_3 A C E) (k1_ndiff_3 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k7_partfun1 (k1_euclid A) C F) = (k7_euclid A (k9_euclid A D F) E)) ) ) ) )  =>  ((r2_ndiff_4 A C B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_funct_1 (k2_ndiff_4 A C B) F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ndiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v2_fdiff_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~  (D = k6_numbers) )  &  ( (~ (r1_xxreal_0 C (k18_complex1 D)))  & (r1_xxreal_0 B (k12_binop_2 (k18_complex1 (k1_seq_1 A D)) (k18_complex1 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r1_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) =>  ((k3_necklace (k2_neckla_2 A B)) = (k1_neckla_2 (k3_necklace A) (k3_necklace B))) ) ) ) ) ) ).
tt(t18_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_orders_2 (k4_necklace A)) = (k2_xboole_0 (a_1_0_necklace A) (a_1_1_necklace A))) ) ) ).
tt(t18_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (~  ( (~  ((k2_net_1 A) = k1_xboole_0) )  &  ( (~  ((k6_net_1 A B) = (k1_tarski B)) )  &  (~  ((k6_net_1 A B) = (k4_net_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t18_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k8_real_1 (k3_newton A) (k3_newton B)) = k6_numbers) ) ) ) ) ) ).
tt(t18_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r3_nfcont_1 B A D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 B) E) C) &  ((v3_normsp_1 E B) & (r2_hidden (k6_normsp_1 B E) C)) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D) A) &  ((k7_partfun1 (u1_struct_0 A) D (k6_normsp_1 B E)) = (k6_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C) & (r1_tarski B A))  => (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D B) C)) ) ) ) ) ) ) ).
tt(t18_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r2_hidden B (k1_relset_1 k1_numbers C)) & (r1_nfcont_4 A C B))  => (r1_nfcont_4 A (k2_nfcont_4 A k1_numbers C) B)) ) ) ) ) ) ) ).
tt(t18_normform,ax, (! [A:$i] : (v1_setwiseo (k5_normform A) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))) ).
tt(t18_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) B C) = (k3_funct_2 k5_numbers (u1_struct_0 A) B D)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_normsp_2 A))) =>  ( ( (C = D)  &  (E = F) )  =>  ((r1_nfcont_1 A B C E) <=> (r1_tmap_1 (k3_normsp_2 A) (k3_normsp_2 B) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_numbers,ax,(r1_tarski k5_numbers k3_numbers)).
tt(t18_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  (~  ( (~  (D = k1_xboole_0) )  &  ((r1_tarski D (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_openlatt A B) (k10_openlatt A C))) &  ((v6_ordinal1 D) &  (! [E:$i] :  (~  ((r2_hidden E (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_openlatt A B) (k10_openlatt A C))) &  (! [F:$i] :  ((r2_hidden F D) => (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k2_oppcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k2_oppcat_1 A))) =>  ( ((k3_graph_1 (k2_oppcat_1 A) C) = (k4_graph_1 (k2_oppcat_1 A) B))  =>  ((k6_oppcat_1 A (k1_cat_1 (k2_oppcat_1 A) B C)) = (k1_cat_1 A (k6_oppcat_1 A C) (k6_oppcat_1 A B))) ) ) ) ) ) ) ) ).
tt(t18_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_orders_1 A) => (v3_orders_1 (k2_relat_1 A))) ) ) ).
tt(t18_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B C) & (r2_hidden B (k1_orders_2 A C))) ) ) ) ) ) ) ) ).
tt(t18_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v3_ordinal1 (k3_tarski A))) ) ).
tt(t18_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_ordinal2 A) = A) ) ) ).
tt(t18_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r1_ordinal1 A B) & (r1_ordinal1 C D))  => (r1_ordinal1 (k10_ordinal2 A C) (k10_ordinal2 B D))) ) ) ) ) ) ) ) ) ).
tt(t18_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k10_ordinal2 B C)) ) ) )  => (v2_ordinal2 A)) ) ) ) ) ).
tt(t18_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal5 A 2) = (k12_ordinal2 A A)) ) ) ).
tt(t18_ordinal6,ax, (! [A:$i] :  ( ((k9_xtuple_0 (k2_ordinal6 A)) = (k1_ordinal6 A))  &  ((k10_xtuple_0 (k2_ordinal6 A)) = (k2_ordinal1 A)) ) ) ).
tt(t18_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t18_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B (k5_algstr_0 B E C) D) =>  ((r1_orders_2 B C D) |  ((k1_ortsp_1 A B D C E) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_osalg_1 A (k11_osafree A B D) (k1_msualg_1 A C)) <=> (r2_hidden D (k3_msualg_1 A C (k8_osafree A B)))) ) ) ) ) ) ) ) ) ).
tt(t18_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_pboole C (u4_struct_0 A) (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k3_osalg_1 A B))) (k3_relat_1 (u2_msualg_1 A) (k3_osalg_1 A B))) => (v12_osalg_1 (k4_osalg_1 A B C) A)) ) ) ) ) ) ).
tt(t18_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r1_tarski (k5_osalg_2 A B C) (k6_osalg_2 A B))) ) ) ) ) ) ).
tt(t18_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) ) )  =>  ((r3_osalg_3 A B C) =>  ((v13_osalg_1 B A) <=> (v13_osalg_1 C A)) ) ) ) ) ) ) ) ).
tt(t18_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r2_msualg_3 A B C D) & (v1_osalg_3 D A))  => (r4_msualg_3 A (k16_osalg_4 A B (k19_osalg_4 A B C D)) C (k21_osalg_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t18_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v1_translac (k2_diraf A))) ) ).
tt(t18_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_parsp_1 A B C B C)) ) ) ) ) ) ).
tt(t18_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_2 A B C D))  &  ((r1_parsp_2 A B C E) &  ((r1_parsp_2 A B D E) &  (~  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B))))  => (r1_tarski (k7_relat_1 D C) (k1_tarski (k1_funct_1 D A)))) ) ) ) ) ).
tt(t18_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( ((r2_hidden D (k1_relset_1 B E)) & (r2_hidden D A))  => (r2_hidden (k7_partfun1 C E D) (k2_relset_1 C (k2_partfun1 B C E A)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  ( ((r1_setfam_1 E F) &  ((r2_hidden B F) &  ((r2_hidden C E) &  ((r2_hidden D B) & (r2_hidden D C)) ) ) )  => (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_relat_1 (k4_relat_1 A)) = A) ) ) ).
tt(t18_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B D) &  ( (~  (C = B) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A B E B F) & (r2_analoaf A C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k2_pboole A B D) (k2_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t18_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_pcomps_1 B A) => (v1_pcomps_1 (k1_pcomps_1 A B) A)) ) ) ) ) ).
tt(t18_pcs_0,ax, (! [A:$i] :  ( ((v14_pcs_0 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( ((v14_pcs_0 B) & (l2_pcs_0 B))  =>  ((r1_tsep_1 A B) => (v8_relat_2 (u1_orders_2 (k18_pcs_0 A B)))) ) ) ) ) ).
tt(t18_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ((r2_relset_1 (k1_euclid A) (k1_euclid 1) E (k3_pdiff_1 A C)) =>  ((r4_pdiff_1 A 1 B E D) <=> (r3_pdiff_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 2) B)) =>  ( ((r3_pdiff_1 2 2 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 A B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 A B))))) &  ((k11_pdiff_1 2 2 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 2) B)) =>  ( ((r2_pdiff_3 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B))))) &  ((k3_pdiff_3 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (E = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 3 F E))  =>  ( (D = (k11_pdiff_1 3 3 F E))  <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (E = (k11_finseq_1 G H I))  &  (? [J:$i] :  ((m1_rcomp_1 J I) &  ((r1_tarski J (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 F E))) &  (? [K:$i] :  ( ((v1_funct_1 K) &  ((v3_fdiff_1 K) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (? [L:$i] :  ( ((v1_funct_1 L) &  ((v2_fdiff_1 L) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( (D = (k1_seq_1 K 1))  &  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_hidden M J) =>  ((k9_real_1 (k1_seq_1 (k1_pdiff_2 3 3 F E) M) (k1_seq_1 (k1_pdiff_2 3 3 F E) I)) = (k7_real_1 (k1_seq_1 K (k9_real_1 M I)) (k1_seq_1 L (k9_real_1 M I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r9_pdiff_5 E D))  =>  ((k9_pdiff_5 E D) = (k1_fdiff_1 (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 E) D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) =>  ((v1_funct_1 (k8_pdiff_1 A B C D)) &  ((v1_funct_2 (k8_pdiff_1 A B C D) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 (k8_pdiff_1 A B C D) (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v1_lopban_1 (k8_pdiff_1 A B C D) (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 (k8_pdiff_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ( (~  (B = (k4_struct_0 (k4_real_ns1 1))) )  &  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A C (k4_struct_0 (k4_real_ns1 A))) B) = (k4_struct_0 (k4_real_ns1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  ( ( (F = (k3_relat_1 C (k4_pdiff_1 E B)))  &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E B)) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) F) D)) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) C) (k11_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t18_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) &  ( (C = (k1_funct_1 B (k12_finseq_1 k5_numbers 1)))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 1))) =>  ( (E = (k12_finseq_1 k1_numbers D))  =>  ((k17_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A) B E) = (k1_rlvect_1 (k4_real_ns1 A) C D)) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 1))) =>  ((k1_normsp_0 (k4_real_ns1 A) (k17_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A) B D)) = (k11_binop_2 (k1_normsp_0 (k4_real_ns1 A) C) (k1_normsp_0 (k4_real_ns1 1) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v11_pencil_1 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v6_pencil_1 (k1_pencil_1 A B C)) &  ((v5_pencil_1 (k1_pencil_1 A B C)) &  (~  (! [D:$i] :  ((m1_subset_1 D A) => (v3_pencil_1 (k1_pencil_1 A B D))) ) ) ) ) ) )  => (v6_pencil_1 (k5_pencil_1 A B))) ) ) ) ) ).
tt(t18_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_pencil_1 C A) => (v1_pencil_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t18_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v13_pencil_1 C))  &  ((v16_pencil_1 C A) & (m3_pboole C A (k12_pralg_1 A B))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A C)))) =>  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  &  ((r2_hidden E (k4_card_3 C)) &  ((k1_tarski (k2_funct_7 E (k3_pencil_1 A C) D)) = (k4_card_3 (k2_funct_7 C (k3_pencil_1 A C) (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A C))) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k1_vectsp_9 A B) C))  &  ((r1_xxreal_0 3 (k1_vectsp_9 A B)) & (v4_pencil_1 (k5_pencil_4 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t18_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v1_abian (k3_power 2 A))) ) ) ).
tt(t18_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_petri B A) <=> (v4_petri (k12_petri A B) (k11_petri A))) ) ) ) ) ).
tt(t18_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r1_pnproc_1 A (k3_pnproc_1 A (k2_pnproc_1 A B C) C) B)) ) ) ) ) ).
tt(t18_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_polyalg1 C A B))  =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) &  ( ((u1_struct_0 C) = D)  & (v3_polyalg1 D A B)) ) ) ) ) ) ) ) ) ).
tt(t18_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k7_polyeq_1 1 k6_numbers A B C) = k6_numbers)  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( (C = (k2_xcmplx_0 D E))  &  ((k7_real_1 (k8_real_1 (k8_real_1 3 E) D) A) = k6_numbers) )  =>  ( ((k2_xcmplx_0 (k1_newton D 3) (k1_newton E 3)) = (k4_xcmplx_0 B))  &  ((k3_xcmplx_0 (k1_newton D 3) (k1_newton E 3)) = (k2_newton (k1_real_1 (k6_real_1 A 3)) 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 k6_numbers (k12_binop_2 (k9_binop_2 (k7_binop_2 A) (k7_square_1 (k9_binop_2 (k5_square_1 A) (k5_square_1 B)))) 2)) & (r1_xxreal_0 k6_numbers (k12_binop_2 (k9_binop_2 A (k7_square_1 (k9_binop_2 (k5_square_1 A) (k5_square_1 B)))) 2))) ) ) ) ) ).
tt(t18_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k3_xcmplx_0 A (k2_newton B F)) (k3_xcmplx_0 C (k2_newton D F))) = E)  &  ( ((k3_xcmplx_0 B D) = k6_numbers)  &  ( (~ (v1_abian F))  &  ( (~  ((k3_xcmplx_0 A C) = k6_numbers) )  &  ( (~  ( (B = k6_numbers)  &  (D = (k1_power F (k7_xcmplx_0 E C))) ) )  &  (~  ( (B = (k1_power F (k7_xcmplx_0 E A)))  &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_polyeq_5 A B C) (k3_polyeq_5 A B C)) (k3_xcmplx_0 (k2_polyeq_5 A B C) (k4_polyeq_5 A B C))) (k3_xcmplx_0 (k3_polyeq_5 A B C) (k4_polyeq_5 A B C))) = B) ) ) ) ) ) ) ).
tt(t18_polyform,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k1_funct_1 (k7_finseq_1 (k7_finseq_1 B C) (k9_finseq_1 A)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_finseq_1 B) (k3_finseq_1 C)) 1)) = A) ) ) ) ) ) ).
tt(t18_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((k3_polynom1 A B D E) = (k4_algstr_0 B (k3_polynom1 A B C E))) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) D (k5_vfunct_1 (k15_pre_poly A) B C))) ) ) ) ) ) ) ) ).
tt(t18_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  => (r3_orders_1 (k17_pre_poly A) (k2_polynom1 (k15_pre_poly A) B C))) ) ) ) ) ) ).
tt(t18_polynom3,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k2_wsierp_1 (k17_finseq_1 k5_numbers B A)) (k2_wsierp_1 (k17_finseq_1 k5_numbers C A)))) ) ) ) ) ) ) ).
tt(t18_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_polynom4 A (k10_polynom3 A) B) = (k5_struct_0 A)) ) ) ) ) ).
tt(t18_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A B 3) (k13_polynom3 A (k13_polynom3 A B B) B))) ) ) ) ).
tt(t18_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l5_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k3_polynom1 A B (k4_polynom7 A B C) (k16_pre_poly A)) = C)  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( (~  (D = (k16_pre_poly A)) )  =>  ((k3_polynom1 A B (k4_polynom7 A B C) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k11_algstr_0 A (k3_polynom8 A C B)) = (k3_polynom8 A C (k4_xcmplx_0 B))) ) ) ) ) ) ) ) ).
tt(t18_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k1_polyred A (k11_pre_poly A E F) C D) (k1_polyred A E C (k1_polyred A F C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 1 (k1_power B A)) & (r1_xxreal_0 (k1_power B A) A)) ) ) ) ) ) ).
tt(t18_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  ( (~  ((k1_msualg_1 B D) = k1_xboole_0) )  => (r2_hidden E (k9_xtuple_0 (k1_pralg_2 (k2_pralg_2 (k12_pralg_2 A B C D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  ((k2_nat_1 (k5_card_1 (k7_trees_2 A C B)) (k5_card_1 (k5_trees_2 A C))) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ) ).
tt(t18_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (B = (k2_nat_1 (k3_nat_1 A (k3_pre_ff k6_numbers)) (k3_nat_1 B (k3_pre_ff 1)))) ) ) ) ) ).
tt(t18_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A B (k1_prelamb A (k2_prelamb A B C) B))) (k2_prelamb A B C))) ) ) ) ) ) ).
tt(t18_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k1_relat_1 B) A) => (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(t18_prepower,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_newton (k1_seq_1 B D) A)) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k2_newton (k2_seq_2 B) A)) ) ) ) ) ) ) ) ) ).
tt(t18_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k2_pre_topc A B))) ) ) ) ).
tt(t18_prob_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ((r2_hidden B C) => (m1_prob_1 B A C)) ) ) ) ) ).
tt(t18_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ( (~  ( (~ (r1_xxreal_0 1 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C))))  & (r1_xxreal_0 (k1_seq_1 D C) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k1_seq_1 D C) k6_numbers))  & (r1_xxreal_0 1 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k1_funct_1 (k3_prob_3 B C) A) (k1_funct_1 (k2_prob_3 B C) A))) ) ) ) ) ).
tt(t18_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xboole_0 (k1_prob_4 A (k9_setfam_1 A) (k3_prob_3 A B) (k2_nat_1 C 1)) (k1_prob_4 A (k9_setfam_1 A) B C))) ) ) ) ) ) ).
tt(t18_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C)) (k6_cqc_lang A (k7_cqc_lang A B C))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t18_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_projdes1 A B C D E))  &  ((r1_projdes1 A B C D F) &  ( (~ (r1_collsp A B C F))  & (r1_projdes1 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) & (r5_projpl_1 A B C D E)) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) => (r4_projpl_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t18_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  ( (~ (r1_incsp_1 A B C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r1_incsp_1 A D C) =>  ((k1_funct_1 (k1_projred1 A C C B) D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E F) I) &  ((r1_incsp_1 A G K) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E G) J) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) L) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E H) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B G F) N) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D F H) O) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C G H) P)) ) ) ) ) ) )  =>  ((r1_incsp_1 A B I) |  ((r1_incsp_1 A B J) |  ((r1_incsp_1 A C J) |  ((r1_incsp_1 A D I) |  ((r1_projred2 A I K J) |  ((r1_projred2 A K J L) |  ( (B = C)  |  ( (C = D)  |  ( (D = B)  |  ( (~  (M = I) )  &  ( (~  (M = J) )  &  ( (~ (r1_incsp_1 A D M))  &  (~ (r1_incsp_1 A C M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  ( (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) => (v2_binop_1 (k9_prvect_1 A B C) (k1_funct_1 A C))) )  => (v2_binop_1 (k13_prvect_1 A B) (k4_card_3 A))) ) ) ) ) ).
tt(t18_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_prvect_3 A B))) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E)) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_prvect_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) E G))  &  (D = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) F H)) )  =>  ((k3_rlvect_1 (k7_prvect_3 A B) C D) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k3_rlvect_1 A E F) (k3_rlvect_1 B G H))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k4_struct_0 (k7_prvect_3 A B)) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_struct_0 A) (k4_struct_0 B)))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_prvect_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E))  =>  ((k4_algstr_0 (k7_prvect_3 A B) C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_algstr_0 A D) (k4_algstr_0 B E))) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_prvect_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E))  =>  ((k1_rlvect_1 (k7_prvect_3 A B) C F) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k1_rlvect_1 A D F) (k1_rlvect_1 B E F))) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_prvect_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (C = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D E))  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid 2)) =>  (~  ( (F = (k2_finseq_4 k1_numbers (k1_normsp_0 A D) (k1_normsp_0 B E)))  &  ((k1_normsp_0 (k7_prvect_3 A B) C) = (k12_euclid F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_pscomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k8_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_rcomp_1 A B)) = (a_2_0_pscomp_1 A B)) ) ) ) ) ).
tt(t18_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) => (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k8_pua2mss1 A D (k2_nat_1 B C)) (k8_pua2mss1 A (k8_pua2mss1 A D B) C))) ) ) ) ) ) ) ) ).
tt(t18_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A B C)) (k2_pzfmisc1 A B C))) ) ) ) ) ).
tt(t18_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ( ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k12_qc_lang1 A)) 1)) = k6_numbers)  &  ( (~  ((v2_qc_lang1 B A) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (m2_subset_1 (k1_funct_1 (k11_qc_lang1 A B) 1) (k6_qc_lang1 A) (k8_qc_lang1 A C))) ) ) ) )  &  ( ((v3_qc_lang1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 1) )  &  ( ((v4_qc_lang1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 2) )  &  ((v5_qc_lang1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t18_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  ( ((k7_qc_lang2 A B C E) = (k5_qc_lang2 A D F))  =>  ( (B = D)  &  ((k5_qc_lang2 A C E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k4_qc_lang2 A B C)) = (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k24_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t18_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (~  ( (~  (C = D) )  &  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) = (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) D))  & (r3_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_lattices A (k6_algstr_0 A (k1_quantal1 A (k1_quantal1 A C B) B) (k1_quantal1 A (k1_quantal1 A D B) B)) (k1_quantal1 A (k1_quantal1 A (k6_algstr_0 A C D) B) B))) ) ) ) ) ) ) ) ).
tt(t18_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni (k26_quaterni A B) C) = (k26_quaterni (k27_quaterni A C) (k27_quaterni B C))) ) ) ) ) ) ) ).
tt(t18_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k29_quaterni (k27_quaterni k4_quatern2 A) (k27_quaterni A k4_quatern2)) = (k6_quaterni k6_numbers k6_numbers (k1_real_1 (k8_real_1 2 (k20_quaterni A))) (k8_real_1 2 (k19_quaterni A)))) ) ) ).
tt(t18_quaterni,ax, ((k10_quaterni k12_quaterni k1_xcmplx_0) = k11_quaterni) ).
tt(t18_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  &  (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers))  <=>  ( (~ (r1_xxreal_0 D (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))))  &  (~ (r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (~  (B = (k11_quofield A)) )  =>  ( ((k9_quofield A B (k14_quofield A B)) = (k12_quofield A))  &  ((k9_quofield A (k14_quofield A B) B) = (k12_quofield A)) ) ) ) ) ) ) ).
tt(t18_radix_1,ax, ((k11_radix_1 k6_numbers) = k6_numbers) ).
tt(t18_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D (k4_radix_3 C)))  =>  ((r2_hidden A (k2_finseq_1 B)) => (m2_subset_1 (k7_radix_3 A C B D) k4_numbers (k4_radix_3 C))) ) ) ) ) ) ) ) ) ).
tt(t18_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r1_xxreal_0 2 C))  =>  ((k8_radix_1 A C (k6_radix_5 A B C)) = (k2_xcmplx_0 (k8_radix_1 A C (k4_radix_5 A B C)) (k8_radix_1 A C (k10_radix_1 C A 1)))) ) ) ) ) ) ) ) ) ).
tt(t18_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 2 B) &  ( (~ (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k8_radix_6 A B C)) k6_numbers))  & (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B C) (k8_radix_1 (k2_xcmplx_0 A 2) B (k2_radix_6 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) => (m1_random_1 (k3_valued_1 A k1_numbers k1_numbers C D) A B)) ) ) ) ) ) ) ) ).
tt(t18_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 (k1_vectsp_7 A B C) (k5_algstr_0 B D E)) => (r1_struct_0 (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E))) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ( ((k2_rat_1 A) = A)  |  ((k1_rat_1 A) = 1) )  => (v1_int_1 A)) ) ) ).
tt(t18_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_ratfunc1 A (k3_polynom5 A B C)) = (k8_group_1 A C (k2_ratfunc1 A B))) ) ) ) ) ) ) ).
tt(t18_rcomp_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_rcomp_1 C B) =>  (~ (r1_tarski C A)) ) ) ) ) ) ) ) ) ).
tt(t18_rcomp_3,ax, (! [A:$i] :  ( ((v5_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ( (~ (r2_hidden (k5_seq_4 A) A))  &  ( (~ (r2_hidden (k4_seq_4 A) A))  &  (~ (r1_tarski A (k2_rcomp_1 (k5_seq_4 A) (k4_seq_4 A)))) ) ) ) ) ) ).
tt(t18_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_seq_1 (k1_real_3 C D) A) = k6_numbers)  =>  ((r1_xxreal_0 B A) |  ((k1_seq_1 (k2_real_3 C D) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) (k1_funcsdom A k1_numbers (k4_real_lat A) B C) C) C)) ) ) ) ) ) ).
tt(t18_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k7_real_ns1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k7_real_ns1 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 (k4_real_ns1 A)) k5_numbers (u1_struct_0 (k7_real_ns1 A)) B C) & (v1_bhsp_3 C (k7_real_ns1 A)))  => (v1_rsspace3 B (k4_real_ns1 A))) ) ) ) ) ) ) ).
tt(t18_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_subset_1 (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C) (u1_struct_0 A))) ) ) ) ) ) ).
tt(t18_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) C D)) = (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t18_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k20_rfunct_3 B (k3_rearran1 A B D C) B) = (k20_rfunct_3 A C A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k1_relat_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k1_relat_1 A) (k1_relat_1 B))) ) ) ) ) ).
tt(t18_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))) => (m1_subset_1 (k5_relset_1 A C D B) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ).
tt(t18_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (a_4_1_relset_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ) ) ).
tt(t18_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_finseq_6 D B) & (m2_finseq_1 D B))  =>  ( ((r2_hidden C (k10_xtuple_0 D)) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k4_finseq_4 D C))) )  =>  ((k7_partfun1 B D A) = (k7_partfun1 B (k1_finseq_6 B D C) (k7_nat_d (k2_nat_1 A (k3_finseq_1 D)) (k4_finseq_4 D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) =>  ( (B = C)  |  ((r2_hidden B (k1_relat_1 A)) & (r2_hidden C (k1_relat_1 A))) ) ) ) ) ) ) ).
tt(t18_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B C) & (r1_rewrite2 A B D E))  => (r1_rewrite2 A C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t18_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [E:$i] :  ((l1_rewrite3 E D) =>  (~  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 D E)))))  & (r1_rewrite3 D E A (k2_flang_1 C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_rfinseq2,ax, (! [A:$i] :  ( ((v1_integra2 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v1_integra2 (k17_finseq_1 k1_numbers B A)) & (m2_finseq_1 (k17_finseq_1 k1_numbers B A) k1_numbers)) ) ) ) ) ).
tt(t18_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ( ((k3_finseq_1 A) = k6_numbers)  |  ((k3_finseq_1 A) = 1) )  => (v8_valued_0 A)) ) ) ).
tt(t18_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k45_valued_1 A B) C) = (k45_valued_1 (k24_valued_1 A C) (k24_valued_1 B C))) ) ) ) ) ) ) ).
tt(t18_rfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v5_xxreal_2 (k2_relset_1 k1_numbers B)) &  ((k4_seq_4 (k2_relset_1 k1_numbers B)) = (k5_seq_4 (k2_relset_1 k1_numbers B))) )  => (v3_funct_1 B)) ) ) ) ) ).
tt(t18_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (v1_setwiseo (k13_rfunct_3 A) (k3_rfunct_3 A k1_numbers))) ) ).
tt(t18_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_partfun1 A k1_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 B k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 B k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k4_finseq_2 B k1_numbers)) =>  ( ( ((k18_rvsum_1 C) = 1)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 C)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 C F)) &  ((k1_seq_1 E F) = (k1_seq_1 A (k1_seq_1 D F))) ) ) ) ) )  => (r1_xxreal_0 (k1_seq_1 A (k18_rvsum_1 (k15_rvsum_1 B C D))) (k18_rvsum_1 (k15_rvsum_1 B C E)))) ) ) ) ) ) ) ) )  <=> (r2_rfunct_3 A k1_numbers)) ) ) ) ).
tt(t18_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (v4_partfun3 A))  => (r1_xxreal_0 k6_numbers (k2_rinfsup1 A))) ) ) ).
tt(t18_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( ((k5_rinfsup2 A) = (k6_rinfsup2 A))  &  ((r2_hidden (k6_rinfsup2 A) k1_numbers) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (v3_rinfsup2 (k1_valued_0 k7_numbers A B))) ) ) ) ) ) ) ) ).
tt(t18_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v2_ring_1 B A) <=>  ( (~ (v2_struct_0 (k2_ring_1 A B)))  &  ( (~ (v6_struct_0 (k2_ring_1 A B)))  &  ((v13_algstr_0 (k2_ring_1 A B)) &  ((v3_group_1 (k2_ring_1 A B)) &  ((v5_group_1 (k2_ring_1 A B)) &  ((v4_vectsp_1 (k2_ring_1 A B)) &  ((v5_vectsp_1 (k2_ring_1 A B)) &  ((v2_rlvect_1 (k2_ring_1 A B)) &  ((v3_rlvect_1 (k2_ring_1 A B)) &  ((v4_rlvect_1 (k2_ring_1 A B)) &  ((v1_vectsp_2 (k2_ring_1 A B)) & (l6_algstr_0 (k2_ring_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k9_ringcat1 A)) =>  ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v36_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rlvect_2 D B) => (r1_rlvect_2 B (k1_rlaffin1 B (k8_rlvect_2 B A D) C) (k8_rlvect_2 B A (k1_rlaffin1 B D C)))) ) ) ) ) ) ) ) ).
tt(t18_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden B C) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k5_rlaffin1 A C (k1_funct_1 (k2_rlaffin2 A) C)) B) = (k10_real_1 1 (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(t18_rlaffin3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_rlaffin1 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [E:$i] :  ((m2_rlaffin3 E B D) =>  (! [F:$i] :  ((m2_rlaffin3 F B (k1_convex1 B D A)) =>  ( ((r2_hidden C (k4_rlaffin1 B D)) &  (F = (k4_vfunct_1 k5_numbers B E A)) )  =>  ( (A = k1_xboole_0)  |  ((k1_rlaffin3 B D E C) = (k1_rlaffin3 B (k1_convex1 B D A) F (k1_rlvect_1 B C A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t18_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ( ((k2_rlsub_2 A (k1_rlsub_1 A) B) = (k1_rlsub_1 A))  &  ((k2_rlsub_2 A B (k1_rlsub_1 A)) = (k1_rlsub_1 A)) ) ) ) ) ) ).
tt(t18_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_convex1 A (k3_convex1 A B) C) = (k3_convex1 A (k1_convex1 A B C))) ) ) ) ) ) ) ).
tt(t18_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_algstr_0 A B) = (k4_algstr_0 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t18_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_rlvect_2 A (k5_subset_1 (u1_struct_0 A) C B)) = (k3_rlvect_1 A (k2_rlvect_2 A (k7_subset_1 (u1_struct_0 A) C B)) (k2_rlvect_2 A (k7_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t18_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ( (B = (u1_struct_0 C))  =>  ((k1_rlvect_3 A B) = C) ) ) ) ) ) ) ) ).
tt(t18_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) =>  ( (B = C)  | (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B (k3_rlvect_1 A C B)) A)) ) ) ) ) ) ) ) ).
tt(t18_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_3 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (D = (k4_subset_1 (u1_struct_0 A) B C))  & (v1_rlvect_3 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k5_rusub_4 B (k2_rlvect_x B (k6_domain_1 (u1_struct_0 B) D)) C)) <=>  (? [E:$i] :  ((v1_int_1 E) &  (A = (k3_rlvect_1 B C (k1_rlvect_1 B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (r1_struct_0 D (k4_struct_0 C))) ) ) ) ) ) ) ) ).
tt(t18_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) => (m1_rmod_2 (k2_rmod_3 A B C E) A (k2_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k3_rmod_4 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t18_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_robbins1 A B B) = B) ) ) ) ) ).
tt(t18_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A B) (k3_robbins1 A (k1_lattices A C B)))) = B) ) ) ) ) ) ) ).
tt(t18_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_robbins1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_robbins1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_robbins1 A) (u1_robbins1 B)) &  (C = D) )  =>  ((k3_robbins1 A C) = (k3_robbins1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t18_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_robbins4)) =>  ( ( (A = (k6_subset_1 3 2))  &  (B = 2) )  =>  ( ((k13_lattice3 k1_robbins4 A B) = 3)  &  ((k12_lattice3 k1_robbins4 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t18_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k3_roughs_1 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t18_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_xxreal_0 k6_numbers (k1_rpr_1 A B))) ) ) ) ).
tt(t18_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  ( (C = (k4_struct_0 (k9_rsspace4 A B)))  =>  (k6_numbers = (k1_normsp_0 (k9_rsspace4 A B) C)) ) ) ) ) ) ) ) ).
tt(t18_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 k1_numbers C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers C) C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C C) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) k1_numbers)))) )  =>  ( ( (B = C)  &  ( (D = (k4_struct_0 A))  &  ( (E = (k1_realset1 (u1_algstr_0 A) B))  &  ( (F = (k5_relat_1 (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B)))  &  (G = (k1_realset1 (u1_bhsp_1 A) B)) ) ) ) )  => (m1_rusub_1 (g1_bhsp_1 C D E F G) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ( ((k2_rusub_2 A (k1_rusub_1 A) B) = (k1_rusub_1 A))  &  ((k2_rusub_2 A B (k1_rusub_1 A)) = (k1_rusub_1 A)) ) ) ) ) ) ).
tt(t18_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((r1_tarski (k3_rlvect_2 A C) (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rlvect_2 D B) =>  ( (D = (k2_partfun1 (u1_struct_0 A) k1_numbers C (u1_struct_0 B)))  =>  ( ((k3_rlvect_2 A C) = (k3_rlvect_2 B D))  &  ((k6_rlvect_2 A C) = (k6_rlvect_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 C (k1_rusub_4 A)) <=>  (? [D:$i] :  ( ((v1_bhsp_1 D) & (m1_rusub_1 D A))  &  ((k1_rusub_4 D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t18_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_rusub_5 A B B) = (k3_tarski (a_2_0_rusub_5 A B))) ) ) ) ) ).
tt(t18_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k1_seq_1 (k6_rvsum_1 B) A) = (k7_binop_2 (k1_seq_1 B A))) ) ) ) ).
tt(t18_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ( ((k8_rvsum_2 A B C) = (k5_finseq_2 k2_numbers A k5_complex1))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t18_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k5_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 k6_numbers)) = (k3_xcmplx_0 B C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ( (~  (E = (k10_ami_3 k6_numbers)) )  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmbsort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k2_scmfsa8c A B)) = (k4_subset_1 k2_scmfsa_2 (k2_sf_mastr B) (k5_scmfsa_m A (k4_scmfsa_2 k6_numbers)))) ) ) ) ) ).
tt(t18_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 1)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t18_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) => (m1_subset_1 (k1_funct_4 A B) (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)))) ) ) ) ).
tt(t18_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k6_scmfsa_2 A B)) = 1) ) ) ) ) ).
tt(t18_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_4 A (k3_scmfsa6a A B)) = (k3_scmfsa6a A B)) ) ) ) ) ).
tt(t18_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 B 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa6b C)) ) ) ) ) ) )  =>  ((r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v6_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((r1_tarski (k3_scmfsa6a C D) A) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k9_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A C) D) (k8_memstr_0 3 k1_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) B)) E) (k5_card_1 C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C D)) B (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) B) 1) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa7b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v6_amistd_1 A 3 k1_scmfsa_2) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r5_scmfsa7b A B C)) ) ) ) ) ) ) ).
tt(t18_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_scmfsa8a A B C) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k2_scmfsa8a A B C)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k8_memstr_0 3 k1_scmfsa_2 A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))  &  ( ( ((k1_funct_1 B E) = k6_numbers)  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b C B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b C B A) F)) ) ) ) )  &  ( (~  ((k1_funct_1 B E) = k6_numbers) )  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b D B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b D B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 C 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 D 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r5_scmfsa7b E C A) &  ((r6_scmfsa7b E C A) &  ((r1_tarski E A) &  ((r1_tarski E B) &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) ) ) )  =>  ((k8_extpro_1 3 k1_scmfsa_2 A C) = (k8_extpro_1 3 k1_scmfsa_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) C) = k6_numbers) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) (k2_nat_1 E 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  ((k1_funct_1 B D) = k6_numbers) )  =>  ((r6_scmfsa7b (k1_scmfsa_9 D C) B A) & (r5_scmfsa7b (k1_scmfsa_9 D C) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((k8_memstr_0 3 k1_scmfsa_2 A) = (k1_scmfsa_m A)) ) ) ) ).
tt(t18_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v3_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_scmfsa_m A)) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A)) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 B C) D) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_scmfsa_m A)) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)))))) ) ) ) ) ) ) ) ) ).
tt(t18_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( (~  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F)) = k6_numbers) )  =>  ( (~ (r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) (k2_nat_1 F 1)))))  &  ((r1_scm_halt B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F) (k1_funct_4 A (k2_scmfsa_9 C B))) & (r2_scm_halt B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F) (k1_funct_4 A (k2_scmfsa_9 C B)))) ) )  &  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) (k2_nat_1 F 1)) (k4_scmfsa_2 k6_numbers)) = 1)  &  ( ( ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F)) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F) C) k6_numbers))  &  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F) C) k6_numbers) =>  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_scmisort D B C A) F)) = k6_numbers) ) ) ) ) ) ) ) )  =>  ((r2_scm_halt (k2_scmfsa_9 C B) D A) & (r1_scm_halt (k2_scmfsa_9 C B) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k9_scmpds_2 C A B)) = 6) ) ) ) ) ) ) ).
tt(t18_scmpds_4,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r2_hidden A (k9_xtuple_0 (k7_memstr_0 2 k1_scmpds_2 B)))) ) ) ) ) ).
tt(t18_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k9_scmpds_2 A B C) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ).
tt(t18_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) &  ((v2_compos_1 E k1_scmpds_2) & (v3_scmpds_4 E)) ) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 E) B) &  ((r1_scmpds_6 E D B) & (r2_scmpds_6 E D B)) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_tarski (k61_valued_1 E F) C) &  ( ((k5_memstr_0 2 k1_scmpds_2 A) = F)  &  ((k6_memstr_0 2 k1_scmpds_2 D) = (k6_memstr_0 2 k1_scmpds_2 A)) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A (k8_extpro_1 2 k1_scmpds_2 B D))) = (k2_nat_1 (k5_card_1 E) F))  &  ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D (k8_extpro_1 2 k1_scmpds_2 B D))) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A (k8_extpro_1 2 k1_scmpds_2 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k5_card_1 D) 2) C))  <=> (r2_hidden C (k9_xtuple_0 (k2_scmpds_8 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t18_scmpds_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_amistd_1 2 k1_scmpds_2 A) = k5_numbers) ) ) ).
tt(t18_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 C (u1_struct_0 (k1_scmring2 A)))) ) ) )  &  ((k1_funct_1 (k2_extpro_1 2 (k1_scmring2 A) B C) (k4_struct_0 (k1_scmring2 A))) = (k4_card_1 (k5_memstr_0 2 (k1_scmring2 A) C))) ) )  & (v2_extpro_1 B 2 (k1_scmring2 A))) ) ) ) ) ) ).
tt(t18_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 6)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (B = (k8_scmring2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t18_scmyciel,ax, (! [A:$i] :  (~  ( ((k3_tarski A) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  &  (~  (A = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t18_scpinvar,ax, ((k5_card_1 k5_scpinvar) = 12) ).
tt(t18_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_analoaf A B D B E) & (r2_analoaf A C D C E))  =>  ((r2_analoaf A B C B D) |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers B C) A) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A) C))) ) ) ) ) ) ).
tt(t18_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) )  => (r1_xxreal_0 (k2_seq_2 A) (k2_seq_2 B))) ) ) ) ) ).
tt(t18_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k8_nat_1 k1_numbers B D) = (k8_nat_1 k1_numbers A D)) ) ) ) ) ) )  | (v2_comseq_2 B)) ) ) ) ) ) ).
tt(t18_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  => (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k5_seqfunc A (k2_seqfunc A C B)) (k2_seqfunc A (k5_seqfunc A C) (k18_complex1 B)))) ) ) ) ) ) ).
tt(t18_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k37_valued_1 k5_numbers k1_numbers B) A) = (k37_valued_1 k5_numbers k1_numbers (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t18_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_series_1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A B))) ) )  => (r1_xxreal_0 k6_numbers (k4_series_1 A))) ) ) ).
tt(t18_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 1)) (k13_newton B 4))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 1)) B) (k2_nat_1 B 1)) (k6_xcmplx_0 (k2_nat_1 (k13_newton B 2) B) 1)) 2)) ) ) ) ) ) ).
tt(t18_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 (k3_xcmplx_0 A B) (k13_complex1 1 4))) ) ) ) ) ).
tt(t18_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 (k2_nat_1 (k4_nat_1 2 B) 1) (k13_newton 3 B))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_nat_1 (k4_nat_1 B (k13_newton 3 (k2_nat_1 B 1))) 1)) ) ) ) ) ) ).
tt(t18_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  => (r1_xxreal_0 (k2_xcmplx_0 (k6_square_1 (k3_xcmplx_0 A C)) (k6_square_1 (k3_xcmplx_0 B D))) (k6_square_1 (k3_xcmplx_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C D))))) ) ) ) ) ) ) ) ).
tt(t18_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_setfam_1 B (k1_tarski A)) =>  (! [C:$i] :  ((r2_hidden C B) => (r1_tarski C A)) ) ) ) ) ).
tt(t18_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A B) k6_numbers) = (k1_kurato_0 A B)) ) ) ) ).
tt(t18_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k7_setlim_2 B D C) A) = (k7_setlim_2 B (k10_nat_1 (k9_setfam_1 B) D A) C)) ) ) ) ) ) ) ) ).
tt(t18_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) & (v2_binop_1 C A)) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k7_setwiseo B A C (k3_setwiseo B E F) D) = (k5_binop_1 A C (k3_funct_2 B A D E) (k3_funct_2 B A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) &  ((v2_binop_1 E B) &  ((v1_setwiseo E B) &  ((v1_finseqop E B) & (r6_binop_1 B F E)) ) ) )  =>  ((k3_funct_2 B B (k10_funcop_1 B B F D (k6_partfun1 B)) (k7_setwiseo A B E C G)) = (k7_setwiseo A B E C (k1_partfun1 A B B B G (k10_funcop_1 B B F D (k6_partfun1 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ((r1_sfmastr2 B A C D) & (r1_xxreal_0 k6_numbers (k1_funct_1 A C)))  =>  ( ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C))  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 A C) E) =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) = k6_numbers)  &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) F) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r5_scmfsa7b E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) F) (k1_funct_4 G (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers)))))) & (r6_scmfsa7b E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) F) (k1_funct_4 G (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers))))))) )  =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) (k2_nat_1 F 1)) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( ( (C = (k16_scmfsa_2 A B))  |  (C = (k17_scmfsa_2 A B)) )  =>  ((k1_sf_mastr C) = (k4_scmfsa_m A)) ) ) ) ) ) ) ) ).
tt(t18_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  ((r1_tarski (u1_struct_0 B) A) & (r1_tarski (u1_sgraph1 B) (k2_sgraph1 (u1_struct_0 B)))) ) ) ) ).
tt(t18_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  =>  ((k6_lattices A) = (k1_sheffer1 A)) ) ) ).
tt(t18_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) D) B) = (k5_sheffer1 A B (k5_sheffer1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t18_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_simplex0 A) => (v1_finset_1 (u1_pre_topc A))) ) ) ).
tt(t18_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) =>  ((k2_struct_0 (k5_simplex1 A B C)) = (k2_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t18_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v4_matroid0 B) &  ((v2_simplex2 B A) & (m1_simplex0 B (u1_struct_0 (k15_euclid A)))) ) ) ) )  =>  ((r1_tarski (k3_simplex1 (k15_euclid A) B) (k2_struct_0 B)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k1_xboole_0))  &  (! [D:$i] :  ((v7_ordinal1 D) => (r1_xxreal_0 C (k3_simplex2 A (k5_simplex1 D (k15_euclid A) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sincos10,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t18_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k5_square_1 (k1_seq_1 k1_sin_cos2 A)) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k1_seq_1 k4_sin_cos2 (k8_real_1 2 A)) 1)))  &  ((k5_square_1 (k1_seq_1 k4_sin_cos2 A)) = (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k1_seq_1 k4_sin_cos2 (k8_real_1 2 A)) 1))) ) ) ) ).
tt(t18_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 k7_complex1 A)) = (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A)) ) ) ).
tt(t18_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) = (k4_xcmplx_0 (k3_xcmplx_0 2 (k3_xcmplx_0 (k17_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k17_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)))))) ) ) ) ) ).
tt(t18_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k20_sin_cos A) = k6_numbers) )  =>  ((k1_sin_cos4 (k8_real_1 3 A)) = (k10_real_1 (k9_real_1 (k8_real_1 3 (k1_sin_cos4 A)) (k2_newton (k1_sin_cos4 A) 3)) (k9_real_1 1 (k8_real_1 3 (k5_square_1 (k1_sin_cos4 A)))))) ) ) ) ).
tt(t18_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k7_real_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A) & (r1_xxreal_0 A (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  => (r1_xxreal_0 k6_numbers (k20_sin_cos A))) ) ) ) ) ).
tt(t18_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k12_binop_2 (k11_binop_2 2 A) (k10_binop_2 1 (k3_square_1 A))) k6_numbers)) ) ) ) ) ).
tt(t18_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k9_sin_cos2 (k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2))))  &  ((k7_xcmplx_0 (k6_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k2_xcmplx_0 (k6_sin_cos2 A) (k6_sin_cos2 B))) = (k9_sin_cos2 (k6_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 B 2)))) ) ) ) ) ) ).
tt(t18_sin_cos9,ax, ( ((k1_seq_1 k30_sin_cos (k10_real_1 k32_sin_cos 4)) = 1)  &  ( ((k2_sin_cos4 (k10_real_1 k32_sin_cos 4)) = 1)  &  ( ((k1_seq_1 k30_sin_cos (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) = (k1_real_1 1))  &  ((k2_sin_cos4 (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) = (k1_real_1 1)) ) ) ) ).
tt(t18_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k8_nat_1 k1_numbers (k4_sin_cos (k17_complex1 A)) B))) ) ) ) ).
tt(t18_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)) &  ((k17_euclid A) = (k17_euclid D)) ) )  =>  ( ((k18_euclid A) = (k18_euclid D))  | (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t18_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 2 (k3_finseq_1 A)) => (r1_tarski (k10_xtuple_0 A) (k3_topreal1 2 A))) ) ) ).
tt(t18_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k10_pscomp_1 A) = (k13_pscomp_1 A))  => (v2_sppol_1 A)) ) ) ).
tt(t18_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)) &  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  (~  ( ((k18_euclid A) = (k18_euclid B))  &  ((k18_euclid C) = (k18_euclid B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k4_finseq_1 C)) & (r2_hidden B (k4_finseq_1 C)))  => (r1_tarski (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B)) (k3_topreal1 2 C))) ) ) ) ) ) ) ).
tt(t18_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t18_square_1,ax, ((k7_square_1 1) = 1) ).
tt(t18_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_stacks_1 A B C) =>  ((r1_stacks_1 A B) |  ((k6_stacks_1 A B) = (k6_stacks_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t18_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_2 C B) & (v1_stirl2_1 C A B))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 B D))  => (r1_xxreal_0 D (k5_nat_1 (k1_stirl2_1 A B C (k1_seq_4 D))))) ) ) ) ) ) ) ) ) ) ).
tt(t18_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) => (r2_relset_1 (k3_qc_lang1 A) B (k3_sublemma A D B C) (k3_sublemma A (k5_sublemma A D) B C))) ) ) ) ) ) ) ) ).
tt(t18_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r1_tarski B (k3_subset_1 A B)) <=>  (B = (k1_subset_1 A)) ) ) ) ) ).
tt(t18_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A B))) =>  ((r1_tarski C D) => (r1_tarski (k4_substlat A B E C) (k4_substlat A B E D))) ) ) ) ) ) ) ) ) ).
tt(t18_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k28_substut1 A (k21_substut1 A B C)) = B) ) ) ) ) ) ) ) ).
tt(t18_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A B C)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((k7_cqc_sim1 A (k6_cqc_lang A B)) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A (k6_cqc_lang A B) C)))) ) ) ) ) ) ) ) ).
tt(t18_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (r1_xxreal_0 (k3_supinf_2 (k11_supinf_2 k7_numbers A B D) (k11_supinf_2 k7_numbers A C E)) (k11_supinf_2 k7_numbers A (k5_supinf_2 B C) (k13_supinf_2 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (F = (k4_struct_0 A)) )  &  (~  ((k1_symsp_1 A B (k4_vectsp_1 A B F D) C E) = (k1_symsp_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k4_relat_1 A) (k2_xboole_0 B (k2_relat_1 B))) =>  ((r1_tarski (k4_relat_1 A) B) & (r1_tarski (k4_relat_1 A) (k2_relat_1 B))) ) ) ) ) ).
tt(t18_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((v2_metric_1 B A) & (v4_metric_1 B A)) )  =>  ((v1_partfun1 (k1_taxonom1 A B C) A) &  ((v1_relat_2 (k1_taxonom1 A B C)) &  ((v3_relat_2 (k1_taxonom1 A B C)) & (m1_subset_1 (k1_taxonom1 A B C) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ) ).
tt(t18_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ( ((r2_hidden D C) & (r1_tarski B D))  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ( ((r2_hidden B E) &  (! [F:$i] :  (~  ((r2_hidden F E) &  ( (~ (r1_tarski F D))  &  ( (~ (r1_tarski D F))  &  (~ (r1_xboole_0 D F)) ) ) ) ) ) )  =>  (! [F:$i] :  ( (! [G:$i] :  ((r2_hidden G F) <=>  ((r2_hidden G E) & (r1_tarski G D)) ) )  =>  ((m1_eqrel_1 (k2_xboole_0 F (k7_subset_1 (k1_zfmisc_1 A) C (k1_tarski D))) A) & (r1_setfam_1 (k2_xboole_0 F (k7_subset_1 (k1_zfmisc_1 A) C (k1_tarski D))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_taylor_1,ax, ((r2_relset_1 k1_numbers k1_numbers k3_taylor_1 (k2_partfun2 k1_numbers k1_numbers k24_sin_cos)) &  ((v2_funct_1 k3_taylor_1) &  ( ((k1_relset_1 k1_numbers k3_taylor_1) = (k3_limfunc1 k6_numbers))  &  ( ((k2_relset_1 k1_numbers k3_taylor_1) = k1_numbers)  &  ((r2_fdiff_1 k3_taylor_1 (k3_limfunc1 k6_numbers)) &  ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_fdiff_1 k3_taylor_1 A)) ) )  &  ( (! [A:$i] :  ((m2_subset_1 A k1_numbers (k3_limfunc1 k6_numbers)) =>  ((k1_fdiff_1 k3_taylor_1 A) = (k10_real_1 1 A)) ) )  &  (! [A:$i] :  ((m2_subset_1 A k1_numbers (k3_limfunc1 k6_numbers)) =>  (~ (r1_xxreal_0 (k1_fdiff_1 k3_taylor_1 A) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t18_taylor_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_fdiff_1 A B) =>  ((k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A) B) = (k32_valued_1 k1_numbers k1_numbers (k2_fdiff_1 A B))) ) ) ) ) ) ).
tt(t18_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v5_tbsp_1 A) <=> (v6_tbsp_1 (k2_struct_0 A) A)) ) ) ).
tt(t18_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v5_tops_1 (k1_struct_0 A) A)) ) ).
tt(t18_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (v1_tops_2 (k1_tdlat_2 A B) A)) ) ) ) ).
tt(t18_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v2_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc B A) &  ( (~  (B = k1_xboole_0) )  &  (~  (B = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k3_polynom1 A C (k5_termord A B C D) (k3_termord A B C D)) = (k3_polynom1 A C D (k3_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(t18_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = B) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t18_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_pre_topc (k1_tex_2 A B)) =>  ((v1_tdlat_3 (k1_tex_2 A B)) & (v2_tdlat_3 (k1_tex_2 A B))) ) ) ) ) ) ).
tt(t18_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v1_tops_3 D B) <=> (v1_tops_3 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t18_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k6_domain_1 (u1_struct_0 A) B) (k2_tex_4 A B))) ) ) ) ).
tt(t18_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_subset_1 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc D A k3_topmetr) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  =>  (~  ( ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D B) = (k1_tarski k6_numbers))  &  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D C) = (k1_tarski 1)) ) ) ) ) ) ) ) ) ) )  => (v10_pre_topc A)) ) ) ).
tt(t18_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((m1_pre_topc B C) =>  ( ((r1_tsep_1 B D) & (r1_tsep_1 D B))  |  ( (~ (r1_tsep_1 C D))  &  (~ (r1_tsep_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  ((m1_toler_1 A B C) => (r1_tarski A B)) ) ) ) ) ).
tt(t18_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 (k15_euclid A) k17_borsuk_1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) k17_borsuk_1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k17_borsuk_1)) =>  ((k1_binop_1 B C D) = (k1_rlvect_1 (k15_euclid A) C D)) ) ) ) )  => (v5_pre_topc B (k2_borsuk_1 (k15_euclid A) k17_borsuk_1) (k15_euclid A))) ) ) ) ) ).
tt(t18_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_borsuk_2 E B C D) =>  (! [F:$i] :  ((m1_borsuk_2 F B C D) => (m1_borsuk_6 (k1_topalg_2 A B E F) B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topalg_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 A (k1_pre_topc B D))) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A (k1_pre_topc B D))) (u1_struct_0 C))))) )  =>  ( ( (F = (k2_partfun1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 C) E (k2_zfmisc_1 (u1_struct_0 A) D)))  & (v5_pre_topc E (k2_borsuk_1 A B) C))  => (v5_pre_topc F (k2_borsuk_1 A (k1_pre_topc B D)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_6 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H) =>  (! [J:$i] :  ((m1_borsuk_2 J B E F) =>  (! [K:$i] :  ((m1_borsuk_2 K B E F) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) J (k4_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) K (k4_topalg_4 A B k5_topmetr H)) & (r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) )  => (m1_borsuk_6 (k4_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) I) B E F J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_6 F A B C D E) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ((v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) A) => (v5_pre_topc (k3_topalg_5 k5_topmetr k5_topmetr A F G) k5_topmetr A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B B) =>  (! [F:$i] :  ((m1_borsuk_2 F C D D) =>  ( ( (B = D)  &  ((r1_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 k5_topmetr) (u1_struct_0 C) E F) & (v3_topalg_6 F C D)) )  => (v3_topalg_6 E A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_topdim_1 (k1_pre_topc A B)) => (v1_topdim_1 B A)) ) ) ) ) ).
tt(t18_topdim_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 1))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k9_finseq_1 B) = A)  =>  ((r1_xxreal_0 C k6_numbers) |  ((k2_tops_1 (k15_euclid 1) (k1_topreal9 1 A C)) = (k2_tarski (k9_finseq_1 (k3_xxreal_3 B C)) (k9_finseq_1 (k1_xxreal_3 B C)))) ) ) ) ) ) ) ) ) ).
tt(t18_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_topgen_1 A B)) <=>  (! [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k9_subset_1 (u1_struct_0 A) B E)) &  (~  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  ((r1_tarski C B) &  ((k1_card_1 C) = (k2_waybel23 A)) ) ) ) ) ) ) ) ).
tt(t18_topgen_3,ax, (! [A:$i] :  ( ((v4_taxonom2 A) &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D C))  & (r1_tarski (k2_rcomp_1 C D) B)) ) ) ) ) ) ) ) ) )  => (v4_card_3 A)) ) ).
tt(t18_topgen_4,ax, (! [A:$i] :  ((v1_xboole_0 k1_xboole_0) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ).
tt(t18_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden (k19_euclid A B) k2_topgen_5) <=> (r1_xxreal_0 k6_numbers B)) ) ) ) ) ).
tt(t18_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k1_topgrp_1 A B)) (k1_topgrp_1 A (k2_group_1 A B)))) ) ) ) ).
tt(t18_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((u1_struct_0 (k4_topmetr A B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(t18_topreal1,ax, ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1))) = (k1_tarski (k19_euclid 1 1))) ).
tt(t18_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A)))  =>  ((k2_topreal1 2 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B) C) = (k2_topreal1 2 A C)) ) ) ) ) ) ) ) ).
tt(t18_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) )  &  ((v4_topreal1 B) &  ((r2_hidden A (k3_topreal1 2 B)) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((v4_topreal1 C) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = A)  &  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) & (r1_tarski (k3_topreal1 2 C) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((v1_topreal2 A) &  ((k25_pscomp_1 A) = (k21_pscomp_1 A)) ) ) ) ) ).
tt(t18_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k2_metric_1 (k1_topreal7 A B) (k2_topreal7 A B C E) (k2_topreal7 A B D F)) = (k2_square_1 (k2_metric_1 A C D) (k2_metric_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_topreal8,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_zfmisc_1 C))  & (m2_finseq_1 C A))  =>  ( ( ((k7_partfun1 A C 1) = (k7_partfun1 A B (k3_finseq_1 B)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  &  ((k7_partfun1 A B D) = (k7_partfun1 A C 1)) ) ) ) ) ) )  =>  ((k1_finseq_6 A (k4_graph_2 A B C) (k7_partfun1 A C 1)) = (k4_graph_2 A C B)) ) ) ) ) ) ) ) ).
tt(t18_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_topreal9 A C B) (k3_topreal9 A C B)) = (k2_topreal9 A C B)) ) ) ) ) ) ) ).
tt(t18_topreala,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers A) = (k4_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)))  &  ((v3_rcomp_1 (k1_relset_1 k1_numbers B)) &  ((v3_rcomp_1 (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B (k1_relset_1 k1_numbers B))) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_relset_1 k1_numbers C))) &  ( (! [D:$i] :  ((r2_hidden D (k1_relset_1 k1_numbers B)) =>  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) )  &  (! [D:$i] :  ((r2_hidden D (k1_relset_1 k1_numbers C)) =>  ((k1_funct_1 A D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A (k1_relset_1 k1_numbers A)))) ) ) ) ) ) ) ).
tt(t18_toprealb,ax,(m1_pre_topc (k8_toprealb 2) (k1_topreala (k1_real_1 1) 1 (k1_real_1 1) 1))).
tt(t18_toprealc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k12_euclid (k9_finseq_1 A)) = (k18_complex1 A)) ) ) ).
tt(t18_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k4_toprns_1 A B (k3_toprns_1 A C)) = (k1_toprns_1 A B C)) ) ) ) ) ) ) ).
tt(t18_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k1_tops_1 A (k1_struct_0 A)) = (k1_struct_0 A)) ) ) ).
tt(t18_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) => (v2_tops_2 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t18_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=> (v2_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t18_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v5_pre_topc C B (k15_euclid A)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (? [F:$i] :  ( ((v3_pre_topc F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D F) & (r1_tarski (k7_relset_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C F) (k1_topreal9 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ((r2_transgeo A B D) & (r2_transgeo A C D))  => (r2_transgeo A (k1_transgeo A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t18_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((v3_tops_2 (k3_treal_1 A B (k2_treal_1 A B) (k1_treal_1 A B)) (k4_topmetr k6_numbers 1) (k4_topmetr A B)) &  ((r2_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k2_tops_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k3_treal_1 A B (k2_treal_1 A B) (k1_treal_1 A B))) (k4_treal_1 A B (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1))) &  ((v3_tops_2 (k4_treal_1 A B (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) (k4_topmetr A B) (k4_topmetr k6_numbers 1)) & (r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr A B)) (k2_tops_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k4_treal_1 A B (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1))) (k3_treal_1 A B (k2_treal_1 A B) (k1_treal_1 A B)))) ) ) ) ) ) ) ) ).
tt(t18_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden B (k1_trees_1 A)) & (r2_hidden C (k1_trees_1 A)))  => (r3_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t18_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((v1_trees_2 A) => (v1_finset_1 (k1_trees_2 A B))) ) ) ) ) ).
tt(t18_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_trees_3 A) & (r1_tarski B A))  => (v1_trees_3 B)) ) ) ).
tt(t18_trees_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k3_trees_4 A C) = (k4_trees_4 B D))  & (v6_trees_3 D))  =>  ( (A = B)  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 D E) = (k1_trees_4 (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((v1_xboole_0 (k7_trees_9 A B)) <=>  ((v1_zfmisc_1 A) &  (~ (r2_hidden (k1_funct_1 A k1_xboole_0) B)) ) ) ) ) ) ).
tt(t18_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_tsep_1 C B) & (m1_pre_topc C B))  =>  ((v1_tsep_1 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ).
tt(t18_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B D) &  ((r2_tsep_2 A C E) &  ((r1_xboole_0 B C) & (r2_tsep_1 A D E)) ) )  => (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tsp_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v6_pre_topc C) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t18_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (u1_struct_0 B))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k9_subset_1 (u1_struct_0 A) D (k4_tex_4 A E)) = (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_turing_1 (k3_finseq_4 k5_numbers C D E) A B) =>  ((r1_turing_1 A B C (k2_nat_1 (k2_nat_1 C D) 2)) & (r1_turing_1 A B (k2_nat_1 (k2_nat_1 C D) 2) (k2_nat_1 (k2_nat_1 (k2_nat_1 C D) E) 4))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_twoscomp,ax, ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 k6_numbers 1 1)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k17_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k17_twoscomp (k11_finseq_1 1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t18_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) ) )  =>  ((k7_unialg_2 A (k2_subset_1 (u1_struct_0 A))) = A) ) ) ).
tt(t18_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  ((k5_unialg_2 A (k7_unialg_2 A (k6_unialg_2 A)) B) = (k7_unialg_2 A (k6_unialg_2 A))) ) ) ) ) ).
tt(t18_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k7_group_1 (k1_uniroots A)) = (k21_binop_2 (k7_group_1 A) 1)) ) ) ).
tt(t18_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) k6_numbers))  &  ((k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t18_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (m1_connsp_2 B A C)) ) )  => (v3_pre_topc B A)) ) ) ) ) ).
tt(t18_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ( (B = C)  & (r1_xxreal_0 k6_numbers C))  =>  ((k8_supinf_2 (k1_integra2 A B)) = (k1_extreal1 C (k8_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t18_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_urysohn3 D A B C) =>  ((v5_pre_topc (k6_urysohn3 A B C D) A k3_topmetr) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k6_urysohn3 A B C D) E)) &  ((r1_xxreal_0 (k1_seq_1 (k6_urysohn3 A B C D) E) 1) &  ( ((r2_hidden E B) =>  ((k1_seq_1 (k6_urysohn3 A B C D) E) = k6_numbers) )  &  ((r2_hidden E C) =>  ((k1_seq_1 (k6_urysohn3 A B C D) E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k7_cqc_lang A D E) F C) <=>  ((r1_valuat_1 A B D F C) & (r1_valuat_1 A B E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_valued_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_funct_1 A) & (v4_valued_0 A)) ) ) )  =>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ).
tt(t18_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((k1_funct_1 (k54_valued_1 A) B) = (k17_complex1 (k1_funct_1 A B))) ) ) ) ).
tt(t18_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k45_valued_1 A B) = (k30_valued_1 (k45_valued_1 B A))) ) ) ) ) ).
tt(t18_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (D = F) )  =>  ((r1_struct_0 D C) |  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) G F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) H (k4_vectsp_1 A B I C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vectsp11,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_vectsp11 A B k1_xboole_0) (k3_struct_0 A))) ) ) ) ).
tt(t18_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k4_struct_0 A) B) = (k4_algstr_0 A B))  &  ((k5_algstr_0 A B (k4_struct_0 A)) = B) ) ) ) ) ) ).
tt(t18_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  ((k1_vectsp_2 A D B) = (k1_vectsp_2 A (k6_algstr_0 A D C) (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_struct_0 D (k4_struct_0 C))) ) ) ) ) ) ) ) ).
tt(t18_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) => (m1_vectsp_4 (k2_vectsp_5 A B C E) A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~  (C = D) )  =>  (! [E:$i] :  ((m2_vectsp_6 E A B (k7_domain_1 (u1_struct_0 B) C D)) =>  ((k4_vectsp_6 A B E) = (k3_rlvect_1 B (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_vectsp_7 A B C) = B)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r1_tarski D C) &  ((v1_vectsp_7 D A B) &  ((k1_vectsp_7 A B D) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((r1_struct_0 (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) C D)) E) &  ( (~ (r1_struct_0 (k1_vectsp_7 A B D) E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r2_hidden F C) & (r1_struct_0 (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) (k4_subset_1 (u1_struct_0 B) C D) (k6_domain_1 (u1_struct_0 B) F)) (k6_domain_1 (u1_struct_0 B) E))) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B C 1) C)) ) ) ) ) ) ).
tt(t18_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B C k6_complex1) C)) ) ) ) ) ) ).
tt(t18_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k6_waybel_0 A B)) <=> (r1_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t18_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((k1_yellow_2 A A (k6_waybel10 A B)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B))) ) ) ) ) ).
tt(t18_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_waybel_0 A B (k6_waybel_0 A D)) => (r1_orders_2 A D (k1_waybel11 A B))) ) ) ) ) ) ) ) ) ).
tt(t18_waybel12,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A C D) => (r1_yellow_4 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) D) B))) ) ) ) ) ) ) ) ) ).
tt(t18_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 E A B) =>  ((r1_lattice3 A C D) <=> (r1_lattice3 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( ((k13_lattice3 (k2_yellow_1 (u1_pre_topc A)) B C) = (k2_xboole_0 B C))  &  ((k12_lattice3 (k2_yellow_1 (u1_pre_topc A)) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(t18_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~  ((v3_waybel_3 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v6_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  =>  (~  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) ) ) ) ) )  &  ( (? [B:$i] :  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v6_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  &  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) )  => (v3_waybel_3 A)) ) ) ) ).
tt(t18_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v3_lattice3 (k2_yellow_1 (k8_waybel_0 A)))) ) ).
tt(t18_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_waybel_0 D A) & (l1_waybel_0 D A)) )  =>  ((v5_orders_3 C A B) => (v8_waybel_0 (k6_waybel_9 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t18_waybel18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  (? [B:$i] :  ( (~ (v1_xboole_0 B))  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B (k7_funcop_1 B k9_waybel18)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B (k7_funcop_1 B k9_waybel18))))))) )  & (v3_tops_2 (k8_waybel18 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18)) C) A (k7_waybel18 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18)) C))) ) ) ) ) ) ).
tt(t18_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_waybel_0 (k1_waybel_3 A C) A) &  (~ (v1_xboole_0 (k1_waybel_3 A C))) ) ) )  & (v2_waybel_3 A)) )  => (v2_waybel_3 B)) ) ) ) ) ).
tt(t18_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) =>  ((r1_yellow_2 (u1_struct_0 A) A (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A)) & (r1_yellow_2 (u1_struct_0 B) B (k3_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ) ).
tt(t18_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((r5_waybel_1 A B) & (v3_lattice3 A))  => (v3_lattice3 B)) ) ) ) ) ).
tt(t18_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v7_yellow_0 B A) => (v3_lattice3 B)) ) ) ) ) ).
tt(t18_waybel22,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((r1_waybel22 B C) &  ((k1_card_1 C) = (k1_card_1 A)) )  => (r5_waybel_1 B (k2_yellow_1 (k8_waybel_0 (k3_yellow_1 A))))) ) ) ) ) ).
tt(t18_waybel23,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t18_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((v22_waybel_0 (k1_waybel24 A B C D E) B C) & (v22_waybel_0 (k2_waybel24 A B C D F) A C)) ) ) ) )  => (v22_waybel_0 D (k3_yellow_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t18_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B)))))) )  =>  ( ( (C = D)  & (v3_tops_2 C A B))  => (v23_waybel_0 D (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ) ) ) ) ).
tt(t18_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_borsuk_1 D B C) => (r1_yellow16 (k1_waybel26 A C) (k1_waybel26 A B) (k3_waybel26 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t18_waybel27,ax, (! [A:$i] : (r5_waybel_1 (k3_yellow_1 A) (k6_yellow_1 A (k3_yellow_1 1)))) ).
tt(t18_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v5_yellow_6 (k3_waybel28 A) A)) ) ).
tt(t18_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v4_waybel11 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((k1_waybel26 A B) = (k3_waybel24 A B)) ) ) ) ) ).
tt(t18_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) )  =>  ((v10_waybel_0 B A) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A B)) A)) ) ) ) ) ).
tt(t18_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k2_pre_topc A C) = (k2_pre_topc B D)) ) ) ) ) ) ) ) ) ) ).
tt(t18_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel_3 B A) =>  (B = (k2_yellow_0 A (k2_waybel_3 A B))) ) ) ) ) ) ).
tt(t18_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v1_waybel11 B A)) ) ) ) ).
tt(t18_waybel33,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel33 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 C (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  ((r2_hidden B C) => (r2_hidden (k1_waybel33 A (k2_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(t18_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( ((k15_functor0 (k4_waybel34 A) (k5_waybel34 A) (k6_waybel34 A)) = (k7_waybel34 A))  &  ((k15_functor0 (k5_waybel34 A) (k4_waybel34 A) (k7_waybel34 A)) = (k6_waybel34 A)) ) ) ) ).
tt(t18_waybel35,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden D C) &  ((r2_hidden (k4_tarski D D) B) & (r1_yellow_0 A (k4_waybel35 A B C D))) )  =>  (D = (k1_yellow_0 A (k4_waybel35 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t18_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r3_orders_2 A C (k1_yellow_0 A D)) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski E D) & (r3_orders_2 A B (k1_yellow_0 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r2_hidden (k7_waybel_4 A B) (u1_struct_0 (k8_waybel_4 A)))) ) ) ) ).
tt(t18_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r2_hidden B (k1_yellow_6 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D B) => (r2_hidden (k1_funct_1 C D) (k1_yellow_6 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) C D E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A D)) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(t18_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k7_subset_1 (u1_struct_0 A) (k3_waybel_6 A) (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))))  => (v4_waybel_6 B A)) ) ) ) ) ).
tt(t18_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_waybel_7 B A) <=>  ( ( (~ (v1_xboole_0 (k3_subset_1 (u1_struct_0 A) B)))  &  ((v2_waybel_0 (k3_subset_1 (u1_struct_0 A) B) A) &  ((v13_waybel_0 (k3_subset_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k3_subset_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  |  ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t18_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v3_waybel_8 A))  => (v3_waybel_8 B)) ) ) ) ) ).
tt(t18_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_waybel_9 A A (k4_waybel_1 A C) B) = (k3_waybel_2 A C B)) ) ) ) ) ) ) ).
tt(t18_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  => (r1_struct_0 (k4_weddwitt A) (k4_struct_0 A))) ) ).
tt(t18_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A B) D) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v4_relat_2 B) => (v4_relat_2 (k2_wellord1 B A))) ) ) ) ).
tt(t18_wellord2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ( (! [B:$i] :  (~  ((r2_hidden B A) &  (B = k1_xboole_0) ) ) )  &  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (B = C)  | (r1_xboole_0 B C)) ) ) )  &  (! [B:$i] :  (? [C:$i] :  ((r2_hidden C A) &  (! [D:$i] :  (~  ((k3_xboole_0 B C) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A (k6_xcmplx_0 B C)) =>  ((r1_xxreal_0 A B) & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t18_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k3_xboole_0 B C)) => (r1_tarski A B)) ) ) ) ).
tt(t18_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k6_xboolean A B)) = (k5_xboolean (k3_xboolean A) (k4_xboolean (k3_xboolean A) B))) ) ) ) ) ).
tt(t18_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 A (k6_xcmplx_0 A B)) = B) ) ) ) ) ).
tt(t18_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 C D)) => (r1_xxreal_0 (k6_xcmplx_0 D C) (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t18_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k13_xtuple_0 B)) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~ (r2_hidden (k6_xtuple_0 A C D E) B)) ) ) ) ) ) ) ) ).
tt(t18_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k3_xxreal_0 A C) (k3_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t18_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_1 A A) = k1_xboole_0) ) ) ).
tt(t18_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m2_xxreal_2 A (k3_xxreal_1 A B))) ) ) ) ).
tt(t18_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k3_xxreal_3 A B) = k1_xxreal_0)  &  ( (~  (A = k1_xxreal_0) )  &  (~  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(t18_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ( (D = (k10_lattice3 A B C))  & (r1_yellow_0 A (k2_tarski B C)))  =>  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) )  &  ( ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) )  =>  ( (D = (k10_lattice3 A B C))  & (r1_yellow_0 A (k2_tarski B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_waybel_3 (k3_yellow_3 A B) (k7_yellow_3 A B C E) (k7_yellow_3 A B D F)) =>  ((r1_waybel_3 A C D) & (r1_waybel_3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_yellow_0 C A) =>  (! [D:$i] :  ((m1_yellow_0 D B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (v6_yellow_0 C A)) )  => (v6_yellow_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t18_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_yellow13 (k9_setfam_1 (u1_struct_0 A)) A B)) ) ) ) ).
tt(t18_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( (~  ( (~ (r1_t_0topsp A B))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B)) ) ) ) ) ) )  =>  ((v2_struct_0 A) <=> (v2_struct_0 B)) ) ) ) ) ) ).
tt(t18_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((k5_setfam_1 A (k2_yellow15 A B)) = A) ) ) ) ).
tt(t18_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_orders_3 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (~  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C) (k3_struct_0 B)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v6_waybel_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) E (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D)) &  ( ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) E (u1_struct_0 (k1_yellow_2 A A E))) = (k3_struct_0 (k1_yellow_2 A A E)))  & (r5_waybel_1 B (k1_yellow_2 A A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B C))))))  =>  ((r1_tarski (k2_struct_0 (k4_waybel18 A B C)) (k3_tarski D)) => (r1_tarski (k2_struct_0 (k3_waybel18 A B)) (k3_tarski (a_4_0_yellow17 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t18_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  ( ((r2_yellow18 A B) &  ((r2_yellow18 C D) & (r1_functor0 A C)) )  => (r1_functor0 B D)) ) ) ) ) ) ) ) ) ).
tt(t18_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k2_pre_topc A C)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_subset_1 D (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  ( (D = (k1_yellow19 A B))  => (r2_waybel_0 A (k3_yellow19 A (k2_struct_0 A) D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow_1,ax, (! [A:$i] :  ((k3_yellow_0 (k3_yellow_1 A)) = k1_xboole_0) ) ).
tt(t18_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A A))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k2_zfmisc_1 A A)) &  ((v1_funct_1 D) & (v1_partfun1 D (k2_zfmisc_1 A A))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (k2_zfmisc_1 B B)) &  ((v1_funct_1 E) & (v1_partfun1 E (k2_zfmisc_1 B B))) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (k2_zfmisc_1 B B)) &  ((v1_funct_1 F) & (v1_partfun1 F (k2_zfmisc_1 B B))) ) )  =>  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B))) &  ((v1_funct_1 G) & (v1_partfun1 G (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B)))) ) )  &  (? [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B))) &  ((v1_funct_1 H) & (v1_partfun1 H (k2_zfmisc_1 (k3_xboole_0 A B) (k3_xboole_0 A B)))) ) )  &  ( (G = (k1_yellow20 C E))  &  ( (H = (k1_yellow20 D F))  &  ((k1_yellow20 (k3_altcat_1 A C D) (k3_altcat_1 B E F)) = (k3_altcat_1 (k3_xboole_0 A B) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_yellow21 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_yellow21 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k7_yellow21 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k7_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k7_yellow21 A) C))) &  ((v22_waybel_0 D (k4_yellow21 (k7_yellow21 A) B) (k4_yellow21 (k7_yellow21 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k7_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k7_yellow21 A) C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v11_quantal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ).
tt(t18_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v1_lattice3 (k3_yellow_3 A B)) =>  ((v1_lattice3 A) & (v1_lattice3 B)) ) ) ) ) ) ).
tt(t18_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_yellow_4 A (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) B D)) (k4_subset_1 (u1_struct_0 A) B (k2_yellow_4 A C D)))) ) ) ) ) ) ) ) ).
tt(t18_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_5 A (k13_lattice3 A B C) D) = (k13_lattice3 A (k1_yellow_5 A B D) (k1_yellow_5 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t18_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  (! [D:$i] :  ((r2_waybel_0 A C D) => (r2_waybel_0 A B D)) ) ) ) ) ) ) ) ).
tt(t18_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))) =>  ( (B = C)  =>  ( ((k12_waybel_0 A B) = (k11_waybel_0 (k7_lattice3 A) C))  &  ((k11_waybel_0 A B) = (k12_waybel_0 (k7_lattice3 A) C)) ) ) ) ) ) ) ) ) ).
tt(t18_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_yellow_8 A (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) B)) ) ) ) ).
tt(t18_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (B = (k2_tarski k1_xboole_0 A))  =>  ( ((k1_cantor_1 A B) = B)  &  ((k2_cantor_1 A B) = B) ) ) ) ) ) ).
tt(t18_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v8_zf_fund1 B A) & (r2_hidden C B))  =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ((r2_hidden (k5_zf_fund1 (k4_zf_lang D E) C) B) & (r2_hidden (k5_zf_fund1 (k5_zf_lang D E) C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t18_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k17_zf_lang B C D A) = (k13_zf_lang B (k13_zf_lang C (k13_zf_lang D A))))  &  ((k17_zf_lang B C D A) = (k15_zf_lang B C (k13_zf_lang D A))) ) ) ) ) ) ) ) ) ) ).
tt(t18_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_zf_lang A) =>  ((k1_funct_1 A 1) = k6_numbers) ) ) ) ).
tt(t18_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_tarski A) (k1_tarski B)) =>  (A = B) ) ) ) ).
tt(t18_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ((v1_ordinal1 A) &  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r2_hidden (k2_tarski B C) A)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B A) => (r2_hidden (k3_tarski B) A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B A) => (r2_hidden (k3_xboole_0 A (k1_zfmisc_1 B)) A)) )  &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) & (r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))))  =>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_hidden (k7_relset_1 A A (k1_zfmodel1 B A C) D) A)) ) ) ) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_xboole_0 C D) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) )  | (v1_zf_model A)) ) ) ) ).
tt(t18_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_zfmodel1 B A) & (r1_zfmodel1 C A))  => (r1_zfmodel1 (k3_relat_1 C B) A)) ) ) ) ) ) ) ).
tt(t18_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r1_zf_model A B (k11_zf_lang C D)) <=>  ((r1_zf_model A B C) => (r1_zf_model A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t18_zfrefle1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  => (r1_tarski (k10_xtuple_0 A) (k4_ordinal2 A))) ) ).
tt(t18_zf_refle,ax, (! [A:$i] : (r1_tarski (k3_ordinal2 A) (k1_ordinal1 (k3_tarski (k2_ordinal1 A))))) ).
tt(t18_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_zmodul01 B A) =>  ( (B = k1_xboole_0)  | (r2_hidden (k4_struct_0 A) B)) ) ) ) ) ) ).
tt(t190_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xxreal_0 C) => (r1_tarski (k6_subset_1 (k22_member_1 A C) (k22_member_1 B C)) (k22_member_1 (k6_subset_1 A B) C))) ) ) ) ) ) ).
tt(t190_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_xcmplx_0 (k7_xcmplx_0 (k4_xcmplx_0 A) B)) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(t190_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 1 (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t190_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 C B) (k1_xxreal_1 A B)) = (k2_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t191_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k22_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k22_member_1 A C) (k22_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t191_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 B)) = (k7_xcmplx_0 A B)) ) ) ) ) ).
tt(t191_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 1 (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t191_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 C B) (k1_xxreal_1 A B)) = (k4_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t192_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k22_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k22_member_1 A C) (k22_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t192_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 (k4_xcmplx_0 A) B) = (k7_xcmplx_0 A (k4_xcmplx_0 B))) ) ) ) ) ).
tt(t192_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 1 (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t192_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k1_xxreal_1 C B) (k3_xxreal_1 A B)) = (k1_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t193_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k5_binop_2 C B) (k23_member_1 A C))) ) ) ) ) ) ) ).
tt(t193_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k4_xcmplx_0 A) = (k7_xcmplx_0 A (k4_xcmplx_0 1))) ) ) ).
tt(t193_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 (k4_xcmplx_0 A) B))  => (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ).
tt(t193_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 C B) (k3_xxreal_1 A B)) = (k3_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t194_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k23_member_1 A B) = (a_2_15_member_1 A B)) ) ) ) ) ).
tt(t194_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (A = (k7_xcmplx_0 (k4_xcmplx_0 A) (k4_xcmplx_0 1))) ) ) ).
tt(t194_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 (k4_xcmplx_0 B) A))  => (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ).
tt(t194_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 C B) (k2_xxreal_1 A B)) = (k2_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t195_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k23_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k5_binop_2 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t195_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 A B) = (k4_xcmplx_0 1))  =>  ( (A = (k4_xcmplx_0 B))  &  (B = (k4_xcmplx_0 A)) ) ) ) ) ) ) ).
tt(t195_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B (k4_xcmplx_0 A)))  => (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ).
tt(t195_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 C B) (k2_xxreal_1 A B)) = (k4_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t196_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski (k23_member_1 A C) (k23_member_1 B C)) =>  ( (C = k6_numbers)  | (r1_tarski A B)) ) ) ) ) ) ) ) ).
tt(t196_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 A B) = (k4_xcmplx_0 A))  =>  ( (A = k6_numbers)  |  (B = (k4_xcmplx_0 1)) ) ) ) ) ) ) ).
tt(t196_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 A (k4_xcmplx_0 B)))  => (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ).
tt(t196_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 C B) (k4_xxreal_1 A B)) = (k1_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t197_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k23_member_1 A C) = (k23_member_1 B C))  =>  ( (C = k6_numbers)  |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t197_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 (k4_xcmplx_0 A) A) = (k4_xcmplx_0 1)) ) ) ) ).
tt(t197_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 A)))  & (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ) ).
tt(t197_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 C B) (k4_xxreal_1 A B)) = (k3_xxreal_1 C A)) ) ) ) ) ) ) ) ).
tt(t198_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k23_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k23_member_1 A C) (k23_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t198_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 A (k4_xcmplx_0 A)) = (k4_xcmplx_0 1)) ) ) ) ).
tt(t198_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 B)))  & (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ) ).
tt(t198_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xboole_0 (k2_xxreal_1 A B) (k2_xxreal_1 C D)))  =>  ((k6_subset_1 (k2_xxreal_1 A B) (k2_xxreal_1 C D)) = (k2_xboole_0 (k2_xxreal_1 A C) (k2_xxreal_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(t199_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k23_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k23_member_1 A C) (k23_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t199_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~  (A = k6_numbers) )  &  ( (A = (k7_xcmplx_0 1 A))  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ).
tt(t199_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k4_xcmplx_0 A) B))  & (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ) ).
tt(t199_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xboole_0 (k3_xxreal_1 A B) (k3_xxreal_1 C D)))  =>  ((k6_subset_1 (k3_xxreal_1 A B) (k3_xxreal_1 C D)) = (k2_xboole_0 (k3_xxreal_1 A C) (k3_xxreal_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(t19_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_abcmiz_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_abcmiz_0 A C B) =>  ( (~ (v1_xboole_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A B) (k5_waybel_0 A C))))  &  ((v1_waybel_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A B) (k5_waybel_0 A C)) A) &  ((v12_waybel_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A B) (k5_waybel_0 A C)) A) & (m1_subset_1 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_abcmiz_0 A B) (k5_waybel_0 A C)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_abcmiz_1,ax, ((k1_abcmiz_1 k2_abcmiz_1) = k2_abcmiz_1) ).
tt(t19_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k10_abcmiz_1)  &  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (~  (B = (k5_trees_4 (k4_tarski k10_abcmiz_1 3) C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  =>  ( (B = C)  | (r1_tarski (k2_aff_1 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ((r1_xxreal_0 (k1_afinsq_1 B) A) =>  ((r1_xxreal_0 (k1_afinsq_1 (k1_ordinal4 B C)) A) |  ((k1_funct_1 (k1_ordinal4 B C) A) = (k1_funct_1 C (k6_xcmplx_0 A (k1_afinsq_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t19_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ((k3_afinsq_2 (k1_ordinal4 A B) (k23_binop_2 (k1_afinsq_1 A) 1) (k23_binop_2 (k1_afinsq_1 A) (k1_afinsq_1 B))) = B) ) ) ) ) ).
tt(t19_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((r2_hidden B (k2_zfmisc_1 (k8_afproj A) (k1_tarski 2))) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k4_tarski (k6_afproj A C) 2))  & (v1_aff_4 C A)) ) ) ) ) ) ) ).
tt(t19_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_afvect0 A B D C)) ) ) ) ) ) ) ) ).
tt(t19_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r1_alg_1 A B C) =>  ((r1_alg_1 (k4_alg_1 A (k6_alg_1 A B C)) B (k7_alg_1 A B C)) & (r2_alg_1 (k4_alg_1 A (k6_alg_1 A B C)) B (k7_alg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t19_algspec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_partfun1 (k1_algspec1 A C) (k1_algspec1 B C))) ) ) ) ).
tt(t19_algstr_4,ax, (! [A:$i] :  ((k11_algstr_4 A 3) = (k2_xboole_0 (k2_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 (k2_zfmisc_1 A A) (k1_tarski 1))) (k1_tarski 1)) (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k1_tarski 1)) A) (k1_tarski 2)))) ) ).
tt(t19_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k8_altcat_1 A B) (k1_altcat_1 A B B))) ) ) ) ).
tt(t19_altcat_2,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v6_altcat_1 A) & (l2_altcat_1 A)) )  =>  (A = k5_altcat_2) ) ) ).
tt(t19_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) &  (? [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) &  ((v2_altcat_3 E A B C) &  ((v2_altcat_3 F A C D) &  (~ (v2_altcat_3 (k5_altcat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v2_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v2_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k5_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(t19_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k4_ami_3 H I))  & (r2_hidden H (k9_xtuple_0 B))) )  =>  ((k6_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I)) = (k6_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_amistd_1 2 k1_ami_3 B (k9_ami_3 C A)) = (k2_tarski C (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t19_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_tarski (k2_amistd_1 A B C) (k1_amistd_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t19_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((v2_amistd_1 C A B) & (r2_hidden D (k2_amistd_4 A B C)))  =>  (D = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 (k4_amistd_1 A))) =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) C) = 1)  =>  ((k1_amistd_1 A (k4_amistd_1 A) B C) = (k6_domain_1 k5_numbers (k5_ami_wstd A (k4_amistd_1 A) B))) ) ) ) ) ) ) ) ).
tt(t19_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((u1_struct_0 (k2_analmetr A B C)) = (u1_struct_0 A))  &  ( ((u1_analoaf (k2_analmetr A B C)) = (k1_diraf (u1_struct_0 A) (k1_analoaf A)))  &  ((u1_analmetr (k2_analmetr A B C)) = (k1_analmetr A B C)) ) ) ) ) ) ) ) ) ).
tt(t19_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) )  =>  ( (~  (B = C) )  &  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_analort A B C D E F G))  => (r2_analort A B C F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k1_anproj_1 A)) =>  ((m1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t19_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  ( ( (A = (k9_domain_1 A F G H I))  &  ( ((k3_funct_2 A k1_numbers B F) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = F)  |  ((k1_funct_1 B J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers C G) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = G)  |  ((k1_funct_1 C J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers D H) = 1)  &  ( (! [J:$i] :  ((r2_hidden J A) =>  ( (J = H)  |  ((k1_funct_1 D J) = k6_numbers) ) ) )  &  ( ((k3_funct_2 A k1_numbers E I) = 1)  &  (! [J:$i] :  ((r2_hidden J A) =>  ( (J = I)  |  ((k1_funct_1 E J) = k6_numbers) ) ) ) ) ) ) ) ) ) ) )  =>  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  (! [J:$i] :  ((m2_funct_2 J A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  (? [L:$i] :  ((m1_subset_1 L k1_numbers) &  (? [M:$i] :  ((m1_subset_1 M k1_numbers) &  (? [N:$i] :  ((m1_subset_1 N k1_numbers) & (r2_funct_2 A k1_numbers J (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K B)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L C))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M D))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) N E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k9_aofa_000 A B (k1_nat_1 C 1)) = (k2_xboole_0 (k9_aofa_000 A B C) (a_3_1_aofa_000 A B C))) ) ) ) ) ) ) ).
tt(t19_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_card_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C A (k1_card_1 A)) &  ((v2_funct_2 C (k1_card_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) )  =>  (! [D:$i] :  ((m6_aofa_i00 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 A k4_numbers) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) )  => (r2_aofa_i00 (k7_freealg k19_aofa_000 k26_aofa_i00) A B D E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_armstrng,ax, (! [A:$i] :  ((v3_armstrng (k4_armstrng A) A) &  ((v8_relat_2 (k4_armstrng A)) &  ((v4_armstrng (k4_armstrng A) A) & (v5_armstrng (k4_armstrng A) A)) ) ) ) ).
tt(t19_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (B = 1)  =>  ((k2_arytm_0 A B) = A) ) ) ) ) ) ).
tt(t19_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( (A = k11_arytm_3)  =>  ( (B = k11_arytm_3)  |  ((k2_arytm_1 A B) = (k4_tarski k11_arytm_3 B)) ) ) ) ) ) ) ).
tt(t19_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( (A = (k7_arytm_2 B C))  => (r1_arytm_2 C A)) ) ) ) ) ) ) ).
tt(t19_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( (~  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) )  => (r1_arytm_3 (k6_ordinal3 A (k3_arytm_3 A B)) (k6_ordinal3 B (k3_arytm_3 A B)))) ) ) ) ) ).
tt(t19_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden A (k7_asympt_0 B)) <=> (r2_hidden B (k6_asympt_0 A))) ) ) ) ) ).
tt(t19_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((k6_asympt_0 A) = (k6_asympt_0 B))  <=> (r2_hidden A (k8_asympt_0 B))) ) ) ) ) ).
tt(t19_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [D:$i] :  ((r2_hidden D (k4_autalg_1 A B C)) => (m2_pboole D A B C)) ) ) ) ) ) ) ) ).
tt(t19_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k6_partfun1 (u1_struct_0 A)) = (k1_group_1 (k5_autgroup A))) ) ) ).
tt(t19_bagorder,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ( ((k1_polynom2 A B) = k1_xboole_0)  =>  (B = (k16_pre_poly A)) ) ) ) ) ).
tt(t19_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (r2_hidden (k4_struct_0 A) (k4_bcialg_1 A))) ) ).
tt(t19_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_bcialg_1 A B C) => (r1_bcialg_1 A (k1_bcialg_2 A B D E) (k1_bcialg_2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v4_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B D)) (k1_bcialg_1 A D C)) = (k4_struct_0 A))  &  ( ((k1_bcialg_1 A B (k4_struct_0 A)) = B)  &  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  => (v1_setwiseo (u1_bcialg_4 A) (u1_struct_0 A))) ) ).
tt(t19_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ((k1_bcialg_2 E F G (k2_nat_1 A 1)) = (k1_bcialg_2 E F G (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_bcialg_6 A (k19_binop_2 C) (k2_bcialg_1 A B)) = (k2_bcialg_1 A (k3_bcialg_6 A (k19_binop_2 C) B))) ) ) ) ) ) ) ).
tt(t19_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m2_bciideal B A) => (r1_tarski (k4_bcialg_1 A) B)) ) ) ) ) ).
tt(t19_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k2_bhsp_1 A B C)) (k8_real_1 (k7_square_1 (k2_bhsp_1 A B B)) (k7_square_1 (k2_bhsp_1 A C C))))) ) ) ) ) ) ).
tt(t19_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 C A) =>  ( ((k1_bhsp_2 A C) = B)  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k3_bhsp_1 A (k5_algstr_0 A (k1_normsp_1 A C F) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_bhsp_3 B A) => (v2_bhsp_3 (k5_vfunct_1 k5_numbers A B) A)) ) ) ) ) ).
tt(t19_bhsp_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((k1_normsp_1 B C (k2_nat_1 A 1)) = (k5_algstr_0 B (k3_bhsp_4 B C (k2_nat_1 A 1)) (k3_bhsp_4 B C A))) ) ) ) ) ) ) ).
tt(t19_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k5_bilinear A B C D E) F) (k5_hahnban1 A C (k7_bilinear A B C D F) (k7_bilinear A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_binari_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k20_binop_2 (k21_binop_2 (k20_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k6_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) (k15_funcop_1 k5_numbers (k4_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k2_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) (k15_funcop_1 k5_numbers (k5_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k2_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E)))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) (k15_funcop_1 k5_numbers (k4_binari_2 (k23_binop_2 A 1) (k3_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) (k1_binari_2 (k23_binop_2 A 1))) k7_margrel1 k6_numbers (k5_series_1 2 (k23_binop_2 A 1)))) = (k21_binop_2 (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D))) (k3_binari_2 (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ( ((k7_partfun1 k6_margrel1 B A) = k8_margrel1)  &  ((k7_partfun1 k6_margrel1 (k4_binarith A B (k1_binari_2 A)) A) = k8_margrel1) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  =>  ((r1_xxreal_0 D A) =>  ( (D = 1)  |  ( ((k7_partfun1 k6_margrel1 B D) = k8_margrel1)  &  ((k7_partfun1 k6_margrel1 (k4_binarith A B (k1_binari_2 A)) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ( (B = (k5_euclid A))  &  (C = (k5_euclid A)) )  => (r1_binarith A B C)) ) ) ) ) ) ) ).
tt(t19_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ((k7_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 D)) (k9_binarith A 1 k6_margrel1 C (k10_binarith k6_margrel1 E))) = (k9_binarith A 1 k6_margrel1 (k7_binarith A B C) (k10_binarith k6_margrel1 (k2_binarith (k2_binarith D E) (k8_binarith A B C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v1_algstr_1 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k6_algstr_0 A (k5_binom A B D) C) = (k5_binom A (k6_algstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t19_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  =>  ((v3_funct_1 C) <=>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden D A) &  ((r2_hidden E A) &  ((r2_hidden F B) & (r2_hidden G B)) ) )  =>  ((k1_binop_1 C D F) = (k1_binop_1 C E G)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  ((k3_finseq_1 (k2_bintree2 A B)) = (k5_series_1 2 B)) ) ) ) ) ).
tt(t19_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A B C) & (r3_lattices A B D))  =>  ((r4_boolealg A C D) | (r1_boolealg A B (k5_lattices A))) ) ) ) ) ) ) ) ) ) ).
tt(t19_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B (k1_valued_0 (k9_setfam_1 A) D (k2_nat_1 E 1)) C)) F) (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B D C)) (k2_nat_1 (k2_nat_1 E 1) F)) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B D C)) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  ((v1_tops_2 C (k2_borsuk_1 A B)) =>  ((v1_tops_2 (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) C) A) & (v1_tops_2 (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) C) B)) ) ) ) ) ) ) ) ).
tt(t19_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) =>  (~  ((m1_setfam_1 D (u1_struct_0 (k2_borsuk_1 B A))) &  ((v1_tops_2 D (k2_borsuk_1 B A)) &  ( (C = (a_3_1_borsuk_3 A B D))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski E C) &  ((v1_finset_1 E) & (m1_setfam_1 E (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) => (m1_subset_1 (k2_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) ) ) ).
tt(t19_borsuk_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v1_rat_1 A)) )  =>  (~ (v1_rat_1 (k4_xcmplx_0 A))) ) ) ).
tt(t19_borsuk_6,ax, ((v4_pre_topc a_0_8_borsuk_6 (k15_euclid 2)) & (m1_subset_1 a_0_8_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ).
tt(t19_borsuk_7,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k39_valued_1 (k14_valued_2 B A)) = (k14_valued_2 (k39_valued_1 B) (k3_square_1 A))) ) ) ) ) ).
tt(t19_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k4_bspace A (k5_struct_0 k2_bspace) B) = B) ) ) ) ).
tt(t19_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t19_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t19_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k2_enumset1 C D E F))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (E = F) )  &  ( ((k15_bvfunc_1 A G (k2_partit1 A E F)) = (k15_bvfunc_1 A H (k2_partit1 A E F)))  & (r1_xboole_0 (k15_bvfunc_1 A H (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A G (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k13_bvfunc_1 A B)) (k14_bvfunc_1 A (k1_bvfunc_1 A B))) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k14_bvfunc_1 A B)) (k13_bvfunc_1 A (k1_bvfunc_1 A B)))) ) ) ) ) ).
tt(t19_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k10_bvfunc_1 A C D)) (k10_bvfunc_1 A (k10_bvfunc_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t19_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc26 A B C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) C)) & (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k5_bvfunc26 A B C)) (k9_bvfunc_1 A B C))) ) ) ) ) ) ) ).
tt(t19_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k7_bvfunc_2 A C B D)) (k6_bvfunc_2 A (k1_bvfunc_1 A C) B D))) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((r3_bvfunc_2 A B C D) => (r1_bvfunc_1 A (k7_bvfunc_2 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B D) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C D) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k10_bvfunc_1 A B D) (k10_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t19_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))))) ) ) ) ) ) ).
tt(t19_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D E)) (k9_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (r2_relset_1 A k1_numbers (k8_c0sp1 A B) B)) ) ) ) ) ).
tt(t19_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k5_algstr_0 (k5_c0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers G H) = (k9_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers E H) (k3_funct_2 (u1_struct_0 A) k1_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) (k1_calcul_1 (k3_cqc_lang A) D)) &  ( ((k6_cqc_lang A B) = (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C)))  &  ( ((k6_cqc_lang A (k2_calcul_1 A C)) = (k2_calcul_1 A D))  &  ((r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C) (k2_calcul_1 A C)) & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) (k2_calcul_1 A D))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) | (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 C (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) )  =>  ((k1_relset_1 k5_numbers (k3_calcul_2 (k3_cqc_lang A) B C)) = (k1_relset_1 k5_numbers B)) ) ) ) ) ) ) ).
tt(t19_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_card_1 (k1_ordinal1 A)) = (k2_card_1 (k3_card_1 A))) ) ) ).
tt(t19_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k1_card_2 (k1_card_2 A B) C) = (k1_card_2 A (k1_card_2 B C))) ) ) ) ) ) ) ).
tt(t19_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k5_xboole_0 (k5_card_3 B A) (k5_card_3 B C)) (k5_card_3 B (k5_xboole_0 A C)))) ) ) ).
tt(t19_card_4,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  ((v1_finset_1 A) |  ( (B = k1_xboole_0)  |  ((r2_wellord2 (k2_zfmisc_1 A B) A) &  ((k1_card_1 (k2_zfmisc_1 A B)) = (k1_card_1 A)) ) ) ) ) ) ) ).
tt(t19_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( ((k1_card_2 A A) = A)  &  ((k2_card_2 A A) = A) ) ) ) ).
tt(t19_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r2_hidden B (k5_card_fil A)) <=> (r2_hidden (k1_card_1 B) (k1_card_1 A))) ) ) ) ) ).
tt(t19_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (~ (v1_xboole_0 (k3_xboole_0 (k9_xtuple_0 C) (k8_relat_1 D (k1_tarski A)))))  =>  ((r2_hidden B (k2_card_fin C D A)) <=>  (! [E:$i] :  ( ((r2_hidden E (k9_xtuple_0 D)) &  ((k1_funct_1 D E) = A) )  => (r2_hidden B (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ).
tt(t19_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~  ((v1_card_lar B A) &  ( (~ (v1_card_lar (k2_card_lar A B) A))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C A) & (r3_card_lar A (a_3_2_card_lar A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k3_tarski (a_2_0_cat_2 A B))))  & (m1_subset_1 (k3_tarski (a_2_0_cat_2 A B)) (k1_zfmisc_1 (u4_struct_0 A)))) ) ) ) ) ).
tt(t19_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 C)) =>  ( (~  (A = B) )  => (r2_funct_2 (k2_tarski A B) (u4_struct_0 C) (k8_cat_3 C (k2_tarski A B) (k5_funct_4 (u4_struct_0 C) A B D E) (k5_funct_4 (u4_struct_0 C) A B F G)) (k5_funct_4 (u4_struct_0 C) A B (k1_cat_1 C F D) (k1_cat_1 C G E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A (k2_cat_4 A B C) B) = k1_xboole_0) )  &  (~  ((k2_cat_1 A (k2_cat_4 A B C) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t19_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) &  ((v4_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) &  ((v4_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B))) ) ) ) ) ) ).
tt(t19_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_catalan1 (k1_nat_1 A 1)) = (k8_real_1 (k8_real_1 2 (k9_real_1 2 (k10_real_1 3 (k1_nat_1 A 1)))) (k1_catalan1 A))) ) ) ) ).
tt(t19_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((r1_tarski (k2_relset_1 k5_numbers B) (k7_domain_1 k5_numbers k6_numbers 1)) &  ((k23_binop_2 (k24_binop_2 2 A) 1) = (k5_nat_1 (a_1_1_catalan2 B))) )  => (v1_catalan2 (k5_relat_1 B (k24_binop_2 2 A)))) ) ) ) ) ).
tt(t19_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k1_msualg_1 (k3_catalg_1 A) (k10_catalg_1 A B C D)) = (k2_finseq_4 (u1_struct_0 (k3_catalg_1 A)) (k9_catalg_1 A C D) (k9_catalg_1 A B C)))  &  ((k2_msualg_1 (k3_catalg_1 A) (k10_catalg_1 A B C D)) = (k9_catalg_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( (C = D)  & (v1_comseq_2 (k2_partfun1 A k2_numbers C A)))  => (r1_xxreal_0 (k17_complex1 (k3_funct_2 A k2_numbers C B)) (k1_normsp_0 (k7_cc0sp1 A) D))) ) ) ) ) ) ) ) ) ).
tt(t19_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ( (~ (v2_struct_0 (k5_cc0sp2 A)))  &  ((v13_algstr_0 (k5_cc0sp2 A)) &  ((v2_rlvect_1 (k5_cc0sp2 A)) &  ((v3_rlvect_1 (k5_cc0sp2 A)) &  ((v4_rlvect_1 (k5_cc0sp2 A)) &  ((v2_clvect_1 (k5_cc0sp2 A)) &  ((v3_clvect_1 (k5_cc0sp2 A)) &  ((v4_clvect_1 (k5_cc0sp2 A)) &  ((v5_clvect_1 (k5_cc0sp2 A)) & (l1_clvect_1 (k5_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k3_funct_2 k5_numbers k2_numbers B D) = (k3_funct_2 k5_numbers k2_numbers A D)) ) ) ) ) ) )  | (v2_comseq_2 B)) ) ) ) ) ) ).
tt(t19_cfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k1_valued_0 k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers B A) (k1_valued_0 k2_numbers C A)))) ) ) ) ) ) ).
tt(t19_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A C) &  ((r2_hidden B C) &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k2_numbers (k9_funct_2 C k2_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k2_numbers (k9_funct_2 C k2_numbers)) =>  (? [F:$i] :  ((m1_subset_1 F k2_numbers) &  (? [G:$i] :  ((m1_subset_1 G k2_numbers) &  ((r2_funct_2 C k2_numbers (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) F D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G E))) (k4_cfuncdom C)) &  (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) D) (k46_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B D) (k19_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t19_cgames_1,ax, (! [A:$i] :  ( ((v1_cgames_1 A) & (l1_cgames_1 A))  =>  ((v2_cgames_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k2_xboole_0 (u1_cgames_1 A) (u2_cgames_1 A))) => (v2_cgames_1 B)) ) ) ) ) ).
tt(t19_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~ (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers C B) A)) ) ) ) ) ) ) ) ) ).
tt(t19_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))) =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  (! [F:$i] :  ((r1_glib_000 A D E F) => (r1_glib_000 C D E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) =>  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 A D))) =>  (! [K:$i] :  ((m1_subset_1 K (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (J = (k5_relat_1 I (u1_struct_0 A)))  &  ((v1_circuit2 (k5_facirc_1 A D J G) A D) &  ( (K = (k5_relat_1 (k5_facirc_1 C F I G) (u1_struct_0 B)))  & (v1_circuit2 (k5_facirc_1 B E K H) B E)) ) )  => (v1_circuit2 (k5_facirc_1 C F I (k2_xcmplx_0 G H)) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msafree2 B A) &  ((v5_circcmb3 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) => (v1_circuit2 (k6_circuit2 A B C) A B)) ) ) ) ) ) ).
tt(t19_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ((r2_circcomb A B C D) => (r2_circcomb B A D C)) ) ) ) ) ) ) ) ) ).
tt(t19_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_circled1 C A) & (m1_rlvect_2 C A))  &  ( ((k6_rlvect_2 A C) = B)  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B D) =>  ((v1_circled1 C A) & (m2_rlvect_2 C A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A B) =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  ((k6_circtrm1 A B (k4_subset_1 (k1_msaterm A B) C D) E) = (k3_circcomb (k1_circtrm1 A B C) (k1_circtrm1 A B D) (k6_circtrm1 A B C E) (k6_circtrm1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C (k3_msafree2 A)) &  ((r2_hidden D (k2_relset_1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A C)))) & (r1_xxreal_0 (k6_circuit1 A B C) (k6_circuit1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  ((v3_funct_1 (k10_funct_6 C)) =>  ((v1_xboole_0 (k2_msafree2 A)) |  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 A B))) => (r8_pboole (u1_struct_0 A) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C D) (k7_circuit1 A B)) (k8_nat_1 (k4_card_3 (u3_msualg_1 A B)) (k9_circuit2 A B C E) (k7_circuit1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_classes1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) &  ((k3_classes1 A B) = (k1_classes1 A)) ) ) ) ).
tt(t19_classes2,ax, (! [A:$i] :  ((v2_classes1 A) => (v4_ordinal1 (k1_card_1 A))) ) ).
tt(t19_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_clvect_1 B A) &  ((k7_clvect_1 A B) = C) )  =>  ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = (k1_normsp_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t19_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_clopban2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_clopban2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_clopban2 A))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( ((k1_algstr_0 (k9_clopban2 A) B C) = (k1_algstr_0 (k9_clopban2 A) C B))  &  ( ((k1_algstr_0 (k9_clopban2 A) (k1_algstr_0 (k9_clopban2 A) B C) D) = (k1_algstr_0 (k9_clopban2 A) B (k1_algstr_0 (k9_clopban2 A) C D)))  &  ( ((k1_algstr_0 (k9_clopban2 A) B (k4_struct_0 (k9_clopban2 A))) = B)  &  ((v10_algstr_0 B (k9_clopban2 A)) &  ( ((k6_algstr_0 (k9_clopban2 A) (k6_algstr_0 (k9_clopban2 A) B C) D) = (k6_algstr_0 (k9_clopban2 A) B (k6_algstr_0 (k9_clopban2 A) C D)))  &  ( ((k6_algstr_0 (k9_clopban2 A) B (k5_struct_0 (k9_clopban2 A))) = B)  &  ( ((k6_algstr_0 (k9_clopban2 A) (k5_struct_0 (k9_clopban2 A)) B) = B)  &  ( ((k6_algstr_0 (k9_clopban2 A) B (k1_algstr_0 (k9_clopban2 A) C D)) = (k1_algstr_0 (k9_clopban2 A) (k6_algstr_0 (k9_clopban2 A) B C) (k6_algstr_0 (k9_clopban2 A) B D)))  &  ( ((k6_algstr_0 (k9_clopban2 A) (k1_algstr_0 (k9_clopban2 A) C D) B) = (k1_algstr_0 (k9_clopban2 A) (k6_algstr_0 (k9_clopban2 A) C B) (k6_algstr_0 (k9_clopban2 A) D B)))  &  ( ((k1_clvect_1 (k9_clopban2 A) (k6_algstr_0 (k9_clopban2 A) B C) E) = (k6_algstr_0 (k9_clopban2 A) (k1_clvect_1 (k9_clopban2 A) B E) C))  &  ( ((k1_clvect_1 (k9_clopban2 A) (k6_algstr_0 (k9_clopban2 A) B C) (k3_xcmplx_0 E F)) = (k6_algstr_0 (k9_clopban2 A) (k1_clvect_1 (k9_clopban2 A) B E) (k1_clvect_1 (k9_clopban2 A) C F)))  &  ( ((k1_clvect_1 (k9_clopban2 A) (k1_algstr_0 (k9_clopban2 A) B C) E) = (k1_algstr_0 (k9_clopban2 A) (k1_clvect_1 (k9_clopban2 A) B E) (k1_clvect_1 (k9_clopban2 A) C E)))  &  ( ((k1_clvect_1 (k9_clopban2 A) B (k2_xcmplx_0 E F)) = (k1_algstr_0 (k9_clopban2 A) (k1_clvect_1 (k9_clopban2 A) B E) (k1_clvect_1 (k9_clopban2 A) B F)))  &  ( ((k1_clvect_1 (k9_clopban2 A) B (k3_xcmplx_0 E F)) = (k1_clvect_1 (k9_clopban2 A) (k1_clvect_1 (k9_clopban2 A) B F) E))  &  ((k1_clvect_1 (k9_clopban2 A) B k6_complex1) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k6_clvect_1 A B C)) (k6_clvect_1 A (k1_bhsp_4 A B) C))) ) ) ) ) ) ).
tt(t19_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v2_clopban3 (k1_clopban4 A (k4_struct_0 A)) A) &  ((k1_clopban3 A (k1_clopban4 A (k4_struct_0 A))) = (k5_struct_0 A)) ) ) ) ).
tt(t19_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  ((v4_closure1 C A B) => (r2_pboole A (k4_pboole A (k2_closure1 A B C D) (k2_closure1 A B C E)) (k16_pralg_1 A C (k4_pboole A D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k3_closure2 (k2_tarski B C)))) =>  ((k1_funct_1 (k3_closure2 (k2_tarski B C)) A) = (k2_tarski (k1_funct_1 B A) (k1_funct_1 C A))) ) ) ) ) ) ) ).
tt(t19_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B B B)) = (k1_clvect_1 A B (k8_complex1 (k8_complex1 k6_complex1 k6_complex1) k6_complex1))) ) ) ) ) ).
tt(t19_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 C A) =>  ( ((k1_clvect_2 A C) = B)  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k13_csspace A (k5_algstr_0 A (k1_normsp_1 A C F) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A B (k2_nat_1 C 1)) = (k5_algstr_0 A (k2_clvect_3 A B (k2_nat_1 C 1)) (k2_clvect_3 A B C))) ) ) ) ) ) ) ).
tt(t19_cohsp_1,ax, (! [A:$i] :  ((k3_tarski (k5_finsub_1 A)) = A) ) ).
tt(t19_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_coh_sp A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k3_tarski B) (k3_tarski C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski B) (k3_tarski C))))) )  =>  ( (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k2_tarski E F) B) => (r2_hidden (k2_tarski (k1_funct_1 D E) (k1_funct_1 D F)) C)) ) )  =>  ( ( ((k3_tarski C) = k1_xboole_0)  &  (~  ((k3_tarski B) = k1_xboole_0) ) )  | (r2_hidden (k4_tarski (k4_tarski B C) D) (k5_coh_sp A))) ) ) ) ) ) ) ) ) ).
tt(t19_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_collsp D A) =>  ( ((r2_hidden B D) & (r2_hidden C D))  =>  ( (B = C)  |  ((k1_collsp A B C) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_incsp_1 B) =>  (! [C:$i] :  ((l1_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 B))) =>  ((k5_combgras A B C D) = (a_4_1_combgras A B C D)) ) ) ) ) ) ) ) ) ).
tt(t19_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_complex1 (k6_xcmplx_0 A B)) = (k9_real_1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k6_xcmplx_0 A B)) = (k9_real_1 (k4_complex1 A) (k4_complex1 B))) ) ) ) ) ) ).
tt(t19_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  ((k1_comptrig A) = k6_numbers) )  =>  ( (~  ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig A)))  & (r1_xxreal_0 (k18_sin_cos (k1_comptrig A)) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k18_sin_cos (k1_comptrig A)) k6_numbers))  & (r1_xxreal_0 k32_sin_cos (k1_comptrig A))) ) ) ) ) ) ).
tt(t19_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k11_algstr_0 k1_complfld (k4_algstr_0 k1_complfld A)) = (k4_algstr_0 k1_complfld (k11_algstr_0 k1_complfld A))) ) ) ) ).
tt(t19_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_complsp2 (k9_seq_4 A B)) = (k9_seq_4 (k1_complsp2 A) (k1_complsp2 B))) ) ) ) ) ) ).
tt(t19_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v4_tbsp_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( (B = C)  =>  ((v4_tbsp_1 (k1_topmetr A B)) <=> (v4_pre_topc C (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(t19_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v4_compos_1 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k2_afinsq_1 (k63_valued_1 B))) &  ((k1_funct_1 (k63_valued_1 B) C) = (k2_compos_1 A)) ) ) ) ) ) ) ) ) ).
tt(t19_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((r2_compos_2 B C) & (r1_compos_2 C D))  => (r1_compos_2 B D)) ) ) ) ) ) ) ) ).
tt(t19_comptrig,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))).
tt(t19_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v2_compts_1 C A) <=> (v2_compts_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v2_margrel1 A))  =>  ( ((k9_xtuple_0 A) = (k1_tarski k1_xboole_0))  =>  ((k18_margrel1 A) = k6_numbers) ) ) ) ).
tt(t19_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A) C))) ) ) ) ) ) ).
tt(t19_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k7_comseq_3 A) B) (k7_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k8_comseq_3 A) B) (k8_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)))) ) ) ) ) ).
tt(t19_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v5_conlat_1 (g2_conlat_1 A (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) A))  &  ((v7_conlat_1 (g2_conlat_1 A (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) A) & (l2_conlat_1 (g2_conlat_1 A (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) A)) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) =>  ( ( ( (~ (v5_conlat_1 (g2_conlat_1 A C D) A))  &  ((v7_conlat_1 (g2_conlat_1 A C D) A) & (l2_conlat_1 (g2_conlat_1 A C D) A)) )  & (r1_tarski B C))  => (r1_tarski (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B) = (k1_funct_1 (k1_conlat_1 (k7_conlat_2 A)) B)) ) ) ) ) ).
tt(t19_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) => (v2_connsp_1 (k2_pre_topc A B) A)) ) ) ) ) ).
tt(t19_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_connsp_2 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))))  =>  (~  ((v2_connsp_1 C (k1_pre_topc A B)) &  ((v3_pre_topc C (k1_pre_topc A B)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v2_connsp_1 D A) &  (C = (k9_subset_1 (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_connsp_3 (k1_struct_0 A) A)) ) ).
tt(t19_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (a_3_3_convex1 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t19_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) => (r1_tarski (k1_convex4 A (k5_convex4 A B C)) (k4_subset_1 (u1_struct_0 A) (k1_convex4 A B) (k1_convex4 A C)))) ) ) ) ) ) ).
tt(t19_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k13_cqc_lang A (k13_qc_lang1 A C) B) = (k13_qc_lang1 A (k13_cqc_lang A C B))) ) ) ) ) ) ) ).
tt(t19_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) => (v1_finset_1 (k24_qc_lang1 A B))) ) ) ) ).
tt(t19_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((k1_cqc_the1 A (k1_cqc_the1 A B)) = (k1_cqc_the1 A B)) ) ) ) ) ).
tt(t19_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) =>  ((r2_hidden D (k24_qc_lang1 A C)) | (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A D B) C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r4_cqc_the3 A B C) & (r4_cqc_the3 A C D))  => (r4_cqc_the3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t19_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  ( (C = (k4_struct_0 (k9_csspace4 A B)))  =>  (k6_numbers = (k1_normsp_0 (k9_csspace4 A B) C)) ) ) ) ) ) ) ) ).
tt(t19_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) & (l1_csspace B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k12_csspace B (k1_clvect_1 B C A) D) = (k12_csspace B C (k1_clvect_1 B D (k15_complex1 A)))) ) ) ) ) ) ) ) ) ).
tt(t19_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_decomp_1 C A B) <=>  ((v5_decomp_1 C A B) & (v15_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t19_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k2_finseq_1 16)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  (~  (A = 16) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_dickson A) & (r2_hidden C (k6_dickson A B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_dickson A))) =>  ((r2_hidden D C) => (r4_waybel_4 B D (u1_orders_2 (k5_dickson A)))) ) ) ) ) ) ) ) ) ).
tt(t19_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 B A) C)) &  ((v1_funct_2 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 B A) C) k1_numbers k1_numbers) & (m1_subset_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 B A) C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t19_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r2_zfmisc_1 A B C D) =>  ( ((k11_diff_1 E A B C D) = (k11_diff_1 E B A C D))  &  ((k11_diff_1 E A B C D) = (k11_diff_1 E B C A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) A) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k7_real_1 (k7_real_1 C (k8_real_1 (k10_real_1 (k5_real_1 A 1) 2) B)) (k10_real_1 B 2))))  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) A) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k9_real_1 (k9_real_1 C (k8_real_1 (k10_real_1 (k5_real_1 A 1) 2) B)) (k10_real_1 B 2)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A B) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))) & (r2_hidden A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_fdiff_9) B) A) = (k1_real_1 (k8_real_1 4 (k13_complex1 (k8_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k18_sin_cos B)) (k8_real_1 (k18_sin_cos (k8_real_1 2 (k7_real_1 A B))) (k18_sin_cos (k8_real_1 2 A))))))) ) ) ) ) ) ).
tt(t19_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  ( ((k1_dilworth A) = 1)  =>  ((v2_dilworth (k2_struct_0 A) A) & (m1_subset_1 (k2_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(t19_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_diraf A B C C B) & (r2_diraf A B C B C)) ) ) ) ) ) ) ).
tt(t19_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  ((k18_rvsum_1 (k4_dist_1 A B)) = 1) ) ) ) ) ).
tt(t19_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k2_zfmisc_1 A B) = (a_2_0_domain_1 A B)) ) ) ) ) ).
tt(t19_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_dynkin B A) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski C D) => (r2_hidden (k7_subset_1 A D C) B)) ) ) ) ) ) ) ) ) ).
tt(t19_ec_pf_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ((k6_int_1 (k3_xcmplx_0 A B) C) = 1) )  =>  ((k11_algstr_0 (k9_int_3 C) D) = (k6_int_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_ec_pf_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ( (E = (k6_int_1 B C))  &  (B = (k2_xcmplx_0 A 1)) ) )  =>  ((k3_rlvect_1 (k9_int_3 C) (k8_group_1 (k9_int_3 C) D F) F) = (k8_group_1 (k9_int_3 C) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ((r2_hidden D (k7_ens_1 A B C)) <=>  ( ((k3_ens_1 A D) = B)  &  ((k4_ens_1 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v2_matrprob A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (v4_partfun3 (k8_matrix_1 k1_numbers A B))) ) ) ) ) ) ).
tt(t19_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k2_enumset1 A B C D) (k1_enumset1 E F G))) ) ) ) ) ) ) ) ).
tt(t19_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r2_hidden B (k6_eqrel_1 A A D C)) <=> (r2_hidden (k4_tarski B C) D)) ) ) ) ) ) ).
tt(t19_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k3_msualg_1 A D C)) =>  ((k1_funct_1 (k5_msualg_1 A D C) E) = (k1_funct_1 (k5_msualg_1 A D B) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  => (r1_tarski (k9_e_siec A) (k2_xboole_0 (k2_zfmisc_1 (k7_e_siec A) (k8_e_siec A)) (k2_zfmisc_1 (k8_e_siec A) (k7_e_siec A))))) ) ).
tt(t19_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k23_rvsum_1 (k1_rlvect_1 (k15_euclid A) B D) C) = (k11_binop_2 D (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t19_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_euclid_3 (k3_xcmplx_0 B A)) = (k1_rlvect_1 (k15_euclid 2) (k1_euclid_3 A) B)) ) ) ) ) ).
tt(t19_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k5_euclid A) B) = k6_numbers) ) ) ) ) ).
tt(t19_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k5_euclid_5 (k4_euclid_5 k6_numbers k6_numbers k6_numbers) (k4_euclid_5 A B C)) = (k4_struct_0 (k15_euclid 3))) ) ) ) ) ) ) ).
tt(t19_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A C)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) B C)))  & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ( (D = C)  |  ( ( ((k4_euclid_3 A C D) = (k4_euclid_3 D C B))  =>  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A D)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) D B))) )  &  ( ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A D)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) D B)))  =>  ((k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) C D) (k5_algstr_0 (k15_euclid 2) B A)) = k6_numbers) )  &  ( ((k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) C D) (k5_algstr_0 (k15_euclid 2) B A)) = k6_numbers)  =>  ((k4_euclid_3 A C D) = (k4_euclid_3 D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ( ((v5_euclid_7 B A) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r2_hidden D B) =>  ((k23_rvsum_1 D C) = k6_numbers) ) ) ) )  =>  (C = (k5_euclid A)) ) ) ) ) ) ) ) ).
tt(t19_euclid_8,ax, ((k5_euclid_8 k4_euclid_8 k3_euclid_8) = (k6_euclid 3 k2_euclid_8)) ).
tt(t19_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (~  ((r2_hidden C (k9_metric_1 (k14_euclid A) D B)) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E k5_numbers))  =>  (~ (r1_tarski (k4_euclid_9 A C (k13_complex1 1 E)) (k9_metric_1 (k14_euclid A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k8_euclid A B C)) (k7_real_1 (k12_euclid (k8_euclid A B D)) (k12_euclid (k8_euclid A D C))))) ) ) ) ) ) ) ) ).
tt(t19_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  ((k8_euclid A (k7_euclid A (k7_euclid A B C) D) (k7_euclid A (k7_euclid A E F) G)) = (k7_euclid A (k7_euclid A (k8_euclid A B E) (k8_euclid A C F)) (k8_euclid A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ( (~  ((k4_struct_0 A) = D) )  &  ( (~  ((k4_struct_0 A) = E) )  &  ((r2_analmetr A D E B C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_analmetr A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 F H)) (k1_rlvect_1 A C (k1_real_1 (k8_real_1 F G)))) B C) & (r2_analmetr A (k5_algstr_0 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) D) (k5_algstr_0 A (k3_rlvect_1 A (k1_rlvect_1 A B (k8_real_1 F H)) (k1_rlvect_1 A C (k1_real_1 (k8_real_1 F G)))) E) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  => (r1_xxreal_0 (k1_euler_1 A) (k6_xcmplx_0 A 1))) ) ) ).
tt(t19_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v1_int_2 B) & (r1_int_2 A B))  =>  ( (A = k1_xboole_0)  |  ((k4_nat_d (k1_newton A B) B) = (k4_nat_d A B)) ) ) ) ) ) ) ).
tt(t19_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  ((v3_exchsort A k1_xboole_0) <=> (v1_xboole_0 A)) ) ) ).
tt(t19_extens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_msafree D A B) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r1_msualg_3 A B C E) &  ((r1_msualg_3 A B C F) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D F))) )  => (r8_pboole (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_extpro_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  (~ (v1_setfam_1 C)) )  =>  ((r1_xxreal_0 A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_memstr_0 D C) &  ((v3_memstr_0 D C) &  ((v3_extpro_1 D C) & (l1_extpro_1 D C)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 D)) & (v1_funct_1 E)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 D)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 C D)) & (v1_partfun1 F (u1_struct_0 D))) ) ) )  =>  ((r1_compos_1 D E (k5_memstr_0 C D (k5_extpro_1 C D E F A))) => (r1_compos_1 D E (k5_memstr_0 C D (k5_extpro_1 C D E F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_extreal2,ax, ( ((k3_extreal1 k1_supinf_1) = k1_supinf_1)  &  ((k3_extreal1 k2_supinf_1) = k1_supinf_1) ) ).
tt(t19_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( (! [E:$i] :  ((r2_hidden E (k10_xtuple_0 (k1_msualg_1 A D))) => (r1_facirc_1 A B C E)) )  => (r1_facirc_1 A B (k6_circuit2 A B C) (k2_msualg_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t19_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k15_facirc_1 A B C)) = (k2_xboole_0 (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) (k1_tarski (k17_facirc_1 A B C)))) ) ) ) ).
tt(t19_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) &  ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) )  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ) ) ).
tt(t19_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) )  =>  ((k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B)) = (k1_rcomp_1 (k5_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k4_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))) ) ) ) ) ) ) ) ).
tt(t19_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) (k7_relset_1 k1_numbers k1_numbers B (k3_limfunc1 A))))) ) ) ) ) ) ).
tt(t19_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k3_taylor_1))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 B k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k3_taylor_1) A) B) = (k10_real_1 1 (k8_real_1 (k1_seq_1 k3_taylor_1 B) B))) ) ) ) ) ) ) ) ).
tt(t19_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k30_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k30_sin_cos) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k1_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t19_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r2_fdiff_1 B A) & (r2_fdiff_1 C A)) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) D) = (k9_real_1 (k1_fdiff_1 B D) (k1_fdiff_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 C B) =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C A) B) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C A) B) (k26_valued_1 k1_numbers k1_numbers (k2_fdiff_1 C B) A))) ) ) ) ) ) ) ) ).
tt(t19_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r3_fdiff_3 A C) & (r3_fdiff_3 B C))  =>  ( ((k1_seq_1 B C) = k6_numbers)  |  ((r3_fdiff_3 (k3_rfunct_1 k1_numbers k1_numbers A B) C) &  ((k2_fdiff_3 C (k3_rfunct_1 k1_numbers k1_numbers A B)) = (k10_real_1 (k9_real_1 (k8_real_1 (k2_fdiff_3 C A) (k1_seq_1 B C)) (k8_real_1 (k2_fdiff_3 C B) (k1_seq_1 A C))) (k5_square_1 (k1_seq_1 B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1)))) &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1)) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1)) B) E) = (k10_real_1 (k8_real_1 2 E) (k9_real_1 (k5_square_1 A) (k2_newton E 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 k3_taylor_1)) =>  ((r2_fdiff_1 k3_taylor_1 A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 k3_taylor_1 A) B) = (k10_real_1 1 B)) ) ) ) ) ) ) ) ).
tt(t19_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) (k10_real_1 1 (k9_real_1 1 (k6_power k8_power A)))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 D (k6_power k8_power A))) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = k8_power)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) (k10_real_1 1 (k9_real_1 1 (k6_power k8_power A)))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)) (k10_real_1 1 (k9_real_1 1 (k6_power k8_power A)))) B) D) = (k10_real_1 (k1_seq_1 k24_sin_cos D) (k10_prepower A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k4_sin_cos6))) &  ((r1_tarski C (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k4_sin_cos6) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k4_sin_cos6) C) E) = (k9_real_1 (k8_real_1 A (k1_seq_1 k4_sin_cos6 E)) (k10_real_1 (k7_real_1 (k8_real_1 A E) B) (k7_square_1 (k9_real_1 1 (k5_square_1 E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t19_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t19_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k8_ff_siec A) (k8_ff_siec A)) = (k8_ff_siec A))  &  ( ((k3_relat_1 (k8_ff_siec A) (k7_ff_siec A)) = (k8_ff_siec A))  &  ( ((k3_relat_1 (k7_ff_siec A) (k7_ff_siec A)) = (k7_ff_siec A))  &  ((k3_relat_1 (k7_ff_siec A) (k8_ff_siec A)) = (k7_ff_siec A)) ) ) ) ) ) ).
tt(t19_fib_num2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_tarski (k9_xtuple_0 A) (k2_finseq_1 B)) &  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ((r1_tarski A D) &  ((k4_finseq_1 D) = (k2_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_nat_1 2 (k1_fib_num3 (k2_nat_1 A 2))) = (k2_nat_1 (k1_fib_num3 A) (k1_fib_num3 (k2_nat_1 A 3)))) ) ) ).
tt(t19_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k2_int_1 (k11_complex1 (k13_complex1 (k3_power k1_fib_num A) (k7_square_1 5)) (k13_complex1 1 2))) = (k1_pre_ff A)) ) ) ) ).
tt(t19_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_finseq_8 A C) =>  ((r2_finseq_8 A B C 1) |  ((k8_finseq_8 A (k1_finseq_8 A B C) C 1) = (k2_nat_1 (k3_finseq_1 B) 1)) ) ) ) ) ) ) ) ) ).
tt(t19_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A B C) = B) ) ) )  &  ((k2_filter_0 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t19_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 (k4_filter_1 A B)))  &  ((v10_lattices (k4_filter_1 A B)) &  ((v14_lattices (k4_filter_1 A B)) & (l3_lattices (k4_filter_1 A B))) ) )  &  ((k6_lattices (k4_filter_1 A B)) = (k5_filter_1 A B (k6_lattices A))) ) ) ) ) ) ).
tt(t19_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_lattice2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_lattice2 A))) =>  ( ((r3_lattices A B C) => (r3_lattices (k1_lattice2 A) (k1_filter_2 A C) (k1_filter_2 A B)))  &  ( ((r3_lattices (k1_lattice2 A) (k1_filter_2 A C) (k1_filter_2 A B)) => (r3_lattices A B C))  &  ( ((r3_lattices (k1_lattice2 A) D E) => (r3_lattices A (k2_filter_2 A E) (k2_filter_2 A D)))  &  ((r3_lattices A (k2_filter_2 A E) (k2_filter_2 A D)) => (r3_lattices (k1_lattice2 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ((m2_finseq_1 C B) &  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ).
tt(t19_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (~  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r3_xboole_0 (k2_finseq_1 A) (k2_finseq_1 B))) ) ) ) ).
tt(t19_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k1_funct_1 A (k4_finseq_4 A B)) = B) ) ) ) ) ).
tt(t19_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k10_xtuple_0 (k16_finseq_1 B A)) (k10_xtuple_0 A))) ) ) ) ).
tt(t19_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ((k4_finseq_4 (k10_finseq_1 A B) A) = 1) ) ) ).
tt(t19_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_finseq_7 A B C C) = B) ) ) ) ) ) ) ).
tt(t19_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) => (r2_finseq_8 A B B 1)) ) ) ) ) ).
tt(t19_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A B) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  => (r2_relset_1 k5_numbers C (k2_finseqop A B C G (k5_finseq_2 A F D) E) (k5_finseq_2 C F (k2_binop_1 A B C G D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((v2_binop_1 C A) =>  ( ( (~ (v1_setwiseo C A))  &  (~  ( (~  (D = k6_numbers) )  &  (~  (E = k6_numbers) ) ) ) )  |  ((k1_finsop_1 A (k5_finseq_2 A (k4_nat_1 D E) B) C) = (k1_finsop_1 A (k5_finseq_2 A E (k1_finsop_1 A (k5_finseq_2 A D B) C)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k8_fintopo2 A C)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D (k6_fintopo2 A B)) =>  ( (~ (r1_xboole_0 D C))  &  (~ (r1_xboole_0 D (k3_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fintopo3 A B k6_numbers) = B) ) ) ) ) ).
tt(t19_fintopo4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v1_fin_topo (k2_fintopo4 A))) ) ) ).
tt(t19_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_orders_2 A) &  ((v1_fin_topo A) &  ((v1_fintopo6 A) &  ( (~  (B = k1_xboole_0) )  &  ( (~  ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0) )  &  ((k6_fin_topo A B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fin_topo A (k3_subset_1 (u1_struct_0 A) B)) = (k5_fin_topo A B)) ) ) ) ) ).
tt(t19_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski (k6_flang_1 A B (k9_subset_1 (k3_catalan2 A) C D)) (k9_subset_1 (k3_catalan2 A) (k6_flang_1 A B C) (k6_flang_1 A B D))) & (r1_tarski (k6_flang_1 A (k9_subset_1 (k3_catalan2 A) C D) B) (k9_subset_1 (k3_catalan2 A) (k6_flang_1 A C B) (k6_flang_1 A D B)))) ) ) ) ) ) ) ) ).
tt(t19_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden B (k1_flang_2 A C D E)) <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) & (r2_hidden B (k7_flang_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k7_flang_1 A (k1_flang_3 A B D) C) = (k1_flang_3 A B (k3_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ).
tt(t19_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k1_funct_2 B C)) => (r1_tarski (k3_tarski A) (k2_zfmisc_1 B C))) ) ) ) ).
tt(t19_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E A) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ( ((v4_fomodel2 F A) & (m2_subset_1 F (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [G:$i] :  ((m2_subset_1 G (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ( (~  ( ((k26_fomodel2 A B G (k30_fomodel2 A (k31_fomodel2 A C) D)) = k8_margrel1)  &  (! [H:$i] :  ((m1_subset_1 H B) =>  (~  ((k26_fomodel2 A B (k37_fomodel2 A B G C H) D) = 1) ) ) ) ) )  &  ( ( (? [H:$i] :  ((m1_subset_1 H B) &  ((k26_fomodel2 A B (k37_fomodel2 A B G C H) D) = 1) ) )  =>  ((k26_fomodel2 A B G (k30_fomodel2 A (k31_fomodel2 A C) D)) = k8_margrel1) )  &  ( ( ((k26_fomodel2 A B G (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) E) F)) = k8_margrel1)  =>  ( ((k26_fomodel2 A B G E) = k7_margrel1)  &  ((k26_fomodel2 A B G F) = k7_margrel1) ) )  &  ( ( ((k26_fomodel2 A B G E) = k7_margrel1)  &  ((k26_fomodel2 A B G F) = k7_margrel1) )  =>  ((k26_fomodel2 A B G (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) E) F)) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 C)) (k1_fomodel4 C)))) =>  ((r2_hidden A (k1_funct_1 (k21_fomodel4 C D) B)) <=>  ((r2_hidden A (k1_fomodel4 C)) & (r2_hidden (k4_tarski B A) D)) ) ) ) ) ) ) ) ).
tt(t19_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) (k1_frechet2 A B) (k1_frechet2 A C)) = (k1_frechet2 A (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t19_frechet,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C A) =>  ((r2_hidden D A) |  ((k8_relat_1 (k1_funct_4 (k6_partfun1 A) (k7_funcop_1 B D)) (k6_subset_1 C (k1_tarski D))) = (k6_subset_1 C B)) ) ) ) ) ) ) ).
tt(t19_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k8_fscirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t19_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( (~  ((k3_fscirc_2 A B C) = (k4_tarski D k2_twoscomp)) )  &  ( (~  ((k3_fscirc_2 A B C) = (k4_tarski D k3_twoscomp)) )  &  (~  ((k3_fscirc_2 A B C) = (k4_tarski D k1_facirc_1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C B A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r5_fsm_1 B A C D E) <=>  (! [F:$i] :  ((m1_subset_1 F B) =>  ( ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) A (u3_fsm_1 B A C) (k1_domain_1 (u1_struct_0 C) B D F)) = (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) A (u3_fsm_1 B A C) (k1_domain_1 (u1_struct_0 C) B E F)))  & (r5_fsm_1 B A C (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k1_domain_1 (u1_struct_0 C) B D F)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k1_domain_1 (u1_struct_0 C) B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_2 D A B))  =>  ((r2_hidden (u2_fsm_1 A D) (u1_fsm_2 A D)) => (r3_fsm_2 A B D C (k3_funct_2 (u1_struct_0 D) B (u4_fsm_1 A B D) (u2_fsm_1 A D)))) ) ) ) ) ) ) ) ) ).
tt(t19_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_3 D A C))  =>  ((r2_hidden B (k6_fsm_3 A C D)) <=>  (~ (r1_xboole_0 (k3_rewrite3 A C D B (u1_fsm_3 A C D)) (u2_fsm_3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t19_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k25_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) (k11_ftacell1 A B C D E)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith G (k9_margrel1 H)) I) K) (k10_margrel1 K (k9_margrel1 J))) (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith G (k9_margrel1 H)) I)))))  &  ((k1_funct_1 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) (k12_ftacell1 A B C D E)) = (k2_binarith (k2_binarith (k2_binarith (k2_binarith G (k9_margrel1 H)) I) (k9_margrel1 J)) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k3_relat_1 A (k2_funcop_1 B C)) = (k2_funcop_1 (k8_relat_1 A B) C)) ) ) ) ) ).
tt(t19_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A C) &  ((r2_hidden B C) &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k1_numbers (k9_funct_2 C k1_numbers)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ((r2_funct_2 C k1_numbers (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) F D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G E))) (k8_funcsdom C)) &  (~  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k9_xtuple_0 (k3_relat_1 (k4_relat_1 A) B)) = (k3_xboole_0 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t19_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((v2_funct_1 C) <=>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) &  ((r2_hidden E A) &  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ).
tt(t19_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_funct_1 (k1_funct_3 A)) &  ((v1_funct_2 (k1_funct_3 A) (k1_zfmisc_1 (k9_xtuple_0 A)) (k1_zfmisc_1 (k10_xtuple_0 A))) & (m1_subset_1 (k1_funct_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k9_xtuple_0 A)) (k1_zfmisc_1 (k10_xtuple_0 A)))))) ) ) ) ).
tt(t19_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k1_funct_4 A B) = B) ) ) ) ) ) ).
tt(t19_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) (k9_xtuple_0 C)) =>  ((r2_hidden A (k9_xtuple_0 (k1_funct_5 C))) &  ((v1_relat_1 (k1_funct_1 (k1_funct_5 C) A)) & (v1_funct_1 (k1_funct_1 (k1_funct_5 C) A))) ) ) ) ) ) ) ).
tt(t19_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k8_relat_1 B (k1_funct_6 (k10_xtuple_0 B)))) <=>  ((r2_hidden A (k9_xtuple_0 B)) &  ((v1_relat_1 (k1_funct_1 B A)) & (v1_funct_1 (k1_funct_1 B A))) ) ) ) ) ) ).
tt(t19_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k3_finseq_2 A) (k3_finseq_2 B)) => (r1_tarski A B)) ) ) ).
tt(t19_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k37_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t19_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D (k9_xtuple_0 C)) =>  ((r2_hidden (k2_xcmplx_0 D A) (k9_xtuple_0 C)) &  ((r2_hidden (k6_xcmplx_0 D A) (k9_xtuple_0 C)) &  ((r2_hidden (k2_xcmplx_0 D B) (k9_xtuple_0 C)) &  ((r2_hidden (k6_xcmplx_0 D B) (k9_xtuple_0 C)) &  ((k1_funct_1 C (k2_xcmplx_0 D A)) = (k1_funct_1 C (k2_xcmplx_0 D B))) ) ) ) ) ) ) )  =>  ( ((k6_xcmplx_0 A B) = k6_numbers)  |  ((v1_funct_9 C (k6_xcmplx_0 A B)) & (v2_funct_9 C)) ) ) ) ) ) ) ) ) ).
tt(t19_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G B) &  ((v1_funct_1 G) & (v1_partfun1 G B)) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H C) &  ((v1_funct_1 H) & (v1_partfun1 H C)) ) )  =>  (! [I:$i] :  ((m1_functor0 I A B D F G) =>  (! [J:$i] :  ((m1_functor0 J A C (k1_partfun1 A B B C D E) (k3_relat_1 D G) H) =>  ( (! [K:$i] :  (~  ((r2_hidden K A) &  ( ((k1_funct_1 (k3_relat_1 D G) K) = k1_xboole_0)  &  ( (~  ((k1_funct_1 F K) = k1_xboole_0) )  &  (~  ((k1_funct_1 (k3_relat_1 (k1_partfun1 A B B C D E) H) K) = k1_xboole_0) ) ) ) ) ) )  => (m1_functor0 (k8_pboole I J) A C (k1_partfun1 A B B C D E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_altcat_2 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) &  ((v1_altcat_2 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  ((k13_functor0 A B A C (k15_functor0 A B C)) = (k12_functor0 A)) ) ) ) ) ) ) ) ).
tt(t19_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  => (r8_pboole (u1_struct_0 A) (k5_functor3 A B C D D (k4_functor2 A B D) E) (k4_functor2 A C (k1_functor3 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 D C))  => (r1_fuzzy_1 (k2_fuzzy_1 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t19_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k1_fuzzy_1 A B (k1_fuzzy_2 A C D)) (k1_fuzzy_2 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t19_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  ( ((v5_relat_1 G (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 D E) & (r1_fuzzy_1 F G))  => (r1_fuzzy_1 (k4_fuzzy_4 A B C D F) (k4_fuzzy_4 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k3_funct_2 (u1_struct_0 A) k7_numbers B (k4_algstr_0 A (k5_struct_0 A))) = k6_numbers) ) ) ) ) ) ).
tt(t19_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_fvsum_1 1 A (k4_matrix_2 (u1_struct_0 A) B) (k4_matrix_2 (u1_struct_0 A) C)) = (k4_matrix_2 (u1_struct_0 A) (k1_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t19_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 (k13_gate_1 A B C)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) & (v1_xboole_0 C)) ) ) ) ) ) ).
tt(t19_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_gcd_1 A (k8_group_1 A D B) (k8_group_1 A D C)) =>  ( (D = (k4_struct_0 A))  | (r4_gcd_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ((r1_xxreal_0 (k3_finseq_1 E) A) =>  ((k9_genealg1 D E F B A C) = (k8_genealg1 D E F B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r2_geomtrap A B C D E F G) & (r2_geomtrap A B C D E H I)) )  =>  ( (D = E)  | (r2_geomtrap A B C F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k7_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t19_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ((k5_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k5_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ( ((k6_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k6_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ((k7_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k7_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v3_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k35_glib_000 A B) = (k5_card_1 (k28_glib_000 A B))) ) ) ) ) ).
tt(t19_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m3_glib_001 E A) =>  (! [F:$i] :  ((m3_glib_001 F B) =>  ( (E = F)  =>  ((r1_glib_001 A C D E) <=> (r1_glib_001 B C D F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ( ((r2_hidden B (k2_glib_002 A E)) & (r2_glib_000 A B D C))  => (r2_hidden D (k2_glib_002 A E))) ) ) ) ) ) ) ) ).
tt(t19_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) & (v1_glib_003 B)) ) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ( (C = D)  &  ((k5_glib_003 A) = (k5_glib_003 B)) )  =>  ((k8_glib_003 A C) = (k8_glib_003 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C))) (k2_glib_002 A B))) ) ) ) ) ) ).
tt(t19_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v1_glib_005 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( (~  (C = B) )  => (r2_glib_005 A (k13_glib_005 A C B) B C)) ) ) ) ) ) ) ).
tt(t19_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( ((k1_matrix_1 C) = (k2_nat_1 A 1))  & (r2_hidden B (k2_finseq_1 A)))  =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 C (k1_matrix_1 C)) B) = (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C B))  & (r2_hidden B (k2_finseq_1 (k1_matrix_1 (k3_goboard1 C (k1_matrix_1 C)))))) ) ) ) ) ) ) ) ) ).
tt(t19_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 1 B)) )  =>  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k3_goboard5 C A B))) ) ) ) ) ) ) ) ).
tt(t19_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers (k1_matrix_1 A))) = (a_1_5_goboard6 A)) ) ) ).
tt(t19_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 (k2_nat_1 E 1) (k1_matrix_1 A))) ) ) ) ) ) )  =>  ((r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D (k2_nat_1 E 1)))) |  ( (B = D)  & (r1_xxreal_0 (k1_int_2 (k9_real_1 C E)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 1))) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 1))) (k13_complex1 1 2)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 1))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t19_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (v1_convex1 (k1_tops_1 (k15_euclid 2) (k5_goboard5 A B)) (k15_euclid 2))) ) ) ) ) ).
tt(t19_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v2_goboard1 A) =>  ((k1_goboard5 A (k3_finseq_1 A)) = (a_1_10_gobrd11 A)) ) ) ) ).
tt(t19_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_tarski (k16_matrix_1 E) (k16_matrix_1 F)) &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 F)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D)) ) ) )  => (r1_tarski (k3_goboard5 F C (k7_nat_d D 1)) (k3_goboard5 E A (k7_nat_d B 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_topreal1 2 A) = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) (k3_goboard9 A)) (k3_goboard9 A))) ) ) ).
tt(t19_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v4_card_3 A) => (v4_card_3 (k3_cqc_lang A))) ) ) ).
tt(t19_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( ((r1_partfun1 (u1_graph_1 A) (u1_graph_1 B)) & (r1_partfun1 (u2_graph_1 A) (u2_graph_1 B)))  =>  ((r4_graph_1 A (k5_graph_1 A B)) & (r4_graph_1 B (k5_graph_1 A B))) ) ) ) ) ) ).
tt(t19_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_graph_2 A) <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 1))  &  (? [B:$i] :  (? [C:$i] :  ( (~  (B = C) )  &  ((k10_xtuple_0 A) = (k2_tarski B C)) ) ) ) ) ) ) ) ).
tt(t19_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r1_xboole_0 B (u4_struct_0 A)))  &  ( (~ (r2_hidden C (k1_graph_3 A B)))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (~  ((r2_hidden D (k1_graph_3 A B)) &  ( (~ (r2_hidden E B))  &  ( (D = (k1_funct_1 (u2_graph_1 A) E))  |  (D = (k1_funct_1 (u1_graph_1 A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  =>  ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) ) ) ) ) ) ).
tt(t19_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  ((r1_tarski (k2_graph_5 B C) A) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r1_tarski (k1_graph_5 B (k7_partfun1 (u4_struct_0 B) C D)) A)) ) ) ) ) ) ) ) ) ).
tt(t19_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k1_seq_1 (k2_graphsp B A C D) A) = D) ) ) ) ) ) ) ) ) ) ).
tt(t19_grcat_1,ax, (! [A:$i] :  ( ((v1_grcat_1 A) &  ((v2_grcat_1 A) & (l1_grcat_1 A)) )  =>  (! [B:$i] :  ( ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  (~  ( ((k7_grcat_1 B) = (k8_grcat_1 A))  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l2_algstr_0 E)) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  (~  ( (A = (g1_grcat_1 C D F))  &  ( (B = (g1_grcat_1 D E G))  &  ((k13_grcat_1 B A) = (g1_grcat_1 C E (k1_partfun1 (u1_struct_0 C) (u1_struct_0 D) (u1_struct_0 D) (u1_struct_0 E) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v1_gr_cy_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ((k6_group_1 A B) = (k7_group_1 A)) ) ) ) ) ) ).
tt(t19_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ( ((k7_group_1 A) = 2)  &  ((k7_group_1 B) = 2) )  => (r2_group_6 A B)) ) ) ) ) ).
tt(t19_gr_cy_3,ax, ((k1_gr_cy_3 3) = 7) ).
tt(t19_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ( ((m1_group_6 C A B) & (m1_group_6 (k5_group_6 B (k1_group_6 A B C)) (k5_group_6 A C) (k10_group_5 (k5_group_6 A C))))  => (m1_group_6 (k1_grnilp_1 A B (k7_group_2 A)) A C)) ) ) ) ) ) ) ).
tt(t19_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (~  ((r2_hidden E (k2_groeb_1 A B C (k7_ideal_1 (k11_polynom1 A C) D))) &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (~  ((r2_hidden F (k2_groeb_1 A B C D)) & (r3_pre_poly A F E)) ) ) ) ) ) ) )  => (r1_tarski (k2_groeb_1 A B C (k7_ideal_1 (k11_polynom1 A C) D)) (k3_groeb_1 A (k2_groeb_1 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t19_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r8_pboole (k15_pre_poly A) (k3_groeb_2 A B C D E) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t19_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  ( ((k2_xboole_0 (k3_groeb_3 A B C D E) (k4_groeb_3 A B C D E)) = (k2_polynom1 (k15_pre_poly A) C D))  &  ((k3_xboole_0 (k3_groeb_3 A B C D E) (k4_groeb_3 A B C D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_11 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 A) (k2_group_11 A B D) (k2_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t19_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A C B))  <=>  ((k6_algstr_0 A (k2_group_1 A B) (k2_group_1 A C)) = (k6_algstr_0 A (k2_group_1 A C) (k2_group_1 A B))) ) ) ) ) ) ) ) ).
tt(t19_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_2 A (k6_domain_1 (u1_struct_0 A) B) (k7_domain_1 (u1_struct_0 A) C D)) = (k7_domain_1 (u1_struct_0 A) (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ).
tt(t19_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_group_3 A B (k1_group_1 A)) = B) ) ) ) ) ).
tt(t19_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  ((k3_finseq_1 C) = (k3_finseq_1 E)) )  =>  ((k4_group_4 A (k8_finseq_1 k4_numbers D E) (k8_finseq_1 (u1_struct_0 A) B C)) = (k8_finseq_1 (u1_struct_0 A) (k4_group_4 A D B) (k4_group_4 A E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_group_5 A (k1_group_1 A) B) = (k1_group_1 A))  &  ((k2_group_5 A B (k1_group_1 A)) = (k1_group_1 A)) ) ) ) ) ) ).
tt(t19_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_group_6 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_group_6 A B))) =>  ((k2_group_2 A (k6_group_6 A B C) (k6_group_6 A B D)) = (k6_algstr_0 (k5_group_6 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(t19_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l3_algstr_0 B)) )  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_group_7 (k10_finseq_1 A B)) & (v4_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ) ) ) ) ) ) ) ).
tt(t19_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ( ( (D = (k10_group_2 A B C))  & (v8_struct_0 A))  => (r1_xxreal_0 (k18_group_2 B D) (k18_group_2 A C))) ) ) ) ) ) ) ) ) ).
tt(t19_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  ((k17_group_9 A B C C) = C) ) ) ) ) ) ).
tt(t19_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (! [E:$i] :  ((m1_group_2 E B) =>  ( ((v2_group_10 D A) &  ((v2_group_10 E A) &  ((u1_struct_0 C) = (k7_group_4 B D E)) ) )  => (v2_group_10 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k6_hahnban1 A B (k6_algstr_0 A C D) E) (k6_hahnban1 A B C (k6_hahnban1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_hahnban B A) &  ((v3_hahnban B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k5_algstr_0 A C D)) = (k9_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B C) (k3_funct_2 (u1_struct_0 A) k1_numbers B D))) ) ) ) ) ) ) ) ) ).
tt(t19_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_hallmar1 D A B C) => (m2_hallmar1 D A B)) ) ) ) ) ) ) ) ).
tt(t19_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) & (r1_xxreal_0 (k1_funct_1 (k6_weierstr A B) C) (k4_metric_1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t19_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  &  ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A B) (k13_glib_001 A C)) = (k1_tarski (k4_glib_001 A B))) )  =>  ((v1_glib_001 B A) |  ((v1_glib_001 C A) |  ( (~ (v1_glib_001 (k7_glib_001 A B C) A))  & (v5_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k4_hahnban1 k1_complfld A B)) (k4_hahnban1 k1_complfld A (k1_hermitan A B)))) ) ) ) ).
tt(t19_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (~  ( ((k10_normform A C (k2_heyting1 A B)) = k1_xboole_0)  &  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden D (k6_heyting1 A C)) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (C = (k2_lattice2 (k4_partfun1 A B) (k5_substlat A B) C (k8_heyting2 A B))) ) ) ) ) ) ).
tt(t19_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 A C) => (r1_tarski (k3_heyting3 A B) (k3_heyting3 C B))) ) ) ) ) ) ) ).
tt(t19_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 C A B) & (r1_taylor_1 D A B))  => (r1_taylor_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t19_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k1_normsp_1 A (k11_polynom3 A (k5_hilbasis A B D) E) (k2_nat_1 C B)) = (k6_algstr_0 A D (k1_normsp_1 A E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k3_hilbert1 C A) (k3_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(t19_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ( ((k4_hilbert1 A B) = (k4_hilbert1 C D))  =>  ( (A = C)  &  (D = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k3_relat_1 C (k15_pralg_1 A B)) = (k15_pralg_1 (k3_relat_1 C A) (k3_relat_1 C B))) ) ) ) ) ) ) ).
tt(t19_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k3_polynom5 A C D)) (k3_polynom5 A (k11_polynom3 A B C) D))) ) ) ) ) ) ) ) ).
tt(t19_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 B A) => (r1_idea_1 B (k8_idea_1 B A))) ) ) ) ) ).
tt(t19_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_subset_1 B (u1_struct_0 A)) <=>  (~ (r2_hidden (k5_struct_0 A) B)) ) ) ) ) ) ).
tt(t19_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) &  ((r1_collsp A B C E) &  ((r1_collsp A B F G) &  ((r1_collsp A B F H) &  ((r1_collsp A C G K) &  ((r1_collsp A F D K) &  ((r1_collsp A C H J) &  ((r1_collsp A E F J) &  ((r1_collsp A D H I) & (r1_collsp A E G I)) ) ) ) ) ) ) ) )  =>  ( (B = D)  |  ( (B = E)  |  ( (D = E)  |  ( (C = D)  |  ( (C = E)  |  ( (B = G)  |  ( (B = H)  |  ( (G = H)  |  ( (F = G)  |  ( (F = H)  |  ((r1_collsp A B C F) | (r1_collsp A I J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k3_incproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k3_incproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k3_incproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k3_incproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 (k3_incproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 (k3_incproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 (k3_incproj A))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k3_incproj A))) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 (k3_incproj A))) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 (k3_incproj A))) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 (k3_incproj A))) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 (k3_incproj A))) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 (k3_incproj A))) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 (k3_incproj A))) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 (k3_incproj A))) =>  (! [S:$i] :  ((m1_subset_1 S (u2_incsp_1 (k3_incproj A))) =>  (! [T:$i] :  ((m1_subset_1 T (u2_incsp_1 (k3_incproj A))) =>  ( ((r2_zfmisc_1 B C D E) &  ((r2_zfmisc_1 B F G H) &  ((r1_incsp_1 (k3_incproj A) B N) &  ((r1_incsp_1 (k3_incproj A) B Q) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) D H I) L) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) E F J) O) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) C G K) R) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) C H J) M) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) E G I) P) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) D F K) S) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) F G H) N) &  ((r4_incsp_1 (k3_incproj A) (k8_domain_1 (u1_incsp_1 (k3_incproj A)) C D E) Q) & (r4_incsp_1 (k3_incproj A) (k7_domain_1 (u1_incsp_1 (k3_incproj A)) I J) T)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (N = Q)  | (r1_incsp_1 (k3_incproj A) K T)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  (~  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  &  ((r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) F) &  ( (~ (r2_incsp_1 A E F))  & (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  ((r1_funct_2 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (u4_struct_0 C) D E) =>  ((k13_index_1 A B D) = (k13_index_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_instalg1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A C D E) => (r3_pua2mss1 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r2_int_1 (k2_xcmplx_0 A B) C D) <=> (r2_int_1 A (k6_xcmplx_0 C B) D)) ) ) ) ) ) ) ) ) ).
tt(t19_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A C) & (r1_int_1 B C))  => (r1_int_1 (k2_int_2 A B) C)) ) ) ) ) ) ) ).
tt(t19_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k4_nat_d (k3_xcmplx_0 B C) (k1_newton B A)) = (k3_xcmplx_0 B (k4_nat_d C (k1_newton B (k7_nat_d A 1))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ((k3_int_2 A B) = 1)  =>  ((r1_xxreal_0 B 2) |  ((r1_int_5 A B) |  ((k6_int_1 (k1_newton A (k3_nat_d (k7_nat_d B 1) 2)) B) = (k6_xcmplx_0 B 1)) ) ) ) ) ) ) ) ).
tt(t19_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_int_2 A B) =>  ((k3_int_2 A (k3_xcmplx_0 B C)) = (k3_int_2 A C)) ) ) ) ) ) ) ) ).
tt(t19_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((v3_group_1 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A))) &  ((v5_group_1 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A))) & (v2_group_1 (g3_algstr_0 (k1_int_7 A) (k2_int_7 A)))) ) ) ) ).
tt(t19_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) k19_sin_cos)) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k10_real_1 1 (k7_real_1 A 1))) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k10_real_1 1 (k7_real_1 A 1))) (k5_seq_4 B)))) ) ) ) ) ).
tt(t19_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ((r1_tarski E (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ( (E = (k1_relset_1 k1_numbers D))  &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)))) & (r2_relset_1 k1_numbers k1_numbers D (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 (k21_binop_2 A 1))) A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2)))))) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((k2_integra5 B D) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos9 (k1_partfun2 k1_numbers D)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2))))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 D)) (k8_real_1 D (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t19_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (C = (k1_rcomp_1 D E))  =>  ((k11_integr15 A C B) = (k12_integr15 D E A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ( ((r1_integr16 A B) &  ((r1_integr16 A C) &  ((r1_tarski A (k1_relset_1 k1_numbers B)) &  ((r1_tarski A (k1_relset_1 k1_numbers C)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k2_numbers B A)) & (v1_comseq_2 (k2_partfun1 k1_numbers k2_numbers C A))) ) ) ) )  =>  ((r1_integr16 A (k2_valued_1 k1_numbers k2_numbers k2_numbers B C)) &  ((r1_integr16 A (k46_valued_1 k1_numbers k2_numbers k2_numbers B C)) &  ( ((k7_integr16 A (k2_valued_1 k1_numbers k2_numbers k2_numbers B C)) = (k3_binop_2 (k7_integr16 A B) (k7_integr16 A C)))  &  ((k7_integr16 A (k46_valued_1 k1_numbers k2_numbers k2_numbers B C)) = (k4_binop_2 (k7_integr16 A B) (k7_integr16 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_integr19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid B) C A) B))  => (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 B k1_numbers C) A))) ) ) ) ) ) ) ).
tt(t19_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k3_integra1 (k2_integra1 B C A)) = (k1_seq_1 (k5_integra1 B (k7_rfunct_1 B B) C) A)) ) ) ) ) ) ) ) ).
tt(t19_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 k6_numbers A))  => (r1_xxreal_0 (k8_real_1 (k8_real_1 A (k5_seq_4 (k1_rvsum_1 C))) (k3_integra1 B)) (k1_seq_1 (k8_integra1 B (k26_valued_1 B k1_numbers C A)) D))) ) ) ) ) ) ) ) ) ).
tt(t19_integra3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers D B)) & (r2_hidden A (k4_finseq_1 C)))  => (r1_xxreal_0 (k5_seq_4 (k1_rvsum_1 D)) (k4_seq_4 (k1_rvsum_1 (k2_partfun1 B k1_numbers D (k2_integra1 B C A)))))) ) ) ) ) ) ) ) ) ).
tt(t19_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v2_seq_2 (k2_partfun1 A k1_numbers C A)) => (v3_xxreal_2 (k1_rvsum_1 (k2_partfun1 A k1_numbers C B)))) ) ) ) ) ) ).
tt(t19_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k1_rcomp_1 C D))  =>  ((k2_integra5 B A) = (k4_integra5 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A D) E) &  ((r1_integra5 (k3_integra5 A D) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A D))) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A D))) &  ((r1_tarski (k3_integra5 A D) (k9_xtuple_0 E)) & (r1_tarski (k3_integra5 A D) (k9_xtuple_0 F))) ) ) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 B C) (k3_valued_1 k1_numbers k1_numbers k1_numbers E F)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers E F) (k3_integra5 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) C) &  ((r1_tarski C (k1_relset_1 k1_numbers D)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D C))) ) )  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B))) &  ((r1_integra5 (k3_integra5 A B) D) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_integra8,ax, ((k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 1) = (k10_real_1 (k7_real_1 (k5_square_1 k8_power) 1) (k8_real_1 2 k8_power))) ).
tt(t19_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 B (k1_taylor_1 A)) = (k9_real_1 (k8_real_1 (k10_real_1 1 (k7_real_1 A 1)) (k2_newton (k4_seq_4 B) (k7_real_1 A 1))) (k8_real_1 (k10_real_1 1 (k7_real_1 A 1)) (k2_newton (k5_seq_4 B) (k7_real_1 A 1))))) ) ) ) ) ).
tt(t19_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r1_interva1 A (k4_interva1 A B B) B)) ) ) ) ).
tt(t19_intpro_1,ax,(r2_hidden k10_intpro_1 k8_intpro_1)).
tt(t19_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((k1_seq_1 (k7_newton C D B) (k2_nat_1 A 1)) = (k3_xcmplx_0 (k3_xcmplx_0 (k6_newton A B) (k3_power C (k6_xcmplx_0 B A))) (k3_power D A))) ) ) ) ) ) ) ) ) ) ).
tt(t19_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  ( ((r1_isocat_1 A B) & (r1_isocat_1 C D))  => (r1_isocat_1 (k8_cat_2 A C) (k8_cat_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t19_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A F))  =>  (! [G:$i] :  ((m2_nattra_1 G B C (k12_cat_2 A B C D (k3_graph_1 A F)) (k12_cat_2 A B C D (k3_graph_1 A E))) =>  ((r2_funct_2 (u1_struct_0 B) (u4_struct_0 C) G (k4_isocat_2 A B C D F)) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 C) (k4_isocat_2 A B C D (k1_cat_1 A F E)) (k7_nattra_1 B C (k12_cat_2 A B C D (k3_graph_1 A F)) (k12_cat_2 A B C D (k3_graph_1 A E)) (k12_cat_2 A B C D (k4_graph_1 A E)) G (k4_isocat_2 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v5_tops_1 C A) &  ((r1_tarski (k1_tops_1 A C) B) & (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t19_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v2_funct_1 B) =>  ((r1_xxreal_0 (k3_finseq_1 B) 1) |  ((v1_graph_4 (k4_jgraph_1 A B) (k1_jgraph_1 A)) &  (~  ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ).
tt(t19_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k2_xcmplx_0 F G)) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~  ( (B = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A))  & (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t19_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid D) (k12_euclid D)) A) (k9_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k17_euclid D) k6_numbers) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t19_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid B)) =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  => (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ).
tt(t19_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r2_hidden E (k1_sppol_2 A B C D))) )  =>  ((r1_xxreal_0 A (k17_euclid E)) &  ((r1_xxreal_0 (k17_euclid E) B) &  ((r1_xxreal_0 C (k18_euclid E)) & (r1_xxreal_0 (k18_euclid E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k18_euclid C) = H)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 E (k17_euclid C)) &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) H)) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_xboole_0 (k1_jordan2c 2 B) (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ).
tt(t19_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_matrix_1 B)) => (v1_convex1 (k2_goboard5 B A) (k15_euclid 2))) ) ) ) ) ).
tt(t19_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_jordan1h A C) & (r2_jordan2c 2 A B))  => (r1_xboole_0 B (k3_topreal1 2 (k1_jordan13 A C)))) ) ) ) ) ) ) ).
tt(t19_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k2_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) =>  ((r2_hidden B (k1_jordan7 A B (k18_pscomp_1 A))) & (r2_hidden (k18_pscomp_1 A) (k1_jordan7 A B (k18_pscomp_1 A)))) ) ) ) ) ) ).
tt(t19_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A C D E B) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A C D B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) & (r1_xxreal_0 (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k4_topreal1 A)))) (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_topreal1 A)))))) ) ) ) ) ) ).
tt(t19_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k1_matrix_1 E))) ) ) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A C)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_3_jordan1 A B C D))  => (v2_connsp_1 E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A 1) (k1_jordan1a (k1_jordan8 A 1)) 1) = (k19_euclid (k13_complex1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 A 1))))) ) ) ).
tt(t19_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) &  ((k18_euclid A) = (k7_pscomp_1 (k1_jordan2c 2 B))) ) ) ) ) ) ) ).
tt(t19_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k19_pscomp_1 B) (k2_gobrd13 (k1_jordan9 B A) (k1_jordan8 B A) C))) ) ) ) ) ) ) ) ).
tt(t19_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) 2)) = (k7_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ).
tt(t19_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k4_finseq_4 (k1_jordan1e B A) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = 1) ) ) ) ) ).
tt(t19_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k1_matrix_1 A) = (k5_card_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A)))) ) ) ).
tt(t19_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1) D))  &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E)) = (k9_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k25_pscomp_1 B) A))  =>  ((k25_pscomp_1 A) = (k25_pscomp_1 B)) ) ) ) ) ) ).
tt(t19_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r1_xboole_0 B C) &  ( (~ (r1_tarski B (k2_jordan2c A C)))  &  (~ (r1_tarski B (k1_jordan2c A C))) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( (~ (r1_jordan5c A B C D E))  &  (~ (r1_jordan5c A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k6_pscomp_1 A) = (k6_pscomp_1 (k9_jordan6 A))) ) ) ).
tt(t19_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))) &  ((k1_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_jordan23 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k4_jordan3 A B C) 1) = B) ) ) ) ) ) ) ) ) ).
tt(t19_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_euclid (k12_finseq_1 k1_numbers A)) = (k12_finseq_1 k1_numbers (k18_complex1 A))) ) ) ).
tt(t19_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden C (k3_topreal1 2 A)) &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k1_jordan3 A C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) C))) ) )  =>  ( (C = (k1_funct_1 A 1))  | (r1_jordan3 B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) C)) ) ) ) ) ) ) ) ).
tt(t19_jordan4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 1 D)) )  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 (k2_nat_1 (k7_nat_d C B) 1) D) |  ((k2_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) D) = (k2_topreal1 2 A (k7_nat_d (k2_nat_1 D B) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan5a,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ( ((k5_seq_4 (k1_rcomp_1 A B)) = A)  &  ((k4_seq_4 (k1_rcomp_1 A B)) = B) ) ) ) ) ) ) ).
tt(t19_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (v4_topreal1 A))  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  | (r2_hidden B (k3_topreal1 2 (k2_jordan3 A B)))) ) ) ) ) ) ).
tt(t19_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_pre_topc B (k15_euclid 2)) &  ((v4_topreal1 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A C))) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) |  ((k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k1_jordan5c (k2_topreal1 2 A C) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(t19_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_0_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k14_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k14_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t19_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) => (r1_tarski (k3_jordan6 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t19_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ((v5_pre_topc F k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 F) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) = A)  &  ( ((k1_funct_1 F k6_numbers) = B)  &  ( ((k1_funct_1 F 1) = C)  &  ( ((k1_funct_1 F G) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  ( ((k1_funct_1 F H) = E)  &  ((r1_xxreal_0 k6_numbers H) &  ((r1_xxreal_0 H 1) & (r1_jordan5c A B C D E)) ) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C)) &  ((r2_hidden D (k16_matrix_1 C)) &  ((r2_hidden D (k3_goboard5 C A B)) &  ( (~  (D = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B)) )  &  ( (~  (D = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) )  &  ( (~  (D = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) )  &  (~  (D = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) => (v2_compts_1 (k1_jordan7 A B (k18_pscomp_1 A)) (k15_euclid 2))) ) ) ) ) ).
tt(t19_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  ((k7_subset_1 (u1_struct_0 (k15_euclid B)) (k2_topreal9 B C A) (k1_topreal9 B C A)) = (k3_topreal9 B C A)) ) ) ) ) ) ) ).
tt(t19_knaster,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_abian (u1_struct_0 B) C A) D) = (k3_knaster B C D A)) ) ) ) ) ) ) ) ) ).
tt(t19_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((v2_prob_1 B) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ( (~ (r1_xxreal_0 E D))  &  (~ (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 A) B E))) ) ) ) ) )  | (r2_hidden C (k2_kurato_0 A B))) ) ) ) ) ) ).
tt(t19_kurato_1,ax, ((k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)))) = (k3_rcomp_1 4 k1_xxreal_0)) ).
tt(t19_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) D E) = (k9_subset_1 (u1_struct_0 A) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C E))) ) )  => (r1_tarski (k1_kurato_2 A D) (k9_subset_1 (u1_struct_0 A) (k1_kurato_2 A B) (k1_kurato_2 A C)))) ) ) ) ) ) ) ) ) ).
tt(t19_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  (! [F:$i] :  ((m1_matrix_1 F D A B) =>  (! [G:$i] :  ((m1_matrix_1 G D B A) =>  ( (G = (k4_matrix_1 D F))  =>  ( ( (B = k1_xboole_0)  &  (~  (A = k1_xboole_0) ) )  |  ((k3_laplace C A B D F E) = (k4_matrix_1 D (k3_matrix11 C B A D G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((k1_funct_1 (k1_latsubgr A) (k10_group_2 A B C)) = (k3_xboole_0 (k1_funct_1 (k1_latsubgr A) B) (k1_funct_1 (k1_latsubgr A) C))) ) ) ) ) ) ) ).
tt(t19_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( ((v1_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) &  ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))) )  &  ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) A) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_latsum_1 A B) &  ( (C = E)  &  (D = F) ) ) ) )  =>  ((k13_lattice3 A C D) = (k13_lattice3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_setwiseo (u1_lattices A) (u1_struct_0 A)) =>  ((k6_lattices A) = (k4_binop_1 (u1_struct_0 A) (u1_lattices A))) ) ) ) ).
tt(t19_lattice3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_lattices B) &  ((v10_lattices B) & (l3_lattices B)) ) )  &  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k3_lattice3 B)) ) ) ) ) ).
tt(t19_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ((k2_lattice4 A (k1_setwiseo (u1_struct_0 A))) = (k6_lattices A)) ) ) ).
tt(t19_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_zfmisc_1 A A (u1_struct_0 B) (u1_struct_0 B))) => (r1_relset_1 (k2_zfmisc_1 A A) (u1_struct_0 B) C (k6_lattice5 A B C D))) ) ) ) ) ) ) ) ).
tt(t19_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v2_lattice6 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k5_lattices A)) )  =>  ((v4_lattice6 B A) <=> (v3_waybel_6 (k4_lattice3 A B) (k3_lattice3 A))) ) ) ) ) ) ).
tt(t19_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((k5_lattice8 A B C D (k1_ordinal1 E)) = (k2_lattice8 (k3_lattice8 A E) B (k10_lattice5 (k3_lattice8 A E) B (k5_lattice8 A B C D E)) (k4_lattice8 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r3_lattices A B (k6_lattices A))) ) ) ) ).
tt(t19_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) & (r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B D))))  =>  ((k1_recdef_1 (k5_lexbfs A B C) E) = (k1_recdef_1 (k5_lexbfs A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_lfuzzy_0 A))) =>  ((k13_lattice3 (k4_lfuzzy_0 A) B C) = (k2_fuzzy_1 A (k5_lfuzzy_0 A B) (k5_lfuzzy_0 A C))) ) ) ) ) ) ) ).
tt(t19_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (v2_lfuzzy_1 (k1_lfuzzy_1 (k2_zfmisc_1 A A) B (k2_fuzzy_4 A A B)) A)) ) ) ) ).
tt(t19_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) & (v2_comseq_2 B))  => (v2_limfunc1 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t19_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A (k7_real_1 A D))))) ) ) )  | (r5_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t19_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) | (r3_limfunc3 B A))  => (r2_limfunc3 (k56_valued_1 k1_numbers k1_numbers B) A)) ) ) ) ) ).
tt(t19_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r2_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t19_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 A B C) => (r1_lmod_6 A (k1_vectsp_4 A B) C)) ) ) ) ) ) ) ).
tt(t19_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_lmod_7 A B C))) => (m1_subset_1 D (u1_struct_0 (k13_lmod_7 A B C)))) ) ) ) ) ) ) ) ).
tt(t19_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) &  ((v1_funct_2 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) A B) &  ((v1_lopban_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) A B) & (m1_subset_1 (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ).
tt(t19_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_lopban_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_lopban_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_lopban_2 A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((k1_algstr_0 (k9_lopban_2 A) B C) = (k1_algstr_0 (k9_lopban_2 A) C B))  &  ( ((k1_algstr_0 (k9_lopban_2 A) (k1_algstr_0 (k9_lopban_2 A) B C) D) = (k1_algstr_0 (k9_lopban_2 A) B (k1_algstr_0 (k9_lopban_2 A) C D)))  &  ( ((k1_algstr_0 (k9_lopban_2 A) B (k4_struct_0 (k9_lopban_2 A))) = B)  &  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_lopban_2 A))) &  ((k1_algstr_0 (k9_lopban_2 A) B G) = (k4_struct_0 (k9_lopban_2 A))) ) )  &  ( ((k6_algstr_0 (k9_lopban_2 A) (k6_algstr_0 (k9_lopban_2 A) B C) D) = (k6_algstr_0 (k9_lopban_2 A) B (k6_algstr_0 (k9_lopban_2 A) C D)))  &  ( ((k6_algstr_0 (k9_lopban_2 A) B (k5_struct_0 (k9_lopban_2 A))) = B)  &  ( ((k6_algstr_0 (k9_lopban_2 A) (k5_struct_0 (k9_lopban_2 A)) B) = B)  &  ( ((k6_algstr_0 (k9_lopban_2 A) B (k1_algstr_0 (k9_lopban_2 A) C D)) = (k1_algstr_0 (k9_lopban_2 A) (k6_algstr_0 (k9_lopban_2 A) B C) (k6_algstr_0 (k9_lopban_2 A) B D)))  &  ( ((k6_algstr_0 (k9_lopban_2 A) (k1_algstr_0 (k9_lopban_2 A) C D) B) = (k1_algstr_0 (k9_lopban_2 A) (k6_algstr_0 (k9_lopban_2 A) C B) (k6_algstr_0 (k9_lopban_2 A) D B)))  &  ( ((k1_rlvect_1 (k9_lopban_2 A) (k6_algstr_0 (k9_lopban_2 A) B C) E) = (k6_algstr_0 (k9_lopban_2 A) (k1_rlvect_1 (k9_lopban_2 A) B E) C))  &  ( ((k1_rlvect_1 (k9_lopban_2 A) (k6_algstr_0 (k9_lopban_2 A) B C) (k3_xcmplx_0 E F)) = (k6_algstr_0 (k9_lopban_2 A) (k1_rlvect_1 (k9_lopban_2 A) B E) (k1_rlvect_1 (k9_lopban_2 A) C F)))  &  ( ((k1_rlvect_1 (k9_lopban_2 A) (k1_algstr_0 (k9_lopban_2 A) B C) E) = (k1_algstr_0 (k9_lopban_2 A) (k1_rlvect_1 (k9_lopban_2 A) B E) (k1_rlvect_1 (k9_lopban_2 A) C E)))  &  ( ((k1_rlvect_1 (k9_lopban_2 A) B (k2_xcmplx_0 E F)) = (k1_algstr_0 (k9_lopban_2 A) (k1_rlvect_1 (k9_lopban_2 A) B E) (k1_rlvect_1 (k9_lopban_2 A) B F)))  &  ( ((k1_rlvect_1 (k9_lopban_2 A) B (k3_xcmplx_0 E F)) = (k1_rlvect_1 (k9_lopban_2 A) (k1_rlvect_1 (k9_lopban_2 A) B F) E))  &  ((k1_rlvect_1 (k9_lopban_2 A) B 1) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k5_normsp_1 A B C)) (k5_normsp_1 A (k1_bhsp_4 A B) C))) ) ) ) ) ) ).
tt(t19_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k1_rlvect_1 A (k6_lopban_3 A (k3_rlvect_1 A C D) B) (k10_real_1 1 (k3_newton B))) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k6_lopban_4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_0 D A) =>  ((r2_hidden (k3_lattices A B C) D) <=>  ((r2_hidden B D) | (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_rfunct_3 D C k1_numbers (k3_rfunct_3 C k1_numbers)) =>  ((k2_lpspace1 C k1_numbers (k13_rfunct_3 C) (k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) A D) (k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) B D)) = (k2_binop_1 k1_numbers (k3_rfunct_3 C k1_numbers) (k3_rfunct_3 C k1_numbers) (k4_lpspace1 C) (k7_real_1 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t19_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (~ (r2_relset_1 A k1_numbers (k26_valued_1 A k1_numbers (k2_mesfun6c D A (k56_valued_1 A k1_numbers B)) (k4_power C D)) (k2_mesfun6c D A (k26_valued_1 A k1_numbers (k56_valued_1 A k1_numbers B) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k3_hilbert1 (k4_hilbert1 A B) (k5_ltlaxio1 (k2_ltlaxio1 B) (k2_ltlaxio1 (k4_ltlaxio1 A (k4_hilbert1 A B))))))) = 1) ) ) ) ) ) ) ) ) ).
tt(t19_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t19_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m1_subset_1 (k16_funcop_1 (k6_finseq_1 A) B) (k4_partfun1 (k3_finseq_2 A) A))) ) ) ) ).
tt(t19_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r1_tarski (k1_mathmorp A D C) (k6_rusub_4 A C B))) ) ) ) ) ) ) ) ) ).
tt(t19_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v1_matrix10 B) &  ((v2_matrix10 C) & (r1_matrix10 (k1_matrix10 B) (k1_matrix10 C))) )  => (v2_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t19_matrix11,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) &  ((v3_funct_2 E (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) &  ((v3_funct_2 F (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)))))) ) )  =>  ( ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) E A) = C)  &  ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) F A) = D)  &  ( ((k1_funct_1 E B) = B)  &  ((k1_funct_1 F B) = B) ) ) )  =>  ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) (k1_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) F E) A) = (k1_partfun1 A A A A D C))  &  ((k1_funct_1 (k1_partfun1 (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) (k2_xboole_0 A (k1_tarski B)) F E) B) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B B) =>  ((r2_hidden A (k4_finseq_1 (k12_matrix_1 C B))) =>  ((r1_xxreal_0 B k6_numbers) |  ((k4_matrix_6 B C E (k5_matrix12 B B C (k12_matrix_1 C B) A D)) = (k5_matrix12 B B C E A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 B k5_numbers)) =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 E) (k10_xtuple_0 F)) (k2_matrix_1 D)) =>  ( ( (B = k6_numbers)  &  (~  (C = k6_numbers) ) )  |  ((k1_matrix13 A D C B E F) = (k4_matrix_1 A (k1_matrix13 A (k4_matrix_1 A D) B C F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) <=>  (? [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) &  ( ((k4_matrix_6 A B D C) = (k12_matrix_1 B A))  &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D A C) =>  ( ((k6_matrix13 D (k1_matrix15 D A B C E F) (k2_finseq_1 A) (k2_finseq_1 (k1_matrix_1 E))) = E)  &  ((k6_matrix13 D (k1_matrix15 D A B C E F) (k2_finseq_1 A) (k7_subset_1 k5_numbers (k2_finseq_1 (k2_nat_1 (k1_matrix_1 E) (k1_matrix_1 F))) (k2_finseq_1 (k1_matrix_1 E)))) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ((m1_matrix_1 G F C C) =>  ( ((v3_matrix16 G F) &  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))) &  ( (D = (k2_xcmplx_0 A 1))  &  (E = (k2_xcmplx_0 B 1)) ) ) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 C B) |  ((k3_matrix_1 F G A B) = (k3_matrix_1 F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (m1_matrix_1 (k10_finseq_1 (k10_finseq_1 B C) (k10_finseq_1 D E)) A 2 2)) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix_2,ax, ((k12_matrix_2 1) = (k1_tarski (k1_finseq_2 1))) ).
tt(t19_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k4_matrix_3 B C (k12_matrix_1 B A)) = C) ) ) ) ) ) ) ).
tt(t19_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 E))  &  ((k1_matrix_4 A B C) = (k1_matrix_4 A D E)) ) ) ) ) ) )  =>  ((k1_matrix_4 A B D) = (k1_matrix_4 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k3_matrix_5 A (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A))) = A) ) ) ).
tt(t19_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ( (C = (k4_matrix_6 A B D C))  & (v1_matrix_6 C A B))  => (r1_matrix_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t19_matrix_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) => (m1_matrix_1 (k5_matrix_1 A (u1_struct_0 B) C) (u1_struct_0 B) A A)) ) ) ) ) ) ).
tt(t19_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B C D) = (k4_matrix_6 A B C E)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrix_9,ax, ((k12_matrix_2 3) = (k4_enumset1 (k3_finseq_4 k5_numbers 1 2 3) (k3_finseq_4 k5_numbers 3 2 1) (k3_finseq_4 k5_numbers 1 3 2) (k3_finseq_4 k5_numbers 2 3 1) (k3_finseq_4 k5_numbers 2 1 3) (k3_finseq_4 k5_numbers 3 1 2))) ).
tt(t19_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k4_finseq_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k4_finseq_2 A k2_numbers)) =>  ((k9_matrix_5 (k5_matrixc1 C D) B) = (k5_binop_2 (k9_matrix_5 C B) (k9_matrix_5 D B))) ) ) ) ) ) ) ) ) ).
tt(t19_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k11_matrixj1 A (k4_matrixj1 A B)) = (k4_matrix_2 k5_numbers (k1_matrix_1 B))) ) ) ) ) ).
tt(t19_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_4 E B C) =>  (! [F:$i] :  ((m1_vectsp_4 F B C) =>  (! [G:$i] :  ((m1_vectsp_4 G B D) =>  (! [H:$i] :  ((m1_vectsp_4 H B D) =>  (! [I:$i] :  ((m1_matrlin I B C) =>  (! [J:$i] :  ((m2_finseq_1 J (u1_struct_0 D)) =>  (! [K:$i] :  ((m1_matrlin K B E) =>  (! [L:$i] :  ((m1_matrlin L B F) =>  (! [M:$i] :  ((m2_finseq_1 M (u1_struct_0 G)) =>  (! [N:$i] :  ((m2_finseq_1 N (u1_struct_0 H)) =>  (! [O:$i] :  ((m1_matrix_1 O (u1_struct_0 B) (k3_finseq_1 I) (k3_finseq_1 J)) =>  (! [P:$i] :  ((m1_matrix_1 P (u1_struct_0 B) (k3_finseq_1 K) (k3_finseq_1 M)) =>  (! [Q:$i] :  ((m1_matrix_1 Q (u1_struct_0 B) (k3_finseq_1 L) (k3_finseq_1 N)) =>  ( ( (I = (k7_finseq_1 K L))  &  ( (J = (k7_finseq_1 M N))  &  ( (O = (k13_matrixj1 (u1_struct_0 B) (k4_struct_0 B) (k5_matrixj1 (u1_struct_0 B) P Q)))  &  ( ((k1_matrix_1 P) = (k3_finseq_1 M))  &  ((k1_matrix_1 Q) = (k3_finseq_1 N)) ) ) ) )  =>  ( ((r2_hidden A (k4_finseq_1 K)) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin2 B C D I J O) (k7_partfun1 (u1_struct_0 C) I A)) = (k3_funct_2 (u1_struct_0 E) (u1_struct_0 G) (k4_matrlin2 B E G K M P) (k7_partfun1 (u1_struct_0 E) K A))) )  &  ((r2_hidden A (k4_finseq_1 L)) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin2 B C D I J O) (k7_partfun1 (u1_struct_0 C) I (k1_nat_1 A (k3_finseq_1 K)))) = (k3_funct_2 (u1_struct_0 F) (u1_struct_0 H) (k4_matrlin2 B F H L N Q) (k7_partfun1 (u1_struct_0 F) L A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrixr1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_matrix_1 D)))  =>  ((k9_matrix_1 (u1_struct_0 B) (k6_matrix_3 B D C) A) = (k10_fvsum_1 (k3_finseq_1 D) B (k9_matrix_1 (u1_struct_0 B) D A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k4_matrix_3 A B (k2_matrix_3 A C)) = (k2_matrix_3 A (k4_matrix_3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D B C) =>  ((r2_hidden A (k4_finseq_1 D)) =>  ((k9_matrlin B C D (k7_partfun1 (u1_struct_0 C) D A)) = (k8_matrix_1 (u1_struct_0 B) (k12_matrix_1 B (k3_finseq_1 D)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_xtuple_0 C) (k9_xtuple_0 C)) &  ((v3_funct_2 F (k9_xtuple_0 C) (k9_xtuple_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 C) (k9_xtuple_0 C))))) ) )  =>  ( (D = (k1_partfun1 (k9_xtuple_0 C) (k9_xtuple_0 C) k5_numbers (u1_struct_0 B) F C))  =>  ((k3_vectsp_6 A B D E) = (k1_partfun1 (k9_xtuple_0 C) (k9_xtuple_0 C) k5_numbers (u1_struct_0 B) F (k3_vectsp_6 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_matroid0 A C B) <=>  ((r1_tarski C B) &  ((k5_card_1 C) = (k4_matroid0 A B)) ) ) ) ) ) ) ) ) ).
tt(t19_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  (~  ( ((k3_finseq_1 E) = C)  &  ( ((k3_finseq_1 F) = C)  &  (! [G:$i] :  ((m1_matrix_1 G A D C) =>  (? [H:$i] :  ((v7_ordinal1 H) &  ((r2_hidden H (k2_finseq_1 D)) &  (~  ( ((r2_hidden H (k2_finseq_1 B)) =>  ((k1_matrprob A G H) = E) )  &  ( (~ (r2_hidden H (k2_finseq_1 B)))  =>  ((k1_matrprob A G H) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k3_finseq_1 (k11_matrix13 B A A (k12_matrix_1 B A))) = A) ) ) ) ) ).
tt(t19_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid A))))  =>  (~  ((v1_rlvect_3 (k2_relset_1 (u1_struct_0 (k15_euclid A)) B) (k15_euclid A)) &  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A A) =>  (~  ((v1_matrix_6 C A k2_vectsp_1) &  ((k17_finseq_1 (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) (k3_finseq_1 B) C) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((v4_matrix_6 (k2_matrtop3 D A B C) D k2_vectsp_1) &  ((k5_matrix_6 D k2_vectsp_1 (k2_matrtop3 D A B C)) = (k2_matrtop3 D (k4_xcmplx_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) C) B) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t19_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k7_pboole A B C) (k1_mboolean A (k6_pboole A B C)))) ) ) ) ) ).
tt(t19_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (k2_zfmisc_1 (k2_tarski B C) (k2_tarski D E))) =>  ( ( ((k1_xtuple_0 A) = B)  |  ((k1_xtuple_0 A) = C) )  &  ( ((k2_xtuple_0 A) = D)  |  ((k2_xtuple_0 A) = E) ) ) ) ) ) ) ) ) ).
tt(t19_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( ((k2_relset_1 (k9_setfam_1 A) D) = (k2_tarski B C))  &  ( ((k1_prob_2 A (k9_setfam_1 A) D k6_numbers) = B)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 E k6_numbers))  =>  ((k1_prob_2 A (k9_setfam_1 A) D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_measure2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k1_funct_1 B k6_numbers) = (k1_funct_1 A k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k1_funct_1 B (k2_nat_1 C 1)) = (k6_subset_1 (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 A C)))  & (r1_tarski (k1_funct_1 A C) (k1_funct_1 A (k2_nat_1 C 1)))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 D C))  => (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t19_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  (! [F:$i] :  ((m1_measure3 F A B C) =>  (! [G:$i] :  ((m1_measure3 G A B C) =>  ( ((k2_xboole_0 D F) = (k2_xboole_0 E G))  =>  ((k12_supinf_2 C D) = (k12_supinf_2 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v4_measure5 A) =>  (A = (k3_xxreal_1 (k7_supinf_2 A) (k8_supinf_2 A))) ) ) ) ).
tt(t19_measure8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_measure4 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) => (r1_xxreal_0 (k1_xxreal_3 (k1_mesfunc9 C (k9_subset_1 A D B)) (k1_mesfunc9 C (k9_subset_1 A D (k6_subset_1 A B)))) (k1_mesfunc9 C D))) )  => (r2_hidden B (k1_measure4 A C))) ) ) ) ) ) ).
tt(t19_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_member_1 (k1_tarski A)) = (k1_tarski (k1_binop_2 A))) ) ) ).
tt(t19_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v1_membered B) =>  ((r1_tarski A B) => (v1_membered A)) ) ) ) ).
tt(t19_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  (C = (k1_funct_4 (k7_memstr_0 A B (k5_memstr_0 A B C)) (k6_memstr_0 A B C))) ) ) ) ) ) ) ) ).
tt(t19_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 J)) (k1_rlvect_1 (k15_euclid 2) C J)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 K)) (k1_rlvect_1 (k15_euclid 2) A K)))  &  ( (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 L)) (k1_rlvect_1 (k15_euclid 2) B L)))  &  ((r1_euclid_6 A D G) &  ((r1_euclid_6 B E G) &  ((r1_euclid_6 B E H) &  ((r1_euclid_6 C F H) &  ((r1_euclid_6 A D I) & (r1_euclid_6 C F I)) ) ) ) ) ) ) )  =>  ((r1_euclid_6 A B C) |  ( (J = 1)  |  ( (K = 1)  |  ( (L = 1)  |  ( (~  ((k11_binop_2 (k11_binop_2 (k9_binop_2 (k10_binop_2 1 K) (k11_binop_2 J K)) (k9_binop_2 (k10_binop_2 1 J) (k11_binop_2 L J))) (k9_binop_2 (k10_binop_2 1 L) (k11_binop_2 K L))) = k6_numbers) )  &  ((k1_euclid_6 H I G) = (k11_binop_2 (k12_binop_2 (k5_square_1 (k10_binop_2 (k11_binop_2 (k11_binop_2 K L) J) (k11_binop_2 (k11_binop_2 (k10_binop_2 1 K) (k10_binop_2 1 L)) (k10_binop_2 1 J)))) (k11_binop_2 (k11_binop_2 (k9_binop_2 (k10_binop_2 1 K) (k11_binop_2 J K)) (k9_binop_2 (k10_binop_2 1 J) (k11_binop_2 L J))) (k9_binop_2 (k10_binop_2 1 L) (k11_binop_2 K L)))) (k1_euclid_6 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  ( ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc1 A C (k4_mesfunc5 A k7_numbers B F) E)) )  &  ((v1_mesfun10 B A) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) => (v10_mesfunc5 (k3_mesfunc5 A B F))) ) ) ) ) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 D E)) |  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B F))) )  &  ((r1_mesfunc5 A C D (k7_mesfunc8 A B)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k12_supinf_2 F G) = (k7_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B G))) ) )  &  ((v10_mesfunc5 F) &  ((k2_mesfunc5 F) = (k7_mesfunc5 A C D (k7_mesfunc8 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((k12_supinf_2 C E) = k6_numbers)  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  & (r1_mesfunc1 A B D F)) ) ) )  | (r1_mesfunc5 A B C (k2_partfun1 A k7_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers C E) D)) ) )  => (r1_mesfunc1 A B (k6_mesfun7c A C) D)) ) ) ) ) ) ) ) ) ).
tt(t19_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r3_mesfunc6 A B C (k4_mesfunc5 A k1_numbers D E))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (r3_mesfunc6 A B C (k4_mesfunc5 A k1_numbers (k2_mesfun9c A D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k8_nat_1 B C G) = (k9_subset_1 A E (k17_mesfunc1 A D (k1_measure6 (k9_real_1 F (k10_real_1 1 (k2_nat_1 G 1))))))) ) )  =>  ((k9_subset_1 A E (k18_mesfunc1 A D (k1_measure6 F))) = (k1_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k12_supinf_2 (k1_mesfunc2 A B) C) = (k12_supinf_2 B C))  =>  ((k12_supinf_2 (k2_mesfunc2 A B) C) = k1_supinf_2) ) ) ) ) ) ) ) ).
tt(t19_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v6_supinf_2 D) & (v6_supinf_2 E))  => (v6_supinf_2 (k3_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc6 A B C E) &  ((r1_mesfunc6 A B D E) & (r1_tarski E (k1_relset_1 A D))) )  => (r2_hidden (k8_subset_1 A (k8_subset_1 A E (k11_mesfunc1 C F)) (k13_mesfunc1 D F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((k1_relset_1 A (k3_mesfunc1 A (k10_mesfunc1 A B) (k10_mesfunc1 A C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  & (r1_tarski (k1_relset_1 A (k10_mesfunc1 A (k3_mesfunc1 A B C))) (k1_relset_1 A (k10_mesfunc1 A B)))) ) ) ) ) ) ) ).
tt(t19_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C E) D)) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers (k4_mesfunc8 A C) E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers C E) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers B E) D))) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (v10_mesfunc5 (k3_mesfunc5 A B E))) ) ) ) )  => (r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k7_mesfunc8 A B) D) (k7_mesfunc8 A C))) ) ) ) ) ) ) ) ).
tt(t19_metric_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k11_metric_1 B C A) = (a_3_5_metric_1 A B C)) ) ) ) ) ) ) ).
tt(t19_metric_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  ((r2_hidden A (k2_metric_2 B)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  (A = (k6_domain_1 (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(t19_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ( ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 A B) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t19_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_metric_6 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) & (r2_hidden D (k2_pcomps_1 A)))  => (r2_metric_6 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k2_waybel23 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc C A) & (v2_tex_2 C A))  => (r1_ordinal1 (k1_card_1 C) B)) ) ) ) ) ) ) ) ).
tt(t19_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  ( (C = B)  =>  ((k4_rlvect_1 (k15_euclid A) B) = (k4_rlvect_1 (k10_funcsdom (k2_finseq_1 A)) C)) ) ) ) ) ) ) ) ).
tt(t19_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_midsp_1 A B C D E) => (r2_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_midsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ( ((r1_midsp_2 (u1_struct_0 B) A C) & (v1_midsp_2 C B A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k1_midsp_1 B (k1_midsp_1 B D E) (k1_midsp_1 B F G)) = (k1_midsp_1 B (k1_midsp_1 B D F) (k1_midsp_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_3 B (k2_nat_1 A 2))) )  =>  (! [C:$i] :  ( ((v4_midsp_2 C B) & (l1_midsp_2 C B))  =>  ((v2_midsp_3 B A) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B C)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B C)))) =>  ((k9_midsp_3 A B C D F) = (k9_midsp_3 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_relset_1 A A D E) &  ((r1_tarski B C) & (r1_relset_1 A A F G)) )  => (r1_tarski (k6_mmlquery A G B D) (k6_mmlquery A F C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mod_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (m1_subset_1 (k1_enumset1 B C D) A)) ) ) ) ) ) ) ) ).
tt(t19_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_mod_3 A B C) = B)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r1_tarski D C) & (v1_mod_3 D A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k3_mod_4 A B)))  &  ((v13_algstr_0 (k3_mod_4 A B)) &  ((v2_rlvect_1 (k3_mod_4 A B)) &  ((v3_rlvect_1 (k3_mod_4 A B)) &  ((v4_rlvect_1 (k3_mod_4 A B)) &  ((v2_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A)) &  ((v4_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A)) & (l1_vectsp_2 (k3_mod_4 A B) (k2_mod_4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( ((k8_trees_2 A (k1_modal_1 A)) = 2)  =>  ((k1_trees_2 A (k1_modal_1 A)) = (k7_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) (k12_finseq_1 k5_numbers k6_numbers) (k12_finseq_1 k5_numbers 1))) ) ) ) ).
tt(t19_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k30_modelc_1 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E)))))) )  =>  ((r4_modelc_1 B C E F D (k7_modelc_1 A)) <=>  (~ (r4_modelc_1 B C E F D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((v2_modelc_2 A) & (r1_modelc_2 B A)) ) ) ) ) ) ).
tt(t19_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ((r2_modelc_3 A C B) => (r1_xxreal_0 (k18_modelc_3 A (u2_modelc_3 A B)) (k9_real_1 (k18_modelc_3 A (u2_modelc_3 A C)) 1))) ) ) ) ) ) ) ).
tt(t19_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  => (r1_xxreal_0 (k11_nat_3 A C) (k11_nat_3 B C))) )  => (r1_nat_d A B)) ) ) ) ) ).
tt(t19_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_monoid_0 B A) =>  ( ((v1_group_1 A) => (v1_group_1 B))  &  ( ((v5_group_1 A) => (v5_group_1 B))  &  ( ((v3_group_1 A) => (v3_group_1 B))  &  ( ((v13_monoid_0 A) => (v13_monoid_0 B))  &  ( ((v17_monoid_0 A) => (v17_monoid_0 B))  &  ((v16_monoid_0 A) => (v16_monoid_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_monoid_1 B A))) =>  ( ((k9_xtuple_0 C) = A)  & (r1_tarski (k10_xtuple_0 C) (u1_struct_0 B))) ) ) ) ) ) ).
tt(t19_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k1_setfam_1 (a_3_8_morph_01 A B C)) (k1_morph_01 A C (k6_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ) ).
tt(t19_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_msaterm E A B (k2_msaterm A B D)) =>  ((r2_hidden (k6_msaterm A B (k2_msaterm A B D) E) (k1_funct_1 (k5_msafree3 A B C) (k2_msualg_1 A D))) <=> (r1_tarski (k2_relset_1 (k5_trees_3 (u1_struct_0 (k5_msafree A B))) E) (k3_card_3 (k5_msafree3 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (? [C:$i] :  ( ((v3_msualg_1 C A) &  ((v4_msualg_1 C A) &  ((v2_msafree C A) & (l3_msualg_1 C A)) ) )  &  (? [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) &  ((r2_msualg_3 A C B D) &  ((k6_msualg_3 A C B D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t19_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  ((k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B) (k5_msaterm A C B D E)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msscyc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (m1_trees_1 (k17_finseq_1 k5_numbers C B) (k9_xtuple_0 A))) ) ) ) ) ) ).
tt(t19_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) & (v2_finset_1 (k6_pboole A C B)))  => (v2_finset_1 C)) ) ) ) ) ) ).
tt(t19_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k12_msualg_1 A B)))))  =>  ( (D = (u1_struct_0 (k12_msualg_1 A C)))  =>  ((u1_unialg_1 (k12_msualg_1 A C)) = (k3_unialg_2 (k12_msualg_1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A C)) => (r1_tarski (k10_xtuple_0 (k5_relat_1 (k5_msualg_1 A B C) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_msualg_2 A C D))) B))) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k9_msualg_2 A C D)) B))) ) ) ) ) ) ) ) ).
tt(t19_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  ((r2_msualg_3 A B C D) <=>  ((k6_msualg_3 A B C D) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k5_lattices (k6_msualg_5 A B)) = (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ) ).
tt(t19_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) C D) =>  (! [F:$i] :  ((m2_msualg_6 F A B C D) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ((r1_msualg_6 A D E B G) => (m2_msualg_6 (k3_relat_1 F G) A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msualg_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  ((v2_msualg_7 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k15_lattice3 A C) = (k15_lattice3 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v1_msualg_7 (k6_msualg_5 A B) (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ) ).
tt(t19_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D)) =>  ( ((r2_msualg_3 A B C E) & (r1_msualg_3 A B D F))  =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ((r8_pboole (u1_struct_0 A) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) (u3_msualg_1 A D) E G) F) => (r1_msualg_3 A C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r2_alg_1 A B C) => (r3_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C))) ) ) ) ) ) ) ).
tt(t19_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_dilworth B (k3_necklace A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_necklace A))))) ) ) ) ) ).
tt(t19_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  ( ((v1_tops_2 (k2_nagata_1 A B) A) &  ((v1_cantor_1 (k2_nagata_1 A B) A) & (m1_subset_1 (k2_nagata_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v3_pre_topc C A) &  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D E) &  ((r1_tarski (k2_pre_topc A E) C) & (r2_hidden E (k2_nagata_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v9_pre_topc A) &  ((v7_pre_topc A) &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  & (v6_nagata_1 B A)) ) ) )  <=> (v3_pcomps_1 A)) ) ) ).
tt(t19_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k2_xcmplx_0 A B) A))  <=> (r1_xxreal_0 1 B)) ) ) ) ) ).
tt(t19_nat_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~  ( (~  (A = 1) )  & (r1_xxreal_0 A 1)) ) ) ) ).
tt(t19_nat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r1_xboole_0 (k1_polynom2 A B) (k1_polynom2 A C)) =>  ((k8_nat_3 A (k11_pre_poly A B C)) = (k24_binop_2 (k8_nat_3 A B) (k8_nat_3 A C))) ) ) ) ) ) ) ).
tt(t19_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A B))  & (r1_nat_d A (k9_newton B))) ) ) ) ) ) ).
tt(t19_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_int_2 A) =>  ((k3_moebius1 (k1_newton A B)) = (a_2_0_nat_5 A B)) ) ) ) ) ) ).
tt(t19_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d A B) = k6_numbers)  =>  ((k3_nat_d (k2_xcmplx_0 A C) B) = (k2_nat_1 (k3_nat_d A B) (k3_nat_d C B))) ) ) ) ) ) ) ) ).
tt(t19_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  ((r1_nattra_1 B A C D) =>  (! [E:$i] :  ((m1_nattra_1 E B A C D) =>  (! [F:$i] :  ((m1_nattra_1 F B A C D) =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k4_nattra_1 B A C D E G) = (k4_nattra_1 B A C D F G)) ) )  => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r3_ncfcont1 B A C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  (! [E:$i] :  ((m1_ncfcont1 E A (k7_partfun1 (u1_struct_0 A) C D)) =>  (? [F:$i] :  ((m1_nfcont_1 F B D) & (r1_tarski (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_ncfcont2 A B C D) => (r7_ncfcont1 B C D A)) ) ) ) ) ) ) ) ).
tt(t19_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A B E) = (k1_rlvect_1 A C (k10_real_1 1 (k7_real_1 E D)))) ) )  =>  ((r1_xxreal_0 D k6_numbers) | (v3_normsp_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k4_vfunct_1 k1_numbers A D B))) & (r2_ndiff_3 A D C))  =>  ((r2_ndiff_3 A (k4_vfunct_1 k1_numbers A D B) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_funct_1 (k2_ndiff_3 A (k4_vfunct_1 k1_numbers A D B) C) E) = (k1_rlvect_1 A (k1_ndiff_3 A D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_ndiff_4 A B C) => (r1_nfcont_4 A B C)) ) ) ) ) ) ) ).
tt(t19_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_tarski (k1_rltopsp1 A D E) (k1_relset_1 (u1_struct_0 A) C)) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden G (k1_rltopsp1 A D E)) => (r1_nfcont_1 A B C G)) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden G (k2_ndiff_5 A D E)) => (r1_ndiff_1 A B C G)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden G (k2_ndiff_5 A D E)) => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 A B) (k3_ndiff_1 A B C G)) F)) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 (u1_struct_0 B) C D))) (k11_binop_2 F (k1_normsp_0 A (k5_algstr_0 A E D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  ((u1_orders_2 (k3_necklace B)) = (k2_wellord1 (u1_orders_2 (k3_necklace A)) (u1_struct_0 (k3_necklace B)))) ) ) ) ) ).
tt(t19_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden B (u1_orders_2 (k4_necklace A))) <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ( (~ (r1_xxreal_0 A (k2_nat_1 C 1)))  &  ( (B = (k4_tarski C (k2_nat_1 C 1)))  |  (B = (k4_tarski (k2_nat_1 C 1) C)) ) ) ) ) ) ) ) ) ).
tt(t19_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  => (r1_tarski (k6_net_1 A B) (k2_net_1 A))) ) ) ) ) ).
tt(t19_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_newton k6_numbers A) = 1) ) ) ).
tt(t19_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r3_nfcont_1 C B D A) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 C) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E A) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (~  ((r2_hidden H A) &  ( (~ (r1_xxreal_0 G (k1_normsp_0 C (k5_algstr_0 C H E))))  & (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D H) (k7_partfun1 (u1_struct_0 B) D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D))) &  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) C B) A) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) D B) A)) )  =>  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) (k6_vfunct_1 k1_numbers A C D) B) A) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) (k2_vfunct_1 k1_numbers A C D) B) A)) ) ) ) ) ) ) ) ) ).
tt(t19_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 C)))))  =>  ( ((r2_hidden B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers (k1_euclid A) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 C) E F))) &  ((r1_nfcont_4 A E B) &  ( (D = (k7_partfun1 (k1_euclid A) E B))  & (r1_nfcont_1 (k4_real_ns1 A) C F D)) ) )  => (r1_nfcont_3 C (k1_partfun1 k1_numbers (k1_euclid A) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 C) E F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_normform,ax, (! [A:$i] :  ((k4_binop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_normform A)) = (k1_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) (k1_setwiseo A) (k1_setwiseo A))) ) ).
tt(t19_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) & (v3_normsp_1 C A))  => (v3_normsp_1 (k2_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t19_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)))))) )  =>  ( (C = D)  =>  ((r3_nfcont_1 A B C (u1_struct_0 A)) <=> (v5_pre_topc D (k3_normsp_2 A) (k3_normsp_2 B))) ) ) ) ) ) ) ) ) ) ).
tt(t19_numbers,ax,(r1_tarski k5_numbers k1_numbers)).
tt(t19_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r3_lattices A B C))  => (r2_hidden (k2_filter_0 A B) (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k10_openlatt A B) (k10_openlatt A C)))) ) ) ) ) ) ) ).
tt(t19_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~  ((k7_oppcat_1 A B D (k5_cat_1 A B C D E F)) = (k1_cat_1 (k2_oppcat_1 A) (k7_oppcat_1 A C D F) (k7_oppcat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_wellord1 A) =>  ((v1_orders_1 A) &  ((v2_orders_1 A) & (v3_orders_1 A)) ) ) ) ) ).
tt(t19_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r2_hidden B (k1_orders_2 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t19_ordinal1,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) =>  ((v3_ordinal1 B) & (r1_tarski B A)) ) )  => (v3_ordinal1 A)) ) ).
tt(t19_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden A B) => (r2_hidden A (k3_ordinal2 B))) ) ) ) ).
tt(t19_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden A B) =>  ( ( (~  ((r1_ordinal1 C D) &  (~  (D = k1_xboole_0) ) ) )  &  (~ (r2_hidden C D)) )  | (r2_hidden (k11_ordinal2 A C) (k11_ordinal2 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t19_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k11_ordinal2 C B)) ) ) )  =>  ( (B = k1_xboole_0)  | (v2_ordinal2 A)) ) ) ) ) ) ).
tt(t19_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k1_ordinal5 A 3) = (k12_ordinal2 A (k12_ordinal2 A A))) ) ) ).
tt(t19_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  ((k10_xtuple_0 (k2_ordinal6 A)) = A) ) ) ).
tt(t19_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t19_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_ortsp_1 A B D C C) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) D)) <=> (r2_hidden (k4_tarski C D) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C))) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_hidden (k4_tarski E D) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C)) => (r2_hidden (k4_tarski C D) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_orders_3 A) &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (v12_osalg_1 B A)) ) ) ) ).
tt(t19_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r2_hidden D (k5_osalg_2 A B C)) <=>  ((v3_msualg_2 D A B) &  ((r2_pboole (u1_struct_0 A) (k3_osalg_2 A B) D) & (r2_pboole (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r2_msualg_3 A B C D) & (v1_osalg_3 D A))  => (r6_msualg_3 A (k16_osalg_4 A B (k19_osalg_4 A B C D)) C)) ) ) ) ) ) ) ) ) ).
tt(t19_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_parsp_1 A B C D E) => (r1_parsp_1 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) &  ((r1_parsp_2 A B C E) & (r1_parsp_2 A B D F)) )  =>  ( (B = C)  |  ( (B = D)  | (r1_parsp_1 A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 D) = (k1_tarski A))  &  ((r2_hidden A B) & (r2_hidden (k1_funct_1 D A) C)) )  =>  ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ) ).
tt(t19_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((r2_relset_1 C B D (k3_partfun2 C B A E)) <=>  ( (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F (k1_relset_1 C D)) <=>  ((r2_hidden F (k1_relset_1 C E)) & (r2_hidden (k7_partfun1 B E F) A)) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F (k1_relset_1 C D)) =>  ((k7_partfun1 B D F) = (k7_partfun1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  ( ((r2_hidden B (k3_partit1 A E F)) &  ((r2_hidden C E) &  ((r2_hidden D B) & (r2_hidden D C)) ) )  => (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_partit_2,ax, (k8_funct_5 = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ).
tt(t19_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_diraf A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B F E) & (r2_analoaf A D E C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k3_pboole A B D) (k3_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t19_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) B) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ).
tt(t19_pcs_0,ax, (! [A:$i] :  ( ((v14_pcs_0 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( ((v14_pcs_0 B) & (l2_pcs_0 B))  =>  ((r1_tsep_1 A B) => (v13_pcs_0 (k18_pcs_0 A B))) ) ) ) ) ).
tt(t19_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ( ((r2_relset_1 (k1_euclid A) (k1_euclid 1) E (k3_pdiff_1 A C)) & (r4_pdiff_1 A 1 B E D))  =>  ((k12_pdiff_1 A 1 B E D) = (k12_finseq_1 k1_numbers (k11_pdiff_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_2,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r3_pdiff_1 2 1 B A) & (r3_pdiff_1 2 1 C A))  => (r3_pdiff_1 2 1 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t19_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 2) B)) =>  ( ((r3_pdiff_3 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B))))) &  ((k4_pdiff_3 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( (D = (k11_finseq_1 A B C))  =>  ((k11_pdiff_1 3 1 E D) = (k1_fdiff_1 (k1_pdiff_2 3 1 E D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r1_pdiff_5 B A) <=> (r3_pdiff_1 3 1 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ).
tt(t19_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) =>  ((v1_funct_1 (k8_pdiff_1 A B C D)) &  ((v1_funct_2 (k8_pdiff_1 A B C D) (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 (k8_pdiff_1 A B C D) B A) &  ((v2_pdiff_6 (k8_pdiff_1 A B C D) B A) & (m1_subset_1 (k8_pdiff_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  (C = (k1_seq_1 (k1_pdiff_1 E A) D)) ) )  =>  ( ((k8_euclid A (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E D) B) D) = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E (k5_euclid A)) (k10_binop_2 B C)))  &  ((k8_euclid A D (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E D) B)) = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E (k5_euclid A)) (k10_binop_2 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)))) =>  ( ( (G = (k3_relat_1 C (k4_pdiff_1 F B)))  &  ( (H = (k3_relat_1 D (k4_pdiff_1 F B)))  &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B)) ) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) G H)) E)) ) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) C D)) (k11_binop_2 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) &  ( (C = (k1_funct_1 B (k12_finseq_1 k5_numbers 1)))  &  ((k1_normsp_0 (k4_real_ns1 A) C) = (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)) B)) ) ) ) ) ) ) ) ).
tt(t19_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_zfmisc_1 B) =>  ((v2_pencil_1 B A) & (v1_pencil_1 B A)) ) ) ) ) ) ).
tt(t19_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_pencil_1 C A) => (v1_pencil_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t19_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  ((k1_funct_1 B D) = (k1_funct_1 C D)) )  =>  ((k1_pencil_3 A B C) = (k1_nat_1 (k1_pencil_3 A B (k2_funct_7 C D (k1_funct_1 B D))) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t19_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k1_vectsp_9 A B) C) | (v5_pencil_1 (k5_pencil_4 A B C))) ) ) ) ) ) ) ) ).
tt(t19_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (v1_abian A))  &  ( (~ (v1_abian B))  & (v1_abian (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t19_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k7_petri A C)) <=>  (~ (r1_xboole_0 (k8_petri A (k6_domain_1 (u4_struct_0 A) B)) C)) ) ) ) ) ) ) ) ).
tt(t19_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A C D))  => (r2_pnproc_1 A (k3_pnproc_1 A C B) (k3_pnproc_1 A D B))) ) ) ) ) ) ) ) ).
tt(t19_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_polyalg1 C A B) &  (! [D:$i] :  ( ((v1_polyalg1 D A) & (m1_polyalg1 D A B))  =>  (~  ((u1_struct_0 D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k7_polyeq_1 1 k6_numbers A B C) = k6_numbers)  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( (C = (k2_xcmplx_0 D E))  &  ( ((k7_real_1 (k8_real_1 (k8_real_1 3 E) D) A) = k6_numbers)  &  ( (~  (C = (k7_real_1 (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))) (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))))) )  &  ( (~  (C = (k7_real_1 (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))) (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))))) )  &  (~  (C = (k7_real_1 (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))) (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 B 2)) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 B) 4) (k2_newton (k6_real_1 A 3) 3))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( ((k1_polyeq_3 A) = B)  &  ((r1_xxreal_0 k6_numbers (k4_complex1 B)) &  ( (~  (A = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) k7_complex1))) )  &  (~  (A = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) k7_complex1))) ) ) ) ) ) ) ) ) ) ).
tt(t19_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k3_xcmplx_0 A (k2_newton B F)) (k3_xcmplx_0 C (k2_newton D F))) = E)  &  ( ((k3_xcmplx_0 B D) = k6_numbers)  &  ((v1_abian F) &  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 E C) k6_numbers))  &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 E A) k6_numbers))  &  ( (~  ((k3_xcmplx_0 A C) = k6_numbers) )  &  ( (~  ( (B = k6_numbers)  &  (D = (k1_power F (k7_xcmplx_0 E C))) ) )  &  ( (~  ( (B = k6_numbers)  &  (D = (k4_xcmplx_0 (k1_power F (k7_xcmplx_0 E C)))) ) )  &  ( (~  ( (B = (k1_power F (k7_xcmplx_0 E A)))  &  (D = k6_numbers) ) )  &  (~  ( (B = (k4_xcmplx_0 (k1_power F (k7_xcmplx_0 E A))))  &  (D = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k2_polyeq_5 A B C) (k3_polyeq_5 A B C)) (k4_polyeq_5 A B C)) = (k4_xcmplx_0 A)) ) ) ) ) ) ) ).
tt(t19_polyform,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D (k3_finseq_1 (k7_finseq_1 A B))) =>  ((r1_xxreal_0 D (k3_finseq_1 A)) |  ((k1_funct_1 (k7_finseq_1 (k7_finseq_1 A B) C) D) = (k1_funct_1 B (k6_xcmplx_0 D (k3_finseq_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) C (k5_vfunct_1 (k15_pre_poly A) B (k5_vfunct_1 (k15_pre_poly A) B C)))) ) ) ) ) ).
tt(t19_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((k2_polynom1 (k15_pre_poly A) B C) = (k1_tarski D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B C E) = (k6_algstr_0 B (k3_polynom1 A B C D) (k3_polynom2 A D B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_polynom3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  =>  ((k17_finseq_1 A (k2_nat_1 C 1) B) = (k7_finseq_1 (k17_finseq_1 A C B) (k9_finseq_1 (k1_funct_1 B (k2_nat_1 C 1))))) ) ) ) ) ) ) ).
tt(t19_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k8_polynom3 A B C) D) = (k3_rlvect_1 A (k2_polynom4 A B D) (k2_polynom4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t19_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A B (k2_nat_1 C 1)) (k13_polynom3 A (k2_polynom5 A B C) B))) ) ) ) ) ) ).
tt(t19_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom7 A B (k4_struct_0 B)) (k7_polynom1 A B))) ) ) ).
tt(t19_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k3_polynom8 A C (k2_xcmplx_0 B 1)) = (k8_group_1 A (k3_polynom8 A C B) (k3_polynom8 A C 1))) ) ) ) ) ) ) ) ).
tt(t19_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k5_polynom7 A B C D)) (k2_polynom1 (k15_pre_poly A) B C))) ) ) ) ) ) ) ) ).
tt(t19_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A (k1_real_1 1)) =>  ((v1_abian B) |  ((r1_xxreal_0 (k1_power B A) (k1_real_1 1)) & (r1_xxreal_0 A (k1_power B A))) ) ) ) ) ) ) ).
tt(t19_pralg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) => (r2_hidden (k3_funct_2 (k3_msualg_1 B D (k14_pralg_2 A B C)) (k4_msualg_1 B D (k14_pralg_2 A B C)) (k5_msualg_1 B D (k14_pralg_2 A B C)) E) (k4_card_3 (k9_pralg_2 A B (k2_msualg_1 B D) C)))) ) ) ) ) ) ) ) ) ).
tt(t19_pre_circ,ax, (! [A:$i] :  ((k5_card_1 (k1_trees_4 A)) = 1) ) ).
tt(t19_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k3_pre_ff D) = (k2_nat_1 (k3_nat_1 B (k3_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1))) (k3_nat_1 C (k3_pre_ff (k2_nat_1 (k2_nat_1 (k4_nat_1 2 A) 1) 1)))))  =>  ((k3_pre_ff D) = (k2_nat_1 (k3_nat_1 B (k3_pre_ff A)) (k3_nat_1 (k2_xcmplx_0 C B) (k3_pre_ff (k1_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t19_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) C) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k2_prelamb A C B)) & (r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k1_prelamb A B C))) ) ) ) ) ) ) ) ).
tt(t19_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  ((k1_card_1 A) = (k1_card_1 (k10_xtuple_0 A))) ) ) ).
tt(t19_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 B))  =>  ( ((k1_newton (k2_prepower B A) B) = A)  &  ((k2_prepower B (k1_newton A B)) = A) ) ) ) ) ) ) ).
tt(t19_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_pre_topc A B) (k2_pre_topc A C))) ) ) ) ) ) ) ).
tt(t19_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) => (m1_prob_1 (k9_subset_1 A C D) A B)) ) ) ) ) ) ) ).
tt(t19_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_prob_2 A B E C D) => (r1_prob_2 A B E D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_3 A (k3_prob_3 A B)) (k2_prob_3 A B))) ) ) ).
tt(t19_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 C) => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_3 A C) C)) ) ) ) ) ) ).
tt(t19_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) B) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t19_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_collsp A E B F) &  ((r1_collsp A E C G) & (r1_collsp A E D H)) )  =>  ((r1_projdes1 A B C D E) |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (~ (r1_collsp A F G H))  &  (~ (r1_projdes1 A F G H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (~  ( (~ (r4_projpl_1 A B C D))  &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B D) F) &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r1_incsp_1 A C D) =>  ((r1_incsp_1 A B D) |  ((r1_incsp_1 A B E) | (m1_subset_1 (k1_funct_1 (k1_projred1 A D E B) C) (u1_incsp_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  (! [N:$i] :  ((m1_subset_1 N (u2_incsp_1 A)) =>  (! [O:$i] :  ((m1_subset_1 O (u2_incsp_1 A)) =>  (! [P:$i] :  ((m1_subset_1 P (u2_incsp_1 A)) =>  (! [Q:$i] :  ((m1_subset_1 Q (u2_incsp_1 A)) =>  (! [R:$i] :  ((m1_subset_1 R (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E F) K) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F G H) M) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) E H I) L) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C H) N) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) E J) O) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B F I) P) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C I J) Q) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) F J D) R) & (r1_incsp_1 A D N)) ) ) ) ) ) ) )  =>  ((r1_incsp_1 A B K) |  ((r1_incsp_1 A B L) |  ((r1_incsp_1 A C M) |  ((r1_incsp_1 A C L) |  ((r1_incsp_1 A D K) |  ((r1_projred2 A K M L) |  ( (B = C)  |  ( (C = D)  |  ( (~ (r1_incsp_1 A C O))  &  ( (~ (r1_incsp_1 A D O))  &  (~  (K = O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 A)) =>  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 A)) => (r3_binop_1 (k1_funct_1 A D) (k8_prvect_1 A C D) (k9_prvect_1 A B D))) )  => (r3_binop_1 (k4_card_3 A) C (k13_prvect_1 A B))) ) ) ) ) ) ) ).
tt(t19_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k10_finseq_1 D E)) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k10_finseq_1 E G))  &  (D = (k10_finseq_1 F H)) )  =>  ((k3_rlvect_1 (k14_prvect_2 (k10_finseq_1 A B)) C D) = (k10_finseq_1 (k3_rlvect_1 A E F) (k3_rlvect_1 B G H))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k4_struct_0 (k14_prvect_2 (k10_finseq_1 A B))) = (k10_finseq_1 (k4_struct_0 A) (k4_struct_0 B)))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k10_finseq_1 D E))  =>  ((k4_algstr_0 (k14_prvect_2 (k10_finseq_1 A B)) C) = (k10_finseq_1 (k4_algstr_0 A D) (k4_algstr_0 B E))) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( (C = (k10_finseq_1 D E))  =>  ((k1_rlvect_1 (k14_prvect_2 (k10_finseq_1 A B)) C F) = (k10_finseq_1 (k1_rlvect_1 A D F) (k1_rlvect_1 B E F))) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (C = (k10_finseq_1 D E))  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid 2)) =>  (~  ( (F = (k2_finseq_4 k1_numbers (k1_normsp_0 A D) (k1_normsp_0 B E)))  &  ((k1_normsp_0 (k14_prvect_2 (k10_finseq_1 A B)) C) = (k12_euclid F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (a_2_1_pscomp_1 B C))  => (v3_pre_topc A (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t19_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k6_pua2mss1 A)) =>  ((v1_partfun1 (k7_pua2mss1 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k7_pua2mss1 A B)) & (v8_relat_2 (k7_pua2mss1 A B))) ) ) ) ) ) ) ).
tt(t19_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k3_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pboole A)) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t19_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) =>  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = k6_numbers) )  &  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 1) )  &  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 2) )  &  (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A B) 1)) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t19_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ((v5_qc_lang1 (k6_qc_lang2 A B C D) A) &  ( ((k21_qc_lang1 A (k6_qc_lang2 A B C D)) = B)  &  ((k22_qc_lang1 A (k6_qc_lang2 A B C D)) = (k15_qc_lang1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k24_qc_lang1 A (k5_qc_lang2 A B C)) = (k7_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A C) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t19_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k3_qc_lang4 A B C) = (a_3_0_qc_lang4 A B C)) ) ) ) ) ) ) ).
tt(t19_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v17_quantal1 B A) =>  ((v1_group_1 A) &  ( ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = (k1_quantal1 A B B))  &  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = (k2_quantal1 A B B)) ) ) ) ) ) ) ) ).
tt(t19_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k28_quaterni A) = (k27_quaterni (k28_quaterni k2_quatern2) A)) ) ) ).
tt(t19_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k26_quaterni (k27_quaterni k4_quatern2 A) (k27_quaterni A k4_quatern2)) = (k6_quaterni (k1_real_1 (k8_real_1 2 (k18_quaterni A))) (k8_real_1 2 (k17_quaterni A)) k6_numbers k6_numbers)) ) ) ).
tt(t19_quaterni,ax, ((k10_quaterni k1_xcmplx_0 k11_quaterni) = (k8_quaterni (k10_quaterni k11_quaterni k1_xcmplx_0))) ).
tt(t19_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  &  (~  ( (~  ( (~ (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C)))  &  ((r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D) & (r1_xxreal_0 D (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) ) )  &  (~  ( (~  ((r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D) & (r1_xxreal_0 D (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) )  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~  ((k12_quofield A) = (k11_quofield A)) ) ) ) ).
tt(t19_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k12_radix_1 k6_numbers A) = k6_numbers) ) ) ).
tt(t19_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 2 A) &  ((r2_hidden B (k3_radix_1 A)) & (r2_hidden C (k4_radix_3 A))) )  => (r2_hidden (k6_radix_3 (k2_xcmplx_0 B C) A) (k3_radix_3 A))) ) ) ) ) ) ) ).
tt(t19_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r1_xxreal_0 2 C))  =>  ((k8_radix_1 (k2_xcmplx_0 A 1) C (k6_radix_5 (k2_xcmplx_0 A 1) (k2_xcmplx_0 B 1) C)) = (k2_xcmplx_0 (k8_radix_1 (k2_xcmplx_0 A 1) C (k6_radix_5 (k2_xcmplx_0 A 1) B C)) (k8_radix_1 (k2_xcmplx_0 A 1) C (k8_radix_5 (k2_xcmplx_0 A 1) B C)))) ) ) ) ) ) ) ) ).
tt(t19_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r1_xxreal_0 2 C))  =>  ((k8_radix_1 A C (k10_radix_6 A B C)) = 1) ) ) ) ) ) ) ) ) ).
tt(t19_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) => (m1_random_1 (k47_valued_1 A k1_numbers k1_numbers C D) A B)) ) ) ) ) ) ) ) ).
tt(t19_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m1_vectsp_4 B A C) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ).
tt(t19_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k2_rat_1 A) = A)  <=>  ((k1_rat_1 A) = 1) ) ) ) ).
tt(t19_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  & (l5_algstr_0 A))  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (B = (k3_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B))) ) ) ) ) ).
tt(t19_rcomp_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k2_rcomp_1 (k6_xcmplx_0 B C) (k2_xcmplx_0 B C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_xxreal_2 A) &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) ) )  =>  (~  ( (~ (r2_hidden (k5_seq_4 A) A))  &  ( (~ (r2_hidden (k4_seq_4 A) A))  &  (~  (A = (k2_rcomp_1 (k5_seq_4 A) (k4_seq_4 A))) ) ) ) ) ) ) ).
tt(t19_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k2_nat_1 (k4_nat_1 (k3_funct_2 k5_numbers k5_numbers (k2_real_3 B A) k6_numbers) A) (k3_funct_2 k5_numbers k5_numbers (k1_real_3 B A) k6_numbers))) ) ) ) ) ) ).
tt(t19_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) (k1_funcsdom A k1_numbers (k4_real_lat A) B C) B) B)) ) ) ) ) ) ).
tt(t19_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t19_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) C D)) = (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) (k5_binop_1 (u1_struct_0 A) (k1_realset3 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t19_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k21_rfunct_3 B (k3_rearran1 A B D C) B) = (k21_rfunct_3 A C A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k1_relat_1 (k3_xboole_0 A B)) (k3_xboole_0 (k1_relat_1 A) (k1_relat_1 B)))) ) ) ) ).
tt(t19_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((r1_tarski B C) => (r2_relset_1 B A (k5_relset_1 B A D C) D)) ) ) ) ) ) ).
tt(t19_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ((r2_hidden A (k9_xtuple_0 (k3_relset_2 B D))) =>  ((k1_funct_1 (k3_relset_2 B D) A) = (k7_relset_1 B C D A)) ) ) ) ) ) ) ).
tt(t19_revrot_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~  ((k16_euclid A) = (k22_euclid A)) ) ) ) ).
tt(t19_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) =>  ((r2_hidden B (k1_relat_1 A)) <=> (r2_hidden C (k1_relat_1 A))) ) ) ) ) ) ).
tt(t19_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B C) & (r2_rewrite2 A B D E))  => (r2_rewrite2 A C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t19_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 D)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 D)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [H:$i] :  ( ((v2_rewrite3 H D G) & (l1_rewrite3 H G))  =>  ( ((r1_rewrite3 G H A E B) & (r1_rewrite3 G H A F C))  =>  ( (E = F)  |  (! [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 D)) =>  ( (~  ((k1_flang_1 D E I) = F) )  &  (~  ((k1_flang_1 D F I) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rfinseq2,ax, (! [A:$i] :  ( ((v1_integra2 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_integra2 B) & (m2_finseq_1 B k1_numbers))  =>  ((r2_classes1 A B) =>  (A = B) ) ) ) ) ) ).
tt(t19_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v8_valued_0 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ((r1_xxreal_0 C B) | (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t19_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k45_valued_1 A B) = (k24_valued_1 (k45_valued_1 B A) (k1_real_1 1))) ) ) ) ) ).
tt(t19_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( ((v5_xxreal_2 (k7_relset_1 B k1_numbers C A)) &  ((k4_seq_4 (k7_relset_1 B k1_numbers C A)) = (k5_seq_4 (k7_relset_1 B k1_numbers C A))) )  => (v3_funct_1 (k2_partfun1 B k1_numbers C A))) ) ) ) ) ) ).
tt(t19_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k6_finseq_1 (k3_rfunct_3 A k1_numbers))) (k4_rfunct_3 A k1_numbers (k2_subset_1 A) k6_numbers))) ) ).
tt(t19_rfunct_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_rfunct_3 A B) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ( (~ (r1_xxreal_0 C D))  &  (~ (r1_xxreal_0 E C)) ) ) ) ) ) ) ) )  | (r1_fcont_1 A C)) ) ) ) ) ) ) ) ).
tt(t19_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (v4_partfun3 A))  => (r1_xxreal_0 k6_numbers (k1_rinfsup1 A))) ) ) ).
tt(t19_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ((v7_mesfunc5 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (v3_rinfsup2 (k1_valued_0 k7_numbers A B))) ) ) ) ) ) ) ).
tt(t19_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( ((v5_group_1 A) & (v3_ring_1 B A))  => (v33_algstr_0 (k2_ring_1 A B))) ) ) ) ) ).
tt(t19_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ((m3_ringcat1 B (k10_ringcat1 A)) =>  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  (~  ( ((k11_ringcat1 A B) = (k12_ringcat1 A C))  &  (! [D:$i] :  ((m2_ringcat1 D A) =>  (! [E:$i] :  ((m2_ringcat1 E A) =>  (! [F:$i] :  ((m2_ringcat1 F A) =>  (~  ((r1_ringcat1 D E) &  ((r1_ringcat1 E F) &  ((m1_ringcat1 B E F) & (m1_ringcat1 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_rlvect_2 A (k1_rlaffin1 A (k1_rlaffin1 A B D) C) (k1_rlaffin1 A B (k3_rlvect_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t19_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden (k1_funct_1 (k2_rlaffin2 A) B) B) <=>  ((k5_card_1 B) = 1) ) ) ) ) ) ).
tt(t19_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m2_rlaffin3 D (k15_euclid A) C) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ( ((k8_matrix13 k2_vectsp_1 E) = A)  =>  (! [F:$i] :  ((m2_rlaffin3 F (k15_euclid B) (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) C)) =>  ( (F = (k4_finseqop (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) D (k3_matrtop1 A B E)))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden G (k4_rlaffin1 (k15_euclid A) C)) =>  ((k1_rlaffin3 (k15_euclid A) C D G) = (k1_rlaffin3 (k15_euclid B) (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) C) F (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (r1_struct_0 A (k4_struct_0 B))) ) ) ) ).
tt(t19_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( ((k2_rlsub_2 A (k1_rlsub_1 A) (k2_rlsub_1 A)) = (k1_rlsub_1 A))  &  ((k2_rlsub_2 A (k2_rlsub_1 A) (k1_rlsub_1 A)) = (k1_rlsub_1 A)) ) ) ) ).
tt(t19_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_convex1 A C) (k2_convex1 A B))) ) ) ) ) ) ) ).
tt(t19_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k4_algstr_0 A B))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t19_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers B C) = k6_numbers)  <=>  (~ (r2_hidden C (k3_rlvect_2 A B))) ) ) ) ) ) ) ) ).
tt(t19_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (u1_struct_0 A))  =>  ((k1_rlvect_3 A B) = A) ) ) ) ) ) ).
tt(t19_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 B) C D) B) =>  ( (C = D)  |  ( (A = k6_numbers)  | (v1_rlvect_3 (k7_domain_1 (u1_struct_0 B) C (k1_rlvect_1 B D A)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (u1_struct_0 B)) => (m1_rlsub_1 (k1_rlvect_3 A C) B)) ) ) ) ) ) ) ).
tt(t19_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k2_rlvect_x B (k7_domain_1 (u1_struct_0 B) C D))) <=>  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((v1_int_1 F) &  (A = (k3_rlvect_1 B (k1_rlvect_1 B C E) (k1_rlvect_1 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) => (r1_struct_0 B (k4_struct_0 C))) ) ) ) ) ) ).
tt(t19_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) => (m1_rmod_2 (k2_rmod_3 A B C E) A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_rmod_4 E A B C) =>  ((r1_tarski C D) => (m2_rmod_4 E A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A B (k6_lattices A)) = (k6_lattices A)) ) ) ) ) ).
tt(t19_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A C))) = C) ) ) ) ) ) ) ).
tt(t19_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_robbins1 B))  =>  ( ( ((g2_robbins1 (u1_struct_0 A) (u2_lattices A) (u1_robbins1 A)) = (g2_robbins1 (u1_struct_0 B) (u2_lattices B) (u1_robbins1 B)))  & (v9_robbins3 A))  => (v9_robbins3 B)) ) ) ) ) ).
tt(t19_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( ( (A = (k6_subset_1 3 1))  &  (B = 2) )  =>  ( ((k3_lattices k2_robbins4 A B) = 3)  &  ((k4_lattices k2_robbins4 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t19_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k4_roughs_1 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t19_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski B C) => (r1_xxreal_0 (k1_rpr_1 A B) (k1_rpr_1 A C))) ) ) ) ) ) ) ).
tt(t19_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_rsspace4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_rsspace4 A B))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_rsspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) &  ((v1_rsspace4 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A (u1_struct_0 B)) &  ((v1_rsspace4 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (F = C)  &  ( (G = D)  &  (H = E) ) )  =>  ( (E = (k1_algstr_0 (k9_rsspace4 A B) C D))  <=>  (! [I:$i] :  ((m1_subset_1 I A) =>  ((k3_funct_2 A (u1_struct_0 B) H I) = (k3_rlvect_1 B (k3_funct_2 A (u1_struct_0 B) F I) (k3_funct_2 A (u1_struct_0 B) G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (m1_rusub_1 A A)) ) ).
tt(t19_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((k2_rusub_2 A (k1_rusub_1 A) (k2_rusub_1 A)) = (k1_rusub_1 A))  &  ((k2_rusub_2 A (k2_rusub_1 A) (k1_rusub_1 A)) = (k1_rusub_1 A)) ) ) ) ).
tt(t19_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  (? [D:$i] :  ((m1_rlvect_2 D A) &  ( ((k3_rlvect_2 B C) = (k3_rlvect_2 A D))  &  ((k6_rlvect_2 B C) = (k6_rlvect_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_rusub_4 A)) & (v1_xboole_0 (k2_rusub_4 A B))) ) ) ) ) ) ).
tt(t19_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k1_rusub_5 A B (k6_domain_1 (u1_struct_0 A) C)) = (k3_tarski (a_2_0_rusub_5 A B))) ) ) ) ) ) ) ) ).
tt(t19_rvsum_1,ax, ((k6_rvsum_1 (k6_finseq_1 k1_numbers)) = (k6_finseq_1 k1_numbers)) ).
tt(t19_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  (B = (k8_rvsum_2 A (k4_rvsum_2 A B C) C)) ) ) ) ) ) ) ).
tt(t19_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k6_ami_3 (k10_ami_3 k6_numbers) (k10_ami_3 1))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 k6_numbers)) = (k5_int_1 B C))  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) (k10_ami_3 1)) = (k6_int_1 B C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (~  ( (~  (E = (k10_ami_3 k6_numbers)) )  &  ( (~  (E = (k10_ami_3 1)) )  &  (~  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_sf_mastr (k1_scmfsa6a A B)) = (k4_sf_mastr A)) ) ) ) ) ).
tt(t19_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 2)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t19_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_funct_1 (k6_scmfsa_1 A B) k5_numbers) = B) ) ) ) ) ).
tt(t19_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k7_scmfsa_2 A B)) = 2) ) ) ) ) ).
tt(t19_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k6_scmfsa6a A B) = (k5_scmfsa6a (k11_compos_1 k1_scmfsa_2 A) B)) ) ) ) ) ).
tt(t19_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v7_amistd_1 C 3 k1_scmfsa_2) & (v1_scmfsa6b C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 B C) D) (k1_funct_4 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))) ) ) ) ) ) ) ) ) ).
tt(t19_scmfsa7b,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v7_amistd_1 A 3 k1_scmfsa_2) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r6_scmfsa7b A B C)) ) ) ) ) ) ) ).
tt(t19_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k5_card_1 (k1_scmfsa6a A B)) = (k5_card_1 A)) ) ) ) ) ).
tt(t19_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r5_scmfsa7b (k2_scmfsa8b E C D) B A) & (r6_scmfsa7b (k2_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k1_funct_1 C (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r5_scmfsa7b E C A) &  ((r6_scmfsa7b E C A) &  ( (! [F:$i] :  ( ((v1_ami_2 F) &  ( (~ (v1_scmfsa_m F))  & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 C F) = (k1_funct_1 D F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 C F) = (k18_scmfsa_2 D F)) ) ) ) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E C A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) C) = k6_numbers)  &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) (k4_scmfsa_2 k6_numbers)) = 1) )  =>  ( ( (~  ((r6_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E)) (k1_funct_4 A (k1_scmfsa_9 C D))) & (r5_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E)) (k1_funct_4 A (k1_scmfsa_9 C D)))) )  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) (k2_nat_1 E 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) (k1_funct_4 A (k1_scmfsa_9 C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r5_scmfsa7b C D A) &  ((r6_scmfsa7b C D A) &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 E))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) E)) 4))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 E))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) E))) ) ) )  =>  ((r1_xxreal_0 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D)) E) |  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k2_nat_1 1 E) 1))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 E 1))) 4))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k2_nat_1 1 E) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m A)) = (k6_memstr_0 3 k1_scmfsa_2 A)) ) ) ) ).
tt(t19_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v3_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa6a C D) A B) (k9_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b D (k1_scmfsa6b C A B) B) (k5_card_1 C)))) ) ) ) ) ) ) ) ).
tt(t19_scmisort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scm_halt A) & (v1_scmfsa7b A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_funct_1 C B) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 C B) (k1_funct_1 (k1_scmfsa6b A C D) B))) ) ) ) ) )  => (v2_scm_halt (k2_scmfsa_9 B A))) ) ) ) ) ).
tt(t19_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k10_scmpds_2 C A B)) = 7) ) ) ) ) ) ) ).
tt(t19_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 C) A) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 A B)) =>  ((k5_extpro_1 2 k1_scmpds_2 A B E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k1_scmpds_4 C D)) B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmpds_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k1_scmpds_6 A))) &  ((k1_funct_1 (k1_scmpds_6 A) k6_numbers) = (k3_scmpds_2 A)) ) ) ) ).
tt(t19_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_scmpds_6 C A B) &  ((r2_scmpds_6 C A B) & (r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)))) )  =>  ((k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A) E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k1_scmpds_4 C D)) (k8_memstr_0 2 k1_scmpds_2 A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k2_scmpds_8 A B C) k6_numbers) = (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2)))  &  ((k1_funct_1 (k2_scmpds_8 A B C) (k2_nat_1 (k5_card_1 C) 1)) = (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 C) 1)))) ) ) ) ) ) ) ) ).
tt(t19_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) =>  ((k9_xtuple_0 B) = k1_ami_2) ) ) ) ) ).
tt(t19_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  ( (B = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))  => (v2_extpro_1 B 2 (k1_scmring2 A))) ) ) ) ) ).
tt(t19_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = 7)  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  (B = (k9_scmring2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_card_1 (k3_tarski A)) = 1)  => (v2_scmyciel A)) ) ) ).
tt(t19_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ( ((k1_funct_1 B (k1_scmp_gcd 1)) = C)  &  ((k1_funct_1 B (k1_scmp_gcd 2)) = D) )  =>  ((r1_xxreal_0 C k6_numbers) |  ((r1_xxreal_0 D k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 k5_scpinvar B A) (k1_scmp_gcd 1)) = (k3_int_2 C D))  &  ( ((k1_funct_1 (k6_scmpds_4 k5_scpinvar B A) (k1_scmp_gcd 2)) = (k3_int_2 C D))  &  ((r1_scmpds_6 k5_scpinvar B A) & (r2_scmpds_6 k5_scpinvar B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C E F) &  ((r2_analoaf A B D E G) &  ((r2_analoaf A B D E H) &  ((r2_analoaf A C D F G) & (r2_analoaf A C D F H)) ) ) )  =>  ((r2_analoaf A B C B D) |  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers B C) A) (k20_valued_1 k5_numbers k1_numbers k1_numbers B (k26_valued_1 k5_numbers k1_numbers C A)))) ) ) ) ) ) ).
tt(t19_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 C D)) & (r1_xxreal_0 (k1_seq_1 C D) (k1_seq_1 B D))) ) )  &  ((k2_seq_2 A) = (k2_seq_2 B)) ) ) )  => (v2_comseq_2 C)) ) ) ) ) ) ) ).
tt(t19_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k8_nat_1 k1_numbers B D) = (k8_nat_1 k1_numbers A D)) ) ) ) ) ) )  |  ((k2_seq_2 A) = (k2_seq_2 B)) ) ) ) ) ) ) ).
tt(t19_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) <=>  ((r1_seqfunc A k1_numbers B C) &  (? [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ( (C = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) =>  ((v2_comseq_2 (k10_seqfunc A B E)) &  ((k2_seq_2 (k10_seqfunc A B E)) = (k1_seq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers B C) A) = (k20_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers B A) (k1_valued_0 k1_numbers C A))) ) ) ) ) ) ) ).
tt(t19_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C))) )  & (v1_series_1 B))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A D) (k3_funct_2 k5_numbers k1_numbers B D))) ) ) ) ) )  | (v1_series_1 A)) ) ) ) ) ) ).
tt(t19_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 5)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k4_nat_1 (k13_newton B 2) (k13_newton (k2_nat_1 B 1) 2)) (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 2 (k13_newton B 2)) (k4_nat_1 2 B)) 1)) 12)) ) ) ) ) ) ).
tt(t19_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 (k13_complex1 1 2) (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)))) ) ) ) ) ).
tt(t19_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k3_xcmplx_0 C (k1_newton A C))) ) )  =>  ( (A = 1)  |  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 (k3_series_1 B) C) = (k6_xcmplx_0 (k7_xcmplx_0 (k3_xcmplx_0 A (k6_xcmplx_0 1 (k1_newton A C))) (k1_newton (k6_xcmplx_0 1 A) 2)) (k7_xcmplx_0 (k3_xcmplx_0 C (k1_newton A (k2_nat_1 C 1))) (k6_xcmplx_0 1 A)))) ) ) ) ) ) ) ) ) ).
tt(t19_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  => (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 4 A) B) C) D) (k3_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 C D)) (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))))) ) ) ) ) ) ) ) ).
tt(t19_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_setfam_1 C (k2_tarski A B)) =>  (! [D:$i] :  (~  ((r2_hidden D C) &  ( (~ (r1_tarski D A))  &  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ).
tt(t19_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B D) A)) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 B) D (k2_nat_1 A E)))) ) ) ) ) ) ) ) ) ).
tt(t19_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k8_setlim_2 B D C) A) = (k8_setlim_2 B (k10_nat_1 (k9_setfam_1 B) D A) C)) ) ) ) ) ) ) ) ).
tt(t19_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) & (v2_binop_1 C A)) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  ((k7_setwiseo B A C (k4_setwiseo B E F G) D) = (k5_binop_1 A C (k5_binop_1 A C (k3_funct_2 B A D E) (k3_funct_2 B A D F)) (k3_funct_2 B A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 D B) &  ((v2_binop_1 D B) &  ((v1_setwiseo D B) & (v1_finseqop D B)) ) )  =>  ((k3_funct_2 B B (k5_finseqop B D) (k7_setwiseo A B D C E)) = (k7_setwiseo A B D C (k1_partfun1 A B B B E (k5_finseqop B D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((k11_card_3 (k2_memstr_0 3 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) k6_numbers) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2)) = (k5_relat_1 A (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2))) ) ) ) ) ) ) ) ) ) ).
tt(t19_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_sfmastr3 F B C D E A))  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 G (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1)) =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) (k4_scmfsa_2 k6_numbers)) = 1)  &  ( ( (~ (r4_scmfsa7b E B))  =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) B) = (k2_xcmplx_0 G (k1_funct_1 A C)))  & (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) B) (k2_xcmplx_0 (k1_funct_1 A D) 1))) )  &  ((k2_xcmplx_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E)))) G) = (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((r2_hidden A (k2_relset_1 (u1_compos_1 k1_scmfsa_2) B)) => (r1_tarski (k1_sf_mastr A) (k2_sf_mastr B))) ) ) ) ) ).
tt(t19_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (~  ((r2_hidden C (u1_sgraph1 B)) &  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D (u1_struct_0 B)) &  ((r2_hidden E (u1_struct_0 B)) &  ( (~  (D = E) )  &  (C = (k2_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  =>  ((k5_lattices A) = (k2_sheffer1 A)) ) ) ).
tt(t19_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C B) B)) = (k5_sheffer1 A B C)) ) ) ) ) ) ) ).
tt(t19_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (~  ((v1_finset_1 (u1_pre_topc A)) &  ( (~ (v2_simplex0 A))  & (v3_matroid0 A)) ) ) ) ) ).
tt(t19_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) =>  ((k3_simplex1 B (k5_simplex1 A B C)) = (k3_simplex1 B C)) ) ) ) ) ) ) ) ).
tt(t19_simplex2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid B))) (u1_struct_0 (k15_euclid (k7_real_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid B))) (u1_struct_0 (k15_euclid (k7_real_1 A B))))))) )  &  ((v3_tops_2 C (k2_borsuk_1 (k15_euclid A) (k15_euclid B)) (k15_euclid (k7_real_1 A B))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid B))) =>  ((k1_binop_1 C D E) = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t19_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k4_sin_cos2 (k7_binop_2 A)) = (k1_seq_1 k4_sin_cos2 A))  &  ( ((k1_seq_1 k1_sin_cos2 (k7_binop_2 A)) = (k1_real_1 (k1_seq_1 k1_sin_cos2 A)))  &  ((k1_seq_1 k7_sin_cos2 (k7_binop_2 A)) = (k1_real_1 (k1_seq_1 k7_sin_cos2 A))) ) ) ) ) ).
tt(t19_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k15_sin_cos (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k24_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k5_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k24_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B)) k7_complex1))) ) ) ) ) ).
tt(t19_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  (~  ((k2_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) = (k7_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t19_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k17_sin_cos A) = k6_numbers) )  =>  ((k2_sin_cos4 (k8_real_1 3 A)) = (k10_real_1 (k9_real_1 (k2_newton (k2_sin_cos4 A) 3) (k8_real_1 3 (k2_sin_cos4 A))) (k9_real_1 (k8_real_1 3 (k5_square_1 (k2_sin_cos4 A))) 1))) ) ) ) ).
tt(t19_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A) & (r1_xxreal_0 A (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  => (r1_xxreal_0 (k20_sin_cos A) k6_numbers)) ) ) ) ) ).
tt(t19_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k5_square_1 (k10_binop_2 1 (k3_square_1 A))) k6_numbers)) ) ) ) ) ).
tt(t19_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k6_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B))) = (k7_xcmplx_0 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k3_sin_cos2 (k6_xcmplx_0 A B)))) ) ) ) ) ).
tt(t19_sin_cos9,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))) => (r2_hidden (k1_seq_1 k29_sin_cos A) (k1_rcomp_1 (k1_real_1 1) 1))) ) ).
tt(t19_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B)) = (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B))  &  ((r1_xxreal_0 B C) =>  ((k18_complex1 (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) C) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B))) = (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) C) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k17_complex1 A))) B))) ) ) ) ) ) ) ) ) ).
tt(t19_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ( (~ (v2_sppol_1 (k2_topreal1 2 B A)))  &  (~ (v1_sppol_1 (k2_topreal1 2 B A))) ) ) ) ) ) ) ) ).
tt(t19_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (v1_xboole_0 A))  =>  ((k3_topreal1 2 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B))) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B))) ) ) ) ) ) ).
tt(t19_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k11_pscomp_1 A) = (k10_pscomp_1 A))  => (v1_sppol_1 A)) ) ) ).
tt(t19_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)) &  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  (~  ( ((k17_euclid A) = (k17_euclid B))  &  ((k17_euclid C) = (k17_euclid B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 B A) |  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 B (k3_finseq_1 C)) =>  ((k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 C A) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t19_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t19_square_1,ax, (~ (r1_xxreal_0 (k7_square_1 2) 1)) ).
tt(t19_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((r1_stacks_1 A B) =>  ((k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B) = (u1_stacks_1 A)) ) ) ) ) ) ).
tt(t19_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v2_funct_2 C A) & (v1_stirl2_1 C B A))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 A D))  => (r1_xxreal_0 (k5_nat_1 (k1_stirl2_1 B A C (k1_seq_4 D))) (k20_binop_2 (k21_binop_2 B A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t19_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) =>  ( (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A D) C E) <=> (r1_sublemma A D B (k1_sublemma A B E (k3_sublemma A D B E)) C)) ) )  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A (k5_sublemma A D)) C E) <=> (r1_sublemma A (k5_sublemma A D) B (k1_sublemma A B E (k3_sublemma A (k5_sublemma A D) B E)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r1_tarski (k3_subset_1 A B) B) <=>  (B = (k2_subset_1 A)) ) ) ) ) ).
tt(t19_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B (k4_substlat A B (k3_substlat A B C) D)) = (k3_substlat A B (k4_substlat A B C D))) ) ) ) ) ) ) ).
tt(t19_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k29_substut1 A (k21_substut1 A B C)) = C) ) ) ) ) ) ) ) ).
tt(t19_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k2_substut2 A (k7_cqc_lang A B C) D) = (k6_sublemma A (k2_substut2 A B D) (k2_substut2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t19_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k9_supinf_2 A (k6_supinf_2 B) (k14_supinf_2 A B C)) = (k6_supinf_2 (k9_supinf_2 A B C))) ) ) ) ) ) ) ).
tt(t19_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_orders_2 B E D) =>  ((r1_orders_2 B C D) |  ( ((k1_symsp_1 A B D (k3_rlvect_1 B C E) F) = (k1_symsp_1 A B D C F))  &  ((k1_symsp_1 A B D C (k3_rlvect_1 B F E)) = (k1_symsp_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k4_relat_1 A) B) => (r1_tarski (k4_relat_1 A) (k2_relat_1 B))) ) ) ) ).
tt(t19_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 C D) => (r1_relset_1 A A (k1_taxonom1 A B C) (k1_taxonom1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t19_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_tarski B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( (! [D:$i] :  (~  ((r2_hidden D C) &  ( (~ (r1_tarski D B))  &  ( (~ (r1_tarski B D))  &  (~ (r1_xboole_0 B D)) ) ) ) ) )  =>  ( (! [D:$i] :  (~  ((r2_hidden D C) & (r1_tarski D B)) ) )  |  (! [D:$i] :  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden E C) & (r1_xboole_0 E B)) ) )  =>  ((m1_eqrel_1 (k2_xboole_0 D (k1_tarski B)) A) &  ((r1_setfam_1 C (k2_xboole_0 D (k1_tarski B))) &  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r1_setfam_1 C E) =>  (! [F:$i] :  ( ((r2_hidden F E) & (r1_tarski B F))  => (r1_setfam_1 (k2_xboole_0 D (k1_tarski B)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 B A) =>  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k24_sin_cos) A) = (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 B A)) (k1_fdiff_1 B A))) ) ) ) ) ) ) ).
tt(t19_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos A) (k4_nat_1 2 B)) = (k26_valued_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k16_sin_cos A) (k2_newton (k1_real_1 1) B)))  &  ( ((k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k26_valued_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k19_sin_cos A) (k2_newton (k1_real_1 1) B)))  &  ( ((k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos A) (k4_nat_1 2 B)) = (k26_valued_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k19_sin_cos A) (k2_newton (k1_real_1 1) B)))  &  ((k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k26_valued_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k16_sin_cos A) (k2_newton (k1_real_1 1) (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ).
tt(t19_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v1_tbsp_1 A) => (v5_tbsp_1 A)) ) ) ).
tt(t19_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v5_tops_1 (k2_struct_0 A) A)) ) ).
tt(t19_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = k1_xboole_0)  <=>  ((k1_tdlat_2 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t19_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v2_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc B A) &  ( (~  (B = k1_xboole_0) )  &  (~  (B = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t19_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( (~  (E = (k3_termord A B C D)) )  =>  ((k3_polynom1 A C (k5_termord A B C D) E) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ((k2_tex_1 A) = (k1_compts_1 A))  <=>  (? [B:$i] :  ((m1_subset_1 B A) &  (A = (k6_domain_1 A B)) ) ) ) ) ) ).
tt(t19_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v2_tex_2 C A)) )  => (v2_tex_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t19_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tex_3 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((m1_pre_topc B C) => (v2_tex_3 C A)) ) ) ) ) ) ) ).
tt(t19_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_tex_4 B A) & (r2_hidden C B))  => (r1_tarski B (k2_tex_4 A C))) ) ) ) ) ) ) ).
tt(t19_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tmap_1 A k3_topmetr B C) <=>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ((r2_hidden C E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F E) & (r1_xxreal_0 D (k18_complex1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B F) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((m1_pre_topc B C) =>  ( ( (~ (r1_tsep_1 C D))  &  (~ (r1_tsep_1 D C)) )  |  ((r1_tsep_1 B D) & (r1_tsep_1 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_toler_1 C A B) =>  (? [D:$i] :  ( ((v1_toler_1 D A B) & (m1_toler_1 D A B))  & (r1_tarski C D)) ) ) ) ) ) ) ).
tt(t19_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A C D))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ((r3_borsuk_2 A B C E F) => (r3_borsuk_2 A B C E (k1_borsuk_2 A B D C (k1_borsuk_2 A B C D F G) (k2_borsuk_2 A C D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_topalg_2 A) & (m1_pre_topc A k2_topalg_2)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) => (m1_borsuk_6 (k3_topalg_2 A D E) A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t19_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_pre_topc E) & (l1_pre_topc E)) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 E C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 E C)) (u1_struct_0 A))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k2_borsuk_1 E D)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 E D)) (u1_struct_0 A))))) )  =>  (! [H:$i] :  ( ((v4_pre_topc H B) & (m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [I:$i] :  ( ((v4_pre_topc I B) & (m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((m1_pre_topc C B) &  ((m1_pre_topc D B) &  ( (H = (k2_struct_0 C))  &  ( (I = (k2_struct_0 D))  &  ( ((k2_xboole_0 (k2_struct_0 C) (k2_struct_0 D)) = (k2_struct_0 B))  &  ((v5_pre_topc F (k2_borsuk_1 E C) A) &  ((v5_pre_topc G (k2_borsuk_1 E D) A) &  ( (! [J:$i] :  ((r2_hidden J (k9_subset_1 (u1_struct_0 (k2_borsuk_1 E D)) (k2_struct_0 (k2_borsuk_1 E C)) (k2_struct_0 (k2_borsuk_1 E D)))) =>  ((k1_funct_1 F J) = (k1_funct_1 G J)) ) )  &  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k2_borsuk_1 E B)) (u1_struct_0 A)) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 E B)) (u1_struct_0 A))))) )  =>  (~  ( (J = (k1_funct_4 F G))  & (v5_pre_topc J (k2_borsuk_1 E B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A C D) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) I (k3_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) J (k3_topalg_4 A B k5_topmetr H)) & (r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) )  => (r3_borsuk_2 A C D I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_6 F A B C D E) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ((v5_pre_topc F (k2_borsuk_1 k5_topmetr k5_topmetr) A) => (v5_pre_topc (k4_topalg_5 k5_topmetr k5_topmetr A F G) k5_topmetr A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_funct_1 k1_xboole_0) &  ((v4_topalg_6 k1_xboole_0 A) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 A))))) ) ) ) ).
tt(t19_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_topdim_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) =>  ((v1_topdim_1 B A) & (r1_xxreal_0 (k2_topdim_1 A B) (k2_topdim_1 A C))) ) ) ) ) ) ) ) ).
tt(t19_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v4_card_3 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v12_pre_topc (k1_pre_topc A B)) =>  ((v1_topdim_1 B A) & (r1_xxreal_0 (k2_topdim_1 A B) k6_numbers)) ) ) ) ) ) ).
tt(t19_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_topgen_1 A B)) <=>  (? [D:$i] :  ( ((v1_yellow_8 D A C) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k9_subset_1 (u1_struct_0 A) B E)) &  (~  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ((v3_pre_topc C (k5_topgen_2 A B)) <=>  (~  ((r2_hidden B C) &  (~ (v1_finset_1 (k3_subset_1 (u1_struct_0 (k5_topgen_2 A B)) C))) ) ) ) ) ) ) ) ).
tt(t19_topgen_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (v4_card_3 (a_1_0_topgen_3 A))) ) ).
tt(t19_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))  =>  ((v3_pre_topc B A) <=> (v1_tops_2 C A)) ) ) ) ) ) ) ) ).
tt(t19_topgen_5,ax,(r1_tarski k1_topgen_5 k2_topgen_5)).
tt(t19_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k2_topgrp_1 A B)) (k2_topgrp_1 A (k2_group_1 A B)))) ) ) ) ).
tt(t19_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (C = (k1_rcomp_1 A B))  =>  ((k4_topmetr A B) = (k1_pre_topc k3_topmetr C)) ) ) ) ) ) ) ) ) ).
tt(t19_topreal1,ax,(r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 k6_numbers)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1)))).
tt(t19_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k2_topreal1 A B C) (k3_topreal1 A B))) ) ) ) ) ) ).
tt(t19_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) &  ((v4_topreal1 B) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) A) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  &  (C = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) ) )  =>  ( ( (~  ( ((k17_euclid A) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  &  (~  ((k18_euclid A) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) )  &  (~  ( (~  ((k17_euclid A) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) )  &  ((k18_euclid A) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) )  |  ((v4_topreal1 C) &  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) & (r1_tarski (k3_topreal1 2 C) (k2_xboole_0 (k3_topreal1 2 B) (k9_metric_1 (k14_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_topreal5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((v1_topreal2 A) &  ((k18_pscomp_1 A) = (k22_pscomp_1 A)) ) ) ) ) ).
tt(t19_topreal6,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ((r1_t_0topsp A B) & (v1_connsp_1 A))  => (v1_connsp_1 B)) ) ) ) ) ).
tt(t19_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_metric_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_topreal7 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_topreal7 A B))) =>  ((k2_metric_1 (k1_topreal7 A B) C D) = (k2_square_1 (k2_metric_1 A (k3_topreal7 A B C) (k3_topreal7 A B D)) (k2_metric_1 B (k4_topreal7 A B C) (k4_topreal7 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t19_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  ((k2_topreal1 2 A 1) = (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) 2 A))) ) ) ).
tt(t19_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xboole_0 (k1_topreal9 A C B) (k3_topreal9 A C B))) ) ) ) ) ) ).
tt(t19_topreala,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( ( (C = B)  & (m1_rcomp_1 B A))  => (m1_connsp_2 C k3_topmetr A)) ) ) ) ) ) ) ).
tt(t19_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A C B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A C B)))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_toprealb A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( (E = F)  =>  ((k3_funct_2 (u1_struct_0 (k8_toprealb A)) (u1_struct_0 (k7_toprealb A C B)) D E) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) F B) C)) ) ) ) ) )  => (v3_tops_2 D (k8_toprealb A) (k7_toprealb A C B))) ) ) ) ) ) ) ) ) ).
tt(t19_toprealc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (m2_finseq_1 A k1_numbers)) ) ).
tt(t19_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k4_toprns_1 A B (k4_toprns_1 A C D)) = (k1_toprns_1 A (k4_toprns_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t19_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k1_tops_1 A B) (k1_tops_1 A C))) ) ) ) ) ) ) ).
tt(t19_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) => (v3_pre_topc (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t19_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (v4_pre_topc C A))  =>  (C = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t19_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C (k15_euclid A) B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ( ((v3_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 B) C D) E) &  (! [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  =>  (~ (r1_tarski (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 B) C (k1_topreal9 A D F)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ((r3_relat_2 C (k2_zfmisc_1 A A)) &  ((r8_relat_2 C (k2_zfmisc_1 A A)) & (r1_transgeo A B C)) )  => (r2_transgeo A B C)) ) ) ) ) ) ) ).
tt(t19_treal_1,ax,(v1_connsp_1 k17_borsuk_1)).
tt(t19_trees_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((r2_hidden A B) => (m2_finseq_1 A k5_numbers)) ) ) ) ).
tt(t19_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (m1_trees_2 k1_xboole_0 A)) ) ).
tt(t19_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_trees_3 A) & (r1_tarski B A))  => (v2_trees_3 B)) ) ) ).
tt(t19_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v6_trees_3 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((r2_hidden (k7_finseq_1 (k12_finseq_1 k5_numbers C) D) (k9_xtuple_0 (k4_trees_4 A B))) =>  ((k1_funct_1 (k4_trees_4 A B) (k7_finseq_1 (k12_finseq_1 k5_numbers C) D)) = (k5_funct_6 B (k2_nat_1 C 1) D)) ) ) ) ) ) ) ) ) ).
tt(t19_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_trees_3 B))  =>  ((r2_hidden A (k9_trees_9 B)) <=>  (? [C:$i] :  ((m1_subset_1 C B) &  (? [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) &  (A = (k5_trees_2 C D)) ) ) ) ) ) ) ) ) ).
tt(t19_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tsep_1 B A) & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) =>  ((v1_tsep_1 B C) & (m1_pre_topc B C)) ) ) ) ) ) ) ) ).
tt(t19_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_2 A B D) &  ((r2_tsep_2 A C E) &  ( ((k4_subset_1 (u1_struct_0 A) D E) = (u1_struct_0 A))  & (r2_tsep_1 A D E)) ) )  => (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v6_pre_topc A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_tsp_1 B A))  &  (! [C:$i] :  ( ((v1_pre_topc C) &  ( (~ (v6_pre_topc C))  & (m1_pre_topc C A)) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t19_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k4_tex_4 A D))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t19_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_turing_1 (k3_finseq_4 k5_numbers C D E) A B) =>  ( ((k1_funct_1 B C) = k6_numbers)  &  ( ((k1_funct_1 B (k2_nat_1 (k2_nat_1 C D) 2)) = k6_numbers)  &  ( ((k1_funct_1 B (k2_nat_1 (k2_nat_1 (k2_nat_1 C D) E) 4)) = k6_numbers)  &  ( (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (~ (r1_xxreal_0 F C))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 C D) 2) F))  &  (~  ((k1_funct_1 B F) = 1) ) ) ) ) ) )  &  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (~ (r1_xxreal_0 F (k2_nat_1 (k2_nat_1 C D) 2)))  &  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k2_nat_1 C D) E) 4) F))  &  (~  ((k1_funct_1 B F) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_twoscomp,ax, ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 k6_numbers 1 1)) = 1)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k18_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k18_twoscomp (k11_finseq_1 1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t19_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (u1_struct_0 B))  =>  ((k7_unialg_2 A C) = B) ) ) ) ) ) ) ) ).
tt(t19_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  ((k5_lattices (k12_unialg_2 A)) = (k7_unialg_2 A (k6_unialg_2 A))) ) ) ).
tt(t19_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (u1_struct_0 (k1_uniroots A))) => (r2_hidden B (u1_struct_0 A))) ) ) ) ).
tt(t19_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_algseq_1 A B) = 1)  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_algseq_1 A (k1_normsp_1 A B k6_numbers))) &  (~  ((k1_normsp_1 A B k6_numbers) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t19_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v7_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v4_pre_topc (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t19_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ( (B = C)  & (r1_xxreal_0 k6_numbers C))  =>  ((k7_supinf_2 (k1_integra2 A B)) = (k1_extreal1 C (k7_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t19_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc D A k3_topmetr) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 D E)) &  ((r1_xxreal_0 (k1_seq_1 D E) 1) &  ( ((r2_hidden E B) =>  ((k1_seq_1 D E) = k6_numbers) )  &  ((r2_hidden E C) =>  ((k1_seq_1 D E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k11_cqc_lang A C E) F D) <=>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k3_valuat_1 A B C (k8_valuat_1 A B F E)) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  => (m2_valued_0 B A B)) ) ) ) ).
tt(t19_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k9_subset_1 k5_numbers (k4_finseq_1 A) (k4_finseq_1 B)))  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(t19_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k50_valued_1 (k18_valued_1 A B) C) = (k18_valued_1 A (k50_valued_1 B C))) ) ) ) ) ) ) ).
tt(t19_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (D = F) )  =>  ((r1_struct_0 D C) |  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 D)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ( ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) G F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) I (k4_vectsp_1 A B K C)))  &  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) H F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) J (k4_vectsp_1 A B L C))) )  =>  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k3_rlvect_1 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) G H) F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) (k3_rlvect_1 D I J) (k4_vectsp_1 A B (k3_rlvect_1 A K L) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_vectsp11,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_vectsp11 A B 1) B)) ) ) ) ).
tt(t19_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k1_algstr_0 A B (k4_algstr_0 A C)) = (k4_struct_0 A))  =>  (B = C) )  &  ( ( (B = C)  =>  ((k1_algstr_0 A B (k4_algstr_0 A C)) = (k4_struct_0 A)) )  &  ( ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  (B = C) )  &  ( (B = C)  =>  ((k5_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k4_algstr_0 A (k1_vectsp_2 A C B)) = (k1_vectsp_2 A (k4_algstr_0 A C) B))  &  ((k1_vectsp_2 A C (k4_algstr_0 A B)) = (k4_algstr_0 A (k1_vectsp_2 A C B))) ) ) ) ) ) ) ) ) ).
tt(t19_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (r1_struct_0 B (k4_struct_0 C))) ) ) ) ) ) ).
tt(t19_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((m1_vectsp_4 C A D) & (m1_vectsp_4 C A E))  => (m1_vectsp_4 C A (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ( ((k1_vectsp_6 A B C) = k1_xboole_0)  =>  ((k4_vectsp_6 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t19_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_vectsp_7 C A B) &  (! [D:$i] :  ((m1_vectsp_7 D A B) =>  (~ (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ( ((g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)) = (k1_vectsp_7 A B C))  & (v1_vectsp_7 D A B))  =>  ((r1_xxreal_0 (k5_card_1 D) (k5_card_1 C)) &  (? [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r1_tarski E C) &  ( ((k5_card_1 E) = (k6_xcmplx_0 (k5_card_1 C) (k5_card_1 D)))  &  ((g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)) = (k1_vectsp_7 A B (k4_subset_1 (u1_struct_0 B) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k2_vfunct_1 A B D E)) (k6_vfunct_1 A B (k2_vfunct_1 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t19_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k2_vfunct_1 A B D E)) (k3_vfunct_2 A B (k2_vfunct_1 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_waybel_0 A B) = (k5_waybel_0 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t19_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k6_waybel10 A (k1_yellow_2 A A B)) B)) ) ) ) ).
tt(t19_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  ((k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) = (a_2_1_waybel11 A B)) ) ) ) ) ).
tt(t19_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_yellow_4 A D C) &  ((v13_waybel_0 B A) & (r1_tarski D B)) )  => (r1_tarski C B)) ) ) ) ) ) ) ) ) ).
tt(t19_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 E A B) =>  ((r2_lattice3 A C D) <=> (r2_lattice3 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((v5_waybel_6 B (k2_yellow_1 (u1_pre_topc A))) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (~  ((r1_tarski (k3_xboole_0 C D) B) &  ( (~ (r1_tarski C B))  &  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k4_waybel_6 (k7_lattice3 A))) <=> (v6_waybel_6 B A)) ) ) ) ) ).
tt(t19_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v1_waybel16 B A) &  ((k2_yellow_0 A (k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B))) = B) ) ) ) ) ) ) ).
tt(t19_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_waybel11 A D)) (k1_waybel11 B (k6_waybel_9 A B C D)))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_yellow_0 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  (~  ((v2_waybel18 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~ (r1_waybel18 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18)))) ) ) ) ) ) ) ).
tt(t19_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((r2_hidden D (u1_pre_topc A)) | (r2_hidden D (u1_pre_topc B)))  => (v3_pre_topc D C)) ) ) ) ) ) ) ) ) ).
tt(t19_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v5_orders_3 C A B) &  ((v5_orders_3 D B A) &  ((r1_yellow_2 (u1_struct_0 A) A (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A)) & (r1_yellow_2 (u1_struct_0 B) B (k3_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C))) ) )  => (v3_waybel_1 (k1_waybel_1 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t19_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v17_waybel_0 B A A) => (v17_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t19_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v8_yellow_0 B A) => (v3_lattice3 B)) ) ) ) ) ).
tt(t19_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r2_yellow_0 A C) => (r2_hidden (k2_yellow_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t19_waybel24,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_yellow_1 A B))) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(t19_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) => (r5_waybel_1 (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ).
tt(t19_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  ((r1_borsuk_1 B C) => (r3_yellow16 (k1_waybel26 A C) (k1_waybel26 A B))) ) ) ) ) ) ) ).
tt(t19_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D (k6_yellow_1 B (k6_yellow_1 A C))) & (m1_yellow_0 D (k6_yellow_1 B (k6_yellow_1 A C)))) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C))) & (m1_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ((v3_waybel27 F) => (v5_orders_3 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v6_yellow_6 (k3_waybel28 A) A)) ) ).
tt(t19_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_funct_1 (k2_tops_2 (u1_struct_0 (k1_waybel26 A k9_waybel18)) (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))) (k4_waybel29 A)) B) = (k5_funct_3 B (u1_struct_0 A))) ) ) ) ) ).
tt(t19_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (~ (v2_struct_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)))  &  ((v7_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)) & (l1_waybel_0 (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C) A)) ) ) ) ) ) ) ) ).
tt(t19_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C A)) )  =>  (! [D:$i] :  ( ((v2_pre_topc D) &  ((v2_waybel19 D) & (m1_yellow_9 D B)) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 B))) =>  ((u1_pre_topc (k2_borsuk_1 C D)) = (k2_waybel19 (k3_yellow_3 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~ (v8_struct_0 A))  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (r1_ordinal1 (k1_card_1 (a_2_0_waybel31 A B)) (k1_card_1 B))) ) ) ) ) ).
tt(t19_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v3_pre_topc (k3_subset_1 (u1_struct_0 B) (k5_waybel_0 B C)) B)) ) ) ) ) ) ).
tt(t19_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (r1_tarski (k5_waybel11 A) (k4_waybel28 A))) ) ).
tt(t19_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ( ((k13_functor0 (k5_waybel34 A) (k4_waybel34 A) (k5_waybel34 A) (k7_waybel34 A) (k6_waybel34 A)) = (k12_functor0 (k5_waybel34 A)))  &  ((k13_functor0 (k4_waybel34 A) (k5_waybel34 A) (k4_waybel34 A) (k6_waybel34 A) (k7_waybel34 A)) = (k12_functor0 (k4_waybel34 A))) ) ) ) ).
tt(t19_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel35 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v3_waybel35 C A B) & (m1_waybel35 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ((r2_orders_2 A D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_orders_2 A D F) &  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) F E) B) &  (F = (k1_yellow_0 A (k4_waybel35 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r3_orders_2 A C (k1_yellow_0 A D)) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski E D) & (r3_orders_2 A B (k1_yellow_0 A E))) ) ) ) ) ) ) )  => (r1_waybel_3 A B C)) ) ) ) ) ) ) ).
tt(t19_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (r2_hidden (k3_yellow_2 A) (u1_struct_0 (k8_waybel_4 A)))) ) ).
tt(t19_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) C D E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A D)) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_waybel_6 B A) & (r1_tarski B C))  => (v4_waybel_6 C A)) ) ) ) ) ) ) ).
tt(t19_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_waybel_7 B A) <=> (r2_hidden B (k4_waybel_6 (k2_yellow_1 (k7_waybel_0 A))))) ) ) ) ) ).
tt(t19_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=>  ((v3_orders_2 (k1_waybel_8 A)) &  ((v4_orders_2 (k1_waybel_8 A)) &  ((v5_orders_2 (k1_waybel_8 A)) &  ((v1_lattice3 (k1_waybel_8 A)) &  ((v2_lattice3 (k1_waybel_8 A)) & (l1_orders_2 (k1_waybel_8 A))) ) ) ) ) ) ) ) ).
tt(t19_waybel_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v1_tops_2 C A)) )  => (v1_tops_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t19_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  => (r1_struct_0 (k4_weddwitt A) (k1_group_1 A))) ) ).
tt(t19_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((r1_xxreal_0 (k4_metric_1 A C D) (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B))) & (r1_xxreal_0 (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B)) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k2_wellord1 (k2_wellord1 C A) B) = (k2_wellord1 C (k3_xboole_0 A B))) ) ) ) ) ).
tt(t19_wellord2,ax, (! [A:$i] : (r1_relat_2 (k1_wellord2 A) A)) ).
tt(t19_wsierp_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k2_finseq_3 1 (k9_finseq_1 A)) = k1_xboole_0)  &  ( ((k2_finseq_3 1 (k10_finseq_1 A B)) = (k9_finseq_1 B))  &  ( ((k2_finseq_3 2 (k10_finseq_1 A B)) = (k9_finseq_1 A))  &  ( ((k2_finseq_3 1 (k11_finseq_1 A B C)) = (k10_finseq_1 B C))  &  ( ((k2_finseq_3 2 (k11_finseq_1 A B C)) = (k10_finseq_1 A C))  &  ((k2_finseq_3 3 (k11_finseq_1 A B C)) = (k10_finseq_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t19_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r1_tarski A C))  => (r1_tarski A (k3_xboole_0 B C))) ) ) ) ).
tt(t19_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k7_xboolean (k7_xboolean A B) C) = (k7_xboolean A (k7_xboolean B C))) ) ) ) ) ) ) ).
tt(t19_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k6_xcmplx_0 A B) = (k6_xcmplx_0 C B))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t19_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) C) <=> (r1_xxreal_0 A (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t19_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k6_xtuple_0 A B C D) E) => (r2_hidden A (k13_xtuple_0 E))) ) ) ) ) ) ).
tt(t19_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k3_xxreal_0 B D) (k3_xxreal_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_1 A A) = k1_xboole_0) ) ) ).
tt(t19_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m2_xxreal_2 A (k2_xxreal_1 A B))) ) ) ) ).
tt(t19_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( ((k3_xxreal_3 A B) = k2_xxreal_0)  &  ( (~  (A = k2_xxreal_0) )  &  (~  (B = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(t19_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ( (D = (k11_lattice3 A B C))  & (r2_yellow_0 A (k2_tarski B C)))  =>  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) )  &  ( ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) )  =>  ( (D = (k11_lattice3 A B C))  & (r2_yellow_0 A (k2_tarski B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_waybel_3 (k3_yellow_3 A B) (k7_yellow_3 A B C E) (k7_yellow_3 A B D F)) <=>  ((r1_waybel_3 A C D) & (r1_waybel_3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (C = D)  & (v3_waybel11 C A)) )  => (v3_waybel11 D B)) ) ) ) ) ) ) ) ) ).
tt(t19_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_yellow13 C A B) =>  (~ (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t19_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (r1_t_0topsp A (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ).
tt(t19_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k2_yellow15 A B)) & (r2_hidden D (k2_yellow15 A B)))  =>  ( (C = D)  | (r1_xboole_0 C D)) ) ) ) ) ) ) ).
tt(t19_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((r2_yellow16 B A C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v22_waybel_0 D A A) &  ((v6_waybel_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  (~  ((r1_yellow16 (k1_yellow_2 A A D) A D) & (r5_waybel_1 B (k1_yellow_2 A A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel18 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_waybel18 A B))) =>  ( ((r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski D)) (k3_tarski E)) &  (! [F:$i] :  (~  ((r2_hidden F (k2_waybel18 A B)) &  ((r2_hidden F E) & (r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski D)) F)) ) ) ) )  => (r1_tarski (k2_struct_0 (k3_waybel18 A B)) (k3_tarski E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  ( ((r2_yellow18 A B) &  ((r2_yellow18 C D) & (r2_functor0 A C)) )  => (r2_functor0 B D)) ) ) ) ) ) ) ) ) ).
tt(t19_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r1_waybel_0 A C B) =>  (! [D:$i] :  ((m2_yellow_6 D A C) => (r1_waybel_0 A D B)) ) ) ) ) ) ) ) ).
tt(t19_yellow_1,ax, (! [A:$i] :  ((k4_yellow_0 (k3_yellow_1 A)) = A) ) ).
tt(t19_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) =>  ((k2_yellow20 A B) = (k2_yellow20 B A)) ) ) ) ) ) ).
tt(t19_yellow21,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_yellow21 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_yellow21 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k8_yellow21 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k8_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k8_yellow21 A) C))) &  ((v22_waybel_0 D (k4_yellow21 (k8_yellow21 A) B) (k4_yellow21 (k8_yellow21 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k8_yellow21 A) B)) (u1_struct_0 (k4_yellow21 (k8_yellow21 A) C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v11_quantal1 B) =>  ((k2_relset_1 (u1_struct_0 A) B) = (a_2_0_yellow_2 A B)) ) ) ) ) ) ).
tt(t19_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v2_lattice3 (k3_yellow_3 A B)) =>  ((v2_lattice3 A) & (v2_lattice3 B)) ) ) ) ) ) ).
tt(t19_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) = (k6_domain_1 (u1_struct_0 A) (k10_lattice3 A B C))) ) ) ) ) ) ) ).
tt(t19_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_orders_2 A B (k3_yellow_0 A)) =>  (B = (k3_yellow_0 A)) ) ) ) ) ) ).
tt(t19_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((r1_waybel_0 A B C) => (r2_waybel_0 A B C)) ) ) ) ) ) ).
tt(t19_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))) =>  ( (B = C)  =>  ( ((k3_waybel_0 A B) = (k4_waybel_0 (k7_lattice3 A) C))  &  ((k4_waybel_0 A B) = (k3_waybel_0 (k7_lattice3 A) C)) ) ) ) ) ) ) ) ) ).
tt(t19_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_yellow_8 A (k6_domain_1 (u1_struct_0 A) B) B)) ) ) ) ).
tt(t19_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( ((r1_tarski C D) => (r1_tarski (k1_cantor_1 A C) (k1_cantor_1 B D)))  &  ( (C = D)  =>  ((k1_cantor_1 A C) = (k1_cantor_1 B D)) ) ) ) ) ) ) ) ) ).
tt(t19_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v8_zf_fund1 B A) & (r2_hidden C B))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r2_hidden (k5_zf_fund1 D C) B) => (r2_hidden (k5_zf_fund1 (k6_zf_lang D) C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t19_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  (! [H:$i] :  ((m2_subset_1 H k5_numbers k1_zf_lang) =>  ( ((k17_zf_lang C D E A) = (k17_zf_lang F G H B))  =>  ( (C = F)  &  ( (D = G)  &  ( (E = H)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_zf_lang A) =>  ((k1_funct_1 A 1) = 1) ) ) ) ).
tt(t19_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r1_tarski (k1_tarski A) (k2_tarski B C)) &  ( (~  (A = B) )  &  (~  (A = C) ) ) ) ) ) ) ) ).
tt(t19_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( (~ (r2_hidden (k2_zf_lang k6_numbers) (k2_zf_model B)))  =>  ((r1_zf_model A C (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (? [E:$i] :  ((m1_subset_1 E A) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r1_zf_model A (k2_zf_lang1 A (k2_zf_lang1 A C (k2_zf_lang 3) D) (k2_zf_lang 4) F) B) <=>  (F = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t19_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r1_zf_model A B (k12_zf_lang C D)) <=>  ((r1_zf_model A B C) <=> (r1_zf_model A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t19_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_ordinal2 A B) & (r2_ordinal2 B C))  => (r2_ordinal2 A C)) ) ) ) ) ) ) ).
tt(t19_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((r2_hidden B A) => (r2_hidden (k3_ordinal2 B) A)) ) ) ) ).
tt(t19_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t1_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_yellow_0 A B) & (r2_hidden (k1_yellow_0 A B) B)) ) ) ) ) ).
tt(t1_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k1_funct_1 B A) (k3_card_3 B))) ) ) ).
tt(t1_abcmiz_a,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  (A = (k4_tarski (k1_xtuple_0 A) (k2_xtuple_0 A))) ) ) ).
tt(t1_abian,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~  ( (~ (v1_abian A))  &  (! [B:$i] :  ((v1_int_1 B) =>  (~  (A = (k2_xcmplx_0 (k3_xcmplx_0 2 B) 1)) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((v1_int_1 B) &  (A = (k2_xcmplx_0 (k3_xcmplx_0 2 B) 1)) ) )  & (v1_abian A)) ) ) ) ) ).
tt(t1_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k18_complex1 A) = A)  |  ((k18_complex1 A) = (k4_xcmplx_0 A)) ) ) ) ).
tt(t1_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t1_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_2 A) <=> (v3_aff_2 A)) ) ) ).
tt(t1_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v1_aff_3 A) => (v2_aff_3 A)) ) ) ).
tt(t1_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( ((r1_aff_1 A B C D) | (r1_aff_1 A B D C))  &  ( (~  (B = C) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A B E F) & (r2_analoaf A C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (A = (k3_xboole_0 A B))  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t1_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden B A) => (m2_subset_1 B k1_numbers k5_numbers)) ) ) ) ).
tt(t1_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  &  (B = (u1_struct_0 A)) )  => (v1_aff_4 B A)) ) ) ) ) ).
tt(t1_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ).
tt(t1_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ).
tt(t1_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (B = (u1_struct_0 A))  =>  ((k3_unialg_2 A B) = (u1_unialg_1 A)) ) ) ) ) ) ).
tt(t1_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k7_card_1 B)) <=>  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(t1_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) (k9_xtuple_0 C)) =>  ((k1_funct_4 (k1_funct_4 A B) C) = (k1_funct_4 (k1_funct_4 B A) C)) ) ) ) ) ) ) ) ).
tt(t1_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A D (k4_struct_0 A)) = D) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k1_algstr_0 A D E) = (k4_struct_0 A)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A D E) F) = (k1_algstr_0 A D (k1_algstr_0 A E F))) ) ) ) ) ) )  &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) )  =>  ((k1_algstr_0 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t1_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k1_algstr_0 A C B)) ) ) ) )  &  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k5_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k5_struct_0 A) B) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B D) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A B D))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = (k6_algstr_0 A D B))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~  (A = B) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((k7_real_1 (k8_real_1 A E) C) = (k7_real_1 (k8_real_1 B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B (k1_yellow_6 A)) & (r1_tarski C (k1_yellow_6 A)))  => (r1_tarski (k2_zfmisc_1 B C) (k1_yellow_6 A))) ) ) ) ).
tt(t1_ali2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_ali2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v1_compts_1 (k3_pcomps_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D)  =>  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_altcat_1,ax, (! [A:$i] : (r2_hidden (k4_relat_1 A) (k1_funct_2 A A))) ).
tt(t1_altcat_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] : (r1_funct_2 (k2_zfmisc_1 A B) (k2_zfmisc_1 (k1_tarski C) (k1_tarski D)) (k2_zfmisc_1 A B) (k1_tarski (k4_tarski C D)) (k16_funct_3 A B (k1_tarski C) (k1_tarski D) (k7_funcop_1 A C) (k7_funcop_1 B D)) (k7_funcop_1 (k2_zfmisc_1 A B) (k4_tarski C D)))) ) ) ) ).
tt(t1_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_altcat_3 (k8_altcat_1 A B) A B B) & (v2_altcat_3 (k8_altcat_1 A B) A B B)) ) ) ) ) ).
tt(t1_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A B D)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  ( ( (F = (k5_altcat_1 A B C D E G))  &  ((k5_altcat_1 A C D C G (k1_altcat_3 A C D G)) = (k8_altcat_1 A C)) )  =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C D) = k1_xboole_0)  |  ( ((k1_altcat_1 A D C) = k1_xboole_0)  |  (E = (k5_altcat_1 A B D C F (k1_altcat_3 A C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ami_3,ax, ((k4_struct_0 k1_ami_3) = k5_numbers) ).
tt(t1_ami_4,ax, ((k9_xtuple_0 k1_ami_4) = 5) ).
tt(t1_ami_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (A = (k10_ami_3 B)) ) ) ) ) ).
tt(t1_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  (~  (A = 8) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_amistd_1 A B D C) = (k6_domain_1 k5_numbers D)) ) )  => (v1_xboole_0 (k2_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(t1_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  ((k5_xtuple_0 B) = k6_numbers) ) ) ) ) ).
tt(t1_amistd_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v3_amistd_1 C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k5_numbers)) =>  ( (D = (k1_tarski A))  =>  ((k1_amistd_3 B C D) = (k16_funcop_1 k6_numbers A)) ) ) ) ) ) ) ) ) ) ).
tt(t1_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_memstr_0 A B E)) =>  ((v4_amistd_1 C A B) =>  ( (E = (k4_struct_0 B))  |  ((k5_memstr_0 A B (k2_extpro_1 A B C D)) = (k5_memstr_0 A B (k2_extpro_1 A B C (k1_amistd_4 A B D E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_amistd_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (v2_amistd_1 (k5_compos_0 (u1_compos_1 B) C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t1_ami_wstd,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_extpro_1 C B)) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_ami_wstd B C D E) & (r1_ami_wstd B C E A))  => (r1_ami_wstd B C D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A D E) =>  ((r2_analmetr A B C D E) <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (B = (k3_rlvect_1 A (k1_rlvect_1 A D F) (k1_rlvect_1 A E G)))  &  (C = (k3_rlvect_1 A (k1_rlvect_1 A D H) (k1_rlvect_1 A E I))) )  =>  ((k7_real_1 (k8_real_1 F H) (k8_real_1 G I)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k5_algstr_0 A B C) (k5_algstr_0 A C D)) = (k5_algstr_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(t1_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k1_analort A B C (k3_rlvect_1 A D E)) = (k3_rlvect_1 A (k1_analort A B C D) (k1_analort A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_anproj_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~  (D = k6_numbers) )  &  (B = (k1_rlvect_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  ( (~ (v9_struct_0 D A))  &  ( (~ (r2_anproj_1 A B C D))  &  (~ (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((r1_tarski D (k9_xtuple_0 A)) &  ((r1_tarski D (k9_xtuple_0 B)) &  ((r1_tarski (k10_xtuple_0 C) D) &  (! [E:$i] :  ((r2_hidden E D) =>  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) ) ) )  =>  ((k3_relat_1 C A) = (k3_relat_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t1_aofa_i00,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ( (~  (D = E) )  &  ( (~  (E = F) )  &  ( (~  (F = D) )  &  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (~  ( ((k1_funct_1 G D) = A)  &  ( ((k1_funct_1 G E) = B)  &  ((k1_funct_1 G F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_arithm,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_xcmplx_0 A k6_numbers) = A) ) ) ).
tt(t1_armstrng,ax, (! [A:$i] :  ((v2_finsub_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))))  =>  ( ((r2_hidden B A) & (r1_tarski C A))  => (r2_hidden (k8_setfam_1 B C) A)) ) ) ) ) ) ).
tt(t1_arrow,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((r1_xxreal_0 2 (k5_card_1 A)) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (~  (! [C:$i] :  ((m1_subset_1 C A) =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(t1_arytm_0,ax,(r1_tarski k2_arytm_2 k1_numbers)).
tt(t1_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((k7_arytm_2 A B) = B)  =>  (A = k11_arytm_3) ) ) ) ) ) ).
tt(t1_arytm_2,ax,(r1_tarski k5_arytm_3 k2_arytm_2)).
tt(t1_arytm_3,ax, (~ (r1_arytm_3 k1_xboole_0 k1_xboole_0)) ).
tt(t1_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A (k2_nat_1 C 1)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B C) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t1_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( ((k1_seq_1 A k6_numbers) = k6_numbers)  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 A C) = (k7_real_1 (k7_real_1 (k9_real_1 (k8_real_1 (k4_nat_1 12 (k5_series_1 C 3)) (k6_power 2 C)) (k8_real_1 5 (k5_square_1 C))) (k5_square_1 (k6_power 2 C))) 36)) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k8_real_1 (k5_series_1 C 3) (k6_power 2 C))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v4_asympt_0 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C A) &  ((r2_funct_2 k5_numbers k1_numbers D B) & (r2_hidden C (k6_asympt_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r4_alg_1 A A (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t1_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 B (k2_group_3 A D C))) ) ) ) )  <=> (v1_group_3 B A)) ) ) ) ) ).
tt(t1_axioms,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (~  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r1_xxreal_0 C D)) ) ) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((v1_xreal_0 D) &  (? [E:$i] :  ((v1_xreal_0 E) &  ((r2_hidden D A) &  ((r2_hidden E B) &  (~  ((r1_xxreal_0 D C) & (r1_xxreal_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bagorder,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden C A) &  ((r2_hidden C B) &  ((k6_subset_1 A (k1_tarski C)) = (k6_subset_1 B (k1_tarski C))) ) )  =>  (A = B) ) ) ) ) ).
tt(t1_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  <=>  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B D)) (k1_bcialg_1 A D C)) = (k4_struct_0 A))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_2 A B C k6_numbers) = B) ) ) ) ) ) ) ).
tt(t1_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ).
tt(t1_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D (k3_bcialg_4 A B C)) & (r1_bcialg_1 A E D))  => (r2_hidden E (k3_bcialg_4 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_bcialg_1 A B C) & (r1_bcialg_1 A C D))  => (r1_bcialg_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t1_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k5_bcialg_1 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A B D)) = (k1_bcialg_1 A D (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t1_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) => (r1_bcialg_1 A (k1_bcialg_1 A E (k1_bcialg_1 A D B)) (k1_bcialg_1 A E (k1_bcialg_1 A D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k2_bhsp_1 A (k4_struct_0 A) (k4_struct_0 A)) = k6_numbers) ) ) ).
tt(t1_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v1_bhsp_2 B A)) ) ) ) ) ).
tt(t1_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v1_bhsp_3 B A)) ) ) ) ) ).
tt(t1_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k2_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t1_bhsp_5,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v2_funct_1 B) &  ((v2_funct_1 C) &  ((k10_xtuple_0 B) = (k10_xtuple_0 C)) ) )  =>  ( ((k4_finseq_1 B) = (k4_finseq_1 C))  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  &  ( (C = (k3_relat_1 D B))  &  ( ((k9_xtuple_0 D) = (k4_finseq_1 B))  &  ((k10_xtuple_0 D) = (k4_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) =>  ((k1_funct_1 C D) = D) ) ) )  =>  ((k1_bhsp_6 A B) = (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) B C)) ) ) ) ) ) ) ) ) ).
tt(t1_bhsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((r1_bhsp_6 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 E))  &  ((r1_tarski E B) &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (v1_xboole_0 F))  &  ((r1_tarski F B) &  ((r1_xboole_0 E F) & (r1_xxreal_0 D (k18_complex1 (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 F C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k2_bilinear A B C D (k1_bilinear A B C)) D)) ) ) ) ) ) ) ) ).
tt(t1_binari_2,ax, (! [A:$i] :  ( ((v3_card_1 A 2) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k9_binarith 1 1 k6_margrel1 (k10_binarith k6_margrel1 k7_margrel1) (k10_binarith k6_margrel1 k7_margrel1)))  =>  ((k3_binari_2 2 A) = k6_numbers) ) ) ) ).
tt(t1_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (~ (r1_xxreal_0 (k5_series_1 2 A) (k6_binarith A B))) ) ) ) ) ).
tt(t1_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k23_binop_2 A 1) (k24_binop_2 A 2))) ) ) ).
tt(t1_binarith,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E C))  =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k7_partfun1 C (k8_finseq_1 C E (k12_finseq_1 C D)) A) = (k7_partfun1 C E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t1_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ( (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F A) & (r2_hidden G B))  =>  ((k1_binop_1 D F G) = (k1_binop_1 E F G)) ) ) )  => (r2_funct_2 (k2_zfmisc_1 A B) C D E)) ) ) ) ) ) ) ) ).
tt(t1_binop_2,ax, ((k4_binop_1 k2_numbers k27_binop_2) = k6_numbers) ).
tt(t1_bintree1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  ((k14_trees_3 (k9_finseq_1 B)) = (k3_pre_poly A (k1_bintree1 A B))) ) ) ) ) ).
tt(t1_bintree2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden B (k3_finseq_2 A)) => (r2_hidden (k5_relat_1 B (k2_finseq_1 C)) (k3_finseq_2 A))) ) ) ) ) ) ).
tt(t1_birkhoff,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) => (r2_pboole (u1_struct_0 A) (k3_funct_6 D) (k3_funct_6 (k1_birkhoff A C B D)))) ) ) ) ) ) ) ) ).
tt(t1_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k3_lattices A B C) D) => (r3_lattices A B D)) ) ) ) ) ) ) ) ) ).
tt(t1_boole,ax, (! [A:$i] :  ((k2_xboole_0 A k1_xboole_0) = A) ) ).
tt(t1_boolmark,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((v1_funct_1 (k1_funct_4 C (k1_margrel1 B D E))) &  ((v1_funct_2 (k1_funct_4 C (k1_margrel1 B D E)) A B) & (m1_subset_1 (k1_funct_4 C (k1_margrel1 B D E)) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bor_cant,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 B 1) =>  ((v1_abian A) |  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 k6_numbers (k7_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_sin_cos (k1_real_1 B)) (k2_nat_1 A 1)) (k3_funct_2 k5_numbers k1_numbers (k4_sin_cos (k1_real_1 B)) (k2_nat_1 A 2))))) ) ) ) ) ) ) ).
tt(t1_borsuk_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ).
tt(t1_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (~  ((m1_pre_topc A D) &  ((m1_pre_topc C D) &  ( ((k2_xboole_0 (k2_struct_0 A) (k2_struct_0 C)) = (k2_struct_0 D))  &  ((v1_compts_1 A) &  ((v1_compts_1 C) &  ((v8_pre_topc D) &  ((v5_pre_topc E A B) &  ((v5_pre_topc F C B) &  ( (! [G:$i] :  ((r2_hidden G (k9_subset_1 (u1_struct_0 C) (k2_struct_0 A) (k2_struct_0 C))) =>  ((k1_funct_1 E G) = (k1_funct_1 F G)) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  (~  ( (G = (k1_funct_4 E F))  & (v5_pre_topc G D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((k2_struct_0 (k2_borsuk_1 A B)) = (k3_borsuk_1 A B (k2_struct_0 A) (k2_struct_0 B))) ) ) ) ) ).
tt(t1_borsuk_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (~  ((v1_zfmisc_1 B) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k6_domain_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t1_borsuk_6,ax, ((u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 k6_numbers 1) (k1_rcomp_1 k6_numbers 1))) ).
tt(t1_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((k3_square_1 A) = (k3_square_1 B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t1_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid A) C D)) = (k3_rlvect_1 (k15_euclid A) B (k1_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) C B) D))) ) ) ) ) ) ) ) ) ).
tt(t1_brouwer,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((r2_hidden C (k1_brouwer A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (C = (k4_borsuk_1 A B D E))  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bspace,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k4_finseq_1 C)) => (r1_struct_0 A (k1_funct_1 C B))) ) ) ) ) ) ) ).
tt(t1_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A C D)) (k2_bvfunc_1 A D B)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A D B)))) ) ) ) ) ) ) ) ).
tt(t1_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((r1_setfam_1 C D) => (r1_tarski (k15_bvfunc_1 A B C) (k15_bvfunc_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((k15_bvfunc_1 A B (k2_partit1 A C D)) = (k9_subset_1 A (k15_bvfunc_1 A B C) (k15_bvfunc_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k9_bvfunc_1 A B C)) (k2_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t1_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B C) (k1_bvfunc_1 A (k2_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t1_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  ((r2_hidden C D) &  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ( ((k9_xtuple_0 E) = B)  &  ( ((k10_xtuple_0 E) = F)  &  ( (! [G:$i] :  ((r2_hidden G B) => (r2_hidden (k1_funct_1 E G) G)) )  &  ( (D = (k8_setfam_1 A F))  &  (~  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A C D) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A B (k9_bvfunc_1 A C D)) => (r1_bvfunc_1 A (k2_bvfunc_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 C (k12_bvfunc_1 A)))  <=> (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t1_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C (k2_bvfunc_1 A B C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t1_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) C)) C)) ) ) ) ) ) ).
tt(t1_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k2_bvfunc_1 A (k2_bvfunc_1 A C D) E)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k9_bvfunc_1 A B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k5_bvfunc_1 A B D))) ) ) ) ) ) ) ) ).
tt(t1_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v3_group_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 F))) =>  ( ( (G = A)  &  ( (D = (k1_realset1 (u1_algstr_0 F) G))  &  ( (E = (k1_realset1 (u2_algstr_0 F) G))  &  ( (B = (k5_struct_0 F))  &  ( (C = (k4_struct_0 F))  & (v1_c0sp1 G F)) ) ) ) )  => (m1_c0sp1 (g6_algstr_0 A D E B C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 A) k1_numbers B C) D) &  ((v3_rcomp_1 D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C E) &  ((v3_pre_topc E A) & (r1_tarski (k7_relset_1 (u1_struct_0 A) k1_numbers B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((r2_calcul_1 A B C) =>  ((r1_tarski (k2_relset_1 (k3_cqc_lang A) B) (k2_relset_1 (k3_cqc_lang A) C)) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k5_numbers)) & (r1_tarski (k2_relset_1 (k3_cqc_lang A) B) (k2_relset_1 (k3_cqc_lang A) (k2_partfun1 k5_numbers (k3_cqc_lang A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k2_calcul_2 B C)) <=>  ((r1_xxreal_0 (k2_nat_1 1 B) A) & (r1_xxreal_0 A (k2_xcmplx_0 C B))) ) ) ) ) ) ) ) ).
tt(t1_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski B (k1_cantor_1 A B))) ) ) ).
tt(t1_card_1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) & (r2_wellord2 A B)) ) ) ).
tt(t1_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (r2_wellord2 B C))  =>  ( (~  (C = k1_xboole_0) )  &  (? [D:$i] : (r2_hidden D C)) ) ) ) ) ) ).
tt(t1_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  ((k1_card_3 A) = A) ) ) ).
tt(t1_card_4,ax, (! [A:$i] :  ((v1_finset_1 A) => (v4_card_3 A)) ) ).
tt(t1_card_5,ax, (! [A:$i] :  ((k2_card_1 (k1_card_1 A)) = (k2_card_1 A)) ) ).
tt(t1_card_fil,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_finset_1 B))  => (r2_hidden (k5_card_1 (k1_tarski A)) (k1_card_1 B))) ) ) ).
tt(t1_cardfin2,ax, (~ (v2_abian (k6_partfun1 k1_xboole_0))) ).
tt(t1_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((r1_tarski A B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t1_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r3_card_lar A B) <=>  ((v2_card_lar B A) & (v1_card_lar B A)) ) ) ) ) ) ).
tt(t1_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden B (k2_cat_1 A C D)) <=>  ( ((k3_graph_1 A B) = C)  &  ((k4_graph_1 A B) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [E:$i] :  ((r2_hidden E A) =>  ((k7_partfun1 B C E) = (k7_partfun1 B D E)) ) )  => (r2_funct_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t1_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v1_cat_4 A) <=>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (v10_cat_1 B A)) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) &  ( ((k3_graph_1 A E) = D)  &  ( ((k3_graph_1 A F) = D)  &  ( ((k4_graph_1 A E) = B)  &  ( ((k4_graph_1 A F) = C)  & (r2_cat_3 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_cat_1 B)) )  =>  ( ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B)))  =>  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) & (v6_cat_1 B)) ) ) ) ) ) ) ) ) ).
tt(t1_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  => (r1_xxreal_0 (k7_nat_d A 1) (k7_nat_d (k4_nat_1 2 A) 3))) ) ) ).
tt(t1_catalan2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  &  (C = (k1_ordinal4 (k5_relat_1 C B) D)) ) ) ) ) ) ) ) ).
tt(t1_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k1_catalg_1 A B (k6_partfun1 (k3_card_3 B))) (k2_msualg_3 A B))) ) ) ).
tt(t1_cayley,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k1_cayley A)) =>  ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(t1_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v2_cfuncdom B) & (l1_cfuncdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 k2_numbers A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers A) A)))) )  =>  ( ( (C = A)  &  ( (D = (k4_struct_0 B))  &  ( (E = (k5_struct_0 B))  &  ( (F = (k1_realset1 (u1_algstr_0 B) C))  &  ( (G = (k1_realset1 (u2_algstr_0 B) C))  &  ( (H = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 B)) (u1_struct_0 B) (u1_clvect_1 B) (k2_zfmisc_1 k2_numbers C)))  & (v1_c0sp1 C B)) ) ) ) ) )  => (m1_cc0sp1 (g1_cfuncdom A G F H E D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ((r2_funct_2 (u1_struct_0 A) k2_numbers C (k1_cc0sp2 A B)) => (v1_cc0sp2 C A)) ) ) ) ) ) ) ).
tt(t1_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_relset_1 k5_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A D) = (k11_complex1 (k3_funct_2 k5_numbers k2_numbers B D) (k3_funct_2 k5_numbers k2_numbers C D))) ) ) ) ) ) ) ) ) ) ).
tt(t1_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r1_funct_2 k5_numbers k1_numbers k5_numbers k2_numbers A B) & (v2_comseq_2 A))  => (v2_comseq_2 B)) ) ) ) ) ).
tt(t1_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((v1_partfun1 A k2_numbers) =>  ( ((k1_relset_1 k2_numbers (k5_comseq_3 k2_numbers A)) = k2_numbers)  &  ((k1_relset_1 k2_numbers (k6_comseq_3 k2_numbers A)) = k2_numbers) ) ) ) ) ).
tt(t1_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) =>  ((r2_funct_2 A k2_numbers B (k1_funcsdom A k2_numbers (k1_cfuncdom A) C D)) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers B E) = (k8_complex1 (k3_funct_2 A k2_numbers C E) (k3_funct_2 A k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers B C))) =>  ((k7_partfun1 k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C) D) = (k8_complex1 (k7_partfun1 k2_numbers B D) (k7_partfun1 k2_numbers C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k2_cgames_1 B)) <=>  (? [C:$i] :  ( ((v1_cgames_1 C) & (l1_cgames_1 C))  &  ( (A = C)  &  (! [D:$i] :  (~  ((r2_hidden D (k2_xboole_0 (u1_cgames_1 C) (u2_cgames_1 C))) &  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r2_hidden E B) & (r2_hidden D (k2_cgames_1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_chain_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_chord,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((v7_ordinal1 (k6_xcmplx_0 A 1)) & (r1_xxreal_0 1 A)) ) ) ).
tt(t1_circcmb2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 B A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B A) A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k5_circcomb D C))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k5_circcomb D C) (k7_circcomb B A D C)))) =>  ((k3_circuit1 (k5_circcomb D C) (k7_circcomb B A D C) F E) = (k3_relat_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((r2_hidden D (k2_msafree2 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k1_funct_1 (k5_facirc_1 A B C E) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_circcomb,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  ((r1_tarski C D) => (r1_tarski (k6_finseq_2 A C) (k6_finseq_2 B D))) ) ) ) ) ) ) ).
tt(t1_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v3_rltopsp1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_rltopsp1 (k1_rusub_5 A B C) A)) ) ) ) ) ) ).
tt(t1_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  ( (E = D)  =>  ((k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E) = (k7_msaterm A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A B) C)) =>  ( ((r2_hidden C (k1_msafree2 A)) & (r2_hidden D (k1_msualg_2 A B C)))  =>  ((k1_funct_1 (k1_circuit1 A B) C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)) (u3_msualg_1 A (k11_msafree A B))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_funcop_1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) E)) =>  (~  ((r2_hidden E (k3_msafree2 A)) &  ( (G = (k4_trees_4 (k4_tarski (k4_msafree2 A E) (u1_struct_0 A)) F))  &  ((r1_msualg_3 A (k11_msafree A B) (k11_msafree A B) C) &  ( (D = (k3_relat_1 (k1_msualg_1 A (k4_msafree2 A E)) C))  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) &  ((v1_finseq_1 H) & (v6_trees_3 H)) ) )  =>  (~  ( (H = (k15_pralg_1 D F))  &  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) E) (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B)) (u3_msualg_1 A (k11_msafree A B)) C E) G) = (k4_trees_4 (k4_tarski (k4_msafree2 A E) (u1_struct_0 A)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_classes1,ax, (! [A:$i] :  ((v2_classes1 A) <=>  ((v1_classes1 A) &  ( (! [B:$i] :  ((r2_hidden B A) => (r2_hidden (k9_setfam_1 B) A)) )  &  (! [B:$i] :  ( ((r1_tarski B A) & (r2_hidden (k1_card_1 B) (k1_card_1 A)))  => (r2_hidden B A)) ) ) ) ) ) ).
tt(t1_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_classes1 A) & (r2_hidden B A))  =>  ( (~ (r2_tarski B A))  & (r2_hidden (k1_card_1 B) (k1_card_1 A))) ) ) ) ).
tt(t1_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A (u1_struct_0 B) (k4_lopban_1 A B) C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t1_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) & (l1_clvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_clopban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_clopban1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 C)) &  ((v13_vectsp_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v1_clopban1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_clvect_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_bhsp_4 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t1_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) &  ((v9_clvect_1 C A) &  ((k7_clvect_1 A (k3_normsp_1 A B C)) = (k4_struct_0 A)) ) )  =>  ((k7_clvect_1 A B) = (k7_clvect_1 A C)) ) ) ) ) ) ) ) ).
tt(t1_closure1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) => (r1_tarski (a_2_0_closure1 A C) (a_2_0_closure1 A B))) ) ) ) ) ).
tt(t1_closure2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r1_tarski B C) => (r1_tarski (k3_funct_2 A A (k6_partfun1 A) B) (k3_funct_2 A A (k6_partfun1 A) C))) ) ) ) ) ) ) ).
tt(t1_closure3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k1_funct_4 B C) = C) ) ) ) ) ) ) ).
tt(t1_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ( (C = k6_numbers)  |  (B = (k4_struct_0 A)) )  =>  ((k1_clvect_1 A B C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t1_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v1_clvect_2 B A)) ) ) ) ) ).
tt(t1_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k16_csspace A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) = (k1_bhsp_4 A (k16_csspace A B C))) ) ) ) ) ) ) ).
tt(t1_cohsp_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (k1_cohsp_1 A)) <=>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  (~  ( (B = (k1_tarski C))  & (r2_hidden C A)) ) ) ) ) ) ) ) ).
tt(t1_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  => (r2_hidden k1_xboole_0 A)) ) ).
tt(t1_collsp,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ( (~  ((k1_tarski B) = A) )  &  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (C = D) )  &  ((r2_hidden C A) & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ).
tt(t1_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ( ((k1_card_1 B) = A)  &  ((k1_card_1 C) = A) )  =>  ( (B = C)  |  ((r2_hidden (k1_card_1 (k3_xboole_0 B C)) A) & (r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 (k2_xboole_0 B C)))) ) ) ) ) ) ) ).
tt(t1_commacat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E)) =>  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  (? [I:$i] :  ((m1_subset_1 I (u4_struct_0 C)) & (r2_hidden I (k2_cat_1 C (k8_cat_1 A C D G) (k8_cat_1 B C E H)))) ) ) ) ) )  =>  ( (F = (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k14_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F) (k15_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F)) (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F)))  &  ((r2_hidden (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F) (k2_cat_1 C (k8_cat_1 A C D (k14_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F)) (k8_cat_1 B C E (k15_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F)))) &  ( ((k3_graph_1 C (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F)) = (k8_cat_1 A C D (k14_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F)))  &  ((k4_graph_1 C (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F)) = (k8_cat_1 B C E (k15_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_compact1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v1_tex_3 (k1_pre_topc A B) A) & (v5_compact1 (k1_pre_topc A B)))  => (v1_tsep_1 (k1_pre_topc A B) A)) ) ) ) ) ).
tt(t1_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t1_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (C = (k2_xcmplx_0 (k3_xcmplx_0 B (k4_xcmplx_0 (k1_int_1 (k13_complex1 A B)))) A))  &  ((r1_xxreal_0 k6_numbers C) &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k3_rlvect_1 k1_complfld A B) = (k3_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((u1_pre_topc (k1_complsp1 A)) = (k27_seq_4 A)) ) ) ).
tt(t1_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ((r2_hidden A (k4_finseq_1 (k9_seq_4 B C))) =>  ((k9_matrix_5 (k9_seq_4 B C) A) = (k3_binop_2 (k9_matrix_5 B A) (k9_matrix_5 C A))) ) ) ) ) ) ) ) ).
tt(t1_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  => (v2_seq_2 (k1_compl_sp A B))) ) ) ) ).
tt(t1_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_compos_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ( ((k2_compos_0 A B) = (k2_compos_0 A C))  &  ( ((k5_xtuple_0 B) = (k5_xtuple_0 C))  &  ((k2_xtuple_0 B) = (k2_xtuple_0 C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t1_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k2_compos_2 A (k8_compos_1 A C D) B) = (k8_compos_1 A C (k2_compos_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t1_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r1_xxreal_0 (k1_real_1 (k17_complex1 A)) (k3_complex1 A))) ) ).
tt(t1_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_compts_1 A) <=> (v2_compts_1 (k2_struct_0 A) A)) ) ) ).
tt(t1_comput_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k2_funct_7 (k10_finseq_1 A B) 1 C) = (k10_finseq_1 C B))  &  ((k2_funct_7 (k10_finseq_1 A B) 2 C) = (k10_finseq_1 A C)) ) ) ) ) ).
tt(t1_comseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [B:$i] :  ((r2_hidden B k5_numbers) => (m1_subset_1 (k1_funct_1 A B) k2_numbers)) ) ) ) ) ) ).
tt(t1_comseq_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( (~  (A = k5_complex1) )  &  ( (~  (B = k5_complex1) )  &  (~  ((k17_complex1 (k11_complex1 (k12_complex1 A) (k12_complex1 B))) = (k10_real_1 (k17_complex1 (k11_complex1 A B)) (k8_real_1 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ) ) ) ) ) ).
tt(t1_comseq_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~  ((k2_nat_1 A 1) = k5_complex1) )  &  (~  ((k3_xcmplx_0 (k2_nat_1 A 1) k7_complex1) = k5_complex1) ) ) ) ) ).
tt(t1_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v4_conaffm A) => (v1_conaffm A)) ) ) ).
tt(t1_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_funct_1 (k1_conlat_1 A) (k1_tarski B)) = (a_2_2_conlat_1 A B)) ) ) ) ) ).
tt(t1_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( ((k5_lattices (k11_conlat_1 A)) = (k6_conlat_1 A))  &  ((k6_lattices (k11_conlat_1 A)) = (k5_conlat_1 A)) ) ) ) ).
tt(t1_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_conmetr1 A) <=>  ((v5_conmetr1 A) & (v6_conmetr1 A)) ) ) ) ).
tt(t1_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r5_analmetr A B C D) &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) => (r1_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t1_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m1_connsp_2 C A B) & (m1_connsp_2 D A B))  => (m1_connsp_2 (k4_subset_1 (u1_struct_0 A) C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t1_connsp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((v2_connsp_1 C A) & (r1_tarski B C)) ) )  => (r1_tarski B (k1_connsp_3 A B))) ) ) ) ) ).
tt(t1_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v1_convex1 B A) => (v1_convex1 (k1_convex1 A B C) A)) ) ) ) ) ) ) ).
tt(t1_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_convex1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_convex1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t1_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v2_convex1 C A) & (m1_rlvect_2 C A))  &  ( ((k6_rlvect_2 A C) = B)  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B D) =>  ((v2_convex1 C A) & (m2_rlvect_2 C A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) k2_numbers B C) = k5_complex1)  <=>  (~ (r2_hidden C (k1_convex4 A B))) ) ) ) ) ) ) ) ).
tt(t1_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_convfun1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) C D))  =>  ((k1_rlvect_1 (k3_convfun1 A B) E F) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k1_rlvect_1 A C F) (k1_rlvect_1 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((r2_hidden B (k2_qc_lang1 A)) <=>  (~  ( (~ (r2_hidden B (k4_qc_lang1 A)))  &  ( (~ (r2_hidden B (k5_qc_lang1 A)))  &  (~ (r2_hidden B (k3_qc_lang1 A))) ) ) ) ) ) ) ) ).
tt(t1_cqc_sim1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k9_relat_1 (k1_funct_4 C (k16_funcop_1 A B)) A) = (k1_tarski B)) ) ) ) ) ).
tt(t1_cqc_the1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((a_1_0_cqc_the1 A) = (k2_xboole_0 (a_1_1_cqc_the1 A) (k1_tarski (k2_nat_1 A 1)))) ) ) ).
tt(t1_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) D) A)) ) ) ) ) ) ) ) ) ).
tt(t1_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r2_hidden B C) => (r3_cqc_the1 A C B)) ) ) ) ) ) ) ).
tt(t1_csspace2,ax, ( ((u1_struct_0 k18_csspace) = k11_csspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  & (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace A)) (k55_valued_1 k5_numbers k2_numbers (k2_csspace A))))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  & (v2_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_comseq_2 k5_numbers (k2_csspace A))))) ) )  &  ( ((k4_struct_0 k18_csspace) = k6_csspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (A = (k2_csspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k1_algstr_0 k18_csspace A B) = (k1_series_1 k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) )  &  ( (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k1_clvect_1 k18_csspace B A) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace B) A)) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  ( ((k4_algstr_0 k18_csspace A) = (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))  & (r2_funct_2 k5_numbers k2_numbers (k2_csspace (k4_algstr_0 k18_csspace A)) (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((k5_algstr_0 k18_csspace A B) = (k46_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  ((v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace A)) (k55_valued_1 k5_numbers k2_numbers (k2_csspace B)))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k18_csspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k18_csspace)) =>  ((k12_csspace k18_csspace C D) = (k11_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace C) (k2_comseq_2 k5_numbers (k2_csspace D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_csspace3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k17_complex1 (k6_xcmplx_0 (k3_funct_2 k5_numbers k2_numbers B D) A))) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k17_complex1 (k6_xcmplx_0 (k3_comseq_2 B) A))) ) ) ) ) ) ) ) ) ).
tt(t1_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A))) = k6_numbers) )  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) ) ) ) ) ).
tt(t1_csspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k2_csspace A) A)) ) ).
tt(t1_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k3_decomp_1 A B) = (k2_decomp_1 A B))  <=>  ((k1_decomp_1 A B) = (k4_decomp_1 A B)) ) ) ) ) ) ).
tt(t1_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D A (k4_finseq_2 C A)) =>  ((r1_xxreal_0 B C) => (m2_finseq_2 (k2_descip_1 A B D) A (k4_finseq_2 B A))) ) ) ) ) ) ) ) ) ).
tt(t1_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((k9_xtuple_0 A) = (k1_tarski B))  =>  (A = (k16_funcop_1 B (k1_funct_1 A B))) ) ) ) ) ).
tt(t1_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers C)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers C)))  =>  ((k1_seq_1 (k3_diff_1 C B) A) = (k9_real_1 (k1_seq_1 C (k7_real_1 A B)) (k1_seq_1 C A))) ) ) ) ) ) ) ) ).
tt(t1_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C A (k7_real_1 A B)) = (k6_real_1 (k1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C B) 1) A) B)) ) ) ) ) ) ) ).
tt(t1_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k5_diff_1 C A) B) = (k9_real_1 (k1_seq_1 (k3_diff_1 C (k10_real_1 A 2)) B) (k1_seq_1 (k3_diff_1 C (k1_real_1 (k10_real_1 A 2))) B))) ) ) ) ) ) ) ).
tt(t1_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k9_real_1 (k6_power k8_power A) (k6_power k8_power B)) = (k5_power k8_power (k13_complex1 A B))) ) ) ) ) ) ) ) ) ).
tt(t1_dilworth,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden C A))  =>  ((k6_subset_1 A (k2_xboole_0 B (k1_tarski C))) = (k6_subset_1 A B)) ) ) ) ) ).
tt(t1_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ).
tt(t1_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_analort A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_analort A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_analort A B C))) =>  ((r2_analoaf (k5_analort A B C) D D F H) &  ((r2_analoaf (k5_analort A B C) D F H H) &  ( (~  ((r2_analoaf (k5_analort A B C) D F E G) &  ((r2_analoaf (k5_analort A B C) D F G E) &  ( (~  (D = F) )  &  (~  (E = G) ) ) ) ) )  &  ( (~  ((r2_analoaf (k5_analort A B C) D F E G) &  ((r2_analoaf (k5_analort A B C) D F E H) &  ( (~ (r2_analoaf (k5_analort A B C) D F G H))  &  (~ (r2_analoaf (k5_analort A B C) D F H G)) ) ) ) )  &  ( ((r2_analoaf (k5_analort A B C) D F E G) => (r2_analoaf (k5_analort A B C) F D G E))  &  ( ( ((r2_analoaf (k5_analort A B C) D F E G) & (r2_analoaf (k5_analort A B C) D F G H))  => (r2_analoaf (k5_analort A B C) D F E H))  &  (~  ((r2_analoaf (k5_analort A B C) D E F G) &  ( (~ (r2_analoaf (k5_analort A B C) F G D E))  &  (~ (r2_analoaf (k5_analort A B C) F G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_analort A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_analort A B C))) &  ( (~  (F = G) )  & (r2_analoaf (k5_analort A B C) F G D E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_analort A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_analort A B C))) &  ( (~  (F = G) )  & (r2_analoaf (k5_analort A B C) D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_dist_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k9_xtuple_0 B) = (k8_relset_1 k5_numbers A B A)) ) ) ) ).
tt(t1_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A (k2_zfmisc_1 B C)) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (~  (A = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_dtconstr,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k5_trees_3 A)) => (m2_finseq_1 B (k4_trees_3 A))) ) ) ) ).
tt(t1_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((r2_hidden C (k10_xtuple_0 B)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((k8_nat_1 (k9_setfam_1 A) B D) = C) ) ) ) ) ) ) ) ) ).
tt(t1_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (m1_ec_pf_1 A A)) ) ).
tt(t1_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k4_algstr_0 A C))  =>  ((k2_binom A B 2) = (k2_binom A C 2)) ) ) ) ) ) ) ) ).
tt(t1_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r1_tarski (k1_endalg A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(t1_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r2_hidden B (k1_ens_1 A)) <=>  (? [C:$i] :  ((m1_subset_1 C A) &  (? [D:$i] :  ((m1_subset_1 D A) &  ( ( (D = k1_xboole_0)  =>  (C = k1_xboole_0) )  &  ((v1_funct_1 B) &  ((v1_funct_2 B C D) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_entropy1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C D) &  ((r1_nat_d A C) & (r1_xxreal_0 (k3_nat_d D A) (k3_nat_d B A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_tarski A B) = (k2_xboole_0 (k1_tarski A) (k1_tarski B))) ) ) ).
tt(t1_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r2_relset_1 A A (k3_eqrel_1 A (k1_eqrel_1 A) B) (k1_eqrel_1 A))) ) ) ).
tt(t1_equation,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((k2_relset_1 C (k1_partfun1 A B B C D E)) = C)  =>  ((k2_relset_1 C E) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_e_siec,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((v2_e_siec (g1_e_siec A B C)) &  ((v3_e_siec (g1_e_siec A B C)) & (l1_e_siec (g1_e_siec A B C))) )  <=>  ((r1_tarski B (k2_zfmisc_1 A A)) &  ((r1_tarski C (k2_zfmisc_1 A A)) &  ( ((k3_relat_1 B B) = B)  &  ( ((k3_relat_1 B C) = B)  &  ( ((k3_relat_1 C C) = C)  &  ( ((k3_relat_1 C B) = C)  &  ( ((k3_relat_1 B (k4_xboole_0 B (k4_relat_1 A))) = k1_xboole_0)  &  ((k3_relat_1 C (k4_xboole_0 C (k4_relat_1 A))) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k1_funct_1 (k14_rvsum_1 C (k5_euclid A)) B) = k6_numbers) ) ) ) ) ) ) ).
tt(t1_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_euclid_3 (k1_euclid_3 A)) = A) ) ) ).
tt(t1_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ( ((k7_euclid A (k9_euclid A B k6_numbers) B) = B)  &  ((k7_euclid A B (k5_euclid A)) = B) ) ) ) ) ) ).
tt(t1_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (A = (k3_finseq_4 k1_numbers B C D)) ) ) ) ) ) ) ) ) ).
tt(t1_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k18_sin_cos (k4_euclid_3 A B C)) = (k18_sin_cos (k4_euclid_3 D E F)))  &  ((k21_sin_cos (k4_euclid_3 A B C)) = (k21_sin_cos (k4_euclid_3 D E F))) )  =>  ((k4_euclid_3 A B C) = (k4_euclid_3 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_euclid_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k9_xtuple_0 (k3_relat_1 B A)) = (k3_xboole_0 (k9_xtuple_0 B) (k8_relat_1 B (k9_xtuple_0 A)))) ) ) ) ) ).
tt(t1_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (A = (k1_euclid_8 (k1_seq_1 A 1) (k1_seq_1 A 2) (k1_seq_1 A 3))) ) ) ).
tt(t1_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  ((v1_xboole_0 B) =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t1_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  ( ((k9_euclid D (k9_euclid D E C) (k10_real_1 A B)) = (k9_euclid D E (k10_real_1 (k8_real_1 A C) B)))  &  ((k9_euclid D (k9_euclid D E C) (k10_real_1 1 B)) = (k9_euclid D E (k10_real_1 C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r5_analmetr A B C D))  =>  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_int_2 A A) <=>  (A = 1) ) ) ) ).
tt(t1_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) <=> (r1_int_2 A B)) ) ) ) ) ).
tt(t1_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((r2_hidden C (k6_subset_1 (k10_ordinal2 A B) A)) <=>  (? [D:$i] :  ((v3_ordinal1 D) &  ( (C = (k10_ordinal2 A D))  & (r2_hidden D B)) ) ) ) ) ) ) ) ) ).
tt(t1_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m3_pboole E A B) =>  ((r2_pboole A B E) => (r6_pboole A (k1_msafree A B C E D) D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_extpro_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k1_extpro_1 A))) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 A (k1_extpro_1 A))) & (v1_partfun1 B (u1_struct_0 (k1_extpro_1 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 (k1_extpro_1 A))) =>  ((k2_extpro_1 A (k1_extpro_1 A) C B) = B) ) ) ) ) ) ) ).
tt(t1_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k1_extreal1 A B) = (k11_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ((k3_extreal1 A) = (k18_complex1 B)) ) ) ) ) ) ).
tt(t1_facirc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (~  ((v2_facirc_1 A) & (v1_facirc_1 (k10_xtuple_0 A))) ) ) ) ).
tt(t1_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = C) )  &  ( (~  (B = C) )  &  (~  ((k6_subset_1 (k2_tarski A B) (k1_tarski C)) = (k2_tarski A B)) ) ) ) ) ) ) ) ).
tt(t1_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden B A) & (r1_fcont_1 C B))  => (r1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A) B)) ) ) ) ) ) ).
tt(t1_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B A))) &  ((r2_hidden F (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B A))) &  ( (~ (r1_xxreal_0 D (k18_complex1 (k9_real_1 E F))))  & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 B E) (k1_seq_1 B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden A (k2_rcomp_1 (k9_real_1 B C) (k7_real_1 B C))) & (r1_xxreal_0 C (k18_complex1 (k9_real_1 A B)))) ) ) ) ) ) ) ) ).
tt(t1_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos B)))) (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t1_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k16_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t1_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) <=> (r2_hidden B k1_numbers)) ) )  <=>  (A = k1_numbers) ) ) ) ).
tt(t1_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ( ((k2_seq_2 A) = (k2_seq_2 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k1_seq_1 C (k4_nat_1 2 D)) = (k1_seq_1 A D))  &  ((k1_seq_1 C (k2_nat_1 (k4_nat_1 2 D) 1)) = (k1_seq_1 B D)) ) ) ) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k2_seq_2 A)) ) ) ) ) ) ) ) ) ).
tt(t1_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k1_rcomp_1 (k9_real_1 B C) B) (k1_relset_1 k1_numbers A))) ) )  &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) B) D) = (k10_real_1 1 (k7_real_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers C D))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k7_real_1 A E))  &  ( ((k1_seq_1 D E) = (k9_real_1 A E))  &  (~  ((k1_seq_1 D E) = k6_numbers) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C D) B) E) = (k10_real_1 (k8_real_1 2 A) (k5_square_1 (k9_real_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_seq_1 k24_sin_cos (k8_real_1 B (k6_power k8_power A))) = (k10_prepower A B)) ) ) ) ) ) ).
tt(t1_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k5_prepower A 2) = (k5_square_1 A)) ) ) ).
tt(t1_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) &  ((k1_seq_1 k19_sin_cos A) = k6_numbers) ) ) ) ) ).
tt(t1_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k19_sin_cos A) = k6_numbers) )  =>  ((r1_fdiff_1 k1_fdiff_9 A) &  ((k1_fdiff_1 k1_fdiff_9 A) = (k10_real_1 (k1_seq_1 k16_sin_cos A) (k5_square_1 (k1_seq_1 k19_sin_cos A)))) ) ) ) ) ).
tt(t1_ff_siec,ax, (! [A:$i] :  (! [B:$i] :  ((r1_xboole_0 A B) =>  ( ((u1_struct_0 (k1_ff_siec A B)) = A)  &  ( ((u4_struct_0 (k1_ff_siec A B)) = B)  &  ((k1_net_1 (k1_ff_siec A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t1_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k1_fib_fusc A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_memstr_0 C 2 k1_ami_3 k6_numbers) & (m1_scm_1 C (k16_afinsq_1 1 B k6_numbers k6_numbers)))  =>  ((r1_extpro_1 2 k1_ami_3 A C) &  ( ( (B = k6_numbers)  =>  ((k8_extpro_1 2 k1_ami_3 A C) = 1) )  &  ( ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k8_extpro_1 2 k1_ami_3 A C) = (k6_xcmplx_0 (k4_nat_1 6 B) 2)) )  &  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A C) (k10_ami_3 3)) = (k1_pre_ff B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fib_num2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k2_nat_1 (k7_nat_d A 1) 2) = (k2_nat_1 A 1)) ) ) ).
tt(t1_fib_num3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k3_power A B) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t1_fib_num4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_power (k13_complex1 A B) C) = (k13_complex1 (k3_power A C) (k3_power B C))) ) ) ) ) ) ) ).
tt(t1_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_int_2 A B) = (k3_int_2 A (k2_nat_1 B A))) ) ) ) ) ).
tt(t1_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((k1_finseq_8 A (k1_finseq_8 A (k1_finseq_8 A B C) D) E) = (k1_finseq_8 A (k1_finseq_8 A B (k1_finseq_8 A C D)) E))  &  ( ((k1_finseq_8 A (k1_finseq_8 A (k1_finseq_8 A B C) D) E) = (k1_finseq_8 A (k1_finseq_8 A B C) (k1_finseq_8 A D E)))  &  ((k1_finseq_8 A (k1_finseq_8 A B (k1_finseq_8 A C D)) E) = (k1_finseq_8 A (k1_finseq_8 A B C) (k1_finseq_8 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k3_lattices A D B) (k3_lattices A D C))) ) ) ) ) ) ) ) ) ).
tt(t1_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v1_xboole_0 (k9_subset_1 (u1_struct_0 A) B C)))  &  ((v19_lattices (k9_subset_1 (u1_struct_0 A) B C) A) &  ((v20_lattices (k9_subset_1 (u1_struct_0 A) B C) A) & (m1_subset_1 (k9_subset_1 (u1_struct_0 A) B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t1_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( (D = (k1_realset1 C B))  =>  ( ((v1_binop_1 C A) => (v1_binop_1 D B))  &  ( ((v3_binop_1 C A) => (v3_binop_1 D B))  &  ((v2_binop_1 C A) => (v2_binop_1 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 k1_numbers (k3_rcomp_1 A k1_xxreal_0)) = (k2_rcomp_1 k2_xxreal_0 A)) ) ) ).
tt(t1_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) <=>  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t1_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((m1_subset_1 (k3_xxreal_0 A B) k5_numbers) & (m1_subset_1 (k4_xxreal_0 A B) k5_numbers)) ) ) ) ) ).
tt(t1_finseq_3,ax, ((k2_finseq_1 3) = (k1_enumset1 1 2 3)) ).
tt(t1_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_finseq_4 A B) => (r2_hidden B (k9_xtuple_0 A))) ) ) ) ).
tt(t1_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) => (m1_subset_1 (k2_xcmplx_0 (k6_xcmplx_0 B A) 1) k5_numbers)) ) ) ) ) ).
tt(t1_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_tarski A (k2_finseq_1 B)) & (r2_hidden 1 A))  =>  ((k1_funct_1 (k14_finseq_1 A) 1) = 1) ) ) ) ) ).
tt(t1_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((r1_xxreal_0 D C) |  (B = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k17_finseq_1 A (k7_nat_d C 1) B) (k9_finseq_1 (k1_funct_1 B C))) (k17_finseq_1 A (k7_nat_d (k7_nat_d D C) 1) (k2_rfinseq A C B))) (k9_finseq_1 (k1_funct_1 B D))) (k2_rfinseq A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((k3_finseq_6 A (k1_finseq_8 A B C) 1 (k3_finseq_1 B)) = B) ) ) ) ) ) ) ) ).
tt(t1_finseqop,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k13_funct_3 k1_xboole_0 A) = k1_xboole_0)  &  ((k13_funct_3 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t1_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A B) & (v1_finset_1 B))  => (v1_finset_1 A)) ) ) ).
tt(t1_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (~  ( ((k8_nat_1 A D 1) = (k1_funct_1 B 1))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~  (k6_numbers = E) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) E))  &  (~  ((k8_nat_1 A D (k2_nat_1 E 1)) = (k1_binop_1 C (k8_nat_1 A D E) (k1_funct_1 B (k2_nat_1 E 1)))) ) ) ) ) ) )  &  ((k1_finsop_1 A B C) = (k8_nat_1 A D (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_finsub_1,ax, (! [A:$i] :  ((v4_finsub_1 A) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((r2_hidden (k2_xboole_0 B C) A) & (r2_hidden (k6_subset_1 B C) A)) ) ) ) ) ) ).
tt(t1_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k8_fin_topo A B) (k8_fin_topo A C))) ) ) ) ) ) ) ).
tt(t1_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) => (r1_tarski B (k12_fin_topo A B))) ) ) ) ) ).
tt(t1_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_tarski (k7_fintopo3 A B C) (k7_fintopo3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t1_fintopo5,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((v2_funct_1 C) =>  ((k7_relat_1 (k2_funct_1 C) (k7_relset_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t1_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fin_topo A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k9_fin_topo A B) (k9_fin_topo A C))) ) ) ) ) ) ) ).
tt(t1_fin_topo,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) | (r1_tarski (k7_partfun1 (k9_setfam_1 A) B C) (k7_partfun1 (k9_setfam_1 A) B (k2_nat_1 C 1)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 B))) )  => (r1_tarski (k7_partfun1 (k9_setfam_1 A) B C) (k7_partfun1 (k9_setfam_1 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t1_flang_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 C B)) )  & (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t1_flang_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 (k2_xcmplx_0 A B) C) &  ((r1_xxreal_0 C (k2_xcmplx_0 D B)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ((k2_xcmplx_0 E B) = C)  &  ((r1_xxreal_0 A E) & (r1_xxreal_0 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k8_flang_1 A C)) =>  ((r1_tarski (k6_flang_1 A (k8_flang_1 A C) B) (k8_flang_1 A C)) & (r1_tarski (k6_flang_1 A B (k8_flang_1 A C)) (k8_flang_1 A C))) ) ) ) ) ) ) ).
tt(t1_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_xboole_0 (k4_finseq_2 C A) (k3_finseq_2 B)) = (k3_xboole_0 (k4_finseq_2 C A) (k4_finseq_2 C B))) ) ) ) ) ).
tt(t1_fomodel1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  ( ((k8_subset_1 (k15_fomodel1 A) (k16_fomodel1 A) (k3_fomodel1 A)) = k1_xboole_0)  &  ( ((k3_xboole_0 (k5_fomodel1 A) (k6_fomodel1 A)) = (k3_fomodel1 A))  &  ( ((k6_subset_1 (k4_fomodel1 A) (k9_fomodel1 A)) = (k6_domain_1 (k17_fomodel1 A) (k18_fomodel1 A)))  &  ((r1_tarski (k9_fomodel1 A) (k17_fomodel1 A)) &  ((r1_tarski (k4_fomodel1 A) (k6_fomodel1 A)) &  ((r1_tarski (k3_fomodel1 A) (k5_fomodel1 A)) &  ((r1_tarski (k16_fomodel1 A) (k5_fomodel1 A)) &  ((r1_tarski (k5_fomodel1 A) (k9_fomodel1 A)) &  ((r1_tarski (k3_fomodel1 A) (k6_fomodel1 A)) & (r1_tarski (k6_fomodel1 A) (k17_fomodel1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v14_fomodel1 B k6_numbers A) & (m2_subset_1 B (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (B = (k12_finseq_1 (k15_fomodel1 A) (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) B))) ) ) ) ) ).
tt(t1_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) (k8_eqrel_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k8_eqrel_1 A B)) =>  ( (~ (r2_subset_1 C D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))))) =>  ( ((r1_tarski D E) & (v3_fomodel4 A C D B))  =>  ( ( (~ (v6_fomodel4 E C))  &  (~ (v6_fomodel4 D C)) )  | (v3_fomodel4 A C E B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_fraenkel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((r2_relset_1 A B (k2_partfun1 A B C E) (k2_partfun1 A B D E)) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) =>  ((k1_funct_1 C F) = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((v1_funct_1 (k2_valued_0 (u1_struct_0 A) C B)) &  ((v1_funct_2 (k2_valued_0 (u1_struct_0 A) C B) k5_numbers (u1_struct_0 A)) & (m1_subset_1 (k2_valued_0 (u1_struct_0 A) C B) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t1_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (m1_subset_1 (k2_relset_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(t1_freealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( ((k6_unialg_2 A) = k1_xboole_0)  &  (B = k1_xboole_0) ) )  =>  ((m1_freealg B A) <=>  ((k7_unialg_2 A B) = A) ) ) ) ) ) ) ).
tt(t1_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k4_fscirc_1 A B C)))) ) ) ).
tt(t1_fscirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  =>  ( ( ((k1_funct_1 C k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 D k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_msualg_1 G))  =>  (! [H:$i] :  ( ((v4_msualg_1 H G) & (l3_msualg_1 H G))  =>  (! [I:$i] :  ( ( (G = (k1_funct_1 C F))  &  ( (H = (k1_funct_1 D F))  &  (I = (k1_funct_1 E F)) ) )  =>  ( ((k1_funct_1 C (k1_nat_1 F 1)) = (k2_circcomb G (k8_fscirc_1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ( ((k1_funct_1 D (k1_nat_1 F 1)) = (k3_circcomb G (k8_fscirc_1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I) H (k9_fscirc_1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ((k1_funct_1 E (k1_nat_1 F 1)) = (k6_fscirc_1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((k1_fscirc_2 F A B) = (k1_funct_1 C F))  &  ( ((k2_fscirc_2 F A B) = (k1_funct_1 D F))  &  ((k3_fscirc_2 F A B) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k2_fsm_1 A B C (k6_finseq_1 A)) = (k12_finseq_1 (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(t1_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_fsm_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k2_fsm_1 A C D (k12_finseq_1 A B)) = (k2_finseq_4 (u1_struct_0 C) D (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) A) (u1_struct_0 C) (u1_fsm_1 A C) (k1_domain_1 (u1_struct_0 C) A D B)))) ) ) ) ) ) ) ) ) ).
tt(t1_fsm_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 B C) A) => (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t1_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_msafree2 (k1_ftacell1 A B C D E)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k12_gfacirc1 A B C)) (k2_enumset1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k9_gfacirc1 A B C))) (k2_tarski (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp) (k12_gfacirc1 (k12_gfacirc1 A B C) E D))) (k2_enumset1 (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp) (k4_tarski (k10_finseq_1 E D) k2_twoscomp) (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp) (k9_gfacirc1 (k12_gfacirc1 A B C) E D)))) ) ) ) ) ) ).
tt(t1_funcop_1,ax, (! [A:$i] :  ((k12_funct_3 A) = (k13_funct_3 (k6_partfun1 A) (k6_partfun1 A))) ) ).
tt(t1_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  ((r2_funct_2 A k1_numbers B (k1_funcsdom A k1_numbers (k5_funcsdom A) C D)) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k1_numbers B E) = (k7_real_1 (k3_funct_2 A k1_numbers C E) (k3_funct_2 A k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) C) <=>  ((r2_hidden A (k9_xtuple_0 C)) &  (B = (k1_funct_1 C A)) ) ) ) ) ) ) ).
tt(t1_funct_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_funct_1 A) &  ((v1_funct_2 A (k9_xtuple_0 A) (k10_xtuple_0 A)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 A) (k10_xtuple_0 A))))) ) ) ) ).
tt(t1_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  ((k4_relat_1 A) = (k5_relat_1 (k4_relat_1 B) A)) ) ) ) ).
tt(t1_funct_4,ax, (! [A:$i] :  (~  ( (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (~  (B = (k4_tarski C D)) ) ) ) ) ) )  &  (! [B:$i] :  (! [C:$i] :  (~ (r1_tarski A (k2_zfmisc_1 B C))) ) ) ) ) ) ).
tt(t1_funct_5,ax, ((k2_funct_4 k1_xboole_0) = k1_xboole_0) ).
tt(t1_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k4_card_3 A) (k1_funct_2 (k9_xtuple_0 A) (k3_card_3 A)))) ) ).
tt(t1_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_tarski (k10_xtuple_0 A) B) =>  ((k3_relat_1 A (k6_partfun1 B)) = A) ) ) ) ) ).
tt(t1_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 A k1_numbers k1_numbers B) <=>  ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k2_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 B (k1_real_1 C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t1_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ((v1_funct_9 B A) <=>  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((r2_hidden (k2_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((r2_hidden (k6_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B (k2_xcmplx_0 C A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_functor0,ax, (! [A:$i] :  ((v1_funct_1 k1_xboole_0) &  ((v1_funct_2 k1_xboole_0 A k1_xboole_0) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (k2_zfmisc_1 A k1_xboole_0)))) ) ) ).
tt(t1_functor1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (C = D)  => (r1_funct_2 C A D A (k6_funct_3 A C) (k1_partfun1 D B B A (k6_funct_3 B D) (k6_funct_3 A B)))) ) ) ) ) ) ) ) ) ).
tt(t1_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_functor0 A B C D D (k8_altcat_1 A D)) = (k8_altcat_1 B (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t1_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A B C)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A B E)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A E D)) =>  ( ( ((k5_altcat_1 A B C D F G) = (k5_altcat_1 A B E D H I))  &  ( ((k5_altcat_1 A C B C (k1_altcat_3 A B C F) F) = (k8_altcat_1 A C))  &  ((k5_altcat_1 A E D E I (k1_altcat_3 A E D I)) = (k8_altcat_1 A E)) ) )  =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C B) = k1_xboole_0)  |  ( ((k1_altcat_1 A C D) = k1_xboole_0)  |  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  |  ((k5_altcat_1 A C B E (k1_altcat_3 A B C F) H) = (k5_altcat_1 A C D E G (k1_altcat_3 A E D I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v5_relat_1 (k7_rfunct_1 A A) (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 (k7_rfunct_1 A A)) &  ((v1_funct_2 (k7_rfunct_1 A A) A k1_numbers) & (m1_subset_1 (k7_rfunct_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) ) ) ) ).
tt(t1_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 C B)) & (r1_xxreal_0 (k1_seq_1 C B) 1)) ) ) ) ) ) ) ).
tt(t1_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((v5_xxreal_2 (k2_relset_1 k1_numbers B)) &  ( (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 (k1_seq_1 B C) (k4_seq_4 (k2_relset_1 k1_numbers B)))) )  &  (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 (k5_seq_4 (k2_relset_1 k1_numbers B)) (k1_seq_1 B C))) ) ) ) ) ) ) ) ).
tt(t1_fvaluat1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( (A = (k2_xxreal_3 A))  =>  (A = k6_numbers) ) ) ) ).
tt(t1_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) )  => (v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A))) ) ).
tt(t1_gate_1,ax, ( ((k1_gate_1 (k1_tarski k1_xboole_0)) = k1_xboole_0)  &  ((k1_gate_1 k1_xboole_0) = (k1_tarski k1_xboole_0)) ) ).
tt(t1_gate_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k8_gate_1 S R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R Q)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T))))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k8_gate_1 V U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U T)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k1_gate_1 Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k1_gate_1 Q)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 (k4_gate_1 Q R))) )  &  ( (~  ( (~ (v1_xboole_0 (k4_gate_1 Q R)))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 (k3_gate_1 (k2_gate_1 S (k1_gate_1 Q)) (k2_gate_1 Q (k4_gate_1 R S))))) )  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 (k2_gate_1 S (k1_gate_1 Q)) (k2_gate_1 Q (k4_gate_1 R S)))))  & (v1_xboole_0 V)) )  &  (~  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 H)) )  &  (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gate_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) (k1_gate_1 I)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) (k1_gate_1 I))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) I))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) I)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k2_gate_1 J (k1_gate_1 I)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 J (k1_gate_1 I))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k2_gate_1 J I))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 J I)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) (k1_gate_1 K)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) (k1_gate_1 K))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) K))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) K)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k2_gate_1 L (k1_gate_1 K)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 L (k1_gate_1 K))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k2_gate_1 L K))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 L K)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k1_gate_1 J))) )  &  ( (~  ( (~ (v1_xboole_0 (k1_gate_1 J)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 L)) )  &  (~  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 C)) )  &  (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (~  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k2_gate_1 A C))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A C)))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 B C) (k2_gate_1 A D) k1_xboole_0)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) k1_xboole_0 K))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) k1_xboole_0 K)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) k1_xboole_0 K))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) k1_xboole_0 K)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 H)) )  &  (~  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k1_gate_5 A B C D))) )  &  ( (~  ( (~ (v1_xboole_0 (k1_gate_5 A B C D)))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k2_gate_5 A B C D))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_5 A B C D)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k3_gate_5 A B C D))) )  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_5 A B C D)))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k4_gate_5 A B C D))) )  &  (~  ( (~ (v1_xboole_0 (k4_gate_5 A B C D)))  & (v1_xboole_0 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ( ((k8_group_1 A B C) = (k8_group_1 A B D))  =>  (C = D) )  &  ( ((k8_group_1 A C B) = (k8_group_1 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_genealg1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D (k3_finseq_1 B)) =>  ((k2_rfinseq A D (k8_finseq_1 A B C)) = (k8_finseq_1 A (k2_rfinseq A D B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t1_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v7_struct_0 (k2_analoaf A)))  &  ((v2_analoaf (k2_analoaf A)) & (l1_analoaf (k2_analoaf A))) ) ) ) ) ) ) ) ) ).
tt(t1_gfacirc1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  ( ((k1_funct_1 k1_gfacirc1 (k10_binarith k6_margrel1 A)) = (k9_margrel1 A))  &  ( ((k1_funct_1 k1_gfacirc1 (k10_binarith k6_margrel1 A)) = (k1_funct_1 k5_twoscomp (k10_finseq_1 A A)))  &  ( ((k1_funct_1 k1_gfacirc1 (k10_binarith k5_numbers k6_numbers)) = 1)  &  ((k1_funct_1 k1_gfacirc1 (k10_binarith k5_numbers 1)) = k6_numbers) ) ) ) ) ) ).
tt(t1_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) )  =>  ( ( ((k1_funct_1 C k6_numbers) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 D k6_numbers) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k1_funct_1 E k6_numbers) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_msualg_1 G))  =>  (! [H:$i] :  ( ((v4_msualg_1 H G) & (l3_msualg_1 H G))  =>  (! [I:$i] :  ( ( (G = (k1_funct_1 C F))  &  ( (H = (k1_funct_1 D F))  &  (I = (k1_funct_1 E F)) ) )  =>  ( ((k1_funct_1 C (k1_nat_1 F 1)) = (k2_circcomb G (k13_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ( ((k1_funct_1 D (k1_nat_1 F 1)) = (k3_circcomb G (k13_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I) H (k14_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)))  &  ((k1_funct_1 E (k1_nat_1 F 1)) = (k9_gfacirc1 (k1_funct_1 A (k1_nat_1 F 1)) (k1_funct_1 B (k1_nat_1 F 1)) I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((k1_gfacirc2 F A B) = (k1_funct_1 C F))  &  ( ((k2_gfacirc2 F A B) = (k1_funct_1 D F))  &  ((k3_gfacirc2 F A B) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_glib_000,ax, ( (k1_glib_000 = 1)  &  ( (k2_glib_000 = 2)  &  ( (k3_glib_000 = 3)  &  (k4_glib_000 = 4) ) ) ) ).
tt(t1_glib_001,ax, (! [A:$i] :  ( ( (~ (v1_abian A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_abian B))  & (m1_subset_1 B k5_numbers))  =>  ( (~ (r1_xxreal_0 B A))  <=> (r1_xxreal_0 (k2_nat_1 A 2) B)) ) ) ) ) ).
tt(t1_glib_003,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v1_funct_1 K) & (v1_finseq_1 K)) )  =>  ( (K = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B)) (k9_finseq_1 C)) (k9_finseq_1 D)) (k9_finseq_1 E)) (k9_finseq_1 F)) (k9_finseq_1 G)) (k9_finseq_1 H)) (k9_finseq_1 I)) (k9_finseq_1 J)))  =>  ( ((k3_finseq_1 K) = 10)  &  ( ((k1_funct_1 K 1) = A)  &  ( ((k1_funct_1 K 2) = B)  &  ( ((k1_funct_1 K 3) = C)  &  ( ((k1_funct_1 K 4) = D)  &  ( ((k1_funct_1 K 5) = E)  &  ( ((k1_funct_1 K 6) = F)  &  ( ((k1_funct_1 K 7) = G)  &  ( ((k1_funct_1 K 8) = H)  &  ( ((k1_funct_1 K 9) = I)  &  ((k1_funct_1 K 10) = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k13_pre_poly (k1_funct_4 A B)) (k2_xboole_0 (k13_pre_poly A) (k13_pre_poly B)))) ) ) ) ).
tt(t1_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ((v3_glib_001 C A) => (r5_glib_005 A B C)) ) ) ) ) ) ) ).
tt(t1_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r1_xxreal_0 2 (k3_finseq_1 A)))  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t1_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A))) ) )  =>  ((r1_xxreal_0 C (k2_nat_1 B 1)) | (r1_xboole_0 (k2_topreal1 2 A B) (k2_topreal1 2 A C))) ) ) ) ) )  => (v3_topreal1 A)) ) ) ).
tt(t1_goboard3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) )  &  ((v2_funct_1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((v1_topreal1 A) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v2_funct_1 C) &  ((v2_topreal1 C) &  ((v3_topreal1 C) &  ((v1_topreal1 C) &  ( ((k3_topreal1 2 A) = (k3_topreal1 2 C))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)))  & (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_goboard4,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) & (r1_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C))) ) ) )  =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B A)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 A))) ) ) ) ) ) ) ) ).
tt(t1_goboard6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r2_hidden B (k9_metric_1 A B C))) ) ) ) ) ) ) ).
tt(t1_goboard7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A B)) C))  &  ((r1_xxreal_0 B (k7_real_1 A C)) & (r1_xxreal_0 A (k7_real_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t1_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_goboard9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r3_connsp_1 A D B) &  ((r3_connsp_1 A D C) &  ( (~  (B = C) )  &  (~ (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_gobrd10 A B) => (r1_gobrd10 (k2_nat_1 A 1) (k2_nat_1 B 1))) ) ) ) ) ).
tt(t1_gobrd11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (v2_connsp_1 B A))  => (r1_tarski B (k1_connsp_1 A C))) ) ) ) ) ) ) ).
tt(t1_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))))  => (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) ) ) ) ) ) ) ).
tt(t1_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  (~  ( (C = (k16_euclid 2))  &  ((r2_jordan2c 2 (k3_topreal1 2 A) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k3_subset_1 (u1_struct_0 (k14_euclid 2)) (k9_metric_1 (k14_euclid 2) C D)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( ((v1_henmodel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))))  =>  ((v1_goedelcp C A) =>  ((r1_henmodel A C B) <=>  (~ (r1_henmodel A C (k6_cqc_lang A B))) ) ) ) ) ) ) ) ) ).
tt(t1_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ( ((k1_relset_1 (u4_struct_0 A) (u1_graph_1 A)) = (u4_struct_0 A))  &  ((k1_relset_1 (u4_struct_0 A) (u2_graph_1 A)) = (u4_struct_0 A)) ) ) ) ).
tt(t1_graph_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 (k1_nat_1 A 1) B) & (r1_xxreal_0 B C))  <=>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 A D) &  ( (~ (r1_xxreal_0 C D))  &  (B = (k2_nat_1 D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_graph_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((v1_abian A) <=> (v1_abian B))  <=> (v1_abian (k6_xcmplx_0 A B))) ) ) ) ) ).
tt(t1_graph_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_graph_4 B C D A) => (r2_graph_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t1_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((r1_tarski (k10_xtuple_0 B) (k10_xtuple_0 C)) &  ((r2_hidden A (k9_xtuple_0 B)) &  (! [D:$i] :  (~  ((r2_hidden D (k9_xtuple_0 C)) &  ((k1_funct_1 B A) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_graphsp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ( (~ (r2_hidden B (k10_xtuple_0 A)))  & (v2_funct_1 A))  <=> (v2_funct_1 (k7_finseq_1 A (k9_finseq_1 B)))) ) ) ) ).
tt(t1_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k3_xtuple_0 B C D) A) & (r2_hidden (k6_xtuple_0 B C D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gr_cy_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  ( (A = k6_numbers)  => (r3_binop_1 k4_numbers A k44_binop_2)) ) ) ).
tt(t1_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k6_group_1 A B) 1))  &  ( (B = (k5_group_1 A D C))  &  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_nat_d C (k3_xcmplx_0 A B)) &  ( (~  (C = 1) )  &  ( (~  (C = A) )  &  ( (~  (C = B) )  &  (~  (C = (k3_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_tarski B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) ) ) ) ).
tt(t1_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_3 A B C) = (k6_algstr_0 A B (k2_group_5 A B C))) ) ) ) ) ) ) ).
tt(t1_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r4_polyred A B C D E F) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  (F = (k6_polynom1 A C D (k9_polynom1 A C G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((r1_xxreal_0 D C) |  ((k1_funct_1 B D) = (k4_struct_0 A)) ) ) ) )  =>  ((k4_rlvect_1 A B) = (k4_rlvect_1 A (k17_finseq_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ).
tt(t1_groeb_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((k1_groeb_2 A (k11_pre_poly A B C) C) = B) ) ) ) ) ) ).
tt(t1_group_10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~  ((r1_ordinal1 (k5_card_1 A) (k1_card_1 B)) & (v1_xboole_0 (k3_group_10 B A))) ) ) ) ) ) ).
tt(t1_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_2 A (k13_group_2 A B C) (k13_group_2 A B D)) = (k13_group_2 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t1_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_group_7 A B C))) =>  ( ( ((k9_xtuple_0 D) = A)  &  ( ((k1_funct_1 D C) = E)  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~  (F = C) )  =>  ((k1_funct_1 D F) = (k1_group_1 (k1_group_7 A B F))) ) ) ) ) )  <=>  (D = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = C)  &  ( ((k6_algstr_0 A B C) = C)  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( ((k6_algstr_0 A C D) = B)  &  ((k6_algstr_0 A D C) = B) ) ) ) ) ) ) ) ) ) )  |  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) ) ) ) ).
tt(t1_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v8_struct_0 A) => (v1_finset_1 B)) ) ) ) ) ).
tt(t1_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k6_algstr_0 A B C) (k2_group_1 A C)) = B)  &  ( ((k6_algstr_0 A (k6_algstr_0 A B (k2_group_1 A C)) C) = B)  &  ( ((k6_algstr_0 A (k6_algstr_0 A (k2_group_1 A C) C) B) = B)  &  ( ((k6_algstr_0 A (k6_algstr_0 A C (k2_group_1 A C)) B) = B)  &  ( ((k6_algstr_0 A B (k6_algstr_0 A C (k2_group_1 A C))) = B)  &  ( ((k6_algstr_0 A B (k6_algstr_0 A (k2_group_1 A C) C)) = B)  &  ( ((k6_algstr_0 A (k2_group_1 A C) (k6_algstr_0 A C B)) = B)  &  ((k6_algstr_0 A C (k6_algstr_0 A (k2_group_1 A C) B)) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (C = E)  =>  ((k5_group_1 B A C) = (k5_group_1 D A E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((r1_struct_0 (k6_group_2 B) A) <=>  (A = (k1_group_1 B)) ) ) ) ) ).
tt(t1_group_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k3_funct_2 A B C D) = (k3_funct_2 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) & (v1_group_7 F)) ) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l3_algstr_0 G))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_group_7 A F))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_group_7 A F))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 G)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 G)) =>  ( ((r2_hidden B A) &  ( (G = (k1_funct_1 F B))  &  ( (C = H)  &  ( (D = I)  &  ( (E = (k6_algstr_0 (k2_group_7 A F) H I))  &  ( ((k1_funct_1 C B) = J)  &  ((k1_funct_1 D B) = K) ) ) ) ) ) )  =>  ((k6_algstr_0 G J K) = (k1_funct_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  (~  ((v1_int_2 A) &  ( ((k7_group_1 B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ((k6_group_1 B C) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ((m1_group_9 D A C) =>  ((r1_struct_0 D B) => (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t1_groupp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k1_newton B C)) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((v1_int_2 C) &  ((r1_int_1 C A) &  (~  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( ((v1_group_3 C D) & (m1_group_6 C A D))  =>  ((v1_group_3 (k10_group_2 A C B) (k10_group_2 A D B)) & (m1_group_6 (k10_group_2 A C B) A (k10_group_2 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t1_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 (k1_rlsub_2 A B C)))) ) ) ) ) ) ).
tt(t1_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((k2_nat_1 (k5_card_1 (k2_xboole_0 A B)) (k5_card_1 (k3_xboole_0 A B))) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t1_hausdorf,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((k4_xxreal_0 A B) = k6_numbers) )  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t1_heine,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_topmetr C k8_metric_1) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( ( (A = D)  &  (B = E) )  =>  ((k4_metric_1 C D E) = (k18_complex1 (k6_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_helly,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  ((k3_graph_2 (k9_finseq_1 (k1_funct_1 A 1)) A) = A) ) ) ).
tt(t1_henmodel,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( ((k2_relset_1 B C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden E (k1_relset_1 A C)) & (r2_hidden D (k1_relset_1 A C)))  =>  ((r1_xxreal_0 E D) | (r2_hidden (k1_funct_1 C D) (k1_funct_1 C E))) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((k4_card_1 D) = A) ) ) )  |  ((k1_funct_1 C (k3_tarski A)) = (k3_tarski (k2_relset_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t1_hermitan,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (A = (k15_complex1 A))  =>  ((k4_complex1 A) = k6_numbers) ) ) ) ).
tt(t1_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C D) =>  ((r1_collsp A C D B) &  ((r1_collsp A D B C) &  ((r1_collsp A C B D) &  ((r1_collsp A B D C) & (r1_collsp A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_heyting1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E A) => (r2_hidden (k3_funct_2 A B D E) C)) )  =>  ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_substlat A B)) & (r2_hidden C D))  =>  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(t1_heyting3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  =>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) & (r1_tarski A (k1_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 B) (k6_domain_1 k5_numbers k6_numbers)))) ) ) ) ).
tt(t1_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_relset_1 k1_numbers (k5_relset_1 k1_numbers k1_numbers B A)) = A) ) ) ) ) ).
tt(t1_hilbasis,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((r1_tarski (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k9_xtuple_0 C)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ( (D = (k3_relat_1 A C))  &  ( (E = (k3_relat_1 B C))  &  ((k3_relat_1 (k7_finseq_1 A B) C) = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) => (r2_hidden k2_hilbert1 (k5_hilbert1 A))) ) ).
tt(t1_hilbert2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ( (! [C:$i] :  ((r2_hidden C A) =>  ((v1_relat_1 (k1_funct_1 B C)) &  ((v4_relat_1 (k1_funct_1 B C) C) &  ((v1_funct_1 (k1_funct_1 B C)) & (v1_partfun1 (k1_funct_1 B C) C)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (C = (k3_card_3 B))  =>  ((k9_xtuple_0 C) = (k3_tarski A)) ) ) ) ) ) ) ) ).
tt(t1_hilbert3,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) <=>  (~ (v1_abian (k6_xcmplx_0 A 1))) ) ) ) ).
tt(t1_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r1_xxreal_0 k6_numbers C) &  (~  ((k8_real_1 (k4_power C A) (k4_power C B)) = (k4_power C (k7_real_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C E) &  ((r1_aff_1 A B C F) &  ((r1_aff_1 A B C G) &  ((r1_aff_1 A B D H) &  ((r1_aff_1 A B D I) &  ((r1_aff_1 A B D J) &  ((r2_analoaf A C D E H) &  ((r2_analoaf A C I E J) &  ((r2_analoaf A F D G H) & (v4_aff_2 A)) ) ) ) ) ) ) ) )  =>  ((r1_aff_1 A B C D) |  ( (D = I)  |  ( (B = I)  |  ( (B = F)  | (r2_analoaf A F I G J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k4_algstr_0 A (k11_algstr_0 A B)) = (k11_algstr_0 A (k4_algstr_0 A B))) ) ) ) ) ) ).
tt(t1_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((v1_int_2 B) &  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  &  ( (~  (A = k6_numbers) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( ((k4_nat_d (k4_nat_1 D A) B) = C)  &  (~ (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k1_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t1_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_incproj B A) <=> (m1_subset_1 B (k1_incproj A))) ) ) ) ).
tt(t1_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C D) B) <=>  ((r1_incsp_1 A C B) & (r1_incsp_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A B))  =>  ((k1_cat_1 A B C) = (k4_tarski (k9_cat_2 A A (k3_graph_1 A B) (k4_graph_1 A C)) (k1_partfun1 (u4_struct_0 (k5_cat_5 A B)) (u4_struct_0 (k6_cat_5 A B)) (u4_struct_0 (k5_cat_5 A C)) (u4_struct_0 (k6_cat_5 A C)) (k1_index_1 A B) (k1_index_1 A C)))) ) ) ) ) ) ) ) ).
tt(t1_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_msaterm D A C (k2_msaterm A C B)) <=> (m1_subset_1 D (k3_msualg_1 A B (k11_msafree A C)))) ) ) ) ) ) ) ) ).
tt(t1_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (A = B)  |  (A = (k4_xcmplx_0 B)) )  => (v1_int_1 A)) ) ) ) ) ).
tt(t1_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A (k2_xcmplx_0 B C)))  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(t1_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  ((k3_funct_2 (u1_struct_0 k1_int_3) k5_numbers k3_int_3 A) = (k2_int_3 A)) ) ) ).
tt(t1_int_4,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r2_tarski A (k2_measure6 A B))) ) ) ) ).
tt(t1_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A C))  => (r1_int_1 A (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t1_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k3_finseq_1 (k1_valued_1 A B)) = (k6_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t1_int_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((k13_pre_poly C) = (k1_tarski B))  => (r6_pboole A C (k2_funct_7 (k8_funcop_1 k5_numbers A k6_numbers) B (k1_funct_1 C B)))) ) ) ) ) ).
tt(t1_integr10,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  ( (~ (r1_xxreal_0 B E))  &  (~ (r1_xxreal_0 C (k8_real_1 (k5_real_1 B E) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_integr11,ax, ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) k1_numbers) A) = (k5_square_1 (k1_seq_1 k16_sin_cos A))) ) ) ) ).
tt(t1_integr12,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 A D) = 1) ) ) )  & (r2_relset_1 k1_numbers k1_numbers B (k1_taylor_1 2))) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) C) D) = (k7_binop_2 (k12_binop_2 (k11_binop_2 2 D) (k5_square_1 (k9_binop_2 1 (k2_newton D 2)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t1_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9)) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos (k10_real_1 1 B)) (k8_real_1 (k5_square_1 B) (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 B)))))) ) ) ) ) ) ) ) ).
tt(t1_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr15 D A B C) =>  ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) => (r1_xxreal_0 (k7_integra1 A B C) (k1_integr15 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t1_integr16,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k3_complex1 (k5_binop_2 B A)) = (k11_binop_2 B (k3_complex1 A)))  &  ((k4_complex1 (k5_binop_2 B A)) = (k11_binop_2 B (k4_complex1 A))) ) ) ) ) ) ).
tt(t1_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (D = (k1_binom A B C)) )  =>  ((k4_rlvect_1 A D) = (k3_rlvect_1 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((r2_hidden B (k3_integra5 A C)) &  ((r1_tarski (k3_integra5 A B) (k3_integra5 A C)) & (r1_tarski (k3_integra5 B C) (k3_integra5 A C))) ) ) ) ) ) ) ) ) ).
tt(t1_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_integr1c C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers C) (k1_relset_1 k2_numbers A)) &  ((r1_tarski (k2_relset_1 k2_numbers C) (k1_relset_1 k2_numbers B)) &  ((r1_integr1c A C) &  ((r1_integr1c B C) &  ((r2_integr1c A C) & (r2_integr1c B C)) ) ) ) )  =>  ((k3_integr1c (k2_valued_1 k2_numbers k2_numbers k2_numbers A B) C) = (k2_xcmplx_0 (k3_integr1c A C) (k3_integr1c B C))) ) ) ) ) ) ) ) ).
tt(t1_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B A) <=>  ((r1_xxreal_0 (k5_seq_4 A) B) & (r1_xxreal_0 B (k4_seq_4 A))) ) ) ) ) ) ).
tt(t1_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ((r1_integra1 B C) => (r1_xxreal_0 (k1_integra3 A C) (k1_integra3 A B))) ) ) ) ) ) ) ).
tt(t1_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ( ((k3_integra1 A) = k6_numbers)  =>  ((k3_finseq_1 B) = 1) ) ) ) ) ) ).
tt(t1_integra5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( ( (B = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers D) A))  |  (B = (k8_finseq_1 k1_numbers A (k12_finseq_1 k1_numbers D))) )  &  ( ( (C = (k8_finseq_1 k1_numbers (k12_finseq_1 k1_numbers E) A))  |  (C = (k8_finseq_1 k1_numbers A (k12_finseq_1 k1_numbers E))) )  &  (~  ((k18_rvsum_1 (k8_rvsum_1 B C)) = (k9_real_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((k2_xcmplx_0 A C) = (k2_xcmplx_0 B D)) ) )  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v4_xxreal_2 (k1_rvsum_1 C)) &  ((v4_xxreal_2 (k1_rvsum_1 D)) &  (! [E:$i] :  ((r2_hidden E B) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 C E) (k1_seq_1 D E))) A)) ) ) )  =>  ((r1_xxreal_0 (k9_real_1 (k4_seq_4 (k1_rvsum_1 C)) (k4_seq_4 (k1_rvsum_1 D))) A) & (r1_xxreal_0 (k9_real_1 (k4_seq_4 (k1_rvsum_1 D)) (k4_seq_4 (k1_rvsum_1 C))) A)) ) ) ) ) ) ) ) ) ) ).
tt(t1_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k18_sin_cos (k7_real_1 A (k8_real_1 (k4_nat_1 2 B) k32_sin_cos))) = (k18_sin_cos A)) ) ) ) ) ).
tt(t1_integra9,ax, ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 1) k6_numbers) k24_sin_cos)) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k1_real_1 1) k6_numbers) k24_sin_cos)) k1_numbers) A) = (k26_sin_cos (k1_real_1 A))) ) ) ) ).
tt(t1_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((r2_hidden D (k1_interva1 A B C)) <=>  ((r1_tarski B D) & (r1_tarski D C)) ) ) ) ) ) ) ) ).
tt(t1_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 B (k3_intpro_1 C B)) (k7_intpro_1 A))) ) ) ) ) ) ).
tt(t1_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((v1_int_2 A) & (v1_rat_1 (k7_square_1 A))) ) ) ) ).
tt(t1_isocat_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) )  => (r2_funct_2 A (k9_funct_2 B C) (k11_funct_5 A B C (k1_isocat_2 A B C D)) D)) ) ) ) ) ) ) ) ).
tt(t1_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))) (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A C)))) = (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))))) ) ) ) ) ) ) ).
tt(t1_jct_misc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r2_hidden A (k1_rcomp_1 C D)) & (r2_hidden B (k1_rcomp_1 C D)))  => (r2_hidden (k6_real_1 (k2_xcmplx_0 A B) 2) (k1_rcomp_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v1_graph_4 B A) & (r3_graph_4 A C B))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) )  =>  ((r1_xxreal_0 E D) |  ( (D = 1)  &  (E = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 D))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 D))) =>  (~  ((m1_pre_topc A D) &  ((m1_pre_topc C D) &  ( (G = (k2_struct_0 A))  &  ( (H = (k2_struct_0 C))  &  ( ((k2_xboole_0 (k2_struct_0 A) (k2_struct_0 C)) = (k2_struct_0 D))  &  ((v4_pre_topc G D) &  ((v4_pre_topc H D) &  ((v5_pre_topc E A B) &  ((v5_pre_topc F C B) &  ( (! [I:$i] :  ((r2_hidden I (k9_subset_1 (u1_struct_0 C) (k2_struct_0 A) (k2_struct_0 C))) =>  ((k1_funct_1 E I) = (k1_funct_1 F I)) ) )  &  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  (~  ( (I = (k1_funct_4 E F))  & (v5_pre_topc I D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k12_euclid A) = (k7_square_1 (k7_real_1 (k5_square_1 (k17_euclid A)) (k5_square_1 (k18_euclid A)))))  &  ((k5_square_1 (k12_euclid A)) = (k7_real_1 (k5_square_1 (k17_euclid A)) (k5_square_1 (k18_euclid A)))) ) ) ) ).
tt(t1_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((v5_pre_topc B A k3_topmetr) &  (C = (a_3_0_jgraph_4 A B D)) )  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k12_euclid A) 1) =>  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) 1)) ) ) ) ) ) ).
tt(t1_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 B C) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) (k19_euclid A B) (k19_euclid A C))))  =>  ( ((k17_euclid D) = A)  &  ((r1_xxreal_0 B (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k18_euclid D) = C)  &  ((r1_xxreal_0 A (k17_euclid D)) & (r1_xxreal_0 (k17_euclid D) B)) )  =>  ((r1_xxreal_0 B A) | (r2_hidden D (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_jgraph_8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C k17_borsuk_1 (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)))))) ) )  =>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  ( ((k1_seq_1 D 1) = k6_numbers)  &  ( ((k1_seq_1 D (k3_finseq_1 D)) = 1)  &  ((r1_xxreal_0 5 (k3_finseq_1 D)) &  ((r1_tarski (k2_relset_1 k1_numbers D) (u1_struct_0 k17_borsuk_1)) &  ((v5_valued_0 D) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  ( (F = (k1_rcomp_1 (k7_partfun1 k1_numbers D E) (k7_partfun1 k1_numbers D (k2_nat_1 E 1))))  &  ( (G = (k7_relset_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid A)) C F))  & (r1_xxreal_0 B (k3_tbsp_1 (k14_euclid A) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v2_connsp_1 E (k15_euclid 2)) &  ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k1_jordan9 E B))) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k1_jordan8 E B))) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 (k1_jordan8 E B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C (k2_nat_1 D 1)))  & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E B)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xxreal_0 1 (k1_jordan11 A))) ) ).
tt(t1_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k7_nat_d A 1) k6_numbers)) ) ) ) ).
tt(t1_jordan14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((k1_jordan2c 2 (k3_topreal1 2 A)) = (k3_goboard9 A))  |  ((k1_jordan2c 2 (k3_topreal1 2 A)) = (k2_goboard9 A)) ) ) ) ).
tt(t1_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (~ (r1_xboole_0 A B))  & (r1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A) (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B))) ) ) ) ) ) ).
tt(t1_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k9_jordan6 A) = (k8_jordan6 A)) ) ) ) ).
tt(t1_jordan17,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r2_hidden B E) &  ((r1_topreal1 (k15_euclid A) C D E) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k1_pre_topc (k15_euclid A) E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k1_pre_topc (k15_euclid A) E)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((v3_tops_2 F k17_borsuk_1 (k1_pre_topc (k15_euclid A) E)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  ((k1_funct_1 F G) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan18,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_square_1 (k6_xcmplx_0 A B)) = (k3_square_1 (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t1_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  ( (A = k6_numbers)  | (r1_xxreal_0 (k10_real_1 (k2_nat_1 B 1) B) (k10_real_1 (k2_nat_1 A 1) A))) ) ) ) ) ) ).
tt(t1_jordan1a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~ (v1_abian (k3_finseq_1 A)))  =>  ((k3_finseq_1 A) = (k9_real_1 (k4_nat_1 2 (k1_jordan1a A)) 1)) ) ) ) ).
tt(t1_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k17_borsuk_1) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 A))))) )  &  ((v5_pre_topc D k17_borsuk_1 A) &  ( (B = (k1_funct_1 D k6_numbers))  &  (C = (k1_funct_1 D 1)) ) ) ) ) ) ) ) )  => (v1_connsp_1 A)) ) ) ).
tt(t1_jordan1b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_xboole_0 A) <=> (v1_xboole_0 (k3_finseq_5 A))) ) ) ).
tt(t1_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A D))) & (r2_hidden (k4_tarski (k3_real_1 B 1) C) (k2_matrix_1 (k1_jordan8 A D))))  =>  ((k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 2 1)) = (k9_real_1 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) (k3_real_1 B 1) C)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan1d,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r1_tarski D B) & (r1_tarski C (k3_tarski D))) ) ) ) ) )  => (r1_tarski (k3_tarski A) (k3_tarski B))) ) ) ).
tt(t1_jordan1e,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k10_xtuple_0 A)) => (r1_sprect_2 B (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A C))) ) ) ) ) ) ) ) ).
tt(t1_jordan1f,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A C)) (k3_topreal1 2 D)))  &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski A C) (k2_matrix_1 E)) &  ((r1_xxreal_0 B C) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 B F) &  ((r1_xxreal_0 F C) &  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A F)) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A C)) (k3_topreal1 2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan1g,ax, (! [A:$i] :  ( ((v1_zfmisc_1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  (! [B:$i] :  (~  (A = (k9_finseq_1 B)) ) ) ) ) ) ) ).
tt(t1_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = B) )  => (r2_hidden A (k2_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k2_tarski A B))))) ) ) ) ) ).
tt(t1_jordan1i,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan9 B A) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) 1)) ) ) ) ) ).
tt(t1_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 A)) &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C E)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan1k,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (? [E:$i] :  ((r2_hidden E A) &  (D = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r2_hidden D A))  =>  ((k5_jordan6 A B C D D) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (v9_rltopsp1 (k6_domain_1 (u1_struct_0 (k15_euclid A)) B) (k15_euclid A))) ) ) ) ).
tt(t1_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k1_jordan19 A) B) (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan9 A k6_numbers))))) ) ) ) ).
tt(t1_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (r1_xxreal_0 1 (k3_finseq_1 (k2_jordan3 A B)))) ) ) ) ) ).
tt(t1_jordan24,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) & (r1_jordan24 2 A B C)) ) ) ) ) ) ).
tt(t1_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr))))) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) C D) = (k7_partfun1 k1_numbers D A)) ) ) ) ) ) ) ) ) ).
tt(t1_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ((r1_xxreal_0 2 (k3_finseq_1 B)) =>  ((r2_hidden (k1_funct_1 B 1) (k3_topreal1 A B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) B 1) (k3_topreal1 A B)) &  ((r2_hidden (k1_funct_1 B (k3_finseq_1 B)) (k3_topreal1 A B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) B (k3_finseq_1 B)) (k3_topreal1 A B))) ) ) ) ) ) ) ) ).
tt(t1_jordan4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 (k2_xcmplx_0 B B) A))  &  ((k4_nat_d A B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t1_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_topreal1 (k15_euclid A) B C D) => (v2_compts_1 D (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t1_jordan5b,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_nat_d A 1))) ) ) ) ).
tt(t1_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r2_hidden E A) &  ( ((k1_funct_1 F G) = E)  &  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers H) &  ( (~ (r1_xxreal_0 G H))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((v3_tops_2 H k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 H k6_numbers) = C)  &  ( ((k1_funct_1 H 1) = D)  &  ( ((k1_funct_1 H I) = E)  &  ((r1_xxreal_0 k6_numbers I) & (r1_xxreal_0 I 1)) ) ) ) )  =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers J) &  ( (~ (r1_xxreal_0 I J))  & (r2_hidden (k1_funct_1 H J) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ((r1_xxreal_0 2 (k3_finseq_1 B)) => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) B (k3_finseq_1 B)) (k2_topreal1 A B (k7_nat_d (k3_finseq_1 B) 1)))) ) ) ) ) ).
tt(t1_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 A (k6_real_1 (k2_xcmplx_0 A B) 2)) & (r1_xxreal_0 (k6_real_1 (k2_xcmplx_0 A B) 2) B)) ) ) ) ) ) ).
tt(t1_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v1_topreal2 A) =>  ((r2_hidden (k18_pscomp_1 A) (k9_jordan6 A)) &  ((r2_hidden (k22_pscomp_1 A) (k9_jordan6 A)) &  ((r2_hidden (k18_pscomp_1 A) (k8_jordan6 A)) & (r2_hidden (k22_pscomp_1 A) (k8_jordan6 A))) ) ) ) ) ) ).
tt(t1_jordan8,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  => (r1_goboard1 A (k6_finseq_1 A) B)) ) ) ).
tt(t1_jordan9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((r3_connsp_1 A E C) &  ((r3_connsp_1 A E D) & (r1_tarski B E)) ) )  =>  ((r1_xboole_0 B C) |  ((r1_xboole_0 B D) |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_jordan_a,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v2_compts_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_rcomp_1 (k7_relset_1 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ).
tt(t1_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = C) )  &  ((k1_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) (k10_real_1 1 2)) = B) ) ) ) ) ) ) ) ) ).
tt(t1_knaster,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( (A = (k2_xboole_0 B C))  & (r1_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)))  =>  ((v2_funct_1 A) <=>  ((v2_funct_1 B) &  ((v2_funct_1 C) & (r1_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_kolmog01,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (~  ((r1_tarski B (k9_xtuple_0 A)) &  ( (~  (B = k1_xboole_0) )  &  ((k10_xtuple_0 (k5_relat_1 A B)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t1_kurato_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (r1_tarski (k4_funct_6 A) (k1_funct_1 A B))) ) ) ) ).
tt(t1_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))))) = (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) ) ) ) ) ).
tt(t1_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((v3_pre_topc (k9_metric_1 (k14_euclid A) B C) (k15_euclid A)) & (m1_subset_1 (k9_metric_1 (k14_euclid A) B C) (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) ) ) ) ) ) ) ).
tt(t1_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  ((k2_xboole_0 (k1_lang1 A) (k2_lang1 A)) = (u1_struct_0 A)) ) ) ).
tt(t1_laplace,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k3_finseq_1 (k2_finseq_3 B A)) = (k7_nat_d (k3_finseq_1 A) 1)) ) ) ) ) ) ).
tt(t1_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((u1_struct_0 (k10_group_2 A B C)) = (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ).
tt(t1_latsum_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden A (k2_xboole_0 C D)) &  ((r2_hidden B (k2_xboole_0 C D)) &  ( (~  ((r2_hidden A (k6_subset_1 C D)) & (r2_hidden B (k6_subset_1 C D))) )  &  ( (~  ((r2_hidden A D) & (r2_hidden B D)) )  &  ( (~  ((r2_hidden A (k6_subset_1 C D)) & (r2_hidden B D)) )  &  (~  ((r2_hidden A D) & (r2_hidden B (k6_subset_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lattice2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k9_xtuple_0 (k2_partfun1 A B D C)) = C) ) ) ) ) ) ) ) ).
tt(t1_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_lattice3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_lattice3 A))) =>  ( ((k1_lattices (k1_lattice3 A) B C) = (k2_xboole_0 B C))  &  ((k2_lattices (k1_lattice3 A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t1_lattice4,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (! [B:$i] :  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski B A) &  ((v6_ordinal1 B) &  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ((r2_hidden D B) => (r1_tarski D C)) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ( (~  (C = B) )  & (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lattice5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  ( (A = (k3_tarski (k10_xtuple_0 B)))  =>  ((k9_xtuple_0 A) = (k3_tarski (k10_xtuple_0 (k2_funct_6 B)))) ) ) ) ) ) ).
tt(t1_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v1_lattice6 A) <=> (v2_lattice6 (k1_lattice2 A))) ) ) ).
tt(t1_lattice7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (m1_lattice7 (k7_domain_1 (u1_struct_0 A) B C) A B C)) ) ) ) ) ) ) ).
tt(t1_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  => (r1_ordinal1 (k1_ordinal1 k1_xboole_0) (k7_lattice5 A B C))) ) ) ) ) ) ).
tt(t1_lexbfs,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  ((v2_funct_1 D) =>  ((k1_card_1 (a_4_0_lexbfs A B C D)) = (k2_nat_1 B 1)) ) ) ) ) ) ) ) ) ) ).
tt(t1_lfuzzy_0,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (? [B:$i] :  ( ((v1_orders_2 B) & (l1_orders_2 B))  &  ( ((u1_struct_0 B) = A)  & (v1_lfuzzy_0 B)) ) ) ) ) ).
tt(t1_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k7_lfuzzy_0 A B D) = (k7_lfuzzy_0 A C D)) ) )  => (r2_relset_1 A k1_numbers B C)) ) ) ) ) ) ) ).
tt(t1_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r1_fcont_1 A B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 B E))  &  ((r2_hidden E (k1_relset_1 k1_numbers A)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden F (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r1_limfunc3 A B)) ) ) ) ) ).
tt(t1_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 A) => (v2_seq_2 A))  &  ((v8_valued_0 A) => (v1_seq_2 A)) ) ) ) ).
tt(t1_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 B) &  ( (~ (r1_xxreal_0 (k2_seq_2 B) A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_xtuple_0 B) (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k10_prob_1 A))) | (r1_tarski (k10_xtuple_0 B) (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k3_limfunc1 A))))  => (r1_tarski (k10_xtuple_0 B) (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A)))) ) ) ) ) ) ) ).
tt(t1_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ((r1_tarski (k2_relset_1 k1_numbers C) (k8_subset_1 k1_numbers (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B A)) D)) =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B A))) &  ((r1_tarski (k2_relset_1 k1_numbers C) D) &  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) &  ((r1_tarski (k2_relset_1 k1_numbers C) (k8_subset_1 k1_numbers (k1_relset_1 k1_numbers B) D)) & (r1_tarski (k2_relset_1 k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers C B)) (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v1_lmod_5 D A B))  => (v1_lmod_5 C A B)) ) ) ) ) ) ) ) ) ).
tt(t1_lmod_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  ( (C = (g1_vectsp_1 B (u1_struct_0 D) (u1_algstr_0 D) (u2_struct_0 D) (u1_vectsp_1 B D)))  =>  ((r1_struct_0 C A) <=> (r1_struct_0 D A)) ) ) ) ) ) ) ) ) ).
tt(t1_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~ (v7_struct_0 A))  &  ((v1_lmod_5 C A B) & (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ) ).
tt(t1_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  ((r2_funct_2 A (u1_struct_0 B) E (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D)) <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A (u1_struct_0 B) E F) = (k1_algstr_0 B (k3_funct_2 A (u1_struct_0 B) C F) (k3_funct_2 A (u1_struct_0 B) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_lopban_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 C)) &  ((v13_vectsp_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v1_lopban_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_normsp_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_bhsp_4 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t1_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) &  ((v3_normsp_1 C A) &  ((k6_normsp_1 A (k3_normsp_1 A B C)) = (k4_struct_0 A)) ) )  =>  ((k6_normsp_1 A B) = (k6_normsp_1 A C)) ) ) ) ) ) ) ) ).
tt(t1_lopban_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v1_comseq_2 A) & (r1_xxreal_0 k6_numbers B))  =>  ((k6_rinfsup1 (k26_valued_1 k5_numbers k1_numbers A B)) = (k8_real_1 B (k6_rinfsup1 A))) ) ) ) ) ) ).
tt(t1_lopban_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 (k6_real_1 B (k7_real_1 1 C)) A))  &  (~ (r1_xxreal_0 B (k6_real_1 B (k7_real_1 1 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k1_lopclset A)) => (v3_pre_topc B A)) ) ) ) ) ).
tt(t1_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) <=>  ((v1_ideal_1 B A) & (v1_lpspace1 B A)) ) ) ) ) ) ).
tt(t1_lpspace2,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (v1_xreal_0 A))  =>  (! [B:$i] :  ( ((v2_xxreal_0 B) & (v1_xreal_0 B))  =>  (~  ( ((k7_real_1 (k10_real_1 1 A) (k10_real_1 1 B)) = 1)  & (r1_xxreal_0 A 1)) ) ) ) ) ) ).
tt(t1_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 (k4_power B C) (k4_power A C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_ltlaxio1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A (k4_xboolean B C)) (k6_xboolean A B)) = 1) ) ) ) ) ) ) ).
tt(t1_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A B D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t1_margrel1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_finseq_1 B) & (v2_card_3 B))  =>  ((r1_tarski A B) =>  ((v3_finseq_1 A) & (v2_card_3 A)) ) ) ) ) ).
tt(t1_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_mathmorp A (k2_mathmorp A B)) = B) ) ) ) ) ).
tt(t1_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ((k4_algstr_0 k2_vectsp_1 A) = (k1_real_1 B)) ) ) ) ) ) ).
tt(t1_matrix11,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_sgraph1 (k2_finseq_1 B))) <=>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden C (k2_finseq_1 B)) &  ((r2_hidden D (k2_finseq_1 B)) &  ( (~ (r1_xxreal_0 D C))  &  (A = (k2_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  ((k1_matrix_1 D) = (k1_matrix_1 E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D A B C) =>  ( ( (B = k6_numbers)  =>  (C = k6_numbers) )  <=>  ( ((k3_finseq_1 D) = B)  &  ((k1_matrix_1 D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) => (m2_finseq_2 B (u1_struct_0 A) (k4_finseq_2 (k3_finseq_1 B) (u1_struct_0 A)))) ) ) ) ).
tt(t1_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 C) = (k3_finseq_1 D))  =>  ((k4_matrix_3 A (k6_matrix_3 A C B) D) = (k6_matrix_3 A (k4_matrix_3 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k9_fvsum_1 A B (k1_group_1 A)) = B) ) ) ) ) ).
tt(t1_matrix17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v12_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) B B) =>  ( ((r2_hidden (k4_tarski C D) (k2_matrix_1 G)) &  ( ((k2_xcmplx_0 C D) = (k2_xcmplx_0 B 1))  &  ( (E = (k6_xcmplx_0 (k2_xcmplx_0 B 1) D))  &  ( (F = (k6_xcmplx_0 (k2_xcmplx_0 B 1) C))  & (v2_matrix17 G A B)) ) ) )  =>  ((k3_matrix_1 (u1_struct_0 A) G C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_matrix_1 (k9_finseq_1 (k12_finseq_1 A B)))) ) ) ) ).
tt(t1_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F E) =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k2_matrix_2 E C D F))) =>  ((k3_matrix_1 E (k2_matrix_2 E C D F) A B) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_matrix_3 C A B))) =>  ((k3_matrix_1 (u1_struct_0 C) (k1_matrix_3 C A B) D E) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k2_matrix_3 A (k2_matrix_3 A B)) = B) ) ) ) ) ).
tt(t1_matrix_5,ax, (1 = (k1_group_1 k1_complfld)) ).
tt(t1_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k4_matrix_3 A (k1_matrix_3 A (k3_finseq_1 B) (k3_finseq_1 B)) B) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ).
tt(t1_matrix_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) &  ((v3_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 2) (k2_finseq_1 2))))) ) )  =>  ( (A = (k10_finseq_1 1 2))  |  (A = (k10_finseq_1 2 1)) ) ) ) ).
tt(t1_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_matrix_8 (k12_matrix_1 B A) A B) & (v3_matrix_8 (k12_matrix_1 B A) A B)) ) ) ) ) ).
tt(t1_matrix_9,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (r2_hidden (k1_tarski A) (k5_finsub_1 B))) ) ) ).
tt(t1_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_matrix_1 C)) ) )  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 C)) <=>  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k8_finseq_1 (u1_struct_0 A) (k3_fvsum_1 A B C) (k3_fvsum_1 A D E)) = (k3_fvsum_1 A (k8_finseq_1 (u1_struct_0 A) B D) (k8_finseq_1 (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k13_matrix_3 A B (k2_matrixj2 B C A)) = (k5_finseq_2 (u1_struct_0 B) A C)) ) ) ) ) ) ) ).
tt(t1_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( (A = C)  &  (B = D) )  =>  ((k7_real_1 A B) = (k3_rlvect_1 k2_vectsp_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k4_rvsum_1 A B) = (k5_euclid (k3_finseq_1 A))) )  =>  ( (A = (k6_rvsum_1 B))  &  (B = (k6_rvsum_1 A)) ) ) ) ) ) ) ).
tt(t1_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (! [F:$i] :  ((m1_vectsp_4 F A E) =>  (! [G:$i] :  ((m1_vectsp_4 G A E) =>  ( ( (F = C)  &  (G = D) )  =>  ( ((k2_vectsp_5 A B C D) = (k2_vectsp_5 A E F G))  &  ((k1_vectsp_5 A B C D) = (k1_vectsp_5 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  =>  ((k3_finseq_1 (k2_finseq_3 (k1_nat_1 A 1) B)) = A) ) ) ) ) ) ).
tt(t1_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((r1_tarski C B) =>  ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t1_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ( ((k3_finseq_1 D) = C)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = B) ) ) ) )  <=>  (D = (k5_finseq_2 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ((k3_fvsum_1 k2_vectsp_1 (k1_matrtop1 A) (k1_matrtop1 B)) = (k4_rvsum_1 A B)) ) ) ) ) ).
tt(t1_matrtop2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((m1_vectsp_6 A k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B)) <=> (m1_rlvect_2 A (k15_euclid B))) ) ) ) ).
tt(t1_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ( ((k12_matrix_3 A B (k5_matrix_1 A (u1_struct_0 B) (k4_matrix11 A A (u1_struct_0 B) D (k5_matrix_1 A (u1_struct_0 B) (k4_matrix11 A A (u1_struct_0 B) D C))))) = (k12_matrix_3 A B C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) =>  ((k3_matrix_1 (u1_struct_0 B) (k5_matrix_1 A (u1_struct_0 B) (k4_matrix11 A A (u1_struct_0 B) D (k5_matrix_1 A (u1_struct_0 B) (k4_matrix11 A A (u1_struct_0 B) D C)))) E F) = (k3_matrix_1 (u1_struct_0 B) C (k1_seq_1 D E) (k1_seq_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_mazurulm,ax, ((v1_tops_1 k2_urysohn1 k5_topmetr) & (m1_subset_1 k2_urysohn1 (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ).
tt(t1_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A B (k1_mboolean A C)) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D B) <=> (r2_pboole A D C)) ) ) ) ) ) ) ) ) ).
tt(t1_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_tarski (k1_enumset1 A B k1_xboole_0)) = (k3_tarski (k2_tarski A B))) ) ) ).
tt(t1_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  => (v6_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C))) ) ) ) ) ) ) ).
tt(t1_measure3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 A) C) (k12_supinf_2 (k18_supinf_2 B) C))) )  => (r1_xxreal_0 (k19_supinf_2 A) (k19_supinf_2 B))) ) ) ) ) ).
tt(t1_measure4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B D F) = (k8_subset_1 A E (k8_nat_1 B C F))) ) )  =>  ((k3_tarski (k2_relset_1 B D)) = (k8_subset_1 A E (k3_tarski (k2_relset_1 B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_measure5,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ( (~ (v1_measure5 A))  &  ( (~ (v2_measure5 A))  &  ( (~ (v3_measure5 A))  &  (~ (v4_measure5 A)) ) ) ) ) ) ) ).
tt(t1_measure6,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_zfmisc_1 k5_numbers k5_numbers))))) )  &  ((v2_funct_1 A) &  ( ((k1_relset_1 k5_numbers A) = k5_numbers)  &  ((k11_funcop_1 k5_numbers k5_numbers k5_numbers A) = (k2_zfmisc_1 k5_numbers k5_numbers)) ) ) ) ) ).
tt(t1_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k12_supinf_2 A B) = k1_supinf_2) ) )  =>  ((k19_supinf_2 A) = k1_supinf_2) ) ) ) ).
tt(t1_measure8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (r2_funct_2 k5_numbers k7_numbers (k18_supinf_2 A) (k2_mesfunc9 A))) ) ).
tt(t1_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r2_hidden B A) <=> (r2_hidden (k2_xxreal_3 B) (k4_member_1 A))) ) ) ) ) ).
tt(t1_membered,ax, (! [A:$i] :  ((v1_membered A) => (r1_tarski A k2_numbers)) ) ).
tt(t1_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ((v13_struct_0 B 1) &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( ((k5_memstr_0 A B C) = (k5_memstr_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k9_binop_2 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k9_binop_2 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(t1_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  => (r1_xxreal_0 (k7_supinf_2 (k17_supinf_2 A)) (k7_supinf_2 (k17_supinf_2 B)))) ) ) ) ) ).
tt(t1_mesfun6c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k3_supinf_2 (k1_measure6 A) (k1_measure6 B)) = (k2_xcmplx_0 A B))  &  ( ((k2_supinf_2 (k1_measure6 A)) = (k4_xcmplx_0 A))  &  ( ((k4_supinf_2 (k1_measure6 A) (k1_measure6 B)) = (k6_xcmplx_0 A B))  &  ((k1_extreal1 (k1_measure6 A) (k1_measure6 B)) = (k3_xcmplx_0 A B)) ) ) ) ) ) ) ) ).
tt(t1_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_funct_2 k5_numbers k1_numbers k5_numbers k7_numbers (k10_seqfunc A B C) (k3_mesfunc5 A (k1_mesfun7c A B) C))) ) ) ) ) ) ).
tt(t1_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((r2_hidden C D) & (v2_comseq_2 (k10_seqfunc A B C)))  => (v2_comseq_2 (k10_seqfunc A (k1_mesfun9c A k1_numbers B D) C))) ) ) ) ) ) ) ) ).
tt(t1_mesfunc1,ax,(r2_tarski k5_numbers k1_mesfunc1)).
tt(t1_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  => (r2_relset_1 A k7_numbers B (k6_mesfunc1 A B 1))) ) ) ) ).
tt(t1_mesfunc3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B)) k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  ( ( ((k4_finseq_1 D) = (k2_finseq_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 D)) &  (! [G:$i] :  ((m2_finseq_1 G k1_numbers) =>  (~  ( ((k4_finseq_1 G) = (k2_finseq_1 B))  &  ( ((k1_seq_1 D F) = (k18_rvsum_1 G))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k1_seq_1 G H) = (k1_seq_1 C (k4_tarski F H))) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k4_finseq_1 E) = (k2_finseq_1 B))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m2_finseq_1 G k1_numbers) =>  (~  ( ((k4_finseq_1 G) = (k2_finseq_1 A))  &  ( ((k1_seq_1 E F) = (k18_rvsum_1 G))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k1_seq_1 G H) = (k1_seq_1 C (k4_tarski H F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k18_rvsum_1 D) = (k18_rvsum_1 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_mesfunc4,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k7_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k7_numbers) =>  ( ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 A D))) ) )  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B D))) ) )  &  ( ((k4_finseq_1 A) = (k4_finseq_1 B))  &  (C = (k3_mesfunc1 k5_numbers A B)) ) ) )  =>  ((k4_extreal1 C) = (k3_supinf_2 (k4_extreal1 A) (k4_extreal1 B))) ) ) ) ) ) ) ) ).
tt(t1_mesfunc5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((k3_extreal1 (k4_supinf_2 A B)) = (k3_extreal1 (k4_supinf_2 B A))) ) ) ) ) ).
tt(t1_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k7_numbers (k10_mesfunc1 A (k1_mesfunc5 A B)) (k1_mesfunc5 A (k56_valued_1 A k1_numbers B)))) ) ) ) ).
tt(t1_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A B)) => (r1_xxreal_0 (k12_supinf_2 B D) (k12_supinf_2 C D))) ) )  => (v6_supinf_2 (k4_mesfunc1 A C B))) ) ) ) ) ) ) ).
tt(t1_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (m2_subset_1 (a_4_0_mesfunc8 A B D E) (k1_zfmisc_1 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v4_mesfunc5 B) & (v4_mesfunc5 C))  =>  ((k1_relset_1 A (k3_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ).
tt(t1_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_metric_1 A B B) = k6_numbers) ) )  <=> (v6_metric_1 A)) ) ) ).
tt(t1_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_metric_2 A B C) & (r3_metric_2 A C D))  => (r3_metric_2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t1_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ( ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) C D) = k6_numbers)  <=>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_metric_6,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k4_metric_1 A B C) (k4_metric_1 A D C))) (k4_metric_1 A B D))) ) ) ) ) ) ) ) ).
tt(t1_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) <=> (r1_metrizts A B (k2_struct_0 A) (k2_struct_0 B))) ) ) ) ) ).
tt(t1_mfold_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (r2_borsuk_3 A (k1_pre_topc A (k2_struct_0 A)))) ) ).
tt(t1_mfold_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k9_xtuple_0 (k6_relat_1 B A)) = (k8_relat_1 A B)) ) ) ) ).
tt(t1_midsp_1,ax, ((u1_struct_0 k2_midsp_1) = 1) ).
tt(t1_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_midsp_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ((v1_midsp_2 D B A) =>  ((k1_midsp_1 B C C) = C) ) ) ) ) ) ) ) ) ) ).
tt(t1_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (~  ( ((k3_finseq_1 D) = (k2_nat_1 (k2_nat_1 A 1) B))  &  (! [E:$i] :  ((m2_finseq_1 E C) =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (~  ( ((k3_finseq_1 E) = A)  &  ( ((k3_finseq_1 F) = B)  &  (D = (k8_finseq_1 C (k8_finseq_1 C E (k12_finseq_1 C G)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_mmlquery,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) <=>  (! [C:$i] : (r1_tarski (k9_relat_1 A C) (k9_relat_1 B C))) ) ) ) ) ) ).
tt(t1_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_mod_2 A))) =>  (B = (k4_struct_0 (k1_mod_2 A))) ) ) ) ) ).
tt(t1_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (~  ((k4_struct_0 A) = (k4_algstr_0 A (k5_struct_0 A))) ) ) ) ).
tt(t1_mod_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((k2_binop_1 B C A D E F) = (k2_binop_1 C B A (k1_mod_4 B C A D) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (~  ( (~  (A = B) )  & (r3_xboole_0 (k12_finseq_1 k5_numbers A) (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) C))) ) ) ) ) ) ) ) ).
tt(t1_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_mod_2 B A) &  ((v3_mod_2 B A) & (l1_mod_2 B A)) )  => (m3_modcat_1 (k1_tarski B) A)) ) ) ) ).
tt(t1_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  <=> (r2_hidden A k12_modelc_1)) ) ).
tt(t1_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  <=> (r2_hidden A k9_modelc_2)) ) ).
tt(t1_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ((r2_hidden A (u2_modelc_3 B C)) =>  ( ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  (~ (v6_modelc_2 A)) ) ) )  |  ((r8_modelc_2 D (k14_modelc_3 B C)) <=> (r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~  (A = 1) )  => (r1_xxreal_0 2 A)) ) ) ).
tt(t1_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v5_monoid_0 B A) <=>  ((v3_monoid_0 B A) & (v4_monoid_0 B A)) ) ) ) ) ) ).
tt(t1_monoid_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k3_relat_1 B (k5_relat_1 A C)) = (k3_relat_1 (k6_relat_1 C B) A)) ) ) ) ) ) ).
tt(t1_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = k1_xboole_0)  =>  ( ((k6_rusub_4 A B C) = C)  &  ( ((k6_rusub_4 A C B) = C)  &  ((k1_morph_01 A B C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t1_msafree1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B (k4_card_3 A)) => (r1_tarski (k10_xtuple_0 B) (k3_card_3 A))) ) ) ) ) ).
tt(t1_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_struct_0 A) & (l1_msualg_1 A)) )  =>  ((k2_msafree2 A) = (u1_struct_0 A)) ) ) ).
tt(t1_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  ( ((v1_msualg_3 C) & (r2_pboole A B (k2_funct_6 C)))  => (r6_pboole A (k1_equation A (k9_pboole A B C) C) B)) ) ) ) ) ) ).
tt(t1_msafree,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k3_finseq_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_finseq_2 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E B (k3_finseq_2 B)) =>  (! [F:$i] :  ( ((r2_hidden F A) &  (E = (k1_funct_1 C F)) )  =>  ((k1_funct_1 (k3_relat_1 C (k6_finseq_2 B D)) F) = (k4_card_3 (k3_relat_1 E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  & (l1_msualg_1 E)) )  =>  (! [F:$i] :  ((m1_msalimit F A E) =>  (! [G:$i] :  ((m2_msalimit G A E F) =>  ( ((r1_orders_2 A C B) & (r1_orders_2 A D C))  => (r8_pboole (u1_struct_0 E) (k3_msualg_3 (u1_struct_0 E) (u3_msualg_1 E (k5_pralg_2 (u1_struct_0 A) E F B)) (u3_msualg_1 E (k5_pralg_2 (u1_struct_0 A) E F C)) (u3_msualg_1 E (k5_pralg_2 (u1_struct_0 A) E F D)) (k1_msalimit A E F G B C) (k1_msalimit A E F G C D)) (k1_msalimit A E F G B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((r2_hidden (k4_trees_4 (k4_tarski C (u1_struct_0 A)) D) (k1_msaterm A B)) & (v6_trees_3 D))  <=> (m1_msaterm D A B (k2_msaterm A B C))) ) ) ) ) ) ) ) ) ).
tt(t1_msinst_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ( (B = (k1_msinst_1 A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_msualg_1 C)) ) ) ) ) ) ) ) ) ).
tt(t1_msscyc_2,ax, (! [A:$i] :  ((l1_msualg_1 A) => (r1_tarski (k1_msscyc_2 A) (k2_zfmisc_1 (u4_struct_0 A) (u1_struct_0 A)))) ) ).
tt(t1_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (~  (B = k1_xboole_0) )  => (r1_tarski (k8_setfam_1 A B) (k5_setfam_1 A B))) ) ) ) ).
tt(t1_mssublat,ax, (! [A:$i] :  ((k3_funct_2 k5_numbers (k3_finseq_2 (k1_tarski A)) (k7_finseq_2 A) k6_numbers) = k1_xboole_0) ) ).
tt(t1_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (~ (v1_xboole_0 (k5_msualg_1 A B C))) ) ) ) ) ) ) ).
tt(t1_msualg_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D A (k3_finseq_2 A)) =>  ((k4_card_3 (k3_relat_1 D (k3_pboole A B C))) = (k3_xboole_0 (k4_card_3 (k3_relat_1 D B)) (k4_card_3 (k3_relat_1 D C)))) ) ) ) ) ) ) ) ) ).
tt(t1_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_msualg_3 B) <=>  (! [C:$i] :  ((r2_hidden C A) => (v2_funct_1 (k1_funct_1 B C))) ) ) ) ) ) ).
tt(t1_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((v3_relat_2 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D C)) &  ((v8_relat_2 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D C)) &  ((v1_partfun1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D C) (k1_funct_1 (u3_msualg_1 A B) C)) & (m1_subset_1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) C) (k1_funct_1 (u3_msualg_1 A B) C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_msualg_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k5_eqrel_1 A B C) (k1_msualg_5 A (k3_eqrel_1 A B C)))) ) ) ) ) ).
tt(t1_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k3_msualg_1 A C B)) =>  ((v1_relat_1 D) & (v1_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t1_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_msualg_4 (k2_msualg_3 A B) A B) & (m1_msualg_4 (k2_msualg_3 A B) A B B)) ) ) ) ) ).
tt(t1_msualg_8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((r2_hidden A (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B))) ) )  &  ( ((r2_hidden A (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B)))  =>  ((r1_xxreal_0 1 A) &  (~ (r1_xxreal_0 (k3_finseq_1 B) A)) ) ) ) ) ) ) ) ).
tt(t1_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 D)) & (r2_hidden (k1_funct_1 D A) (k2_zfmisc_1 B C)))  =>  ((k1_funct_1 D A) = (k4_tarski (k1_funct_1 (k11_mcart_1 D) A) (k1_funct_1 (k12_mcart_1 D) A))) ) ) ) ) ) ) ).
tt(t1_msuhom_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski (k10_xtuple_0 A) C) =>  ((k3_relat_1 A (k5_relat_1 B C)) = (k3_relat_1 A B)) ) ) ) ) ) ) ).
tt(t1_multop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_zfmisc_1 B C D) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 B C D) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_zfmisc_1 B C D) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 B C D) A)))) )  =>  ( (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((r2_hidden G B) &  ((r2_hidden H C) & (r2_hidden I D)) )  =>  ((k1_funct_1 E (k3_xtuple_0 G H I)) = (k1_funct_1 F (k3_xtuple_0 G H I))) ) ) ) )  => (r2_funct_2 (k3_zfmisc_1 B C D) A E F)) ) ) ) ) ) ) ) ) ) ).
tt(t1_mycielsk,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k3_xcmplx_0 A (k1_xreal_0 B C)) = (k1_xreal_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 A C))) ) ) ) ) ) ) ) ).
tt(t1_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (B = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) C)) ) )  => (v1_nagata_1 B A)) ) ) ) ) ).
tt(t1_nagata_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  (A = (k4_nat_1 (k13_newton 2 B) (k2_nat_1 (k4_nat_1 2 C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t1_nat_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ((r2_hidden k6_numbers A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) => (r2_hidden (k2_xcmplx_0 B 1) A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden B A)) ) ) ) ) ).
tt(t1_nat_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 B (k7_xcmplx_0 A (k2_xcmplx_0 (k1_int_1 (k7_xcmplx_0 A B)) 1)))) ) ) ) ) ) ) ).
tt(t1_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_nat_d A C) & (r1_nat_d B D))  => (r1_nat_d (k24_binop_2 A B) (k24_binop_2 C D))) ) ) ) ) ) ) ) ) ).
tt(t1_nat_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k11_binop_2 A A) (k11_binop_2 B B)))  & (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(t1_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k21_binop_2 (k13_newton 2 (k23_binop_2 A 2)) 1) (k13_newton 2 (k23_binop_2 A 1)))) ) ) ).
tt(t1_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k4_nat_d B A))) ) ) ) ) ) ).
tt(t1_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ((k1_lattices k3_nat_lat A B) = (k5_nat_d A B)) ) ) ) ) ).
tt(t1_nattra_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 C)))  =>  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m1_subset_1 H (k1_zfmisc_1 D)))  => (r8_binop_1 G H (k2_zfmisc_1 A B) (k1_nattra_1 (k2_zfmisc_1 C D) (k2_zfmisc_1 A B) (k6_cat_2 C D A B E F) (k8_mcart_1 C D G H)) (k6_cat_2 G H A B (k1_nattra_1 C A E G) (k1_nattra_1 D B F H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A B) (k6_clvect_1 A B (k10_complex1 k6_complex1)))) ) ) ) ).
tt(t1_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r1_ncfcont2 A C D E) & (r1_tarski B A))  => (r1_ncfcont2 B C D E)) ) ) ) ) ) ) ) ) ).
tt(t1_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_nfcont_1 C A B) =>  (! [D:$i] :  ((m1_nfcont_1 D A B) =>  (? [E:$i] :  ((m1_nfcont_1 E A B) &  ((r1_tarski E C) & (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((r1_ndiff_1 B A C D) &  (! [E:$i] :  ((m1_nfcont_1 E B D) =>  (~  ((r1_tarski E (k1_relset_1 (u1_struct_0 B) C)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v2_relat_1 G) &  ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k1_numbers) &  ((v1_fdiff_1 G k6_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v3_funct_1 H) &  ((v1_funct_2 H k5_numbers (u1_struct_0 B)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) H) = (k1_tarski D))  & (r1_tarski (k2_relset_1 (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B F G) H)) E))  =>  ((v3_normsp_1 (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B F G) H) C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) H C)) (k37_valued_1 k5_numbers k1_numbers G)) A) &  ((k17_lopban_1 B A (k3_ndiff_1 B A C D) F) = (k6_normsp_1 A (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B F G) H) C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) H C)) (k37_valued_1 k5_numbers k1_numbers G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A C D)) (k1_seq_1 B D))) )  &  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) )  =>  ((v3_normsp_1 C A) &  ((k6_normsp_1 A C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t1_ndiff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  => (r2_relset_1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers B C) (k7_integr15 A k1_numbers B (k2_nfcont_4 A k1_numbers C)))) ) ) ) ) ) ).
tt(t1_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ((v1_ndiff_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (E = k6_numbers) )  &  ( (~ (r1_xxreal_0 D (k17_complex1 E)))  & (r1_xxreal_0 C (k11_binop_2 (k8_binop_2 (k17_complex1 E)) (k1_normsp_0 A (k10_funct_2 k1_numbers (u1_struct_0 A) B E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_neckla_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))) => (r2_hidden D A)) ) ) ) ) ) ) ).
tt(t1_neckla_3,ax, (! [A:$i] :  (! [B:$i] : (r2_relset_1 A A (k2_partfun1 A A (k6_partfun1 A) B) (k8_subset_1 (k2_zfmisc_1 A A) (k6_partfun1 A) (k2_zfmisc_1 B B)))) ) ).
tt(t1_necklace,ax, (4 = (k2_enumset1 k6_numbers 1 2 3)) ).
tt(t1_net_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_petri B) =>  (~  ( (~  ((k2_net_1 B) = k1_xboole_0) )  &  ((m1_subset_1 A (k2_net_1 B)) &  ( (~ (m1_subset_1 A (u1_struct_0 B)))  &  (~ (m1_subset_1 A (u4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t1_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_finseq_1 A) = (k2_xboole_0 (k2_xboole_0 (k1_tarski 1) (a_1_0_newton A)) (k1_tarski A))) ) ) ) ).
tt(t1_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k2_normsp_1 A B (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ).
tt(t1_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r1_nfcont_2 A C D E) & (r1_tarski B A))  => (r1_nfcont_2 B C D E)) ) ) ) ) ) ) ) ) ).
tt(t1_nfcont_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D)) => (r2_hidden (k1_seq_1 C A) (k1_relset_1 k1_numbers D))) ) ) ) ) ) ) ) ) ).
tt(t1_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( (D = C)  =>  ((r1_nfcont_4 A C B) <=> (r1_nfcont_3 (k4_real_ns1 A) D B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ( ((r1_normform A B C D) & (r1_normform A B D C))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_normsp_0 A (k4_struct_0 A)) = k6_numbers) ) ) ).
tt(t1_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((v4_tbsp_1 A) &  ( ((k5_setfam_1 (u1_struct_0 A) (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) B)) = (u1_struct_0 A))  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r2_hidden (k3_subset_1 (u1_struct_0 A) (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C)) (k2_pcomps_1 A))) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k9_metric_1 A E D) (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_ntalgo_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_int_1 (k6_int_1 A B) B) = (k6_int_1 A B)) ) ) ) ) ).
tt(t1_numbers,ax,(r2_xboole_0 k1_numbers k2_numbers)).
tt(t1_numeral1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_relat_1 (k5_relset_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k1_prepower B) A) C)) &  ((v5_relat_1 (k5_relset_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k1_prepower B) A) C) k5_numbers) &  ((v1_funct_1 (k5_relset_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k1_prepower B) A) C)) &  ((v5_ordinal1 (k5_relset_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k1_prepower B) A) C)) & (v1_finset_1 (k5_relset_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k1_prepower B) A) C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_numerals,ax,(m1_subset_1 k1_xboole_0 k4_ordinal1)).
tt(t1_openlatt,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k9_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 A) B) C))) C)) ) ) ) ) ) ).
tt(t1_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  ( ((k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) B C)) = C)  &  ((k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) B C)) = B) ) ) ) ) ) ) ) ) ).
tt(t1_orders_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~ (r2_hidden k1_xboole_0 (k1_orders_1 A))) ) ) ).
tt(t1_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_orders_2 A B B)) ) ) ) ).
tt(t1_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t1_orders_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((v4_yellow_0 (k2_yellow_1 A) (k2_yellow_1 B)) & (m1_yellow_0 (k2_yellow_1 A) (k2_yellow_1 B))) ) ) ) ) ) ).
tt(t1_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=> (r1_ordinal1 (k1_ordinal1 A) (k1_ordinal1 B))) ) ) ) ) ).
tt(t1_ordinal3,ax, (! [A:$i] : (r1_tarski A (k1_ordinal1 A))) ).
tt(t1_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k9_xtuple_0 A) = (k1_ordinal1 B))  =>  ((r1_ordinal2 (k1_ordinal2 A) A) &  ((k8_ordinal2 A) = (k1_ordinal2 A)) ) ) ) ) ) ) ).
tt(t1_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r1_ordinal1 A (k1_ordinal1 B)) &  ( (~ (r1_ordinal1 A B))  &  (~  (A = (k1_ordinal1 B)) ) ) ) ) ) ) ) ) ).
tt(t1_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) <=>  (! [B:$i] :  ((r2_hidden B A) => (v3_ordinal1 B)) ) ) ) ).
tt(t1_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_o_ring_1 B A) => (v13_o_ring_1 B A)) ) ) ) ) ).
tt(t1_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_orders_2 B (k4_struct_0 B) C)) ) ) ) ) ) ).
tt(t1_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m1_osafree C A B) <=>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r8_pboole (u1_struct_0 A) D (k2_osalg_2 A C)) =>  ((k10_osalg_2 A B D) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_osalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (k3_finseq_2 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k3_finseq_2 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( (~ (v2_struct_0 (g3_osalg_1 A C B D E F)))  &  ( (~ (v11_struct_0 (g3_osalg_1 A C B D E F)))  &  ((v3_orders_2 (g3_osalg_1 A C B D E F)) &  ((v4_orders_2 (g3_osalg_1 A C B D E F)) & (v5_orders_2 (g3_osalg_1 A C B D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) )  =>  ((v1_relat_1 (k3_pboole (u1_struct_0 A) B C)) &  ((v4_relat_1 (k3_pboole (u1_struct_0 A) B C) (u1_struct_0 A)) &  ((v1_funct_1 (k3_pboole (u1_struct_0 A) B C)) &  ((v1_partfun1 (k3_pboole (u1_struct_0 A) B C) (u1_struct_0 A)) & (v11_osalg_1 (k3_pboole (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t1_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v1_funcop_1 B)) ) ) )  =>  ((v1_osalg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A C D) =>  ((r1_tarski (k9_xtuple_0 (k1_funct_1 B C)) (k9_xtuple_0 (k1_funct_1 B D))) & (r1_tarski (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) B C) =>  ((v1_osalg_4 D A B C) =>  ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (u1_struct_0 A)) & (v11_osalg_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((m1_subset_1 B (u1_struct_0 A)) => (m1_subset_1 B (u1_struct_0 (k2_diraf A))))  &  ( ((m1_subset_1 B (u1_struct_0 (k2_diraf A))) => (m1_subset_1 B (u1_struct_0 A)))  &  ( ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_diraf A)))))  &  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_diraf A)))) => (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t1_pardepap,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A E F E G) &  ((r2_analoaf A B F C E) & (r2_analoaf A C G D F)) ) )  => (r2_analoaf A D E B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k2_parsp_1 A B C) = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k3_rlvect_1 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k3_rlvect_1 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)) (k3_rlvect_1 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(t1_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_parsp_1 A)))  &  ((v2_parsp_1 (k9_parsp_1 A)) & (l1_parsp_1 (k9_parsp_1 A))) ) ) ) ).
tt(t1_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( (! [C:$i] :  ((r2_hidden C (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((k2_xboole_0 A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t1_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ( ( ((k1_relset_1 B C) = (k1_relset_1 B D))  &  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B C)) =>  ((k7_partfun1 A C E) = (k7_partfun1 A D E)) ) ) ) )  => (r2_relset_1 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t1_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r1_tarski B (k9_xtuple_0 (k2_funct_1 A))))  =>  ((k7_relat_1 A (k7_relat_1 (k2_funct_1 A) B)) = B) ) ) ) ) ).
tt(t1_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r1_tarski C D)) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t1_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k2_bvfunc_2 A (k1_subset_1 (k1_bvfunc_2 A))) = (k6_partit1 A)) ) ) ).
tt(t1_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C C D) &  ( (~  (C = D) )  &  ( (~  (B = C) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A E C C F) &  ((r2_diraf A E B D F) &  ( (~  (D = F) )  &  (~  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_pboole,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_relat_1 A) => (v1_setfam_1 (k10_xtuple_0 A))) ) ) ).
tt(t1_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k9_metric_1 A B C) (k9_metric_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t1_pcomps_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_wellord1 A B) =>  ((r2_wellord1 (k2_wellord1 A B) B) &  (B = (k1_relat_1 (k2_wellord1 A B))) ) ) ) ) ) ).
tt(t1_pcs_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [D:$i] :  ( ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B))))  =>  ((r1_xboole_0 A B) => (v8_relat_2 (k2_pcs_0 A A B B C D))) ) ) ) ) ) ) ).
tt(t1_pdiff_1,ax, ( (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ( ((k1_relset_1 (k1_euclid B) (k1_pdiff_1 A B)) = (k1_euclid B))  &  ((k1_rvsum_1 (k1_pdiff_1 A B)) = k1_numbers) ) ) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((k1_seq_1 (k1_pdiff_1 1 1) (k12_finseq_1 k1_numbers A)) = A)  &  ((k1_funct_1 (k2_funct_1 (k1_pdiff_1 1 1)) A) = (k12_finseq_1 k1_numbers A)) ) ) ) ) ).
tt(t1_pdiff_2,ax, ( ((k1_relset_1 (k1_euclid 2) (k1_pdiff_1 1 2)) = (k1_euclid 2))  &  ( ((k2_relset_1 k1_numbers (k1_pdiff_1 1 2)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k1_pdiff_1 1 2) (k10_finseq_1 A B)) = A) ) ) ) ) ) ) ).
tt(t1_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r1_pdiff_3 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 D) C) A)) ) ) ) ) ) ) ) ) ).
tt(t1_pdiff_4,ax, ( ((k1_relset_1 (k1_euclid 3) (k1_pdiff_1 1 3)) = (k1_euclid 3))  &  ( ((k1_rvsum_1 (k1_pdiff_1 1 3)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_seq_1 (k1_pdiff_1 1 3) (k11_finseq_1 A B C)) = A) ) ) ) ) ) ) ) ) ).
tt(t1_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r1_pdiff_5 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 E) D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  <=>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ).
tt(t1_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  ((k17_finseq_1 k1_numbers A (k5_euclid B)) = (k5_euclid A)) ) ) ) ) ) ).
tt(t1_pdiff_8,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden B (k2_finseq_1 A)) &  (C = D) )  => (r1_xxreal_0 (k18_complex1 (k7_partfun1 k1_numbers D B)) (k12_euclid C))) ) ) ) ) ) ) ) ) ).
tt(t1_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_xxreal_0 (k1_normsp_0 A E) 1) => (r1_xxreal_0 (k1_normsp_0 B (k17_lopban_1 A B C E)) (k11_binop_2 D (k1_normsp_0 A E)))) ) ) )  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t1_pencil_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k4_card_3 A) = (k4_card_3 B))  & (v2_relat_1 A))  => (v2_relat_1 B)) ) ) ) ) ).
tt(t1_pencil_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k2_relset_1 A (k1_pencil_2 A B C D)) (k2_relset_1 A B))) ) ) ) ) ) ) ).
tt(t1_pencil_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_pencil_1 A C D) => (r1_pencil_1 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t1_pencil_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 3 B) &  ((r1_xxreal_0 B (k1_nat_1 A 1)) &  (~ (r1_xxreal_0 2 A)) ) ) ) ) ) ) ) ) ).
tt(t1_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_int_2 A (k1_nat_1 A 1))) ) ).
tt(t1_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_petri_2 C A B) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E D A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  &  ((v1_finset_1 D) &  (C = (a_4_1_petri_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_petri A B) = (a_2_2_petri A B)) ) ) ) ) ).
tt(t1_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((v1_relat_1 (k1_tarski (k4_tarski A B))) &  ((v1_funct_1 (k1_tarski (k4_tarski A B))) & (v2_finseq_1 (k1_tarski (k4_tarski A B)))) ) ) ) ) ) ).
tt(t1_polyalg1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) A)))) )  =>  ((k9_xtuple_0 C) = (k2_zfmisc_1 A B)) ) ) ) ) ).
tt(t1_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k1_polyeq_1 A B C) = k6_numbers)  =>  ( (A = k6_numbers)  |  (C = (k4_xcmplx_0 (k7_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t1_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k1_polyeq_2 A k6_numbers B k6_numbers C D) = k6_numbers)  =>  ( (A = k6_numbers)  |  ( (C = k6_numbers)  |  ((r1_xxreal_0 (k6_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)) k6_numbers) |  ( (~  (D = k6_numbers) )  &  (~  ( (~  (D = (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) )  &  ( (~  (D = (k6_square_1 (k13_complex1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) )  &  ( (~  (D = (k4_xcmplx_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))))) )  &  (~  (D = (k4_xcmplx_0 (k6_square_1 (k13_complex1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k2_quin_1 A B C)) &  ( ((k2_polyeq_3 A B C D) = k6_numbers)  &  ( (~  (D = (k12_binop_2 (k9_binop_2 (k7_binop_2 B) (k7_square_1 (k2_quin_1 A B C))) (k11_binop_2 2 A))) )  &  ( (~  (D = (k12_binop_2 (k10_binop_2 (k7_binop_2 B) (k7_square_1 (k2_quin_1 A B C))) (k11_binop_2 2 A))) )  &  (~  (D = (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers (k2_quin_1 B A C)) =>  ((r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B)) |  ((r1_xxreal_0 (k7_xcmplx_0 C B) k6_numbers) |  ( (~ (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k7_square_1 (k2_quin_1 B A C))) (k3_xcmplx_0 2 B)) k6_numbers))  &  (~ (r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) (k7_square_1 (k2_quin_1 B A C))) (k3_xcmplx_0 2 B)) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 A A) = (k1_newton A 2)) ) ) ).
tt(t1_polyform,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (! [D:$i] :  (! [E:$i] :  (~  ( (~  (D = E) )  &  (A = (k2_tarski D E)) ) ) ) )  |  ( (B = C)  |  (A = (k2_tarski B C)) ) ) ) ) ) ) ).
tt(t1_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k4_finseq_1 B) = (k4_finseq_1 C))  =>  ((k4_finseq_1 (k3_fvsum_1 A B C)) = (k4_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t1_polynom2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k2_nat_1 C D)) = (k6_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t1_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_funct_1 B C) = (k4_struct_0 A)) ) ) )  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t1_polynom4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  (B = (k7_finseq_1 (k7_finseq_1 (k17_finseq_1 A (k7_nat_d C 1) B) (k9_finseq_1 (k1_funct_1 B C))) (k2_rfinseq A C B))) ) ) ) ) ) ) ) ).
tt(t1_polynom5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~ (r1_xxreal_0 k6_numbers (k7_real_1 (k9_real_1 (k9_real_1 (k4_nat_1 A B) A) B) 1))) ) ) ) ) ) ) ) ).
tt(t1_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( (! [D:$i] :  ((r2_hidden D C) <=>  (? [E:$i] :  ((v3_ordinal1 E) &  ( (D = (k10_ordinal2 A E))  & (r2_hidden E B)) ) ) ) )  =>  ((k10_ordinal2 A B) = (k2_xboole_0 A C)) ) ) ) ) ) ) ).
tt(t1_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) C (k7_polynom1 A B)) <=>  ((k2_polynom1 (k15_pre_poly A) B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t1_polynom8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v4_vectsp_1 B) &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (C = (k4_struct_0 B)) )  &  ((k2_binom B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t1_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_vfunct_1 (k15_pre_poly A) B (k5_polynom1 A B C D)) (k5_polynom1 A B (k5_vfunct_1 (k15_pre_poly A) B C) (k5_vfunct_1 (k15_pre_poly A) B D)))) ) ) ) ) ) ) ).
tt(t1_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (~ (v1_xboole_0 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))  &  ((v6_orders_2 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B) & (m1_subset_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v1_abian B) =>  ((k1_newton (k4_xcmplx_0 A) B) = (k1_newton A B)) ) ) ) ) ) ).
tt(t1_pralg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  ( (~ (v2_struct_0 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))))  &  ((v1_unialg_1 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))) &  ((v2_unialg_1 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))) &  ((v3_unialg_1 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))) &  ((v4_unialg_1 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B))) & (l1_unialg_1 (g1_unialg_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k4_pralg_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_pralg_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 A) = (k1_tarski k1_xboole_0))  =>  ((k1_pralg_2 A) = A) ) ) ) ).
tt(t1_pralg_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r2_hidden A (k4_card_3 B)) => (r2_hidden (k5_relat_1 A C) (k4_card_3 (k5_relat_1 B C)))) ) ) ) ) ) ).
tt(t1_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( ((k9_xtuple_0 A) = (k1_tarski B))  &  ((k10_xtuple_0 A) = (k1_tarski C)) )  =>  (A = (k1_tarski (k4_tarski B C))) ) ) ) ) ) ).
tt(t1_pre_ff,ax, ( ((k1_pre_ff k6_numbers) = k6_numbers)  &  ( ((k1_pre_ff 1) = 1)  &  (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k2_nat_1 (k1_nat_1 A 1) 1)) = (k2_nat_1 (k1_pre_ff A) (k1_pre_ff (k1_nat_1 A 1)))) ) ) ) ) ).
tt(t1_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 1)  => (r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)) (k9_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t1_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_2 B A (k3_finseq_2 A)) =>  ((k5_pre_poly A (k3_pre_poly (k3_finseq_2 A) B)) = B) ) ) ) ).
tt(t1_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 A (k1_seq_1 B C))) ) )  => (r1_xxreal_0 A (k2_seq_2 B))) ) ) ) ) ).
tt(t1_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (r2_hidden k1_xboole_0 (u1_pre_topc A))) ) ).
tt(t1_prgcor_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k7_nat_d (k2_nat_1 A C) (k2_nat_1 B C)) = (k7_nat_d A B)) ) ) ) ) ) ) ).
tt(t1_prgcor_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((r1_tarski k5_numbers A) &  ((v7_ordinal1 (k1_funct_1 B k6_numbers)) & (r2_hidden (k1_funct_1 B k6_numbers) (k1_afinsq_1 B))) )  => (r1_prgcor_2 A B (k12_afinsq_1 A B))) ) ) ) ) ).
tt(t1_prob_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) =>  ((k1_seq_1 B D) = A) ) ) ) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = A) ) ) ) ) ) ) ).
tt(t1_prob_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ( ((k10_real_1 D B) = (k10_real_1 C A))  <=>  ((k8_real_1 D A) = (k8_real_1 C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_prob_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~ (r2_hidden k6_numbers (k1_relset_1 k5_numbers A))) ) ) ).
tt(t1_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (r1_tarski (k4_measure1 A (k9_setfam_1 A) C) B)) ) ) ) ) ).
tt(t1_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k6_cqc_lang A (k7_cqc_lang A B (k6_cqc_lang A B))) (k4_cqc_the1 A))) ) ) ) ).
tt(t1_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C D) =>  ((r1_collsp A C D B) &  ((r1_collsp A D B C) &  ((r1_collsp A C B D) &  ((r1_collsp A B D C) & (r1_collsp A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) => (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C B) E))  &  ( ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E) =>  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B D C) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C B D) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D B) E) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D B C) E) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D C B) E)) ) ) ) )  &  ( ((r2_projpl_1 A B E F) => (r2_projpl_1 A B F E))  &  ((r3_projpl_1 A B E F G) =>  ((r3_projpl_1 A B E G F) &  ((r3_projpl_1 A B F E G) &  ((r3_projpl_1 A B F G E) &  ((r3_projpl_1 A B G E F) & (r3_projpl_1 A B G F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) => (r1_incsp_1 A C B)) ) ) ) ) ) ) ).
tt(t1_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) )  => (r1_projred2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t1_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r3_binop_1 (u1_struct_0 A) (k4_struct_0 A) (u1_algstr_0 A))) ) ).
tt(t1_prvect_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 B D) = (k18_complex1 (k9_real_1 (k1_seq_1 A D) C))) ) )  =>  ( ( ((v2_comseq_2 A) &  ((k2_seq_2 A) = C) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) )  &  ( ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_prvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k2_zfmisc_1 C D)) (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)))))) )  &  ((v2_funct_1 E) &  ((v2_funct_2 E (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) &  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((r2_hidden F A) &  ((r2_hidden G B) &  ((r2_hidden H C) & (r2_hidden I D)) ) )  =>  ((k1_binop_1 E (k4_tarski F G) (k4_tarski H I)) = (k4_tarski (k4_tarski F H) (k4_tarski G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_seq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_pscomp_1 A B) (k1_seq_1 B C))) ) ) ) ) ) ).
tt(t1_pua2mss1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) )  =>  ((r1_tarski (k4_card_3 A) (k4_card_3 B)) =>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(t1_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v1_pythtrip (k4_nat_1 A B)) & (r1_int_2 A B))  =>  ((v1_pythtrip A) & (v1_pythtrip B)) ) ) ) ) ) ).
tt(t1_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_hidden B A) =>  ((k9_xtuple_0 (k1_funct_4 D (k16_funcop_1 B C))) = A) ) ) ) ) ) ) ).
tt(t1_qc_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) => (r1_tarski (k2_zfmisc_1 (k1_tarski C) B) (k2_zfmisc_1 A B))) ) ) ) ) ).
tt(t1_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k18_qc_lang1 A (k13_qc_lang1 A B)) = B) ) ) ) ) ).
tt(t1_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k6_qc_lang1 A)) => (m2_subset_1 B (k6_qc_lang1 A) (k8_qc_lang1 A (k7_qc_lang1 A B)))) ) ) ) ).
tt(t1_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A B C) => (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A B)) (k3_finseq_1 (k11_qc_lang1 A C)))) ) ) ) ) ) ) ).
tt(t1_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k3_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  (! [D:$i] :  ((m1_prob_1 D k1_numbers k12_prob_1) =>  ( (D = (k3_subset_1 k1_numbers (k7_qmax_1 A C)))  =>  ((k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A C) B) (k7_qmax_1 A C)) = (k9_real_1 1 (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A C) B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t1_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k1_lattices A C D) = (k1_lattices B E F))  &  ( ((k2_lattices A C D) = (k2_lattices B E F))  &  ( ((r1_lattices A C D) => (r1_lattices B E F))  &  ((r1_lattices B E F) => (r1_lattices A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k6_quaterni A B C D) = (k26_quaterni (k26_quaterni (k23_quaterni A (k25_quaterni B k1_xcmplx_0)) (k25_quaterni C k11_quaterni)) (k25_quaterni D k12_quaterni))) ) ) ) ) ) ) ) ) ).
tt(t1_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k17_quaterni (k27_quaterni A B)) = (k17_quaterni (k27_quaterni B A))) ) ) ) ) ).
tt(t1_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k9_xtuple_0 (k2_quaterni A B C D E F G H)) = (k2_enumset1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t1_quin_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) = (k6_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 (k2_xcmplx_0 D (k7_xcmplx_0 B (k3_xcmplx_0 2 A))))) (k7_xcmplx_0 (k1_quin_1 A B C) (k3_xcmplx_0 4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t1_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (~ (v1_xboole_0 (k1_quofield A))) ) ) ).
tt(t1_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k4_nat_d A B) = (k6_xcmplx_0 B 1))  =>  ((k4_nat_d (k2_xcmplx_0 A 1) B) = k6_numbers) ) ) ) ) ) ).
tt(t1_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_nat_d A 1) = k6_numbers) ) ) ).
tt(t1_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r2_hidden B (k2_radix_3 A)) =>  ((r1_xxreal_0 (k6_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 (k7_nat_d A 1))) 1) B) & (r1_xxreal_0 B (k1_radix_1 (k7_nat_d A 1)))) ) ) ) ) ) ).
tt(t1_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k1_radix_1 A) 2)) ) ) ) ).
tt(t1_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r2_hidden (k6_xcmplx_0 (k1_radix_1 A) 1) (k3_radix_1 A))) ) ) ).
tt(t1_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 2 C))  =>  ((k8_radix_1 (k2_xcmplx_0 B A) C (k6_radix_5 (k2_xcmplx_0 B A) B C)) = (k8_radix_1 B C (k6_radix_5 B B C))) ) ) ) ) ) ) ) ) ).
tt(t1_ramsey_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ( ((v2_funct_1 D) & (r1_ordinal1 (k5_card_1 A) (k1_card_1 B)))  =>  ((v1_xboole_0 B) |  ((v1_xboole_0 C) |  ((k3_group_10 (k7_relat_1 D E) A) = (k7_relat_1 (k1_ramsey_1 A B C D) (k3_group_10 E A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc5 A B C D) &  ((r1_tarski E (k1_relset_1 A D)) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G E) => (r1_xxreal_0 F (k12_supinf_2 D G))) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C E)) | (r1_xxreal_0 (k1_extreal1 (k1_measure6 F) (k12_supinf_2 C E)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_random_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_xtuple_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_xtuple_0 A))) =>  ((r1_xboole_0 B C) => (r1_xboole_0 (k10_xtuple_0 (k5_relat_1 A B)) (k10_xtuple_0 (k5_relat_1 A C)))) ) ) ) ) ) ) ).
tt(t1_ranknull,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 B) &  ((v2_funct_1 (k5_relat_1 A (k10_xtuple_0 B))) & (r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A))) )  => (v2_funct_1 (k3_relat_1 B A))) ) ) ) ) ).
tt(t1_rat_1,ax, (! [A:$i] :  (~  ((r2_hidden A k3_numbers) &  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (C = k6_numbers) )  &  (A = (k7_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t1_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k7_partfun1 (u1_struct_0 A) D E) = (k6_algstr_0 A B (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) )  =>  ((k4_rlvect_1 A D) = (k6_algstr_0 A B (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden A (k2_rcomp_1 (k6_xcmplx_0 B C) (k2_xcmplx_0 B C))) <=>  (~ (r1_xxreal_0 C (k18_complex1 (k6_xcmplx_0 A B)))) ) ) ) ) ) ) ) ).
tt(t1_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered A) & (v3_xxreal_2 A)) )  =>  (! [B:$i] :  ( ((v2_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) => (r2_hidden (k3_seq_4 A) B)) ) ) ) ) ).
tt(t1_real_1,ax, (k2_arytm_2 = a_0_0_real_1) ).
tt(t1_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k10_real_1 1 A) 1)) ) ) ) ) ).
tt(t1_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (v2_xxreal_0 A))  => (v2_xxreal_0 B)) ) ) ) ) ).
tt(t1_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k1_binop_1 k2_real_lat A B) = (k1_binop_1 k2_real_lat B A)) ) ) ) ) ).
tt(t1_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ( (B = C)  =>  ((k1_normsp_0 (k4_real_ns1 A) B) = (k12_euclid C)) ) ) ) ) ) ) ) ).
tt(t1_realset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r2_hidden B (k2_zfmisc_1 A A)) => (r2_hidden (k1_funct_1 C B) A)) ) ) ) ) ).
tt(t1_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))))  &  ((v13_algstr_0 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))) &  ((v2_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))) &  ((v3_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))) &  ((v4_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A))) & (l2_algstr_0 (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A)))) ) ) ) ) ) ) ).
tt(t1_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k5_realset2 A) (k5_struct_0 A)) = (k5_struct_0 A)) ) ) ).
tt(t1_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ((v3_rearran1 B (k1_zfmisc_1 A)) <=>  ((k3_finseq_1 B) = (k5_card_1 A)) ) ) ) ) ) ).
tt(t1_recdef_2,ax, (! [A:$i] :  ( (? [B:$i] :  (? [C:$i] :  (? [D:$i] :  (A = (k3_xtuple_0 B C D)) ) ) )  =>  (A = (k3_xtuple_0 (k4_xtuple_0 A) (k5_xtuple_0 A) (k2_xtuple_0 A))) ) ) ).
tt(t1_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k9_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) ) ) ) ) ).
tt(t1_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_relat_2 A) <=> (r1_tarski (k4_relat_1 (k1_relat_1 A)) A)) ) ) ).
tt(t1_reloc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k7_ami_3 B) A) = (k7_ami_3 (k2_xcmplx_0 B A))) ) ) ) ) ).
tt(t1_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ((r1_tarski A D) => (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ).
tt(t1_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k10_eqrel_1 B)) <=>  (? [C:$i] :  ( (A = (k1_tarski C))  & (r2_hidden C B)) ) ) ) ) ).
tt(t1_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r2_finseq_4 B (k7_partfun1 A B (k3_finseq_1 B))) =>  ((k4_finseq_4 B (k7_partfun1 A B (k3_finseq_1 B))) = (k3_finseq_1 B)) ) ) ) ) ) ).
tt(t1_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k1_rewrite1 k1_xboole_0 A) = A)  &  ((k1_rewrite1 A k1_xboole_0) = A) ) ) ) ).
tt(t1_rewrite2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden (k1_nat_1 A 1) (k4_finseq_1 B)) =>  ((r2_hidden A (k4_finseq_1 B)) |  (A = k6_numbers) ) ) ) ) ) ) ).
tt(t1_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden B (k4_finseq_1 C)) =>  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) C) (k2_xcmplx_0 B 1)) = (k1_funct_1 C B)) ) ) ) ) ) ) ).
tt(t1_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A (k1_rfinseq2 A))) & (r1_xxreal_0 (k1_seq_1 A B) (k3_rfinseq2 A))) ) ) ) ) ) ).
tt(t1_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_classes1 A B) <=> (r2_classes1 (k7_finseq_1 A C) (k7_finseq_1 B C))) ) ) ) ) ) ) ).
tt(t1_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((r1_tarski (k9_xtuple_0 (k4_rfunct_1 A)) (k9_xtuple_0 A)) &  ((k9_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski k6_numbers)))) = (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski k6_numbers)))) ) ) ) ).
tt(t1_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_relset_1 k5_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers B C)) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A D) = (k9_real_1 (k1_seq_1 B D) (k1_seq_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t1_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (A = (k9_real_1 (k1_rfunct_3 A) (k2_rfunct_3 A))) ) ) ).
tt(t1_rfunct_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k3_xxreal_0 A B) (k4_xxreal_0 A B))) ) ) ) ).
tt(t1_rinfsup1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( (~ (r1_xxreal_0 C (k6_xcmplx_0 A B)))  &  (~ (r1_xxreal_0 (k2_xcmplx_0 A B) C)) )  <=>  (~ (r1_xxreal_0 B (k18_complex1 (k6_xcmplx_0 C A)))) ) ) ) ) ) ) ) ).
tt(t1_rinfsup2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ( (A = B)  & (v4_xxreal_2 B))  =>  ((v4_xxreal_2 A) &  ((k8_supinf_2 A) = (k4_seq_4 B)) ) ) ) ) ) ) ).
tt(t1_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A (k5_algstr_0 A B C) C) = B) ) ) ) ) ) ) ).
tt(t1_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v1_ringcat1 D A B) & (v1_ringcat1 E B C))  => (v1_ringcat1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_convex1 A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t1_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_rlvect_2 D A C) =>  (~  ((v2_convex1 D A) &  ( (~  (B = (k6_rlvect_2 A D)) )  &  ( (~  ((k3_funct_2 (u1_struct_0 A) k1_numbers D B) = k1_xboole_0) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E (k3_convex1 A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B)))) &  ( ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A E (k9_real_1 1 (k3_funct_2 (u1_struct_0 A) k1_numbers D B)))))  &  ((k3_rlvect_1 A (k1_rlvect_1 A (k6_rlvect_2 A D) (k10_real_1 1 (k3_funct_2 (u1_struct_0 A) k1_numbers D B))) (k1_rlvect_1 A E (k9_real_1 1 (k10_real_1 1 (k3_funct_2 (u1_struct_0 A) k1_numbers D B))))) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rlaffin3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k7_finseq_1 (k3_euclid_9 A C) (k3_euclid_9 B C)) = (k3_euclid_9 (k7_finseq_1 A B) C)) ) ) ) ) ) ) ).
tt(t1_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  ( (B = k1_xboole_0)  | (r2_hidden (k4_struct_0 A) B)) ) ) ) ) ) ).
tt(t1_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((r1_struct_0 (k1_rlsub_2 A B C) D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden C B) => (r2_hidden (k1_rlvect_1 A C D) (k1_convex1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t1_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_struct_0 A B)) ) ) ) ).
tt(t1_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_rlvect_2 A B) = B) ) ) ) ) ).
tt(t1_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k6_rlvect_2 A (k7_rlvect_2 A B C)) = (k3_rlvect_1 A (k6_rlvect_2 A B) (k6_rlvect_2 A C))) ) ) ) ) ) ) ).
tt(t1_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_algstr_0 A (k3_rlvect_1 A B C) B) = C)  &  ( ((k5_algstr_0 A (k3_rlvect_1 A C B) B) = C)  &  ( ((k3_rlvect_1 A (k5_algstr_0 A B B) C) = C)  &  ( ((k3_rlvect_1 A (k5_algstr_0 A C B) B) = C)  &  ( ((k3_rlvect_1 A B (k5_algstr_0 A C B)) = C)  &  ( ((k3_rlvect_1 A C (k5_algstr_0 A B B)) = C)  &  ((k5_algstr_0 A B (k5_algstr_0 A B C)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_rlvect_3 D A) &  ((r1_tarski (k3_rlvect_2 A B) D) &  ((r1_tarski (k3_rlvect_2 A C) D) &  ((k6_rlvect_2 A B) = (k6_rlvect_2 A C)) ) ) )  => (r1_rlvect_2 A B C)) ) ) ) ) ) ) ) ) ).
tt(t1_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k4_rlvect_1 A (k1_binom A B C)) = (k3_rlvect_1 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ).
tt(t1_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rmod_2 C A B) =>  ( (C = k1_xboole_0)  | (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ).
tt(t1_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((r1_struct_0 (k1_rmod_3 A B C D) E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((r2_hidden F (k9_xtuple_0 D)) &  (G = (k1_funct_1 E F)) )  =>  ((k1_funct_1 D F) = (k5_vectsp_2 A B C G)) ) ) ) ) ) )  =>  ((k4_rlvect_1 B D) = (k5_vectsp_2 A B C (k4_rlvect_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k4_robbins1 A B C) (k4_robbins1 A B (k3_robbins1 A C))) = B) ) ) ) ) ) ) ).
tt(t1_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A D E)) B)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A C) (k3_robbins1 A (k1_lattices A C F)))))))) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((v2_robbins3 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v9_lattices A)) ) )  =>  ((v5_sheffer1 A) & (v7_robbins1 A)) ) ) ) ).
tt(t1_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  ((k3_lattice3 A) = (k3_lattice3 B)) ) ) ) ) ) ).
tt(t1_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ( ((k1_seq_1 C A) = (k1_seq_1 C B))  &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k2_rcomp_1 A B)) &  ((k1_fdiff_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_roughs_1,ax, (! [A:$i] :  ((r1_relset_1 A A (k1_eqrel_1 A) (k6_partfun1 A)) => (v1_zfmisc_1 A)) ) ).
tt(t1_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  <=>  (! [C:$i] :  ((r1_tarski C B) <=>  ( (C = k1_xboole_0)  |  (C = B) ) ) ) ) ) ) ) ) ).
tt(t1_rsspace2,ax, ( ((u1_struct_0 k13_rsspace) = k11_rsspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace A) (k2_rsspace A)))) ) )  &  ( ((k4_struct_0 k13_rsspace) = k6_rsspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  (A = (k2_rsspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k13_rsspace)) =>  ((k3_rlvect_1 k13_rsspace A B) = (k1_series_1 k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k13_rsspace)) =>  ((k1_rlvect_1 k13_rsspace B A) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace B) A)) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  ( ((k4_algstr_0 k13_rsspace A) = (k32_valued_1 k5_numbers k1_numbers (k2_rsspace A)))  & (r2_funct_2 k5_numbers k1_numbers (k2_rsspace (k4_algstr_0 k13_rsspace A)) (k32_valued_1 k5_numbers k1_numbers (k2_rsspace A)))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k13_rsspace)) =>  ((k5_algstr_0 k13_rsspace A B) = (k47_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k13_rsspace)) =>  ((v1_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace A) (k2_rsspace B))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k13_rsspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k13_rsspace)) =>  ((k1_bhsp_1 k13_rsspace C D) = (k4_series_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace C) (k2_rsspace D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rsspace3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k18_complex1 (k9_real_1 (k1_seq_1 B D) A))) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k18_complex1 (k9_real_1 (k2_seq_2 B) A))) ) ) ) ) ) ) ) ) ) ).
tt(t1_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_comseq_2 A) &  ((k4_seq_4 (k2_relset_1 k1_numbers (k56_valued_1 k5_numbers k1_numbers A))) = k6_numbers) )  <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t1_rsspace,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k2_rsspace A) A)) ) ).
tt(t1_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ( ((r1_struct_0 B D) & (m1_rusub_1 B C))  => (r1_struct_0 C D)) ) ) ) ) ) ) ) ).
tt(t1_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((r1_struct_0 (k1_rusub_2 A B C) D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r1_struct_0 (k1_rusub_3 A B) C) <=>  (? [D:$i] :  ((m2_rlvect_2 D A B) &  (C = (k6_rlvect_2 A D)) ) ) ) ) ) ) ) ) ).
tt(t1_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_struct_0 (k1_rusub_3 A (k4_subset_1 (u1_struct_0 A) B C)) D) &  ( (~ (r1_struct_0 (k1_rusub_3 A C) D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r1_struct_0 (k1_rusub_3 A (k4_subset_1 (u1_struct_0 A) (k7_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) (k6_domain_1 (u1_struct_0 A) E)) (k6_domain_1 (u1_struct_0 A) D))) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_rusub_5 A B B)) ) ) ) ).
tt(t1_rvsum_1,ax,(r3_binop_1 k1_numbers k6_numbers k33_binop_2)).
tt(t1_rvsum_2,ax,(r7_binop_1 k2_numbers k2_rvsum_2 k29_binop_2)).
tt(t1_scheme1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = (k4_nat_1 2 B)) )  &  (~  (A = (k2_nat_1 (k4_nat_1 2 B) 1)) ) ) ) ) ) ) ) ).
tt(t1_scm_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ( ((v5_memstr_0 F 2 k1_ami_3 E) & (m1_scm_1 F (k16_afinsq_1 A B C D)))  =>  ( ((k1_funct_1 F (k10_ami_3 k6_numbers)) = A)  &  ( ((k1_funct_1 F (k10_ami_3 1)) = B)  &  ( ((k1_funct_1 F (k10_ami_3 2)) = C)  &  ((k1_funct_1 F (k10_ami_3 3)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  &  ( (~  (B = C) )  & (r4_scmfsa7b (k2_scmfsa8c B A) C)) ) ) ) ) ) ) ) ) ).
tt(t1_scm_comp,ax, (! [A:$i] :  ((m2_subset_1 A (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (~  ( (~  (A = (k4_tarski k6_numbers k6_numbers)) )  &  ( (~  (A = (k4_tarski k6_numbers 1)) )  &  ( (~  (A = (k4_tarski k6_numbers 2)) )  &  ( (~  (A = (k4_tarski k6_numbers 3)) )  &  (~  (A = (k4_tarski k6_numbers 4)) ) ) ) ) ) ) ) ) ).
tt(t1_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_scmfsa_2)) =>  (~  ((r2_hidden A (k8_struct_0 k1_scmfsa_2)) &  ( (~  ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  &  (~ (m1_scmfsa_2 A)) ) ) ) ) ) ).
tt(t1_scmfsa_1,ax,(r1_tarski k1_ami_2 k1_scmfsa_1)).
tt(t1_scmfsa_2,ax, ((k4_struct_0 k1_scmfsa_2) = k5_numbers) ).
tt(t1_scmfsa_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k11_scmfsa_2 B) A) = (k11_scmfsa_2 (k2_nat_1 B A))) ) ) ) ) ).
tt(t1_scmfsa_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  (~ (v2_compos_1 B k1_scmfsa_2)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 C) & (v4_extpro_1 C 3 k1_scmfsa_2 B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski C D) & (r1_tarski (k9_memstr_0 3 k1_scmfsa_2 C A) E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ((r1_tarski B F) & (r1_tarski (k6_compos_1 k1_scmfsa_2 B A) G))  =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D H)) A) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 G E H)))  &  ( ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k3_extpro_1 3 k1_scmfsa_2 F (k5_extpro_1 3 k1_scmfsa_2 F D H)) A) = (k3_extpro_1 3 k1_scmfsa_2 G (k5_extpro_1 3 k1_scmfsa_2 G E H)))  &  ( ((k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 F D H) (k9_xtuple_0 (k6_memstr_0 3 k1_scmfsa_2 C))) = (k5_relat_1 (k5_extpro_1 3 k1_scmfsa_2 G E H) (k9_xtuple_0 (k6_memstr_0 3 k1_scmfsa_2 C))))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F (k1_funct_4 D (k6_memstr_0 3 k1_scmfsa_2 E)) H)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 G E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (~ (r2_hidden (k2_compos_1 k1_scmfsa_2) (k10_xtuple_0 (k2_scmfsa6a A)))) ) ) ).
tt(t1_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 A (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 A 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski B C) => (r1_extpro_1 3 k1_scmfsa_2 C A)) ) ) ) ) ) ) ).
tt(t1_scmfsa6c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v1_scmfsa6b D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v7_amistd_1 E 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a D E) B C) A) = (k1_funct_1 (k1_scmfsa6b E (k1_scmfsa6b D B C) C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scmfsa_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_scmfsa_7 A B) = (k1_ordinal4 (k2_scmfsa_7 A B) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ) ) ).
tt(t1_scmfsa7b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ( ( (A = (k2_compos_1 k1_scmfsa_2))  =>  ((k1_funct_1 (k2_scmfsa6a (k11_compos_1 k1_scmfsa_2 A)) k6_numbers) = (k11_scmfsa_2 2)) )  &  ( (~  (A = (k2_compos_1 k1_scmfsa_2)) )  =>  ((k1_funct_1 (k2_scmfsa6a (k11_compos_1 k1_scmfsa_2 A)) k6_numbers) = A) ) ) ) ) ).
tt(t1_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r5_scmfsa7b B C A) => (r2_hidden k6_numbers (k9_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t1_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a B A C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E D) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) E)) (k2_afinsq_1 C))) ) )  & (r1_xxreal_0 (k2_scmfsa8a B A C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scmfsa9a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k2_sf_mastr (k16_funcop_1 A B)) = (k1_sf_mastr B)) ) ) ) ) ).
tt(t1_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k1_scmfsa8b B (k3_scmfsa6a A (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k2_nat_1 (k5_card_1 A) 6)) ) ) ) ) ).
tt(t1_scmfsa_i,ax,(r1_tarski k3_scm_inst k2_scmfsa_i)).
tt(t1_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ( (~  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  &  ( (~ (m1_scmfsa_2 B))  &  (~  (B = (k4_struct_0 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ).
tt(t1_scm_inst,ax,(r2_hidden (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) k3_scm_inst)).
tt(t1_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  (~  ( (D = (k1_funct_1 A B))  &  ((k1_sf_mastr D) = (k1_sf_mastr C)) ) ) ) )  |  ((k2_sf_mastr A) = (k2_sf_mastr (k1_funct_4 A (k16_funcop_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t1_scmpds_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 B) = (k5_memstr_0 2 k1_scmpds_2 C))  =>  ((k17_scmpds_2 B A) = (k17_scmpds_2 C A)) ) ) ) ) ) ) ) ).
tt(t1_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((r2_hidden (k2_compos_0 (u1_compos_1 k1_scmpds_2) A) (k4_enumset1 k6_numbers 1 4 5 6 14)) |  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 A B) (k4_struct_0 k1_scmpds_2)) = (k1_ordinal1 (k5_memstr_0 2 k1_scmpds_2 B))) ) ) ) ) ) ).
tt(t1_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k5_memstr_0 2 k1_scmpds_2 A) = B)  =>  ((k17_scmpds_2 A (k6_xcmplx_0 C B)) = C) ) ) ) ) ) ) ) ).
tt(t1_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (A = (k1_scmp_gcd B)) ) ) ) ) ).
tt(t1_scmpds_9,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k5_memstr_0 2 k1_scmpds_2 C) = B)  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 A C) (k4_struct_0 k1_scmpds_2)) = (k1_ordinal1 (k5_memstr_0 2 k1_scmpds_2 C))) ) ) )  =>  ((k1_amistd_1 2 k1_scmpds_2 B A) = (k1_tarski (k1_ordinal1 B))) ) ) ) ) ) ).
tt(t1_scmpds_i,ax, (! [A:$i] :  ((v1_int_1 A) => (r2_hidden A (k2_xboole_0 k2_scm_inst k4_numbers))) ) ).
tt(t1_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_scmpds_2 A B) = (k1_scmp_gcd (k2_nat_1 A B))) ) ) ) ) ).
tt(t1_scmring2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 (k1_scmring2 B))))  <=> (r2_hidden A (k8_struct_0 k1_ami_3))) ) ) ) ).
tt(t1_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  ((k4_memstr_0 2 (k1_scmring2 A) B) = (u1_struct_0 A)) ) ) ) ) ).
tt(t1_scmring4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ((k2_scmring3 B A) = (k1_domain_1 k5_numbers k5_numbers 1 A)) ) ) ) ) ).
tt(t1_scmringi,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 8)) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_scmringi B)) =>  (! [D:$i] :  ((m1_subset_1 D k2_scm_inst) =>  (! [E:$i] :  ((m1_subset_1 E k2_scm_inst) =>  ( (C = (k3_xtuple_0 A k1_xboole_0 (k2_finseq_4 k2_scm_inst D E)))  =>  ( ((k2_scmringi B C) = D)  &  ((k3_scmringi B C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (~ (r2_hidden (k4_tarski A B) B)) ) ) ).
tt(t1_scpinvar,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmpds_4 (k4_scmpds_4 A B) C) k6_numbers) = A)  &  ((k1_funct_1 (k1_scmpds_4 (k4_scmpds_4 A B) C) 1) = B) ) ) ) ) ) ) ) ).
tt(t1_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  ( ((k3_finseq_1 D) = B)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 D)))  =>  ((k1_funct_1 D E) = (k1_funct_1 A (k1_scmp_gcd (k2_nat_1 C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) G)) k6_numbers) |  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_6 E G C D) B A) F) = (k1_funct_1 (k6_scmpds_4 C B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B C B C)) ) ) ) ) ) ).
tt(t1_seq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [B:$i] :  ((r2_hidden B k5_numbers) => (v1_xreal_0 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t1_seq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ( (~ (r1_xxreal_0 B (k4_xcmplx_0 A)))  &  (~ (r1_xxreal_0 A B)) )  <=>  (~ (r1_xxreal_0 A (k18_complex1 B))) ) ) ) ) ) ).
tt(t1_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (~  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden C A) &  ((r2_hidden D B) & (r1_xxreal_0 D C)) ) ) ) ) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((v1_xreal_0 D) &  (? [E:$i] :  ((v1_xreal_0 E) &  ((r2_hidden D A) &  ((r2_hidden E B) &  (~  ((r1_xxreal_0 D C) & (r1_xxreal_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_seqfunc,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  <=>  ( ((k9_xtuple_0 C) = k5_numbers)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((v1_funct_1 (k1_funct_1 C D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t1_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A C) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ) ) ) ).
tt(t1_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers B C) = (k3_power A (k2_nat_1 C 1))) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 1 A) |  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t1_series_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k18_complex1 (k1_newton (k4_xcmplx_0 1) A)) = 1) ) ) ).
tt(t1_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 A B) | (r1_xxreal_0 (k13_complex1 B A) (k13_complex1 (k2_xcmplx_0 B C) (k2_xcmplx_0 A C)))) ) ) ) ) ) ) ) ).
tt(t1_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_newton (k2_xcmplx_0 (k2_xcmplx_0 A B) C) 2) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k1_newton B 2)) (k1_newton C 2)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) C)) (k3_xcmplx_0 (k3_xcmplx_0 2 B) C))) ) ) ) ) ) ) ).
tt(t1_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 4 (k3_xcmplx_0 (k2_xcmplx_0 A B) (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B))))) ) ) ) ).
tt(t1_setfam_1,ax, ((k1_setfam_1 k1_xboole_0) = k1_xboole_0) ).
tt(t1_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  => (r2_hidden (k3_funct_2 k5_numbers C D (k2_nat_1 A B)) (a_3_0_setlim_1 A C D))) ) ) ) ) ) ) ).
tt(t1_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k3_prob_1 B (k10_nat_1 (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t1_setwiseo,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k1_tarski A) (k1_enumset1 A B C))) ) ) ).
tt(t1_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) & (v2_binop_1 E B))  =>  ( (C = D)  |  ((k7_setwiseo A B E (k3_setwiseo A C D) F) = (k5_binop_1 B E (k3_funct_2 A B F C) (k3_funct_2 A B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sfmastr1,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (~  ( (~ (r2_hidden A (k2_sf_mastr B)))  & (r4_scmfsa7b B A)) ) ) ) ) ) ).
tt(t1_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b D (k1_scmfsa_m A) B) & (r6_scmfsa7b D (k1_scmfsa_m A) B))  =>  ((r2_hidden C (k2_sf_mastr D)) |  ((k1_funct_1 (k1_scmfsa6b D A B) C) = (k1_funct_1 (k1_scmfsa_m A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m A) D) & (r6_scmfsa7b C (k1_scmfsa_m A) D))  =>  ((r4_scmfsa7b C B) |  ((k1_funct_1 (k1_scmfsa6b C A D) B) = (k1_funct_1 (k1_scmfsa_m A) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k6_scmfsa_2 A B) = (k6_scmfsa_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((r2_hidden C (k1_sgraph1 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( (C = D)  &  ((r1_xxreal_0 A D) & (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k5_robbins1 A B C)) = (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C))) ) ) ) ) ) ) ).
tt(t1_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A B (k5_sheffer1 A C D)))) (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A B D) D)) (k5_sheffer1 A E (k5_sheffer1 A B (k5_sheffer1 A C D))))) = (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A B D) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_simplex0,ax, (! [A:$i] :  ((v1_classes1 A) <=>  (! [B:$i] :  ((r2_hidden B A) => (r1_tarski (k9_setfam_1 B) A)) ) ) ) ).
tt(t1_simplex1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ( (! [D:$i] :  ((r2_hidden D A) =>  ((k1_card_1 (k9_relat_1 B D)) = C) ) )  =>  ((k1_card_1 B) = (k1_card_2 (k1_card_1 (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) A))) (k2_card_2 C (k1_card_1 A)))) ) ) ) ) ) ) ).
tt(t1_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [C:$i] :  ( ((v1_tops_2 C (k3_pcomps_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [D:$i] :  ((m1_simplex2 D A B) =>  ( ((v1_compts_1 (k3_pcomps_1 A)) &  ((m1_setfam_1 B (u1_struct_0 (k3_pcomps_1 A))) & (r1_tarski B C)) )  => (m1_simplex2 D A C)) ) ) ) ) ) ) ) ) ).
tt(t1_sincos10,ax,(r1_tarski (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers k1_fdiff_9))).
tt(t1_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k8_real_1 2 (k7_square_1 (k11_binop_2 A B))) (k9_binop_2 A B))) ) ) ) ) ).
tt(t1_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A))) = 1) ) ) ).
tt(t1_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos4 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k1_sin_cos4 A))) ) ) ).
tt(t1_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k20_sin_cos A) = k6_numbers) )  =>  ((k3_sin_cos4 A) = (k10_real_1 (k4_sin_cos4 A) (k1_sin_cos4 A))) ) ) ) ).
tt(t1_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B A) |  ((k1_int_1 (k7_xcmplx_0 A B)) = k6_numbers) ) ) ) ) ) ) ).
tt(t1_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k12_binop_2 1 A) = (k3_power A (k19_binop_2 1))) ) ) ) ).
tt(t1_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k9_sin_cos2 A) = (k7_xcmplx_0 (k3_sin_cos2 A) (k6_sin_cos2 A)))  &  ((k9_sin_cos2 k6_numbers) = k6_numbers) ) ) ) ).
tt(t1_sin_cos9,ax,(r1_tarski (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers k29_sin_cos))).
tt(t1_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( ((k3_newton k6_numbers) = 1)  &  ( (~  ((k3_newton A) = k6_numbers) )  &  ((k3_newton (k2_nat_1 A 1)) = (k3_nat_1 (k3_newton A) (k2_nat_1 A 1))) ) ) ) ) ).
tt(t1_sppol_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xxreal_0 A (k5_real_1 B 1))) ) ) ) ) ).
tt(t1_sppol_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k19_euclid A B) = (k19_euclid C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sprect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v3_funct_1 (k7_finseq_1 A B)) =>  ((v3_funct_1 A) & (v3_funct_1 B)) ) ) ) ) ) ).
tt(t1_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( ((r1_xxreal_0 A B) &  ((r2_hidden A (k4_finseq_1 E)) &  ((r2_hidden B (k4_finseq_1 E)) & (r2_hidden C (k4_finseq_1 (k3_finseq_6 D E A B)))) ) )  => (r2_hidden (k7_nat_d (k2_nat_1 C A) 1) (k4_finseq_1 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_sprect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k7_partfun1 A (k8_finseq_1 A C B) (k3_finseq_1 (k8_finseq_1 A C B))) = (k7_partfun1 A B (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(t1_sprect_4,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ((v4_pre_topc B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xboole_0 (k3_topreal1 2 A) B))  &  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) B))  &  (~  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k3_jordan3 A (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) B) = (k1_tarski (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ) ) ).
tt(t1_sprect_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden C (k10_xtuple_0 (k17_finseq_1 A (k4_finseq_4 B D) B))) => (r1_xxreal_0 (k4_finseq_4 B C) (k4_finseq_4 B D))) ) ) ) ) ) ) ) ) ).
tt(t1_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k3_xxreal_0 A B) (k4_xxreal_0 A B)) = (k2_xcmplx_0 A B)) ) ) ) ) ).
tt(t1_stacks_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_finseq_3 A k1_xboole_0) = k1_xboole_0) ) ) ).
tt(t1_stirl2_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  ((k6_seq_4 A) = (k5_nat_1 A)) ) ) ).
tt(t1_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k8_struct_0 A)) <=>  (~ (v9_struct_0 B A)) ) ) ) ) ) ).
tt(t1_sublemma,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r1_tarski (k9_xtuple_0 D) (k9_xtuple_0 C)) & (r1_tarski (k9_xtuple_0 E) (k9_xtuple_0 C)))  =>  ((k1_funct_4 (k1_funct_4 A B) C) = (k1_funct_4 (k1_funct_4 (k1_funct_4 A D) (k1_funct_4 B E)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_subset_1,ax, (! [A:$i] : (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 A))) ).
tt(t1_subset,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (m1_subset_1 A B)) ) ) ).
tt(t1_substlat,ax, (! [A:$i] :  (! [B:$i] : (r2_hidden k1_xboole_0 (k1_substlat A B))) ) ).
tt(t1_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((r2_hidden B (k9_xtuple_0 C)) => (r2_hidden (k1_funct_1 C B) (k3_qc_lang1 A))) ) ) ) ) ) ).
tt(t1_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_substut1 A)) =>  (? [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A C) = (k5_cqc_lang A))  &  ((k19_substut1 A C) = B) ) ) ) ) ) ) ) ).
tt(t1_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C (k3_supinf_1 B)) => (r2_hidden C (k3_supinf_1 A))) ) ) ) ) ) ) ) ).
tt(t1_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k3_supinf_2 A B) = (k7_real_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_orders_2 B (k4_struct_0 B) C)) ) ) ) ) ) ).
tt(t1_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski (k9_xtuple_0 (k3_xboole_0 C (k2_zfmisc_1 A B))) A) & (r1_tarski (k10_xtuple_0 (k3_xboole_0 C (k2_zfmisc_1 A B))) B)) ) ) ) ) ).
tt(t1_t_0topsp,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((r2_hidden E D) &  ((k3_funct_2 A B C E) = (k3_funct_2 A B C F)) )  => (r2_hidden F D)) ) ) ) )  =>  ((k8_relset_1 A B C (k7_relset_1 A B C D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t1_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k11_borsuk_1 A B)))) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B) C) = (k3_tarski C)) ) ) ) ) ) ) ).
tt(t1_tarski,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  ((r2_hidden C A) <=> (r2_hidden C B)) )  =>  (A = B) ) ) ) ).
tt(t1_taxonom1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden (k1_nat_1 B 1) (k4_finseq_1 A)) =>  ((r2_hidden B (k4_finseq_1 A)) |  (B = k6_numbers) ) ) ) ) ) ) ).
tt(t1_taxonom2,ax, (! [A:$i] :  ( (~ (v2_struct_0 (k2_yellow_1 (k1_tarski (k1_tarski A)))))  &  ((v3_orders_2 (k2_yellow_1 (k1_tarski (k1_tarski A)))) &  ((v4_orders_2 (k2_yellow_1 (k1_tarski (k1_tarski A)))) &  ((v5_orders_2 (k2_yellow_1 (k1_tarski (k1_tarski A)))) &  ((v1_taxonom2 (k2_yellow_1 (k1_tarski (k1_tarski A)))) & (v2_taxonom2 (k2_yellow_1 (k1_tarski (k1_tarski A))))) ) ) ) ) ) ).
tt(t1_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_prepower A (k2_xcmplx_0 C B)) = (k3_xcmplx_0 (k4_prepower A C) (k4_prepower A B))) ) ) ) ) ) ) ).
tt(t1_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k18_complex1 (k2_newton A B)) = (k2_newton (k18_complex1 A) B)) ) ) ) ) ).
tt(t1_tbsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) &  (~ (r1_xxreal_0 (k4_power A C) (k4_power A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_tdgroup,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_vectsp_1)) =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_vectsp_1)) &  ((k3_rlvect_1 k1_vectsp_1 B B) = A) ) ) ) ) ).
tt(t1_tdlat_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k2_struct_0 A))  <=> (r1_tarski (k3_subset_1 (u1_struct_0 A) B) C)) ) ) ) ) ) ) ).
tt(t1_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))) (k1_tops_1 A (k2_pre_topc A B))) & (r1_tarski (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))) (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ).
tt(t1_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k3_subset_1 (u1_struct_0 A) (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t1_termord,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A B C) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  & (r6_pboole A C (k11_pre_poly A B D))) ) ) ) ) ) ) ) ).
tt(t1_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_tmap_1 A B)))) =>  ( ( (C = D)  & (v3_pre_topc C A))  => (v3_pre_topc D (k6_tmap_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t1_tex_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_card_1 B 1) =>  ((r1_tarski A B) =>  (A = B) ) ) ) ) ) ).
tt(t1_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ( (~ (v1_xboole_0 B))  <=> (v1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t1_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k1_setfam_1 (a_2_0_tex_4 A B))) ) ) ) ) ).
tt(t1_tietze,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 (k17_complex1 (k6_xcmplx_0 A B)) C) =>  ((r1_xxreal_0 (k6_xcmplx_0 B C) A) & (r1_xxreal_0 A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t1_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ((r1_subset_1 C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ( ((k2_partfun1 C B E (k9_subset_1 A C D)) = (k2_partfun1 D B F (k9_subset_1 A C D)))  &  ( ((k2_partfun1 (k4_subset_1 A C D) B (k1_tmap_1 A B C D E F) C) = E)  &  ((k2_partfun1 (k4_subset_1 A C D) B (k1_tmap_1 A B C D E F) D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_toler_1,ax, (! [A:$i] :  ((k2_relset_1 A (k1_eqrel_1 A)) = A) ) ).
tt(t1_topalg_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((r2_relset_1 A A (k1_partfun1 A B B A C D) (k6_partfun1 A)) & (r2_relset_1 B B (k1_partfun1 B A A B D C) (k6_partfun1 B)))  => (v3_funct_2 D B A)) ) ) ) ) ) ) ).
tt(t1_topalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G B E F) =>  ( ( (C = E)  &  ( (D = F)  & (r1_borsuk_6 B E F)) )  => (m1_borsuk_2 G A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topalg_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((r2_hidden C A) & (r2_hidden D B))  =>  ((v1_funct_1 (k1_funct_4 E (k16_funcop_1 C D))) &  ((v1_funct_2 (k1_funct_4 E (k16_funcop_1 C D)) A B) & (m1_subset_1 (k1_funct_4 E (k16_funcop_1 C D)) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t1_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k5_group_7 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_topmetr A B))) =>  (~  ( (~  ((k9_metric_1 (k2_topmetr A B) D C) = (k1_rcomp_1 A B)) )  &  ( (~  ((k9_metric_1 (k2_topmetr A B) D C) = (k3_rcomp_1 A (k2_xcmplx_0 D C))) )  &  ( (~  ((k9_metric_1 (k2_topmetr A B) D C) = (k4_rcomp_1 (k6_xcmplx_0 D C) B)) )  &  (~  ((k9_metric_1 (k2_topmetr A B) D C) = (k2_rcomp_1 (k6_xcmplx_0 D C) (k2_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topalg_6,ax,(r2_funct_2 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (k1_borsuk_6 k6_numbers 1 k6_numbers 1) (k3_struct_0 (k4_topmetr k6_numbers 1)))).
tt(t1_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))) =>  ( (D = (k9_subset_1 (u1_struct_0 A) B C))  => (r1_tarski (k2_tops_1 (k1_pre_topc A C) D) (k9_subset_1 (u1_struct_0 A) (k2_tops_1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t1_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ((r1_xxreal_0 (k1_topdim_2 B C) A) => (v1_topdim_2 C B)) ) ) ) ) ) ).
tt(t1_topgen_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~ (r1_xboole_0 B (k3_subset_1 (u1_struct_0 A) C)))  &  ((k7_subset_1 (u1_struct_0 A) B C) = k1_xboole_0) ) )  &  (~  ( (~  ((k7_subset_1 (u1_struct_0 A) B C) = k1_xboole_0) )  & (r1_xboole_0 B (k3_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t1_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_tops_2 (a_3_0_topgen_2 A B C) A) &  ((v1_yellow_8 (a_3_0_topgen_2 A B C) A C) & (m1_subset_1 (a_3_0_topgen_2 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t1_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) <=>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D B) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v4_card_3 B) <=> (v4_card_3 (k7_setfam_1 A B))) ) ) ) ).
tt(t1_topgen_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) =>  (! [C:$i] :  ((k8_relat_1 (k1_funct_4 A B) C) = (k2_xboole_0 (k8_relat_1 A C) (k8_relat_1 B C))) ) ) ) ) ) ) ).
tt(t1_topgrp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((k2_relset_1 (u1_struct_0 A) (k3_struct_0 A)) = (k2_struct_0 A)) ) ) ).
tt(t1_topmetr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) &  ((v2_funct_1 B) &  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C (k9_xtuple_0 B)) &  ((r2_hidden D (k6_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 B))) &  ((k1_funct_1 B C) = (k1_funct_1 A D)) ) ) ) ) ) ) )  => (v2_funct_1 (k1_funct_4 A B))) ) ) ) ) ).
tt(t1_topmetr3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( ((v2_tbsp_1 B A) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r2_hidden (k2_tbsp_1 A B D) C)) )  & (v4_pre_topc C (k3_pcomps_1 A))) )  => (r2_hidden (k1_tbsp_1 A B) C)) ) ) ) ) ) ) ).
tt(t1_topmetr,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_setfam_1 B (u1_struct_0 A)) <=> (r1_tarski (u1_struct_0 A) (k3_tarski B))) ) ) ) ) ).
tt(t1_topreal1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_topreal1 A C D B) =>  ((r2_hidden C B) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(t1_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r2_hidden A k1_topreal1) &  ((r2_hidden B k1_topreal1) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) A B C) &  ((r1_topreal1 (k15_euclid 2) A B D) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) C D))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) C D) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topreal3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden 1 (k4_finseq_1 (k11_finseq_1 A B C))) &  ((r2_hidden 2 (k4_finseq_1 (k11_finseq_1 A B C))) & (r2_hidden 3 (k4_finseq_1 (k11_finseq_1 A B C)))) ) ) ) ) ).
tt(t1_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal4 A B C) => (v5_topreal1 A)) ) ) ) ) ) ) ).
tt(t1_topreal5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((v3_pre_topc D A) &  ( (~ (r1_xboole_0 C B))  &  ( (~ (r1_xboole_0 D B))  &  ((r1_tarski B (k4_subset_1 (u1_struct_0 A) C D)) &  ((r1_xboole_0 C D) & (v2_connsp_1 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k6_square_1 (k2_xcmplx_0 A B)) (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B)))) ) ) ) ) ).
tt(t1_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_xxreal_0 (k2_square_1 (k7_real_1 A C) (k7_real_1 B D)) (k7_real_1 (k2_square_1 A B) (k2_square_1 C D)))) ) ) ) ) ) ) ) ).
tt(t1_topreal8,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A (k2_tarski B C)) & (r2_hidden B A))  =>  ((r2_hidden C A) |  (A = (k1_tarski B)) ) ) ) ) ) ).
tt(t1_topreala,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden (k1_funct_1 A B) (k7_relat_1 A C)) & (v2_funct_1 A)) )  => (r2_hidden B C)) ) ) ) ) ).
tt(t1_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k17_sin_cos (k2_xcmplx_0 (k3_xcmplx_0 A B) C)) = (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A C) k16_sin_cos) B)) ) ) ) ) ) ) ).
tt(t1_toprealc,ax, (! [A:$i] :  ((v1_zfmisc_1 A) =>  (! [B:$i] :  ((r2_tarski A B) => (v1_zfmisc_1 B)) ) ) ) ).
tt(t1_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (m1_subset_1 (k1_funct_1 B C) (u1_struct_0 (k15_euclid A)))) ) ) ) ) ) ) ) ).
tt(t1_tops_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k3_subset_1 (u1_struct_0 A) B) = (k3_subset_1 (u1_struct_0 A) C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t1_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski B (k9_setfam_1 (k2_struct_0 A)))) ) ) ) ).
tt(t1_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = (k1_struct_0 A))  =>  ((k3_subset_1 (u1_struct_0 A) B) = (k2_struct_0 A)) )  &  ( ( ((k3_subset_1 (u1_struct_0 A) B) = (k2_struct_0 A))  =>  (B = (k1_struct_0 A)) )  &  ( ( (B = k1_xboole_0)  =>  ((k3_subset_1 (u1_struct_0 A) B) = (u1_struct_0 A)) )  &  ( ((k3_subset_1 (u1_struct_0 A) B) = (u1_struct_0 A))  =>  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t1_tops_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v2_pre_topc C) & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v2_pre_topc D) & (l1_pre_topc D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D)))  &  ( (E = F)  & (v1_t_0topsp E A C)) ) )  => (v1_t_0topsp F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (? [D:$i] :  ((m1_subset_1 D A) &  ((k3_funct_2 A A C D) = B) ) ) ) ) ) ) ) ) ).
tt(t1_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_aff_1 A B C D) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_aff_1 A B C D) &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (C = (k1_rcomp_1 A B))  => (v4_pre_topc C k3_topmetr)) ) ) ) ) ) ) ).
tt(t1_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  (B = (k7_finseq_1 A C)) ) ) ) ) ) ) ) ).
tt(t1_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_tarski A C) & (r1_tarski B C))  => (r3_xboole_0 A B)) ) ) ) ) ) ) ).
tt(t1_trees_3,ax, (! [A:$i] :  ((v1_trees_3 A) <=> (r1_tarski A k1_trees_3)) ) ).
tt(t1_trees_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_tarski (k2_trees_1 A) (k2_trees_1 B)) => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t1_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k5_trees_2 A (k6_finseq_1 k5_numbers)) = A) ) ) ).
tt(t1_trees_a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((k7_finseq_1 A B) = (k7_finseq_1 D C))  => (r3_xboole_0 A D)) ) ) ) ) ) ) ) ) ).
tt(t1_triang_1,ax, (! [A:$i] :  ((k2_wellord1 k1_xboole_0 A) = k1_xboole_0) ) ).
tt(t1_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) => (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(t1_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_subset_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 A) B) (k3_subset_1 (u1_struct_0 A) C)) = (k7_subset_1 (u1_struct_0 A) C B)) ) ) ) ) ) ) ).
tt(t1_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_pre_topc D B) &  (D = (k8_subset_1 (u1_struct_0 A) C (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_tsp_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v1_tsp_2 C A)) )  => (v1_tsp_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t1_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden A (k3_turing_1 B)) <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t1_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k2_twoscomp (k10_finseq_1 A B)) = (k10_margrel1 A B))  &  ( ((k1_funct_1 k3_twoscomp (k10_finseq_1 A B)) = (k10_margrel1 (k9_margrel1 A) B))  &  ((k1_funct_1 k4_twoscomp (k10_finseq_1 A B)) = (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B))) ) ) ) ) ) ) ).
tt(t1_unialg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) )  =>  ((r2_hidden A (k4_finseq_1 (u1_unialg_1 B))) =>  ((v1_funct_1 (k1_funct_1 (u1_unialg_1 B) A)) & (m1_subset_1 (k1_funct_1 (u1_unialg_1 B) A) (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 B)) (u1_struct_0 B))))) ) ) ) ) ) ).
tt(t1_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  ((k3_finseq_1 (u1_unialg_1 A)) = (k3_finseq_1 (u1_unialg_1 B))) ) ) ) ) ) ).
tt(t1_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k1_unialg_3 A)) <=>  (? [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  &  (B = C) ) ) ) ) ) ) ).
tt(t1_uniform1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 A (k10_real_1 1 B))) ) ) ) ) ) ) ) ) ).
tt(t1_uniroots,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ((k5_relat_1 A (k2_finseq_1 1)) = (k9_finseq_1 (k1_funct_1 A 1))) ) ) ) ).
tt(t1_uproots,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ((k1_recdef_1 A B) = k6_numbers) ) ) ) )  =>  ( ((k2_wsierp_1 A) = (k3_finseq_1 A))  <=>  (A = (k5_finseq_2 k5_numbers (k3_finseq_1 A) 1)) ) ) ) ) ).
tt(t1_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k1_urysohn1 A)) =>  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 B 1)) ) ) ) ) ) ).
tt(t1_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((k1_integra2 (k1_integra2 A B) (k2_real_1 B)) = A) ) ) ) ) ) ).
tt(t1_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 D) (k9_setfam_1 (u1_struct_0 A)))))) )  &  ((r1_tarski B (k1_funct_1 E k6_numbers)) &  ( (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_funct_1 E 1)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers (k1_urysohn1 D)) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers (k1_urysohn1 D)) =>  ( (~ (r1_xxreal_0 G F))  =>  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E F) A) &  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E G) A) & (r1_tarski (k2_pre_topc A (k4_urysohn1 A (k1_urysohn1 D) E F)) (k4_urysohn1 A (k1_urysohn1 D) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_valuat_1 A B)) =>  ((v1_funct_1 C) &  ((v1_funct_2 C (k3_qc_lang1 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_qc_lang1 A) B)))) ) ) ) ) ) ) ) ).
tt(t1_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_valued_0 B))  =>  ((r1_tarski A B) => (v1_valued_0 A)) ) ) ) ) ).
tt(t1_valued_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_membered C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k1_funct_1 (k2_valued_1 A B C D E) F) = (k2_xcmplx_0 (k1_funct_1 D F) (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_valued_2,ax, (! [A:$i] : (m1_subset_1 (k3_valued_2 A) (k1_zfmisc_1 (k2_valued_2 A)))) ).
tt(t1_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v1_vectmetr A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ( ((k7_partfun1 (u1_struct_0 A) E 1) = B)  &  ( ((k7_partfun1 (u1_struct_0 A) E (k3_finseq_1 E)) = C)  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F (k9_real_1 (k3_finseq_1 E) 1)) & (r1_xxreal_0 D (k4_metric_1 A (k7_partfun1 (u1_struct_0 A) E F) (k7_partfun1 (u1_struct_0 A) E (k2_nat_1 F 1))))) ) ) ) )  &  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  ( ( ((k3_finseq_1 F) = (k9_real_1 (k3_finseq_1 E) 1))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k3_finseq_1 F)))  =>  ((k7_partfun1 k1_numbers F G) = (k4_metric_1 A (k7_partfun1 (u1_struct_0 A) E G) (k7_partfun1 (u1_struct_0 A) E (k2_nat_1 G 1)))) ) ) ) )  =>  ((k4_metric_1 A B C) = (k18_rvsum_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k4_vectsp_1 A C (k4_struct_0 A) D) = (k4_struct_0 C))  &  ((k4_vectsp_1 A C B (k4_struct_0 C)) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 C))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 C))))  =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 B k5_numbers)) =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 F) (k10_xtuple_0 G)) (k2_matrix_1 D)) =>  ((k1_matrix13 (u1_struct_0 C) (k3_matrix_3 C D E) A B F G) = (k5_matrlin2 A B C (k1_matrix13 (u1_struct_0 C) D A B F G) (k1_matrix13 (u1_struct_0 C) E A B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_vectsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_vectsp_1)) =>  ( ((k3_rlvect_1 k1_vectsp_1 A B) = (k3_rlvect_1 k1_vectsp_1 B A))  &  ( ((k3_rlvect_1 k1_vectsp_1 (k3_rlvect_1 k1_vectsp_1 A B) C) = (k3_rlvect_1 k1_vectsp_1 A (k3_rlvect_1 k1_vectsp_1 B C)))  &  ( ((k3_rlvect_1 k1_vectsp_1 A (k4_struct_0 k1_vectsp_1)) = A)  &  ((k3_rlvect_1 k1_vectsp_1 A (k4_algstr_0 k1_vectsp_1 A)) = (k4_struct_0 k1_vectsp_1)) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_4 C A B) =>  ( (C = k1_xboole_0)  | (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ).
tt(t1_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((r1_struct_0 (k1_vectsp_5 A B C D) E) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_6 D B C) =>  ((r2_hidden A (k1_vectsp_6 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) &  ( (A = E)  &  (~  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v1_vectsp_7 D A B))  => (v1_vectsp_7 C A B)) ) ) ) ) ) ) ) ) ).
tt(t1_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_vectsp_8 A B))))  =>  (~ (v1_xboole_0 (k7_relset_1 (k2_vectsp_8 A B) (k9_setfam_1 (u1_struct_0 B)) (k4_vectsp_8 A B) C))) ) ) ) ) ) ) ).
tt(t1_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_1 D) (k4_finseq_1 D)) &  ((v3_funct_2 F (k4_finseq_1 D) (k4_finseq_1 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 D) (k4_finseq_1 D))))) ) )  =>  ( (E = (k1_partfun1 (k4_finseq_1 D) (k4_finseq_1 D) k5_numbers (u1_struct_0 B) F D))  =>  ((k4_rlvect_1 B (k3_vectsp_6 A B D C)) = (k4_rlvect_1 B (k3_vectsp_6 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k7_subset_1 A (k1_relset_1 A (k3_vfunct_1 A B D C)) (k8_relset_1 A (u1_struct_0 B) (k3_vfunct_1 A B D C) (k1_tarski (k4_struct_0 B)))) = (k9_subset_1 A (k7_subset_1 A (k1_relset_1 A D) (k8_relset_1 A k1_numbers D (k1_tarski k6_numbers))) (k7_subset_1 A (k1_relset_1 A C) (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B)))))) ) ) ) ) ) ) ) ) ).
tt(t1_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ((k7_subset_1 A (k1_relset_1 A (k1_vfunct_2 A B C D)) (k8_relset_1 A (u1_struct_0 B) (k1_vfunct_2 A B C D) (k1_tarski (k4_struct_0 B)))) = (k9_subset_1 A (k7_subset_1 A (k1_relset_1 A C) (k8_relset_1 A k2_numbers C (k1_tarski k6_numbers))) (k7_subset_1 A (k1_relset_1 A D) (k8_relset_1 A (u1_struct_0 B) D (k1_tarski (k4_struct_0 B)))))) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v1_waybel_0 B A))  <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) & (r2_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel10,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((r1_tarski A B) => (r1_tarski (k2_relat_1 A) (k2_relat_1 B)))  &  ( ((r1_tarski (k2_relat_1 A) (k2_relat_1 B)) => (r1_tarski A B))  &  ( ((r1_tarski (k2_relat_1 A) B) => (r1_tarski A (k2_relat_1 B)))  &  ((r1_tarski A (k2_relat_1 B)) => (r1_tarski (k2_relat_1 A) B)) ) ) ) ) ) ) ) ).
tt(t1_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r4_yellow_4 A B C) => (r3_orders_2 A (k2_yellow_0 A B) (k2_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t1_waybel12,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) & (v4_card_3 B))  => (v4_card_3 A)) ) ) ).
tt(t1_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (r1_tarski (k2_waybel_8 A B) (k2_waybel_8 A C))) ) ) ) ) ) ) ).
tt(t1_waybel14,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  &  ((r1_tarski C B) &  ( ((k5_setfam_1 A C) = (k5_setfam_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D C) & (r1_tarski D (k5_setfam_1 A (k7_subset_1 (k1_zfmisc_1 A) C (k6_domain_1 (k1_zfmisc_1 A) D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel15,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ( ((v4_yellow_0 C B) & (m1_yellow_0 C B))  =>  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) ) ) ) ) ) ) ).
tt(t1_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_waybel_0 A C))) = (k13_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t1_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v12_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v5_orders_3 C A B) => (v12_waybel_0 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t1_waybel18,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ( (C = (k7_subset_1 (k1_zfmisc_1 A) B (k1_tarski k1_xboole_0)))  |  (B = (k2_xboole_0 C (k1_tarski k1_xboole_0))) )  =>  ((k1_cantor_1 A B) = (k1_cantor_1 A C)) ) ) ) ) ) ) ).
tt(t1_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (? [B:$i] :  ( ((v2_pre_topc B) &  ((v1_waybel_9 B) & (m1_yellow_9 B A)) )  & (v1_waybel19 B)) ) ) ) ).
tt(t1_waybel_1,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A B C) => (r1_orders_2 A (k12_lattice3 A B D) (k12_lattice3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t1_waybel20,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k6_partfun1 A))) =>  ((k9_xtuple_0 B) = (k10_xtuple_0 B)) ) ) ) ).
tt(t1_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_yellow_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel21 C A B) =>  ((k2_yellow_6 (u1_struct_0 A) B C (k4_yellow_0 A)) = (k4_yellow_0 B)) ) ) ) ) ) ) ).
tt(t1_waybel22,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k8_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k8_waybel_0 A)))))) )  =>  ((k1_yellow_0 (k2_yellow_1 (k8_waybel_0 A)) B) = (k3_tarski B)) ) ) ) ) ).
tt(t1_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_waybel_8 A B) = (k8_subset_1 (u1_struct_0 A) (k1_waybel_3 A B) (u1_struct_0 (k1_waybel_8 A)))) ) ) ) ) ).
tt(t1_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_waybel17 A B)))) =>  ((v1_funct_1 (k1_yellow_0 (k2_waybel17 A B) C)) &  ((v1_funct_2 (k1_yellow_0 (k2_waybel17 A B) C) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_yellow_0 (k2_waybel17 A B) C) A B) & (m1_subset_1 (k1_yellow_0 (k2_waybel17 A B) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t1_waybel25,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k9_waybel18)) =>  ( (A = k6_numbers)  => (v4_pre_topc (k6_domain_1 (u1_struct_0 k9_waybel18) A) k9_waybel18)) ) ) ).
tt(t1_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_waybel26 A B))) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) &  ((v5_pre_topc C A (k1_waybel25 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) ) ) ) ) ) ) ) ) ).
tt(t1_waybel27,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r1_tarski D (k1_funct_2 A (k1_funct_2 B C))) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E D) &  ((v1_funct_1 E) & (v1_partfun1 E D)) ) )  =>  (~  ((v1_waybel27 E) & (r1_tarski (k10_xtuple_0 E) (k1_funct_2 (k2_zfmisc_1 A B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  => (r3_orders_2 A (k1_waybel_9 A B) (k1_waybel11 A B))) ) ) ) ).
tt(t1_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C)))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( ((v2_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 E))) )  => (v1_waybel27 (k2_tops_2 (u1_struct_0 D) (u1_struct_0 E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B))) ) ) ) ) ) ).
tt(t1_waybel30,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k3_xboole_0 A (k3_tarski B)) = (k3_tarski (a_2_0_waybel30 A B))) ) ) ) ).
tt(t1_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (r1_ordinal1 (k1_waybel31 A) (k1_card_1 B))) ) ) ) ).
tt(t1_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_waybel32 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v13_waybel_0 B A)) ) ) ) ) ).
tt(t1_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E (k3_yellow_1 C)) &  ((v13_waybel_0 E (k3_yellow_1 C)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 C))))) ) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v2_waybel_0 F (k3_yellow_1 D)) &  ((v13_waybel_0 F (k3_yellow_1 D)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 D))))) ) )  =>  ( (E = F)  =>  ((k1_waybel33 A C E) = (k1_waybel33 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  &  ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D))) )  =>  (! [E:$i] :  ((m1_waybel_1 E A B) =>  (! [F:$i] :  ((m1_waybel_1 F C D) =>  ( ( (E = F)  & (v3_waybel_1 E A B))  => (v3_waybel_1 F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel35,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_zfmisc_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) => (m1_waybel35 B A C)) ) ) ) ) ) ).
tt(t1_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) => (r3_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t1_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C E) B) & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D F) B))  => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k13_lattice3 A C D) (k13_lattice3 A E F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  &  ((v1_waybel_0 (k1_waybel_3 A B) A) &  ((v12_waybel_0 (k1_waybel_3 A B) A) & (m1_subset_1 (k1_waybel_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A (k1_waybel_3 A B))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) => (r1_tarski (k1_waybel_3 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v19_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k12_lattice3 A D E)) = (k12_lattice3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) =>  ((r3_orders_2 A (k1_yellow_0 A B) (k1_yellow_0 A C)) & (r1_orders_2 A (k2_yellow_0 A C) (k2_yellow_0 A B))) ) ) ) ) ) ).
tt(t1_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A B D) &  ((r3_orders_2 A D C) & (r2_hidden D (u1_struct_0 (k1_waybel_8 A)))) )  => (r1_waybel_3 A B C)) ) ) ) ) ) ) ) ) ).
tt(t1_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  &  ( ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  &  ( (E = F)  & (v5_orders_3 E A B)) ) )  => (v5_orders_3 F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_weddwitt,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k2_newton B A) = 1)  =>  ((r1_xxreal_0 B 1) |  (A = k6_numbers) ) ) ) ) ) ) ).
tt(t1_weierstr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) & (r1_tarski (k4_subset_1 (u1_struct_0 A) (k9_metric_1 A B D) (k9_metric_1 A C E)) (k9_metric_1 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_wellfnd1,ax, (! [A:$i] :  ((v4_funct_1 A) =>  ( (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_partfun1 B C)) ) ) ) )  =>  ((v1_relat_1 (k3_tarski A)) & (v1_funct_1 (k3_tarski A))) ) ) ) ).
tt(t1_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k1_wellord1 C B)) <=>  ( (~  (A = B) )  & (r2_hidden (k4_tarski A B) C)) ) ) ) ) ) ).
tt(t1_wellset1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_hidden A (k1_relat_1 B)) <=>  (~  (! [C:$i] :  ( (~ (r2_hidden (k4_tarski A C) B))  &  (~ (r2_hidden (k4_tarski C A) B)) ) ) ) ) ) ) ) ).
tt(t1_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_newton A 2) = (k3_xcmplx_0 A A))  &  ((k1_newton (k4_xcmplx_0 A) 2) = (k1_newton A 2)) ) ) ) ).
tt(t1_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k5_xboole_0 B C)) <=>  (~  ((r2_hidden A B) <=> (r2_hidden A C)) ) ) ) ) ) ).
tt(t1_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r1_tarski B C))  => (r1_tarski A C)) ) ) ) ).
tt(t1_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k4_xboolean A A) = A) ) ) ).
tt(t1_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 A (k2_xcmplx_0 B C)) = (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t1_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 B A)) ) ) ) ) ).
tt(t1_xregular,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((r2_hidden B A) & (r1_xboole_0 B A)) ) ) ) ).
tt(t1_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k4_tarski A B) = (k4_tarski C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ).
tt(t1_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t1_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k1_xxreal_1 B C)) <=>  ((r1_xxreal_0 B A) & (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(t1_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((m1_xxreal_2 A (k1_tarski B)) <=> (r1_xxreal_0 B A)) ) ) ) ) ).
tt(t1_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  ((v2_xxreal_0 A) &  (~ (v1_xreal_0 A)) ) )  =>  (A = k1_xxreal_0) ) ) ).
tt(t1_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((r1_orders_2 A C D) => (r1_orders_2 B E F))  &  ((r2_orders_2 A C D) => (r2_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((v2_yellow_0 (k3_yellow_3 A B)) =>  ((v2_yellow_0 A) & (v2_yellow_0 B)) ) ) ) ) ) ).
tt(t1_yellow11,ax, (3 = (k8_domain_1 k5_numbers k6_numbers 1 2)) ).
tt(t1_yellow12,ax, (! [A:$i] :  (! [B:$i] : (r1_relset_1 A A (k7_relset_1 A (k2_zfmisc_1 A A) (k12_funct_3 A) B) (k2_zfmisc_1 B B))) ) ).
tt(t1_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v4_pre_topc B A)) ) ) ) ).
tt(t1_yellow14,ax, ((k9_setfam_1 1) = (k2_tarski k6_numbers 1)) ).
tt(t1_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_funct_1 A B))) =>  ( (~ (r1_xboole_0 (k8_relat_1 (k12_card_3 A B) (k1_tarski C)) (k8_relat_1 (k12_card_3 A B) D)))  => (r2_hidden C D)) ) ) ) ) ) ) ).
tt(t1_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_functor0 A B C E) = (k3_functor0 A B D E)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  ((k6_functor0 A B C E F G) = (k6_functor0 A B D E F G)) ) ) ) ) ) ) ) )  =>  ((g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C)) = (g2_functor0 A B (u1_functor0 A B D) (u2_functor0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t1_yellow19,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) &  ((v2_waybel_0 B (k3_yellow_1 A)) &  ((v13_waybel_0 B (k3_yellow_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) ) ) )  =>  (! [C:$i] :  (~  ((r2_hidden C B) & (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t1_yellow_1,ax, (! [A:$i] :  ( ((u1_struct_0 (k2_yellow_1 A)) = A)  &  ((u1_orders_2 (k2_yellow_1 A)) = (k1_yellow_1 A)) ) ) ).
tt(t1_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v7_functor0 C A B) & (v21_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k3_functor0 A B C D) = E)  <=>  ((k3_functor0 B A (k15_functor0 A B C) E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_yellow18 A B) = (u1_struct_0 (k1_yellow21 B))) ) ) ) ) ).
tt(t1_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (k5_waybel_0 A B)) <=> (r2_lattice3 A C B)) ) ) ) ) ) ) ).
tt(t1_yellow_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_relset_1 A B C (k2_zfmisc_1 (k9_xtuple_0 C) (k10_xtuple_0 C)))) ) ) ) ).
tt(t1_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r1_yellow_0 A B))  => (r1_orders_2 A C (k1_yellow_0 A B))) ) ) ) ) ) ).
tt(t1_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_lattice3 A B B) = B) ) ) ) ) ).
tt(t1_yellow_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r2_hidden (k9_xtuple_0 B) A) & (r1_tarski (k10_xtuple_0 B) A))  => (r2_hidden (k4_card_3 B) A)) ) ) ) ) ).
tt(t1_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lattice3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lattice3 A))) =>  ((r1_orders_2 (k7_lattice3 A) B C) <=> (r1_orders_2 A (k9_lattice3 A C) (k9_lattice3 A B))) ) ) ) ) ) ) ).
tt(t1_yellow_8,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k5_finsub_1 A)) & (r1_tarski C B))  => (r2_hidden C (k5_finsub_1 A))) ) ) ) ).
tt(t1_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k3_subset_1 (u1_struct_0 A) (k6_waybel_0 A B))) <=>  (~ (r1_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t1_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k1_yoneda_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k1_yoneda_1 A))) =>  ( ( ((k4_graph_1 (k1_yoneda_1 A) D) = (k3_graph_1 (k1_yoneda_1 A) E))  &  ( ((k4_tarski (k9_cat_2 (k1_yoneda_1 A) (k1_yoneda_1 A) (k3_graph_1 (k1_yoneda_1 A) D) (k4_graph_1 (k1_yoneda_1 A) D)) B) = D)  &  ((k4_tarski (k9_cat_2 (k1_yoneda_1 A) (k1_yoneda_1 A) (k3_graph_1 (k1_yoneda_1 A) E) (k4_graph_1 (k1_yoneda_1 A) E)) C) = E) ) )  =>  ((k4_tarski (k9_cat_2 (k1_yoneda_1 A) (k1_yoneda_1 A) (k3_graph_1 (k1_yoneda_1 A) D) (k4_graph_1 (k1_yoneda_1 A) E)) (k3_relat_1 B C)) = (k1_cat_1 (k1_yoneda_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k1_zf_colla A B) = (a_2_1_zf_colla A B)) ) ) ) ) ).
tt(t1_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski B A) &  ( ((r2_hidden C B) => (m1_subset_1 C A))  &  ( ((r2_hidden C D) & (r2_hidden D B))  => (m1_subset_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t1_zf_fund2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ((v1_ordinal1 A) =>  ((k1_zf_fund2 (k8_zf_lang (k2_zf_lang 2) (k11_zf_lang (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang k6_numbers)) (k5_zf_lang (k2_zf_lang 2) (k2_zf_lang 1)))) A (k2_zf_lang1 A C (k2_zf_lang 1) B)) = (k3_xboole_0 A (k1_zfmisc_1 B))) ) ) ) ) ) ) ) ).
tt(t1_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ( ((k18_zf_lang (k4_zf_lang A B)) = A)  &  ((k19_zf_lang (k4_zf_lang A B)) = B) ) ) ) ) ) ).
tt(t1_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k4_zf_lang A B) = (k4_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t1_zfmisc_1,ax, ((k1_zfmisc_1 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t1_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) => (r2_zf_model A k6_zf_model)) ) ) ).
tt(t1_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  => (r1_tarski (k2_zf_model (k6_zf_lang1 C A B)) (k2_xboole_0 (k7_subset_1 k1_zf_lang (k2_zf_model C) (k1_tarski A)) (k1_tarski B)))) ) ) ) ) ) ).
tt(t1_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v2_zf_lang A) =>  ((k2_zf_model A) = (k2_tarski (k18_zf_lang A) (k19_zf_lang A))) )  &  ( ((v3_zf_lang A) =>  ((k2_zf_model A) = (k2_tarski (k18_zf_lang A) (k19_zf_lang A))) )  &  ( ((v4_zf_lang A) =>  ((k2_zf_model A) = (k2_zf_model (k20_zf_lang A))) )  &  ( ((v5_zf_lang A) =>  ((k2_zf_model A) = (k4_subset_1 k1_zf_lang (k2_zf_model (k21_zf_lang A)) (k2_zf_model (k22_zf_lang A)))) )  &  ((v6_zf_lang A) =>  ((k2_zf_model A) = (k7_subset_1 k1_zf_lang (k2_zf_model (k24_zf_lang A)) (k1_tarski (k23_zf_lang A)))) ) ) ) ) ) ) ) ).
tt(t1_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_zfrefle1 A (k1_subset_1 k9_zf_lang))) ) ).
tt(t1_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_zf_model A k7_zf_model)) ) ).
tt(t1_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ( (A = k6_numbers)  |  (C = (k4_struct_0 B)) )  =>  ((k1_zmodul01 B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t200_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k23_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k23_member_1 A C) (k23_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t200_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k7_xcmplx_0 C A) = (k7_xcmplx_0 D B))  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  |  ( (A = (k4_xcmplx_0 B))  |  ((k7_xcmplx_0 C A) = (k7_xcmplx_0 (k2_xcmplx_0 C D) (k2_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t200_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k4_xcmplx_0 B) A))  & (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ) ).
tt(t200_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k1_xxreal_1 A D) (k2_xboole_0 (k1_xxreal_1 A B) (k1_xxreal_1 C D))) = (k4_xxreal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t201_member_1,ax, (! [A:$i] :  ((v1_membered A) => (r1_tarski (k23_member_1 A k6_numbers) (k1_tarski k6_numbers))) ) ).
tt(t201_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k5_xcmplx_0 A) = (k5_xcmplx_0 B))  =>  (A = B) ) ) ) ) ) ).
tt(t201_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B (k4_xcmplx_0 A)) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ).
tt(t201_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k6_subset_1 (k1_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k3_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t202_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ( (~  (A = k1_xboole_0) )  =>  ((k23_member_1 A k6_numbers) = (k1_tarski k6_numbers)) ) ) ) ).
tt(t202_xcmplx_1,ax, ((k5_xcmplx_0 k6_numbers) = k6_numbers) ).
tt(t202_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A (k4_xcmplx_0 B)) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ).
tt(t202_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C B) |  ((k6_subset_1 (k2_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k4_xxreal_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t203_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k23_member_1 A 1) = A) ) ) ).
tt(t203_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k3_xcmplx_0 (k3_xcmplx_0 B A) (k5_xcmplx_0 A))) ) ) ) ) ) ).
tt(t203_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 A) B) =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ).
tt(t203_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k3_xxreal_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t204_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k23_member_1 A (k5_binop_2 B C)) = (k23_member_1 (k23_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t204_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = (k5_xcmplx_0 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t204_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 B) A) =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 (k7_xcmplx_0 B A) (k4_xcmplx_0 1))) ) ) ) ) ) ).
tt(t204_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~  ((k6_subset_1 (k4_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k4_xxreal_1 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t205_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k23_member_1 (k13_member_1 A B) C) = (k13_member_1 (k23_member_1 A C) B)) ) ) ) ) ) ) ).
tt(t205_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_xcmplx_0 (k3_xcmplx_0 A (k5_xcmplx_0 B))) = (k3_xcmplx_0 (k5_xcmplx_0 A) B)) ) ) ) ) ).
tt(t205_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k4_xcmplx_0 A) B))  & (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t205_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~ (r2_hidden A (k2_xboole_0 (k4_xxreal_1 B A) (k4_xxreal_1 A C)))) ) ) ) ) ) ) ).
tt(t206_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r1_tarski (k23_member_1 A (k3_binop_2 B C)) (k9_member_1 (k23_member_1 A B) (k23_member_1 A C)))) ) ) ) ) ) ).
tt(t206_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_xcmplx_0 (k3_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B))) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t206_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k4_xcmplx_0 B) A))  & (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t206_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~ (r2_hidden A (k2_xboole_0 (k2_xxreal_1 B A) (k4_xxreal_1 A C)))) ) ) ) ) ) ) ).
tt(t207_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r1_tarski (k23_member_1 A (k4_binop_2 B C)) (k11_member_1 (k23_member_1 A B) (k23_member_1 A C)))) ) ) ) ) ) ).
tt(t207_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((k3_xcmplx_0 A (k5_xcmplx_0 B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t207_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 A)))  & (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t207_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~ (r2_hidden A (k2_xboole_0 (k4_xxreal_1 B A) (k3_xxreal_1 A C)))) ) ) ) ) ) ) ).
tt(t208_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k23_member_1 (k9_member_1 A B) C) = (k9_member_1 (k23_member_1 A C) (k23_member_1 B C))) ) ) ) ) ) ) ).
tt(t208_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((k3_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t208_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 B)))  & (r1_xxreal_0 (k4_xcmplx_0 1) (k7_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t208_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~ (r2_hidden A (k2_xboole_0 (k2_xxreal_1 B A) (k3_xxreal_1 A C)))) ) ) ) ) ) ) ).
tt(t209_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k23_member_1 (k11_member_1 A B) C) = (k11_member_1 (k23_member_1 A C) (k23_member_1 B C))) ) ) ) ) ) ) ).
tt(t209_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_xcmplx_0 A (k5_xcmplx_0 B)) = 1)  =>  (A = B) ) ) ) ) ) ).
tt(t209_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_xxreal_0 A (k7_xcmplx_0 B C))) ) ) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t209_xxreal_1,ax, ((k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) = k7_numbers) ).
tt(t20_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r1_abcmiz_0 A B C) => (r3_orders_2 A (k5_abcmiz_0 A B C) B)) ) ) ) ) ) ) ).
tt(t20_abcmiz_1,ax, (! [A:$i] :  ((v1_finset_1 (k6_classes1 A)) => (v1_finset_1 A)) ) ).
tt(t20_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) &  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (~  ( (C = (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)))  &  ( ((k2_msualg_1 A C) = (k1_xtuple_0 C))  & (m1_abcmiz_1 B A (k2_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k1_absvalue (k2_xcmplx_0 A B)) (k3_real_1 (k2_xcmplx_0 (k1_absvalue A) (k1_absvalue B)) 1))) ) ) ) ).
tt(t20_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 C A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = D) )  & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) & (r1_tarski D (k1_aff_4 A B C))) ) )  =>  ((r5_aff_1 A B D) |  ((k1_aff_4 A B D) = (k1_aff_4 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (~  ((r2_hidden A (k2_afinsq_1 (k1_ordinal4 B C))) &  ( (~ (r2_hidden A (k2_afinsq_1 B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k2_afinsq_1 C)) &  (A = (k2_nat_1 (k1_afinsq_1 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  ((k1_afinsq_1 (k4_afinsq_2 A)) = (k5_card_1 A)) ) ) ).
tt(t20_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) <=>  (~  ( (~ (m1_subset_1 B (u1_struct_0 A)))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k5_afproj A C))  & (v1_aff_1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t20_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_afvect0 A B C D) &  ((r2_afvect0 A B E D) &  ( (~  (C = E) )  &  (~ (r1_afvect0 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_alg_1 A B C) => (r4_alg_1 (k4_alg_1 A (k6_alg_1 A B C)) B (k7_alg_1 A B C))) ) ) ) ) ) ) ).
tt(t20_algspec1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k1_algspec1 (k2_xboole_0 A B) C) = (k2_xboole_0 (k1_algspec1 A C) (k1_algspec1 B C))) ) ) ) ) ).
tt(t20_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 2 B) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( ((k3_finseq_1 C) = (k6_xcmplx_0 B 1))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k6_xcmplx_0 B 1)))  =>  ((k1_funct_1 C D) = (k2_zfmisc_1 (k11_algstr_4 A D) (k11_algstr_4 A (k7_nat_d B D)))) ) ) )  &  ((k11_algstr_4 A B) = (k3_card_3 (k2_card_3 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((k5_altcat_1 A B C C D (k8_altcat_1 A C)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t20_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) => (m1_altcat_2 A A)) ) ).
tt(t20_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ( ((v1_altcat_3 D A B C) & (v4_altcat_3 D A B C))  =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C B) = k1_xboole_0)  | (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v3_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v3_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_ami_2,ax, (~ (r2_hidden k5_numbers k2_ami_2)) ).
tt(t20_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~ (v2_extpro_1 (k6_ami_3 A B) 2 k1_ami_3)) ) ) ) ) ).
tt(t20_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k5_ami_3 H I))  & (r2_hidden H (k9_xtuple_0 B))) )  =>  ((k3_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I)) = (k3_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_amistd_1 2 k1_ami_3 (k9_ami_3 B A)) = (k1_tarski B)) ) ) ) ) ).
tt(t20_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 C (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = 1)  => (r8_pboole (u1_struct_0 (k4_amistd_1 A)) (k2_extpro_1 A (k4_amistd_1 A) B C) (k9_memstr_0 A (k4_amistd_1 A) C 1))) ) ) ) ) ) ) ).
tt(t20_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_amistd_1 A (k4_amistd_1 A) B) = (k7_domain_1 k5_numbers B (k5_ami_wstd A (k4_amistd_1 A) B))) ) ) ) ) ).
tt(t20_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_analmetr (k2_analmetr A B C)) = (k2_diraf (k2_analoaf A))) ) ) ) ) ) ) ).
tt(t20_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_analoaf A B C D E))  &  (~ (r1_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r1_analort A E F B B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski B C) (k1_anproj_1 A)) <=>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  & (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t20_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ( (A = (k9_domain_1 A B C D E))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [I:$i] :  ((m2_funct_2 I A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [J:$i] :  ((m2_funct_2 J A k1_numbers (k9_funct_2 A k1_numbers)) &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  (! [N:$i] :  ((m1_subset_1 N k1_numbers) =>  (~ (r2_funct_2 A k1_numbers J (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K F)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L G))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M H))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) N I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((r2_hidden D (k9_aofa_000 A B (k1_nat_1 C 1))) <=>  (~  ( (~ (r2_hidden D (k9_aofa_000 A B C)))  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (~  ( (D = (k1_funct_1 (k2_pua2mss1 A E) F))  &  ((r2_hidden F (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A E))) & (r1_tarski (k2_relset_1 (u1_struct_0 A) F) (k9_aofa_000 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_card_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C A (k1_card_1 A)) &  ((v2_funct_2 C (k1_card_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) )  =>  (! [D:$i] :  ((m6_aofa_i00 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 A k4_numbers) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) A)))) )  => (m2_aofa_i00 E (k7_freealg k19_aofa_000 k26_aofa_i00) A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (v1_finset_1 B)) ) ) ) ).
tt(t20_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((k2_arytm_0 (k2_arytm_0 A B) (k4_arytm_0 B)) = A) ) ) ) ) ) ).
tt(t20_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k7_arytm_2 C (k1_arytm_1 B A)) = (k2_arytm_1 (k7_arytm_2 C B) A)) ) ) ) ) ) ) ) ).
tt(t20_arytm_2,ax, ((r2_hidden k11_arytm_3 k2_arytm_2) & (r2_hidden k12_arytm_3 k2_arytm_2)) ).
tt(t20_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((r1_arytm_3 A B) <=>  ((k3_arytm_3 A B) = 1) ) ) ) ) ) ).
tt(t20_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (r2_hidden A (k7_asympt_0 A))) ) ).
tt(t20_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden A (k8_asympt_0 B)) <=>  ((k8_asympt_0 A) = (k8_asympt_0 B)) ) ) ) ) ) ).
tt(t20_autalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [D:$i] :  ((m2_pboole D A B C) => (r2_hidden D (k4_autalg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t20_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_autgroup A))) =>  ( (B = C)  =>  ((k2_funct_1 B) = (k2_group_1 (k5_autgroup A) C)) ) ) ) ) ) ) ) ).
tt(t20_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r2_hidden B A) =>  ((v1_relat_1 (k5_relat_1 C B)) &  ((v4_relat_1 (k5_relat_1 C B) B) &  ((v1_funct_1 (k5_relat_1 C B)) &  ((v1_partfun1 (k5_relat_1 C B) B) &  ((v4_valued_0 (k5_relat_1 C B)) & (v2_pre_poly (k5_relat_1 C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k4_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k4_bcialg_1 A)) => (r2_hidden (k1_bcialg_1 A B C) (k4_bcialg_1 A))) ) ) ) ) ) ).
tt(t20_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_bcialg_1 A B C) => (r1_bcialg_1 A (k1_bcialg_2 A D C E) (k1_bcialg_2 A D B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_bcialg_1 A B D) & (r1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B)))  => (r1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_bcialg_4 A B k6_numbers) = (k4_struct_0 A)) ) ) ) ) ).
tt(t20_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ((k1_bcialg_2 E F G (k2_nat_1 B 1)) = (k1_bcialg_2 E F G (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (C = (k3_bcialg_6 A D (k2_bcialg_1 A (k2_bcialg_1 A B))))  => (r2_hidden (k3_bcialg_6 A D B) (k7_bcialg_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t20_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (m2_bciideal (k4_bcialg_1 A) A)) ) ).
tt(t20_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) => (r1_bhsp_1 A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t20_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) => (v2_comseq_2 (k2_bhsp_2 A B))) ) ) ) ) ).
tt(t20_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_bhsp_3 B A) & (v2_bhsp_3 C A))  => (v2_bhsp_3 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t20_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_normsp_1 A B 1) = (k5_algstr_0 A (k3_bhsp_4 A B 1) (k3_bhsp_4 A B k6_numbers))) ) ) ) ) ).
tt(t20_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) (k9_bilinear A B C D (k7_hahnban1 A C)) E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( ( ((k7_partfun1 k6_margrel1 B A) = k8_margrel1)  &  ((k7_partfun1 k6_margrel1 (k4_binarith A B (k1_binari_2 A)) A) = k8_margrel1) )  =>  ((k4_binarith A B (k1_binari_2 A)) = (k3_binarith A (k1_binari_2 A))) ) ) ) ) ) ).
tt(t20_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_int_1 (k22_binop_2 B A) A) = k6_numbers) ) ) ) ) ).
tt(t20_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ((m1_subset_1 C k6_margrel1) =>  ((k6_binarith (k1_nat_1 A 1) (k9_binarith A 1 k6_margrel1 B (k10_binarith k6_margrel1 C))) = (k2_nat_1 (k6_binarith A B) (k15_funcop_1 k5_numbers C k7_margrel1 k6_numbers (k5_series_1 2 A)))) ) ) ) ) ) ) ).
tt(t20_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_algstr_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k6_algstr_0 A C (k5_binom A B D)) = (k6_binom A (k6_algstr_0 A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t20_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))))  =>  ( ((r2_relset_1 A B (k1_relset_1 (k2_zfmisc_1 A B) D) (k1_relset_1 (k2_zfmisc_1 A B) E)) &  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k4_tarski F G) (k1_relset_1 (k2_zfmisc_1 A B) D)) =>  ((k1_binop_1 D F G) = (k1_binop_1 E F G)) ) ) ) )  => (r2_relset_1 (k2_zfmisc_1 A B) C D E)) ) ) ) ) ) ) ) ).
tt(t20_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  ((k4_finseq_1 (k2_bintree2 A B)) = (k2_finseq_1 (k5_series_1 2 B))) ) ) ) ) ).
tt(t20_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r4_boolealg A B C))  & (r4_boolealg A (k4_lattices A D B) (k4_lattices A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t20_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k3_funct_2 B k1_numbers C (k1_prob_2 A B (k9_bor_cant A (k2_prob_1 A D)) E)) = (k9_real_1 1 (k3_funct_2 B k1_numbers C (k1_prob_2 A B (k7_bor_cant A D) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  ( ( ((k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) C) = k1_xboole_0)  |  ((k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) C) = k1_xboole_0) )  =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t20_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) =>  (~  ((m1_setfam_1 C (u1_struct_0 (k2_borsuk_1 B A))) &  ((v1_tops_2 C (k2_borsuk_1 B A)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) =>  (~  ((r1_tarski D C) &  ((m1_setfam_1 D (u1_struct_0 (k2_borsuk_1 B A))) & (v1_finset_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_borsuk_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (v1_xboole_0 (k1_seq_4 A)))  &  ((v2_measure5 (k1_seq_4 A)) & (m1_subset_1 (k1_seq_4 A) (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(t20_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~ (v1_rat_1 (k6_xcmplx_0 A B))) ) ) ) ) ).
tt(t20_borsuk_6,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)))))) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_funct_1 A (k4_tarski B C)) = (k10_finseq_1 B C)) ) ) ) ) ) ) ).
tt(t20_borsuk_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ( (~  ((k16_rvsum_1 A) = k6_numbers) )  =>  ((k16_rvsum_1 (k14_valued_2 A (k16_rvsum_1 A))) = 1) ) ) ) ).
tt(t20_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k4_bspace A B (k4_bspace A C D)) = (k4_bspace A (k8_group_1 k2_bspace B C) D)) ) ) ) ) ) ) ) ).
tt(t20_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A B (k5_bvfunc_1 A C (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t20_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k1_enumset1 C D E))  &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  ( (~  (E = C) )  &  ( ((k15_bvfunc_1 A F E) = (k15_bvfunc_1 A G E))  & (r1_xboole_0 (k15_bvfunc_1 A G (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A F (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k11_bvfunc_1 A)) (k11_bvfunc_1 A)) &  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k12_bvfunc_1 A)) (k12_bvfunc_1 A)) &  ((r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A (k11_bvfunc_1 A)) (k11_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A (k12_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t20_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A (k1_bvfunc_1 A B)) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t20_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k6_bvfunc26 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t20_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A C (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A C B E) (k9_bvfunc_1 A (k7_bvfunc_2 A D B E) (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((r3_bvfunc_2 A B C D) => (r1_bvfunc_1 A B (k6_bvfunc_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A C (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A B) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 C (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t20_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t20_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k12_bvfunc_1 A)) B)) ) ) ) ).
tt(t20_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k9_bvfunc_1 A B (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t20_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) =>  ((k1_seq_1 (k10_c0sp1 A) B) = (k4_seq_4 (k9_c0sp1 A B))) ) ) ) ) ) ).
tt(t20_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_nfcont_1 B A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) & (v1_rsspace3 C A)) )  =>  ((v3_normsp_1 C A) & (r2_hidden (k6_normsp_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t20_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B) (k1_calcul_1 (k3_cqc_lang A) C)) &  ((r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B)) & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C) (k2_calcul_1 A C))) )  => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k7_cqc_lang A (k2_calcul_1 A B) (k2_calcul_1 A C)))) ) ) ) ) ) ) ).
tt(t20_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D C) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t20_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k3_card_1 C)) ) ) ) )  =>  ((k3_card_1 A) = (k1_card_1 (k4_ordinal2 B))) ) ) ) ) ) ) ) ).
tt(t20_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k2_card_2 A k6_numbers) = k6_numbers) ) ) ).
tt(t20_card_3,ax, (! [A:$i] :  (! [B:$i] : (r1_ordinal1 (k1_card_1 (k5_card_3 B A)) (k1_card_1 A))) ) ).
tt(t20_card_4,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  (! [D:$i] :  ((v1_card_1 D) =>  ( ((r2_hidden A B) & (r2_hidden C D))  =>  ((r2_hidden (k2_card_2 A C) (k2_card_2 B D)) & (r2_hidden (k2_card_2 C A) (k2_card_2 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t20_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  => (r1_ordinal1 A (k3_card_2 A B))) ) ) ) ).
tt(t20_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ((r1_tarski (k4_card_fil A) B) => (v1_card_fil B A)) ) ) ) ) ).
tt(t20_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (~ (v1_xboole_0 (k2_card_fin B C A)))  => (r1_tarski (k8_relat_1 C (k1_tarski A)) (k9_xtuple_0 B))) ) ) ) ) ) ).
tt(t20_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_card_lar B A) => (r1_ordinal1 (k1_card_5 A) (k1_card_1 B))) ) ) ) ) ).
tt(t20_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k3_tarski (a_2_0_cat_2 A B)))  =>  ( ((v1_funct_1 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C)) &  ((v1_funct_2 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C) C B) & (m1_subset_1 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  &  ( ((v1_funct_1 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C)) &  ((v1_funct_2 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C) C B) & (m1_subset_1 (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  &  ((v1_funct_1 (k1_realset1 (u1_cat_1 A) C)) & (m1_subset_1 (k1_realset1 (u1_cat_1 A) C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  => (r2_funct_2 A (u4_struct_0 B) (k6_cat_3 B A D C) (k8_cat_3 B A D (k8_funcop_1 (u4_struct_0 B) A C)))) ) ) ) ) ) ) ).
tt(t20_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_cat_3 A (k2_cat_4 A B C) (k7_cat_4 A B C) (k8_cat_4 A B C))) ) ) ) ) ) ).
tt(t20_cat_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_cat_5 A))  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_cat_1 B) &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) &  ((v4_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) ) )  &  ((u1_struct_0 B) = A) ) ) ) ) ).
tt(t20_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k1_catalan1 A) k6_numbers)) ) ) ) ).
tt(t20_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((r2_hidden C (k2_catalan2 A B)) <=>  ((v1_catalan2 C) &  ( ((k1_relset_1 k5_numbers C) = A)  &  ((k7_afinsq_2 C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t20_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u1_struct_0 (k3_catalg_1 (u1_struct_0 B))) (k11_catalg_1 A B C) (k9_catalg_1 (u1_struct_0 A) D E)) = (k9_catalg_1 (u1_struct_0 B) (k8_cat_1 A B C D) (k8_cat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cc0sp1 A))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k7_cc0sp1 A) B))) ) ) ) ).
tt(t20_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k1_cc0sp2 A k6_numbers) = (k4_struct_0 (k5_cc0sp2 A))) ) ) ).
tt(t20_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~  ((k3_funct_2 k5_numbers k2_numbers B D) = (k3_funct_2 k5_numbers k2_numbers A D)) ) ) ) ) ) )  |  ((k3_comseq_2 A) = (k3_comseq_2 B)) ) ) ) ) ) ) ).
tt(t20_cfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k1_valued_0 k2_numbers (k36_valued_1 k5_numbers k2_numbers B) A) (k36_valued_1 k5_numbers k2_numbers (k1_valued_0 k2_numbers B A)))) ) ) ) ).
tt(t20_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D C k2_numbers (k9_funct_2 C k2_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k2_numbers (k9_funct_2 C k2_numbers)) =>  ( ( (C = (k2_tarski A B))  &  ( (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 D F) = k6_complex1) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 D F) = k6_numbers) ) ) ) )  &  (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 E F) = k6_numbers) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 E F) = k6_complex1) ) ) ) ) ) )  =>  ( (A = B)  |  (! [F:$i] :  ((m2_funct_2 F C k2_numbers (k9_funct_2 C k2_numbers)) =>  (? [G:$i] :  ((m1_subset_1 G k2_numbers) &  (? [H:$i] :  ((m1_subset_1 H k2_numbers) & (r2_funct_2 C k2_numbers F (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) (k19_valued_1 A k2_numbers k2_numbers B D)) (k19_valued_1 A k2_numbers k2_numbers B (k46_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t20_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((r1_xxreal_0 B 1) | (r2_hidden (k6_xcmplx_0 B 1) (k4_finseq_1 A))) ) ) ) ) ) ).
tt(t20_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers B C) A) & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers B D) A))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t20_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v4_glib_001 B A) <=>  ((k3_finseq_1 B) = (k2_nat_1 (k4_nat_1 2 (k5_card_1 (k14_glib_001 A B))) 1)) ) ) ) ) ) ).
tt(t20_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ( (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 A D))) => (v1_circuit2 (k5_facirc_1 A D I G) A D)) )  &  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) => (v1_circuit2 (k5_facirc_1 B E I H) B E)) ) )  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) => (v1_circuit2 (k5_facirc_1 C F I (k2_xcmplx_0 G H)) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msafree2 B A) &  ((v5_circcmb3 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) => (r8_pboole (u1_struct_0 A) (k1_circcmb3 A B C) (k6_circuit2 A B C))) ) ) ) ) ) ).
tt(t20_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) & (l3_msualg_1 E B))  =>  (! [F:$i] :  ((l3_msualg_1 F C) =>  ( ((r2_circcomb A B D E) &  ((r2_circcomb B C E F) & (r2_circcomb C A F D)) )  => (r2_circcomb (k2_circcomb A B) C (k3_circcomb A B D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ((v1_circled1 D A) & (m1_rlvect_2 D A))  =>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski (k7_domain_1 (u1_struct_0 A) B C) E) &  (~  ((v1_circled1 D A) & (m2_rlvect_2 D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  (! [F:$i] :  ((m1_circtrm1 F A C D B E) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) => (m1_circtrm1 F A C D B (k5_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_classes1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) &  ( ((k3_classes1 A B) = (k1_classes1 A))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C B) &  ((k3_classes1 A C) = (k1_classes1 A)) ) ) ) ) ) ) ) ) ).
tt(t20_classes2,ax, (! [A:$i] :  ((v2_classes1 A) =>  ( (A = k1_xboole_0)  |  ( (~  ((k1_card_1 A) = k6_numbers) )  &  ( (~  ((k1_card_1 A) = k1_xboole_0) )  & (v4_ordinal1 (k1_card_1 A))) ) ) ) ) ).
tt(t20_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k4_struct_0 B)) ) )  => (v2_clopban1 C A B)) ) ) ) ) ) ) ).
tt(t20_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k9_clopban2 A)) &  ((v3_normsp_0 (k9_clopban2 A)) &  ((v8_clvect_1 (k9_clopban2 A)) &  ((v2_rlvect_1 (k9_clopban2 A)) &  ((v3_rlvect_1 (k9_clopban2 A)) &  ((v4_rlvect_1 (k9_clopban2 A)) &  ((v13_algstr_0 (k9_clopban2 A)) &  ((v3_group_1 (k9_clopban2 A)) &  ((v3_vectsp_1 (k9_clopban2 A)) &  ((v1_vectsp_1 (k9_clopban2 A)) &  ((v2_clvect_1 (k9_clopban2 A)) &  ((v3_clvect_1 (k9_clopban2 A)) &  ((v4_clvect_1 (k9_clopban2 A)) &  ((v2_cfuncdom (k9_clopban2 A)) &  ((v2_clvect_1 (k9_clopban2 A)) &  ((v3_clvect_1 (k9_clopban2 A)) &  ((v4_clvect_1 (k9_clopban2 A)) & (v5_clvect_1 (k9_clopban2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_clopban3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((v1_clopban3 (k6_clvect_1 A B C) A) &  ((k1_clopban3 A (k6_clvect_1 A B C)) = (k1_clvect_1 A (k1_clopban3 A B) C)) ) ) ) ) ) ) ) ).
tt(t20_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_normsp_1 A (k1_clopban4 A B) k6_numbers) = (k5_struct_0 A))  &  ((k1_normsp_1 A (k2_clopban4 k6_numbers A B C) k6_numbers) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t20_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((v1_closure1 C A B) & (v1_closure1 D A B))  => (v1_closure1 (k3_closure1 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t20_closure2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_closure2 B C))) =>  ( ((r2_hidden A B) &  (F = (k2_tarski D E)) )  =>  ((k1_funct_1 (k4_closure2 B C F) A) = (k2_tarski (k1_funct_1 D A) (k1_funct_1 E A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ( (B = k1_xboole_0)  | (r2_hidden (k4_struct_0 A) B)) ) ) ) ) ) ).
tt(t20_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) => (v2_comseq_2 (k2_clvect_2 A B))) ) ) ) ) ).
tt(t20_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_normsp_1 A B 1) = (k5_algstr_0 A (k2_clvect_3 A B 1) (k2_clvect_3 A B k6_numbers))) ) ) ) ) ).
tt(t20_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_cohsp_1 A)) )  =>  ((v1_classes1 (k9_xtuple_0 A)) =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k3_tarski (k7_relat_1 A (k5_finsub_1 B)))) ) ) ) ) ) ).
tt(t20_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (B = (k4_tarski (k4_tarski (k6_coh_sp A B) (k7_coh_sp A B)) (k2_xtuple_0 B))) ) ) ) ).
tt(t20_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_collsp D A) =>  (! [E:$i] :  ((m2_collsp E A) =>  ( ((r2_hidden B D) &  ((r2_hidden C D) &  ((r2_hidden B E) & (r2_hidden C E)) ) )  =>  ( (B = C)  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_combgras B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((v6_combgras B A A) & (v1_combgras C A))  => (v1_combgras (k4_combgras A A B C) A)) ) ) ) ) ) ) ).
tt(t20_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k5_xcmplx_0 A)) = (k10_real_1 (k3_complex1 A) (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))))  &  ((k4_complex1 (k5_xcmplx_0 A)) = (k10_real_1 (k1_real_1 (k4_complex1 A)) (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))))) ) ) ) ).
tt(t20_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig A)))  &  ( (~ (r1_xxreal_0 k32_sin_cos (k1_comptrig B)))  & (r1_xxreal_0 k32_sin_cos (k1_comptrig (k2_xcmplx_0 A B)))) ) ) ) ) ) ) ).
tt(t20_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_rlvect_1 k1_complfld (k11_algstr_0 k1_complfld A) (k11_algstr_0 k1_complfld B)) = (k8_group_1 k1_complfld (k3_rlvect_1 k1_complfld A B) (k11_algstr_0 k1_complfld (k8_group_1 k1_complfld A B)))) ) ) ) ) ) ) ) ) ).
tt(t20_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k4_finseq_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k4_finseq_2 A k2_numbers)) =>  ((k9_matrix_5 (k2_complsp2 A C D) B) = (k4_binop_2 (k9_matrix_5 C B) (k9_matrix_5 D B))) ) ) ) ) ) ) ) ) ).
tt(t20_compl_sp,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_compts_1 A) => (v8_compl_sp A)) ) ) ).
tt(t20_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  ( ((k5_card_1 (k7_compos_1 A B C)) = (k6_xcmplx_0 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1))  &  ((k5_card_1 (k7_compos_1 A B C)) = (k7_nat_d (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1)) ) ) ) ) ) ) ) ).
tt(t20_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (B = (k1_funct_4 (k63_valued_1 B) (k16_funcop_1 (k62_valued_1 B) (k2_compos_1 A)))) ) ) ) ) ).
tt(t20_comptrig,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))).
tt(t20_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_pre_topc D A) =>  (! [E:$i] :  ((m1_pre_topc E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 E) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 B))))) )  =>  ( ( ((k2_xboole_0 (k2_struct_0 D) (k2_struct_0 E)) = (k2_struct_0 A))  &  ( ((k9_subset_1 (u1_struct_0 E) (k2_struct_0 D) (k2_struct_0 E)) = (k6_domain_1 (u1_struct_0 A) C))  &  ((v1_compts_1 D) &  ((v1_compts_1 E) &  ((v8_pre_topc A) &  ((v5_pre_topc F D B) &  ((v5_pre_topc G E B) &  ((k1_funct_1 F C) = (k1_funct_1 G C)) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_funct_4 F G)) &  ((v1_funct_2 (k1_funct_4 F G) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_funct_4 F G) A B) & (m1_subset_1 (k1_funct_4 F G) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_comput_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_margrel1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) B)))) )  => (r1_tarski (k1_relset_1 (k3_finseq_2 A) C) (k4_finseq_2 (k19_margrel1 C) A))) ) ) ) ).
tt(t20_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A (k2_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A B) C))) ) ) ) ) ) ).
tt(t20_comseq_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k25_valued_1 k5_numbers k2_numbers B A))) = (k9_complex1 (k15_complex1 A) (k15_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t20_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r2_funct_2 k5_numbers k1_numbers (k7_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k7_comseq_3 A) (k3_complex1 B)) (k26_valued_1 k5_numbers k1_numbers (k8_comseq_3 A) (k4_complex1 B)))) & (r2_funct_2 k5_numbers k1_numbers (k8_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)) (k1_series_1 k1_numbers (k26_valued_1 k5_numbers k1_numbers (k8_comseq_3 A) (k3_complex1 B)) (k26_valued_1 k5_numbers k1_numbers (k7_comseq_3 A) (k4_complex1 B))))) ) ) ) ) ).
tt(t20_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) &  ( (~ (v5_conlat_1 (g2_conlat_1 A B C) A))  &  ((v7_conlat_1 (g2_conlat_1 A B C) A) & (l2_conlat_1 (g2_conlat_1 A B C) A)) ) ) )  <=>  ((k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)) = B) ) ) ) ) ) ).
tt(t20_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  &  ((v2_conlat_1 A) & (l1_conlat_1 A)) )  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k8_conlat_2 (k7_conlat_2 A) (k8_conlat_2 A B)) = B) ) ) ) ) ).
tt(t20_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_connsp_1 A) &  ((v2_connsp_1 B A) &  ( ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) = (k4_subset_1 (u1_struct_0 A) C D))  & (r1_connsp_1 A C D)) ) )  =>  ((v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B C) A) & (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t20_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = (k2_struct_0 A)) )  &  ((r1_tarski B C) &  ((v4_pre_topc B A) &  ((v3_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r1_tarski B D) & (r1_tarski (k2_pre_topc A D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (u1_struct_0 A))  => (m1_connsp_3 B A)) ) ) ) ) ).
tt(t20_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (a_3_4_convex1 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t20_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ( ((m2_convex4 C A B) & (m2_convex4 D A B))  => (m2_convex4 (k5_convex4 A C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t20_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v4_qc_lang1 C A) =>  ((k13_cqc_lang A C B) = (k14_qc_lang1 A (k13_cqc_lang A (k19_qc_lang1 A C) B) (k13_cqc_lang A (k20_qc_lang1 A C) B))) ) ) ) ) ) ) ) ).
tt(t20_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((k13_cqc_sim1 A B) = (k26_qc_lang1 A))  <=> (v6_qc_lang1 B A)) ) ) ) ) ).
tt(t20_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v1_cqc_the1 B A) <=>  ((k1_cqc_the1 A B) = B) ) ) ) ) ) ).
tt(t20_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C B) B) A)) ) ) ) ) ) ) ).
tt(t20_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r4_cqc_the3 A B C) <=>  ((k1_cqc_the1 A B) = (k1_cqc_the1 A C)) ) ) ) ) ) ) ) ).
tt(t20_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_csspace4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_csspace4 A B))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_csspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) &  ((v1_csspace4 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A (u1_struct_0 B)) &  ((v1_csspace4 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (F = C)  &  ( (G = D)  &  (H = E) ) )  =>  ( (E = (k1_algstr_0 (k9_csspace4 A B) C D))  <=>  (! [I:$i] :  ((m1_subset_1 I A) =>  ((k3_funct_2 A (u1_struct_0 B) H I) = (k3_rlvect_1 B (k3_funct_2 A (u1_struct_0 B) F I) (k3_funct_2 A (u1_struct_0 B) G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v2_csspace C) & (l1_csspace C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k12_csspace C (k3_rlvect_1 C (k1_clvect_1 C D A) (k1_clvect_1 C E B)) F) = (k2_xcmplx_0 (k3_xcmplx_0 A (k12_csspace C D F)) (k3_xcmplx_0 B (k12_csspace C E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_decomp_1 C A B) <=>  ((v8_decomp_1 C A B) & (v16_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t20_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k2_finseq_1 32)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  ( (~  (A = 16) )  &  ( (~  (A = 17) )  &  ( (~  (A = 18) )  &  ( (~  (A = 19) )  &  ( (~  (A = 20) )  &  ( (~  (A = 21) )  &  ( (~  (A = 22) )  &  ( (~  (A = 23) )  &  ( (~  (A = 24) )  &  ( (~  (A = 25) )  &  ( (~  (A = 26) )  &  ( (~  (A = 27) )  &  ( (~  (A = 28) )  &  ( (~  (A = 29) )  &  ( (~  (A = 30) )  &  ( (~  (A = 31) )  &  (~  (A = 32) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_wellfnd1 (k5_dickson A)) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  (~ (r2_hidden C (k6_dickson A B))) ) ) ) ) ) ) ) ) ).
tt(t20_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v3_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C B) (k2_nat_1 A 1)) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t20_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v3_funct_1 D) =>  ((k10_diff_1 D A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t20_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C A (k7_real_1 A B)) = (k10_real_1 (k1_seq_1 (k3_diff_1 C B) A) B)) ) ) ) ) ) ) ).
tt(t20_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k9_real_1 A B) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))) & (r2_hidden A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_fdiff_9) B) A) = (k1_real_1 (k8_real_1 4 (k13_complex1 (k8_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 A) B)) (k18_sin_cos B)) (k8_real_1 (k18_sin_cos (k8_real_1 2 A)) (k18_sin_cos (k8_real_1 2 (k9_real_1 A B)))))))) ) ) ) ) ) ).
tt(t20_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  ( ((v1_dilworth (k2_struct_0 A) A) & (m1_subset_1 (k2_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_dilworth A) = 1) ) ) ) ).
tt(t20_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_diraf A B C D D) & (r2_diraf A D D B C)) ) ) ) ) ) ) ) ) ).
tt(t20_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_dist_1 B A) =>  ((m2_subset_1 (k8_dist_1 A B) (k1_zfmisc_1 (k3_finseq_2 A)) (k6_dist_1 A)) &  ((k3_funct_2 (k6_dist_1 A) (k3_finseq_2 k1_numbers) (k7_dist_1 A) (k8_dist_1 A B)) = B) ) ) ) ) ) ).
tt(t20_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((k3_zfmisc_1 A B C) = (a_3_0_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t20_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((m1_dynkin B A) & (v2_finsub_1 B))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ) ).
tt(t20_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( ( (B = k6_numbers)  |  (C = k6_numbers) )  <=>  ((k8_group_1 (k9_int_3 A) B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t20_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( (B = (k6_int_1 2 A))  =>  ((k3_rlvect_1 (k9_int_3 A) C C) = (k8_group_1 (k9_int_3 A) B C)) ) ) ) ) ) ) ) ).
tt(t20_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k2_ens_1 A)) =>  ((r2_hidden D (k7_ens_1 A B C)) => (r2_hidden (k2_xtuple_0 D) (k1_funct_2 B C))) ) ) ) ) ) ) ) ) ).
tt(t20_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k9_matrix_1 k1_numbers (k10_matrixr1 A) B) = (k2_matrprob (k1_seq_1 A B))) ) ) ) ) ) ).
tt(t20_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k3_enumset1 A B C D E) (k2_tarski F G))) ) ) ) ) ) ) ) ).
tt(t20_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden C (k6_eqrel_1 A A B C))) ) ) ) ) ).
tt(t20_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D B (k14_pralg_2 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  (! [F:$i] :  ((r2_hidden F (k3_msualg_1 B E D)) =>  ( ((v1_relat_1 (k1_funct_1 (k5_msualg_1 B E D) F)) & (v1_funct_1 (k1_funct_1 (k5_msualg_1 B E D) F)))  &  ((v1_relat_1 (k1_funct_1 (k5_msualg_1 B E (k14_pralg_2 A B C)) F)) & (v1_funct_1 (k1_funct_1 (k5_msualg_1 B E (k14_pralg_2 A B C)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k10_e_siec A) (k2_zfmisc_1 (k8_e_siec A) (k7_e_siec A))) & (r1_tarski (k11_e_siec A) (k2_zfmisc_1 (k8_e_siec A) (k7_e_siec A)))) ) ) ).
tt(t20_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k23_rvsum_1 B (k1_rlvect_1 (k15_euclid A) C D)) = (k11_binop_2 D (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t20_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k2_euclid_3 (k1_rlvect_1 (k15_euclid 2) B A)) = (k3_xcmplx_0 A (k2_euclid_3 B))) ) ) ) ) ).
tt(t20_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k7_euclid A B C) D) = (k7_real_1 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t20_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k5_euclid_5 (k4_euclid_5 A k6_numbers k6_numbers) (k4_euclid_5 B k6_numbers k6_numbers)) = (k4_struct_0 (k15_euclid 3))) ) ) ) ) ).
tt(t20_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_euclid_6 A B C))  <=>  ((r1_zfmisc_1 A B C) &  ( (~  ((k4_euclid_3 A B C) = k32_sin_cos) )  &  ( (~  ((k4_euclid_3 B C A) = k32_sin_cos) )  &  (~  ((k4_euclid_3 C A B) = k32_sin_cos) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v6_euclid_7 (k6_domain_1 (k1_euclid A) (k5_euclid A)) A)) ) ).
tt(t20_euclid_8,ax, ((k5_euclid_8 k2_euclid_8 k4_euclid_8) = (k6_euclid 3 k3_euclid_8)) ).
tt(t20_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (~  ( (~  (A = k6_numbers) )  &  ((r2_hidden C (k4_euclid_9 A D B)) & (r1_xxreal_0 B (k1_funct_1 (k3_euclid (k8_rvsum_1 C D)) (k1_euclid_9 A C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ((k12_rvsum_1 (k8_rvsum_1 A B)) = (k12_rvsum_1 (k8_rvsum_1 B A))) ) ) ) ) ).
tt(t20_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  ((k9_euclid B (k7_euclid B (k7_euclid B C D) E) A) = (k7_euclid B (k7_euclid B (k9_euclid B C A) (k9_euclid B D A)) (k9_euclid B E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_analmetr B C D) &  (A = (k2_analmetr B C D)) )  => (v5_conaffm A)) ) ) ) ) ) ) ) ) ).
tt(t20_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 A) =>  ((k1_euler_1 A) = (k6_xcmplx_0 A 1)) ) ) ) ).
tt(t20_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_exchsort A) = (k2_ordinal2 (k9_xtuple_0 A))) ) ) ).
tt(t20_extpro_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  (~ (v1_setfam_1 C)) )  =>  ((r1_xxreal_0 A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_memstr_0 D C) &  ((v3_memstr_0 D C) &  ((v3_extpro_1 D C) & (l1_extpro_1 D C)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 D)) & (v1_funct_1 E)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 D)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 C D)) & (v1_partfun1 F (u1_struct_0 D))) ) ) )  =>  ((r1_compos_1 D E (k5_memstr_0 C D (k5_extpro_1 C D E F A))) =>  ((k5_extpro_1 C D E F B) = (k5_extpro_1 C D E F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( ((m1_subset_1 A k1_numbers) | (m1_subset_1 B k1_numbers))  => (r1_xxreal_0 (k4_supinf_2 (k3_extreal1 A) (k3_extreal1 B)) (k3_extreal1 (k4_supinf_2 A B)))) ) ) ) ) ).
tt(t20_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (u1_struct_0 (k2_circcomb A B))) & (r2_hidden C (u1_struct_0 (k2_circcomb B A)))) ) ) ) ) ) ) ).
tt(t20_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  (~  ((k2_msafree2 (k15_facirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t20_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C A) B))) ) ) ) ) ) ).
tt(t20_fcont_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers C) (k1_rcomp_1 (k5_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k4_seq_4 (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))))) ) ) ) ) ) ) ).
tt(t20_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski (k1_limfunc1 A) (k1_relset_1 k1_numbers B)) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_limfunc1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_limfunc1 A)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k1_limfunc1 A))) (k7_relset_1 k1_numbers k1_numbers B (k1_limfunc1 A))))) ) ) ) ) ) ).
tt(t20_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k24_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k24_sin_cos B)) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t20_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k30_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k30_sin_cos) A) B) = (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k2_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t20_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers C A))) & (r2_fdiff_1 C B))  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C A) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers C A) B) D) = (k8_real_1 A (k1_fdiff_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) & (r2_fdiff_1 C A))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) C) (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k2_fdiff_1 C A))))) ) ) ) ) ) ) ) ).
tt(t20_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r3_fdiff_3 A B) =>  ( ((k1_seq_1 A B) = k6_numbers)  |  ((r3_fdiff_3 (k6_rfunct_1 k1_numbers k1_numbers A) B) &  ((k2_fdiff_3 B (k6_rfunct_1 k1_numbers k1_numbers A)) = (k1_real_1 (k10_real_1 (k2_fdiff_3 B A) (k5_square_1 (k1_seq_1 A B))))) ) ) ) ) ) ) ) ).
tt(t20_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = A) ) ) )  &  (D = (k1_taylor_1 3)) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) B) E) = (k8_real_1 3 (k2_newton E 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k3_taylor_1))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k3_taylor_1) A) B) = (k7_real_1 1 (k1_seq_1 k3_taylor_1 B))) ) ) ) ) ) ) ) ).
tt(t20_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1) A) C) = (k10_real_1 (k1_seq_1 k24_sin_cos C) (k7_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t20_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k1_sin_cos6) (k10_real_1 1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = (k8_real_1 2 C))  &  ( (~ (r1_xxreal_0 (k1_seq_1 B C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 B C))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k1_sin_cos6) (k10_real_1 1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k1_sin_cos6) (k10_real_1 1 2)) A) C) = (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 (k8_real_1 2 C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t20_fdiff_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)))) & (r1_xxreal_0 1 A))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)) B) C) = (k10_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 k16_sin_cos C) (k5_real_1 A 1))) (k5_prepower (k1_seq_1 k19_sin_cos C) (k1_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_fdiff_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)))) & (r1_xxreal_0 1 A))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)) B) C) = (k10_real_1 (k4_real_1 A (k1_seq_1 k16_sin_cos C)) (k5_prepower (k1_seq_1 k19_sin_cos C) (k1_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k8_ff_siec A) (k4_xboole_0 (k8_ff_siec A) (k4_relat_1 (k2_net_1 A)))) = k1_xboole_0)  &  ((k3_relat_1 (k7_ff_siec A) (k4_xboole_0 (k7_ff_siec A) (k4_relat_1 (k2_net_1 A)))) = k1_xboole_0) ) ) ) ).
tt(t20_fib_num2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  & (r1_tarski A B)) ) ) ) ).
tt(t20_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_fib_num3 (k1_nat_1 A 1)) = (k2_nat_1 (k1_pre_ff A) (k1_pre_ff (k1_nat_1 A 2)))) ) ) ).
tt(t20_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k1_int_1 (k13_complex1 (k3_power k1_fib_num (k3_xcmplx_0 2 A)) (k7_square_1 5))) = (k1_pre_ff (k3_xcmplx_0 2 A))) ) ) ) ).
tt(t20_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_finseq_8 A C) =>  ((r2_finseq_8 A B C 1) | (r5_finseq_8 A (k1_finseq_8 A B C) C)) ) ) ) ) ) ) ) ).
tt(t20_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  &  ( (~  (B = (k5_lattices A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r2_hidden B C) & (v1_filter_0 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v2_struct_0 (k4_filter_1 A B)))  &  ((v10_lattices (k4_filter_1 A B)) &  ((v17_lattices (k4_filter_1 A B)) & (l3_lattices (k4_filter_1 A B))) ) ) ) ) ) ) ).
tt(t20_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=>  ( (~ (v1_xboole_0 B))  &  ((v19_lattices B (k1_lattice2 A)) &  ((v20_lattices B (k1_lattice2 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A))))) ) ) ) ) ) ) ).
tt(t20_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~  (A = k1_xboole_0) )  <=> (r1_xxreal_0 1 (k3_finseq_1 A))) ) ) ).
tt(t20_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( (B = (k5_relat_1 C (k2_finseq_1 A)))  & (r1_xxreal_0 (k3_finseq_1 C) A))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t20_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k2_finseq_1 B) = (k1_tarski A))  =>  ( (B = 1)  &  (A = 1) ) ) ) ) ) ).
tt(t20_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r2_hidden (k4_finseq_4 A B) (k4_finseq_1 A))) ) ) ) ).
tt(t20_finseq_5,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~ (v1_xboole_0 B))  =>  ((k17_finseq_1 A 1 B) = (k9_finseq_1 (k7_partfun1 A B 1))) ) ) ) ) ).
tt(t20_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k4_finseq_4 (k10_finseq_1 A B) B) = 2) ) ) ) ).
tt(t20_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_finseq_7 A (k2_finseq_7 A B C D) D C) = B) ) ) ) ) ) ) ) ) ).
tt(t20_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_finseq_8 A B C k6_numbers) => (r2_finseq_8 A B C 1)) ) ) ) ) ) ) ).
tt(t20_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A C) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) B)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G E) & (m2_finseq_1 G C))  => (r2_relset_1 k5_numbers B (k1_finseqop A C B F (k5_finseq_2 A E D) G) (k3_finseqop A C B F D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((k3_finseq_1 B) = 1)  =>  ((k1_finsop_1 A B C) = (k1_funct_1 B 1)) ) ) ) ) ) ) ) ).
tt(t20_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k9_fintopo2 A C)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D (k6_fintopo2 A B)) & (r1_xboole_0 D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fintopo3 A B 1) = (k8_fin_topo A B)) ) ) ) ) ).
tt(t20_fintopo4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v3_orders_2 (k4_fintopo4 A))) ) ) ).
tt(t20_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_orders_2 A) &  ((v1_fin_topo A) &  ((v1_fintopo6 A) &  ( (~  (B = k1_xboole_0) )  &  ( (~  ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0) )  &  ((k7_fin_topo A B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k10_fin_topo A C)) & (r2_hidden B (k9_fin_topo A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ) ).
tt(t20_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k4_subset_1 (k3_catalan2 A) (k6_flang_1 A B C) (k6_flang_1 A B D)) = (k6_flang_1 A B (k4_subset_1 (k3_catalan2 A) C D)))  &  ((k4_subset_1 (k3_catalan2 A) (k6_flang_1 A C B) (k6_flang_1 A D B)) = (k6_flang_1 A (k4_subset_1 (k3_catalan2 A) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t20_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D E))  => (r1_tarski (k7_flang_1 A B D) (k1_flang_2 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_flang_1 A (k1_flang_3 A B C)) = (k2_flang_2 A (k1_flang_3 A B C))) ) ) ) ) ) ).
tt(t20_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (A = (a_1_1_fomodel0 A)) ) ) ).
tt(t20_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_fomodel2 E B C)) )  => (r2_relset_1 (k35_fomodel1 B) C (k5_relset_1 (k35_fomodel1 B) C (k10_funct_5 k5_numbers (k35_fomodel1 B) C (k9_funct_2 (k35_fomodel1 B) C) (k8_fomodel2 B C D E) (k1_nat_1 A 1)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A)) (k5_relset_1 (k35_fomodel1 B) C (k10_fomodel2 B C E) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))) (k39_fomodel1 B) A)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v1_orders_4 B) &  ((v11_fomodel1 B) & (l1_fomodel1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))))) =>  (~  ((v12_fomodel4 C 2 B) &  ((v6_fomodel4 C B) &  ((v16_fomodel4 C B) &  ( (~ (v14_fomodel4 A B C))  &  ((r1_tarski A (k33_fomodel2 B)) &  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_subset_1 E (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 D) (k2_xboole_0 D k6_margrel1))) (k16_fomodel2 B D)) =>  (~ (v10_fomodel2 A D B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v3_frechet A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k1_frechet2 A B)) ) ) ) ) ) ).
tt(t20_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  => (v1_frechet (k3_pcomps_1 A))) ) ).
tt(t20_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k3_msafree2 (k8_fscirc_1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k1_facirc_1) (k9_facirc_1 A B C k1_facirc_1)) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) (k1_tarski (k6_fscirc_1 A B C)))) ) ) ) ) ) ) ).
tt(t20_fscirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_facirc_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k2_msafree2 (k1_fscirc_2 (k2_nat_1 C 1) A B)) = (k2_xboole_0 (k2_msafree2 (k1_fscirc_2 C A B)) (k7_subset_1 (u1_struct_0 (k8_fscirc_1 (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 B (k2_nat_1 C 1)) (k3_fscirc_2 C A B))) (k2_msafree2 (k8_fscirc_1 (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 B (k2_nat_1 C 1)) (k3_fscirc_2 C A B))) (k1_tarski (k3_fscirc_2 C A B)))))  &  ((v1_relat_1 (k3_msafree2 (k1_fscirc_2 C A B))) &  (~ (v1_facirc_1 (k2_msafree2 (k1_fscirc_2 C A B)))) ) ) ) ) ) ) ) ) ).
tt(t20_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C B A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r5_fsm_1 B A C D E) =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 F)) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  (~  ( (H = (k1_funct_1 (k2_fsm_1 B C D F) G))  &  ( (I = (k1_funct_1 (k2_fsm_1 B C E F) G))  & (r5_fsm_1 B A C H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_2 D A B))  =>  (~  ((v1_fsm_2 D A) &  ((r2_fsm_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E B) =>  (~ (r3_fsm_2 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  ((k6_fsm_3 A B C) = (k3_fsm_3 A B C (u2_fsm_3 A B C))) ) ) ) ) ) ) ).
tt(t20_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  ( (~  (E = (k4_tarski (k10_finseq_1 D (k24_gfacirc1 A B C)) k4_twoscomp)) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E)))) => (v1_circuit2 (k5_facirc_1 (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E) F 4) (k7_ftacell1 A B C D E) (k8_ftacell1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_funcop_1 (k2_funcop_1 A (k4_tarski B C))) = (k2_funcop_1 A (k4_tarski C B))) ) ) ) ).
tt(t20_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k1_numbers (k9_funct_2 C k1_numbers)) =>  ( ( (C = (k2_tarski A B))  &  ( (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 D F) = 1) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 D F) = k6_numbers) ) ) ) )  &  (! [F:$i] :  ((r2_hidden F C) =>  ( ( (F = A)  =>  ((k1_funct_1 E F) = k6_numbers) )  &  ( (~  (F = A) )  =>  ((k1_funct_1 E F) = 1) ) ) ) ) ) )  =>  ( (A = B)  |  (! [F:$i] :  ((m2_funct_2 F C k1_numbers (k9_funct_2 C k1_numbers)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) & (r2_funct_2 C k1_numbers F (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k3_xboole_0 (k9_xtuple_0 C) B)) =>  ((k1_funct_1 C A) = (k1_funct_1 (k3_relat_1 (k4_relat_1 B) C) A)) ) ) ) ) ) ).
tt(t20_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ((v2_funct_1 (k1_partfun1 A B B C D E)) =>  ( ( (C = k1_xboole_0)  &  (~  (B = k1_xboole_0) ) )  | (v2_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t20_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((v1_funct_1 (k1_funct_3 C)) &  ((v1_funct_2 (k1_funct_3 C) (k1_zfmisc_1 A) (k1_zfmisc_1 B)) & (m1_subset_1 (k1_funct_3 C) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B))))) ) ) ) ) ) ) ).
tt(t20_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_funct_4 k1_xboole_0 A) = A) ) ) ).
tt(t20_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden (k4_tarski A B) (k9_xtuple_0 C)) &  (D = (k1_funct_1 (k1_funct_5 C) A)) )  =>  ((r2_hidden B (k9_xtuple_0 D)) &  ((k1_funct_1 D B) = (k1_binop_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t20_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k1_funct_6 k1_xboole_0) = k1_xboole_0)  &  ( ((k1_funct_6 (k1_tarski A)) = (k1_tarski A))  &  ( ((k1_funct_6 (k2_tarski A B)) = (k2_tarski A B))  &  ((k1_funct_6 (k1_enumset1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_funct_7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden B A) =>  ((r1_xxreal_0 B C) | (r2_hidden C A)) ) ) ) ) )  => (v1_card_1 A)) ) ) ).
tt(t20_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k55_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t20_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((r2_hidden (k2_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((r2_hidden (k6_xcmplx_0 C A) (k9_xtuple_0 B)) &  ((k1_funct_1 B (k2_xcmplx_0 C A)) = (k5_xcmplx_0 (k1_funct_1 B C))) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((v1_funct_9 B (k8_real_1 2 A)) & (v2_funct_9 B)) ) ) ) ) ) ) ).
tt(t20_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l1_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ((v7_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k3_functor0 A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_altcat_2 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) &  ((v1_altcat_2 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  ((k15_functor0 B A (k15_functor0 A B C)) = (g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C))) ) ) ) ) ) ) ) ).
tt(t20_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  ((r1_functor2 A B C D) => (r8_pboole (u1_struct_0 A) (k5_functor3 A B B C D E (k12_functor0 B)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k2_fuzzy_1 A B D) (k2_fuzzy_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t20_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k6_fuzzy_1 A B C) (k1_fuzzy_2 A (k2_fuzzy_1 A B C) (k1_fuzzy_1 A B C)))) ) ) ) ) ) ).
tt(t20_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  ( ((k1_seq_1 (k4_fuzzy_2 A B) C) = k6_numbers)  &  ((k1_seq_1 (k5_fuzzy_2 A B) C) = 1) ) ) ) ) ) ) ) ).
tt(t20_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ((k3_funct_2 (u1_struct_0 A) k7_numbers C (k4_algstr_0 A B)) = (k3_funct_2 (u1_struct_0 A) k7_numbers C B)) ) ) ) ) ) ) ) ).
tt(t20_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k4_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A C) (k5_finseq_2 (u1_struct_0 B) A D)) = (k5_finseq_2 (u1_struct_0 B) A (k1_algstr_0 B C D))) ) ) ) ) ) ) ) ) ).
tt(t20_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 (k14_gate_1 A B C D)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) ) ) ) ) ) ) ).
tt(t20_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k2_gcd_1 A B) (k2_gcd_1 A C)))  =>  ((k2_gcd_1 A B) = (k2_gcd_1 A C)) ) ) ) ) ) ) ) ).
tt(t20_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ((r1_xxreal_0 (k3_finseq_1 E) A) =>  ((k9_genealg1 D E F B C A) = (k8_genealg1 D E F B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~ (r2_geomtrap A B C D E F G))  &  (~ (r2_geomtrap A B C D E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k6_circuit2 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k6_circuit2 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((k5_gfacirc2 (k1_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k2_circcomb (k5_gfacirc2 A B C) (k25_gfacirc1 D E (k7_gfacirc2 A B C))))  &  ( ((k6_gfacirc2 (k1_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k3_circcomb (k5_gfacirc2 A B C) (k25_gfacirc1 D E (k7_gfacirc2 A B C)) (k6_gfacirc2 A B C) (k26_gfacirc1 D E (k7_gfacirc2 A B C))))  &  ((k7_gfacirc2 (k1_nat_1 A 1) (k7_finseq_1 B (k9_finseq_1 D)) (k7_finseq_1 C (k9_finseq_1 E))) = (k21_gfacirc1 D E (k7_gfacirc2 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (~ (v1_xboole_0 (k6_subset_1 (k6_glib_000 A) (k6_domain_1 (k6_glib_000 A) B)))) ) ) ) ) ).
tt(t20_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k5_glib_001 A C E) = (k5_glib_001 B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (r1_tarski (k2_glib_002 A B) (k1_glib_002 A B))) ) ) ) ).
tt(t20_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m1_glib_000 B A)) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ((k8_glib_003 A C) = (k8_glib_003 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k6_glib_004 A (k9_glib_004 A (k10_glib_004 A B) C)) = k1_xboole_0)  <=>  ((k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C))) = (k2_glib_002 A B)) ) ) ) ) ) ) ) ).
tt(t20_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( ((k1_matrix_1 D) = (k2_nat_1 A 1))  &  ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k4_finseq_1 D))) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 D))) &  ( ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 D (k1_matrix_1 D)) C B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C B))  & (r2_hidden (k1_matrix_1 D) (k2_finseq_1 (k1_matrix_1 D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 C) &  ((v5_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 C))) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) A)) (k1_goboard5 C B))) ) ) ) ) ) ) ).
tt(t20_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)) = (a_2_2_goboard6 A B)) ) ) ) ) ) ) ).
tt(t20_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k1_matrix_1 A))) ) ) ) ) ) )  =>  ((r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) |  ( (C = E)  & (r1_xxreal_0 (k1_int_2 (k9_real_1 B D)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 1))) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k2_nat_1 C 1))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k2_nat_1 C 1))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 2))) (k13_complex1 1 2)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 C 2))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t20_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (v1_convex1 (k1_tops_1 (k15_euclid 2) (k4_goboard5 A B)) (k15_euclid 2))) ) ) ) ) ).
tt(t20_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((v2_goboard1 B) & (r1_xxreal_0 1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k1_goboard5 B A) = (a_2_0_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t20_gobrd13,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) => (r1_tarski (k16_matrix_1 (k2_goboard2 B)) (k16_matrix_1 A))) ) ) ) ) ).
tt(t20_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_topreal1 2 A) = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) (k2_goboard9 A)) (k2_goboard9 A))) ) ) ).
tt(t20_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v4_card_3 A) =>  ( (~ (v1_xboole_0 (k1_goedelcp A)))  & (v4_card_3 (k1_goedelcp A))) ) ) ) ).
tt(t20_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( (? [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  &  ((r4_graph_1 A C) & (r4_graph_1 B C)) ) )  =>  ((r4_graph_1 A (k5_graph_1 A B)) & (r4_graph_1 B (k5_graph_1 A B))) ) ) ) ) ) ).
tt(t20_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v1_graph_2 A) & (v2_graph_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v1_graph_2 B) & (v2_graph_2 B)) ) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ((k1_funct_1 A 1) = (k1_funct_1 B 1)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t20_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] : (r1_tarski (k2_graph_3 A B C) (k5_graph_3 A B))) ) ) ) ) ).
tt(t20_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  (~  ( (~ (v1_graph_4 C A))  &  ((r3_graph_4 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ( ((v7_graph_1 F A) & (m2_graph_1 F A))  =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 F)))  &  ((r3_graph_4 A G F) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 G)))  &  ( ((k1_funct_1 B 1) = (k1_funct_1 G 1))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 G (k3_finseq_1 G)))  &  ( ((k15_finseq_1 D) = F)  &  ((k15_finseq_1 E) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (~  ( (~ (r1_tarski (k2_graph_5 B C) A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E (u4_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_1 F (u4_struct_0 B)) =>  (~  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 C)) &  ( (~ (r1_tarski (k1_graph_5 B (k7_partfun1 (u4_struct_0 B) C (k2_nat_1 D 1))) A))  &  ( ((k3_finseq_1 E) = D)  &  ( (C = (k8_finseq_1 (u4_struct_0 B) E F))  & (r1_tarski (k2_graph_5 B E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k4_finseq_1 (k2_graphsp A B C D)) = (k4_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(t20_grcat_1,ax, (! [A:$i] :  ( ((v1_grcat_1 A) &  ((v2_grcat_1 A) & (l1_grcat_1 A)) )  =>  (! [B:$i] :  ( ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  ( ((k7_grcat_1 B) = (k8_grcat_1 A))  =>  ( ((k7_grcat_1 (k13_grcat_1 B A)) = (k7_grcat_1 A))  &  ((k8_grcat_1 (k13_grcat_1 B A)) = (k8_grcat_1 B)) ) ) ) ) ) ) ).
tt(t20_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ((v1_gr_cy_1 A) => (v1_gr_cy_1 B)) ) ) ) ) ).
tt(t20_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  ( ((k7_group_1 A) = 2)  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ((r1_group_2 A B (k6_group_2 A)) |  (B = A) ) ) ) ) ) ) ).
tt(t20_gr_cy_3,ax, ((k1_gr_cy_3 5) = 31) ).
tt(t20_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski C B) (k2_funct_1 A)) <=> (r2_hidden (k4_tarski B C) A)) ) ) ) ) ) ).
tt(t20_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ( ( ((v15_algstr_0 C) & (m1_group_6 C A B))  &  ((v15_algstr_0 (k1_grnilp_1 A B (k7_group_2 A))) & (m1_group_6 (k1_grnilp_1 A B (k7_group_2 A)) A C)) )  => (m1_group_6 (k5_group_6 B (k1_group_6 A B C)) (k5_group_6 A C) (k10_group_5 (k5_group_6 A C)))) ) ) ) ) ) ) ).
tt(t20_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_tarski (k2_groeb_1 A B C (k7_ideal_1 (k11_polynom1 A C) D)) (k3_groeb_1 A (k2_groeb_1 A B C D))) => (v9_rewrite1 (k3_polyred A B C D))) ) ) ) ) ) ) ) ) ).
tt(t20_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r8_pboole (k15_pre_poly A) (k3_groeb_2 A B C D (k7_polynom1 A C)) (k7_polynom1 A C)) & (r8_pboole (k15_pre_poly A) (k3_groeb_2 A B C (k7_polynom1 A C) D) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(t20_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( ((r2_hidden F (k3_groeb_3 A B C D E)) & (r2_hidden G (k4_groeb_3 A B C D E)))  => (r2_termord A B G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k1_group_11 A (k9_subset_1 (u1_struct_0 A) B C) D) = (k9_subset_1 (u1_struct_0 A) (k1_group_11 A B D) (k1_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t20_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A C B))  <=>  ((k6_algstr_0 A B (k2_group_1 A C)) = (k6_algstr_0 A (k2_group_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t20_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_2 A (k7_domain_1 (u1_struct_0 A) B C) (k6_domain_1 (u1_struct_0 A) D)) = (k7_domain_1 (u1_struct_0 A) (k6_algstr_0 A B D) (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t20_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_group_3 A B B) = B) ) ) ) ) ).
tt(t20_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ((r1_tarski (k10_xtuple_0 C) (k8_group_2 A B)) => (r1_struct_0 B (k3_group_4 A (k4_group_4 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t20_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_group_5 A B B) = (k1_group_1 A)) ) ) ) ) ).
tt(t20_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_group_6 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_group_6 A B))) =>  ((k6_group_6 A B (k6_algstr_0 (k5_group_6 A B) C D)) = (k2_group_2 A (k6_group_6 A B C) (k6_group_6 A B D))) ) ) ) ) ) ) ) ) ).
tt(t20_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_group_7 (k10_finseq_1 A B)) &  ((v2_group_7 (k10_finseq_1 A B) (k2_tarski 1 2)) & (v3_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ) ) ) ) ) ) ) ) ).
tt(t20_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (~ (r1_xxreal_0 (k18_group_2 A B) k6_numbers)) ) ) ) ) ).
tt(t20_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (! [E:$i] :  ((m1_group_9 E A B) =>  ((k17_group_9 A B (k17_group_9 A B C D) E) = (k17_group_9 A B C (k17_group_9 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (~  ( ((v1_group_3 D B) & (m1_group_2 D B))  &  ((v2_group_10 C A) &  ((v2_group_10 D A) &  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E B))  =>  (~  ( ((u1_struct_0 E) = (k7_group_4 B C D))  & (v2_group_10 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k6_hahnban1 A B (k5_struct_0 A) C) C)) ) ) ) ) ) ).
tt(t20_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_hahnban B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_struct_0 A)) = k6_numbers) ) ) ) ) ).
tt(t20_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((r2_hidden C (k4_finseq_1 B)) => (m1_hallmar1 (k2_hallmar1 A B C D) A B C)) ) ) ) ) ) ) ) ).
tt(t20_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (v2_compts_1 B (k3_pcomps_1 A)))  => (r1_xxreal_0 (k4_metric_1 A C D) (k1_funct_1 (k5_weierstr A B) C))) ) ) ) ) ) ) ) ) ).
tt(t20_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  &  ( ((k4_glib_001 A C) = (k3_glib_001 A B))  &  ((r1_xboole_0 (k14_glib_001 A B) (k14_glib_001 A C)) &  ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A B) (k13_glib_001 A C)) = (k2_tarski (k4_glib_001 A B) (k3_glib_001 A B))) ) ) )  =>  ((v1_glib_001 B A) |  ((v1_glib_001 C A) | (v8_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ).
tt(t20_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k6_hahnban1 k1_complfld A C B)) (k6_hahnban1 k1_complfld A (k2_complfld C) (k1_hermitan A B)))) ) ) ) ) ) ).
tt(t20_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  (~  ( (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E C) &  (! [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden F D) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) F (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B))) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E (k7_heyting1 A (k3_heyting1 A C) (k3_heyting1 A D))) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) => (r3_lattices (k5_substlat A B) (k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k7_heyting2 A B C) D) C)) ) ) ) ) ) ) ).
tt(t20_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_heyting3 1 A) = (k7_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k1_domain_1 k5_numbers k5_numbers 1 A) (k1_domain_1 k5_numbers k5_numbers 2 A))) ) ) ).
tt(t20_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 C A B) & (r1_taylor_1 D A B))  => (r1_taylor_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t20_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k1_normsp_1 A (k11_polynom3 A E (k5_hilbasis A B D)) (k2_nat_1 C B)) = (k6_algstr_0 A (k1_normsp_1 A E C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r2_hidden (k3_hilbert1 A (k3_hilbert1 B C)) k6_hilbert1) => (r2_hidden (k3_hilbert1 B (k3_hilbert1 A C)) k6_hilbert1)) ) ) ) ) ) ) ).
tt(t20_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ( ((k3_hilbert1 A B) = (k3_hilbert1 C D))  =>  ( (A = C)  &  (D = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_funct_2 k1_xboole_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_funct_2 k1_xboole_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_xboole_0) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_xboole_0)))) )  =>  ((k10_xtuple_0 (k15_pralg_1 C D)) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(t20_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k2_hurwitz A B) = (k4_xcmplx_0 1))  <=> (r2_funct_2 k5_numbers (u1_struct_0 A) B (k9_polynom3 A))) ) ) ) ) ).
tt(t20_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k8_idea_1 A B) = (k8_idea_1 A C))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t20_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_subset_1 B (u1_struct_0 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v1_gcd_1 C A) & (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t20_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A B D) & (r3_incsp_1 A C D)) ) ) )  &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t20_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  ((k12_mcart_1 (k9_index_1 A B C)) = (k8_index_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B)) ) ) ) ) ) ) ).
tt(t20_instalg1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_instalg1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r3_pua2mss1 A B D E) &  ((r1_tarski (k10_xtuple_0 D) (u1_struct_0 C)) & (r1_tarski (k10_xtuple_0 E) (u4_struct_0 C))) )  => (r3_pua2mss1 A C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ( ((k3_xcmplx_0 A B) = C)  & (r2_int_1 D E C))  => (r2_int_1 D E A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (m1_subset_1 (k3_int_2 A B) k5_numbers)) ) ) ) ).
tt(t20_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d (k3_xcmplx_0 A B) (k3_xcmplx_0 A C)) = (k3_xcmplx_0 A (k4_nat_d B C))) ) ) ) ) ) ) ).
tt(t20_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ( ((k3_int_2 A B) = 1)  & (r1_int_5 A B))  =>  ((r1_xxreal_0 B 2) |  ((k6_int_1 (k6_xcmplx_0 (k1_newton A (k3_nat_d (k7_nat_d B 1) 2)) 1) B) = k6_numbers) ) ) ) ) ) ) ).
tt(t20_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_2 A B) => (r1_int_1 (k3_xcmplx_0 A B) (k2_int_2 A B))) ) ) ) ) ).
tt(t20_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_int_7 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_int_7 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k8_group_1 (k3_int_7 A) B C) = (k8_group_1 (k9_int_3 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 k6_numbers k32_sin_cos))  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) k19_sin_cos)) = k6_numbers) ) ) ) ) ) ).
tt(t20_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ((r1_tarski E (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A)))) &  ( (E = (k1_relset_1 k1_numbers D))  & (r2_relset_1 k1_numbers k1_numbers D (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 (k21_binop_2 A 1))) A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2)))))) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((k2_integra5 B D) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A))) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k2_sin_cos9 (k1_partfun2 k1_numbers D)) (k3_rfunct_1 k1_numbers k1_numbers k3_taylor_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2))))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 D)) (k8_real_1 D (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t20_integr15,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (C = (k1_rcomp_1 E D))  =>  ((k6_euclid A (k11_integr15 A C B)) = (k12_integr15 D E A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_integr16,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) &  ((r1_integr16 B C) & (v1_comseq_2 (k2_partfun1 k1_numbers k2_numbers C B))) )  =>  ((r1_integr16 B (k25_valued_1 k1_numbers k2_numbers C A)) &  ((k7_integr16 B (k25_valued_1 k1_numbers k2_numbers C A)) = (k5_binop_2 A (k7_integr16 B C))) ) ) ) ) ) ) ) ) ).
tt(t20_integr19,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid B) C A) B) &  ((r1_integr15 B A C) & (r1_integra5 A (k1_nfcont_4 B k1_numbers C))) ) )  => (r1_xxreal_0 (k12_euclid (k11_integr15 B A C)) (k2_integra5 A (k1_nfcont_4 B k1_numbers C)))) ) ) ) ) ) ) ).
tt(t20_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k3_integra1 (k2_integra1 B C A)) = (k1_seq_1 (k4_integra1 B (k7_rfunct_1 B B) C) A)) ) ) ) ) ) ) ) ).
tt(t20_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k8_real_1 (k8_real_1 A (k4_seq_4 (k1_rvsum_1 C))) (k3_integra1 B)) (k1_seq_1 (k8_integra1 B (k26_valued_1 B k1_numbers C A)) D))) ) ) ) ) ) ) ) ) ).
tt(t20_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v1_fdiff_1 (k2_integra3 A C) k6_numbers) & (v2_relat_1 (k2_integra3 A C))) )  =>  ( ((k3_integra1 A) = k6_numbers)  |  ((v2_comseq_2 (k4_integra2 A B C)) &  ((k2_seq_2 (k4_integra2 A B C)) = (k11_integra1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t20_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) & (v3_integra1 B A))  => (v3_integra1 (k18_rfunct_3 A B) A)) ) ) ) ) ).
tt(t20_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k1_rcomp_1 D C))  =>  ((k1_real_1 (k2_integra5 B A)) = (k4_integra5 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t20_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) )  =>  ((k4_integra5 A D E) = (k7_real_1 (k4_integra5 A C E) (k4_integra5 C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) C) &  ((r1_tarski C (k1_relset_1 k1_numbers D)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D C)) & (r1_integra7 C E D)) ) ) )  =>  ((k1_seq_1 E B) = (k7_real_1 (k4_integra5 A B D) (k1_seq_1 E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v3_fdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k32_valued_1 k1_numbers k1_numbers A)) &  ((v3_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A)) & (m1_subset_1 (k32_valued_1 k1_numbers k1_numbers A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(t20_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 C k1_numbers (k1_integra5 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) C) (k47_valued_1 C k1_numbers k1_numbers (k1_integra5 A C) (k1_integra5 B C)))) ) ) ) ) ) ).
tt(t20_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r1_interva1 A (k3_interva1 A B B) B)) ) ) ) ).
tt(t20_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 A A)) k8_intpro_1)) ) ) ) ).
tt(t20_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 A k6_numbers) |  ((k1_seq_1 (k3_irrat_1 A) B) = (k1_seq_1 (k7_newton 1 (k13_complex1 1 A) A) (k2_nat_1 B 1))) ) ) ) ) ) ) ).
tt(t20_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r1_nattra_1 A B D E) =>  (! [F:$i] :  ((m2_cat_1 F C A) =>  (! [G:$i] :  ((m1_nattra_1 G A B D E) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k4_nattra_1 C B (k9_cat_1 C A B F D) (k9_cat_1 C A B F E) (k3_isocat_1 C A B D E F G) H) = (k4_nattra_1 A B D E G (k8_cat_1 C A F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) E) = (k12_cat_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ( ((k2_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) (k1_tops_1 A (k2_pre_topc A B))))  &  ((k2_tops_1 A B) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) (k2_pre_topc A (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ).
tt(t20_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jgraph_1 A 2) & (v1_graph_4 (k4_jgraph_1 (u1_struct_0 (k15_euclid 2)) A) (k1_jgraph_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((k1_funct_1 A 1) = (k1_funct_1 A (k3_finseq_1 A)))  | (v2_topreal1 A)) ) ) ) ).
tt(t20_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = B) ) )  & (v5_pre_topc C A k3_topmetr)) ) ) ) ) ) ) ).
tt(t20_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (A = (k8_struct_0 (k15_euclid 2)))  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2)))) ) ) ) ).
tt(t20_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid D) (k12_euclid D)) A) (k7_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k17_euclid D) k6_numbers) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t20_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid B)) =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 A (k10_real_1 (k17_euclid B) (k12_euclid B))) |  ( ((k12_euclid B) = k6_numbers)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  =>  ((r1_xxreal_0 k6_numbers (k18_euclid C)) &  (~ (r1_xxreal_0 k6_numbers (k17_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_xxreal_0 k6_numbers C) &  ( (D = a_0_0_jgraph_6)  &  (E = (a_3_0_jgraph_6 A B C)) ) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 C A C B) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 E (k17_euclid C)) &  ((r1_xxreal_0 (k17_euclid C) F) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan10,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k7_setfam_1 (u1_struct_0 (k15_euclid 2)) (k3_jordan10 A)) = (k4_jordan10 A)) ) ) ).
tt(t20_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 B (k1_matrix_1 C)))  => (v1_convex1 (k3_goboard5 C A B) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t20_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_subset_1 (k2_jordan2c 2 A) (k3_topreal1 2 (k1_jordan13 A B)))) ) ) ) ) ).
tt(t20_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k2_jordan1e B A))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F G) &  ((r1_xxreal_0 G E) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) F C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) G C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan16,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) k1_numbers k1_numbers A (k1_fcont_1 B C)) =>  ( (B = k6_numbers)  | (v3_tops_2 A k3_topmetr k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t20_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_jordan17 A C D E B) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (F = B) )  &  ( (~  (F = C) )  & (r1_jordan17 A C E B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) &  ((k2_jordan18 A B) = (k1_jordan18 A B)) ) ) ) ) ) ) ).
tt(t20_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B))) )  => (r1_xxreal_0 (k7_pscomp_1 (k3_topreal1 2 C)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B))))) ) ) ) ) ) ) ).
tt(t20_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_0_jordan1 A))  => (v3_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t20_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A 1) (k1_jordan1a (k1_jordan8 A 1)) (k3_finseq_1 (k1_jordan8 A 1))) = (k19_euclid (k13_complex1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k7_pscomp_1 (k3_topreal1 2 (k1_jordan9 A 1))))) ) ) ).
tt(t20_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) &  ((k17_euclid A) = (k8_pscomp_1 (k1_jordan2c 2 B))) ) ) ) ) ) ) ).
tt(t20_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  & (r2_hidden (k19_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) C))) ) ) ) ) ) ) ) ).
tt(t20_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan9 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) )  =>  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k2_nat_1 C 1))) = (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t20_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan1e B A) (k19_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k1_jordan1e B A) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ) ).
tt(t20_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  => (r1_tarski (k2_topreal1 2 B C) (k3_gobrd13 B A C))) ) ) ) ) ) ) ) ).
tt(t20_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C D))  &  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E)) = (k6_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k24_pscomp_1 B) A))  =>  ((k24_pscomp_1 A) = (k24_pscomp_1 B)) ) ) ) ) ) ).
tt(t20_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_topreal6 2 (k19_euclid k6_numbers k6_numbers) (k1_rlvect_1 (k15_euclid 2) A B)) = (k8_real_1 (k18_complex1 B) (k1_topreal6 2 (k19_euclid k6_numbers k6_numbers) A))) ) ) ) ) ).
tt(t20_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((r1_topreal1 (k15_euclid A) B C D) &  ((r1_topreal1 (k15_euclid A) B C E) & (r1_tarski E D)) )  =>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k8_pscomp_1 A) = (k8_pscomp_1 (k9_jordan6 A))) ) ) ).
tt(t20_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))) &  ((k2_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_jordan23 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k4_jordan3 A B C) (k3_finseq_1 (k4_jordan3 A B C))) = C) ) ) ) ) ) ) ) ) ).
tt(t20_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 1))) =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (A = (k12_finseq_1 k1_numbers B)) ) ) ) ) ).
tt(t20_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (m1_connsp_3 (k1_jordan2c A B) (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B)))) ) ) ) ).
tt(t20_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) &  (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1))) ) )  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ((k2_nat_1 (k2_nat_1 (k1_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) B) (k1_jordan3 A B)) 1) = (k3_finseq_1 A)) ) ) ) ) ) ) ).
tt(t20_jordan4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 1 D)) )  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 (k2_nat_1 (k7_nat_d C B) 1) D) |  ((k2_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C B) D) = (k2_topreal1 2 A (k7_nat_d C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) )  =>  ( ((r1_xxreal_0 A E) &  ((r1_xxreal_0 F B) &  ((v3_tops_2 I (k4_topmetr A B) (k4_topmetr C D)) &  ( ((k1_funct_1 I A) = C)  &  ( ((k1_funct_1 I B) = D)  &  ( (G = (k1_funct_1 I E))  &  (H = (k1_funct_1 I F)) ) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) |  ((k7_relset_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) I (k1_rcomp_1 E F)) = (k1_rcomp_1 G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (v4_topreal1 A))  =>  ( (B = (k1_funct_1 A 1))  | (r2_hidden B (k3_topreal1 2 (k3_jordan3 A B)))) ) ) ) ) ) ).
tt(t20_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_pre_topc B (k15_euclid 2)) &  ((v4_topreal1 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A C))) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) |  ((k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k2_jordan5c (k2_topreal1 2 A C) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(t20_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_0_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k14_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k14_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t20_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) => (r1_tarski (k4_jordan6 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t20_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v1_topreal2 A) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k1_funct_1 C 1) = (k18_pscomp_1 A))  &  ((v2_funct_1 C) &  ((r1_xxreal_0 8 (k3_finseq_1 C)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) C) A) &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) D) | (r1_jordan6 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)))) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k14_euclid 2)))) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  &  ( (E = (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1))))  & (r1_xxreal_0 B (k3_tbsp_1 (k14_euclid 2) E))) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_euclid 2)))) =>  (~  ( (D = (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1)))  & (r1_xxreal_0 B (k3_tbsp_1 (k14_euclid 2) D))) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)))) ) ) ) )  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C))))  &  ((r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2))) &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 E D) |  ((r1_xxreal_0 (k3_finseq_1 C) E) |  ((r1_gobrd10 D E) | (r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1))) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C E) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 E 1))))) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  (~ (r1_xboole_0 (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1)) (k1_jordan7 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_goboard5 C A B)) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_goboard5 C A B)) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)) (k3_goboard5 C A B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_goboard5 C A B))) ) ) ) ) ) ) ) ) ) ).
tt(t20_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B C) => (v2_compts_1 (k1_jordan7 A B C) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t20_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  ((r2_hidden C (k3_topreal9 B D A)) => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid B)) (k1_rltopsp1 (k15_euclid B) D C) (k7_domain_1 (u1_struct_0 (k15_euclid B)) D C)) (k1_topreal9 B D A))) ) ) ) ) ) ) ) ) ).
tt(t20_knaster,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_abian (u1_struct_0 B) C A) D) = (k4_knaster B C D A)) ) ) ) ) ) ) ) ) ).
tt(t20_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  ((k3_kurato_0 A B) = (k2_kurato_0 A B)) ) ) ) ) ).
tt(t20_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1))))) = (k2_rcomp_1 k2_xxreal_0 4)) ).
tt(t20_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) C D) = (k2_pre_topc A (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 A)) B D))) ) )  =>  ((k1_kurato_2 A C) = (k1_kurato_2 A B)) ) ) ) ) ) ) ) ).
tt(t20_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k2_finseq_1 (k1_nat_1 A 1))) & (r2_hidden C (k2_finseq_1 (k1_nat_1 A 1))))  =>  (! [D:$i] :  (~  ( (D = (a_3_0_laplace A B C))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E D (k12_matrix_2 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 D (k12_matrix_2 A))))) )  =>  (~  ((v3_funct_2 E D (k12_matrix_2 A)) &  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 (k1_nat_1 A 1))) =>  ( ((k1_funct_1 F B) = C)  =>  ((k1_funct_1 E F) = (k4_laplace B A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_group_3 A))))  =>  ((r2_hidden (k6_group_2 A) B) => (r1_group_2 A (k2_latsubgr A B) (k6_group_2 A))) ) ) ) ) ).
tt(t20_latsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ( (~ (v1_xboole_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B))))  &  ((v1_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) &  ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))) ) )  => (r2_hidden (k3_yellow_0 B) (u1_struct_0 A))) ) ) ) ) ).
tt(t20_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (r6_binop_1 (u1_struct_0 A) (u2_lattices A) (u2_lattices A))) ) ).
tt(t20_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ((k6_lattice3 (u1_struct_0 A) (k2_lattice3 A)) = (k2_lattice3 (k1_lattice2 A)))  &  ((k7_lattice3 (k3_lattice3 A)) = (k3_lattice3 (k1_lattice2 A))) ) ) ) ).
tt(t20_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k3_lattice2 (u1_struct_0 A) A (k5_setwiseo (u1_struct_0 A) B (k2_setwiseo (u1_struct_0 A) C)) D) = (k4_lattices A (k3_lattice2 (u1_struct_0 A) A B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t20_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (~  ((k7_lattice5 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t20_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (B = (k5_lattices A)) )  &  ( (~  (B = (k6_lattices A)) )  &  (~  ( ((v3_lattice6 B A) => (v2_waybel_6 (k4_lattice3 A B) (k3_lattice3 A)))  &  ( ((v2_waybel_6 (k4_lattice3 A B) (k3_lattice3 A)) => (v3_lattice6 B A))  &  ( ((v4_lattice6 B A) => (v3_waybel_6 (k4_lattice3 A B) (k3_lattice3 A)))  &  ((v3_waybel_6 (k4_lattice3 A B) (k3_lattice3 A)) => (v4_lattice6 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ( ((v5_ordinal1 E) &  ((v1_relat_1 E) & (v1_funct_1 E)) )  =>  (! [F:$i] :  ((v3_ordinal1 F) =>  ( ((v4_ordinal1 F) &  ( ((k9_xtuple_0 E) = F)  &  (! [G:$i] :  ((v3_ordinal1 G) =>  ((r2_hidden G F) =>  ((k1_funct_1 E G) = (k5_lattice8 A B C D G)) ) ) ) ) )  =>  ( (F = k1_xboole_0)  |  ((k5_lattice8 A B C D F) = (k3_tarski (k10_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattices A (k7_lattices A B) B) = (k5_lattices A)) ) ) ) ) ).
tt(t20_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) &  ((k1_recdef_1 (k5_lexbfs A B C) E) = D) )  =>  ((k6_lexbfs A B (k7_nat_d (k39_glib_000 B) D)) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k1_fuzzy_1 A B C) = (k12_lattice3 (k4_lfuzzy_0 A) (k6_lfuzzy_0 A B) (k6_lfuzzy_0 A C))) ) ) ) ) ) ) ).
tt(t20_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( ((v2_lfuzzy_1 C A) & (r1_fuzzy_1 B C))  => (r1_fuzzy_1 (k2_lfuzzy_1 (k2_zfmisc_1 A A) B (k2_fuzzy_4 A A B)) C)) ) ) ) ) ) ) ).
tt(t20_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = B) ) )  => (v1_limfunc1 A)) ) ) ).
tt(t20_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 E (k1_seq_1 C F))) ) ) ) ) ) ) ) ) )  | (r5_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t20_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  ( (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))))  &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) ) )  | (r2_limfunc3 B A)) ) ) ) ) ) ).
tt(t20_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r3_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t20_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 A B C) => (r1_lmod_6 A (k1_vectsp_4 A C) B)) ) ) ) ) ) ) ).
tt(t20_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_lmod_7 A B C))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k18_lmod_7 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = C) )  =>  ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = (k1_normsp_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t20_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k9_lopban_2 A)) &  ((v3_normsp_0 (k9_lopban_2 A)) &  ((v2_normsp_1 (k9_lopban_2 A)) &  ((v2_rlvect_1 (k9_lopban_2 A)) &  ((v3_rlvect_1 (k9_lopban_2 A)) &  ((v4_rlvect_1 (k9_lopban_2 A)) &  ((v13_algstr_0 (k9_lopban_2 A)) &  ((v3_group_1 (k9_lopban_2 A)) &  ((v3_vectsp_1 (k9_lopban_2 A)) &  ((v1_vectsp_1 (k9_lopban_2 A)) &  ((v5_rlvect_1 (k9_lopban_2 A)) &  ((v6_rlvect_1 (k9_lopban_2 A)) &  ((v7_rlvect_1 (k9_lopban_2 A)) &  ((v2_funcsdom (k9_lopban_2 A)) &  ((v5_rlvect_1 (k9_lopban_2 A)) &  ((v6_rlvect_1 (k9_lopban_2 A)) &  ((v7_rlvect_1 (k9_lopban_2 A)) & (v8_rlvect_1 (k9_lopban_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_lopban_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v1_lopban_3 (k5_normsp_1 A B C) A) &  ((k1_lopban_3 A (k5_normsp_1 A B C)) = (k1_rlvect_1 A (k1_lopban_3 A B) C)) ) ) ) ) ) ) ) ).
tt(t20_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v2_lopban_3 (k1_lopban_4 A (k4_struct_0 A)) A) &  ((k1_lopban_3 A (k1_lopban_4 A (k4_struct_0 A))) = (k5_struct_0 A)) ) ) ) ).
tt(t20_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (k8_lopclset A) (k4_lattices A B C)) = (k3_xboole_0 (k1_funct_1 (k8_lopclset A) B) (k1_funct_1 (k8_lopclset A) C))) ) ) ) ) ) ) ).
tt(t20_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) C D)) (k2_lpspace1 A k1_numbers (k13_rfunct_3 A) (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B C) (k2_lpspace1 A k1_numbers (k3_lpspace1 A) B D)))) ) ) ) ) ) ) ) ).
tt(t20_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] : (r2_relset_1 A k1_numbers (k2_mesfun6c C A (k2_partfun1 A k1_numbers B D)) (k2_partfun1 A k1_numbers (k2_mesfun6c C A B) D))) ) ) ) ) ) ) ).
tt(t20_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k3_hilbert1 (k5_ltlaxio1 (k2_ltlaxio1 A) (k2_ltlaxio1 (k4_ltlaxio1 B (k4_hilbert1 B A)))) (k4_hilbert1 B A)))) = 1) ) ) ) ) ) ) ) ) ).
tt(t20_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A B D) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t20_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 (k3_finseq_2 A) A)) =>  ( (C = (k16_funcop_1 (k6_finseq_1 A) B))  =>  ((v4_margrel1 (k17_margrel1 A C) A) &  ((v5_margrel1 (k17_margrel1 A C) A) & (v2_relat_1 (k17_margrel1 A C))) ) ) ) ) ) ) ) ) ).
tt(t20_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_mathmorp A (k6_rusub_4 A B C) C))) ) ) ) ) ) ).
tt(t20_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r1_matrix10 B C) => (v2_matrix10 (k4_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t20_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ((v4_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) =>  ( ((k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B B) = (k1_finseq_2 A))  & (r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B))) ) ) ) ) ) ).
tt(t20_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) B B) =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k4_matrix_6 B D F (k6_matrix12 B B D (k12_matrix_1 D B) A C E)) = (k6_matrix12 B B D F A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_matrix_1 B A 1 1) =>  (B = (k2_matrlin A (k4_matrix_2 A (k3_matrix_1 A B 1 1)))) ) ) ) ) ).
tt(t20_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k13_fvsum_1 A B (k2_matrix14 A (k3_finseq_1 B))) = (k4_struct_0 A)) ) ) ) ) ).
tt(t20_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((r1_xxreal_0 (k8_matrix13 A B) (k8_matrix13 A (k7_matrlin (u1_struct_0 A) B C))) & (r1_xxreal_0 (k8_matrix13 A C) (k8_matrix13 A (k7_matrlin (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ).
tt(t20_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((v3_matrix16 D (u1_struct_0 B)) => (v3_matrix16 (k2_matrix13 A A B D C) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t20_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k1_xboole_0))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((m1_matrix_1 B A (k3_finseq_1 B) C) <=>  (C = (k1_matrix_1 B)) ) ) ) ) ) ) ) ) ).
tt(t20_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_subset_1 (k1_finseq_2 A) (u1_struct_0 (k13_matrix_2 A)))) ) ).
tt(t20_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_matrix_3 A (k5_matrix_2 (u1_struct_0 A) 1 (k4_matrix_2 (u1_struct_0 A) B)) (k5_matrix_2 (u1_struct_0 A) 1 (k4_matrix_2 (u1_struct_0 A) C))) = (k5_matrix_2 (u1_struct_0 A) 1 (k4_matrix_2 (u1_struct_0 A) (k8_group_1 A B C)))) ) ) ) ) ) ) ).
tt(t20_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k3_matrix_3 A B (k1_matrix_4 A C C))) ) ) ) ) ) ) ) ).
tt(t20_matrix_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) )  =>  ((k6_matrix_3 A (k3_matrix_3 A C D) B) = (k3_matrix_3 A (k6_matrix_3 A C B) (k6_matrix_3 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_matrix_1 A (u1_struct_0 B) (k2_matrix_2 (u1_struct_0 B) A A C)) = (k2_matrix_2 (u1_struct_0 B) A A C)) ) ) ) ) ) ) ).
tt(t20_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k3_group_4 A (k8_finseq_1 (u1_struct_0 A) B C))) = (k6_algstr_0 A (k2_group_1 A (k3_group_4 A C)) (k2_group_1 A (k3_group_4 A B)))) ) ) ) ) ) ) ).
tt(t20_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B D C) = (k4_matrix_6 A B E C)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 1 2 3))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) B F J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrixc1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k15_complex1 (k5_binop_1 k2_numbers k27_binop_2 A (k15_complex1 B))) = (k5_binop_1 k2_numbers k27_binop_2 (k15_complex1 A) B)) ) ) ) ) ).
tt(t20_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ((k2_wsierp_1 (k11_matrixj1 A (k5_matrixj1 A B C))) = (k2_nat_1 (k1_matrix_1 B) (k1_matrix_1 C))) ) ) ) ) ) ) ).
tt(t20_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (! [G:$i] :  ( ((v1_matrixj1 G (u1_struct_0 A)) & (m2_finseq_1 G (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( (F = (k13_matrixj1 (u1_struct_0 A) (k4_struct_0 A) G))  =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden H (k4_finseq_1 D)) &  (I = (k1_matrixj1 (k10_matrixj1 (u1_struct_0 A) G) H)) )  =>  ( ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k4_matrlin2 A B C D E F) (k7_partfun1 (u1_struct_0 B) D H)) = (k4_rlvect_1 C (k5_matrlin A C (k8_matrix_1 (u1_struct_0 A) (k2_matrixj1 (u1_struct_0 A) G I) (k7_nat_d H (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) (k6_matrixj1 (u1_struct_0 A) (k7_nat_d I 1) G))))) (k2_rfinseq (u1_struct_0 C) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) (k6_matrixj1 (u1_struct_0 A) (k7_nat_d I 1) G))) (k17_finseq_1 (u1_struct_0 C) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) (k6_matrixj1 (u1_struct_0 A) I G))) E)))))  &  ((k3_finseq_1 (k2_rfinseq (u1_struct_0 C) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) (k6_matrixj1 (u1_struct_0 A) (k7_nat_d I 1) G))) (k17_finseq_1 (u1_struct_0 C) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) (k6_matrixj1 (u1_struct_0 A) I G))) E))) = (k1_matrix_1 (k2_matrixj1 (u1_struct_0 A) G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  =>  ((k8_matrix_1 (u1_struct_0 A) (k6_matrix_3 A C B) D) = (k10_fvsum_1 (k1_matrix_1 C) A (k8_matrix_1 (u1_struct_0 A) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k3_finseq_1 C) = (k1_matrix_1 B)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_3 A B (k1_matrix_4 A C D)) = (k1_matrix_4 A (k4_matrix_3 A B C) (k4_matrix_3 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  ((k9_matrlin A B C (k4_struct_0 B)) = (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 C) (k4_struct_0 A))) ) ) ) ) ) ) ).
tt(t20_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ( ((v2_funct_1 C) & (r1_tarski (k1_vectsp_6 A B D) (k10_xtuple_0 C)))  =>  ((k4_rlvect_1 B (k3_vectsp_6 A B C D)) = (k4_vectsp_6 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_xxreal_0 (k4_matroid0 A B) (k5_card_1 B))) ) ) ) ).
tt(t20_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 (k3_matrprob A)) = (k3_finseq_1 A))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 (k3_finseq_1 A))) =>  ((k1_seq_1 (k3_matrprob A) B) = (k18_rvsum_1 (k8_matrix_1 k1_numbers A B))) ) ) ) ) ) ) ).
tt(t20_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  (! [D:$i] :  ((m1_matrlin D k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  (! [E:$i] :  ((m1_matrlin E k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 B)) =>  ( ( (D = (k11_matrix13 k2_vectsp_1 A A (k12_matrix_1 k2_vectsp_1 A)))  &  (E = (k11_matrix13 k2_vectsp_1 B B (k12_matrix_1 k2_vectsp_1 B))) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 k2_vectsp_1) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ( (F = C)  => (r1_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 (k6_prvect_1 k2_vectsp_1 B)) (k3_matrtop1 A B C) (k4_matrlin2 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k6_prvect_1 k2_vectsp_1 B) D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  ( (D = (k11_matrix13 k2_vectsp_1 A A (k12_matrix_1 k2_vectsp_1 A)))  =>  ((r1_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k2_relset_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (k17_finseq_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) B D))) C) <=>  (C = (k7_finseq_1 (k16_finseq_1 B C) (k5_finseq_2 k5_numbers (k7_nat_d A B) k6_numbers))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ( (E = B)  |  ( (E = C)  |  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) F) E) = (k1_seq_1 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) C) B)) = (k1_normsp_0 A (k5_algstr_0 A C B))) ) ) ) ) ) ) ).
tt(t20_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B (k2_mboolean A C)) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  &  ((r1_pboole A B D) & (r1_pboole A D C)) ) ) ) ) ) ) ) ) ).
tt(t20_mcart_1,ax, (! [A:$i] :  ( (? [B:$i] :  (? [C:$i] :  (A = (k4_tarski B C)) ) )  =>  ( (~  (A = (k1_xtuple_0 A)) )  &  (~  (A = (k2_xtuple_0 A)) ) ) ) ) ).
tt(t20_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (v1_xboole_0 (k2_tarski B C)))  &  ((v4_card_3 (k2_tarski B C)) & (m1_subset_1 (k2_tarski B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ).
tt(t20_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B C E)))  & (r1_tarski (k8_nat_1 B C E) (k8_nat_1 B C (k2_nat_1 E 1)))) ) ) )  =>  ((k5_setfam_1 A (k4_measure1 A B D)) = (k5_setfam_1 A (k4_measure1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t20_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  => (r1_measure3 A (k2_measure3 A B C) (k4_measure3 A B C))) ) ) ) ) ).
tt(t20_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r2_hidden C A) &  ((r2_hidden D B) & (r1_xxreal_0 (k8_supinf_2 A) (k7_supinf_2 B))) )  => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t20_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  => (r1_tarski B (k1_measure4 A (k9_measure8 A B C)))) ) ) ) ) ).
tt(t20_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_member_1 (k2_tarski A B)) = (k2_tarski (k1_binop_2 A) (k1_binop_2 B))) ) ) ) ) ).
tt(t20_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) => (v2_membered A)) ) ) ) ).
tt(t20_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_memstr_0 A B (k7_memstr_0 A B C)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t20_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k18_binop_2 2 3)) (k1_rlvect_1 (k15_euclid 2) C (k18_binop_2 1 3))))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k18_binop_2 2 3)) (k1_rlvect_1 (k15_euclid 2) A (k18_binop_2 1 3))))  &  ( (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k18_binop_2 2 3)) (k1_rlvect_1 (k15_euclid 2) B (k18_binop_2 1 3))))  &  ((r1_euclid_6 A D G) &  ((r1_euclid_6 B E G) &  ((r1_euclid_6 B E H) &  ((r1_euclid_6 C F H) &  ((r1_euclid_6 A D I) & (r1_euclid_6 C F I)) ) ) ) ) ) ) )  =>  ((r1_euclid_6 A B C) |  ((k1_euclid_6 H I G) = (k12_binop_2 (k1_euclid_6 A B C) 7)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfun10 A B C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) =>  ((v10_mesfunc5 (k3_mesfunc5 A B D)) &  ((k2_mesfunc5 (k3_mesfunc5 A B D)) = (k12_supinf_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((k12_supinf_2 C F) = k6_numbers)  =>  ( (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (~  ( (G = (k1_relset_1 A D))  & (r1_mesfunc6 A B D G)) ) ) )  | (r3_mesfunc6 A B C (k2_partfun1 A k1_numbers D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) & (v2_comseq_2 (k10_seqfunc A B C)))  => (v1_rinfsup2 (k3_mesfunc5 A (k5_mesfun7c A B) C))) ) ) ) ) ) ) ).
tt(t20_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k5_comseq_3 A B) C) (k5_comseq_3 A (k2_partfun1 A k2_numbers B C))) & (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k6_comseq_3 A B) C) (k6_comseq_3 A (k2_partfun1 A k2_numbers B C)))) ) ) ) ) ) ).
tt(t20_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  (! [E:$i] :  (! [F:$i] :  ((v1_xreal_0 F) =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k8_nat_1 C D G) = (k9_subset_1 A E (k15_mesfunc1 A B (k1_measure6 (k3_real_1 F (k10_real_1 1 (k2_nat_1 G 1))))))) ) )  =>  ((k9_subset_1 A E (k16_mesfunc1 A B (k1_measure6 F))) = (k1_measure2 A C (k1_measure3 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k12_supinf_2 (k1_mesfunc2 A B) C) = k1_supinf_2) )  =>  ((k12_supinf_2 (k2_mesfunc2 A B) C) = (k2_supinf_2 (k12_supinf_2 B C))) ) ) ) ) ) ) ) ).
tt(t20_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v6_supinf_2 B) =>  ( ((r1_xxreal_0 k6_numbers C) => (v6_supinf_2 (k6_mesfunc1 A B C)))  &  ((r1_xxreal_0 C k6_numbers) => (v2_mesfunc5 (k6_mesfunc1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t20_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r2_relset_1 A k7_numbers (k1_mesfunc5 A (k26_valued_1 A k1_numbers B C)) (k6_mesfunc1 A (k1_mesfunc5 A B) C))) ) ) ) ) ) ).
tt(t20_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  => (r2_relset_1 A k7_numbers (k3_mesfunc1 A (k2_partfun1 A k7_numbers (k10_mesfunc1 A B) (k1_relset_1 A (k10_mesfunc1 A (k3_mesfunc1 A B C)))) (k2_partfun1 A k7_numbers (k10_mesfunc1 A C) (k1_relset_1 A (k10_mesfunc1 A (k3_mesfunc1 A B C))))) (k2_partfun1 A k7_numbers (k3_mesfunc1 A (k10_mesfunc1 A B) (k10_mesfunc1 A C)) (k1_relset_1 A (k10_mesfunc1 A (k3_mesfunc1 A B C)))))) ) ) ) ) ) ).
tt(t20_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C E) D)) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers (k3_mesfunc8 A C) E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((v1_mesfunc8 D A k7_numbers) &  ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers))) &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers D G) C) & (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers E G) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers D G) C))) ) ) ) )  => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_metric_1,ax, (! [A:$i] :  ((k1_binop_1 k3_metric_1 A A) = k6_numbers) ) ).
tt(t20_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden D B) &  ((r2_hidden F C) &  ((r2_hidden E B) & (r2_hidden G C)) ) )  =>  ((k4_metric_1 A D F) = (k4_metric_1 A E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 A B) = (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 B A)) ) ) ) ) ).
tt(t20_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~ (r1_xxreal_0 D k6_numbers))  => (r2_metric_6 A (k9_metric_1 A B D) C)) ) )  <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) & (r2_hidden D (k2_pcomps_1 A)))  => (r2_metric_6 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k2_waybel23 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 C A) => (r1_ordinal1 (k1_card_1 C) B)) ) ) ) ) ) ) ) ).
tt(t20_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlvect_2 B (k10_funcsdom (k2_finseq_1 A))) =>  (! [C:$i] :  ((m1_rlvect_2 C (k15_euclid A)) =>  ((r1_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) k1_numbers C B) =>  ((k6_rlvect_2 (k15_euclid A) C) = (k6_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) B)) ) ) ) ) ) ) ) ).
tt(t20_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) => (r1_midsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_midsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ( ((r1_midsp_2 (u1_struct_0 B) A C) & (v1_midsp_2 C B A))  =>  ( (~ (v2_struct_0 B))  &  ((v2_midsp_1 B) & (l1_midsp_1 B)) ) ) ) ) ) ) ) ) ).
tt(t20_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r2_hidden 1 (k2_finseq_1 (k2_nat_1 A 1)))) ) ).
tt(t20_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_relset_1 A A D E) &  ((r1_tarski B C) & (r1_relset_1 A A F G)) )  => (r1_tarski (k8_mmlquery A G B D) (k8_mmlquery A F C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mod_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m1_subset_1 (k1_ordinal1 B) A)) ) ) ) ).
tt(t20_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (v2_mod_3 B A)) ) ) ) ).
tt(t20_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k5_mod_4 A B)))  &  ((v13_algstr_0 (k5_mod_4 A B)) &  ((v7_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) &  ((v8_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) &  ((v9_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) &  ((v10_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) &  ((v11_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A)) &  ((v2_rlvect_1 (k5_mod_4 A B)) &  ((v3_rlvect_1 (k5_mod_4 A B)) &  ((v4_rlvect_1 (k5_mod_4 A B)) & (l1_vectsp_1 (k5_mod_4 A B) (k2_mod_4 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( (~  (B = (k1_modal_1 A)) )  =>  ((r2_wellord2 (k4_trees_1 A B) (a_2_0_modal_1 A B)) &  (~ (r2_hidden (k1_modal_1 A) (a_2_0_modal_1 A B))) ) ) ) ) ) ) ).
tt(t20_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C))))  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (k30_modelc_1 C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F)))))) )  =>  ((r4_modelc_1 C D F G E (k8_modelc_1 A B)) <=>  ((r4_modelc_1 C D F G E A) & (r4_modelc_1 C D F G E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v3_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  (B = (k10_modelc_2 A)) ) ) ) ) ) ) ).
tt(t20_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ((r3_modelc_3 A C B) => (r1_xxreal_0 (k18_modelc_3 A (u2_modelc_3 A B)) (k9_real_1 (k18_modelc_3 A (u2_modelc_3 A C)) 1))) ) ) ) ) ) ) ).
tt(t20_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  &  ( (~  (B = 1) )  & (r1_nat_d (k1_newton B 2) A)) ) )  => (v1_moebius1 A)) ) ) ).
tt(t20_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v22_algstr_0 B) &  ((v4_vectsp_1 B) & (m1_monoid_0 B A)) )  =>  (! [C:$i] :  ( ((v22_algstr_0 C) &  ((v4_vectsp_1 C) & (m1_monoid_0 C A)) )  =>  (B = C) ) ) ) ) ) ) ).
tt(t20_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_monoid_1 B A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_monoid_1 B A))) =>  ( (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t20_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k3_tarski (a_3_7_morph_01 A B C)) (k1_morph_01 A (k5_setfam_1 (u1_struct_0 A) B) C))) ) ) ) ) ) ).
tt(t20_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B))) =>  ((v3_msualg_2 C A (k11_msafree A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_msaterm E A B (k2_msaterm A B D)) =>  ((r1_tarski (k2_relset_1 (k5_trees_3 (u1_struct_0 (k5_msafree A B))) E) (k3_card_3 C)) => (r2_hidden (k6_msaterm A B (k2_msaterm A B D) E) (k1_funct_1 C (k2_msualg_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_msaterm D A B (k2_msaterm A B C)) =>  ((k7_msaterm A B (k6_msaterm A B (k2_msaterm A B C) D)) = (k2_msualg_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t20_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( (~ (v1_zfmisc_1 C))  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~  ((k1_funct_1 C k1_xboole_0) = (k4_tarski D (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) & (v2_finset_1 (k6_pboole A B C)))  => (v2_finset_1 C)) ) ) ) ) ) ).
tt(t20_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  => (m1_unialg_2 (k12_msualg_1 A C) (k12_msualg_1 A B))) ) ) ) ) ) ).
tt(t20_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((v3_msualg_2 (k9_msualg_2 A B C) A B) & (r2_pboole (u1_struct_0 A) C (k9_msualg_2 A B C))) ) ) ) ) ) ) ).
tt(t20_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D))) =>  ( ((r8_pboole (u1_struct_0 A) D E) & (r1_msualg_3 A B C D))  => (r2_msualg_3 A B (k6_msualg_3 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_msualg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k6_lattices (k6_msualg_5 A B)) = (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ).
tt(t20_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) D E) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r1_msualg_6 A C D B F) =>  (! [G:$i] :  ((m2_msualg_6 G A B D E) => (m2_msualg_6 (k3_relat_1 F G) A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_msualg_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 A B) => (v4_lattice3 (k1_msualg_7 A B))) ) ) ) ) ).
tt(t20_msualg_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v2_msualg_7 (k6_msualg_5 A B) (k5_msualg_5 (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ) ).
tt(t20_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A C (k6_pboole A (k7_funcop_1 A (k1_tarski B)) (k7_funcop_1 A (k1_tarski B)))) => (r6_pboole A (k1_msualg_9 A C (k7_funcop_1 A (k1_tarski B)) (k7_funcop_1 A (k1_tarski B)) D) (k2_msualg_9 A C (k7_funcop_1 A (k1_tarski B)) (k7_funcop_1 A (k1_tarski B)) D))) ) ) ) ) ) ).
tt(t20_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r4_alg_1 A B C) => (r4_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C))) ) ) ) ) ) ) ).
tt(t20_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_dilworth B (k3_necklace A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_necklace A)))))  =>  ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t20_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) =>  ( (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  (~ (v6_nagata_1 B A)) ) )  | (v10_pre_topc A)) ) ) ) ).
tt(t20_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_pcomps_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  (~  ((v1_tops_2 (k2_nagata_1 A C) A) &  ((m1_setfam_1 (k2_nagata_1 A C) (u1_struct_0 A)) &  ((r1_setfam_1 (k2_nagata_1 A C) B) & (v2_nagata_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  => (m2_subset_1 (k6_xcmplx_0 B 1) k1_numbers k5_numbers)) ) ) ) ) ).
tt(t20_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 (k2_xcmplx_0 A A) B) |  ((k3_nat_d B A) = 1) ) ) ) ) ) ) ).
tt(t20_nat_3,ax, (! [A:$i] :  ((k8_nat_3 A (k16_pre_poly A)) = 1) ) ).
tt(t20_nat_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_int_2 C) => (r1_xxreal_0 (k11_nat_3 A C) (k11_nat_3 B C))) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  (B = (k3_nat_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k4_nat_d (k24_binop_2 A C) B) = (k4_nat_d (k24_binop_2 A D) B))  & (v1_int_2 B))  =>  ( (k6_numbers = A)  |  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 B C) |  ((r1_xxreal_0 B D) |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_nat_d (k3_xcmplx_0 B A) A) = B) ) ) ) ) ) ).
tt(t20_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k4_nattra_1 B A C C (k3_nattra_1 B A C) D) = (k4_cat_1 A (k8_cat_1 B A C D))) ) ) ) ) ) ) ) ) ).
tt(t20_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) =>  ( (! [E:$i] :  ((m1_ncfcont1 E A D) =>  (~  ((k9_subset_1 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) C) E) = (k1_tarski D)) ) ) )  | (r1_ncfcont1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r2_ncfcont2 A B C D) => (r8_ncfcont1 C B D A)) ) ) ) ) ) ) ) ).
tt(t20_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A B E) = (k1_rlvect_1 A C (k10_real_1 1 (k7_real_1 E D)))) ) )  =>  ((r1_xxreal_0 D k6_numbers) |  ((k6_normsp_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) & (v3_funct_1 (k2_partfun1 k1_numbers (u1_struct_0 A) C B)))  =>  ((r2_ndiff_3 A C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_funct_1 (k2_ndiff_3 A C B) D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ((r2_ndiff_4 B C A) => (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid B) C A) B)) ) ) ) ) ) ).
tt(t20_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k16_lopban_1 A B))) =>  ( ((r1_tarski (k1_rltopsp1 A D E) (k1_relset_1 (u1_struct_0 A) C)) &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden H (k1_rltopsp1 A D E)) => (r1_nfcont_1 A B C H)) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden H (k2_ndiff_5 A D E)) => (r1_ndiff_1 A B C H)) ) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden H (k2_ndiff_5 A D E)) => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 A B) (k5_algstr_0 (k16_lopban_1 A B) (k3_ndiff_1 A B C H) G)) F)) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 (u1_struct_0 B) C D)) (k17_lopban_1 A B G (k5_algstr_0 A E D)))) (k11_binop_2 F (k1_normsp_0 A (k5_algstr_0 A E D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_necklace A))) =>  ( (B = C)  =>  ((k3_necklace (k5_yellow_0 A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k6_domain_1 (u1_struct_0 A) B)))) = (k5_yellow_0 (k3_necklace A) (k7_subset_1 (u1_struct_0 (k3_necklace A)) (k2_struct_0 (k3_necklace A)) (k6_domain_1 (u1_struct_0 (k3_necklace A)) C)))) ) ) ) ) ) ) ) ).
tt(t20_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k4_necklace A)) = A) ) ) ).
tt(t20_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  => (r1_tarski (k6_net_1 A B) (k2_net_1 A))) ) ) ) ) ).
tt(t20_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 B A) &  (C = (k6_xcmplx_0 A B)) )  =>  ((k5_newton B A) = (k5_newton C A)) ) ) ) ) ) ) ) ).
tt(t20_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r4_nfcont_1 B C A) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_hidden G A) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B G D))))  & (r1_xxreal_0 E (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C G) (k7_partfun1 k1_numbers C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((r1_tarski C (k1_relset_1 k1_numbers E)) &  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) D B) A) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) E C) A)) ) )  =>  ((v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) (k6_vfunct_1 k1_numbers A D E) (k3_xboole_0 B C)) A) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) (k2_vfunct_1 k1_numbers A D E) (k3_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t20_nfcont_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers (u1_struct_0 B) (u1_struct_0 B) k1_numbers C D))) &  ((r1_nfcont_3 B C A) & (r2_nfcont_1 B D (k7_partfun1 (u1_struct_0 B) C A))) )  => (r1_fcont_1 (k1_partfun1 k1_numbers (u1_struct_0 B) (u1_struct_0 B) k1_numbers C D) A)) ) ) ) ) ) ) ) ) ).
tt(t20_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) => (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) (k4_binop_1 (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k5_normform A)) B)) ) ) ).
tt(t20_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) & (v3_normsp_1 C A))  => (v3_normsp_1 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t20_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (B = C)  =>  ((v3_pre_topc B (k3_normsp_2 A)) <=> (v3_pre_topc C (k4_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t20_numbers,ax,(r1_tarski k5_numbers k2_numbers)).
tt(t20_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r3_lattices A B C))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r2_hidden D (k7_openlatt A)) &  ( (~ (r2_hidden C D))  & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_oppcat_1 A B B (k4_cat_1 A B)) = (k4_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A B))) ) ) ) ) ).
tt(t20_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_orders_1 A) =>  ((v1_orders_1 A) & (v2_orders_1 A)) ) ) ) ).
tt(t20_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B C) & (r2_hidden B (k2_orders_2 A C))) ) ) ) ) ) ) ) ).
tt(t20_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r1_tarski A B) &  ( (~  (A = k1_xboole_0) )  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) => (r1_ordinal1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C B) => (r2_hidden C A)) ) )  => (r1_ordinal1 (k3_ordinal2 B) A)) ) ) ) ).
tt(t20_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ((r1_ordinal1 A B) & (r1_ordinal1 C D))  => (r1_ordinal1 (k11_ordinal2 A C) (k11_ordinal2 B D))) ) ) ) ) ) ) ) ) ).
tt(t20_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (~  (A = k1_xboole_0) )  =>  ((k12_ordinal2 k1_xboole_0 A) = k1_xboole_0) ) ) ) ).
tt(t20_ordinal5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k1_ordinal5 k6_numbers (k4_nat_1 2 A)) = 1)  &  ((k1_ordinal5 k6_numbers (k2_nat_1 (k4_nat_1 2 A) 1)) = k6_numbers) ) ) ) ).
tt(t20_ordinal6,ax, (! [A:$i] :  ((k1_card_1 (k9_xtuple_0 (k2_ordinal6 A))) = (k1_card_1 (k2_ordinal1 A))) ) ).
tt(t20_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t20_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((r1_orders_2 B E D) <=>  ((k1_ortsp_1 A B D C E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (? [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) & (r2_hidden (k4_tarski E D) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C))) )  => (r2_hidden (k4_tarski C D) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C))) ) ) ) ) ) ) ) ) ).
tt(t20_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (l3_msualg_1 D A))  =>  ((r2_osalg_1 A B C) => (r1_tarski (k1_funct_1 (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A D)) B) (k1_funct_1 (k6_finseq_2 (u1_struct_0 A) (u3_msualg_1 A D)) C))) ) ) ) ) ) ) ) ) ).
tt(t20_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((r2_hidden C (k6_osalg_2 A B)) <=> (v3_msualg_2 C A B)) ) ) ) ) ) ) ).
tt(t20_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v2_msualg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) A B) &  ((v3_msualg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) A B) & (m1_osalg_4 (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) A B)) ) ) ) ) ) ).
tt(t20_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_parsp_1 A B B C D)) ) ) ) ) ) ) ) ).
tt(t20_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C F) &  ((r1_parsp_2 A B C G) &  ((r1_parsp_2 A D E F) & (r1_parsp_2 A D E G)) ) )  =>  ((r1_parsp_1 A B C D E) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B)))))  =>  ((r2_hidden C (k1_relset_1 A D)) =>  ((k1_funct_1 D C) = B) ) ) ) ) ) ) ).
tt(t20_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden D (k1_relset_1 B (k3_partfun2 B C A E))) <=>  ((r2_hidden D (k1_relset_1 B E)) & (r2_hidden (k7_partfun1 C E D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r1_setfam_1 B C) <=> (r1_tarski (k4_partit1 A B) (k4_partit1 A C))) ) ) ) ) ) ) ).
tt(t20_partit_2,ax, (! [A:$i] :  (! [B:$i] :  ((k1_relat_1 (k1_partit_2 A B)) = k1_xboole_0) ) ) ).
tt(t20_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((r1_diraf A B C D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B E F) & (r2_analoaf A C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D E))  => (r2_pboole A (k2_pboole A B D) (k2_pboole A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_pcomps_1 B A) =>  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B))) ) ) ) ) ) ).
tt(t20_pcs_0,ax, (! [A:$i] :  ( ((v14_pcs_0 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( ((v14_pcs_0 B) & (l2_pcs_0 B))  =>  ((r1_tsep_1 A B) =>  ((v14_pcs_0 (k18_pcs_0 A B)) & (l2_pcs_0 (k18_pcs_0 A B))) ) ) ) ) ) ).
tt(t20_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( ( (C = D)  &  (E = F) )  =>  ((r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C E) <=> (r1_pdiff_1 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_2,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r3_pdiff_1 2 2 B A) & (r3_pdiff_1 2 2 C A))  => (r3_pdiff_1 2 2 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t20_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 2) B)) =>  ( ((r4_pdiff_3 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 2) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B))))) &  ((k5_pdiff_3 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( (D = (k11_finseq_1 A B C))  =>  ((k11_pdiff_1 3 2 E D) = (k1_fdiff_1 (k1_pdiff_2 3 2 E D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r2_pdiff_5 B A) <=> (r3_pdiff_1 3 2 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ).
tt(t20_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  ( ((r1_pdiff_1 B A C E) & (r1_pdiff_1 B A D E))  =>  ((r1_pdiff_1 B A (k7_integr15 A (k1_euclid B) C D) E) & (r2_relset_1 (k1_euclid B) (k1_euclid A) (k8_pdiff_1 B A (k7_integr15 A (k1_euclid B) C D) E) (k7_integr15 A (k1_euclid B) (k8_pdiff_1 B A C E) (k8_pdiff_1 B A D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  (C = (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 D A) E)) ) )  =>  ( ((k5_algstr_0 (k4_real_ns1 A) (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D E) B) E) = (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) (k5_algstr_0 (k4_real_ns1 1) B C)))  &  ((k5_algstr_0 (k4_real_ns1 A) E (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D E) B)) = (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 A D (k4_struct_0 (k4_real_ns1 A))) (k5_algstr_0 (k4_real_ns1 1) C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) & (v3_nfcont_1 D (k4_real_ns1 A))) )  =>  ( ((r7_pdiff_1 A B E C D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k15_pdiff_1 A B E C D) D))  <=>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B))  =>  ((r7_pdiff_1 A 1 E (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 F B)) D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 1)) (k15_pdiff_1 A 1 E (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 F B)) D) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  ((k1_normsp_0 (k4_real_ns1 A) (k17_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A) B C)) = (k11_binop_2 (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)) B) (k1_normsp_0 (k4_real_ns1 1) C))) ) ) ) ) ) ) ).
tt(t20_pencil_1,ax, (! [A:$i] :  ( ((v6_pencil_1 A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_pre_topc A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = B)  => (v1_pencil_1 C A)) ) ) ) ) ) ) ).
tt(t20_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_pencil_2 A C D) =>  ((v1_zfmisc_1 C) |  ((v1_zfmisc_1 D) | (r1_pencil_2 A (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  ((r1_pencil_3 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 E (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [F:$i] :  ((m1_pencil_2 F A B) =>  (! [G:$i] :  ((m1_pencil_2 G A B) =>  ( ( (F = (k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) E C))  &  (G = (k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) E D)) )  => (r1_pencil_3 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k1_vectsp_9 A B) C) | (v6_pencil_1 (k5_pencil_4 A B C))) ) ) ) ) ) ) ) ).
tt(t20_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (v1_abian A))  & (v1_abian (k1_newton A B))) ) ) ) ) ) ).
tt(t20_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k6_petri A C)) <=>  (~ (r1_xboole_0 (k9_petri A (k6_domain_1 (u4_struct_0 A) B)) C)) ) ) ) ) ) ) ) ).
tt(t20_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A B C) => (r1_pnproc_1 A (k3_pnproc_1 A (k2_pnproc_1 A C D) B) (k2_pnproc_1 A (k3_pnproc_1 A C B) D))) ) ) ) ) ) ) ) ).
tt(t20_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r1_tarski E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_polyalg1 F A B) &  ( (E = (u1_struct_0 F))  & (r1_tarski C E)) ) ) ) ) )  => (v3_polyalg1 (k6_setfam_1 (u1_struct_0 B) D) A B)) ) ) ) ) ) ) ) ) ).
tt(t20_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  &  ( ((k7_polyeq_1 k6_numbers A B C D) = k6_numbers)  &  ( (~  (D = (k6_real_1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) )  &  (~  (D = (k6_real_1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( ((k1_polyeq_3 A) = B)  &  ( ((k4_complex1 B) = k6_numbers)  &  ( (~ (r1_xxreal_0 (k3_complex1 B) k6_numbers))  &  ( (~  (A = (k7_square_1 (k3_complex1 B))) )  &  (~  (A = (k7_binop_2 (k7_square_1 (k3_complex1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ( ((k3_xcmplx_0 A (k2_newton B F)) = C)  &  ((k3_xcmplx_0 B D) = E) )  =>  ((v1_abian F) |  ( ((k3_xcmplx_0 C A) = k6_numbers)  |  ( (B = (k1_power F (k7_xcmplx_0 C A)))  &  (D = (k3_xcmplx_0 E (k1_power F (k7_xcmplx_0 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (~  (E = k6_numbers) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 E (k1_newton A 3)) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k2_polyeq_5 (k13_complex1 D E) (k13_complex1 C E) (k13_complex1 B E))) )  &  ( (~  (A = (k3_polyeq_5 (k13_complex1 D E) (k13_complex1 C E) (k13_complex1 B E))) )  &  (~  (A = (k4_polyeq_5 (k13_complex1 D E) (k13_complex1 C E) (k13_complex1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_polyform,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  ((k16_rvsum_1 (k6_polyform (k3_polyform A) B)) = (k2_xcmplx_0 A (k16_rvsum_1 B))) ) ) ) ) ).
tt(t20_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k4_polynom1 A B C D)) (k4_subset_1 (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) B C) (k2_polynom1 (k15_pre_poly A) B D)))) ) ) ) ) ) ) ).
tt(t20_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k7_polynom1 A B) C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t20_polynom3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  =>  ((k18_rvsum_1 (k17_finseq_1 k1_numbers (k2_nat_1 B 1) A)) = (k2_xcmplx_0 (k18_rvsum_1 (k17_finseq_1 k1_numbers B A)) (k1_funct_1 A (k2_nat_1 B 1)))) ) ) ) ) ) ).
tt(t20_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_polynom4 A (k5_vfunct_1 k5_numbers A B) C) = (k4_algstr_0 A (k2_polynom4 A B C))) ) ) ) ) ) ) ).
tt(t20_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A (k9_polynom3 A) (k2_nat_1 B 1)) (k9_polynom3 A))) ) ) ) ).
tt(t20_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l5_algstr_0 B)) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom7 A B (k5_struct_0 B)) (k8_polynom1 A B))) ) ) ).
tt(t20_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k3_polynom8 A C (k6_xcmplx_0 B 1)) = (k8_group_1 A (k3_polynom8 A C B) (k3_polynom8 A C (k4_xcmplx_0 1)))) ) ) ) ) ) ) ) ).
tt(t20_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v9_struct_0 D B))  & (m1_subset_1 D (u1_struct_0 B)))  => (r1_tarski (k2_polynom1 (k15_pre_poly A) B C) (k2_polynom1 (k15_pre_poly A) B (k5_polynom7 A B C D)))) ) ) ) ) ) ) ) ).
tt(t20_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 A (k1_power B A)) &  (~ (r1_xxreal_0 1 (k1_power B A))) ) ) ) ) ) ) ) ).
tt(t20_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  ( (~  ((k1_msualg_1 B E) = k1_xboole_0) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 B E (k14_pralg_2 A B C))) => (m1_subset_1 (k1_funct_1 (k10_funct_6 G) D) (k3_msualg_1 B E (k5_pralg_2 A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pre_circ,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k6_xcmplx_0 (k5_card_1 A) 1) = (k1_xreal_0 (k5_card_1 A) 1)) ) ) ).
tt(t20_pre_ff,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k3_pre_ff D) = (k2_nat_1 (k3_nat_1 B (k3_pre_ff (k4_nat_1 2 A))) (k3_nat_1 C (k3_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1)))))  =>  ((k3_pre_ff D) = (k2_nat_1 (k3_nat_1 (k2_xcmplx_0 B C) (k3_pre_ff A)) (k3_nat_1 C (k3_pre_ff (k1_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t20_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k2_prelamb A B B)) & (r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k1_prelamb A B B))) ) ) ) ) ).
tt(t20_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden D B) &  ((r3_orders_1 C B) &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E B) => (r2_hidden (k1_domain_1 A A D E) C)) ) ) ) )  =>  ((k7_partfun1 A (k7_pre_poly A B C) 1) = D) ) ) ) ) ) ) ) ) ) ).
tt(t20_prepower,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k3_prepower A 1) = 1) ) ) ) ).
tt(t20_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k2_pre_topc A C))) ) ) ) ) ) ) ).
tt(t20_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) => (m1_prob_1 (k3_subset_1 A C) A B)) ) ) ) ) ).
tt(t20_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ((r2_prob_2 A B F C D E) <=>  ( ((k1_seq_1 F (k5_prob_1 A B (k5_prob_1 A B C D) E)) = (k8_real_1 (k8_real_1 (k1_seq_1 F C) (k1_seq_1 F D)) (k1_seq_1 F E)))  &  ((r1_prob_2 A B F C D) &  ((r1_prob_2 A B F D E) & (r1_prob_2 A B F C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_kurato_0 A (k3_prob_3 A B)) = (k1_kurato_0 A B)) ) ) ) ).
tt(t20_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 C) =>  ( ((k1_prob_4 A B (k3_prob_3 A C) k6_numbers) = (k1_prob_4 A B C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_prob_4 A B (k3_prob_3 A C) (k2_nat_1 D 1)) = (k3_measure1 A B (k1_prob_4 A B C (k2_nat_1 D 1)) (k1_prob_4 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t20_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) (k9_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t20_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (~  ((r1_projdes1 A B C D E) &  ( (~ (r1_projdes1 A B C D F))  &  ( (~ (r1_projdes1 A B C F E))  &  ((r1_collsp A E F G) &  ((r1_collsp A E B H) &  ((r1_collsp A E C I) &  ((r1_collsp A B F J) &  ((r1_collsp A H G J) &  ((r1_collsp A C F K) &  ((r1_collsp A I G K) &  ((r1_collsp A D F L) &  ( (~  (E = H) )  &  ( (~  (F = G) )  &  ( (~  (E = I) )  & (r1_collsp A J K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  ( ((r5_projpl_1 A B C D E) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) F) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B D) G) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B E) H)) ) )  => (r1_zfmisc_1 F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A C E) &  (D = (k1_funct_1 (k1_projred1 A E F B) C)) )  =>  ((r1_incsp_1 A B E) |  ((r1_incsp_1 A B F) | (r1_incsp_1 A D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_projred2 A D E F))  &  ((r1_projred2 A D F G) &  ( (~ (r1_incsp_1 A C G))  &  ( (~  (D = G) )  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A I H) &  ( (~ (r1_incsp_1 A I D))  &  ( (~ (r1_incsp_1 A I G))  &  ((k3_relat_1 (k1_projred1 A D F B) (k1_projred1 A F E C)) = (k3_relat_1 (k1_projred1 A D G I) (k1_projred1 A G E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_prvect_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_prvect_1 B A) =>  (! [C:$i] :  ((m2_prvect_1 C A) =>  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 A)) =>  ((r1_finseqop (k1_funct_1 A D) (k10_prvect_1 A C D) (k9_prvect_1 A B D)) & (v1_setwiseo (k9_prvect_1 A B D) (k1_funct_1 A D))) ) )  => (r1_finseqop (k4_card_3 A) (k11_prvect_1 A C) (k13_prvect_1 A B))) ) ) ) ) ) ) ).
tt(t20_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_prvect_2 B)) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B)))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 B))) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( (D = F)  &  ( (E = G)  &  ((k1_funct_1 C (k10_finseq_1 D E)) = (k7_finseq_1 F G)) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))))) =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k3_rlvect_1 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))) D E)) = (k3_rlvect_1 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D) (k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k1_rlvect_1 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))) D E)) = (k1_rlvect_1 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D) E)) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C (k4_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))))) = (k4_struct_0 (k14_prvect_2 (k7_finseq_1 A B))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))))) =>  ((k1_normsp_0 (k14_prvect_2 (k7_finseq_1 A B)) (k3_funct_2 (u1_struct_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B)))) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A B))) C D)) = (k1_normsp_0 (k14_prvect_2 (k10_finseq_1 (k14_prvect_2 A) (k14_prvect_2 B))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_pscomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k8_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_rcomp_1 A B)) = (a_2_2_pscomp_1 A B)) ) ) ) ) ).
tt(t20_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k7_pua2mss1 A B) B)) ) ) ) ).
tt(t20_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r6_pboole A (k3_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pzfmisc1 A B)) | (r6_pboole A (k3_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pzfmisc1 A C)))  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t20_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ( (~ (v2_qc_lang1 (k12_qc_lang1 A) A))  &  ( (~ (v3_qc_lang1 (k12_qc_lang1 A) A))  &  ( (~ (v4_qc_lang1 (k12_qc_lang1 A) A))  &  ( (~ (v5_qc_lang1 (k12_qc_lang1 A) A))  &  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ( (~  ((v2_qc_lang1 B A) & (v3_qc_lang1 B A)) )  &  ( (~  ((v2_qc_lang1 B A) & (v4_qc_lang1 B A)) )  &  ( (~  ((v2_qc_lang1 B A) & (v5_qc_lang1 B A)) )  &  ( (~  ((v3_qc_lang1 B A) & (v4_qc_lang1 B A)) )  &  ( (~  ((v3_qc_lang1 B A) & (v5_qc_lang1 B A)) )  &  (~  ((v4_qc_lang1 B A) & (v5_qc_lang1 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k8_qc_lang2 A B C D E) = (k15_qc_lang1 A B (k6_qc_lang2 A C D E)))  &  ((k9_qc_lang2 A B C D E) = (k5_qc_lang2 A B (k7_qc_lang2 A C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((v6_qc_lang1 (k12_qc_lang1 A) A) & (v6_qc_lang1 (k1_qc_lang2 A) A)) ) ) ).
tt(t20_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A B C) <=>  (~  ((k3_qc_lang4 A C B) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t20_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v17_quantal1 B A) =>  ( ((k1_quantal1 A C D) = (k1_quantal1 A (k6_algstr_0 A C (k2_quantal1 A D B)) B))  &  ((k2_quantal1 A C D) = (k2_quantal1 A (k6_algstr_0 A (k1_quantal1 A D B) C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k27_quaterni (k28_quaterni A) B) = (k28_quaterni (k27_quaterni A B))) ) ) ) ) ).
tt(t20_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k29_quaterni (k27_quaterni k11_quaterni A) (k27_quaterni A k11_quaterni)) = (k6_quaterni k6_numbers (k8_real_1 2 (k20_quaterni A)) k6_numbers (k1_real_1 (k8_real_1 2 (k18_quaterni A))))) ) ) ).
tt(t20_quaterni,ax, ((k10_quaterni k11_quaterni k12_quaterni) = (k8_quaterni (k10_quaterni k12_quaterni k11_quaterni))) ).
tt(t20_quin_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k1_quin_1 A B C) = k6_numbers)  &  ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) = k6_numbers) )  =>  ( (A = k6_numbers)  |  (D = (k4_xcmplx_0 (k7_xcmplx_0 B (k3_xcmplx_0 2 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k15_quofield A) (k5_binop_1 (k7_quofield A) (k15_quofield A) B C) D) = (k5_binop_1 (k7_quofield A) (k15_quofield A) B (k5_binop_1 (k7_quofield A) (k15_quofield A) C D))) ) ) ) ) ) ) ) ) ).
tt(t20_radix_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 2 C) &  ((r2_hidden A (k3_radix_1 C)) & (r2_hidden B (k3_radix_1 C))) )  =>  ((r1_xxreal_0 (k2_xcmplx_0 (k4_xcmplx_0 (k1_radix_1 C)) 2) (k12_radix_1 (k2_xcmplx_0 A B) C)) & (r1_xxreal_0 (k12_radix_1 (k2_xcmplx_0 A B) C) (k6_xcmplx_0 (k1_radix_1 C) 2))) ) ) ) ) ) ) ) ).
tt(t20_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r1_xxreal_0 2 B))  =>  ((k7_radix_3 D B (k2_xcmplx_0 (k2_xcmplx_0 A 1) 1) (k10_radix_3 (k2_xcmplx_0 A 1) B (k10_radix_1 B (k2_xcmplx_0 A 1) C))) = (k7_radix_3 D B (k2_xcmplx_0 A 1) (k10_radix_3 A B (k10_radix_1 B A (k4_nat_d C (k1_newton (k1_radix_1 B) A)))))) ) ) ) ) ) ) ) ) ) ).
tt(t20_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D (k2_xcmplx_0 A 2)) & (m2_finseq_1 D (k3_radix_1 C)))  =>  (~  ((r1_xxreal_0 2 C) &  ((r2_hidden B (k2_finseq_1 (k2_xcmplx_0 A 2))) &  ((r2_radix_6 B A C (k8_radix_6 A C D)) &  ( (~ (r1_xxreal_0 (k4_radix_1 B C (k2_xcmplx_0 A 2) (k8_radix_6 A C D)) k6_numbers))  & (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) C (k8_radix_6 A C D)) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (m1_random_1 (k26_valued_1 A k1_numbers C D) A B)) ) ) ) ) ) ) ) ).
tt(t20_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) => (m1_vectsp_7 C A (k1_vectsp_7 A B C))) ) ) ) ) ) ) ).
tt(t20_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ( ( (~  ((k2_rat_1 A) = A) )  &  (~  ((k1_rat_1 A) = 1) ) )  | (m2_subset_1 A k1_numbers k5_numbers)) ) ) ) ).
tt(t20_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ( ( (~ (v9_struct_0 C A))  & (m1_subset_1 C (u1_struct_0 A)))  =>  ((v5_ratfunc1 (k3_ratfunc1 A (k3_polynom5 A (k4_ratfunc1 A B) C) (k3_polynom5 A (k5_ratfunc1 A B) C)) A) <=> (v5_ratfunc1 B A)) ) ) ) ) ) ) ).
tt(t20_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r2_hidden B A) &  (! [C:$i] :  ((m1_rcomp_1 C B) =>  (~ (r1_tarski C A)) ) ) ) ) ) )  => (v3_rcomp_1 A)) ) ) ).
tt(t20_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_xxreal_2 A) => (r1_tarski A (k1_limfunc1 (k4_seq_4 A)))) ) ) ).
tt(t20_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  =>  ((k13_complex1 B A) = (k3_real_1 (k3_funct_2 k5_numbers k5_numbers (k2_real_3 B A) k6_numbers) (k10_real_1 1 (k13_complex1 A (k3_funct_2 k5_numbers k5_numbers (k1_real_3 B A) k6_numbers))))) ) ) ) ) ) ).
tt(t20_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_real_lat A) B (k1_funcsdom A k1_numbers (k4_real_lat A) C D)) (k1_funcsdom A k1_numbers (k4_real_lat A) (k1_funcsdom A k1_numbers (k5_real_lat A) B C) (k1_funcsdom A k1_numbers (k5_real_lat A) B D)))) ) ) ) ) ) ) ) ).
tt(t20_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ).
tt(t20_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) B B) = (k5_struct_0 A)) ) ) ) ) ).
tt(t20_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ( ((k20_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A) C) = (k20_rfunct_3 B (k15_valued_1 B k1_numbers D A) B))  &  ((k21_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A) C) = (k21_rfunct_3 B (k15_valued_1 B k1_numbers D A) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ((k10_xtuple_0 A) = (k9_xtuple_0 (k2_relat_1 A)))  &  ((k9_xtuple_0 A) = (k10_xtuple_0 (k2_relat_1 A))) ) ) ) ).
tt(t20_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A))) => (m1_subset_1 (k6_relset_1 C A B D) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) ) ) ) ) ).
tt(t20_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_tarski (k10_xtuple_0 (k3_relset_2 A C)) (k9_setfam_1 (k2_relset_1 B C)))) ) ) ) ).
tt(t20_revrot_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 B)) => (r1_tarski (k10_xtuple_0 (k1_goboard1 A)) (k10_xtuple_0 (k1_goboard1 B)))) ) ) ) ) ).
tt(t20_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) <=>  ( (B = C)  | (r2_hidden (k4_tarski B C) (k18_finseq_1 A))) ) ) ) ) ) ).
tt(t20_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (~ (r2_rewrite2 A (k1_partit_2 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C)) ) ) ) ) ) ).
tt(t20_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  ((r2_rewrite3 E F G A B C D) =>  ((r1_struct_0 G A) &  ((r1_struct_0 G C) &  ((r2_hidden B (k8_afinsq_1 E)) &  ((r2_hidden D (k8_afinsq_1 E)) &  ((r2_hidden A (k9_xtuple_0 (k9_xtuple_0 (u1_rewrite3 F G)))) & (r2_hidden C (k10_xtuple_0 (u1_rewrite3 F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rfinseq2,ax, (! [A:$i] :  ( ((v8_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  ((k5_rfinseq2 A) = A) ) ) ).
tt(t20_rfinseq,ax, (! [A:$i] :  ( ((v8_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((v8_valued_0 (k17_finseq_1 k1_numbers B A)) & (m2_finseq_1 (k17_finseq_1 k1_numbers B A) k1_numbers)) ) ) ) ) ).
tt(t20_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k45_valued_1 A (k1_valued_1 B C)) = (k45_valued_1 (k45_valued_1 A B) C)) ) ) ) ) ) ) ).
tt(t20_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ((r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k8_finseq_1 (k3_rfunct_3 A k1_numbers) B (k12_finseq_1 (k3_rfunct_3 A k1_numbers) C))) (k5_rfunct_3 A k1_numbers (k14_rfunct_3 A B) C))) ) ) ) ) ) ).
tt(t20_rfunct_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ( ((r5_rfunct_4 B A) & (r7_rfunct_4 B A))  <=> (r1_fcont_1 B A)) ) ) ) ) ) ).
tt(t20_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) &  ((v4_partfun3 A) &  ((v2_seq_2 B) & (v4_partfun3 B)) ) )  =>  ((v2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) & (r1_xxreal_0 (k8_real_1 (k2_rinfsup1 A) (k2_rinfsup1 B)) (k2_rinfsup1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) ).
tt(t20_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_mesfunc5 B) =>  ((v7_mesfunc5 (k1_valued_0 k7_numbers B A)) &  ((v10_mesfunc5 (k1_valued_0 k7_numbers B A)) &  ((k2_mesfunc5 B) = (k2_mesfunc5 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ) ).
tt(t20_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v33_algstr_0 (k2_ring_1 A B)) => (v3_ring_1 B A)) ) ) ) ) ).
tt(t20_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_ringcat1 A))  =>  (! [B:$i] :  ((m3_ringcat1 B (k10_ringcat1 A)) =>  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 A)) =>  ( ((k11_ringcat1 A B) = (k12_ringcat1 A C))  => (r2_hidden (k6_ringcat1 B C) (k10_ringcat1 A))) ) ) ) ) ) ) ).
tt(t20_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_rlvect_2 A (k1_rlaffin1 A (k4_rlvect_2 A) B) (k4_rlvect_2 A))) ) ) ) ).
tt(t20_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (~ (v1_xboole_0 B))  => (r2_hidden (k1_funct_1 (k2_rlaffin2 A) B) (k1_rlaffin2 A B))) ) ) ) ) ).
tt(t20_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ((m2_rlaffin3 D B C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski E C) & (r2_hidden A (k4_rlaffin1 B C)))  =>  ((r2_hidden A (k4_rlaffin1 B E)) <=>  (! [F:$i] :  ((r2_hidden F (k4_finseq_1 (k1_rlaffin3 B C D A))) =>  ((r2_hidden (k1_funct_1 D F) E) |  ((k1_funct_1 (k1_rlaffin3 B C D A) F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t20_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( ((k2_rlsub_2 A (k2_rlsub_1 A) B) = B)  &  ((k2_rlsub_2 A B (k2_rlsub_1 A)) = B) ) ) ) ) ) ).
tt(t20_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_convex1 A B) (k3_convex1 A C))) ) ) ) ) ) ) ).
tt(t20_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t20_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k4_rlvect_2 A) B) = k6_numbers) ) ) ) ) ).
tt(t20_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (m1_rlsub_1 (k1_rlvect_3 A B) (k1_rlvect_3 A C))) ) ) ) ) ) ) ).
tt(t20_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) =>  ( (B = C)  | (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B (k4_algstr_0 A C)) A)) ) ) ) ) ) ) ) ).
tt(t20_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_rlvect_3 A C) = (k1_rlvect_3 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden B (k2_rlvect_x A (k7_domain_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t20_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( ((r1_struct_0 E C) & (r1_struct_0 E D))  => (r1_struct_0 E (k3_rlvect_1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( ((m1_rmod_2 C A D) & (m1_rmod_2 C A E))  => (m1_rmod_2 C A (k2_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (m2_rmod_4 (k3_rmod_4 A B) A B C)) ) ) ) ) ) ).
tt(t20_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A B (k6_robbins1 A B C)) = B) ) ) ) ) ) ) ).
tt(t20_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A B (k3_robbins1 A (k1_lattices A C (k3_robbins1 A B))))) = (k3_robbins1 A B)) ) ) ) ) ) ) ).
tt(t20_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_robbins1 B))  =>  ( ( ((g4_robbins1 (u1_struct_0 A) (u2_lattices A) (u1_lattices A) (u1_robbins1 A)) = (g4_robbins1 (u1_struct_0 B) (u2_lattices B) (u1_lattices B) (u1_robbins1 B)))  & (v10_robbins1 A))  => (v10_robbins1 B)) ) ) ) ) ).
tt(t20_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( ( (A = (k6_subset_1 3 2))  &  (B = 1) )  =>  ((k3_lattices k2_robbins4 A B) = 3) ) ) ) ) ) ).
tt(t20_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k3_roughs_1 A (k2_struct_0 A)) = (k2_struct_0 A)) ) ) ).
tt(t20_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A (k4_subset_1 A B C)) = (k9_real_1 (k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C)) (k1_rpr_1 A (k9_subset_1 A B C)))) ) ) ) ) ) ) ).
tt(t20_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_rsspace4 A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) &  ((v1_rsspace4 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_rsspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (E = C)  &  (F = D) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (D = (k1_rlvect_1 (k9_rsspace4 A B) C G))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A (u1_struct_0 B) F H) = (k1_rlvect_1 B (k3_funct_2 A (u1_struct_0 B) E H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_bhsp_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) ) )  =>  ( ((m1_rusub_1 A B) & (m1_rusub_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t20_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( ((k2_rusub_2 A (k2_rusub_1 A) B) = B)  &  ((k2_rusub_2 A B (k2_rusub_1 A)) = B) ) ) ) ) ) ).
tt(t20_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (~  ((r1_tarski (k3_rlvect_2 A C) (u1_struct_0 B)) &  (! [D:$i] :  ((m1_rlvect_2 D B) =>  (~  ( ((k3_rlvect_2 B D) = (k3_rlvect_2 A C))  &  ((k6_rlvect_2 B D) = (k6_rlvect_2 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B (k1_rusub_4 A)))  =>  ((k2_rusub_4 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t20_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  &  ( (C = (k1_rusub_5 A B B))  &  ((v3_rusub_4 C A) & (r1_rusub_5 A B C)) ) ) ) ) ) ) ) ).
tt(t20_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_rvsum_1 (k9_finseq_1 A)) = (k12_finseq_1 k1_numbers (k7_binop_2 A))) ) ) ).
tt(t20_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  (B = (k4_rvsum_2 A (k8_rvsum_2 A B C) C)) ) ) ) ) ) ) ).
tt(t20_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k7_ami_3 1)) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmbsort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k2_scmfsa8c A B)) = (k4_sf_mastr B)) ) ) ) ) ).
tt(t20_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 3)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t20_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_scmfsa_1 k2_scmfsa_1) =>  ((k1_funct_1 (k6_scmfsa_1 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ).
tt(t20_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k8_scmfsa_2 A B)) = 3) ) ) ) ) ).
tt(t20_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k6_scmfsa6a A B) = (k4_scmfsa6a A (k11_compos_1 k1_scmfsa_2 B))) ) ) ) ) ).
tt(t20_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v7_amistd_1 C 3 k1_scmfsa_2) & (v1_scmfsa6b C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa6a C D) A B) (k9_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b D (k1_scmfsa6b C A B) B) (k5_card_1 C)))) ) ) ) ) ) ) ) ).
tt(t20_scmfsa7b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (r3_scmfsa7b A B))  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 A C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ).
tt(t20_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((k5_card_1 (k2_scmfsa6a A)) = (k5_card_1 A)) ) ) ).
tt(t20_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B (k1_scmfsa_m E) A) & (r6_scmfsa7b B (k1_scmfsa_m E) A))  =>  ((r1_xxreal_0 (k1_funct_1 E D) k6_numbers) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b D B C) E A) (k1_funct_4 (k1_scmfsa6b B E A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k1_funct_1 C (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r5_scmfsa7b E C A) &  ((r6_scmfsa7b E C A) &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E C A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~ (r1_scmfsa9a A B C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B D C A) E) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b C D A) &  ((r6_scmfsa7b C D A) &  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D))))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D)))) 4)) ) )  =>  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D))))) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 C) 4))) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 B (k4_scmfsa_2 k6_numbers)))  &  ( (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  &  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k18_scmfsa_2 A C) = (k18_scmfsa_2 B C)) ) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 A) = (k6_memstr_0 3 k1_scmfsa_2 B)) ) ) ) ) ) ).
tt(t20_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scm_halt D) & (v3_scm_halt D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v2_scm_halt E)) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa6a D E) A C) B) = (k1_funct_1 (k1_scmfsa6b E (k1_scmfsa6b D A C) C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmisort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scm_halt A) & (v1_scmfsa7b A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (~  ((r1_xxreal_0 (k1_funct_1 C B) (k1_funct_1 (k1_scmfsa6b A C D) B)) &  (~ (r1_xxreal_0 (k1_funct_1 (k1_scmfsa6b A C D) B) k6_numbers)) ) ) ) ) ) )  => (v2_scm_halt (k2_scmfsa_9 B A))) ) ) ) ) ).
tt(t20_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k11_scmpds_2 C A B)) = 8) ) ) ) ) ) ) ).
tt(t20_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (~  ( (C = (k1_funct_4 B (k5_funct_4 (u1_compos_1 k1_scmpds_2) (k5_memstr_0 2 k1_scmpds_2 A) (k1_ordinal1 (k5_memstr_0 2 k1_scmpds_2 A)) (k3_scmpds_2 1) (k3_scmpds_2 (k4_xcmplx_0 1)))))  & (r1_extpro_1 2 k1_scmpds_2 C A)) ) ) ) ) ) ) ) ).
tt(t20_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 C) A) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 A B)) =>  ((k5_extpro_1 2 k1_scmpds_2 A B E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmpds_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scmpds_4 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r1_scmpds_6 A B C)) ) ) ) ) ) ) ).
tt(t20_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_tarski C D) &  ((r1_scmpds_6 C A B) &  ((r2_scmpds_6 C A B) & (r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)))) ) )  =>  ((k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k8_memstr_0 2 k1_scmpds_2 A) E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) & (r2_scmpds_6 (k2_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) =>  ((v2_extpro_1 B 2 (k1_scmring2 A)) =>  (B = (k2_compos_1 (k1_scmring2 A))) ) ) ) ) ) ).
tt(t20_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = k6_numbers)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k6_numbers)) ) ) ) ) ) ).
tt(t20_scmyciel,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes1 A))  => (r2_hidden k1_xboole_0 A)) ) ).
tt(t20_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (D = E) )  &  ( (~  ( (B = D)  &  (C = E) ) )  &  (~  ( (B = E)  &  (C = D) ) ) ) ) ) )  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A B) C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A C) (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t20_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_seq_1 A D) (k1_seq_1 C D)) & (r1_xxreal_0 (k1_seq_1 C D) (k1_seq_1 B D))) ) )  &  ((k2_seq_2 A) = (k2_seq_2 B)) ) ) )  =>  ((k2_seq_2 C) = (k2_seq_2 A)) ) ) ) ) ) ) ) ).
tt(t20_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ((k2_seq_2 (k1_valued_0 k1_numbers B A)) = (k2_seq_2 B)) ) ) ) ) ) ).
tt(t20_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) <=>  ((r1_seqfunc A k1_numbers B C) &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D C) => (v2_comseq_2 (k10_seqfunc A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t20_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers B C) A) = (k52_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers B A) (k1_valued_0 k1_numbers C A))) ) ) ) ) ) ) ).
tt(t20_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C)) & (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A C) (k3_funct_2 k5_numbers k1_numbers B C))) ) )  & (v1_series_1 B))  =>  ((v1_series_1 A) & (r1_xxreal_0 (k4_series_1 A) (k4_series_1 B))) ) ) ) ) ) ).
tt(t20_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 6)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 (k4_nat_1 2 B) 1)) (k2_xcmplx_0 (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton B 4)) (k4_nat_1 6 (k13_newton B 3))) (k4_nat_1 3 B)) 1)) 42)) ) ) ) ) ) ).
tt(t20_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 9 (k8_real_1 (k7_real_1 1 (k13_complex1 1 A)) (k7_real_1 1 (k13_complex1 1 B))))) ) ) ) ) ).
tt(t20_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k7_xcmplx_0 1 (k2_xcmplx_0 (k3_prepower 2 (k2_nat_1 C 1)) (k2_prepower 2 C)))) ) )  =>  ((k1_seq_1 (k3_series_1 B) A) = (k3_prepower 2 (k2_nat_1 A 1))) ) ) ) ) ) ).
tt(t20_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 3 (k8_complex1 (k8_complex1 (k13_complex1 A B) (k13_complex1 B C)) (k13_complex1 C A)))) ) ) ) ) ) ).
tt(t20_setfam_1,ax, (! [A:$i] : (r1_setfam_1 A (k2_setfam_1 A A))) ).
tt(t20_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B D) A)) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) & (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 B) D (k2_nat_1 A E)))) ) ) ) ) ) ) ) ) ).
tt(t20_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k9_setlim_2 B D C) A) = (k9_setlim_2 B (k10_nat_1 (k9_setfam_1 B) D A) C)) ) ) ) ) ) ) ) ).
tt(t20_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) & (v2_binop_1 C A)) )  =>  ( (D = k1_xboole_0)  |  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k7_setwiseo B A C (k5_setwiseo B D (k2_setwiseo B F)) E) = (k5_binop_1 A C (k7_setwiseo B A C D E) (k3_funct_2 B A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((r2_hidden C (k4_finseq_1 D)) =>  ((k1_funct_1 (k1_setwop_2 A D B) C) = (k1_funct_1 D C)) )  &  ( (~ (r2_hidden C (k4_finseq_1 D)))  =>  ((k1_funct_1 (k1_setwop_2 A D B) C) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r6_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E)) (k1_funct_4 B (k1_sfmastr2 C D))) & (r5_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E)) (k1_funct_4 B (k1_sfmastr2 C D)))) )  =>  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k4_scmfsa_m C) (k2_sf_mastr D)))) k6_numbers) |  ((k11_card_3 (k2_memstr_0 3 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) (k2_nat_1 E 1)) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2)) = (k5_relat_1 (k1_scmfsa6b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k1_funct_4 B (k1_sfmastr2 C D))) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_sfmastr3 F B C D E A))  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E)))) k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1) G)) )  &  (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1) G))  & (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 F B C D E A) G) (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E)))) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  => (r1_tarski (k2_sf_mastr (k1_funct_4 A B)) (k4_subset_1 k2_scmfsa_2 (k2_sf_mastr A) (k2_sf_mastr B)))) ) ) ) ).
tt(t20_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k2_tarski C D) (u1_sgraph1 B)) =>  ((r2_hidden C (u1_struct_0 B)) &  ((r2_hidden D (u1_struct_0 B)) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t20_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) &  ((v3_sheffer1 A) & (l3_lattices A)) ) ) )  =>  ((k6_lattices A) = (k1_sheffer1 A)) ) ) ).
tt(t20_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B C) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t20_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v1_matroid0 A) & (v1_finset_1 (u1_pre_topc A)))  => (v2_simplex0 A)) ) ) ).
tt(t20_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) =>  ((k5_simplex1 (k3_real_1 A 1) B C) = (k4_simplex1 B (k5_simplex1 A B C))) ) ) ) ) ) ) ) ).
tt(t20_simplex2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid B))) (u1_struct_0 (k15_euclid (k7_real_1 A B)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid B))) (u1_struct_0 (k15_euclid (k7_real_1 A B))))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid B))) =>  ((k1_binop_1 C D E) = (k7_finseq_1 D E)) ) ) ) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid B))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid (k7_real_1 A B)))) =>  ( (G = (k7_finseq_1 E F))  =>  ((k7_relset_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid B))) (u1_struct_0 (k15_euclid (k7_real_1 A B))) C (k3_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)) (k4_euclid_9 A E D) (k4_euclid_9 B F D))) = (k4_euclid_9 (k7_real_1 A B) G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sincos10,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t20_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_seq_1 k4_sin_cos2 (k9_binop_2 A B)) = (k7_real_1 (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B))))  &  ((k1_seq_1 k4_sin_cos2 (k10_binop_2 A B)) = (k9_real_1 (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ) ).
tt(t20_sin_cos3,ax, ((k15_sin_cos k5_complex1) = 1) ).
tt(t20_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  (~  ((k6_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) = (k7_xcmplx_0 (k17_sin_cos (k6_xcmplx_0 A B)) (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t20_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_square_1 (k17_sin_cos A)) = (k10_real_1 (k9_real_1 1 (k21_sin_cos (k8_real_1 2 A))) 2)) ) ) ).
tt(t20_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A) & (r1_xxreal_0 A (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  => (r1_xxreal_0 k6_numbers (k20_sin_cos A))) ) ) ) ) ).
tt(t20_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 1 (k3_square_1 A)) (k10_binop_2 1 (k3_square_1 A))) 1)) ) ) ) ) ).
tt(t20_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 (k6_xcmplx_0 A B)) (k3_sin_cos2 A)) (k3_sin_cos2 (k2_xcmplx_0 A B))) (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k6_xcmplx_0 A B)) (k6_sin_cos2 A)) (k6_sin_cos2 (k2_xcmplx_0 A B)))) = (k9_sin_cos2 A)) ) ) ) ) ).
tt(t20_sin_cos9,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))) => (r2_hidden (k1_seq_1 k30_sin_cos A) (k1_rcomp_1 (k1_real_1 1) 1))) ) ).
tt(t20_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers (k12_sin_cos A B C))) D)) = (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers (k12_sin_cos A B C))) D)) ) ) ) ) ) ) ) ) ).
tt(t20_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v2_funct_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)) & (v1_zfmisc_1 (k2_topreal1 2 B A))) ) ) ) ) ) ) ) ).
tt(t20_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~ (v1_xboole_0 A))  =>  ((k3_topreal1 2 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k3_topreal1 2 A))) ) ) ) ) ) ).
tt(t20_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k12_pscomp_1 A) = (k13_pscomp_1 A))  => (v1_sppol_1 A)) ) ) ).
tt(t20_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)) &  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  (~  ( ((k18_euclid A) = (k18_euclid B))  &  ((k18_euclid C) = (k18_euclid B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 B (k3_finseq_1 C)))  =>  ((r1_xxreal_0 B A) |  ((k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A (k7_nat_d B 1))) (k2_topreal1 2 C (k7_nat_d B 1)))) ) ) ) ) ) ) ) ) ).
tt(t20_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t20_square_1,ax, ((k7_square_1 4) = 2) ).
tt(t20_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden (k7_stacks_1 A B D) (k11_stacks_1 A C)) => (r2_hidden B (k11_stacks_1 A C)))  &  ((r2_hidden (k5_stacks_1 A B) (k11_stacks_1 A C)) =>  ((r1_stacks_1 A B) | (r2_hidden B (k11_stacks_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_2 C B) &  ((v1_stirl2_1 C A B) &  (A = B) ) )  =>  (C = (k6_partfun1 A)) ) ) ) ) ) ) ) ).
tt(t20_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ( ((k2_sublemma A (k6_sublemma A B C)) = (k7_cqc_lang A (k2_sublemma A B) (k2_sublemma A C)))  &  ((k19_substut1 A (k6_sublemma A B C)) = (k19_substut1 A B)) ) ) ) ) ) ) ) ) ).
tt(t20_subset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((r1_tarski B C) & (r1_tarski B (k3_subset_1 A C)))  =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t20_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B (k4_substlat A B C (k3_substlat A B D))) = (k3_substlat A B (k4_substlat A B C D))) ) ) ) ) ) ) ).
tt(t20_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [D:$i] :  ((m1_substut1 D A B) =>  (! [E:$i] :  ((m1_substut1 E A C) =>  ( ((v3_substut1 B A) &  ((v3_substut1 C A) &  ((k24_substut1 A B D) = (k24_substut1 A C E)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k4_substut2 A (k7_cqc_lang A B C) D E) = (k7_cqc_lang A (k4_substut2 A B D E) (k4_substut2 A C D E)))  &  ( ( ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k4_substut2 A B D E)))  &  ((k7_cqc_sim1 A C) = (k7_cqc_sim1 A (k4_substut2 A C D E))) )  =>  ((k7_cqc_sim1 A (k7_cqc_lang A B C)) = (k7_cqc_sim1 A (k4_substut2 A (k7_cqc_lang A B C) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((k11_supinf_2 k7_numbers A (k6_supinf_2 B) (k14_supinf_2 A B C)) = (k2_supinf_2 (k10_supinf_2 k7_numbers A B C)))  &  ((k10_supinf_2 k7_numbers A (k6_supinf_2 B) (k14_supinf_2 A B C)) = (k2_supinf_2 (k11_supinf_2 k7_numbers A B C))) ) ) ) ) ) ) ) ).
tt(t20_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_orders_2 B E C) & (r1_orders_2 B E F))  =>  ((r1_orders_2 B C D) |  ((k1_symsp_1 A B (k3_rlvect_1 B D E) C F) = (k1_symsp_1 A B D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski B (k2_zfmisc_1 A A)) =>  ( ((k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) = (k6_subset_1 B (k4_relat_1 A)))  &  ((k6_subset_1 B (k4_relat_1 (k10_xtuple_0 B))) = (k6_subset_1 B (k4_relat_1 A))) ) ) ) ) ) ).
tt(t20_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_taxonom1 B A) &  ((v2_metric_1 B A) &  ((v3_metric_1 B A) & (r2_hidden (k4_tarski C D) (k1_taxonom1 A B k6_numbers))) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t20_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((v5_taxonom2 B A) & (m1_taxonom2 B A)) )  =>  (~  ((v6_taxonom2 B A) &  ( (~ (r2_hidden k1_xboole_0 B))  &  ( (! [C:$i] :  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C (k1_partit1 A)) &  ( (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~ (r1_setfam_1 D E))  &  (~ (r1_setfam_1 E D)) ) ) ) ) ) )  &  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  (! [F:$i] :  ((r2_hidden F C) =>  ((r1_setfam_1 F E) & (r1_setfam_1 D F)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_taxonom1 C A) =>  (~  ((k3_tarski C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 B A) =>  ((r1_xxreal_0 (k1_seq_1 B A) k6_numbers) |  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) = (k10_real_1 (k1_fdiff_1 B A) (k1_seq_1 B A))) ) ) ) ) ) ) ) ).
tt(t20_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ( ((k1_seq_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 B) B) C) (k4_nat_1 2 A)) = k6_numbers)  &  ( ((k1_seq_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 B) B) C) (k2_nat_1 (k4_nat_1 2 A) 1)) = (k10_real_1 (k8_real_1 (k2_newton (k1_real_1 1) A) (k2_newton C (k2_nat_1 (k4_nat_1 2 A) 1))) (k3_newton (k2_nat_1 (k4_nat_1 2 A) 1))))  &  ( ((k1_seq_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 B) B) C) (k4_nat_1 2 A)) = (k10_real_1 (k8_real_1 (k2_newton (k1_real_1 1) A) (k2_newton C (k4_nat_1 2 A))) (k3_newton (k4_nat_1 2 A))))  &  ((k1_seq_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 B) B) C) (k2_nat_1 (k4_nat_1 2 A) 1)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_tarski B))  =>  ((k3_tbsp_1 A C) = k6_numbers) ) ) ) ) ) ) ).
tt(t20_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v6_tops_1 (k1_struct_0 A) A)) ) ).
tt(t20_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k1_tarski B))  =>  ((k1_tdlat_2 A C) = (k1_tarski (k1_tops_1 A B))) ) ) ) ) ) ) ) ).
tt(t20_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k1_tarski C))  =>  ((k2_pre_topc A B) = (u1_struct_0 A)) ) ) ) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t20_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) (k2_polynom1 (k15_pre_poly A) C D))) ) ) ) ) ) ) ) ).
tt(t20_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_tex_1 A B)))) =>  ( ((r1_tarski (k6_domain_1 A B) C) => (v4_pre_topc C (k3_tex_1 A B)))  &  ((v4_pre_topc C (k3_tex_1 A B)) =>  ((v1_xboole_0 C) | (r1_tarski (k6_domain_1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t20_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v2_tex_2 C A) <=> (v1_tdlat_3 B)) ) ) ) ) ) ) ) ).
tt(t20_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((m1_pre_topc B C) =>  ((v2_tex_3 B C) & (m1_pre_topc B C)) ) ) ) ) ) ) ) ).
tt(t20_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_tex_4 (k2_tex_4 A B) A)) ) ) ) ).
tt(t20_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 (u1_struct_0 A) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 (u1_struct_0 A) k1_numbers))))) )  =>  ( ((r3_seqfunc (u1_struct_0 A) B (u1_struct_0 A)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_funct_1 (k1_seqfunc (u1_struct_0 A) k1_numbers B C)) &  ((v1_funct_2 (k1_seqfunc (u1_struct_0 A) k1_numbers B C) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k1_seqfunc (u1_struct_0 A) k1_numbers B C) A k3_topmetr) & (m1_subset_1 (k1_seqfunc (u1_struct_0 A) k1_numbers B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) ) )  =>  ((v1_funct_1 (k11_seqfunc (u1_struct_0 A) B (u1_struct_0 A))) &  ((v1_funct_2 (k11_seqfunc (u1_struct_0 A) B (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k11_seqfunc (u1_struct_0 A) B (u1_struct_0 A)) A k3_topmetr) & (m1_subset_1 (k11_seqfunc (u1_struct_0 A) B (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) ) ) ) ) ) ) ).
tt(t20_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((k1_tsep_1 A B B) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ).
tt(t20_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden (k4_tarski C D) B) &  (! [E:$i] :  ( ((v1_toler_1 E A B) & (m1_toler_1 E A B))  =>  (~  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ((r4_borsuk_2 A B C E F) => (r4_borsuk_2 A B C E (k1_borsuk_2 A B D C (k1_borsuk_2 A B C D F G) (k2_borsuk_2 A C D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_pre_topc E) & (l1_pre_topc E)) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k2_borsuk_1 C E)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 C E)) (u1_struct_0 A))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k2_borsuk_1 D E)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 D E)) (u1_struct_0 A))))) )  =>  (! [H:$i] :  ( ((v4_pre_topc H B) & (m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [I:$i] :  ( ((v4_pre_topc I B) & (m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((m1_pre_topc C B) &  ((m1_pre_topc D B) &  ( (H = (k2_struct_0 C))  &  ( (I = (k2_struct_0 D))  &  ( ((k2_xboole_0 (k2_struct_0 C) (k2_struct_0 D)) = (k2_struct_0 B))  &  ((v5_pre_topc F (k2_borsuk_1 C E) A) &  ((v5_pre_topc G (k2_borsuk_1 D E) A) &  ( (! [J:$i] :  ((r2_hidden J (k9_subset_1 (u1_struct_0 (k2_borsuk_1 D E)) (k2_struct_0 (k2_borsuk_1 C E)) (k2_struct_0 (k2_borsuk_1 D E)))) =>  ((k1_funct_1 F J) = (k1_funct_1 G J)) ) )  &  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k2_borsuk_1 B E)) (u1_struct_0 A)) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B E)) (u1_struct_0 A))))) )  =>  (~  ( (J = (k1_funct_4 F G))  & (v5_pre_topc J (k2_borsuk_1 B E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_2 I B E F) =>  (! [J:$i] :  ((m1_borsuk_2 J B E F) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) I (k4_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) J (k4_topalg_4 A B k5_topmetr H)) & (r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) )  => (r3_borsuk_2 B E F I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) (k5_topalg_5 A) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) (k2_topalg_5 A) k12_toprealb))) ) ).
tt(t20_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v4_topalg_6 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 A))))) )  => (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ) ) ).
tt(t20_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_topdim_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xxreal_0 (k2_topdim_1 A B) (k4_topdim_1 A))) ) ) ) ).
tt(t20_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 A 1) =>  ((k4_topdim_1 (k15_euclid A)) = A) ) ) ) ).
tt(t20_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (k7_subset_1 (u1_struct_0 A) B (k2_topgen_1 A B))) <=> (r2_topgen_1 A B C)) ) ) ) ) ) ).
tt(t20_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ((v4_pre_topc C (k5_topgen_2 A B)) <=>  (~  ((r2_hidden B A) &  ( (~ (r2_hidden B C))  &  (~ (v1_finset_1 C)) ) ) ) ) ) ) ) ) ).
tt(t20_topgen_3,ax, ((k1_card_1 a_0_0_topgen_3) = k3_topgen_3) ).
tt(t20_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))  =>  ((v4_pre_topc B A) <=> (v2_tops_2 C A)) ) ) ) ) ) ) ) ).
tt(t20_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((r1_tarski (k1_topreal9 2 (k19_euclid A B) C) k2_topgen_5) <=> (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t20_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v3_tops_2 (k3_struct_0 A) A A)) ) ).
tt(t20_topmetr,ax, ((k4_topmetr k6_numbers 1) = k17_borsuk_1) ).
tt(t20_topreal1,ax,(r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers k6_numbers) (k19_euclid k6_numbers 1)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 k6_numbers) (k19_euclid 1 1)))).
tt(t20_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A)) (k3_topreal1 2 A))) ) ) ) ).
tt(t20_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden (k19_euclid (k17_euclid A) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) (k9_metric_1 (k14_euclid 2) E D)) &  ((v4_topreal1 B) &  ( (C = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k19_euclid (k17_euclid A) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k19_euclid (k17_euclid A) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid A) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) A)) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) )  =>  ( ((k17_euclid A) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  |  ( ((k18_euclid A) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  |  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) & (r1_tarski (k3_topreal1 2 C) (k2_xboole_0 (k3_topreal1 2 B) (k9_metric_1 (k14_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_topreal6,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_compts_1 C A)) ) )  => (v2_compts_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t20_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) & (l1_metric_1 B)) )  => (v6_metric_1 (k1_topreal7 A B))) ) ) ) ).
tt(t20_topreal8,ax, (! [A:$i] :  ( ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  => (v3_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(t20_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (v1_xboole_0 (k1_topreal9 A C B)))  & (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ) ).
tt(t20_topreala,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_topmetr)) =>  (! [B:$i] :  ((m1_connsp_2 B k3_topmetr A) =>  (? [C:$i] :  ((m1_rcomp_1 C A) & (r1_tarski C B)) ) ) ) ) ) ).
tt(t20_toprealb,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r2_borsuk_3 (k7_toprealb A D B) (k7_toprealb A E C))) ) ) ) ) ) ) ) ) ) ).
tt(t20_toprealc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (~  ( (~  ((k12_euclid A) = k6_numbers) )  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (~  ((k1_funct_1 A B) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t20_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k1_toprns_1 A B (k4_toprns_1 A C D)) = (k4_toprns_1 A (k1_toprns_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t20_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k1_tops_1 A C)) (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t20_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_finset_1 B))  => (v3_pre_topc (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t20_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) =>  ((k2_pre_topc A C) = (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ) ).
tt(t20_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) )  =>  ((v5_pre_topc C (k15_euclid A) (k15_euclid B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (? [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  & (r1_tarski (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C (k1_topreal9 A D F)) (k1_topreal9 B (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  ( ((r2_hidden (k4_tarski (k4_tarski F G) (k4_tarski D E)) C) & (r2_hidden (k4_tarski (k4_tarski D E) (k4_tarski H I)) C))  =>  ( (D = E)  | (r2_hidden (k4_tarski (k4_tarski F G) (k4_tarski H I)) C)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) => (r2_hidden (k4_tarski (k4_tarski D D) (k4_tarski E F)) C)) ) ) ) ) )  &  ((r3_relat_2 C (k2_zfmisc_1 A A)) & (r1_transgeo A B C)) ) )  => (r2_transgeo A B C)) ) ) ) ) ) ) ).
tt(t20_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v1_connsp_1 (k4_topmetr A B))) ) ) ) ) ).
tt(t20_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden B A) & (r1_tarski C B))  => (r2_hidden C A)) ) ) ) ) ) ) ).
tt(t20_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (m1_trees_2 (k1_tarski k1_xboole_0) A)) ) ).
tt(t20_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_trees_3 A) & (r1_tarski B A))  => (v3_trees_3 B)) ) ) ).
tt(t20_trees_4,ax, (! [A:$i] :  ( ((k3_trees_4 A k1_xboole_0) = (k1_trees_4 A))  &  ((k4_trees_4 A k1_xboole_0) = (k1_trees_4 A)) ) ) ).
tt(t20_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_trees_3 B))  =>  ((r2_hidden A B) => (r2_hidden A (k9_trees_9 B))) ) ) ) ) ).
tt(t20_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((r2_tsep_1 A B C) <=> (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ).
tt(t20_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (u1_struct_0 B))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k9_subset_1 (u1_struct_0 A) D (k4_tex_4 A E)) = (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) )  => (v3_borsuk_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t20_turing_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( ((k1_gr_cy_1 (k4_turing_1 1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = B)  &  ((k1_gr_cy_1 (k4_turing_1 2 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = (k2_nat_1 B (k7_partfun1 k5_numbers A 1))) ) ) ) ) ) ) ).
tt(t20_twoscomp,ax, ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 k6_numbers 1 1)) = k6_numbers)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k19_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k19_twoscomp (k11_finseq_1 1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t20_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k2_xboole_0 C (u1_struct_0 B)))  =>  ( ( (C = k1_xboole_0)  &  ((k6_unialg_2 A) = k1_xboole_0) )  |  ((k8_unialg_2 A (k7_unialg_2 A C) B) = (k7_unialg_2 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 A))  =>  ((k8_unialg_2 A (k7_unialg_2 A C) B) = (k7_unialg_2 A C)) ) ) ) ) ) ) ) ).
tt(t20_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  => (r1_tarski (u1_struct_0 (k1_uniroots A)) (u1_struct_0 A))) ) ).
tt(t20_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k9_polynom3 A)) (k9_polynom3 A))) ) ) ) ).
tt(t20_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski (k2_pre_topc A B) C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (D = k1_xboole_0) )  &  ((v3_pre_topc D A) &  ((r1_tarski (k2_pre_topc A B) D) & (r1_tarski (k2_pre_topc A D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_urysohn2,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 k6_numbers B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = (k2_measure5 A))  =>  ((k8_real_1 B C) = (k2_measure5 (k1_integra2 A B))) ) ) ) ) ) ) ) ) ).
tt(t20_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc D A k3_topmetr) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 D E)) &  ((r1_xxreal_0 (k1_seq_1 D E) 1) &  ( ((r2_hidden E B) =>  ((k1_seq_1 D E) = k6_numbers) )  &  ((r2_hidden E C) =>  ((k1_seq_1 D E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k11_cqc_lang A C E) F D) <=>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = H) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B D H)) ) ) )  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F E) G) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( ((m2_valued_0 B A C) & (m2_valued_0 C A D))  => (m2_valued_0 B A D)) ) ) ) ) ) ) ) ) ).
tt(t20_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_tarski A B) => (r1_tarski (k61_valued_1 A C) (k61_valued_1 B C))) ) ) ) ) ) ) ).
tt(t20_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k18_valued_1 (k50_valued_1 A B) C) = (k50_valued_1 (k18_valued_1 A C) B)) ) ) ) ) ) ) ).
tt(t20_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [F:$i] :  ((m1_vectsp_4 F A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) =>  ( ( (C = E)  &  (D = F) )  =>  ((r1_struct_0 D C) |  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) G F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) H (k4_vectsp_1 A B J C)))  =>  ((k4_vectsp_5 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k4_vectsp_1 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) I G) F (k1_vectsp_7 A (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) (k6_domain_1 (u1_struct_0 (k1_vectsp_5 A B D (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C)))) E))) = (k1_domain_1 (u1_struct_0 D) (u1_struct_0 B) (k4_vectsp_1 A D I H) (k4_vectsp_1 A B (k8_group_1 A I J) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((l1_struct_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) )  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k1_vectsp11 C D (k2_xcmplx_0 A B)) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 C) (k1_vectsp11 C D A) (k1_vectsp11 C D B)))) ) ) ) ) ) ) ) ).
tt(t20_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k4_vectsp_1 A C (k11_algstr_0 A B) (k4_vectsp_1 A C B D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( ((k3_rlvect_1 A (k1_vectsp_2 A C B) (k1_vectsp_2 A D B)) = (k1_vectsp_2 A (k3_rlvect_1 A C D) B))  &  ((k5_algstr_0 A (k1_vectsp_2 A C B) (k1_vectsp_2 A D B)) = (k1_vectsp_2 A (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((r1_struct_0 E C) & (r1_struct_0 E D))  => (r1_struct_0 E (k3_rlvect_1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( ((k2_vectsp_5 A B (k1_vectsp_4 A B) C) = (k1_vectsp_4 A B))  &  ((k2_vectsp_5 A B C (k1_vectsp_4 A B)) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ) ).
tt(t20_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ( ((k1_vectsp_6 A B D) = (k6_domain_1 (u1_struct_0 B) C))  =>  ((k4_vectsp_6 A B D) = (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C)) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_vectsp_7 A B C) = B)  &  (! [D:$i] :  ((m1_vectsp_7 D A B) =>  (~ (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_matrlin B A) =>  (! [C:$i] :  ((m1_vectsp_7 C A B) => (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(t20_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k6_vfunct_1 A B C (k2_vfunct_1 A B D E)) (k2_vfunct_1 A B (k6_vfunct_1 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k3_vfunct_2 A B C (k2_vfunct_1 A B D E)) (k2_vfunct_1 A B (k3_vfunct_2 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_waybel_0 A B) = (k6_waybel_0 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t20_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_funct_1 (k2_funct_1 (k5_waybel10 A))) &  ((v1_funct_2 (k2_funct_1 (k5_waybel10 A)) (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A))) (u1_struct_0 (k2_waybel10 A))) & (m1_subset_1 (k2_funct_1 (k5_waybel10 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A))) (u1_struct_0 (k2_waybel10 A)))))) ) ) ) ).
tt(t20_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((v1_waybel_0 (k2_relset_1 (u1_struct_0 A) C) A) => (v7_waybel_0 (k3_waybel11 A B C))) ) ) ) ) ) ) ).
tt(t20_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_yellow_4 A C D) &  ((v12_waybel_0 B A) & (r1_tarski D B)) )  => (r1_tarski C B)) ) ) ) ) ) ) ) ) ).
tt(t20_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  ((v17_waybel_0 C A B) & (v18_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(t20_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((v6_waybel_6 B (k2_yellow_1 (u1_pre_topc A))) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (~  ((r1_tarski B (k2_xboole_0 C D)) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel15 B A) <=>  ((v6_waybel_6 B A) &  (~  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ) ).
tt(t20_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_orders_2 A B C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_orders_2 A B D) => (r3_orders_2 A C D)) ) )  &  ((k6_waybel_0 A B) = (k4_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) B) (k6_waybel_0 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_waybel_9 A B C D))) =>  ( ( (F = E)  & (v5_orders_3 C A B))  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k2_yellow_0 A (a_3_0_waybel17 A D E))) (k2_yellow_0 B (a_5_0_waybel17 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ( (E = D)  & (v3_pre_topc D A))  => (v3_pre_topc E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v5_orders_3 C A B) &  ((v5_orders_3 D B A) &  ((r1_yellow_2 (u1_struct_0 A) A (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A)) & (r1_yellow_2 (u1_struct_0 B) B (k3_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C))) ) )  =>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) D (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D))) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) C (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v21_waybel_0 B A A) => (v21_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t20_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D B) & (m1_yellow_0 D B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((u1_struct_0 C) = (u1_struct_0 D))  & (v7_yellow_0 C A)) )  => (v7_yellow_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t20_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r1_yellow_0 A C) => (r2_hidden (k1_yellow_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t20_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) & (l1_waybel_9 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_waybel24 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel24 A B))) =>  ((r1_orders_2 (k3_waybel24 A B) C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_hidden (k4_tarski (k1_funct_1 C E) (k1_funct_1 D E)) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  =>  ((v3_orders_2 (k1_waybel25 A)) &  ((v4_orders_2 (k1_waybel25 A)) &  ((v5_orders_2 (k1_waybel25 A)) &  ((v1_lattice3 (k1_waybel25 A)) &  ((v2_lattice3 (k1_waybel25 A)) &  ((v3_lattice3 (k1_waybel25 A)) &  ((v3_waybel_3 (k1_waybel25 A)) & (l1_orders_2 (k1_waybel25 A))) ) ) ) ) ) ) ) ) ).
tt(t20_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v3_tops_2 D B C) => (v23_waybel_0 (k3_waybel26 A B C D) (k1_waybel26 A B) (k1_waybel26 A C))) ) ) ) ) ) ) ) ) ).
tt(t20_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D (k6_yellow_1 A (k6_yellow_1 B C))) & (m1_yellow_0 D (k6_yellow_1 A (k6_yellow_1 B C)))) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E (k6_yellow_1 (k2_zfmisc_1 A B) C)) & (m1_yellow_0 E (k6_yellow_1 (k2_zfmisc_1 A B) C))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ((v1_waybel27 F) => (v5_orders_3 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k3_waybel28 A)) => (r2_hidden B (k6_yellow_6 A))) ) ) ) ) ).
tt(t20_waybel29,ax, ((k1_waybel25 k9_waybel18) = (k1_waybel29 (k3_yellow_1 1))) ).
tt(t20_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) )  =>  ( ((r1_funct_2 B (u1_struct_0 A) B B C (k6_partfun1 B)) &  (D = (g1_waybel_0 A B (k1_toler_1 (u1_orders_2 A) B) C)) )  => (v10_waybel_0 D A)) ) ) ) ) ) ) ) ) ).
tt(t20_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C (k3_yellow_3 A B))) )  =>  (! [D:$i] :  ( ((v2_pre_topc D) &  ((v2_waybel19 D) & (m1_yellow_9 D A)) )  =>  (! [E:$i] :  ( ((v2_pre_topc E) &  ((v2_waybel19 E) & (m1_yellow_9 E B)) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 B))) =>  ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (k2_borsuk_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel31,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k4_waybel_0 A B)) A) & (v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k3_waybel_0 A B)) A)) ) ) ) ) ).
tt(t20_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc C B) <=>  ( (C = (u1_struct_0 B))  | (r2_hidden C (a_2_1_waybel32 A B))) ) ) ) ) ) ) ) ).
tt(t20_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v2_cantor_1 C A) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ((r1_tarski C (u1_pre_topc B)) & (r2_hidden (u1_struct_0 A) (u1_pre_topc B)))  => (r1_tarski (u1_pre_topc A) (u1_pre_topc B))) ) ) ) ) ) ) ).
tt(t20_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r2_functor0 (k4_waybel34 A) (k5_waybel34 A))) ) ).
tt(t20_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel35 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_waybel35 C A B))  =>  ( ((v4_waybel35 C A) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (r1_yellow_0 A (k4_waybel35 A B C D))) ) )  & (r1_waybel35 A C B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  (D = (k1_yellow_0 A (k4_waybel35 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A C (k1_yellow_0 A D)) => (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r1_yellow_2 (u1_struct_0 A) (k2_yellow_1 (k7_waybel_0 A)) (k7_waybel_4 A B) (k3_yellow_2 A))) ) ) ) ).
tt(t20_waybel_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A B) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ( ((k1_relset_1 A (k6_waybel_5 A B C F)) = A)  &  ( ((k1_relset_1 (k1_funct_1 (k7_funcop_1 A B) D) (k1_waybel_5 A C (k7_funcop_1 A B) (k6_waybel_5 A B C F) D)) = B)  &  ((k2_binop_1 A B C F D E) = (k1_funct_1 (k1_waybel_5 A C (k7_funcop_1 A B) (k6_waybel_5 A B C F) D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  => (v5_waybel_6 (k4_yellow_0 A) A)) ) ).
tt(t20_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v11_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v2_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) | (r2_hidden (k7_waybel_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t20_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v3_waybel_8 A) <=> (v5_waybel_7 (k1_waybel_4 A) A)) ) ) ).
tt(t20_waybel_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v2_tops_2 C A)) )  => (v2_tops_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t20_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k5_card_1 (u1_struct_0 (k4_weddwitt A))) 1)) ) ) ).
tt(t20_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B)) (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B)))) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t20_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((k2_wellord1 (k2_wellord1 C A) B) = (k2_wellord1 (k2_wellord1 C B) A)) ) ) ) ) ).
tt(t20_wellord2,ax, (! [A:$i] : (r8_relat_2 (k1_wellord2 A) A)) ).
tt(t20_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k7_real_1 (k18_rvsum_1 (k4_wsierp_1 k1_numbers A B)) (k1_seq_1 B A)) = (k18_rvsum_1 B)) ) ) ) ) ) ).
tt(t20_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) &  ((r1_tarski A C) &  (! [D:$i] :  ( ((r1_tarski D B) & (r1_tarski D C))  => (r1_tarski D A)) ) ) )  =>  (A = (k3_xboole_0 B C)) ) ) ) ) ).
tt(t20_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k7_xboolean A B)) = (k4_xboolean A B)) ) ) ) ) ).
tt(t20_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k6_xcmplx_0 A B) = (k6_xcmplx_0 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t20_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A (k2_xcmplx_0 B C)) <=> (r1_xxreal_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t20_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k14_xtuple_0 B)) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~ (r2_hidden (k6_xtuple_0 C A D E) B)) ) ) ) ) ) ) ) ).
tt(t20_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 A C))  => (r1_xxreal_0 A (k3_xxreal_0 B C))) ) ) ) ) ) ) ).
tt(t20_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_1 A A) = k1_xboole_0) ) ) ).
tt(t20_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m2_xxreal_2 A (k4_xxreal_1 A B))) ) ) ) ).
tt(t20_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ((r2_hidden (k1_xxreal_3 A B) k1_numbers) &  (~  ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v1_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_yellow_0 A (k2_tarski B C))) ) ) ) ) ) ) ).
tt(t20_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_waybel_3 (k3_yellow_3 A B) C D) =>  ((r1_waybel_3 A (k8_yellow_3 A B C) (k8_yellow_3 A B D)) & (r1_waybel_3 B (k9_yellow_3 A B C) (k9_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( (C = D)  & (v2_waybel11 C A)) )  => (v2_waybel11 D B)) ) ) ) ) ) ) ) ) ).
tt(t20_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_yellow13 (a_2_0_yellow13 A B) A B) & (m1_yellow13 (a_2_0_yellow13 A B) A B)) ) ) ) ) ).
tt(t20_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (k1_tarski B))  & (r1_tarski (k2_pre_topc A D) (k2_pre_topc A E)))  => (r2_hidden B (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((v1_yellow15 C A) & (r1_tarski B C))  => (v1_yellow15 B A)) ) ) ) ) ) ).
tt(t20_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r3_yellow16 B A) => (v24_waybel_0 B)) ) ) ) ) ).
tt(t20_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_waybel18 A B))) =>  ( (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski (k2_struct_0 (k3_waybel18 A B)) (k3_tarski E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel18 A B C))) =>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 D)))  =>  (~  ((r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski E)) (k3_tarski F)) &  (! [G:$i] :  (~  ((r2_hidden G (k2_waybel18 A B)) &  ((r2_hidden G F) & (r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski E)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (E = C)  &  ( (F = D)  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B F E)) &  ( (H = G)  &  (~  ((v1_altcat_3 G A C D) <=> (v2_altcat_3 H B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski B C) & (r2_waybel_7 A B D))  => (r2_waybel_7 A C D)) ) ) ) ) ) ).
tt(t20_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)))))  =>  ((k2_yellow_0 (k3_yellow_1 A) B) = (k1_setfam_1 B)) ) ) ) ).
tt(t20_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) => (m1_altcat_2 (k2_yellow20 A B) A)) ) ) ) ) ).
tt(t20_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  ( ((v11_quantal1 C) & (r1_tarski A (k2_relset_1 (u1_struct_0 B) C)))  =>  ((k7_relset_1 (u1_struct_0 B) (u1_struct_0 B) C A) = A) ) ) ) ) ) ) ).
tt(t20_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v1_waybel_0 (k6_yellow_3 A B C D) (k3_yellow_3 A B)) =>  ((v1_waybel_0 C A) & (v1_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k7_domain_1 (u1_struct_0 A) C D)) = (k7_domain_1 (u1_struct_0 A) (k10_lattice3 A B C) (k10_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t20_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A B C) &  ((r3_orders_2 A B D) &  ((k12_lattice3 A C D) = (k3_yellow_0 A)) ) )  =>  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t20_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  => (r1_waybel_0 A B (u1_struct_0 A))) ) ) ) ).
tt(t20_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lattice3 A))) =>  ( (B = C)  =>  ( ((k5_waybel_0 A B) = (k6_waybel_0 (k7_lattice3 A) C))  &  ((k6_waybel_0 A B) = (k5_waybel_0 (k7_lattice3 A) C)) ) ) ) ) ) ) ) ) ).
tt(t20_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc C A))  => (v4_pre_topc (k2_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) C B) A)) ) ) ) ) ) ) ).
tt(t20_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( ( (C = D)  & (r2_hidden A C))  =>  ((k2_cantor_1 B D) = (k2_xboole_0 (k1_tarski B) (k2_cantor_1 A C))) ) ) ) ) ) ) ) ).
tt(t20_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v8_zf_fund1 B A) & (r2_hidden C B))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_zf_lang E) & (m2_finseq_1 E k5_numbers))  =>  ( ((r2_hidden (k5_zf_fund1 D C) B) & (r2_hidden (k5_zf_fund1 E C) B))  => (r2_hidden (k5_zf_fund1 (k7_zf_lang D E) C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  ( ((k17_zf_lang C D E A) = (k15_zf_lang F G B))  =>  ( (C = F)  &  ( (D = G)  &  ((k13_zf_lang E A) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v4_zf_lang A) =>  ((k1_funct_1 A 1) = 2) ) ) ) ).
tt(t20_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_tarski A B) (k1_tarski C)) =>  (A = C) ) ) ) ) ).
tt(t20_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_zfmodel1 C A) &  ((r1_zfmodel1 D A) & (r1_tarski (k2_zf_model B) (k1_tarski (k2_zf_lang 3)))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k9_xtuple_0 E) = A)  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_zf_model A F B) =>  ((k1_funct_1 E (k3_funct_2 k1_zf_lang A F (k2_zf_lang 3))) = (k1_funct_1 C (k3_funct_2 k1_zf_lang A F (k2_zf_lang 3)))) )  &  ((r1_zf_model A F (k6_zf_lang B)) =>  ((k1_funct_1 E (k3_funct_2 k1_zf_lang A F (k2_zf_lang 3))) = (k1_funct_1 D (k3_funct_2 k1_zf_lang A F (k2_zf_lang 3)))) ) ) ) ) )  => (r1_zfmodel1 E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((r1_zf_model A B (k13_zf_lang D C)) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers k1_zf_lang) =>  ( (~  ((k3_funct_2 k1_zf_lang A E F) = (k3_funct_2 k1_zf_lang A B F)) )  =>  (D = F) ) ) )  & (r1_zf_model A E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_ordinal2 A B) => (r1_ordinal1 B A)) ) ) ) ) ).
tt(t20_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) )  =>  ( ((r2_hidden k4_ordinal1 A) &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((r2_hidden C D) => (r1_tarski (k5_zf_refle A B C) (k5_zf_refle A B D))) ) ) ) )  &  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((v4_ordinal1 C) =>  ( (C = k1_xboole_0)  |  ((k5_zf_refle A B C) = (k3_card_3 (k5_relat_1 B C))) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  &  ((v2_ordinal2 D) &  ((v3_ordinal2 D) &  (! [E:$i] :  ( ((v3_ordinal1 E) & (m1_subset_1 E A))  =>  ( ((k4_ordinal4 A D E) = E)  =>  ( (k1_xboole_0 = E)  |  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang (k5_zf_refle A B E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang (k5_zf_refle A B E))))) )  =>  ((r1_zf_model (k4_zf_refle A B) (k1_zf_lang1 k1_zf_lang (k5_zf_refle A B E) (k4_zf_refle A B) F) C) <=> (r1_zf_model (k5_zf_refle A B E) F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t20_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t210_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k6_xxreal_3 C B) (k24_member_1 A C))) ) ) ) ) ) ) ).
tt(t210_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_xcmplx_0 A B) = 1)  =>  (A = (k5_xcmplx_0 B)) ) ) ) ) ) ).
tt(t210_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C 1))  => (r1_xxreal_0 (k7_xcmplx_0 A C) B)) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t210_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_1 A k2_xxreal_0) = k1_xboole_0) ) ) ).
tt(t211_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k24_member_1 A B) = (a_2_16_member_1 A B)) ) ) ) ) ).
tt(t211_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k2_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = (k3_xcmplx_0 (k2_xcmplx_0 A B) (k5_xcmplx_0 (k3_xcmplx_0 A B)))) ) ) ) ) ) ) ) ) ).
tt(t211_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k5_xcmplx_0 A) 1)) ) ) ).
tt(t211_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_1 A k2_xxreal_0) = k1_xboole_0) ) ) ).
tt(t212_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k24_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k6_xxreal_3 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t212_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k6_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = (k3_xcmplx_0 (k6_xcmplx_0 B A) (k5_xcmplx_0 (k3_xcmplx_0 A B)))) ) ) ) ) ) ) ) ) ).
tt(t212_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 1 (k5_xcmplx_0 A))) ) ) ) ).
tt(t212_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_1 A k2_xxreal_0) = k1_xboole_0) ) ) ).
tt(t213_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k6_binop_2 C B) (k25_member_1 A C))) ) ) ) ) ) ) ).
tt(t213_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_xcmplx_0 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 B A)) ) ) ) ) ).
tt(t213_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A (k4_xcmplx_0 1)) => (r1_xxreal_0 (k4_xcmplx_0 1) (k5_xcmplx_0 A))) ) ) ).
tt(t213_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( (~  (A = k2_xxreal_0) )  =>  ((k1_xxreal_1 A k2_xxreal_0) = k1_xboole_0) ) ) ) ).
tt(t214_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k25_member_1 A B) = (a_2_17_member_1 A B)) ) ) ) ) ).
tt(t214_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B)) = (k7_xcmplx_0 B A)) ) ) ) ) ).
tt(t214_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 1) A))  & (r1_xxreal_0 (k5_xcmplx_0 A) (k4_xcmplx_0 1))) ) ) ) ).
tt(t214_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_1 k1_xxreal_0 A) = k1_xboole_0) ) ) ).
tt(t215_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k25_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k6_binop_2 B D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t215_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 1 A) = (k5_xcmplx_0 A)) ) ) ).
tt(t215_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 A 2) k6_numbers)) ) ) ) ).
tt(t215_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k2_xxreal_1 k1_xxreal_0 A) = k1_xboole_0) ) ) ).
tt(t216_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski (k25_member_1 A C) (k25_member_1 B C)) =>  ( (C = k6_numbers)  | (r1_tarski A B)) ) ) ) ) ) ) ) ).
tt(t216_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 1 (k5_xcmplx_0 A)) = A) ) ) ).
tt(t216_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k7_xcmplx_0 A 2))) ) ) ) ).
tt(t216_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_1 k1_xxreal_0 A) = k1_xboole_0) ) ) ).
tt(t217_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k25_member_1 A C) = (k25_member_1 B C))  =>  ( (C = k6_numbers)  |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t217_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_xcmplx_0 (k7_xcmplx_0 1 A)) = A) ) ) ).
tt(t217_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A (k7_xcmplx_0 1 2)) => (r1_xxreal_0 (k6_xcmplx_0 (k3_xcmplx_0 2 A) 1) k6_numbers)) ) ) ).
tt(t217_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( (~  (A = k1_xxreal_0) )  =>  ((k1_xxreal_1 k1_xxreal_0 A) = k1_xboole_0) ) ) ) ).
tt(t218_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k25_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k25_member_1 A C) (k25_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t218_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 1 A) = (k5_xcmplx_0 B))  =>  (A = B) ) ) ) ) ) ).
tt(t218_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A (k7_xcmplx_0 1 2)) => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 1 (k3_xcmplx_0 2 A)))) ) ) ).
tt(t218_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 A B))  => (r2_hidden A (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t219_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k25_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k25_member_1 A C) (k25_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t219_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 A (k5_xcmplx_0 B)) = (k3_xcmplx_0 A B)) ) ) ) ) ).
tt(t219_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k7_xcmplx_0 1 2) A) => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k3_xcmplx_0 2 A) 1))) ) ) ).
tt(t219_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (r2_hidden B (k1_xxreal_1 A k1_xxreal_0))) ) ) ) ) ).
tt(t21_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r1_abcmiz_0 A B C) => (r2_hidden C (k2_abcmiz_0 A (k5_abcmiz_0 A B C)))) ) ) ) ) ) ) ).
tt(t21_abcmiz_1,ax, (! [A:$i] :  ((k6_classes1 (k1_abcmiz_1 A)) = (k6_classes1 A)) ) ).
tt(t21_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k14_abcmiz_1 A)) =>  ((v5_abcmiz_1 B A (k28_abcmiz_1 A)) <=>  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) &  ((k1_xtuple_0 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0))) = k8_abcmiz_1) ) ) ) ) ) ) ).
tt(t21_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_xcmplx_0 (k1_absvalue A) (k1_absvalue (k13_complex1 1 A))) = 1) ) ) ) ).
tt(t21_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_aff_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((v1_aff_1 E A) &  ((r2_hidden B E) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r1_tarski D (k1_aff_4 A B C)) &  ( (~ (r5_aff_1 A C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) & (v1_funct_1 B)) )  => (r1_ordinal1 (k9_xtuple_0 A) (k9_xtuple_0 (k1_ordinal4 A B)))) ) ) ) ).
tt(t21_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  ((r1_tarski A B) =>  ( (A = k1_xboole_0)  | (r1_xxreal_0 (k1_recdef_1 (k4_afinsq_2 B) k6_numbers) (k1_recdef_1 (k4_afinsq_2 A) k6_numbers))) ) ) ) ) ) ).
tt(t21_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k5_afproj A C))  & (v1_aff_1 C A)) ) ) ) ) ) ) ).
tt(t21_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_afvect0 A B C D)) ) ) ) ) ) ) ) ).
tt(t21_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((r3_alg_1 A B C) => (r5_alg_1 (k4_alg_1 A (k6_alg_1 A B C)) B)) ) ) ) ) ) ) ).
tt(t21_algspec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) A) =>  ((k3_relat_1 C (k1_algspec1 A B)) = (k3_relat_1 C (k1_funct_4 (k6_partfun1 A) B))) ) ) ) ) ) ) ) ).
tt(t21_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 2 C) &  ((r2_hidden B (k11_algstr_4 A C)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( ((k2_xtuple_0 B) = D)  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k6_xcmplx_0 C 1)) &  ((r2_hidden (k1_xtuple_0 (k1_xtuple_0 B)) (k11_algstr_4 A D)) &  ((r2_hidden (k2_xtuple_0 (k1_xtuple_0 B)) (k11_algstr_4 A E)) &  ( (C = (k2_xcmplx_0 D E))  & (r2_hidden B (k2_zfmisc_1 (k2_zfmisc_1 (k11_algstr_4 A D) (k11_algstr_4 A E)) (k1_tarski D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  &  (~  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A B C)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A D E)) =>  ((k5_altcat_1 A B D E (k5_altcat_1 A B C D F G) H) = (k5_altcat_1 A B C E F (k5_altcat_1 A C D E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  (! [C:$i] :  ((l2_altcat_1 C) =>  ( ((m1_altcat_2 A B) & (m1_altcat_2 B C))  => (m1_altcat_2 A C)) ) ) ) ) ) ) ).
tt(t21_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ( ((v2_altcat_3 D A B C) & (v5_altcat_3 D A B C))  =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C B) = k1_xboole_0)  | (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_altcat_3 A D E) => (r2_altcat_3 B (k3_functor0 A B C D) (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ami_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v2_extpro_1 (k7_ami_3 A) 2 k1_ami_3)) ) ) ).
tt(t21_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k6_ami_3 H I))  & (r2_hidden H (k9_xtuple_0 B))) )  =>  ( (H = I)  |  ((k5_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I)) = (k5_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_amistd_1 2 k1_ami_3 A) = (k2_tarski A (k1_ordinal1 A))) ) ) ).
tt(t21_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((v5_amistd_1 C A B) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r2_hidden (k5_memstr_0 A B D) (k1_relset_1 k5_numbers C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ((r1_tarski C E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r2_hidden (k5_memstr_0 A B (k5_extpro_1 A B E D F)) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 B)) =>  ((v3_ami_wstd D A B) =>  ((k1_amistd_1 A B C D) = (k6_domain_1 k5_numbers (k5_ami_wstd A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t21_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A F G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analmetr A F G))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k2_analmetr A F G))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k2_analmetr A F G))) =>  ( ( (H = B)  &  ( (I = C)  &  ( (J = D)  &  (K = E) ) ) )  =>  ((r4_analmetr (k2_analmetr A F G) H J I K) <=> (r3_analmetr A B D C E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ((k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) = D) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_analoaf A B C D E))  &  ( (~ (r1_analoaf A B C E D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( ((r1_analoaf A B C B F) | (r1_analoaf A B C F B))  &  ((r1_analoaf A D E D F) | (r1_analoaf A D E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_analort A E F B B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v9_struct_0 B A))  => (m1_subset_1 (k2_anproj_1 A B) (k3_anproj_1 A))) ) ) ) ) ).
tt(t21_anproj_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ( (A = (k9_domain_1 A B C D E))  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  (! [F:$i] :  ((m2_funct_2 F A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [G:$i] :  ((m2_funct_2 G A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [H:$i] :  ((m2_funct_2 H A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [I:$i] :  ((m2_funct_2 I A k1_numbers (k9_funct_2 A k1_numbers)) =>  (~  ( (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  ((r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) J F)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K G))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L H))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M I))) (k8_funcsdom A)) =>  ( (J = k6_numbers)  &  ( (K = k6_numbers)  &  ( (L = k6_numbers)  &  (M = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [J:$i] :  ((m2_funct_2 J A k1_numbers (k9_funct_2 A k1_numbers)) =>  (? [K:$i] :  ((m1_subset_1 K k1_numbers) &  (? [L:$i] :  ((m1_subset_1 L k1_numbers) &  (? [M:$i] :  ((m1_subset_1 M k1_numbers) &  (? [N:$i] :  ((m1_subset_1 N k1_numbers) & (r2_funct_2 A k1_numbers J (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k1_funcsdom A k1_numbers (k5_funcsdom A) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) K F)) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) L G))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) M H))) (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) N I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k9_aofa_000 A B C) (k9_aofa_000 A B D))) ) ) ) ) ) ) ) ) ).
tt(t21_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_card_3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k9_funct_2 A k4_numbers))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) &  ((v1_funct_2 C A (k1_card_1 A)) &  ((v2_funct_2 C (k1_card_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_card_1 A))))) ) ) )  =>  (! [D:$i] :  ((m6_aofa_i00 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k9_funct_2 A k4_numbers) k4_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A k4_numbers) k4_numbers)))) )  => (m3_aofa_i00 E (k7_freealg k19_aofa_000 k26_aofa_i00) A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t21_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v7_armstrng B A) & (v8_relat_2 B))  =>  ((v3_armstrng B A) & (v4_armstrng B A)) ) ) ) ) ).
tt(t21_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( ((k2_arytm_0 A B) = k6_numbers)  &  ( (~  (A = k6_numbers) )  &  (~  (B = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t21_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( (~ (r1_arytm_2 A B))  =>  ((k2_arytm_1 C (k1_arytm_1 A B)) = (k2_arytm_1 (k7_arytm_2 C B) A)) ) ) ) ) ) ) ) ).
tt(t21_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ((r2_hidden A k5_arytm_3) &  ((r2_hidden B k5_arytm_3) &  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (! [D:$i] :  ((m1_subset_1 D k5_arytm_3) =>  (~  ( (A = C)  &  ( (B = D)  &  ((k8_arytm_2 A B) = (k10_arytm_3 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((k9_ordinal3 (k4_arytm_3 A B) (k3_arytm_3 A B)) = A) ) ) ) ) ).
tt(t21_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k7_asympt_0 B)) & (r2_hidden B (k7_asympt_0 C)))  => (r2_hidden A (k7_asympt_0 C))) ) ) ) ) ) ) ).
tt(t21_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k8_real_1 C (k6_power 2 C))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C B) &  ((r1_tarski (k6_asympt_0 C) (k6_asympt_0 (k3_asympt_1 (k7_real_1 1 A)))) &  (~  ((k6_asympt_0 C) = (k6_asympt_0 (k3_asympt_1 (k7_real_1 1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (r2_hidden (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))) ) ) ) ).
tt(t21_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k6_algstr_0 A B C)) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A B) (k6_autgroup A C)))) ) ) ) ) ) ).
tt(t21_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A C B) => (r1_tarski (k1_polynom2 A C) (k1_polynom2 A B))) ) ) ) ) ) ) ).
tt(t21_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k4_bcialg_1 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B C) B)) ) ) ) ) ) ).
tt(t21_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_2 A B C E) (k1_bcialg_2 A D C E)) (k1_bcialg_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t21_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v4_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_bcialg_1 A B C) & (r1_bcialg_1 A B D))  => (r1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_bcialg_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v2_bcialg_4 B) & (l1_bcialg_4 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k6_bcialg_4 B C (k2_nat_1 A 1)) = (k1_bcialg_4 B (k6_bcialg_4 B C A) C)) ) ) ) ) ) ) ).
tt(t21_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A B B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_bcialg_1 A (k3_bcialg_6 A C B)) = (k2_bcialg_1 A (k3_bcialg_6 A C (k2_bcialg_1 A (k2_bcialg_1 A B))))) ) ) ) ) ) ) ).
tt(t21_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m2_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r1_bcialg_1 A C D))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(t21_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) => (r1_bhsp_1 A (k4_algstr_0 A B) C)) ) ) ) ) ) ) ).
tt(t21_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A C)) &  ((k2_seq_2 (k2_bhsp_2 A C)) = (k3_bhsp_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t21_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_bhsp_3 C A) => (v2_bhsp_3 (k5_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t21_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k4_bhsp_4 A B 1 k6_numbers) = (k1_normsp_1 A B 1)) ) ) ) ) ).
tt(t21_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) (k9_bilinear A B C (k7_hahnban1 A B) D) E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ( (C = (k5_euclid A))  &  ( ((k7_partfun1 k6_margrel1 B A) = k8_margrel1)  &  ((k7_partfun1 k6_margrel1 (k4_binarith A B (k1_binari_2 A)) A) = k8_margrel1) ) )  =>  (B = (k3_binarith A C)) ) ) ) ) ) ) ) ).
tt(t21_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k1_binari_4 C B) (k1_binari_4 C A))) ) ) ) ) ) ) ).
tt(t21_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((k2_nat_1 (k6_binarith A (k7_binarith A B C)) (k15_funcop_1 k5_numbers (k8_binarith A B C) k7_margrel1 k6_numbers (k5_series_1 2 A))) = (k2_nat_1 (k6_binarith A B) (k6_binarith A C))) ) ) ) ) ) ) ).
tt(t21_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v1_algstr_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k6_algstr_0 A (k6_binom A B D) C) = (k6_algstr_0 A B (k5_binom A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  ((k10_xtuple_0 (k2_bintree2 A B)) = (k2_trees_2 A B)) ) ) ) ) ).
tt(t21_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k1_boolealg A B C) D) => (r3_lattices A B (k3_lattices A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_bor_cant A B C (k2_prob_1 A D)) =>  ((k3_funct_2 B k1_numbers C (k1_prob_2 A B (k1_prob_3 A D) E)) = (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B D C)) E)) )  &  ((r1_bor_cant A B C D) =>  ((k9_real_1 1 (k3_funct_2 B k1_numbers C (k1_prob_2 A B (k2_prob_3 A D) E))) = (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B (k2_prob_1 A D) C)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((m1_setfam_1 C (k3_borsuk_1 A B D E)) =>  ( ( (~  (E = k1_xboole_0) )  => (m1_setfam_1 (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) C) D))  &  ( (~  (D = k1_xboole_0) )  => (m1_setfam_1 (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  (! [D:$i] :  ((m1_pre_topc D B) => (m1_pre_topc (k2_borsuk_1 C D) (k2_borsuk_1 A B))) ) ) ) ) ) ) ) ).
tt(t21_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_connsp_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r2_hidden B A) & (r2_hidden D A)) ) )  => (r2_hidden C A)) ) ) ) ) ) ) ) ) ).
tt(t21_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~ (v1_rat_1 (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t21_borsuk_6,ax, ((v4_pre_topc a_0_9_borsuk_6 (k2_borsuk_1 k3_topmetr k3_topmetr)) & (m1_subset_1 a_0_9_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr))))) ).
tt(t21_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ((k9_xtuple_0 (k1_borsuk_7 A B F C D E)) = (k1_enumset1 A B F)) ) ) ) ) ) ) ) ).
tt(t21_bspace,ax, (! [A:$i] : (v2_rlvect_1 (k7_bspace A))) ).
tt(t21_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A C (k5_bvfunc_1 A D B)))) ) ) ) ) ) ) ) ).
tt(t21_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  ( (B = (k3_enumset1 C D E F G))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v3_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((r2_funct_2 A k6_margrel1 B (k11_bvfunc_1 A)) | (r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t21_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) B) C) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t21_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k10_bvfunc_1 A B C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t21_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k9_bvfunc_1 A D C) B E) (k9_bvfunc_1 A (k7_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k9_bvfunc_1 A C (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A B C E) => (r1_bvfunc_1 A (k6_bvfunc_2 A B C D) (k6_bvfunc_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k9_bvfunc_1 A D B) (k9_bvfunc_1 A D C)))) ) ) ) ) ) ) ) ).
tt(t21_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k11_bvfunc_1 A)) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t21_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D C)) (k9_bvfunc_1 A (k5_bvfunc_1 A B D) C))) ) ) ) ) ) ) ) ).
tt(t21_c0sp1,ax, (! [A:$i] :  ((l1_lopban_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v2_funcsdom B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v1_vectsp_1 B) &  ((v3_vectsp_1 B) & (l1_funcsdom B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((g1_funcsdom (u1_struct_0 A) (u2_algstr_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u3_struct_0 A) (u2_struct_0 A)) = B)  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) & (l1_funcsdom A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_c0sp1 (u1_struct_0 A))))) =>  ( (B = (k2_c0sp2 A))  => (v2_nfcont_1 B (k11_c0sp1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t21_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) (k7_cqc_lang A B C)) => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) B)) ) ) ) ) ) ) ) ) ).
tt(t21_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ).
tt(t21_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) <=> (r2_hidden (k3_card_1 A) (k3_card_1 B))) ) ) ) ) ).
tt(t21_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k2_card_2 A 1) = A) ) ) ).
tt(t21_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ((r2_hidden A (k3_card_3 (k2_card_3 B))) &  (! [C:$i] :  (! [D:$i] :  (~  (A = (k4_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t21_card_4,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((k1_card_1 A) = (k2_card_2 k4_ordinal1 (k1_card_1 A))) ) ) ).
tt(t21_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((k3_tarski A) = A) ) ) ).
tt(t21_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ( ((v1_card_fil B A) & (v3_card_fil B A))  => (r1_tarski (k4_card_fil A) B)) ) ) ) ) ).
tt(t21_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (~ (v1_xboole_0 (k2_card_fin B C A)))  =>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D (k8_relat_1 C (k1_tarski A))) &  ((r2_hidden E (k8_relat_1 C (k1_tarski A))) & (r1_xboole_0 (k1_funct_1 B D) (k1_funct_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (! [C:$i] :  ((m1_card_lar C A B) => (v2_card_lar C A)) )  => (v2_card_lar (k6_setfam_1 A B) A)) ) ) ) ) ).
tt(t21_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k4_graph_1 A C) = B)  =>  ((k1_cat_1 A C (k4_cat_1 A B)) = C) ) ) ) ) ) ) ) ).
tt(t21_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = (k3_tarski (a_2_0_cat_2 A B)))  &  ( (D = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C))  &  ( (E = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C))  &  (F = (k1_realset1 (u1_cat_1 A) C)) ) ) )  =>  ((v1_cat_2 (g1_cat_1 B C D E F) A) & (m3_cat_2 (g1_cat_1 B C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  => (r2_funct_2 A (u4_struct_0 B) (k7_cat_3 B A D C) (k8_cat_3 B A (k8_funcop_1 (u4_struct_0 B) A C) D))) ) ) ) ) ) ) ).
tt(t21_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  => (v1_cat_4 A)) ) ).
tt(t21_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_5 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) &  ((v4_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) ) )  =>  ((r1_tarski (u1_struct_0 A) (u1_struct_0 B)) => (m3_cat_2 A B)) ) ) ) ) ).
tt(t21_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k4_nat_1 4 (k1_catalan1 A)) (k1_catalan1 (k1_nat_1 A 1)))) ) ) ) ).
tt(t21_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k2_catalan2 A B) (k1_card_fin A B 1 k6_numbers))) ) ) ) ).
tt(t21_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B))) (k12_catalg_1 A B C) (k8_catalg_1 (u1_struct_0 A) D)) = (k8_catalg_1 (u1_struct_0 B) (k8_cat_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t21_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cc0sp1 A))) =>  ( (B = (k4_struct_0 (k7_cc0sp1 A)))  =>  (k6_numbers = (k1_normsp_0 (k7_cc0sp1 A) B)) ) ) ) ) ) ).
tt(t21_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k5_cc0sp2 A) B))) ) ) ) ).
tt(t21_cfcont_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 B) =>  ((v2_comseq_2 (k1_valued_0 k2_numbers B A)) &  ((k3_comseq_2 (k1_valued_0 k2_numbers B A)) = (k3_comseq_2 B)) ) ) ) ) ) ) ).
tt(t21_cfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k1_valued_0 k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers B C) A) (k19_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers B A) (k1_valued_0 k2_numbers C A)))) ) ) ) ) ) ).
tt(t21_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ( (C = (k2_tarski A B))  &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k2_numbers (k9_funct_2 C k2_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k2_numbers (k9_funct_2 C k2_numbers)) =>  (? [F:$i] :  ((m2_funct_2 F C k2_numbers (k9_funct_2 C k2_numbers)) &  (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k2_numbers) =>  (~ (r2_funct_2 C k2_numbers F (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C) D) (k2_valued_1 A k2_numbers k2_numbers (k25_valued_1 A k2_numbers B D) (k25_valued_1 A k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t21_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v3_cgames_1 A) & (v4_cgames_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ( (~ (r1_xxreal_0 C B))  => (r2_hidden (k9_cgames_1 (k1_funct_1 A B)) (k9_cgames_1 (k1_funct_1 A C)))) ) ) ) ) ) ) ).
tt(t21_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers B C) A) & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers D C) A))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t21_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) B) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) B))) =>  (! [D:$i] :  ((m3_glib_001 D A) =>  ( (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (~  ((r1_xxreal_0 E (k3_finseq_1 D)) & (r2_hidden (k1_funct_1 D E) B)) ) ) )  => (m3_glib_001 D C)) ) ) ) ) ) ) ) ) ).
tt(t21_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  ((r1_xboole_0 (k2_msafree2 B) (k3_msafree2 A)) &  (C = (k2_circcomb A B)) ) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( (H = (k5_relat_1 G (u1_struct_0 A)))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( (I = (k5_relat_1 G (u1_struct_0 B)))  =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ((k5_facirc_1 C F G J) = (k1_funct_4 (k5_facirc_1 A D H J) (k5_facirc_1 B E I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_circcmb3,ax, (! [A:$i] :  ( ((v4_circcmb3 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msafree2 B A) &  ((v5_circcmb3 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) => (r1_xxreal_0 (k2_circcmb3 A B C) 1)) ) ) ) ) ) ).
tt(t21_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_msualg_1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k3_circcomb A A B B) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ).
tt(t21_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_circled1 B A) & (m1_rlvect_2 B A))  =>  (! [C:$i] :  ( ((v1_circled1 C A) & (m1_rlvect_2 C A))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 (k8_real_1 D E) k6_numbers))  =>  ((k3_rlvect_2 A (k7_rlvect_2 A (k8_rlvect_2 A D B) (k8_rlvect_2 A E C))) = (k4_subset_1 (u1_struct_0 A) (k3_rlvect_2 A (k8_rlvect_2 A D B)) (k3_rlvect_2 A (k8_rlvect_2 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  (! [F:$i] :  ((m1_circtrm1 F A C D B E) =>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ((r2_hidden G (k9_trees_9 D)) =>  ((r1_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) (k5_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) E (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) G) &  ((k1_funct_1 (k5_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) E (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) G) = (k7_circtrm1 A B C G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_classes1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = B) )  &  ((r2_hidden A (k1_classes1 B)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ( (~ (r2_hidden A (k3_classes1 B C)))  & (r2_hidden A (k3_classes1 B (k1_ordinal1 C)))) ) ) ) ) ) ) ) ) ).
tt(t21_classes2,ax, (! [A:$i] :  ( (~  ((k1_card_1 (k1_classes1 A)) = k6_numbers) )  &  ( (~  ((k1_card_1 (k1_classes1 A)) = k1_xboole_0) )  & (v4_ordinal1 (k1_card_1 (k1_classes1 A)))) ) ) ).
tt(t21_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  => (v6_clvect_1 (k8_clopban1 A B) (k6_clopban1 A B))) ) ) ) ).
tt(t21_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k7_clopban2 A)) = (k6_clopban2 A)) ) ) ).
tt(t21_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C D) = (k1_normsp_1 A B k6_numbers)) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k1_valued_0 (u1_struct_0 A) B 1)) (k3_normsp_1 A (k1_valued_0 (u1_struct_0 A) (k1_bhsp_4 A B) 1) C))) ) ) ) ) ) ) ).
tt(t21_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) =>  ((k1_normsp_1 A (k4_clopban4 (k2_nat_1 E 1) A B C) D) = (k3_rlvect_1 A (k1_normsp_1 A (k4_clopban4 E A B C) D) (k1_normsp_1 A (k3_clopban4 (k2_nat_1 E 1) A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((v2_closure1 C A B) & (v2_closure1 D A B))  => (v2_closure1 (k3_closure1 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t21_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  ((r2_hidden C D) => (r1_pboole A C (k5_closure2 A B D))) ) ) ) ) ) ) ) ).
tt(t21_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t21_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A C)) &  ((k2_seq_2 (k2_clvect_2 A C)) = (k13_csspace A B)) ) ) ) ) ) ) ) ) ).
tt(t21_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_clvect_3 A B 1 k6_numbers) = (k1_normsp_1 A B 1)) ) ) ) ) ).
tt(t21_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_classes1 (k9_xtuple_0 A)) =>  ((v8_cohsp_1 A) <=>  ((v3_cohsp_1 (k9_xtuple_0 A)) &  ((v6_cohsp_1 A) &  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k1_funct_1 A B)) &  (! [D:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D B) & (r2_hidden C (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  ( (~  ( ((k3_tarski (k7_coh_sp A B)) = k1_xboole_0)  &  (~  ((k3_tarski (k6_coh_sp A B)) = k1_xboole_0) ) ) )  &  ( ((v1_funct_1 (k2_xtuple_0 B)) &  ((v1_funct_2 (k2_xtuple_0 B) (k3_tarski (k6_coh_sp A B)) (k3_tarski (k7_coh_sp A B))) & (m1_subset_1 (k2_xtuple_0 B) (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski (k6_coh_sp A B)) (k3_tarski (k7_coh_sp A B)))))) )  &  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k2_tarski C D) (k6_coh_sp A B)) => (r2_hidden (k2_tarski (k1_funct_1 (k2_xtuple_0 B) C) (k1_funct_1 (k2_xtuple_0 B) D)) (k7_coh_sp A B))) ) ) ) ) ) ) ) ).
tt(t21_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m2_collsp B A) =>  (! [C:$i] :  ((m2_collsp C A) =>  (~  ( (~  (B = C) )  &  ( (~ (r1_xboole_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_xboole_0 B C) = (k6_domain_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_combgras B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((v6_combgras B A A) &  ((v2_funct_2 (u2_combgras A A B) (u2_incsp_1 A)) & (v1_combgras C A)) )  => (v1_combgras (k5_combgras A A B C) A)) ) ) ) ) ) ) ).
tt(t21_complex1,ax, ((k12_complex1 k7_complex1) = (k10_complex1 k7_complex1)) ).
tt(t21_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k1_comptrig A) = k6_numbers)  <=>  ((r1_xxreal_0 k6_numbers (k3_complex1 A)) &  ((k4_complex1 A) = k6_numbers) ) ) ) ) ).
tt(t21_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k5_algstr_0 k1_complfld (k11_algstr_0 k1_complfld A) (k11_algstr_0 k1_complfld B)) = (k8_group_1 k1_complfld (k5_algstr_0 k1_complfld B A) (k11_algstr_0 k1_complfld (k8_group_1 k1_complfld A B)))) ) ) ) ) ) ) ) ) ).
tt(t21_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_complsp2 (k10_seq_4 A B)) = (k10_seq_4 (k1_complsp2 A) (k1_complsp2 B))) ) ) ) ) ) ).
tt(t21_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v3_finset_1 B) &  ((v2_tops_2 B A) &  ((v4_card_3 B) &  ((k6_setfam_1 (u1_struct_0 A) B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t21_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r1_ordinal1 (k2_afinsq_1 B) (k2_afinsq_1 (k7_compos_1 A B C)))) ) ) ) ) ) ).
tt(t21_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ( ((k63_valued_1 B) = (k63_valued_1 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t21_comptrig,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)))).
tt(t21_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_pre_topc C B) =>  (! [D:$i] :  ((m1_pre_topc D B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 D) (u1_struct_0 A)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 A))))) )  =>  ( ( ((k2_xboole_0 (k2_struct_0 C) (k2_struct_0 D)) = (k2_struct_0 B))  &  ( ((k9_subset_1 (u1_struct_0 D) (k2_struct_0 C) (k2_struct_0 D)) = (k7_domain_1 (u1_struct_0 B) E F))  &  ((v1_compts_1 C) &  ((v1_compts_1 D) &  ((v8_pre_topc B) &  ((v5_pre_topc G C A) &  ((v5_pre_topc H D A) &  ( ((k1_funct_1 G E) = (k1_funct_1 H E))  &  ((k1_funct_1 G F) = (k1_funct_1 H F)) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_funct_4 G H)) &  ((v1_funct_2 (k1_funct_4 G H) (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_pre_topc (k1_funct_4 G H) B A) & (m1_subset_1 (k1_funct_4 G H) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) & (v2_margrel1 A)) ) )  => (r1_tarski (k1_relset_1 (k3_finseq_2 k5_numbers) A) (k4_finseq_2 (k19_margrel1 A) k5_numbers))) ) ).
tt(t21_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers A k6_complex1) A)) ) ).
tt(t21_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k7_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k7_comseq_3 A) (k7_comseq_3 B)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k8_comseq_3 A) (k8_comseq_3 B)))) & (r2_funct_2 k5_numbers k1_numbers (k8_comseq_3 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k1_series_1 k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k7_comseq_3 A) (k8_comseq_3 B)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k8_comseq_3 A) (k7_comseq_3 B))))) ) ) ) ) ).
tt(t21_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ( ( (~ (v5_conlat_1 (g2_conlat_1 A (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B) (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B))) A))  &  ((v7_conlat_1 (g2_conlat_1 A (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B) (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B))) A) & (l2_conlat_1 (g2_conlat_1 A (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B) (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B))) A)) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u4_struct_0 A))) =>  ( ( ( (~ (v5_conlat_1 (g2_conlat_1 A C D) A))  &  ((v7_conlat_1 (g2_conlat_1 A C D) A) & (l2_conlat_1 (g2_conlat_1 A C D) A)) )  & (r1_tarski B D))  => (r1_tarski (k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t21_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  => (v3_funct_2 (k9_conlat_2 A) (u1_struct_0 (k1_lattice2 (k11_conlat_1 A))) (u1_struct_0 (k11_conlat_1 (k7_conlat_2 A))))) ) ).
tt(t21_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_connsp_1 A C D) & (v4_pre_topc B A)) )  =>  ((v4_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A) & (v4_pre_topc (k4_subset_1 (u1_struct_0 A) B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t21_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v1_connsp_2 A) & (v10_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((r1_xboole_0 B C) &  ((v2_connsp_1 B A) &  ((v2_connsp_1 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_connsp_1 D A) &  ((v2_connsp_1 E A) &  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (m1_connsp_3 B A))  => (r1_tarski (k1_connsp_1 A C) B)) ) ) ) ) ) ) ).
tt(t21_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (~  ((v2_convex1 B A) &  ((k3_rlvect_2 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t21_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) => (r1_convex4 A (k5_convex4 A B C) (k5_convex4 A C B))) ) ) ) ) ) ).
tt(t21_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ((k13_cqc_lang A (k14_qc_lang1 A C D) B) = (k14_qc_lang1 A (k13_cqc_lang A C B) (k13_cqc_lang A D B))) ) ) ) ) ) ) ) ) ).
tt(t21_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k2_qc_lang3 A B) (k24_qc_lang1 A C)) => (r2_qc_lang1 A B (k13_cqc_sim1 A C))) ) ) ) ) ) ) ).
tt(t21_cqc_the1,ax, ((r2_hidden k6_numbers k2_cqc_the1) &  ((r2_hidden 1 k2_cqc_the1) &  ((r2_hidden 2 k2_cqc_the1) &  ((r2_hidden 3 k2_cqc_the1) &  ((r2_hidden 4 k2_cqc_the1) &  ((r2_hidden 5 k2_cqc_the1) &  ((r2_hidden 6 k2_cqc_the1) &  ((r2_hidden 7 k2_cqc_the1) &  ((r2_hidden 8 k2_cqc_the1) & (r2_hidden 9 k2_cqc_the1)) ) ) ) ) ) ) ) ) ).
tt(t21_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k12_cqc_lang A C B) A) =>  ((r2_hidden C (k24_qc_lang1 A B)) | (v2_cqc_the1 B A)) ) ) ) ) ) ) ) ).
tt(t21_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (k4_subset_1 (k3_cqc_lang A) (k1_cqc_the1 A B) (k1_cqc_the1 A C)) (k1_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) B C)))) ) ) ) ) ) ).
tt(t21_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_csspace4 A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) &  ((v1_csspace4 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_csspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (E = C)  &  (F = D) )  =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( (D = (k1_clvect_1 (k9_csspace4 A B) C G))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A (u1_struct_0 B) F H) = (k1_clvect_1 B (k3_funct_2 A (u1_struct_0 B) E H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v2_csspace C) & (l1_csspace C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k12_csspace C D (k3_rlvect_1 C (k1_clvect_1 C E A) (k1_clvect_1 C F B))) = (k2_xcmplx_0 (k3_xcmplx_0 (k15_complex1 A) (k12_csspace C D E)) (k3_xcmplx_0 (k15_complex1 B) (k12_csspace C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_decomp_1 C A B) <=>  ((v9_decomp_1 C A B) & (v18_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t21_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k2_finseq_1 48)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  ( (~  (A = 16) )  &  ( (~  (A = 17) )  &  ( (~  (A = 18) )  &  ( (~  (A = 19) )  &  ( (~  (A = 20) )  &  ( (~  (A = 21) )  &  ( (~  (A = 22) )  &  ( (~  (A = 23) )  &  ( (~  (A = 24) )  &  ( (~  (A = 25) )  &  ( (~  (A = 26) )  &  ( (~  (A = 27) )  &  ( (~  (A = 28) )  &  ( (~  (A = 29) )  &  ( (~  (A = 30) )  &  ( (~  (A = 31) )  &  ( (~  (A = 32) )  &  ( (~  (A = 33) )  &  ( (~  (A = 34) )  &  ( (~  (A = 35) )  &  ( (~  (A = 36) )  &  ( (~  (A = 37) )  &  ( (~  (A = 38) )  &  ( (~  (A = 39) )  &  ( (~  (A = 40) )  &  ( (~  (A = 41) )  &  ( (~  (A = 42) )  &  ( (~  (A = 43) )  &  ( (~  (A = 44) )  &  ( (~  (A = 45) )  &  ( (~  (A = 46) )  &  ( (~  (A = 47) )  &  (~  (A = 48) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_dickson A))) =>  (~  ((r4_waybel_4 B C (u1_orders_2 (k5_dickson A))) & (v1_xboole_0 (k6_dickson A B))) ) ) ) ) ) ) ) ).
tt(t21_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k26_valued_1 k1_numbers k1_numbers E B) C) (k2_nat_1 A 1)) D) = (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E C) (k2_nat_1 A 1)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~  (A = B) )  =>  ((k9_diff_1 (k1_fcont_1 C D) A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t21_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C (k9_real_1 A B) A) = (k10_real_1 (k1_seq_1 (k4_diff_1 C B) A) B)) ) ) ) ) ) ) ).
tt(t21_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers k2_fdiff_9) (k1_relset_1 k1_numbers k1_fdiff_9))))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_fdiff_9) B) A) = (k1_real_1 (k8_real_1 4 (k13_complex1 (k8_real_1 (k21_sin_cos (k8_real_1 2 A)) (k18_sin_cos B)) (k8_real_1 (k18_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k18_sin_cos (k9_real_1 (k8_real_1 2 A) B))))))) ) ) ) ) ) ).
tt(t21_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  ( ((k2_dilworth A) = 1)  =>  ((v1_dilworth (k2_struct_0 A) A) & (m1_subset_1 (k2_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(t21_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_diraf A B C B D) => (r2_diraf A C B C D)) ) ) ) ) ) ) ) ) ).
tt(t21_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_dist_1 B A) => (v3_funct_1 (k4_dist_1 A B))) ) ) ) ) ).
tt(t21_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((k4_zfmisc_1 A B C D) = (a_4_0_domain_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t21_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D (k5_dynkin A B)) & (v2_finsub_1 B)) )  => (r2_hidden (k9_subset_1 A C D) (k5_dynkin A B))) ) ) ) ) ) ) ) ) ).
tt(t21_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( ((k2_binom (k9_int_3 A) B k6_numbers) = (k1_group_1 (k9_int_3 A)))  &  ((k2_binom (k9_int_3 A) B k6_numbers) = 1) ) ) ) ) ) ).
tt(t21_ec_pf_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ( (E = (k6_int_1 B C))  &  (F = (k6_int_1 (k6_xcmplx_0 A B) C)) ) )  =>  ((k5_algstr_0 (k9_int_3 C) (k8_group_1 (k9_int_3 C) D G) (k8_group_1 (k9_int_3 C) E G)) = (k8_group_1 (k9_int_3 C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( (C = (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B)))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((k3_matrix_1 k1_numbers C D E) = (k8_real_1 (k1_seq_1 A D) (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k5_enumset1 A B C D E F G) = (k2_xboole_0 (k4_enumset1 A B C D E F) (k1_tarski G))) ) ) ) ) ) ) ) ).
tt(t21_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~ (r2_hidden C (k6_eqrel_1 A A B D))) ) ) ) ) ) ) ) ).
tt(t21_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_msualg_2 D A C) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r8_pboole (u1_struct_0 A) E (u3_msualg_1 A D)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) G (k1_msafree (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B) E F)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k3_msualg_1 A H C)) =>  (! [J:$i] :  ((m1_subset_1 J (k3_msualg_1 A H D)) =>  ( (I = J)  =>  ( ((k3_msualg_1 A H D) = k1_xboole_0)  |  ((k5_msualg_3 A C B H F I) = (k5_msualg_3 A D B H G J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k13_e_siec A) (k2_zfmisc_1 (k12_e_siec A) (k12_e_siec A))) & (r1_tarski (k14_e_siec A) (k2_zfmisc_1 (k12_e_siec A) (k12_e_siec A)))) ) ) ).
tt(t21_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k4_algstr_0 (k15_euclid A) B) C) = (k7_binop_2 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t21_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k17_complex1 (k2_euclid_3 A)) = (k7_square_1 (k7_real_1 (k5_square_1 (k17_euclid A)) (k5_square_1 (k18_euclid A))))) ) ) ).
tt(t21_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k23_rvsum_1 (k9_euclid A B D) C) = (k4_real_1 D (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t21_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k5_euclid_5 (k4_euclid_5 k6_numbers A k6_numbers) (k4_euclid_5 k6_numbers B k6_numbers)) = (k4_struct_0 (k15_euclid 3))) ) ) ) ) ).
tt(t21_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k4_euclid_3 A B C) = (k4_euclid_3 D E F))  &  ((k4_euclid_3 C A B) = (k4_euclid_3 F D E)) )  =>  ((r1_euclid_6 A B C) |  ((r1_euclid_6 D E F) |  ( ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D F))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A C)) (k12_euclid (k5_algstr_0 (k15_euclid 2) F E))))  &  ( ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) F E))))  &  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A C)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 D (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ( (C = (k2_euclid_7 (k1_euclid A) B D))  =>  ((k5_euclid_7 A C) = (k5_euclid_7 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t21_euclid_8,ax, ((k5_euclid_8 k3_euclid_8 k2_euclid_8) = (k6_euclid 3 k4_euclid_8)) ).
tt(t21_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) => (r1_tarski (k4_euclid_9 A C (k6_xcmplx_0 B (k1_funct_1 (k3_euclid (k8_rvsum_1 C D)) (k1_euclid_9 A C D)))) (k4_euclid_9 A D B))) ) ) ) ) ) ) ) ).
tt(t21_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_pcomps_1 (k1_euclid A) (k13_euclid A))) ) ).
tt(t21_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid D)) =>  ((k9_euclid D (k7_euclid D (k9_euclid D E B) (k9_euclid D F C)) A) = (k7_euclid D (k9_euclid D E (k8_real_1 A B)) (k9_euclid D F (k8_real_1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r4_analmetr A B E B F) &  ((r4_analmetr A B G B H) &  ((r4_analmetr A C E D F) &  ((r4_analmetr A C G D H) &  (B = D) ) ) ) )  =>  ((r2_analoaf A B G B C) |  ((r2_analoaf A B C B E) | (r4_analmetr A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_int_2 A B) =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 B 1) |  ((k1_euler_1 (k3_xcmplx_0 A B)) = (k4_nat_1 (k1_euler_1 A) (k1_euler_1 B))) ) ) ) ) ) ) ) ).
tt(t21_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (v2_exchsort A (k1_exchsort A))) ) ).
tt(t21_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) & (r1_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E)))) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k6_extpro_1 A B C D) = (k6_extpro_1 A B C (k5_extpro_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) => (r1_xxreal_0 (k3_extreal1 (k4_supinf_2 A B)) (k3_supinf_2 (k3_extreal1 A) (k3_extreal1 B)))) ) ) ) ).
tt(t21_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ((r2_hidden C (k3_msafree2 A)) =>  ((r2_hidden C (k3_msafree2 (k2_circcomb A B))) & (r2_hidden C (k3_msafree2 (k2_circcomb B A)))) ) ) ) ) ) ) ).
tt(t21_facirc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ( ((r1_circcomb A B) &  ((k2_msafree2 A) = (k2_msafree2 B)) )  =>  ((k2_msafree2 (k2_circcomb A B)) = (k2_msafree2 A)) ) ) ) ) ) ).
tt(t21_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers B) A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers B) A))) ) ) ) ) ).
tt(t21_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_limfunc1 A) (k1_relset_1 k1_numbers B)) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_limfunc1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_limfunc1 A)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k2_limfunc1 A))) (k7_relset_1 k1_numbers k1_numbers B (k2_limfunc1 A))))) ) ) ) ) ) ).
tt(t21_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) A) B) = (k10_real_1 (k21_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t21_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k1_fdiff_9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k1_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k1_sin_cos9 B)) (k8_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k1_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t21_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r2_fdiff_1 B A) & (r2_fdiff_1 C A)) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) D) = (k7_real_1 (k8_real_1 (k1_seq_1 C D) (k1_fdiff_1 B D)) (k8_real_1 (k1_seq_1 B D) (k1_fdiff_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) &  ((r2_fdiff_1 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D A) &  ((k1_seq_1 C D) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers B C) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers B C) A) (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) C) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 C A) B)) (k20_valued_1 k1_numbers k1_numbers k1_numbers C C)))) ) ) ) ) ) ) ) ).
tt(t21_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r3_fdiff_3 A B) &  ((r4_fdiff_3 A B) &  ((k2_fdiff_3 B A) = (k1_fdiff_3 B A)) ) )  =>  ((r1_fdiff_1 A B) &  ( ((k1_fdiff_1 A B) = (k2_fdiff_3 B A))  &  ((k1_fdiff_1 A B) = (k1_fdiff_3 B A)) ) ) ) ) ) ) ) ).
tt(t21_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1))) &  ( (D = (k1_taylor_1 3))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = A)  &  (~ (r1_xxreal_0 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) B) E) = (k10_real_1 (k8_real_1 3 (k2_newton E 2)) (k7_real_1 A (k2_newton E 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B k3_taylor_1))) &  ( (B = (k1_taylor_1 2))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) & (r1_xxreal_0 C k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) C) = (k7_real_1 C (k8_real_1 (k8_real_1 2 C) (k1_seq_1 k3_taylor_1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) C) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k3_taylor_1) A) C) = (k10_real_1 (k1_seq_1 k24_sin_cos C) (k9_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k4_sin_cos6) (k10_real_1 1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = (k8_real_1 2 C))  &  ( (~ (r1_xxreal_0 (k1_seq_1 B C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 B C))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k4_sin_cos6) (k10_real_1 1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k4_sin_cos6) (k10_real_1 1 2)) A) C) = (k1_real_1 (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 (k8_real_1 2 C))))))) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A)))) & (r1_xxreal_0 1 A))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A)) B) C) = (k1_real_1 (k10_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 k19_sin_cos C) (k5_real_1 A 1))) (k5_prepower (k1_seq_1 k16_sin_cos C) (k1_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t21_fdiff_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A)))) & (r1_xxreal_0 1 A))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A)) B) C) = (k1_real_1 (k10_real_1 (k4_real_1 A (k1_seq_1 k19_sin_cos C)) (k5_prepower (k1_seq_1 k16_sin_cos C) (k1_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t21_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k9_ff_siec A) (k9_ff_siec A)) = (k9_ff_siec A))  &  ( ((k3_relat_1 (k4_xboole_0 (k9_ff_siec A) (k4_relat_1 (k2_net_1 A))) (k9_ff_siec A)) = k1_xboole_0)  &  ((k2_xboole_0 (k2_xboole_0 (k9_ff_siec A) (k2_relat_1 (k9_ff_siec A))) (k4_relat_1 (k2_net_1 A))) = (k2_xboole_0 (k10_ff_siec A) (k2_relat_1 (k10_ff_siec A)))) ) ) ) ) ).
tt(t21_fib_num2,ax, ((k1_pre_ff 2) = 1) ).
tt(t21_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_fib_num3 A) = (k2_xcmplx_0 (k3_power k1_fib_num A) (k3_power k2_fib_num A))) ) ) ).
tt(t21_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_int_1 (k13_complex1 (k3_power k1_fib_num (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1)) (k7_square_1 5))) = (k1_pre_ff (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1))) ) ) ).
tt(t21_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((k4_finseq_8 A (k6_finseq_1 A) B) = (k6_finseq_1 A))  &  ((k4_finseq_8 A B (k6_finseq_1 A)) = (k6_finseq_1 A)) ) ) ) ) ) ).
tt(t21_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k3_filter_0 A B) = B) ) ) ) ) ).
tt(t21_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B B) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((k5_binop_1 (k2_zfmisc_1 A B) (k6_filter_1 A B G H) (k1_domain_1 A B C E) (k1_domain_1 A B D F)) = (k1_domain_1 A B (k5_binop_1 A G C D) (k5_binop_1 B H E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k3_lattices A C D) B)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r3_lattices A D C))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (A = (k5_relat_1 (k7_finseq_1 A B) (k4_finseq_1 A))) ) ) ) ) ).
tt(t21_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (B = (k5_relat_1 C (k2_finseq_1 A)))  =>  ((k3_finseq_1 B) = (k3_xxreal_0 A (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t21_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k2_finseq_1 C) = (k2_tarski A B))  =>  ( (A = B)  |  ( (C = 2)  &  ((k2_tarski A B) = (k2_tarski 1 2)) ) ) ) ) ) ) ) ).
tt(t21_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ((r1_xxreal_0 1 (k4_finseq_4 A B)) & (r1_xxreal_0 (k4_finseq_4 A B) (k3_finseq_1 A))) ) ) ) ) ).
tt(t21_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((k1_nat_1 A 1) = (k3_finseq_1 C))  =>  (C = (k8_finseq_1 B (k17_finseq_1 B A C) (k12_finseq_1 B (k7_partfun1 B C (k3_finseq_1 C))))) ) ) ) ) ) ) ) ).
tt(t21_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_finseq_4 (k11_finseq_1 A B C) A) = 1) ) ) ) ).
tt(t21_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_finseq_7 A B C D) = (k2_finseq_7 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t21_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_tarski C B) =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k1_funct_1 C 1) = (k1_funct_1 B 1)) ) ) ) ) ) ) ) ) ).
tt(t21_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C A) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G E) & (m2_finseq_1 G C))  =>  ((k3_funcop_1 F G (k5_finseq_2 C E D)) = (k4_funcop_1 F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((k3_finseq_1 B) = 2)  =>  ((k1_finsop_1 A B C) = (k1_binop_1 C (k1_funct_1 B 1) (k1_funct_1 B 2))) ) ) ) ) ) ) ) ).
tt(t21_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k10_fintopo2 A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden D (k6_fintopo2 A B)) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fintopo3 A B 2) = (k8_fin_topo A (k8_fin_topo A B))) ) ) ) ) ).
tt(t21_fintopo4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v1_fin_topo (k4_fintopo4 A))) ) ) ).
tt(t21_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xboole_0 (k6_fin_topo A B) (k7_fin_topo A B))) ) ) ) ).
tt(t21_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  ((k10_fin_topo A B) = k1_xboole_0) )  &  ( (~  ((k1_card_1 B) = 1) )  & (v4_fin_topo B A)) ) ) ) ) ) ) ).
tt(t21_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski (k7_subset_1 (k3_catalan2 A) (k6_flang_1 A B C) (k6_flang_1 A B D)) (k6_flang_1 A B (k7_subset_1 (k3_catalan2 A) C D))) & (r1_tarski (k7_subset_1 (k3_catalan2 A) (k6_flang_1 A C B) (k6_flang_1 A D B)) (k6_flang_1 A (k7_subset_1 (k3_catalan2 A) C D) B))) ) ) ) ) ) ) ) ).
tt(t21_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_flang_2 A B C D) = k1_xboole_0)  <=>  (~  ((r1_xxreal_0 C D) &  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_tarski B (k1_flang_3 A C E)) & (r1_tarski D (k1_flang_3 A C F)))  => (r1_tarski (k6_flang_1 A B D) (k1_flang_3 A C (k2_xcmplx_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) & (v1_partfun1 B A)) )  => (r1_relset_1 A A (k6_partfun1 A) (k3_relat_1 B (k2_relat_1 B)))) ) ) ).
tt(t21_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v13_fomodel1 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  ((k1_funct_1 (k10_fomodel2 A B D) C) = (k1_funct_1 (k4_fomodel2 A B D (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k15_fomodel1 A) (k22_fomodel1 A) C)) (k3_relat_1 (k33_fomodel1 A C) (k10_fomodel2 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t21_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v1_orders_4 B) &  ((v11_fomodel1 B) & (l1_fomodel1 B)) ) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( ((r1_tarski A (k33_fomodel2 B)) & (v13_fomodel2 C A B))  => (v18_fomodel4 C A B)) ) ) ) ) ) ).
tt(t21_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_frechet A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k1_frechet2 A (k1_struct_0 A)) = k1_xboole_0)  &  ((r1_tarski B (k1_frechet2 A B)) &  ( ((k1_frechet2 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k1_frechet2 A B) (k1_frechet2 A C)))  &  ((k1_frechet2 A (k1_frechet2 A B)) = (k1_frechet2 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_frechet,ax,(v1_frechet k3_topmetr)).
tt(t21_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_msualg_1 D))  =>  ( (D = (k8_fscirc_1 A B C))  =>  ((r2_hidden A (u1_struct_0 D)) &  ((r2_hidden B (u1_struct_0 D)) & (r2_hidden C (u1_struct_0 D))) ) ) ) ) ) ) ) ).
tt(t21_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  ((k2_msafree2 (k1_fscirc_2 A B C)) = (k2_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t21_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r6_fsm_1 A B C D D E)) ) ) ) ) ) ) ) ) ) ).
tt(t21_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_2 D A B))  =>  ((r2_fsm_2 A C D) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ( ((r3_fsm_2 A B D C E) & (r3_fsm_2 A B D C F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A B))  =>  ((k6_fsm_3 A B C) = (k5_fsm_3 A B C (u1_fsm_3 A B C))) ) ) ) ) ) ) ).
tt(t21_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_msafree2 (k13_ftacell1 A B C D E)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k36_gfacirc1 A B C)) (k2_enumset1 (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k33_gfacirc1 A B C))) (k2_tarski (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1) (k24_gfacirc1 (k36_gfacirc1 A B C) E D))) (k2_enumset1 (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1) (k4_tarski (k10_finseq_1 E D) k3_twoscomp) (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp) (k21_gfacirc1 (k36_gfacirc1 A B C) E D)))) ) ) ) ) ) ).
tt(t21_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 D) = (k9_xtuple_0 (k3_funcop_1 C A B)))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 (k3_funcop_1 C A B))) =>  ((k1_funct_1 D E) = (k1_binop_1 C (k1_funct_1 A E) (k1_funct_1 B E))) ) ) )  =>  (D = (k3_funcop_1 C A B)) ) ) ) ) ) ) ) ) ) ).
tt(t21_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ( (C = (k2_tarski A B))  &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k1_numbers (k9_funct_2 C k1_numbers)) =>  (? [F:$i] :  ((m2_funct_2 F C k1_numbers (k9_funct_2 C k1_numbers)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~ (r2_funct_2 C k1_numbers F (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k3_relat_1 C (k4_relat_1 B)))) <=>  ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t21_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ((v2_funct_1 C) <=>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E D A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D A)))) )  =>  ((r2_relset_1 D B (k1_partfun1 D A A B E C) (k1_partfun1 D A A B F C)) => (r2_relset_1 D A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k3_funct_3 B))) =>  ((k1_funct_1 (k3_funct_3 B) A) = (k8_relat_1 B A)) ) ) ) ) ).
tt(t21_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_funct_4 A k1_xboole_0) = A) ) ) ).
tt(t21_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) (k9_xtuple_0 C)) =>  ((r2_hidden B (k9_xtuple_0 (k3_funct_5 C))) &  ((v1_relat_1 (k1_funct_1 (k3_funct_5 C) B)) & (v1_funct_1 (k1_funct_1 (k3_funct_5 C) B))) ) ) ) ) ) ) ).
tt(t21_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A (k1_funct_6 B)) =>  ((k1_funct_6 A) = A) ) ) ) ).
tt(t21_funct_7,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (? [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski D C) =>  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(t21_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k55_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t21_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k16_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) ) ).
tt(t21_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B C C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 B C C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_functor0 A B (k9_functor0 A B C D) E) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) &  ((v1_altcat_2 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) &  ((v1_altcat_2 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) &  ((v1_altcat_2 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ( ((v8_functor0 E B C) & (l2_functor0 E B C))  =>  (! [F:$i] :  ( ((v8_functor0 F B A) & (l2_functor0 F B A))  =>  (! [G:$i] :  ( ((v8_functor0 G C B) & (l2_functor0 G C B))  =>  ( ((v21_functor0 E B C) &  ((v21_functor0 D A B) &  ( ((g2_functor0 B A (u1_functor0 B A F) (u2_functor0 B A F)) = (k15_functor0 A B D))  &  ((g2_functor0 C B (u1_functor0 C B G) (u2_functor0 C B G)) = (k15_functor0 B C E)) ) ) )  =>  ((k15_functor0 A C (k13_functor0 A B C D E)) = (k13_functor0 C B A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C B A) & (m2_functor0 C B A))  =>  (! [D:$i] :  ( ((v15_functor0 D B A) & (m2_functor0 D B A))  =>  (! [E:$i] :  ((m1_functor2 E B A C D) =>  ((r1_functor2 B A C D) => (r8_pboole (u1_struct_0 B) (k6_functor3 B B A C D (k12_functor0 B) E) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 D E))  => (r1_fuzzy_1 (k2_fuzzy_1 A B D) (k2_fuzzy_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A (k1_fuzzy_1 A B C) (k3_fuzzy_1 A (k2_fuzzy_1 A B C))) (k3_fuzzy_1 A (k6_fuzzy_1 A B C)))) ) ) ) ) ) ).
tt(t21_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k2_zfmisc_1 A B)) =>  ( ((k1_seq_1 (k4_fuzzy_2 A B) (k4_tarski C D)) = k6_numbers)  &  ((k1_seq_1 (k5_fuzzy_2 A B) (k4_tarski C D)) = 1) ) ) ) ) ) ) ) ) ).
tt(t21_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ( (B = (k4_struct_0 A))  |  ((k3_funct_2 (u1_struct_0 A) k7_numbers C (k11_algstr_0 A B)) = (k2_supinf_2 (k3_funct_2 (u1_struct_0 A) k7_numbers C B))) ) ) ) ) ) ) ) ) ).
tt(t21_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_algstr_1 B) &  ((v2_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k4_fvsum_1 A B C (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = C)  &  (C = (k4_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)) C)) ) ) ) ) ) ) ) ).
tt(t21_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ( (~ (v1_xboole_0 (k15_gate_1 A B C D)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) & (v1_xboole_0 D)) ) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) & (v1_xboole_0 D)) ) ) )  & (v1_xboole_0 (k15_gate_1 A B C D))) ) ) ) ) ) ) ).
tt(t21_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k3_gcd_1 A)) & (v1_xboole_0 B)) ) ) ) ) ) ).
tt(t21_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((r1_xxreal_0 (k3_finseq_1 E) A) & (r1_xxreal_0 (k3_finseq_1 E) B))  =>  ((k9_genealg1 D E F A B C) = (k7_genealg1 D E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_geomtrap A F G B C D E) => (r2_geomtrap A F G D E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k2_twoscomp)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k2_twoscomp)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) ) )  =>  ((k1_twoscomp (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) (k6_circuit2 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D) (k9_gfacirc1 A B C)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((k5_gfacirc2 (k1_nat_1 A 1) B C) = (k2_circcomb (k5_gfacirc2 A B C) (k25_gfacirc1 (k1_funct_1 B (k1_nat_1 A 1)) (k1_funct_1 C (k1_nat_1 A 1)) (k7_gfacirc2 A B C))))  &  ( ((k6_gfacirc2 (k1_nat_1 A 1) B C) = (k3_circcomb (k5_gfacirc2 A B C) (k25_gfacirc1 (k1_funct_1 B (k1_nat_1 A 1)) (k1_funct_1 C (k1_nat_1 A 1)) (k7_gfacirc2 A B C)) (k6_gfacirc2 A B C) (k26_gfacirc1 (k1_funct_1 B (k1_nat_1 A 1)) (k1_funct_1 C (k1_nat_1 A 1)) (k7_gfacirc2 A B C))))  &  ((k7_gfacirc2 (k1_nat_1 A 1) B C) = (k21_gfacirc1 (k1_funct_1 B (k1_nat_1 A 1)) (k1_funct_1 C (k1_nat_1 A 1)) (k7_gfacirc2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t21_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t21_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 (k6_glib_001 A B)))  &  ( ((k1_relset_1 k5_numbers B) = (k1_relset_1 k5_numbers (k6_glib_001 A B)))  &  ((k2_relset_1 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) B) = (k2_relset_1 (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k6_glib_001 A B))) ) ) ) ) ) ) ).
tt(t21_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( (C = D)  => (r1_tarski (k2_glib_002 B D) (k2_glib_002 A C))) ) ) ) ) ) ) ) ) ).
tt(t21_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v3_glib_001 B A) =>  ((k10_glib_003 A B) = k6_numbers) ) ) ) ) ) ).
tt(t21_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)))) = (k6_nat_1 (k1_nat_1 C 1) (k5_card_1 (k2_glib_002 A B)))) ) ) ) ) ) ) ).
tt(t21_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) E B))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) E D))) &  ((r2_hidden C (k4_finseq_1 A)) &  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 E))) & (r2_hidden D (k4_finseq_1 E))) ) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 E) 1) | (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 E B) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k1_matrix_1 C) A) |  ((r1_xxreal_0 (k3_finseq_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B (k2_nat_1 A 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) (k2_nat_1 A 1))) (k3_goboard5 C B A))) ) ) ) ) ) ) ) ) ).
tt(t21_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) k6_numbers)) = (a_1_6_goboard6 A)) ) ) ).
tt(t21_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k1_matrix_1 A))) ) ) ) ) ) )  =>  ((r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) |  ( ( (B = D)  |  (B = (k2_nat_1 D 1)) )  &  ( (C = E)  |  ((k2_nat_1 C 1) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1)) (k17_euclid C))) ) ) )  => (r1_xboole_0 B (k3_topreal1 2 A))) ) ) ) ) ).
tt(t21_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (r1_tarski (k1_tops_1 (k15_euclid 2) (k5_goboard5 A B)) (k2_goboard9 A))) ) ) ) ) ).
tt(t21_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v3_goboard1 A) =>  ((k2_goboard5 A k6_numbers) = (a_1_11_gobrd11 A)) ) ) ) ).
tt(t21_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((k3_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k2_pre_topc (k15_euclid 2) (k3_goboard9 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard9 A) (k3_topreal1 2 A))) ) ) ).
tt(t21_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden C B) => (r1_henmodel A B C)) ) ) ) ) ) ) ).
tt(t21_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_graph_1 D))  =>  ( ((r4_graph_1 A B) &  ((r4_graph_1 C B) & (r1_graph_1 D A C)) )  => (r4_graph_1 D B)) ) ) ) ) ) ) ) ) ).
tt(t21_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v1_graph_2 A) & (v2_graph_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v1_graph_2 B) & (v2_graph_2 B)) ) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 B)) )  =>  ( (A = B)  |  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] : (r1_tarski (k3_graph_3 A B C) (k6_graph_3 A B))) ) ) ) ) ).
tt(t21_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  (~  ((r3_graph_4 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ( ((v7_graph_1 F A) &  ((v3_graph_2 F A) & (m2_graph_1 F A)) )  =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (~  ( ((k15_finseq_1 D) = F)  &  ( ((k15_finseq_1 E) = G)  &  ((r3_graph_4 A G F) &  ( ((k1_funct_1 B 1) = (k1_funct_1 G 1))  &  ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 G (k3_finseq_1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  ((r1_tarski (k10_xtuple_0 B) (k10_xtuple_0 C)) => (r1_tarski (k2_graph_5 A B) (k2_graph_5 A C))) ) ) ) ) ) ) ).
tt(t21_graphsp,ax, (! [A:$i] :  ((m2_funct_2 A (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k4_graphsp (k3_finseq_2 k1_numbers) (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) k6_numbers) B) = B) ) ) ) ) ) ) ) ) ).
tt(t21_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ((v1_grcat_1 E) & (m1_grcat_1 E A B))  =>  (! [F:$i] :  ( ((v1_grcat_1 F) & (m1_grcat_1 F B C))  =>  (! [G:$i] :  ( ((v1_grcat_1 G) & (m1_grcat_1 G C D))  =>  ((k14_grcat_1 A C D G (k14_grcat_1 A B C F E)) = (k14_grcat_1 A B D (k14_grcat_1 B C D G F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  ((v1_int_2 (k7_group_1 A)) =>  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) ) ) ).
tt(t21_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  ( ((k7_group_1 A) = 2)  =>  ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) ) ) ).
tt(t21_gr_cy_3,ax, ((k1_gr_cy_3 7) = 127) ).
tt(t21_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (A = k1_xboole_0)  =>  ((k2_funct_1 A) = k1_xboole_0) ) ) ) ).
tt(t21_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v1_grnilp_1 A) <=>  (? [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_xcmplx_0 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  =>  ( ( (D = (k1_funct_1 B C))  &  (E = (k1_funct_1 B (k2_xcmplx_0 C 1))) )  =>  ((m1_group_6 E A D) & (m1_group_6 (k1_grnilp_1 A D (k7_group_2 A)) A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r2_groeb_1 A B C D E) => (m2_rewrite1 (k3_polyred A B C D) (k3_polyred A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r8_pboole (k15_pre_poly A) (k3_groeb_2 A B C D E) (k7_polynom1 A C)) | (r2_termord A B (k3_termord A B C (k3_groeb_2 A B C D E)) (k2_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k3_groeb_3 A B C D k6_numbers) = k1_xboole_0)  &  ((k4_groeb_3 A B C D k6_numbers) = (k2_polynom1 (k15_pre_poly A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t21_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((r1_tarski B C) => (r1_tarski (k1_group_11 A B D) (k1_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  => (r3_binop_1 (u1_struct_0 A) (k1_group_1 A) (u2_algstr_0 A))) ) ).
tt(t21_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k2_group_2 A (k7_domain_1 (u1_struct_0 A) B C) (k7_domain_1 (u1_struct_0 A) D E)) = (k9_domain_1 (u1_struct_0 A) (k6_algstr_0 A B D) (k6_algstr_0 A B E) (k6_algstr_0 A C D) (k6_algstr_0 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_group_3 A B (k2_group_1 A B)) = B)  &  ((k2_group_3 A (k2_group_1 A B) B) = (k2_group_1 A B)) ) ) ) ) ) ).
tt(t21_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k4_group_4 A (k6_finseq_1 k4_numbers) (k6_finseq_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ).
tt(t21_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_group_5 A B (k2_group_1 A B)) = (k1_group_1 A))  &  ((k2_group_5 A (k2_group_1 A B) B) = (k1_group_1 A)) ) ) ) ) ) ).
tt(t21_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_group_6 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (C = (k13_group_2 A B D))  &  (C = (k14_group_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t21_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((v1_relat_1 (k10_finseq_1 A B)) &  ((v4_relat_1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_funct_1 (k10_finseq_1 A B)) &  ((v1_partfun1 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v1_group_7 (k10_finseq_1 A B)) &  ((v2_group_7 (k10_finseq_1 A B) (k2_tarski 1 2)) &  ((v3_group_7 (k10_finseq_1 A B) (k2_tarski 1 2)) & (v4_group_7 (k10_finseq_1 A B) (k2_tarski 1 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((v8_struct_0 A) =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (! [E:$i] :  ((m1_group_2 E C) =>  ( (E = (k10_group_2 B C D))  =>  (! [F:$i] :  ((m1_group_2 F D) =>  ( (F = (k10_group_2 B C D))  =>  (! [G:$i] :  ((m1_group_2 G B) =>  ( ( (G = (k10_group_2 B C D))  & (r1_int_2 (k18_group_2 B C) (k18_group_2 B D)))  =>  ( ((k18_group_2 B D) = (k18_group_2 C E))  &  ((k18_group_2 B C) = (k18_group_2 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ( ((k17_group_9 A B (k4_group_9 A B) C) = (k4_group_9 A B))  &  ((k17_group_9 A B C (k4_group_9 A B)) = (k4_group_9 A B)) ) ) ) ) ) ) ).
tt(t21_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_group_3 C B) & (m1_group_2 C B))  =>  (! [D:$i] :  ( ((v1_group_3 D B) & (m1_group_2 D B))  =>  (~  ((v2_group_10 C A) &  ((v2_group_10 D A) &  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E B) & (m1_group_2 E B)) )  =>  (~  ( ((u1_struct_0 E) = (k7_group_4 B C D))  & (v2_group_10 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v5_hahnban1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_vectsp_1 k1_complfld A (k1_hahnban1 k6_numbers D) C)) = (k8_real_1 D (k3_funct_2 (u1_struct_0 A) k1_numbers B (k4_vectsp_1 k1_complfld A k2_hahnban1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) &  ((v2_hahnban C B) &  ((v3_hahnban C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D))))) =>  ( (D = E)  =>  ((r1_struct_0 B D) |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) k1_numbers) &  ((v2_hahnban G (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) &  ((v3_hahnban G (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) k1_numbers)))) ) ) )  &  ( ((k2_partfun1 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) k1_numbers G (u1_struct_0 B)) = C)  &  ((k3_funct_2 (u1_struct_0 (k1_rlsub_2 A B (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) D)))) k1_numbers G E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((r2_hidden C (k4_finseq_1 B)) => (m2_hallmar1 (k2_hallmar1 A B C D) A B)) ) ) ) ) ) ) ) ).
tt(t21_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v2_compts_1 B (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r1_xxreal_0 (k4_metric_1 A D C) (k1_funct_1 (k5_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v7_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  ( ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((r1_xxreal_0 D (k3_finseq_1 C)) &  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  ((r1_xxreal_0 E D) =>  ((k1_funct_1 B E) = (k1_funct_1 C E)) ) ) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E D))  =>  ((k1_funct_1 B E) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A (k5_hahnban1 k1_complfld A B C)) (k5_hahnban1 k1_complfld A (k1_hermitan A B) (k1_hermitan A C)))) ) ) ) ) ) ).
tt(t21_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k10_normform A B (k6_heyting1 A B)) = k1_xboole_0) ) ) ) ).
tt(t21_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  ((v1_finset_1 C) =>  (! [D:$i] :  ((r2_hidden D (k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) C)) =>  (D = C) ) ) ) ) ) ) ) ) ).
tt(t21_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (~  ((r2_hidden C (k4_heyting3 (k2_nat_1 A 1) B)) &  (! [D:$i] :  (~  ((r2_hidden D (k4_heyting3 A B)) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_taylor_1 D B C) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers D A) C) B) (k26_valued_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 D C) B) A))) ) ) ) ) ) ) ) ) ).
tt(t21_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_xxreal_0 (k1_algseq_1 A (k11_polynom3 A B C)) (k7_nat_d (k2_nat_1 (k1_algseq_1 A B) (k1_algseq_1 A C)) 1))) ) ) ) ) ) ).
tt(t21_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k3_hilbert1 B C) (k3_hilbert1 A C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t21_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k1_hilbert2 A) = (k1_hilbert2 B))  =>  (A = B) ) ) ) ) ) ).
tt(t21_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r1_tarski (k10_xtuple_0 (k15_pralg_1 D E)) C)) ) ) ) ) ) ) ) ).
tt(t21_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k2_hurwitz A B) = (k2_hurwitz A C)) )  =>  ((k2_hurwitz A (k2_normsp_1 A B C)) = (k4_xxreal_0 (k2_hurwitz A B) (k2_hurwitz A C))) ) ) ) ) ) ) ) ).
tt(t21_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k9_idea_1 C A B) = (k9_idea_1 C B A)) ) ) ) ) ) ) ).
tt(t21_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_subset_1 B (u1_struct_0 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v1_gcd_1 C A) & (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t21_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A B E) &  ((r3_incsp_1 A C E) & (r3_incsp_1 A D E)) ) ) ) )  &  ( (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r1_incsp_1 A E B) &  ((r1_incsp_1 A E C) & (r1_incsp_1 A E D)) ) ) )  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  ((k13_index_1 A C (k9_index_1 A B C)) = B) ) ) ) ) ) ) ).
tt(t21_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ( ((g3_msualg_1 B (u3_msualg_1 B C) (u4_msualg_1 B C)) = (g3_msualg_1 B (u3_msualg_1 B D) (u4_msualg_1 B D)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r3_pua2mss1 A B E F) =>  ((k1_instalg1 A B C E F) = (k1_instalg1 A B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) <=> (r2_int_1 (k2_xcmplx_0 A C) B C)) ) ) ) ) ) ) ).
tt(t21_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (r1_int_1 (k3_int_2 A B) A)) ) ) ) ).
tt(t21_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((v1_int_2 B) &  ((r1_int_2 B C) & (r1_nat_d B (k4_nat_d C (k1_newton B A)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ((k3_int_2 A B) = 1)  =>  ((r1_xxreal_0 B 2) |  ((r1_int_5 A B) |  ((k6_int_1 (k2_xcmplx_0 (k1_newton A (k3_nat_d (k7_nat_d B 1) 2)) 1) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t21_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_int_2 C D) &  ((r2_int_1 A B C) & (r2_int_1 A B D)) )  => (r2_int_1 A B (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t21_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( ((k1_group_1 (k3_int_7 A)) = 1)  &  ((k1_group_1 (k3_int_7 A)) = (k5_struct_0 (k9_int_3 A))) ) ) ) ).
tt(t21_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 k6_numbers (k8_real_1 2 k32_sin_cos)))  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) k19_sin_cos)) = k6_numbers) ) ) ) ) ) ).
tt(t21_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r1_tarski D (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))))))) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k1_sin_cos6) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k1_sin_cos6) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos) (k41_valued_1 k1_numbers k1_numbers k19_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k24_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t21_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos) (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos (k41_valued_1 k1_numbers k1_numbers k19_sin_cos)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k24_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t21_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ((r2_hidden C (k1_relset_1 B (k7_integr15 A B D E))) =>  ((k7_partfun1 (k1_euclid A) (k7_integr15 A B D E) C) = (k7_euclid A (k7_partfun1 (k1_euclid A) D C) (k7_partfun1 (k1_euclid A) E C))) ) ) ) ) ) ) ) ) ) ).
tt(t21_integr16,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) &  ((r1_integr16 B C) & (v1_comseq_2 (k2_partfun1 k1_numbers k2_numbers C B))) )  =>  ((r1_integr16 B (k25_valued_1 k1_numbers k2_numbers C A)) &  ((k7_integr16 B (k25_valued_1 k1_numbers k2_numbers C A)) = (k5_binop_2 A (k7_integr16 B C))) ) ) ) ) ) ) ) ) ).
tt(t21_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid C)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers D)) &  ((r1_integr15 C (k3_integra5 A B) D) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 C k1_numbers D)) & (v3_integr15 (k2_partfun1 k1_numbers (k1_euclid C) D (k3_integra5 A B)) C)) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 A B C D)) (k4_integra5 A B (k1_nfcont_4 C k1_numbers D)))) ) ) ) ) ) ) ) ) ).
tt(t21_integra1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k1_seq_1 C D) = (k7_real_1 (k7_partfun1 k1_numbers A D) (k7_partfun1 k1_numbers B D))) ) ) ) ) )  =>  ((k18_rvsum_1 C) = (k7_real_1 (k18_rvsum_1 A) (k18_rvsum_1 B))) ) ) ) ) ) ) ) ).
tt(t21_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 k6_numbers A))  => (r1_xxreal_0 (k1_seq_1 (k9_integra1 B (k26_valued_1 B k1_numbers C A)) D) (k8_real_1 (k8_real_1 A (k4_seq_4 (k1_rvsum_1 C))) (k3_integra1 B)))) ) ) ) ) ) ) ) ) ).
tt(t21_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v1_fdiff_1 (k2_integra3 A C) k6_numbers) & (v2_relat_1 (k2_integra3 A C))) )  =>  ( ((k3_integra1 A) = k6_numbers)  |  ((v2_comseq_2 (k3_integra2 A B C)) &  ((k2_seq_2 (k3_integra2 A B C)) = (k10_integra1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t21_integra4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k19_rfunct_3 A B) (k18_rfunct_3 A (k32_valued_1 A k1_numbers B)))) ) ) ) ).
tt(t21_integra5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r2_fdiff_1 B D) &  ((r2_fdiff_1 C D) &  ((r1_tarski A D) &  ((r1_integra5 A (k2_fdiff_1 B D)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 B D) A)) &  ((r1_integra5 A (k2_fdiff_1 C D)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 C D) A))) ) ) ) ) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B D) C)) = (k9_real_1 (k9_real_1 (k8_real_1 (k1_seq_1 B (k4_seq_4 A)) (k1_seq_1 C (k4_seq_4 A))) (k8_real_1 (k1_seq_1 B (k5_seq_4 A)) (k1_seq_1 C (k5_seq_4 A)))) (k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k2_fdiff_1 C D))))) ) ) ) ) ) ) ) ) ) ).
tt(t21_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) )  =>  ((r1_tarski (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)) (k9_xtuple_0 (k56_valued_1 k1_numbers k1_numbers E))) &  ((r1_integra5 (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)) (k56_valued_1 k1_numbers k1_numbers E)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers E) (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)))) & (r1_xxreal_0 (k18_complex1 (k4_integra5 C D E)) (k4_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D) (k56_valued_1 k1_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) C) &  ((r1_integra5 (k3_integra5 A B) D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B))) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski C (k1_relset_1 k1_numbers D)) &  ((r1_tarski C (k1_relset_1 k1_numbers E)) &  ((r1_integra7 C F D) & (r1_integra7 C G E)) ) ) ) ) ) ) ) )  =>  ((k9_real_1 (k8_real_1 (k1_seq_1 F B) (k1_seq_1 G B)) (k8_real_1 (k1_seq_1 F A) (k1_seq_1 G A))) = (k7_real_1 (k4_integra5 A B (k20_valued_1 k1_numbers k1_numbers k1_numbers D G)) (k4_integra5 A B (k20_valued_1 k1_numbers k1_numbers k1_numbers F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_fdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k32_valued_1 k1_numbers k1_numbers A)) &  ((v2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A)) & (m1_subset_1 (k32_valued_1 k1_numbers k1_numbers A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ).
tt(t21_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 D k1_numbers (k20_valued_1 D k1_numbers k1_numbers (k1_integra5 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) D) (k1_integra5 C D)) (k1_integra5 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) D))) ) ) ) ) ) ) ) ).
tt(t21_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  => (r1_interva1 A (k4_interva1 A B C) (k4_interva1 A C B))) ) ) ) ) ) ).
tt(t21_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 B B)) k8_intpro_1)) ) ) ) ).
tt(t21_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((v1_series_1 (k3_irrat_1 A)) &  ( ((k4_series_1 (k3_irrat_1 A)) = (k3_power (k2_xcmplx_0 1 (k13_complex1 1 A)) A))  &  ((k4_series_1 (k3_irrat_1 A)) = (k1_seq_1 k4_irrat_1 A)) ) ) ) ) ) ).
tt(t21_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r1_nattra_1 A B D E) =>  (! [F:$i] :  ((m1_nattra_1 F A B D E) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k4_nattra_1 A C (k9_cat_1 A B C D G) (k9_cat_1 A B C E G) (k2_isocat_1 A B C D E F G) H) = (k9_cat_3 B (k8_cat_1 A B D H) (k8_cat_1 A B E H) C G (k4_nattra_1 A B D E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (m2_cat_1 (k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) E) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 (k1_isomichi A B) A) &  ( ((k1_isomichi A B) = (k7_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A B)) (k2_pre_topc A (k1_tops_1 A B))))  &  ((k1_isomichi A B) = (k9_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A B)) (k1_tops_1 A (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ).
tt(t21_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_jgraph_1 (u1_struct_0 (k15_euclid 2)) A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1)))  &  ( ((k1_funct_1 A D) = (k1_funct_1 B C))  &  ((k1_funct_1 A (k2_nat_1 D 1)) = (k1_funct_1 B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k6_xcmplx_0 F G)) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jgraph_3,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A k1_jgraph_3) & (v5_pre_topc A (k15_euclid 2) (k15_euclid 2))) ) ) ).
tt(t21_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid D) (k12_euclid D)) A) (k9_real_1 1 A)))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k17_euclid D) k6_numbers) &  ((r1_xxreal_0 A (k13_complex1 (k18_euclid D) (k12_euclid D))) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t21_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 k6_numbers (k18_euclid B)) & (r1_xxreal_0 k6_numbers (k18_euclid C)))  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  ( ((k12_euclid B) = k6_numbers)  |  ( ((k12_euclid C) = k6_numbers)  |  ((r1_xxreal_0 (k10_real_1 (k17_euclid C) (k12_euclid C)) (k10_real_1 (k17_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) C))  & (r1_xxreal_0 (k10_real_1 (k17_euclid E) (k12_euclid E)) (k10_real_1 (k17_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  (~ (v3_tops_2 C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) )  | (v1_topreal2 B)) ) ) ) ) ) ).
tt(t21_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid C) H)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan10,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k6_setfam_1 (u1_struct_0 (k15_euclid 2)) (k4_jordan10 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan2c 2 A))) ) ) ).
tt(t21_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (v1_convex1 (k5_goboard5 A B) (k15_euclid 2))) ) ) ) ) ).
tt(t21_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_jordan1h A B) => (r1_tarski (k3_topreal1 2 (k1_jordan13 A B)) (k1_jordan2c 2 A))) ) ) ) ) ).
tt(t21_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r1_jordan5c A B C D E))  =>  ( (D = E)  | (r1_topreal1 (k15_euclid 2) D E (k5_jordan6 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B E C D) & (r1_jordan17 A E B C D))  =>  ( (B = C)  |  ( (B = D)  |  ( (E = D)  |  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k1_jordan18 A B) (k2_jordan18 A B)))) ) ) ) ).
tt(t21_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_matrix_1 B))) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A)) (k6_pscomp_1 (k3_topreal1 2 C)))) ) ) ) ) ) ) ).
tt(t21_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_1_jordan1 A))  => (v3_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t21_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 A)) &  ((r2_hidden E (k3_goboard5 A (k3_finseq_1 A) B)) &  ((k17_euclid E) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 A) B) |  ((k3_finseq_1 A) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) &  ((k18_euclid A) = (k9_pscomp_1 (k1_jordan2c 2 B))) ) ) ) ) ) ) ).
tt(t21_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A)))) ) ) ) ) ) ) ) ) ).
tt(t21_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan9 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) )  =>  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k2_nat_1 C 1))) = (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t21_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_xxreal_0 (k4_finseq_4 (k1_jordan1e B A) (k19_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k1_jordan1e B A) (k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ).
tt(t21_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  =>  ((k3_gobrd13 B (k2_goboard2 B) A) = (k5_goboard5 B A)) ) ) ) ) ) ).
tt(t21_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k18_pscomp_1 (k3_topreal1 2 A)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D (k2_nat_1 E 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k18_pscomp_1 B) A))  =>  ((k18_pscomp_1 A) = (k18_pscomp_1 B)) ) ) ) ) ) ).
tt(t21_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k1_topreal6 2 (k3_rlvect_1 (k15_euclid 2) A B) (k3_rlvect_1 (k15_euclid 2) C B)) = (k1_topreal6 2 A C)) ) ) ) ) ) ) ).
tt(t21_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r2_hidden D A))  =>  ( (C = D)  | (r1_topreal1 (k15_euclid 2) D C (k5_jordan6 A B C D C))) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))  &  (~ (v1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) ) ) ) ).
tt(t21_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k1_jordan21 (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ) ).
tt(t21_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (r1_tarski (k3_topreal1 2 (k2_jordan3 A B)) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t21_jordan2b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_rlvect_1 (k15_euclid 1) (k1_jordan2b A) B) = (k1_jordan2b (k8_real_1 B A))) ) ) ) ) ).
tt(t21_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (m1_connsp_3 (k2_jordan2c A B) (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B)))) ) ) ) ).
tt(t21_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) )  =>  ( (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1)))  |  ((k2_nat_1 (k1_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) B) (k1_jordan3 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ) ).
tt(t21_jordan4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k1_jordan4 (k7_nat_d (k3_finseq_1 A) 1) A) = (k7_nat_d (k3_finseq_1 A) 1)) ) ) ).
tt(t21_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xboole_0 A B))  &  ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)) &  ((r1_topreal1 (k15_euclid 2) C D A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ( ((k1_funct_1 F G) = E)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers H) &  ( (~ (r1_xxreal_0 G H))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (v2_funct_1 A))  =>  ((k4_jordan3 A B B) = (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)) ) ) ) ) ) ).
tt(t21_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((v4_topreal1 A) & (r2_hidden (k1_jordan5c (k3_topreal1 2 A) (k2_topreal1 2 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A B))) ) )  =>  ((k1_jordan5c (k3_topreal1 2 A) (k2_topreal1 2 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) ) ) ) ) ) ).
tt(t21_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_1_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k16_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k16_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t21_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k3_jordan6 A B C B) = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t21_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C)) &  ((r2_hidden D (k16_matrix_1 C)) & (r2_hidden D (k3_goboard5 C A B))) ) ) ) )  => (r1_sppol_1 2 D (k3_goboard5 C A B))) ) ) ) ) ) ) ) ) ).
tt(t21_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) A)) ) ) ) ) ) ) ).
tt(t21_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k2_topreal9 C D A) (k1_topreal9 C D B))) ) ) ) ) ) ) ) ) ).
tt(t21_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_abian (u1_struct_0 A) C B)) ) ) ) ) ) ).
tt(t21_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ((k4_kurato_0 A B) = (k1_kurato_0 A B)) ) ) ) ) ).
tt(t21_kurato_1,ax, ((k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)))))) = (k4_rcomp_1 k2_xxreal_0 4)) ).
tt(t21_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  &  ((v3_toprns_1 D A) &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden (k3_funct_2 k5_numbers (u1_struct_0 (k15_euclid A)) D E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))) B E))) )  &  (C = (k6_toprns_1 A D)) ) ) ) )  => (r2_hidden C (k1_kurato_2 (k15_euclid A) B))) ) ) ) ) ) ) ).
tt(t21_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 1))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 (k1_nat_1 A 1))) &  ((k1_funct_1 B E) = F) )  =>  ((k14_matrix_2 C (k1_nat_1 A 1) D B) = (k8_group_1 C (k1_laplace C (k4_group_1 C) (k4_algstr_0 C (k1_group_1 C)) (k2_xcmplx_0 E F)) (k14_matrix_2 C A D (k4_laplace E A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_group_3 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_group_3 A))))  =>  ( (C = (k1_tarski B))  =>  ((k2_latsubgr A C) = B) ) ) ) ) ) ) ) ).
tt(t21_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  (! [D:$i] :  ( ( ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) & (r2_hidden D (u1_struct_0 A))) )  => (r2_hidden C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t21_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  => (r6_binop_1 (u1_struct_0 A) (u2_lattices A) (u1_lattices A))) ) ) ).
tt(t21_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattice3 A B (k7_domain_1 (u1_struct_0 A) C D)) <=> (r3_lattices A B (k4_lattices A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_lattice4 A (k5_setwiseo (u1_struct_0 A) B (k2_setwiseo (u1_struct_0 A) C))) = (k4_lattices A (k2_lattice4 A B) C)) ) ) ) ) ) ) ).
tt(t21_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_lattice5 A k1_xboole_0) = A) ) ) ).
tt(t21_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_lattice6 B A) => (v4_lattice6 B A)) ) ) ) ) ).
tt(t21_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r1_ordinal1 C D) => (r1_tarski (k3_lattice8 A C) (k3_lattice8 A D))) ) ) ) ) ) ) ) ) ).
tt(t21_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattices A (k7_lattices A B) B) = (k6_lattices A)) ) ) ) ) ).
tt(t21_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (r1_xxreal_0 (k39_glib_000 B) D))  &  ( (~ (r1_xxreal_0 C D))  &  (~  ((r2_hidden (k6_lexbfs A B D) (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) &  ((k1_recdef_1 (k5_lexbfs A B C) (k6_lexbfs A B D)) = (k7_nat_d (k39_glib_000 B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_lfuzzy_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_lfuzzy_0 A))) =>  ((k12_lattice3 (k4_lfuzzy_0 A) B C) = (k1_fuzzy_1 A (k5_lfuzzy_0 A B) (k5_lfuzzy_0 A C))) ) ) ) ) ) ) ).
tt(t21_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( ((v2_lfuzzy_1 C A) & (r1_fuzzy_1 C B))  => (r1_fuzzy_1 C (k1_lfuzzy_1 (k2_zfmisc_1 A A) B (k2_fuzzy_4 A A B)))) ) ) ) ) ) ) ).
tt(t21_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k1_real_1 B)) ) )  => (v2_limfunc1 A)) ) ) ).
tt(t21_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r2_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r2_limfunc2 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r3_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r3_limfunc2 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r3_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ((r3_limfunc2 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r2_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  ( (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))))  &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) ) ) )  | (r2_limfunc3 B A)) ) ) ) ) ) ).
tt(t21_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r5_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_seq_1 B E) (k1_limfunc2 B A))) ) ) ) ) ) ) )  | (r2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t21_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 A B C) => (r1_lmod_6 A B (k2_vectsp_4 A C))) ) ) ) ) ) ) ).
tt(t21_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k18_lmod_7 A B E C) = (k18_lmod_7 A B E D))  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k4_struct_0 B)) ) )  => (v2_lopban_1 C A B)) ) ) ) ) ) ) ).
tt(t21_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k7_lopban_2 A)) = (k6_lopban_2 A)) ) ) ).
tt(t21_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A C D) = (k1_normsp_1 A B k6_numbers)) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k1_valued_0 (u1_struct_0 A) B 1)) (k3_normsp_1 A (k1_valued_0 (u1_struct_0 A) (k1_bhsp_4 A B) 1) C))) ) ) ) ) ) ) ).
tt(t21_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) k6_numbers) = (k5_struct_0 A))  &  ((k8_nat_1 (u1_struct_0 A) (k5_lopban_4 k6_numbers A B C) k6_numbers) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t21_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_funct_1 (k8_lopclset A) (k3_lattices A B C)) = (k2_xboole_0 (k1_funct_1 (k8_lopclset A) B) (k1_funct_1 (k8_lopclset A) C))) ) ) ) ) ) ) ).
tt(t21_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_rfunct_3 C B k1_numbers (k3_rfunct_3 B k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D B k1_numbers (k3_rfunct_3 B k1_numbers)) =>  ((k2_lpspace1 B k1_numbers (k3_lpspace1 B) (k2_binop_1 k1_numbers (k3_rfunct_3 B k1_numbers) (k3_rfunct_3 B k1_numbers) (k4_lpspace1 B) A C) D) = (k2_binop_1 k1_numbers (k3_rfunct_3 B k1_numbers) (k3_rfunct_3 B k1_numbers) (k4_lpspace1 B) A (k2_lpspace1 B k1_numbers (k3_lpspace1 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t21_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k4_power (k18_complex1 (k7_real_1 A B)) C) (k8_real_1 (k4_power 2 C) (k7_real_1 (k4_power (k18_complex1 A) C) (k4_power (k18_complex1 B) C))))) ) ) ) ) ) ) ).
tt(t21_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 C (k3_hilbert1 (k4_hilbert1 A B) (k2_ltlaxio1 (k7_ltlaxio1 B))))) = 1) ) ) ) ) ) ) ) ) ).
tt(t21_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) &  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden B (k4_cqc_the1 A))) )  => (r2_hidden D (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t21_margrel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ((k3_xboole_0 (k4_finseq_2 A B) (k4_finseq_2 A C)) = (k4_finseq_2 A C)) ) ) ) ) ) ) ).
tt(t21_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_mathmorp A (k4_struct_0 A) B) = B) ) ) ) ) ).
tt(t21_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v1_matrix10 B) & (v2_matrix10 C))  => (v2_matrix10 (k4_matrix10 A C B))) ) ) ) ) ) ) ).
tt(t21_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k13_matrix_2 A))) &  ( (B = (k3_group_4 (k13_matrix_2 A) C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 A)) =>  (~  ( ((k1_funct_1 C D) = E)  & (v4_matrix_2 E (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k5_matrix_6 B D (k4_matrix12 B B D (k12_matrix_1 D B) A C)) = (k4_matrix12 B B D (k12_matrix_1 D B) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  ( ( (B = 1)  &  (C = 1) )  =>  ((k1_matrix13 A D B C E F) = (k2_matrlin A (k4_matrix_2 A (k3_matrix_1 A D (k1_funct_1 E 1) (k1_funct_1 F 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k13_fvsum_1 A (k2_matrix14 A (k3_finseq_1 B)) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t21_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k8_matrix13 A B)) )  =>  ((k8_matrix13 A B) = (k8_matrix13 A (k7_matrlin (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t21_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v3_matrix16 C (u1_struct_0 B)) & (v3_matrix16 D (u1_struct_0 B)))  => (v3_matrix16 (k2_matrix_6 A B C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t21_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((k3_matrix_1 A B D E) = (k3_matrix_1 A C D E)) ) ) ) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t21_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( ((k3_relat_1 (k1_finseq_2 A) B) = B)  &  ((k3_relat_1 B (k1_finseq_2 A)) = B) ) ) ) ) ) ).
tt(t21_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k4_matrix_3 A (k6_matrix_2 (u1_struct_0 A) B D F H) (k6_matrix_2 (u1_struct_0 A) C E G I)) = (k6_matrix_2 (u1_struct_0 A) (k3_rlvect_1 A (k8_group_1 A B C) (k8_group_1 A D G)) (k3_rlvect_1 A (k8_group_1 A B E) (k8_group_1 A D I)) (k3_rlvect_1 A (k8_group_1 A F C) (k8_group_1 A H G)) (k3_rlvect_1 A (k8_group_1 A F E) (k8_group_1 A H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k1_matrix_4 A (k3_matrix_3 A B C) C)) ) ) ) ) ) ) ) ).
tt(t21_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 A) = (k1_matrix_1 B)) )  =>  ((k7_matrix_5 C (k3_matrix_5 A B)) = (k3_matrix_5 (k7_matrix_5 C A) (k7_matrix_5 C B))) ) ) ) ) ) ) ) ).
tt(t21_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v2_matrix_6 (k2_matrix_2 (u1_struct_0 B) A A C) A B)) ) ) ) ) ) ).
tt(t21_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k4_matrix_7 A (k6_finseq_1 (u1_struct_0 A))) = (k6_finseq_1 (u1_struct_0 A))) ) ) ).
tt(t21_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B D C) = (k11_matrix_1 B A)) )  =>  (D = (k11_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 3 2 1))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) D F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k9_matrix_5 B C) = (k9_matrix_5 A C)) ) ) ) ) ) ) ) ).
tt(t21_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_matrixj1 C B) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 B))))  =>  ((k11_matrixj1 B (k6_matrixj1 B A C)) = (k17_finseq_1 k5_numbers A (k11_matrixj1 B C))) ) ) ) ) ) ) ).
tt(t21_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ((r2_hidden (k3_finseq_1 D) (k4_finseq_1 D)) =>  ((k4_rlvect_1 C (k5_matrlin A C (k8_matrix_1 (u1_struct_0 A) (k2_matrixj2 A B (k3_finseq_1 D)) (k3_finseq_1 D)) D)) = (k4_vectsp_1 A C B (k7_partfun1 (u1_struct_0 C) D (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (~  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k13_fvsum_1 A (k8_matrix_1 (u1_struct_0 A) B E) (k9_matrix_1 (u1_struct_0 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k1_matrix_1 C) = (k3_finseq_1 A)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k6_matrixr1 C (k5_matrixr1 A B)) = (k5_matrixr1 (k6_matrixr1 C A) (k6_matrixr1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  ((k3_finseq_1 C) = (k1_vectsp_9 A B)) ) ) ) ) ) ) ).
tt(t21_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [F:$i] :  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 C)) =>  ( ((r1_tarski (k10_xtuple_0 G) F) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) &  ((v13_vectsp_1 E C B) &  ((v1_mod_2 E A C B) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((r2_hidden H F) =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D H) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) E H)) ) ) ) ) ) ) ) )  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D (k4_rlvect_1 C G)) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) E (k4_rlvect_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc B A) <=>  ((k5_card_1 B) = (k4_matroid0 A B)) ) ) ) ) ) ).
tt(t21_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 A) k6_numbers))  =>  ((k3_matrprob A) = (k4_matrprob (k4_matrix_1 k1_numbers A))) ) ) ) ).
tt(t21_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) B A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 B) (k2_finseq_1 B)) &  ((v3_funct_2 E (k2_finseq_1 B) (k2_finseq_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 B) (k2_finseq_1 B))))) ) )  =>  ( ((k1_funct_1 (k3_matrtop1 B A D) C) = (k1_funct_1 (k3_matrtop1 B A (k4_matrix11 B A (u1_struct_0 k2_vectsp_1) E D)) (k3_relat_1 E C)))  &  ((v3_card_1 (k3_relat_1 E C) B) & (m2_finseq_1 (k3_relat_1 E C) k1_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid A))))  =>  ((v1_rlvect_3 (k2_relset_1 (u1_struct_0 (k15_euclid A)) B) (k15_euclid A)) =>  (! [C:$i] :  ((m1_matrlin C k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  ( (C = (k11_matrix13 k2_vectsp_1 A A (k12_matrix_1 k2_vectsp_1 A)))  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A A) =>  ( ((v1_matrix_6 D A k2_vectsp_1) &  ((k17_finseq_1 (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) (k3_finseq_1 B) D) = B) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 A A D) (k2_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) (k2_relset_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (k17_finseq_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (k3_finseq_1 B) C))))) = (k2_struct_0 (k1_rlvect_3 (k15_euclid A) (k2_relset_1 (u1_struct_0 (k15_euclid A)) B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) B) = (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k20_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k4_xcmplx_0 (k17_sin_cos A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) C) C) = (k1_rlvect_1 A (k5_algstr_0 A B C) 2)) ) ) ) ) ) ) ).
tt(t21_mboolean,ax, (! [A:$i] : (r6_pboole A (k2_mboolean A (k1_pboole A)) (k1_pboole A))) ).
tt(t21_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_hidden A B) =>  (A = (k4_tarski (k1_xtuple_0 A) (k2_xtuple_0 A))) ) ) ) ) ).
tt(t21_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_card_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( (~ (v1_xboole_0 (k7_setfam_1 A B)))  &  ((v4_card_3 (k7_setfam_1 A B)) & (m1_subset_1 (k7_setfam_1 A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(t21_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B C E)))  & (r1_tarski (k8_nat_1 B C E) (k8_nat_1 B C (k2_nat_1 E 1)))) ) ) )  =>  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v3_membered B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k9_member_1 B A)) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r2_hidden D B) &  ((r2_hidden E A) &  (C = (k7_real_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_measure8 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  =>  ((v1_funct_1 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D)) &  ((v1_funct_2 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D) k5_numbers k7_numbers) & (m1_subset_1 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ) ) ) ) ) ).
tt(t21_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r2_hidden B A) => (r2_hidden (k5_xxreal_3 B) (k6_member_1 A))) ) ) ) ) ).
tt(t21_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v3_membered B) =>  ((r1_tarski A B) => (v3_membered A)) ) ) ) ).
tt(t21_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((k7_memstr_0 A B (k2_xcmplx_0 C E)) = (k7_memstr_0 A B (k2_xcmplx_0 D E)))  <=>  ((k7_memstr_0 A B C) = (k7_memstr_0 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) A H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) B I))) ) )  =>  ((r1_euclid_6 A B C) |  ( (G = 1)  |  ( (H = 1)  |  ( (I = 1)  |  ( ((k9_binop_2 (k10_binop_2 1 H) (k11_binop_2 G H)) = k6_numbers)  |  ( ((k9_binop_2 (k10_binop_2 1 G) (k11_binop_2 I G)) = k6_numbers)  |  ( ((k9_binop_2 (k10_binop_2 1 I) (k11_binop_2 H I)) = k6_numbers)  |  ( ((k11_binop_2 (k11_binop_2 (k12_binop_2 G (k10_binop_2 1 G)) (k12_binop_2 H (k10_binop_2 1 H))) (k12_binop_2 I (k10_binop_2 1 I))) = 1)  <=>  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) &  ((r1_euclid_6 A D J) &  ((r1_euclid_6 B E J) & (r1_euclid_6 C F J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfun10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 B A k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (E = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B G))) )  & (r1_mesfun10 A B F)) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 D E)) |  ((r1_mesfunc5 A C D F) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k12_supinf_2 G H) = (k7_mesfunc5 A C D (k4_mesfunc5 A k7_numbers B H))) ) )  &  ((v10_mesfunc5 G) &  ((k2_mesfunc5 G) = (k7_mesfunc5 A C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((k12_supinf_2 C E) = k6_numbers)  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  & (r1_mesfun6c A B D F)) ) ) )  |  ((r2_mesfun6c A B C (k2_partfun1 A k2_numbers D E)) &  ((k1_mesfun6c A B C (k2_partfun1 A k2_numbers D E)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) = D)  &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers C E) D)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (v2_comseq_2 (k10_seqfunc A C E))) ) ) ) )  => (r1_mesfunc1 A B (k8_mesfun7c A C) D)) ) ) ) ) ) ) ) ) ).
tt(t21_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  => (r2_funct_2 k5_numbers (k4_partfun1 A k1_numbers) (k11_mesfun7c A (k1_mesfun9c A k2_numbers C B)) (k1_mesfun9c A k1_numbers (k11_mesfun7c A C) B))) ) ) ) ) ).
tt(t21_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) )  =>  (! [E:$i] :  (! [F:$i] :  ((v1_xreal_0 F) =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k8_nat_1 C D G) = (k9_subset_1 A E (k16_mesfunc1 A B (k1_measure6 (k5_real_1 F (k10_real_1 1 (k2_nat_1 G 1))))))) ) )  =>  ((k9_subset_1 A E (k15_mesfunc1 A B (k1_measure6 F))) = (k2_measure2 A C (k1_measure3 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k12_supinf_2 (k2_mesfunc2 A B) C) = (k2_supinf_2 (k12_supinf_2 B C)))  =>  ((k12_supinf_2 (k1_mesfunc2 A B) C) = k1_supinf_2) ) ) ) ) ) ) ) ).
tt(t21_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [D:$i] :  ((r2_hidden D (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) =>  ((r1_xxreal_0 (k12_supinf_2 C D) (k12_supinf_2 B D)) &  ( (~ (r1_xxreal_0 (k12_supinf_2 C D) k2_supinf_1))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 B D))) ) ) ) )  => (v6_supinf_2 (k4_mesfunc1 A B C))) ) ) ) ) ) ) ).
tt(t21_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_mesfunc6 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r1_mesfunc6 A B (k26_valued_1 A k1_numbers C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((r2_hidden D (k1_relset_1 A (k10_mesfunc1 A (k3_mesfunc1 A B C)))) => (r1_xxreal_0 (k12_supinf_2 (k10_mesfunc1 A (k3_mesfunc1 A B C)) D) (k12_supinf_2 (k3_mesfunc1 A (k10_mesfunc1 A B) (k10_mesfunc1 A C)) D))) ) ) ) ) ) ) ) ).
tt(t21_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc8 A C) F) (k1_measure6 E)))) ) )  =>  ((k2_kurato_0 A D) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k18_mesfunc1 A (k6_mesfunc8 A C) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers))) &  ((v1_mesfunc8 E A k7_numbers) &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F C) => (v1_mesfunc9 (k3_mesfunc5 A D F))) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers E F) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers D F) C))) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F C) => (v1_mesfunc9 (k3_mesfunc5 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  (~  ( (~  (A = B) )  & (r1_xxreal_0 (k1_metric_1 1 1 k3_metric_1 A B) k6_numbers)) ) ) ) ) ) ).
tt(t21_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r4_metric_2 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r2_hidden E B) &  ((r2_hidden F C) &  ((k4_metric_1 A E F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 k1_numbers k1_numbers)) => (r1_xxreal_0 (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 A C) (k7_real_1 (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 A B) (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k16_metric_3 B C)))) ) ) ) ) ) ).
tt(t21_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_tbsp_1 B A) & (v2_tbsp_1 C A))  =>  ((k4_metric_1 A (k1_tbsp_1 A B) (k1_tbsp_1 A C)) = (k2_seq_2 (k3_metric_6 A B C))) ) ) ) ) ) ) ) ).
tt(t21_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k2_waybel23 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xboole_0 D E)) ) ) ) ) ) )  =>  ((r2_hidden k1_xboole_0 C) | (r1_ordinal1 (k1_card_1 C) B)) ) ) ) ) ) ) ) ) ).
tt(t21_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (B = C)  =>  ((v1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A))) <=> (v1_rlvect_3 C (k15_euclid A))) ) ) ) ) ) ) ) ).
tt(t21_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((r2_midsp_1 A B C) & (r2_midsp_1 A B D))  => (r2_midsp_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t21_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (r1_midsp_2 (u1_struct_0 A) (k15_midsp_1 A) (k5_midsp_2 A))) ) ).
tt(t21_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_midsp_3 1 A)) ) ).
tt(t21_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r1_tarski (k9_mmlquery A C B D) (k4_mmlquery A C B))) ) ) ) ) ) ) ).
tt(t21_mod_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((m1_subset_1 k6_numbers A) &  ((m1_subset_1 1 A) & (m1_subset_1 2 A)) ) ) ) ).
tt(t21_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_lmod_5 C A B) &  (! [D:$i] :  ((m1_mod_3 D A B) =>  (~ (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v7_mod_4 B A A) <=>  ((v13_vectsp_1 B A A) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_algstr_0 A C D)) = (k6_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_group_1 A)) = (k1_group_1 A))  &  ((v2_funct_1 B) & (v2_funct_2 B (u1_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t21_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (~  ( (~  (B = (k1_modal_1 A)) )  & (r1_xxreal_0 (k5_card_1 A) (k5_card_1 (k4_trees_1 A B)))) ) ) ) ) ) ).
tt(t21_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C))))  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (k30_modelc_1 C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F)))))) )  =>  ((r4_modelc_1 C D F G E (k13_modelc_1 A B)) <=>  ((r4_modelc_1 C D F G E A) | (r4_modelc_1 C D F G E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v6_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  (B = (k10_modelc_2 A)) ) ) ) ) ) ) ).
tt(t21_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ((r4_modelc_3 A C B) => (r1_xxreal_0 (k21_modelc_3 A B) (k5_real_1 (k21_modelc_3 A C) 1))) ) ) ) ) ) ) ).
tt(t21_moebius1,ax,(v1_moebius1 k6_numbers)).
tt(t21_monoid_0,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ((m3_monoid_0 B A) => (m2_monoid_0 B A)) ) ) ) ).
tt(t21_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_monoid_1 B A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_monoid_1 B A))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k10_monoid_1 B A (k6_algstr_0 (k9_monoid_1 B A) C D) E) = (k6_algstr_0 B (k10_monoid_1 B A C E) (k10_monoid_1 B A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~  (B = k1_xboole_0) )  =>  ((k1_morph_01 A C (k5_setfam_1 (u1_struct_0 A) B)) = (k1_setfam_1 (a_3_8_morph_01 A B C))) ) ) ) ) ) ) ) ).
tt(t21_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  => (v3_msualg_2 (k5_msafree3 A B C) A (k11_msafree A B))) ) ) ) ) ) ).
tt(t21_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ((m1_msaterm D A B (k2_msaterm A B C)) <=> (r1_lang1 (k5_msafree A B) (k2_msaterm A B C) (k1_dtconstr (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) D))) ) ) ) ) ) ) ) ) ).
tt(t21_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msafree C A B) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r2_pboole (u1_struct_0 A) C D) => (m1_msafree D A B)) ) ) ) ) ) ) ) ) ).
tt(t21_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v2_finset_1 B) <=> (v2_finset_1 (k1_mboolean A B))) ) ) ) ).
tt(t21_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((m1_msualg_2 B A C) <=> (m1_msualg_2 B A (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C)))) ) ) ) ) ) ) ).
tt(t21_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) =>  ((k12_msualg_2 A B C) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ) ) ) ).
tt(t21_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A B C D) &  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D))) =>  (~  ((r8_pboole (u1_struct_0 A) D E) & (r2_msualg_3 A B (k6_msualg_3 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_msualg_5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (u1_struct_0 (k2_msualg_5 B))) <=>  ((v1_partfun1 A B) &  ((v3_relat_2 A) &  ((v8_relat_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) ) ).
tt(t21_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 (k1_msualg_1 A E))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A E B)) =>  ((k3_relat_1 (k4_msualg_6 A E F B G) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D (k2_msualg_1 A E))) = (k3_relat_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A E) F)) (k4_msualg_6 A E F C (k5_msualg_3 A B C E D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_msualg_7,ax, (? [A:$i] :  ((m2_nat_lat A (k1_msualg_7 k6_numbers 1)) &  ((v2_msualg_7 A (k1_msualg_7 k6_numbers 1)) &  (~ (v1_msualg_7 A (k1_msualg_7 k6_numbers 1))) ) ) ) ).
tt(t21_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B (k6_pboole A C D)) =>  ((v2_msualg_3 E A B (k6_pboole A C D)) => (v2_msualg_3 (k1_msualg_9 A B C D E) A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_unialg_2 A B) & (r1_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C)))  => (r1_alg_1 A B C)) ) ) ) ) ) ) ).
tt(t21_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_dilworth B (k3_necklace A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_necklace A))))) ) ) ) ) ).
tt(t21_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_binop_1 C D E) = (k18_complex1 (k9_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers B D) (k3_funct_2 (u1_struct_0 A) k1_numbers B E)))) ) ) ) )  => (v1_pscomp_1 C (k2_borsuk_1 A A))) ) ) ) ) ) ) ) ).
tt(t21_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ((v3_pcomps_1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  =>  (~ (v5_nagata_1 B A)) ) ) ) ) ) ) ).
tt(t21_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) => (m2_subset_1 (k6_xcmplx_0 B A) k1_numbers k5_numbers)) ) ) ) ) ).
tt(t21_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_abian A) <=>  ((k4_nat_d A 2) = k6_numbers) ) ) ) ).
tt(t21_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = 1) )  =>  ((k11_nat_3 1 A) = k6_numbers) ) ) ) ).
tt(t21_nat_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_int_2 C) =>  ((k11_nat_3 A C) = (k11_nat_3 B C)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t21_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ((v1_int_2 A) =>  ((k11_nat_3 (k6_nat_d B C) A) = (k3_xxreal_0 (k11_nat_3 B A) (k11_nat_3 C A))) ) ) ) ) ) ) ) ).
tt(t21_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d A B) = (k4_nat_d (k2_xcmplx_0 (k3_xcmplx_0 B C) A) B)) ) ) ) ) ) ) ).
tt(t21_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  ((r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k5_nattra_1 A B C D D E (k3_nattra_1 A B D)) E) & (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k5_nattra_1 A B C C D (k3_nattra_1 A B C) E) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) =>  ( (! [E:$i] :  ((m1_ncfcont1 E A D) =>  (~  ((k9_subset_1 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) C) E) = (k1_tarski D)) ) ) )  | (r2_ncfcont1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t21_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_ncfcont2 A B C D) => (r9_ncfcont1 B C D A)) ) ) ) ) ) ) ) ).
tt(t21_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v1_fdiff_1 B k6_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((v12_struct_0 (k2_ndiff_1 A C B) k5_numbers A) & (v1_ndiff_1 (k2_ndiff_1 A C B) A (k4_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t21_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r1_tarski D (k1_relset_1 k1_numbers E)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F D) =>  ((k7_partfun1 (u1_struct_0 A) E F) = (k3_rlvect_1 A (k1_rlvect_1 A B F) C)) ) ) ) )  =>  ((r2_ndiff_3 A E D) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F D) =>  ((k1_funct_1 (k2_ndiff_3 A E D) F) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ( ((r2_ndiff_4 B D A) & (r1_tarski C A))  => (r2_ndiff_4 B D C)) ) ) ) ) ) ) ) ).
tt(t21_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_prvect_2 A B))) =>  ((k1_normsp_0 (k14_prvect_2 A) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) C)) = (k1_normsp_0 (k11_prvect_2 A B) C)) ) ) ) ) ) ) ).
tt(t21_neckla_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski D E) (u1_orders_2 A)) <=> (r2_hidden (k4_tarski (k1_funct_1 C D) (k1_funct_1 C E)) (u1_orders_2 B))) ) ) ) ) ) )  <=> (r1_necklace A B)) ) ) ) ) ).
tt(t21_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A (k1_nat_1 B 1)))  => (r2_hidden (k4_tarski B (k1_nat_1 B 1)) (u1_orders_2 (k4_necklace A)))) ) ) ) ) ).
tt(t21_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (! [C:$i] :  ((r2_hidden B C) =>  ( ((k2_net_1 A) = k1_xboole_0)  | (r2_hidden (k5_net_1 A B) (k10_net_1 A C))) ) ) ) ) ) ) ).
tt(t21_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_newton A A) = 1) ) ) ).
tt(t21_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_nfcont_1 B C D A) <=> (r3_nfcont_1 B C (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A) A)) ) ) ) ) ) ) ) ).
tt(t21_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers D)) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C))  => (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) (k4_vfunct_1 k1_numbers C D B) A) C)) ) ) ) ) ) ) ) ).
tt(t21_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  ( ( (B = C)  &  (D = E) )  =>  ((r2_nfcont_4 A B D) <=> (r2_nfcont_1 (k4_real_ns1 A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_normform,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden F D) => (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) (k3_funct_2 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) C F) E)) ) )  => (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) (k6_normform B A D C) E)) ) ) ) ) ) ) ) ) ) ).
tt(t21_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 C A) => (v3_normsp_1 (k4_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t21_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (B = C)  =>  ((v4_pre_topc B (k3_normsp_2 A)) <=> (v4_pre_topc C (k4_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t21_numbers,ax, (~  (k1_numbers = k2_numbers) ) ).
tt(t21_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~ (r2_hidden D (k7_openlatt A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  ((k6_oppcat_1 A (k4_cat_1 (k2_oppcat_1 A) B)) = (k4_cat_1 A (k4_oppcat_1 A B))) ) ) ) ) ).
tt(t21_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_orders_1 A) => (v1_orders_1 A)) ) ) ).
tt(t21_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r2_hidden B (k2_orders_2 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t21_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) <=> (r1_ordinal1 (k1_ordinal1 A) B)) ) ) ) ) ).
tt(t21_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  (~  ((r2_hidden A (k3_ordinal2 B)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C B) & (r1_ordinal1 A C)) ) ) ) ) ) ) ) ) ).
tt(t21_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((k10_ordinal2 A B) = (k10_ordinal2 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t21_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k12_ordinal2 B D)) ) ) ) )  => (r1_ordinal2 (k12_ordinal2 B A) C)) ) ) ) ) ) ) ) ) ).
tt(t21_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r1_ordinal1 A B) & (r2_hidden k6_numbers C))  => (r1_ordinal1 (k1_ordinal5 C A) (k1_ordinal5 C B))) ) ) ) ) ) ) ).
tt(t21_ordinal6,ax, (! [A:$i] : (r3_wellord1 (k1_wellord2 (k1_ordinal6 A)) (k1_wellord2 (k2_ordinal1 A)) (k2_ordinal6 A))) ).
tt(t21_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t21_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k8_group_1 A (k1_ortsp_1 A B D C F) (k11_algstr_0 A (k1_ortsp_1 A B D C E))) = (k1_ortsp_1 A B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r3_orders_2 A E F) &  ((r2_hidden C (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) E)) & (r2_hidden D (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) E))) )  =>  ((r2_hidden (k4_tarski D E) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C)) <=> (r2_hidden (k4_tarski D F) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( ((r2_osalg_1 A B C) & (r2_osalg_1 A C D))  => (r2_osalg_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t21_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_orders_2 A D E) => (r2_setfam_1 (k8_osalg_2 A B C D) (k8_osalg_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  =>  ((r8_pboole (u1_struct_0 A) C (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) => (v3_osalg_4 C A B)) ) ) ) ) ) ) ).
tt(t21_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_parsp_1 A B C D E) => (r1_parsp_1 A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) & (r1_parsp_1 A B C D E))  =>  ( (B = C)  | (r1_parsp_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B)))))  =>  ( ((k1_relset_1 A C) = (k1_relset_1 A D))  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t21_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden D (k1_relset_1 B (k3_partfun2 B C A E))) =>  ((k7_partfun1 C (k3_partfun2 B C A E) D) = (k7_partfun1 C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((m2_finseq_1 G A) =>  ( ((r1_tarski D A) &  ((r2_hidden E D) &  ( ((k1_funct_1 G 1) = E)  &  ( ((k1_funct_1 G (k3_finseq_1 G)) = F)  &  ((r1_xxreal_0 1 (k3_finseq_1 G)) &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r1_xxreal_0 1 H) &  ( (~ (r1_xxreal_0 (k3_finseq_1 G) H))  &  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (~  ((r2_hidden I B) &  ((r2_hidden J C) &  ((r2_hidden (k1_funct_1 G H) I) &  ((r2_hidden K I) &  ((r2_hidden K J) & (r2_hidden (k1_funct_1 G (k2_nat_1 H 1)) J)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((r1_partit1 A B D) & (r1_partit1 A C D)) ) ) ) ) ) )  => (r2_hidden F D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) =>  ((v1_relat_2 B) &  ((k1_relat_1 B) = A) ) ) ) ) ) ) ).
tt(t21_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r3_diraf A B C D))  &  ((r1_diraf A B E D) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B F C) & (r2_analoaf A C D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D E))  => (r2_pboole A (k3_pboole A B D) (k3_pboole A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t21_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) & (v2_tops_2 B A))  => (v4_pre_topc (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t21_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((r1_tarski (u1_struct_0 A) (u1_struct_0 (k19_pcs_0 A B))) &  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 (k19_pcs_0 A B))) & (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_pcs_0 A) (u1_pcs_0 (k19_pcs_0 A B)))) ) ) ) ) ).
tt(t21_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ( ( (C = D)  &  ( (E = F)  & (r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C E)) )  =>  ((k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C E) = (k8_pdiff_1 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_1 2 1 A B) => (r1_fcont_1 (k1_pdiff_2 2 1 A B) (k1_seq_1 (k1_pdiff_1 1 2) B))) ) ) ) ) ).
tt(t21_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r1_pdiff_3 B A) & (r1_pdiff_3 C A))  =>  ((r3_pdiff_1 2 1 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) &  ((k11_pdiff_1 2 1 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) = (k7_real_1 (k2_pdiff_3 B A) (k2_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( (D = (k11_finseq_1 A B C))  =>  ((k11_pdiff_1 3 3 E D) = (k1_fdiff_1 (k1_pdiff_2 3 3 E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r3_pdiff_5 B A) <=> (r3_pdiff_1 3 3 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ).
tt(t21_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  ( ((r1_pdiff_1 B A C E) & (r1_pdiff_1 B A D E))  =>  ((r1_pdiff_1 B A (k8_integr15 A (k1_euclid B) C D) E) & (r2_relset_1 (k1_euclid B) (k1_euclid A) (k8_pdiff_1 B A (k8_integr15 A (k1_euclid B) C D) E) (k8_integr15 A (k1_euclid B) (k8_pdiff_1 B A C E) (k8_pdiff_1 B A D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 B))) =>  ( ((r1_ndiff_1 (k4_real_ns1 B) (k4_real_ns1 A) D E) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B)) )  =>  ((r2_pdiff_1 A B C D E) &  ((k9_pdiff_1 B A C D E) = (k3_relat_1 (k7_pdiff_1 B C (k4_struct_0 (k4_real_ns1 B))) (k3_ndiff_1 (k4_real_ns1 B) (k4_real_ns1 A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ((v3_nfcont_1 D (k4_real_ns1 A)) =>  ( ((r2_ndiff_1 D (k4_real_ns1 A) (k4_real_ns1 B) C) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C D) D))  <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E B))  =>  ((r2_ndiff_1 D (k4_real_ns1 A) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 E B))) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 E B)) D) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((v1_pdiff_7 F A) &  ( (E = D)  &  ( (F = G)  & (r2_pdiff_7 A B C D F)) ) ) ) )  =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r2_hidden H F) &  (H = I) )  =>  ((k12_pdiff_1 A B C D H) = (k1_funct_1 (k9_pdiff_1 A B C E I) (k12_finseq_1 k5_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pencil_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_pre_topc A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = B)  => (v2_pencil_1 C A)) ) ) ) ) ) ) ).
tt(t21_pencil_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_pencil_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_pencil_2 A C D) =>  ((v1_zfmisc_1 C) |  ((v1_zfmisc_1 D) | (r1_pencil_2 A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  ((r1_xboole_0 C D) =>  ((r1_pencil_3 A B C D) <=>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  ( ( (C = (k4_card_3 E))  &  (D = (k4_card_3 F)) )  =>  ( ((k3_pencil_1 A E) = (k3_pencil_1 A F))  &  (? [G:$i] :  ((m1_subset_1 G A) &  ( (~  (G = (k3_pencil_1 A E)) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ( (~  (H = G) )  =>  ((k1_funct_1 E H) = (k1_funct_1 F H)) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_pencil_1 A B G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_pencil_1 A B G))) =>  ( ( ((k1_funct_1 E G) = (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B G)) H))  &  ((k1_funct_1 F G) = (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B G)) I)) )  => (r1_pencil_1 (k2_pencil_1 A B G) H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 3 (k1_vectsp_9 A B)))  =>  ((r1_xxreal_0 (k1_vectsp_9 A B) C) |  ( (~ (v2_struct_0 (k5_pencil_4 A B C)))  &  ( (~ (v3_pencil_1 (k5_pencil_4 A B C)))  &  ( (~ (v4_pencil_1 (k5_pencil_4 A B C)))  &  ((v5_pencil_1 (k5_pencil_4 A B C)) &  ((v6_pencil_1 (k5_pencil_4 A B C)) & (l1_pre_topc (k5_pencil_4 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_abian B) =>  ((r1_xxreal_0 A k6_numbers) | (v1_abian (k1_newton B A))) ) ) ) ) ) ).
tt(t21_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A C B))  => (r1_pnproc_1 A B C)) ) ) ) ) ) ).
tt(t21_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_polyalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v3_polyalg1 C A B) =>  ((u1_struct_0 (k2_polyalg1 A B C)) = C) ) ) ) ) ) ) ) ).
tt(t21_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( (B = (k7_xcmplx_0 C A))  &  ( (D = (k7_xcmplx_0 E A))  &  ((k7_polyeq_1 A k6_numbers C E F) = k6_numbers) ) )  =>  ( (A = k6_numbers)  |  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (~  ( (F = (k2_xcmplx_0 G H))  &  ( ((k7_real_1 (k8_real_1 (k8_real_1 3 H) G) B) = k6_numbers)  &  ( (~  (F = (k7_real_1 (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))) (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))))) )  &  ( (~  (F = (k7_real_1 (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))) (k2_power 3 (k7_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))))) )  &  (~  (F = (k7_real_1 (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))) (k2_power 3 (k9_real_1 (k1_real_1 (k6_real_1 E (k8_real_1 2 A))) (k7_square_1 (k7_real_1 (k6_real_1 (k3_square_1 E) (k8_real_1 4 (k3_square_1 A))) (k2_newton (k6_real_1 C (k8_real_1 3 A)) 3))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( ((k1_polyeq_3 A) = B)  &  ( ((k4_complex1 B) = k6_numbers)  &  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 B)))  &  ( (~  (A = (k5_binop_2 (k7_square_1 (k7_binop_2 (k3_complex1 B))) k7_complex1)) )  &  (~  (A = (k1_binop_2 (k5_binop_2 (k7_square_1 (k7_binop_2 (k3_complex1 B))) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( ((k3_xcmplx_0 A (k2_newton B F)) = C)  &  ( ((k3_xcmplx_0 B D) = E)  &  ((v1_abian F) &  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 (k7_xcmplx_0 C A) k6_numbers))  &  ( (~  (A = k6_numbers) )  &  ( (~  ( (B = (k1_power F (k7_xcmplx_0 C A)))  &  (D = (k3_xcmplx_0 E (k1_power F (k7_xcmplx_0 A C)))) ) )  &  (~  ( (B = (k4_xcmplx_0 (k1_power F (k7_xcmplx_0 C A))))  &  (D = (k4_xcmplx_0 (k3_xcmplx_0 E (k1_power F (k7_xcmplx_0 A C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((v1_xcmplx_0 H) =>  (! [I:$i] :  ((v1_xcmplx_0 I) =>  ( ( (A = (k6_xcmplx_0 E (k13_complex1 F 4)))  &  ( (I = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 3 (k1_newton F 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 (k3_xcmplx_0 4 B) F)) (k1_newton F 3)) 64))  &  (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 D) (k3_xcmplx_0 (k3_xcmplx_0 64 F) C)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton F 2)) B)) (k3_xcmplx_0 3 (k1_newton F 4))) 1024)) ) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 F (k1_newton A 3))) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton E 4) (k3_xcmplx_0 (k3_xcmplx_0 4 I) (k1_newton E 2))) (k3_xcmplx_0 (k3_xcmplx_0 8 G) E)) (k3_xcmplx_0 4 H)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_polyform,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ((k16_rvsum_1 (k6_polyform (k6_polyform A B) C)) = (k2_xcmplx_0 (k2_xcmplx_0 (k16_rvsum_1 A) (k16_rvsum_1 B)) (k16_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t21_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B (k4_polynom1 A B C D) E) (k4_polynom1 A B C (k4_polynom1 A B D E)))) ) ) ) ) ) ) ) ) ).
tt(t21_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k8_polynom1 A B) C) = (k5_struct_0 B)) ) ) ) ) ) ) ).
tt(t21_polynom3,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 D (k1_funct_1 A (k2_nat_1 B 1))) &  ((r1_xxreal_0 E (k1_funct_1 A (k2_nat_1 C 1))) &  ((k2_nat_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers B A)) D) = (k2_nat_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers C A)) E)) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) B) |  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k3_normsp_1 A B C) D) = (k5_algstr_0 A (k2_polynom4 A B D) (k2_polynom4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A (k10_polynom3 A) B) (k10_polynom3 A))) ) ) ) ).
tt(t21_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom7 A B C) (k4_polynom7 A B D)) <=>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t21_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (D = (k4_struct_0 A)) )  =>  ((k8_group_1 A (k3_polynom8 A D B) (k3_polynom8 A D C)) = (k3_polynom8 A D (k2_xcmplx_0 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t21_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v9_struct_0 E C))  & (m1_subset_1 E (u1_struct_0 C)))  =>  ((k3_termord A B C (k5_polynom7 A C D E)) = (k3_termord A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A k6_numbers) =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((v1_abian B) |  ((r1_xxreal_0 (k1_power B A) A) &  (~ (r1_xxreal_0 (k1_power B A) (k1_real_1 1))) ) ) ) ) ) ) ) ) ).
tt(t21_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 B E (k14_pralg_2 A B C))) =>  (! [G:$i] :  ((r2_hidden G (k1_relset_1 k5_numbers (k1_msualg_1 B E))) =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ( (H = (k1_funct_1 F G))  =>  ((k1_funct_1 (k1_funct_1 (k10_funct_6 F) D) G) = (k1_funct_1 H D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) <=> (r2_tarski A B)) ) ) ) ) ).
tt(t21_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k2_prelamb A (k2_prelamb A B (k1_prelamb A C B)) C)) & (r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k1_prelamb A C (k1_prelamb A (k2_prelamb A B C) B)))) ) ) ) ) ) ) ).
tt(t21_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden D B) &  ((r3_orders_1 C B) &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E B) => (r2_hidden (k1_domain_1 A A E D) C)) ) ) ) )  =>  ((k7_partfun1 A (k7_pre_poly A B C) (k3_finseq_1 (k7_pre_poly A B C))) = D) ) ) ) ) ) ) ) ) ) ).
tt(t21_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k2_prepower 1 A) = A) ) ) ) ).
tt(t21_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k2_pre_topc A C)))) ) ) ) ) ) ).
tt(t21_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) => (m1_prob_1 (k4_subset_1 A C D) A B)) ) ) ) ) ) ) ).
tt(t21_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ((r2_prob_2 A B F C D E) => (r2_prob_2 A B F D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) C (k1_prob_3 A D)) =>  ( ((k1_prob_2 A B C k6_numbers) = (k1_prob_2 A B D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_prob_2 A B C (k1_nat_1 E 1)) = (k9_subset_1 A (k1_funct_1 C E) (k1_prob_2 A B D (k1_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xboole_0 (k1_prob_4 A B (k3_prob_3 A C) (k2_nat_1 D 1)) (k1_prob_4 A B C D))) ) ) ) ) ) ) ) ).
tt(t21_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) C) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t21_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r1_collsp A B C F) &  ((r1_collsp A B D G) &  ((r1_collsp A B E H) &  ((r1_collsp A C D I) &  ((r1_collsp A F G I) &  ((r1_collsp A D E J) &  ((r1_collsp A G H J) &  ((r1_collsp A C E K) & (r1_collsp A F H K)) ) ) ) ) ) ) )  =>  ((r1_collsp A B C D) |  ((r1_collsp A B D E) |  ((r1_collsp A B C E) |  ( (C = F)  |  ( (D = G)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  | (r1_collsp A J K I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  ( ((v1_projpl_1 A) &  ((r3_projpl_1 A B F G H) &  ((r1_zfmisc_1 F G H) &  ((r2_projpl_1 A C I F) &  ((r2_projpl_1 A D I G) & (r2_projpl_1 A E I H)) ) ) ) )  =>  ((r1_incsp_1 A B I) | (r1_zfmisc_1 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r2_hidden C (k10_xtuple_0 (k1_projred1 A D E B))) =>  ((r1_incsp_1 A B D) |  ((r1_incsp_1 A B E) | (r1_incsp_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_projred2 A D E F))  &  ((r1_projred2 A E F G) &  ( (~ (r1_incsp_1 A B G))  &  ( (~  (E = G) )  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A I H) &  ( (~ (r1_incsp_1 A I E))  &  ( (~ (r1_incsp_1 A I G))  &  ((k3_relat_1 (k1_projred1 A D F B) (k1_projred1 A F E C)) = (k3_relat_1 (k1_projred1 A D G B) (k1_projred1 A G E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B))))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 C D E) = (k1_domain_1 (u1_struct_0 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))) D (k12_finseq_1 (u1_struct_0 B) E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_3 A B))) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C (k3_rlvect_1 (k5_prvect_3 A B) D E)) = (k3_rlvect_1 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C D) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C (k1_rlvect_1 (k5_prvect_3 A B) D E)) = (k1_rlvect_1 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C D) E)) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 A B)) (u1_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B)))) C (k4_struct_0 (k5_prvect_3 A B))) = (k4_struct_0 (k5_prvect_3 A (k10_prvect_2 (k9_finseq_1 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (a_2_3_pscomp_1 B C))  => (v3_pre_topc A (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t21_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k6_pua2mss1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((v1_partfun1 (k8_pua2mss1 A B C) (u1_struct_0 A)) &  ((v3_relat_2 (k8_pua2mss1 A B C)) & (v8_relat_2 (k8_pua2mss1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t21_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k3_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A B C)) (k1_pzfmisc1 A B)) & (r6_pboole A (k3_pboole A (k1_pzfmisc1 A C) (k2_pzfmisc1 A B C)) (k1_pzfmisc1 A C))) ) ) ) ) ) ).
tt(t21_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  ( ((r1_qc_lang1 A B C) & (r1_qc_lang1 A C D))  => (r1_qc_lang1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t21_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [I:$i] :  ((m2_subset_1 I (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k8_qc_lang2 A D F H B) = (k8_qc_lang2 A E G I C))  =>  ( (D = E)  &  ( (F = G)  &  ( (H = I)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v6_qc_lang1 B A) <=> (v6_qc_lang1 (k13_qc_lang1 A B) A)) ) ) ) ) ).
tt(t21_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A C))) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A C))) =>  ( ( (D = (k8_finseq_1 k5_numbers E (k12_finseq_1 k5_numbers B)))  & (v3_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E) A))  =>  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) D) = (k18_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E)))  &  (B = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_quantal1 A))  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (k1_lattice3 k1_xboole_0))  =>  ((v20_quantal1 A) & (v21_quantal1 A)) ) ) ) ).
tt(t21_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k27_quaterni A (k28_quaterni B)) = (k28_quaterni (k27_quaterni A B))) ) ) ) ) ).
tt(t21_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k26_quaterni (k27_quaterni k11_quaterni A) (k27_quaterni A k11_quaterni)) = (k6_quaterni (k1_real_1 (k8_real_1 2 (k19_quaterni A))) k6_numbers (k8_real_1 2 (k17_quaterni A)) k6_numbers)) ) ) ).
tt(t21_quaterni,ax, ((k10_quaterni k12_quaterni k1_xcmplx_0) = (k8_quaterni (k10_quaterni k1_xcmplx_0 k12_quaterni))) ).
tt(t21_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k3_square_1 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 A) B) C)) (k1_quin_1 A C D)) k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 B)) (k3_xcmplx_0 C B)) D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k15_quofield A) B C) = (k5_binop_1 (k7_quofield A) (k15_quofield A) C B)) ) ) ) ) ) ) ).
tt(t21_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_radix_1 1 A B) =>  ((k4_radix_1 1 B 1 (k10_radix_1 B 1 A)) = A) ) ) ) ) ) ).
tt(t21_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 2 B) & (r1_radix_1 A C B))  =>  (C = (k14_radix_3 (k2_xcmplx_0 A 1) B (k10_radix_3 A B (k10_radix_1 B A C)))) ) ) ) ) ) ) ) ) ).
tt(t21_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k7_numbers (k5_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A C)) (k1_mesfunc5 A (k20_valued_1 A k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t21_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((r1_struct_0 (k1_vectsp_7 A B C) D) &  ( (~ (r2_hidden D C))  & (v1_vectsp_7 (k4_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 (k1_rat_1 A) 1))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 (k1_rat_1 A) 1)) ) ) ) ) ).
tt(t21_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (? [C:$i] :  ((m1_ratfunc1 C A) &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  &  ( (B = (k3_ratfunc1 A (k13_polynom3 A D (k4_ratfunc1 A C)) (k13_polynom3 A D (k5_ratfunc1 A C))))  &  ((v5_ratfunc1 C A) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) &  ( (D = (k3_group_4 (k14_polynom3 A) E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) G) &  ((k1_funct_1 E F) = (k3_hurwitz A G 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (~  ((v3_rcomp_1 A) &  ((v4_xxreal_2 A) & (r2_hidden (k4_seq_4 A) A)) ) ) ) ) ).
tt(t21_rcomp_3,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((v4_xxreal_2 A) & (r2_hidden (k4_seq_4 A) A))  =>  ((v3_xxreal_2 A) |  (A = (k1_limfunc1 (k4_seq_4 A))) ) ) ) ) ).
tt(t21_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_funct_2 k5_numbers k5_numbers (k2_real_3 A k6_numbers) (k8_funcop_1 k5_numbers k5_numbers k6_numbers))) ) ).
tt(t21_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  ((k1_binop_1 (k4_real_lat A) B C) = (k1_binop_1 (k4_real_lat A) C B)) ) ) ) ) ) ) ).
tt(t21_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B (k5_struct_0 A)) = B)  &  ((k6_algstr_0 A (k5_struct_0 A) B) = B) ) ) ) ) ) ).
tt(t21_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) C D)) = (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t21_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k1_relset_1 B (k4_rearran1 A B D C)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t21_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k1_relat_1 A) = (k1_relat_1 (k2_relat_1 A))) ) ) ).
tt(t21_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski B C) => (r2_relset_1 A B (k6_relset_1 A B C D) D)) ) ) ) ) ) ).
tt(t21_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((v1_funct_1 (k3_relset_2 A C)) &  ((v1_funct_2 (k3_relset_2 A C) (k9_setfam_1 A) (k9_setfam_1 (k2_relset_1 B C))) & (m1_subset_1 (k3_relset_2 A C) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 (k2_relset_1 B C)))))) ) ) ) ) ) ).
tt(t21_revrot_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  =>  ((k10_xtuple_0 (k1_goboard1 A)) = (k10_xtuple_0 (k1_goboard1 B))) ) ) ) ) ) ).
tt(t21_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) <=> (r1_rewrite1 (k18_finseq_1 A) B C)) ) ) ) ) ).
tt(t21_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (~  ((r2_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C) D E) &  ( (~ (r2_rewrite2 A B D E))  &  (~ (r2_rewrite2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [H:$i] :  ((l1_rewrite3 H F) =>  (! [I:$i] :  ((l1_rewrite3 I G) =>  ( ( ((u1_rewrite3 F H) = (u1_rewrite3 G I))  & (r2_rewrite3 E F H A B C D))  => (r2_rewrite3 E G I A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rfinseq2,ax, (! [A:$i] :  ( ((v1_integra2 A) & (m2_finseq_1 A k1_numbers))  =>  ((k6_rfinseq2 A) = A) ) ) ).
tt(t21_rfinseq,ax, (! [A:$i] :  ( ((v8_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (v8_valued_0 (k2_rfinseq k1_numbers B A))) ) ) ) ).
tt(t21_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k24_valued_1 A 1) = A) ) ) ).
tt(t21_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ((r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k8_finseq_1 (k3_rfunct_3 A k1_numbers) B C)) (k5_rfunct_3 A k1_numbers (k14_rfunct_3 A B) (k14_rfunct_3 A C)))) ) ) ) ) ) ).
tt(t21_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski A (k9_xtuple_0 B)) =>  ( ((r6_rfunct_4 B A) & (r8_rfunct_4 B A))  <=> (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t21_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) &  ((v4_partfun3 A) &  ((v1_seq_2 B) & (v4_partfun3 B)) ) )  =>  ((v1_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) & (r1_xxreal_0 (k1_rinfsup1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k8_real_1 (k1_rinfsup1 A) (k1_rinfsup1 B)))) ) ) ) ) ) ).
tt(t21_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 B) =>  ((v10_mesfunc5 (k1_valued_0 k7_numbers B A)) &  ((k2_mesfunc5 B) = (k2_mesfunc5 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ).
tt(t21_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((v4_ring_1 B A) <=>  ( (~ (v2_struct_0 (k2_ring_1 A B)))  &  ( (~ (v6_struct_0 (k2_ring_1 A B)))  &  ((v13_algstr_0 (k2_ring_1 A B)) &  ((v33_algstr_0 (k2_ring_1 A B)) &  ((v3_group_1 (k2_ring_1 A B)) &  ((v4_vectsp_1 (k2_ring_1 A B)) &  ((v5_vectsp_1 (k2_ring_1 A B)) &  ((v2_rlvect_1 (k2_ring_1 A B)) &  ((v3_rlvect_1 (k2_ring_1 A B)) &  ((v4_rlvect_1 (k2_ring_1 A B)) & (l6_algstr_0 (k2_ring_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k17_ringcat1 A))) =>  ((r2_hidden (k4_tarski C B) (k1_relset_1 (k2_zfmisc_1 (u4_struct_0 (k17_ringcat1 A)) (u4_struct_0 (k17_ringcat1 A))) (u1_cat_1 (k17_ringcat1 A)))) <=>  ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B)) ) ) ) ) ) ) ) ).
tt(t21_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k1_rlaffin1 A B (k4_struct_0 A)) B)) ) ) ) ).
tt(t21_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ((r1_tarski B C) & (r2_hidden (k1_funct_1 (k2_rlaffin2 A) C) (k4_rlaffin1 A B)))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t21_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_rlaffin1 D C) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) )  =>  (! [E:$i] :  ((m2_rlaffin3 E C D) =>  ((r2_hidden A (k4_rlaffin1 C D)) =>  ((r2_hidden A (k4_rlaffin1 C (k7_relset_1 k5_numbers (u1_struct_0 C) E (k2_finseq_1 B)))) <=>  ((k1_rlaffin3 C D E A) = (k7_finseq_1 (k17_finseq_1 k1_numbers B (k1_rlaffin3 C D E A)) (k2_finseq_2 (k7_nat_d (k5_card_1 D) B) k1_xboole_0))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_struct_0 D B) => (r1_struct_0 D (k1_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t21_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k2_rlsub_2 A (k2_rlsub_1 A) (k2_rlsub_1 A)) = A) ) ) ).
tt(t21_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_convex1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 C 1) & (r2_hidden (k4_struct_0 A) B)) )  => (r1_tarski (k1_convex1 A B C) B)) ) ) ) ) ) ) ).
tt(t21_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t21_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_rlvect_2 D A B) =>  ((r1_tarski B C) => (m2_rlvect_2 D A C)) ) ) ) ) ) ) ) ) ).
tt(t21_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k1_rlvect_3 A B) = A)  & (r1_tarski B C))  =>  ((k1_rlvect_3 A C) = A) ) ) ) ) ) ) ) ).
tt(t21_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (~  ( (~  (A = B) )  & (v1_rlvect_3 (k7_domain_1 (u1_struct_0 C) (k1_rlvect_1 C D A) (k1_rlvect_1 C D B)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_struct_0 (k1_rlvect_3 A (k4_subset_1 (u1_struct_0 A) B C)) D) &  ( (~ (r1_struct_0 (k1_rlvect_3 A C) D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r1_struct_0 (k1_rlvect_3 A (k4_subset_1 (u1_struct_0 A) (k7_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) (k6_domain_1 (u1_struct_0 A) E)) (k6_domain_1 (u1_struct_0 A) D))) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden A (k5_rusub_4 B (k2_rlvect_x B (k7_domain_1 (u1_struct_0 B) D E)) C)) <=>  (? [F:$i] :  ((v1_int_1 F) &  (? [G:$i] :  ((v1_int_1 G) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B C (k1_rlvect_1 B D F)) (k1_rlvect_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rmod_2 E A C) =>  ((r1_struct_0 E D) => (r1_struct_0 E (k5_vectsp_2 A C B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ( ((k2_rmod_3 A B (k1_rmod_2 A B) C) = (k1_rmod_2 A B))  &  ((k2_rmod_3 A B C (k1_rmod_2 A B)) = (k1_rmod_2 A B)) ) ) ) ) ) ) ) ).
tt(t21_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_rmod_4 C A B (k1_subset_1 (u1_struct_0 B))) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k3_rmod_4 A B))) ) ) ) ) ) ).
tt(t21_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_robbins1 A B (k5_robbins1 A B C)) = B) ) ) ) ) ) ) ).
tt(t21_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A B B)) = (k3_robbins1 A B)) ) ) ) ) ).
tt(t21_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_robbins1 B))  =>  ( ( ((g4_robbins1 (u1_struct_0 A) (u2_lattices A) (u1_lattices A) (u1_robbins1 A)) = (g4_robbins1 (u1_struct_0 B) (u2_lattices B) (u1_lattices B) (u1_robbins1 B)))  & (v8_robbins3 A))  => (v8_robbins3 B)) ) ) ) ) ).
tt(t21_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( ( (A = (k6_subset_1 3 1))  &  (B = 1) )  =>  ((k3_lattices k2_robbins4 A B) = 3) ) ) ) ) ) ).
tt(t21_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  ((k4_roughs_1 A (k2_struct_0 A)) = (k2_struct_0 A)) ) ) ).
tt(t21_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((k1_rpr_1 A (k4_subset_1 A B C)) = (k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C))) ) ) ) ) ) ) ) ).
tt(t21_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_rsspace4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_normsp_0 (k9_rsspace4 A B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k9_rsspace4 A B))) )  &  ( ( (C = (k4_struct_0 (k9_rsspace4 A B)))  =>  ((k1_normsp_0 (k9_rsspace4 A B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k9_rsspace4 A B) (k1_rlvect_1 (k9_rsspace4 A B) C E)) = (k8_real_1 (k18_complex1 E) (k1_normsp_0 (k9_rsspace4 A B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k9_rsspace4 A B) (k1_algstr_0 (k9_rsspace4 A B) C D)) (k7_real_1 (k1_normsp_0 (k9_rsspace4 A B) C) (k1_normsp_0 (k9_rsspace4 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  ( ((m1_rusub_1 A B) & (m1_rusub_1 B C))  => (m1_rusub_1 A C)) ) ) ) ) ) ) ).
tt(t21_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k2_rusub_2 A (k2_rusub_1 A) (k2_rusub_1 A)) = A) ) ) ).
tt(t21_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 (k1_rusub_3 A B) C)) ) ) ) ) ) ).
tt(t21_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v1_rusub_4 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k2_rusub_4 B C) (k2_rusub_4 A C))) ) ) ) ) ) ).
tt(t21_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (r1_struct_0 (k2_rusub_5 A B) (k4_struct_0 A))) ) ) ) ).
tt(t21_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_rvsum_1 (k2_finseq_2 A B)) = (k5_finseq_2 k1_numbers A (k7_binop_2 B))) ) ) ) ) ).
tt(t21_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k9_rvsum_2 (k9_finseq_1 B) A) = (k12_finseq_1 k2_numbers (k5_binop_2 A B))) ) ) ) ) ).
tt(t21_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k8_ami_3 1 (k10_ami_3 k6_numbers))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 4)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t21_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_scmfsa_1 k3_scmfsa_1) =>  ((k9_scmfsa_1 (k6_scmfsa_1 A B) C) = (k9_scmfsa_1 A C)) ) ) ) ) ) ) ).
tt(t21_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k9_scmfsa_2 A B)) = 4) ) ) ) ) ).
tt(t21_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k3_scmfsa6a A B)) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t21_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (~ (r1_extpro_1 3 k1_scmfsa_2 (k2_funct_7 B (k5_memstr_0 3 k1_scmfsa_2 A) (k11_scmfsa_2 (k5_memstr_0 3 k1_scmfsa_2 A))) A)) ) ) ) ) ).
tt(t21_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((r5_scmfsa7b C A B) =>  ((r4_scmfsa7b C D) |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) E) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A))) =>  ((r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) D) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) D)) &  (~  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) &  ((r5_scmfsa7b D B A) & (r6_scmfsa7b D B A)) )  =>  ((r5_scmfsa7b (k2_scmfsa8b E C D) B A) & (r6_scmfsa7b (k2_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a B A C) =>  ((r1_scmfsa8a (k8_memstr_0 3 k1_scmfsa_2 B) (k1_funct_4 A C) C) &  ((k2_scmfsa8a B A C) = (k2_scmfsa8a (k8_memstr_0 3 k1_scmfsa_2 B) (k1_funct_4 A C) C)) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  ( ((r1_scmfsa9a A C E F) &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 C F E A) G)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D F E B) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k1_scmfsa_9 A B) (k2_nat_1 (k5_card_1 B) 4)) = (k11_scmfsa_2 k6_numbers)) ) ) ) ) ).
tt(t21_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_funct_1 (k1_funct_4 A (k7_memstr_0 3 k1_scmfsa_2 C)) B) = (k1_funct_1 A B)) ) ) ) ) ) ) ).
tt(t21_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scm_halt D) & (v3_scm_halt D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v2_scm_halt E)) ) ) ) ) ) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a D E) A C) B) = (k18_scmfsa_2 (k1_scmfsa6b E (k1_scmfsa6b D A C) C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmisort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v2_scm_halt A) & (v1_scmfsa7b A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k4_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k4_numbers)))) )  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( (~  ( (~ (r1_xxreal_0 (k1_funct_1 C D) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 C D) (k1_funct_1 C (k1_scmfsa6b A D F)))) )  &  ( ( ((k6_memstr_0 3 k1_scmfsa_2 D) = (k6_memstr_0 3 k1_scmfsa_2 E))  =>  ((k1_funct_1 C D) = (k1_funct_1 C E)) )  &  ( ((r1_xxreal_0 (k1_funct_1 C D) k6_numbers) => (r1_xxreal_0 (k1_funct_1 D B) k6_numbers))  &  ((r1_xxreal_0 (k1_funct_1 D B) k6_numbers) => (r1_xxreal_0 (k1_funct_1 C D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) )  => (v2_scm_halt (k2_scmfsa_9 B A))) ) ) ) ) ).
tt(t21_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k12_scmpds_2 C D A B)) = 9) ) ) ) ) ) ) ) ) ).
tt(t21_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ( (C = D)  &  ((r1_tarski B E) &  ((r1_tarski B F) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( (~ (r1_xxreal_0 A G))  => (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 F D G)) (k2_afinsq_1 B))) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 G A) =>  ((k5_extpro_1 2 k1_scmpds_2 E C G) = (k5_extpro_1 2 k1_scmpds_2 F D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmpds_5,ax, (! [A:$i] :  ((v1_int_1 A) => (v6_compos_0 (k3_scmpds_2 A) (u1_compos_1 k1_scmpds_2))) ) ).
tt(t21_scmpds_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v2_scmpds_4 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r2_scmpds_6 A B C)) ) ) ) ) ) ) ).
tt(t21_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A))) &  ((r1_tarski C D) &  ((r1_scmpds_6 C A B) & (r2_scmpds_6 C A B)) ) )  => (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k8_memstr_0 2 k1_scmpds_2 A) E)) (k2_afinsq_1 (k10_compos_1 k1_scmpds_2 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) k6_numbers) =>  ((k6_scmpds_4 (k2_scmpds_8 D F C) B A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k2_compos_1 (k1_scmring2 A)) = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ) ) ).
tt(t21_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 1)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t21_scmyciel,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v3_scmyciel B A) =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((r2_hidden C B) => (r1_xxreal_0 (k5_card_1 C) (k1_nat_1 A 1))) ) ) ) ) ) ) ).
tt(t21_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) )  => (r2_analoaf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(t21_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B) (k20_valued_1 k5_numbers k1_numbers k1_numbers A C)) (k20_valued_1 k5_numbers k1_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t21_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_relat_1 A))  =>  ( ((k2_seq_2 A) = k6_numbers)  | (v2_comseq_2 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ) ).
tt(t21_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 (k1_valued_0 k1_numbers B A)) => (v2_comseq_2 B)) ) ) ) ) ).
tt(t21_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_seqfunc A B C) =>  ((r2_relset_1 A k1_numbers D (k11_seqfunc A B C)) <=>  ( ((k1_relset_1 A D) = C)  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k18_complex1 (k9_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers B H) E) (k1_seq_1 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_valued_0 k1_numbers (k26_valued_1 k5_numbers k1_numbers C B) A) = (k26_valued_1 k5_numbers k1_numbers (k1_valued_0 k1_numbers C A) B)) ) ) ) ) ) ) ).
tt(t21_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) D) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_newton B 7)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k3_xcmplx_0 (k4_nat_1 (k13_newton B 2) (k13_newton (k2_nat_1 B 1) 2)) (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k2_nat_1 (k4_nat_1 3 (k13_newton B 4)) (k4_nat_1 6 (k13_newton B 3))) (k13_newton B 2)) (k4_nat_1 4 B)) 2)) 24)) ) ) ) ) ) ).
tt(t21_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 (k13_complex1 1 4) (k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)))) ) ) ) ) ).
tt(t21_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k2_xcmplx_0 (k13_newton 2 B) (k1_newton (k7_xcmplx_0 1 2) B))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_xcmplx_0 (k6_xcmplx_0 (k13_newton 2 (k2_nat_1 B 1)) (k1_newton (k7_xcmplx_0 1 2) B)) 1)) ) ) ) ) ) ).
tt(t21_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 B C)) (k3_xcmplx_0 C A)) = 1)  => (r1_xxreal_0 (k7_square_1 3) (k2_xcmplx_0 (k2_xcmplx_0 A B) C))) ) ) ) ) ) ) ).
tt(t21_setfam_1,ax, (! [A:$i] : (r1_setfam_1 (k3_setfam_1 A A) A)) ).
tt(t21_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k5_prob_1 B (k9_setfam_1 B) (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) (k2_nat_1 A 1)) (k3_funct_2 k5_numbers (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t21_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 C) => (v2_prob_1 (k5_setlim_2 A C B))) ) ) ) ) ) ).
tt(t21_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) & (v2_binop_1 C A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 B)) =>  (~  ( (~  (E = k1_xboole_0) )  &  ( (~  (F = k1_xboole_0) )  &  (~  ((k7_setwiseo B A C (k5_setwiseo B E F) D) = (k5_binop_1 A C (k7_setwiseo B A C E D) (k7_setwiseo B A C F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k2_partfun1 k5_numbers A (k1_setwop_2 A C B) (k4_finseq_1 C)) = C) ) ) ) ) ) ) ).
tt(t21_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( ((r1_sfmastr2 B A C D) | (v7_amistd_1 D 3 k1_scmfsa_2))  &  ( (~ (r1_xxreal_0 (k1_funct_1 A C) E))  &  ( (~  ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C)) )  &  (~  ((k11_card_3 (k2_memstr_0 3 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) (k2_nat_1 E 1)) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2)) = (k5_relat_1 (k1_scmfsa6b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E) (k1_funct_4 B (k1_sfmastr2 C D))) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_sfmastr3 G B C D E A))  =>  ((r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A D) (k1_funct_1 A C)) 1) F) |  ((k5_relat_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) (k2_nat_1 F 1)) (k2_xboole_0 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E)) k3_scmfsa_2)) = (k5_relat_1 (k1_scmfsa6b (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B C D E A) F) (k1_funct_4 G (k2_scmfsa_9 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k5_scmfsa6a (k5_scmfsa6a E (k7_scmfsa_2 B (k4_scmfsa_2 k6_numbers))) (k8_scmfsa_2 (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E))) (k4_scmfsa_2 k6_numbers)))))) (k2_xboole_0 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m B C D) (k2_sf_mastr E)) k3_scmfsa_2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((r1_xboole_0 (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers B)) =>  ((k2_sf_mastr (k1_funct_4 A B)) = (k4_subset_1 k2_scmfsa_2 (k2_sf_mastr A) (k2_sf_mastr B))) ) ) ) ) ) ).
tt(t21_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  ( ((v1_finset_1 (u1_struct_0 B)) & (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 A)))  &  ((v1_finset_1 (u1_sgraph1 B)) & (m1_subset_1 (u1_sgraph1 B) (k1_zfmisc_1 (k2_sgraph1 (u1_struct_0 B))))) ) ) ) ) ).
tt(t21_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v13_lattices A) &  ((v14_lattices A) &  ((v16_lattices A) &  ((v17_lattices A) &  ((v3_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) )  =>  ((k5_lattices A) = (k2_sheffer1 A)) ) ) ).
tt(t21_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B B)) = B) ) ) ) ) ) ) ).
tt(t21_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_matroid0 A) =>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k5_simplex0 (u1_struct_0 A) (u1_pre_topc A))) ) ) ) ).
tt(t21_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ( ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) & (r1_xxreal_0 (k6_simplex0 B) k1_xboole_0))  =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (k4_simplex1 A B)) ) ) ) ) ) ).
tt(t21_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) &  (? [D:$i] :  ((v1_xreal_0 D) & (r1_tarski B (k4_euclid_9 A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t21_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_seq_1 k1_sin_cos2 (k9_binop_2 A B)) = (k7_real_1 (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B))))  &  ((k1_seq_1 k1_sin_cos2 (k10_binop_2 A B)) = (k9_real_1 (k8_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ) ).
tt(t21_sin_cos3,ax, ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 k5_complex1) = k6_numbers) ).
tt(t21_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  (~  ((k2_xcmplx_0 (k1_sin_cos4 A) (k2_sin_cos4 B)) = (k7_xcmplx_0 (k20_sin_cos (k6_xcmplx_0 A B)) (k3_xcmplx_0 (k20_sin_cos A) (k17_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t21_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_square_1 (k20_sin_cos A)) = (k10_real_1 (k7_real_1 1 (k21_sin_cos (k8_real_1 2 A))) 2)) ) ) ).
tt(t21_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  &  ( ((k17_sin_cos A) = k6_numbers)  &  ( (~  (A = (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) )  &  (~  (A = (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 (k3_square_1 A) 1))  & (r1_xxreal_0 1 (k5_square_1 (k12_binop_2 1 A)))) ) ) ) ).
tt(t21_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k3_sin_cos2 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k9_sin_cos2 C)) (k3_xcmplx_0 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k9_sin_cos2 C))) (k6_sin_cos2 A)) (k6_sin_cos2 B)) (k6_sin_cos2 C)))  &  ( ((k6_sin_cos2 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 1 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B))) (k3_xcmplx_0 (k9_sin_cos2 B) (k9_sin_cos2 C))) (k3_xcmplx_0 (k9_sin_cos2 C) (k9_sin_cos2 A))) (k6_sin_cos2 A)) (k6_sin_cos2 B)) (k6_sin_cos2 C)))  &  ((k9_sin_cos2 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k9_sin_cos2 C)) (k3_xcmplx_0 (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B)) (k9_sin_cos2 C))) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 1 (k3_xcmplx_0 (k9_sin_cos2 B) (k9_sin_cos2 C))) (k3_xcmplx_0 (k9_sin_cos2 C) (k9_sin_cos2 A))) (k3_xcmplx_0 (k9_sin_cos2 A) (k9_sin_cos2 B))))) ) ) ) ) ) ) ) ) ).
tt(t21_sin_cos9,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t21_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers (k12_sin_cos A B E))) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v2_funct_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)) &  ((v2_sppol_1 (k2_topreal1 2 B A)) & (v1_sppol_1 (k2_topreal1 2 B A))) ) ) ) ) ) ) ) ) ).
tt(t21_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_topreal1 2 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) A B)) = (k1_rltopsp1 (k15_euclid 2) A B)) ) ) ) ) ).
tt(t21_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_xxreal_0 (k6_pscomp_1 A) (k8_pscomp_1 A))) ) ).
tt(t21_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r1_sprect_2 A A)) ) ).
tt(t21_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 B)) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k3_topreal1 2 A)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) ) ) )  =>  ( ( (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) )  &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) )  | (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ) ).
tt(t21_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t21_square_1,ax, (~ (r1_xxreal_0 2 (k7_square_1 2))) ).
tt(t21_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k11_stacks_1 A (k7_stacks_1 A B C))) &  ( (~ (r1_stacks_1 A B))  => (r2_hidden B (k11_stacks_1 A (k5_stacks_1 A B)))) ) ) ) ) ) ) ) ).
tt(t21_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( (C = (k6_partfun1 B))  =>  ((r1_xxreal_0 B k6_numbers) | (v1_stirl2_1 C B A)) ) ) ) ) ) ) ) ).
tt(t21_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k19_substut1 A (k6_sublemma A B C)) = (k19_substut1 A B)) ) ) ) ) ) ) ) ).
tt(t21_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r1_tarski (k3_subset_1 A (k4_subset_1 A B C)) (k3_subset_1 A B))) ) ) ) ) ).
tt(t21_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A B))) =>  ((k4_substlat A B C (k4_substlat A B D E)) = (k4_substlat A B (k4_substlat A B C D) E)) ) ) ) ) ) ) ) ) ).
tt(t21_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) =>  ((k31_substut1 A (k24_substut1 A B C)) = (k22_substut1 A B)) ) ) ) ) ) ) ) ).
tt(t21_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A B D)))) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_cqc_sim1 A C) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A C D)))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_cqc_sim1 A (k7_cqc_lang A B C)) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A (k7_cqc_lang A B C) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t21_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_supinf_2 C A B) <=>  ( (~ (r1_xxreal_0 k1_supinf_1 (k10_supinf_2 k7_numbers A B C)))  &  (~ (r1_xxreal_0 (k11_supinf_2 k7_numbers A B C) k2_supinf_1)) ) ) ) ) ) ) ) ) ).
tt(t21_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B (k5_algstr_0 B E C) D) =>  ((r1_orders_2 B C D) |  ((k1_symsp_1 A B D C E) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ((k3_relat_1 (k4_relat_1 A) (k6_subset_1 B (k4_relat_1 A))) = k1_xboole_0)  =>  ((k9_xtuple_0 (k6_subset_1 B (k4_relat_1 A))) = (k6_subset_1 (k9_xtuple_0 B) A)) )  &  ( ((k3_relat_1 (k6_subset_1 B (k4_relat_1 A)) (k4_relat_1 A)) = k1_xboole_0)  =>  ((k10_xtuple_0 (k6_subset_1 B (k4_relat_1 A))) = (k6_subset_1 (k10_xtuple_0 B) A)) ) ) ) ) ) ).
tt(t21_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((v2_metric_1 B A) & (v3_metric_1 B A))  => (r2_hidden (k4_tarski C C) (k1_taxonom1 A B k6_numbers))) ) ) ) ) ) ) ).
tt(t21_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_fdiff_1 (k4_taylor_1 B) A) &  ((k1_fdiff_1 (k4_taylor_1 B) A) = (k3_xcmplx_0 B (k9_prepower A (k5_real_1 B 1)))) ) ) ) ) ) ) ).
tt(t21_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_taylor_1 k16_sin_cos B A) & (r1_taylor_1 k19_sin_cos B A)) ) ) ) ) ).
tt(t21_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tbsp_1 B A) => (r1_xxreal_0 k6_numbers (k3_tbsp_1 A B))) ) ) ) ) ).
tt(t21_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v6_tops_1 (k2_struct_0 A) A)) ) ).
tt(t21_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B C) => (r1_tarski (k1_tdlat_2 A B) (k1_tdlat_2 A C))) ) ) ) ) ) ) ).
tt(t21_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v4_pre_topc B A)) ) ) ) ) ) ).
tt(t21_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) = k1_xboole_0)  |  ((k2_polynom1 (k15_pre_poly A) C (k5_termord A B C D)) = (k1_tarski (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t21_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~ (v1_xboole_0 (k6_subset_1 A (k6_domain_1 A B))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_tex_1 A B)))) =>  ( ( (C = (k6_domain_1 A B))  =>  ((v4_pre_topc C (k3_tex_1 A B)) & (v2_tops_1 C (k3_tex_1 A B))) )  &  ( ((v4_pre_topc C (k3_tex_1 A B)) & (v2_tops_1 C (k3_tex_1 A B)))  =>  ((v1_xboole_0 C) |  (C = (k6_domain_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (u1_struct_0 A))  =>  ((v2_tex_2 B A) <=> (v1_tdlat_3 A)) ) ) ) ) ) ).
tt(t21_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tex_3 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_tex_3 C B) & (m1_pre_topc C B)) )  =>  ((v2_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ).
tt(t21_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_tex_4 A B)) <=>  ((k2_tex_4 A C) = (k2_tex_4 A B)) ) ) ) ) ) ) ) ).
tt(t21_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v2_xxreal_0 C) & (v1_xreal_0 C))  =>  ((r1_tietze B C (u1_struct_0 A)) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k4_xcmplx_0 C) C))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k4_xcmplx_0 C) C)))))) ) ) ) ) ) ) ) ) ).
tt(t21_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((k2_tsep_1 A B B) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ).
tt(t21_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ( ((v1_toler_1 D A B) & (m1_toler_1 D A B))  =>  (~ (r2_hidden C D)) ) ) ) ) ) ) ) ) ).
tt(t21_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A D C))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D C) =>  ((r3_borsuk_2 A B C E F) => (r3_borsuk_2 A B C E (k1_borsuk_2 A B D C (k1_borsuk_2 A B C D F (k2_borsuk_2 A D C G)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k17_borsuk_1)) =>  (! [D:$i] :  ( ((v3_funct_1 D) & (m1_borsuk_2 D A B B))  =>  ((k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 A) D C) = B) ) ) ) ) ) ) ) ) ).
tt(t21_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A C D) =>  (! [K:$i] :  ((m1_borsuk_2 K B E F) =>  (! [L:$i] :  ((m1_borsuk_2 L B E F) =>  (! [M:$i] :  ((m1_borsuk_6 M A C D I J) =>  (! [N:$i] :  ((m1_borsuk_6 N B E F K L) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) I (k3_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) J (k3_topalg_4 A B k5_topmetr H)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) K (k4_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) L (k4_topalg_4 A B k5_topmetr H)) &  ((r3_borsuk_2 A C D I J) & (r3_borsuk_2 B E F K L)) ) ) ) )  => (m1_borsuk_6 (k2_topalg_4 A B (k2_borsuk_1 k5_topmetr k5_topmetr) M N) (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topalg_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2))))) =>  ( ((m1_setfam_1 A (u1_struct_0 (k8_toprealb 2))) & (v1_tops_2 A (k8_toprealb 2)))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 B k5_topmetr)) (u1_struct_0 (k8_toprealb 2))) &  ((v5_pre_topc C (k2_borsuk_1 B k5_topmetr) (k8_toprealb 2)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B k5_topmetr)) (u1_struct_0 (k8_toprealb 2)))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_finseq_1 E k1_numbers))  &  ( ((k1_seq_1 E 1) = k6_numbers)  &  ( ((k1_seq_1 E (k3_finseq_1 E)) = 1)  &  ((v5_valued_0 E) &  (? [F:$i] :  ( ((v3_pre_topc F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r2_hidden D F) &  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden G (k4_finseq_1 E)) &  ((r2_hidden (k1_nat_1 G 1) (k4_finseq_1 E)) &  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2)))))  =>  (~  ((r2_hidden H A) & (r1_tarski (k7_relset_1 (u1_struct_0 (k2_borsuk_1 B k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) C (k2_zfmisc_1 F (k1_rcomp_1 (k1_seq_1 E G) (k1_seq_1 E (k1_nat_1 G 1))))) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) => (m2_subset_1 k1_xboole_0 (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ).
tt(t21_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ( ( (D = C)  & (v1_topdim_1 C A))  =>  ((v1_topdim_1 D (k1_pre_topc A B)) &  ((k2_topdim_1 (k1_pre_topc A B) D) = (k2_topdim_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 (k4_topdim_1 (k15_euclid A)) A)) ) ).
tt(t21_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_topgen_1 A B C) <=>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (E = C) )  &  ((r2_hidden E B) & (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C A) =>  ((v4_pre_topc (k1_tarski C) (k5_topgen_2 A B)) & (m1_subset_1 (k1_tarski C) (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B))))) ) ) ) ) ).
tt(t21_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 1 B))  &  (~ (v1_series_1 (k4_topgen_3 A B))) ) ) ) ) ) ) ).
tt(t21_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_tops_2 B A) & (v2_tops_2 C A))  => (v2_tops_2 (k2_topgen_4 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t21_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 k6_numbers B) =>  ((r1_xxreal_0 C k6_numbers) |  ((r1_xboole_0 (k1_topreal9 2 (k19_euclid A B) C) k1_topgen_5) <=> (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ).
tt(t21_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_connsp_2 (k2_struct_0 A) A B)) ) ) ) ).
tt(t21_topmetr,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  ( (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 A D) = (k7_real_1 (k8_real_1 B D) C)) ) ) ) ) ) )  => (v5_pre_topc A k3_topmetr k3_topmetr)) ) ) ).
tt(t21_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_nat_1 B 1) (k3_finseq_1 C)))  =>  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) C B) (k2_topreal1 A C B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) C (k1_nat_1 B 1)) (k2_topreal1 A C B))) ) ) ) ) ) ) ) ).
tt(t21_topreal3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid B))) =>  ( ((r2_hidden C (k9_metric_1 (k14_euclid B) E A)) & (r2_hidden D (k9_metric_1 (k14_euclid B) E A)))  => (r1_tarski (k1_rltopsp1 (k15_euclid B) C D) (k9_metric_1 (k14_euclid B) E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k18_euclid A)) (k9_metric_1 (k14_euclid 2) E D)) &  ((v4_topreal1 B) &  ( (C = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k18_euclid A)) A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k18_euclid A))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) (k18_euclid A)) A)) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) )  =>  ( ((k17_euclid A) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  |  ( ((k18_euclid A) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))))  |  ((r1_topreal4 (k3_topreal1 2 C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) & (r1_tarski (k3_topreal1 2 C) (k2_xboole_0 (k3_topreal1 2 B) (k9_metric_1 (k14_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_topreal6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k4_card_3 (k4_funct_4 E F A C)) (k4_card_3 (k4_funct_4 E F B D)))) ) ) ) ) ) ) ).
tt(t21_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_metric_1 B) & (l1_metric_1 B)) )  => (v8_metric_1 (k1_topreal7 A B))) ) ) ) ).
tt(t21_topreal8,ax, (! [A:$i] :  ( ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) => (v3_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(t21_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((v1_xboole_0 (k1_topreal9 A C B)) => (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ).
tt(t21_topreala,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_topmetr)) =>  ( ( (A = B)  & (r1_fcont_1 B C))  => (r1_tmap_1 k3_topmetr k3_topmetr A C)) ) ) ) ) ) ) ).
tt(t21_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (~ (m1_subset_1 A (u1_struct_0 (k11_toprealb A)))) ) ) ).
tt(t21_toprealc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  => (r1_xxreal_0 (k18_complex1 (k16_rvsum_1 A)) (k18_rvsum_1 (k3_euclid A)))) ) ).
tt(t21_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_toprns_1 C A) =>  ( (B = k6_numbers)  | (v1_toprns_1 (k2_toprns_1 B A C) A)) ) ) ) ) ) ) ) ).
tt(t21_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_tops_1 A (k7_subset_1 (u1_struct_0 A) B C)) (k7_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k1_tops_1 A C)))) ) ) ) ) ) ).
tt(t21_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_tops_2 B A) & (v1_finset_1 B))  => (v4_pre_topc (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t21_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) => (v1_tops_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t21_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  ((v5_pre_topc B A k3_topmetr) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden C E) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) D) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 A A)))) =>  ( ((r1_transgeo A B D) & (r2_transgeo A C D))  => (r1_transgeo A (k2_transgeo A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t21_treal_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k17_borsuk_1) (u1_struct_0 k17_borsuk_1)) &  ((v5_pre_topc A k17_borsuk_1 k17_borsuk_1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k17_borsuk_1))))) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 k17_borsuk_1)) &  ((k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 k17_borsuk_1) A B) = B) ) ) ) ) ).
tt(t21_trees_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden (k7_finseq_1 A C) B) => (r2_hidden A B)) ) ) ) ) ) ) ).
tt(t21_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m1_trees_2 D A) =>  (~  ((r2_hidden B D) &  ((r2_hidden C D) &  ( (~ (r2_hidden B (k1_trees_1 C)))  &  (~ (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_tarski (k5_trees_3 A) (k4_trees_3 A))) ) ).
tt(t21_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ((k3_trees_4 A (k9_finseq_1 B)) = (k7_trees_2 (k7_funcop_1 (k2_trees_1 1) A) (k12_finseq_1 k5_numbers k6_numbers) (k1_trees_4 B))) ) ) ).
tt(t21_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_trees_3 B))  =>  ((r1_tarski A B) => (r1_tarski (k9_trees_9 A) (k9_trees_9 B))) ) ) ) ) ).
tt(t21_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((k1_tsep_1 A (k1_tsep_1 A B C) D) = (k1_tsep_1 A B (k1_tsep_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t21_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=> (r1_connsp_1 A (k7_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) B) (k7_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) C))) ) ) ) ) ) ) ).
tt(t21_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k4_tex_4 A D))) )  => (v3_borsuk_1 C A B)) ) ) ) ) ) ) ).
tt(t21_turing_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 3 (k3_finseq_1 A)) =>  ( ((k1_gr_cy_1 (k4_turing_1 1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = B)  &  ( ((k1_gr_cy_1 (k4_turing_1 2 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = (k2_nat_1 B (k7_partfun1 k5_numbers A 1)))  &  ( ((k1_gr_cy_1 (k4_turing_1 3 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = (k2_nat_1 (k2_nat_1 B (k7_partfun1 k5_numbers A 1)) (k7_partfun1 k5_numbers A 2)))  &  ((k1_gr_cy_1 (k4_turing_1 4 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) A))) = (k2_nat_1 (k2_nat_1 (k2_nat_1 B (k7_partfun1 k5_numbers A 1)) (k7_partfun1 k5_numbers A 2)) (k7_partfun1 k5_numbers A 3))) ) ) ) ) ) ) ) ) ).
tt(t21_twoscomp,ax, ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 k6_numbers 1 1)) = k6_numbers)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k20_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k20_twoscomp (k11_finseq_1 1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t21_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) =>  (! [C:$i] :  ((m1_unialg_2 C A) =>  ((k8_unialg_2 A B C) = (k8_unialg_2 A C B)) ) ) ) ) ) ) ).
tt(t21_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (u1_struct_0 A))  =>  ((k6_lattices (k12_unialg_2 A)) = (k7_unialg_2 A B)) ) ) ) ) ) ).
tt(t21_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((r2_hidden B (k2_uniroots A)) <=> (m1_comptrig B (k1_group_1 k1_complfld) A)) ) ) ) ) ).
tt(t21_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B C) (k9_polynom3 A)) &  ( (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k9_polynom3 A)))  &  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) C (k9_polynom3 A))) ) ) ) ) ) ) ) ) ) ).
tt(t21_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) <=>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) & (r1_tarski (k2_pre_topc A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k8_real_1 (k13_newton 2 B) A) 1)) ) ) ) ) ) ).
tt(t21_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc D A k3_topmetr) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 D E)) &  ((r1_xxreal_0 (k1_seq_1 D E) 1) &  ( ((r2_hidden E B) =>  ((k1_seq_1 D E) = k6_numbers) )  &  ((r2_hidden E C) =>  ((k1_seq_1 D E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) => (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B D (k6_cqc_lang A (k6_cqc_lang A C))) (k8_valuat_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t21_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((m2_valued_0 C A B) => (r1_tarski (k2_relset_1 A C) (k2_relset_1 A B))) ) ) ) ) ) ).
tt(t21_valued_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k61_valued_1 (k61_valued_1 C B) A) = (k61_valued_1 C (k2_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t21_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k50_valued_1 (k50_valued_1 A B) C) = (k50_valued_1 A (k18_valued_1 B C))) ) ) ) ) ) ) ).
tt(t21_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( ((k4_vectsp10 A B C) = (k3_vectsp_4 A B (k4_struct_0 B) C))  &  ((k4_struct_0 (k6_vectsp10 A B C)) = (k4_vectsp10 A B C)) ) ) ) ) ) ) ) ).
tt(t21_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ( ((k1_funct_1 (k1_vectsp11 B C G) D) = E)  &  ((k1_funct_1 (k1_vectsp11 B C F) E) = E) )  =>  ((k1_funct_1 (k1_vectsp11 B C (k2_xcmplx_0 G (k3_xcmplx_0 A F))) D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k4_algstr_0 B (k4_vectsp_1 A B C D)) = (k4_vectsp_1 A B (k4_algstr_0 A C) D))  &  ((k5_algstr_0 B E (k4_vectsp_1 A B C D)) = (k1_algstr_0 B E (k4_vectsp_1 A B (k4_algstr_0 A C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  ((k1_vectsp_2 A D (k1_vectsp_2 A B C)) = (k1_vectsp_2 A (k6_algstr_0 A D C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_struct_0 E D) => (r1_struct_0 E (k4_vectsp_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ( ((k2_vectsp_5 A B (k2_vectsp_4 A B) C) = C)  &  ((k2_vectsp_5 A B C (k2_vectsp_4 A B)) = C) ) ) ) ) ) ) ) ).
tt(t21_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ( ((k1_vectsp_6 A B E) = (k7_domain_1 (u1_struct_0 B) C D))  =>  ( (C = D)  |  ((k4_vectsp_6 A B E) = (k3_rlvect_1 B (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k4_vectsp_1 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_matrlin B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) => (v1_finset_1 C)) ) ) ) ) ) ) ) ).
tt(t21_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k3_normsp_0 A B (k3_vfunct_1 A B D C)) (k20_valued_1 A k1_numbers k1_numbers (k56_valued_1 A k1_numbers D) (k3_normsp_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t21_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k1_numbers (k3_normsp_0 A B (k1_vfunct_2 A B D C)) (k20_valued_1 A k1_numbers k1_numbers (k55_valued_1 A k2_numbers D) (k3_normsp_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t21_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) => (r1_tarski (k5_waybel_0 A B) (k5_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t21_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_orders_2 B) &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((k1_funct_1 (k2_funct_1 (k5_waybel10 A)) B) = (k6_waybel10 A B)) ) ) ) ) ).
tt(t21_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((r1_tarski B (u1_struct_0 A)) & (v7_waybel_0 (k3_waybel11 A B C)))  => (r2_hidden (k3_waybel11 A B C) (k6_yellow_6 A))) ) ) ) ) ) ) ).
tt(t21_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k4_yellow_4 A B B) = B) ) ) ) ) ).
tt(t21_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ((v17_waybel_0 D A B) &  ( ((v4_yellow_0 B C) &  ((v7_yellow_0 B C) & (m1_yellow_0 B C)) )  &  ((v3_lattice3 C) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((r8_pboole (u1_struct_0 A) D E) & (v17_waybel_0 E A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_waybel_9 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  &  ((v1_tops_2 E B) &  ((v1_yellow_8 E B D) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) )  =>  ((v1_tops_2 E A) &  ((v1_yellow_8 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((k1_waybel15 A) = (k7_subset_1 (u1_struct_0 (k7_lattice3 A)) (k4_waybel_6 (k7_lattice3 A)) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)))) ) ) ).
tt(t21_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (~ (r2_hidden (k4_yellow_0 A) (k1_waybel16 A))) ) ) ).
tt(t21_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  => (r3_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_waybel11 A D)) (k1_waybel11 B (k6_waybel_9 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t21_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ( (E = D)  & (v4_pre_topc D A))  => (v4_pre_topc E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 B) C (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C))) => (v11_quantal1 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t21_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v18_waybel_0 B A A) => (v18_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t21_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D B) & (m1_yellow_0 D B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((u1_struct_0 C) = (u1_struct_0 D))  & (v8_yellow_0 C A)) )  => (v8_yellow_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t21_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r2_yellow_0 A C) =>  ((r2_yellow_0 (k5_yellow_0 A B) C) &  ((k2_yellow_0 (k5_yellow_0 A B) C) = (k2_yellow_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t21_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) & (l1_waybel_9 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  <=> (m1_subset_1 C (u1_struct_0 (k3_waybel24 A B)))) ) ) ) ) ) ).
tt(t21_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) &  ((v5_pre_topc C (k1_waybel25 A) (k1_waybel25 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B)))))) ) )  => (v5_orders_3 C (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ) ).
tt(t21_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ((r1_t_0topsp B C) => (r5_waybel_1 (k1_waybel26 A B) (k1_waybel26 A C))) ) ) ) ) ) ) ).
tt(t21_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D (k6_yellow_1 A (k6_yellow_1 B C))) & (m1_yellow_0 D (k6_yellow_1 A (k6_yellow_1 B C)))) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E (k6_yellow_1 (k2_zfmisc_1 A B) C)) & (m1_yellow_0 E (k6_yellow_1 (k2_zfmisc_1 A B) C))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 E) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 D))))) )  =>  ((v2_waybel27 F) => (v5_orders_3 F E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  (! [C:$i] :  ((m4_yellow_6 C A) =>  ((r1_tarski B C) => (r1_tarski (u1_pre_topc (k13_yellow_6 A C)) (u1_pre_topc (k13_yellow_6 A B)))) ) ) ) ) ) ) ).
tt(t21_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_waybel_3 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ((k1_waybel25 (k3_waybel18 A (k2_funcop_1 A (k1_waybel29 B)))) = (k1_waybel29 (k5_yellow_1 A (k2_funcop_1 A B)))) ) ) ) ) ).
tt(t21_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((m1_subset_1 C (u1_struct_0 (k2_waybel_2 A B D))) <=> (m1_subset_1 C (k5_finsub_1 B))) ) ) ) ) ) ) ).
tt(t21_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) ) ) ) ).
tt(t21_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v2_waybel19 B) & (m1_yellow_9 B A)) )  =>  (! [C:$i] :  ( ((v6_waybel23 C A) & (m1_waybel23 C A))  =>  ((v1_tops_2 (a_2_0_waybel31 A C) B) &  ((v1_cantor_1 (a_2_0_waybel31 A C) B) & (m1_subset_1 (a_2_0_waybel31 A C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ).
tt(t21_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_waybel_0 A C) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) )  & (v3_pre_topc B A))  => (v13_waybel_0 B A)) ) ) ) ) ).
tt(t21_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r1_tarski (k1_waybel19 A) (k4_waybel28 A))) ) ).
tt(t21_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v22_waybel_0 C A B) <=>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E A))  =>  (! [F:$i] :  ( ((v3_pre_topc F D) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))))  =>  ((v3_pre_topc (k4_waybel_0 A (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F)) E) & (m1_subset_1 (k4_waybel_0 A (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F)) (k1_zfmisc_1 (u1_struct_0 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  ((r1_yellow_0 A (k4_waybel35 A B C D)) &  (D = (k1_yellow_0 A (k4_waybel35 A B C D))) ) ) ) )  => (r1_waybel35 A C B)) ) ) ) ) ) ) ).
tt(t21_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A C (k1_yellow_0 A D)) => (r2_hidden B D)) ) )  => (r1_waybel_3 A B C)) ) ) ) ) ) ) ).
tt(t21_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r2_hidden (k3_yellow_0 A) B)) ) ) ) ).
tt(t21_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) (k7_funcop_1 B C) (k6_waybel_5 B C (u1_struct_0 A) D) E)) A)) )  =>  ((k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))) = (k4_yellow_2 A (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) (k7_funcop_1 B C) (k6_waybel_5 B C (u1_struct_0 A) D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  => (v6_waybel_6 (k3_yellow_0 A) A)) ) ).
tt(t21_waybel_7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 A)) &  ((v13_waybel_0 B (k3_yellow_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A))))) ) )  =>  ((v2_waybel_7 B (k3_yellow_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) | (r2_hidden (k6_subset_1 A C) B)) ) ) ) ) ) ) ).
tt(t21_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) => (v5_waybel_6 B A)) ) ) ) ) ).
tt(t21_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_yellow_6 A B))) => (m1_connsp_2 C A B)) ) ) ) ) ) ).
tt(t21_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k5_card_1 (u1_struct_0 (k4_weddwitt A))) = (k5_card_1 (u1_struct_0 A)))  <=> (v5_group_1 A)) ) ) ).
tt(t21_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (E = (k1_funct_1 (k5_weierstr A B) C))  &  (F = (k1_funct_1 (k5_weierstr A B) D)) )  => (r1_xxreal_0 (k18_complex1 (k9_real_1 E F)) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_wellord1 (k2_wellord1 B A) A) = (k2_wellord1 B A)) ) ) ) ).
tt(t21_wellord2,ax, (! [A:$i] : (r4_relat_2 (k1_wellord2 A) A)) ).
tt(t21_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ((r2_hidden A (k4_finseq_1 B)) => (m2_subset_1 (k10_real_1 (k3_wsierp_1 B) (k1_seq_1 B A)) k1_numbers k5_numbers)) ) ) ) ) ).
tt(t21_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_xboole_0 A (k2_xboole_0 A B)) = A) ) ) ).
tt(t21_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k7_xboolean A B)) = (k4_xboolean (k3_xboolean A) (k3_xboolean B))) ) ) ) ) ).
tt(t21_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) C) = (k6_xcmplx_0 (k6_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t21_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C D)) <=> (r1_xxreal_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ).
tt(t21_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k6_xtuple_0 A B C D) E) => (r2_hidden B (k14_xtuple_0 E))) ) ) ) ) ) ).
tt(t21_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  & (r1_xxreal_0 (k3_xxreal_0 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t21_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k4_xxreal_1 A B) (k3_xxreal_1 A B))) ) ) ) ).
tt(t21_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m1_xxreal_2 A (k1_xxreal_1 B A))) ) ) ) ).
tt(t21_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ((r2_hidden (k3_xxreal_3 A B) k1_numbers) &  (~  ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  ((v2_lattice3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_yellow_0 A (k2_tarski B C))) ) ) ) ) ) ) ).
tt(t21_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_waybel_3 (k3_yellow_3 A B) C D) <=>  ((r1_waybel_3 A (k8_yellow_3 A B C) (k8_yellow_3 A B D)) & (r1_waybel_3 B (k9_yellow_3 A B C) (k9_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow12,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v13_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B D) => (r1_xboole_0 (k4_yellow_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t21_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_yellow13 (k1_tarski (u1_struct_0 A)) A B) & (m1_yellow13 (k1_tarski (u1_struct_0 A)) A B)) ) ) ) ) ).
tt(t21_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (k1_tarski C))  &  ((r2_hidden B (k2_pre_topc A D)) &  ((v3_pre_topc E A) & (r2_hidden B E)) ) )  => (r2_hidden C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (v1_yellow15 B A)) ) ) ) ).
tt(t21_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r3_yellow16 B A) => (v3_lattice3 B)) ) ) ) ) ).
tt(t21_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_waybel18 A B))) =>  ( (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski (k2_struct_0 (k3_waybel18 A B)) (k3_tarski E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel18 A B C))) =>  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 D)))  =>  (~  ((r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski E)) (k3_tarski F)) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B C)))) =>  (~  ( (~  (G = (k2_struct_0 (k4_waybel18 A B C))) )  &  ((r2_hidden E G) &  ((r2_hidden (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) G) F) & (v3_pre_topc G (k4_waybel18 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (E = C)  &  ( (F = D)  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B F E)) &  ( (H = G)  &  (~  ((v2_altcat_3 G A C D) <=> (v1_altcat_3 H B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  &  ((r1_waybel_0 A D B) & (r3_waybel_9 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 A)))) =>  ((k1_yellow_0 (k3_yellow_1 A) B) = (k3_tarski B)) ) ) ) ).
tt(t21_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_yellow20 A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_yellow20 A B))) =>  ( ( (G = C)  &  ( (G = E)  &  ( (H = D)  &  (H = F) ) ) )  =>  ((k1_altcat_1 (k2_yellow20 A B) G H) = (k3_xboole_0 (k1_altcat_1 A C D) (k1_altcat_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v11_quantal1 (k3_struct_0 A))) ) ).
tt(t21_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))))  =>  ( (~ (v1_xboole_0 (k4_yellow_3 A B C)))  &  (~ (v1_xboole_0 (k5_yellow_3 A B C))) ) ) ) ) ) ) ) ).
tt(t21_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B D) & (r1_tarski C E))  => (r1_tarski (k1_yellow_4 A B C) (k1_yellow_4 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_yellow_5,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k13_lattice3 A B C) = (k3_yellow_0 A))  =>  ( (B = (k3_yellow_0 A))  &  (C = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ).
tt(t21_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((r2_waybel_0 A B C) =>  ( (~ (v2_struct_0 (k5_yellow_6 A B C)))  & (v7_waybel_0 (k5_yellow_6 A B C))) ) ) ) ) ) ) ).
tt(t21_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A B C) = (k13_lattice3 (k7_lattice3 A) (k8_lattice3 A B) (k8_lattice3 A C))) ) ) ) ) ) ) ).
tt(t21_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v3_yellow_8 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_zfmisc_1 B)) ) ) ) ).
tt(t21_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k1_cantor_1 A (k2_cantor_1 A (k1_cantor_1 A B))) = (k1_cantor_1 A (k2_cantor_1 A B))) ) ) ) ).
tt(t21_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v8_zf_fund1 B A) & (r2_hidden C B))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers k1_zf_lang) =>  ((r2_hidden (k5_zf_fund1 D C) B) => (r2_hidden (k5_zf_fund1 (k8_zf_lang E D) C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((v6_zf_lang (k16_zf_lang B C D A)) &  ( ((k23_zf_lang (k16_zf_lang B C D A)) = B)  &  ((k24_zf_lang (k16_zf_lang B C D A)) = (k14_zf_lang C D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_zf_lang A) =>  ((k1_funct_1 A 1) = 3) ) ) ) ).
tt(t21_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_tarski A B) (k1_tarski C)) =>  ((k2_tarski A B) = (k1_tarski C)) ) ) ) ) ).
tt(t21_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_zfmodel1 B A) & (r2_zfmodel1 C A))  => (r2_zfmodel1 (k3_relat_1 B C) A)) ) ) ) ) ) ) ).
tt(t21_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k14_zf_lang B C A)) <=>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ( (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  (~  ( (~  ((k3_funct_2 k1_zf_lang D F G) = (k3_funct_2 k1_zf_lang D E G)) )  &  ( (~  (B = G) )  &  (~  (C = G) ) ) ) ) ) )  => (r1_zf_model D F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t21_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_ordinal2 A B) & (r2_ordinal2 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t21_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v6_card_fil A) => (v1_zf_model (k4_classes1 A))) ) ) ).
tt(t21_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((u1_struct_0 A) = B)  => (v7_zmodul01 B A)) ) ) ) ) ).
tt(t220_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k25_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k25_member_1 A C) (k25_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t220_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 (k5_xcmplx_0 A) (k7_xcmplx_0 B C)) = (k7_xcmplx_0 B (k3_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(t220_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k7_xcmplx_0 1 2) A) => (r1_xxreal_0 (k6_xcmplx_0 1 (k3_xcmplx_0 2 A)) k6_numbers)) ) ) ).
tt(t220_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (r2_hidden A (k1_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ).
tt(t221_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r1_tarski (k25_member_1 A (k3_binop_2 B C)) (k9_member_1 (k25_member_1 A B) (k25_member_1 A C)))) ) ) ) ) ) ).
tt(t221_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 (k5_xcmplx_0 A) B) = (k5_xcmplx_0 (k3_xcmplx_0 A B))) ) ) ) ) ).
tt(t221_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k7_xcmplx_0 A 3))) ) ) ) ).
tt(t221_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  => (r2_hidden A (k2_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ).
tt(t222_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r1_tarski (k25_member_1 A (k4_binop_2 B C)) (k11_member_1 (k25_member_1 A B) (k25_member_1 A C)))) ) ) ) ) ) ).
tt(t222_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_xcmplx_0 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k5_xcmplx_0 A))) ) ) ).
tt(t222_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 A 3) k6_numbers)) ) ) ) ).
tt(t222_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xxreal_1 A B) = (k2_xboole_0 (k1_xxreal_1 A B) (k1_xxreal_1 B A))) ) ) ) ) ) ).
tt(t223_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden B A) => (r2_hidden (k6_xxreal_3 B C) (k26_member_1 A C))) ) ) ) ) ) ) ).
tt(t223_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~  (A = k6_numbers) )  &  ( (A = (k5_xcmplx_0 A))  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ).
tt(t223_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k7_xcmplx_0 A 4))) ) ) ) ).
tt(t223_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B C) & (r2_hidden A (k2_xboole_0 (k4_xxreal_1 B C) (k4_xxreal_1 C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t224_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k26_member_1 A B) = (a_2_18_member_1 A B)) ) ) ) ) ).
tt(t224_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) B) = (k2_xcmplx_0 A C)) ) ) ) ) ) ) ).
tt(t224_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 A 4) k6_numbers)) ) ) ) ).
tt(t224_xxreal_1,ax, (k1_numbers = (k4_xxreal_1 k2_xxreal_0 k1_xxreal_0)) ).
tt(t225_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k26_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (C = (k6_xxreal_3 D B))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t225_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) C) B) = (k2_xcmplx_0 A C)) ) ) ) ) ) ) ).
tt(t225_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  (A = (k7_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t225_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k4_xxreal_1 A B) k1_numbers)) ) ) ) ).
tt(t226_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_hidden B A) => (r2_hidden (k6_binop_2 B C) (k27_member_1 A C))) ) ) ) ) ) ) ).
tt(t226_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 A B) C) B) = (k6_xcmplx_0 A C)) ) ) ) ) ) ) ).
tt(t226_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ( (~ (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2) A))  &  (~ (r1_xxreal_0 B (k7_xcmplx_0 (k2_xcmplx_0 A B) 2))) ) ) ) ) ) ) ).
tt(t226_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r2_hidden A k1_numbers) => (r1_tarski (k2_xxreal_1 A B) k1_numbers)) ) ) ) ) ).
tt(t227_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k27_member_1 A B) = (a_2_19_member_1 A B)) ) ) ) ) ).
tt(t227_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) C) B) = (k6_xcmplx_0 A C)) ) ) ) ) ) ) ).
tt(t227_xreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t227_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r2_hidden A k1_numbers) => (r1_tarski (k3_xxreal_1 B A) k1_numbers)) ) ) ) ) ).
tt(t228_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  (~  ((r2_hidden C (k27_member_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (C = (k6_binop_2 D B))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t228_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A A) B) = (k4_xcmplx_0 B)) ) ) ) ) ).
tt(t228_xreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D A))  &  ( (~ (r1_xxreal_0 B D))  &  (~ (r1_xxreal_0 C D)) ) ) ) ) )  =>  ((r1_xxreal_0 B A) | (r1_xxreal_0 C A)) ) ) ) ) ) ) ) ).
tt(t228_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers))  => (r1_tarski (k1_xxreal_1 A B) k1_numbers)) ) ) ) ) ).
tt(t229_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r1_tarski (k27_member_1 A C) (k27_member_1 B C)) =>  ( (C = k6_numbers)  | (r1_tarski A B)) ) ) ) ) ) ) ) ).
tt(t229_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) A) B) = (k4_xcmplx_0 B)) ) ) ) ) ).
tt(t229_xreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D A))  &  ( (~ (r1_xxreal_0 B D))  &  (~ (r1_xxreal_0 D C)) ) ) ) ) )  =>  ((r1_xxreal_0 B A) | (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t229_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_1 k2_xxreal_0 A) = (a_1_0_xxreal_1 A)) ) ) ).
tt(t22_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r1_abcmiz_0 A B C) => (r2_hidden (k5_abcmiz_0 A B C) (k3_abcmiz_0 A C))) ) ) ) ) ) ) ).
tt(t22_abcmiz_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k4_classes1 k4_ordinal1))))  => (r2_hidden A (k4_classes1 k4_ordinal1))) ) ).
tt(t22_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ( (~ (v5_abcmiz_1 B A (k28_abcmiz_1 A)))  & (m1_abcmiz_1 B A (k14_abcmiz_1 A)))  <=> (r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k2_abcmiz_1)) ) ) ) ) ).
tt(t22_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k13_complex1 1 (k1_absvalue A)) = (k1_absvalue (k13_complex1 1 A))) ) ) ).
tt(t22_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden B (k2_aff_1 A C D)) =>  ( (C = D)  |  ((r2_hidden E (k2_aff_1 A C D)) <=> (r2_analoaf A C D B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_4 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r1_tarski C B) &  ((r1_tarski D B) &  ( (~ (r5_aff_1 A C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (~  ((r2_hidden A (k2_afinsq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (D = A)  & (r2_hidden (k2_nat_1 (k1_afinsq_1 C) D) (k2_afinsq_1 (k1_ordinal4 C B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_recdef_1 (k4_afinsq_2 (k1_tarski A)) k6_numbers) = A) ) ) ).
tt(t22_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) => (m1_subset_1 B (u1_incsp_1 (k13_afproj A)))) ) ) ) ).
tt(t22_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_afvect0 A B C D) & (r2_afvect0 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) & (r1_xboole_0 (k10_xtuple_0 B) (k9_xtuple_0 A)))  =>  (! [C:$i] :  ((k3_relat_1 (k1_algspec1 C B) A) = (k5_relat_1 A C)) ) ) ) ) ) ) ).
tt(t22_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden B (k11_algstr_4 A D)) & (r2_hidden C (k11_algstr_4 A E)))  => (r2_hidden (k4_tarski (k4_tarski B C) D) (k11_algstr_4 A (k2_xcmplx_0 D E)))) ) ) ) ) ) ) ) ).
tt(t22_altcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  ((v14_altcat_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_altcat_1 A B B) = (k1_tarski (k8_altcat_1 A B))) ) ) ) ) ) ).
tt(t22_altcat_2,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ( ((m1_altcat_2 A B) & (m1_altcat_2 B A))  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B))) ) ) ) ) ) ).
tt(t22_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ((v1_altcat_3 (k5_altcat_1 A B C D E F) A B D) =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C D) = k1_xboole_0)  |  ( ((k1_altcat_1 A D B) = k1_xboole_0)  | (v1_altcat_3 F A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v1_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v2_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ami_2,ax,(r2_hidden k5_numbers k1_ami_2)).
tt(t22_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (v2_extpro_1 (k8_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(t22_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_ami_3)))  =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  ( (J = (k6_ami_3 H I))  & (r2_hidden I (k9_xtuple_0 B))) )  =>  ((k6_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) I)) = (k6_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((r2_hidden (k2_xcmplx_0 A 1) (k3_amistd_1 2 k1_ami_3 A)) &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden B (k3_amistd_1 2 k1_ami_3 A)) => (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t22_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (~  ((v3_ami_wstd C A B) & (v2_extpro_1 C A B)) ) ) ) ) ) ) ) ).
tt(t22_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analmetr A B C))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k2_analmetr A B C))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k2_analmetr A B C))) =>  ( ( (H = D)  &  ( (I = E)  &  ( (J = F)  &  (K = G) ) ) )  =>  ((r2_analoaf (k2_analmetr A B C) H I J K) <=>  (? [L:$i] :  ((m1_subset_1 L k1_numbers) &  (? [M:$i] :  ((m1_subset_1 M k1_numbers) &  ( ((k1_rlvect_1 A (k5_algstr_0 A E D) L) = (k1_rlvect_1 A (k5_algstr_0 A G F) M))  &  (~  ( (L = k6_numbers)  &  (M = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (k1_analoaf A)) <=> (r1_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r1_analort A E F B C D D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  (~  ( ((k2_anproj_1 A B) = (k2_anproj_1 A C))  <=> (r1_anproj_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_anproj_2,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k9_aofa_000 A B D) (k9_aofa_000 A C D))) ) ) ) ) ) ) ) ) ).
tt(t22_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m2_funct_2 F B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers (k42_aofa_i00 A B C D E) F) = (k21_aofa_i00 B k4_numbers F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v3_armstrng B A) & (v4_armstrng B A))  => (v7_armstrng B A)) ) ) ) ).
tt(t22_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k4_arytm_0 (k2_arytm_0 A B)) = (k2_arytm_0 (k4_arytm_0 A) (k4_arytm_0 B))) ) ) ) ) ).
tt(t22_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((r1_arytm_2 A C) |  ((k2_arytm_1 B (k1_arytm_1 A C)) = (k7_arytm_2 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ) ).
tt(t22_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( (~  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) )  => (r1_arytm_3 (k4_arytm_3 A B) (k4_arytm_3 B A))) ) ) ) ) ).
tt(t22_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((r1_xxreal_0 (k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) k6_numbers) |  ((k7_asympt_0 A) = (k7_asympt_0 B)) ) ) ) ) ) ) ).
tt(t22_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 1 A))  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C 1))  =>  ((k1_seq_1 B C) = (k10_real_1 (k5_series_1 C 2) (k6_power 2 C))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C B) &  ((r1_tarski (k6_asympt_0 (k3_asympt_1 (k7_real_1 1 A))) (k6_asympt_0 C)) &  (~  ((k6_asympt_0 (k3_asympt_1 (k7_real_1 1 A))) = (k6_asympt_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_autalg_1 C (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) => (r2_hidden C (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))) ) ) ) ) ) ).
tt(t22_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k1_group_1 A)) (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t22_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_bagorder (k17_pre_poly A) A)) ) ).
tt(t22_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (m1_bcialg_1 A A)) ) ).
tt(t22_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_bcialg_1 A (k1_bcialg_2 A (k1_bcialg_2 A B (k1_bcialg_1 A B C) D) (k1_bcialg_1 A C B) D) B)) ) ) ) ) ) ) ) ).
tt(t22_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ((v7_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A C D) = (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_bcialg_4 A B 1) = B) ) ) ) ) ).
tt(t22_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E D B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k1_bcialg_1 A (k3_bcialg_6 A C B) (k3_bcialg_6 A D B)) = (k3_bcialg_6 A (k21_binop_2 C D) B)) ) ) ) ) ) ) ) ) ).
tt(t22_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m2_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B) => (r2_hidden (k1_bcialg_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) => (r1_bhsp_1 A (k4_algstr_0 A B) (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t22_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A C B))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A C B))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t22_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v2_bhsp_3 B A)) ) ) ) ) ).
tt(t22_bhsp_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((k4_bhsp_4 B C (k2_nat_1 A 1) A) = (k1_normsp_1 B C (k2_nat_1 A 1))) ) ) ) ) ) ) ).
tt(t22_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k9_bilinear A B C D (k7_hahnban1 A C)) (k1_bilinear A B C))) ) ) ) ) ) ) ) ).
tt(t22_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( (B = (k5_euclid A))  =>  ((k4_binarith A (k3_binarith A B) (k1_binari_2 A)) = (k3_binarith A (k1_binari_2 A))) ) ) ) ) ) ).
tt(t22_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k1_binari_4 B C) (k1_binari_4 A C))) ) ) ) ) ) ) ).
tt(t22_binarith,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ((r1_binarith A B C) =>  ((k6_binarith A (k7_binarith A B C)) = (k2_nat_1 (k6_binarith A B) (k6_binarith A C))) ) ) ) ) ) ) ) ).
tt(t22_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_relset_1 k5_numbers (u1_struct_0 A) (k8_binom A B C k6_numbers) (k12_finseq_1 (u1_struct_0 A) (k1_group_1 A)))) ) ) ) ) ) ).
tt(t22_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  ((k1_funct_1 (k2_bintree2 A 1) 1) = (k10_binarith k5_numbers k6_numbers)) ) ) ).
tt(t22_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k1_boolealg A D C) (k1_boolealg A D B))) ) ) ) ) ) ) ) ) ).
tt(t22_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((m1_setfam_1 C D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski E C) &  ((m1_setfam_1 E D) &  (! [F:$i] :  (~  ((r2_hidden F E) & (r1_xboole_0 F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = (k3_borsuk_1 B A E D))  =>  ((g1_pre_topc (u1_struct_0 (k2_borsuk_1 (k1_pre_topc B E) (k1_pre_topc A D))) (u1_pre_topc (k2_borsuk_1 (k1_pre_topc B E) (k1_pre_topc A D)))) = (g1_pre_topc (u1_struct_0 (k1_pre_topc (k2_borsuk_1 B A) C)) (u1_pre_topc (k1_pre_topc (k2_borsuk_1 B A) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_connsp_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_tarski (k1_rcomp_1 B C) A)) ) ) ) ) ) ) ).
tt(t22_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~  ( (~  (A = k6_numbers) )  & (v1_rat_1 (k3_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t22_borsuk_6,ax, ((v4_pre_topc a_0_10_borsuk_6 (k2_borsuk_1 k3_topmetr k3_topmetr)) & (m1_subset_1 a_0_10_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr))))) ).
tt(t22_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) => (r1_tarski (k10_xtuple_0 (k1_borsuk_7 A B F C D E)) (k1_enumset1 C D E))) ) ) ) ) ) ) ).
tt(t22_bspace,ax, (! [A:$i] : (v3_rlvect_1 (k7_bspace A))) ).
tt(t22_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A C (k5_bvfunc_1 A D (k1_bvfunc_1 A B))))) ) ) ) ) ) ) ) ).
tt(t22_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  ( (B = (k3_enumset1 C D E F G))  =>  ( (C = D)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A C E) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v3_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A B) B) & (r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A B) B)) ) ) ) ) ).
tt(t22_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A (k1_bvfunc_1 A B) B)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t22_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B C) (k5_bvfunc26 A (k5_bvfunc26 A B C) (k5_bvfunc26 A B C)))) ) ) ) ) ) ).
tt(t22_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k5_bvfunc_1 A C D) B E) (k5_bvfunc_1 A C (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k9_bvfunc_1 A D C) B E) (k9_bvfunc_1 A (k6_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A B C D) => (r1_bvfunc_1 A (k7_bvfunc_2 A B C D) (k7_bvfunc_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t22_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D E) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t22_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k10_bvfunc_1 A B C)) (k10_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t22_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D E)) (k9_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t22_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_c0sp1 A)))  &  ((v13_algstr_0 (k11_c0sp1 A)) &  ((v2_rlvect_1 (k11_c0sp1 A)) &  ((v3_rlvect_1 (k11_c0sp1 A)) &  ((v4_rlvect_1 (k11_c0sp1 A)) &  ((v5_rlvect_1 (k11_c0sp1 A)) &  ((v6_rlvect_1 (k11_c0sp1 A)) &  ((v7_rlvect_1 (k11_c0sp1 A)) &  ((v2_funcsdom (k11_c0sp1 A)) &  ((v3_group_1 (k11_c0sp1 A)) &  ((v5_group_1 (k11_c0sp1 A)) &  ((v1_vectsp_1 (k11_c0sp1 A)) &  ((v3_vectsp_1 (k11_c0sp1 A)) & (l1_funcsdom (k11_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k5_c0sp2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k5_c0sp2 A)))))) )  =>  ((v1_rsspace3 B (k5_c0sp2 A)) => (v3_normsp_1 B (k5_c0sp2 A))) ) ) ) ) ).
tt(t22_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) (k7_cqc_lang A B C)) => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) C)) ) ) ) ) ) ) ) ) ).
tt(t22_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k7_cqc_lang A B C)))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t22_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k3_card_1 A) = (k3_card_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t22_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k2_card_2 (k2_card_2 A B) C) = (k2_card_2 A (k2_card_2 B C))) ) ) ) ) ) ) ).
tt(t22_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k3_card_3 (k2_card_3 B))) <=>  ((r2_hidden (k2_xtuple_0 A) (k9_xtuple_0 B)) &  ((r2_hidden (k1_xtuple_0 A) (k1_funct_1 B (k2_xtuple_0 A))) &  (A = (k4_tarski (k1_xtuple_0 A) (k2_xtuple_0 A))) ) ) ) ) ) ) ).
tt(t22_card_4,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 A) =>  ( (A = k1_xboole_0)  |  ((v1_finset_1 B) |  ((k2_card_2 (k1_card_1 B) (k1_card_1 A)) = (k1_card_1 B)) ) ) ) ) ) ).
tt(t22_card_5,ax, ((k1_card_5 k4_ordinal1) = k4_ordinal1) ).
tt(t22_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v3_card_fil B A) & (m1_card_fil B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) <=>  (~ (r2_hidden C (k1_card_fil A B))) ) ) ) ) ) ) ) ).
tt(t22_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ((r2_hidden A (k2_card_fin C D B)) &  ((r2_hidden B (k10_xtuple_0 D)) &  (! [E:$i] :  (~  ((r2_hidden E (k9_xtuple_0 D)) &  ( ((k1_funct_1 D E) = B)  & (r2_hidden A (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r2_hidden k4_ordinal1 (k1_card_5 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  => (r2_hidden (k3_ordinal2 (k10_xtuple_0 C)) A)) ) ) ) ) ) ) ).
tt(t22_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = B)  =>  ((k1_cat_1 A (k4_cat_1 A B) C) = C) ) ) ) ) ) ) ) ).
tt(t22_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C))))  =>  ( ((v1_cat_2 (g1_cat_1 B C D E F) A) & (m3_cat_2 (g1_cat_1 B C D E F) A))  =>  ( (C = (k3_tarski (a_2_0_cat_2 A B)))  &  ( (D = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) C))  &  ( (E = (k2_partfun1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) C))  &  (F = (k1_realset1 (u1_cat_1 A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v1_cat_3 D A B C) => (v8_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t22_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (~  ((v1_cat_3 (k7_cat_4 A B C) A (k2_cat_4 A B C) B) & (v1_cat_3 (k8_cat_4 A B C) A (k2_cat_4 A B C) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  ((r1_funct_2 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (u4_struct_0 C) D E) =>  ((k4_cat_5 A B D) = (k4_cat_5 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_xboole_0 (k2_catalan2 A B)) <=>  (~ (r1_xxreal_0 (k24_binop_2 2 B) A)) ) ) ) ) ) ).
tt(t22_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u4_struct_0 (k3_catalg_1 (u1_struct_0 B))) (k12_catalg_1 A B C) (k10_catalg_1 (u1_struct_0 A) D E F)) = (k10_catalg_1 (u1_struct_0 B) (k8_cat_1 A B C D) (k8_cat_1 A B C E) (k8_cat_1 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_cc0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k1_algstr_0 (k7_cc0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A k2_numbers D H) = (k3_binop_2 (k3_funct_2 A k2_numbers B H) (k3_funct_2 A k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_cc0sp2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_cc0sp2 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_cc0sp2 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k3_rlvect_1 (k5_cc0sp2 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers D H) = (k8_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers B H) (k3_funct_2 (u1_struct_0 A) k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r2_relset_1 k5_numbers k2_numbers A (k1_valued_0 k2_numbers B C))) ) )  | (v2_comseq_2 B)) ) ) ) ) ) ).
tt(t22_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_cfdiff_1 C B) =>  ( ((r1_cfdiff_1 A B) & (r1_tarski C (k1_relset_1 k2_numbers A)))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) &  ((v1_cfdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ( ( ((k2_relset_1 k2_numbers E) = (k1_tarski B))  & (r1_tarski (k2_relset_1 k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers D E)) C))  =>  ((v2_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers D) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers D E) A) (k8_funct_2 k5_numbers k2_numbers k2_numbers E A)))) &  ((k2_cfdiff_1 A B) = (k3_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers D) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k8_funct_2 k5_numbers k2_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers D E) A) (k8_funct_2 k5_numbers k2_numbers k2_numbers E A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cfuncdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ( (C = (k2_tarski A B))  &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k2_numbers (k9_funct_2 C k2_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k2_numbers (k9_funct_2 C k2_numbers)) =>  (~  ( (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  ((r2_funct_2 C k2_numbers (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) F D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G E))) (k4_cfuncdom C)) =>  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) )  &  (! [F:$i] :  ((m2_funct_2 F C k2_numbers (k9_funct_2 C k2_numbers)) =>  (? [G:$i] :  ((m1_subset_1 G k2_numbers) &  (? [H:$i] :  ((m1_subset_1 H k2_numbers) & (r2_funct_2 C k2_numbers F (k1_funcsdom C k2_numbers (k1_cfuncdom C) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) G D)) (k2_funcsdom C k2_numbers k2_numbers (k9_funct_2 C k2_numbers) (k3_cfuncdom C) (k1_domain_1 k2_numbers (k9_funct_2 C k2_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers B (k9_complex1 C D)) (k25_valued_1 A k2_numbers (k25_valued_1 A k2_numbers B D) C))) ) ) ) ) ) ) ) ).
tt(t22_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v3_cgames_1 A) & (v4_cgames_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  ((r1_xxreal_0 B C) => (r1_ordinal1 (k9_cgames_1 (k1_funct_1 A B)) (k9_cgames_1 (k1_funct_1 A C)))) ) ) ) ) ) ) ).
tt(t22_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers C B) A) & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers E D) A))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 E D) |  ( (C = E)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( (~  (B = C) )  =>  (! [D:$i] :  ((m3_glib_001 D A) =>  (~  ( ((k13_glib_001 A D) = (k2_tarski B C))  &  (! [E:$i] :  (~ (r1_glib_000 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  ((r1_xboole_0 (k2_msafree2 B) (k3_msafree2 A)) &  (C = (k2_circcomb A B)) ) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) =>  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 A D))) =>  ( (J = (k5_relat_1 I (u1_struct_0 A)))  =>  (! [K:$i] :  ((m1_subset_1 K (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (K = (k5_relat_1 I (u1_struct_0 B)))  &  ((v1_circuit2 (k5_facirc_1 A D J G) A D) & (v1_circuit2 (k5_facirc_1 B E K H) B E)) )  => (v1_circuit2 (k5_facirc_1 C F I (k4_xxreal_0 G H)) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_circcmb3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k4_finseq_2 C A) = (k4_finseq_2 D B))  =>  ( (C = k6_numbers)  |  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ((r2_circcomb A B C D) =>  ((k3_circcomb A B C D) = (k3_circcomb B A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t22_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ( ((v1_circled1 C A) &  ((k3_rlvect_2 A C) = (k6_domain_1 (u1_struct_0 A) B)) )  =>  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers C B) = 1)  &  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ) ) ).
tt(t22_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  ( (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (~  ((r2_hidden E (k9_trees_9 D)) &  ( ((k1_funct_1 E k1_xboole_0) = (k4_tarski F (u1_struct_0 A)))  &  ((k1_msualg_1 A F) = k1_xboole_0) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  (! [F:$i] :  ((m1_circtrm1 F A C D B E) =>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ((r2_hidden G (k9_trees_9 D)) =>  ((r1_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) (k5_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) E (k6_trees_1 (k9_xtuple_0 G))) G) &  ((k1_funct_1 (k5_facirc_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B) E (k6_trees_1 (k9_xtuple_0 G))) G) = (k7_circtrm1 A B C G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_classes1,ax, (! [A:$i] :  ((v1_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (B = k1_xboole_0) )  => (v1_ordinal1 (k3_classes1 A B))) ) ) ) ) ).
tt(t22_classes2,ax, (! [A:$i] :  (! [B:$i] :  ((v2_classes1 A) =>  ( ( (~  ((r2_hidden B A) & (v1_ordinal1 A)) )  &  ( (~  ((r2_hidden B A) & (r1_tarski B A)) )  &  (~  ((r2_hidden (k1_card_1 B) (k1_card_1 A)) & (r1_tarski B A)) ) ) )  | (r1_tarski (k1_funct_2 B A) A)) ) ) ) ).
tt(t22_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  => (m1_clvect_1 (g1_clvect_1 (k8_clopban1 A B) (k10_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k8_csspace (k6_clopban1 A B) (k8_clopban1 A B)) (k9_csspace (k6_clopban1 A B) (k8_clopban1 A B))) (k6_clopban1 A B))) ) ) ) ).
tt(t22_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k8_clopban2 A)) = (k6_clopban2 A)) ) ) ).
tt(t22_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clopban3 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_clopban3 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t22_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_bhsp_4 A (k4_clopban4 (k2_nat_1 D 1) A B C)) D) = (k3_rlvect_1 A (k1_normsp_1 A (k1_bhsp_4 A (k4_clopban4 D A B C)) D) (k1_normsp_1 A (k1_bhsp_4 A (k3_clopban4 (k2_nat_1 D 1) A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t22_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((v3_closure1 C A B) &  ((v3_closure1 D A B) & (r6_pboole A (k3_closure1 A B D C) (k3_closure1 A B C D))) )  => (v3_closure1 (k3_closure1 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t22_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_closure2 A B))) =>  ( (E = (k2_tarski C D))  => (r6_pboole A (k2_mboolean A (k5_closure2 A B E)) (k2_pboole A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t22_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A C B))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A C B))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t22_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_clvect_3 A B (k2_nat_1 C 1) C) = (k1_normsp_1 A B (k2_nat_1 C 1))) ) ) ) ) ) ) ).
tt(t22_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_classes1 (k9_xtuple_0 A)) & (v3_cohsp_1 (k9_xtuple_0 A)))  =>  ((v9_cohsp_1 A) <=>  ((v6_cohsp_1 A) &  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k1_funct_1 A B)) &  (! [D:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D B) &  ((r2_hidden C (k1_funct_1 A D)) &  (! [E:$i] :  ( ((r1_tarski E B) & (r2_hidden C (k1_funct_1 A E)))  => (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  ( ((k6_coh_sp A B) = (k7_coh_sp A C))  =>  ( ((k2_xtuple_0 (k9_coh_sp A C B)) = (k3_relat_1 (k2_xtuple_0 C) (k2_xtuple_0 B)))  &  ( ((k6_coh_sp A (k9_coh_sp A C B)) = (k6_coh_sp A C))  &  ((k7_coh_sp A (k9_coh_sp A C B)) = (k7_coh_sp A B)) ) ) ) ) ) ) ) ) ).
tt(t22_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((k1_collsp A B C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t22_combgras,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((l1_combgras B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 A))) =>  ( ((v7_combgras B A) & (v2_combgras C A))  =>  ((v2_combgras (k4_combgras A A B C) A) & (v2_combgras (k5_combgras A A B C) A)) ) ) ) ) ) ) ) ).
tt(t22_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k4_complex1 A) = k6_numbers)  =>  ( ((k3_complex1 A) = k6_numbers)  |  ( ((k3_complex1 (k5_xcmplx_0 A)) = (k2_real_1 (k3_complex1 A)))  &  ((k4_complex1 (k5_xcmplx_0 A)) = k6_numbers) ) ) ) ) ) ).
tt(t22_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k1_comptrig A) = k32_sin_cos)  <=>  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 A)))  &  ((k4_complex1 A) = k6_numbers) ) ) ) ) ).
tt(t22_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k11_algstr_0 k1_complfld A) = (k3_vectsp_1 k1_complfld (k5_struct_0 k1_complfld) A)) ) ) ) ).
tt(t22_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k1_complsp2 (k1_complsp2 A)) = A) ) ) ).
tt(t22_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v5_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) ) )  =>  (~  ((v2_prob_1 B) &  ((k2_kurato_0 (u1_struct_0 A) B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t22_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r1_tarski (k63_valued_1 B) (k63_valued_1 (k7_compos_1 A B C)))) ) ) ) ) ) ).
tt(t22_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ( ((r2_compos_2 B C) & (r2_compos_2 C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t22_comptrig,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))))).
tt(t22_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  <=>  ((v1_tops_2 B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))))) ) ) ) ) ).
tt(t22_comput_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_margrel1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) )  =>  ( ((v3_margrel1 B A) &  (~ (v1_xboole_0 B)) )  <=>  ((k1_relset_1 (k3_finseq_2 A) B) = (k4_finseq_2 (k19_margrel1 B) A)) ) ) ) ) ).
tt(t22_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers A)) A)) ) ).
tt(t22_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k31_valued_1 k5_numbers k2_numbers A)) = (k10_complex1 (k3_comseq_2 A))) ) ) ).
tt(t22_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k7_comseq_3 (k9_comseq_3 B A)) (k2_valued_0 k1_numbers B (k7_comseq_3 A))) & (r2_funct_2 k5_numbers k1_numbers (k8_comseq_3 (k9_comseq_3 B A)) (k2_valued_0 k1_numbers B (k8_comseq_3 A)))) ) ) ) ) ).
tt(t22_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (~ (v5_conlat_1 (g2_conlat_1 A C B) A))  &  ((v7_conlat_1 (g2_conlat_1 A C B) A) & (l2_conlat_1 (g2_conlat_1 A C B) A)) ) ) )  <=>  ((k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B)) = B) ) ) ) ) ) ).
tt(t22_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  => (r1_filter_1 (k11_conlat_1 (k7_conlat_2 A)) (k1_lattice2 (k11_conlat_1 A)))) ) ).
tt(t22_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_connsp_1 B A) &  ( (~ (r1_xboole_0 B C))  &  ( (~  ((k7_subset_1 (u1_struct_0 A) B C) = (k1_struct_0 A)) )  & (r1_xboole_0 B (k2_tops_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v3_pre_topc D A) &  ((v4_pre_topc D A) & (r2_hidden B D)) ) ) ) )  &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t22_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m1_connsp_3 B A) & (m1_connsp_3 C A))  =>  ((m1_connsp_3 (k4_subset_1 (u1_struct_0 A) B C) A) & (m1_connsp_3 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t22_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v2_convex1 B A) &  ((r1_xxreal_0 (k1_funct_1 B C) k6_numbers) & (r2_hidden C (k3_rlvect_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t22_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) => (r1_convex4 A (k5_convex4 A B (k5_convex4 A C D)) (k5_convex4 A (k5_convex4 A B C) D))) ) ) ) ) ) ) ) ).
tt(t22_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((v5_qc_lang1 C A) &  ((k21_qc_lang1 A C) = B) )  =>  ((k13_cqc_lang A C B) = C) ) ) ) ) ) ) ) ).
tt(t22_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k13_cqc_sim1 A (k5_cqc_lang A)) = (k26_qc_lang1 A)) ) ) ).
tt(t22_cqc_the1,ax,(v1_finset_1 k2_cqc_the1)).
tt(t22_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden F (k24_qc_lang1 A D)) | (v2_cqc_the1 (k8_cqc_lang A B (k12_cqc_lang A F C)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((k1_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) B C)) = (k1_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) (k1_cqc_the1 A B) (k1_cqc_the1 A C)))) ) ) ) ) ) ) ).
tt(t22_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_csspace4 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k1_normsp_0 (k9_csspace4 A B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k9_csspace4 A B))) )  &  ( ( (C = (k4_struct_0 (k9_csspace4 A B)))  =>  ((k1_normsp_0 (k9_csspace4 A B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k9_csspace4 A B) (k1_clvect_1 (k9_csspace4 A B) C E)) = (k8_real_1 (k17_complex1 E) (k1_normsp_0 (k9_csspace4 A B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k9_csspace4 A B) (k1_algstr_0 (k9_csspace4 A B) C D)) (k7_real_1 (k1_normsp_0 (k9_csspace4 A B) C) (k1_normsp_0 (k9_csspace4 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k4_algstr_0 A B) C) = (k12_csspace A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t22_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_decomp_1 C A B) <=>  ((v8_decomp_1 C A B) & (v17_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t22_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k2_finseq_1 56)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  ( (~  (A = 16) )  &  ( (~  (A = 17) )  &  ( (~  (A = 18) )  &  ( (~  (A = 19) )  &  ( (~  (A = 20) )  &  ( (~  (A = 21) )  &  ( (~  (A = 22) )  &  ( (~  (A = 23) )  &  ( (~  (A = 24) )  &  ( (~  (A = 25) )  &  ( (~  (A = 26) )  &  ( (~  (A = 27) )  &  ( (~  (A = 28) )  &  ( (~  (A = 29) )  &  ( (~  (A = 30) )  &  ( (~  (A = 31) )  &  ( (~  (A = 32) )  &  ( (~  (A = 33) )  &  ( (~  (A = 34) )  &  ( (~  (A = 35) )  &  ( (~  (A = 36) )  &  ( (~  (A = 37) )  &  ( (~  (A = 38) )  &  ( (~  (A = 39) )  &  ( (~  (A = 40) )  &  ( (~  (A = 41) )  &  ( (~  (A = 42) )  &  ( (~  (A = 43) )  &  ( (~  (A = 44) )  &  ( (~  (A = 45) )  &  ( (~  (A = 46) )  &  ( (~  (A = 47) )  &  ( (~  (A = 48) )  &  ( (~  (A = 49) )  &  ( (~  (A = 50) )  &  ( (~  (A = 51) )  &  ( (~  (A = 52) )  &  ( (~  (A = 53) )  &  ( (~  (A = 54) )  &  ( (~  (A = 55) )  &  (~  (A = 56) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (~  ((r2_hidden C (k6_dickson A B)) & (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t22_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) B) (k2_nat_1 A 1)) C) = (k7_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) (k2_nat_1 A 1)) C) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E B) (k2_nat_1 A 1)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_zfmisc_1 A B C) =>  ((k10_diff_1 (k1_fcont_1 D E) A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C (k9_real_1 A (k10_real_1 B 2)) (k7_real_1 A (k10_real_1 B 2))) = (k10_real_1 (k1_seq_1 (k5_diff_1 C B) A) B)) ) ) ) ) ) ) ).
tt(t22_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden B (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k19_sin_cos) A B) = (k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) A B)) ) ) ) ) ) ).
tt(t22_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((r2_hidden C (k4_dilworth A B)) & (r2_hidden C (k3_dilworth A B)))  => (r2_hidden C B)) ) ) ) ) ) ).
tt(t22_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_diraf A B C D E) =>  ((r2_diraf A B C E D) &  ((r2_diraf A C B D E) &  ((r2_diraf A C B E D) &  ((r2_diraf A D E B C) &  ((r2_diraf A D E C B) &  ((r2_diraf A E D B C) & (r2_diraf A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v1_dist_1 B A) & (r1_dist_1 A B C))  => (v1_dist_1 C A)) ) ) ) ) ) ) ).
tt(t22_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (B = (a_2_1_domain_1 A B)) ) ) ) ) ).
tt(t22_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((r2_hidden C (k5_dynkin A B)) &  ((r2_hidden D (k5_dynkin A B)) & (v2_finsub_1 B)) )  => (r2_hidden (k9_subset_1 A C D) (k5_dynkin A B))) ) ) ) ) ) ) ) ) ).
tt(t22_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((k2_binom (k9_int_3 A) B 2) = (k8_group_1 (k9_int_3 A) B B)) ) ) ) ) ).
tt(t22_ec_pf_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ( (E = (k6_int_1 B C))  &  (A = (k2_xcmplx_0 B 1)) ) )  =>  ((k5_algstr_0 (k9_int_3 C) (k8_group_1 (k9_int_3 C) D F) (k8_group_1 (k9_int_3 C) E F)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m1_subset_1 B (u1_struct_0 (k11_ens_1 A)))) ) ) ) ).
tt(t22_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( (C = (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B)))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k8_matrix_1 k1_numbers C D) = (k10_rvsum_1 B (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k1_tarski A) (k5_enumset1 B C D E F G H))) ) ) ) ) ) ) ) ) ).
tt(t22_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_2 E) &  ((v3_relat_2 E) &  ((v8_relat_2 E) &  ((v1_partfun1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( ((r2_hidden B (k6_eqrel_1 A A E C)) & (r2_hidden D (k6_eqrel_1 A A E C)))  => (r2_hidden (k4_tarski B D) E)) ) ) ) ) ) ) ).
tt(t22_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_msualg_6 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_msualg_6 D A) & (m1_msualg_2 D A C))  =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r8_pboole (u1_struct_0 A) E (u3_msualg_1 A D)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) =>  ((r1_msualg_3 A C B F) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) G (k1_msafree (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B) E F)) => (r1_msualg_3 A D B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k13_e_siec A) (k13_e_siec A)) = (k13_e_siec A))  &  ( ((k3_relat_1 (k4_xboole_0 (k13_e_siec A) (k4_relat_1 (k12_e_siec A))) (k13_e_siec A)) = k1_xboole_0)  &  ((k2_xboole_0 (k2_xboole_0 (k13_e_siec A) (k2_relat_1 (k13_e_siec A))) (k4_relat_1 (k12_e_siec A))) = (k2_xboole_0 (k14_e_siec A) (k2_relat_1 (k14_e_siec A)))) ) ) ) ) ).
tt(t22_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B (k4_algstr_0 (k15_euclid A) C)) = (k7_binop_2 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t22_euclid_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k3_finseq_1 A) = 2)  =>  ((k12_euclid A) = (k7_square_1 (k7_real_1 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))))) ) ) ) ).
tt(t22_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k23_rvsum_1 B (k9_euclid A C D)) = (k4_real_1 D (k23_rvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t22_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k5_euclid_5 (k4_euclid_5 k6_numbers k6_numbers A) (k4_euclid_5 k6_numbers k6_numbers B)) = (k4_struct_0 (k15_euclid 3))) ) ) ) ) ).
tt(t22_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k4_euclid_3 A B C) = (k4_euclid_3 D E F))  &  ((k4_euclid_3 C A B) = (k4_euclid_3 E F D)) )  =>  ((r1_euclid_6 A B C) |  ((r1_euclid_6 D E F) |  ( ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B C)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D F))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D))))  &  ( ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B C)) (k12_euclid (k5_algstr_0 (k15_euclid 2) F E))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D))))  &  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) F E))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k5_euclid_7 A (k5_finseq_2 (k1_euclid A) B (k5_euclid A))) = (k5_euclid A)) ) ) ) ) ).
tt(t22_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k5_euclid_8 A (k1_euclid_8 k6_numbers k6_numbers k6_numbers)) = (k1_euclid_8 k6_numbers k6_numbers k6_numbers)) ) ) ).
tt(t22_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) => (r1_tarski (k9_metric_1 (k14_euclid A) C B) (k4_euclid_9 A C B))) ) ) ) ) ) ).
tt(t22_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k15_euclid A)) = (k1_euclid A)) ) ) ).
tt(t22_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid E)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid E)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid E)) =>  ((k9_euclid E (k7_euclid E (k7_euclid E (k9_euclid E F B) (k9_euclid E G C)) (k9_euclid E H D)) A) = (k7_euclid E (k7_euclid E (k9_euclid E F (k8_real_1 A B)) (k9_euclid E G (k8_real_1 A C))) (k9_euclid E H (k8_real_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_analmetr B C D) &  (A = (k2_analmetr B C D)) )  => (v7_euclmetr A)) ) ) ) ) ) ) ) ) ).
tt(t22_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  ((k9_xtuple_0 A) = (k6_subset_1 (k2_exchsort A) (k1_exchsort A))) ) ) ).
tt(t22_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_extpro_1 A B C D) <=> (r1_extpro_1 A B C (k5_extpro_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((r2_hidden C (k3_msafree2 B)) => (r2_hidden C (k3_msafree2 (k2_circcomb A B)))) ) ) ) ) ) ).
tt(t22_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (~  ((k2_msafree2 (k19_facirc_1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t22_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((k8_relset_1 k1_numbers k1_numbers B (k1_seq_4 k6_numbers)) = k1_xboole_0) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers B) A))) ) ) ) ).
tt(t22_fcont_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_partfun1 A k1_numbers) =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers A) (k2_relset_1 k1_numbers A)))) ) ) ) ).
tt(t22_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k16_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k21_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t22_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_fdiff_9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k1_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k8_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k2_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t22_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers B A)))  =>  ((r2_fdiff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 B A) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) &  ((k1_seq_1 B C) = k6_numbers) ) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers B) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers B) A) (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k2_fdiff_1 B A) (k20_valued_1 k1_numbers k1_numbers k1_numbers B B))))) ) ) ) ) ) ).
tt(t22_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_fdiff_1 A B) =>  ((r3_fdiff_3 A B) &  ((r4_fdiff_3 A B) &  ( ((k1_fdiff_1 A B) = (k2_fdiff_3 B A))  &  ((k1_fdiff_1 A B) = (k1_fdiff_3 B A)) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k7_real_1 A E))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers))  &  ( ((k1_seq_1 D E) = (k9_real_1 A E))  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) E) = (k10_real_1 (k8_real_1 2 A) (k9_real_1 (k5_square_1 A) (k5_square_1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = A) ) ) )  &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E B) & (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) B) E) = (k10_real_1 (k8_real_1 (k8_real_1 4 A) E) (k2_newton (k9_real_1 A (k2_newton E 2)) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) k3_taylor_1)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) C) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) k3_taylor_1)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) k3_taylor_1)) A) C) = (k10_real_1 (k1_seq_1 k24_sin_cos C) (k9_real_1 1 (k1_seq_1 k24_sin_cos C)))) ) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))))) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ( ((k1_seq_1 C E) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B E) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))) A) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))) A) E) = (k1_real_1 (k8_real_1 E (k10_prepower (k9_real_1 1 (k5_prepower E 2)) (k1_real_1 (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A) B) = (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t22_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers A)) A) B) = (k10_real_1 (k9_real_1 (k1_seq_1 k16_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t22_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k13_ff_siec A) (k2_zfmisc_1 (k12_ff_siec A) (k11_ff_siec A))) & (r1_tarski (k14_ff_siec A) (k2_zfmisc_1 (k12_ff_siec A) (k11_ff_siec A)))) ) ) ).
tt(t22_fib_num2,ax, ((k1_pre_ff 3) = 2) ).
tt(t22_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_1 (k4_nat_1 2 (k1_fib_num3 A)) (k1_fib_num3 (k1_nat_1 A 1))) = (k4_nat_1 5 (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t22_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((r1_xxreal_0 2 A) & (v1_abian A))  =>  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k1_int_1 (k2_xcmplx_0 (k3_xcmplx_0 k1_fib_num (k1_pre_ff A)) 1))) ) ) ) ).
tt(t22_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (r1_filerec1 A B (k6_finseq_1 A) B)) ) ) ) ).
tt(t22_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k3_filter_0 A B) (k3_filter_0 A C))) ) ) ) ) ) ) ).
tt(t22_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 C A) & (v1_binop_1 D B))  <=> (v1_binop_1 (k6_filter_1 A B C D) (k2_zfmisc_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t22_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v18_lattices D A) &  ((v21_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden B D) =>  ((r2_hidden (k4_lattices A B C) D) & (r2_hidden (k4_lattices A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_finseq_1 (k7_finseq_1 A B)) = (k2_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t22_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( ((k3_finseq_1 C) = (k2_xcmplx_0 A B))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ( ((k3_finseq_1 D) = A)  &  ( ((k3_finseq_1 E) = B)  &  (C = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r2_hidden C (k1_relset_1 k5_numbers (k7_finseq_1 A B)))) ) ) ) ) ) ).
tt(t22_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ((m1_subset_1 (k6_xcmplx_0 (k4_finseq_4 A B) 1) k5_numbers) & (m1_subset_1 (k6_xcmplx_0 (k3_finseq_1 A) (k4_finseq_4 A B)) k5_numbers)) ) ) ) ) ).
tt(t22_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r1_xxreal_0 A (k3_finseq_1 C)) =>  ((k17_finseq_1 B A (k8_finseq_1 B C D)) = (k17_finseq_1 B A C)) ) ) ) ) ) ) ) ) ).
tt(t22_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((k4_finseq_4 (k11_finseq_1 A B C) B) = 2) ) ) ) ) ).
tt(t22_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k10_xtuple_0 (k2_finseq_7 A B C D)) = (k10_xtuple_0 B)) ) ) ) ) ) ) ) ) ).
tt(t22_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k3_finseq_1 C) = k6_numbers)  => (r4_finseq_8 A B C)) ) ) ) ) ) ) ).
tt(t22_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A C) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) B)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G E) & (m2_finseq_1 G C))  =>  ((k3_finseqop A C B F D G) = (k3_relat_1 G (k5_funcop_1 F D (k6_partfun1 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k11_fintopo2 A C)) <=>  ((r2_hidden B C) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden D (k6_fintopo2 A B)) & (r1_xboole_0 (k7_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) B)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k5_fintopo3 A (k9_subset_1 (u1_struct_0 A) B C) D) = (k9_subset_1 (u1_struct_0 A) (k5_fintopo3 A B D) (k5_fintopo3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t22_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_fin_topo A B) = (k7_subset_1 (u1_struct_0 A) (k9_fin_topo A B) B)) ) ) ) ) ).
tt(t22_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k8_fin_topo A B) B)) ) ) ) ).
tt(t22_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski (k5_subset_1 (k3_catalan2 A) (k6_flang_1 A B C) (k6_flang_1 A B D)) (k6_flang_1 A B (k5_subset_1 (k3_catalan2 A) C D))) & (r1_tarski (k5_subset_1 (k3_catalan2 A) (k6_flang_1 A C B) (k6_flang_1 A D B)) (k6_flang_1 A (k5_subset_1 (k3_catalan2 A) C D) B))) ) ) ) ) ) ) ) ).
tt(t22_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_flang_2 A B C C) = (k7_flang_1 A B C)) ) ) ) ) ) ).
tt(t22_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_flang_3 A B (k2_xcmplx_0 C D)) = (k6_flang_1 A (k1_flang_3 A B C) (k7_flang_1 A B D))) ) ) ) ) ) ) ) ).
tt(t22_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_finseq_2 (k2_xcmplx_0 B C) A) = (k7_relset_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A) (k11_monoid_0 A) (k2_zfmisc_1 (k4_finseq_2 B A) (k4_finseq_2 C A)))) ) ) ) ) ) ) ).
tt(t22_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( ((v4_fomodel1 B A) & (m1_subset_1 B (k1_fomodel1 A)))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ( ((v4_fomodel2 D A) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  ( (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A B) C)) (k32_fomodel2 A C)))  &  ( (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D)) (k32_fomodel2 A C)))  &  (~ (r1_xxreal_0 (k32_fomodel2 A (k30_fomodel2 A (k30_fomodel2 A (k31_fomodel2 A (k1_fomodel2 A)) C) D)) (k32_fomodel2 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v4_frechet A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_frechet2 A (k1_frechet2 A B)) = (k1_frechet2 A B)) ) ) )  => (v3_frechet A)) ) ) ).
tt(t22_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) C (k8_funcop_1 (u1_struct_0 A) k5_numbers B)) => (r1_frechet A C B)) ) ) ) ) ) ) ).
tt(t22_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k8_fscirc_1 A B C)))) ) ) ).
tt(t22_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k3_twoscomp)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k2_twoscomp)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 A C) k3_twoscomp))) ) )  =>  ((k11_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) (k6_circuit2 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r6_fsm_1 A B C D E F) => (r6_fsm_1 A B C E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_2 C (k2_zfmisc_1 A A) (k1_ordinal1 A)))  =>  ( ((v1_fsm_2 C (k2_zfmisc_1 A A)) &  ( ((u1_struct_0 C) = (k1_ordinal1 A))  &  ( ((u1_fsm_2 (k2_zfmisc_1 A A) C) = A)  &  ( ((u2_fsm_1 (k2_zfmisc_1 A A) C) = A)  &  ( ((u4_fsm_1 (k2_zfmisc_1 A A) (k1_ordinal1 A) C) = (k6_partfun1 (u1_struct_0 C)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) (k2_zfmisc_1 A A)) (u1_struct_0 C) (u1_fsm_1 (k2_zfmisc_1 A A) C) (k1_domain_1 (u1_struct_0 C) (k2_zfmisc_1 A A) (u2_fsm_1 (k2_zfmisc_1 A A) C) (k1_domain_1 A A D E))) = (k5_binop_1 A B D E)) ) ) ) ) ) ) ) ) )  =>  ((v5_fsm_2 C (k2_zfmisc_1 A A)) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r3_fsm_2 (k2_zfmisc_1 A A) (k1_ordinal1 A) C (k1_domain_1 A A D E) (k5_binop_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  (! [E:$i] :  ((m1_rewrite1 E (k1_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) D)) =>  (~  ( ((k2_xtuple_0 (k1_funct_1 E 1)) = (k1_flang_1 A (k3_flang_1 A B) C))  &  ( ((k2_xtuple_0 (k1_funct_1 E (k3_finseq_1 E))) = (k2_flang_1 A))  &  ( (~  ((k2_xtuple_0 (k1_funct_1 E 2)) = (k1_flang_1 A (k3_flang_1 A B) C)) )  &  (~  ((k2_xtuple_0 (k1_funct_1 E 2)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (v1_relat_1 (k3_msafree2 (k13_ftacell1 A B C D E)))) ) ) ) ) ).
tt(t22_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 (k3_funcop_1 C A B))) =>  ((k1_funct_1 (k3_funcop_1 C A B) D) = (k1_binop_1 C (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t22_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ( (C = (k2_tarski A B))  &  ( (~  (A = B) )  &  (! [D:$i] :  ((m2_funct_2 D C k1_numbers (k9_funct_2 C k1_numbers)) =>  (! [E:$i] :  ((m2_funct_2 E C k1_numbers (k9_funct_2 C k1_numbers)) =>  (~  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_funct_2 C k1_numbers (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) F D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G E))) (k8_funcsdom C)) =>  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) )  &  (! [F:$i] :  ((m2_funct_2 F C k1_numbers (k9_funct_2 C k1_numbers)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) & (r2_funct_2 C k1_numbers F (k1_funcsdom C k1_numbers (k5_funcsdom C) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) G D)) (k2_funcsdom C k1_numbers k1_numbers (k9_funct_2 C k1_numbers) (k7_funcsdom C) (k1_domain_1 k1_numbers (k9_funct_2 C k1_numbers) H E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_relat_1 (k4_relat_1 B) (k4_relat_1 A)) = (k4_relat_1 (k3_xboole_0 A B))) ) ) ).
tt(t22_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( ((k2_relset_1 C (k1_partfun1 A B B C D E)) = C)  & (v2_funct_1 E))  =>  ( (C = k1_xboole_0)  |  ((k2_relset_1 B D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t22_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k10_xtuple_0 (k3_funct_3 A)) (k1_zfmisc_1 (k9_xtuple_0 A)))) ) ).
tt(t22_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ((k1_funct_4 (k6_partfun1 A) (k6_partfun1 B)) = (k6_partfun1 (k2_xboole_0 A B))) ) ) ).
tt(t22_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden (k4_tarski A B) (k9_xtuple_0 C)) &  (D = (k1_funct_1 (k3_funct_5 C) B)) )  =>  ((r2_hidden A (k9_xtuple_0 D)) &  ((k1_funct_1 D A) = (k1_binop_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t22_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 B)) &  (C = (k1_funct_1 B A)) )  =>  ((r2_hidden A (k9_xtuple_0 (k2_funct_6 B))) &  ( ((k1_funct_1 (k2_funct_6 B) A) = (k9_xtuple_0 C))  &  ((r2_hidden A (k9_xtuple_0 (k3_funct_6 B))) &  ((k1_funct_1 (k3_funct_6 B) A) = (k10_xtuple_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t22_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 A) = (k2_nat_1 (k3_finseq_1 B) 1))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) <=>  ((r2_hidden C (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A))) ) ) ) ) ) ) ) ) ).
tt(t22_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t22_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k19_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) ) ).
tt(t22_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) D E) = (k4_tarski (k3_functor0 A B C D) (k3_functor0 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F C A) & (m2_functor0 F C A))  =>  (! [G:$i] :  ( ((v15_functor0 G C A) & (m2_functor0 G C A))  =>  (! [H:$i] :  ((m1_functor2 H B C D E) =>  (! [I:$i] :  ((m2_functor2 I C A F G) =>  ( ((r1_functor2 B C D E) & (r2_functor2 C A F G))  => (r8_pboole (u1_struct_0 B) (k7_functor3 B C A D E F G H I) (k3_functor2 B A (k1_functor3 B C A D F) (k1_functor3 B C A D G) (k1_functor3 B C A E G) (k6_functor3 B C A F G D I) (k5_functor3 B C A D E H G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r2_funct_2 A k1_numbers (k2_fuzzy_1 A B C) C)) ) ) ) ) ) ) ).
tt(t22_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A (k6_fuzzy_1 A B C) D) (k2_fuzzy_1 A (k1_fuzzy_2 A B (k2_fuzzy_1 A C D)) (k1_fuzzy_2 A C (k2_fuzzy_1 A B D))))) ) ) ) ) ) ) ) ).
tt(t22_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 C B) k1_numbers (k4_fuzzy_4 C A B (k4_fuzzy_2 C A) D) (k4_fuzzy_2 C B))) ) ) ) ) ) ) ) ).
tt(t22_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ((v3_fvaluat1 A) =>  ( (B = (k4_struct_0 A))  |  ((k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B)) = (k4_supinf_2 (k3_funct_2 (u1_struct_0 A) k7_numbers D C) (k3_funct_2 (u1_struct_0 A) k7_numbers D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ((r2_hidden A (k4_finseq_1 (k5_fvsum_1 B D))) &  (C = (k1_funct_1 D A)) )  =>  ((k1_funct_1 (k5_fvsum_1 B D) A) = (k4_algstr_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t22_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ( (~ (v1_xboole_0 (k16_gate_1 A B C D)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  (~ (v1_xboole_0 D)) ) ) ) )  & (v1_xboole_0 (k16_gate_1 A B C D))) ) ) ) ) ) ) ).
tt(t22_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ((r2_hidden (k5_struct_0 A) B) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) & (r4_gcd_1 A D C)) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  (~  ( (~  (C = D) )  & (r3_gcd_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((r1_xxreal_0 (k3_finseq_1 E) A) & (r1_xxreal_0 (k3_finseq_1 E) B))  =>  ((k9_genealg1 D E F A C B) = (k7_genealg1 D E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_geomtrap A F G B C D E) => (r2_geomtrap A F G C B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_twoscomp (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) (k5_facirc_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D 2) (k9_gfacirc1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E F) (k10_margrel1 F G)) (k10_margrel1 G E)))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) = (k10_margrel1 E F))  &  ( ((k1_funct_1 (k5_facirc_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 F G))  &  ((k1_funct_1 (k5_facirc_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  => (r1_tarski (k3_msafree2 (k5_gfacirc2 A C D)) (k3_msafree2 (k5_gfacirc2 B C D)))) ) ) ) ) ) ) ) ) ).
tt(t22_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  ((k6_glib_000 A) = (k6_domain_1 (k6_glib_000 A) B)) ) ) ) ) ).
tt(t22_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( ((k3_glib_001 A B) = (k4_glib_001 A (k6_glib_001 A B)))  &  ((k4_glib_001 A B) = (k3_glib_001 A (k6_glib_001 A B))) ) ) ) ) ) ).
tt(t22_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( ((r5_glib_000 A B) &  (C = D) )  =>  ((k2_glib_002 A C) = (k2_glib_002 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((r1_glib_000 A B C D) =>  ((k10_glib_003 A (k2_glib_001 A B C D)) = (k1_seq_1 (k5_glib_003 A) D)) ) ) ) ) ) ) ) ) ).
tt(t22_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)) (k21_glib_000 A (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)))))) ) ) ) ) ) ).
tt(t22_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ( ((r2_hidden A (k4_finseq_1 C)) => (r1_xxreal_0 1 (k3_finseq_1 (k17_finseq_1 B A C))))  &  ((r1_goboard1 B C D) => (r1_goboard1 B (k17_finseq_1 B A C) D)) ) ) ) ) ) ) ) ) ).
tt(t22_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k3_goboard5 C A B))) ) ) ) ) ) ) ) ).
tt(t22_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) (k1_matrix_1 A))) = (a_1_7_goboard6 A)) ) ) ).
tt(t22_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k1_matrix_1 A)) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D (k2_nat_1 E 1)))))  &  ( (~  ( (C = E)  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D (k2_nat_1 E 1)))) ) )  &  ( (~  ( (C = (k2_nat_1 E 1))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D (k2_nat_1 E 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C))) ) )  &  (~  ( ((k2_nat_1 C 1) = E)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D (k2_nat_1 E 1)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xxreal_0 (k17_euclid C) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1)))) ) ) )  => (r1_xboole_0 B (k3_topreal1 2 A))) ) ) ) ) ).
tt(t22_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k2_goboard2 (k1_goboard9 A)) = (k2_goboard2 A)) ) ) ).
tt(t22_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v3_goboard1 A) =>  ((k2_goboard5 A (k1_matrix_1 A)) = (a_1_12_gobrd11 A)) ) ) ) ).
tt(t22_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((k2_gobrd13 D E A) = (k3_goboard5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k2_pre_topc (k15_euclid 2) (k2_goboard9 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard9 A) (k3_topreal1 2 A))) ) ) ).
tt(t22_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k2_goedelcp A (k12_cqc_lang A C B)) = C)  &  ((k3_goedelcp A (k12_cqc_lang A C B)) = B) ) ) ) ) ) ) ) ).
tt(t22_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((r4_graph_1 A B) & (r4_graph_1 C B))  => (r4_graph_1 (k5_graph_1 A C) B)) ) ) ) ) ) ) ).
tt(t22_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v1_graph_2 A) & (v2_graph_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v1_graph_2 B) & (v2_graph_2 B)) ) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 B)) )  =>  ( (A = B)  |  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) &  ((v1_graph_2 C) & (v2_graph_2 C)) ) ) )  =>  (~  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k10_xtuple_0 C) = (k10_xtuple_0 A))  &  ( (~  (C = A) )  &  (~  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_card_1 (k5_graph_3 A B)) = (k8_graph_1 A B)) ) ) ) ) ).
tt(t22_graph_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((v2_funct_1 A) &  ((v7_graph_1 A C) & (m2_graph_1 A C)) )  =>  ((v2_funct_1 (k5_relat_1 A (k2_finseq_1 B))) &  ((v7_graph_1 (k5_relat_1 A (k2_finseq_1 B)) C) & (m2_graph_1 (k5_relat_1 A (k2_finseq_1 B)) C)) ) ) ) ) ) ) ) ) ).
tt(t22_graph_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u4_struct_0 C)) =>  ( ((r1_tarski (k10_xtuple_0 D) (k10_xtuple_0 E)) & (r1_tarski (k7_subset_1 (u1_struct_0 C) (k2_graph_5 C E) A) B))  => (r1_tarski (k7_subset_1 (u1_struct_0 C) (k2_graph_5 C D) A) B)) ) ) ) ) ) ) ) ) ).
tt(t22_graphsp,ax, (! [A:$i] :  ((m2_funct_2 A (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [B:$i] :  ((m2_funct_2 B (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k4_graphsp (k3_finseq_2 k1_numbers) (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) B A)) (k2_nat_1 D 1)) C) = (k4_graphsp (k3_finseq_2 k1_numbers) A (k4_graphsp (k3_finseq_2 k1_numbers) B (k4_graphsp (k3_finseq_2 k1_numbers) (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) B A)) D) C)))) ) ) ) ) ) ) ) ) ).
tt(t22_grcat_1,ax, (! [A:$i] :  ( ((v1_grcat_1 A) &  ((v2_grcat_1 A) & (l1_grcat_1 A)) )  =>  (! [B:$i] :  ( ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  (! [C:$i] :  ( ((v1_grcat_1 C) &  ((v2_grcat_1 C) & (l1_grcat_1 C)) )  =>  ( ( ((k7_grcat_1 C) = (k8_grcat_1 B))  &  ((k7_grcat_1 B) = (k8_grcat_1 A)) )  =>  ((k13_grcat_1 C (k13_grcat_1 B A)) = (k13_grcat_1 (k13_grcat_1 C B) A)) ) ) ) ) ) ) ) ).
tt(t22_gr_cy_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_gr_cy_1 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_gr_cy_1 A))) =>  (? [D:$i] :  ((v1_int_1 D) &  (C = (k5_group_1 (k4_gr_cy_1 A) D B)) ) ) ) ) ) ) ) ) ).
tt(t22_gr_cy_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((v1_gr_cy_1 B) &  ((k7_group_1 B) = A) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_nat_d C A) &  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D B))  =>  (~  ( ((k7_group_1 D) = C)  &  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E B))  =>  ( ((k7_group_1 E) = C)  => (r1_group_2 B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_gr_cy_3,ax, ((k1_gr_cy_3 11) = (k4_nat_1 23 89)) ).
tt(t22_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden A B))  <=> (r2_hidden (k4_tarski A (k1_funct_1 C A)) (k5_relat_1 C B))) ) ) ) ) ).
tt(t22_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (! [E:$i] :  ((m1_group_6 E A B) =>  (! [F:$i] :  ( ((v1_group_3 F B) & (m1_group_6 F A B))  =>  ( ((m1_group_6 D A C) &  ((m1_group_6 (k5_group_6 C (k1_group_6 A C D)) (k5_group_6 A D) (k10_group_5 (k5_group_6 A D))) &  ( (E = (k10_group_2 A C B))  &  (F = (k3_group_6 A D B)) ) ) )  => (m1_group_6 (k5_group_6 E (k1_group_6 B E F)) (k5_group_6 B F) (k10_group_5 (k5_group_6 B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_polynom1 A C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_polynom1 A C))) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r1_groeb_1 A B C F) =>  ((r11_polyred (k11_polynom1 A C) (k7_ideal_1 (k11_polynom1 A C) F) D E) <=>  ((k2_rewrite1 (k3_polyred A B C F) D) = (k2_rewrite1 (k3_polyred A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r3_pre_poly A (k3_termord A B C E) (k3_termord A B C D)) => (r8_polyred A B C (k5_polynom7 A C D (k4_termord A B C E)) E (k3_groeb_2 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k3_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) = (k2_polynom1 (k15_pre_poly A) C D))  &  ((k4_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t22_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((r1_tarski B C) => (r1_tarski (k2_group_11 A B D) (k2_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t22_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = (k1_group_1 A)) ) ) ).
tt(t22_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k2_group_1 A C) B)) ) ) )  =>  ((k2_group_2 A B B) = B) ) ) ) ) ) ).
tt(t22_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_3 A B C) = B)  <=>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(t22_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_group_4 B (k12_finseq_1 k4_numbers (k2_group_4 A)) (k12_finseq_1 (u1_struct_0 B) C)) = (k12_finseq_1 (u1_struct_0 B) (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(t22_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k2_group_5 A B C)) = (k2_group_5 A C B)) ) ) ) ) ) ) ).
tt(t22_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ((m1_subset_1 (k14_group_2 A C B) (u1_struct_0 (k5_group_6 A C))) &  ((m1_subset_1 (k13_group_2 A C B) (u1_struct_0 (k5_group_6 A C))) & (m1_subset_1 (k8_group_2 A C) (u1_struct_0 (k5_group_6 A C)))) ) ) ) ) ) ) ) ).
tt(t22_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) & (v1_group_7 (k11_finseq_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) =>  (! [D:$i] :  ((v1_int_1 D) => (r1_struct_0 B (k5_group_1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t22_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  ((k3_tarski (k7_group_9 A B C)) = (u1_struct_0 B)) ) ) ) ) ) ).
tt(t22_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v15_algstr_0 C) &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) )  =>  ( ((r2_group_6 B C) & (v2_group_10 B A))  => (v2_group_10 C A)) ) ) ) ) ) ) ).
tt(t22_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_vectsp_4 B k1_complfld A) => (m1_rlsub_1 (k10_hahnban1 B) (k10_hahnban1 A))) ) ) ) ).
tt(t22_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v1_hahnban C A) &  ((v4_hahnban C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) k1_numbers) &  ((v2_hahnban D B) &  ((v3_hahnban D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (E = F)  => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 B) k1_numbers D E) (k3_funct_2 (u1_struct_0 A) k1_numbers C F))) ) ) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) &  ((v2_hahnban E A) &  ((v3_hahnban E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (~  ( ((k2_partfun1 (u1_struct_0 A) k1_numbers E (u1_struct_0 B)) = D)  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers E F) (k3_funct_2 (u1_struct_0 A) k1_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_hallmar1 C A B) =>  (! [D:$i] :  ((m2_hallmar1 D A C) => (m2_hallmar1 D A B)) ) ) ) ) ) ) ) ).
tt(t22_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (r2_hidden D C)) )  => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A B) D) (k10_weierstr A B C))) ) ) ) ) ) ) ) ) ).
tt(t22_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (~  ( ((k3_glib_001 A B) = (k3_glib_001 A C))  & (v1_abian (k3_finseq_1 (k1_helly B C)))) ) ) ) ) ) ) ) ).
tt(t22_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B C) = (k4_struct_0 k1_complfld))  <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) (k1_hermitan A B) C) = (k4_struct_0 k1_complfld)) ) ) ) ) ) ) ) ).
tt(t22_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) => (r3_lattices (k12_normform A) (k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k11_heyting1 A B) C) B)) ) ) ) ) ).
tt(t22_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_partfun1 A B)) =>  ( ( (D = (k1_tarski F))  &  ( (E = C)  &  ((k4_substlat A B E D) = k1_xboole_0) ) )  => (r3_lattices (k5_substlat A B) (k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) F) (k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k4_heyting2 A B) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r2_hidden (k3_heyting3 A B) (k4_heyting3 (k2_nat_1 A 1) B))) ) ) ) ) ).
tt(t22_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_taylor_1 D B C) => (r1_taylor_1 (k26_valued_1 k1_numbers k1_numbers D A) B C)) ) ) ) ) ) ) ) ) ).
tt(t22_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C A) &  ((v2_ideal_1 C A) &  ((v3_ideal_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_quofield D A B) =>  ( (~ (v1_xboole_0 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))  &  ((v1_ideal_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B) &  ((v2_ideal_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B) &  ((v3_ideal_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B) & (m1_subset_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((r2_hidden (k3_hilbert1 A B) k6_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 B C) (k3_hilbert1 A C)) k6_hilbert1)) ) ) ) ) ) ) ).
tt(t22_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (~  ((k4_hilbert1 A B) = (k3_hilbert1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (C = k1_xboole_0)  &  ( (~  (B = k1_xboole_0) )  &  (~  (A = k1_xboole_0) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B C))))) )  =>  ((k9_xtuple_0 (k2_pralg_2 D)) = (k1_funct_2 A B)) ) ) ) ) ) ) ).
tt(t22_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_xxreal_0 (k2_hurwitz A (k8_polynom3 A B C)) (k4_xxreal_0 (k2_hurwitz A B) (k2_hurwitz A C)))) ) ) ) ) ) ).
tt(t22_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_idea_1 B A) =>  ((k9_idea_1 B 1 A) = A) ) ) ) ) ) ).
tt(t22_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ( (B = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))  |  (B = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t22_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ( ((r3_incsp_1 A B E) & (r3_incsp_1 A C E))  =>  ((r3_incsp_1 A D E) |  ( (B = C)  |  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A D F) &  ((r3_incsp_1 A B F) & (r3_incsp_1 A C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m5_index_1 E (u1_struct_0 D) (u4_struct_0 D) (u1_graph_1 D) (u2_graph_1 D) (u1_cat_1 D) (k7_isocat_1 D)) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((m3_cat_2 (k4_cat_5 A B F) D) &  ((m3_cat_2 (k4_cat_5 A C G) D) & (r1_funct_2 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (u4_struct_0 C) F G)) )  =>  ((k14_index_1 A B D F E) = (k14_index_1 A C D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C B) & (l3_msualg_1 C B))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) => (v4_msualg_1 (k1_instalg1 A B C D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 A B C) <=> (r2_int_1 (k6_xcmplx_0 A C) B C)) ) ) ) ) ) ) ).
tt(t22_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 C A) & (r1_int_1 C B))  => (r1_int_1 C (k3_int_2 A B))) ) ) ) ) ) ) ).
tt(t22_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ( ((k6_int_1 (k6_xcmplx_0 A B) C) = k6_numbers)  <=>  ((k4_nat_d A C) = (k4_nat_d B C)) ) ) ) ) ) ) ) ) ).
tt(t22_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_5 A B) & (r1_int_5 C B))  => (r1_int_5 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t22_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_int_2 A B) &  (! [C:$i] :  ((v1_int_1 C) =>  (~ (r2_int_1 (k3_xcmplx_0 C A) 1 B)) ) ) ) ) ) ) ) ) ).
tt(t22_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_int_7 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( (B = C)  =>  ((k2_group_1 (k3_int_7 A) B) = (k11_algstr_0 (k9_int_3 A) C)) ) ) ) ) ) ) ) ).
tt(t22_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) k16_sin_cos)) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k1_real_1 (k10_real_1 1 (k7_real_1 A 1)))) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k1_real_1 (k10_real_1 1 (k7_real_1 A 1)))) (k5_seq_4 B)))) ) ) ) ) ).
tt(t22_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r1_tarski D (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))))))) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k4_sin_cos6) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k4_sin_cos6) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t22_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t22_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos) (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos (k41_valued_1 k1_numbers k1_numbers k16_sin_cos)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t22_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ((r2_hidden C (k1_relset_1 B (k8_integr15 A B D E))) =>  ((k7_partfun1 (k1_euclid A) (k8_integr15 A B D E) C) = (k8_euclid A (k7_partfun1 (k1_euclid A) D C) (k7_partfun1 (k1_euclid A) E C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k1_rcomp_1 C D))  =>  ((k7_integr16 B A) = (k8_integr16 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t22_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid E)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integr15 E (k3_integra5 A B) F) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 E k1_numbers F)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid E) F (k3_integra5 A B)) E) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)) (k1_nfcont_4 E k1_numbers F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 E k1_numbers F) (k3_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D)))) & (r1_xxreal_0 (k12_euclid (k12_integr15 C D E F)) (k4_integra5 (k3_xxreal_0 C D) (k4_xxreal_0 C D) (k1_nfcont_4 E k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_integra1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k1_seq_1 C D) = (k9_real_1 (k7_partfun1 k1_numbers A D) (k7_partfun1 k1_numbers B D))) ) ) ) ) )  =>  ((k18_rvsum_1 C) = (k9_real_1 (k18_rvsum_1 A) (k18_rvsum_1 B))) ) ) ) ) ) ) ) ).
tt(t22_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 (k1_seq_1 (k9_integra1 B (k26_valued_1 B k1_numbers C A)) D) (k8_real_1 (k8_real_1 A (k5_seq_4 (k1_rvsum_1 C))) (k3_integra1 B)))) ) ) ) ) ) ) ) ) ).
tt(t22_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) & (v3_integra1 B A))  => (v3_integra1 (k19_rfunct_3 A B) A)) ) ) ) ) ).
tt(t22_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) E) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) )  =>  ((r1_tarski (k3_integra5 C D) (k9_xtuple_0 (k56_valued_1 k1_numbers k1_numbers E))) &  ((r1_integra5 (k3_integra5 C D) (k56_valued_1 k1_numbers k1_numbers E)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers E) (k3_integra5 C D))) &  ((r1_xxreal_0 (k18_complex1 (k4_integra5 C D E)) (k4_integra5 C D (k56_valued_1 k1_numbers k1_numbers E))) & (r1_xxreal_0 (k18_complex1 (k4_integra5 D C E)) (k4_integra5 C D (k56_valued_1 k1_numbers k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k1_rcomp_1 A B) C) &  ((r1_tarski C (k1_relset_1 k1_numbers D)) &  ((r1_tarski C (k1_relset_1 k1_numbers E)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E C)) &  ((r1_integra7 C F D) & (r1_integra7 C G E)) ) ) ) ) ) )  =>  ((k9_real_1 (k8_real_1 (k1_seq_1 F B) (k1_seq_1 G B)) (k8_real_1 (k1_seq_1 F A) (k1_seq_1 G A))) = (k7_real_1 (k4_integra5 A B (k20_valued_1 k1_numbers k1_numbers k1_numbers D G)) (k4_integra5 A B (k20_valued_1 k1_numbers k1_numbers k1_numbers F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_fdiff_1 A B) =>  ((r1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A) B) &  ((k1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A) B) = (k1_real_1 (k1_fdiff_1 A B))) ) ) ) ) ) ) ).
tt(t22_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 D k1_numbers (k20_valued_1 D k1_numbers k1_numbers (k1_integra5 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) D) (k1_integra5 C D)) (k1_integra5 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) D))) ) ) ) ) ) ) ) ).
tt(t22_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  => (r1_interva1 A (k3_interva1 A B C) (k3_interva1 A C B))) ) ) ) ) ) ).
tt(t22_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k3_intpro_1 C A) (k3_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t22_irrat_1,ax, ((v2_comseq_2 k4_irrat_1) &  ((k2_seq_2 k4_irrat_1) = k8_power) ) ).
tt(t22_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 B C F G))  => (r2_nattra_1 A C (k9_cat_1 A B C D F) (k9_cat_1 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_funct_2 (u4_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) => (r2_funct_2 (u4_struct_0 (k8_cat_2 A B)) (u4_struct_0 C) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_isomichi B A) <=>  ((v6_tops_1 (k1_tops_1 A B) A) & (v1_xboole_0 (k1_isomichi A B))) ) ) ) ) ) ).
tt(t22_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jgraph_1 (u1_struct_0 (k15_euclid 2)) A B) => (r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) ) ) ).
tt(t22_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = E)  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = (k3_xcmplx_0 E E)) ) ) ) ) )  & (v5_pre_topc C A k3_topmetr)) ) ) ) ) ) ) ) ) ) ).
tt(t22_jgraph_3,ax,(v2_funct_1 k1_jgraph_3)).
tt(t22_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k1_real_1 (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k18_euclid D) (k12_euclid D)) A) (k7_real_1 1 A)))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 (k17_euclid D) k6_numbers) &  ((r1_xxreal_0 (k13_complex1 (k18_euclid D) (k12_euclid D)) A) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t22_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 (k17_euclid B) k6_numbers))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  & (r1_xxreal_0 (k17_euclid C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) => (v2_compts_1 A (k15_euclid 2))) ) ) ).
tt(t22_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 G (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) H) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  =>  ((v1_convex1 (k3_gobrd13 A (k2_goboard2 A) B) (k15_euclid 2)) & (v1_convex1 (k2_gobrd13 A (k2_goboard2 A) B) (k15_euclid 2))) ) ) ) ) ) ).
tt(t22_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A E) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan13 A E))) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A E))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan13 A E) D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) B C))  & (r1_xxreal_0 B 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan16,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_tarski D A) &  ((r1_topreal1 (k15_euclid 2) B C D) &  ((r2_hidden (k18_pscomp_1 A) D) &  ((r2_hidden (k22_pscomp_1 A) D) &  ( (~ (r1_tarski (k8_jordan6 A) D))  &  (~ (r1_tarski (k9_jordan6 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B C D E) & (r1_jordan17 A D C B E))  =>  ( (B = C)  |  ( (C = D)  |  ( (D = E)  |  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k1_jordan2c 2 B)) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k1_jordan18 A B) (k2_jordan18 A B)) B) = (k2_tarski (k1_jordan18 A B) (k2_jordan18 A B))) ) ) ) ) ) ).
tt(t22_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B))) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1)) (k9_pscomp_1 (k3_topreal1 2 C)))) ) ) ) ) ) ) ).
tt(t22_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_2_jordan1 A))  => (v3_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t22_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k1_matrix_1 A) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 A)) &  ((r2_hidden F (k3_goboard5 A B C)) &  ( ((k17_euclid F) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E)))  &  ( (~  (B = D) )  &  (~  (B = (k7_nat_d D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden A (k1_jordan2c 2 B)) &  ((k17_euclid A) = (k6_pscomp_1 (k1_jordan2c 2 B))) ) ) ) ) ) ) ).
tt(t22_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((k21_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A)))) ) ) ) ) ) ) ) ) ).
tt(t22_jordan1e,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan9 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) )  =>  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k2_nat_1 C 1))) = (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t22_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan1e B A) (k21_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k1_jordan1e B A) (k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ) ).
tt(t22_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  => (r1_tarski (k2_topreal1 2 B C) (k2_gobrd13 B A C))) ) ) ) ) ) ) ) ).
tt(t22_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k20_pscomp_1 (k3_topreal1 2 A)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 D 1) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((r1_tarski A B) & (r2_hidden (k19_pscomp_1 B) A))  =>  ((k19_pscomp_1 A) = (k19_pscomp_1 B)) ) ) ) ) ) ).
tt(t22_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  & (r1_xxreal_0 (k1_topreal6 2 A B) k6_numbers)) ) ) ) ) ) ).
tt(t22_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) &  ((r1_jordan5c A B C D E) & (r1_jordan5c A B C E F)) )  =>  ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k5_jordan6 A B C D E) (k5_jordan6 A B C E F)) = (k5_jordan6 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (~ (v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k9_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))  &  (~ (v1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k9_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) ) ) ) ).
tt(t22_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k2_jordan21 (k3_topreal1 2 (k1_jordan9 A B))) = (k2_jordan21 (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ) ).
tt(t22_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) & (v2_jordan23 A)) )  => (r1_tarski (k3_topreal1 2 (k4_jordan3 A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t22_jordan2b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_jordan2b (k2_xcmplx_0 A B)) = (k3_rlvect_1 (k15_euclid 1) (k1_jordan2b A) (k1_jordan2b B))) ) ) ) ) ).
tt(t22_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_jordan2c A B C) => (r1_tarski C (k1_jordan2c A B))) ) ) ) ) ) ) ).
tt(t22_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ((k2_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) B) = (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 A B))) ) ) ) ) ) ).
tt(t22_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k7_nat_d (k3_finseq_1 B) 1)))  =>  ((k1_jordan4 A B) = A) ) ) ) ) ) ).
tt(t22_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xboole_0 A B))  &  ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)) &  ((r1_topreal1 (k15_euclid 2) C D A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ( ((k1_funct_1 F G) = E)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 H 1) &  ( (~ (r1_xxreal_0 H G))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  & (v4_topreal1 A)) ) )  =>  ( (C = (k1_funct_1 A (k3_finseq_1 A)))  | (r2_hidden B (k3_topreal1 2 (k2_jordan3 A C)))) ) ) ) ) ) ) ) ).
tt(t22_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((v4_topreal1 A) & (r2_hidden (k2_jordan5c (k3_topreal1 2 A) (k2_topreal1 2 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A B))) ) )  =>  ((k2_jordan5c (k3_topreal1 2 A) (k2_topreal1 2 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1))) ) ) ) ) ) ).
tt(t22_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_1_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k16_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k16_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t22_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k3_jordan6 A B C C) = A) ) ) ) ) ) ) ) ).
tt(t22_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_xxreal_0 2 (k1_matrix_1 B)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 B)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k1_matrix_1 B)) & (r1_tarski (k2_topreal1 2 C A) (k3_goboard5 B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_jordan_a C A) =>  ((r2_hidden B (k4_finseq_1 C)) => (r1_tarski (k2_jordan_a A B C) A)) ) ) ) ) ) ) ).
tt(t22_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k3_topreal9 C D A) (k1_topreal9 C D B))) ) ) ) ) ) ) ) ) ).
tt(t22_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) =>  (! [D:$i] :  ((v3_ordinal1 D) => (r3_lattices A C (k5_knaster A B C D))) ) ) ) ) ) ) ) ) ).
tt(t22_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_funct_1 B) => (m1_subset_1 (k3_funct_1 B) (k1_zfmisc_1 A))) ) ) ) ).
tt(t22_kurato_1,ax, ((k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) (k2_pre_topc k3_topmetr (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1))))))) = (k2_rcomp_1 4 k1_xxreal_0)) ).
tt(t22_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_funct_1 C D) B)) )  => (r1_tarski (k1_kurato_2 A C) (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(t22_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 1))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 (k1_nat_1 A 1))) &  ((k1_funct_1 B D) = E) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) (k1_nat_1 A 1) (k1_nat_1 A 1)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) A A) =>  ( (G = (k2_laplace D E (k1_nat_1 A 1) C F))  =>  ((k3_funct_2 (k12_matrix_2 (k1_nat_1 A 1)) (u1_struct_0 C) (k11_matrix_3 (k1_nat_1 A 1) C F) B) = (k8_group_1 C (k8_group_1 C (k1_laplace C (k4_group_1 C) (k4_algstr_0 C (k1_group_1 C)) (k2_xcmplx_0 D E)) (k3_matrix_1 (u1_struct_0 C) F D E)) (k3_funct_2 (k12_matrix_2 A) (u1_struct_0 C) (k11_matrix_3 A C G) (k4_laplace D A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_group_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_group_4 A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((k3_lattices (k11_group_4 A) D E) = (k8_group_4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_latsum_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((l1_orders_2 C) =>  (! [D:$i] :  ((l1_orders_2 D) =>  (~  ((r2_hidden (k4_tarski A B) (u1_orders_2 (k1_latsum_1 C D))) &  ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D)) C) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 C) (u1_struct_0 D)) (k1_zfmisc_1 (u1_struct_0 C))))  &  ( (~  ((r2_hidden A (u1_struct_0 C)) & (r2_hidden B (u1_struct_0 C))) )  &  ( (~  ((r2_hidden A (u1_struct_0 D)) & (r2_hidden B (u1_struct_0 D))) )  &  (~  ((r2_hidden A (k6_subset_1 (u1_struct_0 C) (u1_struct_0 D))) & (r2_hidden B (k6_subset_1 (u1_struct_0 D) (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((r6_binop_1 (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) => (v11_lattices A)) ) ) ).
tt(t22_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_lattice3 A B (k7_domain_1 (u1_struct_0 A) C D)) <=> (r3_lattices A (k3_lattices A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t22_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((k3_lattice2 (u1_struct_0 A) A (k8_setwiseo (u1_struct_0 A) (u1_struct_0 A) C B) D) = (k3_lattice2 (u1_struct_0 A) A B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t22_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k8_lattice5 A (k1_ordinal1 B)) = (k5_lattice5 (k8_lattice5 A B))) ) ) ) ) ).
tt(t22_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_lattice6 B A) => (v3_lattice6 B A)) ) ) ) ) ).
tt(t22_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((v1_funct_1 (k5_lattice8 A B C D E)) &  ((v1_funct_2 (k5_lattice8 A B C D E) (k2_zfmisc_1 (k3_lattice8 A E) (k3_lattice8 A E)) (u1_struct_0 B)) & (m1_subset_1 (k5_lattice8 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_lattice8 A E) (k3_lattice8 A E)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_lattices A (k7_lattices A B)) = B) ) ) ) ) ).
tt(t22_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) =>  ( (~ (r1_xxreal_0 C (k7_nat_d (k39_glib_000 B) (k1_recdef_1 (k5_lexbfs A B C) D))))  &  (~ (r1_xxreal_0 (k1_recdef_1 (k5_lexbfs A B C) D) (k7_nat_d (k39_glib_000 B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((k8_lfuzzy_0 A C (k4_fuzzy_4 A B C D E) F G) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (a_7_0_lfuzzy_0 A B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_fuzzy_4 A A A (k5_fuzzy_4 A A) B) B)) ) ) ) ).
tt(t22_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_limfunc1 A) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 C (k1_seq_1 B D))) ) ) ) ) )  | (v1_limfunc1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t22_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r5_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r5_limfunc2 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r6_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ( ((r6_limfunc2 C A) =>  ((r1_xxreal_0 B k6_numbers) | (r6_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) )  &  ((r6_limfunc2 C A) =>  ((r1_xxreal_0 k6_numbers B) | (r5_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  ( (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))))  &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) ) )  | (r3_limfunc3 B A)) ) ) ) ) ) ).
tt(t22_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r6_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_seq_1 B E) (k1_limfunc2 B A))) ) ) ) ) ) ) )  | (r3_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t22_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_lmod_6 A C (k1_vectsp_5 A B C D)) & (r1_lmod_6 A D (k1_vectsp_5 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t22_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_vectsp_4 F A C) =>  ( ((k1_algstr_0 (k17_lmod_7 A C F) (k18_lmod_7 A C F D) (k18_lmod_7 A C F E)) = (k18_lmod_7 A C F (k3_rlvect_1 C D E)))  &  ((k4_vectsp_1 A (k17_lmod_7 A C F) B (k18_lmod_7 A C F D)) = (k18_lmod_7 A C F (k4_vectsp_1 A C B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  => (v1_rlsub_1 (k10_lopban_1 A B) (k8_lopban_1 A B))) ) ) ) ).
tt(t22_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k8_lopban_2 A)) = (k6_lopban_2 A)) ) ) ).
tt(t22_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_lopban_3 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_lopban_3 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t22_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) =>  ((k8_nat_1 (u1_struct_0 A) (k7_lopban_4 (k2_nat_1 E 1) A B C) D) = (k3_rlvect_1 A (k8_nat_1 (u1_struct_0 A) (k7_lopban_4 E A B C) D) (k8_nat_1 (u1_struct_0 A) (k6_lopban_4 (k2_nat_1 E 1) A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  => (r1_tarski (k10_lopclset A) (k9_setfam_1 (k7_lopclset A)))) ) ).
tt(t22_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A D)) =>  (k6_numbers = (k1_funct_1 D E)) ) ) )  =>  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  (E = (k1_relset_1 A D)) ) ) )  |  ((r1_mesfunc5 A B C D) &  ((k7_mesfunc5 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden E (k1_lpspace2 A B C D)) & (r2_hidden F (k1_lpspace2 A B C D)))  =>  ((r3_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers E))) &  ((r3_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers F))) & (r3_mesfunc6 A B C (k3_valued_1 A k1_numbers k1_numbers (k2_mesfun6c D A (k56_valued_1 A k1_numbers E)) (k2_mesfun6c D A (k56_valued_1 A k1_numbers F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((r2_ltlaxio1 C A) & (r2_ltlaxio1 C B))  <=> (r2_ltlaxio1 C (k4_subset_1 k1_hilbert1 A B))) ) ) ) ) ) ) ).
tt(t22_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C D)) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A D E)) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_margrel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v2_margrel1 B) &  ((v3_margrel1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) )  =>  ((k9_xtuple_0 B) = (k4_finseq_2 (k19_margrel1 B) A)) ) ) ) ) ).
tt(t22_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_mathmorp A B (k6_domain_1 (u1_struct_0 A) C)) = (k1_mathmorp A (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t22_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ((v1_matrix10 C) =>  ((r1_xxreal_0 k6_numbers A) | (v2_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ) ).
tt(t22_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((v12_vectsp_1 A) <=>  (~  ((k1_group_1 A) = (k4_algstr_0 A (k1_group_1 A))) ) ) ) ) ).
tt(t22_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( ((r2_hidden A (k4_finseq_1 (k12_matrix_1 D B))) & (r2_hidden C (k4_finseq_1 (k12_matrix_1 D B))))  =>  ( (C = A)  |  ((r1_xxreal_0 B k6_numbers) |  ((k5_matrix_6 B D (k6_matrix12 B B D (k12_matrix_1 D B) A C E)) = (k6_matrix12 B B D (k12_matrix_1 D B) A C (k4_algstr_0 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_matrix_1 B A 2 2) =>  (B = (k6_matrix_2 A (k3_matrix_1 A B 1 1) (k3_matrix_1 A B 1 2) (k3_matrix_1 A B 2 1) (k3_matrix_1 A B 2 2))) ) ) ) ) ).
tt(t22_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_fvsum_1 A (k12_finseq_1 (u1_struct_0 A) (k4_struct_0 A)) (k12_finseq_1 (u1_struct_0 A) B)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t22_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = k1_xboole_0) )  =>  ( ((k7_matrlin (u1_struct_0 A) B C) = C)  &  ((k7_matrlin (u1_struct_0 A) C B) = C) ) ) ) ) ) ) ) ) ).
tt(t22_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((v3_matrix16 C (u1_struct_0 B)) &  ((v3_matrix16 D (u1_struct_0 B)) & (v3_matrix16 E (u1_struct_0 B))) )  => (v3_matrix16 (k2_matrix_6 A B (k2_matrix_6 A B C D) E) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B k1_xboole_0 A) =>  ( ((k3_finseq_1 C) = k1_xboole_0)  &  ( ((k1_matrix_1 C) = k1_xboole_0)  &  ((k2_matrix_1 C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( ((k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B) B) = (k1_finseq_2 A))  &  ((k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B)) = (k1_finseq_2 A)) ) ) ) ) ) ).
tt(t22_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ( ((k1_matrix_1 C) = k6_numbers)  |  ((k4_matrix_1 (u1_struct_0 A) (k4_matrix_3 A B C)) = (k4_matrix_3 A (k4_matrix_1 (u1_struct_0 A) C) (k4_matrix_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k3_matrix_3 A (k1_matrix_4 A B C) C)) ) ) ) ) ) ) ) ).
tt(t22_matrix_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k4_matrix_3 A (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B)) C) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v2_matrix_6 C A B) & (v2_matrix_6 D A B))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_matrix_6 A B C D) <=> (v2_matrix_6 (k4_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_matrix_7 A (k8_finseq_1 (u1_struct_0 A) B C)) = (k8_finseq_1 (u1_struct_0 A) (k4_matrix_7 A B) (k4_matrix_7 A C))) ) ) ) ) ) ) ).
tt(t22_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B D C) = (k11_matrix_1 B A)) )  =>  (D = (k11_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 1 3 2))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) B G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((r1_xxreal_0 1 (k3_finseq_1 (k1_complsp2 A))) =>  ((k1_finsop_1 k2_numbers (k1_complsp2 A) k27_binop_2) = (k15_complex1 (k1_finsop_1 k2_numbers A k27_binop_2))) ) ) ) ).
tt(t22_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  ( (C = k1_xboole_0)  =>  ((k13_matrixj1 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t22_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 D)) =>  ((r2_hidden A (k4_finseq_1 E)) =>  ( (A = (k3_finseq_1 E))  |  ((k4_rlvect_1 D (k5_matrlin B D (k8_matrix_1 (u1_struct_0 B) (k2_matrixj2 B C (k3_finseq_1 E)) A) E)) = (k3_rlvect_1 D (k4_vectsp_1 B D C (k7_partfun1 (u1_struct_0 D) E A)) (k7_partfun1 (u1_struct_0 D) E (k1_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 C) = (k3_finseq_1 D))  =>  ((k4_matrix_3 A C (k6_matrix_3 A D B)) = (k6_matrix_3 A (k4_matrix_3 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers C D E) = (k9_real_1 (k3_matrix_1 k1_numbers A D E) (k3_matrix_1 k1_numbers B D E))) ) ) ) ) ) ) ) ) )  =>  (C = (k5_matrixr1 A B)) ) ) ) ) ) ) ) ).
tt(t22_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D B C) =>  ( ((v1_vectsp_7 (k10_xtuple_0 (k17_finseq_1 (u1_struct_0 C) A D)) B C) & (m1_subset_1 (k10_xtuple_0 (k17_finseq_1 (u1_struct_0 C) A D)) (k1_zfmisc_1 (u1_struct_0 C))))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (E = (k10_xtuple_0 (k17_finseq_1 (u1_struct_0 C) A D)))  => (m1_matrlin (k17_finseq_1 (u1_struct_0 C) A D) B (k1_vectsp_7 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ( ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) &  ((v13_vectsp_1 E C B) & (v1_mod_2 E A C B)) ) )  =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ( ((k4_finseqop (u1_struct_0 C) (u1_struct_0 B) F D) = (k4_finseqop (u1_struct_0 C) (u1_struct_0 B) F E))  =>  ((r1_xxreal_0 (k3_finseq_1 F) k6_numbers) | (r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_matroid0 B A) =>  (! [C:$i] :  ((m1_matroid0 C A) =>  ((k5_card_1 B) = (k5_card_1 C)) ) ) ) ) ) ) ).
tt(t22_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k4_matrprob A) = (k3_matrprob (k4_matrix_1 k1_numbers A))) ) ) ).
tt(t22_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k1_funct_1 (k3_matrtop1 A B E) (k4_rvsum_1 C D)) = (k4_rvsum_1 (k1_funct_1 (k3_matrtop1 A B E) C) (k1_funct_1 (k3_matrtop1 A B E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlvect_3 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ((v1_rlvect_3 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ( ((k1_card_1 B) = (k1_card_1 C))  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A A) =>  (~  ((v1_matrix_6 D A k2_vectsp_1) &  ((k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 A A D) (k2_struct_0 (k1_rlvect_3 (k15_euclid A) B))) = (k2_struct_0 (k1_rlvect_3 (k15_euclid A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) C) = (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k17_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k20_sin_cos A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B) C) C)) = (k11_binop_2 2 (k1_normsp_0 A (k5_algstr_0 A C B)))) ) ) ) ) ) ) ).
tt(t22_mboolean,ax, (! [A:$i] :  (! [B:$i] : (r6_pboole A (k2_mboolean A (k7_funcop_1 A B)) (k7_funcop_1 A (k3_tarski B)))) ) ).
tt(t22_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (C = (k4_tarski (k1_xtuple_0 C) (k2_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(t22_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ( (! [C:$i] :  ((r2_hidden C B) => (r2_hidden (k6_subset_1 A C) B)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((r1_tarski C B) => (r2_hidden (k6_setfam_1 A C) B)) ) ) )  <=>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ).
tt(t22_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B D (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B C E)))  & (r1_tarski (k8_nat_1 B C E) (k8_nat_1 B C (k2_nat_1 E 1)))) ) ) )  =>  ( ((k8_nat_1 B C k6_numbers) = (k8_nat_1 B D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 B C (k2_nat_1 E 1)) = (k1_measure1 A B (k8_nat_1 B D (k2_nat_1 E 1)) (k8_nat_1 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ((k8_supinf_2 A) = (k7_supinf_2 B))  =>  ( ( (~ (r2_hidden (k8_supinf_2 A) A))  &  (~ (r2_hidden (k7_supinf_2 B) B)) )  |  ((v6_xxreal_2 (k4_subset_1 k1_numbers A B)) & (m1_subset_1 (k4_subset_1 k1_numbers A B) (k1_zfmisc_1 k1_numbers))) ) ) ) ) ) ) ).
tt(t22_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  =>  ((v1_funct_1 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D)) &  ((v1_funct_2 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D) k5_numbers k7_numbers) & (m1_subset_1 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k7_numbers C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) ) ) ) ) ) ) ) ) ).
tt(t22_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) => (r1_tarski (k6_member_1 A) (k6_member_1 B))) ) ) ) ) ).
tt(t22_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v4_membered B) =>  ((r1_tarski A B) => (v4_membered A)) ) ) ) ).
tt(t22_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((k7_memstr_0 A B C) = (k7_memstr_0 A B D))  =>  ((k7_memstr_0 A B (k7_nat_d C E)) = (k7_memstr_0 A B (k7_nat_d D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( (D = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k10_binop_2 1 G)) (k1_rlvect_1 (k15_euclid 2) C G)))  &  ( (E = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k10_binop_2 1 H)) (k1_rlvect_1 (k15_euclid 2) A H)))  &  (F = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A (k10_binop_2 1 I)) (k1_rlvect_1 (k15_euclid 2) B I))) ) )  =>  ((r1_euclid_6 A B C) |  ( (G = 1)  |  ( (H = 1)  |  ( (I = 1)  |  ( ((k11_binop_2 (k11_binop_2 (k12_binop_2 G (k10_binop_2 1 G)) (k12_binop_2 H (k10_binop_2 1 H))) (k12_binop_2 I (k10_binop_2 1 I))) = 1)  <=> (r1_menelaus (k4_euclid_4 2 A D) (k4_euclid_4 2 B E) (k4_euclid_4 2 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ( (E = (k1_relset_1 A D))  &  ((r2_mesfun6c A B C D) &  ((k12_supinf_2 C F) = k6_numbers) ) )  =>  ((k1_mesfun6c A B C (k2_partfun1 A k2_numbers D (k7_prob_1 A B E F))) = (k1_mesfun6c A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k1_numbers C k6_numbers)) = E)  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers C F) E)) )  &  ( ((k1_relset_1 A D) = E)  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) =>  ((v2_comseq_2 (k10_seqfunc A C F)) &  ((k12_supinf_2 D F) = (k2_seq_2 (k10_seqfunc A C F))) ) ) ) ) ) ) )  => (r1_mesfunc1 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  => (r2_funct_2 k5_numbers (k4_partfun1 A k1_numbers) (k12_mesfun7c A (k1_mesfun9c A k2_numbers C B)) (k1_mesfun9c A k1_numbers (k12_mesfun7c A C) B))) ) ) ) ) ).
tt(t22_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k8_nat_1 B C G) = (k9_subset_1 A E (k18_mesfunc1 A D (k1_measure6 (k7_real_1 F (k10_real_1 1 (k2_nat_1 G 1))))))) ) )  =>  ((k9_subset_1 A E (k17_mesfunc1 A D (k1_measure6 F))) = (k2_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k12_supinf_2 (k2_mesfunc2 A B) C) = k1_supinf_2) )  =>  ((k12_supinf_2 (k1_mesfunc2 A B) C) = (k12_supinf_2 B C)) ) ) ) ) ) ) ) ).
tt(t22_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v6_supinf_2 B) & (v6_supinf_2 C))  =>  ( ((k1_relset_1 A (k3_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  & (v6_supinf_2 (k3_mesfunc1 A B C))) ) ) ) ) ) ) ) ).
tt(t22_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (v3_valued_0 (k1_mesfunc5 A B))) ) ) ) ).
tt(t22_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A (k3_mesfunc1 A D E)))  & (r1_xxreal_0 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k10_mesfunc1 A (k3_mesfunc1 A D E)) F)) (k3_supinf_2 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k10_mesfunc1 A D) F)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k10_mesfunc1 A E) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k8_nat_1 (k9_setfam_1 A) D F) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k4_mesfunc5 A k7_numbers (k3_mesfunc8 A C) F) (k1_measure6 E)))) ) )  =>  ((k3_tarski (k2_relset_1 B D)) = (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) (k17_mesfunc1 A (k5_mesfunc8 A C) (k1_measure6 E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) & (r1_xxreal_0 D C))  =>  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) D))) & (r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  ((k1_metric_1 1 1 k3_metric_1 A B) = (k1_metric_1 1 1 k3_metric_1 B A)) ) ) ) ) ).
tt(t22_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r4_metric_2 A B C D) => (r4_metric_2 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t22_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ( ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 A B) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t22_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_metric_6 A D B) & (r1_metric_6 A D C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t22_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 (k2_waybel23 A) B) <=> (r1_ordinal1 (k4_topgen_1 A) B)) ) ) ) ) ).
tt(t22_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ( (C = (k8_euclid_7 A))  &  (! [D:$i] :  ((m2_rlvect_2 D (k15_euclid A) C) =>  (~  (B = (k6_rlvect_2 (k15_euclid A) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((r2_midsp_1 A B C) & (r2_midsp_1 A D C))  => (r2_midsp_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t22_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_midsp_1 A B C) = (k8_midsp_1 A D E))  <=>  ((k3_midsp_1 A B E) = (k3_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v4_midsp_2 E B) & (l1_midsp_2 E B))  =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 (u1_midsp_2 B E)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B E)))) =>  ((k9_midsp_3 A B E C F) = (k9_midsp_3 A B E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_relset_1 A A D E) & (r1_tarski B C))  => (r1_tarski (k4_mmlquery A D B) (k4_mmlquery A E C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_mod_2,ax, ( ((k4_struct_0 k18_mod_2) = k6_numbers)  &  ( ((k5_struct_0 k18_mod_2) = 1)  &  ((m1_subset_1 (k4_struct_0 k18_mod_2) (k1_enumset1 k6_numbers 1 2)) &  ((m1_subset_1 (k5_struct_0 k18_mod_2) (k1_enumset1 k6_numbers 1 2)) &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 k18_mod_2) (u1_struct_0 k18_mod_2)) (u1_struct_0 k18_mod_2) (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2) (u1_algstr_0 k18_mod_2) k13_mod_2) & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 k18_mod_2) (u1_struct_0 k18_mod_2)) (u1_struct_0 k18_mod_2) (k2_zfmisc_1 (k1_enumset1 k6_numbers 1 2) (k1_enumset1 k6_numbers 1 2)) (k1_enumset1 k6_numbers 1 2) (u2_algstr_0 k18_mod_2) k14_mod_2)) ) ) ) ) ).
tt(t22_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( ((k1_mod_3 A B C) = B)  &  (! [D:$i] :  ((m1_mod_3 D A B) =>  (~ (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v8_mod_4 B A A) <=>  ((v13_vectsp_1 B A A) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_algstr_0 A C D)) = (k6_algstr_0 A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_group_1 A)) = (k1_group_1 A))  &  ((v2_funct_1 B) & (v2_funct_2 B (u1_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t22_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( ((k1_trees_2 A (k1_modal_1 A)) = (k6_domain_1 A B))  =>  (A = (k5_trees_1 (k2_trees_1 1) (k12_finseq_1 k5_numbers k6_numbers) (k4_trees_1 A B))) ) ) ) ) ) ).
tt(t22_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k30_modelc_1 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E)))))) )  =>  ((r4_modelc_1 B C E F D (k9_modelc_1 A)) <=>  (? [G:$i] :  ((m1_modelc_1 G B C) &  ( ((k3_funct_2 k5_numbers B G k6_numbers) = D)  & (r4_modelc_1 B C E F (k3_funct_2 k5_numbers B G 1) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v4_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  ( (B = (k11_modelc_2 A))  |  (B = (k12_modelc_2 A)) ) ) ) ) ) ) ) ).
tt(t22_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ((r1_xxreal_0 (k21_modelc_3 A B) k6_numbers) =>  ((u2_modelc_3 A B) = (k7_modelc_3 A)) ) ) ) ) ) ).
tt(t22_moebius1,ax, (~ (v1_moebius1 1)) ).
tt(t22_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_algstr_0 B))  =>  ((m2_monoid_0 A A) & (m3_monoid_0 B B)) ) ) ) ) ).
tt(t22_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_group_1 B) & (l3_algstr_0 B)) )  =>  ((k5_struct_0 (k11_monoid_1 B A)) = (k5_monoid_1 (u1_struct_0 B) A (k4_binop_1 (u1_struct_0 B) (u2_algstr_0 B)))) ) ) ) ).
tt(t22_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k1_morph_01 A B D) (k1_morph_01 A C D))) ) ) ) ) ) ) ) ) ).
tt(t22_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  => (r2_pboole (u1_struct_0 A) (k1_equation (u1_struct_0 A) C (k15_msafree A B)) (k5_msafree3 A B C))) ) ) ) ) ) ).
tt(t22_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_msaterm D A B (k2_msaterm A B C)) =>  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) => (m1_dtconstr (k1_funct_1 D E) (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_relat_1 C) & (m1_msafree C A B))  =>  (? [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A C)) (u3_msualg_1 A B)) & (r2_msualg_3 A (k11_msafree A C) B D)) ) ) ) ) ) ) ) ).
tt(t22_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  ( ((v2_finset_1 B) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A C B) => (v2_finset_1 C)) ) ) )  => (v2_finset_1 (k2_mboolean A B))) ) ) ) ).
tt(t22_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ( ((k1_unialg_1 A) = (k1_unialg_1 B))  <=>  ((k6_msualg_1 A) = (k6_msualg_1 B)) ) ) ) ) ) ).
tt(t22_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A C)) =>  ((k12_msualg_2 A B D) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) D (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A C))) => (r3_msualg_3 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t22_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 (k1_msualg_1 A D))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  ((k3_relat_1 (k4_msualg_6 A D E B F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k2_msualg_1 A D))) = (k3_relat_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) E)) (k4_msualg_6 A D E B (k5_msualg_3 A B B D C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_msualg_7,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  &  (? [B:$i] :  ((m2_nat_lat B A) &  ((v2_msualg_7 B A) &  (~ (v1_msualg_7 B A)) ) ) ) ) ) ).
tt(t22_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B (k6_pboole A C D)) =>  ((v2_msualg_3 E A B (k6_pboole A C D)) => (v2_msualg_3 (k2_msualg_9 A B C D E) A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_unialg_2 A B) & (r2_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C)))  => (r3_alg_1 A B C)) ) ) ) ) ) ) ).
tt(t22_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v2_dilworth B (k3_necklace A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_necklace A)))))  =>  ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t22_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((v1_pscomp_1 B A) & (v1_pscomp_1 C A))  => (v1_pscomp_1 (k3_nagata_1 A B C) A)) ) ) ) ) ) ) ).
tt(t22_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v9_pre_topc A) &  ((v7_pre_topc A) &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))))) )  & (v5_nagata_1 B A)) ) ) )  <=> (v3_pcomps_1 A)) ) ) ).
tt(t22_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 (k1_nat_1 B 1) A))  &  ((r1_xxreal_0 B A) &  (~  (A = B) ) ) ) ) ) ) ) ) ).
tt(t22_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_abian A))  <=>  ((k4_nat_d A 2) = 1) ) ) ) ).
tt(t22_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k11_nat_3 A A) = 1) ) ) ) ).
tt(t22_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  ( ((k1_newton A (k11_nat_3 C A)) = (k1_newton B (k11_nat_3 C B)))  =>  ((r1_xxreal_0 (k11_nat_3 C A) k6_numbers) |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t22_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_int_2 A) <=>  ( ((k4_nat_d (k23_binop_2 (k9_newton (k7_nat_d A 1)) 1) A) = k6_numbers)  &  (~ (r1_xxreal_0 A 1)) ) ) ) ) ).
tt(t22_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d (k2_xcmplx_0 A B) C) = (k4_nat_d (k2_nat_1 (k4_nat_d A C) B) C)) ) ) ) ) ) ) ).
tt(t22_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  ( ((r1_nattra_1 A B C D) &  ((r1_nattra_1 A B D E) & (r1_nattra_1 A B E F)) )  =>  (! [G:$i] :  ((m1_nattra_1 G A B C D) =>  (! [H:$i] :  ((m1_nattra_1 H A B D E) =>  (! [I:$i] :  ((m1_nattra_1 I A B E F) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k5_nattra_1 A B C D F G (k5_nattra_1 A B D E F H I)) (k5_nattra_1 A B C E F (k5_nattra_1 A B C D E G H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) =>  ( (! [E:$i] :  ((m1_nfcont_1 E B D) =>  (~  ((k9_subset_1 (u1_struct_0 B) (k1_relset_1 (u1_struct_0 B) C) E) = (k1_tarski D)) ) ) )  | (r3_ncfcont1 B A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers))))  =>  ((r4_ncfcont2 A B C) => (r10_ncfcont1 B C A)) ) ) ) ) ) ).
tt(t22_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=> (r2_hidden C (u1_struct_0 A))) ) )  <=>  (B = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t22_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_ndiff_3 A B C) => (r1_nfcont_3 A B C)) ) ) ) ) ) ) ).
tt(t22_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A))))) )  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) => (r2_ndiff_4 A C B)) ) ) ) ) ) ) ).
tt(t22_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_prvect_2 A B))) =>  ( ((k5_algstr_0 (k14_prvect_2 A) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) D) C) = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) (k5_algstr_0 (k11_prvect_2 A B) D (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C))))  &  ((k5_algstr_0 (k14_prvect_2 A) C (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) D)) = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) (k5_algstr_0 (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  => (r2_necklace B A)) ) ) ) ).
tt(t22_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (u1_struct_0 (k4_necklace A))) & (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t22_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_net_1 A)) =>  (! [C:$i] :  ((r2_hidden B C) =>  ( ((k2_net_1 A) = k1_xboole_0)  | (r2_hidden (k6_net_1 A B) (k11_net_1 A C))) ) ) ) ) ) ) ).
tt(t22_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_newton (k1_nat_1 B 1) (k1_nat_1 A 1)) = (k7_real_1 (k5_newton (k1_nat_1 B 1) A) (k5_newton B A))) ) ) ) ) ).
tt(t22_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r4_nfcont_1 B C A) <=> (r4_nfcont_1 B (k2_partfun1 (u1_struct_0 B) k1_numbers C A) A)) ) ) ) ) ) ).
tt(t22_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) C A) B))  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_normsp_0 k1_numbers B C) A)) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) (k5_vfunct_1 k1_numbers B C) A) B)) ) ) ) ) ) ) ).
tt(t22_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r2_hidden B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers C D))) &  ((r1_nfcont_4 A C B) & (r2_nfcont_4 A D (k7_partfun1 (k1_euclid A) C B))) )  => (r1_fcont_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers C D) B)) ) ) ) ) ) ) ) ) ).
tt(t22_normform,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)))))) )  =>  ( ((k5_relat_1 D C) = (k5_relat_1 E C))  =>  ((k6_normform B A C D) = (k6_normform B A C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v3_normsp_1 C B) => (v3_normsp_1 (k5_normsp_1 B C A) B)) ) ) ) ) ) ) ).
tt(t22_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ((v3_pre_topc B (k4_normsp_2 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (a_3_2_normsp_2 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_numbers,ax, (~  (k3_numbers = k1_numbers) ) ).
tt(t22_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((k1_funct_1 (k8_openlatt A) B) = (k1_funct_1 (k8_openlatt A) C)) ) ) ) ) ) ) ) ) ).
tt(t22_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v7_cat_1 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B)) <=> (v8_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t22_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  => (v2_orders_1 B)) ) ) ).
tt(t22_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A B C) <=> (r2_hidden C (k1_orders_2 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(t22_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k1_ordinal1 B)) <=> (r1_ordinal1 A B)) ) ) ) ) ).
tt(t22_ordinal2,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_ordinal1 (k3_ordinal2 A) (k3_ordinal2 B))) ) ) ).
tt(t22_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden (k10_ordinal2 A B) (k10_ordinal2 A C)) => (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t22_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~  (A = k1_xboole_0) )  &  ((k12_ordinal2 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t22_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((r2_hidden k6_numbers A) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k1_ordinal5 A C)) ) ) ) )  => (v2_ordinal5 B)) ) ) ) ) ).
tt(t22_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v5_ordinal1 D) & (v1_ordinal2 D)) ) )  =>  ( ( (D = (k2_ordinal6 A))  &  ((r2_hidden B (k9_xtuple_0 D)) & (r2_hidden C (k9_xtuple_0 D))) )  =>  ((r1_tarski B C) <=> (r1_tarski (k1_funct_1 D B) (k1_funct_1 D C))) ) ) ) ) ) ) ).
tt(t22_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t22_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k1_ortsp_1 A B D C E) = (k11_algstr_0 A (k1_ortsp_1 A B D E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k4_tarski D F) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) C)) & (r2_hidden (k4_tarski E F) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) D)))  => (r2_hidden (k4_tarski C F) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k4_dtconstr (k2_osafree A B)) (u1_struct_0 A))) (k19_osafree A B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((r6_osalg_1 A B C) & (r6_osalg_1 A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t22_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tarski (k8_osalg_2 A B C D) (k8_msualg_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t22_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_osalg_4 C A B) & (m1_osalg_4 C A B)) )  => (v3_msualg_4 C A B)) ) ) ) ) ) ).
tt(t22_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_parsp_1 A B C D E) => (r1_parsp_1 A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) & (r1_parsp_1 A B C D E))  =>  ( (B = C)  | (r1_parsp_1 A D C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_relset_1 A B (k3_partfun1 C A B) C)) ) ) ) ).
tt(t22_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ( (D = (k7_relset_1 C B E A))  <=>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden F D) <=>  (? [G:$i] :  ((m1_subset_1 G C) &  ((r2_hidden G (k1_relset_1 C E)) &  ((r2_hidden G A) &  (F = (k7_partfun1 B E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E A) &  ( ((k1_funct_1 D 1) = E)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = F)  &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 1 G) &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) G))  &  (! [H:$i] :  (~  ((r2_hidden H A) &  ((r2_hidden (k4_tarski (k1_funct_1 D G) H) (k3_eqrel_1 A B C)) & (r2_hidden (k4_tarski H (k1_funct_1 D (k2_nat_1 G 1))) (k3_eqrel_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_hidden (k4_tarski E F) (k5_eqrel_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r3_relat_2 B A) => (v3_relat_2 B)) ) ) ) ) ).
tt(t22_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B E C D) & (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r6_pboole A (k2_pboole A B C) C)) ) ) ) ) ) ).
tt(t22_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) => (v2_pcomps_1 A)) ) ) ).
tt(t22_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k19_pcs_0 A B))) =>  ( (C = B)  => (r1_orders_2 (k19_pcs_0 A B) C D)) ) ) ) ) ) ) ) ).
tt(t22_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 A))) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  ( ( (E = F)  &  (G = H) )  =>  ((k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k7_pdiff_1 A D G) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) E (k4_pdiff_1 C B))) = (k2_pdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A D H) (k1_partfun1 (k1_euclid A) (k1_euclid B) (k1_euclid B) k1_numbers F (k1_pdiff_1 C B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_1 2 2 A B) => (r1_fcont_1 (k1_pdiff_2 2 2 A B) (k1_seq_1 (k1_pdiff_1 2 2) B))) ) ) ) ) ).
tt(t22_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r2_pdiff_3 B A) & (r2_pdiff_3 C A))  =>  ((r3_pdiff_1 2 2 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) &  ((k11_pdiff_1 2 2 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) = (k7_real_1 (k3_pdiff_3 B A) (k3_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t22_pdiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r1_pdiff_4 B A) =>  ((r1_tarski A (k1_relset_1 (k1_euclid 3) B)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C A) => (r3_pdiff_1 3 1 B C)) ) ) ) ) ) ) ) ).
tt(t22_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r4_pdiff_5 B A) <=> (r3_pdiff_1 3 1 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ).
tt(t22_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_pdiff_1 B A C D) =>  ((r1_pdiff_1 B A (k9_integr15 A E (k1_euclid B) C) D) & (r2_relset_1 (k1_euclid B) (k1_euclid A) (k8_pdiff_1 B A (k9_integr15 A E (k1_euclid B) C) D) (k9_integr15 A E (k1_euclid B) (k8_pdiff_1 B A C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  ( ((r1_pdiff_1 B A D E) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B)) )  =>  ((r4_pdiff_1 B A C D E) &  ((k12_pdiff_1 B A C D E) = (k1_funct_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (k1_euclid B) (k1_euclid A) (k7_pdiff_1 B C (k4_struct_0 (k4_real_ns1 B))) (k8_pdiff_1 B A D E)) (k12_finseq_1 k1_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ((v3_nfcont_1 D (k4_real_ns1 A)) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ((r7_pdiff_1 A B E C D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k15_pdiff_1 A B E C D) D)) ) ) )  <=>  ((r2_ndiff_1 D (k4_real_ns1 A) (k4_real_ns1 B) C) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C D) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((v1_pdiff_7 F A) &  ( (E = D)  &  ( (F = G)  & (r2_pdiff_7 A B C D F)) ) ) ) )  =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k4_real_ns1 A))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k4_real_ns1 A))) =>  ( ( (H = J)  &  ( (I = K)  &  ((r2_hidden H F) & (r2_hidden I F)) ) )  =>  ((k12_euclid (k8_euclid B (k7_partfun1 (k1_euclid B) (k2_pdiff_7 A B C D F) I) (k7_partfun1 (k1_euclid B) (k2_pdiff_7 A B C D F) H))) = (k1_normsp_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k7_partfun1 (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B))) (k15_pdiff_1 A B C E G) K) (k7_partfun1 (u1_struct_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B))) (k15_pdiff_1 A B C E G) J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pencil_1,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  & (l1_pre_topc A))  => (v1_pencil_1 (k2_struct_0 A) A)) ) ).
tt(t22_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  ( ((v2_pencil_1 C (k5_pencil_1 A B)) & (v1_pencil_1 C (k5_pencil_1 A B)))  =>  ((v1_zfmisc_1 C) | (m1_pencil_2 (k3_tarski (a_3_0_pencil_2 A B C)) A B)) ) ) ) ) ) ) ) ) ).
tt(t22_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v9_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_pencil_1 A B C))) =>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  (~  ((m1_pencil_2 (k4_card_3 F) A B) &  ((r8_pboole A E (k2_funct_7 F C (k6_domain_1 (u1_struct_0 (k2_pencil_1 A B C)) D))) &  ( (~ (r2_hidden D (k1_funct_1 F C)))  &  (! [G:$i] :  ((m2_finseq_1 G (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  (~  ( ((k1_funct_1 G 1) = (k4_card_3 E))  &  ( ((k1_funct_1 G (k3_finseq_1 G)) = (k4_card_3 F))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) => (m1_pencil_2 (k1_funct_1 G H) A B)) ) )  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_xxreal_0 1 H) =>  ((r1_xxreal_0 (k3_finseq_1 G) H) |  (! [I:$i] :  ((m1_pencil_2 I A B) =>  (! [J:$i] :  ((m1_pencil_2 J A B) =>  ( ( (I = (k1_funct_1 G H))  &  (J = (k1_funct_1 G (k1_nat_1 H 1))) )  =>  ((r1_xboole_0 I J) & (r1_pencil_3 A B I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 D (k1_vectsp_9 A B)) & (v1_xboole_0 (k6_pencil_4 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_nat_d 2 A) <=> (v1_abian A)) ) ) ).
tt(t22_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r1_pnproc_1 A (k2_pnproc_1 A (k2_pnproc_1 A B C) D) (k2_pnproc_1 A B (k2_pnproc_1 A C D)))) ) ) ) ) ) ) ).
tt(t22_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_polyalg1 A)))))  =>  ( (B = (u1_struct_0 (k14_polynom3 A)))  => (v3_polyalg1 B A (k1_polyalg1 A))) ) ) ) ) ).
tt(t22_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_quin_1 A B C)) &  ( ((k7_polyeq_1 A B C k6_numbers D) = k6_numbers)  &  ( (~  (D = k6_numbers) )  &  ( (~  (D = (k6_real_1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) )  &  (~  (D = (k6_real_1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( ((k1_polyeq_3 A) = B)  &  ( (~ (r1_xxreal_0 k6_numbers (k4_complex1 B)))  &  ( (~  (A = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) k7_complex1))) )  &  (~  (A = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) k7_complex1))) ) ) ) ) ) ) ) ) ) ).
tt(t22_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k4_power A B) = 1)  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(t22_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((v1_xcmplx_0 H) =>  (! [I:$i] :  ((v1_xcmplx_0 I) =>  ( ( (G = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 B C) H) I)))  &  ( (D = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 B C) (k3_xcmplx_0 B H)) (k3_xcmplx_0 B I)) (k3_xcmplx_0 C H)) (k3_xcmplx_0 C I)) (k3_xcmplx_0 H I)))  &  ( (E = (k4_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 B C) H) (k3_xcmplx_0 (k3_xcmplx_0 B C) I)) (k3_xcmplx_0 (k3_xcmplx_0 B H) I)) (k3_xcmplx_0 (k3_xcmplx_0 C H) I))))  &  (F = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 B C) H) I)) ) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 G (k1_newton A 3))) (k3_xcmplx_0 D (k1_newton A 2))) (k3_xcmplx_0 E A)) F) = k6_numbers)  <=>  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = H) )  &  (~  (A = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_polyform,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_bspace)) =>  ((k4_rlvect_1 k2_bspace (k3_pre_poly (u1_struct_0 k2_bspace) A)) = A) ) ) ).
tt(t22_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((k3_polynom1 A B (k7_polynom1 A B) C) = (k4_struct_0 B)) ) ) ) ) ) ).
tt(t22_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k5_vfunct_1 (k15_pre_poly A) B C) D) = (k4_algstr_0 B (k5_polynom2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t22_polynom3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_finseq_2 B)) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  ((r2_hidden F (k4_finseq_1 D)) &  ((r2_hidden G (k4_finseq_1 (k1_funct_1 C E))) &  ((r2_hidden H (k4_finseq_1 (k1_funct_1 D F))) &  ( ((k10_pre_poly A C) = (k10_pre_poly B D))  &  ((k2_nat_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d E 1) (k10_pre_poly A C))) G) = (k2_nat_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d F 1) (k10_pre_poly B D))) H)) ) ) ) ) )  =>  ( (E = F)  &  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_polynom4 A (k1_polynom4 A B) C) = (k6_algstr_0 A (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C (k7_nat_d (k1_algseq_1 A B) 1)))) ) ) ) ) ) ) ).
tt(t22_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_polynom4 A (k2_polynom5 A B D) C) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k2_polynom4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t22_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k2_polynom1 (k15_pre_poly A) B (k4_polynom7 A B C)) = k1_xboole_0)  |  ((k2_polynom1 (k15_pre_poly A) B (k4_polynom7 A B C)) = (k6_domain_1 (k15_pre_poly A) (k16_pre_poly A))) ) ) ) ) ) ) ).
tt(t22_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k3_polynom8 A (k11_algstr_0 A C) B) = (k3_polynom8 A C (k4_xcmplx_0 B))) ) ) ) ) ) ) ) ).
tt(t22_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_polynom7 A B (k1_polyred A D B C) E) (k9_polynom1 A B (k1_polynom7 A B E D) C))) ) ) ) ) ) ) ) ) ) ).
tt(t22_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k5_real_1 (k1_power B A) 1) (k10_real_1 (k5_real_1 A 1) B))) ) ) ) ) ) ).
tt(t22_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( (~  ((k1_msualg_1 B D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( (G = (k3_funct_2 (k3_msualg_1 B D (k14_pralg_2 A B C)) (k4_msualg_1 B D (k14_pralg_2 A B C)) (k5_msualg_1 B D (k14_pralg_2 A B C)) E))  =>  ((k1_funct_1 G F) = (k1_funct_1 (k5_msualg_1 B D (k5_pralg_2 A B C F)) (k1_funct_1 (k10_funct_6 E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pre_circ,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) )  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k5_card_1 (k1_funct_4 A B)) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ).
tt(t22_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k2_prelamb A (k2_prelamb A (k2_prelamb A B C) (k2_prelamb A D C)) (k2_prelamb A B D))) & (r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k1_prelamb A (k1_prelamb A D B) (k1_prelamb A (k1_prelamb A C D) (k1_prelamb A C B))))) ) ) ) ) ) ) ) ) ).
tt(t22_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_card_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (v1_card_1 B)) ) ) ) ) ).
tt(t22_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 1 C)) )  =>  ((k2_prepower C (k3_xcmplx_0 A B)) = (k3_xcmplx_0 (k2_prepower C A) (k2_prepower C B))) ) ) ) ) ) ) ) ).
tt(t22_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) =>  ((k2_pre_topc A B) = B) )  &  ( ((v2_pre_topc A) &  ((k2_pre_topc A B) = B) )  => (v4_pre_topc B A)) ) ) ) ) ) ).
tt(t22_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m1_prob_1 k1_xboole_0 A B)) ) ) ).
tt(t22_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ((r2_prob_2 A B F C D E) => (r2_prob_2 A B F C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) C (k2_prob_3 A D)) =>  ( ((k1_prob_2 A B C k6_numbers) = (k1_prob_2 A B D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_prob_2 A B C (k1_nat_1 E 1)) = (k2_xboole_0 (k1_funct_1 C E) (k1_prob_2 A B D (k1_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((r1_prob_4 A B C) <=> (r1_measure3 A B (k2_prob_4 A B C))) ) ) ) ) ) ) ).
tt(t22_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k7_cqc_lang A B B)) (k4_cqc_the1 A))) ) ) ) ).
tt(t22_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  => (v5_anproj_2 A)) ) ).
tt(t22_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ( ((v1_projpl_1 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) & (r2_projpl_1 A D B C)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~ (r5_projpl_1 A B C D E)) ) ) ) ) ) ) ) )  |  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r1_zfmisc_1 C D E) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A B E))  &  ( (~ (r1_incsp_1 A C E))  &  ( (~ (r1_incsp_1 A C F))  &  (~  ( ((k9_xtuple_0 (k3_relat_1 (k1_projred1 A D E B) (k1_projred1 A E F C))) = (k1_relset_1 (u1_incsp_1 A) (k1_projred1 A D E B)))  &  ((k10_xtuple_0 (k3_relat_1 (k1_projred1 A D E B) (k1_projred1 A E F C))) = (k10_xtuple_0 (k1_projred1 A E F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u2_incsp_1 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u2_incsp_1 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A D H) &  ((r1_incsp_1 A D J) &  ((r1_incsp_1 A E I) &  ((r1_incsp_1 A E J) &  ((r1_incsp_1 A B K) &  ((r1_incsp_1 A E K) &  ((r1_incsp_1 A D L) &  ((r1_incsp_1 A C L) &  ((r1_incsp_1 A F H) &  ((r1_incsp_1 A F K) &  ((r1_incsp_1 A G I) &  ((r1_incsp_1 A G L) &  ((r1_incsp_1 A F M) & (r1_incsp_1 A G M)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_incsp_1 A B H) |  ((r1_incsp_1 A C I) |  ((r1_incsp_1 A B J) |  ((r1_incsp_1 A C J) |  ((r1_incsp_1 A B I) |  ((r1_incsp_1 A C H) |  ((r1_projred2 A H I J) |  ((k3_relat_1 (k1_projred1 A H J B) (k1_projred1 A J I C)) = (k3_relat_1 (k1_projred1 A H M C) (k1_projred1 A M I B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k10_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( (D = F)  &  ( ((k12_finseq_1 (u1_struct_0 B) E) = G)  &  ((k1_binop_1 C D E) = (k7_finseq_1 F G)) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B))) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k3_rlvect_1 (k5_prvect_3 (k10_prvect_2 A) B) D E)) = (k3_rlvect_1 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C D) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k1_rlvect_1 (k5_prvect_3 (k10_prvect_2 A) B) D E)) = (k1_rlvect_1 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C D) E)) ) ) ) )  &  ((k3_funct_2 (u1_struct_0 (k5_prvect_3 (k10_prvect_2 A) B)) (u1_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k4_struct_0 (k5_prvect_3 (k10_prvect_2 A) B))) = (k4_struct_0 (k10_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 A) B) = (k17_euclid B)) ) ) ) ) ) ).
tt(t22_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k9_pua2mss1 A) (k6_pua2mss1 A))) ) ).
tt(t22_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k4_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pzfmisc1 A B)) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t22_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) => (r1_qc_lang1 A B B)) ) ) ) ).
tt(t22_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k8_qc_lang2 A B C D E) = (k15_qc_lang1 A G F))  =>  ( (B = G)  &  ((k6_qc_lang2 A C D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((v6_qc_lang1 B A) & (v6_qc_lang1 C A))  <=> (v6_qc_lang1 (k14_qc_lang1 A B C) A)) ) ) ) ) ) ) ).
tt(t22_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A C))) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A C))) =>  (~  ( (D = (k8_finseq_1 k5_numbers E (k12_finseq_1 k5_numbers B)))  &  ((v4_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E) A) &  ( (~  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) D) = (k19_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E)))  &  (B = k6_numbers) ) )  &  (~  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) D) = (k20_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E)))  &  (B = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_quantal1 A (k5_quantal1 A B)) = B) ) ) ) ) ).
tt(t22_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k27_quaterni (k28_quaterni A) (k28_quaterni B)) = (k27_quaterni A B)) ) ) ) ) ).
tt(t22_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k29_quaterni (k27_quaterni k12_quaterni A) (k27_quaterni A k12_quaterni)) = (k6_quaterni k6_numbers (k1_real_1 (k8_real_1 2 (k19_quaterni A))) (k8_real_1 2 (k18_quaterni A)) k6_numbers)) ) ) ).
tt(t22_quaterni,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A 4 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 4 k1_numbers)))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) & (r1_funct_2 4 k1_numbers (k2_enumset1 k6_numbers 1 2 3) k1_numbers A (k3_quaterni k1_numbers k6_numbers 1 2 3 B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t22_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k1_quin_1 A B C) = k6_numbers)  =>  ((r1_xxreal_0 A k6_numbers) |  ( (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers))  &  (D = (k4_xcmplx_0 (k7_xcmplx_0 B (k3_xcmplx_0 2 A)))) ) )  &  (~  ( (~  (D = (k4_xcmplx_0 (k7_xcmplx_0 B (k3_xcmplx_0 2 A)))) )  & (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k5_binop_1 (k7_quofield A) (k15_quofield A) B (k11_quofield A)) = B)  &  ((k5_binop_1 (k7_quofield A) (k15_quofield A) (k11_quofield A) B) = B) ) ) ) ) ) ).
tt(t22_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_radix_1 B C A) =>  (C = (k8_radix_1 B A (k10_radix_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t22_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) => (m1_random_1 (k20_valued_1 A k1_numbers k1_numbers C D) A B)) ) ) ) ) ) ) ) ).
tt(t22_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_vectsp_7 F A C) =>  ( ((m1_vectsp_7 E A (k1_ranknull A C B D)) & (r1_tarski E F))  => (v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D (k7_subset_1 (u1_struct_0 C) F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 1 (k2_real_1 (k1_rat_1 A))))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 1 (k2_real_1 (k1_rat_1 A)))) ) ) ) ) ).
tt(t22_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A))  =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ( (~ (v1_ratfunc1 D A))  & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ( (B = (k3_ratfunc1 A (k13_polynom3 A D (k4_ratfunc1 A C)) (k13_polynom3 A D (k5_ratfunc1 A C))))  & (v5_ratfunc1 C A))  =>  ( (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k14_polynom3 A))) =>  (~  ( (D = (k3_group_4 (k14_polynom3 A) E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) G) &  ((k1_funct_1 E F) = (k3_hurwitz A G 1)) ) ) ) ) ) ) ) ) ) ) ) )  |  ((k11_ratfunc1 A B) = (k6_ratfunc1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (~  ((v3_rcomp_1 A) &  ((v3_xxreal_2 A) & (r2_hidden (k5_seq_4 A) A)) ) ) ) ) ).
tt(t22_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_xxreal_2 A) =>  ((r2_hidden (k4_seq_4 A) A) | (r1_tarski A (k10_prob_1 (k4_seq_4 A)))) ) ) ) ).
tt(t22_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_funct_2 k5_numbers k5_numbers (k1_real_3 A k6_numbers) (k8_funcop_1 k5_numbers k5_numbers k6_numbers))) ) ).
tt(t22_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  ((k1_binop_1 (k5_real_lat A) B C) = (k1_binop_1 (k5_real_lat A) C B)) ) ) ) ) ) ) ).
tt(t22_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ( ((k8_group_1 A B C) = (k5_struct_0 A))  =>  (C = (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B)) ) ) ) ) ) ) ) ).
tt(t22_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  ( ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) (k5_struct_0 A) B)) = (k5_struct_0 A))  &  ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) (k5_struct_0 A) B) B) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t22_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 A)) & (m2_finseq_1 E (k1_zfmisc_1 A))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ( ((r2_hidden C (k1_funct_1 (k2_rearran1 A E) 1)) =>  ((k1_seq_1 (k4_rearran1 B A E D) C) = (k1_seq_1 (k20_rfunct_3 B D B) 1)) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r2_hidden C (k6_subset_1 (k1_funct_1 (k2_rearran1 A E) (k2_nat_1 F 1)) (k1_funct_1 (k2_rearran1 A E) F))))  =>  ((r1_xxreal_0 (k3_finseq_1 (k2_rearran1 A E)) F) |  ((k1_seq_1 (k4_rearran1 B A E D) C) = (k1_seq_1 (k20_rfunct_3 B D B) (k2_nat_1 F 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_relat_1 (k3_xboole_0 A B)) = (k3_xboole_0 (k2_relat_1 A) (k2_relat_1 B))) ) ) ) ) ).
tt(t22_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v4_relat_2 A) <=> (r1_tarski (k3_xboole_0 A (k2_relat_1 A)) (k4_relat_1 (k9_xtuple_0 A)))) ) ) ).
tt(t22_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((k7_relset_1 A B C A) = (k2_relset_1 B C))  &  ((k8_relset_1 A B C B) = (k1_relset_1 A C)) ) ) ) ) ) ).
tt(t22_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_tarski (k5_setfam_1 B (k7_relset_1 (k9_setfam_1 A) (k9_setfam_1 B) (k4_relset_2 B A C) A)) (k7_relset_1 A B C (k3_tarski A)))) ) ) ) ).
tt(t22_revrot_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 B)) => (r1_tarski (k10_xtuple_0 (k2_goboard1 A)) (k10_xtuple_0 (k2_goboard1 B)))) ) ) ) ) ).
tt(t22_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A B) =>  (! [C:$i] :  (! [D:$i] :  ((r1_rewrite1 A C D) => (r1_rewrite1 B C D)) ) ) ) ) ) ) ) ).
tt(t22_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) => (r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B (k7_rewrite2 A B))) ) ) ).
tt(t22_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  (~  ((r2_rewrite3 C F G A D B E) &  (! [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 C)) =>  (~  ((r1_rewrite3 F G A H B) &  (D = (k1_flang_1 C H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (? [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  & (r2_classes1 A B)) ) ) ) ).
tt(t22_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k45_valued_1 A (k45_valued_1 B C)) = (k1_valued_1 (k45_valued_1 A B) C)) ) ) ) ) ) ) ).
tt(t22_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) & (r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))))  =>  ((r1_xxreal_0 D C) | (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k8_finseq_1 (k3_rfunct_3 A k1_numbers) (k12_finseq_1 (k3_rfunct_3 A k1_numbers) C) B)) (k5_rfunct_3 A k1_numbers C (k14_rfunct_3 A B)))) ) ) ) ) ) ).
tt(t22_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_rfunct_4 B A) => (r4_rfunct_4 B A)) ) ) ) ).
tt(t22_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 A) & (v1_seq_2 A))  => (v1_comseq_2 A)) ) ) ).
tt(t22_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v2_rinfsup2 B) => (v2_rinfsup2 (k1_valued_0 k7_numbers B A)))  &  ((v1_rinfsup2 B) => (v1_rinfsup2 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ).
tt(t22_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m3_ringcat1 C (k10_ringcat1 (k9_ringcat1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_ringcat1 A))) =>  (! [E:$i] :  ((m2_ringcat1 E (k9_ringcat1 A)) =>  ( ((v2_ringcat1 B) & (m3_ringcat1 B (k10_ringcat1 (k9_ringcat1 A))))  &  ((m1_subset_1 C (u4_struct_0 (k17_ringcat1 A))) &  ( ((v36_algstr_0 D) & (m2_ringcat1 D (k9_ringcat1 A)))  & (m1_subset_1 E (u1_struct_0 (k17_ringcat1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) => (r1_tarski (k3_rlvect_2 B (k2_rlaffin1 B C A)) (k1_convex1 B (k3_rlvect_2 B C) A))) ) ) ) ) ) ).
tt(t22_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B C) =>  ((v1_xboole_0 (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) |  ((k1_funct_1 (k2_rlaffin2 A) C) = (k3_rlvect_1 A (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) (k2_rlaffin2 A) (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) (k9_real_1 1 (k10_real_1 1 (k5_card_1 C)))) (k1_rlvect_1 A B (k10_real_1 1 (k5_card_1 C))))) ) ) ) ) ) ) ) ) ).
tt(t22_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_rlaffin1 D C) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C)))) )  =>  (! [E:$i] :  ((m2_rlaffin3 E C D) =>  ( ((r1_xxreal_0 B (k5_card_1 D)) & (r2_hidden A (k4_rlaffin1 C D)))  =>  ((r2_hidden A (k4_rlaffin1 C (k7_subset_1 (u1_struct_0 C) D (k7_relset_1 k5_numbers (u1_struct_0 C) E (k2_finseq_1 B))))) <=>  ((k1_rlaffin3 C D E A) = (k7_finseq_1 (k2_finseq_2 B k1_xboole_0) (k2_rfinseq k1_numbers B (k1_rlaffin3 C D E A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_struct_0 C B) => (r1_struct_0 C (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t22_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (m1_rlsub_1 (k2_rlsub_2 A B C) (k1_rlsub_2 A B C))) ) ) ) ) ) ).
tt(t22_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r1_tarski (k1_rltopsp1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t22_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k5_algstr_0 A C D) = B) ) ) ) ) ) ) ) ) ).
tt(t22_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (m2_rlvect_2 (k4_rlvect_2 A) A B)) ) ) ) ).
tt(t22_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_rlvect_3 A (k4_subset_1 (u1_struct_0 A) B C)) = (k1_rlsub_2 A (k1_rlvect_3 A B) (k1_rlvect_3 A C))) ) ) ) ) ) ) ).
tt(t22_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  (A = 1) )  & (v1_rlvect_3 (k7_domain_1 (u1_struct_0 B) C (k1_rlvect_1 B C A)) B)) ) ) ) ) ) ) ) ).
tt(t22_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ( ((g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)) = (k1_rlvect_3 A B))  & (v1_rlvect_3 C A))  =>  ((r1_xxreal_0 (k5_card_1 C) (k5_card_1 B)) &  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski D B) &  ( ((k5_card_1 D) = (k6_xcmplx_0 (k5_card_1 B) (k5_card_1 C)))  &  ((g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)) = (k1_rlvect_3 A (k4_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden A (k2_rlvect_x B (k8_domain_1 (u1_struct_0 B) C D E))) <=>  (? [F:$i] :  ((v1_int_1 F) &  (? [G:$i] :  ((v1_int_1 G) &  (? [H:$i] :  ((v1_int_1 H) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B (k1_rlvect_1 B C F) (k1_rlvect_1 B D G)) (k1_rlvect_1 B E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_struct_0 D C) => (r1_struct_0 D (k4_algstr_0 B C))) ) ) ) ) ) ) ) ) ).
tt(t22_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ( ((k2_rmod_3 A B (k2_rmod_2 A B) C) = C)  &  ((k2_rmod_3 A B C (k2_rmod_2 A B)) = C) ) ) ) ) ) ) ) ).
tt(t22_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) => (m2_rmod_4 C A B (k2_rmod_4 A B C))) ) ) ) ) ) ).
tt(t22_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k5_robbins1 A (k3_robbins1 A B) C) = (k6_lattices A))  &  ((k5_robbins1 A (k3_robbins1 A C) B) = (k6_lattices A)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t22_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) B)) C)) = (k3_robbins1 A C)) ) ) ) ) ) ) ).
tt(t22_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_robbins3 A) & (l3_robbins3 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) <=> (r1_lattices A B C)) ) ) ) ) ) ) ).
tt(t22_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( ( (A = (k6_subset_1 3 2))  &  (B = 2) )  =>  ((k3_lattices k2_robbins4 A B) = 3) ) ) ) ) ) ).
tt(t22_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A (k9_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k3_roughs_1 A B) (k3_roughs_1 A C))) ) ) ) ) ) ) ).
tt(t22_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ((k1_rpr_1 A B) = (k9_real_1 1 (k1_rpr_1 A (k3_subset_1 A B))))  &  ((k1_rpr_1 A (k3_subset_1 A B)) = (k9_real_1 1 (k1_rpr_1 A B))) ) ) ) ) ) ).
tt(t22_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k9_rsspace4 A B)) &  ((v3_normsp_0 (k9_rsspace4 A B)) & (v2_normsp_1 (k9_rsspace4 A B))) ) ) ) ) ) ).
tt(t22_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_rusub_1 B C)) ) ) ) ) ) ) ).
tt(t22_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (m1_rusub_1 (k2_rusub_2 A B C) (k1_rusub_2 A B C))) ) ) ) ) ) ).
tt(t22_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rlvect_3 C B) =>  ((v1_rlvect_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(t22_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  ((v2_rusub_4 (k2_struct_0 A) A) & (v2_rusub_4 (k1_struct_0 A) A)) ) ) ).
tt(t22_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k2_rusub_5 A (k1_rusub_1 A)) = (k2_rusub_1 A)) ) ) ).
tt(t22_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k5_rvsum_1 A B (k7_rvsum_1 A B)) = (k5_finseq_2 k5_numbers A k6_numbers)) ) ) ) ) ).
tt(t22_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k9_rvsum_2 (k2_finseq_2 A C) B) = (k5_finseq_2 k2_numbers A (k5_binop_2 B C))) ) ) ) ) ) ) ).
tt(t22_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 (k9_ami_3 1 (k10_ami_3 k6_numbers))) (k5_afinsq_1 (k2_compos_1 k1_ami_3))) A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 k6_numbers) & (m1_scm_1 D (k6_afinsq_1 B C)))  =>  ((r1_extpro_1 2 k1_ami_3 A D) &  ( ((k8_extpro_1 2 k1_ami_3 A D) = 1)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A D) E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmbsort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k2_scmfsa8c A B)) = (k2_nat_1 (k5_card_1 B) 12)) ) ) ) ) ).
tt(t22_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 5)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t22_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 (k6_scmfsa_1 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ).
tt(t22_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k10_scmfsa_2 A B)) = 5) ) ) ) ) ).
tt(t22_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v2_compos_1 A k1_scmfsa_2) =>  ((k1_scmfsa6a A B) = A) ) ) ) ) ) ).
tt(t22_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((v1_int_1 B) => (r1_tarski (k10_xtuple_0 (k2_scmfsa_7 A B)) (k1_enumset1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers)) (k7_scmfsa_2 A (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) ) ) ) ).
tt(t22_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1))) = (k5_card_1 C))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1)))) ) ) ) ) ) ) ) ) ).
tt(t22_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_xxreal_0 (k1_funct_1 E D) k6_numbers) &  ((r5_scmfsa7b C (k1_scmfsa_m E) A) & (r6_scmfsa7b C (k1_scmfsa_m E) A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b D B C) E A) (k1_funct_4 (k1_scmfsa6b C E A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 C 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ((r1_tarski E A) & (r1_scmfsa8a C A E))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_tarski (k6_compos_1 k1_scmfsa_2 E F) B) &  ( ((k5_memstr_0 3 k1_scmfsa_2 D) = F)  &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) )  =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_scmfsa8a C A E) G))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k3_extpro_1 3 k1_scmfsa_2 A (k5_extpro_1 3 k1_scmfsa_2 A C G)) F) = (k3_extpro_1 3 k1_scmfsa_2 B (k5_extpro_1 3 k1_scmfsa_2 B D G))) ) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 G (k2_scmfsa8a C A E)) =>  ( ((k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C G)) F) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D G)))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C G)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ((k1_funct_1 B C) = k6_numbers)  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa_9 C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b C B A) &  ((r6_scmfsa7b C B A) &  ((k1_funct_1 B D) = k6_numbers) ) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 D C)) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B)) 3))) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B)) 3)) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 D C)) (k8_memstr_0 3 k1_scmfsa_2 B) E)) (k2_afinsq_1 (k1_scmfsa_9 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2)))  =>  ( (~ (r2_hidden k6_numbers (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m B) A)))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m B) A)) & (r2_hidden (k4_scmfsa_2 C) B)) ) ) ) ) ) ) ) ) ).
tt(t22_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v2_scm_halt B) & (v3_scm_halt B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m (k1_scmfsa6b B C A))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b B C A))) ) ) ) ) ) ) ).
tt(t22_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 D C) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B))) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k13_scmpds_2 C D A B)) = 10) ) ) ) ) ) ) ) ) ).
tt(t22_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_scmpds_4 A B) & (r1_xxreal_0 B C))  => (r1_scmpds_4 A C)) ) ) ) ) ) ) ).
tt(t22_scmpds_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 1)  & (v1_scmpds_5 A)) ) ) ) ).
tt(t22_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 2 k1_scmpds_2 C) = (k6_memstr_0 2 k1_scmpds_2 D))  & (r1_scmpds_6 E C A))  => (r1_scmpds_6 E D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (~  ((r1_tarski C D) &  ((r1_scmpds_6 C A B) &  ((r2_scmpds_6 C A B) &  ( (~  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k8_memstr_0 2 k1_scmpds_2 A) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)))) = (k2_compos_1 k1_scmpds_2)) )  &  (~  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k8_memstr_0 2 k1_scmpds_2 A) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)))) = (k5_card_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k2_scmpds_8 D E C) B A)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k8_struct_0 (k1_scmring2 A)) = (k8_struct_0 k1_ami_3)) ) ) ).
tt(t22_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 2)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t22_scmyciel,ax,(v4_scmyciel (k1_tarski k1_xboole_0))).
tt(t22_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_semi_af1 A B C D) =>  ((r1_semi_af1 A B D C) &  ((r1_semi_af1 A C B D) &  ((r1_semi_af1 A C D B) &  ((r1_semi_af1 A D B C) & (r1_semi_af1 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers B C) A) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A) (k26_valued_1 k5_numbers k1_numbers C A)))) ) ) ) ) ) ).
tt(t22_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_relat_1 A))  =>  ( ((k2_seq_2 A) = k6_numbers)  |  ((k2_seq_2 (k37_valued_1 k5_numbers k1_numbers A)) = (k2_real_1 (k2_seq_2 A))) ) ) ) ) ).
tt(t22_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 (k1_valued_0 k1_numbers B A)) =>  ((k2_seq_2 B) = (k2_seq_2 (k1_valued_0 k1_numbers B A))) ) ) ) ) ) ).
tt(t22_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r3_seqfunc A B C) => (r2_seqfunc A B C)) ) ) ) ) ) ).
tt(t22_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v5_valued_0 A) & (m2_valued_0 B k1_numbers A))  => (v5_valued_0 B)) ) ) ) ) ).
tt(t22_series_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (B = 1) )  =>  ((k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k1_prepower B)) A) = (k10_real_1 (k9_real_1 1 (k3_power B (k2_nat_1 A 1))) (k9_real_1 1 B))) ) ) ) ) ) ).
tt(t22_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 B (k13_newton (k2_nat_1 B 1) 2))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k4_nat_1 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 2)) (k2_nat_1 (k4_nat_1 3 B) 5)) 12)) ) ) ) ) ) ).
tt(t22_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (~  ( ((k2_xcmplx_0 A B) = 1)  & (r1_xxreal_0 1 (k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)))) ) ) ) ) ) ).
tt(t22_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k2_xcmplx_0 (k4_nat_1 (k9_newton B) B) (k7_xcmplx_0 B (k9_newton (k2_nat_1 B 1))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 (k9_newton (k2_nat_1 B 1)) (k7_xcmplx_0 1 (k9_newton (k2_nat_1 B 1))))) ) ) ) ) ) ) ).
tt(t22_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 3 (k8_complex1 (k8_complex1 (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 A B) C) C) (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 B C) A) A)) (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 C A) B) B)))) ) ) ) ) ) ).
tt(t22_setfam_1,ax, (! [A:$i] : (r1_setfam_1 (k4_setfam_1 A A) A)) ).
tt(t22_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k6_prob_1 B (k9_setfam_1 B) (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) (k2_nat_1 A 1)) (k3_funct_2 k5_numbers (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t22_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 C) => (v3_prob_1 (k5_setlim_2 A C B))) ) ) ) ) ) ).
tt(t22_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v3_binop_1 C A)) )  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden F D) =>  ((k5_binop_1 A C (k3_funct_2 B A E F) (k7_setwiseo B A C D E)) = (k7_setwiseo B A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((k2_partfun1 k5_numbers A (k1_setwop_2 A (k8_finseq_1 A C D) B) (k4_finseq_1 C)) = C) ) ) ) ) ) ) ) ) ).
tt(t22_sfmastr1,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden A (k2_sf_mastr (k1_scmfsa6c A B))) & (r2_hidden B (k2_sf_mastr (k1_scmfsa6c A B)))) ) ) ) ) ).
tt(t22_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_xxreal_0 (k1_funct_1 A C) k6_numbers) &  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  =>  ((k5_relat_1 (k1_scmfsa6b (k2_sfmastr2 C D) A B) (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2)) = (k5_relat_1 A (k2_xboole_0 (k2_sf_mastr D) k3_scmfsa_2))) ) ) ) ) ) ) ) ) ) ).
tt(t22_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  => (r1_tarski (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A B C) (k2_sf_mastr D)) (k2_sf_mastr (k2_sfmastr3 A B C D)))) ) ) ) ) ) ) ) ).
tt(t22_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_sf_mastr A) = (k2_sf_mastr (k61_valued_1 A B))) ) ) ) ) ).
tt(t22_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (~  ( (~  (B = (g1_sgraph1 k1_xboole_0 (k1_subset_1 (k2_sgraph1 k1_xboole_0)))) )  &  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_sgraph1 C))) =>  (~  ( (~ (v1_xboole_0 C))  &  (B = (g1_sgraph1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_sheffer1 A B C) <=> (r2_lattices A B C)) ) ) ) ) ) ) ).
tt(t22_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A C (k5_sheffer1 A D B))) = C) ) ) ) ) ) ) ) ) ).
tt(t22_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((k6_simplex0 A) = (k2_xxreal_3 1))  <=> (v4_simplex0 A)) ) ) ).
tt(t22_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ( ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) & (r1_xxreal_0 (k6_simplex0 C) k1_xboole_0))  =>  ((r1_xxreal_0 A k1_xboole_0) |  ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (k5_simplex1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t22_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [C:$i] :  ((m2_rlaffin3 C (k15_euclid A) B) =>  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))))) =>  (~  ( ((k3_finseq_1 D) = (k5_card_1 B))  &  ((v2_tops_2 (k2_relset_1 (k9_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)))) D) (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) &  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k4_finseq_1 D))) => (r1_tarski (k3_convex1 (k15_euclid A) (k7_relset_1 k5_numbers (u1_struct_0 (k15_euclid A)) C E)) (k5_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (k7_relset_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)))) D E)))) )  & (v1_xboole_0 (k6_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (k2_relset_1 (k9_setfam_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)))) D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t22_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_seq_1 k7_sin_cos2 (k9_binop_2 A B)) = (k10_real_1 (k7_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) (k7_real_1 1 (k8_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)))))  &  ((k1_seq_1 k7_sin_cos2 (k10_binop_2 A B)) = (k10_real_1 (k9_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) (k9_real_1 1 (k8_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B))))) ) ) ) ) ) ).
tt(t22_sin_cos3,ax, ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 k5_complex1) = k6_numbers) ).
tt(t22_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  (~  ((k6_xcmplx_0 (k1_sin_cos4 A) (k2_sin_cos4 B)) = (k4_xcmplx_0 (k7_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k3_xcmplx_0 (k20_sin_cos A) (k17_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t22_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k17_sin_cos A) 3) = (k10_real_1 (k9_real_1 (k8_real_1 3 (k17_sin_cos A)) (k18_sin_cos (k8_real_1 3 A))) 4)) ) ) ).
tt(t22_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  &  ( ((k20_sin_cos A) = k6_numbers)  &  ( (~  (A = (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) )  &  (~  (A = (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A 1) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 k6_numbers (k10_binop_2 1 (k3_square_1 A)))) ) ) ) ).
tt(t22_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 2 A)) (k6_sin_cos2 (k3_xcmplx_0 2 B))) (k6_sin_cos2 (k3_xcmplx_0 2 C))) (k6_sin_cos2 (k3_xcmplx_0 2 (k2_xcmplx_0 (k2_xcmplx_0 A B) C)))) = (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 4 (k6_sin_cos2 (k2_xcmplx_0 B C))) (k6_sin_cos2 (k2_xcmplx_0 C A))) (k6_sin_cos2 (k2_xcmplx_0 A B)))) ) ) ) ) ) ) ).
tt(t22_sin_cos9,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t22_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers C D) = (k8_nat_1 k2_numbers (k10_comseq_3 (k12_sin_cos A B D)) D)) ) )  =>  ((v2_comseq_2 C) &  ((k3_comseq_2 C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t22_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v1_finset_1 (a_1_0_sppol_1 A))) ) ).
tt(t22_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k3_topreal1 2 A) = (k3_topreal1 2 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A))) ) ) ).
tt(t22_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_xxreal_0 (k9_pscomp_1 A) (k7_pscomp_1 A))) ) ).
tt(t22_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  => (r1_sprect_2 A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 A B) 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) ) ) ) ) ) ).
tt(t22_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) 1)) ) ) ) ).
tt(t22_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k6_square_1 (k3_square_1 A)) = A) ) ) ) ).
tt(t22_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  ((r1_stacks_1 A C) & (r2_hidden C (k11_stacks_1 A B))) ) ) ) ) ) ) ).
tt(t22_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  =>  (A = k6_numbers) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~ (v1_stirl2_1 C A B)) ) ) ) ) ) ) ) ) ) ).
tt(t22_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A D) = (k19_substut1 A E))  =>  ((r2_relset_1 (k3_qc_lang1 A) B (k3_sublemma A D B C) (k3_sublemma A (k6_sublemma A D E) B C)) & (r2_relset_1 (k3_qc_lang1 A) B (k3_sublemma A E B C) (k3_sublemma A (k6_sublemma A D E) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r1_tarski (k3_subset_1 A B) (k3_subset_1 A (k9_subset_1 A B C)))) ) ) ) ) ).
tt(t22_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k4_partfun1 A B))) =>  ((k4_substlat A B C (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) D E)) = (k1_finsub_1 (k5_finsub_1 (k4_partfun1 A B)) (k4_substlat A B C D) (k4_substlat A B C E))) ) ) ) ) ) ) ) ) ).
tt(t22_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (~  ((v5_substut1 B A) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A B))) (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A (k27_substut1 A B)))))) ) ) ) ) ) ).
tt(t22_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ( ((k2_substut2 A (k11_cqc_lang A C B) D) = (k9_sublemma A (k7_substut2 A B C D) (k8_substut2 A B C D)))  & (v3_substut1 (k7_substut2 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t22_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_supinf_2 C A B) <=> (v2_supinf_2 (k14_supinf_2 A B C) A (k6_supinf_2 B))) ) ) ) ) ) ) ).
tt(t22_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k1_symsp_1 A B D C C) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t22_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ((r1_tarski A (k3_relat_1 A A)) &  ((k3_relat_1 A (k6_subset_1 A (k4_relat_1 (k10_xtuple_0 A)))) = k1_xboole_0) )  => (r1_tarski (k4_relat_1 (k10_xtuple_0 A)) A))  &  ( ((r1_tarski A (k3_relat_1 A A)) &  ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A))) A) = k1_xboole_0) )  => (r1_tarski (k4_relat_1 (k9_xtuple_0 A)) A)) ) ) ) ).
tt(t22_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_relat_2 (k1_taxonom1 A B C) A) & (v4_metric_1 B A))  =>  ((v1_partfun1 (k13_lang1 A (k1_taxonom1 A B C)) A) &  ((v3_relat_2 (k13_lang1 A (k1_taxonom1 A B C))) &  ((v8_relat_2 (k13_lang1 A (k1_taxonom1 A B C))) & (m1_subset_1 (k13_lang1 A (k1_taxonom1 A B C)) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ) ).
tt(t22_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 C A) =>  ((r1_xxreal_0 (k1_seq_1 C A) k6_numbers) |  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 B)) A) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 B)) A) = (k8_real_1 (k4_real_1 B (k10_prepower (k1_seq_1 C A) (k5_real_1 B 1))) (k1_fdiff_1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t22_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers B) &  ((r1_xxreal_0 k6_numbers C) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) =>  ((r1_xxreal_0 F k6_numbers) |  ((r1_xxreal_0 1 F) |  ((r1_xxreal_0 (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D))) (k10_real_1 (k8_real_1 B (k2_newton C D)) (k3_newton D))) & (r1_xxreal_0 (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D))) (k10_real_1 (k8_real_1 B (k2_newton C D)) (k3_newton D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v6_tbsp_1 B A) &  ( ((k3_tbsp_1 A B) = k6_numbers)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (B = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v5_tops_1 (k2_pre_topc A (k1_tops_1 A B)) A)) ) ) ) ).
tt(t22_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_tdlat_2 A (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) = (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_2 A B) (k1_tdlat_2 A C))) ) ) ) ) ) ) ).
tt(t22_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v3_pre_topc B A)) ) ) ) ) ) ).
tt(t22_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r6_pboole A (k2_polynom7 A C (k5_termord A B C D)) (k3_termord A B C D)) &  ((k3_polynom7 A C (k5_termord A B C D)) = (k4_termord A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_tex_1 A B)))) =>  ( ((r1_tarski C (k6_subset_1 A (k6_domain_1 A B))) => (v3_pre_topc C (k3_tex_1 A B)))  &  ((v3_pre_topc C (k3_tex_1 A B)) =>  ( (C = A)  | (r1_tarski C (k6_subset_1 A (k6_domain_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t22_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C B) & (v2_tex_2 B A))  => (v2_tex_2 C A)) ) ) ) ) ) ) ).
tt(t22_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ( ((v2_tex_3 B A) & (m1_pre_topc B A))  <=>  ((v2_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t22_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_subset_1 (k2_tex_4 A B) (k2_tex_4 A C)) |  ((k2_tex_4 A B) = (k2_tex_4 A C)) ) ) ) ) ) ) ) ).
tt(t22_tietze,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  ((r1_tietze (k45_valued_1 C D) A B) => (r1_tietze (k45_valued_1 D C) A B)) ) ) ) ) ) ) ) ).
tt(t22_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc B C) & (m1_pre_topc D E))  => (m1_pre_topc (k1_tsep_1 A B D) (k1_tsep_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r1_relset_1 A A B (k1_eqrel_1 A))) ) ) ).
tt(t22_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D C) =>  ((r4_borsuk_2 A B C E F) => (r4_borsuk_2 A B C E (k1_borsuk_2 A B D C (k1_borsuk_2 A B C D F (k2_borsuk_2 A D C G)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_borsuk_2 C A B B) =>  ( ((k1_funct_1 C k6_numbers) = B)  &  ((k1_funct_1 C 1) = B) ) ) ) ) ) ) ) ).
tt(t22_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [H:$i] :  ((m1_borsuk_2 H (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F)) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A C D) =>  (! [K:$i] :  ((m1_borsuk_2 K B E F) =>  (! [L:$i] :  ((m1_borsuk_2 L B E F) =>  ( ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) I (k3_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) J (k3_topalg_4 A B k5_topmetr H)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) K (k4_topalg_4 A B k5_topmetr G)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) L (k4_topalg_4 A B k5_topmetr H)) &  ((r3_borsuk_2 A C D I J) & (r3_borsuk_2 B E F K L)) ) ) ) )  => (r3_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E) (k4_borsuk_1 A B D F) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topalg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 (k8_toprealb 2)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A (k1_tex_2 k17_borsuk_1 k18_borsuk_1))) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A (k1_tex_2 k17_borsuk_1 k18_borsuk_1))) (u1_struct_0 k2_topalg_2))))) )  =>  (~  ((v5_pre_topc B (k2_borsuk_1 A k5_topmetr) (k8_toprealb 2)) &  ((v5_pre_topc C (k2_borsuk_1 A (k1_tex_2 k17_borsuk_1 k18_borsuk_1)) k2_topalg_2) &  ( ((k2_partfun1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) B (k2_zfmisc_1 (u1_struct_0 A) (k6_domain_1 k1_numbers k6_numbers))) = (k1_partfun1 (u1_struct_0 (k2_borsuk_1 A (k1_tex_2 k17_borsuk_1 k18_borsuk_1))) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) C k12_toprealb))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2))))) )  =>  (~  ((v5_pre_topc D (k2_borsuk_1 A k5_topmetr) k2_topalg_2) &  ((r2_funct_2 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) B (k1_partfun1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) D k12_toprealb)) &  ( ((k2_partfun1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2) D (k2_zfmisc_1 (u1_struct_0 A) (k6_domain_1 k1_numbers k6_numbers))) = C)  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2))))) )  =>  ( ((v5_pre_topc E (k2_borsuk_1 A k5_topmetr) k2_topalg_2) &  ((r2_funct_2 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) B (k1_partfun1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) E k12_toprealb)) &  ((k2_partfun1 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2) E (k2_zfmisc_1 (u1_struct_0 A) (k6_domain_1 k1_numbers k6_numbers))) = C) ) )  => (r2_funct_2 (u1_struct_0 (k2_borsuk_1 A k5_topmetr)) (u1_struct_0 k2_topalg_2) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_2 A B C) => (m2_subset_1 D (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ) ) ) ) ) ) ) ).
tt(t22_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ( ( (D = C)  & (v1_topdim_1 D (k1_pre_topc A B)))  =>  ((v1_topdim_1 C A) &  ((k2_topdim_1 (k1_pre_topc A B) D) = (k2_topdim_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_waybel23 (k1_pre_topc A B)) &  ((v3_topdim_1 (k1_pre_topc A B)) & (r1_xxreal_0 (k2_topdim_1 A B) k6_numbers)) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (~  ((v1_tops_2 C A) &  ((m1_setfam_1 C B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((v1_tops_2 (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) D) A) &  ((m1_setfam_1 (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) D) B) &  ( (! [E:$i] :  ((r2_hidden E C) => (r1_tarski (k1_funct_1 D E) E)) )  &  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E C) & (r2_hidden F C))  =>  ( (E = F)  | (r1_xboole_0 (k1_funct_1 D E) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_topgen_1 A B C) <=>  (? [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((k9_subset_1 (u1_struct_0 A) D B) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t22_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C A) =>  ( (C = B)  |  ((v3_pre_topc (k1_tarski C) (k5_topgen_2 A B)) & (m1_subset_1 (k1_tarski C) (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B))))) ) ) ) ) ) ).
tt(t22_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ((k4_series_1 (k10_nat_1 k1_numbers (k1_prepower A) B)) = (k13_complex1 (k1_newton A B) (k6_xcmplx_0 1 A))) ) ) ) ) ) ) ) ) ).
tt(t22_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_tops_2 B A) & (v2_tops_2 C A))  => (v2_tops_2 (k3_topgen_4 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t22_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  ((r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)) (k6_xcmplx_0 D E)) => (r1_tarski (k1_topreal9 A C E) (k1_topreal9 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_t_0topsp C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_connsp_2 E A D) =>  (? [F:$i] :  ( ((v3_pre_topc F B) & (m1_connsp_2 F B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)))  & (r1_tarski F (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (m1_pre_topc (k1_pre_topc A B) (k1_pre_topc A C))) ) ) ) ) ) ) ).
tt(t22_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ( ( ((k3_finseq_1 B) = k6_numbers)  |  ((k3_finseq_1 B) = 1) )  <=>  ((k3_topreal1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t22_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k14_euclid 2))) =>  ( ( (I = A)  &  ( (A = (k19_euclid D E))  &  ( (B = (k19_euclid F G))  &  ( (C = (k19_euclid F E))  & (r2_hidden B (k9_metric_1 (k14_euclid 2) I H))) ) ) )  => (r2_hidden C (k9_metric_1 (k14_euclid 2) I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  (~  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k9_metric_1 (k14_euclid 2) D C)))  &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k9_metric_1 (k14_euclid 2) D C)) &  ((r2_hidden A (k9_metric_1 (k14_euclid 2) D C)) &  ((v4_topreal1 B) &  ( (~ (r2_hidden A (k3_topreal1 2 B)))  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal4 (k3_topreal1 2 E) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) A) & (r1_tarski (k3_topreal1 2 E) (k2_xboole_0 (k3_topreal1 2 B) (k9_metric_1 (k14_euclid 2) D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) => (m1_subset_1 (k4_card_3 (k5_funct_4 (k1_zfmisc_1 k1_numbers) 1 2 A B)) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ).
tt(t22_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v9_metric_1 B) & (l1_metric_1 B)) )  => (v9_metric_1 (k1_topreal7 A B))) ) ) ) ).
tt(t22_topreal8,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 4))  &  (~ (v2_funct_1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ) ) ).
tt(t22_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (~ (v1_xboole_0 (k2_topreal9 A C B)))  => (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ) ).
tt(t22_topreala,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) k1_numbers k1_numbers A B) & (v1_fcont_1 B))  => (v5_pre_topc A k3_topmetr k3_topmetr)) ) ) ) ) ).
tt(t22_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  ((k11_toprealb A) = (k1_pre_topc (k8_toprealb 2) (k7_subset_1 (u1_struct_0 (k8_toprealb 2)) (k2_struct_0 (k8_toprealb 2)) (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) A)))) ) ) ).
tt(t22_toprealc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v13_struct_0 B 1) & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k6_struct_0 A B C))) ) ) ) ) ) ) ) ).
tt(t22_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_toprns_1 B A) => (v1_toprns_1 (k3_toprns_1 A B) A)) ) ) ) ) ).
tt(t22_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k1_tops_1 A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc D A) &  ((r1_tarski D C) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) => (v4_pre_topc (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t22_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v3_tops_1 (k1_struct_0 A) A)) ) ).
tt(t22_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k3_topmetr) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A))))) )  =>  ((v5_pre_topc B k3_topmetr A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_topmetr)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 A) B C) D) &  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (~ (r1_tarski (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 A) B (k2_rcomp_1 (k6_xcmplx_0 C E) (k2_xcmplx_0 C E))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r3_transgeo A B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t22_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B))) &  ((v5_pre_topc C (k4_topmetr A B) (k4_topmetr A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)))))) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_topmetr A B))) &  ((k3_funct_2 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t22_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((r2_hidden k1_xboole_0 A) & (r2_hidden (k6_finseq_1 k5_numbers) A)) ) ) ).
tt(t22_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m1_trees_2 E A) =>  (~  ((r2_hidden B E) &  ((r2_hidden C E) &  ((r1_tarski D C) &  ( (~ (r2_hidden B (k1_trees_1 D)))  &  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v4_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ( (~ (v1_xboole_0 (k1_funct_1 A B)))  & (v1_trees_1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t22_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((k4_trees_4 A (k9_finseq_1 B)) = (k7_trees_2 (k7_funcop_1 (k2_trees_1 1) A) (k12_finseq_1 k5_numbers k6_numbers) B)) ) ) ) ).
tt(t22_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k9_trees_9 (k1_tarski A)) = (k3_trees_9 A)) ) ) ).
tt(t22_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  => (m1_pre_topc B (k1_tsep_1 A B C))) ) ) ) ) ) ).
tt(t22_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski D B) &  ((r1_tarski E C) &  ( ((k4_subset_1 (u1_struct_0 A) D E) = (k4_subset_1 (u1_struct_0 A) B C))  & (r2_tsep_1 A D E)) ) )  => (r2_tsep_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (v3_borsuk_1 C A B)) ) ) ) ) ) ).
tt(t22_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 D)) & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) D) A B))  => (r1_turing_1 A B C (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) 2))) ) ) ) ) ) ) ) ) ).
tt(t22_twoscomp,ax, ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 k6_numbers 1 1)) = 1)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k25_twoscomp (k11_finseq_1 1 1 k6_numbers)) = 1)  &  ((k1_funct_1 k25_twoscomp (k11_finseq_1 1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t22_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  ((k5_unialg_2 A B (k8_unialg_2 A B C)) = B) ) ) ) ) ) ) ).
tt(t22_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  ((k6_lattices (k12_unialg_2 A)) = A) ) ) ).
tt(t22_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  => (r2_hidden (k1_group_1 k1_complfld) (k2_uniroots A))) ) ).
tt(t22_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k6_polynom5 A B) (k6_polynom5 A C)) (k6_polynom5 A (k13_polynom3 A B C)))) ) ) ) ) ) ).
tt(t22_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v10_pre_topc A) & (v7_pre_topc A))  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  & (r1_tarski (k2_pre_topc A C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k9_real_1 B A) 1))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) => (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B D (k7_cqc_lang A C C)) (k8_valuat_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t22_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A E)) & (m2_valued_0 D A C))  => (m2_valued_0 (k8_funct_2 k5_numbers B A D E) B (k8_funct_2 k5_numbers B A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k61_valued_1 (k3_relat_1 A B) C) = (k3_relat_1 (k61_valued_1 A C) B)) ) ) ) ) ) ) ).
tt(t22_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k24_valued_1 (k30_valued_1 B) A) = (k24_valued_1 B (k4_xcmplx_0 A))) ) ) ) ) ).
tt(t22_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_vectsp10 A B C))) =>  ((m2_vectsp_4 D A B C) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k3_vectsp_4 A B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_4 D B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D))))) )  =>  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 D) (u1_struct_0 D) (u1_struct_0 C) F (k7_matrlin2 B C C D E)) => (r1_funct_2 (u1_struct_0 D) (u1_struct_0 C) (u1_struct_0 D) (u1_struct_0 D) (k7_matrlin2 B C C D (k1_vectsp11 C E A)) (k1_vectsp11 D F A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k4_vectsp_1 A B C (k4_algstr_0 B D)) = (k4_algstr_0 B (k4_vectsp_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t22_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k6_algstr_0 A (k1_vectsp_2 A C B) B) = C) ) ) ) ) ) ) ) ).
tt(t22_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_struct_0 D C) => (r1_struct_0 D (k4_algstr_0 B C))) ) ) ) ) ) ) ) ) ).
tt(t22_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k2_vectsp_5 A B (k2_vectsp_4 A B) (k2_vectsp_4 A B)) = B) ) ) ) ) ).
tt(t22_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k5_vectsp_6 A B D E) C) = (k3_rlvect_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_matrlin B A) =>  (! [C:$i] :  ((m1_vectsp_7 C A B) =>  (! [D:$i] :  ((m1_vectsp_7 D A B) =>  ((k1_card_1 C) = (k1_card_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t22_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r2_relset_1 A k1_numbers (k3_normsp_0 A B (k4_vfunct_1 A B C D)) (k26_valued_1 A k1_numbers (k3_normsp_0 A B C) (k18_complex1 D)))) ) ) ) ) ) ) ) ).
tt(t22_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k1_numbers (k3_normsp_0 A B (k2_vfunct_2 A B C D)) (k26_valued_1 A k1_numbers (k3_normsp_0 A B C) (k17_complex1 D)))) ) ) ) ) ) ) ) ).
tt(t22_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) => (r1_tarski (k6_waybel_0 A C) (k6_waybel_0 A B))) ) ) ) ) ) ) ).
tt(t22_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r5_waybel_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)))) ) ).
tt(t22_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v8_waybel_0 B A) & (l1_waybel_0 B A)) ) ) ) )  =>  ((k1_waybel11 A B) = (k1_waybel_2 A B)) ) ) ) ) ).
tt(t22_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k2_yellow_4 A B B) = B) ) ) ) ) ).
tt(t22_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ((v5_orders_3 D A B) &  ((v22_waybel_0 D A B) &  ( ((v4_yellow_0 B C) &  ((v4_waybel_0 B C) & (m1_yellow_0 B C)) )  &  ((v3_lattice3 C) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((r8_pboole (u1_struct_0 A) D E) & (v22_waybel_0 E A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) => (v13_waybel_0 C A)) ) )  => (v2_compts_1 (k6_waybel_0 A B) A)) ) ) ) ) ).
tt(t22_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_waybel15 C A) =>  ((r3_orders_2 A C B) <=>  (~ (r3_orders_2 A C (k7_waybel_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t22_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  => (r1_tarski (k1_waybel16 A) (k3_waybel_6 A))) ) ).
tt(t22_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=> (v22_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(t22_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B C) & (r1_tarski C (u1_pre_topc A)))  =>  ( ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  &  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(t22_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v3_waybel_1 (k1_waybel_1 A B C D) A B) & (v2_funct_2 C (u1_struct_0 B)))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r3_waybel_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v22_waybel_0 B A A) => (v22_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t22_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D B) & (m1_yellow_0 D B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((u1_struct_0 C) = (u1_struct_0 D))  & (v4_waybel_0 C A)) )  => (v4_waybel_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t22_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r1_yellow_0 A C) =>  ((r1_yellow_0 (k5_yellow_0 A B) C) &  ((k1_yellow_0 (k5_yellow_0 A B) C) = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t22_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (E = (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) (k7_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) C D)))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E F) = (k1_yellow_0 B (k7_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_waybel25 A))) =>  ((k2_pre_topc (k1_waybel25 A) (k6_domain_1 (u1_struct_0 (k1_waybel25 A)) B)) = (k5_waybel_0 (k1_waybel25 A) B)) ) ) ) ) ).
tt(t22_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  ( ((r1_borsuk_1 B C) &  ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B))) )  =>  ((v3_lattice3 (k1_waybel26 A C)) & (v3_waybel_3 (k1_waybel26 A C))) ) ) ) ) ) ) ) ).
tt(t22_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  => (r1_tarski (u1_struct_0 (k2_waybel27 A B)) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)))) ) ) ) ).
tt(t22_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (r1_tarski (k3_waybel28 A) (k2_waybel11 A))) ) ).
tt(t22_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v2_waybel18 B) & (l1_pre_topc B)) ) ) )  =>  ((k1_waybel25 (k3_waybel18 A (k2_funcop_1 A B))) = (k1_waybel29 (k5_yellow_1 A (k2_funcop_1 A (k1_waybel25 B))))) ) ) ) ) ).
tt(t22_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) <=> (m1_subset_1 D (u1_struct_0 (k3_waybel_2 A C B)))) ) ) ) ) ) ) ) ).
tt(t22_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) => (v2_yellow13 A)) ) ) ).
tt(t22_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ((v1_tops_2 (a_3_1_waybel31 A B C) B) &  ((v1_cantor_1 (a_3_1_waybel31 A B C) B) & (m1_subset_1 (a_3_1_waybel31 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ).
tt(t22_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_waybel_9 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_waybel_0 A C) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) => (v12_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(t22_waybel33,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((m2_yellow_9 C A) & (m2_yellow_9 C B))  =>  (! [D:$i] :  ((m3_yellow_9 D A B) => (m2_yellow_9 C D)) ) ) ) ) ) ) ) ) ).
tt(t22_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v22_waybel_0 C A B) => (v1_waybel34 (k1_waybel34 A B C) B A)) ) ) ) ) ) ) ).
tt(t22_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_yellow_0 A (k4_waybel35 A B C D))) )  => (m1_waybel35 (k6_waybel35 A B C) A B)) ) ) ) ) ) ) ).
tt(t22_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (C = (k1_yellow_0 A D))  => (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r2_hidden (k4_yellow_0 A) B)) ) ) ) ).
tt(t22_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_0_waybel_5 A B C D))  => (r1_orders_2 A (k1_yellow_0 A E) (k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_orders_2 A (k2_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v11_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((v1_subset_1 B (u1_struct_0 A)) & (v2_waybel_7 B A))  <=> (v3_waybel_7 B A)) ) ) ) ) ).
tt(t22_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_1 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) => (v5_waybel_6 B A)) ) )  => (v3_waybel_8 A)) ) ) ).
tt(t22_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_yellow_6 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_yellow_6 A B))) => (m1_subset_1 (k3_xboole_0 C D) (u1_struct_0 (k9_yellow_6 A B)))) ) ) ) ) ) ) ) ).
tt(t22_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 (k4_weddwitt A)) = (k2_xboole_0 (u1_struct_0 (k10_group_5 (k1_uniroots A))) (k1_tarski (k4_struct_0 A)))) ) ) ).
tt(t22_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B)) (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A D) B)))) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) =>  ((k2_wellord1 (k2_wellord1 C B) A) = (k2_wellord1 C A)) ) ) ) ) ) ).
tt(t22_wellord2,ax, (! [A:$i] :  ((k1_wellord2 (k1_tarski A)) = (k1_tarski (k4_tarski A A))) ) ).
tt(t22_wsierp_1,ax, (! [A:$i] :  ((v1_rat_1 A) => (r1_int_2 (k2_rat_1 A) (k1_rat_1 A))) ) ).
tt(t22_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_xboole_0 A (k3_xboole_0 A B)) = A) ) ) ).
tt(t22_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k4_xboolean A (k7_xboolean B C)) = (k4_xboolean (k4_xboolean A (k5_xboolean (k3_xboolean B) C)) (k5_xboolean (k3_xboolean C) B))) ) ) ) ) ) ) ).
tt(t22_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A B) = (k6_xcmplx_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t22_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) (k6_xcmplx_0 C D)) => (r1_xxreal_0 (k2_xcmplx_0 A D) (k6_xcmplx_0 C B))) ) ) ) ) ) ) ) ) ).
tt(t22_xtuple_0,ax, (! [A:$i] :  ((v3_xtuple_0 A) =>  (! [B:$i] :  ((v3_xtuple_0 B) =>  ( ( ((k7_xtuple_0 A) = (k7_xtuple_0 B))  &  ( ((k8_xtuple_0 A) = (k8_xtuple_0 B))  &  ( ((k5_xtuple_0 A) = (k5_xtuple_0 B))  &  ((k2_xtuple_0 A) = (k2_xtuple_0 B)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t22_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A (k3_xxreal_0 B C)) => (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(t22_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k4_xxreal_1 A B) (k2_xxreal_1 A B))) ) ) ) ).
tt(t22_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m1_xxreal_2 A (k3_xxreal_1 B A))) ) ) ) ).
tt(t22_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((v1_xreal_0 A) =>  ( ((k1_xxreal_3 (k3_xxreal_3 B A) A) = B)  &  ((k3_xxreal_3 (k1_xxreal_3 B A) A) = B) ) ) ) ) ) ) ).
tt(t22_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k13_lattice3 A B C))  <=>  ((r1_orders_2 A B D) &  ((r1_orders_2 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B E) & (r1_orders_2 A C E))  => (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((v1_waybel_3 C (k3_yellow_3 A B)) =>  ((v1_waybel_3 (k8_yellow_3 A B C) A) & (v1_waybel_3 (k9_yellow_3 A B C) B)) ) ) ) ) ) ) ) ).
tt(t22_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k6_partfun1 (u1_struct_0 A)) (k9_subset_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 A))) (u1_orders_2 A) (u1_orders_2 (k7_lattice3 A))))) ) ).
tt(t22_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_yellow13 C A B) & (m1_yellow13 C A B))  =>  (C = (k1_tarski (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t22_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (k1_tarski B))  &  ( (E = (k1_tarski C))  &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc F A) & (r2_hidden B F))  => (r2_hidden C F)) ) ) ) )  => (r1_tarski (k2_pre_topc A D) (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v1_yellow15 B A) => (m1_eqrel_1 (k2_yellow15 A B) A)) ) ) ) ) ).
tt(t22_yellow16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r3_yellow16 B A) => (v3_waybel_3 B)) ) ) ) ) ).
tt(t22_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_waybel18 A B))) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E A) => (v1_compts_1 (k4_waybel18 A B E))) )  &  ( (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski (k2_struct_0 (k3_waybel18 A B)) (k3_tarski E))) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_waybel18 A B C))) =>  (? [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 D)))  & (r1_tarski (k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) (k1_tarski E)) (k3_tarski F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (E = C)  &  ( (F = D)  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B F E)) &  ( (H = G)  &  ((v1_altcat_3 G A C D) &  ((v2_altcat_3 G A C D) &  (~  ((k1_altcat_3 B F E H) = (k1_altcat_3 A C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) &  ((v3_yellow_6 D A) & (l1_waybel_0 D A)) ) ) )  &  ((r1_waybel_0 A D B) & (r2_hidden C (k10_yellow_6 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))))) =>  ((k1_yellow_0 (k2_yellow_1 (u1_pre_topc A)) B) = (k3_tarski B)) ) ) ) ) ).
tt(t22_yellow20,ax, (! [A:$i] :  ( ((v2_altcat_1 A) & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ((v2_altcat_1 B) & (l2_altcat_1 B))  =>  ((r1_yellow20 A B) => (v2_altcat_1 (k2_yellow20 A B))) ) ) ) ) ).
tt(t22_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r2_hidden C A) =>  ((r3_orders_2 B C (k1_yellow_0 B A)) & (r3_orders_2 B (k2_yellow_0 B A) C)) ) ) ) ) ) ) ).
tt(t22_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((v1_waybel_0 (k4_yellow_3 A B C) A) & (v1_waybel_0 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ).
tt(t22_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice3 A B C) =>  ((k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) = B) ) ) ) ) ) ) ) ).
tt(t22_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_orders_2 A B C) &  ((k12_lattice3 A C D) = (k3_yellow_0 A)) )  =>  ((k12_lattice3 A B D) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t22_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((r2_waybel_0 A B C) => (m2_yellow_6 (k5_yellow_6 A B C) A B)) ) ) ) ) ) ).
tt(t22_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lattice3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lattice3 A))) =>  ((k12_lattice3 A (k9_lattice3 A B) (k9_lattice3 A C)) = (k13_lattice3 (k7_lattice3 A) B C)) ) ) ) ) ) ) ).
tt(t22_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  => (v4_yellow_8 A)) ) ).
tt(t22_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((u1_pre_topc A) = (k1_cantor_1 (u1_struct_0 A) B))  <=>  ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t22_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((v8_zf_fund1 B A) & (r2_hidden C B))  => (r2_hidden (k5_zf_fund1 D C) B)) ) ) ) ) ) ) ) ) ).
tt(t22_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ((v11_zf_lang (k17_zf_lang B C D A)) &  ( ((k23_zf_lang (k17_zf_lang B C D A)) = B)  &  ((k24_zf_lang (k17_zf_lang B C D A)) = (k15_zf_lang C D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_zf_lang A) =>  ((k1_funct_1 A 1) = 4) ) ) ) ).
tt(t22_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r1_tarski (k2_tarski A B) (k2_tarski C D)) &  ( (~  (A = C) )  &  (~  (A = D) ) ) ) ) ) ) ) ) ).
tt(t22_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) &  ((r1_zf_model A E (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang B (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) &  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model C)) &  ((r1_zf_model A E (k8_zf_lang (k2_zf_lang 3) (k13_zf_lang (k2_zf_lang k6_numbers) (k8_zf_lang (k2_zf_lang 4) (k12_zf_lang C (k4_zf_lang (k2_zf_lang 4) (k2_zf_lang k6_numbers))))))) & (r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model D))) ) ) )  =>  ((r2_hidden (k2_zf_lang 4) (k2_zf_model D)) |  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ( ((k9_xtuple_0 F) = A)  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r1_zf_model A (k2_zf_lang1 A E (k2_zf_lang 3) G) D) =>  ((k1_funct_1 F G) = (k3_funct_2 A A (k1_zfmodel1 B A E) G)) )  &  ((r1_zf_model A (k2_zf_lang1 A E (k2_zf_lang 3) G) (k6_zf_lang D)) =>  ((k1_funct_1 F G) = (k3_funct_2 A A (k1_zfmodel1 C A E) G)) ) ) ) ) )  => (r2_zfmodel1 F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  =>  ((r1_zf_model D E (k15_zf_lang B C A)) <=>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_zf_lang D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang D)))) )  &  ( (! [G:$i] :  ((m2_subset_1 G k5_numbers k1_zf_lang) =>  (~  ( (~  ((k3_funct_2 k1_zf_lang D F G) = (k3_funct_2 k1_zf_lang D E G)) )  &  ( (~  (B = G) )  &  (~  (C = G) ) ) ) ) ) )  & (r1_zf_model D F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t22_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ( ((v4_ordinal1 (k9_xtuple_0 B)) &  ((v2_ordinal2 B) & (r1_ordinal2 A B)) )  =>  ( ((k9_xtuple_0 B) = k1_xboole_0)  | (r2_ordinal2 A (k9_xtuple_0 B))) ) ) ) ) ) ).
tt(t22_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v7_zmodul01 B A) &  ((v7_zmodul01 C A) &  (D = (a_3_0_zmodul01 A B C)) ) )  => (v7_zmodul01 D A)) ) ) ) ) ) ) ) ) ).
tt(t230_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k27_member_1 A C) = (k27_member_1 B C))  =>  ( (C = k6_numbers)  |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t230_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) A) = (k4_xcmplx_0 B)) ) ) ) ) ).
tt(t230_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B C))  => (r1_xxreal_0 (k6_xcmplx_0 B A) C)) ) ) ) ) ) ) ).
tt(t230_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_1 A k1_xxreal_0) = (a_1_1_xxreal_1 A)) ) ) ).
tt(t231_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k27_member_1 (k3_xboole_0 A B) C) = (k3_xboole_0 (k27_member_1 A C) (k27_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t231_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) B) A) = (k4_xcmplx_0 B)) ) ) ) ) ).
tt(t231_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t231_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_xxreal_1 k2_xxreal_0 A) = (a_1_2_xxreal_1 A)) ) ) ).
tt(t232_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k27_member_1 (k6_subset_1 A B) C) = (k6_subset_1 (k27_member_1 A C) (k27_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t232_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (~  (A = (k7_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t232_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_xreal_0 A A) = k6_numbers) ) ) ).
tt(t232_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_xxreal_1 A k1_xxreal_0) = (a_1_3_xxreal_1 A)) ) ) ).
tt(t233_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (C = k6_numbers) )  =>  ((k27_member_1 (k5_xboole_0 A B) C) = (k5_xboole_0 (k27_member_1 A C) (k27_member_1 B C))) ) ) ) ) ) ) ) ).
tt(t233_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k7_xcmplx_0 A (k3_xcmplx_0 (k3_xcmplx_0 B C) (k7_xcmplx_0 D E))) = (k3_xcmplx_0 (k7_xcmplx_0 E C) (k7_xcmplx_0 A (k3_xcmplx_0 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t233_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xreal_0 B A) = (k6_xcmplx_0 B A)) ) ) ) ) ) ).
tt(t233_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k4_xxreal_1 k2_xxreal_0 A)) <=>  (~ (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t234_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k27_member_1 (k9_member_1 A B) C) = (k9_member_1 (k27_member_1 A C) (k27_member_1 B C))) ) ) ) ) ) ) ).
tt(t234_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k2_xcmplx_0 (k3_xcmplx_0 (k7_xcmplx_0 (k6_xcmplx_0 A B) C) D) B) = (k2_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 1 (k7_xcmplx_0 D C)) B) (k3_xcmplx_0 (k7_xcmplx_0 D C) A))) ) ) ) ) ) ) ) ) ).
tt(t234_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) &  ((k1_xreal_0 B A) = (k1_xreal_0 C A)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t234_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k3_xxreal_1 k2_xxreal_0 A)) <=> (r1_xxreal_0 B A)) ) ) ) ) ).
tt(t235_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k27_member_1 (k11_member_1 A B) C) = (k11_member_1 (k27_member_1 A C) (k27_member_1 B C))) ) ) ) ) ) ) ).
tt(t235_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k2_xcmplx_0 (k3_xcmplx_0 A B) C) = (k3_xcmplx_0 A (k2_xcmplx_0 B (k7_xcmplx_0 C A)))) ) ) ) ) ) ) ) ).
tt(t235_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((k2_xcmplx_0 (k1_xreal_0 A B) B) = A) ) ) ) ) ) ).
tt(t235_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k4_xxreal_1 A k1_xxreal_0)) <=>  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(t236_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 A C))  & (r1_xxreal_0 (k1_xreal_0 B C) (k1_xreal_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t236_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k2_xxreal_1 A k1_xxreal_0)) <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t237_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_xreal_0 A 1))) ) ) ) ).
tt(t237_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_xxreal_1 B C) (k1_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t238_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 B C) (k1_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t239_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 B C) (k1_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t23_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A D B) & (r2_hidden C (k2_abcmiz_0 A D)))  =>  ((r1_abcmiz_0 A B C) & (r3_orders_2 A D (k5_abcmiz_0 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_abcmiz_1,ax,(r1_tarski k2_abcmiz_1 (k4_classes1 k4_ordinal1))).
tt(t23_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((m1_abcmiz_1 B A (k14_abcmiz_1 A)) <=>  ( ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) &  ((k1_xtuple_0 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0))) = k8_abcmiz_1) )  | (r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k2_abcmiz_1)) ) ) ) ) ) ).
tt(t23_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k5_real_1 (k2_xcmplx_0 (k1_absvalue A) (k1_absvalue B)) 1) (k1_absvalue (k2_xcmplx_0 A B)))) ) ) ) ).
tt(t23_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 D A) & (r2_hidden B D))  =>  ((r2_hidden C D) <=> (r2_aff_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 C A) &  ((r2_hidden B C) &  ((r1_tarski D C) & (r2_hidden B E)) ) )  =>  ( ( (~ (r5_aff_1 A D E))  &  (~ (r5_aff_1 A E D)) )  | (r1_tarski E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ((r2_hidden A (k2_afinsq_1 B)) => (r2_hidden (k2_nat_1 (k1_afinsq_1 C) A) (k2_afinsq_1 (k1_ordinal4 C B)))) ) ) ) ) ) ) ).
tt(t23_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ((r1_afinsq_2 A B) =>  ((k9_subset_1 k1_numbers (k3_xboole_0 A B) k5_numbers) = k1_xboole_0) ) ) ) ).
tt(t23_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k13_afproj A))) <=>  (~  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (B = (k4_tarski C 1))  & (v1_aff_1 C A)) )  &  (~  ( (B = (k4_tarski (k6_afproj A C) 2))  & (v1_aff_4 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t23_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_afvect0 A B C D) & (r1_afvect0 A C E))  => (r2_afvect0 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_algspec1 B A) => (r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A))) ) ) ) ).
tt(t23_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_tarski A B) => (r1_tarski (k11_algstr_4 A C) (k11_algstr_4 B C))) ) ) ) ) ).
tt(t23_altcat_1,ax, ((v14_altcat_1 (k7_altcat_1 1)) & (v13_struct_0 (k7_altcat_1 1) 1)) ).
tt(t23_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_altcat_2 A B))) =>  (C = B) ) ) ) ) ) ) ).
tt(t23_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ((v2_altcat_3 (k5_altcat_1 A B C D E F) A B D) =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C D) = k1_xboole_0)  |  ( ((k1_altcat_1 A D B) = k1_xboole_0)  | (v2_altcat_3 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v2_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v1_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ami_2,ax, (! [A:$i] :  (~  ((r2_hidden A k2_ami_2) &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  (A = (k4_tarski 1 B)) ) ) ) ) ) ) ).
tt(t23_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (v2_extpro_1 (k9_ami_3 B A) 2 k1_ami_3)) ) ) ) ) ).
tt(t23_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  (J = (k8_ami_3 I H)) )  =>  ( (I = (k1_ordinal1 (k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 E C G))))  |  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) = k6_numbers)  <=>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k7_ami_3 A) B) = (k7_ami_3 (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t23_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ((v5_amistd_1 C A B) & (r2_hidden (k1_ami_wstd A B k6_numbers) (k1_relset_1 k5_numbers C)))  => (v4_ami_wstd C A B)) ) ) ) ) ) ) ).
tt(t23_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  ((r4_analmetr (k2_analmetr A B C) D E F G) => (r4_analmetr (k2_analmetr A B C) F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analoaf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analoaf A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analoaf A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analoaf A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analoaf A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analoaf A))) =>  ((r2_analoaf (k2_analoaf A) B C D D) &  ( ((r2_analoaf (k2_analoaf A) B C C B) =>  (B = C) )  &  ( ( ((r2_analoaf (k2_analoaf A) B C F G) & (r2_analoaf (k2_analoaf A) B C H I))  =>  ( (B = C)  | (r2_analoaf (k2_analoaf A) F G H I)) )  &  ( ((r2_analoaf (k2_analoaf A) B C D E) => (r2_analoaf (k2_analoaf A) C B E D))  &  ( ((r2_analoaf (k2_analoaf A) B C C D) => (r2_analoaf (k2_analoaf A) B C B D))  &  (~  ((r2_analoaf (k2_analoaf A) B C B D) &  ( (~ (r2_analoaf (k2_analoaf A) B C C D))  &  (~ (r2_analoaf (k2_analoaf A) B D D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analoaf A))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analoaf A))) &  ( (~ (r2_analoaf (k2_analoaf A) B C D E))  &  (~ (r2_analoaf (k2_analoaf A) B C E D)) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analoaf A))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analoaf A))) &  ((r2_analoaf (k2_analoaf A) B C D E) &  ((r2_analoaf (k2_analoaf A) B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analoaf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analoaf A))) =>  (~  ( (~  (B = D) )  &  ((r2_analoaf (k2_analoaf A) D B B E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analoaf A))) =>  (~  ((r2_analoaf (k2_analoaf A) C B B F) & (r2_analoaf (k2_analoaf A) C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_analort A E F B C D D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((u1_struct_0 (k5_anproj_1 A)) = (k3_anproj_1 A))  &  ((u1_collsp (k5_anproj_1 A)) = (k4_anproj_1 A)) ) ) ) ).
tt(t23_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  ((r1_collsp (k5_anproj_1 A) B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (B = (k2_anproj_1 A E))  &  ( (C = (k2_anproj_1 A F))  &  ( (D = (k2_anproj_1 A G))  &  ( (~ (v9_struct_0 E A))  &  ( (~ (v9_struct_0 F A))  &  ( (~ (v9_struct_0 G A))  & (r2_anproj_1 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((r2_hidden D (k9_aofa_000 A B (k1_nat_1 C 1))) <=>  (~  ( (~ (r2_hidden D B))  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (~  ( (D = (k1_funct_1 (k2_pua2mss1 A E) F))  &  ((r2_hidden F (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A E))) & (r1_tarski (k2_relset_1 (u1_struct_0 A) F) (k9_aofa_000 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m2_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m3_aofa_i00 F A B C D) => (r2_hidden (k44_aofa_i00 A B C D E F) (k18_aofa_000 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) => (v6_armstrng (k5_armstrng A) (u1_armstrng A))) ) ).
tt(t23_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_arytm_0 A (k1_arytm_0 B C)) = (k1_arytm_0 (k1_arytm_0 A B) C)) ) ) ) ) ) ) ).
tt(t23_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  (~  ( (~ (r1_arytm_2 A B))  &  ( (~ (r1_arytm_2 A C))  &  (~  ((k2_arytm_1 B (k1_arytm_1 A C)) = (k2_arytm_1 C (k1_arytm_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((r1_arytm_3 A B) =>  ((k4_arytm_3 A B) = A) ) ) ) ) ) ).
tt(t23_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers) )  =>  ((r2_hidden B (k7_asympt_0 A)) &  (~ (r2_hidden A (k7_asympt_0 B))) ) ) ) ) ) ) ).
tt(t23_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B 1))  =>  ((k1_seq_1 A B) = (k10_real_1 (k5_series_1 B 2) (k6_power 2 B))) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((r1_tarski (k6_asympt_0 B) (k6_asympt_0 (k3_asympt_1 8))) &  (~  ((k6_asympt_0 B) = (k6_asympt_0 (k3_asympt_1 8))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (r1_tarski (k5_autalg_1 A B) (k4_autalg_1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))) ) ) ) ).
tt(t23_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k1_group_1 A)) B) = B) ) ) ) ) ).
tt(t23_bagorder,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_finset_1 A)) )  =>  (~ (v2_wellord1 (k17_pre_poly A))) ) ) ).
tt(t23_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (r2_hidden (k4_struct_0 A) (k5_bcialg_1 A))) ) ).
tt(t23_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A (k2_bcialg_1 A C) (k2_bcialg_1 A B))) ) ) ) ) ) ) ) ).
tt(t23_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ((v7_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A B D)) = (k1_bcialg_1 A D (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_bcialg_4 A B 2) = (k1_bcialg_4 A B B)) ) ) ) ) ).
tt(t23_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~  ((k2_bcialg_5 A B C D) = A) )  &  ( (~  ((k2_bcialg_5 A B C D) = B) )  &  ( (~  ((k2_bcialg_5 A B C D) = C) )  &  (~  ((k2_bcialg_5 A B C D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k3_bcialg_6 A D (k3_bcialg_6 A C B)) = (k3_bcialg_6 A (k22_binop_2 C D) B)) ) ) ) ) ) ) ) ) ).
tt(t23_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((v3_bciideal (k4_bcialg_1 A) A) & (m2_bcialg_1 (k4_bcialg_1 A) A)) ) ) ).
tt(t23_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_bhsp_1 A B (k4_struct_0 A))) ) ) ) ).
tt(t23_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  => (v2_comseq_2 (k3_bhsp_2 A C B))) ) ) ) ) ) ) ).
tt(t23_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 E C) & (r1_xxreal_0 D (k3_bhsp_1 A (k1_normsp_1 A B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v3_bhsp_3 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k3_bhsp_1 A (k5_algstr_0 A (k3_bhsp_4 A B E) (k3_bhsp_4 A B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k9_bilinear A B C (k7_hahnban1 A B) D) (k1_bilinear A B C))) ) ) ) ) ) ) ) ).
tt(t23_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( (C = (k5_euclid A))  =>  ( ((k8_binarith A B (k1_binari_2 A)) = k8_margrel1)  <=>  (B = (k3_binarith A C)) ) ) ) ) ) ) ) ) ).
tt(t23_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k1_binari_4 A 1) = A) ) ) ) ).
tt(t23_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_funct_1 (k8_binom A B C D) 1) = (k2_binom A B D)) ) ) ) ) ) ) ) ) ).
tt(t23_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  ((k1_funct_1 (k2_bintree2 A 1) 2) = (k10_binarith k5_numbers 1)) ) ) ).
tt(t23_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_lattices A B C) & (r3_lattices A D E))  => (r3_lattices A (k1_boolealg A B E) (k1_boolealg A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  (~  ((v1_finset_1 C) &  ((r1_tarski C (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) D)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) =>  (~  ((r1_tarski E D) &  ((v1_finset_1 E) &  (C = (k7_relset_1 (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_borsuk_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v2_compts_1 C A) & (v2_compts_1 D B))  =>  ((v2_compts_1 (k3_borsuk_1 A B C D) (k2_borsuk_1 A B)) & (m1_subset_1 (k3_borsuk_1 A B C D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t23_borsuk_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( (C = (k1_rcomp_1 A B))  => (v4_pre_topc C k5_topmetr)) ) ) ) ) ) ) ).
tt(t23_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~  ( (~  (A = k6_numbers) )  & (v1_rat_1 (k13_complex1 B A))) ) ) ) ) ) ).
tt(t23_borsuk_6,ax, ((v4_pre_topc a_0_11_borsuk_6 (k2_borsuk_1 k3_topmetr k3_topmetr)) & (m1_subset_1 a_0_11_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr))))) ).
tt(t23_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k1_borsuk_7 A A A B C D) = (k16_funcop_1 A D)) ) ) ) ) ).
tt(t23_bspace,ax, (! [A:$i] : (v4_rlvect_1 (k7_bspace A))) ).
tt(t23_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C (k5_bvfunc_1 A D B))))) ) ) ) ) ) ) ) ).
tt(t23_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  ( (B = (k3_enumset1 C D E F G))  =>  ( (C = E)  |  ( (D = E)  |  ( (E = F)  |  ( (E = G)  |  ((k5_bvfunc_2 A E B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k2_bvfunc_1 A B C)) (k2_bvfunc_1 A (k13_bvfunc_1 A B) (k13_bvfunc_1 A C))) & (r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A (k5_bvfunc_1 A B C)) (k5_bvfunc_1 A (k14_bvfunc_1 A B) (k14_bvfunc_1 A C)))) ) ) ) ) ) ) ).
tt(t23_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k9_bvfunc_1 A (k1_bvfunc_1 A B) B) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t23_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k5_bvfunc26 A B C) (k5_bvfunc26 A B D)) (k2_bvfunc_1 A B (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k5_bvfunc_1 A D C) B E) (k5_bvfunc_1 A (k6_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k10_bvfunc_1 A B C) D E) (k10_bvfunc_1 A (k6_bvfunc_2 A B D E) (k6_bvfunc_2 A C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D (k9_bvfunc_1 A C B)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C (k9_bvfunc_1 A D B)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) (k1_bvfunc_1 A B)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t23_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t23_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k1_bvfunc_1 A B) (k10_bvfunc_1 A (k9_bvfunc_1 A B C) (k1_bvfunc_1 A B)))) ) ) ) ) ) ).
tt(t23_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t23_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_c0sp1 A))) =>  ((k1_binop_1 (k5_c0sp1 (k12_funcsdom A) (k6_c0sp1 A)) 1 B) = B) ) ) ) ) ).
tt(t23_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r1_tarski (k13_pre_poly (k3_valued_1 (u1_struct_0 A) k1_numbers k1_numbers B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ) ).
tt(t23_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_substut1 A)) =>  ((r1_sublemma A (k2_substut2 A B F) C E D) <=> (r1_valuat_1 A C B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k7_cqc_lang A B C)))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t23_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=> (r1_ordinal1 (k3_card_1 A) (k3_card_1 B))) ) ) ) ) ).
tt(t23_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k2_card_2 2 A) = (k1_card_2 A A)) ) ) ).
tt(t23_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) => (r1_tarski (k2_card_3 A) (k2_card_3 B))) ) ) ) ) ).
tt(t23_card_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (v1_finset_1 A))  &  ( (~  (B = k6_numbers) )  &  (~  ((r2_wellord2 (k4_finseq_2 B A) A) &  ((k1_card_1 (k4_finseq_2 B A)) = (k1_card_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t23_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((k1_card_5 (k2_card_1 A)) = (k2_card_1 A)) ) ) ).
tt(t23_card_fil,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_card_fil B A) =>  ( ((v3_card_fil B A) & (r1_card_fil A (k1_card_1 A) B))  =>  ((v2_card_fil B A) | (v1_card_fil B A)) ) ) ) ) ) ).
tt(t23_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v1_xboole_0 B) | (v1_xboole_0 (k3_tarski (k10_xtuple_0 B))))  =>  ((k2_card_fin B C A) = (k3_tarski (k10_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t23_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((r2_hidden k4_ordinal1 (k1_card_5 A)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r2_hidden (k1_card_1 B) (k1_card_5 A)) &  (! [C:$i] :  ((m1_card_lar C A B) =>  ((v2_card_lar C A) & (v1_card_lar C A)) ) ) )  =>  ((v2_card_lar (k6_setfam_1 A B) A) & (v1_card_lar (k6_setfam_1 A B) A)) ) ) ) ) ) ) ).
tt(t23_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  (~ (r2_hidden (k1_cat_1 A E F) (k2_cat_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ( ((u1_struct_0 (k8_cat_2 A B)) = (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))  &  ( ((u4_struct_0 (k8_cat_2 A B)) = (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)))  &  ((r1_funct_2 (u4_struct_0 (k8_cat_2 A B)) (u1_struct_0 (k8_cat_2 A B)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_graph_1 (k8_cat_2 A B)) (k6_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_graph_1 A) (u1_graph_1 B))) &  ((r1_funct_2 (u4_struct_0 (k8_cat_2 A B)) (u1_struct_0 (k8_cat_2 A B)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u2_graph_1 (k8_cat_2 A B)) (k6_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u2_graph_1 A) (u2_graph_1 B))) &  ((u1_cat_1 (k8_cat_2 A B)) = (k7_cat_2 (u4_struct_0 A) (u4_struct_0 B) (u1_cat_1 A) (u1_cat_1 B))) ) ) ) ) ) ) ) ) ).
tt(t23_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v2_cat_3 D A B C) => (v7_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t23_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  ((k2_cat_1 A B (k2_cat_4 A C D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_hidden C (k9_cat_5 A B)) <=>  ((k4_graph_1 A C) = B) ) ) ) ) ) ) ) ).
tt(t23_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_catalan2 A k6_numbers) = (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)) (k8_funcop_1 k5_numbers A k6_numbers))) ) ) ).
tt(t23_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (r3_pua2mss1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k11_catalg_1 A B C) (k12_catalg_1 A B C))) ) ) ) ) ) ).
tt(t23_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( (C = E)  &  (D = F) )  =>  ( (F = (k1_clvect_1 (k7_cc0sp1 A) E B))  <=>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k3_funct_2 A k2_numbers D G) = (k5_binop_2 B (k3_funct_2 A k2_numbers C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cc0sp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_cc0sp2 B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_cc0sp2 B))) =>  ( ( (C = E)  &  (D = F) )  =>  ( (F = (k1_clvect_1 (k5_cc0sp2 B) E A))  <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) k2_numbers D G) = (k3_xcmplx_0 A (k3_funct_2 (u1_struct_0 B) k2_numbers C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r2_relset_1 k5_numbers k2_numbers A (k1_valued_0 k2_numbers B C))) ) )  |  ((k3_comseq_2 B) = (k3_comseq_2 A)) ) ) ) ) ) ) ).
tt(t23_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((r1_cfdiff_1 A C) & (r1_cfdiff_1 B C))  =>  ((r1_cfdiff_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  ((k2_cfdiff_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers A B) C) = (k8_complex1 (k2_cfdiff_1 A C) (k2_cfdiff_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t23_cfuncdom,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_clvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ((k3_rlvect_1 A (k1_clvect_1 A B D) (k1_clvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k2_numbers) &  (? [F:$i] :  ((m1_subset_1 F k2_numbers) &  (D = (k3_rlvect_1 A (k1_clvect_1 A B E) (k1_clvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) D) (k46_valued_1 A k2_numbers k2_numbers (k25_valued_1 A k2_numbers B D) (k25_valued_1 A k2_numbers C D)))) ) ) ) ) ) ) ) ).
tt(t23_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v3_cgames_1 B) & (v4_cgames_1 B)) ) ) ) )  =>  ((r2_hidden (k1_funct_1 B (k3_finseq_1 B)) (k2_cgames_1 A)) => (r2_hidden (k1_funct_1 B 1) (k2_cgames_1 A))) ) ) ) ) ).
tt(t23_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r2_hidden B (k3_chain_1 A C D)) <=>  (~  ( (~  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  ((r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E)) & (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 D E))) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  (~  ( (~ (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 D E)))  &  ((r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 D E)) | (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m3_glib_001 D A) =>  ((r1_tarski (k13_glib_001 A D) B) => (m3_glib_001 D C)) ) ) ) ) ) ) ) ) ).
tt(t23_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  ((r1_xboole_0 (k2_msafree2 B) (k3_msafree2 A)) &  (C = (k2_circcomb A B)) ) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 C F))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 A D))) =>  ( (I = (k5_relat_1 H (u1_struct_0 A)))  =>  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 B E))) =>  (~  ( (J = (k5_relat_1 H (u1_struct_0 B)))  &  ( (~  ((v1_circuit2 (k5_facirc_1 A D I G) A D) & (v1_circuit2 (k5_facirc_1 B E J G) B E)) )  & (v1_circuit2 (k5_facirc_1 C F H G) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (m1_subset_1 C (u1_struct_0 (k2_circcomb A B)))) ) ) ) ) ) ).
tt(t23_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) & (l3_msualg_1 E B))  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) & (l3_msualg_1 F C))  =>  ( ((r1_partfun1 (u3_msualg_1 A D) (u3_msualg_1 B E)) &  ((r1_partfun1 (u3_msualg_1 B E) (u3_msualg_1 C F)) & (r1_partfun1 (u3_msualg_1 C F) (u3_msualg_1 A D))) )  =>  ((k3_circcomb (k2_circcomb A B) C (k3_circcomb A B D E) F) = (k3_circcomb A (k2_circcomb B C) D (k3_circcomb B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((v1_circled1 D A) &  ((k3_rlvect_2 A D) = (k7_domain_1 (u1_struct_0 A) B C)) )  =>  ( (B = C)  |  ( ((k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers D B) (k3_funct_2 (u1_struct_0 A) k1_numbers D C)) = 1)  &  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) &  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers D C)) &  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_circtrm1 A B C D) =>  ( ((u1_struct_0 B) = (k7_relat_1 C (u1_struct_0 A)))  &  ((u4_struct_0 B) = (k7_relat_1 D (u4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_classes1,ax, (! [A:$i] :  ((v1_ordinal1 A) => (v1_ordinal1 (k1_classes1 A))) ) ).
tt(t23_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~  ((r2_hidden A (k1_classes1 B)) & (v1_ordinal1 B)) )  &  ( (~  ((r2_hidden A (k1_classes1 B)) & (r1_tarski A (k1_classes1 B))) )  &  (~  ((r2_hidden (k1_card_1 A) (k1_card_1 (k1_classes1 B))) & (r1_tarski A (k1_classes1 B))) ) ) ) )  => (r1_tarski (k9_funct_2 A (k1_classes1 B)) (k1_classes1 B))) ) ) ).
tt(t23_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_clopban1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_clopban1 A B))) =>  ( (E = (k3_rlvect_1 (k9_clopban1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k10_clopban1 A B E F) = (k3_rlvect_1 B (k10_clopban1 A B C F) (k10_clopban1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k9_clopban2 A)) = (k6_clopban2 A)) ) ) ).
tt(t23_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_seq_2 (k3_series_1 (k4_normsp_0 A B))) <=> (v2_clopban3 B A)) ) ) ) ) ).
tt(t23_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_clopban4 A B) D) = (k1_normsp_1 A (k3_clopban4 D A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t23_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m2_pboole C A (k5_mssubfam A B) (k5_mssubfam A B)) =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((v4_closure1 C A B) & (v4_closure1 D A B))  => (v4_closure1 (k3_closure1 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t23_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_closure2 D A B (k2_closure2 A B)) =>  (! [E:$i] :  ((m1_closure2 E A B (k2_closure2 A B)) =>  ( (C = (k2_tarski D E))  => (r6_pboole A (k4_mssubfam A B (k5_closure2 A B C)) (k3_pboole A D E))) ) ) ) ) ) ) ) ) ) ).
tt(t23_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  => (v6_clvect_1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t23_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  => (v2_comseq_2 (k3_clvect_2 A C B))) ) ) ) ) ) ) ).
tt(t23_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) &  ((v4_clvect_2 A) & (l1_csspace A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k13_csspace A (k5_algstr_0 A (k2_clvect_3 A B E) (k2_clvect_3 A B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_classes1 (k9_xtuple_0 A)) & (v3_cohsp_1 (k9_xtuple_0 A)))  =>  ((v10_cohsp_1 A) <=>  ((v6_cohsp_1 A) &  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k1_funct_1 A B)) &  (! [D:$i] :  (~  ((r2_hidden D B) &  ((r2_hidden C (k1_funct_1 A (k1_tarski D))) &  (! [E:$i] :  ( ((r1_tarski E B) & (r2_hidden C (k1_funct_1 A E)))  => (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_coh_sp A)) =>  ( ( ((k6_coh_sp A B) = (k7_coh_sp A C))  &  ((k6_coh_sp A D) = (k7_coh_sp A B)) )  =>  ((k9_coh_sp A (k9_coh_sp A C B) D) = (k9_coh_sp A C (k9_coh_sp A B D))) ) ) ) ) ) ) ) ) ).
tt(t23_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((r1_xxreal_0 2 A) & (r1_ordinal1 (k2_nat_1 A 2) (k1_card_1 B)))  =>  (! [C:$i] :  ((l1_combgras C (k1_combgras A B) (k1_combgras A B)) =>  ((v7_combgras C (k1_combgras A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ((v3_combgras D A B) =>  ((v3_combgras (k4_combgras (k1_combgras A B) (k1_combgras A B) C D) A B) & (v3_combgras (k5_combgras (k1_combgras A B) (k1_combgras A B) C D) A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 A) = k6_numbers)  =>  ( ((k4_complex1 A) = k6_numbers)  |  ( ((k3_complex1 (k5_xcmplx_0 A)) = k6_numbers)  &  ((k4_complex1 (k5_xcmplx_0 A)) = (k1_real_1 (k2_real_1 (k4_complex1 A)))) ) ) ) ) ) ).
tt(t23_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k4_complex1 A) = k6_numbers)  <=>  ( ((k1_comptrig A) = k6_numbers)  |  ((k1_comptrig A) = k32_sin_cos) ) ) ) ) ).
tt(t23_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k3_vectsp_1 k1_complfld A (k5_struct_0 k1_complfld)) = A) ) ) ).
tt(t23_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k1_complsp2 (k11_seq_4 A)) = (k11_seq_4 (k1_complsp2 A))) ) ) ).
tt(t23_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski (k2_relset_1 (k9_setfam_1 (u1_struct_0 A)) C) B) &  ((v2_relat_1 C) &  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v5_compl_sp D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) ) )  =>  (~  ((v2_prob_1 D) &  ( ( ((v1_pcomps_1 B A) & (v2_funct_1 C))  =>  ((k2_kurato_0 (u1_struct_0 A) D) = k1_xboole_0) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) &  ( ((k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) D E) = (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) F)))  &  (F = (a_3_2_compl_sp A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_funct_1 (k7_compos_1 A B C) (k62_valued_1 B)) = (k1_funct_1 (k5_compos_1 A C (k7_nat_d (k5_card_1 B) 1)) k6_numbers)) ) ) ) ) ) ) ).
tt(t23_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  => (r2_compos_2 B (k8_compos_1 A B C))) ) ) ) ) ) ).
tt(t23_comptrig,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))).
tt(t23_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v2_compts_1 B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))))) ) ) ) ) ).
tt(t23_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  =>  ( ((v2_comput_1 A) &  (~ (v1_xboole_0 A)) )  <=>  ((k1_relset_1 (k3_finseq_2 k5_numbers) A) = (k4_finseq_2 (k19_margrel1 A) k5_numbers)) ) ) ) ).
tt(t23_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A (k31_valued_1 k5_numbers k2_numbers B)) (k2_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ).
tt(t23_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_funct_2 k5_numbers k1_numbers (k1_valued_0 k1_numbers (k7_comseq_3 A) B) (k7_comseq_3 (k1_valued_0 k2_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k1_valued_0 k1_numbers (k8_comseq_3 A) B) (k8_comseq_3 (k1_valued_0 k2_numbers A B)))) ) ) ) ) ).
tt(t23_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( ((u2_conlat_1 A (k5_conlat_1 A)) = (u1_struct_0 A))  &  ((u3_conlat_1 A (k6_conlat_1 A)) = (u4_struct_0 A)) ) ) ) ).
tt(t23_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v2_connsp_1 C A) <=> (v2_connsp_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k1_connsp_2 A B))) ) ) ) ).
tt(t23_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (m1_connsp_3 C A)) ) )  => (m1_connsp_3 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t23_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (~  ((v2_convex1 B A) &  (B = (k4_rlvect_2 A)) ) ) ) ) ) ) ).
tt(t23_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (r1_convex4 A (k5_convex4 A B (k2_convex4 A)) B)) ) ) ) ).
tt(t23_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v5_qc_lang1 C A) =>  ( ((k21_qc_lang1 A C) = B)  |  ((k13_cqc_lang A C B) = (k15_qc_lang1 A (k21_qc_lang1 A C) (k13_cqc_lang A (k22_qc_lang1 A C) B))) ) ) ) ) ) ) ) ) ).
tt(t23_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k13_cqc_sim1 A (k6_cqc_lang A B)) = (k13_cqc_sim1 A B)) ) ) ) ) ).
tt(t23_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = k6_numbers) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 1) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 2) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 3) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 4) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 5) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 6) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 7) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 8) )  &  (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 9) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 B A) => (v2_cqc_the1 (k11_cqc_lang A C B) A)) ) ) ) ) ) ) ).
tt(t23_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r4_cqc_the3 A B (k1_cqc_the1 A B))) ) ) ) ).
tt(t23_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k9_csspace4 A B)) &  ((v3_normsp_0 (k9_csspace4 A B)) & (v8_clvect_1 (k9_csspace4 A B))) ) ) ) ) ) ).
tt(t23_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k4_algstr_0 A B) C) = (k4_xcmplx_0 (k12_csspace A B C))) ) ) ) ) ) ) ).
tt(t23_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_decomp_1 C A B) <=>  ((v8_decomp_1 C A B) & (v14_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t23_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k2_finseq_1 64)) &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  ( (~  (A = 16) )  &  ( (~  (A = 17) )  &  ( (~  (A = 18) )  &  ( (~  (A = 19) )  &  ( (~  (A = 20) )  &  ( (~  (A = 21) )  &  ( (~  (A = 22) )  &  ( (~  (A = 23) )  &  ( (~  (A = 24) )  &  ( (~  (A = 25) )  &  ( (~  (A = 26) )  &  ( (~  (A = 27) )  &  ( (~  (A = 28) )  &  ( (~  (A = 29) )  &  ( (~  (A = 30) )  &  ( (~  (A = 31) )  &  ( (~  (A = 32) )  &  ( (~  (A = 33) )  &  ( (~  (A = 34) )  &  ( (~  (A = 35) )  &  ( (~  (A = 36) )  &  ( (~  (A = 37) )  &  ( (~  (A = 38) )  &  ( (~  (A = 39) )  &  ( (~  (A = 40) )  &  ( (~  (A = 41) )  &  ( (~  (A = 42) )  &  ( (~  (A = 43) )  &  ( (~  (A = 44) )  &  ( (~  (A = 45) )  &  ( (~  (A = 46) )  &  ( (~  (A = 47) )  &  ( (~  (A = 48) )  &  ( (~  (A = 49) )  &  ( (~  (A = 50) )  &  ( (~  (A = 51) )  &  ( (~  (A = 52) )  &  ( (~  (A = 53) )  &  ( (~  (A = 54) )  &  ( (~  (A = 55) )  &  ( (~  (A = 56) )  &  ( (~  (A = 57) )  &  ( (~  (A = 58) )  &  ( (~  (A = 59) )  &  ( (~  (A = 60) )  &  ( (~  (A = 61) )  &  ( (~  (A = 62) )  &  ( (~  (A = 63) )  &  (~  (A = 64) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_dickson A) =>  ( ((v16_waybel_0 A) & (v1_wellfnd1 (k5_dickson A)))  <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_card_1 (k6_dickson A B)) = 1) ) ) ) ) ) ) ).
tt(t23_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers D E) B) (k2_nat_1 A 1)) C) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) (k2_nat_1 A 1)) C) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 E B) (k2_nat_1 A 1)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_zfmisc_1 A B C D) =>  ((k11_diff_1 (k1_fcont_1 E F) A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C (k9_real_1 A (k10_real_1 B 2)) (k7_real_1 A (k10_real_1 B 2))) = (k10_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C B) 1) A) B)) ) ) ) ) ) ) ).
tt(t23_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) (k7_real_1 A B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) A))) ) ) ) ) ) ).
tt(t23_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k5_card_1 B) = (k2_dilworth A))  =>  ((k4_subset_1 (u1_struct_0 A) (k4_dilworth A B) (k3_dilworth A B)) = (k2_struct_0 A)) ) ) ) ) ) ).
tt(t23_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  ( (~  ((r2_diraf A B C D E) & (r2_diraf A B C F G)) )  &  ( (~  ((r2_diraf A B C D E) & (r2_diraf A F G B C)) )  &  ( (~  ((r2_diraf A D E B C) & (r2_diraf A F G B C)) )  &  (~  ((r2_diraf A D E B C) & (r2_diraf A B C F G)) ) ) ) ) )  &  (~ (r2_diraf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v1_dist_1 B A) & (v1_dist_1 C A))  => (r1_dist_1 A B C)) ) ) ) ) ) ) ).
tt(t23_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ((k8_mcart_1 A B C D) = (a_4_1_domain_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t23_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v2_finsub_1 B) => (v2_finsub_1 (k5_dynkin A B))) ) ) ) ) ).
tt(t23_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  ( (D = (k4_nat_d A C))  =>  ((k2_binom (k9_int_3 C) D B) = (k4_nat_d (k1_newton A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t23_ec_pf_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 C))) =>  ( ( (D = (k6_int_1 A C))  &  ( (E = (k6_int_1 B C))  &  (A = (k2_xcmplx_0 B 1)) ) )  =>  ((k5_algstr_0 (k9_int_3 C) (k8_group_1 (k9_int_3 C) D F) F) = (k8_group_1 (k9_int_3 C) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) => (m1_subset_1 B A)) ) ) ) ).
tt(t23_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  => (v4_matrprob (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B)))) ) ) ) ).
tt(t23_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k2_tarski A B) (k4_enumset1 C D E F G H))) ) ) ) ) ) ) ) ) ).
tt(t23_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((r2_hidden B (k6_eqrel_1 A A C D)) <=>  ((k6_eqrel_1 A A C D) = (k6_eqrel_1 A A C B)) ) ) ) ) ) ) ) ).
tt(t23_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v4_msualg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m1_msafree D A B) =>  (! [E:$i] :  ( ((v2_relat_1 E) & (m1_msafree E A C))  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r2_pboole (u1_struct_0 A) E (k9_pboole (u1_struct_0 A) D F)) & (r1_msualg_3 A B C F))  => (r2_msualg_3 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u2_e_siec A)))) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))))  &  ((k3_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A)))) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) ) ) ) ).
tt(t23_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k4_algstr_0 (k15_euclid A) B) (k4_algstr_0 (k15_euclid A) C)) = (k23_rvsum_1 B C)) ) ) ) ) ) ) ).
tt(t23_euclid_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k3_finseq_1 A) = 2)  &  (B = A) )  =>  ((k12_euclid B) = (k12_euclid A)) ) ) ) ) ) ).
tt(t23_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k6_euclid A B) C) = (k1_real_1 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t23_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 A (k3_rlvect_1 (k15_euclid 3) B C)) = (k3_rlvect_1 (k15_euclid 3) (k5_euclid_5 A B) (k5_euclid_5 A C))) ) ) ) ) ) ) ).
tt(t23_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_zfmisc_1 A B C) & (r1_xxreal_0 (k4_euclid_3 A B C) k32_sin_cos))  =>  ((r1_xxreal_0 (k4_euclid_3 B C A) k32_sin_cos) & (r1_xxreal_0 (k4_euclid_3 C A B) k32_sin_cos)) ) ) ) ) ) ) ) ).
tt(t23_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  ( ((v5_valued_0 C) &  ((r1_tarski (k2_relset_1 k5_numbers C) (k4_finseq_1 B)) &  ((r2_relset_1 k5_numbers (k1_euclid A) D (k1_partfun1 k5_numbers k5_numbers k5_numbers (k1_euclid A) C B)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((r2_hidden E (k2_relset_1 k5_numbers C)) |  ((k1_funct_1 B E) = (k5_euclid A)) ) ) ) ) ) ) )  =>  ((k5_euclid_7 A B) = (k5_euclid_7 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) =>  ((v3_pre_topc B (k3_pcomps_1 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k5_numbers))  =>  (~ (r1_tarski (k4_euclid_9 A C (k13_complex1 1 D)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) k1_numbers)))) ) ) ) ) ) ).
tt(t23_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid E)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid E)) =>  ((k7_euclid E (k7_euclid E (k9_euclid E F A) (k9_euclid E G B)) (k7_euclid E (k9_euclid E F C) (k9_euclid E G D))) = (k7_euclid E (k9_euclid E F (k7_real_1 A C)) (k9_euclid E G (k7_real_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_analmetr B C D) &  (A = (k2_analmetr B C D)) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) &  ((v1_euclmetr A) &  ((v2_euclmetr A) &  ((v3_euclmetr A) &  ((v4_euclmetr A) &  ((v5_euclmetr A) &  ((v6_euclmetr A) &  ((v7_euclmetr A) & (l1_analmetr A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) )  =>  ( ((k9_xtuple_0 C) = (k6_subset_1 A B))  =>  ((v1_xboole_0 C) |  ( ((k1_exchsort C) = B)  &  ((k2_exchsort C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t23_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) =>  ((k6_extpro_1 A B C D) = (k5_extpro_1 A B C D (k8_extpro_1 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t23_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  ( ((r1_xxreal_0 (k3_extreal1 A) B) & (r1_xxreal_0 (k3_extreal1 C) D))  => (r1_xxreal_0 (k3_extreal1 (k3_supinf_2 A C)) (k3_supinf_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t23_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  ((k2_circcomb A B) = (k2_circcomb B A)) ) ) ) ) ).
tt(t23_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k19_facirc_1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k1_facirc_1) (k9_facirc_1 A B C k1_facirc_1)) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_facirc_1) (k4_tarski (k10_finseq_1 B C) k3_facirc_1) (k4_tarski (k10_finseq_1 C A) k3_facirc_1))) (k1_tarski (k17_facirc_1 A B C)))) ) ) ) ).
tt(t23_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((k8_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A) (k1_seq_4 k6_numbers)) = k1_xboole_0) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers B) A))) ) ) ) ).
tt(t23_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))  =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))) ) ) ) ) ) ) ) ).
tt(t23_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k19_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k18_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t23_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_fdiff_9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k1_sin_cos9 B)) (k8_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k1_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t23_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 D C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 D C) E) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 B A) &  ( ((v3_rcomp_1 (k7_relset_1 k1_numbers k1_numbers B A)) & (m1_subset_1 (k7_relset_1 k1_numbers k1_numbers B A) (k1_zfmisc_1 k1_numbers)))  & (r2_fdiff_1 C (k7_relset_1 k1_numbers k1_numbers B A))) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k2_fdiff_1 C (k7_relset_1 k1_numbers k1_numbers B A))) (k2_fdiff_1 B A)))) ) ) ) ) ) ) ) ).
tt(t23_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k9_real_1 E A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers))  &  ( ((k1_seq_1 D E) = (k7_real_1 E A))  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) E) = (k10_real_1 (k8_real_1 2 A) (k9_real_1 (k5_square_1 E) (k5_square_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) k3_taylor_1))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = A) ) ) )  &  ( (D = (k1_taylor_1 2))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E B) & (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E B) & (r1_xxreal_0 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) E) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) k3_taylor_1) B) E) = (k10_real_1 (k8_real_1 (k8_real_1 4 A) E) (k9_real_1 (k2_newton A 2) (k2_newton E 4)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B) A) C) = (k8_real_1 2 (k26_sin_cos (k8_real_1 2 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t23_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ( ((k1_seq_1 C E) = 1)  &  ( (~ (r1_xxreal_0 (k1_seq_1 B E) k6_numbers))  &  (~  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))) A) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))) A) E) = (k1_seq_1 k1_sin_cos6 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A) B) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t23_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers A)) A) B) = (k10_real_1 (k9_real_1 (k1_seq_1 k19_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t23_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k9_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A))) & (r1_tarski (k10_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A)))) ) ) ).
tt(t23_fib_num2,ax, ((k1_pre_ff 4) = 3) ).
tt(t23_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_xcmplx_0 (k1_fib_num3 (k1_nat_1 A 3)) (k4_nat_1 2 (k1_fib_num3 A))) = (k4_nat_1 5 (k1_pre_ff A))) ) ) ).
tt(t23_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((v1_abian A) |  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k2_int_1 (k6_xcmplx_0 (k3_xcmplx_0 k1_fib_num (k1_pre_ff A)) 1))) ) ) ) ) ).
tt(t23_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_finseq_1 D A) =>  (! [E:$i] :  ((m1_finseq_1 E A) =>  (! [F:$i] :  ((m1_finseq_1 F A) =>  ( ( (F = (k9_finseq_1 C))  &  ( (D = (k11_finseq_1 C B C))  &  (E = (k10_finseq_1 B C)) ) )  =>  ( (B = C)  |  ((r1_filerec1 A F D F) & (r1_filerec1 A E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B C) => (r1_tarski (k2_filter_0 A B) (k3_filter_0 A C))) ) ) ) ) ) ) ).
tt(t23_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v2_binop_1 C A) & (v2_binop_1 D B))  <=> (v2_binop_1 (k6_filter_1 A B C D) (k2_zfmisc_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t23_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_hidden C B)) ) ) ) ) ) ).
tt(t23_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 (k2_nat_1 (k3_finseq_1 A) 1) C) & (r1_xxreal_0 C (k2_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))))  =>  ((k1_funct_1 (k7_finseq_1 A B) C) = (k1_funct_1 B (k6_xcmplx_0 C (k3_finseq_1 A)))) ) ) ) ) ) ) ) ).
tt(t23_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (~  ( ((k3_finseq_1 D) = (k2_xcmplx_0 A B))  &  (! [E:$i] :  ((m2_finseq_1 E C) =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  (~  ( ((k3_finseq_1 E) = A)  &  ( ((k3_finseq_1 F) = B)  &  (D = (k8_finseq_1 C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k1_relset_1 k5_numbers A)) => (m1_subset_1 B k5_numbers)) ) ) ) ).
tt(t23_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r2_hidden (k4_finseq_4 A B) (k8_relat_1 A (k1_tarski B)))) ) ) ) ).
tt(t23_finseq_5,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k17_finseq_1 A (k3_finseq_1 B) (k8_finseq_1 A B C)) = B) ) ) ) ) ) ).
tt(t23_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  (~  ((k4_finseq_4 (k11_finseq_1 A C B) B) = 3) ) ) ) ) ) ) ) ).
tt(t23_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k2_finseq_7 A (k2_finseq_4 A B C) 1 2) = (k2_finseq_4 A C B)) ) ) ) ) ) ) ).
tt(t23_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r4_finseq_8 A B C) => (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(t23_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C A) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C A) B)))) )  =>  (! [G:$i] :  ( ((v3_card_1 G E) & (m2_finseq_1 G C))  =>  ((k4_funcop_1 F G D) = (k3_relat_1 G (k4_funcop_1 F (k6_partfun1 C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k12_fintopo2 A C)) <=>  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D (k6_fintopo2 A B)) & (r1_xboole_0 (k7_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) B)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski B (k3_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t23_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_fintopo4 A B C) => (r1_xboole_0 (k7_fin_topo A B) C)) ) ) ) ) ) ) ).
tt(t23_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_fin_topo B A) => (v3_fin_topo (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t23_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_flang_1 A B (k2_xcmplx_0 C 1)) = (k6_flang_1 A (k7_flang_1 A B C) B)) ) ) ) ) ) ).
tt(t23_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 E F))  => (r1_tarski (k1_flang_2 A B D E) (k1_flang_2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A B (k1_flang_3 A B C)) = (k6_flang_1 A (k1_flang_3 A B C) B)) ) ) ) ) ) ).
tt(t23_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k8_relat_1 (k2_xboole_0 B C) A) = (k2_xboole_0 (k8_relat_1 B A) (k8_relat_1 C A))) ) ) ) ) ) ).
tt(t23_fomodel2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v4_fomodel2 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v4_fomodel2 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ( (~ (v15_fomodel1 D B))  =>  ( (D = (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) E) C))  <=>  ( (A = (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) D))  &  ( (E = (k40_fomodel2 B D))  &  (C = (k41_fomodel2 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_frechet A) =>  ((v3_frechet A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k1_frechet2 A (k1_struct_0 A)) = k1_xboole_0)  &  ((r1_tarski B (k1_frechet2 A B)) &  ( ((k1_frechet2 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k1_frechet2 A B) (k1_frechet2 A C)))  &  ((k1_frechet2 A (k1_frechet2 A B)) = (k1_frechet2 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_frechet A) => (v3_frechet A)) ) ) ).
tt(t23_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k8_fscirc_1 A B C)))) ) ) ) ) ) ) ).
tt(t23_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k4_fscirc_1 A B C) (k7_fscirc_1 A B C) D 2) (k4_fscirc_1 A B C) (k7_fscirc_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r6_fsm_1 A B C D E G) & (r6_fsm_1 A B C E F G))  => (r6_fsm_1 A B C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers)))  =>  ( ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C B) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = B) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C B))  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = C) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r3_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C) (k2_square_1 B C))) ) ) ) ) ) ) ).
tt(t23_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) C)) =>  (~  ( ((k2_xtuple_0 (k1_funct_1 D 1)) = B)  &  ( ((k2_xtuple_0 (k1_funct_1 D (k3_finseq_1 D))) = (k2_flang_1 A))  & (r1_xxreal_0 (k3_finseq_1 D) (k1_afinsq_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (~  ((k2_msafree2 (k13_ftacell1 A B C D E)) = (k3_enumset1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((k5_relat_1 A D) = (k5_relat_1 B D))  =>  ((k5_relat_1 (k3_funcop_1 E A C) D) = (k5_relat_1 (k3_funcop_1 E B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_funcsdom,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k10_xtuple_0 A) = (k9_xtuple_0 B))  &  ((k3_relat_1 A B) = A) )  =>  (B = (k4_relat_1 (k9_xtuple_0 B))) ) ) ) ) ) ).
tt(t23_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((r2_relset_1 A A (k1_partfun1 A B B A C D) (k6_partfun1 A)) =>  ((v2_funct_1 C) & (v2_funct_2 D A)) ) ) ) ) ) ) ) ).
tt(t23_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k7_relat_1 (k3_funct_3 B) A) (k1_zfmisc_1 (k9_xtuple_0 B)))) ) ) ).
tt(t23_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k5_relat_1 (k1_funct_4 A B) (k9_xtuple_0 B)) = B) ) ) ) ) ).
tt(t23_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k9_xtuple_0 (k3_funct_5 A)) = (k10_xtuple_0 (k9_xtuple_0 A))) ) ) ).
tt(t23_funct_6,ax, ( ((k2_funct_6 k1_xboole_0) = k1_xboole_0)  &  ((k3_funct_6 k1_xboole_0) = k1_xboole_0) ) ).
tt(t23_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_funcop_1 (k7_finseq_1 A B)) =>  ((v1_funcop_1 A) & (v1_funcop_1 B)) ) ) ) ) ) ).
tt(t23_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r1_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t23_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k1_fdiff_9 (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) ) ).
tt(t23_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_functor0 A B C) D E) = (k4_tarski (k3_functor0 A B C E) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  ((r1_functor2 A B C D) => (r8_pboole (u1_struct_0 A) (k7_functor3 A B B C D (k12_functor0 B) (k12_functor0 B) E (k4_functor2 B B (k12_functor0 B))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k1_fuzzy_1 A B C) (k2_fuzzy_1 A B C))) ) ) ) ) ) ).
tt(t23_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A (k1_fuzzy_2 A B (k2_fuzzy_1 A C D)) (k1_fuzzy_1 A (k1_fuzzy_1 A B C) D)) (k1_fuzzy_2 A B (k6_fuzzy_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t23_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A C) k1_numbers (k4_fuzzy_4 A B C D (k4_fuzzy_2 B C)) (k4_fuzzy_2 A C))) ) ) ) ) ) ) ) ).
tt(t23_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ((v3_fvaluat1 A) =>  ( (B = (k4_struct_0 A))  |  ( (C = (k4_struct_0 A))  |  ((k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A B C)) = (k2_supinf_2 (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  (D = (k1_funct_1 E A)) )  =>  ((k1_funct_1 (k6_fvsum_1 B C E) A) = (k4_algstr_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 (k17_gate_1 A B C D)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) & (v1_xboole_0 D)) ) ) ) ) ) ) ) ).
tt(t23_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  ((r4_gcd_1 A C D) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t23_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((r1_xxreal_0 (k3_finseq_1 E) A) & (r1_xxreal_0 (k3_finseq_1 E) B))  =>  ((k9_genealg1 D E F C A B) = (k7_genealg1 D E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_geomtrap A B C D E D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k7_gfacirc1 A B C) (k8_gfacirc1 A B C) D 2) (k7_gfacirc1 A B C) (k8_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k3_msafree2 (k5_gfacirc2 (k1_nat_1 A 1) B C)) = (k2_xboole_0 (k3_msafree2 (k5_gfacirc2 A B C)) (k3_msafree2 (k25_gfacirc1 (k1_funct_1 B (k1_nat_1 A 1)) (k1_funct_1 C (k1_nat_1 A 1)) (k7_gfacirc2 A B C))))) ) ) ) ) ) ) ).
tt(t23_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v3_glib_000 A) & (v4_glib_000 A)) ) ) ) ) )  =>  ((k7_glib_000 A) = k1_xboole_0) ) ) ).
tt(t23_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_001 A C D B) <=> (r1_glib_001 A D C (k6_glib_001 A B))) ) ) ) ) ) ) ).
tt(t23_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_002 B) & (m1_glib_000 B A))  =>  ((v9_glib_000 B A) => (v1_glib_002 A)) ) ) ) ) ).
tt(t23_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((k10_glib_003 A B) = (k10_glib_003 A (k6_glib_001 A B))) ) ) ) ) ).
tt(t23_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_glib_003 D) &  ((v4_glib_003 D A) & (m2_glib_000 D A (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C))) (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)))) )  =>  ((r1_glib_004 A D B) &  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)))) =>  ((k1_glib_004 A B E) = (k1_seq_1 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k9_glib_004 A (k10_glib_004 A B) C)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  ( ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 A)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 C D F G)) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 B)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B E) = (k3_matrix_1 C D F G)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B) E) = (k3_matrix_1 C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 B) &  ((v5_goboard1 B) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B))) )  =>  ((v3_relat_1 B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_goboard5 B A) (k1_goboard5 B (k2_nat_1 A 1))) = (a_2_10_goboard5 A B)) ) ) ) ) ) ) ).
tt(t23_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 B (k3_finseq_1 B) A)) = (a_2_3_goboard6 A B)) ) ) ) ) ) ) ).
tt(t23_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 A)) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))))  &  ( (~  ( (B = D)  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1) C)) = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) ) )  &  ( (~  ( (B = (k2_nat_1 D 1))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C))) ) )  &  (~  ( ((k2_nat_1 B 1) = D)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1)) (k18_euclid C))) ) ) )  => (r1_xboole_0 B (k3_topreal1 2 A))) ) ) ) ) ).
tt(t23_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_goboard9 A) = (k2_goboard9 (k1_goboard9 A))) ) ) ).
tt(t23_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((v3_goboard1 B) & (r1_xxreal_0 1 A))  =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k2_goboard5 B A) = (a_2_1_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t23_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C)) ) ) ) ) ) )  =>  ((k3_gobrd13 D E A) = (k3_goboard5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k3_goboard9 B)) & (r1_xxreal_0 (k17_euclid A) (k6_pscomp_1 (k3_topreal1 2 B)))) ) ) ) ) ) ).
tt(t23_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_henmodel A B (k5_cqc_lang A))) ) ) ) ).
tt(t23_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_graph_1 B) & (l1_graph_1 B)) )  =>  ((r4_graph_1 A B) =>  ( ((k5_graph_1 A B) = B)  &  ((k5_graph_1 B A) = B) ) ) ) ) ) ) ).
tt(t23_graph_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~  (A = B) )  &  ( (~ (r1_xxreal_0 C 1))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_finseq_1 D) &  ((v1_graph_2 D) & (v2_graph_2 D)) ) ) )  =>  (~  ( ((k10_xtuple_0 D) = (k2_tarski A B))  &  ( ((k3_finseq_1 D) = C)  &  ((k1_funct_1 D 1) = A) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_card_1 (k6_graph_3 A B)) = (k9_graph_1 A B)) ) ) ) ) ).
tt(t23_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) )  =>  ((v2_funct_1 B) &  ((v7_graph_1 B A) & (m2_graph_1 B A)) ) ) ) ) ) ).
tt(t23_graph_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u4_struct_0 C)) =>  ((r1_tarski (k7_subset_1 (u1_struct_0 C) (k2_graph_5 C (k8_finseq_1 (u4_struct_0 C) D E)) A) B) =>  ((r1_tarski (k7_subset_1 (u1_struct_0 C) (k2_graph_5 C D) A) B) & (r1_tarski (k7_subset_1 (u1_struct_0 C) (k2_graph_5 C E) A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k8_graph_5)))) )  =>  ((r1_xxreal_0 k6_numbers (k12_graphsp A B C D)) <=>  (? [E:$i] :  ((r2_hidden E (u4_struct_0 A)) & (r1_graph_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  ( ((k7_grcat_1 (k11_grcat_1 A)) = A)  &  ( ((k8_grcat_1 (k11_grcat_1 A)) = A)  &  ( (! [B:$i] :  ( ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  ( ((k8_grcat_1 B) = A)  =>  ((k13_grcat_1 (k11_grcat_1 A) B) = B) ) ) )  &  (! [B:$i] :  ( ((v1_grcat_1 B) &  ((v2_grcat_1 B) & (l1_grcat_1 B)) )  =>  ( ((k7_grcat_1 B) = A)  =>  ((k13_grcat_1 B (k11_grcat_1 A)) = B) ) ) ) ) ) ) ) ) ).
tt(t23_gr_cy_1,ax, (k2_gr_cy_1 = (k5_group_4 k2_gr_cy_1 (k6_domain_1 (u1_struct_0 k2_gr_cy_1) (k5_gr_cy_1 1)))) ).
tt(t23_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (A = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) &  ((v1_group_6 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) )  =>  ((r1_struct_0 (k10_group_6 C A D) B) => (v2_funct_2 D (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t23_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~  (A = 2) )  =>  ((k4_nat_d (k1_gr_cy_3 A) (k4_nat_1 2 A)) = 1) ) ) ) ).
tt(t23_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) =>  ((k5_relat_1 B (k9_xtuple_0 A)) = A) ) ) ) ) ) ).
tt(t23_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k13_group_2 B (k2_grsolv_1 A B C D) (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k13_group_2 A D (k6_algstr_0 A E F))))  &  ((k5_group_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F) (k14_group_2 B (k2_grsolv_1 A B C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k5_group_2 A F (k14_group_2 A D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r1_groeb_1 A B C E) =>  ((r2_hidden D (k7_ideal_1 (k11_polynom1 A C) E)) <=> (r1_rewrite1 (k3_polyred A B C E) D (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_groeb_1 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) &  ((r2_hidden F D) & (r4_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) G)) )  => (r8_pboole (k15_pre_poly A) G (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))))  => (r2_hidden (k3_termord A B C D) (k3_groeb_3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k1_group_11 A B D) (k1_group_11 A C D)) (k1_group_11 A (k4_subset_1 (u1_struct_0 A) B C) D))) ) ) ) ) ) ) ) ).
tt(t23_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r1_finseqop (u1_struct_0 A) (k3_group_1 A) (u2_algstr_0 A))) ) ).
tt(t23_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k2_group_1 A C) B)) ) )  =>  ((k1_group_2 A B) = B) ) ) ) ) ) ).
tt(t23_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_3 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A (k2_group_3 A B D) (k2_group_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t23_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k4_group_4 C (k2_finseq_4 k4_numbers (k2_group_4 A) (k2_group_4 B)) (k2_finseq_4 (u1_struct_0 C) D E)) = (k2_finseq_4 (u1_struct_0 C) (k5_group_1 C A D) (k5_group_1 C B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_3 A (k2_group_5 A B C) D) = (k2_group_5 A (k2_group_3 A B D) (k2_group_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t23_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  ((r1_struct_0 (k5_group_6 A C) B) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (B = (k13_group_2 A C D))  &  (B = (k14_group_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_group_7 (k11_finseq_1 A B C)) & (v2_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (~  ( (~  (A = (k6_group_2 A)) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_group_1 A)) ) ) ) ) ) ) ).
tt(t23_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) &  ((v4_group_9 D A B) & (m1_group_9 D A B)) )  =>  (? [E:$i] :  ( ((v2_group_9 E A) &  ((v4_group_9 E A B) & (m1_group_9 E A B)) )  &  ((u1_struct_0 E) = (k2_group_2 B (k15_group_9 A B C) (k15_group_9 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t23_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  ((v2_group_10 B A) => (r1_xxreal_0 (k2_groupp_1 A C) (k2_groupp_1 A B))) ) ) ) ) ) ) ).
tt(t23_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ) ) ).
tt(t23_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (u1_normsp_0 A)) &  ((v1_funct_2 (u1_normsp_0 A) (u1_struct_0 A) k1_numbers) &  ((v1_hahnban (u1_normsp_0 A) A) &  ((v6_hahnban (u1_normsp_0 A) A) & (m1_subset_1 (u1_normsp_0 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ) ) ).
tt(t23_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v2_relat_1 B) & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m3_hallmar1 D A B C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((k1_funct_1 D C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (r2_hidden D C)) )  => (r1_xxreal_0 (k1_funct_1 (k5_weierstr A B) D) (k10_weierstr A B C))) ) ) ) ) ) ) ) ) ).
tt(t23_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k3_glib_001 A B) = (k3_glib_001 A C))  =>  ((r1_tarski B C) | (r1_xxreal_0 (k2_nat_1 (k3_finseq_1 (k1_helly B C)) 2) (k3_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t23_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  ((k8_vectsp10 k1_complfld A B) = (k8_vectsp10 k1_complfld A (k1_hermitan A B))) ) ) ) ) ).
tt(t23_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  ((k4_lattices (k12_normform A) B (k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k8_heyting1 A) B)) = (k5_lattices (k12_normform A))) ) ) ) ).
tt(t23_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k4_partfun1 A B)))  => (r2_hidden C (k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) C))) ) ) ) ) ).
tt(t23_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_tarski (k2_heyting3 A B) (k2_heyting3 C B)) =>  (A = C) ) ) ) ) ) ) ) ).
tt(t23_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 B A) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 1) (k2_fdiff_1 B A))) ) ) ) ) ).
tt(t23_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield C A B) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t23_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ( ((r2_hidden (k3_hilbert1 A B) k6_hilbert1) & (r2_hidden (k3_hilbert1 B C) k6_hilbert1))  => (r2_hidden (k3_hilbert1 A C) k6_hilbert1)) ) ) ) ) ) ) ).
tt(t23_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (~  ((k4_hilbert1 A B) = k2_hilbert1) ) ) ) ) ) ).
tt(t23_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (C = k1_xboole_0)  &  ( (~  (B = k1_xboole_0) )  &  (~  (A = k1_xboole_0) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B C))))) )  => (r1_tarski (k10_xtuple_0 (k2_pralg_2 D)) (k1_funct_2 A C))) ) ) ) ) ) ).
tt(t23_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  (B = (k9_polynom3 A)) )  &  ( (~  (C = (k9_polynom3 A)) )  &  (~  ((k2_hurwitz A (k11_polynom3 A B C)) = (k2_xcmplx_0 (k2_hurwitz A B) (k2_hurwitz A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_idea_1 A B) &  ((r1_idea_1 A C) & (r1_idea_1 A D)) ) )  =>  ((k9_idea_1 A (k9_idea_1 A B C) D) = (k9_idea_1 A B (k9_idea_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t23_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_ideal_1 D A B) => (m1_ideal_1 (k9_fvsum_1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t23_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A D C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A B D) & (r3_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) =>  ((k14_index_1 A B B C D) = (k13_index_1 A E (k9_cat_1 A B E C (k9_index_1 B D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((l3_msualg_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 B)) =>  ( (G = (k1_funct_1 D F))  =>  ((k5_msualg_1 A F (k1_instalg1 A B E C D)) = (k5_msualg_1 B G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 C A))  =>  ((r1_xxreal_0 B (k5_real_1 A 1)) |  ((r1_xxreal_0 C (k5_real_1 A 1)) |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t23_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~  ( (A = k6_numbers)  &  (B = k6_numbers) ) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (A = (k3_xcmplx_0 (k3_int_2 A B) C))  &  ( (B = (k3_xcmplx_0 (k3_int_2 A B) D))  & (r1_int_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ( ((k4_nat_d A C) = (k4_nat_d B C))  <=> (r1_int_1 C (k6_xcmplx_0 A B))) ) ) ) ) ) ) ) ).
tt(t23_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~ (r1_xxreal_0 B 2))  &  ( ((k3_int_2 A B) = 1)  &  ( ((k3_int_2 C B) = 1)  &  ((r1_int_5 A B) &  ( (~ (r1_int_5 C B))  & (r1_int_5 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ( (~ (v2_relat_1 A))  &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  ((k19_rvsum_1 A) = k6_numbers) ) ) ).
tt(t23_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k7_group_1 (k3_int_7 A)) = (k6_xcmplx_0 A 1)) ) ) ).
tt(t23_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 k6_numbers (k8_real_1 2 k32_sin_cos)))  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) k16_sin_cos)) = k6_numbers) ) ) ) ) ) ).
tt(t23_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r1_tarski G (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 D H) = (k9_binop_2 (k11_binop_2 A H) B))  &  ((k1_seq_1 E H) = 1) ) ) ) )  &  ( (G = (k1_relset_1 k1_numbers F))  & (r2_relset_1 k1_numbers k1_numbers F (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k1_sin_cos6 A) (k3_rfunct_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))))))) ) ) )  =>  ((k2_integra5 C F) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_sin_cos6) (k4_seq_4 C)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_sin_cos6) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos)) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t23_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1))) &  ( (B = (k1_relset_1 k1_numbers k29_sin_cos))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos A))) ) )  =>  ((k2_integra5 A k29_sin_cos) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t23_integr15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden C (k1_relset_1 B (k9_integr15 A E B D))) =>  ((k7_partfun1 (k1_euclid A) (k9_integr15 A E B D) C) = (k9_euclid A (k7_partfun1 (k1_euclid A) D C) E)) ) ) ) ) ) ) ) ) ) ).
tt(t23_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k1_rcomp_1 D C))  =>  ((k1_binop_2 (k7_integr16 B A)) = (k8_integr16 C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t23_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid E)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 E (k3_integra5 A B) F) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 E k1_numbers F)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid E) F (k3_integra5 A B)) E) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 C D) (k1_nfcont_4 E k1_numbers F)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 E k1_numbers F) (k3_integra5 C D))) &  ((r1_xxreal_0 (k12_euclid (k12_integr15 C D E F)) (k4_integra5 C D (k1_nfcont_4 E k1_numbers F))) & (r1_xxreal_0 (k12_euclid (k12_integr15 D C E F)) (k4_integra5 C D (k1_nfcont_4 E k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ((k18_rvsum_1 (k5_integra1 A (k7_rfunct_1 A A) B)) = (k3_integra1 A)) ) ) ) ) ).
tt(t23_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers)))) )  =>  (! [E:$i] :  ((m1_integra1 E C) =>  ( ((r2_hidden B (k4_finseq_1 E)) &  ((v1_seq_2 (k2_partfun1 C k1_numbers D C)) & (r1_xxreal_0 k6_numbers A)) )  =>  ((k1_seq_1 (k4_integra1 C (k26_valued_1 C k1_numbers D A) E) B) = (k8_real_1 A (k1_seq_1 (k4_integra1 C D E) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) & (v3_integra1 B A))  =>  ((v3_integra1 (k56_valued_1 A k1_numbers B) A) & (r1_xxreal_0 (k18_complex1 (k12_integra1 A B)) (k12_integra1 A (k56_valued_1 A k1_numbers B)))) ) ) ) ) ) ).
tt(t23_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 C D)) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 F G)) E)) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k18_complex1 (k4_integra5 C D F)) (k3_xcmplx_0 E (k6_xcmplx_0 D C))) & (r1_xxreal_0 (k18_complex1 (k4_integra5 D C F)) (k3_xcmplx_0 E (k6_xcmplx_0 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_integra7,ax,(r1_integra7 k1_numbers k16_sin_cos k19_sin_cos)).
tt(t23_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers A))) & (r2_fdiff_1 A B))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers A) B) C) = (k1_real_1 (k1_fdiff_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 D k1_numbers (k20_valued_1 D k1_numbers k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) D) (k1_integra5 C D)) (k20_valued_1 D k1_numbers k1_numbers (k1_integra5 A D) (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D)))) ) ) ) ) ) ) ) ).
tt(t23_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_interva1 D A))  => (r1_interva1 A (k4_interva1 A (k4_interva1 A B C) D) (k4_interva1 A B (k4_interva1 A C D)))) ) ) ) ) ) ) ) ).
tt(t23_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 A (k3_intpro_1 B C)) k8_intpro_1) => (r2_hidden (k3_intpro_1 B (k3_intpro_1 A C)) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t23_irrat_1,ax, ((v1_series_1 k5_irrat_1) &  ((k4_series_1 k5_irrat_1) = (k26_sin_cos 1)) ) ).
tt(t23_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r2_nattra_1 A B D E) =>  (! [F:$i] :  ((m2_nattra_1 F A B D E) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k4_nattra_1 A C (k9_cat_1 A B C D G) (k9_cat_1 A B C E G) (k4_isocat_1 A B C D E F G) H) = (k9_cat_3 B (k8_cat_1 A B D H) (k8_cat_1 A B E H) C G (k4_nattra_1 A B D E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_nattra_1 (k8_cat_2 A B) C D E) =>  (! [F:$i] :  ((m2_nattra_1 F (k8_cat_2 A B) C D E) =>  ((r2_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) &  (? [G:$i] :  ((m2_nattra_1 G A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C))))) )  =>  ((r1_funct_2 (u1_struct_0 (k8_cat_2 A B)) (u4_struct_0 C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) F H) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k4_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E) G I) = (k4_tarski (k9_cat_2 (k11_nattra_1 B C) (k11_nattra_1 B C) (k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) I) (k8_cat_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C E) I)) (k10_funct_5 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k9_funct_2 (u1_struct_0 B) (u4_struct_0 C)) (k11_funct_5 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_isomichi B A) <=>  ((v5_tops_1 (k2_pre_topc A B) A) & (v1_xboole_0 (k1_isomichi A B))) ) ) ) ) ) ).
tt(t23_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jgraph_1 (u1_struct_0 (k15_euclid 2)) A B) => (r1_tarski (k3_topreal1 2 B) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t23_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((v5_pre_topc B A k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k3_xcmplx_0 C F)) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_2_jgraph_3)  &  (B = a_0_3_jgraph_3) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = B) ) ) ) ) ) ).
tt(t23_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (C = a_0_0_jgraph_4)  &  (B = (a_1_0_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k17_euclid B)) =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 A (k10_real_1 (k18_euclid B) (k12_euclid B))) |  ( ((k12_euclid B) = k6_numbers)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  =>  ((r1_xxreal_0 k6_numbers (k17_euclid C)) &  (~ (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (D = (a_3_0_jgraph_6 A B C))  =>  ((r1_xxreal_0 C k6_numbers) | (v1_topreal2 D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid B) H) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (? [E:$i] :  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski E)) )  &  ( (~ (r2_hidden D (k3_topreal1 2 C)))  &  ( (~ (r1_xboole_0 (k3_topreal1 2 C) (k1_rltopsp1 (k15_euclid 2) A D)))  &  (~ (r1_xboole_0 (k3_topreal1 2 C) (k1_rltopsp1 (k15_euclid 2) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A E) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan13 A E))) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A E))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan13 A E) D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) B C))  & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 A E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( (~  (D = B) )  &  ( (~  (D = C) )  &  ( (~  (E = B) )  &  ( (~  (E = C) )  &  ( (~  (D = E) )  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) D E F) &  ((r1_tarski F A) & (r1_subset_1 F (k2_tarski B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B C D E) & (r1_jordan17 A E C D B))  =>  ( (B = C)  |  ( (B = D)  |  ( (C = E)  |  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r2_hidden A (k1_jordan2c 2 C)) & (r2_hidden B (k1_jordan2c 2 C)))  =>  ( ((k17_euclid A) = (k17_euclid B))  | (r2_zfmisc_1 (k1_jordan18 A C) (k2_jordan18 B C) (k1_jordan18 B C) (k2_jordan18 A C))) ) ) ) ) ) ) ) ).
tt(t23_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_matrix_1 B))) )  => (r1_xxreal_0 (k8_pscomp_1 (k3_topreal1 2 C)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A)))) ) ) ) ) ) ) ).
tt(t23_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_3_jordan1 A))  => (v3_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t23_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 A)) &  ((r2_hidden E (k3_goboard5 A B (k1_matrix_1 A))) &  ((k18_euclid E) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) B) |  ((k1_matrix_1 A) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k1_jordan2c 2 A)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 A C)) D))  &  ( (~ (r1_xxreal_0 E 1))  &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A C)) E))  &  ( (~  ((k17_euclid B) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A C) D E))) )  &  ((r2_hidden B (k3_goboard5 (k1_jordan8 A C) D E)) & (r1_tarski (k3_goboard5 (k1_jordan8 A C) D E) (k1_jordan2c 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A))) (k10_xtuple_0 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t23_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_xxreal_0 (k4_finseq_4 (k1_jordan1e B A) (k21_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k1_jordan1e B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ).
tt(t23_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  =>  ((k2_gobrd13 B (k2_goboard2 B) A) = (k4_goboard5 B A)) ) ) ) ) ) ).
tt(t23_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k22_pscomp_1 (k3_topreal1 2 A)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D (k2_nat_1 E 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k7_pscomp_1 A) (k7_pscomp_1 B)) =>  ((k7_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k7_pscomp_1 B)) ) ) ) ) ) ).
tt(t23_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k1_topreal6 2 (k5_algstr_0 (k15_euclid 2) A B) (k5_algstr_0 (k15_euclid 2) C B)) = (k1_topreal6 2 A C)) ) ) ) ) ) ) ).
tt(t23_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) &  ((r1_jordan5c A B C D E) & (r1_jordan5c A B C E F)) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k5_jordan6 A B C D E) (k5_jordan6 A B C E F)) = (k1_tarski E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((r1_tarski B A) &  ((r2_hidden (k18_pscomp_1 A) B) &  ((r2_hidden (k22_pscomp_1 A) B) &  ( (~ (r1_tarski (k8_jordan6 A) B))  &  (~ (r1_tarski (k9_jordan6 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k18_euclid (k1_jordan21 (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) (k18_euclid (k1_jordan21 A)))) ) ) ) ) ) ).
tt(t23_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 A) (k4_finseq_1 (k3_graph_2 A B)))) ) ) ) ).
tt(t23_jordan2b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_jordan2b A) = (k1_jordan2b B))  =>  (A = B) ) ) ) ) ) ).
tt(t23_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_jordan2c A B C) => (r1_tarski C (k2_jordan2c A B))) ) ) ) ) ) ) ).
tt(t23_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ( ((k1_funct_1 (k2_jordan3 A B) 1) = B)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 C (k3_finseq_1 (k2_jordan3 A B))) =>  ((r1_xxreal_0 C 1) |  ( ( (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1)))  =>  ((k1_funct_1 (k2_jordan3 A B) C) = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) C))) )  &  ( (~  (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1))) )  =>  ((k1_funct_1 (k2_jordan3 A B) C) = (k1_funct_1 A (k9_real_1 (k2_nat_1 (k1_jordan3 A B) C) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k1_jordan4 A B) = (k1_jordan4 (k2_nat_1 A (k7_nat_d (k3_finseq_1 B) 1)) B))  &  ((k1_jordan4 A B) = (k1_jordan4 (k2_nat_1 (k7_nat_d (k3_finseq_1 B) 1) A) B)) ) ) ) ) ) ).
tt(t23_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = B)  =>  ((v2_rcomp_1 A) <=> (v4_pre_topc B k3_topmetr)) ) ) ) ) ) ).
tt(t23_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = (k1_funct_1 A (k3_finseq_1 A))) )  &  ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  ((v4_topreal1 A) &  ( (~ (r2_hidden B (k3_topreal1 2 (k2_jordan3 A C))))  &  (~ (r2_hidden C (k3_topreal1 2 (k2_jordan3 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v4_topreal1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A))) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)))) ) ) ) ) ).
tt(t23_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_4_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t23_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k4_jordan6 A B C C) = (k1_tarski C)) ) ) ) ) ) ) ) ).
tt(t23_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_xxreal_0 2 (k1_matrix_1 B)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r2_hidden D (k16_matrix_1 B)) &  ((r2_hidden D (k2_topreal1 2 C A)) &  ( (~  (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A)) )  &  (~  (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden C (k2_jordan_a A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_xreal_0 C))  =>  ((k2_pre_topc (k15_euclid A) (k1_topreal9 A B C)) = (k2_topreal9 A B C)) ) ) ) ) ) ) ).
tt(t23_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) C) =>  (! [D:$i] :  ((v3_ordinal1 D) => (r3_lattices A (k6_knaster A B C D) C)) ) ) ) ) ) ) ) ) ).
tt(t23_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) &  ((v3_kurato_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [C:$i] :  ((r2_hidden C (k4_kurato_0 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 A) B (k2_nat_1 D E)))) ) ) ) ) ) ) ) ) ).
tt(t23_kurato_1,ax, ((k1_tops_1 k3_topmetr k6_kurato_1) = (k4_subset_1 k1_numbers (k2_rcomp_1 4 5) (k2_rcomp_1 5 k1_xxreal_0))) ).
tt(t23_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) )  =>  ((k1_kurato_2 A B) = (k2_pre_topc A C)) ) ) ) ) ) ) ) ).
tt(t23_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_finseq_1 A)) & (r2_hidden D (k2_finseq_1 A)))  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k12_matrix_2 A))) =>  ( (E = (a_3_1_laplace A C D))  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  ((k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) E (k11_matrix_3 A B F)) = (k8_group_1 B (k3_matrix_1 (u1_struct_0 B) F C D) (k6_laplace C D A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_group_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_group_4 A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((k4_lattices (k11_group_4 A) D E) = (k10_group_2 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B))) =>  ( ( ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r1_orders_2 (k1_latsum_1 A B) C D) & (r2_hidden D (u1_struct_0 A))) )  => (r2_hidden C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t23_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  => (r6_binop_1 (u1_struct_0 A) (u1_lattices A) (u2_lattices A))) ) ) ).
tt(t23_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r4_lattice3 B C A) <=> (r3_lattice3 B (k7_lattices B C) (a_2_0_lattice3 A B))) ) ) ) ) ) ).
tt(t23_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((k4_lattices A (k2_lattice4 A B) (k2_lattice4 A C)) = (k2_lattice4 A (k5_setwiseo (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t23_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((v4_ordinal1 C) &  ( ((k9_xtuple_0 B) = C)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D C) =>  ((k1_funct_1 B D) = (k8_lattice5 A D)) ) ) ) ) )  =>  ( (C = k1_xboole_0)  |  ((k8_lattice5 A C) = (k3_tarski (k10_xtuple_0 B))) ) ) ) ) ) ) ) ) ).
tt(t23_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v8_lattice6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k15_lattice3 A (a_3_0_lattice6 A B C))) ) ) ) ) ) ) ) ).
tt(t23_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) => (r1_relset_1 (k2_zfmisc_1 A A) (u1_struct_0 B) C (k6_lattice8 A B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t23_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_lattices A (k4_lattices A B C)) = (k3_lattices A (k7_lattices A B) (k7_lattices A C))) ) ) ) ) ) ) ).
tt(t23_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) & (r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))))  =>  ((r1_xxreal_0 (k1_recdef_1 (k5_lexbfs A B C) E) (k1_recdef_1 (k5_lexbfs A B C) D)) | (r2_hidden E (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B (k7_nat_d (k39_glib_000 B) (k1_recdef_1 (k5_lexbfs A B C) D)))))) ) ) ) ) ) ) ) ) ) ).
tt(t23_lfuzzy_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v5_relat_1 F (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B C) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) k1_numbers)))) ) )  =>  (! [G:$i] :  ( ((v5_relat_1 G (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C D) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C D) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A D) k1_numbers (k4_fuzzy_4 A C D (k4_fuzzy_4 A B C E F) G) (k4_fuzzy_4 A B D E (k4_fuzzy_4 B C D F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_fuzzy_4 A A A B (k5_fuzzy_4 A A)) B)) ) ) ) ).
tt(t23_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_limfunc1 A) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 C (k1_seq_1 B D))) ) ) ) ) )  | (v2_limfunc1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t23_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) | (r3_limfunc2 B A))  => (r2_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A)) ) ) ) ) ).
tt(t23_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  ( (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))))  &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) ) ) )  | (r3_limfunc3 B A)) ) ) ) ) ) ).
tt(t23_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r5_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k1_seq_1 B E) (k2_limfunc2 B A))) ) ) ) ) ) ) )  | (r5_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t23_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_lmod_6 A (k2_vectsp_5 A B C D) C) & (r1_lmod_6 A (k2_vectsp_5 A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t23_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( (~ (v2_struct_0 (k17_lmod_7 A B C)))  &  ((v13_algstr_0 (k17_lmod_7 A B C)) &  ((v7_vectsp_1 (k17_lmod_7 A B C) A) &  ((v8_vectsp_1 (k17_lmod_7 A B C) A) &  ((v9_vectsp_1 (k17_lmod_7 A B C) A) &  ((v10_vectsp_1 (k17_lmod_7 A B C) A) &  ((v11_vectsp_1 (k17_lmod_7 A B C) A) &  ((v2_rlvect_1 (k17_lmod_7 A B C)) &  ((v3_rlvect_1 (k17_lmod_7 A B C)) &  ((v4_rlvect_1 (k17_lmod_7 A B C)) & (l1_vectsp_1 (k17_lmod_7 A B C) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  => (m1_rlsub_1 (g1_rlvect_1 (k10_lopban_1 A B) (k10_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k8_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B)) (k9_rsspace (k8_lopban_1 A B) (k10_lopban_1 A B))) (k8_lopban_1 A B))) ) ) ) ).
tt(t23_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k9_lopban_2 A)) = (k6_lopban_2 A)) ) ) ).
tt(t23_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_seq_2 (k3_series_1 (k4_normsp_0 A B))) <=> (v2_lopban_3 B A)) ) ) ) ) ).
tt(t23_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k7_lopban_4 (k2_nat_1 D 1) A B C)) D) = (k3_rlvect_1 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k7_lopban_4 D A B C)) D) (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k6_lopban_4 (k2_nat_1 D 1) A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t23_lopclset,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) ) )  =>  ((r2_hidden A (k10_lopclset B)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  ((k3_funct_2 (u1_struct_0 B) (k9_setfam_1 (k7_lopclset B)) (k9_lopclset B) C) = A) ) ) ) ) ) ) ).
tt(t23_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) & (r2_hidden E (k9_lpspace1 A B C)))  => (r2_hidden (k3_valued_1 A k1_numbers k1_numbers D E) (k9_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ( ((v1_funct_1 (k8_lpspace1 A k6_numbers)) & (m1_subset_1 (k8_lpspace1 A k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  & (r2_hidden (k8_lpspace1 A k6_numbers) (k1_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t23_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((r1_ltlaxio1 B A) <=> (r2_ltlaxio1 B (k6_domain_1 k1_hilbert1 A))) ) ) ) ) ).
tt(t23_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k5_cqc_lang A)) (k4_cqc_the1 A))) ) ) ) ).
tt(t23_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A B (k6_rusub_4 A C D)) = (k3_mathmorp A (k3_mathmorp A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t23_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ((v2_matrix10 C) =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ) ).
tt(t23_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v12_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) =>  ((k2_matrix11 A C B) = (k1_group_1 C)) )  &  ( ( ((k2_matrix11 A C B) = (k1_group_1 C))  => (v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))))  &  ( ( (~ (v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))))  =>  ((k2_matrix11 A C B) = (k4_algstr_0 C (k1_group_1 C))) )  &  (~  ( ((k2_matrix11 A C B) = (k4_algstr_0 C (k1_group_1 C)))  & (v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((r2_hidden A (k4_finseq_1 (k12_matrix_1 C B))) =>  ( (D = (k4_struct_0 C))  |  ((r1_xxreal_0 B k6_numbers) |  ((k5_matrix_6 B C (k5_matrix12 B B C (k12_matrix_1 C B) A D)) = (k5_matrix12 B B C (k12_matrix_1 C B) A (k11_algstr_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  ( ( (B = 2)  &  (C = 2) )  =>  ((k1_matrix13 A D B C E F) = (k6_matrix_2 A (k3_matrix_1 A D (k1_funct_1 E 1) (k1_funct_1 F 1)) (k3_matrix_1 A D (k1_funct_1 E 1) (k1_funct_1 F 2)) (k3_matrix_1 A D (k1_funct_1 E 2) (k1_funct_1 F 1)) (k3_matrix_1 A D (k1_funct_1 E 2) (k1_funct_1 F 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_finseq_1 (k3_matrix14 A B C)) = B) ) ) ) ) ) ) ).
tt(t23_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( (D = (k1_matrix_3 B (k3_finseq_1 C) A))  =>  ((k8_matrix13 B C) = (k8_matrix13 B (k7_matrlin (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  ( ((v3_matrix16 E (u1_struct_0 B)) & (v3_matrix16 F (u1_struct_0 B)))  => (v3_matrix16 (k2_matrix_6 A B (k2_matrix13 A A B E C) (k2_matrix13 A A B F D)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (~ (r1_xxreal_0 A k1_xboole_0))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  ( ((k3_finseq_1 D) = A)  &  ( ((k1_matrix_1 D) = B)  &  ((k2_matrix_1 D) = (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) => (m1_subset_1 (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B) (u1_struct_0 (k13_matrix_2 A)))) ) ) ) ).
tt(t23_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 B)) =>  ( ((v1_binop_1 D C) &  ((v2_binop_1 D C) & (v1_binop_1 E C)) )  =>  ( ( ((k8_matrix_3 B A I H) = k1_xboole_0)  &  (~ (v1_setwiseo D C)) )  |  ((k7_setwiseo (k2_zfmisc_1 A B) C D (k8_matrix_3 A B H I) (k9_matrix_3 A B C E F G)) = (k7_setwiseo (k2_zfmisc_1 B A) C D (k8_matrix_3 B A I H) (k9_matrix_3 B A C E G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k3_matrix_3 A B D) = (k3_matrix_3 A (k3_matrix_3 A B C) (k1_matrix_4 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ((k1_matrix_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k6_matrix_5 (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A)) B) = (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 B))) ) ) ) ) ) ) ) ).
tt(t23_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k5_matrix_1 A (u1_struct_0 B) (k2_matrix_6 A B C D)) = (k2_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) (k5_matrix_1 A (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_matrix_7 A (k4_matrix_2 (u1_struct_0 A) B)) = (k4_matrix_2 (u1_struct_0 A) (k2_group_1 A B))) ) ) ) ) ).
tt(t23_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v2_matrix_8 C A B) & (r1_matrix_6 A B C D))  =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix_8 (k4_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 2 3 1))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) C G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ((k17_rvsum_1 (k1_complsp2 A)) = (k15_complex1 (k17_rvsum_1 A))) ) ) ) ).
tt(t23_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m1_matrix_1 E A (k2_wsierp_1 (k10_matrixj1 A (k5_matrixj1 A C D))) (k2_wsierp_1 (k11_matrixj1 A (k5_matrixj1 A C D)))) =>  ( (E = (k13_matrixj1 A B (k5_matrixj1 A C D)))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden F (k4_finseq_1 C)) =>  ((k8_matrix_1 A E F) = (k8_finseq_1 A (k8_matrix_1 A C F) (k5_finseq_2 A (k1_matrix_1 D) B))) )  &  ((r2_hidden F (k4_finseq_1 D)) =>  ((k8_matrix_1 A E (k1_nat_1 F (k3_finseq_1 C))) = (k8_finseq_1 A (k5_finseq_2 A (k1_matrix_1 C) B) (k8_matrix_1 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E B) &  ((v9_vectsp_1 E B) &  ((v10_vectsp_1 E B) &  ((v11_vectsp_1 E B) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v1_matrlin E B) & (l1_vectsp_1 E B)) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrlin F B D) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 E)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) (k3_finseq_1 F) (k3_finseq_1 G)) =>  ( (H = (k2_matrixj2 B C A))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k4_finseq_1 F)) =>  ( ( (I = (k3_finseq_1 F))  =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) (k4_matrlin2 B D E F G H) (k7_partfun1 (u1_struct_0 D) F I)) = (k4_vectsp_1 B E C (k7_partfun1 (u1_struct_0 E) G I))) )  &  ( (~  (I = (k3_finseq_1 F)) )  =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) (k4_matrlin2 B D E F G H) (k7_partfun1 (u1_struct_0 D) F I)) = (k3_rlvect_1 E (k4_vectsp_1 B E C (k7_partfun1 (u1_struct_0 E) G I)) (k7_partfun1 (u1_struct_0 E) G (k1_nat_1 I 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrixr1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ( (C = D)  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k4_tarski E F) (k2_matrix_1 C)) =>  ((k3_matrix_1 A C E F) = (k3_matrix_1 B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k10_matrixr1 (k8_rvsum_1 A B)) = (k5_matrixr1 (k10_matrixr1 A) (k10_matrixr1 B))) ) ) ) ) ) ).
tt(t23_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D B C) =>  ( ((v1_vectsp_7 (k10_xtuple_0 (k2_rfinseq (u1_struct_0 C) A D)) B C) & (m1_subset_1 (k10_xtuple_0 (k2_rfinseq (u1_struct_0 C) A D)) (k1_zfmisc_1 (u1_struct_0 C))))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (E = (k10_xtuple_0 (k2_rfinseq (u1_struct_0 C) A D)))  => (m1_matrlin (k2_rfinseq (u1_struct_0 C) A D) B (k1_vectsp_7 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_matrix_1 F E A B) =>  (! [G:$i] :  ((m1_matrix_1 G E C B) =>  ((r2_hidden D (k9_xtuple_0 F)) =>  ((k8_matrix_1 E (k8_matrlin E A C B F G) D) = (k8_matrix_1 E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_matroid0 C A) & (r1_tarski B C)) ) ) ) ) ) ).
tt(t23_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = k6_numbers)  =>  ((k5_matrprob A) = k6_numbers) ) ) ) ).
tt(t23_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k1_funct_1 (k3_matrtop1 A B E) (k10_rvsum_1 D C)) = (k10_rvsum_1 (k1_funct_1 (k3_matrtop1 A B E) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (! [D:$i] :  ( ((v1_rlvect_3 D (k15_euclid B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))))  =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  => (v1_rlvect_3 (k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D) (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t23_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) |  ((k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D A B C)) E) = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k16_finseq_1 (k7_nat_d B 1) E) (k4_matrix_2 k1_numbers (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k20_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k4_xcmplx_0 (k17_sin_cos A)))))) (k16_finseq_1 (k7_nat_d (k7_nat_d C B) 1) (k1_rfinseq B E))) (k4_matrix_2 k1_numbers (k7_real_1 (k8_real_1 (k1_seq_1 E B) (k17_sin_cos A)) (k8_real_1 (k1_seq_1 E C) (k20_sin_cos A))))) (k1_rfinseq C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k1_mazurulm A B)) (k1_mazurulm A B))) ) ) ) ).
tt(t23_mboolean,ax, (! [A:$i] :  (! [B:$i] : (r6_pboole A (k2_mboolean A (k7_funcop_1 A (k1_tarski B))) (k7_funcop_1 A B))) ) ).
tt(t23_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_zfmisc_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k4_tarski A C) (k4_tarski A D) (k4_tarski B C) (k4_tarski B D))) ) ) ) ) ).
tt(t23_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (~ (v1_xboole_0 (k4_measure1 A B C)))  &  ((v4_card_3 (k4_measure1 A B C)) & (m1_subset_1 (k4_measure1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ).
tt(t23_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_tarski (k8_nat_1 B D E) (k8_nat_1 B D (k2_nat_1 E 1)))) )  =>  ((k1_funct_1 C (k5_setfam_1 A (k4_measure1 A B D))) = (k8_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers D C)))) ) ) ) ) ) ) ) ) ).
tt(t23_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_measure6 (k2_measure6 A B) (k4_xcmplx_0 B)) = A) ) ) ) ) ).
tt(t23_measure8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D C) => (r1_xxreal_0 (k1_mesfunc9 A D) (k1_mesfunc9 B D))) ) )  => (r1_xxreal_0 (k1_mesfunc9 (k18_supinf_2 A) C) (k1_mesfunc9 (k18_supinf_2 B) C))) ) ) ) ) ) ) ).
tt(t23_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k6_member_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k6_member_1 A) (k6_member_1 B))) ) ) ) ) ).
tt(t23_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v5_membered B) =>  ((r1_tarski A B) => (v5_membered A)) ) ) ) ).
tt(t23_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v4_memstr_0 C A B)) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_partfun1 C (k7_memstr_0 A B D))) ) ) ) ) ) ) ) ).
tt(t23_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r2_mesfun6c A B C D) => (r2_mesfun6c A B C (k2_partfun1 A k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers))) =>  ((r2_funct_2 k5_numbers k1_numbers (k10_seqfunc A (k11_mesfun7c A B) C) (k7_comseq_3 (k9_mesfun7c A B C))) & (r2_funct_2 k5_numbers k1_numbers (k10_seqfunc A (k12_mesfun7c A B) C) (k8_comseq_3 (k9_mesfun7c A B C)))) ) ) ) ) ) ) ) ).
tt(t23_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((v1_mesfunc8 D A k2_numbers) &  ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k2_numbers D k6_numbers))) &  ((r2_hidden B C) & (v2_comseq_2 (k9_mesfun7c A D B))) ) )  => (v2_comseq_2 (k9_mesfun7c A (k1_mesfun9c A k2_numbers D C) B))) ) ) ) ) ) ) ) ).
tt(t23_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B C F) = (k9_subset_1 A E (k17_mesfunc1 A D (k1_measure6 F)))) ) )  =>  ((k9_subset_1 A E (k19_mesfunc1 A D k1_supinf_1)) = (k1_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  => (r2_relset_1 A k7_numbers B (k4_mesfunc1 A (k1_mesfunc2 A B) (k2_mesfunc2 A B)))) ) ) ) ).
tt(t23_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v6_supinf_2 B) &  ((v6_supinf_2 C) & (v6_supinf_2 D)) )  =>  ( ((k1_relset_1 A (k3_mesfunc1 A (k3_mesfunc1 A B C) D)) = (k9_subset_1 A (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)) (k1_relset_1 A D)))  &  ((v6_supinf_2 (k3_mesfunc1 A (k3_mesfunc1 A B C) D)) &  (! [E:$i] :  ((r2_hidden E (k9_subset_1 A (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)) (k1_relset_1 A D))) =>  ((k12_supinf_2 (k3_mesfunc1 A (k3_mesfunc1 A B C) D) E) = (k3_supinf_2 (k3_supinf_2 (k12_supinf_2 B E) (k12_supinf_2 C E)) (k12_supinf_2 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_relset_1 A k7_numbers (k1_mesfunc5 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k3_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A C))) &  ((r2_relset_1 A k7_numbers (k1_mesfunc5 A (k47_valued_1 A k1_numbers k1_numbers B C)) (k4_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A C))) &  ( ((k1_relset_1 A (k1_mesfunc5 A (k3_valued_1 A k1_numbers k1_numbers B C))) = (k9_subset_1 A (k1_relset_1 A (k1_mesfunc5 A B)) (k1_relset_1 A (k1_mesfunc5 A C))))  &  ( ((k1_relset_1 A (k1_mesfunc5 A (k47_valued_1 A k1_numbers k1_numbers B C))) = (k9_subset_1 A (k1_relset_1 A (k1_mesfunc5 A B)) (k1_relset_1 A (k1_mesfunc5 A C))))  &  ( ((k1_relset_1 A (k1_mesfunc5 A (k3_valued_1 A k1_numbers k1_numbers B C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ((k1_relset_1 A (k1_mesfunc5 A (k47_valued_1 A k1_numbers k1_numbers B C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] : (r2_relset_1 A k7_numbers (k1_mesfunc2 A (k3_mesfunc2 B A)) (k3_mesfunc2 B A))) ) ) ).
tt(t23_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C E) D)) ) )  => (r1_mesfunc1 A B (k6_mesfunc8 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t23_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) &  ( ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) D) = k1_supinf_1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 E C) &  ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B E) D) = k1_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  (! [C:$i] :  ((m1_subset_1 C 1) => (r1_xxreal_0 (k1_metric_1 1 1 k3_metric_1 A C) (k7_real_1 (k1_metric_1 1 1 k3_metric_1 A B) (k1_metric_1 1 1 k3_metric_1 B C)))) ) ) ) ) ) ).
tt(t23_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k3_metric_2 A B C)) <=> (r4_metric_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t23_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  ((k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 A B) = (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 B A)) ) ) ) ) ).
tt(t23_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v2_tbsp_1 B A)) ) ) ) ) ).
tt(t23_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  (! [C:$i] :  ( ((v1_cantor_1 C A) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 D A) &  ((m1_setfam_1 D (u1_struct_0 A)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski E D) &  ((m1_setfam_1 E (u1_struct_0 A)) & (r1_ordinal1 (k1_card_1 E) B)) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_cantor_1 D A) &  ((v1_tops_2 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  ((r1_tarski D C) & (r1_ordinal1 (k1_card_1 D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m1_rlvect_3 (k8_euclid_7 A) (k15_euclid A))) ) ).
tt(t23_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((r2_midsp_1 A B C) & (r2_midsp_1 A C D))  => (r2_midsp_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t23_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_midsp_1 A B C) = D)  <=>  ((k8_midsp_1 A B D) = (k8_midsp_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t23_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [F:$i] :  ( ((v4_midsp_2 F B) & (l1_midsp_2 F B))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (u1_midsp_2 B F))) =>  (! [H:$i] :  ((m2_finseq_2 H (u1_struct_0 (u1_midsp_2 B F)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B F)))) =>  ( ( ((k8_midsp_3 A B F C E) = H)  &  ( ((k9_midsp_2 B F C D) = G)  &  ((k10_midsp_3 A B F H) = G) ) )  =>  ((k4_midsp_3 A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k2_mmlquery A C B)) <=>  (? [E:$i] :  ((m1_subset_1 E A) &  ((r2_hidden D (k1_mmlquery A C E)) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_mod_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_mod_2)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_enumset1 k6_numbers 1 2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_enumset1 k6_numbers 1 2)) =>  ( ( (C = A)  &  (D = B) )  =>  ( ((k1_algstr_0 k18_mod_2 A B) = (k11_mod_2 C D))  &  ( ((k6_algstr_0 k18_mod_2 A B) = (k12_mod_2 C D))  &  ((k4_algstr_0 k18_mod_2 A) = (k10_mod_2 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((v1_ringcat1 C A B) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_algstr_0 A D)) = (k4_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k5_algstr_0 A D E)) = (k5_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_modal_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v3_trees_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  ( ((k1_trees_2 (k9_xtuple_0 B) (k1_modal_1 (k9_xtuple_0 B))) = (k6_domain_1 (k9_xtuple_0 B) C))  =>  (B = (k7_trees_2 (k8_funcop_1 A (k2_trees_1 1) (k2_modal_1 A B)) (k12_finseq_1 k5_numbers k6_numbers) (k5_trees_2 B C))) ) ) ) ) ) ) ) ).
tt(t23_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k30_modelc_1 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 B C E)))))) )  =>  ((r4_modelc_1 B C E F D (k10_modelc_1 A)) <=>  (? [G:$i] :  ((m1_modelc_1 G B C) &  ( ((k3_funct_2 k5_numbers B G k6_numbers) = D)  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) => (r4_modelc_1 B C E F (k3_funct_2 k5_numbers B G H) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v5_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  ( (B = (k11_modelc_2 A))  |  (B = (k12_modelc_2 A)) ) ) ) ) ) ) ) ).
tt(t23_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (~  ( (~ (r1_xxreal_0 (k21_modelc_3 A B) k6_numbers))  &  ((u2_modelc_3 A B) = (k7_modelc_3 A)) ) ) ) ) ) ) ).
tt(t23_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (~ (v1_moebius1 A)) ) ) ).
tt(t23_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m3_monoid_0 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 A)) & (r1_tarski (u1_struct_0 C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t23_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ((v5_group_1 A) => (v5_group_1 (k9_monoid_1 A B)))  &  ( ((v3_group_1 A) => (v3_group_1 (k9_monoid_1 A B)))  &  ( ((v10_monoid_0 A) => (v10_monoid_0 (k9_monoid_1 A B)))  &  ( ((v13_monoid_0 A) => (v13_monoid_0 (k9_monoid_1 A B)))  &  ( ((v16_monoid_0 A) => (v16_monoid_0 (k9_monoid_1 A B)))  &  ((v17_monoid_0 A) => (v17_monoid_0 (k9_monoid_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t23_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k1_morph_01 A D C) (k1_morph_01 A D B))) ) ) ) ) ) ) ) ) ).
tt(t23_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))))) (k1_msaterm A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k1_funct_1 (k5_msafree3 A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))) B) D)) => (r2_hidden C (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) D))) ) ) ) ) ) ) ) ) ).
tt(t23_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_msaterm D A B (k2_msaterm A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ( (F = (k1_funct_1 D E))  =>  ( (F = (k7_partfun1 (k1_msaterm A B) D E))  &  ( ((k7_msaterm A B F) = (k1_funct_1 (k1_msualg_1 A C) E))  &  ((k7_msaterm A B F) = (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_relat_1 C) & (m1_msafree C A B))  =>  (~  ( (~ (v4_msafree2 B A))  & (v4_msafree2 (k11_msafree A C) A)) ) ) ) ) ) ) ) ).
tt(t23_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v2_finset_1 (k2_mboolean A B)) =>  ((v2_finset_1 B) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A C B) => (v2_finset_1 C)) ) ) ) ) ) ) ) ).
tt(t23_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ( ((u1_struct_0 A) = (k1_tarski k6_numbers))  =>  ((k6_msualg_1 (k12_msualg_1 A B)) = (g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A))) ) ) ) ) ) ).
tt(t23_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  ((k11_msualg_2 A B (k12_msualg_2 A B (k2_msualg_2 A B)) C) = (k12_msualg_2 A B (k2_msualg_2 A B))) ) ) ) ) ) ) ).
tt(t23_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A B C D) &  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D))) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A (k6_msualg_3 A B C D)) (u3_msualg_1 A C)) =>  (~  ((r2_msualg_3 A B (k6_msualg_3 A B C D) E) &  ((r3_msualg_3 A (k6_msualg_3 A B C D) C F) & (r8_pboole (u1_struct_0 A) D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k6_msualg_3 A B C D)) (u3_msualg_1 A C) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (~  ((r1_msualg_6 A E F B G) &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) F)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) F))))) )  =>  (~  ((r1_msualg_6 A E F C H) &  ((k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) H) = (k3_relat_1 G (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_msualg_7,ax, (? [A:$i] :  ((m2_nat_lat A (k1_msualg_7 k6_numbers 1)) &  ((v1_msualg_7 A (k1_msualg_7 k6_numbers 1)) &  (~ (v2_msualg_7 A (k1_msualg_7 k6_numbers 1))) ) ) ) ).
tt(t23_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) ) )  =>  (! [F:$i] :  ((m2_pboole F A B (k6_pboole A D E)) =>  ((r1_pboole A C (k2_funct_6 F)) =>  (! [G:$i] :  ((r2_hidden G A) =>  ((k1_funct_1 (k16_pralg_1 A F C) G) = (k4_tarski (k1_funct_1 (k16_pralg_1 A (k1_msualg_9 A B D E F) C) G) (k1_funct_1 (k16_pralg_1 A (k2_msualg_9 A B D E F) C) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_unialg_2 A B) & (r3_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C)))  => (r2_alg_1 A B C)) ) ) ) ) ) ) ).
tt(t23_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v3_dilworth A) & (l1_orders_2 A)) )  =>  ((k1_dilworth A) = (k2_dilworth (k3_necklace A))) ) ) ).
tt(t23_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers))))) )  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k1_binop_1 B C D) = (k3_nagata_1 A C D)) ) ) ) )  =>  ((v1_setwiseo B (k9_funct_2 (u1_struct_0 A) k1_numbers)) &  ((v1_binop_1 B (k9_funct_2 (u1_struct_0 A) k1_numbers)) & (v2_binop_1 B (k9_funct_2 (u1_struct_0 A) k1_numbers))) ) ) ) ) ) ) ).
tt(t23_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 2 A))  &  ( (~  (A = k6_numbers) )  &  (~  (A = 1) ) ) ) ) ) ) ).
tt(t23_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 B C) & (r1_nat_d (k4_nat_1 2 A) B)) )  =>  ((v1_abian (k3_nat_d C A)) <=> (v1_abian (k3_nat_d (k7_nat_d C B) A))) ) ) ) ) ) ) ) ).
tt(t23_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 B A))  &  ( (~  (B = 1) )  &  (~  ((k11_nat_3 A B) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t23_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ( ((k9_real_1 A 1) = (k4_nat_1 B (k13_newton C E)))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((v1_int_2 C) &  ( ((k4_nat_d (k13_newton G (k7_nat_d A 1)) A) = 1)  &  ((v1_int_2 F) &  ((r1_nat_d F A) &  ( (~ (r1_nat_d F (k7_nat_d (k13_newton G (k3_nat_d (k7_nat_d A 1) C)) 1)))  &  (~  ((k4_nat_d F (k13_newton C E)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((v1_int_2 A) &  ( ((k4_nat_d A 4) = 1)  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k23_binop_2 (k1_pepin B) (k1_pepin C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_nat_d (k2_xcmplx_0 A B) C) = (k4_nat_d (k1_nat_1 A (k4_nat_d B C)) C)) ) ) ) ) ) ) ).
tt(t23_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r2_nattra_1 A B C D) & (r2_nattra_1 A B D E))  => (r2_nattra_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k9_subset_1 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) C) (k1_relset_1 (u1_struct_0 A) D))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k3_vfunct_2 (u1_struct_0 A) B C D)) (k2_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k2_vfunct_1 (u1_struct_0 A) B C D)) (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r5_ncfcont2 A B C) => (r11_ncfcont1 B C A)) ) ) ) ) ) ).
tt(t23_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((v1_partfun1 C (u1_struct_0 A)) =>  ((v2_ndiff_1 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (F = (k4_struct_0 A)) )  &  ( (~ (r1_xxreal_0 E (k1_normsp_0 A F)))  & (r1_xxreal_0 D (k8_real_1 (k2_real_1 (k1_normsp_0 A F)) (k1_normsp_0 B (k7_partfun1 (u1_struct_0 B) C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ((r2_ndiff_3 A C B) => (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) C B) A)) ) ) ) ) ) ).
tt(t23_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ((v1_partfun1 B k1_numbers) =>  ((v1_ndiff_3 B (k4_real_ns1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (E = k6_numbers) )  &  ( (~ (r1_xxreal_0 D (k17_complex1 E)))  & (r1_xxreal_0 C (k11_binop_2 (k8_binop_2 (k17_complex1 E)) (k1_normsp_0 (k4_real_ns1 A) (k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) B E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  (~  ((v3_nfcont_1 D (k14_prvect_2 A)) &  ((r2_hidden C D) &  (! [E:$i] :  ((m1_nfcont_1 E (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_prvect_2 A B))) &  ((r2_hidden F E) &  (~ (r2_hidden (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v1_neckla_2 A) => (v1_neckla_2 B)) ) ) ) ) ).
tt(t23_necklace,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (v3_orders_3 (k4_necklace A))) ) ) ).
tt(t23_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski C (k2_net_1 A)) =>  ((r2_hidden B (k12_net_1 A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k2_net_1 A)) &  ((r2_hidden D C) & (r2_hidden B (k5_net_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t23_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k5_newton 1 A) = A) ) ) ) ).
tt(t23_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r3_nfcont_1 C D E A) & (r1_tarski B A))  => (r3_nfcont_1 C D E B)) ) ) ) ) ) ) ) ) ).
tt(t23_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((v1_partfun1 B k1_numbers) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k7_partfun1 (u1_struct_0 A) B (k2_xcmplx_0 C D)) = (k3_rlvect_1 A (k7_partfun1 (u1_struct_0 A) B C) (k7_partfun1 (u1_struct_0 A) B D))) ) ) ) ) )  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~ (r1_nfcont_3 A B C)) ) )  | (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) B k1_numbers) A)) ) ) ) ) ) ).
tt(t23_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( (B = C)  =>  ((v1_nfcont_3 B (k4_real_ns1 A)) <=> (v1_nfcont_4 C A)) ) ) ) ) ) ) ) ).
tt(t23_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ((r2_hidden B (k7_normform A)) <=> (r1_xboole_0 (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B))) ) ) ) ).
tt(t23_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) => (v2_comseq_2 (k4_normsp_0 A B))) ) ) ) ) ).
tt(t23_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (D = (a_3_2_normsp_2 A B C))  => (v3_pre_topc D (k4_normsp_2 A))) ) ) ) ) ) ) ) ) ).
tt(t23_numbers,ax, (~  (k3_numbers = k2_numbers) ) ).
tt(t23_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k9_openlatt A) (k13_openlatt A) (k14_openlatt A))))  &  ((v10_lattices (g3_lattices (k9_openlatt A) (k13_openlatt A) (k14_openlatt A))) & (l3_lattices (g3_lattices (k9_openlatt A) (k13_openlatt A) (k14_openlatt A)))) ) ) ) ).
tt(t23_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v8_cat_1 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B)) <=> (v7_cat_1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t23_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  => (v1_orders_1 B)) ) ) ).
tt(t23_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A B C) <=> (r2_hidden B (k2_orders_2 A (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(t23_ordinal1,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v3_ordinal1 B)) )  => (v3_ordinal1 (k3_tarski A))) ) ).
tt(t23_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_ordinal2 (k1_tarski A)) = (k1_ordinal1 A)) ) ) ).
tt(t23_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 (k10_ordinal2 A B) (k10_ordinal2 A C)) => (r1_ordinal1 B C)) ) ) ) ) ) ) ).
tt(t23_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden 1 A) => (r2_hidden (k12_ordinal2 A B) (k12_ordinal2 A (k1_ordinal1 B)))) ) ) ) ) ).
tt(t23_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden k6_numbers A) & (r2_hidden k6_numbers B))  => (r1_ordinal1 A (k1_ordinal5 A B))) ) ) ) ) ).
tt(t23_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v5_ordinal1 D) & (v1_ordinal2 D)) ) )  =>  ( ( (D = (k2_ordinal6 A))  &  ((r2_hidden B (k9_xtuple_0 D)) & (r2_hidden C (k9_xtuple_0 D))) )  =>  ((r2_hidden B C) <=> (r2_hidden (k1_funct_1 D B) (k1_funct_1 D C))) ) ) ) ) ) ) ).
tt(t23_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t23_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B C (k3_rlvect_1 B E D)) =>  ((r1_orders_2 B C D) |  ((k1_ortsp_1 A B D C E) = (k4_algstr_0 A (k1_ortsp_1 A B E C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski C E) (k1_funct_1 (k19_osafree A B) D)) =>  ((r2_hidden C (k4_dtconstr (k2_osafree A B))) &  ((r2_hidden D (k4_dtconstr (k2_osafree A B))) & (r2_hidden E (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t23_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r6_osalg_1 A B C) & (r6_osalg_1 A C D))  => (r6_osalg_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t23_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k1_funct_1 (u3_msualg_1 A B) D) (k8_osalg_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t23_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) &  ((v13_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_osalg_4 C A B)) )  => (v3_osalg_4 C A B)) ) ) ) ) ) ).
tt(t23_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_parsp_1 A B C D E) =>  ((r1_parsp_1 A C B D E) &  ((r1_parsp_1 A B C E D) &  ((r1_parsp_1 A C B E D) &  ((r1_parsp_1 A D E B C) &  ((r1_parsp_1 A E D B C) &  ((r1_parsp_1 A D E C B) & (r1_parsp_1 A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C E) &  ((r1_parsp_2 A B D F) &  ((r1_parsp_2 A B D G) &  ((r1_parsp_1 A C D E F) & (r1_parsp_1 A C D E G)) ) ) )  =>  ((r1_parsp_2 A B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k1_relset_1 A (k3_partfun1 C A B)) (k9_xtuple_0 C)) & (r1_tarski (k10_xtuple_0 (k3_partfun1 C A B)) (k10_xtuple_0 C))) ) ) ) ) ).
tt(t23_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden D (k7_relset_1 B C E A)) <=>  (? [F:$i] :  ((m1_subset_1 F B) &  ((r2_hidden F (k1_relset_1 B E)) &  ((r2_hidden F A) &  (D = (k7_partfun1 C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((k4_partit1 A (k3_partit1 A B C)) = (k5_eqrel_1 A (k4_partit1 A B) (k4_partit1 A C))) ) ) ) ) ) ) ).
tt(t23_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v3_relat_2 C) => (r3_relat_2 C B)) ) ) ) ) ) ) ).
tt(t23_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C D E) &  ( (~ (r3_diraf A B C D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B F E) & (r1_diraf A C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r6_pboole A (k3_pboole A B C) B)) ) ) ) ) ) ).
tt(t23_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_pcomps_1 A) &  ((v4_pre_topc B A) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc E A) &  ((v3_pre_topc F A) &  ((r1_tarski C E) &  ((r2_hidden D F) & (r1_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski C D) &  ((r1_tarski B E) & (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k19_pcs_0 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k19_pcs_0 A B))) =>  ( ( (C = E)  &  ( (D = F)  & (r1_orders_2 A C D)) )  => (r1_orders_2 (k19_pcs_0 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 B))) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid B)) =>  ( ( (E = F)  &  (G = H) )  =>  ((r5_pdiff_1 B A C D E G) <=> (r6_pdiff_1 B A C D F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r3_pdiff_3 B A) & (r3_pdiff_3 C A))  =>  ((r3_pdiff_1 2 1 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) &  ((k11_pdiff_1 2 1 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) = (k7_real_1 (k4_pdiff_3 B A) (k4_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t23_pdiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r2_pdiff_4 B A) =>  ((r1_tarski A (k1_relset_1 (k1_euclid 3) B)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C A) => (r3_pdiff_1 3 2 B C)) ) ) ) ) ) ) ) ).
tt(t23_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r5_pdiff_5 B A) <=> (r3_pdiff_1 3 2 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ).
tt(t23_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = C)  =>  ((a_3_0_pdiff_6 A B D) = (a_3_1_pdiff_6 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r1_pdiff_7 A C D) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A)) )  =>  ((r3_pdiff_1 A B C D) &  ( ((k11_pdiff_1 A B C D) = (k1_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A B D) C) (k1_seq_1 (k1_pdiff_1 B A) D)))  &  ((k11_pdiff_1 A B C D) = (k1_seq_1 (k1_pdiff_7 A C D) (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A B (k5_euclid A)) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k1_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((v1_pdiff_7 F A) &  ( (E = D)  &  (F = G) ) ) ) )  =>  ( ( ((r2_pdiff_7 A B C D F) & (r4_pdiff_7 A B (k2_pdiff_7 A B C D F) F))  =>  ((r7_pdiff_1 A B C E G) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k15_pdiff_1 A B C E G) G)) )  &  ( ((r7_pdiff_1 A B C E G) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 B)) (k15_pdiff_1 A B C E G) G))  =>  ((r2_pdiff_7 A B C D F) & (r4_pdiff_7 A B (k2_pdiff_7 A B C D F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_hidden C (k4_card_3 B)) & (r2_hidden D (k4_card_3 B)))  =>  (! [E:$i] :  ( (~  (E = (k3_pencil_1 A B)) )  =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) &  ( (~ (v1_zfmisc_1 D))  &  ((v2_pencil_1 D (k5_pencil_1 A B)) &  ((v1_pencil_1 D (k5_pencil_1 A B)) &  (C = (k3_tarski (a_3_0_pencil_2 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v9_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  ((r1_xboole_0 C D) =>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  ( ( (C = (k4_card_3 E))  &  (D = (k4_card_3 F)) )  =>  ( ((k3_pencil_1 A E) = (k3_pencil_1 A F))  <=>  (? [G:$i] :  ((m2_finseq_1 G (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) &  ( ((k1_funct_1 G 1) = C)  &  ( ((k1_funct_1 G (k3_finseq_1 G)) = D)  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) => (m1_pencil_2 (k1_funct_1 G H) A B)) ) )  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_xxreal_0 1 H) =>  ((r1_xxreal_0 (k3_finseq_1 G) H) |  (! [I:$i] :  ((m1_pencil_2 I A B) =>  (! [J:$i] :  ((m1_pencil_2 J A B) =>  ( ( (I = (k1_funct_1 G H))  &  (J = (k1_funct_1 G (k1_nat_1 H 1))) )  =>  ((r1_xboole_0 I J) & (r1_pencil_3 A B I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( ((k2_vectsp_4 A B) = (k2_vectsp_4 A C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_vectsp_9 A B D) = (k2_vectsp_9 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_abian (k3_xcmplx_0 A B)) &  ( (~ (v1_abian A))  &  (~ (v1_abian B)) ) ) ) ) ) ) ) ).
tt(t23_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A D E))  => (r2_pnproc_1 A (k2_pnproc_1 A B D) (k2_pnproc_1 A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t23_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ((g6_algstr_0 (u1_struct_0 (k3_polyalg1 A)) (u1_algstr_0 (k3_polyalg1 A)) (u2_algstr_0 (k3_polyalg1 A)) (u3_struct_0 (k3_polyalg1 A)) (u2_struct_0 (k3_polyalg1 A))) = (k14_polynom3 A)) ) ) ).
tt(t23_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 B A)))  &  ( ((k7_polyeq_1 A k6_numbers B k6_numbers C) = k6_numbers)  &  ( (~  (C = k6_numbers) )  &  ( (~  (C = (k6_square_1 (k4_xcmplx_0 (k7_xcmplx_0 B A)))) )  &  (~  (C = (k4_xcmplx_0 (k6_square_1 (k4_xcmplx_0 (k7_xcmplx_0 B A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( ((k1_polyeq_3 A) = B)  &  ( (~  (A = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) k7_complex1))) )  &  ( (~  (A = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) k7_complex1))) )  &  ( (~  (A = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) k7_complex1))) )  &  (~  (A = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 B) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 B)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) 2)) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k4_power A B) = A)  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  (B = 1) ) ) ) ) ) ) ) ).
tt(t23_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( ( (B = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton D 2)) (k6_xcmplx_0 (k1_newton G 2) E) (k3_xcmplx_0 2 G))))  &  ( (C = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton D 2)) (k6_xcmplx_0 (k1_newton G 2) E) (k3_xcmplx_0 2 G))))  &  (F = (k10_complex1 (k13_complex1 D (k3_xcmplx_0 B C)))) ) )  =>  ( (D = k6_numbers)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 (k3_xcmplx_0 4 G) (k1_newton A 2))) (k3_xcmplx_0 (k3_xcmplx_0 8 D) A)) (k3_xcmplx_0 4 E)) = k6_numbers)  <=>  (~  ( (~  (A = (k2_xcmplx_0 (k2_xcmplx_0 B C) F)) )  &  ( (~  (A = (k6_xcmplx_0 (k6_xcmplx_0 B C) F)) )  &  ( (~  (A = (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) C) F)) )  &  (~  (A = (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_polyform,ax, (! [A:$i] :  (! [B:$i] : (m2_funct_2 (k8_funcop_1 (u1_struct_0 k2_bspace) (k2_zfmisc_1 A B) (k5_struct_0 k2_bspace)) (k2_zfmisc_1 A B) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace)) (k9_funct_2 (k2_zfmisc_1 A B) (k2_tarski (k4_struct_0 k2_bspace) (k5_struct_0 k2_bspace))))) ) ).
tt(t23_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B C (k7_polynom1 A B)) C)) ) ) ) ) ).
tt(t23_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k5_polynom1 A B C D) E) = (k3_rlvect_1 B (k5_polynom2 A B C E) (k5_polynom2 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_algseq_1 A B) C) <=> (r1_algseq_1 A B C)) ) ) ) ) ) ) ).
tt(t23_polynom4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k13_polynom3 A (k1_polynom4 A B) C) D) = (k8_group_1 A (k2_polynom4 A (k1_polynom4 A B) D) (k2_polynom4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t23_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_algseq_1 A (k2_polynom5 A B C)) = (k7_real_1 (k9_real_1 (k4_nat_1 C (k1_algseq_1 A B)) C) 1)) ) ) ) ) ) ) ) ).
tt(t23_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k2_polynom7 A B (k4_polynom7 A B C)) = (k16_pre_poly A))  &  ((k3_polynom7 A B (k4_polynom7 A B C)) = C) ) ) ) ) ) ) ).
tt(t23_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_group_1 A (k3_polynom8 A B (k3_xcmplx_0 (k6_xcmplx_0 C 1) (k6_xcmplx_0 E 1))) (k3_polynom8 A B (k4_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 D 1) (k6_xcmplx_0 E 1))))) = (k3_polynom8 A B (k3_xcmplx_0 (k6_xcmplx_0 C D) (k6_xcmplx_0 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v3_polynom7 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden (k3_termord A B C D) (k2_polynom1 (k15_pre_poly A) C E)) => (r2_hidden (k3_termord A B C (k9_polynom1 A C F D)) (k2_polynom1 (k15_pre_poly A) C (k9_polynom1 A C F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_power,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k8_nat_1 k1_numbers A C) = (k1_power C B)) ) ) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((v2_comseq_2 A) &  ((k2_seq_2 A) = 1) ) ) ) ) ) ) ) ).
tt(t23_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 B D (k14_pralg_2 A B C))) =>  ( (~  ((k1_msualg_1 B D) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k5_msualg_3 B (k14_pralg_2 A B C) (k5_pralg_2 A B C F) D (k2_pralg_3 A B C F) E) = (k1_funct_1 (k10_funct_6 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pre_circ,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (v1_finset_1 (a_1_0_pre_circ A))) ) ) ).
tt(t23_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) B) =>  ((r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k2_prelamb A C (k2_prelamb A C B))) & (r2_prelamb A (k6_finseq_1 (u1_struct_0 A)) (k1_prelamb A (k1_prelamb A B C) C))) ) ) ) ) ) ) ) ).
tt(t23_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k1_card_3 (k5_relat_1 A B)) = (k5_relat_1 (k1_card_3 A) B)) ) ) ) ).
tt(t23_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 A k6_numbers) |  ((k3_prepower B (k10_real_1 1 A)) = (k10_real_1 1 (k2_prepower B A))) ) ) ) ) ) ) ).
tt(t23_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) =>  ((k2_pre_topc A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) )  &  ( ((v2_pre_topc A) &  ((k2_pre_topc A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) )  => (v3_pre_topc B A)) ) ) ) ) ) ).
tt(t23_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m1_prob_1 A A B)) ) ) ).
tt(t23_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( (E = k1_xboole_0)  => (r1_prob_2 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  => (r1_tarski (k1_funct_1 (k1_prob_3 B D) A) (k1_funct_1 D A))) ) ) ) ) ) ) ).
tt(t23_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((m1_prob_4 D A B C) <=> (m1_measure3 D A B (k2_prob_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t23_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k10_cqc_lang A B C) (k8_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t23_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  <=>  ((v1_projpl_1 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) & (r2_projpl_1 A D B C)) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) & (r5_projpl_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  ( ((r1_incsp_1 A E C) &  ((r1_incsp_1 A F C) &  ( ((k1_funct_1 (k1_projred1 A C D B) E) = G)  &  ( ((k1_funct_1 (k1_projred1 A C D B) F) = H)  &  (G = H) ) ) ) )  =>  ((r1_incsp_1 A B C) |  ((r1_incsp_1 A B D) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B E))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_incsp_1 A B G))  &  ( (~ (r1_incsp_1 A C G))  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  ((r1_incsp_1 A D H) &  ( (~ (r1_incsp_1 A D E))  &  ( (~  (D = C) )  &  ( (~ (r1_projred2 A E F G))  &  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (~  ((r1_projred2 A E G I) &  ( (~ (r1_incsp_1 A C I))  &  ( (~ (r1_incsp_1 A D I))  &  ((k3_relat_1 (k1_projred1 A E G B) (k1_projred1 A G F C)) = (k3_relat_1 (k1_projred1 A E I D) (k1_projred1 A I F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_prvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B))))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 C D E) = (k1_domain_1 (u1_struct_0 A) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))) D (k12_finseq_1 (u1_struct_0 B) E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_prvect_3 A B))) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C (k3_rlvect_1 (k7_prvect_3 A B) D E)) = (k3_rlvect_1 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C D) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C (k1_rlvect_1 (k7_prvect_3 A B) D E)) = (k1_rlvect_1 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C D) E)) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C (k4_struct_0 (k7_prvect_3 A B))) = (k4_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 A B))) =>  ((k1_normsp_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 A B)) (u1_struct_0 (k7_prvect_3 A (k14_prvect_2 (k9_finseq_1 B)))) C D)) = (k1_normsp_0 (k7_prvect_3 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 A) B) = (k18_euclid B)) ) ) ) ) ) ).
tt(t23_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_pua2mss1 B (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A))) => (r2_pua2mss1 (u1_struct_0 A) B (k10_eqrel_1 (u1_struct_0 A)))) ) ) ) ).
tt(t23_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k4_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) (k1_pboole A)) => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t23_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ( ((r1_qc_lang1 A B C) & (r1_qc_lang1 A C B))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t23_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k8_qc_lang2 A B C D E) = (k6_qc_lang2 A G H F))  =>  ( (B = G)  &  ( (C = H)  &  ((k15_qc_lang1 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v6_qc_lang1 (k15_qc_lang1 A B C) A) <=> (r1_tarski (k24_qc_lang1 A C) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t23_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A C))) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A C))) =>  ( ( (D = (k8_finseq_1 k5_numbers E (k12_finseq_1 k5_numbers B)))  & (v5_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E) A))  =>  ( ((k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) D) = (k22_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A C) E)))  &  (B = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k5_quantal1 A C) (k5_quantal1 A B))) ) ) ) ) ) ) ).
tt(t23_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni (k29_quaterni A B) C) = (k29_quaterni (k27_quaterni A C) (k27_quaterni B C))) ) ) ) ) ) ) ).
tt(t23_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k26_quaterni (k27_quaterni k12_quaterni A) (k27_quaterni A k12_quaterni)) = (k6_quaterni (k1_real_1 (k8_real_1 2 (k20_quaterni A))) k6_numbers k6_numbers (k8_real_1 2 (k17_quaterni A)))) ) ) ).
tt(t23_quaterni,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k17_quaterni (k6_quaterni A B C D)) = A)  &  ( ((k18_quaterni (k6_quaterni A B C D)) = B)  &  ( ((k19_quaterni (k6_quaterni A B C D)) = C)  &  ((k20_quaterni (k6_quaterni A B C D)) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k3_square_1 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 2 A) B) C)) (k1_quin_1 A C D)) k6_numbers))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 B)) (k3_xcmplx_0 C B)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k16_quofield A) (k5_binop_1 (k7_quofield A) (k16_quofield A) B C) D) = (k5_binop_1 (k7_quofield A) (k16_quofield A) B (k5_binop_1 (k7_quofield A) (k16_quofield A) C D))) ) ) ) ) ) ) ) ) ).
tt(t23_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_radix_1 1 A B) & (r1_radix_1 1 C B))  =>  ((k11_radix_1 (k2_xcmplx_0 (k4_radix_1 1 B 1 (k10_radix_1 B 1 A)) (k4_radix_1 1 B 1 (k10_radix_1 B 1 C)))) = (k11_radix_1 (k2_xcmplx_0 A C))) ) ) ) ) ) ) ) ).
tt(t23_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers D) & (v6_supinf_2 C))  => (m1_random_1 (k2_mesfun6c D A C) A B)) ) ) ) ) ) ) ) ) ).
tt(t23_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (m2_vectsp_6 (k15_funct_7 (u1_struct_0 B) (u1_struct_0 A) D E F) A B (k4_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k2_rat_1 A) = (k1_rat_1 A))  <=>  (A = 1) ) ) ) ).
tt(t23_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k11_ratfunc1 A (k7_ratfunc1 A)) = (k7_ratfunc1 A)) ) ) ).
tt(t23_rcomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (~  ((v3_rcomp_1 A) &  ((v5_xxreal_2 A) &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_tarski (k1_rcomp_1 B C) A)) ) ) ) )  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  (A = (k2_rcomp_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v4_xxreal_2 A) =>  ((v3_xxreal_2 A) |  ((r2_hidden (k4_seq_4 A) A) |  (A = (k10_prob_1 (k4_seq_4 A))) ) ) ) ) ) ).
tt(t23_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_funct_2 k5_numbers k5_numbers (k2_real_3 k6_numbers A) (k8_funcop_1 k5_numbers k5_numbers k6_numbers))) ) ).
tt(t23_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_real_lat A))) =>  ( ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) C D) B))  &  ( ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) B C) D))  &  ( ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) C B) D))  &  ( ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) D B) C))  &  ( ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) D C) B))  &  ((k1_binop_1 (k4_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k4_real_lat A) B D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (B = (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B))) ) ) ) ) ).
tt(t23_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) B C) = (k1_funct_1 (k5_realset2 A) (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) C B))) ) ) ) ) ) ) ).
tt(t23_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k1_rvsum_1 (k4_rearran1 A B D C)) = (k1_rvsum_1 (k20_rfunct_3 A C A))) ) ) ) ) ) ) ) ) ) ).
tt(t23_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_relat_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k2_relat_1 A) (k2_relat_1 B))) ) ) ) ) ).
tt(t23_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ( ((k7_relset_1 B A C (k8_relset_1 B A C A)) = (k2_relset_1 A C))  &  ((k8_relset_1 B A C (k7_relset_1 B A C B)) = (k1_relset_1 B C)) ) ) ) ) ) ).
tt(t23_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((k7_relset_1 (k9_setfam_1 A) (k9_setfam_1 B) (k4_relset_2 B A D) (k10_eqrel_1 C)) = k1_xboole_0)  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t23_revrot_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  =>  ((k10_xtuple_0 (k2_goboard1 A)) = (k10_xtuple_0 (k2_goboard1 B))) ) ) ) ) ) ).
tt(t23_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_rewrite1 A C D) <=> (r1_rewrite1 (k2_xboole_0 A (k4_relat_1 B)) C D)) ) ) ) ) ) ).
tt(t23_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k8_afinsq_1 A)) =>  ((m1_rewrite1 D (k7_rewrite2 A B)) =>  ((m1_rewrite1 (k5_rewrite2 A C D) (k7_rewrite2 A B)) & (m1_rewrite1 (k4_rewrite2 A C D) (k7_rewrite2 A B))) ) ) ) ) ) ) ) ) ).
tt(t23_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ((l1_rewrite3 F E) =>  ((r1_rewrite3 E F A B C) <=> (r2_rewrite3 D E F A B C (k2_flang_1 D))) ) ) ) ) ) ) ) ) ) ).
tt(t23_rfinseq,ax, (! [A:$i] :  ( ((v8_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v8_valued_0 B) & (m2_finseq_1 B k1_numbers))  =>  ((r2_classes1 A B) =>  (A = B) ) ) ) ) ) ).
tt(t23_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k1_valued_1 A (k45_valued_1 B C)) = (k45_valued_1 (k1_valued_1 A B) C)) ) ) ) ) ) ) ).
tt(t23_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) & (r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))))  =>  ((r1_xxreal_0 D C) | (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k2_finseq_4 (k3_rfunct_3 A k1_numbers) B C)) (k5_rfunct_3 A k1_numbers B C))) ) ) ) ) ) ).
tt(t23_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_rfunct_4 B A) => (r2_rfunct_4 B A)) ) ) ) ).
tt(t23_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 A) & (v2_seq_2 A))  => (v1_comseq_2 A)) ) ) ).
tt(t23_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((r1_xxreal_0 (k2_rinfsup2 B) (k12_supinf_2 B A)) & (r1_xxreal_0 (k12_supinf_2 B A) (k1_rinfsup2 B))) ) ) ) ) ).
tt(t23_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_rlvect_2 B (k2_rlaffin1 B C A)) = (k1_convex1 B (k3_rlvect_2 B C) A)) ) ) ) ) ) ) ) ).
tt(t23_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_tarski (k3_convex1 A B) (k3_convex1 A C)) &  ( (~ (v1_xboole_0 C))  &  ((r1_xboole_0 (k3_convex1 A B) (k1_rlaffin2 A C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_xboole_0 D C) & (r1_tarski (k3_convex1 A B) (k3_convex1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m2_rlaffin3 C (k15_euclid A) B) =>  ( ((r2_hidden (k5_euclid A) B) &  ((k1_funct_1 C (k3_finseq_1 C)) = (k5_euclid A)) )  =>  ( ((k2_relset_1 (u1_struct_0 (k15_euclid A)) (k17_finseq_1 (u1_struct_0 (k15_euclid A)) (k7_nat_d (k5_card_1 B) 1) C)) = (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (k1_euclid A) (k5_euclid A))))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)))) =>  ( (B = D)  => (m1_matrlin (k17_finseq_1 (u1_struct_0 (k15_euclid A)) (k7_nat_d (k5_card_1 B) 1) C) k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t23_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ((k1_rlsub_2 A (k2_rlsub_2 A B C) C) = C) ) ) ) ) ) ) ).
tt(t23_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (v1_convex1 (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t23_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k5_algstr_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t23_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_rlvect_2 B A (k1_subset_1 (u1_struct_0 A))) => (r2_funct_2 (u1_struct_0 A) k1_numbers B (k4_rlvect_2 A))) ) ) ) ).
tt(t23_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (m1_rlsub_1 (k1_rlvect_3 A (k9_subset_1 (u1_struct_0 A) B C)) (k2_rlsub_2 A (k1_rlvect_3 A B) (k1_rlvect_3 A C)))) ) ) ) ) ) ).
tt(t23_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C (k5_algstr_0 A D B)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) =>  (! [B:$i] :  ((m1_rlvect_3 B A) => (v1_finset_1 B)) ) ) ) ) ).
tt(t23_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden B (k2_rlvect_x A (k8_domain_1 (u1_struct_0 A) B C D))) &  ((r2_hidden C (k2_rlvect_x A (k8_domain_1 (u1_struct_0 A) B C D))) & (r2_hidden D (k2_rlvect_x A (k8_domain_1 (u1_struct_0 A) B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t23_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( ((r1_struct_0 E C) & (r1_struct_0 E D))  => (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((k2_rmod_3 A B (k2_rmod_2 A B) (k2_rmod_2 A B)) = B) ) ) ) ) ).
tt(t23_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((r2_hidden C (k9_xtuple_0 E)) &  (D = (k1_funct_1 E C)) )  =>  ((k1_funct_1 (k4_rmod_4 A B E F) C) = (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F D) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k5_robbins1 A B C) = (k6_lattices A))  &  ((k6_robbins1 A B C) = (k7_robbins1 A)) )  =>  ((k3_robbins1 A B) = C) ) ) ) ) ) ) ) ).
tt(t23_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A B)) = B) ) ) ) ) ).
tt(t23_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins3 A) & (l3_robbins3 A)) ) )  =>  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k3_lattice3 A)) ) ) ).
tt(t23_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  ( ( (A = k6_numbers)  =>  ((k3_robbins1 k2_robbins4 A) = 3) )  &  ( ( (A = 3)  =>  ((k3_robbins1 k2_robbins4 A) = k6_numbers) )  &  ( ( (A = 1)  =>  ((k3_robbins1 k2_robbins4 A) = (k6_subset_1 3 1)) )  &  ( ( (A = (k6_subset_1 3 1))  =>  ((k3_robbins1 k2_robbins4 A) = 1) )  &  ( ( (A = 2)  =>  ((k3_robbins1 k2_robbins4 A) = (k6_subset_1 3 2)) )  &  ( (A = (k6_subset_1 3 2))  =>  ((k3_robbins1 k2_robbins4 A) = 2) ) ) ) ) ) ) ) ) ).
tt(t23_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k4_roughs_1 A B) (k4_roughs_1 A C))) ) ) ) ) ) ) ).
tt(t23_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A (k7_subset_1 A B C)) = (k9_real_1 (k1_rpr_1 A B) (k1_rpr_1 A (k9_subset_1 A B C)))) ) ) ) ) ) ) ).
tt(t23_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_rsspace4 A B)))  &  ((v13_algstr_0 (k9_rsspace4 A B)) &  ((v2_rlvect_1 (k9_rsspace4 A B)) &  ((v3_rlvect_1 (k9_rsspace4 A B)) &  ((v4_rlvect_1 (k9_rsspace4 A B)) &  ((v5_rlvect_1 (k9_rsspace4 A B)) &  ((v6_rlvect_1 (k9_rsspace4 A B)) &  ((v7_rlvect_1 (k9_rsspace4 A B)) &  ((v8_rlvect_1 (k9_rsspace4 A B)) &  ((v3_normsp_0 (k9_rsspace4 A B)) &  ((v4_normsp_0 (k9_rsspace4 A B)) &  ((v2_normsp_1 (k9_rsspace4 A B)) & (l1_normsp_1 (k9_rsspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 C D)) ) )  => (m1_rusub_1 B C)) ) ) ) ) ) ) ).
tt(t23_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ((k1_rusub_2 A (k2_rusub_2 A B C) C) = C) ) ) ) ) ) ) ).
tt(t23_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_rlvect_3 C A) & (r1_tarski C (u1_struct_0 B)))  =>  ((v1_rlvect_3 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t23_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_rusub_4 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t23_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k2_rusub_5 A (k2_rusub_1 A)) = (k1_rusub_1 A)) ) ) ).
tt(t23_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ( ((k5_rvsum_1 A B C) = (k5_finseq_2 k5_numbers A k6_numbers))  =>  (B = (k7_rvsum_1 A C)) ) ) ) ) ) ) ) ).
tt(t23_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ((k9_rvsum_2 C (k3_binop_2 A B)) = (k3_rvsum_2 (k9_rvsum_2 C A) (k9_rvsum_2 C B))) ) ) ) ) ) ) ).
tt(t23_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  => (m1_scm_1 A (k6_finseq_1 k4_numbers))) ) ).
tt(t23_scmbsort,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ((k5_card_1 (k5_scmfsa6a (k6_scmfsa6a A B) C)) = 6) ) ) ) ) ) ) ).
tt(t23_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 6)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) A))) = (k1_tarski 1)) ) ) ) ).
tt(t23_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k2_scmfsa_1) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_funct_1 (k7_scmfsa_1 A B C) k5_numbers) = (k1_funct_1 A k5_numbers)) ) ) ) ) ) ) ).
tt(t23_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k11_scmfsa_2 A)) = 6) ) ) ).
tt(t23_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k6_compos_1 k1_scmfsa_2 (k2_scmfsa6a A) B) = (k1_scmfsa6a (k6_compos_1 k1_scmfsa_2 A B) (k2_nat_1 (k5_card_1 A) B))) ) ) ) ) ).
tt(t23_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((v1_int_1 B) => (r1_tarski (k10_xtuple_0 (k1_scmfsa_7 A B)) (k2_enumset1 (k2_compos_1 k1_scmfsa_2) (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers)) (k7_scmfsa_2 A (k4_scmfsa_2 k6_numbers)) (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers))))) ) ) ) ).
tt(t23_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  => (r1_scmfsa8a A B (k2_scmfsa6a C))) ) ) ) ) ) ) ).
tt(t23_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v7_amistd_1 (k2_scmfsa8b E C D) 3 k1_scmfsa_2) &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B E) k6_numbers))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3)))))  &  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D))  & (r1_scmfsa8a C A E))  => (r1_scmfsa8a D B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r2_scmfsa9a A (k1_scmfsa_m B) C D) =>  ( ( (~ (r1_scmfsa9a A (k1_scmfsa_m B) C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa_9 C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 (k1_scmfsa_m B) D C A) (k1_scmfsa9a A (k1_scmfsa_m B) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B C D A) (k2_nat_1 E 1)) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 B C D A) E) C D A) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~ (r1_xxreal_0 (k6_seq_4 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m B) (k2_nat_1 A 1))) (k6_seq_4 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m B) A)))) ) ) ) ) ).
tt(t23_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scm_halt D) & (v3_scm_halt D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_scmfsa6c E) & (m1_subset_1 E (u1_compos_1 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a D E) A C) B) = (k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 E (k1_scmfsa6b D A C)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v1_scmfsa7b C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k2_scmfsa_9 D C)) =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 D C) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 D C) (k1_scmfsa6b C B A) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k14_scmpds_2 C D A B)) = 11) ) ) ) ) ) ) ) ) ).
tt(t23_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k5_card_1 A) B)) => (v3_scmpds_4 (k3_scmpds_4 A (k3_scmpds_2 B)))) ) ) ) ) ).
tt(t23_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 C) A) =>  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t23_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 2 k1_scmpds_2 C) = (k6_memstr_0 2 k1_scmpds_2 D))  &  ((r1_scmpds_6 E C A) & (r2_scmpds_6 E C A)) )  =>  ((r1_scmpds_6 E D B) & (r2_scmpds_6 E D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r2_scmpds_6 C A B) &  ((r1_scmpds_6 D (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 A) B) B) & (r2_scmpds_6 D (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 A) B) B)) )  =>  ((r1_scmpds_6 D (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A))) (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C))) & (r2_scmpds_6 D (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A))) (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) k6_numbers) =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_8 D F C) B A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_scmring2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 (k1_scmring2 B))))  <=> (r2_hidden A (k8_struct_0 (k1_scmring2 B)))) ) ) ) ).
tt(t23_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 3)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t23_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((v1_finset_1 (k3_tarski A)) => (v1_finset_1 A)) ) ) ).
tt(t23_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  &  ((r2_analoaf A B C E F) &  ((r2_analoaf A B D E G) &  ( (~  (E = F) )  &  ( (~  (E = G) )  & (r1_semi_af1 A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers C (k3_xcmplx_0 A B)) (k26_valued_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers C B) A))) ) ) ) ) ) ).
tt(t23_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k2_seq_2 B) = k6_numbers)  | (v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t23_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~  ((k2_seq_2 A) = k6_numbers) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (v2_relat_1 (k1_valued_0 k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t23_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C D) & (r1_seqfunc A k1_numbers B D))  =>  ( (C = k1_xboole_0)  | (r1_seqfunc A k1_numbers B C)) ) ) ) ) ) ) ) ).
tt(t23_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v6_valued_0 A) & (m2_valued_0 B k1_numbers A))  => (v6_valued_0 B)) ) ) ) ) ).
tt(t23_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers B (k2_nat_1 C 1)) = (k4_real_1 A (k3_funct_2 k5_numbers k1_numbers B C))) ) )  =>  ( (A = 1)  |  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers (k3_series_1 B) C) = (k10_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers B k6_numbers) (k9_real_1 1 (k3_power A (k2_nat_1 C 1)))) (k9_real_1 1 A))) ) ) ) ) ) ) ) ) ).
tt(t23_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 (k4_nat_1 B (k13_newton (k2_nat_1 B 1) 2)) (k2_nat_1 B 2))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k4_nat_1 (k4_nat_1 (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 2)) (k2_nat_1 B 3)) (k2_nat_1 (k4_nat_1 2 B) 3)) 10)) ) ) ) ) ) ).
tt(t23_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 (k13_complex1 25 4) (k3_xcmplx_0 (k2_xcmplx_0 A (k13_complex1 1 A)) (k2_xcmplx_0 B (k13_complex1 1 B))))) ) ) ) ) ).
tt(t23_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ( ((k1_seq_1 B C) = (k1_newton (k7_xcmplx_0 A (k6_xcmplx_0 A 1)) C))  &  ((k1_seq_1 B k6_numbers) = k6_numbers) ) ) ) )  =>  ( (A = 1)  |  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k1_seq_1 (k3_series_1 B) C) = (k3_xcmplx_0 A (k6_xcmplx_0 (k1_newton (k7_xcmplx_0 A (k6_xcmplx_0 A 1)) C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t23_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k3_square_1 (k2_xcmplx_0 (k6_square_1 (k3_xcmplx_0 A B)) (k13_complex1 1 (k6_square_1 (k3_xcmplx_0 A B))))) (k3_xcmplx_0 (k2_xcmplx_0 A (k13_complex1 1 A)) (k2_xcmplx_0 B (k13_complex1 1 B))))) ) ) ) ).
tt(t23_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r1_xboole_0 A B))  =>  ((k3_xboole_0 (k1_setfam_1 A) (k1_setfam_1 B)) = (k1_setfam_1 (k3_setfam_1 A B))) ) ) ) ).
tt(t23_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (v3_prob_1 (k2_setlim_1 A B))) ) ) ).
tt(t23_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 C A) => (v1_setlim_1 (k5_setlim_2 A C B) A)) ) ) ) ) ) ).
tt(t23_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v3_binop_1 C A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 B)) =>  ((r1_tarski E F) =>  ( (E = k1_xboole_0)  |  ((k5_binop_1 A C (k7_setwiseo B A C E D) (k7_setwiseo B A C F D)) = (k7_setwiseo B A C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k10_xtuple_0 (k1_setwop_2 A C B)) = (k2_xboole_0 (k10_xtuple_0 C) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t23_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (C = D) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k1_funct_1 B C))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k2_sfmastr1 C D) B A) D) = (k1_pre_ff E))  &  ((k1_funct_1 (k1_scmfsa6b (k2_sfmastr1 C D) B A) C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k1_funct_1 A C) = E)  =>  ( ( (~ (r1_sfmastr2 B A C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ( ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C))  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_sfmastr2 C D) A B)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k3_sfmastr2 B A D C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (~  ( (~  (A = B) )  &  ( (~  (B = (k9_scmfsa_m 1 (k4_subset_1 k2_scmfsa_2 (k6_scmfsa_m A C D) (k2_sf_mastr E)))) )  &  ( (~ (r4_scmfsa7b E B))  & (r4_scmfsa7b (k2_sfmastr3 A C D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_sf_mastr A) = (k1_sf_mastr (k5_compos_0 (u1_compos_1 k1_scmfsa_2) A B))) ) ) ) ) ).
tt(t23_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_sgraph1 B))) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_sgraph1 (k2_xboole_0 B (k1_tarski D))))))  =>  ( ((r2_hidden (g1_sgraph1 B C) (k3_sgraph1 A)) & (r2_hidden D A))  => (r2_hidden (g1_sgraph1 (k2_xboole_0 B (k1_tarski D)) E) (k3_sgraph1 A))) ) ) ) ) ) ) ) ) ).
tt(t23_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  => (v16_lattices A)) ) ).
tt(t23_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A D B)) = B) ) ) ) ) ) ) ) ) ).
tt(t23_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) => (r1_xxreal_0 (k2_xxreal_3 1) (k6_simplex0 A))) ) ).
tt(t23_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  (! [D:$i] :  ( ( (~ (v3_pencil_1 D))  & (m2_simplex0 D (u1_struct_0 B) C))  =>  ( ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) & (r1_tarski (k3_simplex1 B D) (k2_struct_0 D)))  => (m2_simplex0 (k5_simplex1 A B D) (u1_struct_0 B) (k5_simplex1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t23_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k5_card_1 B) = (k3_real_1 A 1))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)))) &  ((v5_pre_topc C (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)) (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))))))) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) &  ((r2_hidden D (k1_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) C)) &  ((k1_funct_1 C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t23_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k1_sin_cos2 (k8_real_1 2 A)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k1_sin_cos2 A)) (k1_seq_1 k4_sin_cos2 A)))  &  ( ((k1_seq_1 k4_sin_cos2 (k8_real_1 2 A)) = (k9_real_1 (k8_real_1 2 (k5_square_1 (k1_seq_1 k4_sin_cos2 A))) 1))  &  ((k1_seq_1 k7_sin_cos2 (k8_real_1 2 A)) = (k10_real_1 (k8_real_1 2 (k1_seq_1 k7_sin_cos2 A)) (k7_real_1 1 (k5_square_1 (k1_seq_1 k7_sin_cos2 A))))) ) ) ) ) ).
tt(t23_sin_cos3,ax, ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 k5_complex1) = 1) ).
tt(t23_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  (~  ((k2_xcmplx_0 (k2_sin_cos4 A) (k2_sin_cos4 B)) = (k7_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)))) ) ) ) ) ) ) ) ) ).
tt(t23_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k20_sin_cos A) 3) = (k10_real_1 (k7_real_1 (k8_real_1 3 (k20_sin_cos A)) (k21_sin_cos (k8_real_1 3 A))) 4)) ) ) ).
tt(t23_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k17_sin_cos A) = (k1_real_1 1))  =>  (A = (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k6_real_1 A (k8_real_1 2 k32_sin_cos)))))) ) ) ) ).
tt(t23_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))) k6_numbers)) ) ) ) ).
tt(t23_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 A) (k3_sin_cos2 B)) (k3_sin_cos2 (k6_xcmplx_0 B A))) (k3_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 B) (k3_sin_cos2 C)) (k3_sin_cos2 (k6_xcmplx_0 C B)))) (k3_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 C) (k3_sin_cos2 A)) (k3_sin_cos2 (k6_xcmplx_0 A C)))) (k3_xcmplx_0 (k3_xcmplx_0 (k3_sin_cos2 (k6_xcmplx_0 B A)) (k3_sin_cos2 (k6_xcmplx_0 C B))) (k3_sin_cos2 (k6_xcmplx_0 A C)))) = k6_numbers) ) ) ) ) ) ) ).
tt(t23_sin_cos9,ax,(r1_tarski (k1_rcomp_1 (k1_real_1 1) 1) (k1_relset_1 k1_numbers k1_sin_cos9))).
tt(t23_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_sin_cos (k2_xcmplx_0 A B)) = (k9_complex1 (k15_sin_cos A) (k15_sin_cos B))) ) ) ) ) ).
tt(t23_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (v1_finset_1 (a_1_1_sppol_1 A))) ) ).
tt(t23_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (~  ((k3_topreal1 2 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ).
tt(t23_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)) = (a_1_0_sprect_1 A)) ) ) ).
tt(t23_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  => (r1_sprect_2 A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ).
tt(t23_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 A) &  ((r2_hidden C (k2_topreal1 2 B A)) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) C))) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_jordan5c (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) D C)) ) ) ) ) ) ) ) ) ) ).
tt(t23_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t23_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A k6_numbers) =>  ((k6_square_1 (k3_square_1 A)) = (k4_xcmplx_0 A)) ) ) ) ).
tt(t23_stacks_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_rewrite1 C B) =>  ((r2_hidden (k1_funct_1 C 1) A) <=> (v5_relat_1 C A)) ) ) ) ) ) ) ).
tt(t23_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  =>  (A = k6_numbers) )  &  ((r1_xxreal_0 B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ((v2_funct_2 C B) & (v1_stirl2_1 C A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k39_substut1 A (k6_sublemma A B C)) = (k7_cqc_lang A (k39_substut1 A B) (k39_substut1 A C))) ) ) ) ) ) ) ) ).
tt(t23_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) <=> (r1_tarski B (k3_subset_1 A C))) ) ) ) ) ) ).
tt(t23_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) => (r1_tarski C (k4_substlat A B C C))) ) ) ) ).
tt(t23_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v6_substut1 B A) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A B))) (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A (k28_substut1 A B))))))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A B))) (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A (k29_substut1 A B)))))) ) ) ) ) ) ) ).
tt(t23_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A B D)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  ((k7_cqc_sim1 A (k11_cqc_lang A C B)) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A (k11_cqc_lang A C B) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t23_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_supinf_2 C A B) <=> (v1_supinf_2 (k14_supinf_2 A B C) A (k6_supinf_2 B))) ) ) ) ) ) ) ).
tt(t23_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((r1_orders_2 B E D) <=>  ((k1_symsp_1 A B D C E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ((r1_tarski A (k3_relat_1 A A)) &  ((k3_relat_1 A (k6_subset_1 A (k4_relat_1 (k10_xtuple_0 A)))) = k1_xboole_0) )  =>  ((k3_xboole_0 A (k4_relat_1 (k10_xtuple_0 A))) = (k4_relat_1 (k10_xtuple_0 A))) )  &  ( ((r1_tarski A (k3_relat_1 A A)) &  ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A))) A) = k1_xboole_0) )  =>  ((k3_xboole_0 A (k4_relat_1 (k9_xtuple_0 A))) = (k4_relat_1 (k9_xtuple_0 A))) ) ) ) ) ).
tt(t23_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  ( ((v1_taxonom1 B A) &  ((v2_metric_1 B A) & (v3_metric_1 B A)) )  => (r2_relset_1 A A (k13_lang1 A (k1_taxonom1 A B k6_numbers)) (k1_taxonom1 A B k6_numbers))) ) ) ) ) ).
tt(t23_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_taylor_1 A C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D C) => (r1_taylor_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C D) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 1 F))  &  (~  ( (~ (r1_xxreal_0 B (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D)))))  &  (~ (r1_xxreal_0 B (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A)) D) (k8_real_1 F E)) (k2_newton E D)) (k3_newton D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k3_tbsp_1 A (k9_metric_1 A B C)) (k8_real_1 2 C))) ) ) ) ) ) ) ).
tt(t23_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v6_tops_1 (k1_tops_1 A (k2_pre_topc A B)) A)) ) ) ) ).
tt(t23_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k1_tdlat_2 A (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_2 A B) (k1_tdlat_2 A C)))) ) ) ) ) ) ).
tt(t23_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((k2_pre_topc A B) = B) ) ) ) ) ) ) ).
tt(t23_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r6_pboole A (k3_termord A B C D) (k2_polynom7 A C D)) &  ( ((k4_termord A B C D) = (k3_polynom7 A C D))  & (r8_pboole (k15_pre_poly A) (k5_termord A B C D) D)) ) ) ) ) ) ) ) ) ) ).
tt(t23_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~ (v1_xboole_0 (k6_subset_1 A (k6_domain_1 A B))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_tex_1 A B)))) =>  ( ( (C = (k6_subset_1 A (k6_domain_1 A B)))  =>  ((v3_pre_topc C (k3_tex_1 A B)) & (v1_tops_1 C (k3_tex_1 A B))) )  &  ( ((v3_pre_topc C (k3_tex_1 A B)) & (v1_tops_1 C (k3_tex_1 A B)))  =>  ( (C = A)  |  (C = (k6_subset_1 A (k6_domain_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_tex_2 B A) | (v2_tex_2 C A))  => (v2_tex_2 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t23_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v1_tops_1 B A) &  ((v3_pre_topc B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tsep_1 C A) &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v4_pre_topc B A) & (r2_hidden C B))  => (r1_tarski (k2_tex_4 A C) B)) ) ) ) ) ) ) ).
tt(t23_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc A B)) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) )  =>  (~  ((v5_pre_topc C (k1_pre_topc A B) (k4_topmetr (k1_real_1 1) 1)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) &  ((v5_pre_topc D A (k4_topmetr (k1_real_1 1) 1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) ) )  =>  (~  ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) D B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc B D) & (m1_pre_topc C E))  =>  ((r1_tsep_1 B C) | (m1_pre_topc (k2_tsep_1 A B C) (k2_tsep_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r1_relset_1 A A (k6_partfun1 A) B)) ) ) ).
tt(t23_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A D B))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D B) =>  ((r3_borsuk_2 A B C E F) => (r3_borsuk_2 A B C E (k1_borsuk_2 A B B C (k1_borsuk_2 A B D B (k2_borsuk_2 A D B G) G) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_borsuk_6 A D E) => (r1_borsuk_6 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_borsuk_2 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) =>  (! [J:$i] :  ((m1_borsuk_2 J (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) =>  (! [K:$i] :  ((m1_borsuk_2 K A C D) =>  (! [L:$i] :  ((m1_borsuk_2 L A D E) =>  ( ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) &  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) K (k3_topalg_4 A B k5_topmetr I)) & (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) L (k3_topalg_4 A B k5_topmetr J))) ) )  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_topalg_4 A B k5_topmetr (k1_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H) I J)) (k1_borsuk_2 A C D E K L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topalg_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_topalg_2)) =>  (! [D:$i] :  ((m1_borsuk_2 D (k8_toprealb 2) A B) =>  (~  ((r2_hidden C (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) A))) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2))))) )  =>  (~  ( ((k1_seq_1 E k6_numbers) = C)  &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) D (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) E k12_toprealb)) &  ((v5_pre_topc E k5_topmetr k2_topalg_2) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2))))) )  =>  ( ((v5_pre_topc F k5_topmetr k2_topalg_2) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 2)) D (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) F k12_toprealb)) &  ((k1_seq_1 F k6_numbers) = C) ) )  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((v1_funct_1 B) &  ((v4_topalg_6 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t23_topdim_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v9_pre_topc B) =>  ( ((v3_topdim_1 B) & (r1_xxreal_0 (k4_topdim_1 B) A))  <=>  (! [C:$i] :  ( ((v4_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ( (~ (r2_hidden D C))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_metrizts B (k6_domain_1 (u1_struct_0 B) D) C E) &  ((v1_topdim_1 E B) & (r1_xxreal_0 (k2_topdim_1 B E) (k5_real_1 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ( ((v5_waybel23 B) &  ((v3_topdim_1 B) & (r1_xxreal_0 (k4_topdim_1 B) A)) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  (~  ((v1_tops_2 C B) &  ((m1_setfam_1 C (u1_struct_0 B)) &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  (~  ((v1_tops_2 D B) &  ((m1_setfam_1 D (u1_struct_0 B)) &  ((r1_setfam_1 D C) &  ((r1_xxreal_0 (k5_card_1 D) (k4_nat_1 (k5_card_1 C) (k1_nat_1 A 1))) & (r1_xxreal_0 (k1_topdim_2 (u1_struct_0 B) D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_topgen_1 B A) <=> (v3_pre_topc (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t23_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_finset_1 A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  (~  ( (C = (k1_tarski B))  & (v3_pre_topc C (k5_topgen_2 A B))) ) ) ) ) ) ) ).
tt(t23_topgen_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k4_series_1 (k10_nat_1 k1_numbers (k1_prepower (k13_complex1 1 2)) (k2_nat_1 A 1))) = (k1_newton (k13_complex1 1 2) A)) ) ) ).
tt(t23_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_tops_2 C A))  => (v1_tops_2 (k2_topgen_4 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t23_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((r1_xxreal_0 B C) => (r1_tarski (k1_topreal9 2 (k19_euclid A B) B) (k1_topreal9 2 (k19_euclid A C) C))) ) ) ) ) ) ) ).
tt(t23_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_connsp_2 E A D))  =>  (? [F:$i] :  ((m1_connsp_2 F B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) & (r1_tarski F (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) )  => (v1_t_0topsp C A B)) ) ) ) ) ) ) ).
tt(t23_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr C D)))) =>  ( ((r1_xxreal_0 C A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B D) &  (E = (k1_rcomp_1 A B)) ) ) )  =>  ((k4_topmetr A B) = (k1_pre_topc (k4_topmetr C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((k3_topreal1 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t23_topreal3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden (k19_euclid A B) (k9_metric_1 (k14_euclid 2) E C)) & (r2_hidden (k19_euclid A D) (k9_metric_1 (k14_euclid 2) E C)))  => (r2_hidden (k19_euclid A (k6_real_1 (k2_xcmplx_0 B D) 2)) (k9_metric_1 (k14_euclid 2) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r1_topreal4 E C D) &  ((r1_tarski E A) &  ((r2_hidden B (k9_metric_1 (k14_euclid 2) G F)) &  ((r2_hidden D (k9_metric_1 (k14_euclid 2) G F)) &  ((r1_tarski (k9_metric_1 (k14_euclid 2) G F) A) &  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal4 H C B) & (r1_tarski H A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((k12_euclid (k19_euclid k6_numbers A)) = (k18_complex1 A))  &  ((k12_euclid (k19_euclid A k6_numbers)) = (k18_complex1 A)) ) ) ) ).
tt(t23_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  ((k2_borsuk_1 (k3_pcomps_1 A) (k3_pcomps_1 B)) = (k3_pcomps_1 (k1_topreal7 A B))) ) ) ) ) ).
tt(t23_topreal8,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 4))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ((v1_xboole_0 (k2_topreal9 A C B)) & (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ) ) ).
tt(t23_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((v4_pre_topc (k1_rcomp_1 B C) (k4_topmetr A D)) & (m1_subset_1 (k1_rcomp_1 B C) (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A D))))) ) ) ) ) ) ) ) ) ) ).
tt(t23_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) =>  ( (~  (A = B) )  => (m1_subset_1 B (u1_struct_0 (k11_toprealb A)))) ) ) ) ) ).
tt(t23_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden C (k1_topreal9 A D B)) <=> (r2_hidden (k4_algstr_0 (k15_euclid A) C) (k1_topreal9 A (k4_algstr_0 (k15_euclid A) D) B))) ) ) ) ) ) ) ) ) ).
tt(t23_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k12_euclid (k4_struct_0 (k15_euclid A))) = k6_numbers) ) ) ).
tt(t23_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc D B) =>  ((k1_tops_1 B D) = D) )  &  ( ((k1_tops_1 A C) = C)  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ) ) ).
tt(t23_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) => (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t23_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_tops_1 B A) &  (B = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t23_tops_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr))))) )  =>  ((v5_pre_topc A k3_topmetr k3_topmetr) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_topmetr)) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (? [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  & (r1_tarski (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A (k2_rcomp_1 (k6_xcmplx_0 B D) (k2_xcmplx_0 B D))) (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A B) C) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 k3_topmetr) A B) C)))) ) ) ) ) ) ) ) ) ).
tt(t23_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_transgeo A) & (l1_analoaf A)) )  => (r3_transgeo A (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t23_treal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (m1_pre_topc A k3_topmetr))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B k3_topmetr))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (~  ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r1_xxreal_0 D E) &  ((r1_tarski (k1_rcomp_1 D E) (u1_struct_0 A)) &  ((r1_tarski (k1_rcomp_1 D E) (u1_struct_0 B)) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_rcomp_1 D E)) (k1_rcomp_1 D E))) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_trees_1,ax, ( (~ (v1_xboole_0 (k1_tarski k1_xboole_0)))  & (v1_trees_1 (k1_tarski k1_xboole_0))) ).
tt(t23_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_trees_2 C A))  =>  (~  ( (~ (r1_xxreal_0 (k5_card_1 C) B))  &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ((r2_hidden D C) & (r1_xxreal_0 B (k3_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v5_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ( (~ (v1_xboole_0 (k1_funct_1 A B)))  &  ((v1_finset_1 (k1_funct_1 A B)) & (v1_trees_1 (k1_funct_1 A B))) ) ) ) ) ) ) ).
tt(t23_trees_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ( (~  ((r2_hidden C (k10_xtuple_0 A)) & (r2_hidden C (k4_trees_2 A))) )  =>  ((k9_trees_4 A B C) = A) ) ) ) ) ) ) ).
tt(t23_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_trees_3 A))  =>  ((k9_trees_9 A) = (k3_tarski (a_1_3_trees_9 A))) ) ) ).
tt(t23_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((m1_pre_topc B C) <=>  ((k1_tsep_1 A B C) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) ) ) ) ) ) ) ) ).
tt(t23_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=> (r1_connsp_1 A (k7_subset_1 (u1_struct_0 A) B (k9_subset_1 (u1_struct_0 A) B C)) (k7_subset_1 (u1_struct_0 A) C (k9_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t23_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  => (r1_borsuk_1 A B)) ) ) ) ).
tt(t23_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r1_xxreal_0 3 (k3_finseq_1 D)) & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) D) A B))  =>  ((r1_turing_1 A B C (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) 2)) &  ((r1_turing_1 A B (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) 2) (k2_nat_1 (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) (k7_partfun1 k5_numbers D 2)) 4)) & (r1_turing_1 A B (k2_nat_1 (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) (k7_partfun1 k5_numbers D 2)) 4) (k2_nat_1 (k2_nat_1 (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) (k7_partfun1 k5_numbers D 2)) (k7_partfun1 k5_numbers D 3)) 6))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_twoscomp,ax, ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 k6_numbers 1 1)) = 1)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k26_twoscomp (k11_finseq_1 1 1 k6_numbers)) = 1)  &  ((k1_funct_1 k26_twoscomp (k11_finseq_1 1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t23_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  ((k8_unialg_2 A (k5_unialg_2 A B C) C) = C) ) ) ) ) ) ) ).
tt(t23_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  => (v4_lattice3 (k12_unialg_2 A))) ) ).
tt(t23_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((r2_hidden B (k2_uniroots A)) =>  ((k17_complex1 B) = 1) ) ) ) ) ) ).
tt(t23_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k6_polynom5 A (k13_polynom3 A B C)) = (k4_subset_1 (u1_struct_0 A) (k6_polynom5 A B) (k6_polynom5 A C))) ) ) ) ) ) ) ).
tt(t23_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc B A) &  ((v4_pre_topc C A) &  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r1_tarski C D) & (r1_tarski (k2_pre_topc A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r1_tarski (k1_urysohn1 A) k2_urysohn1)) ) ).
tt(t23_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k8_cqc_lang A D E) F C) <=>  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F D) C) = k7_margrel1)  |  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B F E) C) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_valued_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers C)))) ) )  =>  ((k8_nat_1 C D A) = (k8_nat_1 C D B)) ) ) ) ) ) ) ) ).
tt(t23_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k61_valued_1 (k1_funct_4 A B) C) = (k1_funct_4 (k61_valued_1 A C) (k61_valued_1 B C))) ) ) ) ) ) ) ).
tt(t23_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k24_valued_1 (k30_valued_1 B) A) = (k30_valued_1 (k24_valued_1 B A))) ) ) ) ) ).
tt(t23_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((m2_vectsp_4 (k3_vectsp_4 A B D C) A B C) & (m1_subset_1 (k3_vectsp_4 A B D C) (u1_struct_0 (k6_vectsp10 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t23_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D C) &  ((v9_vectsp_1 D C) &  ((v10_vectsp_1 D C) &  ((v11_vectsp_1 D C) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D C)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 D)) &  ((v13_vectsp_1 E D D) &  ((v1_mod_2 E C D D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D))))) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 D) (k1_vectsp11 D E A) F) = (k4_struct_0 D))  =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 D) (k1_vectsp11 D E (k2_xcmplx_0 A B)) F) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k4_vectsp_1 A B C (k5_algstr_0 B D E)) = (k5_algstr_0 B (k4_vectsp_1 A B C D) (k4_vectsp_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_vectsp_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_vectsp_2 A))) =>  ( ((k4_vectsp_1 A (k3_vectsp_2 A) B (k3_rlvect_1 (k3_vectsp_2 A) D E)) = (k3_rlvect_1 (k3_vectsp_2 A) (k4_vectsp_1 A (k3_vectsp_2 A) B D) (k4_vectsp_1 A (k3_vectsp_2 A) B E)))  &  ( ((k4_vectsp_1 A (k3_vectsp_2 A) (k3_rlvect_1 A B C) D) = (k3_rlvect_1 (k3_vectsp_2 A) (k4_vectsp_1 A (k3_vectsp_2 A) B D) (k4_vectsp_1 A (k3_vectsp_2 A) C D)))  &  ( ((k4_vectsp_1 A (k3_vectsp_2 A) (k6_algstr_0 A B C) D) = (k4_vectsp_1 A (k3_vectsp_2 A) B (k4_vectsp_1 A (k3_vectsp_2 A) C D)))  &  ((k4_vectsp_1 A (k3_vectsp_2 A) (k5_struct_0 A) D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((r1_struct_0 E C) & (r1_struct_0 E D))  => (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (m1_vectsp_4 (k2_vectsp_5 A B C D) A (k1_vectsp_5 A B C D))) ) ) ) ) ) ) ) ).
tt(t23_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) => (r1_tarski (k1_vectsp_6 A B (k5_vectsp_6 A B C D)) (k4_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B C) (k1_vectsp_6 A B D)))) ) ) ) ) ) ) ) ).
tt(t23_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (v1_matrlin (k1_vectsp_4 A B) A)) ) ) ) ).
tt(t23_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B C) (k4_vfunct_1 A B C (k1_real_1 1)))) ) ) ) ) ) ).
tt(t23_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B C) (k2_vfunct_2 A B C (k10_complex1 k6_complex1)))) ) ) ) ) ) ).
tt(t23_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) <=> (r1_tarski (k3_waybel_0 A B) B)) ) ) ) ) ).
tt(t23_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_waybel_0 C B))  &  ( ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_waybel_0 C B)) ) ) ) ) ) ) ) ).
tt(t23_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  ((k4_yellow_6 A B) = (k1_waybel11 A B)) ) ) ) ) ).
tt(t23_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~ (v1_xboole_0 (a_2_0_waybel12 A B))) ) ) ) ) ).
tt(t23_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A)))))  &  ((v4_yellow_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))) (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) &  ((v7_yellow_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))) (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) &  ((v4_waybel_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))) (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) & (m1_yellow_0 (k2_yellow_1 (k7_waybel_0 (k1_waybel_8 A))) (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A))))) ) ) ) ) ) ).
tt(t23_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((k5_waybel11 A) = (u1_pre_topc A)) ) ) ).
tt(t23_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_0_waybel15 A B C))) ) ) ) ) ) ) ).
tt(t23_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) => (v2_waybel_6 B A)) ) ) ) ) ).
tt(t23_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_waybel_3 A F D) & (r1_waybel_3 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v2_cantor_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_tops_2 E B) &  ((v2_cantor_1 E B) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ((v1_tops_2 (k2_xboole_0 D E) C) &  ((v2_cantor_1 (k2_xboole_0 D E) C) & (m1_subset_1 (k2_xboole_0 D E) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r3_waybel_1 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) E)))) )  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C) (k3_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t23_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v21_waybel_0 C A B) => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t23_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D B) & (m1_yellow_0 D B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ( ((u1_struct_0 C) = (u1_struct_0 D))  & (v3_waybel_0 C A)) )  => (v3_waybel_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t23_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  ((r2_yellow_0 A (k7_domain_1 B C D)) =>  ((r2_yellow_0 (k5_yellow_0 A B) (k7_domain_1 B C D)) &  ((k2_yellow_0 (k5_yellow_0 A B) (k7_domain_1 B C D)) = (k2_yellow_0 A (k7_domain_1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel24,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k4_waybel_3 A B (k2_yellow_0 (k5_yellow_1 A B) C) D) = (k2_yellow_0 (k3_waybel_3 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v3_pre_topc B (k1_waybel25 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_waybel25 A)))))  => (v13_waybel_0 B (k1_waybel25 A))) ) ) ) ).
tt(t23_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) &  ((v6_pre_topc C) &  ((v1_waybel25 C) & (l1_pre_topc C)) ) ) )  =>  ( ((r1_waybel18 B C) &  ((v3_lattice3 (k1_waybel26 A C)) & (v3_waybel_3 (k1_waybel26 A C))) )  =>  ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B))) ) ) ) ) ) ) ) ).
tt(t23_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_waybel27 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_waybel27 A B))) =>  ((r3_orders_2 (k2_waybel27 A B) C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r3_orders_2 B (k3_waybel27 A B C E) (k3_waybel27 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel28,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r2_hidden A (k1_yellow_6 B))) ) ) ).
tt(t23_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel24 A C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_waybel24 A C))) =>  ((r3_orders_2 (k3_waybel24 A C) D E) => (r1_tarski (k5_waybel26 D) (k5_waybel26 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_waybel_0 C A))  =>  ((k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A (k3_waybel_2 A B C))) = (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A C)))) ) ) ) ) ) ) ).
tt(t23_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) =>  ((v8_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)))) =>  ( (B = (u1_orders_2 A))  => (v4_pre_topc B (k2_borsuk_1 A A))) ) ) ) ) ) ) ).
tt(t23_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (~  ( (~ (v1_finset_1 C))  & (v1_finset_1 (a_3_2_waybel31 A B C))) ) ) ) ) ) ) ) ).
tt(t23_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A (k2_waybel32 A B))) = (a_2_2_waybel32 A B)) ) ) ) ) ).
tt(t23_waybel33,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_yellow_9 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc C A) =>  ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  &  ((v4_pre_topc C A) =>  ((v4_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t23_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_waybel_3 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v1_waybel34 (k1_waybel34 A B C) B A) => (v22_waybel_0 C A B)) ) ) ) ) ) ) ).
tt(t23_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_yellow_0 A (k4_waybel35 A B C D))) )  => (v4_waybel35 (k6_waybel35 A B C) A)) ) ) ) ) ) ) ).
tt(t23_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel_3 B A)) )  <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k5_waybel_0 A (k3_yellow_0 A)) = (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) ) ) ).
tt(t23_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_0_waybel_5 A B C D))  =>  ((k5_yellow_2 A (k4_waybel_5 A (k6_waybel_5 B C (u1_struct_0 A) D))) = (k1_yellow_0 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_waybel_6 B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r3_orders_2 A B (k1_yellow_0 A C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r3_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r1_subset_1 B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v1_waybel_7 D A) &  ((r1_tarski B D) & (r1_subset_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k2_struct_0 (k1_waybel_8 A))) (k2_struct_0 (k1_waybel_8 (k1_yellow_2 A A B))))) ) ) ) ) ).
tt(t23_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_yellow_6 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_yellow_6 A B))) => (m1_subset_1 (k2_xboole_0 C D) (u1_struct_0 (k9_yellow_6 A B)))) ) ) ) ) ) ) ) ).
tt(t23_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (u1_struct_0 (k5_weddwitt A B)) (u1_struct_0 A))) ) ) ) ).
tt(t23_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (E = (k1_funct_1 (k6_weierstr A B) C))  &  (F = (k1_funct_1 (k6_weierstr A B) D)) )  => (r1_xxreal_0 (k18_complex1 (k9_real_1 E F)) (k4_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k2_wellord1 A (k1_relat_1 A)) = A) ) ) ).
tt(t23_wellord2,ax, (! [A:$i] : (r1_tarski (k1_wellord2 A) (k2_zfmisc_1 A A))) ).
tt(t23_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( ( (C = (k7_xcmplx_0 B A))  & (r1_int_2 B A))  =>  ( (A = k6_numbers)  |  ( (B = (k2_rat_1 C))  &  (A = (k1_rat_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t23_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 A (k2_xboole_0 B C)) = (k2_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(t23_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k5_xboolean A (k7_xboolean B C)) = (k4_xboolean (k5_xboolean (k5_xboolean A (k3_xboolean B)) C) (k5_xboolean (k5_xboolean A (k3_xboolean C)) B))) ) ) ) ) ) ) ).
tt(t23_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 A C)) = (k6_xcmplx_0 C B)) ) ) ) ) ) ) ).
tt(t23_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) (k2_xcmplx_0 C D)) => (r1_xxreal_0 (k6_xcmplx_0 A D) (k2_xcmplx_0 C B))) ) ) ) ) ) ) ) ) ).
tt(t23_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k9_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) ) ) ).
tt(t23_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 (k3_xxreal_0 B C) A))  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ) ).
tt(t23_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k3_xxreal_1 A B) (k1_xxreal_1 A B))) ) ) ) ).
tt(t23_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m1_xxreal_2 A (k2_xxreal_1 B A))) ) ) ) ).
tt(t23_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( ( (A = k1_xxreal_0)  =>  ((k2_xxreal_3 A) = k2_xxreal_0) )  &  ( ( ((k2_xxreal_3 A) = k2_xxreal_0)  =>  (A = k1_xxreal_0) )  &  ( ( (A = k2_xxreal_0)  =>  ((k2_xxreal_3 A) = k1_xxreal_0) )  &  ( ((k2_xxreal_3 A) = k1_xxreal_0)  =>  (A = k2_xxreal_0) ) ) ) ) ) ) ).
tt(t23_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (D = (k12_lattice3 A B C))  <=>  ((r1_orders_2 A D B) &  ((r1_orders_2 A D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A E B) & (r1_orders_2 A E C))  => (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ( ((v1_waybel_3 (k8_yellow_3 A B C) A) & (v1_waybel_3 (k9_yellow_3 A B C) B))  => (v1_waybel_3 C (k3_yellow_3 A B))) ) ) ) ) ) ) ).
tt(t23_yellow12,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  => (r1_relset_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 A)) (k9_subset_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 A))) (u1_orders_2 A) (u1_orders_2 (k7_lattice3 A))) (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t23_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_yellow_8 C A B) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (m1_yellow13 C A B)) ) ) ) ) ) ).
tt(t23_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v3_yellow_8 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  &  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) )  => (v3_yellow_8 D B)) ) ) ) ) ) ) ) ) ).
tt(t23_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_waybel23 (k2_struct_0 A) A) & (v4_waybel23 (k2_struct_0 A) A)) ) ) ).
tt(t23_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r4_yellow16 B A) => (v24_waybel_0 B)) ) ) ) ) ).
tt(t23_yellow17,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v1_compts_1 (k4_waybel18 A B C))) )  => (v1_compts_1 (k3_waybel18 A B))) ) ) ) ) ).
tt(t23_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_yellow18 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A D C) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (E = C)  &  ( (F = D)  &  (? [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B F E)) &  ( (H = G)  &  (~  ((v3_altcat_3 G A C D) <=> (v3_altcat_3 H B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r1_waybel_0 A C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_waybel_9 A C D) => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k3_yellow_0 (k2_yellow_1 (u1_pre_topc A))) = k1_xboole_0) ) ) ).
tt(t23_yellow20,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((l2_altcat_1 B) =>  ((r1_yellow20 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_yellow20 A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_yellow20 A B))) =>  ( ( (G = C)  &  ( (G = E)  &  ( (H = D)  &  (H = F) ) ) )  =>  ( ((k1_altcat_1 A C D) = k1_xboole_0)  |  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A C D)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 B E F)) =>  ( (I = J)  => (r2_hidden I (k1_altcat_1 (k2_yellow20 A B) G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t23_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] : (r1_yellow_0 A B))  <=>  (! [B:$i] : (r2_yellow_0 A B)) ) ) ) ).
tt(t23_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v2_waybel_0 (k6_yellow_3 A B C D) (k3_yellow_3 A B)) =>  ((v2_waybel_0 C A) & (v2_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t23_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_lattice3 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) C)) ) ) ) ) ) ).
tt(t23_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_yellow_5 A (k3_yellow_0 A) B) = (k3_yellow_0 A)) ) ) ) ) ).
tt(t23_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ( (D = (k5_yellow_6 A B C))  => (r1_waybel_0 A D C)) ) ) ) ) ) ) ) ).
tt(t23_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A B C) = (k12_lattice3 (k7_lattice3 A) (k8_lattice3 A B) (k8_lattice3 A C))) ) ) ) ) ) ) ).
tt(t23_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t23_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  <=>  ((v1_tops_2 (k2_cantor_1 (u1_struct_0 A) B) A) &  ((v1_cantor_1 (k2_cantor_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k2_cantor_1 (u1_struct_0 A) B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t23_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k4_ordinal1) =>  ((v8_zf_fund1 B A) =>  ((r2_hidden C B) &  ((r2_hidden (k2_ordinal4 A) B) & (r2_hidden (k3_ordinal4 A) B)) ) ) ) ) ) ) ) ) ).
tt(t23_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_zf_lang A) =>  ((k21_zf_lang A) = (k20_zf_lang (k21_zf_lang (k20_zf_lang A)))) ) ) ) ).
tt(t23_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~  ((v2_zf_lang A) &  ((k1_funct_1 A 1) = k6_numbers) ) )  &  ( (~  ((v3_zf_lang A) &  ((k1_funct_1 A 1) = 1) ) )  &  ( (~  ((v4_zf_lang A) &  ((k1_funct_1 A 1) = 2) ) )  &  ( (~  ((v5_zf_lang A) &  ((k1_funct_1 A 1) = 3) ) )  &  (~  ((v6_zf_lang A) &  ((k1_funct_1 A 1) = 4) ) ) ) ) ) ) ) ) ) ).
tt(t23_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k5_xboole_0 (k1_tarski A) (k1_tarski B)) = (k2_tarski A B)) ) ) ) ).
tt(t23_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_zfmodel1 (k6_partfun1 A) A)) ) ).
tt(t23_zf_model,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((r2_zf_model C (k8_zf_lang B A)) <=> (r2_zf_model C A)) ) ) ) ) ) ) ).
tt(t23_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r2_ordinal2 (k1_ordinal1 A) 1)) ) ).
tt(t23_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ( ((r1_struct_0 C B) & (m1_zmodul01 C D))  => (r1_struct_0 D B)) ) ) ) ) ) ) ) ).
tt(t240_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 B C) (k1_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t241_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 B C) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t242_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k1_xxreal_1 B C) (k3_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t243_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k2_xxreal_1 B C) (k3_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t244_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 B C) (k3_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t245_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 B C) (k3_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t246_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 B C) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t247_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 B C) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t248_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k2_xxreal_1 B C) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t249_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k1_xxreal_1 B C) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t24_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r2_hidden C (k2_abcmiz_0 A B)) =>  ((r1_abcmiz_0 A B C) &  ((k5_abcmiz_0 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(t24_abcmiz_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_abcmiz_1)))  =>  ((v1_finset_1 (k1_abcmiz_1 A)) & (m1_subset_1 (k1_abcmiz_1 A) (k1_zfmisc_1 k2_abcmiz_1))) ) ) ).
tt(t24_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ((v6_abcmiz_1 B A) &  ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A))) )  <=>  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) &  ((k1_xtuple_0 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0))) = k7_abcmiz_1) ) ) ) ) ) ) ).
tt(t24_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_absvalue A) = (k1_absvalue (k13_complex1 1 A))) ) ) ).
tt(t24_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (k2_aff_1 A B C))  =>  ( (B = C)  |  ((v1_aff_1 D A) &  ((r2_hidden B D) &  ((r2_hidden C D) &  (~  (B = C) ) ) ) ) ) )  &  ( ((v1_aff_1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  =>  ( (B = C)  |  ( (~  (B = C) )  &  (D = (k2_aff_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 D A) &  ((v1_aff_4 E A) &  ((r2_hidden B D) &  ((r2_hidden C D) &  ((r2_hidden B E) & (r2_hidden C E)) ) ) ) )  =>  ( (D = E)  |  ( (B = C)  | (v1_aff_1 (k9_subset_1 (u1_struct_0 A) D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k1_ordinal4 A B)))) ) ) ) ).
tt(t24_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  ((r1_afinsq_2 A B) => (r1_xboole_0 A B)) ) ) ) ) ).
tt(t24_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k14_afproj A))) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k6_afproj A C))  & (v1_aff_4 C A)) ) ) ) ) ) ) ).
tt(t24_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_afvect0 A B C D) &  ((r2_afvect0 A B E F) & (r1_afvect0 A C E)) )  =>  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((m1_algspec1 B A) =>  (! [C:$i] :  ((r2_hidden C (k10_xtuple_0 A)) =>  ((r2_hidden (k1_funct_1 B C) (k9_xtuple_0 A)) &  ((k1_funct_1 A (k1_funct_1 B C)) = C) ) ) ) ) ) ) ) ).
tt(t24_algstr_4,ax, (! [A:$i] :  ( (A = k1_xboole_0)  <=>  ((k12_algstr_4 A) = k1_xboole_0) ) ) ).
tt(t24_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_altcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_altcat_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_altcat_1 A))) =>  ( (~  ( (B = C)  &  (C = D) ) )  =>  ((k4_altcat_1 (u1_struct_0 (k9_altcat_1 A)) (u1_altcat_1 (k9_altcat_1 A)) (u2_altcat_1 (k9_altcat_1 A)) B C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t24_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) & (m1_altcat_2 C A)) )  =>  ( ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) & (r2_altcat_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C)) (u1_altcat_1 B) (u1_altcat_1 C)))  => (m1_altcat_2 B C)) ) ) ) ) ) ) ).
tt(t24_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) => (v1_altcat_3 D A B C)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (~ (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ((v3_altcat_3 F A D E) =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v3_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ami_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden (k4_tarski 1 A) k2_ami_2)) ) ).
tt(t24_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) <=>  (~  ( (~  (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k2_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k3_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k4_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k5_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k6_ami_3 B C)) ) ) ) ) )  &  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  (A = (k7_ami_3 B)) ) ) )  &  ( (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k8_ami_3 C B)) ) ) ) ) )  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k9_ami_3 C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_ami_3)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) &  ((v1_finset_1 B) & (v4_extpro_1 B 2 k1_ami_3 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_ami_3)))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  (! [J:$i] :  ((m1_subset_1 J (u1_compos_1 k1_ami_3)) =>  ( ( (J = (k3_extpro_1 2 k1_ami_3 E (k5_extpro_1 2 k1_ami_3 E C G)))  &  (J = (k9_ami_3 I H)) )  =>  ( (I = (k1_ordinal1 (k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 E C G))))  |  ( (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 F D G) H) k6_numbers))  & (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 E C G) H) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k8_ami_3 B A) C) = (k8_ami_3 (k2_xcmplx_0 B C) A)) ) ) ) ) ) ) ).
tt(t24_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) ) )  => (v5_amistd_1 (k16_funcop_1 (k1_ami_wstd A B k6_numbers) (k2_compos_1 B)) A B)) ) ) ) ).
tt(t24_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  ((r4_analmetr (k2_analmetr A B C) D E F G) => (r4_analmetr (k2_analmetr A B C) D E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ((k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) = D) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_analoaf A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analoaf A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analoaf A))) =>  (~  ( (~ (r2_analoaf (k2_analoaf A) B C D E))  &  ( (~ (r2_analoaf (k2_analoaf A) B C E D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analoaf A))) =>  (~  ( ((r2_analoaf (k2_analoaf A) B C B F) | (r2_analoaf (k2_analoaf A) B C F B))  &  ((r2_analoaf (k2_analoaf A) D E D F) | (r2_analoaf (k2_analoaf A) D E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) => (r3_analmetr A D E (k2_analort A B C D) (k2_analort A B C E) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_anproj_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v7_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) & (l1_rlvect_1 D)) ) ) ) ) ) ) ) ) )  =>  (~  ((r2_hidden (k3_xtuple_0 A B C) (u1_collsp (k5_anproj_1 D))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (~  ( (A = (k2_anproj_1 D E))  &  ( (B = (k2_anproj_1 D F))  &  ( (C = (k2_anproj_1 D G))  &  ( (~ (v9_struct_0 E D))  &  ( (~ (v9_struct_0 F D))  &  ( (~ (v9_struct_0 G D))  & (r2_anproj_1 D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  ((r1_collsp (k5_anproj_1 A) B C D) =>  ((r1_collsp (k5_anproj_1 A) B D C) &  ((r1_collsp (k5_anproj_1 A) C B D) &  ((r1_collsp (k5_anproj_1 A) D C B) &  ((r1_collsp (k5_anproj_1 A) D B C) & (r1_collsp (k5_anproj_1 A) C D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (C = (k3_tarski (a_2_1_aofa_000 A B)))  & (v1_unialg_2 C A)) ) ) ) ) ) ) ).
tt(t24_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m2_aofa_i00 F A B D E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k44_aofa_i00 A B D E F G)) (k3_funct_2 (k9_funct_2 B k4_numbers) B F C)) = (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = (k3_funct_2 (k9_funct_2 B k4_numbers) B F C)) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k44_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v6_armstrng (a_2_0_armstrng A B) A) & (m1_subset_1 (a_2_0_armstrng A B) (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) ) ) ).
tt(t24_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden (k5_arytm_0 A B) k1_numbers) =>  (B = k6_numbers) ) ) ) ) ) ).
tt(t24_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k2_arytm_1 B (k7_arytm_2 A C)) = (k2_arytm_1 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ).
tt(t24_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( ((k4_arytm_3 A 1) = A)  &  ((k4_arytm_3 1 A) = 1) ) ) ) ).
tt(t24_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_limfunc1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ( (~ (r2_hidden B (k7_asympt_0 A)))  & (r2_hidden A (k7_asympt_0 B))) ) ) ) ) ) ).
tt(t24_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k4_power (k7_real_1 (k9_real_1 (k5_square_1 B) B) 1) 4)) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((k6_asympt_0 (k3_asympt_1 8)) = (k6_asympt_0 B)) ) ) ) ) ) ) ) ) ).
tt(t24_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (r2_hidden (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) (k5_autalg_1 A B))) ) ) ) ).
tt(t24_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k2_group_1 A B)) (k6_autgroup A B)) (k6_autgroup A (k1_group_1 A)))) ) ) ) ).
tt(t24_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_bagorder (k4_bagorder A) A)) ) ).
tt(t24_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = B) ) ) ) ) ) ) ) ).
tt(t24_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 (k2_bcialg_1 A B) A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A C B) =>  ((k2_bcialg_1 A B) = (k2_bcialg_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t24_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ((v7_bcialg_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A C (k1_bcialg_1 A B D)) => (r1_bcialg_1 A D (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_bcialg_4 A B 3) = (k1_bcialg_4 A (k1_bcialg_4 A B B) B)) ) ) ) ) ).
tt(t24_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~  ((k3_bcialg_5 A B C D) = A) )  &  ( (~  ((k3_bcialg_5 A B C D) = B) )  &  ( (~  ((k3_bcialg_5 A B C D) = C) )  &  (~  ((k3_bcialg_5 A B C D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k3_bcialg_6 A (k20_binop_2 C D) B) = (k1_bcialg_1 A (k3_bcialg_6 A C B) (k2_bcialg_1 A (k3_bcialg_6 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t24_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v19_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A)) ) ) ) ).
tt(t24_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) =>  ((k2_bhsp_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A B C)) = (k7_real_1 (k2_bhsp_1 A B B) (k2_bhsp_1 A C C))) ) ) ) ) ) ) ) ).
tt(t24_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  =>  ((v2_comseq_2 (k3_bhsp_2 A C B)) &  ((k2_seq_2 (k3_bhsp_2 A C B)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t24_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) => (v2_bhsp_3 B A)) ) ) ) ) ).
tt(t24_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v3_bhsp_3 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k3_bhsp_1 A (k4_bhsp_4 A B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k7_bilinear A B C (k9_bilinear A B C D E) F) (k6_hahnban1 A C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( (B = (k5_euclid A))  =>  ((k7_binarith A (k3_binarith A B) (k1_binari_2 A)) = B) ) ) ) ) ) ).
tt(t24_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A (k5_series_1 2 B)) =>  ((k1_binari_4 B A) = B) ) ) ) ) ) ).
tt(t24_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_funct_1 (k8_binom A B C D) (k2_nat_1 D 1)) = (k2_binom A C D)) ) ) ) ) ) ) ) ) ).
tt(t24_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k5_series_1 2 (k2_nat_1 B 1))) =>  (! [D:$i] :  ((m2_finseq_2 D k6_margrel1 (k4_finseq_2 B k6_margrel1)) =>  ( (D = (k1_funct_1 (k2_bintree2 A B) (k3_nat_d (k2_nat_1 C 1) 2)))  =>  ((k1_funct_1 (k2_bintree2 A (k2_nat_1 B 1)) C) = (k7_finseq_1 D (k10_binarith k5_numbers (k4_nat_d (k2_nat_1 C 1) 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B (k3_lattices A C D)) => (r3_lattices A (k1_boolealg A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t24_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~  ((k3_borsuk_1 A B C D) = k1_xboole_0) )  =>  ( ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 A)) (k8_borsuk_1 A B) (k3_borsuk_1 A B C D)) = C)  &  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))) (k9_setfam_1 (u1_struct_0 B)) (k9_borsuk_1 A B) (k3_borsuk_1 A B C D)) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ((r1_xxreal_0 A B) =>  ( (~ (v1_xboole_0 (k1_rcomp_1 A B)))  &  ((v2_connsp_1 (k1_rcomp_1 A B) k5_topmetr) &  ((v2_compts_1 (k1_rcomp_1 A B) k5_topmetr) & (m1_subset_1 (k1_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) ) ) ) ) ) ) ).
tt(t24_borsuk_5,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v1_rat_1 B)) )  =>  (~  ( (~  (A = k6_numbers) )  & (v1_rat_1 (k13_complex1 A B))) ) ) ) ) ) ).
tt(t24_borsuk_6,ax, ( (~ (v1_xboole_0 a_0_12_borsuk_6))  &  ((v4_pre_topc a_0_12_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr)) & (m1_subset_1 a_0_12_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))) ) ).
tt(t24_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k1_borsuk_7 A A B C D E) = (k4_funct_4 A B D E)) ) ) ) ) ) ).
tt(t24_bspace,ax, (! [A:$i] : (v13_algstr_0 (k7_bspace A))) ).
tt(t24_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B (k5_bvfunc_1 A C (k1_bvfunc_1 A D))) (k9_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t24_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  ( (B = (k3_enumset1 C D E F G))  =>  ( (C = F)  |  ( (D = F)  |  ( (E = F)  |  ( (F = G)  |  ((k5_bvfunc_2 A F B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v3_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k9_bvfunc_1 A C B)) (k9_bvfunc_1 A C (k13_bvfunc_1 A B))) & (r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k9_bvfunc_1 A B C)) (k9_bvfunc_1 A (k14_bvfunc_1 A B) C))) ) ) ) ) ) ) ).
tt(t24_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k9_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t24_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) C) (k1_bvfunc_1 A (k2_bvfunc_1 A B D))))) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k5_bvfunc_1 A D C) B E) (k5_bvfunc_1 A (k7_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k2_bvfunc_1 A B C) D E) (k2_bvfunc_1 A B (k6_bvfunc_2 A C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D (k9_bvfunc_1 A C B)) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 C (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D B) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t24_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k1_bvfunc_1 A C)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C (k1_bvfunc_1 A B)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t24_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k10_bvfunc_1 A (k10_bvfunc_1 A (k10_bvfunc_1 A B C) (k10_bvfunc_1 A C B)) B))) ) ) ) ) ) ).
tt(t24_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k1_bvfunc_1 A B) (k10_bvfunc_1 A (k9_bvfunc_1 A C B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t24_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A C F) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k9_bvfunc_1 A E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_c0sp1 A)))  &  ((v13_algstr_0 (k11_c0sp1 A)) &  ((v2_rlvect_1 (k11_c0sp1 A)) &  ((v3_rlvect_1 (k11_c0sp1 A)) &  ((v4_rlvect_1 (k11_c0sp1 A)) &  ((v5_rlvect_1 (k11_c0sp1 A)) &  ((v6_rlvect_1 (k11_c0sp1 A)) &  ((v7_rlvect_1 (k11_c0sp1 A)) &  ((v8_rlvect_1 (k11_c0sp1 A)) & (l1_rlvect_1 (k11_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r1_tarski (k13_pre_poly (k26_valued_1 (u1_struct_0 A) k1_numbers C B)) (k13_pre_poly C))) ) ) ) ) ) ).
tt(t24_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_valuat_1 F A E) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) E (k2_valuat_1 A E)) =>  ((r1_valuat_1 A E (k4_substut2 A B C D) F G) <=>  (? [H:$i] :  ((m1_subset_1 H E) &  ( ((k3_funct_2 (k3_qc_lang1 A) E G D) = H)  & (r1_valuat_1 A E B F (k1_sublemma A E G (k12_sublemma A E C H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t24_card_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) &  ((r1_tarski B C) & (r2_wellord2 A C)) )  =>  ((r2_wellord2 A B) & (r2_wellord2 B C)) ) ) ) ) ).
tt(t24_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k2_card_2 A (k1_card_2 B C)) = (k1_card_2 (k2_card_2 A B) (k2_card_2 A C))) ) ) ) ) ) ) ).
tt(t24_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) => (r1_tarski (k3_card_3 A) (k3_card_3 B))) ) ) ) ) ).
tt(t24_card_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_finset_1 A))  =>  ((k1_card_1 A) = (k1_card_1 (k3_finseq_2 A))) ) ) ) ).
tt(t24_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  => (r1_ordinal1 k4_ordinal1 (k1_card_5 A))) ) ).
tt(t24_card_fil,ax, (! [A:$i] :  ((v1_card_1 A) => (r1_ordinal1 (k2_card_1 A) (k3_card_2 2 A))) ) ).
tt(t24_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k5_relat_1 B (k8_relat_1 C (k1_tarski A))) = (k7_funcop_1 (k8_relat_1 C (k1_tarski A)) (k3_tarski (k10_xtuple_0 B))))  =>  ((k2_card_fin B C A) = (k3_tarski (k10_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t24_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ((r2_hidden k4_ordinal1 (k1_card_5 A)) & (v1_card_lar B A))  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ( ((v3_ordinal1 D) &  ((v4_ordinal1 D) &  (~ (v1_finset_1 D)) ) )  =>  (~  ((r2_hidden D A) &  ((r2_hidden C D) & (r2_hidden D (k2_card_lar A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  ((k2_cat_1 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v1_cat_3 E A B C) & (v1_cat_3 F A C D))  => (v1_cat_3 (k5_cat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_cat_4 A B C (k2_cat_4 A B C) (k7_cat_4 A B C) (k8_cat_4 A B C)) = (k4_cat_1 A (k2_cat_4 A B C))) ) ) ) ) ) ) ).
tt(t24_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_hidden C (k10_cat_5 A B)) <=>  ((k3_graph_1 A C) = B) ) ) ) ) ) ) ) ).
tt(t24_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 A k6_numbers)) = 1) ) ) ).
tt(t24_catalg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((l3_msualg_1 B (k3_catalg_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_msualg_1 (k3_catalg_1 A) (k8_catalg_1 A C) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ).
tt(t24_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_cc0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k6_algstr_0 (k7_cc0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A k2_numbers D H) = (k5_binop_2 (k3_funct_2 A k2_numbers B H) (k3_funct_2 A k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_cc0sp2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_cc0sp2 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_cc0sp2 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k8_group_1 (k5_cc0sp2 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers D H) = (k9_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers B H) (k3_funct_2 (u1_struct_0 A) k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~  ((k3_comseq_2 A) = k6_numbers) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (v2_relat_1 (k1_valued_0 k2_numbers A B))) ) ) ) ) ) ) ) ).
tt(t24_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((r1_cfdiff_1 A C) & (r1_cfdiff_1 B C))  =>  ((r1_cfdiff_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  ((k2_cfdiff_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers A B) C) = (k11_complex1 (k2_cfdiff_1 A C) (k2_cfdiff_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t24_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_cfuncdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_cfuncdom A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cfuncdom A))) =>  ( ((k1_algstr_0 (k7_cfuncdom A) B C) = (k1_algstr_0 (k7_cfuncdom A) C B))  &  ( ((k1_algstr_0 (k7_cfuncdom A) (k1_algstr_0 (k7_cfuncdom A) B C) D) = (k1_algstr_0 (k7_cfuncdom A) B (k1_algstr_0 (k7_cfuncdom A) C D)))  &  ( ((k1_algstr_0 (k7_cfuncdom A) B (k4_struct_0 (k7_cfuncdom A))) = B)  &  ((v10_algstr_0 B (k7_cfuncdom A)) &  ( ((k6_algstr_0 (k7_cfuncdom A) B C) = (k6_algstr_0 (k7_cfuncdom A) C B))  &  ( ((k6_algstr_0 (k7_cfuncdom A) (k6_algstr_0 (k7_cfuncdom A) B C) D) = (k6_algstr_0 (k7_cfuncdom A) B (k6_algstr_0 (k7_cfuncdom A) C D)))  &  ( ((k6_algstr_0 (k7_cfuncdom A) B (k5_struct_0 (k7_cfuncdom A))) = B)  &  ( ((k6_algstr_0 (k7_cfuncdom A) (k5_struct_0 (k7_cfuncdom A)) B) = B)  &  ( ((k6_algstr_0 (k7_cfuncdom A) B (k1_algstr_0 (k7_cfuncdom A) C D)) = (k1_algstr_0 (k7_cfuncdom A) (k6_algstr_0 (k7_cfuncdom A) B C) (k6_algstr_0 (k7_cfuncdom A) B D)))  &  ((k6_algstr_0 (k7_cfuncdom A) (k1_algstr_0 (k7_cfuncdom A) C D) B) = (k1_algstr_0 (k7_cfuncdom A) (k6_algstr_0 (k7_cfuncdom A) C B) (k6_algstr_0 (k7_cfuncdom A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) (k25_valued_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers C B) (k10_complex1 k6_complex1)))) ) ) ) ) ) ).
tt(t24_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (r2_hidden A (k10_cgames_1 A))) ) ).
tt(t24_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) )  =>  ((r2_hidden D (k3_chain_1 A B C)) <=>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  ((r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 D E)) & (r1_xxreal_0 (k1_seq_1 D E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ( (C = D)  & (v8_glib_001 C A))  => (v8_glib_001 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) &  ((r1_xboole_0 (k2_msafree2 B) (k3_msafree2 A)) &  (C = (k2_circcomb A B)) ) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ( (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 A D))) => (v1_circuit2 (k5_facirc_1 A D I G) A D)) )  &  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) => (v1_circuit2 (k5_facirc_1 B E I H) B E)) ) )  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 C F))) => (v1_circuit2 (k5_facirc_1 C F I (k4_xxreal_0 G H)) C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 (k2_circcomb A B)))) ) ) ) ) ) ).
tt(t24_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v4_msafree2 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) &  ((v4_msafree2 D B) & (l3_msualg_1 D B)) )  =>  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) => (v4_msafree2 (k3_circcomb A B C D) (k2_circcomb A B))) ) ) ) ) ) ) ) ) ).
tt(t24_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_rlvect_2 C A (k6_domain_1 (u1_struct_0 A) B)) =>  ((v1_circled1 C A) =>  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers C B) = 1)  &  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ) ) ).
tt(t24_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_circtrm1 A B C D) =>  ( ((k10_xtuple_0 C) = (u1_struct_0 B))  &  ((k10_xtuple_0 D) = (u4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k1_classes1 B)) => (r2_hidden (k1_card_1 A) (k1_card_1 (k1_classes1 B)))) ) ) ).
tt(t24_classes2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) & (v1_funct_1 A)) )  =>  ( ((v4_ordinal1 (k9_xtuple_0 A)) &  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k4_classes1 B)) ) ) ) )  =>  ((k4_classes1 (k9_xtuple_0 A)) = (k3_card_3 A)) ) ) ) ).
tt(t24_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_clopban1 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (D = (k1_clvect_1 (k9_clopban1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k10_clopban1 A B D F) = (k1_clvect_1 B (k10_clopban1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clopban3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) E) (k1_normsp_1 A (k1_bhsp_4 A B) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A (k3_rlvect_1 A C D))) B) = (k1_normsp_1 A (k1_bhsp_4 A (k4_clopban4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_closure1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m2_pboole E B (k5_mssubfam B C) (k5_mssubfam B C)) =>  ( ((v1_closure1 E B C) &  ((r2_hidden A B) &  (D = (k1_funct_1 E A)) ) )  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) => (r1_tarski F (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m3_pboole D A B) =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r2_hidden E C) => (r2_pboole A D E)) ) )  => (r2_pboole A D (k4_mssubfam A B (k5_closure2 A B C)))) ) ) ) ) ) ) ) ).
tt(t24_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((u1_struct_0 A) = B)  => (v6_clvect_1 B A)) ) ) ) ) ).
tt(t24_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  =>  ((v2_comseq_2 (k3_clvect_2 A C B)) &  ((k2_seq_2 (k3_clvect_2 A C B)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t24_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) &  ((v4_clvect_2 A) & (l1_csspace A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k13_csspace A (k3_clvect_3 A B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k5_cohsp_1 A)) <=>  ((v1_finset_1 B) &  ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden C (k1_funct_1 A B))) ) ) ) ) ) ) ).
tt(t24_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_coh_sp A)) =>  ( ((k2_xtuple_0 (k8_coh_sp A B)) = (k6_partfun1 (k3_tarski B)))  &  ( ((k6_coh_sp A (k8_coh_sp A B)) = B)  &  ((k7_coh_sp A (k8_coh_sp A B)) = B) ) ) ) ) ) ).
tt(t24_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (A = 1)  & (r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)))  =>  (! [C:$i] :  ((l1_combgras C (k1_combgras A B) (k1_combgras A B)) =>  (~  ((v7_combgras C (k1_combgras A B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (~  ((g1_combgras (k1_combgras A B) (k1_combgras A B) (u1_combgras (k1_combgras A B) (k1_combgras A B) C) (u2_combgras (k1_combgras A B) (k1_combgras A B) C)) = (k8_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k3_complex1 (k13_complex1 A B)) = (k13_complex1 (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))) (k7_real_1 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B)))))  &  ((k4_complex1 (k13_complex1 A B)) = (k13_complex1 (k9_real_1 (k8_real_1 (k3_complex1 B) (k4_complex1 A)) (k8_real_1 (k3_complex1 A) (k4_complex1 B))) (k7_real_1 (k5_square_1 (k3_complex1 B)) (k5_square_1 (k4_complex1 B))))) ) ) ) ) ) ).
tt(t24_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 (k1_comptrig A) k32_sin_cos) => (r1_xxreal_0 k6_numbers (k4_complex1 A))) ) ) ).
tt(t24_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k3_vectsp_1 k1_complfld A A) = (k5_struct_0 k1_complfld)) ) ) ) ).
tt(t24_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_binop_2 A (k15_complex1 A)) = (k11_binop_2 2 (k3_complex1 A))) ) ) ).
tt(t24_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 (k6_xcmplx_0 (k5_card_1 B) 1) D))  =>  ((k1_funct_1 (k5_compos_1 A B (k7_nat_d (k5_card_1 B) 1)) D) = (k1_funct_1 (k5_compos_1 A (k7_compos_1 A B C) (k7_nat_d (k5_card_1 B) 1)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t24_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r1_tarski B C) => (r1_compos_2 B C)) ) ) ) ) ) ).
tt(t24_comptrig,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))))).
tt(t24_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v2_margrel1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_tarski (k1_relset_1 (k3_finseq_2 A) B) (k4_finseq_2 C A)) =>  ((k19_margrel1 B) = C) ) ) ) ) ) ) ) ).
tt(t24_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A B) C))) ) ) ) ) ) ).
tt(t24_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k31_valued_1 k5_numbers k2_numbers A))) = (k10_complex1 (k15_complex1 (k3_comseq_2 A)))) ) ) ).
tt(t24_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A B) = k5_complex1) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k10_comseq_3 A) B) = k5_complex1) ) ) ) ) ) ).
tt(t24_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  =>  ( ( ((u2_conlat_1 A B) = k1_xboole_0)  => (v9_conlat_1 B A))  &  ( ((u3_conlat_1 A B) = k1_xboole_0)  => (v8_conlat_1 B A)) ) ) ) ) ) ).
tt(t24_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B C) A) & (v2_connsp_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) )  =>  ((v2_connsp_1 B A) & (v2_connsp_1 C A)) ) ) ) ) ) ) ) ).
tt(t24_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc C A) &  ((v4_pre_topc C A) &  ((r2_hidden B C) & (r1_tarski C (k1_connsp_2 A B))) ) )  =>  (C = (k1_connsp_2 A B)) ) ) ) ) ) ) ) ).
tt(t24_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (m1_connsp_3 C A)) ) )  => (m1_connsp_3 (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t24_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_rlvect_2 C A (k6_domain_1 (u1_struct_0 A) B)) =>  ((v2_convex1 C A) =>  ( ((k1_funct_1 C B) = 1)  &  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k1_funct_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t24_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ( (~  (B = k5_complex1) )  =>  ((k1_convex4 A (k7_convex4 A B C)) = (k1_convex4 A C)) ) ) ) ) ) ) ) ).
tt(t24_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k13_cqc_lang A (k15_qc_lang1 A B C) B) = (k15_qc_lang1 A B C)) ) ) ) ) ) ) ).
tt(t24_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_qc_lang1 A (k13_cqc_sim1 A B) (k13_cqc_sim1 A (k7_cqc_lang A B C))) & (r1_qc_lang1 A (k13_cqc_sim1 A C) (k13_cqc_sim1 A (k7_cqc_lang A B C)))) ) ) ) ) ) ) ).
tt(t24_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (~  ((r2_cqc_the1 A B C) &  ((k10_xtuple_0 C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t24_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A B (k11_cqc_lang A C B)) A)) ) ) ) ) ) ) ).
tt(t24_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) => (r4_cqc_the3 A (k4_subset_1 (k3_cqc_lang A) B C) (k4_subset_1 (k3_cqc_lang A) (k1_cqc_the1 A B) (k1_cqc_the1 A C)))) ) ) ) ) ) ).
tt(t24_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_csspace4 A B)))  &  ((v13_algstr_0 (k9_csspace4 A B)) &  ((v2_rlvect_1 (k9_csspace4 A B)) &  ((v3_rlvect_1 (k9_csspace4 A B)) &  ((v4_rlvect_1 (k9_csspace4 A B)) &  ((v3_normsp_0 (k9_csspace4 A B)) &  ((v4_normsp_0 (k9_csspace4 A B)) &  ((v2_clvect_1 (k9_csspace4 A B)) &  ((v3_clvect_1 (k9_csspace4 A B)) &  ((v4_clvect_1 (k9_csspace4 A B)) &  ((v5_clvect_1 (k9_csspace4 A B)) &  ((v8_clvect_1 (k9_csspace4 A B)) & (l2_clvect_1 (k9_csspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A B (k4_algstr_0 A C)) = (k4_xcmplx_0 (k12_csspace A B C))) ) ) ) ) ) ) ).
tt(t24_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v9_decomp_1 C A B) <=>  ((v8_decomp_1 C A B) & (v19_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t24_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (A = (k4_subset_1 k5_numbers (k6_domain_1 k5_numbers k6_numbers) (k7_subset_1 k5_numbers (k2_finseq_1 A) (k1_tarski A)))) ) ) ).
tt(t24_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((r2_wellord1 (u1_orders_2 A) (u1_struct_0 A)) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_card_1 (k6_dickson A B)) = 1) ) ) ) ) ) ).
tt(t24_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers F B) (k26_valued_1 k1_numbers k1_numbers G C)) D) (k2_nat_1 A 1)) E) = (k7_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 F D) (k2_nat_1 A 1)) E)) (k8_real_1 C (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 G D) (k2_nat_1 A 1)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k1_fcont_1 A B) C) D) = (k8_real_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t24_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k10_diff_1 C (k9_real_1 B A) B (k7_real_1 B A)) = (k10_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) 2) B) (k8_real_1 (k8_real_1 2 A) A))) ) ) ) ) ) ) ) ).
tt(t24_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) A) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t24_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r5_waybel_4 A (k3_dilworth A C) B) => (r5_waybel_4 A (k2_struct_0 A) B)) ) ) ) ) ) ) ).
tt(t24_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_diraf A B C B D)) ) ) ) ) ) ) ) ) ).
tt(t24_dist_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k10_dist_1 A) = (k8_dist_1 A (k11_dist_1 A))) ) ) ).
tt(t24_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 C)) =>  ((k9_mcart_1 A B C D E F) = (a_6_0_domain_1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v2_finsub_1 B) =>  (! [C:$i] :  ((m1_dynkin C A) =>  ((r1_tarski B C) => (r1_tarski (k9_prob_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t24_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_binom A B (k1_nat_1 C 1)) = (k6_algstr_0 A (k2_binom A B C) B)) ) ) ) ) ) ) ).
tt(t24_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( (B = (k6_int_1 2 A))  =>  ((k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B C) C) = C) ) ) ) ) ) ) ) ).
tt(t24_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) => (m1_subset_1 B (u4_struct_0 (k11_ens_1 A)))) ) ) ) ).
tt(t24_entropy1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_entropy1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_entropy1 (k8_matrix_1 k1_numbers B C) C)) ) ) ) ) ) ) ) ).
tt(t24_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k1_enumset1 A B C) (k3_enumset1 D E F G H))) ) ) ) ) ) ) ) ) ).
tt(t24_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden D A) &  ( (~  ((k6_eqrel_1 A A B C) = (k6_eqrel_1 A A B D)) )  &  (~ (r1_xboole_0 (k6_eqrel_1 A A B C) (k6_eqrel_1 A A B D))) ) ) ) ) ) ) ) ) ).
tt(t24_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v4_msualg_1 D A) &  ((v2_msafree D A) & (l3_msualg_1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r2_msualg_3 A B C E) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A D C F) &  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A B)) =>  (~  ((r1_msualg_3 A D B G) & (r8_pboole (u1_struct_0 A) F (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A B) (u3_msualg_1 A C) G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ( ((k3_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0)  &  ((k3_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) = k1_xboole_0) ) ) ) ) ) ).
tt(t24_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k5_algstr_0 (k15_euclid A) B C) D) = (k10_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t24_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k12_euclid (k1_euclid_3 A)) = (k7_square_1 (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))))) ) ) ).
tt(t24_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 B (k6_euclid A C)) = (k1_real_1 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t24_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 (k3_rlvect_1 (k15_euclid 3) A B) C) = (k3_rlvect_1 (k15_euclid 3) (k5_euclid_5 A C) (k5_euclid_5 B C))) ) ) ) ) ) ) ).
tt(t24_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_zfmisc_1 A B C) =>  ((r1_xxreal_0 (k4_euclid_3 A B C) k32_sin_cos) |  ( (~ (r1_xxreal_0 (k4_euclid_3 B C A) k32_sin_cos))  &  (~ (r1_xxreal_0 (k4_euclid_3 C A B) k32_sin_cos)) ) ) ) ) ) ) ) ) ) ).
tt(t24_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  ( ((v2_funct_1 C) &  ((r1_tarski (k2_relset_1 k5_numbers C) (k4_finseq_1 B)) &  ((r2_relset_1 k5_numbers (k1_euclid A) D (k1_partfun1 k5_numbers k5_numbers k5_numbers (k1_euclid A) C B)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((r2_hidden E (k2_relset_1 k5_numbers C)) |  ((k1_funct_1 B E) = (k5_euclid A)) ) ) ) ) ) ) )  =>  ((k5_euclid_7 A B) = (k5_euclid_7 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t24_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k4_euclid_9 A C D) B)) ) ) ) ) ) ) )  => (v3_pre_topc B (k3_pcomps_1 (k14_euclid A)))) ) ) ) ) ).
tt(t24_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (m2_finseq_1 B k1_numbers)) ) ) ) ).
tt(t24_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid G)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid G)) =>  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid G)) =>  ((k7_euclid G (k7_euclid G (k7_euclid G (k9_euclid G H A) (k9_euclid G I B)) (k9_euclid G J C)) (k7_euclid G (k7_euclid G (k9_euclid G H D) (k9_euclid G I E)) (k9_euclid G J F))) = (k7_euclid G (k7_euclid G (k9_euclid G H (k7_real_1 A D)) (k9_euclid G I (k7_real_1 B E))) (k9_euclid G J (k7_real_1 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_exchsort,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ( ((k1_exchsort A) = k1_xboole_0)  &  ( ((k2_exchsort A) = (k9_xtuple_0 A))  &  ((k3_exchsort A) = (k9_xtuple_0 A)) ) ) ) ) ).
tt(t24_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k3_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k2_compos_1 B))  =>  ((k5_extpro_1 A B C D (k8_extpro_1 A B C D)) = (k5_extpro_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( ((m1_subset_1 A k1_numbers) | (m1_subset_1 B k1_numbers))  => (r1_xxreal_0 (k3_extreal1 (k4_supinf_2 (k3_extreal1 A) (k3_extreal1 B))) (k3_extreal1 (k4_supinf_2 A B)))) ) ) ) ) ).
tt(t24_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  ((k3_circcomb A B C D) = (k3_circcomb B A D C)) ) ) ) ) ) ) ) ) ).
tt(t24_facirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ( ((k1_xtuple_0 (k5_facirc_2 C A B)) = k1_xboole_0)  &  ( ((k2_xtuple_0 (k5_facirc_2 C A B)) = (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1))  &  ((k9_xtuple_0 (k2_xtuple_0 (k5_facirc_2 C A B))) = (k4_finseq_2 k6_numbers k6_margrel1)) ) )  |  ( ((k1_card_1 (k1_xtuple_0 (k5_facirc_2 C A B))) = 3)  &  ( ((k2_xtuple_0 (k5_facirc_2 C A B)) = k4_facirc_1)  &  ((k9_xtuple_0 (k2_xtuple_0 (k5_facirc_2 C A B))) = (k4_finseq_2 3 k6_margrel1)) ) ) ) ) ) ) ) ) ) ).
tt(t24_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C))) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) &  ( ((k8_relset_1 k1_numbers k1_numbers B (k1_seq_4 k6_numbers)) = k1_xboole_0)  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ).
tt(t24_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))  =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))) ) ) ) ) ) ).
tt(t24_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) A) B) = (k10_real_1 (k18_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t24_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_fdiff_9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k2_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k8_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k2_sin_cos9 B))) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t24_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fdiff_1 A B) => (r1_fcont_1 A B)) ) ) ) ) ).
tt(t24_fdiff_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C A) & (r2_hidden D A))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 B C) (k1_seq_1 B D))) (k5_square_1 (k9_real_1 C D)))) ) ) ) ) )  =>  ((r2_fdiff_1 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_fdiff_1 B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t24_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers D E) k3_taylor_1))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ( ((k1_seq_1 D F) = (k9_real_1 F A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D F) k6_numbers))  &  ( ((k1_seq_1 E F) = (k9_real_1 F B))  &  (~ (r1_xxreal_0 (k1_seq_1 E F) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers D E) k3_taylor_1) C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers D E) k3_taylor_1) C) F) = (k10_real_1 (k9_real_1 A B) (k8_real_1 (k9_real_1 F A) (k9_real_1 F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 B k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1) A) B) = (k8_real_1 (k10_real_1 1 (k5_square_1 B)) (k9_real_1 1 (k1_seq_1 k3_taylor_1 B)))) ) ) ) ) ) ) ) ).
tt(t24_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)))) &  ( (B = (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 C D) = 1) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) D) = (k10_real_1 (k26_sin_cos D) (k7_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))))) &  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ( ((k1_seq_1 C E) = 1)  &  ( (~ (r1_xxreal_0 (k1_seq_1 B E) k6_numbers))  &  (~  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))) A) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k4_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2)))) A) E) = (k1_seq_1 k4_sin_cos6 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)) A) B) = (k10_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t24_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t24_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k16_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A))) & (r1_tarski (k15_ff_siec A) (k2_zfmisc_1 (k2_net_1 A) (k2_net_1 A)))) ) ) ).
tt(t24_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 2)) = (k2_nat_1 (k1_pre_ff A) (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t24_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_1 (k1_fib_num3 A) (k1_pre_ff A)) = (k4_nat_1 2 (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t24_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k1_int_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k1_pre_ff A) (k3_xcmplx_0 (k7_square_1 5) (k1_pre_ff A))) 1) 2))) ) ) ) ).
tt(t24_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) => (r1_tarski B (k1_finseq_8 A B C))) ) ) ) ) ) ).
tt(t24_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (k6_domain_1 (u1_struct_0 A) B))  =>  ((k3_filter_0 A C) = (k2_filter_0 A B)) ) ) ) ) ) ) ) ).
tt(t24_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r1_binop_1 A C E) & (r1_binop_1 B D F))  <=> (r1_binop_1 (k2_zfmisc_1 A B) (k1_domain_1 A B C D) (k6_filter_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v13_lattices A) => (r2_hidden (k5_lattices A) B)) ) ) ) ) ).
tt(t24_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 C (k3_finseq_1 (k7_finseq_1 A B))) =>  ((r1_xxreal_0 C (k3_finseq_1 A)) |  ((k1_funct_1 (k7_finseq_1 A B) C) = (k1_funct_1 B (k6_xcmplx_0 C (k3_finseq_1 A)))) ) ) ) ) ) ) ) ) ).
tt(t24_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C B) => (m2_finseq_1 C A)) ) ) ) ) ).
tt(t24_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k1_relset_1 k5_numbers A)) &  (B = k6_numbers) ) ) ) ) ) ).
tt(t24_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ( (~ (r1_xxreal_0 (k4_finseq_4 A B) C))  &  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(t24_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  ((r2_hidden B (k10_xtuple_0 D)) =>  ((k7_finseq_1 (k5_finseq_4 D B) (k12_finseq_1 A B)) = (k17_finseq_1 C (k4_finseq_4 D B) D)) ) ) ) ) ) ) ) ) ).
tt(t24_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_finseq_5 (k7_finseq_1 (k9_finseq_1 A) B)) = (k7_finseq_1 (k3_finseq_5 B) (k9_finseq_1 A))) ) ) ) ).
tt(t24_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k2_finseq_7 A (k3_finseq_4 A B C D) 1 2) = (k3_finseq_4 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t24_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r4_finseq_8 A B C) =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 B)) &  ((k3_finseq_6 A B (k7_nat_d (k2_nat_1 (k3_finseq_1 B) 1) (k3_finseq_1 C)) (k3_finseq_1 B)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t24_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v2_binop_1 F B) => (r2_funct_2 A B (k1_partfun1 A B B B (k6_funcop_1 B A F D E) (k10_funcop_1 B B F C (k6_partfun1 B))) (k6_funcop_1 B A F (k1_partfun1 A B B B D (k10_funcop_1 B B F C (k6_partfun1 B))) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k9_fintopo2 A B) (k9_fintopo2 A C))) ) ) ) ) ) ) ).
tt(t24_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k5_fintopo3 A B C) B)) ) ) ) ) ) ) ).
tt(t24_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ((r1_xboole_0 B C) &  ((r1_xboole_0 (k7_fin_topo A B) C) & (r1_xboole_0 (k7_fin_topo A C) B)) ) )  => (r1_fintopo4 A B C)) ) ) ) ) ) ) ).
tt(t24_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fin_topo B A) => (v2_fin_topo (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t24_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k7_flang_1 A B k6_numbers) = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ).
tt(t24_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D E))  =>  ((k1_flang_2 A B C E) = (k4_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B C D) (k1_flang_2 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k7_flang_1 A B C) (k1_flang_3 A B D)) = (k6_flang_1 A (k1_flang_3 A B D) (k7_flang_1 A B C))) ) ) ) ) ) ) ) ).
tt(t24_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((k8_relset_1 B k6_margrel1 (k9_fomodel0 A B) (k1_tarski k1_xboole_0)) = (k6_subset_1 B A))  &  ((k8_relset_1 B k6_margrel1 (k9_fomodel0 A B) (k6_domain_1 k5_numbers 1)) = (k3_xboole_0 A B)) ) ) ) ).
tt(t24_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 B) (k3_rfunct_3 (k3_finseq_2 C) (k2_xboole_0 C k6_margrel1))) (k16_fomodel2 B C)) => (r2_hidden (k24_fomodel2 B C A D) (k9_funct_2 (k25_fomodel2 B A) k6_margrel1))) ) ) ) ) ) ) ) ).
tt(t24_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v2_frechet B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k2_frechet A B) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) => (r1_tarski (k2_frechet A C) B)) ) ) ) ) ) ) ) ).
tt(t24_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k1_fscirc_1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ((k1_funct_1 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F G)) (k10_margrel1 (k9_margrel1 E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k1_fscirc_1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ((k1_funct_1 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k6_fscirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 E) F) (k10_margrel1 F G)) (k10_margrel1 (k9_margrel1 E) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ((r5_fsm_1 B C D E F) => (r6_fsm_1 B C D E F A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers)))  =>  ( ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C B))  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = B) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C B) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = C) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r3_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C) (k1_square_1 B C))) ) ) ) ) ) ) ).
tt(t24_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  (! [E:$i] :  ((m1_rewrite1 E (k1_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) D)) =>  (~  ( ((k2_xtuple_0 (k1_funct_1 E 1)) = (k1_flang_1 A B C))  &  ( ((k2_xtuple_0 (k1_funct_1 E (k3_finseq_1 E))) = (k2_flang_1 A))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  ((k2_xtuple_0 (k1_funct_1 E F)) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden B (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden C (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden D (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden E (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k36_gfacirc1 A B C) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k33_gfacirc1 A B C) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k24_gfacirc1 (k36_gfacirc1 A B C) E D) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k3_twoscomp) (u1_struct_0 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp) (u1_struct_0 (k13_ftacell1 A B C D E))) & (r2_hidden (k21_gfacirc1 (k36_gfacirc1 A B C) E D) (u1_struct_0 (k13_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((k5_relat_1 A D) = (k5_relat_1 B D))  =>  ((k5_relat_1 (k3_funcop_1 E C A) D) = (k5_relat_1 (k3_funcop_1 E C B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_struct_0 (k11_funcsdom A)) = (k9_funcsdom A)) ) ) ).
tt(t24_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) & (v2_funct_1 B))  => (v2_funct_1 (k3_relat_1 A B))) ) ) ) ) ).
tt(t24_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v2_funct_1 (k1_partfun1 A B B C D E)) &  ((k2_relset_1 B D) = B) )  =>  ( ( (C = k1_xboole_0)  &  (~  (B = k1_xboole_0) ) )  |  ((v2_funct_1 D) & (v2_funct_1 E)) ) ) ) ) ) ) ) ) ) ).
tt(t24_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k8_relat_1 (k3_funct_3 B) A) (k1_zfmisc_1 (k10_xtuple_0 B)))) ) ) ).
tt(t24_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k5_relat_1 (k1_funct_4 A B) (k6_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 B))) A)) ) ) ) ).
tt(t24_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  =>  ( ((k2_zfmisc_1 A B) = k1_xboole_0)  |  ( ((k9_xtuple_0 (k1_funct_5 C)) = A)  &  ((k9_xtuple_0 (k3_funct_5 C)) = B) ) ) ) ) ) ) ) ).
tt(t24_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k2_funct_6 (k7_funcop_1 A B)) = (k7_funcop_1 A (k9_xtuple_0 B)))  &  ((k3_funct_6 (k7_funcop_1 A B)) = (k7_funcop_1 A (k10_xtuple_0 B))) ) ) ) ) ).
tt(t24_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k3_xboole_0 B C)) =>  ((k1_funct_7 A B) = (k1_funct_7 A C)) ) ) ) ) ).
tt(t24_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r2_funct_8 A k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t24_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k2_fdiff_9 (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) ) ).
tt(t24_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B C C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 B C C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  ((k1_funct_1 (k4_functor0 A B (k9_functor0 A B C D) E F) G) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C B A) & (m2_functor0 C B A))  =>  (! [D:$i] :  ( ((v15_functor0 D B A) & (m2_functor0 D B A))  =>  (! [E:$i] :  ((m1_functor2 E B A C D) =>  ((r1_functor2 B A C D) => (r8_pboole (u1_struct_0 B) (k7_functor3 B B A (k12_functor0 B) (k12_functor0 B) C D (k4_functor2 B B (k12_functor0 B)) E) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 B D))  => (r1_fuzzy_1 B (k1_fuzzy_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t24_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k2_fuzzy_1 A B (k1_fuzzy_2 A C B)) C)) ) ) ) ) ) ) ).
tt(t24_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_fuzzy_4 A A A B (k4_fuzzy_2 A A)) (k4_fuzzy_4 A A A (k4_fuzzy_2 A A) B))) ) ) ) ).
tt(t24_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B))))  =>  ( (B = (k4_struct_0 A))  | (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D B) (k3_funct_2 (u1_struct_0 A) k7_numbers D C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_fvsum_1 1 A (k4_matrix_2 (u1_struct_0 A) B)) = (k4_matrix_2 (u1_struct_0 A) (k4_algstr_0 A B))) ) ) ) ) ).
tt(t24_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 (k18_gate_1 A B C D E)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) => (m2_subset_1 (k4_struct_0 A) (u1_struct_0 A) B)) ) ) ) ).
tt(t24_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((r1_xxreal_0 (k3_finseq_1 E) A) &  ((r1_xxreal_0 (k3_finseq_1 E) B) & (r1_xxreal_0 (k3_finseq_1 E) C)) )  =>  ((k9_genealg1 D E F A B C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_geomtrap A B C D E F G) &  ((r2_geomtrap A B C D E F H) &  ( (~  (D = E) )  &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k10_gfacirc1 A B C)) = (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) (k1_tarski (k12_gfacirc1 A B C)))) ) ) ) ).
tt(t24_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((k8_gfacirc2 (k1_nat_1 B 1) A C D) = (k24_gfacirc1 (k1_funct_1 C (k1_nat_1 B 1)) (k1_funct_1 D (k1_nat_1 B 1)) (k7_gfacirc2 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( ((k7_glib_000 A) = k1_xboole_0)  => (v7_glib_000 A)) ) ) ).
tt(t24_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) =>  ( ((k1_funct_1 B C) = (k1_funct_1 (k6_glib_001 A B) (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1)))  & (r2_hidden (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1) (k1_relset_1 k5_numbers (k6_glib_001 A B)))) ) ) ) ) ) ) ) ).
tt(t24_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k5_setfam_1 (k6_glib_000 A) (k3_glib_002 A)) = (k6_glib_000 A)) ) ) ).
tt(t24_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k10_glib_003 A (k7_glib_001 A B C)) = (k2_xcmplx_0 (k10_glib_003 A B) (k10_glib_003 A C))) ) ) ) ) ) ) ) ).
tt(t24_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (v13_glib_000 (k10_glib_004 A B))) ) ) ) ).
tt(t24_goboard1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  ( ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 E 1) (k4_finseq_1 A)))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((r2_hidden (k4_tarski H I) (k2_matrix_1 D)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) = (k3_matrix_1 C D F G))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)) = (k3_matrix_1 C D H I)) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 F H)) (k18_complex1 (k6_xcmplx_0 G I))) = 1) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 B)) & (r2_hidden (k2_nat_1 E 1) (k4_finseq_1 B)))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((r2_hidden (k4_tarski H I) (k2_matrix_1 D)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B E) = (k3_matrix_1 C D F G))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 E 1)) = (k3_matrix_1 C D H I)) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 F H)) (k18_complex1 (k6_xcmplx_0 G I))) = 1) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 D)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k3_matrix_1 C D E F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k3_matrix_1 C D G H))  &  ((r2_hidden (k3_finseq_1 A) (k4_finseq_1 A)) & (r2_hidden 1 (k4_finseq_1 B))) ) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 E G)) (k18_complex1 (k6_xcmplx_0 F H))) = 1) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) & (r2_hidden (k2_nat_1 E 1) (k4_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) &  ((r2_hidden (k4_tarski H I) (k2_matrix_1 D)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B) E) = (k3_matrix_1 C D F G))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B) (k2_nat_1 E 1)) = (k3_matrix_1 C D H I)) ) ) )  =>  ((k2_xcmplx_0 (k18_complex1 (k6_xcmplx_0 F H)) (k18_complex1 (k6_xcmplx_0 G I))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 B) &  ((v4_goboard1 B) & (r1_xxreal_0 (k2_nat_1 A 1) (k1_matrix_1 B))) )  =>  ((v3_relat_1 B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard5 B A) (k2_goboard5 B (k2_nat_1 A 1))) = (a_2_11_goboard5 A B)) ) ) ) ) ) ) ).
tt(t24_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)) = (a_2_4_goboard6 A B)) ) ) ) ) ) ) ).
tt(t24_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 A)) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))))  &  ( (~  ( (C = E)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C))) ) )  &  (~  ( ((k2_nat_1 C 1) = E)  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1) E))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xxreal_0 (k18_euclid C) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A)))))) ) ) )  => (r1_xboole_0 B (k3_topreal1 2 A))) ) ) ) ) ).
tt(t24_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_goboard9 (k1_goboard9 A)) = (k2_goboard9 A)) ) ) ).
tt(t24_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_goboard5 A k6_numbers k6_numbers) = (a_1_13_gobrd11 A)) ) ) ).
tt(t24_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C)) ) ) ) ) ) )  =>  ((k2_gobrd13 D E A) = (k3_goboard5 E B (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k3_goboard9 B)) & (r1_xxreal_0 (k8_pscomp_1 (k3_topreal1 2 B)) (k17_euclid A))) ) ) ) ) ) ).
tt(t24_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r1_henmodel A B (k6_cqc_lang A (k5_cqc_lang A))) <=>  (~ (v1_henmodel B A)) ) ) ) ) ) ).
tt(t24_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( ((r1_partfun1 (u1_graph_1 A) (u1_graph_1 B)) & (r1_partfun1 (u2_graph_1 A) (u2_graph_1 B)))  =>  ( ( (~  ((k5_graph_1 A B) = B) )  &  (~  ((k5_graph_1 B A) = B) ) )  | (r4_graph_1 A B)) ) ) ) ) ) ).
tt(t24_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  ( ((r1_tarski (k10_xtuple_0 B) (k1_relset_1 k5_numbers A)) &  ((r1_tarski (k10_xtuple_0 C) (k1_relset_1 k5_numbers A)) &  ( (D = (k3_relat_1 B A))  &  ( (E = (k3_relat_1 C A))  &  (F = (k3_relat_1 (k7_finseq_1 B C) A)) ) ) ) )  =>  (F = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_graph_1 A B) = (k7_graph_3 A B (u4_struct_0 A))) ) ) ) ) ).
tt(t24_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  =>  ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) ) )  &  ( ( ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) )  =>  ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) ) )  &  ( ((v7_graph_1 B A) &  ((v3_graph_2 B A) & (m2_graph_1 B A)) )  =>  ((v2_funct_1 B) &  ((v7_graph_1 B A) & (m2_graph_1 B A)) ) ) ) ) ) ) ) ) ).
tt(t24_graph_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ( ( (~  (D = (k1_funct_1 (u1_graph_1 B) (k1_funct_1 C A))) )  &  (~  (D = (k1_funct_1 (u2_graph_1 B) (k1_funct_1 C A))) ) )  | (r2_hidden D (k2_graph_5 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) k8_graph_5) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) k8_graph_5)))) )  =>  ( ((k12_graphsp A B C D) = (k1_real_1 1))  <=>  (! [E:$i] :  (~  ((r2_hidden E (u4_struct_0 A)) & (r1_graph_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_grcat_1,ax, (! [A:$i] :  ( ((v1_grcat_1 A) &  ((v2_grcat_1 A) & (l1_grcat_1 A)) )  =>  ( (~ (v1_xboole_0 (k1_tarski A)))  & (v4_grcat_1 (k1_tarski A))) ) ) ).
tt(t24_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  ((k7_group_1 A) = (k3_xcmplx_0 2 B)) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( ((k6_group_1 A B) = 2)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_group_1 A C) = 2)  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~  (A = 2) )  =>  ((k4_nat_d (k1_gr_cy_3 A) 8) = 7) ) ) ) ).
tt(t24_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden (k1_funct_1 C A) B))  <=> (r2_hidden (k4_tarski A (k1_funct_1 C A)) (k6_relat_1 B C))) ) ) ) ) ).
tt(t24_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_group_6 G B (k10_group_6 A B C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k10_group_6 A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k10_group_6 A B C))) =>  ( ( (H = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))  &  ( (I = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))  &  (G = (k2_grsolv_1 A B C D)) ) )  =>  ((k13_group_2 (k10_group_6 A B C) G (k6_algstr_0 (k10_group_6 A B C) H I)) = (k13_group_2 B (k2_grsolv_1 A B C D) (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r2_groeb_1 A B C E D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden F D) => (r1_rewrite1 (k3_polyred A B C E) F (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) &  ((r2_hidden F D) & (r4_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) G)) )  => (r8_pboole (k15_pre_poly A) G (k7_polynom1 A C))) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  => (r1_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  ((r1_tarski (k4_groeb_3 A B C D E) (k2_polynom1 (k15_pre_poly A) C D)) &  ( ((k5_card_1 (k4_groeb_3 A B C D E)) = (k6_xcmplx_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( ((r2_hidden F (k4_groeb_3 A B C D E)) &  ((r2_hidden G (k2_polynom1 (k15_pre_poly A) C D)) & (r1_termord A B G F)) )  => (r2_hidden G (k4_groeb_3 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_11 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 A) (k2_group_11 A B D) (k2_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t24_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k5_finseqop (u1_struct_0 A) (u2_algstr_0 A)) (k3_group_1 A))) ) ).
tt(t24_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  =>  ((k6_algstr_0 A D E) = (k6_algstr_0 A E D)) ) ) ) ) )  =>  ((k2_group_2 A B C) = (k2_group_2 A C B)) ) ) ) ) ) ) ) ).
tt(t24_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_3 A (k2_group_3 A B C) D) = (k2_group_3 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t24_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) & (l3_algstr_0 D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ((k4_group_4 D (k3_finseq_4 k4_numbers (k2_group_4 A) (k2_group_4 B) (k2_group_4 C)) (k3_finseq_4 (u1_struct_0 D) E F G)) = (k3_finseq_4 (u1_struct_0 D) (k5_group_1 D A E) (k5_group_1 D B F) (k5_group_1 D C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B C) = (k6_algstr_0 A (k6_algstr_0 A (k5_group_1 A 2 (k2_group_1 A B)) (k5_group_1 A 2 (k6_algstr_0 A B (k2_group_1 A C)))) (k5_group_1 A 2 C))) ) ) ) ) ) ) ).
tt(t24_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((k1_group_1 (k5_group_6 A B)) = (k8_group_2 A B)) ) ) ) ) ).
tt(t24_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_group_1 C) & (l3_algstr_0 C)) )  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_group_7 (k11_finseq_1 A B C)) & (v3_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (A = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (~  ( (~  (C = (k6_group_2 A)) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_struct_0 C (k5_group_1 A D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_struct_0 (k18_group_9 A B C) D) <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))) &  ( (G = (k1_group_9 A (u1_struct_0 B) (u1_group_9 A B) C))  &  ( ((k3_finseq_1 E) = (k3_finseq_1 F))  &  ((r1_tarski (k2_relset_1 (u1_struct_0 B) E) G) &  ((k3_group_4 B (k4_group_4 B F E)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((v2_group_10 B A) &  ((k2_groupp_1 A B) = k6_numbers) )  =>  (B = (k6_group_2 B)) ) ) ) ) ) ).
tt(t24_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v3_hahnban1 B k1_complfld A) &  ((v6_hahnban1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v1_hahnban B (k10_hahnban1 A)) &  ((v4_hahnban B (k10_hahnban1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t24_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) &  ((v2_hahnban C B) &  ((v3_hahnban C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) ) ) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (D = E)  => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 B) k1_numbers C D) (k1_normsp_0 A E))) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) &  ((v2_hahnban D A) &  ((v3_hahnban D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (~  ( ((k2_partfun1 (u1_struct_0 A) k1_numbers D (u1_struct_0 B)) = C)  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers D E) (k1_normsp_0 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v2_relat_1 B) & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m3_hallmar1 E A B C) =>  (! [F:$i] :  ((m3_hallmar1 F A E D) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  =>  ( ((k1_funct_1 F C) = k1_xboole_0)  |  ( ((k1_funct_1 E D) = k1_xboole_0)  |  ((m3_hallmar1 F A B D) & (m3_hallmar1 F A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( ( (D = (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) C))  &  ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A))) )  => (v4_xxreal_2 D)) ) ) ) ) ) ) ) ) ).
tt(t24_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v5_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (~  ( ((k3_glib_001 A B) = (k3_glib_001 A C))  &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  ((k1_funct_1 B (k2_nat_1 (k3_finseq_1 (k1_helly B C)) 2)) = (k1_funct_1 C (k2_nat_1 (k3_finseq_1 (k1_helly B C)) 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  => (v1_vectsp_4 (k8_vectsp10 k1_complfld A B) k1_complfld A)) ) ) ) ).
tt(t24_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) => (r3_lattices (k12_normform A) (k4_lattices (k12_normform A) B (k5_binop_1 (u1_struct_0 (k12_normform A)) (k9_heyting1 A) B C)) C)) ) ) ) ) ).
tt(t24_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (~  ( (! [F:$i] :  (~  ((r2_hidden F D) &  (! [G:$i] :  (~  ((r2_hidden G E) & (r1_tarski G (k2_xboole_0 F C))) ) ) ) ) )  &  (! [F:$i] :  (~  ((r2_hidden F (k3_heyting2 A B D E)) & (r1_tarski F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_tarski (k3_heyting3 A B) (k2_heyting3 C B)) <=>  (~ (r1_xxreal_0 C A)) ) ) ) ) ) ) ) ).
tt(t24_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 1 A) & (r1_taylor_1 C A B))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C B) 1) (k2_fdiff_1 C B))) ) ) ) ) ) ) ).
tt(t24_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_ideal_1 F A C) =>  (! [G:$i] :  ((m1_ideal_1 G B D) =>  (! [H:$i] :  ((m2_finseq_1 H (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((v1_quofield E A B) &  ( ((k3_finseq_1 F) = (k3_finseq_1 G))  &  ((r1_ideal_1 A C F H) &  (! [I:$i] :  ((r2_hidden I (k4_finseq_1 G)) =>  ((k1_funct_1 G I) = (k6_algstr_0 B (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) H I))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) H I)))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) H I))))) ) ) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k4_rlvect_1 A F)) = (k4_rlvect_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B C)) (k3_hilbert1 (k3_hilbert1 D B) (k3_hilbert1 A (k3_hilbert1 D C)))) k6_hilbert1)) ) ) ) ) ) ) ) ).
tt(t24_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (~  ((k4_hilbert1 B C) = (k1_hilbert2 A)) ) ) ) ) ) ) ) ).
tt(t24_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (C = k1_xboole_0)  &  ( (~  (B = k1_xboole_0) )  &  (~  (A = k1_xboole_0) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B C))))) )  =>  ((v1_funct_1 (k2_pralg_2 D)) &  ((v1_funct_2 (k2_pralg_2 D) (k1_funct_2 A B) (k1_funct_2 A C)) & (m1_subset_1 (k2_pralg_2 D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_2 A B) (k1_funct_2 A C))))) ) ) ) ) ) ) ) ).
tt(t24_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( ((k2_hurwitz A B) = k6_numbers)  & (v1_polynom5 B A)) ) ) ) ) ) ).
tt(t24_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_idea_1 C (k9_idea_1 C A B))) ) ) ) ) ) ).
tt(t24_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_ideal_1 D A B) => (m1_ideal_1 (k1_polynom1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t24_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (~  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) <=>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) => (m4_index_1 E (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (k14_index_1 A B B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((l3_msualg_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 B)) =>  ( (G = (k1_funct_1 D F))  =>  ( ((k3_msualg_1 B G E) = (k3_msualg_1 A F (k1_instalg1 A B E C D)))  &  ((k4_msualg_1 A F (k1_instalg1 A B E C D)) = (k4_msualg_1 B G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 A C))  =>  ((r1_xxreal_0 (k3_real_1 A 1) B) |  ((r1_xxreal_0 (k3_real_1 A 1) C) |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_int_2 A B) =>  ( ((k3_int_2 (k3_xcmplx_0 C A) (k3_xcmplx_0 C B)) = (k1_int_2 C))  &  ( ((k3_int_2 (k3_xcmplx_0 C A) (k3_xcmplx_0 B C)) = (k1_int_2 C))  &  ( ((k3_int_2 (k3_xcmplx_0 A C) (k3_xcmplx_0 C B)) = (k1_int_2 C))  &  ((k3_int_2 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C)) = (k1_int_2 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v1_int_2 B) & (r1_int_2 B C))  =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B (k3_square_1 D)) C) (k1_newton B A)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( ((k3_int_2 A B) = 1)  &  ((k3_int_2 C B) = 1) )  =>  ((r1_xxreal_0 B 2) |  ((r1_int_5 A B) |  ((r1_int_5 C B) | (r1_int_5 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B (k3_finseq_1 A)) =>  ((r1_xxreal_0 B k6_numbers) |  ((v1_relat_1 (k16_finseq_1 B A)) &  ((v5_relat_1 (k16_finseq_1 B A) k4_numbers) &  ((v1_funct_1 (k16_finseq_1 B A)) &  ( (~ (v1_xboole_0 (k16_finseq_1 B A)))  &  ((v1_finseq_1 (k16_finseq_1 B A)) &  ((v1_partfun3 (k16_finseq_1 B A)) & (v1_int_6 (k16_finseq_1 B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~ (v4_group_1 B A))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( ((k5_group_1 A C B) = (k5_group_1 A D B))  &  (D = (k2_xcmplx_0 (k4_nat_1 E (k6_group_1 A B)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) k16_sin_cos)) = k6_numbers) ) ) ) ) ) ).
tt(t24_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r1_tarski G (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 D H) = (k9_binop_2 (k11_binop_2 A H) B))  &  ((k1_seq_1 E H) = 1) ) ) ) )  &  ( (G = (k1_relset_1 k1_numbers F))  & (r2_relset_1 k1_numbers k1_numbers F (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k4_sin_cos6 A) (k3_rfunct_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers E (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))))))) ) ) )  =>  ((k2_integra5 C F) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k4_sin_cos6) (k4_seq_4 C)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k4_sin_cos6) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos) (k41_valued_1 k1_numbers k1_numbers k16_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k24_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t24_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1))) &  ( (B = (k1_relset_1 k1_numbers k30_sin_cos))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) A))) ) )  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k30_sin_cos)) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t24_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m2_subset_1 F k1_numbers k5_numbers))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid F)))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_integr15 F (k3_integra5 A B) G) &  ((r1_integra5 (k3_integra5 A B) (k1_nfcont_4 F k1_numbers G)) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid F) G (k3_integra5 A B)) F) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers G)) &  ((r2_hidden C (k3_integra5 A B)) &  ((r2_hidden D (k3_integra5 A B)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 C D)) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid F) G H)) E)) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k12_euclid (k12_integr15 C D F G)) (k11_binop_2 E (k10_binop_2 D C))) & (r1_xxreal_0 (k12_euclid (k12_integr15 D C F G)) (k11_binop_2 E (k10_binop_2 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  ((k18_rvsum_1 (k4_integra1 A (k7_rfunct_1 A A) B)) = (k3_integra1 A)) ) ) ) ) ).
tt(t24_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers)))) )  =>  (! [E:$i] :  ((m1_integra1 E C) =>  ( ((r2_hidden B (k4_finseq_1 E)) &  ((v1_seq_2 (k2_partfun1 C k1_numbers D C)) & (r1_xxreal_0 A k6_numbers)) )  =>  ((k1_seq_1 (k5_integra1 C (k26_valued_1 C k1_numbers D A) E) B) = (k8_real_1 A (k1_seq_1 (k4_integra1 C D E) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_integra4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden D B) & (r2_hidden E B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 C D) (k1_seq_1 C E))) A)) ) ) ) )  => (r1_xxreal_0 (k9_real_1 (k4_seq_4 (k1_rvsum_1 C)) (k5_seq_4 (k1_rvsum_1 C))) A)) ) ) ) ) ) ) ).
tt(t24_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) E) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E (k3_integra5 A B))) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 E)) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) ) ) ) )  =>  ( ((k4_integra5 C D (k3_valued_1 k1_numbers k1_numbers k1_numbers E F)) = (k7_real_1 (k4_integra5 C D E) (k4_integra5 C D F)))  &  ((k4_integra5 C D (k47_valued_1 k1_numbers k1_numbers k1_numbers E F)) = (k9_real_1 (k4_integra5 C D E) (k4_integra5 C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_real_1 (k1_seq_1 k16_sin_cos A) (k1_seq_1 k16_sin_cos B)) = (k4_integra5 B A k19_sin_cos)) ) ) ) ) ).
tt(t24_integra8,ax,(r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) k1_numbers)).
tt(t24_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ((k1_integra9 C A B) = (k1_integra9 C B A)) ) ) ) ) ) ) ).
tt(t24_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_interva1 D A))  => (r1_interva1 A (k3_interva1 A (k3_interva1 A B C) D) (k3_interva1 A B (k3_interva1 A C D)))) ) ) ) ) ) ) ) ).
tt(t24_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 A C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t24_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B C) = (k1_seq_1 (k3_series_1 (k3_irrat_1 C)) A)) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = (k1_seq_1 (k3_series_1 k5_irrat_1) A)) ) ) ) ) ) ) ).
tt(t24_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ((r2_nattra_1 A B D E) =>  (! [F:$i] :  ((m2_cat_1 F C A) =>  (! [G:$i] :  ((m2_nattra_1 G A B D E) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k4_nattra_1 C B (k9_cat_1 C A B F D) (k9_cat_1 C A B F E) (k5_isocat_1 C A B D E F G) H) = (k4_nattra_1 A B D E G (k8_cat_1 C A F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) (k6_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D)) (k6_isocat_2 A B C D D (k6_nattra_1 (k8_cat_2 A B) C D)))) ) ) ) ) ) ) ) ).
tt(t24_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ((v6_tops_1 (k1_tops_1 A B) A) &  ((v5_tops_1 (k2_pre_topc A B) A) & (v1_xboole_0 (k1_isomichi A B))) ) ) ) ) ) ) ).
tt(t24_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 A) & (r1_jgraph_1 (u1_struct_0 (k15_euclid 2)) A B))  => (v1_topreal1 B)) ) ) ) ) ).
tt(t24_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((v5_pre_topc B A k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k2_xcmplx_0 F C)) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (B = a_0_2_jgraph_3)  & (v3_tops_2 C (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) A)))  => (v1_topreal2 A)) ) ) ) ) ) ) ).
tt(t24_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (C = a_0_0_jgraph_4)  &  (B = (a_1_1_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 k6_numbers (k17_euclid B)) & (r1_xxreal_0 k6_numbers (k17_euclid C)))  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  ( ((k12_euclid B) = k6_numbers)  |  ( ((k12_euclid C) = k6_numbers)  |  ((r1_xxreal_0 (k10_real_1 (k18_euclid C) (k12_euclid C)) (k10_real_1 (k18_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k7_jgraph_4 A) C))  & (r1_xxreal_0 (k10_real_1 (k18_euclid E) (k12_euclid E)) (k10_real_1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k6_jgraph_6 k6_numbers k6_numbers A) = (a_1_0_jgraph_6 A))  &  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k5_jgraph_6 k6_numbers k6_numbers A) = (a_1_1_jgraph_6 A)) )  &  ( ((k8_jgraph_6 k6_numbers k6_numbers A) = (a_1_2_jgraph_6 A))  &  ( ((k7_jgraph_6 k6_numbers k6_numbers A) = (a_1_3_jgraph_6 A))  &  ((k9_jgraph_6 k6_numbers k6_numbers A) = (a_1_4_jgraph_6 A)) ) ) ) ) ) ) ).
tt(t24_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 E (k17_euclid B)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) |  ((r1_xxreal_0 (k17_euclid D) (k17_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) & (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) C D)))  =>  ((r2_subset_1 (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) C D)) |  ((k17_euclid A) = (k17_euclid C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A E) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan13 A E))) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A E))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan13 A E) D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) B C))  & (r1_xxreal_0 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r2_hidden D A))  =>  ( (B = D)  | (r1_topreal1 (k15_euclid 2) B D (k5_jordan6 A B C B D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B E C D) & (r1_jordan17 A B C E D))  =>  ( (B = C)  |  ( (B = D)  |  ( (E = D)  |  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r1_jordan18 A B C C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 B (k1_matrix_1 C)) & (v1_xboole_0 (k3_goboard5 C A B))) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_2_jordan1 A B C D))  => (v3_pre_topc E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 A)) &  ((r2_hidden F (k3_goboard5 A B C)) &  ( ((k18_euclid F) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E)))  &  ( (~  (C = E) )  &  (~  (C = (k7_nat_d E 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v9_rltopsp1 A (k15_euclid 2)) & (v1_xboole_0 (k2_jordan2c 2 A))) ) ) ) ).
tt(t24_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((k23_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k3_finseq_1 (k1_jordan8 B A)) C)) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k4_finseq_4 (k1_jordan1e B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = (k3_finseq_1 (k1_jordan1e B A))) ) ) ) ) ).
tt(t24_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 B)) A) &  ( (~  (A = (k3_goboard9 B)) )  &  (~  (A = (k2_goboard9 B)) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k24_pscomp_1 (k3_topreal1 2 A)))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 B)) &  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 D 1) E))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k8_pscomp_1 A) (k8_pscomp_1 B)) =>  ((k8_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k8_pscomp_1 B)) ) ) ) ) ) ).
tt(t24_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_topreal6 2 A B) = (k1_topreal6 2 (k4_algstr_0 (k15_euclid 2) A) (k4_algstr_0 (k15_euclid 2) B))) ) ) ) ) ).
tt(t24_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k5_jordan6 A B C B C) = A) ) ) ) ) ) ) ) ).
tt(t24_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((k1_jordan21 A) = (k18_pscomp_1 A)) ) ) ) ).
tt(t24_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k18_euclid (k2_jordan21 A)) (k18_euclid (k2_jordan21 (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))))) ) ) ) ) ) ).
tt(t24_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 B) (k4_finseq_1 (k3_graph_2 A B)))) ) ) ) ).
tt(t24_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (a_1_0_jordan2b B))  => (v3_pre_topc A k3_topmetr)) ) ) ) ) ).
tt(t24_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (r1_xboole_0 (k1_jordan2c A B) (k2_jordan2c A B))) ) ) ) ).
tt(t24_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ( ((k1_funct_1 (k3_jordan3 A B) (k3_finseq_1 (k3_jordan3 A B))) = B)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_jordan3 A B)))  =>  ((k1_funct_1 (k3_jordan3 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r3_jordan4 A B C D) =>  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 A D))  &  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 B E) = (k1_funct_1 A (k1_jordan4 (k7_nat_d (k2_nat_1 C E) 1) A))) ) ) )  |  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ((k1_funct_1 B E) = (k1_funct_1 A (k1_jordan4 (k7_nat_d (k2_nat_1 (k3_finseq_1 A) C) E) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = B)  =>  ((k6_measure6 A) = (k2_pre_topc k3_topmetr B)) ) ) ) ) ) ).
tt(t24_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) & (v4_topreal1 A)) )  => (r1_tarski (k3_topreal1 2 (k4_jordan3 A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t24_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_topreal1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) ) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C))) ) ) ) ) ) ) ).
tt(t24_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_3_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k17_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k17_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t24_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k4_jordan6 A B C B) = A) ) ) ) ) ) ) ) ).
tt(t24_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 D))) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D) C)))) ) ) ) ) ) ) ) ) ).
tt(t24_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((r1_gobrd10 C D) | (r1_subset_1 (k2_jordan_a A C B) (k2_jordan_a A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_xreal_0 C))  =>  ((k2_tops_1 (k15_euclid A) (k1_topreal9 A B C)) = (k3_topreal9 A B C)) ) ) ) ) ) ) ).
tt(t24_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r1_ordinal1 D E) => (r3_lattices A (k5_knaster A B C D) (k5_knaster A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_kurato_1,ax, ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) = (k3_rcomp_1 4 k1_xxreal_0)) ).
tt(t24_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) )  =>  ((k1_kurato_2 A B) = C) ) ) ) ) ) ) ) ).
tt(t24_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r2_hidden E (k2_finseq_1 A)))  =>  ((k5_laplace D E A B C) = (k5_laplace E D A B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_group_4 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( (B = C)  =>  ((v15_algstr_0 C) & (m1_group_2 C A)) ) ) ) ) ) ) ) ).
tt(t24_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((r1_latsum_1 A B) &  ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) A) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_orders_2 B) & (v5_orders_2 B)) ) ) ) ) )  => (v5_orders_2 (k1_latsum_1 A B))) ) ) ) ) ).
tt(t24_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((r6_binop_1 (u1_struct_0 A) (u1_lattices A) (u2_lattices A)) => (v11_lattices A)) ) ) ).
tt(t24_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r3_lattice3 B C A) <=> (r4_lattice3 B (k7_lattices B C) (a_2_0_lattice3 A B))) ) ) ) ) ) ).
tt(t24_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden (k6_lattices A) B) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((r1_tarski C B) => (r2_hidden (k2_lattice4 A C) B)) ) ) ) ) ) ) ) ).
tt(t24_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) => (r1_tarski A (k8_lattice5 A B))) ) ) ) ).
tt(t24_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v9_lattice6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k16_lattice3 A (a_3_1_lattice6 A B C))) ) ) ) ) ) ) ) ).
tt(t24_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  (! [F:$i] :  ((m1_lattice5 F A B C) =>  ((r1_ordinal1 D E) => (r1_relset_1 (k2_zfmisc_1 (k3_lattice8 A D) (k3_lattice8 A D)) (u1_struct_0 B) (k6_lattice8 A B C F D) (k6_lattice8 A B C F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_lattices A (k3_lattices A B C)) = (k4_lattices A (k7_lattices A B) (k7_lattices A C))) ) ) ) ) ) ) ).
tt(t24_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_lexbfs B A) & (m1_lexbfs B A))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B C))) &  ( (~ (r1_xxreal_0 (k1_recdef_1 (k5_lexbfs A B C) E) (k1_recdef_1 (k5_lexbfs A B C) D)))  & (r2_hidden D (k1_relset_1 (k6_glib_000 A) (k5_lexbfs A B (k7_nat_d (k39_glib_000 B) (k1_recdef_1 (k5_lexbfs A B C) E)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_lfuzzy_1 A B k6_numbers) (k5_fuzzy_4 A A))) ) ) ) ).
tt(t24_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) & (v2_limfunc1 B))  => (v1_limfunc1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t24_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) | (r6_limfunc2 B A))  => (r5_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A)) ) ) ) ) ).
tt(t24_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 C)) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r2_limfunc3 C A)) ) ) ) ) ) ) ) ).
tt(t24_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r6_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k1_seq_1 B E) (k2_limfunc2 B A))) ) ) ) ) ) ) )  | (r6_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t24_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A C D) => (r1_lmod_6 A (k2_vectsp_5 A B C E) (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_lopban_1 A B))) =>  ( (E = (k3_rlvect_1 (k11_lopban_1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k12_lopban_1 A B E F) = (k3_rlvect_1 B (k12_lopban_1 A B C F) (k12_lopban_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_lopban_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) E) (k1_normsp_1 A (k1_bhsp_4 A B) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) (k1_lopban_4 A B) D) = (k8_nat_1 (u1_struct_0 A) (k6_lopban_4 D A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t24_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v1_filter_0 C A) &  ( (~ (r2_hidden C (k3_funct_2 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A) B)))  & (r2_hidden B C)) ) ) ) ) ) ) ) ) ).
tt(t24_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_hidden E (k9_lpspace1 B C D)) => (r2_hidden (k26_valued_1 B k1_numbers E A) (k9_lpspace1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D))) => (r1_xxreal_0 (k1_seq_1 (k2_mesfun6c B A (k56_valued_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers C D))) E) (k1_seq_1 (k26_valued_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k2_mesfun6c B A (k56_valued_1 A k1_numbers C)) (k2_mesfun6c B A (k56_valued_1 A k1_numbers D))) (k4_power 2 B)) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r3_ltlaxio1 C A) & (r3_ltlaxio1 C (k3_hilbert1 A B)))  => (r3_ltlaxio1 C B)) ) ) ) ) ) ) ).
tt(t24_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C)) (k8_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t24_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A B (k6_rusub_4 A C D)) = (k3_mathmorp A (k3_mathmorp A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t24_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v4_matrix10 B) => (v3_matrix10 (k2_matrix10 A B))) ) ) ) ) ).
tt(t24_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 (k1_nat_1 A 2))) =>  ((r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) E (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) D C)) =>  ((k2_matrix11 A B E) = (k8_group_1 B (k2_matrix11 A B C) (k2_matrix11 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 A)))  =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 D k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 B k5_numbers)) =>  ( ((r2_hidden C (k2_finseq_1 D)) & (r1_tarski (k10_xtuple_0 G) (k2_finseq_1 (k1_matrix_1 E))))  =>  ((k8_matrix_1 A (k1_matrix13 A E D B F G) C) = (k1_partfun1 k5_numbers k5_numbers k5_numbers A G (k8_matrix_1 A E (k1_funct_1 F C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B C))  =>  ((k1_funct_1 (k3_matrix14 A C B) B) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t24_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k8_matrix13 A B) = (k8_matrix13 A (k7_matrlin (u1_struct_0 A) B C)))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski D (k4_finseq_1 B)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E D) =>  ((k8_matrix_1 (u1_struct_0 A) B E) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 B) (k4_struct_0 A))) ) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E D) =>  ((k8_matrix_1 (u1_struct_0 A) C E) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 C) (k4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v3_matrix16 F (u1_struct_0 B)) &  ((v3_matrix16 G (u1_struct_0 B)) & (v3_matrix16 H (u1_struct_0 B))) )  => (v3_matrix16 (k2_matrix_6 A B (k2_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) =>  ( ((k3_finseq_1 C) = A)  &  ( ((k1_matrix_1 C) = A)  &  ((k2_matrix_1 C) = (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_finseq_2 A) = (k1_group_1 (k13_matrix_2 A))) ) ) ).
tt(t24_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  ( ((v1_binop_1 D A) & (v2_binop_1 D A))  =>  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I C) =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C (k2_setwiseo B H) (k2_setwiseo C I)) (k9_matrix_3 B C A E F G)) = (k7_setwiseo B A D (k2_setwiseo B H) (k9_funcop_1 A B E F (k7_setwiseo C A D (k2_setwiseo C I) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k3_matrix_3 A B C) D) = (k3_matrix_3 A (k1_matrix_4 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((k6_matrix_3 A B (k4_struct_0 A)) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ) ).
tt(t24_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v2_matrix_6 C A B) & (v2_matrix_6 D A B))  => (v2_matrix_6 (k2_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k3_group_4 A (k8_finseq_1 (u1_struct_0 A) B (k4_matrix_7 A (k4_finseq_5 (u1_struct_0 A) B)))) = (k1_group_1 A)) ) ) ) ) ).
tt(t24_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v2_matrix_8 C A B) &  ((v2_matrix_8 D A B) &  ((r1_matrix_6 A B C D) &  ((k4_matrix_6 A B C D) = (k11_matrix_1 B A)) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix_8 (k2_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 2 1 3))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) C E J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_complsp2 (k5_matrixc1 A (k1_complsp2 B))) = (k5_matrixc1 B (k1_complsp2 A))) ) ) ) ) ) ).
tt(t24_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m1_matrix_1 E A (k2_wsierp_1 (k10_matrixj1 A (k5_matrixj1 A C D))) (k2_wsierp_1 (k11_matrixj1 A (k5_matrixj1 A C D)))) =>  ( (E = (k13_matrixj1 A B (k5_matrixj1 A C D)))  <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden F (k2_finseq_1 (k1_matrix_1 C))) =>  ((k9_matrix_1 A E F) = (k8_finseq_1 A (k9_matrix_1 A C F) (k5_finseq_2 A (k3_finseq_1 D) B))) )  &  ((r2_hidden F (k2_finseq_1 (k1_matrix_1 D))) =>  ((k9_matrix_1 A E (k1_nat_1 F (k1_matrix_1 C))) = (k8_finseq_1 A (k5_finseq_2 A (k3_finseq_1 C) B) (k9_matrix_1 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_matrixj2 G A B) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 F)) =>  ( (H = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) G))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ( ((r2_hidden I (k4_finseq_1 E)) &  (J = (k1_matrixj1 (k10_matrixj1 (u1_struct_0 A) G) I)) )  =>  ( ( (I = (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) (k7_matrixj2 A B J G))))  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin2 A C D E F H) (k7_partfun1 (u1_struct_0 C) E I)) = (k4_vectsp_1 A D B (k7_partfun1 (u1_struct_0 D) F I))) )  &  ( (~  (I = (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) (k7_matrixj2 A B J G)))) )  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin2 A C D E F H) (k7_partfun1 (u1_struct_0 C) E I)) = (k3_rlvect_1 D (k4_vectsp_1 A D B (k7_partfun1 (u1_struct_0 D) F I)) (k7_partfun1 (u1_struct_0 D) F (k1_nat_1 I 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrixr1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ((k2_matrix_1 (k3_matrix_3 A B C)) = (k2_matrix_1 B)) ) ) ) ) ) ) ).
tt(t24_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k9_matrixr1 (k8_rvsum_1 A B)) = (k5_matrixr1 (k9_matrixr1 A) (k9_matrixr1 B))) ) ) ) ) ) ) ).
tt(t24_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrlin F A D) =>  (! [G:$i] :  ((m1_matrlin G A (k1_vectsp_5 A B C D)) =>  ( (G = (k7_finseq_1 E F))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_vectsp_5 A B C D))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k1_vectsp_5 A B C D))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k1_vectsp_5 A B C D))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 C)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 D)) =>  ( ( (H = (k3_rlvect_1 (k1_vectsp_5 A B C D) I J))  &  ( (I = K)  &  (J = L) ) )  =>  ((k9_matrlin A (k1_vectsp_5 A B C D) G H) = (k8_finseq_1 (u1_struct_0 A) (k9_matrlin A C E K) (k9_matrlin A D F L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D C B) =>  ( ((k1_matrix_1 E) = (k1_matrix_1 F))  =>  ((k1_matrix_1 (k8_matrlin D A C B E F)) = (k1_matrix_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_xxreal_0 (k4_matroid0 A B) (k4_matroid0 A C))) ) ) ) ) ) ) ).
tt(t24_matrprob,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A k6_numbers) =>  ((k5_matrprob B) = k6_numbers) ) ) ) ) ).
tt(t24_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k1_funct_1 (k3_matrtop1 A B E) (k8_rvsum_1 C D)) = (k8_rvsum_1 (k1_funct_1 (k3_matrtop1 A B E) C) (k1_funct_1 (k3_matrtop1 A B E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (! [D:$i] :  ( ((v1_rlaffin1 D (k15_euclid B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))))  =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  => (v1_rlaffin1 (k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D) (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t24_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 (k3_square_1 A) (k7_real_1 (k5_square_1 (k1_seq_1 E B)) (k5_square_1 (k1_seq_1 E C)))) &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D F B C)) E) B) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_mazurulm C A B) => (r3_nfcont_1 A B C (k1_relset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t24_mboolean,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r6_pboole A (k2_mboolean A (k7_funcop_1 A (k2_tarski (k1_tarski B) (k1_tarski C)))) (k7_funcop_1 A (k2_tarski B C)))) ) ) ).
tt(t24_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  ( (~  (C = (k1_xtuple_0 C)) )  &  (~  (C = (k2_xtuple_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  => (m2_subset_1 (k5_setfam_1 A (k4_measure1 A B C)) (k1_zfmisc_1 A) B)) ) ) ) ) ).
tt(t24_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = k1_numbers)  =>  ((k2_measure6 B A) = B) ) ) ) ) ) ).
tt(t24_measure8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_measure4 A B)) &  ((v1_prob_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_measure4 A B))))) ) )  =>  ((r2_hidden (k5_setfam_1 A (k4_measure1 A (k1_measure4 A B) C)) (k1_measure4 A B)) &  ((k1_mesfunc9 B (k5_setfam_1 A (k4_measure1 A (k1_measure4 A B) C))) = (k3_mesfunc9 (k1_partfun1 k5_numbers (k1_measure4 A B) (k9_setfam_1 A) k7_numbers C B))) ) ) ) ) ) ) ).
tt(t24_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) => (r1_tarski (k6_member_1 (k3_xboole_0 A B)) (k3_xboole_0 (k6_member_1 A) (k6_member_1 B)))) ) ) ) ).
tt(t24_membered,ax, (! [A:$i] :  (! [B:$i] :  ((v6_membered B) =>  ((r1_tarski A B) => (v6_membered A)) ) ) ) ).
tt(t24_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  ((k9_xtuple_0 C) = (k2_xboole_0 (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) (k9_xtuple_0 (k6_memstr_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t24_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r2_mesfun6c A B C D) & (r1_xboole_0 E F))  =>  ((k1_mesfun6c A B C (k2_partfun1 A k2_numbers D (k6_prob_1 A B E F))) = (k2_xcmplx_0 (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D E)) (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers (k11_mesfun7c A B) C) (k5_comseq_3 A (k4_mesfunc5 A k2_numbers B C))) & (r2_relset_1 A k1_numbers (k4_mesfunc5 A k1_numbers (k12_mesfun7c A B) C) (k6_comseq_3 A (k4_mesfunc5 A k2_numbers B C)))) ) ) ) ) ) ) ).
tt(t24_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((v1_mesfunc8 B A k2_numbers) <=> (v1_mesfunc8 (k11_mesfun7c A B) A k1_numbers)) ) ) ) ) ).
tt(t24_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B C F) = (k9_subset_1 A E (k15_mesfunc1 A D (k1_measure6 F)))) ) )  =>  ((k9_subset_1 A E (k15_mesfunc1 A D k1_supinf_1)) = (k2_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  => (r2_relset_1 A k7_numbers (k10_mesfunc1 A B) (k3_mesfunc1 A (k1_mesfunc2 A B) (k2_mesfunc2 A B)))) ) ) ) ).
tt(t24_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) & (v3_mesfunc5 C))  =>  ( ((k1_relset_1 A (k3_mesfunc1 A (k1_mesfunc2 A (k3_mesfunc1 A B C)) (k2_mesfunc2 A B))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_mesfunc1 A (k2_mesfunc2 A (k3_mesfunc1 A B C)) (k1_mesfunc2 A B))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_mesfunc1 A (k3_mesfunc1 A (k1_mesfunc2 A (k3_mesfunc1 A B C)) (k2_mesfunc2 A B)) (k2_mesfunc2 A C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_mesfunc1 A (k3_mesfunc1 A (k2_mesfunc2 A (k3_mesfunc1 A B C)) (k1_mesfunc2 A B)) (k1_mesfunc2 A C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ((v6_supinf_2 (k3_mesfunc1 A (k1_mesfunc2 A (k3_mesfunc1 A B C)) (k2_mesfunc2 A B))) & (v6_supinf_2 (k3_mesfunc1 A (k2_mesfunc2 A (k3_mesfunc1 A B C)) (k1_mesfunc2 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k3_numbers B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k3_numbers B)))) )  =>  ( (! [H:$i] :  ((v1_rat_1 H) =>  ((k1_funct_1 G H) = (k9_subset_1 A (k8_subset_1 A E (k11_mesfunc1 C H)) (k8_subset_1 A E (k11_mesfunc1 D (k9_real_1 F H))))) ) )  =>  ((k8_subset_1 A E (k11_mesfunc1 (k3_valued_1 A k1_numbers k1_numbers C D) F)) = (k3_tarski (k2_relset_1 B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C D)))  =>  ((r1_mesfunc5 A B C (k3_mesfunc2 D A)) &  ( ((k7_mesfunc5 A B C (k3_mesfunc2 D A)) = (k12_supinf_2 C D))  &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k3_mesfunc2 D A) D)) = (k12_supinf_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = D)  &  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C E) D)) ) )  => (r1_mesfunc1 A B (k5_mesfunc8 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t24_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  (~  ((v2_mesfunc9 B A) &  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) &  ( ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) E) = k1_supinf_1)  &  ((r1_xxreal_0 D C) &  ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B D) E) = k2_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B 1) =>  (! [C:$i] :  ((m1_subset_1 C 1) => (r1_xxreal_0 (k1_metric_1 1 1 k3_metric_1 A C) (k4_xxreal_0 (k1_metric_1 1 1 k3_metric_1 A B) (k1_metric_1 1 1 k3_metric_1 B C)))) ) ) ) ) ) ).
tt(t24_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A))) =>  ((r2_hidden C (k4_metric_2 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) &  (? [E:$i] :  ((m1_subset_1 E (k2_metric_2 A)) &  ( (C = (k1_domain_1 (k2_metric_2 A) (k2_metric_2 A) D E))  & (r4_metric_2 A D E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 k1_numbers k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 k1_numbers k1_numbers)) => (r1_xxreal_0 (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 A C) (k7_real_1 (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 A B) (k1_metric_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k2_zfmisc_1 k1_numbers k1_numbers) k18_metric_3 B C)))) ) ) ) ) ) ).
tt(t24_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_metric_6 A C B) & (m2_valued_0 D (u1_struct_0 A) C))  => (r1_metric_6 A D B)) ) ) ) ) ) ) ) ) ).
tt(t24_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  ((v1_metrizts A) &  (! [C:$i] :  ( ((v1_cantor_1 C A) &  ((v1_tops_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  ((r1_tarski C B) & (v4_card_3 C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_hidden B (u1_pre_topc (k15_euclid A))) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k1_xboole_0))  & (r1_tarski (k1_topreal9 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_midsp_1 A B C) =>  ((r2_midsp_1 A D B) <=> (r2_midsp_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_midsp_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 B))) =>  (! [F:$i] :  ( ((v4_midsp_2 F B) & (l1_midsp_2 F B))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (u1_midsp_2 B F))) =>  (! [H:$i] :  ((m2_finseq_2 H (u1_struct_0 (u1_midsp_2 B F)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 B F)))) =>  ( ( ((k7_midsp_3 A B F C H) = E)  &  ( ((k10_midsp_2 B F C G) = D)  &  ((k4_midsp_3 A B C E) = D) ) )  =>  ((k10_midsp_3 A B F H) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  (~  ((k3_mmlquery A D (k16_mmlquery A B C)) = (k15_mmlquery A (k3_mmlquery A D B) (k3_mmlquery A D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_mod_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_mod_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k18_mod_2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_enumset1 k6_numbers 1 2)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_enumset1 k6_numbers 1 2)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_enumset1 k6_numbers 1 2)) =>  ( ( (D = A)  &  ( (E = B)  &  (F = C) ) )  =>  ( ((k1_algstr_0 k18_mod_2 (k1_algstr_0 k18_mod_2 A B) C) = (k11_mod_2 (k11_mod_2 D E) F))  &  ( ((k1_algstr_0 k18_mod_2 A (k1_algstr_0 k18_mod_2 B C)) = (k11_mod_2 D (k11_mod_2 E F)))  &  ( ((k6_algstr_0 k18_mod_2 (k6_algstr_0 k18_mod_2 A B) C) = (k12_mod_2 (k12_mod_2 D E) F))  &  ((k6_algstr_0 k18_mod_2 A (k6_algstr_0 k18_mod_2 B C)) = (k12_mod_2 D (k12_mod_2 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((v2_mod_4 C A B) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_algstr_0 A D)) = (k4_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k5_algstr_0 A D E)) = (k5_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_modal_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (! [C:$i] :  ((m1_trees_1 C A) =>  ( ( (B = (k12_finseq_1 k5_numbers k6_numbers))  &  ( (C = (k12_finseq_1 k5_numbers 1))  &  ((k1_trees_2 A (k1_modal_1 A)) = (k7_domain_1 A B C)) ) )  =>  (A = (k5_trees_1 (k5_trees_1 (k2_trees_1 2) (k12_finseq_1 k5_numbers k6_numbers) (k4_trees_1 A B)) (k12_finseq_1 k5_numbers 1) (k4_trees_1 A C))) ) ) ) ) ) ) ) ).
tt(t24_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_1 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_partfun1 D C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C))))  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (k30_modelc_1 C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 (k48_modelc_1 C D F)))))) )  =>  ((r4_modelc_1 C D F G E (k11_modelc_1 A B)) <=>  (? [H:$i] :  ((m1_modelc_1 H C D) &  ( ((k3_funct_2 k5_numbers C H k6_numbers) = E)  &  (? [I:$i] :  ((m1_subset_1 I k5_numbers) &  ( (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  ( (~ (r1_xxreal_0 I J))  => (r4_modelc_1 C D F G (k3_funct_2 k5_numbers C H J) A)) ) )  & (r4_modelc_1 C D F G (k3_funct_2 k5_numbers C H I) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v7_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  ( (B = (k11_modelc_2 A))  |  (B = (k12_modelc_2 A)) ) ) ) ) ) ) ) ).
tt(t24_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (? [C:$i] :  ((v7_ordinal1 C) &  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  (? [E:$i] :  ( ((v1_modelc_3 E A) & (l1_modelc_3 E A))  &  ((r1_xxreal_0 1 C) &  ( ((k3_finseq_1 D) = C)  &  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D C) = E)  &  ( ((u2_modelc_3 A E) = (k7_modelc_3 A))  & (r5_modelc_3 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_moebius1 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (r1_xxreal_0 (k11_nat_3 A B) 1)) ) ) ) ) ).
tt(t24_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B))) ) ) ) ) ).
tt(t24_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m2_monoid_0 C B))  => (m2_monoid_0 (k9_monoid_1 C A) (k9_monoid_1 B A))) ) ) ) ) ).
tt(t24_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k1_morph_01 A (k5_rusub_4 A C B) D) = (k1_morph_01 A C (k5_rusub_4 A D B)))  &  ((k1_morph_01 A (k5_rusub_4 A C B) D) = (k5_rusub_4 A (k1_morph_01 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  => (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k1_msafree3 A B)) (k5_msafree3 A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))) B))) ) ) ) ).
tt(t24_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  |  ((k4_finseq_1 D) = (k4_finseq_1 (k1_msualg_1 A C))) )  &  ( ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( (F = (k1_funct_1 D E))  &  ((k7_msaterm A B F) = (k1_funct_1 (k1_msualg_1 A C) E)) ) ) ) ) ) ) ) )  |  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( (F = (k1_funct_1 D E))  &  ((k7_msaterm A B F) = (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)) ) ) ) ) ) ) ) ) )  &  (~ (m1_msaterm D A B (k2_msaterm A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (u1_msualg_1 A) C) = k1_xboole_0)  =>  ((k9_xtuple_0 (k5_msualg_1 A C B)) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(t24_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v2_finset_1 (k2_funct_6 B)) => (v2_finset_1 (k3_funct_6 B))) ) ) ) ).
tt(t24_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  ( ((k12_msualg_1 A B) = (k12_msualg_1 A C))  =>  ((g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C))) ) ) ) ) ) ) ) ).
tt(t24_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) E (k2_pboole (u1_struct_0 A) D (u3_msualg_1 A C))) =>  ((k13_msualg_2 A B (k12_msualg_2 A B D) C) = (k12_msualg_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_msualg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D B)) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ( ( (F = G)  &  ((r2_hidden F (k3_msualg_1 A D B)) & (r2_hidden H (k3_msualg_1 A D C))) )  =>  ( (H = (k5_msualg_3 A B C D E F))  <=>  (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k9_xtuple_0 G)) =>  ((k1_funct_1 H I) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) E (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A D) I)) (k1_funct_1 G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (~  ((r1_msualg_6 A D E B F) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E))))) )  =>  (~  ((r1_msualg_6 A D E B G) &  ((k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D) G) = (k3_relat_1 F (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_msualg_7,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  &  (? [B:$i] :  ((m2_nat_lat B A) &  ((v1_msualg_7 B A) &  (~ (v2_msualg_7 B A)) ) ) ) ) ) ).
tt(t24_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k7_msafree2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k3_msualg_1 A D B)) =>  ( ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k7_msafree2 A)) C (k2_msualg_1 A D)) (k3_funct_2 (k3_msualg_1 A D B) (k4_msualg_1 A D B) (k5_msualg_1 A D B) E)) = k6_numbers)  &  ((k3_funct_2 (k3_msualg_1 A D (k7_msafree2 A)) (k4_msualg_1 A D (k7_msafree2 A)) (k5_msualg_1 A D (k7_msafree2 A)) (k5_msualg_3 A B (k7_msafree2 A) D C E)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_unialg_2 A B) & (r4_msualg_3 (k6_msualg_1 A) (k9_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)) (k2_msuhom_1 A B C)))  => (r4_alg_1 A B C)) ) ) ) ) ) ) ).
tt(t24_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v4_dilworth A) & (l1_orders_2 A)) )  =>  ((k2_dilworth A) = (k1_dilworth (k3_necklace A))) ) ) ).
tt(t24_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers))))) )  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k1_binop_1 B C D) = (k3_nagata_1 A C D)) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) k1_numbers (k9_funct_2 (u1_struct_0 A) k1_numbers)) =>  ((r3_binop_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) C B) => (v1_pscomp_1 C A)) ) ) ) ) ) ) ) ).
tt(t24_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (B = (k3_xcmplx_0 C A))  =>  ( (A = k6_numbers)  | (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t24_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k3_nat_d A C) (k3_nat_d B C))) ) ) ) ) ) ) ).
tt(t24_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~  (A = 1) )  &  ( (~  (A = B) )  &  (~  ((k11_nat_3 B A) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t24_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k9_real_1 A 1) = (k4_nat_1 B C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_nat_d D B) &  ((v1_int_2 D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( ((k4_nat_d (k13_newton E (k7_nat_d A 1)) A) = 1)  &  ((k6_nat_d (k7_nat_d (k13_newton E (k3_nat_d (k7_nat_d A 1) D)) 1) A) = 1) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 B C) |  ((r1_xxreal_0 C k6_numbers) | (v1_int_2 A)) ) ) ) ) ) ) ) ) ).
tt(t24_nat_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers)))  =>  ((r1_funct_2 k5_numbers k5_numbers k5_numbers k1_numbers A B) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (~ (r1_tarski C (k2_finseq_1 D))) ) )  |  ((k3_uproots C (k1_nat_5 k5_numbers A C)) = (k18_rvsum_1 (k4_bhsp_5 k1_numbers k5_numbers B (k14_finseq_1 C)))) ) ) ) ) ) ) ) ) ).
tt(t24_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k4_nat_d A B) = A) ) ) ) ) ) ).
tt(t24_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r2_nattra_1 A B C D) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ((r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k7_nattra_1 A B C D D E (k6_nattra_1 A B D)) E) & (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k7_nattra_1 A B C C D (k6_nattra_1 A B C) E) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k9_subset_1 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) C) (k1_relset_1 (u1_struct_0 A) D))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k6_vfunct_1 (u1_struct_0 A) B C D)) (k2_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k2_vfunct_1 (u1_struct_0 A) B C D)) (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k2_numbers))))  =>  ((r6_ncfcont2 A B C) => (r12_ncfcont1 B C A)) ) ) ) ) ) ).
tt(t24_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_ndiff_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v12_struct_0 D k5_numbers A) &  ((v1_ndiff_1 D A (k4_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) B) &  ((k6_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((r2_ndiff_3 A D B) & (r1_tarski C B))  => (r2_ndiff_3 A D C)) ) ) ) ) ) ) ) ).
tt(t24_ndiff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) & (r1_ndiff_3 (k4_real_ns1 B) C D)) )  =>  ((r1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 A B)) D) &  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 A B) (k1_ndiff_3 (k4_real_ns1 B) C D)) = (k1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 A B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  ((v3_nfcont_1 E (k14_prvect_2 A)) =>  ((r2_ndiff_5 A B C D E) <=>  ((r1_tarski E (k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  ((r2_hidden F E) => (r1_ndiff_5 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  ((r2_necklace (k4_necklace 4) A) <=> (r2_necklace (k4_necklace 4) (k3_necklace A))) ) ) ).
tt(t24_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden (k4_tarski B C) (u1_orders_2 (k4_necklace A))) &  ( (~  (B = (k1_nat_1 C 1)) )  &  (~  (C = (k1_nat_1 B 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski C (k2_net_1 A)) =>  ((r2_hidden B (k13_net_1 A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k2_net_1 A)) &  ((r2_hidden D C) & (r2_hidden B (k6_net_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t24_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) &  (B = (k5_real_1 A 1)) )  =>  ((k5_newton B A) = A) ) ) ) ) ) ).
tt(t24_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) => (r3_nfcont_1 B A C (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t24_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( ((v1_rcomp_1 (k1_relset_1 k1_numbers B)) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) B (k1_relset_1 k1_numbers B)) A))  => (v1_nfcont_1 (k2_relset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t24_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) =>  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) <=>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r2_hidden G B) &  ( (~ (r1_xxreal_0 F (k18_complex1 (k10_binop_2 G D))))  & (r1_xxreal_0 E (k12_euclid (k8_euclid A (k7_partfun1 (k1_euclid A) C G) (k7_partfun1 (k1_euclid A) C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ( ((r2_hidden B (k7_normform A)) & (r2_hidden C (k7_normform A)))  =>  ((r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C) (k7_normform A)) <=>  ((k5_setwiseo A (k3_finsub_1 (k5_finsub_1 A) (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) C)) (k3_finsub_1 (k5_finsub_1 A) (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) C) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B))) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t24_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 C A) &  ((k6_normsp_1 A C) = B) )  =>  ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A C B))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A C B))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t24_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  ( (D = (a_3_3_normsp_2 A B C))  => (v4_pre_topc D (k3_normsp_2 A))) ) ) ) ) ) ) ) ) ).
tt(t24_numbers,ax, (~  (k4_numbers = k3_numbers) ) ).
tt(t24_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  ((u1_struct_0 (k15_openlatt A)) = (k9_openlatt A)) ) ) ).
tt(t24_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B)) <=> (v9_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t24_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((v6_relat_2 B) => (v3_orders_1 B)) ) ) ) ).
tt(t24_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k3_orders_2 A D C)) <=>  ((r2_orders_2 A B C) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t24_ordinal1,ax, (! [A:$i] :  (~  ( (! [B:$i] :  ((r2_hidden B A) => (v3_ordinal1 B)) )  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~ (r1_tarski A B)) ) ) ) ) ) ).
tt(t24_ordinal2,ax, (! [A:$i] : (r1_ordinal1 (k2_ordinal2 A) (k3_ordinal2 A))) ).
tt(t24_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A (k10_ordinal2 A B)) & (r1_ordinal1 B (k10_ordinal2 A B))) ) ) ) ) ).
tt(t24_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden 1 A) & (r2_hidden B C))  => (r2_hidden (k12_ordinal2 A B) (k12_ordinal2 A C))) ) ) ) ) ) ) ).
tt(t24_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden 1 A) =>  ((r1_xxreal_0 C B) | (r2_hidden (k1_ordinal5 A B) (k1_ordinal5 A C))) ) ) ) ) ) ) ) ).
tt(t24_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  (! [B:$i] :  ((v1_ordinal6 B) =>  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden C D)) ) )  => (r3_wellord1 (k1_wellord2 (k10_ordinal2 (k1_ordinal6 A) (k1_ordinal6 B))) (k1_wellord2 (k2_xboole_0 A B)) (k1_ordinal4 (k2_ordinal6 A) (k2_ordinal6 B)))) ) ) ) ) ).
tt(t24_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t24_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k1_ortsp_1 A B E D C) = (k8_group_1 A (k11_algstr_0 A (k1_ortsp_1 A B D C E)) (k1_ortsp_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k2_osalg_4 A)) =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) (k5_osalg_4 A (k8_osafree A B) (k20_osafree A B) C)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r2_hidden F C) & (r2_hidden (k4_tarski D F) (k1_funct_1 (k19_osafree A B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (l3_msualg_1 D A))  =>  ((r3_orders_2 A (k2_msualg_1 A B) (k2_msualg_1 A C)) => (r1_tarski (k4_msualg_1 A B D) (k4_msualg_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t24_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r2_pboole (u1_struct_0 A) (k2_pboole (u1_struct_0 A) (k3_osalg_2 A B) C) (k9_osalg_2 A B C))) ) ) ) ) ) ).
tt(t24_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) &  ((v13_osalg_1 C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ( ((r1_msualg_3 A B C D) & (v1_osalg_3 D A))  => (v3_osalg_4 (k19_osalg_4 A B C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t24_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_parsp_1 A B C B D) =>  ((r1_parsp_1 A B D B C) &  ((r1_parsp_1 A C B B D) &  ((r1_parsp_1 A B C D B) &  ((r1_parsp_1 A B D C B) &  ((r1_parsp_1 A C B D B) &  ((r1_parsp_1 A D B B C) &  ((r1_parsp_1 A D B C B) &  ((r1_parsp_1 A C B C D) &  ((r1_parsp_1 A B C C D) &  ((r1_parsp_1 A C B D C) &  ((r1_parsp_1 A C D C B) &  ((r1_parsp_1 A B C D C) &  ((r1_parsp_1 A D C C B) &  ((r1_parsp_1 A C D B C) &  ((r1_parsp_1 A D C B C) &  ((r1_parsp_1 A D B D C) &  ((r1_parsp_1 A B D D C) &  ((r1_parsp_1 A D B C D) &  ((r1_parsp_1 A B D C D) &  ((r1_parsp_1 A D C D B) &  ((r1_parsp_1 A C D D B) &  ((r1_parsp_1 A D C B D) & (r1_parsp_1 A C D B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) & (r1_parsp_2 A B C E))  =>  ( (B = C)  | (r1_parsp_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k1_relset_1 B (k3_partfun1 D B C))) <=>  ((r2_hidden A (k9_xtuple_0 D)) &  ((r2_hidden A B) & (r2_hidden (k1_funct_1 D A) C)) ) ) ) ) ) ) ) ).
tt(t24_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r2_hidden C (k1_relset_1 A D)) =>  ((k9_relat_1 D C) = (k1_tarski (k7_partfun1 B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((k4_partit1 A (k2_partit1 A B C)) = (k4_eqrel_1 A (k4_partit1 A B) (k4_partit1 A C))) ) ) ) ) ) ) ).
tt(t24_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v4_relat_2 C) => (r4_relat_2 C B)) ) ) ) ) ) ) ).
tt(t24_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v6_pasch A)) ) ).
tt(t24_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r2_pboole A (k3_pboole A B C) (k2_pboole A B D))) ) ) ) ) ) ) ).
tt(t24_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v8_pre_topc A) & (v2_pcomps_1 A))  => (v9_pre_topc A)) ) ) ).
tt(t24_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k19_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k19_pcs_0 A B))) =>  ( ( (C = D)  & (r1_orders_2 (k19_pcs_0 A B) D E))  =>  ( (C = B)  |  ((r2_hidden B (u1_struct_0 A)) |  ((r2_hidden E (u1_struct_0 A)) &  (~  (E = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_real_ns1 B))) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid B)) =>  ( ( (E = F)  &  ( (G = H)  & (r5_pdiff_1 B A C D E G)) )  =>  ((k1_funct_1 (k13_pdiff_1 B A C D E G) (k12_finseq_1 k5_numbers 1)) = (k9_finseq_1 (k14_pdiff_1 B A C D F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r4_pdiff_3 B A) & (r4_pdiff_3 C A))  =>  ((r3_pdiff_1 2 2 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) &  ((k11_pdiff_1 2 2 (k3_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) = (k7_real_1 (k5_pdiff_3 B A) (k5_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t24_pdiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r3_pdiff_4 B A) =>  ((r1_tarski A (k1_relset_1 (k1_euclid 3) B)) &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((r2_hidden C A) => (r3_pdiff_1 3 3 B C)) ) ) ) ) ) ) ) ).
tt(t24_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r6_pdiff_5 B A) <=> (r3_pdiff_1 3 3 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ).
tt(t24_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_euclid A) (k1_euclid B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_euclid A) (k1_euclid B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  =>  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 E B A) &  ((v2_pdiff_6 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  ((r1_tarski (a_3_2_pdiff_6 A D G) (k1_relset_1 (k1_euclid A) C)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid A)) =>  (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid B)) =>  (~  ( (~  (J = (k5_euclid A)) )  &  ( (~ (r1_xxreal_0 I (k12_euclid J)))  &  ( (K = (k1_pdiff_6 A B F J))  & (r1_xxreal_0 H (k8_real_1 (k2_real_1 (k12_euclid J)) (k12_euclid K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  ( (~ (r1_xxreal_0 G (k12_euclid (k8_euclid A H D))))  =>  ((k8_euclid B (k7_partfun1 (k1_euclid B) C H) (k7_partfun1 (k1_euclid B) C D)) = (k7_euclid B (k1_pdiff_6 A B E (k8_euclid A H D)) (k1_pdiff_6 A B F (k8_euclid A H D)))) ) ) ) ) ) ) ) ) )  |  ((r1_pdiff_1 A B C D) & (r2_funct_2 (k1_euclid A) (k1_euclid B) (k8_pdiff_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  ( ( ((k4_finseq_1 B) = (k4_finseq_1 C))  & (r2_relset_1 k5_numbers (k1_euclid A) D (k7_integr15 A k5_numbers B C)))  =>  ((k5_euclid_7 A D) = (k7_euclid A (k5_euclid_7 A B) (k5_euclid_7 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ( (E = F)  &  ((v1_pdiff_7 E A) &  (C = D) ) )  =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G A))  =>  ((r2_pdiff_7 A B G C E) & (r4_pdiff_7 A B (k2_pdiff_7 A B G C E) E)) ) ) )  <=>  ((r2_ndiff_1 F (k4_real_ns1 A) (k4_real_ns1 B) D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) D F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_pre_topc (k5_pencil_1 A B))) <=>  (? [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  &  ( (C = (k4_card_3 D))  & (m1_subset_1 (k1_funct_1 D (k3_pencil_1 A D)) (u1_pre_topc (k2_pencil_1 A B (k3_pencil_1 A D))))) ) ) ) ) ) ) ) ) ).
tt(t24_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 D (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  => (m1_pencil_2 (k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) D C) A B)) ) ) ) ) ) ) ) ) ).
tt(t24_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  (! [E:$i] :  ((m1_pencil_2 E A B) =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  (! [G:$i] :  ( ( (~ (v13_pencil_1 G))  &  ((v16_pencil_1 G A) & (m3_pboole G A (k12_pralg_1 A B))) )  =>  (! [H:$i] :  ( ( (~ (v13_pencil_1 H))  &  ((v16_pencil_1 H A) & (m3_pboole H A (k12_pralg_1 A B))) )  =>  (! [I:$i] :  ( ( (~ (v13_pencil_1 I))  &  ((v16_pencil_1 I A) & (m3_pboole I A (k12_pralg_1 A B))) )  =>  ( ( (D = (k4_card_3 F))  &  ( (E = (k4_card_3 G))  &  ( ((k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) C D) = (k4_card_3 H))  &  ( ((k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) C E) = (k4_card_3 I))  &  ((k3_pencil_1 A F) = (k3_pencil_1 A G)) ) ) ) )  =>  ((k3_pencil_1 A H) = (k3_pencil_1 A I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_vectsp_9 A B)) & (r1_tarski (k2_vectsp_9 A B D) (k2_vectsp_9 A C D))) )  =>  ((k2_vectsp_4 A B) = (k2_vectsp_4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_newton A 2) = (k3_square_1 A)) ) ) ).
tt(t24_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A B C) => (r2_pnproc_1 A (k3_pnproc_1 A C B) C)) ) ) ) ) ) ).
tt(t24_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  ((k1_group_1 (k1_polyalg1 A)) = (k10_polynom3 A)) ) ) ).
tt(t24_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( ((k3_polyeq_1 A B k6_numbers C) = k6_numbers)  &  ( (~  (C = (k1_binop_2 (k6_binop_2 B A))) )  &  (~  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k6_power A C) = k6_numbers)  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  ((r1_xxreal_0 C k6_numbers) |  (C = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((v1_xcmplx_0 H) =>  (! [I:$i] :  ((v1_xcmplx_0 I) =>  (! [J:$i] :  ((v1_xcmplx_0 J) =>  (! [K:$i] :  ((v1_xcmplx_0 K) =>  ( ( (K = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 3 (k1_newton G 2))) 32))  &  ( (H = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 (k3_xcmplx_0 4 B) G)) (k1_newton G 3)) 64))  &  ( (I = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 D) (k3_xcmplx_0 (k3_xcmplx_0 64 G) C)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton G 2)) B)) (k3_xcmplx_0 3 (k1_newton G 4))) 1024))  &  ( (E = (k1_polyeq_5 2 (k2_polyeq_5 (k4_xcmplx_0 (k1_newton H 2)) (k6_xcmplx_0 (k1_newton K 2) I) (k3_xcmplx_0 2 K))))  &  ( (F = (k1_polyeq_5 2 (k3_polyeq_5 (k4_xcmplx_0 (k1_newton H 2)) (k6_xcmplx_0 (k1_newton K 2) I) (k3_xcmplx_0 2 K))))  &  (J = (k10_complex1 (k13_complex1 H (k3_xcmplx_0 E F)))) ) ) ) ) )  =>  ( (H = k6_numbers)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 G (k1_newton A 3))) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 E F) J) (k13_complex1 G 4))) )  &  ( (~  (A = (k6_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 E F) J) (k13_complex1 G 4))) )  &  ( (~  (A = (k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 E) F) J) (k13_complex1 G 4))) )  &  (~  (A = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 E) F) J) (k13_complex1 G 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 1)))  &  ( (~ (r1_xxreal_0 (k7_polyform A) B))  &  (~  ((v7_ordinal1 (k2_xcmplx_0 B 1)) &  ((r1_xxreal_0 1 (k2_xcmplx_0 B 1)) & (r1_xxreal_0 (k2_xcmplx_0 B 1) (k7_polyform A))) ) ) ) ) ) ) ) ) ) ).
tt(t24_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k6_polynom1 A B C C) (k7_polynom1 A B))) ) ) ) ) ).
tt(t24_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k6_polynom1 A B C D) E) = (k5_algstr_0 B (k5_polynom2 A B C E) (k5_polynom2 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_algseq_1 A B D) & (r1_algseq_1 A C D))  => (r1_algseq_1 A (k2_normsp_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t24_polynom4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k13_polynom3 A B C) D) = (k8_group_1 A (k2_polynom4 A B D) (k2_polynom4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t24_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k1_algseq_1 A (k3_polynom5 A B (k4_struct_0 A))) = k6_numbers) ) ) ) ) ).
tt(t24_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v4_polynom7 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B C D) = (k3_polynom7 A B C)) ) ) ) ) ) ) ) ) ).
tt(t24_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_polynom8 A B (k4_nat_1 C D)) = (k3_polynom8 A (k3_polynom8 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t24_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((k11_bagorder (g1_orders_2 (k15_pre_poly A) B) (k2_polyred A B C D)) = (k3_termord A B C D)) ) ) ) ) ) ) ) ) ).
tt(t24_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_power A k6_numbers) = 1) ) ) ).
tt(t24_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_pralg_2 D A B) => (r1_msualg_3 B (k14_pralg_2 A B D) (k5_pralg_2 A B D C) (k2_pralg_3 A B D C))) ) ) ) ) ) ) ) ).
tt(t24_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k2_prelamb A B (k2_prelamb A C C))) B)) ) ) ) ) ) ).
tt(t24_pre_poly,ax, (! [A:$i] :  ((k1_card_3 (k9_finseq_1 A)) = (k9_finseq_1 (k1_card_1 A))) ) ).
tt(t24_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 C))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k2_prepower C (k13_complex1 A B)) = (k13_complex1 (k2_prepower C A) (k2_prepower C B))) ) ) ) ) ) ) ) ) ).
tt(t24_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  ( (~ (v2_struct_0 A))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r2_hidden C D) & (r1_xboole_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) => (m1_prob_1 (k7_subset_1 A C D) A B)) ) ) ) ) ) ) ).
tt(t24_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) => (r1_prob_2 A B D C (k4_prob_1 A B))) ) ) ) ) ) ) ) ).
tt(t24_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  => (r1_tarski (k1_funct_1 D A) (k1_funct_1 (k2_prob_3 B D) A))) ) ) ) ) ) ) ).
tt(t24_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) => (m1_prob_4 k1_xboole_0 A B C)) ) ) ) ) ) ).
tt(t24_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k10_cqc_lang A B C) (k8_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t24_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ( (~  (C = D) )  =>  ((r1_incsp_1 A (k2_projpl_1 A C D) C) &  ((r1_incsp_1 A (k2_projpl_1 A C D) D) &  ( ((k2_projpl_1 A C D) = (k2_projpl_1 A D C))  &  ( ((r1_incsp_1 A B C) & (r1_incsp_1 A B D))  =>  (B = (k2_projpl_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A C D) & (r1_incsp_1 A C E))  =>  ((r1_incsp_1 A B D) |  ((r1_incsp_1 A B E) |  ((k1_funct_1 (k1_projred1 A D E B) C) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B E))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_incsp_1 A B G))  &  ( (~ (r1_incsp_1 A C G))  &  ( (~  (B = C) )  &  ((r1_incsp_1 A B H) &  ((r1_incsp_1 A C H) &  ((r1_incsp_1 A D H) &  ( (~ (r1_incsp_1 A D F))  &  ( (~  (D = B) )  &  ( (~ (r1_projred2 A E F G))  &  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (~  ((r1_projred2 A F G I) &  ( (~ (r1_incsp_1 A B I))  &  ( (~ (r1_incsp_1 A D I))  &  ((k3_relat_1 (k1_projred1 A E G B) (k1_projred1 A G F C)) = (k3_relat_1 (k1_projred1 A E I B) (k1_projred1 A I F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_prvect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_prvect_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))))) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  (? [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  &  ( (D = F)  &  ( ((k12_finseq_1 (u1_struct_0 B) E) = G)  &  ((k1_binop_1 C D E) = (k7_finseq_1 F G)) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B))) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k3_rlvect_1 (k7_prvect_3 (k14_prvect_2 A) B) D E)) = (k3_rlvect_1 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C D) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C E))) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k1_rlvect_1 (k7_prvect_3 (k14_prvect_2 A) B) D E)) = (k1_rlvect_1 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C D) E)) ) ) ) )  &  ( ((k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C (k4_struct_0 (k7_prvect_3 (k14_prvect_2 A) B))) = (k4_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B))) =>  ((k1_normsp_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B))) (k3_funct_2 (u1_struct_0 (k7_prvect_3 (k14_prvect_2 A) B)) (u1_struct_0 (k14_prvect_2 (k7_finseq_1 A (k9_finseq_1 B)))) C D)) = (k1_normsp_0 (k7_prvect_3 (k14_prvect_2 A) B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden A B) =>  ((r1_xxreal_0 (k6_pscomp_1 B) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) (k8_pscomp_1 B)) &  ((r1_xxreal_0 (k9_pscomp_1 B) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k7_pscomp_1 B))) ) ) ) ) ) ) ) ).
tt(t24_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m1_pua2mss1 B (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) (k1_pua2mss1 (u1_struct_0 A) (u1_unialg_1 A))) => (r2_pua2mss1 (u1_struct_0 A) B (k8_eqrel_1 (u1_struct_0 A) (k9_pua2mss1 A)))) ) ) ) ).
tt(t24_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k4_pboole A (k1_pzfmisc1 A B) (k2_pzfmisc1 A B C)) (k1_pboole A)) & (r6_pboole A (k4_pboole A (k1_pzfmisc1 A C) (k2_pzfmisc1 A B C)) (k1_pboole A))) ) ) ) ) ) ).
tt(t24_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ((r1_qc_lang1 A B C) | (r1_qc_lang1 A C B)) ) ) ) ) ) ) ).
tt(t24_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [I:$i] :  ((m2_subset_1 I (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k9_qc_lang2 A D F H B) = (k9_qc_lang2 A E G I C))  =>  ( (D = E)  &  ( (F = G)  &  ( (H = I)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v6_qc_lang1 C A) => (v6_qc_lang1 (k15_qc_lang1 A B C) A)) ) ) ) ) ) ) ).
tt(t24_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((v3_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) A) =>  ((r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)) (k9_xtuple_0 (k2_qc_lang4 A B))) &  ((k1_funct_1 (k2_qc_lang4 A B) (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers))) = (k18_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t24_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((k5_quantal1 A (k15_lattice3 A B)) = (k16_lattice3 A (a_2_0_quantal1 A B))) ) ) ) ).
tt(t24_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni A (k29_quaterni B C)) = (k29_quaterni (k27_quaterni A B) (k27_quaterni A C))) ) ) ) ) ) ) ).
tt(t24_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k17_quaterni (k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A))) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k17_quaterni A))) ) ) ).
tt(t24_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (A = (k6_quaterni (k17_quaterni A) (k18_quaterni A) (k19_quaterni A) (k20_quaterni A))) ) ) ).
tt(t24_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((k1_quin_1 A B C) = k6_numbers)  =>  ((r1_xxreal_0 k6_numbers A) |  ( (~  ( (~ (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C)))  &  (D = (k4_xcmplx_0 (k7_xcmplx_0 B (k3_xcmplx_0 2 A)))) ) )  &  (~  ( (~  (D = (k4_xcmplx_0 (k7_xcmplx_0 B (k3_xcmplx_0 2 A)))) )  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k16_quofield A) B C) = (k5_binop_1 (k7_quofield A) (k16_quofield A) C B)) ) ) ) ) ) ) ).
tt(t24_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_radix_1 (k2_xcmplx_0 B 1) A C) =>  ((k4_radix_1 (k2_xcmplx_0 B 1) C (k2_xcmplx_0 B 1) (k10_radix_1 C (k2_xcmplx_0 B 1) A)) = (k3_nat_d A (k1_newton (k1_radix_1 C) B))) ) ) ) ) ) ) ) ).
tt(t24_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) => (m1_random_1 (k56_valued_1 A k1_numbers C) A B)) ) ) ) ) ) ).
tt(t24_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) => (r1_vectsp_6 A B C (k6_ranknull A B C (k1_vectsp_6 A B C)))) ) ) ) ) ) ).
tt(t24_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k2_rat_1 A) = (k1_real_1 (k1_rat_1 A)))  <=>  (A = (k1_real_1 1)) ) ) ) ).
tt(t24_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k11_ratfunc1 A (k8_ratfunc1 A)) = (k8_ratfunc1 A)) ) ) ).
tt(t24_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_xxreal_2 A) => (r1_tarski A (k2_limfunc1 (k5_seq_4 A)))) ) ) ).
tt(t24_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_funct_2 k5_numbers k5_numbers (k1_real_3 k6_numbers A) (k8_funcop_1 k5_numbers k5_numbers k6_numbers))) ) ).
tt(t24_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_real_lat A))) =>  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) C D) B))  &  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) B C) D))  &  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) C B) D))  &  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) D B) C))  &  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) D C) B))  &  ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k5_real_lat A) C D)) = (k1_binop_1 (k5_real_lat A) (k1_binop_1 (k5_real_lat A) B D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((m2_subset_1 (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C) (u1_struct_0 A) (k8_struct_0 A)) & (m2_subset_1 (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B) (u1_struct_0 A) (k8_struct_0 A))) ) ) ) ) ) ) ).
tt(t24_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_binop_1 (k2_realset3 A) (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B) C) = (k1_funct_1 (k5_realset2 A) (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C))) ) ) ) ) ) ) ).
tt(t24_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  => (r2_classes1 (k4_rearran1 A B D C) (k20_rfunct_3 A C A))) ) ) ) ) ) ) ) ) ).
tt(t24_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_relat_1 (k6_subset_1 A B)) = (k6_subset_1 (k2_relat_1 A) (k2_relat_1 B))) ) ) ) ) ).
tt(t24_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) <=>  (? [E:$i] :  ((m1_subset_1 E B) & (r2_hidden (k4_tarski D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r2_hidden C (k6_relset_2 A B D E)) =>  (! [F:$i] :  ((r2_hidden F D) => (r2_hidden C (k1_relset_2 A B E F))) ) ) ) ) ) ) ) ) ) ).
tt(t24_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 C)) & (r1_xxreal_0 1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) C B)) A) |  ((k2_topreal1 2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) C B) A) = (k2_topreal1 2 C (k2_nat_1 (k7_nat_d A 1) (k4_finseq_4 C B)))) ) ) ) ) ) ) ) ) ).
tt(t24_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) => (r1_rewrite1 (k2_relat_1 A) C B)) ) ) ) ) ).
tt(t24_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k8_afinsq_1 A)) =>  ((m1_rewrite1 E (k7_rewrite2 A B)) => (m1_rewrite1 (k5_rewrite2 A D (k4_rewrite2 A C E)) (k7_rewrite2 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t24_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  ((r1_rewrite3 F G A D B) <=> (r2_rewrite3 C F G A (k1_flang_1 C D E) B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v8_valued_0 A) => (v1_integra2 (k6_rvsum_1 A))) ) ) ).
tt(t24_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((k8_relset_1 k5_numbers k1_numbers A (k1_tarski (k10_real_1 C B))) = (k8_relset_1 k5_numbers k1_numbers (k10_rvsum_1 A B) (k1_tarski C))) ) ) ) ) ) ) ) ).
tt(t24_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k54_valued_1 (k18_valued_1 A B)) = (k18_valued_1 (k54_valued_1 A) (k54_valued_1 B))) ) ) ) ) ).
tt(t24_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ((r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) & (r1_xxreal_0 C D)) )  => (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t24_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_rfunct_3 C A k1_numbers (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_rfunct_3 D A k1_numbers (k3_rfunct_3 A k1_numbers)) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A (k3_finseq_4 (k3_rfunct_3 A k1_numbers) B C D)) (k5_rfunct_3 A k1_numbers (k5_rfunct_3 A k1_numbers B C) D))) ) ) ) ) ) ) ) ).
tt(t24_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_rfunct_3 B A) => (r3_rfunct_4 B A)) ) ) ) ).
tt(t24_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 A) & (v1_seq_2 A))  =>  ((k2_seq_2 A) = (k1_rinfsup1 A)) ) ) ) ).
tt(t24_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (r1_xxreal_0 (k2_rinfsup2 A) (k1_rinfsup2 A))) ) ).
tt(t24_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k17_ringcat1 A))) =>  (! [D:$i] :  ((m3_ringcat1 D (k10_ringcat1 (k9_ringcat1 A))) =>  (! [E:$i] :  ((m3_ringcat1 E (k10_ringcat1 (k9_ringcat1 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ( ( ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B))  =>  ((k11_ringcat1 (k9_ringcat1 A) E) = (k12_ringcat1 (k9_ringcat1 A) D)) )  &  ( ( ((k11_ringcat1 (k9_ringcat1 A) E) = (k12_ringcat1 (k9_ringcat1 A) D))  =>  ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B)) )  &  ( ( ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B))  => (r2_hidden (k4_tarski E D) (k1_relset_1 (k2_zfmisc_1 (k10_ringcat1 (k9_ringcat1 A)) (k10_ringcat1 (k9_ringcat1 A))) (k16_ringcat1 (k9_ringcat1 A)))))  &  ( ((r2_hidden (k4_tarski E D) (k1_relset_1 (k2_zfmisc_1 (k10_ringcat1 (k9_ringcat1 A)) (k10_ringcat1 (k9_ringcat1 A))) (k16_ringcat1 (k9_ringcat1 A)))) =>  ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B)) )  &  ( ( ((k3_graph_1 (k17_ringcat1 A) C) = (k4_graph_1 (k17_ringcat1 A) B))  =>  ((k1_cat_1 (k17_ringcat1 A) B C) = (k6_ringcat1 E D)) )  &  ( ( ((k3_graph_1 (k17_ringcat1 A) B) = (k3_graph_1 (k17_ringcat1 A) C))  =>  ((k11_ringcat1 (k9_ringcat1 A) D) = (k11_ringcat1 (k9_ringcat1 A) E)) )  &  ( ( ((k11_ringcat1 (k9_ringcat1 A) D) = (k11_ringcat1 (k9_ringcat1 A) E))  =>  ((k3_graph_1 (k17_ringcat1 A) B) = (k3_graph_1 (k17_ringcat1 A) C)) )  &  ( ( ((k4_graph_1 (k17_ringcat1 A) B) = (k4_graph_1 (k17_ringcat1 A) C))  =>  ((k12_ringcat1 (k9_ringcat1 A) D) = (k12_ringcat1 (k9_ringcat1 A) E)) )  &  ( ((k12_ringcat1 (k9_ringcat1 A) D) = (k12_ringcat1 (k9_ringcat1 A) E))  =>  ((k4_graph_1 (k17_ringcat1 A) B) = (k4_graph_1 (k17_ringcat1 A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  (! [D:$i] :  ((m1_rlvect_2 D B) => (r1_rlvect_2 B (k2_rlaffin1 B (k7_rlvect_2 B C D) A) (k7_rlvect_2 B (k2_rlaffin1 B C A) (k2_rlaffin1 B D A)))) ) ) ) ) ) ) ) ).
tt(t24_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (~  ( (~  ((k6_rlvect_2 A B) = (k6_rlvect_2 A C)) )  &  ( ((k3_rlaffin1 A B) = (k3_rlaffin1 A C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers B D) (k3_funct_2 (u1_struct_0 A) k1_numbers C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m2_rlaffin3 C (k15_euclid A) B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)))) =>  ( ( (B = D)  &  ((r2_hidden (k5_euclid A) B) &  ((k1_funct_1 C (k3_finseq_1 C)) = (k5_euclid A)) ) )  =>  (! [E:$i] :  ((m1_matrlin E k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) D)) =>  ( (E = (k17_finseq_1 (u1_struct_0 (k15_euclid A)) (k7_nat_d (k5_card_1 B) 1) C))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) D))) =>  ((k9_matrlin k2_vectsp_1 (k1_vectsp_7 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) D) E F) = (k17_finseq_1 k1_numbers (k7_nat_d (k5_card_1 B) 1) (k1_rlaffin3 (k15_euclid A) B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 k1_numbers C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers C) C)))) )  =>  ( ( (B = C)  &  ( (D = (k4_struct_0 A))  &  ( (E = (k1_realset1 (u1_algstr_0 A) B))  &  (F = (k5_relat_1 (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B))) ) ) )  => (m1_rlsub_1 (g1_rlvect_1 C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ((k2_rlsub_2 A C (k1_rlsub_2 A C B)) = C) ) ) ) ) ) ) ).
tt(t24_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k5_rusub_4 A B D) C))  <=> (r2_hidden D (k7_rusub_4 A C (k2_rltopsp1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t24_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_rlvect_1 B (k4_algstr_0 B C) A) = (k1_rlvect_1 B C (k4_xcmplx_0 A))) ) ) ) ) ) ) ).
tt(t24_rlvect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ( ((r2_hidden A (k1_relset_1 k5_numbers D)) &  (C = (k1_funct_1 D A)) )  =>  ((k1_funct_1 (k5_rlvect_2 B D E) A) = (k1_rlvect_1 B C (k3_funct_2 (u1_struct_0 B) k1_numbers E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B C) &  ((v1_rlvect_3 C A) &  ((k1_rlvect_3 A C) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B (k5_algstr_0 A C B) (k5_algstr_0 A D B)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t24_rlvect_x,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r2_hidden A (k5_rusub_4 B (k2_rlvect_x B (k8_domain_1 (u1_struct_0 B) D E F)) C)) <=>  (? [G:$i] :  ((v1_int_1 G) &  (? [H:$i] :  ((v1_int_1 H) &  (? [I:$i] :  ((v1_int_1 I) &  (A = (k3_rlvect_1 B (k3_rlvect_1 B (k3_rlvect_1 B C (k1_rlvect_1 B D G)) (k1_rlvect_1 B E H)) (k1_rlvect_1 B F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  => (m1_rmod_2 B A B)) ) ) ) ).
tt(t24_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (m1_rmod_2 (k2_rmod_3 A B C D) A (k1_rmod_3 A B C D))) ) ) ) ) ) ) ) ).
tt(t24_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k4_rmod_4 A B (k6_finseq_1 (u1_struct_0 B)) C) = (k6_finseq_1 (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t24_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k6_robbins1 A (k6_robbins1 A B C) D) (k6_robbins1 A (k6_robbins1 A B C) (k3_robbins1 A D))) (k6_robbins1 A (k6_robbins1 A B (k3_robbins1 A C)) D)) (k6_robbins1 A (k6_robbins1 A B (k3_robbins1 A C)) (k3_robbins1 A D))) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) (k3_robbins1 A D))) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) (k3_robbins1 A D))) = (k6_lattices A)) ) ) ) ) ) ) ) ) ).
tt(t24_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) B)) C) = (k3_robbins1 A (k3_robbins1 A C))) ) ) ) ) ) ) ).
tt(t24_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v6_oposet_1 A) & (l2_qmax_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  ( (C = (k10_lattice3 A B C))  &  (B = (k11_lattice3 A B C)) ) ) ) ) ) ) ) ) ).
tt(t24_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ((r3_lattices k2_robbins4 A B) <=> (r1_tarski A B)) ) ) ) ) ).
tt(t24_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_roughs_1 A B) (k3_roughs_1 A C))) ) ) ) ) ) ) ).
tt(t24_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski C B) =>  ((k1_rpr_1 A (k7_subset_1 A B C)) = (k9_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C))) ) ) ) ) ) ) ) ).
tt(t24_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_rsspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_rsspace4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_rsspace4 A B))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_rsspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) &  ((v1_rsspace4 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A (u1_struct_0 B)) &  ((v1_rsspace4 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (F = C)  &  ( (G = D)  &  (H = E) ) )  =>  ( (E = (k5_algstr_0 (k9_rsspace4 A B) C D))  <=>  (! [I:$i] :  ((m1_subset_1 I A) =>  ((k3_funct_2 A (u1_struct_0 B) H I) = (k5_algstr_0 B (k3_funct_2 A (u1_struct_0 B) F I) (k3_funct_2 A (u1_struct_0 B) G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t24_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ((k2_rusub_2 A C (k1_rusub_2 A C B)) = C) ) ) ) ) ) ) ).
tt(t24_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_3 C B) =>  (? [D:$i] :  ((m1_rusub_3 D A) & (r1_tarski C D)) ) ) ) ) ) ) ) ).
tt(t24_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((v2_rusub_4 (k3_rusub_4 A B) A) & (r2_hidden (k4_struct_0 A) (u1_struct_0 B))) ) ) ) ) ).
tt(t24_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (C = (k4_struct_0 A)) )  &  ((r1_struct_0 B C) & (r1_struct_0 (k2_rusub_5 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t24_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ( ((k30_valued_1 A) = (k30_valued_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t24_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  ((k10_rvsum_2 A B k5_complex1) = (k5_finseq_2 k2_numbers A k5_complex1)) ) ) ) ) ).
tt(t24_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 7)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) A))) = (k1_tarski 1)) ) ) ) ).
tt(t24_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k2_scmfsa_1) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_funct_1 (k7_scmfsa_1 A B C) B) = C) ) ) ) ) ) ) ).
tt(t24_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k12_scmfsa_2 A B)) = 7) ) ) ) ) ).
tt(t24_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_scmfsa6a (k3_scmfsa6a A B)) = (k3_scmfsa6a A (k2_scmfsa6a B))) ) ) ) ) ).
tt(t24_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  ((k2_scmfsa8a A B (k2_scmfsa6a C)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1)) ) ) ) ) ) ) ) ).
tt(t24_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B E) k6_numbers))  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b C B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b C B A) F)) ) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b D B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b D B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r1_scmfsa8a B A C) <=> (r1_scmfsa8a (k1_scmfsa_m B) A C)) ) ) ) ) ) ) ) ).
tt(t24_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k2_scmfsa_9 A B)) = (k1_finsub_1 (k1_zfmisc_1 k2_scmfsa_2) (k4_scmfsa_m A) (k2_sf_mastr B))) ) ) ) ) ).
tt(t24_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_seq_4 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m C) B)) (k6_seq_4 (k3_funct_2 k5_numbers (k1_zfmisc_1 k5_numbers) (k8_scmfsa_m C) A)))) ) ) ) ) ) ) ) ).
tt(t24_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scm_halt D) & (v3_scm_halt D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_scmfsa6c E) & (m1_subset_1 E (u1_compos_1 k1_scmfsa_2)))  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa6a D E) A C) B) = (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 E (k1_scmfsa6b D A C)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 E C) B A) D) = (k18_scmfsa_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k15_scmpds_2 C D A B)) = 12) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k5_card_1 A) C)) => (v3_scmpds_4 (k3_scmpds_4 A (k7_scmpds_2 D B C)))) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B) D))  => (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B D)) (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r1_scmpds_6 C B A) <=> (r1_scmpds_6 C (k8_memstr_0 2 k1_scmpds_2 B) (k1_funct_4 A D))) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  ( ((r1_scmpds_6 C A B) &  ((r2_scmpds_6 C A B) &  ((r1_scmpds_6 D (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 A) B) B) & (r2_scmpds_6 D (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 A) B) B)) ) )  =>  ((r1_scmpds_6 (k1_scmpds_4 C D) A B) & (r2_scmpds_6 (k1_scmpds_4 C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  =>  ( ( (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_recdef_1 I J) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers)) ) )  &  ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 B J))) ) )  &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  ( ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 J L))) ) )  &  ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L H) =>  ((k1_funct_1 J L) = (k1_funct_1 B L)) ) ) )  &  ((k1_funct_1 J D) = (k1_funct_1 B D)) ) )  =>  ((r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C J K) D) = (k1_funct_1 J D))  &  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) &  ( (~ (r1_xxreal_0 (k1_recdef_1 I J) (k1_recdef_1 I (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C J K)))))  &  ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 (k6_scmpds_4 C J K) L))) ) )  &  (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L H) =>  ((k1_funct_1 (k6_scmpds_4 C J K) L) = (k1_funct_1 J L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) & (r2_scmpds_6 (k2_scmpds_8 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k2_memstr_0 2 (k1_scmring2 A)) = (k3_relat_1 k3_ami_2 (k1_scmring1 A))) ) ) ).
tt(t24_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 4)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t24_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((r2_hidden B (k3_tarski A)) <=> (r2_hidden (k1_tarski B) A)) ) ) ) ).
tt(t24_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) )  => (r1_semi_af1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t24_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers B C) A) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A) (k26_valued_1 k5_numbers k1_numbers C A)))) ) ) ) ) ) ).
tt(t24_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k2_seq_2 B) = k6_numbers)  |  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k10_real_1 (k2_seq_2 A) (k2_seq_2 B))) ) ) ) ) ) ) ).
tt(t24_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~  ((k2_seq_2 A) = k6_numbers) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((m2_valued_0 B k1_numbers A) & (v2_relat_1 B)) ) ) ) ) ) ) ) ) ).
tt(t24_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C D) & (r2_seqfunc A B D))  =>  ( (C = k1_xboole_0)  |  ((r2_seqfunc A B C) & (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k11_seqfunc A B D) C) (k11_seqfunc A B C))) ) ) ) ) ) ) ) ) ).
tt(t24_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 A) & (m2_valued_0 B k1_numbers A))  => (v7_valued_0 B)) ) ) ) ) ).
tt(t24_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k18_complex1 A)))  =>  ((v1_series_1 (k1_prepower A)) &  ((k4_series_1 (k1_prepower A)) = (k10_real_1 1 (k9_real_1 1 A))) ) ) ) ) ).
tt(t24_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k13_newton 2 B))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 (k3_xcmplx_0 (k13_newton 2 (k2_nat_1 B 1)) (k2_xcmplx_0 (k6_xcmplx_0 (k13_newton B 2) B) 2)) 4)) ) ) ) ) ) ).
tt(t24_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k18_complex1 A) B) => (r1_xxreal_0 (k3_square_1 A) (k3_square_1 B))) ) ) ) ) ).
tt(t24_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k3_xcmplx_0 (k13_newton 2 B) (k7_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 3 B) 1) 4)))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k2_xcmplx_0 (k3_xcmplx_0 (k13_newton 2 B) (k7_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 3 B) 4) 2)) 2)) ) ) ) ) ) ) ).
tt(t24_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 C A) B) (k8_complex1 (k8_complex1 (k13_complex1 (k3_xcmplx_0 A B) C) (k13_complex1 (k3_xcmplx_0 C B) A)) (k13_complex1 (k3_xcmplx_0 C A) B)))) ) ) ) ) ) ).
tt(t24_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (B = k1_xboole_0) )  =>  ((k2_xboole_0 A (k1_setfam_1 B)) = (k1_setfam_1 (k2_setfam_1 (k1_tarski A) B))) ) ) ) ).
tt(t24_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (v2_prob_1 (k4_setlim_1 A B))) ) ) ).
tt(t24_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 C) => (v2_prob_1 (k6_setlim_2 A C B))) ) ) ) ) ) ).
tt(t24_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v3_binop_1 C A)) )  =>  ( (D = k1_xboole_0)  |  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (! [G:$i] :  ((m1_subset_1 G B) =>  ((r2_hidden G D) =>  ((k3_funct_2 B A E G) = F) ) ) )  =>  ((k7_setwiseo B A C D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E B) => (r2_funct_2 k5_numbers A (k1_partfun1 k5_numbers B B A (k1_setwop_2 B E C) D) (k1_setwop_2 A (k4_finseqop B A E D) (k3_funct_2 B A D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t24_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~ (r1_sfmastr2 B A C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ((r5_scmfsa7b (k2_sfmastr2 C D) A B) & (r6_scmfsa7b (k2_sfmastr2 C D) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 A D)) |  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden G (k4_subset_1 k2_scmfsa_2 (k5_scmfsa_m C D) (k2_sf_mastr E))) =>  ( (G = B)  |  ((k1_funct_1 (k1_scmfsa6b (k2_sfmastr3 B C D E) A F) G) = (k1_funct_1 A G)) ) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_sfmastr3 B C D E) A F) G) = (k18_scmfsa_2 A G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_sf_mastr A) = (k2_sf_mastr (k5_compos_1 k1_scmfsa_2 A B))) ) ) ) ) ).
tt(t24_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_sgraph1 B))) =>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ( (~  (D = E) )  &  ((r2_hidden (g1_sgraph1 B C) (k3_sgraph1 A)) &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_sgraph1 B))))  =>  (~  ( (F = (k2_xboole_0 C (k1_tarski (k2_tarski D E))))  & (r2_hidden (g1_sgraph1 B F) (k3_sgraph1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) & (l3_lattices A)) ) ) ) ) )  => (v4_sheffer1 A)) ) ).
tt(t24_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A C (k5_sheffer1 A B D))) = C) ) ) ) ) ) ) ) ) ).
tt(t24_simplex0,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc B A) => (r1_xxreal_0 (k5_card_1 B) (k1_xxreal_3 (k6_simplex0 A) 1))) ) ) ) ) ).
tt(t24_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex0 C (u1_struct_0 B))) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) => (r1_tarski (k4_simplex0 C) (k4_simplex0 (k5_simplex1 A B C)))) ) ) ) ) ) ) ).
tt(t24_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k5_card_1 B) = (k3_real_1 A 1))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)))) &  ((v5_pre_topc C (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B)) (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k3_convex1 (k15_euclid A) B))))))) ) )  => (v2_abian C)) ) ) ) ) ) ) ).
tt(t24_sincos10,ax,(v2_funct_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t24_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k9_real_1 (k5_square_1 (k1_seq_1 k1_sin_cos2 A)) (k5_square_1 (k1_seq_1 k1_sin_cos2 B))) = (k8_real_1 (k1_seq_1 k1_sin_cos2 (k9_binop_2 A B)) (k1_seq_1 k1_sin_cos2 (k10_binop_2 A B))))  &  ( ((k8_real_1 (k1_seq_1 k1_sin_cos2 (k9_binop_2 A B)) (k1_seq_1 k1_sin_cos2 (k10_binop_2 A B))) = (k9_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) (k5_square_1 (k1_seq_1 k4_sin_cos2 B))))  &  ((k9_real_1 (k5_square_1 (k1_seq_1 k1_sin_cos2 A)) (k5_square_1 (k1_seq_1 k1_sin_cos2 B))) = (k9_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) (k5_square_1 (k1_seq_1 k4_sin_cos2 B)))) ) ) ) ) ) ) ).
tt(t24_sin_cos3,ax, ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 k5_complex1) = 1) ).
tt(t24_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  (~  ((k6_xcmplx_0 (k2_sin_cos4 A) (k2_sin_cos4 B)) = (k4_xcmplx_0 (k7_xcmplx_0 (k17_sin_cos (k6_xcmplx_0 A B)) (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t24_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k17_sin_cos A) 4) = (k10_real_1 (k7_real_1 (k9_real_1 3 (k8_real_1 4 (k21_sin_cos (k8_real_1 2 A)))) (k21_sin_cos (k8_real_1 4 A))) 8)) ) ) ).
tt(t24_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k17_sin_cos A) = 1)  =>  (A = (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k6_real_1 A (k8_real_1 2 k32_sin_cos)))))) ) ) ) ).
tt(t24_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 k6_numbers (k9_binop_2 (k11_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 B) 1))) (k11_binop_2 B (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)))))) ) ) ) ) ).
tt(t24_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k3_sin_cos2 (k7_xcmplx_0 A 2)) = (k6_square_1 (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) 1) 2))) ) ) ) ).
tt(t24_sin_cos9,ax,(r1_tarski (k1_rcomp_1 (k1_real_1 1) 1) (k1_relset_1 k1_numbers k2_sin_cos9))).
tt(t24_sin_cos,ax, ( ((k1_relset_1 k1_numbers k16_sin_cos) = k1_numbers)  &  ((k1_relset_1 k1_numbers k19_sin_cos) = k1_numbers) ) ).
tt(t24_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (a_1_0_sppol_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(t24_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k3_topreal1 2 A) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ).
tt(t24_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)) = (a_1_1_sprect_1 A)) ) ) ).
tt(t24_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sprect_2 A B) & (r1_sprect_2 A C))  => (r1_sprect_2 A (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B C))) ) ) ) ) ) ) ).
tt(t24_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v3_pre_topc (k2_goboard9 A) (k15_euclid 2)) & (v3_pre_topc (k3_goboard9 A) (k15_euclid 2))) ) ) ).
tt(t24_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t24_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((k6_square_1 A) = k6_numbers) )  =>  (A = k6_numbers) ) ) ) ).
tt(t24_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_rewrite1 C (k12_stacks_1 A)) =>  ( (B = (k1_funct_1 C 1))  => (r1_tarski (k10_xtuple_0 C) (k11_stacks_1 A B))) ) ) ) ) ) ) ).
tt(t24_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (v1_finset_1 (a_2_0_stirl2_1 A B))) ) ) ) ).
tt(t24_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k16_substut1 A) (k38_substut1 A)) =>  ( ((k19_substut1 A E) = (k19_substut1 A F))  =>  ( ((r1_sublemma A E B (k1_sublemma A B D (k3_sublemma A E B D)) C) & (r1_sublemma A F B (k1_sublemma A B D (k3_sublemma A F B D)) C))  <=> (r1_sublemma A (k6_sublemma A E F) B (k1_sublemma A B D (k3_sublemma A (k6_sublemma A E F) B D)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B (k3_subset_1 A C)) <=> (r1_tarski B C)) ) ) ) ) ) ).
tt(t24_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  ((k3_substlat A B (k4_substlat A B C C)) = (k3_substlat A B C)) ) ) ) ) ).
tt(t24_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (~  ((v7_substut1 B A) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A B))) (k3_finseq_1 (k11_qc_lang1 A (k18_substut1 A (k31_substut1 A B)))))) ) ) ) ) ) ).
tt(t24_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_substut1 A)) =>  ((k7_cqc_sim1 A (k5_cqc_lang A)) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A (k5_cqc_lang A) B)))) ) ) ) ) ).
tt(t24_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_supinf_2 C A B) <=> (v3_supinf_2 (k14_supinf_2 A B C) A (k6_supinf_2 B))) ) ) ) ) ) ) ).
tt(t24_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k8_group_1 A (k1_symsp_1 A B D C F) (k11_algstr_0 A (k1_symsp_1 A B D C E))) = (k1_symsp_1 A B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ((k3_relat_1 B (k6_subset_1 B (k4_relat_1 A))) = k1_xboole_0)  =>  ((k3_relat_1 B (k6_subset_1 B (k4_relat_1 (k10_xtuple_0 B)))) = k1_xboole_0) )  &  ( ((k3_relat_1 (k6_subset_1 B (k4_relat_1 A)) B) = k1_xboole_0)  =>  ((k3_relat_1 (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) B) = k1_xboole_0) ) ) ) ) ) ).
tt(t24_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((r2_relset_1 A A C (k13_lang1 A (k1_taxonom1 A B k6_numbers))) &  ((v1_taxonom1 B A) &  ((v2_metric_1 B A) & (v3_metric_1 B A)) ) )  =>  (C = (k4_relat_1 A)) ) ) ) ) ) ) ) ).
tt(t24_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_taylor_1 A C B) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski (k2_rcomp_1 D E) B) =>  ((r1_xxreal_0 E D) | (r2_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A B) C) (k2_rcomp_1 D E)) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A (k2_rcomp_1 D E)) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C D) &  (? [E:$i] :  ((v1_xreal_0 E) &  ((r2_hidden E (k2_rcomp_1 (k1_real_1 A) A)) &  (~  ( (~ (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k1_seq_1 k16_sin_cos E) (k1_seq_1 (k3_series_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) E)) D)))))  &  (~ (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k1_seq_1 k19_sin_cos E) (k1_seq_1 (k3_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) E)) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tbsp_1 B A) & (r1_tarski C B))  => (r1_xxreal_0 (k3_tbsp_1 A C) (k3_tbsp_1 A B))) ) ) ) ) ) ) ).
tt(t24_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) => (v5_tops_1 (k2_pre_topc A B) A)) ) ) ) ) ).
tt(t24_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_tdlat_2 A B) (k1_tdlat_2 A C)) (k1_tdlat_2 A (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)))) ) ) ) ) ) ).
tt(t24_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  ((k1_tops_1 A B) = B) ) ) ) ) ) ) ).
tt(t24_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v4_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r6_pboole A (k3_termord A B C D) (k16_pre_poly A)) &  ((k4_termord A B C D) = (k3_polynom1 A C D (k16_pre_poly A))) ) ) ) ) ) ) ) ) ) ).
tt(t24_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 (k3_tex_1 A B)) (u1_pre_topc (k3_tex_1 A B))))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((r1_tarski (k6_domain_1 A B) D) => (v4_pre_topc D C))  &  ((v4_pre_topc D C) =>  ((v1_xboole_0 D) | (r1_tarski (k6_domain_1 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_pre_topc C A))  =>  ((v3_pre_topc (k9_subset_1 (u1_struct_0 A) B C) A) & (v3_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) &  ((v3_pre_topc C A) &  ((v2_tex_2 B A) & (v2_tex_2 C A)) ) )  => (v2_tex_2 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t24_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_tex_3 B A) <=>  (? [C:$i] :  ( ((v1_pre_topc C) &  ((v1_tsep_1 C A) &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) )  & (m1_pre_topc C B)) ) ) ) ) ) ) ).
tt(t24_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_pre_topc B A) & (r2_hidden C B))  => (r1_tarski (k2_tex_4 A C) B)) ) ) ) ) ) ) ).
tt(t24_tietze,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc A B)) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) &  ((v5_pre_topc C (k1_pre_topc A B) (k4_topmetr (k1_real_1 1) 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) &  ((v5_pre_topc D A (k4_topmetr (k1_real_1 1) 1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) ) )  &  ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) D B) = C) ) ) ) ) ) )  => (v10_pre_topc A)) ) ) ).
tt(t24_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( ((m1_pre_topc B C) & (m1_pre_topc D C))  => (m1_pre_topc (k1_tsep_1 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t24_toler_1,ax, (! [A:$i] :  (? [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B (k3_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) )  &  (! [C:$i] :  ((r2_hidden C A) => (m1_toler_1 C (k3_tarski A) B)) ) ) ) ) ).
tt(t24_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D B) =>  ((r4_borsuk_2 A B C E F) => (r4_borsuk_2 A B C E (k1_borsuk_2 A B B C (k1_borsuk_2 A B D B (k2_borsuk_2 A D B G) G) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) =>  ((r1_borsuk_6 A D E) => (m1_borsuk_2 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) F C) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_borsuk_2 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) =>  (! [J:$i] :  ((m1_borsuk_2 J (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k7_topalg_4 A B C E F H (k1_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H) I J)) (k1_borsuk_2 A C D E (k7_topalg_4 A B C D F G I) (k7_topalg_4 A B D E G H J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topalg_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) =>  (! [C:$i] :  ((m1_borsuk_2 C (k8_toprealb 2) A B) =>  (! [D:$i] :  ((m1_borsuk_2 D (k8_toprealb 2) A B) =>  (! [E:$i] :  ((m1_borsuk_6 E (k8_toprealb 2) A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k2_topalg_2)) =>  (~  ((r4_borsuk_2 (k8_toprealb 2) A B C D) &  ((r2_hidden F (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) A))) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k2_topalg_2)) =>  (! [H:$i] :  ((m1_borsuk_2 H k2_topalg_2 F G) =>  (! [I:$i] :  ((m1_borsuk_2 I k2_topalg_2 F G) =>  (! [J:$i] :  ((m1_borsuk_6 J k2_topalg_2 F G H I) =>  (~  ((r4_borsuk_2 k2_topalg_2 F G H I) &  ((r2_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) E (k1_partfun1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) J k12_toprealb)) &  ((r2_hidden G (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) B))) &  (! [K:$i] :  ((m1_borsuk_6 K k2_topalg_2 F G H I) =>  ((r2_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 (k8_toprealb 2)) E (k1_partfun1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) K k12_toprealb)) => (r2_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k2_topalg_2) J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topalg_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((r1_tarski (k9_xtuple_0 B) k1_numbers) & (r1_tarski (k10_xtuple_0 B) (k2_struct_0 A))) ) ) ) ) ).
tt(t24_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) =>  ((v3_topdim_1 A) <=> (v3_topdim_1 B)) ) ) ) ) ) ).
tt(t24_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ((v3_topdim_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_xxreal_0 (k2_topdim_1 B (k3_subset_1 (u1_struct_0 B) C)) A) & (v5_waybel23 (k1_pre_topc B (k3_subset_1 (u1_struct_0 B) C))))  =>  (! [D:$i] :  ( ((v4_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v4_pre_topc E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ( (C = (k4_subset_1 (u1_struct_0 B) D E))  &  (! [F:$i] :  ( ((v4_pre_topc F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [G:$i] :  ( ((v4_pre_topc G B) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ( ((k2_struct_0 B) = (k4_subset_1 (u1_struct_0 B) F G))  &  ((r1_tarski D F) &  ((r1_tarski E G) &  ( ((k9_subset_1 (u1_struct_0 B) D G) = (k9_subset_1 (u1_struct_0 B) D E))  &  ( ((k9_subset_1 (u1_struct_0 B) D E) = (k9_subset_1 (u1_struct_0 B) F E))  & (r1_xxreal_0 (k2_topdim_1 B (k7_subset_1 (u1_struct_0 B) (k9_subset_1 (u1_struct_0 B) F G) (k9_subset_1 (u1_struct_0 B) D E))) (k3_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = k1_xboole_0)  =>  ((k3_topgen_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t24_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ((v1_finset_1 C) =>  ((k2_pre_topc (k5_topgen_2 A B) C) = C) ) ) ) ) ) ).
tt(t24_topgen_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (r1_xxreal_0 (k4_series_1 (k4_topgen_3 B A)) (k4_series_1 (k1_prepower A)))) ) ) ) ) ) ) ).
tt(t24_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) & (v1_tops_2 C A))  => (v1_tops_2 (k3_topgen_4 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t24_topgen_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_topgen_2 C A) =>  (! [D:$i] :  ((m1_topgen_2 D B) =>  ( (C = D)  =>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ) ) ) ) ) ).
tt(t24_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v4_pre_topc D B) <=> (v4_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topmetr,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B 1) &  (C = (k1_rcomp_1 A B)) ) ) )  =>  ((k4_topmetr A B) = (k1_pre_topc k5_topmetr C)) ) ) ) ) ) ) ) ).
tt(t24_topreal1,ax, (? [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) &  (? [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k2_tarski (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k19_euclid k6_numbers k6_numbers))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k19_euclid 1 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k19_euclid k6_numbers k6_numbers))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k19_euclid 1 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topreal3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden (k19_euclid A B) (k9_metric_1 (k14_euclid 2) E C)) & (r2_hidden (k19_euclid D B) (k9_metric_1 (k14_euclid 2) E C)))  => (r2_hidden (k19_euclid (k6_real_1 (k2_xcmplx_0 A D) 2) B) (k9_metric_1 (k14_euclid 2) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal4 A (k15_euclid 2)) &  (B = (a_2_0_topreal4 A C)) )  => (v3_pre_topc B (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t24_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( (A = (k4_struct_0 (k15_euclid 2)))  &  (A = B) )  =>  ( (B = (k2_finseq_4 k5_numbers k6_numbers k6_numbers))  &  ( ((k17_euclid B) = k6_numbers)  &  ((k18_euclid B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t24_topreal7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (C = D)  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  & (r1_tarski (k9_metric_1 B D F) (k9_metric_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (C = D)  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  & (r1_tarski (k9_metric_1 A C F) (k9_metric_1 B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k3_pcomps_1 A) = (k3_pcomps_1 B)) ) ) ) ) ) ).
tt(t24_topreal8,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 A) 4) | (v2_funct_1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t24_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  ( ( ((k2_xcmplx_0 B C) = 1)  &  ( ((k7_real_1 (k18_complex1 B) (k18_complex1 C)) = 1)  &  ((r2_hidden E (k2_topreal9 A F D)) & (r2_hidden G (k1_topreal9 A F D))) ) )  =>  ( (C = k6_numbers)  | (r2_hidden (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) E B) (k1_rlvect_1 (k15_euclid A) G C)) (k1_topreal9 A F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((v3_pre_topc (k2_rcomp_1 B C) (k4_topmetr A D)) & (m1_subset_1 (k2_rcomp_1 B C) (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A D))))) ) ) ) ) ) ) ) ) ) ).
tt(t24_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k11_toprealb k9_toprealb))) &  ((k18_euclid A) = k6_numbers) )  =>  (A = k10_toprealb) ) ) ) ).
tt(t24_toprealc,ax, (! [A:$i] :  ((v1_valued_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((r2_hidden (k30_valued_1 B) A) <=> (r2_hidden B (k2_toprealc A))) ) ) ) ) ).
tt(t24_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k12_euclid B) = k6_numbers)  =>  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t24_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (r1_tarski B C))  => (r1_tarski B (k1_tops_1 A C))) ) ) ) ) ) ) ).
tt(t24_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 B) D (k2_struct_0 B)) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) => (v3_tops_1 (k2_pre_topc A B) A)) ) ) ) ) ).
tt(t24_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ((v5_pre_topc B (k15_euclid A) k3_topmetr) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  & (r1_tarski (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B (k1_topreal9 A C E)) (k2_rcomp_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B C) D) (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) B C) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_transgeo A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r3_transgeo A B) => (r3_transgeo A (k2_funct_2 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t24_treal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (m1_pre_topc A k3_topmetr))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B k3_topmetr))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (~  ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ((r1_xxreal_0 D E) &  ((r1_tarski (k1_rcomp_1 D E) (u1_struct_0 A)) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_rcomp_1 D E)) (k1_rcomp_1 D E))) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (~ (v1_xboole_0 (k2_xboole_0 A B)))  & (v1_trees_1 (k2_xboole_0 A B))) ) ) ) ) ).
tt(t24_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) => (m1_trees_2 (a_2_2_trees_2 A B) A)) ) ) ) ).
tt(t24_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v6_trees_3 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((v1_relat_1 (k1_funct_1 A B)) &  ((v1_funct_1 (k1_funct_1 A B)) & (v3_trees_2 (k1_funct_1 A B))) ) ) ) ) ) ) ).
tt(t24_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ( ((k9_xtuple_0 (k8_trees_3 A B C)) = (k9_xtuple_0 C))  &  ((k9_xtuple_0 (k9_trees_3 A B C)) = (k9_xtuple_0 C)) ) ) ) ) ) ) ) ).
tt(t24_trees_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v3_trees_3 C))  =>  ((r2_hidden A (k12_trees_9 C B)) <=>  (? [D:$i] :  ((m1_subset_1 D C) &  (? [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 D)) &  ( (A = (k5_trees_2 D E))  &  (~  ((r2_hidden E (k3_trees_1 (k9_xtuple_0 D))) &  (~ (r2_hidden (k1_funct_1 D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  ((v1_borsuk_1 (k1_tsep_1 A B C) A) & (m1_pre_topc (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ).
tt(t24_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski D B) &  ((r1_tarski E C) &  ( ((k9_subset_1 (u1_struct_0 A) D E) = (k9_subset_1 (u1_struct_0 A) B C))  & (r2_tsep_1 A B C)) ) )  => (r2_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k2_pre_topc B (k6_domain_1 (u1_struct_0 B) D))) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ) ).
tt(t24_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_turing_1 A)) =>  ( ((k1_funct_1 B C) = D)  => (r2_funct_2 k4_numbers (u1_turing_1 A) (k5_turing_1 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t24_twoscomp,ax, ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 k6_numbers 1 1)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k27_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k27_twoscomp (k11_finseq_1 1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t24_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (v1_binop_1 (k10_unialg_2 A) (k9_unialg_2 A))) ) ).
tt(t24_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (B = (k4_relat_1 (u1_struct_0 A)))  =>  ((k5_unialg_3 A A B) = (k4_relat_1 (u1_struct_0 (k12_unialg_2 A)))) ) ) ) ) ) ).
tt(t24_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((r2_hidden B (k2_uniroots A)) <=>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (B = (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C) A)))) ) ) ) ) ) ) ) ).
tt(t24_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_polynom3 A))) =>  ( (B = C)  =>  ((k5_vfunct_1 k5_numbers A B) = (k4_algstr_0 (k14_polynom3 A) C)) ) ) ) ) ) ) ) ).
tt(t24_urysohn1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v10_pre_topc A) =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~  (B = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_urysohn1 D) (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 D) (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski B (k1_funct_1 E k6_numbers)) &  ( (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_funct_1 E 1)))  &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers (k1_urysohn1 D)) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers (k1_urysohn1 D)) =>  ( (~ (r1_xxreal_0 G F))  =>  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E F) A) &  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 D) E G) A) & (r1_tarski (k2_pre_topc A (k4_urysohn1 A (k1_urysohn1 D) E F)) (k4_urysohn1 A (k1_urysohn1 D) E G))) ) ) ) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_urysohn1 (k2_nat_1 D 1)) (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_urysohn1 (k2_nat_1 D 1)) (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  (~  ((r1_tarski B (k1_funct_1 F k6_numbers)) &  ( (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k1_funct_1 F 1)))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers (k1_urysohn1 (k2_nat_1 D 1))) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers (k1_urysohn1 (k2_nat_1 D 1))) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers (k1_urysohn1 (k2_nat_1 D 1))) =>  ( (~ (r1_xxreal_0 H G))  =>  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F G) A) &  ((v3_pre_topc (k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F H) A) &  ((r1_tarski (k2_pre_topc A (k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F G)) (k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F H)) &  ((r2_hidden I (k1_urysohn1 D)) =>  ((k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F I) = (k1_funct_1 E I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 B 1) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C k2_urysohn1) &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k8_cqc_lang A D E) F C) <=>  ((r1_valuat_1 A B D F C) => (r1_valuat_1 A B E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 A B C) = (k8_nat_1 A B D)) ) ) ) )  => (v3_funct_1 B)) ) ) ) ) ).
tt(t24_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) => (r2_hidden (k2_xcmplx_0 C B) (k1_relset_1 k5_numbers (k61_valued_1 A B)))) ) ) ) ) ) ) ).
tt(t24_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k24_valued_1 B (k4_xcmplx_0 A)) = (k30_valued_1 (k24_valued_1 B A))) ) ) ) ) ).
tt(t24_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m2_vectsp_4 D A B C) => (m1_subset_1 D (u1_struct_0 (k6_vectsp10 A B C)))) ) ) ) ) ) ) ) ).
tt(t24_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_struct_0 (k2_vectsp11 A B C) D) <=>  (? [E:$i] :  ((v7_ordinal1 E) &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B C E) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k11_algstr_0 A (k11_algstr_0 A B)) = B) ) ) ) ) ) ).
tt(t24_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_vectsp_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_vectsp_2 A))) =>  ( ((k5_vectsp_2 A (k4_vectsp_2 A) B (k3_rlvect_1 (k4_vectsp_2 A) D E)) = (k3_rlvect_1 (k4_vectsp_2 A) (k5_vectsp_2 A (k4_vectsp_2 A) B D) (k5_vectsp_2 A (k4_vectsp_2 A) B E)))  &  ( ((k5_vectsp_2 A (k4_vectsp_2 A) (k3_rlvect_1 A B C) D) = (k3_rlvect_1 (k4_vectsp_2 A) (k5_vectsp_2 A (k4_vectsp_2 A) B D) (k5_vectsp_2 A (k4_vectsp_2 A) C D)))  &  ( ((k5_vectsp_2 A (k4_vectsp_2 A) (k6_algstr_0 A C B) D) = (k5_vectsp_2 A (k4_vectsp_2 A) B (k5_vectsp_2 A (k4_vectsp_2 A) C D)))  &  ((k5_vectsp_2 A (k4_vectsp_2 A) (k1_group_1 A) D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (m1_vectsp_4 B A B)) ) ) ) ).
tt(t24_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ((k1_vectsp_5 A B (k2_vectsp_5 A B C D) D) = D) ) ) ) ) ) ) ) ) ).
tt(t24_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ( ((m2_vectsp_6 D A B C) & (m2_vectsp_6 E A B C))  => (m2_vectsp_6 (k5_vectsp_6 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((v1_matrlin B A) => (v1_matrlin C A)) ) ) ) ) ) ) ).
tt(t24_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B (k5_vfunct_1 A B C)) C)) ) ) ) ) ) ).
tt(t24_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B (k5_vfunct_1 A B C)) C)) ) ) ) ) ) ).
tt(t24_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v13_waybel_0 B A) <=> (r1_tarski (k4_waybel_0 A B) B)) ) ) ) ) ).
tt(t24_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ((v22_waybel_0 (k6_waybel10 A B) A A) <=> (v4_waybel_0 B A)) ) ) ) ) ).
tt(t24_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  => (r1_waybel11 A B (k4_yellow_6 A B))) ) ) ) ).
tt(t24_waybel12,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel_0 (a_2_1_waybel12 A B) A) & (m1_subset_1 (a_2_1_waybel12 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t24_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A))))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))))))) )  &  ((v17_waybel_0 B A (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) &  ((v22_waybel_0 B A (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) &  ((v2_funct_1 B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (u1_struct_0 (k1_waybel_8 A)))) B C) = (k2_waybel_8 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k5_waybel11 A)) <=> (v3_pre_topc B A)) ) ) ) ) ).
tt(t24_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_waybel15 B A) & (v1_waybel15 C A))  =>  ( (B = C)  |  ((k12_lattice3 A B C) = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ).
tt(t24_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_yellow_0 A C) &  (B = (k2_yellow_0 A C)) )  => (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(t24_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_3_waybel17 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ((m3_yellow_9 E A B) =>  (! [F:$i] :  ((m3_yellow_9 F C D) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 E) (u1_struct_0 F)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) )  =>  ( ( (I = G)  &  ( (I = H)  &  ((v5_pre_topc G A C) & (v5_pre_topc H B D)) ) )  => (v5_pre_topc I E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) =>  ((v2_funct_2 C (u1_struct_0 B)) <=> (v2_funct_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel_0 D A) => (v2_waybel_0 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k10_yellow_6 A C)) (k10_yellow_6 B (k6_waybel_9 A B D C)))) ) ) ) ) ) ) ) ) ).
tt(t24_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  ((r1_yellow_0 A (k7_domain_1 B C D)) =>  ((r1_yellow_0 (k5_yellow_0 A B) (k7_domain_1 B C D)) &  ((k1_yellow_0 (k5_yellow_0 A B) (k7_domain_1 B C D)) = (k1_yellow_0 A (k7_domain_1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (E = (k2_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) (k7_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) C D)))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E F) = (k2_yellow_0 B (k7_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_funct_1 (u1_waybel_0 (k1_waybel25 B) (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C E)) D) = (k1_funct_1 (k2_yellow_6 (u1_struct_0 C) (k3_waybel24 A (k1_waybel25 B)) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C) D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) ) )  =>  ( (~ (v7_pre_topc A))  => (r1_waybel18 k9_waybel18 A)) ) ) ).
tt(t24_waybel27,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((k2_waybel27 A B) = (k2_waybel17 A B)) ) ) ) ) ).
tt(t24_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k4_waybel17 A B) (k6_yellow_6 A))) ) ) ) ).
tt(t24_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v4_waybel11 C) &  ((v3_waybel_3 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_waybel_9 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D (k3_waybel24 A C)))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)))))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D)))))) )  &  ((v1_waybel27 E) &  ((v2_funct_1 E) &  ((v2_funct_2 E (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) &  ((v2_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 (k3_waybel24 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v4_waybel11 C) &  ((v3_waybel_3 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_waybel_9 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D (k3_waybel24 A C)))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 B D)) (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)))))) )  &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_waybel24 (k2_borsuk_1 B A) C)) (u1_struct_0 (k3_waybel24 B D)))))) )  &  ((v1_waybel27 E) &  ((v23_waybel_0 E (k3_waybel24 B D) (k3_waybel24 (k2_borsuk_1 B A) C)) &  ((v2_waybel27 F) & (v23_waybel_0 F (k3_waybel24 (k2_borsuk_1 B A) C) (k3_waybel24 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (! [D:$i] : (r1_yellow_0 A (k7_relset_1 B (u1_struct_0 A) C D)))  => (r1_tarski (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A (k2_waybel_2 A B C))) (k11_waybel_0 A (k2_relset_1 (u1_struct_0 A) C)))) ) ) ) ) ) ).
tt(t24_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k1_waybel30 A B) (k1_waybel30 A C))) ) ) ) ) ) ) ).
tt(t24_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  ((k1_waybel31 A) = (k2_waybel23 B)) ) ) ) ) ).
tt(t24_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((k1_waybel_2 A (k2_waybel32 A B)) = (k1_waybel11 A B)) ) ) ) ) ).
tt(t24_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r1_tarski (k2_waybel19 A) (k4_waybel28 A))) ) ).
tt(t24_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_waybel34 C A B) <=> (v1_t_0topsp (k8_waybel18 A B C) A (k7_waybel18 A B C))) ) ) ) ) ) ) ).
tt(t24_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel35 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v3_waybel35 C A B) & (m1_waybel35 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k6_waybel35 A B C)) =>  (D = (k1_yellow_0 A (a_4_0_waybel35 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k1_waybel_3 A B)))  & (v1_waybel_0 (k1_waybel_3 A B) A)) ) )  =>  ((v2_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A B C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A D B) &  (~ (r3_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k6_waybel_0 A (k4_yellow_0 A)) = (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))) ) ) ).
tt(t24_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_waybel_5 A) & (l1_orders_2 A)) ) ) ) ) )  => (v3_waybel_3 A)) ) ).
tt(t24_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) => (v2_waybel_6 B A)) ) ) ) ) ).
tt(t24_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r2_hidden C B))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v1_waybel_7 D A) &  ((r1_tarski B D) &  (~ (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) =>  ((v3_orders_2 (k1_yellow_2 A A B)) &  ((v4_orders_2 (k1_yellow_2 A A B)) &  ((v5_orders_2 (k1_yellow_2 A A B)) &  ((v1_lattice3 (k1_yellow_2 A A B)) &  ((v2_lattice3 (k1_yellow_2 A A B)) &  ((v2_waybel_8 (k1_yellow_2 A A B)) & (l1_orders_2 (k1_yellow_2 A A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r2_hidden B (k10_yellow_6 A C)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A C)))  => (r2_hidden B (k2_pre_topc A D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (u1_struct_0 (k5_weddwitt A B))) <=>  ((k6_algstr_0 A C B) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ) ).
tt(t24_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  | (v5_pre_topc (k5_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ) ) ).
tt(t24_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v1_wellord1 B) => (v1_wellord1 (k2_wellord1 B A))) ) ) ) ).
tt(t24_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (? [C:$i] :  ((v1_rat_1 C) &  (A = (k1_newton C B)) ) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k1_newton C B)) ) ) ) ) ) ) ) ) ) ).
tt(t24_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_xboole_0 A (k3_xboole_0 B C)) = (k3_xboole_0 (k2_xboole_0 A B) (k2_xboole_0 A C))) ) ) ) ).
tt(t24_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k7_xboolean A B)) = (k4_xboolean (k4_xboolean (k3_xboolean A) (k3_xboolean B)) (k5_xboolean (k3_xboolean A) B))) ) ) ) ) ).
tt(t24_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k6_xcmplx_0 A B) = (k6_xcmplx_0 C D))  =>  ((k6_xcmplx_0 A C) = (k6_xcmplx_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t24_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) <=> (r1_xxreal_0 (k4_xcmplx_0 B) (k4_xcmplx_0 A))) ) ) ) ) ).
tt(t24_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k9_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))) ) ).
tt(t24_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) &  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 D B) & (r1_xxreal_0 D C))  => (r1_xxreal_0 D A)) ) ) ) )  =>  (A = (k3_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t24_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k2_xxreal_1 A B) (k1_xxreal_1 A B))) ) ) ) ).
tt(t24_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (m1_xxreal_2 A (k4_xxreal_1 B A))) ) ) ) ).
tt(t24_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((v1_xreal_0 A) =>  (B = (k3_xxreal_3 (k1_xxreal_3 B A) A)) ) ) ) ) ) ).
tt(t24_yellow_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k13_lattice3 A B C))  <=> (r1_orders_2 A C B)) ) ) ) ) ) ) ).
tt(t24_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ( ((k4_yellow_3 A B (k4_yellow_4 (k3_yellow_3 A B) C D)) = (k4_yellow_4 A (k4_yellow_3 A B C) (k4_yellow_3 A B D)))  &  ((k5_yellow_3 A B (k4_yellow_4 (k3_yellow_3 A B) C D)) = (k4_yellow_4 B (k5_yellow_3 A B C) (k5_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ((r2_yellow_0 A (k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k4_waybel_2 A) B)) => (r3_waybel_0 (k3_yellow_3 A A) A (k4_waybel_2 A) B)) ) ) ) ) ).
tt(t24_yellow13,ax, (! [A:$i] :  ((l1_pre_topc A) => (m2_yellow13 (k9_setfam_1 (u1_struct_0 A)) A)) ) ).
tt(t24_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  &  ( (E = F)  &  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (r1_yellow_8 A E C)) ) )  => (r1_yellow_8 B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v6_waybel23 (k2_struct_0 A) A) & (v7_waybel23 (k2_struct_0 A) A)) ) ) ).
tt(t24_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r4_yellow16 B A) => (v3_lattice3 B)) ) ) ) ) ).
tt(t24_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  ( ((r2_yellow18 A B) & (r2_yellow18 C D))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  ((r1_functor3 B C E F) => (r1_functor3 A D (k2_functor3 A B D (k2_yellow18 A B) (k3_functor3 B C D F (k2_yellow18 C D))) (k2_functor3 A B D (k2_yellow18 A B) (k3_functor3 B C D E (k2_yellow18 C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v3_yellow_6 C A) & (l1_waybel_0 C A)) ) ) )  =>  ((r1_waybel_0 A C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k10_yellow_6 A C)) => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_yellow_0 (k2_yellow_1 (u1_pre_topc A))) = (u1_struct_0 A)) ) ) ).
tt(t24_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  ((r1_yellow20 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_yellow20 A B))) =>  ( ( (E = C)  &  ( (E = D)  &  ((k8_altcat_1 A C) = (k8_altcat_1 B D)) ) )  => (r2_hidden (k8_altcat_1 A C) (k1_altcat_1 (k2_yellow20 A B) E E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] : (r1_yellow_0 A B))  => (v3_lattice3 A)) ) ) ).
tt(t24_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((v2_waybel_0 (k4_yellow_3 A B C) A) & (v2_waybel_0 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ).
tt(t24_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_yellow_0 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B)) & (r2_yellow_0 A B))  => (r3_orders_2 A (k13_lattice3 A C (k2_yellow_0 A B)) (k2_yellow_0 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B)))) ) ) ) ) ) ) ).
tt(t24_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_yellow_5 A B C) & (r1_orders_2 A C D))  => (r2_yellow_5 A B D)) ) ) ) ) ) ) ) ) ).
tt(t24_yellow_6,ax, (! [A:$i] :  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m3_yellow_6 C A B) <=>  (! [D:$i] :  ((r2_hidden D A) =>  ( (~ (v2_struct_0 (k1_funct_1 C D)))  &  ((v4_orders_2 (k1_funct_1 C D)) &  ((v7_waybel_0 (k1_funct_1 C D)) & (l1_waybel_0 (k1_funct_1 C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t24_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_lattice3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lattice3 A))) =>  ((k13_lattice3 A (k9_lattice3 A B) (k9_lattice3 A C)) = (k12_lattice3 (k7_lattice3 A) B C)) ) ) ) ) ) ) ).
tt(t24_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_yellow_8 A) & (l1_pre_topc A)) ) )  => (v6_pre_topc A)) ) ).
tt(t24_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 (k1_cantor_1 (u1_struct_0 A) B) A) &  ((v2_cantor_1 (k1_cantor_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k1_cantor_1 (u1_struct_0 A) B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t24_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_relat_1 (k2_tarski (k4_tarski A B) (k4_tarski B B)) (k1_tarski (k4_tarski B C))) = (k2_tarski (k4_tarski A C) (k4_tarski B C))) ) ) ) ).
tt(t24_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_zf_lang A) =>  ((k22_zf_lang A) = (k20_zf_lang (k22_zf_lang (k20_zf_lang A)))) ) ) ) ).
tt(t24_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 A 1) = k6_numbers)  => (v2_zf_lang A)) ) ) ).
tt(t24_zfmisc_1,ax, (! [A:$i] :  ((k1_zfmisc_1 (k1_tarski A)) = (k2_tarski k1_xboole_0 (k1_tarski A))) ) ).
tt(t24_zfmodel2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_zfmodel1 (k6_partfun1 A) A)) ) ).
tt(t24_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r2_ordinal2 A (k1_ordinal1 B)) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  (A = (k1_ordinal1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t24_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_struct_0 C B) => (r1_struct_0 A B)) ) ) ) ) ) ).
tt(t250_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 B C) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t251_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_xxreal_1 B C) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t252_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 B C) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ) ).
tt(t253_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_xxreal_1 C A) (k1_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t254_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 C A) (k1_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t255_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 C A) (k1_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t256_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 C A) (k1_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t257_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 C A) (k2_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t258_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 C A) (k3_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t259_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k3_xxreal_1 C A) (k3_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t25_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_abcmiz_0 A)) =>  ( ((r1_abcmiz_0 A B C) & (r1_abcmiz_0 A (k5_abcmiz_0 A B C) D))  =>  ((r1_abcmiz_0 A B D) &  ((r1_abcmiz_0 A (k5_abcmiz_0 A B D) C) &  ((k5_abcmiz_0 A (k5_abcmiz_0 A B D) C) = (k5_abcmiz_0 A (k5_abcmiz_0 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_abcmiz_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden (k4_tarski k1_xboole_0 A) k2_abcmiz_1)) ) ).
tt(t25_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  ((v7_abcmiz_1 B A) <=>  ((k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) = k10_abcmiz_1) ) ) ) ) ) ).
tt(t25_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_absvalue (k13_complex1 A B)) = (k13_complex1 (k1_absvalue A) (k1_absvalue B))) ) ) ) ) ).
tt(t25_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 E A) &  ((r2_hidden B E) &  ((r2_hidden C E) & (r1_aff_1 A B C D)) ) )  =>  ( (B = C)  | (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 E A) &  ((v1_aff_4 F A) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ((r2_hidden D E) &  ((r2_hidden B F) &  ((r2_hidden C F) & (r2_hidden D F)) ) ) ) ) ) )  =>  ((r1_aff_1 A B C D) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k1_ordinal4 B A)))) ) ) ) ).
tt(t25_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_afinsq_2 B C) => (r1_afinsq_2 (k3_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(t25_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k14_afproj A))) => (m1_subset_1 (k4_tarski B 2) (u2_incsp_1 (k13_afproj A)))) ) ) ) ).
tt(t25_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_afvect0 A B C D) & (r2_afvect0 A E C F))  => (r2_analoaf A B E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) => (m1_algspec1 (k2_funct_1 A) A)) ) ) ).
tt(t25_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k12_algstr_4 A)) => (r2_hidden B (k2_zfmisc_1 (k11_algstr_4 A (k2_xtuple_0 B)) (k1_tarski (k2_xtuple_0 B))))) ) ) ) ).
tt(t25_altcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_altcat_1 A))) =>  ((k4_altcat_1 (u1_struct_0 (k9_altcat_1 A)) (u1_altcat_1 (k9_altcat_1 A)) (u2_altcat_1 (k9_altcat_1 A)) B B B) = (k17_funcop_1 (k4_relat_1 B) (k4_relat_1 B) (k4_relat_1 B))) ) ) ) ) ).
tt(t25_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( ((u1_struct_0 B) = (u1_struct_0 A))  &  ((u1_altcat_1 B) = (u1_altcat_1 A)) )  =>  ((g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B)) = (g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A))) ) ) ) ) ) ).
tt(t25_altcat_3,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v6_altcat_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((r2_hidden D (k1_altcat_1 A B C)) &  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  ((r2_hidden E (k1_altcat_1 A B C)) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_altcat_3 A D E) => (r2_altcat_3 B (k3_functor0 A B C E) (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  ((v2_extpro_1 A 2 k1_ami_3) =>  (A = (k2_compos_1 k1_ami_3)) ) ) ) ).
tt(t25_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ( ((k5_memstr_0 2 k1_ami_3 A) = (k5_memstr_0 2 k1_ami_3 B))  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t25_ami_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k9_ami_3 B A) C) = (k9_ami_3 (k2_xcmplx_0 B C) A)) ) ) ) ) ) ) ).
tt(t25_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (v5_ami_wstd (k16_funcop_1 (k1_ami_wstd A B k6_numbers) C) A B)) ) ) ) ) ) ).
tt(t25_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) => (r4_analmetr (k2_analmetr A B C) D E F F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) &  ( ((r2_analoaf A B C C B) =>  (B = C) )  &  ( ( ((r2_analoaf A B C F G) & (r2_analoaf A B C H I))  =>  ( (B = C)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C D E) => (r2_analoaf A C B E D))  &  ( ((r2_analoaf A B C C D) => (r2_analoaf A B C B D))  &  (~  ((r2_analoaf A B C B D) &  ( (~ (r2_analoaf A B C C D))  &  (~ (r2_analoaf A B D D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~ (r2_analoaf A B C D E))  &  (~ (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = D) )  &  ((r2_analoaf A D B B E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) ) ) ) ) ).
tt(t25_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_analort A D E B C (k2_analort A D E B) (k2_analort A D E C))) ) ) ) ) ) ) ) ) ) ).
tt(t25_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  ( (~ (v9_struct_0 D A))  &  (~  ((r2_hidden (k3_xtuple_0 (k2_anproj_1 A B) (k2_anproj_1 A C) (k2_anproj_1 A D)) (u1_collsp (k5_anproj_1 A))) <=> (r2_anproj_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  => (v3_anproj_2 (k5_anproj_1 A))) ) ) ).
tt(t25_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_unialg_2 C A) & (r1_tarski B C))  => (r1_tarski (k3_tarski (a_2_1_aofa_000 A B)) C)) ) ) ) ) ) ) ).
tt(t25_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k51_aofa_i00 A B D E F G)) F) = G)  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k51_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) (k8_armstrng A B) B)) ) ) ).
tt(t25_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_arytm_0 (k1_arytm_0 A B)) = (k1_arytm_0 (k3_arytm_0 A) (k3_arytm_0 B))) ) ) ) ) ).
tt(t25_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 C B))  =>  ((k2_arytm_1 (k1_arytm_1 B C) A) = (k2_arytm_1 (k1_arytm_1 B A) C)) ) ) ) ) ) ) ) ).
tt(t25_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (~  ( (~  (A = k1_xboole_0) )  &  ((k4_arytm_3 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t25_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v3_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v3_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden B (k7_asympt_0 A)) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k8_real_1 C (k1_seq_1 A D)) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B (k1_asympt_1 (k7_real_1 1 A) 1 k6_numbers)) &  ((r1_tarski (k6_asympt_0 (k3_asympt_1 8)) (k6_asympt_0 B)) &  (~  ((k6_asympt_0 (k3_asympt_1 8)) = (k6_asympt_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_autalg_1 C (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) => (r2_hidden (k4_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C) (k5_autalg_1 A B))) ) ) ) ) ) ).
tt(t25_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A B) (k6_autgroup A (k2_group_1 A B))) (k6_autgroup A (k1_group_1 A)))) ) ) ) ).
tt(t25_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_wellord1 (k4_bagorder A))) ) ).
tt(t25_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 (k2_bcialg_1 A B) A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D)))) = (k1_bcialg_1 A (k2_bcialg_1 A C) (k2_bcialg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t25_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A C D) B) => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D (k1_bcialg_1 A D C))) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  ((k6_bcialg_4 A (k4_struct_0 A) 2) = (k4_struct_0 A)) ) ) ).
tt(t25_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (A = (k2_bcialg_5 A B C D))  =>  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 A C) & (r1_xxreal_0 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_6 B A) => (v1_bcialg_6 (k2_bcialg_1 A (k2_bcialg_1 A B)) A)) ) ) ) ) ).
tt(t25_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((k4_bcialg_1 A) = (u1_struct_0 A)) ) ) ).
tt(t25_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) =>  ((k2_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A B C)) = (k7_real_1 (k2_bhsp_1 A B B) (k2_bhsp_1 A C C))) ) ) ) ) ) ) ) ).
tt(t25_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k2_normsp_1 A D E))) &  ((k2_seq_2 (k2_bhsp_2 A (k2_normsp_1 A D E))) = (k3_bhsp_1 A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_bhsp_3 B A) & (r2_bhsp_3 A B C))  => (v2_bhsp_3 C A)) ) ) ) ) ) ) ).
tt(t25_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_bhsp_4 B A) & (v2_bhsp_4 C A))  => (v2_bhsp_4 (k6_bhsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t25_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_bilinear A B C (k9_bilinear A B C D E) F) (k6_hahnban1 A B (k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) E F) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_binari_3 A k6_numbers) = (k5_euclid A)) ) ) ).
tt(t25_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A (k5_series_1 2 B)))  & (r1_xxreal_0 (k1_binari_4 B A) B)) ) ) ) ) ) ).
tt(t25_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v1_algstr_1 A) &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binom A (k3_rlvect_1 A B C) D) = (k4_rlvect_1 A (k8_binom A B C D))) ) ) ) ) ) ) ) ) ).
tt(t25_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_lattices A (k7_lattices A B) (k7_lattices A (k4_lattices A B C)))) ) ) ) ) ) ).
tt(t25_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v2_compts_1 D B) =>  (! [E:$i] :  ((m2_connsp_2 E (k2_borsuk_1 B A) (k3_borsuk_1 B A D (k6_domain_1 (u1_struct_0 A) C))) =>  (? [F:$i] :  ((m2_connsp_2 F B D) &  (? [G:$i] :  ((m1_connsp_2 G A C) & (r1_tarski (k6_borsuk_1 B A D C F G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = A)  =>  ((v4_xxreal_2 B) & (v3_xxreal_2 B)) ) ) ) ) ) ).
tt(t25_borsuk_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v1_rat_1 A)) )  =>  (~ (v1_rat_1 (k4_int_1 A))) ) ) ).
tt(t25_borsuk_6,ax, ( (~ (v1_xboole_0 a_0_13_borsuk_6))  &  ((v4_pre_topc a_0_13_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr)) & (m1_subset_1 a_0_13_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))) ) ).
tt(t25_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  (A = B) )  =>  ((k1_borsuk_7 A B A C D E) = (k4_funct_4 A B E D)) ) ) ) ) ) ) ).
tt(t25_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_bspace A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_bspace A))) =>  ((k4_vectsp_1 k2_bspace (k7_bspace A) B (k1_algstr_0 (k7_bspace A) C D)) = (k1_algstr_0 (k7_bspace A) (k4_vectsp_1 k2_bspace (k7_bspace A) B C) (k4_vectsp_1 k2_bspace (k7_bspace A) B D))) ) ) ) ) ) ) ) ).
tt(t25_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)) (k9_bvfunc_1 A C (k5_bvfunc_1 A D B))))) ) ) ) ) ) ) ) ).
tt(t25_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t25_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  ( (B = (k3_enumset1 C D E F G))  =>  ( (C = G)  |  ( (D = G)  |  ( (E = G)  |  ( (F = G)  |  ((k5_bvfunc_2 A G B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v3_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  =>  ((r2_funct_2 A k6_margrel1 (k13_bvfunc_1 A (k5_bvfunc_1 A C B)) (k5_bvfunc_1 A C (k13_bvfunc_1 A B))) &  ((r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A (k2_bvfunc_1 A C B)) (k2_bvfunc_1 A C (k14_bvfunc_1 A B))) & (r2_funct_2 A k6_margrel1 (k14_bvfunc_1 A (k2_bvfunc_1 A B C)) (k2_bvfunc_1 A (k14_bvfunc_1 A B) C))) ) ) ) ) ) ) ) ).
tt(t25_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D B)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t25_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k9_bvfunc_1 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t25_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k2_bvfunc_1 A C D) B E) (k2_bvfunc_1 A C (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)) (k9_bvfunc_1 A (k6_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k6_bvfunc_2 A B D E) C) (k7_bvfunc_2 A (k9_bvfunc_1 A B C) D E))) ) ) ) ) ) ) ) ) ) ).
tt(t25_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k12_bvfunc_1 A) (k9_bvfunc_1 A (k12_bvfunc_1 A) B)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t25_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A B) C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A C) B) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t25_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k10_bvfunc_1 A (k9_bvfunc_1 A B C) C))) ) ) ) ) ) ).
tt(t25_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k10_bvfunc_1 A (k10_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A C B)) B))) ) ) ) ) ) ).
tt(t25_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k9_bvfunc_1 A D G)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A E B) (k9_bvfunc_1 A F C)) (k9_bvfunc_1 A G D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_funcop_1 k5_numbers A k6_numbers) = (k4_struct_0 (k11_c0sp1 A))) ) ) ).
tt(t25_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r1_tarski (k13_pre_poly (k20_valued_1 (u1_struct_0 A) k1_numbers k1_numbers B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ) ).
tt(t25_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ( ((k2_calcul_1 A D) = (k11_cqc_lang A C B))  & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) (k2_calcul_1 A D)))  =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) D) (k4_substut2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B)))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t25_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_zfmisc_1 A) B) =>  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) &  (~ (r2_wellord2 A B)) ) ) ) ) ).
tt(t25_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k3_card_2 A k6_numbers) = 1) ) ) ).
tt(t25_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((k3_card_3 (k2_card_3 (k7_funcop_1 A B))) = (k2_zfmisc_1 B A)) ) ) ).
tt(t25_card_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( ((k1_card_5 k6_numbers) = k6_numbers)  &  ((k1_card_5 (k5_card_1 (k2_nat_1 A 1))) = 1) ) ) ) ).
tt(t25_card_fil,ax,(v4_card_fil k4_ordinal1)).
tt(t25_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k2_card_fin B C A) = (k3_tarski (k10_xtuple_0 B)))  =>  ((v1_xboole_0 (k3_tarski (k10_xtuple_0 B))) |  ((k5_relat_1 B (k8_relat_1 C (k1_tarski A))) = (k7_funcop_1 (k8_relat_1 C (k1_tarski A)) (k3_tarski (k10_xtuple_0 B)))) ) ) ) ) ) ) ) ).
tt(t25_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( ((r2_hidden k4_ordinal1 (k1_card_5 A)) & (v1_card_lar B A))  => (v1_card_lar (k2_card_lar A B) A)) ) ) ) ) ).
tt(t25_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  (! [G:$i] :  ((m1_cat_1 G A C D) =>  (! [H:$i] :  ((m1_cat_1 H A D E) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  (~  ((k5_cat_1 A B C E F (k5_cat_1 A C D E G H)) = (k5_cat_1 A B D E (k5_cat_1 A B C D F G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_cat_2 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k9_cat_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v2_cat_3 E A B C) & (v2_cat_3 F A C D))  => (v2_cat_3 (k5_cat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  (! [G:$i] :  ((m1_cat_1 G A B D) =>  (! [H:$i] :  ((m1_cat_1 H A E B) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A E B) = k1_xboole_0) )  &  (~  ((k9_cat_4 A C D E (k5_cat_1 A E B C H F) (k5_cat_1 A E B D H G)) = (k5_cat_1 A E B (k2_cat_4 A C D) H (k9_cat_4 A C D B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_cat_1 A B C) = (k9_subset_1 (u4_struct_0 A) (k10_cat_5 A B) (k9_cat_5 A C))) ) ) ) ) ) ) ).
tt(t25_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_tarski (k2_relset_1 k5_numbers A) (k2_tarski k6_numbers B)) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k1_afinsq_1 A) = (k1_afinsq_1 C))  &  ((r1_tarski (k2_relset_1 k5_numbers C) (k2_tarski k6_numbers B)) &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D (k1_afinsq_1 A)) =>  ((k8_complex1 (k7_afinsq_2 (k5_relat_1 A D)) (k7_afinsq_2 (k5_relat_1 C D))) = (k24_binop_2 B D)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_afinsq_1 A)) =>  ((k1_recdef_1 C D) = (k21_binop_2 B (k1_recdef_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k8_catalg_1 (u1_struct_0 A) B) (k13_catalg_1 A)) = (k2_cat_1 A B B)) ) ) ) ) ).
tt(t25_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_cc0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( ((k1_normsp_0 (k7_cc0sp1 A) C) = k6_numbers)  =>  (C = (k4_struct_0 (k7_cc0sp1 A))) )  &  ( ( (C = (k4_struct_0 (k7_cc0sp1 A)))  =>  ((k1_normsp_0 (k7_cc0sp1 A) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k7_cc0sp1 A) (k1_clvect_1 (k7_cc0sp1 A) C B)) = (k11_binop_2 (k17_complex1 B) (k1_normsp_0 (k7_cc0sp1 A) C)))  & (r1_xxreal_0 (k1_normsp_0 (k7_cc0sp1 A) (k1_algstr_0 (k7_cc0sp1 A) C D)) (k9_binop_2 (k1_normsp_0 (k7_cc0sp1 A) C) (k1_normsp_0 (k7_cc0sp1 A) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  ((k1_normsp_0 (k5_cc0sp2 A) (k4_struct_0 (k5_cc0sp2 A))) = k6_numbers) ) ) ).
tt(t25_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~  ((k3_comseq_2 A) = k6_numbers) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((m2_valued_0 B k2_numbers A) & (v2_relat_1 B)) ) ) ) ) ) ) ) ) ).
tt(t25_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r1_cfdiff_1 B C) =>  ((r1_cfdiff_1 (k25_valued_1 k2_numbers k2_numbers B A) C) &  ((k2_cfdiff_1 (k25_valued_1 k2_numbers k2_numbers B A) C) = (k9_complex1 A (k2_cfdiff_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t25_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_cfuncdom A)))  &  ((v13_algstr_0 (k7_cfuncdom A)) &  ((v2_rlvect_1 (k7_cfuncdom A)) &  ((v3_rlvect_1 (k7_cfuncdom A)) &  ((v4_rlvect_1 (k7_cfuncdom A)) &  ((v3_group_1 (k7_cfuncdom A)) &  ((v5_group_1 (k7_cfuncdom A)) &  ((v4_vectsp_1 (k7_cfuncdom A)) &  ((v5_vectsp_1 (k7_cfuncdom A)) & (l6_algstr_0 (k7_cfuncdom A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers B (k2_valued_1 A k2_numbers k2_numbers C D)) (k46_valued_1 A k2_numbers k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) D))) ) ) ) ) ) ) ) ).
tt(t25_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v3_cgames_1 A) & (v4_cgames_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ((v1_relat_1 (k16_finseq_1 B A)) &  ((v1_funct_1 (k16_finseq_1 B A)) &  ( (~ (v1_xboole_0 (k16_finseq_1 B A)))  &  ((v1_finseq_1 (k16_finseq_1 B A)) &  ((v3_cgames_1 (k16_finseq_1 B A)) & (v4_cgames_1 (k16_finseq_1 B A))) ) ) ) ) ) ) ) ) ).
tt(t25_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( (~  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) )  =>  ((r2_hidden D (k3_chain_1 A C B)) <=>  (? [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) &  ( (~ (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E)))  &  ((r1_xxreal_0 (k1_seq_1 D E) (k1_seq_1 B E)) | (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  (~  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B C) = (k1_funct_1 B D))  &  ( (~  (C = D) )  &  ( (~  ( (C = 1)  &  (D = (k3_finseq_1 B)) ) )  &  (~  ( (C = (k3_finseq_1 B))  &  (D = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_circcmb3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  => (m1_circcmb3 (k5_circcomb C D) B)) ) ) ) ) ) ) ) ).
tt(t25_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 A C))) =>  (! [E:$i] :  ( ((v4_msualg_1 E B) & (l3_msualg_1 E B))  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 B E))) =>  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B E)) => (r2_hidden (k1_funct_4 D F) (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_rlvect_2 D A (k7_domain_1 (u1_struct_0 A) B C)) =>  ((v1_circled1 D A) =>  ( (B = C)  |  ( ((k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers D B) (k3_funct_2 (u1_struct_0 A) k1_numbers D C)) = 1)  &  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) &  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers D C)) &  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (r1_circtrm1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)))) ) ).
tt(t25_classes1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A (k1_classes1 B)) & (r2_tarski A (k1_classes1 B))) ) ) ) ).
tt(t25_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A (k2_ordinal1 B)))  =>  ((r2_hidden (k1_card_1 (k4_classes1 A)) (k1_card_1 B)) & (r2_hidden (k4_classes1 A) B)) ) ) ) ) ).
tt(t25_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k9_clopban1 A B)) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(t25_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) D) (k1_normsp_1 A (k1_bhsp_4 A B) C))) (k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 (k4_normsp_0 A B)) D) (k1_seq_1 (k3_series_1 (k4_normsp_0 A B)) C))))) ) ) ) ) ) ) ) ) ).
tt(t25_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k5_algstr_0 A (k6_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A C)) B) (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A D)) B)) (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A (k3_rlvect_1 A C D))) B)) = (k1_normsp_1 A (k1_bhsp_4 A (k5_clopban4 A C D B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_closure1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m2_pboole E B (k5_mssubfam B C) (k5_mssubfam B C)) =>  ( ((v2_closure1 E B C) &  ((r2_hidden A B) &  (D = (k1_funct_1 E A)) ) )  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) =>  ((r1_tarski F G) => (r1_tarski (k1_funct_1 D F) (k1_funct_1 D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k5_closure2 A B (k2_closure2 A B)) (k5_mssubfam A B))) ) ) ).
tt(t25_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_clvect_1 B A) &  ((v6_clvect_1 C A) &  (D = (a_3_0_clvect_1 A B C)) ) )  => (v6_clvect_1 D A)) ) ) ) ) ) ) ) ) ).
tt(t25_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k16_csspace A D E))) &  ((k2_seq_2 (k2_clvect_2 A (k16_csspace A D E))) = (k13_csspace A (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_clvect_3 B A) & (v2_clvect_3 C A))  => (v2_clvect_3 (k16_csspace A B C) A)) ) ) ) ) ) ) ).
tt(t25_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v6_cohsp_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden C (k9_xtuple_0 A)) &  ((r1_tarski B C) & (v1_finset_1 C)) )  =>  (! [D:$i] :  ((r2_hidden (k4_tarski B D) (k5_cohsp_1 A)) => (r2_hidden (k4_tarski C D) (k5_cohsp_1 A))) ) ) ) ) ) ) ).
tt(t25_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_coh_sp A)) =>  ( ((k9_coh_sp A (k8_coh_sp A (k6_coh_sp A B)) B) = B)  &  ((k9_coh_sp A B (k8_coh_sp A (k7_coh_sp A B))) = B) ) ) ) ) ).
tt(t25_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((k1_card_1 B) = (k2_nat_1 A 1))  =>  ((r1_xxreal_0 A 1) |  (! [C:$i] :  ((l1_combgras C (k1_combgras A B) (k1_combgras A B)) =>  (~  ((v7_combgras C (k1_combgras A B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (~  ((g1_combgras (k1_combgras A B) (k1_combgras A B) (u1_combgras (k1_combgras A B) (k1_combgras A B) C) (u2_combgras (k1_combgras A B) (k1_combgras A B) C)) = (k8_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k4_complex1 A) = k6_numbers)  &  ((k4_complex1 B) = k6_numbers) )  =>  ( ((k3_complex1 B) = k6_numbers)  |  ( ((k3_complex1 (k13_complex1 A B)) = (k13_complex1 (k3_complex1 A) (k3_complex1 B)))  &  ((k4_complex1 (k13_complex1 A B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t25_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( (~  (A = k6_numbers) )  =>  ( ((k21_sin_cos (k1_comptrig (k10_complex1 A))) = (k1_real_1 (k21_sin_cos (k1_comptrig A))))  &  ((k18_sin_cos (k1_comptrig (k10_complex1 A))) = (k1_real_1 (k18_sin_cos (k1_comptrig A)))) ) ) ) ) ).
tt(t25_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k3_vectsp_1 k1_complfld (k4_struct_0 k1_complfld) A) = (k4_struct_0 k1_complfld)) ) ) ) ).
tt(t25_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k9_matrix_5 (k45_valued_1 B C) A) = (k4_binop_2 (k9_matrix_5 B A) (k9_matrix_5 C A))) ) ) ) ) ) ) ) ).
tt(t25_compl_sp,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (~  ( (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k8_nat_1 A C D) (k8_nat_1 (k9_setfam_1 A) B D))) )  &  ((v1_finset_1 (k2_relset_1 A C)) & (v1_xboole_0 (k2_kurato_0 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t25_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  ((k5_compos_1 B (k4_compos_1 B) A) = (k4_compos_1 B)) ) ) ) ) ).
tt(t25_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((r2_compos_2 B C) =>  (! [D:$i] :  ((r1_tarski C D) => (r1_compos_2 B D)) ) ) ) ) ) ) ) ) ).
tt(t25_comptrig,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos)))).
tt(t25_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_margrel1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k1_relset_1 (k3_finseq_2 A) B) = (k4_finseq_2 C A))  =>  ((k19_margrel1 B) = C) ) ) ) ) ) ) ) ).
tt(t25_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers A B) C))) ) ) ) ) ) ).
tt(t25_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A B) = k5_complex1) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)) B) = k6_numbers) ) ) ) ) ) ).
tt(t25_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ( ( ((u2_conlat_1 A B) = k1_xboole_0)  =>  (B = (k6_conlat_1 A)) )  &  ( ((u3_conlat_1 A B) = k1_xboole_0)  =>  (B = (k5_conlat_1 A)) ) ) ) ) ) ) ).
tt(t25_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_connsp_1 C A)) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = (k1_struct_0 A)) )  &  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D B) &  ( (~  (D = C) )  & (r1_connsp_1 A C D)) ) ) ) ) ) ) ) ) )  | (v2_connsp_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ) ).
tt(t25_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v4_pre_topc (k1_connsp_2 A B) A)) ) ) ) ).
tt(t25_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m1_connsp_3 B A) & (m1_connsp_3 C A))  => (m1_connsp_3 (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t25_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_rlvect_2 D A (k7_domain_1 (u1_struct_0 A) B C)) =>  ((v2_convex1 D A) =>  ( (B = C)  |  ( ((k2_xcmplx_0 (k1_funct_1 D B) (k1_funct_1 D C)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 D B)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 D C)) &  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 D B)) (k1_rlvect_1 A C (k1_funct_1 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (r1_convex4 A (k7_convex4 A k5_complex1 B) (k2_convex4 A))) ) ) ) ).
tt(t25_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( (~  (B = C) )  =>  ((k13_cqc_lang A (k15_qc_lang1 A B D) C) = (k15_qc_lang1 A B (k13_cqc_lang A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t25_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k14_cqc_sim1 A (k5_cqc_lang A)) = (k5_cqc_lang A)) ) ) ).
tt(t25_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ((r2_cqc_the1 A B C) => (r1_xxreal_0 1 (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t25_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden E (k24_qc_lang1 A D)) | (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A E B) C) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r4_cqc_the3 A B C) => (r4_cqc_the3 A (k4_subset_1 (k3_cqc_lang A) B D) (k4_subset_1 (k3_cqc_lang A) C D))) ) ) ) ) ) ) ) ) ).
tt(t25_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_csspace4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_csspace4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_csspace4 A B))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) &  ((v1_csspace4 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) &  ((v1_csspace4 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A (u1_struct_0 B)) &  ((v1_csspace4 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) ) )  =>  ( ( (F = C)  &  ( (G = D)  &  (H = E) ) )  =>  ( (E = (k5_algstr_0 (k9_csspace4 A B) C D))  <=>  (! [I:$i] :  ((m1_subset_1 I A) =>  ((k3_funct_2 A (u1_struct_0 B) H I) = (k5_algstr_0 B (k3_funct_2 A (u1_struct_0 B) F I) (k3_funct_2 A (u1_struct_0 B) G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k4_algstr_0 A B) (k4_algstr_0 A C)) = (k12_csspace A B C)) ) ) ) ) ) ) ).
tt(t25_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  ((v7_decomp_1 C A B) & (v10_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t25_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B A) &  ( (~  (B = k6_numbers) )  &  (~  ((r2_hidden B (k2_finseq_1 A)) &  (~  (B = A) ) ) ) ) ) ) ) ) ) ).
tt(t25_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) => (r1_dickson A (k1_subset_1 (u1_struct_0 A)) k1_xboole_0)) ) ).
tt(t25_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) 1) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k10_real_1 A 2)) B) (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k1_real_1 (k10_real_1 A 2))) B))) ) ) ) ) ) ) ).
tt(t25_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k1_fcont_1 A B) C) D) = (k8_real_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t25_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) A B) = (k9_real_1 (k9_diff_1 C A B) (k9_diff_1 D A B))) ) ) ) ) ) ) ) ) ).
tt(t25_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) (k7_real_1 A (k13_complex1 B 2))) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k16_sin_cos) (k9_real_1 A (k13_complex1 B 2))))) ) ) ) ) ) ).
tt(t25_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_waybel_4 A (k4_dilworth A C) B) => (r3_waybel_4 A (k2_struct_0 A) B)) ) ) ) ) ) ) ).
tt(t25_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_diraf A B C D E) &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 C)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 D)) =>  ((k10_mcart_1 A B C D E F G H) = (a_8_0_domain_1 A B C D E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 B))) =>  (~  ( (~  (C = k6_numbers) )  &  ((k2_binom (k9_int_3 B) C A) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t25_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  ( (B = (k6_int_1 2 A))  =>  ((k2_binom (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) C D) 2) = (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) C 2) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B C) D)) (k2_binom (k9_int_3 A) D 2))) ) ) ) ) ) ) ) ) ) ).
tt(t25_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k11_ens_1 A))) => (m1_subset_1 B (k2_ens_1 A))) ) ) ) ).
tt(t25_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k1_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((r1_entropy1 (k8_matrix_1 k1_numbers B C) C) &  ((k1_seq_1 (k8_matrix_1 k1_numbers B C) C) = (k1_seq_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k2_enumset1 A B C D) (k2_enumset1 E F G H))) ) ) ) ) ) ) ) ) ).
tt(t25_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  ((k6_eqrel_1 A A (k6_partfun1 A) B) = (k1_tarski B)) ) ) ) ).
tt(t25_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_pralg_2 D B A) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E B) =>  (? [F:$i] :  ( ((v3_msualg_1 F A) &  ((v4_msualg_1 F A) &  ((v3_msafree2 F A) & (m1_msualg_2 F A C)) ) )  &  (F = (k5_pralg_2 B A D E)) ) ) ) )  &  (! [E:$i] :  ( ((v3_msualg_1 E A) &  ((v4_msualg_1 E A) &  ((v3_msafree2 E A) & (m1_msualg_2 E A C)) ) )  =>  (~  (! [F:$i] :  ((m1_subset_1 F B) => (m1_msualg_2 (k5_pralg_2 B A D F) A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))))) = k1_xboole_0)  &  ((k3_relat_1 (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))) = k1_xboole_0) ) ) ) ).
tt(t25_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D B) (k1_rlvect_1 (k15_euclid A) E C)) F) = (k9_binop_2 (k11_binop_2 B (k23_rvsum_1 D F)) (k11_binop_2 C (k23_rvsum_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k17_complex1 (k2_euclid_3 A)) = (k12_euclid A)) ) ) ).
tt(t25_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k6_euclid A B) (k6_euclid A C)) = (k23_rvsum_1 B C)) ) ) ) ) ) ) ).
tt(t25_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 A A) = (k4_struct_0 (k15_euclid 3))) ) ) ).
tt(t25_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((k4_euclid_3 B D C) = (k4_euclid_3 A D C)) )  =>  ((r1_euclid_6 B C D) |  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ((k6_euclid_7 A B) = (k6_euclid_7 A C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t25_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k9_euclid 3 k2_euclid_8 A) = (k1_euclid_8 A k6_numbers k6_numbers)) ) ) ).
tt(t25_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_funct_2 (k2_finseq_1 A) k1_numbers) = (k4_card_3 (k12_pralg_1 (k2_finseq_1 A) (k7_funcop_1 (k2_finseq_1 A) k3_topmetr)))) ) ) ).
tt(t25_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ((k13_rvsum_1 A (k10_euclid A B)) = (k11_euclid A B)) ) ) ) ) ).
tt(t25_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid E)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid E)) =>  ((k8_euclid E (k7_euclid E (k9_euclid E F A) (k9_euclid E G B)) (k7_euclid E (k9_euclid E F C) (k9_euclid E G D))) = (k7_euclid E (k9_euclid E F (k9_real_1 A C)) (k9_euclid E G (k9_real_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_exchsort A)) ) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden (k1_ordinal1 B) (k9_xtuple_0 A)))  => (r2_xboole_0 (k1_funct_1 A (k1_ordinal1 B)) (k1_funct_1 A B))) ) )  => (v4_exchsort A)) ) ) ).
tt(t25_extpro_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_setfam_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v3_extpro_1 C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 C)) & (v1_funct_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 C)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 B C)) & (v1_partfun1 E (u1_struct_0 C))) ) ) )  =>  ( ((r1_xxreal_0 (k8_extpro_1 B C D E) A) & (r1_extpro_1 B C D E))  =>  ((k5_extpro_1 B C D E A) = (k5_extpro_1 B C D E (k8_extpro_1 B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_extreal1 A B)) =>  ((k3_extreal1 (k3_supinf_2 A B)) = (k3_supinf_2 (k3_extreal1 A) (k3_extreal1 B))) ) ) ) ) ) ).
tt(t25_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v1_circcomb C) &  ((v2_circcomb C) &  ((v3_circcomb C) & (l1_msualg_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D A) &  ((v6_circcomb D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msafree2 E B) &  ((v6_circcomb E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msafree2 F C) &  ((v6_circcomb F C) & (l3_msualg_1 F C)) )  =>  ((k3_circcomb (k2_circcomb A B) C (k3_circcomb A B D E) F) = (k3_circcomb A (k2_circcomb B C) D (k3_circcomb B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( (~  ((k5_facirc_2 A B C) = (k4_tarski D k3_facirc_1)) )  &  (~  ((k5_facirc_2 A B C) = (k4_tarski D k1_facirc_1)) ) ) ) ) ) ) ) ) ) ).
tt(t25_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k7_relset_1 k1_numbers k1_numbers B A))))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A))) ) ) ) ) ) ).
tt(t25_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))  =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))) ) ) ) ) ) ).
tt(t25_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k8_real_1 (k1_seq_1 k16_sin_cos B) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t25_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k1_sin_cos9) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k1_sin_cos9 B)) (k10_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t25_fdiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 B A) => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t25_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden D (k2_rcomp_1 A B)) & (r2_hidden E (k2_rcomp_1 A B)))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 C D) (k1_seq_1 C E))) (k5_square_1 (k9_real_1 D E)))) ) ) ) )  & (r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)))  =>  ((r2_fdiff_1 C (k2_rcomp_1 A B)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B)))) ) ) ) ) ) ) ) ).
tt(t25_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers D (k10_real_1 1 (k9_real_1 A B))))) &  ( (D = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers E F) k3_taylor_1))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G C) =>  ( ((k1_seq_1 E G) = (k9_real_1 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E G) k6_numbers))  &  ( ((k1_seq_1 F G) = (k9_real_1 G B))  &  ( (~ (r1_xxreal_0 (k1_seq_1 F G) k6_numbers))  &  (~  ((k9_real_1 A B) = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers D (k10_real_1 1 (k9_real_1 A B))) C) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G C) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers D (k10_real_1 1 (k9_real_1 A B))) C) G) = (k10_real_1 1 (k8_real_1 (k9_real_1 G A) (k9_real_1 G B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k6_rfunct_1 k1_numbers k1_numbers k3_taylor_1))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k3_taylor_1 B) = k6_numbers) ) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k3_taylor_1) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 B (k5_square_1 (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t25_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) B) A) C) = (k8_real_1 2 (k26_sin_cos (k8_real_1 2 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k10_real_1 D A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)) B) D) = (k7_real_1 (k1_seq_1 k1_sin_cos6 (k10_real_1 D A)) (k10_real_1 D (k8_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 (k10_real_1 D A)))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)) A) B) = (k10_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t25_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) A) B) = (k9_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t25_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ((r1_tarski (k9_xtuple_0 (k16_ff_siec A)) (k2_net_1 A)) &  ((r1_tarski (k10_xtuple_0 (k16_ff_siec A)) (k2_net_1 A)) &  ((r1_tarski (k9_xtuple_0 (k15_ff_siec A)) (k2_net_1 A)) & (r1_tarski (k10_xtuple_0 (k15_ff_siec A)) (k2_net_1 A))) ) ) ) ) ).
tt(t25_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 3)) = (k2_nat_1 (k1_pre_ff (k1_nat_1 A 2)) (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t25_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_1 (k4_nat_1 3 (k1_pre_ff A)) (k1_fib_num3 A)) = (k4_nat_1 2 (k1_pre_ff (k1_nat_1 A 2)))) ) ) ).
tt(t25_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k2_int_1 (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k1_pre_ff A) (k3_xcmplx_0 (k7_square_1 5) (k1_pre_ff A))) 1) 2))) ) ) ) ).
tt(t25_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) => (r1_tarski B (k9_finseq_8 A B C))) ) ) ) ) ) ).
tt(t25_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  & (r2_hidden (k5_lattices A) B))  =>  ( ((k3_filter_0 A B) = (k1_filter_0 A))  &  ((k3_filter_0 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t25_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r2_binop_1 A C E) & (r2_binop_1 B D F))  <=> (r2_binop_1 (k2_zfmisc_1 A B) (k1_domain_1 A B C D) (k6_filter_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v13_lattices A) =>  ( (~ (v1_xboole_0 (k6_domain_1 (u1_struct_0 A) (k5_lattices A))))  &  ((v18_lattices (k6_domain_1 (u1_struct_0 A) (k5_lattices A)) A) &  ((v21_lattices (k6_domain_1 (u1_struct_0 A) (k5_lattices A)) A) & (m1_subset_1 (k6_domain_1 (u1_struct_0 A) (k5_lattices A)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t25_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 (k7_finseq_1 A B))) &  ( (~ (r2_hidden C (k4_finseq_1 A)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  (C = (k2_nat_1 (k3_finseq_1 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) B)))) )  => (m2_finseq_1 C B)) ) ) ) ) ) ).
tt(t25_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) <=>  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t25_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  ((k1_finseq_4 A B) = (k4_finseq_4 A B)) ) ) ) ) ).
tt(t25_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) => (r1_xxreal_0 (k3_finseq_1 (k2_rfinseq B A C)) (k3_finseq_1 C))) ) ) ) ) ) ).
tt(t25_finseq_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_finseq_5 (k3_finseq_5 A)) = A) ) ) ).
tt(t25_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k2_finseq_7 A (k3_finseq_4 A B C D) 1 3) = (k3_finseq_4 A D C B)) ) ) ) ) ) ) ) ) ).
tt(t25_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ( (~ (r1_xxreal_0 (k3_finseq_1 C) k6_numbers))  =>  ((r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 B)) &  ((k3_finseq_6 A B (k7_nat_d (k2_nat_1 (k3_finseq_1 B) 1) (k3_finseq_1 C)) (k3_finseq_1 B)) = C) ) )  => (r4_finseq_8 A B C)) ) ) ) ) ) ) ).
tt(t25_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v2_binop_1 F B) => (r2_funct_2 A B (k1_partfun1 A B B B (k6_funcop_1 B A F D E) (k9_funcop_1 B B F (k6_partfun1 B) C)) (k6_funcop_1 B A F D (k1_partfun1 A B B B E (k9_funcop_1 B B F (k6_partfun1 B) C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k10_fintopo2 A B) (k10_fintopo2 A C))) ) ) ) ) ) ) ).
tt(t25_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k3_fintopo3 A B C) (k3_fintopo3 A B (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t25_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v4_fin_topo (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t25_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k7_flang_1 A B 1) = B) ) ) ) ).
tt(t25_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D E))  =>  ((k1_flang_2 A B C E) = (k4_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B C D) (k1_flang_2 A B (k2_xcmplx_0 D 1) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k6_flang_1 A (k1_flang_2 A B C D) (k1_flang_3 A B E)) = (k6_flang_1 A (k1_flang_3 A B E) (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k1_funct_1 B A))  <=> (r2_hidden A (k8_relat_1 B (k1_tarski C)))) ) ) ) ) ) ).
tt(t25_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v4_fomodel1 E A) & (m1_subset_1 E (k1_fomodel1 A)))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_fomodel2 F A B)) )  =>  ( (~ (r2_hidden E (k10_xtuple_0 C)))  =>  ((k1_funct_1 (k10_fomodel2 A B (k5_fomodel2 F E D)) C) = (k1_funct_1 (k10_fomodel2 A B F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_frechet A B C) <=>  ((v2_frechet B A) &  (C = (k2_frechet2 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_frechet C A) & (r1_tarski (k2_relset_1 (u1_struct_0 A) C) B))  => (r1_tarski (k2_frechet A C) B)) ) )  => (v4_pre_topc B A)) ) )  => (v4_frechet A)) ) ) ).
tt(t25_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k8_fscirc_1 A B C) (k9_fscirc_1 A B C))) ) ) ) ) ) ) ) ).
tt(t25_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k8_fscirc_1 A B C) (k9_fscirc_1 A B C) D 2) (k8_fscirc_1 A B C) (k9_fscirc_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (r6_fsm_1 A B C D E k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t25_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers)))  =>  ( ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = (k7_real_1 B C)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r3_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C) (k7_real_1 B C))) ) ) ) ) ) ) ).
tt(t25_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 C)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C)))))  =>  (! [H:$i] :  ((m1_rewrite1 H (k1_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G)) =>  (~  ( ((k1_funct_1 H 1) = (k4_tarski A (k1_flang_1 C D E)))  &  ( ((k1_funct_1 H (k3_finseq_1 H)) = (k4_tarski B (k1_flang_1 C F E)))  &  (! [I:$i] :  ((m1_rewrite1 I (k1_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G)) =>  (~  ( ((k1_funct_1 I 1) = (k4_tarski A D))  &  ((k1_funct_1 I (k3_finseq_1 I)) = (k4_tarski B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k36_gfacirc1 A B C) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_gfacirc1) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k33_gfacirc1 A B C) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k4_gfacirc1) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k24_gfacirc1 (k36_gfacirc1 A B C) E D) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k36_gfacirc1 A B C) E) k3_gfacirc1) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k3_twoscomp) (k3_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp) (k3_msafree2 (k13_ftacell1 A B C D E))) & (r2_hidden (k21_gfacirc1 (k36_gfacirc1 A B C) E D) (k3_msafree2 (k13_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k3_relat_1 C (k3_funcop_1 D A B)) = (k3_funcop_1 D (k3_relat_1 C A) (k3_relat_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t25_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_funcsdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_funcsdom A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_funcsdom A))) =>  ( ((k1_algstr_0 (k11_funcsdom A) B C) = (k1_algstr_0 (k11_funcsdom A) C B))  &  ( ((k1_algstr_0 (k11_funcsdom A) (k1_algstr_0 (k11_funcsdom A) B C) D) = (k1_algstr_0 (k11_funcsdom A) B (k1_algstr_0 (k11_funcsdom A) C D)))  &  ( ((k1_algstr_0 (k11_funcsdom A) B (k4_struct_0 (k11_funcsdom A))) = B)  &  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_funcsdom A))) &  ((k1_algstr_0 (k11_funcsdom A) B E) = (k4_struct_0 (k11_funcsdom A))) ) )  &  ( ((k6_algstr_0 (k11_funcsdom A) B C) = (k6_algstr_0 (k11_funcsdom A) C B))  &  ( ((k6_algstr_0 (k11_funcsdom A) (k6_algstr_0 (k11_funcsdom A) B C) D) = (k6_algstr_0 (k11_funcsdom A) B (k6_algstr_0 (k11_funcsdom A) C D)))  &  ( ((k6_algstr_0 (k11_funcsdom A) B (k5_struct_0 (k11_funcsdom A))) = B)  &  ( ((k6_algstr_0 (k11_funcsdom A) (k5_struct_0 (k11_funcsdom A)) B) = B)  &  ( ((k6_algstr_0 (k11_funcsdom A) B (k1_algstr_0 (k11_funcsdom A) C D)) = (k1_algstr_0 (k11_funcsdom A) (k6_algstr_0 (k11_funcsdom A) B C) (k6_algstr_0 (k11_funcsdom A) B D)))  &  ((k6_algstr_0 (k11_funcsdom A) (k1_algstr_0 (k11_funcsdom A) C D) B) = (k1_algstr_0 (k11_funcsdom A) (k6_algstr_0 (k11_funcsdom A) C B) (k6_algstr_0 (k11_funcsdom A) D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 (k3_relat_1 B A)) & (r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A)))  => (v2_funct_1 B)) ) ) ) ) ).
tt(t25_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_1 C) &  ((k2_relset_1 B C) = B) )  =>  ((v1_funct_1 (k2_funct_1 C)) &  ((v1_funct_2 (k2_funct_1 C) B A) & (m1_subset_1 (k2_funct_1 C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ).
tt(t25_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k3_tarski (k7_relat_1 (k3_funct_3 B) A)) (k8_relat_1 B (k3_tarski A)))) ) ) ).
tt(t25_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski A (k1_funct_4 B A))) ) ) ) ).
tt(t25_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) =>  ((r1_tarski (k9_xtuple_0 (k1_funct_5 C)) A) & (r1_tarski (k9_xtuple_0 (k3_funct_5 C)) B)) ) ) ) ) ) ).
tt(t25_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (~  (B = k1_xboole_0) )  =>  ((r2_hidden A (k4_funct_6 B)) <=>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) => (r2_hidden A (k1_funct_1 B C))) ) ) ) ) ) ) ).
tt(t25_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] : (r1_funct_7 A A B)) ) ) ).
tt(t25_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_8 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 B k1_numbers k1_numbers C) => (r1_funct_8 B k1_numbers k1_numbers (k9_valued_1 k1_numbers k1_numbers C A))) ) ) ) ) ) ) ).
tt(t25_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k29_sin_cos (k8_real_1 k32_sin_cos A))) ) ).
tt(t25_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 B C C)) =>  (! [E:$i] :  ( ((v8_functor0 E A B) &  ((v10_functor0 E A B) & (l2_functor0 E A B)) )  =>  ( (E = (k9_functor0 A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A F G)) =>  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  =>  ((k6_functor0 A B E F G H) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F C A) & (m2_functor0 F C A))  =>  (! [G:$i] :  ((m1_functor2 G B C D E) =>  ((r1_functor2 B C D E) => (r8_pboole (u1_struct_0 B) (k5_functor3 B C A D E G F) (k7_functor3 B C A D E F F G (k4_functor2 C A F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k1_fuzzy_1 A B D) (k1_fuzzy_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t25_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A (k6_fuzzy_1 A B C) (k1_fuzzy_1 A B C)) (k2_fuzzy_1 A B C))) ) ) ) ) ) ).
tt(t25_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ( (C = D)  =>  ((k1_fuzzy_4 A B (k5_fuzzy_4 A B) C D) = 1) )  &  ( (~  (C = D) )  =>  ((k1_fuzzy_4 A B (k5_fuzzy_4 A B) C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A B C)) k6_numbers))  =>  ( (B = (k4_struct_0 A))  |  ( (C = (k4_struct_0 A))  | (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k6_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A C)) = (k5_finseq_2 (u1_struct_0 B) A (k4_algstr_0 B C))) ) ) ) ) ) ) ).
tt(t25_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  ( (~ (v1_xboole_0 (k19_gate_1 A B C D E)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) & (v1_xboole_0 E)) ) ) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) & (v1_xboole_0 E)) ) ) ) )  & (v1_xboole_0 (k19_gate_1 A B C D E))) ) ) ) ) ) ) ) ).
tt(t25_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ( ((k4_gcd_1 A B (k4_struct_0 A)) = (k4_struct_0 A))  &  ((k4_gcd_1 A B (k5_struct_0 A)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t25_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((k9_genealg1 D E F A B C) = (k9_genealg1 D E F B A C))  &  ((k9_genealg1 D E F A B C) = (k9_genealg1 D E F A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_geomtrap A B C D E F G))  =>  ( (D = E)  |  ( ( (~ (r2_geomtrap A B C D E F H))  &  (~ (r2_geomtrap A B C D E H F)) )  |  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k10_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k10_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k10_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k10_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k14_twoscomp) C) k14_twoscomp) (u1_struct_0 (k10_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t25_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (v1_relat_1 (k3_msafree2 (k5_gfacirc2 A B C)))) ) ) ) ) ) ).
tt(t25_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (r1_xxreal_0 1 (k15_glib_000 A))) ) ).
tt(t25_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k1_relset_1 k5_numbers (k6_glib_001 A B))) =>  ( ((k1_funct_1 (k6_glib_001 A B) C) = (k1_funct_1 B (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1)))  & (r2_hidden (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) C) 1) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ).
tt(t25_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) <=>  ((k3_glib_002 A) = (k1_tarski (k6_glib_000 A))) ) ) ) ).
tt(t25_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((r2_hidden C (k28_glib_000 A (k4_glib_001 A B))) =>  ((k10_glib_003 A (k10_glib_001 A B C)) = (k2_xcmplx_0 (k10_glib_003 A B) (k1_seq_1 (k5_glib_003 A) C))) ) ) ) ) ) ) ).
tt(t25_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k2_nat_1 (k39_glib_000 (k10_glib_004 A B)) 1) = (k5_card_1 (k2_glib_002 A B))) ) ) ) ) ).
tt(t25_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 B))) & (r1_xboole_0 (k10_xtuple_0 C) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) B A)))) )  =>  ((r1_xxreal_0 (k1_matrix_1 B) 1) | (r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k3_goboard1 B A))) ) ) ) ) ) ) ) ).
tt(t25_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 C A B) (k3_goboard5 C (k2_nat_1 A 1) B)) = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B))) = (a_2_5_goboard6 A B)) ) ) ) ) ) ) ).
tt(t25_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 E)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 E)) & (r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C (k2_nat_1 D 1))))) ) ) ) ) ) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 (k2_goboard2 A))))  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 1) 1)) (k13_complex1 1 2)) (k19_euclid k6_numbers 1)) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 1) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 2) 1)) (k13_complex1 1 2)) (k19_euclid k6_numbers 1))) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t25_goboard9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)))  => (r1_tarski (k1_tops_1 (k15_euclid 2) (k4_goboard5 A B)) (k3_goboard9 A))) ) ) ) ) ).
tt(t25_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_goboard5 A k6_numbers (k1_matrix_1 A)) = (a_1_14_gobrd11 A)) ) ) ).
tt(t25_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k3_gobrd13 D E A) = (k3_goboard5 E B (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k3_goboard9 B)) & (r1_xxreal_0 (k7_pscomp_1 (k3_topreal1 2 B)) (k18_euclid A))) ) ) ) ) ) ).
tt(t25_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) | (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) D) (k12_finseq_1 (k3_cqc_lang A) (k2_calcul_1 A C))) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_graph_1 B) & (l1_graph_1 B)) )  =>  ((r4_graph_1 A B) => (v2_graph_1 A)) ) ) ) ) ).
tt(t25_graph_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r1_tarski (k1_relset_1 k5_numbers C) (k4_finseq_1 B)) & (r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t25_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (~  ( (~  ((k7_graph_3 B C A) = k6_numbers) )  & (v1_xboole_0 (k4_graph_3 B C A))) ) ) ) ) ) ) ).
tt(t25_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 B) = 1)  =>  ((k2_graph_5 A B) = (k1_graph_5 A (k7_partfun1 (u4_struct_0 A) B 1))) ) ) ) ) ) ).
tt(t25_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 B) k8_graph_5) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) k8_graph_5)))) )  =>  ( ((r2_hidden A (u4_struct_0 B)) & (r1_graph_4 B C D A))  =>  ((k12_graphsp B C D E) = (k1_funct_1 E A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_grcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  ((m4_grcat_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_grcat_1 D) & (m1_grcat_1 D B C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  ((k7_group_1 A) = (k3_xcmplx_0 2 B)) ) )  &  (! [B:$i] :  ((m1_group_2 B A) =>  (~  ( ((k7_group_1 B) = 2)  &  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v1_gr_cy_1 B) & (l3_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v2_gr_cy_3 A)) )  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( ((k4_nat_d A 4) = 3)  &  (! [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v1_gr_cy_3 B)) )  =>  (~ (r1_nat_d B (k1_gr_cy_3 A))) ) ) ) ) ) ) ) ).
tt(t25_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski A B) & (v2_funct_1 B))  =>  ((k6_relat_1 (k10_xtuple_0 A) B) = A) ) ) ) ) ) ).
tt(t25_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  =>  (! [F:$i] :  ( ((v15_algstr_0 F) & (m1_group_6 F B (k10_group_6 A B C)))  =>  (! [G:$i] :  ( ((v15_algstr_0 G) &  ((v1_group_3 G (k10_group_6 A B C)) & (m1_group_6 G B (k10_group_6 A B C))) )  =>  ( ( ((v15_algstr_0 E) & (m1_group_6 E A D))  &  ((m1_group_6 (k5_group_6 D (k1_group_6 A D E)) (k5_group_6 A E) (k10_group_5 (k5_group_6 A E))) &  ((r1_group_2 B F (k2_grsolv_1 A B C D)) & (r1_group_2 B G (k2_grsolv_1 A B C E))) ) )  => (m1_group_6 (k5_group_6 F (k1_group_6 (k10_group_6 A B C) F G)) (k5_group_6 (k10_group_6 A B C) G) (k10_group_5 (k5_group_6 (k10_group_6 A B C) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden F E) => (r1_rewrite1 (k3_polyred A B C D) F (k7_polynom1 A C))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden F E) => (r7_polyred A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  => (r1_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) (k7_polynom1 A C))) ) ) ) )  =>  ((r2_hidden (k7_polynom1 A C) D) | (r1_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  ( ((k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E)) = (k3_groeb_3 A B C D E))  &  ((k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E)) = (k4_groeb_3 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 C D) => (r1_tarski (k1_group_11 A B D) (k1_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t25_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A k6_numbers B) = (k1_group_1 A)) ) ) ) ) ).
tt(t25_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k2_group_2 A B C) = (k2_group_2 A C B)) ) ) ) ) ) ) ) ).
tt(t25_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_3 A (k2_group_3 A B C) (k2_group_1 A C)) = B)  &  ((k2_group_3 A (k2_group_3 A B (k2_group_1 A C)) C) = B) ) ) ) ) ) ) ) ).
tt(t25_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k4_group_4 A (k5_finseq_2 k4_numbers (k3_finseq_1 B) (k2_group_4 1)) B) = B) ) ) ) ) ).
tt(t25_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_5 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A (k2_group_3 A (k2_group_5 A B D) C) (k2_group_5 A C D))) ) ) ) ) ) ) ) ) ).
tt(t25_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_group_3 C A) & (m1_group_2 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_group_6 A C))) =>  ( (D = (k13_group_2 A C B))  =>  ((k2_group_1 (k5_group_6 A C) D) = (k13_group_2 A C (k2_group_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t25_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v5_group_1 C) & (l3_algstr_0 C)) )  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_group_7 (k11_finseq_1 A B C)) & (v4_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_gr_cy_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v1_gr_cy_1 B) & (l3_algstr_0 B)) ) ) ) ) ) ) ) ).
tt(t25_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  ((k18_group_9 A B (k15_group_9 A B C)) = C) ) ) ) ) ) ).
tt(t25_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((v2_group_10 B A) &  ((k2_groupp_1 A B) = 1) )  => (v1_gr_cy_1 B)) ) ) ) ) ).
tt(t25_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hahnban1 B k1_complfld A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k11_hahnban1 A B)) &  ((v1_funct_2 (k11_hahnban1 A B) (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v2_hahnban (k11_hahnban1 A B) (k10_hahnban1 A)) &  ((v3_hahnban (k11_hahnban1 A B) (k10_hahnban1 A)) & (m1_subset_1 (k11_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t25_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (m1_hallmar1 B A B C)) ) ) ) ) ).
tt(t25_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( ( (D = (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) C))  &  ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A))) )  => (v4_xxreal_2 D)) ) ) ) ) ) ) ) ) ).
tt(t25_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (~  ( (~ (v3_glib_001 B A))  & (v1_glib_001 B A)) ) ) ) ) ) ).
tt(t25_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_vectsp_4 B k1_complfld A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 C A k1_complfld) &  ((v1_hermitan C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((r1_tarski (u1_struct_0 B) (k8_vectsp10 k1_complfld A (k1_hermitan A C))) => (v1_hermitan (k10_vectsp10 k1_complfld A B C) (k6_vectsp10 k1_complfld A B))) ) ) ) ) ) ) ).
tt(t25_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ( ((k10_normform A (k3_heyting1 A C) (k2_heyting1 A B)) = k1_xboole_0)  => (r3_lattices (k12_normform A) (k3_funct_2 (k7_normform A) (u1_struct_0 (k12_normform A)) (k4_heyting1 A) B) (k3_funct_2 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k8_heyting1 A) C))) ) ) ) ) ) ).
tt(t25_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k4_partfun1 A B)))  =>  ( ( (! [F:$i] :  ((m1_subset_1 F (k4_partfun1 A B)) =>  ((r2_hidden F C) => (r1_partfun1 F E)) ) )  & (r3_lattices (k5_substlat A B) (k4_lattices (k5_substlat A B) C (k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) E)) D))  => (r3_lattices (k5_substlat A B) (k3_funct_2 (k4_partfun1 A B) (u1_struct_0 (k5_substlat A B)) (k8_heyting2 A B) E) (k5_binop_1 (u1_struct_0 (k5_substlat A B)) (k5_heyting2 A B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (m1_subset_1 (k4_heyting3 A B) (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers B))))) ) ) ) ).
tt(t25_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers k16_sin_cos B) D) C) A) = (k8_real_1 B (k1_seq_1 k16_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 C k32_sin_cos) 2))))) ) ) ) ) ) ) ) ) ) ).
tt(t25_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_quofield C A B) => (v4_quofield (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t25_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 (k3_hilbert1 A B) C) (k3_hilbert1 B C)) k6_hilbert1)) ) ) ) ) ) ).
tt(t25_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (~  ((k3_hilbert1 A B) = k2_hilbert1) ) ) ) ) ) ).
tt(t25_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  => (v3_funct_2 (k16_funct_3 A B A B C D) (k2_zfmisc_1 A B) (k2_zfmisc_1 A B))) ) ) ) ) ) ).
tt(t25_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~  (C = k6_numbers) )  =>  ( ((k1_normsp_1 A (k3_hurwitz A B C) k6_numbers) = (k4_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)))  &  ((k1_normsp_1 A (k3_hurwitz A B C) C) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ).
tt(t25_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k8_idea_1 B A) = 1)  =>  (A = 1) ) ) ) ) ) ).
tt(t25_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) => (m1_ideal_1 C A B)) ) ) ) ) ) ).
tt(t25_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  &  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  (~  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  ((r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) F) <=>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) => (m3_cat_2 (k10_index_1 A (k14_index_1 A B B C D)) E)) ) ) ) ) ) ) ) ) ) ).
tt(t25_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((k1_instalg1 A A B (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A))) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ).
tt(t25_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_int_1 A) = A)  <=> (v1_int_1 A)) ) ) ).
tt(t25_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A (k3_xcmplx_0 B C)) & (r1_int_2 B A))  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(t25_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v1_int_2 B) & (r1_int_2 B C))  =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B D) C) (k1_newton B A)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~  ((k2_int_5 A B) = 1) )  &  ( (~  ((k2_int_5 A B) = k6_numbers) )  &  (~  ((k2_int_5 A B) = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ) ).
tt(t25_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (C = (k7_xcmplx_0 (k19_rvsum_1 A) (k1_funct_1 A B)))  => (r1_int_2 C (k1_funct_1 A B))) ) ) ) ) ) ) ) ).
tt(t25_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v8_struct_0 A) &  ( ((k6_group_1 A B) = D)  &  ( ((k6_group_1 A C) = E)  &  ((k3_int_2 D E) = 1) ) ) )  =>  ((k6_group_1 A (k8_group_1 A B C)) = (k3_xcmplx_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~  ((k7_real_1 A B) = k6_numbers) )  &  ( (~  ((k9_real_1 A B) = k6_numbers) )  &  (~  ((k2_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 B k6_numbers) k19_sin_cos))) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) (k4_seq_4 C)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 C G) = 1)  &  ( ((k1_seq_1 D G) = (k12_binop_2 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D G))) ) ) ) ) ) )  &  ( (F = (k1_relset_1 k1_numbers E))  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B)) & (r2_relset_1 k1_numbers k1_numbers E (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6) (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k41_valued_1 k1_numbers k1_numbers D)) (k4_taylor_1 (k18_binop_2 1 2))) A))))) ) ) )  =>  ((k2_integra5 B E) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6)) (k4_seq_4 B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_sin_cos6)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos))))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t25_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1))) &  ( (B = (k1_relset_1 k1_numbers k30_sin_cos))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k30_sin_cos A))) ) )  =>  ((k2_integra5 A k30_sin_cos) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1)) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t25_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) )  =>  ((k12_integr15 D E A (k9_integr15 A F k1_numbers G)) = (k9_euclid A (k12_integr15 D E A G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v2_seq_2 (k2_partfun1 A k1_numbers C A)) => (r1_xxreal_0 (k8_real_1 (k5_seq_4 (k1_rvsum_1 C)) (k3_integra1 A)) (k7_integra1 A C B))) ) ) ) ) ) ) ).
tt(t25_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers)))) )  =>  (! [E:$i] :  ((m1_integra1 E C) =>  ( ((r2_hidden B (k4_finseq_1 E)) &  ((v2_seq_2 (k2_partfun1 C k1_numbers D C)) & (r1_xxreal_0 k6_numbers A)) )  =>  ((k1_seq_1 (k5_integra1 C (k26_valued_1 C k1_numbers D A) E) B) = (k8_real_1 A (k1_seq_1 (k5_integra1 C D E) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integra4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) &  ((r1_xxreal_0 k6_numbers A) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 D E) (k1_seq_1 D F))) (k8_real_1 A (k18_complex1 (k9_real_1 (k1_seq_1 C E) (k1_seq_1 C F)))))) ) ) ) ) ) )  => (r1_xxreal_0 (k9_real_1 (k4_seq_4 (k1_rvsum_1 D)) (k5_seq_4 (k1_rvsum_1 D))) (k8_real_1 A (k9_real_1 (k4_seq_4 (k1_rvsum_1 C)) (k5_seq_4 (k1_rvsum_1 C)))))) ) ) ) ) ) ) ) ) ).
tt(t25_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) F) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden C (k3_integra5 A B)) & (r2_hidden D (k3_integra5 A B))) ) ) ) )  =>  ((k4_integra5 C D (k26_valued_1 k1_numbers k1_numbers F E)) = (k4_real_1 E (k4_integra5 C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_integra7,ax,(r1_integra7 k1_numbers (k26_valued_1 k1_numbers k1_numbers k19_sin_cos (k1_real_1 1)) k16_sin_cos)).
tt(t25_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) A) &  ((k1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) A) = (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A)) ) ) ) ).
tt(t25_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D) &  ((v1_comseq_2 (k2_partfun1 D k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D)) &  ((v3_integra1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D) &  ((v1_comseq_2 (k2_partfun1 D k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D)) & (v3_integra1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D)) ) ) ) )  =>  ((k1_integra9 D (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) = (k7_real_1 (k1_integra9 D A C) (k1_integra9 D B C))) ) ) ) ) ) ) ) ) ) ).
tt(t25_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski B C) =>  ( (~ (v1_xboole_0 (k2_interva1 A B C)))  &  ((v1_interva1 (k2_interva1 A B C) A) & (m1_subset_1 (k2_interva1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ) ) ).
tt(t25_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 A B) k8_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 A C)) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t25_irrat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  ((k2_seq_2 B) = A) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 (k1_seq_1 B E) (k6_xcmplx_0 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  ((r2_nattra_1 B A C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((k2_cat_1 A (k8_cat_1 B A C E) (k8_cat_1 B A D E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  (! [F:$i] :  ((m2_cat_1 F (k8_cat_2 A B) C) =>  ( ((r2_nattra_1 (k8_cat_2 A B) C D E) & (r2_nattra_1 (k8_cat_2 A B) C E F))  =>  (! [G:$i] :  ((m2_nattra_1 G (k8_cat_2 A B) C D E) =>  (! [H:$i] :  ((m2_nattra_1 H (k8_cat_2 A B) C E F) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) (k6_isocat_2 A B C D F (k7_nattra_1 (k8_cat_2 A B) C D E F G H)) (k7_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E) (k5_isocat_2 A B C F) (k6_isocat_2 A B C D E G) (k6_isocat_2 A B C E F H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k4_rcomp_1 k2_xxreal_0 B))  =>  ((k1_tops_1 k3_topmetr A) = (k2_rcomp_1 k2_xxreal_0 B)) ) ) ) ) ) ).
tt(t25_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 A) &  ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ( (~  ((k1_funct_1 A 1) = (k1_funct_1 A (k3_finseq_1 A))) )  &  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((v1_topreal1 B) &  ((v2_funct_1 B) &  ((r1_tarski (k3_topreal1 2 B) (k3_topreal1 2 A)) &  ( ((k1_funct_1 A 1) = (k1_funct_1 B 1))  &  ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B (k3_finseq_1 B)))  & (r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k3_xcmplx_0 F G)) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (A = a_0_2_jgraph_3)  =>  ((v1_topreal2 A) & (v2_compts_1 A (k15_euclid 2))) ) ) ) ).
tt(t25_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_2_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t25_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  & (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_6_jgraph_6)  &  (B = a_0_7_jgraph_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = B) ) ) ) ) ) ).
tt(t25_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 E (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) H)) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)))  &  ( ((k18_euclid B) = (k18_euclid C))  &  ( ((k18_euclid C) = (k18_euclid A))  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)))  &  (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A E) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan13 A E))) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A E))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan13 A E) D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A E) B C))  & (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A E)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B C D E) & (r1_jordan17 A B E D C))  =>  ( (B = C)  |  ( (C = D)  |  ( (D = E)  |  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((r1_jordan18 A B C D E F) => (r1_jordan18 A B D C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 B (k1_matrix_1 C)))  => (v2_connsp_1 (k3_goboard5 C A B) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t25_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_3_jordan1 A B C D))  => (v3_pre_topc E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k3_finseq_1 (k1_jordan8 B A)))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ).
tt(t25_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k3_finseq_1 (k1_jordan8 B A)) C)) ) ) ) ) ) ) ) ) ).
tt(t25_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k4_finseq_4 (k2_jordan1e B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = 1) ) ) ) ) ).
tt(t25_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  =>  ((r1_tarski (k1_tops_1 (k15_euclid 2) (k2_gobrd13 B A C)) (k3_goboard9 B)) & (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_gobrd13 B A C)) (k2_goboard9 B))) ) ) ) ) ) ) ) ) ).
tt(t25_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_sprect_2 A) <=> (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k18_pscomp_1 (k3_topreal1 2 A))) 2) (k14_pscomp_1 (k3_topreal1 2 A)))) ) ) ).
tt(t25_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k9_pscomp_1 A) (k9_pscomp_1 B)) =>  ((k9_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k9_pscomp_1 A)) ) ) ) ) ) ).
tt(t25_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k1_topreal6 2 (k5_algstr_0 (k15_euclid 2) A B) (k5_algstr_0 (k15_euclid 2) A C)) = (k1_topreal6 2 B C)) ) ) ) ) ) ) ).
tt(t25_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) C D A) &  ((r1_topreal1 (k15_euclid 2) E F B) &  ((r1_jordan5c A C D E F) & (r1_tarski B A)) ) )  =>  (B = (k5_jordan6 A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((k1_jordan21 A) = (k22_pscomp_1 A)) ) ) ) ).
tt(t25_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k18_euclid (k1_jordan21 (k3_topreal1 2 (k1_jordan9 A C)))) (k18_euclid (k1_jordan21 (k3_topreal1 2 (k1_jordan9 A B)))))) ) ) ) ) ) ) ).
tt(t25_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v3_funct_1 (k3_graph_2 A B)) => (v3_funct_1 A)) ) ) ) ) ).
tt(t25_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (a_1_1_jordan2b B))  => (v3_pre_topc A k3_topmetr)) ) ) ) ) ).
tt(t25_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (r1_tarski (k1_jordan2c A B) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) ) ) ) ).
tt(t25_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ( ( (~  (B = (k1_funct_1 A 1)) )  =>  ((k3_finseq_1 (k3_jordan3 A B)) = (k2_nat_1 (k1_jordan3 A B) 1)) )  &  ( (B = (k1_funct_1 A 1))  =>  ((k3_finseq_1 (k3_jordan3 A B)) = (k1_jordan3 A B)) ) ) ) ) ) ) ) ).
tt(t25_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_jordan4 A B C D) & (r1_xxreal_0 C D))  =>  ( ((k3_finseq_1 B) = (k2_nat_1 (k7_nat_d D C) 1))  &  (B = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = B)  =>  ((v1_rcomp_1 A) <=> (v2_compts_1 B k3_topmetr)) ) ) ) ) ) ).
tt(t25_jordan5b,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 A))))  =>  ((r1_xxreal_0 C B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A)))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A))))) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t25_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_topreal1 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k2_topreal1 2 A C))) ) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) B)) ) ) ) ) ) ) ).
tt(t25_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_3_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k17_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k17_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t25_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k4_jordan6 A B C D) = (k3_jordan6 A C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 D))) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C (k1_matrix_1 D))))) ) ) ) ) ) ) ) ) ).
tt(t25_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k7_nat_d (k3_finseq_1 B) 1) C))  &  (~ (r1_subset_1 (k2_jordan_a A (k3_finseq_1 B) B) (k2_jordan_a A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t25_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v4_pre_topc B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (r2_hidden C B))  &  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  (~ (r1_xboole_0 (k1_topreal9 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r1_ordinal1 D E) => (r3_lattices A (k6_knaster A B C E) (k6_knaster A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_kurato_1,ax, ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) = (k2_rcomp_1 4 k1_xxreal_0)) ).
tt(t25_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v9_rltopsp1 C (k15_euclid A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))) B D) C)) ) )  => (v9_rltopsp1 (k1_kurato_2 (k15_euclid A) B) (k15_euclid A))) ) ) ) ) ) ) ).
tt(t25_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ((k12_matrix_3 A B D) = (k4_rlvect_1 B (k8_laplace A C B D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_group_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_group_4 A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((r3_lattices (k11_group_4 A) D E) <=> (r1_tarski (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((v13_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) A) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 A))))  &  ( ((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B) & (m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B))))  &  ((r1_latsum_1 A B) &  ((v4_orders_2 A) & (v4_orders_2 B)) ) ) )  => (v4_orders_2 (k1_latsum_1 A B))) ) ) ) ) ).
tt(t25_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (r6_binop_1 (u1_struct_0 A) (u1_lattices A) (u1_lattices A))) ) ).
tt(t25_lattice3,ax, (! [A:$i] : (v4_lattice3 (k1_lattice3 A))) ).
tt(t25_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A (k2_lattice4 A B) C) = (k2_lattice4 A (k8_setwiseo (u1_struct_0 A) (u1_struct_0 A) (k9_funcop_1 (u1_struct_0 A) (u1_struct_0 A) (u2_lattices A) (k3_struct_0 A) C) B))) ) ) ) ) ) ) ).
tt(t25_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_lattice5 E A B D) =>  ((r2_hidden C (k7_lattice5 A B D)) <=> (r2_hidden C (k9_xtuple_0 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v9_lattice6 B A) <=> (v4_waybel_6 (k1_lattice6 A B) (k3_lattice3 A))) ) ) ) ) ).
tt(t25_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v2_lattice5 C A B) =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) => (v2_lattice5 (k6_lattice8 A B C D E) (k3_lattice8 A E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_lattices A B C) = (k5_lattices A))  <=> (r3_lattices A B (k7_lattices A C))) ) ) ) ) ) ) ).
tt(t25_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) C))))  =>  ((k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) D) = (k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k11_lexbfs A B C E)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_lfuzzy_1 A B 1) B)) ) ) ) ).
tt(t25_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) | (v2_limfunc1 A))  => (v1_limfunc1 (k56_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t25_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 A D))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A)))) ) ) ) )  | (r2_limfunc2 B A)) ) ) ) ) ) ).
tt(t25_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc3 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 C)) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc3 C A)) ) ) ) ) ) ) ) ).
tt(t25_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r2_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k2_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r5_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t25_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A C D) => (r1_lmod_6 A (k2_vectsp_5 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (D = (k1_rlvect_1 (k11_lopban_1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k12_lopban_1 A B D F) = (k1_rlvect_1 B (k12_lopban_1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) D) (k1_normsp_1 A (k1_bhsp_4 A B) C))) (k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 (k4_normsp_0 A B)) D) (k1_seq_1 (k3_series_1 (k4_normsp_0 A B)) C))))) ) ) ) ) ) ) ) ) ).
tt(t25_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A (k3_rlvect_1 A C D))) B) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k7_lopban_4 B A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k7_lopclset A) (k3_funct_2 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A) B)) = (k3_funct_2 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A) (k7_lattices A B))) ) ) ) ) ).
tt(t25_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k10_lpspace1 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k10_lpspace1 A B C))) =>  ( ( (D = F)  &  (E = G) )  =>  ((k3_valued_1 A k1_numbers k1_numbers D E) = (k3_rlvect_1 (k10_lpspace1 A B C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) & (r2_hidden E (k1_lpspace2 A B C F)))  => (r2_hidden (k3_valued_1 A k1_numbers k1_numbers D E) (k1_lpspace2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r3_ltlaxio1 B A) => (r3_ltlaxio1 B (k2_ltlaxio1 A))) ) ) ) ) ).
tt(t25_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) B) (k4_cqc_the1 A))) ) ) ) ).
tt(t25_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k6_rusub_4 A B (k3_mathmorp A C D)) (k3_mathmorp A (k6_rusub_4 A B C) D))) ) ) ) ) ) ) ) ).
tt(t25_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v2_matrix10 B) => (v3_matrix10 B)) ) ) ) ) ).
tt(t25_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  ( ( ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) & (v5_matrix_2 C (k11_matrix_2 (k12_matrix_2 A))))  |  ( (~ (v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))))  &  (~ (v5_matrix_2 C (k11_matrix_2 (k12_matrix_2 A)))) ) )  <=> (v5_matrix_2 (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) C B) (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ) ) ).
tt(t25_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 A)))  =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 D k5_numbers)) =>  (! [H:$i] :  ((m2_finseq_2 H k5_numbers (k4_finseq_2 B k5_numbers)) =>  ( ((r2_hidden C (k2_finseq_1 D)) &  ((r2_hidden E (k2_finseq_1 D)) &  ((k1_funct_1 G C) = (k1_funct_1 G E)) ) )  =>  ((k8_matrix_1 A (k1_matrix13 A F D B G H) C) = (k8_matrix_1 A (k1_matrix13 A F D B G H) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C D))  =>  ( (B = C)  |  ((k1_funct_1 (k3_matrix14 A D B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( (C = (k2_matrix15 A B))  <=>  ( ((k8_matrix_1 A C 1) = B)  &  ((k3_finseq_1 C) = 1) ) ) ) ) ) ) ) ) ).
tt(t25_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v3_matrix16 C (u1_struct_0 B)) => (v3_matrix16 (k1_matrix_6 A B C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t25_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  ( ((k3_finseq_1 D) = A)  &  ((k2_matrix_1 D) = (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 (k1_matrix_1 D)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v5_matrix_2 (k6_partfun1 (k2_finseq_1 A)) A)) ) ).
tt(t25_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 B)) =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 C)) =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ((v1_setwiseo D A) &  ((v1_finseqop D A) & (r6_binop_1 A E D)) ) ) )  =>  (! [J:$i] :  ((m1_subset_1 J B) =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C (k2_setwiseo B J) I) (k9_matrix_3 B C A E F G)) = (k7_setwiseo B A D (k2_setwiseo B J) (k9_funcop_1 A B E F (k7_setwiseo C A D I G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k3_matrix_3 A (k1_matrix_4 A B C) D) = (k3_matrix_3 A (k1_matrix_4 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((k7_matrix_5 k6_numbers A) = (k8_matrix_5 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ).
tt(t25_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ( ((v1_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A))  &  ((v2_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A)) )  => (v2_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t25_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k3_group_4 A (k8_finseq_1 (u1_struct_0 A) (k4_matrix_7 A (k4_finseq_5 (u1_struct_0 A) B)) B)) = (k1_group_1 A)) ) ) ) ) ).
tt(t25_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v2_matrix_8 C A B) &  ((v2_matrix_8 D A B) &  ((k4_matrix_6 A B C D) = (k1_matrix_6 A B (k4_matrix_6 A B D C))) ) )  =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix_8 (k2_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  (! [L:$i] :  ((m1_matrix_2 L (k12_matrix_2 3)) =>  ( (L = (k3_finseq_4 k5_numbers 3 1 2))  =>  ((k10_matrix_3 3 A K L) = (k3_finseq_4 (u1_struct_0 A) D E I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k5_matrixc1 A (k12_seq_4 B C)) = (k12_seq_4 (k5_matrixc1 A B) C)) ) ) ) ) ) ) ) ).
tt(t25_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E A) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 A))))  => (m1_subset_1 (k2_matrix_1 (k13_matrixj1 A B D)) (k1_zfmisc_1 (k2_matrix_1 (k13_matrixj1 A C (k3_matrixj1 A D E)))))) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_matrixj2 D A (k4_struct_0 A)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) (k3_finseq_1 C) (k3_finseq_1 C)) =>  ( (E = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) D))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 D)) => (r1_xxreal_0 (k3_finseq_1 (k14_matrixj1 (u1_struct_0 A) D G)) F)) ) )  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_vectsp11 B (k4_matrlin2 A B B C C E) F) (k6_grcat_1 B B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 (k3_matrixr1 A B)) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 (k3_matrixr1 A B)) = (k1_matrix_1 A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers (k3_matrixr1 A B) C D) = (k7_real_1 (k3_matrix_1 k1_numbers A C D) (k3_matrix_1 k1_numbers B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 A) = (k1_matrix_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k8_matrix_1 k1_numbers (k5_matrixr1 A B) C) = (k8_rvsum_1 (k8_matrix_1 k1_numbers A C) (k8_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t25_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( (D = (k2_vectsp_4 A B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_matrlin G A D) =>  ( ( (F = E)  &  (C = G) )  =>  ((k9_matrlin A B C F) = (k9_matrlin A D G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ((m1_matrix_1 G F A B) =>  (! [H:$i] :  ((m1_matrix_1 H F C B) =>  ( ((r2_hidden D (k9_xtuple_0 H)) &  (E = (k2_nat_1 (k3_finseq_1 G) D)) )  =>  ((k8_matrix_1 F (k8_matrlin F A C B G H) E) = (k8_matrix_1 F H D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xxreal_0 (k2_xcmplx_0 (k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B C)) (k4_matroid0 A (k9_subset_1 (u1_struct_0 A) B C))) (k2_xcmplx_0 (k4_matroid0 A B) (k4_matroid0 A C)))) ) ) ) ) ) ).
tt(t25_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers B A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers C A) =>  ((k3_matrprob (k8_matrlin k1_numbers B C A D E)) = (k8_finseq_1 k1_numbers (k3_matrprob D) (k3_matrprob E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k1_funct_1 (k3_matrtop1 A B (k5_matrlin2 A B k2_vectsp_1 D E)) C) = (k4_rvsum_1 (k1_funct_1 (k3_matrtop1 A B D) C) (k1_funct_1 (k3_matrtop1 A B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (! [D:$i] :  ( ((v1_rlaffin1 D (k15_euclid B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))))  =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid B))) =>  ((r2_hidden E (k4_rlaffin1 (k15_euclid B) D)) =>  ((r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 B A C) E) (k4_rlaffin1 (k15_euclid A) (k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D))) &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v3_card_1 F B) &  ((v1_finseq_1 F) & (v3_valued_0 F)) ) ) )  =>  ((k1_funct_1 (k5_rlaffin1 (k15_euclid B) D E) F) = (k1_funct_1 (k5_rlaffin1 (k15_euclid A) (k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D) (k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 B A C) E)) (k1_funct_1 (k3_matrtop1 B A C) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid D))) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 (k3_square_1 A) (k7_real_1 (k5_square_1 (k1_seq_1 E B)) (k5_square_1 (k1_seq_1 E C)))) &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid D)) (u1_struct_0 (k15_euclid D)) (k3_matrtop1 D D (k2_matrtop3 D F B C)) E) C) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B C) => (r2_pboole A B (k2_mboolean A C))) ) ) ) ) ) ).
tt(t25_measure1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  =>  ((v6_supinf_2 D) => (v6_supinf_2 (k1_partfun1 A B B k7_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(t25_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_measure6 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t25_measure8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_measure4 A B)) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (r2_hidden (k1_prob_1 A C) (k1_measure4 A B))) ) ) ) ) ).
tt(t25_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  ((k4_member_1 (k6_member_1 A)) = (k6_member_1 (k4_member_1 A))) ) ) ).
tt(t25_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v1_membered B)) )  => (v1_membered (k3_tarski A))) ) ).
tt(t25_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  ((k9_xtuple_0 C) = (k2_xboole_0 (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) (k9_xtuple_0 (k6_memstr_0 A B C)))) ) ) ) ) ) ) ).
tt(t25_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r2_mesfun6c A B C D) &  (E = (k7_subset_1 A (k1_relset_1 A D) F)) )  =>  ((r2_mesfun6c A B C (k2_partfun1 A k2_numbers D F)) &  ((k1_mesfun6c A B C D) = (k2_xcmplx_0 (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D F)) (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k2_numbers B k6_numbers))) => (v2_comseq_2 (k9_mesfun7c A B C))) ) )  =>  ( ((k8_mesfun7c A (k11_mesfun7c A B)) = (k5_comseq_3 A (k10_mesfun7c A B)))  &  ((k8_mesfun7c A (k12_mesfun7c A B)) = (k6_comseq_3 A (k10_mesfun7c A B))) ) ) ) ) ) ) ).
tt(t25_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((v1_mesfunc8 (k11_mesfun7c A B) A k1_numbers) <=> (v1_mesfunc8 (k12_mesfun7c A B) A k1_numbers)) ) ) ) ) ).
tt(t25_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B C F) = (k9_subset_1 A E (k15_mesfunc1 A D (k1_measure6 (k1_real_1 F))))) ) )  =>  ((k9_subset_1 A E (k19_mesfunc1 A D k2_supinf_1)) = (k1_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t25_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((r1_mesfunc1 A C B D) => (r1_mesfunc1 A C (k1_mesfunc2 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t25_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) &  ((v4_mesfunc5 B) &  ((v3_mesfunc5 C) & (v4_mesfunc5 C)) ) )  => (r2_relset_1 A k7_numbers (k3_mesfunc1 A (k3_mesfunc1 A (k1_mesfunc2 A (k3_mesfunc1 A B C)) (k2_mesfunc2 A B)) (k2_mesfunc2 A C)) (k3_mesfunc1 A (k3_mesfunc1 A (k2_mesfunc2 A (k3_mesfunc1 A B C)) (k1_mesfunc2 A B)) (k1_mesfunc2 A C)))) ) ) ) ) ) ) ).
tt(t25_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r1_mesfunc6 A B C E) &  ((r1_mesfunc6 A B D E) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k3_numbers B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k3_numbers B)))) )  =>  (~  (! [H:$i] :  ((v1_rat_1 H) =>  ((k1_funct_1 G H) = (k9_subset_1 A (k8_subset_1 A E (k11_mesfunc1 C H)) (k8_subset_1 A E (k11_mesfunc1 D (k9_real_1 F H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k5_prob_1 A B D E))))  =>  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k3_mesfunc2 D A) E)) = (k12_supinf_2 C (k5_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = D)  &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C E) D)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (v10_mesfunc5 (k3_mesfunc5 A C E))) ) ) ) )  => (r1_mesfunc1 A B (k7_mesfunc8 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t25_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (~  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) &  ( ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) D) = k2_supinf_1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 E C) &  ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B E) D) = k2_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k2_metric_1 A B C) k6_numbers)) ) ) ) ) )  <=> (v11_metric_1 A)) ) ) ).
tt(t25_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k5_metric_2 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) &  (? [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) & (r4_metric_2 A C D B)) ) ) ) ) ) ) ) ) ).
tt(t25_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ( ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 A B) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t25_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_tbsp_1 B A) & (m2_valued_0 C (u1_struct_0 A) B))  => (v3_tbsp_1 C A)) ) ) ) ) ) ) ).
tt(t25_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_connsp_1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~ (r2_metrizts A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (k3_rltopsp1 (k15_euclid A) B) (k2_mfold_2 A C D)) = (k2_mfold_2 A C (k3_rlvect_1 (k15_euclid A) B D))) ) ) ) ) ) ) ) ) ).
tt(t25_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( (~ (v1_xboole_0 (a_2_0_midsp_1 A B)))  & (m1_subset_1 (a_2_0_midsp_1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ).
tt(t25_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((r1_midsp_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k5_binop_1 A (k6_midsp_2 A B C) D E) = F)  <=>  ((k2_binop_1 A A (u1_struct_0 B) C D F) = (k2_binop_1 A A (u1_struct_0 B) C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [G:$i] :  ( ((v4_midsp_2 G C) & (l1_midsp_2 G C))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (u1_midsp_2 C G))) =>  (! [I:$i] :  ((m2_finseq_2 I (u1_struct_0 (u1_midsp_2 C G)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C G)))) =>  ( ( ((k8_midsp_3 A C G D F) = I)  &  ((k9_midsp_2 C G D E) = H) )  =>  ((k8_midsp_3 A C G D (k6_midsp_3 A C F B E)) = (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C G)) (k2_nat_1 A 1) I B H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((r1_tarski B C) & (r1_relset_1 A A D E))  => (r1_tarski (k2_mmlquery A D B) (k2_mmlquery A E C))) ) ) ) ) ) ) ) ) ) ).
tt(t25_mod_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_enumset1 k6_numbers 1 2)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_enumset1 k6_numbers 1 2)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_enumset1 k6_numbers 1 2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_enumset1 k6_numbers 1 2)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_enumset1 k6_numbers 1 2)) =>  ( ( (D = k6_numbers)  &  (E = 1) )  =>  ( ((k11_mod_2 A B) = (k11_mod_2 B A))  &  ( ((k11_mod_2 (k11_mod_2 A B) C) = (k11_mod_2 A (k11_mod_2 B C)))  &  ( ((k11_mod_2 A D) = A)  &  ( ((k11_mod_2 A (k10_mod_2 A)) = D)  &  ( ((k12_mod_2 A B) = (k12_mod_2 B A))  &  ( ((k12_mod_2 (k12_mod_2 A B) C) = (k12_mod_2 A (k12_mod_2 B C)))  &  ( ((k12_mod_2 E A) = A)  &  ( (~  ( (~  (A = D) )  &  (! [F:$i] :  ((m1_subset_1 F (k1_enumset1 k6_numbers 1 2)) =>  (~  ((k12_mod_2 A F) = E) ) ) ) ) )  &  ( (~  (D = E) )  &  ((k12_mod_2 A (k11_mod_2 B C)) = (k11_mod_2 (k12_mod_2 A B) (k12_mod_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((v8_mod_4 (k3_struct_0 A) A A) <=>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_modal_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) =>  ( ( (C = (k12_finseq_1 k5_numbers k6_numbers))  &  ( (D = (k12_finseq_1 k5_numbers 1))  &  ((k1_trees_2 (k9_xtuple_0 B) (k1_modal_1 (k9_xtuple_0 B))) = (k7_domain_1 (k9_xtuple_0 B) C D)) ) )  =>  (B = (k7_trees_2 (k7_trees_2 (k8_funcop_1 A (k2_trees_1 2) (k2_modal_1 A B)) (k12_finseq_1 k5_numbers k6_numbers) (k5_trees_2 B C)) (k12_finseq_1 k5_numbers 1) (k5_trees_2 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ((m1_modelc_1 D A B) &  ((k3_funct_2 k5_numbers A D k6_numbers) = C) ) ) ) ) ) ) ) ) ).
tt(t25_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((v8_modelc_2 A) =>  ((r1_modelc_2 B A) <=>  ( (B = (k11_modelc_2 A))  |  (B = (k12_modelc_2 A)) ) ) ) ) ) ) ) ).
tt(t25_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) & (l1_modelc_3 C A))  =>  ((r4_modelc_3 A C B) =>  ((r1_tarski (u1_modelc_3 A C) (u1_modelc_3 A B)) & (r1_tarski (u3_modelc_3 A C) (u3_modelc_3 A B))) ) ) ) ) ) ) ) ).
tt(t25_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (v1_moebius1 (k24_binop_2 A B)))  & (v1_moebius1 A)) ) ) ) ) ) ).
tt(t25_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 B C D) = (k6_algstr_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m2_monoid_0 C B))  =>  ((r2_hidden (k4_binop_1 (u1_struct_0 B) (u2_algstr_0 B)) (u1_struct_0 C)) => (m3_monoid_0 (k9_monoid_1 C A) (k11_monoid_1 B A))) ) ) ) ) ) ).
tt(t25_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_morph_01 A (k1_morph_01 A B C) D) = (k1_morph_01 A B (k2_morph_01 A C D))) ) ) ) ) ) ) ) ) ).
tt(t25_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((k10_msualg_2 A (k11_msafree A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers)))) (k5_msafree3 A (k2_pboole (u1_struct_0 A) B (k8_funcop_1 (k1_zfmisc_1 k5_numbers) (u1_struct_0 A) (k6_domain_1 k5_numbers k6_numbers))) B)) = (k1_msafree3 A B)) ) ) ) ) ).
tt(t25_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  |  ((k4_finseq_1 D) = (k4_finseq_1 (k1_msualg_1 A C))) )  &  ( ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ( (F = (k1_funct_1 D E))  =>  ((k7_msaterm A B F) = (k1_funct_1 (k1_msualg_1 A C) E)) ) ) ) ) ) )  |  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ( (F = (k1_funct_1 D E))  =>  ((k7_msaterm A B F) = (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)) ) ) ) ) ) ) )  &  (~ (m1_msaterm D A B (k2_msaterm A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v4_msscyc_1 A) => (v1_finset_1 (k1_msualg_2 A B C))) ) ) ) ) ) ) ).
tt(t25_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  ( ((r2_pboole A B (k3_funct_6 C)) &  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden D A) &  (E = (k1_funct_1 C D)) )  => (v1_finset_1 (k8_relat_1 E (k1_funct_1 B D)))) ) ) ) )  => (v2_finset_1 B)) ) ) ) ) ) ).
tt(t25_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ( ((u1_struct_0 A) = (k1_tarski k6_numbers))  =>  ((u3_msualg_1 A B) = (u3_msualg_1 (k6_msualg_1 (k12_msualg_1 A B)) (k9_msualg_1 (k12_msualg_1 A B)))) ) ) ) ) ) ).
tt(t25_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A B)) =>  ((k13_msualg_2 A B (k12_msualg_2 A B D) C) = (k12_msualg_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) E F) =>  (! [G:$i] :  ((m2_msualg_6 G A B E F) =>  (? [H:$i] :  ((m2_msualg_6 H A C E F) & (r2_funct_2 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) F) (k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) E) (k1_funct_1 (u3_msualg_1 A C) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D E) H) (k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) F) (k1_funct_1 (u3_msualg_1 A B) F) (k1_funct_1 (u3_msualg_1 A C) F) G (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C) D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k7_msafree2 A))) => (r2_msualg_3 A B (k7_msafree2 A) C)) ) ) ) ) ) ).
tt(t25_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r8_pboole (u1_struct_0 (k6_msualg_1 A)) (k2_msuhom_1 A A (k6_partfun1 (u1_struct_0 A))) (k2_msualg_3 (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A))))) ) ).
tt(t25_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((v5_dilworth B (k3_necklace A)) & (m1_eqrel_1 B (u1_struct_0 (k3_necklace A)))) ) ) ) ) ).
tt(t25_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) (k9_funct_2 (u1_struct_0 A) k1_numbers)) (k9_funct_2 (u1_struct_0 A) k1_numbers))))) )  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k1_binop_1 B C D) = (k3_nagata_1 A C D)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k9_funct_2 (u1_struct_0 A) k1_numbers)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k3_finseq_1 C)) =>  ( (k6_numbers = D)  |  ((v1_funct_1 (k1_funct_1 C D)) &  ((v1_funct_2 (k1_funct_1 C D) (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 (k1_funct_1 C D) A) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ) ) )  =>  ((v1_funct_1 (k1_finsop_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) C B)) &  ((v1_funct_2 (k1_finsop_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) C B) (u1_struct_0 A) k1_numbers) &  ((v1_pscomp_1 (k1_finsop_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) C B) A) & (m1_subset_1 (k1_finsop_1 (k9_funct_2 (u1_struct_0 A) k1_numbers) C B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 1) &  ( (~  (A = k6_numbers) )  &  (~  (A = 1) ) ) ) ) ) ) ).
tt(t25_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A (k4_nat_1 2 B)) => (r1_xxreal_0 (k3_nat_d (k1_nat_1 A 1) 2) B)) ) ) ) ) ).
tt(t25_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k11_nat_3 (k1_newton A B) A) = B) ) ) ) ) ) ).
tt(t25_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k9_real_1 A 1) = (k4_nat_1 (k13_newton F D) C))  &  ((v1_int_2 F) &  ( ((k4_nat_d (k13_newton E (k7_nat_d A 1)) A) = 1)  &  ((k6_nat_d (k7_nat_d (k13_newton E (k3_nat_d (k7_nat_d A 1) F)) 1) A) = 1) ) ) )  =>  ((r1_xxreal_0 (k13_newton F D) C) |  ((r1_xxreal_0 C k6_numbers) | (v1_int_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_nat_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ( (C = B)  =>  ((k3_uproots D (k1_nat_5 A C D)) = (k21_rfunct_3 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_nat_d A A) = k6_numbers) ) ) ).
tt(t25_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  (! [E:$i] :  ((m2_cat_1 E B A) =>  ( ((r2_nattra_1 B A C D) & (r2_nattra_1 B A D E))  =>  (! [F:$i] :  ((m2_nattra_1 F B A C D) =>  (! [G:$i] :  ((m2_nattra_1 G B A D E) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((k4_nattra_1 B A C E (k7_nattra_1 B A C D E F G) H) = (k5_cat_1 A (k8_cat_1 B A C H) (k8_cat_1 B A D H) (k8_cat_1 B A E H) (k4_nattra_1 B A C D F H) (k4_nattra_1 B A D E G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) E) (k9_subset_1 (u1_struct_0 B) (k1_relset_1 (u1_struct_0 B) C) (k1_relset_1 (u1_struct_0 B) D))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E (k3_vfunct_2 (u1_struct_0 B) A C D)) (k2_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D))) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E (k2_vfunct_1 (u1_struct_0 B) A C D)) (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r13_ncfcont1 B C A D) => (r1_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t25_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_partfun1 C (u1_struct_0 A)) & (v1_partfun1 D (u1_struct_0 A)))  =>  ((r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k6_vfunct_1 (u1_struct_0 A) B C D)) (k2_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E (k2_vfunct_1 (u1_struct_0 A) B C D)) (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_ndiff_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  &  ( ((k7_partfun1 (u1_struct_0 A) B k6_numbers) = (k4_struct_0 A))  & (r1_nfcont_3 A B k6_numbers)) ) ) ) ) ).
tt(t25_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_ndiff_3 (k4_real_ns1 A) B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  => (r1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) B (k4_pdiff_1 D A)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden E (k4_finseq_1 A)) & (r2_ndiff_5 A B E C D))  => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A))))) ) ) ) ) ) ) ) ) ).
tt(t25_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  ((v1_neckla_2 A) <=> (v1_neckla_2 (k3_necklace A))) ) ) ).
tt(t25_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (u1_struct_0 (k4_necklace A))) & (r2_hidden C (u1_struct_0 (k4_necklace A))))  =>  ( ( (~  (B = (k1_nat_1 C 1)) )  &  (~  (C = (k1_nat_1 B 1)) ) )  | (r2_hidden (k4_tarski B C) (u1_orders_2 (k4_necklace A)))) ) ) ) ) ) ) ) ).
tt(t25_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_net_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  =>  ((r2_hidden C (k12_net_1 A B)) <=>  (~  ( (~  ((r2_hidden C B) & (r2_hidden C (u1_struct_0 A))) )  &  (! [D:$i] :  ((m1_subset_1 D (k2_net_1 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden D (u4_struct_0 A)) & (r1_net_1 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (m2_subset_1 (k5_newton B A) k1_numbers k5_numbers)) ) ) ) ).
tt(t25_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r3_nfcont_1 B A D C) & (r3_nfcont_1 B A E C))  =>  ((r3_nfcont_1 B A (k6_vfunct_1 (u1_struct_0 B) A D E) C) & (r3_nfcont_1 B A (k2_vfunct_1 (u1_struct_0 B) A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) &  ((v1_rcomp_1 C) & (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 A) B C) A)) )  => (v1_nfcont_1 (k7_relset_1 k1_numbers (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t25_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (r1_tarski C B))  => (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D C) A)) ) ) ) ) ) ) ).
tt(t25_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) => (r1_xboole_0 (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B))) ) ) ).
tt(t25_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) & (v3_normsp_1 C A))  =>  ((k6_normsp_1 A (k2_normsp_1 A B C)) = (k3_rlvect_1 A (k6_normsp_1 A B) (k6_normsp_1 A C))) ) ) ) ) ) ) ) ).
tt(t25_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_normsp_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_normsp_2 A))) =>  ( ( (B = C)  &  (D = E) )  =>  ( ((v1_yellow_8 C (k4_normsp_2 A) E) &  ((v1_tops_2 C (k4_normsp_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))))) )  <=>  ((v1_yellow_8 B (k3_normsp_2 A) D) &  ((v1_tops_2 B (k3_normsp_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_numbers,ax, (~  (k4_numbers = k1_numbers) ) ).
tt(t25_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_openlatt A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_openlatt A))) =>  ( ((k3_lattices (k15_openlatt A) B C) = (k2_xboole_0 B C))  &  ((k4_lattices (k15_openlatt A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(t25_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_cat_1 B A) <=> (v10_cat_1 (k3_oppcat_1 A B) (k2_oppcat_1 A))) ) ) ) ) ).
tt(t25_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_orders_1 A) => (v1_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t25_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_orders_2 A (k1_struct_0 A) B) = k1_xboole_0) ) ) ) ) ).
tt(t25_ordinal1,ax, (! [A:$i] :  (~  (! [B:$i] :  ((r2_hidden B A) <=> (v3_ordinal1 B)) ) ) ) ).
tt(t25_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  ((r2_hidden A (k9_xtuple_0 B)) => (v3_ordinal1 (k1_funct_1 B A))) ) ) ) ) ).
tt(t25_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A B) =>  ((r2_hidden A (k10_ordinal2 B C)) & (r2_hidden A (k10_ordinal2 C B))) ) ) ) ) ) ) ) ).
tt(t25_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden 1 B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k12_ordinal2 B C)) ) ) ) )  => (v2_ordinal2 A)) ) ) ) ) ).
tt(t25_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((r2_hidden 1 A) &  ((r1_ordinal1 (k9_xtuple_0 B) k4_ordinal1) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 B C) = (k1_ordinal5 A C)) ) ) ) ) )  => (v2_ordinal2 B)) ) ) ) ) ).
tt(t25_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  (! [B:$i] :  ((v1_ordinal6 B) =>  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden C D)) ) )  =>  ((k2_ordinal6 (k2_xboole_0 A B)) = (k1_ordinal4 (k2_ordinal6 A) (k2_ordinal6 B))) ) ) ) ) ) ).
tt(t25_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t25_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B C E))  &  ( (~ (r1_orders_2 B F D))  &  ( (~ (r1_orders_2 B F E))  &  (~  ((k8_group_1 A (k1_ortsp_1 A B D F C) (k1_ortsp_1 A B C D E)) = (k8_group_1 A (k1_ortsp_1 A B F D E) (k1_ortsp_1 A B E F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (u3_msualg_1 A (k8_osafree A B)) C)) =>  ((k8_osalg_4 A (k8_osafree A B) (k20_osafree A B) C D) = (k9_xtuple_0 (k1_funct_1 (k19_osafree A B) D))) ) ) ) ) ) ) ) ) ).
tt(t25_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (l3_msualg_1 D A))  =>  ((r2_osalg_1 A (k1_msualg_1 A B) (k1_msualg_1 A C)) => (r1_tarski (k3_msualg_1 A B D) (k3_msualg_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t25_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((v2_relat_1 (k2_pboole (u1_struct_0 A) (k3_osalg_2 A B) C)) => (v2_relat_1 (k9_osalg_2 A B C))) ) ) ) ) ) ) ).
tt(t25_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_osalg_4 E A B)) )  =>  ( ((r1_msualg_3 A B C D) &  ((v1_osalg_3 D A) & (r2_pboole (u1_struct_0 A) E (k19_osalg_4 A B C D))) )  =>  ((r1_msualg_3 A (k16_osalg_4 A B E) C (k23_osalg_4 A B C D E)) & (v1_osalg_3 (k23_osalg_4 A B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (D = E) )  &  ( (~  ( (B = D)  &  (C = E) ) )  &  (~  ( (B = E)  &  (C = D) ) ) ) ) ) )  => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) & (r1_parsp_2 A B D E))  =>  ( (B = D)  | (r1_parsp_2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 D)) &  ((r2_hidden A B) & (r2_hidden (k1_funct_1 D A) C)) )  =>  ((k1_funct_1 (k3_partfun1 D B C) A) = (k1_funct_1 D A)) ) ) ) ) ) ) ).
tt(t25_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden C (k1_relset_1 A E)) & (r2_hidden D (k1_relset_1 A E)))  =>  ((k7_relset_1 A B E (k2_tarski C D)) = (k2_tarski (k7_partfun1 B E C) (k7_partfun1 B E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( ((k4_partit1 A B) = (k4_partit1 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t25_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r4_relat_2 B A) => (v4_relat_2 B)) ) ) ) ) ).
tt(t25_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_diraf A B C D E) &  ((r2_diraf A B D C E) &  ( (~ (r3_diraf A B C D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r3_diraf A F B E) & (r3_diraf A F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r6_pboole A (k2_pboole A B (k3_pboole A D C)) (k3_pboole A (k2_pboole A B D) C))) ) ) ) ) ) ) ) ).
tt(t25_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v8_pre_topc A) & (v2_pcomps_1 A))  => (v10_pre_topc A)) ) ) ).
tt(t25_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_pcs_0 A B))) =>  ( (~  (C = B) )  => (r2_hidden C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t25_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ((r7_pdiff_1 B A C E D) => (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t25_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r1_pdiff_3 B A) & (r1_pdiff_3 C A))  =>  ((r3_pdiff_1 2 1 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) &  ((k11_pdiff_1 2 1 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) = (k9_real_1 (k2_pdiff_3 B A) (k2_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t25_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 3) B)) =>  ( ((r3_pdiff_1 3 1 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 A B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k1_rvsum_1 E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 3) B)))  & (r1_tarski (k1_rvsum_1 (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 A B))))) &  ((k11_pdiff_1 3 1 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r7_pdiff_5 B A) <=> (r3_pdiff_1 3 1 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ).
tt(t25_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((r1_tarski (a_3_2_pdiff_6 A D E) (k1_relset_1 (k1_euclid A) C)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_euclid A) (k1_euclid B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k1_euclid A) (k1_euclid B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) )  &  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k1_euclid A) (k1_euclid B)) &  ((v1_pdiff_6 F B A) &  ((v2_pdiff_6 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B))))) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid A)) =>  (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid B)) =>  (~  ( (~  (J = (k5_euclid A)) )  &  ( (~ (r1_xxreal_0 I (k12_euclid J)))  &  ( (K = (k1_pdiff_6 A B G J))  & (r1_xxreal_0 H (k8_real_1 (k2_real_1 (k12_euclid J)) (k12_euclid K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  ( (~ (r1_xxreal_0 E (k12_euclid (k8_euclid A H D))))  =>  ((k8_euclid B (k7_partfun1 (k1_euclid B) C H) (k7_partfun1 (k1_euclid B) C D)) = (k7_euclid B (k1_pdiff_6 A B F (k8_euclid A H D)) (k1_pdiff_6 A B G (k8_euclid A H D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  ((r2_relset_1 k5_numbers (k1_euclid A) D (k9_integr15 A B k5_numbers C)) =>  ((k5_euclid_7 A D) = (k9_euclid A (k5_euclid_7 A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((v1_pdiff_7 E A) &  ((r1_tarski E (k1_relset_1 (k1_euclid A) C)) &  ( (D = C)  &  (E = F) ) ) )  =>  ( ( ((r2_ndiff_1 F (k4_real_ns1 A) (k4_real_ns1 B) D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) D F) F))  =>  ((r1_pdiff_6 E B A C) &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r2_hidden G E) &  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid A)) =>  ((r2_hidden J E) =>  ((r1_xxreal_0 I (k12_euclid (k8_euclid A J G))) |  (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k8_euclid B (k1_pdiff_6 A B (k8_pdiff_1 A B C J) K) (k1_pdiff_6 A B (k8_pdiff_1 A B C G) K))) (k11_binop_2 H (k12_euclid K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ((r1_pdiff_6 E B A C) &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r2_hidden G E) &  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid A)) =>  ((r2_hidden J E) =>  ((r1_xxreal_0 I (k12_euclid (k8_euclid A J G))) |  (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k8_euclid B (k1_pdiff_6 A B (k8_pdiff_1 A B C J) K) (k1_pdiff_6 A B (k8_pdiff_1 A B C G) K))) (k11_binop_2 H (k12_euclid K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_ndiff_1 F (k4_real_ns1 A) (k4_real_ns1 B) D) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) D F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((m1_subset_1 C (u1_struct_0 (k5_pencil_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_pencil_1 A B D))) => (m1_subset_1 (k2_funct_7 C D E) (u1_struct_0 (k5_pencil_1 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pencil_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ((m1_pencil_2 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 D (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  => (m1_pencil_2 (k8_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) D C) A B)) ) ) ) ) ) ) ) ) ).
tt(t25_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k3_funct_2 A A D E) = F)  <=>  (! [G:$i] :  ((m1_pencil_2 G A B) =>  (! [H:$i] :  ( ( (~ (v13_pencil_1 H))  &  ((v16_pencil_1 H A) & (m3_pboole H A (k12_pralg_1 A B))) )  =>  (! [I:$i] :  ( ( (~ (v13_pencil_1 I))  &  ((v16_pencil_1 I A) & (m3_pboole I A (k12_pralg_1 A B))) )  =>  ( ( (G = (k4_card_3 H))  &  ( ((k7_relset_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) C G) = (k4_card_3 I))  &  ((k3_pencil_1 A H) = E) ) )  =>  ((k3_pencil_1 A I) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 D (k1_vectsp_9 A B)) & (v3_pencil_1 (k7_pencil_4 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k1_newton A B) 1)) ) ) ) ) ) ) ).
tt(t25_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) &  ((r2_pnproc_1 A D E) & (r2_pnproc_1 A E B)) )  => (r2_pnproc_1 A (k3_pnproc_1 A B E) (k3_pnproc_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k3_polyeq_1 A k6_numbers B C) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (D = (k1_binop_2 (k6_binop_2 B A)))  &  ( (~  (C = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) k7_complex1))) )  &  ( (~  (C = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) k7_complex1))) )  &  ( (~  (C = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) k7_complex1))) )  &  (~  (C = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k6_power A C) = 1)  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  ((r1_xxreal_0 C k6_numbers) |  (C = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  (! [H:$i] :  ((v1_xcmplx_0 H) =>  (! [I:$i] :  ((v1_xcmplx_0 I) =>  ( ( (I = (k13_complex1 (k6_xcmplx_0 (k3_xcmplx_0 8 B) (k3_xcmplx_0 3 (k1_newton F 2))) 32))  &  ( (G = (k13_complex1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 8 C) (k3_xcmplx_0 (k3_xcmplx_0 4 B) F)) (k1_newton F 3)) 64))  &  ( (G = k6_numbers)  &  ( (H = (k13_complex1 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 256 D) (k3_xcmplx_0 (k3_xcmplx_0 64 F) C)) (k3_xcmplx_0 (k3_xcmplx_0 16 (k1_newton F 2)) B)) (k3_xcmplx_0 3 (k1_newton F 4))) 1024))  &  (E = (k1_polyeq_5 2 (k6_xcmplx_0 (k1_newton I 2) H))) ) ) ) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 F (k1_newton A 3))) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k6_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k6_xcmplx_0 I E)))) (k13_complex1 F 4))) )  &  ( (~  (A = (k6_xcmplx_0 (k4_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k6_xcmplx_0 I E))))) (k13_complex1 F 4))) )  &  ( (~  (A = (k6_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k2_xcmplx_0 I E)))) (k13_complex1 F 4))) )  &  (~  (A = (k6_xcmplx_0 (k4_xcmplx_0 (k1_polyeq_5 2 (k4_xcmplx_0 (k3_xcmplx_0 2 (k2_xcmplx_0 I E))))) (k13_complex1 F 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (v1_xboole_0 (k8_polyform A B)))  <=>  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B (k7_polyform A))) ) ) ) ) ) ).
tt(t25_polynom1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_vectsp_1 B) & (l5_algstr_0 B)) )  =>  ( ((k3_polynom1 A B (k8_polynom1 A B) (k16_pre_poly A)) = (k5_struct_0 B))  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (~  (C = (k16_pre_poly A)) )  =>  ((k3_polynom1 A B (k8_polynom1 A B) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t25_polynom2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B C D) E) = (k8_group_1 B (k5_polynom2 A B C E) (k5_polynom2 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r1_tarski (k2_algseq_1 A (k2_normsp_1 A B C)) (k4_subset_1 k5_numbers (k2_algseq_1 A B) (k2_algseq_1 A C)))) ) ) ) ) ) ).
tt(t25_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k3_polynom5 A B C)) = (k1_algseq_1 A B)) ) ) ) ) ) ) ) ).
tt(t25_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k4_polynom7 A B C) D) = C) ) ) ) ) ) ) ) ) ).
tt(t25_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k3_polynom8 A (k11_algstr_0 A B) C) = (k11_algstr_0 A (k3_polynom8 A B C))) ) ) ) ) ) ) ) ).
tt(t25_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_polyred A B C D D)) ) ) ) ) ) ) ) ).
tt(t25_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_power A 1) = A) ) ) ).
tt(t25_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_pralg_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) & (v1_funcop_1 G)) ) ) )  =>  ( (! [H:$i] :  ((m1_subset_1 H A) =>  (? [I:$i] :  ((m2_pboole I (u1_struct_0 B) (u3_msualg_1 B F) (u3_msualg_1 B (k5_pralg_2 A B D H))) &  ( (I = (k1_funct_1 G H))  & (r1_msualg_3 B F (k5_pralg_2 A B D H) I)) ) ) ) )  =>  ((r2_hidden G (k1_funct_2 A (k1_funct_2 (u1_struct_0 B) (a_3_2_pralg_3 A B G)))) &  ((k1_funct_1 (k1_funct_1 (k10_funct_6 G) E) C) = (k1_funct_1 (k1_funct_1 G C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_prelamb A (k2_prelamb A B C) (k2_prelamb A B (k1_prelamb A (k2_prelamb A B C) B)))) ) ) ) ) ) ).
tt(t25_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k1_card_3 (k7_finseq_1 A B)) = (k7_finseq_1 (k1_card_3 A) (k1_card_3 B))) ) ) ) ) ).
tt(t25_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 1 C)) )  =>  ((k2_prepower B (k2_prepower C A)) = (k2_prepower (k4_nat_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t25_pre_topc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t25_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ( ((v5_relat_1 B C) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (m1_prob_1 (k8_nat_1 (k9_setfam_1 A) B D) A C)) ) ) ) ) ) ) ) ).
tt(t25_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_prob_2 A B E C D) => (r1_prob_2 A B E C (k7_prob_1 A B (k4_prob_1 A B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E D) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  ((r2_hidden C (k1_funct_1 (k1_prob_3 B E) A)) <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 F A) => (r2_hidden C (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  (! [F:$i] :  ((m1_prob_4 F A B C) =>  (! [G:$i] :  ((m1_prob_4 G A B C) =>  ( ((k2_xboole_0 D F) = (k2_xboole_0 E G))  =>  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A (k9_cqc_lang A B C) D) (k9_cqc_lang A B (k9_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t25_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r1_incsp_1 A B D) =>  ( (D = E)  |  ((r1_incsp_1 A C D) |  ( (B = (k2_projpl_1 A D E))  |  ((r1_incsp_1 A (k2_projpl_1 A (k1_projpl_1 A C B) E) E) &  (~ (r1_incsp_1 A (k2_projpl_1 A (k1_projpl_1 A C B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B E))  &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ( (~ (r1_incsp_1 A C G))  &  ((r1_incsp_1 A D E) &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A D G) &  ( (~  (E = G) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A H E))  &  ( (~ (r1_incsp_1 A H G))  &  ((k3_relat_1 (k1_projred1 A E F B) (k1_projred1 A F G C)) = (k1_projred1 A E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k17_euclid (k10_pscomp_1 A)) = (k17_euclid (k11_pscomp_1 A))) ) ) ).
tt(t25_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  => (m3_pua2mss1 (k8_eqrel_1 (u1_struct_0 A) (k9_pua2mss1 A)) A)) ) ).
tt(t25_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C)) => (r6_pboole A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C))) ) ) ) ) ) ).
tt(t25_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  ((r2_qc_lang1 A B C) <=>  (~ (r1_qc_lang1 A C B)) ) ) ) ) ) ) ) ).
tt(t25_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k9_qc_lang2 A B C D E) = (k5_qc_lang2 A G F))  =>  ( (B = G)  &  ((k7_qc_lang2 A C D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((v6_qc_lang1 B A) & (v6_qc_lang1 C A))  <=> (v6_qc_lang1 (k3_qc_lang2 A B C) A)) ) ) ) ) ) ) ).
tt(t25_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((v4_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) A) =>  ((r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)) (k9_xtuple_0 (k2_qc_lang4 A B))) &  ( ((k1_funct_1 (k2_qc_lang4 A B) (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers))) = (k19_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C)))  &  ((r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)) (k9_xtuple_0 (k2_qc_lang4 A B))) &  ((k1_funct_1 (k2_qc_lang4 A B) (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1))) = (k20_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((k5_quantal1 A (k16_lattice3 A B)) = (k15_lattice3 A (a_2_0_quantal1 A B))) ) ) ) ).
tt(t25_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k31_quaterni (k6_quaterni A B C D)) = (k6_quaterni A (k1_real_1 B) (k1_real_1 C) (k1_real_1 D))) ) ) ) ) ) ) ) ) ).
tt(t25_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k18_quaterni (k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A))) = (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k18_quaterni A)))) ) ) ).
tt(t25_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ( ((k17_quaterni A) = (k17_quaterni B))  &  ( ((k18_quaterni A) = (k18_quaterni B))  &  ( ((k19_quaterni A) = (k19_quaterni B))  &  ((k20_quaterni A) = (k20_quaterni B)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t25_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  & (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) ) ) ) ) ) ) ) ) ).
tt(t25_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k5_binop_1 (k7_quofield A) (k16_quofield A) B (k12_quofield A)) = B)  &  ((k5_binop_1 (k7_quofield A) (k16_quofield A) (k12_quofield A) B) = B) ) ) ) ) ) ).
tt(t25_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 2 A) &  ((r1_radix_1 1 B A) & (r1_radix_1 1 C A)) )  =>  ((k8_radix_1 1 A (k14_radix_1 1 A (k10_radix_1 A 1 B) (k10_radix_1 A 1 C))) = (k12_radix_1 (k2_xcmplx_0 B C) A)) ) ) ) ) ) ) ) ).
tt(t25_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_random_1 C A B) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 k6_numbers D) => (m1_random_1 (k2_mesfun6c D A (k7_random_1 A B C)) A B)) ) ) ) ) ) ) ) ) ).
tt(t25_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E D) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k6_ranknull A B C D) E) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k4_xcmplx_0 (k2_rat_1 A)) = (k1_rat_1 A))  <=>  (A = (k1_real_1 1)) ) ) ) ).
tt(t25_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  &  ((v5_ratfunc1 B A) & (m1_ratfunc1 B A)) )  =>  ((k11_ratfunc1 A B) = (k6_ratfunc1 A B)) ) ) ) ) ).
tt(t25_rcomp_3,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((v3_xxreal_2 A) & (r2_hidden (k5_seq_4 A) A))  =>  ((v4_xxreal_2 A) |  (A = (k2_limfunc1 (k5_seq_4 A))) ) ) ) ) ).
tt(t25_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((v7_ordinal1 C) &  ( ((k1_seq_1 (k2_real_3 A B) C) = k6_numbers)  &  ((k1_seq_1 (k1_real_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t25_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  ( ((k1_binop_1 (k4_real_lat A) (k1_binop_1 (k5_real_lat A) B C) C) = C)  &  ( ((k1_binop_1 (k4_real_lat A) C (k1_binop_1 (k5_real_lat A) B C)) = C)  &  ( ((k1_binop_1 (k4_real_lat A) C (k1_binop_1 (k5_real_lat A) C B)) = C)  &  ((k1_binop_1 (k4_real_lat A) (k1_binop_1 (k5_real_lat A) C B) C) = C) ) ) ) ) ) ) ) ) ) ).
tt(t25_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t25_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k8_struct_0 A)) =>  ( ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) B D) = (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) C E))  <=>  ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B E) = (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k20_rfunct_3 B (k4_rearran1 A B D C) B) = (k20_rfunct_3 A C A)) ) ) ) ) ) ) ) ) ) ).
tt(t25_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k3_relat_1 A B)) (k9_xtuple_0 A))) ) ) ) ).
tt(t25_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  (! [D:$i] :  ((r2_hidden D (k2_relset_1 A C)) <=>  (? [E:$i] :  ((m1_subset_1 E B) & (r2_hidden (k4_tarski E D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((r2_hidden D (k6_relset_2 B A C E)) <=>  (! [F:$i] :  ((r2_hidden F C) => (r2_hidden D (k1_relset_2 B A E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 C)) & (r1_xxreal_0 (k4_finseq_4 C B) A))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((k2_topreal1 2 C A) = (k2_topreal1 2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) C B) (k2_nat_1 (k7_nat_d A (k4_finseq_4 C B)) 1))) ) ) ) ) ) ) ) ) ).
tt(t25_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) =>  ((r2_rewrite1 A B C) & (r2_rewrite1 A C B)) ) ) ) ) ) ).
tt(t25_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  ( ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))))  => (r2_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A B) (k3_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A B)))) ) ) ) ).
tt(t25_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [H:$i] :  ((l1_rewrite3 H G) =>  ((r2_rewrite3 C G H A D B E) => (r2_rewrite3 C G H A (k1_flang_1 C D F) B (k1_flang_1 C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((v1_integra2 A) => (v8_valued_0 (k6_rvsum_1 A))) ) ) ).
tt(t25_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k8_relset_1 k5_numbers k1_numbers (k10_rvsum_1 A k6_numbers) (k1_tarski k6_numbers)) = (k4_finseq_1 A)) ) ) ).
tt(t25_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k54_valued_1 (k24_valued_1 A B)) = (k24_valued_1 (k54_valued_1 A) (k18_complex1 B))) ) ) ) ) ).
tt(t25_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) &  ((r2_hidden D (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers B))) & (r1_xxreal_0 C D)) )  => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t25_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) =>  ((r2_classes1 B C) => (r2_relset_1 A k1_numbers (k14_rfunct_3 A B) (k14_rfunct_3 A C))) ) ) ) ) ) ) ).
tt(t25_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_rfunct_4 B A) => (r3_rfunct_4 B A)) ) ) ) ).
tt(t25_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 A) & (v2_seq_2 A))  =>  ((k2_seq_2 A) = (k2_rinfsup1 A)) ) ) ) ).
tt(t25_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v8_valued_0 B) =>  ((v8_valued_0 (k1_valued_0 k7_numbers B A)) &  ((k2_rinfsup2 B) = (k2_rinfsup2 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ).
tt(t25_ringcat1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k17_ringcat1 A))) =>  (! [C:$i] :  ((m2_ringcat1 C (k9_ringcat1 A)) =>  ( (B = C)  =>  ((k4_cat_1 (k17_ringcat1 A) B) = (k13_ringcat1 (k9_ringcat1 A) C)) ) ) ) ) ) ) ) ).
tt(t25_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_rlvect_2 D C) => (r1_rlvect_2 C (k8_rlvect_2 C A (k2_rlaffin1 C D B)) (k2_rlaffin1 C (k8_rlvect_2 C A D) B))) ) ) ) ) ) ) ) ).
tt(t25_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rlvect_2 E C) =>  (! [F:$i] :  ((m1_rlvect_2 F C) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_xxreal_0 (k3_funct_2 (u1_struct_0 C) k1_numbers (k7_rlvect_2 C (k8_rlvect_2 C A E) (k8_rlvect_2 C (k9_real_1 1 A) F)) D) G) &  ((r1_xxreal_0 G (k3_funct_2 (u1_struct_0 C) k1_numbers (k7_rlvect_2 C (k8_rlvect_2 C B E) (k8_rlvect_2 C (k9_real_1 1 B) F)) D)) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( ((k3_funct_2 (u1_struct_0 C) k1_numbers (k7_rlvect_2 C (k8_rlvect_2 C H E) (k8_rlvect_2 C (k9_real_1 1 H) F)) D) = G)  &  ( ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 A H) & (r1_xxreal_0 H B)) )  &  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 B H) & (r1_xxreal_0 H A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [E:$i] :  ((m2_rlaffin3 E (k15_euclid A) C) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r1_xxreal_0 B A) &  ( ((k5_card_1 C) = (k23_binop_2 A 1))  &  (F = (a_5_0_rlaffin3 A B C D E)) ) )  =>  ((v3_pre_topc D (k15_euclid B)) <=> (v3_pre_topc F (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (m1_rlsub_1 A A)) ) ).
tt(t25_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) => (m1_rlsub_1 (k1_rlsub_2 A (k2_rlsub_2 A B C) (k2_rlsub_2 A C D)) (k2_rlsub_2 A C (k1_rlsub_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t25_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t25_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_rlvect_1 B (k4_algstr_0 B C) A) = (k4_algstr_0 B (k1_rlvect_1 B C A))) ) ) ) ) ) ) ).
tt(t25_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r2_relset_1 k5_numbers (u1_struct_0 A) (k5_rlvect_2 A (k2_pre_poly (u1_struct_0 A)) B) (k2_pre_poly (u1_struct_0 A)))) ) ) ) ).
tt(t25_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rlvect_3 A B) = A)  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) &  ((v1_rlvect_3 C A) &  ((k1_rlvect_3 A C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C (k3_rlvect_1 A D B)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) =>  (! [B:$i] :  ((m1_rlvect_3 B A) =>  (! [C:$i] :  ((m1_rlvect_3 C A) =>  ((k1_card_1 B) = (k1_card_1 C)) ) ) ) ) ) ) ) ).
tt(t25_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (k2_rlvect_x A B)) <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v5_relat_1 F k4_numbers) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) )  &  ( (C = (k4_rlvect_1 A E))  &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) B) &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 F))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k3_finseq_1 D))) =>  ((k7_partfun1 (u1_struct_0 A) E G) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) D G) (k1_seq_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_vectsp_2 C A) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) ) )  =>  ( ((m1_rmod_2 C A B) & (m1_rmod_2 B A C))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t25_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ((k1_rmod_3 A B (k2_rmod_3 A B C D) D) = D) ) ) ) ) ) ) ) ) ).
tt(t25_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k4_rmod_4 A B (k12_finseq_1 (u1_struct_0 B) C) D) = (k12_finseq_1 (u1_struct_0 B) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C))) ) ) ) ) ) ) ) ) ).
tt(t25_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k6_robbins1 A (k6_robbins1 A B D) (k6_robbins1 A C (k3_robbins1 A D))) = (k7_robbins1 A))  &  ( ((k6_robbins1 A (k6_robbins1 A (k6_robbins1 A B C) D) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) D)) = (k7_robbins1 A))  &  ( ((k6_robbins1 A (k6_robbins1 A (k6_robbins1 A B (k3_robbins1 A C)) D) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) D)) = (k7_robbins1 A))  &  ( ((k6_robbins1 A (k6_robbins1 A (k6_robbins1 A B C) D) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) D)) = (k7_robbins1 A))  &  ((k6_robbins1 A (k6_robbins1 A (k6_robbins1 A B C) (k3_robbins1 A D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) (k3_robbins1 A D))) = (k7_robbins1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A (k1_lattices A B C))) = (k1_lattices A C B)) ) ) ) ) ) ) ).
tt(t25_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v10_robbins3 A) & (l4_robbins3 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_lattice3 A B C) = (k5_robbins3 A B C)) ) ) ) ) ) ) ).
tt(t25_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( (A = k6_numbers)  =>  ((k4_lattices k2_robbins4 A B) = A) ) ) ) ) ) ).
tt(t25_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k4_roughs_1 A B) (k4_roughs_1 A C))) ) ) ) ) ) ) ).
tt(t25_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r1_xxreal_0 (k1_rpr_1 A (k4_subset_1 A B C)) (k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C)))) ) ) ) ) ) ).
tt(t25_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_lopban_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k9_rsspace4 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k9_rsspace4 A B)))))) )  =>  ((v1_rsspace3 C (k9_rsspace4 A B)) => (v3_normsp_1 C (k9_rsspace4 A B))) ) ) ) ) ) ) ) ).
tt(t25_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t25_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) => (m1_rusub_1 (k1_rusub_2 A (k2_rusub_2 A B C) (k2_rusub_2 A C D)) (k2_rusub_2 A C (k1_rusub_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t25_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (D = (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C)))  & (r1_struct_0 (k1_rusub_3 A D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k4_struct_0 A) B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden C B) => (r2_hidden (k1_rlvect_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski B (u1_struct_0 (k2_rusub_5 A (k3_rusub_5 A B))))) ) ) ) ).
tt(t25_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 A k1_numbers)) =>  ( ((k5_rvsum_1 A B C) = (k5_rvsum_1 A D C))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t25_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k11_rvsum_2 (k6_finseq_1 k2_numbers) A) = (k6_finseq_1 k2_numbers)) ) ) ).
tt(t25_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 8)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) A))) = (k1_tarski 1)) ) ) ) ).
tt(t25_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k2_scmfsa_1) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_scmfsa_1 k2_scmfsa_1) =>  ( (~  (D = B) )  =>  ((k1_funct_1 (k7_scmfsa_1 A B C) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k13_scmfsa_2 A B)) = 8) ) ) ) ) ).
tt(t25_scmfsa6a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmfsa6a (k3_scmfsa6a A B) C) = (k3_scmfsa6a A (k3_scmfsa6a B C))) ) ) ) ) ) ) ).
tt(t25_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k3_scmfsa6a (k2_scmfsa6a A) B) = (k3_scmfsa6a A B)) ) ) ) ) ).
tt(t25_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) |  ((r5_scmfsa7b (k3_scmfsa8b E C D) B A) & (r6_scmfsa7b (k3_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k2_afinsq_1 (k1_scmfsa8b A B C))) &  ((r2_hidden 1 (k2_afinsq_1 (k1_scmfsa8b A B C))) &  ((r2_hidden k6_numbers (k2_afinsq_1 (k2_scmfsa8b A B C))) & (r2_hidden 1 (k2_afinsq_1 (k2_scmfsa8b A B C)))) ) ) ) ) ) ) ) ) ).
tt(t25_scmfsa9a,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k2_scmfsa_9 A B)) = (k4_sf_mastr B)) ) ) ) ) ).
tt(t25_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) (k2_nat_1 k6_numbers 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k1_scmfsa_9 C B)) B) (k8_memstr_0 3 k1_scmfsa_2 D)) 3)))) ) ) ) ) ) ) ) ).
tt(t25_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~ (r2_hidden (k9_scmfsa_m A B) B)) ) ) ) ) ).
tt(t25_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r1_scm_halt A B C)) ) ) ) ) ) ) ).
tt(t25_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa_9 E C) B A) D) = (k1_funct_1 (k1_scmfsa_m B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmpds_2) (k16_scmpds_2 C D A B)) = 13) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k5_card_1 A) C)) => (v3_scmpds_4 (k3_scmpds_4 A (k8_scmpds_2 D B C)))) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_tarski C A) & (r1_xxreal_0 D (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)))  =>  ((k5_extpro_1 2 k1_scmpds_2 A B D) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)) =>  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B E)) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B E))) ) ) )  &  ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_tarski C D) &  ((r1_scmpds_6 C A B) & (r2_scmpds_6 C A B)) )  =>  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B D) (k8_memstr_0 2 k1_scmpds_2 A) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)))) = (k5_card_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  =>  ( ( (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_recdef_1 I J) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers)) ) )  &  ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 B J))) ) )  &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 J) &  ((v5_funct_1 J (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 J (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 J 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K k5_numbers) &  ((v5_relat_1 K (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 K) & (v1_partfun1 K k5_numbers)) ) ) )  =>  ( ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 J L))) ) )  &  ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L H) =>  ((k1_funct_1 J L) = (k1_funct_1 B L)) ) ) )  &  ((k1_funct_1 J D) = (k1_funct_1 B D)) ) )  =>  ((r1_xxreal_0 (k1_funct_1 J (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C J K) D) = (k1_funct_1 J D))  &  ((r1_scmpds_6 C J K) &  ((r2_scmpds_6 C J K) &  ( (~ (r1_xxreal_0 (k1_recdef_1 I J) (k1_recdef_1 I (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C J K)))))  &  ( (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 (k6_scmpds_4 C J K) (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 (k6_scmpds_4 C J K) L))) ) )  &  (! [L:$i] :  ( ((v1_ami_2 L) & (m1_subset_1 L (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden L H) =>  ((k1_funct_1 (k6_scmpds_4 C J K) L) = (k1_funct_1 J L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ((k6_scmpds_4 (k2_scmpds_8 D E C) B A) = (k6_scmpds_4 (k2_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k6_subset_1 (u1_struct_0 (k1_scmring2 A)) (k1_tarski k5_numbers)) = k2_ami_2) ) ) ).
tt(t25_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 5)  =>  ((k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t25_scmyciel,ax, (! [A:$i] : (v4_scmyciel (k2_tarski k1_xboole_0 (k1_tarski A)))) ).
tt(t25_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_semi_af1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers B C) A) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A) C))) ) ) ) ) ) ).
tt(t25_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k2_seq_2 A) = k6_numbers) ) )  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t25_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v3_funct_1 B) =>  ( ( (~ (r2_hidden A (k1_rvsum_1 B)))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k8_nat_1 k1_numbers B C) = A) ) ) ) )  |  ((k2_seq_2 B) = A) ) ) ) ) ) ) ).
tt(t25_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C D) & (r3_seqfunc A B D))  =>  ( (C = k1_xboole_0)  | (r3_seqfunc A B C)) ) ) ) ) ) ) ) ).
tt(t25_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 A) & (m2_valued_0 B k1_numbers A))  => (v8_valued_0 B)) ) ) ) ) ).
tt(t25_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers B (k2_nat_1 C 1)) = (k4_real_1 A (k3_funct_2 k5_numbers k1_numbers B C))) ) )  =>  ((r1_xxreal_0 1 (k18_complex1 A)) |  ((v1_series_1 B) &  ((k4_series_1 B) = (k10_real_1 (k3_funct_2 k5_numbers k1_numbers B k6_numbers) (k9_real_1 1 A))) ) ) ) ) ) ) ) ).
tt(t25_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 1 (k3_xcmplx_0 (k6_xcmplx_0 B 1) (k2_nat_1 B 1))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 2 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k11_complex1 (k13_complex1 3 4) (k13_complex1 1 (k4_nat_1 2 B))) (k13_complex1 1 (k4_nat_1 2 (k2_nat_1 B 1))))) ) ) ) ) ) ) ).
tt(t25_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A (k18_complex1 B)) => (r1_xxreal_0 (k3_square_1 A) (k3_square_1 B))) ) ) ) ) ).
tt(t25_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k7_xcmplx_0 (k2_nat_1 C 1) (k2_nat_1 C 2))) ) )  =>  ((k1_seq_1 (k1_series_3 B) A) = (k7_xcmplx_0 1 (k2_nat_1 A 2))) ) ) ) ) ) ).
tt(t25_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_square_1 A) B) (k3_xcmplx_0 (k3_square_1 B) C)) (k3_xcmplx_0 (k3_square_1 C) A)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 B)) (k3_xcmplx_0 B (k3_square_1 C))) (k3_xcmplx_0 C (k3_square_1 A))))) ) ) ) ) ) ) ) ) ).
tt(t25_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_xboole_0 A (k3_tarski B)) = (k3_tarski (k3_setfam_1 (k1_tarski A) B))) ) ) ).
tt(t25_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 (k2_setlim_1 A B) A) & (v1_setlim_1 (k4_setlim_1 A B) A)) ) ) ) ).
tt(t25_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 C) => (v3_prob_1 (k6_setlim_2 A C B))) ) ) ) ) ) ).
tt(t25_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 C B) &  ((v2_binop_1 C B) & (v3_binop_1 C B)) )  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ( ((k7_relset_1 A B E D) = (k1_tarski F))  =>  ((k7_setwiseo A B C D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_setwiseo B A) =>  ((k1_finsop_1 A (k5_finseq_2 A C (k4_binop_1 A B)) B) = (k4_binop_1 A B)) ) ) ) ) ) ) ) ).
tt(t25_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 A C) k6_numbers) =>  ((k1_funct_1 (k1_scmfsa6b (k4_sfmastr2 C) A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t25_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 G) & (v1_partfun1 G k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  &  (F = (k2_xcmplx_0 (k6_xcmplx_0 (k1_funct_1 A C) (k1_funct_1 A D)) 1)) )  =>  ( ( (~ (r1_sfmastr3 G B D C E A))  &  (~ (v7_amistd_1 E 3 k1_scmfsa_2)) )  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_sfmastr3 B D C E) A G)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k1_sfmastr3 G B D C E A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_sf_mastr A) = (k2_sf_mastr (k6_compos_1 k1_scmfsa_2 A B))) ) ) ) ) ).
tt(t25_sgraph1,ax, (! [A:$i] : (r2_sgraph1 A (k3_sgraph1 A))) ).
tt(t25_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  <=>  ((v2_sheffer1 A) &  ((v1_sheffer1 A) &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v3_sheffer1 A) & (v4_sheffer1 A)) ) ) ) ) ) ) ) ) ).
tt(t25_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A C B)) = B) ) ) ) ) ) ) ) ) ).
tt(t25_simplex0,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( (~  ((v3_pencil_1 B) &  (~ (r1_xxreal_0 (k2_xxreal_3 1) A)) ) )  =>  ((r1_xxreal_0 (k6_simplex0 B) A) <=>  ((v3_matroid0 B) &  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v3_pre_topc C B) => (r1_xxreal_0 (k5_card_1 C) (k1_xxreal_3 A 1))) ) ) ) ) ) ) ) ) ) ).
tt(t25_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matroid0 B) & (m1_simplex0 B (u1_struct_0 A)))  =>  ((v2_simplex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C B) & (v3_pre_topc D B))  =>  ((r1_xboole_0 (k1_rlaffin2 A (k1_simplex1 A B C)) (k1_rlaffin2 A (k1_simplex1 A B D))) |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k5_card_1 B) = (k3_real_1 A 1))  =>  ((k2_topdim_1 (k15_euclid A) (k3_convex1 (k15_euclid A) B)) = A) ) ) ) ) ) ).
tt(t25_sincos10,ax, ((k2_relset_1 k1_numbers k1_sincos10) = (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) ).
tt(t25_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_real_1 (k5_square_1 (k1_seq_1 k1_sin_cos2 A)) (k5_square_1 (k1_seq_1 k4_sin_cos2 B))) = (k8_real_1 (k1_seq_1 k4_sin_cos2 (k9_binop_2 A B)) (k1_seq_1 k4_sin_cos2 (k10_binop_2 A B))))  &  ( ((k8_real_1 (k1_seq_1 k4_sin_cos2 (k9_binop_2 A B)) (k1_seq_1 k4_sin_cos2 (k10_binop_2 A B))) = (k7_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) (k5_square_1 (k1_seq_1 k1_sin_cos2 B))))  &  ((k7_real_1 (k5_square_1 (k1_seq_1 k1_sin_cos2 A)) (k5_square_1 (k1_seq_1 k4_sin_cos2 B))) = (k7_real_1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)) (k5_square_1 (k1_seq_1 k1_sin_cos2 B)))) ) ) ) ) ) ) ).
tt(t25_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k15_sin_cos A) = (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A))) ) ) ).
tt(t25_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos B)))) ) ) ) ) ).
tt(t25_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_newton (k20_sin_cos A) 4) = (k10_real_1 (k7_real_1 (k7_real_1 3 (k8_real_1 4 (k21_sin_cos (k8_real_1 2 A)))) (k21_sin_cos (k8_real_1 4 A))) 8)) ) ) ).
tt(t25_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k20_sin_cos A) = (k1_real_1 1))  =>  (A = (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k6_real_1 A (k8_real_1 2 k32_sin_cos)))))) ) ) ) ).
tt(t25_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k10_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))) k6_numbers)) ) ) ) ).
tt(t25_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k3_sin_cos2 (k7_xcmplx_0 A 2)) = (k4_xcmplx_0 (k6_square_1 (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) 1) 2)))) ) ) ) ).
tt(t25_sin_cos9,ax, ((k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))))) ).
tt(t25_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k15_sin_cos (k3_xcmplx_0 A k7_complex1)) = (k2_xcmplx_0 (k21_sin_cos A) (k3_xcmplx_0 (k18_sin_cos A) k7_complex1))) ) ) ).
tt(t25_sppol_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) => (m1_subset_1 (a_1_1_sppol_1 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(t25_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden B (k2_topreal1 2 A C)) =>  ((k3_topreal1 2 A) = (k3_topreal1 2 (k5_finseq_5 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ) ).
tt(t25_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)) = (a_1_2_sprect_1 A)) ) ) ).
tt(t25_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r1_sprect_2 A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(t25_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_subset_1 (k3_goboard9 A) (k3_topreal1 2 A))) ) ).
tt(t25_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k21_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t25_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k6_square_1 A) k6_numbers)) ) ) ) ).
tt(t25_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k11_stacks_1 A B) = (a_2_0_stacks_1 A B)) ) ) ) ) ).
tt(t25_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (m1_subset_1 (k1_card_1 (a_2_0_stirl2_1 A B)) k5_numbers)) ) ) ) ).
tt(t25_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ( ( ((k19_substut1 A D) = (k19_substut1 A E))  &  ( (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A D) C F) <=> (r1_sublemma A D B (k1_sublemma A B F (k3_sublemma A D B F)) C)) ) )  &  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A E) C F) <=> (r1_sublemma A E B (k1_sublemma A B F (k3_sublemma A E B F)) C)) ) ) ) )  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A (k6_sublemma A D E)) C F) <=> (r1_sublemma A (k6_sublemma A D E) B (k1_sublemma A B F (k3_sublemma A (k6_sublemma A D E) B F)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((r1_xboole_0 B C) & (r1_xboole_0 (k3_subset_1 A B) (k3_subset_1 A C)))  =>  (B = (k3_subset_1 A C)) ) ) ) ) ) ) ).
tt(t25_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ((k3_substlat A B (k4_substlat A B C C)) = C) ) ) ) ) ).
tt(t25_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ( ((v2_substut1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = k6_numbers) )  &  ( (~  ((v4_substut1 B A) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (m2_subset_1 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1) (k6_qc_lang1 A) (k8_qc_lang1 A C))) ) ) ) )  &  ( ((v5_substut1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 1) )  &  ( ((v6_substut1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 2) )  &  ((v7_substut1 B A) =>  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t25_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  ((k7_cqc_sim1 A B) = (k7_cqc_sim1 A (k39_substut1 A (k2_substut2 A B C)))) ) ) ) ) ) ) ).
tt(t25_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_xxreal_0 k2_supinf_1 (k12_supinf_2 C D)) & (r1_xxreal_0 (k12_supinf_2 C D) k1_supinf_1)) ) ) ) ) ) ) ) ) ).
tt(t25_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k1_symsp_1 A B D C E) = (k11_algstr_0 A (k1_symsp_1 A B D E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden (k4_tarski A B) (k1_sysrel C)) =>  ((r2_hidden A (k9_xtuple_0 (k1_sysrel C))) &  (A = B) ) ) ) ) ) ) ).
tt(t25_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((r2_relset_1 A A C (k13_lang1 A (k1_taxonom1 A B k6_numbers))) &  ((v1_taxonom1 B A) &  ((v2_metric_1 B A) & (v3_metric_1 B A)) ) )  =>  ((k8_eqrel_1 A C) = (k10_eqrel_1 A)) ) ) ) ) ) ) ) ).
tt(t25_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E))) )  =>  ((r1_xxreal_0 E D) |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers G) = (k2_subset_1 k1_numbers))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k1_seq_1 G H) = (k9_real_1 (k9_real_1 (k1_seq_1 B E) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C H E)) A)) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 E H) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) )  &  ((k9_real_1 (k9_real_1 (k1_seq_1 B E) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C D E)) A)) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 E D) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1)))) = k6_numbers) ) )  =>  ((r2_fdiff_1 G (k2_rcomp_1 D E)) &  ( ((k1_seq_1 G D) = k6_numbers)  &  ( ((k1_seq_1 G E) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers G (k1_rcomp_1 D E))) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 G H) = (k7_real_1 (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) H) (k2_newton (k9_real_1 E H) A)) (k3_newton A))) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 E H) A)) (k3_newton A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( ((k1_seq_1 (k3_series_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) (k2_nat_1 (k4_nat_1 2 C) 1)) = (k1_seq_1 (k3_series_1 (k22_sin_cos B)) C))  &  ((k1_seq_1 (k3_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) (k2_nat_1 (k4_nat_1 2 C) 1)) = (k1_seq_1 (k3_series_1 (k23_sin_cos B)) C)) ) ) ) ) ) ) ) ) ).
tt(t25_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tbsp_1 B A) & (v6_tbsp_1 C A))  =>  ((r1_xboole_0 B C) | (r1_xxreal_0 (k3_tbsp_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k7_real_1 (k3_tbsp_1 A B) (k3_tbsp_1 A C)))) ) ) ) ) ) ) ) ).
tt(t25_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) => (v6_tops_1 (k1_tops_1 A B) A)) ) ) ) ) ).
tt(t25_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((r1_tarski (k1_tops_1 A C) (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B))) & (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k1_tops_1 A C))) ) ) ) ) ) ) ) ).
tt(t25_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k1_tarski C))  => (v3_pre_topc (k2_pre_topc A B) A)) ) ) ) )  => (v3_tdlat_3 A)) ) ) ).
tt(t25_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((r6_pboole A (k3_termord A B C (k4_polynom7 A C D)) (k16_pre_poly A)) &  ((k4_termord A B C (k4_polynom7 A C D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t25_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 (k3_tex_1 A B)) (u1_pre_topc (k3_tex_1 A B))))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((r1_tarski D (k6_subset_1 A (k6_domain_1 A B))) => (v3_pre_topc D C))  &  ((v3_pre_topc D C) =>  ( (D = A)  | (r1_tarski D (k6_subset_1 A (k6_domain_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v4_pre_topc C A))  =>  ((v4_pre_topc (k9_subset_1 (u1_struct_0 A) B C) A) & (v4_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((v2_tex_2 B A) & (v2_tex_2 C A)) ) )  => (v2_tex_2 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t25_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ((v1_tex_3 B A) | (v1_tex_3 C A))  =>  ((v1_tex_3 (k1_tsep_1 A B C) A) & (m1_pre_topc (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t25_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k2_tex_4 A B) (k1_setfam_1 (a_2_4_tex_4 A B)))) ) ) ) ).
tt(t25_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( ((m1_pre_topc B D) & (m1_pre_topc C D))  =>  ((r1_tsep_1 B C) | (m1_pre_topc (k2_tsep_1 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B (k3_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C (k3_tarski A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) )  =>  ( ( (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) B) <=>  (? [F:$i] :  ((r2_hidden F A) &  ((r2_hidden D F) & (r2_hidden E F)) ) ) ) ) )  &  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) C) <=>  (? [F:$i] :  ((r2_hidden F A) &  ((r2_hidden D F) & (r2_hidden E F)) ) ) ) ) ) )  => (r2_relset_1 (k3_tarski A) (k3_tarski A) B C)) ) ) ) ) ) ).
tt(t25_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A B D))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A B D) =>  ((r3_borsuk_2 A B C E F) => (r3_borsuk_2 A B C E (k1_borsuk_2 A B B C (k1_borsuk_2 A B D B G (k2_borsuk_2 A B D G)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) => (m1_borsuk_2 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) F C) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_borsuk_2 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) =>  (! [J:$i] :  ((m1_borsuk_2 J (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) =>  (! [K:$i] :  ((m1_borsuk_2 K B F G) =>  (! [L:$i] :  ((m1_borsuk_2 L B G H) =>  ( ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) &  ((r1_borsuk_6 (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) K (k4_topalg_4 A B k5_topmetr I)) & (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) L (k4_topalg_4 A B k5_topmetr J))) ) )  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) (k4_topalg_4 A B k5_topmetr (k1_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H) I J)) (k1_borsuk_2 B F G H K L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_topalg_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_borsuk_2 B k2_topalg_2 (k4_toprealb k6_numbers) (k4_toprealb A)) =>  ((k1_funct_1 k7_topalg_5 A) = (k6_eqrel_1 (k2_topalg_1 (k8_toprealb 2) k9_toprealb) (k2_topalg_1 (k8_toprealb 2) k9_toprealb) (k4_topalg_1 (k8_toprealb 2) k9_toprealb) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 k2_topalg_2) (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) B k12_toprealb))) ) ) ) ) ).
tt(t25_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_2 A B C) =>  ((v7_topalg_6 D A) & (m2_subset_1 D (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ) ) ) ) ) ) ) ) ).
tt(t25_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( ((r1_borsuk_3 A B) & (v3_topdim_1 A))  =>  ((k4_topdim_1 A) = (k4_topdim_1 B)) ) ) ) ) ) ).
tt(t25_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))  =>  ((k3_topgen_1 A C) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_topgen_1 A B))) ) ) ) ) ) ) ) ).
tt(t25_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v4_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v4_pre_topc (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C)) A) =>  ((k2_pre_topc A B) = (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t25_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k4_series_1 (k10_nat_1 k1_numbers (k4_topgen_3 A (k13_complex1 1 2)) (k2_nat_1 B 1))) (k1_newton (k13_complex1 1 2) B))) ) ) ).
tt(t25_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_ordinal1 (k1_card_1 (k2_topgen_4 A B C)) (k1_card_1 (k2_zfmisc_1 B C)))) ) ) ) ) ).
tt(t25_topgen_5,ax, ((v3_pre_topc (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) k3_topgen_5) & (m1_subset_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t25_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc D A) <=> (v3_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_topreal1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) => (r1_topreal1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k3_topreal1 2 A))) ) ) ).
tt(t25_topreal3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_euclid 2))) =>  (~  ((r2_hidden (k19_euclid A B) (k9_metric_1 (k14_euclid 2) F C)) &  ((r2_hidden (k19_euclid D E) (k9_metric_1 (k14_euclid 2) F C)) &  ( (~ (r2_hidden (k19_euclid A E) (k9_metric_1 (k14_euclid 2) F C)))  &  (~ (r2_hidden (k19_euclid D B) (k9_metric_1 (k14_euclid 2) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v2_topreal4 B (k15_euclid 2)) &  ((r2_hidden A B) &  (C = (a_2_1_topreal4 A B)) ) )  => (v3_pre_topc C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t25_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( (A = (k16_euclid 2))  &  (B = C) )  =>  ((k4_metric_1 (k14_euclid 2) A B) = (k12_euclid C)) ) ) ) ) ) ) ) ).
tt(t25_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_t_0topsp (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B))) (k3_pcomps_1 (k14_euclid (k2_nat_1 A B))))) ) ) ) ).
tt(t25_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_topreal1 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) )  => (v1_topreal1 (k2_graph_2 (u1_struct_0 (k15_euclid 2)) C A B))) ) ) ) ) ) ).
tt(t25_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (! [C:$i] :  ( ((v1_convex1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  => (v1_convex1 (k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B C) (k15_euclid A))) ) ) ) ) ) ).
tt(t25_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 A C))  =>  ((v3_pre_topc (k4_rcomp_1 C B) (k4_topmetr A B)) & (m1_subset_1 (k4_rcomp_1 C B) (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) ) ) ) ) ) ) ) ).
tt(t25_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((m1_subset_1 A (u1_struct_0 (k11_toprealb k10_toprealb))) &  ((k18_euclid A) = k6_numbers) )  =>  (A = k9_toprealb) ) ) ) ).
tt(t25_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k2_rltopsp1 (k15_euclid A) B) = (k2_toprealc B)) ) ) ) ) ).
tt(t25_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 k6_numbers (k12_euclid B))) ) ) ) ).
tt(t25_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  (! [C:$i] :  ((r2_hidden C B) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((v3_pre_topc D A) &  ((r1_tarski D B) & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((v3_pre_topc B A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (D = B)  => (v3_pre_topc D C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_tops_1 B A) & (v1_tops_1 B A)) ) ) ) ) ) ).
tt(t25_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v5_pre_topc B k3_topmetr (k15_euclid A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_topmetr)) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (? [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  & (r1_tarski (k7_relset_1 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)) B (k2_rcomp_1 (k6_xcmplx_0 C E) (k2_xcmplx_0 C E))) (k1_topreal9 A (k3_funct_2 (u1_struct_0 k3_topmetr) (u1_struct_0 (k15_euclid A)) B C) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_transgeo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_transgeo A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r3_transgeo A B) & (r3_transgeo A C))  => (r3_transgeo A (k1_transgeo (u1_struct_0 A) C B))) ) ) ) ) ) ) ).
tt(t25_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (~ (v1_xboole_0 (k3_xboole_0 A B)))  & (v1_trees_1 (k3_xboole_0 A B))) ) ) ) ) ).
tt(t25_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ( ((v2_trees_2 D A) & (m1_trees_2 D A))  =>  ( ((r1_tarski B C) & (r2_hidden C D))  => (r2_hidden B D)) ) ) ) ) ) ) ) ) ).
tt(t25_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((v4_trees_3 A) & (v4_trees_3 B))  <=> (v4_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(t25_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ((k8_trees_3 A B (k2_trees_4 (k2_zfmisc_1 A B) (k1_domain_1 A B C D))) = (k2_trees_4 A C))  &  ((k9_trees_3 A B (k2_trees_4 (k2_zfmisc_1 A B) (k1_domain_1 A B C D))) = (k2_trees_4 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_trees_3 B))  =>  ((v1_xboole_0 (k12_trees_9 B A)) <=>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v1_zfmisc_1 C) &  (~ (r2_hidden (k1_funct_1 C k1_xboole_0) A)) ) ) ) ) ) ) ) ).
tt(t25_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  ((v1_tsep_1 (k1_tsep_1 A B C) A) & (m1_pre_topc (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ).
tt(t25_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))) =>  ( ( (E = B)  &  (F = C) )  =>  ((r1_connsp_1 A B C) <=> (r1_connsp_1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k6_domain_1 (u1_struct_0 B) D)) = (k4_tex_4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (B = (k3_xtuple_0 C D E))  =>  ( (C = (u5_turing_1 A))  |  ((k9_turing_1 A B) = (k3_xtuple_0 (k1_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 A B)) (k2_xcmplx_0 (k7_turing_1 A B) (k6_turing_1 A (k8_turing_1 A B))) (k5_turing_1 A (k3_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) B) (k7_turing_1 A B) (k2_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k8_turing_1 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t25_twoscomp,ax, ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 k6_numbers 1 1)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 1 k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k28_twoscomp (k11_finseq_1 1 1 k6_numbers)) = 1)  &  ((k1_funct_1 k28_twoscomp (k11_finseq_1 1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t25_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (v2_binop_1 (k10_unialg_2 A) (k9_unialg_2 A))) ) ).
tt(t25_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((r2_hidden B (k2_uniroots A)) & (r2_hidden C (k2_uniroots A)))  => (r2_hidden (k5_binop_2 B C) (k2_uniroots A))) ) ) ) ) ) ) ).
tt(t25_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_polynom3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_polynom3 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_normsp_1 A B C) = (k5_algstr_0 (k14_polynom3 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C k3_urysohn1) &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_funct_2 E (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k3_valuat_1 A B C E) D) = k8_margrel1)  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 E D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_nat_1 A B C) = (k8_nat_1 A B (k1_nat_1 C 1))) ) )  => (v3_funct_1 B)) ) ) ) ) ).
tt(t25_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k10_xtuple_0 (k61_valued_1 A B)) (k10_xtuple_0 A))) ) ) ) ).
tt(t25_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k18_valued_1 A B)) = (k18_valued_1 (k30_valued_1 A) B)) ) ) ) ) ).
tt(t25_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_vectsp10 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (D = (k3_vectsp_4 A B E C))  =>  ((k4_vectsp_1 A (k6_vectsp10 A B C) F D) = (k3_vectsp_4 A B (k4_vectsp_1 A B F E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  => (m1_vectsp_4 (k1_ranknull B C C (k1_vectsp11 C D A)) B (k2_vectsp11 B C D))) ) ) ) ) ) ) ) ).
tt(t25_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ( (~  ((k11_algstr_0 A B) = (k4_struct_0 A)) )  &  (~  ((k4_algstr_0 A (k11_algstr_0 A B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t25_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_vectsp_2 C A B))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  ( ((k4_vectsp_1 A C D (k1_algstr_0 C H I)) = (k1_algstr_0 C (k4_vectsp_1 A C D H) (k4_vectsp_1 A C D I)))  &  ( ((k4_vectsp_1 A C (k3_rlvect_1 A D E) H) = (k1_algstr_0 C (k4_vectsp_1 A C D H) (k4_vectsp_1 A C E H)))  &  ( ((k4_vectsp_1 A C (k6_algstr_0 A D E) H) = (k4_vectsp_1 A C D (k4_vectsp_1 A C E H)))  &  ( ((k4_vectsp_1 A C (k1_group_1 A) H) = H)  &  ( ((k5_vectsp_2 B C F (k1_algstr_0 C H I)) = (k1_algstr_0 C (k5_vectsp_2 B C F H) (k5_vectsp_2 B C F I)))  &  ( ((k5_vectsp_2 B C (k3_rlvect_1 B F G) H) = (k1_algstr_0 C (k5_vectsp_2 B C F H) (k5_vectsp_2 B C G H)))  &  ( ((k5_vectsp_2 B C (k6_algstr_0 B G F) H) = (k5_vectsp_2 B C F (k5_vectsp_2 B C G H)))  &  ( ((k5_vectsp_2 B C (k1_group_1 B) H) = H)  &  ((k4_vectsp_1 A C D (k5_vectsp_2 B C F H)) = (k5_vectsp_2 B C F (k4_vectsp_1 A C D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  ((v4_vectsp_2 C B) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (v5_vectsp_2 C A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v7_vectsp_1 C A) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( ((m1_vectsp_4 C A B) & (m1_vectsp_4 B A C))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t25_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ((k2_vectsp_5 A B D (k1_vectsp_5 A B D C)) = D) ) ) ) ) ) ) ) ) ).
tt(t25_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) => (r1_vectsp_6 A B (k5_vectsp_6 A B C D) (k5_vectsp_6 A B D C))) ) ) ) ) ) ) ) ).
tt(t25_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (r1_xxreal_0 (k1_vectsp_9 A C) (k1_vectsp_9 A B))) ) ) ) ) ) ).
tt(t25_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) (k6_vfunct_1 A B C (k5_vfunct_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t25_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) (k3_vfunct_2 A B C (k5_vfunct_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t25_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ( ((v12_waybel_0 C A) => (v12_waybel_0 D B))  &  ((v13_waybel_0 C A) => (v13_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) <=> (v4_waybel_0 (k1_yellow_2 A A B) A)) ) ) ) ) ).
tt(t25_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel11 A B))) =>  (C = B) ) ) ) ) ) ) ).
tt(t25_waybel12,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v13_waybel_0 (a_2_2_waybel12 A B) A) & (m1_subset_1 (a_2_2_waybel12 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t25_waybel13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v1_yellow_0 (k3_waybel_3 A B C)) &  ((v2_waybel_8 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) ) )  =>  ((v3_orders_2 (k5_yellow_1 A B)) &  ((v4_orders_2 (k5_yellow_1 A B)) &  ((v5_orders_2 (k5_yellow_1 A B)) &  ((v1_lattice3 (k5_yellow_1 A B)) &  ((v2_lattice3 (k5_yellow_1 A B)) &  ((v1_yellow_0 (k5_yellow_1 A B)) &  ((v2_waybel_8 (k5_yellow_1 A B)) & (l1_orders_2 (k5_yellow_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) =>  (! [C:$i] :  ( ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (B = (a_2_2_waybel14 A C))  => (v1_waybel_0 B (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) ).
tt(t25_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (k1_waybel15 A)) =>  ((r2_hidden B C) <=>  ((v1_waybel15 B A) & (r3_orders_2 A B (k1_yellow_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t25_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) => (r1_tarski (k1_waybel16 A) B)) ) ) ) ) ).
tt(t25_waybel17,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_4_waybel17 A B C D))) ) )  => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t25_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden D E) & (r2_hidden E B))  => (r1_waybel_0 A C E)) ) )  => (r2_hidden D (k10_yellow_6 A C))) ) ) ) ) ) ) ) ) ).
tt(t25_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v3_waybel_1 (k1_waybel_1 A B C D) A B) & (v2_funct_2 D (u1_struct_0 A)))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_waybel_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v17_waybel_0 D A B) & (v17_waybel_0 E B C))  => (v17_waybel_0 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ( (~ (v1_xboole_0 (a_2_0_waybel21 A B)))  &  ((v1_waybel_0 (a_2_0_waybel21 A B) A) & (m1_subset_1 (a_2_0_waybel21 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t25_waybel23,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v2_lattice3 (k5_yellow_0 A B))) ) ) ) ).
tt(t25_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_yellow_1 (u1_struct_0 A) B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) D) = (k1_yellow_0 B (a_4_1_waybel24 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t25_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) &  ((v10_waybel_0 C (k3_waybel24 A (k1_waybel25 B))) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v10_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D) (k1_waybel25 B))) ) ) ) ) ) ) ) ).
tt(t25_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) ) )  =>  (~  ((v1_lattice3 (k1_waybel26 A B)) & (v7_pre_topc B)) ) ) ) ) ) ).
tt(t25_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D))) )  =>  ((k2_waybel27 A C) = (k2_waybel27 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_yellow_6 C A (k4_waybel17 A B)) =>  ((k1_waybel11 A C) = (k1_yellow_0 A B)) ) ) ) ) ) ) ).
tt(t25_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (v23_waybel_0 (k3_waybel29 B A) (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 B A))) (k3_waybel24 B (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))))) ) ) ) ) ).
tt(t25_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  => (r1_tarski (k2_relset_1 (u1_struct_0 A) C) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A (k2_waybel_2 A B C))))) ) ) ) ) ).
tt(t25_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_waybel30 A (k6_waybel_0 A B)) = (k2_waybel_3 A B)) ) ) ) ) ).
tt(t25_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v2_waybel19 B) & (m1_yellow_9 B A)) )  =>  ((k1_waybel31 A) = (k2_waybel23 B)) ) ) ) ) ).
tt(t25_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_waybel_2 A (k2_waybel32 A B)) = (k1_waybel11 A (k5_waybel_9 A B C))) ) ) ) ) ) ) ).
tt(t25_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel33 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v2_waybel19 C) & (m1_yellow_9 C A)) )  => (m2_yellow_9 B C)) ) ) ) ) ) ).
tt(t25_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E A))  =>  (! [F:$i] :  ( ((v3_pre_topc F D) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))))  =>  ((k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F) = (k9_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) (k1_waybel34 A B C)) (k4_waybel_0 A (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel35 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v3_waybel35 C A B) & (m1_waybel35 C A B))  => (r1_waybel35 A (k6_waybel35 A B C) B)) ) ) ) ) ) ).
tt(t25_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) <=> (r1_tarski (k1_waybel_3 A B) (k1_waybel_3 A C))) ) ) ) ) ) ) ).
tt(t25_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_funct_1 (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A)))) &  ((v1_funct_2 (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) ) ) ) ).
tt(t25_waybel_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_yellow_0 A C) &  ((r1_yellow_0 A D) &  (D = (a_3_0_waybel_5 A B C)) ) )  => (r1_orders_2 A (k1_yellow_0 A D) (k12_lattice3 A B (k1_yellow_0 A C)))) ) ) ) ) ) ) ) ) ).
tt(t25_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) <=>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski C)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski C))))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski C))) D E) = k1_xboole_0)  <=> (r3_orders_2 A E B)) ) )  =>  ((v19_waybel_0 D A (k3_yellow_1 (k1_tarski C))) & (v20_waybel_0 D A (k3_yellow_1 (k1_tarski C)))) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r1_subset_1 B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D A) &  ((v13_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v2_waybel_7 D A) &  ((r1_tarski C D) & (r1_subset_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k2_struct_0 (k1_waybel_8 A))) = (k2_struct_0 (k1_waybel_8 (k1_yellow_2 A A B)))) ) ) ) ) ) ).
tt(t25_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v3_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_pre_topc C A A) => (r2_hidden (k2_yellow_6 (u1_struct_0 A) A C (k11_yellow_6 A B)) (k10_yellow_6 A (k6_waybel_9 A A C B)))) ) ) ) ) ) ) ).
tt(t25_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (u1_struct_0 (k4_weddwitt A)) (u1_struct_0 (k5_weddwitt A B)))) ) ) ) ).
tt(t25_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) D) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t25_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v2_wellord1 B) => (v2_wellord1 (k2_wellord1 B A))) ) ) ) ).
tt(t25_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (? [C:$i] :  ((v1_rat_1 C) &  (A = (k1_newton C B)) ) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  (A = (k1_newton C B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_xboole_0 (k2_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 B C)) (k3_xboole_0 C A)) = (k3_xboole_0 (k3_xboole_0 (k2_xboole_0 A B) (k2_xboole_0 B C)) (k2_xboole_0 C A))) ) ) ) ).
tt(t25_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k4_xboolean (k3_xboolean A) (k7_xboolean B C)) = (k4_xboolean (k4_xboolean (k3_xboolean A) (k5_xboolean (k3_xboolean B) C)) (k5_xboolean (k3_xboolean C) B))) ) ) ) ) ) ) ).
tt(t25_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k2_xcmplx_0 A (k6_xcmplx_0 B B))) ) ) ) ) ).
tt(t25_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A (k4_xcmplx_0 B)) => (r1_xxreal_0 B (k4_xcmplx_0 A))) ) ) ) ) ).
tt(t25_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) (k9_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t25_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_xxreal_0 A (k4_xxreal_0 A B))) ) ) ) ).
tt(t25_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) => (r1_tarski (k4_xxreal_1 A B) (k1_xxreal_1 A B))) ) ) ) ).
tt(t25_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k2_xxreal_2 (k1_xxreal_1 A B)) = A) ) ) ) ) ) ).
tt(t25_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k2_xxreal_3 (k1_xxreal_3 A B)) = (k3_xxreal_3 (k2_xxreal_3 B) A)) ) ) ) ) ).
tt(t25_yellow_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k12_lattice3 A B C))  <=> (r3_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t25_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ( ((k4_yellow_3 A B (k2_yellow_4 (k3_yellow_3 A B) C D)) = (k2_yellow_4 A (k4_yellow_3 A B C) (k4_yellow_3 A B D)))  &  ((k5_yellow_3 A B (k2_yellow_4 (k3_yellow_3 A B) C D)) = (k2_yellow_4 B (k5_yellow_3 A B C) (k5_yellow_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t25_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ((r1_yellow_0 A (k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k5_waybel_2 A) B)) => (r4_waybel_0 (k3_yellow_3 A A) A (k5_waybel_2 A) B)) ) ) ) ) ).
tt(t25_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m2_yellow13 B A) =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(t25_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  &  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v2_compts_1 C A)) )  => (v2_compts_1 D B)) ) ) ) ) ) ) ) ) ).
tt(t25_yellow15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  => (m1_waybel23 (k2_struct_0 A) A)) ) ).
tt(t25_yellow16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r4_yellow16 B A) => (v3_waybel_3 B)) ) ) ) ) ).
tt(t25_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  ( ((r2_yellow18 A B) &  ((r2_yellow18 C D) & (r1_yellow18 A C)) )  => (r1_yellow18 B D)) ) ) ) ) ) ) ) ) ).
tt(t25_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_subset_1 D (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  &  ((r2_hidden B D) & (r1_waybel_7 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t25_yellow_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) <=> (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))))) ) ) ) ) ).
tt(t25_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ( ((r1_yellow20 A B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k8_altcat_1 A C) = (k8_altcat_1 B D)) ) ) ) ) ) )  =>  ((v2_struct_0 (k2_yellow20 A B)) |  ((v2_altcat_1 (k2_yellow20 A B)) &  ((v3_altcat_2 (k2_yellow20 A B) A) & (m1_altcat_2 (k2_yellow20 A B) A)) ) ) ) ) ) ) ) ).
tt(t25_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] : (r2_yellow_0 A B))  => (v3_lattice3 A)) ) ) ).
tt(t25_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v13_waybel_0 (k6_yellow_3 A B C D) (k3_yellow_3 A B)) =>  ((v13_waybel_0 C A) & (v13_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t25_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r2_lattice3 A B (k1_yellow_0 A (k2_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t25_yellow_5,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_lattice3 A B (k3_yellow_0 A)) = (k3_yellow_0 A)) ) ) ) ) ).
tt(t25_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) =>  ( ((r2_hidden B (k6_yellow_6 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_hidden (k7_yellow_6 (u1_struct_0 B) A C D) (k6_yellow_6 A))) ) )  => (r2_hidden (k8_yellow_6 A B C) (k6_yellow_6 A))) ) ) ) ) ) ) ).
tt(t25_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_1 A) <=> (v2_waybel_1 (k7_lattice3 A))) ) ) ).
tt(t25_yellow_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_yellow_8 A)))) =>  ((v4_pre_topc B (k1_yellow_8 A)) <=>  ( (B = A)  | (v1_finset_1 B)) ) ) ) ) ) ).
tt(t25_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) )  =>  ((u1_pre_topc A) = (u1_pre_topc B)) ) ) ) ) ) ) ) ).
tt(t25_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  (A = B) )  =>  ((k3_relat_1 (k2_tarski (k4_tarski C A) (k4_tarski D B)) (k2_tarski (k4_tarski A E) (k4_tarski B F))) = (k2_tarski (k4_tarski C E) (k4_tarski D F))) ) ) ) ) ) ) ) ).
tt(t25_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  ((k25_zf_lang A) = (k21_zf_lang (k20_zf_lang A))) ) ) ) ).
tt(t25_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 A 1) = 1)  => (v3_zf_lang A)) ) ) ).
tt(t25_zfmisc_1,ax, (! [A:$i] :  ((k3_tarski (k1_tarski A)) = A) ) ).
tt(t25_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_ordinal2 A B) =>  ((v4_ordinal1 A) <=> (v4_ordinal1 B)) ) ) ) ) ) ).
tt(t25_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t260_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k1_xxreal_1 C A) (k2_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t261_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k3_xxreal_1 C A) (k2_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t262_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 C A) (k2_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t263_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k4_xxreal_1 C A) (k4_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t264_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k3_xxreal_1 C A) (k4_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t265_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_xxreal_1 C A) (k3_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t266_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 C A) (k3_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t267_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  => (r1_tarski (k1_xxreal_1 C A) (k4_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t268_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_xxreal_1 C A) (k4_xxreal_1 k2_xxreal_0 B))) ) ) ) ) ) ) ).
tt(t269_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k3_xboole_0 (k4_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A k1_xxreal_0)) = (k4_xxreal_1 A B)) ) ) ) ) ).
tt(t26_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_abcmiz_0 A C B) =>  ( (~ (v1_xboole_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_abcmiz_0 A B) (k5_waybel_0 A C))))  &  ((v1_waybel_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_abcmiz_0 A B) (k5_waybel_0 A C)) A) &  ((v12_waybel_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_abcmiz_0 A B) (k5_waybel_0 A C)) A) & (m1_subset_1 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_abcmiz_0 A B) (k5_waybel_0 A C)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t26_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k2_abcmiz_1)) =>  ((k1_abcmiz_1 (k1_tarski (k4_tarski (k1_abcmiz_1 B) A))) = (k2_xboole_0 (k1_abcmiz_1 B) (k1_tarski (k4_tarski (k1_abcmiz_1 B) A)))) ) ) ) ) ).
tt(t26_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ((v9_abcmiz_1 B A) & (m1_abcmiz_1 B A (k12_abcmiz_1 A)))  <=>  ((r2_hidden (k1_xtuple_0 (k1_funct_1 B k1_xboole_0)) k20_abcmiz_1) &  ((k1_xtuple_0 (k1_xtuple_0 (k1_funct_1 B k1_xboole_0))) = k6_abcmiz_1) ) ) ) ) ) ) ).
tt(t26_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 k6_numbers (k3_real_1 A (k18_complex1 A)))) ) ).
tt(t26_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_aff_1 A C D B)) ) ) )  => (v1_aff_1 B A)) ) ) ) ) ).
tt(t26_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) &  ((v1_aff_4 C A) &  ((v1_aff_1 D A) &  ((v1_aff_1 E A) &  ((r1_tarski D B) &  ((r1_tarski E B) &  ((r1_tarski D C) & (r1_tarski E C)) ) ) ) ) ) )  =>  ( (D = E)  |  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((k10_xtuple_0 (k1_ordinal4 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t26_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (? [C:$i] :  ((r2_hidden C A) & (r2_afinsq_2 (k1_tarski C) B)) )  &  (~ (r1_xxreal_0 (k1_recdef_1 (k4_afinsq_2 A) k6_numbers) (k1_recdef_1 (k4_afinsq_2 B) k6_numbers))) ) ) ) ) ) ) ) ).
tt(t26_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ( (B = D)  &  ((k4_tarski C 1) = E) )  =>  ((r1_incsp_1 (k13_afproj A) D E) <=>  ((v1_aff_1 C A) & (r2_hidden B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_afvect0 A B C D) &  ((r2_afvect0 A E F G) & (r1_afvect0 A C F)) )  => (r2_analoaf A B E G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  (! [B:$i] :  ((m1_algspec1 B A) =>  (B = (k2_funct_1 A)) ) ) ) ) ) ).
tt(t26_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k12_algstr_4 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k12_algstr_4 A)) => (m1_subset_1 (k4_tarski (k4_tarski (k4_tarski (k1_xtuple_0 B) (k1_xtuple_0 C)) (k2_xtuple_0 B)) (k2_xcmplx_0 (k2_xtuple_0 B) (k2_xtuple_0 C))) (k12_algstr_4 A))) ) ) ) ) ) ).
tt(t26_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) & (m1_altcat_2 C A)) )  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 C))  &  ((u1_altcat_1 B) = (u1_altcat_1 C)) )  =>  ((g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B)) = (g2_altcat_1 (u1_struct_0 C) (u1_altcat_1 C) (u2_altcat_1 C))) ) ) ) ) ) ) ) ).
tt(t26_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v6_altcat_3 B A) & (v6_altcat_3 C A))  => (r2_altcat_3 A B C)) ) ) ) ) ) ) ).
tt(t26_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v1_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v1_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_ami_2) =>  ( (A = k5_numbers)  | (r2_hidden A k2_ami_2)) ) ) ).
tt(t26_ami_3,ax, ((k2_compos_1 k1_ami_3) = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0)) ).
tt(t26_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v5_ami_wstd C A B)) ) ) ) ) )  => (r2_hidden (k1_ami_wstd A B k6_numbers) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ).
tt(t26_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analmetr A B C))) =>  (~  ((r4_analmetr (k2_analmetr A B C) D E F G) &  ((r2_analoaf (k2_analmetr A B C) D E H I) &  ( (~  (D = E) )  &  (~ (r4_analmetr (k2_analmetr A B C) F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_analoaf A)))  &  ((v2_analoaf (k2_analoaf A)) & (l1_analoaf (k2_analoaf A))) ) ) ) ) ).
tt(t26_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_analort A D E B C (k1_analort A D E B) (k1_analort A D E C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_anproj_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((m1_subset_1 A (u1_struct_0 (k5_anproj_1 B))) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  ( (~ (v9_struct_0 C B))  &  (A = (k2_anproj_1 B C)) ) ) ) ) ) ) ) ).
tt(t26_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_anproj_1 A))) =>  (~  ((r1_collsp (k5_anproj_1 A) B C D) &  ((r1_collsp (k5_anproj_1 A) E F D) &  ((r1_collsp (k5_anproj_1 A) B E G) &  ((r1_collsp (k5_anproj_1 A) C F G) &  ((r1_collsp (k5_anproj_1 A) B F H) &  ((r1_collsp (k5_anproj_1 A) C E H) &  ((r1_collsp (k5_anproj_1 A) G D H) &  ( (~ (r1_collsp (k5_anproj_1 A) B C F))  &  ( (~ (r1_collsp (k5_anproj_1 A) B C E))  &  ( (~ (r1_collsp (k5_anproj_1 A) B E F))  &  (~ (r1_collsp (k5_anproj_1 A) C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k10_aofa_000 A)) <=>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  (~ (r2_hidden B (k2_relset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t26_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k47_aofa_i00 A B D E F G)) F) = (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k47_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k4_armstrng A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (~  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (~  ((r2_hidden (k6_armstrng A D E) (k8_armstrng A C)) & (r3_armstrng A (k6_armstrng A D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 A B) =>  ((k8_arytm_2 C (k1_arytm_1 B A)) = (k2_arytm_1 (k8_arytm_2 C B) (k8_arytm_2 C A))) ) ) ) ) ) ) ) ).
tt(t26_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( ((k4_arytm_3 k1_xboole_0 A) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  =>  ((k4_arytm_3 A k1_xboole_0) = 1) ) ) ) ) ).
tt(t26_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k7_asympt_0 (k1_asympt_0 A B)) = (k7_asympt_0 (k5_asympt_0 A B))) ) ) ) ) ).
tt(t26_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 A C) = (k4_power C (k6_power 2 C))) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k4_power C (k7_square_1 C))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v4_asympt_0 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C A) &  ((r2_funct_2 k5_numbers k1_numbers D B) &  ((r1_tarski (k6_asympt_0 C) (k6_asympt_0 D)) &  (~  ((k6_asympt_0 C) = (k6_asympt_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_autalg_1 C (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  (! [D:$i] :  ((m1_autalg_1 D (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) => (r2_hidden (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (u3_msualg_1 A B) D C) (k5_autalg_1 A B))) ) ) ) ) ) ) ) ).
tt(t26_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_autgroup A (k2_group_1 A B)) = (k2_funct_1 (k6_autgroup A B))) ) ) ) ) ).
tt(t26_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ( ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden (k4_tarski C D) B) => (r2_hidden (k4_tarski (k11_pre_poly A C E) (k11_pre_poly A D E)) B)) ) ) ) ) ) )  & (r7_relat_2 B (k15_pre_poly A)))  => (v2_bagorder (k5_bagorder A B) A)) ) ) ) ) ).
tt(t26_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A D C)) (k1_bcialg_1 A C (k1_bcialg_1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t26_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v3_bcialg_2 (k4_struct_0 A) A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v10_bcialg_1 B A)) ) ) ) ) ).
tt(t26_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) &  ((v8_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) ) )  =>  ((m1_bcialg_3 B C) => (m2_bcialg_1 B C)) ) ) ) ) ) ) ).
tt(t26_bcialg_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v2_bcialg_4 B) & (l1_bcialg_4 B)) ) ) ) ) )  =>  ((k6_bcialg_4 B (k4_struct_0 B) A) = (k4_struct_0 B)) ) ) ) ) ).
tt(t26_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 A (k3_bcialg_5 A B C D)) &  ((r1_xxreal_0 B (k3_bcialg_5 A B C D)) &  ((r1_xxreal_0 C (k3_bcialg_5 A B C D)) & (r1_xxreal_0 D (k3_bcialg_5 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v1_bcialg_6 B A) &  ((k4_bcialg_6 A B) = C) )  =>  ((k3_bcialg_6 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t26_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) D) = (k1_bcialg_1 B C D)) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t26_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_bhsp_1 A B) = k6_numbers)  <=>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t26_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k2_normsp_1 A D E) (k3_rlvect_1 A B C)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k2_normsp_1 A D E) (k3_rlvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_bhsp_3 B A) & (m2_valued_0 C (u1_struct_0 A) B))  => (v2_bhsp_3 C A)) ) ) ) ) ) ) ).
tt(t26_bhsp_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v2_bhsp_4 C B) => (v2_bhsp_4 (k5_normsp_1 B C A) B)) ) ) ) ) ) ) ).
tt(t26_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v2_bilinear G A B C) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G (k1_algstr_0 B D E) F) = (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) B))  =>  ((k1_funct_1 (k1_binari_3 (k2_xcmplx_0 A 1) B) (k2_xcmplx_0 A 1)) = k7_margrel1) ) ) ) ) ) ).
tt(t26_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_binari_4 A k6_numbers) = (k5_euclid A)) ) ) ).
tt(t26_binom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k5_numbers A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k5_numbers A) B)))) )  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k2_binop_1 k5_numbers A B E k6_numbers F) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k2_binop_1 k5_numbers A B E (k2_nat_1 G 1) F) = (k2_binop_1 A B B D F (k2_binop_1 k5_numbers A B E G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_lattices A (k7_lattices A (k3_lattices A B C)) (k7_lattices A B))) ) ) ) ) ) ).
tt(t26_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k10_borsuk_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (B = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r2_hidden C B) &  (B = A) )  =>  ((r1_xxreal_0 (k5_seq_4 B) C) & (r1_xxreal_0 C (k4_seq_4 B))) ) ) ) ) ) ) ) ).
tt(t26_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_rat_1 C) =>  (! [D:$i] :  ((v1_rat_1 D) =>  (~  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 D C))  &  (~ (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_borsuk_6,ax, ( (~ (v1_xboole_0 a_0_14_borsuk_6))  &  ((v4_pre_topc a_0_14_borsuk_6 (k2_borsuk_1 k5_topmetr k5_topmetr)) & (m1_subset_1 a_0_14_borsuk_6 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))) ) ).
tt(t26_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k1_borsuk_7 A B B C D E) = (k4_funct_4 A B C E)) ) ) ) ) ) ).
tt(t26_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_bspace A))) =>  ((k4_vectsp_1 k2_bspace (k7_bspace A) (k3_rlvect_1 k2_bspace B C) D) = (k1_algstr_0 (k7_bspace A) (k4_vectsp_1 k2_bspace (k7_bspace A) B D) (k4_vectsp_1 k2_bspace (k7_bspace A) C D))) ) ) ) ) ) ) ) ).
tt(t26_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B (k5_bvfunc_1 A C (k1_bvfunc_1 A D))) (k9_bvfunc_1 A C (k5_bvfunc_1 A D B))))) ) ) ) ) ) ) ) ).
tt(t26_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( (F = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B H) (k16_funcop_1 C I)) (k16_funcop_1 D J)) (k16_funcop_1 E K)) (k16_funcop_1 A G)))  =>  ( (A = B)  |  ( (A = C)  |  ( (A = D)  |  ( (A = E)  |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (C = D)  |  ( (C = E)  |  ( (D = E)  |  ( ((k1_funct_1 F A) = G)  &  ( ((k1_funct_1 F B) = H)  &  ( ((k1_funct_1 F C) = I)  &  ( ((k1_funct_1 F D) = J)  &  ((k1_funct_1 F E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 (k3_funct_2 A k6_margrel1 (k13_bvfunc_1 A B) C) (k3_funct_2 A k6_margrel1 B C))) ) ) ) ) ) ).
tt(t26_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t26_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A (k12_bvfunc_1 A) B) (k11_bvfunc_1 A))) ) ) ) ).
tt(t26_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k2_bvfunc_1 A D C) B E) (k2_bvfunc_1 A (k6_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k6_bvfunc_2 A (k5_bvfunc_1 A (k1_bvfunc_1 A C) D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t26_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k6_bvfunc_2 A B D E) (k6_bvfunc_2 A C D E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A B C)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t26_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k5_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t26_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k10_bvfunc_1 A (k9_bvfunc_1 A C B) B))) ) ) ) ) ) ).
tt(t26_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k10_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A B))) (k12_bvfunc_1 A))) ) ) ) ).
tt(t26_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C E)) (k1_bvfunc_1 A (k2_bvfunc_1 A D E))) (k1_bvfunc_1 A (k2_bvfunc_1 A B C))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t26_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 A))) =>  ( ( (C = D)  & (v1_comseq_2 (k2_partfun1 A k1_numbers C A)))  => (r1_xxreal_0 (k18_complex1 (k1_seq_1 C B)) (k1_normsp_0 (k11_c0sp1 A) D))) ) ) ) ) ) ) ) ) ).
tt(t26_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_c0sp2 A)))  & (m1_subset_1 (k6_c0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k12_funcsdom (u1_struct_0 A)))))) ) ) ).
tt(t26_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((r1_tarski F (k3_qc_lang1 A)) =>  ((r2_hidden B F) | (r2_relset_1 (k3_qc_lang1 A) C (k2_partfun1 (k3_qc_lang1 A) C (k1_sublemma A C D (k12_sublemma A C B E)) F) (k2_partfun1 (k3_qc_lang1 A) C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B))) (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t26_card_1,ax, (! [A:$i] :  ((r2_wellord2 A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ).
tt(t26_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_card_2 k6_numbers A) = k6_numbers) ) ) ) ).
tt(t26_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k4_card_3 A) = k1_xboole_0)  <=> (r2_hidden k1_xboole_0 (k10_xtuple_0 A))) ) ) ).
tt(t26_card_5,ax, (! [A:$i] :  (! [B:$i] :  ((v1_card_1 B) =>  ( ((r1_tarski A B) & (r2_hidden (k1_card_1 A) (k1_card_5 B)))  =>  ((r2_hidden (k3_ordinal2 A) B) & (r2_hidden (k3_tarski A) B)) ) ) ) ) ).
tt(t26_card_fil,ax,(v5_card_fil k4_ordinal1)).
tt(t26_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k2_card_fin B k1_xboole_0 A) = (k3_tarski (k10_xtuple_0 B))) ) ) ) ).
tt(t26_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v5_card_lar A) => (v4_card_lar A)) ) ) ).
tt(t26_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A C D) =>  (! [F:$i] :  ((m1_cat_1 F A D B) =>  ((v1_cat_3 (k5_cat_1 A C D B E F) A C B) =>  ( ((k2_cat_1 A C D) = k1_xboole_0)  |  ( ((k2_cat_1 A D C) = k1_xboole_0)  | (v1_cat_3 F A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  (! [G:$i] :  ((m1_cat_1 G A B D) =>  (! [H:$i] :  ((m1_cat_1 H A B D) =>  ( ((k9_cat_4 A C D B E G) = (k9_cat_4 A C D B F H))  =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A B D) = k1_xboole_0)  |  ( (E = F)  &  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((r2_hidden B (k10_cat_5 A (k3_graph_1 A B))) & (r2_hidden B (k9_cat_5 A (k4_graph_1 A B)))) ) ) ) ) ).
tt(t26_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 (k6_newton A B) k6_numbers)) ) ) ) ) ) ).
tt(t26_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C D) (k13_catalg_1 A)) = (k4_card_3 (k2_finseq_4 (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A C D) (k2_cat_1 A B C))))  &  ((k4_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C D) (k13_catalg_1 A)) = (k2_cat_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_cc0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_cc0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_cc0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k5_algstr_0 (k7_cc0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A k2_numbers D H) = (k4_binop_2 (k3_funct_2 A k2_numbers B H) (k3_funct_2 A k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  ( ((k1_normsp_0 (k5_cc0sp2 A) B) = k6_numbers)  =>  (B = (k4_struct_0 (k5_cc0sp2 A))) ) ) ) ) ) ).
tt(t26_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v3_funct_1 A) => (v2_comseq_2 A)) ) ) ).
tt(t26_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((r1_cfdiff_1 A C) & (r1_cfdiff_1 B C))  =>  ((r1_cfdiff_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  ((k2_cfdiff_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers A B) C) = (k8_complex1 (k9_complex1 (k7_partfun1 k2_numbers B C) (k2_cfdiff_1 A C)) (k9_complex1 (k7_partfun1 k2_numbers A C) (k2_cfdiff_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t26_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_cfuncdom A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_cfuncdom A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_cfuncdom A))) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  ( ((k1_algstr_0 (k8_cfuncdom A) B C) = (k1_algstr_0 (k8_cfuncdom A) C B))  &  ( ((k1_algstr_0 (k8_cfuncdom A) (k1_algstr_0 (k8_cfuncdom A) B C) D) = (k1_algstr_0 (k8_cfuncdom A) B (k1_algstr_0 (k8_cfuncdom A) C D)))  &  ( ((k1_algstr_0 (k8_cfuncdom A) B (k4_struct_0 (k8_cfuncdom A))) = B)  &  ((v10_algstr_0 B (k8_cfuncdom A)) &  ( ((k6_algstr_0 (k8_cfuncdom A) B C) = (k6_algstr_0 (k8_cfuncdom A) C B))  &  ( ((k6_algstr_0 (k8_cfuncdom A) (k6_algstr_0 (k8_cfuncdom A) B C) D) = (k6_algstr_0 (k8_cfuncdom A) B (k6_algstr_0 (k8_cfuncdom A) C D)))  &  ( ((k6_algstr_0 (k8_cfuncdom A) B (k5_struct_0 (k8_cfuncdom A))) = B)  &  ( ((k6_algstr_0 (k8_cfuncdom A) B (k1_algstr_0 (k8_cfuncdom A) C D)) = (k1_algstr_0 (k8_cfuncdom A) (k6_algstr_0 (k8_cfuncdom A) B C) (k6_algstr_0 (k8_cfuncdom A) B D)))  &  ( ((k1_clvect_1 (k8_cfuncdom A) (k6_algstr_0 (k8_cfuncdom A) B C) E) = (k6_algstr_0 (k8_cfuncdom A) (k1_clvect_1 (k8_cfuncdom A) B E) C))  &  ( ((k1_clvect_1 (k8_cfuncdom A) (k1_algstr_0 (k8_cfuncdom A) B C) E) = (k1_algstr_0 (k8_cfuncdom A) (k1_clvect_1 (k8_cfuncdom A) B E) (k1_clvect_1 (k8_cfuncdom A) C E)))  &  ( ((k1_clvect_1 (k8_cfuncdom A) B (k8_complex1 E F)) = (k1_algstr_0 (k8_cfuncdom A) (k1_clvect_1 (k8_cfuncdom A) B E) (k1_clvect_1 (k8_cfuncdom A) B F)))  &  ((k1_clvect_1 (k8_cfuncdom A) B (k9_complex1 E F)) = (k1_clvect_1 (k8_cfuncdom A) (k1_clvect_1 (k8_cfuncdom A) B F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers B k6_complex1) B)) ) ) ) ).
tt(t26_cgames_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v3_cgames_1 A) & (v4_cgames_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v3_cgames_1 B) & (v4_cgames_1 B)) ) ) ) )  =>  ( (? [C:$i] :  ((v2_cgames_1 C) &  ( (C = (k1_funct_1 B 1))  & (r2_hidden (k1_funct_1 A (k3_finseq_1 A)) (k8_cgames_1 C))) ) )  =>  ((v1_relat_1 (k7_finseq_1 A B)) &  ((v1_funct_1 (k7_finseq_1 A B)) &  ( (~ (v1_xboole_0 (k7_finseq_1 A B)))  &  ((v1_finseq_1 (k7_finseq_1 A B)) &  ((v3_cgames_1 (k7_finseq_1 A B)) & (v4_cgames_1 (k7_finseq_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t26_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r2_hidden B (k3_chain_1 A B C)) & (r2_hidden C (k3_chain_1 A B C))) ) ) ) ) ) ) ).
tt(t26_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  ( (~ (v1_glib_001 B A))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( (E = (k3_glib_001 A B))  & (r1_glib_000 A C E D))  =>  ((r2_hidden C (k13_glib_001 A B)) | (v5_glib_001 (k7_glib_001 A (k2_glib_001 A C E D) B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t26_circcmb3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  => (m2_circcmb3 (k7_circcomb A B C D) B (k4_circcmb3 A B C D))) ) ) ) ) ) ) ) ).
tt(t26_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  ((r2_hidden (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)) (k4_card_3 (u3_msualg_1 A C))) & (r2_hidden (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)) (k4_card_3 (u3_msualg_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_circtrm1 A B C D) => (r1_circtrm1 B A (k2_funct_1 C) (k2_funct_1 D))) ) ) ) ) ) ) ) ) ).
tt(t26_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k1_classes1 A)) & (r2_hidden C (k1_classes1 A)))  =>  ((r2_hidden (k1_tarski B) (k1_classes1 A)) & (r2_hidden (k2_tarski B C) (k1_classes1 A))) ) ) ) ) ).
tt(t26_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden A (k2_ordinal1 (k1_classes1 B))) =>  ((r2_hidden (k1_card_1 (k4_classes1 A)) (k1_card_1 (k1_classes1 B))) & (r2_hidden (k4_classes1 A) (k1_classes1 B))) ) ) ) ) ).
tt(t26_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) &  ((v2_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (v4_xxreal_2 (k12_clopban1 A B C))) ) ) ) ) ) ).
tt(t26_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clopban3 B A) => (v1_clopban3 B A)) ) ) ) ) ).
tt(t26_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k4_sin_cos (k1_normsp_0 A B)) C))) ) ) ) ) ) ).
tt(t26_closure1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m2_pboole E B (k5_mssubfam B C) (k5_mssubfam B C)) =>  ( ((v3_closure1 E B C) &  ((r2_hidden A B) &  (D = (k1_funct_1 E A)) ) )  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) =>  ((k1_funct_1 D F) = (k1_funct_1 D (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_funct_1 (k6_partfun1 (k6_closure2 A B))) &  ((v1_funct_2 (k6_partfun1 (k6_closure2 A B)) (k6_closure2 A B) (k6_closure2 A B)) &  ((v7_closure2 (k6_partfun1 (k6_closure2 A B)) A B) & (m1_subset_1 (k6_partfun1 (k6_closure2 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) ) ) ) ).
tt(t26_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_clvect_1 B A) & (v6_clvect_1 C A))  => (v6_clvect_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t26_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k16_csspace A D E) (k3_rlvect_1 A B C)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k16_csspace A D E) (k3_rlvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((v2_clvect_3 B A) => (v2_clvect_3 (k6_clvect_1 A B C) A)) ) ) ) ) ) ) ).
tt(t26_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden (k4_tarski D E) (k6_cohsp_1 A B C)) & (r2_hidden (k4_tarski D F) (k6_cohsp_1 A B C)))  => (r2_hidden (k2_tarski E F) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( ( ((k1_card_1 D) = (k5_real_1 A 1))  &  (C = (a_3_0_combgras A B D)) )  =>  (D = (k1_setfam_1 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k3_complex1 A) = k6_numbers)  &  ((k3_complex1 B) = k6_numbers) )  =>  ( ((k4_complex1 B) = k6_numbers)  |  ( ((k3_complex1 (k13_complex1 A B)) = (k13_complex1 (k4_complex1 A) (k4_complex1 B)))  &  ((k4_complex1 (k13_complex1 A B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t26_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ( ((k21_sin_cos (k1_comptrig A)) = (k13_complex1 (k3_complex1 A) (k17_complex1 A)))  &  ((k18_sin_cos (k1_comptrig A)) = (k13_complex1 (k4_complex1 A) (k17_complex1 A))) ) ) ) ) ).
tt(t26_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k3_vectsp_1 k1_complfld B A) = (k4_struct_0 k1_complfld))  =>  ( (A = (k4_struct_0 k1_complfld))  |  (B = (k4_struct_0 k1_complfld)) ) ) ) ) ) ) ).
tt(t26_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k9_matrix_5 (k1_valued_1 B C) A) = (k3_binop_2 (k9_matrix_5 B A) (k9_matrix_5 C A))) ) ) ) ) ) ) ) ).
tt(t26_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) & (v1_setfam_1 B))  => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t26_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  ((k61_valued_1 (k4_compos_1 B) A) = (k16_funcop_1 A (k2_compos_1 B))) ) ) ) ) ).
tt(t26_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k62_valued_1 B) C))  <=> (r2_hidden C (k9_xtuple_0 (k63_valued_1 B)))) ) ) ) ) ) ) ).
tt(t26_comptrig,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))))).
tt(t26_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_comput_1 A)) ) )  =>  ( ((k3_finseq_1 A) = k6_numbers)  =>  ((k1_comput_1 A) = k6_numbers) ) ) ) ).
tt(t26_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers A) B) (k31_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) & (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k31_valued_1 k5_numbers k2_numbers B)) (k31_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ) ).
tt(t26_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k11_complex1 (k3_comseq_2 A) (k3_comseq_2 B))) ) ) ) ) ).
tt(t26_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k3_series_1 (k7_comseq_3 A)) (k7_comseq_3 (k10_comseq_3 A))) & (r2_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_comseq_3 A)) (k8_comseq_3 (k10_comseq_3 A)))) ) ) ).
tt(t26_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v6_conlat_1 B A) & (l2_conlat_1 B A))  =>  (~  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  &  ( (~ (v8_conlat_1 B A))  &  (~ (v9_conlat_1 B A)) ) ) ) ) ) ) ) ).
tt(t26_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_connsp_1 C A)) ) )  =>  ( ((k6_setfam_1 (u1_struct_0 A) B) = (k1_struct_0 A))  | (v2_connsp_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ) ).
tt(t26_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k1_connsp_1 A B) (k1_connsp_2 A B))) ) ) ) ).
tt(t26_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden C (k6_connsp_3 A B C))) ) ) ) ) ) ) ).
tt(t26_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_rlvect_2 E A (k8_domain_1 (u1_struct_0 A) B C D)) =>  ((v2_convex1 E A) =>  ( (B = C)  |  ( (C = D)  |  ( (D = B)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k1_funct_1 E B) (k1_funct_1 E C)) (k1_funct_1 E D)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E B)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E C)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E D)) &  ((k6_rlvect_2 A E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 E B)) (k1_rlvect_1 A C (k1_funct_1 E C))) (k1_rlvect_1 A D (k1_funct_1 E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ((m2_convex4 D A B) => (m2_convex4 (k7_convex4 A C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t26_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((k5_qc_lang3 A C) = k1_xboole_0)  =>  ((k13_cqc_lang A C B) = C) ) ) ) ) ) ) ) ).
tt(t26_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ((k14_cqc_sim1 A (k4_cqc_lang B A D C)) = (k4_cqc_lang B A D C)) ) ) ) ) ) ) ) ) ).
tt(t26_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (~  ((r2_cqc_the1 A B C) &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = k6_numbers) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 1) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 2) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 3) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 4) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 5) )  &  (~  ((k2_xtuple_0 (k1_funct_1 C 1)) = 6) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A C B)) A)) ) ) ) ) ) ) ) ) ).
tt(t26_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r4_cqc_the3 A B C) & (r2_cqc_the3 A (k4_subset_1 (k3_cqc_lang A) B D) E))  => (r2_cqc_the3 A (k4_subset_1 (k3_cqc_lang A) C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_clopban1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k9_csspace4 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k9_csspace4 A B)))))) )  =>  ((v1_csspace3 C (k9_csspace4 A B)) => (v9_clvect_1 C (k9_csspace4 A B))) ) ) ) ) ) ) ) ).
tt(t26_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k12_csspace A (k5_algstr_0 A B C) D) = (k6_xcmplx_0 (k12_csspace A B D) (k12_csspace A C D))) ) ) ) ) ) ) ) ) ).
tt(t26_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  ((v5_decomp_1 C A B) & (v11_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t26_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A 16) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  (~  (A = 15) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  (~  ((r1_dickson A B C) & (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t26_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) A) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) A) (k7_real_1 C (k8_real_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t26_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k1_fcont_1 A B) C) D) = (k8_real_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t26_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers D A) E) B C) = (k7_real_1 (k8_real_1 A (k9_diff_1 D B C)) (k9_diff_1 E B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden B (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k16_sin_cos) A B) = (k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) A B)) ) ) ) ) ) ).
tt(t26_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (r1_tarski (k5_dilworth A) B))  & (r1_tarski (k5_dilworth A) (k4_dilworth A B))) ) ) ) ) ) ).
tt(t26_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_diraf A B C D E) & (r2_diraf A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k1_subset_1 A) = (a_1_1_domain_1 A)) ) ) ).
tt(t26_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k8_group_1 A B B) = (k8_group_1 A C C))  <=>  ( (B = C)  |  (B = (k4_algstr_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t26_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  ( (B = (k6_int_1 2 A))  =>  ((k2_binom (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) C D) 2) = (k3_rlvect_1 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) C 2) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B C) D)) (k2_binom (k9_int_3 A) D 2))) ) ) ) ) ) ) ) ) ) ).
tt(t26_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k11_ens_1 A))) =>  ( ((k3_graph_1 (k11_ens_1 A) B) = (k3_ens_1 A (k15_ens_1 A B)))  &  ((k4_graph_1 (k11_ens_1 A) B) = (k4_ens_1 A (k15_ens_1 A B))) ) ) ) ) ) ).
tt(t26_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( (C = (k6_matrixr1 (k1_entropy1 A) B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) =>  ((k3_matrix_1 k1_numbers C D E) = (k8_real_1 (k1_seq_1 A D) (k3_matrix_1 k1_numbers B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k3_enumset1 A B C D E) (k1_enumset1 F G H))) ) ) ) ) ) ) ) ) ).
tt(t26_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  ((k6_eqrel_1 A A (k1_eqrel_1 A) B) = A) ) ) ) ).
tt(t26_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v4_msualg_1 C A) &  ((v3_msafree2 C A) & (m1_msualg_2 C A B)) ) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v4_msualg_1 D A) &  ((v3_msafree2 D A) & (m1_msualg_2 D A B)) ) )  =>  (? [E:$i] :  ( ((v3_msualg_1 E A) &  ((v4_msualg_1 E A) &  ((v3_msafree2 E A) & (m1_msualg_2 E A B)) ) )  &  ((m1_msualg_2 C A E) & (m1_msualg_2 D A E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u2_e_siec A)))))) = (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))))  &  ((k3_relat_1 (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A)))))) = (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))) ) ) ) ).
tt(t26_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B (k3_rlvect_1 (k15_euclid A) C D)) = (k9_binop_2 (k23_rvsum_1 B C) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t26_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( (A = (k2_euclid_3 B))  |  (B = (k1_euclid_3 A)) )  =>  ((k1_comptrig A) = (k3_euclid_3 B)) ) ) ) ) ) ).
tt(t26_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k8_euclid A B C) D) = (k9_real_1 (k23_rvsum_1 B D) (k23_rvsum_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t26_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 (k3_rlvect_1 (k15_euclid 3) A B) (k3_rlvect_1 (k15_euclid 3) C D)) = (k3_rlvect_1 (k15_euclid 3) (k3_rlvect_1 (k15_euclid 3) (k3_rlvect_1 (k15_euclid 3) (k5_euclid_5 A C) (k5_euclid_5 A D)) (k5_euclid_5 B C)) (k5_euclid_5 B D))) ) ) ) ) ) ) ) ) ).
tt(t26_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) & (r1_xxreal_0 (k4_euclid_3 B D C) k32_sin_cos))  =>  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)) | (r1_xxreal_0 (k4_euclid_3 A D C) (k4_euclid_3 B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k11_euclid A (k6_euclid_7 A B)) = (k6_euclid_7 A B)) ) ) ) ) ).
tt(t26_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k9_euclid 3 k3_euclid_8 A) = (k1_euclid_8 k6_numbers A k6_numbers)) ) ) ).
tt(t26_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A)))))) =>  ( (B = (k2_waybel18 (k2_finseq_1 A) (k7_funcop_1 (k2_finseq_1 A) k3_topmetr)))  => (v2_cantor_1 B (k3_pcomps_1 (k14_euclid A)))) ) ) ) ) ) ).
tt(t26_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) D) = (k3_rlvect_1 (k15_euclid A) B (k3_rlvect_1 (k15_euclid A) C D))) ) ) ) ) ) ) ) ) ).
tt(t26_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid G)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid G)) =>  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid G)) =>  ((k8_euclid G (k7_euclid G (k7_euclid G (k9_euclid G H A) (k9_euclid G I B)) (k9_euclid G J C)) (k7_euclid G (k7_euclid G (k9_euclid G H D) (k9_euclid G I E)) (k9_euclid G J F))) = (k7_euclid G (k7_euclid G (k9_euclid G H (k9_real_1 A D)) (k9_euclid G I (k9_real_1 B E))) (k9_euclid G J (k9_real_1 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  ( ( ((k3_exchsort A) = k4_ordinal1)  &  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden B (k9_xtuple_0 A)) & (r2_hidden (k1_ordinal1 B) (k9_xtuple_0 A)))  => (r2_xboole_0 (k1_funct_1 A (k1_ordinal1 B)) (k1_funct_1 A B))) ) ) )  => (v4_exchsort A)) ) ) ).
tt(t26_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 B)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) &  ((v1_partfun1 E (u1_struct_0 B)) & (v5_memstr_0 E A B C)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 B)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ((r1_tarski (k16_funcop_1 C D) F) =>  ((k4_extpro_1 A B E F) = (k2_extpro_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~  (A = k1_supinf_1) )  &  ( (~  (B = k1_supinf_1) )  &  ( (~  ( (A = k1_supinf_1)  &  (B = k1_supinf_1) ) )  &  ( (~  ( (A = k2_supinf_1)  &  (B = k2_supinf_1) ) )  &  (~  ((k3_xxreal_0 A B) = (k2_extreal1 (k4_supinf_2 (k3_supinf_2 A B) (k3_extreal1 (k4_supinf_2 A B))) (k1_measure6 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) &  ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  ((m1_subset_1 (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)) (k4_card_3 (u3_msualg_1 A C))) & (m1_subset_1 (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)) (k4_card_3 (u3_msualg_1 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_facirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_facirc_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k2_msafree2 (k3_facirc_2 (k2_nat_1 C 1) A B)) = (k2_xboole_0 (k2_msafree2 (k3_facirc_2 C A B)) (k7_subset_1 (u1_struct_0 (k19_facirc_1 (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 B (k2_nat_1 C 1)) (k5_facirc_2 C A B))) (k2_msafree2 (k19_facirc_1 (k1_funct_1 A (k2_nat_1 C 1)) (k1_funct_1 B (k2_nat_1 C 1)) (k5_facirc_2 C A B))) (k1_tarski (k5_facirc_2 C A B)))))  &  ((v1_relat_1 (k3_msafree2 (k3_facirc_2 C A B))) &  (~ (v1_facirc_1 (k2_msafree2 (k3_facirc_2 C A B)))) ) ) ) ) ) ) ) ) ).
tt(t26_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C D) (k9_subset_1 k1_numbers A (k8_relset_1 k1_numbers k1_numbers C B))))) ) ) ) ) ) ) ).
tt(t26_fcont_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers))))  =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers)))) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers A))) ) ) ) ).
tt(t26_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B)))) (k8_real_1 (k1_seq_1 k19_sin_cos B) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t26_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9) A) B) = (k9_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k2_sin_cos9 B)) (k10_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t26_fdiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_fdiff_1 C A) & (r1_tarski B A))  => (r2_fdiff_1 C B)) ) ) ) ) ) ).
tt(t26_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k10_prob_1 A)) & (r2_hidden D (k10_prob_1 A)))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 B C) (k1_seq_1 B D))) (k5_square_1 (k9_real_1 C D)))) ) ) ) ) )  =>  ((r2_fdiff_1 B (k10_prob_1 A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) ) ) ) ) ) ).
tt(t26_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1))) &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k9_real_1 E A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers))  &  (~  (E = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D) k3_taylor_1) B) E) = (k10_real_1 (k9_real_1 (k8_real_1 2 A) E) (k8_real_1 E (k9_real_1 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)))) &  ( (B = (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_taylor_1 2)) C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) D) = (k10_real_1 (k26_sin_cos D) (k9_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k10_real_1 D A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C D) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 C D))) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)) B) D) = (k9_real_1 (k1_seq_1 k4_sin_cos6 (k10_real_1 D A)) (k10_real_1 D (k8_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 (k10_real_1 D A)))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  (~  (A = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) D) = (k10_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  (~  (A = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers B)) B) D) = (k10_real_1 (k9_real_1 (k1_seq_1 k16_sin_cos (k8_real_1 A D)) (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A D)))) (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k16_ff_siec A) (k16_ff_siec A)) = (k16_ff_siec A))  &  ( ((k3_relat_1 (k16_ff_siec A) (k15_ff_siec A)) = (k16_ff_siec A))  &  ( ((k3_relat_1 (k15_ff_siec A) (k15_ff_siec A)) = (k15_ff_siec A))  &  ((k3_relat_1 (k15_ff_siec A) (k16_ff_siec A)) = (k15_ff_siec A)) ) ) ) ) ) ).
tt(t26_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 4)) = (k2_nat_1 (k1_pre_ff (k1_nat_1 A 2)) (k1_pre_ff (k1_nat_1 A 3)))) ) ) ).
tt(t26_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k4_nat_1 2 (k1_fib_num3 (k2_nat_1 A B))) = (k2_nat_1 (k4_nat_1 (k1_fib_num3 A) (k1_fib_num3 B)) (k4_nat_1 (k4_nat_1 5 (k1_pre_ff A)) (k1_pre_ff B)))) ) ) ) ) ).
tt(t26_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k13_complex1 (k2_xcmplx_0 (k1_pre_ff A) (k6_square_1 (k2_xcmplx_0 (k3_xcmplx_0 5 (k1_pepin (k1_pre_ff A))) (k3_xcmplx_0 4 (k3_power (k4_xcmplx_0 1) A))))) 2)) ) ) ).
tt(t26_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((r4_finseq_8 A B C) => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 (k3_finseq_1 B) (k3_finseq_1 C)))) ) ) ) ) ) ) ).
tt(t26_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  & (r2_hidden (k5_lattices A) B))  =>  ( (B = (k1_filter_0 A))  &  (B = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t26_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r3_binop_1 A C E) & (r3_binop_1 B D F))  <=> (r3_binop_1 (k2_zfmisc_1 A B) (k1_domain_1 A B C D) (k6_filter_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k6_domain_1 (u1_struct_0 A) B)))  &  ((v18_lattices (k6_domain_1 (u1_struct_0 A) B) A) &  ((v21_lattices (k6_domain_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_domain_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v13_lattices A)) ) ) ) ) ).
tt(t26_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 A) (k4_finseq_1 (k7_finseq_1 A B)))) ) ) ) ).
tt(t26_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 B) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) A)))) ) ) ) ) ) ).
tt(t26_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) <=>  ((m1_subset_1 (k6_xcmplx_0 B 1) k5_numbers) & (m1_subset_1 (k6_xcmplx_0 (k3_finseq_1 A) B) k5_numbers)) ) ) ) ) ) ).
tt(t26_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ( (~  (C = (k4_finseq_4 A B)) )  &  ((k1_funct_1 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t26_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  ((r2_hidden A (k4_finseq_1 (k2_rfinseq C B D))) => (r2_hidden (k2_xcmplx_0 B A) (k4_finseq_1 D))) ) ) ) ) ) ) ) ).
tt(t26_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k5_finseq_4 (k10_finseq_1 A B) B) = (k9_finseq_1 A)) ) ) ) ).
tt(t26_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k2_finseq_7 A (k3_finseq_4 A B C D) 2 3) = (k3_finseq_4 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t26_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) & (r1_tarski C B))  => (r2_finseq_8 A B C 1)) ) ) ) ) ) ) ).
tt(t26_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k4_finseqop A A (k1_finseqop A A A F D E) (k10_funcop_1 A A F B (k6_partfun1 A))) (k1_finseqop A A A F (k4_finseqop A A D (k10_funcop_1 A A F B (k6_partfun1 A))) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k9_fintopo2 A C)) (k9_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t26_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k5_fintopo3 A B (k2_nat_1 C 1)) (k5_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t26_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_fintopo6 A B) &  (B = (k1_struct_0 A)) ) ) ) ) ) ) ).
tt(t26_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k7_flang_1 A B 2) = (k6_flang_1 A B B)) ) ) ) ).
tt(t26_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C (k2_xcmplx_0 D 1)) =>  ((k1_flang_2 A B C (k2_xcmplx_0 D 1)) = (k4_subset_1 (k3_catalan2 A) (k1_flang_2 A B C D) (k7_flang_1 A B (k2_xcmplx_0 D 1)))) ) ) ) ) ) ) ) ) ).
tt(t26_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_tarski C (k6_flang_1 A C (k1_flang_3 A B D))) & (r1_tarski C (k6_flang_1 A (k1_flang_3 A B D) C))) ) ) ) ) ) ) ) ) ).
tt(t26_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v5_relat_1 B A) & (v1_finseq_1 B))  => (m2_finseq_1 B A)) ) ) ) ).
tt(t26_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_fomodel1 C A) & (m1_subset_1 C (k1_fomodel1 A)))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_fomodel2 D A B)) )  =>  (? [E:$i] :  ((m1_subset_1 E B) &  ( (E = (k1_funct_1 (k4_fomodel2 A B D C) k1_xboole_0))  &  ((k5_fomodel2 D C E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_frechet2,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_pcomps_1 A)))))) ) ) ) ) ) ).
tt(t26_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_frechet A) => (v4_frechet A)) ) ) ).
tt(t26_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k1_fscirc_2 A B C) (k2_fscirc_2 A B C)))) => (v1_circuit2 (k5_facirc_1 (k1_fscirc_2 A B C) (k2_fscirc_2 A B C) D (k2_nat_1 1 (k4_nat_1 2 A))) (k1_fscirc_2 A B C) (k2_fscirc_2 A B C))) ) ) ) ) ) ) ) ).
tt(t26_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r6_fsm_1 A B C D E (k2_xcmplx_0 F G)) => (r6_fsm_1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers)))  =>  ( ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  ((r1_xxreal_0 B k6_numbers) & (r1_xxreal_0 C k6_numbers)) )  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = 1) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 B k6_numbers) & (r1_xxreal_0 C k6_numbers))  =>  ( ( (~  (B = k6_numbers) )  &  (~  (C = k6_numbers) ) )  |  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = k6_numbers) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 k6_numbers C))  &  (~  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r3_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C) (k2_square_1 (k2_absvalue B) (k2_absvalue C)))) ) ) ) ) ) ) ).
tt(t26_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 C)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C)))))  =>  ((r1_rewrite1 (k1_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G) (k4_tarski A (k1_flang_1 C D E)) (k4_tarski B (k1_flang_1 C F E))) => (r1_rewrite1 (k1_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G) (k4_tarski A D) (k4_tarski B F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (~  ((r2_hidden A (k2_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden B (k2_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden C (k2_msafree2 (k13_ftacell1 A B C D E))) &  ((r2_hidden D (k2_msafree2 (k13_ftacell1 A B C D E))) & (r2_hidden E (k2_msafree2 (k13_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k4_funcop_1 B A C) = (k3_funcop_1 B A (k2_funcop_1 (k9_xtuple_0 A) C))) ) ) ) ) ) ).
tt(t26_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_funcsdom A)))  &  ((v13_algstr_0 (k11_funcsdom A)) &  ((v3_group_1 (k11_funcsdom A)) &  ((v5_group_1 (k11_funcsdom A)) &  ((v4_vectsp_1 (k11_funcsdom A)) &  ((v5_vectsp_1 (k11_funcsdom A)) &  ((v2_rlvect_1 (k11_funcsdom A)) &  ((v3_rlvect_1 (k11_funcsdom A)) &  ((v4_rlvect_1 (k11_funcsdom A)) & (l6_algstr_0 (k11_funcsdom A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 (k3_relat_1 B A)) &  ((k10_xtuple_0 B) = (k9_xtuple_0 A)) )  =>  ((v2_funct_1 B) & (v2_funct_1 A)) ) ) ) ) ) ).
tt(t26_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_1 D) & (r2_hidden C A))  =>  ( (B = k1_xboole_0)  |  ((k1_funct_1 (k2_funct_1 D) (k1_funct_1 D C)) = C) ) ) ) ) ) ) ) ).
tt(t26_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A (k1_zfmisc_1 (k10_xtuple_0 B))) =>  ((k3_tarski (k7_relat_1 (k3_funct_3 B) A)) = (k8_relat_1 B (k3_tarski A))) ) ) ) ) ).
tt(t26_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_partfun1 A (k1_funct_4 B C)) => (r1_partfun1 (k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 C))) B)) ) ) ) ) ) ) ).
tt(t26_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k1_funct_2 A B)) =>  ( ((k9_xtuple_0 (k2_funct_5 C)) = (k2_zfmisc_1 (k9_xtuple_0 C) A))  &  ((k9_xtuple_0 (k4_funct_5 C)) = (k2_zfmisc_1 A (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t26_funct_6,ax, (! [A:$i] :  ( ((k3_card_3 (k7_funcop_1 k1_xboole_0 A)) = k1_xboole_0)  &  ((k4_funct_6 (k7_funcop_1 k1_xboole_0 A)) = k1_xboole_0) ) ) ).
tt(t26_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_funct_7 A B C) => (r1_funct_7 B A C)) ) ) ) ) ) ).
tt(t26_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_8 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 B k1_numbers k1_numbers C) => (r1_funct_8 B k1_numbers k1_numbers (k15_valued_1 k1_numbers k1_numbers C A))) ) ) ) ) ) ) ).
tt(t26_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 k30_sin_cos (k8_real_1 k32_sin_cos A))) ) ).
tt(t26_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 B C C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  ((k8_functor0 A B (k9_functor0 A B C D) E F G) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ((m1_functor2 G B C E F) =>  ((r1_functor2 B C E F) => (r8_pboole (u1_struct_0 A) (k6_functor3 A B C E F D G) (k7_functor3 A B C D D E F (k4_functor2 A B D) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 D E))  => (r1_fuzzy_1 (k1_fuzzy_1 A B D) (k1_fuzzy_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k1_fuzzy_2 A B C) (k4_fuzzy_1 A)) => (r1_fuzzy_1 B C)) ) ) ) ) ) ) ).
tt(t26_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((k1_fuzzy_4 B A (k2_fuzzy_4 B A E) D C) = (k1_fuzzy_4 A B E C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B)) k6_numbers))  =>  ( (B = (k4_struct_0 A))  | (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D C) (k3_funct_2 (u1_struct_0 A) k7_numbers D B))) ) ) ) ) ) ) ) ) ) ).
tt(t26_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k4_fvsum_1 A B C (k6_fvsum_1 A B C)) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)))  &  ((k4_fvsum_1 A B (k6_fvsum_1 A B C) C) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t26_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  ( (~ (v1_xboole_0 (k20_gate_1 A B C D E)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  (~ (v1_xboole_0 E)) ) ) ) ) )  & (v1_xboole_0 (k20_gate_1 A B C D E))) ) ) ) ) ) ) ) ).
tt(t26_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=>  (C = (k4_gcd_1 A B C)) ) ) ) ) ) ) ) ).
tt(t26_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ((k9_genealg1 D E F A B C) = (k9_genealg1 D E F C A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) & (r2_geomtrap A B C D E F G))  => (r2_geomtrap A B C D E (k1_geomtrap A D F) (k1_geomtrap A E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k10_gfacirc1 A B C))) & (r2_hidden (k12_gfacirc1 A B C) (k3_msafree2 (k10_gfacirc1 A B C)))) ) ) ) ).
tt(t26_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v2_facirc_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k2_msafree2 (k5_gfacirc2 (k1_nat_1 C 1) A B)) = (k2_xboole_0 (k2_msafree2 (k5_gfacirc2 C A B)) (k7_subset_1 (u1_struct_0 (k25_gfacirc1 (k1_funct_1 A (k1_nat_1 C 1)) (k1_funct_1 B (k1_nat_1 C 1)) (k7_gfacirc2 C A B))) (k2_msafree2 (k25_gfacirc1 (k1_funct_1 A (k1_nat_1 C 1)) (k1_funct_1 B (k1_nat_1 C 1)) (k7_gfacirc2 C A B))) (k1_tarski (k7_gfacirc2 C A B)))))  &  ((v1_relat_1 (k3_msafree2 (k5_gfacirc2 C A B))) &  (~ (v1_facirc_1 (k2_msafree2 (k5_gfacirc2 C A B)))) ) ) ) ) ) ) ) ) ).
tt(t26_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ( ((k15_glib_000 A) = 1)  <=> (v4_glib_000 A)) ) ) ).
tt(t26_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  ((k3_glib_002 A) = (k3_glib_002 B)) ) ) ) ) ) ).
tt(t26_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) &  ((v1_glib_003 B) & (v7_glib_003 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( ( (C = D)  &  ((k5_glib_003 A) = (k5_glib_003 B)) )  =>  ((k10_glib_003 A C) = (k10_glib_003 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k11_glib_004 A B))) = (k2_glib_002 A B)) ) ) ) ) ).
tt(t26_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k1_matrix_1 C) A) |  ((r1_xxreal_0 (k3_finseq_1 C) B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 C B A) (k3_goboard5 C B (k2_nat_1 A 1))) = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B (k2_nat_1 A 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) (k2_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t26_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) |  ((k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) = (a_3_0_goboard6 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 E)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 E)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 E)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 E)) & (r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 A 1) B)) (k10_real_1 1 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 C 1) D)))) ) ) ) ) ) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1) (k19_euclid 1 1)) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 1)) (k13_complex1 1 2)) (k19_euclid k6_numbers 1))) (k3_topreal1 2 A))) ) ).
tt(t26_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k3_goboard5 B k6_numbers A) = (a_2_2_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t26_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k2_gobrd13 D E A) = (k3_goboard5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k3_goboard9 B)) & (r1_xxreal_0 (k18_euclid A) (k9_pscomp_1 (k3_topreal1 2 B)))) ) ) ) ) ) ).
tt(t26_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k6_goedelcp A (k6_domain_1 (k3_cqc_lang A) B)) = (k24_qc_lang1 A B)) ) ) ) ) ).
tt(t26_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_graph_1 B) & (l1_graph_1 B)) )  =>  ((r4_graph_1 A B) => (v3_graph_1 A)) ) ) ) ) ).
tt(t26_graph_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) => (m1_subset_1 B (k1_zfmisc_1 B))) ) ) ).
tt(t26_graph_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_graph_1 C) & (l1_graph_1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (~  ((r2_hidden A (u4_struct_0 C)) &  ( (~ (r2_hidden A B))  &  ( ( (D = (k1_funct_1 (u2_graph_1 C) A))  |  (D = (k1_funct_1 (u1_graph_1 C) A)) )  &  ((k10_graph_1 C D) = (k7_graph_3 C D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 A)) =>  ((r1_tarski (k2_graph_5 A B) (k2_graph_5 A (k8_finseq_1 (u4_struct_0 A) B C))) & (r1_tarski (k2_graph_5 A C) (k2_graph_5 A (k8_finseq_1 (u4_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t26_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) => (r1_tarski (k13_graphsp B A) (k2_finseq_1 A))) ) ) ) ).
tt(t26_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_grcat_1 C) & (m1_grcat_1 C A B))  => (m4_grcat_1 (k1_tarski C) A B)) ) ) ) ) ) ).
tt(t26_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v1_gr_cy_1 B) => (v1_gr_cy_1 (k10_group_6 B A C))) ) ) ) ) ) ) ).
tt(t26_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v2_gr_cy_3 A)) )  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( ((k4_nat_d A 4) = 1)  &  (! [B:$i] :  ( ((v7_ordinal1 B) &  ((v1_int_2 B) & (v1_gr_cy_3 B)) )  =>  (~  ((k4_nat_d (k1_gr_cy_3 A) B) = (k6_xcmplx_0 B 2)) ) ) ) ) ) ) ) ) ).
tt(t26_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k8_relat_1 C B)) <=>  ((r2_hidden (k4_tarski A (k1_funct_1 C A)) C) & (r2_hidden (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t26_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  ((v15_algstr_0 (k2_grsolv_1 A B C D)) &  ((v1_group_3 (k2_grsolv_1 A B C D) (k10_group_6 A B C)) & (m1_group_6 (k2_grsolv_1 A B C D) B (k10_group_6 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( ((r1_tarski E D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden F D) => (r7_polyred A B C F E)) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden F D) => (r10_polyred A B C F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden E D) =>  ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) )  =>  ((r2_hidden (k7_polynom1 A C) D) | (r1_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  ((r1_tarski (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E)) (k2_polynom1 (k15_pre_poly A) C D)) & (r1_tarski (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E)) (k2_polynom1 (k15_pre_poly A) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 C D) => (r1_tarski (k2_group_11 A B C) (k2_group_11 A B D))) ) ) ) ) ) ) ) ) ).
tt(t26_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A 1 B) = B) ) ) ) ) ).
tt(t26_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_group_2 A (k3_group_2 A B C)) = (k3_group_2 A (k1_group_2 A B) (k1_group_2 A C))) ) ) ) ) ) ) ).
tt(t26_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_3 A (k2_group_1 A B) C) = (k2_group_1 A (k2_group_3 A B C))) ) ) ) ) ) ) ).
tt(t26_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k4_group_4 A (k5_finseq_2 k4_numbers (k3_finseq_1 B) (k2_group_4 k6_numbers)) B) = (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 B) (k1_group_1 A))) ) ) ) ) ).
tt(t26_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_5 A B (k6_algstr_0 A C D)) = (k6_algstr_0 A (k2_group_5 A B D) (k2_group_3 A (k2_group_5 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t26_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((k7_struct_0 (k5_group_6 A B)) = (k17_group_2 A B)) ) ) ) ) ).
tt(t26_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_group_7 (k11_finseq_1 A B C)) &  ((v2_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) & (v3_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (m1_group_9 (k18_group_9 A B C) A (k18_group_9 A B D))) ) ) ) ) ) ) ) ).
tt(t26_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v2_group_10 A B) &  ( ((k2_groupp_1 B A) = 2)  &  ((k6_group_1 A C) = (k1_newton B 2)) ) )  => (v5_group_1 A)) ) ) ) ) ) ) ).
tt(t26_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hahnban1 B k1_complfld A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((v1_funct_1 (k12_hahnban1 A B)) &  ((v1_funct_2 (k12_hahnban1 A B) (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v2_hahnban (k12_hahnban1 A B) (k10_hahnban1 A)) &  ((v3_hahnban (k12_hahnban1 A B) (k10_hahnban1 A)) & (m1_subset_1 (k12_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t26_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) => (m2_hallmar1 B A B)) ) ) ).
tt(t26_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v2_compts_1 B (k3_pcomps_1 A)) => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A B) C) (k1_funct_1 (k5_weierstr A B) C))) ) ) ) ) ) ) ).
tt(t26_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  (~  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 B A k1_complfld) &  ((v1_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B))))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = (k3_vectsp_4 k1_complfld A D (k9_vectsp10 k1_complfld A (k1_hermitan A B))))  =>  ((k3_funct_2 (u1_struct_0 (k6_vectsp10 k1_complfld A (k9_vectsp10 k1_complfld A (k1_hermitan A B)))) (u1_struct_0 k1_complfld) (k2_hermitan A B) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_normform A))) =>  ( ( (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((r2_hidden E C) => (r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) E B) (k7_normform A))) ) )  & (r3_lattices (k12_normform A) (k4_lattices (k12_normform A) C (k3_funct_2 (k7_normform A) (u1_struct_0 (k12_normform A)) (k4_heyting1 A) B)) D))  => (r3_lattices (k12_normform A) (k3_funct_2 (k7_normform A) (u1_struct_0 (k12_normform A)) (k4_heyting1 A) B) (k5_binop_1 (u1_struct_0 (k12_normform A)) (k9_heyting1 A) C D))) ) ) ) ) ) ) ) ).
tt(t26_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  ((k4_lattices (k5_substlat A B) C (k3_funct_2 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k4_heyting2 A B) C)) = (k5_lattices (k5_substlat A B))) ) ) ) ) ) ).
tt(t26_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_heyting3 1 A) = (k7_domain_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers A)) (k2_heyting3 1 A) (k3_heyting3 1 A))) ) ) ).
tt(t26_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers k19_sin_cos B) D) C) A) = (k8_real_1 B (k1_seq_1 k19_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 C k32_sin_cos) 2))))) ) ) ) ) ) ) ) ) ) ).
tt(t26_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_quofield D A B) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k7_ideal_1 A C)) = (k7_ideal_1 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B C)) (k3_hilbert1 B (k3_hilbert1 A C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t26_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (~  ((k3_hilbert1 B C) = (k1_hilbert2 A)) ) ) ) ) ) ) ) ).
tt(t26_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k1_funct_1 (k2_funct_2 (k9_funct_2 A B) (k1_hilbert3 A B C D)) E) = (k1_partfun1 A A A B C (k1_partfun1 A B B B E (k2_funct_2 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~  (C = D) )  &  (~  ((k1_normsp_1 A (k3_hurwitz A B D) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r1_xxreal_0 4 (k3_finseq_1 B)) =>  ((r1_idea_1 A (k1_recdef_1 (k11_idea_1 A B C) 1)) &  ((r1_idea_1 A (k1_recdef_1 (k11_idea_1 A B C) 2)) &  ((r1_idea_1 A (k1_recdef_1 (k11_idea_1 A B C) 3)) & (r1_idea_1 A (k1_recdef_1 (k11_idea_1 A B C) 4))) ) ) ) ) ) ) ) ) ) ).
tt(t26_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_ideal_1 D A B) => (m2_ideal_1 (k9_fvsum_1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t26_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B C))  &  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ( ((r2_incsp_1 A B E) & (r3_incsp_1 A C E))  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) (u1_cat_1 C) (k7_isocat_1 C)) =>  ((k14_index_1 A B B D (k14_index_1 B C C E F)) = (k14_index_1 A C C (k9_cat_1 A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((k2_instalg1 A A B) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ).
tt(t26_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 A (k1_int_1 A)))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 A (k1_int_1 A))) ) ) ) ) ).
tt(t26_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_2 A B) & (r1_int_2 C B))  => (r1_int_2 (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t26_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B C) D) A) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [E:$i] :  ((v1_int_1 E) =>  ( ( ((r1_int_2 B A) &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B E) D) A) = k6_numbers) )  => (r2_hidden E (k6_eqrel_1 k4_numbers k4_numbers (k1_int_4 A) C)))  &  ((r2_hidden E (k6_eqrel_1 k4_numbers k4_numbers (k1_int_4 A) C)) =>  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B E) D) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (~  ((k6_int_1 A B) = k6_numbers) )  =>  ((k2_int_5 (k1_pepin A) B) = 1) ) ) ) ) ) ).
tt(t26_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_int_6 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) => (r2_int_1 (k1_funct_1 B C) 1 (k1_funct_1 A C))) ) ) ) ) ) ) ).
tt(t26_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_xxreal_0 k6_numbers (k2_hurwitz A B)) => (v1_uproots B A)) ) ) ) ) ).
tt(t26_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~  ((k7_real_1 A B) = k6_numbers) )  &  ( (~  ((k9_real_1 A B) = k6_numbers) )  &  (~  ((k2_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 B k6_numbers) k16_sin_cos))) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B))))) (k4_seq_4 C)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B))))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 C G) = 1)  &  ( ((k1_seq_1 D G) = (k12_binop_2 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 D G))) ) ) ) ) ) )  &  ( (F = (k1_relset_1 k1_numbers E))  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B)) & (r2_relset_1 k1_numbers k1_numbers E (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6) (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k41_valued_1 k1_numbers k1_numbers D)) (k4_taylor_1 (k18_binop_2 1 2))) A))))) ) ) )  =>  ((k2_integra5 B E) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6)) (k4_seq_4 B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k4_sin_cos6)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k32_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos)))))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t26_integr14,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = (k10_real_1 (k4_real_1 A (k1_seq_1 k16_sin_cos E)) (k5_prepower (k1_seq_1 k19_sin_cos E) (k3_real_1 A 1)))) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)))) &  ((r1_xxreal_0 1 A) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_taylor_1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t26_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) F) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) )  =>  ((k12_integr15 D E A (k2_nfcont_4 A k1_numbers F)) = (k6_euclid A (k12_integr15 D E A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_seq_2 (k2_partfun1 B k1_numbers D B)) & (r2_hidden A (k4_finseq_1 C)))  => (r1_xxreal_0 (k8_real_1 (k4_seq_4 (k1_rvsum_1 (k2_partfun1 B k1_numbers D (k2_integra1 B C A)))) (k3_integra1 (k2_integra1 B C A))) (k8_real_1 (k4_seq_4 (k1_rvsum_1 D)) (k3_integra1 (k2_integra1 B C A))))) ) ) ) ) ) ) ) ) ).
tt(t26_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers)))) )  =>  (! [E:$i] :  ((m1_integra1 E C) =>  ( ((r2_hidden B (k4_finseq_1 E)) &  ((v2_seq_2 (k2_partfun1 C k1_numbers D C)) & (r1_xxreal_0 A k6_numbers)) )  =>  ((k1_seq_1 (k4_integra1 C (k26_valued_1 C k1_numbers D A) E) B) = (k8_real_1 A (k1_seq_1 (k5_integra1 C D E) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integra4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers D B)) &  ((r1_xxreal_0 k6_numbers A) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r2_hidden F B) & (r2_hidden G B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 E F) (k1_seq_1 E G))) (k8_real_1 A (k7_real_1 (k18_complex1 (k9_real_1 (k1_seq_1 C F) (k1_seq_1 C G))) (k18_complex1 (k9_real_1 (k1_seq_1 D F) (k1_seq_1 D G))))))) ) ) ) ) ) ) )  => (r1_xxreal_0 (k9_real_1 (k4_seq_4 (k1_rvsum_1 E)) (k5_seq_4 (k1_rvsum_1 E))) (k8_real_1 A (k7_real_1 (k9_real_1 (k4_seq_4 (k1_rvsum_1 C)) (k5_seq_4 (k1_rvsum_1 C))) (k9_real_1 (k4_seq_4 (k1_rvsum_1 D)) (k5_seq_4 (k1_rvsum_1 D))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 D)) &  (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden E (k3_integra5 A B)) =>  ((k1_seq_1 D E) = C) ) ) ) ) )  =>  ((r1_integra5 (k3_integra5 A B) D) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers D (k3_integra5 A B))) &  ((k4_integra5 A B D) = (k3_xcmplx_0 C (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_real_1 (k1_seq_1 k19_sin_cos A) (k1_seq_1 k19_sin_cos B)) = (k4_integra5 A B k16_sin_cos)) ) ) ) ) ).
tt(t26_integra8,ax, ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A k1_numbers) =>  ((k1_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) A) = (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A)) ) ) ) ) ).
tt(t26_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D) &  ((v1_comseq_2 (k2_partfun1 D k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D)) &  ((v3_integra1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A C) D) D) &  ((v1_comseq_2 (k2_partfun1 D k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D)) & (v3_integra1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D) D)) ) ) ) )  =>  ((k1_integra9 D (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) C) = (k9_real_1 (k1_integra9 D A C) (k1_integra9 D B C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ).
tt(t26_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ( ((r2_hidden (k3_intpro_1 A B) k8_intpro_1) & (r2_hidden (k3_intpro_1 B C) k8_intpro_1))  => (r2_hidden (k3_intpro_1 A C) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t26_irrat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 (k1_seq_1 B E) (k6_xcmplx_0 A C))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  |  ((v2_comseq_2 B) &  ((k2_seq_2 B) = A) ) ) ) ) ) ) ) ).
tt(t26_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  ((r2_nattra_1 B A C D) =>  (! [E:$i] :  ((m2_nattra_1 E B A C D) =>  (! [F:$i] :  ((m2_nattra_1 F B A C D) =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k4_nattra_1 B A C D E G) = (k4_nattra_1 B A C D F G)) ) )  => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_nattra_1 (k8_cat_2 A B) C D E) =>  (! [F:$i] :  ((m2_nattra_1 F (k8_cat_2 A B) C D E) =>  (! [G:$i] :  ((m2_nattra_1 G (k8_cat_2 A B) C D E) =>  ((r2_funct_2 (u1_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) (k6_isocat_2 A B C D E F) (k6_isocat_2 A B C D E G)) => (r2_funct_2 (u1_struct_0 (k8_cat_2 A B)) (u4_struct_0 C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k3_rcomp_1 B k1_xxreal_0))  =>  ((k1_tops_1 k3_topmetr A) = (k2_rcomp_1 B k1_xxreal_0)) ) ) ) ) ) ).
tt(t26_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 A) &  ((v1_topreal1 B) &  ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ( (~  ((k1_funct_1 A 1) = (k1_funct_1 A (k3_finseq_1 A))) )  &  ( (~  ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B))) )  &  ((r1_goboard4 (k1_goboard1 A) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k1_goboard1 B) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k2_goboard1 A) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) &  ((r1_goboard4 (k2_goboard1 B) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) & (r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) = k6_numbers) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = E)  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = (k10_real_1 1 E)) ) ) ) ) )  & (v5_pre_topc C A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (A = a_0_3_jgraph_3)  => (v1_topreal2 A)) ) ) ).
tt(t26_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_3_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t26_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k10_real_1 (k17_euclid B) (k12_euclid B)) A))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  (~ (r1_xxreal_0 (k17_euclid C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_8_jgraph_6)  &  (B = a_0_9_jgraph_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = B) ) ) ) ) ) ).
tt(t26_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 E (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid C) F) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)))  &  ( ((k17_euclid B) = (k17_euclid C))  &  ( ((k17_euclid C) = (k17_euclid A))  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C)))  &  (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A B) & (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A B)) (k3_jordan11 A B))) ) ) ) ) ) ).
tt(t26_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan17 A B C D E) & (r1_jordan17 A B C E D))  =>  ( (B = C)  |  ( (B = D)  |  ( (C = E)  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((r1_jordan18 A B C D E F) => (r1_jordan18 A B C D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 (k17_euclid B) (k6_pscomp_1 A)))  &  ( (~ (r1_xxreal_0 (k8_pscomp_1 A) (k17_euclid B)))  &  ((r2_hidden B (k3_jordan19 A)) & (r2_hidden B (k4_jordan19 A))) ) ) ) ) ) ) ) ).
tt(t26_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k3_finseq_1 B)) & (v9_rltopsp1 (k3_goboard5 B A k6_numbers) (k15_euclid 2))) ) ) ) ) ) ).
tt(t26_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_2_jordan1 A B C D))  &  (F = (a_4_3_jordan1 A B C D)) )  => (r1_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k3_finseq_1 (k1_jordan8 B A)))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ).
tt(t26_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k3_finseq_1 (k1_jordan8 B A)) C) (k10_xtuple_0 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t26_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k2_jordan1e B A) (k23_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k2_jordan1e B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ) ).
tt(t26_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 E)) &  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C D)) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_sprect_2 A) <=> (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k22_pscomp_1 (k3_topreal1 2 A))) 2) (k16_pscomp_1 (k3_topreal1 2 A)))) ) ) ).
tt(t26_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k6_pscomp_1 A) (k6_pscomp_1 B)) =>  ((k6_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k6_pscomp_1 A)) ) ) ) ) ) ).
tt(t26_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_topreal6 2 (k1_rlvect_1 (k15_euclid 2) A C) (k1_rlvect_1 (k15_euclid 2) B C)) = (k8_real_1 (k18_complex1 C) (k1_topreal6 2 A B))) ) ) ) ) ) ) ).
tt(t26_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_jordan20 A B C D G) &  ( ((k17_euclid E) = G)  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) D E) A) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) D E))) ) )  => (r1_jordan20 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((k2_jordan21 A) = (k18_pscomp_1 A)) ) ) ) ).
tt(t26_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k18_euclid (k2_jordan21 (k3_topreal1 2 (k1_jordan9 A B)))) (k18_euclid (k2_jordan21 (k3_topreal1 2 (k1_jordan9 A C)))))) ) ) ) ) ) ) ).
tt(t26_jordan23,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((v3_funct_1 (k3_graph_2 A B)) &  ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1)) )  =>  ( (A = k1_xboole_0)  | (v3_funct_1 B)) ) ) ) ) ) ).
tt(t26_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (a_2_0_jordan2b B C))  => (v3_pre_topc A k3_topmetr)) ) ) ) ) ) ) ).
tt(t26_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (r1_tarski (k2_jordan2c A B) (k3_subset_1 (u1_struct_0 (k15_euclid A)) B))) ) ) ) ).
tt(t26_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ( ( (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1)))  =>  ((k3_finseq_1 (k2_jordan3 A B)) = (k9_real_1 (k3_finseq_1 A) (k1_jordan3 A B))) )  &  ( (~  (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1))) )  =>  ((k3_finseq_1 (k2_jordan3 A B)) = (k7_real_1 (k9_real_1 (k3_finseq_1 A) (k1_jordan3 A B)) 1)) ) ) ) ) ) ) ) ).
tt(t26_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) =>  ((r1_xxreal_0 C D) |  ( ((k3_finseq_1 B) = (k7_nat_d (k2_nat_1 (k3_finseq_1 A) D) C))  &  ( (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C (k7_nat_d (k3_finseq_1 A) 1)) (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) D A)))  &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C (k7_nat_d (k3_finseq_1 A) 1)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan5a,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = B) )  <=>  ((k6_measure6 (k2_rcomp_1 A B)) = (k1_rcomp_1 A B)) ) ) ) ) ) ).
tt(t26_jordan5b,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))))  =>  ((r1_xxreal_0 C B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A))))) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t26_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v4_topreal1 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) & (r2_hidden B (k2_topreal1 2 A C))) ) )  => (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t26_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_2_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k15_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k15_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t26_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((k5_jordan6 A B C D E) = (a_5_0_jordan6 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v1_topreal1 C) &  ((r1_tarski (k3_topreal1 2 D) (k3_topreal1 2 C)) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_gobrd13 C B A) (k3_topreal1 2 D)))  |  (E = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_gobrd13 C B A) (k3_topreal1 2 D))) )  => (v2_connsp_1 E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_gobrd10 C D))  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan_a A C B) (k2_jordan_a A D B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v9_rltopsp1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (? [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  & (r1_tarski B (k1_topreal9 A C D))) ) ) ) ) ) ) ) ).
tt(t26_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r2_xboole_0 D E) &  ( (~ (r2_abian (u1_struct_0 A) (k5_knaster A B C E) B))  &  ((k5_knaster A B C D) = (k5_knaster A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_kurato_1,ax, ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) = (k2_rcomp_1 2 k1_xxreal_0)) ).
tt(t26_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v9_rltopsp1 B (k15_euclid 2)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A C) B)) ) )  => (v2_compts_1 (k1_kurato_2 (k15_euclid 2) A) (k15_euclid 2))) ) ) ) ) ).
tt(t26_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k9_laplace A D B C) = (k8_laplace A D B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_group_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_group_4 A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((r3_lattices (k11_group_4 A) D E) <=> (m1_group_6 B A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (r1_lattice2 (u1_struct_0 A) (u2_lattices A) (u1_lattices A))) ) ).
tt(t26_lattice3,ax, (! [A:$i] : (v5_lattice3 (k1_lattice3 A))) ).
tt(t26_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v3_filter_0 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r3_lattices A (k4_lattices A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_filter_0 B D E))) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t26_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  ((k11_lattice5 A B C D k1_xboole_0) = C) ) ) ) ) ) ) ) ) ).
tt(t26_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v8_lattice6 B A) => (r1_tarski (k6_lattice6 A) B)) ) ) ) ) ).
tt(t26_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v1_lattice5 C A B) =>  (! [D:$i] :  ((m1_lattice5 D A B C) =>  (! [E:$i] :  ((v3_ordinal1 E) => (v1_lattice5 (k6_lattice8 A B C D E) (k3_lattice8 A E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k7_lattices A C) (k7_lattices A B))) ) ) ) ) ) ) ).
tt(t26_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B))) =>  ((k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k11_lexbfs A B C E)) D) = (k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_lfuzzy_1 A B (k1_nat_1 C 1)) (k4_fuzzy_4 A A A (k4_lfuzzy_1 A B C) B))) ) ) ) ) ) ).
tt(t26_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) & (m2_valued_0 B k1_numbers A))  => (v1_limfunc1 B)) ) ) ) ) ).
tt(t26_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 A D))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A)))) ) ) ) ) )  | (r2_limfunc2 B A)) ) ) ) ) ) ).
tt(t26_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_limfunc3 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))) (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r2_limfunc3 C A)) ) ) ) ) ) ) ) ).
tt(t26_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r3_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k2_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r6_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t26_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((r1_lmod_6 A C D) & (r1_lmod_6 A C E))  => (r1_lmod_6 A C (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k11_lopban_1 A B)) = (k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B))) ) ) ) ) ).
tt(t26_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_lopban_3 B A) => (v1_lopban_3 B A)) ) ) ) ) ).
tt(t26_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lopban_4 A C D) =>  ((k5_algstr_0 A (k6_algstr_0 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A C)) B) (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A D)) B)) (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A (k3_rlvect_1 A C D))) B)) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k8_lopban_4 A C D B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t26_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k3_tarski (k10_lopclset A)) = (k7_lopclset A)) ) ) ).
tt(t26_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k10_lpspace1 B C D))) =>  ( (E = F)  =>  ((k26_valued_1 B k1_numbers E A) = (k1_rlvect_1 (k10_lpspace1 B C D) F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ((r2_hidden D (k1_lpspace2 A B C F)) => (r2_hidden (k26_valued_1 A k1_numbers D E) (k1_lpspace2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r3_ltlaxio1 B A) => (r3_ltlaxio1 B (k6_ltlaxio1 A))) ) ) ) ) ).
tt(t26_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A C) (k6_cqc_lang A B))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t26_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B (k6_rusub_4 A C D)) = (k6_rusub_4 A (k6_rusub_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t26_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v3_matrix10 B) & (v3_matrix10 C))  => (v3_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t26_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  ((k14_matrix_2 B (k1_nat_1 A 2) C D) = (k8_group_1 B (k2_matrix11 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t26_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 (u1_struct_0 D))))  =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ((r2_hidden C (k2_finseq_1 B)) &  ((k1_funct_1 E A) = (k1_funct_1 E C)) ) )  =>  ( (A = C)  |  ((k12_matrix_3 B D (k1_matrix13 (u1_struct_0 D) G B B E F)) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B C))  =>  ((k1_funct_1 (k12_matrix_1 A C) B) = (k3_matrix14 A C B)) ) ) ) ) ) ) ) ).
tt(t26_matrix15,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( (~  ( ((k3_finseq_1 C) = k1_xboole_0)  &  ((k3_finseq_1 B) = k1_xboole_0) ) )  =>  ( (C = (k3_matrix15 A B))  <=>  ( ((k9_matrix_1 A C 1) = B)  &  ((k1_matrix_1 C) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v3_matrix16 C (u1_struct_0 B)) & (v3_matrix16 D (u1_struct_0 B)))  => (v3_matrix16 (k3_matrix_6 A B C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t26_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  (! [E:$i] :  ((m1_matrix_1 E C A B) =>  ((k2_matrix_1 D) = (k2_matrix_1 E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (k12_matrix_2 A))) ) ).
tt(t26_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 B)) =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 C)) =>  ( ((v1_setwiseo D A) &  ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ((v1_finseqop D A) & (r6_binop_1 A E D)) ) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C H I) (k9_matrix_3 B C A E F G)) = (k7_setwiseo B A D H (k9_funcop_1 A B E F (k7_setwiseo C A D I G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k3_matrix_3 A B D) = (k1_matrix_4 A (k3_matrix_3 A B C) (k1_matrix_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k2_numbers)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k6_numbers))  &  (! [E:$i] :  ((m2_finseq_1 E k2_numbers) =>  (~  ( ((k3_finseq_1 E) = (k3_finseq_1 D))  &  ( ((k9_matrix_5 E 1) = (k5_binop_2 (k3_matrix_1 k2_numbers C A 1) (k3_matrix_1 k2_numbers D 1 B)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 D) F) |  ((k9_matrix_5 E (k23_binop_2 F 1)) = (k3_binop_2 (k9_matrix_5 E F) (k5_binop_2 (k3_matrix_1 k2_numbers C A (k23_binop_2 F 1)) (k3_matrix_1 k2_numbers D (k23_binop_2 F 1) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ((k5_matrix_1 B (u1_struct_0 A) (k1_matrix_6 B A C)) = (k1_matrix_6 B A (k5_matrix_1 B (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t26_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k2_group_1 A (k3_group_4 A B)) = (k3_group_4 A (k4_matrix_7 A (k4_finseq_5 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t26_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v2_matrix_8 C A B) =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix_8 (k5_matrix_1 A (u1_struct_0 B) C) A B)) ) ) ) ) ) ) ) ).
tt(t26_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_finsop_1 (u1_struct_0 A) (k3_finseq_4 (u1_struct_0 A) B C D) (u2_algstr_0 A)) = (k8_group_1 A (k8_group_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t26_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k5_matrixc1 (k12_seq_4 A C) B) = (k12_seq_4 (k5_matrixc1 A B) C)) ) ) ) ) ) ) ) ).
tt(t26_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_matrixj1 E C) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 C))))  =>  (! [F:$i] :  ( ((v1_matrixj1 F C) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 C))))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k13_matrixj1 C D E))) =>  ((k3_matrix_1 C (k13_matrixj1 C D E) A B) = (k3_matrix_1 C (k13_matrixj1 C D (k3_matrixj1 C E F)) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A C) =>  (! [E:$i] :  ((m1_matrixj2 E A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 D)) =>  ( (F = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) E))  =>  ((v2_matrixj2 (k4_matrlin2 A C C D D F) A C) <=>  ( ((k3_finseq_1 D) = k1_xboole_0)  |  (B = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers C D E) = (k7_real_1 (k3_matrix_1 k1_numbers A D E) (k3_matrix_1 k1_numbers B D E))) ) ) ) ) ) ) )  =>  (C = (k3_matrixr1 A B)) ) ) ) ) ) ) ) ).
tt(t26_matrixr2,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 A) = (k1_matrix_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 A)))  =>  ((k9_matrix_1 k1_numbers (k5_matrixr1 A B) C) = (k8_rvsum_1 (k9_matrix_1 k1_numbers A C) (k9_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t26_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrlin F A D) => (m1_matrlin (k7_finseq_1 E F) A (k1_vectsp_5 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D C B) =>  ( ((k1_matrix_1 E) = (k1_matrix_1 F))  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k1_matrix_1 E))) =>  ((k9_matrix_1 D (k8_matrlin D A C B E F) G) = (k8_finseq_1 D (k9_matrix_1 D E G) (k9_matrix_1 D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_xxreal_0 (k4_matroid0 A B) (k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B C))) & (r1_xxreal_0 (k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) D))) (k1_nat_1 (k4_matroid0 A B) 1))) ) ) ) ) ) ) ) ) ).
tt(t26_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k4_rvsum_1 (k3_matrprob A) (k3_matrprob B)) = (k3_matrprob (k7_matrlin k1_numbers A B))) ) ) ) ) ).
tt(t26_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E A) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 k2_vectsp_1) A B) =>  ( (C = D)  =>  ((k10_rvsum_1 (k1_funct_1 (k3_matrtop1 A B F) E) C) = (k1_funct_1 (k3_matrtop1 A B (k2_matrix13 A B k2_vectsp_1 F D)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (! [D:$i] :  ( ((v1_rlvect_3 D (k15_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  => (v1_rlvect_3 (k7_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D) (k15_euclid B))) ) ) ) ) ) ) ) ) ).
tt(t26_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) | (v1_matrtop3 (k3_matrtop1 D D (k2_matrtop3 D A B C)) (k4_matrix13 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k2_mboolean A B) (k2_mboolean A C))) ) ) ) ) ) ).
tt(t26_mcart_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ( ((r2_hidden C A) | (r2_hidden D A))  &  (B = (k3_xtuple_0 C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k7_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ( (F = k1_xboole_0)  =>  ((k12_supinf_2 E F) = C) )  &  ( (~  (F = k1_xboole_0) )  =>  ((k12_supinf_2 E F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v1_measure5 A) <=> (v1_measure5 (k2_measure6 A B))) ) ) ) ) ).
tt(t26_measure8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 D) =>  ((k2_mesfunc5 (k11_measure8 A B D C)) = (k1_mesfunc9 C (k4_kurato_0 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k6_member_1 (k1_tarski A)) = (k1_tarski (k5_xxreal_3 A))) ) ) ).
tt(t26_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v2_membered B)) )  => (v2_membered (k3_tarski A))) ) ).
tt(t26_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  (C = (k1_funct_4 (k6_memstr_0 A B C) (k7_memstr_0 A B (k5_memstr_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t26_mesfun6c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 B) C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( ((v6_supinf_2 E) & (r1_xxreal_0 k6_numbers A))  => (v6_supinf_2 (k2_mesfun6c A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k2_numbers C k6_numbers)) = D)  &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers C E) D)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (v2_comseq_2 (k9_mesfun7c A C E))) ) ) ) )  => (r1_mesfun6c A B (k10_mesfun7c A C) D)) ) ) ) ) ) ) ) ) ).
tt(t26_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((v1_mesfunc8 C A k2_numbers) &  ( (B = (k1_relset_1 A (k4_mesfunc5 A k2_numbers C k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) => (v2_comseq_2 (k9_mesfun7c A C D))) ) ) ) )  => (r2_relset_1 A k2_numbers (k2_partfun1 A k2_numbers (k10_mesfun7c A C) B) (k10_mesfun7c A (k1_mesfun9c A k2_numbers C B)))) ) ) ) ) ) ).
tt(t26_mesfunc1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B C F) = (k9_subset_1 A E (k17_mesfunc1 A D (k1_measure6 (k1_real_1 F))))) ) )  =>  ((k9_subset_1 A E (k17_mesfunc1 A D k2_supinf_1)) = (k2_measure2 A B (k1_measure3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  ( ((r1_mesfunc1 A C B D) & (r1_tarski D (k1_relset_1 A B)))  => (r1_mesfunc1 A C (k2_mesfunc2 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t26_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((r2_relset_1 A k7_numbers (k1_mesfunc2 A (k6_mesfunc1 A B C)) (k6_mesfunc1 A (k1_mesfunc2 A B) C)) & (r2_relset_1 A k7_numbers (k2_mesfunc2 A (k6_mesfunc1 A B C)) (k6_mesfunc1 A (k2_mesfunc2 A B) C))) ) ) ) ) ) ) ) ).
tt(t26_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc6 A B C E) & (r1_mesfunc6 A B D E))  => (r1_mesfunc6 A B (k3_valued_1 A k1_numbers k1_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ((r1_mesfunc5 A B C D) &  ((r1_tarski E (k1_relset_1 A D)) &  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H E) =>  ((r1_xxreal_0 F (k12_supinf_2 D H)) & (r1_xxreal_0 (k12_supinf_2 D H) G)) ) ) ) ) )  =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C E)) |  ((r1_xxreal_0 (k1_extreal1 (k1_measure6 F) (k12_supinf_2 C E)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D E))) & (r1_xxreal_0 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D E)) (k1_extreal1 (k1_measure6 G) (k12_supinf_2 C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 C A k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)) = E)  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers C F) E)) )  &  ( ((k1_relset_1 A D) = E)  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) =>  ((v10_mesfunc5 (k3_mesfunc5 A C F)) &  ((k12_supinf_2 D F) = (k2_mesfunc5 (k3_mesfunc5 A C F))) ) ) ) ) ) ) )  => (r1_mesfunc1 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  (~  ((v2_mesfunc9 B A) &  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) &  ( ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) E) = k2_supinf_1)  &  ((r1_xxreal_0 D C) &  ((k1_mesfunc9 (k4_mesfunc5 A k7_numbers B D) E) = k1_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v11_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k2_metric_1 A B C))) ) ) ) ) ) ).
tt(t26_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  ((r2_hidden B (k6_metric_2 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) & (r4_metric_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t26_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 A B) = (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 B A)) ) ) ) ) ).
tt(t26_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v3_tbsp_1 B A)) ) ) ) ) ).
tt(t26_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v4_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_tarski C E) &  ((r1_tarski D F) & (r1_xboole_0 (k2_pre_topc A E) (k2_pre_topc A F))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (~  ( (G = (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A E)))  &  ( (H = (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A F)))  &  ((r2_metrizts (k1_pre_topc A B) G H I) &  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_metrizts A C D J) & (r1_tarski (k9_subset_1 (u1_struct_0 A) B J) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  &  (! [C:$i] :  ( ((v1_rlvect_3 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ( ((k1_card_1 C) = (k10_binop_2 A 1))  &  ((k2_struct_0 (k1_rlvect_3 (k15_euclid A) C)) = (k2_mfold_2 A B (k4_struct_0 (k15_euclid A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_hidden B (k4_midsp_1 A C)) <=> (r2_midsp_1 A B C)) ) ) ) ) ) ) ).
tt(t26_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((r1_midsp_2 A B C) => (v1_midsp_2 (k7_midsp_2 A B C) (g1_midsp_1 A (k6_midsp_2 A B C)) B)) ) ) ) ) ) ) ).
tt(t26_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [G:$i] :  ( ((v4_midsp_2 G C) & (l1_midsp_2 G C))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (u1_midsp_2 C G))) =>  (! [I:$i] :  ((m2_finseq_2 I (u1_struct_0 (u1_midsp_2 C G)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C G)))) =>  ( ( ((k7_midsp_3 A C G D I) = F)  &  ((k10_midsp_2 C G D H) = E) )  =>  ((k7_midsp_3 A C G D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C G)) (k2_nat_1 A 1) I B H)) = (k6_midsp_3 A C F B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relset_1 A A C D) => (r1_tarski (k3_mmlquery A C B) (k3_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t26_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B C) = (k1_algstr_0 A C B))  &  ( ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D)))  &  ( ((k1_algstr_0 A B (k4_struct_0 A)) = B)  &  ( ((k1_algstr_0 A B (k4_algstr_0 A B)) = (k4_struct_0 A))  &  ( ((k6_algstr_0 A B C) = (k6_algstr_0 A C B))  &  ( ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D)))  &  ( ((k6_algstr_0 A (k5_struct_0 A) B) = B)  &  ( ((k6_algstr_0 A B (k5_struct_0 A)) = B)  &  ( (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A B E) = (k5_struct_0 A)) ) ) ) ) )  &  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((v8_mod_4 (k3_struct_0 A) A A) <=>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_modal_1,ax,(r1_subset_1 k4_modal_1 k3_modal_1)).
tt(t26_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_partfun1 B A) <=>  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r2_hidden D A) & (r2_hidden (k4_tarski C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r1_modelc_2 A B) &  ( (~ (v3_modelc_2 B))  &  ( (~ (v6_modelc_2 B))  &  ( (~ (v4_modelc_2 B))  &  ( (~ (v5_modelc_2 B))  &  ( (~ (v7_modelc_2 B))  &  (~ (v8_modelc_2 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((r5_modelc_3 D B) &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  (C = (k5_relat_1 B (k2_finseq_1 A))) ) )  => (r5_modelc_3 D C)) ) ) ) ) ) ) ) ) ).
tt(t26_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (v1_moebius1 A))  &  ((r1_nat_d B A) & (v1_moebius1 B)) ) ) ) ) ) ) ).
tt(t26_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m2_monoid_0 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ).
tt(t26_monoid_1,ax, (! [A:$i] :  ( ((u1_struct_0 (k13_monoid_1 A)) = (k9_funct_2 A k5_numbers))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k13_monoid_1 A)) (u1_struct_0 (k13_monoid_1 A))) (u1_struct_0 (k13_monoid_1 A)) (k2_zfmisc_1 (k9_funct_2 A k5_numbers) (k9_funct_2 A k5_numbers)) (k9_funct_2 A k5_numbers) (u2_algstr_0 (k13_monoid_1 A)) (k8_monoid_1 k5_numbers k5_numbers k5_numbers k47_binop_2 A)) &  ((k5_struct_0 (k13_monoid_1 A)) = (k5_monoid_1 k5_numbers A k6_numbers)) ) ) ) ).
tt(t26_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A C) (k5_setfam_1 (u1_struct_0 A) B)) = (k3_tarski (a_3_9_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t26_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_msualg_2 D A (k11_msafree A B)) =>  (! [E:$i] :  ((m1_msualg_2 E A (k11_msafree A C)) =>  ((r8_pboole (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A E)) =>  ((g3_msualg_1 A (u3_msualg_1 A D) (u4_msualg_1 A D)) = (g3_msualg_1 A (u3_msualg_1 A E) (u4_msualg_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  ((r2_pboole (u1_struct_0 A) B C) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) => (m1_dtconstr D (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C))) ) ) ) ) ) ) ) ) ).
tt(t26_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_0_msscyc_1 A B C) = (k2_xboole_0 (k12_msafree A B C) (k1_msualg_2 A (k11_msafree A B) C))) ) ) ) ) ) ) ).
tt(t26_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((v2_finset_1 B) &  ((r2_pboole A B (k6_pboole A C D)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  (~  ((v2_finset_1 E) &  ((r2_pboole A E C) &  ((v2_finset_1 F) &  ((r2_pboole A F D) & (r2_pboole A B (k6_pboole A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mssublat,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v13_struct_0 A 1) &  ((v5_msualg_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ( ((u1_struct_0 A) = (k1_tarski k6_numbers))  =>  ((k9_msualg_1 (k12_msualg_1 A B)) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ) ).
tt(t26_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D A B) =>  ((k13_msualg_2 A B C D) = (k13_msualg_2 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t26_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) D E) =>  (! [F:$i] :  ((m2_msualg_6 F A B D E) =>  (? [G:$i] :  ((m2_msualg_6 G A B D E) & (r2_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E) (k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D) G) (k1_partfun1 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) E) (k1_funct_1 (u3_msualg_1 A B) E) F (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ( (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  & (r8_pboole (u1_struct_0 A) (u3_msualg_1 A B) (k1_pzfmisc1 (u1_struct_0 A) C))) )  => (r6_msualg_3 A B (k7_msafree2 A))) ) ) ) ) ).
tt(t26_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  ( ((r1_unialg_2 A B) & (r1_unialg_2 B C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((k8_pboole (k2_msuhom_1 A B D) (k2_msuhom_1 B C E)) = (k2_msuhom_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v5_dilworth B (k3_necklace A)) & (m1_eqrel_1 B (u1_struct_0 (k3_necklace A))))  =>  ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(t26_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_funct_1 (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C D)) &  ((v1_funct_2 (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C D) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C D) A B) & (m1_subset_1 (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k3_funct_2 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)) D E)) &  ((v3_pre_topc (k3_funct_2 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)) D E) A) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden F (k3_funct_2 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)) D G)) =>  ((k1_funct_1 (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C F) F) = (k1_funct_1 (k3_funct_2 (u1_struct_0 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)) C G) F)) ) ) ) ) ) ) ) ) )  => (v5_pre_topc (k4_nagata_1 (u1_struct_0 A) (u1_struct_0 B) C) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t26_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 2) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  (~  (A = 2) ) ) ) ) ) ) ) ).
tt(t26_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_abian A) =>  ((k3_nat_d A 2) = (k3_nat_d (k1_nat_1 A 1) 2)) ) ) ) ).
tt(t26_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A (k1_newton A (k11_nat_3 B A))) =>  ( (A = 1)  |  ( (B = k6_numbers)  | (r1_nat_d A B)) ) ) ) ) ) ) ).
tt(t26_nat_4,ax,(v1_int_2 7)).
tt(t26_nat_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ((r1_xboole_0 C D) =>  ((k3_uproots (k4_subset_1 A C D) (k1_nat_5 A B (k4_subset_1 A C D))) = (k23_binop_2 (k3_uproots C (k1_nat_5 A B C)) (k3_uproots D (k1_nat_5 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t26_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (k6_numbers = (k4_nat_d k6_numbers A)) ) ) ).
tt(t26_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_nattra_1 G A B C D) =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  ( ((r2_nattra_1 A B C D) &  ((r2_nattra_1 A B D E) & (r2_nattra_1 A B E F)) )  =>  (! [I:$i] :  ((m2_nattra_1 I A B E F) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k7_nattra_1 A B C D F G (k7_nattra_1 A B D E F H I)) (k7_nattra_1 A B C E F (k7_nattra_1 A B C D E G H) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k2_vfunct_2 (u1_struct_0 A) B C E)) (k6_clvect_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ((r14_ncfcont1 C B A D) => (r2_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t26_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((v1_partfun1 C (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k4_vfunct_1 (u1_struct_0 A) B C E)) (k5_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v3_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski B (k1_relset_1 k1_numbers C)) => (r2_ndiff_3 A C B)) ) ) ) ) ) ) ).
tt(t26_ndiff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) & (r1_ndiff_4 B C D)) )  =>  ((r1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid B) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 A B)) D) &  ((k1_funct_1 (k4_pdiff_1 A B) (k1_ndiff_4 B C D)) = (k1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid B) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 A B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ((r2_hidden F (k4_finseq_1 A)) =>  ((r2_relset_1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) (k6_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D)) (k6_vfunct_1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) B (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) C) (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) D))) & (r2_relset_1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) (k2_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D)) (k2_vfunct_1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) B (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) C) (k1_partfun1 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A F))) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A (k5_ndiff_5 A F) E) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_rewrite1 (u1_orders_2 A) B C) => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(t26_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_card_1 (a_1_1_necklace A)) = (k5_real_1 A 1)) ) ) ) ).
tt(t26_net_1,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_net_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_net_1 A)) =>  ( (~  ((k2_net_1 A) = k1_xboole_0) )  =>  ((r2_hidden C (k13_net_1 A B)) <=>  (~  ( (~  ((r2_hidden C B) & (r2_hidden C (u1_struct_0 A))) )  &  (! [D:$i] :  ((m1_subset_1 D (k2_net_1 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden D (u4_struct_0 A)) & (r2_net_1 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 C) = B)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  (E = (k5_real_1 (k2_xcmplx_0 A D) 1)) )  =>  ((k1_funct_1 C D) = (k5_newton A E)) ) ) ) ) ) )  =>  ( (B = k6_numbers)  |  ((k18_rvsum_1 C) = (k5_newton (k1_nat_1 A 1) (k2_xcmplx_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t26_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r3_nfcont_1 B A E C) & (r3_nfcont_1 B A F D))  =>  ((r3_nfcont_1 B A (k6_vfunct_1 (u1_struct_0 B) A E F) (k3_xboole_0 C D)) & (r3_nfcont_1 B A (k2_vfunct_1 (u1_struct_0 B) A E F) (k3_xboole_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) C A) B) <=>  (? [D:$i] :  ((v1_xreal_0 D) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r2_hidden E (k1_relset_1 A (k2_partfun1 k1_numbers (u1_struct_0 B) C A))) & (r2_hidden F (k1_relset_1 A (k2_partfun1 k1_numbers (u1_struct_0 B) C A))))  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 (u1_struct_0 B) C F))) (k4_real_1 D (k18_complex1 (k6_xcmplx_0 E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers D))) &  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A)) )  =>  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k7_integr15 A k1_numbers C D) B) A) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers C D) B) A)) ) ) ) ) ) ) ) ) ).
tt(t26_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ((r1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C) => (m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))) ) ) ) ) ) ).
tt(t26_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) & (v3_normsp_1 C A))  =>  ((k6_normsp_1 A (k3_normsp_1 A B C)) = (k5_algstr_0 A (k6_normsp_1 A B) (k6_normsp_1 A C))) ) ) ) ) ) ) ) ).
tt(t26_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_normsp_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_normsp_2 A))) =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 (k3_normsp_2 A)) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) &  (D = E) )  =>  ((r1_frechet (k4_normsp_2 A) C E) <=> (r1_frechet (k3_normsp_2 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_numbers,ax, (~  (k4_numbers = k2_numbers) ) ).
tt(t26_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_openlatt A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_openlatt A))) =>  ((r3_lattices (k15_openlatt A) B C) <=> (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t26_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_cat_1 (k3_oppcat_1 A B) (k2_oppcat_1 A)) <=> (v10_cat_1 B A)) ) ) ) ) ).
tt(t26_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v2_orders_1 A) => (v2_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t26_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~ (r2_hidden B (k3_orders_2 A C B))) ) ) ) ) ) ) ).
tt(t26_ordinal1,ax, (! [A:$i] :  (~  (! [B:$i] :  ((v3_ordinal1 B) => (r2_hidden B A)) ) ) ) ).
tt(t26_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ( ((k4_ordinal2 A) = (k3_ordinal2 (k10_xtuple_0 A)))  &  ((k5_ordinal2 A) = (k2_ordinal2 (k10_xtuple_0 A))) ) ) ) ).
tt(t26_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k10_ordinal2 A B) = k1_xboole_0)  =>  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t26_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden 1 A) & (v4_ordinal1 B))  =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k12_ordinal2 A D)) ) ) ) )  =>  ((k12_ordinal2 A B) = (k4_ordinal2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden 1 A) & (r2_hidden 1 B))  => (r2_hidden A (k1_ordinal5 A B))) ) ) ) ) ).
tt(t26_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) =>  (! [B:$i] :  ((v1_ordinal6 B) =>  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden C D)) ) )  =>  ((k1_ordinal6 (k2_xboole_0 A B)) = (k10_ordinal2 (k1_ordinal6 A) (k1_ordinal6 B))) ) ) ) ) ) ).
tt(t26_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t26_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B C E))  &  ( (~ (r1_orders_2 B F D))  &  ( (~ (r1_orders_2 B F E))  &  ( (~ (r1_orders_2 B G D))  &  (~  ((k8_group_1 A (k8_group_1 A (k1_ortsp_1 A B D G C) (k1_ortsp_1 A B C D E)) (k1_ortsp_1 A B E C H)) = (k8_group_1 A (k8_group_1 A (k1_ortsp_1 A B D G F) (k1_ortsp_1 A B F D E)) (k1_ortsp_1 A B E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B))) =>  ((r8_pboole (u1_struct_0 A) C (k20_osafree A B)) <=>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((r2_hidden F (k1_funct_1 B D)) =>  ( ((r3_orders_2 A D E) => (r2_hidden (k4_tarski (k1_trees_4 (k4_tarski F D)) (k1_trees_4 (k4_tarski F D))) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B)) C E)))  &  (! [G:$i] :  ( ((r2_hidden (k4_tarski (k1_trees_4 (k4_tarski F D)) G) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B)) C E)) | (r2_hidden (k4_tarski G (k1_trees_4 (k4_tarski F D))) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B)) C E)))  =>  ((r3_orders_2 A D E) &  (G = (k1_trees_4 (k4_tarski F D))) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A D (k8_osafree A B))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A E (k8_osafree A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r2_hidden (k4_tarski (k3_funct_2 (k3_msualg_1 A D (k8_osafree A B)) (k4_msualg_1 A D (k8_osafree A B)) (k5_msualg_1 A D (k8_osafree A B)) F) (k3_funct_2 (k3_msualg_1 A E (k8_osafree A B)) (k4_msualg_1 A E (k8_osafree A B)) (k5_msualg_1 A E (k8_osafree A B)) G)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B)) C H)) <=>  ((r1_osalg_1 A D E) &  ( ((k3_finseq_1 (k1_msualg_1 A D)) = (k3_finseq_1 (k1_msualg_1 A E)))  &  ((r3_orders_2 A (k2_msualg_1 A D) H) &  ((r3_orders_2 A (k2_msualg_1 A E) H) &  (? [I:$i] :  ((m2_finseq_2 I (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) &  ( ((k4_finseq_1 I) = (k4_finseq_1 F))  &  (! [J:$i] :  ((v7_ordinal1 J) =>  ((r2_hidden J (k4_finseq_1 I)) => (r2_hidden (k4_tarski (k1_funct_1 F J) (k1_funct_1 G J)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A (k8_osafree A B)) C (k7_partfun1 (u1_struct_0 A) I J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (l3_msualg_1 D A))  =>  ((r6_osalg_1 A B C) =>  ((r1_tarski (k3_msualg_1 A B D) (k3_msualg_1 A C D)) & (r1_tarski (k4_msualg_1 A B D) (k4_msualg_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  (! [E:$i] :  ((m2_osalg_2 E A B) =>  ((r2_hidden E (k5_osalg_2 A B D)) => (r1_tarski (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_osalg_2 A B D))) C) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) E)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_parsp_1 A D E B C) & (r1_parsp_1 A B C F G))  =>  ( (B = C)  | (r1_parsp_1 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) =>  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (D = B) )  &  ( (~  (B = E) )  &  ( (~  (C = E) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k1_relset_1 B (k3_partfun1 D B C))) =>  ((k1_funct_1 (k3_partfun1 D B C) A) = (k1_funct_1 D A)) ) ) ) ) ) ) ).
tt(t26_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ( (D = (k8_relset_1 C B E A))  <=>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) <=>  ((r2_hidden F (k1_relset_1 C E)) & (r2_hidden (k7_partfun1 B E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ((k3_partit1 A (k3_partit1 A B C) D) = (k3_partit1 A B (k3_partit1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t26_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v8_relat_2 C) => (r8_relat_2 C B)) ) ) ) ) ) ) ).
tt(t26_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_diraf A B C D E) &  ( (~ (r3_diraf A B C D))  &  ((r3_diraf A F B E) &  ((r3_diraf A F C D) & (r3_diraf A F B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A B (k2_pboole A C D)) <=>  ((r2_pboole A C B) &  ((r2_pboole A D B) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A C E) & (r2_pboole A D E))  => (r2_pboole A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k9_metric_1 A B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t26_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k19_pcs_0 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k19_pcs_0 A B))) =>  ( ( (C = E)  &  ( (D = F)  & (r1_orders_2 (k19_pcs_0 A B) E F)) )  =>  ( (C = B)  | (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ((r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) (k6_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E)) (k6_vfunct_1 (u1_struct_0 (k4_real_ns1 1)) (k4_real_ns1 A) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) D) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) E))) & (r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) (k2_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E)) (k2_vfunct_1 (u1_struct_0 (k4_real_ns1 1)) (k4_real_ns1 A) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) D) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r2_pdiff_3 B A) & (r2_pdiff_3 C A))  =>  ((r3_pdiff_1 2 2 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) &  ((k11_pdiff_1 2 2 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A) = (k9_real_1 (k3_pdiff_3 B A) (k3_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t26_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 3) B)) =>  ( ((r3_pdiff_1 3 2 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 A B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k1_rvsum_1 E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 3) B)))  & (r1_tarski (k1_rvsum_1 (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 A B))))) &  ((k11_pdiff_1 3 2 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r8_pdiff_5 B A) <=> (r3_pdiff_1 3 2 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ).
tt(t26_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 B A) (k3_rlvect_1 (k4_real_ns1 A) C D)) = (k3_rlvect_1 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 B A) C) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 B A) D))) ) ) ) ) ) ) ) ) ).
tt(t26_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  ( ( ((k3_finseq_1 B) = (k23_binop_2 (k3_finseq_1 C) 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k7_partfun1 (k1_euclid A) C D) = (k8_euclid A (k7_partfun1 (k1_euclid A) B D) (k7_partfun1 (k1_euclid A) B (k23_binop_2 D 1)))) ) ) ) )  =>  ((k8_euclid A (k7_partfun1 (k1_euclid A) B 1) (k7_partfun1 (k1_euclid A) B (k3_finseq_1 B))) = (k5_euclid_7 A C)) ) ) ) ) ) ) ) ).
tt(t26_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ( ((v1_pdiff_7 C A) & (r1_tarski C (k1_relset_1 (k1_euclid A) D)))  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ((r2_pdiff_7 A B E D C) & (r4_pdiff_7 A B (k2_pdiff_7 A B E D C) C)) ) ) )  <=>  ((r1_pdiff_6 C B A D) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E C) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  ((r2_hidden H C) =>  ((r1_xxreal_0 G (k12_euclid (k8_euclid A H E))) |  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k8_euclid B (k1_pdiff_6 A B (k8_pdiff_1 A B D H) I) (k1_pdiff_6 A B (k8_pdiff_1 A B D E) I))) (k11_binop_2 F (k12_euclid I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ( (~ (v13_pencil_1 C))  & (v16_pencil_1 C A)) ) ) ) )  =>  ((r1_ordinal1 2 (k1_card_1 (k3_xboole_0 (k4_card_3 B) (k4_card_3 C)))) =>  ( ((k3_pencil_1 A B) = (k3_pencil_1 A C))  &  (! [D:$i] :  ( (~  (D = (k3_pencil_1 A B)) )  =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ((m1_pencil_2 D A B) =>  (! [E:$i] :  ((m1_pencil_2 E A B) =>  ( ((r1_xboole_0 D E) & (r1_pencil_3 A B D E))  =>  (! [F:$i] :  ( ( (~ (v13_pencil_1 F))  &  ((v16_pencil_1 F A) & (m3_pboole F A (k12_pralg_1 A B))) )  =>  (! [G:$i] :  ( ( (~ (v13_pencil_1 G))  &  ((v16_pencil_1 G A) & (m3_pboole G A (k12_pralg_1 A B))) )  =>  ( ( ((k4_card_3 F) = D)  &  ((k4_card_3 G) = E) )  => (r1_funct_2 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A F))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A F)))) (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A G))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A G)))) (k3_pencil_3 A B C F) (k3_pencil_3 A B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 (k1_vectsp_9 A B) D))  & (v4_pencil_1 (k7_pencil_4 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k1_newton A B) = (k3_xcmplx_0 A (k1_newton A (k7_nat_d B 1)))) ) ) ) ) ) ) ) ) ).
tt(t26_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A B C) => (r1_pnproc_1 A C (k2_pnproc_1 A (k3_pnproc_1 A C B) B))) ) ) ) ) ) ).
tt(t26_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ( ((k3_polyeq_1 A B C D) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (~  ( (E = (k4_binop_2 (k1_polyeq_3 (k6_binop_2 B (k5_binop_2 2 A))) (k6_binop_2 C A)))  &  ( (F = (k6_binop_2 B (k5_binop_2 2 A)))  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 E) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 E)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2)) k7_complex1)) F)) )  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 E) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 E)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2))) k7_complex1)) F)) )  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 E) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 E)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2))) k7_complex1)) F)) )  &  (~  (D = (k4_binop_2 (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 E) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 E)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 E)) (k5_square_1 (k4_complex1 E))))) 2)) k7_complex1)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k5_polyeq_5 A B C D) (k6_polyeq_5 A B C D)) (k7_polyeq_5 A B C D)) (k8_polyeq_5 A B C D)) = (k4_xcmplx_0 D)) ) ) ) ) ) ) ) ) ).
tt(t26_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 (k7_polyform A) B))  & (r1_xxreal_0 (k7_polyform A) (k6_xcmplx_0 B 1))) ) ) ) ) ) ).
tt(t26_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B C (k5_polynom1 A B D E)) (k5_polynom1 A B (k9_polynom1 A B C D) (k9_polynom1 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t26_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_normsp_1 A (k2_normsp_1 A B C) D) (k2_normsp_1 A B (k2_normsp_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t26_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A B (k4_struct_0 A)) (k9_polynom3 A))) ) ) ) ).
tt(t26_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l5_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_polynom7 A B C D) (k6_polynom7 A B C D))) ) ) ) ) ) ) ).
tt(t26_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k3_polynom8 A B (k3_xcmplx_0 C D)) = (k3_polynom8 A (k3_polynom8 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r1_polyred A B C D E) & (r1_polyred A B C E D))  <=>  ((k2_polynom1 (k15_pre_poly A) C D) = (k2_polynom1 (k15_pre_poly A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_power 1 A) = 1) ) ) ).
tt(t26_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v4_msualg_1 E B) & (l3_msualg_1 E B))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) & (v1_funcop_1 F)) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (? [H:$i] :  ((m2_pboole H (u1_struct_0 B) (u3_msualg_1 B E) (u3_msualg_1 B (k5_pralg_2 A B C G))) &  ( (H = (k1_funct_1 F G))  & (r1_msualg_3 B E (k5_pralg_2 A B C G) H)) ) ) ) )  => (r2_hidden (k1_funct_1 (k10_funct_6 F) D) (k1_funct_2 A (k1_funct_2 (k1_funct_1 (u3_msualg_1 B E) D) (k3_tarski (a_3_1_pralg_3 A B C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_prelamb A (k2_prelamb A B (k3_prelamb A C D)) (k2_prelamb A (k2_prelamb A B D) C))) ) ) ) ) ) ) ) ).
tt(t26_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_pre_poly A) <=>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) ) ) ) ) ).
tt(t26_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 1 C)) )  =>  ((k3_xcmplx_0 (k2_prepower B A) (k2_prepower C A)) = (k2_prepower (k4_nat_1 B C) (k1_newton A (k2_nat_1 B C)))) ) ) ) ) ) ) ) ).
tt(t26_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v2_pre_topc C) & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((v5_pre_topc D A C) & (m1_pre_topc C B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (E = D)  => (v5_pre_topc E A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  ( ((v5_relat_1 B C) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (m1_prob_1 (k1_prob_1 A B) A C)) ) ) ) ) ) ).
tt(t26_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_prob_2 A B E C D) => (r1_prob_2 A B E (k7_prob_1 A B (k4_prob_1 A B) C) (k7_prob_1 A B (k4_prob_1 A B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E D) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  ((r2_hidden C (k1_funct_1 (k2_prob_3 B E) A)) <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ((r1_xxreal_0 F A) & (r2_hidden C (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_4 D A B C) => (r2_hidden D (k4_prob_4 A B C))) ) ) ) ) ) ) ) ).
tt(t26_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k7_cqc_lang A B C) D) (k7_cqc_lang A B (k7_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t26_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (r4_projpl_1 A B C D))  => (r1_zfmisc_1 B C D)) ) ) ) ) ) ) ) ) ).
tt(t26_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k17_euclid (k13_pscomp_1 A)) = (k17_euclid (k12_pscomp_1 A))) ) ) ).
tt(t26_pua2mss1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k7_finseq_1 (k7_finseq_1 D (k9_finseq_1 F)) E) (k4_card_3 C)) =>  ( (! [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) =>  (~  ((r2_hidden F H) & (r2_hidden G H)) ) ) )  | (r2_hidden (k7_finseq_1 (k7_finseq_1 D (k9_finseq_1 G)) E) (k4_card_3 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A (k2_pzfmisc1 A B C) (k1_pzfmisc1 A D)) =>  ((r6_pboole A B D) & (r6_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t26_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (~  ( (~ (r2_qc_lang1 A B C))  &  ( (~  (B = C) )  &  (~ (r2_qc_lang1 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t26_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((k9_qc_lang2 A B C D E) = (k7_qc_lang2 A G H F))  =>  ( (B = G)  &  ( (C = H)  &  ((k5_qc_lang2 A D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((v6_qc_lang1 B A) & (v6_qc_lang1 C A))  <=> (v6_qc_lang1 (k2_qc_lang2 A B C) A)) ) ) ) ) ) ) ).
tt(t26_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((v5_qc_lang1 (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C) A) =>  ((r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)) (k9_xtuple_0 (k2_qc_lang4 A B))) &  ((k1_funct_1 (k2_qc_lang4 A B) (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers))) = (k22_qc_lang1 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t26_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_quantal1 A (k3_lattices A B C)) = (k4_lattices A (k5_quantal1 A B) (k5_quantal1 A C)))  &  ((k5_quantal1 A (k4_lattices A B C)) = (k3_lattices A (k5_quantal1 A B) (k5_quantal1 A C))) ) ) ) ) ) ) ) ).
tt(t26_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k31_quaterni (k31_quaterni A)) = A) ) ) ).
tt(t26_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k19_quaterni (k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A))) = (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k19_quaterni A)))) ) ) ).
tt(t26_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ( ((k17_quaterni A) = k6_numbers)  &  ( ((k18_quaterni A) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ((k20_quaterni A) = k6_numbers) ) ) )  =>  (A = k21_quaterni) ) ) ) ).
tt(t26_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C)))  <=>  ( (~ (r1_xxreal_0 D (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A))))  &  (~ (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k16_quofield A) (k5_binop_1 (k7_quofield A) (k15_quofield A) B C) D) = (k5_binop_1 (k7_quofield A) (k15_quofield A) (k5_binop_1 (k7_quofield A) (k16_quofield A) B D) (k5_binop_1 (k7_quofield A) (k16_quofield A) C D))) ) ) ) ) ) ) ) ) ).
tt(t26_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 2 B) &  ((r1_radix_1 A C B) & (r1_radix_1 A D B)) )  =>  ((k2_xcmplx_0 C D) = (k2_xcmplx_0 (k8_radix_1 A B (k14_radix_1 A B (k10_radix_1 B A C) (k10_radix_1 B A D))) (k3_xcmplx_0 (k1_newton (k1_radix_1 B) A) (k11_radix_1 (k2_xcmplx_0 (k4_radix_1 A B A (k10_radix_1 B A C)) (k4_radix_1 A B A (k10_radix_1 B A D))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) =>  (! [E:$i] :  ((m1_random_1 E A B) =>  ( ((r1_random_1 A B D C) & (r1_random_1 A B E C))  =>  ((k8_random_1 A B C (k3_random_1 A B D E)) = (k7_real_1 (k8_random_1 A B C D) (k8_random_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~ (r2_hidden E D))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k6_ranknull A B C D) E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rat_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k6_real_1 (k3_xcmplx_0 (k2_rat_1 B) A) (k8_real_1 (k1_rat_1 B) A))) ) ) ) ) ) ).
tt(t26_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k11_ratfunc1 A (k3_ratfunc1 A (k13_polynom3 A (k3_hurwitz A C 1) (k4_ratfunc1 A B)) (k13_polynom3 A (k3_hurwitz A C 1) (k5_ratfunc1 A B)))) = (k11_ratfunc1 A B)) ) ) ) ) ) ) ).
tt(t26_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_xxreal_2 A) =>  ((r2_hidden (k5_seq_4 A) A) | (r1_tarski A (k3_limfunc1 (k5_seq_4 A)))) ) ) ) ).
tt(t26_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 B) (k1_nat_1 A 1)) = (k10_real_1 1 (k9_real_1 (k1_seq_1 (k3_real_3 B) A) (k1_seq_1 (k4_real_3 B) A)))) ) ) ) ) ).
tt(t26_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k4_real_lat A) B C)) = B)  &  ( ((k1_binop_1 (k5_real_lat A) (k1_binop_1 (k4_real_lat A) C B) B) = B)  &  ( ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k4_real_lat A) C B)) = B)  &  ((k1_binop_1 (k5_real_lat A) (k1_binop_1 (k4_real_lat A) B C) B) = B) ) ) ) ) ) ) ) ) ) ).
tt(t26_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k8_group_1 A B C) = (k8_group_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t26_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) (k5_struct_0 A) B) = (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B)) ) ) ) ) ).
tt(t26_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((k21_rfunct_3 B (k4_rearran1 A B D C) B) = (k21_rfunct_3 A C A)) ) ) ) ) ) ) ) ) ) ).
tt(t26_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k10_xtuple_0 (k3_relat_1 A B)) (k10_xtuple_0 B))) ) ) ) ).
tt(t26_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (~  ( (~  ((k1_relset_1 A C) = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~ (r2_hidden D (k2_relset_1 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((k7_relset_1 (k9_setfam_1 A) (k9_setfam_1 B) (k4_relset_2 B A E) (k10_eqrel_1 C)) = k1_xboole_0)  =>  ((k6_relset_2 A B (k4_subset_1 A C D) E) = (k6_relset_2 A B D E)) ) ) ) ) ) ) ) ) ) ).
tt(t26_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((k28_seq_4 (k1_goboard1 B)) = (k28_seq_4 (k1_goboard1 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)))) ) ) ) ) ).
tt(t26_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] : (r2_rewrite1 A B B)) ) ) ).
tt(t26_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B C) => (r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A B) (k7_rewrite2 A C))) ) ) ) ) ) ).
tt(t26_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  ((r2_rewrite3 C F G A D B E) => (r1_xxreal_0 (k1_afinsq_1 E) (k1_afinsq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  =>  ( ( (A = (k3_relat_1 C B))  & (r1_xxreal_0 1 (k3_finseq_1 B)))  =>  ((k6_rvsum_1 A) = (k3_relat_1 C (k6_rvsum_1 B))) ) ) ) ) ) ) ) ).
tt(t26_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ((v2_funct_1 A) & (v2_funct_1 B)) )  => (r2_classes1 A B)) ) ) ) ) ).
tt(t26_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k4_rfunct_1 (k4_rfunct_1 A)) = (k5_relat_1 A (k9_xtuple_0 (k4_rfunct_1 A)))) ) ) ).
tt(t26_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_xboole_0 A (k1_relset_1 k1_numbers B)) =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) &  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) & (v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ) ) ) ).
tt(t26_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_rfunct_3 A B C D) =>  ( (E = k6_numbers)  | (r1_rfunct_3 A B (k17_finseq_1 (k3_rfunct_3 A B) E C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rfunct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_rfunct_4 B A) & (v2_funct_1 B))  => (r4_rfunct_4 B A)) ) ) ) ).
tt(t26_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 B) => (v1_seq_2 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t26_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_valued_0 B) =>  ((v7_valued_0 (k1_valued_0 k7_numbers B A)) &  ((k1_rinfsup2 B) = (k1_rinfsup2 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ) ).
tt(t26_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  => (r1_rlvect_2 B (k2_rlaffin1 B (k4_rlvect_2 B) A) (k4_rlvect_2 B))) ) ) ) ).
tt(t26_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k3_convex1 A D)) &  ((r2_hidden C (k3_convex1 A D)) &  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r2_hidden E D) &  ((r2_hidden F (k3_convex1 A (k7_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) E)))) &  ((r1_xxreal_0 k1_xboole_0 G) &  ( (~ (r1_xxreal_0 1 G))  &  ((k3_rlvect_1 A (k1_rlvect_1 A C G) (k1_rlvect_1 A F (k9_real_1 1 G))) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ( ((v1_rlaffin1 D (k15_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [F:$i] :  ((m2_rlaffin3 F (k15_euclid A) D) =>  ( ((r1_xxreal_0 B A) &  ( ((k5_card_1 D) = (k23_binop_2 A 1))  &  (C = (a_5_0_rlaffin3 A B D E F)) ) )  =>  ((v4_pre_topc E (k15_euclid B)) <=> (v4_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_rlvect_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( ((m1_rlsub_1 A B) & (m1_rlsub_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t26_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) =>  ((k2_rlsub_2 A C (k1_rlsub_2 A B D)) = (k1_rlsub_2 A (k2_rlsub_2 A B C) (k2_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v3_rltopsp1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t26_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_rlvect_1 B (k4_algstr_0 B C) (k4_xcmplx_0 A)) = (k1_rlvect_1 B C A)) ) ) ) ) ) ) ).
tt(t26_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r2_relset_1 k5_numbers (u1_struct_0 A) (k5_rlvect_2 A (k3_pre_poly (u1_struct_0 A) B) C) (k3_pre_poly (u1_struct_0 A) (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers C B))))) ) ) ) ) ) ).
tt(t26_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_rlvect_3 C A) =>  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t26_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B (k3_rlvect_1 A C B) (k3_rlvect_1 A D B)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v1_rlvect_5 (k1_rlsub_1 A))) ) ).
tt(t26_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k3_rlvect_x A B)) <=>  (? [D:$i] :  ( ((v3_card_1 D (k3_finseq_1 B)) & (m2_finseq_1 D (u1_struct_0 A)))  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E k4_numbers) &  ((v1_funct_1 E) &  ((v3_card_1 E (k3_finseq_1 B)) & (v1_finseq_1 E)) ) ) )  &  ( (C = (k4_rlvect_1 A D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 B))) =>  ((k7_partfun1 (u1_struct_0 A) D F) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) B F) (k1_seq_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_2 D A) & (l1_vectsp_2 D A)) ) ) ) ) )  =>  ( ((m1_rmod_2 B A C) & (m1_rmod_2 C A D))  => (m1_rmod_2 B A D)) ) ) ) ) ) ) ) ) ).
tt(t26_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ((k2_rmod_3 A B D (k1_rmod_3 A B D C)) = D) ) ) ) ) ) ) ) ) ).
tt(t26_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k4_rmod_4 A B (k2_finseq_4 (u1_struct_0 B) C D) E) = (k2_finseq_4 (u1_struct_0 B) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k6_robbins1 A B C) (k6_robbins1 A B D)) = (k5_robbins1 A (k5_robbins1 A (k6_robbins1 A (k6_robbins1 A B C) D) (k6_robbins1 A (k6_robbins1 A B C) (k3_robbins1 A D))) (k6_robbins1 A (k6_robbins1 A B (k3_robbins1 A C)) D))) ) ) ) ) ) ) ) ) ).
tt(t26_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A B (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A C D)) (k3_robbins1 A (k1_lattices A C B))))) = (k3_robbins1 A (k3_robbins1 A (k1_lattices A C B)))) ) ) ) ) ) ) ) ) ).
tt(t26_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v10_robbins3 A) & (l4_robbins3 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k11_lattice3 A B C) = (k4_robbins3 A B C)) ) ) ) ) ) ) ).
tt(t26_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( (A = k6_numbers)  =>  ((k3_lattices k2_robbins4 A B) = B) ) ) ) ) ) ).
tt(t26_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k3_roughs_1 A B) (k3_roughs_1 A C)) (k3_roughs_1 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t26_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A B) = (k7_real_1 (k1_rpr_1 A (k9_subset_1 A B C)) (k1_rpr_1 A (k9_subset_1 A B (k3_subset_1 A C))))) ) ) ) ) ) ) ).
tt(t26_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v3_lopban_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_rsspace4 A B)))  &  ((v13_algstr_0 (k9_rsspace4 A B)) &  ((v2_rlvect_1 (k9_rsspace4 A B)) &  ((v3_rlvect_1 (k9_rsspace4 A B)) &  ((v4_rlvect_1 (k9_rsspace4 A B)) &  ((v5_rlvect_1 (k9_rsspace4 A B)) &  ((v6_rlvect_1 (k9_rsspace4 A B)) &  ((v7_rlvect_1 (k9_rsspace4 A B)) &  ((v8_rlvect_1 (k9_rsspace4 A B)) &  ((v3_normsp_0 (k9_rsspace4 A B)) &  ((v4_normsp_0 (k9_rsspace4 A B)) &  ((v2_normsp_1 (k9_rsspace4 A B)) &  ((v3_lopban_1 (k9_rsspace4 A B)) & (l1_normsp_1 (k9_rsspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  =>  (B = A) ) ) ) ) ) ).
tt(t26_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) =>  ((k2_rusub_2 A C (k1_rusub_2 A B D)) = (k1_rusub_2 A (k2_rusub_2 A B C) (k2_rusub_2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_3 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (D = (k4_subset_1 (u1_struct_0 A) B C))  & (v1_rlvect_3 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden (k4_struct_0 A) B) =>  ((v3_rusub_4 B A) &  (B = (u1_struct_0 (k1_rlvect_3 A B))) ) ) ) ) ) ) ).
tt(t26_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (u1_struct_0 (k3_rusub_5 A C)) (u1_struct_0 (k3_rusub_5 A B)))) ) ) ) ) ) ) ).
tt(t26_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k6_rvsum_1 (k4_rvsum_1 A B)) = (k4_rvsum_1 (k6_rvsum_1 A) (k6_rvsum_1 B))) ) ) ) ) ).
tt(t26_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k11_rvsum_2 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k2_numbers (k5_binop_2 A B))) ) ) ) ) ).
tt(t26_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ( (D = (k1_funct_1 B C))  =>  ((r1_xxreal_0 (k5_card_1 B) C) |  ((k1_funct_1 (k3_scmfsa6a A B) (k2_nat_1 (k5_card_1 A) C)) = (k5_compos_0 (u1_compos_1 k1_scmfsa_2) D (k5_card_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 9)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t26_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k2_scmfsa_1) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m2_subset_1 D k1_scmfsa_1 k3_scmfsa_1) =>  ((k9_scmfsa_1 (k7_scmfsa_1 A B C) D) = (k9_scmfsa_1 A D)) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k14_scmfsa_2 B C A)) = 9) ) ) ) ) ) ) ).
tt(t26_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_scmfsa6a (k3_scmfsa6a B C) A) = (k3_scmfsa6a B (k5_scmfsa6a C A))) ) ) ) ) ) ) ).
tt(t26_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A))) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) E)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k8_memstr_0 3 k1_scmfsa_2 A) E)))  &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) E)) = (k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k8_memstr_0 3 k1_scmfsa_2 A) E))) ) ) ) )  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1))))  &  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1))) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k8_memstr_0 3 k1_scmfsa_2 A) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k8_memstr_0 3 k1_scmfsa_2 A)) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmfsa8b A B C) k6_numbers) = (k12_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A))  &  ( ((k1_funct_1 (k1_scmfsa8b A B C) 1) = (k11_scmfsa_2 2))  &  ( ((k1_funct_1 (k2_scmfsa8b A B C) k6_numbers) = (k13_scmfsa_2 (k2_nat_1 (k5_card_1 C) 3) A))  &  ((k1_funct_1 (k2_scmfsa8b A B C) 1) = (k11_scmfsa_2 2)) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  => (r3_scmfsa9a A B C D)) ) ) ) ) ) ) ) ).
tt(t26_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k5_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E)) = k6_numbers)  & (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) F)))  =>  ((r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E) (k8_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E))) & (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) (k2_nat_1 E 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 F (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k1_scmfsa_9 C B)) B) (k8_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E))) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmfsa_m,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~  ( (~  (A = B) )  &  ((k9_scmfsa_m A C) = (k9_scmfsa_m B C)) ) ) ) ) ) ) ) ) ).
tt(t26_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v2_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r2_scm_halt A B C)) ) ) ) ) ) ) ).
tt(t26_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v1_scmfsa7b C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k2_scmfsa_9 E C)) =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 E C) B A) D) = (k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 E C) (k1_scmfsa6b C B A) A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 14)  &  (! [B:$i] :  ((v1_int_1 B) =>  (~  (A = (k3_scmpds_2 B)) ) ) ) ) ) ) ) ).
tt(t26_scmpds_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v3_scmpds_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k5_card_1 A) C)) => (v3_scmpds_4 (k3_scmpds_4 A (k9_scmpds_2 D B C)))) ) ) ) ) ) ) ) ) ).
tt(t26_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  ((r1_tarski C A) =>  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t26_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_scmpds_6 C A B) & (r2_scmpds_6 C A B))  =>  ((r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A)) D) | (r2_hidden (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 B (k10_compos_1 k1_scmpds_2 C)) (k8_memstr_0 2 k1_scmpds_2 A) D)) (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_scmpds_6 B C A) &  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C)) D))  &  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C) D)) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  =>  ( ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_recdef_1 G H) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers)) ) )  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  ( (~ (r1_xxreal_0 (k1_recdef_1 G H) (k1_recdef_1 G (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C H I)))))  &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J F) =>  ((k1_funct_1 (k6_scmpds_4 C H I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) &  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers))  =>  ((k6_scmpds_4 (k2_scmpds_8 D E C) B A) = (k6_scmpds_4 (k2_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 6)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B))) = (k1_tarski 1)) ) ) ) ) ) ).
tt(t26_scmyciel,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v4_scmyciel A))  => (r1_xxreal_0 (k2_scmyciel A) (k5_card_1 A))) ) ).
tt(t26_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) & (r1_semi_af1 A B C E))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A (k3_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A B) C))) ) ) ) ) ) ).
tt(t26_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k2_seq_2 A) = k6_numbers) ) )  =>  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers) ) ) ) ) ) ).
tt(t26_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v3_funct_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k2_seq_2 A) = (k8_nat_1 k1_numbers A B)) ) ) ) ) ) ).
tt(t26_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r1_seqfunc A k1_numbers B C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D C) => (r1_seqfunc A k1_numbers B (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t26_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seqm_3 A) & (m2_valued_0 B k1_numbers A))  => (v1_seqm_3 B)) ) ) ) ) ).
tt(t26_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A C) k6_numbers))  &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k10_real_1 (k3_funct_2 k5_numbers k1_numbers A (k2_nat_1 C 1)) (k3_funct_2 k5_numbers k1_numbers A C))) ) ) )  & (v2_comseq_2 B))  =>  ((r1_xxreal_0 1 (k2_seq_2 B)) | (v1_series_1 A)) ) ) ) ) ) ).
tt(t26_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 1 (k3_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 2 B) 1) (k2_nat_1 (k4_nat_1 2 B) 1))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 B (k2_nat_1 (k4_nat_1 2 B) 1))) ) ) ) ) ) ) ).
tt(t26_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k18_complex1 A) (k18_complex1 B))) (k7_real_1 (k18_complex1 A) (k18_complex1 B)))) ) ) ) ).
tt(t26_series_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k7_xcmplx_0 1 (k2_nat_1 C 1))) ) )  =>  ((k1_seq_1 (k1_series_3 B) A) = (k7_xcmplx_0 1 (k9_newton (k2_nat_1 A 1)))) ) ) ) ) ) ).
tt(t26_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k13_complex1 B (k6_xcmplx_0 A B)) (k13_complex1 C (k6_xcmplx_0 A C)))) ) ) ) ) ) ) ) ) ).
tt(t26_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (B = k1_xboole_0) )  =>  ((k6_subset_1 A (k3_tarski B)) = (k1_setfam_1 (k4_setfam_1 (k1_tarski A) B))) ) ) ) ).
tt(t26_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k3_prob_1 B C) (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A))) ) ) ) ) ).
tt(t26_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 C A) => (v1_setlim_1 (k6_setlim_2 A C B) A)) ) ) ) ) ) ).
tt(t26_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 C B) &  ((v2_binop_1 C B) & (v3_binop_1 C B)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 A)) =>  ( ((k7_relset_1 A B D F) = (k7_relset_1 A B E G))  =>  ( (F = k1_xboole_0)  |  ((k7_setwiseo A B C F D) = (k7_setwiseo A B C G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((v2_binop_1 C A) =>  ( ( (~  ((r1_xxreal_0 1 D) & (r1_xxreal_0 1 E)) )  &  (~ (v1_setwiseo C A)) )  |  ((k1_finsop_1 A (k5_finseq_2 A (k2_xcmplx_0 D E) B) C) = (k5_binop_1 A C (k1_finsop_1 A (k5_finseq_2 A D B) C) (k1_finsop_1 A (k5_finseq_2 A E B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 A C)) =>  ((k1_funct_1 (k1_scmfsa6b (k4_sfmastr2 C) A B) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t26_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v1_scmfsa7b E)) ) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~ (r1_sfmastr3 F B C D E A))  &  (~ (v7_amistd_1 E 3 k1_scmfsa_2)) )  |  ((r5_scmfsa7b (k2_sfmastr3 B C D E) A F) & (r6_scmfsa7b (k2_sfmastr3 B C D E) A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((k2_sf_mastr A) = (k2_sf_mastr (k2_scmfsa6a A))) ) ) ).
tt(t26_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_sgraph1 A B) => (r1_tarski (k3_sgraph1 A) B)) ) ) ).
tt(t26_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) &  ((v8_robbins1 A) &  ((v9_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v10_sheffer1 A)) ) ).
tt(t26_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B D)) D) = (k5_sheffer1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t26_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((k6_simplex0 (k5_simplex0 A (k6_domain_1 (k1_zfmisc_1 A) B))) = (k3_xxreal_3 (k5_card_1 B) 1)) ) ) ) ).
tt(t26_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C B) & (v3_pre_topc D B))  =>  ((r1_xboole_0 (k1_rlaffin2 A (k1_simplex1 A B C)) (k3_convex1 A (k1_simplex1 A B D))) | (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(t26_simplex2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_topdim_1 (k15_euclid A)) = A) ) ) ).
tt(t26_sincos10,ax, ((k2_relset_1 k1_numbers k2_sincos10) = (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) ).
tt(t26_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k1_sin_cos2 (k7_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))) (k1_seq_1 k4_sin_cos2 (k9_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))))  &  ((k9_real_1 (k1_seq_1 k1_sin_cos2 A) (k1_seq_1 k1_sin_cos2 B)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k1_sin_cos2 (k9_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))) (k1_seq_1 k4_sin_cos2 (k7_real_1 (k6_real_1 A 2) (k6_real_1 B 2))))) ) ) ) ) ) ).
tt(t26_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k15_sin_cos (k1_binop_2 A)) = (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A))) ) ) ).
tt(t26_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k20_sin_cos A) (k17_sin_cos B)))) ) ) ) ) ).
tt(t26_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k18_sin_cos (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k9_real_1 1 (k20_sin_cos A)) 2)))  |  ((k18_sin_cos (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k9_real_1 1 (k20_sin_cos A)) 2)))) ) ) ) ).
tt(t26_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k20_sin_cos A) = 1)  =>  (A = (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k6_real_1 A (k8_real_1 2 k32_sin_cos))))) ) ) ) ).
tt(t26_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k18_complex1 B) (k18_complex1 A))) )  => (r1_xxreal_0 k6_numbers (k10_binop_2 (k11_binop_2 B (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))) (k11_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 B) 1)))))) ) ) ) ) ).
tt(t26_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k3_sin_cos2 (k3_xcmplx_0 2 A)) = (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_sin_cos2 A)) (k6_sin_cos2 A)))  &  ( ((k6_sin_cos2 (k3_xcmplx_0 2 A)) = (k6_xcmplx_0 (k3_xcmplx_0 2 (k5_square_1 (k6_sin_cos2 A))) 1))  &  ((k9_sin_cos2 (k3_xcmplx_0 2 A)) = (k7_xcmplx_0 (k3_xcmplx_0 2 (k9_sin_cos2 A)) (k2_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A))))) ) ) ) ) ).
tt(t26_sin_cos9,ax, ((k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))))) ).
tt(t26_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k15_complex1 (k15_sin_cos (k3_xcmplx_0 A k7_complex1))) = (k15_sin_cos (k4_xcmplx_0 (k3_xcmplx_0 A k7_complex1)))) ) ) ).
tt(t26_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (A = (k3_tarski (a_1_1_sppol_1 B)))  => (v4_pre_topc A (k15_euclid 2))) ) ) ) ) ).
tt(t26_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k3_finseq_1 A) 2) => (v2_topreal1 A)) ) ) ).
tt(t26_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)) = (a_1_3_sprect_1 A)) ) ) ).
tt(t26_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r1_sprect_2 A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(t26_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_subset_1 (k2_goboard9 A) (k3_topreal1 2 A))) ) ).
tt(t26_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t26_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k6_square_1 A) (k6_square_1 B))) ) ) ) ) ).
tt(t26_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((r1_stacks_1 A B) =>  ((k13_stacks_1 A B) = B) ) ) ) ) ) ).
tt(t26_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_stirl2_1 A A) = 1) ) ) ).
tt(t26_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) =>  ( ((k18_substut1 A (k24_substut1 A B C)) = (k15_qc_lang1 A (k23_substut1 A B) (k18_substut1 A (k22_substut1 A B))))  &  ((k19_substut1 A (k24_substut1 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t26_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((r1_tarski B C) & (r1_xboole_0 D C))  => (r1_tarski B (k3_subset_1 A D))) ) ) ) ) ) ) ) ).
tt(t26_substlat,ax, (! [A:$i] :  (! [B:$i] :  ((k5_lattices (k5_substlat A B)) = k1_xboole_0) ) ) ).
tt(t26_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v4_substut1 B A) =>  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = k6_numbers) )  &  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 1) )  &  ( (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 2) )  &  (~  ((k1_xtuple_0 (k1_funct_1 (k11_qc_lang1 A (k18_substut1 A B)) 1)) = 3) ) ) ) ) ) ) ) ) ) ).
tt(t26_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((v2_qc_lang1 B A) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v5_relat_1 E (k3_qc_lang1 A)) &  ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A))) )  =>  (~  (B = (k4_cqc_lang C A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_tarski B k1_numbers) =>  ( (~ (r1_xxreal_0 (k12_supinf_2 C D) k2_supinf_1))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_orders_2 B C (k3_rlvect_1 B E D)) =>  ((r1_orders_2 B C D) |  ((k1_symsp_1 A B D C E) = (k1_symsp_1 A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k9_xtuple_0 (k1_sysrel A)) = (k10_xtuple_0 (k1_sysrel A))) ) ) ).
tt(t26_taxonom1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k2_relset_1 k1_numbers B))  & (r1_xxreal_0 (k1_xxreal_2 C) D))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers A) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers A) => (r1_xxreal_0 (k1_metric_1 A A B E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k1_seq_1 F G) = (k9_real_1 (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C G D)) A)) (k10_real_1 (k8_real_1 E (k2_newton (k9_real_1 D G) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ( ((k1_seq_1 (k3_series_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) (k4_nat_1 2 C)) = (k1_seq_1 (k3_series_1 (k22_sin_cos B)) (k5_real_1 C 1)))  &  ((k1_seq_1 (k3_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) (k4_nat_1 2 C)) = (k1_seq_1 (k3_series_1 (k23_sin_cos B)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_tbsp_1 B A) => (v6_tbsp_1 (k2_relset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t26_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) => (v5_tops_1 (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) A)) ) ) ) ) ).
tt(t26_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k5_setfam_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t26_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v1_tdlat_3 A) <=>  ((v3_tdlat_3 A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = (k1_tarski C))  => (v4_pre_topc B A)) ) ) ) ) ) ) ) ) ).
tt(t26_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r6_pboole A (k3_termord A B C (k5_termord A B C D)) (k3_termord A B C D))) ) ) ) ) ) ) ) ).
tt(t26_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 (k3_tex_1 A B)) (u1_pre_topc (k3_tex_1 A B))))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))))  =>  ((k2_pre_topc C D) = (k2_xboole_0 D (k6_domain_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ((v2_tex_3 B A) | (v2_tex_3 C A))  =>  ((v2_tex_3 (k1_tsep_1 A B C) A) & (m1_pre_topc (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t26_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k2_tex_4 A B) (k1_setfam_1 (a_2_5_tex_4 A B)))) ) ) ) ).
tt(t26_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~  ( ((r1_tsep_1 B C) | (r1_tsep_1 C B))  &  ( (~  ((r1_tsep_1 D C) & (r1_tsep_1 C D)) )  &  (~  ( ((k2_tsep_1 A (k1_tsep_1 A B D) C) = (k2_tsep_1 A D C))  &  ((k2_tsep_1 A C (k1_tsep_1 A B D)) = (k2_tsep_1 A C D)) ) ) ) ) )  &  (~  ( (~  ((r1_tsep_1 B C) & (r1_tsep_1 C B)) )  &  ( ((r1_tsep_1 D C) | (r1_tsep_1 C D))  &  (~  ( ((k2_tsep_1 A (k1_tsep_1 A B D) C) = (k2_tsep_1 A B C))  &  ((k2_tsep_1 A C (k1_tsep_1 A B D)) = (k2_tsep_1 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (! [D:$i] :  ( ((v1_toler_1 D A B) & (m1_toler_1 D A B))  <=>  ((v1_toler_1 D A C) & (m1_toler_1 D A C)) ) )  => (r2_relset_1 A A B C)) ) ) ) ) ) ).
tt(t26_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A B D) =>  ((r4_borsuk_2 A B C E F) => (r4_borsuk_2 A B C E (k1_borsuk_2 A B B C (k1_borsuk_2 A B D B G (k2_borsuk_2 A B D G)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A D D) => (m1_borsuk_2 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) E C) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_borsuk_2 I (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G)) =>  (! [J:$i] :  ((m1_borsuk_2 J (k2_borsuk_1 A B) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H)) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) (k8_topalg_4 A B C E F H (k1_borsuk_2 (k2_borsuk_1 A B) (k4_borsuk_1 A B C F) (k4_borsuk_1 A B D G) (k4_borsuk_1 A B E H) I J)) (k1_borsuk_2 B F G H (k8_topalg_4 A B C D F G I) (k8_topalg_4 A B D E G H J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topalg_5,ax,(v3_funct_2 k7_topalg_5 (u1_struct_0 k2_gr_cy_1) (u1_struct_0 (k5_topalg_1 (k8_toprealb 2) k9_toprealb)))).
tt(t26_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (m2_subset_1 (k5_relat_1 B (k1_rcomp_1 C D)) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ) ) ) ) ) ) ).
tt(t26_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_metrizts A B C D) =>  ((v1_topdim_1 C A) <=> (v1_topdim_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t26_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B C) => (r1_tarski (k3_topgen_1 A B) (k3_topgen_1 A C))) ) ) ) ) ) ) ).
tt(t26_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ( (~ (v1_finset_1 C))  =>  ((k2_pre_topc (k5_topgen_2 A B) C) = (k2_xboole_0 C (k1_tarski B))) ) ) ) ) ) ) ).
tt(t26_topgen_3,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k4_series_1 (k4_topgen_3 A (k13_complex1 1 2))) (k8_nat_1 k1_numbers (k3_series_1 (k4_topgen_3 A (k13_complex1 1 2))) B))) ) ) ) ) ).
tt(t26_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_ordinal1 (k1_card_1 (k3_topgen_4 A B C)) (k1_card_1 (k2_zfmisc_1 B C)))) ) ) ) ) ).
tt(t26_topgen_5,ax, ((v4_pre_topc k1_topgen_5 k3_topgen_5) & (m1_subset_1 k1_topgen_5 (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t26_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) <=> (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v5_topreal1 A) &  (A = k1_xboole_0) ) ) ) ) ).
tt(t26_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k9_metric_1 (k14_euclid 2) C B)))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k9_real_1 (k3_finseq_1 A) 1)) &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k9_real_1 (k3_finseq_1 A) 1)))  =>  ( ((k9_subset_1 (u1_struct_0 (k14_euclid 2)) (k2_topreal1 2 A E) (k9_metric_1 (k14_euclid 2) C B)) = k1_xboole_0)  | (r1_xxreal_0 D E)) ) ) )  & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k9_metric_1 (k14_euclid 2) C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r2_hidden A B) &  (C = (a_2_1_topreal4 A B)) )  => (r1_tarski C B)) ) ) ) ) ) ) ).
tt(t26_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_rlvect_1 (k15_euclid 2) B A) = (k19_euclid (k8_real_1 A (k17_euclid B)) (k8_real_1 A (k18_euclid B)))) ) ) ) ) ).
tt(t26_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) (u1_struct_0 (k3_pcomps_1 (k14_euclid (k2_nat_1 A B))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) (u1_struct_0 (k3_pcomps_1 (k14_euclid (k2_nat_1 A B)))))))) )  &  ((v3_tops_2 C (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B))) (k3_pcomps_1 (k14_euclid (k2_nat_1 A B)))) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ((r2_hidden (k4_tarski D E) (k1_relset_1 (u1_struct_0 (k2_borsuk_1 (k3_pcomps_1 (k14_euclid A)) (k3_pcomps_1 (k14_euclid B)))) C)) =>  ((k1_binop_1 C D E) = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  &  ((v1_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  => (v1_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t26_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((r2_hidden D (k4_topreal9 A B C)) <=>  (? [E:$i] :  ((v1_xreal_0 E) &  ( (D = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 E)) (k1_rlvect_1 (k15_euclid A) C E)))  & (r1_xxreal_0 k6_numbers E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C B))  =>  ((v3_pre_topc (k3_rcomp_1 A C) (k4_topmetr A B)) & (m1_subset_1 (k3_rcomp_1 A C) (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) ) ) ) ) ) ) ) ).
tt(t26_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((m1_subset_1 B (u1_struct_0 (k11_toprealb A))) =>  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) 1)) ) ) ) ) ) ) ) ).
tt(t26_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (A = k6_numbers) )  &  ((r2_hidden C (k1_topreal9 A D B)) & (r1_xxreal_0 (k3_xcmplx_0 A B) (k18_complex1 (k16_rvsum_1 (k5_algstr_0 (k15_euclid A) C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k12_euclid (k4_algstr_0 (k15_euclid A) B)) = (k12_euclid B)) ) ) ) ) ).
tt(t26_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k1_tops_1 A B)) = (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))) ) ) ) ) ).
tt(t26_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((v4_pre_topc B A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (D = B)  => (v4_pre_topc D C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_tops_1 B A) & (r1_tarski C B))  => (v3_tops_1 C A)) ) ) ) ) ) ) ).
tt(t26_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v1_transgeo A)) ) ).
tt(t26_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k2_xboole_0 A B)))  &  ((v1_finset_1 (k2_xboole_0 A B)) & (v1_trees_1 (k2_xboole_0 A B))) ) ) ) ) ) ).
tt(t26_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v2_trees_2 B A) & (m1_trees_2 B A))  => (r2_hidden k1_xboole_0 B)) ) ) ) ).
tt(t26_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((v5_trees_3 A) & (v5_trees_3 B))  <=> (v5_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(t26_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ((k13_funct_3 (k1_trees_4 A) (k1_trees_4 B)) = (k1_trees_4 (k4_tarski A B))) ) ) ).
tt(t26_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((k12_trees_9 (k1_tarski A) B) = (k7_trees_9 A B)) ) ) ) ).
tt(t26_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( ( (~ (r1_tsep_1 B C))  =>  ((k2_tsep_1 A B C) = (k2_tsep_1 A C B)) )  &  ( ( ( (~ (r1_tsep_1 B C))  &  (~ (r1_tsep_1 (k2_tsep_1 A B C) D)) )  |  ( (~ (r1_tsep_1 C D))  &  (~ (r1_tsep_1 B (k2_tsep_1 A C D))) ) )  =>  ((k2_tsep_1 A (k2_tsep_1 A B C) D) = (k2_tsep_1 A B (k2_tsep_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))) =>  ( ( (E = (k9_subset_1 (u1_struct_0 A) (u1_struct_0 D) B))  &  ( (F = (k9_subset_1 (u1_struct_0 A) (u1_struct_0 D) C))  & (r1_connsp_1 A B C)) )  => (r1_connsp_1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = C)  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) D) = (k3_tex_4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_turing_1 A)) =>  (! [E:$i] :  ( ((k1_funct_1 (k5_turing_1 A B C D) C) = D)  &  ( (~  (E = C) )  =>  ((k1_funct_1 (k5_turing_1 A B C D) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_twoscomp,ax, ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 k6_numbers k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 k6_numbers k6_numbers 1)) = 1)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 k6_numbers 1 k6_numbers)) = 1)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 k6_numbers 1 1)) = k6_numbers)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k33_twoscomp (k11_finseq_1 1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k33_twoscomp (k11_finseq_1 1 1 1)) = 1) ) ) ) ) ) ) ) ).
tt(t26_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  => (v1_binop_1 (k11_unialg_2 A) (k9_unialg_2 A))) ) ).
tt(t26_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k2_uniroots A) = (a_1_1_uniroots A)) ) ) ).
tt(t26_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A (k11_polynom3 A B C) (k11_polynom3 A B D)) (k11_polynom3 A B (k3_normsp_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t26_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ((r1_tarski A (k1_xxreal_1 B C)) =>  ((r1_xxreal_0 B (k7_supinf_2 A)) & (r1_xxreal_0 (k8_supinf_2 A) C)) ) ) ) ) ) ) ) ).
tt(t26_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (? [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) &  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (H = C) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B E H)) ) ) )  &  ((k3_funct_2 (k3_qc_lang1 A) B G C) = (k3_funct_2 (k3_qc_lang1 A) B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ( ((v3_funct_1 B) & (m2_valued_0 C A B))  => (r2_funct_2 k5_numbers A B C)) ) ) ) ) ) ) ).
tt(t26_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k9_xtuple_0 A) k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k10_xtuple_0 (k61_valued_1 A B)) = (k10_xtuple_0 A)) ) ) ) ) ) ).
tt(t26_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k50_valued_1 A B)) = (k50_valued_1 (k30_valued_1 A) B)) ) ) ) ) ).
tt(t26_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_vectsp10 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_vectsp10 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ( (D = (k3_vectsp_4 A B F C))  &  (E = (k3_vectsp_4 A B G C)) )  =>  ((k3_rlvect_1 (k6_vectsp10 A B C) D E) = (k3_vectsp_4 A B (k3_rlvect_1 B F G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D C) &  ((v9_vectsp_1 D C) &  ((v10_vectsp_1 D C) &  ((v11_vectsp_1 D C) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D C)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 D)) &  ((v13_vectsp_1 E D D) &  ((v1_mod_2 E C D D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D))))) ) ) )  => (m1_vectsp_4 (k1_ranknull C D D (k1_vectsp11 D E A)) C (k1_ranknull C D D (k1_vectsp11 D E (k2_xcmplx_0 A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp_1,ax, (~  ((k3_rlvect_1 k2_vectsp_1 (k5_struct_0 k2_vectsp_1) (k5_struct_0 k2_vectsp_1)) = (k4_struct_0 k2_vectsp_1)) ) ).
tt(t26_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k6_vectsp_2 A B)))  &  ((v13_algstr_0 (k6_vectsp_2 A B)) &  ((v8_vectsp_1 (k6_vectsp_2 A B) A) &  ((v9_vectsp_1 (k6_vectsp_2 A B) A) &  ((v10_vectsp_1 (k6_vectsp_2 A B) A) &  ((v11_vectsp_1 (k6_vectsp_2 A B) A) &  ((v2_rlvect_1 (k6_vectsp_2 A B)) &  ((v3_rlvect_1 (k6_vectsp_2 A B)) &  ((v4_rlvect_1 (k6_vectsp_2 A B)) &  ((v4_vectsp_2 (k6_vectsp_2 A B) B) &  ((v5_vectsp_2 (k6_vectsp_2 A B) A B) & (l2_vectsp_2 (k6_vectsp_2 A B) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  ( ((m1_vectsp_4 B A C) & (m1_vectsp_4 C A D))  => (m1_vectsp_4 B A D)) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (m1_vectsp_4 (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E)) A (k2_vectsp_5 A B D (k1_vectsp_5 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) => (r1_vectsp_6 A B (k5_vectsp_6 A B C (k5_vectsp_6 A B D E)) (k5_vectsp_6 A B (k5_vectsp_6 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t26_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_7 C A B) =>  ((k1_card_1 C) = (k1_vectsp_9 A (k1_vectsp_7 A B C))) ) ) ) ) ) ) ) ).
tt(t26_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k5_vfunct_1 A B D)) (k6_vfunct_1 A B C D))) ) ) ) ) ) ) ) ).
tt(t26_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k2_vfunct_1 A B C (k5_vfunct_1 A B D)) (k3_vfunct_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t26_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v12_waybel_0 C A)) ) )  =>  ((v12_waybel_0 (k5_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k5_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t26_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_waybel10 A))) <=>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v22_waybel_0 B A A) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t26_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel11 A B))) =>  ((k2_waybel_0 A (k4_waybel11 A B) C) = B) ) ) ) ) ) ) ).
tt(t26_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_waybel_6 B A) & (v12_waybel_0 B A))  => (v2_waybel_0 B A)) ) ) ) ) ).
tt(t26_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  => (r5_waybel_1 A B)) ) ) ) ) ).
tt(t26_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc C A) & (r2_hidden B C))  => (r1_waybel_3 A (k2_yellow_0 A C) B)) ) ) ) ) ) ) ).
tt(t26_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B (k1_waybel15 A)) & (r1_tarski C (k1_waybel15 A)))  =>  ((r1_tarski B C) <=> (r3_orders_2 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ) ) ).
tt(t26_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r3_waybel_4 A (k6_subset_1 (u1_struct_0 A) (k6_waybel_0 A C)) B)) )  => (v1_waybel16 B A)) ) ) ) ) ).
tt(t26_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_5_waybel17 A B C D))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_6_waybel17 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t26_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_waybel_0 A B C) => (r1_tarski (k10_yellow_6 A B) (k2_pre_topc A C))) ) ) ) ) ) ) ).
tt(t26_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_waybel_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) E)))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t26_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v21_waybel_0 D A B) & (v21_waybel_0 E B C))  => (v21_waybel_0 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v8_waybel_0 B A) & (l1_waybel_0 B A)) ) ) ) )  =>  ( (~ (v1_xboole_0 (a_2_1_waybel21 A B)))  &  ((v1_waybel_0 (a_2_1_waybel21 A B) A) & (m1_subset_1 (a_2_1_waybel21 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t26_waybel23,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (v1_lattice3 (k5_yellow_0 A B))) ) ) ) ).
tt(t26_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_waybel_9 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_funct_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) D) = (k1_yellow_0 B (a_4_2_waybel24 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t26_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_waybel_9 (k1_waybel25 B) (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D))) )  => (r1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C)))) ) ) ) ) ) ) ).
tt(t26_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) ) )  =>  ( ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B)))  => (v3_waybel_3 (k2_yellow_1 (u1_pre_topc A)))) ) ) ) ) ).
tt(t26_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v8_yellow_0 (k2_waybel27 A B) (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 (k2_waybel27 A B) (k6_yellow_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t26_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k4_tarski (k4_waybel17 A B) (k1_yellow_0 A B)) (k3_waybel28 A))) ) ) ) ).
tt(t26_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k1_waybel29 (k2_yellow_1 (u1_pre_topc A))))) &  ((v5_pre_topc C B (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))))))) ) )  =>  ((v3_pre_topc (k5_waybel26 C) (k2_borsuk_1 B A)) & (m1_subset_1 (k5_waybel26 C) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B A))))) ) ) ) ) ) ) ) ).
tt(t26_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((r1_yellow_0 A (k2_relset_1 (u1_struct_0 A) C)) &  ((r1_yellow_0 A (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A (k2_waybel_2 A B C)))) &  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) => (r1_yellow_0 A (k7_relset_1 B (u1_struct_0 A) C D))) ) ) )  =>  ((k4_yellow_2 A C) = (k1_waybel_2 A (k2_waybel_2 A B C))) ) ) ) ) ) ) ).
tt(t26_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k1_tops_1 A B) (k1_waybel30 A B))) ) ) ) ).
tt(t26_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((r5_waybel_1 A B) =>  ((k1_card_1 (u1_struct_0 A)) = (k1_card_1 (u1_struct_0 B))) ) ) ) ) ) ).
tt(t26_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_waybel_0 A (k2_waybel32 A B) C) => (r1_waybel_0 A B C)) ) ) ) ) ) ) ).
tt(t26_waybel33,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel33 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  => (r2_waybel_7 A B (k1_waybel33 A (k2_struct_0 A) B))) ) ) ) ).
tt(t26_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E A))  =>  ( (! [F:$i] :  ( ((v3_pre_topc F D) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))))  =>  ((v3_pre_topc (k4_waybel_0 A (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F)) E) & (m1_subset_1 (k4_waybel_0 A (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) F)) (k1_zfmisc_1 (u1_struct_0 E)))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 B) (u1_struct_0 A) F (k1_waybel34 A B C)) => (v2_waybel34 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel35 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v3_waybel35 C A B) & (m1_waybel35 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ((r2_orders_2 A D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k6_waybel35 A B C)) &  ((r2_orders_2 A D F) & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) F E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_waybel_3,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel_3 B A)) )  => (v2_waybel_3 A)) ) ) ).
tt(t26_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (r2_hidden (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) (u1_struct_0 (k8_waybel_4 A)))) ) ).
tt(t26_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_waybel_5 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_1_waybel_5 A B C))) ) ) ) ) ) ) ).
tt(t26_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_yellow_0 A)) )  =>  ((v5_waybel_6 B A) <=>  ( (~ (v1_xboole_0 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B))))  &  ((v2_waybel_0 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) &  ((v13_waybel_0 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) & (m1_subset_1 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t26_waybel_7,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v11_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 A)) &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r1_tarski B C) & (v3_waybel_7 C A)) ) ) ) ) ) ) ).
tt(t26_waybel_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) <=> (r1_tarski B A)) ) ) ).
tt(t26_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v3_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v5_pre_topc (k4_waybel_1 A C) A A) => (r2_hidden (k12_lattice3 A C (k11_yellow_6 A B)) (k10_yellow_6 A (k3_waybel_2 A C B)))) ) ) ) ) ) ) ).
tt(t26_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (u1_struct_0 (k4_weddwitt A))) & (r2_hidden D (u1_struct_0 (k5_weddwitt A B))))  => (r2_hidden (k6_algstr_0 A C D) (u1_struct_0 (k5_weddwitt A B)))) ) ) ) ) ) ) ) ) ).
tt(t26_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) D) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k5_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((v2_wellord1 C) => (r3_xboole_0 (k1_wellord1 C A) (k1_wellord1 C B))) ) ) ) ) ).
tt(t26_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_nat_d (k1_newton B A) (k1_newton C A)) =>  ((r1_xxreal_0 A k6_numbers) | (r1_nat_d B C)) ) ) ) ) ) ) ) ).
tt(t26_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k3_xboole_0 A C) (k3_xboole_0 B C))) ) ) ) ).
tt(t26_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k7_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t26_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k6_xcmplx_0 (k2_xcmplx_0 A B) B)) ) ) ) ) ).
tt(t26_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 A) B) => (r1_xxreal_0 (k4_xcmplx_0 B) A)) ) ) ) ) ).
tt(t26_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) (k9_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t26_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k4_xxreal_0 A C) (k4_xxreal_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t26_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k3_xxreal_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t26_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_xxreal_2 (k2_xxreal_1 A B)) = A) ) ) ) ) ) ).
tt(t26_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k2_xxreal_3 (k3_xxreal_3 A B)) = (k1_xxreal_3 (k2_xxreal_3 A) B))  &  ((k2_xxreal_3 (k3_xxreal_3 A B)) = (k3_xxreal_3 B A)) ) ) ) ) ) ).
tt(t26_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((r1_yellow_0 A C) =>  ((k1_yellow_0 A C) = (k1_yellow_0 B C)) ) ) ) ) ) ) ) ).
tt(t26_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) => (r1_tarski (k3_waybel_0 (k3_yellow_3 A B) C) (k6_yellow_3 A B (k3_waybel_0 A (k4_yellow_3 A B C)) (k3_waybel_0 B (k5_yellow_3 A B C))))) ) ) ) ) ) ).
tt(t26_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_yellow_0 (k5_yellow_0 A B) A) => (v2_waybel_0 B A)) ) ) ) ) ).
tt(t26_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m2_yellow13 B A) => (r1_tarski (u1_pre_topc A) (k1_cantor_1 (u1_struct_0 A) (k1_tdlat_2 A B)))) ) ) ) ).
tt(t26_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v4_yellow_8 A))  => (v4_yellow_8 B)) ) ) ) ) ).
tt(t26_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v8_struct_0 A) =>  ((u1_struct_0 A) = (u1_struct_0 (k1_waybel_8 A))) ) ) ) ).
tt(t26_yellow16,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_yellow_0 C B) =>  ((v4_yellow_0 C B) <=>  ((v4_yellow_0 C A) & (m1_yellow_0 C A)) ) ) ) ) ) ) ) ).
tt(t26_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r2_functor0 A B) => (r3_yellow18 A B)) ) ) ) ) ).
tt(t26_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (? [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 D (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  &  ((r2_hidden B D) & (r2_waybel_7 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t26_yellow_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) & (v1_yellow_1 A)) ) ) )  =>  ((k5_yellow_1 k1_xboole_0 A) = (g1_orders_2 (k1_tarski k1_xboole_0) (k6_partfun1 (k1_tarski k1_xboole_0)))) ) ) ).
tt(t26_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  ((v2_altcat_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  (F = D) )  =>  ((k1_altcat_1 B E F) = (k1_altcat_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r2_yellow_0 A B)) )  =>  (! [B:$i] :  ((r2_yellow_0 A B) &  ((k2_yellow_0 A B) = (k2_yellow_0 A (k3_xboole_0 B (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t26_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v13_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((v13_waybel_0 (k4_yellow_3 A B C) A) & (v13_waybel_0 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ).
tt(t26_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_lattice3 A D B) & (r1_lattice3 A E C))  => (r1_lattice3 A (k2_yellow_4 A D E) (k13_lattice3 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t26_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_yellow_5 A B (k12_lattice3 A C D)) => (r2_yellow_5 A B C)) ) ) ) ) ) ) ) ) ).
tt(t26_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) =>  ((u1_struct_0 (k8_yellow_6 A B C)) = (k2_zfmisc_1 (u1_struct_0 B) (k4_card_3 (k12_pralg_1 (u1_struct_0 B) C)))) ) ) ) ) ) ) ).
tt(t26_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v2_waybel_0 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A))))) ) ) ) ) ).
tt(t26_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v7_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ) ).
tt(t26_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((v1_tops_2 C B) &  ((v2_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) )  =>  ((u1_pre_topc A) = (u1_pre_topc B)) ) ) ) ) ) ) ) ).
tt(t26_zf_fund1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ( ((k4_zf_fund1 (k6_domain_1 k1_zf_lang A)) = (k6_domain_1 k5_numbers (k3_zf_fund1 A)))  &  ((k4_zf_fund1 (k7_domain_1 k1_zf_lang A B)) = (k7_domain_1 k5_numbers (k3_zf_fund1 A) (k3_zf_fund1 B))) ) ) ) ) ) ).
tt(t26_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  ((k26_zf_lang A) = (k20_zf_lang (k22_zf_lang (k20_zf_lang A)))) ) ) ) ).
tt(t26_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 A 1) = 2)  => (v4_zf_lang A)) ) ) ).
tt(t26_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_tarski (k2_tarski (k1_tarski A) (k1_tarski B))) = (k2_tarski A B)) ) ) ).
tt(t26_zfrefle1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_ordinal2 A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ) ).
tt(t26_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t270_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xboole_0 (k3_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A k1_xxreal_0)) = (k3_xxreal_1 A B)) ) ) ) ) ).
tt(t271_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 B k1_xxreal_0)) = (k2_xxreal_1 B A)) ) ) ) ) ).
tt(t272_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 B k1_xxreal_0)) = (k1_xxreal_1 B A)) ) ) ) ) ).
tt(t273_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) => (r1_xboole_0 (k2_xxreal_1 C A) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t274_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) => (r1_xboole_0 (k2_xxreal_1 C A) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t275_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) => (r1_xboole_0 (k4_xxreal_1 C A) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t276_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) => (r1_xboole_0 (k4_xxreal_1 C A) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t277_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xboole_0 (k1_xxreal_1 C A) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t278_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xboole_0 (k1_xxreal_1 C A) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t279_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xboole_0 (k3_xxreal_1 C A) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t27_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_abcmiz_0 A B (k1_subset_1 (u1_abcmiz_0 A))) = B) ) ) ) ) ).
tt(t27_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  ((k1_abcmiz_1 (k6_domain_1 k2_abcmiz_1 A)) = (k4_subset_1 k2_abcmiz_1 (k3_abcmiz_1 A) (k6_domain_1 k2_abcmiz_1 A))) ) ) ).
tt(t27_abcmiz_a,ax, ( ((k23_abcmiz_1 k8_abcmiz_a) = k6_abcmiz_1)  &  ( ((k25_abcmiz_1 k8_abcmiz_a) = k1_xboole_0)  &  ((k26_abcmiz_1 k8_abcmiz_a) = k6_numbers) ) ) ).
tt(t27_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 k6_numbers (k3_real_1 (k4_xcmplx_0 A) (k18_complex1 A)))) ) ).
tt(t27_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B F) &  ((r2_hidden C F) & (v1_aff_1 F A)) )  =>  ( (B = C)  |  ((r2_aff_1 A D E F) <=> (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 C A) => (v1_aff_1 (k2_aff_4 A B C) A)) ) ) ) ) ) ) ).
tt(t27_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ((k1_ordinal4 (k1_ordinal4 A B) C) = (k1_ordinal4 A (k1_ordinal4 B C))) ) ) ) ) ) ) ).
tt(t27_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (v6_membered C))  =>  ((r1_afinsq_2 B C) =>  ((r1_xxreal_0 (k5_card_1 B) A) |  ( ((k2_relset_1 (k10_xtuple_0 (k4_afinsq_2 (k2_xboole_0 B C))) (k5_relat_1 (k4_afinsq_2 (k2_xboole_0 B C)) (k5_card_1 B))) = B)  &  ((k1_recdef_1 (k5_relat_1 (k4_afinsq_2 (k2_xboole_0 B C)) (k5_card_1 B)) A) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t27_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  (~  ( (B = D)  &  ( ((k4_tarski (k6_afproj A C) 2) = E)  & (r1_incsp_1 (k13_afproj A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_afvect0 A B C) = D)  <=> (r2_analoaf A C B B D)) ) ) ) ) ) ) ) ) ).
tt(t27_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) =>  (! [C:$i] :  ((m1_algspec1 C A) =>  (! [D:$i] :  ((m1_algspec1 D B) => (m1_algspec1 (k1_funct_4 C D) (k1_funct_4 A B))) ) ) ) ) ) ) ) ) ).
tt(t27_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k12_algstr_4 A) (k12_algstr_4 B))) ) ) ).
tt(t27_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ((v2_altcat_2 B A) & (m1_altcat_2 B A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  =>  ((g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B)) = (g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A))) ) ) ) ) ) ).
tt(t27_altcat_3,ax, (! [A:$i] :  ((l1_altcat_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_altcat_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A C B)) &  ((r2_hidden D (k1_altcat_1 A C B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) =>  ((r2_hidden E (k1_altcat_1 A C B)) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v2_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v2_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ami_2,ax, ((k9_xtuple_0 (k3_relat_1 k3_ami_2 k4_ami_2)) = k1_ami_2) ).
tt(t27_ami_3,ax, ((k8_struct_0 k1_ami_3) = k2_ami_2) ).
tt(t27_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v2_ami_wstd C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 C)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v5_ami_wstd D B C)) ) ) ) )  =>  ( (~ (r1_xxreal_0 (k5_card_1 D) A))  <=> (r2_hidden (k1_ami_wstd B C A) (k1_relset_1 k5_numbers D))) ) ) ) ) ) ) ) ) ).
tt(t27_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) &  ((r4_analmetr (k2_analmetr A B C) D E F G) &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) &  ( ((r2_analoaf A B C C B) =>  (B = C) )  &  ( ( ((r2_analoaf A B C F G) & (r2_analoaf A B C H I))  =>  ( (B = C)  | (r2_analoaf A F G H I)) )  &  ( ((r2_analoaf A B C D E) => (r2_analoaf A C B E D))  &  ( ((r2_analoaf A B C C D) => (r2_analoaf A B C B D))  &  (~  ((r2_analoaf A B C B D) &  ( (~ (r2_analoaf A B C C D))  &  (~ (r2_analoaf A B D D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (~ (r2_analoaf A B C D E))  &  (~ (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (B = D) )  &  ((r2_analoaf A D B B E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  ( (~ (r2_analoaf A B C E D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( ((r2_analoaf A B C B F) | (r2_analoaf A B C F B))  &  ((r2_analoaf A D E D F) | (r2_analoaf A D E F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) &  ((v3_analoaf A) & (l1_analoaf A)) ) ) ) ) ) ).
tt(t27_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((r1_analoaf A D E F G) <=>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~  (H = I) )  &  ((r1_analort A B C H I D E) & (r1_analort A B C H I F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) &  ((r1_collsp (k5_anproj_1 A) B C F) & (r1_collsp (k5_anproj_1 A) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_unialg_2 B A) => (r1_tarski (k6_unialg_2 A) B)) ) ) ) ) ).
tt(t27_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k48_aofa_i00 A B D E F G)) F) = (k21_aofa_i00 B k4_numbers C G))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k48_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r4_armstrng A B C D) <=>  ((r2_hidden (k6_armstrng A C D) B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (~  ((r2_hidden (k6_armstrng A E F) B) &  ( (~  ( (C = E)  &  (D = F) ) )  & (r3_armstrng A (k6_armstrng A E F) (k6_armstrng A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  (~  ( (~ (r1_arytm_2 A B))  &  ( (~  (C = k11_arytm_3) )  &  (~  ((k4_tarski k11_arytm_3 (k8_arytm_2 C (k1_arytm_1 A B))) = (k2_arytm_1 (k8_arytm_2 C B) (k8_arytm_2 C A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( (~  (A = k1_xboole_0) )  =>  ((k4_arytm_3 A A) = 1) ) ) ) ).
tt(t27_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k8_asympt_0 A) = (a_1_2_asympt_0 A)) ) ) ).
tt(t27_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_seq_1 A B) = (k4_power B (k7_square_1 B))) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((r2_funct_2 k5_numbers k1_numbers C (k1_asympt_1 2 1 k6_numbers)) &  ((r1_tarski (k6_asympt_0 B) (k6_asympt_0 C)) &  (~  ((k6_asympt_0 B) = (k6_asympt_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_pboole B (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A))) =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) =>  ( (B = (k16_funcop_1 k6_numbers C))  => (r2_hidden B (k5_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) ) ) ) ) ) ) ).
tt(t27_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k1_group_1 A)) (k6_autgroup A B)) (k6_autgroup A B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A B) (k6_autgroup A (k1_group_1 A))) (k6_autgroup A B))) ) ) ) ) ).
tt(t27_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_bagorder (k6_bagorder A) A)) ) ).
tt(t27_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B E) (k1_bcialg_1 A D C)) (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (v4_bcialg_2 B A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_bcialg_2 B A)) ) ) ) ) ).
tt(t27_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_bcialg_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A C D)) B) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A D (k1_bcialg_1 A D C)) (k1_bcialg_1 A C D)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) C) C) = (k1_bcialg_1 A B (k6_bcialg_4 A C 3))) ) ) ) ) ) ) ).
tt(t27_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( ( (A = (k2_bcialg_5 A B C D))  &  (A = B) )  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A A A A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_6 B A) &  ((k4_bcialg_6 A B) = 1) ) ) ) ) ) ) ).
tt(t27_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B C (k1_bcialg_1 B D C)) = C) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t27_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_bhsp_1 B (k1_rlvect_1 B C A)) = (k8_real_1 (k18_complex1 A) (k3_bhsp_1 B C))) ) ) ) ) ) ) ).
tt(t27_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k3_normsp_1 A D E))) &  ((k2_seq_2 (k2_bhsp_2 A (k3_normsp_1 A D E))) = (k3_bhsp_1 A (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (m2_valued_0 C (u1_struct_0 A) B))  => (v1_bhsp_2 C A)) ) ) ) ) ) ) ).
tt(t27_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k2_bhsp_2 B C) D) (k1_seq_1 A D))) )  & (v1_series_1 A))  => (v2_bhsp_4 C B)) ) ) ) ) ) ) ).
tt(t27_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v1_bilinear G A B C) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D (k1_algstr_0 C E F)) = (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D E) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) B))  =>  ((k1_binari_3 (k2_xcmplx_0 A 1) B) = (k9_binarith A 1 k6_margrel1 (k1_binari_3 A B) (k10_binarith k6_margrel1 k7_margrel1))) ) ) ) ) ) ).
tt(t27_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 B (k21_binop_2 (k5_series_1 2 (k7_nat_d A 1)) 1)) & (r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d A 1))) B))  =>  ((k3_binari_2 A (k2_binari_4 A B)) = B) ) ) ) ) ) ).
tt(t27_binom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) B)))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A k5_numbers) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A k5_numbers) B)))) )  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((k2_binop_1 A k5_numbers B E F k6_numbers) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k2_binop_1 A k5_numbers B E F (k2_nat_1 G 1)) = (k2_binop_1 B A B D (k2_binop_1 A k5_numbers B E F G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B (k1_boolealg A C B)) => (r1_boolealg A B (k5_lattices A))) ) ) ) ) ) ) ).
tt(t27_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r2_hidden (k3_tarski C) (u1_pre_topc A)) <=> (r2_hidden C (u1_pre_topc (k11_borsuk_1 A B)))) ) ) ) ) ) ) ).
tt(t27_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( (A = B)  =>  ((v2_rcomp_1 A) <=> (v4_pre_topc B k5_topmetr)) ) ) ) ) ) ).
tt(t27_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ( ((v1_xreal_0 C) &  (~ (v1_rat_1 C)) )  =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 A B))) =>  ((m1_subset_1 (k1_xtuple_0 C) (u1_struct_0 A)) & (m1_subset_1 (k2_xtuple_0 C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t27_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (~  ( (~  (A = B) )  &  ( (~  (A = F) )  &  (~  ((k1_funct_1 (k1_borsuk_7 A B F C D E) A) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_bspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_bspace A))) =>  ((k4_vectsp_1 k2_bspace (k7_bspace A) (k8_group_1 k2_bspace B C) D) = (k4_vectsp_1 k2_bspace (k7_bspace A) B (k4_vectsp_1 k2_bspace (k7_bspace A) C D))) ) ) ) ) ) ) ) ).
tt(t27_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B (k5_bvfunc_1 A C (k1_bvfunc_1 A D))) (k9_bvfunc_1 A C (k5_bvfunc_1 A D (k1_bvfunc_1 A B)))))) ) ) ) ) ) ) ) ).
tt(t27_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( (F = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B H) (k16_funcop_1 C I)) (k16_funcop_1 D J)) (k16_funcop_1 E K)) (k16_funcop_1 A G)))  =>  ((k9_xtuple_0 F) = (k3_enumset1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 (k3_funct_2 A k6_margrel1 B C) (k3_funct_2 A k6_margrel1 (k14_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t27_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B (k1_bvfunc_1 A C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t27_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A (k11_bvfunc_1 A) B) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t27_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k2_bvfunc_1 A C D) B E) (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k1_bvfunc_1 A (k7_bvfunc_2 A (k2_bvfunc_1 A C (k1_bvfunc_1 A D)) B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k7_bvfunc_2 A B D E) (k7_bvfunc_2 A C D E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t27_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t27_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k10_bvfunc_1 A (k10_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A C B)) B))) ) ) ) ) ) ).
tt(t27_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k9_bvfunc_1 A B C) B) B) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t27_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C F)) (k9_bvfunc_1 A D G)) (k1_bvfunc_1 A (k2_bvfunc_1 A E F))) (k1_bvfunc_1 A (k2_bvfunc_1 A E G))) (k1_bvfunc_1 A (k2_bvfunc_1 A F G))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A (k2_bvfunc_1 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B D))) (k1_bvfunc_1 A (k2_bvfunc_1 A C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_c0sp1 A))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k11_c0sp1 A) B))) ) ) ) ).
tt(t27_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k12_funcsdom (u1_struct_0 A))))))  =>  ( (B = (k6_c0sp2 A))  => (v4_c0sp1 B (k12_funcsdom (u1_struct_0 A)))) ) ) ) ) ).
tt(t27_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( ((r2_relset_1 (k3_qc_lang1 A) B (k2_partfun1 (k3_qc_lang1 A) B E (k3_calcul_1 A D)) (k2_partfun1 (k3_qc_lang1 A) B F (k3_calcul_1 A D))) & (r9_calcul_1 A D B C E))  => (r9_calcul_1 A D B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k8_cqc_lang A B C))))) ) ) ) ) ) ) ) ) ).
tt(t27_card_1,ax, ((k1_card_1 k1_xboole_0) = k1_xboole_0) ).
tt(t27_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ( ((k3_card_2 A 1) = A)  &  ((k3_card_2 1 A) = 1) ) ) ) ).
tt(t27_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 B C))) ) )  => (r1_tarski (k4_card_3 A) (k4_card_3 B))) ) ) ) ) ).
tt(t27_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  ((r1_tarski (k10_xtuple_0 C) B) & (r2_hidden A (k1_card_5 B))) )  =>  ((r2_hidden (k4_ordinal2 C) B) & (r2_hidden (k3_card_3 C) B)) ) ) ) ) ) ) ) ).
tt(t27_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v5_card_fil A) => (v2_card_1 A)) ) ) ).
tt(t27_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  => (r1_tarski (k2_card_fin C D A) (k2_card_fin C (k5_relat_1 D B) A))) ) ) ) ) ) ).
tt(t27_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v4_card_lar A) => (v1_card_5 A)) ) ) ).
tt(t27_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k4_cat_1 A B) (k2_cat_1 A B B))) ) ) ) ).
tt(t27_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k8_cat_2 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) &  (C = (k10_cat_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((v2_cat_3 (k5_cat_1 A B C D E F) A B D) =>  ( ((k2_cat_1 A C D) = k1_xboole_0)  |  ( ((k2_cat_1 A D C) = k1_xboole_0)  | (v2_cat_3 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A B D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  ( ((v7_cat_1 E A B C) | (v7_cat_1 F A B D))  &  (~ (v7_cat_1 (k9_cat_4 A C D B E F) A B (k2_cat_4 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u4_struct_0 A) (k9_cat_5 A (k3_graph_1 A B))) => (r2_hidden (k1_cat_1 A C B) (k9_cat_5 A (k4_graph_1 A B)))) ) ) ) ) ) ).
tt(t27_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k24_binop_2 2 (k23_binop_2 A 1)) B) =>  ((k5_card_1 (k7_subset_1 (k9_funct_2 B (k2_tarski 1 k6_numbers)) (k1_card_fin B (k23_binop_2 A 1) 1 k6_numbers) (k2_catalan2 B (k23_binop_2 A 1)))) = (k5_card_1 (k1_card_fin B A 1 k6_numbers))) ) ) ) ) ) ).
tt(t27_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m2_pboole (k1_catalg_1 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) C) (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k1_instalg1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k13_catalg_1 B) (k11_catalg_1 A B C) (k12_catalg_1 A B C))))) ) ) ) ) ) ).
tt(t27_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k7_cc0sp1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k7_cc0sp1 A)))))) )  =>  ((v1_csspace3 B (k7_cc0sp1 A)) => (v9_clvect_1 B (k7_cc0sp1 A))) ) ) ) ) ).
tt(t27_cc0sp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_compts_1 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 B))) =>  ((k1_normsp_0 (k5_cc0sp2 B) (k1_clvect_1 (k5_cc0sp2 B) C A)) = (k8_real_1 (k18_complex1 A) (k1_normsp_0 (k5_cc0sp2 B) C))) ) ) ) ) ) ) ).
tt(t27_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ( ((v3_funct_1 B) & (r2_hidden A (k2_relset_1 k2_numbers B)))  |  ((v3_funct_1 B) &  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((k3_funct_2 k5_numbers k2_numbers B C) = A) ) ) ) )  =>  ((k3_comseq_2 B) = A) ) ) ) ) ) ).
tt(t27_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v6_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k2_numbers A)) &  ((k5_relset_1 k2_numbers k2_numbers A B) = (k6_partfun1 B)) )  =>  ((r2_cfdiff_1 A B) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r2_hidden C B) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 A B) C) = k6_complex1) ) ) ) ) ) ) ) ) ) ).
tt(t27_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k8_cfuncdom A)))  &  ((v13_algstr_0 (k8_cfuncdom A)) &  ((v2_rlvect_1 (k8_cfuncdom A)) &  ((v3_rlvect_1 (k8_cfuncdom A)) &  ((v4_rlvect_1 (k8_cfuncdom A)) &  ((v2_clvect_1 (k8_cfuncdom A)) &  ((v3_clvect_1 (k8_cfuncdom A)) &  ((v4_clvect_1 (k8_cfuncdom A)) &  ((v3_group_1 (k8_cfuncdom A)) &  ((v5_group_1 (k8_cfuncdom A)) &  ((v1_vectsp_1 (k8_cfuncdom A)) &  ((v3_vectsp_1 (k8_cfuncdom A)) &  ((v2_cfuncdom (k8_cfuncdom A)) & (l1_cfuncdom (k8_cfuncdom A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers B (k46_valued_1 A k2_numbers k2_numbers C D)) (k2_valued_1 A k2_numbers k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) D))) ) ) ) ) ) ) ) ).
tt(t27_cgames_1,ax, (! [A:$i] :  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k10_cgames_1 B)) <=>  (~  ( (~  (A = B) )  &  (! [C:$i] :  ((v2_cgames_1 C) =>  (~  ((r2_hidden C (k8_cgames_1 B)) & (r2_hidden A (k10_cgames_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t27_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ((k3_chain_1 A B B) = (k6_domain_1 (k1_euclid A) B)) ) ) ) ) ).
tt(t27_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ( ((r1_xboole_0 (k14_glib_001 A B) (k14_glib_001 A C)) &  ( ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A B) (k13_glib_001 A C)) = (k7_domain_1 (k6_glib_000 A) (k3_glib_001 A B) (k4_glib_001 A B)))  &  ( ((k3_glib_001 A C) = (k4_glib_001 A B))  &  ((k4_glib_001 A C) = (k3_glib_001 A B)) ) ) )  =>  ((v1_glib_001 B A) |  ((v3_glib_001 C A) |  ((v1_glib_001 C A) | (v8_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t27_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  (! [C:$i] :  ((m1_circcmb3 C A) =>  (! [D:$i] :  ((m2_circcmb3 D A B) =>  (! [E:$i] :  ((m2_circcmb3 E A C) => (r2_circcomb B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t27_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k2_circcomb A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ( (E = F)  => (r1_funct_2 (k3_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k4_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k3_msualg_1 B F D) (k4_msualg_1 B F D) (k5_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k5_msualg_1 B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ((r1_circtrm1 A B D E) & (r1_circtrm1 B C F G))  => (r1_circtrm1 A C (k3_relat_1 D F) (k3_relat_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k1_classes1 A)) & (r2_hidden C (k1_classes1 A)))  => (r2_hidden (k4_tarski B C) (k1_classes1 A))) ) ) ) ).
tt(t27_classes2,ax, (! [A:$i] :  ((v2_classes1 A) => (r1_tarski (k4_classes1 (k1_card_1 A)) A)) ) ).
tt(t27_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v2_clopban1 C A B) <=> (v4_xxreal_2 (k12_clopban1 A B C))) ) ) ) ) ) ) ).
tt(t27_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_series_1 B) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  (~ (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A C E)) (k1_seq_1 B E))) ) ) ) ) )  | (v2_clopban3 C A)) ) ) ) ) ) ) ) ).
tt(t27_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A B)) C)) (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C)) &  ((r1_xxreal_0 (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C) (k4_series_1 (k4_sin_cos (k1_normsp_0 A B)))) & (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A (k1_bhsp_4 A (k1_clopban4 A B)) C)) (k4_series_1 (k4_sin_cos (k1_normsp_0 A B))))) ) ) ) ) ) ) ) ).
tt(t27_closure1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m2_pboole E B (k5_mssubfam B C) (k5_mssubfam B C)) =>  ( ((v4_closure1 E B C) &  ((r2_hidden A B) &  (D = (k1_funct_1 E A)) ) )  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) =>  (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 (k1_funct_1 C A)) (k9_setfam_1 (k1_funct_1 C A))) =>  ((k1_funct_1 D (k4_subset_1 (k1_funct_1 C A) F G)) = (k2_xboole_0 (k1_funct_1 D F) (k1_funct_1 D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_funct_1 (k6_partfun1 (k6_closure2 A B))) &  ((v1_funct_2 (k6_partfun1 (k6_closure2 A B)) (k6_closure2 A B) (k6_closure2 A B)) &  ((v8_closure2 (k6_partfun1 (k6_closure2 A B)) A B) & (m1_subset_1 (k6_partfun1 (k6_closure2 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) ) ) ) ).
tt(t27_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  (! [D:$i] :  ( ((r1_struct_0 B D) & (m1_clvect_1 B C))  => (r1_struct_0 C D)) ) ) ) ) ) ) ) ).
tt(t27_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k3_normsp_1 A D E))) &  ((k2_seq_2 (k2_clvect_2 A (k3_normsp_1 A D E))) = (k13_csspace A (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers (k2_clvect_2 A B) D) (k8_nat_1 k1_numbers C D))) )  & (v1_series_1 C))  => (v2_clvect_3 B A)) ) ) ) ) ) ) ).
tt(t27_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v6_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) (k6_cohsp_1 A B C)) & (r2_hidden (k4_tarski E G) (k6_cohsp_1 A B C)))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k15_coh_sp B)) <=>  (? [C:$i] :  ((r1_tarski C B) &  ((v1_partfun1 A C) &  ((v1_relat_2 A) &  ((v3_relat_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) ) ) ) ) ) ) ).
tt(t27_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ((v3_combgras C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( (D = (k1_setfam_1 C))  =>  ( ((k1_card_1 D) = (k5_real_1 A 1))  &  (C = (a_3_0_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k15_complex1 A)) = (k3_complex1 A))  &  ((k4_complex1 (k15_complex1 A)) = (k1_real_1 (k4_complex1 A))) ) ) ) ).
tt(t27_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_comptrig (k3_xcmplx_0 A B)) = (k1_comptrig A)) ) ) ) ) ) ).
tt(t27_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k8_group_1 k1_complfld (k3_vectsp_1 k1_complfld C A) (k3_vectsp_1 k1_complfld D B)) = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld C D) (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k4_binop_2 A (k15_complex1 A)) = (k5_binop_2 (k11_binop_2 2 (k4_complex1 A)) k7_complex1)) ) ) ).
tt(t27_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_pcomps_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((k1_card_1 C) = 1) ) ) ) )  => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t27_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  ((k8_compos_1 A B (k4_compos_1 A)) = B) ) ) ) ) ).
tt(t27_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k62_valued_1 B) C))  =>  ((k1_funct_1 (k63_valued_1 B) C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(t27_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden (k1_seq_1 k16_sin_cos A) (k1_rcomp_1 (k1_real_1 1) 1)) & (r2_hidden (k1_seq_1 k19_sin_cos A) (k1_rcomp_1 (k1_real_1 1) 1))) ) ) ).
tt(t27_comput_1,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k2_comput_1 A))) ).
tt(t27_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k36_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(t27_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k1_series_1 k2_numbers (k10_comseq_3 A) (k10_comseq_3 B)) (k10_comseq_3 (k1_series_1 k2_numbers A B)))) ) ) ) ).
tt(t27_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v6_conlat_1 B A) & (l2_conlat_1 B A))  =>  (~  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  &  ( (~  (B = (k5_conlat_1 A)) )  &  (~  (B = (k6_conlat_1 A)) ) ) ) ) ) ) ) ) ).
tt(t27_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v2_connsp_1 (k2_struct_0 A) A) <=> (v1_connsp_1 A)) ) ) ).
tt(t27_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_pre_topc A B)) <=>  (! [D:$i] :  ((m1_connsp_2 D A C) =>  (~ (r1_xboole_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k6_connsp_3 A B C) = (k1_connsp_1 (k1_pre_topc A B) (k2_connsp_3 A B C))) ) ) ) ) ) ) ) ).
tt(t27_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ( ((v2_convex1 C A) &  ((k3_rlvect_2 A C) = (k6_domain_1 (u1_struct_0 A) B)) )  =>  ((k1_funct_1 C B) = 1) ) ) ) ) ) ) ) ).
tt(t27_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_convex4 D A) => (r1_convex4 A (k7_convex4 A (k2_xcmplx_0 B C) D) (k5_convex4 A (k7_convex4 A B D) (k7_convex4 A C D)))) ) ) ) ) ) ) ) ).
tt(t27_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k13_cqc_lang A C B) = C) ) ) ) ) ) ) ).
tt(t27_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_qc_lang1 B A) =>  ((k14_cqc_sim1 A B) = B) ) ) ) ) ) ).
tt(t27_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (! [E:$i] :  ((m2_finseq_1 E (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 D)))  =>  ((r1_cqc_the1 A D B C) <=> (r1_cqc_the1 A (k8_finseq_1 (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1) D E) B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden E (k24_qc_lang1 A D)) |  ((r2_hidden F (k24_qc_lang1 A B)) | (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A E B) (k11_cqc_lang A F C)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r4_cqc_the3 A B C) & (r2_cqc_the3 A D B))  => (r2_cqc_the3 A D C)) ) ) ) ) ) ) ) ) ).
tt(t27_csspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v3_clopban1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k9_csspace4 A B)))  &  ((v13_algstr_0 (k9_csspace4 A B)) &  ((v2_rlvect_1 (k9_csspace4 A B)) &  ((v3_rlvect_1 (k9_csspace4 A B)) &  ((v4_rlvect_1 (k9_csspace4 A B)) &  ((v3_normsp_0 (k9_csspace4 A B)) &  ((v4_normsp_0 (k9_csspace4 A B)) &  ((v2_clvect_1 (k9_csspace4 A B)) &  ((v3_clvect_1 (k9_csspace4 A B)) &  ((v4_clvect_1 (k9_csspace4 A B)) &  ((v5_clvect_1 (k9_csspace4 A B)) &  ((v8_clvect_1 (k9_csspace4 A B)) &  ((v3_clopban1 (k9_csspace4 A B)) & (l2_clvect_1 (k9_csspace4 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k12_csspace A B (k5_algstr_0 A C D)) = (k6_xcmplx_0 (k12_csspace A B C) (k12_csspace A B D))) ) ) ) ) ) ) ) ) ).
tt(t27_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  ((v6_decomp_1 C A B) & (v12_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t27_descip_1,ax, (! [A:$i] :  (~  ((r2_hidden A 64) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  ( (~  (A = 14) )  &  ( (~  (A = 15) )  &  ( (~  (A = 16) )  &  ( (~  (A = 17) )  &  ( (~  (A = 18) )  &  ( (~  (A = 19) )  &  ( (~  (A = 20) )  &  ( (~  (A = 21) )  &  ( (~  (A = 22) )  &  ( (~  (A = 23) )  &  ( (~  (A = 24) )  &  ( (~  (A = 25) )  &  ( (~  (A = 26) )  &  ( (~  (A = 27) )  &  ( (~  (A = 28) )  &  ( (~  (A = 29) )  &  ( (~  (A = 30) )  &  ( (~  (A = 31) )  &  ( (~  (A = 32) )  &  ( (~  (A = 33) )  &  ( (~  (A = 34) )  &  ( (~  (A = 35) )  &  ( (~  (A = 36) )  &  ( (~  (A = 37) )  &  ( (~  (A = 38) )  &  ( (~  (A = 39) )  &  ( (~  (A = 40) )  &  ( (~  (A = 41) )  &  ( (~  (A = 42) )  &  ( (~  (A = 43) )  &  ( (~  (A = 44) )  &  ( (~  (A = 45) )  &  ( (~  (A = 46) )  &  ( (~  (A = 47) )  &  ( (~  (A = 48) )  &  ( (~  (A = 49) )  &  ( (~  (A = 50) )  &  ( (~  (A = 51) )  &  ( (~  (A = 52) )  &  ( (~  (A = 53) )  &  ( (~  (A = 54) )  &  ( (~  (A = 55) )  &  ( (~  (A = 56) )  &  ( (~  (A = 57) )  &  ( (~  (A = 58) )  &  ( (~  (A = 59) )  &  ( (~  (A = 60) )  &  ( (~  (A = 61) )  &  ( (~  (A = 62) )  &  (~  (A = 63) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v1_wellfnd1 (k5_dickson A)) & (v16_waybel_0 A))  => (v4_dickson A)) ) ) ).
tt(t27_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) (k4_nat_1 2 A)) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) (k4_nat_1 2 A)) (k7_real_1 C (k8_real_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t27_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers F G) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 G)) (k8_real_1 B G)) C)) ) )  =>  ( (D = E)  |  ((k9_diff_1 F D E) = (k7_real_1 (k8_real_1 A (k7_real_1 D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers D A) E) B C) = (k9_real_1 (k8_real_1 A (k9_diff_1 D B C)) (k9_diff_1 E B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) (k7_real_1 A B)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) A))) ) ) ) ) ) ).
tt(t27_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~ (r1_tarski (k6_dilworth A) B))  & (r1_tarski (k6_dilworth A) (k3_dilworth A B))) ) ) ) ) ) ).
tt(t27_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_diraf A B C C D) &  ( (~  (C = B) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_diraf A E C C F) & (r2_diraf A E B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k3_subset_1 A B) = (a_2_2_domain_1 A B)) ) ) ) ) ).
tt(t27_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( ((k3_rlvect_1 (k9_int_3 A) B B) = (k4_struct_0 (k9_int_3 A)))  =>  ((r1_xxreal_0 A 2) |  (B = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ).
tt(t27_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  ( (B = (k6_int_1 2 A))  =>  ((k2_binom (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C E) (k8_group_1 (k9_int_3 A) D F)) 2) = (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) C 2) (k2_binom (k9_int_3 A) E 2)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B C) D) E) F)) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k2_binom (k9_int_3 A) F 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  ((k2_cat_1 (k11_ens_1 A) B C) = (k7_ens_1 A (k13_ens_1 A B) (k13_ens_1 A C))) ) ) ) ) ) ) ).
tt(t27_entropy1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( (C = (k6_matrixr1 (k1_entropy1 A) B))  <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k8_matrix_1 k1_numbers C D) = (k11_rvsum_1 (k1_matrix_1 B) (k8_matrix_1 k1_numbers B D) (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k4_enumset1 A B C D E F) (k2_tarski G H))) ) ) ) ) ) ) ) ) ).
tt(t27_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (? [C:$i] :  ((k6_eqrel_1 A A B C) = A) )  => (r2_relset_1 A A B (k1_eqrel_1 A))) ) ) ) ).
tt(t27_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( (C = (a_2_0_equation A B))  =>  (! [D:$i] :  ((m1_pralg_2 D C A) =>  (~  ( (! [E:$i] :  ((r2_hidden E C) =>  (E = (k1_funct_1 D E)) ) )  &  (! [E:$i] :  ( ((v3_msualg_1 E A) &  ((v4_msualg_1 E A) & (m1_msualg_2 E A (k14_pralg_2 C A D))) )  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A E) (u3_msualg_1 A B)) =>  (~ (r2_msualg_3 A E B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u2_e_siec A))))) = k1_xboole_0)  &  ((k3_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))) (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A))))) = k1_xboole_0) ) ) ) ).
tt(t27_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B (k5_algstr_0 (k15_euclid A) C D)) = (k10_binop_2 (k23_rvsum_1 B C) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t27_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( (A = (k8_real_1 (k12_euclid C) (k21_sin_cos (k3_euclid_3 C))))  &  (B = (k8_real_1 (k12_euclid C) (k18_sin_cos (k3_euclid_3 C)))) )  =>  (C = (k19_euclid A B)) ) ) ) ) ) ) ) ).
tt(t27_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k7_euclid A (k9_euclid A D B) (k9_euclid A E C)) F) = (k7_real_1 (k4_real_1 B (k23_rvsum_1 D F)) (k4_real_1 C (k23_rvsum_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (A = (k3_finseq_4 k1_numbers (k1_euclid_5 A) (k2_euclid_5 A) (k3_euclid_5 A))) ) ) ).
tt(t27_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)) |  ((r1_xxreal_0 (k4_euclid_3 B D C) k32_sin_cos) |  ( (A = C)  | (r1_xxreal_0 (k4_euclid_3 B D C) (k4_euclid_3 A D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ((k18_rvsum_1 (k6_euclid_7 B A)) = 1) ) ) ) ) ) ).
tt(t27_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k9_euclid 3 k4_euclid_8 A) = (k1_euclid_8 k6_numbers k6_numbers A)) ) ) ).
tt(t27_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A)))))) =>  ( (B = (k2_waybel18 (k2_finseq_1 A) (k7_funcop_1 (k2_finseq_1 A) k3_topmetr)))  => (v1_tops_2 B (k3_pcomps_1 (k14_euclid A)))) ) ) ) ) ).
tt(t27_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k3_rlvect_1 (k15_euclid A) (k4_struct_0 (k15_euclid A)) B) = B)  &  ((k3_rlvect_1 (k15_euclid A) B (k4_struct_0 (k15_euclid A))) = B) ) ) ) ) ) ).
tt(t27_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid D)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid D)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid D)) =>  ( ((k7_real_1 (k7_real_1 A B) C) = 1)  =>  ((k7_euclid D (k7_euclid D (k9_euclid D E A) (k9_euclid D F B)) (k9_euclid D G C)) = (k7_euclid D (k7_euclid D E (k9_euclid D (k8_euclid D F E) B)) (k9_euclid D (k8_euclid D G E) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_exchsort,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ( ((v4_exchsort A) & (v1_finset_1 (k1_funct_1 A k1_xboole_0)))  => (v1_finset_1 A)) ) ) ).
tt(t27_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( (D = (k4_extpro_1 A B D C))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k5_extpro_1 A B C D E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~  (A = k2_supinf_1) )  &  ( (~  (B = k2_supinf_1) )  &  ( (~  ( (A = k1_supinf_1)  &  (B = k1_supinf_1) ) )  &  ( (~  ( (A = k2_supinf_1)  &  (B = k2_supinf_1) ) )  &  (~  ((k4_xxreal_0 A B) = (k2_extreal1 (k3_supinf_2 (k3_supinf_2 A B) (k3_extreal1 (k4_supinf_2 A B))) (k1_measure6 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  ((k3_msafree2 (k2_circcomb A B)) = (k2_xboole_0 (k3_msafree2 A) (k3_msafree2 B))) ) ) ) ) ).
tt(t27_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  ((k2_msafree2 (k3_facirc_2 A B C)) = (k2_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t27_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_partfun1 A k1_numbers) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_seq_1 A (k2_xcmplx_0 B C)) = (k7_real_1 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) )  =>  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~ (r1_fcont_1 A B)) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A k1_numbers))) ) ) ) ).
tt(t27_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k8_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t27_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9) A) B) = (k7_real_1 (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k1_sin_cos9 B))) (k10_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t27_fdiff_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v2_fdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( ((k1_seq_1 A k6_numbers) = k6_numbers)  & (r1_fcont_1 A k6_numbers)) ) ) ).
tt(t27_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k3_limfunc1 A)) & (r2_hidden D (k3_limfunc1 A)))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 B C) (k1_seq_1 B D))) (k5_square_1 (k9_real_1 C D)))) ) ) ) ) )  =>  ((r2_fdiff_1 B (k3_limfunc1 A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) ) ) ) ) ) ).
tt(t27_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) B) D) = (k8_real_1 (k10_real_1 3 2) (k10_prepower (k7_real_1 A D) (k10_real_1 1 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)) A) C) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos C)) (k9_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t27_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))))) &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers D E)) &  ((r2_relset_1 k1_numbers k1_numbers E (k1_taylor_1 2)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) B) F) = (k1_real_1 (k8_real_1 F (k10_prepower (k9_real_1 (k5_square_1 A) (k5_prepower F 2)) (k1_real_1 (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  (~  (A = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) D) = (k10_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k8_real_1 A D))  &  (~  (A = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers B)) B) D) = (k10_real_1 (k9_real_1 (k1_seq_1 k19_sin_cos (k8_real_1 A D)) (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A D)))) (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k16_ff_siec A) (k4_xboole_0 (k16_ff_siec A) (k4_relat_1 (k2_net_1 A)))) = k1_xboole_0)  &  ((k3_relat_1 (k15_ff_siec A) (k4_xboole_0 (k15_ff_siec A) (k4_relat_1 (k2_net_1 A)))) = k1_xboole_0) ) ) ) ).
tt(t27_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 5)) = (k2_nat_1 (k1_pre_ff (k1_nat_1 A 3)) (k1_pre_ff (k1_nat_1 A 4)))) ) ) ).
tt(t27_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_nat_1 (k1_fib_num3 (k2_nat_1 A 3)) (k1_fib_num3 A)) = (k6_xcmplx_0 (k13_newton (k1_fib_num3 (k2_nat_1 A 2)) 2) (k13_newton (k1_fib_num3 (k2_nat_1 A 1)) 2))) ) ) ).
tt(t27_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_pre_ff (k2_xcmplx_0 A 1)) = (k1_int_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k1_pre_ff A) 1) (k6_square_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 5 (k1_pepin (k1_pre_ff A))) (k3_xcmplx_0 2 (k1_pre_ff A))) 1))) 2))) ) ) ) ).
tt(t27_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((r4_finseq_8 A C B) =>  (C = (k9_finseq_8 A C B)) ) ) ) ) ) ) ) ).
tt(t27_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A (k4_lattices A B (k3_lattices A (k7_lattices A B) C)) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k4_lattices A B D) C) => (r3_lattices A D (k3_lattices A (k7_lattices A B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r4_binop_1 A C D) & (r4_binop_1 B E F))  <=> (r4_binop_1 (k2_zfmisc_1 A B) (k6_filter_1 A B C E) (k6_filter_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v18_lattices (u1_struct_0 A) A) &  ((v21_lattices (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t27_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (D = A)  & (r2_hidden (k2_nat_1 (k3_finseq_1 C) D) (k4_finseq_1 (k7_finseq_1 C B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  => (m2_finseq_1 (k2_partfun1 k5_numbers B C (k2_finseq_1 A)) B)) ) ) ) ) ) ).
tt(t27_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ( (~  (C = (k4_finseq_4 A B)) )  &  ((k1_funct_1 A C) = B) ) ) ) ) ) )  => (r2_finseq_4 A B)) ) ) ) ).
tt(t27_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  ((r2_hidden A (k4_finseq_1 (k2_rfinseq C B D))) =>  ((k7_partfun1 C (k2_rfinseq C B D) A) = (k7_partfun1 C D (k2_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t27_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((k5_finseq_4 (k11_finseq_1 A B C) B) = (k9_finseq_1 A)) ) ) ) ) ).
tt(t27_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((r1_xxreal_0 D C) |  ((k2_finseq_7 A B C D) = (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k17_finseq_1 A (k7_nat_d C 1) B) (k12_finseq_1 A (k7_partfun1 A B D))) (k17_finseq_1 A (k7_nat_d (k7_nat_d D C) 1) (k2_rfinseq A C B))) (k12_finseq_1 A (k7_partfun1 A B C))) (k2_rfinseq A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r2_finseq_8 A B C D))  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((k3_finseq_6 A B E (k2_nat_1 (k7_nat_d E 1) (k3_finseq_1 C))) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k4_finseqop A A (k1_finseqop A A A F D E) (k9_funcop_1 A A F (k6_partfun1 A) B)) (k1_finseqop A A A F D (k4_finseqop A A E (k9_funcop_1 A A F (k6_partfun1 A) B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k9_fintopo2 A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k9_fintopo2 A C)))) ) ) ) ) ) ).
tt(t27_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_subset_1 (u1_struct_0 A) (k5_fintopo3 A (k3_subset_1 (u1_struct_0 A) B) C)) = (k3_fintopo3 A B C)) ) ) ) ) ) ) ).
tt(t27_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_fin_topo B A) &  ((v3_fin_topo C A) & (r1_xboole_0 B C)) )  => (r1_fintopo4 A B C)) ) ) ) ) ) ) ).
tt(t27_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k7_flang_1 A B C) = k1_xboole_0)  <=>  ( (~ (r1_xxreal_0 C k6_numbers))  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t27_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((k1_flang_2 A B C D) = (k4_subset_1 (k8_afinsq_1 A) (k7_flang_1 A B C) (k1_flang_2 A B (k2_xcmplx_0 C 1) D))) ) ) ) ) ) ) ) ) ).
tt(t27_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k1_flang_3 A B D)) = (k6_flang_1 A (k1_flang_3 A B D) (k1_flang_3 A B C))) ) ) ) ) ) ) ) ).
tt(t27_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  (! [F:$i] :  ( ((v1_funct_2 F A D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A D))))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((v1_funct_1 (k4_relset_1 B A A D (k4_relset_1 B C C A (k4_relset_1 B A A C G E) (k3_relset_1 A C E)) F)) => (r2_relset_1 B D (k4_relset_1 B A A D (k4_relset_1 B C C A (k4_relset_1 B A A C G E) (k3_relset_1 A C E)) F) (k4_relset_1 B A A D G F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_fomodel2 C A) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))))  =>  (! [D:$i] :  ((m2_subset_1 D (k9_funct_2 (k37_fomodel1 A) (k3_rfunct_3 (k3_finseq_2 B) (k2_xboole_0 B k6_margrel1))) (k16_fomodel2 A B)) =>  ( ((k26_fomodel2 A B D C) = 1)  <=> (v10_fomodel2 (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C) B A D)) ) ) ) ) ) ) ) ) ).
tt(t27_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t27_frechet,ax,(m1_subset_1 k1_numbers (u1_struct_0 k3_frechet))).
tt(t27_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C B A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r6_fsm_1 B A C D E F) <=>  ((r6_fsm_1 B A C D E 1) &  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( (H = (k6_xcmplx_0 F 1))  => (r6_fsm_1 B A C (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k1_domain_1 (u1_struct_0 C) B D G)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k1_domain_1 (u1_struct_0 C) B E G)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k7_domain_1 k5_numbers k6_numbers 1) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k7_domain_1 k5_numbers k6_numbers 1) A)))) )  =>  ((k2_fsm_2 B A (k1_fsm_2 B A k6_numbers 1 D) C) = (k1_funct_1 D 1)) ) ) ) ) ) ) ) ) ).
tt(t27_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 C)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C)))))  =>  ((r3_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G A (k1_flang_1 C D E) B (k1_flang_1 C F E)) => (r3_rewrite3 C (k4_subset_1 (k3_catalan2 C) (k9_flang_1 C) (k4_flang_1 C (k2_flang_1 C))) G A D B F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  (I = (k1_funct_1 F C)) ) )  =>  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) (k15_ftacell1 A B C D E)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 G) H) (k10_margrel1 H (k9_margrel1 I))) (k10_margrel1 (k9_margrel1 I) (k9_margrel1 G)))))  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) (k16_ftacell1 A B C D E)) = (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k9_xtuple_0 (k4_funcop_1 B A D))) =>  ((k1_funct_1 (k4_funcop_1 B A D) C) = (k1_binop_1 B (k1_funct_1 A C) D)) ) ) ) ) ) ) ) ).
tt(t27_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_struct_0 (k12_funcsdom A)) = (k9_funcsdom A)) ) ) ).
tt(t27_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A)) &  ((r1_tarski (k10_xtuple_0 C) (k9_xtuple_0 A)) &  ( ((k9_xtuple_0 B) = (k9_xtuple_0 C))  &  ((k3_relat_1 B A) = (k3_relat_1 C A)) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t27_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v2_funct_2 D B) & (v2_funct_2 E C))  => (v2_funct_2 (k1_partfun1 A B B C D E) C)) ) ) ) ) ) ) ) ) ) ).
tt(t27_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k3_tarski (k8_relat_1 (k3_funct_3 B) A)) (k7_relat_1 B (k3_tarski A)))) ) ) ).
tt(t27_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_partfun1 A (k1_funct_4 B C)) => (r1_partfun1 A C)) ) ) ) ) ) ) ).
tt(t27_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  (! [C:$i] :  (~ (r2_hidden (k4_tarski B C) (k9_xtuple_0 A))) ) )  =>  ( ((k1_funct_5 A) = k1_xboole_0)  &  ((k3_funct_5 A) = k1_xboole_0) ) ) ) ) ).
tt(t27_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = k1_xboole_0) )  =>  ( ((k3_card_3 (k7_funcop_1 A B)) = B)  &  ((k4_funct_6 (k7_funcop_1 A B)) = B) ) ) ) ) ).
tt(t27_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((r1_funct_7 A B D) & (r1_funct_7 B C D))  => (r1_funct_7 A C D)) ) ) ) ) ) ) ) ).
tt(t27_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t27_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) (k8_real_1 k32_sin_cos A))) ) ).
tt(t27_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_functor0 B A (k10_functor0 A B) C) = C) ) ) ) ) ) ) ).
tt(t27_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ( ((v15_functor0 H B C) & (m2_functor0 H B C))  =>  (! [I:$i] :  ( ((v15_functor0 I C D) & (m2_functor0 I C D))  =>  (! [J:$i] :  ( ((v15_functor0 J C D) & (m2_functor0 J C D))  =>  (! [K:$i] :  ((m1_functor2 K A B E F) =>  (! [L:$i] :  ((m1_functor2 L B C G H) =>  (! [M:$i] :  ((m1_functor2 M C D I J) =>  ( ((r1_functor2 A B E F) &  ((r1_functor2 B C G H) & (r1_functor2 C D I J)) )  => (r8_pboole (u1_struct_0 A) (k7_functor3 A B D E F (k1_functor3 B C D G I) (k1_functor3 B C D H J) K (k7_functor3 B C D G H I J L M)) (k7_functor3 A C D (k1_functor3 A B C E G) (k1_functor3 A B C F H) I J (k7_functor3 A B C E F G H K L) M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r2_funct_2 A k1_numbers (k1_fuzzy_1 A B C) B)) ) ) ) ) ) ) ).
tt(t27_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k1_fuzzy_1 A B C) (k4_fuzzy_1 A)) => (r2_funct_2 A k1_numbers (k1_fuzzy_2 A B C) B)) ) ) ) ) ) ) ).
tt(t27_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ((v3_fvaluat1 A) => (r1_xxreal_0 (k3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D B) (k3_funct_2 (u1_struct_0 A) k7_numbers D C)) (k3_funct_2 (u1_struct_0 A) k7_numbers D (k3_rlvect_1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t27_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k4_fvsum_1 A B C D) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)))  =>  ( (C = (k6_fvsum_1 A B D))  &  (D = (k6_fvsum_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 (k21_gate_1 A B C D E)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) & (v1_xboole_0 E)) ) ) ) ) ) ) ) ) ) ).
tt(t27_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ((v2_gcd_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  ((r2_gcd_1 A D C) =>  ( (D = (k4_struct_0 A))  | (r2_hidden (k1_gcd_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((k9_genealg1 D E F A A B) = (k7_genealg1 D E F B))  &  ( ((k9_genealg1 D E F A C A) = (k7_genealg1 D E F C))  &  ((k9_genealg1 D E F A C C) = (k7_genealg1 D E F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_geomtrap A B C D E F G) &  ( (~ (r2_geomtrap A B C D E (k1_geomtrap A D G) (k1_geomtrap A E F)))  &  (~ (r2_geomtrap A B C D E (k1_geomtrap A E F) (k1_geomtrap A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  ((r2_hidden A (k2_msafree2 (k10_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k10_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k10_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t27_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  ((k2_msafree2 (k5_gfacirc2 A B C)) = (k2_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t27_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ( ((k15_glib_000 A) = 1)  <=>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  ((k6_glib_000 A) = (k6_domain_1 (k6_glib_000 A) B)) ) ) ) ) ) ).
tt(t27_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ((k6_glib_001 A C) = (k6_glib_001 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k3_glib_002 A)) =>  ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A)))) ) ) ) ) ).
tt(t27_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m1_glib_000 B A)) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  ( (C = D)  =>  ((k10_glib_003 A C) = (k10_glib_003 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ( ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m2_glib_000 C A (k1_relset_1 (k6_glib_000 A) (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k11_glib_004 A B))) (k3_domain_1 (k3_rfunct_3 (k6_glib_000 A) k1_numbers) (k1_zfmisc_1 (k7_glib_000 A)) (k11_glib_004 A B)))) )  =>  ((r1_glib_004 A C B) &  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k2_glib_002 A B)) =>  ((r2_hidden D (k24_glib_000 A C)) &  ((k1_glib_004 A B D) = (k1_seq_1 (k5_glib_004 (k6_glib_000 A) k1_numbers (k1_zfmisc_1 (k7_glib_000 A)) (k11_glib_004 A B)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((r2_hidden A (k4_finseq_1 D)) &  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 D)) &  ((r2_hidden B (k4_finseq_1 C)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C B))) &  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C B))))  &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C E))) &  ((r2_hidden E (k4_finseq_1 C)) &  (~  ((k18_complex1 (k6_xcmplx_0 B E)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 (k2_goboard2 D))) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) (k2_nat_1 C 1))) ) ) ) ) )  =>  ( ((k5_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B C))  &  ((k4_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) (k2_nat_1 B 1) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 C)) &  ((r2_hidden B (k1_tops_1 (k15_euclid 2) (k2_goboard5 C A))) & (r1_xxreal_0 (k18_euclid B) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 C))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 C)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k1_matrix_1 C)) & (r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k10_real_1 1 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C D (k2_nat_1 E 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1)) (k13_complex1 1 2)) (k19_euclid k6_numbers 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1) (k19_euclid 1 (k4_xcmplx_0 1)))) (k3_topreal1 2 A))) ) ).
tt(t27_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_goboard5 A (k3_finseq_1 A) k6_numbers) = (a_1_15_gobrd11 A)) ) ) ).
tt(t27_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k3_gobrd13 D E A) = (k3_goboard5 E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) &  ((v1_sprect_2 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k3_goboard9 C)) &  ((r2_hidden B (k2_goboard9 C)) & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) A B) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ).
tt(t27_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((k6_goedelcp A (k4_subset_1 (k3_cqc_lang A) B C)) = (k4_subset_1 (k3_qc_lang1 A) (k6_goedelcp A B) (k6_goedelcp A C))) ) ) ) ) ) ) ).
tt(t27_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_graph_1 B) & (l1_graph_1 B)) )  =>  ((r4_graph_1 A B) => (v4_graph_1 A)) ) ) ) ) ).
tt(t27_graph_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) => (m1_subset_1 (k5_relat_1 D B) (k1_zfmisc_1 C))) ) ) ) ) ) ).
tt(t27_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C D) =>  ((k5_card_1 (k2_graph_3 A B (k6_subset_1 D C))) = (k6_xcmplx_0 (k5_card_1 (k2_graph_3 A B D)) (k5_card_1 (k2_graph_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t27_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ( ( (C = (k8_finseq_1 (u4_struct_0 A) D B))  &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ((k3_finseq_1 B) = 1) ) )  =>  ((k2_graph_5 A C) = (k2_xboole_0 (k2_graph_5 A D) (k1_tarski (k1_funct_1 (u2_graph_1 A) (k1_funct_1 B 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t27_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) => (r1_tarski (k7_graphsp B A) (k13_graphsp B A))) ) ) ) ).
tt(t27_grcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_grcat_1 A B) & (r1_grcat_1 A C))  =>  (B = C) ) ) ) ) ).
tt(t27_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ( ((r2_group_6 A B) & (v1_gr_cy_1 A))  => (v1_gr_cy_1 B)) ) ) ) ) ).
tt(t27_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A 1))  => (r1_int_1 (k6_xcmplx_0 A 1) (k6_xcmplx_0 (k1_newton A B) 1))) ) ) ) ) ).
tt(t27_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) & (r1_tarski B C))  =>  ((k5_relat_1 B A) = (k5_relat_1 C A)) ) ) ) ) ) ) ).
tt(t27_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (? [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_xcmplx_0 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  ( (D = (k1_funct_1 B C))  =>  ((k1_grnilp_1 A D (k7_group_2 A)) = (k1_funct_1 B (k2_xcmplx_0 C 1))) ) ) ) ) ) ) ) ) ) ) )  => (v1_grnilp_1 A)) ) ) ).
tt(t27_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden F E) => (r10_polyred A B C F D)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (~  ((r2_hidden F (k2_groeb_1 A B C E)) &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r2_hidden G (k2_groeb_1 A B C D)) & (r3_pre_poly A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (m2_ideal_1 (k17_finseq_1 (u1_struct_0 A) D C) A B)) ) ) ) ) ) ) ) ).
tt(t27_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))))  => (r1_tarski (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E)) (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  => (r1_tarski (k2_group_2 A (k1_group_11 A B D) (k1_group_11 A C D)) (k1_group_11 A (k2_group_2 A B C) D))) ) ) ) ) ) ) ) ).
tt(t27_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A 2 B) = (k6_algstr_0 A B B)) ) ) ) ) ).
tt(t27_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k4_group_2 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B D E))  & (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k2_group_3 A (k5_group_1 A D B) C) = (k5_group_1 A D (k2_group_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t27_group_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ( ((k3_finseq_1 C) = A)  =>  ((k4_group_4 B C (k5_finseq_2 (u1_struct_0 B) A (k1_group_1 B))) = (k5_finseq_2 (u1_struct_0 B) A (k1_group_1 B))) ) ) ) ) ) ) ) ).
tt(t27_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A (k2_group_1 A B) C) = (k2_group_3 A (k2_group_5 A C B) (k2_group_1 A B))) ) ) ) ) ) ) ).
tt(t27_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((v1_finset_1 (k15_group_2 A B)) =>  ((k7_struct_0 (k5_group_6 A B)) = (k18_group_2 A B)) ) ) ) ) ) ).
tt(t27_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v5_group_1 C) & (l3_algstr_0 C)) ) ) )  =>  ((v1_relat_1 (k11_finseq_1 A B C)) &  ((v4_relat_1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_funct_1 (k11_finseq_1 A B C)) &  ((v1_partfun1 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v1_group_7 (k11_finseq_1 A B C)) &  ((v2_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) &  ((v3_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3)) & (v4_group_7 (k11_finseq_1 A B C) (k1_enumset1 1 2 3))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((u1_struct_0 (k18_group_9 A B C)) = (k1_setfam_1 (a_3_0_group_9 A B C))) ) ) ) ) ) ).
tt(t27_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (v2_groupp_1 (k6_group_2 A) B)) ) ) ) ).
tt(t27_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k10_hahnban1 A)) k1_numbers) &  ((v2_hahnban B (k10_hahnban1 A)) &  ((v3_hahnban B (k10_hahnban1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_hahnban1 A)) k1_numbers)))) ) ) )  =>  ((v1_funct_1 (k16_hahnban1 A B)) &  ((v1_funct_2 (k16_hahnban1 A B) (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 (k16_hahnban1 A B) A k1_complfld) &  ((v1_hahnban1 (k16_hahnban1 A B) k1_complfld A) & (m1_subset_1 (k16_hahnban1 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) ) ) ) ) ) ).
tt(t27_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_relat_1 B) & (m2_finseq_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((m4_hallmar1 C A B) <=>  ( ((k9_xtuple_0 C) = (k4_finseq_1 B))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) => (m3_hallmar1 C A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) B) = (k1_seq_4 k6_numbers)) ) ) ) ) ).
tt(t27_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ( ((v5_glib_001 D A) & (m3_glib_001 D A))  =>  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  ( ((r1_glib_001 A B C D) & (r1_glib_001 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_complfld)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  ((v2_hermitan F A B) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) F C (k4_vectsp_1 k1_complfld B E D)) = (k8_group_1 k1_complfld (k2_complfld E) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k12_normform A))) =>  ((k4_filter_0 (k12_normform A) B C) = (k2_lattice2 (u1_struct_0 (k12_normform A)) (k12_normform A) (k10_heyting1 A B) (k6_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (u1_lattices (k12_normform A)) (k8_heyting1 A) (k9_funcop_1 (u1_struct_0 (k12_normform A)) (u1_struct_0 (k12_normform A)) (k9_heyting1 A) (k11_heyting1 A B) C)))) ) ) ) ) ) ).
tt(t27_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) => (r3_lattices (k5_substlat A B) (k4_lattices (k5_substlat A B) C (k5_binop_1 (u1_struct_0 (k5_substlat A B)) (k5_heyting2 A B) C D)) D)) ) ) ) ) ) ) ).
tt(t27_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((k4_heyting3 1 A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t27_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers k24_sin_cos B) D) C) A) = (k8_real_1 B (k1_seq_1 k24_sin_cos A))) ) ) ) ) ) ) ) ) ) ).
tt(t27_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v4_quofield C A B) & (v6_ideal_1 A))  => (v6_ideal_1 B)) ) ) ) ) ) ) ).
tt(t27_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 A B)) (k3_hilbert1 A B)) k6_hilbert1)) ) ) ) ).
tt(t27_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( (~  ((k4_hilbert1 A B) = A) )  &  (~  ((k4_hilbert1 A B) = B) ) ) ) ) ) ) ).
tt(t27_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  => (r2_funct_2 (k9_funct_2 A B) (k9_funct_2 A B) (k2_funct_2 (k9_funct_2 A B) (k1_hilbert3 A B C D)) (k1_hilbert3 A B (k2_funct_2 A C) (k2_funct_2 B D)))) ) ) ) ) ) ) ) ).
tt(t27_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_hurwitz A (k3_hurwitz A B C)) = C) ) ) ) ) ) ) ).
tt(t27_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 4 (k3_finseq_1 A)) =>  ((r1_idea_1 C (k1_recdef_1 (k12_idea_1 C A B) 1)) &  ((r1_idea_1 C (k1_recdef_1 (k12_idea_1 C A B) 2)) &  ((r1_idea_1 C (k1_recdef_1 (k12_idea_1 C A B) 3)) & (r1_idea_1 C (k1_recdef_1 (k12_idea_1 C A B) 4))) ) ) ) ) ) ) ) ) ) ).
tt(t27_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_ideal_1 D A B) => (m1_ideal_1 (k1_polynom1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t27_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A D C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ( ((r3_incsp_1 A B E) & (r3_incsp_1 A C E))  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_cat_1 E) &  ((v3_cat_1 E) &  ((v4_cat_1 E) &  ((v5_cat_1 E) &  ((v6_cat_1 E) &  ((v3_cat_5 E) & (l1_cat_1 E)) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G C E) =>  ((r1_funct_2 (u4_struct_0 C) (u4_struct_0 D) (u4_struct_0 C) (u4_struct_0 E) F G) =>  ((k15_index_1 A B C D F) = (k15_index_1 A B C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ((r3_pua2mss1 B C F G) =>  (! [H:$i] :  ((l3_msualg_1 H C) =>  ((k1_instalg1 A C H (k3_relat_1 D F) (k3_relat_1 E G)) = (k1_instalg1 A B (k1_instalg1 B C H F G) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A (k5_real_1 (k1_int_1 A) 1)))  &  (~ (r1_xxreal_0 (k3_real_1 A 1) (k1_int_1 A))) ) ) ) ).
tt(t27_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_int_1 B A) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(t27_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (~  (C = k6_numbers) )  &  ((r1_int_2 A C) &  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 A D) B) C) = k6_numbers)  &  (! [E:$i] :  ((v1_int_1 E) =>  (~ (r2_hidden (k4_tarski D (k3_xcmplx_0 B E)) (k1_int_4 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k2_int_5 1 A) = 1) ) ) ).
tt(t27_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_int_6 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  =>  ( (C = D)  | (r2_int_1 (k1_funct_1 B C) k6_numbers (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_xxreal_0 k6_numbers (k2_hurwitz A B)) =>  ((v1_finset_1 (k6_polynom5 A B)) &  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( (D = (k2_hurwitz A B))  &  ( (C = (k1_card_1 (k6_polynom5 A B)))  & (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~  ((k7_real_1 A B) = k6_numbers) )  &  ( (~  ((k9_real_1 A B) = k6_numbers) )  &  (~  ((k2_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 B k6_numbers) k19_sin_cos))) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k19_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B))))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k19_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) (k4_seq_4 C)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k19_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B))))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k19_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ((r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k21_binop_2 A 1))) A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k23_binop_2 A 1))))) &  ((r1_xxreal_0 1 A) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)))) &  (D = (k1_relset_1 k1_numbers C)) ) ) ) )  =>  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_taylor_1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos)) A) B) = (k10_real_1 1 (k8_real_1 B (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t27_integr14,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = (k10_real_1 (k4_real_1 A (k1_seq_1 k19_sin_cos E)) (k5_prepower (k1_seq_1 k16_sin_cos E) (k3_real_1 A 1)))) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A)))) &  ((r1_xxreal_0 1 A) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A))) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k1_taylor_1 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) F) &  ((r1_integr15 A (k3_integra5 B C) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B C)) A) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) ) ) ) )  =>  ((k12_integr15 D E A (k7_integr15 A k1_numbers F G)) = (k7_euclid A (k12_integr15 D E A F) (k12_integr15 D E A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_seq_2 (k2_partfun1 A k1_numbers C A)) => (r1_xxreal_0 (k6_integra1 A C B) (k8_real_1 (k4_seq_4 (k1_rvsum_1 C)) (k3_integra1 A)))) ) ) ) ) ) ) ).
tt(t27_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_seq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 k6_numbers A))  =>  ((k6_integra1 B (k26_valued_1 B k1_numbers C A) D) = (k8_real_1 A (k6_integra1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_integra4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) &  ((v3_integra1 C B) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers D B)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden E B) & (r2_hidden F B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 D E) (k1_seq_1 D F))) (k8_real_1 A (k18_complex1 (k9_real_1 (k1_seq_1 C E) (k1_seq_1 C F)))))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) | (v3_integra1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ( (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k3_integra5 A B)) =>  ((k1_seq_1 F G) = C) ) ) )  &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 F)) &  ((r2_hidden D (k3_integra5 A B)) & (r2_hidden E (k3_integra5 A B))) ) ) )  =>  ((k4_integra5 D E F) = (k3_xcmplx_0 C (k6_xcmplx_0 E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_integra7,ax,(r1_integra7 k1_numbers k24_sin_cos k24_sin_cos)).
tt(t27_integra8,ax, ((k2_fdiff_1 k16_sin_cos k1_numbers) = k19_sin_cos) ).
tt(t27_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)))) )  =>  ((k1_integra9 C (k32_valued_1 k1_numbers k1_numbers A) B) = (k1_real_1 (k1_integra9 C A B))) ) ) ) ) ) ) ) ).
tt(t27_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_interva1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( (D = (k2_interva1 A B C))  =>  ( ((k7_interva1 A D) = B)  &  ((k8_interva1 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A (k3_intpro_1 B C)) (k3_intpro_1 (k3_intpro_1 D B) (k3_intpro_1 A (k3_intpro_1 D C)))) k8_intpro_1)) ) ) ) ) ) ) ) ).
tt(t27_irrat_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) C) (k6_xcmplx_0 (k4_series_1 A) B))) ) ) ) ) ) ) ) ) ).
tt(t27_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D B C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G C A) =>  (! [H:$i] :  ((m2_nattra_1 H B C D E) =>  (! [I:$i] :  ((m2_nattra_1 I B C E F) =>  ( ((r2_nattra_1 B C D E) & (r2_nattra_1 B C E F))  => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) (k4_isocat_1 B C A D F (k7_nattra_1 B C D E F H I) G) (k7_nattra_1 B A (k9_cat_1 B C A D G) (k9_cat_1 B C A E G) (k9_cat_1 B C A F G) (k4_isocat_1 B C A D E H G) (k4_isocat_1 B C A E F I G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k11_nattra_1 B C)) =>  (? [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) & (r2_funct_2 (u4_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) D (k5_isocat_2 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t27_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 B) (k3_borsuk_5 B C)) (k3_rcomp_1 C k1_xxreal_0)))  =>  ((k2_pre_topc k3_topmetr A) = (u1_struct_0 k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t27_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 A C) &  ((r1_xxreal_0 C B) &  ((r1_xxreal_0 A D) & (r1_xxreal_0 D B)) ) )  => (r1_xxreal_0 (k18_complex1 (k9_real_1 C D)) (k9_real_1 B A))) ) ) ) ) ) ) ) ) ).
tt(t27_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = k6_numbers) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k7_xcmplx_0 F G)) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_4_jgraph_3)  &  (B = a_0_5_jgraph_3) )  => (r1_tarski (k8_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 B) A)) ) ) ) ) ).
tt(t27_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_0_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 (k18_euclid B) k6_numbers) & (r1_xxreal_0 (k18_euclid C) k6_numbers))  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  ( ((k12_euclid B) = k6_numbers)  |  ( ((k12_euclid C) = k6_numbers)  |  ((r1_xxreal_0 (k10_real_1 (k17_euclid C) (k12_euclid C)) (k10_real_1 (k17_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C))  & (r1_xxreal_0 (k10_real_1 (k17_euclid E) (k12_euclid E)) (k10_real_1 (k17_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_10_jgraph_6)  &  (B = a_0_1_jgraph_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = B) ) ) ) ) ) ).
tt(t27_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 E (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid C) H)) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) & (r2_hidden B (k1_rltopsp1 (k15_euclid 2) A C))) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan14,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B C) & (r1_xxreal_0 1 B))  =>  ((k3_jordan1h A C) = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d C B)) (k9_real_1 (k3_jordan1h A B) 2)) 2)) ) ) ) ) ) ) ) ).
tt(t27_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k2_jordan1e B A))) &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( (~ (r1_jordan17 A B C D E))  &  ( (~ (r1_jordan17 A B C E D))  &  ( (~ (r1_jordan17 A B D C E))  &  ( (~ (r1_jordan17 A B D E C))  &  ( (~ (r1_jordan17 A B E C D))  &  (~ (r1_jordan17 A B E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r1_jordan18 A B C D C E)) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan19,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k17_euclid B) = (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2))  &  ((r2_hidden B (k3_jordan19 A)) & (r2_hidden B (k4_jordan19 A))) ) ) ) ) ) ) ).
tt(t27_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k3_finseq_1 B)) & (v9_rltopsp1 (k3_goboard5 B A (k1_matrix_1 B)) (k15_euclid 2))) ) ) ) ) ) ).
tt(t27_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((a_4_4_jordan1 A B C D) = (a_4_0_jordan1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t27_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) (k3_finseq_1 (k1_jordan8 B A)))) (k8_jordan6 B))) ) ) ) ) ).
tt(t27_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((k25_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1)) ) ) ) ) ) ) ) ) ).
tt(t27_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_xxreal_0 (k4_finseq_4 (k2_jordan1e B A) (k23_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k2_jordan1e B A) (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ).
tt(t27_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C D) => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B) D)) ) ) ) ) ) ) ) ) ).
tt(t27_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_sprect_2 A) <=> (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k24_pscomp_1 (k3_topreal1 2 A))) 2) (k17_pscomp_1 (k3_topreal1 2 A)))) ) ) ).
tt(t27_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k7_pscomp_1 B) (k7_pscomp_1 A)))  =>  ((k20_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k20_pscomp_1 B)) ) ) ) ) ) ).
tt(t27_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C 1) =>  ((k1_topreal6 2 A (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A C) (k1_rlvect_1 (k15_euclid 2) B (k9_real_1 1 C)))) = (k8_real_1 (k9_real_1 1 C) (k1_topreal6 2 A B))) ) ) ) ) ) ) ) ).
tt(t27_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r2_jordan20 A B C D G) &  ( ((k17_euclid E) = G)  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) D E) A) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) D E))) ) )  => (r2_jordan20 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ((k2_jordan21 A) = (k22_pscomp_1 A)) ) ) ) ).
tt(t27_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k18_euclid (k1_jordan21 (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A C))))) (k18_euclid (k1_jordan21 (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))))) ) ) ) ) ) ) ) ).
tt(t27_jordan23,ax, (! [A:$i] :  ( ((v1_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (v1_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ).
tt(t27_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 1))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k9_finseq_1 C) = A)  =>  ((k9_metric_1 (k14_euclid 1) A B) = (a_2_2_jordan2b B C)) ) ) ) ) ) ) ) ).
tt(t27_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_jordan2c A B) (k2_jordan2c A B)) = (k3_subset_1 (u1_struct_0 (k15_euclid A)) B)) ) ) ) ) ).
tt(t27_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_jordan3 A B C D) & (r2_jordan3 A B D C))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_jordan4 A B C D) & (r1_xxreal_0 D C))  =>  ( ((k3_finseq_1 B) = (k2_nat_1 (k7_nat_d C D) 1))  &  (B = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan5a,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  ((r1_funct_2 (u1_struct_0 A) k1_numbers (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) =>  ((v1_pscomp_1 B A) <=> (v5_pre_topc C A k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t27_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) =>  ((k2_jordan3 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) = A) ) ) ) ).
tt(t27_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r2_hidden (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A D)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A E)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) & (r2_hidden C B)) ) ) ) ) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) |  ( ((k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = C)  |  ((r1_xxreal_0 D E) &  ( (D = E)  => (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_2_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k15_pscomp_1 (k3_topreal1 2 A))) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k15_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ) ).
tt(t27_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r1_jordan5c A C B E D))  => (r1_jordan5c A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan9,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  =>  ((r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_gobrd13 B A C) (k3_topreal1 2 B)) (k3_goboard9 B)) & (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_gobrd13 B A C) (k3_topreal1 2 B)) (k2_goboard9 B))) ) ) ) ) ) ) ) ) ).
tt(t27_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) D))  &  ((r1_gobrd10 C D) & (r2_subset_1 (k2_jordan_a A C B) (k2_jordan_a A D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_jordan,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) => (v2_funct_2 C (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t27_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r2_xboole_0 D E) &  ( (~ (r2_abian (u1_struct_0 A) (k6_knaster A B C E) B))  &  ((k6_knaster A B C D) = (k6_knaster A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_kurato_1,ax, ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k3_rcomp_1 2 k1_xxreal_0)) ).
tt(t27_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A)))))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A)))) D E) = (k3_borsuk_1 (k15_euclid A) (k15_euclid A) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))) B E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid A))) C E))) ) )  =>  ((k3_borsuk_1 (k15_euclid A) (k15_euclid A) (k1_kurato_2 (k15_euclid A) B) (k1_kurato_2 (k15_euclid A) C)) = (k1_kurato_2 (k2_borsuk_1 (k15_euclid A) (k15_euclid A)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ((k12_matrix_3 A B D) = (k4_rlvect_1 B (k9_laplace A C B D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v4_lattice3 (k11_group_4 A))) ) ).
tt(t27_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  => (r1_lattice2 (u1_struct_0 A) (u1_lattices A) (u2_lattices A))) ) ).
tt(t27_lattice3,ax, (! [A:$i] : (v6_lattice3 (k1_lattice3 A))) ).
tt(t27_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v3_filter_0 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((v2_funct_1 C) & (r3_lattices A (k4_lattices A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E)) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C F)))  => (r3_lattices A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C (k4_filter_0 B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_lattice5 E A B D) =>  ((k11_lattice5 A B D E (k1_ordinal1 C)) = (k6_lattice5 (k8_lattice5 A C) B (k10_lattice5 (k8_lattice5 A C) B (k11_lattice5 A B D E C)) (k9_lattice5 A B D E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v9_lattice6 B A) => (r1_tarski (k5_lattice6 A) B)) ) ) ) ) ).
tt(t27_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v1_yellow11 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ( ((v1_lattice5 C A B) & (v3_lattice5 C A B))  =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((m1_lattice5 E A B C) =>  ((r1_ordinal1 D (k7_lattice5 A B C)) => (v3_lattice5 (k6_lattice8 A B C E D) (k3_lattice8 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v19_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (B = (k2_struct_0 A)) ) ) ) ) ).
tt(t27_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) =>  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B))) |  ((k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k11_lexbfs A B C E)) D) = (k2_xboole_0 (k1_funct_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) D) (k6_domain_1 k5_numbers (k7_nat_d (k15_glib_000 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_lfuzzy_1 A B (k2_xcmplx_0 C D)) (k4_fuzzy_4 A A A (k4_lfuzzy_1 A B C) (k4_lfuzzy_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t27_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) & (m2_valued_0 B k1_numbers A))  => (v2_limfunc1 B)) ) ) ) ) ).
tt(t27_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 A D))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A)))) ) ) ) )  | (r3_limfunc2 B A)) ) ) ) ) ) ).
tt(t27_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r3_limfunc3 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))) (k3_xboole_0 (k9_xtuple_0 C) (k9_xtuple_0 B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc3 C A)) ) ) ) ) ) ) ) ).
tt(t27_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r2_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k4_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  | (v4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t27_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_lmod_6 A (k2_vectsp_5 A B C D) (k1_vectsp_5 A B C D))) ) ) ) ) ) ) ) ).
tt(t27_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (v4_xxreal_2 (k14_lopban_1 A B C))) ) ) ) ) ) ).
tt(t27_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_series_1 B) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  (~ (r1_xxreal_0 (k1_normsp_0 A (k1_normsp_1 A C E)) (k1_seq_1 B E))) ) ) ) ) )  | (v2_lopban_3 C A)) ) ) ) ) ) ) ) ).
tt(t27_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k8_nat_1 k1_numbers (k4_sin_cos (k1_normsp_0 A B)) C))) ) ) ) ) ) ).
tt(t27_lopclset,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) => (v1_xboole_0 B)) ) ) ) ) ).
tt(t27_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k10_lpspace1 A B C))) =>  ( (D = E)  =>  ( ((k3_rlvect_1 (k10_lpspace1 A B C) E (k1_rlvect_1 (k10_lpspace1 A B C) E (k1_real_1 1))) = (k2_partfun1 A k1_numbers (k8_lpspace1 A k6_numbers) (k1_relset_1 A D)))  &  (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  (? [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden F (k9_lpspace1 A B C)) &  ((r2_hidden G (k9_lpspace1 A B C)) &  ( (F = (k3_rlvect_1 (k10_lpspace1 A B C) E (k1_rlvect_1 (k10_lpspace1 A B C) E (k1_real_1 1))))  &  ((r2_relset_1 A k1_numbers G (k8_lpspace1 A k6_numbers)) & (r1_lpspace1 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) & (r2_hidden E (k1_lpspace2 A B C F)))  => (r2_hidden (k47_valued_1 A k1_numbers k1_numbers D E) (k1_lpspace2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r3_ltlaxio1 C (k3_hilbert1 A B)) & (r3_ltlaxio1 C (k3_hilbert1 A (k2_ltlaxio1 A))))  => (r3_ltlaxio1 C (k3_hilbert1 A (k6_ltlaxio1 B)))) ) ) ) ) ) ) ).
tt(t27_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A B))) (k4_cqc_the1 A))) ) ) ) ).
tt(t27_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_mathmorp A D (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k1_mathmorp A D B) (k1_mathmorp A D C))) ) ) ) ) ) ) ) ) ).
tt(t27_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 B (k2_matrix10 A C)) => (v3_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t27_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 (k1_nat_1 A 2))) =>  (~  ((v4_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) & (v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2))))) ) ) ) ) ) ).
tt(t27_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( (~ (v2_funct_1 C))  =>  ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) E A A C D)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A)) ) )  =>  ((k3_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) C D) = (k1_funct_1 (k3_matrix14 B A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k3_matrix_3 A (k2_matrix15 (u1_struct_0 A) B) (k2_matrix15 (u1_struct_0 A) C)) = (k2_matrix15 (u1_struct_0 A) (k3_fvsum_1 A B C))) ) ) ) ) ) ) ) ).
tt(t27_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  ( ((v3_matrix16 E (u1_struct_0 B)) & (v3_matrix16 F (u1_struct_0 B)))  => (v3_matrix16 (k3_matrix_6 A B (k2_matrix13 A A B E C) (k2_matrix13 A A B F D)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  (! [E:$i] :  ((m1_matrix_1 E C A B) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) =>  ((k3_matrix_1 C D F G) = (k3_matrix_1 C E F G)) ) ) ) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) & (v1_binop_1 E A)) )  =>  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I C) =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C (k2_setwiseo B H) (k2_setwiseo C I)) (k9_matrix_3 B C A E F G)) = (k7_setwiseo C A D (k2_setwiseo C I) (k10_funcop_1 A C E (k7_setwiseo B A D (k2_setwiseo B H) F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A B D) = (k1_matrix_4 A (k3_matrix_3 A B C) (k3_matrix_3 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ((v2_matrix_6 C B A) => (v2_matrix_6 (k1_matrix_6 B A C) B A)) ) ) ) ) ) ) ).
tt(t27_matrix_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k13_matrix_2 A))) =>  ( ( (C = B)  & (r1_xxreal_0 1 A))  =>  ((k3_matrix_7 A B) = (k2_group_1 (k13_matrix_2 A) C)) ) ) ) ) ) ) ) ).
tt(t27_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v2_matrix_8 C A B) & (v1_matrix_8 C A B))  =>  (C = (k11_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t27_matrix_9,ax, ((r2_hidden (k3_finseq_4 k5_numbers 1 3 2) (k12_matrix_2 3)) &  ((r2_hidden (k3_finseq_4 k5_numbers 2 3 1) (k12_matrix_2 3)) &  ((r2_hidden (k3_finseq_4 k5_numbers 2 1 3) (k12_matrix_2 3)) &  ((r2_hidden (k3_finseq_4 k5_numbers 3 1 2) (k12_matrix_2 3)) &  ((r2_hidden (k3_finseq_4 k5_numbers 1 2 3) (k12_matrix_2 3)) & (r2_hidden (k3_finseq_4 k5_numbers 3 2 1) (k12_matrix_2 3))) ) ) ) ) ).
tt(t27_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_complsp2 (k5_matrixc1 A B)) = (k5_matrixc1 (k1_complsp2 A) (k1_complsp2 B))) ) ) ) ) ) ).
tt(t27_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_matrixj1 F C) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 C))))  =>  (! [G:$i] :  ( ((v1_matrixj1 G C) & (m2_finseq_1 G (k3_finseq_2 (k3_finseq_2 C))))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k13_matrixj1 C D F))) <=>  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  ( (~ (r1_xxreal_0 B k1_xboole_0))  & (r2_hidden (k4_tarski (k1_nat_1 A (k2_wsierp_1 (k10_matrixj1 C G))) (k1_nat_1 B (k2_wsierp_1 (k11_matrixj1 C G)))) (k2_matrix_1 (k13_matrixj1 C E (k3_matrixj1 C G F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_matrixj2 D A (k4_struct_0 A)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) (k3_finseq_1 C) (k3_finseq_1 C)) =>  ( (E = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) D))  =>  ((r1_xxreal_0 (k3_finseq_1 C) k1_xboole_0) |  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 B)) &  ((v2_matrixj2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) F (k4_matrlin2 A B B C C E)) =>  ( (? [G:$i] :  ((v7_ordinal1 G) &  ((r2_hidden G (k4_finseq_1 D)) &  ((k3_finseq_1 (k14_matrixj1 (u1_struct_0 A) D G)) = (k9_matrixj2 A B F)) ) ) )  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k4_finseq_1 D)) => (r1_xxreal_0 (k3_finseq_1 (k14_matrixj1 (u1_struct_0 A) D G)) (k9_matrixj2 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 (k7_matrixr1 A B)) = (k3_finseq_1 B))  &  ((k1_matrix_1 (k7_matrixr1 A B)) = (k1_matrix_1 B)) ) ) ) ) ) ).
tt(t27_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A B) =>  (! [F:$i] :  ((m1_matrix_1 F k1_numbers B C) =>  (! [G:$i] :  ((m1_matrix_1 G k1_numbers C D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ((k6_matrixr1 (k6_matrixr1 E F) G) = (k6_matrixr1 E (k6_matrixr1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 F B C) &  ((v1_mod_2 F A B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [G:$i] :  ((m1_vectsp_4 G A B) =>  (! [H:$i] :  ((m1_vectsp_4 H A B) =>  (! [I:$i] :  ((m1_vectsp_4 I A C) =>  (! [J:$i] :  ((m1_vectsp_4 J A C) =>  ((r1_vectsp_5 A C I J) =>  ( ( ((k1_vectsp_9 A G) = k1_xboole_0)  &  (~  ((k1_vectsp_9 A I) = k1_xboole_0) ) )  |  ( ( ((k1_vectsp_9 A H) = k1_xboole_0)  &  (~  ((k1_vectsp_9 A J) = k1_xboole_0) ) )  |  (! [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K (u1_struct_0 G) (u1_struct_0 I)) &  ((v13_vectsp_1 K G I) &  ((v1_mod_2 K A G I) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 G) (u1_struct_0 I))))) ) ) )  =>  (! [L:$i] :  ( ((v1_funct_1 L) &  ((v1_funct_2 L (u1_struct_0 H) (u1_struct_0 J)) &  ((v13_vectsp_1 L H J) &  ((v1_mod_2 L A H J) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 H) (u1_struct_0 J))))) ) ) )  =>  ( ( (K = (k2_matrlin2 G F))  &  (L = (k2_matrlin2 H F)) )  =>  (! [M:$i] :  ((m1_matrlin M A G) =>  (! [N:$i] :  ((m1_matrlin N A H) =>  (! [O:$i] :  ((m1_matrlin O A I) =>  (! [P:$i] :  ((m1_matrlin P A J) =>  ( ( ((k7_finseq_1 M N) = D)  &  ((k7_finseq_1 O P) = E) )  =>  ((k1_matrlin2 A B C F D E) = (k13_matrixj1 (u1_struct_0 A) (k4_struct_0 A) (k5_matrixj1 (u1_struct_0 A) (k1_matrlin2 A G I K M O) (k1_matrlin2 A H J L N P)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E D) &  ((v9_vectsp_1 E D) &  ((v10_vectsp_1 E D) &  ((v11_vectsp_1 E D) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E D)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) A B) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) C B) =>  ((k6_matrlin E (k8_matrlin (u1_struct_0 E) A C B F G)) = (k8_finseq_1 (u1_struct_0 E) (k6_matrlin E F) (k6_matrlin E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C))) = (k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) D))))  &  ((k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) D))) = (k4_matroid0 A B)) )  =>  ((k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k7_domain_1 (u1_struct_0 A) C D))) = (k4_matroid0 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k9_binop_2 (k5_matrprob A) (k5_matrprob B)) = (k5_matrprob (k7_matrlin k1_numbers A B))) ) ) ) ) ) ).
tt(t27_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) (k1_algstr_0 (k15_euclid A) C D)) = (k1_algstr_0 (k15_euclid B) (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) C) (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (! [D:$i] :  ( ((v1_rlaffin1 D (k15_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k8_matrix13 k2_vectsp_1 C) = B)  => (v1_rlaffin1 (k7_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A C) D) (k15_euclid B))) ) ) ) ) ) ) ) ) ).
tt(t27_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (v2_matrtop3 (k3_matrtop1 B B (k1_matrtop3 B A)) B)) ) ) ) ) ).
tt(t27_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_mboolean A (k2_pboole A B C)) (k2_pboole A (k2_mboolean A B) (k2_mboolean A C)))) ) ) ) ) ).
tt(t27_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ( (D = k1_xboole_0)  =>  ((k12_supinf_2 C D) = k1_supinf_2) )  &  ( (~  (D = k1_xboole_0) )  =>  ((k12_supinf_2 C D) = k1_supinf_1) ) ) ) ) ) ) ) ) ) ).
tt(t27_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v2_measure5 A) <=> (v2_measure5 (k2_measure6 A B))) ) ) ) ) ).
tt(t27_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_measure8 D A B) =>  ((v3_prob_1 D) => (v7_valued_0 (k10_measure8 A B D C))) ) ) ) ) ) ) ) ).
tt(t27_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_member_1 (k2_tarski A B)) = (k2_tarski (k5_xxreal_3 A) (k5_xxreal_3 B))) ) ) ) ) ).
tt(t27_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v3_membered B)) )  => (v3_membered (k3_tarski A))) ) ).
tt(t27_memstr_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_memstr_0 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 B C))) ) )  => (r2_hidden (k4_struct_0 C) (k9_xtuple_0 (k1_funct_4 D (k7_memstr_0 B C A))))) ) ) ) ) ) ) ) ).
tt(t27_mesfun6c,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 B) C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((v6_supinf_2 E) =>  ((k4_power (k1_seq_1 E A) (k10_real_1 1 2)) = (k7_square_1 (k1_seq_1 E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 C A k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k2_numbers C k6_numbers)) = E)  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers C F) E)) )  &  ( ((k1_relset_1 A D) = E)  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F E) =>  ((v2_comseq_2 (k9_mesfun7c A C F)) &  ((k1_funct_1 D F) = (k3_comseq_2 (k9_mesfun7c A C F))) ) ) ) ) ) ) )  => (r1_mesfun6c A B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((v1_mesfunc8 E A k2_numbers) &  ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k2_numbers E k6_numbers))) &  (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers E F) C)) ) ) )  => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers (k1_mesfun9c A k2_numbers E C) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski D (k9_xtuple_0 C)) =>  ((r1_mesfunc1 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k9_subset_1 A D (k18_mesfunc1 A C (k1_measure6 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r1_mesfunc1 A B (k10_mesfunc1 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t27_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((r2_relset_1 A k7_numbers (k1_mesfunc2 A (k6_mesfunc1 A B (k1_real_1 C))) (k6_mesfunc1 A (k2_mesfunc2 A B) C)) & (r2_relset_1 A k7_numbers (k2_mesfunc2 A (k6_mesfunc1 A B (k1_real_1 C))) (k6_mesfunc1 A (k1_mesfunc2 A B) C))) ) ) ) ) ) ) ) ).
tt(t27_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k7_numbers (k4_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A C)) (k3_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A (k32_valued_1 A k1_numbers C))))) ) ) ) ) ) ).
tt(t27_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A C)) =>  ((v7_mesfunc5 (k3_mesfunc5 A B D)) &  ((k12_supinf_2 C D) = (k2_mesfunc5 (k3_mesfunc5 A B D))) ) ) ) )  => (v3_valued_0 C)) ) ) ) ) ) ) ).
tt(t27_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v2_mesfunc9 B A) =>  ( ((k9_subset_1 A (k8_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) (k1_tarski k2_supinf_1)) (k8_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers B (k1_nat_1 C 1)) (k1_tarski k1_supinf_1))) = k1_xboole_0)  &  ((k9_subset_1 A (k8_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) (k1_tarski k1_supinf_1)) (k8_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers B (k1_nat_1 C 1)) (k1_tarski k2_supinf_1))) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t27_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 2) =>  (! [B:$i] :  ((m1_subset_1 B 2) =>  ((k1_metric_1 2 2 k12_metric_1 A B) = k6_numbers) ) ) ) ) ).
tt(t27_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  ((r2_hidden B (k7_metric_2 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) & (r4_metric_2 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t27_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) => (r1_xxreal_0 (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 A C) (k7_real_1 (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 A B) (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k20_metric_3 B C)))) ) ) ) ) ) ).
tt(t27_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_tbsp_1 B A) => (v1_metric_6 B A)) ) ) ) ) ).
tt(t27_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  &  ( (~  (C = (k4_struct_0 (k15_euclid A))) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ((v3_tops_2 D (k15_euclid A) (k15_euclid A)) &  ((k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) D (k2_mfold_2 A B (k4_struct_0 (k15_euclid A)))) = (k2_mfold_2 A C (k4_struct_0 (k15_euclid A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_midsp_1 A B C) =>  ((k4_midsp_1 A B) = (k4_midsp_1 A C)) ) ) ) ) ) ) ) ).
tt(t27_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_midsp_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  <=>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_midsp_2 B) & (l2_algstr_0 B)) ) ) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 B))))) )  &  ((r1_midsp_2 (u1_struct_0 A) B C) & (v1_midsp_2 C A B)) ) ) ) ) ) ) ) ).
tt(t27_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ((r1_midsp_3 A B C) <=>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  ((k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B (k11_midsp_2 C D))) = (k11_midsp_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k3_mmlquery A (k15_mmlquery (k2_zfmisc_1 A A) C D) B) = (k15_mmlquery A (k3_mmlquery A C B) (k3_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t27_mod_2,ax, ( (~ (v2_struct_0 k18_mod_2))  &  ( (~ (v6_struct_0 k18_mod_2))  &  ((v13_algstr_0 k18_mod_2) &  ((v33_algstr_0 k18_mod_2) &  ((v3_group_1 k18_mod_2) &  ((v5_group_1 k18_mod_2) &  ((v4_vectsp_1 k18_mod_2) &  ((v5_vectsp_1 k18_mod_2) &  ((v12_vectsp_1 k18_mod_2) &  ((v2_rlvect_1 k18_mod_2) &  ((v3_rlvect_1 k18_mod_2) &  ((v4_rlvect_1 k18_mod_2) & (l6_algstr_0 k18_mod_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) => (m1_subset_1 (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 1) (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) (k12_finseq_1 k5_numbers k6_numbers) A) k6_modal_1)) ) ).
tt(t27_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_hidden (k4_tarski C D) B) &  (! [E:$i] :  ((m1_modelc_1 E A B) =>  (~  ( ((k3_funct_2 k5_numbers A E k6_numbers) = C)  &  ((k3_funct_2 k5_numbers A E 1) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  => (r2_modelc_2 A A)) ) ).
tt(t27_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  (~  ((r5_modelc_3 D B) &  ( (~ (r2_hidden C (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 B 1) D))))  &  ( (~ (r1_xxreal_0 A 1))  &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  ((r2_hidden C (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 B A) D))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 A E))  &  ( (~ (r2_hidden C (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 B E) D))))  & (r2_hidden C (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 B (k1_nat_1 E 1)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d C (k3_nat_d B A)))  =>  ((v1_moebius1 B) |  ((r1_nat_d C B) &  (~ (r1_nat_d A C)) ) ) ) ) ) ) ) ) ) ).
tt(t27_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m3_monoid_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m3_monoid_0 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g4_algstr_0 (u1_struct_0 B) (u2_algstr_0 B) (u3_struct_0 B)) = (g4_algstr_0 (u1_struct_0 C) (u2_algstr_0 C) (u3_struct_0 C))) ) ) ) ) ) ) ) ).
tt(t27_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 A (u1_struct_0 (k13_monoid_1 B))) <=>  ((v1_funct_1 A) &  ((v1_funct_2 A B k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 B k5_numbers)))) ) ) ) ) ).
tt(t27_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A D) B) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A D) C))) ) ) ) ) ) ) ) ) ).
tt(t27_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) => (r2_pboole (u1_struct_0 A) (k2_msafree3 A D) B)) ) ) ) ) ) ) ) ).
tt(t27_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) => (m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) ) ) ) ) ) ) ) ).
tt(t27_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  (! [G:$i] :  ((m1_msaterm G A B (k2_msaterm A B E)) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (! [I:$i] :  ((m1_subset_1 I (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) D)) =>  (~  ( (F = (k4_trees_4 (k4_tarski E (u1_struct_0 A)) G))  &  ((r2_hidden H (k4_finseq_1 G)) &  ( (I = (k1_funct_1 G H))  & (r1_xxreal_0 (k8_msafree2 A B C F) (k8_msafree2 A B D I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((v2_finset_1 B) &  ((r2_pboole A B (k6_pboole A C D)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  (~  ((v2_finset_1 E) &  ((r2_pboole A E C) & (r2_pboole A B (k6_pboole A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B (k6_msualg_1 A)) &  ((v4_msualg_1 B (k6_msualg_1 A)) & (m1_msualg_2 B (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  ( ((u1_struct_0 (k6_msualg_1 A)) = (k1_tarski k6_numbers))  => (m1_unialg_2 (k12_msualg_1 (k6_msualg_1 A) B) A)) ) ) ) ) ).
tt(t27_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D A B) =>  ((k11_msualg_2 A B C (k13_msualg_2 A B C D)) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t27_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((v2_msualg_6 C A B) <=>  ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t27_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  => (m3_pboole C (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))) ) ) ) ) ) ).
tt(t27_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v5_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((v6_dilworth B (k3_necklace A)) & (m1_eqrel_1 B (u1_struct_0 (k3_necklace A)))) ) ) ) ) ).
tt(t27_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((v1_pscomp_1 C A) => (v1_pscomp_1 (k5_nagata_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t27_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 3) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  (~  (A = 3) ) ) ) ) ) ) ) ) ).
tt(t27_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_nat_d (k3_nat_d A B) C) = (k3_nat_d A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t27_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = 1) )  =>  ( ( (~  (B = k6_numbers) )  &  ((k11_nat_3 B A) = k6_numbers) )  <=>  (~ (r1_nat_d A B)) ) ) ) ) ) ) ).
tt(t27_nat_4,ax,(v1_int_2 11)).
tt(t27_nat_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  ( (D = (k1_tarski B))  =>  ((k3_uproots D (k1_nat_5 A C D)) = (k1_recdef_1 C B)) ) ) ) ) ) ) ) ).
tt(t27_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k3_nat_d A B) = k6_numbers) ) ) ) ) ) ).
tt(t27_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ( ((r2_nattra_1 A B C D) & (v1_nattra_1 E A B C D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k4_nattra_1 A B D C (k9_nattra_1 A B C D E) F) = (k6_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B D F) (k4_nattra_1 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k4_vfunct_1 (u1_struct_0 A) B C E)) (k5_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r15_ncfcont1 B C A D) => (r3_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t27_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_nfcont_1 B A C D) <=>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 B) E) (k1_relset_1 (u1_struct_0 B) C)) &  ((v3_normsp_1 E B) &  ( ((k6_normsp_1 B E) = D)  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 B E F) = D) ) ) ) ) ) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E C) A) &  ((k7_partfun1 (u1_struct_0 A) C D) = (k6_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_ndiff_4 A B C) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  => (r1_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid A) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) B (k4_pdiff_1 D A)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t27_ndiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v2_prvect_2 B) & (v1_ndiff_5 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 B))) =>  (! [F:$i] :  ((r2_hidden F (k4_finseq_1 B)) => (r2_relset_1 (u1_struct_0 (k11_prvect_2 B (k5_ndiff_5 B F))) (u1_struct_0 C) (k4_vfunct_1 (u1_struct_0 (k11_prvect_2 B (k5_ndiff_5 B F))) C (k1_partfun1 (u1_struct_0 (k11_prvect_2 B (k5_ndiff_5 B F))) (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 C) (k4_ndiff_5 B (k5_ndiff_5 B F) E) D) A) (k1_partfun1 (u1_struct_0 (k11_prvect_2 B (k5_ndiff_5 B F))) (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 C) (k4_ndiff_5 B (k5_ndiff_5 B F) E) (k4_vfunct_1 (u1_struct_0 (k14_prvect_2 B)) C D A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_neckla_3,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 (u1_orders_2 A) B C) => (r1_rewrite1 (u1_orders_2 A) C B)) ) ) ) ) ).
tt(t27_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k5_card_1 (u1_orders_2 (k4_necklace A))) = (k8_real_1 2 (k5_real_1 A 1))) ) ) ) ).
tt(t27_newton,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_newton A B k6_numbers) = (k12_finseq_1 k5_numbers 1)) ) ) ) ) ).
tt(t27_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r3_nfcont_1 B A E D) => (r3_nfcont_1 B A (k4_vfunct_1 (u1_struct_0 B) A E C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C) & (r1_tarski B A))  => (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D B) C)) ) ) ) ) ) ) ).
tt(t27_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((r1_tarski C (k1_relset_1 k1_numbers E)) &  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) E C) A)) ) )  =>  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k7_integr15 A k1_numbers D E) (k3_xboole_0 B C)) A) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers D E) (k3_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t27_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  (~  ((r2_hidden C (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B)) & (r2_hidden C (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B))) ) ) ) ) ) ).
tt(t27_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 C A) =>  ((k6_normsp_1 A (k4_normsp_1 A C B)) = (k5_algstr_0 A (k6_normsp_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t27_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 (k3_normsp_2 A)) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) =>  ((v2_frechet C (k4_normsp_2 A)) <=> (v2_frechet B (k3_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t27_numbers,ax, (~  (k5_numbers = k4_numbers) ) ).
tt(t27_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  => (r1_filter_1 A (k15_openlatt A))) ) ).
tt(t27_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B C) (k6_oppcat_1 A D)) = (k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) C D)) ) ) ) ) ) ) ) ) ).
tt(t27_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v3_orders_1 A) => (v3_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t27_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_orders_2 A B C) => (r1_tarski (k3_orders_2 A D B) (k3_orders_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t27_ordinal1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) &  ( (~ (r2_hidden B A))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (~ (r2_hidden C A))  => (r1_ordinal1 B C)) ) ) ) ) ) ) ).
tt(t27_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k10_ordinal2 A k1_xboole_0) = A) ) ) ).
tt(t27_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r1_ordinal1 A B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  (B = (k10_ordinal2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t27_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 B C) =>  ( (A = k1_xboole_0)  | (r1_ordinal1 (k12_ordinal2 A B) (k12_ordinal2 A C))) ) ) ) ) ) ) ) ).
tt(t27_ordinal5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k12_ordinal2 A B) = (k1_newton A B)) ) ) ) ) ).
tt(t27_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_abian A B) => (r2_hidden A (k10_xtuple_0 B))) ) ) ) ).
tt(t27_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t27_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  ( (~ (r1_orders_2 B F D))  &  (~  ((k8_group_1 A (k1_ortsp_1 A B D C E) (k1_ortsp_1 A B E D F)) = (k8_group_1 A (k1_ortsp_1 A B D C F) (k1_ortsp_1 A B F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v3_osalg_4 (k20_osafree A B) A (k8_osafree A B))) ) ) ) ).
tt(t27_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((v13_osalg_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r6_osalg_1 A C D) => (r1_relset_1 (k3_msualg_1 A C B) (k4_msualg_1 A C B) (k5_msualg_1 A C B) (k5_msualg_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t27_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  (! [E:$i] :  ((m2_osalg_2 E A B) =>  ((r2_hidden E (k5_osalg_2 A B D)) => (r1_tarski (k10_xtuple_0 (k5_relat_1 (k5_msualg_1 A C B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_osalg_2 A B D))) C))) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r1_parsp_1 A B C B D))  =>  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (~  (D = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) =>  ( (~ (r1_parsp_2 A B C D))  &  ( (~ (r1_parsp_2 A C B E))  &  ( (~ (r1_parsp_2 A D E B))  &  (~ (r1_parsp_2 A E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_tarski C D) => (r1_relset_1 A B (k3_partfun1 C A B) (k3_partfun1 D A B))) ) ) ) ) ) ) ).
tt(t27_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  &  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B C)) =>  ((k3_funct_2 B A D E) = (k7_partfun1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((k2_partit1 A B (k3_partit1 A B C)) = B) ) ) ) ) ) ) ).
tt(t27_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r8_relat_2 B A) => (v8_relat_2 B)) ) ) ) ) ).
tt(t27_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B C D) &  ((r1_diraf A C E F) &  ( (~ (r3_diraf A B C F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_diraf A B G F) & (r1_diraf A G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A B (k3_pboole A C D)) <=>  ((r2_pboole A B C) &  ((r2_pboole A B D) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A E C) & (r2_pboole A E D))  => (r2_pboole A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((v9_metric_1 A) &  ((r2_hidden B (k9_metric_1 A C D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  & (r1_tarski (k9_metric_1 A B E) (k9_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k19_pcs_0 A B))) =>  ( (C = B)  =>  ((r1_pcs_0 (k19_pcs_0 A B) C D) & (r1_pcs_0 (k19_pcs_0 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) => (r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) (k4_vfunct_1 (u1_struct_0 (k4_real_ns1 1)) (k4_real_ns1 A) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) E) D) (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A)) (k7_pdiff_1 B C F) (k4_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r3_pdiff_3 B A) & (r3_pdiff_3 C A))  =>  ((r3_pdiff_1 2 1 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) &  ((k11_pdiff_1 2 1 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) = (k9_real_1 (k4_pdiff_3 B A) (k4_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 3 3) B)) =>  ( ((r3_pdiff_1 3 3 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 A B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k1_rvsum_1 E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 3 3) B)))  & (r1_tarski (k1_rvsum_1 (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 A B))))) &  ((k11_pdiff_1 3 3 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 A B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r9_pdiff_5 B A) <=> (r3_pdiff_1 3 3 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ).
tt(t27_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 B A) (k1_rlvect_1 (k4_real_ns1 A) C D)) = (k1_rlvect_1 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 B A) C) D)) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k1_euclid A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k7_partfun1 (k1_euclid A) D E) = (k8_euclid A (k7_partfun1 (k1_euclid A) B E) (k7_partfun1 (k1_euclid A) C E))) ) ) ) ) )  =>  ((k5_euclid_7 A D) = (k8_euclid A (k5_euclid_7 A B) (k5_euclid_7 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t27_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  ( ( (D = E)  & (r1_pdiff_6 C B A D))  =>  ((k1_pdiff_9 A B C D) = (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ( (~ (v13_pencil_1 B))  & (v16_pencil_1 B A)) ) ) ) )  =>  (! [C:$i] :  ( (~ (v1_zfmisc_1 C))  =>  ((v16_pencil_1 (k2_funct_7 B (k3_pencil_1 A B) C) A) &  (~ (v13_pencil_1 (k2_funct_7 B (k3_pencil_1 A B) C))) ) ) ) ) ) ) ) ).
tt(t27_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (! [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  =>  (! [E:$i] :  ( ( (~ (v13_pencil_1 E))  &  ((v16_pencil_1 E A) & (m3_pboole E A (k12_pralg_1 A B))) )  =>  ( ((m1_pencil_2 (k4_card_3 D) A B) &  ((m1_pencil_2 (k4_card_3 E) A B) &  ((k3_pencil_1 A D) = (k3_pencil_1 A E)) ) )  => (r1_funct_2 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A D)))) (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A E))) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A (k2_pencil_3 A B C) (k3_pencil_1 A E)))) (k3_pencil_3 A B C D) (k3_pencil_3 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k1_vectsp_9 A B)))  =>  ((r1_xxreal_0 D C) | (v5_pencil_1 (k7_pencil_4 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k4_nat_d B 2) = k6_numbers)  =>  ((k3_square_1 (k1_newton A (k3_nat_d B 2))) = (k1_newton A B)) ) ) ) ) ) ).
tt(t27_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r1_pnproc_1 A (k3_pnproc_1 A (k2_pnproc_1 A B C) B) C)) ) ) ) ) ).
tt(t27_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k1_newton A 3) = (k5_binop_2 (k5_binop_2 A A) A))  &  ( ((k1_newton A 3) = (k5_binop_2 (k1_polyeq_3 A) A))  &  ((k1_newton A 3) = (k3_polyeq_3 A)) ) ) ) ) ).
tt(t27_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k6_polyeq_5 A B C D)) (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k7_polyeq_5 A B C D))) (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k8_polyeq_5 A B C D))) (k3_xcmplx_0 (k6_polyeq_5 A B C D) (k7_polyeq_5 A B C D))) (k3_xcmplx_0 (k6_polyeq_5 A B C D) (k8_polyeq_5 A B C D))) (k3_xcmplx_0 (k7_polyeq_5 A B C D) (k8_polyeq_5 A B C D))) = C) ) ) ) ) ) ) ) ) ).
tt(t27_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k4_finseq_1 (k10_polyform A B)) = (k2_finseq_1 (k11_polyform A B))) ) ) ) ) ).
tt(t27_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B (k9_polynom1 A B C D) E) (k9_polynom1 A B C (k9_polynom1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k3_normsp_1 A B C) D) = (k5_algstr_0 A (k1_normsp_1 A B D) (k1_normsp_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t27_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A B (k5_struct_0 A)) B)) ) ) ) ).
tt(t27_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k5_polynom7 A B C D) (k9_polynom1 A B (k4_polynom7 A B D) C))) ) ) ) ) ) ) ) ).
tt(t27_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((k3_polynom8 A B (k3_xcmplx_0 C (k6_xcmplx_0 D 1))) = (k3_polynom8 A (k2_binom A B C) (k6_xcmplx_0 D 1))) ) ) ) ) ) ) ) ) ) ).
tt(t27_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r1_polyred A B C D E) & (r1_polyred A B C E F))  => (r1_polyred A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power A (k2_xcmplx_0 B C)) = (k3_xcmplx_0 (k3_power A B) (k3_power A C))) ) ) ) ) ) ) ) ).
tt(t27_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_pralg_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) & (v1_funcop_1 G)) ) ) )  =>  ( (! [H:$i] :  ((m1_subset_1 H A) =>  (? [I:$i] :  ((m2_pboole I (u1_struct_0 B) (u3_msualg_1 B F) (u3_msualg_1 B (k5_pralg_2 A B D H))) &  ( (I = (k1_funct_1 G H))  & (r1_msualg_3 B F (k5_pralg_2 A B D H) I)) ) ) ) )  =>  (! [H:$i] :  ((m2_pboole H (u1_struct_0 B) (u3_msualg_1 B F) (u3_msualg_1 B (k5_pralg_2 A B D C))) =>  ( (H = (k1_funct_1 G C))  =>  (! [I:$i] :  ((r2_hidden I (k1_funct_1 (u3_msualg_1 B F) E)) =>  (! [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  =>  ( (J = (k1_funct_1 (k10_funct_6 (k1_funct_1 (k10_funct_6 G) E)) I))  =>  ((k1_funct_1 J C) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 B) (u3_msualg_1 B F) (u3_msualg_1 B (k5_pralg_2 A B D C)) H E) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) (k3_prelamb A B (k2_prelamb A C D))) (k2_prelamb A (k3_prelamb A B C) D))) ) ) ) ) ) ) ) ).
tt(t27_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  ((k3_finseq_1 (k5_pre_poly A B)) = (k2_wsierp_1 (k10_pre_poly A B))) ) ) ) ).
tt(t27_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 1 C)) )  => (r1_xxreal_0 (k2_prepower C A) (k2_prepower C B))) ) ) ) ) ) ) ).
tt(t27_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_pre_topc D B) =>  ((v5_pre_topc C A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  ( (E = C)  => (v5_pre_topc E A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_prob_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( ((k9_xtuple_0 D) = C)  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden E C) =>  ( ((r2_hidden B E) =>  ((k1_funct_1 D E) = 1) )  &  ( (~ (r2_hidden B E))  =>  ((k1_funct_1 D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ( ((r1_prob_2 A B F C D) &  ((r1_prob_2 A B F C E) & (r1_xboole_0 D E)) )  => (r1_prob_2 A B F C (k6_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (v2_prob_1 (k1_prob_3 A C))) ) ) ) ) ).
tt(t27_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((k4_prob_4 A B C) = (k2_measure3 A B (k2_prob_4 A B C))) ) ) ) ) ) ) ).
tt(t27_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B (k9_cqc_lang A C D)) (k9_cqc_lang A (k9_cqc_lang A B C) D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t27_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((r5_projpl_1 A B C D E) => (r2_zfmisc_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k18_euclid (k11_pscomp_1 A)) = (k18_euclid (k12_pscomp_1 A))) ) ) ).
tt(t27_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m3_pua2mss1 B A) => (r1_setfam_1 B (k8_eqrel_1 (u1_struct_0 A) (k9_pua2mss1 A)))) ) ) ) ).
tt(t27_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A (k2_pzfmisc1 A B C) (k1_pzfmisc1 A D)) => (r6_pboole A (k2_pzfmisc1 A B C) (k1_pzfmisc1 A D))) ) ) ) ) ) ) ) ).
tt(t27_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) => (r2_qc_lang1 A B (k28_qc_lang1 A B))) ) ) ) ).
tt(t27_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ((v5_qc_lang1 (k8_qc_lang2 A B C D E) A) &  ( ((k21_qc_lang1 A (k8_qc_lang2 A B C D E)) = B)  &  ((k22_qc_lang1 A (k8_qc_lang2 A B C D E)) = (k6_qc_lang2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((v6_qc_lang1 B A) & (v6_qc_lang1 C A))  <=> (v6_qc_lang1 (k4_qc_lang2 A B C) A)) ) ) ) ) ) ) ).
tt(t27_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 (k2_qc_lang4 A C))) =>  ( ((r2_hidden E (k3_qc_lang4 A B C)) & (r2_hidden F (k3_qc_lang4 A C D)))  => (r2_hidden (k8_finseq_1 k5_numbers E F) (k3_qc_lang4 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((k6_algstr_0 A B (k15_lattice3 A C)) = (k15_lattice3 A (a_3_8_quantal1 A B C)))  &  ((k9_quantal1 A B (k16_lattice3 A C)) = (k16_lattice3 A (a_3_9_quantal1 A B C))) ) ) ) ) ) ) ).
tt(t27_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k6_quatern2 A B) = (k26_quaterni (k26_quaterni (k23_quaterni (k10_real_1 (k7_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni B) (k17_quaterni A)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni B) (k19_quaterni A))) (k8_real_1 (k20_quaterni B) (k20_quaterni A))) (k5_square_1 (k3_quatern2 B))) (k25_quaterni (k10_real_1 (k7_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni B) (k18_quaterni A)) (k8_real_1 (k18_quaterni B) (k17_quaterni A))) (k8_real_1 (k19_quaterni B) (k20_quaterni A))) (k8_real_1 (k20_quaterni B) (k19_quaterni A))) (k5_square_1 (k3_quatern2 B))) k4_quatern2)) (k25_quaterni (k10_real_1 (k9_real_1 (k9_real_1 (k7_real_1 (k8_real_1 (k17_quaterni B) (k19_quaterni A)) (k8_real_1 (k18_quaterni B) (k20_quaterni A))) (k8_real_1 (k19_quaterni B) (k17_quaterni A))) (k8_real_1 (k20_quaterni B) (k18_quaterni A))) (k5_square_1 (k3_quatern2 B))) k11_quaterni)) (k25_quaterni (k10_real_1 (k9_real_1 (k7_real_1 (k9_real_1 (k8_real_1 (k17_quaterni B) (k20_quaterni A)) (k8_real_1 (k18_quaterni B) (k19_quaterni A))) (k8_real_1 (k19_quaterni B) (k18_quaterni A))) (k8_real_1 (k20_quaterni B) (k17_quaterni A))) (k5_square_1 (k3_quatern2 B))) k12_quaterni))) ) ) ) ) ).
tt(t27_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k20_quaterni (k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A))) = (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k20_quaterni A)))) ) ) ).
tt(t27_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( (A = k6_numbers)  =>  ((k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A))) = k6_numbers) ) ) ) ).
tt(t27_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_quin_1 A B C) k6_numbers))  &  (~  ( (~  ( (~ (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers))  &  ((r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D) & (r1_xxreal_0 D (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) ) )  &  (~  ( (~  ((r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)) D) & (r1_xxreal_0 D (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k3_xcmplx_0 2 A)))) )  & (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ((k5_binop_1 (k7_quofield A) (k16_quofield A) B (k5_binop_1 (k7_quofield A) (k15_quofield A) C D)) = (k5_binop_1 (k7_quofield A) (k15_quofield A) (k5_binop_1 (k7_quofield A) (k16_quofield A) B C) (k5_binop_1 (k7_quofield A) (k16_quofield A) B D))) ) ) ) ) ) ) ) ) ).
tt(t27_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A C) =>  (! [E:$i] :  ((m1_random_1 E A C) =>  ((r1_random_1 A C E D) =>  ((k8_random_1 A C D (k5_random_1 A C E B)) = (k8_real_1 B (k8_random_1 A C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_vectsp_6 E A B D) =>  ((r1_tarski C D) => (r1_vectsp_6 A B E (k5_vectsp_6 A B (k6_ranknull A B E C) (k6_ranknull A B E (k7_subset_1 (u1_struct_0 B) D C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (C = (k6_real_1 B A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (B = (k4_real_1 (k2_rat_1 C) D))  &  (A = (k4_nat_1 (k1_rat_1 C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  ((k11_ratfunc1 A (k11_ratfunc1 A B)) = (k11_ratfunc1 A B)) ) ) ) ) ).
tt(t27_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v3_xxreal_2 A) =>  ((v4_xxreal_2 A) |  ((r2_hidden (k5_seq_4 A) A) |  (A = (k3_limfunc1 (k5_seq_4 A))) ) ) ) ) ) ).
tt(t27_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( ((k1_seq_1 (k3_real_3 C) A) = k6_numbers)  & (r1_xxreal_0 A B))  =>  ((k1_seq_1 (k3_real_3 C) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t27_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_real_lat A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_real_lat A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_real_lat A))) =>  ((k1_binop_1 (k5_real_lat A) B (k1_binop_1 (k4_real_lat A) C D)) = (k1_binop_1 (k4_real_lat A) (k1_binop_1 (k5_real_lat A) B C) (k1_binop_1 (k5_real_lat A) B D))) ) ) ) ) ) ) ) ) ).
tt(t27_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_binop_1 (k2_realset3 A) B (k5_struct_0 A)) = B) ) ) ) ) ).
tt(t27_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ( ((k20_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A) C) = (k20_rfunct_3 B (k15_valued_1 B k1_numbers D A) B))  &  ((k21_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A) C) = (k21_rfunct_3 B (k15_valued_1 B k1_numbers D A) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k9_xtuple_0 (k3_relat_1 A B)) = (k9_xtuple_0 A)) ) ) ) ) ) ).
tt(t27_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_relat_2 A) <=> (r1_tarski (k3_relat_1 A A) A)) ) ) ).
tt(t27_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  (~  ( (~  ((k2_relset_1 A C) = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~ (r2_hidden D (k1_relset_1 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k6_relset_2 A B (k4_subset_1 A C D) E) = (k9_subset_1 B (k6_relset_2 A B C E) (k6_relset_2 A B D E))) ) ) ) ) ) ) ) ) ).
tt(t27_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((k28_seq_4 (k2_goboard1 B)) = (k28_seq_4 (k2_goboard1 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)))) ) ) ) ) ).
tt(t27_rewrite1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_rewrite1 k1_xboole_0 A B) =>  (A = B) ) ) ) ).
tt(t27_rewrite2,ax, (! [A:$i] : (r2_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A (k6_rewrite2 (k8_afinsq_1 A))) (k6_rewrite2 (k8_afinsq_1 A)))) ).
tt(t27_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 F))) =>  (! [H:$i] :  ((l1_rewrite3 H G) =>  ( ( ((v1_relat_1 (u1_rewrite3 G H)) & (v1_funct_1 (u1_rewrite3 G H)))  &  ((r2_rewrite3 F G H A B C D) & (r2_rewrite3 F G H A B E D)) )  =>  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_classes1 A B) => (r2_classes1 (k6_rvsum_1 A) (k6_rvsum_1 B))) ) ) ) ) ).
tt(t27_rfinseq,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k2_rfinseq A (k3_finseq_1 B) B) = k1_xboole_0) ) ) ) ).
tt(t27_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k4_rfunct_1 (k18_valued_1 A B)) = (k18_valued_1 (k4_rfunct_1 A) (k4_rfunct_1 B))) ) ) ) ) ).
tt(t27_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers C (k3_xboole_0 A B)))) ) ) ) ) ).
tt(t27_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_rfunct_3 A B C D) => (r1_rfunct_3 A B (k2_rfinseq (k3_rfunct_3 A B) E C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 B) => (v2_seq_2 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t27_rinfsup2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((k12_supinf_2 (k4_rinfsup2 B) A) = (k1_rinfsup2 (k1_valued_0 k7_numbers B A)))  &  ((k12_supinf_2 (k3_rinfsup2 B) A) = (k2_rinfsup2 (k1_valued_0 k7_numbers B A))) ) ) ) ) ) ).
tt(t27_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_rlvect_2 D C) => (r1_rlvect_2 C (k2_rlaffin1 C (k2_rlaffin1 C D B) A) (k2_rlaffin1 C D (k8_real_1 A B)))) ) ) ) ) ) ) ) ).
tt(t27_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 (k4_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B)) A) <=>  ((v1_rlaffin1 C A) &  (~  ( (~ (r2_hidden B C))  & (r2_hidden B (k4_rlaffin1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t27_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [E:$i] :  ((m2_rlaffin3 E (k15_euclid A) C) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C))))) =>  ( (F = (a_5_1_rlaffin3 A B C D E))  =>  ((r1_xxreal_0 (k5_card_1 C) B) |  ((v3_pre_topc D (k15_euclid B)) <=> (v3_pre_topc F (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  ( ((m1_rlsub_1 A B) & (m1_rlsub_1 B C))  => (m1_rlsub_1 A C)) ) ) ) ) ) ) ).
tt(t27_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) => (m1_rlsub_1 (k1_rlsub_2 A B (k2_rlsub_2 A C D)) (k2_rlsub_2 A (k1_rlsub_2 A C B) (k1_rlsub_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t27_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k4_struct_0 A) B)) ) ) ) ).
tt(t27_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A B (k1_algstr_0 A C D)) = (k5_algstr_0 A (k5_algstr_0 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t27_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r2_relset_1 k5_numbers (u1_struct_0 A) (k5_rlvect_2 A (k2_finseq_4 (u1_struct_0 A) B C) D) (k2_finseq_4 (u1_struct_0 A) (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers D C))))) ) ) ) ) ) ) ) ).
tt(t27_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rlvect_3 A B) = A)  &  (! [C:$i] :  ((m1_rlvect_3 C A) =>  (~ (r1_tarski C B)) ) ) ) ) ) ) ) ) ).
tt(t27_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 B) C D E) B) =>  ( (C = E)  |  ( (C = D)  |  ( (E = D)  |  ( (A = k6_numbers)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 B) C D (k1_rlvect_1 B E A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((v1_rlvect_5 A) => (v1_rlvect_5 B)) ) ) ) ) ).
tt(t27_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k4_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k4_numbers) =>  ( ((r2_hidden C (k3_rlvect_x A B)) & (r2_hidden D (k3_rlvect_x A B)))  => (r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D F)) (k3_rlvect_x A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) => (m1_rmod_2 C A D)) ) ) ) ) ) ) ) ) ).
tt(t27_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) => (m1_rmod_2 (k1_rmod_3 A B (k2_rmod_3 A B C D) (k2_rmod_3 A B D E)) A (k2_rmod_3 A B D (k1_rmod_3 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k4_rmod_4 A B (k3_finseq_4 (u1_struct_0 B) C D E) F) = (k3_finseq_4 (u1_struct_0 B) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F C) C) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F D) D) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F E) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k6_robbins1 A B (k5_robbins1 A C D))) = (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k5_robbins1 A (k6_robbins1 A (k6_robbins1 A B (k3_robbins1 A C)) (k3_robbins1 A D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) C) (k3_robbins1 A D))) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) D)) (k6_robbins1 A (k6_robbins1 A (k3_robbins1 A B) (k3_robbins1 A C)) (k3_robbins1 A D)))) ) ) ) ) ) ) ) ) ).
tt(t27_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_lattices A B C) = (k1_lattices A C B)) ) ) ) ) ) ) ).
tt(t27_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v6_oposet_1 A) &  ((v10_oposet_1 A) &  ((v10_robbins3 A) &  ((v11_robbins3 A) & (l4_robbins3 A)) ) ) ) ) ) ) )  => (v10_robbins1 A)) ) ).
tt(t27_robbins4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_robbins4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_robbins4)) =>  ( (A = 3)  =>  ((k3_lattices k2_robbins4 A B) = A) ) ) ) ) ) ).
tt(t27_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_roughs_1 A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k4_roughs_1 A B) (k4_roughs_1 A C)))) ) ) ) ) ) ).
tt(t27_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A B) = (k9_real_1 (k1_rpr_1 A (k4_subset_1 A B C)) (k1_rpr_1 A (k7_subset_1 A C B)))) ) ) ) ) ) ) ).
tt(t27_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=> (r1_struct_0 A C)) ) )  =>  (B = A) ) ) ) ) ) ).
tt(t27_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) => (m1_rusub_1 (k1_rusub_2 A C (k2_rusub_2 A B D)) (k2_rusub_2 A (k1_rusub_2 A B C) (k1_rusub_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t27_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (u1_struct_0 B)) => (m1_rusub_1 (k1_rusub_3 A C) B)) ) ) ) ) ) ) ).
tt(t27_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (v3_rusub_4 (k3_rusub_4 A B) A)) ) ) ) ).
tt(t27_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (u1_struct_0 B))  =>  ((k3_rusub_5 A C) = (k2_rusub_5 A B)) ) ) ) ) ) ) ) ).
tt(t27_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 B k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k4_finseq_2 B k1_numbers)) =>  ((k1_seq_1 (k9_rvsum_1 B C D) A) = (k10_binop_2 (k1_seq_1 C A) (k1_seq_1 D A))) ) ) ) ) ) ) ) ).
tt(t27_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ((k11_rvsum_2 (k2_finseq_2 A B) C) = (k10_rvsum_2 A C B)) ) ) ) ) ) ) ).
tt(t27_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v4_compos_0 C (u1_compos_1 k1_scmfsa_2)) & (m1_subset_1 C (u1_compos_1 k1_scmfsa_2)))  =>  ( (~  (C = (k2_compos_1 k1_scmfsa_2)) )  =>  ((k1_funct_1 (k3_scmfsa6a (k5_scmfsa6a A C) B) (k5_card_1 A)) = C) ) ) ) ) ) ) ) ).
tt(t27_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 10)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t27_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k3_scmfsa_1) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ((k9_scmfsa_1 (k8_scmfsa_1 A B C) B) = C) ) ) ) ) ) ) ).
tt(t27_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k15_scmfsa_2 C B A)) = 10) ) ) ) ) ) ) ).
tt(t27_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmfsa6a (k5_scmfsa6a B A) C) = (k3_scmfsa6a B (k4_scmfsa6a A C))) ) ) ) ) ) ) ).
tt(t27_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B))  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E)))  &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E)) = (k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) E))) ) ) ) )  &  ( ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))))  &  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k3_scmfsa6a C D)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r5_scmfsa7b D B A) & (r6_scmfsa7b D B A)) )  =>  ((r5_scmfsa7b (k3_scmfsa8b E C D) B A) & (r6_scmfsa7b (k3_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3) D))  =>  ((r2_hidden D (k2_afinsq_1 (k1_scmfsa8b A B C))) &  (~  ((k1_funct_1 (k1_scmfsa8b A B C) D) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r3_scmfsa9a A B C D) & (r4_scmfsa9a A B C D))  =>  ((r6_scmfsa7b (k2_scmfsa_9 C D) B A) & (r5_scmfsa7b (k2_scmfsa_9 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r5_scmfsa7b B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E) (k1_funct_4 A (k1_scmfsa_9 C B))) & (r6_scmfsa7b B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) E) (k1_funct_4 A (k1_scmfsa_9 C B)))) ) )  =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  =>  (~  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) (k1_nat_1 F 1)))) &  (~  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers) ) ) )  &  ( (~  ( ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers)  &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F) C) = k6_numbers) ) )  &  ( (~  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F) C) = k6_numbers) )  =>  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers) ) ) ) ) ) ) ) )  |  ((r6_scmfsa7b (k1_scmfsa_9 C B) D A) & (r5_scmfsa7b (k1_scmfsa_9 C B) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k3_scmfsa_2)) =>  ( ((k5_relat_1 A (k2_xboole_0 C D)) = (k5_relat_1 B (k2_xboole_0 C D)))  <=>  ( (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden E C) =>  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) )  &  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((r2_hidden E D) =>  ((k18_scmfsa_2 A E) = (k18_scmfsa_2 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((r1_scm_halt C B A) &  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) & (r1_tarski C A)) )  =>  ((r4_scmfsa7b C D) |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A B E) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v1_scmfsa7b C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k2_scmfsa_9 E C)) =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa_9 E C) B A) D) = (k1_funct_1 (k1_scmfsa6b (k2_scmfsa_9 E C) (k1_scmfsa6b C B A) A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 1)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (~  (A = (k4_scmpds_2 B)) ) ) ) ) ) ) ) ).
tt(t27_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ( ((k5_memstr_0 2 k1_scmpds_2 A) = D)  &  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 D E)) &  ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 A) C) = (k5_memstr_0 2 k1_scmpds_2 B)) ) )  =>  ((k2_nat_1 (k17_scmpds_2 A E) C) = (k17_scmpds_2 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (~  ((r1_tarski C A) &  ( (~  ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))) = (k2_compos_1 k1_scmpds_2)) )  &  (~  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 A B (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))) = (k5_card_1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_scmpds_6 B D A) & (r2_scmpds_6 B D A))  =>  ((r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D) E) |  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D E)) = (k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 B C))) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 B C))) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_scmpds_6 B D A) &  ((r2_scmpds_6 B D A) &  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) D) E))  &  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 B C))) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 B C))) D E)) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  (! [H:$i] :  ( ( (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 B I))) ) )  &  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 I) &  ((v5_funct_1 I (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 I (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 I 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J k5_numbers) &  ((v5_relat_1 J (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 J) & (v1_partfun1 J k5_numbers)) ) ) )  =>  ( ( (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden K G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 I K))) ) )  &  ( (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden K H) =>  ((k1_funct_1 I K) = (k1_funct_1 B K)) ) ) )  &  ((k1_funct_1 I D) = (k1_funct_1 B D)) ) )  =>  ((r1_xxreal_0 (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C I J) D) = (k1_funct_1 I D))  &  ((r1_scmpds_6 C I J) &  ((r2_scmpds_6 C I J) &  ( (~ (r1_xxreal_0 (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) E)) (k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 (k1_funct_1 B D) E))))  &  ( (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden K G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 (k6_scmpds_4 C I J) K))) ) )  &  (! [K:$i] :  ( ((v1_ami_2 K) & (m1_subset_1 K (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden K H) =>  ((k1_funct_1 (k6_scmpds_4 C I J) K) = (k1_funct_1 I K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) &  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers))  =>  ((k6_scmpds_4 (k2_scmpds_8 D E C) B A) = (k6_scmpds_4 (k2_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k1_scmring2 A)))) =>  ( (B = 7)  =>  ((k9_xtuple_0 (k10_card_3 (k3_compos_0 (u1_compos_1 (k1_scmring2 A)) B))) = (k1_tarski 1)) ) ) ) ) ) ).
tt(t27_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (A = (k2_xboole_0 (k2_xboole_0 (k1_tarski k1_xboole_0) (k9_bspace (k3_tarski A))) (k1_scmyciel A))) ) ) ).
tt(t27_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  &  ((r2_analoaf A B C D E) & (r1_semi_af1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers A 1) A)) ) ).
tt(t27_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers A)) = (k17_complex1 (k3_comseq_2 A))) ) ) ) ).
tt(t27_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( ((k2_seq_2 A) = k6_numbers)  |  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((m2_valued_0 B k1_numbers A) & (v2_relat_1 B))  =>  ((k2_seq_2 (k37_valued_1 k5_numbers k1_numbers B)) = (k8_binop_2 (k2_seq_2 A))) ) ) ) ) ) ) ) ).
tt(t27_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D C) => (r1_seqfunc A k1_numbers B (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t27_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (m2_valued_0 B k1_numbers A))  => (v1_seq_2 B)) ) ) ) ) ).
tt(t27_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A B) k6_numbers)) ) )  &  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 1 (k10_real_1 (k3_funct_2 k5_numbers k1_numbers A (k2_nat_1 C 1)) (k3_funct_2 k5_numbers k1_numbers A C)))) ) ) ) )  & (v1_series_1 A)) ) ) ) ) ).
tt(t27_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 1 (k3_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 3 B) 2) (k2_nat_1 (k4_nat_1 3 B) 1))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 B (k2_nat_1 (k4_nat_1 3 B) 1))) ) ) ) ) ) ) ).
tt(t27_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k3_xcmplx_0 (k3_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B)) (k6_square_1 C)) (k8_complex1 (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B)) (k13_complex1 1 C)))) ) ) ) ) ) ) ).
tt(t27_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = B)  &  ((k1_seq_1 A k6_numbers) = 1) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k1_series_3 A) B) = (k9_newton B)) ) ) ) ) ) ) ).
tt(t27_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 C D))  & (r1_xxreal_0 (k13_complex1 C (k2_xcmplx_0 C B)) (k13_complex1 D (k2_xcmplx_0 D A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (B = k1_xboole_0) )  =>  ((k6_subset_1 A (k1_setfam_1 B)) = (k3_tarski (k4_setfam_1 (k1_tarski A) B))) ) ) ) ).
tt(t27_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) (k1_kurato_0 B C))) ) ) ) ) ).
tt(t27_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 C) => (v3_prob_1 (k7_setlim_2 A C B))) ) ) ) ) ) ).
tt(t27_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (r6_binop_1 A D C)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  ( (~  (E = k1_xboole_0) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k5_binop_1 A D G (k7_setwiseo B A C E F)) = (k7_setwiseo B A C E (k10_funcop_1 A B D G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_binop_1 C A) & (v2_binop_1 C A))  =>  ( ( (~  ((r1_xxreal_0 1 D) & (r1_xxreal_0 1 E)) )  &  (~ (v1_setwiseo C A)) )  |  ((k1_finsop_1 A (k5_finseq_2 A (k3_xcmplx_0 D E) B) C) = (k1_finsop_1 A (k5_finseq_2 A E (k1_finsop_1 A (k5_finseq_2 A D B) C)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (C = D) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k1_funct_1 A C))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k5_sfmastr2 C D) A B) D) = (k1_pre_ff E))  &  ((k1_funct_1 (k1_scmfsa6b (k5_sfmastr2 C D) A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~  ( (~  (A = B) )  & (r4_scmfsa7b (k3_sfmastr3 B C A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k3_scmfsa6a A B)) = (k4_subset_1 k2_scmfsa_2 (k2_sf_mastr A) (k2_sf_mastr B))) ) ) ) ) ).
tt(t27_sgraph1,ax, (! [A:$i] :  ((r2_sgraph1 A (k3_sgraph1 A)) &  (! [B:$i] :  ((r2_sgraph1 A B) => (r1_tarski (k3_sgraph1 A) B)) ) ) ) ).
tt(t27_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) &  ((v8_robbins1 A) &  ((v9_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v11_sheffer1 A)) ) ).
tt(t27_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B (k5_sheffer1 A C D)))) = (k5_sheffer1 A B (k5_sheffer1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t27_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  (! [D:$i] :  ((m2_simplex0 D A C) => (m2_simplex0 D A B)) ) ) ) ) ) ) ).
tt(t27_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C B) &  ((v1_rlaffin1 (k1_simplex1 A B C) A) & (v3_pre_topc D B)) )  =>  ((r1_tarski (k1_rlaffin2 A (k1_simplex1 A B C)) (k3_convex1 A (k1_simplex1 A B D))) <=> (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_sincos10,ax, ((k2_relset_1 k1_numbers k3_sincos10) = (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) ).
tt(t27_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k4_sin_cos2 (k7_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))) (k1_seq_1 k4_sin_cos2 (k9_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))))  &  ((k9_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k1_sin_cos2 (k9_real_1 (k6_real_1 A 2) (k6_real_1 B 2)))) (k1_seq_1 k1_sin_cos2 (k7_real_1 (k6_real_1 A 2) (k6_real_1 B 2))))) ) ) ) ) ) ).
tt(t27_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k15_sin_cos (k3_binop_2 A (k5_binop_2 (k11_binop_2 2 k32_sin_cos) k7_complex1))) = (k15_sin_cos A)) ) ) ).
tt(t27_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k3_xcmplx_0 2 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)))) ) ) ) ) ).
tt(t27_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k21_sin_cos (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k7_real_1 1 (k20_sin_cos A)) 2)))  |  ((k21_sin_cos (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k7_real_1 1 (k20_sin_cos A)) 2)))) ) ) ) ).
tt(t27_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) &  ((k17_sin_cos A) = (k1_real_1 1)) ) )  =>  (A = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) ).
tt(t27_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  &  ( (~ (r1_xxreal_0 1 (k3_square_1 B)))  &  ((k11_binop_2 A B) = (k19_binop_2 1)) ) ) ) ) ) ) ) ).
tt(t27_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k3_sin_cos2 (k3_xcmplx_0 2 A)) = (k7_xcmplx_0 (k3_xcmplx_0 2 (k9_sin_cos2 A)) (k6_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A)))))  &  ( ((k3_sin_cos2 (k3_xcmplx_0 3 A)) = (k3_xcmplx_0 (k3_sin_cos2 A) (k6_xcmplx_0 (k3_xcmplx_0 4 (k5_square_1 (k6_sin_cos2 A))) 1)))  &  ( ((k3_sin_cos2 (k3_xcmplx_0 3 A)) = (k6_xcmplx_0 (k3_xcmplx_0 3 (k3_sin_cos2 A)) (k3_xcmplx_0 (k3_xcmplx_0 2 (k3_sin_cos2 A)) (k6_xcmplx_0 1 (k6_sin_cos2 (k3_xcmplx_0 2 A))))))  &  ( ((k6_sin_cos2 (k3_xcmplx_0 2 A)) = (k2_xcmplx_0 1 (k3_xcmplx_0 2 (k5_square_1 (k3_sin_cos2 A)))))  &  ( ((k6_sin_cos2 (k3_xcmplx_0 2 A)) = (k2_xcmplx_0 (k5_square_1 (k6_sin_cos2 A)) (k5_square_1 (k3_sin_cos2 A))))  &  ( ((k6_sin_cos2 (k3_xcmplx_0 2 A)) = (k7_xcmplx_0 (k2_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A))) (k6_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A)))))  &  ( ((k6_sin_cos2 (k3_xcmplx_0 3 A)) = (k3_xcmplx_0 (k6_sin_cos2 A) (k2_xcmplx_0 (k3_xcmplx_0 4 (k5_square_1 (k3_sin_cos2 A))) 1)))  &  ((k9_sin_cos2 (k3_xcmplx_0 3 A)) = (k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 3 (k9_sin_cos2 A)) (k2_newton (k9_sin_cos2 A) 3)) (k2_xcmplx_0 1 (k3_xcmplx_0 3 (k5_square_1 (k9_sin_cos2 A)))))) ) ) ) ) ) ) ) ) ) ).
tt(t27_sin_cos9,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t27_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((k17_complex1 (k15_sin_cos (k3_xcmplx_0 A k7_complex1))) = 1)  &  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k18_complex1 (k17_sin_cos B)) 1) & (r1_xxreal_0 (k18_complex1 (k20_sin_cos B)) 1)) ) ) ) ) ) ).
tt(t27_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)))) ) ) ) )  =>  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1))) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 2)))) ) ) ) ) ) ).
tt(t27_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_topreal1 A))  => (v2_topreal1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t27_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A))) = (k1_tarski (k11_pscomp_1 A))) ) ) ).
tt(t27_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r1_sprect_2 A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k13_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(t27_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k8_jordan5d A) (k7_jordan5d A))) ) ) ).
tt(t27_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t27_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_square_1 B) (k6_square_1 A))) ) ) ) ) ) ) ).
tt(t27_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_stacks_1 A (k7_stacks_1 A B C)) = (k13_stacks_1 A B)) ) ) ) ) ) ) ).
tt(t27_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_stirl2_1 k6_numbers A) = k6_numbers) ) ) ) ).
tt(t27_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) => (v7_substut1 (k9_sublemma A B C) A)) ) ) ) ) ) ) ).
tt(t27_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D B) => (r2_hidden D C)) )  => (r1_tarski B C)) ) ) ) ) ) ).
tt(t27_substlat,ax, (! [A:$i] :  (! [B:$i] :  ((k6_lattices (k5_substlat A B)) = (k1_tarski k1_xboole_0)) ) ) ).
tt(t27_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ( (~  ((v4_substut1 B A) & (v5_substut1 B A)) )  &  ( (~  ((v4_substut1 B A) & (v6_substut1 B A)) )  &  ( (~  ((v4_substut1 B A) & (v7_substut1 B A)) )  &  ( (~  ((v5_substut1 B A) & (v6_substut1 B A)) )  &  ( (~  ((v5_substut1 B A) & (v7_substut1 B A)) )  &  ( (~  ((v6_substut1 B A) & (v7_substut1 B A)) )  &  ( (~  ((v2_substut1 B A) & (v4_substut1 B A)) )  &  ( (~  ((v2_substut1 B A) & (v5_substut1 B A)) )  &  ( (~  ((v2_substut1 B A) & (v6_substut1 B A)) )  &  (~  ((v2_substut1 B A) & (v7_substut1 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_substut2 E A C D) =>  (~  ((r2_qc_lang2 A C D) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 E)) &  (! [F:$i] :  ((m1_subset_1 F (k9_qc_lang1 A)) =>  (~  ( (F = (k1_funct_1 E B))  & (r2_qc_lang2 A F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_xxreal_0 (k11_supinf_2 k7_numbers A B C) (k12_supinf_2 C D)) & (r1_xxreal_0 (k12_supinf_2 C D) (k10_supinf_2 k7_numbers A B C))) ) ) ) ) ) ) ) ) ).
tt(t27_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  (~  ((k1_symsp_1 A B E D C) = (k8_group_1 A (k4_algstr_0 A (k11_algstr_0 A (k1_symsp_1 A B D C E))) (k1_symsp_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((r2_hidden A (k9_xtuple_0 (k1_sysrel B))) =>  ((r2_hidden A (k9_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B)) )  &  ( ( ((r2_hidden A (k9_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B))  => (r2_hidden A (k9_xtuple_0 (k1_sysrel B))))  &  ( ((r2_hidden A (k10_xtuple_0 (k1_sysrel B))) =>  ((r2_hidden A (k9_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B)) )  &  ( ( ((r2_hidden A (k9_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B))  => (r2_hidden A (k10_xtuple_0 (k1_sysrel B))))  &  ( ((r2_hidden A (k10_xtuple_0 (k1_sysrel B))) =>  ((r2_hidden A (k10_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B)) )  &  ( ( ((r2_hidden A (k10_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B))  => (r2_hidden A (k10_xtuple_0 (k1_sysrel B))))  &  ( ((r2_hidden A (k9_xtuple_0 (k1_sysrel B))) =>  ((r2_hidden A (k10_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B)) )  &  ( ((r2_hidden A (k10_xtuple_0 B)) & (r2_hidden (k4_tarski A A) B))  => (r2_hidden A (k9_xtuple_0 (k1_sysrel B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_taxonom1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k2_relset_1 k1_numbers B))  & (r1_xxreal_0 (k1_xxreal_2 C) D))  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A E (k13_lang1 A (k1_taxonom1 A B D))) =>  ((k8_eqrel_1 A E) = (k1_tarski A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) &  ((r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden F (k2_rcomp_1 D E)) &  ((k1_seq_1 B E) = (k7_real_1 (k1_seq_1 (k3_series_1 (k6_taylor_1 B C D E)) A) (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) F) (k2_newton (k9_real_1 E D) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_seq_1 (k3_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)) (k4_nat_1 2 C)) = (k1_seq_1 (k3_series_1 (k23_sin_cos B)) C)) ) ) ) ) ) ) ) ).
tt(t27_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) => (v6_tops_1 (k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B)) A)) ) ) ) ) ).
tt(t27_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k6_setfam_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t27_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v4_pre_topc (k1_tops_1 A B) A)) ) ) ) ) ) ).
tt(t27_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k4_termord A B C (k5_termord A B C D)) = (k4_termord A B C D)) ) ) ) ) ) ) ) ) ).
tt(t27_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 (k3_tex_1 A B)) (u1_pre_topc (k3_tex_1 A B))))  <=>  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (~  (D = A) )  =>  ((k1_tops_1 C D) = (k7_subset_1 (u1_struct_0 C) D (k6_domain_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ((v2_tex_3 B A) & (v2_tex_3 C A))  =>  ((v2_tex_3 (k2_tsep_1 A B C) A) & (m1_pre_topc (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t27_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (v3_tex_4 B A))  =>  (B = (k2_tex_4 A C)) ) ) ) ) ) ) ) ).
tt(t27_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ((m1_pre_topc B D) => (m1_pre_topc (k2_tsep_1 A B C) (k2_tsep_1 A D C)))  &  ((m1_pre_topc C D) => (m1_pre_topc (k2_tsep_1 A B C) (k2_tsep_1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((r2_hidden D (k9_relat_1 C B)) <=> (r2_hidden (k4_tarski B D) C)) ) ) ) ) ) ).
tt(t27_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A D C))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ((r3_borsuk_2 A B D (k1_borsuk_2 A B C D E G) (k1_borsuk_2 A B C D F G)) => (r3_borsuk_2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) =>  (! [I:$i] :  ((m1_borsuk_2 I B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) =>  ( ((r3_borsuk_2 A D E F G) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) H (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) F C)) & (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) I (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) G C))) )  => (r3_borsuk_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)))) =>  (! [F:$i] :  ((m1_borsuk_2 F (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D)) =>  ( (E = (k6_eqrel_1 (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k4_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) F))  =>  ((k3_funct_2 (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))) (k11_topalg_4 A B C D) E) = (k10_finseq_1 (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) (k9_topalg_4 A B C D F)) (k6_eqrel_1 (k2_topalg_1 B D) (k2_topalg_1 B D) (k4_topalg_1 B D) (k10_topalg_4 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_topalg_5,ax, (! [A:$i] :  ( ((v1_toprealb A) & (m1_pre_topc A (k15_euclid 2)))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_group_6 k2_gr_cy_1 (k5_topalg_1 A B))) ) ) ) ).
tt(t27_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((k9_xtuple_0 B) = (k1_rcomp_1 (k2_xxreal_2 (k9_xtuple_0 B)) (k1_xxreal_2 (k9_xtuple_0 B)))) ) ) ) ) ).
tt(t27_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_metrizts A B C D) & (v1_topdim_1 C A))  =>  ((k2_topdim_1 A C) = (k2_topdim_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t27_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k3_topgen_1 A (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)) = (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k3_topgen_1 A B) (k3_topgen_1 A C))) ) ) ) ) ) ) ).
tt(t27_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ((v1_finset_1 (k3_subset_1 (u1_struct_0 (k5_topgen_2 A B)) C)) =>  ((k1_tops_1 (k5_topgen_2 A B) C) = C) ) ) ) ) ) ).
tt(t27_topgen_3,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ( ((k4_series_1 (k4_topgen_3 A (k13_complex1 1 2))) = (k4_series_1 (k4_topgen_3 B (k13_complex1 1 2))))  =>  (A = B) ) ) ) ) ) ).
tt(t27_topgen_4,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k3_tarski (k2_setfam_1 A B)) (k2_xboole_0 (k3_tarski A) (k3_tarski B)))) ) ).
tt(t27_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ((v3_pre_topc (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_topreal9 2 (k19_euclid A B) B) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k19_euclid A k6_numbers))) k3_topgen_5) & (m1_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_topreal9 2 (k19_euclid A B) B) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k19_euclid A k6_numbers))) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ) ) ) ) ).
tt(t27_topgrp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (r1_tarski (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_tops_1 B D)) (k1_tops_1 A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t27_topreal1,ax, (? [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((v5_topreal1 A) &  ((v5_topreal1 B) &  ( (k1_topreal1 = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) = (k2_tarski (k19_euclid k6_numbers k6_numbers) (k19_euclid 1 1))) ) ) ) ) ) ) ) ).
tt(t27_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid A) = (k18_euclid B))  =>  ( ((k18_euclid C) = (k18_euclid B))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k19_euclid (k17_euclid B) (k18_euclid C))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid B) (k18_euclid C)) C)) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t27_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v2_topreal4 B (k15_euclid 2)) &  ((r2_hidden A B) &  (C = (a_2_1_topreal4 A B)) ) )  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t27_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( (B = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k9_real_1 1 A)) (k1_rlvect_1 (k15_euclid 2) D A)))  &  ( (~  (B = C) )  &  ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_topreal8,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v2_topreal1 A) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 4))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A 1) (k3_topreal1 2 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) 1 A))) = (k2_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) ) ) ) ).
tt(t27_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r2_hidden B (k4_topreal9 A B C))) ) ) ) ) ) ).
tt(t27_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))) = (k2_zfmisc_1 (k1_rcomp_1 A B) (k1_rcomp_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t27_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((m1_subset_1 A (u1_struct_0 (k11_toprealb k9_toprealb))) =>  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid A)) &  (~ (r1_xxreal_0 1 (k17_euclid A))) ) ) ) ) ).
tt(t27_toprealc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A (k1_algstr_0 A B C) C) = B) ) ) ) ) ) ) ).
tt(t27_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = (k12_euclid (k5_algstr_0 (k15_euclid A) C B))) ) ) ) ) ) ) ).
tt(t27_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))) = (k2_pre_topc A B)) ) ) ) ) ) ).
tt(t27_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((v1_tops_2 B A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C)))) =>  ( (D = B)  => (v1_tops_2 D C)) ) ) ) ) ) ) ) ) ) ).
tt(t27_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B C) &  ((v4_pre_topc C A) & (v2_tops_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t27_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v2_transgeo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t27_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) )  =>  ( (~ (v1_xboole_0 (k3_xboole_0 B A)))  &  ((v1_finset_1 (k3_xboole_0 B A)) & (v1_trees_1 (k3_xboole_0 B A))) ) ) ) ) ) ).
tt(t27_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m1_trees_2 D A) =>  ( ((r2_hidden B D) &  ((r2_hidden C D) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) )  => (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t27_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((v6_trees_3 A) & (v6_trees_3 B))  <=> (v6_trees_3 (k7_finseq_1 A B))) ) ) ) ) ).
tt(t27_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_trees_3 E (k2_zfmisc_1 A B)))  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_trees_3 F A))  =>  (! [G:$i] :  ((m2_finseq_1 G E) =>  (! [H:$i] :  ((m2_finseq_1 H F) =>  ( ( ((k4_finseq_1 H) = (k4_finseq_1 G))  &  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ((r2_hidden I (k4_finseq_1 G)) =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v5_relat_1 J (k2_zfmisc_1 A B)) &  ((v1_funct_1 J) & (v3_trees_2 J)) ) )  =>  ( (J = (k1_funct_1 G I))  =>  ((k1_funct_1 H I) = (k8_trees_3 A B J)) ) ) ) ) ) ) )  =>  ((k8_trees_3 A B (k4_trees_4 (k1_domain_1 A B C D) G)) = (k4_trees_4 C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_trees_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_trees_3 B))  =>  ((k12_trees_9 B A) = (k3_tarski (a_2_2_trees_9 A B))) ) ) ) ).
tt(t27_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  =>  ((m1_pre_topc (k2_tsep_1 A B C) B) & (m1_pre_topc (k2_tsep_1 A B C) C)) ) ) ) ) ) ) ) ).
tt(t27_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))) =>  ( ( (E = B)  &  (F = C) )  =>  ((r2_tsep_1 A B C) <=> (r2_tsep_1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C))) = (k4_tex_4 A C)) ) ) ) ) ) ) ).
tt(t27_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k14_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k14_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( (A = (k4_domain_1 k5_numbers k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)) k6_numbers C B))  & (r2_turing_1 (k3_finseq_4 k5_numbers C D E) k14_turing_1 B))  =>  ((v2_turing_1 A k14_turing_1) &  ( ((k2_mcart_1 (u2_turing_1 k14_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)) (k11_turing_1 k14_turing_1 A)) = (k2_nat_1 1 C))  & (r2_turing_1 (k2_finseq_4 k5_numbers (k2_nat_1 1 C) (k2_nat_1 D E)) k14_turing_1 (k3_mcart_1 (u2_turing_1 k14_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k14_turing_1)) (k11_turing_1 k14_turing_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((u1_struct_0 (k34_twoscomp A B)) = (k2_xboole_0 (k2_tarski A B) (k1_tarski (k4_tarski (k10_finseq_1 A B) k15_twoscomp)))) ) ) ) ) ).
tt(t27_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  => (v2_binop_1 (k11_unialg_2 A) (k9_unialg_2 A))) ) ).
tt(t27_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k1_card_1 (k2_uniroots A)) = A) ) ) ).
tt(t27_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k9_polynom3 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(t27_urysohn2,ax, ((r2_hidden k6_numbers k2_urysohn1) & (r2_hidden 1 k2_urysohn1)) ).
tt(t27_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ( (~ (r2_hidden C (k24_qc_lang1 A D)))  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = H) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B F H)) ) ) )  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E D) F) = (k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B E D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A D)) => (r2_funct_2 k5_numbers B (k1_valued_0 B (k8_funct_2 k5_numbers B A C D) E) (k8_funct_2 k5_numbers B A (k1_valued_0 A C E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_valued_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) & (v1_funct_1 B)) )  => (r2_tarski (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers (k61_valued_1 B A)))) ) ) ) ).
tt(t27_valued_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k30_valued_1 (k50_valued_1 A B)) = (k50_valued_1 A (k30_valued_1 B))) ) ) ) ) ).
tt(t27_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) &  ((v13_vectsp_1 D C A) &  ((v1_hahnban1 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E))))) =>  ( (E = F)  =>  ((r1_struct_0 C E) |  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (? [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E)))) (u1_struct_0 A)) &  ((v13_vectsp_1 H (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E))) A) &  ((v1_hahnban1 H A (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E)))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E)))) (u1_struct_0 A))))) ) ) )  &  ( ((k5_relset_1 (u1_struct_0 (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E)))) (u1_struct_0 A) H (u1_struct_0 C)) = D)  &  ((k3_funct_2 (u1_struct_0 (k1_vectsp_5 A B C (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) E)))) (u1_struct_0 A) H F) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (? [D:$i] :  ((v7_ordinal1 D) &  ((k2_vectsp11 A B C) = (k1_ranknull A B B (k1_vectsp11 B C D))) ) ) ) ) ) ) ) ) ).
tt(t27_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t27_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) =>  ((k5_struct_0 A) = (k1_group_1 A)) ) ) ) ).
tt(t27_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_tarski (u1_struct_0 C) (u1_struct_0 D)) => (m1_vectsp_4 C A D)) ) ) ) ) ) ) ) ) ).
tt(t27_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) =>  ((k2_vectsp_5 A B D (k1_vectsp_5 A B C E)) = (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ((r1_vectsp_6 A B (k5_vectsp_6 A B C (k2_vectsp_6 A B)) C) & (r1_vectsp_6 A B (k5_vectsp_6 A B (k2_vectsp_6 A B) C) C)) ) ) ) ) ) ) ).
tt(t27_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k1_vectsp_9 A B) = (k1_vectsp_9 A (k2_vectsp_4 A B))) ) ) ) ) ).
tt(t27_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k6_vfunct_1 B C D E) A) (k6_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A) (k2_partfun1 B (u1_struct_0 C) E A))) &  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k6_vfunct_1 B C D E) A) (k6_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A) E)) & (r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k6_vfunct_1 B C D E) A) (k6_vfunct_1 B C D (k2_partfun1 B (u1_struct_0 C) E A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k3_vfunct_2 A B C D) E) (k3_vfunct_2 A B (k2_partfun1 A (u1_struct_0 B) C E) (k2_partfun1 A (u1_struct_0 B) D E))) &  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k3_vfunct_2 A B C D) E) (k3_vfunct_2 A B (k2_partfun1 A (u1_struct_0 B) C E) D)) & (r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k3_vfunct_2 A B C D) E) (k3_vfunct_2 A B C (k2_partfun1 A (u1_struct_0 B) D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v12_waybel_0 B A) & (v12_waybel_0 C A))  =>  ((v12_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A) & (v12_waybel_0 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t27_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_waybel10 A))) <=>  ((v1_orders_2 B) &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) ) ) ) ) ) ) ).
tt(t27_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r1_waybel_0 A (k4_waybel11 A B) C) <=> (r2_hidden B C)) ) ) ) ) ) ).
tt(t27_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r3_orders_2 A C D))  &  (~ (r3_orders_2 A D C)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B))) )  => (r2_hidden (k2_yellow_0 A C) C)) ) ) ) ) ) ) ).
tt(t27_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_waybel_3 A D E) <=> (r1_waybel_3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ( (C = B)  =>  ((v6_waybel_6 C (k2_yellow_1 (k5_waybel11 A))) <=>  ((v2_waybel_0 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ) ) ) ).
tt(t27_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=>  (? [B:$i] : (r5_waybel_1 A (k3_yellow_1 B))) ) ) ) ).
tt(t27_waybel16,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_orders_2 A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_orders_2 A B E) => (r1_orders_2 A C E)) ) ) )  =>  ((r1_orders_2 A D B) |  ((k13_lattice3 A B D) = (k13_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_8 A) & (v2_waybel_8 B))  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_hidden E (u1_struct_0 (k1_waybel_8 B))) =>  ((r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r2_hidden F (u1_struct_0 (k1_waybel_8 A))) &  ((r3_orders_2 A F D) & (r3_orders_2 B E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((u1_waybel_0 A (k2_yellow_9 A B)) = (k4_relat_1 B))  &  ((u1_waybel_0 A (k3_yellow_9 A B)) = (k4_relat_1 B)) ) ) ) ) ) ).
tt(t27_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) =>  ((v2_funct_1 C) <=> (v2_funct_2 D (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v18_waybel_0 D A B) & (v18_waybel_0 E B C))  => (v18_waybel_0 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_waybel_0 B A))  =>  (! [C:$i] :  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) C) => (r1_waybel_0 A B C)) ) ) ) ) ) ).
tt(t27_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((k2_yellow_0 (k5_yellow_0 A B) C) = (k2_yellow_0 A C)) ) ) ) ) ) ) ).
tt(t27_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_yellow_1 (u1_struct_0 A) B)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k7_relat_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) D) = (a_4_3_waybel24 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t27_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v1_waybel25 A))  => (v1_waybel25 B)) ) ) ) ) ).
tt(t27_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) &  ((v6_pre_topc C) &  ((v1_waybel25 C) & (l1_pre_topc C)) ) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_waybel26 A C)) (u1_struct_0 (k1_waybel26 A C))) &  ((v22_waybel_0 D (k1_waybel26 A C) (k1_waybel26 A C)) &  ((v6_waybel_1 D (k1_waybel26 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A C)) (u1_struct_0 (k1_waybel26 A C)))))) ) ) )  &  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  =>  ((k1_funct_1 D E) = (k6_struct_0 A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) E B))) ) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_pre_topc E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) E (k6_struct_0 A A B)) & (r2_funct_2 (u1_struct_0 (k1_waybel26 A C)) (u1_struct_0 (k1_waybel26 A C)) D (k4_waybel26 C A A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_waybel27 A B)))) =>  ((k1_yellow_0 (k2_waybel27 A B) C) = (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C)) ) ) ) ) ) ) ).
tt(t27_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k4_waybel28 A)) => (v3_waybel11 B A)) ) ) ) ) ).
tt(t27_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) <=>  ((v3_pre_topc (a_1_0_waybel29 A) (k2_borsuk_1 (k1_waybel29 (k2_yellow_1 (u1_pre_topc A))) A)) & (m1_subset_1 (a_1_0_waybel29 A) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k1_waybel29 (k2_yellow_1 (u1_pre_topc A))) A))))) ) ) ) ).
tt(t27_waybel_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v10_waybel_0 B A) => (v10_waybel_0 (k3_waybel_2 A C B) A)) ) ) ) ) ) ) ).
tt(t27_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k1_waybel30 A B) (k1_waybel30 A C)) (k1_waybel30 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t27_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ( ((k1_card_1 B) = (k1_waybel31 A))  =>  ((k1_waybel31 A) = (k1_waybel31 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ) ) ).
tt(t27_waybel32,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_waybel_0 A B C) => (r1_waybel_0 A (k2_waybel32 A B) C)) ) ) ) ) ) ) ).
tt(t27_waybel33,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v1_waybel33 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_compts_1 A) & (v7_pre_topc A)) ) ) ).
tt(t27_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E A))  =>  (! [F:$i] :  ( ((v4_waybel11 F) & (m1_yellow_9 F (k1_yellow_2 B A (k1_waybel34 A B C))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 D) (u1_struct_0 F)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 F))))) )  =>  ( ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 B) (u1_struct_0 A) G (k1_waybel34 A B C)) &  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 F) (u1_struct_0 D) (u1_struct_0 E) H G) & (v2_waybel34 G D E)) )  => (v1_t_0topsp H D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) <=>  ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D A) => (m1_subset_1 (k1_funct_1 C D) (u1_struct_0 (k3_waybel_3 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r2_hidden (k1_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))) (k8_funcop_1 (k1_zfmisc_1 (u1_struct_0 A)) (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) (k7_waybel_4 A B)) (u1_orders_2 (k8_waybel_4 A)))) ) ) ) ).
tt(t27_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ( (! [E:$i] :  ((m1_subset_1 E B) => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k1_waybel_5 B (u1_struct_0 A) C D E)) A)) )  => (v1_waybel_0 (k2_relset_1 (u1_struct_0 A) (k5_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D))) A)) ) ) ) ) ) ) ) ) ).
tt(t27_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) <=> (v2_waybel_6 B A)) ) ) ) ) ).
tt(t27_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (u1_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (u1_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))))) ) ) )  =>  (! [C:$i] :  ((r1_waybel_7 A B C) <=> (r2_waybel_7 A B C)) ) ) ) ) ) ).
tt(t27_waybel_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_1 A))) =>  ((r1_waybel_3 (k3_yellow_1 A) B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ((r1_tarski C (k5_setfam_1 A D)) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski B (k3_tarski E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A C) A A)) )  => (v4_pre_topc (k6_waybel_0 A B) A)) ) ) ) ) ).
tt(t27_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((m1_subset_1 (k4_struct_0 A) (u1_struct_0 (k5_weddwitt A B))) & (m1_subset_1 (k1_group_1 A) (u1_struct_0 (k5_weddwitt A B)))) ) ) ) ) ).
tt(t27_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((v2_compts_1 B (k3_pcomps_1 A)) =>  ( (B = k1_xboole_0)  | (v5_pre_topc (k6_weierstr A B) (k3_pcomps_1 A) k3_topmetr)) ) ) ) ) ) ).
tt(t27_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((v2_wellord1 C) & (r2_hidden A (k1_wellord1 C B)))  =>  ((k1_wellord1 (k2_wellord1 C (k1_wellord1 C B)) A) = (k1_wellord1 C A)) ) ) ) ) ) ).
tt(t27_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ((k3_int_2 A B) = (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t27_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k3_xboole_0 A C) (k3_xboole_0 B D))) ) ) ) ) ).
tt(t27_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k7_xboolean A B)) = (k6_xboolean A (k6_xboolean A B))) ) ) ) ) ).
tt(t27_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (A = (k2_xcmplx_0 (k6_xcmplx_0 A B) B)) ) ) ) ) ).
tt(t27_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((k2_xcmplx_0 A B) = k6_numbers) ) )  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t27_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k10_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ).
tt(t27_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k4_xxreal_0 B D) (k4_xxreal_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k2_xxreal_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t27_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_xxreal_2 (k3_xxreal_1 A B)) = A) ) ) ) ) ) ).
tt(t27_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((k2_xxreal_3 (k1_xxreal_3 (k2_xxreal_3 A) B)) = (k3_xxreal_3 A B))  &  ((k2_xxreal_3 (k1_xxreal_3 (k2_xxreal_3 A) B)) = (k1_xxreal_3 A (k2_xxreal_3 B))) ) ) ) ) ) ).
tt(t27_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((r2_yellow_0 A C) =>  ((k2_yellow_0 A C) = (k2_yellow_0 B C)) ) ) ) ) ) ) ) ).
tt(t27_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k6_yellow_3 A B (k3_waybel_0 A C) (k3_waybel_0 B D)) = (k3_waybel_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t27_yellow12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_yellow_0 (k5_yellow_0 A B) A) => (v1_waybel_0 B A)) ) ) ) ) ).
tt(t27_yellow13,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_cantor_1 B A) &  ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (m2_yellow13 B A)) ) ) ) ).
tt(t27_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v6_waybel_3 A))  => (v6_waybel_3 B)) ) ) ) ) ).
tt(t27_yellow15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~ (v1_finset_1 B))  =>  ((k1_card_1 B) = (k1_card_1 (k11_waybel_0 A B))) ) ) ) ) ) ).
tt(t27_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_waybel_0 C B) & (m1_yellow_0 C B)) )  =>  ((v4_waybel_0 C A) & (m1_yellow_0 C A)) ) ) ) ) ) ) ).
tt(t27_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  ((r2_yellow18 A B) =>  ((r1_yellow18 A C) <=> (r3_yellow18 B C)) ) ) ) ) ) ) ) ).
tt(t27_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_subset_1 C (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  ((r2_hidden B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_waybel_7 A C D) => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((k6_yellow_1 k1_xboole_0 A) = (g1_orders_2 (k1_tarski k1_xboole_0) (k6_partfun1 (k1_tarski k1_xboole_0)))) ) ) ).
tt(t27_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B C D) = k1_xboole_0) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 B C D)) =>  ((k6_functor0 B A (k10_functor0 A B) C D E) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_yellow_0 A B)) )  =>  (! [B:$i] :  ((r1_yellow_0 A B) &  ((k1_yellow_0 A B) = (k1_yellow_0 A (k3_xboole_0 B (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t27_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v12_waybel_0 (k6_yellow_3 A B C D) (k3_yellow_3 A B)) =>  ((v12_waybel_0 C A) & (v12_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_lattice3 A D B) & (r2_lattice3 A E C))  => (r2_lattice3 A (k2_yellow_4 A D E) (k13_lattice3 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_yellow_5 A B (k1_yellow_5 A C D)) => (r2_yellow_5 A B C)) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_yellow_1 (u1_struct_0 B) C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_yellow_6 A B C))) =>  ( (F = (k7_yellow_3 B (k5_yellow_1 (u1_struct_0 B) C) D E))  =>  ((k2_waybel_0 A (k8_yellow_6 A B C) F) = (k3_funct_2 (u1_struct_0 (k3_waybel_3 (u1_struct_0 B) C D)) (u1_struct_0 A) (u1_waybel_0 A (k7_yellow_6 (u1_struct_0 B) A C D)) (k4_waybel_3 (u1_struct_0 B) C E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v1_waybel_0 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))))  <=>  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t27_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B (k1_tops_1 A C)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((r1_tarski D C) & (r2_hidden B (k1_tops_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t27_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 B A) &  ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t27_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_tarski A B))  <=>  (C = (k2_tarski (k4_tarski A (k1_funct_1 C A)) (k4_tarski B (k1_funct_1 C B)))) ) ) ) ) ) ).
tt(t27_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  ( ((k27_zf_lang A) = (k25_zf_lang (k21_zf_lang A)))  &  ((k27_zf_lang A) = (k26_zf_lang (k22_zf_lang A))) ) ) ) ) ).
tt(t27_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 A 1) = 3)  => (v5_zf_lang A)) ) ) ).
tt(t27_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (~ (r2_ordinal2 (k2_ordinal1 A) B)) ) ) ) ) ).
tt(t27_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((k4_struct_0 B) = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t280_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xboole_0 (k3_xxreal_1 C A) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t281_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 k2_xxreal_0 B)) = (k3_xxreal_1 B A)) ) ) ) ) ).
tt(t282_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 k2_xxreal_0 B)) = (k4_xxreal_1 B A)) ) ) ) ) ).
tt(t283_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 k2_xxreal_0 B)) = (k3_xxreal_1 B A)) ) ) ) ) ).
tt(t284_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 B k1_xxreal_0)) = (k2_xxreal_1 A B)) ) ) ) ) ).
tt(t285_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 B k1_xxreal_0)) = (k4_xxreal_1 A B)) ) ) ) ) ).
tt(t286_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 k2_xxreal_0 B)) = (k1_xxreal_1 B A)) ) ) ) ) ).
tt(t287_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 k2_xxreal_0 B)) = (k2_xxreal_1 B A)) ) ) ) ) ).
tt(t288_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 k2_xxreal_0 B)) = (k4_xxreal_1 B A)) ) ) ) ) ).
tt(t289_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 k2_xxreal_0 B)) = (k1_xxreal_1 B A)) ) ) ) ) ).
tt(t28_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_abcmiz_0 A B (k6_finseq_1 (u1_abcmiz_0 A))) = (k12_finseq_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t28_abcmiz_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) => (r2_hidden (k4_tarski (k4_subset_1 k2_abcmiz_1 (k3_abcmiz_1 B) (k6_domain_1 k2_abcmiz_1 B)) A) k2_abcmiz_1)) ) ) ) ).
tt(t28_abcmiz_a,ax, (k20_abcmiz_1 = (k2_zfmisc_1 (k1_enumset1 k6_abcmiz_1 k7_abcmiz_1 k8_abcmiz_1) (k2_zfmisc_1 k4_abcmiz_1 k5_numbers))) ).
tt(t28_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( ((k18_complex1 A) = (k18_complex1 B))  &  ( (~  (A = B) )  &  (~  (A = (k4_xcmplx_0 B)) ) ) ) ) ) ) ) ) ).
tt(t28_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_aff_1 A B C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~  (E = F) )  &  ((r2_hidden E D) &  ((r2_hidden F D) & (r2_analoaf A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 C A) &  ((v1_aff_1 D A) &  ((r2_hidden B C) & (r1_tarski D C)) ) )  => (r1_tarski (k2_aff_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t28_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ( ( ((k1_ordinal4 A B) = (k1_ordinal4 C B))  |  ((k1_ordinal4 B A) = (k1_ordinal4 B C)) )  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t28_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (v6_membered C))  =>  ( ((r1_afinsq_2 B C) & (r2_hidden A (k5_card_1 B)))  => (r2_hidden (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 B C)) A) B)) ) ) ) ) ) ) ).
tt(t28_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ( (D = (k5_afproj A B))  &  ( ((k4_tarski C 1) = E)  &  ((v1_aff_1 B A) & (v1_aff_1 C A)) ) )  =>  ((r1_incsp_1 (k13_afproj A) D E) <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_afvect0 A B C) = C)  <=>  ( (C = B)  | (r1_afvect0 A C B)) ) ) ) ) ) ) ) ).
tt(t28_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) =>  (! [C:$i] :  ((m1_algspec1 C A) =>  (? [D:$i] :  ((m1_algspec1 D B) & (r1_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t28_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_tarski (k2_zfmisc_1 (k11_algstr_4 A B) (k1_tarski B)) (k12_algstr_4 A))) ) ) ) ).
tt(t28_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_2 B A) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_altcat_1 A C D) = (k1_altcat_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_altcat_3 B A) & (v7_altcat_3 C A))  => (r2_altcat_3 A B C)) ) ) ) ) ) ) ).
tt(t28_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v3_altcat_3 (k6_functor0 A B C D E F) B (k3_functor0 A B C D) (k3_functor0 A B C E))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v3_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ami_2,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ((k9_xtuple_0 A) = k1_ami_2) ) ) ).
tt(t28_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  => (r2_hidden A (k8_struct_0 k1_ami_3))) ) ).
tt(t28_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  => (r2_hidden (k6_ami_wstd A B C) (k1_relset_1 k5_numbers C))) ) ) ) ) ) ).
tt(t28_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analmetr A B C))) =>  (~  ((r1_analmetr A B C) &  ((r4_analmetr (k2_analmetr A B C) D E F G) &  ((r4_analmetr (k2_analmetr A B C) D E H I) &  ( (~  (D = E) )  &  (~ (r2_analoaf (k2_analmetr A B C) F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((k3_rlvect_1 A (k1_rlvect_1 A B D) (k1_rlvect_1 A C E)) = (k4_struct_0 A))  =>  ( (D = k6_numbers)  &  (E = k6_numbers) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_analoaf A)))  &  ((v2_analoaf (k2_analoaf A)) &  ((v3_analoaf (k2_analoaf A)) & (l1_analoaf (k2_analoaf A))) ) ) ) ) ) ).
tt(t28_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((r1_analoaf A D E F G) <=>  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) &  ( (~  (H = I) )  &  ((r2_analort A B C H I D E) & (r2_analort A B C H I F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) &  ((r1_collsp (k5_anproj_1 A) B C F) & (r1_collsp (k5_anproj_1 A) D E F)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) &  ((r1_collsp (k5_anproj_1 A) B C F) & (r1_collsp (k5_anproj_1 A) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( ((k6_unialg_2 A) = k1_xboole_0)  => (v1_unialg_2 (k1_struct_0 A) A)) ) ) ).
tt(t28_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k57_aofa_i00 A B D E G F)) G) = (k2_xcmplx_0 (k21_aofa_i00 B k4_numbers C G) F))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = G) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k57_aofa_i00 A B D E G F)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v6_armstrng B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ((v8_armstrng (k8_armstrng A B) A) &  ((v9_armstrng (k8_armstrng A B) A) & (v10_armstrng (k8_armstrng A B) A)) ) ) ) ) ) ).
tt(t28_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ((r1_arytm_2 B A) =>  ( ((k1_arytm_1 A B) = k11_arytm_3)  |  ( (C = k11_arytm_3)  |  ((k2_arytm_1 (k8_arytm_2 C B) (k8_arytm_2 C A)) = (k4_tarski k11_arytm_3 (k8_arytm_2 C (k1_arytm_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  ( (~  (A = k1_xboole_0) )  =>  ((k4_arytm_3 (k9_ordinal3 B A) (k9_ordinal3 C A)) = (k4_arytm_3 B C)) ) ) ) ) ) ) ) ).
tt(t28_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  => (r2_hidden A (k8_asympt_0 A))) ) ).
tt(t28_asympt_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((r2_funct_2 k5_numbers k1_numbers A (k1_asympt_1 2 1 k6_numbers)) &  ((r2_funct_2 k5_numbers k1_numbers B (k1_asympt_1 2 1 1)) &  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ) ).
tt(t28_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_autalg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_autalg_1 A B))) =>  (! [E:$i] :  ((m1_autalg_1 E (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  (! [F:$i] :  ((m1_autalg_1 F (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 (k7_autalg_1 A B) C D) = (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (u3_msualg_1 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k4_autgroup A)) =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k6_autgroup A (k1_group_1 A)) B) B) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B (k6_autgroup A (k1_group_1 A))) B)) ) ) ) ) ).
tt(t28_bagorder,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_finset_1 A)) )  =>  (~ (v2_wellord1 (k6_bagorder A))) ) ) ).
tt(t28_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k2_bcialg_1 A C) (k2_bcialg_1 A B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(t28_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_bcialg_2 (k1_bcialg_1 A B (k2_bcialg_1 A (k2_bcialg_1 A B))) A) & (m1_subset_1 (k1_bcialg_1 A B (k2_bcialg_1 A (k2_bcialg_1 A B))) (u1_struct_0 A))) ) ) ) ) ).
tt(t28_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A (k1_bcialg_1 A B C) C)) ) ) ) ) ) ) ) ).
tt(t28_bcialg_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v2_bcialg_4 B) & (l1_bcialg_4 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_2 B C D A) = (k1_bcialg_1 B C (k6_bcialg_4 B D A))) ) ) ) ) ) ) ) ) ).
tt(t28_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (A = (k2_bcialg_5 A B C D))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D A) |  ((v8_bcialg_1 E) & (m1_bcialg_5 E A (k2_nat_1 A 1) A (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  ( ((v1_bcialg_6 B A) &  ((v1_bcialg_6 C A) & (r2_hidden B (k7_bcialg_1 A C))) )  =>  ((k4_bcialg_6 A B) = (k4_bcialg_6 A C)) ) ) ) ) ) ) ) ).
tt(t28_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B C (k1_bcialg_1 B C D)) = (k1_bcialg_1 B D (k1_bcialg_1 B D C))) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t28_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k3_bhsp_1 A B))) ) ) ) ).
tt(t28_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k3_normsp_1 A D E) (k5_algstr_0 A B C)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k3_normsp_1 A D E) (k5_algstr_0 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((m2_valued_0 B (u1_struct_0 A) C) & (v1_bhsp_2 C A))  =>  ((k1_bhsp_2 A B) = (k1_bhsp_2 A C)) ) ) ) ) ) ) ) ).
tt(t28_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~  ((k1_normsp_1 B C D) = (k4_struct_0 B)) )  &  ((k1_seq_1 A D) = (k10_real_1 (k3_bhsp_1 B (k1_normsp_1 B C (k2_nat_1 D 1))) (k3_bhsp_1 B (k1_normsp_1 B C D)))) ) ) )  & (v2_comseq_2 A))  =>  ((r1_xxreal_0 1 (k2_seq_2 A)) | (v2_bhsp_4 C B)) ) ) ) ) ) ) ) ).
tt(t28_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear H A B C) &  ((v2_bilinear H A B C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H (k1_algstr_0 B D E) (k1_algstr_0 C F G)) = (k1_algstr_0 A (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H D F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H D G)) (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H E F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_binari_3 (k2_xcmplx_0 A 1) (k5_series_1 2 A)) = (k7_finseq_1 (k5_euclid A) (k10_binarith k5_numbers 1))) ) ) ).
tt(t28_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((k6_int_1 B (k5_series_1 2 A)) = (k6_int_1 C (k5_series_1 2 A)))  =>  ( ( (~  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C)) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  (~ (r1_xxreal_0 k6_numbers C)) ) ) )  |  ((k2_binari_4 A B) = (k2_binari_4 A C)) ) ) ) ) ) ) ) ) ).
tt(t28_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r1_boolealg A C (k3_lattices A B (k1_boolealg A C B)))) ) ) ) ) ) ) ).
tt(t28_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B) C))) ) ) ) ) ) ).
tt(t28_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  => (r1_xxreal_0 (k5_seq_4 A) (k4_seq_4 A))) ) ).
tt(t28_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k1_borsuk_5)  =>  ((k2_pre_topc k3_topmetr A) = (u1_struct_0 k3_topmetr)) ) ) ) ).
tt(t28_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  ( ( (A = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 k6_numbers (k10_real_1 1 2)) (k1_rcomp_1 k6_numbers 1)))  &  (B = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 (k10_real_1 1 2) 1) (k1_rcomp_1 k6_numbers 1))) )  =>  ((k2_xboole_0 (k2_struct_0 (k1_pre_topc (k2_borsuk_1 k5_topmetr k5_topmetr) A)) (k2_struct_0 (k1_pre_topc (k2_borsuk_1 k5_topmetr k5_topmetr) B))) = (k2_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) ) ) ) ) ) ).
tt(t28_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ((r1_zfmisc_1 A B F) =>  ( ((k1_funct_1 (k1_borsuk_7 A B F C D E) A) = C)  &  ( ((k1_funct_1 (k1_borsuk_7 A B F C D E) B) = D)  &  ((k1_funct_1 (k1_borsuk_7 A B F C D E) F) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_bspace A))) =>  ((k4_vectsp_1 k2_bspace (k7_bspace A) (k1_group_1 k2_bspace) B) = B) ) ) ) ).
tt(t28_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( (F = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B H) (k16_funcop_1 C I)) (k16_funcop_1 D J)) (k16_funcop_1 E K)) (k16_funcop_1 A G)))  =>  ((k10_xtuple_0 F) = (k3_enumset1 (k1_funct_1 F A) (k1_funct_1 F B) (k1_funct_1 F C) (k1_funct_1 F D) (k1_funct_1 F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_bvfunc_1 A B (k10_eqrel_1 A))) ) ) ) ).
tt(t28_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A B) (k10_bvfunc_1 A (k1_bvfunc_1 A C) (k9_bvfunc_1 A C B))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t28_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_funct_2 A k6_margrel1 (k6_bvfunc26 A (k11_bvfunc_1 A) (k11_bvfunc_1 A)) (k12_bvfunc_1 A)) &  ((r2_funct_2 A k6_margrel1 (k6_bvfunc26 A (k11_bvfunc_1 A) (k12_bvfunc_1 A)) (k11_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A (k12_bvfunc_1 A) (k12_bvfunc_1 A)) (k11_bvfunc_1 A))) ) ) ) ).
tt(t28_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_1 A C D) B E) (k6_bvfunc_1 A C (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k7_bvfunc_2 A C B E) (k1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E) (k6_bvfunc_2 A (k9_bvfunc_1 A C (k1_bvfunc_1 A D)) B E))))) ) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B D) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A (k5_bvfunc_1 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t28_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C E)) (k5_bvfunc_1 A (k1_bvfunc_1 A D) (k1_bvfunc_1 A E))) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t28_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A B C) B)) ) ) ) ) ) ).
tt(t28_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_c0sp1 A))) =>  ( (B = (k4_struct_0 (k11_c0sp1 A)))  =>  (k6_numbers = (k1_normsp_0 (k11_c0sp1 A) B)) ) ) ) ) ) ).
tt(t28_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v1_rlsub_1 (k6_c0sp2 A) (k10_funcsdom (u1_struct_0 A)))) ) ).
tt(t28_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) E (k2_valuat_1 A E)) =>  (! [G:$i] :  ((m1_subset_1 G E) =>  ( (~ (r2_hidden C (k24_qc_lang1 A (k11_cqc_lang A D B))))  => (r2_relset_1 (k3_qc_lang1 A) E (k2_partfun1 (k3_qc_lang1 A) E (k1_sublemma A E (k1_sublemma A E F (k12_sublemma A E C G)) (k12_sublemma A E D G)) (k24_qc_lang1 A B)) (k2_partfun1 (k3_qc_lang1 A) E (k1_sublemma A E F (k12_sublemma A E D G)) (k24_qc_lang1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C B)))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) (k5_calcul_2 A (k4_finseq_5 (k3_cqc_lang A) B)))))) ) ) ) ) ) ) ).
tt(t28_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 A (k1_tarski B)) <=>  (? [C:$i] :  (A = (k1_tarski C)) ) ) ) ) ).
tt(t28_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k3_card_2 A (k1_card_2 B C)) = (k2_card_2 (k3_card_2 A B) (k3_card_2 A C))) ) ) ) ) ) ) ).
tt(t28_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_card_1 (k1_funct_1 A B)) = (k1_funct_1 A B)) ) ) ) ) ).
tt(t28_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((r2_hidden (k1_card_5 A) A) => (v2_card_1 A)) ) ) ).
tt(t28_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( (r3_card_fil & (v2_card_1 A))  => (v5_card_fil A)) ) ) ).
tt(t28_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((k8_relat_1 C (k1_tarski A)) = (k8_relat_1 (k5_relat_1 C B) (k1_tarski A)))  =>  ((k2_card_fin D C A) = (k2_card_fin D (k5_relat_1 C B) A)) ) ) ) ) ) ) ) ).
tt(t28_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v4_card_lar A) => (v2_card_1 A)) ) ) ).
tt(t28_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((k5_cat_1 A B C C D (k4_cat_1 A C)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t28_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( ((k3_graph_1 (k8_cat_2 A B) (k10_cat_2 A B C D)) = (k9_cat_2 A B (k3_graph_1 A C) (k3_graph_1 B D)))  &  ((k4_graph_1 (k8_cat_2 A B) (k10_cat_2 A B C D)) = (k9_cat_2 A B (k4_graph_1 A C) (k4_graph_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t28_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( ((v1_cat_3 D A B C) & (v7_cat_1 D A B C))  => (v9_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t28_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B (k2_cat_4 A B (k1_cat_4 A))) = k1_xboole_0) )  &  (~  ((k2_cat_1 A B (k2_cat_4 A (k1_cat_4 A) B)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t28_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u4_struct_0 A) (k10_cat_5 A (k4_graph_1 A B))) => (r2_hidden (k1_cat_1 A B C) (k10_cat_5 A (k3_graph_1 A B)))) ) ) ) ) ) ).
tt(t28_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k24_binop_2 2 (k23_binop_2 A 1)) B) =>  ((k5_card_1 (k2_catalan2 B (k23_binop_2 A 1))) = (k21_binop_2 (k6_newton (k23_binop_2 A 1) B) (k6_newton A B))) ) ) ) ) ) ).
tt(t28_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C D) (k13_catalg_1 A))) <=>  (? [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) &  ( (E = (k2_finseq_4 (u4_struct_0 A) F G))  &  ( ((k3_graph_1 A G) = B)  &  ( ((k4_graph_1 A G) = C)  &  ( ((k3_graph_1 A F) = C)  &  ((k4_graph_1 A F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k7_cc0sp1 A)))  &  ((v13_algstr_0 (k7_cc0sp1 A)) &  ((v2_rlvect_1 (k7_cc0sp1 A)) &  ((v3_rlvect_1 (k7_cc0sp1 A)) &  ((v4_rlvect_1 (k7_cc0sp1 A)) &  ((v3_group_1 (k7_cc0sp1 A)) &  ((v1_vectsp_1 (k7_cc0sp1 A)) &  ((v3_vectsp_1 (k7_cc0sp1 A)) &  ((v3_normsp_0 (k7_cc0sp1 A)) &  ((v4_normsp_0 (k7_cc0sp1 A)) &  ((v2_clvect_1 (k7_cc0sp1 A)) &  ((v3_clvect_1 (k7_cc0sp1 A)) &  ((v4_clvect_1 (k7_cc0sp1 A)) &  ((v5_clvect_1 (k7_cc0sp1 A)) &  ((v8_clvect_1 (k7_cc0sp1 A)) &  ((v2_cfuncdom (k7_cc0sp1 A)) &  ((v5_clopban2 (k7_cc0sp1 A)) & (l1_clopban2 (k7_cc0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_cc0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cc0sp2 A))) => (r1_xxreal_0 (k1_normsp_0 (k5_cc0sp2 A) (k3_rlvect_1 (k5_cc0sp2 A) B C)) (k7_real_1 (k1_normsp_0 (k5_cc0sp2 A) B) (k1_normsp_0 (k5_cc0sp2 A) C)))) ) ) ) ) ) ).
tt(t28_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v3_funct_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_comseq_2 A) = (k3_funct_2 k5_numbers k2_numbers A B)) ) ) ) ) ) ).
tt(t28_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v6_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski C (k1_relset_1 k2_numbers (k2_valued_1 k2_numbers k2_numbers k2_numbers A B))) &  ((r2_cfdiff_1 A C) & (r2_cfdiff_1 B C)) )  =>  ((r2_cfdiff_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_hidden D C) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers A B) C) D) = (k8_complex1 (k2_cfdiff_1 A D) (k2_cfdiff_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_struct_0 (k7_cfuncdom A)) = (k5_cfuncdom A)) ) ) ).
tt(t28_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B (k46_valued_1 A k2_numbers k2_numbers C D)) (k46_valued_1 A k2_numbers k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C) D))) ) ) ) ) ) ) ) ).
tt(t28_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden A (k10_cgames_1 B)) &  ( (~  (A = B) )  &  (~ (r2_hidden (k9_cgames_1 A) (k9_cgames_1 B))) ) ) ) ) ) ) ) ).
tt(t28_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 C F))) )  =>  ((r1_tarski (k3_chain_1 A D E) (k3_chain_1 A B C)) <=>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) &  ((r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 E F)) & (r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k15_glib_001 A (k7_glib_001 A B C)) = (k2_nat_1 (k15_glib_001 A B) (k15_glib_001 A C))) ) ) ) ) ) ) ) ).
tt(t28_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  (! [C:$i] :  ((m1_circcmb3 C A) =>  (! [D:$i] :  ((m2_circcmb3 D A B) =>  (! [E:$i] :  ((m2_circcmb3 E A C) =>  ((v4_msafree2 (k3_circcomb B C D E) (k2_circcomb B C)) & (l3_msualg_1 (k3_circcomb B C D E) (k2_circcomb B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ( ((r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D)) & (r1_partfun1 (u4_msualg_1 A C) (u4_msualg_1 B D)))  =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k2_circcomb A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( (E = F)  => (r1_funct_2 (k3_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k4_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k3_msualg_1 A F C) (k4_msualg_1 A F C) (k5_msualg_1 (k2_circcomb A B) E (k3_circcomb A B C D)) (k5_msualg_1 A F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_circtrm1 A B C D) =>  ( ((k7_relat_1 C (k2_msafree2 A)) = (k2_msafree2 B))  &  ((k7_relat_1 C (k3_msafree2 A)) = (k3_msafree2 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A (k1_classes1 B)) & (r1_tarski C (k1_classes1 B)))  => (r1_tarski (k2_zfmisc_1 A C) (k1_classes1 B))) ) ) ) ).
tt(t28_classes2,ax, (! [A:$i] : (r1_tarski (k4_classes1 (k1_card_1 (k1_classes1 A))) (k1_classes1 A))) ).
tt(t28_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) &  ((v2_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k11_clopban1 A B C) C)) ) ) ) ) ) ).
tt(t28_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k4_normsp_0 A B) D)) & (r1_xxreal_0 (k1_seq_1 (k4_normsp_0 A B) D) (k1_seq_1 (k4_normsp_0 A C) D))) ) )  & (v2_clopban3 C A))  =>  ((v2_clopban3 B A) & (r1_xxreal_0 (k4_series_1 (k4_normsp_0 A B)) (k4_series_1 (k4_normsp_0 A C)))) ) ) ) ) ) ) ) ).
tt(t28_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 1 (k4_series_1 (k4_sin_cos (k1_normsp_0 A B))))) ) ) ) ).
tt(t28_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B B) =>  ( ((r1_pboole A C B) & (r6_pboole A (k16_pralg_1 A D C) C))  <=> (r1_pboole A C (k5_closure1 A B D))) ) ) ) ) ) ) ) ).
tt(t28_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_funct_1 (k6_partfun1 (k6_closure2 A B))) &  ((v1_funct_2 (k6_partfun1 (k6_closure2 A B)) (k6_closure2 A B) (k6_closure2 A B)) &  ((v9_closure2 (k6_partfun1 (k6_closure2 A B)) A B) & (m1_subset_1 (k6_partfun1 (k6_closure2 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) ) ) ) ).
tt(t28_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((r1_struct_0 B C) => (r1_struct_0 A C)) ) ) ) ) ) ).
tt(t28_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k3_normsp_1 A D E) (k5_algstr_0 A B C)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k3_normsp_1 A D E) (k5_algstr_0 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~  ((k1_normsp_1 A B D) = (k4_struct_0 A)) )  &  ((k8_nat_1 k1_numbers C D) = (k10_real_1 (k13_csspace A (k1_normsp_1 A B (k2_nat_1 D 1))) (k13_csspace A (k1_normsp_1 A B D)))) ) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_clvect_3 B A)) ) ) ) ) ) ) ) ).
tt(t28_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v8_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v8_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( ((k6_cohsp_1 A B C) = (k6_cohsp_1 A B D))  => (r2_funct_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t28_coh_sp,ax, (! [A:$i] : (r2_hidden (k1_eqrel_1 A) (k14_coh_sp A))) ).
tt(t28_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_incsp_1 (k1_combgras A B)))) =>  ( ((v3_combgras C A B) &  ((v3_combgras D A B) &  ((k1_setfam_1 C) = (k1_setfam_1 D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_complex1,ax, ((k15_complex1 k6_numbers) = k6_numbers) ).
tt(t28_complex2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers B))  =>  ((k1_comptrig (k3_xcmplx_0 A B)) = (k1_comptrig (k4_xcmplx_0 A))) ) ) ) ) ) ).
tt(t28_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k8_group_1 k1_complfld B (k3_vectsp_1 k1_complfld C A)) = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld B C) A)) ) ) ) ) ) ) ) ).
tt(t28_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k1_valued_1 A (k1_valued_1 B C)) = (k1_valued_1 (k1_valued_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t28_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_finset_1 B))  & (v1_xboole_0 (k2_topgen_1 A B))) ) ) ) ) ) ) ).
tt(t28_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  ((k8_compos_1 A (k4_compos_1 A) B) = B) ) ) ) ) ).
tt(t28_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_compos_2 B C) =>  ((r1_xxreal_0 (k62_valued_1 B) D) |  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_comptrig,ax, ((k10_xtuple_0 k16_sin_cos) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t28_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  => (m2_rfunct_3 A (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers))) ) ).
tt(t28_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k11_complex1 (k15_complex1 (k3_comseq_2 A)) (k15_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t28_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers (k10_comseq_3 A) (k10_comseq_3 B)) (k10_comseq_3 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ).
tt(t28_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) )  =>  ((r2_conlat_1 A B C) <=> (r1_tarski (u3_conlat_1 A C) (u3_conlat_1 A B))) ) ) ) ) ) ) ).
tt(t28_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_connsp_1 A B C)) ) ) )  => (v1_connsp_1 A)) ) ) ).
tt(t28_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (m2_connsp_2 (k2_struct_0 A) A B)) ) ) ) ).
tt(t28_connsp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v3_pre_topc (k4_connsp_3 A B C) (k1_pre_topc A C))) ) ) ) ) ) ) ).
tt(t28_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((v2_convex1 D A) &  ((k3_rlvect_2 A D) = (k7_domain_1 (u1_struct_0 A) B C)) )  =>  ( (B = C)  |  ( ((k2_xcmplx_0 (k1_funct_1 D B) (k1_funct_1 D C)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 D B)) & (r1_xxreal_0 k6_numbers (k1_funct_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) => (r1_convex4 A (k7_convex4 A B (k5_convex4 A C D)) (k5_convex4 A (k7_convex4 A B C) (k7_convex4 A B D)))) ) ) ) ) ) ) ) ).
tt(t28_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k6_qc_lang3 A (k13_cqc_lang A C B)) = (k6_qc_lang3 A C)) ) ) ) ) ) ) ).
tt(t28_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k14_cqc_sim1 A (k6_cqc_lang A B)) = (k6_cqc_lang A (k14_cqc_sim1 A B))) ) ) ) ) ).
tt(t28_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (! [E:$i] :  ((m2_finseq_1 E (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 D)) & (r1_cqc_the1 A D B C)) )  => (r1_cqc_the1 A (k8_finseq_1 (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1) E D) (k2_nat_1 B (k3_finseq_1 E)) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden C (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C B) (k12_cqc_lang A D B)) A)) ) ) ) ) ) ) ) ) ).
tt(t28_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r5_cqc_the3 A B C) & (r5_cqc_the3 A C D))  => (r5_cqc_the3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t28_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_2 A) & (v1_comseq_2 B))  => (v1_comseq_2 (k2_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(t28_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k12_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) = (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k12_csspace A B D) (k12_csspace A B E)) (k12_csspace A C D)) (k12_csspace A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_decomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  ((v8_decomp_1 C A B) & (v13_decomp_1 C A B)) ) ) ) ) ) ) ) ).
tt(t28_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (? [J:$i] :  ((m2_finseq_1 J A) &  ((v3_card_1 J 8) &  ( ((k1_funct_1 J 1) = B)  &  ( ((k1_funct_1 J 2) = C)  &  ( ((k1_funct_1 J 3) = D)  &  ( ((k1_funct_1 J 4) = E)  &  ( ((k1_funct_1 J 5) = F)  &  ( ((k1_funct_1 J 6) = G)  &  ( ((k1_funct_1 J 7) = H)  &  ((k1_funct_1 J 8) = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 B)) &  ((v4_dickson A) &  ((u1_struct_0 A) = (u1_struct_0 B)) ) )  => (v4_dickson B)) ) ) ) ) ).
tt(t28_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) (k2_nat_1 (k4_nat_1 2 A) 1)) C) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) (k2_nat_1 (k4_nat_1 2 A) 1)) (k7_real_1 (k7_real_1 C (k8_real_1 A B)) (k10_real_1 B 2)))) ) ) ) ) ) ) ) ) ).
tt(t28_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers G H) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 H)) (k8_real_1 B H)) C)) ) )  & (r1_zfmisc_1 D E F))  =>  ((k10_diff_1 G D E F) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers D (k26_valued_1 k1_numbers k1_numbers E A)) B C) = (k7_real_1 (k9_diff_1 D B C) (k8_real_1 A (k9_diff_1 E B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) A) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t28_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_dilworth C (k5_yellow_0 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)))))  =>  ((v1_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t28_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_diraf A B C D) => (r3_diraf A B C D)) ) ) ) ) ) ) ) ) ).
tt(t28_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k9_subset_1 A B C) = (a_3_1_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t28_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 B))) =>  ( (~  (C = k6_numbers) )  =>  ((k2_binom (k9_int_3 B) (k11_algstr_0 (k9_int_3 B) C) A) = (k11_algstr_0 (k9_int_3 B) (k2_binom (k9_int_3 B) C A))) ) ) ) ) ) ) ) ).
tt(t28_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( (C = (k6_int_1 2 A))  =>  ((r1_xxreal_0 A 2) |  ( (~  (C = (k4_struct_0 (k9_int_3 A))) )  &  (~  ((k2_binom (k9_int_3 A) C B) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_ens_1 A))) =>  ( ((k3_graph_1 (k11_ens_1 A) B) = (k4_graph_1 (k11_ens_1 A) C))  =>  ((k1_cat_1 (k11_ens_1 A) C B) = (k6_ens_1 A (k15_ens_1 A C) (k15_ens_1 A B))) ) ) ) ) ) ) ) ).
tt(t28_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  => (v4_matrprob (k6_matrixr1 (k1_entropy1 A) B))) ) ) ) ) ).
tt(t28_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k6_enumset1 A B C D E F G H) = (k2_xboole_0 (k5_enumset1 A B C D E F G) (k1_tarski H))) ) ) ) ) ) ) ) ) ).
tt(t28_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [E:$i] :  ( ((v3_relat_2 E) &  ((v8_relat_2 E) &  ((v1_partfun1 E B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  ((r2_hidden A B) =>  ((r2_hidden (k4_tarski A C) (k5_eqrel_1 B D E)) <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  ((r1_xxreal_0 1 (k3_finseq_1 F)) &  ( (A = (k1_funct_1 F 1))  &  ( (C = (k1_funct_1 F (k3_finseq_1 F)))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 1 G) =>  ((r1_xxreal_0 (k3_finseq_1 F) G) | (r2_hidden (k4_tarski (k1_funct_1 F G) (k1_funct_1 F (k2_nat_1 G 1))) (k3_eqrel_1 B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v2_msafree B A) &  ((v1_msualg_6 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v1_msafree C A B) & (m1_msafree C A B))  =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( ((r2_pboole (u1_struct_0 A) D C) & (v1_msualg_6 (k12_msualg_2 A B D) A))  => (v2_msafree (k12_msualg_2 A B D) A)) ) ) ) ) ) ) ) ) ).
tt(t28_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u2_e_siec A)))) (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A))))) = k1_xboole_0)  &  ((k3_relat_1 (k4_relat_1 (k4_xboole_0 (u1_struct_0 A) (k10_xtuple_0 (u1_e_siec A)))) (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A))))) = k1_xboole_0) ) ) ) ).
tt(t28_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k3_rlvect_1 (k15_euclid A) B C) (k3_rlvect_1 (k15_euclid A) D E)) = (k9_binop_2 (k9_binop_2 (k9_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_euclid_3,ax, ((k3_euclid_3 (k4_struct_0 (k15_euclid 2))) = k6_numbers) ).
tt(t28_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 B (k7_euclid A C D)) = (k7_real_1 (k23_rvsum_1 B C) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t28_euclid_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = 3)  &  ((k3_finseq_1 B) = 3) )  =>  ((k14_rvsum_1 A B) = (k3_finseq_4 k1_numbers (k8_real_1 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k8_real_1 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k8_real_1 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ) ).
tt(t28_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ( (~ (r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) B C)) &  ((k4_euclid_3 B D E) = (k4_euclid_3 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ((k12_euclid (k6_euclid_7 B A)) = 1) ) ) ) ) ) ).
tt(t28_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k9_euclid 3 A 1) = A) ) ) ).
tt(t28_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_pcomps_1 (k14_euclid A)) = (k3_waybel18 (k2_finseq_1 A) (k7_funcop_1 (k2_finseq_1 A) k3_topmetr))) ) ) ).
tt(t28_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_rlvect_1 (k15_euclid A) (k4_struct_0 (k15_euclid A)) B) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ).
tt(t28_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid C)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid C)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid C)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid C)) =>  (~  ( (D = (k7_euclid C (k7_euclid C E (k9_euclid C (k8_euclid C F E) A)) (k9_euclid C (k8_euclid C G E) B)))  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (D = (k7_euclid C (k7_euclid C (k9_euclid C E H) (k9_euclid C F A)) (k9_euclid C G B)))  &  ((k7_real_1 (k7_real_1 H A) B) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_exchsort,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) & (v1_funct_1 A)) )  =>  ( ((v4_exchsort A) &  ((v1_finset_1 (k1_funct_1 A k1_xboole_0)) &  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  ((k1_funct_1 A B) = k1_xboole_0) )  => (r2_hidden (k1_ordinal1 B) (k9_xtuple_0 A))) ) ) ) )  =>  ((k4_exchsort A) = k1_xboole_0) ) ) ) ).
tt(t28_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_compos_1 B)) =>  ((k1_funct_1 (k2_extpro_1 A B (k3_compos_1 B C (k5_memstr_0 A B D)) D) (k4_struct_0 B)) = (k5_memstr_0 A B (k4_extpro_1 A B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((k3_supinf_2 (k2_extreal2 A B) (k1_extreal2 A B)) = (k3_supinf_2 A B)) ) ) ) ) ).
tt(t28_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 B) (k2_msafree2 A)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 A C))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)))  =>  ((k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) (k6_circuit2 (k2_circcomb A B) (k3_circcomb A B C D) E) (u1_struct_0 A)) = (k6_circuit2 A C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k3_facirc_1)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k3_facirc_1)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 C A) k3_facirc_1))) ) )  =>  ((k11_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) (k6_circuit2 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D) (k17_facirc_1 A B C)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_rcomp_1 (k1_relset_1 k1_numbers A)) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A (k1_relset_1 k1_numbers A))))  => (v1_rcomp_1 (k2_relset_1 k1_numbers A))) ) ) ).
tt(t28_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B)))) (k8_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t28_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9) A) B) = (k9_real_1 (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k2_sin_cos9 B))) (k10_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t28_fdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v4_fdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) => (r2_fdiff_1 B A)) ) ) ) ) ).
tt(t28_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_partfun1 A k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 A B) (k1_seq_1 A C))) (k5_square_1 (k9_real_1 B C)))) ) ) ) )  =>  ((r2_fdiff_1 A (k2_subset_1 k1_numbers)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers)))) ) ) ) ).
tt(t28_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) B) D) = (k10_prepower (k7_real_1 A D) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ( (B = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos C) (k1_taylor_1 2)) k24_sin_cos) k3_taylor_1))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos C) D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 B A) D) = (k10_real_1 (k7_real_1 (k1_seq_1 k24_sin_cos D) 1) (k9_real_1 (k1_seq_1 k24_sin_cos D) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))))) &  ((r2_relset_1 k1_numbers k1_numbers D (k47_valued_1 k1_numbers k1_numbers k1_numbers E F)) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ( ((k1_seq_1 E G) = (k5_square_1 A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers))  &  ( ((k1_seq_1 C G) = (k10_real_1 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C G) (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 C G)))  &  ( (~  (G = k6_numbers) )  &  (~ (r1_xxreal_0 A k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))) B) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k1_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))) B) G) = (k1_seq_1 k1_sin_cos6 (k10_real_1 G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k29_sin_cos))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k29_sin_cos) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k29_sin_cos) C) E) = (k7_real_1 (k10_real_1 (k8_real_1 A (k1_seq_1 k16_sin_cos E)) (k1_seq_1 k19_sin_cos E)) (k10_real_1 (k7_real_1 (k8_real_1 A E) B) (k5_square_1 (k1_seq_1 k19_sin_cos E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_fdiff_9))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_fdiff_9) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k1_fdiff_9) C) E) = (k7_real_1 (k10_real_1 A (k1_seq_1 k19_sin_cos E)) (k10_real_1 (k8_real_1 (k7_real_1 (k8_real_1 A E) B) (k1_seq_1 k16_sin_cos E)) (k5_square_1 (k1_seq_1 k19_sin_cos E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ff_siec,ax, (! [A:$i] :  ( ((v1_net_1 A) & (l1_petri A))  =>  ( ((k3_relat_1 (k17_ff_siec A) (k17_ff_siec A)) = (k17_ff_siec A))  &  ( ((k3_relat_1 (k4_xboole_0 (k17_ff_siec A) (k4_relat_1 (k2_net_1 A))) (k17_ff_siec A)) = k1_xboole_0)  &  ((k2_xboole_0 (k2_xboole_0 (k17_ff_siec A) (k2_relat_1 (k17_ff_siec A))) (k4_relat_1 (k2_net_1 A))) = (k2_xboole_0 (k10_ff_siec A) (k2_relat_1 (k10_ff_siec A)))) ) ) ) ) ).
tt(t28_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 2)) = (k6_xcmplx_0 (k1_pre_ff (k1_nat_1 A 3)) (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t28_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k4_nat_1 2 A)) = (k4_nat_1 (k1_pre_ff A) (k1_fib_num3 A))) ) ) ).
tt(t28_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_pre_ff A) = (k1_int_1 (k3_xcmplx_0 (k13_complex1 1 k1_fib_num) (k2_xcmplx_0 (k1_pre_ff (k2_xcmplx_0 A 1)) (k13_complex1 1 2))))) ) ) ) ).
tt(t28_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((r5_finseq_8 A C B) =>  (C = (k9_finseq_8 A C B)) ) ) ) ) ) ) ) ).
tt(t28_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_filter_0 A B B) = (k6_lattices A)) ) ) ) ) ).
tt(t28_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r5_binop_1 A C D) & (r5_binop_1 B E F))  <=> (r5_binop_1 (k2_zfmisc_1 A B) (k6_filter_1 A B C E) (k6_filter_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k6_filter_2 A C)) <=> (r3_lattices A B C)) ) ) ) ) ) ) ).
tt(t28_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden A (k4_finseq_1 B)) => (r2_hidden (k2_nat_1 (k3_finseq_1 C) A) (k4_finseq_1 (k7_finseq_1 C B)))) ) ) ) ) ) ) ).
tt(t28_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (C = (k2_partfun1 k5_numbers B D (k2_finseq_1 A)))  =>  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t28_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((r2_hidden B (k10_xtuple_0 A)) &  ((k1_tarski (k4_finseq_4 A B)) = (k8_relat_1 A (k1_tarski B))) ) ) ) ) ) ).
tt(t28_finseq_5,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k2_rfinseq A k6_numbers B) = B) ) ) ) ).
tt(t28_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  (~  ((k5_finseq_4 (k11_finseq_1 A C B) B) = (k10_finseq_1 A C)) ) ) ) ) ) ) ) ).
tt(t28_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((r1_xxreal_0 C 1) |  ((k2_finseq_7 A B 1 C) = (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k12_finseq_1 A (k7_partfun1 A B C)) (k17_finseq_1 A (k7_nat_d C 2) (k2_rfinseq A 1 B))) (k12_finseq_1 A (k7_partfun1 A B 1))) (k2_rfinseq A C B))) ) ) ) ) ) ) ) ) ).
tt(t28_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (r5_finseq_8 A B B)) ) ) ) ).
tt(t28_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v3_card_1 E B) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k1_finseqop A A A F (k1_finseqop A A A F C D) E) (k1_finseqop A A A F C (k1_finseqop A A A F D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k10_fintopo2 A B) (k10_fintopo2 A C)) (k10_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t28_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_subset_1 (u1_struct_0 A) (k3_fintopo3 A (k3_subset_1 (u1_struct_0 A) B) C)) = (k5_fintopo3 A B C)) ) ) ) ) ) ) ).
tt(t28_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  & (r1_fintopo4 A B C)) )  =>  ((v2_fin_topo B A) & (v3_fin_topo B A)) ) ) ) ) ) ) ) ).
tt(t28_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k7_flang_1 A (k4_flang_1 A (k2_flang_1 A)) B) = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ).
tt(t28_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_flang_2 A B C (k2_xcmplx_0 C 1)) = (k4_subset_1 (k3_catalan2 A) (k7_flang_1 A B C) (k7_flang_1 A B (k2_xcmplx_0 C 1)))) ) ) ) ) ) ).
tt(t28_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B (k1_flang_3 A C D)) =>  ((r1_xxreal_0 E k6_numbers) | (r1_tarski (k7_flang_1 A B E) (k1_flang_3 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (v1_xboole_0 A))  =>  ((k1_funct_1 (k7_finseq_1 A B) 1) = (k1_funct_1 A 1)) ) ) ) ) ) ).
tt(t28_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_fomodel1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_finseq_2 (k15_fomodel1 A)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) =>  ((v7_fomodel2 B (k6_domain_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) C) A) <=> (r2_hidden B (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t28_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_pcomps_1 A))) =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_pcomps_1 A)) B D) &  (C = E) )  =>  ((r1_metric_6 A B C) <=> (r1_frechet (k3_pcomps_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_frechet,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_frechet))) =>  ( ((v3_pre_topc A k3_frechet) & (r2_hidden k1_numbers A))  <=>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) &  ((v3_pre_topc B k3_topmetr) &  ((r1_tarski k5_numbers B) &  (A = (k2_xboole_0 (k7_subset_1 (u1_struct_0 k3_topmetr) B k5_numbers) (k1_tarski k1_numbers))) ) ) ) ) ) ) ) ).
tt(t28_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  => (r1_setfam_1 (k7_fsm_1 B C D (k2_nat_1 A 1)) (k7_fsm_1 B C D A))) ) ) ) ) ) ) ) ).
tt(t28_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ((v5_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers))) ) )  =>  ( ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C B) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = B) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C B))  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = C) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C)) = (k2_square_1 B C)) ) ) ) ) ) ) ) ).
tt(t28_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (~  ((r4_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) D E (k1_flang_1 A B C) F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  (~  ((r4_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) D E B G) & (r4_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) D G C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) (k36_gfacirc1 A B C)) = (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)))  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 2) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((k5_relat_1 A C) = (k5_relat_1 B C))  =>  ((k5_relat_1 (k4_funcop_1 D A E) C) = (k5_relat_1 (k4_funcop_1 D B E) C)) ) ) ) ) ) ) ) ) ) ).
tt(t28_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = A)  &  ( ((k9_xtuple_0 C) = A)  &  ((r1_tarski (k10_xtuple_0 C) A) &  ((v2_funct_1 B) &  ((k3_relat_1 C B) = B) ) ) ) )  =>  (C = (k4_relat_1 A)) ) ) ) ) ) ) ).
tt(t28_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ( ((k2_relset_1 B C) = B)  &  ((v2_funct_1 C) &  (! [E:$i] :  (! [F:$i] :  ( ( ((r2_hidden E B) &  ((k1_funct_1 D E) = F) )  =>  ((r2_hidden F A) &  ((k1_funct_1 C F) = E) ) )  &  ( ((r2_hidden F A) &  ((k1_funct_1 C F) = E) )  =>  ((r2_hidden E B) &  ((k1_funct_1 D E) = F) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  (D = (k2_funct_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t28_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski A (k1_zfmisc_1 (k9_xtuple_0 B))) & (v2_funct_1 B))  =>  ((k3_tarski (k8_relat_1 (k3_funct_3 B) A)) = (k7_relat_1 B (k3_tarski A))) ) ) ) ) ).
tt(t28_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=> (r1_tarski A (k1_funct_4 A B))) ) ) ) ) ).
tt(t28_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  (~  ((r2_hidden B (k9_xtuple_0 A)) &  ((v1_relat_1 (k1_funct_1 A B)) & (v1_funct_1 (k1_funct_1 A B))) ) ) )  =>  ( ((k2_funct_5 A) = k1_xboole_0)  &  ((k4_funct_5 A) = k1_xboole_0) ) ) ) ) ).
tt(t28_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A B) & (r2_hidden C (k9_xtuple_0 D)))  =>  ((k5_funct_6 (k7_funcop_1 B D) A C) = (k1_funct_1 D C)) ) ) ) ) ) ) ).
tt(t28_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_funct_7 A B C) =>  ((k6_subset_1 (k9_xtuple_0 A) C) = (k6_subset_1 (k9_xtuple_0 B) C)) ) ) ) ) ) ) ).
tt(t28_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_funct_8 A k1_numbers k1_numbers B) => (r1_funct_8 A k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers B))) ) ) ) ) ).
tt(t28_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k55_valued_1 k1_numbers k1_numbers k19_sin_cos) (k8_real_1 k32_sin_cos A))) ) ).
tt(t28_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_tarski (k1_altcat_1 B C D) (k1_altcat_1 A (k3_functor0 B A (k10_functor0 A B) C) (k3_functor0 B A (k10_functor0 A B) D)))) ) ) ) ) ) ) ) ).
tt(t28_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F C A) & (m2_functor0 F C A))  =>  (! [G:$i] :  ((m2_functor2 G B C D E) =>  ((r2_functor2 B C D E) => (m2_functor2 (k5_functor3 B C A D E G F) B A (k1_functor3 B C A D F) (k1_functor3 B C A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) &  ((r1_fuzzy_1 B D) & (r2_funct_2 A k1_numbers (k1_fuzzy_1 A C D) (k4_fuzzy_1 A))) )  => (r2_funct_2 A k1_numbers B (k4_fuzzy_1 A))) ) ) ) ) ) ) ) ) ).
tt(t28_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 (k2_fuzzy_2 A B B) B) & (r1_fuzzy_1 B (k3_fuzzy_2 A B B))) ) ) ) ) ).
tt(t28_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ((v3_fvaluat1 A) =>  ((r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D C) (k3_funct_2 (u1_struct_0 A) k7_numbers D B)) |  ((k3_funct_2 (u1_struct_0 A) k7_numbers D B) = (k3_funct_2 (u1_struct_0 A) k7_numbers D (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k6_fvsum_1 A B (k6_fvsum_1 A B C)) = C) ) ) ) ) ) ) ).
tt(t28_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~ (v1_xboole_0 (k22_gate_1 A B C D E F)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_gcd_1 A E (k5_gcd_1 A B C D)) =>  ((r2_gcd_1 A E C) & (r2_gcd_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) => (m1_genealg1 (k4_genealg1 E F G A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  ( ( (D = (k1_geomtrap A E I))  &  ( (D = (k1_geomtrap A F J))  &  ( (D = (k1_geomtrap A G K))  &  ( (D = (k1_geomtrap A H L))  & (r2_geomtrap A B C E F G H)) ) ) )  => (r2_geomtrap A B C I J K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) = (k2_binarith E F))  &  ( ((k1_funct_1 (k6_circuit2 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D) A) = E)  &  ( ((k1_funct_1 (k6_circuit2 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D) B) = F)  &  ((k1_funct_1 (k6_circuit2 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k5_gfacirc2 A B C) (k6_gfacirc2 A B C)))) => (v1_circuit2 (k5_facirc_1 (k5_gfacirc2 A B C) (k6_gfacirc2 A B C) D (k2_nat_1 1 (k4_nat_1 2 A))) (k5_gfacirc2 A B C) (k6_gfacirc2 A B C))) ) ) ) ) ) ) ) ).
tt(t28_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k10_glib_000 A) B) C) | (r2_hidden (k1_funct_1 (k11_glib_000 A) B) C)) )  <=> (r2_hidden B (k20_glib_000 A C))) ) ) ) ) ).
tt(t28_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((k2_nat_1 (k3_finseq_1 (k7_glib_001 A B C)) 1) = (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t28_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) <=>  ((k4_glib_002 A) = 1) ) ) ) ).
tt(t28_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 (k9_glib_003 A B))) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k9_glib_003 A B) C))) ) ) ) ) ) ) ).
tt(t28_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))) =>  (~  ( (~  ((k12_glib_004 A B) = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~ (r2_hidden C (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B)))  &  ((k14_glib_004 A B) = (k4_tarski (k4_subset_1 (k6_glib_000 A) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k6_domain_1 (k6_glib_000 A) C)) (k2_xboole_0 (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k1_tarski (k10_subset_1 (k12_glib_004 A B)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)))) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((r2_hidden A (k4_finseq_1 C)) &  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 C)) &  ((r2_hidden B (k4_finseq_1 D)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D B) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C A))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D E) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C A))))  => (r1_xxreal_0 E B)) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden (k2_nat_1 B 1) (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 B 1)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t28_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) B (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) (k2_nat_1 C 1))) ) ) ) ) )  =>  ( ((k5_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B (k2_nat_1 C 1)))  &  ((k4_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_matrix_1 C) A))  &  ((r2_hidden B (k1_tops_1 (k15_euclid 2) (k2_goboard5 C A))) & (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 (k2_nat_1 A 1))) (k18_euclid B))) ) ) ) ) ) ) ) ) ).
tt(t28_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 C)) & (r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 (k2_goboard2 A))))  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid k6_numbers 1)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 B 2) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid k6_numbers 1))) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t28_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_goboard5 A (k3_finseq_1 A) (k1_matrix_1 A)) = (a_1_16_gobrd11 A)) ) ) ).
tt(t28_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k2_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_gobrd14,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_sprect_1 A))) = (k4_card_3 (k5_funct_4 (k1_zfmisc_1 k1_numbers) 1 2 (k1_rcomp_1 (k6_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) (k8_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A)))) (k1_rcomp_1 (k9_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) (k7_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))))))) ) ) ).
tt(t28_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_qc_lang1 A))) =>  (~  ((v1_finset_1 B) &  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(t28_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_graph_1 B) & (l1_graph_1 B)) )  =>  ((r2_hidden B (k11_graph_1 A)) <=> (r4_graph_1 B A)) ) ) ) ) ).
tt(t28_graph_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 C)) =>  ( ( ((k15_finseq_1 E) = C)  &  ( ((k15_finseq_1 G) = D)  &  (F = (k5_relat_1 E (k10_xtuple_0 (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k1_relset_1 k5_numbers E)) (k1_relset_1 k5_numbers G))))) ) )  =>  ((k15_finseq_1 F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C D) =>  ((k5_card_1 (k3_graph_3 A B (k6_subset_1 D C))) = (k6_xcmplx_0 (k5_card_1 (k3_graph_3 A B D)) (k5_card_1 (k3_graph_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t28_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  (~  ( (~  (B = (k1_funct_1 (u1_graph_1 A) (k1_funct_1 C 1))) )  &  ((r2_hidden B (k2_graph_5 A C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 C)) &  (B = (k1_funct_1 (u2_graph_1 A) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) => (r1_tarski (k7_graphsp B A) (k2_finseq_1 A))) ) ) ) ).
tt(t28_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (? [B:$i] :  ((r2_hidden B A) & (r1_grcat_1 B k3_algstr_0)) ) ) ) ).
tt(t28_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v7_ordinal1 (k6_xcmplx_0 (k1_newton A B) 1)) & (v1_int_2 (k6_xcmplx_0 (k1_newton A B) 1)))  =>  ((r1_xxreal_0 B 1) |  ( (A = 2)  &  ((v7_ordinal1 B) & (v1_int_2 B)) ) ) ) ) ) ) ) ).
tt(t28_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k5_relat_1 A (k1_tarski B)) = (k1_tarski (k4_tarski B (k1_funct_1 A B)))) ) ) ) ) ).
tt(t28_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (? [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_xcmplx_0 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  =>  ( ( (D = (k1_funct_1 B C))  &  (E = (k1_funct_1 B (k2_xcmplx_0 C 1))) )  =>  ((m1_group_6 E A D) &  ( (~ (v2_struct_0 (k5_group_6 A E)))  &  ((v2_group_1 (k5_group_6 A E)) &  ((v3_group_1 (k5_group_6 A E)) &  ((v5_group_1 (k5_group_6 A E)) & (l3_algstr_0 (k5_group_6 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v1_grnilp_1 A)) ) ) ).
tt(t28_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (~  ((r2_hidden F (k2_groeb_1 A B C E)) &  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r2_hidden G (k2_groeb_1 A B C D)) & (r3_pre_poly A G F)) ) ) ) ) ) ) )  => (r1_tarski (k2_groeb_1 A B C E) (k3_groeb_1 A (k2_groeb_1 A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (m2_ideal_1 (k2_rfinseq (u1_struct_0 A) D C) A B)) ) ) ) ) ) ) ) ).
tt(t28_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C D)) =>  ( ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E))) | (r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E))))  &  (~ (r2_hidden F (k3_xboole_0 (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E)) (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E (k2_group_11 A (k2_group_2 A B C) D)) & (r1_xboole_0 (k13_group_2 A D E) (k2_group_2 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A 3 B) = (k6_algstr_0 A (k6_algstr_0 A B B) B)) ) ) ) ) ).
tt(t28_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k5_group_2 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B E D))  & (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_int_1 D) =>  ((k2_group_3 A (k5_group_1 A D B) C) = (k5_group_1 A D (k2_group_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t28_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_struct_0 (k5_group_4 A C) B) <=>  (? [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m2_finseq_1 E k4_numbers) &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ((r1_tarski (k10_xtuple_0 D) C) &  ((k3_group_4 A (k4_group_4 A E D)) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B (k2_group_1 A C)) = (k2_group_3 A (k2_group_5 A C B) (k2_group_1 A C))) ) ) ) ) ) ) ).
tt(t28_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((m1_group_6 C A B) => (m1_group_2 (k5_group_6 B (k1_group_6 A B C)) (k5_group_6 A C))) ) ) ) ) ) ) ).
tt(t28_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)) (k4_group_7 A B) (k4_group_7 A C)) = (k4_group_7 A (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t28_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) &  ((v4_group_9 D A B) & (m1_group_9 D A B)) )  =>  ((k16_group_9 A B C D) = (k16_group_9 A B D C)) ) ) ) ) ) ) ) ).
tt(t28_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((k7_group_1 B) = A)  => (v3_groupp_1 B A)) ) ) ) ) ).
tt(t28_hahnban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v3_hahnban1 B k1_complfld A) &  ((v6_hahnban1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C k1_complfld A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 D C k1_complfld) &  ((v1_hahnban1 D k1_complfld C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 k1_complfld))))) ) ) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (F = E)  => (r1_xxreal_0 (k17_complex1 (k3_funct_2 (u1_struct_0 C) (u1_struct_0 k1_complfld) D E)) (k3_funct_2 (u1_struct_0 A) k1_numbers B F))) ) ) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 k1_complfld)) &  ((v13_vectsp_1 E A k1_complfld) &  ((v1_hahnban1 E k1_complfld A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) ) ) )  =>  (~  ( ((k5_relset_1 (u1_struct_0 A) (u1_struct_0 k1_complfld) E (u1_struct_0 C)) = D)  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r1_xxreal_0 (k17_complex1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) E F)) (k3_funct_2 (u1_struct_0 A) k1_numbers B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (! [D:$i] :  ((m2_hallmar1 D A B) =>  ((r1_hallmar1 A D C) => (r1_hallmar1 A B C)) ) ) ) ) ) ) ) ).
tt(t28_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  => (r1_xxreal_0 k6_numbers (k8_weierstr A B C))) ) ) ) ) ) ) ).
tt(t28_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ( ((k3_glib_001 A (k2_helly A B C)) = B)  &  ((k4_glib_001 A (k2_helly A B C)) = C) ) ) ) ) ) ) ) ).
tt(t28_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k1_complfld))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) (k9_bilinear k1_complfld A A B (k1_hermitan A B)) C C) = (k5_square_1 (k17_complex1 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 k1_complfld) B C)))) ) ) ) ) ) ) ).
tt(t28_heyting1,ax, (! [A:$i] :  ((k6_lattices (k12_normform A)) = (k1_tarski (k4_tarski k1_xboole_0 k1_xboole_0))) ) ).
tt(t28_heyting2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_substlat A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_substlat A B))) =>  ((k4_filter_0 (k5_substlat A B) C D) = (k2_lattice2 (u1_struct_0 (k5_substlat A B)) (k5_substlat A B) (k6_heyting2 A B C) (k6_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (u1_lattices (k5_substlat A B)) (k4_heyting2 A B) (k9_funcop_1 (u1_struct_0 (k5_substlat A B)) (u1_struct_0 (k5_substlat A B)) (k5_heyting2 A B) (k7_heyting2 A B C) D)))) ) ) ) ) ) ) ) ).
tt(t28_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (m1_subset_1 (k6_domain_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers B)) (k2_heyting3 A B)) (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers B))))) ) ) ) ).
tt(t28_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k1_taylor_1 A) B) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k9_real_1 A 1)) A) B))) ) ) ) ).
tt(t28_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k11_polynom1 k6_numbers A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k11_polynom1 k6_numbers A)))))) )  & (v4_quofield B A (k11_polynom1 k6_numbers A))) ) ) ) ).
tt(t28_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 A (k3_hilbert1 (k3_hilbert1 A B) B)) k6_hilbert1)) ) ) ) ).
tt(t28_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( (~  ((k3_hilbert1 A B) = A) )  &  (~  ((k3_hilbert1 A B) = B) ) ) ) ) ) ) ).
tt(t28_hilbert3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) &  ((v3_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C C) &  ((v3_funct_2 G C C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  =>  ((k16_pralg_1 A (k1_partfun1 A (k9_funct_2 B C) (k9_funct_2 B C) (k9_funct_2 B C) D (k1_hilbert3 B C F G)) (k1_partfun1 A B B B E F)) = (k3_relat_1 (k16_pralg_1 A D E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k2_hurwitz A B) = 1)  <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (~  (C = (k4_struct_0 A)) )  & (r2_funct_2 k5_numbers (u1_struct_0 A) B (k3_polynom5 A (k3_hurwitz A D 1) C))) ) ) ) ) ) ) ) ) ) ).
tt(t28_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) & (r1_idea_1 A (k1_recdef_1 B 4))) ) ) )  =>  ((r1_idea_1 A (k1_recdef_1 (k13_idea_1 B) 1)) &  ((r1_idea_1 A (k1_recdef_1 (k13_idea_1 B) 2)) &  ((r1_idea_1 A (k1_recdef_1 (k13_idea_1 B) 3)) & (r1_idea_1 A (k1_recdef_1 (k13_idea_1 B) 4))) ) ) ) ) ) ) ) ).
tt(t28_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m3_ideal_1 C A B) => (m1_ideal_1 C A B)) ) ) ) ) ) ).
tt(t28_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  ( (~  (B = C) )  =>  ((k1_incsp_1 A B C) = (k1_incsp_1 A C B)) ) ) ) ) ) ) ) ).
tt(t28_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) => (m4_index_1 (k4_cat_5 C D E) (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (k15_index_1 A B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t28_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_instalg1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_instalg1 C B))  =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  ((k2_instalg1 A C D) = (k2_instalg1 B C (k2_instalg1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t28_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_xcmplx_0 (k1_int_1 A) B) = (k1_int_1 (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t28_int_2,ax,(v1_int_2 2)).
tt(t28_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_int_2 A B) =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 B 1) |  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((k6_int_1 (k9_real_1 (k8_real_1 A D) C) B) = k6_numbers)  => (r2_hidden (k4_tarski D (k4_real_1 C (k13_newton A (k7_nat_d (k1_euler_1 B) 1)))) (k1_int_4 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ((k3_int_2 A B) = 1)  =>  ((r1_xxreal_0 B 2) | (r2_int_1 (k2_int_5 A B) (k1_newton A (k3_nat_d (k7_nat_d B 1) 2)) B)) ) ) ) ) ) ).
tt(t28_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_1 A) &  ((v1_partfun3 A) & (v1_int_6 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_int_6 B A) =>  (! [C:$i] :  ((m1_int_6 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) => (r2_int_1 (k1_funct_1 B D) (k1_funct_1 C D) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t28_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_int_7 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ( (B = C)  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k2_binop_1 (u1_struct_0 (k3_int_7 A)) k5_numbers (u1_struct_0 (k3_int_7 A)) (k4_group_1 (k3_int_7 A)) B D) = (k2_binop_1 (u1_struct_0 (k9_int_3 A)) k5_numbers (u1_struct_0 (k9_int_3 A)) (k4_group_1 (k9_int_3 A)) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos))) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos) (k10_real_1 1 (k5_square_1 A))) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 A) k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos))) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos) (k10_real_1 1 (k5_square_1 A))) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 A) k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos))) (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t28_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ((r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k21_binop_2 A 1))) A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k23_binop_2 A 1))))) &  ((r1_xxreal_0 1 A) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A)))) &  (D = (k1_relset_1 k1_numbers C)) ) ) ) )  =>  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A))) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos (k1_taylor_1 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers C) (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos))))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t28_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k19_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k16_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t28_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) F) &  ((r1_integr15 A (k3_integra5 B C) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B C)) A) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) ) ) ) )  =>  ((k12_integr15 D E A (k8_integr15 A k1_numbers F G)) = (k8_euclid A (k12_integr15 D E A F) (k12_integr15 D E A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) => (r1_xxreal_0 (k7_integra1 A C B) (k6_integra1 A C B))) ) ) ) ) ) ) ).
tt(t28_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v1_seq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 A k6_numbers))  =>  ((k7_integra1 B (k26_valued_1 B k1_numbers C A) D) = (k8_real_1 A (k6_integra1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t28_integra4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) &  ((v3_integra1 C B) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers D B)) &  ((v3_integra1 D B) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers E B)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r2_hidden F B) & (r2_hidden G B))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 E F) (k1_seq_1 E G))) (k8_real_1 A (k7_real_1 (k18_complex1 (k9_real_1 (k1_seq_1 C F) (k1_seq_1 C G))) (k18_complex1 (k9_real_1 (k1_seq_1 D F) (k1_seq_1 D G))))))) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) | (v3_integra1 E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) C) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 C)) &  ((r1_tarski (k2_rcomp_1 A B) (k9_xtuple_0 E)) &  ( (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F (k2_rcomp_1 A B)) =>  ((k1_seq_1 E F) = (k4_integra5 A F C)) ) ) )  &  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_fcont_1 C D)) ) ) ) ) ) )  =>  ((r1_fdiff_1 E D) &  ((k1_fdiff_1 E D) = (k1_seq_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos B)) = (k4_integra5 B A k24_sin_cos)) ) ) ) ) ).
tt(t28_integra8,ax, ((k2_fdiff_1 k19_sin_cos k1_numbers) = (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) ).
tt(t28_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) D)) &  ((r1_integra5 D (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)) & (r1_tarski D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) )  =>  ((k1_integra9 D (k26_valued_1 k1_numbers k1_numbers B A) C) = (k8_real_1 A (k1_integra9 D B C))) ) ) ) ) ) ) ) ) ) ).
tt(t28_interva1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((r2_hidden B C) <=>  ((r1_tarski (k7_interva1 A C) B) & (r1_tarski B (k8_interva1 A C))) ) ) ) ) ) ).
tt(t28_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 (k3_intpro_1 A B) C) (k3_intpro_1 B C)) k8_intpro_1)) ) ) ) ) ) ).
tt(t28_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k1_seq_1 k4_irrat_1 A) (k4_series_1 k5_irrat_1))) ) ) ).
tt(t28_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_nattra_1 H B C E F) =>  (! [I:$i] :  ((m2_nattra_1 I B C F G) =>  ( ((r2_nattra_1 B C E F) & (r2_nattra_1 B C F G))  => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k5_isocat_1 A B C E G D (k7_nattra_1 B C E F G H I)) (k7_nattra_1 A C (k9_cat_1 A B C D E) (k9_cat_1 A B C D F) (k9_cat_1 A B C D G) (k5_isocat_1 A B C E F D H) (k5_isocat_1 A B C F G D I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m2_cat_1 E (k8_cat_2 A B) C) =>  ((r2_nattra_1 A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) =>  (! [F:$i] :  ((m2_nattra_1 F A (k11_nattra_1 B C) (k5_isocat_2 A B C D) (k5_isocat_2 A B C E)) =>  ((r2_nattra_1 (k8_cat_2 A B) C D E) &  (? [G:$i] :  ((m2_nattra_1 G (k8_cat_2 A B) C D E) & (r2_funct_2 (u1_struct_0 A) (u4_struct_0 (k11_nattra_1 B C)) F (k6_isocat_2 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_borsuk_5 B C))  =>  ((k1_tops_1 k3_topmetr A) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t28_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( ( (D = B)  &  (E = C) )  =>  ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = (k4_metric_1 (k14_euclid A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = k6_numbers) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k7_xcmplx_0 (k7_xcmplx_0 F G) G)) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ( (A = (k4_struct_0 (k15_euclid 2)))  =>  ((k1_funct_1 (k2_funct_1 k1_jgraph_3) A) = (k4_struct_0 (k15_euclid 2))) )  &  ( (~  ( ( ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k1_real_1 (k17_euclid A)) (k18_euclid A)))  |  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k1_real_1 (k17_euclid A)))) )  &  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  &  (~  ((k1_funct_1 (k2_funct_1 k1_jgraph_3) A) = (k19_euclid (k8_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))) (k8_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))))) ) ) ) )  &  (~  ( (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k1_real_1 (k17_euclid A)) (k18_euclid A))) )  &  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k1_real_1 (k17_euclid A)))) )  &  (~  ((k1_funct_1 (k2_funct_1 k1_jgraph_3) A) = (k19_euclid (k8_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))) (k8_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))))) ) ) ) ) ) ) ) ) ).
tt(t28_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_1_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ( ((k6_pscomp_1 A) = (k1_real_1 1))  &  ( ((k8_pscomp_1 A) = 1)  &  ( ((k9_pscomp_1 A) = (k1_real_1 1))  &  ((k7_pscomp_1 A) = 1) ) ) ) ) ) ) ).
tt(t28_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (A = a_0_11_jgraph_6)  &  (B = a_0_12_jgraph_6) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = B) ) ) ) ) ) ).
tt(t28_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 (k18_euclid D) (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) &  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) &  ((r1_xxreal_0 (k18_euclid D) (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) & (r1_xxreal_0 (k17_euclid D) (k17_euclid C))) ) ) ) ) )  =>  ( ((k17_euclid A) = (k17_euclid C))  |  ( ((k18_euclid D) = (k18_euclid B))  |  ((r1_xxreal_0 (k17_euclid D) (k17_euclid A)) | (r1_jordan17 (k1_sppol_2 (k17_euclid A) (k17_euclid C) (k18_euclid D) (k18_euclid B)) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C)))  &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( ( ( ((k17_euclid B) = (k17_euclid C))  &  ((k17_euclid C) = (k17_euclid D)) )  |  ( ((k18_euclid B) = (k18_euclid C))  &  ((k18_euclid C) = (k18_euclid D)) ) )  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) D A)))  &  (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) D A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan14,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B C) & (r1_jordan1h A B))  => (r1_jordan1h A C)) ) ) ) ) ) ) ).
tt(t28_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r1_jordan18 A B C D E D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k1_matrix_1 (k1_jordan8 B A)) = (k2_nat_1 (k13_newton 2 A) 3)) ) ) ) ) ).
tt(t28_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((a_4_5_jordan1 A B C D) = (a_4_1_jordan1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t28_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) (k3_finseq_1 (k1_jordan8 B A)))) (k9_jordan6 B))) ) ) ) ) ).
tt(t28_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1)) ) ) ) ) ) ) ) ) ).
tt(t28_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k2_jordan1e B A) (k25_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k2_jordan1e B A) (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ) ).
tt(t28_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_seq_1 (k7_pre_poly k1_numbers (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B)) k1_jordan1h) A) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1))) ) ) ) ) ) ).
tt(t28_jordan1i,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_topreal2 C) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k17_euclid D) = (k10_real_1 (k7_real_1 (k6_pscomp_1 C) (k8_pscomp_1 C)) 2))  &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k1_jordan8 C A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) (k1_jordan1a (k1_jordan8 C A)) B) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 C A)))) &  ( ((k18_euclid D) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C 1) (k1_jordan1a (k1_jordan8 C 1)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) (k1_jordan1a (k1_jordan8 C A)) B)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 C A)))))))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 C A))) &  (D = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) (k1_jordan1a (k1_jordan8 C A)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k7_pscomp_1 B) (k7_pscomp_1 A)))  =>  ((k21_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k21_pscomp_1 B)) ) ) ) ) ) ).
tt(t28_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((k1_topreal6 2 A (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B C) (k1_rlvect_1 (k15_euclid 2) A (k9_real_1 1 C)))) = (k8_real_1 C (k1_topreal6 2 B A))) ) ) ) ) ) ) ) ).
tt(t28_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r3_jordan20 A B C D G) &  ( ((k17_euclid E) = G)  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) D E) A) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) D E))) ) )  => (r3_jordan20 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2)))) => (r1_xxreal_0 (k18_euclid A) (k18_euclid (k1_jordan21 B)))) ) ) ) ) ).
tt(t28_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k18_euclid (k2_jordan21 (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) (k18_euclid (k2_jordan21 (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A C))))))) ) ) ) ) ) ) ) ).
tt(t28_jordan23,ax, (! [A:$i] :  ( ((v2_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (v2_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ).
tt(t28_jordan2b,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 1)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 1)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 1))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 1)) (u1_struct_0 k3_topmetr) A B) = (k7_partfun1 k1_numbers B 1)) ) )  => (v3_tops_2 A (k15_euclid 1) k3_topmetr)) ) ) ).
tt(t28_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (B = (k1_euclid A))  => (v2_connsp_1 B (k15_euclid A))) ) ) ) ) ).
tt(t28_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ( (A = B)  |  ( ((r2_jordan3 A B C D) | (r3_jordan3 A B D C))  &  (~  ((r2_jordan3 A B C D) & (r3_jordan3 A B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_jordan4 A B C D) =>  ((r1_xxreal_0 D C) |  ( ((k3_finseq_1 B) = (k7_nat_d (k2_nat_1 (k3_finseq_1 A) C) D))  &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C 1) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k7_nat_d (k3_finseq_1 A) 1) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) =>  ((k3_jordan3 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = A) ) ) ) ).
tt(t28_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((v4_topreal1 A) &  ((v4_pre_topc B (k15_euclid 2)) &  ((r2_hidden (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k2_topreal1 2 A D)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r2_hidden C (k2_topreal1 2 A E)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) & (r2_hidden C B)) ) ) ) ) ) ) )  =>  ((r1_xboole_0 (k3_topreal1 2 A) B) |  ( ((k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) = C)  |  ((r1_xxreal_0 E D) &  ( (D = E)  => (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) C (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_5_jordan5d A))  =>  ((k5_seq_4 B) = (k1_pscomp_1 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t28_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k3_jordan6 A B C D) = (k4_jordan6 A C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan8 A B))) &  ((r2_hidden (k20_pscomp_1 A) (k3_goboard5 (k1_jordan8 A B) C (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) &  (~  ((k20_pscomp_1 A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan_a A (k3_finseq_1 B) B) (k2_jordan_a A 1 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) ) ) ) ).
tt(t28_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) => (v2_connsp_1 (k2_relset_1 (u1_struct_0 A) D) A)) ) ) ) ) ) ) ) ) ).
tt(t28_knaster,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v4_lattice3 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v14_quantal1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r3_lattices B D (k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) C D)) & (r2_abian (u1_struct_0 B) (k5_knaster B C D A) C))  =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r1_ordinal1 A E) =>  ((k5_knaster B C D A) = (k5_knaster B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) ) ).
tt(t28_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  => (r1_tarski (k3_kurato_0 (u1_struct_0 (k15_euclid 2)) A) (k1_kurato_2 (k15_euclid 2) A))) ) ).
tt(t28_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_2 E (k12_matrix_2 A)) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ( ((k3_finseq_1 C) = A)  & (r2_hidden F (k2_finseq_1 A)))  =>  ((k11_fvsum_1 B (k8_matrix_1 (u1_struct_0 B) (k7_laplace A B D) F) C) = (k8_laplace A F B (k3_matrix11 F A A (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r2_funct_2 (u1_struct_0 (k11_group_4 A)) (u1_struct_0 (k11_group_4 A)) (k3_latsubgr A A (k6_partfun1 (u1_struct_0 A))) (k6_partfun1 (u1_struct_0 (k11_group_4 A))))) ) ).
tt(t28_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((r2_hidden C D) => (r3_lattices A (k3_funct_2 B (u1_struct_0 A) E C) (k2_lattice2 B A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r3_lattice3 B C A) <=> (r1_lattice3 (k3_lattice3 B) A (k4_lattice3 B C))) ) ) ) ) ) ).
tt(t28_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v3_filter_0 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  ((v3_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) =>  ((v3_filter_0 A) & (r1_lattice4 B A C)) ) ) ) ) ) ) ) ).
tt(t28_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_ordinal1 C)) )  =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_lattice5 F A B E) =>  ( ((v4_ordinal1 D) &  ( ((k9_xtuple_0 C) = D)  &  (! [G:$i] :  ((v3_ordinal1 G) =>  ((r2_hidden G D) =>  ((k1_funct_1 C G) = (k11_lattice5 A B E F G)) ) ) ) ) )  =>  ( (D = k1_xboole_0)  |  ((k11_lattice5 A B E F D) = (k3_tarski (k10_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((m1_lattice5 E A B C) =>  ((r1_ordinal1 D (k7_lattice5 A B C)) =>  ((v1_funct_1 (k6_lattice8 A B C E D)) &  ((v1_funct_2 (k6_lattice8 A B C E D) (k2_zfmisc_1 (k3_lattice8 A D) (k3_lattice8 A D)) (u1_struct_0 B)) &  ((v1_lattice5 (k6_lattice8 A B C E D) (k3_lattice8 A D) B) &  ((v2_lattice5 (k6_lattice8 A B C E D) (k3_lattice8 A D) B) &  ((v3_lattice5 (k6_lattice8 A B C E D) (k3_lattice8 A D) B) & (m1_subset_1 (k6_lattice8 A B C E D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k3_lattice8 A D) (k3_lattice8 A D)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v2_lexbfs (k16_lexbfs A))) ) ).
tt(t28_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers (k4_lfuzzy_1 A B (k3_xcmplx_0 C D)) (k4_lfuzzy_1 A (k4_lfuzzy_1 A B D) C))) ) ) ) ) ) ) ) ).
tt(t28_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) & (v2_comseq_2 B))  =>  ((r1_xxreal_0 (k2_seq_2 B) k6_numbers) | (v1_limfunc1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t28_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 A D))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 (k9_real_1 A C) A)))) ) ) ) ) )  | (r3_limfunc2 B A)) ) ) ) ) ) ).
tt(t28_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc3 C A) =>  ( ((k1_limfunc3 C A) = B)  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A F)) k6_numbers))  &  ( (~ (r1_xxreal_0 E (k18_complex1 (k9_real_1 A F))))  &  ((r2_hidden F (k9_xtuple_0 C)) & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 C F) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r3_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k4_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  | (v5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t28_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (r1_lmod_6 A (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E)) (k2_vectsp_5 A B D (k1_vectsp_5 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  ((v2_lopban_1 C A B) <=> (v4_xxreal_2 (k14_lopban_1 A B C))) ) ) ) ) ) ) ).
tt(t28_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 (k4_normsp_0 A B) D)) & (r1_xxreal_0 (k1_seq_1 (k4_normsp_0 A B) D) (k1_seq_1 (k4_normsp_0 A C) D))) ) )  & (v2_lopban_3 C A))  =>  ((v2_lopban_3 B A) & (r1_xxreal_0 (k4_series_1 (k4_normsp_0 A B)) (k4_series_1 (k4_normsp_0 A C)))) ) ) ) ) ) ) ) ).
tt(t28_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_normsp_0 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A B)) C)) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C)) &  ((r1_xxreal_0 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C) (k4_series_1 (k4_sin_cos (k1_normsp_0 A B)))) & (r1_xxreal_0 (k1_normsp_0 A (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k1_lopban_4 A B)) C)) (k4_series_1 (k4_sin_cos (k1_normsp_0 A B))))) ) ) ) ) ) ) ) ).
tt(t28_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden (k5_lattices A) (k3_filter_0 A B)) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski C B) &  ((k2_lattice4 A C) = (k5_lattices A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r1_lpspace1 A B C D D)) ) ) ) ) ) ) ) ).
tt(t28_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ((r2_hidden D (k1_lpspace2 A B C E)) => (r2_hidden (k56_valued_1 A k1_numbers D) (k1_lpspace2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 (k10_nat_1 (k1_zfmisc_1 k10_ltlaxio1) D B)) (k1_domain_1 k5_numbers k1_hilbert1 C A)) = (k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 D) (k1_domain_1 k5_numbers k1_hilbert1 (k2_nat_1 B C) A))) ) ) ) ) ) ) ) ) ).
tt(t28_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C) (k8_cqc_lang A B C)) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t28_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_mathmorp A D (k9_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k1_mathmorp A D B) (k1_mathmorp A D C))) ) ) ) ) ) ) ) ) ).
tt(t28_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 B C) => (v3_matrix10 (k4_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t28_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E C B A) =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 B)) =>  ( ( ( (G = D)  &  ((k3_finseq_1 F) = (k1_matrix_1 E)) )  =>  ((k8_matrix_1 C (k3_matrix11 D B A C E F) G) = F) )  &  ( (~  (G = D) )  =>  ((k8_matrix_1 C (k3_matrix11 D B A C E F) G) = (k8_matrix_1 C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 A)))  =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 D k5_numbers)) =>  ( ((r2_hidden C (k2_finseq_1 D)) & (r1_tarski (k10_xtuple_0 F) (k2_finseq_1 (k3_finseq_1 E))))  =>  ((k9_matrix_1 A (k1_matrix13 A E B D F G) C) = (k1_partfun1 k5_numbers k5_numbers k5_numbers A F (k9_matrix_1 A E (k1_funct_1 G C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (C = (k11_matrix_1 B A))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A)) ) )  =>  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k3_matrix_3 A (k3_matrix15 (u1_struct_0 A) B) (k3_matrix15 (u1_struct_0 A) C)) = (k3_matrix15 (u1_struct_0 A) (k3_fvsum_1 A B C))) ) ) ) ) ) ) ) ).
tt(t28_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v3_matrix16 F (u1_struct_0 B)) &  ((v3_matrix16 G (u1_struct_0 B)) & (v3_matrix16 H (u1_struct_0 B))) )  => (v3_matrix16 (k3_matrix_6 A B (k2_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 C)) => (r2_hidden (k4_tarski E D) (k2_matrix_1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 B)) =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 C)) =>  ( ((v1_setwiseo D A) &  ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ((v1_finseqop D A) &  ((r6_binop_1 A E D) & (v1_binop_1 E A)) ) ) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C H I) (k9_matrix_3 B C A E F G)) = (k7_setwiseo C A D I (k10_funcop_1 A C E (k7_setwiseo B A D H F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 E))  &  ((k3_matrix_3 A B C) = (k3_matrix_3 A D E)) ) ) ) ) ) )  =>  ((k1_matrix_4 A B D) = (k1_matrix_4 A E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((v2_matrix_6 C B A) & (v2_matrix_6 D B A))  => (v2_matrix_6 (k3_matrix_6 B A C D) B A)) ) ) ) ) ) ) ) ) ).
tt(t28_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ((r1_xxreal_0 1 A) =>  ((v5_matrix_2 B (k11_matrix_2 (k12_matrix_2 A))) <=> (v5_matrix_2 (k3_matrix_7 A B) (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ) ).
tt(t28_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k11_matrix_1 B A) = (k12_matrix_1 B A)) ) ) ) ) ) ) ).
tt(t28_matrix_9,ax, ((k2_funct_1 (k3_finseq_4 k5_numbers 2 3 1)) = (k3_finseq_4 k5_numbers 3 1 2)) ).
tt(t28_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k17_rvsum_1 (k12_seq_4 A B)) = (k5_binop_2 B (k17_rvsum_1 A))) ) ) ) ) ).
tt(t28_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_matrixj1 E C) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 C))))  =>  (! [F:$i] :  ( ((v1_matrixj1 F C) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 C))))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k13_matrixj1 C D E))) =>  ((k3_matrix_1 C (k13_matrixj1 C D E) A B) = (k3_matrix_1 C (k13_matrixj1 C D (k3_matrixj1 C F E)) (k1_nat_1 A (k2_wsierp_1 (k10_matrixj1 C F))) (k1_nat_1 B (k2_wsierp_1 (k11_matrixj1 C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 G B C) &  ((v1_mod_2 G A B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ((r2_hidden H (k4_finseq_1 D)) &  ( (~  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) G (k7_partfun1 (u1_struct_0 B) D H)) = (k4_vectsp_1 A C F (k7_partfun1 (u1_struct_0 C) E H))) )  &  (~  ((r2_hidden (k1_nat_1 H 1) (k4_finseq_1 D)) &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) G (k7_partfun1 (u1_struct_0 B) D H)) = (k3_rlvect_1 C (k4_vectsp_1 A C F (k7_partfun1 (u1_struct_0 C) E H)) (k7_partfun1 (u1_struct_0 C) E (k1_nat_1 H 1)))) ) ) ) ) ) ) )  &  (! [H:$i] :  ( ((v2_relat_1 H) & (m1_matrixj2 H A F))  =>  (~  ((k1_matrlin2 A B C G D E) = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k2_matrix_1 (k7_matrixr1 A B)) = (k2_matrix_1 B)) ) ) ) ) ).
tt(t28_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((k1_matrixr2 A (k1_matrixr2 A B C) D) = (k1_matrixr2 A B (k1_matrixr2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t28_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  ((k1_matrlin2 A B B (k3_struct_0 B) C C) = (k12_matrix_1 A (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t28_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (! [F:$i] :  ((m1_matrix_1 F D C B) =>  ( ((k1_matrix_1 E) = (k1_matrix_1 F))  =>  ((k4_matrix_1 D (k8_matrlin D A C B E F)) = (k7_matrlin D (k4_matrix_1 D E) (k4_matrix_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_matroid0 A C B)) ) ) ) ) ) ) ).
tt(t28_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k5_matrprob A) = (k5_matrprob (k4_matrix_1 k1_numbers A))) ) ) ).
tt(t28_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) (k5_algstr_0 (k15_euclid A) C D)) = (k5_algstr_0 (k15_euclid B) (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) C) (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 C D))  =>  ((r1_xxreal_0 C B) | (v3_matrtop3 (k3_matrtop1 D D (k2_matrtop3 D A B C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k2_mboolean A (k3_pboole A B C)) (k3_pboole A (k2_mboolean A B) (k2_mboolean A C)))) ) ) ) ) ).
tt(t28_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) )  &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((k12_supinf_2 C D) = k1_supinf_2) ) ) ) ) ) ) ) ).
tt(t28_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v3_measure5 A) <=> (v3_measure5 (k2_measure6 A B))) ) ) ) ) ).
tt(t28_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_measure8 D A B) =>  ((v2_prob_1 D) => (v8_valued_0 (k10_measure8 A B D C))) ) ) ) ) ) ) ) ).
tt(t28_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r2_hidden B A) <=> (r2_hidden (k2_binop_2 B) (k7_member_1 A))) ) ) ) ) ).
tt(t28_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v4_membered B)) )  => (v4_membered (k3_tarski A))) ) ).
tt(t28_memstr_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_memstr_0 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 B C)) & (v1_partfun1 D (u1_struct_0 C))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 C)) &  ((v1_funct_1 E) & (v5_funct_1 E (k2_memstr_0 B C))) ) )  =>  ((r1_tarski (k1_funct_4 E (k7_memstr_0 B C A)) D) =>  ((k5_memstr_0 B C D) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski C (k1_relset_1 A D)) =>  ((k8_subset_1 A C (k11_mesfunc1 D E)) = (k7_subset_1 A C (k8_subset_1 A C (k14_mesfunc1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r2_relset_1 A k2_numbers (k2_partfun1 A k2_numbers (k25_valued_1 A k2_numbers C D) B) (k25_valued_1 A k2_numbers (k2_partfun1 A k2_numbers C B) D))) ) ) ) ) ) ) ).
tt(t28_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k2_numbers D k6_numbers))) &  ((v1_mesfunc8 D A k2_numbers) &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) => (v1_comseq_3 (k9_mesfun7c A D E))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) => (v1_comseq_3 (k9_mesfun7c A (k1_mesfun9c A k2_numbers D C) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc1 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k9_subset_1 A D (k16_mesfunc1 A C (k1_measure6 E))) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) => (v3_valued_0 (k3_mesfunc2 C A))) ) ) ) ) ) ).
tt(t28_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((r2_relset_1 A k7_numbers (k1_mesfunc2 A (k2_partfun1 A k7_numbers B C)) (k2_partfun1 A k7_numbers (k1_mesfunc2 A B) C)) & (r2_relset_1 A k7_numbers (k2_mesfunc2 A (k2_partfun1 A k7_numbers B C)) (k2_partfun1 A k7_numbers (k2_mesfunc2 A B) C))) ) ) ) ) ) ).
tt(t28_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_relset_1 A k7_numbers (k7_mesfunc1 A (k1_mesfunc5 A B)) (k1_mesfunc5 A (k26_valued_1 A k1_numbers B (k1_real_1 1)))) & (r2_relset_1 A k7_numbers (k7_mesfunc1 A (k1_mesfunc5 A B)) (k1_mesfunc5 A (k32_valued_1 A k1_numbers B)))) ) ) ) ) ).
tt(t28_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 D A k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers)) = F)  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers D G) F) & (v3_valued_0 (k4_mesfunc5 A k7_numbers D G))) ) )  &  ( ((k1_relset_1 A E) = F)  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G F) =>  ((v7_mesfunc5 (k3_mesfunc5 A D G)) &  ((k12_supinf_2 E G) = (k2_mesfunc5 (k3_mesfunc5 A D G))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C F)) |  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m2_subset_1 I (k1_zfmisc_1 A) B) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  (~  ((r1_tarski I F) &  ( (~ (r1_xxreal_0 G (k12_supinf_2 C I)))  &  (! [K:$i] :  ((v7_ordinal1 K) =>  ( (~ (r1_xxreal_0 K J))  =>  (! [L:$i] :  ((m1_subset_1 L A) =>  (~  ((r2_hidden L (k7_prob_1 A B F I)) & (r1_xxreal_0 H (k3_extreal1 (k4_supinf_2 (k12_supinf_2 (k4_mesfunc5 A k7_numbers D K) L) (k12_supinf_2 E L))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v2_mesfunc9 B A) =>  ((k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C)) = (k1_setfam_1 (a_3_0_mesfunc9 A B C))) ) ) ) ) ) ) ) ).
tt(t28_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 2) =>  (! [B:$i] :  ((m1_subset_1 B 2) =>  ((k1_metric_1 2 2 k12_metric_1 A B) = (k1_metric_1 2 2 k12_metric_1 B A)) ) ) ) ) ).
tt(t28_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A))) =>  ((r2_hidden B (k8_metric_2 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) &  (? [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k1_domain_1 (k2_metric_2 A) (k2_metric_2 A) C D))  & (r4_metric_2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ( ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 A B) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t28_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_tbsp_1 B A) => (v1_metric_6 B A)) ) ) ) ) ).
tt(t28_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_euclid_7 (k23_binop_2 A 1) (k23_binop_2 A 1)) = (k7_finseq_1 (k4_struct_0 (k15_euclid A)) (k12_finseq_1 k5_numbers 1))) ) ) ).
tt(t28_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((k4_midsp_1 A B) = (k4_midsp_1 A C))  => (r2_midsp_1 A B C)) ) ) ) ) ) ) ).
tt(t28_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_midsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((r1_midsp_2 (u1_struct_0 B) A C) & (v1_midsp_2 C B A))  =>  ( ((k1_midsp_1 B D E) = (k1_midsp_1 B F G))  <=>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D E) = (k3_rlvect_1 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ((r2_midsp_3 A B C) <=>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  ((k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B (k1_midsp_2 (u1_midsp_2 C D) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) E B)))) = (k1_midsp_2 (u1_midsp_2 C D) (k10_midsp_3 A C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_tarski B C) =>  ( (B = k1_xboole_0)  | (r1_tarski (k3_mmlquery A D C) (k3_mmlquery A D B))) ) ) ) ) ) ) ) ) ).
tt(t28_mod_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((r2_hidden A C) & (r2_hidden B C))  => (r2_hidden D C)) ) ) ) ) ) ) ) ) ).
tt(t28_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_ringcat1 C A B) <=> (v2_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t28_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) => (m1_subset_1 (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 1) (k1_domain_1 k5_numbers k5_numbers 1 1)) (k12_finseq_1 k5_numbers k6_numbers) A) k6_modal_1)) ) ).
tt(t28_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B D))) =>  ((r3_modelc_1 A B D C (k25_modelc_1 (k48_modelc_1 A B D) E)) <=>  (? [F:$i] :  ((m1_subset_1 F A) &  ((r2_hidden (k4_tarski C F) B) & (r3_modelc_1 A B D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r1_modelc_2 A B) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t28_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ( ((r4_modelc_3 B D C) & (r2_hidden A (u1_modelc_3 B C)))  =>  ((r2_hidden A (u1_modelc_3 B D)) | (r1_modelc_3 B D C A)) ) ) ) ) ) ) ) ) ) ).
tt(t28_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d C B))  =>  ((r1_nat_d A C) | (r1_nat_d C (k3_nat_d B A))) ) ) ) ) ) ) ) ).
tt(t28_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m2_monoid_0 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m5_monoid_0 B A C)) ) ) ) ) ) ) ).
tt(t28_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))) =>  ( ((k9_xtuple_0 B) = A)  & (r1_tarski (k10_xtuple_0 B) k5_numbers)) ) ) ) ).
tt(t28_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A C) (k5_rusub_4 A D B)) = (k5_rusub_4 A (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A C) D) B)) ) ) ) ) ) ) ) ) ).
tt(t28_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) => (r2_pboole (u1_struct_0 A) (k4_msafree3 A B C) B)) ) ) ) ) ) ).
tt(t28_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  ( (~ (v1_zfmisc_1 C))  => (m2_msaterm C A B)) ) ) ) ) ) ) ).
tt(t28_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) ) )  =>  (~  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r1_pboole A C B) &  ((r1_pboole A D B) &  ( (~ (r2_pboole A C D))  &  (~ (r2_pboole A D C)) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((r1_pboole A C B) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D B) => (r2_pboole A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) & (m1_unialg_2 B A))  =>  (! [C:$i] :  ( ((v1_unialg_1 C) & (m1_unialg_2 C A))  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k6_msualg_1 A)) &  ((v4_msualg_1 D (k6_msualg_1 A)) & (m1_msualg_2 D (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  (! [E:$i] :  ( ((v3_msualg_1 E (k6_msualg_1 A)) &  ((v4_msualg_1 E (k6_msualg_1 A)) & (m1_msualg_2 E (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  ( ( (D = (k9_msualg_1 B))  &  (E = (k9_msualg_1 C)) )  =>  ((k2_pboole (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) D) (u3_msualg_1 (k6_msualg_1 A) E)) = (k16_funcop_1 k6_numbers (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_msualg_2 D A B) =>  ((k13_msualg_2 A B (k11_msualg_2 A B C D) D) = (g3_msualg_1 A (u3_msualg_1 A D) (u4_msualg_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t28_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((v3_msualg_6 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_rewrite1 (k3_msualg_6 A) D E) =>  (! [F:$i] :  ((m2_msualg_6 F A B D E) =>  (! [G:$i] :  (! [H:$i] :  ((r2_hidden (k4_tarski G H) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D)) => (r2_hidden (k4_tarski (k1_funct_1 F G) (k1_funct_1 F H)) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_msualg_5 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))))) =>  ( (C = D)  =>  ((v2_msualg_4 (k4_mssubfam (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) (k5_closure2 (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) D)) A B) &  ((v3_msualg_4 (k4_mssubfam (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) (k5_closure2 (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) D)) A B) & (m1_msualg_4 (k4_mssubfam (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) (k5_closure2 (u1_struct_0 A) (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) D)) (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_mycielsk,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v6_dilworth B (k3_necklace A)) & (m1_eqrel_1 B (u1_struct_0 (k3_necklace A))))  =>  ((v5_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(t28_nagata_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k1_metric_1 A A B C C) = k6_numbers)  & (r1_xxreal_0 (k1_metric_1 A A B C E) (k7_real_1 (k1_metric_1 A A B C D) (k1_metric_1 A A B E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 4) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  (~  (A = 4) ) ) ) ) ) ) ) ) ) ).
tt(t28_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (v1_zfmisc_1 A))  <=>  ( (~ (v1_xboole_0 A))  &  (~  (A = 1) ) ) ) ) ) ).
tt(t28_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((k11_nat_3 (k24_binop_2 B C) A) = (k23_binop_2 (k11_nat_3 B A) (k11_nat_3 C A))) ) ) ) ) ) ) ).
tt(t28_nat_4,ax,(v1_int_2 13)).
tt(t28_nat_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  ((k3_uproots (k8_mcart_1 A A D E) (k1_nat_5 (k2_zfmisc_1 A A) (k1_partfun1 (k2_zfmisc_1 A A) (k2_zfmisc_1 k5_numbers k5_numbers) (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers (k16_funct_3 A A k5_numbers k5_numbers B C) k48_binop_2) (k8_mcart_1 A A D E))) = (k24_binop_2 (k3_uproots D (k1_nat_5 A B D)) (k3_uproots E (k1_nat_5 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k6_nat_d B A) = (k6_nat_d A (k4_nat_d B A))) ) ) ) ) ) ).
tt(t28_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r3_nattra_1 A B C D) => (r3_nattra_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t28_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) (k1_relset_1 (u1_struct_0 B) C)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) D (k2_vfunct_2 (u1_struct_0 B) A C E)) (k6_clvect_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_ncfcont1 D A) & (r7_ncfcont1 A B C D))  => (r1_ncfcont2 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t28_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_ndiff_1 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v1_funct_1 (k6_vfunct_1 (u1_struct_0 B) A C D)) &  ((v2_ndiff_1 (k6_vfunct_1 (u1_struct_0 B) A C D) B A) & (m1_subset_1 (k6_vfunct_1 (u1_struct_0 B) A C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((v1_funct_1 (k2_vfunct_1 (u1_struct_0 B) A C D)) &  ((v2_ndiff_1 (k2_vfunct_1 (u1_struct_0 B) A C D) B A) & (m1_subset_1 (k2_vfunct_1 (u1_struct_0 B) A C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 C))))))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r2_ndiff_3 (k4_real_ns1 C) D A)) )  =>  ((r2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) D (k4_pdiff_1 B C)) A) & (r2_relset_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) (k2_ndiff_3 (k4_real_ns1 C) D A) (k4_pdiff_1 B C)) (k2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) D (k4_pdiff_1 B C)) A))) ) ) ) ) ) ) ) ) ).
tt(t28_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ( ((r2_hidden F (k4_finseq_1 A)) &  ((r1_ndiff_5 A B F C E) & (r1_ndiff_5 A B F D E)) )  =>  ((r1_ndiff_5 A B F (k6_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D) E) &  ((k6_ndiff_5 A B F (k6_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D) E) = (k3_rlvect_1 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A F)) B) (k6_ndiff_5 A B F C E) (k6_ndiff_5 A B F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k1_neckla_3 A B)) => (r2_hidden (k4_tarski B C) (k1_msualg_5 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ) ) ) ).
tt(t28_necklace,ax,(r5_waybel_1 (k4_necklace 1) (k3_necklace (k4_necklace 1)))).
tt(t28_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_funct_1 (k7_newton B C A) 1) = (k1_newton B A)) ) ) ) ) ) ) ).
tt(t28_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r3_nfcont_1 B C D A) =>  ((r4_nfcont_1 B (k3_normsp_0 (u1_struct_0 B) C D) A) & (r3_nfcont_1 B C (k5_vfunct_1 (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t28_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C) & (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) E B) C))  => (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) (k6_vfunct_1 k1_numbers C D E) (k3_xboole_0 A B)) C)) ) ) ) ) ) ) ) ) ).
tt(t28_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers D)) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A))  => (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k9_integr15 A C k1_numbers D) B) A)) ) ) ) ) ) ) ) ).
tt(t28_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ( (~ (r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C) (k7_normform A)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  ((r2_hidden D (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B)) & (r2_hidden D (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) C))) )  &  (~  ((r2_hidden D (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) C)) & (r2_hidden D (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v3_normsp_1 C B) =>  ((k6_normsp_1 B (k5_normsp_1 B C A)) = (k1_rlvect_1 B (k6_normsp_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t28_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k3_normsp_2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_normsp_2 A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 (k3_normsp_2 A)) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) & (v2_frechet C (k4_normsp_2 A)))  =>  ( ((k2_frechet (k3_normsp_2 A) B) = (k2_frechet (k4_normsp_2 A) C))  &  ((k2_frechet2 (k3_normsp_2 A) B) = (k2_frechet2 (k4_normsp_2 A) C)) ) ) ) ) ) ) ) ) ).
tt(t28_numbers,ax, (~  (k5_numbers = k3_numbers) ) ).
tt(t28_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_openlatt A)) (k16_openlatt A) (k6_lattices A)) = (k7_openlatt A)) ) ) ).
tt(t28_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) D) = (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) (k3_oppcat_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t28_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_wellord1 A B) =>  ((r1_orders_1 A B) &  ((r2_orders_1 A B) & (r3_orders_1 A B)) ) ) ) ) ) ).
tt(t28_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C D) => (r1_tarski (k3_orders_2 A C B) (k3_orders_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t28_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) <=>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) => (r2_hidden (k1_ordinal1 B) A)) ) ) ) ) ) ).
tt(t28_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k10_ordinal2 A (k1_ordinal1 B)) = (k1_ordinal1 (k10_ordinal2 A B))) ) ) ) ) ).
tt(t28_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ((r2_hidden A B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ( (B = (k10_ordinal2 A C))  &  (~  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k12_ordinal2 A C) (k12_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t28_ordinal5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k1_ordinal5 A B) B)) ) ) ) ) ) ).
tt(t28_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((k2_ordinal1 (a_1_0_ordinal6 A)) = (a_1_0_ordinal6 A)) ) ) ).
tt(t28_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t28_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (E = (k4_struct_0 B))  =>  ((r1_orders_2 B C D) |  ((k2_ortsp_1 A B E F D C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k21_osafree A B C) = (a_3_3_osafree A B C)) ) ) ) ) ) ) ).
tt(t28_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  ( ((v1_orders_3 A) | (v6_osalg_1 A))  => (v13_osalg_1 B A)) ) ) ) ) ).
tt(t28_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_osalg_2 D A B) => (r1_tarski (k10_xtuple_0 (k5_relat_1 (k5_msualg_1 A C B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k9_osalg_2 A B D))) C))) (k1_funct_1 (k3_relat_1 (u2_msualg_1 A) (k9_osalg_2 A B D)) C))) ) ) ) ) ) ) ) ).
tt(t28_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~ (r1_parsp_1 A B C D E))  =>  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) =>  ( (~ (r1_parsp_2 A B C D))  &  ( (~ (r1_parsp_2 A C B E))  &  ( (~ (r1_parsp_2 A D E B))  &  ( (~ (r1_parsp_2 A E D C))  &  ( (~ (r1_parsp_2 A B D C))  &  ( (~ (r1_parsp_2 A C B D))  &  ( (~ (r1_parsp_2 A C D B))  &  ( (~ (r1_parsp_2 A D B C))  &  ( (~ (r1_parsp_2 A D C B))  &  ( (~ (r1_parsp_2 A C E B))  &  ( (~ (r1_parsp_2 A B C E))  &  ( (~ (r1_parsp_2 A B E C))  &  ( (~ (r1_parsp_2 A E B C))  &  ( (~ (r1_parsp_2 A E C B))  &  ( (~ (r1_parsp_2 A D B E))  &  ( (~ (r1_parsp_2 A B D E))  &  ( (~ (r1_parsp_2 A B E D))  &  ( (~ (r1_parsp_2 A E B D))  &  ( (~ (r1_parsp_2 A E D B))  &  ( (~ (r1_parsp_2 A E C D))  &  ( (~ (r1_parsp_2 A C D E))  &  ( (~ (r1_parsp_2 A C E D))  &  ( (~ (r1_parsp_2 A D C E))  &  (~ (r1_parsp_2 A D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_tarski A B) => (r1_relset_1 A C (k3_partfun1 D A C) (k3_partfun1 D B C))) ) ) ) ) ) ).
tt(t28_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ((r1_partfun1 C D) <=>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k9_subset_1 B (k1_relset_1 B C) (k1_relset_1 B D))) =>  ((k7_partfun1 A C E) = (k7_partfun1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((k3_partit1 A B (k2_partit1 A B C)) = B) ) ) ) ) ) ) ).
tt(t28_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v5_relat_2 C) => (r5_relat_2 C B)) ) ) ) ) ) ) ).
tt(t28_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v4_pasch A)) ) ).
tt(t28_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k2_pboole A (k2_pboole A B C) D) (k2_pboole A B (k2_pboole A C D)))) ) ) ) ) ) ) ).
tt(t28_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((v9_metric_1 A) &  ((r2_hidden D (k9_subset_1 (u1_struct_0 A) (k9_metric_1 A E B) (k9_metric_1 A F C))) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_tarski (k9_metric_1 A D G) (k9_metric_1 A E B)) & (r1_tarski (k9_metric_1 A D G) (k9_metric_1 A F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k19_pcs_0 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k19_pcs_0 A B))) =>  ( ( (C = E)  &  ( (D = F)  & (r1_pcs_0 A C D)) )  => (r1_pcs_0 (k19_pcs_0 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ( ((r2_pdiff_1 A B C D F) & (r2_pdiff_1 A B C E F))  =>  ((r2_pdiff_1 A B C (k6_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E) F) &  ((k9_pdiff_1 B A C (k6_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E) F) = (k3_rlvect_1 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)) (k9_pdiff_1 B A C D F) (k9_pdiff_1 B A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r4_pdiff_3 B A) & (r4_pdiff_3 C A))  =>  ((r3_pdiff_1 2 2 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) &  ((k11_pdiff_1 2 2 (k47_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A) = (k9_real_1 (k5_pdiff_3 B A) (k5_pdiff_3 C A))) ) ) ) ) ) ) ) ) ).
tt(t28_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 B A) & (r3_pdiff_1 3 1 C A))  => (r3_pdiff_1 3 1 (k20_valued_1 (k1_euclid 3) k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t28_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r1_pdiff_5 B A) =>  ((k1_pdiff_5 B A) = (k11_pdiff_1 3 1 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ) ).
tt(t28_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) & (r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C D)) )  =>  ((r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 E B)) D) &  ((k3_relat_1 (k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C D) (k4_pdiff_1 E B)) = (k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 E B)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (? [F:$i] :  ((m2_finseq_1 F (k1_euclid A)) &  (? [G:$i] :  ((m2_finseq_1 G (k1_euclid B)) &  ( ((k3_finseq_1 F) = (k23_binop_2 A 1))  &  ( ((k3_finseq_1 G) = A)  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 F)) =>  ((k7_partfun1 (k1_euclid A) F H) = (k8_finseq_1 k1_numbers (k17_finseq_1 k1_numbers (k7_nat_d (k23_binop_2 A 1) H) E) (k5_euclid (k7_nat_d H 1)))) ) ) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k7_partfun1 (k1_euclid B) G H) = (k8_euclid B (k7_partfun1 (k1_euclid B) C (k7_euclid A D (k7_partfun1 (k1_euclid A) F H))) (k7_partfun1 (k1_euclid B) C (k7_euclid A D (k7_partfun1 (k1_euclid A) F (k23_binop_2 H 1)))))) ) ) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) =>  ( ((r2_hidden H (k4_finseq_1 F)) &  ((k7_partfun1 (k1_euclid A) F H) = I) )  => (r1_xxreal_0 (k12_euclid I) (k12_euclid E))) ) ) ) )  &  ((k8_euclid B (k7_partfun1 (k1_euclid B) C (k7_euclid A D E)) (k7_partfun1 (k1_euclid B) C D)) = (k5_euclid_7 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ( (E = F)  &  ((v1_pdiff_7 E A) &  (C = D) ) )  =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G A))  =>  ((r2_pdiff_7 A B G C E) & (r4_pdiff_7 A B (k2_pdiff_7 A B G C E) E)) ) ) )  <=>  ((r1_pdiff_6 E B A C) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) D F) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pencil_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v6_pencil_1 A) &  ((v8_pencil_1 A) & (l1_pre_topc A)) ) ) )  =>  ((v10_pencil_1 A) => (v9_pencil_1 A)) ) ) ).
tt(t28_pencil_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v10_pencil_1 (k2_pencil_1 A B C))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B))) &  ((v1_pencil_2 C (k5_pencil_1 A B) (k5_pencil_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)))))) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) & (v1_funcop_1 E)) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((v1_funct_1 (k1_funct_1 E F)) &  ((v1_funct_2 (k1_funct_1 E F) (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F)))) & (m1_subset_1 (k1_funct_1 E F) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F))))))) )  &  ( (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F))))))) )  =>  ( (G = (k1_funct_1 E F))  => (v1_pencil_2 G (k2_pencil_1 A B F) (k2_pencil_1 A B (k3_funct_2 A A D F)))) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_pencil_1 A B))) =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) & (v1_partfun1 H A)) ) )  =>  ( (H = G)  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I A) &  ((v1_funct_1 I) & (v1_partfun1 I A)) ) )  =>  ( (I = (k3_funct_2 (u1_struct_0 (k5_pencil_1 A B)) (u1_struct_0 (k5_pencil_1 A B)) C G))  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F)))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B F)) (u1_struct_0 (k2_pencil_1 A B (k3_funct_2 A A D F))))))) )  =>  ( (J = (k1_funct_1 E F))  =>  ((k1_funct_1 I (k3_funct_2 A A D F)) = (k1_funct_1 J (k1_funct_1 H F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k1_nat_1 C 1) (k1_vectsp_9 A B)) => (v6_pencil_1 (k7_pencil_4 A B C (k1_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t28_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 B) =>  ( (A = k6_numbers)  |  ((k3_nat_d (k1_newton A B) A) = (k1_newton A (k7_nat_d B 1))) ) ) ) ) ) ) ).
tt(t28_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ((r2_pnproc_1 A (k2_pnproc_1 A B C) D) => (r1_pnproc_1 A (k3_pnproc_1 A (k3_pnproc_1 A D B) C) (k3_pnproc_1 A D (k2_pnproc_1 A B C)))) ) ) ) ) ) ) ) ).
tt(t28_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( ((k7_polyeq_1 A B k6_numbers k6_numbers C) = k6_numbers)  &  ( (~  (C = (k1_binop_2 (k6_binop_2 B A))) )  &  (~  (C = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k6_polyeq_5 A B C D)) (k7_polyeq_5 A B C D)) (k3_xcmplx_0 (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k6_polyeq_5 A B C D)) (k8_polyeq_5 A B C D))) (k3_xcmplx_0 (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k7_polyeq_5 A B C D)) (k8_polyeq_5 A B C D))) (k3_xcmplx_0 (k3_xcmplx_0 (k6_polyeq_5 A B C D) (k7_polyeq_5 A B C D)) (k8_polyeq_5 A B C D))) = (k4_xcmplx_0 B)) ) ) ) ) ) ) ) ) ).
tt(t28_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_finseq_1 (k10_polyform A B)) = (k11_polyform A B)) ) ) ) ) ).
tt(t28_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B C (k7_polynom1 A B)) (k7_polynom1 A B))) ) ) ) ) ) ).
tt(t28_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_normsp_1 A B (k9_polynom3 A)) B)) ) ) ) ).
tt(t28_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k9_polynom3 A) B) (k9_polynom3 A))) ) ) ) ).
tt(t28_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k6_polynom7 A B C D) (k9_polynom1 A B C (k4_polynom7 A B D)))) ) ) ) ) ) ) ) ).
tt(t28_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  ( ((k3_finseq_1 (k4_polynom8 A B C)) = A)  &  ( ((k1_matrix_1 (k4_polynom8 A B C)) = 1)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 A D))  =>  ((k3_matrix_1 (u1_struct_0 B) (k4_polynom8 A B C) (k1_nat_1 D 1) 1) = (k8_nat_1 (u1_struct_0 B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_polyred A B C D E) | (r1_polyred A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power A (k4_xcmplx_0 B)) = (k10_real_1 1 (k3_power A B))) ) ) ) ) ) ).
tt(t28_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v4_msualg_1 E B) & (l3_msualg_1 E B))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) & (v1_funcop_1 F)) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (? [H:$i] :  ((m2_pboole H (u1_struct_0 B) (u3_msualg_1 B E) (u3_msualg_1 B (k5_pralg_2 A B C G))) &  ( (H = (k1_funct_1 F G))  & (r1_msualg_3 B E (k5_pralg_2 A B C G) H)) ) ) ) )  =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 (u3_msualg_1 B E) D)) => (r2_hidden (k1_funct_1 (k10_funct_6 (k1_funct_1 (k10_funct_6 F) D)) G) (k4_card_3 (k9_pralg_2 A B D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) (k2_prelamb A (k3_prelamb A B C) C)) & (r2_prelamb A (k12_finseq_1 (u1_struct_0 A) B) (k1_prelamb A C (k3_prelamb A C B)))) ) ) ) ) ) ) ).
tt(t28_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_finseq_2 B)) =>  ( ((k10_pre_poly A C) = (k10_pre_poly B D))  =>  ((k3_finseq_1 (k5_pre_poly A C)) = (k3_finseq_1 (k5_pre_poly B D))) ) ) ) ) ) ) ) ).
tt(t28_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_prepower C B) (k2_prepower C A))) ) ) ) ) ) ) ) ) ) ).
tt(t28_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v2_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) => (v2_pre_topc A)) ) ) ).
tt(t28_prob_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers)))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden E C) =>  ( ((r2_hidden B E) =>  ((k1_seq_1 D E) = 1) )  &  ( (~ (r2_hidden B E))  =>  ((k1_seq_1 D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (~  ((r1_prob_2 A B C D E) &  ( (~ (r1_xxreal_0 1 (k1_seq_1 C D)))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 C E)))  & (r1_xxreal_0 1 (k1_seq_1 C (k6_prob_1 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (v3_prob_1 (k2_prob_3 A C))) ) ) ) ) ).
tt(t28_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) => (r1_tarski B (k4_prob_4 A B C))) ) ) ) ) ) ).
tt(t28_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C (k7_cqc_lang A B C))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t28_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~  ( ((k1_projpl_1 A B D) = (k1_projpl_1 A C E))  &  ( (~  (B = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  (~  ((k1_projpl_1 A B D) = (k1_projpl_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k18_euclid (k10_pscomp_1 A)) = (k18_euclid (k13_pscomp_1 A))) ) ) ).
tt(t28_pua2mss1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  => (r3_pua2mss1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)))) ) ).
tt(t28_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k1_mboolean A (k1_pzfmisc1 A B)) (k2_pzfmisc1 A (k1_pboole A) (k1_pzfmisc1 A B)))) ) ) ).
tt(t28_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_qc_lang1 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_qc_lang1 A))))  =>  ((r1_tarski B C) => (r1_qc_lang1 A (k25_qc_lang1 A C) (k25_qc_lang1 A B))) ) ) ) ) ) ) ).
tt(t28_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ((v4_qc_lang2 (k7_qc_lang2 A B C E) A) & (v4_qc_lang2 (k9_qc_lang2 A B C D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v6_qc_lang1 (k5_qc_lang2 A B C) A) <=> (r1_tarski (k24_qc_lang1 A C) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t28_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_trees_1 E (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  ( ((r2_hidden E (k3_qc_lang4 A B C)) & (r2_hidden (k7_finseq_1 E F) (k3_qc_lang4 A B D)))  => (r2_hidden F (k3_qc_lang4 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((k6_algstr_0 A (k15_lattice3 A C) B) = (k15_lattice3 A (a_3_10_quantal1 A B C)))  &  ((k9_quantal1 A (k16_lattice3 A C) B) = (k16_lattice3 A (a_3_11_quantal1 A B C))) ) ) ) ) ) ) ).
tt(t28_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_quatern2 A) = (k29_quaterni (k29_quaterni (k24_quaterni (k10_real_1 (k17_quaterni A) (k5_square_1 (k3_quatern2 A))) (k25_quaterni (k10_real_1 (k18_quaterni A) (k5_square_1 (k3_quatern2 A))) k4_quatern2)) (k25_quaterni (k10_real_1 (k19_quaterni A) (k5_square_1 (k3_quatern2 A))) k11_quaterni)) (k25_quaterni (k10_real_1 (k20_quaterni A) (k5_square_1 (k3_quatern2 A))) k12_quaterni))) ) ) ).
tt(t28_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A)) = (k6_quaterni (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k17_quaterni A)) (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k18_quaterni A))) (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k19_quaterni A))) (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k20_quaterni A))))) ) ) ).
tt(t28_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A))) = k6_numbers)  =>  (A = k21_quaterni) ) ) ) ).
tt(t28_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( ((k5_binop_1 (k7_quofield A) (k15_quofield A) B (k3_funct_2 (k7_quofield A) (k7_quofield A) (k17_quofield A) B)) = (k11_quofield A))  &  ((k5_binop_1 (k7_quofield A) (k15_quofield A) (k3_funct_2 (k7_quofield A) (k7_quofield A) (k17_quofield A) B) B) = (k11_quofield A)) ) ) ) ) ) ).
tt(t28_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_random_1 D A B) =>  (! [E:$i] :  ((m1_random_1 E A B) =>  ( ((r1_random_1 A B D C) & (r1_random_1 A B E C))  =>  ((k8_random_1 A B C (k4_random_1 A B D E)) = (k9_real_1 (k8_random_1 A B C D) (k8_random_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_xboole_0 D (k1_vectsp_6 A B C)) => (r1_tarski (k5_ranknull A B C D) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t28_rat_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (C = (k7_xcmplx_0 A B))  &  ( (~  (B = k6_numbers) )  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (A = (k3_xcmplx_0 (k2_rat_1 C) D))  &  (B = (k8_real_1 (k1_rat_1 C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A))  =>  ((v5_ratfunc1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (C = (k4_struct_0 A)) )  &  ((k4_tarski (k3_polynom5 A (k4_ratfunc1 A B) C) (k3_polynom5 A (k5_ratfunc1 A B) C)) = (k11_ratfunc1 A B)) ) ) ) ) ) ) ) ) ).
tt(t28_rcomp_3,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ( (~ (v4_xxreal_2 A))  &  ( (~ (v3_xxreal_2 A))  &  (~  (A = k1_numbers) ) ) ) ) ) ) ).
tt(t28_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( ((k1_seq_1 (k3_real_3 C) A) = k6_numbers)  & (r1_xxreal_0 A B))  =>  ((k1_seq_1 (k4_real_3 C) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t28_real_lat,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k6_real_lat A)))  &  ((v10_lattices (k6_real_lat A)) &  ((v11_lattices (k6_real_lat A)) & (l3_lattices (k6_real_lat A))) ) ) ) ) ).
tt(t28_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C) = D)  <=>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) D B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t28_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 B) = (k5_card_1 A)) )  =>  ((r2_classes1 (k4_rearran1 A B D C) (k3_rearran1 A B D C)) &  ( ((k20_rfunct_3 B (k4_rearran1 A B D C) B) = (k20_rfunct_3 B (k3_rearran1 A B D C) B))  &  ((k21_rfunct_3 B (k4_rearran1 A B D C) B) = (k21_rfunct_3 B (k3_rearran1 A B D C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k9_xtuple_0 A) (k10_xtuple_0 B)) =>  ((k10_xtuple_0 (k3_relat_1 B A)) = (k10_xtuple_0 A)) ) ) ) ) ) ).
tt(t28_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_relat_2 A) <=> (r1_tarski (k4_xboole_0 (k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)) (k4_relat_1 (k1_relat_1 A))) (k2_xboole_0 A (k2_relat_1 A)))) ) ) ).
tt(t28_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k4_tarski F G) (k4_relset_1 A B B C D E)) <=>  (? [H:$i] :  ((m1_subset_1 H B) &  ((r2_hidden (k4_tarski F H) D) & (r2_hidden (k4_tarski H G) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_relset_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (m1_subset_1 (a_4_2_relset_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) ) ) ) ) ) ).
tt(t28_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) )  =>  ((k2_goboard2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) = (k2_goboard2 B)) ) ) ) ) ).
tt(t28_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) =>  ((r2_hidden B (k1_relat_1 A)) |  (B = C) ) ) ) ) ) ) ).
tt(t28_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) => (r2_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k6_rewrite2 (k8_afinsq_1 A)))) (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) (k7_rewrite2 A B) (k6_rewrite2 (k8_afinsq_1 A))))) ) ) ).
tt(t28_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ((l1_rewrite3 F E) =>  (~  ( (~ (r2_hidden (k2_flang_1 D) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))))  & (r2_rewrite3 D E F A B C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k5_rfinseq2 (k6_rvsum_1 A)) = (k6_rvsum_1 (k6_rfinseq2 A))) ) ) ).
tt(t28_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ( ((k1_funct_1 A C) = (k1_funct_1 B D))  &  ( ((k1_funct_1 A D) = (k1_funct_1 B C))  &  ((r2_hidden C (k9_xtuple_0 A)) &  ((r2_hidden D (k9_xtuple_0 A)) &  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 A)) =>  ( (E = C)  |  ( (E = D)  |  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) )  => (r2_classes1 A B)) ) ) ) ) ) ) ).
tt(t28_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (B = k6_numbers) )  =>  ((k4_rfunct_1 (k24_valued_1 A B)) = (k24_valued_1 (k4_rfunct_1 A) (k5_xcmplx_0 B))) ) ) ) ) ) ).
tt(t28_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) & (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) ).
tt(t28_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) =>  ( (~  ((k3_finseq_1 C) = k6_numbers) )  =>  ((r1_rfunct_3 A k1_numbers C B) <=> (r2_hidden B (k1_relset_1 A (k14_rfunct_3 A C)))) ) ) ) ) ) ) ) ).
tt(t28_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 B) => (v1_comseq_2 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t28_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_funct_2 k5_numbers k7_numbers (k4_rinfsup2 (k1_valued_0 k7_numbers A B)) (k1_valued_0 k7_numbers (k4_rinfsup2 A) B)) &  ((k5_rinfsup2 (k1_valued_0 k7_numbers A B)) = (k5_rinfsup2 A)) ) ) ) ) ) ).
tt(t28_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k2_rlaffin1 A B 1) B)) ) ) ) ).
tt(t28_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_rlaffin1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_tarski C D) & (r2_hidden B C))  =>  ((v1_rlaffin1 (k2_xboole_0 (k7_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) B)) (k1_tarski (k1_funct_1 (k2_rlaffin2 A) C))) A) & (m1_subset_1 (k2_xboole_0 (k7_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) B)) (k1_tarski (k1_funct_1 (k2_rlaffin2 A) C))) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [E:$i] :  ((m2_rlaffin3 E (k15_euclid A) C) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C))))) =>  ( (F = (a_5_1_rlaffin3 A B C D E))  =>  ((r1_xxreal_0 (k5_card_1 C) B) |  ((v4_pre_topc D (k15_euclid B)) <=> (v4_pre_topc F (k1_pre_topc (k15_euclid A) (k4_rlaffin1 (k15_euclid A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_rlsub_1 B C)) ) ) ) ) ) ) ).
tt(t28_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) =>  ((k1_rlsub_2 A C (k2_rlsub_2 A B D)) = (k2_rlsub_2 A (k1_rlsub_2 A B C) (k1_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t28_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k18_complex1 C) = 1)  =>  ((k1_convex1 A B C) = B) ) ) ) ) ) ) ) ).
tt(t28_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k5_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t28_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  => (r2_relset_1 k5_numbers (u1_struct_0 A) (k5_rlvect_2 A (k3_finseq_4 (u1_struct_0 A) B C D) E) (k3_finseq_4 (u1_struct_0 A) (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers E B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers E C)) (k1_rlvect_1 A D (k3_funct_2 (u1_struct_0 A) k1_numbers E D))))) ) ) ) ) ) ) ) ) ) ).
tt(t28_rlvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_orders_1 B A) =>  ( (~ (r2_hidden k1_xboole_0 A))  =>  ((k9_xtuple_0 B) = A) ) ) ) ) ) ).
tt(t28_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 C) D E F) C) =>  ( (D = F)  |  ( (D = E)  |  ( (F = E)  |  ( (A = k6_numbers)  |  ( (B = k6_numbers)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 C) D (k1_rlvect_1 C E A) (k1_rlvect_1 C F B)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (r1_xxreal_0 (k1_rlvect_5 B) (k1_rlvect_5 A))) ) ) ) ).
tt(t28_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( (B = (k8_funcop_1 (u1_struct_0 A) (k2_finseq_1 (k3_finseq_1 B)) (k4_struct_0 A)))  =>  ((k4_rlvect_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t28_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) => (r1_struct_0 D E)) ) )  => (m1_rmod_2 C A D)) ) ) ) ) ) ) ) ) ).
tt(t28_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) =>  ((k2_rmod_3 A B D (k1_rmod_3 A B C E)) = (k1_rmod_3 A B (k2_rmod_3 A B C D) (k2_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((k4_rmod_4 A B (k8_finseq_1 (u1_struct_0 B) C D) E) = (k8_finseq_1 (u1_struct_0 B) (k4_rmod_4 A B C E) (k4_rmod_4 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k5_robbins1 A (k6_robbins1 A B C) (k6_robbins1 A B D)) (k3_robbins1 A (k6_robbins1 A B (k5_robbins1 A C D)))) = (k6_lattices A)) ) ) ) ) ) ) ) ) ).
tt(t28_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) B)) C) = C) ) ) ) ) ) ) ).
tt(t28_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins3 A))  =>  ( ((v8_robbins3 A) &  ((v9_robbins3 A) &  ((v10_robbins1 A) &  ((v10_lattices A) & (v10_robbins3 A)) ) ) )  =>  ((v12_oposet_1 A) & (v6_oposet_1 A)) ) ) ) ).
tt(t28_robbins4,ax, ((k6_lattices k2_robbins4) = 3) ).
tt(t28_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A (k3_subset_1 (u1_struct_0 A) B)) = (k3_subset_1 (u1_struct_0 A) (k4_roughs_1 A B))) ) ) ) ) ).
tt(t28_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A (k9_subset_1 A (k3_subset_1 A B) C))) = (k7_real_1 (k1_rpr_1 A C) (k1_rpr_1 A (k9_subset_1 A (k3_subset_1 A C) B)))) ) ) ) ) ) ) ).
tt(t28_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((u1_struct_0 B) = C)  => (v1_rlsub_1 C A)) ) ) ) ) ) ) ).
tt(t28_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) =>  ((k1_rusub_2 A C (k2_rusub_2 A B D)) = (k2_rusub_2 A (k1_rusub_2 A B C) (k1_rusub_2 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t28_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_rusub_3 A C) = (k1_rusub_3 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r2_hidden (k4_struct_0 A) B) =>  (B = (u1_struct_0 (k1_rusub_3 A B))) ) ) ) ) ) ).
tt(t28_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_rusub_5 A B) = (k2_rusub_5 A (k2_rusub_5 A (k3_rusub_5 A B)))) ) ) ) ) ).
tt(t28_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ( ((k8_rvsum_1 (k6_finseq_1 k1_numbers) A) = (k6_finseq_1 k1_numbers))  &  ((k8_rvsum_1 A (k6_finseq_1 k1_numbers)) = (k6_finseq_1 k1_numbers)) ) ) ) ).
tt(t28_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k11_rvsum_2 (k2_finseq_2 A B) (k2_finseq_2 A C)) = (k5_finseq_2 k2_numbers A (k5_binop_2 B C))) ) ) ) ) ) ) ).
tt(t28_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ((k1_funct_1 (k3_scmfsa6a (k5_scmfsa6a A C) B) (k2_nat_1 (k5_card_1 A) 1)) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 A) 2))) ) ) ) ) ) ) ).
tt(t28_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 11)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t28_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k3_scmfsa_1) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_scmfsa_1 k3_scmfsa_1) =>  ( (~  (D = B) )  =>  ((k9_scmfsa_1 (k8_scmfsa_1 A B C) D) = (k9_scmfsa_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k16_scmfsa_2 B A)) = 11) ) ) ) ) ).
tt(t28_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_scmfsa6a (k5_scmfsa6a C A) B) = (k3_scmfsa6a C (k6_scmfsa6a A B))) ) ) ) ) ) ) ).
tt(t28_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))) =>  ((r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) D) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) D)) &  (~  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r5_scmfsa7b D (k1_scmfsa_m B) A) & (r6_scmfsa7b D (k1_scmfsa_m B) A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3) D))  =>  ((r2_hidden D (k2_afinsq_1 (k2_scmfsa8b A B C))) &  (~  ((k1_funct_1 (k2_scmfsa8b A B C) D) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((r4_scmfsa9a A B C D) =>  ((r6_scmfsa7b (k2_scmfsa_9 C D) B A) & (r5_scmfsa7b (k2_scmfsa_9 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) (k1_nat_1 F 1)))) &  (~  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers) ) ) )  &  ( (~  ( ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers)  &  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F) C) = k6_numbers) ) )  &  ( (~  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F) C) = k6_numbers) )  =>  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D B C A) F)) = k6_numbers) ) ) ) ) ) ) )  =>  ((r6_scmfsa7b (k1_scmfsa_9 C B) D A) & (r5_scmfsa7b (k1_scmfsa_9 C B) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)) =>  ( ((k5_relat_1 A (k2_xboole_0 C k3_scmfsa_2)) = (k5_relat_1 B (k2_xboole_0 C k3_scmfsa_2)))  <=>  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden D C) =>  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ((k18_scmfsa_2 A D) = (k18_scmfsa_2 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_scmfsa6c C) &  ((v2_scmfsa6c C) & (m1_subset_1 C (u1_compos_1 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k4_scmfsa6a C D) B A) E) = (k1_funct_1 (k1_scmfsa6b D (k2_extpro_1 3 k1_scmfsa_2 C (k1_scmfsa_m B)) A) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k2_sf_mastr (k2_scmisort A)) = (k5_enumset1 (k4_scmfsa_2 k6_numbers) (k4_scmfsa_2 1) (k4_scmfsa_2 2) (k4_scmfsa_2 3) (k4_scmfsa_2 4) (k4_scmfsa_2 5) (k4_scmfsa_2 6))) ) ) ).
tt(t28_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 2)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k5_scmpds_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_compos_1 k1_scmpds_2)) =>  ( ( ((k5_memstr_0 2 k1_scmpds_2 A) = D)  &  ((r1_scmpds_4 E D) &  ( ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 A) C) = (k5_memstr_0 2 k1_scmpds_2 B))  &  ((k6_memstr_0 2 k1_scmpds_2 A) = (k6_memstr_0 2 k1_scmpds_2 B)) ) ) )  =>  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) E) = 1)  |  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) E) = 3)  |  ( ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 E A)) C) = (k5_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 E B)))  &  ((k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 E A)) = (k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_tarski C A) &  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B) D))  &  ((k3_extpro_1 2 k1_scmpds_2 A (k5_extpro_1 2 k1_scmpds_2 A B D)) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_scmpds_6 B C A) &  ((r2_scmpds_6 B C A) &  ( (~ (r1_xxreal_0 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C)) D))  &  ((k3_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C) D)) = (k2_compos_1 k1_scmpds_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) &  ((r2_scmpds_6 C B A) &  ((r1_scmpds_6 D (k6_scmpds_4 C B A) A) & (r2_scmpds_6 D (k6_scmpds_4 C B A) A)) ) )  =>  ((k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B) = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k10_compos_1 k1_scmpds_2 D)) (k8_memstr_0 2 k1_scmpds_2 (k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))))) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 G) &  ((v5_funct_1 G (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 G (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 G 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H k5_numbers) &  ((v5_relat_1 H (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 H) & (v1_partfun1 H k5_numbers)) ) ) )  =>  ( ( (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 G I) = (k1_funct_1 B I)) ) ) )  &  ((k1_funct_1 G D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C G H) D) = (k1_funct_1 G D))  &  ((r1_scmpds_6 C G H) &  ((r2_scmpds_6 C G H) &  ( (~ (r1_xxreal_0 (k1_funct_1 G (k2_scmpds_2 (k1_funct_1 B D) E)) (k1_funct_1 (k6_scmpds_4 C G H) (k2_scmpds_2 (k1_funct_1 B D) E))))  &  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden I F) =>  ((k1_funct_1 (k6_scmpds_4 C G H) I) = (k1_funct_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) &  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers))  =>  ((k6_scmpds_4 (k2_scmpds_8 D E C) B A) = (k6_scmpds_4 (k2_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 (k1_scmring2 A)) (k2_compos_0 (u1_compos_1 (k1_scmring2 A)) (k8_scmring2 A B)))) 1) = k5_numbers) ) ) ) ) ).
tt(t28_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ( ((k3_tarski A) = k1_xboole_0)  => (v1_scmyciel A)) ) ) ).
tt(t28_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  &  ((r2_analoaf A B C D E) &  ( (~  (D = E) )  &  ((r1_semi_af1 A D E F) & (r1_semi_af1 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k17_complex1 (k8_complex1 (k3_comseq_2 A) (k3_comseq_2 B)))) ) ) ) ) ).
tt(t28_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k12_binop_2 1 (k9_binop_2 C A))) ) ) )  => (v2_comseq_2 B)) ) ) ) ) ).
tt(t28_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r1_seqfunc A k1_numbers B (k1_tarski D)) & (r1_seqfunc A k1_numbers C (k1_tarski D)))  =>  ((r2_relset_1 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B D) (k10_seqfunc A C D)) (k10_seqfunc A (k6_seqfunc A B C) D)) &  ((r2_relset_1 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B D) (k10_seqfunc A C D)) (k10_seqfunc A (k7_seqfunc A B C) D)) & (r2_relset_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B D) (k10_seqfunc A C D)) (k10_seqfunc A (k8_seqfunc A B C) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (m2_valued_0 B k1_numbers A))  => (v2_seq_2 B)) ) ) ) ) ).
tt(t28_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C)) &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers A C))) ) ) )  & (v2_comseq_2 B))  =>  ((r1_xxreal_0 1 (k2_seq_2 B)) | (v1_series_1 A)) ) ) ) ) ) ).
tt(t28_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 2 B) 1) (k2_nat_1 (k4_nat_1 2 B) 1)) (k2_nat_1 (k4_nat_1 2 B) 3))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 1 12) (k13_complex1 1 (k4_nat_1 (k4_nat_1 4 (k2_nat_1 (k4_nat_1 2 B) 1)) (k2_nat_1 (k4_nat_1 2 B) 3))))) ) ) ) ) ) ) ).
tt(t28_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = k6_numbers)  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 k6_numbers C) | (r1_xxreal_0 (k8_real_1 6 (k3_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k1_newton B 3)) (k1_newton C 3)))) (k1_newton (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k1_newton B 2)) (k1_newton C 2)) 3))) ) ) ) ) ) ) ) ) ) ).
tt(t28_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ( ((k1_seq_1 B C) = (k7_xcmplx_0 A C))  &  ((k1_seq_1 B k6_numbers) = 1) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k1_seq_1 (k1_series_3 B) C) = (k7_xcmplx_0 (k1_newton A C) (k9_newton C))) ) ) ) ) ) ) ) ) ).
tt(t28_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 C D)) (k3_xcmplx_0 (k6_square_1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 C))) (k6_square_1 (k2_xcmplx_0 (k3_square_1 B) (k3_square_1 D)))))) ) ) ) ) ) ) ) ).
tt(t28_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_tarski (k3_setfam_1 A B)) = (k3_xboole_0 (k3_tarski A) (k3_tarski B))) ) ) ).
tt(t28_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (m1_subset_1 (a_3_3_setlim_1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(t28_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 C) => (v2_prob_1 (k7_setlim_2 A C B))) ) ) ) ) ) ).
tt(t28_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (r6_binop_1 A D C)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  ( (~  (E = k1_xboole_0) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k5_binop_1 A D (k7_setwiseo B A C E F) G) = (k7_setwiseo B A C E (k9_funcop_1 A B D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  ( ((v1_setwiseo C B) &  ((v1_setwiseo D A) &  ( ((k3_funct_2 B A E (k4_binop_1 B C)) = (k4_binop_1 A D))  &  (! [G:$i] :  ((m1_subset_1 G B) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  ((k3_funct_2 B A E (k5_binop_1 B C G H)) = (k5_binop_1 A D (k3_funct_2 B A E G) (k3_funct_2 B A E H))) ) ) ) ) ) ) )  =>  ((k3_funct_2 B A E (k1_finsop_1 B F C)) = (k1_finsop_1 A (k4_finseqop B A F E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) &  ( (~ (v1_scmfsa_m A))  & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2))) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) => (r1_tarski (k6_scmfsa_m B C A) (k2_sf_mastr (k3_sfmastr3 B C A D)))) ) ) ) ) ) ) ) ).
tt(t28_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ((k2_sf_mastr (k11_compos_1 k1_scmfsa_2 A)) = (k1_sf_mastr A)) ) ) ).
tt(t28_sgraph1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (? [D:$i] :  ((v1_finset_1 D) &  ( (D = (a_3_0_sgraph1 A B C))  &  ((k4_sgraph1 A B C) = (k5_card_1 D)) ) ) ) ) ) ) ) ) ).
tt(t28_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) &  ((v8_robbins1 A) &  ((v9_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v12_sheffer1 A)) ) ).
tt(t28_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B D))) C) = (k5_sheffer1 A C (k5_sheffer1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t28_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v5_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C))))  =>  ((r1_tarski (k2_simplex0 C D) (u1_pre_topc B)) =>  ((v1_pre_topc (k5_simplex0 C D)) & (m2_simplex0 (k5_simplex0 C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t28_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) => (v1_simplex1 (k4_simplex1 A B) A)) ) ) ) ) ).
tt(t28_sincos10,ax, ((k2_relset_1 k1_numbers k4_sincos10) = (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) ).
tt(t28_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) = (k10_real_1 (k1_seq_1 k1_sin_cos2 (k9_binop_2 A B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B))))  &  ((k9_real_1 (k1_seq_1 k7_sin_cos2 A) (k1_seq_1 k7_sin_cos2 B)) = (k10_real_1 (k1_seq_1 k1_sin_cos2 (k10_binop_2 A B)) (k8_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k4_sin_cos2 B)))) ) ) ) ) ) ).
tt(t28_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) A) k7_complex1)) = 1) ) ) ).
tt(t28_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k4_xcmplx_0 (k3_xcmplx_0 2 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B))))) ) ) ) ) ).
tt(t28_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k18_sin_cos (k6_real_1 A 2)) = k6_numbers) )  =>  ((k1_sin_cos4 (k6_real_1 A 2)) = (k10_real_1 (k9_real_1 1 (k20_sin_cos A)) (k17_sin_cos A))) ) ) ) ).
tt(t28_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) &  ((k17_sin_cos A) = 1) ) )  =>  (A = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t28_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  &  ( (~ (r1_xxreal_0 1 (k3_square_1 B)))  &  ((k11_binop_2 A B) = 1) ) ) ) ) ) ) ) ).
tt(t28_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 5 A)) (k3_xcmplx_0 2 (k3_sin_cos2 (k3_xcmplx_0 3 A)))) (k3_sin_cos2 A)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 7 A)) (k3_xcmplx_0 2 (k3_sin_cos2 (k3_xcmplx_0 5 A)))) (k3_sin_cos2 (k3_xcmplx_0 3 A)))) = (k7_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 3 A)) (k3_sin_cos2 (k3_xcmplx_0 5 A)))) ) ) ).
tt(t28_sin_cos9,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t28_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k7_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos A)) (k5_square_1 (k1_seq_1 k16_sin_cos A))) = 1)  &  ((k7_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos A) (k1_seq_1 k19_sin_cos A)) (k8_real_1 (k1_seq_1 k16_sin_cos A) (k1_seq_1 k16_sin_cos A))) = 1) ) ) ) ).
tt(t28_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)))) ) ) ) )  =>  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1))) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 2)))) ) ) ) ) ) ).
tt(t28_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_topreal1 A) => (v2_topreal1 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A))) ) ) ).
tt(t28_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k12_pscomp_1 A) (k13_pscomp_1 A))) = (k1_tarski (k12_pscomp_1 A))) ) ) ).
tt(t28_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r1_sprect_2 A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k10_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(t28_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 A)) B))  &  ((k20_pscomp_1 (k3_topreal1 2 A)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A)))) ) ) ) ) ) ) ).
tt(t28_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k18_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t28_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((k6_square_1 A) = (k6_square_1 B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t28_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( (~ (r1_stacks_1 A B))  =>  ((k13_stacks_1 A (k5_stacks_1 A B)) = (k13_stacks_1 A B)) ) ) ) ) ) ).
tt(t28_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k3_stirl2_1 k6_numbers A) = 1)  <=>  (A = k6_numbers) ) ) ) ).
tt(t28_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  ((v7_substut1 B A) =>  ((k39_substut1 A B) = (k11_sublemma A B (k39_substut1 A (k10_sublemma A B)))) ) ) ) ) ) ).
tt(t28_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (r2_hidden C B)) )  =>  (A = B) ) ) ) ) ).
tt(t28_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v5_substut1 B A) =>  ((k37_substut1 A B) = (k13_qc_lang1 A (k37_substut1 A (k27_substut1 A B)))) ) ) ) ) ) ).
tt(t28_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_substut2 E A D C) =>  ( ((r2_qc_lang2 A D C) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 E))) )  => (m2_subset_1 (k1_funct_1 E B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski B k1_numbers) =>  ((v1_supinf_2 C A B) <=> (r2_hidden (k10_supinf_2 k7_numbers A B C) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t28_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B C E))  &  ( (~ (r1_orders_2 B F E))  &  (~  ((k8_group_1 A (k1_symsp_1 A B C D E) (k1_symsp_1 A B F E D)) = (k8_group_1 A (k1_symsp_1 A B D C F) (k1_symsp_1 A B E F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k1_sysrel A) = (k4_relat_1 (k9_xtuple_0 (k1_sysrel A)))) ) ) ).
tt(t28_taxonom1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k2_relset_1 k1_numbers B))  & (r1_xxreal_0 (k1_xxreal_2 C) D))  => (r2_relset_1 A A (k13_lang1 A (k1_taxonom1 A B D)) (k1_taxonom1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t28_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E))) )  =>  ((r1_xxreal_0 E D) |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((k1_relset_1 k1_numbers G) = (k2_subset_1 k1_numbers))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k1_seq_1 G H) = (k9_real_1 (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C H D)) A)) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 D H) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) )  &  ((k9_real_1 (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k6_taylor_1 B C E D)) A)) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 D E) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1)))) = k6_numbers) ) )  =>  ((r2_fdiff_1 G (k2_rcomp_1 D E)) &  ( ((k1_seq_1 G E) = k6_numbers)  &  ( ((k1_seq_1 G D) = k6_numbers)  &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers G (k1_rcomp_1 D E))) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H (k2_rcomp_1 D E)) =>  ((k1_fdiff_1 G H) = (k7_real_1 (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) H) (k2_newton (k9_real_1 D H) A)) (k3_newton A))) (k10_real_1 (k8_real_1 F (k2_newton (k9_real_1 D H) A)) (k3_newton A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((v2_comseq_2 (k3_series_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B))) &  ( ((k1_seq_1 k16_sin_cos B) = (k4_series_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B)))  &  ((v2_comseq_2 (k3_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B))) &  ((k1_seq_1 k19_sin_cos B) = (k4_series_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B))) ) ) ) ) ) ) ) ) ).
tt(t28_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_tops_1 B A) &  ((v5_tops_1 C A) & (v5_tops_1 D A)) )  =>  ((k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) C D)))))) = (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k1_tops_1 A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t28_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) &  ((v3_pre_topc C A) & (r1_xboole_0 B C)) )  => (r1_xboole_0 (k2_pre_topc A B) (k2_pre_topc A C))) ) ) ) ) ) ) ) ).
tt(t28_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r8_pboole (k15_pre_poly A) (k5_termord A B C (k5_termord A B C D)) (k5_termord A B C D))) ) ) ) ) ) ) ) ).
tt(t28_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k3_tex_1 A B) = (k2_tex_1 A))  <=>  (A = (k6_domain_1 A B)) ) ) ) ) ) ).
tt(t28_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tex_2 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tdlat_3 C) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t28_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ( ((v2_tex_3 B A) & (v1_tex_3 C A))  |  ((v1_tex_3 B A) & (v2_tex_3 C A)) )  =>  ((v1_tex_3 (k2_tsep_1 A B C) A) & (m1_pre_topc (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t28_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_tex_4 A B) = (k3_tex_4 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t28_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ((m1_pre_topc B C) =>  ( ( (~ (r1_tsep_1 C D))  &  (~ (r1_tsep_1 D C)) )  |  ( ((k2_tsep_1 A C (k1_tsep_1 A B D)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ((k2_tsep_1 A C (k1_tsep_1 A D B)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden B E) &  ((v1_toler_1 E A C) & (m1_toler_1 E A C)) ) ) )  =>  ((k9_relat_1 C B) = (k3_tarski D)) ) ) ) ) ) ) ).
tt(t28_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ((r4_borsuk_2 A B D (k1_borsuk_2 A B C D E G) (k1_borsuk_2 A B C D F G)) => (r4_borsuk_2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) =>  (! [I:$i] :  ((m1_borsuk_2 I B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) =>  (! [J:$i] :  ((m1_borsuk_6 J A D E F G) =>  ( ((r3_borsuk_2 A D E F G) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) H (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) F C)) & (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) I (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) G C))) )  => (m1_borsuk_6 (k1_partfun1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) J C) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_borsuk_2 E (k2_borsuk_1 A B) (k4_borsuk_1 A B C D) (k4_borsuk_1 A B C D)) =>  ((k1_funct_1 (k11_topalg_4 A B C D) (k6_eqrel_1 (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k2_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k4_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) E)) = (k10_finseq_1 (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) (k9_topalg_4 A B C D E)) (k6_eqrel_1 (k2_topalg_1 B D) (k2_topalg_1 B D) (k4_topalg_1 B D) (k10_topalg_4 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ( ((k9_xtuple_0 B) = (k1_rcomp_1 k6_numbers 1))  => (m1_borsuk_2 B A (k2_topalg_6 A B) (k3_topalg_6 A B))) ) ) ) ) ).
tt(t28_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((v3_topdim_1 (k2_borsuk_1 A B)) =>  ((v3_topdim_1 (k2_borsuk_1 B A)) &  ((k4_topdim_1 (k2_borsuk_1 A B)) = (k4_topdim_1 (k2_borsuk_1 B A))) ) ) ) ) ) ) ).
tt(t28_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_topgen_1 A B) (k2_pre_topc A B))) ) ) ) ).
tt(t28_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))) =>  ( (~ (v1_finset_1 (k3_subset_1 (u1_struct_0 (k5_topgen_2 A B)) C)))  =>  ((k1_tops_1 (k5_topgen_2 A B) C) = (k7_subset_1 (u1_struct_0 (k5_topgen_2 A B)) C (k1_tarski B))) ) ) ) ) ) ) ).
tt(t28_topgen_3,ax, (! [A:$i] :  ((v4_card_3 A) => (v4_card_3 (k5_finsub_1 A))) ) ).
tt(t28_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ((k2_xboole_0 (k3_tarski A) (k3_tarski B)) = (k3_tarski (k2_setfam_1 A B))) ) ) ) ) ) ) ).
tt(t28_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((v3_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_topreal9 2 (k19_euclid A B) C) k2_topgen_5) k3_topgen_5) & (m1_subset_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_topreal9 2 (k19_euclid A B) C) k2_topgen_5) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ) ) ) ) ) ) ).
tt(t28_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_tops_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_tops_2 C A B) => (v1_tops_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t28_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v5_topreal1 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~ (r1_topreal1 (k15_euclid 2) B C A)) ) ) ) ) ) ) ) ) ).
tt(t28_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid A) = (k17_euclid B))  =>  ( ((k17_euclid C) = (k17_euclid B))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k19_euclid (k17_euclid C) (k18_euclid B))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid C) (k18_euclid B)) C)) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t28_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((v2_topreal4 B (k15_euclid 2)) &  ((r2_hidden A B) &  (C = (a_2_1_topreal4 A B)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t28_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( (B = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C (k9_real_1 1 A)) (k1_rlvect_1 (k15_euclid 2) D A)))  &  ( (~  (B = D) )  &  ((r1_xxreal_0 A 1) & (r1_xxreal_0 1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  =>  ((k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) A) = (k2_topreal1 2 B A)) ) ) ) ) ) ) ) ).
tt(t28_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r2_hidden B (k4_topreal9 A C B))) ) ) ) ) ) ).
tt(t28_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k19_euclid A B) = (k4_funct_4 1 2 A B)) ) ) ) ) ).
tt(t28_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((m1_subset_1 A (u1_struct_0 (k11_toprealb k10_toprealb))) =>  ( (~ (r1_xxreal_0 (k17_euclid A) (k1_real_1 1)))  & (r1_xxreal_0 (k17_euclid A) 1)) ) ) ) ).
tt(t28_toprealc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k5_algstr_0 A B C) C) = B) ) ) ) ) ) ) ).
tt(t28_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t28_tops_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_tops_1 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) & (r2_hidden C D))  =>  ( (~ (r1_xboole_0 B D))  &  (~ (r1_xboole_0 (k3_subset_1 (u1_struct_0 A) B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((v2_tops_2 B A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C)))) =>  ( (D = B)  => (v2_tops_2 D C)) ) ) ) ) ) ) ) ) ) ).
tt(t28_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v3_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski D C) &  ( (~  (D = k1_xboole_0) )  &  ((v3_pre_topc D A) & (r1_xboole_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v2_transgeo (k6_partfun1 (u1_struct_0 A)) A)) ) ).
tt(t28_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B A))  => (r2_hidden (k12_finseq_1 k5_numbers A) (k2_trees_1 B))) ) ) ) ) ).
tt(t28_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) =>  (? [C:$i] :  ( ((v2_trees_2 C A) & (m1_trees_2 C A))  & (r1_tarski B C)) ) ) ) ) ) ).
tt(t28_trees_3,ax, (! [A:$i] :  ((v4_trees_3 (k9_finseq_1 A)) <=>  ( (~ (v1_xboole_0 A))  & (v1_trees_1 A)) ) ) ).
tt(t28_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_trees_3 E (k2_zfmisc_1 A B)))  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_trees_3 F B))  =>  (! [G:$i] :  ((m2_finseq_1 G E) =>  (! [H:$i] :  ((m2_finseq_1 H F) =>  ( ( ((k4_finseq_1 H) = (k4_finseq_1 G))  &  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ((r2_hidden I (k4_finseq_1 G)) =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v5_relat_1 J (k2_zfmisc_1 A B)) &  ((v1_funct_1 J) & (v3_trees_2 J)) ) )  =>  ( (J = (k1_funct_1 G I))  =>  ((k1_funct_1 H I) = (k9_trees_3 A B J)) ) ) ) ) ) ) )  =>  ((k9_trees_3 A B (k4_trees_4 (k1_domain_1 A B C D) G)) = (k4_trees_4 D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  ( ((k3_finseq_1 (k2_trees_9 A B)) = (k3_finseq_1 (k1_trees_9 (k9_xtuple_0 A) B)))  &  ((k4_finseq_1 (k2_trees_9 A B)) = (k4_finseq_1 (k1_trees_9 (k9_xtuple_0 A) B))) ) ) ) ) ) ).
tt(t28_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ((m1_pre_topc B C) =>  ((k2_tsep_1 A B C) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) )  &  ( ( ((k2_tsep_1 A B C) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  => (m1_pre_topc B C))  &  ( ((m1_pre_topc C B) =>  ((k2_tsep_1 A B C) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) )  &  ( ((k2_tsep_1 A B C) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)))  => (m1_pre_topc C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))) =>  ( ( (E = (k9_subset_1 (u1_struct_0 A) (u1_struct_0 D) B))  &  ( (F = (k9_subset_1 (u1_struct_0 A) (u1_struct_0 D) C))  & (r2_tsep_1 A B C)) )  => (r2_tsep_1 D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_relat_1 (k1_tsp_2 A B) C) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k4_tex_4 A C))) ) ) ) ) ) ) ).
tt(t28_turing_1,ax,(r1_tarski (k9_xtuple_0 k15_comput_1) (k4_finseq_2 2 k5_numbers))).
tt(t28_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  => (r2_hidden (k4_tarski (k10_finseq_1 A B) k15_twoscomp) (k3_msafree2 (k34_twoscomp A B)))) ) ) ) ).
tt(t28_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_nat_d B A) => (r1_tarski (k2_uniroots B) (k2_uniroots A))) ) ) ) ) ).
tt(t28_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B C) (k11_polynom3 A B D)) =>  ( (B = (k9_polynom3 A))  | (r2_funct_2 k5_numbers (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t28_urysohn2,ax,(r1_tarski k2_urysohn1 (k1_xxreal_1 k6_numbers 1))).
tt(t28_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B E F D) =>  ((r2_hidden C (k24_qc_lang1 A E)) |  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = H) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B D H)) ) ) )  => (r1_valuat_1 A B E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (r2_hidden (k8_nat_1 A B C) (k2_relset_1 A B))) ) ) ) ) ) ).
tt(t28_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) & (v1_funct_1 A)) )  =>  ((k61_valued_1 A k6_numbers) = A) ) ) ).
tt(t28_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k9_xtuple_0 (k14_valued_2 B A)) = (k9_xtuple_0 B)) ) ) ) ) ).
tt(t28_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ( (~ (v3_funct_1 C))  &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ( (~  (D = (k4_struct_0 B)) )  &  (~  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  ((v1_funct_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D)) &  ((v1_funct_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A)))) &  ((v13_vectsp_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (k1_ranknull B C C (k1_vectsp11 C D A)) (k1_ranknull B C C (k1_vectsp11 C D A))) &  ((v1_mod_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) B (k1_ranknull B C C (k1_vectsp11 C D A)) (k1_ranknull B C C (k1_vectsp11 C D A))) & (m1_subset_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C D A)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C D A))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k4_algstr_0 A B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t28_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_algstr_0 A (k5_struct_0 A))) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(t28_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) => (r1_struct_0 D E)) ) )  => (m1_vectsp_4 C A D)) ) ) ) ) ) ) ) ) ).
tt(t28_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (m1_vectsp_4 (k1_vectsp_5 A B C (k2_vectsp_5 A B D E)) A (k2_vectsp_5 A B (k1_vectsp_5 A B D C) (k1_vectsp_5 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t28_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) => (r1_tarski (k1_vectsp_6 A B (k6_vectsp_6 A B C D)) (k1_vectsp_6 A B D))) ) ) ) ) ) ) ) ).
tt(t28_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ( ((k1_vectsp_9 A B) = (k1_vectsp_9 A C))  <=>  ((k2_vectsp_4 A B) = (k2_vectsp_4 A C)) ) ) ) ) ) ) ) ).
tt(t28_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k3_vfunct_1 B C E D) A) (k3_vfunct_1 B C (k2_partfun1 B k1_numbers E A) (k2_partfun1 B (u1_struct_0 C) D A))) &  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k3_vfunct_1 B C E D) A) (k3_vfunct_1 B C (k2_partfun1 B k1_numbers E A) D)) & (r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k3_vfunct_1 B C E D) A) (k3_vfunct_1 B C E (k2_partfun1 B (u1_struct_0 C) D A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k1_vfunct_2 A B E C) D) (k1_vfunct_2 A B (k2_partfun1 A k2_numbers E D) (k2_partfun1 A (u1_struct_0 B) C D))) &  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k1_vfunct_2 A B E C) D) (k1_vfunct_2 A B (k2_partfun1 A k2_numbers E D) C)) & (r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k1_vfunct_2 A B E C) D) (k1_vfunct_2 A B E (k2_partfun1 A (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v13_waybel_0 C A)) ) )  =>  ((v13_waybel_0 (k5_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k5_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t28_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((k1_yellow_2 (k7_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k2_tmap_1 (k2_waybel10 A) (k1_waybel10 (k3_waybel10 A) (k4_waybel10 A)) (k5_waybel10 A) (k7_waybel10 A))) = (k1_waybel10 (k4_waybel10 A) (k8_waybel10 A))) ) ) ).
tt(t28_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_waybel11 A (k4_waybel11 A B))) ) ) ) ) ).
tt(t28_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r3_orders_2 A C D))  &  (~ (r3_orders_2 A D C)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B))) )  => (r2_hidden (k1_yellow_0 A C) C)) ) ) ) ) ) ) ).
tt(t28_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_waybel_3 D A) <=> (v1_waybel_3 (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ( (C = B)  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  (B = (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A D))) ) ) )  |  ((v5_waybel_6 C (k2_yellow_1 (k5_waybel11 A))) &  (~  (C = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=> (v2_waybel_8 A)) ) ) ).
tt(t28_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_orders_2 A B C) &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_orders_2 A B E) => (r3_orders_2 A C E)) ) )  &  ( (~ (r3_orders_2 A D B))  & (r3_orders_2 A (k12_lattice3 A D C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_8 A) & (v2_waybel_8 B))  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_5_waybel17 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k5_waybel_0 A B)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t28_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v7_waybel_1 B A) &  ((r2_yellow_0 A C) & (r1_tarski C (k2_relset_1 (u1_struct_0 A) B))) )  =>  ((k2_yellow_0 A C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k2_yellow_0 A C))) ) ) ) ) ) ) ) ).
tt(t28_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v22_waybel_0 D A B) & (v22_waybel_0 E B C))  => (v22_waybel_0 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_waybel11 A (k3_yellow_9 A B)) = (k2_yellow_0 A B)) ) ) ) ) ).
tt(t28_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((k1_yellow_0 (k5_yellow_0 A B) C) = (k1_yellow_0 A C)) ) ) ) ) ) ) ).
tt(t28_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k7_relat_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) D) = (a_4_4_waybel24 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t28_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((r2_borsuk_3 A B) => (v1_waybel25 B)) ) ) ) ) ).
tt(t28_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  ( ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B)))  =>  ((v3_lattice3 (k1_waybel25 B)) & (v3_waybel_3 (k1_waybel25 B))) ) ) ) ) ) ).
tt(t28_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) & (l1_orders_2 D)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v3_orders_2 E) &  ((v4_orders_2 E) &  ((v5_orders_2 E) & (l1_orders_2 E)) ) ) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v3_orders_2 F) &  ((v4_orders_2 F) &  ((v5_orders_2 F) & (l1_orders_2 F)) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) &  ((v22_waybel_0 G B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 A) (u1_struct_0 B)) &  ((v22_waybel_0 H A B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 D) (u1_struct_0 E)) &  ((v22_waybel_0 I D E) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 E) (u1_struct_0 F)) &  ((v22_waybel_0 J E F) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 F))))) ) )  => (r2_funct_2 (u1_struct_0 (k2_waybel27 C D)) (u1_struct_0 (k2_waybel27 A F)) (k1_partfun1 (u1_struct_0 (k2_waybel27 C D)) (u1_struct_0 (k2_waybel27 B E)) (u1_struct_0 (k2_waybel27 B E)) (u1_struct_0 (k2_waybel27 A F)) (k4_waybel27 B C D E G I) (k4_waybel27 A B E F H J)) (k4_waybel27 A C D F (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) H G) (k1_partfun1 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 F) I J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k5_waybel11 A)) => (r2_hidden B (k4_waybel28 A))) ) ) ) ) ).
tt(t28_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_connsp_2 C A B))  =>  (? [D:$i] :  ( ((v3_pre_topc D (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_waybel29 (k2_yellow_1 (u1_pre_topc A)))))))  &  ((r2_hidden C D) & (m1_connsp_2 (k1_setfam_1 D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) => (r3_orders_2 A B (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C)))) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B))) ) ) ) ) ) ) ) ).
tt(t28_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_subset_1 (u1_struct_0 A) (k1_waybel30 A B) (k1_waybel30 A C)) = (k1_waybel30 A (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t28_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r1_ordinal1 (k1_waybel31 A) (k1_waybel31 (k2_yellow_1 (k5_waybel11 A))))) ) ).
tt(t28_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_waybel32 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A C (k1_waybel11 A B)) => (r3_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(t28_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_1 C) =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v4_waybel11 E) & (m1_yellow_9 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 E) (u1_struct_0 B) (u1_struct_0 A) F (k1_waybel34 A B C)) =>  ((v22_waybel_0 C A B) <=> (v1_t_0topsp F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  ((r1_orders_2 (k5_yellow_1 A B) C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_orders_2 (k3_waybel_3 A B E) (k4_waybel_3 A B C E) (k4_waybel_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v5_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C) => (r1_yellow_2 (u1_struct_0 A) (k2_yellow_1 (k7_waybel_0 A)) (k7_waybel_4 A B) (k7_waybel_4 A C))) ) ) ) ) ) ) ).
tt(t28_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((k4_waybel_6 A) = (k3_waybel_6 A)) ) ) ).
tt(t28_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_subset_1 D (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))) &  ((v2_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))))) ) ) )  =>  (~  ((r2_hidden B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r1_waybel_7 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_waybel_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  ((v1_finset_1 B) <=> (v1_waybel_3 B (k3_yellow_1 A))) ) ) ) ).
tt(t28_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A C) A A)) )  => (v4_pre_topc (k5_waybel_0 A B) A)) ) ) ) ) ).
tt(t28_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r1_xxreal_0 (k5_card_1 (u1_struct_0 (k5_weddwitt A B))) 1)) ) ) ) ) ).
tt(t28_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) D) = (k2_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((v2_wellord1 B) & (r1_tarski A (k1_relat_1 B)))  =>  ( (~  ( (~  (A = (k1_relat_1 B)) )  &  (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 B)) &  (A = (k1_wellord1 B C)) ) ) ) ) )  <=>  (! [C:$i] :  ((r2_hidden C A) =>  (! [D:$i] :  ((r2_hidden (k4_tarski D C) B) => (r2_hidden D A)) ) ) ) ) ) ) ) ) ).
tt(t28_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ((k3_int_2 A B) = (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t28_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  ((k3_xboole_0 A B) = A) ) ) ) ).
tt(t28_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k7_xboolean A B)) = (k6_xboolean B A)) ) ) ) ) ).
tt(t28_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 A B) = (k2_xcmplx_0 (k2_xcmplx_0 A C) (k6_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t28_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A k6_numbers) &  ((r1_xxreal_0 B k6_numbers) &  ((k2_xcmplx_0 A B) = k6_numbers) ) )  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t28_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ).
tt(t28_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C B))  => (r1_xxreal_0 (k4_xxreal_0 A C) B)) ) ) ) ) ) ) ).
tt(t28_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k4_xxreal_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t28_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_xxreal_2 (k4_xxreal_1 A B)) = A) ) ) ) ) ) ).
tt(t28_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 k1_xxreal_0 A) |  (B = (k3_xxreal_3 (k1_xxreal_3 B A) A)) ) ) ) ) ) ) ).
tt(t28_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((k1_yellow_0 A B) = (k15_lattice3 (k14_lattice3 A) B))  &  ((k2_yellow_0 A B) = (k16_lattice3 (k14_lattice3 A) B)) ) ) ) ) ).
tt(t28_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((r1_tarski (k4_yellow_3 A B (k3_waybel_0 (k3_yellow_3 A B) C)) (k3_waybel_0 A (k4_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k3_waybel_0 (k3_yellow_3 A B) C)) (k3_waybel_0 B (k5_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t28_yellow12,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_yellow_4 A (k4_waybel_0 A C) B) => (r1_tarski (k4_waybel_0 A B) (k4_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t28_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_yellow13 A) & (l1_waybel_9 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) ) ) ) ).
tt(t28_yellow14,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  & (v1_compts_1 A))  => (v1_compts_1 B)) ) ) ) ) ).
tt(t28_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) ) )  => (r1_ordinal1 (k1_card_1 (u1_struct_0 A)) (k1_card_1 (u1_pre_topc A)))) ) ).
tt(t28_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C A) &  ((v4_waybel_0 C A) & (m1_yellow_0 C A)) ) )  =>  ((m1_yellow_0 B C) =>  ((v4_yellow_0 B C) &  ((v4_waybel_0 B C) & (m1_yellow_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t28_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  ( ((r3_yellow18 A B) & (r1_yellow18 B C))  => (r3_yellow18 A C)) ) ) ) ) ) ) ).
tt(t28_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 C (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  ((r2_hidden B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_waybel_7 A C D) => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_orders_2 B) =>  ((k1_funct_2 A (u1_struct_0 B)) = (u1_struct_0 (k6_yellow_1 A B))) ) ) ) ).
tt(t28_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  =>  (! [D:$i] :  ((l2_functor0 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( (F = E)  =>  ((k3_functor0 C B (k14_functor0 A B C D) F) = (k3_functor0 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r2_yellow_0 A B)) )  => (v3_lattice3 A)) ) ) ).
tt(t28_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v12_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  =>  ((v12_waybel_0 (k4_yellow_3 A B C) A) & (v12_waybel_0 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ).
tt(t28_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_yellow_0 A (k2_yellow_4 A B C)) = (k13_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t28_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r1_yellow_5 A B (k3_yellow_0 A))) ) ) ) ) ).
tt(t28_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m3_yellow_6 C (u1_struct_0 B) A) => (r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A (k8_yellow_6 A B C))) (k3_tarski (a_3_0_yellow_6 A B C)))) ) ) ) ) ) ).
tt(t28_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v13_waybel_0 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A))))) ) ) ) ) ).
tt(t28_yellow_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) =>  ((v6_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden B (k1_tops_1 A C)) & (v2_compts_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t28_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  => (v1_tops_2 B A)) ) ) ) ).
tt(t28_zf_fund1,ax, ( ((k1_relset_1 k4_ordinal1 k2_zf_fund1) = k4_ordinal1)  &  ( ((k2_relset_1 k1_zf_lang k2_zf_fund1) = k1_zf_lang)  &  ((v2_funct_1 k2_zf_fund1) &  ((v2_funct_1 (k2_funct_1 k2_zf_fund1)) &  ( ((k9_xtuple_0 (k2_funct_1 k2_zf_fund1)) = k1_zf_lang)  &  ((k10_xtuple_0 (k2_funct_1 k2_zf_fund1)) = k4_ordinal1) ) ) ) ) ) ).
tt(t28_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  ( ((k28_zf_lang A) = (k26_zf_lang (k21_zf_lang A)))  &  ((k28_zf_lang A) = (k25_zf_lang (k22_zf_lang A))) ) ) ) ) ).
tt(t28_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( ((k1_funct_1 A 1) = 4)  => (v6_zf_lang A)) ) ) ).
tt(t28_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 (k1_tarski C) (k1_tarski D))) <=>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ).
tt(t28_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((r2_hidden k4_ordinal1 A) &  ((v2_ordinal2 C) &  ((v3_ordinal2 C) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  (~  ((r2_hidden B D) &  ((k4_ordinal4 A C D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t28_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k3_rlvect_1 D E F) = (k3_rlvect_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t290_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 k2_xxreal_0 B)) = (k2_xxreal_1 B A)) ) ) ) ) ).
tt(t291_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 B k1_xxreal_0)) = (k1_xxreal_1 A B)) ) ) ) ) ).
tt(t292_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 B k1_xxreal_0)) = (k3_xxreal_1 A B)) ) ) ) ) ).
tt(t293_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 B k1_xxreal_0)) = (k2_xxreal_1 A B)) ) ) ) ) ).
tt(t294_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 B k1_xxreal_0)) = (k4_xxreal_1 A B)) ) ) ) ) ).
tt(t295_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 B k1_xxreal_0)) = (k1_xxreal_1 A B)) ) ) ) ) ).
tt(t296_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 B k1_xxreal_0)) = (k3_xxreal_1 A B)) ) ) ) ) ).
tt(t297_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k6_subset_1 (k4_xxreal_1 A D) (k4_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t298_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 D C) |  ((k6_subset_1 (k2_xxreal_1 A D) (k4_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t299_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A D) (k4_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((k7_abcmiz_0 A B (k12_finseq_1 (u1_abcmiz_0 A) C)) = (k10_finseq_1 B (k5_abcmiz_0 A B C))) ) ) ) ) ) ) ).
tt(t29_abcmiz_1,ax,(r2_hidden (k2_pre_poly k2_abcmiz_1) k4_abcmiz_1)).
tt(t29_abcmiz_a,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k2_abcmiz_1 k4_abcmiz_1) =>  ((r2_hidden (k4_tarski (k2_relset_1 k2_abcmiz_1 B) A) k2_abcmiz_1) & (m2_finseq_2 (k7_finseq_1 B (k9_finseq_1 (k4_tarski (k2_relset_1 k2_abcmiz_1 B) A))) k2_abcmiz_1 k4_abcmiz_1)) ) ) ) ) ).
tt(t29_absvalue,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (A = (k18_complex1 A)) ) ) ).
tt(t29_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  => (r2_aff_1 A B C (k2_aff_1 A B C))) ) ) ) ) ) ) ).
tt(t29_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 F A) &  ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D F) & (r2_analoaf A B C D E)) ) ) )  =>  ( (B = C)  | (r2_hidden E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (v6_membered C))  =>  ((r1_afinsq_2 B C) =>  ((r1_xxreal_0 (k1_afinsq_1 (k4_afinsq_2 B)) A) |  ((k1_recdef_1 (k4_afinsq_2 B) A) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ).
tt(t29_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ( (D = (k5_afproj A B))  &  ( (E = (k4_tarski (k6_afproj A C) 2))  &  ((v1_aff_1 B A) & (v1_aff_4 C A)) ) )  =>  ((r1_incsp_1 (k13_afproj A) D E) <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_afvect0 A B (k1_afvect0 A B C)) = C) ) ) ) ) ) ) ).
tt(t29_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k1_funct_1 (k1_algspec1 (u4_struct_0 A) C) D) = (k1_funct_1 (k1_algspec1 (u4_struct_0 A) C) E))  =>  ( ((k3_relat_1 (k1_msualg_1 A D) (k1_algspec1 (u1_struct_0 A) B)) = (k3_relat_1 (k1_msualg_1 A E) (k1_algspec1 (u1_struct_0 A) B)))  &  ((k1_funct_1 (k1_algspec1 (u1_struct_0 A) B) (k2_msualg_1 A D)) = (k1_funct_1 (k1_algspec1 (u1_struct_0 A) B) (k2_msualg_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (m1_algstr_4 (k14_algstr_4 B) (k14_algstr_4 A))) ) ) ).
tt(t29_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t29_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v8_altcat_3 B A) & (v8_altcat_3 C A))  => (r2_altcat_3 A B C)) ) ) ) ) ) ) ).
tt(t29_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (r2_altcat_3 B (k3_functor0 A B C D) (k3_functor0 A B C E))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (r2_altcat_3 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k3_ami_2 k4_ami_2))) =>  ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) ) ) ) ).
tt(t29_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) ) )  =>  ((r1_tarski C D) => (r1_ami_wstd A B (k6_ami_wstd A B C) (k6_ami_wstd A B D))) ) ) ) ) ) ) ) ) ).
tt(t29_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A B C))) =>  ( ((r1_analmetr A B C) &  ((r4_analmetr (k2_analmetr A B C) D E F G) & (r4_analmetr (k2_analmetr A B C) D E F H)) )  => (r4_analmetr (k2_analmetr A B C) D E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((r3_analmetr A D E F G B C) <=>  ((r1_analort A B C D E F G) | (r1_analort A B C D E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_collsp B) &  ((v3_collsp B) &  ((v4_collsp B) &  ((v2_anproj_2 B) &  ((v3_anproj_2 B) & (l1_collsp B)) ) ) ) ) )  =>  (~  ( (B = (k5_anproj_1 A))  & (v7_anproj_2 B)) ) ) ) ) ) ) ) ).
tt(t29_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( ((k6_unialg_2 A) = k1_xboole_0)  =>  (! [B:$i] :  ((m1_freealg B A) =>  (~  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t29_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k53_aofa_i00 A B D E F G)) F) = (k2_xcmplx_0 (k21_aofa_i00 B k4_numbers C F) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k53_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((v8_armstrng B A) &  ((v9_armstrng B A) &  ((v10_armstrng B A) &  (C = (a_2_1_armstrng A B)) ) ) )  =>  ((r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B (k8_armstrng A C)) &  ((v6_armstrng C A) &  (! [D:$i] :  ( ((v6_armstrng D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ((r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B (k8_armstrng A D)) => (r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (~  ( (~ (r2_hidden A k4_ordinal1))  &  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  (! [C:$i] :  ((m1_subset_1 C k4_ordinal1) =>  (~  ( (A = (k4_tarski B C))  &  ((r1_arytm_3 B C) &  ( (~  (C = k1_xboole_0) )  &  (~  (C = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden A (k8_asympt_0 B)) => (r2_hidden B (k8_asympt_0 A))) ) ) ) ) ).
tt(t29_asympt_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((r2_funct_2 k5_numbers k1_numbers A (k1_asympt_1 2 1 k6_numbers)) &  ((r2_funct_2 k5_numbers k1_numbers B (k1_asympt_1 2 2 k6_numbers)) &  ((r1_tarski (k6_asympt_0 A) (k6_asympt_0 B)) &  (~  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ) ) ) ).
tt(t29_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) = (k1_group_1 (k7_autalg_1 A B))) ) ) ) ) ).
tt(t29_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r2_group_6 (k5_autgroup A) (k5_group_6 A (k10_group_5 A)))) ) ).
tt(t29_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_bagorder (k7_bagorder A) A)) ) ).
tt(t29_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  ((k2_bcialg_1 A (k2_bcialg_1 A B)) = B) ) ) ) ) ) ).
tt(t29_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 B A) <=>  ((k2_bcialg_1 A (k2_bcialg_1 A B)) = B) ) ) ) ) ) ).
tt(t29_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) = (k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))))) ) ) ) ) ) ) ) ).
tt(t29_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_finsop_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) B) (u1_bcialg_4 A)) = B) ) ) ) ) ).
tt(t29_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( ( (A = (k2_bcialg_5 A B C D))  &  ( (A = D)  &  (A = C) ) )  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A A A A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v1_bcialg_6 B A) &  ((k4_bcialg_6 A B) = C) )  =>  ((r2_hidden (k3_bcialg_6 A D B) (k4_bcialg_1 A)) <=> (r1_int_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) D) = (k1_bcialg_1 B (k1_bcialg_1 B C E) (k1_bcialg_1 B D E))) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t29_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k2_bhsp_1 A B C)) (k8_real_1 (k3_bhsp_1 A B) (k3_bhsp_1 A C)))) ) ) ) ) ) ).
tt(t29_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k5_normsp_1 A D C))) &  ((k2_seq_2 (k2_bhsp_2 A (k5_normsp_1 A D C))) = (k3_bhsp_1 A (k1_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_3 B A) & (m2_valued_0 C (u1_struct_0 A) B))  => (v1_bhsp_3 C A)) ) ) ) ) ) ) ).
tt(t29_bhsp_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 A (k3_bhsp_1 B (k1_normsp_1 B C E)))) ) ) ) )  &  ((v1_bhsp_2 C B) &  ((k1_bhsp_2 B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D E (k4_struct_0 C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k5_series_1 2 A) B) =>  ((r1_xxreal_0 (k5_series_1 2 (k2_xcmplx_0 A 1)) B) |  ((k1_funct_1 (k1_binari_3 (k2_xcmplx_0 A 1) B) (k2_xcmplx_0 A 1)) = k8_margrel1) ) ) ) ) ) ) ).
tt(t29_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r2_int_1 B C (k5_series_1 2 A)) =>  ( ( (~  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C)) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  (~ (r1_xxreal_0 k6_numbers C)) ) ) )  |  ((k2_binari_4 A B) = (k2_binari_4 A C)) ) ) ) ) ) ) ) ) ).
tt(t29_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k1_boolealg A B C) (k5_lattices A)) <=> (r3_lattices A B C)) ) ) ) ) ) ) ).
tt(t29_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_borsuk_1 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B) D) = C) ) ) ) ) ) ) ) ) ).
tt(t29_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_connsp_1 A k5_topmetr) &  ((v2_compts_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ( (A = B)  & (r1_tarski (k1_rcomp_1 (k5_seq_4 B) (k4_seq_4 B)) B))  =>  ((k1_rcomp_1 (k5_seq_4 B) (k4_seq_4 B)) = B) ) ) ) ) ) ).
tt(t29_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k2_borsuk_5 A B)) <=>  ((v1_rat_1 C) &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)))) =>  ( ( (A = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 k6_numbers (k10_real_1 1 2)) (k1_rcomp_1 k6_numbers 1)))  &  (B = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 (k10_real_1 1 2) 1) (k1_rcomp_1 k6_numbers 1))) )  =>  ((k9_subset_1 (u1_struct_0 (k1_pre_topc (k2_borsuk_1 k5_topmetr k5_topmetr) B)) (k2_struct_0 (k1_pre_topc (k2_borsuk_1 k5_topmetr k5_topmetr) A)) (k2_struct_0 (k1_pre_topc (k2_borsuk_1 k5_topmetr k5_topmetr) B))) = (k2_zfmisc_1 (k1_tarski (k10_real_1 1 2)) (k1_rcomp_1 k6_numbers 1))) ) ) ) ) ) ).
tt(t29_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ( ((k9_xtuple_0 G) = (k1_enumset1 A B F))  &  ( ((k1_funct_1 G A) = C)  &  ( ((k1_funct_1 G B) = D)  &  ((k1_funct_1 G F) = E) ) ) )  =>  (G = (k1_borsuk_7 A B F C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bspace,ax, (! [A:$i] :  ((v8_vectsp_1 (k7_bspace A) k2_bspace) &  ((v9_vectsp_1 (k7_bspace A) k2_bspace) &  ((v10_vectsp_1 (k7_bspace A) k2_bspace) & (v11_vectsp_1 (k7_bspace A) k2_bspace)) ) ) ) ).
tt(t29_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k3_enumset1 C D E F G))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (F = G) )  & (r1_xboole_0 (k15_bvfunc_1 A I (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G)) (k15_bvfunc_1 A H C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v3_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) ) )  => (r2_bvfunc_1 A B (k6_partit1 A))) ) ) ) ).
tt(t29_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A (k9_bvfunc_1 A B D) C) C)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t29_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B B) (k1_bvfunc_1 A B)) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc26 A B B)) B)) ) ) ) ) ).
tt(t29_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_1 A D C) B E) (k6_bvfunc_1 A (k6_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k7_bvfunc_2 A C B E) (k1_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E)) (k1_bvfunc_1 A (k7_bvfunc_2 A (k2_bvfunc_1 A C (k1_bvfunc_1 A D)) B E)))))) ) ) ) ) ) ) ) ) ) ).
tt(t29_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A)) &  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A))) )  => (r2_funct_2 A k6_margrel1 D (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t29_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A (k5_bvfunc_1 A B C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t29_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A B D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t29_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) C)) ) ) ) ) ) ) ) ) ).
tt(t29_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_c0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_c0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k1_algstr_0 (k11_c0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_seq_1 D H) = (k7_real_1 (k1_seq_1 B H) (k1_seq_1 C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_rlsub_1 (k7_c0sp2 A) (k10_funcsdom (u1_struct_0 A)))) ) ).
tt(t29_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ( ((k2_calcul_1 A E) = (k4_substut2 A B C D))  & (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E) (k2_calcul_1 A E)))  =>  ((r2_hidden D (k3_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E))) |  ((r2_hidden D (k24_qc_lang1 A (k11_cqc_lang A C B))) | (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E) (k11_cqc_lang A C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C)) &  ((v3_funct_2 D (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C))))) ) )  =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k3_calcul_2 (k3_cqc_lang A) C D) (k12_finseq_1 (k3_cqc_lang A) (k5_calcul_2 A (k4_finseq_5 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))))))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k3_calcul_2 (k3_cqc_lang A) C D) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t29_card_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_card_1 A) = (k1_card_1 (k1_tarski B)))  <=>  (? [C:$i] :  (A = (k1_tarski C)) ) ) ) ) ).
tt(t29_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k3_card_2 (k2_card_2 A B) C) = (k2_card_2 (k3_card_2 A C) (k3_card_2 B C))) ) ) ) ) ) ) ).
tt(t29_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_card_1 (k1_funct_1 (k2_card_3 A) B)) = (k1_funct_1 A B)) ) ) ) ) ).
tt(t29_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (~  ((r2_hidden (k1_card_5 A) A) &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  (~  ( ((k9_xtuple_0 B) = (k1_card_5 A))  &  ((r1_tarski (k10_xtuple_0 B) A) &  ((v2_ordinal2 B) &  ( (A = (k4_ordinal2 B))  &  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  &  (~ (r2_hidden k6_numbers (k10_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_card_fil,ax,(v6_card_fil k4_ordinal1)).
tt(t29_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  => (r1_tarski (k2_card_fin (k5_relat_1 C A) D B) (k2_card_fin C D B))) ) ) ) ) ) ).
tt(t29_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v4_card_lar A) => (v4_card_fil A)) ) ) ).
tt(t29_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((k5_cat_1 A B B C (k4_cat_1 A B) D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t29_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ( ( ((k3_graph_1 A D) = (k4_graph_1 A C))  &  ((k3_graph_1 B F) = (k4_graph_1 B E)) )  =>  ((k1_cat_1 (k8_cat_2 A B) (k10_cat_2 A B C E) (k10_cat_2 A B D F)) = (k10_cat_2 A B (k1_cat_1 A C D) (k1_cat_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( ((v2_cat_3 D A B C) & (v8_cat_1 D A B C))  => (v9_cat_1 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t29_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_cat_1 A B (k2_cat_4 A (k1_cat_4 A) B) B (k11_cat_4 A B) (k10_cat_4 A B)) = (k4_cat_1 A B))  &  ( ((k5_cat_1 A (k2_cat_4 A (k1_cat_4 A) B) B (k2_cat_4 A (k1_cat_4 A) B) (k10_cat_4 A B) (k11_cat_4 A B)) = (k4_cat_1 A (k2_cat_4 A (k1_cat_4 A) B)))  &  ( ((k5_cat_1 A B (k2_cat_4 A B (k1_cat_4 A)) B (k13_cat_4 A B) (k12_cat_4 A B)) = (k4_cat_1 A B))  &  ((k5_cat_1 A (k2_cat_4 A B (k1_cat_4 A)) B (k2_cat_4 A B (k1_cat_4 A)) (k12_cat_4 A B) (k13_cat_4 A B)) = (k4_cat_1 A (k2_cat_4 A B (k1_cat_4 A)))) ) ) ) ) ) ) ) ).
tt(t29_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k11_cat_5 A B))) =>  ( (C = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A (k14_cat_5 A B C) (k15_cat_5 A B C)) (k13_cat_5 A B C)))  &  ( ((k3_graph_1 A (k15_cat_5 A B C)) = (k4_graph_1 A (k13_cat_5 A B C)))  &  ( ((k14_cat_5 A B C) = (k1_cat_1 A (k13_cat_5 A B C) (k15_cat_5 A B C)))  &  ( ((k3_graph_1 (k11_cat_5 A B) C) = (k14_cat_5 A B C))  &  ((k4_graph_1 (k11_cat_5 A B) C) = (k15_cat_5 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k24_binop_2 2 A) B) =>  ((k5_card_1 (k2_catalan2 B A)) = (k11_binop_2 (k13_complex1 (k21_binop_2 (k23_binop_2 B 1) (k24_binop_2 2 A)) (k21_binop_2 (k23_binop_2 B 1) A)) (k6_newton A B))) ) ) ) ) ) ).
tt(t29_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ( ((r2_hidden G (k2_cat_1 A D E)) & (r2_hidden H (k2_cat_1 A E F)))  =>  (! [I:$i] :  ((m1_subset_1 I (k3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) D E F) (k13_catalg_1 A))) =>  ( (I = (k2_finseq_4 (u4_struct_0 A) H G))  =>  (! [J:$i] :  ((m2_pboole J (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k1_instalg1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k13_catalg_1 B) (k11_catalg_1 A B C) (k12_catalg_1 A B C)))) =>  ((r8_pboole (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) J (k1_catalg_1 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) C)) =>  ((k5_msualg_3 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A) (k1_instalg1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k13_catalg_1 B) (k11_catalg_1 A B C) (k12_catalg_1 A B C)) (k10_catalg_1 (u1_struct_0 A) D E F) J I) = (k2_finseq_4 (u4_struct_0 B) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C H) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_cc0sp2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_cc0sp2 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_cc0sp2 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k5_algstr_0 (k5_cc0sp2 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers D H) = (k11_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers B H) (k3_funct_2 (u1_struct_0 A) k2_numbers C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  ( ((k3_comseq_2 A) = k6_numbers)  |  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((m2_valued_0 B k2_numbers A) & (v2_relat_1 B))  =>  ((k3_comseq_2 (k36_valued_1 k5_numbers k2_numbers B)) = (k12_complex1 (k3_comseq_2 A))) ) ) ) ) ) ) ) ).
tt(t29_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v6_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski C (k1_relset_1 k2_numbers (k46_valued_1 k2_numbers k2_numbers k2_numbers A B))) &  ((r2_cfdiff_1 A C) & (r2_cfdiff_1 B C)) )  =>  ((r2_cfdiff_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_hidden D C) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers A B) C) D) = (k11_complex1 (k2_cfdiff_1 A D) (k2_cfdiff_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k5_struct_0 (k8_cfuncdom A)) = (k5_cfuncdom A)) ) ) ).
tt(t29_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k1_numbers (k55_valued_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C)) (k20_valued_1 A k1_numbers k1_numbers (k55_valued_1 A k2_numbers B) (k55_valued_1 A k2_numbers C)))) ) ) ) ) ) ).
tt(t29_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k10_cgames_1 B)) => (r1_ordinal1 (k9_cgames_1 A) (k9_cgames_1 B))) ) ) ) ) ).
tt(t29_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 B F))) ) )  =>  ((r1_tarski (k3_chain_1 A C B) (k3_chain_1 A D E)) <=>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 E F)) &  ( (~ (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 E F)))  & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  ((r1_tarski C B) =>  (! [D:$i] :  ((m2_glib_000 D A B (k21_glib_000 A B)) =>  (! [E:$i] :  ((m2_glib_000 E D C (k21_glib_000 D C)) => (m2_glib_000 E A C (k21_glib_000 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  (! [C:$i] :  ((m1_circcmb3 C A) =>  (! [D:$i] :  ((m2_circcmb3 D A B) =>  (! [E:$i] :  ((m2_circcmb3 E A C) => (v4_circcomb (k3_circcomb B C D E) (k2_circcomb B C))) ) ) ) ) ) ) ) ) ) ).
tt(t29_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B)))  =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 B)) =>  ( (I = J)  =>  ((k3_circuit1 C F G I) = (k3_circuit1 B E H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  ( ((r2_circtrm1 A B) & (r2_circtrm1 B C))  => (r2_circtrm1 A C)) ) ) ) ) ) ) ).
tt(t29_classes1,ax, ((k4_classes1 k1_xboole_0) = k1_xboole_0) ).
tt(t29_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_classes1 A) &  ((v1_ordinal1 A) & (r2_hidden B A)) )  => (r2_hidden (k6_classes1 B) A)) ) ) ).
tt(t29_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_clopban1 C A B) &  ((v2_clopban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((k1_seq_1 (k13_clopban1 A B) C) = (k4_seq_4 (k12_clopban1 A B C))) ) ) ) ) ) ) ).
tt(t29_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 (k4_normsp_0 A B) C) k6_numbers)) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D)))) ) ) ) )  & (v2_clopban3 B A)) ) ) ) ) ) ) ).
tt(t29_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k18_complex1 (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C)) = (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))  &  ((r1_xxreal_0 C D) =>  ((k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) D) (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))) = (k9_real_1 (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) D) (k1_seq_1 (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k5_closure1 A B (k2_msualg_3 A B)) B)) ) ) ).
tt(t29_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_funct_1 (k6_partfun1 (k6_closure2 A B))) &  ((v1_funct_2 (k6_partfun1 (k6_closure2 A B)) (k6_closure2 A B) (k6_closure2 A B)) &  ((v10_closure2 (k6_partfun1 (k6_closure2 A B)) A B) & (m1_subset_1 (k6_partfun1 (k6_closure2 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) ) ) ) ) ) ).
tt(t29_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t29_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k6_clvect_1 A D C))) &  ((k2_seq_2 (k2_clvect_2 A (k6_clvect_1 A D C))) = (k13_csspace A (k1_clvect_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 C (k13_csspace A (k1_normsp_1 A B E)))) ) ) ) )  &  ((v1_clvect_2 B A) &  ((k1_clvect_2 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B)))) =>  (~  ( (! [D:$i] :  ((r2_hidden D C) => (v1_finset_1 (k1_xtuple_0 D))) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D A))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E A))  =>  ((r1_tarski D E) =>  (! [F:$i] :  ((r2_hidden (k4_tarski D F) C) => (r2_hidden (k4_tarski E F) C)) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D A))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden (k4_tarski D E) C) & (r2_hidden (k4_tarski D F) C))  => (r2_hidden (k2_tarski E F) B)) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v8_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  (C = (k6_cohsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_coh_sp,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k15_coh_sp A))) ).
tt(t29_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ( ((k5_card_1 C) = (k5_real_1 A 1))  => (v3_combgras (k7_combgras A B C) A B)) ) ) ) ) ) ) ) ).
tt(t29_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k15_complex1 A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t29_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 A B) = (k2_xcmplx_0 (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B))) (k3_xcmplx_0 (k7_real_1 (k1_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B))) (k8_real_1 (k4_complex1 A) (k3_complex1 B))) k7_complex1))) ) ) ) ) ).
tt(t29_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k3_vectsp_1 k1_complfld B A) = (k5_struct_0 k1_complfld))  =>  ( (A = (k4_struct_0 k1_complfld))  |  (B = A) ) ) ) ) ) ) ).
tt(t29_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k1_valued_1 A B) = (k1_valued_1 B A)) ) ) ) ) ) ).
tt(t29_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  ((v8_compl_sp A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v1_finset_1 B))  &  ((v4_card_3 B) & (v1_xboole_0 (k2_topgen_1 A B))) ) ) ) ) ) ) ) ).
tt(t29_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k8_compos_1 A (k8_compos_1 A B C) D) = (k8_compos_1 A B (k8_compos_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t29_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  ((k62_valued_1 B) = (k6_xcmplx_0 (k5_card_1 B) 1)) ) ) ) ) ).
tt(t29_comptrig,ax, ((k10_xtuple_0 k19_sin_cos) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t29_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) &  ((v2_margrel1 A) & (v2_comput_1 A)) ) ) ) )  =>  ((v3_margrel1 A k5_numbers) & (m2_rfunct_3 A (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers))) ) ) ).
tt(t29_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  <=> (v2_relat_1 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(t29_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r2_funct_2 k5_numbers k2_numbers (k10_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)) (k25_valued_1 k5_numbers k2_numbers (k10_comseq_3 A) B))) ) ) ) ).
tt(t29_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) )  =>  ((r2_conlat_1 A C B) <=> (r1_tarski (u3_conlat_1 A B) (u3_conlat_1 A C))) ) ) ) ) ) ) ).
tt(t29_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_connsp_1 A B C)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_connsp_1 A B C)) ) ) ) ) ) ) ).
tt(t29_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_connsp_2 C A B) => (r1_tarski B C)) ) ) ) ) ) ).
tt(t29_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  ((k2_pre_topc (k1_pre_topc A C) (k4_connsp_3 A B C)) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A B) C)) ) ) ) ) ) ) ) ).
tt(t29_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rlvect_2 E A) =>  ( ((v2_convex1 E A) &  ((k3_rlvect_2 A E) = (k8_domain_1 (u1_struct_0 A) B C D)) )  =>  ( (B = C)  |  ( (C = D)  |  ( (D = B)  |  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k1_funct_1 E B) (k1_funct_1 E C)) (k1_funct_1 E D)) = 1)  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E B)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E C)) &  ((r1_xxreal_0 k6_numbers (k1_funct_1 E D)) &  ((k6_rlvect_2 A E) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B (k1_funct_1 E B)) (k1_rlvect_1 A C (k1_funct_1 E C))) (k1_rlvect_1 A D (k1_funct_1 E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_convex4 D A) => (r1_convex4 A (k7_convex4 A B (k7_convex4 A C D)) (k7_convex4 A (k3_xcmplx_0 B C) D))) ) ) ) ) ) ) ) ).
tt(t29_cqc_lang,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k17_funcop_1 A B C) = (k16_funcop_1 (k4_tarski A B) C)) ) ) ) ).
tt(t29_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v3_qc_lang1 B A) &  (C = (k18_qc_lang1 A B)) )  =>  ((k14_cqc_sim1 A B) = (k6_cqc_lang A (k14_cqc_sim1 A C))) ) ) ) ) ) ) ) ).
tt(t29_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( ((r2_cqc_the1 A B C) & (r2_cqc_the1 A B D))  => (r2_cqc_the1 A B (k8_finseq_1 (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1) C D))) ) ) ) ) ) ) ) ) ).
tt(t29_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden E (k24_qc_lang1 A C)) |  ((r2_hidden F (k24_qc_lang1 A D)) | (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A E B) (k12_cqc_lang A F C)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r5_cqc_the3 A B C) <=> (r4_cqc_the3 A (k6_domain_1 (k3_cqc_lang A) B) (k6_domain_1 (k3_cqc_lang A) C))) ) ) ) ) ) ) ).
tt(t29_csspace4,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 B) => (v1_comseq_2 (k25_valued_1 k5_numbers k2_numbers B A))) ) ) ) ) ).
tt(t29_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_csspace A (k4_struct_0 A) B) = k6_numbers) ) ) ) ) ).
tt(t29_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  (! [L:$i] :  ((m1_subset_1 L A) =>  (! [M:$i] :  ((m1_subset_1 M A) =>  (! [N:$i] :  ((m1_subset_1 N A) =>  (! [O:$i] :  ((m1_subset_1 O A) =>  (! [P:$i] :  ((m1_subset_1 P A) =>  (! [Q:$i] :  ((m1_subset_1 Q A) =>  (? [R:$i] :  ((m2_finseq_1 R A) &  ((v3_card_1 R 16) &  ( ((k1_funct_1 R 1) = B)  &  ( ((k1_funct_1 R 2) = C)  &  ( ((k1_funct_1 R 3) = D)  &  ( ((k1_funct_1 R 4) = E)  &  ( ((k1_funct_1 R 5) = F)  &  ( ((k1_funct_1 R 6) = G)  &  ( ((k1_funct_1 R 7) = H)  &  ( ((k1_funct_1 R 8) = I)  &  ( ((k1_funct_1 R 9) = J)  &  ( ((k1_funct_1 R 10) = K)  &  ( ((k1_funct_1 R 11) = L)  &  ( ((k1_funct_1 R 12) = M)  &  ( ((k1_funct_1 R 13) = N)  &  ( ((k1_funct_1 R 14) = O)  &  ( ((k1_funct_1 R 15) = P)  &  ((k1_funct_1 R 16) = Q) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v4_dickson A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r1_orders_2 A (k8_nat_1 (u1_struct_0 A) B C) (k8_nat_1 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C A B) = (k9_diff_1 C B A)) ) ) ) ) ) ) ).
tt(t29_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H k1_numbers k1_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers H I) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 I)) (k8_real_1 B I)) C)) ) )  & (r2_zfmisc_1 D E F G))  =>  ((k11_diff_1 H D E F G) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers D (k26_valued_1 k1_numbers k1_numbers E A)) B C) = (k9_real_1 (k9_diff_1 D B C) (k8_real_1 A (k9_diff_1 E B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) (k7_real_1 A (k13_complex1 B 2))) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k19_sin_cos) (k9_real_1 A (k13_complex1 B 2))))) ) ) ) ) ) ).
tt(t29_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_dilworth (k9_subset_1 (u1_struct_0 A) C B) (k5_yellow_0 A B)) & (m1_subset_1 (k9_subset_1 (u1_struct_0 A) C B) (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B))))) ) ) ) ) ) ) ).
tt(t29_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_diraf A B C D) &  ( (~ (r1_diraf A B C D))  &  ( (~ (r1_diraf A C B D))  &  (~ (r1_diraf A B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k4_subset_1 A B C) = (a_3_2_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t29_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots (k9_int_3 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (B = C)  =>  ((k5_group_1 (k1_uniroots (k9_int_3 A)) D B) = (k2_binom (k9_int_3 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  ( (D = (k6_int_1 3 A))  =>  ((r1_xxreal_0 A 3) |  ( (~  (D = (k4_struct_0 (k9_int_3 A))) )  &  (~  ((k2_binom (k9_int_3 A) D B) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ((k4_cat_1 (k11_ens_1 A) B) = (k5_ens_1 A (k13_ens_1 A B))) ) ) ) ) ).
tt(t29_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k3_finseq_1 (k1_matrprob A C D)) = (k4_nat_1 D (k1_matrix_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_enumset1,ax, (! [A:$i] :  ((k2_tarski A A) = (k1_tarski A)) ) ).
tt(t29_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A D (k3_eqrel_1 A B C)) =>  (! [E:$i] :  (~  ((r2_hidden E A) &  ( (~  ((k6_eqrel_1 A A D E) = (k6_eqrel_1 A A B E)) )  &  (~  ((k6_eqrel_1 A A D E) = (k6_eqrel_1 A A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_funct_1 (k4_equation A) B)) => (r2_hidden (k1_xtuple_0 C) (k1_funct_1 (u3_msualg_1 A (k3_equation A)) B))) ) ) ) ) ) ).
tt(t29_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k15_e_siec A) (k15_e_siec A)) = (k15_e_siec A))  &  ( ((k3_relat_1 (k15_e_siec A) (k16_e_siec A)) = (k15_e_siec A))  &  ( ((k3_relat_1 (k16_e_siec A) (k15_e_siec A)) = (k16_e_siec A))  &  ((k3_relat_1 (k16_e_siec A) (k16_e_siec A)) = (k16_e_siec A)) ) ) ) ) ) ).
tt(t29_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k5_algstr_0 (k15_euclid A) B C) (k5_algstr_0 (k15_euclid A) D E)) = (k9_binop_2 (k10_binop_2 (k10_binop_2 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  =>  ( ( (~ (r1_xxreal_0 k32_sin_cos (k3_euclid_3 A)))  =>  ((k3_euclid_3 (k4_algstr_0 (k15_euclid 2) A)) = (k7_real_1 (k3_euclid_3 A) k32_sin_cos)) )  &  ((r1_xxreal_0 k32_sin_cos (k3_euclid_3 A)) =>  ((k3_euclid_3 (k4_algstr_0 (k15_euclid 2) A)) = (k9_real_1 (k3_euclid_3 A) k32_sin_cos)) ) ) ) ) ) ).
tt(t29_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 B (k8_euclid A C D)) = (k9_real_1 (k23_rvsum_1 B C) (k23_rvsum_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t29_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k23_rvsum_1 A B) = (k7_real_1 (k7_real_1 (k8_real_1 (k1_euclid_5 A) (k1_euclid_5 B)) (k8_real_1 (k2_euclid_5 A) (k2_euclid_5 B))) (k8_real_1 (k3_euclid_5 A) (k3_euclid_5 B)))) ) ) ) ) ).
tt(t29_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((r2_hidden A (k6_jgraph_6 C D E)) &  ((r2_hidden B (k8_jgraph_6 C D E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~ (r2_hidden F (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k5_jgraph_6 C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ( (A = C)  |  ((k23_rvsum_1 (k6_euclid_7 B A) (k6_euclid_7 B C)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t29_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k1_rlvect_1 (k15_euclid A) B 1) = B)  &  ((k1_rlvect_1 (k15_euclid A) B k6_numbers) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t29_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ((k21_euclid A) = (k5_euclid A)) ) ) ) ) ).
tt(t29_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((k1_funct_1 (k10_funct_7 C A B) A) = (k1_funct_1 C B)) ) ) ) ) ) ).
tt(t29_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) <=>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((k3_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k2_compos_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (~  ( ((k3_extreal1 A) = k1_supinf_1)  &  ( (~  (A = k1_supinf_1) )  &  (~  (A = k2_supinf_1) ) ) ) ) ) ) ).
tt(t29_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 A) (k2_msafree2 B)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 B D))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)))  =>  ((k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) (k6_circuit2 (k2_circcomb A B) (k3_circcomb A B C D) E) (u1_struct_0 B)) = (k6_circuit2 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k15_facirc_1 A B C) (k18_facirc_1 A B C) D 2) (k15_facirc_1 A B C) (k18_facirc_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t29_fcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  ((v1_rcomp_1 A) & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) )  => (v1_rcomp_1 (k7_relset_1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t29_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k8_real_1 (k1_seq_1 k24_sin_cos B) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t29_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k1_sin_cos9 B) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 (k1_seq_1 k29_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t29_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k10_prob_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) ) ) ) )  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) & (v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) ) ) ) ) ) ).
tt(t29_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k9_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3))) B) D) = (k10_prepower (k9_real_1 A D) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) (k1_taylor_1 2)) A) C) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos C)) (k7_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t29_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))))) &  ((r2_relset_1 k1_numbers k1_numbers D (k47_valued_1 k1_numbers k1_numbers k1_numbers E F)) &  ((r2_relset_1 k1_numbers k1_numbers F (k1_taylor_1 2)) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ( ((k1_seq_1 E G) = (k5_square_1 A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers))  &  ( ((k1_seq_1 C G) = (k10_real_1 G A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 C G) (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 C G)))  &  ( (~  (G = k6_numbers) )  &  (~ (r1_xxreal_0 A k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))) B) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k4_sin_cos6)) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 1 2)))) B) G) = (k1_seq_1 k4_sin_cos6 (k10_real_1 G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k30_sin_cos))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k30_sin_cos) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k30_sin_cos) C) E) = (k9_real_1 (k10_real_1 (k8_real_1 A (k1_seq_1 k19_sin_cos E)) (k1_seq_1 k16_sin_cos E)) (k10_real_1 (k7_real_1 (k8_real_1 A E) B) (k5_square_1 (k1_seq_1 k16_sin_cos E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers D k2_fdiff_9))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k2_fdiff_9) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k2_fdiff_9) C) E) = (k9_real_1 (k10_real_1 A (k1_seq_1 k16_sin_cos E)) (k10_real_1 (k8_real_1 (k7_real_1 (k8_real_1 A E) B) (k1_seq_1 k19_sin_cos E)) (k5_square_1 (k1_seq_1 k16_sin_cos E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff (k1_nat_1 A 1)) = (k6_xcmplx_0 (k1_pre_ff (k1_nat_1 A 2)) (k1_pre_ff A))) ) ) ).
tt(t29_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_nat_1 2 (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1))) = (k2_nat_1 (k4_nat_1 (k1_fib_num3 (k2_nat_1 A 1)) (k1_pre_ff A)) (k4_nat_1 (k1_fib_num3 A) (k1_pre_ff (k2_nat_1 A 1))))) ) ) ).
tt(t29_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( ((r1_xxreal_0 B A) &  (~ (r1_xxreal_0 B 1)) )  |  ( (B = 1)  &  (~ (r1_xxreal_0 A B)) ) )  =>  ((k1_int_1 (k2_xcmplx_0 (k3_xcmplx_0 (k3_power k1_fib_num B) (k1_pre_ff A)) (k13_complex1 1 2))) = (k1_pre_ff (k2_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t29_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((r5_finseq_8 A B C) => (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 B))) ) ) ) ) ) ) ).
tt(t29_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((r2_hidden B D) & (r2_hidden (k4_filter_0 A B C) D))  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ).
tt(t29_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r6_binop_1 A C D) & (r6_binop_1 B E F))  <=> (r6_binop_1 (k2_zfmisc_1 A B) (k6_filter_1 A B C E) (k6_filter_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_filter_2 A B) = (k2_filter_0 (k1_lattice2 A) (k1_filter_2 A B)))  &  ((k6_filter_2 (k1_lattice2 A) (k1_filter_2 A B)) = (k2_filter_0 A B)) ) ) ) ) ) ).
tt(t29_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k7_finseq_1 A B)))) ) ) ) ).
tt(t29_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski (k10_xtuple_0 A) (k9_xtuple_0 C)) &  (B = (k3_relat_1 A C)) )  =>  ((k3_finseq_1 B) = (k3_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(t29_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  <=>  ((k1_relset_1 k5_numbers A) = (k1_relset_1 k5_numbers B)) ) ) ) ) ) ).
tt(t29_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r2_hidden B (k10_xtuple_0 A)))  =>  ((k1_tarski (k4_finseq_4 A B)) = (k8_relat_1 A (k1_tarski B))) ) ) ) ) ).
tt(t29_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~ (v1_xboole_0 B))  =>  (B = (k8_finseq_1 A (k12_finseq_1 A (k7_partfun1 A B 1)) (k2_rfinseq A 1 B))) ) ) ) ) ) ).
tt(t29_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ((k6_finseq_4 (k10_finseq_1 A B) A) = (k9_finseq_1 B)) ) ) ).
tt(t29_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) |  ((k2_finseq_7 A B C (k3_finseq_1 B)) = (k8_finseq_1 A (k8_finseq_1 A (k8_finseq_1 A (k17_finseq_1 A (k7_nat_d C 1) B) (k12_finseq_1 A (k7_partfun1 A B (k3_finseq_1 B)))) (k17_finseq_1 A (k7_nat_d (k7_nat_d (k3_finseq_1 B) C) 1) (k2_rfinseq A C B))) (k12_finseq_1 A (k7_partfun1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t29_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k2_finseqop A A A F (k3_finseqop A A A F B E) C) (k3_finseqop A A A F B (k2_finseqop A A A F E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k10_fintopo2 A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k10_fintopo2 A B) (k10_fintopo2 A C)))) ) ) ) ) ) ).
tt(t29_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k4_subset_1 (u1_struct_0 A) (k3_fintopo3 A B D) (k3_fintopo3 A C D)) = (k3_subset_1 (u1_struct_0 A) (k5_fintopo3 A (k3_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t29_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_fintopo4 A B C) &  ((r1_tarski D B) & (r1_tarski E C)) )  => (r1_fintopo4 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k7_flang_1 A B C) = (k4_flang_1 A (k2_flang_1 A)))  <=>  ( (C = k6_numbers)  |  (B = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ) ) ) ) ).
tt(t29_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B C) => (r1_tarski (k1_flang_2 A B D E) (k1_flang_2 A C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t29_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B (k1_flang_3 A C D)) =>  ((r1_xxreal_0 E k6_numbers) | (r1_tarski (k1_flang_3 A B E) (k1_flang_3 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((k5_xboole_0 B A) = k1_xboole_0)  <=>  (B = A) ) ) ) ).
tt(t29_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_pcomps_1 A)) B C) =>  ((v2_tbsp_1 B A) <=> (v2_frechet C (k3_pcomps_1 A))) ) ) ) ) ) ) ) ).
tt(t29_frechet,ax, (! [A:$i] :  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_frechet))) =>  ((r2_hidden k1_numbers A) |  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) &  ((k8_subset_1 k1_numbers k5_numbers A) = k1_xboole_0) ) ) )  &  ( ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) &  ((k8_subset_1 k1_numbers k5_numbers A) = k1_xboole_0) )  =>  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_frechet))) &  (~ (r2_hidden k1_numbers A)) ) ) ) ) ).
tt(t29_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k8_eqrel_1 (u1_struct_0 C) (k6_fsm_1 A B C D)) = (k8_eqrel_1 (u1_struct_0 C) (k6_fsm_1 A B C (k1_nat_1 D 1))))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k8_eqrel_1 (u1_struct_0 C) (k6_fsm_1 A B C (k2_xcmplx_0 D E))) = (k8_eqrel_1 (u1_struct_0 C) (k6_fsm_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ((v5_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers))) ) )  =>  ( ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C B))  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = B) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 C B) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = C) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C)) = (k1_square_1 B C)) ) ) ) ) ) ) ) ).
tt(t29_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 B)) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  ((k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E (k1_flang_1 B C D) A) = (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E D (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E C A))) ) ) ) ) ) ) ) ) ) ).
tt(t29_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k37_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) (k17_ftacell1 A B C D E)) = (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) (k9_margrel1 K)) (k10_margrel1 (k9_margrel1 K) J)) (k10_margrel1 J (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)))))  &  ((k1_funct_1 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) (k18_ftacell1 A B C D E)) = (k9_margrel1 (k2_binarith (k2_binarith (k2_binarith (k2_binarith (k9_margrel1 G) H) (k9_margrel1 I)) J) (k9_margrel1 K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k3_relat_1 B (k4_funcop_1 C A D)) = (k4_funcop_1 C (k3_relat_1 B A) D)) ) ) ) ) ) ) ) ).
tt(t29_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k10_xtuple_0 (k3_relat_1 B A)) = (k10_xtuple_0 A))  & (v2_funct_1 A))  => (r1_tarski (k9_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t29_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( ((k2_relset_1 B C) = B)  & (v2_funct_1 C))  =>  ( (B = k1_xboole_0)  |  ( ((k3_relat_1 C (k2_funct_1 C)) = (k6_partfun1 A))  &  ((k3_relat_1 (k2_funct_1 C) C) = (k6_partfun1 B)) ) ) ) ) ) ) ) ).
tt(t29_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k7_relat_1 (k3_funct_3 B) A) (k8_relat_1 (k1_funct_3 B) A))) ) ) ).
tt(t29_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k1_funct_4 A B) (k2_xboole_0 A B))) ) ) ) ).
tt(t29_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( (~  ((k2_zfmisc_1 A B) = k1_xboole_0) )  &  ( ((k9_xtuple_0 D) = (k2_zfmisc_1 A B))  &  ((r2_hidden C A) &  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (~  ( ((k1_funct_1 (k1_funct_5 D) C) = E)  &  ( ((k9_xtuple_0 E) = B)  &  ((r1_tarski (k10_xtuple_0 E) (k10_xtuple_0 D)) &  (! [F:$i] :  ((r2_hidden F B) =>  ((k1_funct_1 E F) = (k1_binop_1 D C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k9_xtuple_0 (k6_funct_6 A)) = (k4_funct_6 (k2_funct_6 A)))  & (r1_tarski (k10_xtuple_0 (k6_funct_6 A)) (k4_card_3 (k3_funct_6 A)))) ) ) ).
tt(t29_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski (k9_xtuple_0 B) C) => (r1_funct_7 A (k1_funct_4 A B) C)) ) ) ) ) ) ).
tt(t29_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k52_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t29_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k55_valued_1 k1_numbers k1_numbers k16_sin_cos) (k55_valued_1 k1_numbers k1_numbers k19_sin_cos)) (k8_real_1 (k10_real_1 k32_sin_cos 2) A))) ) ).
tt(t29_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_functor0 A A (k11_functor0 A) B) = B) ) ) ) ) ).
tt(t29_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ((m2_functor2 G B C E F) =>  ((r2_functor2 B C E F) => (m2_functor2 (k6_functor3 A B C E F D G) A C (k1_functor3 A B C D E) (k1_functor3 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k2_fuzzy_1 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A B D)) B) => (r1_fuzzy_1 B (k2_fuzzy_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t29_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k2_fuzzy_2 A (k2_fuzzy_2 A B C) D) (k2_fuzzy_2 A B (k2_fuzzy_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t29_fvaluat1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_realset2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_fvaluat1 D B) =>  ((v3_fvaluat1 B) =>  ( (C = (k4_struct_0 B))  |  ((k3_funct_2 (u1_struct_0 B) k7_numbers D (k3_fvaluat1 B C A)) = (k4_xxreal_3 A (k3_funct_2 (u1_struct_0 B) k7_numbers D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k6_fvsum_1 A B C) = (k6_fvsum_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t29_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  ( (~ (v1_xboole_0 (k23_gate_1 A B C D E F)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) & (v1_xboole_0 F)) ) ) ) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) & (v1_xboole_0 F)) ) ) ) ) )  & (v1_xboole_0 (k23_gate_1 A B C D E F))) ) ) ) ) ) ) ) ) ).
tt(t29_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_gcd_1 A B C D) = (k5_gcd_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t29_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((k10_genealg1 E F G k6_numbers A B C) = (k9_genealg1 E G F A B C))  &  ( ((k10_genealg1 E F G D k6_numbers B C) = (k9_genealg1 E G F D B C))  &  ( ((k10_genealg1 E F G D A k6_numbers C) = (k9_genealg1 E G F D A C))  &  ((k10_genealg1 E F G D A B k6_numbers) = (k9_genealg1 E G F D A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k4_geomtrap A B C D E) = (k4_geomtrap A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k14_twoscomp)))  &  (H = (k1_funct_1 D C)) )  =>  ((k1_twoscomp (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) (k6_circuit2 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D) (k12_gfacirc1 A B C)) = (k2_binarith E H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r1_tarski (k18_glib_000 A B) (k20_glib_000 A B)) & (r1_tarski (k19_glib_000 A B) (k20_glib_000 A B))) ) ) ) ).
tt(t29_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ((r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 (k7_glib_001 A B C))) & (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ).
tt(t29_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  ((k4_glib_002 A) = (k4_glib_002 B)) ) ) ) ) ) ).
tt(t29_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (r1_xxreal_0 k6_numbers (k10_glib_003 A B))) ) ) ) ).
tt(t29_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)))) =>  ((r1_tarski (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k14_glib_004 A B))) & (r1_tarski (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) B) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k14_glib_004 A B)))) ) ) ) ) ).
tt(t29_goboard1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A)) ) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B D) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A C)))) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 2 (k3_finseq_1 B)) & (r1_xboole_0 (k3_topreal1 2 B) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A C)))) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r2_hidden E (k4_finseq_1 B)) &  ((r2_hidden F (k4_finseq_1 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B E) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))) &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r2_hidden G (k4_finseq_1 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B G) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))))  => (r1_xxreal_0 G E)) ) )  &  ( (~ (r1_xxreal_0 F E))  &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B F) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A D))) & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) B (k2_nat_1 C 1))) ) ) ) ) )  =>  ( ((k5_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B C))  &  ((k4_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 C)) &  ((r2_hidden B (k1_tops_1 (k15_euclid 2) (k1_goboard5 C A))) & (r1_xxreal_0 (k17_euclid B) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) )  =>  (~  ((r2_hidden A (k4_finseq_1 B)) &  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1))) ) ) ) ) ) ) ) ).
tt(t29_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A))) (k19_euclid (k4_xcmplx_0 1) 1)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 2 (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid k6_numbers 1))) (k3_topreal1 2 A))) ) ).
tt(t29_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((k3_goboard5 B (k3_finseq_1 B) A) = (a_2_3_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t29_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B C)) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_gobrd13 B C A) (k2_gobrd13 B C A)) = (k2_topreal1 2 B A)) ) ) ) ) ) ) ) ).
tt(t29_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_pre_topc (k15_euclid 2) (k3_goboard9 A))) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k3_topreal1 2 A))) ) ) ).
tt(t29_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r1_tarski B C) => (r1_tarski (k6_goedelcp A B) (k6_goedelcp A C))) ) ) ) ) ) ) ).
tt(t29_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  => (r2_hidden A (k11_graph_1 A))) ) ).
tt(t29_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_graph_1 A B C D) => (r2_graph_1 A C B D)) ) ) ) ) ) ) ) ).
tt(t29_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C D) =>  ((k7_graph_3 A B (k6_subset_1 D C)) = (k6_xcmplx_0 (k7_graph_3 A B D) (k7_graph_3 A B C))) ) ) ) ) ) ) ) ).
tt(t29_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ((r1_graph_5 A D B C) =>  ((r2_hidden B (k2_graph_5 A D)) & (r2_hidden C (k2_graph_5 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ( (B = (k15_graphsp (k7_graphsp C A) C A))  =>  ( ((k7_graphsp C A) = k1_xboole_0)  |  ((r2_hidden B (k4_finseq_1 C)) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ( (~  ((k1_seq_1 C B) = (k1_real_1 1)) )  &  (~  ((k1_seq_1 C (k2_nat_1 A B)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden k3_algstr_0 (k17_grcat_1 A))) ) ).
tt(t29_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((v7_ordinal1 (k1_gr_cy_3 A)) & (v1_int_2 (k1_gr_cy_3 A)))  =>  ((r1_xxreal_0 A 1) |  ((v7_ordinal1 A) & (v1_int_2 A)) ) ) ) ) ).
tt(t29_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ((k1_funct_1 A C) = (k1_funct_1 B C)) )  =>  ((k5_relat_1 A (k1_tarski C)) = (k5_relat_1 B (k1_tarski C))) ) ) ) ) ) ) ).
tt(t29_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (? [B:$i] :  ((m2_finseq_1 B (k2_grnilp_1 A)) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( ((k1_funct_1 B 1) = (k7_group_2 A))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k6_group_2 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden (k2_xcmplx_0 C 1) (k4_finseq_1 B)))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  =>  ( ( (D = (k1_funct_1 B C))  &  (E = (k1_funct_1 B (k2_xcmplx_0 C 1))) )  =>  ((m1_group_6 E A D) &  ( (~ (v2_struct_0 (k5_group_6 A E)))  &  ((v2_group_1 (k5_group_6 A E)) &  ((v3_group_1 (k5_group_6 A E)) &  ((v1_gr_cy_1 (k5_group_6 A E)) & (l3_algstr_0 (k5_group_6 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v1_grnilp_1 A)) ) ) ).
tt(t29_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ( ((r1_tarski E D) & (r1_tarski (k2_groeb_1 A B C D) (k3_groeb_1 A (k2_groeb_1 A B C E))))  => (r2_groeb_1 A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m2_ideal_1 D A B) =>  ((r1_tarski B C) => (m2_ideal_1 D A C)) ) ) ) ) ) ) ) ) ).
tt(t29_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ( ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E))) & (r2_hidden G (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E))))  => (r2_termord A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  =>  ((k2_group_2 A (k2_group_11 A B D) (k2_group_11 A C D)) = (k2_group_11 A (k2_group_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t29_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_group_1 A 2 B) = (k1_group_1 A))  <=>  ((k2_group_1 A B) = B) ) ) ) ) ) ).
tt(t29_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k2_group_2 A (k4_group_2 A D B) C) = (k4_group_2 A D (k2_group_2 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t29_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k2_group_3 A B C) = B) ) ) ) ) ) ) ) ).
tt(t29_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B C) => (r1_struct_0 (k5_group_4 A C) B)) ) ) ) ) ) ) ).
tt(t29_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_5 A (k2_group_1 A B) (k2_group_1 A C)) = (k2_group_3 A (k2_group_5 A B C) (k2_group_1 A (k6_algstr_0 A B C))))  &  ((k2_group_5 A (k2_group_1 A B) (k2_group_1 A C)) = (k2_group_3 A (k2_group_5 A B C) (k2_group_1 A (k6_algstr_0 A C B)))) ) ) ) ) ) ) ) ).
tt(t29_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((m1_group_6 C A B) =>  ((v1_group_3 (k5_group_6 B (k1_group_6 A B C)) (k5_group_6 A C)) & (m1_group_2 (k5_group_6 B (k1_group_6 A B C)) (k5_group_6 A C))) ) ) ) ) ) ) ) ).
tt(t29_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k6_algstr_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)) (k5_group_7 A B C E) (k5_group_7 A B D F)) = (k5_group_7 A B (k6_algstr_0 A C D) (k6_algstr_0 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((k19_group_9 A B C D) = (k18_group_9 A B (k16_group_9 A B C D))) ) ) ) ) ) ) ) ).
tt(t29_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v2_groupp_1 B A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k5_group_1 B (k1_newton A E) (k6_algstr_0 B C D)) = (k6_algstr_0 B (k5_group_1 B (k1_newton A E) C) (k5_group_1 B (k1_newton A E) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_hahnban1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_binop_1 (k4_group_1 k1_complfld) (k1_hahnban1 A k6_numbers) B) = (k1_hahnban1 (k3_power A B) k6_numbers)) ) ) ) ) ) ).
tt(t29_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  ((v1_hallmar1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 2 (k5_card_1 (k1_funct_1 B C))) &  (! [D:$i] :  (~  ((r2_hidden D (k1_funct_1 B C)) & (v1_hallmar1 (k2_hallmar1 A B C D) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((k8_weierstr A B B) = k6_numbers) ) ) ) ) ).
tt(t29_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k13_glib_001 A (k2_helly A B C))) & (r2_hidden C (k13_glib_001 A (k2_helly A B C)))) ) ) ) ) ) ) ).
tt(t29_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k3_hermitan A B C)) C)) ) ) ) ) ) ).
tt(t29_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_heyting3 B (k6_domain_1 k5_numbers A)))) =>  ((r2_hidden C D) =>  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k6_domain_1 k5_numbers A))))) ) ) ) ) ) ) ) ).
tt(t29_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((r1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 B)) A) &  ((k1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 B)) A) = (k1_real_1 (k10_real_1 (k8_real_1 B (k5_prepower A (k9_real_1 B 1))) (k5_square_1 (k5_prepower A B))))) ) ) ) ) ) ) ).
tt(t29_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly B) (u1_struct_0 A)) &  ((v1_polynom1 D (k15_pre_poly B) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k11_polynom1 B A))) =>  (~  ( (D = (k4_rlvect_1 (k11_polynom1 B A) E))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k11_polynom1 B A)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_polynom1 B A)) (u1_struct_0 A))))) )  =>  (~  ( (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly B) (u1_struct_0 A)) &  ((v1_polynom1 G (k15_pre_poly B) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly B) (u1_struct_0 A))))) ) )  =>  ((k1_funct_1 F G) = (k3_polynom1 B A G C)) ) )  &  ((k3_polynom1 B A D C) = (k4_rlvect_1 A (k4_finseqop (u1_struct_0 (k11_polynom1 B A)) (u1_struct_0 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ( ((r2_hidden (k3_hilbert1 A (k3_hilbert1 B C)) k6_hilbert1) & (r2_hidden B k6_hilbert1))  => (r2_hidden (k3_hilbert1 A C) k6_hilbert1)) ) ) ) ) ) ) ).
tt(t29_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  (k2_hilbert1 = (k1_hilbert2 A)) ) ) ) ).
tt(t29_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((k3_hilbert3 A k2_hilbert1) = 1) ) ) ).
tt(t29_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_polynom4 A (k3_hurwitz A C 1) B) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t29_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ((r1_idea_1 A (k1_recdef_1 C 1)) &  ((r1_idea_1 A (k1_recdef_1 C 2)) &  ((r1_idea_1 A (k1_recdef_1 C 3)) &  ((r1_idea_1 A (k1_recdef_1 C 4)) &  ( ((k1_recdef_1 D 1) = (k10_idea_1 A (k1_recdef_1 C 1)))  &  ( ((k1_recdef_1 D 2) = (k6_idea_1 A (k1_recdef_1 C 2)))  &  ( ((k1_recdef_1 D 3) = (k6_idea_1 A (k1_recdef_1 C 3)))  &  ((k1_recdef_1 D 4) = (k10_idea_1 A (k1_recdef_1 C 4))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k11_idea_1 A (k11_idea_1 A B C) D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t29_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m3_ideal_1 D A B) => (m3_ideal_1 (k1_polynom1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t29_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k2_incsp_1 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) => (m4_index_1 D (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (k15_index_1 A B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t29_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((l3_msualg_1 E B) =>  (! [F:$i] :  ((l3_msualg_1 F B) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 B) (u3_msualg_1 B E) (u3_msualg_1 B F)) => (m2_pboole (k3_relat_1 C G) (u1_struct_0 A) (u3_msualg_1 A (k1_instalg1 A B E C D)) (u3_msualg_1 A (k1_instalg1 A B F C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k3_real_1 (k1_int_1 A) 1) A)) ) ) ).
tt(t29_int_2,ax, (~ (v1_int_2 4)) ).
tt(t29_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ((r1_int_1 (k3_int_2 B A) C) &  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (~  ( ((k3_finseq_1 D) = (k3_int_2 B A))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 B (k1_funct_1 D E)) C) A) = k6_numbers) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k5_numbers D)) &  ((r2_hidden F (k1_relset_1 k5_numbers D)) &  ( (~  (E = F) )  & (r2_int_1 (k1_funct_1 D E) (k1_funct_1 D F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( ((k3_int_2 A B) = 1)  & (r2_int_1 A C B))  =>  ((r1_xxreal_0 B 2) |  ((k2_int_5 A B) = (k2_int_5 C B)) ) ) ) ) ) ) ) ) ).
tt(t29_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  (! [C:$i] :  ((m1_int_6 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) => (r2_int_1 (k16_rvsum_1 (k18_valued_1 A C)) (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_int_7 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_int_7 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k6_group_1 (k3_int_7 A) B) = D)  &  ((k5_group_1 (k3_int_7 A) D C) = 1) )  =>  ((r1_xxreal_0 D k6_numbers) | (m1_subset_1 C (u1_struct_0 (k5_group_4 (k3_int_7 A) (k6_domain_1 (u1_struct_0 (k3_int_7 A)) B))))) ) ) ) ) ) ) ) ) ) ).
tt(t29_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k2_integra5 B (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos))) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k10_real_1 1 (k5_square_1 A))) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 A) k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos))) (k4_seq_4 B)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k10_real_1 1 (k5_square_1 A))) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 A) k6_numbers) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos))) (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t29_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos))) &  ((r2_relset_1 k1_numbers k1_numbers D (k3_rfunct_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos)) (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos)))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k11_binop_2 A F))  &  (~  (A = k6_numbers) ) ) ) ) )  &  (E = (k1_relset_1 k1_numbers D)) ) ) ) )  =>  ((k2_integra5 B D) = (k10_binop_2 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos) (k12_binop_2 1 A)) (k1_partfun2 k1_numbers E)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k29_sin_cos) (k12_binop_2 1 A)) (k1_partfun2 k1_numbers E)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t29_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k16_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos D) (k1_seq_1 k19_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t29_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r1_xxreal_0 B C) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers D)) &  (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F (k3_integra5 B C)) =>  ((k1_funct_1 D F) = E) ) ) ) ) )  =>  ((r1_integr15 A (k3_integra5 B C) D) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) D (k3_integra5 B C)) A) &  ((k12_integr15 B C A D) = (k9_euclid A E (k10_binop_2 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ( ((k3_finseq_1 B) = 1)  => (r1_integra1 B C)) ) ) ) ) ) ) ).
tt(t29_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v2_seq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 k6_numbers A))  =>  ((k7_integra1 B (k26_valued_1 B k1_numbers C A) D) = (k8_real_1 A (k7_integra1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v3_integra1 B A) &  ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) & (v3_integra1 C A)) ) )  => (v3_integra1 (k20_valued_1 A k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t29_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_integra5 (k3_integra5 A B) C) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k3_integra5 A B))) &  ((r1_tarski (k3_integra5 A B) (k9_xtuple_0 C)) &  ((r2_hidden D (k2_rcomp_1 A B)) &  ((r1_fcont_1 C D) &  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k2_rcomp_1 A B) (k9_xtuple_0 E)) &  ( (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F (k2_rcomp_1 A B)) =>  ((k1_seq_1 E F) = (k4_integra5 A F C)) ) ) )  &  ((r1_fdiff_1 E D) &  ((k1_fdiff_1 E D) = (k1_seq_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_integra7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r1_integra7 k1_numbers (k1_taylor_1 (k2_nat_1 A 1)) (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 A) (k2_nat_1 A 1)))) ) ).
tt(t29_integra8,ax, ((k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) k1_numbers) = k16_sin_cos) ).
tt(t29_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_measure5 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) E)) &  ((r1_integra5 E (k20_valued_1 k1_numbers k1_numbers k1_numbers C D)) & (r1_tarski E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers C D)))) )  =>  ((k1_integra9 E (k26_valued_1 k1_numbers k1_numbers C A) (k26_valued_1 k1_numbers k1_numbers D B)) = (k8_real_1 (k8_real_1 A B) (k1_integra9 E C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_interva1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k2_setfam_1 B (k3_setfam_1 C D)) = (k3_setfam_1 (k2_setfam_1 B C) (k2_setfam_1 B D))) ) ) ) ) ) ) ) ).
tt(t29_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A (k3_intpro_1 B C)) (k3_intpro_1 B (k3_intpro_1 A C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t29_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_series_1 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  => (r1_xxreal_0 (k1_seq_1 (k3_series_1 B) A) (k4_series_1 B))) ) ) ) ) ).
tt(t29_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G C D) =>  (! [H:$i] :  ((m2_cat_1 H C D) =>  (! [I:$i] :  ((m2_nattra_1 I C D G H) =>  ((r2_nattra_1 C D G H) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 D) (k5_isocat_1 A B D (k9_cat_1 B C D F G) (k9_cat_1 B C D F H) E (k5_isocat_1 B C D G H F I)) (k5_isocat_1 A C D G H (k9_cat_1 A B C E F) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  => (r1_isocat_1 (k11_nattra_1 (k8_cat_2 A B) C) (k11_nattra_1 A (k11_nattra_1 B C)))) ) ) ) ) ) ).
tt(t29_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_borsuk_5 B C))  =>  ((k1_tops_1 k3_topmetr A) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t29_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k5_square_1 (k12_euclid A)) = (k7_real_1 (k5_square_1 (k17_euclid A)) (k5_square_1 (k18_euclid A)))) ) ) ).
tt(t29_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k1_funct_1 k4_pscomp_1 C)) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t29_jgraph_3,ax, ((v1_funct_1 (k2_funct_1 k1_jgraph_3)) &  ((v1_funct_2 (k2_funct_1 k1_jgraph_3) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k2_funct_1 k1_jgraph_3) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) ) ).
tt(t29_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_0_jgraph_4) )  => (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ).
tt(t29_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((k18_pscomp_1 A) = (k19_euclid (k1_real_1 1) k6_numbers)) ) ) ) ).
tt(t29_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [I:$i] :  ( ( (~ (v1_xboole_0 I))  &  ((v2_compts_1 I (k15_euclid 2)) & (m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ( (I = (k5_jgraph_6 k6_numbers k6_numbers 1))  &  ( (A = (k6_jgraph_6 k6_numbers k6_numbers 1))  &  ( (B = (k8_jgraph_6 k6_numbers k6_numbers 1))  &  ( (C = (k7_jgraph_6 k6_numbers k6_numbers 1))  &  ( (D = (k9_jgraph_6 k6_numbers k6_numbers 1))  &  ( (E = (k1_jgraph_6 (k1_real_1 1) 1 (k1_real_1 1) 1))  &  ( (F = (k3_jgraph_6 (k1_real_1 1) 1 (k1_real_1 1) 1))  &  ( (G = (k2_jgraph_6 (k1_real_1 1) 1 (k1_real_1 1) 1))  &  ( (H = (k4_jgraph_6 (k1_real_1 1) 1 (k1_real_1 1) 1))  & (r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J k1_jgraph_3)) ) ) ) ) ) ) ) )  =>  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1)) = I)  &  ( ((k7_relat_1 (k2_funct_1 J) I) = (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1))  &  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J E) = A)  &  ( ((k7_relat_1 (k2_funct_1 J) A) = E)  &  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J F) = B)  &  ( ((k7_relat_1 (k2_funct_1 J) B) = F)  &  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J G) = C)  &  ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) J H) = D)  &  ( ((k7_relat_1 (k2_funct_1 J) C) = G)  &  ((k7_relat_1 (k2_funct_1 J) D) = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 E (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) F) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( ( ( ((k17_euclid A) = (k17_euclid B))  &  ((k17_euclid C) = (k17_euclid D)) )  |  ( ((k18_euclid A) = (k18_euclid B))  &  ((k18_euclid C) = (k18_euclid D)) ) )  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) C D)) = (k1_tarski E))  &  ( (~  (E = A) )  &  ( (~  (E = B) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan14,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ((v1_topreal1 B) &  ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 D (k1_matrix_1 A))) ) )  => (v2_connsp_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 A C D) (k3_topreal1 2 B)) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t29_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r1_jordan18 A B C D D E)) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 C B)) (k3_finseq_1 (k1_jordan8 C A)))) ) ) ) ) ) ) ) ).
tt(t29_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (m1_subset_1 (a_4_4_jordan1 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ) ) ) ).
tt(t29_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k3_finseq_1 (k1_jordan8 B A)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ) ) ) ) ).
tt(t29_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k10_xtuple_0 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t29_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_xxreal_0 (k4_finseq_4 (k2_jordan1e B A) (k25_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k4_finseq_4 (k2_jordan1e B A) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))))) ) ) ) ).
tt(t29_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k1_matrix_1 B)))  =>  ((k1_seq_1 (k7_pre_poly k1_numbers (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B)) k1_jordan1h) A) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A))) ) ) ) ) ) ).
tt(t29_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k8_pscomp_1 B) (k8_pscomp_1 A)))  =>  ((k23_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k23_pscomp_1 B)) ) ) ) ) ) ).
tt(t29_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ((k7_real_1 (k1_topreal6 2 B A) (k1_topreal6 2 A C)) = (k1_topreal6 2 B C)) ) ) ) ) ) ) ) ).
tt(t29_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r4_jordan20 A B C D G) &  ( ((k17_euclid E) = G)  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) D E) A) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) D E))) ) )  => (r4_jordan20 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2)))) => (r1_xxreal_0 (k18_euclid (k2_jordan21 B)) (k18_euclid A))) ) ) ) ) ).
tt(t29_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k18_pscomp_1 A) (k3_jordan19 A))) ) ).
tt(t29_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_topreal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (v1_topreal1 (k2_jordan3 A B))) ) ) ) ) ) ).
tt(t29_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 k1_numbers A 1) = (k17_euclid A))  &  ((k7_partfun1 k1_numbers A 2) = (k18_euclid A)) ) ) ) ).
tt(t29_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ((r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B)) | (r2_hidden C (k3_topreal1 2 (k2_jordan3 A B)))) ) ) ) ) ) ) ) ).
tt(t29_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) => (r2_jordan4 A (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) B) D C)) ) ) ) ) ) ) ) ) ).
tt(t29_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1))))) ) ) ) ) ).
tt(t29_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden B (k2_topreal1 2 A D)) &  ((r2_hidden C (k2_topreal1 2 A D)) &  ((v4_topreal1 A) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) & (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B C)) ) ) ) )  => (r1_jordan5c (k2_topreal1 2 A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) B C)) ) ) ) ) ) ) ) ) ).
tt(t29_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_4_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A)) (k3_pscomp_1 (k15_euclid 2) k4_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t29_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal1 (k15_euclid 2) B C A) =>  ((k5_jordan6 A B C D E) = (k5_jordan6 A C B E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k1_nat_1 C 1) (k3_finseq_1 (k1_jordan8 A B))) &  ((r2_hidden (k20_pscomp_1 A) (k3_goboard5 (k1_jordan8 A B) C (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k1_nat_1 D 1) (k3_finseq_1 (k1_jordan8 A B))) & (r2_hidden (k20_pscomp_1 A) (k3_goboard5 (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1)))) ) ) ) )  =>  ( ((k20_pscomp_1 A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1)))  |  ( ((k20_pscomp_1 A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1)))  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (~ (r2_subset_1 (k2_jordan_a A (k3_finseq_1 B) B) (k2_jordan_a A 1 B))) ) ) ) ) ).
tt(t29_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ( ( (C = E)  &  ( (D = F)  &  ((r1_borsuk_6 A C D) & (r1_tarski (k2_relset_1 (u1_struct_0 A) G) (u1_struct_0 B))) ) )  =>  ((r1_borsuk_6 B E F) & (m1_borsuk_2 G B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_knaster,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v4_lattice3 B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v14_quantal1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r3_lattices B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 B) C D) D) & (r2_abian (u1_struct_0 B) (k6_knaster B C D A) C))  =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r1_ordinal1 A E) =>  ((k6_knaster B C D A) = (k6_knaster B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k2_pre_topc k3_topmetr k6_kurato_1)) ) ).
tt(t29_kurato_2,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_tops_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan2c 2 (k3_topreal1 2 (k1_jordan9 A B))))) = (k3_topreal1 2 (k1_jordan9 A B))) ) ) ) ) ).
tt(t29_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) B B) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k13_fvsum_1 D (k8_matrix_1 (u1_struct_0 D) E C) (k9_matrix_1 (u1_struct_0 D) (k5_matrix_1 B (u1_struct_0 D) (k7_laplace B D E)) A)) = (k12_matrix_3 B D (k3_matrix11 A B B (u1_struct_0 D) E (k8_matrix_1 (u1_struct_0 D) E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_1 C) => (v2_funct_1 (k3_latsubgr A B C))) ) ) ) ) ) ) ).
tt(t29_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (? [F:$i] :  ((m1_subset_1 F C) &  ((r2_hidden F D) & (r3_lattices A B (k3_funct_2 C (u1_struct_0 A) E F))) ) )  => (r3_lattices A B (k2_lattice2 C A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 B))) =>  ((r1_lattice3 (k3_lattice3 B) A C) <=> (r3_lattice3 B (k5_lattice3 B C) A)) ) ) ) ) ) ).
tt(t29_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  ((k7_lattices A (k6_lattices A)) = (k5_lattices A)) ) ) ).
tt(t29_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 B C) => (r1_tarski (k8_lattice5 A B) (k8_lattice5 A C))) ) ) ) ) ) ) ).
tt(t29_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) (u1_struct_0 B)) &  ((v1_lattice5 E D B) &  ((v2_lattice5 E D B) &  ((v3_lattice5 E D B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) (u1_struct_0 B))))) ) ) ) )  =>  ((r2_lattice8 A B C D E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ((r3_orders_2 B (k3_lattice5 A B C F G) (k13_lattice3 B H I)) &  (! [J:$i] :  ((m1_subset_1 J D) =>  (! [K:$i] :  ((m1_subset_1 K D) =>  (~  ( ((k1_binop_1 E F J) = H)  &  ( ((k3_lattice5 D B E J K) = (k12_lattice3 B (k13_lattice3 B (k3_lattice5 A B C F G) H) I))  &  ((k1_binop_1 E K G) = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (! [C:$i] :  (~  ( (~ (r2_hidden C (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B))))  &  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)) = (k6_glib_000 A)) )  &  (~ (r1_termord k5_numbers (k4_bagorder k5_numbers) (k2_uproots k5_numbers (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) C) 1) (k2_uproots k5_numbers (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) B) (k10_lexbfs A B)) 1))) ) ) ) ) ) ) ) ) ).
tt(t29_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k7_lfuzzy_0 (k2_zfmisc_1 A A) (k5_lfuzzy_1 A B) (k1_domain_1 A A C D)) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (k5_card_3 (k1_domain_1 A A C D) (a_2_0_lfuzzy_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t29_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) =>  ((v1_seq_2 A) | (v1_limfunc1 A)) ) ) ) ).
tt(t29_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) )  | (r5_limfunc2 B A)) ) ) ) ) ) ).
tt(t29_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc3 B A) =>  ((r1_limfunc2 B A) &  ((r4_limfunc2 B A) &  ( ((k1_limfunc2 B A) = (k2_limfunc2 B A))  &  ( ((k1_limfunc3 B A) = (k1_limfunc2 B A))  &  ((k1_limfunc3 B A) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t29_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r5_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k4_limfunc1 A))) ) ) ) )  | (v4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t29_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A C D) =>  ((k2_vectsp_5 A B D (k1_vectsp_5 A B C E)) = (k1_vectsp_5 A B (k2_vectsp_5 A B C D) (k2_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k13_lopban_1 A B C) C)) ) ) ) ) ) ).
tt(t29_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 (k4_normsp_0 A B) C) k6_numbers)) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D)))) ) ) ) )  & (v2_lopban_3 B A)) ) ) ) ) ) ) ).
tt(t29_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 1 (k4_series_1 (k4_sin_cos (k1_normsp_0 A B))))) ) ) ) ).
tt(t29_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v1_filter_0 B A) & (r2_hidden (k5_lattices A) B)) ) ) ) ) ) ).
tt(t29_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r1_lpspace1 A B C D E) => (r1_lpspace1 A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_lpspace2 A B C F))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_lpspace2 A B C F))) =>  ( ( (D = G)  &  (E = H) )  =>  ((k3_valued_1 A k1_numbers k1_numbers D E) = (k3_rlvect_1 (k2_lpspace2 A B C F) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ((r2_ltlaxio1 C A) => (r2_ltlaxio1 (k10_nat_1 (k1_zfmisc_1 k10_ltlaxio1) C B) A)) ) ) ) ) ) ) ).
tt(t29_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A C))) (k8_cqc_lang A B C)) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A C)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t29_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A B (k4_subset_1 (u1_struct_0 A) C D)) = (k9_subset_1 (u1_struct_0 A) (k3_mathmorp A B C) (k3_mathmorp A B D))) ) ) ) ) ) ) ) ) ).
tt(t29_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 A k6_numbers) & (v1_matrix10 C))  => (v3_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t29_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D B A) =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  ( ((k3_finseq_1 F) = (k1_matrix_1 E))  =>  (! [G:$i] :  ((m2_finseq_2 G D (k3_finseq_2 D)) =>  ( (F = G)  =>  ((k3_matrix11 C B A D E F) = (k1_finseq_7 (k3_finseq_2 D) E C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 A)))  =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [H:$i] :  ((m2_finseq_2 H k5_numbers (k4_finseq_2 D k5_numbers)) =>  ( ((r2_hidden C (k2_finseq_1 D)) &  ((r2_hidden E (k2_finseq_1 D)) &  ((k1_funct_1 H C) = (k1_funct_1 H E)) ) )  =>  ((k9_matrix_1 A (k1_matrix13 A F B D G H) C) = (k9_matrix_1 A (k1_matrix13 A F B D G H) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (C = (k12_matrix_1 B A))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A)) ) )  =>  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k15_funcop_1 (u1_struct_0 B) D E (k5_struct_0 B) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k2_matrix13 1 (k3_finseq_1 C) A (k2_matrix15 (u1_struct_0 A) C) B) = (k2_matrix15 (u1_struct_0 A) (k9_fvsum_1 A C B))) ) ) ) ) ) ) ).
tt(t29_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v3_matrix16 F (u1_struct_0 B)) &  ((v3_matrix16 G (u1_struct_0 B)) & (v3_matrix16 H (u1_struct_0 B))) )  => (v3_matrix16 (k3_matrix_6 A B (k3_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l6_algstr_0 D))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k11_matrix_1 D C))) =>  ((k3_matrix_1 (u1_struct_0 D) (k11_matrix_1 D C) A B) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 C)) =>  ( ((v1_setwiseo D A) &  ((v1_binop_1 D A) & (v2_binop_1 D A)) )  =>  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (! [I:$i] :  ((m1_subset_1 I B) =>  ((k3_funct_2 B A F I) = (k7_setwiseo C A D G (k10_funct_5 B C A (k9_funct_2 C A) (k11_funct_5 B C A E) I))) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C (k2_setwiseo B H) G) E) = (k7_setwiseo B A D (k2_setwiseo B H) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 E))  &  ((k1_matrix_4 A B D) = (k1_matrix_4 A E C)) ) ) ) ) ) )  =>  ((k3_matrix_3 A B C) = (k3_matrix_3 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v12_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ( ((v2_matrix_6 C B A) & (v3_matrix_6 C B A))  =>  (C = (k1_matrix_3 A B B)) ) ) ) ) ) ) ) ).
tt(t29_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_xxreal_0 1 A) =>  ((k14_matrix_2 B A D C) = (k14_matrix_2 B A D (k3_matrix_7 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((v2_matrix_8 C A B) & (v1_matrix_6 C A B)) ) ) ) ) ) ) ) ) ).
tt(t29_matrix_9,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k13_matrix_2 3))) =>  ( (A = (k3_finseq_4 k5_numbers 2 3 1))  =>  ((k2_group_1 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ) ).
tt(t29_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ( (A = B)  & (r1_xxreal_0 1 (k3_finseq_1 A)))  =>  ((k1_finsop_1 k1_numbers A k33_binop_2) = (k1_finsop_1 k2_numbers B k27_binop_2)) ) ) ) ) ) ).
tt(t29_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_matrixj1 E C) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 C))))  =>  (! [F:$i] :  ( ((v1_matrixj1 F C) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 C))))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 (k13_matrixj1 C D (k3_matrixj1 C E F)))) =>  ( ( (~  ((r1_xxreal_0 A (k2_wsierp_1 (k10_matrixj1 C E))) &  (~ (r1_xxreal_0 B (k2_wsierp_1 (k11_matrixj1 C E)))) ) )  &  (~  ( (~ (r1_xxreal_0 A (k2_wsierp_1 (k10_matrixj1 C E))))  & (r1_xxreal_0 B (k2_wsierp_1 (k11_matrixj1 C E)))) ) )  |  ((k3_matrix_1 C (k13_matrixj1 C D (k3_matrixj1 C E F)) A B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) &  ((v2_matrixj2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) ) )  =>  (? [D:$i] :  ( ((v2_relat_1 D) & (m1_matrixj2 D A (k4_struct_0 A)))  &  (? [E:$i] :  ((m1_matrlin E A B) &  ((k1_matrlin2 A B B C E E) = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  ((k3_matrix_1 k1_numbers (k7_matrixr1 A B) C D) = (k8_real_1 A (k3_matrix_1 k1_numbers B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C A B B) =>  ((k5_matrix_1 B A (k5_matrix_1 B A C)) = C) ) ) ) ) ) ) ).
tt(t29_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_matrlin D A B) =>  ((v1_matrix_6 (k3_matrlin2 A B B (k3_struct_0 B) C D) (k3_finseq_1 C) A) &  ((k3_matrlin2 A B B (k3_struct_0 B) D C) = (k5_matrix_6 (k3_finseq_1 C) A (k3_matrlin2 A B B (k3_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ((k3_fvsum_1 B (k6_matrlin B C) (k6_matrlin B D)) = (k6_matrlin B (k7_matrlin (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t29_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_tarski B C) & (r2_matroid0 A D B))  => (r2_matroid0 A D C)) ) ) ) ) ) ) ) ) ).
tt(t29_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k5_matrprob A) = (k18_rvsum_1 (k4_matrprob A))) ) ) ).
tt(t29_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B C) (k4_struct_0 (k15_euclid A))) = (k4_struct_0 (k15_euclid B))) ) ) ) ) ) ) ).
tt(t29_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 C (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((k3_matrtop3 A (k1_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C B)) = (k4_matrix_6 A k2_vectsp_1 (k3_matrtop3 A C) (k3_matrtop3 A B))) ) ) ) ) ) ) ).
tt(t29_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k2_mboolean A (k1_mboolean A B)) B)) ) ) ).
tt(t29_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v4_measure5 A) <=> (v4_measure5 (k2_measure6 A B))) ) ) ) ) ).
tt(t29_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v3_prob_1 D) => (v7_valued_0 (k11_measure8 A B D C))) ) ) ) ) ) ) ) ).
tt(t29_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r2_hidden (k2_binop_2 B) A) <=> (r2_hidden B (k7_member_1 A))) ) ) ) ) ).
tt(t29_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v5_membered B)) )  => (v5_membered (k3_tarski A))) ) ).
tt(t29_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((v5_memstr_0 D A B C) <=> (r1_tarski (k7_memstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t29_mesfun6c,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 B) C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( ((v6_supinf_2 E) &  ((r1_xxreal_0 k6_numbers A) &  ((r1_tarski D (k1_relset_1 B E)) & (r1_mesfunc6 B C E D)) ) )  => (r1_mesfunc6 B C (k2_mesfun6c A B E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_xxreal_0 k6_numbers D) &  ((r1_tarski E (k1_relset_1 A C)) & (r1_mesfun6c A B C E)) )  => (r1_mesfunc6 A B (k2_mesfun6c D A (k55_valued_1 A k2_numbers C)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((r2_funct_2 k5_numbers (k4_partfun1 A k1_numbers) (k2_mesfun9c A (k11_mesfun7c A B)) (k11_mesfun7c A (k3_mesfun9c A B))) & (r2_funct_2 k5_numbers (k4_partfun1 A k1_numbers) (k2_mesfun9c A (k12_mesfun7c A B)) (k12_mesfun7c A (k3_mesfun9c A B)))) ) ) ) ) ).
tt(t29_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_tarski D (k9_xtuple_0 C)) =>  ((r1_mesfunc1 A B C D) <=>  (! [E:$i] :  ((v1_xreal_0 E) => (r2_hidden (k9_subset_1 A D (k17_mesfunc1 A C (k1_measure6 E))) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) => (r1_mesfunc1 A B (k3_mesfunc2 C A) D)) ) ) ) ) ) ) ) ).
tt(t29_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((r1_tarski D (k1_relset_1 A (k3_mesfunc1 A B C))) =>  ( ((k1_relset_1 A (k2_partfun1 A k7_numbers (k3_mesfunc1 A B C) D)) = D)  &  ( ((k1_relset_1 A (k3_mesfunc1 A (k2_partfun1 A k7_numbers B D) (k2_partfun1 A k7_numbers C D))) = D)  & (r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k3_mesfunc1 A B C) D) (k3_mesfunc1 A (k2_partfun1 A k7_numbers B D) (k2_partfun1 A k7_numbers C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc6 A B C E) &  ((r1_mesfunc6 A B D E) & (r1_tarski E (k1_relset_1 A D))) )  => (r1_mesfunc6 A B (k47_valued_1 A k1_numbers k1_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A B E F) = (k6_subset_1 C (k3_funct_2 A B D F))) ) )  =>  ((k3_tarski (k2_relset_1 B E)) = (k6_subset_1 C (k1_setfam_1 (k2_relset_1 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v2_mesfunc9 B A) & (v1_mesfunc8 B A k7_numbers))  =>  ((k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) ) ) ) ) ) ) ) ).
tt(t29_metric_1,ax, (! [A:$i] :  ((m1_subset_1 A 2) =>  (! [B:$i] :  ((m1_subset_1 B 2) =>  (! [C:$i] :  ((m1_subset_1 C 2) => (r1_xxreal_0 (k1_metric_1 2 2 k12_metric_1 A C) (k7_real_1 (k1_metric_1 2 2 k12_metric_1 A B) (k1_metric_1 2 2 k12_metric_1 B C)))) ) ) ) ) ) ).
tt(t29_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (k2_metric_2 A) (k2_metric_2 A) k1_numbers)) =>  ((r2_hidden B (k9_metric_2 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) &  (? [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (B = (k4_domain_1 (k2_metric_2 A) (k2_metric_2 A) k1_numbers C D E))  & (r4_metric_2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  ((k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 A B) = (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 B A)) ) ) ) ) ).
tt(t29_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v6_tbsp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski B (k9_metric_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t29_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid (k23_binop_2 A 1)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid (k23_binop_2 A 1)))) =>  ( (~  (B = (k4_struct_0 (k15_euclid (k23_binop_2 A 1)))) )  => (r1_mfold_2 (k15_euclid A) (k3_mfold_2 (k23_binop_2 A 1) B C))) ) ) ) ) ) ) ).
tt(t29_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k4_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C)) = (k4_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)))  =>  ((k3_midsp_1 A B E) = (k3_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_midsp_2 A) & (l2_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_midsp_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_midsp_2 (u1_struct_0 B) A C) & (v1_midsp_2 C B A))  =>  ( ((k1_midsp_1 B D E) = F)  <=>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D E) = (k1_midsp_2 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  ( ((r1_midsp_3 A B C) & (r3_midsp_3 A B C))  => (r2_midsp_3 A B C)) ) ) ) ) ) ) ).
tt(t29_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_mmlquery A B D) = (k1_mmlquery A C D)) ) )  => (r2_relset_1 A A B C)) ) ) ) ) ) ).
tt(t29_mod_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((r2_hidden (u1_struct_0 k18_mod_2) A) &  ((r2_hidden (u1_algstr_0 k18_mod_2) A) &  ((r2_hidden (k5_vectsp_1 k18_mod_2) A) &  ((r2_hidden (k4_struct_0 k18_mod_2) A) &  ((r2_hidden (u2_algstr_0 k18_mod_2) A) & (r2_hidden (k5_struct_0 k18_mod_2) A)) ) ) ) ) ) ) ).
tt(t29_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v2_mod_4 C A B) <=> (v1_ringcat1 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t29_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) => (m1_subset_1 (k7_trees_2 (k7_trees_2 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 2) (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) (k12_finseq_1 k5_numbers k6_numbers) A) (k12_finseq_1 k5_numbers 1) B) k6_modal_1)) ) ) ) ).
tt(t29_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( ((k51_modelc_1 A B C D) = (k51_modelc_1 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_modelc_2 A B) => (r3_modelc_2 A B)) ) ) ) ) ).
tt(t29_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  (~  ((r5_modelc_3 D B) &  ((r2_hidden C (u2_modelc_3 D (k10_modelc_3 (k1_funct_1 B 1) D))) &  ( (~ (r1_xxreal_0 A 1))  &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  ( (~ (r2_hidden C (u2_modelc_3 D (k10_modelc_3 (k1_funct_1 B A) D))))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden C (u2_modelc_3 D (k10_modelc_3 (k1_funct_1 B E) D))) &  (~ (r2_hidden C (u2_modelc_3 D (k10_modelc_3 (k1_funct_1 B (k1_nat_1 E 1)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A B) =>  ((v1_moebius1 B) |  ((a_2_2_moebius1 A B) = (a_2_3_moebius1 A B)) ) ) ) ) ) ) ).
tt(t29_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m3_monoid_0 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m3_monoid_0 C A))  =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m7_monoid_0 B A C)) ) ) ) ) ) ) ).
tt(t29_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k13_monoid_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k15_monoid_1 A (k6_algstr_0 (k13_monoid_1 A) B C) D) = (k2_nat_1 (k15_monoid_1 A B D) (k15_monoid_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t29_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A C) (k6_setfam_1 (u1_struct_0 A) B)) = (k1_setfam_1 (a_3_10_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t29_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ( (D = E)  =>  ((k7_msaterm A B D) = (k7_msaterm A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) => (m1_dtconstr (k5_trees_2 C D) (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ) ) ) ) ).
tt(t29_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) ) )  =>  (~  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r1_pboole A C B) &  ((r1_pboole A D B) &  ( (~ (r2_pboole A C D))  &  (~ (r2_pboole A D C)) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((r1_pboole A C B) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D B) => (r2_pboole A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) &  ((v4_unialg_1 B) & (m1_unialg_2 B A)) )  =>  (! [C:$i] :  ( ((v1_unialg_1 C) &  ((v4_unialg_1 C) & (m1_unialg_2 C A)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k6_msualg_1 A)) &  ((v4_msualg_1 D (k6_msualg_1 A)) & (m1_msualg_2 D (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  (! [E:$i] :  ( ((v3_msualg_1 E (k6_msualg_1 A)) &  ((v4_msualg_1 E (k6_msualg_1 A)) & (m1_msualg_2 E (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  ( ( (D = (k9_msualg_1 B))  &  (E = (k9_msualg_1 C)) )  =>  ((k3_pboole (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) D) (u3_msualg_1 (k6_msualg_1 A) E)) = (k16_funcop_1 k6_numbers (k3_xboole_0 (u1_struct_0 B) (u1_struct_0 C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v1_binop_1 (k15_msualg_2 A B) (k14_msualg_2 A B))) ) ) ) ).
tt(t29_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_hidden (k4_tarski E F) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (k6_msualg_6 A B C) D)) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) G)) &  (? [I:$i] :  ((m1_subset_1 I (k1_funct_1 (u3_msualg_1 A B) G)) &  (? [J:$i] :  ((m2_msualg_6 J A B G D) &  ((r1_rewrite1 (k3_msualg_6 A) G D) &  ((r2_hidden (k4_tarski H I) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C G)) &  ( (E = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) D) J H))  &  (F = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) D) J I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((r8_pboole (u1_struct_0 A) C (k6_pboole (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) => (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (k1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ) ) ) ) ).
tt(t29_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v1_mycielsk A) & (l1_orders_2 A)) )  =>  ((k2_mycielsk A) = (k3_mycielsk (k3_necklace A))) ) ) ).
tt(t29_nagata_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 k6_numbers (k1_metric_1 A A B C D))) ) ) ) ) ) ) ) ).
tt(t29_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 5) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  (~  (A = 5) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_nat_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (v7_ordinal1 A))  => (r1_xxreal_0 2 A)) ) ).
tt(t29_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((k1_newton A (k11_nat_3 (k24_binop_2 B C) A)) = (k24_binop_2 (k1_newton A (k11_nat_3 B A)) (k1_newton A (k11_nat_3 C A)))) ) ) ) ) ) ) ).
tt(t29_nat_4,ax,(v1_int_2 19)).
tt(t29_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_nat_5 A 1) = 1) ) ) ).
tt(t29_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_xcmplx_0 A B) = (k4_nat_1 (k5_nat_d A B) (k6_nat_d A B))) ) ) ) ) ).
tt(t29_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r3_nattra_1 A B C D) & (r3_nattra_1 A B D E))  => (r3_nattra_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) =>  ((r2_funct_2 k5_numbers k1_numbers (k4_normsp_0 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D (k3_normsp_0 (u1_struct_0 A) B C))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_vfunct_1 k5_numbers B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k5_vfunct_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_ncfcont1 D B) & (r8_ncfcont1 B A C D))  => (r2_ncfcont2 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t29_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v1_funct_1 (k4_vfunct_1 (u1_struct_0 B) A D C)) &  ((v2_ndiff_1 (k4_vfunct_1 (u1_struct_0 B) A D C) B A) & (m1_subset_1 (k4_vfunct_1 (u1_struct_0 B) A D C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t29_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid C)))))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r2_ndiff_4 C D A)) )  =>  ((r2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid C) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) D (k4_pdiff_1 B C)) A) & (r2_relset_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (k1_partfun1 k1_numbers (k1_euclid C) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) (k2_ndiff_4 C D A) (k4_pdiff_1 B C)) (k2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid C) (u1_struct_0 (k4_real_ns1 C)) (u1_struct_0 (k4_real_ns1 1)) D (k4_pdiff_1 B C)) A))) ) ) ) ) ) ) ) ) ).
tt(t29_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ( ((r2_hidden F (k4_finseq_1 A)) &  ((r1_ndiff_5 A B F C E) & (r1_ndiff_5 A B F D E)) )  =>  ((r1_ndiff_5 A B F (k2_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D) E) &  ((k6_ndiff_5 A B F (k2_vfunct_1 (u1_struct_0 (k14_prvect_2 A)) B C D) E) = (k5_algstr_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A F)) B) (k6_ndiff_5 A B F C E) (k6_ndiff_5 A B F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (C = (k1_neckla_3 A B))  <=>  (! [D:$i] :  ((r2_hidden D C) <=> (r2_hidden (k4_tarski B D) (k1_msualg_5 (u1_struct_0 A) (u1_orders_2 A)))) ) ) ) ) ) ) ) ).
tt(t29_necklace,ax,(r5_waybel_1 (k4_necklace 4) (k3_necklace (k4_necklace 4)))).
tt(t29_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_funct_1 (k7_newton B C A) (k1_nat_1 A 1)) = (k1_newton C A)) ) ) ) ) ) ) ).
tt(t29_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((v1_partfun1 C (u1_struct_0 B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k7_partfun1 (u1_struct_0 A) C (k3_rlvect_1 B D E)) = (k3_rlvect_1 A (k7_partfun1 (u1_struct_0 A) C D) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~ (r1_nfcont_1 B A C D)) ) )  | (r3_nfcont_1 B A C (u1_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t29_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C) & (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) E B) C))  => (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) (k2_vfunct_1 k1_numbers C D E) (k3_xboole_0 A B)) C)) ) ) ) ) ) ) ) ) ).
tt(t29_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers C)) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A))  =>  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 A k1_numbers C) B)) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k2_nfcont_4 A k1_numbers C) B) A)) ) ) ) ) ) ) ).
tt(t29_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  ((r1_xboole_0 (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B) (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B)) => (m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))) ) ) ) ).
tt(t29_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_normsp_2 A))) =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) &  (D = E) )  =>  ((r1_frechet (k4_normsp_2 A) C E) <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B H) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_numbers,ax, (~  (k5_numbers = k1_numbers) ) ).
tt(t29_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k15_openlatt A)) (k16_openlatt A) (k5_lattices A)) = k1_xboole_0) ) ) ).
tt(t29_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k4_oppcat_1 A D)) = (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t29_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_orders_1 A B) =>  ((r1_orders_1 A B) & (r2_orders_1 A B)) ) ) ) ) ).
tt(t29_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_orders_2 C A B) => (r1_tarski C B)) ) ) ) ) ) ).
tt(t29_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( (~  ( (~ (v4_ordinal1 A))  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  (A = (k1_ordinal1 B)) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((v3_ordinal1 B) &  (A = (k1_ordinal1 B)) ) )  & (v4_ordinal1 A)) ) ) ) ) ).
tt(t29_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k10_ordinal2 B D)) ) ) ) )  =>  ((k10_ordinal2 B A) = (k4_ordinal2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  | (v4_ordinal1 (k10_ordinal2 B A))) ) ) ) ) ) ).
tt(t29_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden 1 A) =>  ( (B = k1_xboole_0)  | (r2_hidden 1 (k12_ordinal2 A B))) ) ) ) ) ) ).
tt(t29_ordinal5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k1_ordinal5 A k4_ordinal1) = k4_ordinal1) ) ) ) ).
tt(t29_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((r2_hidden A (k9_xtuple_0 (k3_ordinal6 B))) => (r1_abian (k1_funct_1 (k3_ordinal6 B) A) B)) ) ) ) ).
tt(t29_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t29_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ( ((k2_ortsp_1 A B E F D C) = (k4_struct_0 A))  <=> (r1_orders_2 B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v2_relat_1 (k22_osafree A B))) ) ) ) ).
tt(t29_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v4_msualg_1 (k6_osalg_1 A B C) A) & (v13_osalg_1 (k6_osalg_1 A B C) A)) ) ) ) ) ) ) ).
tt(t29_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((v3_msualg_2 (k9_osalg_2 A B C) A B) & (r2_pboole (u1_struct_0 A) C (k9_osalg_2 A B C))) ) ) ) ) ) ) ).
tt(t29_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r1_parsp_1 A B C B D))  =>  ( (~ (r1_parsp_1 A B D B C))  &  ( (~ (r1_parsp_1 A C B B D))  &  ( (~ (r1_parsp_1 A B C D B))  &  ( (~ (r1_parsp_1 A B D C B))  &  ( (~ (r1_parsp_1 A C B D B))  &  ( (~ (r1_parsp_1 A D B B C))  &  ( (~ (r1_parsp_1 A D B C B))  &  ( (~ (r1_parsp_1 A C B C D))  &  ( (~ (r1_parsp_1 A B C C D))  &  ( (~ (r1_parsp_1 A C B D C))  &  ( (~ (r1_parsp_1 A C D C B))  &  ( (~ (r1_parsp_1 A C B D C))  &  ( (~ (r1_parsp_1 A D C C B))  &  ( (~ (r1_parsp_1 A C D B C))  &  ( (~ (r1_parsp_1 A D C B C))  &  ( (~ (r1_parsp_1 A D B D C))  &  ( (~ (r1_parsp_1 A B D D C))  &  ( (~ (r1_parsp_1 A D B C D))  &  ( (~ (r1_parsp_1 A B D C D))  &  ( (~ (r1_parsp_1 A D C D B))  &  ( (~ (r1_parsp_1 A C D D B))  &  ( (~ (r1_parsp_1 A D C B D))  &  (~ (r1_parsp_1 A C D B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_parsp_2 A B C D E) &  ((r1_parsp_2 A B C F) & (r1_parsp_2 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_tarski A B) => (r1_relset_1 C A (k3_partfun1 D C A) (k3_partfun1 D C B))) ) ) ) ) ) ).
tt(t29_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden D C) =>  ((k7_partfun1 B (k4_partfun2 A B C E) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ( ((r1_setfam_1 B D) & (r1_setfam_1 C D))  => (r1_setfam_1 (k3_partit1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t29_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r5_relat_2 B A) => (v5_relat_2 B)) ) ) ) ) ).
tt(t29_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_diraf A B C D) &  ((r1_diraf A B E F) &  ( (~ (r3_diraf A B C F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_diraf A C G F) & (r1_diraf A E G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k3_pboole A (k3_pboole A B C) D) (k3_pboole A B (k3_pboole A C D)))) ) ) ) ) ) ) ).
tt(t29_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((v9_metric_1 A) => (r2_hidden (k9_metric_1 A B C) (k2_pcomps_1 A))) ) ) ) ) ) ) ).
tt(t29_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k19_pcs_0 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k19_pcs_0 A B))) =>  ( ( (C = E)  &  ( (D = F)  & (r1_pcs_0 (k19_pcs_0 A B) E F)) )  =>  ( (C = B)  |  ( (D = B)  | (r1_pcs_0 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r3_pdiff_1 A B C E) & (r3_pdiff_1 A B D E))  =>  ((r3_pdiff_1 A B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) &  ((k11_pdiff_1 A B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) = (k7_real_1 (k11_pdiff_1 A B C E) (k11_pdiff_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r1_pdiff_3 C B) =>  ((r3_pdiff_1 2 1 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 1 2 C) A) B) &  ((k11_pdiff_1 2 1 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 1 2 C) A) B) = (k8_real_1 A (k2_pdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t29_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 2 B A) & (r3_pdiff_1 3 2 C A))  => (r3_pdiff_1 3 2 (k20_valued_1 (k1_euclid 3) k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t29_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r2_pdiff_5 B A) =>  ((k2_pdiff_5 B A) = (k11_pdiff_1 3 2 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ) ).
tt(t29_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  ((r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) C D) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E B))  => (r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) (k1_partfun1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 E B)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  (? [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  & (r2_relset_1 (k1_euclid A) (k1_euclid 1) B (k3_pdiff_1 A C))) ) ) ) ) ) ).
tt(t29_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r3_pdiff_7 A B C E) & (r3_pdiff_7 A B D E))  =>  ((r3_pdiff_7 A B (k7_integr15 B (k1_euclid A) C D) E) & (r3_pdiff_7 A B (k8_integr15 B (k1_euclid A) C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pencil_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v15_pencil_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_pencil_1 A B)))) =>  ( ( (~ (v1_zfmisc_1 C))  &  ((v2_pencil_1 C (k5_pencil_1 A B)) & (v1_pencil_1 C (k5_pencil_1 A B))) )  <=>  (? [D:$i] :  ( ( (~ (v13_pencil_1 D))  &  ((v16_pencil_1 D A) & (m3_pboole D A (k12_pralg_1 A B))) )  &  ( (C = (k4_card_3 D))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_pencil_1 A B (k3_pencil_1 A D))))) =>  ( (E = (k1_funct_1 D (k3_pencil_1 A D)))  =>  ((v2_pencil_1 E (k2_pencil_1 A B (k3_pencil_1 A D))) & (v1_pencil_1 E (k2_pencil_1 A B (k3_pencil_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k1_vectsp_9 A B) (k1_nat_1 C 1)) |  ( (~ (v2_struct_0 (k7_pencil_4 A B C (k1_nat_1 C 1))))  &  ( (~ (v3_pencil_1 (k7_pencil_4 A B C (k1_nat_1 C 1))))  &  ( (~ (v4_pencil_1 (k7_pencil_4 A B C (k1_nat_1 C 1))))  &  ((v5_pencil_1 (k7_pencil_4 A B C (k1_nat_1 C 1))) &  ((v6_pencil_1 (k7_pencil_4 A B C (k1_nat_1 C 1))) & (l1_pre_topc (k7_pencil_4 A B C (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k13_newton 2 (k1_nat_1 A 1)) = (k2_xcmplx_0 (k2_newton 2 A) (k2_newton 2 A))) ) ) ).
tt(t29_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  ( ((r2_pnproc_1 A B C) & (r2_pnproc_1 A C D))  => (r1_pnproc_1 A (k3_pnproc_1 A D (k3_pnproc_1 A C B)) (k2_pnproc_1 A (k3_pnproc_1 A D C) B))) ) ) ) ) ) ) ) ).
tt(t29_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k7_polyeq_1 A k6_numbers B k6_numbers C) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (D = (k1_binop_2 (k6_binop_2 B A)))  &  ( (~  (C = k6_numbers) )  &  ( (~  (C = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) k7_complex1))) )  &  ( (~  (C = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) k7_complex1))) )  &  ( (~  (C = (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) k7_complex1))) )  &  (~  (C = (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 D) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 D)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 D)) (k5_square_1 (k4_complex1 D))))) 2)) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 (k5_polyeq_5 A B C D) (k6_polyeq_5 A B C D)) (k7_polyeq_5 A B C D)) (k8_polyeq_5 A B C D)) = A) ) ) ) ) ) ) ) ) ).
tt(t29_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k10_xtuple_0 (k10_polyform A B)) = (k8_polyform A B)) ) ) ) ) ).
tt(t29_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B C (k8_polynom1 A B)) C)) ) ) ) ) ) ).
tt(t29_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B B) (k9_polynom3 A))) ) ) ) ).
tt(t29_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k10_polynom3 A) B) (k3_algseq_1 A B))) ) ) ) ).
tt(t29_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k5_polynom7 A B C D) E) = (k8_group_1 B D (k5_polynom2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A 1) =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 A E))  =>  ((k3_matrix_1 (u1_struct_0 B) D (k1_nat_1 E 1) 1) = (k8_nat_1 (u1_struct_0 B) C E)) ) ) )  =>  ((k4_polynom8 A B C) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_polyred A B C D E) <=>  (~ (r2_polyred A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power A (k6_xcmplx_0 B C)) = (k13_complex1 (k3_power A B) (k3_power A C))) ) ) ) ) ) ) ) ).
tt(t29_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) & (v1_funcop_1 E)) ) ) )  =>  (~  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (? [G:$i] :  ((m2_pboole G (u1_struct_0 B) (u3_msualg_1 B D) (u3_msualg_1 B (k5_pralg_2 A B C F))) &  ( (G = (k1_funct_1 E F))  & (r1_msualg_3 B D (k5_pralg_2 A B C F) G)) ) ) ) )  &  (! [F:$i] :  ((m2_pboole F (u1_struct_0 B) (u3_msualg_1 B D) (u3_msualg_1 B (k14_pralg_2 A B C))) =>  (~  ((r1_msualg_3 B D (k14_pralg_2 A B C) F) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k3_msualg_3 (u1_struct_0 B) (u3_msualg_1 B D) (u3_msualg_1 B (k14_pralg_2 A B C)) (u3_msualg_1 B (k5_pralg_2 A B C G)) F (k2_pralg_3 A B C G)) = (k1_funct_1 E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_prelamb A) & (l2_prelamb A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_prelamb A (k3_prelamb A (k3_prelamb A B C) D) (k3_prelamb A B (k3_prelamb A C D)))) ) ) ) ) ) ) ) ).
tt(t29_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  (! [C:$i] :  (~  ((r2_hidden C (k4_finseq_1 (k5_pre_poly A B))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) &  ((r2_hidden E (k4_finseq_1 (k1_funct_1 B D))) &  ( (C = (k2_nat_1 (k2_wsierp_1 (k10_pre_poly A (k17_finseq_1 (k3_finseq_2 A) (k7_nat_d D 1) B))) E))  &  ((k1_funct_1 (k1_funct_1 B D) E) = (k1_funct_1 (k5_pre_poly A B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 1 (k2_prepower B A)) & (r1_xxreal_0 (k2_prepower B A) A)) ) ) ) ) ) ).
tt(t29_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) => (m1_pre_topc B A)) ) ) ) ).
tt(t29_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ((v1_funct_1 (k3_relat_1 C D)) &  ((v1_funct_2 (k3_relat_1 C D) k5_numbers k1_numbers) & (m1_subset_1 (k3_relat_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) ) ) ) ) ) ) ).
tt(t29_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers))  =>  ((k1_seq_1 C (k5_prob_1 A B E D)) = (k8_real_1 (k1_seq_1 (k3_prob_2 A B C D) E) (k1_seq_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k3_prob_1 A (k1_prob_3 A C)) = (k3_prob_1 A C)) ) ) ) ) ) ).
tt(t29_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k4_prob_4 A B C)) =>  ((k6_prob_4 A B C D) = (k3_measure3 A B (k2_prob_4 A B C) (k5_prob_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t29_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A C B) (k10_cqc_lang A B C))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t29_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~  ( ((k1_projpl_1 A B D) = (k1_projpl_1 A C E))  &  ( (~  (B = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  (~ (r1_incsp_1 A B (k1_projpl_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k17_euclid (k10_pscomp_1 A)) = (k17_euclid (k18_pscomp_1 A)))  &  ( ((k17_euclid (k10_pscomp_1 A)) = (k17_euclid (k19_pscomp_1 A)))  &  ( ((k17_euclid (k18_pscomp_1 A)) = (k17_euclid (k19_pscomp_1 A)))  &  ( ((k17_euclid (k18_pscomp_1 A)) = (k17_euclid (k11_pscomp_1 A)))  &  ((k17_euclid (k19_pscomp_1 A)) = (k17_euclid (k11_pscomp_1 A))) ) ) ) ) ) ) ).
tt(t29_pua2mss1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ((l1_msualg_1 B) =>  (! [C:$i] :  ((l1_msualg_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ((r3_pua2mss1 A B D F) & (r3_pua2mss1 B C E G))  => (r3_pua2mss1 A C (k3_relat_1 D E) (k3_relat_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r2_pboole A (k1_pzfmisc1 A B) (k1_mboolean A B))) ) ) ).
tt(t29_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  ( ((r1_qc_lang1 A B C) & (r2_qc_lang1 A C D))  => (r2_qc_lang1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t29_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((k10_qc_lang2 A (k3_qc_lang2 A B C)) = B)  &  ( ((k11_qc_lang2 A (k3_qc_lang2 A B C)) = C)  &  ((k18_qc_lang1 A (k3_qc_lang2 A B C)) = (k14_qc_lang1 A (k13_qc_lang1 A B) (k13_qc_lang1 A C))) ) ) ) ) ) ) ) ) ).
tt(t29_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v6_qc_lang1 C A) => (v6_qc_lang1 (k5_qc_lang2 A B C) A)) ) ) ) ) ) ) ).
tt(t29_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) => (r1_tarski (a_4_0_qc_lang4 A B C D) (k3_qc_lang4 A B D))) ) ) ) ) ) ) ) ).
tt(t29_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k9_quantal1 A B (k4_lattices A C D)) = (k4_lattices A (k9_quantal1 A B C) (k9_quantal1 A B D)))  &  ((k9_quantal1 A (k4_lattices A C D) B) = (k4_lattices A (k9_quantal1 A C B) (k9_quantal1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t29_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k8_quatern2 A)) = (k10_real_1 (k17_quaterni A) (k5_square_1 (k3_quatern2 A))))  &  ( ((k18_quaterni (k8_quatern2 A)) = (k1_real_1 (k10_real_1 (k18_quaterni A) (k5_square_1 (k3_quatern2 A)))))  &  ( ((k19_quaterni (k8_quatern2 A)) = (k1_real_1 (k10_real_1 (k19_quaterni A) (k5_square_1 (k3_quatern2 A)))))  &  ((k20_quaterni (k8_quatern2 A)) = (k1_real_1 (k10_real_1 (k20_quaterni A) (k5_square_1 (k3_quatern2 A))))) ) ) ) ) ) ).
tt(t29_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k27_quaterni A (k25_quaterni (k10_real_1 1 (k5_square_1 (k3_quatern2 A))) (k31_quaterni A))) = (k6_quaterni (k10_real_1 (k5_square_1 (k3_quatern2 A)) (k5_square_1 (k3_quatern2 A))) k6_numbers k6_numbers k6_numbers)) ) ) ).
tt(t29_quaterni,ax, ( ((k17_quaterni k22_quaterni) = 1)  &  ( ((k18_quaterni k22_quaterni) = k6_numbers)  &  ( ((k19_quaterni k22_quaterni) = k6_numbers)  &  ((k20_quaterni k22_quaterni) = k6_numbers) ) ) ) ).
tt(t29_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_quofield A)) (k7_quofield A)) =>  ( (~  (B = (k11_quofield A)) )  =>  ( ((k5_binop_1 (k7_quofield A) (k16_quofield A) B (k3_funct_2 (k7_quofield A) (k7_quofield A) (k18_quofield A) B)) = (k12_quofield A))  &  ((k5_binop_1 (k7_quofield A) (k16_quofield A) (k3_funct_2 (k7_quofield A) (k7_quofield A) (k18_quofield A) B) B) = (k12_quofield A)) ) ) ) ) ) ) ).
tt(t29_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  => (m1_random_1 B A (k1_random_1 A))) ) ) ) ).
tt(t29_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A C) => (m2_vectsp_6 (k8_ranknull A C B E D) A B (k2_ranknull C B D (k1_vectsp_6 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ( ((k2_rat_1 A) = (k4_real_1 C B))  &  ((k1_rat_1 A) = (k4_nat_1 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) => (r1_xxreal_0 (k12_ratfunc1 A B) (k4_xxreal_0 (k2_hurwitz A (k4_ratfunc1 A B)) (k2_hurwitz A (k5_ratfunc1 A B))))) ) ) ) ).
tt(t29_rcomp_3,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (~  ( (~ (v1_xboole_0 A))  &  ( (~  (A = k1_numbers) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~  (A = (k1_limfunc1 B)) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~  (A = (k10_prob_1 B)) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~  (A = (k2_limfunc1 B)) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (~  (A = (k3_limfunc1 B)) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 B C) &  (A = (k1_rcomp_1 B C)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (A = (k3_rcomp_1 B C)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (A = (k4_rcomp_1 B C)) ) ) ) ) ) )  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (A = (k2_rcomp_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 B) (k1_nat_1 A 1)) = k6_numbers) ) ) ) ) ).
tt(t29_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ( ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B D) = C)  <=>  ((k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) C D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t29_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ((r2_classes1 (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A))) &  ( ((k20_rfunct_3 C (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) C) = (k20_rfunct_3 B (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B))  &  ((k21_rfunct_3 C (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) C) = (k21_rfunct_3 B (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) => (r1_tarski (k3_relat_1 C A) (k3_relat_1 C B))) ) ) ) ) ) ) ).
tt(t29_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k7_relset_1 C A D B)) <=>  (? [F:$i] :  ((m1_subset_1 F C) &  ((r2_hidden (k4_tarski F E) D) & (r2_hidden F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( (C = k1_xboole_0)  =>  ((k6_relset_2 A B C D) = B) ) ) ) ) ) ) ) ).
tt(t29_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) = (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_goboard9 B) A)) ) ) ) ) ).
tt(t29_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) A) => (r2_rewrite1 A B C)) ) ) ) ) ).
tt(t29_rewrite2,ax, (! [A:$i] : (r2_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A (k1_partit_2 (k8_afinsq_1 A) (k8_afinsq_1 A))) (k1_partit_2 (k8_afinsq_1 A) (k8_afinsq_1 A)))) ).
tt(t29_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ((l1_rewrite3 G F) =>  (~  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 F G)))))  &  ((r2_rewrite3 C F G A D B E) & (r1_xxreal_0 (k1_afinsq_1 D) (k1_afinsq_1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k6_rfinseq2 (k6_rvsum_1 A)) = (k6_rvsum_1 (k5_rfinseq2 A))) ) ) ).
tt(t29_rfinseq,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_finseq_1 (k2_rfinseq A C B)) = (k1_xreal_0 (k3_finseq_1 B) C)) ) ) ) ) ) ) ).
tt(t29_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k4_rfunct_1 (k30_valued_1 A)) = (k24_valued_1 (k4_rfunct_1 A) (k1_real_1 1))) ) ) ).
tt(t29_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) & (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) ).
tt(t29_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_rfunct_3 A k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k17_rfunct_3 A (k17_finseq_1 (k3_rfunct_3 A k1_numbers) D B) C) = (k17_finseq_1 k1_numbers D (k17_rfunct_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t29_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (m1_subset_1 (a_2_0_rinfsup1 A B) (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(t29_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_funct_2 k5_numbers k7_numbers (k3_rinfsup2 (k1_valued_0 k7_numbers A B)) (k1_valued_0 k7_numbers (k3_rinfsup2 A) B)) &  ((k6_rinfsup2 (k1_valued_0 k7_numbers A B)) = (k6_rinfsup2 A)) ) ) ) ) ) ).
tt(t29_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_xboole_0 (k3_rlvect_2 A B) (k10_xtuple_0 C)) =>  ((k18_rvsum_1 (k4_finseqop (u1_struct_0 A) k1_numbers C B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t29_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_ordinal1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( ((v1_finset_1 (k5_setfam_1 (u1_struct_0 A) B)) & (v1_rlaffin1 (k5_setfam_1 (u1_struct_0 A) B) A))  =>  ((v1_rlaffin1 (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) A) & (m1_subset_1 (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t29_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~ (r2_hidden A C))  => (r1_funct_2 (u1_struct_0 B) (u1_struct_0 k3_topmetr) (k2_struct_0 B) (k1_tarski k1_xboole_0) (k2_rlaffin3 B C A) (k7_funcop_1 (k2_struct_0 B) k1_xboole_0))) ) ) ) ) ) ).
tt(t29_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 C D)) ) )  => (m1_rlsub_1 B C)) ) ) ) ) ) ) ).
tt(t29_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B C))  =>  ((k1_rlsub_2 A B (k2_rlsub_2 A D C)) = (k2_rlsub_2 A (k1_rlsub_2 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v4_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (v3_rltopsp1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t29_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A B (k5_algstr_0 A C D)) = (k3_rlvect_1 A (k5_algstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t29_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~  (B = k1_xboole_0) )  & (v1_rlsub_1 B A))  <=>  (! [C:$i] :  ((m2_rlvect_2 C A B) => (r2_hidden (k6_rlvect_2 A C) B)) ) ) ) ) ) ) ).
tt(t29_rlvect_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  ((r1_struct_0 (k1_rlsub_1 B) A) <=>  (A = (k4_struct_0 B)) ) ) ) ) ).
tt(t29_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C (k4_algstr_0 A D)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlvect_3 B A) =>  ((k1_card_1 B) = (k1_rlvect_5 (k1_rlvect_3 A B))) ) ) ) ) ) ).
tt(t29_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k2_finseq_1 (k3_finseq_1 B))) &  (B = (k1_funct_4 (k8_funcop_1 (u1_struct_0 A) (k2_finseq_1 (k3_finseq_1 B)) (k4_struct_0 A)) (k8_funcop_1 (u1_struct_0 A) (k1_tarski D) C))) )  =>  ((k4_rlvect_1 A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t29_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t29_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) => (m1_rmod_2 (k1_rmod_3 A B C (k2_rmod_3 A B D E)) A (k2_rmod_3 A B (k1_rmod_3 A B D C) (k1_rmod_3 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~  ((k4_struct_0 A) = (k1_group_1 A)) )  =>  ( ( (~  (C = k1_xboole_0) )  & (v1_rmod_2 C A B))  <=>  (! [D:$i] :  ((m2_rmod_4 D A B C) => (r2_hidden (k5_rmod_4 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_robbins1 A (k5_robbins1 A (k6_robbins1 A B C) (k6_robbins1 A B D)) (k3_robbins1 A (k6_robbins1 A B (k5_robbins1 A C D)))) = (k7_robbins1 A)) ) ) ) ) ) ) ) ) ).
tt(t29_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) C)) B) = B) ) ) ) ) ) ) ).
tt(t29_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v10_robbins3 B) & (m3_robbins3 B A))  => (v12_oposet_1 B)) ) ) ) ).
tt(t29_robbins4,ax, ((k5_lattices k2_robbins4) = k6_numbers) ).
tt(t29_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A (k3_subset_1 (u1_struct_0 A) B)) = (k3_subset_1 (u1_struct_0 A) (k3_roughs_1 A B))) ) ) ) ) ).
tt(t29_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k1_rpr_1 A (k4_subset_1 A (k4_subset_1 A B C) D)) = (k7_real_1 (k9_real_1 (k7_real_1 (k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C)) (k1_rpr_1 A D)) (k7_real_1 (k7_real_1 (k1_rpr_1 A (k9_subset_1 A B C)) (k1_rpr_1 A (k9_subset_1 A B D))) (k1_rpr_1 A (k9_subset_1 A C D)))) (k1_rpr_1 A (k9_subset_1 A (k9_subset_1 A B C) D)))) ) ) ) ) ) ) ) ) ).
tt(t29_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v1_rlsub_1 B A) &  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ( ((v1_bhsp_1 B) & (m1_rusub_1 B D))  =>  ((k1_rusub_2 A B (k2_rusub_2 A C D)) = (k2_rusub_2 A (k1_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r1_struct_0 (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) B)) C) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  (C = (k1_rlvect_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t29_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (v3_rusub_4 (k4_rusub_4 A B) A)) ) ) ) ).
tt(t29_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_square_1 (k3_bhsp_1 A (k3_rlvect_1 A B C))) = (k7_real_1 (k7_real_1 (k5_square_1 (k3_bhsp_1 A B)) (k8_real_1 2 (k2_bhsp_1 A B C))) (k5_square_1 (k3_bhsp_1 A C))))  &  ((k5_square_1 (k3_bhsp_1 A (k5_algstr_0 A B C))) = (k7_real_1 (k9_real_1 (k5_square_1 (k3_bhsp_1 A B)) (k8_real_1 2 (k2_bhsp_1 A B C))) (k5_square_1 (k3_bhsp_1 A C)))) ) ) ) ) ) ) ) ).
tt(t29_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k8_rvsum_1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k1_numbers (k10_binop_2 A B))) ) ) ) ) ).
tt(t29_rvsum_2,ax, ((k17_rvsum_1 (k6_finseq_1 k2_numbers)) = k5_complex1) ).
tt(t29_scmfsa10,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_scmfsa_2))) =>  ( (A = 12)  =>  ((k3_compos_0 (u1_compos_1 k1_scmfsa_2) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t29_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  (! [B:$i] :  ((m2_subset_1 B k1_scmfsa_1 k3_scmfsa_1) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_scmfsa_1 k2_scmfsa_1) =>  ((k1_funct_1 (k8_scmfsa_1 A B C) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ).
tt(t29_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k17_scmfsa_2 B A)) = 12) ) ) ) ) ).
tt(t29_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmfsa6a (k4_scmfsa6a A B) C) = (k4_scmfsa6a A (k3_scmfsa6a B C))) ) ) ) ) ) ) ).
tt(t29_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B))  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k5_card_1 C))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B (k2_scmfsa6a C)) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B C) (k1_funct_4 A (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1)))) ) ) ) ) ) ) ) ) ).
tt(t29_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b D B A) & (r6_scmfsa7b D B A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r5_scmfsa7b (k3_scmfsa8b E C D) B A) & (r6_scmfsa7b (k3_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a B A (k2_scmfsa6a C)) =>  ((r5_scmfsa7b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) B A) &  ((r6_scmfsa7b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) B A) &  ( ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B)) = (k2_scmfsa8a B A (k2_scmfsa6a C)))  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_scmfsa8a B A (k2_scmfsa6a C)) D))  =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) D)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B) D))) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k2_scmfsa8a B A (k2_scmfsa6a C))) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) D)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 D 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  ( ((r1_tarski (k2_scmfsa_9 B C) A) & (r1_xxreal_0 (k1_funct_1 D B) k6_numbers))  =>  ( ((k8_extpro_1 3 k1_scmfsa_2 A D) = 4)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A D E)) = (k6_memstr_0 3 k1_scmfsa_2 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( (~  ((r1_xxreal_0 (k1_funct_1 C D) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers C (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k4_scmfsa_9 D A B E) 1))) &  (~  ((k1_funct_1 C D) = k6_numbers) ) ) )  &  ( (~  ( ((k1_funct_1 C D) = k6_numbers)  &  ((k1_funct_1 D B) = k6_numbers) ) )  &  ( (~  ((k1_funct_1 D B) = k6_numbers) )  =>  ((k1_funct_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) )  => (v7_amistd_1 (k1_scmfsa_9 B A) 3 k1_scmfsa_2)) ) ) ) ) ).
tt(t29_scmfsa_m,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden A (k9_xtuple_0 (k1_funct_4 (k16_funcop_1 (k4_scmfsa_2 B) C) (k7_memstr_0 3 k1_scmfsa_2 D)))) &  ( (~  (A = (k4_scmfsa_2 B)) )  &  (~  (A = (k4_struct_0 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_scmfsa6c C) &  ((v2_scmfsa6c C) & (m1_subset_1 C (u1_compos_1 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa6a C D) B A) E) = (k18_scmfsa_2 (k1_scmfsa6b D (k2_extpro_1 3 k1_scmfsa_2 C (k1_scmfsa_m B)) A) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k4_sf_mastr (k2_scmisort A)) = (k1_tarski A)) ) ) ).
tt(t29_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 3)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  (A = (k6_scmpds_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) &  ((v2_scmpds_4 E) & (v3_scmpds_4 E)) ) ) ) ) ) ) )  =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 E) B) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 E) F) C) &  ( ((k5_memstr_0 2 k1_scmpds_2 A) = F)  &  ((k6_memstr_0 2 k1_scmpds_2 D) = (k6_memstr_0 2 k1_scmpds_2 A)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) F) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ( ((k3_extpro_1 2 k1_scmpds_2 B (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k3_extpro_1 2 k1_scmpds_2 C (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)) =>  ((k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k1_scmpds_4 C D)) B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v2_compos_1 B k1_scmpds_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_scmpds_6 B C A) & (r2_scmpds_6 B C A))  =>  ((k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 B)) (k8_memstr_0 2 k1_scmpds_2 C)))) = (k5_card_1 B)) ) ) ) ) ) ) ) ).
tt(t29_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) &  ((r2_scmpds_6 C B A) &  ((r1_scmpds_6 D (k6_scmpds_4 C B A) A) & (r2_scmpds_6 D (k6_scmpds_4 C B A) A)) ) )  =>  ((k6_scmpds_4 (k1_scmpds_4 C D) B A) = (k9_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A) (k5_card_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ( ( (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden H G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 B H))) ) )  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 H J))) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ((r1_xxreal_0 (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  ( (~ (r1_xxreal_0 (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)) (k1_funct_1 (k6_scmpds_4 C H I) (k2_scmpds_2 (k1_funct_1 B D) E))))  &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) => (r1_xxreal_0 (k2_xcmplx_0 F (k1_funct_1 (k6_scmpds_4 C H I) (k2_scmpds_2 (k1_funct_1 B D) E))) (k1_funct_1 (k6_scmpds_4 C H I) J))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D E C) B A) &  ((r2_scmpds_6 (k2_scmpds_8 D E C) B A) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers))  =>  ((k6_scmpds_4 (k2_scmpds_8 D E C) B A) = (k6_scmpds_4 (k2_scmpds_8 D E C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 (k1_scmring2 A)) (k2_compos_0 (u1_compos_1 (k1_scmring2 A)) (k9_scmring2 A C B)))) 1) = k5_numbers) ) ) ) ) ) ) ).
tt(t29_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (~  ((r2_hidden B A) &  ( (~  (B = k1_xboole_0) )  &  ( (! [C:$i] :  (~  ( (B = (k1_tarski C))  & (r2_hidden C (k3_tarski A))) ) )  &  (~ (r2_hidden B (k1_scmyciel A))) ) ) ) ) ) ) ) ).
tt(t29_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C E) & (r1_semi_af1 A B D E))  =>  ((r1_semi_af1 A B C D) |  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A (k32_valued_1 k5_numbers k1_numbers B)) (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ).
tt(t29_seq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A))) = (k8_real_1 (k17_complex1 A) (k17_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t29_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k12_binop_2 1 (k9_binop_2 C A))) ) ) )  =>  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ).
tt(t29_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k5_seqfunc A B) C) (k56_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C))) & (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k4_seqfunc A B) C) (k32_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ).
tt(t29_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_comseq_2 A) & (m2_valued_0 B k1_numbers A))  => (v1_comseq_2 B)) ) ) ) ) ).
tt(t29_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C)) &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers A C))) ) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k3_funct_2 k5_numbers k1_numbers B D))) ) ) ) )  & (v1_series_1 A)) ) ) ) ) ) ) ).
tt(t29_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 1 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k4_nat_1 3 B) 2) (k2_nat_1 (k4_nat_1 3 B) 1)) (k2_nat_1 (k4_nat_1 3 B) 4))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 1 24) (k13_complex1 1 (k4_nat_1 (k4_nat_1 6 (k2_nat_1 (k4_nat_1 3 B) 1)) (k2_nat_1 (k4_nat_1 3 B) 4))))) ) ) ) ) ) ) ).
tt(t29_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k8_real_1 2 (k3_power A (k6_square_1 (k3_xcmplx_0 B C)))) (k2_xcmplx_0 (k3_power A B) (k3_power A C)))) ) ) ) ) ) ) ).
tt(t29_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ( ((k1_seq_1 B C) = A)  &  ((k1_seq_1 B k6_numbers) = 1) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k1_seq_1 (k1_series_3 B) C) = (k1_newton A C)) ) ) ) ) ) ) ) ) ).
tt(t29_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) => (r1_xxreal_0 (k3_square_1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 C D)) (k3_xcmplx_0 E F))) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 C)) (k3_square_1 E)) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 B) (k3_square_1 D)) (k3_square_1 F))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~ (r1_tarski (k2_xboole_0 (k1_setfam_1 A) (k1_setfam_1 B)) (k1_setfam_1 (k2_setfam_1 A B)))) ) ) ) ) ) ).
tt(t29_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_kurato_0 A B) = (k3_subset_1 A (k3_prob_1 A (k2_prob_1 A B)))) ) ) ) ).
tt(t29_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 C A) => (v1_setlim_1 (k7_setlim_2 A C B) A)) ) ) ) ) ) ).
tt(t29_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v3_binop_1 D A) &  ((v1_binop_1 D A) & (v2_binop_1 D A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  ( (~  (E = k1_xboole_0) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  ((k7_setwiseo C A D (k8_setwiseo B C F E) G) = (k7_setwiseo B A D E (k1_partfun1 B C C A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((v1_setwiseo B A) &  ( ((k3_funct_2 A A C (k4_binop_1 A B)) = (k4_binop_1 A B))  & (r7_binop_1 A C B)) )  =>  ((k3_funct_2 A A C (k1_finsop_1 A D B)) = (k1_finsop_1 A (k4_finseqop A A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t29_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r5_scmfsa7b (k3_sfmastr3 C D B E) A F) & (r6_scmfsa7b (k3_sfmastr3 C D B E) A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k4_scmfsa6a A B)) = (k2_xboole_0 (k1_sf_mastr A) (k2_sf_mastr B))) ) ) ) ) ).
tt(t29_sgraph1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (~  ((r2_hidden C (u1_struct_0 B)) &  (! [D:$i] :  ((v1_finset_1 D) =>  (~  ( (D = (u1_struct_0 B))  &  (~ (r1_xxreal_0 (k5_card_1 D) (k4_sgraph1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_sheffer1 A) & (l3_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D))) = (k5_sheffer1 A (k5_sheffer1 A (k6_sheffer1 A C) B) (k5_sheffer1 A (k6_sheffer1 A D) B))) ) ) ) ) ) ) ) ) ).
tt(t29_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A E (k5_sheffer1 A C B)))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) & (m1_simplex0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v5_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 C))))  =>  ((r1_tarski D (u1_pre_topc B)) =>  ((v1_pre_topc (k5_simplex0 C D)) & (m2_simplex0 (k5_simplex0 C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t29_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) => (v2_simplex1 (k4_simplex1 A B) A)) ) ) ) ) ).
tt(t29_sincos10,ax, ( ((k1_seq_1 k16_sin_cos (k10_real_1 k32_sin_cos 4)) = (k10_real_1 1 (k7_square_1 2)))  &  ((k1_seq_1 k19_sin_cos (k10_real_1 k32_sin_cos 4)) = (k10_real_1 1 (k7_square_1 2))) ) ).
tt(t29_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_newton (k7_real_1 (k1_seq_1 k4_sin_cos2 A) (k1_seq_1 k1_sin_cos2 A)) B) = (k7_real_1 (k1_seq_1 k4_sin_cos2 (k11_binop_2 B A)) (k1_seq_1 k1_sin_cos2 (k11_binop_2 B A)))) ) ) ) ) ).
tt(t29_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k7_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) A)) k7_complex1)) = 1) ) ) ).
tt(t29_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) = (k4_xcmplx_0 (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k6_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B)))))) ) ) ) ) ).
tt(t29_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k21_sin_cos (k6_real_1 A 2)) = k6_numbers) )  =>  ((k1_sin_cos4 (k6_real_1 A 2)) = (k6_real_1 (k17_sin_cos A) (k7_real_1 1 (k20_sin_cos A)))) ) ) ) ).
tt(t29_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) &  ((k20_sin_cos A) = (k1_real_1 1)) ) )  =>  (A = k32_sin_cos) ) ) ) ).
tt(t29_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  (A = k6_numbers) )  &  ((k25_sin_cos A) = 1) ) ) ) ) ).
tt(t29_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k9_sin_cos2 (k7_xcmplx_0 A 2)) = (k6_square_1 (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) 1) (k2_xcmplx_0 (k6_sin_cos2 A) 1)))) ) ) ) ).
tt(t29_sin_cos9,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t29_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k2_xcmplx_0 (k3_square_1 (k20_sin_cos A)) (k3_square_1 (k17_sin_cos A))) = 1)  &  ((k2_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos A)) (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos A))) = 1) ) ) ) ).
tt(t29_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ( (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A))  &  ( (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)))  &  ( (E = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 2)))  &  ( (~  ( ((k17_euclid C) = (k17_euclid D))  &  (~  ((k17_euclid E) = (k17_euclid D)) ) ) )  &  (~  ( ((k18_euclid C) = (k18_euclid D))  &  (~  ((k18_euclid E) = (k18_euclid D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 A) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k2_topreal1 2 A 1)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) )  => (v2_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) A))) ) ) ) ) ).
tt(t29_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A))) = (k1_tarski (k13_pscomp_1 A))) ) ) ).
tt(t29_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v2_funct_1 B) &  ((v1_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) )  =>  (! [C:$i] :  ( ((v2_funct_1 C) &  ((v1_topreal1 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) )  =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r2_sprect_2 A B) &  ((r3_sprect_2 A C) & (r1_xboole_0 (k3_topreal1 2 B) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) &  ((v1_sprect_2 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ( ((r2_hidden A (k4_finseq_1 (k2_goboard2 B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) A (k1_matrix_1 (k2_goboard2 B))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k20_pscomp_1 (k3_topreal1 2 B))) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) (k2_nat_1 A 1) (k1_matrix_1 (k2_goboard2 B))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k7_nat_d (k3_finseq_1 B) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) A (k7_nat_d (k1_matrix_1 (k2_goboard2 B)) 1))) ) ) ) ) ) ) ).
tt(t29_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t29_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((k6_square_1 (k3_xcmplx_0 A B)) = (k3_xcmplx_0 (k6_square_1 A) (k6_square_1 B))) ) ) ) ) ) ).
tt(t29_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (r2_hidden (k13_stacks_1 A B) (k11_stacks_1 A B))) ) ) ) ).
tt(t29_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k3_stirl2_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t29_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) =>  ((v3_substut1 B A) =>  ((k10_sublemma A (k9_sublemma A B C)) = (k8_sublemma A B)) ) ) ) ) ) ) ) ).
tt(t29_subset_1,ax, (! [A:$i] :  ( (~  (A = k1_xboole_0) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~ (r2_hidden C B))  => (r2_hidden C (k3_subset_1 A B))) ) ) ) ) ) ) ).
tt(t29_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((k37_substut1 A (k20_substut1 A B)) = (k13_qc_lang1 A (k37_substut1 A B))) ) ) ) ) ).
tt(t29_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_substut2 F A D E) =>  (~  ((r1_xxreal_0 (k7_cqc_sim1 A E) B) &  ((r2_qc_lang2 A D E) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 F)) &  (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ( (G = (k1_funct_1 F C))  & (r1_xxreal_0 (k7_cqc_sim1 A G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski B k1_numbers) =>  ((v2_supinf_2 C A B) <=> (r2_hidden (k11_supinf_2 k7_numbers A B C) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t29_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B C E))  &  ( (~ (r1_orders_2 B F D))  &  ( (~ (r1_orders_2 B F E))  &  (~  ((k8_group_1 A (k1_symsp_1 A B D F C) (k1_symsp_1 A B C D E)) = (k8_group_1 A (k1_symsp_1 A B E F C) (k1_symsp_1 A B F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ( ( ((k3_relat_1 C C) = C)  &  ( ((k3_relat_1 C (k6_subset_1 C (k1_sysrel C))) = k1_xboole_0)  & (r2_hidden (k4_tarski A B) C)) )  =>  ( (A = B)  |  ((r2_hidden A (k6_subset_1 (k9_xtuple_0 C) (k9_xtuple_0 (k1_sysrel C)))) & (r2_hidden B (k9_xtuple_0 (k1_sysrel C)))) ) )  &  ( ( ((k3_relat_1 C C) = C)  &  ( ((k3_relat_1 (k6_subset_1 C (k1_sysrel C)) C) = k1_xboole_0)  & (r2_hidden (k4_tarski A B) C)) )  =>  ( (A = B)  |  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 C) (k9_xtuple_0 (k1_sysrel C)))) & (r2_hidden A (k9_xtuple_0 (k1_sysrel C)))) ) ) ) ) ) ) ) ).
tt(t29_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C))  =>  ( ((r1_relat_2 (k1_taxonom1 A B C) A) & (v4_metric_1 B A))  =>  (~ (v1_xboole_0 (k2_taxonom1 A B))) ) ) ) ) ) ) ) ).
tt(t29_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B A C))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ((r1_tarski (k1_rcomp_1 D E) C) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B C) A) (k1_rcomp_1 D E))) &  ((r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 D E)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden F (k2_rcomp_1 D E)) &  ((k1_seq_1 B D) = (k7_real_1 (k1_seq_1 (k3_series_1 (k6_taylor_1 B C E D)) A) (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 D E)) (k2_nat_1 A 1)) F) (k2_newton (k9_real_1 D E) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tops_1 B A) &  ((v6_tops_1 C A) & (v6_tops_1 D A)) )  =>  ((k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) C D)))))) = (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)) (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)))) ) ) ) ).
tt(t29_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A)) ) )  =>  ((k4_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k1_tops_1 A C)) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t29_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) &  ((v1_algstr_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r2_hidden (k11_pre_poly A (k3_termord A B C D) (k3_termord A B C E)) (k2_polynom1 (k15_pre_poly A) C (k9_polynom1 A C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k3_tex_1 A B) = (k1_compts_1 A))  <=>  (A = (k6_domain_1 A B)) ) ) ) ) ) ).
tt(t29_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_tex_2 B A)) ) ) ) ).
tt(t29_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v3_tex_3 B A) <=> (v2_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t29_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r1_xboole_0 (k2_tex_4 A C) (k3_tex_4 A B)))  & (r1_xboole_0 (k2_tex_4 A C) B)) ) ) ) ) ) ) ) ).
tt(t29_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ((m1_pre_topc B D) =>  ( (~ (r1_tsep_1 (k2_tsep_1 A D C) B))  &  (~ (r1_tsep_1 (k2_tsep_1 A C D) B)) ) )  &  ((m1_pre_topc C D) =>  ( (~ (r1_tsep_1 (k2_tsep_1 A B D) C))  &  (~ (r1_tsep_1 (k2_tsep_1 A D B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( (! [E:$i] :  ((r2_hidden E D) <=>  ((r2_hidden B E) & (m1_toler_1 E A C)) ) )  =>  ((k9_relat_1 C B) = (k3_tarski D)) ) ) ) ) ) ) ).
tt(t29_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A B D))  =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D B) =>  ((r3_borsuk_2 A D C (k1_borsuk_2 A D B C G E) (k1_borsuk_2 A D B C G F)) => (r3_borsuk_2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H A E F) =>  (! [I:$i] :  ((m1_borsuk_2 I B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) =>  (! [J:$i] :  ((m1_borsuk_2 J B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F)) =>  ( ((r1_borsuk_6 A D E) &  ((r1_borsuk_6 A E F) &  ((r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) I (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) G C)) & (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) J (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) H C))) ) )  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 B) (k1_borsuk_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C F) I J) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k1_borsuk_2 A D E F G H) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (v3_funct_2 (k11_topalg_4 A B C D) (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D)))))) ) ) ) ) ) ) ) ).
tt(t29_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  => (m1_borsuk_2 (k3_relat_1 (k1_borsuk_6 k6_numbers 1 (k2_xxreal_2 (k9_xtuple_0 B)) (k1_xxreal_2 (k9_xtuple_0 B))) B) A (k2_topalg_6 A B) (k3_topalg_6 A B))) ) ) ) ).
tt(t29_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B))))) =>  ( ((v2_topdim_1 D (k1_pre_topc A B)) &  (D = C) )  =>  ((v2_topdim_1 C A) &  ((k3_topdim_1 A C) = (k3_topdim_1 (k1_pre_topc A B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k4_subset_1 (u1_struct_0 A) B (k2_topgen_1 A B))) ) ) ) ) ).
tt(t29_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  (? [C:$i] :  ( ((v1_tops_2 C (k5_topgen_2 A B)) &  ((v1_cantor_1 C (k5_topgen_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))))) )  &  (C = (k2_xboole_0 (k7_subset_1 (k1_zfmisc_1 A) (k10_eqrel_1 A) (k1_tarski (k1_tarski B))) (a_1_1_topgen_2 A))) ) ) ) ) ).
tt(t29_topgen_3,ax, (k3_topgen_3 = (k3_card_2 2 k4_ordinal1)) ).
tt(t29_topgen_4,ax, (! [A:$i] :  ((k2_setfam_1 k1_xboole_0 A) = k1_xboole_0) ) ).
tt(t29_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ((r1_xxreal_0 C B) =>  ((v3_pre_topc (k1_topreal9 2 (k19_euclid A B) C) k3_topgen_5) & (m1_subset_1 (k1_topreal9 2 (k19_euclid A B) C) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ) ) ) ) ) ) ) ).
tt(t29_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_tops_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v3_tops_2 C A B) => (v1_tops_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t29_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v5_topreal1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~ (v3_tops_2 B k5_topmetr (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ).
tt(t29_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k17_euclid A) (k18_euclid B))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid A) (k18_euclid B)) B)) = (k1_tarski (k19_euclid (k17_euclid A) (k18_euclid B)))) ) ) ) ) ).
tt(t29_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v2_topreal4 C (k15_euclid 2)) &  ((r2_hidden A C) &  ((r2_hidden B C) &  ( (~  (A = B) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal4 D A B) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (A = B)  |  ( (A = C)  |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) |  ( (~ (r1_xxreal_0 (k17_euclid A) (k17_euclid B)))  &  (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 A 1)) |  ((k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) (k2_nat_1 (k3_finseq_1 B) A)) = (k2_topreal1 2 C (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ).
tt(t29_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k4_topreal9 A B B) = (k1_tarski B)) ) ) ) ) ).
tt(t29_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_funct_1 (k19_euclid A B) 1) = A)  &  ((k1_funct_1 (k19_euclid A B) 2) = B) ) ) ) ) ) ).
tt(t29_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) => (r1_borsuk_3 (k11_toprealb A) k1_borsuk_4)) ) ).
tt(t29_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((k31_valued_2 A C D B) = (k52_valued_2 A C D (k7_funcop_1 (k1_relset_1 A D) B))) ) ) ) ) ) ) ) ).
tt(t29_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C)) (k7_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t29_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A B) = (k2_tops_1 A (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t29_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (m1_subset_1 (k9_subset_1 (u1_struct_0 A) B C) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C))))) ) ) ) ) ) ).
tt(t29_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) => (v3_tops_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t29_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v2_transgeo B A) => (v2_transgeo (k2_funct_2 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t29_trees_1,ax, ((k2_trees_1 k6_numbers) = (k1_tarski k1_xboole_0)) ).
tt(t29_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_trees_2 C A))  &  ((k5_card_1 C) = B) ) ) ) )  &  ( (! [B:$i] :  ((m1_trees_1 B A) => (v1_finset_1 (k1_trees_2 A B))) )  &  (! [B:$i] :  ((m1_trees_2 B A) => (v1_finset_1 B)) ) ) ) ) ) ) ).
tt(t29_trees_3,ax, (! [A:$i] :  ((v5_trees_3 (k9_finseq_1 A)) <=>  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) ) ) ) ).
tt(t29_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_trees_3 E (k2_zfmisc_1 A B)))  =>  (! [F:$i] :  ((m2_finseq_1 F E) =>  (? [G:$i] :  ((m2_finseq_1 G (k4_trees_3 A)) &  ( ((k4_finseq_1 G) = (k4_finseq_1 F))  &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 F)) &  (! [I:$i] :  ((m1_subset_1 I E) =>  (~  ( (I = (k1_funct_1 F H))  &  ((k1_funct_1 G H) = (k8_trees_3 A B I)) ) ) ) ) ) ) ) )  &  ((k8_trees_3 A B (k4_trees_4 (k1_domain_1 A B C D) F)) = (k4_trees_4 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v5_trees_3 A)) ) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_trees_1 B (k11_trees_3 A)))  =>  ((k5_card_1 (k1_trees_2 (k11_trees_3 A) B)) = (k3_finseq_1 A)) ) ) ) ) ).
tt(t29_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  ( (~ (r1_tsep_1 B C))  =>  ((v1_borsuk_1 (k2_tsep_1 A B C) A) & (m1_pre_topc (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t29_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r3_tsep_2 A B C) <=>  ((r1_tsep_1 B C) &  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k1_tsep_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t29_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C)) = (k3_tex_4 A C)) ) ) ) ) ) ) ).
tt(t29_turing_1,ax,(r3_turing_1 k14_turing_1 k15_comput_1)).
tt(t29_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((r2_hidden A (k2_msafree2 (k34_twoscomp A B))) & (r2_hidden B (k2_msafree2 (k34_twoscomp A B)))) ) ) ) ) ).
tt(t29_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (C = B)  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 (u1_struct_0 (k1_uniroots A)) k5_numbers (u1_struct_0 (k1_uniroots A)) (k4_group_1 (k1_uniroots A)) B D) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  (C = (k9_polynom3 A)) )  &  ((k2_polynom5 A C B) = (k9_polynom3 A)) ) ) ) ) ) ) ) ) ).
tt(t29_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) => (r1_tarski (k1_urysohn1 A) (k1_urysohn1 B))) ) ) ) ) ).
tt(t29_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r1_valuat_1 A B (k11_cqc_lang A C E) F D) <=>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( (! [H:$i] :  ((m2_subset_1 H (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = H) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B G H) = (k3_funct_2 (k3_qc_lang1 A) B D H)) ) ) )  => (r1_valuat_1 A B E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((v1_partfun1 D A) => (r2_funct_2 k5_numbers B (k8_funct_2 k5_numbers B A (k1_valued_0 A C E) D) (k1_valued_0 B (k8_funct_2 k5_numbers B A C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  & (r2_hidden k6_numbers (k1_relset_1 k5_numbers (k61_valued_1 A B)))) ) ) ) ) ) ).
tt(t29_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k1_funct_1 (k14_valued_2 C B) A) = (k7_xcmplx_0 (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t29_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_vectsp_5 E A B (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) =>  ( (~  (C = (k4_struct_0 B)) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_vectsp10 A B C E) (k4_vectsp_1 A B D C)) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((v1_funct_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D)) &  ((v1_funct_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)))) &  ((v13_vectsp_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) &  ((v1_mod_2 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) B (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) & (m1_subset_1 (k8_matrlin2 B C C (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) (u1_struct_0 (k1_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k4_struct_0 A))  =>  ((k5_algstr_0 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t29_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v6_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_algstr_0 A (k5_struct_0 A)) B) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(t29_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t29_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) =>  ((k1_vectsp_5 A B D (k2_vectsp_5 A B C E)) = (k2_vectsp_5 A B (k1_vectsp_5 A B C D) (k1_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k1_vectsp_6 A B (k6_vectsp_6 A B C D)) = (k1_vectsp_6 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t29_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_vectsp_9 A B) = k6_numbers)  <=>  ((k2_vectsp_4 A B) = (k1_vectsp_4 A B)) ) ) ) ) ) ).
tt(t29_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k5_vfunct_1 B C D) A) (k5_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A))) & (r2_relset_1 B k1_numbers (k2_partfun1 B k1_numbers (k3_normsp_0 B C D) A) (k3_normsp_0 B C (k2_partfun1 B (u1_struct_0 C) D A)))) ) ) ) ) ) ) ) ).
tt(t29_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k5_vfunct_1 A B C) D) (k5_vfunct_1 A B (k2_partfun1 A (u1_struct_0 B) C D))) & (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k3_normsp_0 A B C) D) (k3_normsp_0 A B (k2_partfun1 A (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ).
tt(t29_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v13_waybel_0 B A) & (v13_waybel_0 C A))  =>  ((v13_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A) & (v13_waybel_0 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t29_waybel10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r5_waybel_1 (k7_waybel10 A) (k1_waybel10 (k4_waybel10 A) (k8_waybel10 A)))) ) ).
tt(t29_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k4_waybel11 A B) (k6_yellow_6 A))) ) ) ) ).
tt(t29_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r4_yellow_4 A C B) => (r4_yellow_4 A (k12_waybel_0 A C) (k12_waybel_0 A B))) ) ) ) ) ) ) ).
tt(t29_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_waybel_8 A D)) = (k2_waybel_8 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  (~  ( (C = B)  &  ((v1_waybel14 (k5_waybel_2 A) A) &  ((v5_waybel_6 C (k2_yellow_1 (k5_waybel11 A))) &  ( (~  (C = (u1_struct_0 A)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  (B = (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=> (v3_waybel_3 A)) ) ) ).
tt(t29_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_2 (k7_lattice3 A)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) =>  ( (~ (v1_xboole_0 (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A B))))  &  ((v2_waybel_0 (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) &  ((v13_waybel_0 (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) &  ((v1_waybel_6 (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) & (m1_subset_1 (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) => (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(t29_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v1_waybel19 B) & (m1_yellow_9 B A)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C A))  =>  (! [D:$i] :  ( ((v2_pre_topc D) & (m1_yellow_9 D A))  =>  ((v2_waybel19 D) <=> (m3_yellow_9 D C B)) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v8_waybel_1 B A) &  ((r1_yellow_0 A C) & (r1_tarski C (k2_relset_1 (u1_struct_0 A) B))) )  =>  ((k1_yellow_0 A C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_yellow_0 A C))) ) ) ) ) ) ) ) ).
tt(t29_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_yellow_0 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) )  => (v1_yellow_0 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t29_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v25_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v25_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k1_waybel11 B (k6_waybel_9 A B D (k3_yellow_9 A C))) = (k2_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t29_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_waybel_0 B A)) ) ) ) ).
tt(t29_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  =>  ((v1_funct_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C)) &  ((v1_funct_2 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) A B) & (m1_subset_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t29_waybel25,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  => (v1_waybel25 A)) ) ).
tt(t29_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) &  ((v4_waybel_3 C) & (v1_waybel18 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B C)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((k1_funct_1 (k10_funct_6 D) E) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B C)) (u1_struct_0 (k3_waybel18 B C)) (u1_struct_0 (k4_waybel18 B C E)) D (k6_waybel18 B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel27,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  => (r2_funct_2 (u1_struct_0 (k2_waybel27 A B)) (u1_struct_0 (k2_waybel27 A B)) (k4_waybel27 A A B B (k3_struct_0 A) (k3_struct_0 B)) (k3_struct_0 (k2_waybel27 A B)))) ) ) ) ).
tt(t29_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v13_waybel_0 B A) & (r2_hidden B (k4_waybel28 A)))  => (r2_hidden B (k5_waybel11 A))) ) ) ) ) ).
tt(t29_waybel29,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ((v23_waybel_0 D A C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((r1_funct_2 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 C) E D) & (v23_waybel_0 E B C))  =>  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ( (! [B:$i] :  ( ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k11_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B))) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_yellow_0 A B) =>  ((k11_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) (k11_waybel_0 A B)))) ) ) ) ) ) ) ) ) ).
tt(t29_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v4_waybel11 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski (k1_tops_1 A (k4_waybel_0 A B)) (k3_tarski (a_2_2_waybel30 A B)))) ) ) ) ).
tt(t29_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~ (v8_struct_0 A))  =>  ((k1_waybel31 A) = (k1_waybel31 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(t29_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_waybel32 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v10_waybel_0 B A) & (l1_waybel_0 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A C (k1_waybel11 A B)) <=> (r3_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(t29_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v17_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B)) &  ((v18_waybel_0 (k3_waybel_1 A A B) (k1_yellow_2 A A B) A) &  ((r2_funct_2 (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 A) (k1_waybel34 A (k1_yellow_2 A A B) (k2_waybel_1 A A B)) (k3_waybel_1 A A B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A A B)) (k2_waybel34 A (k1_yellow_2 A A B) (k3_waybel_1 A A B)) (k2_waybel_1 A A B))) ) ) ) ) ) ) ).
tt(t29_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v4_orders_2 (k3_waybel_3 A B C))) )  => (v4_orders_2 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t29_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) C D) => (r1_tarski (k5_waybel_4 A B C) (k5_waybel_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v17_waybel_0 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v11_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_yellow_0 A)) )  =>  ((v5_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A B C) =>  (C = (k4_yellow_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) &  ((v3_waybel_7 D (k3_yellow_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))))) ) ) )  =>  (~  ((r2_hidden B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r2_waybel_7 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_waybel_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  ((k2_waybel_8 (k3_yellow_1 A) B) = (a_2_1_waybel_8 A B)) ) ) ) ).
tt(t29_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k10_yellow_6 A B)) => (r3_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(t29_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_uniroots A))) =>  ( (C = B)  =>  ((u1_struct_0 (k5_weddwitt A B)) = (k2_xboole_0 (u1_struct_0 (k1_weddwitt (k1_uniroots A) C)) (k1_tarski (k4_struct_0 A)))) ) ) ) ) ) ) ) ).
tt(t29_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_pcomps_1 A))) =>  (~  ((r2_hidden D C) &  ((k3_funct_2 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) D) = (k3_weierstr (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k6_weierstr A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((v2_wellord1 C) &  ((r2_hidden A (k1_relat_1 C)) & (r2_hidden B (k1_relat_1 C))) )  =>  ((r2_hidden (k4_tarski A B) C) <=> (r1_tarski (k1_wellord1 C A) (k1_wellord1 C B))) ) ) ) ) ) ).
tt(t29_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A (k3_xcmplx_0 B C)) &  ((k3_int_2 A B) = 1) )  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(t29_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k3_xboole_0 A B) (k2_xboole_0 A C))) ) ) ).
tt(t29_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean (k3_xboolean A) (k7_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t29_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 (k2_xcmplx_0 A B) C) = (k2_xcmplx_0 (k6_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t29_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 B A) B)) ) ) ) ) ) ).
tt(t29_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k10_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t29_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 B (k4_xxreal_0 A C))) ) ) ) ) ) ) ) ) ).
tt(t29_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_xxreal_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t29_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_xxreal_2 (k1_xxreal_1 A B)) = B) ) ) ) ) ) ).
tt(t29_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (A = k1_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  (~  ((k1_xxreal_3 (k1_xxreal_3 A B) C) = (k1_xxreal_3 A (k1_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((k15_lattice3 A B) = (k1_yellow_0 (k3_lattice3 A) B))  &  ((k16_lattice3 A B) = (k2_yellow_0 (k3_lattice3 A) B)) ) ) ) ) ).
tt(t29_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v3_orders_2 B) & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((k4_yellow_3 A B (k3_waybel_0 (k3_yellow_3 A B) C)) = (k3_waybel_0 A (k4_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t29_yellow12,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_4 A B (k3_waybel_0 A C)) => (r1_tarski (k3_waybel_0 A B) (k3_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t29_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel18 A B))) =>  ((r2_hidden C (k2_pre_topc (k3_waybel18 A B) (k6_domain_1 (u1_struct_0 (k3_waybel18 A B)) D))) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_hidden (k5_waybel18 A B C E) (k2_pre_topc (k4_waybel18 A B E) (k6_domain_1 (u1_struct_0 (k4_waybel18 A B E)) (k5_waybel18 A B D E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow15,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  (~  ((r2_hidden D (k2_yellow15 (u1_struct_0 A) C)) &  ( (~ (r1_xboole_0 B D))  &  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r2_lattice3 (k5_yellow_1 A B) D C) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_lattice3 (k3_waybel_3 A B E) (k5_waybel_3 A B E D) (k4_waybel_3 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  ( ((r3_yellow18 A B) & (r3_yellow18 B C))  => (r1_yellow18 A C)) ) ) ) ) ) ) ).
tt(t29_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_9 A B C) <=>  (! [D:$i] :  ((m1_yellow19 D A B) => (r2_hidden C (k2_pre_topc A D))) ) ) ) ) ) ) ) ) ).
tt(t29_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ( ( (G = E)  &  (H = F) )  =>  ( ((k1_altcat_1 C G H) = k1_xboole_0)  |  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A E F)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 C G H)) =>  ( (J = I)  =>  ((k6_functor0 C B (k4_yellow20 A B C D) G H J) = (k6_functor0 A B D E F I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_orders_3 B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (a_2_1_yellow_2 A B))  =>  ((v3_orders_2 (k5_yellow_0 A C)) &  ((v4_orders_2 (k5_yellow_0 A C)) &  ((v5_orders_2 (k5_yellow_0 A C)) &  ((v1_lattice3 (k5_yellow_0 A C)) &  ((v2_lattice3 (k5_yellow_0 A C)) &  ((v3_lattice3 (k5_yellow_0 A C)) & (l1_orders_2 (k5_yellow_0 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r2_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) (k7_yellow_3 A B E F)) =>  ((r2_lattice3 A C E) & (r2_lattice3 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski B (k3_waybel_0 A (k2_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t29_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_yellow_5 A B D))  &  ((r1_orders_2 A C D) & (r1_yellow_5 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_yellow_6 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = C)  &  ((r2_hidden B D) & (v3_pre_topc D A)) ) ) ) ) ) ) ) ) ) ).
tt(t29_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v12_waybel_0 B (k7_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))))  <=>  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t29_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) A) &  ((v2_cantor_1 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) A) & (m1_subset_1 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t29_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)))  => (r2_tarski A (k4_zf_fund1 A))) ) ).
tt(t29_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v11_zf_lang A) =>  ( ((k23_zf_lang A) = (k23_zf_lang (k20_zf_lang A)))  &  ((k24_zf_lang A) = (k20_zf_lang (k24_zf_lang (k20_zf_lang A)))) ) ) ) ) ).
tt(t29_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (A = (k7_finseq_1 B C))  =>  (A = B) ) ) ) ) ) ) ) ).
tt(t29_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_zfmisc_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k4_tarski A B))) ) ) ).
tt(t29_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((r2_hidden k4_ordinal1 A) &  ((v2_ordinal2 C) &  ((v3_ordinal2 C) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  (~  ((r2_hidden B D) &  ( ((k4_ordinal4 A C D) = D)  & (r2_ordinal2 D k4_ordinal1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t29_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (E = B)  =>  ((k1_zmodul01 D E C) = (k1_zmodul01 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  (! [B:$i] :  ((l1_abcmiz_0 B) =>  ( ( ((u1_abcmiz_0 A) = (u1_abcmiz_0 B))  & (v4_abcmiz_0 A))  => (v4_abcmiz_0 B)) ) ) ) ) ).
tt(t2_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k3_card_3 B) = k1_xboole_0)  =>  ((k1_funct_1 B A) = k1_xboole_0) ) ) ) ) ).
tt(t2_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  ((k1_abcmiz_1 (k3_abcmiz_1 A)) = (k3_abcmiz_1 A)) ) ) ).
tt(t2_abian,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  ((r2_hidden k6_numbers A) =>  ((k6_seq_4 A) = k6_numbers) ) ) ) ).
tt(t2_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (A = k6_numbers)  <=>  ((k18_complex1 A) = k6_numbers) ) ) ) ).
tt(t2_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) & (r2_analoaf A B C B C)) ) ) ) ) ) ) ).
tt(t2_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) <=> (v5_aff_2 A)) ) ) ).
tt(t2_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v2_aff_3 A) => (v1_aff_3 A)) ) ) ).
tt(t2_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B D) =>  ( ( (~ (r2_aff_1 A B C D))  &  (~ (r2_aff_1 A C B D)) )  | (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_xboole_0 A (k1_tarski A)) = (k1_nat_1 A 1)) ) ) ).
tt(t2_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski A B)) ) ) ) ).
tt(t2_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  & (v1_aff_4 B A))  =>  (B = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t2_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_analoaf A B B B B)) ) ) ) ).
tt(t2_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((k4_finseqop (u1_struct_0 A) (u1_struct_0 B) (k6_finseq_1 (u1_struct_0 A)) C) = (k6_finseq_1 (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t2_algseq_1,ax, ( ((k7_card_1 k6_numbers) = k1_xboole_0)  &  ( ((k7_card_1 1) = (k1_tarski k6_numbers))  &  ((k7_card_1 2) = (k2_tarski k6_numbers 1)) ) ) ).
tt(t2_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A B) & (r1_tarski (k3_xboole_0 (k10_xtuple_0 C) (k9_xtuple_0 B)) (k9_xtuple_0 A)))  =>  ((k3_relat_1 C B) = (k3_relat_1 C A)) ) ) ) ) ) ) ) ).
tt(t2_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A C (k4_struct_0 A)) = C) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_algstr_0 A C D) = (k4_struct_0 A)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A C D) E) = (k1_algstr_0 A C (k1_algstr_0 A D E))) ) ) ) ) ) ) ) )  =>  ((k1_algstr_0 A (k4_struct_0 A) B) = (k1_algstr_0 A B (k4_struct_0 A))) ) ) ) ) ) ).
tt(t2_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k1_algstr_2 A C)) = (k1_algstr_2 A (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t2_algstr_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_algstr_3)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( (A = D)  &  ( (B = E)  &  (C = F) ) )  =>  ((k1_algstr_3 k3_algstr_3 A B C) = (k7_real_1 (k8_real_1 D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v1_algstr_4 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B C) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B D))  &  ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B F)) )  =>  ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k6_algstr_0 A C E)) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k6_algstr_0 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_altcat_1,ax, ((k1_funct_2 k1_xboole_0 k1_xboole_0) = (k1_tarski (k4_relat_1 k1_xboole_0))) ).
tt(t2_altcat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k2_funct_4 (k3_relat_1 A B)) = (k3_relat_1 (k2_funct_4 A) B)) ) ) ) ) ).
tt(t2_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v1_altcat_3 D A B C) &  ((v2_altcat_3 D A B C) &  (~  ( ((k5_altcat_1 A B C B D (k1_altcat_3 A B C D)) = (k8_altcat_1 A B))  &  ((k5_altcat_1 A C B C (k1_altcat_3 A B C D) D) = (k8_altcat_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D C)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D B)) =>  ( ( (F = (k5_altcat_1 A D B C G E))  &  ((k5_altcat_1 A B D B (k1_altcat_3 A D B G) G) = (k8_altcat_1 A B)) )  =>  ( ((k1_altcat_1 A D B) = k1_xboole_0)  |  ( ((k1_altcat_1 A B D) = k1_xboole_0)  |  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  (E = (k5_altcat_1 A B D C (k1_altcat_3 A D B G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k2_ami_3 A B) C) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 C)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k2_ami_3 A B) C) A) = (k1_funct_1 C B))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k2_ami_3 A B) C) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A C)) = k6_numbers)  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1))) = 1)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 k6_numbers)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 k6_numbers)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 1)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 2)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ami_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (~  (A = (k4_struct_0 k1_ami_3)) ) ) ) ).
tt(t2_ami_6,ax, ((k5_xtuple_0 (k2_compos_1 k1_ami_3)) = k1_xboole_0) ).
tt(t2_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 B)) =>  ((v2_extpro_1 D A B) =>  ((k1_amistd_1 A B C D) = (k6_domain_1 k5_numbers C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_amistd_1 A B D C) = (k1_tarski (k1_ordinal1 D))) ) )  => (v1_xboole_0 (k2_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(t2_amistd_3,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  ((k2_amistd_3 A B (k4_compos_1 B)) = (k8_funcop_1 k5_numbers k8_trees_1 k6_numbers)) ) ) ) ) ).
tt(t2_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_amistd_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k4_memstr_0 A B E)) =>  ((v4_amistd_1 C A B) =>  ( (E = (k4_struct_0 B))  |  ((k5_memstr_0 A B (k2_extpro_1 A B C (k1_amistd_4 A B D E F))) = (k5_memstr_0 A B (k1_amistd_4 A B (k2_extpro_1 A B C D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 (k4_amistd_1 A))) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A (k4_amistd_1 A))) & (v1_partfun1 C (u1_struct_0 (k4_amistd_1 A)))) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r8_pboole (u1_struct_0 (k4_amistd_1 A)) (k2_extpro_1 A (k4_amistd_1 A) B (k9_memstr_0 A (k4_amistd_1 A) C D)) (k9_memstr_0 A (k4_amistd_1 A) (k2_extpro_1 A (k4_amistd_1 A) B C) D))) ) ) ) ) ) ) ) ).
tt(t2_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ((v3_funct_2 C k5_numbers k5_numbers) &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) <=> (r1_ami_wstd A B (k3_funct_2 k5_numbers k5_numbers C E) (k3_funct_2 k5_numbers k5_numbers C F))) ) ) ) )  &  ((v3_funct_2 D k5_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) <=> (r1_ami_wstd A B (k3_funct_2 k5_numbers k5_numbers D E) (k3_funct_2 k5_numbers k5_numbers D F))) ) ) ) ) ) ) )  => (r2_funct_2 k5_numbers k5_numbers C D)) ) ) ) ) ) ) ) ) ).
tt(t2_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analmetr A B C B C)) ) ) ) ) ) ).
tt(t2_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A D E))  =>  ((k5_algstr_0 A B E) = (k5_algstr_0 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_analmetr A B C) =>  ((k1_analort A B C (k1_rlvect_1 A D E)) = (k1_rlvect_1 A (k1_analort A B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_anproj_1 A B C) & (r1_anproj_1 A C D))  => (r1_anproj_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t2_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v9_struct_0 B A))  &  ( (~ (v9_struct_0 C A))  &  ( (~ (r1_anproj_1 A B C))  &  ( (~ (v9_struct_0 D A))  &  ( (~ (v9_struct_0 E A))  &  ( (~ (r1_anproj_1 A D E))  &  ( (~ (r2_anproj_1 A B C D))  &  (~ (r2_anproj_1 A D E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k19_margrel1 (k1_aofa_000 A A (k4_finseq_2 C A) B)) = C) ) ) ) ) ) ) ).
tt(t2_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_aofa_i00 A B C)) <=>  (~  ((k1_funct_1 D B) = C) ) ) ) ) ) ) ) ) ).
tt(t2_arithm,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 A k6_numbers) = k6_numbers) ) ) ).
tt(t2_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_2 A) & (v8_relat_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_relat_1 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C B) =>  (~ (r2_waybel_4 B C A)) ) ) ) ) ) ) ) ) ).
tt(t2_arrow,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((r1_xxreal_0 3 (k5_card_1 A)) =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] :  ((m1_subset_1 D A) &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  ( (~  (A = k11_arytm_3) )  => (r2_hidden (k4_tarski k11_arytm_3 A) k1_numbers)) ) ) ).
tt(t2_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (~  ( ((k8_arytm_2 A B) = k11_arytm_3)  &  ( (~  (A = k11_arytm_3) )  &  (~  (B = k11_arytm_3) ) ) ) ) ) ) ) ) ).
tt(t2_arytm_2,ax,(r1_tarski k4_ordinal1 k2_arytm_2)).
tt(t2_arytm_3,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_arytm_3 1 A)) ) ).
tt(t2_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ( ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers)  |  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B A)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B A)) = (k2_real_1 (k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) ) ) ).
tt(t2_asympt_1,ax, (! [A:$i] :  ( ((v1_asympt_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_asympt_0 B) & (m1_subset_1 B k1_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B 1))  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 E k6_numbers))  =>  ((k1_seq_1 C E) = (k6_power A E)) ) ) )  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 E k6_numbers))  =>  ((k1_seq_1 D E) = (k6_power B E)) ) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) &  ((v4_asympt_0 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) &  ((v4_asympt_0 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers E C) &  ((r2_funct_2 k5_numbers k1_numbers F D) &  ((k6_asympt_0 E) = (k6_asympt_0 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r1_tarski (k1_autalg_1 A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(t2_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (r1_tarski (k1_autgroup A) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 A)))) ) ).
tt(t2_axioms,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r2_hidden A k5_numbers) & (r2_hidden B k5_numbers))  => (r2_hidden (k2_xcmplx_0 A B) k5_numbers)) ) ) ) ) ).
tt(t2_bagorder,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k2_finseq_1 A)) <=>  ((m2_subset_1 (k9_real_1 B 1) k1_numbers k5_numbers) &  (~ (r1_xxreal_0 A (k9_real_1 B 1))) ) ) ) ) ) ) ).
tt(t2_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k4_struct_0 A)) = B) ) ) ) ) ).
tt(t2_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_2 A B C 1) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ).
tt(t2_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) C) & (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) B)) ) ) ) ) ) ) ).
tt(t2_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k3_bcialg_4 A B C)) &  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k3_bcialg_4 A B C)) => (r1_bcialg_1 A E D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_bcialg_1 A B C) & (r1_bcialg_1 A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_bcialg_6 A (k23_binop_2 C 1) B) = (k1_bcialg_1 A B (k2_bcialg_1 A (k3_bcialg_6 A C B)))) ) ) ) ) ) ) ).
tt(t2_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A C D)) (k1_bcialg_1 A B (k1_bcialg_1 A C E))) (k1_bcialg_1 A D E))) ) ) ) ) ) ) ) ) ) ).
tt(t2_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_bhsp_1 A B (k3_rlvect_1 A C D)) = (k7_real_1 (k2_bhsp_1 A B C) (k2_bhsp_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t2_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r1_xxreal_0 D E) &  (~  ((k1_normsp_1 A C E) = (k1_normsp_1 A B E)) ) ) ) ) ) )  | (v1_bhsp_2 C A)) ) ) ) ) ) ) ) ).
tt(t2_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k3_bhsp_1 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) (k1_bhsp_4 A (k3_normsp_1 A B C)))) ) ) ) ) ) ).
tt(t2_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (m1_bhsp_5 k1_xboole_0 A)) ) ).
tt(t2_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (D = (k4_subset_1 (u1_struct_0 A) B C))  =>  ((k1_bhsp_6 A D) = (k3_rlvect_1 A (k1_bhsp_6 A B) (k1_bhsp_6 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bhsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_bhsp_5 B A))  =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((r1_tarski B (k9_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) = D) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski B (k9_xtuple_0 D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E B) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers D E) = (k2_bhsp_1 A E E)) ) ) ) )  =>  ((k2_bhsp_1 A (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) B C) (k5_bhsp_5 (u1_struct_0 A) (u1_struct_0 A) (u1_algstr_0 A) B C)) = (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k2_bilinear A B C (k2_bilinear A B C D E) F) (k2_bilinear A B C D (k2_bilinear A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_binari_2,ax, (! [A:$i] :  ( ((v3_card_1 A 2) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k9_binarith 1 1 k6_margrel1 (k10_binarith k6_margrel1 k8_margrel1) (k10_binarith k6_margrel1 k7_margrel1)))  =>  ((k3_binari_2 2 A) = 1) ) ) ) ).
tt(t2_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ((k6_binarith A B) = (k6_binarith A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 A (k5_series_1 2 A))) ) ).
tt(t2_binarith,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D B))  =>  ((k7_partfun1 B (k8_finseq_1 B D (k12_finseq_1 B C)) (k1_nat_1 A 1)) = C) ) ) ) ) ) ) ) ) ).
tt(t2_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_algstr_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t2_binop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A B) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  ((k1_binop_1 D F G) = (k1_binop_1 E F G)) ) ) ) )  => (r2_funct_2 (k2_zfmisc_1 A B) C D E)) ) ) ) ) ) ) ) ).
tt(t2_binop_2,ax, ((k4_binop_1 k1_numbers k33_binop_2) = k6_numbers) ).
tt(t2_bintree1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((k14_trees_3 (k10_finseq_1 B C)) = (k4_pre_poly A (k1_bintree1 A B) (k1_bintree1 A C))) ) ) ) ) ) ) ).
tt(t2_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) => (m2_finseq_1 B k6_margrel1)) ) ) ) ).
tt(t2_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_lattices A (k4_lattices A B C) (k3_lattices A B D))) ) ) ) ) ) ) ) ).
tt(t2_boole,ax, (! [A:$i] :  ((k3_xboole_0 A k1_xboole_0) = k1_xboole_0) ) ).
tt(t2_boolmark,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_xboole_0 (k7_relat_1 E C) (k7_relat_1 E D)) => (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bor_cant,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r1_xxreal_0 (k7_real_1 1 A) (k3_funct_2 k1_numbers k1_numbers k24_sin_cos A))) ) ).
tt(t2_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (r1_tarski (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_tops_1 B D)) (k1_tops_1 A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ).
tt(t2_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) => (v1_t_0topsp (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t2_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_funct_1 (k6_struct_0 B A C)) &  ((v1_funct_2 (k6_struct_0 B A C) (u1_struct_0 B) (u1_struct_0 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) &  ((v5_pre_topc (k6_struct_0 B A C) B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) & (m1_subset_1 (k6_struct_0 B A C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C))))))) ) ) ) ) ) ) ) ) ).
tt(t2_borsuk_4,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  (~  (! [C:$i] :  ((m1_subset_1 C A) =>  (C = B) ) ) ) ) ) ) ).
tt(t2_borsuk_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k4_enumset1 A B C D E F) = (k2_xboole_0 (k1_enumset1 A C F) (k1_enumset1 B D E))) ) ) ) ) ) ) ).
tt(t2_borsuk_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A C) & (r1_xxreal_0 C B))  => (r2_hidden (k7_xcmplx_0 (k6_xcmplx_0 C A) (k6_xcmplx_0 B A)) (u1_struct_0 (k4_topmetr k6_numbers 1)))) ) ) ) ) ) ) ).
tt(t2_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_int_1 B) (k4_int_1 A)) =>  ((k4_int_1 (k6_xcmplx_0 A B)) = (k9_real_1 (k4_int_1 A) (k4_int_1 B))) ) ) ) ) ) ).
tt(t2_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden B (k4_topreal9 A C D)) &  ((r2_hidden E (k4_topreal9 A C D)) &  ((k12_euclid (k5_algstr_0 (k15_euclid A) B C)) = (k12_euclid (k5_algstr_0 (k15_euclid A) E C))) ) )  =>  (B = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_brouwer,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k2_topreal9 A B k6_numbers) = (k1_tarski B)) ) ) ) ) ).
tt(t2_bspace,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_struct_0 A (k1_funct_1 B C))) ) )  => (m2_finseq_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(t2_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) (k2_bvfunc_1 A C (k1_bvfunc_1 A D))) (k2_bvfunc_1 A D (k1_bvfunc_1 A B))) (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A C (k1_bvfunc_1 A B)) (k2_bvfunc_1 A D (k1_bvfunc_1 A C))) (k2_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t2_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r1_tarski (k15_bvfunc_1 A B C) (k15_bvfunc_1 A B (k3_partit1 A C D)))) ) ) ) ) ) ) ) ).
tt(t2_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ( (B = (k2_tarski C D))  =>  ( (C = D)  |  ((k2_bvfunc_2 A B) = (k2_partit1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k12_bvfunc_1 A)) (k11_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k11_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ) ).
tt(t2_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k9_bvfunc_1 A C B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t2_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B C) (k1_bvfunc_1 A (k5_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t2_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden C D) & (r1_bvfunc_2 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E)) (k2_bvfunc_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t2_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A B C) D) => (r1_bvfunc_1 A B (k9_bvfunc_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t2_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k12_bvfunc_1 A) B) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t2_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A C B) (k10_bvfunc_1 A B C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t2_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B (k1_bvfunc_1 A C))) (k1_bvfunc_1 A B))) ) ) ) ) ) ).
tt(t2_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k5_bvfunc_1 A (k5_bvfunc_1 A C D) E)) (k5_bvfunc_1 A (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k9_bvfunc_1 A B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t2_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A B (k9_bvfunc_1 A B C)) C)) ) ) ) ) ) ).
tt(t2_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_c0sp1 B A) & (v3_c0sp1 B A))  =>  ((v1_xboole_0 B) |  ( (~ (v2_struct_0 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))))  &  ((v13_algstr_0 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v2_rlvect_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v3_rlvect_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v4_rlvect_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v3_group_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v4_vectsp_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) &  ((v5_vectsp_1 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B))) & (l6_algstr_0 (g6_algstr_0 B (k1_c0sp1 A B) (k2_c0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m2_c0sp1 (k3_c0sp2 A) (k12_funcsdom (u1_struct_0 A)))) ) ).
tt(t2_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ( ((k2_nat_1 (k3_finseq_1 (k1_calcul_1 (k3_cqc_lang A) B)) 1) = (k3_finseq_1 B))  &  (~ (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 (k1_calcul_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ).
tt(t2_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_calcul_2 A k6_numbers) = k1_xboole_0) ) ) ).
tt(t2_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_tops_2 (u1_pre_topc A) A) &  ((v1_cantor_1 (u1_pre_topc A) A) & (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(t2_card_1,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ( (A = B)  <=> (r2_wellord2 A B)) ) ) ) ) ).
tt(t2_card_2,ax, (! [A:$i] :  ((r2_wellord2 (k1_zfmisc_1 A) (k1_zfmisc_1 (k1_card_1 A))) &  ((k1_card_1 (k1_zfmisc_1 A)) = (k1_card_1 (k1_zfmisc_1 (k1_card_1 A)))) ) ) ).
tt(t2_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((k1_card_3 (k7_funcop_1 A B)) = (k7_funcop_1 A (k1_card_1 B))) ) ) ).
tt(t2_card_4,ax,(v4_card_3 k4_ordinal1)).
tt(t2_card_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k3_card_3 B)) <=>  (? [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) & (r2_hidden A (k1_funct_1 B C))) ) ) ) ) ) ).
tt(t2_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ( (~ (v1_xboole_0 (k1_tarski A)))  & (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 (k1_zfmisc_1 A))))  &  ( (~ (r2_hidden k1_xboole_0 (k1_tarski A)))  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ( ((r2_hidden B (k1_tarski A)) & (r2_hidden C (k1_tarski A)))  => (r2_hidden (k9_subset_1 A B C) (k1_tarski A)))  &  ( ((r2_hidden B (k1_tarski A)) & (r1_tarski B C))  => (r2_hidden C (k1_tarski A))) ) ) ) ) ) ) ) ) ) ).
tt(t2_cardfin2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 1 (k25_sin_cos A))) ) ) ) ).
tt(t2_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  (! [D:$i] :  (~  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  ( (~ (r2_hidden C A))  &  (~  ((k5_card_1 (k1_funct_2 A B)) = (k1_card_1 (a_4_0_card_fin A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_tarski B (k3_ordinal2 B))) ) ) ) ).
tt(t2_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (~  ((k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t2_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((r2_hidden B A) =>  ((k7_partfun1 C (k8_funcop_1 C A D) B) = D) ) ) ) ) ) ) ) ).
tt(t2_cat_4,ax, (! [A:$i] :  (! [B:$i] :  ((g1_cat_1 (u1_struct_0 (k5_cat_4 A B)) (u4_struct_0 (k5_cat_4 A B)) (u1_graph_1 (k5_cat_4 A B)) (u2_graph_1 (k5_cat_4 A B)) (u1_cat_1 (k5_cat_4 A B))) = (k3_cat_1 A B)) ) ) ).
tt(t2_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_5 A) & (l1_cat_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_graph_1 A B) = (k13_mcart_1 B))  &  ( ((k4_graph_1 A B) = (k14_mcart_1 B))  &  (B = (k4_tarski (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k3_graph_1 A B) (k4_graph_1 A B)) (k2_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t2_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 (k7_nat_d A 1) (k7_nat_d (k4_nat_1 2 A) 2))) ) ) ).
tt(t2_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((v1_catalan2 B) => (r1_xxreal_0 (k24_binop_2 2 (k7_afinsq_2 (k5_relat_1 B A))) A)) ) ) ) ) ).
tt(t2_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_pboole A (k3_funct_6 (k1_catalg_1 A B D)) C) =>  ((k1_catalg_1 A B (k3_relat_1 D E)) = (k8_pboole (k1_catalg_1 A B D) (k1_catalg_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_cayley,ax, (! [A:$i] : (r1_tarski (k1_cayley A) (k1_funct_2 A A))) ).
tt(t2_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_c0sp1 B A) &  ((v1_cc0sp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_cc0sp1 (g1_cfuncdom B (k2_c0sp1 A B) (k1_c0sp1 A B) (k1_cc0sp1 A B) (k4_c0sp1 A B) (k3_c0sp1 A B)) A)) ) ) ) ).
tt(t2_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ((v1_cc0sp2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k2_numbers)) =>  ((v6_cfdiff_1 C) => (v3_pre_topc (k8_relset_1 (u1_struct_0 A) k2_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t2_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r2_relset_1 k5_numbers k2_numbers (k9_comseq_3 C (k2_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k2_valued_1 k5_numbers k2_numbers k2_numbers (k9_comseq_3 C A) (k9_comseq_3 C B))) &  ((r2_relset_1 k5_numbers k2_numbers (k9_comseq_3 C (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k9_comseq_3 C A) (k9_comseq_3 C B))) & (r2_relset_1 k5_numbers k2_numbers (k9_comseq_3 C (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k19_valued_1 k5_numbers k2_numbers k2_numbers (k9_comseq_3 C A) (k9_comseq_3 C B)))) ) ) ) ) ) ) ) ).
tt(t2_cfdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v2_comseq_2 (k1_cfdiff_1 A))) ) ) ).
tt(t2_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid 2)) =>  ( ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden (k3_binop_2 H (k5_binop_2 I k7_complex1)) (k1_relset_1 k2_numbers A)) =>  ((r2_hidden (k10_finseq_1 H I) (k1_relset_1 (k1_euclid 2) B)) &  ((k1_seq_1 B (k10_finseq_1 H I)) = (k1_seq_1 (k5_comseq_3 k2_numbers A) (k3_binop_2 H (k5_binop_2 I k7_complex1)))) ) ) ) ) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ((r2_hidden (k3_binop_2 H (k5_binop_2 I k7_complex1)) (k1_relset_1 k2_numbers A)) =>  ((r2_hidden (k10_finseq_1 H I) (k1_relset_1 (k1_euclid 2) C)) &  ((k1_seq_1 C (k10_finseq_1 H I)) = (k1_seq_1 (k6_comseq_3 k2_numbers A) (k3_binop_2 H (k5_binop_2 I k7_complex1)))) ) ) ) ) ) )  &  ( (D = (k3_binop_2 E (k5_binop_2 F k7_complex1)))  &  ( (G = (k10_finseq_1 E F))  & (r1_cfdiff_1 A D)) ) ) )  =>  ((r3_pdiff_1 2 1 B G) &  ((r3_pdiff_1 2 2 B G) &  ((r3_pdiff_1 2 1 C G) &  ((r3_pdiff_1 2 2 C G) &  ( ((k3_complex1 (k2_cfdiff_1 A D)) = (k11_pdiff_1 2 1 B G))  &  ( ((k3_complex1 (k2_cfdiff_1 A D)) = (k11_pdiff_1 2 2 C G))  &  ( ((k4_complex1 (k2_cfdiff_1 A D)) = (k1_real_1 (k11_pdiff_1 2 2 B G)))  &  ((k4_complex1 (k2_cfdiff_1 A D)) = (k11_pdiff_1 2 1 C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k2_numbers (k9_funct_2 A k2_numbers)) =>  ((r2_funct_2 A k2_numbers B (k1_funcsdom A k2_numbers (k2_cfuncdom A) C D)) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers B E) = (k9_complex1 (k3_funct_2 A k2_numbers C E) (k3_funct_2 A k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k1_relset_1 A (k46_valued_1 A k2_numbers k2_numbers B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k46_valued_1 A k2_numbers k2_numbers B C))) =>  ((k7_partfun1 k2_numbers (k46_valued_1 A k2_numbers k2_numbers B C) D) = (k11_complex1 (k7_partfun1 k2_numbers B D) (k7_partfun1 k2_numbers C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_cgames_1,ax, ((k2_cgames_1 k1_xboole_0) = (k1_tarski k1_cgames_1)) ).
tt(t2_chain_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t2_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_abian A)) )  =>  ((v7_ordinal1 (k6_xcmplx_0 A 1)) & (r1_xxreal_0 1 A)) ) ) ).
tt(t2_circcmb2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 B A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 B A) A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb D C) (k7_circcomb B A D C)))) => (v1_circuit2 (k6_circuit2 (k5_circcomb D C) (k7_circcomb B A D C) E) (k5_circcomb D C) (k7_circcomb B A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circcmb3 C A B) => (r8_pboole (u1_struct_0 A) (k1_circcmb3 A B C) (k5_facirc_1 A B C (k2_circcmb3 A B C)))) ) ) ) ) ) ) ).
tt(t2_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k1_funct_1 (k6_finseq_2 A (k7_funcop_1 A B)) C) = (k4_finseq_2 (k3_finseq_1 C) B)) ) ) ) ) ) ).
tt(t2_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v3_rltopsp1 B A) => (v3_rltopsp1 (k1_convex1 A B C) A)) ) ) ) ) ) ) ).
tt(t2_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((v11_struct_0 (k1_circtrm1 A B C)) <=>  (! [D:$i] :  ((m2_subset_1 D (k1_msaterm A B) C) =>  ((v1_zfmisc_1 D) &  (~ (r2_hidden (k1_funct_1 D k1_xboole_0) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_pboole C (k2_msafree2 A) (k7_funcop_1 (k2_msafree2 A) k5_numbers) (k5_relat_1 (u3_msualg_1 A B) (k2_msafree2 A))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((v1_msafree2 A) => (m1_msafree2 (k1_funct_1 (k10_funct_6 C) D) A B)) ) ) ) ) ) ) ) ) ).
tt(t2_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D)) =>  (! [F:$i] :  ( ((r2_hidden D (k7_subset_1 (u1_struct_0 A) (k3_msafree2 A) (k1_msafree2 A))) &  (E = (k1_trees_4 (k4_tarski F D))) )  =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B C) D) E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_classes1,ax, (! [A:$i] : (r2_hidden A (k1_classes1 A))) ).
tt(t2_classes2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v2_classes1 A) &  ((r2_hidden B A) & (r2_hidden C A)) )  =>  ((r2_hidden (k1_tarski B) A) & (r2_hidden (k2_tarski B C) A)) ) ) ) ) ).
tt(t2_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (C = (k1_funct_1 (k2_clopban1 A B) (k4_tarski E D)))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A (u1_struct_0 B) C F) = (k1_clvect_1 B (k3_funct_2 A (u1_struct_0 B) D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_clopban1 D A B) &  ((v2_clopban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_clopban1 E B C) &  ((v2_clopban1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  ( ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 C)) &  ((v13_vectsp_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v1_clopban1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v2_clopban1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_xxreal_0 (k1_normsp_0 C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) F)) (k4_real_1 (k3_xcmplx_0 (k1_funct_1 (k13_clopban1 B C) E) (k1_funct_1 (k13_clopban1 A B) D)) (k1_normsp_0 A F))) & (r1_xxreal_0 (k1_funct_1 (k13_clopban1 A C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) (k3_xcmplx_0 (k1_funct_1 (k13_clopban1 B C) E) (k1_funct_1 (k13_clopban1 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k4_normsp_0 A B) C))) ) ) ) ) ) ).
tt(t2_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A B D) = C) ) )  =>  ((k7_clvect_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t2_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ( (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (r1_pboole A C B)) )  => (v2_relat_1 B)) ) ) ) ).
tt(t2_closure2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A B) => (r1_tarski (k10_xtuple_0 C) (k3_tarski (k10_xtuple_0 (k5_mssubfam A B))))) ) ) ) ) ) ).
tt(t2_closure3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) =>  ((r2_hidden C D) => (r2_pboole A (k4_mssubfam A B (k5_closure2 A B D)) C)) ) ) ) ) ) ) ) ).
tt(t2_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (~  ( ((k1_clvect_1 A B C) = (k4_struct_0 A))  &  ( (~  (C = k6_numbers) )  &  (~  (B = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  (~  ((k1_normsp_1 A C E) = (k1_normsp_1 A B E)) ) ) ) ) ) )  | (v1_clvect_2 C A)) ) ) ) ) ) ) ) ).
tt(t2_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k3_normsp_1 A (k1_bhsp_4 A B) (k1_bhsp_4 A C)) = (k1_bhsp_4 A (k3_normsp_1 A B C))) ) ) ) ) ) ) ).
tt(t2_cohsp_1,ax, (! [A:$i] :  ((k3_tarski (k1_cohsp_1 A)) = A) ) ).
tt(t2_coh_sp,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k9_setfam_1 A)))  &  ((v1_classes1 (k9_setfam_1 A)) & (v1_coh_sp (k9_setfam_1 A))) ) ) ).
tt(t2_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) )  => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ).
tt(t2_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ( ( ((k1_card_1 C) = (k2_nat_1 A B))  &  ((k1_card_1 D) = (k2_nat_1 A B)) )  =>  ( ((k1_card_1 (k3_xboole_0 C D)) = A)  <=>  ((k1_card_1 (k2_xboole_0 C D)) = (k2_nat_1 A (k4_nat_1 2 B))) ) ) ) ) ) ) ) ) ).
tt(t2_commacat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))) (k2_commacat A B C D E)) =>  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  (? [I:$i] :  ((m1_subset_1 I (u4_struct_0 C)) & (r2_hidden I (k2_cat_1 C (k8_cat_1 A C D G) (k8_cat_1 B C E H)))) ) ) ) ) )  =>  ( (F = (k1_domain_1 (k2_zfmisc_1 (k1_commacat A B C D E) (k1_commacat A B C D E)) (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B)) (k1_domain_1 (k1_commacat A B C D E) (k1_commacat A B C D E) (k3_commacat A B C D E F) (k4_commacat A B C D E F)) (k1_domain_1 (u4_struct_0 A) (u4_struct_0 B) (k16_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F) (k17_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F))))  &  ( ((k3_graph_1 A (k16_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)) = (k14_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k3_commacat A B C D E F)))  &  ( ((k4_graph_1 A (k16_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)) = (k14_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k4_commacat A B C D E F)))  &  ( ((k3_graph_1 B (k17_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)) = (k15_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k3_commacat A B C D E F)))  &  ( ((k4_graph_1 B (k17_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)) = (k15_domain_1 (u1_struct_0 A) (u1_struct_0 B) (u4_struct_0 C) (k4_commacat A B C D E F)))  &  ((k1_cat_1 C (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) D (k16_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)) (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) (k4_commacat A B C D E F))) = (k1_cat_1 C (k3_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C) (k3_commacat A B C D E F)) (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) E (k17_domain_1 (k8_mcart_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u4_struct_0 C)) (k1_commacat A B C D E) (k1_commacat A B C D E)) (u4_struct_0 A) (u4_struct_0 B) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k2_struct_0 A) (k2_struct_0 B)) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_yellow_9 B A) C) = C) ) ) ) ) ) ) ) ).
tt(t2_complex1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A 2 k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 2 k1_numbers)))) )  =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) & (r1_funct_2 2 k1_numbers (k2_tarski k6_numbers 1) k1_numbers A (k5_funct_4 k1_numbers k6_numbers 1 B C))) ) ) ) ) ) ).
tt(t2_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 A B) |  ((r1_xxreal_0 A C) |  (! [D:$i] :  ((v1_int_1 D) =>  ( (B = (k2_xcmplx_0 C (k3_xcmplx_0 A D)))  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (A = B)  =>  ((k4_algstr_0 k1_complfld A) = (k1_binop_2 B)) ) ) ) ) ) ).
tt(t2_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((u1_struct_0 (k1_complsp1 A)) = (k14_seq_4 A)) ) ) ).
tt(t2_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ((r2_hidden A (k4_finseq_1 (k10_seq_4 B C))) =>  ((k9_matrix_5 (k10_seq_4 B C) A) = (k4_binop_2 (k9_matrix_5 B A) (k9_matrix_5 C A))) ) ) ) ) ) ) ) ).
tt(t2_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  =>  ((v2_prob_1 B) =>  ((v1_seq_2 (k1_compl_sp A B)) & (v8_valued_0 (k1_compl_sp A B))) ) ) ) ) ) ).
tt(t2_compos_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_compos_1)) =>  ((k2_compos_0 (u1_compos_1 k1_compos_1) A) = k6_numbers) ) ) ).
tt(t2_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k8_compos_1 A (k2_compos_2 A C B) D) = (k8_compos_1 A C (k1_compos_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t2_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r1_xxreal_0 (k1_real_1 (k17_complex1 A)) (k4_complex1 A))) ) ).
tt(t2_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (k2_struct_0 B)) =>  ((v2_compts_1 C A) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = C)  => (v2_compts_1 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_comput_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((k2_funct_7 E A B) = (k2_funct_7 F A C))  =>  ((k2_funct_7 E A D) = (k2_funct_7 F A D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_comseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (m1_subset_1 (k1_funct_1 A B) k2_numbers)) ) ) ) ) ) ).
tt(t2_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D B) & (r1_xxreal_0 C (k17_complex1 (k8_nat_1 k2_numbers A D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = k6_numbers) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B) = k6_numbers) ) ) ) ) ) ).
tt(t2_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v4_conaffm A) => (v2_conaffm A)) ) ) ).
tt(t2_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k1_funct_1 (k2_conlat_1 A) (k1_tarski B)) = (a_2_3_conlat_1 A B)) ) ) ) ) ).
tt(t2_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) (k5_setfam_1 (u1_struct_0 A) B)) = (k1_setfam_1 (a_2_0_conlat_2 A B))) ) ) ) ) ).
tt(t2_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v3_conmetr1 A) <=>  ((v1_conmetr1 A) & (v2_conmetr1 A)) ) ) ) ).
tt(t2_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r5_analmetr A B C D) &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_connsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) &  ((v4_pre_topc C A) & (r1_xboole_0 B C)) )  => (r1_connsp_1 A B C)) ) ) ) ) ) ) ).
tt(t2_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((m1_connsp_2 C A B) & (m1_connsp_2 D A B))  <=> (m1_connsp_2 (k9_subset_1 (u1_struct_0 A) C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t2_connsp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_connsp_1 C A) & (r1_tarski B C)) ) ) )  =>  ((k1_connsp_3 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t2_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_convex1 B A) & (v1_convex1 C A))  => (v1_convex1 (k7_rusub_4 A B C) A)) ) ) ) ) ) ) ).
tt(t2_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (B = (a_3_0_convex2 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t2_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ((v2_convex1 D A) & (m1_rlvect_2 D A))  =>  (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski (k7_domain_1 (u1_struct_0 A) B C) E) &  (~  ((v2_convex1 D A) & (m2_rlvect_2 D A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers (k2_convex4 A) B) = k5_complex1) ) ) ) ) ).
tt(t2_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rlvect_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_convfun1 A B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k3_convfun1 A B))) =>  ( ( (G = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) C E))  &  (H = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) D F)) )  =>  ((k1_algstr_0 (k3_convfun1 A B) G H) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k1_algstr_0 A C D) (k1_algstr_0 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  ((v1_funct_1 (k16_funcop_1 C B)) & (m1_subset_1 (k16_funcop_1 C B) (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A))))) ) ) ) ) ) ) ).
tt(t2_cqc_sim1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  => (r1_tarski (k7_relat_1 (k1_funct_4 E (k7_funcop_1 B D)) A) (k2_xboole_0 (k7_relat_1 E A) (k1_tarski D)))) ) ) ) ) ) ).
tt(t2_cqc_the1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_finset_1 (a_1_1_cqc_the1 A))) ) ).
tt(t2_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A C B) D) A)) ) ) ) ) ) ) ) ) ).
tt(t2_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r1_tarski B (k1_cqc_the1 A C)) => (r1_tarski (k1_cqc_the1 A B) (k1_cqc_the1 A C))) ) ) ) ) ) ) ).
tt(t2_csspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k18_csspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k18_csspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k18_csspace)) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( ((k12_csspace k18_csspace A A) = k6_numbers)  =>  (A = (k4_struct_0 k18_csspace)) )  &  ( ( (A = (k4_struct_0 k18_csspace))  =>  ((k12_csspace k18_csspace A A) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k3_complex1 (k12_csspace k18_csspace A A))) &  ( ((k4_complex1 (k12_csspace k18_csspace A A)) = k6_numbers)  &  ( ((k12_csspace k18_csspace A B) = (k15_complex1 (k12_csspace k18_csspace B A)))  &  ( ((k12_csspace k18_csspace (k1_algstr_0 k18_csspace A B) C) = (k2_xcmplx_0 (k12_csspace k18_csspace A C) (k12_csspace k18_csspace B C)))  &  ((k12_csspace k18_csspace (k1_clvect_1 k18_csspace A D) B) = (k3_xcmplx_0 D (k12_csspace k18_csspace A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_csspace3,ax, (! [A:$i] :  ((l2_clvect_1 A) =>  ( ( (~ (v2_struct_0 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))))  &  ((v13_algstr_0 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v2_rlvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v3_rlvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v4_rlvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v2_clvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v3_clvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v4_clvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) &  ((v5_clvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A))) & (l1_clvect_1 (g1_clvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_clvect_1 A)))) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_csspace4,ax, ( ((u1_struct_0 k3_csspace4) = k1_csspace4)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  & (v1_comseq_2 (k2_csspace A))) ) )  &  ( ((k4_struct_0 k3_csspace4) = k6_csspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  (A = (k2_csspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_csspace4)) =>  ((k1_algstr_0 k3_csspace4 A B) = (k2_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) )  &  ( (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_csspace4)) =>  ((k1_clvect_1 k3_csspace4 B A) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace B) A)) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  ( ((k4_algstr_0 k3_csspace4 A) = (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))  & (r2_funct_2 k5_numbers k2_numbers (k2_csspace (k4_algstr_0 k3_csspace4 A)) (k31_valued_1 k5_numbers k2_numbers (k2_csspace A)))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_csspace4)) =>  ((k5_algstr_0 k3_csspace4 A B) = (k46_valued_1 k5_numbers k2_numbers k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) => (v1_comseq_2 (k2_csspace A))) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  ((k1_normsp_0 k3_csspace4 A) = (k4_seq_4 (k2_relset_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers (k2_csspace A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  ((k1_algstr_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) A B) = (k1_series_1 k2_numbers (k2_csspace A) (k2_csspace B))) ) ) ) ) ).
tt(t2_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_decomp_1 B A) <=>  (B = (k3_decomp_1 A B)) ) ) ) ) ) ).
tt(t2_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 C A)) =>  ( ((r1_xxreal_0 B C) &  (D = (k6_xcmplx_0 C B)) )  => (m2_finseq_2 (k3_descip_1 A B E) A (k4_finseq_2 D A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_dickson,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_ordinal1 A (k1_nat_1 A 1))) ) ).
tt(t2_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 B A) C)) &  ((v1_funct_2 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 B A) C) k1_numbers k1_numbers) & (m1_subset_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 B A) C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t2_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k10_diff_1 C B (k7_real_1 B A) (k7_real_1 B (k8_real_1 2 A))) = (k6_real_1 (k1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) 2) B) (k8_real_1 2 (k5_square_1 A)))) ) ) ) ) ) ) ) ).
tt(t2_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k3_diff_1 C (k1_real_1 (k10_real_1 A 2))) B) = (k1_real_1 (k1_seq_1 (k4_diff_1 C (k10_real_1 A 2)) B))) ) ) ) ) ) ) ).
tt(t2_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k7_real_1 (k6_power k8_power A) (k6_power k8_power B)) = (k6_power k8_power (k8_real_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t2_dilworth,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) => (m1_subset_1 (k2_xboole_0 C D) (k1_zfmisc_1 (k1_zfmisc_1 (k2_xboole_0 A B))))) ) ) ) ) ) ).
tt(t2_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) =>  ((r2_analoaf A C B E D) &  ((r2_analoaf A D E B C) & (r2_analoaf A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_analort A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k6_analort A B C))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k6_analort A B C))) =>  ((r2_analoaf (k6_analort A B C) D D F H) &  ((r2_analoaf (k6_analort A B C) D F H H) &  ( (~  ((r2_analoaf (k6_analort A B C) D F E G) &  ((r2_analoaf (k6_analort A B C) D F G E) &  ( (~  (D = F) )  &  (~  (E = G) ) ) ) ) )  &  ( (~  ((r2_analoaf (k6_analort A B C) D F E G) &  ((r2_analoaf (k6_analort A B C) D F E H) &  ( (~ (r2_analoaf (k6_analort A B C) D F G H))  &  (~ (r2_analoaf (k6_analort A B C) D F H G)) ) ) ) )  &  ( ((r2_analoaf (k6_analort A B C) D F E G) => (r2_analoaf (k6_analort A B C) F D G E))  &  ( ( ((r2_analoaf (k6_analort A B C) D F E G) & (r2_analoaf (k6_analort A B C) D F G H))  => (r2_analoaf (k6_analort A B C) D F E H))  &  (~  ((r2_analoaf (k6_analort A B C) D E F G) &  ( (~ (r2_analoaf (k6_analort A B C) F G D E))  &  (~ (r2_analoaf (k6_analort A B C) F G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_analort A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k6_analort A B C))) &  ( (~  (F = G) )  & (r2_analoaf (k6_analort A B C) F G D E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_analort A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_analort A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_analort A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k6_analort A B C))) &  ( (~  (F = G) )  & (r2_analoaf (k6_analort A B C) D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_dist_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 B)) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~ (r2_hidden C (k1_dist_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t2_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  ( ( ((k1_xtuple_0 C) = (k1_xtuple_0 D))  &  ((k2_xtuple_0 C) = (k2_xtuple_0 D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t2_dtconstr,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k4_finseq_1 C)) => (r2_hidden (k1_funct_1 C B) A)) ) ) ) ) ).
tt(t2_dynkin,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (v1_finset_1 A)) ) ).
tt(t2_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l6_algstr_0 B))  =>  ( ((m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A))) &  ( ((u1_algstr_0 B) = (k1_realset1 (u1_algstr_0 A) (u1_struct_0 B)))  &  ( ((u2_algstr_0 B) = (k1_realset1 (u2_algstr_0 A) (u1_struct_0 B)))  &  ( ((k5_struct_0 B) = (k5_struct_0 A))  &  ( ((k4_struct_0 B) = (k4_struct_0 A))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) & (v33_algstr_0 B)) ) ) ) ) ) )  =>  ((v6_struct_0 B) | (m1_ec_pf_1 B A)) ) ) ) ) ) ).
tt(t2_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k11_algstr_0 A (k5_struct_0 A)) = (k5_struct_0 A)) ) ) ).
tt(t2_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r2_hidden (k6_partfun1 (u1_struct_0 A)) (k1_endalg A))) ) ).
tt(t2_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_tarski (k1_funct_2 B C) (k1_ens_1 A))) ) ) ) ) ) ).
tt(t2_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_xxreal_0 (k1_seq_1 k3_taylor_1 A) (k9_real_1 A 1)) &  ( ( (A = 1)  =>  ((k1_seq_1 k3_taylor_1 A) = (k9_real_1 A 1)) )  &  ( ( ((k1_seq_1 k3_taylor_1 A) = (k9_real_1 A 1))  =>  (A = 1) )  &  ( (~  ( (~  (A = 1) )  & (r1_xxreal_0 (k9_real_1 A 1) (k1_seq_1 k3_taylor_1 A))) )  &  (~  ( (~ (r1_xxreal_0 (k9_real_1 A 1) (k1_seq_1 k3_taylor_1 A)))  &  (A = 1) ) ) ) ) ) ) ) ) ) ).
tt(t2_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k2_xboole_0 (k1_tarski A) (k2_tarski B C))) ) ) ) ).
tt(t2_eqrel_1,ax, (! [A:$i] :  ((r1_relat_2 (k6_partfun1 A) A) &  ((r3_relat_2 (k6_partfun1 A) A) & (r8_relat_2 (k6_partfun1 A) A)) ) ) ).
tt(t2_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  ((v2_msualg_3 (k3_msualg_3 A B C D E F) A B D) => (v2_msualg_3 F A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_e_siec,ax, (! [A:$i] :  ((v2_e_siec (g1_e_siec A k1_xboole_0 k1_xboole_0)) &  ((v3_e_siec (g1_e_siec A k1_xboole_0 k1_xboole_0)) & (l1_e_siec (g1_e_siec A k1_xboole_0 k1_xboole_0))) ) ) ).
tt(t2_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k14_rvsum_1 B (k5_euclid A)) = (k5_euclid A)) ) ) ) ) ).
tt(t2_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k1_euclid_3 (k2_euclid_3 A)) = A) ) ) ).
tt(t2_euclid_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k9_euclid B (k5_euclid B) A) = (k5_euclid B)) ) ) ) ) ).
tt(t2_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k1_euclid_5 (k4_euclid_5 A B C)) = A)  &  ( ((k2_euclid_5 (k4_euclid_5 A B C)) = B)  &  ((k3_euclid_5 (k4_euclid_5 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t2_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k18_sin_cos (k4_euclid_3 A B C)) = (k1_real_1 (k18_sin_cos (k4_euclid_3 C B A)))) ) ) ) ) ) ) ).
tt(t2_euclid_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_tarski (k10_xtuple_0 A) B) =>  ((k8_relat_1 A B) = (k9_xtuple_0 A)) ) ) ) ) ).
tt(t2_euclid_8,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k3_finseq_1 A) = 3)  => (m2_finseq_2 A k1_numbers (k1_euclid 3))) ) ) ).
tt(t2_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  => (r2_hidden B (k1_euclid A))) ) ) ) ).
tt(t2_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ( ((k8_euclid A B B) = (k5_euclid A))  &  ((k7_euclid A B (k6_euclid A B)) = (k5_euclid A)) ) ) ) ) ) ).
tt(t2_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r6_analmetr A B C F) & (r6_analmetr A D E F))  =>  ((r2_analoaf A B C D E) & (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_int_2 B) =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 B A) | (r1_int_2 A B)) ) ) ) ) ) ) ).
tt(t2_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 1 (k3_xcmplx_0 A B)) => (r1_xxreal_0 1 B)) ) ) ) ) ).
tt(t2_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden A B) &  ((r2_hidden C D) &  ( (~  ( (~  (C = A) )  &  ( (~  (C = B) )  &  ( (~  (D = A) )  &  (~  (D = B) ) ) ) ) )  &  ( (~  ((r2_hidden C A) &  (D = A) ) )  &  ( (~  ((r2_hidden C A) &  (D = B) ) )  &  ( (~  ( (C = A)  & (r2_hidden D B)) )  &  ( (~  ( (C = A)  &  (D = B) ) )  &  ( (~  ( (C = A)  & (r2_hidden B D)) )  &  ( (~  ((r2_hidden A C) &  (D = B) ) )  &  (~  ( (C = B)  & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A B) =>  (! [E:$i] :  ((m2_pboole E A B C) => (r2_pboole A (k9_pboole A D E) (k9_pboole A B E))) ) ) ) ) ) ) ) ) ).
tt(t2_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((k5_extpro_1 A B C D k6_numbers) = D) ) ) ) ) ) ) ) ) ).
tt(t2_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k2_extreal1 A B) = (k12_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( ((k3_extreal1 A) = A)  |  ((k3_extreal1 A) = (k2_supinf_2 A)) ) ) ) ).
tt(t2_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ( ((r1_circcomb A B) &  ((v1_relat_1 (k3_msafree2 A)) & (v1_relat_1 (k3_msafree2 B))) )  => (v1_relat_1 (k3_msafree2 (k2_circcomb A B)))) ) ) ) ) ).
tt(t2_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = (k4_tarski (k10_finseq_1 A B) C)) )  &  (~  (B = (k4_tarski (k10_finseq_1 A B) C)) ) ) ) ) ) ).
tt(t2_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fcont_1 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) &  ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = A)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((k1_seq_1 C D) = A) ) ) ) ) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C B)) &  ((k1_seq_1 B A) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers C B))) ) ) ) ) ) ) ) ) ) ).
tt(t2_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_tarski B A))  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) ) ).
tt(t2_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden A (k2_rcomp_1 (k9_real_1 B C) (k7_real_1 B C))) => (r2_hidden (k9_real_1 A B) (k2_rcomp_1 (k4_xcmplx_0 C) C))) ) ) ) ) ) ) ).
tt(t2_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos B)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t2_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k16_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_sin_cos9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t2_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v3_fdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v3_fdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((v1_funct_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((v3_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (m1_subset_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((v3_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (m1_subset_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ).
tt(t2_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 2 B)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ) ) ).
tt(t2_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k1_rcomp_1 B (k7_real_1 B C)) (k1_relset_1 k1_numbers A))) ) )  &  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k9_real_1 D A))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) B) D) = (k10_real_1 1 (k9_real_1 D A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers C D))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k9_real_1 E A))  &  ( ((k1_seq_1 D E) = (k7_real_1 E A))  &  (~  ((k1_seq_1 D E) = k6_numbers) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers C D) B) E) = (k10_real_1 (k8_real_1 2 A) (k5_square_1 (k7_real_1 E A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_seq_1 k24_sin_cos (k1_real_1 (k8_real_1 B (k6_power k8_power A)))) = (k10_prepower A (k1_real_1 B))) ) ) ) ) ) ).
tt(t2_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k10_prepower A (k10_real_1 1 2)) = (k7_square_1 A)) ) ) ) ).
tt(t2_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) &  ((k1_seq_1 k16_sin_cos A) = k6_numbers) ) ) ) ) ).
tt(t2_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k16_sin_cos A) = k6_numbers) )  =>  ((r1_fdiff_1 k2_fdiff_9 A) &  ((k1_fdiff_1 k2_fdiff_9 A) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos A) (k5_square_1 (k1_seq_1 k16_sin_cos A))))) ) ) ) ) ).
tt(t2_ff_siec,ax, (! [A:$i] :  ( ((u1_struct_0 (k2_ff_siec A)) = A)  &  ( ((u4_struct_0 (k2_ff_siec A)) = k1_xboole_0)  &  ((k1_net_1 (k2_ff_siec A)) = k1_xboole_0) ) ) ) ).
tt(t2_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k3_fib_fusc A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v5_memstr_0 C 2 k1_ami_3 k6_numbers) & (m1_scm_1 C (k16_afinsq_1 2 B 1 k6_numbers)))  =>  ((r1_extpro_1 2 k1_ami_3 A C) &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A C) (k10_ami_3 3)) = (k3_pre_ff B))  &  ((k8_extpro_1 2 k1_ami_3 A C) = (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 B)) 1)) 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fib_num2,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  ((k3_power (k4_xcmplx_0 1) A) = (k4_xcmplx_0 1)) ) ) ).
tt(t2_fib_num3,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  ((k3_xcmplx_0 (k6_square_1 A) (k6_square_1 A)) = A) ) ) ).
tt(t2_fib_num4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (A = k6_numbers) )  =>  ((k3_power A (k2_xcmplx_0 B C)) = (k3_xcmplx_0 (k3_power A B) (k3_power A C))) ) ) ) ) ) ) ) ).
tt(t2_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_int_2 A B) = 1)  =>  ((k3_int_2 A (k4_nat_1 B C)) = (k3_int_2 A C)) ) ) ) ) ) ) ) ).
tt(t2_filerec1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k17_finseq_1 A (k3_finseq_1 B) B) = B) ) ) ) ).
tt(t2_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k4_lattices A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t2_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_filter_0 A B) = (k2_filter_0 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m2_subset_1 F A B) =>  ( ( (D = (k1_realset1 C B))  &  (F = E) )  =>  ( ((r1_binop_1 A E C) => (r1_binop_1 B F D))  &  ( ((r2_binop_1 A E C) => (r2_binop_1 B F D))  &  ((r3_binop_1 A E C) => (r3_binop_1 B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 A)) = (k3_rcomp_1 A k1_xxreal_0)) ) ) ).
tt(t2_finseq_1,ax, ( ((k2_finseq_1 1) = (k1_tarski 1))  &  ((k2_finseq_1 2) = (k2_tarski 1 2)) ) ).
tt(t2_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (A = (k3_xxreal_0 B C))  =>  ((k9_subset_1 k5_numbers (k2_finseq_1 B) (k2_finseq_1 C)) = (k2_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(t2_finseq_3,ax, ((k2_finseq_1 4) = (k2_enumset1 1 2 3 4)) ).
tt(t2_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_finseq_4 A B) <=>  ((r2_hidden B (k9_xtuple_0 A)) &  ((k8_relat_1 A (k1_tarski (k1_funct_1 A B))) = (k1_tarski B)) ) ) ) ) ) ).
tt(t2_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (r2_hidden (k2_xcmplx_0 (k6_xcmplx_0 B A) 1) (k2_finseq_1 B))) ) ) ) ) ).
tt(t2_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 A C))  &  ((k1_funct_1 B C) = (k1_funct_1 B A)) ) ) ) ) ) )  =>  ((k4_finseq_4 B (k1_funct_1 B A)) = A) ) ) ) ) ) ).
tt(t2_finseq_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  & (r1_xxreal_0 A (k3_finseq_1 (k7_finseq_1 C B))))  =>  ((r1_xxreal_0 A (k3_finseq_1 C)) |  ((k1_funct_1 (k7_finseq_1 C B) A) = (k1_funct_1 (k7_finseq_1 D B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_finseq_8,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) =>  ((k2_rfinseq A C B) = (k6_finseq_1 A)) ) ) ) ) ) ) ).
tt(t2_finseqop,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k15_funct_3 k1_xboole_0 A) = k1_xboole_0)  &  ((k15_funct_3 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t2_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 A) & (v1_finset_1 B))  => (v1_finset_1 (k2_xboole_0 A B))) ) ) ).
tt(t2_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (~  ( ((k8_nat_1 A E 1) = (k1_funct_1 C 1))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~  (k6_numbers = F) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) F))  &  (~  ((k8_nat_1 A E (k2_nat_1 F 1)) = (k1_binop_1 D (k8_nat_1 A E F) (k1_funct_1 C (k2_nat_1 F 1)))) ) ) ) ) ) )  &  (B = (k8_nat_1 A E (k3_finseq_1 C))) ) ) ) ) )  |  (B = (k1_finsop_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v4_finsub_1 C))  =>  ( ((m1_subset_1 A C) & (m1_subset_1 B C))  => (m1_subset_1 (k3_xboole_0 A B) C)) ) ) ) ) ).
tt(t2_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fin_topo A B) = (k9_subset_1 (u1_struct_0 A) (k9_fin_topo A B) (k3_subset_1 (u1_struct_0 A) (k8_fin_topo A B)))) ) ) ) ) ).
tt(t2_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_fintopo3 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k3_subset_1 (u1_struct_0 A) B)) & (r2_hidden C (k1_fin_topo A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_tarski (k3_fintopo3 A B C) (k3_fintopo3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t2_fintopo5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((k2_finseq_1 A) = k1_xboole_0) ) )  &  (~  ( (~  ((k2_finseq_1 A) = k1_xboole_0) )  & (r1_xxreal_0 A k6_numbers)) ) ) ) ) ).
tt(t2_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((k9_fin_topo A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t2_fin_topo,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) | (r1_tarski (k7_partfun1 (k9_setfam_1 A) B C) (k7_partfun1 (k9_setfam_1 A) B (k2_nat_1 C 1)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 D (k3_finseq_1 B)) & (r1_tarski (k7_partfun1 (k9_setfam_1 A) B D) (k7_partfun1 (k9_setfam_1 A) B C))) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 C E) & (r1_xxreal_0 E D))  =>  ((k7_partfun1 (k9_setfam_1 A) B D) = (k7_partfun1 (k9_setfam_1 A) B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_flang_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 C 1)) =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(t2_flang_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 (k2_xcmplx_0 A C) E) &  ((r1_xxreal_0 E (k2_xcmplx_0 B D)) &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ( ((k2_xcmplx_0 F G) = E)  &  ((r1_xxreal_0 A F) &  ((r1_xxreal_0 F B) &  ((r1_xxreal_0 C G) & (r1_xxreal_0 G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden B (k1_flang_3 A C D)) <=>  (? [E:$i] :  ((v7_ordinal1 E) &  ((r1_xxreal_0 D E) & (r2_hidden B (k7_flang_1 A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t2_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_xboole_0 (k4_finseq_2 C A) (k3_finseq_2 B)) = (k4_finseq_2 C (k3_xboole_0 A B))) ) ) ) ) ).
tt(t2_fomodel1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (r1_tarski (k1_funct_1 (k25_fomodel1 B) A) (k27_fomodel1 B))) ) ) ) ).
tt(t2_fomodel2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_fomodel2 C A B)) )  => (r2_hidden (k5_relat_1 C (k37_fomodel1 A)) (k16_fomodel2 A B))) ) ) ) ) ) ).
tt(t2_fomodel3,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k35_fomodel1 A))) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) & (m2_subset_1 B (k3_finseq_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k2_fomodel0 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0)) (k8_nat_1 (k9_setfam_1 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 A)) (k1_tarski k1_xboole_0))) (k39_fomodel1 A) C)))) ) ) ) ) ) ).
tt(t2_fomodel4,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v11_fomodel1 A) & (l1_fomodel1 A)) )  =>  (! [B:$i] :  ((v2_fomodel4 B A) =>  (! [C:$i] :  ((v1_fomodel4 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 (k1_fomodel4 A)) (k1_fomodel4 A)))) =>  ((r2_hidden (k4_tarski B C) D) => (r2_hidden C (k1_funct_1 (k21_fomodel4 A D) B))) ) ) ) ) ) ) ) ) ).
tt(t2_fraenkel,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k1_funct_2 A B) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ).
tt(t2_frechet2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_funct_2 k5_numbers k1_numbers k5_numbers k5_numbers A (k6_partfun1 k5_numbers)) =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ) ) ).
tt(t2_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) (u1_struct_0 B)) =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t2_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((r1_tarski (k1_lang1 (k3_freealg A B)) B) &  ((k2_lang1 (k3_freealg A B)) = (k4_finseq_1 A)) ) ) ) ) ).
tt(t2_fscirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k4_fscirc_1 A B C)))) ) ) ) ) ) ) ).
tt(t2_fscirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k1_fscirc_2 k6_numbers A B) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ( ((k2_fscirc_2 k6_numbers A B) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0))  &  ((k3_fscirc_2 k6_numbers A B) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1))) ) ) ) ) ) ) ).
tt(t2_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_fsm_1 A B (k6_finseq_1 A) C C)) ) ) ) ) ) ).
tt(t2_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_fsm_1 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ((k2_fsm_1 A D E (k2_finseq_4 A B C)) = (k3_finseq_4 (u1_struct_0 D) E (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 D) A) (u1_struct_0 D) (u1_fsm_1 A D) (k1_domain_1 (u1_struct_0 D) A E B)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 D) A) (u1_struct_0 D) (u1_fsm_1 A D) (k1_domain_1 (u1_struct_0 D) A (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 D) A) (u1_struct_0 D) (u1_fsm_1 A D) (k1_domain_1 (u1_struct_0 D) A E B)) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fsm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k7_finseq_1 A B) = A)  |  ((k7_finseq_1 B A) = A) )  =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t2_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (v1_relat_1 (k3_msafree2 (k1_ftacell1 A B C D E)))) ) ) ) ) ).
tt(t2_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k13_funct_3 A B) = (k1_funcop_1 (k13_funct_3 B A))) ) ) ) ) ).
tt(t2_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_funct_2 D A k1_numbers (k9_funct_2 A k1_numbers)) =>  ((r2_funct_2 A k1_numbers B (k1_funcsdom A k1_numbers (k6_funcsdom A) C D)) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k1_numbers B E) = (k8_real_1 (k3_funct_2 A k1_numbers C E) (k3_funct_2 A k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t2_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k10_xtuple_0 B) A) =>  ((v1_funct_1 B) &  ((v1_funct_2 B (k9_xtuple_0 B) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) A)))) ) ) ) ) ) ).
tt(t2_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A (k9_xtuple_0 (k3_relat_1 B C))) => (r1_tarski (k7_relat_1 B A) (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t2_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k3_relat_1 B A) = (k3_relat_1 B (k5_relat_1 A (k10_xtuple_0 B)))) ) ) ) ) ).
tt(t2_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ((r2_hidden A (k9_xtuple_0 (k2_funct_4 B))) &  (! [C:$i] :  (! [D:$i] :  (~  (A = (k4_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t2_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ((r1_tarski E (k7_relset_1 A B C D)) => (r1_tarski (k8_relset_1 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_funct_8 A k1_numbers k1_numbers B) <=>  ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k6_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 B (k1_real_1 C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t2_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 B A) & (v1_funct_9 C A))  => (v1_funct_9 (k1_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t2_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k3_relat_1 (k6_partfun1 A) B) = B) ) ) ) ).
tt(t2_functor1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ((v1_funct_1 (k2_funct_1 C)) &  ((v1_funct_2 (k2_funct_1 C) B A) & (m1_subset_1 (k2_funct_1 C) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ).
tt(t2_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  (! [E:$i] :  ((m2_functor0 E A B) =>  ( ((r1_functor2 A B C D) & (r1_functor2 A B D E))  => (r1_functor2 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) &  ((v10_functor0 D A B) & (l2_functor0 D A B)) )  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k4_functor0 A C (k13_functor0 A B C D E) F G) = (k3_relat_1 (k5_functor0 A B D F G) (k4_functor0 B C E (k3_functor0 A B D F) (k3_functor0 A B D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers B C) <=>  ((r1_fuzzy_1 B C) & (r1_fuzzy_1 C B)) ) ) ) ) ) ) ) ).
tt(t2_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r2_funct_2 A k1_numbers (k2_fuzzy_1 A B (k1_fuzzy_1 A D C)) (k1_fuzzy_1 A (k2_fuzzy_1 A B D) C))) ) ) ) ) ) ) ) ) ).
tt(t2_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( (! [D:$i] :  ((r2_hidden D A) => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 C D))) )  => (r1_xxreal_0 (k4_seq_4 (k2_relset_1 k1_numbers B)) (k4_seq_4 (k2_relset_1 k1_numbers C)))) ) ) ) ) ) ) ).
tt(t2_fvaluat1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ( ((k1_xxreal_3 A A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t2_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  => (v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A))) ) ).
tt(t2_gate_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k1_gate_1 A)))  <=> (v1_xboole_0 A)) ) ).
tt(t2_gate_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k2_gate_1 A B) (k2_gate_1 C B) (k2_gate_1 D B))))  & (v1_xboole_0 (k2_gate_1 (k8_gate_1 A C D) B))) )  &  (~  ( (~ (v1_xboole_0 (k2_gate_1 (k8_gate_1 A C D) B)))  & (v1_xboole_0 (k8_gate_1 (k2_gate_1 A B) (k2_gate_1 C B) (k2_gate_1 D B)))) ) ) ) ) ) ) ).
tt(t2_gate_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) (k1_gate_1 I)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) (k1_gate_1 I))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) I))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) I)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k2_gate_1 J (k1_gate_1 I)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 J (k1_gate_1 I))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k2_gate_1 J I))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 J I)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) (k1_gate_1 K)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) (k1_gate_1 K))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) K))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 L) K)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k2_gate_1 L (k1_gate_1 K)))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 L (k1_gate_1 K))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k2_gate_1 L K))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 L K)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) M))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 J) M)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k2_gate_1 I M))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 I M)))  & (v1_xboole_0 L)) )  &  (~  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k2_gate_1 A M))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A M)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k2_gate_1 B M))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 B M)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k2_gate_1 D M))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 D M)))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k3_gate_1 (k2_gate_1 C M) (k1_gate_1 M)))) )  &  (~  ( (~ (v1_xboole_0 (k3_gate_1 (k2_gate_1 C M) (k1_gate_1 M))))  & (v1_xboole_0 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (! [W:$i] :  (! [X:$i] :  (! [Y:$i] :  (~  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k2_gate_1 A D))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A D)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0)))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 Q))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) k1_xboole_0)))  & (v1_xboole_0 Q)) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 (k10_gate_1 O (k2_gate_1 A F) P))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 O (k2_gate_1 A F) P)))  & (v1_xboole_0 R)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k11_gate_1 O (k2_gate_1 A F) P))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 O (k2_gate_1 A F) P)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 S))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) Q)))  & (v1_xboole_0 S)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) Q)))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 (k10_gate_1 S k1_xboole_0 T))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 S k1_xboole_0 T)))  & (v1_xboole_0 V)) )  &  ( (~  ( (~ (v1_xboole_0 X))  & (v1_xboole_0 (k11_gate_1 S k1_xboole_0 T))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 S k1_xboole_0 T)))  & (v1_xboole_0 X)) )  &  ( (~  ( (~ (v1_xboole_0 W))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C F) X U))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C F) X U)))  & (v1_xboole_0 W)) )  &  ( (~  ( (~ (v1_xboole_0 Y))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C F) X U))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C F) X U)))  & (v1_xboole_0 Y)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 R)) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 V)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 W)) )  &  ( (~  ( (~ (v1_xboole_0 W))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 Y)) )  &  ( (~  ( (~ (v1_xboole_0 Y))  & (v1_xboole_0 L)) )  &  (~  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k5_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k5_gate_5 A B C D E)))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k6_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k6_gate_5 A B C D E)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k10_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_5 A B C D E F)))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k11_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_5 A B C D E F)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k12_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k12_gate_5 A B C D E F)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k13_gate_5 A B C D E F))) )  &  (~  ( (~ (v1_xboole_0 (k13_gate_5 A B C D E F)))  & (v1_xboole_0 L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_gcd_1 A B C) & (r1_gcd_1 A C D))  => (r1_gcd_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t2_genealg1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k17_finseq_1 A (k2_nat_1 (k3_finseq_1 B) D) (k8_finseq_1 A B C)) = (k8_finseq_1 A B (k17_finseq_1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t2_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analoaf A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analoaf A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analoaf A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analoaf A))) =>  ( ( (F = B)  &  ( (G = C)  &  ( (H = D)  &  (I = E) ) ) )  =>  ((r2_analoaf (k2_analoaf A) F G H I) <=> (r1_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_gfacirc1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  ( ((k1_funct_1 k2_gfacirc1 (k10_binarith k6_margrel1 A)) = A)  &  ( ((k1_funct_1 k2_gfacirc1 (k10_binarith k6_margrel1 A)) = (k1_funct_1 k2_twoscomp (k10_finseq_1 A A)))  &  ( ((k1_funct_1 k2_gfacirc1 (k10_binarith k5_numbers k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k2_gfacirc1 (k10_binarith k5_numbers 1)) = 1) ) ) ) ) ) ).
tt(t2_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k1_gfacirc2 k6_numbers A B) = (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ( ((k2_gfacirc2 k6_numbers A B) = (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0))  &  ((k3_gfacirc2 k6_numbers A B) = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1))) ) ) ) ) ) ) ).
tt(t2_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (r1_tarski k5_glib_000 (k1_relset_1 k5_numbers A))) ) ).
tt(t2_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v1_glib_002 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (~ (v10_glib_000 B A)) ) ) ) ) ).
tt(t2_glib_003,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) )  => (r1_xxreal_0 (k18_rvsum_1 (k1_glib_003 k1_numbers A B)) (k18_rvsum_1 A))) ) ) ) ) ).
tt(t2_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] : (r1_tarski (k13_pre_poly (k1_funct_4 A (k16_funcop_1 B C))) (k2_xboole_0 (k13_pre_poly A) (k1_tarski B)))) ) ) ) ).
tt(t2_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r5_glib_005 A B C) => (r5_glib_005 A B (k8_glib_001 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden C (k2_finseq_1 (k1_matrix_1 B))))  =>  ((k1_funct_1 (k9_matrix_1 A B C) D) = (k1_funct_1 (k8_matrix_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((v2_funct_1 A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k2_topreal1 2 A B)) &  ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A))) ) ) ) )  =>  ((k2_nat_1 B 1) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t2_goboard3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B D E)) ) ) ) ) ) ) ) ) ) )  &  ((v4_topreal1 A) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((v4_topreal1 C) &  ( ((k3_topreal1 2 A) = (k3_topreal1 2 C))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)))  & (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard4,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) & (r1_xboole_0 (k3_topreal1 2 B) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v2_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C))) ) ) )  =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B A)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B 1))) ) ) ) ) ) ) ) ).
tt(t2_goboard6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (B = C)  =>  ((r1_xxreal_0 D k6_numbers) | (m1_connsp_2 (k9_metric_1 (k14_euclid A) B D) (k15_euclid A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k18_complex1 (k9_real_1 A B)) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t2_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_goboard9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))) =>  ( (B = D)  =>  ((k1_pre_topc A B) = (k1_pre_topc (k1_pre_topc A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_gobrd10 A B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B)) )  => (r1_gobrd10 (k7_nat_d A 1) (k7_nat_d B 1))) ) ) ) ) ).
tt(t2_gobrd11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 D A) &  ((r1_tarski B D) & (v2_connsp_1 C A)) )  =>  ((r1_xboole_0 (k2_pre_topc A B) (k2_pre_topc A C)) | (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))))  =>  ((k2_pre_topc (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k4_connsp_3 (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 (k2_goboard2 A) B C) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) ) ) ) ) ) ) ) ).
tt(t2_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  ( (~  ((k3_topreal1 A B) = k1_xboole_0) )  => (r1_xxreal_0 2 (k3_finseq_1 B))) ) ) ) ) ).
tt(t2_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k9_cqc_lang A (k6_cqc_lang A B) C)))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t2_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (u1_struct_0 A))) ) ) ) ).
tt(t2_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (A = (k5_relat_1 B (k2_finseq_1 C)))  =>  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 A)))  =>  ((k1_funct_1 B D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_graph_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 (k1_graph_2 A B C))) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 A)) &  ( ((k1_funct_1 A E) = (k1_funct_1 (k1_graph_2 A B C) D))  &  ( ((k2_nat_1 E 1) = (k2_nat_1 B D))  &  ((r1_xxreal_0 B E) & (r1_xxreal_0 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_graph_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_graph_4 B C D A) & (r1_graph_4 B E F A))  =>  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_graph_5,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (C = (a_2_0_graph_5 A B))  => (v1_finset_1 C)) ) ) ) ) ) ).
tt(t2_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (r2_hidden (k1_funct_1 B C) A)) ) ) ) ) ) ).
tt(t2_grcat_1,ax, ( ((k1_binop_1 k9_funct_5 k1_xboole_0 k1_xboole_0) = k1_xboole_0)  &  ( ((k1_funct_1 k8_funct_5 k1_xboole_0) = k1_xboole_0)  &  (k5_funct_5 = k1_xboole_0) ) ) ).
tt(t2_gr_cy_1,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  ((k16_rvsum_1 A) = (k1_finsop_1 k4_numbers A k44_binop_2)) ) ) ).
tt(t2_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_struct_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)) B)) ) ) ) ).
tt(t2_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  => (r1_xxreal_0 5 A)) ) ).
tt(t2_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) <=>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t2_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k2_group_5 A B C)) = (k2_group_3 A (k2_group_5 A B (k2_group_1 A C)) C)) ) ) ) ) ) ) ).
tt(t2_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r4_polyred A B C D E F) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ( (F = (k6_polynom1 A C D (k10_polynom1 A C G E)))  &  ( (~ (r2_hidden (k3_termord A B C (k10_polynom1 A C G E)) (k2_polynom1 (k15_pre_poly A) C F)))  & (r1_termord A B (k3_termord A B C (k10_polynom1 A C G E)) (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_groeb_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k4_rlvect_1 A (k2_finseq_7 (u1_struct_0 A) B C D)) = (k4_rlvect_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t2_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r1_termord A B C D) => (r1_termord A B (k11_pre_poly A C E) (k11_pre_poly A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_10,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ( (~  (C = D) )  =>  ((k1_card_1 (k1_card_fin A B C D)) = (k5_card_1 (k3_group_10 A B))) ) ) ) ) ) ) ) ).
tt(t2_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k13_group_2 A B C)) =>  ((k13_group_2 A B C) = (k13_group_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((r2_hidden D (k1_group_12 A B C)) <=>  (? [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_group_7 A B C))) &  ( (E = D)  &  ( ((k9_xtuple_0 E) = A)  &  ( ((k1_funct_1 E C) = F)  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ( (~  (G = C) )  =>  ((k1_funct_1 E G) = (k1_group_1 (k1_group_7 A B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A B D) = C) ) )  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k6_algstr_0 A D B) = C) ) ) ) ) ) ) ) )  =>  ((v3_group_1 A) & (v2_group_1 A)) ) ) ) ).
tt(t2_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A (k1_group_2 B C)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ( (A = (k2_group_1 B D))  & (r2_hidden D C)) ) ) ) ) ) ) ) ) ).
tt(t2_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=> (v1_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ) ).
tt(t2_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (C = E)  =>  ((k5_group_1 B A C) = (k5_group_1 D A E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k2_group_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t2_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_6 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (E = C)  =>  ( ((k13_group_2 B D E) = (k13_group_2 A D C))  &  ((k14_group_2 B D E) = (k14_group_2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_group_7 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  ( ((r2_hidden B A) &  ( (D = (k1_funct_1 C B))  & (v2_group_1 (k2_group_7 A C))) )  => (v2_group_1 D)) ) ) ) ) ) ) ).
tt(t2_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_algstr_0 B C D) = (k6_algstr_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) => (m1_subset_1 D (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t2_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_int_1 B (k1_newton A C)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (B = (k1_newton A D))  & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C B) & (m1_group_6 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_group_2 B (k13_group_2 B C D) (k13_group_2 B C E)) = (k13_group_2 B C (k6_algstr_0 B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_hahnban1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_xcmplx_0 (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1)) (k2_xcmplx_0 C (k3_xcmplx_0 D k7_complex1))) = (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D)) (k3_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 C B)) k7_complex1))) ) ) ) ) ) ) ) ) ).
tt(t2_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) )  =>  ((k4_rlsub_2 A D B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_hallmar1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v2_relat_1 B) & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((k1_funct_1 B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t2_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_funct_1 (k4_weierstr A B) B) = k6_numbers) ) ) ) ) ).
tt(t2_heine,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v5_valued_0 B) & (r1_tarski (k10_xtuple_0 B) k5_numbers))  => (r1_xxreal_0 A (k1_seq_1 B A))) ) ) ) ) ).
tt(t2_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) <=>  ((k1_helly A B) = A) ) ) ) ) ) ).
tt(t2_henmodel,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  =>  ((r2_hidden (k3_tarski A) A) &  (! [B:$i] :  (~  ((r2_hidden B A) &  ( (~ (r2_hidden B (k3_tarski A)))  &  (~  (B = (k3_tarski A)) ) ) ) ) ) ) ) ) ).
tt(t2_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( (~  (A = k5_complex1) )  =>  ( ((k17_complex1 (k8_complex1 (k13_complex1 (k3_complex1 A) (k17_complex1 A)) (k9_complex1 (k13_complex1 (k1_real_1 (k4_complex1 A)) (k17_complex1 A)) k7_complex1))) = 1)  &  ( ((k3_complex1 (k9_complex1 (k8_complex1 (k13_complex1 (k3_complex1 A) (k17_complex1 A)) (k9_complex1 (k13_complex1 (k1_real_1 (k4_complex1 A)) (k17_complex1 A)) k7_complex1)) A)) = (k17_complex1 A))  &  ((k4_complex1 (k9_complex1 (k8_complex1 (k13_complex1 (k3_complex1 A) (k17_complex1 A)) (k9_complex1 (k13_complex1 (k1_real_1 (k4_complex1 A)) (k17_complex1 A)) k7_complex1)) A)) = k6_numbers) ) ) ) ) ) ).
tt(t2_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) & (r1_collsp A B C E))  =>  ( (B = C)  | (r1_collsp A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  ( (B = k1_xboole_0)  =>  ((k9_normform A B) = k1_xboole_0) ) ) ) ) ).
tt(t2_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k4_partfun1 A B)))  => (r2_hidden (k1_tarski C) (k1_substlat A B))) ) ) ) ).
tt(t2_heyting3,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (~  (! [B:$i] :  ( ( (~ (v1_abian B))  & (m1_subset_1 B k5_numbers))  => (r2_hidden B A)) ) ) ) ) ).
tt(t2_hfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (r2_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers A) (k32_valued_1 k1_numbers k1_numbers B)) (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ).
tt(t2_hilbasis,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k6_numbers) &  ((v1_funct_1 A) &  ((v1_partfun1 A k6_numbers) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  ((k21_pre_poly k6_numbers A) = (k9_finseq_1 (k10_finseq_1 k1_xboole_0 k1_xboole_0))) ) ) ).
tt(t2_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 B (k3_hilbert1 C (k4_hilbert1 B C))) (k5_hilbert1 A))) ) ) ) ) ) ).
tt(t2_hilbert2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((k7_finseq_1 (k9_finseq_1 A) C) = (k7_finseq_1 (k9_finseq_1 B) D))  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t2_hilbert3,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (v1_abian A))  <=> (v1_abian (k6_xcmplx_0 A 1))) ) ) ).
tt(t2_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r1_xxreal_0 k6_numbers C) &  (~  ((k4_power (k4_power C A) B) = (k4_power C (k8_real_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ((r1_aff_1 A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v6_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v4_aff_2 A)) ) ) ).
tt(t2_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k4_algstr_0 A (k1_group_1 A)) B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t2_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( ((k4_nat_d B A) = (k4_nat_d C A))  &  ((r1_xxreal_0 B C) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((k6_xcmplx_0 C B) = (k4_nat_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k4_struct_0 A) B)) ) ) ) ).
tt(t2_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  ( ((u1_incsp_1 (k3_incproj A)) = (u1_struct_0 A))  &  ( ((u2_incsp_1 (k3_incproj A)) = (k1_incproj A))  &  ((u3_incsp_1 (k3_incproj A)) = (k2_incproj A)) ) ) ) ) ).
tt(t2_incsp_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D E) B) <=>  ((r1_incsp_1 A C B) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) &  ((v3_cat_5 C) & (l1_cat_1 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  ((r1_funct_2 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (u4_struct_0 C) D E) => (r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 C) (k7_cat_1 A B D) (k7_cat_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~  ( (~  ((k3_msualg_1 A D B) = k1_xboole_0) )  &  ((k3_msualg_1 A D C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((v1_int_1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = B) )  &  (~  (A = (k1_real_1 B)) ) ) ) ) ) ) ) ) ).
tt(t2_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_int_1 A B) => (r1_int_1 A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t2_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_int_3)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_int_3)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_int_3)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k1_int_3)) =>  ( ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 C B) E))  &  ((r1_xxreal_0 (k4_struct_0 k1_int_3) E) &  ( (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 D B) F))  & (r1_xxreal_0 (k4_struct_0 k1_int_3) F)) ) )  =>  ( (B = (k4_struct_0 k1_int_3))  |  ((r1_xxreal_0 (k2_int_3 B) E) |  ((r1_xxreal_0 (k2_int_3 B) F) |  ( (C = D)  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_int_4,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_card_1 A) = (k1_card_1 (k2_measure6 A B))) ) ) ) ) ).
tt(t2_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A (k6_xcmplx_0 B C)))  => (r1_int_1 A C)) ) ) ) ) ) ) ).
tt(t2_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k3_finseq_1 (k45_valued_1 A B)) = (k6_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t2_int_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v3_valued_0 D)) ) ) )  =>  ( ( ((k3_xboole_0 (k13_pre_poly B) (k13_pre_poly C)) = k1_xboole_0)  &  ( ((k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)) = (k13_pre_poly D))  &  ( ((k5_relat_1 B (k13_pre_poly B)) = (k5_relat_1 D (k13_pre_poly B)))  &  ((k5_relat_1 C (k13_pre_poly C)) = (k5_relat_1 D (k13_pre_poly C))) ) ) )  => (r6_pboole A (k11_pre_poly A B C) D)) ) ) ) ) ) ) ) ).
tt(t2_integr10,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  ( (~ (r1_xxreal_0 B E))  &  (~ (r1_xxreal_0 C (k8_real_1 (k9_real_1 E A) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_integr11,ax, ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) k1_numbers) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k10_real_1 1 2) k6_numbers) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 2 k6_numbers) k16_sin_cos) (k10_real_1 1 4))) k1_numbers) A) = (k5_square_1 (k1_seq_1 k19_sin_cos A))) ) ) ) ).
tt(t2_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A F) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D)) E)) &  ((r2_relset_1 k1_numbers k1_numbers E k2_sin_cos9) &  ((r1_tarski F (k2_rcomp_1 (k19_binop_2 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 C G) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 E G) k6_numbers)) ) ) ) )  &  (F = (k1_relset_1 k1_numbers B)) ) ) ) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k3_taylor_1)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k3_taylor_1)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k32_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t2_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_fdiff_9)) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t2_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr15 D A B C) =>  ((v1_seq_2 (k2_partfun1 A k1_numbers B A)) => (r1_xxreal_0 (k1_integr15 A B C D) (k6_integra1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t2_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) => (r2_relset_1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers (k2_partfun1 k1_numbers k2_numbers A B)) (k2_partfun1 k1_numbers k1_numbers (k5_comseq_3 k1_numbers A) B))) ) ) ) ).
tt(t2_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  & (r2_relset_1 k5_numbers (u1_struct_0 A) D (k2_vfunct_1 k5_numbers A B C)))  =>  ((k4_rlvect_1 A D) = (k5_algstr_0 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_integr19,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) & (r1_tarski (k3_integra5 B E) A)) ) )  => (r1_tarski (k3_integra5 C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers B) (k1_relset_1 k2_numbers A)) &  ((r1_integr1c A B) & (r2_integr1c A B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k3_integr1c (k25_valued_1 k2_numbers k2_numbers A C) B) = (k3_xcmplx_0 C (k3_integr1c A B))) ) ) ) ) ) ) ) ).
tt(t2_integra2,ax, (! [A:$i] :  ( ((v1_integra2 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) & (r1_xxreal_0 B C)) )  => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 A C))) ) ) ) ) ) ) ).
tt(t2_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (~  ( (~  ((k3_integra1 A) = k6_numbers) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (~ (r1_xxreal_0 (k3_integra1 (k2_integra1 A B C)) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v3_integra1 (k7_rfunct_1 A A) A) &  ((k12_integra1 A (k7_rfunct_1 A A)) = (k3_integra1 A)) ) ) ) ).
tt(t2_integra5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( ((k3_finseq_1 (k4_rvsum_1 A B)) = (k3_finseq_1 A))  &  ( ((k3_finseq_1 (k8_rvsum_1 A B)) = (k3_finseq_1 A))  &  ( ((k18_rvsum_1 (k4_rvsum_1 A B)) = (k7_real_1 (k18_rvsum_1 A) (k18_rvsum_1 B)))  &  ((k18_rvsum_1 (k8_rvsum_1 A B)) = (k9_real_1 (k18_rvsum_1 A) (k18_rvsum_1 B))) ) ) ) ) ) ) ) ) ).
tt(t2_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_tarski (k2_rcomp_1 (k6_xcmplx_0 C A) (k2_xcmplx_0 C A)) (k2_rcomp_1 (k6_xcmplx_0 C B) (k2_xcmplx_0 C B)))) ) ) ) ) ) ) ).
tt(t2_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v3_xxreal_2 (k1_rvsum_1 C)) &  ((v3_xxreal_2 (k1_rvsum_1 D)) &  (! [E:$i] :  ((r2_hidden E B) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 C E) (k1_seq_1 D E))) A)) ) ) )  =>  ((r1_xxreal_0 (k9_real_1 (k5_seq_4 (k1_rvsum_1 C)) (k5_seq_4 (k1_rvsum_1 D))) A) & (r1_xxreal_0 (k9_real_1 (k5_seq_4 (k1_rvsum_1 D)) (k5_seq_4 (k1_rvsum_1 C))) A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k18_sin_cos (k7_real_1 A (k8_real_1 (k2_nat_1 (k4_nat_1 2 B) 1) k32_sin_cos))) = (k1_real_1 (k18_sin_cos A))) ) ) ) ) ).
tt(t2_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos) (k10_real_1 1 A)) k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos) (k10_real_1 1 A)) k1_numbers) B) = (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos) B)) ) ) ) ) ) ) ).
tt(t2_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~  ((k1_interva1 A B C) = k1_xboole_0) )  =>  ((r2_hidden B (k1_interva1 A B C)) & (r2_hidden C (k1_interva1 A B C))) ) ) ) ) ) ) ).
tt(t2_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  (! [D:$i] :  ((m1_subset_1 D k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 B (k3_intpro_1 C D)) (k3_intpro_1 (k3_intpro_1 B C) (k3_intpro_1 B D))) (k7_intpro_1 A))) ) ) ) ) ) ) ) ).
tt(t2_irrat_1,ax, (? [A:$i] :  ((v1_xreal_0 A) &  (? [B:$i] :  ((v1_xreal_0 B) &  ( (~ (v1_rat_1 A))  &  ( (~ (v1_rat_1 B))  & (v1_rat_1 (k3_power A B))) ) ) ) ) ) ).
tt(t2_isocat_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k9_funct_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k2_binop_1 A B C (k1_isocat_2 A B C D) E F) = (k3_funct_2 B C (k10_funct_5 A B C (k9_funct_2 B C) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C)))) = (k4_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A C))))) ) ) ) ) ) ) ).
tt(t2_jct_misc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k18_complex1 (k6_xcmplx_0 A B)) (k18_complex1 (k6_xcmplx_0 C D)))) (k7_real_1 (k18_complex1 (k6_xcmplx_0 A C)) (k18_complex1 (k6_xcmplx_0 B D))))) ) ) ) ) ) ) ) ).
tt(t2_jgraph_1,ax, (! [A:$i] :  ((u1_struct_0 (k1_jgraph_1 A)) = A) ) ).
tt(t2_jgraph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (C = B)  =>  ((k9_metric_1 (k14_euclid A) B D) = (a_3_0_jgraph_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_jgraph_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k7_relat_1 (k5_relat_1 A B) C) = (k7_relat_1 A (k3_xboole_0 C B))) ) ) ) ) ).
tt(t2_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((v5_pre_topc B A k3_topmetr) &  (C = (a_3_1_jgraph_4 A B D)) )  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t2_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k12_euclid A) 1) =>  ( ((k17_euclid A) = k6_numbers)  |  ( ((k18_euclid A) = k6_numbers)  |  ( (~ (r1_xxreal_0 (k17_euclid A) (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 (k17_euclid A)))  &  ( (~ (r1_xxreal_0 (k18_euclid A) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k18_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t2_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k17_euclid D) = A)  &  ((r1_xxreal_0 B (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) C)) )  =>  ((r1_xxreal_0 C B) | (r2_hidden D (k1_rltopsp1 (k15_euclid 2) (k19_euclid A B) (k19_euclid A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t2_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ((v5_pre_topc E k5_topmetr (k15_euclid A)) &  ((v2_funct_1 E) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid A)) E) = B)  &  ( ((k1_funct_1 E k6_numbers) = C)  &  ((k1_funct_1 E 1) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jgraph_8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r1_tarski D (k1_rltopsp1 (k15_euclid A) B C)) &  ((r2_hidden B D) &  ((r2_hidden C D) & (v2_connsp_1 D (k15_euclid A))) ) )  =>  (D = (k1_rltopsp1 (k15_euclid A) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v2_connsp_1 E (k15_euclid 2)) &  ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k1_jordan9 E B))) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k1_jordan8 E B))) &  ((r2_hidden (k4_tarski C (k2_nat_1 D 1)) (k2_matrix_1 (k1_jordan8 E B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C D))  & (r1_xxreal_0 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xxreal_0 (k2_jordan11 A) 1)) ) ) ).
tt(t2_jordan12,ax, (~ (v1_abian 1)) ).
tt(t2_jordan14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((k2_jordan2c 2 (k3_topreal1 2 A)) = (k3_goboard9 A))  |  ((k2_jordan2c 2 (k3_topreal1 2 A)) = (k2_goboard9 A)) ) ) ) ).
tt(t2_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xboole_0 A B) &  ((r1_tarski A (k7_jordan6 C)) & (r1_tarski B (k7_jordan6 C))) )  => (r1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A) (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B))) ) ) ) ) ) ) ).
tt(t2_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) => (r1_tarski (k5_jordan6 A B C D E) A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_jordan6 A (k18_pscomp_1 A) (k22_pscomp_1 A))) ) ).
tt(t2_jordan18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_tops_2 C A B) & (v2_compts_1 D B))  => (v2_compts_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t2_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A)))) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) (k1_matrix_1 (k1_jordan8 B A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) D)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B C) (k1_jordan1a (k1_jordan8 B C)) (k1_matrix_1 (k1_jordan8 B C))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) D)))) ) ) ) ) ) ) ) ) ).
tt(t2_jordan1a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v1_abian (k3_finseq_1 A)) =>  ((k3_finseq_1 A) = (k9_real_1 (k4_nat_1 2 (k1_jordan1a A)) 2)) ) ) ) ).
tt(t2_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k1_pre_topc A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k1_pre_topc A B)))))) )  =>  (~  ((v5_pre_topc E k17_borsuk_1 (k1_pre_topc A B)) &  ( (C = (k1_funct_1 E k6_numbers))  &  (D = (k1_funct_1 E 1)) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v2_connsp_1 B A)) ) ) ) ) ).
tt(t2_jordan1b,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) & (v1_xboole_0 (k3_finseq_6 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan1c,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k1_jordan8 A D))) & (r2_hidden (k4_tarski B (k3_real_1 C 1)) (k2_matrix_1 (k1_jordan8 A D))))  =>  ((k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) 1 2)) = (k9_real_1 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) B (k3_real_1 C 1))) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A D) B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (B = k6_numbers) )  =>  ((k8_real_1 (k10_real_1 1 B) (k1_newton B (k2_nat_1 A 1))) = (k1_newton B A)) ) ) ) ) ) ).
tt(t2_jordan1e,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k10_xtuple_0 A)) => (r1_sprect_2 B (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A C))) ) ) ) ) ) ) ) ).
tt(t2_jordan1f,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A C)) (k3_topreal1 2 D)))  &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski A C) (k2_matrix_1 E)) &  ((r1_xxreal_0 B C) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 B F) &  ((r1_xxreal_0 F C) &  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A F)) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A C)) (k3_topreal1 2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan1g,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ((r1_goboard1 A B C) => (r1_goboard1 A (k1_finseq_5 A B D) C)) ) ) ) ) ) ) ) ).
tt(t2_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = B) )  =>  ((k2_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k2_tarski A B))) = (k1_rltopsp1 (k15_euclid 2) A B)) ) ) ) ) ) ).
tt(t2_jordan1i,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan9 B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) 1)) ) ) ) ) ).
tt(t2_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 E D))  &  ((r1_xxreal_0 E (k1_matrix_1 A)) & (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C E)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan1k,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (? [E:$i] :  ((m1_subset_1 E A) &  (D = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ((r1_xxreal_0 (k17_euclid A) D) & (r1_xxreal_0 (k17_euclid B) D)) )  => (r1_xxreal_0 (k17_euclid C) D)) ) ) ) ) ) ) ) ) ).
tt(t2_jordan21,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_0_jordan21 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t2_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k2_jordan19 A) B) (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan9 A k6_numbers))))) ) ) ) ).
tt(t2_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (r1_xxreal_0 1 (k3_finseq_1 (k3_jordan3 A B)))) ) ) ) ).
tt(t2_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_pcomps_1 (k14_euclid 2))) (u1_struct_0 (k3_pcomps_1 (k14_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid 2))) (u1_struct_0 (k3_pcomps_1 (k14_euclid 2))))))) )  =>  ((r1_funct_2 (u1_struct_0 (k3_pcomps_1 (k14_euclid 2))) (u1_struct_0 (k3_pcomps_1 (k14_euclid 2))) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k1_jordan24 A)) =>  ((v2_funct_2 B (u1_struct_0 (k3_pcomps_1 (k14_euclid 2)))) & (v1_jordan24 B (k14_euclid 2))) ) ) ) ) ) ).
tt(t2_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden B (k2_finseq_1 A)) =>  ((k7_partfun1 k1_numbers (k4_struct_0 (k15_euclid A)) B) = k6_numbers) ) ) ) ) ) ).
tt(t2_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( ( ((k17_euclid A) = (k17_euclid B))  |  ((k18_euclid A) = (k18_euclid B)) )  &  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (~  ((k17_euclid C) = (k17_euclid D)) )  &  (~  ((k18_euclid C) = (k18_euclid D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B A) =>  ((r1_xxreal_0 (k2_xcmplx_0 B B) A) |  ( ((k4_nat_d A B) = (k6_xcmplx_0 A B))  &  ((k4_nat_d A B) = (k7_nat_d A B)) ) ) ) ) ) ) ) ).
tt(t2_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( ((k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid A) C D)) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 E)) (k1_rlvect_1 (k15_euclid A) C E)))  &  ( (~  (D = E) )  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan5b,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k1_nat_1 A 1) B) => (r1_xxreal_0 1 (k7_nat_d B A))) ) ) ) ) ).
tt(t2_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C A) &  ((r1_topreal1 (k15_euclid 2) D E A) &  (B = (k1_tarski C)) ) )  =>  ((k1_jordan5c A B D E) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_jordan5d,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 3 A) =>  ((k4_nat_d A (k7_nat_d A 1)) = 1) ) ) ) ).
tt(t2_jordan6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc D A) &  (C = (k9_subset_1 (u1_struct_0 A) D B)) )  => (v4_pre_topc C (k1_pre_topc A B))) ) ) ) ) ) ) ) ) ).
tt(t2_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r1_jordan6 A B (k18_pscomp_1 A)))  =>  (B = (k18_pscomp_1 A)) ) ) ) ) ) ).
tt(t2_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ((r1_goboard1 B C D) => (r1_goboard1 B (k2_rfinseq B A C) D)) ) ) ) ) ) ) ) ) ).
tt(t2_jordan9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k17_finseq_1 A D B) = (k17_finseq_1 A D C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_jordan_a,ax, (! [A:$i] :  ( ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski B A) => (r2_hidden (k5_seq_4 B) A)) ) ) ) ) ).
tt(t2_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A)))  & (r1_xxreal_0 (k18_euclid (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) A B) (k10_real_1 1 2))) (k18_euclid A))) ) ) ) ) ) ).
tt(t2_knaster,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r1_abian B (k1_abian A D C)) => (r1_abian (k1_funct_1 D B) (k1_abian A D C))) ) ) ) ) ) ) ).
tt(t2_kolmog01,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( ((k3_xcmplx_0 A A) = A)  &  ( (~  (A = k6_numbers) )  &  (~  (A = 1) ) ) ) ) ) ) ).
tt(t2_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( (~ (r1_xboole_0 A B))  &  ( (~ (r1_xboole_0 C D))  & (r1_xboole_0 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) ) ) ) ) ) ) ).
tt(t2_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_kurato_1 A B) = (k2_xboole_0 (k1_kurato_1 A B) (k1_kurato_1 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t2_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( (B = D)  &  ((r2_hidden C (k9_metric_1 (k14_euclid A) B E)) & (r1_xxreal_0 E (k12_euclid (k5_algstr_0 (k15_euclid A) C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r1_lang1 A B C) => (r2_lang1 A (k1_pre_poly (u1_struct_0 A) (k1_pre_poly (u1_struct_0 A) D (k3_pre_poly (u1_struct_0 A) B)) E) (k1_pre_poly (u1_struct_0 A) (k1_pre_poly (u1_struct_0 A) D C) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_laplace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) D D) =>  ((r2_hidden B (k4_finseq_1 E)) =>  ((k3_finseq_1 (k9_matrix_2 B C D A E)) = (k7_nat_d D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k1_group_3 A)) <=>  (? [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  &  (B = C) ) ) ) ) ) ) ).
tt(t2_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 (k1_latsum_1 A B))) & (r1_relset_1 (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 B) (u1_orders_2 (k1_latsum_1 A B)))) ) ) ) ) ).
tt(t2_lattice2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((k2_partfun1 A B D C) = (k2_partfun1 A B E C))  <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F C) =>  ((k1_funct_1 E F) = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_lattice3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_lattice3 A))) =>  ((r1_lattices (k1_lattice3 A) B C) <=> (r1_tarski B C)) ) ) ) ) ) ).
tt(t2_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C))) & (r1_tarski C (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t2_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k2_zfmisc_1 (k3_tarski A) (k3_tarski B)) = (k3_tarski (a_2_0_lattice5 A B))) ) ) ) ) ).
tt(t2_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (C = D) )  =>  ( ( ((r1_lattice6 A C B) & (r1_lattice6 A D B))  =>  (B = (k4_lattices A D C)) )  &  ( ((r1_lattice6 A B C) & (r1_lattice6 A B D))  =>  (B = (k3_lattices A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_orders_2 A B C) & (r1_xxreal_0 (k1_lattice7 A C) (k1_lattice7 A B))) ) ) ) ) ) ) ) ).
tt(t2_lattice8,ax, (! [A:$i] :  ( ((v7_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v1_yellow11 A)) ) ).
tt(t2_lexbfs,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 B C) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k7_nat_d C A) (k7_nat_d C B))) ) ) ) ) ) ) ) ) ).
tt(t2_lfuzzy_0,ax, (! [A:$i] :  ( ((v1_lfuzzy_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_lfuzzy_0 B) & (l1_orders_2 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B))) ) ) ) ) ) ).
tt(t2_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k8_lfuzzy_0 A B C E F) = (k8_lfuzzy_0 A B D E F)) ) ) ) )  => (r2_relset_1 (k2_zfmisc_1 A B) k1_numbers C D)) ) ) ) ) ) ) ) ) ).
tt(t2_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((r4_limfunc2 A B) &  ((k2_limfunc2 A B) = C) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E B))  & (r2_hidden E (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) )  &  ( ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E B))  & (r2_hidden E (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) )  =>  ((r4_limfunc2 A B) &  ((k2_limfunc2 A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t2_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v7_valued_0 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) ) ) ) ).
tt(t2_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 B) &  ( (~ (r1_xxreal_0 A (k2_seq_2 B)))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 A (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A (k1_seq_1 B D))) k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 1 (k2_nat_1 D 1)) (k18_complex1 (k9_real_1 A (k1_seq_1 B D)))))  & (r2_hidden (k1_seq_1 B D) (k9_xtuple_0 C))) ) ) )  =>  ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  &  ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 C)) & (r1_tarski (k10_xtuple_0 B) (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A)))) ) ) ) ) ) ) ) ) ) ).
tt(t2_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ((r1_tarski (k2_relset_1 k1_numbers C) (k7_subset_1 k1_numbers (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B A)) D)) =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B A))) &  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) &  ((r1_tarski (k2_relset_1 k1_numbers C) (k7_subset_1 k1_numbers (k1_relset_1 k1_numbers B) D)) & (r1_tarski (k2_relset_1 k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers C B)) (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  &  ((v1_lmod_5 C A B) & (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ) ).
tt(t2_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_vectsp_1 A (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C) (u1_vectsp_1 A C)))) =>  ( (D = E)  =>  ((k4_vectsp_1 A C B D) = (k4_vectsp_1 A (g1_vectsp_1 A (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C) (u1_vectsp_1 A C)) B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_vectsp_6 E A B D) =>  ( (~ (r2_hidden C D))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_funct_2 A (u1_struct_0 B) C (k2_funcsdom A (u1_struct_0 B) k1_numbers (k9_funct_2 A (u1_struct_0 B)) (k3_lopban_1 A B) (k1_domain_1 k1_numbers (k9_funct_2 A (u1_struct_0 B)) E D))) <=>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A (u1_struct_0 B) C F) = (k1_rlvect_1 B (k3_funct_2 A (u1_struct_0 B) D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) &  ((v2_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_lopban_1 E B C) &  ((v2_lopban_1 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) )  =>  ( ((v1_funct_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 C)) &  ((v13_vectsp_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v1_lopban_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) &  ((v2_lopban_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_xxreal_0 (k1_normsp_0 C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) F)) (k8_real_1 (k8_real_1 (k1_seq_1 (k15_lopban_1 B C) E) (k1_seq_1 (k15_lopban_1 A B) D)) (k1_normsp_0 A F))) & (r1_xxreal_0 (k1_seq_1 (k15_lopban_1 A C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) (k8_real_1 (k1_seq_1 (k15_lopban_1 B C) E) (k1_seq_1 (k15_lopban_1 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k4_normsp_0 A B) C))) ) ) ) ) ) ).
tt(t2_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) B D) = C) ) )  =>  ((k6_normsp_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t2_lopban_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v1_comseq_2 A) & (r1_xxreal_0 k6_numbers B))  =>  ((k5_rinfsup1 (k26_valued_1 k5_numbers k1_numbers A B)) = (k8_real_1 B (k5_rinfsup1 A))) ) ) ) ) ) ).
tt(t2_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_lopban_5 A B C) = (k5_rusub_4 A (k1_lopban_5 A (k4_struct_0 A) C) B)) ) ) ) ) ) ) ).
tt(t2_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k1_lopclset A)) => (v4_pre_topc B A)) ) ) ) ) ).
tt(t2_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 k1_numbers B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers B) B)))) )  =>  ( ( (C = (k4_struct_0 A))  &  ( (D = (k1_realset1 (u1_algstr_0 A) B))  &  (E = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_rlvect_1 A) (k2_zfmisc_1 k1_numbers B))) ) )  =>  ((v2_rlvect_1 (g1_rlvect_1 B C D E)) &  ((v3_rlvect_1 (g1_rlvect_1 B C D E)) &  ((v4_rlvect_1 (g1_rlvect_1 B C D E)) &  ((v5_rlvect_1 (g1_rlvect_1 B C D E)) &  ((v6_rlvect_1 (g1_rlvect_1 B C D E)) &  ((v7_rlvect_1 (g1_rlvect_1 B C D E)) & (v8_rlvect_1 (g1_rlvect_1 B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (D = (k1_relset_1 A E))  &  ((r1_mesfunc1 A B E D) & (v6_supinf_2 E)) )  =>  ((r2_hidden (k7_mesfunc5 A B C E) k1_numbers) <=> (r1_mesfunc5 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space (k1_series_1 k1_numbers B C) A)) D) (k10_real_1 1 A)) (k7_real_1 (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space B A)) D) (k10_real_1 1 A)) (k4_power (k1_seq_1 (k3_series_1 (k1_lp_space C A)) D) (k10_real_1 1 A))))) ) ) ) ) ) ) ) ) ).
tt(t2_ltlaxio1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean A (k6_xboolean B C)) (k6_xboolean (k4_xboolean A B) C)) = 1) ) ) ) ) ) ) ).
tt(t2_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A B D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t2_margrel1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v3_finseq_1 (k1_tarski A)) & (v2_card_3 (k1_tarski A))) ) ) ).
tt(t2_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_mathmorp A B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t2_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 C)) =>  ((k3_matrix_1 k1_numbers (k4_matrixr1 C) A B) = (k1_real_1 (k3_matrix_1 k1_numbers C A B))) ) ) ) ) ) ) ) ).
tt(t2_matrix11,ax, ( ((k2_sgraph1 (k2_finseq_1 k1_xboole_0)) = k1_xboole_0)  &  ((k2_sgraph1 (k2_finseq_1 1)) = k1_xboole_0) ) ).
tt(t2_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) B A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) B A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r2_hidden C (k4_finseq_1 F)) &  ((r2_hidden D (k4_finseq_1 F)) &  ((r2_hidden H (k4_finseq_1 F)) &  (G = (k1_matrix12 B A E F C D)) ) ) )  =>  ( ( (H = C)  =>  ((k8_matrix_1 (u1_struct_0 E) G H) = (k8_matrix_1 (u1_struct_0 E) F D)) )  &  ( ( (H = D)  =>  ((k8_matrix_1 (u1_struct_0 E) G H) = (k8_matrix_1 (u1_struct_0 E) F C)) )  &  (~  ( (~  (H = C) )  &  ( (~  (H = D) )  &  (~  ((k8_matrix_1 (u1_struct_0 E) G H) = (k8_matrix_1 (u1_struct_0 E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v2_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A))  <=>  ((v1_matrix_2 (k5_matrix_1 A (u1_struct_0 B) C) A B) & (m1_matrix_1 (k5_matrix_1 A (u1_struct_0 B) C) (u1_struct_0 B) A A)) ) ) ) ) ) ) ) ).
tt(t2_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k3_finseq_1 (k3_fvsum_1 A B C)) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t2_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k6_matrix_3 A D (k1_group_1 A)) = D)  &  ((k6_matrix_3 A (k6_matrix_3 A D C) B) = (k6_matrix_3 A D (k8_group_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k9_fvsum_1 A B (k4_algstr_0 A (k1_group_1 A))) = (k5_fvsum_1 A B)) ) ) ) ) ).
tt(t2_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_matrix17 (u1_struct_0 B) (k2_matrix_2 (u1_struct_0 B) A A C) (k5_finseq_2 (u1_struct_0 B) A C))) ) ) ) ) ) ).
tt(t2_matrix_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) => (v1_matrix_1 (k2_finseq_2 B (k2_finseq_2 C A)))) ) ) ) ) ).
tt(t2_matrix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k14_matrix_1 B A (k2_matrix_2 (u1_struct_0 B) A A C) (k2_matrix_2 (u1_struct_0 B) A A D)) = (k2_matrix_2 (u1_struct_0 B) A A (k1_algstr_0 B C D))) ) ) ) ) ) ) ) ) ).
tt(t2_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k3_matrix_3 A B C) = (k3_matrix_3 A C B)) ) ) ) ) ) ) ) ).
tt(t2_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k3_matrix_3 A B (k2_matrix_3 A B)) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ).
tt(t2_matrix_5,ax, ((k4_struct_0 k1_complfld) = k6_numbers) ).
tt(t2_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  =>  ((k4_matrix_3 A B (k1_matrix_3 A (k1_matrix_1 B) (k1_matrix_1 B))) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ) ).
tt(t2_matrix_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ( (A = (k10_finseq_1 1 2))  |  (A = (k10_finseq_1 2 1)) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) &  ((v3_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 2) (k2_finseq_1 2))))) ) ) ) ) ) ).
tt(t2_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((v1_matrix_8 (k11_matrix_1 B A) A B) & (v2_matrix_8 (k11_matrix_1 B A) A B)) ) ) ) ) ).
tt(t2_matrix_9,ax, ( ((k1_funct_1 (k3_finseq_5 (k1_finseq_2 2)) 1) = 2)  &  ((k1_funct_1 (k3_finseq_5 (k1_finseq_2 2)) 2) = 1) ) ).
tt(t2_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k4_wsierp_1 B A (k8_finseq_1 B C D)) = (k8_finseq_1 B (k4_wsierp_1 B A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k12_matrix_3 A B (k2_matrixj2 B C A)) = (k1_laplace B (k4_group_1 B) C A)) ) ) ) ) ) ) ).
tt(t2_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( (A = C)  &  (B = D) )  =>  ((k8_real_1 A B) = (k8_group_1 k2_vectsp_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( (E = (k1_funct_1 D B))  &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 D)) &  ((k3_finseq_1 E) = (k1_matrix_1 D)) ) ) ) ) )  =>  ((k3_matrix_1 A D B C) = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  =>  (! [E:$i] :  ( ((v1_vectsp_7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))))  =>  (! [F:$i] :  ( ((v1_vectsp_7 F A D) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 D))))  =>  ((v1_vectsp_7 (k2_xboole_0 E F) A (k1_vectsp_5 A B C D)) & (m1_subset_1 (k2_xboole_0 E F) (k1_zfmisc_1 (u1_struct_0 (k1_vectsp_5 A B C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C (k1_nat_1 A 1) B) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_matrix_1 D) = (k1_matrix_1 (k1_matrlin C (k1_nat_1 A 1) D))) )  &  ( (E = (k9_finseq_1 (k1_funct_1 D (k1_nat_1 A 1))))  =>  ((k1_matrix_1 D) = (k1_matrix_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_matroid0,ax, (! [A:$i] :  ( ((v1_matroid0 A) & (l1_pre_topc A))  =>  ( (~ (v3_pencil_1 A))  <=> (r2_hidden k1_xboole_0 (k1_matroid0 A))) ) ) ).
tt(t2_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (? [F:$i] :  ((m2_finseq_1 F A) &  ( ((k3_finseq_1 F) = C)  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 C)) =>  ( ((r2_hidden G (k2_finseq_1 B)) =>  ((k1_funct_1 F G) = D) )  &  ( (~ (r2_hidden G (k2_finseq_1 B)))  =>  ((k1_funct_1 F G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  ((k1_partfun3 (k7_finseq_1 A B)) = (k7_finseq_1 (k1_partfun3 A) (k1_partfun3 B))) ) ) ) ) ).
tt(t2_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_vectsp_6 B k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C (k15_euclid A)) =>  ((r1_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 k2_vectsp_1) C B) =>  ((k3_rlvect_2 (k15_euclid A) C) = (k1_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) B)) ) ) ) ) ) ) ) ).
tt(t2_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_matrix_1 C B) & (m1_matrix_1 C (u1_struct_0 B) A A))  =>  ((k5_matrix_1 A (u1_struct_0 B) C) = C) ) ) ) ) ) ) ).
tt(t2_mazurulm,ax, ((k6_measure6 k2_urysohn1) = (k1_xxreal_1 k6_numbers 1)) ).
tt(t2_mboolean,ax, (! [A:$i] : (r6_pboole A (k1_mboolean A (k1_pboole A)) (k7_funcop_1 A (k1_tarski k1_xboole_0)))) ).
tt(t2_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (m1_subset_1 (k2_tarski B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(t2_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_measure2 C A B) =>  ((r2_hidden (k6_setfam_1 A C) B) & (r2_hidden (k5_setfam_1 A C) B)) ) ) ) ) ) ).
tt(t2_measure3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k12_supinf_2 (k18_supinf_2 A) C) = (k12_supinf_2 (k18_supinf_2 B) C)) ) )  =>  ((k19_supinf_2 A) = (k19_supinf_2 B)) ) ) ) ) ) ).
tt(t2_measure4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 B D (k2_nat_1 E 1)) = (k2_xboole_0 (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B D E))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B E k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k8_nat_1 B E (k2_nat_1 F 1)) = (k6_subset_1 (k8_nat_1 B C (k2_nat_1 F 1)) (k8_nat_1 B D F))) ) ) )  =>  ((k3_tarski (k2_relset_1 B C)) = (k3_tarski (k2_relset_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C k1_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_measure6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) => (r1_xxreal_0 k1_supinf_2 (k19_supinf_2 A))) ) ) ).
tt(t2_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A B) (k12_supinf_2 (k18_supinf_2 A) B))) ) ) ) ) ).
tt(t2_measure8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  ((v1_mesfunc9 A) &  ((k19_supinf_2 A) = (k3_mesfunc9 A)) ) ) ) ) ).
tt(t2_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r2_hidden (k2_xxreal_3 B) A) <=> (r2_hidden B (k4_member_1 A))) ) ) ) ) ).
tt(t2_membered,ax, (! [A:$i] :  ((v2_membered A) => (r1_tarski A k7_numbers)) ) ).
tt(t2_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) & (l1_memstr_0 B A)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t2_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k17_euclid (k1_rlvect_1 (k15_euclid 2) A B)) = (k11_binop_2 B (k17_euclid A)))  &  ((k18_euclid (k1_rlvect_1 (k15_euclid 2) A B)) = (k11_binop_2 B (k18_euclid A))) ) ) ) ) ) ).
tt(t2_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (r1_xxreal_0 (k12_supinf_2 A D) (k12_supinf_2 B D))) )  =>  ((r1_xxreal_0 (k12_supinf_2 (k3_rinfsup2 A) C) (k12_supinf_2 (k3_rinfsup2 B) C)) & (r1_xxreal_0 (k12_supinf_2 (k4_rinfsup2 A) C) (k12_supinf_2 (k4_rinfsup2 B) C))) ) ) ) ) ) ) ) ).
tt(t2_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_relset_1 A k1_numbers (k26_valued_1 A k1_numbers (k5_comseq_3 A B) C) (k5_comseq_3 A (k25_valued_1 A k2_numbers B C))) & (r2_relset_1 A k1_numbers (k26_valued_1 A k1_numbers (k6_comseq_3 A B) C) (k6_comseq_3 A (k25_valued_1 A k2_numbers B C)))) ) ) ) ) ) ) ).
tt(t2_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k2_mesfun7c A B))) =>  ((k12_supinf_2 (k2_mesfun7c A B) C) = (k7_supinf_2 (k17_supinf_2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C))))) ) ) ) ) ) ) ) ).
tt(t2_mesfun9c,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A B))))) )  =>  ((v1_mesfunc8 D A B) => (v1_mesfunc8 (k1_mesfun9c A B D C) A B)) ) ) ) ) ) ).
tt(t2_mesfunc1,ax, (k4_numbers = (k4_subset_1 k1_numbers k1_mesfunc1 k5_numbers)) ).
tt(t2_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_valued_0 B) | (v3_valued_0 C))  =>  ( ((k1_relset_1 A (k3_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ((k1_relset_1 A (k4_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t2_mesfunc3,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (A = B)  =>  ((k4_extreal1 A) = (k18_rvsum_1 B)) ) ) ) ) ) ).
tt(t2_mesfunc4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ( ((v1_prob_2 F) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k7_numbers) =>  ( ((r1_mesfunc2 A B E) &  ( (! [I:$i] :  ((r2_hidden I (k9_xtuple_0 E)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 E I))) )  &  ((r1_mesfunc3 A B E F G) &  ( ((k4_finseq_1 H) = (k4_finseq_1 F))  &  ( (! [I:$i] :  ((v7_ordinal1 I) =>  ((r2_hidden I (k4_finseq_1 H)) =>  ((k12_supinf_2 H I) = (k1_extreal1 (k12_supinf_2 G I) (k12_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers F C) I))) ) ) )  &  ((k3_finseq_1 F) = D) ) ) ) ) )  =>  ( ((k9_xtuple_0 E) = k1_xboole_0)  |  ((k1_mesfunc3 A B C E) = (k4_extreal1 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mesfunc5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) => (r1_xxreal_0 (k4_supinf_2 B A) (k3_extreal1 (k4_supinf_2 A B)))) ) ) ) ).
tt(t2_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden (k1_relset_1 A D) B) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A D)) =>  ((k12_supinf_2 D F) = E) ) ) )  => (r1_mesfunc2 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k6_mesfunc1 A C D) B) (k6_mesfunc1 A (k2_partfun1 A k7_numbers C B) D))) ) ) ) ) ) ) ).
tt(t2_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k8_nat_1 (k9_setfam_1 A) (k4_setlim_1 A B) C) = (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) (k10_nat_1 (k9_setfam_1 A) B C))))  &  ((k8_nat_1 (k9_setfam_1 A) (k2_setlim_1 A B) C) = (k6_setfam_1 A (k2_relset_1 (k9_setfam_1 A) (k10_nat_1 (k9_setfam_1 A) B C)))) ) ) ) ) ) ) ) ).
tt(t2_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v4_mesfunc5 B) & (v3_mesfunc5 C))  =>  ((k1_relset_1 A (k4_mesfunc1 A B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ) ).
tt(t2_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_metric_1 A B C) = k6_numbers)  =>  (B = C) ) ) ) ) )  <=> (v7_metric_1 A)) ) ) ).
tt(t2_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_metric_2 A B)) <=> (r3_metric_2 A C B)) ) ) ) ) ) ) ).
tt(t2_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  ((k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) C D) = (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) D C)) ) ) ) ) ) ) ) ) ).
tt(t2_metric_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 k6_numbers (k1_metric_1 A A B C D))) ) ) ) ) ) ) ) ) ).
tt(t2_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)) (u1_struct_0 (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))))))) )  =>  ( (E = (k5_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))  => (v3_tops_2 E (k1_pre_topc A C) (k1_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B (k15_euclid A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc C B k3_topmetr) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( (E = F)  &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k1_funct_1 D F) = (k1_rlvect_1 (k15_euclid A) F G)) ) ) ) ) ) ) )  & (v5_pre_topc D B (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mfold_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski C B) =>  ((k8_relat_1 (k6_relat_1 B A) C) = (k8_relat_1 A C)) ) ) ) ) ) ).
tt(t2_midsp_1,ax,(r1_funct_2 (k2_zfmisc_1 (u1_struct_0 k2_midsp_1) (u1_struct_0 k2_midsp_1)) (u1_struct_0 k2_midsp_1) (k2_zfmisc_1 1 1) 1 (u1_midsp_1 k2_midsp_1) k9_funct_5)).
tt(t2_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 C))))) )  =>  ((r1_midsp_2 A C D) =>  ((k2_binop_1 A A (u1_struct_0 C) D B B) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r2_hidden A (k2_finseq_1 B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (B = (k2_nat_1 (k2_nat_1 C 1) D))  &  (A = (k2_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_mmlquery B D C) <=> (r2_hidden D (k1_mmlquery A C B))) ) ) ) ) ) ) ) ).
tt(t2_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_vectsp_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( ((v1_mod_2 E A B C) & (v1_mod_2 F A C D))  => (v1_mod_2 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r1_tarski (k1_vectsp_6 A B C) D) &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (~  ((v2_funct_1 E) &  ( ((k10_xtuple_0 E) = D)  &  ((k4_vectsp_6 A B C) = (k4_rlvect_1 B (k3_vectsp_6 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( ((g2_algstr_0 (u1_struct_0 (k2_mod_4 A)) (u1_algstr_0 (k2_mod_4 A)) (u2_struct_0 (k2_mod_4 A))) = (g2_algstr_0 (u1_struct_0 A) (u1_algstr_0 A) (u2_struct_0 A)))  &  ( ( ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (v13_algstr_0 A)) )  => (r1_funct_2 (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 (k2_mod_4 A)) (u1_struct_0 A) (u1_struct_0 A) (k5_vectsp_1 (k2_mod_4 A)) (k5_vectsp_1 A)))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_mod_4 A))) <=> (m1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(t2_modal_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (A = (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t2_modcat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  ((m5_modcat_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v2_mod_2 E B) & (m1_mod_2 E B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~ (v2_modelc_1 A))  &  ( (~ (v3_modelc_1 A))  &  ( (~ (v4_modelc_1 A))  &  ( (~ (v5_modelc_1 A))  &  ( (~ (v6_modelc_1 A))  &  (~ (v7_modelc_1 A)) ) ) ) ) ) ) ) ) ).
tt(t2_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ( (~ (v2_modelc_2 A))  &  ( (~ (v3_modelc_2 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (k25_modelc_2 k43_modelc_2)) =>  ((r2_hidden A (u2_modelc_3 B C)) =>  ( ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) )  |  ((r8_modelc_2 D (k14_modelc_3 B C)) <=>  ((r8_modelc_2 D (k14_modelc_3 B (k5_modelc_3 B C A))) | (r8_modelc_2 D (k14_modelc_3 B (k6_modelc_3 B C A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 A) =>  ((r2_hidden C (k2_finseq_1 B)) <=> (r2_hidden (k24_binop_2 A C) (k2_finseq_1 (k24_binop_2 A B)))) ) ) ) ) ) ) ) ).
tt(t2_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v8_monoid_0 B A) <=>  ((v6_monoid_0 B A) & (v7_monoid_0 B A)) ) ) ) ) ) ).
tt(t2_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F E A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 E A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G E B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 E B)))) )  =>  (! [H:$i] :  ((r2_hidden H E) =>  ((k1_monoid_1 (k8_monoid_1 A B C D E) F G H) = (k1_binop_1 D (k1_funct_1 F H) (k1_funct_1 G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = k1_xboole_0)  =>  ( (B = k1_xboole_0)  |  ((k1_morph_01 A C B) = C) ) ) ) ) ) ) ) ) ).
tt(t2_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k4_msafree A B)) =>  ((r2_hidden C (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) & (r2_hidden D (k13_finseq_1 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B)))))) ) ) ) ) ) ) ) ).
tt(t2_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k2_msafree2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (~  ((k2_msualg_1 A C) = B) ) ) ) ) ) ) ) ) ).
tt(t2_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden (k4_tarski A D) (u1_struct_0 (k5_msafree B C))) <=> (r2_hidden A (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(t2_msafree,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((r2_hidden C A) =>  ( (~  ( (~  ((k1_funct_1 B C) = k1_xboole_0) )  &  ((k1_funct_1 (k3_msafree A B) C) = k1_xboole_0) ) )  &  (~  ( (~  ((k1_funct_1 (k3_msafree A B) C) = k1_xboole_0) )  &  ((k1_funct_1 B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t2_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_orders_2 A F E) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 B) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C E)) (u3_msualg_1 B (k5_pralg_2 (u1_struct_0 A) B C F))) =>  ((r8_pboole (u1_struct_0 B) G (k1_msalimit A B C D E F)) => (r1_msualg_3 B (k5_pralg_2 (u1_struct_0 A) B C E) (k5_pralg_2 (u1_struct_0 A) B C F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  (~  ((k1_funct_1 C k1_xboole_0) = (k4_tarski E D)) ) ) ) ) )  &  (~ (r2_hidden (k1_funct_1 C k1_xboole_0) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(t2_msinst_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  ((r2_hidden C (k2_msinst_1 B A)) =>  ((r2_hidden (u3_msualg_1 B C) (k9_funct_2 (u1_struct_0 B) (k1_zfmisc_1 A))) & (r2_hidden (u4_msualg_1 B C) (k1_funct_2 (u4_struct_0 B) (k4_partfun1 (k4_partfun1 k5_numbers A) A)))) ) ) ) ) ) ) ) ).
tt(t2_msscyc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ((k1_graph_2 B 1 A) = (k1_graph_2 (k7_finseq_1 B C) 1 A)) ) ) ) ) ) ) ) ).
tt(t2_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 1 D) =>  ( (~  ( (? [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) &  ((k8_msafree2 A B C E) = D) ) )  &  (! [E:$i] :  ( ((v7_graph_1 E (k4_msscyc_2 A)) & (m1_graph_1 E (k4_msscyc_2 A)))  =>  (~  ( ((k3_finseq_1 E) = D)  &  ((k1_funct_1 (k7_graph_2 (k4_msscyc_2 A) E) (k2_nat_1 (k3_finseq_1 E) 1)) = C) ) ) ) ) ) )  &  (~  ( (? [E:$i] :  ( ((v7_graph_1 E (k4_msscyc_2 A)) & (m1_graph_1 E (k4_msscyc_2 A)))  &  ( ((k3_finseq_1 E) = D)  &  ((k1_funct_1 (k7_graph_2 (k4_msscyc_2 A) E) (k2_nat_1 (k3_finseq_1 E) 1)) = C) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k11_msafree A B)) C)) =>  (~  ((k8_msafree2 A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden B C) => (r1_tarski (k8_setfam_1 A C) B)) ) ) ) ) ).
tt(t2_mssublat,ax, (! [A:$i] :  ((k3_funct_2 k5_numbers (k3_finseq_2 (k1_tarski A)) (k7_finseq_2 A) 1) = (k9_finseq_1 A)) ) ).
tt(t2_msualg_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ((v1_funct_1 (k1_partfun1 A B B C D E)) &  ((v1_funct_2 (k1_partfun1 A B B C D E) (k9_xtuple_0 D) C) & (m1_subset_1 (k1_partfun1 A B B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 D) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A C)) =>  (! [E:$i] :  ((m3_pboole E (u1_struct_0 A) (u3_msualg_1 A C)) =>  ((r2_pboole (u1_struct_0 A) D E) => (r1_tarski (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) D)) B) (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) E)) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  ( ((k9_xtuple_0 (k8_pboole E F)) = A)  &  (! [G:$i] :  ((r2_hidden G A) =>  ((k1_funct_1 (k8_pboole E F) G) = (k3_relat_1 (k1_funct_1 E G) (k1_funct_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v2_msualg_4 D A C) &  ((v3_msualg_4 D A C) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A C))) )  =>  (! [E:$i] :  (~  ((r2_hidden E (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k4_msualg_4 A C D))) B)) &  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  (~  (E = (k6_msualg_4 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_relset_1 A A (k1_msualg_5 A B) B)) ) ) ).
tt(t2_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k3_msualg_1 A C B)) =>  ( ((k9_xtuple_0 D) = (k4_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 (k1_msualg_1 A C))) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 (u3_msualg_1 A B) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v1_msualg_4 (k6_pboole A B B) A B) & (m1_msualg_4 (k6_pboole A B B) A B B)) ) ) ) ) ).
tt(t2_msualg_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_msualg_5 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_msualg_5 A))) =>  (! [D:$i] :  ( ((v1_partfun1 D A) &  ((v3_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [E:$i] :  ( ((v1_partfun1 E A) &  ((v3_relat_2 E) &  ((v8_relat_2 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((r3_lattices (k2_msualg_5 A) B C) <=> (r1_relset_1 A A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_msualg_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_tarski B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))))) )  =>  ((k2_relset_1 (k1_tarski B) C) = (k1_tarski B)) ) ) ) ) ) ).
tt(t2_msuhom_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_tarski (k3_finseq_2 B) (k3_finseq_2 A))) ) ) ).
tt(t2_multop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_zfmisc_1 A B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_zfmisc_1 A B C) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I C) =>  ((k3_funct_2 (k3_zfmisc_1 A B C) D E (k4_domain_1 A B C G H I)) = (k3_funct_2 (k3_zfmisc_1 A B C) D F (k4_domain_1 A B C G H I))) ) ) ) ) ) )  => (r2_funct_2 (k3_zfmisc_1 A B C) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k6_subset_1 B C)) <=>  ((r1_xxreal_0 C A) &  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ) ) ) ).
tt(t2_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B C) & (v1_nagata_1 C A))  => (v1_nagata_1 B A)) ) ) ) ) ) ) ).
tt(t2_nagata_2,ax,(v3_funct_2 k1_nagata_2 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers)).
tt(t2_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 k6_numbers A)) ) ).
tt(t2_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_nat_d k6_numbers A) = k6_numbers) ) ) ).
tt(t2_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A 1))  => (r1_xxreal_0 B (k1_newton A B))) ) ) ) ) ).
tt(t2_nat_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ((r1_xxreal_0 (k11_binop_2 A A) B) & (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t2_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~  ((v1_abian A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (v1_abian C))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (A = (k24_binop_2 (k2_newton 2 B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (B = (k2_nat_1 (k3_nat_1 A (k3_nat_d B A)) (k4_nat_d B A))) ) ) ) ) ) ).
tt(t2_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ((k2_lattices k3_nat_lat A B) = (k6_nat_d A B)) ) ) ) ) ).
tt(t2_nattra_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 A A C C) C))))  =>  ( (G = (k1_realset1 E C))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k8_mcart_1 B B D D) D))))  =>  ( (H = (k1_realset1 F D))  =>  ((k2_nattra_1 A B C D G H) = (k1_realset1 (k7_cat_2 A B E F) (k8_mcart_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (m1_ncfcont1 (a_3_0_ncfcont1 A B C) A B)) ) ) ) ) ) ) ).
tt(t2_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C)))))  =>  ( ((r2_ncfcont2 A C D E) & (r1_tarski B A))  => (r2_ncfcont2 B C D E)) ) ) ) ) ) ) ) ) ).
tt(t2_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_nfcont_1 D A C) =>  (~ (r1_tarski D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_ndiff_1 B A C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v2_relat_1 F) &  ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k1_numbers) &  ((v1_fdiff_1 F k6_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v3_funct_1 G) &  ((v1_funct_2 G k5_numbers (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) G) = (k1_tarski D))  & (r1_tarski (k2_relset_1 (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B E F) G)) (k1_relset_1 (u1_struct_0 B) C)))  =>  ((v3_normsp_1 (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B E F) G) C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) G C)) (k37_valued_1 k5_numbers k1_numbers F)) A) &  ((k17_lopban_1 B A (k3_ndiff_1 B A C D) E) = (k6_normsp_1 A (k1_ndiff_1 A (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) (k2_normsp_1 B (k2_ndiff_1 B E F) G) C) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) G C)) (k37_valued_1 k5_numbers k1_numbers F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_ndiff_1 A (k1_valued_0 (u1_struct_0 A) D B) (k1_valued_0 k1_numbers C B)) (k1_valued_0 (u1_struct_0 A) (k1_ndiff_1 A D C) B))) ) ) ) ) ) ) ) ).
tt(t2_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (C = B)  =>  ((r1_ndiff_4 A B D) <=> (r1_ndiff_3 (k4_real_ns1 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_ndiff_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ( ((k7_partfun1 (u1_struct_0 A) B k6_numbers) = (k4_struct_0 A))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 D (k17_complex1 E)))  => (r1_xxreal_0 (k1_normsp_0 A (k7_partfun1 (u1_struct_0 A) B E)) (k11_binop_2 C (k17_complex1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_neckla_2,ax, ((u1_orders_2 (k4_necklace 4)) = (k4_enumset1 (k4_tarski k6_numbers 1) (k4_tarski 1 k6_numbers) (k4_tarski 1 2) (k4_tarski 2 1) (k4_tarski 2 3) (k4_tarski 3 2))) ).
tt(t2_neckla_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k6_partfun1 (k2_enumset1 A B C D)) = (k2_enumset1 (k4_tarski A A) (k4_tarski B B) (k4_tarski C C) (k4_tarski D D))) ) ) ) ) ).
tt(t2_necklace,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k2_zfmisc_1 (k1_enumset1 A B C) (k1_enumset1 D E F)) = (k7_enumset1 (k4_tarski A D) (k4_tarski A E) (k4_tarski A F) (k4_tarski B D) (k4_tarski B E) (k4_tarski B F) (k4_tarski C D) (k4_tarski C E) (k4_tarski C F))) ) ) ) ) ) ) ).
tt(t2_net_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_petri B) =>  ((m1_subset_1 A (u1_struct_0 B)) =>  ( ((u1_struct_0 B) = k1_xboole_0)  | (m1_subset_1 A (k2_net_1 B))) ) ) ) ) ).
tt(t2_newton,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k3_finseq_1 (k10_rvsum_1 B A)) = (k3_finseq_1 B)) ) ) ) ) ).
tt(t2_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A B) (k5_normsp_1 A B (k1_real_1 1)))) ) ) ) ).
tt(t2_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r1_nfcont_2 A C D E) & (r1_nfcont_2 B C D F))  => (r1_nfcont_2 (k3_xboole_0 A B) C D (k6_vfunct_1 (u1_struct_0 C) D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D (k6_vfunct_1 k1_numbers A B C)) (k2_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C))) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D (k2_vfunct_1 k1_numbers A B C)) (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t2_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r2_hidden C B) & (r1_nfcont_4 A D C))  => (r1_nfcont_4 A (k2_partfun1 k1_numbers (k1_euclid A) D B) C)) ) ) ) ) ) ) ) ).
tt(t2_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ( ((r1_normform A B C D) & (r1_normform A B D E))  => (r1_normform A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_normsp_0 A (k4_algstr_0 A B)) = (k1_normsp_0 A B)) ) ) ) ) ).
tt(t2_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_normsp_2 A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (D = B)  &  ((k9_metric_1 (k2_normsp_2 A) B C) = (a_3_0_normsp_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  ((k1_ntalgo_1 A B) = (k3_int_2 A B)) ) ) ) ) ).
tt(t2_numbers,ax,(r2_xboole_0 k3_numbers k1_numbers)).
tt(t2_numeral1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_nat_d B (k1_recdef_1 A C))) ) )  => (r1_nat_d B (k7_afinsq_2 A))) ) ) ) ) ).
tt(t2_openlatt,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc D A) & (r1_tarski (k9_subset_1 (u1_struct_0 A) B D) C))  => (r1_tarski D (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) (k3_subset_1 (u1_struct_0 A) B) C)))) ) ) ) ) ) ) ) ) ).
tt(t2_oposet_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_orders_2 A) => (v2_oposet_1 A)) ) ) ).
tt(t2_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_oppcat_1 (k2_oppcat_1 A) (k3_oppcat_1 A B)) = B) ) ) ) ) ).
tt(t2_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_tarski B A) <=> (r2_hidden B (k1_orders_1 A))) ) ) ) ).
tt(t2_orders_2,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_orders_2 A B C) & (r1_orders_2 A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_orders_3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_2 A) &  ((v4_relat_2 A) &  ((v8_relat_2 A) &  ((v1_partfun1 A (k1_tarski B)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski B) (k1_tarski B))))) ) ) )  =>  (A = (k6_partfun1 (k1_tarski B))) ) ) ) ) ).
tt(t2_orders_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_orders_4 A B C) => (r1_xboole_0 B C)) ) ) ) ) ).
tt(t2_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_tarski (k1_ordinal1 A)) = A) ) ) ).
tt(t2_ordinal3,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_ordinal1 A) B) => (r1_tarski A B)) ) ) ).
tt(t2_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  => (r1_tarski (k10_xtuple_0 (k1_ordinal4 A B)) (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t2_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v5_ordinal1 C)) )  =>  (~  ( ((k9_xtuple_0 C) = (k10_ordinal2 A B))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v5_ordinal1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v5_ordinal1 E)) )  =>  (~  ( (C = (k1_ordinal4 D E))  &  ( ((k9_xtuple_0 D) = A)  &  ((k9_xtuple_0 E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) <=>  ((k2_ordinal1 A) = A) ) ) ).
tt(t2_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_o_ring_1 B A) =>  ((v3_o_ring_1 B A) &  ((v5_o_ring_1 B A) &  ((v7_o_ring_1 B A) &  ((v9_o_ring_1 B A) &  ((v11_o_ring_1 B A) & (v13_o_ring_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_orders_2 B C D) => (r1_orders_2 B D C)) ) ) ) ) ) ) ) ) ).
tt(t2_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))) =>  ((r2_hidden (k4_tarski (k4_tarski C (u1_struct_0 A)) D) (k1_osafree A B)) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((r2_hidden (k1_funct_1 D E) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k4_tarski F (u1_struct_0 A)) = (k1_funct_1 D E))  => (r3_orders_2 A (k2_msualg_1 A F) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E))) ) ) )  &  (~  ((r2_hidden (k1_funct_1 D E) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r3_orders_2 A F (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)) & (r2_hidden (k1_funct_1 D E) (k2_msafree (u1_struct_0 A) B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r1_osalg_1 A B C) & (r1_osalg_1 A C D))  => (r1_osalg_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t2_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) )  =>  ((v1_relat_1 (k2_pboole (u1_struct_0 A) B C)) &  ((v4_relat_1 (k2_pboole (u1_struct_0 A) B C) (u1_struct_0 A)) &  ((v1_funct_1 (k2_pboole (u1_struct_0 A) B C)) &  ((v1_partfun1 (k2_pboole (u1_struct_0 A) B C) (u1_struct_0 A)) & (v11_osalg_1 (k2_pboole (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) B C) =>  ((v1_osalg_3 D A) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r3_orders_2 A E F) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 B E)) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) B C D E) G) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) B C D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (r2_hidden (k4_tarski B C) (k1_osalg_4 A))) ) ) ) ) ) ) ).
tt(t2_papdesaf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_diraf A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_diraf A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_diraf A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ((r3_diraf A B C D) <=> (r1_aff_1 (k2_diraf A) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pardepap,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A B E B F) &  ((r2_analoaf A B G B H) &  ((r2_analoaf A C E D F) & (r2_analoaf A C G D H)) ) ) )  =>  ((r2_analoaf A B C B E) |  ((r2_analoaf A B C B G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k2_parsp_1 A (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C D) (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E F G)) = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k3_rlvect_1 A B E) (k3_rlvect_1 A C F) (k3_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) =>  ((r1_parsp_1 (k9_parsp_1 A) B C D E) <=>  (? [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [H:$i] :  ((m1_subset_1 H (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  (? [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) &  ( ((k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C D E) = (k6_xtuple_0 F G H I))  &  (~  ( (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ( ((k8_group_1 A J (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) = (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I)))  &  ( ((k8_group_1 A J (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) = (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I)))  &  ((k8_group_1 A J (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))) = (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I))) ) ) ) ) )  &  (~  ( ((k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) = (k4_struct_0 A))  &  ( ((k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) = (k4_struct_0 A))  &  ((k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k2_xboole_0 A B) = C)  =>  (! [D:$i] :  ((r2_hidden D (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((r2_hidden A (k2_relset_1 B D)) <=>  (? [E:$i] :  ((m1_subset_1 E C) &  ((r2_hidden E (k1_relset_1 C D)) &  (A = (k7_partfun1 B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_partfun3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) ) )  =>  ((k9_xtuple_0 (k4_rfunct_1 A)) = (k9_xtuple_0 A)) ) ) ).
tt(t2_partit1,ax, (! [A:$i] :  ((k3_tarski (k6_subset_1 A (k1_tarski k1_xboole_0))) = (k3_tarski A)) ) ).
tt(t2_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r1_relset_1 A A (k3_eqrel_1 A B C) (k4_relset_1 A A A A B C))) ) ) ) ) ) ).
tt(t2_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B D) &  ( (~  (B = D) )  &  ( (~  (C = B) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A B E B F) &  ((r2_diraf A E C D F) &  (~  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pboole,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_relat_1 A) <=>  ( (A = k1_xboole_0)  |  ((k10_xtuple_0 A) = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t2_pcomps_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~  ((k2_pre_topc A B) = k1_xboole_0) )  &  (B = k1_xboole_0) ) )  &  (~  ( (~  (B = k1_xboole_0) )  &  ((k2_pre_topc A B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t2_pcomps_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v9_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 C A) &  ((m1_setfam_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E B) & (r1_tarski (k2_pre_topc A D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  ((v2_struct_0 A) =>  ((g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A)) = k5_pcs_0) ) ) ) ).
tt(t2_pdiff_1,ax, ( ((v1_funct_1 (k2_funct_1 (k1_pdiff_1 1 1))) &  ((v1_funct_2 (k2_funct_1 (k1_pdiff_1 1 1)) k1_numbers (k1_euclid 1)) & (m1_subset_1 (k2_funct_1 (k1_pdiff_1 1 1)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 1))))) )  &  ((v2_funct_1 (k2_funct_1 (k1_pdiff_1 1 1))) &  ( ((k9_xtuple_0 (k2_funct_1 (k1_pdiff_1 1 1))) = k1_numbers)  &  ( ((k10_xtuple_0 (k2_funct_1 (k1_pdiff_1 1 1))) = (k1_euclid 1))  &  (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers (k1_euclid 1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 1))))) )  &  ((v3_funct_2 A k1_numbers (k1_euclid 1)) &  ((k2_funct_1 (k1_pdiff_1 1 1)) = A) ) ) ) ) ) ) ) ).
tt(t2_pdiff_2,ax, ( ((k1_relset_1 (k1_euclid 2) (k1_pdiff_1 2 2)) = (k1_euclid 2))  &  ( ((k2_relset_1 k1_numbers (k1_pdiff_1 2 2)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k1_pdiff_1 2 2) (k10_finseq_1 A B)) = B) ) ) ) ) ) ) ).
tt(t2_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r2_pdiff_3 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 D) C) B)) ) ) ) ) ) ) ) ) ).
tt(t2_pdiff_4,ax, ( ((k1_relset_1 (k1_euclid 3) (k1_pdiff_1 2 3)) = (k1_euclid 3))  &  ( ((k1_rvsum_1 (k1_pdiff_1 2 3)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_seq_1 (k1_pdiff_1 2 3) (k11_finseq_1 A B C)) = B) ) ) ) ) ) ) ) ) ).
tt(t2_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r2_pdiff_5 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 E) D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ( ( (C = D)  &  (E = F) )  =>  ((r1_pdiff_1 B A C E) <=> (r1_ndiff_1 (k4_real_ns1 B) (k4_real_ns1 A) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 A B) =>  ((k17_finseq_1 k1_numbers (k7_nat_d A 1) (k5_euclid B)) = (k5_euclid (k7_nat_d A 1))) ) ) ) ) ) ).
tt(t2_pdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  ( (B = (k12_finseq_1 k1_numbers A))  =>  ((k1_normsp_0 (k4_real_ns1 1) B) = (k18_complex1 A)) ) ) ) ) ) ).
tt(t2_pdiff_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r4_nfcont_1 B C A) <=>  ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) A) &  ((v3_normsp_1 D B) & (r2_hidden (k6_normsp_1 B D) A)) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 B) D C)) &  ((k7_partfun1 k1_numbers C (k6_normsp_1 B D)) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pencil_1,ax, (! [A:$i] :  ((r1_ordinal1 2 (k1_card_1 A)) <=>  (? [B:$i] :  (? [C:$i] :  ((r2_hidden B A) &  ((r2_hidden C A) &  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t2_pencil_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  =>  ((k3_finseq_1 (k1_pencil_2 A B C D)) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) D) C) 1)) ) ) ) ) ) ) ) ) ).
tt(t2_pencil_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v2_pralg_1 C) & (v14_pencil_1 C)) ) ) ) )  =>  (~ (v7_struct_0 (k10_pralg_1 A C B))) ) ) ) ) ) ) ).
tt(t2_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (m1_vectsp_4 C A (k2_vectsp_4 A B))) ) ) ) ) ) ).
tt(t2_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_int_2 B) &  ( (~ (r1_int_2 A B))  &  (~  ((k6_nat_d A B) = B) ) ) ) ) ) ) ) ) ).
tt(t2_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_petri_2 D A C) =>  (~  ((r1_tarski A B) &  (! [E:$i] :  ((m1_petri_2 E B C) =>  (~ (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (k6_petri A B)) <=>  (? [D:$i] :  ((m1_petri D (u4_struct_0 A) (u1_struct_0 A) (u2_petri A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_hidden E B) &  (D = (k4_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ( (A = k1_xboole_0)  <=>  ((k15_finseq_1 A) = k1_xboole_0) ) ) ) ).
tt(t2_polyalg1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) B)))) )  =>  ((k9_xtuple_0 C) = (k2_zfmisc_1 A B)) ) ) ) ) ).
tt(t2_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_polyeq_1 k6_numbers k6_numbers A) = k6_numbers) ) ) ).
tt(t2_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( (E = (k2_xcmplx_0 D (k13_complex1 1 D)))  &  ((k1_polyeq_2 A B C B A D) = k6_numbers) )  =>  ( (A = k6_numbers)  |  ( (~  (D = k6_numbers) )  &  ((k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 E)) (k3_xcmplx_0 B E)) C) (k3_xcmplx_0 2 A)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k2_quin_1 A B C)))  &  ( ((k2_polyeq_3 A B C D) = k6_numbers)  &  ( (~  (D = (k3_binop_2 (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A))) (k5_binop_2 (k12_binop_2 (k7_square_1 (k7_binop_2 (k2_quin_1 A B C))) (k11_binop_2 2 A)) k7_complex1))) )  &  (~  (D = (k3_binop_2 (k7_binop_2 (k12_binop_2 B (k11_binop_2 2 A))) (k5_binop_2 (k7_binop_2 (k12_binop_2 (k7_square_1 (k7_binop_2 (k2_quin_1 A B C))) (k11_binop_2 2 A))) k7_complex1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers (k2_quin_1 B A C)) =>  ((r1_xxreal_0 (k7_xcmplx_0 A B) k6_numbers) |  ((r1_xxreal_0 (k7_xcmplx_0 C B) k6_numbers) |  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 A) (k7_square_1 (k2_quin_1 B A C))) (k3_xcmplx_0 2 B))))  &  (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 A) (k7_square_1 (k2_quin_1 B A C))) (k3_xcmplx_0 2 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 (k3_xcmplx_0 A A) A) = (k1_newton A 3)) ) ) ).
tt(t2_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))) =>  ((k4_finseq_1 (k6_matrlin A B)) = (k4_finseq_1 B)) ) ) ) ) ).
tt(t2_polynom2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B))  => (r2_hidden C (k4_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(t2_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A B) = (k4_rlvect_1 A (k4_finseq_5 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t2_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k9_polynom3 A) B) (k9_polynom3 A))) ) ) ) ).
tt(t2_polynom5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k13_complex1 (k3_xxreal_0 A B) (k4_xxreal_0 A B)) 1)) ) ) ) ) ).
tt(t2_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ((r1_pre_poly A B C) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 (k1_funct_1 C D) (k1_funct_1 B D)))  &  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E D) =>  ((k1_funct_1 B E) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_polynom7,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_struct_0 B))  =>  ( (~  ( (~ (v7_struct_0 B))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((k2_polynom1 (k15_pre_poly A) B C) = k1_xboole_0) ) ) ) )  &  (~  ( (~  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((k2_polynom1 (k15_pre_poly A) B C) = k1_xboole_0) ) ) )  & (v7_struct_0 B)) ) ) ) ) ) ).
tt(t2_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  ((k11_algstr_0 A (k8_group_1 A B C)) = (k8_group_1 A (k11_algstr_0 A B) (k11_algstr_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_algstr_1 B) & (l2_algstr_0 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B (k7_polynom1 A B) C) C)) ) ) ) ) ).
tt(t2_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_poset_1 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v6_orders_2 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r3_orders_2 B (k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k1_yellow_0 A C)))) ) ) ) ) ) ) ) ).
tt(t2_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (v1_abian B))  =>  ((k1_newton (k4_xcmplx_0 A) B) = (k4_xcmplx_0 (k1_newton A B))) ) ) ) ) ) ).
tt(t2_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k11_funcop_1 (k2_zfmisc_1 A B) B A (k6_pralg_1 A B)) = (k2_zfmisc_1 B A)) ) ) ) ) ).
tt(t2_pralg_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  => (r6_pboole B (k3_relat_1 E (k6_pboole A C D)) (k6_pboole B (k3_relat_1 E C) (k3_relat_1 E D)))) ) ) ) ) ) ) ) ) ).
tt(t2_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ((m1_pralg_2 F E B) =>  ( ((k5_relat_1 C E) = F)  =>  ((k9_pralg_2 E B D F) = (k5_relat_1 (k9_pralg_2 A B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pre_circ,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k1_funct_1 (k6_finseq_2 A B) (k6_finseq_1 A)) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t2_pre_ff,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k5_int_1 A 1) = A) ) ) ).
tt(t2_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  ( ((k8_trees_2 (k9_xtuple_0 B) C) = 2)  =>  ((r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)) (k9_xtuple_0 B)) & (r2_hidden (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers 1)) (k9_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(t2_pre_poly,ax, (! [A:$i] :  ((k5_pre_poly A (k2_pre_poly (k3_finseq_2 A))) = (k2_pre_poly A)) ) ).
tt(t2_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 B C) A)) ) )  => (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ).
tt(t2_pre_topc,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) B (k3_subset_1 (u1_struct_0 A) B)) = (k2_struct_0 A)) ) ) ) ) ).
tt(t2_prgcor_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 B (k4_nat_d A (k4_nat_1 2 B))) =>  ((r1_xxreal_0 B k6_numbers) |  ( ((k6_xcmplx_0 (k4_nat_d A (k4_nat_1 2 B)) B) = (k4_nat_d A B))  &  ((k2_nat_1 (k4_nat_d A B) B) = (k4_nat_d A (k4_nat_1 2 B))) ) ) ) ) ) ) ) ).
tt(t2_prgcor_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_tarski k5_numbers A) &  ( (~ (r1_xxreal_0 C (k3_finseq_1 B)))  &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((k1_afinsq_1 D) = C)  & (r1_prgcor_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (m1_subset_1 (k2_tarski B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(t2_prob_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 B) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k9_real_1 A (k8_nat_1 k1_numbers B D))) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = (k9_real_1 A (k2_seq_2 B))) ) ) ) ) ) ) ) ) ).
tt(t2_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden A (k1_relset_1 k5_numbers B)) <=>  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 A (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t2_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  <=>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) ) ) ) ) ) ) ).
tt(t2_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k9_cqc_lang A B (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ).
tt(t2_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ).
tt(t2_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v1_projpl_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) => (r1_incsp_1 A B C)) ) ) ) ) ) ) ).
tt(t2_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  ((r1_projred2 A B C D) =>  ((r1_projred2 A B D C) &  ((r1_projred2 A C B D) &  ((r1_projred2 A C D B) &  ((r1_projred2 A D B C) & (r1_projred2 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  => (r1_finseqop (u1_struct_0 A) (k5_vectsp_1 A) (u1_algstr_0 A))) ) ).
tt(t2_prvect_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 A))) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 A C)) & (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) ) )  => (r1_xxreal_0 (k12_euclid A) (k12_euclid B))) ) ) ) ) ).
tt(t2_prvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( ((k9_xtuple_0 B) = (k6_domain_1 k5_numbers 1))  &  ( ((k1_funct_1 B 1) = A)  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k4_card_3 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k4_card_3 B))))) )  =>  (~  ((v2_funct_1 C) &  ((v2_funct_2 C (k4_card_3 B)) &  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k9_finseq_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_seq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 C (k1_seq_1 B D))) )  => (r1_xxreal_0 C (k1_pscomp_1 A B))) ) ) ) ) ) ) ).
tt(t2_pua2mss1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) & (v1_funct_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) & (v1_funct_1 B)) )  =>  ( ((k4_card_3 A) = (k4_card_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t2_pythtrip,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) <=> (v1_abian (k1_pepin A))) ) ) ).
tt(t2_pzfmisc1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (A = k1_xboole_0)  =>  ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) & (v1_partfun1 A k1_xboole_0)) ) ) ) ) ) ).
tt(t2_qc_lang1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_tarski (k2_zfmisc_1 (k1_enumset1 C D E) B) (k2_zfmisc_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t2_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k14_qc_lang1 A B C) = (k14_qc_lang1 A D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  ((k23_qc_lang1 A B) = (k1_qc_lang3 A B (k3_qc_lang1 A))) ) ) ) ) ).
tt(t2_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((r2_qc_lang2 A B C) &  ((k3_finseq_1 (k11_qc_lang1 A B)) = (k3_finseq_1 (k11_qc_lang1 A C))) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t2_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  ((r4_qmax_1 A B C) <=>  (! [D:$i] :  ((m1_subset_1 D (k3_qmax_1 A)) =>  ((k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A B) D) (k7_qmax_1 A B)) = (k3_funct_2 k12_prob_1 k1_numbers (k4_qmax_1 A (k6_qmax_1 A C) D) (k7_qmax_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( (C = D)  =>  ( ((r3_lattice3 A C E) => (r3_lattice3 B D E))  &  ( ((r3_lattice3 B D E) => (r3_lattice3 A C E))  &  ( ((r4_lattice3 A C E) => (r4_lattice3 B D E))  &  ((r4_lattice3 B D E) => (r4_lattice3 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k26_quaterni (k26_quaterni A B) C) = (k26_quaterni A (k26_quaterni B C))) ) ) ) ) ) ) ).
tt(t2_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((m1_subset_1 A k1_numbers) =>  ((k26_quaterni A B) = (k26_quaterni (k26_quaterni (k23_quaterni (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k25_quaterni (k18_quaterni B) k4_quatern2)) (k25_quaterni (k19_quaterni B) k11_quaterni)) (k25_quaterni (k20_quaterni B) k12_quaterni))) ) ) ) ) ) ).
tt(t2_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] : (r1_tarski (k10_xtuple_0 (k2_quaterni A B C D E F G H)) (k2_enumset1 E F G H))) ) ) ) ) ) ) ) ).
tt(t2_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k1_quin_1 A B C) k6_numbers) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (~  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t2_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k6_xcmplx_0 B 1) (k4_nat_d A B)))  =>  ((k4_nat_d (k2_xcmplx_0 A 1) B) = (k2_xcmplx_0 (k4_nat_d A B) 1)) ) ) ) ) ) ).
tt(t2_radix_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k6_int_1 (k2_xcmplx_0 (k6_int_1 A C) (k6_int_1 B C)) C) = (k6_int_1 (k2_xcmplx_0 A (k6_int_1 B C)) C)) ) ) ) ) ) ) ) ).
tt(t2_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k1_radix_3 A) (k2_radix_3 A))) ) ).
tt(t2_radix_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 3 C) =>  ((k5_radix_3 (k2_xcmplx_0 (k5_radix_3 A C) (k5_radix_3 B C)) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t2_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((r1_xxreal_0 A 1) | (r2_hidden (k7_nat_d A 1) (k2_finseq_1 B))) ) ) ) ) ) ).
tt(t2_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 2 B) & (r1_xxreal_0 (k8_radix_1 A B (k6_radix_5 A A B)) k6_numbers)) ) ) ) ) ) ) ).
tt(t2_ramsey_1,ax, (! [A:$i] :  ((r1_tarski A k4_ordinal1) =>  ((v1_finset_1 A) |  ((k1_card_1 A) = k4_ordinal1) ) ) ) ).
tt(t2_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r3_mesfunc6 A B C D) &  ((r1_tarski E (k1_relset_1 A D)) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G E) => (r1_xxreal_0 F (k1_seq_1 D G))) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C E)) | (r1_xxreal_0 (k1_extreal1 (k1_measure6 F) (k12_supinf_2 C E)) (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_random_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k10_xtuple_0 (k3_relat_1 B A)) (k10_xtuple_0 (k5_relat_1 A (k10_xtuple_0 B))))) ) ) ) ).
tt(t2_ranknull,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B C) & (v2_funct_1 (k5_relat_1 A C)))  => (v2_funct_1 (k5_relat_1 A B))) ) ) ) ) ).
tt(t2_rat_1,ax, (! [A:$i] :  (~  ((v1_rat_1 A) &  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (~  ( (~  (C = k6_numbers) )  &  (A = (k7_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (D = (k6_xcmplx_0 C 1)) )  =>  ((k5_finseq_5 (u1_struct_0 A) (k1_polynom3 (u1_struct_0 A) C B) (k7_partfun1 (u1_struct_0 A) B C) D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t2_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden A (k1_rcomp_1 B C)) <=> (r1_xxreal_0 (k18_complex1 (k5_real_1 (k2_xcmplx_0 B C) (k8_real_1 2 A))) (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t2_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v3_membered A) & (v4_xxreal_2 A)) )  =>  (! [B:$i] :  ( ((v2_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) => (r2_hidden (k2_seq_4 A) B)) ) ) ) ) ).
tt(t2_real_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 (k3_real_1 A 1) B) |  ((k1_int_1 B) = A) ) ) ) ) ) ) ).
tt(t2_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (v3_xxreal_0 B))  => (v3_xxreal_0 A)) ) ) ) ) ).
tt(t2_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ((k1_binop_1 k1_real_lat A B) = (k1_binop_1 k1_real_lat B A)) ) ) ) ) ).
tt(t2_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_algstr_0 (k4_real_ns1 A) B C) = (k7_euclid A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_realset1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_realset1 C A B) =>  ((v1_funct_1 (k1_realset1 B C)) &  ((v1_funct_2 (k1_realset1 B C) (k2_zfmisc_1 C C) C) & (m1_subset_1 (k1_realset1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) ) ) ) ) ) ) ).
tt(t2_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B (k4_struct_0 A)) = B)  &  ((k3_rlvect_1 A (k4_struct_0 A) B) = B) ) ) ) ) ) ).
tt(t2_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_funct_1 (k5_realset2 A) (k1_binop_1 (k4_realset2 A) B (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) C))) = (k1_binop_1 (k4_realset2 A) C (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B))) ) ) ) ) ) ) ).
tt(t2_rearran1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_rearran1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 B C) &  ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A))) )  => (r1_tarski (k1_funct_1 A B) (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(t2_recdef_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k3_zfmisc_1 B C D)) =>  ((r2_hidden (k4_xtuple_0 A) B) &  ((r2_hidden (k5_xtuple_0 A) C) & (r2_hidden (k2_xtuple_0 A) D)) ) ) ) ) ) ) ).
tt(t2_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)))) ) ) ) ).
tt(t2_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_relat_2 A) <=> (r1_xboole_0 (k4_relat_1 (k1_relat_1 A)) A)) ) ) ).
tt(t2_reloc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k8_ami_3 B C) A) = (k8_ami_3 (k2_xcmplx_0 B A) C)) ) ) ) ) ) ) ).
tt(t2_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  (~  ((r2_hidden A D) &  (! [E:$i] :  (! [F:$i] :  (~  ( (A = (k4_tarski E F))  &  ((r2_hidden E B) & (r2_hidden F C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_relset_2,ax, (! [A:$i] :  ( (A = k1_xboole_0)  <=>  ((k10_eqrel_1 A) = k1_xboole_0) ) ) ).
tt(t2_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k2_rfinseq A (k3_finseq_1 B) B) = k1_xboole_0) ) ) ) ) ).
tt(t2_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (~  (A = k1_xboole_0) )  =>  ((k1_rewrite1 (k7_finseq_1 B (k9_finseq_1 C)) A) = (k7_finseq_1 B A)) ) ) ) ) ) ) ).
tt(t2_rewrite2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (~ (r1_xxreal_0 A (k3_finseq_1 B)))  &  ((r1_xxreal_0 A (k3_finseq_1 (k7_finseq_1 B C))) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (A = (k2_nat_1 (k3_finseq_1 B) D))  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rewrite3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  (~  ( (A = (k7_finseq_1 B (k9_finseq_1 C)))  &  ((k3_finseq_1 A) = (k2_xcmplx_0 (k3_finseq_1 B) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t2_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((r1_xxreal_0 (k1_seq_1 A (k2_rfinseq2 A)) (k1_seq_1 A B)) & (r1_xxreal_0 (k4_rfinseq2 A) (k1_seq_1 A B))) ) ) ) ) ) ).
tt(t2_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r2_classes1 (k7_finseq_1 A B) (k7_finseq_1 B A))) ) ) ) ).
tt(t2_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k6_subset_1 (k9_xtuple_0 (k18_valued_1 A B)) (k8_relat_1 (k18_valued_1 A B) (k1_tarski k6_numbers))) = (k9_subset_1 (k9_xtuple_0 B) (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski k6_numbers))) (k6_subset_1 (k9_xtuple_0 B) (k8_relat_1 B (k1_tarski k6_numbers))))) ) ) ) ) ).
tt(t2_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers C (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k2_valued_0 k1_numbers C A) (k2_valued_0 k1_numbers C B))) &  ((r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers C (k47_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k2_valued_0 k1_numbers C A) (k2_valued_0 k1_numbers C B))) & (r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers C (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k2_valued_0 k1_numbers C A) (k2_valued_0 k1_numbers C B)))) ) ) ) ) ) ) ) ).
tt(t2_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k18_complex1 A) = (k7_real_1 (k1_rfunct_3 A) (k2_rfunct_3 A))) ) ) ).
tt(t2_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k14_rvsum_1 (k8_finseq_1 k1_numbers B (k12_finseq_1 k1_numbers D)) (k8_finseq_1 k1_numbers C (k12_finseq_1 k1_numbers E))) = (k8_finseq_1 k1_numbers (k15_rvsum_1 A B C) (k12_finseq_1 k1_numbers (k11_binop_2 D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A B) B) A)) ) ) ) ).
tt(t2_rinfsup2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ( (A = B)  & (v4_xxreal_2 A))  =>  ((v4_xxreal_2 B) &  ((k8_supinf_2 A) = (k4_seq_4 B)) ) ) ) ) ) ) ).
tt(t2_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k5_algstr_0 A B (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t2_ringcat1,ax, (! [A:$i] :  ( ((v3_ringcat1 A) & (l1_ringcat1 A))  =>  (! [B:$i] :  ( ((v3_ringcat1 B) & (l1_ringcat1 B))  =>  (~  ( ((k1_ringcat1 A) = (k2_ringcat1 B))  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v3_group_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) )  =>  (~  ((r1_ringcat1 C D) &  ((r1_ringcat1 D E) &  ((m1_ringcat1 (g1_ringcat1 (u1_ringcat1 A) (u2_ringcat1 A) (u3_ringcat1 A)) D E) & (m1_ringcat1 (g1_ringcat1 (u1_ringcat1 B) (u2_ringcat1 B) (u3_ringcat1 B)) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_convex1 A B))) ) ) ) ).
tt(t2_rlaffin2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v1_rlaffin1 F C) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 C))))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 C)) =>  ( ((r2_hidden D (k3_convex1 C F)) &  ((r2_hidden E (k3_convex1 C F)) &  ((r2_hidden I (k3_convex1 C (k7_subset_1 (u1_struct_0 C) F (k6_domain_1 (u1_struct_0 C) G)))) &  ((r2_hidden J (k3_convex1 C (k7_subset_1 (u1_struct_0 C) F (k6_domain_1 (u1_struct_0 C) H)))) &  ( ((k3_rlvect_1 C (k1_rlvect_1 C E A) (k1_rlvect_1 C I (k9_real_1 1 A))) = D)  &  ((k3_rlvect_1 C (k1_rlvect_1 C E B) (k1_rlvect_1 C J (k9_real_1 1 B))) = D) ) ) ) ) )  =>  ((r2_hidden E (k3_convex1 C (k7_subset_1 (u1_struct_0 C) F (k6_domain_1 (u1_struct_0 C) G)))) |  ((r2_hidden E (k3_convex1 C (k7_subset_1 (u1_struct_0 C) F (k6_domain_1 (u1_struct_0 C) H)))) |  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 1 B) |  ( (I = J)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden A (k4_card_3 (k7_finseq_1 B C))) <=>  (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  (? [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  &  ( (A = (k7_finseq_1 D E))  &  ((r2_hidden D (k4_card_3 B)) & (r2_hidden E (k4_card_3 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k4_algstr_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t2_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_struct_0 B D) | (r1_struct_0 C D))  => (r1_struct_0 (k1_rlsub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t2_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_setfam_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D E) & (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k5_binop_1 (u1_struct_0 A) (u1_algstr_0 A) B C)) ) ) ) ) ) ) ).
tt(t2_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 D E) = (k3_rlvect_1 A (k7_partfun1 (u1_struct_0 A) B E) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) )  =>  ((k4_rlvect_1 A D) = (k3_rlvect_1 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlvect_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ((k6_rlvect_2 B (k8_rlvect_2 B A C)) = (k1_rlvect_1 B (k6_rlvect_2 B C) A)) ) ) ) ) ) ) ).
tt(t2_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k5_algstr_0 A D C))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t2_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_rlvect_3 B A) &  (! [C:$i] :  ((m1_rlvect_3 C A) =>  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t2_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  & (r2_relset_1 k5_numbers (u1_struct_0 A) D (k2_vfunct_1 k5_numbers A B C)))  =>  ((k4_rlvect_1 A D) = (k5_algstr_0 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t2_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D C) => (r2_hidden (k4_algstr_0 B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_struct_0 C E) | (r1_struct_0 D E))  => (r1_struct_0 (k1_rmod_3 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_vectsp_2 A B C (k4_rlvect_1 B (k6_finseq_1 (u1_struct_0 B)))) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t2_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A B)) = (k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A (k3_robbins1 A B)))) ) ) ) ) ).
tt(t2_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A D B)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A C) (k3_robbins1 A (k1_lattices A C E)))))))) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((v2_robbins3 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v9_lattices A)) ) )  =>  ((v6_lattices A) & (v4_lattices A)) ) ) ) ).
tt(t2_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_lattices A B (k3_robbins1 A B)) = (k6_lattices A))  &  ((k4_lattices A B (k3_robbins1 A B)) = (k5_lattices A)) ) ) ) ) ) ).
tt(t2_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k1_rcomp_1 A (k7_real_1 A B)) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A (k7_real_1 A B)))) &  ( ((k1_seq_1 C A) = (k1_seq_1 C (k7_real_1 A B)))  &  ((r2_fdiff_1 C (k2_rcomp_1 A (k7_real_1 A B))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 1 D))  &  ((k1_fdiff_1 C (k7_real_1 A (k8_real_1 D B))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_roughs_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k6_partfun1 (u1_struct_0 A)) (u1_orders_2 A))) ) ).
tt(t2_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v3_card_1 D 1) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (~  ( (D = (k4_subset_1 A B C))  &  ( (~  (B = C) )  &  ( (~  ( (B = k1_xboole_0)  &  (C = D) ) )  &  (~  ( (B = D)  &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rsspace2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k13_rsspace)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k13_rsspace)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k13_rsspace)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( ((k1_bhsp_1 k13_rsspace A A) = k6_numbers)  =>  (A = (k4_struct_0 k13_rsspace)) )  &  ( ( (A = (k4_struct_0 k13_rsspace))  =>  ((k1_bhsp_1 k13_rsspace A A) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_bhsp_1 k13_rsspace A A)) &  ( ((k1_bhsp_1 k13_rsspace A B) = (k1_bhsp_1 k13_rsspace B A))  &  ( ((k1_bhsp_1 k13_rsspace (k3_rlvect_1 k13_rsspace A B) C) = (k7_real_1 (k1_bhsp_1 k13_rsspace A C) (k1_bhsp_1 k13_rsspace B C)))  &  ((k1_bhsp_1 k13_rsspace (k1_rlvect_1 k13_rsspace A D) B) = (k8_real_1 D (k1_bhsp_1 k13_rsspace A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rsspace3,ax, (! [A:$i] :  ((l1_normsp_1 A) =>  ( ( (~ (v2_struct_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))))  &  ((v13_algstr_0 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v2_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v3_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v4_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v5_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v6_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v7_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) &  ((v8_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) & (l1_rlvect_1 (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rsspace4,ax, ( ((u1_struct_0 k3_rsspace4) = k1_rsspace4)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) <=>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  & (v1_comseq_2 (k2_rsspace A))) ) )  &  ( ((k4_struct_0 k3_rsspace4) = k6_rsspace)  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  (A = (k2_rsspace A)) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_rsspace4)) =>  ((k1_algstr_0 k3_rsspace4 A B) = (k3_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_rsspace4)) =>  ((k1_rlvect_1 k3_rsspace4 B A) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace B) A)) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  ( ((k4_algstr_0 k3_rsspace4 A) = (k32_valued_1 k5_numbers k1_numbers (k2_rsspace A)))  & (r2_funct_2 k5_numbers k1_numbers (k2_rsspace (k4_algstr_0 k3_rsspace4 A)) (k32_valued_1 k5_numbers k1_numbers (k2_rsspace A)))) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_rsspace4)) =>  ((k5_algstr_0 k3_rsspace4 A B) = (k47_valued_1 k5_numbers k1_numbers k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) => (v1_comseq_2 (k2_rsspace A))) )  &  (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  ((k1_normsp_0 k3_rsspace4 A) = (k4_seq_4 (k2_relset_1 k1_numbers (k56_valued_1 k5_numbers k1_numbers (k2_rsspace A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  ((k1_algstr_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) A B) = (k1_series_1 k1_numbers (k2_rsspace A) (k2_rsspace B))) ) ) ) ) ).
tt(t2_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((r1_struct_0 B C) => (r1_struct_0 A C)) ) ) ) ) ) ).
tt(t2_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_struct_0 B D) | (r1_struct_0 C D))  => (r1_struct_0 (k1_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t2_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C B) => (r1_struct_0 (k1_rusub_3 A B) C)) ) ) ) ) ) ).
tt(t2_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ( ((g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)) = (k1_rusub_3 A B))  & (v1_rlvect_3 C A))  =>  ((r1_xxreal_0 (k5_card_1 C) (k5_card_1 B)) &  (? [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski D B) &  ( ((k5_card_1 D) = (k6_xcmplx_0 (k5_card_1 B) (k5_card_1 C)))  &  ((g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)) = (k1_rusub_3 A (k4_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_rusub_5 A B C) => (r1_rusub_5 A C B)) ) ) ) ) ) ) ).
tt(t2_rvsum_1,ax,(r3_binop_1 k1_numbers 1 k35_binop_2)).
tt(t2_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r7_binop_1 k2_numbers (k7_seq_4 A) k27_binop_2)) ) ).
tt(t2_scheme1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = (k4_nat_1 3 B)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 3 B) 1)) )  &  (~  (A = (k2_nat_1 (k4_nat_1 3 B) 2)) ) ) ) ) ) ) ) ) ).
tt(t2_scm_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v5_memstr_0 D 2 k1_ami_3 C) & (m1_scm_1 D (k6_afinsq_1 A B)))  =>  ( ((k1_funct_1 D (k10_ami_3 k6_numbers)) = A)  &  ((k1_funct_1 D (k10_ami_3 1)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t2_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k14_scmfsa_2 D C B) A) D) = (k7_partfun1 k4_numbers (k18_scmfsa_2 A B) (k18_complex1 (k1_funct_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(t2_scm_comp,ax, ((m2_subset_1 (k4_tarski k6_numbers k6_numbers) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 1) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 2) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) &  ((m2_subset_1 (k4_tarski k6_numbers 3) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) & (m2_subset_1 (k4_tarski k6_numbers 4) (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp))) ) ) ) ).
tt(t2_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k6_scmfsa_2 A B) = (k3_xtuple_0 1 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(t2_scmfsa_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k12_scmfsa_2 B C) A) = (k12_scmfsa_2 (k2_nat_1 B A) C)) ) ) ) ) ) ) ).
tt(t2_scmfsa6a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k6_compos_1 k1_scmfsa_2 (k2_scmfsa6a B) A) = (k3_relat_1 (k6_compos_1 k1_scmfsa_2 B A) (k1_funct_4 (k6_partfun1 (u1_compos_1 k1_scmfsa_2)) (k16_funcop_1 (k2_compos_1 k1_scmfsa_2) (k11_scmfsa_2 (k2_nat_1 A (k5_card_1 B))))))) ) ) ) ) ).
tt(t2_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski B C) => (r1_extpro_1 3 k1_scmfsa_2 C A)) ) ) ) ) ) ) ) ).
tt(t2_scmfsa6c,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v1_scmfsa6b D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v7_amistd_1 E 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a D E) B C) A) = (k18_scmfsa_2 (k1_scmfsa6b E (k1_scmfsa6b D B C) C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_scmfsa_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_scmfsa_7 A 1) = (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ).
tt(t2_scmfsa7b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ((k1_funct_1 (k2_scmfsa6a (k11_compos_1 k1_scmfsa_2 A)) 1) = (k11_scmfsa_2 2)) ) ) ).
tt(t2_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k5_card_1 A) C) =>  ((r1_xxreal_0 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) C) |  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ( (D = (k1_funct_1 B (k7_nat_d C (k5_card_1 A))))  =>  ((k1_funct_1 (k3_scmfsa6a A B) C) = (k5_compos_0 (u1_compos_1 k1_scmfsa_2) D (k5_card_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_scmfsa9a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k4_sf_mastr (k16_funcop_1 A B)) = (k3_sf_mastr B)) ) ) ) ) ).
tt(t2_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k2_scmfsa8b B (k3_scmfsa6a A (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2))) = (k2_nat_1 (k5_card_1 A) 6)) ) ) ) ) ).
tt(t2_scmfsa_i,ax, (! [A:$i] :  ((m1_subset_1 A k2_scmfsa_i) =>  ((r1_xxreal_0 (k4_xtuple_0 A) 8) => (r2_hidden A k3_scm_inst)) ) ) ).
tt(t2_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  &  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k18_scmfsa_2 A C) = (k18_scmfsa_2 B C)) ) ) )  <=>  ((k6_memstr_0 3 k1_scmfsa_2 A) = (k6_memstr_0 3 k1_scmfsa_2 B)) ) ) ) ) ) ).
tt(t2_scm_halt,ax,(v2_scm_halt (k11_compos_1 k1_scmfsa_2 (k2_compos_1 k1_scmfsa_2)))).
tt(t2_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r2_hidden (k3_xtuple_0 6 (k12_finseq_1 k5_numbers A) k1_xboole_0) k3_scm_inst)) ) ).
tt(t2_scmisort,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmfsa8b A (k3_scmfsa6a B (k1_scmfsa8a k6_numbers)) (k4_compos_1 k1_scmfsa_2)) (k2_nat_1 (k5_card_1 B) 4)) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 B) 4))) ) ) ) ) ).
tt(t2_scmpds_2,ax, ((k4_struct_0 k1_scmpds_2) = k5_numbers) ).
tt(t2_scmpds_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k6_memstr_0 2 k1_scmpds_2 C) = (k6_memstr_0 2 k1_scmpds_2 D))  =>  ((k1_funct_1 C (k2_scmpds_2 (k1_funct_1 C B) A)) = (k1_funct_1 D (k2_scmpds_2 (k1_funct_1 D B) A))) ) ) ) ) ) ) ) ) ) ).
tt(t2_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ( ((k5_memstr_0 2 k1_scmpds_2 A) = (k5_memstr_0 2 k1_scmpds_2 B))  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t2_scmpds_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmpds_2)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k3_scmpds_4 (k3_scmpds_4 (k2_scmpds_4 A D) B) C) = (k2_scmpds_4 A (k3_scmpds_4 (k3_scmpds_4 D B) C))) ) ) ) ) ) ) ) ) ).
tt(t2_scmpds_9,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_amistd_1 2 k1_scmpds_2 B A) = (k1_tarski (k1_ordinal1 B))) ) )  => (v1_xboole_0 (k2_amistd_1 2 k1_scmpds_2 A))) ) ) ).
tt(t2_scmpds_i,ax,(r2_hidden (k3_xtuple_0 14 k1_xboole_0 (k12_finseq_1 k5_numbers k6_numbers)) k1_scmpds_i)).
tt(t2_scmp_gcd,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_scmpds_2 A) = (k2_nat_1 B C))  =>  ((k17_scmpds_2 A (k4_xcmplx_0 C)) = B) ) ) ) ) ) ) ) ).
tt(t2_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((k1_funct_1 (k3_relat_1 k3_ami_2 (k1_scmring1 A)) k5_numbers) = k5_numbers) ) ) ).
tt(t2_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (m1_subset_1 (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) (u1_compos_1 (k1_scmring2 A)))) ) ).
tt(t2_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (~  (B = (k4_struct_0 (k1_scmring2 A))) ) ) ) ) ) ).
tt(t2_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (B = (k2_scmring3 A C)) ) ) ) ) ) ) ).
tt(t2_scmringi,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 8)) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_scmringi B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (C = (k3_xtuple_0 A (k12_finseq_1 k5_numbers D) k1_xboole_0))  =>  ((k4_scmringi B C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t2_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (~  ((k4_tarski A B) = B) ) ) ) ).
tt(t2_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 D (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ( ((k1_funct_1 D A) = (k1_funct_1 D B))  =>  ((k1_funct_1 C D) = k6_numbers) )  &  ( (~  ((k1_funct_1 D A) = (k1_funct_1 D B)) )  =>  ((k1_funct_1 C D) = (k4_xxreal_0 (k1_int_2 (k1_funct_1 D A)) (k1_int_2 (k1_funct_1 D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (? [D:$i] :  ((m2_finseq_1 D k4_numbers) &  ( ((k3_finseq_1 D) = B)  & (r1_scpisort D A C)) ) ) ) ) ) ) ) ) ).
tt(t2_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_scmpds_6 D B A) &  ((r2_scmpds_6 D B A) &  ( (G = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 D)) (k8_memstr_0 2 k1_scmpds_2 B)) 2))  & (r6_pboole (u1_struct_0 k1_scmpds_2) C (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k2_scmpds_8 E F D))) (k8_memstr_0 2 k1_scmpds_2 B) G))) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F)) k6_numbers) |  ( ((k6_memstr_0 2 k1_scmpds_2 C) = (k6_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 B) A)))  & (r6_pboole (u1_struct_0 k1_scmpds_2) (k8_memstr_0 2 k1_scmpds_2 C) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_seq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  <=>  ( ((k9_xtuple_0 A) = k5_numbers)  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (v1_xreal_0 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t2_seq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k18_complex1 (k6_xcmplx_0 (k5_xcmplx_0 A) (k5_xcmplx_0 B))) = (k10_real_1 (k18_complex1 (k6_xcmplx_0 A B)) (k8_real_1 (k18_complex1 A) (k18_complex1 B)))) ) ) ) ) ) ) ) ) ).
tt(t2_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C B) => (r2_hidden (k9_binop_2 C A) B)) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~ (r2_hidden C B)) ) )  |  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((v1_xreal_0 D) &  ((r2_hidden D B) &  (~ (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) B (k9_seqfunc A D C)) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers B E) (k3_rfunct_1 A k1_numbers (k1_seqfunc A k1_numbers C E) (k1_seqfunc A k1_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)) (k8_nat_1 k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t2_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_power (k18_complex1 A) B) = (k18_complex1 (k3_power A B))) ) ) ) ) ).
tt(t2_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_newton (k2_xcmplx_0 A 1) 3) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 3 (k1_newton A 2))) (k3_xcmplx_0 3 A)) 1))  &  ( ((k1_newton (k2_xcmplx_0 A 1) 4) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 4) (k3_xcmplx_0 4 (k1_newton A 3))) (k3_xcmplx_0 6 (k1_newton A 2))) (k3_xcmplx_0 4 A)) 1))  &  ((k1_newton (k2_xcmplx_0 A 1) 5) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 5) (k3_xcmplx_0 5 (k1_newton A 4))) (k3_xcmplx_0 10 (k1_newton A 3))) (k3_xcmplx_0 10 (k1_newton A 2))) (k3_xcmplx_0 5 A)) 1)) ) ) ) ) ).
tt(t2_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k6_square_1 (k3_xcmplx_0 A B)) (k13_complex1 (k2_xcmplx_0 A B) 2))) ) ) ) ).
tt(t2_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_newton (k2_xcmplx_0 A B) 3) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton A 2)) B)) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton B 2)) A)) (k1_newton B 3))) ) ) ) ) ).
tt(t2_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k1_newton A 3) B) (k3_xcmplx_0 A (k1_newton B 3))) (k2_xcmplx_0 (k1_newton A 4) (k1_newton B 4)))) ) ) ) ).
tt(t2_setfam_1,ax, (! [A:$i] : (r1_tarski (k1_setfam_1 A) (k3_tarski A))) ).
tt(t2_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ((a_3_0_setlim_1 A B C) = (k2_xboole_0 (a_3_1_setlim_1 A B C) (k1_tarski (k3_funct_2 k5_numbers B C A)))) ) ) ) ) ) ).
tt(t2_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k1_prob_1 B (k10_nat_1 (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t2_setwiseo,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k2_tarski A B) (k1_enumset1 A B C))) ) ) ).
tt(t2_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) & (v2_binop_1 E B))  =>  ( ( (D = k1_xboole_0)  &  (~ (v1_setwiseo E B)) )  |  ((r2_hidden C D) |  ((k7_setwiseo A B E (k5_setwiseo A D (k2_setwiseo A C)) F) = (k5_binop_1 B E (k7_setwiseo A B E D F) (k3_funct_2 A B F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r6_scmfsa7b C (k1_scmfsa_m B) A) &  ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b D (k1_scmfsa6b C B A) A)) )  => (r5_scmfsa7b (k3_scmfsa6a C D) (k1_scmfsa_m B) A)) ) ) ) ) ) ) ) ) ).
tt(t2_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b D (k1_scmfsa_m A) B) & (r6_scmfsa7b D (k1_scmfsa_m A) B))  =>  ((r2_hidden C (k4_sf_mastr D)) |  ((k18_scmfsa_2 (k1_scmfsa6b D A B) C) = (k18_scmfsa_2 (k1_scmfsa_m A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k4_compos_1 k1_scmfsa_2) A B)) = (k6_memstr_0 3 k1_scmfsa_2 A)) ) ) ) ) ) ).
tt(t2_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k7_scmfsa_2 A B) = (k7_scmfsa_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k1_sgraph1 A B)) <=>  ((r1_xxreal_0 A C) & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t2_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v1_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattices A B (k3_sheffer1 A B)) = (k1_sheffer1 A)) ) ) ) ) ).
tt(t2_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A D C) C)) (k5_sheffer1 A B C)) (k5_sheffer1 A B C))) D) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A D C) C))) ) ) ) ) ) ) ) ) ).
tt(t2_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k1_simplex0 B)) <=>  (? [C:$i] :  ((r1_tarski A C) & (r2_hidden C B)) ) ) ) ) ).
tt(t2_simplex1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  ( ((k1_card_1 A) = (k3_real_1 (k5_card_1 B) 1))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ((v2_funct_2 C B) &  (! [D:$i] :  (~  ((r2_hidden D B) &  ( ((k1_card_1 (k8_relset_1 A B C (k1_tarski D))) = 2)  &  (! [E:$i] :  ((r2_hidden E B) =>  ( (E = D)  |  ((k1_card_1 (k8_relset_1 A B C (k1_tarski E))) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [C:$i] :  ( ((v1_tops_2 C (k3_pcomps_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [D:$i] :  ((m1_simplex2 D A B) =>  ( ((v1_compts_1 (k3_pcomps_1 A)) &  ((m1_setfam_1 B (u1_struct_0 (k3_pcomps_1 A))) & (r1_setfam_1 B C)) )  => (m1_simplex2 D A C)) ) ) ) ) ) ) ) ) ).
tt(t2_sincos10,ax,(r1_tarski (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos) (k1_relset_1 k1_numbers k1_fdiff_9))).
tt(t2_sin_cos2,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t2_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_binop_2 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A)) = (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k1_binop_2 A))) ) ) ).
tt(t2_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_sin_cos4 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k7_xcmplx_0 1 (k17_sin_cos A)))) ) ) ).
tt(t2_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k17_sin_cos A) = k6_numbers) )  =>  ((k20_sin_cos A) = (k4_real_1 (k17_sin_cos A) (k2_sin_cos4 A))) ) ) ) ).
tt(t2_sin_cos6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v2_funct_1 (k5_relat_1 A B)) & (r1_tarski C B))  => (v2_funct_1 (k5_relat_1 A C))) ) ) ) ) ).
tt(t2_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 1 (k5_square_1 (k12_binop_2 (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)) A)))) ) ) ) ).
tt(t2_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k3_sin_cos2 A) = (k7_xcmplx_0 1 (k3_sin_cos5 A)))  &  ( ((k6_sin_cos2 A) = (k7_xcmplx_0 1 (k2_sin_cos5 A)))  &  ((k9_sin_cos2 A) = (k7_xcmplx_0 1 (k1_sin_cos5 A))) ) ) ) ) ).
tt(t2_sin_cos9,ax,(r1_tarski (k2_rcomp_1 k6_numbers k32_sin_cos) (k1_relset_1 k1_numbers k30_sin_cos))).
tt(t2_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_nat_1 (k3_newton (k7_nat_d A 1)) A) = (k3_newton A)) )  &  ((r1_xxreal_0 A B) =>  ((k8_real_1 (k3_newton (k7_nat_d B A)) (k9_real_1 (k2_nat_1 B 1) A)) = (k3_newton (k7_nat_d (k2_nat_1 B 1) A))) ) ) ) ) ) ) ).
tt(t2_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 (k9_real_1 A B)) & (r1_xxreal_0 (k9_real_1 A B) C))  =>  ((r2_hidden (k9_real_1 A B) (k2_finseq_1 C)) & (m2_subset_1 (k9_real_1 A B) k1_numbers k5_numbers)) ) ) ) ) ) ) ) ).
tt(t2_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k2_xcmplx_0 B C) = (k3_finseq_1 A))  =>  ((k2_topreal1 2 A B) = (k2_topreal1 2 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) C)) ) ) ) ) ) ) ) ).
tt(t2_sprect_1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_funct_1 (k10_finseq_1 A B)) =>  (A = B) ) ) ) ).
tt(t2_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( ((r2_hidden A (k4_finseq_1 E)) &  ((r2_hidden B (k4_finseq_1 E)) & (r2_hidden C (k4_finseq_1 (k3_finseq_6 D E A B)))) )  =>  ((r1_xxreal_0 A B) | (r2_hidden (k2_nat_1 (k7_nat_d A C) 1) (k4_finseq_1 E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_sprect_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_matrix_1 (k3_matrix_2 A B C D)) = (k2_enumset1 (k4_tarski 1 1) (k4_tarski 1 2) (k4_tarski 2 1) (k4_tarski 2 2))) ) ) ) ) ).
tt(t2_sprect_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) )  =>  ((k3_topreal1 2 (k2_jordan3 A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t2_sprect_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C (k10_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 B)) & (r1_xxreal_0 (k4_finseq_4 B C) (k4_finseq_4 B D))) )  =>  ((k4_finseq_4 (k2_finseq_5 A B C) D) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_finseq_4 B D) (k4_finseq_4 B C)) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t2_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k4_xxreal_0 A B) (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t2_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  (~  ((v2_stacks_1 A) &  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (~ (r1_stacks_1 A B)) ) ) ) ) ) ) ).
tt(t2_stirl2_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ((k6_nat_1 (k6_seq_4 A) (k6_seq_4 B)) = (k6_seq_4 (k4_subset_1 k5_numbers A B))) ) ) ) ) ).
tt(t2_struct_0,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  & (l4_struct_0 A))  => (r2_hidden (k5_struct_0 A) (k8_struct_0 A))) ) ).
tt(t2_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden B (k9_xtuple_0 C)) =>  ((k1_funct_4 (k5_relat_1 C (k6_subset_1 (k9_xtuple_0 C) (k6_domain_1 (k3_qc_lang1 A) B))) (k16_funcop_1 B (k1_funct_1 C B))) = C) ) ) ) ) ) ) ) ).
tt(t2_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) => (r2_hidden D C)) ) )  => (r1_tarski B C)) ) ) ) ) ) ).
tt(t2_subset,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 A B) =>  ((v1_xboole_0 B) | (r2_hidden A B)) ) ) ) ).
tt(t2_substlat,ax, (! [A:$i] :  (! [B:$i] : (r2_hidden (k1_tarski k1_xboole_0) (k1_substlat A B))) ) ).
tt(t2_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k9_substut1 A (k5_cqc_lang A)) = k1_xboole_0) ) ) ).
tt(t2_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) =>  (? [F:$i] :  ((m2_subset_1 F (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A F) = (k4_cqc_lang B A C D))  &  ((k19_substut1 A F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_supinf_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden C (k4_supinf_1 B)) => (r2_hidden C (k4_supinf_1 A))) ) ) ) ) ) ) ) ).
tt(t2_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ((k2_supinf_2 A) = (k1_real_1 B)) ) ) ) ) ) ).
tt(t2_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_orders_2 B C D) => (r1_orders_2 B D C)) ) ) ) ) ) ) ) ) ).
tt(t2_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_xboole_0 A B) => (r1_xboole_0 (k9_xtuple_0 (k3_xboole_0 C (k2_zfmisc_1 A B))) (k10_xtuple_0 (k3_xboole_0 C (k2_zfmisc_1 A B))))) ) ) ) ) ).
tt(t2_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_t_0topsp A)))) =>  ((v3_pre_topc B (k3_t_0topsp A)) <=> (r2_hidden (k3_tarski B) (u1_pre_topc A))) ) ) ) ) ).
tt(t2_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k11_borsuk_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k3_tarski C))  =>  ((v4_pre_topc C (k11_borsuk_1 A B)) <=> (v4_pre_topc D A)) ) ) ) ) ) ) ) ) ) ).
tt(t2_tarski,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A B) &  (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_taxonom1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 A)) & (r2_hidden (k1_nat_1 D 1) (k4_finseq_1 A)))  =>  ((k1_funct_1 A D) = (k1_funct_1 A (k1_nat_1 D 1))) ) ) ) ) )  =>  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t2_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden E (k6_eqrel_1 A A B C)) & (r2_hidden E (k6_eqrel_1 A A B D)))  =>  ((k6_eqrel_1 A A B C) = (k6_eqrel_1 A A B D)) ) ) ) ) ) ) ) ) ).
tt(t2_taylor_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fdiff_1 (k1_taylor_1 A) B) &  ((k1_fdiff_1 (k1_taylor_1 A) B) = (k3_xcmplx_0 A (k4_prepower B (k5_real_1 A 1)))) ) ) ) ) ) ).
tt(t2_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_tarski (k2_rcomp_1 (k1_real_1 C) C) (k9_xtuple_0 B)) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 (k1_real_1 C) C)))  =>  ((r1_xxreal_0 C k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k2_rcomp_1 (k1_real_1 C) C)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 1 E))  &  ((k1_seq_1 B D) = (k7_real_1 (k1_seq_1 (k3_series_1 (k1_taylor_2 B (k2_rcomp_1 (k1_real_1 C) C) D)) A) (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 (k1_real_1 C) C)) (k2_nat_1 A 1)) (k8_real_1 E D)) (k2_newton D (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_tbsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k4_power A B) 1) &  (~ (r1_xxreal_0 (k4_power A B) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t2_tdgroup,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_vectsp_1)) =>  ( ((k3_rlvect_1 k1_vectsp_1 A A) = (k4_struct_0 k1_vectsp_1))  =>  (A = (k4_struct_0 k1_vectsp_1)) ) ) ) ).
tt(t2_tdlat_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_xboole_0 B C) <=> (r1_tarski C (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t2_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k2_pre_topc A (k1_tops_1 A B)) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B)))) & (r1_tarski (k1_tops_1 A (k2_pre_topc A B)) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))))) ) ) ) ) ).
tt(t2_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) = (k3_subset_1 (u1_struct_0 A) (k1_tops_1 A B))) ) ) ) ) ).
tt(t2_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r8_pboole (k15_pre_poly A) (k9_polynom1 A B (k7_polynom1 A B) C) (k7_polynom1 A B))) ) ) ) ) ) ).
tt(t2_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k6_tmap_1 A B)))) =>  ( ( (C = D)  & (v4_pre_topc C A))  => (v4_pre_topc D (k6_tmap_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t2_tex_2,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  (! [B:$i] :  ( (~ (v1_xboole_0 (k3_xboole_0 A B)))  => (r1_tarski A B)) ) ) ) ).
tt(t2_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v1_tops_1 B A) <=> (v2_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t2_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k1_setfam_1 (a_2_1_tex_4 A B))) ) ) ) ) ).
tt(t2_tietze,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ((r1_tarski A B) => (r1_tarski (k45_valued_1 C A) (k45_valued_1 C B))) ) ) ) ) ) ) ).
tt(t2_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_subset_1 A C D) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_subset_1 A C D) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G D B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ( ( ((k2_partfun1 (k4_subset_1 A C D) B E C) = F)  &  ((k2_partfun1 (k4_subset_1 A C D) B E D) = G) )  => (r2_funct_2 (k4_subset_1 A C D) B E (k1_tmap_1 A B C D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k4_tarski B C) (k1_eqrel_1 A))) ) ) ) ).
tt(t2_topalg_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k17_borsuk_1)) =>  ( (A = (k4_rcomp_1 B 1))  =>  ((k3_subset_1 (u1_struct_0 k17_borsuk_1) A) = (k1_rcomp_1 k6_numbers B)) ) ) ) ) ) ).
tt(t2_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_borsuk_2 E B C D) =>  (! [F:$i] :  ((m1_borsuk_2 F B C D) => (r4_borsuk_2 B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topalg_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v2_funct_1 (k5_relat_1 A B)) & (r2_hidden C (k10_xtuple_0 (k5_relat_1 A B))))  =>  ((k1_funct_1 (k3_relat_1 (k2_funct_1 (k5_relat_1 A B)) A) C) = C) ) ) ) ) ) ).
tt(t2_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))) (k1_topalg_4 A B C D E F) (k5_group_7 A B G H)) = (k5_group_7 C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) E G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 D) F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topalg_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A B) &  (! [C:$i] :  ( ((v1_cantor_1 C (k4_topmetr A B)) &  ((v1_tops_2 C (k4_topmetr A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))) )  =>  (~  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 (k4_topmetr A B)))) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_topmetr A B))) =>  ( ((k1_funct_1 D E) = (a_3_0_topalg_5 A B E))  &  (C = (k3_card_3 D)) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  ((r2_hidden D C) => (v2_connsp_1 D (k4_topmetr A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topalg_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 F E) | (r2_funct_2 (u1_struct_0 (k4_topmetr E F)) (u1_struct_0 (k4_topmetr C D)) (k1_partfun1 (u1_struct_0 (k4_topmetr E F)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)) (k1_borsuk_6 E F A B) (k1_borsuk_6 A B C D)) (k1_borsuk_6 E F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v10_pre_topc A) <=>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 (k2_pre_topc A D) (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ((r1_xxreal_0 (k1_topdim_2 B C) A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( ((r1_tarski D C) & (r2_hidden (k1_nat_1 A 1) (k1_card_1 D)))  => (v1_xboole_0 (k6_setfam_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t2_topgen_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  ((v1_orders_4 A) <=> (r1_ordinal1 (k1_card_1 (k2_struct_0 A)) k4_ordinal1)) ) ) ).
tt(t2_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_tops_2 (k1_funct_1 B C) A) &  ((v1_yellow_8 (k1_funct_1 B C) A C) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) )  =>  ((v1_tops_2 (k3_card_3 B) A) &  ((v1_cantor_1 (k3_card_3 B) A) & (m1_subset_1 (k3_card_3 B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t2_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v1_topgen_3 B A) & (v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ((l1_pre_topc C) =>  ( ( ((u1_struct_0 C) = A)  &  ((u1_pre_topc C) = (k1_cantor_1 A B)) )  =>  ( ((v2_pre_topc C) & (l1_pre_topc C))  &  ((v1_tops_2 B C) &  ((v1_cantor_1 B C) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ).
tt(t2_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_topgen_1 A B) = (a_2_0_topgen_4 A B)) ) ) ) ) ).
tt(t2_topgen_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  (! [C:$i] :  ((k8_relat_1 (k1_funct_4 A B) C) = (k2_xboole_0 (k8_relat_1 A C) (k8_relat_1 B C))) ) ) ) ) ) ) ).
tt(t2_topgrp_1,ax, (! [A:$i] :  ((l1_struct_0 A) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A)) (k3_struct_0 A))) ) ).
tt(t2_topmetr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k7_relat_1 A (k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B))) (k10_xtuple_0 B)) =>  ((k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) = (k10_xtuple_0 (k1_funct_4 A B))) ) ) ) ) ) ).
tt(t2_topmetr3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_funct_1 (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) D C)) &  ((v1_funct_2 (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) D C) k5_numbers (u1_struct_0 B)) & (m1_subset_1 (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) D C) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t2_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((v8_pre_topc A) => (v8_pre_topc B)) ) ) ) ) ).
tt(t2_topreal1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_topreal1 A D E B) &  ((r1_topreal1 A E F C) &  ((k9_subset_1 (u1_struct_0 A) B C) = (k1_tarski E)) ) )  => (r1_topreal1 A D F (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topreal2,ax,(v2_compts_1 k1_topreal1 (k15_euclid 2))).
tt(t2_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k7_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k3_rlvect_1 (k15_euclid 2) A B)) = (k7_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(t2_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal4 A B C) => (r1_topreal1 (k15_euclid 2) B C A)) ) ) ) ) ) ) ).
tt(t2_topreal5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v2_connsp_1 (k2_struct_0 (k4_topmetr A B)) (k4_topmetr A B))) ) ) ) ) ).
tt(t2_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A B))  => (r1_xxreal_0 (k18_complex1 A) (k18_complex1 B))) ) ) ) ) ).
tt(t2_topreal7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_xxreal_0 A (k7_real_1 B C)) & (r1_xxreal_0 D (k7_real_1 E F)))  => (r1_xxreal_0 (k2_square_1 A D) (k7_real_1 (k2_square_1 B E) (k2_square_1 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) 1)) ) ) ).
tt(t2_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((k3_rlvect_1 (k15_euclid A) B C) = (k3_rlvect_1 (k15_euclid A) B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t2_topreala,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden (k3_real_1 B 1) (k4_finseq_1 A)) &  ( (~ (r2_hidden B (k4_finseq_1 A)))  &  (~  (B = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t2_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k20_sin_cos (k2_xcmplx_0 (k3_xcmplx_0 A B) C)) = (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A C) k19_sin_cos) B)) ) ) ) ) ) ) ).
tt(t2_toprealc,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k24_valued_1 C (k2_xcmplx_0 A B)) = (k1_valued_1 (k24_valued_1 C A) (k24_valued_1 C B))) ) ) ) ) ) ) ).
tt(t2_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_toprns_1 B A) <=>  (! [C:$i] :  (~  ((r2_hidden C k5_numbers) &  ((k1_funct_1 B C) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t2_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k2_pre_topc A (k2_struct_0 A)) = (k2_struct_0 A)) ) ) ).
tt(t2_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((r1_tarski C B) => (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t2_tops_3,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = (k2_struct_0 A))  =>  ((k3_subset_1 (u1_struct_0 A) B) = (k1_struct_0 A)) )  &  ( ( ((k3_subset_1 (u1_struct_0 A) B) = (k1_struct_0 A))  =>  (B = (k2_struct_0 A)) )  &  ( ( (B = (u1_struct_0 A))  =>  ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0) )  &  ( ((k3_subset_1 (u1_struct_0 A) B) = k1_xboole_0)  =>  (B = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t2_tops_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v3_pre_topc B (k15_euclid A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~ (r1_tarski (k1_topreal9 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k3_funct_2 A A D B) = C)  <=>  ((k3_funct_2 A A (k2_funct_2 A D) C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t2_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((v1_translac A) &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) &  ( (~ (r1_aff_1 A B C D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A C D F) & (r1_aff_1 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v1_borsuk_1 (k4_topmetr A B) k3_topmetr)) ) ) ) ) ).
tt(t2_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((r1_tarski A B) &  ((k3_finseq_1 A) = (k3_finseq_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t2_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_xboole_0 A C) & (r1_tarski B C))  => (r3_xboole_0 A B)) ) ) ) ) ) ) ).
tt(t2_trees_3,ax, (! [A:$i] :  ((v2_trees_3 A) <=> (r1_tarski A k2_trees_3)) ) ).
tt(t2_trees_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k2_trees_1 A) = (k2_trees_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t2_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden (k8_finseq_1 k5_numbers B C) A) =>  ((k4_trees_1 A (k8_finseq_1 k5_numbers B C)) = (k4_trees_1 (k4_trees_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t2_trees_a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m4_trees_1 C A) =>  ( (~  (C = k1_xboole_0) )  =>  ((k1_trees_a A B C) = (k2_xboole_0 (a_2_0_trees_a A C) (a_3_0_trees_a A B C))) ) ) ) ) ) ) ) ).
tt(t2_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_finset_1 B) &  ( (~  (B = k1_xboole_0) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~ (r3_orders_2 A C D))  &  (~ (r3_orders_2 A D C)) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_pre_topc A A)) ) ).
tt(t2_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tsep_2 A B C) <=>  ((r1_xboole_0 B C) &  ((k4_subset_1 (u1_struct_0 A) B C) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t2_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v4_pre_topc D B) &  (D = (k8_subset_1 (u1_struct_0 A) C (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_2 B A) => (v1_tops_1 B A)) ) ) ) ) ).
tt(t2_turing_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  (E = B) )  =>  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 (k4_tarski B C) D)) (k4_tarski E F)) = (k1_funct_1 A (k4_tarski E F))) ) ) ) ) ) ) ) ) ).
tt(t2_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k5_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k10_margrel1 A B)))  &  ( ((k1_funct_1 k6_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k10_margrel1 (k9_margrel1 A) B)))  &  ((k1_funct_1 k7_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k10_margrel1 (k9_margrel1 A) (k9_margrel1 B)))) ) ) ) ) ) ) ).
tt(t2_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  ( ((r1_unialg_2 A B) & (r1_unialg_2 B C))  => (r1_unialg_2 A C)) ) ) ) ) ) ) ).
tt(t2_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ( ((k19_margrel1 C) = k6_numbers)  =>  ((r2_unialg_2 A B C) <=> (r2_hidden (k1_funct_1 C k1_xboole_0) B)) ) ) ) ) ) ) ) ).
tt(t2_uniform1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ((v5_pre_topc C A (k3_pcomps_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)))) =>  ( (F = (k9_metric_1 B E D))  => (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_uniroots,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k17_complex1 (k7_partfun1 (u1_struct_0 k1_complfld) A C)) = (k1_funct_1 B C)) ) ) ) )  =>  ((k17_complex1 (k3_group_4 k1_complfld A)) = (k21_rvsum_1 B)) ) ) ) ) ) ).
tt(t2_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( ((r1_xxreal_0 2 (k3_finseq_1 B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((r1_xxreal_0 C 2) |  ((k1_funct_1 B C) = (k4_struct_0 A)) ) ) ) ) )  =>  ((k4_rlvect_1 A B) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B 1) (k7_partfun1 (u1_struct_0 A) B 2))) ) ) ) ) ) ).
tt(t2_urysohn1,ax, ((k1_urysohn1 k6_numbers) = (k7_domain_1 k1_numbers k6_numbers 1)) ).
tt(t2_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  (A = k6_numbers) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = k1_numbers)  =>  ((k1_integra2 B A) = B) ) ) ) ) ) ) ).
tt(t2_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  ( (B = k1_xboole_0)  |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_urysohn3 E A B C D) =>  (? [F:$i] :  ((m1_urysohn3 F A B C (k2_nat_1 D 1)) &  (! [G:$i] :  ((m2_subset_1 G k1_numbers (k1_urysohn1 (k2_nat_1 D 1))) =>  ((r2_hidden G (k1_urysohn1 D)) =>  ((k4_urysohn1 A (k1_urysohn1 (k2_nat_1 D 1)) F G) = (k1_funct_1 E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_funct_2 E (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k3_valuat_1 A B C E) D) = k7_margrel1)  <=>  (? [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) &  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 E F) = k7_margrel1)  &  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = G) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B F G) = (k3_funct_2 (k3_qc_lang1 A) B D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v2_valued_0 B))  =>  ((r1_tarski A B) => (v2_valued_0 A)) ) ) ) ) ).
tt(t2_valued_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers (k8_valued_1 A B C D) E) = (k2_xcmplx_0 D (k3_funct_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_valued_2,ax, (! [A:$i] : (m1_subset_1 (k5_valued_2 A) (k1_zfmisc_1 (k4_valued_2 A)))) ).
tt(t2_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v2_funct_2 (k3_struct_0 A) (u1_struct_0 A)) & (v3_vectmetr (k3_struct_0 A) A)) ) ) ).
tt(t2_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  &  ((r1_struct_0 C E) & (r1_struct_0 D E)) )  =>  (E = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski C (k2_finseq_1 A)) =>  ((k6_matrix13 (u1_struct_0 B) (k12_matrix_1 B A) C C) = (k12_matrix_1 B (k5_card_1 C))) ) ) ) ) ) ) ) ).
tt(t2_vectsp_1,ax, ((k5_struct_0 k2_vectsp_1) = 1) ).
tt(t2_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k3_rlvect_1 A B C) = D)  =>  (B = (k5_algstr_0 A D C)) )  &  ( ( (B = (k5_algstr_0 A D C))  =>  ((k3_rlvect_1 A B C) = D) )  &  ( ( ((k3_rlvect_1 A B C) = D)  =>  (C = (k5_algstr_0 A D B)) )  &  ( (C = (k5_algstr_0 A D B))  =>  ((k3_rlvect_1 A B C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D C) => (r2_hidden (k4_algstr_0 B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_struct_0 C E) | (r1_struct_0 D E))  => (r1_struct_0 (k1_vectsp_5 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ( ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) = (k4_struct_0 A))  <=>  (~ (r2_hidden C (k1_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t2_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_vectsp_7 C A B) & (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ).
tt(t2_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  => (r2_hidden (k4_struct_0 B) (k1_funct_1 (k4_vectsp_8 A B) C))) ) ) ) ) ) ).
tt(t2_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ((r1_xboole_0 (k1_vectsp_6 A B C) (k10_xtuple_0 D)) =>  ((k4_rlvect_1 B (k3_vectsp_6 A B D C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t2_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( ((k8_relset_1 A k1_numbers (k3_normsp_0 A B C) (k1_tarski k6_numbers)) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B))))  &  ((k8_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B C) (k1_tarski (k4_struct_0 B))) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t2_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( ((k8_relset_1 A k1_numbers (k3_normsp_0 A B C) (k1_tarski k6_numbers)) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B))))  &  ((k8_relset_1 A (u1_struct_0 B) (k5_vfunct_1 A B C) (k1_tarski (k4_struct_0 B))) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t2_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v1_xboole_0 B))  & (v2_waybel_0 B A))  <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) & (r1_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((m1_yellow_0 B A) => (m1_yellow_0 (k7_lattice3 B) (k7_lattice3 A)))  &  ( ((m1_yellow_0 (k7_lattice3 B) (k7_lattice3 A)) => (m1_yellow_0 B A))  &  ( ((m1_yellow_0 (k7_lattice3 B) A) => (m1_yellow_0 B (k7_lattice3 A)))  &  ((m1_yellow_0 B (k7_lattice3 A)) => (m1_yellow_0 (k7_lattice3 B) A)) ) ) ) ) ) ) ) ).
tt(t2_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_yellow_4 A B C) => (r3_orders_2 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t2_waybel12,ax, (! [A:$i] :  ((v5_card_3 A) => (r2_tarski k5_numbers A)) ) ).
tt(t2_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_subset_1 (k2_waybel_8 A B) (k1_zfmisc_1 (u1_struct_0 (k1_waybel_8 A))))) ) ) ) ).
tt(t2_waybel14,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k3_subset_1 (u1_struct_0 A) B) = (u1_struct_0 A))  <=> (v1_xboole_0 B)) ) ) ) ) ).
tt(t2_waybel15,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  ((k6_waybel_0 (k3_yellow_1 A) B) = (a_2_0_waybel15 A B)) ) ) ) ).
tt(t2_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k5_waybel_0 A C))) = (k12_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t2_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v13_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v5_orders_3 C A B) => (v13_waybel_0 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t2_waybel18,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  <=>  ((v1_tops_2 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B (k1_tarski k1_xboole_0)) A) &  ((v1_cantor_1 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B (k1_tarski k1_xboole_0)) A) & (m1_subset_1 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B (k1_tarski k1_xboole_0)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t2_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_waybel19 B) & (l1_waybel_9 B)) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((u1_pre_topc A) = (u1_pre_topc B)) ) ) ) ) ) ).
tt(t2_waybel_1,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A B C) => (r1_orders_2 A (k13_lattice3 A B D) (k13_lattice3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t2_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_partfun1 (k8_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 B)) A) &  ((v3_relat_2 (k8_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 B))) &  ((v8_relat_2 (k8_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 B))) & (m1_subset_1 (k8_relset_1 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k16_funct_3 A A B B C C) (k6_partfun1 B)) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ) ) ).
tt(t2_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v19_waybel_0 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t2_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_waybel16 D A B) =>  (! [E:$i] :  ((m1_waybel16 E B C) => (m1_waybel16 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k11_waybel_0 A B) (k11_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t2_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) )  =>  ((k3_yellow_0 (k7_yellow_1 A B)) = (k6_struct_0 A B (k3_yellow_0 B))) ) ) ) ) ).
tt(t2_waybel25,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k9_waybel18)) =>  (~  ( (A = 1)  & (v4_pre_topc (k6_domain_1 (u1_struct_0 k9_waybel18) A) k9_waybel18)) ) ) ) ).
tt(t2_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_waybel26 A B))) <=>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t2_waybel27,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r1_tarski D (k1_funct_2 (k2_zfmisc_1 A B) C)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E D) &  ((v1_funct_1 E) & (v1_partfun1 E D)) ) )  =>  (~  ((v2_waybel27 E) &  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  => (r1_tarski (k10_xtuple_0 E) (k1_funct_2 A (k1_funct_2 B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m2_yellow_6 D A B) =>  (C = (k1_waybel11 A D)) ) )  =>  ( (C = (k1_waybel11 A B))  &  (! [D:$i] :  ((m2_yellow_6 D A B) => (r1_orders_2 A (k1_waybel_9 A D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C)))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 E) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 D))))) )  =>  ( ((v1_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 D))) )  => (v2_waybel27 (k2_tops_2 (u1_struct_0 E) (u1_struct_0 D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_yellow_0 A (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B))) ) ) ) ) ) ).
tt(t2_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k7_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))))) )  =>  ( (~ (v1_xboole_0 (k3_tarski B)))  &  ((v1_waybel_0 (k3_tarski B) A) &  ((v12_waybel_0 (k3_tarski B) A) & (m1_subset_1 (k3_tarski B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t2_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (? [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  &  ((k1_card_1 B) = (k1_waybel31 A)) ) ) ) ) ).
tt(t2_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  ((v1_waybel32 A) => (v2_waybel32 A)) ) ) ).
tt(t2_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((l1_waybel_0 C A) =>  (? [D:$i] :  ( ((v6_waybel_0 D B) & (l1_waybel_0 D B))  &  ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) D) = (k2_yellow_0 A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k6_waybel_0 B D)))) ) ) ) ) ) ) ) ) ).
tt(t2_waybel35,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D C) &  ((r2_hidden E C) & (r2_orders_2 A D E)) )  => (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_orders_2 A B C) &  ((r1_waybel_3 A C D) & (r3_orders_2 A D E)) )  => (r1_waybel_3 A B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k2_waybel_4 A))) ) ) ) ).
tt(t2_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  &  ((r3_orders_2 A B (k1_yellow_0 A C)) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r3_orders_2 A B (k1_yellow_0 A D)) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v20_waybel_0 C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k13_lattice3 A D E)) = (k13_lattice3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_waybel_7,ax, (! [A:$i] :  ((u1_struct_0 (k3_yellow_1 A)) = (k9_setfam_1 A)) ) ).
tt(t2_waybel_8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v1_xboole_0 (k6_waybel_0 A B)))  &  ((v2_waybel_0 (k6_waybel_0 A B) A) &  ((v13_waybel_0 (k6_waybel_0 A B) A) &  ((v1_waybel_6 (k6_waybel_0 A B) A) & (m1_subset_1 (k6_waybel_0 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  <=> (v1_waybel_3 B A)) ) ) ) ) ).
tt(t2_waybel_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  &  ( ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  &  ( (E = F)  & (v5_waybel_0 E A B)) ) )  => (v5_waybel_0 F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_weddwitt,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k2_newton D (k2_xcmplx_0 (k3_xcmplx_0 A B) C)) = (k3_xcmplx_0 (k2_newton D A) (k2_newton D (k2_nat_1 (k3_nat_1 A (k7_nat_d B 1)) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_weierstr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ((v1_topmetr C A) &  ( ((k10_xtuple_0 D) = C)  &  ( ((k4_finseq_1 D) = (k2_finseq_1 (k1_nat_1 B 1)))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_finset_1 E) &  ((v1_topmetr E A) &  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  &  ( ((k10_xtuple_0 F) = E)  &  ( ((k4_finseq_1 F) = (k2_finseq_1 B))  &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) & (r1_tarski (k5_setfam_1 (u1_struct_0 A) C) (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) E) (k9_metric_1 A G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_wellfnd1,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) & (v1_card_5 A)) )  =>  (! [B:$i] :  ( ((r1_tarski B A) & (r2_hidden (k1_card_1 B) A))  => (r2_hidden (k3_ordinal2 B) A)) ) ) ) ).
tt(t2_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_hidden A (k1_relat_1 B)) |  ((k1_wellord1 B A) = k1_xboole_0) ) ) ) ) ).
tt(t2_wellset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( (C = (k2_zfmisc_1 A B))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ((k1_relat_1 C) = (k2_xboole_0 A B)) ) ) ) ) ) ) ) ).
tt(t2_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_newton (k4_xcmplx_0 A) (k4_nat_1 2 B)) = (k1_newton A (k4_nat_1 2 B)))  &  ((k1_newton (k4_xcmplx_0 A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k4_xcmplx_0 (k1_newton A (k2_nat_1 (k4_nat_1 2 B) 1)))) ) ) ) ) ) ).
tt(t2_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (! [D:$i] :  ( (~ (r2_hidden D A))  <=>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (A = (k5_xboole_0 B C)) ) ) ) ) ).
tt(t2_xboole_1,ax, (! [A:$i] : (r1_tarski k1_xboole_0 A)) ).
tt(t2_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k4_xboolean A B)) = (k4_xboolean A B)) ) ) ) ) ).
tt(t2_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k2_xcmplx_0 A B) = (k2_xcmplx_0 C B))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t2_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t2_xregular,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((r2_hidden B A) &  (! [C:$i] :  ((r2_hidden C B) => (r1_xboole_0 C A)) ) ) ) ) ) ).
tt(t2_xtuple_0,ax, (! [A:$i] :  ((v1_xtuple_0 A) =>  (! [B:$i] :  ((v1_xtuple_0 B) =>  ( ( ((k1_xtuple_0 A) = (k1_xtuple_0 B))  &  ((k2_xtuple_0 A) = (k2_xtuple_0 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t2_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  => (r1_xxreal_0 A C)) ) ) ) ) ) ) ).
tt(t2_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k3_xxreal_1 B C)) <=>  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(t2_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((m2_xxreal_2 A (k1_tarski B)) <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t2_xxreal_3,ax, (! [A:$i] :  ( ((v1_xxreal_0 A) &  ((v3_xxreal_0 A) &  (~ (v1_xreal_0 A)) ) )  =>  (A = k2_xxreal_0) ) ) ).
tt(t2_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = E)  =>  ( ((r2_lattice3 A C D) => (r2_lattice3 B C E))  &  ((r1_lattice3 A C D) => (r1_lattice3 B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ((v1_yellow_0 (k3_yellow_3 A B)) =>  ((v1_yellow_0 A) & (v1_yellow_0 B)) ) ) ) ) ) ).
tt(t2_yellow11,ax, ((k6_subset_1 2 1) = (k6_domain_1 k5_numbers 1)) ).
tt(t2_yellow12,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k8_relset_1 A (k2_zfmisc_1 A A) (k12_funct_3 A) (k2_zfmisc_1 B B)) B)) ) ).
tt(t2_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  => (v10_pre_topc A)) ) ).
tt(t2_yellow14,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_relset_1 A (k2_partfun1 A A (k6_partfun1 A) B)) = B) ) ) ) ).
tt(t2_yellow16,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_yellow_0 C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ( ((r1_funct_2 A (u1_struct_0 B) A (u1_struct_0 C) F D) &  ((r1_funct_2 A (u1_struct_0 B) A (u1_struct_0 C) G E) & (r1_yellow_2 A C D E)) )  => (r1_yellow_2 A B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_funct_1 A C)) & (r2_hidden B (k4_card_3 A)))  => (r2_hidden (k2_funct_7 B C D) (k4_card_3 A))) ) ) ) ) ) ) ).
tt(t2_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_functor0 A B C E) = (k3_functor0 A B D E)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  ((k8_functor0 A B C E F G) = (k8_functor0 A B D E F G)) ) ) ) ) ) ) ) )  =>  ((g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C)) = (g2_functor0 A B (u1_functor0 A B D) (u2_functor0 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k1_yellow19 A B)) <=> (m1_connsp_2 C A B)) ) ) ) ) ) ).
tt(t2_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_1 A))) =>  ((r3_orders_2 (k3_yellow_1 A) B C) <=> (r1_tarski B C)) ) ) ) ) ) ).
tt(t2_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v10_functor0 C A B) & (l2_functor0 C A B)) )  =>  (! [D:$i] :  ( ((v8_functor0 D B A) &  ((v10_functor0 D B A) & (l2_functor0 D B A)) )  =>  ( ((v21_functor0 C A B) &  (D = (k15_functor0 A B C)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B (k3_functor0 A B C E) (k3_functor0 A B C F))) =>  ( ((k6_functor0 A B C E F G) = H)  <=>  ((k6_functor0 B A D (k3_functor0 A B C E) (k3_functor0 A B C F) H) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v3_yellow18 A) &  ((v1_yellow21 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_altcat_1 A B) = (k3_struct_0 (k1_yellow21 B))) ) ) ) ) ).
tt(t2_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (k6_waybel_0 A B)) <=> (r1_lattice3 A C B)) ) ) ) ) ) ) ).
tt(t2_yellow_3,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B D) & (r1_orders_2 A C E))  => (r1_orders_2 A (k12_lattice3 A B C) (k12_lattice3 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_yellow_0 A B))  => (r1_orders_2 A (k2_yellow_0 A B) C)) ) ) ) ) ) ).
tt(t2_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_lattice3 A B B) = B) ) ) ) ) ).
tt(t2_yellow_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_pralg_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k1_funct_1 (k12_pralg_1 A B) C) = (u1_struct_0 (k10_pralg_1 A B C))) ) ) ) ) ) ) ).
tt(t2_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_lattice3 A))) =>  ( ((r1_orders_2 A B (k9_lattice3 A C)) => (r1_orders_2 (k7_lattice3 A) C (k8_lattice3 A B)))  &  ( ((r1_orders_2 (k7_lattice3 A) C (k8_lattice3 A B)) => (r1_orders_2 A B (k9_lattice3 A C)))  &  ( ((r1_orders_2 A (k9_lattice3 A C) B) => (r1_orders_2 (k7_lattice3 A) (k8_lattice3 A B) C))  &  ((r1_orders_2 (k7_lattice3 A) (k8_lattice3 A B) C) => (r1_orders_2 A (k9_lattice3 A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t2_yellow_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski B (k5_finsub_1 A)) => (r2_hidden (k6_setfam_1 A B) (k5_finsub_1 A))) ) ) ) ).
tt(t2_yellow_9,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k3_subset_1 (u1_struct_0 A) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) = (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k3_subset_1 (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ).
tt(t2_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (r2_nattra_1 A (k1_yoneda_1 A) (k2_yoneda_1 A (k4_graph_1 A B)) (k2_yoneda_1 A (k3_graph_1 A B)))) ) ) ) ).
tt(t2_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  (~ (r2_hidden C B)) ) )  <=> (r2_hidden B (k1_zf_colla A k1_xboole_0))) ) ) ) ) ).
tt(t2_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (! [D:$i] :  ((v8_zf_fund1 B A) =>  ( ((r2_hidden C B) => (r2_hidden (k1_tarski C) B))  &  ( ((r2_hidden (k1_tarski C) B) => (r2_hidden C B))  &  ((r2_hidden D B) => (r2_hidden (k3_tarski D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t2_zf_fund2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_zf_refle B A)) ) ) ) )  =>  ( ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((r2_hidden C D) => (r1_tarski (k5_zf_refle A B C) (k5_zf_refle A B D))) ) ) ) )  &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((r2_hidden (k5_zf_refle A B C) (k4_zf_refle A B)) & (v1_ordinal1 (k5_zf_refle A B C))) ) )  & (v1_zf_fund2 (k4_zf_refle A B))) )  => (r2_zf_model (k4_zf_refle A B) k10_zf_model)) ) ) ) ) ).
tt(t2_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ( ((k18_zf_lang (k5_zf_lang A B)) = A)  &  ((k19_zf_lang (k5_zf_lang A B)) = B) ) ) ) ) ) ).
tt(t2_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k5_zf_lang A B) = (k5_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t2_zfmisc_1,ax, ((k3_tarski k1_xboole_0) = k1_xboole_0) ).
tt(t2_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ((r2_zf_model A k7_zf_model) <=>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) => (r2_hidden (k2_tarski B C) A)) ) ) ) ) ) ) ) ).
tt(t2_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( (~ (r2_hidden A (k4_zf_lang1 C)))  =>  ( ((r2_hidden B (k2_zf_model C)) =>  ((k2_zf_model (k6_zf_lang1 C B A)) = (k2_xboole_0 (k7_subset_1 k1_zf_lang (k2_zf_model C) (k1_tarski B)) (k1_tarski A))) )  &  ( (~ (r2_hidden B (k2_zf_model C)))  =>  ((k2_zf_model (k6_zf_lang1 C B A)) = (k2_zf_model C)) ) ) ) ) ) ) ) ) ) ).
tt(t2_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((k3_funct_2 k1_zf_lang A D B) = (k3_funct_2 k1_zf_lang A D C))  <=> (r2_hidden D (k5_zf_model (k4_zf_lang B C) A))) ) ) ) ) ) ) ) ) ).
tt(t2_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k9_zf_lang)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k9_zf_lang)) =>  ( ((r1_tarski B C) & (r1_zfrefle1 A C))  => (r1_zfrefle1 A B)) ) ) ) ) ) ) ).
tt(t2_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_zf_model A k8_zf_model)) ) ).
tt(t2_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_algstr_0 A B) = (k1_zmodul01 A B (k4_xcmplx_0 1))) ) ) ) ) ).
tt(t300_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k1_xxreal_1 A D) (k4_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t301_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k4_xxreal_1 A D) (k2_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t302_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k2_xxreal_1 A D) (k2_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k2_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t303_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A D) (k2_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t304_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k1_xxreal_1 A D) (k2_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k1_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t305_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k6_subset_1 (k4_xxreal_1 A D) (k3_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t306_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 D C) |  ((k6_subset_1 (k2_xxreal_1 A D) (k3_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t307_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A D) (k3_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t308_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k1_xxreal_1 A D) (k3_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t309_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k4_xxreal_1 A D) (k1_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_abcmiz_0 A B (k6_finseq_1 (u1_abcmiz_0 A))) = B) ) ) ) ) ).
tt(t30_abcmiz_1,ax, (! [A:$i] :  ( ((v2_funct_1 A) & (m2_finseq_1 A k2_abcmiz_1))  =>  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) <=>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  (C = (k1_funct_1 A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D k2_abcmiz_1) =>  (~  ((r2_hidden D (k3_abcmiz_1 C)) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 A)) &  ( (~ (r1_xxreal_0 B E))  &  (D = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_abcmiz_a,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ((m2_finseq_2 B k2_abcmiz_1 k4_abcmiz_1) &  ((k3_finseq_1 B) = A) ) ) ) ) ).
tt(t30_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A k6_numbers) =>  ((k18_complex1 A) = (k4_xcmplx_0 A)) ) ) ) ).
tt(t30_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_aff_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_aff_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (~  (E = F) )  &  ((r2_hidden E D) &  ((r2_hidden F D) & (r2_analoaf A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 C A) =>  ((r2_hidden B C) <=>  ((k2_aff_4 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(t30_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( ((k1_ordinal4 A B) = k1_xboole_0)  =>  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t30_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (v6_membered C))  =>  ((r1_afinsq_2 B C) =>  ((r1_xxreal_0 (k5_card_1 C) A) |  ( ((k2_relset_1 k5_numbers (k2_afinsq_2 (k4_afinsq_2 (k2_xboole_0 B C)) (k5_card_1 B))) = C)  &  ((k1_recdef_1 (k2_afinsq_2 (k4_afinsq_2 (k2_xboole_0 B C)) (k5_card_1 B)) A) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 B C)) (k23_binop_2 A (k5_card_1 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) =>  ( ((v1_aff_1 B A) &  ( (C = (k5_afproj A B))  &  (D = (k4_tarski B 1)) ) )  => (r1_incsp_1 (k13_afproj A) C D)) ) ) ) ) ) ) ) ) ).
tt(t30_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_afvect0 A B C) = (k1_afvect0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t30_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) <=> (r1_algspec1 A (k1_algspec1 (u1_struct_0 A) B) (k1_algspec1 (u4_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t30_algstr_4,ax, (! [A:$i] :  (A = (a_1_0_algstr_4 A)) ) ).
tt(t30_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_2 B A) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_2 C A) & (m1_altcat_2 C A)) )  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g2_altcat_1 (u1_struct_0 B) (u1_altcat_1 B) (u2_altcat_1 B)) = (g2_altcat_1 (u1_struct_0 C) (u1_altcat_1 C) (u2_altcat_1 C))) ) ) ) ) ) ) ) ).
tt(t30_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ( ((v9_altcat_3 E A B C) & (v9_altcat_3 F A C D))  => (v9_altcat_3 (k5_altcat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v1_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v2_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_ami_3,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) => (r1_xxreal_0 (k2_compos_0 k3_scm_inst A) 8)) ) ).
tt(t30_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r1_ami_wstd A B D (k6_ami_wstd A B C))) ) ) ) ) ) ) ) ) ).
tt(t30_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  ( ((r1_analmetr A B C) & (r4_analmetr (k2_analmetr A B C) D E D E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) &  ((r1_analort A B C D E G F) &  ( (~  (D = E) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J))) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) =>  (~  ( (~ (r1_collsp (k5_anproj_1 A) B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_anproj_1 A))) &  ((r1_collsp (k5_anproj_1 A) E F H) &  ((r1_collsp (k5_anproj_1 A) C D G) & (r1_collsp (k5_anproj_1 A) B H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_freealg B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((v7_ordinal1 D) & (r2_hidden C (k9_aofa_000 A B D))) ) ) ) ) ) ) ) ) ).
tt(t30_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k81_aofa_i00 A B D E F G)) F) = (k2_xcmplx_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k81_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (B = (a_2_2_armstrng A C))  =>  ((k2_xboole_0 (k1_tarski (k4_tarski C A)) (a_2_3_armstrng A C)) = (k8_armstrng A B)) ) ) ) ) ) ) ) ).
tt(t30_arytm_3,ax, (! [A:$i] :  (! [B:$i] :  (~ (v3_ordinal1 (k4_tarski A B))) ) ) ).
tt(t30_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k8_asympt_0 B)) & (r2_hidden B (k8_asympt_0 C)))  => (r2_hidden A (k8_asympt_0 C))) ) ) ) ) ) ) ).
tt(t30_asympt_1,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((r2_funct_2 k5_numbers k1_numbers A (k1_asympt_1 2 2 k6_numbers)) &  ((r1_tarski (k6_asympt_0 A) (k6_asympt_0 (k5_asympt_1 k6_numbers))) &  (~  ((k6_asympt_0 A) = (k6_asympt_0 (k5_asympt_1 k6_numbers))) ) ) ) ) ) ).
tt(t30_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_autalg_1 C (u1_struct_0 A) (u3_msualg_1 A B) (k5_autalg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_autalg_1 A B))) =>  ( (C = D)  =>  ((k4_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C) = (k2_group_1 (k7_autalg_1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t30_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_autgroup A))) =>  (B = (k1_group_1 (k5_autgroup A))) ) ) ) ) ) ).
tt(t30_bagorder,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v2_wellord1 (k7_bagorder A))) ) ).
tt(t30_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k1_bcialg_1 A C B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(t30_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_bcialg_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k2_bcialg_1 A C)) ) ) ) ) ) ) ) ).
tt(t30_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B (k1_bcialg_1 A B C)))) ) ) ) ) ) ) ) ).
tt(t30_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k7_bcialg_4 A (k8_finseq_1 (u1_struct_0 A) B C)) = (k1_bcialg_4 A (k7_bcialg_4 A B) (k7_bcialg_4 A C))) ) ) ) ) ) ) ).
tt(t30_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (A = D)  =>  ((r1_xxreal_0 B C) |  ((v8_bcialg_1 E) & (m1_bcialg_5 E A (k2_nat_1 C 1) C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((v1_bcialg_6 B A) &  ((v1_bcialg_6 (k3_bcialg_6 A C B) A) &  ((k4_bcialg_6 A B) = D) ) )  =>  ((r1_xxreal_0 C k6_numbers) |  ((k4_bcialg_6 A (k3_bcialg_6 A C B)) = (k5_int_1 D (k6_nat_d C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B D C)) = (k1_bcialg_1 B C D)) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t30_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k3_bhsp_1 A (k3_rlvect_1 A B C)) (k7_real_1 (k3_bhsp_1 A B) (k3_bhsp_1 A C)))) ) ) ) ) ) ).
tt(t30_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_normsp_1 A D C) (k1_rlvect_1 A B C)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_normsp_1 A D C) (k1_rlvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k1_valued_0 (u1_struct_0 A) B C) D) = (k1_valued_0 (u1_struct_0 A) (k1_valued_0 (u1_struct_0 A) B D) C)) ) ) ) ) ) ) ) ) ).
tt(t30_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k3_bhsp_1 A (k1_normsp_1 A B (k2_nat_1 D 1))) (k3_bhsp_1 A (k1_normsp_1 A B D))))) ) ) ) )  & (v1_bhsp_4 B A)) ) ) ) ) ) ) ).
tt(t30_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D (k4_struct_0 B) E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k5_series_1 2 A) B) =>  ((r1_xxreal_0 (k5_series_1 2 (k2_xcmplx_0 A 1)) B) |  ((k1_binari_3 (k2_xcmplx_0 A 1) B) = (k9_binarith A 1 k6_margrel1 (k1_binari_3 A (k7_nat_d B (k5_series_1 2 A))) (k10_binarith k6_margrel1 k8_margrel1))) ) ) ) ) ) ) ).
tt(t30_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d B (k5_series_1 2 A)) = (k4_nat_d C (k5_series_1 2 A)))  =>  ((k1_binari_3 A B) = (k1_binari_3 A C)) ) ) ) ) ) ) ) ).
tt(t30_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A B (k3_lattices A C D)) & (r1_boolealg A (k4_lattices A B D) (k5_lattices A)))  => (r3_lattices A B C)) ) ) ) ) ) ) ) ) ).
tt(t30_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B (u1_struct_0 A)))  =>  ((k2_relset_1 (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B)) = (u1_struct_0 (k11_borsuk_1 A B))) ) ) ) ) ).
tt(t30_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_connsp_1 A k5_topmetr) &  ((v2_compts_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) )  =>  ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) ) ) ) ).
tt(t30_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C (k3_borsuk_5 A B)) <=>  ( (~ (v1_rat_1 C))  &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_borsuk_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((v1_xboole_0 k1_xboole_0) &  ((v2_compts_1 k1_xboole_0 A) & (m1_subset_1 k1_xboole_0 (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ).
tt(t30_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k11_finseq_1 A B C) = (k1_borsuk_7 1 2 3 A B C)) ) ) ) ) ).
tt(t30_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((m2_subset_1 B (u1_struct_0 (k7_bspace A)) (k9_bspace A)) => (v3_card_1 B 1)) ) ) ) ) ).
tt(t30_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C D) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k3_enumset1 C D E F G))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (F = G) )  &  ( ((k15_bvfunc_1 A H (k2_partit1 A (k2_partit1 A E F) G)) = (k15_bvfunc_1 A I (k2_partit1 A (k2_partit1 A E F) G)))  & (r1_xboole_0 (k15_bvfunc_1 A I (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A H (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r2_bvfunc_1 A (k16_bvfunc_1 A B C) C)) ) ) ) ) ) ).
tt(t30_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k10_bvfunc_1 A B (k2_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t30_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc26 A B C)) (k5_bvfunc_1 A B C))) ) ) ) ) ) ).
tt(t30_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k10_bvfunc_1 A C D) B E) (k10_bvfunc_1 A C (k6_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E)) (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t30_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A D E)) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A C E)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A (k5_bvfunc_1 A B C)) (k1_bvfunc_1 A B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t30_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_c0sp1 A))) =>  ( ( (C = E)  &  (D = F) )  =>  ( (F = (k1_rlvect_1 (k11_c0sp1 A) E B))  <=>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((k1_seq_1 D G) = (k8_real_1 B (k1_seq_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((r2_hidden B (k6_c0sp2 A)) => (r2_hidden B (k6_c0sp1 (u1_struct_0 A)))) ) ) ) ).
tt(t30_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) => (r10_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) B (k12_finseq_1 (k3_cqc_lang A) (k5_cqc_lang A)))) (k2_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) B (k12_finseq_1 (k3_cqc_lang A) (k5_cqc_lang A)))))) ) ) ) ).
tt(t30_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C)) &  ((v3_funct_2 D (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers C) (k1_relset_1 k5_numbers C))))) ) )  =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k3_calcul_2 (k3_cqc_lang A) C D) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t30_card_1,ax, (! [A:$i] :  ((k1_card_1 (k1_tarski A)) = 1) ) ).
tt(t30_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  (! [C:$i] :  ((v1_card_1 C) =>  ((k3_card_2 A (k2_card_2 B C)) = (k3_card_2 (k3_card_2 A B) C)) ) ) ) ) ) ) ).
tt(t30_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 B C))) ) )  => (r1_ordinal1 (k6_card_3 A) (k6_card_3 B))) ) ) ) ) ).
tt(t30_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v1_card_5 k4_ordinal1) & (v1_card_5 (k2_card_1 A))) ) ) ).
tt(t30_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v6_card_fil A) => (v4_card_fil A)) ) ) ).
tt(t30_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k10_xtuple_0 C)) & (r1_tarski (k8_relat_1 C (k1_tarski A)) B))  =>  ((k2_card_fin (k5_relat_1 D B) C A) = (k2_card_fin D C A)) ) ) ) ) ) ) ) ).
tt(t30_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v5_card_lar A) => (v5_card_fil A)) ) ) ).
tt(t30_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_cat_1 A B B B (k4_cat_1 A B) (k4_cat_1 A B)) = (k4_cat_1 A B)) ) ) ) ) ).
tt(t30_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ( ((k3_graph_1 (k8_cat_2 A B) (k10_cat_2 A B D F)) = (k4_graph_1 (k8_cat_2 A B) (k10_cat_2 A B C E)))  =>  ((k1_cat_1 (k8_cat_2 A B) (k10_cat_2 A B C E) (k10_cat_2 A B D F)) = (k10_cat_2 A B (k1_cat_1 A C D) (k1_cat_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 D A B C) <=>  ((v1_cat_3 D A B C) & (v2_cat_3 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_cat_1 A B (k2_cat_4 A B (k1_cat_4 A))) & (r1_cat_1 A B (k2_cat_4 A (k1_cat_4 A) B))) ) ) ) ) ).
tt(t30_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u4_struct_0 A) (k9_cat_5 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_cat_5 A B))) =>  ( (D = C)  =>  ((k4_cat_1 (k11_cat_5 A B) D) = (k1_domain_1 (u1_struct_0 (k8_cat_2 (k11_cat_5 A B) (k11_cat_5 A B))) (u4_struct_0 A) (k9_cat_2 (k11_cat_5 A B) (k11_cat_5 A B) D D) (k4_cat_1 A (k3_graph_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 (k23_binop_2 2 A) 1)) = (k23_binop_2 A 1)) ) ) ).
tt(t30_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((r2_hidden E (k2_cat_1 A B C)) & (r2_hidden F (k2_cat_1 A C D)))  =>  ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C D) (k13_catalg_1 A)) (k2_finseq_4 (u4_struct_0 A) F E)) = (k1_cat_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_ncfcont1 B A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) B) & (v1_csspace3 C A)) )  =>  ((v9_clvect_1 C A) & (r2_hidden (k7_clvect_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t30_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v3_funct_1 A) & (v2_comseq_2 B))  =>  ( ((k3_comseq_2 (k2_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k8_complex1 (k3_funct_2 k5_numbers k2_numbers A k6_numbers) (k3_comseq_2 B)))  &  ( ((k3_comseq_2 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k11_complex1 (k3_funct_2 k5_numbers k2_numbers A k6_numbers) (k3_comseq_2 B)))  &  ( ((k3_comseq_2 (k46_valued_1 k5_numbers k2_numbers k2_numbers B A)) = (k11_complex1 (k3_comseq_2 B) (k3_funct_2 k5_numbers k2_numbers A k6_numbers)))  &  ((k3_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k9_complex1 (k3_funct_2 k5_numbers k2_numbers A k6_numbers) (k3_comseq_2 B))) ) ) ) ) ) ) ) ) ).
tt(t30_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v6_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski C (k1_relset_1 k2_numbers (k25_valued_1 k2_numbers k2_numbers B A))) & (r2_cfdiff_1 B C))  =>  ((r2_cfdiff_1 (k25_valued_1 k2_numbers k2_numbers B A) C) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_hidden D C) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 (k25_valued_1 k2_numbers k2_numbers B A) C) D) = (k9_complex1 A (k2_cfdiff_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) => (r2_relset_1 A k1_numbers (k55_valued_1 A k2_numbers (k25_valued_1 A k2_numbers B C)) (k26_valued_1 A k1_numbers (k55_valued_1 A k2_numbers B) (k17_complex1 C)))) ) ) ) ) ) ).
tt(t30_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ( ((r2_hidden A B) &  (! [C:$i] :  ((v2_cgames_1 C) =>  ((r2_hidden C B) => (r1_tarski (k8_cgames_1 C) B)) ) ) )  => (r1_tarski (k10_cgames_1 A) B)) ) ) ) ).
tt(t30_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 C F))) )  &  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 D F))) ) ) )  =>  ((r1_tarski (k3_chain_1 A B C) (k3_chain_1 A E D)) <=>  (~  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 D F)))  &  (~ (r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  ((r1_tarski C B) =>  (! [D:$i] :  ((m2_glib_000 D A B (k21_glib_000 A B)) =>  (! [E:$i] :  ((m2_glib_000 E A C (k21_glib_000 A C)) => (m2_glib_000 E D C (k21_glib_000 D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_circcmb3 B A) =>  (! [C:$i] :  ((m1_circcmb3 C A) =>  (! [D:$i] :  ((m2_circcmb3 D A B) =>  (! [E:$i] :  ((m2_circcmb3 E A C) =>  ((v3_funct_1 (u3_msualg_1 (k2_circcomb B C) (k3_circcomb B C D E))) &  ((k3_funct_1 (u3_msualg_1 (k2_circcomb B C) (k3_circcomb B C D E))) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ( (C = (k2_circcomb A B))  & (r1_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 C)) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 A)) =>  ( (I = J)  =>  ((k3_circuit1 C F G I) = (k3_circuit1 A D H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (m1_subset_1 (k1_funct_1 C E) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k4_classes1 (k1_ordinal1 A)) = (k9_setfam_1 (k4_classes1 A))) ) ) ).
tt(t30_classes2,ax, (! [A:$i] :  ( ((v2_classes1 A) & (v1_ordinal1 A))  => (r1_tarski A (k4_classes1 (k1_card_1 A)))) ) ).
tt(t30_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) = (k4_struct_0 (k14_clopban1 A B))) ) ) ) ) ).
tt(t30_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_clopban3 B A)) ) ) ) ) ) ) ) ).
tt(t30_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k18_complex1 (k1_seq_1 (k3_series_1 (k4_normsp_0 A (k5_clopban4 A B C D))) E)) = (k1_seq_1 (k3_series_1 (k4_normsp_0 A (k5_clopban4 A B C D))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) )  =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) B)) =>  ((r6_pboole (u1_struct_0 A) D (k5_closure1 (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) C)) =>  ((v9_closure1 (g1_closure1 A B D) A) & (l1_closure1 (g1_closure1 A B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t30_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_closure2 C A B (k2_closure2 A B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((r6_pboole A C B) & (v7_closure2 D A B))  => (r6_pboole A C (k7_closure2 A B D C))) ) ) ) ) ) ) ) ).
tt(t30_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t30_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k6_clvect_1 A D C) (k1_clvect_1 A B C)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k6_clvect_1 A D C) (k1_clvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k13_csspace A (k1_normsp_1 A B (k2_nat_1 D 1))) (k13_csspace A (k1_normsp_1 A B D))))) ) ) ) )  & (v1_clvect_3 B A)) ) ) ) ) ) ) ).
tt(t30_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v8_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A B C D) = (k7_relat_1 (k6_cohsp_1 A B C) (k3_cohsp_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t30_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r2_hidden (k1_eqrel_1 A) (k15_coh_sp B))) ) ) ).
tt(t30_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ( ((k5_card_1 C) = (k5_real_1 A 1))  =>  ((k1_setfam_1 (k7_combgras A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t30_complex1,ax, ((k15_complex1 k6_complex1) = k6_complex1) ).
tt(t30_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k1_complex2 A A) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 A)) (k8_real_1 (k4_complex1 A) (k4_complex1 A))))  &  ((k1_complex2 A A) = (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) ) ) ) ).
tt(t30_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  (B = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld B A) A)) ) ) ) ) ) ).
tt(t30_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k12_seq_4 (k9_seq_4 B C) A) = (k9_seq_4 (k12_seq_4 B A) (k12_seq_4 C A))) ) ) ) ) ) ) ) ).
tt(t30_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xxreal_0 B (k4_metric_1 A D E))) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_hidden E C) & (r2_hidden D (k9_metric_1 A E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  ((k62_valued_1 (k11_compos_1 A B)) = 1) ) ) ) ) ).
tt(t30_comptrig,ax, ((k10_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t30_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((r1_tarski (k10_xtuple_0 B) (k2_comput_1 A)) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_margrel1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_margrel1 D)) )  =>  ( ((r2_hidden C (k10_xtuple_0 B)) & (r2_hidden D (k10_xtuple_0 B)))  =>  ((k19_margrel1 C) = (k19_margrel1 D)) ) ) ) ) ) )  => (v3_comput_1 B)) ) ) ) ) ).
tt(t30_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers A) (k36_valued_1 k5_numbers k2_numbers B)) (k36_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ).
tt(t30_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k9_complex1 (k3_comseq_2 A) (k3_comseq_2 B))) ) ) ) ) ).
tt(t30_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 A) B)) (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)) B))) ) ) ) ).
tt(t30_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) )  =>  ((r2_conlat_1 A B (k5_conlat_1 A)) & (r2_conlat_1 A (k6_conlat_1 A) B)) ) ) ) ) ).
tt(t30_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_connsp_1 A B C)) ) ) )  => (v1_connsp_1 A)) ) ) ).
tt(t30_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ((k2_pre_topc (k1_pre_topc A B) C) = (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k5_connsp_3 A B C)) B)) ) ) ) ) ) ) ).
tt(t30_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_convex1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k3_convex1 A B) C)) ) ) ) ) ) ) ).
tt(t30_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (r1_convex4 A (k7_convex4 A k6_complex1 B) B)) ) ) ) ).
tt(t30_cqc_lang,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_binop_1 (k17_funcop_1 A B C) A B) = C) ) ) ) ).
tt(t30_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) B (k13_cqc_sim1 A B) (k1_setwiseo (k3_qc_lang1 A)) (k11_cqc_sim1 (k3_qc_lang1 A))) (k15_cqc_sim1 A B))) ) ) ) ).
tt(t30_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( ((r2_cqc_the1 A B D) & (r1_tarski B C))  => (r2_cqc_the1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t30_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k8_cqc_lang A B C)) (k8_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t30_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r5_cqc_the3 A B C) & (r3_cqc_the1 A D B))  => (r3_cqc_the1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t30_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_2 A) <=> (v1_comseq_2 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(t30_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_csspace A B (k4_struct_0 A)) = k6_numbers) ) ) ) ) ).
tt(t30_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_dickson A))) =>  ( ((v3_dickson A) &  ((r2_hidden C B) & (r1_tarski (k9_subset_1 (u1_struct_0 A) (k1_wellord1 (u1_orders_2 A) C) B) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_dickson A) C))) )  => (r4_waybel_4 B C (u1_orders_2 (k5_dickson A)))) ) ) ) ) ) ) ).
tt(t30_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v3_funct_1 C) =>  ((k9_diff_1 C A B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t30_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I k1_numbers k1_numbers) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers I J) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 J)) (k8_real_1 B J)) C)) ) )  & (r3_zfmisc_1 D E F G H))  =>  ((k1_diff_2 I D E F G H) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers E A) (k26_valued_1 k1_numbers k1_numbers F B)) C D) = (k9_real_1 (k8_real_1 A (k9_diff_1 E C D)) (k8_real_1 B (k9_diff_1 F C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k9_diff_1 k3_taylor_1 A B) = (k13_complex1 (k1_seq_1 k3_taylor_1 (k13_complex1 A B)) (k9_real_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t30_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v2_dilworth C (k5_yellow_0 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)))))  =>  ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t30_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_diraf A B C D) =>  ((r3_diraf A B D C) &  ((r3_diraf A C B D) &  ((r3_diraf A C D B) &  ((r3_diraf A D B C) & (r3_diraf A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k7_subset_1 A B C) = (a_3_3_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t30_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~  (C = (k4_struct_0 (k9_int_3 A))) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  (C = (k2_binom (k9_int_3 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  ( (~ (r1_xxreal_0 A 3))  &  (~  ((k4_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ).
tt(t30_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ( (B = k1_xboole_0)  => (v11_cat_1 B (k11_ens_1 A))) ) ) ) ) ).
tt(t30_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ((r2_hidden E (k4_finseq_1 C)) & (r1_xxreal_0 D E)) )  => (r1_tarski (k4_finseq_1 (k1_matrprob A C D)) (k4_finseq_1 (k1_matrprob A C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k1_enumset1 A A B) = (k2_tarski A B)) ) ) ).
tt(t30_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (~  ((r2_relset_1 A A (k3_eqrel_1 A B C) (k1_eqrel_1 A)) &  ( (~ (r2_relset_1 A A B (k1_eqrel_1 A)))  &  (~ (r2_relset_1 A A C (k1_eqrel_1 A))) ) ) ) ) ) ) ) ) ).
tt(t30_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_funct_1 (k4_equation A) B)) => (r2_hidden (k2_xtuple_0 C) (k1_funct_1 (u3_msualg_1 A (k3_equation A)) B))) ) ) ) ) ) ).
tt(t30_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k15_e_siec A) (k4_xboole_0 (k15_e_siec A) (k4_relat_1 (k12_e_siec A)))) = k1_xboole_0)  &  ((k3_relat_1 (k16_e_siec A) (k4_xboole_0 (k16_e_siec A) (k4_relat_1 (k12_e_siec A)))) = k1_xboole_0) ) ) ) ).
tt(t30_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k3_rlvect_1 (k15_euclid A) B C) (k3_rlvect_1 (k15_euclid A) B C)) = (k9_binop_2 (k9_binop_2 (k23_rvsum_1 B B) (k11_binop_2 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t30_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k3_euclid_3 A) = k6_numbers)  =>  ( (A = (k19_euclid (k12_euclid A) k6_numbers))  &  ((k18_euclid A) = k6_numbers) ) ) ) ) ).
tt(t30_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k7_euclid A B C) (k7_euclid A D E)) = (k7_real_1 (k7_real_1 (k7_real_1 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k23_rvsum_1 (k4_euclid_5 C D A) (k4_euclid_5 E F B)) = (k7_real_1 (k7_real_1 (k8_real_1 C E) (k8_real_1 D F)) (k8_real_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) A B)) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) A C))) ) ) )  =>  ( (B = C)  |  (D = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A))  =>  ((k23_rvsum_1 C (k6_euclid_7 A B)) = (k1_seq_1 C B)) ) ) ) ) ) ) ) ).
tt(t30_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_rlvect_1 (k15_euclid A) B (k11_binop_2 C D)) = (k1_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B D) C)) ) ) ) ) ) ) ) ) ).
tt(t30_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((v1_euclid_4 B A) &  ((r2_hidden C B) & (r2_hidden D B)) )  =>  ( (C = D)  |  (B = (k2_euclid_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_exchsort D)) ) )  =>  ( ((r2_hidden B (k9_xtuple_0 D)) & (r2_hidden C (k9_xtuple_0 D)))  =>  ((k7_partfun1 A (k10_funct_7 D B C) B) = (k7_partfun1 A D C)) ) ) ) ) ) ) ).
tt(t30_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E))) = (k2_compos_1 B)) ) )  => (r1_extpro_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t30_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (~ (r1_xxreal_0 k1_supinf_1 (k3_extreal1 A)))  <=> (r2_hidden A k1_numbers)) ) ) ).
tt(t30_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 B) (k2_msafree2 A)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 A C))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)))  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) (k5_facirc_1 (k2_circcomb A B) (k3_circcomb A B C D) E G) (u1_struct_0 A)) = (k5_facirc_1 A C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_facirc_1 A B C) (k20_facirc_1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_facirc_1 A B C) (k20_facirc_1 A B C) D 2) (k12_facirc_1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ((k1_funct_1 (k5_facirc_1 (k19_facirc_1 A B C) (k20_facirc_1 A B C) D 2) (k17_facirc_1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E F) (k10_margrel1 F G)) (k10_margrel1 G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ( (~  ((k1_relset_1 k1_numbers A) = k1_xboole_0) )  &  ((v1_rcomp_1 (k1_relset_1 k1_numbers A)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A (k1_relset_1 k1_numbers A))) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden B (k1_relset_1 k1_numbers A)) &  ((r2_hidden C (k1_relset_1 k1_numbers A)) &  ( ((k1_seq_1 A B) = (k4_seq_4 (k2_relset_1 k1_numbers A)))  &  ((k1_seq_1 A C) = (k5_seq_4 (k2_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k8_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t30_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_sin_cos9) A) B) = (k9_real_1 (k10_real_1 (k1_seq_1 k2_sin_cos9 B) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 (k1_seq_1 k29_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t30_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k10_prob_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) ) ) )  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) & (v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) ) ) ) ) ) ).
tt(t30_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k7_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2) B) D) = (k10_prepower (k7_real_1 A D) (k1_real_1 (k10_real_1 1 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ( (B = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos C) (k1_taylor_1 2)) k24_sin_cos) k3_taylor_1))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 C D) = 1) ) ) ) ) )  =>  ((r2_fdiff_1 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 B A) D) = (k10_real_1 (k9_real_1 (k1_seq_1 k24_sin_cos D) 1) (k7_real_1 (k1_seq_1 k24_sin_cos D) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)) (k1_real_1 (k10_real_1 1 A))))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C B) &  ((k1_seq_1 k16_sin_cos C) = k6_numbers) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)) (k1_real_1 (k10_real_1 1 A))) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)) (k1_real_1 (k10_real_1 1 A))) B) C) = (k10_real_1 (k1_seq_1 k19_sin_cos C) (k5_prepower (k1_seq_1 k16_sin_cos C) (k3_real_1 A 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) A) B) = (k7_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B)) (k10_real_1 (k1_seq_1 k24_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t30_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) A) B) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k19_sin_cos B)) B) (k10_real_1 (k8_real_1 (k1_seq_1 k3_taylor_1 B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t30_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_pre_ff A) = (k6_xcmplx_0 (k1_pre_ff (k1_nat_1 A 2)) (k1_pre_ff (k1_nat_1 A 1)))) ) ) ).
tt(t30_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k6_xcmplx_0 (k4_nat_1 5 (k13_newton (k1_pre_ff A) 2)) (k13_newton (k1_fib_num3 A) 2)) = (k3_xcmplx_0 4 (k3_power (k4_xcmplx_0 1) (k2_nat_1 A 1)))) ) ) ).
tt(t30_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_fib_num3 A) = (k1_int_1 (k2_xcmplx_0 (k3_power k1_fib_num A) (k13_complex1 1 2)))) ) ) ) ).
tt(t30_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 (k9_finseq_8 A B C))) & (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 (k9_finseq_8 A B C)))) ) ) ) ) ) ) ).
tt(t30_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden B D) => (r2_hidden (k4_filter_0 A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t30_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((r1_lattice2 A C D) & (r1_lattice2 B E F))  <=> (r1_lattice2 (k2_zfmisc_1 A B) (k6_filter_1 A B C E) (k6_filter_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k6_filter_2 A B)) &  ((r2_hidden (k4_lattices A B C) (k6_filter_2 A B)) & (r2_hidden (k4_lattices A C B) (k6_filter_2 A B))) ) ) ) ) ) ) ) ).
tt(t30_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k7_finseq_1 B A)))) ) ) ) ).
tt(t30_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( (B = (k2_finseq_1 A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r1_xxreal_0 A (k3_finseq_1 C)) =>  ((v1_relat_1 (k3_relat_1 D C)) &  ((v1_funct_1 (k3_relat_1 D C)) & (v1_finseq_1 (k3_relat_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B)) <=> (r1_tarski (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers B))) ) ) ) ) ).
tt(t30_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((k3_finseq_1 (k1_finseq_3 A (k1_tarski B))) = (k6_xcmplx_0 (k3_finseq_1 A) 1)) ) ) ) ) ).
tt(t30_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((k1_nat_1 A 1) = (k3_finseq_1 C))  =>  ((k2_rfinseq B A C) = (k12_finseq_1 B (k7_partfun1 B C (k3_finseq_1 C)))) ) ) ) ) ) ) ) ).
tt(t30_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((k6_finseq_4 (k11_finseq_1 A B C) B) = (k9_finseq_1 C)) ) ) ) ) ).
tt(t30_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( (C = D)  |  ( (E = D)  |  ((k7_partfun1 A (k2_finseq_7 A B C E) D) = (k7_partfun1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k1_finseqop A A A F (k2_finseqop A A A F D B) E) (k1_finseqop A A A F D (k3_finseqop A A A F B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C (k6_fintopo2 A B)) &  ((r2_hidden D (k6_fintopo2 A B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E (k6_fintopo2 A B)) & (r1_tarski E (k9_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k9_fintopo2 A C))) ) ) ) ) ) ) ) ).
tt(t30_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k9_subset_1 (u1_struct_0 A) (k5_fintopo3 A B D) (k5_fintopo3 A C D)) = (k3_subset_1 (u1_struct_0 A) (k3_fintopo3 A (k3_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t30_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_fintopo4 A B C) & (r1_fintopo4 A B D))  => (r1_fintopo4 A B (k4_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t30_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) => (r2_hidden (k2_flang_1 A) (k7_flang_1 A B C))) ) ) ) ) ) ).
tt(t30_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden A C) &  ( (~  (A = (k2_flang_1 B)) )  &  ( (~  ((r1_xxreal_0 D k6_numbers) & (r1_xxreal_0 E k6_numbers)) )  &  ((k1_flang_2 B C D E) = (k4_flang_1 B (k2_flang_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k6_flang_1 A (k8_flang_1 A B) B) = (k1_flang_3 A B 1)) ) ) ) ).
tt(t30_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r2_hidden B (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0))) <=>  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  &  (~ (v1_xboole_0 B)) ) ) ) ) ) ).
tt(t30_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k3_pcomps_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_pcomps_1 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k3_pcomps_1 A)) B C) & (v2_tbsp_1 B A))  =>  ((k1_tbsp_1 A B) = (k2_frechet2 (k3_pcomps_1 A) C)) ) ) ) ) ) ) ) ).
tt(t30_frechet,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_frechet))) =>  ( (A = B)  =>  ( ( ( ((k9_subset_1 (u1_struct_0 k3_topmetr) k5_numbers A) = k1_xboole_0)  & (v3_pre_topc A k3_topmetr))  =>  ( (~ (r2_hidden k1_numbers B))  & (v3_pre_topc B k3_frechet)) )  &  ((v3_pre_topc B k3_frechet) =>  ((r2_hidden k1_numbers B) |  ( ((k9_subset_1 (u1_struct_0 k3_topmetr) k5_numbers A) = k1_xboole_0)  & (v3_pre_topc A k3_topmetr)) ) ) ) ) ) ) ) ) ).
tt(t30_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  =>  ( ((k7_fsm_1 B C D A) = (k7_fsm_1 B C D (k2_nat_1 A 1)))  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k7_fsm_1 B C D (k2_nat_1 A E)) = (k7_fsm_1 B C D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ((v5_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers))) ) )  =>  ( ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = (k7_real_1 B C)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C)) = (k7_real_1 B C)) ) ) ) ) ) ) ) ).
tt(t30_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_rewrite3 B (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  ( (~ (v2_struct_0 (k1_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B)))  & (l1_rewrite3 (k1_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B) (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))))) ) ) ) ) ).
tt(t30_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  ( (~  (E = (k4_tarski (k10_finseq_1 D (k36_gfacirc1 A B C)) k2_twoscomp)) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E)))) => (v1_circuit2 (k5_facirc_1 (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E) F 4) (k13_ftacell1 A B C D E) (k14_ftacell1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k3_relat_1 (k6_partfun1 B) (k4_funcop_1 C A D)) = (k4_funcop_1 C (k5_relat_1 A B) D)) ) ) ) ) ) ) ).
tt(t30_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ( ((k2_relset_1 B C) = B)  &  ((r2_relset_1 A A (k1_partfun1 A B B A C D) (k6_partfun1 A)) & (v2_funct_1 C)) )  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  (D = (k2_funct_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v2_funct_1 B) =>  ((k7_relat_1 (k3_funct_3 B) A) = (k8_relat_1 (k1_funct_3 B) A)) ) ) ) ) ).
tt(t30_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=>  ((k2_xboole_0 A B) = (k1_funct_4 A B)) ) ) ) ) ) ).
tt(t30_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k1_funct_5 B))) =>  ((v1_relat_1 (k1_funct_1 (k1_funct_5 B) A)) & (v1_funct_1 (k1_funct_1 (k1_funct_5 B) A))) ) ) ) ) ).
tt(t30_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k6_funct_6 B))) =>  ((v1_relat_1 (k1_funct_1 (k6_funct_6 B) A)) & (v1_funct_1 (k1_funct_1 (k6_funct_6 B) A))) ) ) ) ) ).
tt(t30_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((k9_xtuple_0 (k2_funct_7 A C B)) = (k9_xtuple_0 A)) ) ) ) ) ).
tt(t30_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r1_funct_8 A k1_numbers k1_numbers C))  => (r1_funct_8 A k1_numbers k1_numbers (k52_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t30_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) (k8_real_1 k32_sin_cos A))) ) ).
tt(t30_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((k1_funct_1 (k4_functor0 A A (k11_functor0 A) B C) D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t30_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ((m2_functor2 H A B D E) =>  (! [I:$i] :  ((m2_functor2 I B C F G) =>  ( ((r2_functor2 A B D E) & (r2_functor2 B C F G))  =>  ((r2_functor2 A C (k1_functor3 A B C D F) (k1_functor3 A B C E G)) & (m2_functor2 (k7_functor3 A B C D E F G H I) A C (k1_functor3 A B C D F) (k1_functor3 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r2_funct_2 A k1_numbers (k1_fuzzy_1 A C D) (k4_fuzzy_1 A)))  => (r2_funct_2 A k1_numbers (k1_fuzzy_1 A B D) (k4_fuzzy_1 A))) ) ) ) ) ) ) ) ) ).
tt(t30_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_2 A (k3_fuzzy_2 A B C) D) (k3_fuzzy_2 A B (k3_fuzzy_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t30_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C (k3_rlvect_1 A (k5_struct_0 A) B))))  => (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C B))) ) ) ) ) ) ) ).
tt(t30_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ( ((k4_fvsum_1 A B D C) = (k4_fvsum_1 A B E C))  |  ((k4_fvsum_1 A B D C) = (k4_fvsum_1 A B C E)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  ( (~ (v1_xboole_0 (k24_gate_1 A B C D E F)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  (~ (v1_xboole_0 F)) ) ) ) ) ) )  & (v1_xboole_0 (k24_gate_1 A B C D E F))) ) ) ) ) ) ) ) ) ).
tt(t30_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_gcd_1 A B C (k4_struct_0 A)) = (k4_gcd_1 A B C))  &  ((k5_gcd_1 A B (k4_struct_0 A) C) = (k4_gcd_1 A B C)) ) ) ) ) ) ) ) ).
tt(t30_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((k10_genealg1 E F G k6_numbers k6_numbers A B) = (k8_genealg1 E F G A B))  &  ( ((k10_genealg1 E F G k6_numbers C k6_numbers B) = (k8_genealg1 E F G C B))  &  ( ((k10_genealg1 E F G k6_numbers C A k6_numbers) = (k8_genealg1 E F G C A))  &  ( ((k10_genealg1 E F G D k6_numbers A k6_numbers) = (k8_genealg1 E F G D A))  &  ( ((k10_genealg1 E F G D k6_numbers k6_numbers B) = (k8_genealg1 E F G D B))  &  ((k10_genealg1 E F G D C k6_numbers k6_numbers) = (k8_genealg1 E F G D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k4_geomtrap A B C D (k3_rlvect_1 A E F)) = (k7_real_1 (k4_geomtrap A B C D E) (k4_geomtrap A B C D F)))  &  ( ((k4_geomtrap A B C D (k5_algstr_0 A E F)) = (k9_real_1 (k4_geomtrap A B C D E) (k4_geomtrap A B C D F)))  &  ( ((k4_geomtrap A B C (k5_algstr_0 A E F) D) = (k9_real_1 (k4_geomtrap A B C E D) (k4_geomtrap A B C F D)))  &  ((k4_geomtrap A B C (k3_rlvect_1 A E F) D) = (k7_real_1 (k4_geomtrap A B C E D) (k4_geomtrap A B C F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_twoscomp (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) (k5_facirc_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D 2) (k12_gfacirc1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ( ((k1_funct_1 (k5_facirc_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) = (k2_binarith E F))  &  ( ((k1_funct_1 (k5_facirc_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D 2) A) = E)  &  ( ((k1_funct_1 (k5_facirc_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D 2) B) = F)  &  ((k1_funct_1 (k5_facirc_1 (k10_gfacirc1 A B C) (k11_gfacirc1 A B C) D 2) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k7_glib_000 A) = (k20_glib_000 A (k6_glib_000 A))) ) ) ).
tt(t30_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  ( ((k3_glib_001 A (k7_glib_001 A B C)) = (k3_glib_001 A B))  &  ( ((k4_glib_001 A (k7_glib_001 A B C)) = (k4_glib_001 A C))  & (r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A C) (k7_glib_001 A B C))) ) ) ) ) ) ) ) ) ).
tt(t30_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( ((v4_glib_002 A A) & (m1_glib_000 A A))  <=> (v1_glib_002 A)) ) ) ).
tt(t30_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) => (r1_xxreal_0 (k10_glib_003 A C) (k10_glib_003 A B))) ) ) ) ) ) ).
tt(t30_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (~ (v1_xboole_0 (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))))  & (m1_subset_1 (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k1_zfmisc_1 (k6_glib_000 A))))  & (r1_tarski (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k21_glib_000 A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))))) ) ) ) ) ).
tt(t30_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B) &  ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k2_finseq_1 (k1_matrix_1 B))) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) (k2_nat_1 C 1)) (k2_matrix_1 (k2_goboard2 D))) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 (k2_goboard2 D))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 B 1) C)) ) ) ) ) )  =>  ( ((k5_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) (k2_nat_1 B 1) C))  &  ((k4_goboard5 D A) = (k3_goboard5 (k2_goboard2 D) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) A))  &  ((r2_hidden B (k1_tops_1 (k15_euclid 2) (k1_goboard5 C A))) & (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) 1)) (k17_euclid B))) ) ) ) ) ) ) ) ) ).
tt(t30_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r2_hidden B (k4_finseq_1 A)) &  (~  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) ) ) ) ) ) ) ).
tt(t30_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k7_nat_d (k3_finseq_1 (k2_goboard2 A)) 1) (k1_matrix_1 (k2_goboard2 A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid k6_numbers 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A))) (k19_euclid 1 1))) (k3_topreal1 2 A))) ) ).
tt(t30_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k3_goboard5 B A k6_numbers) = (a_2_4_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t30_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B C)) )  => (v4_pre_topc (k2_gobrd13 B C A) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t30_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_pre_topc (k15_euclid 2) (k3_goboard9 A))) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k3_topreal1 2 A))) ) ) ).
tt(t30_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((k6_goedelcp A (k2_relset_1 (k3_cqc_lang A) B)) = (k3_calcul_1 A B)) ) ) ) ) ).
tt(t30_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_graph_1 B) & (l1_graph_1 B)) )  =>  ((r4_graph_1 B A) <=> (r1_tarski (k11_graph_1 B) (k11_graph_1 A))) ) ) ) ) ).
tt(t30_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  (~  ((r2_graph_1 A B C F) &  ((r2_graph_1 A D E F) &  ( (~  ( (B = D)  &  (C = E) ) )  &  (~  ( (B = E)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k2_graph_3 B C A) = (k2_graph_3 B C (k3_xboole_0 A (u4_struct_0 B))))  &  ((k3_graph_3 B C A) = (k3_graph_3 B C (k3_xboole_0 A (u4_struct_0 B)))) ) ) ) ) ) ) ).
tt(t30_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k3_graph_5 B C D)) <=>  (? [E:$i] :  ( ((v7_graph_1 E B) & (m2_graph_1 E B))  &  ( (E = A)  & (r1_graph_5 B E C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) => (r1_xxreal_0 (k15_graphsp (k7_graphsp B A) B A) A)) ) ) ) ).
tt(t30_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k17_grcat_1 A)) =>  ( (~ (v2_struct_0 B))  &  ((v8_algstr_0 B) &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) ) ) ) ) ) ).
tt(t30_gr_cy_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_int_1 (k1_newton A B) C) = (k6_int_1 (k1_newton (k6_int_1 A C) B) C)) ) ) ) ) ) ) ).
tt(t30_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ( ((k1_funct_1 A C) = (k1_funct_1 B C))  &  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) )  =>  ((k5_relat_1 A (k2_tarski C D)) = (k5_relat_1 B (k2_tarski C D))) ) ) ) ) ) ) ) ).
tt(t30_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  => (r2_groeb_1 A B C (k1_groeb_1 A C (k7_polynom1 A C)) (k1_groeb_1 A C (k7_polynom1 A C)))) ) ) ) ) ) ).
tt(t30_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)))))  =>  (! [E:$i] :  ((m2_ideal_1 E (k11_polynom1 A B) D) =>  ((r2_groeb_2 A B C D E) => (r1_tarski (k2_polynom1 (k15_pre_poly A) B C) (k3_tarski (a_4_1_groeb_2 A B D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))))  => (r2_hidden (k3_termord A B C D) (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k2_group_11 A (k1_group_11 A (k2_group_11 A B C) C) C)) & (r1_xboole_0 (k13_group_2 A C D) (k1_group_11 A (k2_group_11 A B C) C))) ) ) ) ) ) ) ) ) ) ).
tt(t30_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_xxreal_0 A k6_numbers) =>  ((k5_group_1 B A C) = (k2_group_1 B (k5_group_1 B (k1_int_2 A) C))) ) ) ) ) ) ) ) ).
tt(t30_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k2_group_2 A (k5_group_2 A D B) C) = (k2_group_2 A B (k4_group_2 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t30_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_3 A B C) = B) ) ) ) )  => (v5_group_1 A)) ) ) ).
tt(t30_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r1_group_2 A (k5_group_4 A (k1_subset_1 (u1_struct_0 A))) (k6_group_2 A))) ) ).
tt(t30_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B (k2_group_3 A C (k2_group_1 A B))) = (k2_group_5 A C (k2_group_1 A B))) ) ) ) ) ) ) ).
tt(t30_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  ( ( (~ (v2_struct_0 (k5_group_6 A B)))  &  ((v2_group_1 (k5_group_6 A B)) &  ((v3_group_1 (k5_group_6 A B)) &  ((v5_group_1 (k5_group_6 A B)) & (l3_algstr_0 (k5_group_6 A B))) ) ) )  <=> (m1_group_6 (k9_group_5 A) A B)) ) ) ) ) ).
tt(t30_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 C)) =>  ((k6_algstr_0 (k2_group_7 (k1_enumset1 1 2 3) (k11_finseq_1 A B C)) (k6_group_7 A B C D F H) (k6_group_7 A B C E G I)) = (k6_group_7 A B C (k6_algstr_0 A D E) (k6_algstr_0 B F G) (k6_algstr_0 C H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ( ((k16_group_9 A B C D) = (k16_group_9 A B D C))  =>  ((u1_struct_0 (k19_group_9 A B C D)) = (k16_group_9 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t30_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  (! [E:$i] :  ((m1_group_2 E B) =>  ( ((v3_groupp_1 D A) &  ((v3_groupp_1 E A) &  ((u1_struct_0 C) = (k7_group_4 B D E)) ) )  => (v3_groupp_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((v1_hallmar1 B A) &  (! [D:$i] :  ((m3_hallmar1 D A B C) =>  (~ (v1_hallmar1 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  => (r1_xxreal_0 k6_numbers (k9_weierstr A B C))) ) ) ) ) ) ) ).
tt(t30_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k13_glib_001 A (k2_helly A B B)) = (k1_tarski B)) ) ) ) ) ).
tt(t30_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k1_bilinear k1_complfld A B)) (k1_bilinear k1_complfld A B))) ) ) ) ).
tt(t30_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  ((r1_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) (k5_heyting3 A) B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden (k1_domain_1 k5_numbers k5_numbers D A) C) & (v1_abian D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_xxreal_0 1 A) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k1_taylor_1 A) B) 2) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k9_real_1 A 2)) (k8_real_1 A (k9_real_1 A 1))) B))) ) ) ) ) ).
tt(t30_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) =>  ((k3_funct_2 (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (k6_hilbasis A B) (k3_funct_2 (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)) (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (k7_hilbasis A B) C)) = C) ) ) ) ) ) ) ).
tt(t30_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) => (r2_hidden (k3_hilbert1 A (k4_hilbert1 A A)) k6_hilbert1)) ) ).
tt(t30_hilbert2,ax, ((k3_hilbert2 k2_hilbert1) = (k2_trees_4 k1_hilbert1 k2_hilbert1)) ).
tt(t30_hilbert3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((k3_hilbert3 B (k1_hilbert2 A)) = (k1_funct_1 B A)) ) ) ) ) ).
tt(t30_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_polynom5 A (k3_hurwitz A B 1) B)) ) ) ) ).
tt(t30_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ((r1_idea_1 A (k1_recdef_1 C 1)) &  ((r1_idea_1 A (k1_recdef_1 C 2)) &  ((r1_idea_1 A (k1_recdef_1 C 3)) &  ((r1_idea_1 A (k1_recdef_1 C 4)) &  ( ((k1_recdef_1 D 1) = (k10_idea_1 A (k1_recdef_1 C 1)))  &  ( ((k1_recdef_1 D 2) = (k6_idea_1 A (k1_recdef_1 C 3)))  &  ( ((k1_recdef_1 D 3) = (k6_idea_1 A (k1_recdef_1 C 2)))  &  ((k1_recdef_1 D 4) = (k10_idea_1 A (k1_recdef_1 C 4))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k11_idea_1 A (k13_idea_1 (k11_idea_1 A (k13_idea_1 B) C)) D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t30_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m3_ideal_1 D A B) => (m1_ideal_1 (k9_fvsum_1 A D C) A B)) ) ) ) ) ) ) ) ).
tt(t30_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k2_incsp_1 A C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t30_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) => (m3_cat_2 (k10_index_1 A (k15_index_1 A B C D E)) (k4_cat_5 C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t30_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_instalg1 B A))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) => (m2_pboole (k5_relat_1 E (u1_struct_0 B)) (u1_struct_0 B) (u3_msualg_1 B (k2_instalg1 A B C)) (u3_msualg_1 B (k2_instalg1 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k2_int_1 A) = A)  <=> (v1_int_1 A)) ) ) ).
tt(t30_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_int_2 A) &  ((v1_int_2 B) &  ( (~ (r1_int_2 A B))  &  (~  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t30_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ((k3_finseq_1 A) = (k7_real_1 D 1)) )  => (r2_relset_1 k5_numbers k1_numbers (k5_wsierp_1 k1_numbers k5_numbers C (k1_wsierp_1 k1_numbers k5_numbers A (k12_finseq_1 k5_numbers B))) (k1_wsierp_1 k1_numbers k5_numbers (k5_wsierp_1 k1_numbers k5_numbers C A) (k12_finseq_1 k5_numbers B)))) ) ) ) ) ) ) ) ) ).
tt(t30_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( ((k3_int_2 A B) = 1)  &  ((k3_int_2 C B) = 1) )  =>  ((r1_xxreal_0 B 2) |  ((k2_int_5 (k3_xcmplx_0 A C) B) = (k3_xcmplx_0 (k2_int_5 A B) (k2_int_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t30_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  (! [C:$i] :  ((m1_int_6 C B) =>  (! [D:$i] :  ((m1_int_6 D B) => (r2_int_1 (k16_rvsum_1 (k18_valued_1 A C)) (k16_rvsum_1 (k18_valued_1 A D)) (k19_rvsum_1 B))) ) ) ) ) ) ) ) ) ).
tt(t30_int_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v8_struct_0 A) &  ((k6_group_1 A B) = (k4_nat_1 C D)) )  =>  ((k6_group_1 A (k5_group_1 A C B)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t30_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k1_sin_cos2)) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k4_sin_cos2) k1_sin_cos2) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k4_sin_cos2) k1_sin_cos2) (k5_seq_4 A)))) ) ) ).
tt(t30_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos))) &  ((r2_relset_1 k1_numbers k1_numbers D (k3_rfunct_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k19_sin_cos)) (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos)))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k11_binop_2 A F))  &  (~  (A = k6_numbers) ) ) ) ) )  &  (E = (k1_relset_1 k1_numbers D)) ) ) ) )  =>  ((k2_integra5 B D) = (k10_binop_2 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos) (k7_binop_2 (k12_binop_2 1 A))) (k1_partfun2 k1_numbers E)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k30_sin_cos) (k7_binop_2 (k12_binop_2 1 A))) (k1_partfun2 k1_numbers E)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos))))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t30_integr14,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = (k10_real_1 (k9_real_1 (k1_seq_1 k16_sin_cos (k8_real_1 A F)) (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A F)))) (k5_square_1 (k1_seq_1 k19_sin_cos (k8_real_1 A F))))) ) ) )  &  ((r1_tarski E (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers E)))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 D F) = (k8_real_1 A F))  &  (~  (A = k6_numbers) ) ) ) ) )  &  ( (E = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers E)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k1_fdiff_9) (k10_real_1 1 A)) (k1_partfun2 k1_numbers E)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  ( ((r1_xxreal_0 B C) &  ( (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 B C)) =>  ((k1_funct_1 F H) = G) ) ) )  &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) )  =>  ((k12_integr15 D E A F) = (k9_euclid A G (k10_binop_2 E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_seq_2 (k2_partfun1 A k1_numbers D A)) &  ((k3_finseq_1 B) = 1) )  => (r1_xxreal_0 (k6_integra1 A D C) (k6_integra1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t30_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [D:$i] :  ((m1_integra1 D B) =>  ( ((v2_seq_2 (k2_partfun1 B k1_numbers C B)) & (r1_xxreal_0 A k6_numbers))  =>  ((k6_integra1 B (k26_valued_1 B k1_numbers C A) D) = (k8_real_1 A (k7_integra1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v3_integra1 B A) & (v1_comseq_2 (k2_partfun1 A k1_numbers (k6_rfunct_1 A k1_numbers B) A))) )  =>  ((r2_hidden k6_numbers (k1_rvsum_1 B)) | (v3_integra1 (k6_rfunct_1 A k1_numbers B) A)) ) ) ) ) ) ).
tt(t30_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k9_real_1 (k1_seq_1 (k1_taylor_1 (k2_nat_1 C 1)) A) (k1_seq_1 (k1_taylor_1 (k2_nat_1 C 1)) B)) = (k4_integra5 B A (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 C) (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t30_integra8,ax, ((k2_fdiff_1 k1_sin_cos2 k1_numbers) = k4_sin_cos2) ).
tt(t30_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ((k1_integra9 D (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) = (k1_integra9 D A (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t30_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_interva1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k3_setfam_1 B (k2_setfam_1 C D)) = (k2_setfam_1 (k3_setfam_1 B C) (k3_setfam_1 B D))) ) ) ) ) ) ) ) ).
tt(t30_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A (k3_intpro_1 A B)) (k3_intpro_1 A B)) k8_intpro_1)) ) ) ) ).
tt(t30_irrat_1,ax, ((v2_comseq_2 k4_irrat_1) &  ((k2_seq_2 k4_irrat_1) = (k4_series_1 k5_irrat_1)) ) ).
tt(t30_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G C D) =>  (! [H:$i] :  ((m2_cat_1 H D B) =>  (! [I:$i] :  ((m2_nattra_1 I C D F G) =>  ((r2_nattra_1 C D F G) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k5_isocat_1 A C B (k9_cat_1 C D B F H) (k9_cat_1 C D B G H) E (k4_isocat_1 C D B F G I H)) (k4_isocat_1 A D B (k9_cat_1 A C D E F) (k9_cat_1 A C D E G) (k5_isocat_1 A C D F G E I) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  ((r2_nattra_1 A B D E) =>  (! [G:$i] :  ((m2_nattra_1 G A B D E) =>  ((k4_isocat_1 A B C D E G F) = (k3_relat_1 G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_isomichi,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((k3_borsuk_5 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t30_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid A) = (k7_square_1 (k7_real_1 (k5_square_1 (k17_euclid A)) (k5_square_1 (k18_euclid A))))) ) ) ).
tt(t30_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k1_funct_1 k5_pscomp_1 C)) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t30_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  =>  ( ( ( ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A)))  |  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  =>  ((k1_funct_1 (k2_funct_1 k1_jgraph_3) A) = (k19_euclid (k8_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))) (k8_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))))) )  &  (~  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A))) )  &  ( (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  &  (~  ((k1_funct_1 (k2_funct_1 k1_jgraph_3) A) = (k19_euclid (k8_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))) (k8_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))))) ) ) ) ) ) ) ) ) ).
tt(t30_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_0_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((k22_pscomp_1 A) = (k19_euclid 1 k6_numbers)) ) ) ) ).
tt(t30_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) = (a_3_5_jgraph_6 A C D))  &  ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D)) = (a_3_6_jgraph_6 A B D))  &  ( ((k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C)) = (a_3_6_jgraph_6 A B C))  &  ((k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D)) = (a_3_5_jgraph_6 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 (k18_euclid B) H) & (r1_xxreal_0 G (k18_euclid D))) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ( (~ (v3_funct_1 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k1_rltopsp1 (k15_euclid 2) B C)) = (k1_tarski A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden E (k1_rltopsp1 (k15_euclid 2) B C)))  &  ( (~ (r2_hidden B (k3_topreal1 2 D)))  &  ( (~ (r2_hidden C (k3_topreal1 2 D)))  &  ( ( ( ((k17_euclid B) = (k17_euclid C))  &  ((k17_euclid B) = (k17_euclid E)) )  |  ( ((k18_euclid B) = (k18_euclid C))  &  ((k18_euclid B) = (k18_euclid E)) ) )  &  ( (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 (k2_nat_1 F 1) (k3_finseq_1 D)) &  ( ((r2_hidden E (k2_gobrd13 D (k2_goboard2 D) F)) | (r2_hidden E (k3_gobrd13 D (k2_goboard2 D) F)))  & (r2_hidden A (k2_topreal1 2 D F))) ) ) ) )  &  ( (~ (r2_hidden E (k3_topreal1 2 D)))  &  ( (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D)) F) &  ((r2_hidden E F) & (r2_hidden B F)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D)) F) &  ((r2_hidden E F) & (r2_hidden C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_jordan1h A B) &  ((r1_xxreal_0 (k3_jordan11 A B) C) & (r1_xxreal_0 C (k2_nat_1 (k4_nat_1 (k13_newton 2 (k7_nat_d B (k1_jordan11 A))) (k7_nat_d (k2_jordan11 A) 2)) 2))) )  => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 (k1_jordan8 A B) (k7_nat_d (k3_jordan1h A B) 1) C) (k3_topreal1 2 (k1_jordan13 A B))) (k1_jordan2c 2 (k3_topreal1 2 (k1_jordan13 A B))))) ) ) ) ) ) ) ).
tt(t30_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) => (r1_jordan18 A B C D E C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 C A)) (k3_finseq_1 (k1_jordan8 C B)))) ) ) ) ) ) ) ).
tt(t30_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (m1_subset_1 (a_4_5_jordan1 A B C D) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ) ) ) ).
tt(t30_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k3_finseq_1 (k1_jordan8 B A)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ) ) ) ) ).
tt(t30_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 1 C)) ) ) ) ) ) ) ) ) ).
tt(t30_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k4_finseq_4 (k2_jordan1e B A) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = (k3_finseq_1 (k2_jordan1e B A))) ) ) ) ) ).
tt(t30_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski 1 C) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 C) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski (k3_finseq_1 B) C) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) C) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ).
tt(t30_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k8_pscomp_1 B) (k8_pscomp_1 A)))  =>  ((k22_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k22_pscomp_1 B)) ) ) ) ) ) ).
tt(t30_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ( (~  (A = B) )  & (r1_xxreal_0 (k1_topreal6 2 B C) (k1_topreal6 2 A C))) ) ) ) ) ) ) ) ) ).
tt(t30_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r1_topreal4 A B C) &  ( (~ (r1_xxreal_0 E (k17_euclid B)))  &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  ( (~ (r1_jordan20 A B C D E))  &  (~ (r2_jordan20 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ((v1_jordan21 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r2_hidden (k1_jordan21 A) A)) ) ).
tt(t30_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k22_pscomp_1 A) (k3_jordan19 A))) ) ).
tt(t30_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_topreal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (v1_topreal1 (k3_jordan3 A B))) ) ) ) ) ) ).
tt(t30_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 k1_numbers A 1) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))  &  ((k7_partfun1 k1_numbers A 2) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A)) ) ) ) ).
tt(t30_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_jordan3 C D A B) =>  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) A D)) & (r2_hidden A (k1_rltopsp1 (k15_euclid 2) C B))) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_jordan4 A B C D) => (r1_jordan4 A (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) B) D C)) ) ) ) ) ) ) ) ) ).
tt(t30_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((v2_funct_1 A) &  ((r1_xxreal_0 2 (k3_finseq_1 A)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k2_topreal1 2 A B))) ) ) )  =>  (B = 1) ) ) ) ) ) ).
tt(t30_jordan5c,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) & (v4_topreal1 A)) )  =>  ( (B = C)  |  ((r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B C) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden B (k2_topreal1 2 A D)) &  ((r2_hidden C (k2_topreal1 2 A E)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A))) ) ) ) )  =>  ((r1_xxreal_0 D E) &  ( (D = E)  => (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1)) B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_jordan5d,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( (B = (a_1_5_jordan5d A))  =>  ((k4_seq_4 B) = (k2_pscomp_1 (k1_pre_topc (k15_euclid 2) (k3_topreal1 2 A)) (k3_pscomp_1 (k15_euclid 2) k5_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ) ) ).
tt(t30_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v4_pre_topc (k6_jordan6 A) (k15_euclid 2)) & (v4_pre_topc (k7_jordan6 A) (k15_euclid 2))) ) ) ).
tt(t30_jordan9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 C)))  =>  ((r1_xboole_0 (k3_gobrd13 C (k1_jordan8 A B) D) A) &  (~ (r1_xboole_0 (k2_gobrd13 C (k1_jordan8 A B) D) A)) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k1_matrix_1 (k1_jordan8 A B))))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 D 1) (k1_matrix_1 (k1_jordan8 A B))))  &  ((r2_hidden (k20_pscomp_1 A) (k3_goboard5 (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) &  (~  ((k20_pscomp_1 A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k7_nat_d (k1_matrix_1 (k1_jordan8 A B)) 1))) ) ) ) ) ) ) ) ) )  |  ((k20_pscomp_1 (k3_topreal1 2 C)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1)) ) ) ) ) ) ) ) ) ).
tt(t30_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan_a A (k3_finseq_1 B) B) (k2_jordan_a A (k7_nat_d (k3_finseq_1 B) 1) B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) ).
tt(t30_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  ( ( (C = E)  &  ( (D = F)  & (r1_tarski (k2_relset_1 (u1_struct_0 A) G) (u1_struct_0 B))) )  =>  ((r1_borsuk_6 B E F) & (m1_borsuk_2 G B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r3_lattices A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r1_ordinal1 (k1_card_1 D) (k1_card_1 (u1_struct_0 A))) & (r2_abian (u1_struct_0 A) (k5_knaster A B C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)))) ) ).
tt(t30_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = D)  =>  ((r1_frechet2 (k15_euclid A) B C) <=>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r1_xxreal_0 F G) & (r2_hidden (k3_funct_2 k5_numbers (u1_struct_0 (k15_euclid A)) B G) (k9_metric_1 (k14_euclid A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  ((k4_matrix_6 A B C (k1_matrix_7 A B (k5_matrix_1 A (u1_struct_0 B) (k7_laplace A B C)) (k11_algstr_0 B (k12_matrix_3 A B C)))) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t30_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k1_funct_1 (k3_latsubgr A B C) (k6_group_2 A)) = (k6_group_2 B)) ) ) ) ) ) ) ).
tt(t30_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) =>  ((k3_funct_2 C (u1_struct_0 A) E F) = B) ) ) )  =>  ( (D = k1_xboole_0)  |  ((k2_lattice2 C A D E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r4_lattice3 B C A) <=> (r2_lattice3 (k3_lattice3 B) A (k4_lattice3 B C))) ) ) ) ) ) ).
tt(t30_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  ((k7_lattices A (k5_lattices A)) = (k6_lattices A)) ) ) ).
tt(t30_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_lattice5 E A B D) =>  ((v1_funct_1 (k11_lattice5 A B D E C)) &  ((v1_funct_2 (k11_lattice5 A B D E C) (k2_zfmisc_1 (k8_lattice5 A C) (k8_lattice5 A C)) (u1_struct_0 B)) & (m1_subset_1 (k11_lattice5 A B D E C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_lattice5 A C) (k8_lattice5 A C)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((m1_lattice8 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k1_xtuple_0 (k1_funct_1 D E)) (k1_xtuple_0 (k1_funct_1 D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)))) =>  (~  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)) = (k6_glib_000 A)) )  & (r2_hidden (k10_lexbfs A B) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) B)))) ) ) ) ) ) ).
tt(t30_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  => (r1_fuzzy_1 B (k5_lfuzzy_1 A B))) ) ) ) ).
tt(t30_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 A) =>  ((v2_seq_2 A) | (v2_limfunc1 A)) ) ) ) ).
tt(t30_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) )  | (r5_limfunc2 B A)) ) ) ) ) ) ).
tt(t30_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r4_limfunc2 B A) &  ((k1_limfunc2 B A) = (k2_limfunc2 B A)) ) )  =>  ((r1_limfunc3 B A) &  ( ((k1_limfunc3 B A) = (k1_limfunc2 B A))  &  ((k1_limfunc3 B A) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) ).
tt(t30_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r6_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k4_limfunc1 A))) ) ) ) )  | (v5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t30_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) => (r1_lmod_6 A (k1_vectsp_5 A B C (k2_vectsp_5 A B D E)) (k2_vectsp_5 A B (k1_vectsp_5 A B D C) (k1_vectsp_5 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((k1_seq_1 (k15_lopban_1 A B) C) = (k4_seq_4 (k14_lopban_1 A B C))) ) ) ) ) ) ) ).
tt(t30_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_lopban_3 B A)) ) ) ) ) ) ) ) ).
tt(t30_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C)) = (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))  &  ((r1_xxreal_0 C D) =>  ((k18_complex1 (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) D) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))) = (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) D) (k8_nat_1 k1_numbers (k3_series_1 (k4_sin_cos (k1_normsp_0 A B))) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A) (k5_lattices A)) = k1_xboole_0) ) ) ).
tt(t30_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r1_lpspace1 A B C D E) & (r1_lpspace1 A B C E F))  => (r1_lpspace1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_lpspace2 A B C F))) =>  ( (D = G)  =>  ((k26_valued_1 A k1_numbers D E) = (k1_rlvect_1 (k2_lpspace2 A B C F) G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r3_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 A)) B) <=> (r3_ltlaxio1 C (k3_hilbert1 (k6_ltlaxio1 A) B))) ) ) ) ) ) ) ).
tt(t30_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A C)) (k8_cqc_lang A C (k6_cqc_lang A B))) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t30_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B (k4_subset_1 (u1_struct_0 A) C D)) = (k4_subset_1 (u1_struct_0 A) (k6_rusub_4 A B C) (k6_rusub_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t30_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 k6_numbers A) & (v2_matrix10 C))  => (v3_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t30_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_matrix_1 E D A B) =>  (E = (k3_matrix11 C A B D E (k8_matrix_1 D E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 (u1_struct_0 D))))  =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ((r2_hidden C (k2_finseq_1 B)) &  ((k1_funct_1 E A) = (k1_funct_1 E C)) ) )  =>  ( (A = C)  |  ((k12_matrix_3 B D (k1_matrix13 (u1_struct_0 D) G B B F E)) = (k4_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k5_matrix_1 A (u1_struct_0 B) (k4_matrix_6 A B C D)) = (k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) D) (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ).
tt(t30_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k2_matrix13 (k3_finseq_1 C) 1 A (k3_matrix15 (u1_struct_0 A) C) B) = (k3_matrix15 (u1_struct_0 A) (k9_fvsum_1 A C B))) ) ) ) ) ) ) ).
tt(t30_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 B) A A) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ( ((v3_matrix16 F (u1_struct_0 B)) &  ((v3_matrix16 G (u1_struct_0 B)) & (v3_matrix16 H (u1_struct_0 B))) )  => (v3_matrix16 (k2_matrix_6 A B (k3_matrix_6 A B (k2_matrix13 A A B F C) (k2_matrix13 A A B G D)) (k2_matrix13 A A B H E)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  ((m1_subset_1 A (k10_matrix_1 C B)) <=> (m1_matrix_1 A (u1_struct_0 C) B B)) ) ) ) ) ) ).
tt(t30_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 C)) =>  ( ( (! [I:$i] :  ((m1_subset_1 I B) =>  ((k3_funct_2 B A F I) = (k7_setwiseo C A D H (k10_funct_5 B C A (k9_funct_2 C A) (k11_funct_5 B C A E) I))) ) )  &  ((v1_setwiseo D A) &  ((v1_binop_1 D A) & (v2_binop_1 D A)) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C G H) E) = (k7_setwiseo B A D G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 E))  &  ((k3_matrix_3 A B C) = (k1_matrix_4 A D E)) ) ) ) ) ) )  =>  ((k3_matrix_3 A B E) = (k1_matrix_4 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v12_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((v3_matrix_6 D B A) & (r2_hidden C (k2_finseq_1 B)))  =>  ((k3_matrix_1 (u1_struct_0 A) D C C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k1_finsop_1 (u1_struct_0 A) (k8_finseq_1 (u1_struct_0 A) B C) (u2_algstr_0 A)) = (k8_group_1 A (k1_finsop_1 (u1_struct_0 A) B (u2_algstr_0 A)) (k1_finsop_1 (u1_struct_0 A) C (u2_algstr_0 A)))) ) ) ) ) ) ) ).
tt(t30_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v4_matrix_8 C A B) => (v3_matrix_8 C A B)) ) ) ) ) ) ) ).
tt(t30_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  ( (A = (k3_finseq_4 k5_numbers 1 3 2))  => (v4_matrix_2 A 3)) ) ) ).
tt(t30_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ( (A = B)  & (r1_xxreal_0 1 (k3_finseq_1 A)))  =>  ((k18_rvsum_1 A) = (k17_rvsum_1 B)) ) ) ) ) ) ).
tt(t30_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden D (k4_finseq_1 C)) & (r2_hidden (k4_tarski E F) (k2_matrix_1 (k2_matrixj1 A C D))))  =>  ((r2_hidden (k4_tarski (k1_nat_1 E (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d D 1) (k10_matrixj1 A C)))) (k1_nat_1 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d D 1) (k11_matrixj1 A C))))) (k2_matrix_1 (k13_matrixj1 A B C))) &  ((k3_matrix_1 A (k2_matrixj1 A C D) E F) = (k3_matrix_1 A (k13_matrixj1 A B C) (k1_nat_1 E (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d D 1) (k10_matrixj1 A C)))) (k1_nat_1 F (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d D 1) (k11_matrixj1 A C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D B) &  ((v9_vectsp_1 D B) &  ((v10_vectsp_1 D B) &  ((v11_vectsp_1 D B) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D B)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 D)) &  ((v13_vectsp_1 E D D) &  ((v1_mod_2 E B D D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 D))))) ) ) )  =>  (! [F:$i] :  ( ((v1_matrlin F B) & (m1_vectsp_4 F B D))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 F) (u1_struct_0 F)) &  ((v13_vectsp_1 G F F) &  ((v1_mod_2 G B F F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 F) (u1_struct_0 F))))) ) ) )  =>  (~  ( (F = (k1_ranknull B D D (k1_vectsp11 D (k3_matrlin B D D E (k4_matrlin B D D (k3_struct_0 D) (k4_algstr_0 B C))) A)))  &  ((r1_funct_2 (u1_struct_0 F) (u1_struct_0 D) (u1_struct_0 F) (u1_struct_0 F) (k8_matrlin2 B D D F E) G) &  (! [H:$i] :  ( ((v2_relat_1 H) & (m1_matrixj2 H B C))  =>  (! [I:$i] :  ((m1_matrlin I B F) =>  (~  ((k1_matrlin2 B F F G I I) = (k20_matrixj1 (u1_struct_0 B) (k4_struct_0 B) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  =>  ((k4_matrix_1 k1_numbers (k7_matrixr1 A B)) = (k7_matrixr1 A (k4_matrix_1 k1_numbers B))) ) ) ) ) ) ).
tt(t30_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((k5_matrix_1 A k1_numbers (k1_matrixr2 A B C)) = (k1_matrixr2 A (k5_matrix_1 A k1_numbers C) (k5_matrix_1 A k1_numbers B))) ) ) ) ) ) ) ).
tt(t30_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C B) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D B C) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 F) = (k3_finseq_1 G))  &  ( ((k3_finseq_1 F) = (k3_finseq_1 E))  &  ((r2_hidden A (k4_finseq_1 D)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k1_funct_1 G H) = (k1_funct_1 (k9_matrlin B C D (k7_partfun1 (u1_struct_0 C) E H)) A)) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 F) k1_xboole_0) |  ((k13_fvsum_1 B F G) = (k1_funct_1 (k9_matrlin B C D (k4_rlvect_1 C (k5_matrlin B C F E))) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  =>  ((k4_rlvect_1 B (k3_fvsum_1 B C D)) = (k3_rlvect_1 B (k4_rlvect_1 B C) (k4_rlvect_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k6_matroid0 A B)) <=>  ((k4_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C))) = (k4_matroid0 A B)) ) ) ) ) ) ) ) ).
tt(t30_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k14_rvsum_1 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t30_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) B A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ((k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A D) (k5_rusub_4 (k15_euclid B) E C)) = (k5_rusub_4 (k15_euclid A) (k2_ranknull (k15_euclid B) (k15_euclid A) (k3_matrtop1 B A D) E) (k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 B A D) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_matrtop3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid C))) =>  (~  ((r2_hidden B A) &  ((r2_hidden B (k2_finseq_1 C)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid C)) (u1_struct_0 (k15_euclid C))) &  ((v13_vectsp_1 E (k15_euclid C) (k15_euclid C)) &  ((v1_topreal9 E C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid C)) (u1_struct_0 (k15_euclid C)))))) ) ) )  =>  (~  ((v1_matrtop3 E A) &  ((v3_matrtop3 E C) &  ( ( (~ (r1_xxreal_0 (k5_card_1 (k9_subset_1 k5_numbers A (k2_finseq_1 C))) 1))  => (r1_xxreal_0 k1_xboole_0 (k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid C)) (u1_struct_0 (k15_euclid C)) E D) B)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k9_subset_1 k5_numbers A (k2_finseq_1 C))) =>  ( (F = B)  |  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid C)) (u1_struct_0 (k15_euclid C)) E D) F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r2_pboole A B (k1_mboolean A (k2_mboolean A B)))) ) ) ).
tt(t30_mcart_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (~  ( ((r2_hidden C A) | (r2_hidden D A))  &  (B = (k6_xtuple_0 C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_xboole_0 D E) =>  ((k12_supinf_2 C (k1_measure1 A B D E)) = (k3_supinf_2 (k12_supinf_2 C D) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v6_xxreal_2 (k2_measure6 A B)) & (m1_subset_1 (k2_measure6 A B) (k1_zfmisc_1 k1_numbers))) ) ) ) ) ).
tt(t30_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v2_prob_1 D) => (v8_valued_0 (k11_measure8 A B D C))) ) ) ) ) ) ) ) ).
tt(t30_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((r1_tarski A B) <=> (r1_tarski (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(t30_membered,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v6_membered B)) )  => (v6_membered (k3_tarski A))) ) ).
tt(t30_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  => (r1_tarski (k7_memstr_0 A B (k5_memstr_0 A B C)) C)) ) ) ) ) ) ).
tt(t30_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((r1_mesfun6c A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r1_mesfunc6 A B (k55_valued_1 A k2_numbers C) D)) ) ) ) ) ) ) ) ) ).
tt(t30_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k7_numbers (k5_mesfunc1 A (k1_mesfunc5 A B) (k1_mesfunc5 A C)) (k1_mesfunc5 A (k20_valued_1 A k1_numbers k1_numbers B C)))) ) ) ) ) ) ).
tt(t30_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k2_numbers (k3_mesfun9c A E) B))) & (r1_xxreal_0 C B))  =>  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k2_numbers (k3_mesfun9c A E) C))) & (r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k2_numbers E C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_tarski E D) & (r1_mesfunc1 A B C D))  => (r1_mesfunc1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ( ((v1_prob_2 C) & (m2_finseq_1 C B))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) &  ((v1_prob_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) ) )  =>  (~  ( ((k3_tarski (k10_xtuple_0 C)) = (k2_measure2 A B (k1_measure3 A B D)))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 C)) =>  ((k1_funct_1 C E) = (k8_nat_1 B D E)) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r2_hidden E (k9_xtuple_0 C)))  =>  ((k8_nat_1 B D E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ((k19_mesfunc1 A B C) = (k8_relset_1 A k7_numbers B (k1_tarski C))) ) ) ) ) ) ) ).
tt(t30_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((k1_mesfunc2 A (k1_mesfunc5 A B)) = (k18_rfunct_3 A B))  &  ((k2_mesfunc2 A (k1_mesfunc5 A B)) = (k19_rfunct_3 A B)) ) ) ) ) ) ).
tt(t30_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 D A k7_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers)) = F)  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers D G) F)) )  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (? [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) &  ((r1_tarski H F) &  ( ((k12_supinf_2 C (k7_prob_1 A B F H)) = k6_numbers)  &  (! [I:$i] :  ((m1_subset_1 I A) =>  (~  ((r2_hidden I H) & (r1_xxreal_0 k1_xxreal_0 (k3_extreal1 (k12_supinf_2 (k4_mesfunc5 A k7_numbers D G) I)))) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C F)) |  ( (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (~  ((r1_tarski G F) &  ( ((k12_supinf_2 C (k7_prob_1 A B F G)) = k6_numbers)  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H F) => (v7_mesfunc5 (k3_mesfunc5 A D H))) ) )  &  ( ((k1_relset_1 A E) = F)  &  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H G) =>  ((k12_supinf_2 E H) = (k2_mesfunc5 (k3_mesfunc5 A D H))) ) ) ) ) ) ) ) ) ) )  |  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) =>  (~  ((r1_tarski H F) &  ((r1_xxreal_0 (k12_supinf_2 C (k7_prob_1 A B F H)) G) &  (! [I:$i] :  ((v1_xreal_0 I) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((v7_ordinal1 J) =>  (? [K:$i] :  ((v7_ordinal1 K) &  ( (~ (r1_xxreal_0 K J))  &  (? [L:$i] :  ((m1_subset_1 L A) &  ((r2_hidden L H) & (r1_xxreal_0 I (k3_extreal1 (k4_supinf_2 (k12_supinf_2 (k4_mesfunc5 A k7_numbers D K) L) (k12_supinf_2 E L))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers B C))) )  => (v2_mesfunc9 B A)) ) ) ) ) ).
tt(t30_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_metric_1 A B C D) => (r1_metric_1 A D C B)) ) ) ) ) ) ) ) ) ).
tt(t30_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((k6_metric_2 A) = (k7_metric_2 A)) ) ) ).
tt(t30_metric_3,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers)) => (r1_xxreal_0 (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 A C) (k7_real_1 (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 A B) (k1_metric_1 (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) (k3_zfmisc_1 k1_numbers k1_numbers k1_numbers) k22_metric_3 B C)))) ) ) ) ) ) ).
tt(t30_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid (k23_binop_2 A 1)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid (k23_binop_2 A 1)))) =>  ( (~  (B = (k4_struct_0 (k15_euclid (k23_binop_2 A 1)))) )  => (v3_mfold_1 (k3_mfold_2 (k23_binop_2 A 1) B C) A)) ) ) ) ) ) ) ).
tt(t30_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) => (r2_hidden B (k4_midsp_1 A B))) ) ) ) ).
tt(t30_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k3_midsp_1 A C D) = (k3_midsp_1 A E F))  <=>  ((k9_midsp_2 A B C D) = (k1_algstr_0 (u1_midsp_2 A B) (k9_midsp_2 A B C E) (k9_midsp_2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ((r1_midsp_3 A B C) =>  ((r3_midsp_3 A B C) <=>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (u1_midsp_2 C D))) =>  ((k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B (k1_algstr_0 (u1_midsp_2 C D) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) E B) F))) = (k1_algstr_0 (u1_midsp_2 C D) (k10_midsp_3 A C D E) (k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k2_mmlquery A B D) = (k2_mmlquery A C D)) ) )  => (r2_relset_1 A A B C)) ) ) ) ) ) ).
tt(t30_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_mod_4 C A B) <=> (v4_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t30_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_subset_1 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 k6_numbers) (k1_domain_1 k5_numbers k5_numbers 3 A)) k6_modal_1)) ) ).
tt(t30_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((k52_modelc_1 A B C D) = (k52_modelc_1 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v3_modelc_2 A) | (v6_modelc_2 A))  => (r2_modelc_2 (k10_modelc_2 A) A)) ) ) ).
tt(t30_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ( ((r4_modelc_3 B D C) & (r2_hidden A (u2_modelc_3 B D)))  =>  ((r2_hidden A (u2_modelc_3 B C)) | (r1_modelc_3 B D C A)) ) ) ) ) ) ) ) ) ) ).
tt(t30_moebius1,ax, ((k2_moebius1 1) = 1) ).
tt(t30_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ( ((v1_group_1 A) & (r2_hidden (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) (u1_struct_0 B)))  =>  ((v1_group_1 B) &  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = (k4_binop_1 (u1_struct_0 B) (u2_algstr_0 B))) ) ) ) ) ) ) ).
tt(t30_monoid_1,ax, (! [A:$i] :  (! [B:$i] : (m1_subset_1 (k5_funct_3 A B) (u1_struct_0 (k13_monoid_1 B)))) ) ).
tt(t30_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A D) B) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A D) C))) ) ) ) ) ) ) ) ) ).
tt(t30_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ((r2_pboole (u1_struct_0 A) (k4_msafree3 A C D) B) => (m1_dtconstr D (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ) ) ) ) ) ).
tt(t30_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 C D)) =>  (~  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ((v2_finset_1 C) &  ((r2_pboole A C (k3_funct_6 B)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r2_pboole A D (k2_funct_6 B)) &  ((v2_finset_1 D) & (r6_pboole A (k9_pboole A D B) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_unialg_1 A) &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) &  ((v4_unialg_1 B) & (m1_unialg_2 B A)) )  =>  (! [C:$i] :  ( ((v1_unialg_1 C) &  ((v4_unialg_1 C) & (m1_unialg_2 C A)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k6_msualg_1 A)) &  ((v4_msualg_1 D (k6_msualg_1 A)) & (m1_msualg_2 D (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  (! [E:$i] :  ( ((v3_msualg_1 E (k6_msualg_1 A)) &  ((v4_msualg_1 E (k6_msualg_1 A)) & (m1_msualg_2 E (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  ( ( (D = (k9_msualg_1 B))  &  (E = (k9_msualg_1 C)) )  =>  ((k9_msualg_1 (k8_unialg_2 A B C)) = (k13_msualg_2 (k6_msualg_1 A) (k9_msualg_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v2_binop_1 (k15_msualg_2 A B) (k14_msualg_2 A B))) ) ) ) ).
tt(t30_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  => (v4_msualg_6 (k6_msualg_6 A B C) A B)) ) ) ) ) ) ).
tt(t30_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) => (r8_pboole (u1_struct_0 A) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B (k17_msualg_4 A B C D))) (u3_msualg_1 A C) (k15_msualg_4 A B (k17_msualg_4 A B C D)) (k19_msualg_4 A B C D)) D)) ) ) ) ) ) ) ) ) ).
tt(t30_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v2_mycielsk A) & (l1_orders_2 A)) )  =>  ((k3_mycielsk A) = (k2_mycielsk (k3_necklace A))) ) ) ).
tt(t30_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ((r1_nagata_1 (u1_struct_0 A) C) =>  ((r1_xxreal_0 B k6_numbers) | (r1_nagata_1 (u1_struct_0 A) (k5_nagata_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B C))) ) ) ) ) ) ) ) ).
tt(t30_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 6) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  (~  (A = 6) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k7_nat_d (k7_nat_d A B) C) = (k7_nat_d A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t30_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((r1_nat_d C B) => (r1_xxreal_0 (k11_nat_3 C A) (k11_nat_3 B A))) ) ) ) ) ) ) ).
tt(t30_nat_4,ax,(v1_int_2 23)).
tt(t30_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_int_2 A) =>  ((k5_nat_5 (k1_newton A B)) = (k18_binop_2 (k21_binop_2 (k1_newton A (k23_binop_2 B 1)) 1) (k21_binop_2 A 1))) ) ) ) ) ) ).
tt(t30_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) |  ((k3_int_2 A B) = (k3_int_2 B (k6_int_1 A B))) ) ) ) ) ) ) ).
tt(t30_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m3_nattra_1 (k6_nattra_1 A B C) A B C C)) ) ) ) ) ) ).
tt(t30_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k1_relset_1 (u1_struct_0 A) C)) =>  ((r2_funct_2 k5_numbers k1_numbers (k4_normsp_0 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 A) D (k3_normsp_0 (u1_struct_0 A) B C))) & (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_vfunct_1 k5_numbers B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D C)) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) D (k5_vfunct_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_nfcont_1 D A) & (r9_ncfcont1 A B C D))  => (r3_ncfcont2 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t30_ndiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r2_ndiff_1 A B C D) => (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ).
tt(t30_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B))))))  =>  ((r2_ndiff_3 (k4_real_ns1 B) C A) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  => (r2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 D B)) A)) ) ) ) ) ) ) ) ) ).
tt(t30_ndiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v2_prvect_2 B) & (v1_ndiff_5 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 B)) (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 B))) =>  (! [F:$i] :  ( ((r2_hidden F (k4_finseq_1 B)) & (r1_ndiff_5 B C F D E))  =>  ((r1_ndiff_5 B C F (k4_vfunct_1 (u1_struct_0 (k14_prvect_2 B)) C D A) E) &  ((k6_ndiff_5 B C F (k4_vfunct_1 (u1_struct_0 (k14_prvect_2 B)) C D A) E) = (k1_rlvect_1 (k16_lopban_1 (k11_prvect_2 B (k5_ndiff_5 B F)) C) (k6_ndiff_5 B C F D E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) ) )  =>  (~  ( (~ (v1_neckla_3 A))  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v1_necklace B) &  ((v3_necklace B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_orders_2 C) &  ((v1_necklace C) &  ((v3_necklace C) & (l1_orders_2 C)) ) ) )  =>  (~  ((r1_subset_1 (u1_struct_0 B) (u1_struct_0 C)) &  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k1_neckla_2 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_necklace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r5_waybel_1 (k4_necklace A) (k3_necklace (k4_necklace A))) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  (~  (A = 4) ) ) ) ) ) ) ) ).
tt(t30_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_newton (k2_xcmplx_0 B C) A) = (k18_rvsum_1 (k7_newton B C A))) ) ) ) ) ) ) ).
tt(t30_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((v1_nfcont_1 (k1_relset_1 (u1_struct_0 B) C) B) & (r3_nfcont_1 B A C (k1_relset_1 (u1_struct_0 B) C)))  => (v1_nfcont_1 (k2_relset_1 (u1_struct_0 A) C) A)) ) ) ) ) ) ) ).
tt(t30_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 C)))))  =>  ( ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) D A) C) & (r1_tarski A (k1_relset_1 k1_numbers D)))  => (v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 C) (k4_vfunct_1 k1_numbers C D B) A) C)) ) ) ) ) ) ) ) ).
tt(t30_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v1_partfun1 B k1_numbers) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k7_partfun1 (k1_euclid A) B (k9_binop_2 C D)) = (k7_euclid A (k7_partfun1 (k1_euclid A) B C) (k7_partfun1 (k1_euclid A) B D))) ) ) ) ) )  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~ (r1_nfcont_4 A B C)) ) )  | (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) B k1_numbers) A)) ) ) ) ) ) ).
tt(t30_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C (k2_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B)) & (r1_tarski D (k3_domain_1 (k5_finsub_1 A) (k5_finsub_1 A) B)))  => (m2_subset_1 (k4_tarski C D) (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A))) ) ) ) ) ) ).
tt(t30_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) =>  ((v2_frechet C (k4_normsp_2 A)) <=> (v3_normsp_1 B A)) ) ) ) ) ) ) ) ).
tt(t30_numbers,ax, (~  (k5_numbers = k2_numbers) ) ).
tt(t30_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (r1_tarski (k9_openlatt A) (k9_setfam_1 (k7_openlatt A)))) ) ).
tt(t30_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_orders_1 A B) => (r1_orders_1 A B)) ) ) ) ).
tt(t30_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~  (B = k1_xboole_0) )  & (m1_orders_2 B A B)) )  &  (~  ( (~ (m1_orders_2 B A B))  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t30_ordinal1,ax, (! [A:$i] :  ((v1_relat_1 k1_xboole_0) &  ((v5_relat_1 k1_xboole_0 A) &  ((v1_funct_1 k1_xboole_0) & (v5_ordinal1 k1_xboole_0)) ) ) ) ).
tt(t30_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k10_ordinal2 k1_xboole_0 A) = A) ) ) ).
tt(t30_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k10_ordinal2 (k10_ordinal2 A B) C) = (k10_ordinal2 A (k10_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t30_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k12_ordinal2 A (k10_ordinal2 B C)) = (k11_ordinal2 (k12_ordinal2 A C) (k12_ordinal2 A B))) ) ) ) ) ) ) ).
tt(t30_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_hidden 1 A) => (v4_ordinal1 (k1_ordinal5 A k4_ordinal1))) ) ) ).
tt(t30_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ( ((k10_xtuple_0 (k3_ordinal6 A)) = (a_1_0_ordinal6 A))  & (r1_tarski (k10_xtuple_0 (k3_ordinal6 A)) (k10_xtuple_0 A))) ) ) ).
tt(t30_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t30_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k2_ortsp_1 A B E F D C) = (k2_ortsp_1 A B F E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k23_osafree A B C) = (a_3_4_osafree A B C)) ) ) ) ) ) ) ).
tt(t30_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_osalg_1 A B C) <=> (r2_hidden C (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (u1_osalg_1 A) B))) ) ) ) ) ) ) ).
tt(t30_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ( ((k10_osalg_2 A B C) = (k10_msualg_2 A B (k9_osalg_2 A B C)))  & (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k10_osalg_2 A B C)) (k9_osalg_2 A B C))) ) ) ) ) ) ) ).
tt(t30_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_1 A B C D E))  &  ((r1_parsp_1 A B C F G) &  ((r1_parsp_1 A D E H I) &  ( (~  (F = G) )  &  ( (~  (H = I) )  & (r1_parsp_1 A F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) => (r2_parsp_2 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_relset_1 A C (k3_partfun1 E A C) (k3_partfun1 E B D))) ) ) ) ) ) ) ).
tt(t30_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ( (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B D)) =>  ((k7_partfun1 A D E) = C) ) ) )  => (r2_relset_1 B A D (k4_partfun2 B A (k1_relset_1 B D) C))) ) ) ) ) ) ) ) ) ).
tt(t30_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ( ((r1_setfam_1 D B) & (r1_setfam_1 D C))  => (r1_setfam_1 D (k2_partit1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t30_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ((v2_relat_2 C) & (r1_tarski (k1_relat_1 C) B))  => (r2_relat_2 C B)) ) ) ) ) ) ) ).
tt(t30_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v5_pasch A)) ) ).
tt(t30_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k3_pboole A B (k2_pboole A B C)) B)) ) ) ) ) ).
tt(t30_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) => (r2_hidden (u1_struct_0 A) (k2_pcomps_1 A))) ) ).
tt(t30_pcs_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (u1_struct_0 A)))  => (v4_orders_2 (k19_pcs_0 A B))) ) ) ) ).
tt(t30_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ( ((r2_pdiff_1 A B C D F) & (r2_pdiff_1 A B C E F))  =>  ((r2_pdiff_1 A B C (k2_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E) F) &  ((k9_pdiff_1 B A C (k2_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) D E) F) = (k5_algstr_0 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)) (k9_pdiff_1 B A C D F) (k9_pdiff_1 B A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r2_pdiff_3 C B) =>  ((r3_pdiff_1 2 2 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 1 2 C) A) B) &  ((k11_pdiff_1 2 2 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 1 2 C) A) B) = (k8_real_1 A (k3_pdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t30_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 3 B A) & (r3_pdiff_1 3 3 C A))  => (r3_pdiff_1 3 3 (k20_valued_1 (k1_euclid 3) k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t30_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r3_pdiff_5 B A) =>  ((k3_pdiff_5 B A) = (k11_pdiff_1 3 3 (k1_pdiff_3 1 3 B) A)) ) ) ) ) ) ).
tt(t30_pdiff_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 C))))))  =>  ( (D = E)  =>  ((r1_pdiff_6 A C B D) <=> (r2_ndiff_1 A (k4_real_ns1 B) (k4_real_ns1 C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r2_hidden E (k1_relset_1 (k1_euclid A) C)) &  ( (E = F)  &  (C = D) ) )  =>  ((k7_partfun1 (k1_euclid B) C E) = (k7_partfun1 (u1_struct_0 (k4_real_ns1 B)) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r3_pdiff_7 A B C D) => (r3_pdiff_7 A B (k9_integr15 B E (k1_euclid A) C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_newton A B) = (k1_newton A C))  =>  ((r1_xxreal_0 A 1) |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t30_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ((m1_pnproc_1 C A) =>  (! [D:$i] :  ((m1_pnproc_1 D A) =>  ((r2_pnproc_1 A (k2_pnproc_1 A (k4_pnproc_1 A C) (k4_pnproc_1 A D)) B) => (r1_pnproc_1 A (k6_pnproc_1 A (k6_pnproc_1 A B C) D) (k2_pnproc_1 A (k2_pnproc_1 A (k3_pnproc_1 A (k3_pnproc_1 A B (k4_pnproc_1 A C)) (k4_pnproc_1 A D)) (k5_pnproc_1 A C)) (k5_pnproc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t30_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ( ((k7_polyeq_1 A B C k6_numbers D) = k6_numbers)  =>  ( (A = k6_numbers)  |  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k2_numbers) =>  (~  ( (F = (k4_binop_2 (k1_polyeq_3 (k6_binop_2 B (k5_binop_2 2 A))) (k6_binop_2 C A)))  &  ( (G = (k6_binop_2 B (k5_binop_2 2 A)))  &  ( (~  (D = k6_numbers) )  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 F) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2)) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 F)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2)) k7_complex1)) G)) )  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 F) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2))) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 F)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2))) k7_complex1)) G)) )  &  ( (~  (D = (k4_binop_2 (k3_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 F) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2)) (k5_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 F)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2))) k7_complex1)) G)) )  &  (~  (D = (k4_binop_2 (k3_binop_2 (k7_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k3_complex1 F) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2))) (k5_binop_2 (k7_square_1 (k12_binop_2 (k9_binop_2 (k7_binop_2 (k3_complex1 F)) (k7_square_1 (k9_binop_2 (k5_square_1 (k3_complex1 F)) (k5_square_1 (k4_complex1 F))))) 2)) k7_complex1)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( (~  (F = k6_numbers) )  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 F (k1_newton A 4)) (k3_xcmplx_0 E (k1_newton A 3))) (k3_xcmplx_0 B (k1_newton A 2))) (k3_xcmplx_0 C A)) D) = k6_numbers)  <=>  (~  ( (~  (A = (k5_polyeq_5 (k13_complex1 D F) (k13_complex1 C F) (k13_complex1 B F) (k13_complex1 E F))) )  &  ( (~  (A = (k6_polyeq_5 (k13_complex1 D F) (k13_complex1 C F) (k13_complex1 B F) (k13_complex1 E F))) )  &  ( (~  (A = (k7_polyeq_5 (k13_complex1 D F) (k13_complex1 C F) (k13_complex1 B F) (k13_complex1 E F))) )  &  (~  (A = (k8_polyeq_5 (k13_complex1 D F) (k13_complex1 C F) (k13_complex1 B F) (k13_complex1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k11_polyform A (k4_xcmplx_0 1)) = 1) ) ) ).
tt(t30_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B (k8_polynom1 A B) C) C)) ) ) ) ) ) ).
tt(t30_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  =>  ( ((k1_normsp_1 A (k10_polynom3 A) k6_numbers) = (k5_struct_0 A))  &  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (B = k6_numbers) )  =>  ((k8_nat_1 (u1_struct_0 A) (k10_polynom3 A) B) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t30_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k3_polynom5 A B C) D) = (k8_group_1 A C (k2_polynom4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t30_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v5_algstr_0 B) &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_vectsp_2 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k5_polynom7 A B C D) E) = (k6_algstr_0 B D (k5_polynom2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_polynom8 A (k4_struct_0 A) B)) ) ) ) ) ).
tt(t30_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_polyred A B C (k7_polynom1 A C) D)) ) ) ) ) ) ) ) ).
tt(t30_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k3_power (k3_xcmplx_0 A B) C) = (k3_xcmplx_0 (k3_power A C) (k3_power B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  (! [D:$i] :  ( ((v3_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r6_msualg_3 B (k14_pralg_2 A B C) (k14_pralg_2 (k8_eqrel_1 A D) B (k4_pralg_3 (k8_eqrel_1 A D) B (k6_partfun1 (k8_eqrel_1 A D)) (k3_pralg_3 A B C D))))) ) ) ) ) ) ) ) ).
tt(t30_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 (k1_funct_1 B C))))  =>  ((r2_hidden (k2_nat_1 (k2_wsierp_1 (k10_pre_poly A (k17_finseq_1 (k3_finseq_2 A) (k7_nat_d C 1) B))) D) (k4_finseq_1 (k5_pre_poly A B))) &  ((k1_funct_1 (k1_funct_1 B C) D) = (k1_funct_1 (k5_pre_poly A B) (k2_nat_1 (k2_wsierp_1 (k10_pre_poly A (k17_finseq_1 (k3_finseq_2 A) (k7_nat_d C 1) B))) D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 A (k2_prepower B A)) &  (~ (r1_xxreal_0 1 (k2_prepower B A))) ) ) ) ) ) ) ) ).
tt(t30_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v3_pre_topc B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))))) ) ) ) ) ).
tt(t30_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  ((k1_seq_1 C (k4_prob_1 A B)) = 1) ) ) ) ) ) ) ).
tt(t30_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C (k5_prob_1 A B D E)) k6_numbers))  =>  ((k1_seq_1 C (k5_prob_1 A B (k5_prob_1 A B D E) F)) = (k8_real_1 (k8_real_1 (k1_seq_1 C D) (k1_seq_1 (k3_prob_2 A B C D) E)) (k1_seq_1 (k3_prob_2 A B C (k5_prob_1 A B D E)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k1_kurato_0 A (k2_prob_3 A C)) = (k1_kurato_0 A C)) ) ) ) ) ) ).
tt(t30_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k4_prob_4 A B C)) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k6_prob_4 A B C D)) & (r2_hidden F (k6_prob_4 A B C D)))  =>  ((k1_funct_1 C E) = (k1_funct_1 C F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k10_cqc_lang A (k9_cqc_lang A B C) (k9_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t30_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A C E) & (r1_incsp_1 A D E))  =>  ( (C = D)  |  ((r1_incsp_1 A B E) |  ( (~  ((k1_projpl_1 A C B) = (k1_projpl_1 A D B)) )  &  (~  ((k1_projpl_1 A B C) = (k1_projpl_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k18_euclid (k10_pscomp_1 A)) (k18_euclid (k18_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k10_pscomp_1 A)) (k18_euclid (k19_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k10_pscomp_1 A)) (k18_euclid (k11_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k18_pscomp_1 A)) (k18_euclid (k19_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k18_pscomp_1 A)) (k18_euclid (k11_pscomp_1 A))) & (r1_xxreal_0 (k18_euclid (k19_pscomp_1 A)) (k18_euclid (k11_pscomp_1 A)))) ) ) ) ) ) ) ).
tt(t30_pua2mss1,ax, (! [A:$i] :  ((l1_msualg_1 A) =>  (! [B:$i] :  ((l1_msualg_1 B) =>  (! [C:$i] :  ((l1_msualg_1 C) =>  ( ((r4_pua2mss1 A B) & (r4_pua2mss1 B C))  => (r4_pua2mss1 A C)) ) ) ) ) ) ) ).
tt(t30_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k2_mboolean A (k1_pzfmisc1 A B)) B)) ) ) ).
tt(t30_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  ( ((r2_qc_lang1 A B C) & (r1_qc_lang1 A C D))  => (r2_qc_lang1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t30_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((k12_qc_lang2 A (k2_qc_lang2 A B C)) = B)  &  ( ((k11_qc_lang2 A (k2_qc_lang2 A B C)) = C)  &  ((k18_qc_lang1 A (k2_qc_lang2 A B C)) = (k14_qc_lang1 A B (k13_qc_lang1 A C))) ) ) ) ) ) ) ) ) ).
tt(t30_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) &  ((k2_qc_lang3 A C) = B) ) ) ) ) ) ) ).
tt(t30_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((k5_trees_2 (k2_qc_lang4 A B) C) = (k2_qc_lang4 A (k3_trees_2 (k9_qc_lang1 A) (k2_qc_lang4 A B) C))) ) ) ) ) ) ) ).
tt(t30_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_lattices A B C) & (r3_lattices A D E))  => (r3_lattices A (k9_quantal1 A B D) (k9_quantal1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k17_quaterni (k6_quatern2 A B)) = (k10_real_1 (k7_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni B) (k17_quaterni A)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni B) (k19_quaterni A))) (k8_real_1 (k20_quaterni B) (k20_quaterni A))) (k5_square_1 (k3_quatern2 B))))  &  ( ((k18_quaterni (k6_quatern2 A B)) = (k10_real_1 (k7_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k17_quaterni B) (k18_quaterni A)) (k8_real_1 (k18_quaterni B) (k17_quaterni A))) (k8_real_1 (k19_quaterni B) (k20_quaterni A))) (k8_real_1 (k20_quaterni B) (k19_quaterni A))) (k5_square_1 (k3_quatern2 B))))  &  ( ((k19_quaterni (k6_quatern2 A B)) = (k10_real_1 (k9_real_1 (k9_real_1 (k7_real_1 (k8_real_1 (k17_quaterni B) (k19_quaterni A)) (k8_real_1 (k18_quaterni B) (k20_quaterni A))) (k8_real_1 (k19_quaterni B) (k17_quaterni A))) (k8_real_1 (k20_quaterni B) (k18_quaterni A))) (k5_square_1 (k3_quatern2 B))))  &  ((k20_quaterni (k6_quatern2 A B)) = (k10_real_1 (k9_real_1 (k7_real_1 (k9_real_1 (k8_real_1 (k17_quaterni B) (k20_quaterni A)) (k8_real_1 (k18_quaterni B) (k19_quaterni A))) (k8_real_1 (k19_quaterni B) (k18_quaterni A))) (k8_real_1 (k20_quaterni B) (k17_quaterni A))) (k5_square_1 (k3_quatern2 B)))) ) ) ) ) ) ) ) ).
tt(t30_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k5_square_1 (k3_quatern2 (k27_quaterni (k27_quaterni A B) C))) = (k8_real_1 (k8_real_1 (k5_square_1 (k3_quatern2 A)) (k5_square_1 (k3_quatern2 B))) (k5_square_1 (k3_quatern2 C)))) ) ) ) ) ) ) ).
tt(t30_quaterni,ax, ( ((k17_quaterni k1_xcmplx_0) = k6_numbers)  &  ( ((k18_quaterni k1_xcmplx_0) = 1)  &  ( ((k19_quaterni k1_xcmplx_0) = k6_numbers)  &  ((k20_quaterni k1_xcmplx_0) = k6_numbers) ) ) ) ).
tt(t30_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((u1_struct_0 (k19_quofield A)) = (k7_quofield A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k19_quofield A)) (u1_struct_0 (k19_quofield A))) (u1_struct_0 (k19_quofield A)) (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A) (u1_algstr_0 (k19_quofield A)) (k15_quofield A)) &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k19_quofield A)) (u1_struct_0 (k19_quofield A))) (u1_struct_0 (k19_quofield A)) (k2_zfmisc_1 (k7_quofield A) (k7_quofield A)) (k7_quofield A) (u2_algstr_0 (k19_quofield A)) (k16_quofield A)) &  ( ((k4_struct_0 (k19_quofield A)) = (k11_quofield A))  &  ((k5_struct_0 (k19_quofield A)) = (k12_quofield A)) ) ) ) ) ) ) ).
tt(t30_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ((m1_random_1 C A (k1_random_1 A)) => (r1_random_1 A (k1_random_1 A) C B)) ) ) ) ) ) ).
tt(t30_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A C) => (r1_tarski (k1_vectsp_6 A B (k8_ranknull A C B E D)) (k2_ranknull C B D (k1_vectsp_6 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t30_rat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( ( (C = (k6_real_1 B A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  (? [E:$i] :  ((v1_int_1 E) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ( (B = (k4_real_1 E D))  &  (A = (k4_nat_1 F D)) ) ) ) ) ) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ( (A = (k1_rat_1 C))  &  (B = (k2_rat_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v4_ratfunc1 B A))  & (m1_ratfunc1 B A))  =>  ((v5_ratfunc1 B A) <=>  ((k12_ratfunc1 A B) = (k4_xxreal_0 (k2_hurwitz A (k4_ratfunc1 A B)) (k2_hurwitz A (k5_ratfunc1 A B)))) ) ) ) ) ) ).
tt(t30_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (~ (r2_hidden A B))  &  ( (~ (r1_xxreal_0 A (k5_seq_4 B)))  &  (~ (r1_xxreal_0 (k4_seq_4 B) A)) ) ) ) ) ) ) ) ).
tt(t30_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) k6_numbers) = B)  &  ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 1)) = k6_numbers) ) ) ) ) ) ).
tt(t30_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_binop_1 (k2_realset3 A) B (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) C D)) = (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t30_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ((r2_classes1 (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A))) &  ( ((k20_rfunct_3 C (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) C) = (k20_rfunct_3 B (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B))  &  ((k21_rfunct_3 C (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A)) C) = (k21_rfunct_3 B (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski A B) => (r1_tarski (k3_relat_1 A C) (k3_relat_1 B C))) ) ) ) ) ) ) ).
tt(t30_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_relat_2 A) <=>  ((k2_zfmisc_1 (k1_relat_1 A) (k1_relat_1 A)) = (k2_xboole_0 A (k2_relat_1 A))) ) ) ) ).
tt(t30_relset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k8_relset_1 A C D B)) <=>  (? [F:$i] :  ((m1_subset_1 F C) &  ((r2_hidden (k4_tarski E F) D) & (r2_hidden F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( (E = (a_4_3_relset_2 A B C D))  =>  ((k6_relset_2 A B (k5_setfam_1 A D) C) = (k8_setfam_1 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_revrot_1,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 4))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 1)) (k2_topreal1 2 A 1)) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) ) ) ) ).
tt(t30_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_rewrite1 A B C) & (r2_rewrite1 A C D))  => (r2_rewrite1 A B D)) ) ) ) ) ) ).
tt(t30_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r2_rewrite2 A (k7_rewrite2 A B) C D) => (r2_rewrite2 A B C D)) ) ) ) ) ) ) ) ).
tt(t30_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~ (v1_xboole_0 G))  =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k8_afinsq_1 G))) =>  (! [I:$i] :  ( ((v2_rewrite3 I G H) & (l1_rewrite3 I H))  =>  ( ((r2_rewrite3 G H I A B C D) & (r2_rewrite3 G H I A B E F))  =>  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k4_finseq_1 (k5_rfinseq2 A)) = (k4_finseq_1 A))  &  ((k3_finseq_1 (k5_rfinseq2 A)) = (k3_finseq_1 A)) ) ) ) ).
tt(t30_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((r2_classes1 A B) &  (! [D:$i] :  (~  ((r2_hidden D (k4_finseq_1 B)) &  ((k1_funct_1 A C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k4_rfunct_1 (k54_valued_1 A)) = (k54_valued_1 (k4_rfunct_1 A))) ) ) ).
tt(t30_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) & (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) ).
tt(t30_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_rfunct_3 A k1_numbers (k15_rfunct_3 A B) C)) ) ) ) ) ) ).
tt(t30_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k2_relset_1 k1_numbers (k1_valued_0 k1_numbers B A)) = (a_2_1_rinfsup1 A B)) ) ) ) ) ).
tt(t30_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v8_valued_0 A) =>  ((r1_xxreal_0 (k12_supinf_2 A B) k2_supinf_1) |  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 A B)) |  ((v2_rinfsup2 (k1_valued_0 k7_numbers A B)) &  ((k1_rinfsup2 (k1_valued_0 k7_numbers A B)) = (k12_supinf_2 A B)) ) ) ) ) ) ) ) ) ).
tt(t30_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v2_funct_1 C) & (r1_tarski (k3_rlvect_2 A B) (k10_xtuple_0 C)))  =>  ((k3_rlaffin1 A B) = (k18_rvsum_1 (k4_finseqop (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ) ).
tt(t30_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_ordinal1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( ((v1_rlaffin1 (k5_setfam_1 (u1_struct_0 A) B) A) & (v1_finset_1 (k5_setfam_1 (u1_struct_0 A) B)))  => (r1_tarski (k1_rlaffin2 A (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B)) (k1_rlaffin2 A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t30_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r1_funct_2 (u1_struct_0 B) (u1_struct_0 k3_topmetr) (k2_struct_0 B) (k1_tarski k1_xboole_0) (k2_rlaffin3 B C A) (k7_funcop_1 (k2_struct_0 B) k1_xboole_0)) & (r2_hidden A C)) ) ) ) ) ) ) ).
tt(t30_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t30_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ( ((k1_rlsub_2 A B C) = C)  <=>  ((k2_rlsub_2 A B C) = B) ) ) ) ) ) ) ) ).
tt(t30_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v4_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (v3_rltopsp1 (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t30_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k1_algstr_0 A B C)) = (k5_algstr_0 A (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t30_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k6_rlvect_2 A (k4_rlvect_2 A)) = (k4_struct_0 A)) ) ) ).
tt(t30_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 (k2_rlsub_2 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t30_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B C D) A) =>  ( (B = D)  |  ( (B = C)  |  ( (D = C)  | (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) B (k4_algstr_0 A C) (k4_algstr_0 A D)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k1_rlvect_5 A) = (k1_rlvect_5 (k2_rlsub_1 A))) ) ) ).
tt(t30_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 B))) => (r2_hidden (k7_partfun1 (u1_struct_0 A) B C) (k3_rlvect_x A B))) ) ) ) ) ) ) ).
tt(t30_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) <=> (r1_struct_0 D E)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t30_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) =>  ((k1_rmod_3 A B D (k2_rmod_3 A B C E)) = (k2_rmod_3 A B (k1_rmod_3 A B C D) (k1_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ((k5_rmod_4 A B (k3_rmod_4 A B)) = (k4_struct_0 B)) ) ) ) ) ).
tt(t30_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_robbins1 A B (k5_robbins1 A C D)) = (k5_robbins1 A (k6_robbins1 A B C) (k6_robbins1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t30_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A C B)) C))) = B) ) ) ) ) ) ) ).
tt(t30_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ( ((v17_lattices A) &  ((v8_robbins1 A) & (v10_lattices A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) ) ) ) ) ).
tt(t30_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_robbins4 A B B) <=>  (B = (k5_lattices A)) ) ) ) ) ) ).
tt(t30_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A (k3_roughs_1 A (k4_roughs_1 A B))) = (k4_roughs_1 A B)) ) ) ) ) ).
tt(t30_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ((r1_xboole_0 B C) &  ((r1_xboole_0 B D) & (r1_xboole_0 C D)) )  =>  ((k1_rpr_1 A (k4_subset_1 A (k4_subset_1 A B C) D)) = (k7_real_1 (k7_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C)) (k1_rpr_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ((k1_rusub_1 B) = (k1_rusub_1 A)) ) ) ) ) ).
tt(t30_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  ( ((k1_rusub_2 A B C) = C)  <=>  ((k2_rusub_2 A B C) = B) ) ) ) ) ) ) ) ).
tt(t30_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_struct_0 (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) B)) B)) ) ) ) ).
tt(t30_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rusub_4 A B) = C)  =>  ((k3_rlsub_1 A D B) = (k5_rusub_4 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t30_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bhsp_1 A B C) =>  ((k5_square_1 (k3_bhsp_1 A (k3_rlvect_1 A B C))) = (k7_real_1 (k5_square_1 (k3_bhsp_1 A B)) (k5_square_1 (k3_bhsp_1 A C)))) ) ) ) ) ) ) ) ).
tt(t30_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k8_rvsum_1 (k2_finseq_2 A B) (k2_finseq_2 A C)) = (k5_finseq_2 k1_numbers A (k10_binop_2 B C))) ) ) ) ) ) ) ).
tt(t30_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k16_rvsum_1 (k9_finseq_1 A)) = A) ) ) ).
tt(t30_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) (k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k11_scmfsa_2 A)))) 1) = k5_numbers) ) ) ).
tt(t30_scmfsa_1,ax,(r1_subset_1 k3_scmfsa_1 k1_ami_2)).
tt(t30_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 1)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k6_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_scmfsa6a (k4_scmfsa6a A C) B) = (k4_scmfsa6a A (k5_scmfsa6a C B))) ) ) ) ) ) ) ).
tt(t30_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b A C B) & (r6_scmfsa7b A C B))  =>  ((r5_scmfsa7b (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2)) C B) & (r6_scmfsa7b (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2)) C B)) ) ) ) ) ) ) ) ).
tt(t30_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b D (k1_scmfsa_m B) A) & (r6_scmfsa7b D (k1_scmfsa_m B) A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scmfsa8a B A (k2_scmfsa6a C)) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_scmfsa8a B A (k2_scmfsa6a C))))) ) ) ) ) ) ) ) ).
tt(t30_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r5_scmfsa7b D B A) & (r6_scmfsa7b D B A))  =>  ((r1_xxreal_0 (k1_funct_1 B C) k6_numbers) |  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C D)) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B)) 3))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k8_memstr_0 3 k1_scmfsa_2 B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmfsa_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r4_scmfsa7b (k16_funcop_1 A (k11_scmfsa_2 B)) C)) ) ) ) ) ) ) ).
tt(t30_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) A) =>  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ).
tt(t30_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r1_scm_halt C B A) <=> (r5_scmfsa7b C (k1_scmfsa_m B) A)) ) ) ) ) ) ) ).
tt(t30_scmisort,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ((k5_card_1 (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a A B) C) D)) = 8) ) ) ) ) ) ) ) ) ).
tt(t30_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 4)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  (A = (k7_scmpds_2 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)) =>  ((k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B E) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((r1_scmpds_6 B D A) & (r2_scmpds_6 B D A))  =>  ((r2_scmpds_6 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C) D A) & (r1_scmpds_6 (k1_scmpds_4 (k1_scmpds_4 B (k1_scmpds_6 (k2_nat_1 (k5_card_1 C) 1))) C) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_compos_1 D k1_scmpds_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v3_scmpds_4 E)) ) ) ) ) ) )  =>  ( ((r1_scmpds_6 D C B) &  ((r2_scmpds_6 D C B) &  ((r1_scmpds_6 E (k6_scmpds_4 D C B) B) & (r2_scmpds_6 E (k6_scmpds_4 D C B) B)) ) )  =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 D E) C B) A) = (k1_funct_1 (k6_scmpds_4 E (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 D C B)) B) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_amistd_1 2 (k1_scmring2 A) C (k8_scmring2 A B)) = (k1_tarski B)) ) ) ) ) ) ) ).
tt(t30_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((k3_tarski A) = (k1_tarski B))  =>  (A = (k2_tarski k1_xboole_0 (k1_tarski B))) ) ) ) ) ).
tt(t30_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) &  ((r1_semi_af1 A B C E) & (r1_semi_af1 A B D F)) )  =>  ( (B = C)  |  ( (B = D)  | (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k3_valued_1 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A B) C))) ) ) ) ) ) ).
tt(t30_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers A))) = (k17_complex1 (k3_comseq_2 A))) ) ) ).
tt(t30_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = (k18_binop_2 1 (k2_nat_1 B 1))) ) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) ) ) ) ).
tt(t30_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r1_seqfunc A k1_numbers C (k1_tarski D)) => (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k2_seqfunc A C B) D) (k26_valued_1 k5_numbers k1_numbers (k10_seqfunc A C D) B))) ) ) ) ) ) ) ) ) ).
tt(t30_seqm_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v5_valued_0 B) =>  ((r1_xxreal_0 A k6_numbers) | (v5_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) )  &  ( ( (k6_numbers = A)  => (v3_funct_1 (k26_valued_1 k5_numbers k1_numbers B A)))  &  ((v5_valued_0 B) =>  ((r1_xxreal_0 k6_numbers A) | (v6_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ) ) ).
tt(t30_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C)) &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers A C))) ) ) )  &  ((v2_comseq_2 B) &  ( (~ (r1_xxreal_0 (k2_seq_2 B) 1))  & (v1_series_1 A)) ) ) ) ) ) ) ) ).
tt(t30_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k6_xcmplx_0 (k4_nat_1 2 B) 1) (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 2)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k8_complex1 (k11_complex1 (k13_complex1 3 4) (k13_complex1 2 (k2_nat_1 B 2))) (k13_complex1 1 (k4_nat_1 (k4_nat_1 2 (k2_nat_1 B 1)) (k2_nat_1 B 2))))) ) ) ) ) ) ) ).
tt(t30_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((r1_xxreal_0 B A) & (r1_xxreal_0 C B))  => (r1_xxreal_0 (k3_power (k3_xcmplx_0 (k3_xcmplx_0 A B) C) (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) 3)) (k3_xcmplx_0 (k3_xcmplx_0 (k3_power A A) (k3_power B B)) (k3_power C C)))) ) ) ) ) ) ) ).
tt(t30_series_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 2 B) =>  ( ((k1_seq_1 A B) = (k6_xcmplx_0 1 (k7_xcmplx_0 1 (k13_newton B 2))))  &  ( ((k1_seq_1 A k6_numbers) = 1)  &  ((k1_seq_1 A 1) = 1) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 2 B) =>  ((k1_seq_1 (k1_series_3 A) B) = (k7_xcmplx_0 (k2_nat_1 B 1) (k4_nat_1 2 B))) ) ) ) ) ) ) ).
tt(t30_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 9 A) B) C) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C))) (k2_xcmplx_0 (k2_xcmplx_0 A B) C))) ) ) ) ) ) ).
tt(t30_setfam_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k1_setfam_1 (k4_setfam_1 A B)) (k6_subset_1 (k1_setfam_1 A) (k1_setfam_1 B)))) ) ).
tt(t30_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k3_subset_1 B (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B (k2_prob_1 B C)) A))) ) ) ) ) ) ).
tt(t30_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 C) => (v2_prob_1 (k8_setlim_2 A C B))) ) ) ) ) ) ).
tt(t30_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 C B) &  ((v2_binop_1 C B) & (v3_binop_1 C B)) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) D)))) )  =>  ( ((v1_binop_1 E D) &  ((v2_binop_1 E D) & (v3_binop_1 E D)) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B D) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B D)))) )  =>  ( (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  ((k3_funct_2 B D G (k5_binop_1 B C H I)) = (k5_binop_1 D E (k3_funct_2 B D G H) (k3_funct_2 B D G I))) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 A)) =>  ( (~  (H = k1_xboole_0) )  =>  ((k3_funct_2 B D G (k7_setwiseo A B C H F)) = (k7_setwiseo A D E H (k1_partfun1 A B B D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ((v1_finseqop C A) & (r6_binop_1 A D C)) ) )  =>  ((k3_funct_2 A A (k10_funcop_1 A A D B (k6_partfun1 A)) (k1_finsop_1 A E C)) = (k1_finsop_1 A (k4_finseqop A A E (k10_funcop_1 A A D B (k6_partfun1 A))) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( (C = B)  |  ( (D = B)  |  ( ((k18_scmfsa_2 (k1_scmfsa6b (k3_sfmastr3 C D B E) A F) E) = (k18_scmfsa_2 A E))  &  ( ((k1_funct_1 (k1_scmfsa6b (k3_sfmastr3 C D B E) A F) C) = (k1_funct_1 A C))  &  ((k1_funct_1 (k1_scmfsa6b (k3_sfmastr3 C D B E) A F) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k2_sf_mastr (k5_scmfsa6a B A)) = (k2_xboole_0 (k2_sf_mastr B) (k1_sf_mastr A))) ) ) ) ) ).
tt(t30_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden D (u1_sgraph1 B)) &  ( ((k4_sgraph1 A B C) = k6_numbers)  & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(t30_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_sheffer1 A) & (l3_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k6_sheffer1 A (k6_sheffer1 A B))) ) ) ) ) ).
tt(t30_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B D))) C) = (k5_sheffer1 A C (k5_sheffer1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t30_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v5_finset_1 B) & (r1_setfam_1 B C))  => (m2_simplex0 (k5_simplex0 A B) A (k5_simplex0 A C))) ) ) ) ) ) ).
tt(t30_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B (u1_struct_0 A))) ) )  =>  ( ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 C (k6_simplex0 B)) &  (! [D:$i] :  ( ((v3_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ( ((k5_card_1 D) = (k3_real_1 C 1))  & (v1_rlaffin1 (k1_simplex1 A B D) A)) ) ) ) ) ) ) ) )  =>  ((k6_simplex0 B) = (k6_simplex0 (k4_simplex1 A B))) ) ) ) ) ) ).
tt(t30_sincos10,ax, ( ((k1_seq_1 k16_sin_cos (k1_real_1 (k10_real_1 k32_sin_cos 4))) = (k1_real_1 (k10_real_1 1 (k7_square_1 2))))  &  ( ((k1_seq_1 k19_sin_cos (k1_real_1 (k10_real_1 k32_sin_cos 4))) = (k10_real_1 1 (k7_square_1 2)))  &  ( ((k1_seq_1 k16_sin_cos (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) = (k10_real_1 1 (k7_square_1 2)))  &  ((k1_seq_1 k19_sin_cos (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) = (k1_real_1 (k10_real_1 1 (k7_square_1 2)))) ) ) ) ).
tt(t30_sin_cos2,ax, ( ((k1_relset_1 k1_numbers k1_sin_cos2) = k1_numbers)  &  ( ((k1_relset_1 k1_numbers k4_sin_cos2) = k1_numbers)  &  ((k1_relset_1 k1_numbers k7_sin_cos2) = k1_numbers) ) ) ).
tt(t30_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k11_binop_2 (k23_binop_2 (k24_binop_2 2 A) 1) k32_sin_cos) k7_complex1)) = (k19_binop_2 1)) ) ) ).
tt(t30_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k2_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))))) ) ) ) ) ).
tt(t30_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_sin_cos4 (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k9_real_1 1 (k20_sin_cos A)) (k7_real_1 1 (k20_sin_cos A)))))  |  ((k1_sin_cos4 (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k9_real_1 1 (k20_sin_cos A)) (k7_real_1 1 (k20_sin_cos A)))))) ) ) ) ).
tt(t30_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 2) A))  & (r1_xxreal_0 1 (k17_sin_cos A))) ) ) ) ) ).
tt(t30_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  (k6_numbers = A) )  &  ((k10_binop_2 (k3_square_1 (k25_sin_cos A)) 1) = k6_numbers) ) ) ) ) ).
tt(t30_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k9_sin_cos2 (k7_xcmplx_0 A 2)) = (k4_xcmplx_0 (k6_square_1 (k7_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 A) 1) (k2_xcmplx_0 (k6_sin_cos2 A) 1))))) ) ) ) ).
tt(t30_sin_cos9,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)) (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t30_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k19_sin_cos k6_numbers) = 1)  &  ( ((k1_seq_1 k16_sin_cos k6_numbers) = k6_numbers)  &  ( ((k1_seq_1 k19_sin_cos (k4_xcmplx_0 A)) = (k1_seq_1 k19_sin_cos A))  &  ((k1_seq_1 k16_sin_cos (k4_xcmplx_0 A)) = (k1_real_1 (k1_seq_1 k16_sin_cos A))) ) ) ) ) ) ).
tt(t30_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ( (C = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A))  &  ( (D = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)))  &  ( (E = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 2)))  &  ( (~  ( ((k17_euclid D) = (k17_euclid E))  &  (~  ((k17_euclid C) = (k17_euclid D)) ) ) )  &  (~  ( ((k18_euclid D) = (k18_euclid E))  &  (~  ((k18_euclid C) = (k18_euclid D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v2_topreal1 A) &  ( ((k2_nat_1 C 1) = (k3_finseq_1 A))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) )  => (v2_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)))) ) ) ) ) ) ) ).
tt(t30_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k10_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A))) = (k1_tarski (k10_pscomp_1 A))) ) ) ).
tt(t30_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  =>  ((v1_sprect_2 A) <=> (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2) (k15_pscomp_1 (k3_topreal1 2 A)))) ) ) ) ).
tt(t30_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 B (k3_finseq_1 C)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) C A B))) &  ( (~  (A = 1) )  &  (~  (B = (k3_finseq_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) 1)) ) ) ) ).
tt(t30_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((k6_square_1 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 (k6_square_1 A) (k6_square_1 B))) ) ) ) ) ) ).
tt(t30_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (? [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) &  ( ((k9_stacks_1 A D) = C)  & (r2_hidden D (k11_stacks_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t30_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k3_stirl2_1 A k6_numbers) = 1)  <=>  (A = k6_numbers) ) ) ) ).
tt(t30_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ((v3_substut1 (k7_sublemma A C B) A) =>  ( ((k10_sublemma A (k9_sublemma A (k7_sublemma A C B) D)) = C)  &  ((k11_sublemma A (k9_sublemma A (k7_sublemma A C B) D) (k39_substut1 A (k10_sublemma A (k9_sublemma A (k7_sublemma A C B) D)))) = (k11_sublemma A (k9_sublemma A (k7_sublemma A C B) D) (k39_substut1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=>  (~ (r2_hidden D C)) ) ) )  =>  (B = (k3_subset_1 A C)) ) ) ) ) ) ) ).
tt(t30_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v6_substut1 B A) =>  ((k37_substut1 A B) = (k14_qc_lang1 A (k37_substut1 A (k28_substut1 A B)) (k37_substut1 A (k29_substut1 A B)))) ) ) ) ) ) ).
tt(t30_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ( ((k7_cqc_sim1 A C) = B)  & (r2_qc_lang2 A D C))  => (r1_xxreal_0 (k7_cqc_sim1 A D) B)) ) ) ) ) ) ) ) ) ).
tt(t30_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski B k1_numbers) =>  ((v3_supinf_2 C A B) <=>  ((r2_hidden (k11_supinf_2 k7_numbers A B C) k1_numbers) & (r2_hidden (k10_supinf_2 k7_numbers A B C) k1_numbers)) ) ) ) ) ) ) ) ) ).
tt(t30_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B C E))  &  ( (~ (r1_orders_2 B F D))  &  ( (~ (r1_orders_2 B F E))  &  ( (~ (r1_orders_2 B G D))  &  (~  ((k8_group_1 A (k8_group_1 A (k1_symsp_1 A B D G C) (k1_symsp_1 A B C D E)) (k1_symsp_1 A B E C H)) = (k8_group_1 A (k8_group_1 A (k1_symsp_1 A B D G F) (k1_symsp_1 A B F D E)) (k1_symsp_1 A B E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ( ( ((k3_relat_1 C C) = C)  &  ( ((k3_relat_1 C (k6_subset_1 C (k4_relat_1 (k9_xtuple_0 C)))) = k1_xboole_0)  & (r2_hidden (k4_tarski A B) C)) )  =>  ( (A = B)  |  ((r2_hidden A (k6_subset_1 (k9_xtuple_0 C) (k9_xtuple_0 (k1_sysrel C)))) & (r2_hidden B (k9_xtuple_0 (k1_sysrel C)))) ) )  &  ( ( ((k3_relat_1 C C) = C)  &  ( ((k3_relat_1 (k6_subset_1 C (k4_relat_1 (k9_xtuple_0 C))) C) = k1_xboole_0)  & (r2_hidden (k4_tarski A B) C)) )  =>  ( (A = B)  |  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 C) (k9_xtuple_0 (k1_sysrel C)))) & (r2_hidden A (k9_xtuple_0 (k1_sysrel C)))) ) ) ) ) ) ) ) ).
tt(t30_taxonom1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ( ((v4_metric_1 B A) & (v1_taxonom1 B A))  => (r2_hidden (k1_tarski A) (k2_taxonom1 A B))) ) ) ) ) ).
tt(t30_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski C B) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_taylor_1 A D B) => (r2_relset_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A B) D) C) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 A C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A))))  &  ((v10_lattices (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A))) &  ((v15_lattices (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A))) &  ((v16_lattices (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A))) & (l3_lattices (g3_lattices (k1_tdlat_1 A) (k2_tdlat_1 A) (k3_tdlat_1 A)))) ) ) ) ) ) ).
tt(t30_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 B) =>  ((k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)) = (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B))) ) ) ) ) ) ).
tt(t30_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((k2_pre_topc A B) = (k1_tops_1 A (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(t30_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) B (k9_polynom1 A B C D)) (a_4_0_termord A B C D))) ) ) ) ) ) ) ) ).
tt(t30_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_tex_1 A B)))) =>  ( (C = (k6_domain_1 A B))  =>  ((k1_compts_1 A) = (k6_tmap_1 (k3_tex_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t30_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_tex_2 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t30_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) &  (! [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  =>  (~  ((v3_tex_3 C A) &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k2_tex_4 A C) (k3_tex_4 A B)))  => (r1_tarski (k2_tex_4 A C) (k3_tex_4 A B))) ) ) ) ) ) ) ).
tt(t30_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc B C) & (m1_pre_topc D E))  =>  ( ( (~ (r1_tsep_1 C E))  &  (~ (r1_tsep_1 (k2_tsep_1 A C E) (k1_tsep_1 A B D))) )  |  ((r1_tsep_1 C D) & (r1_tsep_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_tarski (k4_toler_1 A B) (k4_toler_1 A C)) => (r1_relset_1 A A B C)) ) ) ) ) ) ).
tt(t30_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D B) =>  ((r4_borsuk_2 A D C (k1_borsuk_2 A D B C G E) (k1_borsuk_2 A D B C G F)) => (r4_borsuk_2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ((m1_borsuk_2 E A C C) =>  ((k1_funct_1 (k3_topalg_3 A B C D) (k6_eqrel_1 (k2_topalg_1 A C) (k2_topalg_1 A C) (k4_topalg_1 A C) E)) = (k6_eqrel_1 (k2_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k2_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k4_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C)) (k2_topalg_3 A B C E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r2_group_6 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C D)) (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B D))))) ) ) ) ) ) ) ) ).
tt(t30_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((m1_borsuk_2 (k3_relat_1 (k1_borsuk_6 k6_numbers 1 (k2_xxreal_2 (k9_xtuple_0 B)) (k1_xxreal_2 (k9_xtuple_0 B))) B) A C D) & (r1_borsuk_2 A C D))  =>  ( (C = (k2_topalg_6 A B))  &  (D = (k3_topalg_6 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B))))) =>  ( ((v2_topdim_1 C A) &  (D = C) )  =>  ((v2_topdim_1 D (k1_pre_topc A B)) &  ((k3_topdim_1 A C) = (k3_topdim_1 (k1_pre_topc A B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_topgen_1 A B) (k2_topgen_1 A C))) ) ) ) ) ) ) ).
tt(t30_topgen_2,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((k1_card_1 (k5_finsub_1 A)) = (k1_card_1 A)) ) ) ).
tt(t30_topgen_3,ax,(r2_hidden k4_ordinal1 k3_topgen_3)).
tt(t30_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  (~  ( ((k2_setfam_1 A B) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t30_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_topgen_5)) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  (? [D:$i] :  ( ((v3_pre_topc D k3_topgen_5) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))))  &  ((r2_hidden A D) &  ((r2_hidden C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E D) & (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) => (m3_topgrp_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A)) ) ) ) ).
tt(t30_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_topreal1 A) = (a_1_0_topreal1 A)) ) ) ).
tt(t30_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k17_euclid B) (k18_euclid A))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid B) (k18_euclid A)) B)) = (k1_tarski (k19_euclid (k17_euclid B) (k18_euclid A)))) ) ) ) ) ).
tt(t30_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) =>  ( (A = B)  |  ( (A = C)  |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid B)) |  ( (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B)))  &  (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  =>  ((k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (k3_finseq_1 A)) = (k2_topreal1 2 B 1)) ) ) ) ) ) ).
tt(t30_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k4_topreal9 A C D)) => (r1_tarski (k4_topreal9 A C B) (k4_topreal9 A C D))) ) ) ) ) ) ) ) ) ).
tt(t30_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k2_jgraph_6 A B C D) = (k4_card_3 (k4_funct_4 1 2 (k1_rcomp_1 A B) (k1_rcomp_1 C D)))) ) ) ) ) ) ) ) ) ).
tt(t30_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k8_toprealb 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_toprealb 2))) => (r2_borsuk_3 (k11_toprealb A) (k11_toprealb B))) ) ) ) ).
tt(t30_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((k37_valued_2 A C D B) = (k58_valued_2 A C D (k7_funcop_1 (k1_relset_1 A D) B))) ) ) ) ) ) ) ) ).
tt(t30_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)) (k7_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t30_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A B) = (k4_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) B) (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A B) B))) ) ) ) ) ).
tt(t30_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski C D) => (r1_tarski (k1_tops_2 A B C) (k1_tops_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t30_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_tops_1 B A) & (v2_tops_1 C A))  => (v2_tops_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t30_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v2_transgeo B A) & (v2_transgeo C A))  => (v2_transgeo (k1_transgeo (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t30_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (~  ((r2_hidden B (k2_trees_1 A)) &  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (B = (k12_finseq_1 k5_numbers C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_2 A)) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_trees_2 C A))  &  ((k5_card_1 C) = B) ) ) ) )  &  (! [B:$i] :  ((m1_trees_2 B A) => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t30_trees_3,ax, (! [A:$i] :  ((v6_trees_3 (k9_finseq_1 A)) <=>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) ) ) ).
tt(t30_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_trees_3 E (k2_zfmisc_1 A B)))  =>  (! [F:$i] :  ((m2_finseq_1 F E) =>  (? [G:$i] :  ((m2_finseq_1 G (k4_trees_3 B)) &  ( ((k4_finseq_1 G) = (k4_finseq_1 F))  &  ( (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden H (k4_finseq_1 F)) &  (! [I:$i] :  ((m1_subset_1 I E) =>  (~  ( (I = (k1_funct_1 F H))  &  ((k1_funct_1 G H) = (k9_trees_3 A B I)) ) ) ) ) ) ) ) )  &  ((k9_trees_3 A B (k4_trees_4 (k1_domain_1 A B C D) F)) = (k4_trees_4 D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v3_trees_2 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v6_trees_3 C)) ) )  =>  ( (A = (k4_trees_4 B C))  =>  (! [D:$i] :  ( ((v1_xboole_0 D) & (m1_trees_1 D (k9_xtuple_0 A)))  =>  ((k2_trees_9 A D) = (k14_trees_3 C)) ) ) ) ) ) ) ) ) ).
tt(t30_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  ( (~ (r1_tsep_1 B C))  =>  ((v1_tsep_1 (k2_tsep_1 A B C) A) & (m1_pre_topc (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ).
tt(t30_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (~ (r3_tsep_2 A B B)) ) ) ) ) ).
tt(t30_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ).
tt(t30_turing_1,ax, ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))  &  ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 1 1))  &  ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))  &  ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))  &  ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))  &  ( ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 3 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 1 (k1_real_1 1)))  &  ((k1_funct_1 k15_turing_1 (k1_domain_1 k5_numbers k5_numbers 3 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 4 k6_numbers k6_numbers)) ) ) ) ) ) ) ).
tt(t30_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (~ (v1_facirc_1 (k2_msafree2 (k34_twoscomp A B)))) ) ) ) ) ).
tt(t30_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots k1_complfld))) =>  (~  ((r2_hidden B (k2_uniroots A)) & (v4_group_1 B (k1_uniroots k1_complfld))) ) ) ) ) ) ).
tt(t30_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k13_polynom3 A (k2_polynom5 A D B) (k2_polynom5 A D C)) (k2_polynom5 A D (k2_nat_1 B C)))) ) ) ) ) ) ) ) ).
tt(t30_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D A))  &  ( (~ (r1_xxreal_0 B D))  & (r1_xxreal_0 (k9_real_1 B A) (k18_complex1 (k9_real_1 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [G:$i] :  ((m1_valuat_1 G A B) =>  (! [H:$i] :  ((m1_subset_1 H (k9_qc_lang1 A)) =>  ( ( (E = (k13_cqc_lang A H C))  &  (F = (k13_cqc_lang A H D)) )  =>  ( (C = D)  |  (! [I:$i] :  ((m2_funct_2 I (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( ((k3_funct_2 (k3_qc_lang1 A) B I C) = (k3_funct_2 (k3_qc_lang1 A) B I D))  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B G E) I) = (k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B G F) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r1_tarski (k2_relset_1 A C) (k1_relset_1 A D)) =>  ((k7_relset_1 A B D (k2_relset_1 A C)) = (k2_relset_1 B (k8_funct_2 k5_numbers B A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  => (r2_hidden (k62_valued_1 A) (k1_relset_1 k5_numbers A))) ) ).
tt(t30_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k14_valued_2 (k30_valued_1 B) A) = (k30_valued_1 (k14_valued_2 B A))) ) ) ) ) ).
tt(t30_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_5 E A B (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) =>  ((r1_struct_0 E D) =>  ( (C = (k4_struct_0 B))  |  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_vectsp10 A B C E) D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  ((v1_funct_1 (k8_matrlin2 A B B (k2_vectsp11 A B C) C)) &  ((v1_funct_2 (k8_matrlin2 A B B (k2_vectsp11 A B C) C) (u1_struct_0 (k2_vectsp11 A B C)) (u1_struct_0 (k2_vectsp11 A B C))) &  ((v13_vectsp_1 (k8_matrlin2 A B B (k2_vectsp11 A B C) C) (k2_vectsp11 A B C) (k2_vectsp11 A B C)) &  ((v1_mod_2 (k8_matrlin2 A B B (k2_vectsp11 A B C) C) A (k2_vectsp11 A B C) (k2_vectsp11 A B C)) & (m1_subset_1 (k8_matrlin2 A B B (k2_vectsp11 A B C) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_vectsp11 A B C)) (u1_struct_0 (k2_vectsp11 A B C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k5_algstr_0 A (k8_group_1 A B D) C) = (k4_struct_0 A))  =>  ( (B = (k4_struct_0 A))  |  (D = (k8_group_1 A C (k11_algstr_0 A B))) ) )  &  ( ((k5_algstr_0 A C (k8_group_1 A D B)) = (k4_struct_0 A))  =>  ( (B = (k4_struct_0 A))  |  (D = (k8_group_1 A C (k11_algstr_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k4_vectsp_1 A C B D) = (k4_struct_0 C))  <=>  ( (B = (k4_struct_0 A))  |  (D = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) <=> (r1_struct_0 D E)) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ((m1_vectsp_4 E A C) =>  ((k1_vectsp_5 A B E (k2_vectsp_5 A B D C)) = (k2_vectsp_5 A B (k1_vectsp_5 A B E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) => (r1_vectsp_6 A B (k6_vectsp_6 A B (k4_struct_0 A) C) (k2_vectsp_6 A B))) ) ) ) ) ) ).
tt(t30_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_vectsp_9 A B) = 1)  <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  ( (~  (C = (k4_struct_0 B)) )  &  ((k2_vectsp_4 A B) = (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ).
tt(t30_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k2_vfunct_1 B C D E) A) (k2_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A) (k2_partfun1 B (u1_struct_0 C) E A))) &  ((r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k2_vfunct_1 B C D E) A) (k2_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A) E)) & (r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k2_vfunct_1 B C D E) A) (k2_vfunct_1 B C D (k2_partfun1 B (u1_struct_0 C) E A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) E) (k2_vfunct_1 A B (k2_partfun1 A (u1_struct_0 B) C E) (k2_partfun1 A (u1_struct_0 B) D E))) &  ((r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) E) (k2_vfunct_1 A B (k2_partfun1 A (u1_struct_0 B) C E) D)) & (r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) E) (k2_vfunct_1 A B C (k2_partfun1 A (u1_struct_0 B) D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_waybel_0 B A) <=> (v1_waybel_0 (k3_waybel_0 A B) A)) ) ) ) ) ).
tt(t30_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (a_2_2_waybel11 A B))  =>  ( (~ (v1_xboole_0 C))  & (v1_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(t30_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_waybel12 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r4_yellow_4 A D C) & (r4_yellow_4 A B D))  => (m1_waybel12 D A B)) ) ) ) ) ) ) ) ) ).
tt(t30_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ( ((r5_waybel_1 A B) & (v24_waybel_0 A))  => (v24_waybel_0 B)) ) ) ) ) ).
tt(t30_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) => (v1_waybel14 (k5_waybel_2 A) A)) ) ) ).
tt(t30_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=>  ((v3_waybel_3 A) & (v3_waybel_3 (k7_lattice3 A))) ) ) ) ).
tt(t30_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_2 (k7_lattice3 A)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v1_waybel16 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C (u1_struct_0 (k1_waybel_8 A))) & (r3_waybel_4 A (k6_subset_1 (u1_struct_0 A) (k6_waybel_0 A C)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_tops_2 (k2_xboole_0 (k5_waybel11 A) (a_1_2_waybel19 A)) A) &  ((v2_cantor_1 (k2_xboole_0 (k5_waybel11 A) (a_1_2_waybel19 A)) A) & (m1_subset_1 (k2_xboole_0 (k5_waybel11 A) (a_1_2_waybel19 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(t30_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (r1_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A B C)) (u1_struct_0 A) (u1_struct_0 B) (k2_waybel_1 A B C) C)) ) ) ) ) ) ).
tt(t30_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v2_yellow_0 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) )  => (v2_yellow_0 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t30_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_waybel_9 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ( (E = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))  => (m2_yellow_6 (k6_waybel_9 A B D (k3_yellow_9 A C)) B (k3_yellow_9 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_waybel_0 B A)) ) ) ) ).
tt(t30_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_yellow_0 B (a_4_6_waybel24 A B C D)) = (k1_yellow_0 B (a_4_8_waybel24 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t30_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  => (v24_waybel_0 (k1_waybel25 A))) ) ).
tt(t30_waybel26,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] : (r6_pboole B (k12_pralg_1 B (k7_funcop_1 B A)) (k7_funcop_1 B (u1_struct_0 A)))) ) ) ).
tt(t30_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v1_lattice3 D) &  ((v2_lattice3 D) &  ((v3_lattice3 D) & (l1_orders_2 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v22_waybel_0 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v22_waybel_0 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) )  => (v22_waybel_0 (k4_waybel27 A B C D E F) (k2_waybel27 B C) (k2_waybel27 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v12_waybel_0 B A) =>  ((r2_hidden (k3_subset_1 (u1_struct_0 A) B) (k4_waybel28 A)) <=> (v2_waybel11 B A)) ) ) ) ) ) ).
tt(t30_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) <=>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k5_waybel11 (k3_yellow_3 B A)) = (u1_pre_topc (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A)))) ) ) ) ) ) ).
tt(t30_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) (k11_waybel_0 A B)))) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B))) ) ) ) ) ) ) ) ).
tt(t30_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  ((v2_waybel_2 A) & (v8_pre_topc A)) ) ) ) ).
tt(t30_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) <=> (v22_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t30_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) => (v5_orders_2 (k3_waybel_3 A B C))) )  => (v5_orders_2 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t30_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (r1_funct_2 (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (k9_xtuple_0 (k9_waybel_4 A)) (k9_xtuple_0 (k9_waybel_4 A)) (k1_partfun1 (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (k9_waybel_4 A) (k10_waybel_4 A)) (k6_partfun1 (k9_xtuple_0 (k9_waybel_4 A))))) ) ).
tt(t30_waybel_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  ((r2_relset_1 B B (k1_partfun1 B C C B D E) (k6_partfun1 B)) =>  ((k8_pboole (k7_waybel_5 B C A D) (k7_waybel_5 C B A E)) = (k2_msualg_3 A (k7_funcop_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t30_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_yellow_0 A)) )  =>  ((v5_waybel_6 B A) <=>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) &  ((v1_waybel_6 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  & (r3_waybel_4 A (k3_subset_1 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(t30_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( ((r1_tarski B C) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (u1_struct_0 A))) &  ((v3_waybel_7 D (k3_yellow_1 (u1_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (u1_struct_0 A)))))) ) ) )  =>  (~  ((r2_hidden B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) & (r2_waybel_7 A D E)) ) ) ) ) ) ) ) )  => (r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C)) ) ) ) ) ) ) ).
tt(t30_waybel_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((r2_hidden B (u1_struct_0 (k1_waybel_8 (k3_yellow_1 A)))) <=> (v1_finset_1 B)) ) ) ) ).
tt(t30_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r3_waybel_9 A B C)) ) ) ) ) ) ).
tt(t30_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_uniroots A))) =>  ( (C = B)  =>  ((k7_group_1 (k1_weddwitt (k1_uniroots A) C)) = (k6_xcmplx_0 (k5_card_1 (u1_struct_0 (k5_weddwitt A B))) 1)) ) ) ) ) ) ) ) ).
tt(t30_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E C) &  ((k4_metric_1 A D E) = (k7_weierstr A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((v2_wellord1 C) &  ((r2_hidden A (k1_relat_1 C)) & (r2_hidden B (k1_relat_1 C))) )  =>  ((r1_tarski (k1_wellord1 C A) (k1_wellord1 C B)) <=>  ( (A = B)  | (r2_hidden A (k1_wellord1 C B))) ) ) ) ) ) ) ).
tt(t30_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k3_int_2 A B) = 1)  & (r1_nat_d A (k3_xcmplx_0 B C)))  => (r1_nat_d A C)) ) ) ) ) ) ) ).
tt(t30_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) =>  ((k2_xboole_0 A (k3_xboole_0 C B)) = (k3_xboole_0 (k2_xboole_0 A C) B)) ) ) ) ) ).
tt(t30_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean A (k7_xboolean B C)) = (k4_xboolean (k5_xboolean (k5_xboolean (k3_xboolean A) (k3_xboolean B)) C) (k5_xboolean (k5_xboolean (k3_xboolean A) B) (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t30_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k6_xcmplx_0 A B) C) = (k2_xcmplx_0 (k6_xcmplx_0 C B) A)) ) ) ) ) ) ) ).
tt(t30_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 B (k2_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t30_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k10_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t30_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 (k4_xxreal_0 A B) C) => (r1_xxreal_0 A C)) ) ) ) ) ) ) ).
tt(t30_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r1_xxreal_0 A B) & (v1_xboole_0 (k1_xxreal_1 A B))) ) ) ) ) ) ).
tt(t30_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_xxreal_2 (k3_xxreal_1 A B)) = B) ) ) ) ) ) ).
tt(t30_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (A = k1_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  (~  ((k3_xxreal_3 (k1_xxreal_3 A B) C) = (k1_xxreal_3 A (k3_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( ( (B = (k1_yellow_0 A C))  & (r1_yellow_0 A C))  =>  ((r2_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A C D) => (r1_orders_2 A B D)) ) ) ) )  &  ( ((r2_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A C D) => (r1_orders_2 A B D)) ) ) )  =>  ( (B = (k1_yellow_0 A C))  & (r1_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(t30_yellow10,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((k5_yellow_3 A B (k3_waybel_0 (k3_yellow_3 A B) C)) = (k3_waybel_0 B (k5_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t30_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B C) => (r1_tarski (k6_waybel_0 A B) (k4_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t30_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A B)))) =>  ((r2_hidden C (k2_pre_topc (k3_waybel18 A (k7_funcop_1 A B)) (k6_domain_1 (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A B))) D))) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_hidden (k2_yellow14 A B C E) (k2_pre_topc B (k6_domain_1 (u1_struct_0 B) (k2_yellow14 A B D E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow15,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v6_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v8_struct_0 A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~ (v1_finset_1 B)) ) ) ) ) ) ).
tt(t30_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r1_lattice3 (k5_yellow_1 A B) D C) <=>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_lattice3 (k3_waybel_3 A B E) (k5_waybel_3 A B E D) (k4_waybel_3 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow18,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k1_funct_2 A B)) <=>  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( ((k9_xtuple_0 C) = A)  & (r1_tarski (k10_xtuple_0 C) B)) ) ) ) ) ) ).
tt(t30_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) => (v2_tops_2 (k2_cantor_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t30_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) )  =>  (! [D:$i] :  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ( ( (G = E)  &  (H = F) )  =>  ( ((k1_altcat_1 C G H) = k1_xboole_0)  |  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A E F)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 C G H)) =>  ( (J = I)  =>  ((k8_functor0 C B (k5_yellow20 A B C D) G H J) = (k8_functor0 A B D E F I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_lattice3 A C E) & (r2_lattice3 B D F))  => (r2_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) (k7_yellow_3 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k13_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B C) = (k3_waybel_0 A (k2_yellow_4 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((r1_yellow_5 A B C) & (r1_yellow_5 A B D)) )  & (r1_yellow_5 A B (k12_lattice3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t30_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C (u1_struct_0 (k9_yellow_6 A B))) <=>  ((r2_hidden B C) & (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t30_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_yellow_0 A) <=> (v2_yellow_0 (k7_lattice3 A))) ) ) ).
tt(t30_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ((v1_tops_2 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) A) &  ((v1_cantor_1 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) A) & (m1_subset_1 (k2_xboole_0 B (k1_tarski (u1_struct_0 A))) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t30_zf_fund1,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) =>  (A = (k3_zf_fund1 (k2_zf_lang (k5_card_1 A)))) ) ) ).
tt(t30_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((k20_zf_lang (k10_zf_lang A B)) = (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)))  &  ( ((k25_zf_lang (k10_zf_lang A B)) = (k6_zf_lang A))  &  ((k26_zf_lang (k10_zf_lang A B)) = B) ) ) ) ) ) ) ).
tt(t30_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k7_zf_lang A B) = (k7_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k2_zfmisc_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k4_tarski A B) (k4_tarski A C)))  &  ((k2_zfmisc_1 (k2_tarski A B) (k1_tarski C)) = (k2_tarski (k4_tarski A C) (k4_tarski B C))) ) ) ) ) ).
tt(t30_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) )  =>  (~  ((r2_hidden k4_ordinal1 A) &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((r2_hidden C D) => (r1_tarski (k5_zf_refle A B C) (k5_zf_refle A B D))) ) ) ) )  &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((v4_ordinal1 C) =>  ( (C = k1_xboole_0)  |  ((k5_zf_refle A B C) = (k3_card_3 (k5_relat_1 B C))) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 C) &  ((v3_ordinal2 C) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ( ((k4_ordinal4 A C D) = D)  =>  ( (k1_xboole_0 = D)  | (r3_zfrefle1 (k5_zf_refle A B D) (k4_zf_refle A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t30_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (D = B)  =>  ((k4_algstr_0 A B) = (k4_algstr_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t310_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k2_xxreal_1 A D) (k1_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k4_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t311_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A D) (k1_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t312_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_subset_1 (k1_xxreal_1 A D) (k1_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k3_xxreal_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t313_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k6_subset_1 (k4_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k4_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t314_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k6_subset_1 (k2_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k4_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t315_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k3_xxreal_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t316_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k6_subset_1 (k1_xxreal_1 A C) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k3_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t317_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 C B) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A B) (k4_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k1_tarski B))) ) ) ) ) ) ) ) ) ).
tt(t318_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C B))  =>  ((k6_subset_1 (k1_xxreal_1 A B) (k4_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k1_tarski B))) ) ) ) ) ) ) ) ).
tt(t319_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 C B) =>  ((r1_xxreal_0 B A) |  ((k6_subset_1 (k3_xxreal_1 A B) (k2_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k1_tarski B))) ) ) ) ) ) ) ) ) ).
tt(t31_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((k8_abcmiz_0 A B (k12_finseq_1 (u1_abcmiz_0 A) C)) = (k5_abcmiz_0 A B C)) ) ) ) ) ) ) ).
tt(t31_abcmiz_1,ax, (! [A:$i] :  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) =>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) =>  ((m2_finseq_2 (k8_finseq_1 k2_abcmiz_1 A (k3_pre_poly k2_abcmiz_1 B)) k2_abcmiz_1 k4_abcmiz_1) <=>  ( (~ (r2_hidden B (k2_relset_1 k2_abcmiz_1 A)))  & (r1_tarski (k3_abcmiz_1 B) (k2_relset_1 k2_abcmiz_1 A))) ) ) ) ) ) ).
tt(t31_abcmiz_a,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_abcmiz_1)))  =>  (? [B:$i] :  ((m2_finseq_2 B k2_abcmiz_1 k4_abcmiz_1) &  ((k2_relset_1 k2_abcmiz_1 B) = (k1_abcmiz_1 A)) ) ) ) ) ).
tt(t31_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_aff_1 F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_aff_1 A B C F) & (r2_aff_1 A D E F))  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_1 D A) =>  ((k2_aff_4 A B D) = (k2_aff_4 A B (k2_aff_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 (k1_ordinal4 A B)) &  ((v5_relat_1 (k1_ordinal4 A B) C) &  ((v5_ordinal1 (k1_ordinal4 A B)) &  ((v1_funct_1 (k1_ordinal4 A B)) & (v1_finset_1 (k1_ordinal4 A B))) ) ) )  =>  ( ((v1_relat_1 A) &  ((v5_relat_1 A C) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  &  ((v1_relat_1 B) &  ((v5_relat_1 B C) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (v6_membered C))  =>  ((r1_afinsq_2 B C) =>  ((r1_xxreal_0 (k1_afinsq_1 (k4_afinsq_2 C)) A) |  ((k1_recdef_1 (k4_afinsq_2 C) A) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 B C)) (k23_binop_2 A (k1_afinsq_1 (k4_afinsq_2 B))))) ) ) ) ) ) ) ) ) ).
tt(t31_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_4 C A) &  ((r1_tarski B C) &  ( (D = (k5_afproj A B))  &  (E = (k4_tarski (k6_afproj A C) 2)) ) ) ) )  => (r1_incsp_1 (k13_afproj A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_afvect0 A B D) = C) ) ) ) ) ) ) ) ) ).
tt(t31_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) => (r1_algspec1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t31_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_algstr_4 A))) =>  ( (~ (v1_xboole_0 A))  =>  ((k6_algstr_0 (k14_algstr_4 A) B C) = (k4_tarski (k4_tarski (k4_tarski (k1_xtuple_0 B) (k1_xtuple_0 C)) (k2_xtuple_0 B)) (k2_xcmplx_0 (k15_algstr_4 A B) (k15_algstr_4 A C)))) ) ) ) ) ) ) ).
tt(t31_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  => (r1_tarski (k1_altcat_1 B E F) (k1_altcat_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v2_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v1_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v5_ami_wstd C A B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) ) )  =>  ( ((r1_tarski C D) &  ((k6_ami_wstd A B C) = (k6_ami_wstd A B D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t31_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) =>  ( ((r1_analmetr A B C) &  ((r4_analmetr (k2_analmetr A B C) D E F G) & (r4_analmetr (k2_analmetr A B C) F E G D)) )  => (r4_analmetr (k2_analmetr A B C) G E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) &  ((r2_analort A B C D E G F) &  ( (~  (D = E) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ((v4_collsp (k5_anproj_1 A)) &  ((v3_anproj_2 (k5_anproj_1 A)) &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_anproj_1 A))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_anproj_1 A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_anproj_1 A))) &  ( (~ (r1_collsp (k5_anproj_1 A) B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_anproj_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k5_anproj_1 A))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k5_anproj_1 A))) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_anproj_1 A))) &  ((r1_collsp (k5_anproj_1 A) E F H) &  ((r1_collsp (k5_anproj_1 A) C D G) & (r1_collsp (k5_anproj_1 A) B H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_collsp B) &  ((v3_collsp B) &  ((v4_collsp B) &  ((v2_anproj_2 B) &  ((v3_anproj_2 B) & (l1_collsp B)) ) ) ) ) )  =>  (~  ( (B = (k5_anproj_1 A))  & (v8_anproj_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t31_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_freealg C A) =>  ((r1_tarski C B) => (m1_freealg B A)) ) ) ) ) ) ) ).
tt(t31_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k58_aofa_i00 A B D E G F)) G) = (k3_xcmplx_0 (k21_aofa_i00 B k4_numbers C G) F))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = G) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k58_aofa_i00 A B D E G F)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((r2_hidden B (k9_armstrng A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ( (B = D)  & (r4_armstrng A C E D)) ) ) ) ) ) ) ) ) ) ).
tt(t31_arytm_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_hidden A k5_arytm_3) => (r2_hidden A k4_ordinal1)) ) ) ).
tt(t31_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v3_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v3_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden B (k8_asympt_0 A)) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k8_real_1 D (k1_seq_1 A E)) (k1_seq_1 B E)) & (r1_xxreal_0 (k1_seq_1 B E) (k8_real_1 C (k1_seq_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_asympt_1,ax, ((r1_tarski (k6_asympt_0 (k5_asympt_1 k6_numbers)) (k6_asympt_0 (k5_asympt_1 1))) &  (~  ((k6_asympt_0 (k5_asympt_1 k6_numbers)) = (k6_asympt_0 (k5_asympt_1 1))) ) ) ).
tt(t31_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k1_msuhom_1 (k6_msualg_1 A) (k6_msualg_1 B) (k9_msualg_1 B)))) =>  ((v1_funct_1 (k1_funct_1 C k6_numbers)) &  ((v1_funct_2 (k1_funct_1 C k6_numbers) (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 (k1_funct_1 C k6_numbers) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t31_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_partfun1 C (k15_pre_poly (k1_nat_1 A 1))) &  ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k1_nat_1 A 1)) (k15_pre_poly (k1_nat_1 A 1)))))) ) ) )  =>  (! [D:$i] :  ( ((v1_partfun1 D (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1)))) &  ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))) (k15_pre_poly (k7_nat_d B (k1_nat_1 A 1))))))) ) ) )  =>  ( ((v2_bagorder C (k1_nat_1 A 1)) & (v2_bagorder D (k7_nat_d B (k1_nat_1 A 1))))  => (v2_bagorder (k8_bagorder A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t31_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A (k1_bcialg_1 A B C))) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(t31_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v1_bcialg_2 B A) & (m1_subset_1 B (u1_struct_0 A)))  <=>  ((v5_bcialg_2 B A) &  ((k2_bcialg_2 A B) = 1) ) ) ) ) ) ) ).
tt(t31_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D)) (k1_bcialg_1 A (k1_bcialg_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t31_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_bcialg_4 A (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) C))) = (k1_bcialg_4 A (k7_bcialg_4 A B) C)) ) ) ) ) ) ) ).
tt(t31_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (A = D)  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A B B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v1_bcialg_6 B A) & (v1_bcialg_6 (k2_bcialg_1 A B) A))  =>  ((k4_bcialg_6 A B) = (k4_bcialg_6 A (k2_bcialg_1 A B))) ) ) ) ) ) ).
tt(t31_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B (k1_bcialg_1 B C D) (k1_bcialg_1 B D C))) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((u1_struct_0 A) = (k4_bcialg_1 A)) ) ) ) ).
tt(t31_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_bhsp_1 A (k4_algstr_0 A B)) = (k3_bhsp_1 A B)) ) ) ) ) ).
tt(t31_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k5_vfunct_1 k5_numbers A C))) &  ((k2_seq_2 (k2_bhsp_2 A (k5_vfunct_1 k5_numbers A C))) = (k3_bhsp_1 A (k4_algstr_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t31_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k1_valued_0 (u1_struct_0 A) B C) D) = (k1_valued_0 (u1_struct_0 A) B (k2_nat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t31_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 B C D) = (k4_struct_0 B)) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A D) = (k10_real_1 (k3_bhsp_1 B (k1_normsp_1 B C (k2_nat_1 D 1))) (k3_bhsp_1 B (k1_normsp_1 B C D)))) ) )  &  ((v2_comseq_2 A) &  ( (~ (r1_xxreal_0 (k2_seq_2 A) 1))  & (v1_bhsp_4 C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v4_bilinear G A B C) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G (k4_vectsp_1 A B F D) E) = (k6_algstr_0 A F (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) B))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( (C = (k5_euclid A))  =>  ( ((k1_binari_3 A B) = (k3_binarith A C))  <=>  (B = (k6_xcmplx_0 (k5_series_1 2 A) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t31_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_int_1 B C (k5_series_1 2 A)) =>  ((k1_binari_3 A B) = (k1_binari_3 A C)) ) ) ) ) ) ) ) ).
tt(t31_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_lattices A B C) (k3_lattices A (k1_boolealg A B C) C))) ) ) ) ) ) ).
tt(t31_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D (k13_borsuk_1 A B C)) &  ( (~ (r2_hidden D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_hidden E (k2_struct_0 B)))  &  (D = (k6_domain_1 (u1_struct_0 A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_connsp_1 A k5_topmetr) &  ((v2_compts_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) &  ((r1_xxreal_0 B C) &  (A = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ).
tt(t31_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_borsuk_5 B C))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t31_borsuk_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B C))  =>  ((v1_xboole_0 (k1_rcomp_1 B C)) &  ((v2_compts_1 (k1_rcomp_1 B C) A) & (m1_subset_1 (k1_rcomp_1 B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t31_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ((r1_zfmisc_1 A B F) =>  ((k4_card_3 (k1_borsuk_7 A B F (k1_tarski C) (k1_tarski D) (k1_tarski E))) = (k1_tarski (k1_borsuk_7 A B F C D E))) ) ) ) ) ) ) ) ) ).
tt(t31_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k11_bspace A (k1_bspace (k7_bspace A)) B) = (k1_bspace k2_bspace)) ) ) ) ) ).
tt(t31_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r2_bvfunc_1 A (k17_bvfunc_1 A B C) C)) ) ) ) ) ) ).
tt(t31_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C B) (k12_bvfunc_1 A)))  <=> (r2_funct_2 A k6_margrel1 B C)) ) ) ) ) ) ) ).
tt(t31_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k1_bvfunc_1 A B)) (k11_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k6_bvfunc26 A B (k1_bvfunc_1 A B))) (k12_bvfunc_1 A))) ) ) ) ) ).
tt(t31_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k10_bvfunc_1 A D C) B E) (k10_bvfunc_1 A (k6_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) (k1_bvfunc_1 A (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E))) (k1_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k9_bvfunc_1 A C B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t31_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B B) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t31_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_c0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_c0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k6_algstr_0 (k11_c0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_seq_1 D H) = (k8_real_1 (k1_seq_1 B H) (k1_seq_1 C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((r2_hidden B (k6_c0sp2 A)) => (r2_hidden B (k2_c0sp2 A))) ) ) ) ).
tt(t31_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = k6_numbers) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 1) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 2) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 3) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 4) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 5) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 6) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 7) )  &  ( (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 8) )  &  (~  ((k2_xtuple_0 (k1_funct_1 B C)) = 9) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_calcul_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((r1_xxreal_0 1 A) =>  ((k10_xtuple_0 (k2_finseq_2 A B)) = (k10_xtuple_0 (k9_finseq_1 B))) ) ) ) ) ).
tt(t31_card_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_xboole_0 A B) &  ((r1_xboole_0 C D) &  ((r2_wellord2 A C) & (r2_wellord2 B D)) ) )  => (r2_wellord2 (k2_xboole_0 A B) (k2_xboole_0 C D))) ) ) ) ) ).
tt(t31_card_2,ax, (! [A:$i] :  ((k3_card_2 2 (k1_card_1 A)) = (k1_card_1 (k1_zfmisc_1 A))) ) ).
tt(t31_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  ((r2_hidden k1_xboole_0 (k10_xtuple_0 A)) <=>  ((k7_card_3 A) = k1_xboole_0) ) ) ) ).
tt(t31_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((r1_ordinal1 A B) =>  ((k3_card_2 A B) = (k3_card_2 2 B)) ) ) ) ) ) ).
tt(t31_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ( (r3_card_fil & (v4_card_fil A))  => (v6_card_fil A)) ) ) ).
tt(t31_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k8_relat_1 C (k1_tarski B))) => (r1_tarski (k2_card_fin D C B) (k1_funct_1 D A))) ) ) ) ) ) ) ).
tt(t31_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v5_card_lar A) => (v6_card_fil A)) ) ) ).
tt(t31_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((v7_cat_1 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A E B) =>  (! [G:$i] :  ((m1_cat_1 G A E B) =>  ( ((k5_cat_1 A E B C F D) = (k5_cat_1 A E B C G D))  =>  ( ((k2_cat_1 A E B) = k1_xboole_0)  |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k4_cat_1 (k8_cat_2 A B) (k9_cat_2 A B C D)) = (k10_cat_2 A B (k4_cat_1 A C) (k4_cat_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t31_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A C D) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  ((v1_cat_3 E A C D) => (v1_cat_3 (k9_cat_3 A C D B F E) B (k8_cat_1 A B F C) (k8_cat_1 A B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k2_cat_1 A (k2_cat_4 A B C) (k2_cat_4 A C B)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t31_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k12_cat_5 A B))) =>  ( (C = (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A (k17_cat_5 A B C) (k18_cat_5 A B C)) (k16_cat_5 A B C)))  &  ( ((k3_graph_1 A (k16_cat_5 A B C)) = (k4_graph_1 A (k17_cat_5 A B C)))  &  ( ((k1_cat_1 A (k17_cat_5 A B C) (k16_cat_5 A B C)) = (k18_cat_5 A B C))  &  ( ((k3_graph_1 (k12_cat_5 A B) C) = (k17_cat_5 A B C))  &  ((k4_graph_1 (k12_cat_5 A B) C) = (k18_cat_5 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 (k23_binop_2 4 A) 2)) = (k13_complex1 (k24_binop_2 (k23_binop_2 A 1) (k23_binop_2 A 4)) 2)) ) ) ).
tt(t31_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ( ((r2_hidden F (k2_cat_1 A B C)) &  ((r2_hidden G (k2_cat_1 A C D)) & (r2_hidden H (k2_cat_1 A D E))) )  =>  ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B D E) (k13_catalg_1 A)) (k10_finseq_1 H (k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C D) (k13_catalg_1 A)) (k2_finseq_4 (u4_struct_0 A) G F)))) = (k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C E) (k13_catalg_1 A)) (k10_finseq_1 (k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) C D E) (k13_catalg_1 A)) (k2_finseq_4 (u4_struct_0 A) H G)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k7_cc0sp1 (u1_struct_0 A))))) =>  ( (B = (k2_cc0sp2 A))  => (v2_ncfcont1 B (k7_cc0sp1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t31_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_cfcont_1 B A) <=>  ((r2_hidden A (k1_relset_1 k2_numbers B)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers C) (k1_relset_1 k2_numbers B)) &  ((v2_comseq_2 C) &  ( ((k3_comseq_2 C) = A)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((k3_funct_2 k5_numbers k2_numbers C D) = A) ) ) ) ) ) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C B)) &  ((k7_partfun1 k2_numbers B A) = (k3_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v6_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski C (k1_relset_1 k2_numbers (k19_valued_1 k2_numbers k2_numbers k2_numbers A B))) &  ((r2_cfdiff_1 A C) & (r2_cfdiff_1 B C)) )  =>  ((r2_cfdiff_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers A B) C) &  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_hidden D C) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers A B) C) D) = (k8_complex1 (k9_complex1 (k7_partfun1 k2_numbers B D) (k2_cfdiff_1 A D)) (k9_complex1 (k7_partfun1 k2_numbers A D) (k2_cfdiff_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k31_valued_1 A k2_numbers B) (k25_valued_1 A k2_numbers B (k10_complex1 k6_complex1)))) ) ) ) ).
tt(t31_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k10_cgames_1 B)) => (r1_tarski (k10_cgames_1 A) (k10_cgames_1 B))) ) ) ) ) ).
tt(t31_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 C F))) )  |  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 C F))) ) ) )  =>  ( ((k3_chain_1 A B C) = (k3_chain_1 A D E))  <=>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  ((r1_tarski C B) =>  (! [D:$i] :  ((m2_glib_000 D A B (k21_glib_000 A B)) =>  ((k21_glib_000 D C) = (k21_glib_000 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t31_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden (k6_classes1 A) (k6_classes1 (k4_tarski A B))) & (r2_hidden (k6_classes1 B) (k6_classes1 (k4_tarski A B)))) ) ) ).
tt(t31_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( (C = (k2_circcomb A B))  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ( (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 A D))) =>  ( (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  =>  ( ( (~ (r2_hidden H (k3_msafree2 A)))  &  (~  ((r2_hidden H (u1_struct_0 A)) & (r2_hidden H (k2_msafree2 C))) ) )  |  ((k1_funct_1 (k6_circuit2 C F G) H) = (k1_funct_1 (k6_circuit2 A D I) H)) ) ) ) )  &  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B)))  =>  ( ( (~ (r2_hidden H (k3_msafree2 B)))  &  (~  ((r2_hidden H (u1_struct_0 B)) & (r2_hidden H (k2_msafree2 C))) ) )  |  ((k1_funct_1 (k6_circuit2 C F G) H) = (k1_funct_1 (k6_circuit2 B E I) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) => (m1_subset_1 (k1_funct_1 D E) (u4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ((r2_hidden B (k4_classes1 A)) <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ((r2_hidden C A) & (r2_hidden B (k4_classes1 C))) ) ) ) ) ) ) ) ) ).
tt(t31_classes2,ax, (! [A:$i] :  ( ((v2_classes1 A) & (v1_ordinal1 A))  =>  ((k4_classes1 (k1_card_1 A)) = A) ) ) ).
tt(t31_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_clopban1 D A B) &  ((v2_clopban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ( (D = C)  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E)) (k8_real_1 (k1_normsp_0 (k14_clopban1 A B) C) (k1_normsp_0 A E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 1 (k1_seq_1 C E))) ) ) ) )  & (v1_series_1 (k4_normsp_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t31_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k18_complex1 (k1_seq_1 (k3_series_1 (k4_normsp_0 A (k5_clopban4 A B C F))) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v5_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (? [E:$i] :  ( ((v2_relat_1 E) & (m3_pboole E A (k1_mboolean A B)))  &  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  ((r1_pboole A F E) <=>  ((r1_pboole A F C) & (r2_pboole A D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((v7_closure2 C A B) &  (! [D:$i] :  ((m1_closure2 D A B (k6_closure2 A B)) => (r2_pboole A (k7_closure2 A B C D) D)) ) )  => (v9_closure2 C A B)) ) ) ) ) ) ).
tt(t31_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((k4_struct_0 B) = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t31_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k5_vfunct_1 k5_numbers A C))) &  ((k2_seq_2 (k2_clvect_2 A (k5_vfunct_1 k5_numbers A C))) = (k13_csspace A (k4_algstr_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t31_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A B D) = (k4_struct_0 A)) ) ) )  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k10_real_1 (k13_csspace A (k1_normsp_1 A B (k2_nat_1 D 1))) (k13_csspace A (k1_normsp_1 A B D)))) ) )  &  ((v2_comseq_2 C) &  ( (~ (r1_xxreal_0 (k2_seq_2 C) 1))  & (v1_clvect_3 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k7_cohsp_1 A)) <=>  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k1_funct_1 A B)) &  (! [D:$i] :  ( ((r2_hidden D (k9_xtuple_0 A)) &  ((r1_tarski D B) & (r2_hidden C (k1_funct_1 A D))) )  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t31_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r2_hidden (k6_partfun1 A) (k15_coh_sp B))) ) ) ).
tt(t31_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 3) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((l1_combgras C (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B)) =>  (~  ((v7_combgras C (k1_combgras (k2_nat_1 A 1) B)) &  (! [D:$i] :  ((l1_combgras D (k1_combgras A B) (k1_combgras A B)) =>  (~  ((v7_combgras D (k1_combgras A B)) &  ((r1_funct_2 (u2_incsp_1 (k1_combgras A B)) (u2_incsp_1 (k1_combgras A B)) (u1_incsp_1 (k1_combgras (k2_nat_1 A 1) B)) (u1_incsp_1 (k1_combgras (k2_nat_1 A 1) B)) (u2_combgras (k1_combgras A B) (k1_combgras A B) D) (u1_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k1_combgras A B))) =>  (! [F:$i] :  ((v1_finset_1 F) =>  ( (F = E)  =>  ((k2_combgras (k1_combgras A B) (k1_combgras A B) D E) = (k1_setfam_1 (k4_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) C (k7_combgras (k2_nat_1 A 1) B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_complex1,ax, ((k15_complex1 k7_complex1) = (k10_complex1 k7_complex1)) ).
tt(t31_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k1_complex2 A A) = (k5_square_1 (k17_complex1 A)))  &  ((k5_square_1 (k17_complex1 A)) = (k3_complex1 (k1_complex2 A A))) ) ) ) ).
tt(t31_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k11_algstr_0 k1_complfld (k3_vectsp_1 k1_complfld A B)) = (k3_vectsp_1 k1_complfld B A)) ) ) ) ) ) ) ) ) ).
tt(t31_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k45_valued_1 A B) = (k1_valued_1 A (k30_valued_1 B))) ) ) ) ) ) ).
tt(t31_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v1_tbsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xxreal_0 B (k4_metric_1 A D E))) ) ) ) ) )  =>  ((r1_xxreal_0 B k6_numbers) | (v1_finset_1 C)) ) ) ) ) ) ) ) ) ).
tt(t31_compos_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_compos_1)) =>  ((k5_xtuple_0 A) = k6_numbers) ) ) ).
tt(t31_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  ((k62_valued_1 (k3_compos_2 A B C)) = 2) ) ) ) ) ) ) ).
tt(t31_comptrig,ax, ((k10_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t31_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k3_comput_1 A B) (k2_comput_1 k5_numbers))) ) ) ) ).
tt(t31_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B A) A) B)) ) ) ) ) ).
tt(t31_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 A) B) (k8_nat_1 k2_numbers (k10_comseq_3 A) C))) (k18_complex1 (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)) B) (k8_nat_1 k1_numbers (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)) C))))) ) ) ) ) ) ).
tt(t31_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k8_conlat_1 A)) <=>  ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) ) ) ) ) ) ).
tt(t31_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) <=>  ((v2_connsp_1 D A) & (r2_hidden B D)) ) ) )  &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t31_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_pre_topc (k1_pre_topc A C) (k4_connsp_3 A B C)) (k2_pre_topc A B))) ) ) ) ) ) ) ).
tt(t31_convex1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((v2_funct_1 A) &  ( ((k10_xtuple_0 A) = (k1_enumset1 B C D))  &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~  (D = B) )  &  ( (~  (A = (k11_finseq_1 B C D)) )  &  ( (~  (A = (k11_finseq_1 B D C)) )  &  ( (~  (A = (k11_finseq_1 C B D)) )  &  ( (~  (A = (k11_finseq_1 C D B)) )  &  ( (~  (A = (k11_finseq_1 D B C)) )  &  (~  (A = (k11_finseq_1 D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers (k8_convex4 A C) B) = (k10_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers C B))) ) ) ) ) ) ) ).
tt(t31_cqc_lang,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_funct_4 A A B C) = (k16_funcop_1 A C)) ) ) ) ).
tt(t31_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k6_cqc_lang A C) D E F) (k15_cqc_sim1 A B)) => (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C D E F) (k15_cqc_sim1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ( ((r2_cqc_the1 A C D) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 D))) )  => (r2_hidden (k1_xtuple_0 (k1_funct_1 D B)) (k1_cqc_the1 A C))) ) ) ) ) ) ) ) ) ).
tt(t31_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k11_cqc_lang A D (k8_cqc_lang A B C)) A) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t31_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r4_cqc_the3 A (k7_domain_1 (k3_cqc_lang A) B C) (k6_domain_1 (k3_cqc_lang A) (k7_cqc_lang A B C)))) ) ) ) ) ) ).
tt(t31_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_funct_2 k5_numbers k2_numbers A (k46_valued_1 k5_numbers k2_numbers k2_numbers B C)) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A D) = (k11_complex1 (k3_funct_2 k5_numbers k2_numbers B D) (k3_funct_2 k5_numbers k2_numbers C D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k3_rlvect_1 A B C) (k3_rlvect_1 A B C)) = (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k12_csspace A B B) (k12_csspace A B C)) (k12_csspace A C B)) (k12_csspace A C C))) ) ) ) ) ) ) ).
tt(t31_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v3_dickson A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r1_orders_2 A (k8_nat_1 (u1_struct_0 A) B C) (k8_nat_1 (u1_struct_0 A) B D))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_finset_1 (k6_dickson A B)) &  (~ (v1_xboole_0 (k6_dickson A B))) ) ) ) ) ) ) ).
tt(t31_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k26_valued_1 k1_numbers k1_numbers D A) B C) = (k8_real_1 A (k9_diff_1 D B C))) ) ) ) ) ) ) ) ) ).
tt(t31_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 F)) (k8_real_1 B F)) C)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k1_funct_1 (k3_diff_1 E D) F) = (k7_real_1 (k7_real_1 (k8_real_1 (k8_real_1 (k8_real_1 2 A) D) F) (k8_real_1 A (k5_square_1 D))) (k8_real_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k7_real_1 (k8_real_1 (k3_funct_2 k1_numbers k1_numbers C B) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D A) 1) B)) (k8_real_1 (k3_funct_2 k1_numbers k1_numbers D (k9_real_1 B A)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) 1) B)))) ) ) ) ) ) ) ) ) ).
tt(t31_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k7_real_1 A B) k6_numbers))  &  (~  ((k1_seq_1 (k3_diff_1 k3_taylor_1 B) A) = (k1_seq_1 k3_taylor_1 (k7_real_1 1 (k13_complex1 B A)))) ) ) ) ) ) ) ) ) ).
tt(t31_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v2_dilworth C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_dilworth (k9_subset_1 (u1_struct_0 A) C B) (k5_yellow_0 A B)) & (m1_subset_1 (k9_subset_1 (u1_struct_0 A) C B) (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B))))) ) ) ) ) ) ) ).
tt(t31_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_diraf A B B C) &  ((r3_diraf A B C C) & (r3_diraf A B C B)) ) ) ) ) ) ) ) ).
tt(t31_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k5_subset_1 A B C) = (a_3_4_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t31_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( (~  (B = k6_numbers) )  => (v2_ec_pf_1 (k2_binom (k9_int_3 A) B 2) A)) ) ) ) ) ).
tt(t31_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  (D = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k4_ec_pf_2 A B C D) (k5_ec_pf_2 A B C D) (k6_ec_pf_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t31_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ( ((r2_hidden k1_xboole_0 A) & (v11_cat_1 B (k11_ens_1 A)))  =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t31_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  ( ((k3_finseq_1 (k1_matrprob A C 1)) = (k1_matrix_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski 1 D) (k2_matrix_1 B)) =>  ((r2_hidden D (k4_finseq_1 (k1_matrprob A C 1))) &  ((k1_funct_1 (k1_matrprob A C 1) D) = (k3_matrix_1 A B 1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_enumset1 A A B C) = (k1_enumset1 A B C)) ) ) ) ).
tt(t31_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (A = k1_xboole_0)  =>  ((k7_eqrel_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(t31_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (k4_equation A) C)) =>  (! [E:$i] :  ( ((v3_msualg_1 E A) &  ((v4_msualg_1 E A) & (m1_msualg_2 E A B)) )  =>  ((r1_equation A B C D) => (r1_equation A E C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k17_e_siec A) (k2_zfmisc_1 (k12_e_siec A) (k12_e_siec A))) & (r1_tarski (k14_e_siec A) (k2_zfmisc_1 (k12_e_siec A) (k12_e_siec A)))) ) ) ).
tt(t31_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k5_algstr_0 (k15_euclid A) B C) (k5_algstr_0 (k15_euclid A) B C)) = (k9_binop_2 (k10_binop_2 (k23_rvsum_1 B B) (k11_binop_2 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t31_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  =>  ( (~ (r1_xxreal_0 k32_sin_cos (k3_euclid_3 A)))  <=> (r1_xxreal_0 k32_sin_cos (k3_euclid_3 (k4_algstr_0 (k15_euclid 2) A)))) ) ) ) ).
tt(t31_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k8_euclid A B C) (k8_euclid A D E)) = (k7_real_1 (k9_real_1 (k9_real_1 (k23_rvsum_1 B D) (k23_rvsum_1 B E)) (k23_rvsum_1 C D)) (k23_rvsum_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ( ((k6_euclid_5 A A B) = k6_numbers)  &  ((k6_euclid_5 B A B) = k6_numbers) ) ) ) ) ) ).
tt(t31_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ( (D = (k19_euclid E F))  &  ((r2_hidden D (k1_rltopsp1 (k15_euclid 2) C B)) &  ( (~  (A = C) )  &  ( (~  ((k8_real_1 2 (k4_euclid_3 A C B)) = (k4_euclid_3 A D B)) )  &  (~  ((k8_real_1 2 (k9_real_1 (k4_euclid_3 A C B) k32_sin_cos)) = (k4_euclid_3 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (B = (k5_euclid_7 A (k7_euclid_7 A B))) ) ) ) ) ).
tt(t31_euclid_8,ax, ((k6_euclid 3 k2_euclid_8) = (k1_euclid_8 (k19_binop_2 1) k6_numbers k6_numbers)) ).
tt(t31_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( ((k1_rlvect_1 (k15_euclid A) B C) = (k4_struct_0 (k15_euclid A)))  &  ( (~  (C = k6_numbers) )  &  (~  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden B (k2_euclid_4 A D E)) &  ((r2_hidden C (k2_euclid_4 A D E)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((k8_euclid A C B) = (k9_euclid A (k8_euclid A E D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((k1_funct_1 (k10_funct_7 C A B) B) = (k1_funct_1 C A)) ) ) ) ) ) ).
tt(t31_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E))) = (k2_compos_1 B))  =>  ((k6_extpro_1 A B C D) = (k5_extpro_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 A) (k2_msafree2 B)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 B D))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)))  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) (k5_facirc_1 (k2_circcomb A B) (k3_circcomb A B C D) E G) (u1_struct_0 B)) = (k5_facirc_1 B D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_facirc_1)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k1_facirc_1)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_facirc_1 A B C) (k20_facirc_1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k19_facirc_1 A B C) (k20_facirc_1 A B C) D 2) (k19_facirc_1 A B C) (k20_facirc_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_tarski B (k1_relset_1 k1_numbers A)) &  ((v1_rcomp_1 B) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B)) &  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( ((k1_seq_1 A C) = (k4_seq_4 (k7_relset_1 k1_numbers k1_numbers A B)))  &  ((k1_seq_1 A D) = (k5_seq_4 (k7_relset_1 k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k9_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos B)) (k8_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t31_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_sin_cos9) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k1_seq_1 k1_sin_cos9 B) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 (k1_seq_1 k30_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t31_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k10_prob_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k10_prob_1 A)) => (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) ) )  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) ) ) ) ) ).
tt(t31_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k9_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) B) D) = (k10_prepower (k9_real_1 A D) (k1_real_1 (k10_real_1 1 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k1_taylor_1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k1_taylor_1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k1_taylor_1 2)) A) C) = (k1_real_1 (k8_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos C)) (k9_real_1 1 (k1_seq_1 k24_sin_cos C))))) ) ) ) ) ) ) ) ) ) ).
tt(t31_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)) (k10_real_1 1 A)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C B) &  ((k1_seq_1 k19_sin_cos C) = k6_numbers) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)) (k10_real_1 1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)) (k10_real_1 1 A)) B) C) = (k10_real_1 (k1_seq_1 k16_sin_cos C) (k5_prepower (k1_seq_1 k19_sin_cos C) (k3_real_1 A 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos) A) B) = (k9_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k1_seq_1 k16_sin_cos B)) (k10_real_1 (k1_seq_1 k24_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t31_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) A) B) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k16_sin_cos B)) B) (k10_real_1 (k8_real_1 (k1_seq_1 k3_taylor_1 B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t31_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_xcmplx_0 (k4_nat_1 (k1_pre_ff A) (k1_pre_ff (k1_nat_1 A 2))) (k1_pepin (k1_pre_ff (k1_nat_1 A 1)))) = (k1_newton (k4_xcmplx_0 1) (k1_nat_1 A 1))) ) ) ).
tt(t31_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1)) = (k6_xcmplx_0 (k4_nat_1 (k1_pre_ff (k2_nat_1 A 1)) (k1_fib_num3 (k2_nat_1 A 1))) (k4_nat_1 (k1_pre_ff A) (k1_fib_num3 A)))) ) ) ).
tt(t31_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_fib_num3 A) = (k2_int_1 (k6_xcmplx_0 (k3_power k1_fib_num A) (k13_complex1 1 2)))) ) ) ) ).
tt(t31_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (C = (k1_finseq_8 A (k4_finseq_8 A B C) (k7_finseq_8 A B C))) ) ) ) ) ) ) ).
tt(t31_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_hidden B D) & (r2_hidden C E))  =>  ((r2_hidden (k4_lattices A B C) (k5_filter_0 A D E)) & (r2_hidden (k4_lattices A C B) (k5_filter_0 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k8_filter_1 A)) <=> (r3_lattices A B C)) ) ) ) ) ) ) ).
tt(t31_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v14_lattices A) => (r1_filter_2 (u1_struct_0 A) (k5_filter_2 A) (k6_filter_2 A (k6_lattices A)))) ) ) ).
tt(t31_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k10_xtuple_0 (k7_finseq_1 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t31_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (B = (k2_finseq_1 A))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ((m2_finseq_1 E B) =>  ((r1_xxreal_0 A (k3_finseq_1 D)) => (m2_finseq_1 (k1_partfun1 k5_numbers B k5_numbers C E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r2_hidden 1 (k1_relset_1 k5_numbers A))) ) ) ) ).
tt(t31_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 (k1_finseq_3 A (k1_tarski B)))) =>  ( ( (~ (r1_xxreal_0 (k4_finseq_4 A B) C))  =>  ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A C)) )  &  ((r1_xxreal_0 (k4_finseq_4 A B) C) =>  ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A (k1_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ).
tt(t31_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( ( ((k1_nat_1 A 1) = B)  & (r2_hidden B (k4_finseq_1 D)))  =>  ((k8_finseq_1 C (k12_finseq_1 C (k7_partfun1 C D B)) (k2_rfinseq C B D)) = (k2_rfinseq C A D)) ) ) ) ) ) ) ) ) ) ).
tt(t31_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k6_finseq_4 (k11_finseq_1 A B C) A) = (k10_finseq_1 B C)) ) ) ) ).
tt(t31_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ( ((k7_partfun1 A (k2_finseq_7 A B C D) C) = (k7_partfun1 A B D))  &  ((k7_partfun1 A (k2_finseq_7 A B C D) D) = (k7_partfun1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k3_finseqop A A A F (k5_binop_1 A F B C) E) (k3_finseqop A A A F B (k3_finseqop A A A F C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C (k6_fintopo2 A B)) &  ((r2_hidden D (k6_fintopo2 A B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E (k6_fintopo2 A B)) & (r1_tarski E (k9_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_subset_1 (u1_struct_0 A) (k10_fintopo2 A B) (k10_fintopo2 A C)) = (k10_fintopo2 A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t31_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k7_fintopo3 A B (k2_nat_1 C 1)) = (k12_fin_topo A (k7_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t31_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ( (~  (B = (k1_struct_0 A)) )  &  ( (~  (C = (k1_struct_0 A)) )  &  ((v3_fin_topo B A) &  ((v3_fin_topo C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) )  => (v1_fintopo6 A)) ) ) ).
tt(t31_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) (k7_flang_1 A B C)) =>  ((r1_xxreal_0 C k6_numbers) | (r2_hidden (k2_flang_1 A) B)) ) ) ) ) ) ) ).
tt(t31_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_flang_2 A B C D) = (k4_flang_1 A (k2_flang_1 A)))  <=>  (~  ( (~  ((r1_xxreal_0 C D) &  (B = (k4_flang_1 A (k2_flang_1 A))) ) )  &  ( (~  ( (C = k6_numbers)  &  (D = k6_numbers) ) )  &  (~  ( (C = k6_numbers)  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k8_flang_1 A B) (k7_flang_1 A B C)) = (k1_flang_3 A B C)) ) ) ) ) ) ).
tt(t31_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((k1_funct_1 (k5_fomodel0 A C) (k12_finseq_1 A B)) = B)  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  ( (~ (v1_xboole_0 D))  =>  ((k1_funct_1 (k5_fomodel0 A C) (k7_finseq_1 D (k12_finseq_1 A B))) = (k1_binop_1 C (k1_funct_1 (k5_fomodel0 A C) D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m2_valued_0 D (u1_struct_0 A) B) & (r1_frechet A D C)) )  => (r1_frechet2 A B C)) ) ) ) ) ) ) ).
tt(t31_frechet,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_frechet))) =>  ( (A = (k1_tarski k1_numbers))  => (v4_pre_topc A k3_frechet)) ) ) ).
tt(t31_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  =>  ( (~  ((k7_fsm_1 B C D (k2_nat_1 A 1)) = (k7_fsm_1 B C D A)) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 E A) &  ((k7_fsm_1 B C D (k2_nat_1 E 1)) = (k7_fsm_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fsm_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) &  ((v5_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers)) & (l2_fsm_2 A (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers))) ) )  =>  ( ( ((u1_struct_0 A) = (k1_ordinal1 k1_numbers))  &  ( ((u1_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) = k1_numbers)  &  ( ((u4_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A) = (k6_partfun1 (u1_struct_0 A)))  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  ((r1_xxreal_0 B k6_numbers) & (r1_xxreal_0 C k6_numbers)) )  =>  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = 1) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 B k6_numbers) & (r1_xxreal_0 C k6_numbers))  =>  ( ( (~  (B = k6_numbers) )  &  (~  (C = k6_numbers) ) )  |  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = k6_numbers) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 k6_numbers C))  &  (~  ((k3_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers)) (u1_struct_0 A) (u1_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 (u1_struct_0 A) (k2_zfmisc_1 k1_numbers k1_numbers) (u2_fsm_1 (k2_zfmisc_1 k1_numbers k1_numbers) A) (k1_domain_1 k1_numbers k1_numbers B C))) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_fsm_2 (k2_zfmisc_1 k1_numbers k1_numbers) (k1_ordinal1 k1_numbers) A (k1_domain_1 k1_numbers k1_numbers B C)) = (k2_square_1 (k2_absvalue B) (k2_absvalue C))) ) ) ) ) ) ) ) ).
tt(t31_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 B)) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  ((k3_rewrite3 B (k9_flang_1 B) (k1_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E) C (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 E)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E D A))) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 E)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) E (k1_flang_1 B D C) A))) ) ) ) ) ) ) ) ) ) ).
tt(t31_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_msafree2 (k19_ftacell1 A B C D E)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k48_gfacirc1 A B C)) (k2_enumset1 (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k45_gfacirc1 A B C))) (k2_tarski (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp) (k48_gfacirc1 (k48_gfacirc1 A B C) E D))) (k2_enumset1 (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp) (k4_tarski (k10_finseq_1 E D) k4_twoscomp) (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp) (k45_gfacirc1 (k48_gfacirc1 A B C) E D)))) ) ) ) ) ) ).
tt(t31_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k5_funcop_1 B C A) = (k3_funcop_1 B (k2_funcop_1 (k9_xtuple_0 A) C) A)) ) ) ) ) ) ).
tt(t31_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ((k3_relat_1 A B) = (k4_relat_1 (k9_xtuple_0 A))) ) )  => (v2_funct_1 A)) ) ) ).
tt(t31_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  & (r2_relset_1 A A (k1_partfun1 A B B A C D) (k6_partfun1 A))) )  &  (~ (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(t31_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_tarski B (k1_zfmisc_1 (k9_xtuple_0 A))) => (r1_tarski (k8_relat_1 (k3_funct_3 A) B) (k7_relat_1 (k1_funct_3 A) B))) ) ) ) ).
tt(t31_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k2_xboole_0 A B) = (k1_funct_4 A B)) ) ) ) ) ) ).
tt(t31_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 (k1_funct_5 B))) &  (C = (k1_funct_1 (k1_funct_5 B) A)) )  =>  ( ((k9_xtuple_0 C) = (k10_xtuple_0 (k3_xboole_0 (k9_xtuple_0 B) (k2_zfmisc_1 (k1_tarski A) (k10_xtuple_0 (k9_xtuple_0 B))))))  &  ((r1_tarski (k9_xtuple_0 C) (k10_xtuple_0 (k9_xtuple_0 B))) &  ((r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B)) &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ( ((k1_funct_1 C D) = (k1_binop_1 B A D))  & (r2_hidden (k4_tarski A D) (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 (k6_funct_6 B))) &  (C = (k1_funct_1 (k6_funct_6 B) A)) )  =>  ( ((k9_xtuple_0 C) = (k8_relat_1 B (k1_funct_6 (k10_xtuple_0 B))))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((r2_hidden (k4_tarski D A) (k9_xtuple_0 (k2_funct_5 B))) &  ((k1_funct_1 C D) = (k1_binop_1 (k2_funct_5 B) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 (k2_funct_7 A C B) C) = B) ) ) ) ) ) ).
tt(t31_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) & (r1_funct_8 A k1_numbers k1_numbers C))  => (r2_funct_8 A k1_numbers k1_numbers (k52_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t31_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) (k8_real_1 k32_sin_cos A))) ) ).
tt(t31_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ( ((v8_functor0 D A A) &  ((v10_functor0 D A A) & (l2_functor0 D A A)) )  =>  ( (D = (k11_functor0 A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  ((k6_functor0 A A D B C E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F A B) & (m2_functor0 F A B))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ( ((v15_functor0 H B C) & (m2_functor0 H B C))  =>  (! [I:$i] :  ( ((v15_functor0 I B C) & (m2_functor0 I B C))  =>  (! [J:$i] :  ((m2_functor2 J B C G H) =>  (! [K:$i] :  ((m2_functor2 K B C H I) =>  (! [L:$i] :  ((m1_functor2 L A B D E) =>  (! [M:$i] :  ((m1_functor2 M A B E F) =>  ( ((r2_functor2 A B D E) &  ((r2_functor2 A B E F) &  ((r2_functor2 B C G H) & (r2_functor2 B C H I)) ) )  => (r8_pboole (u1_struct_0 A) (k7_functor3 A B C D F G I (k3_functor2 A B D E F L M) (k5_functor2 B C G H I J K)) (k3_functor2 A C (k1_functor3 A B C D G) (k1_functor3 A B C E H) (k1_functor3 A B C F I) (k7_functor3 A B C D E G H L J) (k7_functor3 A B C E F H I M K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B (k4_fuzzy_1 A)) => (r2_funct_2 A k1_numbers B (k4_fuzzy_1 A))) ) ) ) ) ).
tt(t31_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 (k2_fuzzy_2 A B (k3_fuzzy_2 A B C)) B) & (r1_fuzzy_1 B (k3_fuzzy_2 A B (k2_fuzzy_2 A B C)))) ) ) ) ) ) ) ).
tt(t31_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C (k5_algstr_0 A (k5_struct_0 A) B))))  => (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C B))) ) ) ) ) ) ) ).
tt(t31_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k6_fvsum_1 A B (k4_fvsum_1 A B C D)) = (k4_fvsum_1 A B (k6_fvsum_1 A B C) (k6_fvsum_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t31_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~ (v1_xboole_0 (k25_gate_1 A B C D E F)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) & (v1_xboole_0 F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  ((k5_gcd_1 A B (k4_struct_0 A) (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ).
tt(t31_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((k10_genealg1 E F G A k6_numbers k6_numbers k6_numbers) = (k7_genealg1 E G F A))  &  ( ((k10_genealg1 E F G k6_numbers B k6_numbers k6_numbers) = (k7_genealg1 E G F B))  &  ( ((k10_genealg1 E F G k6_numbers k6_numbers C k6_numbers) = (k7_genealg1 E G F C))  &  ((k10_genealg1 E F G k6_numbers k6_numbers k6_numbers D) = (k7_genealg1 E G F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((k4_geomtrap A B C (k1_rlvect_1 A D F) E) = (k8_real_1 F (k4_geomtrap A B C D E)))  &  ( ((k4_geomtrap A B C D (k1_rlvect_1 A E F)) = (k8_real_1 F (k4_geomtrap A B C D E)))  &  ( ((k4_geomtrap A B C (k1_rlvect_1 A D F) E) = (k8_real_1 (k4_geomtrap A B C D E) F))  &  ((k4_geomtrap A B C D (k1_rlvect_1 A E F)) = (k8_real_1 (k4_geomtrap A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k13_gfacirc1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) (k1_tarski (k12_gfacirc1 A B C))) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) (k1_tarski (k9_gfacirc1 A B C)))) ) ) ) ).
tt(t31_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k7_glib_000 A)) &  ((r2_hidden (k1_funct_1 (k10_glib_000 A) B) C) & (r2_hidden (k1_funct_1 (k11_glib_000 A) B) C)) )  <=> (r2_hidden B (k21_glib_000 A C))) ) ) ) ) ).
tt(t31_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_glib_001 A D E B) & (r1_glib_001 A E F C))  => (r1_glib_001 A D F (k7_glib_001 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t31_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  ((k25_glib_000 A B) = (k21_glib_000 A (k24_glib_000 A B))) ) ) ) ) ).
tt(t31_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v8_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ((r2_hidden B (k7_glib_000 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k5_glib_003 A) B))) ) ) ) ).
tt(t31_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_glib_000 C A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))) => (v1_glib_002 C)) ) ) ) ) ) ).
tt(t31_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((r2_hidden A (k4_finseq_1 D)) &  ((r2_hidden (k2_nat_1 A 1) (k4_finseq_1 D)) &  ((r2_hidden B (k2_finseq_1 (k1_matrix_1 C))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C B))) &  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C B))))  &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C E))) &  ((r2_hidden E (k2_finseq_1 (k1_matrix_1 C))) &  (~  ((k18_complex1 (k6_xcmplx_0 B E)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k5_goboard5 B A) (k4_goboard5 B A)) = (k2_topreal1 2 B A)) ) ) ) ) ) ).
tt(t31_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 C))) ) )  => (r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)))) ) ) ) ) ) ) ).
tt(t31_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r2_hidden B (k4_finseq_1 A)) &  (~  ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) ) ) ) ) ) ) ).
tt(t31_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k1_matrix_1 (k2_goboard2 A))))  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 B 1))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k2_nat_1 B 2))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t31_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((k3_goboard5 B A (k1_matrix_1 B)) = (a_2_5_gobrd11 A B)) ) ) ) ) ) ) ).
tt(t31_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C D) & (r1_xxreal_0 (k2_nat_1 A 1) B)) ) )  =>  ( ((k3_gobrd13 C D A) = (k3_gobrd13 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) D A))  &  ((k2_gobrd13 C D A) = (k2_gobrd13 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  => (r1_tarski (k3_goboard9 A) (k3_goboard9 (k1_sprect_1 (k3_topreal1 2 A))))) ) ).
tt(t31_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (~  ((v4_card_3 A) &  ((v1_finset_1 (k6_goedelcp A B)) &  (! [C:$i] :  ( ((v1_henmodel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (~  ((r1_tarski B C) & (v2_goedelcp C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  => (r1_tarski (k1_tarski A) (k11_graph_1 A))) ) ).
tt(t31_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  ((r1_graph_2 A B C) =>  ( (C = k1_xboole_0)  |  ((k5_graph_2 A (k10_xtuple_0 C)) = (k10_xtuple_0 B)) ) ) ) ) ) ) ) ) ).
tt(t31_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k7_graph_3 B C A) = (k7_graph_3 B C (k3_xboole_0 A (u4_struct_0 B)))) ) ) ) ) ) ).
tt(t31_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v7_graph_1 E B) & (m2_graph_1 E B))  =>  ((r2_graph_5 B C D E A) =>  ( (C = D)  | (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~  (A = (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1)) )  &  (~  ((k1_seq_1 (k6_graphsp (k16_graphsp B) C) A) = (k1_seq_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ((m3_grcat_1 B (k18_grcat_1 A)) =>  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  (~  ( ((k19_grcat_1 A B) = (k20_grcat_1 A C))  &  (! [D:$i] :  ( ((v8_algstr_0 D) & (m2_grcat_1 D A))  =>  (! [E:$i] :  ( ((v8_algstr_0 E) & (m2_grcat_1 E A))  =>  (! [F:$i] :  ( ((v8_algstr_0 F) & (m2_grcat_1 F A))  =>  (~  ((m1_grcat_1 B E F) & (m1_grcat_1 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_gr_cy_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_2 A C) & (r2_int_1 A B C))  => (r1_int_2 B C)) ) ) ) ) ) ) ).
tt(t31_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ( ((k1_funct_1 A C) = (k1_funct_1 B C))  &  ( ((k1_funct_1 A D) = (k1_funct_1 B D))  &  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) )  =>  ((k5_relat_1 A (k1_enumset1 C D E)) = (k5_relat_1 B (k1_enumset1 C D E))) ) ) ) ) ) ) ) ) ).
tt(t31_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r2_groeb_1 A B C (k1_groeb_1 A C D) (k7_ideal_1 (k11_polynom1 A C) (k1_groeb_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t31_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 D (k15_pre_poly A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A B)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A B) E) =>  (! [G:$i] :  ((m2_ideal_1 G (k11_polynom1 A B) E) =>  ( ((r2_groeb_2 A B C E F) & (r2_groeb_2 A B D E G))  => (r2_groeb_2 A B (k4_polynom1 A B C D) E (k5_groeb_2 A B E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E))) =>  ( ((k3_polynom1 A C (k6_groeb_3 A B C D E) F) = (k3_polynom1 A C D F))  &  ((k3_polynom1 A C (k5_groeb_3 A B C D E) F) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_group_11 A (k2_group_11 A B C) C)) => (r1_tarski (k13_group_2 A C D) (k2_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t31_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((k5_group_1 B A (k1_group_1 B)) = (k1_group_1 B)) ) ) ) ) ).
tt(t31_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k5_group_2 A D (k2_group_2 A B C)) = (k2_group_2 A B (k5_group_2 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t31_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A (k3_group_3 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (A = (k2_group_3 B E F))  &  ((r2_hidden E C) & (r2_hidden F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r1_group_2 A (k5_group_4 A (k8_group_2 A B)) B)) ) ) ) ).
tt(t31_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A (k2_group_3 A B (k2_group_1 A C)) C) = (k2_group_5 A (k2_group_1 A C) B)) ) ) ) ) ) ) ).
tt(t31_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k1_group_1 A)) = (k1_group_1 B)) ) ) ) ) ) ) ).
tt(t31_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  ((k1_group_1 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))) = (k4_group_7 A (k1_group_1 A))) ) ) ).
tt(t31_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) &  ((v4_group_9 D A B) & (m1_group_9 D A B)) )  =>  ((u1_struct_0 (k19_group_9 A B C D)) = (k16_group_9 A B C D)) ) ) ) ) ) ) ) ).
tt(t31_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D B) & (m1_group_2 D B)) )  =>  (~  ((m1_group_6 D B (k10_group_5 B)) &  ((v3_groupp_1 C A) &  ((v3_groupp_1 D A) &  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E B))  =>  (~  ( ((u1_struct_0 E) = (k7_group_4 B C D))  & (v3_groupp_1 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (~  ((v1_hallmar1 B A) &  (! [C:$i] :  ((m4_hallmar1 C A B) =>  (~ (v1_hallmar1 C A)) ) ) ) ) ) ) ) ) ).
tt(t31_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (r2_hidden D B)) )  => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A C) D) (k8_weierstr A C B))) ) ) ) ) ) ) ) ) ).
tt(t31_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k6_glib_001 A (k2_helly A B C)) = (k2_helly A C B)) ) ) ) ) ) ) ).
tt(t31_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k6_bilinear k1_complfld A B C D)) (k6_bilinear k1_complfld A B (k3_hermitan A B C) (k3_hermitan A B D)))) ) ) ) ) ) ) ) ).
tt(t31_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A))))) =>  ( ((r1_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) D B) & (r1_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) D C))  => (r1_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) D (k13_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) B C))) ) ) ) ) ) ) ) ) ).
tt(t31_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_xxreal_0 2 A) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k1_taylor_1 A) B) 3) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k9_real_1 A 3)) (k8_real_1 (k8_real_1 A (k9_real_1 A 1)) (k9_real_1 A 2))) B))) ) ) ) ) ).
tt(t31_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_polynom3 (k11_polynom1 B A))) (u1_struct_0 (k11_polynom1 (k2_nat_1 B 1) A)))))) )  & (v4_quofield C (k14_polynom3 (k11_polynom1 B A)) (k11_polynom1 (k2_nat_1 B 1) A))) ) ) ) ) ) ).
tt(t31_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r2_hidden (k4_hilbert1 A B) k6_hilbert1) <=>  ((r2_hidden A k6_hilbert1) & (r2_hidden B k6_hilbert1)) ) ) ) ) ) ).
tt(t31_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_hilbert2 (k1_hilbert2 A)) = (k2_trees_4 k1_hilbert1 (k1_hilbert2 A))) ) ) ).
tt(t31_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((k3_hilbert3 C (k4_hilbert1 A B)) = (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B))) ) ) ) ) ) ) ).
tt(t31_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k2_hurwitz A (k4_hurwitz A B C)) = (k6_xcmplx_0 C 1)) ) ) ) ) ) ) ) ).
tt(t31_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ( ((k1_recdef_1 D 5) = (k1_recdef_1 C 5))  &  ((k1_recdef_1 D 6) = (k1_recdef_1 C 6)) ) ) ) ) ) )  =>  ((k12_idea_1 A (k12_idea_1 A B C) D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t31_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v5_group_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_ideal_1 C A B) =>  ((m2_ideal_1 C A B) & (m3_ideal_1 C A B)) ) ) ) ) ) ) ).
tt(t31_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k2_incsp_1 A C D B)) ) ) ) ) ) ) ) ) ) ).
tt(t31_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_cat_1 E) &  ((v3_cat_1 E) &  ((v4_cat_1 E) &  ((v5_cat_1 E) &  ((v6_cat_1 E) &  ((v3_cat_5 E) & (l1_cat_1 E)) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G D E) =>  ((k15_index_1 A B C E (k9_cat_1 C D E F G)) = (k15_index_1 A (k15_index_1 A B C D F) D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((l3_msualg_1 E B) =>  ((k3_relat_1 C (k2_msualg_3 (u1_struct_0 B) (u3_msualg_1 B E))) = (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k1_instalg1 A B E C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 (k2_int_1 A) A))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 (k2_int_1 A) A)) ) ) ) ) ).
tt(t31_int_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 2 A) &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((v1_int_2 B) & (r1_int_1 B A)) ) ) ) ) ) ) ) ).
tt(t31_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 2 (k3_finseq_1 A)) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k1_relset_1 k5_numbers A)) & (r2_hidden C (k1_relset_1 k5_numbers A)))  =>  ( (B = C)  |  ((k6_nat_d (k1_recdef_1 A B) (k1_recdef_1 A C)) = 1) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) =>  ((k6_nat_d (k3_wsierp_1 (k5_wsierp_1 k1_numbers k5_numbers B A)) (k1_recdef_1 A B)) = 1) ) ) ) ) ) ) ).
tt(t31_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (~  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  ( (~  ((k1_funct_1 A B) = 1) )  &  ( (~  ((k1_funct_1 A B) = k6_numbers) )  &  (~  ((k1_funct_1 A B) = (k4_xcmplx_0 1)) ) ) ) ) ) ) )  &  ( (~  ((k19_rvsum_1 A) = 1) )  &  ( (~  ((k19_rvsum_1 A) = k6_numbers) )  &  (~  ((k19_rvsum_1 A) = (k4_xcmplx_0 1)) ) ) ) ) ) ) ) ).
tt(t31_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  ((r1_xxreal_0 k6_numbers (k2_int_6 A B)) &  (~ (r1_xxreal_0 (k19_rvsum_1 B) (k2_int_6 A B))) ) ) ) ) ) ) ).
tt(t31_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (v2_struct_0 (k3_int_7 A)))  &  ((v2_group_1 (k3_int_7 A)) &  ((v3_group_1 (k3_int_7 A)) &  ((v1_gr_cy_1 (k3_int_7 A)) & (l3_algstr_0 (k3_int_7 A))) ) ) ) ) ) ).
tt(t31_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k4_sin_cos2)) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k1_sin_cos2) k4_sin_cos2) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_fcont_1 1 k6_numbers) k1_sin_cos2) k4_sin_cos2) (k5_seq_4 A)))) ) ) ).
tt(t31_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 D G) = (k9_binop_2 (k11_binop_2 A G) B)) ) ) )  &  ( (F = (k1_relset_1 k1_numbers E))  & (r2_relset_1 k1_numbers k1_numbers E (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) (k3_rfunct_1 k1_numbers k1_numbers D (k41_valued_1 k1_numbers k1_numbers k19_sin_cos))))) ) )  =>  ((k2_integra5 C E) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k29_sin_cos) (k4_seq_4 C)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k29_sin_cos) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos)) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t31_integr14,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = (k10_real_1 (k9_real_1 (k1_seq_1 k19_sin_cos (k8_real_1 A F)) (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A F)))) (k5_square_1 (k1_seq_1 k16_sin_cos (k8_real_1 A F))))) ) ) )  &  ((r1_tarski E (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers E)))) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 D F) = (k8_real_1 A F))  &  (~  (A = k6_numbers) ) ) ) ) )  &  ( (E = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers E)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k2_fdiff_9) (k1_real_1 (k10_real_1 1 A))) (k1_partfun2 k1_numbers E)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) F) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) F (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) )  =>  ((k12_integr15 B E A F) = (k7_euclid A (k12_integr15 B D A F) (k12_integr15 D E A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v2_seq_2 (k2_partfun1 A k1_numbers D A)) &  ((k3_finseq_1 B) = 1) )  => (r1_xxreal_0 (k7_integra1 A D B) (k7_integra1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t31_integra2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 B k1_numbers C B)) & (v3_integra1 C B))  =>  ((v3_integra1 (k26_valued_1 B k1_numbers C A) B) &  ((k12_integra1 B (k26_valued_1 B k1_numbers C A)) = (k8_real_1 A (k12_integra1 B C))) ) ) ) ) ) ) ) ) ).
tt(t31_integra7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_integra5 (k3_integra5 A B) (k1_seqfunc k1_numbers k1_numbers C E)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers C E) (k3_integra5 A B))) &  ((k1_seq_1 D E) = (k4_integra5 A B (k1_seqfunc k1_numbers k1_numbers C E))) ) ) ) )  & (r3_seqfunc k1_numbers C (k3_integra5 A B)))  =>  ((r1_xxreal_0 B A) |  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k11_seqfunc k1_numbers C (k3_integra5 A B)) (k3_integra5 A B))) &  ((r1_integra5 (k3_integra5 A B) (k11_seqfunc k1_numbers C (k3_integra5 A B))) &  ((v2_comseq_2 D) &  ((k2_seq_2 D) = (k4_integra5 A B (k11_seqfunc k1_numbers C (k3_integra5 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_integra8,ax, ((k2_fdiff_1 k4_sin_cos2 k1_numbers) = k1_sin_cos2) ).
tt(t31_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A A)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers B B))) ) ) ) ) ) ) )  =>  ((k1_integra9 C (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k7_real_1 (k1_integra9 C A A) (k8_real_1 2 (k1_integra9 C A B))) (k1_integra9 C B B))) ) ) ) ) ) ) ) ).
tt(t31_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_interva1 D A))  => (r1_interva1 A (k4_interva1 A B (k3_interva1 A C D)) (k3_interva1 A (k4_interva1 A B C) (k4_interva1 A B D)))) ) ) ) ) ) ) ) ).
tt(t31_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 A (k3_intpro_1 (k3_intpro_1 A B) B)) k8_intpro_1)) ) ) ) ).
tt(t31_irrat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((v1_rat_1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 B) & (v1_int_1 (k3_xcmplx_0 (k9_newton B) A))) ) ) ) ) ) ) ) ).
tt(t31_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G D A) =>  (! [H:$i] :  ((m2_cat_1 H A B) =>  (! [I:$i] :  ((m2_nattra_1 I C D E F) =>  ((r2_nattra_1 C D E F) => (r2_funct_2 (u1_struct_0 C) (u4_struct_0 B) (k4_isocat_1 C D B E F I (k9_cat_1 D A B G H)) (k4_isocat_1 C A B (k9_cat_1 C D A E G) (k9_cat_1 C D A F G) (k4_isocat_1 C D A E F I G) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  ((r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_isocat_2 A B C (k8_isocat_2 A B C D E)) D) & (r2_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k10_isocat_2 A B C (k8_isocat_2 A B C D E)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_isomichi,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_tarski (k3_borsuk_5 A B) (k3_rcomp_1 A k1_xxreal_0))) ) ) ) ).
tt(t31_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (r1_xxreal_0 (k12_euclid A) (k7_real_1 (k18_complex1 (k17_euclid A)) (k18_complex1 (k18_euclid A))))) ) ).
tt(t31_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 1 (k17_euclid C))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t31_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = k6_numbers) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k4_real_1 F (k7_square_1 (k7_real_1 1 (k3_square_1 (k7_xcmplx_0 F G)))))) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_1_jgraph_4) )  => (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ).
tt(t31_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) A B) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B)) ) )  => (v5_pre_topc A (k15_euclid 2) k3_topmetr)) ) ) ).
tt(t31_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C))) = (k1_tarski (k19_euclid A C))) ) ) ) ) ) ) ) ) ) ).
tt(t31_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 G (k18_euclid C)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k1_rltopsp1 (k15_euclid 2) B C)) = (k1_tarski D))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden B (k3_topreal1 2 A)))  &  ( (~ (r2_hidden C (k3_topreal1 2 A)))  &  ( ( ( ((k17_euclid B) = (k17_euclid C))  &  ( ((k17_euclid B) = (k17_euclid E))  &  ((k17_euclid E) = (k17_euclid F)) ) )  |  ( ((k18_euclid B) = (k18_euclid C))  &  ( ((k18_euclid B) = (k18_euclid E))  &  ((k18_euclid E) = (k18_euclid F)) ) ) )  &  ( (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 (k2_nat_1 G 1) (k3_finseq_1 A)) &  ((r2_hidden E (k3_gobrd13 A (k2_goboard2 A) G)) &  ((r2_hidden F (k2_gobrd13 A (k2_goboard2 A) G)) & (r2_hidden D (k2_topreal1 2 A G))) ) ) ) ) )  &  ( (~ (r2_hidden E (k3_topreal1 2 A)))  &  ( (~ (r2_hidden F (k3_topreal1 2 A)))  &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) G) &  ((r2_hidden B G) & (r2_hidden C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan14,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C B) &  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 A C)) (k2_nat_1 D 1)))  & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 A B)) (k7_real_1 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B C)) (k9_real_1 D 2)) 2) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan18,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden D A) &  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  & (r1_jordan18 2 A B C D D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 D A)) C) |  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2) 1))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 D B)) (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_6_jordan1 A B C D))  => (v1_convex1 E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) (k3_finseq_1 (k1_jordan8 B A)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t31_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((k19_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 1 C)) ) ) ) ) ) ) ) ) ).
tt(t31_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e B A) 2)) = (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ).
tt(t31_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski C 1) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C 1) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski C (k1_matrix_1 B)) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k1_matrix_1 B)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ).
tt(t31_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k9_pscomp_1 B) (k9_pscomp_1 A)))  =>  ((k25_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k25_pscomp_1 A)) ) ) ) ) ) ).
tt(t31_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  ( (B = (k19_euclid k6_numbers k6_numbers))  =>  ((k9_metric_1 (k14_euclid 2) B A) = (a_1_0_jordan1k A)) ) ) ) ) ) ).
tt(t31_jordan20,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r1_topreal4 A B C) &  ( (~ (r1_xxreal_0 (k17_euclid C) E))  &  ((r2_hidden D A) &  ( ((k17_euclid D) = E)  &  ( (~ (r3_jordan20 A B C D E))  &  (~ (r4_jordan20 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ((v1_jordan21 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r2_hidden (k2_jordan21 A) A)) ) ).
tt(t31_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k18_pscomp_1 A) (k4_jordan19 A))) ) ).
tt(t31_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 A) & (v2_jordan23 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  => (v1_topreal1 (k4_jordan3 A B C))) ) ) ) ) ) ) ) ).
tt(t31_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) &  ((r2_hidden C (k3_topreal1 2 A)) &  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) ) )  =>  ( (B = C)  | (r2_hidden C (k3_topreal1 2 (k2_jordan3 A B)))) ) ) ) ) ) ) ) ).
tt(t31_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 (k3_finseq_1 A) C) | (r1_jordan4 A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) B C)) ) ) ) ) ) ) ) ).
tt(t31_jordan5b,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 A))) &  (C = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B))) ) )  => (r1_topreal4 C (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B))) ) ) ) ) ) ) ).
tt(t31_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden A (k3_topreal1 2 B)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 B)))) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) 1 C)) (k17_euclid A))) ) ) ) ) ) ) ).
tt(t31_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k6_jordan6 A)) <=>  ((k17_euclid B) = A) ) ) ) ) ) ).
tt(t31_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k1_jordan9 C B)))) )  =>  ((r1_xboole_0 (k3_gobrd13 (k1_jordan9 C B) (k1_jordan8 C B) A) C) &  (~ (r1_xboole_0 (k2_gobrd13 (k1_jordan9 C B) (k1_jordan8 C B) A) C)) ) ) ) ) ) ) ) ) ).
tt(t31_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (~ (r2_subset_1 (k2_jordan_a A (k3_finseq_1 B) B) (k2_jordan_a A (k7_nat_d (k3_finseq_1 B) 1) B))) ) ) ) ) ).
tt(t31_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) =>  ((k2_relset_1 (u1_struct_0 A) D) = (k2_relset_1 (u1_struct_0 A) (k2_borsuk_2 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r3_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) C) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r1_ordinal1 (k1_card_1 D) (k1_card_1 (u1_struct_0 A))) & (r2_abian (u1_struct_0 A) (k6_knaster A B C D) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) ) ).
tt(t31_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  => (r1_tarski (k1_kurato_2 A B) (k2_kurato_2 A B))) ) ) ) ).
tt(t31_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( ((k3_finseq_1 D) = A)  & (r2_hidden E (k2_finseq_1 A)))  =>  ((k11_fvsum_1 B (k9_matrix_1 (u1_struct_0 B) (k7_laplace A B C) E) D) = (k8_laplace A E B (k3_matrix11 E A A (u1_struct_0 B) (k5_matrix_1 A (u1_struct_0 B) C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_1 C) => (m3_vectsp_8 (k3_latsubgr A B C) (k11_group_4 A) (k11_group_4 B))) ) ) ) ) ) ) ).
tt(t31_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ((r3_lattices A (k2_lattice2 C A D E) B) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) => (r3_lattices A (k3_funct_2 C (u1_struct_0 A) E F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_lattice3 B))) =>  ((r2_lattice3 (k3_lattice3 B) A C) <=> (r4_lattice3 B (k5_lattice3 B C) A)) ) ) ) ) ) ).
tt(t31_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ((m1_lattice4 C B A) =>  ((v2_funct_2 C (u1_struct_0 A)) =>  ((v17_lattices A) & (r4_lattice4 B A C)) ) ) ) ) ) ) ) ).
tt(t31_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_lattice5 E A B D) => (r1_relset_1 (k2_zfmisc_1 A A) (u1_struct_0 B) D (k12_lattice5 A B D E C))) ) ) ) ) ) ) ) ) ) ).
tt(t31_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow11 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((m1_lattice8 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k2_xtuple_0 (k1_funct_1 D E)) (k2_xtuple_0 (k1_funct_1 D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B))))))  =>  ((k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) (k1_nat_1 B 1))) = (k1_funct_4 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) (k16_funcop_1 (k10_lexbfs A (k13_lexbfs A (k16_lexbfs A) B)) (k7_nat_d (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))))))) ) ) ) ) ) ).
tt(t31_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_fuzzy_1 (k4_lfuzzy_1 A B C) (k5_lfuzzy_1 A B))) ) ) ) ) ) ) ).
tt(t31_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_valued_0 A) =>  ((v1_seq_2 A) | (v1_limfunc1 A)) ) ) ) ).
tt(t31_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) )  | (r6_limfunc2 B A)) ) ) ) ) ) ).
tt(t31_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc3 C A) =>  ((r1_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A) &  ((k1_limfunc3 (k26_valued_1 k1_numbers k1_numbers C B) A) = (k8_real_1 B (k1_limfunc3 C A))) ) ) ) ) ) ) ) ) ).
tt(t31_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r2_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k5_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  | (v7_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t31_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A C D) =>  ((k1_vectsp_5 A B D (k2_vectsp_5 A B C E)) = (k2_vectsp_5 A B (k1_vectsp_5 A B C D) (k1_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((k8_funcop_1 (u1_struct_0 B) (u1_struct_0 A) (k4_struct_0 B)) = (k4_struct_0 (k16_lopban_1 A B))) ) ) ) ) ).
tt(t31_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 1 (k1_seq_1 C E))) ) ) ) )  & (v1_series_1 (k4_normsp_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t31_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k4_normsp_0 A (k8_lopban_4 A B C D))) E)) = (k8_nat_1 k1_numbers (k3_series_1 (k4_normsp_0 A (k8_lopban_4 A B C D))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (k9_setfam_1 (k7_lopclset A)) (k9_lopclset A) (k6_lattices A)) = (k7_lopclset A)) ) ) ).
tt(t31_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r1_lpspace1 A B C D E) & (r1_lpspace1 A B C F G))  => (r1_lpspace1 A B C (k3_valued_1 A k1_numbers k1_numbers D F) (k3_valued_1 A k1_numbers k1_numbers E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_lpspace2 A B C E))) =>  ( (D = F)  =>  ( ((k3_rlvect_1 (k2_lpspace2 A B C E) F (k1_rlvect_1 (k2_lpspace2 A B C E) F (k1_real_1 1))) = (k2_partfun1 A k1_numbers (k8_lpspace1 A k6_numbers) (k1_relset_1 A D)))  &  (? [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  (? [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden G (k1_lpspace2 A B C E)) &  ((r2_hidden H (k1_lpspace2 A B C E)) &  ( (G = (k3_rlvect_1 (k2_lpspace2 A B C E) F (k1_rlvect_1 (k2_lpspace2 A B C E) F (k1_real_1 1))))  &  ((r2_relset_1 A k1_numbers H (k8_lpspace1 A k6_numbers)) & (r1_lpspace1 A B C G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_ltlaxio1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_hilbert1 k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  ((k3_funct_2 k1_hilbert1 k6_margrel1 (k12_ltlaxio1 A) (k4_ltlaxio1 B C)) = (k10_margrel1 (k3_funct_2 k1_hilbert1 k6_margrel1 (k12_ltlaxio1 A) B) (k3_funct_2 k1_hilbert1 k6_margrel1 (k12_ltlaxio1 A) C))) ) ) ) ) ) ) ).
tt(t31_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) C) (k8_cqc_lang A (k6_cqc_lang A C) B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t31_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k3_mathmorp A B C) (k3_mathmorp A D C)) (k3_mathmorp A (k4_subset_1 (u1_struct_0 A) B D) C))) ) ) ) ) ) ) ) ).
tt(t31_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 k6_numbers A) & (v3_matrix10 C))  => (v3_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t31_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_matrix_2 H (k12_matrix_2 A)) =>  ( ((r2_hidden E (k2_finseq_1 A)) &  ( ((k3_finseq_1 F) = A)  &  ((k3_finseq_1 G) = A) ) )  =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 B) A A) =>  ((k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I (k3_fvsum_1 B (k9_fvsum_1 B F C) (k9_fvsum_1 B G D))) H) (u2_algstr_0 B)) = (k3_rlvect_1 B (k8_group_1 B C (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I F) H) (u2_algstr_0 B))) (k8_group_1 B D (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I G) H) (u2_algstr_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( (~ (v2_funct_1 C))  =>  ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) E A A D C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) =>  ((v1_matrix_6 (k5_matrix_1 A (u1_struct_0 B) C) A B) &  ((k5_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C)) = (k5_matrix_1 A (u1_struct_0 B) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t31_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k2_matrix15 (u1_struct_0 B) (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = (k1_matrix_3 B 1 A)) ) ) ) ) ).
tt(t31_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_matrix16 B (u1_struct_0 A)) => (v2_matrix16 (k5_fvsum_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(t31_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k14_matrix_1 B A C D) = (k14_matrix_1 B A D C)) ) ) ) ) ) ) ) ) ).
tt(t31_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 B)) =>  ( ((v1_setwiseo D A) &  ((v1_binop_1 D A) & (v2_binop_1 D A)) )  =>  (! [H:$i] :  ((m1_subset_1 H C) =>  ( (! [I:$i] :  ((m1_subset_1 I C) =>  ((k3_funct_2 C A F I) = (k7_setwiseo B A D G (k10_funct_5 C B A (k9_funct_2 B A) (k12_funct_5 B C A E) I))) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C G (k2_setwiseo C H)) E) = (k7_setwiseo C A D (k2_setwiseo C H) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A B (k3_matrix_3 A C D)) = (k1_matrix_4 A (k1_matrix_4 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((v3_matrix_6 C B A) & (v3_matrix_6 D B A))  => (v3_matrix_6 (k2_matrix_6 B A C D) B A)) ) ) ) ) ) ) ) ) ).
tt(t31_matrix_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r2_classes1 B C) =>  ((k1_finsop_1 (u1_struct_0 A) B (u2_algstr_0 A)) = (k1_finsop_1 (u1_struct_0 A) C (u2_algstr_0 A))) ) ) ) ) ) ) ) ).
tt(t31_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  => (v4_matrix_8 (k12_matrix_1 B A) A B)) ) ) ) ).
tt(t31_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  ( (A = (k3_finseq_4 k5_numbers 2 1 3))  => (v4_matrix_2 A 3)) ) ) ).
tt(t31_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k17_rvsum_1 (k10_seq_4 A B)) = (k4_binop_2 (k17_rvsum_1 A) (k17_rvsum_1 B))) ) ) ) ) ) ).
tt(t31_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_matrixj1 D B) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 B))))  =>  ((r2_hidden A (k4_finseq_1 D)) =>  ((k2_matrixj1 B D A) = (k6_matrix13 B (k13_matrixj1 B C D) (k7_subset_1 k5_numbers (k2_finseq_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers A (k10_matrixj1 B D)))) (k2_finseq_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d A 1) (k10_matrixj1 B D))))) (k7_subset_1 k5_numbers (k2_finseq_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers A (k11_matrixj1 B D)))) (k2_finseq_1 (k2_wsierp_1 (k17_finseq_1 k5_numbers (k7_nat_d A 1) (k11_matrixj1 B D))))))) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrixj2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_polynom5 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (? [D:$i] :  ( ((v2_relat_1 D) &  ((v1_matrixj2 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A))))) )  &  (? [E:$i] :  ((m1_matrlin E A B) &  ( ((k1_matrlin2 A B B C E E) = (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) D))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((m1_vectsp11 F A B C) <=>  (? [G:$i] :  ((v7_ordinal1 G) &  ((r2_hidden G (k4_finseq_1 D)) &  ((k14_matrixj1 (u1_struct_0 A) D G) = (k2_matrixj2 A F (k3_finseq_1 (k14_matrixj1 (u1_struct_0 A) D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ((r2_hidden B (k4_finseq_1 C)) =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ( (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  (D = (k1_funct_1 C B)) ) )  &  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (D = (k1_funct_1 C B))  =>  ((k1_funct_1 (k7_matrixr1 A C) B) = (k10_rvsum_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 C) = A)  &  ((k1_matrix_1 C) = B) )  =>  ((k3_matrixr1 (k4_matrixr1 C) C) = (k8_matrixr1 A B)) ) ) ) ) ) ) ) ).
tt(t31_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrlin F A B) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ((v13_vectsp_1 D C B) & (v1_mod_2 D A C B))  =>  ((r1_xxreal_0 (k3_finseq_1 E) k1_xboole_0) |  ((k4_matrix_3 A (k2_matrix15 (u1_struct_0 A) (k9_matrlin A C E G)) (k1_matrlin2 A C B D E F)) = (k2_matrix15 (u1_struct_0 A) (k9_matrlin A B F (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  =>  ((k3_rlvect_1 B (k4_rlvect_1 B (k6_matrlin B C)) (k4_rlvect_1 B (k6_matrlin B D))) = (k4_rlvect_1 B (k6_matrlin B (k7_matrlin (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k6_matroid0 A B))) ) ) ) ).
tt(t31_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k14_rvsum_1 (k5_finseq_2 k5_numbers A 1) B) = B) ) ) ) ) ).
tt(t31_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ((k7_ranknull (k15_euclid A) (k15_euclid B) (k3_matrtop1 A B D) (k5_rusub_4 (k15_euclid B) E (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B D) C))) = (k5_rusub_4 (k15_euclid A) (k7_ranknull (k15_euclid A) (k15_euclid B) (k3_matrtop1 A B D) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((k2_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B C) = (k6_partfun1 C))  => (r1_funct_2 (u1_struct_0 (k1_rlvect_3 (k15_euclid A) C)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k1_rlvect_3 (k15_euclid A) C)) (u1_struct_0 (k1_rlvect_3 (k15_euclid A) C)) (k2_tmap_1 (k15_euclid A) (k15_euclid A) B (k1_rlvect_3 (k15_euclid A) C)) (k3_struct_0 (k1_rlvect_3 (k15_euclid A) C)))) ) ) ) ) ) ) ).
tt(t31_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A (k2_mboolean A B) C) & (r1_pboole A D B))  => (r2_pboole A D C)) ) ) ) ) ) ) ) ).
tt(t31_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  (C = k1_xboole_0) ) ) )  <=>  (~  ((k3_zfmisc_1 A B C) = k1_xboole_0) ) ) ) ) ) ).
tt(t31_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_tarski D E) => (r1_xxreal_0 (k12_supinf_2 C D) (k12_supinf_2 C E))) ) ) ) ) ) ) ) ) ) ).
tt(t31_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( (B = C)  =>  ((k8_supinf_2 (k2_measure6 A B)) = (k3_supinf_2 C (k8_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t31_measure8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v2_prob_1 D) =>  ((r1_xxreal_0 k1_supinf_1 (k1_mesfunc9 C (k1_prob_2 A B D k6_numbers))) |  ((k2_mesfunc5 (k11_measure8 A B D C)) = (k1_mesfunc9 C (k4_kurato_0 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ( ((k7_member_1 A) = (k7_member_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t31_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v1_membered B))  => (v1_membered (k1_setfam_1 A))) ) ) ).
tt(t31_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  ((k1_funct_4 C (k7_memstr_0 A B (k5_memstr_0 A B C))) = C) ) ) ) ) ) ) ).
tt(t31_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( (E = (k1_relset_1 A D))  & (r1_mesfun6c A B D E)) ) )  =>  ((r2_mesfun6c A B C D) <=> (r3_mesfunc6 A B C (k55_valued_1 A k2_numbers D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( ((k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)) = C)  &  ((r1_mesfunc6 A B D C) & (r1_mesfunc6 A B E C)) )  => (r1_mesfunc6 A B (k20_valued_1 A k1_numbers k1_numbers D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((k1_relset_1 A (k4_mesfunc5 A k2_numbers (k3_mesfun9c A C) B)) = (k1_setfam_1 (a_3_1_mesfun9c A B C))) ) ) ) ) ) ) ).
tt(t31_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc1 A B C D) & (r1_mesfunc1 A B C E))  => (r1_mesfunc1 A B C (k6_prob_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v1_prob_2 C) & (m2_finseq_1 C B))  => (r2_hidden (k3_tarski (k10_xtuple_0 C)) B)) ) ) ) ) ) ) ).
tt(t31_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((v3_mesfunc5 C) &  ((v3_mesfunc5 D) &  ((r1_mesfunc1 A B C E) & (r1_mesfunc1 A B D E)) ) )  => (r1_mesfunc1 A B (k3_mesfunc1 A C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k18_rfunct_3 A B) C))) ) ) ) ) ) ).
tt(t31_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ( ((v2_mesfunc9 B A) &  (! [E:$i] :  ((v7_ordinal1 E) => (r2_relset_1 A k7_numbers (k4_mesfunc5 A k7_numbers C E) (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers B E) D))) ) )  => (v2_mesfunc9 C A)) ) ) ) ) ) ) ) ).
tt(t31_metric_1,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_metric_1 A B C D) =>  ( (~ (r1_metric_1 A C B D))  &  (~ (r1_metric_1 A B D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  => (r1_tarski (k9_metric_2 A) (k9_mcart_1 (k2_metric_2 A) (k2_metric_2 A) k1_numbers (k6_metric_2 A) (k7_metric_2 A) (k5_metric_2 A)))) ) ).
tt(t31_mfold_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_pre_topc C (k15_euclid A)) =>  ( ( ((k2_struct_0 C) = (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1) (k1_tarski B)))  & (r2_hidden B (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1)))  => (v3_tops_2 (k5_mfold_2 A B C) C (k3_mfold_2 A B (k4_struct_0 (k15_euclid A))))) ) ) ) ) ) ) ).
tt(t31_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (? [B:$i] :  ((m1_midsp_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ((r2_hidden C B) <=>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) C) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) C)) ) ) ) ) ) ) ) ).
tt(t31_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_midsp_1 A C D) = E)  <=>  ((k9_midsp_2 A B C D) = (k1_midsp_2 (u1_midsp_2 A B) (k9_midsp_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [F:$i] :  ( ((v4_midsp_2 F C) & (l1_midsp_2 F C))  =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 (u1_midsp_2 C F)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C F)))) =>  ( ( ((k8_midsp_3 A C F D E) = G)  & (r1_xxreal_0 B A))  =>  ((k8_midsp_3 A C F D (k6_midsp_3 A C E (k2_nat_1 B 1) (k5_midsp_3 A (u1_struct_0 C) E B))) = (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C F)) (k2_nat_1 A 1) G (k2_nat_1 B 1) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C F)) G B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_mmlquery A (k19_mmlquery A C D) B) = (k15_mmlquery A (k1_mmlquery A C B) (k1_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t31_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_mod_4 C A B) <=> (v3_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t31_modal_1,ax,(m1_subset_1 (k8_funcop_1 (k2_zfmisc_1 k5_numbers k5_numbers) (k2_trees_1 k6_numbers) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) k6_modal_1)).
tt(t31_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k52_modelc_1 A B C (k51_modelc_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t31_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  =>  ((r2_modelc_2 (k11_modelc_2 A) A) & (r2_modelc_2 (k12_modelc_2 A) A)) ) ) ) ).
tt(t31_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_modelc_2 D) & (m2_finseq_1 D k5_numbers))  =>  ( ((r5_modelc_3 D C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 B (k3_finseq_1 C))) ) )  =>  ((r1_tarski (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 C A) D)) (u1_modelc_3 D (k10_modelc_3 (k1_funct_1 C B) D))) & (r1_tarski (u3_modelc_3 D (k10_modelc_3 (k1_funct_1 C A) D)) (u3_modelc_3 D (k10_modelc_3 (k1_funct_1 C B) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_moebius1,ax, ((k2_moebius1 2) = (k1_real_1 1)) ).
tt(t31_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m3_monoid_0 B A))  => (v4_vectsp_1 B)) ) ) ) ).
tt(t31_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((k15_monoid_1 A (k18_monoid_1 A B) B) = 1)  &  ( (~  (C = B) )  =>  ((k15_monoid_1 A (k18_monoid_1 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t31_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A C) (k5_rusub_4 A D B)) = (k5_rusub_4 A (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A C) D) B)) ) ) ) ) ) ) ) ) ).
tt(t31_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ((k1_msafree3 A B) = (k11_msafree A B)) ) ) ) ) ).
tt(t31_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) F)) =>  ( (D = (k1_trees_4 (k4_tarski G F)))  => (r1_msaterm A B C D E (k2_trees_4 (k1_funct_1 (u3_msualg_1 A B) F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((v3_relat_1 (k1_pboole A)) &  ((v2_finset_1 (k1_pboole A)) & (m3_pboole (k1_pboole A) A (k1_mboolean A B))) ) ) ) ) ).
tt(t31_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_unialg_1 B) &  ((v4_unialg_1 B) & (m1_unialg_2 B A)) )  =>  (! [C:$i] :  ( ((v1_unialg_1 C) &  ((v4_unialg_1 C) & (m1_unialg_2 C A)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D (k6_msualg_1 A)) &  ((v4_msualg_1 D (k6_msualg_1 A)) & (m1_msualg_2 D (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  (! [E:$i] :  ( ((v3_msualg_1 E (k6_msualg_1 A)) &  ((v4_msualg_1 E (k6_msualg_1 A)) & (m1_msualg_2 E (k6_msualg_1 A) (k9_msualg_1 A))) )  =>  ( ( (D = (k9_msualg_1 B))  &  (E = (k9_msualg_1 C)) )  =>  ((k9_msualg_1 (k5_unialg_2 A B C)) = (k11_msualg_2 (k6_msualg_1 A) (k9_msualg_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v1_binop_1 (k16_msualg_2 A B) (k14_msualg_2 A B))) ) ) ) ).
tt(t31_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_hidden (k4_tarski E F) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (k7_msualg_6 A B C) D)) <=>  (? [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) D)) &  (? [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) D)) &  (? [I:$i] :  ((m1_msualg_6 I A B) &  ((r2_hidden (k4_tarski G H) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D)) &  ( (E = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) I D) G))  &  (F = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) I D) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) D)) =>  (? [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) &  (E = (k3_msualg_4 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_mycielsk,ax, (! [A:$i] :  ( ((v1_mycielsk A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A))) )  =>  (! [C:$i] :  (~  ((r2_hidden C B) &  ( ((k5_card_1 B) = (k2_mycielsk A))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E B) =>  (~  ( (~  (E = C) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F (k4_mycielsk A D)) & (r2_hidden F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ((r1_pcomps_1 (u1_struct_0 A) C) =>  ((r1_xxreal_0 B k6_numbers) | (r1_pcomps_1 (u1_struct_0 A) (k5_nagata_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) B C))) ) ) ) ) ) ) ) ).
tt(t31_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 7) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  (~  (A = 7) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((r1_nat_d C B) =>  ((k11_nat_3 (k3_nat_d B C) A) = (k7_nat_d (k11_nat_3 B A) (k11_nat_3 C A))) ) ) ) ) ) ) ) ).
tt(t31_nat_4,ax,(v1_int_2 37)).
tt(t31_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ((r1_nat_d A B) =>  ( (B = A)  |  ( (A = 1)  | (r1_xxreal_0 (k23_binop_2 (k23_binop_2 1 A) B) (k5_nat_5 B))) ) ) ) ) ) ) ).
tt(t31_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_nat_d A A) = A) ) ) ).
tt(t31_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  ( ((r3_nattra_1 A B C D) & (r3_nattra_1 A B D E))  =>  (! [F:$i] :  ((m3_nattra_1 F A B C D) =>  (! [G:$i] :  ((m3_nattra_1 G A B D E) => (m3_nattra_1 (k7_nattra_1 A B C D E F G) A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) (k1_relset_1 (u1_struct_0 B) C)) =>  ((r2_funct_2 k5_numbers k1_numbers (k4_normsp_0 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) D C)) (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 B) D (k3_normsp_0 (u1_struct_0 B) A C))) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) D C)) (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) D (k5_vfunct_1 (u1_struct_0 B) A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  ((v1_ncfcont1 D A) & (r1_ncfcont2 D A B C)) )  => (v1_ncfcont1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t31_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 D A) =>  ((r2_ndiff_1 D A B C) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) => (r1_ndiff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ((r2_ndiff_4 B C A) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  => (r2_ndiff_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (k1_euclid B) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 D B)) A)) ) ) ) ) ) ) ) ) ).
tt(t31_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) => (r1_xxreal_0 (k1_normsp_0 (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C)) (k1_normsp_0 (k14_prvect_2 A) C))) ) ) ) ) ) ).
tt(t31_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) ) )  =>  (~  ( (~ (v1_neckla_3 (k3_necklace A)))  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_orders_2 B) &  ((v1_necklace B) &  ((v3_necklace B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_orders_2 C) &  ((v1_necklace C) &  ((v3_necklace C) & (l1_orders_2 C)) ) ) )  =>  (~  ((r1_subset_1 (u1_struct_0 B) (u1_struct_0 C)) &  ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (k2_neckla_2 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k8_newton A) = (k7_newton 1 1 A)) ) ) ).
tt(t31_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ( ((v1_nfcont_1 (k1_relset_1 (u1_struct_0 A) B) A) & (r4_nfcont_1 A B (k1_relset_1 (u1_struct_0 A) B)))  => (v1_rcomp_1 (k2_relset_1 k1_numbers B))) ) ) ) ) ).
tt(t31_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) C A) B) =>  ((v2_nfcont_3 (k5_vfunct_1 k1_numbers B (k2_partfun1 k1_numbers (u1_struct_0 B) C A)) B) &  ((v2_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) (k5_vfunct_1 k1_numbers B C) A) B) & (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_normsp_0 k1_numbers B C) A))) ) ) ) ) ) ) ) ).
tt(t31_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((v1_rcomp_1 (k1_relset_1 k1_numbers B)) &  ((v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) B (k1_relset_1 k1_numbers B)) A) &  (C = (k2_relset_1 (k1_euclid A) B)) ) )  => (v1_nfcont_1 C (k4_real_ns1 A))) ) ) ) ) ) ) ).
tt(t31_normform,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k8_normform A))) ).
tt(t31_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k4_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_normsp_2 A)))))) )  =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k4_normsp_2 A)) B C) & (v2_frechet C (k4_normsp_2 A)))  =>  ( ((k2_frechet (k4_normsp_2 A) C) = (k6_domain_1 (u1_struct_0 A) (k6_normsp_1 A B)))  &  ((k2_frechet2 (k4_normsp_2 A) C) = (k6_normsp_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t31_numbers,ax,(r1_tarski k1_numbers k7_numbers)).
tt(t31_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  ((u1_struct_0 (k6_openlatt (k17_openlatt A))) = (a_1_1_openlatt A)) ) ) ).
tt(t31_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t31_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_orders_1 A) => (r1_orders_1 A (k1_relat_1 A))) ) ) ).
tt(t31_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((m1_orders_2 B A C) & (m1_orders_2 C A B)) ) ) ) ) ) ) ) ) ).
tt(t31_ordinal1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v3_ordinal1 (k9_xtuple_0 A)) =>  ((v1_relat_1 A) &  ((v5_relat_1 A (k10_xtuple_0 A)) &  ((v1_funct_1 A) & (v5_ordinal1 A)) ) ) ) ) ) ).
tt(t31_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k10_ordinal2 A 1) = (k1_ordinal1 A)) ) ) ).
tt(t31_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( ((k11_ordinal2 A B) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t31_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k12_ordinal2 (k12_ordinal2 A B) C) = (k12_ordinal2 A (k11_ordinal2 C B))) ) ) ) ) ) ) ).
tt(t31_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_hidden k6_numbers A) =>  ((k12_ordinal2 A (k1_ordinal5 A k4_ordinal1)) = (k1_ordinal5 A k4_ordinal1)) ) ) ) ).
tt(t31_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((r2_hidden A (k9_xtuple_0 (k3_ordinal6 B))) => (r1_tarski A (k1_funct_1 (k3_ordinal6 B) A))) ) ) ) ).
tt(t31_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t31_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k2_ortsp_1 A B E (k4_vectsp_1 A B G F) D C) = (k8_group_1 A G (k2_ortsp_1 A B E F D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v2_relat_1 (k24_osafree A B))) ) ) ) ).
tt(t31_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_osalg_1 A B C) <=>  ((k8_osalg_1 A B) = (k8_osalg_1 A C)) ) ) ) ) ) ) ) ).
tt(t31_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ( ((k12_msualg_2 A B C) = (k10_msualg_2 A B (k9_msualg_2 A B C)))  & (r8_pboole (u1_struct_0 A) (u3_msualg_1 A (k12_msualg_2 A B C)) (k9_msualg_2 A B C))) ) ) ) ) ) ) ).
tt(t31_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_1 A B C B D))  &  ((r1_parsp_1 A B C E F) &  ((r1_parsp_1 A B D E G) &  ((r1_parsp_1 A C D F G) &  ( (~  (E = F) )  & (r1_parsp_1 A E F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) => (r2_parsp_2 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski (k9_xtuple_0 C) A) & (r1_tarski (k10_xtuple_0 C) B))  =>  (C = (k3_partfun1 C A B)) ) ) ) ) ) ).
tt(t31_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden E (k1_relset_1 B F)) => (r2_relset_1 A C (k1_partfun1 A B B C (k4_partfun2 A B D E) F) (k4_partfun2 A C D (k7_partfun1 C F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k10_eqrel_1 A) = (a_1_0_partit1 A)) ) ) ).
tt(t31_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r2_relat_2 B A) => (v2_relat_2 B)) ) ) ) ) ).
tt(t31_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_diraf A B C D) &  ((r2_analoaf A B C E F) &  ((r3_diraf A E F G) &  ((r2_analoaf A B E C F) & (r2_analoaf A B E D G)) ) ) )  =>  ((r3_diraf A B C E) | (r1_diraf A E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A B (k3_pboole A B C)) B)) ) ) ) ) ).
tt(t31_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B (k2_pcomps_1 A)) & (r2_hidden C (k2_pcomps_1 A)))  => (r2_hidden (k9_subset_1 (u1_struct_0 A) B C) (k2_pcomps_1 A))) ) ) ) ) ) ) ).
tt(t31_pcs_0,ax, (! [A:$i] :  ( ((v13_pcs_0 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (u1_struct_0 A)))  => (v13_pcs_0 (k19_pcs_0 A B))) ) ) ) ).
tt(t31_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r3_pdiff_1 A B C E) & (r3_pdiff_1 A B D E))  =>  ((r3_pdiff_1 A B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) &  ((k11_pdiff_1 A B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) = (k9_real_1 (k11_pdiff_1 A B C E) (k11_pdiff_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r3_pdiff_3 C B) =>  ((r3_pdiff_1 2 1 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 2 2 C) A) B) &  ((k11_pdiff_1 2 1 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 2 2 C) A) B) = (k8_real_1 A (k4_pdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t31_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 1 A B) => (r1_fcont_1 (k1_pdiff_2 3 1 A B) (k1_seq_1 (k1_pdiff_1 1 3) B))) ) ) ) ) ).
tt(t31_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r4_pdiff_5 B A) =>  ((k4_pdiff_5 B A) = (k11_pdiff_1 3 1 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ) ).
tt(t31_pdiff_6,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid C)))))  =>  ((r1_pdiff_6 A C B D) => (m1_subset_1 A (k1_zfmisc_1 (k1_euclid B)))) ) ) ) ) ) ) ) ).
tt(t31_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  ((v1_pdiff_7 B A) <=>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (a_3_0_pdiff_7 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r3_pdiff_7 A B C D) => (r3_pdiff_7 A B (k2_nfcont_4 B (k1_euclid A) C) D)) ) ) ) ) ) ) ) ) ).
tt(t31_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) <=> (r1_nat_d (k2_newton 2 A) (k2_newton 2 B))) ) ) ) ) ).
tt(t31_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_pnproc_1 B A) => (r1_tarski (k10_xtuple_0 (k7_pnproc_1 A B)) (k9_funct_2 A k5_numbers))) ) ) ).
tt(t31_polyeq_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_newton (k3_binop_2 (k20_sin_cos A) (k5_binop_2 (k17_sin_cos A) k7_complex1)) B) = (k3_binop_2 (k21_sin_cos (k11_binop_2 B A)) (k5_binop_2 (k18_sin_cos (k11_binop_2 B A)) k7_complex1))) ) ) ) ) ).
tt(t31_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k11_polyform A (k7_polyform A)) = 1) ) ) ).
tt(t31_polynom1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v3_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k11_polynom1 A B)) = (k8_polynom1 A B)) ) ) ) ) ).
tt(t31_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k8_polynom3 A C D)) (k8_polynom3 A (k11_polynom3 A B C) (k11_polynom3 A B D)))) ) ) ) ) ) ) ) ).
tt(t31_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((k2_polynom4 A B (k4_struct_0 A)) = (k3_funct_2 k5_numbers (u1_struct_0 A) B k6_numbers)) ) ) ) ) ).
tt(t31_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k6_polynom7 A B C D) E) = (k8_group_1 B (k5_polynom2 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom8 A C B) => (r1_polynom8 A (k11_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t31_polyred,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  &  ((r2_hidden E D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden F D) => (r1_polyred A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k3_power (k13_complex1 A B) C) = (k13_complex1 (k3_power A C) (k3_power B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (m2_finseq_1 (k8_pboole C (k8_funcop_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) (k4_finseq_1 C) D)) (k3_finseq_2 B))) ) ) ) ) ) ) ) ).
tt(t31_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k5_real_1 (k2_prepower B A) 1) (k10_real_1 (k5_real_1 A 1) B))) ) ) ) ) ) ).
tt(t31_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v4_pre_topc B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))))) ) ) ) ) ).
tt(t31_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((k7_real_1 (k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)) (k1_seq_1 D C)) = 1) ) ) ) ) ) ) ) ) ).
tt(t31_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  ( (F = (k3_subset_1 A E))  =>  ((r1_xxreal_0 (k1_seq_1 C E) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 C F) k6_numbers) |  ((k1_seq_1 C D) = (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B C E) D) (k1_seq_1 C E)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B C F) D) (k1_seq_1 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) C (k3_prob_3 A D)) =>  ( ((k1_prob_2 A B C k6_numbers) = (k1_prob_2 A B D k6_numbers))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_prob_2 A B C (k1_nat_1 E 1)) = (k7_subset_1 A (k1_prob_2 A B D (k1_nat_1 E 1)) (k1_funct_1 (k2_prob_3 A D) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_prob_4 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_prob_4 A B C))))) )  =>  (? [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r2_hidden (k1_prob_4 A B E F) (k6_prob_4 A B C (k3_funct_2 k5_numbers (k4_prob_4 A B C) D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k7_cqc_lang A B C) D) (k8_cqc_lang A B (k8_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t31_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ( ((r1_incsp_1 A B D) & (r1_incsp_1 A B E))  =>  ( (D = E)  |  ((r1_incsp_1 A B C) |  ( (~  ((k2_projpl_1 A C D) = (k2_projpl_1 A C E)) )  &  (~  ((k2_projpl_1 A D C) = (k2_projpl_1 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k14_pscomp_1 B)) =>  ( ((k17_euclid A) = (k17_euclid (k18_pscomp_1 B)))  &  ((v2_compts_1 B (k15_euclid 2)) =>  ((r1_xxreal_0 (k18_euclid (k18_pscomp_1 B)) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k18_euclid (k19_pscomp_1 B)))) ) ) ) ) ) ) ) ).
tt(t31_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m3_pua2mss1 B A) => (r7_pua2mss1 A (k11_pua2mss1 A B))) ) ) ) ).
tt(t31_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_mboolean A (k2_pzfmisc1 A (k1_pzfmisc1 A B) (k1_pzfmisc1 A C))) (k2_pzfmisc1 A B C))) ) ) ) ) ).
tt(t31_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) => (r1_qc_lang1 A C (k30_qc_lang1 A C B))) ) ) ) ) ) ).
tt(t31_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((k13_qc_lang2 A (k4_qc_lang2 A B C)) = B)  &  ( ((k14_qc_lang2 A (k4_qc_lang2 A B C)) = C)  &  ( ((k19_qc_lang1 A (k4_qc_lang2 A B C)) = (k2_qc_lang2 A B C))  &  ((k20_qc_lang1 A (k4_qc_lang2 A B C)) = (k2_qc_lang2 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t31_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((k3_qc_lang3 A C) = B) ) ) ) ) ) ) ).
tt(t31_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 (k2_qc_lang4 A B))) =>  ((r2_hidden D (k3_qc_lang4 A B C)) <=>  ((k5_trees_2 (k2_qc_lang4 A B) D) = (k2_qc_lang4 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t31_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k9_quantal1 A (k9_quantal1 A B C) D) = (k9_quantal1 A B (k9_quantal1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t31_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( (~  (A = k6_numbers) )  =>  ((k27_quaterni A (k8_quatern2 A)) = 1) ) ) ) ).
tt(t31_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k17_quaterni (k27_quaterni (k27_quaterni A B) C)) = (k17_quaterni (k27_quaterni (k27_quaterni C A) B))) ) ) ) ) ) ) ).
tt(t31_quaterni,ax, ( ((k17_quaterni k11_quaterni) = k6_numbers)  &  ( ((k18_quaterni k11_quaterni) = k6_numbers)  &  ( ((k19_quaterni k11_quaterni) = 1)  &  ( ((k20_quaterni k11_quaterni) = k6_numbers)  &  ( ((k17_quaterni k12_quaterni) = k6_numbers)  &  ( ((k18_quaterni k12_quaterni) = k6_numbers)  &  ( ((k19_quaterni k12_quaterni) = k6_numbers)  &  ((k20_quaterni k12_quaterni) = 1) ) ) ) ) ) ) ) ).
tt(t31_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) => (m1_subset_1 (k1_binop_1 (k15_quofield A) B C) (u1_struct_0 (k19_quofield A)))) ) ) ) ) ) ).
tt(t31_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ((m1_random_1 C A (k1_random_1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_seq_1 D F) = (k8_real_1 (k1_seq_1 C (k1_funct_1 E F)) (k1_seq_1 B (k1_tarski (k1_funct_1 E F))))) ) ) ) ) ) ) )  =>  ((k8_random_1 A (k1_random_1 A) B C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((r1_xboole_0 (k1_vectsp_6 A B C) (k1_vectsp_6 A B D)) =>  ((k1_vectsp_6 A B (k5_vectsp_6 A B C D)) = (k4_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B C) (k1_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  & (r1_xxreal_0 (k1_real_1 (k1_rat_1 A)) (k2_rat_1 A))) )  &  (~  ( (~ (r1_xxreal_0 (k1_real_1 (k1_rat_1 A)) (k2_rat_1 A)))  & (r1_xxreal_0 (k1_real_1 1) A)) ) ) ) ) ).
tt(t31_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_ratfunc1 A (k7_ratfunc1 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t31_rcomp_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v5_xxreal_2 A) &  ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v5_xxreal_2 B) &  ((v6_xxreal_2 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) ) )  =>  ( ((r1_xxreal_0 (k5_seq_4 A) (k5_seq_4 B)) & (r1_xxreal_0 (k4_seq_4 B) (k4_seq_4 A)))  =>  ( ( ((k5_seq_4 A) = (k5_seq_4 B))  &  ((r2_hidden (k5_seq_4 B) B) &  (~ (r2_hidden (k5_seq_4 A) A)) ) )  |  ( ( ((k4_seq_4 A) = (k4_seq_4 B))  &  ((r2_hidden (k4_seq_4 B) B) &  (~ (r2_hidden (k4_seq_4 A) A)) ) )  | (r1_tarski B A)) ) ) ) ) ) ) ).
tt(t31_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  ( ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k10_real_1 1 B)) 1) = B)  &  ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k10_real_1 1 B)) (k1_nat_1 A 2)) = k6_numbers) ) ) ) ) ) ) ).
tt(t31_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_binop_1 (k2_realset3 A) B (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) C D)) = (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) (k2_binop_1 (u1_struct_0 A) (k8_struct_0 A) (u1_struct_0 A) (k2_realset3 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t31_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ( ((k3_finseq_1 (k20_rfunct_3 B (k3_rearran1 A B D C) B)) = (k5_card_1 B))  & (r1_xxreal_0 1 (k3_finseq_1 (k20_rfunct_3 B (k3_rearran1 A B D C) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k3_relat_1 A C) (k3_relat_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t31_relat_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v8_relat_2 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski B C) A) & (r2_hidden (k4_tarski C D) A))  => (r2_hidden (k4_tarski B D) A)) ) ) ) ) ) ) ).
tt(t31_relset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (! [D:$i] :  ((r2_hidden D A) =>  ((k9_relat_1 B D) = (k9_relat_1 C D)) ) )  => (r2_relset_1 A A B C)) ) ) ) ) ) ).
tt(t31_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski C D) => (r1_tarski (k6_relset_2 A B D E) (k6_relset_2 A B C E))) ) ) ) ) ) ) ) ) ).
tt(t31_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden B (k10_xtuple_0 C)) & (r1_xxreal_0 (k3_finseq_1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) C B)) A))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((k2_topreal1 2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) C B) A) = (k2_topreal1 2 C (k7_nat_d (k2_nat_1 A (k4_finseq_4 C B)) (k3_finseq_1 C)))) ) ) ) ) ) ) ) ) ).
tt(t31_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) => (r2_rewrite1 A C B)) ) ) ) ) ).
tt(t31_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) => (r2_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k7_rewrite2 A (k7_rewrite2 A B)) (k7_rewrite2 A B))) ) ) ).
tt(t31_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E D))  =>  (~  ((r2_hidden (k4_tarski A B) (k1_rewrite3 C D E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  (! [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 C)) =>  (~  ( (A = (k4_tarski F G))  &  (B = (k4_tarski H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k4_finseq_1 (k6_rfinseq2 A)) = (k4_finseq_1 A))  &  ((k3_finseq_1 (k6_rfinseq2 A)) = (k3_finseq_1 A)) ) ) ) ).
tt(t31_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_classes1 A B) <=> (r2_classes1 (k7_finseq_1 C A) (k7_finseq_1 C B))) ) ) ) ) ) ) ).
tt(t31_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k1_rfunct_1 A B) = (k18_valued_1 A (k4_rfunct_1 B))) ) ) ) ) ).
tt(t31_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) & (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C B)))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) ).
tt(t31_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ((r1_rfunct_3 A k1_numbers C B) => (r1_rfunct_3 A k1_numbers (k16_rfunct_3 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t31_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (a_2_0_rinfsup1 A B))  => (v4_xxreal_2 C)) ) ) ) ) ) ) ) ).
tt(t31_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v7_valued_0 A) =>  ((r1_xxreal_0 (k12_supinf_2 A B) k2_supinf_1) |  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 A B)) |  ((v1_rinfsup2 (k1_valued_0 k7_numbers A B)) &  ((k2_rinfsup2 (k1_valued_0 k7_numbers A B)) = (k12_supinf_2 A B)) ) ) ) ) ) ) ) ) ).
tt(t31_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k3_rlaffin1 A (k4_rlvect_2 A)) = k6_numbers) ) ) ).
tt(t31_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))))  =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) (k2_rlaffin3 (k15_euclid B) C A) (k4_rlaffin1 (k15_euclid B) C))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) (k2_rlaffin3 (k15_euclid B) C A) (k4_rlaffin1 (k15_euclid B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid B) (k4_rlaffin1 (k15_euclid B) C))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k2_partfun1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) (k2_rlaffin3 (k15_euclid B) C A) (k4_rlaffin1 (k15_euclid B) C)) (k1_pre_topc (k15_euclid B) (k4_rlaffin1 (k15_euclid B) C)) k3_topmetr) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) (k2_rlaffin3 (k15_euclid B) C A) (k4_rlaffin1 (k15_euclid B) C)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid B) (k4_rlaffin1 (k15_euclid B) C))) (u1_struct_0 k3_topmetr))))) ) ) ) ) ) ) ) ).
tt(t31_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t31_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  (! [D:$i] :  ( ((v1_rlvect_1 D) & (m1_rlsub_1 D A))  =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 (k1_rlsub_2 A B D) (k1_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t31_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k3_rlvect_1 A B C)) =>  (? [E:$i] :  ((m1_connsp_2 E A B) &  (? [F:$i] :  ((m1_connsp_2 F A C) & (r1_tarski (k7_rusub_4 A E F) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k1_algstr_0 A B C)) = (k1_algstr_0 A (k4_algstr_0 A C) (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t31_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_rlvect_2 B A (k1_subset_1 (u1_struct_0 A))) =>  ((k6_rlvect_2 A B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t31_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((m1_rlsub_1 B C) & (m1_rlsub_1 B D))  => (m1_rlsub_1 B (k2_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t31_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  ( (~  (A = B) )  & (v1_rlvect_3 (k8_domain_1 (u1_struct_0 C) (k1_rlvect_1 C D A) (k1_rlvect_1 C D B) E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ( ((k1_rlvect_5 A) = (k1_rlvect_5 B))  <=>  ((k2_rlsub_1 A) = (k2_rlsub_1 B)) ) ) ) ) ) ).
tt(t31_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) => (r1_tarski (k2_relset_1 (u1_struct_0 A) B) (k3_rlvect_x A B))) ) ) ) ).
tt(t31_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 B))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t31_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  ((m1_rmod_2 E A C) =>  ((k1_rmod_3 A B E (k2_rmod_3 A B D C)) = (k2_rmod_3 A B (k1_rmod_3 A B E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_rmod_4 C A B (k1_subset_1 (u1_struct_0 B))) =>  ((k5_rmod_4 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t31_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k6_robbins1 A C D)) = (k6_robbins1 A (k5_robbins1 A B C) (k5_robbins1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t31_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A C))) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A C) C))) = (k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)))) ) ) ) ) ) ) ).
tt(t31_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_robbins4 A B C) & (r1_robbins4 A B D))  =>  ((r1_robbins4 A B (k4_lattices A C D)) & (r1_robbins4 A B (k3_lattices A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A (k4_roughs_1 A (k3_roughs_1 A B))) = (k3_roughs_1 A B)) ) ) ) ) ).
tt(t31_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r1_xxreal_0 (k9_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C)) (k1_rpr_1 A (k7_subset_1 A B C)))) ) ) ) ) ) ).
tt(t31_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k1_rusub_1 B) = (k1_rusub_1 C)) ) ) ) ) ) ) ).
tt(t31_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (! [D:$i] :  ( ((v1_bhsp_1 D) & (m1_rusub_1 D A))  =>  ((m1_rusub_1 B C) => (m1_rusub_1 (k1_rusub_2 A B D) (k1_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t31_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k3_rusub_1 A B (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) C)))) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (D = (k3_rlvect_1 A B (k1_rlvect_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v2_rusub_4 (k5_rusub_4 A B C) A)) ) ) ) ) ) ).
tt(t31_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_real_1 (k5_square_1 (k3_bhsp_1 A (k3_rlvect_1 A B C))) (k5_square_1 (k3_bhsp_1 A (k5_algstr_0 A B C)))) = (k7_real_1 (k8_real_1 2 (k5_square_1 (k3_bhsp_1 A B))) (k8_real_1 2 (k5_square_1 (k3_bhsp_1 A C))))) ) ) ) ) ) ) ).
tt(t31_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k8_rvsum_1 A B) = (k4_rvsum_1 A (k6_rvsum_1 B))) ) ) ) ) ).
tt(t31_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k16_rvsum_1 (k7_finseq_1 B (k9_finseq_1 A))) = (k3_binop_2 (k16_rvsum_1 B) A)) ) ) ) ) ).
tt(t31_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) (k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k12_scmfsa_2 A B)))) 1) = k5_numbers) ) ) ) ) ).
tt(t31_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 2)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k7_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k3_scmfsa6a (k6_scmfsa6a A B) C) = (k4_scmfsa6a A (k4_scmfsa6a B C))) ) ) ) ) ) ) ).
tt(t31_scmfsa8a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_hidden k6_numbers (k2_afinsq_1 (k1_scmfsa8a A))) &  ((k1_funct_1 (k1_scmfsa8a A) k6_numbers) = (k11_scmfsa_2 A)) ) ) ) ).
tt(t31_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v7_amistd_1 (k3_scmfsa8b E C D) 3 k1_scmfsa_2) &  ( ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B E)))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7)))))  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_scmfsa8a B A (k2_scmfsa6a C)))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_scmfsa8a B A (k2_scmfsa6a C))))) ) ) ) ) ) ) ) ).
tt(t31_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) C) k6_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) (k2_nat_1 E 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmfsa_9,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ( (~ (r3_scmfsa7b A (k4_scmfsa_2 k6_numbers)))  => (v1_scmfsa7b (k11_compos_1 k1_scmfsa_2 A))) ) ) ).
tt(t31_scmfsa_m,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ((k9_xtuple_0 (k1_scmfsa_m (k16_funcop_1 B A))) = (k8_domain_1 (u1_struct_0 k1_scmfsa_2) (k4_scmfsa_2 k6_numbers) (k4_struct_0 k1_scmfsa_2) B)) ) ) ) ) ).
tt(t31_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_scm_halt C B A) <=> (r6_scmfsa7b C (k1_scmfsa_m B) A)) ) ) ) ) ) ) ).
tt(t31_scmisort,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_compos_1 k1_scmfsa_2)) =>  ((k5_card_1 (k5_scmfsa6a (k5_scmfsa6a (k5_scmfsa6a (k6_scmfsa6a A B) C) D) E)) = 10) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 5)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  (A = (k8_scmpds_2 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmpds_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 E (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 F (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 F 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v4_relat_1 G k5_numbers) &  ((v5_relat_1 G (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 G) &  ((v1_finset_1 G) &  ((v1_afinsq_1 G) &  ((v2_scmpds_4 G) & (v3_scmpds_4 G)) ) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 G) C) &  (E = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 D (k10_compos_1 k1_scmpds_2 G)) F A)) )  =>  ((k2_extpro_1 2 k1_scmpds_2 (k3_extpro_1 2 k1_scmpds_2 C E) (k9_memstr_0 2 k1_scmpds_2 E B)) = (k9_memstr_0 2 k1_scmpds_2 (k4_extpro_1 2 k1_scmpds_2 E C) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) & (v3_scmpds_4 E)) ) ) ) ) ) )  =>  ( ((r1_tarski (k10_compos_1 k1_scmpds_2 E) B) & (r1_scmpds_6 E D B))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_tarski (k61_valued_1 (k10_compos_1 k1_scmpds_2 E) F) C) &  ( ((k5_memstr_0 2 k1_scmpds_2 A) = F)  &  ((k6_memstr_0 2 k1_scmpds_2 D) = (k6_memstr_0 2 k1_scmpds_2 A)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((k2_nat_1 (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) F) = (k5_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ( ((k3_extpro_1 2 k1_scmpds_2 B (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k3_extpro_1 2 k1_scmpds_2 C (k5_extpro_1 2 k1_scmpds_2 C A G)))  &  ((k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 B D G)) = (k6_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 C A G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_compos_1 D k1_scmpds_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v4_scmpds_4 E) &  ((v1_scmpds_5 E) & (m1_subset_1 E (u1_compos_1 k1_scmpds_2))) )  =>  ( ((r1_scmpds_6 D C B) & (r2_scmpds_6 D C B))  =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 D E) C B) A) = (k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 E (k6_scmpds_4 D C B)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_amistd_1 2 (k1_scmring2 A) (k8_scmring2 A B)) = (k1_tarski B)) ) ) ) ) ).
tt(t31_scmyciel,ax, (! [A:$i] :  (? [B:$i] :  ((v4_scmyciel B) &  ((v2_scmyciel B) &  ((k3_tarski B) = A) ) ) ) ) ).
tt(t31_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C F) &  ((r1_semi_af1 A B C G) &  ((r1_semi_af1 A D E F) & (r1_semi_af1 A D E G)) ) )  =>  ((r2_analoaf A B C D E) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A B) C))) ) ) ) ) ) ).
tt(t31_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k17_complex1 (k11_complex1 (k3_comseq_2 A) (k3_comseq_2 B)))) ) ) ) ) ).
tt(t31_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k12_binop_2 B (k9_binop_2 D A))) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t31_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((r1_seqfunc A k1_numbers B D) & (r1_seqfunc A k1_numbers C D))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) =>  ((r2_relset_1 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k6_seqfunc A B C) E)) &  ((r2_relset_1 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k7_seqfunc A B C) E)) & (r2_relset_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k8_seqfunc A B C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_seqm_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v6_valued_0 B) =>  ((r1_xxreal_0 A k6_numbers) | (v6_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) )  &  ((v6_valued_0 B) =>  ((r1_xxreal_0 k6_numbers A) | (v5_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ) ).
tt(t31_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A C)) &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k8_real_1 (k5_series_1 2 C) (k3_funct_2 k5_numbers k1_numbers A (k5_series_1 2 C)))) ) ) ) )  =>  ((v1_series_1 A) <=> (v1_series_1 B)) ) ) ) ) ) ).
tt(t31_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k2_nat_1 B 2) (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k2_nat_1 B 3)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k11_complex1 (k11_complex1 (k13_complex1 29 36) (k13_complex1 1 (k2_nat_1 B 3))) (k13_complex1 3 (k4_nat_1 (k4_nat_1 2 (k2_nat_1 B 2)) (k2_nat_1 B 3)))) (k13_complex1 4 (k4_nat_1 (k4_nat_1 (k4_nat_1 3 (k2_nat_1 B 1)) (k2_nat_1 B 2)) (k2_nat_1 B 3))))) ) ) ) ) ) ) ).
tt(t31_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) )  =>  (! [C:$i] :  ( ((v1_xreal_0 C) &  (~ (v3_xxreal_0 C)) )  => (r1_xxreal_0 (k3_real_1 (k1_newton B (k2_nat_1 A 2)) (k8_real_1 (k8_real_1 (k2_nat_1 A 2) (k1_newton B (k2_nat_1 A 1))) C)) (k1_newton (k2_xcmplx_0 B C) (k2_nat_1 A 2)))) ) ) ) ) ) ).
tt(t31_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) (k2_xcmplx_0 (k2_xcmplx_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B)) 3)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 B C)) (k3_square_1 C)) 3))) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_xcmplx_0 C A)) (k3_square_1 A)) 3))))) ) ) ) ) ) ).
tt(t31_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(t31_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k3_subset_1 B (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B (k2_prob_1 B C)) A))) ) ) ) ) ) ).
tt(t31_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 C) => (v3_prob_1 (k8_setlim_2 A C B))) ) ) ) ) ) ).
tt(t31_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v1_setwiseo C A)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((k7_setwiseo B A C (k1_setwiseo B) D) = (k4_binop_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t31_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((v1_binop_1 B A) &  ((v2_binop_1 B A) &  ((v1_setwiseo B A) & (v1_finseqop B A)) ) )  =>  ((k3_funct_2 A A (k5_finseqop A B) (k1_finsop_1 A C B)) = (k1_finsop_1 A (k4_finseqop A A C (k5_finseqop A B)) B)) ) ) ) ) ) ) ) ).
tt(t31_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m1_scmfsa_2 E) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 1 (k1_funct_1 A C)) &  ((r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 A D)) &  ((r1_xxreal_0 (k1_funct_1 A D) (k3_finseq_1 (k18_scmfsa_2 A E))) &  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) ) ) )  =>  ( (C = B)  |  ( (D = B)  |  ((k1_funct_1 (k1_scmfsa6b (k3_sfmastr3 C D B E) A F) B) = (k8_graph_2 (k18_scmfsa_2 A E) (k1_int_2 (k1_funct_1 A C)) (k1_int_2 (k1_funct_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k2_sf_mastr (k6_scmfsa6a A B)) = (k5_setwiseo k2_scmfsa_2 (k1_sf_mastr A) (k1_sf_mastr B))) ) ) ) ) ).
tt(t31_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  ( ( (D = (u1_struct_0 B))  &  ((r2_hidden C D) &  ((k2_nat_1 1 (k4_sgraph1 A B C)) = (k5_card_1 D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E D) =>  (~  ( (~  (C = E) )  &  (! [F:$i] :  (~  ((r2_hidden F (u1_sgraph1 B)) &  (F = (k2_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B C) = (k5_sheffer1 A C B)) ) ) ) ) ) ) ).
tt(t31_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A E (k5_sheffer1 A C B)))) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) => (r1_tarski (k4_simplex0 C) (k4_simplex0 B))) ) ) ) ) ).
tt(t31_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) )  =>  ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) =>  ((k6_simplex0 B) = (k6_simplex0 (k4_simplex1 A B))) ) ) ) ) ) ).
tt(t31_sincos10,ax, ( ((k1_seq_1 k1_fdiff_9 k6_numbers) = 1)  &  ( ((k1_seq_1 k1_fdiff_9 (k10_real_1 k32_sin_cos 4)) = (k7_square_1 2))  &  ( ((k1_seq_1 k1_fdiff_9 (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) = (k1_real_1 (k7_square_1 2)))  &  ((k1_seq_1 k1_fdiff_9 k32_sin_cos) = (k1_real_1 1)) ) ) ) ).
tt(t31_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k1_sin_cos2 A) &  ((k1_fdiff_1 k1_sin_cos2 A) = (k1_seq_1 k4_sin_cos2 A)) ) ) ) ).
tt(t31_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k7_binop_2 (k11_binop_2 (k23_binop_2 (k24_binop_2 2 A) 1) k32_sin_cos)) k7_complex1)) = (k19_binop_2 1)) ) ) ).
tt(t31_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k20_sin_cos A) (k17_sin_cos B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k6_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))))) ) ) ) ) ).
tt(t31_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k21_sin_cos (k6_real_1 A 2)) = k6_numbers) )  =>  ((k2_sin_cos4 (k6_real_1 A 2)) = (k10_real_1 (k7_real_1 1 (k20_sin_cos A)) (k17_sin_cos A))) ) ) ) ).
tt(t31_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) A))  & (r1_xxreal_0 (k17_sin_cos A) (k1_real_1 1))) ) ) ) ) ).
tt(t31_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 1 (k12_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k9_binop_2 (k3_square_1 A) 1)))) ) ) ).
tt(t31_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k2_newton (k3_sin_cos2 A) 3) = (k7_xcmplx_0 (k6_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 3 A)) (k3_xcmplx_0 3 (k3_sin_cos2 A))) 4))  &  ( ((k2_newton (k3_sin_cos2 A) 4) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 4 A)) (k3_xcmplx_0 4 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 3) 8))  &  ( ((k2_newton (k3_sin_cos2 A) 5) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 5 A)) (k3_xcmplx_0 5 (k3_sin_cos2 (k3_xcmplx_0 3 A)))) (k3_xcmplx_0 10 (k3_sin_cos2 A))) 16))  &  ( ((k2_newton (k3_sin_cos2 A) 6) = (k7_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 6 A)) (k3_xcmplx_0 6 (k6_sin_cos2 (k3_xcmplx_0 4 A)))) (k3_xcmplx_0 15 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 10) 32))  &  ( ((k2_newton (k3_sin_cos2 A) 7) = (k7_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_sin_cos2 (k3_xcmplx_0 7 A)) (k3_xcmplx_0 7 (k3_sin_cos2 (k3_xcmplx_0 5 A)))) (k3_xcmplx_0 21 (k3_sin_cos2 (k3_xcmplx_0 3 A)))) (k3_xcmplx_0 35 (k3_sin_cos2 A))) 64))  &  ((k2_newton (k3_sin_cos2 A) 8) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 8 A)) (k3_xcmplx_0 8 (k6_sin_cos2 (k3_xcmplx_0 6 A)))) (k3_xcmplx_0 28 (k6_sin_cos2 (k3_xcmplx_0 4 A)))) (k3_xcmplx_0 56 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 35) 128)) ) ) ) ) ) ) ) ).
tt(t31_sin_cos9,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) k1_sin_cos9) = (k1_partfun2 k1_numbers (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(t31_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k21_sin_cos k6_numbers) = 1)  &  ( ((k18_sin_cos k6_numbers) = k6_numbers)  &  ( ((k20_sin_cos (k4_xcmplx_0 A)) = (k20_sin_cos A))  &  ((k17_sin_cos (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k17_sin_cos A))) ) ) ) ) ) ).
tt(t31_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) & (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 2))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B A) (k2_topreal1 2 B (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ).
tt(t31_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v2_topreal1 A) &  ((v2_topreal1 B) &  ( ((k2_nat_1 C 1) = (k3_finseq_1 A))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)) (k2_topreal1 2 B 1)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) ) ) )  => (v2_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ) ) ).
tt(t31_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (r1_xxreal_0 (k8_pscomp_1 A) (k6_pscomp_1 A))) ) ) ).
tt(t31_sprect_2,ax, ((k7_pscomp_1 k1_topreal1) = 1) ).
tt(t31_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2)) (k3_topreal1 2 (k1_sprect_1 (k3_topreal1 2 A))))) ) ) ).
tt(t31_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t31_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ( ((k6_square_1 (k2_xcmplx_0 A B)) = k6_numbers)  <=>  ( (A = k6_numbers)  &  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(t31_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r2_hidden B (k11_stacks_1 A C)) =>  ((k13_stacks_1 A B) = (k13_stacks_1 A C)) ) ) ) ) ) ) ) ).
tt(t31_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_stirl2_1 A k6_numbers) = k6_numbers) ) ) ) ).
tt(t31_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ((v3_substut1 (k7_sublemma A C B) A) =>  ((k11_sublemma A (k9_sublemma A (k7_sublemma A C B) D) (k39_substut1 A C)) = (k11_cqc_lang A (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) (k39_substut1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t31_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~ (r2_hidden D B))  <=> (r2_hidden D C)) ) )  =>  (B = (k3_subset_1 A C)) ) ) ) ) ) ) ).
tt(t31_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ((k19_substut1 A B) = (k19_substut1 A C))  =>  ((k37_substut1 A (k21_substut1 A B C)) = (k14_qc_lang1 A (k37_substut1 A B) (k37_substut1 A C))) ) ) ) ) ) ) ) ).
tt(t31_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_qc_lang2 A D C) =>  ((k7_cqc_sim1 A D) = B) ) ) )  =>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(t31_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((v1_supinf_2 D A B) & (v1_supinf_2 E A C))  => (v1_supinf_2 (k13_supinf_2 A B C D E) A (k5_supinf_2 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~ (r1_orders_2 B E D))  &  ( (~ (r1_orders_2 B F D))  &  (~  ((k8_group_1 A (k1_symsp_1 A B D C E) (k1_symsp_1 A B E D F)) = (k8_group_1 A (k4_algstr_0 A (k1_symsp_1 A B D C F)) (k1_symsp_1 A B F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ( ((k3_relat_1 A A) = A)  &  ((k3_relat_1 A (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A)))) = k1_xboole_0) )  =>  ( ((k9_xtuple_0 (k1_sysrel A)) = (k10_xtuple_0 A))  &  ((k10_xtuple_0 (k1_sysrel A)) = (k10_xtuple_0 A)) ) )  &  ( ( ((k3_relat_1 A A) = A)  &  ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A))) A) = k1_xboole_0) )  =>  ( ((k9_xtuple_0 (k1_sysrel A)) = (k9_xtuple_0 A))  &  ((k10_xtuple_0 (k1_sysrel A)) = (k9_xtuple_0 A)) ) ) ) ) ) ).
tt(t31_taxonom1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers))))  => (m1_taxonom1 (k2_taxonom1 A B) A)) ) ) ) ).
tt(t31_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_taylor_1 A (k1_nat_1 D 1) B) => (r1_taylor_1 A (k1_nat_1 D 1) C)) ) ) ) ) ) ) ) ) ) ).
tt(t31_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (r1_tarski (k5_tdlat_1 A) (k1_tdlat_1 A))) ) ).
tt(t31_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_pcomps_1 A (k1_tdlat_2 A B)) = (a_2_2_tdlat_2 A B)) ) ) ) ) ).
tt(t31_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  ((k1_tops_1 A B) = (k2_pre_topc A (k1_tops_1 A B))) ) ) ) ) ) ) ).
tt(t31_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r6_pboole A (k3_termord A B C (k9_polynom1 A C D E)) (k11_pre_poly A (k3_termord A B C D) (k3_termord A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t31_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (u1_struct_0 A)) )  & (v1_tops_1 B A)) ) ) ) ) ) ) ).
tt(t31_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) )  => (v2_tex_2 B A)) ) ) ) ) ).
tt(t31_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r3_tsep_2 A B C) =>  ((v1_tex_3 B A) <=> (v3_tex_3 C A)) ) ) ) ) ) ) ) ).
tt(t31_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_tex_4 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ).
tt(t31_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc (k1_tsep_1 A B C) (k1_tsep_1 A D E)) &  ((m1_pre_topc (k2_tsep_1 A D (k1_tsep_1 A B C)) B) & (m1_pre_topc (k2_tsep_1 A E (k1_tsep_1 A B C)) C)) )  =>  ((m1_pre_topc B C) |  ((m1_pre_topc C B) |  ( (~ (r1_tsep_1 D (k1_tsep_1 A B C)))  &  (~ (r1_tsep_1 E (k1_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k4_toler_1 A B) = (k4_toler_1 A C))  => (r2_relset_1 A A B C)) ) ) ) ) ) ).
tt(t31_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) & (r1_borsuk_6 A E F)) ) )  =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r3_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J) (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E G (k1_borsuk_2 A C D E H I)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_tops_2 D A B) => (v3_funct_2 (k3_topalg_3 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C))))) ) ) ) ) ) ) ) ) ).
tt(t31_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A D))) &  ((v1_group_6 G (k5_topalg_1 A C) (k5_topalg_1 A D)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A D)))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k5_topalg_1 B E)) (u1_struct_0 (k5_topalg_1 B F))) &  ((v1_group_6 H (k5_topalg_1 B E) (k5_topalg_1 B F)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 B E)) (u1_struct_0 (k5_topalg_1 B F)))))) ) )  =>  ( ((v3_funct_2 G (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A D))) & (v3_funct_2 H (u1_struct_0 (k5_topalg_1 B E)) (u1_struct_0 (k5_topalg_1 B F))))  => (v3_funct_2 (k1_partfun1 (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B E)))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A C) (k5_topalg_1 B E)))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A D) (k5_topalg_1 B F)))) (k11_topalg_4 A B C E) (k1_topalg_4 (k5_topalg_1 A C) (k5_topalg_1 B E) (k5_topalg_1 A D) (k5_topalg_1 B F) G H)) (u1_struct_0 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A D) (k5_topalg_1 B F)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((r2_hidden (k2_topalg_6 A B) (k10_xtuple_0 B)) & (r2_hidden (k3_topalg_6 A B) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t31_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v3_topdim_1 A) & (r1_xxreal_0 (k4_topdim_1 A) B))  <=>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) =>  ((v1_topdim_1 (k2_tops_1 A D) A) & (r1_xxreal_0 (k2_topdim_1 A (k2_tops_1 A D)) (k5_real_1 B 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_topgen_1 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k2_topgen_1 A B) (k2_topgen_1 A C))) ) ) ) ) ) ) ).
tt(t31_topgen_2,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  ((k1_card_1 (a_1_2_topgen_2 A)) = (k1_card_1 A)) ) ) ).
tt(t31_topgen_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ((r2_hidden (k1_card_1 A) k3_topgen_3) => (r2_hidden (k1_card_1 (a_1_1_topgen_3 A)) k3_topgen_3)) ) ) ).
tt(t31_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  (~  ( ((k3_setfam_1 A B) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t31_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (? [D:$i] :  ((v1_rat_1 D) &  (? [E:$i] :  ((v1_rat_1 E) &  ((r2_hidden (k19_euclid D E) (k1_topreal9 2 (k19_euclid A B) C)) &  (~  ((k19_euclid D E) = (k19_euclid A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) =>  (! [C:$i] :  ((m3_topgrp_1 C A) => (m3_topgrp_1 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B) A)) ) ) ) ) ) ).
tt(t31_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_topreal1 A) = (a_1_1_topreal1 A)) ) ) ).
tt(t31_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid A) = (k17_euclid B))  =>  ( ((k18_euclid A) = (k18_euclid B))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k17_euclid A) (k10_real_1 (k7_real_1 (k18_euclid A) (k18_euclid B)) 2))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid A) (k10_real_1 (k7_real_1 (k18_euclid A) (k18_euclid B)) 2)) B)) = (k1_tarski (k19_euclid (k17_euclid A) (k10_real_1 (k7_real_1 (k18_euclid A) (k18_euclid B)) 2)))) ) ) ) ) ) ) ).
tt(t31_topreal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k6_pscomp_1 A) (k17_euclid C)))  &  (~  (B = C) ) ) ) ) ) ) ) ) ).
tt(t31_topreal8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ( ( (~ (v1_zfmisc_1 C))  & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))  =>  ((r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 A 1)) |  ((k2_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) (k2_nat_1 (k3_finseq_1 B) A)) = (k2_topreal1 2 C (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ).
tt(t31_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k4_topreal9 A C D)) =>  ( (B = C)  |  ((k4_topreal9 A C D) = (k4_topreal9 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r2_hidden (k19_euclid A C) (k2_jgraph_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t31_toprealb,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_funct_1 k12_toprealb B) = (k1_funct_1 k12_toprealb (k2_xcmplx_0 B A))) ) ) ) ) ).
tt(t31_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((k42_valued_2 A C D B) = (k63_valued_2 A C D (k7_funcop_1 (k1_relset_1 A D) B))) ) ) ) ) ) ) ) ).
tt(t31_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k9_real_1 (k12_euclid B) (k12_euclid C)) (k12_euclid (k3_rlvect_1 (k15_euclid A) B C)))) ) ) ) ) ) ).
tt(t31_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k4_subset_1 (u1_struct_0 A) B (k2_tops_1 A B))) ) ) ) ) ).
tt(t31_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r2_hidden B D) => (r2_hidden (k9_subset_1 (u1_struct_0 A) B C) (k1_tops_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t31_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v1_tops_3 (k2_struct_0 A) A)) ) ).
tt(t31_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v3_transgeo B A) & (v2_transgeo B A)) ) ) ) ) ) ).
tt(t31_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k4_trees_1 A (k6_finseq_1 k5_numbers)) = A) ) ) ).
tt(t31_trees_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t31_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v4_trees_3 (k10_finseq_1 A B)) <=>  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  &  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) ) ) ) ).
tt(t31_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E (k5_trees_3 (k2_zfmisc_1 A B))) =>  (? [F:$i] :  ((m2_finseq_1 F (k5_trees_3 A)) &  ( ((k4_finseq_1 F) = (k4_finseq_1 E))  &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 E)) &  (! [H:$i] :  ((m1_subset_1 H (k5_trees_3 (k2_zfmisc_1 A B))) =>  (~  ( (H = (k1_funct_1 E G))  &  ((k1_funct_1 F G) = (k8_trees_3 A B H)) ) ) ) ) ) ) ) )  &  ((k8_trees_3 A B (k8_trees_4 (k2_zfmisc_1 A B) (k1_domain_1 A B C D) E)) = (k8_trees_4 A C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 (k5_trees_2 A B))) =>  ((k2_trees_9 A (k8_finseq_1 k5_numbers B C)) = (k2_trees_9 (k5_trees_2 A B) C)) ) ) ) ) ) ) ).
tt(t31_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( (~ (r1_tsep_1 B C))  => (m1_pre_topc (k2_tsep_1 A B C) (k1_tsep_1 A B C))) ) ) ) ) ) ) ).
tt(t31_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( ((r4_tsep_2 A B C) & (r4_tsep_2 A C D))  =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D))) ) ) ) ) ) ) ) ) ) ).
tt(t31_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k4_subset_1 (u1_struct_0 A) C D)) = (k4_subset_1 (u1_struct_0 B) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t31_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k16_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k16_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( (A = (k4_domain_1 k5_numbers k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)) k6_numbers C B))  & (r2_turing_1 (k2_finseq_4 k5_numbers C D) k16_turing_1 B))  =>  ((v2_turing_1 A k16_turing_1) &  ( ((k2_mcart_1 (u2_turing_1 k16_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)) (k11_turing_1 k16_turing_1 A)) = C)  & (r2_turing_1 (k2_finseq_4 k5_numbers C (k2_nat_1 D 1)) k16_turing_1 (k3_mcart_1 (u2_turing_1 k16_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k16_turing_1)) (k11_turing_1 k16_turing_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((u1_struct_0 (k37_twoscomp A B)) = (k2_xboole_0 (k2_tarski A B) (k1_tarski (k4_tarski (k10_finseq_1 A B) k3_twoscomp)))) ) ) ) ) ).
tt(t31_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_uniroots k1_complfld))) =>  ( (C = (k1_hahnban1 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A)) (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A))))  =>  ((k6_group_1 (k1_uniroots k1_complfld) C) = (k3_nat_d A (k6_nat_d B A))) ) ) ) ) ) ) ) ).
tt(t31_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l5_algstr_0 A))  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k10_polynom3 A) (k3_algseq_1 A (k5_struct_0 A)))) ) ).
tt(t31_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k4_subset_1 k1_numbers k2_urysohn1 (k3_limfunc1 1))) &  ((r2_hidden D (k4_subset_1 k1_numbers k2_urysohn1 (k3_limfunc1 1))) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (~ (r1_xxreal_0 A (k9_real_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (~  ( (~  (B = C) )  &  ( (~ (r2_hidden B (k24_qc_lang1 A D)))  & (r2_hidden B (k24_qc_lang1 A (k13_cqc_lang A D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r1_tarski (k2_relset_1 A D) (k1_relset_1 A (k1_partfun1 A B B C E F))) => (r2_funct_2 k5_numbers C (k8_funct_2 k5_numbers C B (k8_funct_2 k5_numbers B A D E) F) (k8_funct_2 k5_numbers C A D (k1_partfun1 A B B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) )  =>  ((r1_tarski A B) => (r1_xxreal_0 (k62_valued_1 A) (k62_valued_1 B))) ) ) ) ) ).
tt(t31_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k14_valued_2 B (k4_xcmplx_0 A)) = (k30_valued_1 (k14_valued_2 B A))) ) ) ) ) ).
tt(t31_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_vectsp_5 F A B (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) C))) =>  ((r1_struct_0 F D) =>  ( (C = (k4_struct_0 B))  |  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_vectsp10 A B C F) (k3_rlvect_1 B (k4_vectsp_1 A B E C) D)) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_funct_1 (k8_matrlin2 A B B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) C)) &  ((v1_funct_2 (k8_matrlin2 A B B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) C) (u1_struct_0 (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D)))) (u1_struct_0 (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))))) &  ((v13_vectsp_1 (k8_matrlin2 A B B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) C) (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D)))) &  ((v1_mod_2 (k8_matrlin2 A B B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) C) A (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D)))) & (m1_subset_1 (k8_matrlin2 A B B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D))) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D)))) (u1_struct_0 (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) D)))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_algstr_0 A B C) = (k4_algstr_0 A (k1_algstr_0 A (k4_algstr_0 A C) (k4_algstr_0 A B)))) ) ) ) ) ) ) ).
tt(t31_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k4_vectsp_1 A C (k11_algstr_0 A B) (k4_vectsp_1 A C B D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t31_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ( ((u1_struct_0 C) = (u1_struct_0 B))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t31_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  ( ((k1_vectsp_5 A B C D) = D)  <=>  ((k2_vectsp_5 A B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t31_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ((m2_vectsp_6 E A B D) => (m2_vectsp_6 (k6_vectsp_6 A B C E) A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_vectsp_9 A B) = 2)  <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  ( (~  (C = D) )  &  ((v1_vectsp_7 (k7_domain_1 (u1_struct_0 B) C D) A B) &  ((k2_vectsp_4 A B) = (k1_vectsp_7 A B (k7_domain_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r2_relset_1 B (u1_struct_0 C) (k2_partfun1 B (u1_struct_0 C) (k4_vfunct_1 B C D E) A) (k4_vfunct_1 B C (k2_partfun1 B (u1_struct_0 C) D A) E))) ) ) ) ) ) ) ) ) ).
tt(t31_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] : (r2_relset_1 A (u1_struct_0 B) (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_2 A B C D) E) (k2_vfunct_2 A B (k2_partfun1 A (u1_struct_0 B) C E) D))) ) ) ) ) ) ) ) ) ).
tt(t31_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattice3 A B C) <=> (r2_lattice3 A (k3_waybel_0 A B) C)) ) ) ) ) ) ) ).
tt(t31_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (u1_pre_topc (k13_yellow_6 A (k2_waybel11 A)))) <=>  ((v1_waybel11 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ).
tt(t31_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 A) C) = B)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) D E) = (k2_yellow_0 A (a_3_0_waybel12 A C E))) ) ) )  => (r4_yellow_4 A (k2_relset_1 (u1_struct_0 A) D) B)) ) ) ) ) ) ) ) ) ).
tt(t31_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ( ((r5_waybel_1 A B) &  ((v3_lattice3 A) & (v1_waybel_8 A)) )  => (v1_waybel_8 B)) ) ) ) ) ).
tt(t31_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_waybel14 (k5_waybel_2 A) A) => (v4_yellow_8 A)) ) ) ).
tt(t31_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=> (v1_waybel_5 A)) ) ) ).
tt(t31_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A C B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v1_waybel16 D A) &  ((r3_orders_2 A B D) &  (~ (r3_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_tops_2 (k2_xboole_0 (k5_waybel11 A) (a_1_3_waybel19 A)) A) &  ((v2_cantor_1 (k2_xboole_0 (k5_waybel11 A) (a_1_3_waybel19 A)) A) & (m1_subset_1 (k2_xboole_0 (k5_waybel11 A) (a_1_3_waybel19 A)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(t31_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_orders_3 C A B) => (v5_orders_3 (k2_waybel_1 A B C) A (k1_yellow_2 A B C))) ) ) ) ) ) ) ).
tt(t31_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_yellow_0 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k4_waybel_3 A B (k3_yellow_0 (k5_yellow_1 A B)) C) = (k3_yellow_0 (k3_waybel_3 A B C))) ) ) ) ) ) ) ) ).
tt(t31_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_waybel_9 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_waybel_9 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  ( (E = (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))  => (r1_tarski (k10_yellow_6 B (k3_yellow_9 B E)) (k10_yellow_6 B (k6_waybel_9 A B D (k3_yellow_9 A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=> (v1_waybel23 B A)) ) ) ) ) ).
tt(t31_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_yellow_0 B (k7_relat_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) D)) = (k1_funct_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) (k1_yellow_0 A D))) ) ) ) ) ) ) ) ) ).
tt(t31_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v7_waybel_0 B) &  ((v10_waybel_0 B (k1_waybel25 A)) & (l1_waybel_0 B (k1_waybel25 A))) ) )  => (r1_waybel_9 (k1_waybel25 A) B)) ) ) ) ).
tt(t31_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k3_waybel18 C (k7_funcop_1 C B)))) &  ((v5_pre_topc D A (k3_waybel18 C (k7_funcop_1 C B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 C (k7_funcop_1 C B))))))) ) )  =>  ((v1_funct_1 (k10_funct_6 D)) &  ((v1_funct_2 (k10_funct_6 D) C (u1_struct_0 (k1_waybel26 A B))) & (m1_subset_1 (k10_funct_6 D) (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 (k1_waybel26 A B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel27,ax,(v4_waybel11 (k1_waybel25 k9_waybel18))).
tt(t31_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k5_waybel11 (k3_yellow_3 B A)) = (u1_pre_topc (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A)))) ) )  <=>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((g1_pre_topc (u1_struct_0 (k1_waybel29 (k3_yellow_3 B A))) (u1_pre_topc (k1_waybel29 (k3_yellow_3 B A)))) = (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A))) ) ) ) ) ) ).
tt(t31_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_3 A A))) =>  ((k3_funct_2 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k4_waybel_2 A) B) = (k11_lattice3 A (k8_yellow_3 A A B) (k9_yellow_3 A A B))) ) ) ) ) ).
tt(t31_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v2_yellow13 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_yellow_0 (k5_yellow_0 A B) A) => (v5_yellow_0 (k5_yellow_0 A (k2_pre_topc A B)) A)) ) ) ) ) ).
tt(t31_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) <=>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k1_yellow_2 A A B)))  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc E C) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))))  =>  ((v3_pre_topc (k4_waybel_0 A E) D) & (m1_subset_1 (k4_waybel_0 A E) (k1_zfmisc_1 (u1_struct_0 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) )  =>  ((v3_orders_2 (k5_yellow_1 A B)) &  ((v4_orders_2 (k5_yellow_1 A B)) &  ((v5_orders_2 (k5_yellow_1 A B)) &  ((v1_lattice3 (k5_yellow_1 A B)) &  ((v2_lattice3 (k5_yellow_1 A B)) &  ((v3_lattice3 (k5_yellow_1 A B)) & (l1_orders_2 (k5_yellow_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (r2_funct_2 (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k8_waybel_4 A)) (k1_partfun1 (u1_struct_0 (k8_waybel_4 A)) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k2_yellow_1 (k3_waybel_4 A))) (u1_struct_0 (k8_waybel_4 A)) (k10_waybel_4 A) (k9_waybel_4 A)) (k6_partfun1 (u1_struct_0 (k8_waybel_4 A))))) ) ).
tt(t31_waybel_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E A D (k7_funcop_1 A B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  => (m2_pboole (k8_pboole E (k7_waybel_5 B C A F)) A D (k7_funcop_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel_6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_funct_1 (k5_funct_3 B (u1_struct_0 A))) &  ((v1_funct_2 (k5_funct_3 B (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski k1_xboole_0)))) & (m1_subset_1 (k5_funct_3 B (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski k1_xboole_0))))))) ) ) ) ) ) ).
tt(t31_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((r1_tarski C D) =>  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) C D) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (~  ((r1_tarski D (k3_tarski E)) &  (! [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 E)))  =>  (~ (r1_tarski C (k3_tarski F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_waybel_8,ax, (! [A:$i] : (v2_waybel_8 (k3_yellow_1 A))) ).
tt(t31_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_waybel_9 A C D) => (r3_waybel_9 A B D)) ) ) ) ) ) ) ) ) ).
tt(t31_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k5_card_1 (u1_struct_0 A)) = (k1_newton (k5_card_1 (u1_struct_0 (k4_weddwitt A))) (k1_vectsp_9 (k4_weddwitt A) (k6_weddwitt A)))) ) ) ).
tt(t31_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E C) &  ((k4_metric_1 A D E) = (k9_weierstr A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((v2_wellord1 B) & (r1_tarski A (k1_relat_1 B)))  =>  ((k1_relat_1 (k2_wellord1 B A)) = A) ) ) ) ) ).
tt(t31_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((k3_int_2 A B) = (k6_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_tarski (k2_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 A C)) (k2_xboole_0 B C))) ) ) ).
tt(t31_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k9_xboolean A A) = (k3_xboolean A)) ) ) ).
tt(t31_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 A B) = (k6_xcmplx_0 (k2_xcmplx_0 A C) (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t31_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 B (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t31_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k11_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k11_xtuple_0 A) (k11_xtuple_0 B))) ) ) ).
tt(t31_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C (k4_xxreal_0 A B)))  & (r1_xxreal_0 C A)) ) ) ) ) ) ) ) ).
tt(t31_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (v1_xboole_0 (k2_xxreal_1 A B))) ) ) ) ) ) ).
tt(t31_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_xxreal_2 (k2_xxreal_1 A B)) = B) ) ) ) ) ) ).
tt(t31_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (A = k1_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  (~  ((k3_xxreal_3 (k3_xxreal_3 A B) C) = (k3_xxreal_3 A (k1_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( ( (B = (k2_yellow_0 A C))  & (r2_yellow_0 A C))  =>  ((r1_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A C D) => (r1_orders_2 A D B)) ) ) ) )  &  ( ((r1_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A C D) => (r1_orders_2 A D B)) ) ) )  =>  ( (B = (k2_yellow_0 A C))  & (r2_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(t31_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) => (r1_tarski (k4_waybel_0 (k3_yellow_3 A B) C) (k6_yellow_3 A B (k4_waybel_0 A (k4_yellow_3 A B C)) (k4_waybel_0 B (k5_yellow_3 A B C))))) ) ) ) ) ) ).
tt(t31_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B C) => (r1_tarski (k5_waybel_0 A B) (k3_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t31_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_waybel_3 C) & (v1_waybel18 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel18 A C))) =>  ((k5_card_3 B (k2_pre_topc (k3_waybel18 A C) (k6_domain_1 (u1_struct_0 (k3_waybel18 A C)) D))) = (k2_pre_topc (k4_waybel18 A C B) (k6_domain_1 (u1_struct_0 (k4_waybel18 A C B)) (k5_waybel18 A C D B)))) ) ) ) ) ) ) ) ) ).
tt(t31_yellow15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_struct_0 A) =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_setfam_1 (a_2_1_yellow15 A C)) B)) ) ) ) ) ) ) ).
tt(t31_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r1_yellow_0 (k5_yellow_1 A B) C) <=>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_yellow_0 (k2_yellow16 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ).
tt(t31_yellow18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_altcat_1 A))) =>  ((k8_altcat_1 (k7_altcat_1 A) B) = (k6_partfun1 B)) ) ) ) ) ).
tt(t31_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v3_waybel_7 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_waybel_7 A B C)) ) ) ) ) ) ) ).
tt(t31_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ( ((v10_functor0 C A B) & (v4_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_functor0 A B C D) = (k3_functor0 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v8_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r2_lattice3 (k3_yellow_3 A B) C (k7_yellow_3 A B D E)) <=>  ((r2_lattice3 A (k4_yellow_3 A B C) D) & (r2_lattice3 B (k5_yellow_3 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ((k3_tarski (a_2_0_yellow_4 A B)) = (k1_yellow_4 A (k4_yellow_3 A A B) (k5_yellow_3 A A B))) ) ) ) ) ).
tt(t31_yellow_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A B C) & (r3_orders_2 A B D))  =>  ((r1_yellow_5 A C D) |  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_yellow_6 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_yellow_6 A B))) =>  ((r1_orders_2 (k9_yellow_6 A B) C D) <=> (r1_tarski D C)) ) ) ) ) ) ) ) ) ).
tt(t31_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v1_yellow_0 (k7_lattice3 A)) <=> (v2_yellow_0 A)) ) ) ).
tt(t31_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E B) &  ((r2_hidden D E) & (r1_tarski E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k4_ordinal1)))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( ((k1_relset_1 A (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A)) = A)  &  ((r1_tarski (k2_relset_1 B (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A)) B) &  ((r2_hidden (k2_partfun1 k4_ordinal1 B (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C) A) (k9_funct_2 A B)) &  ((k1_relset_1 k4_ordinal1 (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang B k2_zf_fund1 C)) = k4_ordinal1) ) ) ) ) ) ) ) ) ) ).
tt(t31_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k20_zf_lang (k11_zf_lang A B)) = (k7_zf_lang A (k6_zf_lang B))) ) ) ) ) ).
tt(t31_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k10_zf_lang A B) = (k10_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t31_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_tarski A) B) <=> (r2_hidden A B)) ) ) ).
tt(t31_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  => (r2_hidden (k4_classes1 B) A)) ) ) ) ).
tt(t31_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k5_algstr_0 D E F) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t320_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C B))  =>  ((k6_subset_1 (k1_xxreal_1 A B) (k2_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k1_tarski B))) ) ) ) ) ) ) ) ).
tt(t321_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C A) |  ((k6_subset_1 (k2_xxreal_1 A C) (k4_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k2_xxreal_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t322_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 A C))  =>  ((k6_subset_1 (k1_xxreal_1 A C) (k4_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k1_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t323_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C A) |  ((k6_subset_1 (k2_xxreal_1 A C) (k3_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k4_xxreal_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t324_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 A C))  =>  ((k6_subset_1 (k1_xxreal_1 A C) (k3_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k3_xxreal_1 B C))) ) ) ) ) ) ) ) ).
tt(t325_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A C)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t326_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A C)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t327_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A C)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t328_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A C)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t329_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 A C)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t32_abcmiz_0,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k1_funct_1 (k1_rewrite1 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t32_abcmiz_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((m2_finseq_2 (k7_finseq_1 A B) k2_abcmiz_1 k4_abcmiz_1) =>  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) & (m2_finseq_1 B k2_abcmiz_1)) ) ) ) ) ) ).
tt(t32_abcmiz_a,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v6_trees_3 C)) ) )  =>  ((r2_hidden (k4_trees_4 B C) A) =>  ( (! [D:$i] :  ( ((v1_instalg1 D) &  ((v1_abcmiz_1 D) &  ((v3_abcmiz_1 D) & (l1_msualg_1 D)) ) )  =>  (~  (A = (k3_card_3 (u3_msualg_1 D (k1_msafree3 D (k28_abcmiz_1 D))))) ) ) )  | (m2_finseq_1 C A)) ) ) ) ) ) ).
tt(t32_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C F) & (r2_analoaf A B C D E))  =>  ( (B = C)  | (r2_aff_1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r5_aff_1 A C D) =>  ((k2_aff_4 A B C) = (k2_aff_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_afinsq_1,ax, (! [A:$i] :  ((k5_afinsq_1 A) = (k1_tarski (k4_tarski k6_numbers A))) ) ).
tt(t32_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  ((r1_afinsq_2 A B) =>  ( (B = k1_xboole_0)  |  ((k1_recdef_1 (k4_afinsq_2 B) k6_numbers) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 A B)) (k1_afinsq_1 (k4_afinsq_2 A)))) ) ) ) ) ) ) ).
tt(t32_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 (k13_afproj A))) =>  ( ((v1_aff_4 B A) &  ((r1_tarski C B) &  ((r5_aff_1 A D C) &  ( (E = (k5_afproj A D))  &  (F = (k4_tarski (k6_afproj A B) 2)) ) ) ) )  => (r1_incsp_1 (k13_afproj A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C (k1_afvect0 A D C) (k1_afvect0 A D B))) ) ) ) ) ) ) ) ).
tt(t32_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_algspec1 A B k1_xboole_0)) ) ) ) ).
tt(t32_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  ( (~ (v1_xboole_0 A))  =>  ( (B = (k4_tarski (k1_xtuple_0 B) (k2_xtuple_0 B)))  & (r1_xxreal_0 1 (k15_algstr_4 A B))) ) ) ) ) ).
tt(t32_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~  ((k1_altcat_1 B C D) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 B D E) = k1_xboole_0) )  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (F = C)  &  ( (G = D)  &  ( (H = E)  &  (? [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A F G)) &  (? [J:$i] :  ((m1_subset_1 J (k1_altcat_1 A G H)) &  (? [K:$i] :  ((m1_subset_1 K (k1_altcat_1 B C D)) &  (? [L:$i] :  ((m1_subset_1 L (k1_altcat_1 B D E)) &  ( (I = K)  &  ( (J = L)  &  (~  ((k5_altcat_1 A F G H I J) = (k5_altcat_1 B C D E K L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (v3_altcat_3 (k8_functor0 A B C D E F) B (k3_functor0 A B C E) (k3_functor0 A B C D))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (v3_altcat_3 F A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v5_ami_wstd C A B)) ) ) ) ) )  =>  ((k6_ami_wstd A B C) = (k1_ami_wstd A B (k7_nat_d (k5_card_1 C) 1))) ) ) ) ) ) ) ).
tt(t32_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_analmetr A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_analmetr A B C))) =>  ((r1_analmetr A B C) =>  ( (D = E)  |  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_analmetr A B C))) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_analmetr A B C))) &  ((r2_analoaf (k2_analmetr A B C) D E D G) & (r4_analmetr (k2_analmetr A B C) D E G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) &  ((r1_analort A B C D E F H) &  ( (~ (r1_analort A B C D E G H))  &  (~ (r1_analort A B C D E H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J))) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_collsp B) &  ((v3_collsp B) &  ((v4_collsp B) &  ((v2_anproj_2 B) &  ((v3_anproj_2 B) & (l1_collsp B)) ) ) ) ) )  =>  (~  ( (B = (k5_anproj_1 A))  & (v8_anproj_2 B)) ) ) ) ) ) ) ) ).
tt(t32_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m5_margrel1 D (u1_struct_0 A) (k1_unialg_2 A)) =>  (~ (r2_hidden C (k2_relset_1 (u1_struct_0 A) D))) ) )  => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t32_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k54_aofa_i00 A B D E F G)) F) = (k3_xcmplx_0 (k21_aofa_i00 B k4_numbers C F) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k54_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v6_armstrng B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ((v1_armstrng (k9_armstrng A B) A) & (v2_finsub_1 (k9_armstrng A B))) ) ) ) ) ).
tt(t32_arytm_3,ax, (! [A:$i] :  (! [B:$i] :  (~ (r2_hidden (k4_tarski A B) k4_ordinal1)) ) ) ).
tt(t32_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k8_asympt_0 (k1_asympt_0 A B)) = (k8_asympt_0 (k5_asympt_0 A B))) ) ) ) ) ).
tt(t32_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_seq_1 A B) = (k5_series_1 B B)) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((r1_tarski (k6_asympt_0 (k5_asympt_1 1)) (k6_asympt_0 B)) &  (~  ((k6_asympt_0 (k5_asympt_1 1)) = (k6_asympt_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) => (m2_pboole (k16_funcop_1 k6_numbers B) (u1_struct_0 (k6_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)) (u3_msualg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) ) ) ) ).
tt(t32_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) = (k15_pre_poly A)) ) ) ).
tt(t32_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden B (k5_bcialg_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B D))) = (k1_bcialg_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_bcialg_2 A B) = 1)  & (v5_bcialg_2 B A)) ) ) ) ) ) ).
tt(t32_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A (k1_bcialg_1 A B C) C))) ) ) ) ) ) ) ).
tt(t32_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_bcialg_4 A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) C) B)) = (k1_bcialg_4 A C (k7_bcialg_4 A B))) ) ) ) ) ) ) ).
tt(t32_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( ((v8_bcialg_1 G) & (m1_bcialg_5 G A B C D))  =>  ( ((r1_xxreal_0 B E) & (r1_xxreal_0 D F))  =>  ((v8_bcialg_1 G) & (m1_bcialg_5 G F E E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k5_bcialg_1 A)) =>  ( ((v1_bcialg_6 (k1_bcialg_1 A B C) A) &  ((r2_hidden B (k7_bcialg_1 A D)) & (r2_hidden C (k7_bcialg_1 A D))) )  =>  ((k4_bcialg_6 A (k1_bcialg_1 A B C)) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t32_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((v3_bciideal (u1_struct_0 A) A) & (m2_bcialg_1 (u1_struct_0 A) A)) ) ) ).
tt(t32_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k9_real_1 (k3_bhsp_1 A B) (k3_bhsp_1 A C)) (k3_bhsp_1 A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t32_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 C A) &  ((k1_bhsp_2 A C) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_vfunct_1 k5_numbers A C) (k4_algstr_0 A B)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_vfunct_1 k5_numbers A C) (k4_algstr_0 A B)))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t32_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k6_bhsp_1 A B C) D) = (k6_bhsp_1 A (k1_valued_0 (u1_struct_0 A) B D) (k1_valued_0 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t32_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A D) = (k2_power D (k3_bhsp_1 B (k1_normsp_1 B C D)))) ) )  & (v2_comseq_2 A))  =>  ((r1_xxreal_0 1 (k2_seq_2 A)) | (v2_bhsp_4 C B)) ) ) ) ) ) ) ) ).
tt(t32_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ((v3_bilinear G A B C) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D (k4_vectsp_1 A C F E)) = (k6_algstr_0 A F (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) (k2_xcmplx_0 B 1)))  =>  ((k8_binarith A (k1_binari_3 A B) (k1_binari_2 A)) = k7_margrel1) ) ) ) ) ) ).
tt(t32_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((k7_partfun1 k6_margrel1 (k2_binari_4 (k23_binop_2 A 1) B) C) = (k7_partfun1 k6_margrel1 (k2_binari_4 A B) C)) ) ) ) ) ) ) ) ).
tt(t32_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k3_lattices A B C)) (k5_lattices A))) ) ) ) ) ) ).
tt(t32_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_hidden D (u1_struct_0 B)))  => (r2_hidden (k6_domain_1 (u1_struct_0 A) D) (k13_borsuk_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t32_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( (A = (u1_struct_0 k1_borsuk_4))  =>  (k1_borsuk_4 = (k1_pre_topc k5_topmetr A)) ) ) ) ).
tt(t32_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_borsuk_5 B C))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t32_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) =>  ((v2_compts_1 (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 A B) (k1_rcomp_1 C D)) (k2_borsuk_1 k5_topmetr k5_topmetr)) & (m1_subset_1 (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 A B) (k1_rcomp_1 C D)) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))))) ) ) ) ) ) ) ) ) ).
tt(t32_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((r1_tarski D E) &  ((r1_tarski F G) & (r1_tarski H I)) )  => (r1_tarski (k4_card_3 (k1_borsuk_7 A B C D F H)) (k4_card_3 (k1_borsuk_7 A B C E G I)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_bspace A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_bspace A))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_bspace (k3_rlvect_1 (k7_bspace A) B C) D) = (k3_rlvect_1 k2_bspace (k3_bspace B D) (k3_bspace C D))) ) ) ) ) ) ) ) ).
tt(t32_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C E) F) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r1_bvfunc_1 A (k16_bvfunc_1 A B C) B)) ) ) ) ) ) ).
tt(t32_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 B (k9_bvfunc_1 A (k1_bvfunc_1 A B) B))) ) ) ) ).
tt(t32_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k6_bvfunc_1 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t32_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k5_bvfunc_1 A C D) B E) (k5_bvfunc_1 A C (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F) (k6_bvfunc_2 A (k9_bvfunc_1 A D E) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A C E) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A C) (k1_bvfunc_1 A B))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t32_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A B)) C) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t32_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_c0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_c0sp1 A))) =>  ( ( ((k1_normsp_0 (k11_c0sp1 A) C) = k6_numbers)  =>  (C = (k4_struct_0 (k11_c0sp1 A))) )  &  ( ( (C = (k4_struct_0 (k11_c0sp1 A)))  =>  ((k1_normsp_0 (k11_c0sp1 A) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k11_c0sp1 A) (k1_rlvect_1 (k11_c0sp1 A) C B)) = (k8_real_1 (k18_complex1 B) (k1_normsp_0 (k11_c0sp1 A) C)))  & (r1_xxreal_0 (k1_normsp_0 (k11_c0sp1 A) (k1_algstr_0 (k11_c0sp1 A) C D)) (k7_real_1 (k1_normsp_0 (k11_c0sp1 A) C) (k1_normsp_0 (k11_c0sp1 A) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_struct_0 (k7_c0sp2 A)) = (k1_c0sp2 A k6_numbers)) ) ) ).
tt(t32_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r5_calcul_1 A B C) => (r7_calcul_1 A C B)) ) ) ) ) ) ) ).
tt(t32_calcul_2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 1 D) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k6_calcul_2 (k3_cqc_lang A) D B)) (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_card_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (r2_hidden C B))  => (r2_wellord2 (k6_subset_1 B (k1_tarski A)) (k6_subset_1 B (k1_tarski C)))) ) ) ) ).
tt(t32_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k3_card_2 A 2) = (k2_card_2 A A)) ) ) ).
tt(t32_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 B C))) ) )  => (r1_ordinal1 (k7_card_3 A) (k7_card_3 B))) ) ) ) ) ).
tt(t32_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ((k3_card_2 (k2_card_1 A) B) = (k2_card_2 (k3_card_2 A B) (k2_card_1 A))) ) ) ) ) ).
tt(t32_card_fil,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v4_ordinal1 A))  =>  (! [B:$i] :  ( ((r1_tarski B A) &  ((k3_ordinal2 B) = A) )  =>  ((k3_tarski B) = A) ) ) ) ) ).
tt(t32_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden A (k8_relat_1 C (k1_tarski B))) =>  ((k8_subset_1 (k3_tarski (k10_xtuple_0 D)) (k2_card_fin D (k5_relat_1 C (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A))) B) (k1_funct_1 D A)) = (k2_card_fin D C B)) ) ) ) ) ) ) ) ).
tt(t32_card_lar,ax, (! [A:$i] :  ( (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ((r1_tarski B C) & (v1_card_1 C)) ) ) ) ) ) )  => (v1_card_1 (k3_tarski A))) ) ).
tt(t32_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v7_cat_1 E A B C) & (v7_cat_1 F A C D))  => (v7_cat_1 (k5_cat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k2_cat_1 (k8_cat_2 A B) (k9_cat_2 A B C E) (k9_cat_2 A B D F)) = (k2_zfmisc_1 (k2_cat_1 A C D) (k2_cat_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A C D) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  ((v2_cat_3 E A C D) => (v2_cat_3 (k9_cat_3 A C D B F E) B (k8_cat_1 A B F C) (k8_cat_1 A B F D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_cat_1 A (k2_cat_4 A C B) (k2_cat_4 A B C) (k2_cat_4 A C B) (k14_cat_4 A C B) (k14_cat_4 A B C)) = (k4_cat_1 A (k2_cat_4 A C B))) ) ) ) ) ) ) ).
tt(t32_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u4_struct_0 A) (k10_cat_5 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k12_cat_5 A B))) =>  ( (D = C)  =>  ((k4_cat_1 (k12_cat_5 A B) D) = (k1_domain_1 (u1_struct_0 (k8_cat_2 (k12_cat_5 A B) (k12_cat_5 A B))) (u4_struct_0 A) (k9_cat_2 (k12_cat_5 A B) (k12_cat_5 A B) D D) (k4_cat_1 A (k4_graph_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 (k23_binop_2 6 A) 3)) = (k13_complex1 (k24_binop_2 (k24_binop_2 (k23_binop_2 A 1) (k23_binop_2 A 5)) (k23_binop_2 A 6)) 6)) ) ) ).
tt(t32_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((r2_hidden D (k2_cat_1 A B C)) =>  ( ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B C C) (k13_catalg_1 A)) (k2_finseq_4 (u4_struct_0 A) (k4_cat_1 A C) D)) = D)  &  ((k1_funct_1 (k5_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k10_catalg_1 (u1_struct_0 A) B B C) (k13_catalg_1 A)) (k2_finseq_4 (u4_struct_0 A) D (k4_cat_1 A B))) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k5_cc0sp2 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k5_cc0sp2 A)))))) )  =>  ((v1_csspace3 B (k5_cc0sp2 A)) => (v9_clvect_1 B (k5_cc0sp2 A))) ) ) ) ) ).
tt(t32_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_cfcont_1 B A) <=>  ((r2_hidden A (k1_relset_1 k2_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k2_numbers B)) &  ( (~ (r1_xxreal_0 D (k17_complex1 (k11_complex1 E A))))  & (r1_xxreal_0 C (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers B E) (k7_partfun1 k2_numbers B A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v6_cfdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k2_numbers A)) & (v3_funct_1 (k5_relset_1 k2_numbers k2_numbers A B)))  =>  ((r2_cfdiff_1 A B) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((r2_hidden C B) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 A B) C) = k5_complex1) ) ) ) ) ) ) ) ) ) ).
tt(t32_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k10_cgames_1 B)) => (r1_tarski (k11_cgames_1 A) (k11_cgames_1 B))) ) ) ) ) ).
tt(t32_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ((r1_xxreal_0 A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid B))) =>  ((r2_hidden D (k4_chain_1 B C A)) <=>  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid B)) &  ( (D = (k3_chain_1 B E F))  &  (~  ( (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_finseq_1 B))) =>  (~  ( ((k5_card_1 G) = A)  &  (! [H:$i] :  ((m2_subset_1 H k5_numbers (k2_finseq_1 B)) =>  ( ((r2_hidden H G) &  ( (~ (r1_xxreal_0 (k1_seq_1 F H) (k1_seq_1 E H)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 E H) (k1_seq_1 F H)) (k2_chain_1 B C H))) )  |  ( (~ (r2_hidden H G))  &  ( ((k1_seq_1 E H) = (k1_seq_1 F H))  & (r2_hidden (k1_seq_1 E H) (k2_chain_1 B C H))) ) ) ) ) ) ) ) )  &  (~  ( (A = B)  &  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 B)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 E G) (k1_seq_1 F G)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 E G) (k1_seq_1 F G)) (k2_chain_1 B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v5_glib_001 B A) =>  ((v1_glib_001 B A) | (v6_glib_001 B A)) ) ) ) ) ) ).
tt(t32_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v5_circcomb A) & (l1_msualg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  ((v4_circcomb B A) => (v3_circcmb3 B A)) ) ) ) ) ).
tt(t32_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k3_msafree2 A) (k2_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  &  (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B))) )  =>  ((k6_circuit2 C F G) = (k1_funct_4 (k6_circuit2 A D H) (k6_circuit2 B E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) => (r1_tarski (k7_relat_1 C (k3_msafree2 A)) (k3_msafree2 B))) ) ) ) ) ) ) ) ) ).
tt(t32_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski A (k4_classes1 B)) <=> (r2_hidden A (k4_classes1 (k1_ordinal1 B)))) ) ) ) ).
tt(t32_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A (k2_ordinal1 B)))  => (r1_ordinal1 (k1_card_1 (k4_classes1 A)) (k1_card_1 B))) ) ) ) ).
tt(t32_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k14_clopban1 A B) C))) ) ) ) ) ) ).
tt(t32_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  &  ((v2_comseq_2 C) &  ( (~ (r1_xxreal_0 (k2_seq_2 C) 1))  & (v2_clopban3 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t32_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_normsp_1 A D E) = (k1_normsp_1 A (k1_bhsp_4 A (k5_clopban4 A B C E)) E)) ) )  =>  ((v9_clvect_1 D A) &  ((k7_clvect_1 A D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v5_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ( ((v2_relat_1 E) & (m3_pboole E A (k1_mboolean A B)))  =>  ( (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) & (v1_partfun1 F A)) ) )  =>  ((r1_pboole A F E) <=>  ((r1_pboole A F C) & (r2_pboole A D F)) ) ) )  =>  (! [F:$i] :  (! [G:$i] :  ( (~ (v1_xboole_0 G))  =>  ( ((r2_hidden F A) &  (G = (k1_funct_1 C F)) )  =>  ((k1_funct_1 E F) = (a_5_0_closure1 A B D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_closure2 C A B (k2_closure2 A B)) =>  (! [D:$i] :  ((m1_closure2 D A B (k2_closure2 A B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [F:$i] :  ((m1_closure2 F A B (k6_closure2 A B)) =>  ( ((r6_pboole A F (k3_pboole A C D)) & (v8_closure2 E A B))  => (r2_pboole A (k7_closure2 A B E F) (k3_pboole A (k7_closure2 A B E C) (k7_closure2 A B E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k3_rlvect_1 D E F) = (k3_rlvect_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 C A) &  ((k1_clvect_2 A C) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k5_vfunct_1 k5_numbers A C) (k4_algstr_0 A B)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k5_vfunct_1 k5_numbers A C) (k4_algstr_0 A B)))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t32_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k2_power D (k13_csspace A (k1_normsp_1 A B D)))) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_clvect_3 B A)) ) ) ) ) ) ) ) ).
tt(t32_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_cohsp_1 A)) )  =>  ((v1_classes1 (k9_xtuple_0 A)) => (r1_tarski (k7_cohsp_1 A) (k5_cohsp_1 A))) ) ) ).
tt(t32_coh_sp,ax, (! [A:$i] : (r2_hidden (k1_eqrel_1 A) (k15_coh_sp A))) ).
tt(t32_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 3) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((l1_combgras C (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B)) =>  ((v7_combgras C (k1_combgras (k2_nat_1 A 1) B)) =>  (! [D:$i] :  ((l1_combgras D (k1_combgras A B) (k1_combgras A B)) =>  ((r1_funct_2 (u2_incsp_1 (k1_combgras A B)) (u2_incsp_1 (k1_combgras A B)) (u1_incsp_1 (k1_combgras (k2_nat_1 A 1) B)) (u1_incsp_1 (k1_combgras (k2_nat_1 A 1) B)) (u2_combgras (k1_combgras A B) (k1_combgras A B) D) (u1_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B B) &  ((v3_funct_2 E B B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  ( ((g1_combgras (k1_combgras A B) (k1_combgras A B) (u1_combgras (k1_combgras A B) (k1_combgras A B) D) (u2_combgras (k1_combgras A B) (k1_combgras A B) D)) = (k8_combgras A B E))  =>  ((g1_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) (u1_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) C) (u2_combgras (k1_combgras (k2_nat_1 A 1) B) (k1_combgras (k2_nat_1 A 1) B) C)) = (k8_combgras (k2_nat_1 A 1) B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_complex1 (k2_xcmplx_0 A B)) = (k8_complex1 (k15_complex1 A) (k15_complex1 B))) ) ) ) ) ).
tt(t32_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k17_complex1 (k1_complex2 A B)) = (k8_real_1 (k17_complex1 A) (k17_complex1 B))) ) ) ) ) ).
tt(t32_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_vectsp_1 k1_complfld (k11_algstr_0 k1_complfld A) (k11_algstr_0 k1_complfld B)) = (k3_vectsp_1 k1_complfld B A)) ) ) ) ) ) ) ) ) ).
tt(t32_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_valued_1 A B) = (k17_seq_4 (k3_finseq_1 A))) )  =>  ( (A = (k30_valued_1 B))  &  (B = (k30_valued_1 A)) ) ) ) ) ) ) ).
tt(t32_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v8_compl_sp (k3_pcomps_1 A)) => (v1_tbsp_1 A)) ) ) ).
tt(t32_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((k9_xtuple_0 (k6_compos_1 A C B)) = (k9_xtuple_0 (k61_valued_1 C B))) ) ) ) ) ) ) ).
tt(t32_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  ((k62_valued_1 (k2_compos_2 A (k3_compos_2 A B C) D)) = 3) ) ) ) ) ) ) ) ) ).
tt(t32_comptrig,ax, ((k10_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t32_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k19_margrel1 (k3_comput_1 A B)) = A) ) ) ) ) ).
tt(t32_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B) (k51_valued_1 k5_numbers k2_numbers k2_numbers C D)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A C) (k19_valued_1 k5_numbers k2_numbers k2_numbers B D)))) ) ) ) ) ) ) ) ).
tt(t32_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k9_complex1 (k15_complex1 (k3_comseq_2 A)) (k15_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t32_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_funct_2 k5_numbers k1_numbers (k1_valued_0 k1_numbers (k3_series_1 (k7_comseq_3 A)) B) (k7_comseq_3 (k1_valued_0 k2_numbers (k10_comseq_3 A) B))) & (r2_funct_2 k5_numbers k1_numbers (k1_valued_0 k1_numbers (k3_series_1 (k8_comseq_3 A)) B) (k8_comseq_3 (k1_valued_0 k2_numbers (k10_comseq_3 A) B)))) ) ) ) ) ).
tt(t32_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  ((k1_binop_1 (k9_conlat_1 A) B C) = (k1_binop_1 (k9_conlat_1 A) C B)) ) ) ) ) ) ) ).
tt(t32_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_connsp_1 B A) &  (B = (k1_struct_0 A)) ) ) ) ) ) ) ).
tt(t32_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ((r1_tarski C B) =>  ((k4_connsp_3 A (k5_connsp_3 A B C) B) = C) ) ) ) ) ) ) ) ).
tt(t32_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_convex1 A B 1) = B) ) ) ) ) ).
tt(t32_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((r1_convex4 A (k5_convex4 A B C) (k2_convex4 A)) => (r1_convex4 A C (k8_convex4 A B))) ) ) ) ) ) ) ).
tt(t32_cqc_lang,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (B = D) )  =>  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 B C)) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ).
tt(t32_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k7_cqc_lang A C D) E F G) (k15_cqc_sim1 A B)) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C E F G) (k15_cqc_sim1 A B)) & (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D (k30_qc_lang1 A E (k7_cqc_sim1 A C)) F G) (k15_cqc_sim1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) =>  ((r2_cqc_the1 A B C) => (r2_hidden (k3_cqc_the1 A C) (k1_cqc_the1 A B))) ) ) ) ) ) ) ).
tt(t32_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k10_cqc_lang A B C)) (k10_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t32_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r5_cqc_the3 A (k7_cqc_lang A B C) (k7_cqc_lang A C B))) ) ) ) ) ) ).
tt(t32_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k3_rlvect_1 A B C) (k5_algstr_0 A B C)) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k12_csspace A B B) (k12_csspace A B C)) (k12_csspace A C B)) (k12_csspace A C C))) ) ) ) ) ) ) ).
tt(t32_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v3_dickson A) &  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_finset_1 (k6_dickson A B)) &  (~ (v1_xboole_0 (k6_dickson A B))) ) ) ) )  => (v4_dickson A)) ) ) ).
tt(t32_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) A B) = (k7_real_1 (k9_diff_1 C A B) (k9_diff_1 D A B))) ) ) ) ) ) ) ) ) ).
tt(t32_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 F)) (k8_real_1 B F)) C)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k1_funct_1 (k4_diff_1 E D) F) = (k7_real_1 (k9_real_1 (k8_real_1 (k8_real_1 (k8_real_1 2 A) D) F) (k8_real_1 A (k5_square_1 D))) (k8_real_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_zfmisc_1 A B C) =>  ((k10_diff_1 D A B C) = (k10_diff_1 D A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t32_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k9_real_1 A B) k6_numbers))  &  (~  ((k1_seq_1 (k4_diff_1 k3_taylor_1 B) A) = (k1_seq_1 k3_taylor_1 (k7_real_1 1 (k13_complex1 B (k9_real_1 A B))))) ) ) ) ) ) ) ) ) ).
tt(t32_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( (D = E)  & (r3_waybel_4 (k5_yellow_0 A B) C D))  => (r3_waybel_4 A C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r3_diraf A B C D) &  ((r3_diraf A B C E) & (r3_diraf A B C F)) )  =>  ( (B = C)  | (r3_diraf A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k5_subset_1 A B C) = (a_3_5_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t32_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((v3_ec_pf_1 B A) <=>  ((k2_ec_pf_1 A B) = (k4_xcmplx_0 1)) ) ) ) ) ) ).
tt(t32_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( (D = E)  <=>  ( ((k4_ec_pf_2 A B C D) = (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E))  &  ( ((k5_ec_pf_2 A B C D) = (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E))  &  ((k6_ec_pf_2 A B C D) = (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ens_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ((v11_cat_1 B (k11_ens_1 A)) =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t32_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) D) |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 (k1_matrprob A C D))) =>  ((k1_funct_1 (k1_matrprob A C D) E) = (k1_funct_1 (k1_matrprob A C (k2_nat_1 D 1)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_enumset1 A A B C D) = (k2_enumset1 A B C D)) ) ) ) ) ).
tt(t32_eqrel_1,ax, (! [A:$i] :  ((m1_eqrel_1 A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ).
tt(t32_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (k4_equation A)) =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v4_msualg_1 D A) & (m1_msualg_2 D A B)) )  =>  ((r2_equation A B C) => (r2_equation A D C)) ) ) ) ) ) ) ) ) ).
tt(t32_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ( ((k3_relat_1 (k17_e_siec A) (k17_e_siec A)) = (k17_e_siec A))  &  ( ((k3_relat_1 (k4_xboole_0 (k17_e_siec A) (k4_relat_1 (k12_e_siec A))) (k17_e_siec A)) = k1_xboole_0)  &  ((k2_xboole_0 (k2_xboole_0 (k17_e_siec A) (k2_relat_1 (k17_e_siec A))) (k4_relat_1 (k12_e_siec A))) = (k2_xboole_0 (k14_e_siec A) (k2_relat_1 (k14_e_siec A)))) ) ) ) ) ).
tt(t32_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B (k4_struct_0 (k15_euclid A))) = k6_numbers) ) ) ) ) ).
tt(t32_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  ( (A = B)  &  ((k5_algstr_0 (k15_euclid 2) A B) = (k4_struct_0 (k15_euclid 2))) ) )  =>  ( (~ (r1_xxreal_0 k32_sin_cos (k3_euclid_3 (k5_algstr_0 (k15_euclid 2) A B))))  <=> (r1_xxreal_0 k32_sin_cos (k3_euclid_3 (k5_algstr_0 (k15_euclid 2) B A)))) ) ) ) ) ) ).
tt(t32_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k7_euclid A B C) (k7_euclid A B C)) = (k7_real_1 (k7_real_1 (k23_rvsum_1 B B) (k8_real_1 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t32_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k5_euclid_5 A (k5_euclid_5 B C)) = (k5_algstr_0 (k15_euclid 3) (k1_rlvect_1 (k15_euclid 3) B (k23_rvsum_1 A C)) (k1_rlvect_1 (k15_euclid 3) C (k23_rvsum_1 A B)))) ) ) ) ) ) ) ).
tt(t32_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden A (k5_jgraph_6 B C D)) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = E) )  &  ((r2_hidden E (k5_jgraph_6 B C D)) & (r2_hidden (k19_euclid B C) (k1_rltopsp1 (k15_euclid 2) A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_euclid_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~  ((k8_euclid_7 A) = k1_xboole_0) ) ) ) ).
tt(t32_euclid_8,ax, ((k6_euclid 3 k3_euclid_8) = (k1_euclid_8 k6_numbers (k19_binop_2 1) k6_numbers)) ).
tt(t32_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) D) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B D) (k1_rlvect_1 (k15_euclid A) C D))) ) ) ) ) ) ) ) ) ).
tt(t32_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r1_euclidlp A B C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~  (D = k6_numbers) )  &  (B = (k9_euclid A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D A) &  ((v1_funct_1 D) & (v1_exchsort D)) ) )  =>  ( ((r2_hidden B (k9_xtuple_0 D)) & (r2_hidden C (k9_xtuple_0 D)))  =>  ((k7_partfun1 A (k10_funct_7 D B C) C) = (k7_partfun1 A D B)) ) ) ) ) ) ) ).
tt(t32_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D (k2_nat_1 E 1)))) = (k2_compos_1 B))  =>  ( ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E))) = (k2_compos_1 B))  |  ( ((k8_extpro_1 A B C D) = (k2_nat_1 E 1))  & (r1_extpro_1 A B C D)) ) )  &  ( ( ((k8_extpro_1 A B C D) = (k2_nat_1 E 1))  & (r1_extpro_1 A B C D))  =>  ( (~  ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D E))) = (k2_compos_1 B)) )  &  ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D (k2_nat_1 E 1)))) = (k2_compos_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 B) (k2_msafree2 A)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 A C))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)))  =>  (! [G:$i] :  ((r2_hidden G (u1_struct_0 A)) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_funct_1 (k5_facirc_1 (k2_circcomb A B) (k3_circcomb A B C D) E H) G) = (k1_funct_1 (k5_facirc_1 A C F H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k3_facirc_2 A B C) (k4_facirc_2 A B C)))) => (v1_circuit2 (k5_facirc_1 (k3_facirc_2 A B C) (k4_facirc_2 A B C) D (k2_nat_1 1 (k4_nat_1 2 A))) (k3_facirc_2 A B C) (k4_facirc_2 A B C))) ) ) ) ) ) ) ) ).
tt(t32_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r2_hidden D (k1_relset_1 A (k2_partfun1 k1_numbers k1_numbers B A))) & (r2_hidden E (k1_relset_1 A (k2_partfun1 k1_numbers k1_numbers B A))))  => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k1_seq_1 B D) (k1_seq_1 B E))) (k4_real_1 C (k18_complex1 (k6_xcmplx_0 D E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k9_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 k16_sin_cos B)) (k8_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t32_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_sin_cos9) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k1_seq_1 k2_sin_cos9 B) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 (k1_seq_1 k30_sin_cos B) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t32_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k10_prob_1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k10_prob_1 A)) => (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) ) ) )  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A)))) ) ) ) ) ).
tt(t32_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 A))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ( ((k1_seq_1 D E) = (k7_real_1 B (k8_real_1 A E)))  &  ( (~  (A = k6_numbers) )  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 A))) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 A))) C) E) = (k10_prepower (k7_real_1 B (k8_real_1 A E)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ( (B = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C k24_sin_cos) (k1_taylor_1 2))) k3_taylor_1))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C k24_sin_cos) D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 B A) D) = (k10_real_1 (k7_real_1 1 (k1_seq_1 k24_sin_cos D)) (k9_real_1 1 (k1_seq_1 k24_sin_cos D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 B k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 B)) B)) ) ) ) ) ) ) ) ).
tt(t32_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k29_sin_cos) A) B) = (k7_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B)) B) (k10_real_1 (k1_seq_1 k3_taylor_1 B) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t32_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_fdiff_9) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k19_sin_cos B)) (k5_square_1 B))) (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos B) B) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t32_fib_num2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k6_xcmplx_0 (k4_nat_1 (k1_pre_ff (k7_nat_d A 1)) (k1_pre_ff (k2_nat_1 A 1))) (k1_pepin (k1_pre_ff A))) = (k1_newton (k4_xcmplx_0 1) A)) ) ) ).
tt(t32_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k3_fib_num3 A B k6_numbers) = A)  &  ( ((k3_fib_num3 A B 1) = B)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_fib_num3 A B (k2_nat_1 (k1_nat_1 C 1) 1)) = (k2_nat_1 (k3_fib_num3 A B C) (k3_fib_num3 A B (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(t32_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_fib_num3 (k3_xcmplx_0 2 A)) = (k2_int_1 (k3_power k1_fib_num (k3_xcmplx_0 2 A)))) ) ) ) ).
tt(t32_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k5_finseq_8 A B C) = (k1_finseq_8 A (k6_finseq_8 A B C) C)) ) ) ) ) ) ) ).
tt(t32_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden B (k5_filter_0 A C D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (B = (k4_lattices A E F))  &  ((r2_hidden E C) & (r2_hidden F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ((k9_xtuple_0 (k8_filter_1 A)) = (u1_struct_0 A))  &  ( ((k10_xtuple_0 (k8_filter_1 A)) = (u1_struct_0 A))  &  ((k1_relat_1 (k8_filter_1 A)) = (u1_struct_0 A)) ) ) ) ) ).
tt(t32_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_filter_2 A B) <=> (v1_filter_0 (k3_filter_2 A B) (k1_lattice2 A))) ) ) ) ) ).
tt(t32_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k7_finseq_1 (k7_finseq_1 A B) C) = (k7_finseq_1 A (k7_finseq_1 B C))) ) ) ) ) ) ) ).
tt(t32_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (m2_finseq_1 (k1_partfun1 k5_numbers A A B C D) B)) ) ) ) ) ) ).
tt(t32_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~  ((k10_xtuple_0 A) = k1_xboole_0) )  => (r2_hidden 1 (k1_relset_1 k5_numbers A))) ) ) ).
tt(t32_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r2_hidden B (k10_xtuple_0 A)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 (k1_finseq_3 A (k1_tarski B)))) =>  ( (~  ( ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A C))  & (r1_xxreal_0 (k4_finseq_4 A B) C)) )  &  ( ( (~ (r1_xxreal_0 (k4_finseq_4 A B) C))  =>  ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A C)) )  &  ( ( ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A (k1_nat_1 C 1)))  => (r1_xxreal_0 (k4_finseq_4 A B) C))  &  ((r1_xxreal_0 (k4_finseq_4 A B) C) =>  ((k1_funct_1 (k1_finseq_3 A (k1_tarski B)) C) = (k1_funct_1 A (k1_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) => (v1_xboole_0 (k2_rfinseq B A C))) ) ) ) ) ) ).
tt(t32_finseq_6,ax, (! [A:$i] :  ( ((k6_finseq_4 (k9_finseq_1 A) A) = k1_xboole_0)  &  ((k5_finseq_4 (k9_finseq_1 A) A) = k1_xboole_0) ) ) ).
tt(t32_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B))) ) )  =>  ((k1_finseq_7 A (k2_finseq_7 A B D E) D C) = (k2_finseq_7 A (k1_finseq_7 A B E C) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 F A) => (r2_relset_1 k5_numbers A (k2_finseqop A A A F E (k5_binop_1 A F B C)) (k2_finseqop A A A F (k2_finseqop A A A F E B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E (k6_fintopo2 A D)) &  ((r2_hidden F (k6_fintopo2 A D)) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden G (k6_fintopo2 A D)) & (r1_tarski G (k9_subset_1 (u1_struct_0 A) E F))) ) ) ) ) ) ) ) ) ) ) ) )  => (r1_tarski (k8_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C)) (k4_subset_1 (u1_struct_0 A) (k8_fintopo2 A B) (k8_fintopo2 A C)))) ) ) ) ) ) ) ).
tt(t32_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_fintopo3 A B k6_numbers) = B) ) ) ) ) ).
tt(t32_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_fintopo6 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ( (~  (B = (k1_struct_0 A)) )  &  ( (~  (C = (k1_struct_0 A)) )  &  ((v3_fin_topo B A) &  ((v3_fin_topo C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k7_flang_1 A B C) B) = (k6_flang_1 A B (k7_flang_1 A B C))) ) ) ) ) ) ).
tt(t32_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_2 A B C D) (k8_flang_1 A B))) ) ) ) ) ) ) ).
tt(t32_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k8_flang_1 A B)) = (k6_flang_1 A (k8_flang_1 A B) (k1_flang_3 A B C))) ) ) ) ) ) ).
tt(t32_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((k1_funct_1 (k8_fomodel0 B) A) = (k1_funct_1 (k5_fomodel0 (k3_finseq_2 B) (k11_monoid_0 B)) A)) ) ) ) ).
tt(t32_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_frechet A B C) => (r1_frechet2 A B C)) ) ) ) ) ) ) ).
tt(t32_frechet,ax, (~ (v1_frechet k3_frechet)) ).
tt(t32_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D B C)) )  =>  (~  ( (~  ((k7_fsm_1 B C D A) = (k7_fsm_1 B C D (k2_nat_1 A 1))) )  & (r1_xxreal_0 (k5_card_1 (k7_fsm_1 B C D (k2_nat_1 A 1))) (k5_card_1 (k7_fsm_1 B C D A)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_fsm_3 D B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  ((k3_rewrite3 B (k9_flang_1 B) (k2_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D) C (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D (k2_flang_1 B) A))) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D C A))) ) ) ) ) ) ) ) ).
tt(t32_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (v1_relat_1 (k3_msafree2 (k19_ftacell1 A B C D E)))) ) ) ) ) ).
tt(t32_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k9_xtuple_0 (k5_funcop_1 B D A))) =>  ((k1_funct_1 (k5_funcop_1 B D A) C) = (k1_binop_1 B D (k1_funct_1 A C))) ) ) ) ) ) ) ) ).
tt(t32_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (B = (k2_funct_1 A))  <=>  ( ((k9_xtuple_0 B) = (k10_xtuple_0 A))  &  (! [C:$i] :  (! [D:$i] :  ( ( ((r2_hidden C (k10_xtuple_0 A)) &  (D = (k1_funct_1 B C)) )  =>  ((r2_hidden D (k9_xtuple_0 A)) &  (C = (k1_funct_1 A D)) ) )  &  ( ((r2_hidden D (k9_xtuple_0 A)) &  (C = (k1_funct_1 A D)) )  =>  ((r2_hidden C (k10_xtuple_0 A)) &  (D = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski C A) =>  ( ( (B = k1_xboole_0)  &  (~  (A = k1_xboole_0) ) )  |  ((v1_funct_1 (k2_partfun1 A B D C)) &  ((v1_funct_2 (k2_partfun1 A B D C) C B) & (m1_subset_1 (k2_partfun1 A B D C) (k1_zfmisc_1 (k2_zfmisc_1 C B)))) ) ) ) ) ) ) ) ) ).
tt(t32_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v2_funct_1 A) => (r1_tarski (k7_relat_1 (k1_funct_3 A) B) (k8_relat_1 (k3_funct_3 A) B))) ) ) ) ).
tt(t32_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) => (r1_tarski A (k1_funct_4 A B))) ) ) ) ) ).
tt(t32_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( (~  ((k2_zfmisc_1 A B) = k1_xboole_0) )  &  ( ((k9_xtuple_0 D) = (k2_zfmisc_1 A B))  &  ((r2_hidden C B) &  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (~  ( ((k1_funct_1 (k3_funct_5 D) C) = E)  &  ( ((k9_xtuple_0 E) = A)  &  ((r1_tarski (k10_xtuple_0 E) (k10_xtuple_0 D)) &  (! [F:$i] :  ((r2_hidden F A) =>  ((k1_funct_1 E F) = (k1_binop_1 D F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k6_funct_6 B))) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C (k10_xtuple_0 B)) => (r2_hidden A (k9_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t32_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (C = D) )  =>  ((k1_funct_1 (k2_funct_7 A C B) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ).
tt(t32_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) & (r2_funct_8 A k1_numbers k1_numbers C))  => (r2_funct_8 A k1_numbers k1_numbers (k52_valued_1 k1_numbers k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t32_funct_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_int_1 A))  => (v1_funct_9 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k8_real_1 k32_sin_cos A))) ) ).
tt(t32_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_altcat_2 D) & (l1_altcat_1 D)) )  =>  (! [E:$i] :  ( ((v8_functor0 E A B) & (l2_functor0 E A B))  =>  (! [F:$i] :  ( ((v8_functor0 F B C) & (l2_functor0 F B C))  =>  (! [G:$i] :  ((l2_functor0 G C D) =>  ((k13_functor0 A B D E (k13_functor0 B C D F G)) = (k13_functor0 A C D (k13_functor0 A B C E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C B A) & (m2_functor0 C B A))  =>  (! [D:$i] :  ( ((v15_functor0 D B A) & (m2_functor0 D B A))  =>  (! [E:$i] :  ((m2_functor2 E B A C D) =>  ( ((r2_functor2 B A C D) &  ((r1_functor2 B A D C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (v3_altcat_3 (k2_functor2 B A C D E F) A (k3_functor0 B A C F) (k3_functor0 B A D F))) ) ) )  =>  ((r2_functor2 B A D C) &  (? [F:$i] :  ((m2_functor2 F B A D C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((k1_funct_1 F G) = (k1_altcat_3 A (k3_functor0 B A C G) (k3_functor0 B A D G) (k2_functor2 B A C D E G)))  & (v3_altcat_3 (k2_functor2 B A D C F G) A (k3_functor0 B A D G) (k3_functor0 B A C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k2_fuzzy_1 A B C) (k4_fuzzy_1 A)) <=>  ((r2_funct_2 A k1_numbers B (k4_fuzzy_1 A)) & (r2_funct_2 A k1_numbers C (k4_fuzzy_1 A))) ) ) ) ) ) ) ) ).
tt(t32_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_2 A B (k3_fuzzy_2 A C D)) (k3_fuzzy_2 A (k2_fuzzy_2 A B C) (k2_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t32_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers D B) (k3_funct_2 (u1_struct_0 A) k7_numbers D C)))  =>  ( (B = (k4_struct_0 A))  | (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers D (k1_vectsp_2 A C B)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  ( ((r2_hidden A (k4_finseq_1 (k7_fvsum_1 B E F))) &  ( (C = (k1_funct_1 E A))  &  (D = (k1_funct_1 F A)) ) )  =>  ((k1_funct_1 (k7_fvsum_1 B E F) A) = (k5_algstr_0 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~ (v1_xboole_0 (k26_gate_1 A B C D E F G)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_gcd_1 A B C (k5_struct_0 A)) = (k5_struct_0 A))  &  ((k5_gcd_1 A B (k5_struct_0 A) C) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t32_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_genealg1 B A) =>  (! [C:$i] :  ((m1_genealg1 C A) =>  ((k10_genealg1 A B C k6_numbers k6_numbers k6_numbers k6_numbers) = B) ) ) ) ) ) ) ).
tt(t32_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analmetr A D E B C) <=>  ((k4_geomtrap A B C D E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k13_gfacirc1 A B C)))) ) ) ).
tt(t32_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden B C) &  ((r2_hidden D C) & (r1_glib_000 A B D E)) )  => (r2_hidden E (k21_glib_000 A C))) ) ) ) ) ) ) ).
tt(t32_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ( ((k1_funct_1 (k7_glib_001 A B C) D) = (k1_funct_1 B D))  & (r2_hidden D (k1_relset_1 k5_numbers (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ( ((v4_glib_002 C A) & (m1_glib_000 C A))  =>  ( ((k24_glib_000 A B) = (k24_glib_000 A C))  <=> (r5_glib_000 B C)) ) ) ) ) ) ) ).
tt(t32_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) =>  ((k6_glib_003 (k12_glib_003 A B C)) = (k1_funct_4 (k6_glib_003 A) (k16_funcop_1 B C))) ) ) ) ) ) ).
tt(t32_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_glib_000 C A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k21_glib_000 A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)))) => (v1_glib_002 C)) ) ) ) ) ) ).
tt(t32_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k1_matrix_1 C)))) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 C))) &  ((r2_hidden (k2_nat_1 A 1) (k2_finseq_1 (k1_matrix_1 C))) &  ((r2_hidden B (k4_finseq_1 D)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D B) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C A))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D E) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C A))))  => (r1_xxreal_0 E B)) ) ) ) ) ) ) ) ) )  =>  ((r2_hidden (k2_nat_1 B 1) (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 B 1)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t32_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  => (r2_hidden (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B))))) ) ) ) ) ).
tt(t32_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 A)) 1)) ) ) ).
tt(t32_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1) (k19_euclid 1 1)) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 2)) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ).
tt(t32_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) |  ((k3_goboard5 C A B) = (a_3_0_gobrd11 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B C))) &  ((r1_xxreal_0 B (k3_finseq_1 C)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) C D)) ) )  =>  ( ((k3_gobrd13 C D (k2_nat_1 A B)) = (k3_gobrd13 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B C) D A))  &  ((k2_gobrd13 C D (k2_nat_1 A B)) = (k2_gobrd13 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B C) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  => (v2_compts_1 (k2_pre_topc (k15_euclid 2) (k3_goboard9 A)) (k15_euclid 2))) ) ).
tt(t32_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r1_henmodel A B D) & (r1_tarski B C))  => (r1_henmodel A C D)) ) ) ) ) ) ) ) ) ).
tt(t32_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_graph_1 B) & (l1_graph_1 B)) )  =>  (~  ((r1_partfun1 (u1_graph_1 A) (u1_graph_1 B)) &  ((r1_partfun1 (u2_graph_1 A) (u2_graph_1 B)) &  ((r1_tarski (k11_graph_1 (k5_graph_1 A B)) (k2_xboole_0 (k11_graph_1 A) (k11_graph_1 B))) &  ( (~ (r4_graph_1 A B))  &  (~ (r4_graph_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t32_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_graph_2 A (k12_finseq_1 (u1_struct_0 A) B) k1_xboole_0)) ) ) ) ).
tt(t32_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_graph_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((r1_graph_2 A D C) =>  ((v1_xboole_0 C) |  ((r2_hidden B (k10_xtuple_0 D)) <=>  (~  ((k7_graph_3 A B (k10_xtuple_0 C)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_graph_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ((v7_graph_1 F C) & (m2_graph_1 F C))  =>  ( ((r2_graph_5 C D E F A) & (r1_tarski A B))  => (r2_graph_5 C D E F B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((k1_seq_1 C A) = (k1_real_1 1)) )  =>  ( (A = (k2_nat_1 (k2_nat_1 (k4_nat_1 B B) (k4_nat_1 3 B)) 1))  |  ((k1_seq_1 (k6_graphsp (k16_graphsp B) C) A) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ).
tt(t32_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_grcat_1 A))  =>  (! [B:$i] :  ((m3_grcat_1 B (k18_grcat_1 A)) =>  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 A)) =>  ( ((k19_grcat_1 A B) = (k20_grcat_1 A C))  => (r2_hidden (k13_grcat_1 B C) (k18_grcat_1 A))) ) ) ) ) ) ) ).
tt(t32_gr_cy_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ( ((r1_int_2 A C) & (r2_int_1 A (k3_xcmplx_0 B B) C))  => (r1_int_2 B C)) ) ) ) ) ) ) ).
tt(t32_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k6_subset_1 (k9_xtuple_0 B) (k9_xtuple_0 C))) =>  ((k1_funct_1 (k6_subset_1 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ).
tt(t32_groeb_1,ax, (! [A:$i] :  ( ((v1_partfun1 A (k15_pre_poly k1_xboole_0)) &  ((v1_relat_2 A) &  ((v4_relat_2 A) &  ((v6_relat_2 A) &  ((v8_relat_2 A) &  ((v2_bagorder A k1_xboole_0) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly k1_xboole_0) (k15_pre_poly k1_xboole_0))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C (k11_polynom1 k1_xboole_0 B)) &  ((v2_ideal_1 C (k11_polynom1 k1_xboole_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 k1_xboole_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 k1_xboole_0 B)))))  =>  ((r1_tarski D C) =>  ( (D = (k1_groeb_1 k1_xboole_0 B (k7_polynom1 k1_xboole_0 B)))  | (r2_groeb_1 k1_xboole_0 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r3_groeb_2 A B C D E F G) => (r2_groeb_2 A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k5_groeb_3 A B C D E))) =>  ( ((k3_polynom1 A C (k5_groeb_3 A B C D E) F) = (k3_polynom1 A C D F))  &  ((k3_polynom1 A C (k6_groeb_3 A B C D E) F) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k2_group_11 A (k2_group_11 A B C) C)) & (r1_xboole_0 (k13_group_2 A C D) (k2_group_11 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t32_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A (k19_binop_2 1) B) = (k2_group_1 A B)) ) ) ) ) ).
tt(t32_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k4_group_2 A (k6_algstr_0 A C D) B) = (k4_group_2 A C (k4_group_2 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t32_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ((k3_group_3 A B C) = k1_xboole_0) )  <=>  ( (~  (B = k1_xboole_0) )  &  (~  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t32_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (m1_group_2 (k5_group_4 A B) (k5_group_4 A C))) ) ) ) ) ) ) ).
tt(t32_group_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_5 B (k5_group_1 B A C) D) = (k6_algstr_0 B (k5_group_1 B (k4_xcmplx_0 A) C) (k5_group_1 B A (k2_group_3 B C D)))) ) ) ) ) ) ) ) ) ).
tt(t32_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k2_group_1 A C)) = (k2_group_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t32_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  ((k1_group_1 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) = (k5_group_7 A B (k1_group_1 A) (k1_group_1 B))) ) ) ) ) ).
tt(t32_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) &  ((v4_group_9 D A B) & (m1_group_9 D A B)) )  =>  ((v4_group_9 (k19_group_9 A B C D) A B) & (m1_group_9 (k19_group_9 A B C D) A B)) ) ) ) ) ) ) ) ).
tt(t32_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_group_3 C B) & (m1_group_2 C B))  =>  (! [D:$i] :  ( ((v1_group_3 D B) & (m1_group_2 D B))  =>  (~  ((m1_group_6 D B (k10_group_5 B)) &  ((v3_groupp_1 C A) &  ((v3_groupp_1 D A) &  (! [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E B) & (m1_group_2 E B)) )  =>  (~  ( ((u1_struct_0 E) = (k7_group_4 B C D))  & (v3_groupp_1 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_hallmar1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  ( (? [C:$i] : (r1_hallmar1 A B C))  <=> (v1_hallmar1 B A)) ) ) ) ) ).
tt(t32_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (r2_hidden D B)) )  => (r1_xxreal_0 (k1_funct_1 (k6_weierstr A C) D) (k1_hausdorf A B C))) ) ) ) ) ) ) ) ) ).
tt(t32_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k13_glib_001 A (k2_helly A B C)) = (k13_glib_001 A (k2_helly A C B))) ) ) ) ) ) ) ).
tt(t32_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k4_bilinear k1_complfld A B C)) (k4_bilinear k1_complfld A B (k3_hermitan A B C)))) ) ) ) ) ) ).
tt(t32_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  ((r2_hidden k1_xboole_0 B) =>  (B = (k1_tarski k1_xboole_0)) ) ) ) ) ) ).
tt(t32_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r1_xxreal_0 A B))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k1_taylor_1 A) C) B) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 (k9_real_1 A B)) (k8_real_1 (k6_newton B A) (k3_newton B))) C))) ) ) ) ) ) ) ).
tt(t32_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  ((v6_ideal_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (v6_ideal_1 (k11_polynom1 B A))) ) ) ) ) ).
tt(t32_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((r2_hidden (k4_hilbert1 A B) k6_hilbert1) => (r2_hidden (k4_hilbert1 B A) k6_hilbert1)) ) ) ) ) ).
tt(t32_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k3_hilbert2 (k4_hilbert1 A B)) = (k6_trees_4 (k4_hilbert1 A B) (k3_hilbert2 A) (k3_hilbert2 B))) ) ) ) ) ).
tt(t32_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((k3_hilbert3 C (k3_hilbert1 A B)) = (k9_funct_2 (k3_hilbert3 C A) (k3_hilbert3 C B))) ) ) ) ) ) ) ).
tt(t32_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 C 1))  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k3_hurwitz A B 1) (k4_hurwitz A B C)) (k3_hurwitz A B C))) ) ) ) ) ) ) ).
tt(t32_idea_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ((r1_xxreal_0 4 (k3_finseq_1 A)) =>  ((k13_idea_1 (k13_idea_1 A)) = A) ) ) ) ).
tt(t32_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_ideal_1 C A B))  =>  (? [D:$i] :  ((m1_ideal_1 D A B) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k8_finseq_1 (u1_struct_0 A) D (k12_finseq_1 (u1_struct_0 A) E))) & (m1_ideal_1 (k12_finseq_1 (u1_struct_0 A) E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k2_incsp_1 A D B C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m5_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) C) =>  ((m4_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) C) =>  ((k16_index_1 A B C D) = (k14_index_1 A E B (k9_index_1 A C E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_instalg1 B A))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((k5_relat_1 (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A C)) (u1_struct_0 B)) = (k2_msualg_3 (u1_struct_0 B) (u3_msualg_1 B (k2_instalg1 A B C)))) ) ) ) ) ) ) ).
tt(t32_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k2_int_1 A) (k5_real_1 A 1)))  &  (~ (r1_xxreal_0 (k3_real_1 (k2_int_1 A) 1) A)) ) ) ) ).
tt(t32_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ( ((k6_int_1 (k1_int_2 A) (k1_int_2 B)) = (k6_int_1 A B))  &  ((k5_int_1 (k1_int_2 A) (k1_int_2 B)) = (k5_int_1 A B)) ) ) ) ) ) ) ).
tt(t32_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) => (r1_nat_d (k1_recdef_1 A B) (k3_wsierp_1 A))) ) ) ) ) ).
tt(t32_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) => (r2_int_1 (k1_funct_1 B D) (k1_funct_1 C D) A)) ) ) )  => (r2_int_1 (k19_rvsum_1 B) (k19_rvsum_1 C) A)) ) ) ) ) ) ) ).
tt(t32_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) => (r2_int_1 A (k1_funct_1 (k1_int_6 A B) C) (k1_funct_1 B C))) ) ) ) ) ) ) ).
tt(t32_integr11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  ( (~  ((k8_real_1 A (k7_real_1 C 1)) = k6_numbers) )  =>  ((k2_integra5 D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A B) (k1_taylor_1 C))) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A B) (k1_taylor_1 (k7_real_1 C 1))) (k10_real_1 1 (k8_real_1 A (k7_real_1 C 1)))) (k4_seq_4 D)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A B) (k1_taylor_1 (k7_real_1 C 1))) (k10_real_1 1 (k8_real_1 A (k7_real_1 C 1)))) (k5_seq_4 D)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 D G) = (k9_binop_2 (k11_binop_2 A G) B)) ) ) )  &  ( (F = (k1_relset_1 k1_numbers E))  & (r2_relset_1 k1_numbers k1_numbers E (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) A) (k3_rfunct_1 k1_numbers k1_numbers D (k41_valued_1 k1_numbers k1_numbers k16_sin_cos))))) ) )  =>  ((k2_integra5 C E) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k30_sin_cos) (k4_seq_4 C)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers D k30_sin_cos) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k41_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos)))) &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k30_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t32_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k19_sin_cos D)) D) (k10_real_1 (k8_real_1 (k1_seq_1 k3_taylor_1 D) (k1_seq_1 k16_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t32_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr15 A (k3_integra5 B C) G) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) G (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) &  ((r2_hidden E (k3_integra5 B C)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 (k3_xxreal_0 D E) (k4_xxreal_0 D E))) => (r1_xxreal_0 (k12_euclid (k7_partfun1 (k1_euclid A) G H)) F)) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k12_euclid (k12_integr15 D E A G)) (k11_binop_2 (k11_binop_2 A F) (k18_complex1 (k10_binop_2 E D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (~  ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_measure5 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( (D = (k1_rcomp_1 (k5_seq_4 B) (k1_seq_1 C A)))  &  ( (E = (k1_rcomp_1 (k1_seq_1 C A) (k4_seq_4 B)))  &  (B = (k4_subset_1 k1_numbers D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) )  => (r1_xxreal_0 k6_numbers (k12_integra1 A B))) ) ) ) ) ).
tt(t32_integra8,ax, ((k2_fdiff_1 k24_sin_cos k1_numbers) = k24_sin_cos) ).
tt(t32_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A A)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers B B)) & (r1_integra9 C A B)) ) ) ) ) ) ) ) )  =>  ((k1_integra9 C (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) = (k7_real_1 (k1_integra9 C A A) (k1_integra9 C B B))) ) ) ) ) ) ) ) ).
tt(t32_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_interva1 D A))  => (r1_interva1 A (k3_interva1 A B (k4_interva1 A C D)) (k4_interva1 A (k3_interva1 A B C) (k3_interva1 A B D)))) ) ) ) ) ) ) ) ).
tt(t32_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ( ((r2_hidden (k3_intpro_1 A (k3_intpro_1 B C)) k8_intpro_1) & (r2_hidden B k8_intpro_1))  => (r2_hidden (k3_intpro_1 A C) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t32_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_xcmplx_0 (k9_newton A) (k1_seq_1 k5_irrat_1 B)) = (k13_complex1 (k9_newton A) (k9_newton B))) ) ) ) ) ).
tt(t32_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k5_isocat_1 A B C E E D (k6_nattra_1 B C E)) (k6_nattra_1 A C (k9_cat_1 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  (! [E:$i] :  ((m2_cat_1 E A (k8_cat_2 B C)) =>  ( ((r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_isocat_2 A B C D) (k9_isocat_2 A B C E)) & (r2_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k10_isocat_2 A B C D) (k10_isocat_2 A B C E)))  => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 (k8_cat_2 B C)) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k2_borsuk_5 C D)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k1_tops_1 k3_topmetr A) = (k2_rcomp_1 k2_xxreal_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) (k7_real_1 (k18_complex1 (k9_real_1 (k17_euclid A) (k17_euclid B))) (k18_complex1 (k9_real_1 (k18_euclid A) (k18_euclid B)))))) ) ) ) ).
tt(t32_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 1 (k18_euclid C))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t32_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = k6_numbers) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B E) = F)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C E) = G) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) D E) = (k4_real_1 G (k7_square_1 (k7_real_1 1 (k3_square_1 (k7_xcmplx_0 F G)))))) ) ) ) ) ) ) )  & (v5_pre_topc D A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_1_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jgraph_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 k3_topmetr) A B) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 B)) ) )  => (v5_pre_topc A (k15_euclid 2) k3_topmetr)) ) ) ).
tt(t32_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))) = (k1_tarski (k19_euclid B C))) ) ) ) ) ) ) ) ) ) ).
tt(t32_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 B) (k1_rltopsp1 (k15_euclid 2) C D)) = (k1_tarski A))  & (r1_subset_1 (k10_xtuple_0 B) (k1_rltopsp1 (k15_euclid 2) C D)))  =>  ( ( (~  ((k17_euclid C) = (k17_euclid D)) )  &  (~  ((k18_euclid C) = (k18_euclid D)) ) )  |  ((r2_hidden C (k3_topreal1 2 B)) |  ((r2_hidden D (k3_topreal1 2 B)) |  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 B)) E) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_jordan1h A B) &  ((r1_xxreal_0 B C) & (r1_xboole_0 (k3_goboard9 (k1_jordan13 A B)) (k3_goboard9 (k1_jordan13 A C)))) ) ) ) ) ) ) ) ) ).
tt(t32_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan18,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) &  ((r2_hidden C A) & (r1_jordan18 2 A B C D E)) )  =>  ( (B = C)  | (r1_jordan18 2 A D E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 D A)) C) |  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2) 1))  &  (~ (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 D B)) (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_7_jordan1 A B C D))  => (v2_connsp_1 E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_jordan1b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k1_jordan1a (k1_jordan8 B A)) (k3_finseq_1 (k1_jordan8 B A)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t32_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 1 C) (k10_xtuple_0 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t32_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e B A) 2)) = (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ).
tt(t32_jordan1h,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (A = (k1_goboard2 (k7_pre_poly k1_numbers (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A)) k1_jordan1h) (k7_pre_poly k1_numbers (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) A)) k1_jordan1h))) ) ) ).
tt(t32_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k9_pscomp_1 B) (k9_pscomp_1 A)))  =>  ((k24_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k24_pscomp_1 A)) ) ) ) ) ) ).
tt(t32_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 B C B D) A) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A B) (k19_euclid C D))) ) ) ) ) ) ) ) ) ).
tt(t32_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k1_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k7_pscomp_1 A))))) ) ).
tt(t32_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k22_pscomp_1 A) (k4_jordan19 A))) ) ).
tt(t32_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_topreal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (v2_topreal1 (k2_jordan3 A B))) ) ) ) ) ) ).
tt(t32_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ( (B = (k1_funct_1 A 1))  | (r1_jordan3 (k3_jordan3 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) B)) ) ) ) ) ) ).
tt(t32_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B C))  =>  ((r1_xxreal_0 (k3_finseq_1 A) C) | (r2_jordan4 A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C B) C B)) ) ) ) ) ) ) ) ).
tt(t32_jordan5b,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  (C = (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A))))) ) )  => (r1_topreal4 C (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B (k1_matrix_1 (k2_goboard2 A))))) ) ) ) ) ) ) ).
tt(t32_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden A (k3_topreal1 2 B)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 B)))) )  => (r1_xxreal_0 (k17_euclid A) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) (k3_finseq_1 (k2_goboard2 B)) C)))) ) ) ) ) ) ) ).
tt(t32_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k7_jordan6 A)) <=>  ((k18_euclid B) = A) ) ) ) ) ) ).
tt(t32_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((v2_connsp_1 B (k15_euclid 2)) =>  ((k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) 1)) ) ) ) ) ) ).
tt(t32_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_jordan_a 2 (k2_jordan_a A C B)) (k4_jordan_a A B))) ) ) ) ) ) ).
tt(t32_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((k2_relset_1 (u1_struct_0 A) D) = (k2_relset_1 (u1_struct_0 A) (k2_borsuk_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t32_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_abian (u1_struct_0 A) C B) &  ((r2_abian (u1_struct_0 A) D B) &  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r1_ordinal1 (k1_card_1 E) (k1_card_1 (u1_struct_0 A))) &  ((r2_abian (u1_struct_0 A) (k5_knaster A B (k3_lattices A C D) E) B) &  ((r3_lattices A C (k5_knaster A B (k3_lattices A C D) E)) & (r3_lattices A D (k5_knaster A B (k3_lattices A C D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) = (k1_tops_1 k3_topmetr k6_kurato_1)) ) ).
tt(t32_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B D))) )  &  ((m2_valued_0 C (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A) &  (! [D:$i] :  ((m2_valued_0 D (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B) =>  (~  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) C E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) B B) =>  ( ((r2_hidden A (k2_finseq_1 B)) & (r2_hidden C (k2_finseq_1 B)))  =>  ((k13_fvsum_1 D (k8_matrix_1 (u1_struct_0 D) (k5_matrix_1 B (u1_struct_0 D) (k7_laplace B D E)) A) (k9_matrix_1 (u1_struct_0 D) E C)) = (k12_matrix_3 B D (k3_matrix11 A B B (u1_struct_0 D) (k5_matrix_1 B (u1_struct_0 D) E) (k8_matrix_1 (u1_struct_0 D) (k5_matrix_1 B (u1_struct_0 D) E) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (m4_vectsp_8 (k3_latsubgr A B C) (k11_group_4 A) (k11_group_4 B))) ) ) ) ) ) ).
tt(t32_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) => (r3_lattices A (k3_funct_2 C (u1_struct_0 A) E F) B)) ) )  =>  ( (D = k1_xboole_0)  | (r3_lattices A (k2_lattice2 C A D E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] : (r3_lattices A (k15_lattice3 A (a_3_2_lattice3 A B C)) (k4_lattices A B (k15_lattice3 A C)))) ) ) ) ) ).
tt(t32_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_lattice4 D A) =>  ( ((r2_hidden B D) & (r2_hidden C D))  => (r2_hidden (k3_lattices A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t32_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_lattice5 F A B E) =>  ((r1_ordinal1 C D) => (r1_relset_1 (k2_zfmisc_1 (k8_lattice5 A C) (k8_lattice5 A C)) (u1_struct_0 B) (k12_lattice5 A B E F C) (k12_lattice5 A B E F D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow11 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_lattice8 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k3_tarski (a_2_0_lattice8 A B)))  =>  ((v1_funct_1 (k3_tarski (a_2_1_lattice8 A B))) &  ((v1_funct_2 (k3_tarski (a_2_1_lattice8 A B)) (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 (k3_tarski (a_2_1_lattice8 A B)) C A) &  ((v2_lattice5 (k3_tarski (a_2_1_lattice8 A B)) C A) &  ((v3_lattice5 (k3_tarski (a_2_1_lattice8 A B)) C A) & (m1_subset_1 (k3_tarski (a_2_1_lattice8 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B (k15_glib_000 A)) =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))) = B) ) ) ) ) ) ).
tt(t32_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k9_lfuzzy_0 A (k1_yellow_0 (k4_lfuzzy_0 A) B) C) = (k1_yellow_0 (k1_lfuzzy_0 (k1_rcomp_1 k6_numbers 1)) (k5_card_3 C B))) ) ) ) ) ) ) ).
tt(t32_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) =>  ((v2_seq_2 A) | (v2_limfunc1 A)) ) ) ) ).
tt(t32_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  & (r2_hidden D (k1_relset_1 k1_numbers B))) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C)))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k2_rcomp_1 A (k7_real_1 A C))))) ) ) ) ) )  | (r6_limfunc2 B A)) ) ) ) ) ) ).
tt(t32_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc3 B A) =>  ((r1_limfunc3 (k32_valued_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc3 (k32_valued_1 k1_numbers k1_numbers B) A) = (k1_real_1 (k1_limfunc3 B A))) ) ) ) ) ) ) ).
tt(t32_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r3_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k5_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  | (v8_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t32_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A C D) => (r1_lmod_6 A C (k1_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) &  ((v2_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ( (D = C)  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E)) (k8_real_1 (k1_normsp_0 (k16_lopban_1 A B) C) (k1_normsp_0 A E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k2_power D (k1_seq_1 (k4_normsp_0 A B) D))) ) )  &  ((v2_comseq_2 C) &  ( (~ (r1_xxreal_0 (k2_seq_2 C) 1))  & (v2_lopban_3 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t32_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) & (r1_xxreal_0 D (k18_complex1 (k8_nat_1 k1_numbers (k3_series_1 (k4_normsp_0 A (k8_lopban_4 A B C F))) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lopclset,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) ) )  =>  (~  ( ((k7_lopclset B) = (k3_tarski A))  &  ((m1_subset_1 A (k1_zfmisc_1 (k10_lopclset B))) &  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (~  ((k7_lopclset B) = (k3_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r1_lpspace1 B C D E F) => (r1_lpspace1 B C D (k26_valued_1 B k1_numbers E A) (k26_valued_1 B k1_numbers F A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ( ((k4_struct_0 (k2_lpspace2 A B C D)) = (k8_lpspace1 A k6_numbers))  & (r2_hidden (k4_struct_0 (k2_lpspace2 A B C D)) (k3_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t32_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_hilbert1 k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_hilbert1 k6_margrel1)))) )  =>  ( (! [E:$i] :  ((r2_hidden E k1_hilbert1) =>  ((k1_funct_1 D E) = (k1_funct_1 (k11_ltlaxio1 C) (k4_tarski B E))) ) )  =>  ((k3_funct_2 k1_hilbert1 k6_margrel1 (k12_ltlaxio1 D) A) = (k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t32_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k6_cqc_lang A B)) (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ).
tt(t32_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 A) (k6_rusub_4 A B D) (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t32_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 A k6_numbers) & (v4_matrix10 C))  => (v3_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t32_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_matrix_2 H (k12_matrix_2 A)) =>  ( ((r2_hidden E (k2_finseq_1 A)) &  ( ((k3_finseq_1 F) = A)  &  ((k3_finseq_1 G) = A) ) )  =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 B) A A) =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I (k3_fvsum_1 B (k9_fvsum_1 B F C) (k9_fvsum_1 B G D)))) H) = (k3_rlvect_1 B (k8_group_1 B C (k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I F)) H)) (k8_group_1 B D (k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) I G)) H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (~  ((v2_funct_1 B) &  ((v2_funct_1 C) &  ( ((k10_xtuple_0 B) = (k10_xtuple_0 C))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  (~  (C = (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers k5_numbers D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B D) = C)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  =>  ( (E = D)  |  ((k1_funct_1 B E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) )  =>  ((k4_rlvect_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t32_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k3_matrix15 (u1_struct_0 B) (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = (k1_matrix_3 B A 1)) ) ) ) ) ).
tt(t32_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v2_matrix16 B (u1_struct_0 A)) =>  ((k1_matrix16 (u1_struct_0 A) (k5_fvsum_1 A B)) = (k1_matrix_6 (k3_finseq_1 B) A (k1_matrix16 (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(t32_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k14_matrix_1 B A (k14_matrix_1 B A C D) E) = (k14_matrix_1 B A C (k14_matrix_1 B A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B C) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B C) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 C)) =>  ( ( (! [I:$i] :  ((m1_subset_1 I C) =>  ((k3_funct_2 C A F I) = (k7_setwiseo B A D G (k10_funct_5 C B A (k9_funct_2 B A) (k12_funct_5 B C A E) I))) ) )  &  ((v1_setwiseo D A) &  ((v1_binop_1 D A) & (v2_binop_1 D A)) ) )  =>  ((k7_setwiseo (k2_zfmisc_1 B C) A D (k8_matrix_3 B C G H) E) = (k7_setwiseo C A D H F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A B (k1_matrix_4 A C D)) = (k3_matrix_3 A (k1_matrix_4 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ((v3_matrix_6 C B A) => (v3_matrix_6 (k1_matrix_6 B A C) B A)) ) ) ) ) ) ) ).
tt(t32_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = A)  &  (E = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) k5_numbers (u1_struct_0 B) C D)) )  => (r2_classes1 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v4_matrix_8 C A B) & (v1_matrix_8 C A B))  =>  (C = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t32_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  ( (A = (k3_finseq_4 k5_numbers 3 2 1))  => (v4_matrix_2 A 3)) ) ) ).
tt(t32_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k5_matrixc1 (k10_seq_4 A B) C) = (k10_seq_4 (k5_matrixc1 A C) (k5_matrixc1 B C))) ) ) ) ) ) ) ) ).
tt(t32_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  (C = (k6_matrix13 A (k13_matrixj1 A B (k3_matrixj1 A (k4_matrixj1 A C) D)) (k2_finseq_1 (k3_finseq_1 C)) (k2_finseq_1 (k1_matrix_1 C)))) ) ) ) ) ) ) ) ) ).
tt(t32_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_polynom5 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (? [D:$i] :  ( ((v2_relat_1 D) &  ((v1_matrixj2 D B) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B))))) )  &  (? [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) &  ( ((k2_wsierp_1 (k10_matrixj1 (u1_struct_0 B) D)) = A)  &  ((v1_matrix_6 E A B) &  (C = (k4_matrix_3 B (k4_matrix_3 B E (k20_matrixj1 (u1_struct_0 B) (k4_struct_0 B) D)) (k5_matrix_6 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k7_matrixr1 1 A) = A) ) ) ).
tt(t32_matrixr2,ax, (! [A:$i] :  ((m1_matrix_1 A k1_numbers 2 2) =>  ((k3_matrixr2 2 A) = (k9_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 1) (k3_matrix_1 k1_numbers A 2 2)) (k8_real_1 (k3_matrix_1 k1_numbers A 1 2) (k3_matrix_1 k1_numbers A 2 1)))) ) ) ).
tt(t32_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A C) =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k1_xboole_0))  =>  ((k2_matrix15 (u1_struct_0 A) (k9_matrlin A B E (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k4_matrlin2 A C B D E G) F))) = (k4_matrix_3 A (k2_matrix15 (u1_struct_0 A) (k9_matrlin A C D F)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  ((k4_rlvect_1 B (k6_matrlin B C)) = (k4_rlvect_1 B (k6_matrlin B (k4_matrix_1 (u1_struct_0 B) C)))) ) ) ) ) ) ) ).
tt(t32_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k6_matroid0 A B) (k6_matroid0 A C))) ) ) ) ) ) ) ).
tt(t32_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k14_rvsum_1 (k5_finseq_2 k5_numbers (k3_finseq_1 A) 1) A) = A) ) ) ).
tt(t32_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) (k1_matrix_1 D) C) =>  (~  ( ( (A = k6_numbers)  =>  (B = k6_numbers) )  &  ( ( (B = k6_numbers)  =>  (C = k6_numbers) )  &  (~  ((k1_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid (k1_matrix_1 D))) (u1_struct_0 (k15_euclid C)) (k3_matrtop1 A B D) (k3_matrtop1 (k1_matrix_1 D) C E)) = (k3_matrtop1 (k3_finseq_1 D) (k1_matrix_1 E) (k5_matrix_3 A B C k2_vectsp_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 C (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v2_matrtop3 C A) &  ((k2_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C D) = (k6_partfun1 D)) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden E (k2_finseq_1 A)) & (r1_struct_0 (k1_rlvect_3 (k15_euclid A) D) (k6_matrixr2 A E)))  =>  ((k1_seq_1 (k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C B) E) = (k1_seq_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D C) => (r2_pboole A D B)) ) )  => (r2_pboole A (k2_mboolean A C) B)) ) ) ) ) ) ).
tt(t32_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k3_zfmisc_1 A B C) = (k3_zfmisc_1 D E F))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ( (C = k1_xboole_0)  |  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_tarski D E) =>  ((r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C D)) |  ((k12_supinf_2 C (k3_measure1 A B E D)) = (k4_supinf_2 (k12_supinf_2 C E) (k12_supinf_2 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_measure6,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( (B = C)  =>  ((k7_supinf_2 (k2_measure6 A B)) = (k3_supinf_2 C (k7_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t32_measure8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ( (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_prob_1 A B) k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A (k9_prob_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_prob_1 A B) k7_numbers)))) ) ) ) )  & (r1_measure8 A B (k9_prob_1 A B) C D)) )  => (v1_measure8 C A B)) ) ) ) ) ) ) ).
tt(t32_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k7_member_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(t32_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v2_membered B))  => (v2_membered (k1_setfam_1 A))) ) ) ).
tt(t32_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  => (r1_tarski (k9_xtuple_0 C) (k2_xboole_0 (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) (k9_xtuple_0 (k6_memstr_0 A B C))))) ) ) ) ) ) ).
tt(t32_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r2_mesfun6c A B C D) & (r2_mesfun6c A B C E))  => (r2_hidden (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers D E)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A k1_numbers (k5_comseq_3 A (k19_valued_1 A k2_numbers k2_numbers B C)) (k47_valued_1 A k1_numbers k1_numbers (k20_valued_1 A k1_numbers k1_numbers (k5_comseq_3 A B) (k5_comseq_3 A C)) (k20_valued_1 A k1_numbers k1_numbers (k6_comseq_3 A B) (k6_comseq_3 A C)))) & (r2_relset_1 A k1_numbers (k6_comseq_3 A (k19_valued_1 A k2_numbers k2_numbers B C)) (k3_valued_1 A k1_numbers k1_numbers (k20_valued_1 A k1_numbers k1_numbers (k6_comseq_3 A B) (k5_comseq_3 A C)) (k20_valued_1 A k1_numbers k1_numbers (k5_comseq_3 A B) (k6_comseq_3 A C))))) ) ) ) ) ) ) ).
tt(t32_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((v1_mesfunc8 C A k2_numbers) =>  ((k1_relset_1 A (k4_mesfunc5 A k2_numbers (k3_mesfun9c A C) B)) = (k1_relset_1 A (k4_mesfunc5 A k2_numbers C k6_numbers))) ) ) ) ) ) ) ) ).
tt(t32_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k9_xtuple_0 C)))  => (r2_hidden (k9_subset_1 A (k9_subset_1 A D (k17_mesfunc1 A C (k1_measure6 E))) (k15_mesfunc1 A C (k1_measure6 F))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v3_valued_0 B) => (m1_subset_1 (k2_relset_1 k7_numbers B) (k1_zfmisc_1 k1_numbers))) ) ) ) ) ).
tt(t32_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B D) &  ( ((k1_relset_1 A D) = k1_xboole_0)  &  (! [E:$i] :  ( ((v1_prob_2 E) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ((m2_finseq_1 F k7_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  (~  ((r1_mesfunc3 A B D E F) &  ( ((k12_supinf_2 F 1) = k6_numbers)  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r1_xxreal_0 2 H) & (r2_hidden H (k1_relset_1 k5_numbers F)))  =>  ( (~ (r1_xxreal_0 (k12_supinf_2 F H) k6_numbers))  &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 F H))) ) ) ) )  &  ( ((k1_relset_1 k5_numbers G) = (k1_relset_1 k5_numbers E))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k1_relset_1 k5_numbers G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k12_supinf_2 F H) (k12_supinf_2 (k4_finseqop B k7_numbers E C) H))) ) ) )  &  ((k4_extreal1 G) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k19_rfunct_3 A B) C))) ) ) ) ) ) ).
tt(t32_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v2_mesfunc9 B A) &  ((v1_mesfunc8 B A k7_numbers) &  ((r1_tarski E (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) & (r2_hidden D E)) ) )  =>  ((k1_mesfunc9 (k2_mesfunc9 (k3_mesfunc5 A B D)) C) = (k1_mesfunc9 (k3_mesfunc5 A (k4_mesfunc9 A B) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_metric_1,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_metric_1 A B C D) & (r1_metric_1 A B D E))  =>  ((r1_metric_1 A B C E) & (r1_metric_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r4_metric_2 A B C D) & (r4_metric_2 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_midsp_1 A) = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B B))) ) ) ) ) ).
tt(t32_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (u1_midsp_2 A B))) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k9_midsp_2 A B C E) = D) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k9_midsp_2 A B C D) = (k9_midsp_2 A B C E))  =>  (D = E) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_algstr_0 (u1_midsp_2 A B) (k9_midsp_2 A B C D) (k9_midsp_2 A B D E)) = (k9_midsp_2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 C) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 C))) =>  (! [F:$i] :  ( ((v4_midsp_2 F C) & (l1_midsp_2 F C))  =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 (u1_midsp_2 C F)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C F)))) =>  ( ( ((k7_midsp_3 A C F D G) = E)  & (r1_xxreal_0 B A))  =>  ((k7_midsp_3 A C F D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C F)) (k2_nat_1 A 1) G (k2_nat_1 B 1) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C F)) G B))) = (k6_midsp_3 A C E (k2_nat_1 B 1) (k5_midsp_3 A (u1_struct_0 C) E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_mmlquery A (k20_mmlquery A C D) B) = (k16_mmlquery A (k1_mmlquery A C B) (k1_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t32_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_mod_4 C A B) <=> (v6_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t32_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k3_modal_1) =>  ( ((k16_modal_1 A) = (k16_modal_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t32_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((k51_modelc_1 A B C (k52_modelc_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t32_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_modelc_2 A B) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t32_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) & (l1_modelc_3 C B))  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) & (l1_modelc_3 D B))  =>  ((r1_modelc_3 B D C A) => (r2_hidden A (u1_modelc_3 B C))) ) ) ) ) ) ) ) ) ).
tt(t32_moebius1,ax, ((k2_moebius1 3) = (k1_real_1 1)) ).
tt(t32_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ((v5_group_1 A) => (v5_group_1 B)) ) ) ) ) ).
tt(t32_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k13_monoid_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k13_monoid_1 A))) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k15_monoid_1 A B D) = (k15_monoid_1 A C D)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t32_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A B) (k6_subset_1 (u1_struct_0 A) C)) = (k6_subset_1 (u1_struct_0 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A B) C)))  &  ((k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A B) (k6_subset_1 (u1_struct_0 A) C)) = (k6_subset_1 (u1_struct_0 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A B) C))) ) ) ) ) ) ) ) ).
tt(t32_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) => (r2_pboole (u1_struct_0 A) (k4_msafree3 A B (k8_msaterm A B C D)) (k4_msafree3 A B C))) ) ) ) ) ) ) ) ).
tt(t32_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 C F)) =>  ( (D = (k1_trees_4 (k4_tarski G F)))  => (r1_msaterm A B C D E (k2_trees_4 (k1_funct_1 (u3_msualg_1 A B) F) (k3_funct_2 (k1_funct_1 C F) (k1_funct_1 (u3_msualg_1 A B) F) (k1_msualg_3 (u1_struct_0 A) C (u3_msualg_1 A B) E F) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ((m3_pboole D B (k1_mboolean B C)) =>  ((r2_hidden A B) => (m1_subset_1 (k1_funct_1 D A) (k1_zfmisc_1 (k1_zfmisc_1 (k1_funct_1 C A))))) ) ) ) ) ) ) ).
tt(t32_mssublat,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v2_unialg_2 A) & (l1_unialg_1 A)) ) ) ) )  => (r1_filter_1 (k12_unialg_2 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) (k17_msualg_2 (k6_msualg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A))) (k9_msualg_1 (g1_unialg_1 (u1_struct_0 A) (u1_unialg_1 A)))))) ) ).
tt(t32_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v2_binop_1 (k16_msualg_2 A B) (k14_msualg_2 A B))) ) ) ) ).
tt(t32_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) => (v4_msualg_6 (k6_msualg_6 A B (k7_msualg_6 A B C)) A B)) ) ) ) ) ) ).
tt(t32_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r2_pboole (u1_struct_0 A) C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((r2_hidden (k4_tarski F G) (k2_msualg_4 A B C E)) =>  ((r1_tarski (k3_msualg_4 A B C E F) (k3_msualg_4 A B D E G)) &  ((v4_msualg_1 B A) => (r1_tarski (k3_msualg_4 A B C E G) (k3_msualg_4 A B D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ((r2_hidden (k4_tarski B C) (u1_orders_2 (k5_mycielsk A))) <=>  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t32_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 8) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  (~  (A = 8) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((k11_nat_3 (k1_newton C A) B) = (k24_binop_2 A (k11_nat_3 C B))) ) ) ) ) ) ) ).
tt(t32_nat_4,ax,(v1_int_2 43)).
tt(t32_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ( ((r1_nat_d A C) & (r1_nat_d B C))  =>  ( (C = A)  |  ( (C = B)  |  ( (A = 1)  |  ( (B = 1)  |  ( (A = B)  | (r1_xxreal_0 (k23_binop_2 (k23_binop_2 (k23_binop_2 1 A) B) C) (k5_nat_5 C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_nat_d A A) = A) ) ) ).
tt(t32_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ((r2_nattra_1 A B C D) <=> (r2_hidden (k4_tarski (k4_tarski C D) E) (k10_nattra_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_ncfcont1 A B C E) & (r1_ncfcont1 A B D E))  =>  ((r1_ncfcont1 A B (k3_vfunct_2 (u1_struct_0 A) B C D) E) & (r1_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski D (k1_relset_1 (u1_struct_0 B) C)) &  ((v1_ncfcont1 D B) & (r2_ncfcont2 D A B C)) )  => (v1_nfcont_1 (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t32_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_ndiff_1 D A B C) => (v3_nfcont_1 D A)) ) ) ) ) ) ) ) ) ).
tt(t32_ndiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers A (k1_pdiff_1 1 1)) => (r2_nfcont_1 (k4_real_ns1 1) A B)) ) ) ) ) ).
tt(t32_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  ((v3_nfcont_1 D (k14_prvect_2 A)) =>  ((r2_ndiff_5 A B C E D) <=>  ((r1_tarski D (k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  ((r2_hidden F D) => (r1_ndiff_5 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_neckla_3,ax, (! [A:$i] :  ( ((v3_necklace A) & (l1_orders_2 A))  =>  ((r2_hidden A k4_neckla_2) => (r2_hidden (k3_necklace A) k4_neckla_2)) ) ) ).
tt(t32_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_newton 2 A) = (k18_rvsum_1 (k8_newton A))) ) ) ).
tt(t32_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski D (k1_relset_1 (u1_struct_0 B) C)) &  ((v1_nfcont_1 D B) & (r3_nfcont_1 B A C D)) )  => (v1_nfcont_1 (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t32_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k2_relset_1 (u1_struct_0 A) B) = (k1_tarski C)) ) )  => (v1_nfcont_3 B A)) ) ) ) ) ).
tt(t32_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ( ((r1_tarski C (k1_relset_1 k1_numbers B)) &  ( (D = (k7_relset_1 k1_numbers (k1_euclid A) B C))  &  ((v1_rcomp_1 C) & (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) B C) A)) ) )  => (v1_nfcont_1 D (k4_real_ns1 A))) ) ) ) ) ) ) ) ) ).
tt(t32_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  ( ((r2_hidden D (k8_normform A)) &  ((r2_hidden B D) &  ((r2_hidden C D) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t32_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (B = C)  =>  ((v2_nfcont_1 B A) <=> (v4_pre_topc C (k4_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t32_numbers,ax, (~  (k1_numbers = k7_numbers) ) ).
tt(t32_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (r1_tarski (k9_openlatt A) (u1_struct_0 (k6_openlatt (k17_openlatt A))))) ) ).
tt(t32_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k3_graph_1 A D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k4_graph_1 A D)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t32_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_orders_1 A B) & (r1_tarski C B))  => (r1_orders_1 A C)) ) ) ) ) ).
tt(t32_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_orders_2 A B C) &  ((r2_hidden B D) &  ((r2_hidden C E) & (m1_orders_2 E A D)) ) )  => (r2_hidden B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v5_ordinal1 C)) ) )  =>  ((v1_relat_1 C) &  ((v5_relat_1 C B) &  ((v1_funct_1 C) & (v5_ordinal1 C)) ) ) ) ) ) ) ) ).
tt(t32_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A B) => (r2_hidden (k10_ordinal2 C A) (k10_ordinal2 C B))) ) ) ) ) ) ) ).
tt(t32_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A B) =>  ( (C = k1_xboole_0)  |  ((r2_hidden A (k11_ordinal2 B C)) & (r2_hidden A (k11_ordinal2 C B))) ) ) ) ) ) ) ) ) ).
tt(t32_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden 1 A) => (r1_ordinal1 B (k12_ordinal2 A B))) ) ) ) ) ).
tt(t32_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden k6_numbers A) & (r1_ordinal1 k4_ordinal1 B))  =>  ((k1_ordinal5 A B) = (k1_ordinal5 A k4_ordinal1)) ) ) ) ) ) ).
tt(t32_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  => (r1_ordinal1 (k9_xtuple_0 (k3_ordinal6 A)) (k9_xtuple_0 A))) ) ).
tt(t32_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t32_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (~ (r1_orders_2 B C D))  =>  ((k2_ortsp_1 A B E (k3_rlvect_1 B F G) D C) = (k3_rlvect_1 A (k2_ortsp_1 A B E F D C) (k2_ortsp_1 A B E G D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) => (r2_hidden D (k25_osafree A B C D))) ) ) ) ) ) ) ) ).
tt(t32_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u4_struct_0 A)) (k7_osalg_1 A)) <=>  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  (B = (k8_osalg_1 A C)) ) ) ) ) ) ) ).
tt(t32_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (r2_pboole (u1_struct_0 A) (u3_msualg_1 A (k12_msualg_2 A B C)) (u3_msualg_1 A (k10_osalg_2 A B C)))) ) ) ) ) ) ).
tt(t32_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_parsp_1 A B D E F) & (r1_parsp_1 A C D E F))  =>  ((r1_parsp_1 A B C B D) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) => (r2_parsp_2 A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (A = (k3_partfun1 A (k9_xtuple_0 A) (k10_xtuple_0 A))) ) ) ).
tt(t32_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((v1_partfun1 (k1_partfun2 A B) A) <=>  (B = A) ) ) ) ) ) ).
tt(t32_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ((r1_setfam_1 B (k6_partit1 A)) & (r1_setfam_1 (k10_eqrel_1 A) B)) ) ) ) ) ).
tt(t32_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k3_pboole A B (k2_pboole A C D)) (k2_pboole A (k3_pboole A B C) (k3_pboole A B D)))) ) ) ) ) ) ) ).
tt(t32_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k2_pcomps_1 A)) => (r2_hidden (k5_setfam_1 (u1_struct_0 A) B) (k2_pcomps_1 A))) ) ) ) ) ).
tt(t32_pcs_0,ax, (! [A:$i] :  ( ((v14_pcs_0 A) & (l2_pcs_0 A))  =>  (! [B:$i] :  ( (~ (r2_hidden B (u1_struct_0 A)))  =>  ((v14_pcs_0 (k19_pcs_0 A B)) & (l2_pcs_0 (k19_pcs_0 A B))) ) ) ) ) ).
tt(t32_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ((r2_pdiff_1 A B C E F) =>  ((r2_pdiff_1 A B C (k4_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) E D) F) &  ((k9_pdiff_1 B A C (k4_vfunct_1 (u1_struct_0 (k4_real_ns1 B)) (k4_real_ns1 A) E D) F) = (k1_rlvect_1 (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 A)) (k9_pdiff_1 B A C E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ((r4_pdiff_3 C B) =>  ((r3_pdiff_1 2 2 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 2 2 C) A) B) &  ((k11_pdiff_1 2 2 (k26_valued_1 (k1_euclid 2) k1_numbers (k1_pdiff_3 2 2 C) A) B) = (k8_real_1 A (k5_pdiff_3 C B))) ) ) ) ) ) ) ) ) ).
tt(t32_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 2 A B) => (r1_fcont_1 (k1_pdiff_2 3 2 A B) (k1_seq_1 (k1_pdiff_1 2 3) B))) ) ) ) ) ).
tt(t32_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r5_pdiff_5 B A) =>  ((k5_pdiff_5 B A) = (k11_pdiff_1 3 2 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ) ).
tt(t32_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid A))) =>  ( (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) &  ( (D = E)  & (v3_nfcont_1 E (k4_real_ns1 A))) ) )  =>  ((r1_pdiff_6 D B A C) <=>  ((r1_tarski D (k1_relset_1 (k1_euclid A) C)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E D) => (r1_pdiff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid C) (k1_euclid D)))))  =>  ((r2_pdiff_7 C D A E B) => (m1_subset_1 B (k1_zfmisc_1 (k1_euclid C)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r3_pdiff_7 A B C D) => (r2_nfcont_4 A (k1_nfcont_4 B (k1_euclid A) C) D)) ) ) ) ) ) ) ) ) ).
tt(t32_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((v1_int_2 A) &  ((r1_nat_d B (k1_newton A C)) &  ( (~  (B = 1) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  (B = (k3_nat_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  =>  (! [C:$i] :  ((m1_pnproc_1 C A) =>  (! [D:$i] :  ((m1_pnproc_1 D A) =>  ((k6_pnproc_1 A (k6_pnproc_1 A B D) C) = (k1_funct_1 (k3_relat_1 (k7_pnproc_1 A D) (k7_pnproc_1 A C)) B)) ) ) ) ) ) ) ) ).
tt(t32_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_newton A B) = (k3_binop_2 (k11_binop_2 (k3_power (k17_complex1 A) B) (k21_sin_cos (k11_binop_2 B (k1_comptrig A)))) (k5_binop_2 (k11_binop_2 (k3_power (k17_complex1 A) B) (k18_sin_cos (k11_binop_2 B (k1_comptrig A)))) k7_complex1))) ) ) ) ) ).
tt(t32_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B (k7_polyform A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  (? [D:$i] :  ((v7_ordinal1 D) &  ( (C = (k15_polyform A B D))  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k11_polyform A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k8_polynom3 A B C) D) (k8_polynom3 A (k11_polynom3 A B D) (k11_polynom3 A C D)))) ) ) ) ) ) ) ) ).
tt(t32_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_funct_2 k5_numbers (u1_struct_0 A) (k3_algseq_1 A B) k6_numbers) = B)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) (k3_algseq_1 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t32_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v5_algstr_0 B) &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_vectsp_2 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k6_polynom7 A B C D) E) = (k8_group_1 B (k5_polynom2 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom8 A C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D B) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) &  ( (~  (D = E) )  &  ((k3_polynom8 A C (k6_xcmplx_0 D E)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_polyred A B C D E) <=>  (~  ( (~  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) D (k7_polynom1 A C)) &  (~  (E = (k7_polynom1 A C)) ) ) )  &  ( (~ (r2_termord A B (k3_termord A B C D) (k3_termord A B C E)))  &  (~  ( ((k3_termord A B C D) = (k3_termord A B C E))  & (r2_polyred A B C (k6_termord A B C D) (k6_termord A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power (k10_real_1 1 A) B) = (k3_power A (k4_xcmplx_0 B))) ) ) ) ) ) ).
tt(t32_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (? [E:$i] :  ((m2_finseq_1 E (k3_finseq_2 B)) &  ( (E = (k8_pboole C (k8_funcop_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)) (k4_finseq_1 C) D)))  &  ((k4_finseqop A B (k5_pre_poly A C) D) = (k5_pre_poly B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k2_prepower 2 A) = (k6_square_1 A)) ) ) ) ).
tt(t32_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 B))))) )  =>  ( (C = D)  =>  ((v5_pre_topc C A B) <=> (v5_pre_topc D (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t32_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((k1_seq_1 D (k7_prob_1 A B (k4_prob_1 A B) C)) = (k9_real_1 1 (k1_seq_1 D C))) ) ) ) ) ) ) ) ) ).
tt(t32_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  (! [G:$i] :  ((m1_prob_1 G A B) =>  ( ((r1_xboole_0 E F) &  (G = (k3_subset_1 A (k6_prob_1 A B E F))) )  =>  ((r1_xxreal_0 (k1_seq_1 C E) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 C F) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 C G) k6_numbers) |  ((k1_seq_1 C D) = (k7_real_1 (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B C E) D) (k1_seq_1 C E)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B C F) D) (k1_seq_1 C F))) (k8_real_1 (k1_seq_1 (k3_prob_2 A B C G) D) (k1_seq_1 C G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D B) &  ((v4_prob_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E D) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  ((r2_hidden C (k1_funct_1 (k3_prob_3 B E) A)) <=>  ((r2_hidden C (k1_funct_1 E A)) &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( (~ (r1_xxreal_0 A F))  & (r2_hidden C (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_prob_4 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_prob_4 A B C))))) )  =>  (! [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k9_setfam_1 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k1_prob_4 A (k9_setfam_1 A) F G) = (k6_subset_1 (k3_funct_2 k5_numbers (k4_prob_4 A B C) D G) (k1_prob_4 A B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k8_cqc_lang A C D)) (k8_cqc_lang A (k7_cqc_lang A B C) D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t32_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ( ((r1_incsp_1 A D (k1_projpl_1 A B C)) & (r1_incsp_1 A D (k1_projpl_1 A B E)))  =>  ( (D = B)  |  ( (E = B)  |  ( (B = C)  | (r1_incsp_1 A E (k1_projpl_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k14_pscomp_1 A) (k1_rltopsp1 (k15_euclid 2) (k18_pscomp_1 A) (k19_pscomp_1 A)))) ) ).
tt(t32_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  (! [D:$i] :  ((m2_pua2mss1 D (u4_struct_0 B)) =>  ((r6_pua2mss1 A B C D) =>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [F:$i] :  ((m2_finseq_1 F (k10_xtuple_0 (u3_msualg_1 B C))) =>  (~  ((r1_tarski (k4_card_3 F) (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A E))) &  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 B)) =>  (~  ( ((k3_relat_1 (k1_msualg_1 B G) (u3_msualg_1 B C)) = F)  & (r2_hidden G (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_mboolean A (k2_pzfmisc1 A B C)) (k2_pboole A B C))) ) ) ) ) ).
tt(t32_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k18_qc_lang1 A (k5_qc_lang2 A B C)) = (k15_qc_lang1 A B (k13_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t32_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k4_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t32_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k3_qc_lang4 A B C) = (a_3_1_qc_lang4 A B C)) ) ) ) ) ) ) ).
tt(t32_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B (k4_quantal1 A)) = B)  &  ((k6_algstr_0 A (k4_quantal1 A) B) = B) ) ) ) ) ) ).
tt(t32_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( (~  (A = k6_numbers) )  =>  ((k27_quaterni (k8_quatern2 A) A) = 1) ) ) ) ).
tt(t32_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k3_quatern2 (k27_quaterni A A)) = (k3_quatern2 (k27_quaterni (k31_quaterni A) (k31_quaterni A)))) ) ) ).
tt(t32_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ( ((k17_quaterni (k7_quaterni (k7_quaterni (k7_quaterni A B) C) D)) = (k7_real_1 (k7_real_1 (k7_real_1 (k17_quaterni A) (k17_quaterni B)) (k17_quaterni C)) (k17_quaterni D)))  &  ( ((k18_quaterni (k7_quaterni (k7_quaterni (k7_quaterni A B) C) D)) = (k7_real_1 (k7_real_1 (k7_real_1 (k18_quaterni A) (k18_quaterni B)) (k18_quaterni C)) (k18_quaterni D)))  &  ( ((k19_quaterni (k7_quaterni (k7_quaterni (k7_quaterni A B) C) D)) = (k7_real_1 (k7_real_1 (k7_real_1 (k19_quaterni A) (k19_quaterni B)) (k19_quaterni C)) (k19_quaterni D)))  &  ((k20_quaterni (k7_quaterni (k7_quaterni (k7_quaterni A B) C) D)) = (k7_real_1 (k7_real_1 (k7_real_1 (k20_quaterni A) (k20_quaterni B)) (k20_quaterni C)) (k20_quaterni D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) => (m1_subset_1 (k1_funct_1 (k17_quofield A) B) (u1_struct_0 (k19_quofield A)))) ) ) ) ).
tt(t32_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ((m1_random_1 C A (k1_random_1 A)) =>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  (? [E:$i] :  ((m2_finseq_1 E A) &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_seq_1 D F) = (k8_real_1 (k1_seq_1 C (k1_funct_1 E F)) (k1_seq_1 B (k1_tarski (k1_funct_1 E F))))) ) ) )  &  ((k8_random_1 A (k1_random_1 A) B C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((r1_xboole_0 (k1_vectsp_6 A B C) (k1_vectsp_6 A B D)) =>  ((k1_vectsp_6 A B (k8_vectsp_6 A B C D)) = (k4_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B C) (k1_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t32_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((r1_xxreal_0 A (k1_real_1 1)) <=> (r1_xxreal_0 (k2_rat_1 A) (k1_real_1 (k1_rat_1 A)))) ) ) ).
tt(t32_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_ratfunc1 A (k8_ratfunc1 A) B) = (k5_struct_0 A)) ) ) ) ) ).
tt(t32_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( ((r1_xxreal_0 A B) &  (C = (k1_rcomp_1 A B)) )  =>  ((k2_tops_1 k2_topalg_2 C) = (k2_tarski A B)) ) ) ) ) ) ) ) ).
tt(t32_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  ( ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) k6_numbers) = k6_numbers)  &  ( ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) 1) = B)  &  ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 (k10_real_1 1 B)) (k1_nat_1 A 2)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t32_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ( ((k5_card_1 B) = (k5_card_1 C))  & (r2_hidden A (k4_finseq_1 E))) )  =>  ((k17_finseq_1 k1_numbers A (k20_rfunct_3 C (k3_rearran1 B C E D) C)) = (k20_rfunct_3 C (k3_rearran1 B C E D) (k1_funct_1 E A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k3_relat_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k3_relat_1 A B) (k3_relat_1 A C))) ) ) ) ) ) ) ).
tt(t32_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A))) =>  ((r1_xboole_0 B C) =>  ((k5_relset_1 C A D B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t32_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_tarski (k4_subset_1 B (k6_relset_2 A B C E) (k6_relset_2 A B D E)) (k6_relset_2 A B (k9_subset_1 A C D) E))) ) ) ) ) ) ) ) ).
tt(t32_revrot_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden B (k10_xtuple_0 C)) & (r1_xxreal_0 1 A))  =>  ((r1_xxreal_0 (k4_finseq_4 C B) A) |  ((k2_topreal1 2 C A) = (k2_topreal1 2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) C B) (k7_nat_d (k2_nat_1 A (k3_finseq_1 C)) (k4_finseq_4 C B)))) ) ) ) ) ) ) ) ) ).
tt(t32_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) =>  ( (B = C)  |  ((r2_hidden B (k1_relat_1 A)) & (r2_hidden C (k1_relat_1 A))) ) ) ) ) ) ) ).
tt(t32_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) => (r3_rewrite2 A B C C)) ) ) ) ) ).
tt(t32_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ((r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C D)) (k1_rewrite3 E F G)) =>  ((r1_struct_0 G A) &  ((r1_struct_0 G C) &  ((r2_hidden B (k8_afinsq_1 E)) &  ((r2_hidden D (k8_afinsq_1 E)) &  ((r2_hidden A (k9_xtuple_0 (k9_xtuple_0 (u1_rewrite3 F G)))) & (r2_hidden C (k10_xtuple_0 (u1_rewrite3 F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( ((k1_rfinseq2 (k5_rfinseq2 A)) = 1)  &  ( ((k2_rfinseq2 (k6_rfinseq2 A)) = 1)  &  ( ((k1_seq_1 (k5_rfinseq2 A) 1) = (k3_rfinseq2 A))  &  ((k1_seq_1 (k6_rfinseq2 A) 1) = (k4_rfinseq2 A)) ) ) ) ) ) ) ).
tt(t32_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_classes1 A B) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F C))  =>  ((k1_funct_1 A F) = (k1_funct_1 B F)) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F (k3_finseq_1 A)) =>  ((r1_xxreal_0 F D) |  ((k1_funct_1 A F) = (k1_funct_1 B F)) ) ) ) )  &  ( (~ (r1_xxreal_0 E C))  &  ((r1_xxreal_0 E D) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 F C))  &  ((r1_xxreal_0 F D) &  ((k1_funct_1 A E) = (k1_funct_1 B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k1_rfunct_1 A B) C) = (k1_rfunct_1 (k24_valued_1 A C) B)) ) ) ) ) ) ) ).
tt(t32_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) =>  ((r1_xxreal_0 B k6_numbers) | (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) )  &  ( ( (B = k6_numbers)  => (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A)))  &  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) =>  ((r1_xxreal_0 k6_numbers B) | (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ) ) ) ).
tt(t32_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_rfunct_3 A k1_numbers (k16_rfunct_3 A (k15_rfunct_3 A B) C) D)) ) ) ) ) ) ) ) ).
tt(t32_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (a_2_0_rinfsup1 A B))  => (v3_xxreal_2 C)) ) ) ) ) ) ) ) ).
tt(t32_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 A B))) )  => (v8_mesfunc5 A)) ) ) ).
tt(t32_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tarski (k3_rlvect_2 A B) (k6_domain_1 (u1_struct_0 A) C)) =>  ((k3_rlaffin1 A B) = (k1_seq_1 B C)) ) ) ) ) ) ) ) ).
tt(t32_rlaffin3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_rlaffin1 C (k15_euclid B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))))  =>  ( ((k5_card_1 C) = (k23_binop_2 B 1))  => (v5_pre_topc (k2_rlaffin3 (k15_euclid B) C A) (k15_euclid B) k3_topmetr)) ) ) ) ) ) ).
tt(t32_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  =>  (B = A) ) ) ) ) ) ).
tt(t32_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( (~  ( (? [D:$i] :  ((m1_rlsub_1 D A) &  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) )  &  ( (~ (m1_rlsub_1 B C))  &  (~ (m1_rlsub_1 C B)) ) ) )  &  (~  ( ((m1_rlsub_1 B C) | (m1_rlsub_1 C B))  &  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (~  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k1_rlvect_1 A C B)) =>  (? [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  &  (? [F:$i] :  ((m1_connsp_2 F A C) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( (~ (r1_xxreal_0 E (k18_complex1 (k9_real_1 G B))))  => (r1_tarski (k1_convex1 A F G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A (k4_algstr_0 A B) C) = (k5_algstr_0 A (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t32_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_rlvect_2 C A (k6_domain_1 (u1_struct_0 A) B)) =>  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ).
tt(t32_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((m1_rlsub_1 B C) & (m1_rlsub_1 D C))  => (m1_rlsub_1 (k1_rlsub_2 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t32_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ( (~  (A = 1) )  & (v1_rlvect_3 (k8_domain_1 (u1_struct_0 B) C (k1_rlvect_1 B C A) D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t32_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rlvect_5 A) = k6_numbers)  <=>  ((k2_rlsub_1 A) = (k1_rlsub_1 A)) ) ) ) ).
tt(t32_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E k4_numbers) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) (k3_rlvect_x A B)) &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 C))) =>  ((k7_partfun1 (u1_struct_0 A) D F) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) C F) (k1_seq_1 E F))) ) ) ) ) ) )  => (r2_hidden (k4_rlvect_1 A D) (k3_rlvect_x A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 C D)) )  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t32_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  ( ((k1_rmod_3 A B C D) = D)  <=>  ((k2_rmod_3 A B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t32_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_rmod_4 D A B (k6_domain_1 (u1_struct_0 B) C)) =>  ((k5_rmod_4 A B D) = (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C)) ) ) ) ) ) ) ) ) ).
tt(t32_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v8_robbins1 A) & (l4_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A B)) = B) ) ) ) ) ).
tt(t32_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) (k3_robbins1 A (k5_robbins1 A C (k3_robbins1 A C)))) = (k3_robbins1 A (k5_robbins1 A B C))) ) ) ) ) ) ) ).
tt(t32_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r3_lattices A (k3_robbins1 A C) B) &  ((k4_lattices A B C) = (k5_lattices A)) )  =>  (B = (k3_robbins1 A C)) ) ) ) ) ) ) ) ) ).
tt(t32_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_roughs_1 A B) = (k5_roughs_1 A (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t32_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_rpr_1 A (k2_subset_1 A) B) = (k1_rpr_1 A B)) ) ) ) ) ).
tt(t32_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (m1_rusub_1 (k1_rusub_1 B) A)) ) ) ) ).
tt(t32_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ( (~  ( (? [D:$i] :  ((m1_rusub_1 D A) &  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) )  &  ( (~ (m1_rusub_1 B C))  &  (~ (m1_rusub_1 C B)) ) ) )  &  (~  ( ((m1_rusub_1 B C) | (m1_rusub_1 C B))  &  (! [D:$i] :  ((m1_rusub_1 D A) =>  (~  ((u1_struct_0 D) = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r1_struct_0 (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) B C)) D) <=>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k4_rusub_4 A B) = C)  =>  ((k3_rusub_1 A D B) = (k5_rusub_4 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_rusub_1 C A) &  ((u1_struct_0 C) = (a_2_3_rusub_5 A B)) ) ) ) ) ) ) ).
tt(t32_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k9_rvsum_1 A B (k5_finseq_2 k1_numbers A k6_numbers)) = B) ) ) ) ) ).
tt(t32_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k16_rvsum_1 (k7_finseq_1 A B)) = (k3_binop_2 (k16_rvsum_1 A) (k16_rvsum_1 B))) ) ) ) ) ).
tt(t32_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r1_tarski (k2_xboole_0 (k4_sf_mastr A) (k2_sf_mastr A)) (k9_xtuple_0 B))) ) ) ) ).
tt(t32_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k10_card_3 (k3_compos_0 (u1_compos_1 k1_scmfsa_2) (k2_compos_0 (u1_compos_1 k1_scmfsa_2) (k13_scmfsa_2 A B)))) 1) = k5_numbers) ) ) ) ) ).
tt(t32_scmfsa_1,ax, ((k9_xtuple_0 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1)) = k1_scmfsa_1) ).
tt(t32_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 3)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k8_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ((k5_scmfsa6a (k6_scmfsa6a A B) C) = (k4_scmfsa6a A (k6_scmfsa6a B C))) ) ) ) ) ) ) ).
tt(t32_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A (k1_scmfsa_m B) C) & (r6_scmfsa7b A (k1_scmfsa_m B) C))  =>  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1))) = (k5_card_1 A)) ) ) ) ) ) ) ) ).
tt(t32_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b C B A))) ) ) ) ) ) ) ).
tt(t32_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa8b C A B) (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 3)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(t32_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~  ((r6_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E)) (k1_funct_4 A (k2_scmfsa_9 C D))) & (r5_scmfsa7b D (k1_scmfsa_m (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E)) (k1_funct_4 A (k2_scmfsa_9 C D)))) )  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) C) k6_numbers) |  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) (k2_nat_1 E 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b D (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) (k1_funct_4 A (k2_scmfsa_9 C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 6 C))  => (r2_hidden C (k2_afinsq_1 (k2_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t32_scmfsa_m,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m1_scmfsa_2 B) => (r1_xboole_0 (k9_xtuple_0 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k9_xtuple_0 (k16_funcop_1 B A)))) ) ) ) ).
tt(t32_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b B C A) (k1_scmfsa6b B (k1_scmfsa_m C) A))) ) ) ) ) ) ).
tt(t32_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k5_card_1 (k2_scmisort A)) = 82) ) ) ).
tt(t32_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 6)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  (A = (k9_scmpds_2 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_tarski (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D)) A) =>  ((k9_memstr_0 2 k1_scmpds_2 (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k10_compos_1 k1_scmpds_2 D)) (k8_memstr_0 2 k1_scmpds_2 (k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B)) E) (k5_card_1 C)) = (k5_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 C (k1_scmpds_6 (k2_nat_1 (k5_card_1 D) 1))) D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t32_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k1_scmpds_7 A B C D)) = (k2_nat_1 (k5_card_1 D) 3)) ) ) ) ) ) ) ) ) ).
tt(t32_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden C (k1_amistd_1 2 (k1_scmring2 A) D (k9_scmring2 A C B))) & (r1_tarski (k1_amistd_1 2 (k1_scmring2 A) D (k9_scmring2 A C B)) (k2_tarski C (k1_ordinal1 D)))) ) ) ) ) ) ) ) ) ).
tt(t32_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  => (r2_hidden (k2_tarski B C) A)) ) )  =>  (A = (k5_scmyciel (k3_tarski A))) ) ) ) ).
tt(t32_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) & (r2_analoaf A B C D E))  =>  ( (B = C)  | (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers A) B) (k32_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A (k32_valued_1 k5_numbers k1_numbers B)) (k32_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ).
tt(t32_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k8_real_1 (k17_complex1 (k3_comseq_2 A)) (k17_complex1 (k3_comseq_2 B)))) ) ) ) ) ).
tt(t32_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k12_binop_2 1 (k9_binop_2 (k4_nat_1 C C) A))) ) ) )  => (v2_comseq_2 B)) ) ) ) ) ).
tt(t32_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k5_seqfunc A B) C) (k56_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C))) & (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k4_seqfunc A B) C) (k32_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ).
tt(t32_seqm_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((v7_valued_0 B) & (r1_xxreal_0 k6_numbers A))  => (v7_valued_0 (k26_valued_1 k5_numbers k1_numbers B A)))  &  ( ((v7_valued_0 B) & (r1_xxreal_0 A k6_numbers))  => (v8_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ).
tt(t32_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B C) = (k10_real_1 1 (k3_power C A))) ) ) )  =>  ((r1_xxreal_0 A 1) | (v1_series_1 B)) ) ) ) ) ) ).
tt(t32_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k4_nat_1 (k2_nat_1 B 1) (k13_newton 2 B)) (k4_nat_1 (k2_nat_1 B 2) (k2_nat_1 B 3)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 (k13_newton 2 (k2_nat_1 B 1)) (k2_nat_1 B 3)) (k13_complex1 1 2))) ) ) ) ) ) ).
tt(t32_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 (k1_newton (k13_complex1 (k2_xcmplx_0 A B) 2) C) (k13_complex1 (k2_xcmplx_0 (k1_newton A C) (k1_newton B C)) 2))) ) ) ) ) ) ).
tt(t32_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 A B)) (k3_square_1 B)) 3)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 B C)) (k3_square_1 C)) 3))) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 C) (k3_xcmplx_0 C A)) (k3_square_1 A)) 3))) (k2_xcmplx_0 (k2_xcmplx_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 B) (k3_square_1 C)) 2))) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 A)) 2))))) ) ) ) ) ) ).
tt(t32_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((k7_setfam_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t32_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_1 A (k2_setlim_1 A B)) (k4_setlim_1 A (k2_prob_1 A B)))) ) ) ).
tt(t32_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 C A) => (v1_setlim_1 (k8_setlim_2 A C B) A)) ) ) ) ) ) ).
tt(t32_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v1_setwiseo C A)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k7_setwiseo B A C (k5_setwiseo B D (k2_setwiseo B F)) E) = (k5_binop_1 A C (k7_setwiseo B A C D E) (k3_funct_2 B A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ( (B = (k4_binop_1 A C))  &  ( ((k5_binop_1 A D B B) = B)  &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  ((k5_binop_1 A C (k5_binop_1 A D G H) (k5_binop_1 A D I J)) = (k5_binop_1 A D (k5_binop_1 A C G I) (k5_binop_1 A C H J))) ) ) ) ) ) ) ) )  &  ((k3_finseq_1 E) = (k3_finseq_1 F)) ) ) ) ) ) )  =>  ((k5_binop_1 A D (k1_finsop_1 A E C) (k1_finsop_1 A F C)) = (k1_finsop_1 A (k1_finseqop A A A D E F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~  ( (~  (A = (k9_scmfsa_m 1 (k5_scmfsa_m B C))) )  &  ( (~  (A = (k9_scmfsa_m 2 (k5_scmfsa_m B C))) )  & (r4_scmfsa7b (k4_sfmastr3 D B C) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ( (~  ( (~  (D = (k2_compos_1 k1_scmfsa_2)) )  &  ( (~  (D = (k6_scmfsa_2 A B)) )  &  ( (~  (D = (k7_scmfsa_2 A B)) )  &  ( (~  (D = (k8_scmfsa_2 A B)) )  &  ( (~  (D = (k9_scmfsa_2 A B)) )  &  ( (~  (D = (k10_scmfsa_2 A B)) )  &  ( (~  (D = (k11_scmfsa_2 C)) )  &  ( (~  (D = (k12_scmfsa_2 C A)) )  &  (~  (D = (k13_scmfsa_2 C A)) ) ) ) ) ) ) ) ) ) )  =>  ((k3_sf_mastr D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t32_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((r2_hidden E (k5_sgraph1 A B C D)) <=>  (? [F:$i] :  ((m2_finseq_2 F (u1_struct_0 B) (k3_finseq_2 (u1_struct_0 B))) &  ( (E = F)  & (r3_sgraph1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A B B)) = (k5_sheffer1 A C (k5_sheffer1 A C C))) ) ) ) ) ) ) ).
tt(t32_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B C))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ).
tt(t32_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) => (r1_xxreal_0 (k6_simplex0 C) (k6_simplex0 B))) ) ) ) ) ).
tt(t32_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v1_simplex1 C B) & (m1_simplex0 C (u1_struct_0 B))) ) ) )  =>  ((r1_tarski (k3_simplex1 B C) (k2_struct_0 C)) =>  ((k6_simplex0 C) = (k6_simplex0 (k5_simplex1 A B C))) ) ) ) ) ) ) ) ).
tt(t32_sincos10,ax, ( ((k1_seq_1 k2_fdiff_9 (k1_real_1 (k10_real_1 k32_sin_cos 2))) = (k1_real_1 1))  &  ( ((k1_seq_1 k2_fdiff_9 (k1_real_1 (k10_real_1 k32_sin_cos 4))) = (k1_real_1 (k7_square_1 2)))  &  ( ((k1_seq_1 k2_fdiff_9 (k10_real_1 k32_sin_cos 4)) = (k7_square_1 2))  &  ((k1_seq_1 k2_fdiff_9 (k10_real_1 k32_sin_cos 2)) = 1) ) ) ) ).
tt(t32_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k4_sin_cos2 A) &  ((k1_fdiff_1 k4_sin_cos2 A) = (k1_seq_1 k1_sin_cos2 A)) ) ) ) ).
tt(t32_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k11_binop_2 (k15_binop_2 (k24_binop_2 2 A) (k18_binop_2 1 2)) k32_sin_cos) k7_complex1)) = k7_complex1) ) ) ).
tt(t32_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) = (k3_xcmplx_0 (k7_xcmplx_0 1 2) (k2_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))))) ) ) ) ) ).
tt(t32_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k18_sin_cos (k6_real_1 A 2)) = k6_numbers) )  =>  ((k2_sin_cos4 (k6_real_1 A 2)) = (k6_real_1 (k17_sin_cos A) (k9_real_1 1 (k20_sin_cos A)))) ) ) ) ).
tt(t32_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))  &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) & (r1_xxreal_0 (k17_sin_cos A) (k1_real_1 1))) ) ) ) ) ).
tt(t32_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A (k19_binop_2 1)))  &  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k12_binop_2 (k9_binop_2 A 1) (k10_binop_2 1 A)) k6_numbers)) ) ) ) ) ).
tt(t32_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k2_newton (k6_sin_cos2 A) 3) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 3 A)) (k3_xcmplx_0 3 (k6_sin_cos2 A))) 4))  &  ( ((k2_newton (k6_sin_cos2 A) 4) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 4 A)) (k3_xcmplx_0 4 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 3) 8))  &  ( ((k2_newton (k6_sin_cos2 A) 5) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 5 A)) (k3_xcmplx_0 5 (k6_sin_cos2 (k3_xcmplx_0 3 A)))) (k3_xcmplx_0 10 (k6_sin_cos2 A))) 16))  &  ( ((k2_newton (k6_sin_cos2 A) 6) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 6 A)) (k3_xcmplx_0 6 (k6_sin_cos2 (k3_xcmplx_0 4 A)))) (k3_xcmplx_0 15 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 10) 32))  &  ( ((k2_newton (k6_sin_cos2 A) 7) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 7 A)) (k3_xcmplx_0 7 (k6_sin_cos2 (k3_xcmplx_0 5 A)))) (k3_xcmplx_0 21 (k6_sin_cos2 (k3_xcmplx_0 3 A)))) (k3_xcmplx_0 35 (k6_sin_cos2 A))) 64))  &  ((k2_newton (k6_sin_cos2 A) 8) = (k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 8 A)) (k3_xcmplx_0 8 (k6_sin_cos2 (k3_xcmplx_0 6 A)))) (k3_xcmplx_0 28 (k6_sin_cos2 (k3_xcmplx_0 4 A)))) (k3_xcmplx_0 56 (k6_sin_cos2 (k3_xcmplx_0 2 A)))) 35) 128)) ) ) ) ) ) ) ) ).
tt(t32_sin_cos9,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)) k2_sin_cos9) = (k1_partfun2 k1_numbers (k2_rcomp_1 k6_numbers k32_sin_cos))) ).
tt(t32_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((k1_newton A (k4_nat_1 2 B)) = (k1_newton (k1_newton A B) 2))  &  ((k1_newton A (k4_nat_1 2 B)) = (k1_newton (k1_newton A 2) B)) ) ) ) ) ) ).
tt(t32_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) & (v2_sppol_1 (k2_topreal1 2 B A))) ) ) )  => (v1_sppol_1 (k2_topreal1 2 B (k2_nat_1 A 1)))) ) ) ) ) ).
tt(t32_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v2_topreal1 A) & (r2_hidden B (k2_topreal1 2 A C)))  => (v2_topreal1 (k5_finseq_5 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ).
tt(t32_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~ (r1_xxreal_0 (k7_pscomp_1 A) (k9_pscomp_1 A))) ) ) ).
tt(t32_sprect_2,ax, ((k6_pscomp_1 k1_topreal1) = k6_numbers) ).
tt(t32_sprect_3,ax, (! [A:$i] :  ( ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) &  ( (~  ((k17_euclid B) = (k6_pscomp_1 (k3_topreal1 2 A))) )  &  ( (~  ((k17_euclid B) = (k8_pscomp_1 (k3_topreal1 2 A))) )  &  ( (~  ((k18_euclid B) = (k9_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k18_euclid B) = (k7_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t32_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k6_square_1 (k7_xcmplx_0 1 A)) = (k7_xcmplx_0 1 (k6_square_1 A))) ) ) ) ).
tt(t32_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r2_hidden B (k11_stacks_1 A C)) &  ((r2_hidden D (k11_stacks_1 A C)) &  ((k9_stacks_1 A B) = (k9_stacks_1 A D)) ) )  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t32_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_stirl2_1 A 1) = 1) ) ) ) ).
tt(t32_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  ((r2_hidden B (k9_xtuple_0 (k19_substut1 A E))) =>  ((k1_funct_1 D (k1_funct_1 (k2_substut1 A (k19_substut1 A E)) B)) = (k3_funct_2 (k3_qc_lang1 A) C (k1_sublemma A C D (k3_sublemma A E C D)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_hidden D B) <=> (r2_hidden D C)) ) ) )  =>  (B = (k3_subset_1 A C)) ) ) ) ) ) ) ).
tt(t32_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v7_substut1 B A) =>  ((k37_substut1 A B) = (k36_substut1 A B (k37_substut1 A (k31_substut1 A B)))) ) ) ) ) ) ).
tt(t32_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_qc_lang2 A C B) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  (C = (k11_cqc_lang A D E)) ) ) ) ) ) ) ) )  =>  ((k7_cqc_sim1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t32_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((v2_supinf_2 D A B) & (v2_supinf_2 E A C))  => (v2_supinf_2 (k13_supinf_2 A B C D E) A (k5_supinf_2 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (E = (k4_struct_0 B))  =>  ( ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A))  |  ((r1_orders_2 B C D) |  ((k2_symsp_1 A B E F D C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r1_tarski (k9_xtuple_0 (k1_sysrel A)) (k9_xtuple_0 A)) &  ((r1_tarski (k10_xtuple_0 (k1_sysrel A)) (k10_xtuple_0 A)) &  ((r1_tarski (k10_xtuple_0 (k1_sysrel A)) (k9_xtuple_0 A)) & (r1_tarski (k9_xtuple_0 (k1_sysrel A)) (k10_xtuple_0 A))) ) ) ) ) ).
tt(t32_taxonom1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ( ((r2_hidden (k10_eqrel_1 A) (k2_taxonom1 A B)) &  ((v4_metric_1 B A) & (v1_taxonom1 B A)) )  => (m2_taxonom1 (k2_taxonom1 A B) A)) ) ) ) ) ).
tt(t32_taylor_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A C) = (k1_seq_1 (k3_series_1 (k6_taylor_1 A B C C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  ((k5_binop_1 (k5_tdlat_1 A) (k6_tdlat_1 A) B C) = (k1_binop_1 (k2_tdlat_1 A) B C)) ) ) ) ) ) ) ).
tt(t32_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_tdlat_2 A (k1_pcomps_1 A B)) = (a_2_3_tdlat_2 A B)) ) ) ) ) ).
tt(t32_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ((v4_pre_topc B A) & (v3_pre_topc B A)) ) ) ) ) ) ) ).
tt(t32_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((k4_termord A B C (k9_polynom1 A C D E)) = (k6_algstr_0 C (k4_termord A B C D) (k4_termord A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (u1_struct_0 A)) )  & (v1_tops_3 B A)) ) ) ) ) ) ) ).
tt(t32_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) &  ((v3_pre_topc C A) &  ((v2_tex_2 B A) & (v2_tex_2 C A)) ) )  => (v2_tex_2 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t32_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r4_tsep_2 A B C) =>  ((v3_tex_3 B A) <=> (v1_tex_3 C A)) ) ) ) ) ) ) ) ).
tt(t32_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_tex_4 A B))) ) ) ) ).
tt(t32_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (m1_pre_topc F A))  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k1_tsep_1 A (k1_tsep_1 A D E) F))  &  ((m1_pre_topc (k2_tsep_1 A D (k1_tsep_1 A B C)) B) &  ((m1_pre_topc (k2_tsep_1 A E (k1_tsep_1 A B C)) C) & (m1_pre_topc (k2_tsep_1 A F (k1_tsep_1 A B C)) (k2_tsep_1 A B C))) ) )  =>  ((r1_tsep_1 B C) |  ((m1_pre_topc B C) |  ((m1_pre_topc C B) |  ( (~ (r1_tsep_1 D (k1_tsep_1 A B C)))  &  (~ (r1_tsep_1 E (k1_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k3_tarski (k4_toler_1 A B)) = A) ) ) ) ).
tt(t32_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r4_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J) (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E G (k1_borsuk_2 A C D E H I)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [F:$i] :  ((m1_borsuk_2 F B D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B D))) &  ((v1_group_6 G (k5_topalg_1 A C) (k5_topalg_1 B D)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B D)))))) ) )  =>  ( ((v3_tops_2 E A B) &  ((r1_borsuk_6 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) D) & (r2_funct_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B D)) G (k1_partfun1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C))) (u1_struct_0 (k5_topalg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C))) (u1_struct_0 (k5_topalg_1 B D)) (k3_topalg_3 A B C E) (k6_topalg_1 B D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) F)))) )  => (v3_funct_2 G (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) => (r2_group_6 (k5_topalg_1 (k2_borsuk_1 A B) (k4_borsuk_1 A B C E)) (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 (k5_topalg_1 A D) (k5_topalg_1 B F))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) =>  ((r1_borsuk_2 A D E) =>  ((r1_xxreal_0 C B) |  ((v7_topalg_6 (k1_partfun1 (u1_struct_0 (k4_topmetr B C)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k1_borsuk_6 B C k6_numbers 1) F) A) & (m2_subset_1 (k1_partfun1 (u1_struct_0 (k4_topmetr B C)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k1_borsuk_6 B C k6_numbers 1) F) (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( ((v7_pre_topc A) &  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v4_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v4_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 D E) &  ( ((k4_subset_1 (u1_struct_0 A) D E) = (k2_struct_0 A))  &  ((r1_tarski B D) & (r1_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_topdim_1 A) & (r1_xxreal_0 (k4_topdim_1 A) k6_numbers)) ) ) ) ).
tt(t32_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_pre_topc A) => (r1_tarski (k2_topgen_1 A (k2_topgen_1 A B)) (k2_topgen_1 A B))) ) ) ) ) ).
tt(t32_topgen_2,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_tops_2 C (k5_topgen_2 A B)) &  ((v1_cantor_1 C (k5_topgen_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))))) )  =>  ( (C = (k2_xboole_0 (k7_subset_1 (k1_zfmisc_1 A) (k10_eqrel_1 A) (k1_tarski (k1_tarski B))) (a_1_2_topgen_2 A)))  =>  ((k1_card_1 C) = (k1_card_1 A)) ) ) ) ) ) ) ).
tt(t32_topgen_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  (~  ((r2_hidden (k1_card_1 A) k3_topgen_3) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (~ (r2_hidden (k3_rcomp_1 B C) (k1_cantor_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topgen_4,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k1_setfam_1 (k2_setfam_1 A B)) (k2_xboole_0 (k1_setfam_1 A) (k1_setfam_1 B)))) ) ).
tt(t32_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))) =>  ( (A = (k8_subset_1 (u1_struct_0 (k15_euclid 2)) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k4_card_3 (k10_finseq_1 k3_numbers k3_numbers))))  =>  (! [B:$i] :  ((k2_pre_topc k3_topgen_5 (k7_subset_1 (u1_struct_0 k3_topgen_5) A (k1_tarski B))) = (k2_struct_0 k3_topgen_5)) ) ) ) ) ).
tt(t32_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) =>  (! [C:$i] :  ((m3_topgrp_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_topgrp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_topgrp_1 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k5_topgrp_1 A) D E) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k5_topreal1 A) = (a_1_2_topreal1 A)) ) ) ).
tt(t32_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k18_euclid A) = (k18_euclid B))  =>  ( ((k17_euclid A) = (k17_euclid B))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid A) (k17_euclid B)) 2) (k18_euclid A))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid A) (k17_euclid B)) 2) (k18_euclid A)) B)) = (k1_tarski (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid A) (k17_euclid B)) 2) (k18_euclid A)))) ) ) ) ) ) ) ).
tt(t32_topreal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k17_euclid C) (k8_pscomp_1 A)))  &  (~  (B = C) ) ) ) ) ) ) ) ) ).
tt(t32_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 A) B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A B) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) = (k2_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)))) ) ) ) ) ) ) ).
tt(t32_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_tarski (k1_rltopsp1 (k15_euclid A) B C) (k4_topreal9 A B C))) ) ) ) ) ) ).
tt(t32_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (v2_struct_0 (k1_topreala A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_toprealb,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_funct_1 k12_toprealb A) = k9_toprealb) ) ) ).
tt(t32_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((k48_valued_2 A C D B) = (k69_valued_2 A C D (k7_funcop_1 (k1_relset_1 A D) B))) ) ) ) ) ) ) ) ).
tt(t32_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k9_real_1 (k12_euclid B) (k12_euclid C)) (k12_euclid (k5_algstr_0 (k15_euclid A) B C)))) ) ) ) ) ) ).
tt(t32_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k9_subset_1 (u1_struct_0 A) B C)) (k4_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_tops_1 A C)))) ) ) ) ) ) ).
tt(t32_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k5_setfam_1 (u1_struct_0 A) D)) => (r1_tarski (k9_subset_1 (u1_struct_0 A) B C) (k5_setfam_1 (u1_struct_0 (k1_pre_topc A C)) (k1_tops_2 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t32_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) => (v1_tops_3 (k1_tops_1 A B) A)) ) ) ) ) ).
tt(t32_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v3_transgeo B A) => (v3_transgeo (k2_funct_2 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t32_trees_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  ((r2_hidden A B) =>  ((k5_trees_1 B A C) = (k2_xboole_0 (a_2_0_trees_1 A B) (a_2_1_trees_1 A C))) ) ) ) ) ) ) ) ).
tt(t32_trees_2,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  ((r2_hidden A (k9_xtuple_0 B)) => (r1_tarski (k10_xtuple_0 (k5_trees_2 B A)) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t32_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v5_trees_3 (k10_finseq_1 A B)) <=>  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_trees_1 B)) ) ) ) ) ) ).
tt(t32_trees_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E (k5_trees_3 (k2_zfmisc_1 A B))) =>  (? [F:$i] :  ((m2_finseq_1 F (k5_trees_3 B)) &  ( ((k4_finseq_1 F) = (k4_finseq_1 E))  &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 E)) &  (! [H:$i] :  ((m1_subset_1 H (k5_trees_3 (k2_zfmisc_1 A B))) =>  (~  ( (H = (k1_funct_1 E G))  &  ((k1_funct_1 F G) = (k9_trees_3 A B H)) ) ) ) ) ) ) ) )  &  ((k9_trees_3 A B (k8_trees_4 (k2_zfmisc_1 A B) (k1_domain_1 A B C D) E)) = (k8_trees_4 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_trees_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  &  ( (C = (k5_relat_1 B (k2_finseq_1 A)))  & (r1_tarski C B)) ) ) ) ) ) ) ).
tt(t32_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (~  ( (~ (r1_tsep_1 B D))  &  ( (~ (r1_tsep_1 D C))  &  (~  ( ((k2_tsep_1 A (k1_tsep_1 A B C) D) = (k1_tsep_1 A (k2_tsep_1 A B D) (k2_tsep_1 A C D)))  &  ((k2_tsep_1 A D (k1_tsep_1 A B C)) = (k1_tsep_1 A (k2_tsep_1 A D B) (k2_tsep_1 A D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A B D) & (r4_tsep_2 A C E))  =>  ( ((k1_tsep_1 A D E) = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))  <=> (r1_tsep_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc C A) | (v3_pre_topc D A))  =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k9_subset_1 (u1_struct_0 A) C D)) = (k9_subset_1 (u1_struct_0 B) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t32_turing_1,ax,(r3_turing_1 k16_turing_1 (k4_comput_1 1 1))).
tt(t32_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  => (r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k3_msafree2 (k37_twoscomp A B)))) ) ) ) ).
tt(t32_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  => (r1_tarski (k2_uniroots A) (u1_struct_0 (k1_uniroots k1_complfld)))) ) ).
tt(t32_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k3_algseq_1 A (k5_struct_0 A))) B)) ) ) ) ).
tt(t32_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_xxreal_2 (k1_integra2 A B)) =>  ((r1_xxreal_0 B k6_numbers) | (v4_xxreal_2 A)) ) ) ) ) ) ).
tt(t32_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) => (r1_valuat_1 A B (k5_cqc_lang A) D C)) ) ) ) ) ) ) ) ).
tt(t32_valued_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) )  =>  (! [C:$i] :  ((m1_valued_0 C B) => (r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t32_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 B (k62_valued_1 A))) ) ) ) ) ).
tt(t32_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k14_valued_2 B (k4_xcmplx_0 A)) = (k14_valued_2 (k30_valued_1 B) A)) ) ) ) ) ).
tt(t32_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k5_hahnban1 A B C D) E) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  ((v1_funct_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C D A)) D)) &  ((v1_funct_2 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C D A)) D) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C D A)))) &  ((v13_vectsp_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C D A)) D) (k3_ranknull B C C (k1_vectsp11 C D A)) (k3_ranknull B C C (k1_vectsp11 C D A))) &  ((v1_mod_2 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C D A)) D) B (k3_ranknull B C C (k1_vectsp11 C D A)) (k3_ranknull B C C (k1_vectsp11 C D A))) & (m1_subset_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C D A)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C D A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C D A))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k1_algstr_0 A C B) (k1_algstr_0 A D B)) = (k5_algstr_0 A C D)) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k5_vectsp_2 A B (k4_struct_0 A) D) = (k4_struct_0 B))  &  ( ((k5_vectsp_2 A B (k4_algstr_0 A (k1_group_1 A)) D) = (k4_algstr_0 B D))  &  ((k5_vectsp_2 A B C (k4_struct_0 B)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_struct_0 C D)) )  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t32_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ((m1_vectsp_4 C A D) => (m1_vectsp_4 (k1_vectsp_5 A B C E) A (k1_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) => (r1_vectsp_6 A B (k6_vectsp_6 A B (k3_rlvect_1 A C D) E) (k5_vectsp_6 A B (k6_vectsp_6 A B C E) (k6_vectsp_6 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t32_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k2_xcmplx_0 (k1_vectsp_9 A (k1_vectsp_5 A B C D)) (k1_vectsp_9 A (k2_vectsp_5 A B C D))) = (k2_xcmplx_0 (k1_vectsp_9 A C) (k1_vectsp_9 A D))) ) ) ) ) ) ) ) ) ).
tt(t32_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( ( ((v1_partfun1 C A) & (v1_partfun1 D A))  => (v1_partfun1 (k6_vfunct_1 A B C D) A))  &  ( ((v1_partfun1 (k6_vfunct_1 A B C D) A) =>  ((v1_partfun1 C A) & (v1_partfun1 D A)) )  &  ( ( ((v1_partfun1 C A) & (v1_partfun1 D A))  => (v1_partfun1 (k2_vfunct_1 A B C D) A))  &  ((v1_partfun1 (k2_vfunct_1 A B C D) A) =>  ((v1_partfun1 C A) & (v1_partfun1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ( ( ((v1_partfun1 C A) & (v1_partfun1 D A))  => (v1_partfun1 (k3_vfunct_2 A B C D) A))  &  ( ((v1_partfun1 (k3_vfunct_2 A B C D) A) =>  ((v1_partfun1 C A) & (v1_partfun1 D A)) )  &  ( ( ((v1_partfun1 C A) & (v1_partfun1 D A))  => (v1_partfun1 (k2_vfunct_1 A B C D) A))  &  ((v1_partfun1 (k2_vfunct_1 A B C D) A) =>  ((v1_partfun1 C A) & (v1_partfun1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_0 A B) <=> (r1_yellow_0 A (k3_waybel_0 A B))) ) ) ) ) ).
tt(t32_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k13_yellow_6 A (k2_waybel11 A))) ) ) ).
tt(t32_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_waybel12 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 A) D) = C)  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) E F) = (k2_yellow_0 A (a_3_0_waybel12 A D F))) ) ) )  => (m1_waybel12 (k2_relset_1 (u1_struct_0 A) E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ( ((r5_waybel_1 A B) &  ((v1_yellow_0 A) & (v2_waybel_8 A)) )  => (v2_waybel_8 B)) ) ) ) ) ).
tt(t32_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) =>  ((v1_compts_1 A) &  ((v6_waybel_3 A) &  ((v4_yellow_8 A) & (v2_yellow_8 A)) ) ) ) ) ) ).
tt(t32_waybel15,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_8 A) <=>  ((v3_lattice3 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski C (k1_waybel15 A)) &  (B = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v4_waybel_6 (k1_waybel16 A) A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_waybel_6 B A) => (r1_tarski (k1_waybel16 A) B)) ) ) ) ) ) ).
tt(t32_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_tops_2 (a_1_4_waybel19 A) A) &  ((v1_cantor_1 (a_1_4_waybel19 A) A) & (m1_subset_1 (a_1_4_waybel19 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(t32_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 A) (k2_waybel_1 A A B) (k3_waybel_1 A A B)) B)) ) ) ) ).
tt(t32_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v2_yellow_0 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k4_waybel_3 A B (k4_yellow_0 (k5_yellow_1 A B)) C) = (k4_yellow_0 (k3_waybel_3 A B C))) ) ) ) ) ) ) ) ).
tt(t32_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((u1_waybel_0 A (k4_waybel17 A B)) = (k6_partfun1 B))  &  ( ((u1_struct_0 (k4_waybel17 A B)) = B)  &  ((v4_yellow_0 (k4_waybel17 A B) A) & (m1_yellow_0 (k4_waybel17 A B) A)) ) ) ) ) ) ) ).
tt(t32_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=> (v2_waybel23 B A)) ) ) ) ) ).
tt(t32_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_waybel24 A B)))))  => (r2_hidden (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) B) C) (u1_struct_0 (k3_waybel24 A B)))) ) ) ) ) ) ).
tt(t32_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v10_waybel_0 B (k1_waybel25 A)) & (l1_waybel_0 B (k1_waybel25 A))) ) ) )  => (r2_hidden (k1_waybel_2 (k1_waybel25 A) B) (k10_yellow_6 (k1_waybel25 A) B))) ) ) ) ).
tt(t32_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (r1_tarski (u1_struct_0 (k1_waybel26 A B)) (k9_funct_2 (u1_struct_0 A) (u1_struct_0 B)))) ) ) ) ).
tt(t32_waybel27,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((k1_waybel26 A k9_waybel18) = (k2_waybel27 A (k3_yellow_1 1))) ) ) ).
tt(t32_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k5_waybel11 (k3_yellow_3 B A)) = (u1_pre_topc (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A)))) ) )  <=>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k1_waybel29 (k3_yellow_3 B A)) = (k1_waybel25 (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A)))) ) ) ) ) ) ).
tt(t32_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k4_waybel_2 A) (k6_yellow_3 A A B C)) = (k3_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(t32_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (? [D:$i] :  ( ((v1_tops_2 D B) &  ((v1_yellow_8 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E D) =>  ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E B) &  ((v13_waybel_0 E B) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) )  <=> (v3_waybel30 A)) ) ) ) ) ).
tt(t32_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v8_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  ( (F = D)  & (r1_waybel_3 A C D)) )  => (r1_waybel_3 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k4_waybel_3 A B (k1_yellow_0 (k5_yellow_1 A B) C) D) = (k1_yellow_0 (k3_waybel_3 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k2_funct_1 (k9_waybel_4 A)) = (k10_waybel_4 A)) ) ) ).
tt(t32_waybel_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m2_pboole E A D (k7_funcop_1 A B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ((k2_funct_6 (k3_msualg_3 A D (k7_funcop_1 A B) (k7_funcop_1 A C) E (k7_waybel_5 B C A F))) = (k2_funct_6 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (k2_tarski k1_xboole_0 1) (k5_funct_3 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) (u1_struct_0 A)) C) = k1_xboole_0)  <=> (r1_orders_2 A C B)) ) ) ) ) ) ) ).
tt(t32_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) &  ((v12_waybel_0 D A) &  ((v1_waybel_7 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((r3_orders_2 A C (k1_yellow_0 A D)) => (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r3_waybel_9 A B C) &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  (~ (r2_hidden C (k10_yellow_6 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k1_vectsp_9 (k4_weddwitt A) (k6_weddwitt A)) k6_numbers)) ) ) ).
tt(t32_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E C) &  ((k4_metric_1 A D E) = (k8_weierstr A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v2_wellord1 B) =>  ((k1_relat_1 (k2_wellord1 B (k1_wellord1 B A))) = (k1_wellord1 B A)) ) ) ) ) ).
tt(t32_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( ((k3_int_2 A B) = 1)  &  ( ((k1_newton C A) = (k1_newton D B))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (C = (k1_newton E B))  &  (D = (k1_newton E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 A B) = (k4_xboole_0 B A))  =>  (A = B) ) ) ) ).
tt(t32_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k4_xboolean A B)) = (k3_xboolean A)) ) ) ) ) ).
tt(t32_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A B) = (k6_xcmplx_0 (k2_xcmplx_0 A C) (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t32_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A k6_numbers) => (r1_xxreal_0 (k2_xcmplx_0 A B) B)) ) ) ) ) ).
tt(t32_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k11_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k11_xtuple_0 A) (k11_xtuple_0 B)))) ) ).
tt(t32_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C B) &  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A D) & (r1_xxreal_0 C D))  => (r1_xxreal_0 B D)) ) ) ) )  =>  (B = (k4_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(t32_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (v1_xboole_0 (k3_xxreal_1 A B))) ) ) ) ) ) ).
tt(t32_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_xxreal_2 (k4_xxreal_1 A B)) = B) ) ) ) ) ) ).
tt(t32_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (A = k1_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  (~  ((k1_xxreal_3 (k3_xxreal_3 A B) C) = (k3_xxreal_3 A (k3_xxreal_3 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (B = (k1_yellow_0 A C))  <=>  ((r2_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A C D) => (r1_orders_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t32_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k6_yellow_3 A B (k4_waybel_0 A C) (k4_waybel_0 B D)) = (k4_waybel_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t32_yellow12,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t32_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A C)))) =>  ((k5_card_3 B (k2_pre_topc (k3_waybel18 A (k7_funcop_1 A C)) (k6_domain_1 (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A C))) D))) = (k2_pre_topc C (k6_domain_1 (u1_struct_0 C) (k2_yellow14 A C D B)))) ) ) ) ) ) ) ) ) ).
tt(t32_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r2_yellow_0 (k5_yellow_1 A B) C) <=>  (! [D:$i] :  ((m1_subset_1 D A) => (r2_yellow_0 (k2_yellow16 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ).
tt(t32_yellow18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_altcat_1 A))) =>  ((k3_yellow18 (k7_altcat_1 A) B) = B) ) ) ) ) ).
tt(t32_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))) &  ((v2_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 B (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_waybel_7 A B C)) ) ) ) ) ) ) ).
tt(t32_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l1_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v10_functor0 C A B) & (l2_functor0 C A B)) )  =>  ((v17_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  ( ((k6_functor0 A B C D E F) = (k6_functor0 A B C D E G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v18_waybel_0 C A B) => (v8_yellow_0 (k1_yellow_2 A B C) B)) ) ) ) ) ) ) ).
tt(t32_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) (k7_yellow_3 A B E F)) =>  ((r1_lattice3 A C E) & (r1_lattice3 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_waybel_0 A (k2_yellow_4 A (k3_waybel_0 A B) (k3_waybel_0 A C))) (k3_waybel_0 A (k2_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t32_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_yellow_5 A B C))  & (r1_yellow_5 A (k12_lattice3 A B D) (k12_lattice3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t32_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) => (r1_tarski (k10_yellow_6 A B) (k10_yellow_6 A C))) ) ) ) ) ) ).
tt(t32_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_yellow_0 A) <=> (v3_yellow_0 (k7_lattice3 A))) ) ) ).
tt(t32_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B (u1_pre_topc A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E B) &  ((r2_hidden D E) & (r1_tarski E C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t32_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ( ((k3_funct_2 k5_numbers k1_zf_lang k2_zf_fund1 (k3_zf_fund1 C)) = C)  &  ( ((k1_funct_1 (k2_funct_1 k2_zf_fund1) C) = (k3_zf_fund1 C))  &  ((k3_funct_2 k5_numbers A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 B) (k3_zf_fund1 C)) = (k3_funct_2 k1_zf_lang A B C)) ) ) ) ) ) ) ) ) ).
tt(t32_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((k21_zf_lang (k12_zf_lang A B)) = (k11_zf_lang A B))  &  ((k22_zf_lang (k12_zf_lang A B)) = (k11_zf_lang B A)) ) ) ) ) ) ).
tt(t32_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k11_zf_lang A B) = (k11_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t32_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_tarski A B) C) <=>  ((r2_hidden A C) & (r2_hidden B C)) ) ) ) ) ).
tt(t32_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  ( (~  (B = k1_xboole_0) )  =>  ( (~ (v1_xboole_0 (k4_classes1 B)))  & (m1_subset_1 (k4_classes1 B) A)) ) ) ) ) ) ).
tt(t32_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  => (m1_zmodul01 A A)) ) ).
tt(t330_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 A C)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t331_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k1_xxreal_1 A C)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t332_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k1_xxreal_1 A C)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t333_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A C)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t334_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A C)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t335_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A C)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t336_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A C)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t337_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 A C)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t338_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 A C)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t339_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 B) (k1_xxreal_1 A C)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t33_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  =>  ((k1_funct_1 (k1_rewrite1 A B) (k2_nat_1 (k3_finseq_1 A) C)) = (k1_funct_1 B (k1_nat_1 C 1))) ) ) ) ) ) ) ) ).
tt(t33_abcmiz_1,ax, (! [A:$i] :  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) =>  ((k1_abcmiz_1 (k2_relset_1 k2_abcmiz_1 A)) = (k2_relset_1 k2_abcmiz_1 A)) ) ) ).
tt(t33_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) => (m1_abcmiz_a B A B)) ) ) ) ).
tt(t33_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_aff_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r2_aff_1 A B B C)) ) ) ) ) ) ).
tt(t33_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  ( ( (~  ((v1_aff_1 B A) & (v1_aff_1 C A)) )  &  (~  ((v1_aff_4 B A) & (v1_aff_4 C A)) ) )  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t33_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( (B = (k5_afinsq_1 A))  <=>  ( ((k2_afinsq_1 B) = 1)  &  ((k10_xtuple_0 B) = (k1_tarski A)) ) ) ) ) ) ).
tt(t33_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_finset_1 E) & (v6_membered E))  =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 (k1_afinsq_1 (k4_afinsq_2 E)) B))  &  ( ((k1_recdef_1 (k4_afinsq_2 E) B) = D)  &  ( ((k1_recdef_1 (k4_afinsq_2 E) C) = A)  & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) =>  (~  ( (D = (k4_tarski (k6_afproj A B) 2))  &  ((v1_aff_4 B A) &  ((r1_incsp_1 (k13_afproj A) C D) & (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) <=> (r2_analoaf A (k1_afvect0 A F B) (k1_afvect0 A F C) (k1_afvect0 A F D) (k1_afvect0 A F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_funct_1 B) & (r1_tarski (k3_xboole_0 (u4_struct_0 A) (k10_xtuple_0 B)) (k9_xtuple_0 B)))  => (r1_algspec1 A C B)) ) ) ) ) ) ) ).
tt(t33_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_algstr_4 A))) =>  ((k15_algstr_4 A (k6_algstr_0 (k14_algstr_4 A) B C)) = (k2_xcmplx_0 (k15_algstr_4 A B) (k15_algstr_4 A C))) ) ) ) ) ) ).
tt(t33_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_altcat_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 B E F)) => (m1_subset_1 G (k1_altcat_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v18_functor0 C A B) &  ((v17_functor0 C A B) & (r2_altcat_3 B (k3_functor0 A B C E) (k3_functor0 A B C D))) )  =>  ( ((k1_altcat_1 A D E) = k1_xboole_0)  |  ( ((k1_altcat_1 A E D) = k1_xboole_0)  | (r2_altcat_3 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k3_amistd_1 A B C) = k5_numbers)  => (r1_ami_wstd A B C D)) ) ) ) ) ) ) ) ) ).
tt(t33_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v2_struct_0 (k2_analmetr A B C)))  &  ((v2_analmetr (k2_analmetr A B C)) & (l1_analmetr (k2_analmetr A B C))) ) ) ) ) ) ) ) ) ).
tt(t33_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) &  ((r2_analort A B C D E F H) &  ( (~ (r2_analort A B C D E G H))  &  (~ (r2_analort A B C D E H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_collsp B) &  ((v3_collsp B) &  ((v4_collsp B) &  ((v2_anproj_2 B) &  ((v3_anproj_2 B) & (l1_collsp B)) ) ) ) ) )  =>  (~  ( (B = (k5_anproj_1 A))  &  (~ (v7_anproj_2 B)) ) ) ) ) ) ) ) ) ).
tt(t33_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) => (r1_tarski (k10_aofa_000 A) B)) ) ) ) ).
tt(t33_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k82_aofa_i00 A B D E F G)) F) = (k3_xcmplx_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k82_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (v6_armstrng (k10_armstrng A B) A)) ) ) ) ) ).
tt(t33_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) =>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  ((r2_hidden (k4_tarski A B) k5_arytm_3) <=>  ((r1_arytm_3 A B) &  ( (~  (B = k1_xboole_0) )  &  (~  (B = 1) ) ) ) ) ) ) ) ) ).
tt(t33_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((r1_xxreal_0 (k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) k6_numbers) | (r2_hidden A (k8_asympt_0 B))) ) ) ) ) ) ).
tt(t33_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 B D) = (k6_series_1 (k3_asympt_1 C) D)) ) )  => (r1_xxreal_0 (k10_real_1 (k5_series_1 A (k2_nat_1 C 1)) (k2_nat_1 C 1)) (k1_seq_1 B A))) ) ) ) ) ) ) ) ).
tt(t33_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 B) = (k1_autalg_1 A))  &  (! [C:$i] :  ((r2_hidden C (k1_autalg_1 A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_autalg_1 A)) (u1_struct_0 (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) &  ((v1_group_6 B (k3_autalg_1 A) (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_autalg_1 A)) (u1_struct_0 (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))))))) ) ) ) ) ) ) ) ).
tt(t33_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k9_bagorder A) = (k5_yellow_1 A (k7_funcop_1 A k11_dickson))) ) ) ).
tt(t33_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k1_bcialg_1 A B C) (k5_bcialg_1 A))) ) ) ) ) ) ).
tt(t33_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (v10_bcialg_1 (k1_bcialg_2 A (k4_struct_0 A) (k2_bcialg_1 A B) C) A)) ) ) ) ) ) ).
tt(t33_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) (k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ).
tt(t33_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_bcialg_4 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k1_bcialg_4 A B C)) ) ) ) ) ) ) ).
tt(t33_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ( ((v8_bcialg_1 F) & (m1_bcialg_5 F A B C D))  =>  ((r1_xxreal_0 (k3_bcialg_5 A B C D) E) =>  ((v8_bcialg_1 F) & (m1_bcialg_5 F E E E E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k5_bcialg_1 A)) =>  ( ((v1_bcialg_6 (k6_bcialg_1 A D E) A) &  ((v1_bcialg_6 B A) &  ((v1_bcialg_6 C A) &  ((v1_bcialg_6 D A) &  ((v1_bcialg_6 E A) &  ((r2_hidden B (k7_bcialg_1 A D)) & (r2_hidden C (k7_bcialg_1 A E))) ) ) ) ) )  => (r1_int_1 (k4_bcialg_6 A (k6_bcialg_1 A D E)) (k5_nat_d (k4_bcialg_6 A B) (k4_bcialg_6 A C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( ((v3_bciideal B A) & (m2_bcialg_1 B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A C D) B) => (r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D (k1_bcialg_1 A D C))) B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k3_bhsp_1 A B) (k3_bhsp_1 A C))) (k3_bhsp_1 A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t33_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k5_vfunct_1 k5_numbers A B) C) = (k5_vfunct_1 k5_numbers A (k1_valued_0 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t33_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A D) = (k2_power D (k1_seq_1 (k2_bhsp_2 B C) D))) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 1 (k1_seq_1 A E))) ) ) ) )  & (v1_bhsp_4 C B)) ) ) ) ) ) ) ) ) ).
tt(t33_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D (k4_struct_0 B) E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) (k2_xcmplx_0 B 1)))  =>  ((k1_binari_3 A (k2_xcmplx_0 B 1)) = (k7_binarith A (k1_binari_3 A B) (k1_binari_2 A))) ) ) ) ) ) ).
tt(t33_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (? [C:$i] :  ((m1_subset_1 C k6_margrel1) &  ((k2_binari_4 (k23_binop_2 A 1) B) = (k8_finseq_1 k6_margrel1 (k2_binari_4 A B) (k12_finseq_1 k6_margrel1 C))) ) ) ) ) ) ) ).
tt(t33_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k4_lattices A B C)) (k1_boolealg A B C))) ) ) ) ) ) ).
tt(t33_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A (k13_borsuk_1 A B C))) (k12_borsuk_1 A (k13_borsuk_1 A B C)) D) = (k1_funct_1 (k12_borsuk_1 B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t33_borsuk_4,ax, ((u1_struct_0 k1_borsuk_4) = (k6_subset_1 (u1_struct_0 k5_topmetr) (k2_tarski k6_numbers 1))) ).
tt(t33_borsuk_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_connsp_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) &  ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (B = k1_xboole_0)  |  (B = (k2_struct_0 A)) ) ) ) ) ) ).
tt(t33_borsuk_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ( ((k1_funct_1 (k1_borsuk_6 A B C D) A) = C)  &  ((k1_funct_1 (k1_borsuk_6 A B C D) B) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_borsuk_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ((v1_xcmplx_0 I) =>  ( ((r1_zfmisc_1 A B I) &  ((r2_hidden C D) &  ((r2_hidden E F) & (r2_hidden G H)) ) )  => (r2_hidden (k1_borsuk_7 A B I C E G) (k4_card_3 (k1_borsuk_7 A B I D F H)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_bspace A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_bspace A))) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k11_bspace A (k8_finseq_1 (u1_struct_0 (k7_bspace A)) B (k12_finseq_1 (u1_struct_0 (k7_bspace A)) C)) D) = (k8_finseq_1 (u1_struct_0 k2_bspace) (k11_bspace A B D) (k12_finseq_1 (u1_struct_0 k2_bspace) (k3_bspace C D)))) ) ) ) ) ) ) ) ) ).
tt(t33_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A E B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) F) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r1_bvfunc_1 A B (k17_bvfunc_1 A B C))) ) ) ) ) ) ).
tt(t33_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k9_bvfunc_1 A (k9_bvfunc_1 A B C) B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t33_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k2_bvfunc_1 A C D)) (k5_bvfunc_1 A (k1_bvfunc_1 A (k5_bvfunc_1 A B C)) (k1_bvfunc_1 A (k5_bvfunc_1 A B D))))) ) ) ) ) ) ) ) ).
tt(t33_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k5_bvfunc_1 A D C) B E) (k5_bvfunc_1 A (k7_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F) (k7_bvfunc_2 A (k2_bvfunc_1 A E C) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E D) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k1_bvfunc_1 A C)) (k9_bvfunc_1 A C (k1_bvfunc_1 A B))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t33_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k5_bvfunc_1 A (k1_bvfunc_1 A B) C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t33_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k6_margrel1) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k6_margrel1) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H A k6_margrel1) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) H) B) & (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) F) G) H) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v4_normsp_0 (k11_c0sp1 A)) &  ((v3_normsp_0 (k11_c0sp1 A)) & (v2_normsp_1 (k11_c0sp1 A))) ) ) ) ).
tt(t33_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_struct_0 (k9_c0sp2 A)) = (k1_c0sp2 A k6_numbers)) ) ) ).
tt(t33_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((r1_calcul_1 (k1_calcul_1 (k3_cqc_lang A) B) (k2_calcul_1 A B)) => (r4_calcul_1 A B)) ) ) ) ) ).
tt(t33_card_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) & (v2_funct_1 B))  => (r2_wellord2 A (k7_relat_1 B A))) ) ) ) ).
tt(t33_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k3_card_2 (k1_card_2 A B) 2) = (k1_card_2 (k1_card_2 (k2_card_2 A A) (k2_card_2 (k2_card_2 2 A) B)) (k2_card_2 B B))) ) ) ) ) ).
tt(t33_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ((r1_tarski A B) => (r1_ordinal1 (k6_card_3 A) (k6_card_3 B))) ) ) ) ) ).
tt(t33_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  => (r1_ordinal1 (k6_card_3 (k2_card_5 B A)) (k3_card_2 B A))) ) ) ) ).
tt(t33_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) => (v1_card_5 A)) ) ) ).
tt(t33_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((k8_relat_1 D (k1_tarski A)) = (k8_relat_1 E (k1_tarski B)))  =>  ((k2_card_fin C D A) = (k2_card_fin C E B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_card_lar,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( ((r2_hidden (k1_card_1 A) (k1_card_5 B)) &  (! [C:$i] :  ((r2_hidden C A) => (r2_hidden (k1_card_1 C) B)) ) )  => (r2_hidden (k1_card_1 (k3_tarski A)) B)) ) ) ) ).
tt(t33_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((v7_cat_1 (k5_cat_1 A B C D E F) A B D) =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A C D) = k1_xboole_0)  | (v7_cat_1 E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_cat_1 H B F G) =>  (~  ( (~  ((k2_cat_1 A C D) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 B F G) = k1_xboole_0) )  &  (~ (m1_cat_1 (k10_cat_2 A B E H) (k8_cat_2 A B) (k9_cat_2 A B C F) (k9_cat_2 A B D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v1_cat_3 D A B C) <=> (v2_cat_3 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t33_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_cat_1 A (k2_cat_4 A B C) (k2_cat_4 A C B))) ) ) ) ) ) ).
tt(t33_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A B))  =>  ((k19_cat_5 A (k1_cat_1 A B C)) = (k1_partfun1 (u4_struct_0 (k11_cat_5 A (k3_graph_1 A B))) (u4_struct_0 (k11_cat_5 A (k4_graph_1 A B))) (u4_struct_0 (k11_cat_5 A (k3_graph_1 A C))) (u4_struct_0 (k11_cat_5 A (k4_graph_1 A C))) (k19_cat_5 A B) (k19_cat_5 A C))) ) ) ) ) ) ) ) ).
tt(t33_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 (k24_binop_2 2 A) A)) = (k13_complex1 (k6_newton A (k24_binop_2 2 A)) (k23_binop_2 A 1))) ) ) ).
tt(t33_catalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (? [D:$i] :  ((m2_pboole D (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k1_instalg1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k13_catalg_1 B) (k11_catalg_1 A B C) (k12_catalg_1 A B C)))) &  ((r8_pboole (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) D (k1_catalg_1 (u1_struct_0 (k3_catalg_1 (u1_struct_0 A))) (u3_msualg_1 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A)) C)) & (r1_msualg_3 (k3_catalg_1 (u1_struct_0 A)) (k13_catalg_1 A) (k1_instalg1 (k3_catalg_1 (u1_struct_0 A)) (k3_catalg_1 (u1_struct_0 B)) (k13_catalg_1 B) (k11_catalg_1 A B C) (k12_catalg_1 A B C)) D)) ) ) ) ) ) ) ) ) ).
tt(t33_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  => (r1_tarski (k13_pre_poly (k11_pre_poly (u1_struct_0 A) B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ) ).
tt(t33_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_cfcont_1 B A) & (r1_cfcont_1 C A))  =>  ((r1_cfcont_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers B C) A) &  ((r1_cfcont_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers B C) A) & (r1_cfcont_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers B C) A)) ) ) ) ) ) ) ) ) ).
tt(t33_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [D:$i] :  ( ((v6_cfdiff_1 D) & (m1_subset_1 D (k1_zfmisc_1 k2_numbers)))  =>  ( ((r1_tarski D (k1_relset_1 k2_numbers C)) &  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ((r2_hidden E D) =>  ((k7_partfun1 k2_numbers C E) = (k8_complex1 (k9_complex1 A E) B)) ) ) ) )  =>  ((r2_cfdiff_1 C D) &  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ((r2_hidden E D) =>  ((k7_partfun1 k2_numbers (k3_cfdiff_1 C D) E) = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers B (k31_valued_1 A k2_numbers C)) (k2_valued_1 A k2_numbers k2_numbers B C))) ) ) ) ) ) ).
tt(t33_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (r1_tarski (k8_cgames_1 A) (k11_cgames_1 A))) ) ).
tt(t33_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_chain_1 E B) =>  ((r1_xxreal_0 A B) =>  ((r2_hidden (k3_chain_1 B C D) (k4_chain_1 B E A)) <=>  (~  ( (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_finseq_1 B))) =>  (~  ( ((k5_card_1 F) = A)  &  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 B)) =>  ( ((r2_hidden G F) &  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k1_seq_1 C G)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 C G) (k1_seq_1 D G)) (k2_chain_1 B E G))) )  |  ( (~ (r2_hidden G F))  &  ( ((k1_seq_1 C G) = (k1_seq_1 D G))  & (r2_hidden (k1_seq_1 C G) (k2_chain_1 B E G))) ) ) ) ) ) ) ) )  &  (~  ( (A = B)  &  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 D F)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 C F) (k1_seq_1 D F)) (k2_chain_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (~  ( (~ (v1_glib_001 B A))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 3))  &  (? [C:$i] :  ((r1_glib_000 A (k4_glib_001 A B) (k3_glib_001 A B) C) &  (~ (v8_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t33_circcmb3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ((r2_hidden D (k9_xtuple_0 A)) & (r2_hidden E (k9_xtuple_0 A))) ) )  =>  ((k3_relat_1 (k7_finseq_4 B C D E) A) = (k7_finseq_4 (k1_funct_1 A B) (k1_funct_1 A C) (k1_funct_1 A D) (k1_funct_1 A E))) ) ) ) ) ) ) ) ).
tt(t33_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_xboole_0 (k3_msafree2 B) (k2_msafree2 A)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  &  (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B))) )  =>  ((k6_circuit2 C F G) = (k1_funct_4 (k6_circuit2 B E I) (k6_circuit2 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k3_msafree2 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (F = (k1_funct_1 C E))  =>  ((k4_msafree2 B F) = (k1_funct_1 D (k4_msafree2 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_tarski (k4_classes1 A) (k4_classes1 (k1_ordinal1 A)))) ) ).
tt(t33_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden A (k2_ordinal1 (k1_classes1 B))) => (r1_ordinal1 (k1_card_1 (k4_classes1 A)) (k1_card_1 (k1_classes1 B)))) ) ) ) ).
tt(t33_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  ( (C = (k4_struct_0 (k14_clopban1 A B)))  =>  (k6_numbers = (k1_normsp_0 (k14_clopban1 A B) C)) ) ) ) ) ) ) ) ).
tt(t33_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 (k4_normsp_0 A B)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k4_power 2 D) (k1_seq_1 (k4_normsp_0 A B) (k4_power 2 D)))) ) ) )  =>  ((v2_clopban3 B A) <=> (v1_series_1 C)) ) ) ) ) ) ) ) ).
tt(t33_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_clopban4 A B) = (k1_clopban3 A (k1_clopban4 A B))) ) ) ) ) ).
tt(t33_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v5_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (? [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) &  (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  (! [F:$i] :  ( ((v2_relat_1 F) & (m3_pboole F A (k1_mboolean A B)))  =>  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) & (v1_partfun1 G A)) ) )  =>  ((r1_pboole A G F) <=>  ((r1_pboole A G C) & (r2_pboole A E G)) ) ) )  => (r6_pboole A (k2_closure1 A B D E) (k4_mssubfam A B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_closure2 C A B (k2_closure2 A B)) =>  (! [D:$i] :  ((m1_closure2 D A B (k2_closure2 A B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [F:$i] :  ((m1_closure2 F A B (k6_closure2 A B)) =>  ( ((r6_pboole A F (k4_pboole A C D)) & (v10_closure2 E A B))  => (r2_pboole A (k4_pboole A (k7_closure2 A B E C) (k7_closure2 A B E D)) (k7_closure2 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  ( (E = B)  =>  ((k1_clvect_1 D E C) = (k1_clvect_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k2_power D (k8_nat_1 k1_numbers (k2_clvect_2 A B) D))) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 1 (k8_nat_1 k1_numbers C E))) ) ) ) )  & (v1_clvect_3 B A)) ) ) ) ) ) ) ) ) ).
tt(t33_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v8_cohsp_1 A)) )  =>  ((v1_classes1 (k9_xtuple_0 A)) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k7_cohsp_1 A)) => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t33_coh_sp,ax, (! [A:$i] : (r2_hidden (k6_partfun1 A) (k15_coh_sp A))) ).
tt(t33_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ((r1_xxreal_0 2 A) & (r1_ordinal1 (k2_nat_1 A 2) (k1_card_1 B)))  =>  (! [C:$i] :  ((l1_combgras C (k1_combgras A B) (k1_combgras A B)) =>  (~  ((v7_combgras C (k1_combgras A B)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (~  ((g1_combgras (k1_combgras A B) (k1_combgras A B) (u1_combgras (k1_combgras A B) (k1_combgras A B) C) (u2_combgras (k1_combgras A B) (k1_combgras A B) C)) = (k8_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_complex1 (k4_xcmplx_0 A)) = (k10_complex1 (k15_complex1 A))) ) ) ).
tt(t33_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k1_complex2 A A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t33_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k3_vectsp_1 k1_complfld B (k11_algstr_0 k1_complfld A)) = (k8_group_1 k1_complfld B A)) ) ) ) ) ) ).
tt(t33_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k1_valued_1 A (k17_seq_4 (k3_finseq_1 A))) = A) ) ) ).
tt(t33_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v1_tbsp_1 A) => (v5_waybel23 (k3_pcomps_1 A))) ) ) ).
tt(t33_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((k9_xtuple_0 (k6_compos_1 A C B)) = (a_3_0_compos_1 A B C)) ) ) ) ) ) ) ).
tt(t33_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  ((k62_valued_1 (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E)) = 4) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_comptrig,ax, ((k10_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos)))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t33_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k4_comput_1 A B) (k2_comput_1 k5_numbers))) ) ) ) ).
tt(t33_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  => (v2_relat_1 (k51_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(t33_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  (~  ( (~  ((k3_comseq_2 A) = k5_complex1) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers A C)) (k10_real_1 (k17_complex1 (k3_comseq_2 A)) 2))) ) ) ) ) ) ) ) ) ).
tt(t33_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A C) = (k8_nat_1 k2_numbers B k6_numbers)) ) )  => (r2_funct_2 k5_numbers k2_numbers (k10_comseq_3 (k1_valued_0 k2_numbers B 1)) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers (k10_comseq_3 B) 1) A))) ) ) ) ) ).
tt(t33_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  ((k1_binop_1 (k10_conlat_1 A) B C) = (k1_binop_1 (k10_conlat_1 A) C B)) ) ) ) ) ) ) ).
tt(t33_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) => (v4_pre_topc B A)) ) ) ) ) ).
tt(t33_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (v2_connsp_1 (k6_connsp_3 A B C) A)) ) ) ) ) ) ) ).
tt(t33_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_convex1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t33_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (r1_convex4 A (k8_convex4 A (k8_convex4 A B)) B)) ) ) ) ).
tt(t33_cqc_lang,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  (B = C) )  =>  ( ((k1_funct_1 (k1_funct_4 A (k4_funct_4 B C D E)) B) = D)  &  ((k1_funct_1 (k1_funct_4 A (k4_funct_4 B C D E)) C) = E) ) ) ) ) ) ) ) ) ).
tt(t33_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_qc_lang1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k11_cqc_lang A D C) E F G) (k15_cqc_sim1 A B)) => (r2_hidden (k6_xtuple_0 C (k28_qc_lang1 A E) (k2_xboole_0 F (k6_domain_1 (k3_qc_lang1 A) D)) (k1_funct_4 G (k16_funcop_1 D (k2_qc_lang3 A E)))) (k15_cqc_sim1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski B (a_2_0_cqc_the1 A B))) ) ) ) ).
tt(t33_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k11_cqc_lang A D (k10_cqc_lang A B C)) A) => (v2_cqc_the1 (k10_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t33_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D (k7_cqc_lang A B C)) <=>  ((r3_cqc_the1 A D B) & (r3_cqc_the1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t33_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A B C)) = (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k12_csspace A B B) (k12_csspace A B C)) (k12_csspace A C B)) (k12_csspace A C C))) ) ) ) ) ) ) ).
tt(t33_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( ((v3_dickson A) & (v4_dickson A))  => (v1_wellfnd1 (k5_dickson A))) ) ) ).
tt(t33_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers E A) (k26_valued_1 k1_numbers k1_numbers F B)) C D) = (k7_real_1 (k8_real_1 A (k9_diff_1 E C D)) (k8_real_1 B (k9_diff_1 F C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k7_real_1 (k7_real_1 (k8_real_1 A (k5_square_1 F)) (k8_real_1 B F)) C)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k1_funct_1 (k5_diff_1 E D) F) = (k7_real_1 (k8_real_1 (k8_real_1 (k8_real_1 2 A) D) F) (k8_real_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 k1_numbers k1_numbers)) &  ((v1_diff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) )  =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_xxreal_0 G F) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers E F) G) = (k8_real_1 (k8_real_1 (k6_newton G F) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) G) B)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D A) (k7_nat_d F G)) (k9_real_1 B (k4_real_1 G A))))) ) ) ) ) )  =>  ( ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k6_series_1 (k12_diff_1 E 1) 1))  &  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 2) B) = (k6_series_1 (k12_diff_1 E 2) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 (k7_real_1 A (k13_complex1 B 2)) k6_numbers))  &  ( (~ (r1_xxreal_0 (k9_real_1 A (k13_complex1 B 2)) k6_numbers))  &  (~  ((k1_seq_1 (k5_diff_1 k3_taylor_1 B) A) = (k1_seq_1 k3_taylor_1 (k7_real_1 1 (k13_complex1 B (k9_real_1 A (k13_complex1 B 2)))))) ) ) ) ) ) ) ) ) ).
tt(t33_dilworth,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( (D = E)  & (r5_waybel_4 (k5_yellow_0 A B) C D))  => (r5_waybel_4 A C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_diraf A B C D) & (r2_diraf A B C D E))  =>  ( (B = C)  | (r3_diraf A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k5_subset_1 A B C) = (a_3_6_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t33_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ((v2_ec_pf_1 B A) <=>  ((k2_ec_pf_1 A B) = 1) ) ) ) ) ) ).
tt(t33_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  ( (G = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D E F))  =>  ( ((k4_ec_pf_2 A B C G) = D)  &  ( ((k5_ec_pf_2 A B C G) = E)  &  ((k6_ec_pf_2 A B C G) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  ( (? [C:$i] :  (B = (k1_tarski C)) )  => (v10_cat_1 B (k11_ens_1 A))) ) ) ) ) ).
tt(t33_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ((r2_hidden E (k4_finseq_1 C)) & (r1_xxreal_0 D E)) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k4_finseq_1 (k1_matrprob A C D))) =>  ((k1_funct_1 (k1_matrprob A C D) F) = (k1_funct_1 (k1_matrprob A C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k4_enumset1 A A B C D E) = (k3_enumset1 A B C D E)) ) ) ) ) ) ).
tt(t33_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (m1_eqrel_1 (k7_eqrel_1 A B) A)) ) ) ).
tt(t33_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (k4_equation A) D)) =>  ( ((r6_msualg_3 A B C) & (r1_equation A B D E))  => (r1_equation A C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k2_relat_1 (k4_xboole_0 (u1_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_zfmisc_1 (k7_e_siec A) (k8_e_siec A))) & (r1_tarski (k2_relat_1 (k4_xboole_0 (u2_e_siec A) (k4_relat_1 (u1_struct_0 A)))) (k2_zfmisc_1 (k7_e_siec A) (k8_e_siec A)))) ) ) ).
tt(t33_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 (k4_struct_0 (k15_euclid A)) B) = k6_numbers) ) ) ) ) ).
tt(t33_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden (k3_euclid_3 A) (k2_rcomp_1 k6_numbers k32_sin_cos)) <=>  (~ (r1_xxreal_0 (k18_euclid A) k6_numbers)) ) ) ) ).
tt(t33_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k23_rvsum_1 (k8_euclid A B C) (k8_euclid A B C)) = (k7_real_1 (k9_real_1 (k23_rvsum_1 B B) (k8_real_1 2 (k23_rvsum_1 B C))) (k23_rvsum_1 C C))) ) ) ) ) ) ) ).
tt(t33_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k6_euclid_5 A B C) = (k6_euclid_5 B C A)) ) ) ) ) ) ) ).
tt(t33_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ( (D = (k19_euclid E F))  &  ( (~  (A = C) )  &  ( (~  (B = C) )  &  ( (~  ((k8_real_1 2 (k4_euclid_3 A C B)) = (k4_euclid_3 A D B)) )  &  (~  ((k8_real_1 2 (k9_real_1 (k4_euclid_3 A C B) k32_sin_cos)) = (k4_euclid_3 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_euclid_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k7_real_ns1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k7_real_ns1 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_real_ns1 A))) =>  (! [F:$i] :  ((m2_rlvect_2 F (k7_real_ns1 A) D) =>  ( ((v2_funct_1 C) &  ((v1_euclid_7 D) &  ( ((k2_relset_1 (u1_struct_0 (k7_real_ns1 A)) C) = (k3_rlvect_2 (k7_real_ns1 A) F))  &  ((r2_hidden E D) &  ((r2_hidden B (k4_finseq_1 (k5_rlvect_2 (k7_real_ns1 A) C F))) &  (E = (k1_funct_1 C B)) ) ) ) ) )  =>  ((k1_binop_1 (k6_real_ns1 A) E (k4_rlvect_1 (k7_real_ns1 A) (k5_rlvect_2 (k7_real_ns1 A) C F))) = (k1_binop_1 (k6_real_ns1 A) E (k1_rlvect_1 (k7_real_ns1 A) E (k1_seq_1 F (k7_partfun1 (u1_struct_0 (k7_real_ns1 A)) C B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_euclid_8,ax, ((k6_euclid 3 k4_euclid_8) = (k1_euclid_8 k6_numbers k6_numbers (k19_binop_2 1))) ).
tt(t33_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_rlvect_1 (k15_euclid A) B (k9_binop_2 C D)) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B C) (k1_rlvect_1 (k15_euclid A) B D))) ) ) ) ) ) ) ) ) ).
tt(t33_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r2_euclidlp A B C) & (r2_euclidlp A C D))  => (r2_euclidlp A B D)) ) ) ) ) ) ) ) ) ).
tt(t33_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  (~  ((k1_funct_1 (k10_funct_7 D B C) A) = (k1_funct_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t33_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k3_compos_1 B C (k5_memstr_0 A B (k5_extpro_1 A B C D (k2_nat_1 E 1)))) = (k2_compos_1 B))  =>  ( ((k5_memstr_0 A B (k5_extpro_1 A B C D E)) = (k5_memstr_0 A B (k5_extpro_1 A B C D (k2_nat_1 E 1))))  |  ((k8_extpro_1 A B C D) = (k2_nat_1 E 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  ((r1_xboole_0 (k3_msafree2 A) (k2_msafree2 B)) =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 B D))) =>  ( (F = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)))  =>  (! [G:$i] :  ((r2_hidden G (u1_struct_0 B)) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_funct_1 (k5_facirc_1 (k2_circcomb A B) (k3_circcomb A B C D) E H) G) = (k1_funct_1 (k5_facirc_1 B D F H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_nat_1 A 1)) & (v1_finseq_1 B)) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  &  (? [D:$i] :  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ).
tt(t33_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_tarski B A))  => (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) ) ).
tt(t33_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k9_real_1 (k7_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos B)) (k8_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t33_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k1_sin_cos9) A) B) = (k7_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k1_sin_cos9 B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t33_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k3_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) ) ) ) )  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) & (v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) ) ) ) ) ) ).
tt(t33_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 (k8_real_1 3 A)))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ( ((k1_seq_1 D E) = (k9_real_1 B (k8_real_1 A E)))  &  ( (~  (A = k6_numbers) )  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 (k8_real_1 3 A)))) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 (k8_real_1 3 A)))) C) E) = (k10_prepower (k9_real_1 B (k8_real_1 A E)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) &  ( (B = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C k24_sin_cos) (k1_taylor_1 2))) k3_taylor_1))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 C D) = 1) ) ) ) ) )  =>  ((r2_fdiff_1 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 B A) D) = (k10_real_1 (k9_real_1 1 (k1_seq_1 k24_sin_cos D)) (k7_real_1 1 (k1_seq_1 k24_sin_cos D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 B k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B)) B))) ) ) ) ) ) ) ) ).
tt(t33_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k30_sin_cos) A) B) = (k9_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B)) B) (k10_real_1 (k1_seq_1 k3_taylor_1 B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t33_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_fdiff_9))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_fdiff_9) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k16_sin_cos B)) (k5_square_1 B))) (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t33_fib_num2,ax, (~ (r1_xxreal_0 k1_fib_num k6_numbers)) ).
tt(t33_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k13_newton (k2_nat_1 (k3_fib_num3 A B (k1_nat_1 C 1)) (k3_fib_num3 A B (k2_nat_1 (k1_nat_1 C 1) 1))) 2) = (k2_nat_1 (k2_nat_1 (k13_newton (k3_fib_num3 A B (k1_nat_1 C 1)) 2) (k4_nat_1 (k4_nat_1 2 (k3_fib_num3 A B (k1_nat_1 C 1))) (k3_fib_num3 A B (k2_nat_1 (k1_nat_1 C 1) 1)))) (k13_newton (k3_fib_num3 A B (k2_nat_1 (k1_nat_1 C 1) 1)) 2))) ) ) ) ) ) ) ).
tt(t33_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k1_fib_num3 (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1)) = (k1_int_1 (k3_power k1_fib_num (k2_xcmplx_0 (k3_xcmplx_0 2 A) 1)))) ) ) ) ).
tt(t33_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  ((k9_finseq_8 A C B) = (k1_finseq_8 A (k6_finseq_8 A C B) B)) ) ) ) ) ) ) ).
tt(t33_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k5_filter_0 A B C) = (k5_filter_0 A C B)) ) ) ) ) ) ) ).
tt(t33_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) & (l3_lattices C)) )  =>  ( ((r1_filter_1 A B) & (r1_filter_1 B C))  => (r1_filter_1 A C)) ) ) ) ) ) ) ).
tt(t33_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v14_lattices A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r1_tarski B C) & (r2_filter_2 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ((k7_finseq_1 A B) = (k7_finseq_1 C B))  |  ((k7_finseq_1 B A) = (k7_finseq_1 B C)) )  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t33_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (C = (k1_partfun1 k5_numbers A A B D E))  =>  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (~  (k1_xboole_0 = (k10_finseq_1 A B)) ) ) ) ).
tt(t33_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  (C = (k6_xcmplx_0 (k4_finseq_4 A B) 1)) )  =>  ((k5_relat_1 A (k2_finseq_1 C)) = (k5_finseq_4 A B)) ) ) ) ) ) ) ).
tt(t33_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) => (r1_tarski (k10_xtuple_0 (k2_rfinseq B A C)) (k10_xtuple_0 C))) ) ) ) ) ) ).
tt(t33_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k6_finseq_4 (k10_finseq_1 A B) B) = k1_xboole_0) ) ) ) ).
tt(t33_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 B))) ) )  =>  ( (D = E)  |  ( (F = E)  |  ((k2_finseq_7 A (k1_finseq_7 A B E C) D F) = (k1_finseq_7 A (k2_finseq_7 A B D F) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 E A) => (r2_relset_1 k5_numbers A (k1_finseqop A A A E C D) (k1_finseqop A A A E D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ( ((v2_fintopo2 A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k8_fintopo2 A B) (k8_fintopo2 A C))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C (k6_fintopo2 A B)) &  ((r2_hidden D (k6_fintopo2 A B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E (k6_fintopo2 A B)) & (r1_tarski E (k9_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_fintopo3 A B 1) = (k12_fin_topo A B)) ) ) ) ) ).
tt(t33_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_orders_2 A) &  ((v4_fin_topo B A) &  ((r1_tarski B (k4_subset_1 (u1_struct_0 A) C D)) &  ((r1_fintopo4 A C D) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_flang_1 A B (k2_xcmplx_0 C D)) = (k6_flang_1 A (k7_flang_1 A B C) (k7_flang_1 A B D))) ) ) ) ) ) ) ) ).
tt(t33_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k2_flang_1 A) (k1_flang_2 A B C D)) <=>  ( (C = k6_numbers)  |  ((r1_xxreal_0 C D) & (r2_hidden (k2_flang_1 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 C D) =>  ((k6_flang_1 A (k1_flang_3 A B E) (k1_flang_2 A B C D)) = (k1_flang_3 A B (k2_xcmplx_0 E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) & (v1_finseq_1 C)) ) )  =>  ((v5_relat_1 B (k3_finseq_2 A)) =>  ((k1_funct_1 (k8_fomodel0 A) (k7_finseq_1 B (k9_finseq_1 C))) = (k7_finseq_1 (k1_funct_1 (k8_fomodel0 A) B) C)) ) ) ) ) ) ) ) ).
tt(t33_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (D = (a_2_0_frechet2 A C))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) B) D))  => (r1_frechet A B C)) ) ) ) ) ) ) ) ) ).
tt(t33_frechet,ax,(v3_frechet k3_frechet)).
tt(t33_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k6_eqrel_1 (u1_struct_0 C) (u1_struct_0 C) (k6_fsm_1 A B C k6_numbers) D) = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(t33_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((r2_hidden A (u2_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) C)) & (r2_hidden A D))  => (r2_hidden D (u2_fsm_3 B (k9_flang_1 B) (k4_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) C)))) ) ) ) ) ) ) ) ).
tt(t33_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (~  ((k2_msafree2 (k19_ftacell1 A B C D E)) = (k3_enumset1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((k5_relat_1 A C) = (k5_relat_1 B C))  =>  ((k5_relat_1 (k5_funcop_1 D E A) C) = (k5_relat_1 (k5_funcop_1 D E B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t33_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ( ((k10_xtuple_0 A) = (k9_xtuple_0 (k2_funct_1 A)))  &  ((k9_xtuple_0 A) = (k10_xtuple_0 (k2_funct_1 A))) ) ) ) ) ).
tt(t33_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski A C) => (r2_relset_1 A B (k2_partfun1 A B D C) D)) ) ) ) ) ) ).
tt(t33_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 A) & (r1_tarski B (k1_zfmisc_1 (k9_xtuple_0 A))))  =>  ((k8_relat_1 (k3_funct_3 A) B) = (k7_relat_1 (k1_funct_3 A) B)) ) ) ) ) ).
tt(t33_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k5_relat_1 (k1_funct_4 A B) (k9_xtuple_0 A)) = A) ) ) ) ) ) ).
tt(t33_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k3_funct_5 B))) =>  ((v1_relat_1 (k1_funct_1 (k3_funct_5 B) A)) & (v1_funct_1 (k1_funct_1 (k3_funct_5 B) A))) ) ) ) ) ).
tt(t33_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B (k10_xtuple_0 C)) &  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k10_xtuple_0 C)) => (r2_hidden A (k9_xtuple_0 D))) ) ) )  => (r2_hidden A (k9_xtuple_0 (k6_funct_6 C)))) ) ) ) ) ) ).
tt(t33_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~  (D = E) )  =>  ((k2_funct_7 (k2_funct_7 A D B) E C) = (k2_funct_7 (k2_funct_7 A E C) D B)) ) ) ) ) ) ) ) ).
tt(t33_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_funct_8 A k1_numbers k1_numbers) => (v6_funct_8 (k32_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t33_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_int_1 C))  => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k16_sin_cos B) A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ).
tt(t33_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l2_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v6_functor0 D A B) &  ((v8_functor0 D A B) & (l2_functor0 D A B)) )  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_functor0 A C (k13_functor0 A B C D E) F) = (k3_functor0 B C E (k3_functor0 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  ( ((r1_functor3 A B C D) & (r1_functor3 A B D E))  => (r1_functor3 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers B (k2_fuzzy_1 A C D)) <=>  ((r1_fuzzy_1 C B) &  ((r1_fuzzy_1 D B) &  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 C E) & (r1_fuzzy_1 D E))  => (r1_fuzzy_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_2 A (k3_fuzzy_2 A B C) (k3_fuzzy_2 A B D)) (k3_fuzzy_2 A B (k2_fuzzy_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t33_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden k1_xxreal_0 (k2_relset_1 k7_numbers B))) ) ) ) ) ).
tt(t33_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ( (D = (k1_funct_1 F A))  &  (E = (k1_funct_1 G A)) ) )  =>  ((k1_funct_1 (k8_fvsum_1 B C F G) A) = (k5_algstr_0 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~  ( (~ (v1_xboole_0 (k27_gate_1 A B C D E F G)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) & (v1_xboole_0 G)) ) ) ) ) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) & (v1_xboole_0 G)) ) ) ) ) ) )  & (v1_xboole_0 (k27_gate_1 A B C D E F G))) ) ) ) ) ) ) ) ) ) ).
tt(t33_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_gcd_1 A B C D) = (k4_struct_0 A))  <=>  ( (C = (k4_struct_0 A))  &  (D = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((r1_xxreal_0 (k3_finseq_1 F) A) =>  ((k10_genealg1 E F G A B C D) = (k9_genealg1 E F G B C D)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) B) =>  ((k10_genealg1 E F G A B C D) = (k9_genealg1 E F G A C D)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) C) =>  ((k10_genealg1 E F G A B C D) = (k9_genealg1 E F G A B D)) )  &  ((r1_xxreal_0 (k3_finseq_1 F) D) =>  ((k10_genealg1 E F G A B C D) = (k9_genealg1 E F G A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r3_analmetr A D E F G B C) <=>  ((k4_geomtrap A B C (k5_algstr_0 A E D) (k5_algstr_0 A G F)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  ((k2_msafree2 (k13_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t33_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] : (r1_tarski (k21_glib_000 A B) (k20_glib_000 A B))) ) ) ).
tt(t33_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  ( ((k4_glib_001 A B) = (k3_glib_001 A C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 C) D))  =>  ( ((k1_funct_1 (k7_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) D)) = (k1_funct_1 C (k2_nat_1 D 1)))  & (r2_hidden (k2_nat_1 (k3_finseq_1 B) D) (k1_relset_1 k5_numbers (k7_glib_001 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden C (k24_glib_000 A B)) <=>  ((k24_glib_000 A B) = (k1_glib_002 A C)) ) ) ) ) ) ) ) ).
tt(t33_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) =>  ((k1_funct_1 (k6_glib_003 (k12_glib_003 A B C)) B) = C) ) ) ) ) ) ).
tt(t33_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k1_glib_002 A (k10_subset_1 (k6_glib_000 A))))) ) ) ) ).
tt(t33_goboard1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A)) ) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B D) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A C)))) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  ((r1_xxreal_0 2 (k3_finseq_1 B)) & (r1_xboole_0 (k3_topreal1 2 B) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A C)))) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 A)) &  ((r2_hidden E (k4_finseq_1 B)) &  ((r2_hidden F (k4_finseq_1 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B E) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))) &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r2_hidden G (k4_finseq_1 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B G) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))))  => (r1_xxreal_0 G E)) ) )  &  ( (~ (r1_xxreal_0 F E))  &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B F) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A D))) & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  => (r2_hidden (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)))) ) ) ) ) ).
tt(t33_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 A)) 1)) ) ) ).
tt(t33_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k7_nat_d (k1_matrix_1 (k2_goboard2 A)) 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A))) (k19_euclid (k4_xcmplx_0 1) 1))) (k3_topreal1 2 A))) ) ).
tt(t33_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  => (v4_pre_topc (k3_goboard5 C A B) (k15_euclid 2))) ) ) ) ) ) ).
tt(t33_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) C B)) )  =>  ((r1_tarski (k3_gobrd13 C B A) (k5_goboard5 C A)) & (r1_tarski (k2_gobrd13 C B A) (k4_goboard5 C A))) ) ) ) ) ) ) ) ).
tt(t33_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~ (v9_rltopsp1 (k2_goboard9 A) (k15_euclid 2))) ) ) ).
tt(t33_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (~  ((v4_card_3 A) &  ((v2_goedelcp B A) &  (! [C:$i] :  ( ((v1_henmodel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (~  ((r1_tarski B C) &  ((v1_goedelcp C A) & (v2_goedelcp C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ( ((r1_partfun1 (u1_graph_1 A) (u1_graph_1 B)) & (r1_partfun1 (u2_graph_1 A) (u2_graph_1 B)))  => (r1_tarski (k2_xboole_0 (k11_graph_1 A) (k11_graph_1 B)) (k11_graph_1 (k5_graph_1 A B)))) ) ) ) ) ).
tt(t33_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  (? [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) & (r1_graph_2 A C B)) ) ) ) ) ) ).
tt(t33_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k10_graph_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t33_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v7_graph_1 F A) & (m2_graph_1 F A))  =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 F)) &  ((r1_graph_5 A F C D) &  ((r1_graph_4 A D E (k1_funct_1 B 1)) &  ( ((k3_finseq_1 B) = 1)  &  (! [G:$i] :  ( ((v7_graph_1 G A) & (m2_graph_1 G A))  =>  (~  ( (G = (k8_finseq_1 (u4_struct_0 A) F B))  & (r1_graph_5 A G C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k4_finseq_1 (k6_graphsp (k16_graphsp A) B)) = (k4_finseq_1 B)) ) ) ) ) ).
tt(t33_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k25_grcat_1 A))) =>  ((r2_hidden (k4_tarski C B) (k9_xtuple_0 (u1_cat_1 (k25_grcat_1 A)))) <=>  ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B)) ) ) ) ) ) ) ) ).
tt(t33_gr_cy_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ( ((r1_int_2 A C) & (r2_int_1 A (k3_xcmplx_0 B B) C))  => (r1_int_2 B C)) ) ) ) ) ) ) ).
tt(t33_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A B) & (r1_tarski A C))  =>  ((k5_relat_1 B (k9_xtuple_0 A)) = (k5_relat_1 C (k9_xtuple_0 A))) ) ) ) ) ) ) ) ).
tt(t33_groeb_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (~  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) => (r1_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t33_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [G:$i] :  ((m2_ideal_1 G (k11_polynom1 A C) F) =>  (! [H:$i] :  ((m2_ideal_1 H (k11_polynom1 A C) F) =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I A) &  ((v1_funct_1 I) &  ((v1_partfun1 I A) &  ((v4_valued_0 I) & (v2_pre_poly I)) ) ) ) )  =>  ( ((r3_groeb_2 A B C D F G I) & (r3_groeb_2 A B C E F H I))  => (r3_groeb_2 A B C (k4_polynom1 A C D E) F (k5_groeb_2 A C F G H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k4_polynom1 A C (k5_groeb_3 A B C D E) (k6_groeb_3 A B C D E)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k2_group_11 A (k1_group_11 A B C) C)) & (r1_xboole_0 (k13_group_2 A C D) (k1_group_11 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t33_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k5_group_1 C (k20_binop_2 A B) D) = (k6_algstr_0 C (k5_group_1 C A D) (k5_group_1 C B D))) ) ) ) ) ) ) ) ) ).
tt(t33_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k5_group_2 A D (k4_group_2 A C B)) = (k4_group_2 A C (k5_group_2 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t33_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_group_3 A B C) (k2_group_2 A (k2_group_2 A (k1_group_2 A C) B) C))) ) ) ) ) ) ).
tt(t33_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (m1_group_2 (k5_group_4 A (k9_subset_1 (u1_struct_0 A) B C)) (k10_group_2 A (k5_group_4 A B) (k5_group_4 A C)))) ) ) ) ) ) ).
tt(t33_group_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_5 B C (k5_group_1 B A D)) = (k6_algstr_0 B (k5_group_1 B (k4_xcmplx_0 A) (k2_group_3 B D C)) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ).
tt(t33_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k2_group_3 A C D)) = (k2_group_3 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) & (l3_algstr_0 C)) )  =>  ((k1_group_1 (k2_group_7 (k1_enumset1 1 2 3) (k11_finseq_1 A B C))) = (k6_group_7 A B C (k1_group_1 A) (k1_group_1 B) (k1_group_1 C))) ) ) ) ) ) ) ).
tt(t33_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  ( ((k19_group_9 A B (k4_group_9 A B) C) = C)  &  ((k19_group_9 A B C (k4_group_9 A B)) = C) ) ) ) ) ) ) ).
tt(t33_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  ( ((r1_group_6 B C) & (v2_groupp_1 B A))  => (v2_groupp_1 C A)) ) ) ) ) ) ) ).
tt(t33_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (v2_compts_1 D (k3_pcomps_1 A))) )  => (r1_xxreal_0 (k8_weierstr A B D) (k7_real_1 (k1_hausdorf A B C) (k1_hausdorf A C D)))) ) ) ) ) ) ) ) ) ).
tt(t33_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ( ((v3_glib_002 D) & (m1_glib_000 D A))  =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 D)) =>  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 D)) =>  ( ( (B = E)  &  (C = F) )  =>  ((k2_helly A B C) = (k2_helly D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k3_bilinear k1_complfld A B C D)) (k3_bilinear k1_complfld A B (k3_hermitan A B C) (k2_complfld D)))) ) ) ) ) ) ) ) ).
tt(t33_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))))  =>  (~  ( (~  (B = (k1_tarski k1_xboole_0)) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) )  =>  (~  ((r2_hidden C B) &  (~  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_taylor_1 C A B) =>  ((r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k32_valued_1 k1_numbers k1_numbers C) B) A) (k32_valued_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C B) A))) & (r1_taylor_1 (k32_valued_1 k1_numbers k1_numbers C) A B)) ) ) ) ) ) ) ) ).
tt(t33_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v6_ideal_1 A)) ) ).
tt(t33_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 (k4_hilbert1 A B) C) (k3_hilbert1 A (k3_hilbert1 B C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t33_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ((k3_hilbert2 (k3_hilbert1 A B)) = (k6_trees_4 (k3_hilbert1 A B) (k3_hilbert2 A) (k3_hilbert2 B))) ) ) ) ) ).
tt(t33_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_hilbert3 B A) => (r2_funct_2 (k3_hilbert3 A k2_hilbert1) (k3_hilbert3 A k2_hilbert1) (k5_hilbert3 A B k2_hilbert1) (k6_partfun1 (k3_hilbert3 A k2_hilbert1)))) ) ) ) ).
tt(t33_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_polynom5 A B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~ (r2_funct_2 k5_numbers (u1_struct_0 A) B (k13_polynom3 A (k3_hurwitz A C 1) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ((r1_idea_1 A (k1_recdef_1 C 1)) &  ((r1_idea_1 A (k1_recdef_1 C 2)) &  ((r1_idea_1 A (k1_recdef_1 C 3)) &  ((r1_idea_1 A (k1_recdef_1 C 4)) &  ( ((k1_recdef_1 D 1) = (k10_idea_1 A (k1_recdef_1 C 1)))  &  ( ((k1_recdef_1 D 2) = (k6_idea_1 A (k1_recdef_1 C 3)))  &  ( ((k1_recdef_1 D 3) = (k6_idea_1 A (k1_recdef_1 C 2)))  &  ( ((k1_recdef_1 D 4) = (k10_idea_1 A (k1_recdef_1 C 4)))  &  ( ((k1_recdef_1 D 5) = (k1_recdef_1 C 5))  &  ((k1_recdef_1 D 6) = (k1_recdef_1 C 6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_partfun1 k14_idea_1 k14_idea_1 k14_idea_1 k14_idea_1 (k15_idea_1 A C) (k16_idea_1 A D)) B) = B) ) ) ) ) ) ) ) ) ) ).
tt(t33_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_ideal_1 C A B))  =>  (? [D:$i] :  ((m2_ideal_1 D A B) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k8_finseq_1 (u1_struct_0 A) D (k12_finseq_1 (u1_struct_0 A) E))) & (m2_ideal_1 (k12_finseq_1 (u1_struct_0 A) E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k2_incsp_1 A D C B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) &  ((v3_cat_5 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m5_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) =>  ((m4_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) C) =>  ((k16_index_1 A B C D) = (k15_index_1 A C B E (k9_index_1 B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  (! [E:$i] :  ((l3_msualg_1 E B) =>  (! [F:$i] :  ((l3_msualg_1 F B) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 B) (u3_msualg_1 B E) (u3_msualg_1 B F)) =>  (! [H:$i] :  ((m2_pboole H (u1_struct_0 A) (u3_msualg_1 A (k1_instalg1 A B E C D)) (u3_msualg_1 A (k1_instalg1 A B F C D))) =>  ( (H = (k3_relat_1 C G))  =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 B)) =>  ( (J = (k1_funct_1 D I))  =>  ( ((k3_msualg_1 B J E) = k1_xboole_0)  |  ( ((k3_msualg_1 B J F) = k1_xboole_0)  |  (! [K:$i] :  ((m1_subset_1 K (k3_msualg_1 B J E)) =>  (! [L:$i] :  ((m1_subset_1 L (k3_msualg_1 A I (k1_instalg1 A B E C D))) =>  ( (K = L)  =>  ((k5_msualg_3 A (k1_instalg1 A B E C D) (k1_instalg1 A B F C D) I H L) = (k5_msualg_3 B E F J G K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_xcmplx_0 (k2_int_1 A) B) = (k2_int_1 (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t33_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k2_int_2 A B) = (k2_int_2 (k1_int_2 A) (k1_int_2 B))) ) ) ) ) ).
tt(t33_int_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden C (k1_relset_1 k5_numbers B)) & (r1_nat_d A (k1_recdef_1 B C)))  => (r1_nat_d A (k3_wsierp_1 B))) ) ) ) ) ) ) ).
tt(t33_int_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 B)) => (r2_int_1 (k1_funct_1 B D) (k4_xcmplx_0 (k1_funct_1 C D)) A)) ) ) )  => (r2_int_1 (k19_rvsum_1 B) (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k3_finseq_1 B)) (k19_rvsum_1 C)) A)) ) ) ) ) ) ) ).
tt(t33_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k1_funct_1 (k4_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) D) (k2_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t33_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers B (k10_real_1 1 2)))) &  (B = (k1_taylor_1 2)) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers B (k10_real_1 1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers B (k10_real_1 1 2)) A) C) = C) ) ) ) ) ) ) ) ) ) ).
tt(t33_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k12_binop_2 (k5_square_1 (k1_seq_1 k16_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D)))) ) ) )  &  ((r1_tarski C (k1_relset_1 C (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers C)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers C)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers C)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t33_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k5_square_1 D) (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 D))))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t33_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k16_sin_cos D)) D) (k10_real_1 (k8_real_1 (k1_seq_1 k3_taylor_1 D) (k1_seq_1 k19_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t33_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((k12_integr15 B C A D) = (k6_euclid A (k12_integr15 C B A D))) ) ) ) ) ) ) ) ) ).
tt(t33_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (~  ((r2_hidden A (k4_finseq_1 C)) &  ((r1_integra1 C D) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  ((k1_seq_1 C A) = (k1_seq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v3_integra1 B A) &  ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) & (v3_integra1 C A)) ) )  =>  ((v3_integra1 (k47_valued_1 A k1_numbers k1_numbers B C) A) &  ((k12_integra1 A (k47_valued_1 A k1_numbers k1_numbers B C)) = (k9_real_1 (k12_integra1 A B) (k12_integra1 A C))) ) ) ) ) ) ) ) ) ).
tt(t33_integra8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 k29_sin_cos)) =>  ((r2_fdiff_1 k29_sin_cos A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 k29_sin_cos A) B) = (k10_real_1 1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t33_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) B) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) B)) &  ((v3_integra1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) C))) ) ) ) ) )  => (r1_xxreal_0 k6_numbers (k1_integra9 B A A))) ) ) ) ) ).
tt(t33_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k3_setfam_1 B (k2_setfam_1 B C)) = B) ) ) ) ) ) ).
tt(t33_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) => (r2_hidden (k3_intpro_1 A (k4_intpro_1 A A)) k8_intpro_1)) ) ).
tt(t33_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k13_complex1 (k9_newton A) (k9_newton B)) k6_numbers)) ) ) ) ) ).
tt(t33_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k4_isocat_1 A B C D D (k6_nattra_1 A B D) E) (k6_nattra_1 A C (k9_cat_1 A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A (k8_cat_2 B C)) =>  (! [E:$i] :  ((m2_cat_1 E A (k8_cat_2 B C)) =>  (! [F:$i] :  ((m2_cat_1 F A (k8_cat_2 B C)) =>  (! [G:$i] :  ((m2_cat_1 G A (k8_cat_2 B C)) =>  ( ((r2_nattra_1 A (k8_cat_2 B C) D E) & (r2_nattra_1 A (k8_cat_2 B C) F G))  =>  (! [H:$i] :  ((m2_nattra_1 H A (k8_cat_2 B C) D E) =>  (! [I:$i] :  ((m2_nattra_1 I A (k8_cat_2 B C) F G) =>  ( ((r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k11_isocat_2 A B C D E H) (k11_isocat_2 A B C F G I)) & (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k12_isocat_2 A B C D E H) (k12_isocat_2 A B C F G I)))  => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 (k8_cat_2 B C)) H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_isomichi,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  (k1_numbers = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 A) (k1_rcomp_1 A B)) (k2_rcomp_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t33_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_complex1 (k17_euclid A)) (k12_euclid A)) & (r1_xxreal_0 (k18_complex1 (k18_euclid A)) (k12_euclid A))) ) ) ).
tt(t33_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k10_real_1 (k18_euclid C) (k17_euclid C)) (k17_euclid C))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t33_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k8_real_1 (k17_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid C) (k17_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t33_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B)) = (k12_euclid B)) ) ) ) ) ).
tt(t33_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((r1_tarski (k8_jordan6 A) A) & (r1_tarski (k9_jordan6 A) A)) ) ) ) ).
tt(t33_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))) = (k1_tarski (k19_euclid B D))) ) ) ) ) ) ) ) ) ) ).
tt(t33_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = E)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) & (r1_xxreal_0 (k17_euclid B) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r2_jordan12 2 A B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  =>  ( ((v1_abian (k1_card_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k2_topreal1 2 B C)))) & (m1_subset_1 (k1_card_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k2_topreal1 2 B C))) k5_numbers))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) D) &  ((r2_hidden (k1_funct_1 B C) D) & (r2_hidden (k1_funct_1 B (k2_nat_1 C 1)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan14,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) & (v1_topreal1 B))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 D (k1_matrix_1 A)))  => (r1_tarski (k1_tops_1 (k15_euclid 2) (k3_goboard5 A C D)) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan18,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ( (~  (B = C) )  &  ( (~  (D = B) )  &  ( (~  (D = C) )  &  ( (~  (E = B) )  &  ( (~  (E = C) )  &  ((r1_jordan18 2 A B C D E) & (r1_jordan18 2 A B D C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E A)) C) |  ((r1_xxreal_0 D 1) |  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 E A)) D) |  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (F = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2))  &  (G = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 D 2)) 2)) )  =>  ((k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E A) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_6_jordan1 A B C D))  => (v3_pre_topc E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_matrix_1 A)) & (v9_rltopsp1 (k3_goboard5 A k6_numbers B) (k15_euclid 2))) ) ) ) ) ) ).
tt(t33_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = (k2_xcmplx_0 (k6_pscomp_1 B) (k8_pscomp_1 B))) ) ) ) ) ).
tt(t33_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B)))  &  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k2_jordan1h (u1_struct_0 (k15_euclid 2)) B))) )  =>  (B = (k2_goboard2 A)) ) ) ) ) ) ).
tt(t33_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k6_pscomp_1 B) (k6_pscomp_1 A)))  =>  ((k18_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_pscomp_1 A)) ) ) ) ) ) ).
tt(t33_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 C (k17_euclid A) C (k18_euclid A)) B) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B C) A)) ) ) ) ) ) ) ).
tt(t33_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) (k2_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k9_pscomp_1 A))))) ) ).
tt(t33_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k1_jordan21 A) (k3_jordan19 A))) ) ).
tt(t33_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v2_topreal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (v2_topreal1 (k3_jordan3 A B))) ) ) ) ) ) ).
tt(t33_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (~  ((r1_xxreal_0 1 A) &  ( (B = (k1_euclid A))  & (v6_tbsp_1 B (k14_euclid A))) ) ) ) ) ) ) ).
tt(t33_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  | (r1_jordan3 (k2_jordan3 A B) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) ) ) ) ).
tt(t33_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 B C) |  ((r1_xxreal_0 (k3_finseq_1 A) B) | (r1_jordan4 A (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B (k7_nat_d (k3_finseq_1 A) 1)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 C)) B C)) ) ) ) ) ) ) ) ) ).
tt(t33_jordan5b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  =>  ( ((r1_xxreal_0 (k1_jordan3 A C) (k1_jordan3 A B)) &  (~  ( ((k1_jordan3 A B) = (k1_jordan3 A C))  & (r2_jordan3 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k1_jordan3 A B)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1)) B C)) ) )  |  ( (B = C)  | (r1_tarski (k3_topreal1 2 (k4_jordan3 A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ).
tt(t33_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden A (k3_topreal1 2 B)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 B)))) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) C 1)) (k18_euclid A))) ) ) ) ) ) ) ).
tt(t33_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v1_topreal2 A) &  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) B) &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c C (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 C (k3_jordan_a 2 (k2_jordan_a A D B)))) ) )  & (r1_xxreal_0 C (k4_jordan_a A B))) ) ) ) ) ) ) ) ).
tt(t33_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A C D))  => (r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_abian (u1_struct_0 A) C B) &  ((r2_abian (u1_struct_0 A) D B) &  (! [E:$i] :  ((v3_ordinal1 E) =>  (~  ((r1_ordinal1 (k1_card_1 E) (k1_card_1 (u1_struct_0 A))) &  ((r2_abian (u1_struct_0 A) (k6_knaster A B (k4_lattices A C D) E) B) &  ((r3_lattices A (k6_knaster A B (k4_lattices A C D) E) C) & (r3_lattices A (k6_knaster A B (k4_lattices A C D) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) = (k2_pre_topc k3_topmetr k6_kurato_1)) ) ).
tt(t33_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B D))) )  &  ((m2_valued_0 C (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B) &  (! [D:$i] :  ((m2_valued_0 D (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A) =>  (~  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) D E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  ((k4_matrix_6 A B (k1_matrix_7 A B (k5_matrix_1 A (u1_struct_0 B) (k7_laplace A B C)) (k11_algstr_0 B (k12_matrix_3 A B C))) C) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ).
tt(t33_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_1 C) => (m1_lattice4 (k3_latsubgr A B C) (k11_group_4 A) (k11_group_4 B))) ) ) ) ) ) ) ).
tt(t33_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden F C) => (r3_lattices A (k3_funct_2 B (u1_struct_0 A) D F) (k3_funct_2 B (u1_struct_0 A) E F))) ) )  =>  ( (C = k1_xboole_0)  | (r3_lattices A (k2_lattice2 B A C D) (k2_lattice2 B A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((v5_lattice3 A) <=>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_lattices A (k4_lattices A C (k15_lattice3 A B)) (k15_lattice3 A (a_3_3_lattice3 A B C)))) ) ) ) ) ) ).
tt(t33_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_lattice4 D A) =>  ( ((r2_hidden B D) & (r2_hidden C D))  => (r2_hidden (k4_filter_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t33_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v2_lattice5 D A B) =>  (! [E:$i] :  ((m1_lattice5 E A B D) => (v2_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow11 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_lattice8 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 D C A) &  ((v2_lattice5 D C A) &  ((v3_lattice5 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ( (C = (k3_tarski (a_2_0_lattice8 A B)))  &  ( (D = (k3_tarski (a_2_1_lattice8 A B)))  &  ((r3_orders_2 A (k3_lattice5 C A D E F) (k13_lattice3 A G H)) &  (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  (~  ( ((k3_lattice5 C A D E I) = G)  &  ( ((k3_lattice5 C A D I J) = (k12_lattice3 A (k13_lattice3 A (k3_lattice5 C A D E F) G) H))  &  ((k3_lattice5 C A D J F) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k15_glib_000 A) B) =>  ((k13_lexbfs A (k16_lexbfs A) (k15_glib_000 A)) = (k13_lexbfs A (k16_lexbfs A) B)) ) ) ) ) ) ).
tt(t33_lfuzzy_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v9_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_0_lfuzzy_1 A B C))) ) ) ) ) ) ) ).
tt(t33_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v1_seqm_3 A) &  ( (~ (v2_comseq_2 A))  &  ( (~ (v1_limfunc1 A))  &  (~ (v2_limfunc1 A)) ) ) ) ) ) ) ).
tt(t33_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r2_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t33_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc3 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc3 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k7_real_1 (k1_limfunc3 B A) (k1_limfunc3 C A))) ) ) ) ) ) ) ) ) ).
tt(t33_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r5_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k5_limfunc1 A))) ) ) ) )  | (v7_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t33_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((r1_lmod_6 A C D) & (r1_lmod_6 A E D))  => (r1_lmod_6 A (k1_vectsp_5 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) => (r1_xxreal_0 k6_numbers (k1_normsp_0 (k16_lopban_1 A B) C))) ) ) ) ) ) ).
tt(t33_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v8_valued_0 (k4_normsp_0 A B)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 C D) = (k8_real_1 (k4_power 2 D) (k1_seq_1 (k4_normsp_0 A B) (k4_power 2 D)))) ) ) )  =>  ((v2_lopban_3 B A) <=> (v1_series_1 C)) ) ) ) ) ) ) ) ).
tt(t33_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 (u1_struct_0 A) D E) = (k8_nat_1 (u1_struct_0 A) (k1_bhsp_4 A (k8_lopban_4 A B C E)) E)) ) )  =>  ((v3_normsp_1 D A) &  ((k6_normsp_1 A D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k10_lopclset A) = (k1_lopclset (k11_lopclset A))) ) ) ).
tt(t33_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r2_relset_1 B k1_numbers (k3_valued_1 B k1_numbers k1_numbers (k8_lpspace1 B k6_numbers) (k8_lpspace1 B k6_numbers)) (k8_lpspace1 B k6_numbers)) & (r2_relset_1 B k1_numbers (k26_valued_1 B k1_numbers (k8_lpspace1 B k6_numbers) A) (k8_lpspace1 B k6_numbers))) ) ) ) ) ).
tt(t33_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_lpspace2 A B C F))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k4_lpspace2 A B C F))) =>  ( ( (D = G)  &  (E = H) )  =>  ((k3_valued_1 A k1_numbers k1_numbers D E) = (k1_algstr_0 (k4_lpspace2 A B C F) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((v1_ltlaxio1 A) => (r3_ltlaxio1 B A)) ) ) ) ) ).
tt(t33_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A B) (k8_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t33_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A (k9_subset_1 (u1_struct_0 A) B C) D) = (k9_subset_1 (u1_struct_0 A) (k3_mathmorp A B D) (k3_mathmorp A C D))) ) ) ) ) ) ) ) ) ).
tt(t33_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) => (v4_matrix10 (k1_matrix10 B))) ) ) ) ).
tt(t33_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) =>  ( ((r2_hidden E (k2_finseq_1 A)) &  ( ((k3_finseq_1 F) = A)  &  ((k3_finseq_1 G) = A) ) )  =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 B) A A) =>  ((k12_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) H (k3_fvsum_1 B (k9_fvsum_1 B F C) (k9_fvsum_1 B G D)))) = (k3_rlvect_1 B (k8_group_1 B C (k12_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) H F))) (k8_group_1 B D (k12_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) H G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_finseq_1 C) (k2_finseq_1 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))))) )  =>  ( (E = (k1_partfun1 (k2_finseq_1 C) (k2_finseq_1 C) k5_numbers k5_numbers H F))  =>  ((k1_matrix13 A D C B E G) = (k4_matrix11 C B A H (k1_matrix13 A D C B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k4_finseq_1 (k11_fvsum_1 A B C)) = (k9_subset_1 k5_numbers (k4_finseq_1 B) (k4_finseq_1 C)))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 (k11_fvsum_1 A B C))) =>  ((k1_funct_1 (k11_fvsum_1 A B C) D) = (k8_group_1 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 (k4_matrix15 A B C)))  =>  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) ) ) ) ) ) ) ).
tt(t33_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v2_matrix16 B (u1_struct_0 A)) &  ((v2_matrix16 C (u1_struct_0 A)) &  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) )  => (v2_matrix16 (k3_fvsum_1 A B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t33_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k14_matrix_1 B A C (k11_matrix_1 B A)) = C) ) ) ) ) ) ) ).
tt(t33_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k1_matrix_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 C) = (k3_finseq_1 D)) )  =>  ((k4_matrix_3 A (k4_matrix_3 A B C) D) = (k4_matrix_3 A B (k4_matrix_3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A B (k1_matrix_4 A C D)) = (k3_matrix_3 A B (k1_matrix_4 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((v3_matrix_6 C B A) & (v3_matrix_6 D B A))  => (v3_matrix_6 (k3_matrix_6 B A C D) B A)) ) ) ) ) ) ) ) ) ).
tt(t33_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ((r1_xxreal_0 1 A) &  ( ((k3_finseq_1 D) = A)  &  (E = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) k5_numbers (u1_struct_0 B) C D)) ) )  =>  ((k1_finsop_1 (u1_struct_0 B) D (u2_algstr_0 B)) = (k1_finsop_1 (u1_struct_0 B) E (u2_algstr_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v4_matrix_8 C A B) & (v2_matrix_6 C A B))  => (v4_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t33_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  (~  ((r2_funct_2 (k2_finseq_1 A) (k2_finseq_1 A) B (k6_partfun1 (k2_finseq_1 A))) & (v4_matrix_2 B A)) ) ) ) ) ) ).
tt(t33_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k5_matrixc1 A (k10_seq_4 B C)) = (k10_seq_4 (k5_matrixc1 A B) (k5_matrixc1 A C))) ) ) ) ) ) ) ) ).
tt(t33_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  (C = (k6_matrix13 A (k13_matrixj1 A B (k3_matrixj1 A D (k4_matrixj1 A C))) (k7_subset_1 k5_numbers (k2_finseq_1 (k2_nat_1 (k3_finseq_1 C) (k2_wsierp_1 (k10_matrixj1 A D)))) (k2_finseq_1 (k2_wsierp_1 (k10_matrixj1 A D)))) (k7_subset_1 k5_numbers (k2_finseq_1 (k2_nat_1 (k1_matrix_1 C) (k2_wsierp_1 (k11_matrixj1 A D)))) (k2_finseq_1 (k2_wsierp_1 (k11_matrixj1 A D)))))) ) ) ) ) ) ) ) ) ).
tt(t33_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k3_matrixr1 A A) = (k7_matrixr1 2 A)) ) ) ).
tt(t33_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k3_finseq_1 B) = A)  &  ( ((k3_finseq_1 C) = A)  &  ((k3_finseq_1 D) = A) ) )  => (v1_matrix_1 (k11_finseq_1 B C D))) ) ) ) ) ) ) ) ) ).
tt(t33_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ( ((k3_finseq_1 D) = k1_xboole_0)  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k4_matrlin2 A B C D E G) F) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D C) &  ((v9_vectsp_1 D C) &  ((v10_vectsp_1 D C) &  ((v11_vectsp_1 D C) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D C) & (l1_vectsp_1 D C)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 C)) &  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 C)) &  ( ((k3_finseq_1 F) = A)  &  ( ((k3_finseq_1 G) = B)  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k9_xtuple_0 G)) =>  ((k7_partfun1 (u1_struct_0 C) G H) = (k4_rlvect_1 C (k11_fvsum_1 C F (k9_matrix_1 (u1_struct_0 C) E H)))) ) ) )  &  (? [H:$i] :  ((m2_finseq_1 H (u1_struct_0 D)) &  (? [I:$i] :  ((m2_finseq_1 I (u1_struct_0 D)) &  ( ((k3_finseq_1 H) = B)  &  ( ((k3_finseq_1 I) = A)  &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  ((r2_hidden J (k9_xtuple_0 I)) =>  ((k7_partfun1 (u1_struct_0 D) I J) = (k4_rlvect_1 D (k5_matrlin C D (k8_matrix_1 (u1_struct_0 C) E J) H))) ) ) )  &  (~  ((k4_rlvect_1 D (k5_matrlin C D F I)) = (k4_rlvect_1 D (k5_matrlin C D G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_matroid0 A (k6_matroid0 A B)) = (k4_matroid0 A B)) ) ) ) ) ).
tt(t33_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 (k14_rvsum_1 A B))) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k14_rvsum_1 A B) C))) ) ) ) ) ) ) ) ).
tt(t33_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (k3_matrtop1 A A (k12_matrix_1 k2_vectsp_1 A)) (k3_struct_0 (k15_euclid A)))) ) ).
tt(t33_matrtop3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v2_matrtop3 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) )  =>  ( ((v1_matrtop3 D A) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k9_subset_1 k5_numbers A (k2_finseq_1 B))) =>  ((k1_seq_1 C E) = k1_xboole_0) ) ) ) )  =>  ((k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) D C) = C) ) ) ) ) ) ) ) ) ).
tt(t33_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D C) => (r6_pboole A (k3_pboole A D B) (k1_pboole A))) ) )  => (r6_pboole A (k3_pboole A (k2_mboolean A C) B) (k1_pboole A))) ) ) ) ) ) ).
tt(t33_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k3_zfmisc_1 A B C) = (k3_zfmisc_1 D E F))  =>  ( ((k3_zfmisc_1 A B C) = k1_xboole_0)  |  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) => (r1_xxreal_0 (k12_supinf_2 C (k1_measure1 A B D E)) (k3_supinf_2 (k12_supinf_2 C D) (k12_supinf_2 C E)))) ) ) ) ) ) ) ) ) ).
tt(t33_measure6,ax, (! [A:$i] :  ( ((v6_xxreal_2 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k2_measure5 A) = (k2_measure5 (k2_measure6 A B))) ) ) ) ) ).
tt(t33_measure8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (~  ((v1_measure8 C A B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_prob_1 A B) k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A (k9_prob_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_prob_1 A B) k7_numbers)))) ) ) ) )  =>  (~  ((r1_measure8 A B (k9_prob_1 A B) C D) &  (D = (k2_partfun1 (k1_measure4 A (k9_measure8 A B C)) k7_numbers (k3_measure4 A (k9_measure8 A B C)) (k9_prob_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k7_member_1 (k3_xboole_0 A B)) = (k3_xboole_0 (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(t33_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v3_membered B))  => (v3_membered (k1_setfam_1 A))) ) ) ).
tt(t33_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (C = (k5_relat_1 C (k4_subset_1 (u1_struct_0 B) (k8_struct_0 B) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B))))) ) ) ) ) ) ) ).
tt(t33_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r2_mesfun6c A B C D) & (r2_mesfun6c A B C E))  => (r2_mesfun6c A B C (k2_valued_1 A k2_numbers k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ( ((k9_subset_1 A (k1_relset_1 A C) (k1_relset_1 A D)) = E)  &  ((r1_mesfun6c A B C E) & (r1_mesfun6c A B D E)) )  => (r1_mesfun6c A B (k19_valued_1 A k2_numbers k2_numbers C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((v1_mesfunc8 E A k2_numbers) &  ((r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k2_numbers E k6_numbers))) & (r2_hidden C D)) )  =>  ((k8_nat_1 k2_numbers (k10_comseq_3 (k9_mesfun7c A E C)) B) = (k8_nat_1 k2_numbers (k9_mesfun7c A (k3_mesfun9c A E) C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k9_xtuple_0 C)))  => (r2_hidden (k9_subset_1 A D (k19_mesfunc1 A C k1_supinf_1)) B)) ) ) ) ) ) ) ) ) ).
tt(t33_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  ((v1_prob_2 (k5_relat_1 D (k2_finseq_1 C))) & (m2_finseq_1 (k5_relat_1 D (k2_finseq_1 C)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r2_hidden (k9_subset_1 A (k9_subset_1 A D (k18_mesfunc1 A C (k1_measure6 E))) (k15_mesfunc1 A C (k1_measure6 F))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k19_rfunct_3 A B) (k18_rfunct_3 A (k32_valued_1 A k1_numbers B)))) ) ) ) ).
tt(t33_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v2_mesfunc9 B A) &  ((v1_mesfunc8 B A k7_numbers) &  ((r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) & (r2_hidden C D)) ) )  =>  ( ((v7_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))) => (v7_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)))  &  ( ((v7_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)) => (v7_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))))  &  ( ((v8_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))) => (v8_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)))  &  ( ((v8_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)) => (v8_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))))  &  ( ((v9_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))) => (v9_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)))  &  ( ((v9_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)) => (v9_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))))  &  ( ((v10_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C))) => (v10_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)))  &  ((v10_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C)) => (v10_mesfunc5 (k2_mesfunc9 (k3_mesfunc5 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k14_metric_1 A B C)) <=> (r1_metric_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t33_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) & (r4_metric_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t33_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (! [D:$i] :  ((m1_midsp_1 D A) =>  (! [E:$i] :  ((m1_midsp_1 E A) =>  (~  ( (? [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ( (B = (k5_midsp_1 A F))  &  ( (C = (k5_midsp_1 A G))  &  ( ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) G))  &  (D = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) G)))) ) ) ) ) ) ) )  &  ( (? [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) &  ( (B = (k5_midsp_1 A F))  &  ( (C = (k5_midsp_1 A G))  &  ( ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) G))  &  (E = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) F) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) G)))) ) ) ) ) ) ) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (u1_midsp_2 A B))) =>  ( ((k9_midsp_2 A B C C) = (k11_midsp_2 A B))  &  ( ( ((k9_midsp_2 A B C D) = (k11_midsp_2 A B))  =>  (C = D) )  &  ( ((k9_midsp_2 A B C D) = (k4_algstr_0 (u1_midsp_2 A B) (k9_midsp_2 A B D C)))  &  ( ( ((k9_midsp_2 A B C D) = (k9_midsp_2 A B E F))  =>  ((k9_midsp_2 A B D C) = (k9_midsp_2 A B F E)) )  &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (u1_midsp_2 A B))) =>  (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ((k9_midsp_2 A B J H) = I) ) ) ) ) ) )  &  ( ( ((k9_midsp_2 A B D C) = (k9_midsp_2 A B E C))  =>  (D = E) )  &  ( ( ((k3_midsp_1 A C D) = E)  =>  ((k9_midsp_2 A B C E) = (k9_midsp_2 A B E D)) )  &  ( ( ((k9_midsp_2 A B C E) = (k9_midsp_2 A B E D))  =>  ((k3_midsp_1 A C D) = E) )  &  ( ( ((k3_midsp_1 A C D) = (k3_midsp_1 A E F))  =>  ((k9_midsp_2 A B C F) = (k9_midsp_2 A B E D)) )  &  ( ( ((k9_midsp_2 A B C F) = (k9_midsp_2 A B E D))  =>  ((k3_midsp_1 A C D) = (k3_midsp_1 A E F)) )  &  ( ( ((k9_midsp_2 A B C D) = G)  =>  ((k10_midsp_2 A B C G) = D) )  &  ( ((k10_midsp_2 A B C G) = D)  =>  ((k9_midsp_2 A B C D) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_midsp_3 B A) =>  (! [C:$i] :  ((m2_midsp_3 C A) =>  (! [D:$i] :  ( ((v4_midsp_2 D C) & (l1_midsp_2 D C))  =>  ((r1_xxreal_0 B A) =>  ((r4_midsp_3 A B C) <=>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 (u1_midsp_2 C D)) (k4_finseq_2 (k2_nat_1 A 1) (u1_struct_0 (u1_midsp_2 C D)))) =>  ((k10_midsp_3 A C D (k1_midsp_3 (u1_struct_0 (u1_midsp_2 C D)) (k2_nat_1 A 1) E (k2_nat_1 B 1) (k5_midsp_3 A (u1_struct_0 (u1_midsp_2 C D)) E B))) = (k11_midsp_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_mmlquery A (k21_mmlquery A C D) B) = (k17_mmlquery A (k1_mmlquery A C B) (k1_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t33_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v6_mod_4 C A B) <=> (v5_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t33_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ( ((k10_modal_1 A) = (k10_modal_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t33_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( ((k51_modelc_1 A B C (k3_robbins1 (k48_modelc_1 A B C) D)) = (k6_subset_1 A (k51_modelc_1 A B C D)))  &  ( ((k51_modelc_1 A B C (k2_lattices (k48_modelc_1 A B C) D E)) = (k9_subset_1 A (k51_modelc_1 A B C D) (k51_modelc_1 A B C E)))  &  ((k51_modelc_1 A B C (k28_modelc_1 (k48_modelc_1 A B C) D E)) = (k4_subset_1 A (k51_modelc_1 A B C D) (k51_modelc_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_modelc_2 A B) &  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~ (r1_modelc_2 C B)) ) ) ) ) ) ) ) ) ).
tt(t33_modelc_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((r5_modelc_3 B A) &  ((r1_xxreal_0 1 (k3_finseq_1 A)) &  ((u2_modelc_3 B (k10_modelc_3 (k1_funct_1 A (k3_finseq_1 A)) B)) = (k7_modelc_3 B)) ) )  => (r1_tarski (u2_modelc_3 B (k10_modelc_3 (k1_funct_1 A 1) B)) (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 A (k3_finseq_1 A)) B)))) ) ) ) ) ).
tt(t33_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (v1_moebius1 A))  &  ((k2_moebius1 A) = k6_numbers) ) ) ) ) ).
tt(t33_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ((v3_group_1 A) => (v3_group_1 B)) ) ) ) ) ).
tt(t33_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (m1_subset_1 (k18_monoid_1 A B) (u1_struct_0 (k19_monoid_1 A)))) ) ) ) ).
tt(t33_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A B) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A C) D)) = (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A B) C)) D))  &  ((k3_funct_2 (k9_setfam_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A B) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A C) D)) = (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k4_morph_01 A (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k3_morph_01 A B) C)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t33_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ( (~ (v3_relat_1 B))  &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B)))) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) => (m1_subset_1 (k5_trees_2 C D) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A B))))) ) ) ) ) ) ) ) ).
tt(t33_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_msaterm F A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finseq_1 G) & (v6_trees_3 G)) ) )  =>  (~  ( ((k3_finseq_1 G) = (k3_finseq_1 F))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((m1_dtconstr I (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (~  ((r2_hidden H (k4_finseq_1 F)) &  ( (I = (k1_funct_1 F H))  &  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v1_funct_1 J) &  ((v1_finset_1 J) & (v3_trees_2 J)) ) )  =>  (~  ( (J = (k1_funct_1 G H))  & (r1_msaterm A B C I D J)) ) ) ) ) ) ) ) ) ) )  &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) &  ((v1_finset_1 H) & (v3_trees_2 H)) ) )  =>  (~  ( (H = (k4_trees_4 (k1_funct_1 (k5_msualg_1 A E B) (k14_trees_3 G)) G))  & (r1_msaterm A B C (k6_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E) F) D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A C)) =>  ((r1_pboole A B D) => (m3_pboole B A C)) ) ) ) ) ) ) ) ).
tt(t33_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (v15_lattices (k17_msualg_2 A B))) ) ) ) ).
tt(t33_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  => (r8_pboole (u1_struct_0 A) (k6_msualg_6 A B C) C)) ) ) ) ) ) ).
tt(t33_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ( ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C)) (k15_msualg_4 A B C) D) E) = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C)) (k15_msualg_4 A B C) D) F))  <=> (r2_hidden (k4_tarski E F) (k2_msualg_4 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_dilworth (k5_mycielsk A)) = A) ) ) ).
tt(t33_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 9) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  (~  (A = 9) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 (k12_nat_3 A))) =>  ((v7_ordinal1 B) & (v1_int_2 B)) ) ) ) ) ).
tt(t33_nat_4,ax,(v1_int_2 83)).
tt(t33_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ( ( ((k5_nat_5 B) = (k23_binop_2 B A))  & (r1_nat_d A B))  =>  ( (B = A)  |  ( (A = 1)  & (v1_int_2 B)) ) ) ) ) ) ) ).
tt(t33_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~  (A = k6_numbers) )  & (v1_int_1 (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t33_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 (k11_nattra_1 A B))) =>  ( (F = (k4_tarski (k4_tarski C D) E))  =>  ( ((k3_graph_1 (k11_nattra_1 A B) F) = C)  &  ((k4_graph_1 (k11_nattra_1 A B) F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_ncfcont1 A B C E) & (r2_ncfcont1 A B D E))  =>  ((r2_ncfcont1 A B (k6_vfunct_1 (u1_struct_0 A) B C D) E) & (r2_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) &  ((v1_nfcont_1 D A) & (r3_ncfcont2 D A B C)) )  => (v1_ncfcont1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t33_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_nfcont_1 D A) & (r1_tarski D (k1_relset_1 (u1_struct_0 A) C)))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((k2_relset_1 (u1_struct_0 B) C) = (k1_tarski E)) ) ) )  |  ((r2_ndiff_1 D A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) (k4_ndiff_1 A B C D) E) = (k4_struct_0 (k16_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  => (r1_nfcont_3 (k4_real_ns1 1) B A)) ) ) ) ) ).
tt(t33_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_prvect_2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  ( (E = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) D))  =>  ( ( (B = C)  =>  ((k1_ndiff_5 A E C) = D) )  &  ( (~  (B = C) )  =>  ((k1_ndiff_5 A E C) = (k4_struct_0 (k11_prvect_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_neckla_3,ax, (! [A:$i] :  ( ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) )  =>  ( ( ((k1_card_1 (u1_struct_0 A)) = 2)  & (r2_hidden (u1_struct_0 A) k13_classes2))  => (r2_hidden (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) k4_neckla_2)) ) ) ).
tt(t33_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 B (k3_xcmplx_0 B A))) ) ) ) ) ).
tt(t33_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (~  ( (~  ((k1_relset_1 (u1_struct_0 A) B) = k1_xboole_0) )  &  ((v1_nfcont_1 (k1_relset_1 (u1_struct_0 A) B) A) &  ((r4_nfcont_1 A B (k1_relset_1 (u1_struct_0 A) B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) &  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) B)) &  ( ((k7_partfun1 k1_numbers B C) = (k4_seq_4 (k2_relset_1 k1_numbers B)))  &  ((k7_partfun1 k1_numbers B D) = (k5_seq_4 (k2_relset_1 k1_numbers B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_nfcont_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F A) =>  ((k7_partfun1 (u1_struct_0 B) C F) = (k3_rlvect_1 B (k1_rlvect_1 B D F) E)) ) ) )  => (v1_nfcont_3 (k2_partfun1 k1_numbers (u1_struct_0 B) C A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v2_nfcont_4 B A) <=>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r2_hidden D (k1_relset_1 k1_numbers B)) & (r2_hidden E (k1_relset_1 k1_numbers B)))  => (r1_xxreal_0 (k12_euclid (k8_euclid A (k7_partfun1 (k1_euclid A) B D) (k7_partfun1 (k1_euclid A) B E))) (k11_binop_2 C (k18_complex1 (k10_binop_2 D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  ( (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) C D)) )  =>  (C = D) ) ) ) ) )  => (r2_hidden B (k8_normform A))) ) ) ) ).
tt(t33_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  ( (B = C)  =>  ((v3_nfcont_1 B A) <=> (v3_pre_topc C (k4_normsp_2 A))) ) ) ) ) ) ) ) ).
tt(t33_numbers,ax,(r2_xboole_0 k1_numbers k7_numbers)).
tt(t33_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k6_openlatt (k17_openlatt A))) (k18_openlatt A) (k4_filter_0 A B C)) = (k4_filter_0 (k6_openlatt (k17_openlatt A)) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k6_openlatt (k17_openlatt A))) (k18_openlatt A) B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k6_openlatt (k17_openlatt A))) (k18_openlatt A) C))) ) ) ) ) ) ) ).
tt(t33_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A D))  =>  ((k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_orders_1 A B) => (v1_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t33_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B C) & (m1_orders_2 C A D))  =>  ((k3_orders_2 A C B) = (k3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) & (v5_ordinal1 B)) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((v1_relat_1 (k5_relat_1 B C)) &  ((v5_relat_1 (k5_relat_1 B C) A) &  ((v1_funct_1 (k5_relat_1 B C)) & (v5_ordinal1 (k5_relat_1 B C))) ) ) ) ) ) ) ) ).
tt(t33_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k10_ordinal2 C A) (k10_ordinal2 C B))) ) ) ) ) ) ) ).
tt(t33_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((k11_ordinal2 A B) = (k11_ordinal2 C B))  =>  ( (B = k1_xboole_0)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t33_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( ((k2_ordinal4 A) = k1_xboole_0)  &  ((k3_ordinal4 A) = 1) ) ) ) ).
tt(t33_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (? [B:$i] :  ((v3_ordinal1 B) &  ((r2_hidden A B) & (v4_ordinal5 B)) ) ) ) ) ).
tt(t33_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  (~  ((r1_abian A B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C (k9_xtuple_0 (k3_ordinal6 B))) &  (A = (k1_funct_1 (k3_ordinal6 B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t33_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k1_funct_1 B C)) &  (D = (k1_trees_4 (k4_tarski E C))) )  =>  ((r2_hidden F (k25_osafree A B (k20_osafree A B) D)) <=>  (F = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u4_struct_0 A)) (k7_osalg_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((m1_osalg_1 C A B) <=>  ((k8_osalg_1 A C) = B) ) ) ) ) ) ) ) ).
tt(t33_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m2_osalg_2 C A B) => (m1_msualg_2 (k12_msualg_2 A B C) A (k10_osalg_2 A B C))) ) ) ) ) ) ).
tt(t33_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_1 A B D B E) & (r1_parsp_1 A C D C E))  =>  ((r1_parsp_1 A B C B D) |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) =>  ((r2_parsp_2 A B D C E) &  ((r2_parsp_2 A D E B C) &  ((r2_parsp_2 A C B E D) &  ((r2_parsp_2 A D B E C) &  ((r2_parsp_2 A E C D B) &  ((r2_parsp_2 A C E B D) & (r2_parsp_2 A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k3_partfun1 C A B) = C) ) ) ) ) ).
tt(t33_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (~  ((v1_partfun1 (k4_partfun2 A B C D) A) &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_partit1 A (k6_partit1 A)) = (k1_eqrel_1 A)) ) ) ).
tt(t33_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k2_pboole A B (k3_pboole A C D)) (k3_pboole A (k2_pboole A B C) (k2_pboole A B D)))) ) ) ) ) ) ) ).
tt(t33_pcomps_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ((v2_pre_topc (g1_pre_topc (u1_struct_0 A) (k2_pcomps_1 A))) & (l1_pre_topc (g1_pre_topc (u1_struct_0 A) (k2_pcomps_1 A)))) ) ) ).
tt(t33_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k20_pcs_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k20_pcs_0 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_orders_2 A B C) <=> (r1_orders_2 (k20_pcs_0 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_pdiff_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r3_pdiff_1 A B D E) =>  ((r3_pdiff_1 A B (k26_valued_1 (k1_euclid A) k1_numbers D C) E) &  ((k11_pdiff_1 A B (k26_valued_1 (k1_euclid A) k1_numbers D C) E) = (k8_real_1 C (k11_pdiff_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r1_pdiff_3 B A) & (r1_pdiff_3 C A))  => (r3_pdiff_1 2 1 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A)) ) ) ) ) ) ) ).
tt(t33_pdiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((r3_pdiff_1 3 3 A B) => (r1_fcont_1 (k1_pdiff_2 3 3 A B) (k1_seq_1 (k1_pdiff_1 3 3) B))) ) ) ) ) ).
tt(t33_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r6_pdiff_5 B A) =>  ((k6_pdiff_5 B A) = (k11_pdiff_1 3 3 (k1_pdiff_3 2 3 B) A)) ) ) ) ) ) ).
tt(t33_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid A))) =>  (~  ((r1_pdiff_6 D B A C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  (~  ( (D = E)  & (v3_nfcont_1 E (k4_real_ns1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ( (D = E)  =>  ((r2_pdiff_7 A B C D F) <=> (r7_pdiff_1 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ( ((r4_pdiff_7 A B D C) & (r4_pdiff_7 A B E C))  =>  ((r4_pdiff_7 A B (k7_integr15 B (k1_euclid A) D E) C) & (r4_pdiff_7 A B (k8_integr15 B (k1_euclid A) D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v1_int_2 A) =>  ((r1_xxreal_0 (k1_newton A (k1_nat_1 B 1)) C) |  ((r1_nat_d C (k1_newton A (k1_nat_1 B 1))) <=> (r1_nat_d C (k1_newton A B))) ) ) ) ) ) ) ) ) ).
tt(t33_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  ((k8_pnproc_1 A B (k2_pre_poly B)) = (k6_partfun1 (k9_funct_2 A k5_numbers))) ) ) ) ).
tt(t33_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((k1_newton (k3_binop_2 (k21_sin_cos (k12_binop_2 (k9_binop_2 C (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B)) A)) (k5_binop_2 (k18_sin_cos (k12_binop_2 (k9_binop_2 C (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B)) A)) k7_complex1)) A) = (k3_binop_2 (k21_sin_cos C) (k5_binop_2 (k18_sin_cos C) k7_complex1))) ) ) ) ) ) ) ) ).
tt(t33_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) => (v2_funct_1 (k10_polyform A B))) ) ) ) ).
tt(t33_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k11_polynom3 A B C) D) (k11_polynom3 A B (k11_polynom3 A C D)))) ) ) ) ) ) ) ) ).
tt(t33_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k3_algseq_1 A B)) = 1) ) ) ) ) ) ).
tt(t33_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B (k4_polynom7 A B D) C) E) = (k8_group_1 B D (k5_polynom2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k6_polynom8 A B (k9_polynom3 B) C) (k9_polynom3 B))) ) ) ) ) ) ).
tt(t33_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r2_polyred A B C (k6_termord A B C D) (k5_termord A B C D))) ) ) ) ) ) ) ) ).
tt(t33_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power (k3_power A B) C) = (k3_power A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t33_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v3_valued_0 D)) ) ) )  =>  ( (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 B E) = (k9_binop_2 (k1_funct_1 C E) (k1_funct_1 D E))) ) )  => (r6_pboole A B (k11_pre_poly A C D))) ) ) ) ) ) ) ) ).
tt(t33_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k1_seq_1 B C) = (k2_prepower C A)) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((v2_comseq_2 B) &  ((k2_seq_2 B) = 1) ) ) ) ) ) ) ) ).
tt(t33_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))))))) )  =>  ( (C = D)  =>  ((v5_pre_topc C A B) <=> (v5_pre_topc D A (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_tarski C D) =>  ((k1_seq_1 E (k7_prob_1 A B D C)) = (k9_real_1 (k1_seq_1 E D) (k1_seq_1 E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers))  =>  ( ((k1_seq_1 (k3_prob_2 A B C E) D) = (k1_seq_1 C D))  <=> (r1_prob_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  => (r1_tarski (k1_funct_1 (k3_prob_3 B D) A) (k1_funct_1 D A))) ) ) ) ) ) ) ).
tt(t33_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (~  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (m1_prob_4 (k1_prob_4 A (k9_setfam_1 A) D E) A B C)) )  &  (! [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (~  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_tarski (k1_prob_4 A (k9_setfam_1 A) D F) (k1_prob_4 A B E F)) &  ((k3_funct_2 B k1_numbers C (k1_prob_4 A B E F)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A B D) (k8_cqc_lang A B (k7_cqc_lang A C D)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t33_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r1_incsp_1 A D (k1_projpl_1 A B C)) =>  ( (B = D)  | (r1_incsp_1 A C (k1_projpl_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t33_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k18_pscomp_1 A) (k19_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)))) ) ).
tt(t33_pua2mss1,ax, (! [A:$i] :  ( ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) )  =>  (! [B:$i] :  ((m3_pua2mss1 B A) =>  ( (B = (k8_eqrel_1 (u1_struct_0 A) (k9_pua2mss1 A)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_msualg_1 C)) )  =>  ((r7_pua2mss1 A C) => (r5_pua2mss1 (k11_pua2mss1 A B) C)) ) ) ) ) ) ) ) ).
tt(t33_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A (k1_pzfmisc1 A B) C) <=> (r1_pboole A B C)) ) ) ) ) ) ).
tt(t33_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v1_qc_lang2 B A) =>  ((v2_qc_lang2 B A) &  ((v3_qc_lang1 B A) &  ((v4_qc_lang1 (k18_qc_lang1 A B) A) &  ((v3_qc_lang1 (k19_qc_lang1 A (k18_qc_lang1 A B)) A) & (v3_qc_lang1 (k20_qc_lang1 A (k18_qc_lang1 A B)) A)) ) ) ) ) ) ) ) ) ).
tt(t33_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k4_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t33_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_trees_2 E (k9_xtuple_0 (k2_qc_lang4 A B))) =>  (~  ((r2_hidden C (a_3_2_qc_lang4 A B E)) &  ((r2_hidden D (a_3_2_qc_lang4 A B E)) &  ( (~ (r2_qc_lang2 A C D))  &  (~ (r2_qc_lang2 A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) &  ((v20_quantal1 A) &  ((v21_quantal1 A) & (l3_quantal1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k9_quantal1 A B (k3_quantal1 A)) = B)  &  ((k9_quantal1 A (k3_quantal1 A) B) = B) ) ) ) ) ) ).
tt(t33_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( (~  (A = k1_quatern2) )  =>  ((k6_quatern2 A A) = k2_quatern2) ) ) ) ).
tt(t33_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k3_quatern2 (k27_quaterni (k31_quaterni A) (k31_quaterni A))) = (k5_square_1 (k3_quatern2 A))) ) ) ).
tt(t33_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ( ((k17_quaterni (k10_quaterni A k1_xcmplx_0)) = k6_numbers)  &  ( ((k18_quaterni (k10_quaterni A k1_xcmplx_0)) = B)  &  ( ((k19_quaterni (k10_quaterni A k1_xcmplx_0)) = k6_numbers)  &  ((k20_quaterni (k10_quaterni A k1_xcmplx_0)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t33_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) => (m1_subset_1 (k1_binop_1 (k16_quofield A) B C) (u1_struct_0 (k19_quofield A)))) ) ) ) ) ) ).
tt(t33_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m2_prob_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ((m1_random_1 C A (k1_random_1 A)) =>  (? [D:$i] :  ((m2_finseq_1 D k1_numbers) &  (? [E:$i] :  ((m2_finseq_1 E A) &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ((v2_funct_1 E) &  ( ((k2_relset_1 A E) = A)  &  ( ((k3_finseq_1 E) = (k5_card_1 A))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  ((k1_seq_1 D F) = (k8_real_1 (k1_seq_1 C (k1_funct_1 E F)) (k1_seq_1 B (k1_tarski (k1_funct_1 E F))))) ) ) )  &  ((k8_random_1 A (k1_random_1 A) B C) = (k18_rvsum_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (m1_vectsp_7 D A B))  => (r1_vectsp_5 A B (k1_vectsp_7 A B C) (k1_vectsp_7 A B (k7_subset_1 (u1_struct_0 B) D C)))) ) ) ) ) ) ) ) ) ).
tt(t33_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 (k1_real_1 1) A))  & (r1_xxreal_0 (k4_xcmplx_0 (k2_rat_1 A)) (k1_rat_1 A))) )  &  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 (k2_rat_1 A)) (k1_rat_1 A)))  & (r1_xxreal_0 (k1_real_1 1) A)) ) ) ) ) ).
tt(t33_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_polynom4 A (k5_ratfunc1 A B) D) = (k4_struct_0 A)) )  &  ( (~  ((k2_polynom4 A (k5_ratfunc1 A C) D) = (k4_struct_0 A)) )  &  (~  ((k13_ratfunc1 A (k9_ratfunc1 A B C) D) = (k3_rlvect_1 A (k13_ratfunc1 A B D) (k13_ratfunc1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k2_rcomp_1 A B))  =>  ((r1_xxreal_0 B A) |  ((k2_tops_1 k2_topalg_2 C) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ).
tt(t33_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_seq_1 (k4_real_3 B) C) = k6_numbers) ) )  =>  ((k1_seq_1 (k3_real_3 B) A) = k6_numbers) ) ) ) ) ) ).
tt(t33_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 B) = (k5_card_1 C)) )  => (r2_relset_1 C k1_numbers (k3_rearran1 B C E (k15_valued_1 B k1_numbers D A)) (k15_valued_1 C k1_numbers (k3_rearran1 B C E D) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k3_relat_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k3_relat_1 A B) (k3_relat_1 A C)))) ) ) ) ) ) ).
tt(t33_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k6_relset_2 A B C (k9_subset_1 (k2_zfmisc_1 A B) D E)) = (k9_subset_1 B (k6_relset_2 A B C D) (k6_relset_2 A B C E))) ) ) ) ) ) ) ) ) ).
tt(t33_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((k3_topreal1 2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) = (k3_topreal1 2 B)) ) ) ) ) ).
tt(t33_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r3_rewrite1 A B) & (r1_rewrite1 A B C))  =>  (B = C) ) ) ) ) ) ).
tt(t33_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r2_rewrite2 A B C D) => (r3_rewrite2 A B C D)) ) ) ) ) ) ) ) ).
tt(t33_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D C))  =>  (~  ((r2_hidden A (k1_rewrite3 B C D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 B)) =>  (! [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 B)) =>  (~  (A = (k4_tarski (k4_tarski E G) (k4_tarski F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_rfinseq,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (? [B:$i] :  ((m2_finseq_1 B k1_numbers) &  ((r2_classes1 A B) &  ((m2_finseq_1 B k4_numbers) & (v8_valued_0 B)) ) ) ) ) ) ).
tt(t33_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k18_valued_1 (k1_rfunct_1 A B) B) = (k5_relat_1 A (k9_xtuple_0 (k4_rfunct_1 B)))) ) ) ) ) ).
tt(t33_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) =>  ((r1_xxreal_0 B k6_numbers) | (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) )  &  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) =>  ((r1_xxreal_0 k6_numbers B) | (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ) ) ).
tt(t33_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_rfunct_3 A k1_numbers)) =>  ((r1_rfunct_3 A k1_numbers C B) =>  ((k1_seq_1 (k14_rfunct_3 A C) B) = (k18_rvsum_1 (k17_rfunct_3 A C B))) ) ) ) ) ) ) ) ).
tt(t33_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (a_2_0_rinfsup1 A B))  => (v5_xxreal_2 C)) ) ) ) ) ) ) ) ).
tt(t33_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A B) k2_supinf_1)) )  => (v9_mesfunc5 A)) ) ) ).
tt(t33_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski (k3_rlvect_2 A B) (k7_domain_1 (u1_struct_0 A) C D)) =>  ( (C = D)  |  ((k3_rlaffin1 A B) = (k7_real_1 (k1_seq_1 B C) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_rlaffin1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((k5_card_1 B) = (k23_binop_2 A 1))  => (v3_pre_topc (k1_rlaffin2 (k15_euclid A) B) (k15_euclid A))) ) ) ) ) ).
tt(t33_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=> (r1_struct_0 A C)) ) )  =>  (B = A) ) ) ) ) ) ).
tt(t33_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (r2_hidden A (k3_rlsub_2 A))) ) ).
tt(t33_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_rltopsp1 A B) C) = (k5_rusub_4 A C B)) ) ) ) ) ) ) ).
tt(t33_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k5_algstr_0 A B C)) = (k1_algstr_0 A C (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t33_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m2_rlvect_2 D A (k7_domain_1 (u1_struct_0 A) B C)) =>  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 B (k1_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t33_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C)) B) =>  ( (B = (k4_struct_0 A))  |  ((k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B)) = (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t33_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rlvect_5 A) = 1)  <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  ( (~  (B = (k4_struct_0 A)) )  &  ((k2_rlsub_1 A) = (k1_rlvect_3 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t33_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 A)))  =>  ((k2_rlvect_x A (k2_relset_1 (u1_struct_0 A) B)) = (k3_rlvect_x A B)) ) ) ) ) ).
tt(t33_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( ((u1_struct_0 D) = C)  => (v1_rmod_2 C A B)) ) ) ) ) ) ) ) ) ).
tt(t33_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  ((m1_rmod_2 C A D) => (m1_rmod_2 (k1_rmod_3 A B C E) A (k1_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (~  (C = D) )  =>  (! [E:$i] :  ((m2_rmod_4 E A B (k7_domain_1 (u1_struct_0 B) C D)) =>  ((k5_rmod_4 A B E) = (k3_rlvect_1 B (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v15_lattices A) &  ((v8_robbins1 A) & (l4_robbins1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A B C) = (k3_robbins1 A (k3_lattices A (k3_robbins1 A B) (k3_robbins1 A C)))) ) ) ) ) ) ) ).
tt(t33_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A C) C))) = (k3_robbins1 A (k5_robbins1 A B C))) ) ) ) ) ) ) ).
tt(t33_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_robbins4 A B C) &  ((k3_lattices A B C) = (k6_lattices A)) )  =>  (B = (k3_robbins1 A C)) ) ) ) ) ) ) ) ) ).
tt(t33_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A (k3_roughs_1 A B)) = (k3_roughs_1 A B)) ) ) ) ) ).
tt(t33_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  ((k2_rpr_1 A (k2_subset_1 A) (k2_subset_1 A)) = 1) ) ) ).
tt(t33_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (m1_rusub_1 (k1_rusub_1 A) B)) ) ) ) ).
tt(t33_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  => (r2_hidden A (k3_rusub_2 A))) ) ).
tt(t33_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) B C)) B) & (r1_struct_0 (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) B C)) C)) ) ) ) ) ) ) ).
tt(t33_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_rusub_4 A (k6_domain_1 (u1_struct_0 A) C) B) = (k5_rusub_4 A B C)) ) ) ) ) ) ) ).
tt(t33_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_xxreal_0 C D) => (r1_tarski (k4_bhsp_2 A B C) (k4_bhsp_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t33_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k9_rvsum_1 A (k5_finseq_2 k1_numbers A k6_numbers) B) = (k7_rvsum_1 A B)) ) ) ) ) ).
tt(t33_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k16_rvsum_1 (k7_finseq_1 (k9_finseq_1 A) B)) = (k3_binop_2 A (k16_rvsum_1 B))) ) ) ) ) ).
tt(t33_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ((k18_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) D) = (k18_scmfsa_2 (k1_scmfsa6b C B A) D)) ) ) ) ) ) ) ) ) ).
tt(t33_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_amistd_1 3 k1_scmfsa_2 B (k11_scmfsa_2 A)) = (k1_tarski A)) ) ) ) ) ).
tt(t33_scmfsa_1,ax, (! [A:$i] :  ((m1_subset_1 A (k4_card_3 (k3_relat_1 k4_scmfsa_1 k5_scmfsa_1))) =>  ((k9_xtuple_0 A) = k1_scmfsa_1) ) ) ).
tt(t33_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 4)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k9_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k4_scmfsa6a A B)) = (k2_nat_1 (k5_card_1 B) 2)) ) ) ) ) ).
tt(t33_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A (k1_scmfsa_m B) C) & (r6_scmfsa7b A (k1_scmfsa_m B) C))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1)))) ) ) ) ) ) ) ) ).
tt(t33_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) (k1_scmfsa6b C B A))) ) ) ) ) ) ).
tt(t33_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k2_scmfsa8b C A B) (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 3)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ).
tt(t33_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( (~ (r3_scmfsa9a A B C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 6 C))  => (r2_hidden (k2_nat_1 (k5_card_1 B) C) (k2_afinsq_1 (k2_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t33_scmfsa_m,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r1_tarski (k1_scmfsa_m (k16_funcop_1 B A)) C) =>  ( ((k18_scmfsa_2 C B) = A)  &  ((k1_funct_1 C (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ).
tt(t33_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r1_scm_halt C B A) & (r2_scm_halt C B A)) )  =>  ((r1_scm_halt (k1_scmfsa8b E C D) B A) & (r2_scm_halt (k1_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmisort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 82 B))  => (r2_hidden B (k9_xtuple_0 (k2_scmisort A)))) ) ) ) ) ).
tt(t33_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 7)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  (A = (k10_scmpds_2 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  ((k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 C D))) B) = (k2_nat_1 (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B) (k8_extpro_1 2 k1_scmpds_2 (k1_funct_4 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) (k10_compos_1 k1_scmpds_2 D)) (k8_memstr_0 2 k1_scmpds_2 (k6_extpro_1 2 k1_scmpds_2 (k1_funct_4 A (k10_compos_1 k1_scmpds_2 C)) B))))) ) ) ) ) ) ) ) ) ).
tt(t33_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((k6_scmpds_4 (k1_scmpds_4 (k1_scmpds_4 C (k1_scmpds_6 (k2_nat_1 (k5_card_1 D) 1))) D) B A) = (k1_funct_4 (k6_scmpds_4 C B A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k5_card_1 E) 3) D))  <=> (r2_hidden D (k2_afinsq_1 (k1_scmpds_7 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_amistd_1 2 (k1_scmring2 A) C (k9_scmring2 A D B)) = (k2_tarski D (k1_ordinal1 C))) ) ) ) ) ) ) ) ) ).
tt(t33_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B A) => (r2_hidden (k1_tarski B) (k5_scmyciel A))) ) ) ).
tt(t33_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) & (r2_analoaf A B C D E))  =>  ( (B = C)  | (r2_analoaf A D C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t33_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_relat_1 A))  =>  ( ((k3_comseq_2 A) = k5_complex1)  |  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers A))) = (k2_real_1 (k17_complex1 (k3_comseq_2 A)))) ) ) ) ) ).
tt(t33_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers B C) = (k12_binop_2 1 (k9_binop_2 (k4_nat_1 C C) A))) ) ) )  =>  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ).
tt(t33_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((r1_seqfunc A k1_numbers C D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k2_seqfunc A C B) E) (k26_valued_1 k5_numbers k1_numbers (k10_seqfunc A C E) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_seqm_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((v8_valued_0 B) & (r1_xxreal_0 k6_numbers A))  => (v8_valued_0 (k26_valued_1 k5_numbers k1_numbers B A)))  &  ( ((v8_valued_0 B) & (r1_xxreal_0 A k6_numbers))  => (v7_valued_0 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ).
tt(t33_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((r1_xxreal_0 A 1) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((k3_funct_2 k5_numbers k1_numbers B C) = (k10_real_1 1 (k3_power C A))) ) ) )  & (v1_series_1 B)) ) ) ) ) ) ) ).
tt(t33_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k4_nat_1 (k13_newton B 2) (k13_newton 4 B)) (k4_nat_1 (k2_nat_1 B 1) (k2_nat_1 B 2)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k8_complex1 (k13_complex1 2 3) (k13_complex1 (k3_xcmplx_0 (k6_xcmplx_0 B 1) (k13_newton 4 (k2_nat_1 B 1))) (k4_nat_1 3 (k2_nat_1 B 2))))) ) ) ) ) ) ) ).
tt(t33_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) k6_numbers)) ) ) ) ) ) ).
tt(t33_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 B) (k3_square_1 C)) 2))) (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 C) (k3_square_1 A)) 2))) (k6_square_1 (k3_xcmplx_0 3 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)))))) ) ) ) ) ) ).
tt(t33_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (~  (B = k1_xboole_0) )  =>  ((k7_subset_1 A (k2_subset_1 A) (k5_setfam_1 A B)) = (k6_setfam_1 A (k7_setfam_1 A B))) ) ) ) ) ).
tt(t33_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_1 A (k4_setlim_1 A B)) (k2_setlim_1 A (k2_prob_1 A B)))) ) ) ).
tt(t33_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A (k5_setlim_2 A C B)) = (k9_subset_1 A B (k3_prob_1 A C))) ) ) ) ) ) ).
tt(t33_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_binop_1 C A) &  ((v1_binop_1 C A) &  ((v2_binop_1 C A) & (v1_setwiseo C A)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 B)) =>  ((k7_setwiseo B A C (k5_setwiseo B E F) D) = (k5_binop_1 A C (k7_setwiseo B A C E D) (k7_setwiseo B A C F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m2_finseq_2 F A (k4_finseq_2 E A)) =>  (! [G:$i] :  ((m2_finseq_2 G A (k4_finseq_2 E A)) =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ( (B = (k4_binop_1 A C))  &  ( ((k5_binop_1 A D B B) = B)  &  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  ((k5_binop_1 A C (k5_binop_1 A D H I) (k5_binop_1 A D J K)) = (k5_binop_1 A D (k5_binop_1 A C H J) (k5_binop_1 A C I K))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_binop_1 A D (k1_finsop_1 A F C) (k1_finsop_1 A G C)) = (k1_finsop_1 A (k1_finseqop A A A D F G) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 1 (k1_funct_1 A B)) &  ((r1_xxreal_0 (k1_funct_1 A B) (k3_finseq_1 (k18_scmfsa_2 A D))) &  ((r1_xxreal_0 1 (k1_funct_1 A C)) &  ((r1_xxreal_0 (k1_funct_1 A C) (k3_finseq_1 (k18_scmfsa_2 A D))) &  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_sfmastr3 D B C) A E) D) = (k2_funct_7 (k2_funct_7 (k18_scmfsa_2 A D) (k1_funct_1 A B) (k1_funct_1 (k18_scmfsa_2 A D) (k1_funct_1 A C))) (k1_funct_1 A C) (k1_funct_1 (k18_scmfsa_2 A D) (k1_funct_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  ( ( (D = (k14_scmfsa_2 A B C))  |  (D = (k15_scmfsa_2 A B C)) )  =>  ((k3_sf_mastr D) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t33_sgraph1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_sgraph1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k3_finseq_2 (u1_struct_0 B))) =>  ((r3_sgraph1 A B C D E) => (r2_hidden E (k5_sgraph1 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t33_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v4_lattices A)) ) ).
tt(t33_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C D)) = (k5_sheffer1 A B (k5_sheffer1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t33_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  ((v7_simplex0 C A B) <=> (r1_tarski (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 B)) (k9_setfam_1 (k2_struct_0 C)) (u1_pre_topc B)) (u1_pre_topc C))) ) ) ) ) ) ).
tt(t33_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  ((v1_setfam_1 C) =>  ((k1_card_1 C) = (k1_card_1 (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) C))) ) ) ) ) ) ) ) ).
tt(t33_sincos10,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))) => (r2_hidden (k1_seq_1 k1_fdiff_9 A) (k1_rcomp_1 1 (k7_square_1 2)))) ) ).
tt(t33_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k7_sin_cos2 A) &  ((k1_fdiff_1 k7_sin_cos2 A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)))) ) ) ) ).
tt(t33_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k15_sin_cos (k5_binop_2 (k7_binop_2 (k11_binop_2 (k15_binop_2 (k24_binop_2 2 A) (k18_binop_2 1 2)) k32_sin_cos)) k7_complex1)) = (k1_binop_2 (k5_binop_2 1 k7_complex1))) ) ) ).
tt(t33_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k17_sin_cos C)) = (k3_xcmplx_0 (k7_xcmplx_0 1 4) (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 B C) A))) (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 C A) B))) (k17_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C))))) ) ) ) ) ) ) ).
tt(t33_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k2_sin_cos4 (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k7_real_1 1 (k20_sin_cos A)) (k9_real_1 1 (k20_sin_cos A)))))  |  ((k2_sin_cos4 (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k7_real_1 1 (k20_sin_cos A)) (k9_real_1 1 (k20_sin_cos A)))))) ) ) ) ).
tt(t33_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A (k10_real_1 k32_sin_cos 2)))  &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) & (r1_xxreal_0 1 (k17_sin_cos A))) ) ) ) ) ).
tt(t33_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k1_sin_cos7 A) = (k2_sin_cos7 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)))) ) ) ) ).
tt(t33_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k2_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 2 A)) (k20_sin_cos (k3_xcmplx_0 2 B))) = (k2_xcmplx_0 2 (k3_xcmplx_0 2 (k6_xcmplx_0 (k5_square_1 (k3_sin_cos2 A)) (k3_square_1 (k17_sin_cos B))))))  &  ((k6_xcmplx_0 (k6_sin_cos2 (k3_xcmplx_0 2 A)) (k20_sin_cos (k3_xcmplx_0 2 B))) = (k3_xcmplx_0 2 (k2_xcmplx_0 (k5_square_1 (k3_sin_cos2 A)) (k3_square_1 (k17_sin_cos B))))) ) ) ) ) ) ).
tt(t33_sin_cos9,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) k1_sin_cos9) = (k1_partfun2 k1_numbers (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(t33_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k1_newton (k3_xcmplx_0 B k7_complex1) (k4_nat_1 2 A)) = (k8_real_1 (k2_newton (k1_real_1 1) A) (k2_newton B (k4_nat_1 2 A))))  &  ((k1_newton (k3_xcmplx_0 B k7_complex1) (k2_nat_1 (k4_nat_1 2 A) 1)) = (k3_xcmplx_0 (k8_real_1 (k2_newton (k1_real_1 1) A) (k2_newton B (k2_nat_1 (k4_nat_1 2 A) 1))) k7_complex1)) ) ) ) ) ) ).
tt(t33_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) & (v1_sppol_1 (k2_topreal1 2 B A))) ) ) )  => (v2_sppol_1 (k2_topreal1 2 B (k2_nat_1 A 1)))) ) ) ) ) ).
tt(t33_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k3_finseq_1 A) 2) => (v3_topreal1 A)) ) ) ).
tt(t33_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(t33_sprect_2,ax, ((k8_pscomp_1 k1_topreal1) = 1) ).
tt(t33_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k2_goboard9 A)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k3_goboard9 A)) & (r2_subset_1 (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ).
tt(t33_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t33_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_xcmplx_0 (k6_square_1 A) A) = (k7_xcmplx_0 1 (k6_square_1 A))) ) ) ) ).
tt(t33_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) &  ((k9_subset_1 (u4_struct_0 A) (k11_stacks_1 A B) (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) C)) = (k6_domain_1 (u4_struct_0 A) D)) ) ) ) ) ) ) ) ) ).
tt(t33_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  ( ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  |  (A = B) )  & (r1_xxreal_0 (k3_stirl2_1 B A) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k3_stirl2_1 B A) k6_numbers))  &  ( (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B)) )  &  (~  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t33_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  ((r2_hidden B (k1_relset_1 (k3_qc_lang1 A) (k2_substut1 A (k19_substut1 A C)))) => (m2_subset_1 (k1_funct_1 (k2_substut1 A (k19_substut1 A C)) B) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ) ) ) ) ) ).
tt(t33_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k1_tarski B) (k1_zfmisc_1 A))) ) ) ) ).
tt(t33_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((v2_substut1 B A) => (m2_subset_1 (k37_substut1 A B) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ).
tt(t33_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r2_qc_lang2 A C B) &  ((k7_cqc_sim1 A C) = 1) ) ) ) )  =>  ((k7_cqc_sim1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t33_supinf_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k7_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((v3_supinf_2 D A B) & (v3_supinf_2 E A C))  => (v3_supinf_2 (k13_supinf_2 A B C D E) A (k5_supinf_2 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  (~  ( ((k2_symsp_1 A B E F D C) = (k4_struct_0 A))  <=> (r1_orders_2 B F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r1_tarski (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))) (k4_relat_1 (k9_xtuple_0 A))) & (r1_tarski (k4_relat_1 (k10_xtuple_0 (k1_sysrel A))) (k4_relat_1 (k9_xtuple_0 A)))) ) ) ).
tt(t33_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((v1_xreal_0 B) => (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_taxonom1 A B) (k1_taxonom1 (u1_struct_0 A) (u1_metric_1 A) B))) ) ) ) ).
tt(t33_taylor_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_tarski (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D)) (k1_relset_1 k1_numbers B)) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))))  =>  ((r1_xxreal_0 D k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 1 F))  &  ((k1_seq_1 B E) = (k7_real_1 (k1_seq_1 (k3_series_1 (k6_taylor_1 B (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D)) C E)) A) (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))) (k2_nat_1 A 1)) (k7_real_1 C (k8_real_1 F (k9_real_1 E C)))) (k2_newton (k9_real_1 E C) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k5_tdlat_1 A)) =>  ((k5_binop_1 (k5_tdlat_1 A) (k7_tdlat_1 A) B C) = (k1_binop_1 (k3_tdlat_1 A) B C)) ) ) ) ) ) ) ).
tt(t33_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B))) = (a_2_4_tdlat_2 A B)) ) ) ) ) ).
tt(t33_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ((v5_tops_1 B A) & (v6_tops_1 B A)) ) ) ) ) ) ) ).
tt(t33_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r8_pboole (k15_pre_poly A) (k5_termord A B C (k9_polynom1 A C D E)) (k9_polynom1 A C (k5_termord A B C D) (k5_termord A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~  ( (~ (v3_tdlat_3 A))  &  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) & (v4_pre_topc B A)) ) ) ) ) )  &  (~  ( (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v2_tops_1 B A) & (v4_pre_topc B A)) ) )  & (v3_tdlat_3 A)) ) ) ) ) ).
tt(t33_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) &  ((v4_pre_topc C A) &  ((v2_tex_2 B A) & (v2_tex_2 C A)) ) )  => (v2_tex_2 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t33_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v3_tex_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (u1_struct_0 B)) => (v2_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t33_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_tex_4 A B) = (k3_tex_4 A (k3_tex_4 A B))) ) ) ) ) ).
tt(t33_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (m1_pre_topc F A))  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k1_tsep_1 A (k1_tsep_1 A D E) F))  &  ((m1_pre_topc (k2_tsep_1 A D (k1_tsep_1 A B C)) B) &  ((m1_pre_topc (k2_tsep_1 A E (k1_tsep_1 A B C)) C) & (m1_pre_topc (k2_tsep_1 A F (k1_tsep_1 A B C)) (k2_tsep_1 A B C))) ) )  =>  ((r1_tsep_1 B C) |  ((m1_pre_topc B C) |  ((m1_pre_topc C B) |  ((m1_pre_topc (k1_tsep_1 A B C) (k1_tsep_1 A D E)) |  ( (~ (r1_tsep_1 (k1_tsep_1 A D E) (k1_tsep_1 A B C)))  &  (~ (r1_tsep_1 F (k1_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((k3_tarski (k3_toler_1 A B)) = A) ) ) ) ).
tt(t33_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) & (r1_borsuk_6 A E F)) ) )  =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r3_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J) (k1_borsuk_2 A B C F G (k1_borsuk_2 A C E F (k1_borsuk_2 A C D E H I) J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v1_borsuk_2 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_borsuk_3 A B) => (r2_group_6 (k5_topalg_1 A C) (k5_topalg_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t33_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  => (r1_borsuk_2 A (k2_topalg_6 A B) (k3_topalg_6 A B))) ) ) ) ).
tt(t33_topdim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( ((k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) B)) = (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) C)))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~  (D = E) )  => (r1_xboole_0 (k8_nat_1 (k9_setfam_1 A) C D) (k8_nat_1 (k9_setfam_1 A) C E))) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (? [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))))  &  ( (E = (a_3_0_topdim_1 A B D))  &  ((k8_nat_1 (k9_setfam_1 A) C D) = (k7_subset_1 A (k8_nat_1 (k9_setfam_1 A) B D) (k5_setfam_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_pre_topc A) =>  ((k2_pre_topc A (k2_topgen_1 A B)) = (k2_topgen_1 A B)) ) ) ) ) ) ).
tt(t33_topgen_2,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_tops_2 C (k5_topgen_2 A B)) &  ((v1_cantor_1 C (k5_topgen_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))))) )  => (r1_ordinal1 (k1_card_1 A) (k1_card_1 C))) ) ) ) ) ).
tt(t33_topgen_3,ax, ((k2_waybel23 k2_topgen_3) = k3_topgen_3) ).
tt(t33_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ((k1_setfam_1 (k2_setfam_1 A B)) = (k2_xboole_0 (k1_setfam_1 A) (k1_setfam_1 B))) ) ) ) ) ) ) ).
tt(t33_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))) =>  ( (A = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5))  =>  (! [B:$i] :  ((k2_pre_topc k3_topgen_5 (k7_subset_1 (u1_struct_0 k3_topgen_5) A (k1_tarski B))) = (k2_struct_0 k3_topgen_5)) ) ) ) ) ).
tt(t33_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ((k4_topgrp_1 A) = (k1_group_1 (k5_topgrp_1 A))) ) ) ).
tt(t33_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k5_topreal1 A) = (a_1_3_topreal1 A)) ) ) ).
tt(t33_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (v4_topreal1 A))  =>  ((r1_xxreal_0 B 2) | (v4_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t33_topreal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k18_euclid C) (k7_pscomp_1 A)))  &  (~  (B = C) ) ) ) ) ) ) ) ) ).
tt(t33_topreal8,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  &  ((v2_funct_1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  &  ((v2_funct_1 B) &  ((v2_topreal1 B) &  ((v3_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) )  =>  ( ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k2_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) ) )  => (v1_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t33_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden C (k3_topreal9 A D B)) & (r2_hidden E (k1_topreal9 A D B)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) C E) (k3_topreal9 A D B)) = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_topreala,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((k7_relset_1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)) k2_topreala (k2_zfmisc_1 A B)) = (k4_card_3 (k4_funct_4 1 2 A B))) ) ) ) ) ).
tt(t33_toprealb,ax, ((k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k6_domain_1 (u1_struct_0 (k8_toprealb 2)) k9_toprealb)) = k4_numbers) ).
tt(t33_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k17_valued_2 A (u1_struct_0 (k15_euclid B)) C)) &  ((v1_funct_2 (k17_valued_2 A (u1_struct_0 (k15_euclid B)) C) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k17_valued_2 A (u1_struct_0 (k15_euclid B)) C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ).
tt(t33_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t33_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k4_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_tops_1 A C)))) ) ) ) ) ) ).
tt(t33_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k5_setfam_1 (u1_struct_0 A) C)) =>  (B = (k5_setfam_1 (u1_struct_0 (k1_pre_topc A B)) (k1_tops_2 A B C))) ) ) ) ) ) ) ) ).
tt(t33_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) => (v1_tops_1 B A)) ) ) ) ) ).
tt(t33_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v2_transgeo B A) & (v3_transgeo C A))  =>  ((v3_transgeo (k1_transgeo (u1_struct_0 A) C B) A) & (v3_transgeo (k1_transgeo (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t33_trees_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  ((r2_hidden A B) =>  (C = (k4_trees_1 (k5_trees_1 B A C) A)) ) ) ) ) ) ) ) ).
tt(t33_trees_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  ((r2_hidden B A) =>  ( (~ (v1_xboole_0 B))  & (v1_trees_1 B)) ) )  =>  ( (~ (v1_xboole_0 (k3_tarski A)))  & (v1_trees_1 (k3_tarski A))) ) ) ) ).
tt(t33_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v6_trees_3 (k10_finseq_1 A B)) <=>  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) ) ) ) ).
tt(t33_trees_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 B)) &  ( (C = (k5_relset_1 k5_numbers A B (k2_finseq_1 (k2_nat_1 E 1))))  &  ( (D = (k5_relset_1 k5_numbers A B (k2_finseq_1 E)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  (C = (k7_finseq_1 D (k12_finseq_1 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ((k1_tsep_1 A (k2_tsep_1 A B C) D) = (k2_tsep_1 A (k1_tsep_1 A B D) (k1_tsep_1 A C D)))  &  ((k1_tsep_1 A D (k2_tsep_1 A B C)) = (k2_tsep_1 A (k1_tsep_1 A D B) (k1_tsep_1 A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r4_tsep_2 A B C) =>  ((v1_tsep_1 B A) <=> (v1_borsuk_1 C A)) ) ) ) ) ) ) ) ).
tt(t33_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc C A) | (v4_pre_topc D A))  =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) (k9_subset_1 (u1_struct_0 A) C D)) = (k9_subset_1 (u1_struct_0 B) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t33_turing_1,ax, ( ((k1_funct_1 k17_turing_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))  &  ( ((k1_funct_1 k17_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 1 1))  &  ( ((k1_funct_1 k17_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))  &  ( ((k1_funct_1 k17_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 3 k6_numbers (k1_real_1 1)))  &  ((k1_funct_1 k17_turing_1 (k1_domain_1 k5_numbers k5_numbers 3 1)) = (k4_domain_1 k5_numbers k5_numbers k1_numbers 4 1 (k1_real_1 1))) ) ) ) ) ).
tt(t33_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((r2_hidden A (k2_msafree2 (k37_twoscomp A B))) & (r2_hidden B (k2_msafree2 (k37_twoscomp A B)))) ) ) ) ) ).
tt(t33_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots k1_complfld))) &  ((k6_group_1 (k1_uniroots k1_complfld) B) = A) ) ) ) ) ).
tt(t33_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( ((k1_algseq_1 A B) = k6_numbers)  |  ((k1_algseq_1 A C) = k6_numbers) )  =>  ((k1_algseq_1 A (k11_polynom3 A B C)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t33_urysohn2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v3_xxreal_2 (k1_integra2 A B)) =>  ((r1_xxreal_0 B k6_numbers) | (v3_xxreal_2 A)) ) ) ) ) ) ).
tt(t33_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) => (r1_valuat_1 A B (k8_cqc_lang A (k7_cqc_lang A D E) (k7_cqc_lang A E D)) F C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  => (r2_hidden (k64_valued_1 A) (k1_relset_1 k5_numbers A))) ) ).
tt(t33_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((v2_relat_1 C) &  ((k14_valued_2 C A) = (k14_valued_2 C B)) )  =>  ( (C = k1_xboole_0)  |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  => (v1_vectsp_4 (k8_vectsp10 A B C) A B)) ) ) ) ) ) ).
tt(t33_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((v1_funct_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D)) &  ((v1_funct_2 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)))) &  ((v13_vectsp_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) &  ((v1_mod_2 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) B (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) & (m1_subset_1 (k8_matrlin2 B C C (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))) (u1_struct_0 (k3_ranknull B C C (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k1_algstr_0 A (k4_algstr_0 A B) C)) = (k1_algstr_0 A (k4_algstr_0 A C) B)) ) ) ) ) ) ) ).
tt(t33_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k4_algstr_0 B (k5_vectsp_2 A B C D)) = (k5_vectsp_2 A B (k4_algstr_0 A C) D))  &  ((k5_algstr_0 B E (k5_vectsp_2 A B C D)) = (k1_algstr_0 B E (k5_vectsp_2 A B (k4_algstr_0 A C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((u1_struct_0 C) = D)  => (v1_vectsp_4 D A B)) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((m1_vectsp_4 C A D) => (m1_vectsp_4 C A (k1_vectsp_5 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) => (r1_vectsp_6 A B (k6_vectsp_6 A B C (k5_vectsp_6 A B D E)) (k5_vectsp_6 A B (k6_vectsp_6 A B C D) (k6_vectsp_6 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t33_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r1_xxreal_0 (k6_xcmplx_0 (k2_xcmplx_0 (k1_vectsp_9 A C) (k1_vectsp_9 A D)) (k1_vectsp_9 A B)) (k1_vectsp_9 A (k2_vectsp_5 A B C D)))) ) ) ) ) ) ) ) ).
tt(t33_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_partfun1 D A) & (v1_partfun1 C A))  <=> (v1_partfun1 (k3_vfunct_1 A B D C) A)) ) ) ) ) ) ) ) ) ).
tt(t33_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_partfun1 D A) & (v1_partfun1 C A))  <=> (v1_partfun1 (k1_vfunct_2 A B D C) A)) ) ) ) ) ) ) ) ) ).
tt(t33_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_0 A B) =>  ((k1_yellow_0 A B) = (k1_yellow_0 A (k3_waybel_0 A B))) ) ) ) ) ) ).
tt(t33_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k13_yellow_6 A (k2_waybel11 A)))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((v1_waybel11 B A) & (v13_waybel_0 B A)) ) ) ) ) ) ) ).
tt(t33_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) &  ((v1_waybel_6 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_tarski (k4_yellow_4 A B C) B) &  ((r2_hidden D B) &  ( (? [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_waybel12 E A C))  & (v4_card_3 E)) )  &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E A) &  ((v13_waybel_0 E A) &  ((v1_waybel_6 E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (~  ((r1_tarski E B) &  ((r2_hidden D E) & (r1_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v17_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) & (v18_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ).
tt(t33_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_waybel_3 A) & (r2_hidden B (k5_waybel11 A)))  =>  (B = (k3_tarski (a_2_3_waybel14 A B))) ) ) ) ) ) ).
tt(t33_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k2_yellow_0 A (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k1_waybel16 A)))) ) ) ) ) ).
tt(t33_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((k2_waybel19 A) = (k1_cantor_1 (u1_struct_0 A) (k2_cantor_1 (u1_struct_0 A) (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) (k5_waybel11 A) (k1_waybel19 A))))) ) ) ).
tt(t33_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v11_quantal1 B) => (r2_funct_2 (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 (k1_yellow_2 A A B)) (k1_partfun1 (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A A B)) (k3_waybel_1 A A B) (k2_waybel_1 A A B)) (k3_struct_0 (k1_yellow_2 A A B)))) ) ) ) ) ).
tt(t33_waybel20,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) &  ((v3_waybel_3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) ) )  => (v3_waybel_3 (k5_yellow_1 A B))) ) ) ) ) ).
tt(t33_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_waybel11 B (k6_waybel_9 A B C (k4_waybel17 A D))) = (k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t33_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_waybel23 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_waybel23 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t33_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((k3_yellow_0 (k6_yellow_1 (u1_struct_0 A) B)) = (k6_struct_0 A B (k3_yellow_0 B))) ) ) ) ) ).
tt(t33_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v10_waybel_0 B (k1_waybel25 A)) & (l1_waybel_0 B (k1_waybel25 A))) ) ) )  => (v3_yellow_6 B (k1_waybel25 A))) ) ) ) ).
tt(t33_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 (k1_waybel26 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 (k1_waybel26 A B)))))) )  =>  ((v1_funct_1 (k10_funct_6 D)) &  ((v1_funct_2 (k10_funct_6 D) (u1_struct_0 A) (u1_struct_0 (k3_waybel18 C (k7_funcop_1 C B)))) &  ((v5_pre_topc (k10_funct_6 D) A (k3_waybel18 C (k7_funcop_1 C B))) & (m1_subset_1 (k10_funct_6 D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 C (k7_funcop_1 C B))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_waybel27 A (k3_yellow_1 1))) (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel27 A (k3_yellow_1 1))) (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))))) )  &  ((v23_waybel_0 B (k2_waybel27 A (k3_yellow_1 1)) (k2_yellow_1 (k5_waybel11 A))) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 1))) &  ((v22_waybel_0 C A (k3_yellow_1 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 1)))))) ) )  =>  ((k1_funct_1 B C) = (k8_relset_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 1)) C (k1_tarski 1))) ) ) ) ) ) ) ) ).
tt(t33_waybel29,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) <=>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((k1_waybel29 (k3_yellow_3 B A)) = (k1_waybel25 (k2_borsuk_1 (k1_waybel29 B) (k1_waybel29 A)))) ) ) ) ) ) ).
tt(t33_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k3_yellow_3 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((k1_yellow_0 A (k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k4_waybel_2 A) B)) = (k1_yellow_0 A (k4_yellow_4 A (k4_yellow_3 A A B) (k5_yellow_3 A A B)))) ) ) ) ) ).
tt(t33_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (a_3_2_waybel30 A B C) (a_2_3_waybel30 A C))) ) ) ) ) ) ).
tt(t33_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v22_waybel_0 B A A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_yellow_2 A A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_yellow_2 A A B))) =>  ( ( (E = C)  &  (F = D) )  =>  ((r1_waybel_3 A C D) <=> (r1_waybel_3 (k1_yellow_2 A A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_waybel_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v3_orders_2 (k3_waybel_3 A B C)) &  ((v4_orders_2 (k3_waybel_3 A B C)) &  ((v5_orders_2 (k3_waybel_3 A B C)) &  ((v1_lattice3 (k3_waybel_3 A B C)) &  ((v2_lattice3 (k3_waybel_3 A B C)) &  ((v3_lattice3 (k3_waybel_3 A B C)) & (l1_orders_2 (k3_waybel_3 A B C))) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_yellow_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_yellow_1 A B))) =>  ((r1_waybel_3 (k5_yellow_1 A B) C D) <=>  ( (! [E:$i] :  ((m1_subset_1 E A) => (r1_waybel_3 (k3_waybel_3 A B E) (k4_waybel_3 A B C E) (k4_waybel_3 A B D E))) )  &  (? [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 A)))  &  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~ (r2_hidden F E))  =>  ((k4_waybel_3 A B C F) = (k3_yellow_0 (k3_waybel_3 A B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v23_waybel_0 (k9_waybel_4 A) (k2_yellow_1 (k3_waybel_4 A)) (k8_waybel_4 A))) ) ).
tt(t33_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  ((v17_waybel_0 C A B) &  ((v22_waybel_0 C A B) & (v2_funct_2 C (u1_struct_0 B))) ) ) )  =>  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski k1_xboole_0)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski k1_xboole_0))))))) )  =>  (! [C:$i] :  ( ((v5_waybel_6 C A) & (m1_subset_1 C (u1_struct_0 A)))  =>  ((r1_funct_2 (u1_struct_0 A) (k2_tarski k1_xboole_0 1) (u1_struct_0 A) (u1_struct_0 (k3_yellow_1 (k1_tarski k1_xboole_0))) (k5_funct_3 (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A C)) (u1_struct_0 A)) B) =>  ((v19_waybel_0 B A (k3_yellow_1 (k1_tarski k1_xboole_0))) & (v20_waybel_0 B A (k3_yellow_1 (k1_tarski k1_xboole_0)))) ) ) ) ) ) ) ) ).
tt(t33_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) => (v1_waybel_7 (k5_waybel_0 A B) A)) ) ) ) ) ).
tt(t33_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v1_compts_1 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_waybel_9 A B C) & (r3_waybel_9 A B D))  =>  (C = D) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_9 A B C) => (r2_hidden C (k10_yellow_6 A B))) ) ) ) ) ) ) ) ).
tt(t33_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_card_1 (u1_struct_0 (k5_weddwitt A B))) = (k1_newton (k5_card_1 (u1_struct_0 (k4_weddwitt A))) (k1_vectsp_9 (k4_weddwitt A) (k7_weddwitt A B)))) ) ) ) ) ).
tt(t33_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_compts_1 B (k3_pcomps_1 A)) &  ( (~  (C = k1_xboole_0) )  &  ((v2_compts_1 C (k3_pcomps_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden E C) &  ((k4_metric_1 A D E) = (k10_weierstr A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_wellord1 A) =>  (! [B:$i] :  ( (! [C:$i] :  ( ((r2_hidden C (k1_relat_1 A)) & (r1_tarski (k1_wellord1 A C) B))  => (r2_hidden C B)) )  => (r1_tarski (k1_relat_1 A) B)) ) ) ) ) ).
tt(t33_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (? [D:$i] :  ((v1_int_1 D) &  (? [E:$i] :  ((v1_int_1 E) &  ((k2_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 B E)) = C) ) ) ) )  <=> (r1_int_1 (k3_int_2 A B) C)) ) ) ) ) ) ) ).
tt(t33_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k4_xboole_0 A C) (k4_xboole_0 B C))) ) ) ) ).
tt(t33_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k5_xboolean A B)) = (k4_xboolean (k3_xboolean A) (k3_xboolean B))) ) ) ) ) ).
tt(t33_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k2_xcmplx_0 A B) = (k2_xcmplx_0 C D))  =>  ((k6_xcmplx_0 A C) = (k6_xcmplx_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 k6_numbers (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t33_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k11_xtuple_0 A) (k11_xtuple_0 B)) (k11_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t33_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k3_xxreal_0 (k3_xxreal_0 A B) C) = (k3_xxreal_0 A (k3_xxreal_0 B C))) ) ) ) ) ) ) ).
tt(t33_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (v1_xboole_0 (k4_xxreal_1 A B))) ) ) ) ) ) ).
tt(t33_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((v1_xxreal_2 (k1_xxreal_1 A B)) & (v2_xxreal_2 (k1_xxreal_1 A B))) ) ) ) ) ) ).
tt(t33_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((v1_xreal_0 A) =>  ((k3_xxreal_3 (k1_xxreal_3 A B) (k1_xxreal_3 A C)) = (k3_xxreal_3 B C)) ) ) ) ) ) ) ) ).
tt(t33_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (B = (k2_yellow_0 A C))  <=>  ((r1_lattice3 A C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A C D) => (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t33_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((r1_tarski (k4_yellow_3 A B (k4_waybel_0 (k3_yellow_3 A B) C)) (k4_waybel_0 A (k4_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k4_waybel_0 (k3_yellow_3 A B) C)) (k4_waybel_0 B (k5_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t33_yellow12,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ((v1_tops_2 C B) &  ((v2_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ).
tt(t33_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) C (k3_struct_0 A)) &  ((r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D (k3_struct_0 A)) &  ((v5_pre_topc C A B) & (v5_pre_topc D B A)) ) )  =>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ) ) ) ) ) ).
tt(t33_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r1_yellow_0 (k5_yellow_1 A B) C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k4_waybel_3 A B (k1_yellow_0 (k5_yellow_1 A B) C) D) = (k1_yellow_0 (k3_waybel_3 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t33_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((v2_yellow18 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k1_altcat_1 A B C) (k1_funct_2 (k3_yellow18 A B) (k3_yellow18 A C)))) ) ) ) ) ) ) ).
tt(t33_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r3_waybel_9 A B C)) ) ) ) ) ) ) ).
tt(t33_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v10_functor0 C A B) & (l2_functor0 C A B))  =>  ((v20_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B D E)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A G H)) &  ( (D = (k3_functor0 A B C G))  &  ( (E = (k3_functor0 A B C H))  &  ( (~  ((k1_altcat_1 A G H) = k1_xboole_0) )  &  (F = (k6_functor0 A B C G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_waybel_0 C A B) => (v7_yellow_0 (k1_yellow_2 A B C) B)) ) ) ) ) ) ) ).
tt(t33_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_lattice3 A C E) & (r1_lattice3 B D F))  => (r1_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) (k7_yellow_3 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_waybel_0 A (k2_yellow_4 A (k3_waybel_0 A B) (k3_waybel_0 A C))) = (k3_waybel_0 A (k2_yellow_4 A B C))) ) ) ) ) ) ) ).
tt(t33_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k13_lattice3 A (k13_lattice3 A (k12_lattice3 A B C) (k12_lattice3 A C D)) (k12_lattice3 A D B)) = (k12_lattice3 A (k12_lattice3 A (k13_lattice3 A B C) (k13_lattice3 A C D)) (k13_lattice3 A D B))) ) ) ) ) ) ) ) ) ).
tt(t33_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  => (r2_hidden (k4_yellow_6 A B) (k10_yellow_6 A B))) ) ) ) ).
tt(t33_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ( ((k8_lattice3 A (k3_yellow_0 A)) = (k4_yellow_0 (k7_lattice3 A)))  &  ((k9_lattice3 A (k4_yellow_0 (k7_lattice3 A))) = (k3_yellow_0 A)) ) ) ) ).
tt(t33_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E C) => (v4_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k3_subset_1 (u1_struct_0 B) E)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_zf_lang)))  =>  ((r2_hidden A (k4_zf_fund1 B)) <=>  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  ((r2_hidden C B) &  (A = (k3_zf_fund1 C)) ) ) ) ) ) ) ) ).
tt(t33_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k20_zf_lang (k13_zf_lang B A)) = (k8_zf_lang B (k6_zf_lang A))) ) ) ) ) ).
tt(t33_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k12_zf_lang A B) = (k12_zf_lang C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A (k1_tarski B)) <=>  ( (A = k1_xboole_0)  |  (A = (k1_tarski B)) ) ) ) ) ).
tt(t33_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 B) &  ((v3_ordinal2 B) &  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ( ((k4_ordinal4 A B C) = C)  &  (D = (k4_classes1 C)) )  =>  ( (k1_xboole_0 = C)  | (r3_zfrefle1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t33_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) => (r1_struct_0 B (k4_struct_0 A))) ) ) ) ).
tt(t340_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k1_xxreal_1 A C)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 C B))) ) ) ) ) ) ) ) ).
tt(t341_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k1_tarski A)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 A B))) ) ) ) ) ) ).
tt(t342_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k1_tarski A)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 A B))) ) ) ) ) ) ).
tt(t343_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A B)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t344_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A B)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t345_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 k2_xxreal_0 B)) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k1_xxreal_1 B A))) ) ) ) ) ).
tt(t346_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 k2_xxreal_0 B)) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k3_xxreal_1 B A))) ) ) ) ) ).
tt(t347_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 k2_xxreal_0 A)) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k2_xxreal_1 A B))) ) ) ) ) ).
tt(t348_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 k2_xxreal_0 A)) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k4_xxreal_1 A B))) ) ) ) ) ).
tt(t349_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k4_xxreal_1 k2_xxreal_0 B) (k1_tarski A)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 A B))) ) ) ) ) ) ).
tt(t34_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((k7_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) = (k1_rewrite1 (k7_abcmiz_0 A B C) (k7_abcmiz_0 A (k8_abcmiz_0 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t34_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  ((m2_finseq_2 (k3_pre_poly k2_abcmiz_1 A) k2_abcmiz_1 k4_abcmiz_1) <=>  ((k3_abcmiz_1 A) = k1_xboole_0) ) ) ) ).
tt(t34_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  ((k10_abcmiz_a B (k35_abcmiz_1 A B)) = k1_xboole_0) ) ) ) ) ).
tt(t34_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_1 A B C D) => (r2_aff_1 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t34_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_4 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E B) &  (~ (r1_aff_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( (B = (k5_afinsq_1 A))  <=>  ( ((k1_afinsq_1 B) = 1)  &  ((k1_funct_1 B k6_numbers) = A) ) ) ) ) ) ).
tt(t34_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  ((r1_afinsq_2 A B) =>  ( (A = k1_xboole_0)  |  ((k1_recdef_1 (k4_afinsq_2 A) k6_numbers) = (k1_recdef_1 (k4_afinsq_2 (k2_xboole_0 A B)) k6_numbers)) ) ) ) ) ) ) ).
tt(t34_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) =>  ( ( (D = (k4_tarski B 1))  &  ((v1_aff_1 B A) & (r1_incsp_1 (k13_afproj A) C D)) )  =>  ((m1_subset_1 C (u1_struct_0 A)) |  (C = (k5_afproj A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_afvect0 A B C) <=> (r1_afvect0 A (k1_afvect0 A D B) (k1_afvect0 A D C))) ) ) ) ) ) ) ) ) ).
tt(t34_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_funct_1 B) & (r1_xboole_0 (k10_xtuple_0 B) (u4_struct_0 A)))  => (r1_algspec1 A C B)) ) ) ) ) ) ) ).
tt(t34_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  (~  ((r1_xxreal_0 2 (k15_algstr_4 A B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_algstr_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_algstr_4 A))) =>  (~  ( (B = (k6_algstr_0 (k14_algstr_4 A) C D))  &  ( (~ (r1_xxreal_0 (k15_algstr_4 A B) (k15_algstr_4 A C)))  &  (~ (r1_xxreal_0 (k15_algstr_4 A B) (k15_algstr_4 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_altcat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  =>  ((k8_altcat_1 B C) = (k8_altcat_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_altcat_4,ax, (! [A:$i] :  ((l2_altcat_1 A) =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u1_altcat_1 A) = (u1_altcat_1 B)) )  => (v2_altcat_2 B A)) ) ) ) ) ).
tt(t34_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k7_ami_wstd A B C k6_numbers) = C) ) ) ) ) ) ) ).
tt(t34_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v2_struct_0 (k2_analmetr A B C)))  &  ((v3_analmetr (k2_analmetr A B C)) & (l1_analmetr (k2_analmetr A B C))) ) ) ) ) ) ) ) ) ).
tt(t34_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analort A F G B C D E) => (r1_analort A F G C B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J))) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_collsp B) &  ((v3_collsp B) &  ((v4_collsp B) &  ((v2_anproj_2 B) &  ((v3_anproj_2 B) & (l1_collsp B)) ) ) ) ) )  =>  (~  ( (B = (k5_anproj_1 A))  &  ( (~ (v7_anproj_2 B))  & (v8_anproj_2 B)) ) ) ) ) ) ) ) ) ).
tt(t34_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_freealg B A) & (m1_freealg B A))  =>  (B = (k10_aofa_000 A)) ) ) ) ) ).
tt(t34_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k76_aofa_i00 A B D E F G)) D) = 1) )  &  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k76_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  ( ((r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k77_aofa_i00 A B D E F G)) D) = 1) )  &  ( ( (~ (r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k77_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = D) )  =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k76_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k77_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski B (k9_armstrng A (k10_armstrng A B)))) ) ) ) ).
tt(t34_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) => (r1_arytm_3 (k6_arytm_3 A) (k7_arytm_3 A))) ) ).
tt(t34_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers) )  =>  ((r2_hidden A (k6_asympt_0 B)) &  (~ (r2_hidden A (k8_asympt_0 B))) ) ) ) ) ) ) ).
tt(t34_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k8_real_1 C (k6_power 2 C))) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 A C) = (k6_power 2 (k9_newton C))) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C B) & (r2_hidden A (k8_asympt_0 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k3_autalg_1 A)) (u1_struct_0 (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) &  ((v1_group_6 B (k3_autalg_1 A) (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_autalg_1 A)) (u1_struct_0 (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))))))) ) )  =>  ( (! [C:$i] :  ((r2_hidden C (k1_autalg_1 A)) =>  ((k1_funct_1 B C) = (k16_funcop_1 k6_numbers C)) ) )  => (v3_funct_2 B (u1_struct_0 (k3_autalg_1 A)) (u1_struct_0 (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A))))) ) ) ) ) ).
tt(t34_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  ((v2_bagorder B A) =>  ((r1_relset_1 (u1_struct_0 (k9_bagorder A)) (u1_struct_0 (k9_bagorder A)) (u1_orders_2 (k9_bagorder A)) B) & (v2_wellord1 B)) ) ) ) ) ) ).
tt(t34_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k2_bcialg_1 A B) (k5_bcialg_1 A))) ) ) ) ).
tt(t34_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_bcialg_2 B A) =>  ((k2_bcialg_2 A B) = (k2_bcialg_2 A (k2_bcialg_1 A B))) ) ) ) ) ) ).
tt(t34_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  &  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_bcialg_4 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k1_bcialg_4 A (k1_bcialg_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t34_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( ((r1_xxreal_0 A C) & (r1_xxreal_0 B D))  =>  ((v8_bcialg_1 E) & (m1_bcialg_5 E A B A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_bcialg_1 A C D) = (k1_bcialg_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  ( ((r1_tarski B C) &  ((v3_bciideal B A) & (m2_bcialg_1 B A)) )  =>  ((v3_bciideal C A) & (m2_bcialg_1 C A)) ) ) ) ) ) ) ) ).
tt(t34_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_bhsp_1 A B B) = k6_numbers) ) ) ) ) ).
tt(t34_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A D C))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A D C))) = (k3_bhsp_1 A (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k3_normsp_1 A B C) D) = (k3_normsp_1 A (k1_valued_0 (u1_struct_0 A) B D) (k1_valued_0 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t34_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 A D) = (k2_power D (k1_seq_1 (k2_bhsp_2 B C) D))) ) )  &  ((v2_comseq_2 A) &  ( (~ (r1_xxreal_0 (k2_seq_2 A) 1))  & (v1_bhsp_4 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D E (k4_struct_0 C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_binari_3 (k2_xcmplx_0 A 1) B) = (k7_finseq_1 (k10_binarith k5_numbers (k4_nat_d B 2)) (k1_binari_3 A (k3_nat_d B 2)))) ) ) ) ) ).
tt(t34_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((m1_subset_1 C k6_margrel1) &  ((k1_binari_3 (k23_binop_2 A 1) B) = (k8_finseq_1 k6_margrel1 (k1_binari_3 A B) (k12_finseq_1 k6_margrel1 C))) ) ) ) ) ) ) ).
tt(t34_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k4_lattices A (k1_boolealg A B C) C) (k5_lattices A))) ) ) ) ) ) ).
tt(t34_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r2_hidden D (u1_struct_0 B)))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A (k13_borsuk_1 A B C))) (k12_borsuk_1 A (k13_borsuk_1 A B C)) D) = (k6_domain_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_borsuk_4,ax,(v1_tsep_1 k1_borsuk_4 k5_topmetr)).
tt(t34_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (~  ((v4_pre_topc A k3_topmetr) &  ((v3_pre_topc A k3_topmetr) &  ( (~  (A = k1_xboole_0) )  &  (~  (A = k1_numbers) ) ) ) ) ) ) ) ).
tt(t34_borsuk_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  ((v1_funct_1 (k1_borsuk_6 A B C D)) &  ((v1_funct_2 (k1_borsuk_6 A B C D) (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D))) &  ((v5_pre_topc (k1_borsuk_6 A B C D) (k4_topmetr A B) (k4_topmetr C D)) & (m1_subset_1 (k1_borsuk_6 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr C D)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k12_toprealc 3 A) = (k11_finseq_1 (k5_square_1 (k1_euclid_5 A)) (k5_square_1 (k2_euclid_5 A)) (k5_square_1 (k3_euclid_5 A)))) ) ) ).
tt(t34_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_bspace A))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_bspace (k4_rlvect_1 (k7_bspace A) B) C) = (k4_rlvect_1 k2_bspace (k11_bspace A B C))) ) ) ) ) ) ) ).
tt(t34_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t34_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A F B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k16_bvfunc_1 A B C)) (k17_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t34_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 B (k9_bvfunc_1 A (k9_bvfunc_1 A B C) B))) ) ) ) ) ) ).
tt(t34_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc_1 A C D)) (k1_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)))) ) ) ) ) ) ) ) ).
tt(t34_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k2_bvfunc_1 A C D) B E) (k2_bvfunc_1 A C (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C (k1_bvfunc_1 A D)) B F) (k6_bvfunc_2 A (k9_bvfunc_1 A E D) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A E (k1_bvfunc_1 A C)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k1_bvfunc_1 A B) C) (k9_bvfunc_1 A (k1_bvfunc_1 A C) B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t34_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B C) (k1_bvfunc_1 A (k9_bvfunc_1 A B (k1_bvfunc_1 A C)))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t34_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r1_bvfunc_1 A B C) & (r1_bvfunc_1 A D E))  => (r1_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_c0sp1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_c0sp1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k11_c0sp1 A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ( (G = (k5_algstr_0 (k11_c0sp1 A) E F))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k1_seq_1 D H) = (k9_real_1 (k1_seq_1 B H) (k1_seq_1 C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_c0sp2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_c0sp2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_c0sp2 B))) =>  ( ( ((k1_normsp_0 (k9_c0sp2 B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k9_c0sp2 B))) )  &  ( ( (C = (k4_struct_0 (k9_c0sp2 B)))  =>  ((k1_normsp_0 (k9_c0sp2 B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k9_c0sp2 B) (k1_rlvect_1 (k9_c0sp2 B) C A)) = (k8_real_1 (k18_complex1 A) (k1_normsp_0 (k9_c0sp2 B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k9_c0sp2 B) (k1_algstr_0 (k9_c0sp2 B) C D)) (k7_real_1 (k1_normsp_0 (k9_c0sp2 B) C) (k1_normsp_0 (k9_c0sp2 B) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((r3_calcul_1 A B D) <=> (r3_calcul_1 A (k8_finseq_1 (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_card_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_wellord2 A B) &  ((r2_hidden C A) & (r2_hidden D B)) )  => (r2_wellord2 (k6_subset_1 A (k1_tarski C)) (k6_subset_1 B (k1_tarski D)))) ) ) ) ) ).
tt(t34_card_2,ax, (! [A:$i] :  (! [B:$i] : (r1_ordinal1 (k1_card_1 (k2_xboole_0 A B)) (k1_card_2 (k1_card_1 A) (k1_card_1 B)))) ) ).
tt(t34_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ((r1_tarski A B) =>  ((r2_hidden k1_xboole_0 (k10_xtuple_0 B)) | (r1_ordinal1 (k7_card_3 A) (k7_card_3 B))) ) ) ) ) ) ).
tt(t34_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( ((v2_card_1 A) & (r2_hidden B (k1_card_5 A)))  =>  ((k3_card_2 A B) = (k6_card_3 (k2_card_5 A B))) ) ) ) ) ) ).
tt(t34_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k6_card_fil A) A) (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k6_card_fil A) A) (k9_setfam_1 A))))) )  & (r4_card_fil A B)) ) ) ) ).
tt(t34_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k8_relat_1 B (k1_tarski A)) = k1_xboole_0)  =>  ((k2_card_fin C B A) = (k3_tarski (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t34_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((v6_card_fil A) & (r2_hidden B A))  => (r2_hidden (k1_card_1 (k4_classes1 B)) A)) ) ) ) ) ).
tt(t34_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  (! [E:$i] :  ((m1_cat_1 E A C B) =>  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A C B) = k1_xboole_0)  | (v7_cat_1 E A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (m2_cat_1 (k1_funct_1 (k1_funct_5 D) (k4_cat_1 A E)) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v2_cat_3 D A B C) <=> (v1_cat_3 (k7_oppcat_1 A B C D) (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t34_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k2_cat_1 A B (k2_cat_4 A B B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t34_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A B))  =>  ((k20_cat_5 A (k1_cat_1 A B C)) = (k1_partfun1 (u4_struct_0 (k12_cat_5 A (k4_graph_1 A C))) (u4_struct_0 (k12_cat_5 A (k3_graph_1 A C))) (u4_struct_0 (k12_cat_5 A (k4_graph_1 A B))) (u4_struct_0 (k12_cat_5 A (k3_graph_1 A B))) (k20_cat_5 A C) (k20_cat_5 A B))) ) ) ) ) ) ) ) ).
tt(t34_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_catalan2 (k24_binop_2 2 A) A)) = (k1_catalan1 (k23_binop_2 A 1))) ) ) ).
tt(t34_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  => (r1_tarski (k13_pre_poly (k25_valued_1 (u1_struct_0 A) k2_numbers C B)) (k13_pre_poly C))) ) ) ) ) ) ).
tt(t34_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_cfcont_1 C A) => (r1_cfcont_1 (k25_valued_1 k2_numbers k2_numbers C B) A)) ) ) ) ) ) ) ).
tt(t34_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((r1_cfdiff_1 A B) => (r1_cfcont_1 A B)) ) ) ) ) ).
tt(t34_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_cfunct_1 A (k2_cfunct_1 A B)) (k2_partfun1 A k2_numbers B (k1_relset_1 A (k2_cfunct_1 A B))))) ) ) ) ).
tt(t34_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (r1_tarski (k8_cgames_1 A) (k10_cgames_1 A))) ) ).
tt(t34_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_chain_1 E B) =>  (~  ((r1_xxreal_0 A B) &  ((r2_hidden (k3_chain_1 B C D) (k4_chain_1 B E A)) &  ( (? [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) &  ( (~  ( (~ (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 C F) (k1_seq_1 D F)) (k2_chain_1 B E F))) )  &  (~  ( ((k1_seq_1 C F) = (k1_seq_1 D F))  & (r2_hidden (k1_seq_1 C F) (k2_chain_1 B E F))) ) ) ) )  &  (~  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 D F)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 C F) (k1_seq_1 D F)) (k2_chain_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) =>  ( ( ((k3_glib_001 A C) = (k3_glib_001 A B))  &  ((k12_glib_001 A C) = (k12_glib_001 A B)) )  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t34_circcmb3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k9_xtuple_0 A)) &  ((r2_hidden D (k9_xtuple_0 A)) &  ((r2_hidden E (k9_xtuple_0 A)) & (r2_hidden F (k9_xtuple_0 A))) ) ) )  =>  ((k3_relat_1 (k8_finseq_4 B C D E F) A) = (k8_finseq_4 (k1_funct_1 A B) (k1_funct_1 A C) (k1_funct_1 A D) (k1_funct_1 A E) (k1_funct_1 A F))) ) ) ) ) ) ) ) ) ).
tt(t34_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_tarski (k2_msafree2 A) (k2_msafree2 B)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  &  (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B))) )  =>  ((k6_circuit2 C F G) = (k1_funct_4 (k6_circuit2 B E I) (k6_circuit2 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (r4_circtrm1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)) B B)) ) ) ) ).
tt(t34_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_tarski (k3_tarski (k4_classes1 A)) (k4_classes1 A))) ) ).
tt(t34_classes2,ax, (! [A:$i] :  ((v2_classes1 A) =>  ((k1_card_1 A) = (k1_card_1 (k4_classes1 (k1_card_1 A)))) ) ) ).
tt(t34_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_clopban1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_clopban1 A B))) =>  ( (E = (k1_algstr_0 (k14_clopban1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k15_clopban1 A B E F) = (k3_rlvect_1 B (k15_clopban1 A B C F) (k15_clopban1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((k1_seq_1 (k4_normsp_0 A B) D) = (k10_real_1 1 (k4_power D C))) ) ) )  =>  ((r1_xxreal_0 C 1) | (v2_clopban3 B A)) ) ) ) ) ) ) ) ).
tt(t34_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ( ((k7_clopban4 A (k3_rlvect_1 A B C)) = (k6_algstr_0 A (k7_clopban4 A B) (k7_clopban4 A C)))  &  ( ((k7_clopban4 A (k3_rlvect_1 A C B)) = (k6_algstr_0 A (k7_clopban4 A C) (k7_clopban4 A B)))  &  ( ((k7_clopban4 A (k3_rlvect_1 A B C)) = (k7_clopban4 A (k3_rlvect_1 A C B)))  & (r1_lopban_4 A (k7_clopban4 A B) (k7_clopban4 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t34_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v5_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m2_pboole E A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((r1_pboole A D C) &  (! [F:$i] :  ((m1_pboole F A (k5_mssubfam A B)) =>  (! [G:$i] :  ( ((v2_relat_1 G) & (m3_pboole G A (k1_mboolean A B)))  =>  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) & (v1_partfun1 H A)) ) )  =>  ((r1_pboole A H G) <=>  ((r1_pboole A H C) & (r2_pboole A F H)) ) ) )  => (r6_pboole A (k2_closure1 A B E F) (k4_mssubfam A B G))) ) ) ) ) )  => (r6_pboole A (k2_closure1 A B E D) D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((v7_closure2 C A B) & (v7_closure2 D A B))  => (v7_closure2 (k8_closure2 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t34_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (D = B)  =>  ((k4_algstr_0 A B) = (k4_algstr_0 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A D C))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A D C))) = (k13_csspace A (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k2_power D (k8_nat_1 k1_numbers (k2_clvect_2 A B) D))) ) )  &  ((v2_comseq_2 C) &  ( (~ (r1_xxreal_0 (k2_seq_2 C) 1))  & (v1_clvect_3 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t34_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v6_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) (k8_cohsp_1 A B C)) & (r2_hidden (k4_tarski E G) (k8_cohsp_1 A B C)))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_coh_sp,ax, (! [A:$i] : (r2_hidden (k4_tarski k1_xboole_0 k1_xboole_0) (k16_coh_sp A))) ).
tt(t34_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B B) &  ((v3_funct_2 C B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  => (v7_combgras (k8_combgras A B C) (k1_combgras A B))) ) ) ) ) ) ) ) ).
tt(t34_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_complex1 (k6_xcmplx_0 A B)) = (k11_complex1 (k15_complex1 A) (k15_complex1 B))) ) ) ) ) ).
tt(t34_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 A B) = (k15_complex1 (k1_complex2 B A))) ) ) ) ) ).
tt(t34_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_vectsp_1 k1_complfld (k11_algstr_0 k1_complfld A) B) = (k11_algstr_0 k1_complfld (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ).
tt(t34_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k1_valued_1 A (k30_valued_1 A)) = (k17_seq_4 (k3_finseq_1 A))) ) ) ).
tt(t34_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v5_waybel23 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((r1_tarski C B) &  ((m1_setfam_1 C (u1_struct_0 A)) & (v4_card_3 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ((k61_valued_1 (k5_compos_1 A D B) C) = (k5_compos_1 A (k61_valued_1 D C) B)) ) ) ) ) ) ) ) ) ).
tt(t34_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k62_valued_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F)) = 5) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 k6_numbers (k1_comptrig A)) &  (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k1_comptrig A))) ) ) ) ).
tt(t34_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k19_margrel1 (k4_comput_1 A B)) = A) ) ) ) ) ).
tt(t34_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k51_valued_1 k5_numbers k2_numbers k2_numbers B A))) ) ) ) ).
tt(t34_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v2_relat_1 A) =>  ( ((k3_comseq_2 A) = k5_complex1)  | (v2_comseq_2 (k36_valued_1 k5_numbers k2_numbers A))) ) ) ) ).
tt(t34_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (v7_valued_0 (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A)))) ) ).
tt(t34_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_conlat_1 D A) &  ( (~ (v5_conlat_1 D A))  &  ((v7_conlat_1 D A) & (l2_conlat_1 D A)) ) )  =>  ((k1_binop_1 (k9_conlat_1 A) B (k1_binop_1 (k9_conlat_1 A) C D)) = (k1_binop_1 (k9_conlat_1 A) (k1_binop_1 (k9_conlat_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t34_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_connsp_1 B A) &  ((v3_connsp_1 C A) &  ( (~  (B = C) )  &  (~ (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_connsp_3 B A))  =>  ((v2_connsp_1 B A) => (v3_connsp_1 B A)) ) ) ) ) ).
tt(t34_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_convex1 A B k6_numbers) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ).
tt(t34_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ((k3_funct_2 (u1_struct_0 A) k2_numbers (k9_convex4 A C D) B) = (k11_complex1 (k3_funct_2 (u1_struct_0 A) k2_numbers C B) (k3_funct_2 (u1_struct_0 A) k2_numbers D B))) ) ) ) ) ) ) ) ) ).
tt(t34_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (~  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C B F E) (k15_cqc_sim1 A D)) &  ( (~  ((k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C B F E) = (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D (k13_cqc_sim1 A D) (k1_setwiseo (k3_qc_lang1 A)) (k11_cqc_sim1 (k3_qc_lang1 A)))) )  &  ( (~ (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k6_cqc_lang A C) B F E) (k15_cqc_sim1 A D)))  &  ( (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~ (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k7_cqc_lang A C G) B F E) (k15_cqc_sim1 A D))) ) )  &  ( (! [G:$i] :  ((m2_subset_1 G (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_qc_lang1 A)) =>  (~  ( (B = (k30_qc_lang1 A H (k7_cqc_sim1 A G)))  & (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k7_cqc_lang A G C) H F E) (k15_cqc_sim1 A D))) ) ) ) ) )  &  (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_qc_lang1 A)) =>  (! [I:$i] :  ((m2_funct_2 I (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (~  ( ((k28_qc_lang1 A H) = B)  &  ( ((k1_funct_4 I (k8_funcop_1 (k3_qc_lang1 A) (k6_domain_1 (k3_qc_lang1 A) G) (k2_qc_lang3 A H))) = E)  &  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k11_cqc_lang A G C) H F I) (k15_cqc_sim1 A D)) | (r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k1_zfmisc_1 F) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k11_cqc_lang A G C) H (k6_subset_1 F (k6_domain_1 (k3_qc_lang1 A) G)) I) (k15_cqc_sim1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( (B = (a_2_0_cqc_the1 A C))  => (v1_cqc_the1 B A)) ) ) ) ) ) ) ).
tt(t34_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k8_cqc_lang A B C)) (k8_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t34_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r5_cqc_the3 A B C) & (r5_cqc_the3 A D E))  => (r5_cqc_the3 A (k7_cqc_lang A B D) (k7_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k17_complex1 (k12_csspace A B B)) = (k3_complex1 (k12_csspace A B B))) ) ) ) ) ).
tt(t34_descip_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_finseq_1 A)) &  ((v1_descip_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k2_finseq_1 A))))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 A C))  =>  ( ((k1_funct_1 B C) = (k1_nat_1 C 1))  & (r2_hidden C (k1_relset_1 A B))) ) ) ) ) ) ) ) ).
tt(t34_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_dickson A) &  (! [C:$i] :  (~  ((r1_dickson A B C) &  (! [D:$i] :  ((r1_dickson A B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_zfmisc_1 A B C) =>  ( ((k10_diff_1 D A B C) = (k10_diff_1 D B C A))  &  ((k10_diff_1 D A B C) = (k10_diff_1 D C B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k10_real_1 A E)) ) )  =>  ( (B = C)  |  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ((k9_diff_1 D B C) = (k1_real_1 (k10_real_1 A (k8_real_1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k7_real_1 (k8_real_1 (k3_funct_2 k1_numbers k1_numbers C (k7_real_1 B (k10_real_1 A 2))) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D A) 1) B)) (k8_real_1 (k3_funct_2 k1_numbers k1_numbers D (k9_real_1 B (k10_real_1 A 2))) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) 1) B)))) ) ) ) ) ) ) ) ) ).
tt(t34_diff_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k25_sin_cos (k6_xcmplx_0 A B)) = (k13_complex1 (k25_sin_cos A) (k25_sin_cos B))) ) ) ) ) ).
tt(t34_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_dilworth C (k5_yellow_0 A (k3_dilworth A B))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A (k3_dilworth A B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~  (D = E) )  &  (~ (r1_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_diraf A B C D) & (r3_diraf A B C E))  => (r2_diraf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k5_subset_1 A B C) = (a_3_7_domain_1 A B C)) ) ) ) ) ) ) ).
tt(t34_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( (B = k6_numbers)  <=>  ((k2_ec_pf_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t34_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ((r1_ec_pf_2 A D (k5_ec_pf_1 A B C)) <=> (m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t34_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (~  ( (~  (A = (k1_tarski k1_xboole_0)) )  &  ((v10_cat_1 B (k11_ens_1 A)) &  (! [C:$i] :  (~  (B = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 C) D) |  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k2_finseq_1 (k1_matrix_1 B))) =>  ((r2_hidden (k2_nat_1 (k4_nat_1 D (k1_matrix_1 B)) E) (k4_finseq_1 (k1_matrprob A C (k2_nat_1 D 1)))) &  ((k1_funct_1 (k1_matrprob A C (k2_nat_1 D 1)) (k2_nat_1 (k4_nat_1 D (k1_matrix_1 B)) E)) = (k1_funct_1 (k1_matrprob A B (k2_nat_1 D 1)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k5_enumset1 A A B C D E F) = (k4_enumset1 A B C D E F)) ) ) ) ) ) ) ).
tt(t34_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (? [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  &  (B = (k7_eqrel_1 A C)) ) ) ) ) ) ).
tt(t34_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (k4_equation A)) =>  ( ((r6_msualg_3 A B C) & (r2_equation A B D))  => (r2_equation A C D)) ) ) ) ) ) ) ) ) ).
tt(t34_e_siec,ax, (! [A:$i] :  ( ((v2_e_siec A) &  ((v3_e_siec A) & (l1_e_siec A)) )  =>  ((r1_tarski (k19_e_siec A) (k2_zfmisc_1 (k7_e_siec A) (k8_e_siec A))) & (r1_tarski (k18_e_siec A) (k2_zfmisc_1 (k7_e_siec A) (k8_e_siec A)))) ) ) ).
tt(t34_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k23_rvsum_1 (k4_struct_0 (k15_euclid A)) (k4_struct_0 (k15_euclid A))) = k6_numbers) ) ) ).
tt(t34_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 k32_sin_cos (k3_euclid_3 A)))  &  ( (~ (r1_xxreal_0 k32_sin_cos (k3_euclid_3 B)))  & (r1_xxreal_0 k32_sin_cos (k3_euclid_3 (k3_rlvect_1 (k15_euclid 2) A B)))) ) ) ) ) ) ) ).
tt(t34_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k5_square_1 (k12_euclid (k7_euclid A B C))) = (k7_real_1 (k7_real_1 (k5_square_1 (k12_euclid B)) (k8_real_1 2 (k23_rvsum_1 B C))) (k5_square_1 (k12_euclid C)))) ) ) ) ) ) ) ).
tt(t34_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k6_euclid_5 A B C) = (k6_euclid_5 C A B)) ) ) ) ) ) ) ).
tt(t34_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ((r2_hidden A (k5_jgraph_6 E F G)) &  ((r2_hidden B (k5_jgraph_6 E F G)) &  ((r2_hidden C (k5_jgraph_6 E F G)) &  ((r2_hidden D (k5_jgraph_6 E F G)) &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  ((k4_euclid_3 A C B) = (k4_euclid_3 A D B)) )  &  ( (~  ((k4_euclid_3 A C B) = (k9_real_1 (k4_euclid_3 A D B) k32_sin_cos)) )  &  (~  ((k4_euclid_3 A C B) = (k7_real_1 (k4_euclid_3 A D B) k32_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_euclid_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k7_real_ns1 A))) =>  ( (B = C)  =>  ((k5_euclid_7 A B) = (k4_rlvect_1 (k7_real_ns1 A) C)) ) ) ) ) ) ) ) ).
tt(t34_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k9_euclid 3 A k6_numbers) = (k1_euclid_8 k6_numbers k6_numbers k6_numbers)) ) ) ).
tt(t34_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( ((k1_rlvect_1 (k15_euclid A) B D) = (k1_rlvect_1 (k15_euclid A) C D))  &  ( (~  (D = k6_numbers) )  &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r3_euclidlp A B C) =>  ( (~  (B = (k5_euclid A)) )  &  (~  (C = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ).
tt(t34_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ((r2_hidden B (k9_xtuple_0 E)) =>  ( (B = C)  |  ( (B = D)  |  ((k7_partfun1 A (k10_funct_7 E C D) B) = (k7_partfun1 A E B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_extpro_1 A B C (k5_extpro_1 A B C D E)) =>  ((r1_xxreal_0 (k8_extpro_1 A B C (k5_extpro_1 A B C D E)) k6_numbers) |  ((k8_extpro_1 A B C D) = (k2_nat_1 E (k8_extpro_1 A B C (k5_extpro_1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_circcomb A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  ((v4_circcomb B A) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k1_funct_1 (k6_circuit2 A B C) (k2_msualg_1 A D)) = (k1_funct_1 (k2_xtuple_0 D) (k3_relat_1 (k1_msualg_1 A D) C))) ) ) ) ) ) ) ) ) ) ).
tt(t34_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B (k2_nat_1 A 1)) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) &  ((v1_finseq_1 C) & (v2_facirc_1 C)) ) ) )  &  (? [D:$i] :  ( (~ (v1_xtuple_0 D))  &  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ) ).
tt(t34_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t34_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k9_real_1 (k9_real_1 (k5_square_1 (k1_seq_1 k19_sin_cos B)) (k8_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t34_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 k2_sin_cos9) A) B) = (k9_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t34_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k3_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) ) ) )  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) & (v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) ) ) ) ) ) ).
tt(t34_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))))) &  ( (C = (k3_valued_1 k1_numbers k1_numbers k1_numbers D E))  &  ( (E = (k1_taylor_1 2))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) B) F) = (k8_real_1 F (k10_prepower (k7_real_1 (k5_square_1 A) (k2_newton F 2)) (k1_real_1 (k10_real_1 1 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1))) &  ( (B = (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 C D) = (k1_real_1 D)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) D) = (k10_real_1 (k9_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))) (k7_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k19_sin_cos (k1_seq_1 k24_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t34_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 B))) (k10_real_1 (k10_real_1 1 B) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t34_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t34_fib_num2,ax, (k2_fib_num = (k3_power (k4_xcmplx_0 k1_fib_num) (k4_xcmplx_0 1))) ).
tt(t34_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_nat_1 (k3_fib_num3 A B C) (k3_fib_num3 A B (k1_nat_1 C 1))) = (k3_fib_num3 A B (k1_nat_1 C 2))) ) ) ) ) ) ) ).
tt(t34_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((v1_abian A) |  ((k1_fib_num3 (k2_xcmplx_0 A 1)) = (k1_int_1 (k2_xcmplx_0 (k3_xcmplx_0 k1_fib_num (k1_fib_num3 A)) 1))) ) ) ) ) ).
tt(t34_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  ( (D = (k1_finseq_8 A B C))  =>  ((r2_finseq_8 A D B 1) & (r2_finseq_8 A D C 1)) ) ) ) ) ) ) ) ) ) ).
tt(t34_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) (k3_filter_0 A B) C)))  &  ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B (k3_filter_0 A C)))) ) ) ) ) ) ) ) ).
tt(t34_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_lattices B))  =>  ( ( (~ (v2_struct_0 (k7_filter_1 A B)))  &  ((v10_lattices (k7_filter_1 A B)) & (l3_lattices (k7_filter_1 A B))) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) ) ) ) ) ) ) ) ).
tt(t34_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A B C) = B) ) ) )  &  ((k6_filter_2 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t34_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k7_finseq_1 A k1_xboole_0) = A)  &  ((k7_finseq_1 k1_xboole_0 A) = A) ) ) ) ).
tt(t34_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k3_relat_1 (k9_finseq_1 A) B) = (k9_finseq_1 (k1_funct_1 B A))) ) ) ) ) ).
tt(t34_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  (k1_xboole_0 = (k11_finseq_1 A B C)) ) ) ) ) ).
tt(t34_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k3_finseq_1 (k5_finseq_4 A B)) = (k6_xcmplx_0 (k4_finseq_4 A B) 1)) ) ) ) ) ).
tt(t34_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((v2_funct_1 C) => (r1_xboole_0 (k10_xtuple_0 (k17_finseq_1 B A C)) (k10_xtuple_0 (k2_rfinseq B A C)))) ) ) ) ) ) ) ).
tt(t34_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  (~  ((k6_finseq_4 (k11_finseq_1 A C B) B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t34_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) ) ) )  =>  ( (C = D)  |  ( (E = D)  |  ((k2_finseq_7 A (k2_finseq_7 A B C E) E D) = (k2_finseq_7 A (k2_finseq_7 A B C D) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 E A) => (r2_relset_1 k5_numbers A (k3_finseqop A A A E B D) (k2_finseqop A A A E D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k11_fintopo2 A C)) <=>  ((r2_hidden B C) &  (~ (r2_hidden B (k9_fintopo2 A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ) ) ).
tt(t34_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_fintopo3 A B 2) = (k12_fin_topo A (k12_fin_topo A B))) ) ) ) ) ).
tt(t34_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_fin_topo A) &  ((v4_fin_topo B A) & (v4_fin_topo C A)) )  =>  ((r1_fintopo4 A B C) | (v4_fin_topo (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t34_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_flang_1 A (k7_flang_1 A B C) D) = (k7_flang_1 A B (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ).
tt(t34_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden (k2_flang_1 A) B) & (r1_xxreal_0 C D))  =>  ((k1_flang_2 A B C D) = (k7_flang_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t34_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((k6_flang_1 A (k8_flang_1 A B) (k1_flang_2 A B C D)) = (k1_flang_3 A B C)) ) ) ) ) ) ) ) ) ).
tt(t34_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ( (C = D)  =>  ((k18_fomodel0 B D A (k12_finseq_1 B C)) = (k9_finseq_1 A)) )  &  ( (~  (C = D) )  =>  ((k18_fomodel0 B D A (k12_finseq_1 B C)) = (k12_finseq_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 (u1_struct_0 A) B E) = D)  & (r1_frechet A B C)) ) )  => (r2_hidden C (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) D)))) ) ) ) ) ) ) ) ) ).
tt(t34_frechet,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  &  ((v3_frechet A) &  (~ (v1_frechet A)) ) ) ) ).
tt(t34_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  ((k7_fsm_1 A B C k6_numbers) = (k1_tarski (u1_struct_0 C))) ) ) ) ) ) ) ).
tt(t34_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  (~  ((r2_hidden A (u2_fsm_3 B (k9_flang_1 B) (k4_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) C))) & (r1_xboole_0 A (u2_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) C))) ) ) ) ) ) ) ).
tt(t34_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden B (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden C (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden D (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden E (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k48_gfacirc1 A B C) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k45_gfacirc1 A B C) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k48_gfacirc1 (k48_gfacirc1 A B C) E D) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp) (u1_struct_0 (k19_ftacell1 A B C D E))) & (r2_hidden (k45_gfacirc1 (k48_gfacirc1 A B C) E D) (u1_struct_0 (k19_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k3_relat_1 B (k5_funcop_1 C D A)) = (k5_funcop_1 C D (k3_relat_1 B A))) ) ) ) ) ) ) ) ).
tt(t34_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 B) & (r2_hidden A (k9_xtuple_0 B)))  =>  ( (A = (k1_funct_1 (k2_funct_1 B) (k1_funct_1 B A)))  &  (A = (k1_funct_1 (k3_relat_1 B (k2_funct_1 B)) A)) ) ) ) ) ) ).
tt(t34_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((r2_hidden C A) & (r2_hidden (k1_funct_1 E C) D))  =>  ( (B = k1_xboole_0)  |  ((k1_funct_1 (k6_relset_1 A B D E) C) = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ).
tt(t34_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v2_funct_1 B) =>  ((k3_funct_3 (k3_relat_1 A B)) = (k3_relat_1 (k3_funct_3 B) (k3_funct_3 A))) ) ) ) ) ) ).
tt(t34_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=>  ((k1_funct_4 A B) = (k1_funct_4 B A)) ) ) ) ) ) ).
tt(t34_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 (k3_funct_5 B))) &  (C = (k1_funct_1 (k3_funct_5 B) A)) )  =>  ( ((k9_xtuple_0 C) = (k9_xtuple_0 (k3_xboole_0 (k9_xtuple_0 B) (k2_zfmisc_1 (k9_xtuple_0 (k9_xtuple_0 B)) (k1_tarski A)))))  &  ((r1_tarski (k9_xtuple_0 C) (k9_xtuple_0 (k9_xtuple_0 B))) &  ((r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B)) &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ( ((k1_funct_1 C D) = (k1_binop_1 B D A))  & (r2_hidden (k4_tarski D A) (k9_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  ( (D = (k1_funct_1 C A))  &  ((r2_hidden B (k9_xtuple_0 (k6_funct_6 C))) &  (E = (k1_funct_1 (k6_funct_6 C) B)) ) ) )  =>  ((k1_funct_1 D B) = (k1_funct_1 E A)) ) ) ) ) ) ) ) ) ) ).
tt(t34_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_funct_7 (k2_funct_7 A D B) D C) = (k2_funct_7 A D C)) ) ) ) ) ) ).
tt(t34_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k32_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t34_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_int_1 C))  => (v1_funct_9 (k15_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k16_sin_cos A) B) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ).
tt(t34_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v6_functor0 D A B) &  ((v8_functor0 D A B) & (l2_functor0 D A B)) )  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k4_functor0 A C (k13_functor0 A B C D E) F F) = (k3_relat_1 (k4_functor0 A B D F F) (k4_functor0 B C E (k3_functor0 A B D F) (k3_functor0 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ((m1_functor3 F A B C D) =>  (! [G:$i] :  ((m1_functor3 G A B D E) =>  ( ((r1_functor3 A B C D) & (r1_functor3 A B D E))  => (m1_functor3 (k5_functor2 A B C D E F G) A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers B (k1_fuzzy_1 A C D)) <=>  ((r1_fuzzy_1 B C) &  ((r1_fuzzy_1 B D) &  (! [E:$i] :  ( ((v5_relat_1 E (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 E) &  ((v1_funct_2 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 E C) & (r1_fuzzy_1 E D))  => (r1_fuzzy_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k2_fuzzy_2 A B C)) (k3_fuzzy_2 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C)))) ) ) ) ) ) ).
tt(t34_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( ((k3_funct_2 (u1_struct_0 A) k7_numbers C B) = 1)  =>  ((k1_fvaluat1 (k2_relset_1 k7_numbers C)) = 1) ) ) ) ) ) ) ) ).
tt(t34_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k8_fvsum_1 1 A (k4_matrix_2 (u1_struct_0 A) B) (k4_matrix_2 (u1_struct_0 A) C)) = (k4_matrix_2 (u1_struct_0 A) (k5_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t34_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~  ( (~ (v1_xboole_0 (k28_gate_1 A B C D E F G)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  (~ (v1_xboole_0 G)) ) ) ) ) ) ) )  & (v1_xboole_0 (k28_gate_1 A B C D E F G))) ) ) ) ) ) ) ) ) ) ).
tt(t34_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r4_gcd_1 A D E) =>  ((r4_gcd_1 A (k5_gcd_1 A B C D) (k5_gcd_1 A B C E)) & (r4_gcd_1 A (k5_gcd_1 A B D C) (k5_gcd_1 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) & (r1_xxreal_0 (k3_finseq_1 F) B))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G C D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) & (r1_xxreal_0 (k3_finseq_1 F) C))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G B D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) & (r1_xxreal_0 (k3_finseq_1 F) D))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G B C)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) B) & (r1_xxreal_0 (k3_finseq_1 F) C))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G A D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) B) & (r1_xxreal_0 (k3_finseq_1 F) D))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G A C)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) C) & (r1_xxreal_0 (k3_finseq_1 F) D))  =>  ((k10_genealg1 E F G A B C D) = (k8_genealg1 E F G A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k8_real_1 2 (k4_geomtrap A B C D (k1_geomtrap A E F))) = (k7_real_1 (k4_geomtrap A B C D E) (k4_geomtrap A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k13_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t34_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((k7_glib_000 A) = (k21_glib_000 A (k6_glib_000 A))) ) ) ).
tt(t34_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k5_numbers (k7_glib_001 A B C))) &  ( (~ (r2_hidden D (k1_relset_1 k5_numbers B)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) E))  &  (D = (k2_nat_1 (k3_finseq_1 B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_glib_002 B A) & (m1_glib_000 B A))  =>  (! [C:$i] :  ( ((v4_glib_002 C A) & (m1_glib_000 C A))  =>  (! [D:$i] :  ( ((r2_hidden D (k24_glib_000 A B)) & (r2_hidden D (k24_glib_000 A C)))  => (r5_glib_000 B C)) ) ) ) ) ) ) ) ).
tt(t34_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] : (r5_glib_000 A (k12_glib_003 A B C))) ) ) ) ).
tt(t34_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B C) =>  ((r1_tarski (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) C))) & (r1_tarski (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) C)))) ) ) ) ) ) ) ) ).
tt(t34_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k2_finseq_1 (k1_matrix_1 C))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1))) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D E) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C A))))  => (r1_xxreal_0 B E)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r1_xxreal_0 E B))  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r2_hidden F (k2_finseq_1 (k1_matrix_1 C))) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D E) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) C F))))  => (r1_xxreal_0 F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k1_matrix_1 B)))  => (r2_hidden (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B (k3_finseq_1 B) A)))) ) ) ) ) ).
tt(t34_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 A) 4)) ) ) ).
tt(t34_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k1_matrix_1 (k2_goboard2 A))))  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 B 1))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k2_nat_1 B 2))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t34_gobrd11,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) & (r1_xxreal_0 1 (k1_matrix_1 A))) ) ) ).
tt(t34_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((k5_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  => (r2_jordan2c 2 (k3_topreal1 2 A) (k2_goboard9 A))) ) ).
tt(t34_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_henmodel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (~  ((v4_card_3 A) &  ((v1_finset_1 (k6_goedelcp A B)) &  (! [C:$i] :  ( ((v1_henmodel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [D:$i] :  ((m1_henmodel D A C) =>  (~ (r6_calcul_1 A B (k1_henmodel A) D (k3_henmodel A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((r2_hidden A (k11_graph_1 B)) & (r2_hidden C (k11_graph_1 B)))  => (r2_hidden (k5_graph_1 A C) (k11_graph_1 B))) ) ) ) ) ) ) ).
tt(t34_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_graph_1 D A) =>  ( ((r1_graph_2 A B D) & (r1_graph_2 A C D))  =>  ( (D = k1_xboole_0)  |  ( (B = C)  |  ( (~  ((k1_funct_1 B 1) = (k1_funct_1 C 1)) )  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ((r1_graph_2 A E D) &  ( (~  (E = B) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (u4_struct_0 A) (u4_struct_0 (k8_graph_3 A B C))) &  ( ((u4_struct_0 A) = (k6_subset_1 (u4_struct_0 (k8_graph_3 A B C)) (k1_tarski (u4_struct_0 A))))  &  ( ((k1_funct_1 (u1_graph_1 (k8_graph_3 A B C)) (u4_struct_0 A)) = B)  &  ((k1_funct_1 (u2_graph_1 (k8_graph_3 A B C)) (u4_struct_0 A)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t34_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v7_graph_1 G B) & (m2_graph_1 G B))  =>  (! [H:$i] :  ( ((v7_graph_1 H B) & (m2_graph_1 H B))  =>  ( ( (G = (k8_finseq_1 (u4_struct_0 B) H C))  &  ((r1_xxreal_0 1 (k3_finseq_1 H)) &  ( ((k3_finseq_1 C) = 1)  &  ((r2_graph_5 B D E H A) & (r1_graph_4 B E F (k1_funct_1 C 1))) ) ) )  => (r2_graph_5 B D F G (k2_xboole_0 A (k1_tarski E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (~  ( (~  ((k7_graphsp B A) = k1_xboole_0) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k7_graphsp B A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((k1_seq_1 (k6_graphsp (k16_graphsp A) B) C) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m3_grcat_1 C (k18_grcat_1 (k17_grcat_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k25_grcat_1 A))) =>  (! [E:$i] :  ((m2_grcat_1 E (k17_grcat_1 A)) =>  ( ((v1_grcat_1 B) & (m3_grcat_1 B (k18_grcat_1 (k17_grcat_1 A))))  &  ((m1_subset_1 C (u4_struct_0 (k25_grcat_1 A))) &  ( ((v8_algstr_0 D) & (m2_grcat_1 D (k17_grcat_1 A)))  & (m1_subset_1 E (u1_struct_0 (k25_grcat_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_gr_cy_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_int_1 A B C) =>  ( (C = k6_numbers)  | (r2_int_1 (k1_newton A D) (k1_newton B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) =>  (A = (k5_relat_1 B (k9_xtuple_0 A))) ) ) ) ) ) ).
tt(t34_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (g1_orders_2 (k15_pre_poly A) (k4_groeb_1 A))))) =>  (? [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k15_pre_poly A))))  & (r1_dickson (g1_orders_2 (k15_pre_poly A) (k4_groeb_1 A)) B C)) ) ) ) ) ) ).
tt(t34_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [G:$i] :  ((m2_ideal_1 G (k11_polynom1 A C) F) =>  (! [H:$i] :  ((m2_ideal_1 H (k11_polynom1 A C) F) =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I A) &  ((v1_funct_1 I) &  ((v1_partfun1 I A) &  ((v4_valued_0 I) & (v2_pre_poly I)) ) ) ) )  =>  (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  ( ((r3_groeb_2 A B C D F G I) &  ( (H = (k17_finseq_1 (u1_struct_0 (k11_polynom1 A C)) J G))  &  (E = (k4_rlvect_1 (k11_polynom1 A C) (k2_rfinseq (u1_struct_0 (k11_polynom1 A C)) J G))) ) )  => (r3_groeb_2 A B C (k6_polynom1 A C D E) F H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k5_groeb_3 A B C D k6_numbers) (k7_polynom1 A C)) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_groeb_3 A B C D k6_numbers) D)) ) ) ) ) ) ) ) ) ).
tt(t34_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k1_group_11 A (k1_group_11 A B C) C) = (k1_group_11 A B C)) ) ) ) ) ) ) ).
tt(t34_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k5_group_1 B (k20_binop_2 A 1) C) = (k6_algstr_0 B (k5_group_1 B A C) C))  &  ((k5_group_1 B (k20_binop_2 A 1) C) = (k6_algstr_0 B C (k5_group_1 B A C))) ) ) ) ) ) ) ) ).
tt(t34_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_group_1 A) =>  ((k5_group_2 A D (k5_group_2 A C B)) = (k5_group_2 A (k6_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_group_3 A (k2_group_2 A B C) D) (k2_group_2 A (k3_group_3 A B D) (k3_group_3 A C D)))) ) ) ) ) ) ) ) ).
tt(t34_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((u1_struct_0 (k5_group_4 A B)) = (k1_setfam_1 (a_2_0_group_4 A B))) ) ) ) ) ).
tt(t34_group_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_5 B (k5_group_1 B A C) D) = (k6_algstr_0 B (k5_group_1 B (k4_xcmplx_0 A) C) (k5_group_1 B A (k2_group_3 B C D)))) ) ) ) ) ) ) ) ) ).
tt(t34_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k2_group_5 A C D)) = (k2_group_5 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_group_1 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)) (k4_group_7 A B)) = (k4_group_7 A (k2_group_1 A B))) ) ) ) ) ).
tt(t34_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ( ((k19_group_9 A B (k5_group_9 A B) C) = (k5_group_9 A B))  &  ((k19_group_9 A B C (k5_group_9 A B)) = (k5_group_9 A B)) ) ) ) ) ) ) ).
tt(t34_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v15_algstr_0 C) &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) ) )  =>  ( ((r2_group_6 B C) & (v3_groupp_1 B A))  => (v3_groupp_1 C A)) ) ) ) ) ) ) ).
tt(t34_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (v2_compts_1 D (k3_pcomps_1 A))) )  => (r1_xxreal_0 (k8_weierstr A D B) (k7_real_1 (k1_hausdorf A B C) (k1_hausdorf A C D)))) ) ) ) ) ) ) ) ) ).
tt(t34_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ( ((v3_glib_002 D) & (m1_glib_000 D A))  =>  ( ((r2_hidden B (k24_glib_000 A D)) & (r2_hidden C (k24_glib_000 A D)))  => (r1_tarski (k13_glib_001 A (k2_helly A B C)) (k24_glib_000 A D))) ) ) ) ) ) ) ) ) ).
tt(t34_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld) (k3_hermitan A B (k5_bilinear k1_complfld A B C D)) (k5_bilinear k1_complfld A B (k3_hermitan A B C) (k3_hermitan A B D)))) ) ) ) ) ) ) ) ).
tt(t34_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers A)))) =>  ( (B = C)  =>  ( (B = (k1_tarski k1_xboole_0))  |  ( (~ (v1_xboole_0 (k1_heyting2 k5_numbers (k6_domain_1 k5_numbers A) C)))  &  ((v1_finset_1 (k1_heyting2 k5_numbers (k6_domain_1 k5_numbers A) C)) & (m1_subset_1 (k1_heyting2 k5_numbers (k6_domain_1 k5_numbers A) C) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ) ) ) ) ) ).
tt(t34_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ( ((k1_seq_1 (k6_taylor_1 k16_sin_cos D A B) C) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 C k32_sin_cos) 2))) (k2_newton (k9_real_1 B A) C)) (k3_newton C)))  &  ((k1_seq_1 (k6_taylor_1 k19_sin_cos D A B) C) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos (k7_real_1 A (k10_real_1 (k8_real_1 C k32_sin_cos) 2))) (k2_newton (k9_real_1 B A) C)) (k3_newton C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_hilbasis,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (v6_ideal_1 (k11_polynom1 B A))) ) ) ) ).
tt(t34_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B C)) (k3_hilbert1 (k4_hilbert1 A B) C)) k6_hilbert1)) ) ) ) ) ) ).
tt(t34_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((k1_funct_1 (k3_hilbert2 A) k1_xboole_0) = A) ) ) ).
tt(t34_hilbert3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ((m1_hilbert3 C B) =>  ((k5_hilbert3 B C (k1_hilbert2 A)) = (k1_funct_1 C A)) ) ) ) ) ) ) ).
tt(t34_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  (C = (k9_polynom3 A)) )  =>  ((r1_hurwitz A B C) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  & (r2_funct_2 k5_numbers (u1_struct_0 A) (k13_polynom3 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ((r1_idea_1 A (k1_recdef_1 C 1)) &  ((r1_idea_1 A (k1_recdef_1 C 2)) &  ((r1_idea_1 A (k1_recdef_1 C 3)) &  ((r1_idea_1 A (k1_recdef_1 C 4)) &  ( ((k1_recdef_1 D 1) = (k10_idea_1 A (k1_recdef_1 C 1)))  &  ( ((k1_recdef_1 D 2) = (k6_idea_1 A (k1_recdef_1 C 2)))  &  ( ((k1_recdef_1 D 3) = (k6_idea_1 A (k1_recdef_1 C 3)))  &  ((k1_recdef_1 D 4) = (k10_idea_1 A (k1_recdef_1 C 4))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_partfun1 k14_idea_1 k14_idea_1 k14_idea_1 k14_idea_1 (k19_idea_1 C A) (k20_idea_1 D A)) B) = B) ) ) ) ) ) ) ) ) ) ).
tt(t34_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m3_ideal_1 C A B))  =>  (? [D:$i] :  ((m3_ideal_1 D A B) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k8_finseq_1 (u1_struct_0 A) D (k12_finseq_1 (u1_struct_0 A) E))) & (m3_ideal_1 (k12_finseq_1 (u1_struct_0 A) E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r1_incsp_1 A D B) & (r1_incsp_1 A D C)) ) )  &  (~  ((k4_incsp_1 A B C) = (k4_incsp_1 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) &  ((v3_cat_5 F) & (l1_cat_1 F)) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m2_cat_1 G E F) =>  ((k14_index_1 A B B C (k15_index_1 B D E F G)) = (k15_index_1 A (k14_index_1 A B B C D) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  ((r1_msualg_3 A C D E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (~  ((r3_pua2mss1 B A F G) &  (! [H:$i] :  ((m2_pboole H (u1_struct_0 B) (u3_msualg_1 B (k1_instalg1 B A C F G)) (u3_msualg_1 B (k1_instalg1 B A D F G))) =>  (~  ((r8_pboole (u1_struct_0 B) H (k3_relat_1 F E)) & (r1_msualg_3 B (k1_instalg1 B A C F G) (k1_instalg1 B A D F G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_int_1 A) = (k2_int_1 A))  <=> (v1_int_1 A)) ) ) ).
tt(t34_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_int_2 A B) = (k3_int_2 (k1_int_2 A) (k1_int_2 B))) ) ) ) ) ).
tt(t34_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k3_finseq_1 A) = (k7_real_1 B 1))  &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B)) )  =>  ((k1_recdef_1 (k5_wsierp_1 k1_numbers k5_numbers C A) B) = (k1_recdef_1 A (k3_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(t34_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k3_int_2 (k1_recdef_1 B C) A) = 1) ) ) )  &  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (~  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k2_int_5 (k1_recdef_1 B D) A)) ) ) )  &  ((k2_int_5 (k3_wsierp_1 B) A) = (k19_rvsum_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k1_funct_1 (k18_valued_1 (k1_int_6 A C) (k1_int_6 B C)) D) (k3_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t34_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (C = (k1_taylor_1 2))  &  (B = (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers C (k10_real_1 1 2)))) ) )  =>  ((k2_integra5 A (k1_partfun2 k1_numbers B)) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers C (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers C (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t34_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k12_binop_2 (k5_square_1 (k1_seq_1 k19_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D)))) ) ) )  &  ((r1_tarski C (k1_relset_1 C (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers C)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers C)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers C)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t34_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k29_sin_cos)) A) B) = (k10_real_1 1 (k8_real_1 (k5_square_1 B) (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 B)))))) ) ) ) ) ) ) ) ).
tt(t34_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k19_sin_cos D)) (k5_square_1 D)) (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos D) D) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k1_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t34_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( (B = C)  =>  ((v3_integr15 B A) <=> (v1_integr19 C (k4_real_ns1 A) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t34_integra1,ax, (! [A:$i] :  ( ((v5_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 B (k3_finseq_1 A)) =>  ((v5_valued_0 (k2_rfinseq k1_numbers B A)) & (m2_finseq_1 (k2_rfinseq k1_numbers B A) k1_numbers)) ) ) ) ) ) ).
tt(t34_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v3_integra1 B A) &  ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) &  ((v3_integra1 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) => (r1_xxreal_0 (k1_seq_1 C D) (k1_seq_1 B D))) ) ) ) ) ) )  => (r1_xxreal_0 (k12_integra1 A C) (k12_integra1 A B))) ) ) ) ) ) ) ).
tt(t34_integra8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 k30_sin_cos)) =>  ((r2_fdiff_1 k30_sin_cos A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 k30_sin_cos A) B) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t34_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers k32_sin_cos))  => (r1_integra9 A k16_sin_cos k19_sin_cos)) ) ) ).
tt(t34_interva1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k2_setfam_1 (k3_setfam_1 B C) C) = C) ) ) ) ) ) ).
tt(t34_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((r2_hidden (k4_intpro_1 A B) k8_intpro_1) <=>  ((r2_hidden A k8_intpro_1) & (r2_hidden B k8_intpro_1)) ) ) ) ) ) ).
tt(t34_irrat_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v1_series_1 A) &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers)) ) )  & (r1_xxreal_0 (k4_series_1 A) k6_numbers)) ) ) ) ) ).
tt(t34_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  (! [E:$i] :  ((m2_nattra_1 E B A C D) =>  ((r2_nattra_1 B A C D) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) (k5_isocat_1 B B A C D (k10_cat_1 B) E) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_cat_1 H A F G) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k8_cat_2 B C)) (k8_isocat_2 A B C D E) H) = (k10_cat_2 B C (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) D H) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_isomichi,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 B) (k1_rcomp_1 C D)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k1_tops_1 k3_topmetr A) = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k2_rcomp_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_complex1 (k9_real_1 (k17_euclid A) (k17_euclid B))) (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) & (r1_xxreal_0 (k18_complex1 (k9_real_1 (k18_euclid A) (k18_euclid B))) (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)))) ) ) ) ) ).
tt(t34_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k10_real_1 (k10_real_1 (k17_euclid C) (k18_euclid C)) (k18_euclid C))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t34_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k8_real_1 (k18_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid C) (k17_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k17_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t34_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_0_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k3_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t34_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((k8_jordan6 A) = (a_1_0_jgraph_5 A)) ) ) ) ).
tt(t34_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) = (k1_tarski (k19_euclid A D))) ) ) ) ) ) ) ) ) ) ).
tt(t34_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = H)  &  ((r1_xxreal_0 E (k17_euclid A)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) |  ((r1_xxreal_0 (k17_euclid D) (k17_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan12,ax, (! [A:$i] :  ( ((v1_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ((v1_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ( ((v1_topreal1 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ( ( ( (~ (v1_xboole_0 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)))  &  ( (~ (v3_funct_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)))  &  ((v1_finseq_6 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v2_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v1_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v2_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) & (m2_finseq_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  &  ((r2_jordan12 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) C) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((v2_topreal1 C) & (v3_topreal1 C)) ) ) )  =>  ( ((v1_abian (k1_card_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 C)))) & (m1_subset_1 (k1_card_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 C))) k5_numbers))  <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) D) &  ((r2_hidden (k1_funct_1 C 1) D) & (r2_hidden (k1_funct_1 C (k3_finseq_1 C)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_jordan1h A B) & (r1_xxreal_0 B C))  => (r1_tarski (k3_topreal1 2 (k1_jordan13 A C)) (k2_pre_topc (k15_euclid 2) (k2_goboard9 (k1_jordan13 A B))))) ) ) ) ) ) ) ).
tt(t34_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 D A)) (k2_nat_1 C 1)) |  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 1)) 2) 1))  & (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 1)) 2) (k3_finseq_1 (k1_jordan8 D B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_7_jordan1 A B C D))  => (v3_pre_topc E (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan1b,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 B (k1_matrix_1 A)) & (v9_rltopsp1 (k3_goboard5 A (k3_finseq_1 A) B) (k15_euclid 2))) ) ) ) ) ) ).
tt(t34_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k2_xcmplx_0 (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k7_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) = (k2_xcmplx_0 (k9_pscomp_1 B) (k7_pscomp_1 B))) ) ) ) ) ).
tt(t34_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) A B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski 1 C) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 C) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski C 1) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C 1) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski (k3_finseq_1 B) C) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) C) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden (k4_tarski C (k1_matrix_1 B)) (k2_matrix_1 B)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B C (k1_matrix_1 B)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ) )  |  (B = (k2_goboard2 A)) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (~ (r1_xxreal_0 (k6_pscomp_1 B) (k6_pscomp_1 A)))  =>  ((k19_pscomp_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B)) = (k19_pscomp_1 A)) ) ) ) ) ) ).
tt(t34_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_euclid 2) (k1_euclid 2) (k1_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 (k10_real_1 1 A) (k1_real_1 (k10_real_1 C A)) (k10_real_1 1 B) (k1_real_1 (k10_real_1 D B))) (k2_jgraph_2 A C B D)) (k6_partfun1 (k1_euclid 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ((v1_jordan21 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k1_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k7_pscomp_1 A))) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan21 A))) ) ) ).
tt(t34_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k2_jordan21 A) (k4_jordan19 A))) ) ).
tt(t34_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 A) & (v2_jordan23 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A)))  => (v2_topreal1 (k4_jordan3 A B C))) ) ) ) ) ) ) ) ).
tt(t34_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) <=>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden D B) & (r1_xxreal_0 C (k12_euclid D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  | (v4_topreal1 (k2_jordan3 A B))) ) ) ) ) ) ).
tt(t34_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 (k3_finseq_1 A) C) | (r2_jordan4 A (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B 1) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k7_nat_d (k3_finseq_1 A) 1) C)) B C)) ) ) ) ) ) ) ) ) ).
tt(t34_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden A (k3_topreal1 2 B)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 B)))) )  => (r1_xxreal_0 (k18_euclid A) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 B) C (k1_matrix_1 (k2_goboard2 B)))))) ) ) ) ) ) ) ).
tt(t34_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  ( (A = (k6_subset_1 (u1_struct_0 k17_borsuk_1) (k2_tarski k6_numbers 1)))  => (v3_pre_topc A k17_borsuk_1)) ) ) ).
tt(t34_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m1_jordan_a C A) => (r1_xxreal_0 B (k4_jordan_a A C))) ) ) ) ) ) ) ) ).
tt(t34_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) => (r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A C D) & (r2_abian (u1_struct_0 A) D B))  =>  (! [E:$i] :  ((v3_ordinal1 E) => (r3_lattices A (k5_knaster A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) = (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)))) ) ).
tt(t34_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A C) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B C))) )  => (r1_tarski (k2_kurato_2 (k15_euclid 2) A) (k2_kurato_2 (k15_euclid 2) B))) ) ) ) ) ).
tt(t34_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) <=>  (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t34_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((k2_partfun1 B (u1_struct_0 A) D C) = (k2_partfun1 B (u1_struct_0 A) E C))  =>  ( (C = k1_xboole_0)  |  ((k2_lattice2 B A C D) = (k2_lattice2 B A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (B = (k16_lattice3 A C))  <=>  ((r3_lattice3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattice3 A D C) => (r3_lattices A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  => (m2_lattice4 (u1_struct_0 A) A)) ) ).
tt(t34_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ((v1_lattice5 D A B) =>  (! [E:$i] :  ((m1_lattice5 E A B D) => (v1_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow11 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_lattice8 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 D C A) &  ((v2_lattice5 D C A) &  ((v3_lattice5 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C))) &  ((v19_waybel_0 E A (k1_lattice5 C)) &  ((v20_waybel_0 E A (k1_lattice5 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C)))))) ) ) )  =>  (! [F:$i] :  ( ((v1_partfun1 F C) &  ((v3_relat_2 F) &  ((v8_relat_2 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  =>  (! [G:$i] :  ( ((v1_partfun1 G C) &  ((v3_relat_2 G) &  ((v8_relat_2 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  =>  (! [H:$i] :  (! [I:$i] :  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C)) E (k4_lattice5 C A D)) &  ( (C = (k3_tarski (a_2_0_lattice8 A B)))  &  ( (D = (k3_tarski (a_2_1_lattice8 A B)))  &  ((r2_hidden F (u1_struct_0 (k1_yellow_2 A (k1_lattice5 C) E))) &  ((r2_hidden G (u1_struct_0 (k1_yellow_2 A (k1_lattice5 C) E))) &  ((r2_hidden (k4_tarski H I) (k5_eqrel_1 C F G)) &  (! [J:$i] :  ( ( (~ (v1_xboole_0 J))  & (m2_finseq_1 J C))  =>  (~  ( ((k3_finseq_1 J) = (k2_nat_1 2 2))  & (r1_lattice5 C J H I F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 (k15_glib_000 A) B) & (r1_xxreal_0 B C))  =>  ((k13_lexbfs A (k16_lexbfs A) B) = (k13_lexbfs A (k16_lexbfs A) C)) ) ) ) ) ) ) ) ).
tt(t34_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  ((k4_fuzzy_4 A A A B (k5_lfuzzy_0 (k2_zfmisc_1 A A) (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) C))) = (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) (a_3_1_lfuzzy_1 A B C))) ) ) ) ) ) ) ).
tt(t34_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) | (v2_limfunc1 A))  =>  ((v2_comseq_2 (k37_valued_1 k5_numbers k1_numbers A)) &  ((k2_seq_2 (k37_valued_1 k5_numbers k1_numbers A)) = k6_numbers) ) ) ) ) ).
tt(t34_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A))) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t34_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc3 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc3 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k9_real_1 (k1_limfunc3 B A) (k1_limfunc3 C A))) ) ) ) ) ) ) ) ) ).
tt(t34_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r6_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k5_limfunc1 A))) ) ) ) )  | (v8_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t34_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (r1_lmod_6 A (k1_mod_3 A B C) (k1_mod_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t34_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  ( (C = (k4_struct_0 (k16_lopban_1 A B)))  =>  (k6_numbers = (k1_normsp_0 (k16_lopban_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t34_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((k1_seq_1 (k4_normsp_0 A B) D) = (k10_real_1 1 (k4_power D C))) ) ) )  =>  ((r1_xxreal_0 C 1) | (v2_lopban_3 B A)) ) ) ) ) ) ) ) ).
tt(t34_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_lopban_4 A B) = (k1_lopban_3 A (k1_lopban_4 A B))) ) ) ) ) ).
tt(t34_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  ((k2_relset_1 (u1_struct_0 (k12_lopclset A)) (k13_lopclset A)) = (u1_struct_0 (k12_lopclset A))) ) ) ).
tt(t34_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ( ((k4_struct_0 (k10_lpspace1 A B C)) = (k8_lpspace1 A k6_numbers))  & (r2_hidden (k4_struct_0 (k10_lpspace1 A B C)) (k11_lpspace1 A B C))) ) ) ) ) ) ) ).
tt(t34_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k4_lpspace2 A B C F))) =>  ( (D = G)  =>  ((k26_valued_1 A k1_numbers D E) = (k1_rlvect_1 (k4_lpspace2 A B C F) G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 A (k3_hilbert1 B A)) k13_ltlaxio1)) ) ) ) ).
tt(t34_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) <=> (r2_hidden (k8_cqc_lang A (k6_cqc_lang A C) (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t34_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k6_rusub_4 A (k9_subset_1 (u1_struct_0 A) B C) D) (k9_subset_1 (u1_struct_0 A) (k6_rusub_4 A B D) (k6_rusub_4 A C D)))) ) ) ) ) ) ) ) ).
tt(t34_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v1_matrix10 B) => (v4_matrix10 B)) ) ) ) ) ).
tt(t34_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) B B) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ((k3_finseq_1 E) = B) )  =>  ((k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) F (k9_fvsum_1 C E D))) = (k8_group_1 C D (k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 C k5_numbers)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_finseq_1 C) (k2_finseq_1 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))))) )  =>  ( (F = (k1_partfun1 (k2_finseq_1 C) (k2_finseq_1 C) k5_numbers k5_numbers H G))  =>  ((k4_matrix_1 A (k1_matrix13 A D B C E F)) = (k1_partfun1 (k2_finseq_1 C) (k2_finseq_1 C) k5_numbers (k3_finseq_2 A) H (k4_matrix_1 A (k1_matrix13 A D B C E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ( ((k3_finseq_1 C) = A)  &  ( (D = (k11_fvsum_1 B C (k3_matrix14 B A E)))  &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A)) ) )  =>  ( ((k1_funct_1 D E) = (k1_funct_1 C E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F A))  =>  ( (F = E)  |  ((k1_funct_1 D F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((r2_hidden C (k4_matrix15 B D E)) &  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 C))) &  ((k9_matrix_1 (u1_struct_0 B) C A) = (k5_finseq_2 (u1_struct_0 B) (k3_finseq_1 C) (k4_struct_0 B))) ) )  =>  ((k9_matrix_1 (u1_struct_0 B) E A) = (k5_finseq_2 (u1_struct_0 B) (k3_finseq_1 E) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((v2_matrix16 B (u1_struct_0 A)) & (v2_matrix16 C (u1_struct_0 A))) )  =>  ((k1_matrix16 (u1_struct_0 A) (k3_fvsum_1 A B C)) = (k3_matrix_3 A (k1_matrix16 (u1_struct_0 A) B) (k1_matrix16 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t34_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k14_matrix_1 B A C (k13_matrix_1 B A C)) = (k11_matrix_1 B A)) ) ) ) ) ) ) ).
tt(t34_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k12_matrix_3 1 A (k5_matrix_2 (u1_struct_0 A) 1 (k4_matrix_2 (u1_struct_0 A) B))) = B) ) ) ) ) ).
tt(t34_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k1_matrix_4 A B D) = (k3_matrix_3 A (k1_matrix_4 A B C) (k1_matrix_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v3_matrix_6 (k3_matrix_6 A B C (k5_matrix_1 A (u1_struct_0 B) C)) A B)) ) ) ) ) ) ) ).
tt(t34_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ((r1_xxreal_0 1 A) &  ((k3_finseq_1 D) = A) )  => (m2_finseq_1 (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) k5_numbers (u1_struct_0 B) C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t34_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((r1_matrix_8 A B C D) & (r1_matrix_8 A B D E))  => (r1_matrix_8 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  (~  ( (A = (k3_finseq_4 k5_numbers 3 1 2))  & (v4_matrix_2 A 3)) ) ) ) ).
tt(t34_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k5_matrixc1 A (k9_seq_4 B C)) = (k9_seq_4 (k5_matrixc1 A B) (k5_matrixc1 A C))) ) ) ) ) ) ) ) ).
tt(t34_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ((k13_matrixj1 A B (k4_matrixj1 A C)) = C) ) ) ) ) ) ) ).
tt(t34_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k3_matrixr1 (k3_matrixr1 A A) A) = (k7_matrixr1 3 A)) ) ) ).
tt(t34_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ( ((k3_finseq_1 C) = B)  &  ( ((k3_finseq_1 D) = B)  &  ((k3_finseq_1 E) = B) ) )  => (m1_matrix_1 (k11_finseq_1 C D E) A 3 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ( ((v13_vectsp_1 D B C) & (v1_mod_2 D A B C))  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k4_matrlin2 A B C E F (k1_matrlin2 A B C D E F)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k9_matrlin A B C D) = (k9_matrlin A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_matroid0 A C (k6_matroid0 A B)) => (r2_matroid0 A C B)) ) ) ) ) ) ) ).
tt(t34_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 k2_vectsp_1) (k4_finseq_2 A (u1_struct_0 k2_vectsp_1))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 k2_vectsp_1) (k4_finseq_2 A (u1_struct_0 k2_vectsp_1))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k15_rvsum_1 A B C) = (k12_fvsum_1 A k2_vectsp_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) A B) =>  ((r2_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) (k3_matrtop1 A B C) (k3_matrtop1 A B D)) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t34_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid B))) =>  (~  ((r2_hidden A (k2_finseq_1 B)) &  ((r1_xxreal_0 2 B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v13_vectsp_1 D (k15_euclid B) (k15_euclid B)) &  ((v1_topreal9 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) ) )  =>  (~  ((v3_matrtop3 D B) &  ((k3_funct_2 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) D C) = (k2_funct_7 C A (k1_real_1 (k1_seq_1 C A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 (k2_pboole A B C)) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r1_pboole A D (k2_pboole A B C)) & (r1_pboole A E (k2_pboole A B C)))  =>  ( (D = E)  | (r6_pboole A (k3_pboole A D E) (k1_pboole A))) ) ) ) ) ) )  => (r6_pboole A (k2_mboolean A (k3_pboole A B C)) (k3_pboole A (k2_mboolean A B) (k2_mboolean A C)))) ) ) ) ) ) ).
tt(t34_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_zfmisc_1 A A A) = (k3_zfmisc_1 B B B))  =>  (A = B) ) ) ) ).
tt(t34_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((r2_hidden k1_xboole_0 B) &  ((r2_hidden A B) &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D B) & (r2_hidden E B))  =>  ((r2_hidden (k6_subset_1 A D) B) &  ((r2_hidden (k2_xboole_0 D E) B) & (r2_hidden (k3_xboole_0 D E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_measure6,ax, (! [A:$i] :  ( ((v1_setfam_1 A) & (v6_ordinal1 A))  =>  ((v1_xboole_0 A) | (v3_finset_1 A)) ) ) ).
tt(t34_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_measure8 E A B) =>  (~  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~ (r1_xxreal_0 k1_supinf_1 (k1_mesfunc9 C (k1_measure8 A B E F)))) ) )  & (r1_xxreal_0 k1_supinf_1 (k1_mesfunc9 C (k8_nat_1 (k9_setfam_1 A) (k2_prob_3 A E) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k7_member_1 (k6_subset_1 A B)) = (k6_subset_1 (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(t34_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v4_membered B))  => (v4_membered (k1_setfam_1 A))) ) ) ).
tt(t34_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ( ((k5_relat_1 C (k4_subset_1 (u1_struct_0 B) (k8_struct_0 B) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)))) = (k5_relat_1 D (k4_subset_1 (u1_struct_0 B) (k8_struct_0 B) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)))))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t34_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r3_mesfunc6 A B C D) & (r3_mesfunc6 A B C E))  => (r3_mesfunc6 A B C (k47_valued_1 A k1_numbers k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v6_supinf_2 D) &  ((v6_supinf_2 E) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F (k1_relset_1 A E)) => (r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 D F))) ) ) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  &  ( (F = (k1_relset_1 A E))  &  ((r1_mesfunc6 A B D F) & (r1_mesfunc6 A B E F)) ) ) ) ) )  | (r1_xxreal_0 (k1_mesfunc6 A B C E) (k1_mesfunc6 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ((v1_mesfunc8 B A k2_numbers) => (v1_mesfunc8 (k3_mesfun9c A B) A k2_numbers)) ) ) ) ) ).
tt(t34_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc1 A B C D) => (r2_hidden (k9_subset_1 A D (k19_mesfunc1 A C k2_supinf_1)) B)) ) ) ) ) ) ) ) ) ).
tt(t34_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((r1_mesfunc2 A C B) => (r1_mesfunc1 A C B D)) ) ) ) ) ) ) ) ) ).
tt(t34_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ((r1_mesfunc2 A B D) => (r1_mesfunc2 A B (k2_partfun1 A k7_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) =>  ((r1_xxreal_0 (k1_seq_1 (k18_rfunct_3 A B) C) k6_numbers) |  ((k1_seq_1 (k19_rfunct_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t34_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((v2_mesfunc9 B A) &  ((v1_mesfunc8 B A k7_numbers) &  ((r1_tarski (k1_relset_1 A C) (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) &  ((r2_hidden D (k1_relset_1 A C)) &  ((v1_mesfunc9 (k3_mesfunc5 A B D)) &  ((k1_mesfunc9 C D) = (k3_mesfunc9 (k3_mesfunc5 A B D))) ) ) ) ) )  =>  ((k1_mesfunc9 C D) = (k2_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t34_metric_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k15_metric_1 A B C)) <=>  (~  ( (~ (r1_metric_1 A B D C))  &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  ( ((k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) B C) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t34_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k5_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t34_midsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ( ((v4_midsp_2 B A) & (l1_midsp_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_midsp_2 A B C (k11_midsp_2 A B)) = C) ) ) ) ) ) ) ).
tt(t34_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_mmlquery A (k22_mmlquery A C D) B) = (k2_mmlquery A D (k1_mmlquery A C B))) ) ) ) ) ) ) ) ).
tt(t34_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v7_mod_4 C A B) <=> (v8_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t34_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ( ((k11_modal_1 A) = (k11_modal_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t34_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r1_tarski D E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F (k52_modelc_1 A B C D)) => (r3_modelc_1 A B C F (k52_modelc_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r3_modelc_2 A B) & (r3_modelc_2 B C))  => (r3_modelc_2 A C)) ) ) ) ) ) ) ).
tt(t34_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r5_modelc_3 C B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  ((u2_modelc_3 C (k10_modelc_3 (k1_funct_1 B (k3_finseq_1 B)) C)) = (k7_modelc_3 C)) ) ) )  => (r1_tarski (u2_modelc_3 C (k10_modelc_3 (k1_funct_1 B A) C)) (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 B (k3_finseq_1 B)) C)))) ) ) ) ) ) ) ).
tt(t34_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k2_moebius1 A) = (k1_real_1 1)) ) ) ).
tt(t34_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ((v10_monoid_0 A) => (v10_monoid_0 B)) ) ) ) ) ).
tt(t34_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((k1_relset_1 k5_numbers (k6_relat_1 (k1_tarski A) (k7_finseq_1 C (k9_finseq_1 A)))) = (k4_subset_1 k5_numbers (k1_relset_1 k5_numbers (k6_relset_1 k5_numbers B (k1_tarski A) C)) (k6_domain_1 k5_numbers (k2_nat_1 (k3_finseq_1 C) 1)))) ) ) ) ) ) ).
tt(t34_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 (k5_msafree A B)) (k2_relset_1 (u1_struct_0 (k5_msafree A B)) C)) =>  (D = (k4_tarski (k1_xtuple_0 D) (k2_xtuple_0 D))) ) ) ) ) ) ) ) ) ).
tt(t34_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  ((r1_msaterm A B C E D F) =>  (! [G:$i] :  ((m1_trees_1 G (k9_xtuple_0 E)) =>  (! [H:$i] :  ((m1_trees_1 H (k9_xtuple_0 F)) =>  ( (H = G)  => (r1_msaterm A B C (k8_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E G) D (k5_trees_2 F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) => (m3_pboole (k2_pboole A C D) A (k1_mboolean A B))) ) ) ) ) ) ) ).
tt(t34_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k5_lattices (k17_msualg_2 A B)) = (k12_msualg_2 A B (k2_msualg_2 A B))) ) ) ) ) ).
tt(t34_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  => (r8_pboole (u1_struct_0 A) (k7_msualg_6 A B C) C)) ) ) ) ) ) ).
tt(t34_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D))) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) F)) =>  ( (G = (k3_msualg_4 A B C F H))  =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B D)) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D)) E F) G) = (k3_msualg_4 A B D F H)) ) ) ) ) ) ) )  => (r8_pboole (u1_struct_0 A) (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D)) (k15_msualg_4 A B C) E) (k15_msualg_4 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_mycielsk,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k2_dilworth (k5_mycielsk A)) = 1) ) ) ).
tt(t34_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 10) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  (~  (A = 10) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden B (k13_pre_poly (k12_nat_3 A))) =>  ((v7_ordinal1 B) & (v1_int_2 B)) ) ) ) ) ).
tt(t34_nat_4,ax,(v1_int_2 139)).
tt(t34_nat_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ((v1_nat_5 A) &  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_xboole_0 C)) )  =>  ((k1_recdef_1 B C) = (k3_uproots (k3_moebius1 C) (k1_nat_5 k5_numbers A (k3_moebius1 C)))) ) ) )  => (v1_nat_5 B)) ) ) ) ) ).
tt(t34_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k7_nat_d (k2_xcmplx_0 A B) B) = A) ) ) ) ) ).
tt(t34_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_nattra_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_nattra_1 A B))) =>  (! [E:$i] :  ((m1_cat_1 E (k11_nattra_1 A B) C D) =>  (~  ( (~  ((k2_cat_1 (k11_nattra_1 A B) C D) = k1_xboole_0) )  &  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_cat_1 G A B) =>  (! [H:$i] :  ((m2_nattra_1 H A B F G) =>  (~  ( (C = F)  &  ( (D = G)  &  (E = (k4_tarski (k4_tarski F G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r3_ncfcont1 B A C E) & (r3_ncfcont1 B A D E))  =>  ((r3_ncfcont1 B A (k3_vfunct_2 (u1_struct_0 B) A C D) E) & (r3_ncfcont1 B A (k2_vfunct_1 (u1_struct_0 B) A C D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  ((v1_ncfcont1 C A) &  ((r5_ncfcont2 C A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( ((k7_partfun1 k1_numbers B D) = (k4_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C)))  &  ((k7_partfun1 k1_numbers B E) = (k5_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_nfcont_1 E A D) =>  ( ((r1_ndiff_1 A B C D) & (r1_tarski E (k1_relset_1 (u1_struct_0 A) C)))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (u1_struct_0 A)) &  ((v12_struct_0 F k5_numbers A) &  ((v1_ndiff_1 F A (k4_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v3_funct_1 G) &  ((v1_funct_2 G k5_numbers (u1_struct_0 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( ((k2_relset_1 (u1_struct_0 A) G) = (k1_tarski D))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) (k2_normsp_1 A F G)) E))  =>  ((v3_normsp_1 (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A F G) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) G C)) B) &  ((k6_normsp_1 B (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A F G) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) G C))) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E (k1_relset_1 (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) k1_numbers k1_numbers (u1_struct_0 B) C D))) &  ((r2_nfcont_1 A C E) & (r1_nfcont_3 B D (k7_partfun1 k1_numbers C E))) )  => (r1_nfcont_1 A B (k1_partfun1 (u1_struct_0 A) k1_numbers k1_numbers (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_prvect_2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_prvect_2 A B))) =>  ((k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) (k3_rlvect_1 (k11_prvect_2 A B) C D)) = (k3_rlvect_1 (k14_prvect_2 A) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) C) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) D))) ) ) ) ) ) ) ) ) ).
tt(t34_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((r2_hidden A k4_neckla_2) => (v1_necklace A)) ) ) ).
tt(t34_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k3_xcmplx_0 C A) B))  => (r1_xxreal_0 C B)) ) ) ) ) ) ) ).
tt(t34_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (~  ( (~  ((k1_relset_1 (u1_struct_0 B) C) = k1_xboole_0) )  &  ((v1_nfcont_1 (k1_relset_1 (u1_struct_0 B) C) B) &  ((r3_nfcont_1 B A C (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) &  ((r2_hidden E (k1_relset_1 (u1_struct_0 B) C)) &  ( ((k7_partfun1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) D) = (k4_seq_4 (k2_relset_1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C))))  &  ((k7_partfun1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) E) = (k5_seq_4 (k2_relset_1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( (B = C)  =>  ((v2_nfcont_4 B A) <=> (v2_nfcont_3 C (k4_real_ns1 A))) ) ) ) ) ) ) ) ).
tt(t34_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  (~  ((r2_hidden B (k10_normform A C D)) &  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r2_hidden E C) &  ((r2_hidden F D) &  (B = (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_normsp_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_normsp_2 A))) =>  ( ( (B = C)  &  (D = E) )  =>  ((m1_connsp_2 B (k3_normsp_2 A) D) <=> (m1_connsp_2 C (k4_normsp_2 A) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (r1_lattice4 A (k6_openlatt (k17_openlatt A)) (k18_openlatt A))) ) ).
tt(t34_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C (k2_oppcat_1 A) B) => (m1_oppcat_1 (k9_oppcat_1 A B C) A B)) ) ) ) ) ) ).
tt(t34_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_orders_1 A) => (r2_orders_1 A (k1_relat_1 A))) ) ) ).
tt(t34_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B C) &  ((r2_wellord1 (u1_orders_2 A) C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E B) & (r2_orders_2 A D E))  => (r2_hidden D B)) ) ) ) )  &  ( (~  (B = C) )  &  (~ (m1_orders_2 B A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_ordinal1,ax, (! [A:$i] :  ( ( (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) ) ) )  & (v6_ordinal1 A))  =>  ((v1_relat_1 (k3_tarski A)) &  ((v1_funct_1 (k3_tarski A)) & (v5_ordinal1 (k3_tarski A))) ) ) ) ).
tt(t34_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k10_ordinal2 A C) (k10_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t34_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden (k11_ordinal2 A B) (k11_ordinal2 C B)) => (r2_hidden A C)) ) ) ) ) ) ) ).
tt(t34_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  => (r2_hidden B (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t34_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k2_ordinal5 A) (k2_ordinal5 B))) ) ) ) ) ).
tt(t34_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ((r2_hidden A (k9_xtuple_0 (k3_ordinal6 C))) &  ((r1_abian B C) & (r2_hidden (k1_funct_1 (k3_ordinal6 C) A) B)) )  => (r2_hidden (k1_ordinal1 A) (k9_xtuple_0 (k3_ordinal6 C)))) ) ) ) ) ) ) ).
tt(t34_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t34_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_hidden E (k25_osafree A B C D)) <=>  ((k25_osafree A B C D) = (k25_osafree A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ( ((r1_osalg_1 A B C) &  ((r2_osalg_1 A D (k1_msualg_1 A B)) & (r2_osalg_1 A D (k1_msualg_1 A C))) )  =>  ((k2_osalg_1 A B D) = (k2_osalg_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) =>  ((k10_osalg_2 A B C) = B) ) ) ) ) ) ) ) ).
tt(t34_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_parsp_1 A B C E F) &  ((r1_parsp_1 A B D E G) &  ((r1_parsp_1 A B D E H) &  ((r1_parsp_1 A C D F G) & (r1_parsp_1 A C D F H)) ) ) )  =>  ((r1_parsp_1 A B C B D) |  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_2 A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_parsp_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_partfun1 k1_xboole_0 A B) = k1_xboole_0) ) ) ).
tt(t34_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_partfun1 (k4_partfun2 B A C D) B) <=>  (C = B) ) ) ) ) ) ) ) ) ) ).
tt(t34_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_partit1 A (k10_eqrel_1 A)) = (k4_relat_1 A)) ) ) ).
tt(t34_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k2_pboole A (k3_pboole A B C) (k3_pboole A B D)) B) => (r2_pboole A B (k2_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t34_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  => (v8_pre_topc (k3_pcomps_1 A))) ) ).
tt(t34_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k20_pcs_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k20_pcs_0 A))) =>  (~  ( (B = D)  &  ( (C = E)  &  ((r1_pcs_0 A B C) & (r1_pcs_0 (k20_pcs_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r2_pdiff_3 B A) & (r2_pdiff_3 C A))  => (r3_pdiff_1 2 2 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 1 2 B) (k1_pdiff_3 1 2 C)) A)) ) ) ) ) ) ) ).
tt(t34_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((k4_pdiff_4 B A) = (k1_euclid_8 (k11_pdiff_1 3 1 B A) (k11_pdiff_1 3 2 B A) (k11_pdiff_1 3 3 B A))) ) ) ) ) ).
tt(t34_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r7_pdiff_5 B A) =>  ((k7_pdiff_5 B A) = (k11_pdiff_1 3 1 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ) ).
tt(t34_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_euclid A))) =>  ( ((v1_pdiff_7 E A) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A)) )  =>  ((r2_pdiff_7 A B C D E) <=>  ((r1_tarski E (k1_relset_1 (k1_euclid A) D)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F E) => (r4_pdiff_1 A B C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((r4_pdiff_7 A B E C) => (r4_pdiff_7 A B (k9_integr15 B D (k1_euclid A) E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((v1_int_2 A) &  ((r1_nat_d B (k1_newton A C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (B = (k1_newton A D))  & (r1_xxreal_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  ((k8_pnproc_1 A B (k3_pre_poly B C)) = (k7_pnproc_1 A C)) ) ) ) ) ) ).
tt(t34_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~  (B = k6_numbers) )  =>  (A = (k1_newton (k3_binop_2 (k11_binop_2 (k2_power B (k17_complex1 A)) (k21_sin_cos (k12_binop_2 (k9_binop_2 (k1_comptrig A) (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C)) B))) (k5_binop_2 (k11_binop_2 (k2_power B (k17_complex1 A)) (k18_sin_cos (k12_binop_2 (k9_binop_2 (k1_comptrig A) (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C)) B))) k7_complex1)) B)) ) ) ) ) ) ) ) ).
tt(t34_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k11_polyform A B)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k11_polyform A B)) &  ((k15_polyform A B D) = (k15_polyform A B C)) ) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t34_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k9_polynom3 A)) (k9_polynom3 A))) ) ) ) ).
tt(t34_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_algseq_1 A (k4_struct_0 A)) (k9_polynom3 A))) ) ).
tt(t34_polynom7,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_algstr_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ((k5_polynom2 A B (k10_polynom1 A B C (k4_polynom7 A B D)) E) = (k8_group_1 B (k5_polynom2 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_polynom8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) &  ((v1_algseq_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_funct_2 k5_numbers (u1_struct_0 B) (k2_polynom8 B (k6_polynom8 A B C E) (k6_polynom8 A B D E)) (k6_polynom8 A B (k13_polynom3 B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t34_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_polyred A B C (k5_termord A B C D) D)) ) ) ) ) ) ) ) ).
tt(t34_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k3_power A B) k6_numbers)) ) ) ) ) ) ).
tt(t34_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v4_valued_0 D)) ) ) )  =>  ( (! [E:$i] :  ((r2_hidden E A) =>  ((k1_funct_1 B E) = (k7_nat_d (k1_funct_1 C E) (k1_funct_1 D E))) ) )  => (r6_pboole A B (k12_pre_poly A C D))) ) ) ) ) ) ) ) ).
tt(t34_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_prepower A k6_numbers) = 1) ) ) ).
tt(t34_pre_topc,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) (u1_struct_0 (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))))))) )  =>  ( (C = D)  =>  ((v5_pre_topc C A B) <=> (v5_pre_topc D (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ) ) ) ) ) ).
tt(t34_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((r1_tarski C D) => (r1_xxreal_0 (k1_seq_1 E C) (k1_seq_1 E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( ((k1_seq_1 (k3_prob_2 A B C E) D) = (k1_seq_1 (k3_prob_2 A B C (k7_prob_1 A B (k4_prob_1 A B) E)) D))  =>  ((r1_xxreal_0 (k1_seq_1 C E) k6_numbers) |  ((r1_xxreal_0 1 (k1_seq_1 C E)) | (r1_prob_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  => (r1_tarski (k1_funct_1 (k3_prob_3 B D) A) (k1_funct_1 (k2_prob_3 B D) A))) ) ) ) ) ) ) ).
tt(t34_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  ((r2_hidden F B) &  (? [G:$i] :  ((m1_prob_4 G A B C) &  (E = (k2_xboole_0 F G)) ) ) ) ) ) )  =>  ( (~ (v1_xboole_0 D))  &  ((v1_prob_1 D A) &  ((v4_prob_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k9_cqc_lang A B C) D) (k9_cqc_lang A (k8_cqc_lang A B D) (k8_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t34_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (~  ( (~  (D = E) )  &  ((r1_incsp_1 A D F) &  ((r1_incsp_1 A E F) &  ( (~ (r1_incsp_1 A B F))  &  ( (~ (r1_incsp_1 A C F))  &  ((k1_projpl_1 A B D) = (k1_projpl_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k18_pscomp_1 A) (k14_pscomp_1 A)) & (r2_hidden (k19_pscomp_1 A) (k14_pscomp_1 A))) ) ) ).
tt(t34_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A (k2_pzfmisc1 A B C) D) <=>  ((r1_pboole A B D) & (r1_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t34_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang2 B A) =>  ((v3_qc_lang1 B A) &  ((v4_qc_lang1 (k18_qc_lang1 A B) A) & (v3_qc_lang1 (k20_qc_lang1 A (k18_qc_lang1 A B)) A)) ) ) ) ) ) ) ).
tt(t34_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t34_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m2_qc_lang4 D A B C) =>  (! [E:$i] :  ((m2_qc_lang4 E A B C) =>  (~  ( (~  (D = E) )  & (r3_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ((v14_quantal1 B A) &  ((v11_quantal1 B) &  ((v15_quantal1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v4_lattice3 C) & (l3_lattices C)) ) )  =>  (~  ( ((u1_struct_0 C) = (k2_relset_1 (u1_struct_0 A) B))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k15_lattice3 C D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k15_lattice3 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_quatern2 (k28_quaterni A)) = (k28_quaterni (k8_quatern2 A))) ) ) ).
tt(t34_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k3_quatern2 (k27_quaterni (k27_quaterni A B) C)) = (k8_real_1 (k8_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k3_quatern2 C))) ) ) ) ) ) ) ).
tt(t34_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ( ((k17_quaterni (k10_quaterni A k11_quaterni)) = k6_numbers)  &  ( ((k18_quaterni (k10_quaterni A k11_quaterni)) = k6_numbers)  &  ( ((k19_quaterni (k10_quaterni A k11_quaterni)) = B)  &  ((k20_quaterni (k10_quaterni A k11_quaterni)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t34_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) => (m1_subset_1 (k1_funct_1 (k18_quofield A) B) (u1_struct_0 (k19_quofield A)))) ) ) ) ).
tt(t34_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_random_1 B A (k1_random_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ( ((k3_finseq_1 C) = (k5_card_1 A))  &  ((v2_funct_1 D) &  ( ((k2_relset_1 A D) = A)  &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_seq_1 C E) = (k1_seq_1 B (k1_funct_1 D E))) ) ) ) ) ) ) )  =>  ((k8_random_1 A (k1_random_1 A) (k2_random_1 A) B) = (k13_complex1 (k18_rvsum_1 C) (k5_card_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t34_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m2_vectsp_6 F A C E) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (~  ((v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D E)) &  ((r2_hidden G E) &  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 C))) =>  (~  ((r1_xboole_0 H E) &  ((k7_ranknull C B D (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D G))) = (k4_subset_1 (u1_struct_0 C) (k6_domain_1 (u1_struct_0 C) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((r1_xxreal_0 A (k1_real_1 1)) <=> (r1_xxreal_0 (k1_rat_1 A) (k4_xcmplx_0 (k2_rat_1 A)))) ) ) ).
tt(t34_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_ratfunc1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_polynom4 A (k5_ratfunc1 A B) D) = (k4_struct_0 A)) )  &  ( (~  ((k2_polynom4 A (k5_ratfunc1 A C) D) = (k4_struct_0 A)) )  &  (~  ((k13_ratfunc1 A (k10_ratfunc1 A B C) D) = (k8_group_1 A (k13_ratfunc1 A B D) (k13_ratfunc1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k3_rcomp_1 A B))  =>  ((r1_xxreal_0 B A) |  ((k2_tops_1 k2_topalg_2 C) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ).
tt(t34_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) )  =>  (A = k6_numbers) ) ) ) ).
tt(t34_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ((r2_classes1 (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A))) &  ( ((k20_rfunct_3 C (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) C) = (k20_rfunct_3 B (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B))  &  ((k21_rfunct_3 C (k18_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) C) = (k21_rfunct_3 B (k18_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k6_subset_1 (k3_relat_1 A B) (k3_relat_1 A C)) (k3_relat_1 A (k6_subset_1 B C)))) ) ) ) ) ) ).
tt(t34_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) =>  ((k7_relset_1 A B (k5_setfam_1 (k2_zfmisc_1 A B) D) C) = (k3_tarski (a_4_4_relset_2 A B C D))) ) ) ) ) ) ) ).
tt(t34_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B C) <=> (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A) C)) ) ) ) ) ) ) ).
tt(t34_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( (~ (r2_hidden B (k1_relat_1 A)))  => (r3_rewrite1 A B)) ) ) ) ).
tt(t34_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r1_rewrite2 A B C D) => (r3_rewrite2 A B C D)) ) ) ) ) ) ) ) ).
tt(t34_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E C))  =>  ( ((u1_rewrite3 B D) = (u1_rewrite3 C E))  =>  ((k1_rewrite3 A B D) = (k1_rewrite3 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k18_valued_1 (k1_rfunct_1 A B) (k1_rfunct_1 C D)) = (k1_rfunct_1 (k18_valued_1 A C) (k18_valued_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t34_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_xxreal_0 k6_numbers B))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A)))  &  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_xxreal_0 B k6_numbers))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ) ).
tt(t34_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_relset_1 A k1_numbers B (k47_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B))) &  ((r2_relset_1 A k1_numbers (k56_valued_1 A k1_numbers B) (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B))) & (r2_relset_1 A k1_numbers (k26_valued_1 A k1_numbers (k18_rfunct_3 A B) 2) (k3_valued_1 A k1_numbers k1_numbers B (k56_valued_1 A k1_numbers B)))) ) ) ) ) ) ).
tt(t34_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (a_2_0_rinfsup1 A B))  =>  ((k5_seq_4 C) = (k1_seq_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t34_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v8_valued_0 A) &  (k2_supinf_1 = (k2_rinfsup2 A)) )  =>  ((v9_mesfunc5 A) &  ((k2_mesfunc5 A) = k2_supinf_1) ) ) ) ) ).
tt(t34_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k3_rlaffin1 A (k7_rlvect_2 A B C)) = (k7_real_1 (k3_rlaffin1 A B) (k3_rlaffin1 A C))) ) ) ) ) ) ) ).
tt(t34_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( ((u1_struct_0 C) = B)  => (v1_rlsub_1 B A)) ) ) ) ) ) ) ).
tt(t34_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) => (m1_rlsub_2 C A B)) ) ) ) ) ) ) ).
tt(t34_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_relset_1 (u1_struct_0 A) (k3_rltopsp1 A B)) = (k2_struct_0 A)) ) ) ) ) ).
tt(t34_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_rlvect_1 B (k5_algstr_0 B C D) A) = (k5_algstr_0 B (k1_rlvect_1 B C A) (k1_rlvect_1 B D A))) ) ) ) ) ) ) ) ) ).
tt(t34_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ( ((k3_rlvect_2 A B) = k1_xboole_0)  =>  ((k6_rlvect_2 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t34_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ((k5_rlvect_2 A (k8_finseq_1 (u1_struct_0 A) B C) D) = (k8_finseq_1 (u1_struct_0 A) (k5_rlvect_2 A B D) (k5_rlvect_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t34_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) &  ((r1_struct_0 (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) D E)) B) & (r1_struct_0 (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) D E)) C)) )  =>  ( (B = C)  |  ( ((k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) D E)) = (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) B C)))  &  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) D E) A) &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_rlvect_5 A) = 2)  <=>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  &  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) &  ((k2_rlsub_1 A) = (k1_rlvect_3 A (k7_domain_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ) ).
tt(t34_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_rlvect_3 A (k2_rlvect_x A B)) = (k1_rlvect_3 A B)) ) ) ) ) ).
tt(t34_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v1_rmod_2 C A B) &  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  (~  (C = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((m1_rmod_2 C A D) => (m1_rmod_2 C A (k1_rmod_3 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ( ((k2_rmod_4 A B C) = k1_xboole_0)  =>  ((k5_rmod_4 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t34_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_robbins1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_robbins1 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ( ((k4_robbins1 A B C) = (k2_lattices (k8_robbins1 A) D E))  &  ( ((k1_lattices A B C) = (k1_lattices (k8_robbins1 A) D E))  &  ((k3_robbins1 A B) = (k3_robbins1 (k8_robbins1 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)))) C)) = (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A C) C))) ) ) ) ) ) ) ).
tt(t34_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A C B) =>  ((k4_lattices A B (k3_lattices A (k3_robbins1 A B) C)) = C) ) ) ) ) ) ) ) ) ).
tt(t34_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A (k3_roughs_1 A B)) = (k4_roughs_1 A (k3_roughs_1 A B))) ) ) ) ) ).
tt(t34_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  => (r1_xxreal_0 (k2_rpr_1 A C B) 1)) ) ) ) ) ) ) ).
tt(t34_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) => (m1_rusub_1 (k1_rusub_1 B) C)) ) ) ) ) ) ).
tt(t34_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) => (m1_rusub_2 C A B)) ) ) ) ) ) ) ).
tt(t34_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r2_hidden E (k3_rusub_1 A B (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) C D)))) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A B (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v2_rusub_4 (k7_rusub_4 A (k6_domain_1 (u1_struct_0 A) C) B) A)) ) ) ) ) ) ).
tt(t34_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_tarski (k4_bhsp_2 A B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t34_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k8_rvsum_1 A (k6_rvsum_1 B)) = (k4_rvsum_1 A B)) ) ) ) ) ).
tt(t34_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k16_rvsum_1 (k10_finseq_1 A B)) = (k3_binop_2 A B)) ) ) ) ) ).
tt(t34_scmbsort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k2_sf_mastr (k1_scmbsort A)) = (k5_enumset1 (k4_scmfsa_2 k6_numbers) (k4_scmfsa_2 1) (k4_scmfsa_2 2) (k4_scmfsa_2 3) (k4_scmfsa_2 4) (k4_scmfsa_2 5) (k4_scmfsa_2 6))) ) ) ).
tt(t34_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_amistd_1 3 k1_scmfsa_2 (k11_scmfsa_2 A)) = (k1_tarski A)) ) ) ).
tt(t34_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 5)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k10_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k5_scmfsa6a B A)) = (k2_nat_1 (k5_card_1 B) 2)) ) ) ) ) ).
tt(t34_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A (k1_scmfsa_m B) C) & (r6_scmfsa7b A (k1_scmfsa_m B) C))  => (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))) ) ) ) ) ) ) ).
tt(t34_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ( (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = E) )  =>  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) )  &  ( (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((k18_scmfsa_2 A E) = (k18_scmfsa_2 B E)) ) )  &  ((k5_memstr_0 3 k1_scmfsa_2 A) = (k5_memstr_0 3 k1_scmfsa_2 B)) ) )  =>  ((r1_scmfsa7b C D) |  ( (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = E) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 C A) E) = (k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 C B) E)) ) ) )  &  ( (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 C A) E) = (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 C B) E)) ) )  &  ((k5_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 C A)) = (k5_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa8b C A B) (k2_nat_1 (k5_card_1 B) 2)) = (k11_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 3))) ) ) ) ) ) ) ).
tt(t34_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  ( ((r3_scmfsa9a A C E F) &  ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D)) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 C F E A) G)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D F E B) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmfsa_9 A B) (k2_nat_1 (k5_card_1 B) 5)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ).
tt(t34_scmfsa_m,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r1_tarski (k8_domain_1 (u1_struct_0 k1_scmfsa_2) B (k4_struct_0 k1_scmfsa_2) A) (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t34_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r1_scm_halt C B A) & (r2_scm_halt C B A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmisort,ax, ((v3_scm_halt (k2_scmisort (k5_scmfsa_2 k6_numbers))) & (v2_scm_halt (k2_scmisort (k5_scmfsa_2 k6_numbers)))) ).
tt(t34_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 8)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  (A = (k11_scmpds_2 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v2_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  ((k6_scmpds_4 (k1_scmpds_4 C D) B A) = (k9_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A) (k5_card_1 C))) ) ) ) ) ) ) ) ) ).
tt(t34_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k5_card_1 C)) ) ) ) ) ) ) ) ).
tt(t34_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((k1_funct_1 (k1_scmpds_7 A B C D) k6_numbers) = (k9_scmpds_2 A B (k2_nat_1 (k5_card_1 D) 3)))  &  ( ((k1_funct_1 (k1_scmpds_7 A B C D) (k2_nat_1 (k5_card_1 D) 1)) = (k11_scmpds_2 A B C))  &  ((k1_funct_1 (k1_scmpds_7 A B C D) (k2_nat_1 (k5_card_1 D) 2)) = (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 D) 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_amistd_1 2 (k1_scmring2 A) (k9_scmring2 A C B)) = (k1_tarski C)) ) ) ) ) ) ) ).
tt(t34_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k2_tarski B C) (k5_scmyciel A))) ) ) ) ).
tt(t34_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C E) &  ((r1_semi_af1 A B D F) &  ((r1_semi_af1 A B D G) &  ((r2_analoaf A C D E F) & (r2_analoaf A C D E G)) ) ) )  =>  ((r1_semi_af1 A B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k3_comseq_2 B) = k5_complex1)  |  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k10_real_1 (k17_complex1 (k3_comseq_2 A)) (k17_complex1 (k3_comseq_2 B)))) ) ) ) ) ) ) ).
tt(t34_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = (k18_binop_2 1 (k2_nat_1 (k4_nat_1 B B) 1))) ) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) ) ) ) ).
tt(t34_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((r2_seqfunc A B D) & (r2_seqfunc A C D))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) =>  ((r2_relset_1 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k6_seqfunc A B C) E)) &  ((r2_relset_1 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k7_seqfunc A B C) E)) & (r2_relset_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k10_seqfunc A B E) (k10_seqfunc A C E)) (k10_seqfunc A (k8_seqfunc A B C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((v5_valued_0 A) & (v5_valued_0 B))  => (v5_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ( ((v6_valued_0 A) & (v6_valued_0 B))  => (v6_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ( ((v7_valued_0 A) & (v7_valued_0 B))  => (v7_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ((v8_valued_0 A) & (v8_valued_0 B))  => (v8_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t34_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) C) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 A) B))) (k18_complex1 (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) C) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B))))) ) ) ) ) ) ) ).
tt(t34_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k2_nat_1 B 2) (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k13_newton 2 B)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 1 (k13_complex1 1 (k4_nat_1 (k2_nat_1 B 1) (k13_newton 2 B))))) ) ) ) ) ) ) ).
tt(t34_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ).
tt(t34_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_xxreal_0 (k6_square_1 (k3_xcmplx_0 3 (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)))) (k8_complex1 (k8_complex1 (k13_complex1 (k3_xcmplx_0 B C) A) (k13_complex1 (k3_xcmplx_0 C A) B)) (k13_complex1 (k3_xcmplx_0 A B) C)))) ) ) ) ) ) ).
tt(t34_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (~  (B = k1_xboole_0) )  =>  ((k5_setfam_1 A (k7_setfam_1 A B)) = (k7_subset_1 A (k2_subset_1 A) (k6_setfam_1 A B))) ) ) ) ) ).
tt(t34_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B E) = (k6_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E) (k3_funct_2 k5_numbers (k9_setfam_1 A) D E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r1_tarski (k6_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A C) E) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A D) E)) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A B) E))) ) ) ) ) ) ) ) ) ) ).
tt(t34_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A (k6_setlim_2 A C B)) = (k4_subset_1 A B (k3_prob_1 A C))) ) ) ) ) ) ).
tt(t34_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 C B) &  ((v2_binop_1 C B) &  ((v3_binop_1 C B) & (v1_setwiseo C B)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 A)) =>  ( ((k8_setwiseo A B D F) = (k8_setwiseo A B E G))  =>  ((k7_setwiseo A B C F D) = (k7_setwiseo A B C G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((v1_binop_1 B A) &  ((v2_binop_1 B A) &  ((v1_setwiseo B A) &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) ) )  =>  ((k5_binop_1 A B (k1_finsop_1 A C B) (k1_finsop_1 A D B)) = (k1_finsop_1 A (k1_finseqop A A A B C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t34_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 1 (k1_funct_1 A B)) &  ((r1_xxreal_0 (k1_funct_1 A B) (k3_finseq_1 (k18_scmfsa_2 A D))) &  ((r1_xxreal_0 1 (k1_funct_1 A C)) &  ((r1_xxreal_0 (k1_funct_1 A C) (k3_finseq_1 (k18_scmfsa_2 A D))) &  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) )  =>  ( ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k4_sfmastr3 D B C) A E) D) (k1_funct_1 A B)) = (k1_funct_1 (k18_scmfsa_2 A D) (k1_funct_1 A C)))  &  ((k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k4_sfmastr3 D B C) A E) D) (k1_funct_1 A C)) = (k1_funct_1 (k18_scmfsa_2 A D) (k1_funct_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ( ( (C = (k16_scmfsa_2 A B))  |  (C = (k17_scmfsa_2 A B)) )  =>  ((k3_sf_mastr C) = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t34_sgraph1,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k2_sgraph1 (k2_finseq_1 3)))) &  ( (A = (k4_setwiseo (k5_finsub_1 k5_numbers) (k3_setwiseo k5_numbers 1 2) (k3_setwiseo k5_numbers 2 3) (k3_setwiseo k5_numbers 3 1)))  &  (k8_sgraph1 = (g1_sgraph1 (k2_finseq_1 3) A)) ) ) ) ).
tt(t34_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v6_lattices A)) ) ).
tt(t34_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B (k5_sheffer1 A D (k5_sheffer1 A C B))))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ) ) ).
tt(t34_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  (! [D:$i] :  ((m2_simplex0 D A C) =>  ( ((v7_simplex0 C A B) & (v7_simplex0 D A C))  =>  ((v7_simplex0 D A B) & (m2_simplex0 D A B)) ) ) ) ) ) ) ) ) ).
tt(t34_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_tops_2 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  ( ((r1_tarski (k3_simplex1 A B) (k2_struct_0 B)) &  ((v1_setfam_1 C) &  ( ((v3_pre_topc (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) D) (k4_simplex1 A B)) & (m1_subset_1 (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) D) (k1_zfmisc_1 (u1_struct_0 (k4_simplex1 A B)))))  & (r1_tarski (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) C) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) D))) ) )  =>  ((r1_tarski C D) & (v6_ordinal1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_sincos10,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)) => (r2_hidden (k1_seq_1 k1_fdiff_9 A) (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ) ).
tt(t34_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k1_sin_cos2 k1_numbers) &  ((k1_fdiff_1 k1_sin_cos2 A) = (k1_seq_1 k4_sin_cos2 A)) ) ) ) ).
tt(t34_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k3_binop_2 A (k11_binop_2 (k24_binop_2 2 B) k32_sin_cos))) = (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A)) ) ) ) ) ).
tt(t34_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k20_sin_cos C)) = (k3_xcmplx_0 (k7_xcmplx_0 1 4) (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 A B) C))) (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 B C) A))) (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 C A) B))) (k20_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C))))) ) ) ) ) ) ) ).
tt(t34_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  ((k18_sin_cos (k6_real_1 A 2)) = k6_numbers) )  &  ( (~  ((k21_sin_cos (k6_real_1 A 2)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k5_square_1 (k1_sin_cos4 (k6_real_1 A 2)))) = k6_numbers) )  &  ( (~  ((k4_sin_cos4 (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k8_real_1 2 (k4_sin_cos4 A)) (k7_real_1 (k4_sin_cos4 A) 1)))) )  &  (~  ((k4_sin_cos4 (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k8_real_1 2 (k4_sin_cos4 A)) (k7_real_1 (k4_sin_cos4 A) 1))))) ) ) ) ) ) ) ) ) ).
tt(t34_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) A))  & (r1_xxreal_0 1 (k20_sin_cos A))) ) ) ) ) ).
tt(t34_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_sin_cos7 A) = (k3_sin_cos7 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)))) ) ) ) ).
tt(t34_sin_cos9,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)) k2_sin_cos9) = (k1_partfun2 k1_numbers (k2_rcomp_1 k6_numbers k32_sin_cos))) ).
tt(t34_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k3_newton A) = (k3_newton A)) ) ) ).
tt(t34_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ( (~  ((v2_sppol_1 (k2_topreal1 2 B A)) & (v1_sppol_1 (k2_topreal1 2 B (k2_nat_1 A 1)))) )  &  (~  ((v1_sppol_1 (k2_topreal1 2 B A)) & (v2_sppol_1 (k2_topreal1 2 B (k2_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (v3_topreal1 A))  => (v3_topreal1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t34_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(t34_sprect_2,ax, ((k9_pscomp_1 k1_topreal1) = k6_numbers) ).
tt(t34_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((k1_sprect_1 (k3_topreal1 2 A)) = A) ) ) ).
tt(t34_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t34_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_xcmplx_0 A (k6_square_1 A)) = (k6_square_1 A)) ) ) ) ).
tt(t34_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k14_stacks_1 A))) =>  (? [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) &  (B = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) C)) ) ) ) ) ) ) ).
tt(t34_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k23_binop_2 A 1) (k23_binop_2 B 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) (k23_binop_2 B 1))))) )  =>  ( ((v2_funct_2 C (k23_binop_2 B 1)) &  ((v1_stirl2_1 C (k23_binop_2 A 1) (k23_binop_2 B 1)) &  ((k1_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) C (k6_domain_1 (k23_binop_2 B 1) (k2_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) C A))) = (k1_seq_4 A)) ) )  =>  ((k2_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) C A) = B) ) ) ) ) ) ) ) ).
tt(t34_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r1_tarski (k2_zfmisc_1 (k9_qc_lang1 A) (k1_substut1 A)) (k9_xtuple_0 (k15_substut1 A)))) ) ).
tt(t34_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k2_tarski B C) (k1_zfmisc_1 A))) ) ) ) ) ) ).
tt(t34_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  <=>  ((m2_finseq_1 C (k3_qc_lang1 A)) &  ((k3_finseq_1 C) = B) ) ) ) ) ) ) ) ) ).
tt(t34_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r1_xxreal_0 1 (k7_cqc_sim1 A B)) &  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r2_qc_lang2 A C B) &  ((k7_cqc_sim1 A C) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_supinf_2,ax, ( ((v1_funct_1 (k6_funct_3 k1_numbers k5_numbers)) &  ((v1_funct_2 (k6_funct_3 k1_numbers k5_numbers) k5_numbers k7_numbers) & (m1_subset_1 (k6_funct_3 k1_numbers k5_numbers) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ((v2_funct_1 (k6_funct_3 k1_numbers k5_numbers)) &  ( (k5_numbers = (k2_relset_1 k1_numbers (k6_funct_3 k1_numbers k5_numbers)))  &  ( (~ (v1_xboole_0 (k2_relset_1 k1_numbers (k6_funct_3 k1_numbers k5_numbers))))  & (m1_subset_1 (k2_relset_1 k1_numbers (k6_funct_3 k1_numbers k5_numbers)) (k1_zfmisc_1 k7_numbers))) ) ) ) ).
tt(t34_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  (~  ((k2_symsp_1 A B E F D C) = (k4_algstr_0 A (k2_symsp_1 A B F E D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r1_tarski (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))) A) & (r1_tarski (k4_relat_1 (k10_xtuple_0 (k1_sysrel A))) A)) ) ) ).
tt(t34_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) C (k3_taxonom1 A B)) & (r1_xxreal_0 k6_numbers B))  =>  ((v1_partfun1 C (u1_struct_0 A)) &  ((v1_relat_2 C) &  ((v3_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t34_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (g3_lattices (k5_tdlat_1 A) (k6_tdlat_1 A) (k7_tdlat_1 A))))  &  ((v10_lattices (g3_lattices (k5_tdlat_1 A) (k6_tdlat_1 A) (k7_tdlat_1 A))) &  ((v17_lattices (g3_lattices (k5_tdlat_1 A) (k6_tdlat_1 A) (k7_tdlat_1 A))) & (l3_lattices (g3_lattices (k5_tdlat_1 A) (k6_tdlat_1 A) (k7_tdlat_1 A)))) ) ) ) ) ).
tt(t34_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B))) = (a_2_5_tdlat_2 A B)) ) ) ) ) ).
tt(t34_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ((k1_tops_1 A (k2_pre_topc A B)) = (k2_pre_topc A (k1_tops_1 A B))) ) ) ) ) ) ) ).
tt(t34_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_termord A B (k3_termord A B C (k4_polynom1 A C D E)) (k2_termord A B (k3_termord A B C D) (k3_termord A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t34_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~  ( (~ (v3_tdlat_3 A))  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (u1_struct_0 A)) )  &  ((v1_tops_1 B A) & (v3_pre_topc B A)) ) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) &  ( (~  (B = (u1_struct_0 A)) )  &  ((v1_tops_1 B A) & (v3_pre_topc B A)) ) ) )  & (v3_tdlat_3 A)) ) ) ) ) ).
tt(t34_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (v2_tex_2 B A))  => (v3_pre_topc B A)) ) ) ) ) ).
tt(t34_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ( ((v3_tex_3 B A) & (m1_pre_topc C B))  => (v3_tex_3 C A)) ) ) ) ) ) ) ).
tt(t34_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k3_tex_4 A C)) => (r1_tarski (k3_tex_4 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ).
tt(t34_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~  ( (~ (r1_tsep_1 (k1_tsep_1 A B C) D))  &  ((r1_tsep_1 B D) & (r1_tsep_1 C D)) ) )  &  ( (~  ( (~  ((r1_tsep_1 B D) & (r1_tsep_1 C D)) )  & (r1_tsep_1 (k1_tsep_1 A B C) D)) )  &  ( (~  ( (~ (r1_tsep_1 D (k1_tsep_1 A B C)))  &  ((r1_tsep_1 D B) & (r1_tsep_1 D C)) ) )  &  (~  ( (~  ((r1_tsep_1 D B) & (r1_tsep_1 D C)) )  & (r1_tsep_1 D (k1_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (! [C:$i] :  ((r2_hidden C A) => (m1_toler_1 (k9_relat_1 B C) A B)) )  => (v8_relat_2 B)) ) ) ) ).
tt(t34_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r4_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D G H) I) J) (k1_borsuk_2 A B C F G (k1_borsuk_2 A C E F (k1_borsuk_2 A C D E H I) J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A D E) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  ( ( (B = F)  &  ( (C = G)  & (r1_borsuk_2 A D E)) )  =>  ((r1_topalg_6 A B C) <=> (r3_borsuk_2 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( ((v3_topdim_1 A) &  ((r1_xxreal_0 (k4_topdim_1 A) k6_numbers) & (v1_metrizts A)) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v4_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v4_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 D E) &  ( ((k4_subset_1 (u1_struct_0 A) D E) = (k2_struct_0 A))  &  ((r1_tarski B D) & (r1_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k3_topgen_1 A B)) (k2_topgen_1 A (k5_setfam_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t34_topgen_2,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((k2_waybel23 (k5_topgen_2 A B)) = (k1_card_1 A)) ) ) ) ).
tt(t34_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_topgen_3 A)))) =>  ((v3_pre_topc B (k5_topgen_3 A)) <=>  ( (B = k11_arytm_3)  | (v1_finset_1 (k3_subset_1 (u1_struct_0 (k5_topgen_3 A)) B))) ) ) ) ) ).
tt(t34_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  (~  ((k3_xboole_0 (k1_setfam_1 A) (k1_setfam_1 B)) = (k1_setfam_1 (k3_setfam_1 A B))) ) ) ) ) ) ) ).
tt(t34_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))) =>  ( (A = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5))  =>  ((k2_pre_topc k3_topgen_5 A) = (k2_struct_0 k3_topgen_5)) ) ) ) ).
tt(t34_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m3_topgrp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_topgrp_1 A))) =>  ( (B = C)  =>  ((k2_group_1 (k5_topgrp_1 A) C) = (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t34_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k6_topreal1 A) = (a_1_4_topreal1 A)) ) ) ).
tt(t34_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k11_finseq_1 A (k19_euclid (k17_euclid A) (k18_euclid B)) B))  =>  ( ((k17_euclid A) = (k17_euclid B))  |  ( ((k18_euclid A) = (k18_euclid B))  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = A)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = B)  & (v4_topreal1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_topreal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (~ (r1_xxreal_0 (k9_pscomp_1 A) (k18_euclid C)))  &  (~  (B = C) ) ) ) ) ) ) ) ) ).
tt(t34_topreal8,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 A) &  ((v2_topreal1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 1)) (k2_topreal1 2 B 1)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) )  => (v2_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t34_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden C (k3_topreal9 A D B)) & (r2_hidden E (k3_topreal9 A D B)))  => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) C E) (k2_tarski C E)) (k1_topreal9 A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_topreala,ax,(v3_tops_2 k2_topreala (k2_borsuk_1 k3_topmetr k3_topmetr) (k15_euclid 2))).
tt(t34_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k4_int_1 A) = (k10_real_1 1 2))  =>  ((k1_funct_1 k12_toprealb A) = (k19_euclid (k1_real_1 1) k6_numbers)) ) ) ) ).
tt(t34_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C)) &  ((v1_funct_2 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ).
tt(t34_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)) (k7_real_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B D)) (k12_euclid (k5_algstr_0 (k15_euclid A) D C))))) ) ) ) ) ) ) ) ).
tt(t34_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k2_tops_1 A B)) (k2_tops_1 A B))) ) ) ) ).
tt(t34_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 (k1_pre_topc A B)) (k1_tops_2 A B C)) (k5_setfam_1 (u1_struct_0 A) C))) ) ) ) ) ) ).
tt(t34_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_3 B A) &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t34_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_diraf A C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t34_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (r2_tarski (k1_trees_1 A) (k4_finseq_1 A))) ) ).
tt(t34_trees_2,ax, (! [A:$i] :  ( ( (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) & (v1_funct_1 B)) ) )  & (v6_ordinal1 A))  =>  ((v1_relat_1 (k3_tarski A)) & (v1_funct_1 (k3_tarski A))) ) ) ).
tt(t34_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((v4_trees_3 (k2_finseq_2 B A)) <=>  ( (~ (v1_xboole_0 A))  & (v1_trees_1 A)) ) ) ) ) ) ).
tt(t34_trees_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  ( (C = (k5_relset_1 k5_numbers A B (k2_finseq_1 1)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  (C = (k12_finseq_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v4_pre_topc C A))  =>  ((r1_xboole_0 B C) <=> (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ).
tt(t34_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r4_tsep_2 A B C) =>  ((v1_borsuk_1 B A) <=> (v1_tsep_1 C A)) ) ) ) ) ) ) ) ).
tt(t34_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) => (v3_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) B)) ) ) ) ) ) ) ).
tt(t34_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k18_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ( (A = (k4_domain_1 k5_numbers k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) k6_numbers C B))  & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) D) k18_turing_1 B)) )  =>  ((v2_turing_1 A k18_turing_1) &  ( ((k2_mcart_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) (k11_turing_1 k18_turing_1 A)) = C)  & (r2_turing_1 (k2_finseq_4 k5_numbers C k6_numbers) k18_turing_1 (k3_mcart_1 (u2_turing_1 k18_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) (k11_turing_1 k18_turing_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (~ (v1_facirc_1 (k2_msafree2 (k37_twoscomp A B)))) ) ) ) ) ).
tt(t34_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots k1_complfld))) =>  ((r1_nat_d (k6_group_1 (k1_uniroots k1_complfld) B) A) <=> (r2_hidden B (k2_uniroots A))) ) ) ) ) ).
tt(t34_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((v1_uproots (k11_polynom3 A B C) A) =>  ((v1_uproots B A) & (v1_uproots C A)) ) ) ) ) ) ) ) ).
tt(t34_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r1_valuat_1 A B (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A D) D) D) E C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) )  =>  ((r1_tarski A B) => (r1_xxreal_0 (k64_valued_1 B) (k64_valued_1 A))) ) ) ) ) ).
tt(t34_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k24_valued_1 C A) B) = (k24_valued_1 C (k7_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t34_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) &  ((v1_hahnban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  ((r1_tarski (u1_struct_0 C) (k8_vectsp10 A B D)) => (v1_hahnban1 (k10_vectsp10 A B C D) A (k6_vectsp10 A B C))) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  ( ((k2_vectsp11 B C D) = (k1_ranknull B C C (k1_vectsp11 C D A)))  =>  ((k2_vectsp_5 B C (k1_ranknull B C C (k1_vectsp11 C D A)) (k3_ranknull B C C (k1_vectsp11 C D A))) = (k1_vectsp_4 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A (k5_algstr_0 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_vectsp_2 A B C (k4_algstr_0 B D)) = (k4_algstr_0 B (k5_vectsp_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v1_vectsp_4 C A B) &  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  (~  (C = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((m1_vectsp_4 C A D) & (m1_vectsp_4 E A D))  => (m1_vectsp_4 (k1_vectsp_5 A B C E) A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) => (r1_vectsp_6 A B (k6_vectsp_6 A B C (k6_vectsp_6 A B D E)) (k6_vectsp_6 A B (k6_algstr_0 A C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t34_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) =>  ((k1_vectsp_9 A B) = (k2_xcmplx_0 (k1_vectsp_9 A C) (k1_vectsp_9 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t34_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k4_vfunct_1 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t34_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k2_vfunct_2 A B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t34_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_yellow_0 A (k5_waybel_0 A B)) &  ((k1_yellow_0 A (k5_waybel_0 A B)) = B) ) ) ) ) ) ).
tt(t34_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (k13_yellow_6 A (k2_waybel11 A)))  => (v4_waybel11 A)) ) ) ).
tt(t34_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) &  ((v1_waybel_6 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_tarski (k4_yellow_4 A B C) B) &  ((r2_hidden D B) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_waybel_0 E A) &  ((v13_waybel_0 E A) &  ((v1_waybel_6 E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (~  ((r1_tarski (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) D) C) E) &  ((r1_tarski E B) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~  ((v2_waybel_8 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_1 B)) & (m1_yellow_0 C (k3_yellow_1 B)))  =>  (~  ((v7_yellow_0 C (k3_yellow_1 B)) &  ((v4_waybel_0 C (k3_yellow_1 B)) & (r5_waybel_1 A C)) ) ) ) ) ) ) ) )  &  ( (? [B:$i] :  (? [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_1 B)) & (m1_yellow_0 C (k3_yellow_1 B)))  &  ((v7_yellow_0 C (k3_yellow_1 B)) &  ((v4_waybel_0 C (k3_yellow_1 B)) & (r5_waybel_1 A C)) ) ) ) )  => (v2_waybel_8 A)) ) ) ) ).
tt(t34_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k5_waybel11 A)) =>  (B = (k3_tarski (a_2_3_waybel14 A B))) ) ) )  => (v3_waybel_3 A)) ) ) ).
tt(t34_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_waybel16 C A) &  (C = (k2_yellow_0 A B)) )  => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t34_waybel19,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v1_waybel19 B) & (m1_yellow_9 B A)) )  =>  (! [C:$i] :  ( ((v2_pre_topc C) &  ((v4_waybel11 C) & (m1_yellow_9 C A)) )  =>  (! [D:$i] :  ((m3_yellow_9 D C B) =>  ((k2_waybel19 A) = (u1_pre_topc D)) ) ) ) ) ) ) ) ) ).
tt(t34_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ((v6_waybel_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (~  ((v5_orders_3 D A C) &  ((v2_funct_2 D (u1_struct_0 C)) &  ((v5_orders_3 E C A) &  ((v2_funct_1 E) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D E)) & (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k3_struct_0 C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel16 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ( (D = (k8_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 (k3_yellow_3 B B)) (k1_waybel20 A A B B C C) (k6_partfun1 (u1_struct_0 B))))  =>  ( (~ (v2_struct_0 (k5_yellow_0 (k3_yellow_3 A A) D)))  &  ((v4_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) D) (k3_yellow_3 A A)) &  ((v7_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) D) (k3_yellow_3 A A)) &  ((v4_waybel_0 (k5_yellow_0 (k3_yellow_3 A A) D) (k3_yellow_3 A A)) & (m1_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) D) (k3_yellow_3 A A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_waybel17 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_waybel17 A B))) =>  ((r3_orders_2 (k4_waybel17 A B) C D) <=> (r3_orders_2 A (k2_waybel_0 A (k4_waybel17 A B) C) (k2_waybel_0 A (k4_waybel17 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t34_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_waybel23 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_waybel23 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t34_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v2_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((k4_yellow_0 (k6_yellow_1 (u1_struct_0 A) B)) = (k6_struct_0 A B (k4_yellow_0 B))) ) ) ) ) ).
tt(t34_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v10_waybel_0 B (k1_waybel25 A)) & (l1_waybel_0 B (k1_waybel25 A))) ) ) )  =>  ((r1_waybel_9 (k1_waybel25 A) B) & (r2_hidden (k1_waybel_2 (k1_waybel25 A) B) (k10_yellow_6 (k1_waybel25 A) B))) ) )  => (v1_waybel25 A)) ) ) ).
tt(t34_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel26 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18)))) (u1_struct_0 (k5_yellow_1 B (k7_funcop_1 B (k1_waybel26 A k9_waybel18))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel26 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18)))) (u1_struct_0 (k5_yellow_1 B (k7_funcop_1 B (k1_waybel26 A k9_waybel18)))))))) )  &  ((v23_waybel_0 C (k1_waybel26 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18))) (k5_yellow_1 B (k7_funcop_1 B (k1_waybel26 A k9_waybel18)))) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B (k7_funcop_1 B k9_waybel18)))) &  ((v5_pre_topc D A (k3_waybel18 B (k7_funcop_1 B k9_waybel18))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_waybel18 B (k7_funcop_1 B k9_waybel18))))))) ) )  =>  ((k1_funct_1 C D) = (k10_funct_6 D)) ) ) ) ) ) ) ) ) ) ).
tt(t34_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  => (r5_waybel_1 (k2_waybel27 A (k3_yellow_1 1)) (k2_yellow_1 (k5_waybel11 A)))) ) ).
tt(t34_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_3 A A))) =>  ((k3_funct_2 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k5_waybel_2 A) B) = (k10_lattice3 A (k8_yellow_3 A A B) (k9_yellow_3 A A B))) ) ) ) ) ).
tt(t34_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_3_waybel30 A B C) = (a_2_4_waybel30 A C)) ) ) ) ) ) ) ).
tt(t34_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v3_waybel_3 (k1_yellow_2 A A B)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_yellow_2 A A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_yellow_2 A A B))) =>  ( ( (E = C)  &  (F = D) )  =>  ((r1_waybel_3 A C D) <=> (r1_waybel_3 (k1_yellow_2 A A B) E F)) ) ) ) ) ) ) ) ) ) )  => (v22_waybel_0 B A A)) ) ) ) ) ).
tt(t34_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 D A) &  ((r1_tarski C (k5_setfam_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski B (k3_tarski E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_setfam_1 (a_2_0_waybel_4 A B)) = (k1_waybel_3 A B)) ) ) ) ) ).
tt(t34_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v4_waybel_6 (k4_waybel_6 A) A) =>  ((v2_waybel_1 A) & (v2_waybel_2 A)) ) ) ) ).
tt(t34_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_waybel_6 B A) => (v4_waybel_7 B A)) ) ) ) ) ).
tt(t34_waybel_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r3_waybel_9 A C B) &  ((v4_pre_topc D A) & (r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A C)) D)) )  => (r2_hidden B D)) ) ) ) ) ) ) ) ) ).
tt(t34_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r1_xxreal_0 (k1_vectsp_9 (k4_weddwitt A) (k7_weddwitt A B)) k6_numbers)) ) ) ) ) ).
tt(t34_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  =>  ((r1_xxreal_0 (k7_weierstr A B C) (k4_metric_1 A D E)) & (r1_xxreal_0 (k4_metric_1 A D E) (k10_weierstr A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((v2_wellord1 C) &  ((r2_hidden A (k1_relat_1 C)) &  ((r2_hidden B (k1_relat_1 C)) &  (! [D:$i] :  ((r2_hidden D (k1_wellord1 C A)) =>  ((r2_hidden (k4_tarski D B) C) &  (~  (D = B) ) ) ) ) ) ) )  => (r2_hidden (k4_tarski A B) C)) ) ) ) ) ).
tt(t34_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D)) = E)  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  |  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((v1_int_1 G) =>  (~  ( ((k2_xcmplx_0 (k3_xcmplx_0 A F) (k3_xcmplx_0 B G)) = E)  &  (! [H:$i] :  ((v1_int_1 H) =>  (~  ( (F = (k2_xcmplx_0 C (k3_xcmplx_0 H (k7_xcmplx_0 B (k3_int_2 A B)))))  &  (G = (k6_xcmplx_0 D (k3_xcmplx_0 H (k7_xcmplx_0 A (k3_int_2 A B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k4_xboole_0 C B) (k4_xboole_0 C A))) ) ) ) ).
tt(t34_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k9_xboolean A B)) = (k4_xboolean (k3_xboolean A) B)) ) ) ) ) ).
tt(t34_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k6_xcmplx_0 A B) = (k6_xcmplx_0 C D))  =>  ((k2_xcmplx_0 A D) = (k2_xcmplx_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k2_xcmplx_0 A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t34_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k11_xtuple_0 A) (k11_xtuple_0 B)) (k11_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t34_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k4_xxreal_0 (k4_xxreal_0 A B) C) = (k4_xxreal_0 A (k4_xxreal_0 B C))) ) ) ) ) ) ) ).
tt(t34_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k1_xxreal_1 B C) (k1_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t34_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  => (v1_xxreal_2 (k2_xxreal_1 A B))) ) ) ) ) ).
tt(t34_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((v1_xreal_0 A) =>  ((k1_xxreal_3 (k3_xxreal_3 B A) (k3_xxreal_3 A C)) = (k3_xxreal_3 B C)) ) ) ) ) ) ) ) ).
tt(t34_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B C) &  ((r1_yellow_0 A B) & (r1_yellow_0 A C)) )  => (r1_orders_2 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ).
tt(t34_yellow10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v3_orders_2 B) & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((k4_yellow_3 A B (k4_waybel_0 (k3_yellow_3 A B) C)) = (k4_waybel_0 A (k4_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t34_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(t34_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc (k8_waybel18 A B C) A (k7_waybel18 A B C)) => (v5_pre_topc C A B)) ) ) ) ) ) ) ).
tt(t34_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_yellow16 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))) =>  ((r2_yellow_0 (k5_yellow_1 A B) C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k4_waybel_3 A B (k2_yellow_0 (k5_yellow_1 A B) C) D) = (k2_yellow_0 (k3_waybel_3 A B D) (k5_waybel_3 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v1_funct_1 D) &  ((v1_funct_2 D (k3_yellow18 A B) (k3_yellow18 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_yellow18 A B) (k3_yellow18 A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (~  ((r2_hidden B (k6_yellow_6 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r3_waybel_9 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ( ((v11_functor0 C A B) & (v4_functor0 C A B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_functor0 A B C D) = (k3_functor0 A B C E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v18_waybel_0 C A B) | (v17_waybel_0 C A B))  =>  ((v3_orders_2 (k1_yellow_2 A B C)) &  ((v4_orders_2 (k1_yellow_2 A B C)) &  ((v5_orders_2 (k1_yellow_2 A B C)) &  ((v1_lattice3 (k1_yellow_2 A B C)) &  ((v2_lattice3 (k1_yellow_2 A B C)) &  ((v3_lattice3 (k1_yellow_2 A B C)) & (l1_orders_2 (k1_yellow_2 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_lattice3 (k3_yellow_3 A B) C (k7_yellow_3 A B D E)) <=>  ((r1_lattice3 A (k4_yellow_3 A B C) D) & (r1_lattice3 B (k5_yellow_3 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_waybel_0 A (k2_yellow_4 A (k4_waybel_0 A B) (k4_waybel_0 A C))) (k4_waybel_0 A (k2_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t34_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k12_lattice3 A B (k7_waybel_1 A B)) = (k3_yellow_0 A))  &  ((k13_lattice3 A B (k7_waybel_1 A B)) = (k4_yellow_0 A)) ) ) ) ) ) ).
tt(t34_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k10_yellow_6 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ( (E = (a_3_1_yellow_6 A B D))  & (r2_hidden C (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ( ((k8_lattice3 A (k4_yellow_0 A)) = (k3_yellow_0 (k7_lattice3 A)))  &  ((k9_lattice3 A (k3_yellow_0 (k7_lattice3 A))) = (k4_yellow_0 A)) ) ) ) ).
tt(t34_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v1_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E C) => (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_zf_fund1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_zf_lang)))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_zf_lang)))  =>  ( ((k4_zf_fund1 (k4_subset_1 k1_zf_lang A B)) = (k4_subset_1 k4_ordinal1 (k4_zf_fund1 A) (k4_zf_fund1 B)))  &  ((k4_zf_fund1 (k7_subset_1 k1_zf_lang A B)) = (k7_subset_1 k4_ordinal1 (k4_zf_fund1 A) (k4_zf_fund1 B))) ) ) ) ) ) ).
tt(t34_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_zf_lang A) =>  ((v9_zf_lang A) &  ((v4_zf_lang A) &  ((v5_zf_lang (k20_zf_lang A)) &  ((v4_zf_lang (k21_zf_lang (k20_zf_lang A))) & (v4_zf_lang (k22_zf_lang (k20_zf_lang A)))) ) ) ) ) ) ) ).
tt(t34_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ( ((k13_zf_lang A C) = (k13_zf_lang B D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) =>  ((r2_hidden C A) | (r1_tarski A (k4_xboole_0 B (k1_tarski C)))) ) ) ) ) ).
tt(t34_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (~  ((r2_hidden B C) &  ( (D = (k4_classes1 C))  & (r3_zfrefle1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t34_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t350_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 A) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 B) (k3_xxreal_1 B A))) ) ) ) ) ) ).
tt(t351_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A B)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t352_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t353_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t354_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t355_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t356_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t357_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t358_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t359_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t35_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 (k7_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) E) = (k1_funct_1 (k7_abcmiz_0 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) =>  ((m2_finseq_2 (k4_pre_poly k2_abcmiz_1 A B) k2_abcmiz_1 k4_abcmiz_1) <=>  ( ((k3_abcmiz_1 A) = k1_xboole_0)  &  ( (~  (A = B) )  & (r1_tarski (k3_abcmiz_1 B) (k6_domain_1 k2_abcmiz_1 A))) ) ) ) ) ) ) ).
tt(t35_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_trees_4 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k1_msualg_1 A B)))  =>  ((k10_abcmiz_a A (k36_abcmiz_1 A B C)) = B) ) ) ) ) ) ) ) ).
tt(t35_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_aff_1 A B C D) &  ( (~ (r2_hidden B D))  & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 B A) &  ((v1_aff_4 C A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (~ (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((k1_funct_1 (k1_ordinal4 (k5_afinsq_1 A) B) k6_numbers) = A) ) ) ) ).
tt(t35_afinsq_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v6_membered A))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (v6_membered B))  =>  ((r1_afinsq_2 A B) <=>  ((k4_afinsq_2 (k2_xboole_0 A B)) = (k1_ordinal4 (k4_afinsq_2 A) (k4_afinsq_2 B))) ) ) ) ) ) ).
tt(t35_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k13_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ( (E = (k4_tarski B 1))  &  ((v1_aff_1 B A) &  ((r1_incsp_1 (k13_afproj A) C E) & (r1_incsp_1 (k13_afproj A) D E)) ) )  =>  ( (D = C)  |  ((m1_subset_1 C (u1_struct_0 A)) | (m1_subset_1 D (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_afvect0 A B C D) <=> (r2_afvect0 A (k1_afvect0 A E B) (k1_afvect0 A E C) (k1_afvect0 A E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) =>  ((k1_partfun1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 B)) (u1_msualg_1 A) (k12_lang1 (u1_struct_0 A) (u1_struct_0 B) C)) = (k3_relat_1 D (u1_msualg_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t35_algstr_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_algstr_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_algstr_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_algstr_4 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_algstr_4 A))) =>  ( ((k6_algstr_0 (k14_algstr_4 A) B C) = (k6_algstr_0 (k14_algstr_4 A) D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_altcat_2 B A) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u1_altcat_1 A) = (u1_altcat_1 B)) )  => (v3_altcat_2 B A)) ) ) ) ) ).
tt(t35_ami_wstd,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v2_ami_wstd C B) & (l1_extpro_1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k7_ami_wstd B C (k4_ami_wstd B C D A) A) = D) ) ) ) ) ) ) ) ) ).
tt(t35_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) <=> (m1_subset_1 B (u1_struct_0 (k3_analmetr A)))) ) ) ) ).
tt(t35_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analort A F G B C D E) => (r2_analort A F G C B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_collsp A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ((v7_anproj_2 A) & (l1_collsp A)) ) ) ) ) ) )  <=>  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_collsp A B C F) & (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((r1_alg_1 A C D) &  ((r1_alg_1 A C E) & (r2_relset_1 (u1_struct_0 A) (u1_struct_0 C) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 C) D B) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 C) E B))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 C) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E F G)) D) = 1) )  &  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = D) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v1_armstrng B A) & (v2_finsub_1 B))  =>  ( (B = (k9_armstrng A (k10_armstrng A B)))  &  (! [C:$i] :  ( ((v6_armstrng C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  ( (B = (k9_armstrng A C))  => (r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) C (k10_armstrng A B))) ) ) ) ) ) ) ) ) ).
tt(t35_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (~  ((k7_arytm_3 A) = k1_xboole_0) ) ) ) ).
tt(t35_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v4_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_limfunc1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((r2_hidden A (k7_asympt_0 B)) &  (~ (r2_hidden A (k8_asympt_0 B))) ) ) ) ) ) ) ).
tt(t35_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) &  ((v6_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k6_int_1 C 2) = k6_numbers)  =>  ((k1_seq_1 B C) = 1) )  &  ( ((k6_int_1 C 2) = 1)  =>  ((k1_seq_1 B C) = C) ) ) ) )  & (r2_hidden B (k8_asympt_0 A))) ) ) ) ) ) ).
tt(t35_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r2_group_6 (k3_autalg_1 A) (k7_autalg_1 (k6_msualg_1 A) (k9_msualg_1 A)))) ) ).
tt(t35_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((r2_hidden (k1_domain_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)) B C) (k3_tarski (k10_xtuple_0 (k12_bagorder A)))) <=>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  ( (~  ((k11_bagorder A B) = (k11_bagorder A C)) )  & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k11_bagorder A B) (k11_bagorder A C)) (u1_orders_2 A))) ) ) )  &  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  ( ((k11_bagorder A B) = (k11_bagorder A C))  & (r2_hidden (k1_domain_1 (k1_zfmisc_1 B) (k1_zfmisc_1 C) (k6_subset_1 B (k6_domain_1 (u1_struct_0 A) (k11_bagorder A B))) (k6_subset_1 C (k6_domain_1 (u1_struct_0 A) (k11_bagorder A C)))) (k3_tarski (k10_xtuple_0 (k12_bagorder A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) & (r1_bcialg_1 A C B)) ) ) ) ) ) ).
tt(t35_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  ((v12_bcialg_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)) A) & (m2_bcialg_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)) A)) ) ) ) ) ).
tt(t35_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(t35_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A B (k7_bcialg_4 A (k2_finseq_4 (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ).
tt(t35_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ((r1_xxreal_0 A C) =>  ((r1_xxreal_0 D A) |  ((v8_bcialg_1 E) & (m1_bcialg_5 E A B A (k2_nat_1 A 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t35_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  <=>  ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A)) ) ) ) ).
tt(t35_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k4_bhsp_1 A B C) (k7_real_1 (k4_bhsp_1 A B D) (k4_bhsp_1 A D C)))) ) ) ) ) ) ) ) ).
tt(t35_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k2_bhsp_2 A (k4_normsp_1 A (k4_normsp_1 A D C) (k5_algstr_0 A B C)))) &  ((k2_seq_2 (k2_bhsp_2 A (k4_normsp_1 A (k4_normsp_1 A D C) (k5_algstr_0 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_valued_0 (u1_struct_0 A) (k5_normsp_1 A C B) D) = (k5_normsp_1 A (k1_valued_0 (u1_struct_0 A) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t35_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (v7_valued_0 (k3_series_1 (k2_bhsp_2 A B)))) ) ) ) ).
tt(t35_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear G A B C) &  ((v4_bilinear G A B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G (k5_algstr_0 B D E) F) = (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k5_series_1 2 A) B))  =>  ((k6_binarith A (k1_binari_3 A B)) = B) ) ) ) ) ) ).
tt(t35_binari_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ( ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 C)) (k20_binop_2 A B)) &  ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) A) & (r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) B)) )  =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 k6_numbers B) |  ((k7_partfun1 k6_margrel1 (k4_binarith (k23_binop_2 C 1) (k2_binari_4 (k23_binop_2 C 1) A) (k2_binari_4 (k23_binop_2 C 1) B)) (k23_binop_2 C 1)) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(t35_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_lattices A B (k1_boolealg A C B)) (k3_lattices A B C))) ) ) ) ) ) ).
tt(t35_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A (k13_borsuk_1 A B C))) (k12_borsuk_1 A (k13_borsuk_1 A B C)) D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A (k13_borsuk_1 A B C))) (k12_borsuk_1 A (k13_borsuk_1 A B C)) E))  =>  ((r2_hidden D (u1_struct_0 B)) |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_borsuk_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (u1_struct_0 k1_borsuk_4)) <=>  ( (~ (r1_xxreal_0 A k6_numbers))  &  (~ (r1_xxreal_0 1 A)) ) ) ) ) ).
tt(t35_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k3_rcomp_1 B C))  =>  ( (B = C)  |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t35_borsuk_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) |  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r1_xxreal_0 A E) & (r1_xxreal_0 E B))  =>  ((k1_funct_1 (k1_borsuk_6 A B C D) E) = (k2_xcmplx_0 (k3_xcmplx_0 (k7_xcmplx_0 (k6_xcmplx_0 D C) (k6_xcmplx_0 B A)) (k6_xcmplx_0 E A)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  ((k16_rvsum_1 (k12_toprealc 3 A)) = (k7_real_1 (k7_real_1 (k5_square_1 (k1_euclid_5 A)) (k5_square_1 (k2_euclid_5 A))) (k5_square_1 (k3_euclid_5 A)))) ) ) ).
tt(t35_bspace,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_vectsp_6 B k2_bspace (k7_bspace A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_bspace A))) =>  ((r2_hidden C (k1_vectsp_6 k2_bspace (k7_bspace A) B)) =>  ((k10_bspace k2_bspace (k7_bspace A) B C) = (k1_group_1 k2_bspace)) ) ) ) ) ) ) ) ).
tt(t35_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A G B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k16_bvfunc_1 A B (k6_partit1 A)) (k13_bvfunc_1 A B))) ) ) ) ).
tt(t35_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 B (k2_bvfunc_1 A (k9_bvfunc_1 A C B) (k9_bvfunc_1 A (k1_bvfunc_1 A C) B)))) ) ) ) ) ) ).
tt(t35_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k10_bvfunc_1 A C D)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k6_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t35_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k2_bvfunc_1 A D C) B E) (k2_bvfunc_1 A (k7_bvfunc_2 A D B E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F) (k6_bvfunc_2 A (k9_bvfunc_1 A E (k1_bvfunc_1 A D)) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A E (k1_bvfunc_1 A C)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k1_bvfunc_1 A B)) (k1_bvfunc_1 A B)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t35_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A (k9_bvfunc_1 A B (k1_bvfunc_1 A C))) (k2_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t35_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r1_bvfunc_1 A (k2_bvfunc_1 A B C) D) => (r1_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A D)) (k1_bvfunc_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t35_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k11_c0sp1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k11_c0sp1 A)))))) )  =>  ((v1_rsspace3 B (k11_c0sp1 A)) => (v3_normsp_1 B (k11_c0sp1 A))) ) ) ) ) ).
tt(t35_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v2_normsp_1 (k9_c0sp2 A))) ) ).
tt(t35_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  (! [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1)) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 C)) & (r3_calcul_1 A C B)) )  => (r3_calcul_1 A (k8_finseq_1 (k2_zfmisc_1 (k4_calcul_1 A) k2_cqc_the1) D C) (k2_nat_1 B (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ).
tt(t35_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 (k1_ordinal1 A) (k1_ordinal1 B)) => (r2_wellord2 A B)) ) ) ).
tt(t35_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((r1_xboole_0 A B) =>  ((k1_card_1 (k2_xboole_0 A B)) = (k1_card_2 (k1_card_1 A) (k1_card_1 B))) ) ) ) ).
tt(t35_card_3,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k6_card_3 (k7_funcop_1 k1_xboole_0 A)) = k1_xboole_0) ) ) ).
tt(t35_card_5,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_finset_1 B))  & (v1_card_1 B))  =>  ( ((r1_ordinal1 (k1_card_5 A) B) & (r2_hidden B A))  =>  ((k3_card_2 A B) = (k3_card_2 (k6_card_3 (k2_card_5 A B)) (k1_card_5 A))) ) ) ) ) ) ).
tt(t35_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  (! [B:$i] :  ((m2_card_fil B A) =>  (~  ((r2_card_fil A A B) &  ((r1_tarski (k5_card_fil A) B) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( ((k1_card_1 C) = A)  &  ( (! [D:$i] :  (~  ((r2_hidden D C) & (r2_hidden D B)) ) )  &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D C) & (r2_hidden E C))  =>  ( (D = E)  | (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((k1_tarski A) = (k8_relat_1 C (k1_tarski B)))  =>  ((k2_card_fin D C B) = (k1_funct_1 D A)) ) ) ) ) ) ) ) ).
tt(t35_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v6_card_fil A) =>  ((k1_card_1 (k4_classes1 A)) = A) ) ) ) ).
tt(t35_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v7_cat_1 (k4_cat_1 A B) A B B)) ) ) ) ).
tt(t35_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (m2_cat_1 (k1_funct_1 (k3_funct_5 D) (k4_cat_1 B E)) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v10_cat_1 B A) =>  ( ((k3_graph_1 A (k10_cat_3 A C B)) = C)  &  ((k4_graph_1 A (k10_cat_3 A C B)) = B) ) ) ) ) ) ) ) ) ).
tt(t35_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((k9_cat_4 A C C B D D) = (k5_cat_1 A B C (k2_cat_4 A C C) D (k15_cat_4 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t35_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_card_1 (a_1_3_catalan2 A)) = (k6_newton A (k24_binop_2 2 A))) ) ) ).
tt(t35_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  => (r1_tarski (k13_pre_poly (k19_valued_1 (u1_struct_0 A) k2_numbers k2_numbers B C)) (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C)))) ) ) ) ) ) ).
tt(t35_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_cfcont_1 B A) => (r1_cfcont_1 (k31_valued_1 k2_numbers k2_numbers B) A)) ) ) ) ) ).
tt(t35_cfdiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfdiff_1 B A) => (r2_cfcont_1 B A)) ) ) ) ).
tt(t35_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_cfunct_1 A (k19_valued_1 A k2_numbers k2_numbers B C)) (k19_valued_1 A k2_numbers k2_numbers (k2_cfunct_1 A B) (k2_cfunct_1 A C)))) ) ) ) ) ) ).
tt(t35_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k11_cgames_1 B)) => (r1_tarski (k10_cgames_1 A) (k11_cgames_1 B))) ) ) ) ) ).
tt(t35_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_chain_1 E B) =>  ( ((r1_xxreal_0 A B) & (r2_hidden (k3_chain_1 B C D) (k4_chain_1 B E A)))  =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) =>  ((r2_hidden (k1_seq_1 C F) (k2_chain_1 B E F)) & (r2_hidden (k1_seq_1 D F) (k2_chain_1 B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m4_glib_001 C A B) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  =>  (C = B) ) ) ) ) ) ) ) ).
tt(t35_circcmb3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ((m1_circcmb3 E B) =>  ((r1_tarski (k10_xtuple_0 D) (u1_struct_0 E)) =>  ((r2_hidden (k3_circcmb3 (k4_circcmb3 A B C D)) (k2_msafree2 E)) |  ((k2_msafree2 (k6_circcmb3 B E (k4_circcmb3 A B C D))) = (k2_msafree2 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_msafree2 C) & (l1_msualg_1 C)) ) )  =>  ( ((r1_tarski (k2_msafree2 B) (k2_msafree2 A)) &  (C = (k2_circcomb A B)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) &  ((v4_msafree2 D A) & (l3_msualg_1 D A)) )  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F C) &  ((v4_msafree2 F C) & (l3_msualg_1 F C)) )  =>  ( ((r2_circcomb A B D E) &  (F = (k3_circcomb A B D E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 C F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A D))) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (H = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 A)))  &  (I = (k11_card_3 (u3_msualg_1 C F) G (u1_struct_0 B))) )  =>  ((k6_circuit2 C F G) = (k1_funct_4 (k6_circuit2 A D H) (k6_circuit2 B E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v4_msualg_1 H A) & (l3_msualg_1 H A))  =>  (! [I:$i] :  ( ((v4_msualg_1 I B) & (l3_msualg_1 I B))  =>  (! [J:$i] :  ( ((v4_msualg_1 J C) & (l3_msualg_1 J C))  =>  ( ((r4_circtrm1 A B D E H I) & (r4_circtrm1 B C F G I J))  => (r4_circtrm1 A C (k3_relat_1 D F) (k3_relat_1 E G) H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k4_classes1 B)) => (r2_hidden (k3_tarski A) (k4_classes1 B))) ) ) ) ).
tt(t35_classes2,ax, (! [A:$i] :  ((k1_card_1 (k1_classes1 A)) = (k1_card_1 (k4_classes1 (k1_card_1 (k1_classes1 A))))) ) ).
tt(t35_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_clopban1 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (D = (k1_clvect_1 (k14_clopban1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k15_clopban1 A B D F) = (k1_clvect_1 B (k15_clopban1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 C 1) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((k1_seq_1 (k4_normsp_0 A B) D) = (k10_real_1 1 (k4_power D C))) ) ) )  & (v2_clopban3 B A)) ) ) ) ) ) ) ) ) ).
tt(t35_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ((k6_algstr_0 A B (k7_clopban4 A C)) = (k6_algstr_0 A (k7_clopban4 A C) B)) ) ) ) ) ) ) ) ).
tt(t35_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m1_pboole D A (k5_mssubfam A B)) =>  (! [E:$i] :  ((m2_pboole E A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( ((r6_pboole A (k2_closure1 A B E D) D) &  (! [F:$i] :  ((m1_pboole F A (k5_mssubfam A B)) =>  (! [G:$i] :  ( ((v2_relat_1 G) & (m3_pboole G A (k1_mboolean A B)))  =>  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) & (v1_partfun1 H A)) ) )  =>  ((r1_pboole A H G) <=>  ((r1_pboole A H C) & (r2_pboole A F H)) ) ) )  => (r6_pboole A (k2_closure1 A B E F) (k4_mssubfam A B G))) ) ) ) ) )  => (r1_pboole A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((v8_closure2 C A B) & (v8_closure2 D A B))  => (v8_closure2 (k8_closure2 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t35_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k5_algstr_0 D E F) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k2_clvect_2 A (k4_normsp_1 A (k4_normsp_1 A D C) (k5_algstr_0 A B C)))) &  ((k2_seq_2 (k2_clvect_2 A (k4_normsp_1 A (k4_normsp_1 A D C) (k5_algstr_0 A B C)))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (v7_valued_0 (k3_series_1 (k2_clvect_2 A B)))) ) ) ) ).
tt(t35_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v7_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) (k8_cohsp_1 A B C)) & (r2_hidden (k4_tarski E F) (k8_cohsp_1 A B C)))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r2_hidden (k4_tarski (k6_partfun1 A) A) (k16_coh_sp B))) ) ) ).
tt(t35_combgras,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_ordinal1 (k2_nat_1 A 1) (k1_card_1 B)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((l1_combgras C (k1_combgras A B) (k1_combgras A B)) =>  ((v7_combgras C (k1_combgras A B)) <=>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B B) &  ((v3_funct_2 D B B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  &  ((g1_combgras (k1_combgras A B) (k1_combgras A B) (u1_combgras (k1_combgras A B) (k1_combgras A B) C) (u2_combgras (k1_combgras A B) (k1_combgras A B) C)) = (k8_combgras A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_complex1 (k3_xcmplx_0 A B)) = (k9_complex1 (k15_complex1 A) (k15_complex1 B))) ) ) ) ) ).
tt(t35_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 (k8_complex1 A B) C) = (k8_complex1 (k1_complex2 A C) (k1_complex2 B C))) ) ) ) ) ) ) ).
tt(t35_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k8_group_1 k1_complfld (k11_algstr_0 k1_complfld A) (k3_vectsp_1 k1_complfld C B)) = (k3_vectsp_1 k1_complfld C (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k30_valued_1 (k1_valued_1 A B)) = (k1_valued_1 (k30_valued_1 A) (k30_valued_1 B))) ) ) ) ) ) ).
tt(t35_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v1_compts_1 (k3_pcomps_1 A)) <=> (v8_compl_sp (k3_pcomps_1 A))) ) ) ).
tt(t35_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_compos_1 B)) =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  (E = (k1_funct_1 C A)) )  =>  ((k5_compos_0 (u1_compos_1 B) E D) = (k1_funct_1 (k6_compos_1 B C D) (k2_xcmplx_0 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k62_valued_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G)) = 6) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k1_comptrig A) = k6_numbers) ) ) ) ).
tt(t35_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k5_comput_1 A B) (k2_comput_1 k5_numbers))) ) ) ) ).
tt(t35_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A (k51_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B) C))) ) ) ) ) ) ).
tt(t35_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_relat_1 A))  =>  ( ((k3_comseq_2 A) = k5_complex1)  |  ((k3_comseq_2 (k36_valued_1 k5_numbers k2_numbers A)) = (k12_complex1 (k3_comseq_2 A))) ) ) ) ) ).
tt(t35_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D C) =>  ((k8_nat_1 k2_numbers A D) = (k8_nat_1 k2_numbers B D)) ) ) )  =>  ((k8_nat_1 k2_numbers (k10_comseq_3 A) C) = (k8_nat_1 k2_numbers (k10_comseq_3 B) C)) ) ) ) ) ) ) ) ).
tt(t35_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_conlat_1 D A) &  ( (~ (v5_conlat_1 D A))  &  ((v7_conlat_1 D A) & (l2_conlat_1 D A)) ) )  =>  ((k1_binop_1 (k10_conlat_1 A) B (k1_binop_1 (k10_conlat_1 A) C D)) = (k1_binop_1 (k10_conlat_1 A) (k1_binop_1 (k10_conlat_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t35_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_connsp_1 B A) &  ((v3_connsp_1 C A) &  ( (~  (B = C) )  &  (~ (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = B) ) ) ) ) ).
tt(t35_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) => (r1_tarski (k1_convex4 A (k9_convex4 A B C)) (k4_subset_1 (u1_struct_0 A) (k1_convex4 A B) (k1_convex4 A C)))) ) ) ) ) ) ).
tt(t35_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C D E F) (k15_cqc_sim1 A B)) => (r2_qc_lang2 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((a_2_0_cqc_the1 A B) = (k1_cqc_the1 A B)) ) ) ) ) ).
tt(t35_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k11_cqc_lang A D (k8_cqc_lang A B C)) A) => (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t35_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r3_cqc_the1 A C (k11_cqc_lang A D B)) <=> (r3_cqc_the1 A C B)) ) ) ) ) ) ) ) ) ).
tt(t35_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k17_complex1 (k12_csspace A B C)) (k8_real_1 (k7_square_1 (k17_complex1 (k12_csspace A B B))) (k7_square_1 (k17_complex1 (k12_csspace A C C)))))) ) ) ) ) ) ).
tt(t35_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v4_dickson A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((m2_valued_0 C (u1_struct_0 A) B) & (v2_dickson C A)) ) ) ) ) ) ) ) ) ) ).
tt(t35_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((r1_zfmisc_1 A B C) =>  ( ((k10_diff_1 D A B C) = (k10_diff_1 D C A B))  &  ((k10_diff_1 D A B C) = (k10_diff_1 D B A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k10_real_1 A F)) ) )  & (r1_zfmisc_1 B C D))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ( (D = k6_numbers)  |  ((k10_diff_1 E B C D) = (k10_real_1 A (k8_real_1 (k8_real_1 B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 k1_numbers k1_numbers)) &  ((v1_diff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) )  =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_xxreal_0 G F) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers E F) G) = (k8_real_1 (k8_real_1 (k6_newton G F) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) G) (k7_real_1 B (k4_real_1 (k7_nat_d F G) (k10_real_1 A 2))))) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D A) (k7_nat_d F G)) (k9_real_1 B (k4_real_1 G (k10_real_1 A 2)))))) ) ) ) ) )  =>  ( ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k6_series_1 (k12_diff_1 E 1) 1))  &  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 2) B) = (k6_series_1 (k12_diff_1 E 2) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers C B))) ) ) ) ) ) ) ).
tt(t35_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_dilworth C (k5_yellow_0 A (k4_dilworth A B))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A (k4_dilworth A B))))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~  (D = E) )  &  (~ (r1_orders_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r3_diraf A D E B) &  ((r3_diraf A D E C) & (r3_diraf A B C F)) )  =>  ( (B = C)  | (r3_diraf A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( (~  (B = k6_numbers) )  =>  ((k2_ec_pf_1 A (k2_binom (k9_int_3 A) B 2)) = 1) ) ) ) ) ) ).
tt(t35_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C)) =>  ((k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k5_ec_pf_2 A B C D) 2) (k6_ec_pf_2 A B C D)) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k4_ec_pf_2 A B C D) 3) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B (k4_ec_pf_2 A B C D)) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A B C D) 2))) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) (k6_ec_pf_2 A B C D) 3)))) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ).
tt(t35_ens_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (~  ((v10_cat_1 B (k11_ens_1 A)) &  (! [C:$i] :  (~  (B = (k1_tarski C)) ) ) ) ) ) ) ) ) ).
tt(t35_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((r2_hidden (k7_real_1 (k8_real_1 (k9_real_1 D 1) (k1_matrix_1 B)) E) (k4_finseq_1 (k1_matrprob A C D))) &  ((k3_matrix_1 A B D E) = (k1_funct_1 (k1_matrprob A C D) (k7_real_1 (k8_real_1 (k9_real_1 D 1) (k1_matrix_1 B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((k6_enumset1 A A B C D E F G) = (k5_enumset1 A B C D E F G)) ) ) ) ) ) ) ) ).
tt(t35_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((r2_hidden (k4_tarski D B) C) <=>  ((k6_eqrel_1 A A C D) = (k6_eqrel_1 A A C B)) ) ) ) ) ) ) ) ).
tt(t35_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (k4_equation A) C)) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((r1_equation A B C D) => (r1_equation A (k13_msualg_4 A B E) C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 k6_numbers (k23_rvsum_1 B B))) ) ) ) ).
tt(t35_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k4_euclid_3 A B C) = (k4_euclid_3 (k5_algstr_0 (k15_euclid 2) A B) (k4_struct_0 (k15_euclid 2)) (k5_algstr_0 (k15_euclid 2) C B))) ) ) ) ) ) ) ).
tt(t35_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k5_square_1 (k12_euclid (k8_euclid A B C))) = (k7_real_1 (k9_real_1 (k5_square_1 (k12_euclid B)) (k8_real_1 2 (k23_rvsum_1 B C))) (k5_square_1 (k12_euclid C)))) ) ) ) ) ) ) ).
tt(t35_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 3))) =>  ((k6_euclid_5 A B C) = (k23_rvsum_1 (k5_euclid_5 A B) C)) ) ) ) ) ) ) ).
tt(t35_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((r2_hidden A (k5_jgraph_6 D E F)) &  ((r2_hidden B (k5_jgraph_6 D E F)) &  ((r2_hidden C (k5_jgraph_6 D E F)) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  ((k4_euclid_3 A B C) = k32_sin_cos) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlsub_1 B (k10_funcsdom (k2_finseq_1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden C (u1_struct_0 B)) => (r2_hidden (k9_euclid A C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t35_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid E)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid E)) =>  ( ((r3_euclidlp E F G) &  ((k7_euclid E (k9_euclid E F A) (k9_euclid E G B)) = (k7_euclid E (k9_euclid E F C) (k9_euclid E G D))) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((k10_funct_7 C A B) = (k10_funct_7 C B A)) ) ) ) ) ) ).
tt(t35_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_extpro_1 A B C (k5_extpro_1 A B C D E)) =>  ((k6_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k6_extpro_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) &  ((v4_circcomb B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden (k4_tarski D E) (u4_struct_0 A)) =>  ((k1_funct_1 (k6_circuit2 A B C) (k4_tarski D E)) = (k1_funct_1 E (k3_relat_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_facirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ( ((k3_funct_2 k5_numbers k5_numbers B k6_numbers) = 1)  &  ( ((k3_funct_2 k5_numbers k5_numbers B 1) = 2)  &  ((k3_funct_2 k5_numbers k5_numbers B 2) = A) ) ) ) ) ) ) ).
tt(t35_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t35_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k19_sin_cos (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t35_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k1_sin_cos9) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k1_sin_cos9 B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t35_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k3_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 A)) => (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) ) )  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) ) ) ) ) ).
tt(t35_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2)))))) &  ( (C = (k47_valued_1 k1_numbers k1_numbers k1_numbers D E))  &  ( (E = (k1_taylor_1 2))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2)))) B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2)))) B) F) = (k8_real_1 F (k10_prepower (k9_real_1 (k5_square_1 A) (k2_newton F 2)) (k1_real_1 (k10_real_1 1 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1))) &  ( (B = (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k24_sin_cos)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = (k1_real_1 D))  &  (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) A) D) = (k10_real_1 (k7_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))) (k9_real_1 (k26_sin_cos D) (k26_sin_cos (k1_real_1 D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k1_seq_1 k16_sin_cos (k1_seq_1 k24_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t35_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k30_sin_cos))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k30_sin_cos) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 B))) (k10_real_1 (k10_real_1 1 B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ) ).
tt(t35_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k19_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t35_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_power (k4_xcmplx_0 k1_fib_num) (k3_xcmplx_0 (k4_xcmplx_0 1) A)) = (k3_power (k3_power (k4_xcmplx_0 k1_fib_num) (k4_xcmplx_0 1)) A)) ) ) ).
tt(t35_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_nat_1 (k3_fib_num3 A B (k1_nat_1 C 1)) (k3_fib_num3 A B (k1_nat_1 C 2))) = (k3_fib_num3 A B (k1_nat_1 C 3))) ) ) ) ) ) ) ).
tt(t35_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((r1_xxreal_0 2 A) & (v1_abian A))  =>  ((k1_fib_num3 (k2_xcmplx_0 A 1)) = (k2_int_1 (k6_xcmplx_0 (k3_xcmplx_0 k1_fib_num (k1_fib_num3 A)) 1))) ) ) ) ).
tt(t35_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  (! [E:$i] :  ((m1_finseq_1 E A) =>  ( (E = (k1_finseq_8 A (k1_finseq_8 A B C) D))  =>  ((r2_finseq_8 A E B 1) &  ((r2_finseq_8 A E C 1) & (r2_finseq_8 A E D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (a_3_1_filter_0 A B C)) ) ) ) ) ) ) ).
tt(t35_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((k3_lattices (k7_filter_1 A B) (k9_filter_1 A B C E) (k9_filter_1 A B D F)) = (k9_filter_1 A B (k3_lattices A C D) (k3_lattices B E F)))  &  ((k4_lattices (k7_filter_1 A B) (k9_filter_1 A B C E) (k9_filter_1 A B D F)) = (k9_filter_1 A B (k4_lattices A C D) (k4_lattices B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v14_lattices A) &  ( (~  (B = (k6_lattices A)) )  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r2_hidden B C) & (r2_filter_2 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k7_finseq_1 A B) = k1_xboole_0)  =>  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t35_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( (D = (k9_finseq_1 A))  =>  ((k1_partfun1 k5_numbers B B C D E) = (k9_finseq_1 (k1_funct_1 E A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((k9_finseq_1 A) = (k10_finseq_1 B C)) ) ) ) ) ).
tt(t35_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  (C = (k6_xcmplx_0 (k4_finseq_4 A B) 1)) )  =>  ((k4_finseq_1 (k5_finseq_4 A B)) = (k2_finseq_1 C)) ) ) ) ) ) ) ).
tt(t35_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k6_finseq_4 C B) = (k2_rfinseq A (k4_finseq_4 C B) C)) ) ) ) ) ) ) ) ).
tt(t35_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden A (k10_xtuple_0 C)) & (r2_hidden B (k10_xtuple_0 (k5_finseq_4 C A))))  =>  ((k5_finseq_4 (k5_finseq_4 C A) B) = (k5_finseq_4 C B)) ) ) ) ) ) ).
tt(t35_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 B))) ) ) ) ) ) )  =>  ( (C = D)  |  ( (E = D)  |  ( (F = C)  |  ( (F = E)  |  ((k2_finseq_7 A (k2_finseq_7 A B C E) D F) = (k2_finseq_7 A (k2_finseq_7 A B D F) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((r6_binop_1 B F G) => (r2_funct_2 A B (k10_funcop_1 B A F (k5_binop_1 B G C D) E) (k6_funcop_1 B A G (k10_funcop_1 B A F C E) (k10_funcop_1 B A F D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ((v2_fintopo2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k9_fintopo2 A B))) ) ) ) ) ).
tt(t35_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k7_fintopo3 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 A) (k7_fintopo3 A B D) (k7_fintopo3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t35_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_fin_topo A) &  ((v4_fin_topo C A) &  ((r1_tarski C B) & (r1_tarski B (k9_fin_topo A C))) ) )  => (v4_fin_topo B A)) ) ) ) ) ) ) ).
tt(t35_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_xxreal_0 C k6_numbers) | (r1_tarski B (k7_flang_1 A B C))) ) ) ) ) ) ) ).
tt(t35_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k6_flang_1 A (k1_flang_2 A B C D) (k7_flang_1 A B E)) = (k6_flang_1 A (k7_flang_1 A B E) (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t35_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_3 A (k7_flang_1 A B C) D) (k1_flang_3 A B (k3_xcmplx_0 C D)))) ) ) ) ) ) ) ).
tt(t35_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ( (B = C)  =>  ((k1_funct_1 (k20_fomodel0 A C D) (k12_finseq_1 A B)) = (k12_finseq_1 A D)) )  &  ( (~  (B = C) )  =>  ((k1_funct_1 (k20_fomodel0 A C D) (k12_finseq_1 A B)) = (k12_finseq_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (C = (a_2_0_frechet2 A B))  &  ((r1_xboole_0 (k2_relset_1 (u1_struct_0 A) D) C) &  ((r1_frechet A D B) &  (! [E:$i] :  ((m2_valued_0 E (u1_struct_0 A) D) =>  (~ (v2_funct_1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_frechet,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) =>  ((k10_xtuple_0 (k1_funct_4 A B)) = (k2_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t35_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D B C)) )  =>  ( ((k2_nat_1 A 1) = (k5_card_1 (u1_struct_0 D)))  =>  ((k7_fsm_1 B C D (k2_nat_1 A 1)) = (k7_fsm_1 B C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t35_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_fsm_3 B A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  ((u1_fsm_3 A (k9_flang_1 A) (k4_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B)) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) (k3_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B (k2_flang_1 A) (u1_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B)))) ) ) ) ) ).
tt(t35_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k48_gfacirc1 A B C) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k45_gfacirc1 A B C) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k14_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k48_gfacirc1 (k48_gfacirc1 A B C) E D) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k48_gfacirc1 A B C) E) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp) (k3_msafree2 (k19_ftacell1 A B C D E))) & (r2_hidden (k45_gfacirc1 (k48_gfacirc1 A B C) E D) (k3_msafree2 (k19_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k3_relat_1 (k6_partfun1 B) (k5_funcop_1 C D A)) = (k5_funcop_1 C D (k5_relat_1 A B))) ) ) ) ) ) ) ).
tt(t35_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 B) & (r2_hidden A (k10_xtuple_0 B)))  =>  ( (A = (k1_funct_1 B (k1_funct_1 (k2_funct_1 B) A)))  &  (A = (k1_funct_1 (k3_relat_1 (k2_funct_1 B) B) A)) ) ) ) ) ) ).
tt(t35_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (~  (B = k1_xboole_0) )  =>  (! [E:$i] :  ( (? [F:$i] :  ((r2_hidden F A) &  ((r2_hidden F C) &  (E = (k1_funct_1 D F)) ) ) )  => (r2_hidden E (k7_relset_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t35_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v1_funct_1 (k3_funct_3 A)) &  ((v1_funct_2 (k3_funct_3 A) (k1_zfmisc_1 (k10_xtuple_0 A)) (k1_zfmisc_1 (k9_xtuple_0 A))) & (m1_subset_1 (k3_funct_3 A) (k1_zfmisc_1 (k2_zfmisc_1 (k1_zfmisc_1 (k10_xtuple_0 A)) (k1_zfmisc_1 (k9_xtuple_0 A)))))) ) ) ) ).
tt(t35_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k1_funct_4 A B) = (k1_funct_4 B A)) ) ) ) ) ) ).
tt(t35_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  =>  ((r1_tarski (k10_xtuple_0 (k1_funct_5 C)) (k1_funct_2 B (k10_xtuple_0 C))) & (r1_tarski (k10_xtuple_0 (k3_funct_5 C)) (k1_funct_2 A (k10_xtuple_0 C)))) ) ) ) ) ) ).
tt(t35_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  ( ((v1_relat_1 (k1_funct_1 C A)) & (v1_funct_1 (k1_funct_1 C A)))  & (r2_hidden B (k9_xtuple_0 (k6_funct_6 C)))) )  =>  ((k5_funct_6 C A B) = (k5_funct_6 (k6_funct_6 C) B A)) ) ) ) ) ) ).
tt(t35_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k2_funct_7 A B (k1_funct_1 A B)) = A) ) ) ) ).
tt(t35_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_funct_8 A k1_numbers k1_numbers) => (v6_funct_8 (k37_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t35_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_int_1 C))  => (v1_funct_9 (k9_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k19_sin_cos B) A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ).
tt(t35_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  ((v21_functor0 (k15_functor0 A B C) B A) & (v8_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ) ).
tt(t35_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D B C) & (m2_functor0 D B C))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F C A) & (m2_functor0 F C A))  =>  (! [G:$i] :  ((m1_functor3 G B C D E) =>  ((r1_functor3 B C D E) =>  ((r1_functor3 B A (k1_functor3 B C A D F) (k1_functor3 B C A E F)) & (m1_functor3 (k5_functor3 B C A D E G F) B A (k1_functor3 B C A D F) (k1_functor3 B C A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B (k2_fuzzy_1 A C D)) & (r2_funct_2 A k1_numbers (k1_fuzzy_1 A B D) (k4_fuzzy_1 A)))  => (r1_fuzzy_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t35_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k3_fuzzy_2 A B C)) (k2_fuzzy_2 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C)))) ) ) ) ) ) ).
tt(t35_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (v1_int_1 (k1_fvaluat1 (k2_relset_1 k7_numbers B)))) ) ) ) ) ).
tt(t35_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k8_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A C) (k5_finseq_2 (u1_struct_0 B) A D)) = (k5_finseq_2 (u1_struct_0 B) A (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ).
tt(t35_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (~ (v1_xboole_0 (k29_gate_1 A B C D E F G)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) & (v1_xboole_0 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_gcd_1 A B (k5_gcd_1 A B C D) E) = (k5_gcd_1 A B C (k5_gcd_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) &  ((r1_xxreal_0 (k3_finseq_1 F) B) & (r1_xxreal_0 (k3_finseq_1 F) C)) )  =>  ((k10_genealg1 E F G A B C D) = (k7_genealg1 E F G D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) &  ((r1_xxreal_0 (k3_finseq_1 F) B) & (r1_xxreal_0 (k3_finseq_1 F) D)) )  =>  ((k10_genealg1 E F G A B C D) = (k7_genealg1 E F G C)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 F) A) &  ((r1_xxreal_0 (k3_finseq_1 F) C) & (r1_xxreal_0 (k3_finseq_1 F) D)) )  =>  ((k10_genealg1 E F G A B C D) = (k7_genealg1 E F G B)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 F) B) &  ((r1_xxreal_0 (k3_finseq_1 F) C) & (r1_xxreal_0 (k3_finseq_1 F) D)) )  =>  ((k10_genealg1 E F G A B C D) = (k7_genealg1 E F G A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (D = E) )  &  ((k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A D E)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k13_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t35_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((k6_subset_1 (k7_glib_000 A) (k20_glib_000 A B)) = (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) B))) ) ) ) ).
tt(t35_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D A) =>  (! [E:$i] :  ((m3_glib_001 E B) =>  (! [F:$i] :  ((m3_glib_001 F B) =>  ( ( (C = E)  &  (D = F) )  =>  ((k7_glib_001 A C D) = (k7_glib_001 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ( (~ (v5_glib_002 B A))  <=>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) => (r1_ordinal1 (k4_glib_002 C) (k4_glib_002 A))) ) ) ) ) ) ) ).
tt(t35_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v2_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k5_glib_003 A) = (k5_glib_003 (k12_glib_003 A B C))) ) ) ) ) ).
tt(t35_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k12_glib_004 A (k15_glib_004 A (k16_glib_004 A) B)) = k1_xboole_0)  <=>  ((k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) = (k1_glib_002 A (k10_subset_1 (k6_glib_000 A)))) ) ) ) ) ) ).
tt(t35_goboard1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) &  ( (~ (r1_xxreal_0 (k1_matrix_1 A) 1))  &  ((r1_xxreal_0 1 (k3_finseq_1 B)) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 A (k1_matrix_1 A)) 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard1 A (k1_matrix_1 A)) (k1_matrix_1 (k3_goboard1 A (k1_matrix_1 A)))))) &  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k3_goboard1 A (k1_matrix_1 A))) & (r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k1_matrix_1 B)))  => (r2_hidden (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)))) ) ) ) ) ).
tt(t35_goboard7,ax, (! [A:$i] :  ( ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) )  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) 4))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1) (k19_euclid 1 (k4_xcmplx_0 1))) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 2)) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers))) (k3_topreal1 2 A))) ) ).
tt(t35_gobrd11,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 C)) & (r1_xxreal_0 B (k1_matrix_1 C)))  =>  ((k3_goboard5 C A B) = (k2_pre_topc (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)))) ) ) ) ) ) ) ) ).
tt(t35_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((k4_gobrd13 D E A) = (k3_goboard5 E B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  => (r1_jordan2c 2 (k3_topreal1 2 A) (k3_goboard9 A))) ) ).
tt(t35_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ( ((r6_calcul_1 A B D E F) & (r1_tarski C B))  => (r6_calcul_1 A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  ( ((r2_graph_2 A C) & (r1_graph_2 A B C))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  ((k1_funct_1 B D) = (k1_funct_1 B (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (u4_struct_0 B)) =>  ( ((k1_funct_1 (u1_graph_1 (k8_graph_3 B C D)) A) = (k1_funct_1 (u1_graph_1 B) A))  &  ((k1_funct_1 (u2_graph_1 (k8_graph_3 B C D)) A) = (k1_funct_1 (u2_graph_1 B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t35_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  (~  ( (D = k1_xboole_0)  & (r3_graph_5 A D B C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k4_finseq_1 (k6_graphsp (k19_graphsp A) B)) = (k4_finseq_1 B)) ) ) ) ) ).
tt(t35_gr_cy_3,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( ((k6_int_1 (k3_xcmplx_0 A A) B) = 1)  &  ( (~ (r2_int_1 A 1 B))  &  (~ (r2_int_1 A (k4_xcmplx_0 1) B)) ) ) ) ) ) ) ) ).
tt(t35_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski C D) &  ((r2_hidden A B) & (r1_tarski (k3_xboole_0 B (k9_xtuple_0 D)) (k9_xtuple_0 C))) )  =>  ((k1_funct_1 D A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t35_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (? [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  & (r2_groeb_1 A B C E D)) ) ) ) ) ) ) ) ) ) ).
tt(t35_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [G:$i] :  ((m2_ideal_1 G (k11_polynom1 A C) F) =>  (! [H:$i] :  ((m2_ideal_1 H (k11_polynom1 A C) F) =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I A) &  ((v1_funct_1 I) &  ((v1_partfun1 I A) &  ((v4_valued_0 I) & (v2_pre_poly I)) ) ) ) )  =>  (! [J:$i] :  ((m1_subset_1 J k5_numbers) =>  ( ((r3_groeb_2 A B C D F G I) &  ( (H = (k2_rfinseq (u1_struct_0 (k11_polynom1 A C)) J G))  &  ( (E = (k4_rlvect_1 (k11_polynom1 A C) (k17_finseq_1 (u1_struct_0 (k11_polynom1 A C)) J G)))  & (r1_xxreal_0 J (k3_finseq_1 G))) ) )  => (r3_groeb_2 A B C (k6_polynom1 A C D E) F H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k5_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) D) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_groeb_3 A B C D (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ).
tt(t35_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k2_group_11 A B C) = (k2_group_11 A (k2_group_11 A B C) C)) ) ) ) ) ) ) ).
tt(t35_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k5_group_1 C (k22_binop_2 A B) D) = (k5_group_1 C B (k5_group_1 C A D))) ) ) ) ) ) ) ) ) ).
tt(t35_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_group_2 A B (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0)  &  ((k4_group_2 A B (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ) ) ) ).
tt(t35_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_group_3 A (k3_group_3 A B C) D) = (k3_group_3 A B (k2_group_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t35_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_group_2 A (k5_group_4 A B) (k5_group_4 A (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) (k1_group_1 A)))))) ) ) ) ).
tt(t35_group_5,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_5 B C (k5_group_1 B A D)) = (k6_algstr_0 B (k5_group_1 B (k4_xcmplx_0 A) (k2_group_3 B D C)) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ).
tt(t35_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_group_5 A C D E)) = (k3_group_5 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_group_1 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B)) (k5_group_7 A B C D)) = (k5_group_7 A B (k2_group_1 A C) (k2_group_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t35_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((m1_group_9 C A (k19_group_9 A B C D)) & (m1_group_9 D A (k19_group_9 A B C D))) ) ) ) ) ) ) ) ).
tt(t35_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((v2_group_10 B A) &  ((k2_groupp_1 A B) = k6_numbers) )  => (v3_groupp_1 B A)) ) ) ) ) ).
tt(t35_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  => (r1_xxreal_0 k6_numbers (k1_hausdorf A B C))) ) ) ) ) ) ) ).
tt(t35_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (! [F:$i] :  ( ((v7_ordinal1 F) &  (~ (v1_abian F)) )  =>  ( ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k3_finseq_1 B)) &  ( ((k1_funct_1 B E) = C)  &  ((k1_funct_1 B F) = D) ) ) )  =>  ((k2_helly A C D) = (k8_glib_001 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear F k1_complfld A B) &  ((v2_hermitan F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) F C (k5_algstr_0 B D E)) = (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) F C D) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) F C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ( (D = (k1_heyting2 k5_numbers (k6_domain_1 k5_numbers A) C))  &  (C = B) )  =>  (! [E:$i] :  ((r2_hidden E B) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 F (k1_nat_1 (k1_xxreal_2 D) 1)))  & (r2_hidden (k1_domain_1 k5_numbers k5_numbers F A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ( ((k1_seq_1 (k1_taylor_2 k16_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B) C) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k10_real_1 (k8_real_1 C k32_sin_cos) 2)) (k2_newton B C)) (k3_newton C)))  &  ((k1_seq_1 (k1_taylor_2 k19_sin_cos (k2_rcomp_1 (k1_real_1 A) A) B) C) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos (k10_real_1 (k8_real_1 C k32_sin_cos) 2)) (k2_newton B C)) (k3_newton C))) ) ) ) ) ) ) ) ) ).
tt(t35_hilbasis,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  (~ (v1_finset_1 B)) )  =>  (~ (v6_ideal_1 (k11_polynom1 B A))) ) ) ) ) ).
tt(t35_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k3_hilbert1 A C) (k3_hilbert1 A (k4_hilbert1 B C)))) k6_hilbert1)) ) ) ) ) ) ).
tt(t35_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 (k3_hilbert2 A))) =>  ((k5_trees_2 (k3_hilbert2 A) B) = (k3_hilbert2 (k3_trees_2 k1_hilbert1 (k3_hilbert2 A) B))) ) ) ) ) ).
tt(t35_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) => (r1_funct_2 (k3_hilbert3 C (k4_hilbert1 A B)) (k3_hilbert3 C (k4_hilbert1 A B)) (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B)) (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B)) (k5_hilbert3 C D (k4_hilbert1 A B)) (k16_funct_3 (k3_hilbert3 C A) (k3_hilbert3 C B) (k3_hilbert3 C A) (k3_hilbert3 C B) (k5_hilbert3 C D A) (k5_hilbert3 C D B)))) ) ) ) ) ) ) ) ).
tt(t35_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) => (r1_hurwitz A B (k3_hurwitz A C 1))) ) ) ) ) ) ) ).
tt(t35_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) &  ((r1_idea_1 A (k1_recdef_1 B 4)) &  ((r1_idea_1 A (k1_recdef_1 C 1)) &  ((r1_idea_1 A (k1_recdef_1 C 2)) &  ((r1_idea_1 A (k1_recdef_1 C 3)) &  ((r1_idea_1 A (k1_recdef_1 C 4)) &  ( ((k1_recdef_1 D 1) = (k10_idea_1 A (k1_recdef_1 C 1)))  &  ( ((k1_recdef_1 D 2) = (k6_idea_1 A (k1_recdef_1 C 2)))  &  ( ((k1_recdef_1 D 3) = (k6_idea_1 A (k1_recdef_1 C 3)))  &  ( ((k1_recdef_1 D 4) = (k10_idea_1 A (k1_recdef_1 C 4)))  &  ( ((k1_recdef_1 D 5) = (k1_recdef_1 C 5))  &  ((k1_recdef_1 D 6) = (k1_recdef_1 C 6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_partfun1 k14_idea_1 k14_idea_1 k14_idea_1 k14_idea_1 (k21_idea_1 A C) (k22_idea_1 A D)) B) = B) ) ) ) ) ) ) ) ) ) ).
tt(t35_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_ideal_1 C A B) =>  (? [D:$i] :  ((m2_finseq_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) & (r1_ideal_1 A B C D)) ) ) ) ) ) ) ) ).
tt(t35_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r1_incsp_1 A D (k1_incsp_1 A B C)) =>  ( (B = C)  | (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t35_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) &  ((v3_cat_5 D) & (l1_cat_1 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E C D) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 D) (u4_struct_0 D) (u1_graph_1 D) (u2_graph_1 D) (u1_cat_1 D) (k7_isocat_1 D)) =>  ((k16_index_1 A C B (k14_index_1 C D D E F)) = (k16_index_1 A D (k15_index_1 A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_instalg1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  & (m1_instalg1 B A))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (~  ((r1_msualg_3 A C D E) &  (! [F:$i] :  ((m2_pboole F (u1_struct_0 B) (u3_msualg_1 B (k2_instalg1 A B C)) (u3_msualg_1 B (k2_instalg1 A B D))) =>  (~  ( (F = (k5_relat_1 E (u1_struct_0 B)))  & (r1_msualg_3 B (k2_instalg1 A B C) (k2_instalg1 A B D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 (k2_int_1 A) (k1_int_1 A)))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 (k2_int_1 A) (k1_int_1 A))) ) ) ) ) ).
tt(t35_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k1_relset_1 k5_numbers A)) &  ((r2_hidden C (k1_relset_1 k5_numbers A)) & (r1_xxreal_0 1 (k3_finseq_1 A))) )  =>  ( (B = C)  | (r1_nat_d (k1_recdef_1 A C) (k3_wsierp_1 (k5_wsierp_1 k1_numbers k5_numbers B A)))) ) ) ) ) ) ) ) ).
tt(t35_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ( ( ((k3_int_2 A C) = 1)  &  ((k3_int_2 B C) = 1) )  =>  ((r1_xxreal_0 C 2) |  ((k2_int_5 (k4_nat_1 (k1_pepin A) B) C) = (k2_int_5 B C)) ) ) ) ) ) ) ) ) ).
tt(t35_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k2_int_6 (k4_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) C) (k2_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t35_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  (D = k6_numbers) )  &  ((k1_seq_1 C D) = (k1_real_1 (k10_real_1 1 (k5_square_1 D)))) ) ) ) )  &  ( ((k9_xtuple_0 C) = B)  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) )  =>  ((r2_hidden k6_numbers B) |  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) (k4_seq_4 A)) (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ).
tt(t35_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ( ((k1_seq_1 B D) = (k12_binop_2 1 (k11_binop_2 D (k9_binop_2 1 (k5_square_1 (k1_seq_1 k3_taylor_1 D))))))  &  ( (~ (r1_xxreal_0 (k1_seq_1 k3_taylor_1 D) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k3_taylor_1 D))) ) ) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k1_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t35_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 1 (k8_real_1 (k5_square_1 D) (k5_square_1 (k1_seq_1 k19_sin_cos (k10_real_1 1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k29_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t35_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k1_seq_1 k16_sin_cos D)) (k5_square_1 D)) (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos D) D) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t35_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) D B) (k4_real_ns1 A) k1_numbers) & (v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) E C) (k4_real_ns1 A) k1_numbers))  =>  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) D E) (k3_xboole_0 B C)) (k4_real_ns1 A) k1_numbers) & (v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (k2_vfunct_1 k1_numbers (k4_real_ns1 A) D E) (k3_xboole_0 B C)) (k4_real_ns1 A) k1_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t35_integra1,ax, (! [A:$i] :  ( ((v5_valued_0 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 A)) & (r1_xxreal_0 B C))  =>  ((v5_valued_0 (k3_finseq_6 k1_numbers A B C)) & (m2_finseq_1 (k3_finseq_6 k1_numbers A B C) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t35_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (v3_xxreal_2 (k1_rvsum_1 (k8_integra1 A B)))) ) ) ) ) ).
tt(t35_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r1_tarski (k10_xtuple_0 (k8_funcop_1 k1_numbers k1_numbers A)) k1_numbers)) ) ).
tt(t35_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k8_real_1 k32_sin_cos 2)))  => (r1_integra9 A k16_sin_cos k19_sin_cos)) ) ) ).
tt(t35_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  => (r1_interva1 A (k3_interva1 A B (k4_interva1 A B C)) B)) ) ) ) ) ) ).
tt(t35_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((r2_hidden (k4_intpro_1 A B) k8_intpro_1) <=> (r2_hidden (k4_intpro_1 B A) k8_intpro_1)) ) ) ) ) ).
tt(t35_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k3_xcmplx_0 (k9_newton A) (k4_series_1 (k1_valued_0 k1_numbers k5_irrat_1 (k2_nat_1 A 1)))) k6_numbers)) ) ) ).
tt(t35_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ((r2_nattra_1 A B C D) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k4_isocat_1 A B B C D E (k10_cat_1 B)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k8_cat_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D E) F) = (k9_cat_2 B C (k8_cat_1 A B D F) (k8_cat_1 A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_isomichi,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r3_xboole_0 A B) &  ( (~ (r1_tarski A B))  &  (~ (r2_xboole_0 B A)) ) ) ) ) ) ).
tt(t35_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid A) C D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers E) &  ((r1_xxreal_0 E 1) &  (B = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) C (k9_real_1 1 E)) (k1_rlvect_1 (k15_euclid A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ((v5_pre_topc D (k1_pre_topc (k15_euclid 2) A) k3_topmetr) &  ((v5_pre_topc E (k1_pre_topc (k15_euclid 2) A) k3_topmetr) &  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  ( ((r2_hidden (k19_euclid F G) A) &  ( (H = (k1_funct_1 D (k19_euclid F G)))  &  (I = (k1_funct_1 E (k19_euclid F G))) ) )  =>  ((k1_funct_1 C (k19_euclid F G)) = (k19_euclid H I)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k8_real_1 (k18_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid C) (k18_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t35_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_1_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k3_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t35_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = a_0_6_jgraph_5)  =>  ((k9_jordan6 A) = (a_1_1_jgraph_5 A)) ) ) ) ).
tt(t35_jgraph_6,ax, (a_0_13_jgraph_6 = a_0_14_jgraph_6) ).
tt(t35_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid C) F) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) H)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan12,ax, (! [A:$i] :  ( ((v1_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ((v1_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ( ((v1_topreal1 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  (! [D:$i] :  ( ((v1_topreal1 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2))))  =>  ( ( ( (~ (v1_xboole_0 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)))  &  ( (~ (v3_funct_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)))  &  ((v1_finseq_6 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v2_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v1_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v2_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) & (m2_finseq_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  &  ( ( (~ (v1_xboole_0 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)))  &  ( (~ (v3_funct_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)))  &  ((v1_finseq_6 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D) (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)) &  ((v2_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)) &  ((v1_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)) &  ((v2_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D)) & (m2_finseq_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  &  ((r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 D)) &  ((r1_xboole_0 (k3_topreal1 2 B) (k3_topreal1 2 C)) & (r2_jordan12 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B) (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k1_funct_1 A 1) = E)  &  ( ((k1_funct_1 A (k3_finseq_1 A)) = F)  &  ( ((k1_funct_1 C 1) = G)  &  ( ((k1_funct_1 C (k3_finseq_1 C)) = H)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D 1))  &  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B))) &  ((r2_hidden G (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 C) (k3_topreal1 2 D))) &  ( (? [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) I) &  ((r2_hidden G I) & (r2_hidden H I)) ) ) )  &  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r3_connsp_1 (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) C D))) I) &  ((r2_hidden E I) & (r2_hidden F I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_jordan1h A B) & (r1_xxreal_0 B C))  => (r1_tarski (k3_goboard9 (k1_jordan13 A B)) (k3_goboard9 (k1_jordan13 A C)))) ) ) ) ) ) ) ).
tt(t35_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 D A)) (k2_nat_1 C 1)) |  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 1)) 2) 1))  & (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 1)) 2) (k1_matrix_1 (k1_jordan8 D B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_6_jordan1 A B C D))  &  (F = (a_4_7_jordan1 A B C D)) )  => (r1_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B (k1_matrix_1 (k1_jordan8 A C))) => (r1_tarski (k3_goboard5 (k1_jordan8 A C) k6_numbers B) (k2_jordan2c 2 A))) ) ) ) ) ) ) ).
tt(t35_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 A B))))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k1_jordan1a (k1_jordan8 A B)) C)) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) ) ) ) ) ) ) ) ) ).
tt(t35_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (m2_subset_1 (k1_int_1 (k7_real_1 (k10_real_1 (k9_real_1 A 2) (k13_newton 2 (k7_nat_d B C))) 2)) k1_numbers k5_numbers)) ) ) ) ) ) ) ).
tt(t35_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k2_jordan3 A B) (k3_finseq_1 (k2_jordan3 A B))) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t35_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  ( ( (C = (k19_euclid k6_numbers k6_numbers))  &  (D = A) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 B (k17_euclid A) B (k18_euclid A)) (k9_metric_1 (k14_euclid 2) C 1)) = (k9_metric_1 (k14_euclid 2) D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan21,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ((v1_jordan21 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k2_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k9_pscomp_1 A))) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan21 A))) ) ) ).
tt(t35_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_tarski (k3_jordan19 A) A)) ) ).
tt(t35_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r2_hidden C (k3_topreal1 2 A)) &  (B = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k1_jordan3 A C)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) C))) ) ) ) ) )  =>  ( (C = (k1_funct_1 A 1))  | (r1_jordan3 B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) C)) ) ) ) ) ) ) ) ).
tt(t35_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) & (v9_rltopsp1 (k2_struct_0 (k15_euclid A)) (k15_euclid A))) ) ) ) ).
tt(t35_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ( (B = (k1_funct_1 A 1))  | (v4_topreal1 (k3_jordan3 A B))) ) ) ) ) ) ).
tt(t35_jordan4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A))) ) )  => (r1_tarski (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (k3_topreal1 2 A))) ) ) ) ) ) ) ).
tt(t35_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k17_euclid D) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B C)))  & (r2_hidden D (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k2_rcomp_1 B C))  => (v3_pre_topc A k3_topmetr)) ) ) ) ) ) ) ).
tt(t35_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  &  ( (C = (a_2_3_jordan_a A B))  &  ((k5_jordan_a A B) = (k2_xxreal_2 C)) ) ) ) ) ) ) ) ).
tt(t35_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A C D) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A C D))  => (r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A C D) & (r2_abian (u1_struct_0 A) C B))  =>  (! [E:$i] :  ((v3_ordinal1 E) => (r3_lattices A C (k6_knaster A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) = (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) ) ).
tt(t35_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) C D) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B D))) ) )  => (r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_kurato_2 (k15_euclid 2) A) (k2_kurato_2 (k15_euclid 2) B)) (k2_kurato_2 (k15_euclid 2) C))) ) ) ) ) ) ) ).
tt(t35_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  ((k5_matrix_6 A B C) = (k1_matrix_7 A B (k5_matrix_1 A (u1_struct_0 B) (k7_laplace A B C)) (k11_algstr_0 B (k12_matrix_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t35_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (~  (D = k1_xboole_0) )  =>  ((k3_lattices A B (k2_lattice2 C A D E)) = (k2_lattice2 C A D (k10_funcop_1 (u1_struct_0 A) C (u2_lattices A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] : (r3_lattices A (k3_lattices A B (k16_lattice3 A C)) (k16_lattice3 A (a_3_4_lattice3 A B C)))) ) ) ) ) ).
tt(t35_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m2_lattice4 B A) =>  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t35_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) )  =>  ( ((v1_lattice5 D A B) & (v3_lattice5 D A B))  =>  (! [E:$i] :  ((m1_lattice5 E A B D) =>  ((r1_ordinal1 C (k7_lattice5 A B D)) => (v3_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow11 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (r1_lattice8 A 2)) ) ).
tt(t35_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v3_lexbfs (k16_lexbfs A))) ) ).
tt(t35_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A))))) =>  ((k4_fuzzy_4 A A A (k5_lfuzzy_0 (k2_zfmisc_1 A A) (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) C)) B) = (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) (a_3_2_lfuzzy_1 A B C))) ) ) ) ) ) ) ).
tt(t35_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) )  | (v1_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ) ).
tt(t35_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r5_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t35_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((k8_relat_1 B (k1_tarski k6_numbers)) = k1_xboole_0) )  =>  ( ((k1_limfunc3 B A) = k6_numbers)  |  ((r1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k1_limfunc3 B A))) ) ) ) ) ) ) ) ).
tt(t35_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  ((v4_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t35_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (r1_lmod_6 A (k1_mod_3 A B (k9_subset_1 (u1_struct_0 B) C D)) (k2_vectsp_5 A B (k1_mod_3 A B C) (k1_mod_3 A B D)))) ) ) ) ) ) ) ) ).
tt(t35_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 A B))) =>  ( (E = (k1_algstr_0 (k16_lopban_1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k17_lopban_1 A B E F) = (k3_rlvect_1 B (k17_lopban_1 A B C F) (k17_lopban_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 C 1) &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((k1_seq_1 (k4_normsp_0 A B) D) = (k10_real_1 1 (k4_power D C))) ) ) )  & (v2_lopban_3 B A)) ) ) ) ) ) ) ) ) ).
tt(t35_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ( ((k10_lopban_4 A (k3_rlvect_1 A B C)) = (k6_algstr_0 A (k10_lopban_4 A B) (k10_lopban_4 A C)))  &  ( ((k10_lopban_4 A (k3_rlvect_1 A C B)) = (k6_algstr_0 A (k10_lopban_4 A C) (k10_lopban_4 A B)))  &  ( ((k10_lopban_4 A (k3_rlvect_1 A B C)) = (k10_lopban_4 A (k3_rlvect_1 A C B)))  & (r1_lopban_4 A (k10_lopban_4 A B) (k10_lopban_4 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t35_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  => (r1_filter_1 A (k12_lopclset A))) ) ).
tt(t35_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k12_lpspace1 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k12_lpspace1 A B C))) =>  ( ( (D = F)  &  (E = G) )  =>  ((k3_valued_1 A k1_numbers k1_numbers D E) = (k1_algstr_0 (k12_lpspace1 A B C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  (~  ((r2_hidden D (k1_lpspace2 A B C E)) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A F)) = k6_numbers)  &  ( ((k1_relset_1 A D) = F)  & (r1_mesfunc6 A B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A (k3_hilbert1 B C)) (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 A C))) k13_ltlaxio1)) ) ) ) ) ) ).
tt(t35_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A C B) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t35_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k6_rusub_4 A B (k9_subset_1 (u1_struct_0 A) C D)) (k9_subset_1 (u1_struct_0 A) (k6_rusub_4 A B C) (k6_rusub_4 A B D)))) ) ) ) ) ) ) ) ).
tt(t35_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((v3_matrix10 B) => (v4_matrix10 (k2_matrix10 A B))) ) ) ) ) ).
tt(t35_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B B) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) E (k10_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E A) D))) = (k8_group_1 C D (k12_matrix_3 B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 B))))  =>  (! [G:$i] :  ((m1_matrix_2 G (k12_matrix_2 A)) =>  ( (C = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) k5_numbers k5_numbers G D))  =>  ( ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) F A A C E)) = (k14_matrix_2 B A (k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) F A A D E)) G))  &  ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) F A A E C)) = (k14_matrix_2 B A (k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) F A A E D)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  ( ( ((k3_finseq_1 D) = A)  &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A)) )  =>  ( ((k13_fvsum_1 C D (k3_matrix14 C A B)) = (k1_funct_1 D B))  &  ((k13_fvsum_1 C D (k3_matrix14 C A B)) = (k7_partfun1 (u1_struct_0 C) D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  ((r2_hidden C (k4_matrix15 A D E)) =>  ((r2_hidden (k6_matrix_3 A C B) (k4_matrix15 A D (k6_matrix_3 A E B))) & (r2_hidden C (k4_matrix15 A (k6_matrix_3 A D B) (k6_matrix_3 A E B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v4_matrix16 B (u1_struct_0 A)) => (v4_matrix16 (k5_fvsum_1 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(t35_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l6_algstr_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) k1_xboole_0 A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) k1_xboole_0 B) =>  (D = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k2_matrix_3 A B) = (k2_matrix_3 A C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_matrix_6 A B C D) <=>  ((k4_matrix_6 A B (k2_matrix_6 A B C D) (k2_matrix_6 A B C D)) = (k2_matrix_6 A B (k2_matrix_6 A B (k2_matrix_6 A B (k4_matrix_6 A B C C) (k4_matrix_6 A B C D)) (k4_matrix_6 A B C D)) (k4_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_xxreal_0 1 A) =>  ((k10_matrix_3 A B (k5_matrix_1 A (u1_struct_0 B) D) (k3_matrix_7 A C)) = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) k5_numbers (u1_struct_0 B) (k3_matrix_7 A C) (k10_matrix_3 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((r1_matrix_8 A B C D) & (v1_matrix_8 D A B))  => (v1_matrix_8 C A B)) ) ) ) ) ) ) ) ) ).
tt(t35_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  (~  ( (A = (k3_finseq_4 k5_numbers 2 3 1))  & (v4_matrix_2 A 3)) ) ) ) ).
tt(t35_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k5_matrixc1 (k9_seq_4 A B) C) = (k9_seq_4 (k5_matrixc1 A C) (k5_matrixc1 B C))) ) ) ) ) ) ) ) ).
tt(t35_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k13_matrixj1 A B (k3_matrixj1 A C D)) = (k13_matrixj1 A B (k3_matrixj1 A (k4_matrixj1 A (k13_matrixj1 A B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t35_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ((k5_matrixr1 A (k4_matrixr1 B)) = (k3_matrixr1 A B)) ) ) ) ) ).
tt(t35_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) => (m1_matrix_1 (k11_finseq_1 (k3_finseq_4 A B C D) (k3_finseq_4 A E F G) (k3_finseq_4 A H I J)) A 3 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((k1_matrix_1 C) = (k3_finseq_1 D)) )  =>  ((k4_matrix_3 B (k2_matrix15 (u1_struct_0 B) (k8_matrix_1 (u1_struct_0 B) C A)) D) = (k2_matrix15 (u1_struct_0 B) (k8_matrix_1 (u1_struct_0 B) (k4_matrix_3 B C D) A))) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (D = (k4_rlvect_1 B (k5_matrlin A B (k9_matrlin A B C D) C))) ) ) ) ) ) ) ) ) ).
tt(t35_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_matroid0 A (k6_matroid0 A B)) = (k6_matroid0 A B)) ) ) ) ) ).
tt(t35_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 k2_vectsp_1)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( (A = C)  &  (B = D) ) )  =>  ((k14_rvsum_1 A B) = (k11_fvsum_1 k2_vectsp_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 k2_vectsp_1) C B) =>  ( ((k1_funct_1 (k3_matrtop1 (k2_xcmplx_0 A C) B (k8_matrlin (u1_struct_0 k2_vectsp_1) A C B E F)) (k7_finseq_1 D (k5_finseq_2 k1_numbers C k6_numbers))) = (k1_funct_1 (k3_matrtop1 A B E) D))  &  ((k1_funct_1 (k3_matrtop1 (k2_xcmplx_0 C A) B (k8_matrlin (u1_struct_0 k2_vectsp_1) C A B F E)) (k7_finseq_1 (k5_finseq_2 k1_numbers C k6_numbers) D)) = (k1_funct_1 (k3_matrtop1 A B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v13_vectsp_1 C (k15_euclid B) (k15_euclid B)) &  ((v1_topreal9 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) ) )  =>  (~  ((v1_matrtop3 C (k3_matrix13 A)) &  ((v2_matrtop3 C B) &  ( (~  ((k3_matrtop3 B C) = (k1_matrtop3 B A)) )  &  (~  ((k3_matrtop3 B C) = (k12_matrix_1 k2_vectsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  ( ((r2_pboole A C (k2_mboolean A (k2_pboole A B D))) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E D) => (r6_pboole A (k3_pboole A E C) (k1_pboole A))) ) ) )  => (r2_pboole A C (k2_mboolean A B))) ) ) ) ) ) ) ) ).
tt(t35_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_zfmisc_1 (k1_tarski A) (k1_tarski B) (k1_tarski C)) = (k1_tarski (k3_xtuple_0 A B C))) ) ) ) ).
tt(t35_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v4_card_3 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( (! [E:$i] :  ((r2_hidden E D) => (r2_hidden E B)) )  =>  ((r2_hidden (k5_setfam_1 A D) B) & (r2_hidden (k6_setfam_1 A D) B)) ) ) ) ) ) ) ) ) ).
tt(t35_measure6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden C (k6_setfam_1 A (k7_relset_1 (k9_setfam_1 B) (k9_setfam_1 A) (k3_measure6 A B E) D))) => (r2_hidden (k1_funct_1 E C) (k6_setfam_1 B D))) ) ) ) ) ) ) ) ).
tt(t35_measure8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((v1_measure8 C A B) =>  ( (! [D:$i] :  ((m2_measure8 D A B) =>  (~  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~ (r1_xxreal_0 k1_supinf_1 (k1_mesfunc9 C (k1_measure8 A B D E)))) ) )  &  (A = (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) D))) ) ) ) )  |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k9_prob_1 A B) k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A (k9_prob_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k9_prob_1 A B) k7_numbers)))) ) ) ) )  =>  ((r1_measure8 A B (k9_prob_1 A B) C D) =>  (D = (k2_partfun1 (k1_measure4 A (k9_measure8 A B C)) k7_numbers (k3_measure4 A (k9_measure8 A B C)) (k9_prob_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k7_member_1 (k5_xboole_0 A B)) = (k5_xboole_0 (k7_member_1 A) (k7_member_1 B))) ) ) ) ) ).
tt(t35_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v5_membered B))  => (v5_membered (k1_setfam_1 A))) ) ) ).
tt(t35_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  (C = (k1_funct_4 (k7_memstr_0 A B (k5_memstr_0 A B C)) (k6_memstr_0 A B C))) ) ) ) ) ) ) ) ).
tt(t35_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r2_mesfun6c A B C D) & (r2_mesfun6c A B C E))  => (r2_mesfun6c A B C (k46_valued_1 A k2_numbers k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ( (E = (k1_relset_1 A D))  & (r1_mesfun6c A B D E)) ) )  & (r3_mesfunc6 A B C (k55_valued_1 A k2_numbers D))) ) ) ) ) ) ) ) ) ) ).
tt(t35_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ((v1_mesfunc8 D A k2_numbers) &  ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k2_numbers D k6_numbers))) & (r2_hidden B C)) )  =>  ((v2_comseq_2 (k10_comseq_3 (k9_mesfun7c A D B))) <=> (v2_comseq_2 (k9_mesfun7c A (k3_mesfun9c A D) B))) ) ) ) ) ) ) ) ) ).
tt(t35_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k9_xtuple_0 C)))  => (r2_hidden (k9_subset_1 A (k9_subset_1 A D (k17_mesfunc1 A C k2_supinf_1)) (k15_mesfunc1 A C k1_supinf_1)) B)) ) ) ) ) ) ) ) ) ).
tt(t35_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ( ((k1_relset_1 k5_numbers D) = (k1_relset_1 k5_numbers E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 E F) = (k9_subset_1 A (k1_funct_1 D F) C)) ) ) ) )  =>  ((v1_prob_2 E) & (m2_finseq_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) =>  ((r1_xxreal_0 (k1_seq_1 (k19_rfunct_3 A B) C) k6_numbers) |  ((k1_seq_1 (k18_rfunct_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t35_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers C E))) )  =>  ((v2_mesfunc9 C A) & (r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t35_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  ((k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) B C) = (k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) C B)) ) ) ) ) ) ) ).
tt(t35_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k8_midsp_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t35_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_mmlquery A (k23_mmlquery A C D) B) = (k3_mmlquery A D (k1_mmlquery A C B))) ) ) ) ) ) ) ) ).
tt(t35_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v8_mod_4 C A B) <=> (v7_mod_4 (k7_mod_4 A B C) A (k2_mod_4 B))) ) ) ) ) ) ) ).
tt(t35_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  (! [D:$i] :  ((m1_subset_1 D k6_modal_1) =>  ( ((k12_modal_1 A B) = (k12_modal_1 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F D) => (r3_modelc_1 A B C F E)) ) )  => (r1_tarski (k51_modelc_1 A B C D) (k51_modelc_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r2_modelc_2 A B) & (r2_modelc_2 B C))  => (r2_modelc_2 A C)) ) ) ) ) ) ) ).
tt(t35_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r5_modelc_3 C B) & (r1_xxreal_0 1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r4_modelc_3 C (k10_modelc_3 (k1_funct_1 B A) C) (k10_modelc_3 (k1_funct_1 B (k1_nat_1 A 1)) C))) ) ) ) ) ) ) ) ).
tt(t35_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_int_2 A B) =>  ((k2_moebius1 (k4_nat_1 A B)) = (k11_binop_2 (k2_moebius1 A) (k2_moebius1 B))) ) ) ) ) ) ).
tt(t35_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ((v16_monoid_0 A) => (v16_monoid_0 B)) ) ) ) ) ).
tt(t35_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( (~  (A = B) )  =>  ((k1_relset_1 k5_numbers (k6_relat_1 (k1_tarski A) (k7_finseq_1 D (k9_finseq_1 B)))) = (k1_relset_1 k5_numbers (k6_relset_1 k5_numbers C (k1_tarski A) D))) ) ) ) ) ) ) ) ).
tt(t35_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ( (~ (v3_relat_1 C))  &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 B (k1_msafree3 B C)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden A (k1_funct_1 (k2_msafree3 B D) E)) => (r2_hidden (k4_tarski A E) (k10_xtuple_0 D)))  &  ((r2_hidden (k4_tarski A E) (k10_xtuple_0 D)) =>  ((r2_hidden A (k1_funct_1 (k2_msafree3 B D) E)) & (r2_hidden A (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_msaterm F A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finset_1 G) & (v3_trees_2 G)) ) )  =>  (~  ((r1_msaterm A B C (k6_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E) F) D G) &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) &  ((v1_finseq_1 H) & (v6_trees_3 H)) ) )  =>  (~  ( ((k3_finseq_1 H) = (k3_finseq_1 F))  &  ( (G = (k4_trees_4 (k1_funct_1 (k5_msualg_1 A E B) (k14_trees_3 H)) H))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((m1_dtconstr J (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (~  ((r2_hidden I (k4_finseq_1 F)) &  ( (J = (k1_funct_1 F I))  &  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v1_funct_1 K) &  ((v1_finset_1 K) & (v3_trees_2 K)) ) )  =>  (~  ( (K = (k1_funct_1 H I))  & (r1_msaterm A B C J D K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) => (m3_pboole (k3_pboole A C D) A (k1_mboolean A B))) ) ) ) ) ) ) ).
tt(t35_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) =>  ((k6_lattices (k17_msualg_2 A B)) = (k12_msualg_2 A B C)) ) ) ) ) ) ) ) ).
tt(t35_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_6 C A B) &  ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  => (r8_pboole (u1_struct_0 A) (k8_msualg_6 A B C) C)) ) ) ) ) ) ).
tt(t35_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D))) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) F)) =>  ( (G = (k3_msualg_4 A B C F H))  =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B C)) F) (k1_funct_1 (u3_msualg_1 A (k13_msualg_4 A B D)) F) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B C)) (u3_msualg_1 A (k13_msualg_4 A B D)) E F) G) = (k3_msualg_4 A B D F H)) ) ) ) ) ) ) )  => (r2_msualg_3 A (k13_msualg_4 A B C) (k13_msualg_4 A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_mycielsk (k5_mycielsk A)) = A) ) ) ).
tt(t35_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 11) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  (~  (A = 11) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~  (B = k6_numbers) )  &  (~  ((k1_funct_1 (k12_nat_3 B) A) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t35_nat_4,ax,(v1_int_2 163)).
tt(t35_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_nat_5 (k2_nat_5 A))) ) ).
tt(t35_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k7_nat_d A B) A)) ) ) ) ).
tt(t35_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_nattra_1 G A B E F) =>  (! [H:$i] :  ((m2_nattra_1 H A B C D) =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 (k11_nattra_1 A B))) =>  (! [J:$i] :  ((m1_subset_1 J (u4_struct_0 (k11_nattra_1 A B))) =>  ( ( (I = (k4_tarski (k4_tarski E F) G))  &  (J = (k4_tarski (k4_tarski C D) H)) )  =>  ((r2_hidden (k10_cat_2 (k11_nattra_1 A B) (k11_nattra_1 A B) J I) (k9_xtuple_0 (u1_cat_1 (k11_nattra_1 A B)))) <=> (r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((r1_ncfcont1 A B C D) => (r1_ncfcont1 A B (k2_vfunct_2 (u1_struct_0 A) B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))  => (r1_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t35_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_ndiff_1 B A C E) & (r1_ndiff_1 B A D E))  =>  ((r1_ndiff_1 B A (k6_vfunct_1 (u1_struct_0 B) A C D) E) &  ((k3_ndiff_1 B A (k6_vfunct_1 (u1_struct_0 B) A C D) E) = (k3_rlvect_1 (k16_lopban_1 B A) (k3_ndiff_1 B A C E) (k3_ndiff_1 B A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers B (k1_pdiff_1 1 1)) &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  & (r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) F (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B E))) ) ) )  =>  ((r1_nfcont_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) <=> (r1_nfcont_3 (k4_real_ns1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) (k3_rlvect_1 (k14_prvect_2 A) C D)) = (k3_rlvect_1 (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t35_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  ( (A = (k1_neckla_2 B C))  &  ((r1_subset_1 (u1_struct_0 B) (u1_struct_0 C)) & (r2_hidden (k1_domain_1 (u1_struct_0 B) (u1_struct_0 C) D E) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  => (r1_nat_d A (k9_newton A))) ) ) ).
tt(t35_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  => (r2_relset_1 (u1_struct_0 B) k1_numbers (k2_partfun1 (u1_struct_0 B) k1_numbers (k3_normsp_0 (u1_struct_0 B) C D) A) (k3_normsp_0 (u1_struct_0 B) C (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))) ) ) ) ) ) ) ).
tt(t35_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) <=>  (? [D:$i] :  ((v1_xreal_0 D) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r2_hidden E (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers (k1_euclid A) C B))) & (r2_hidden F (k1_relset_1 k1_numbers (k2_partfun1 k1_numbers (k1_euclid A) C B))))  => (r1_xxreal_0 (k12_euclid (k8_euclid A (k7_partfun1 (k1_euclid A) C E) (k7_partfun1 (k1_euclid A) C F))) (k11_binop_2 D (k18_complex1 (k10_binop_2 E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k7_normform A))) =>  ( ((r2_hidden B D) &  ((r2_hidden C E) & (r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C) (k7_normform A))) )  => (r2_hidden (k1_normform (k5_finsub_1 A) (k5_finsub_1 A) B C) (k10_normform A D E))) ) ) ) ) ) ) ) ) ) ).
tt(t35_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_normsp_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_normsp_2 A))) =>  ( ((r1_funct_2 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)) (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)) C D) &  (E = F) )  =>  ((r1_tmap_1 (k3_normsp_2 A) (k3_normsp_2 B) C E) <=> (r1_tmap_1 (k4_normsp_2 A) (k4_normsp_2 B) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (r2_lattice4 A (k6_openlatt (k17_openlatt A)) (k18_openlatt A))) ) ).
tt(t35_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_oppcat_1 D A B) =>  (! [E:$i] :  ((m1_oppcat_1 E B C) => (m2_cat_1 (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_orders_1 A B) & (r1_tarski C B))  => (r2_orders_1 A C)) ) ) ) ) ).
tt(t35_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B C) &  ((r2_wellord1 (u1_orders_2 A) C) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden E B) &  ((r2_hidden D C) & (r2_orders_2 A D E)) )  => (r2_hidden D B)) ) ) ) )  &  ( (~  (B = C) )  &  (~ (m1_orders_2 B A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~ (r2_xboole_0 A B))  &  ( (~  (A = B) )  &  (~ (r2_xboole_0 B A)) ) ) ) ) ) ) ) ).
tt(t35_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k11_ordinal2 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t35_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 (k11_ordinal2 A B) (k11_ordinal2 C B)) =>  ( (B = k1_xboole_0)  | (r1_ordinal1 A C)) ) ) ) ) ) ) ) ).
tt(t35_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden (k9_xtuple_0 A) B) & (r1_tarski (k10_xtuple_0 A) B))  => (r2_hidden (k4_ordinal2 A) B)) ) ) ) ) ).
tt(t35_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden A B) & (r2_hidden B (k2_ordinal5 A)))  =>  ((k2_ordinal5 B) = (k2_ordinal5 A)) ) ) ) ) ) ).
tt(t35_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ((r2_hidden (k1_ordinal1 A) (k9_xtuple_0 (k3_ordinal6 C))) &  ((r1_abian B C) & (r2_hidden (k1_funct_1 (k3_ordinal6 C) A) B)) )  => (r1_ordinal1 (k1_funct_1 (k3_ordinal6 C) (k1_ordinal1 A)) B)) ) ) ) ) ) ) ).
tt(t35_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t35_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_msualg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  =>  (! [D:$i] :  ( ((v2_msualg_4 D A (k8_osafree A B)) &  ((v3_msualg_4 D A (k8_osafree A B)) & (m1_osalg_4 D A (k8_osafree A B))) )  =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_pboole (u1_struct_0 A) C D) => (r1_tarski (k25_osafree A B C E) (k25_osafree A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) & (l3_osalg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_osalg_1 A C (k1_msualg_1 A B)) => (r6_osalg_1 A (k2_osalg_1 A B C) B)) ) ) ) ) ) ) ).
tt(t35_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v12_osalg_1 C A) & (m1_msualg_2 C A B)) )  =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A C)) =>  ((k10_osalg_2 A B D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t35_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_parsp_1 A B C B D) & (r1_parsp_1 A B C B E))  => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_parsp_2 A B C D E) & (r2_parsp_2 A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  => (r1_relset_1 C B (k1_partfun1 C A A B (k3_partfun1 D C A) (k3_partfun1 E A B)) (k3_partfun1 (k3_relat_1 D E) C B))) ) ) ) ) ) ) ).
tt(t35_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((v3_funct_1 (k2_partfun1 C B D A)) <=>  (? [E:$i] :  ((m1_subset_1 E B) &  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F (k9_subset_1 C A (k1_relset_1 C D))) =>  ((k7_partfun1 B D F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_setfam_1 (k10_eqrel_1 A) (k6_partit1 A))) ) ).
tt(t35_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k3_pboole A (k2_pboole A B C) (k2_pboole A B D)) B) => (r2_pboole A (k3_pboole A C D) B)) ) ) ) ) ) ) ) ).
tt(t35_pcomps_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) <=>  ((v6_metric_1 (g1_metric_1 A B)) &  ((v7_metric_1 (g1_metric_1 A B)) &  ((v8_metric_1 (g1_metric_1 A B)) &  ((v9_metric_1 (g1_metric_1 A B)) & (l1_metric_1 (g1_metric_1 A B))) ) ) ) ) ) ) ) ).
tt(t35_pcs_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k20_pcs_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k20_pcs_0 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_pcs_0 (k20_pcs_0 A) D E) | (r1_pcs_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r3_pdiff_3 B A) & (r3_pdiff_3 C A))  => (r3_pdiff_1 2 1 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A)) ) ) ) ) ) ) ).
tt(t35_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 B A) &  ((r3_pdiff_1 3 2 B A) &  ((r3_pdiff_1 3 3 B A) &  ((r3_pdiff_1 3 1 C A) &  ((r3_pdiff_1 3 2 C A) & (r3_pdiff_1 3 3 C A)) ) ) ) )  =>  ((k4_pdiff_4 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers B C) A) = (k7_euclid 3 (k4_pdiff_4 B A) (k4_pdiff_4 C A))) ) ) ) ) ) ) ) ).
tt(t35_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r8_pdiff_5 B A) =>  ((k8_pdiff_5 B A) = (k11_pdiff_1 3 2 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ) ).
tt(t35_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ( ( (C = D)  &  (E = F) )  =>  ((r3_pdiff_7 A B C E) <=> (r1_nfcont_1 (k4_real_ns1 A) (k4_real_ns1 B) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((r4_pdiff_7 A B D C) => (r4_pdiff_7 A B (k2_nfcont_4 B (k1_euclid A) D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k4_nat_d B A) = 1)  =>  ((r1_xxreal_0 A 1) |  ((k4_nat_d (k1_newton B C) A) = 1) ) ) ) ) ) ) ) ) ).
tt(t35_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  ((k3_relat_1 (k6_partfun1 (k9_funct_2 A k5_numbers)) (k7_pnproc_1 A C)) = (k7_pnproc_1 A C)) ) ) ) ) ) ).
tt(t35_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (m1_comptrig (k3_binop_2 (k11_binop_2 (k2_power B (k17_complex1 A)) (k21_sin_cos (k12_binop_2 (k9_binop_2 (k1_comptrig A) (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C)) B))) (k5_binop_2 (k11_binop_2 (k2_power B (k17_complex1 A)) (k18_sin_cos (k12_binop_2 (k9_binop_2 (k1_comptrig A) (k11_binop_2 (k11_binop_2 2 k32_sin_cos) C)) B))) k7_complex1)) A B)) ) ) ) ) ) ).
tt(t35_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  ((k3_bspace (k4_struct_0 (k17_polyform A B)) C) = (k4_struct_0 k2_bspace)) ) ) ) ) ) ) ).
tt(t35_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A B (k10_polynom3 A)) B)) ) ) ) ).
tt(t35_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k3_algseq_1 A B) (k3_algseq_1 A C)) (k3_algseq_1 A (k8_group_1 A B C)))) ) ) ) ) ) ).
tt(t35_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B C) =>  ((k4_matrix_3 A (k12_matrix_1 A B) D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t35_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r2_polyred A B C (k6_termord A B C D) D)) ) ) ) ) ) ) ) ).
tt(t35_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k3_power A B) 1)) ) ) ) ) ) ) ).
tt(t35_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v3_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v3_valued_0 D)) ) ) )  => (r6_pboole A (k11_pre_poly A (k11_pre_poly A B C) D) (k11_pre_poly A B (k11_pre_poly A C D)))) ) ) ) ) ) ) ).
tt(t35_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_prepower A 1) = A) ) ) ).
tt(t35_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ((m1_pre_topc A B) <=> (m1_pre_topc A (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))) ) ) ) ) ).
tt(t35_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_1 D A B) => (r1_xxreal_0 (k1_seq_1 D C) 1)) ) ) ) ) ) ) ) ).
tt(t35_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers))  => (r1_xxreal_0 (k10_real_1 (k9_real_1 (k7_real_1 (k1_seq_1 C D) (k1_seq_1 C E)) 1) (k1_seq_1 C E)) (k1_seq_1 (k3_prob_2 A B C E) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_prob_3 A (k3_prob_3 A C)) (k2_prob_3 A C))) ) ) ) ) ).
tt(t35_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((r2_hidden D (k4_prob_4 A B C)) <=>  (? [E:$i] :  (? [F:$i] :  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r1_tarski E D) &  ((r1_tarski D F) &  ((k1_funct_1 C (k6_subset_1 F E)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k8_cqc_lang A D C) (k8_cqc_lang A (k9_cqc_lang A B D) C))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t35_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A B (k1_projpl_1 A C D)) &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (~ (r1_incsp_1 A C (k1_projpl_1 A D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k18_pscomp_1 A)) A) = (k1_tarski (k18_pscomp_1 A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_pscomp_1 A) (k11_pscomp_1 A)) A) = (k1_tarski (k19_pscomp_1 A))) ) ) ) ).
tt(t35_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (~  ( (~ (r6_pboole A B (k1_pboole A)))  &  ( (~ (r6_pboole A B (k1_pzfmisc1 A C)))  &  ( (~ (r6_pboole A B (k1_pzfmisc1 A D)))  &  (~ (r6_pboole A B (k2_pzfmisc1 A C D))) ) ) ) )  => (r2_pboole A B (k2_pzfmisc1 A C D))) ) ) ) ) ) ) ) ).
tt(t35_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang2 B A) =>  ((v4_qc_lang1 B A) &  ((v2_qc_lang2 (k19_qc_lang1 A B) A) & (v2_qc_lang2 (k20_qc_lang1 A B) A)) ) ) ) ) ) ) ).
tt(t35_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A B (k12_qc_lang1 A)) = k1_xboole_0) ) ) ) ) ).
tt(t35_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m2_qc_lang4 D A B C) => (r2_hidden D (k4_qc_lang4 A B C))) ) ) ) ) ) ) ) ).
tt(t35_quatern2,ax, ((k4_struct_0 k15_quatern2) = k1_quatern2) ).
tt(t35_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) => (r1_xxreal_0 (k3_quatern2 (k26_quaterni (k26_quaterni A B) C)) (k7_real_1 (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k3_quatern2 C)))) ) ) ) ) ) ).
tt(t35_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = B)  =>  ( ((k17_quaterni (k10_quaterni A k12_quaterni)) = k6_numbers)  &  ( ((k18_quaterni (k10_quaterni A k12_quaterni)) = k6_numbers)  &  ( ((k19_quaterni (k10_quaterni A k12_quaterni)) = k6_numbers)  &  ((k20_quaterni (k10_quaterni A k12_quaterni)) = B) ) ) ) ) ) ) ) ) ).
tt(t35_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  ((k1_algstr_0 (k19_quofield A) B C) = (k1_binop_1 (k15_quofield A) B C)) ) ) ) ) ) ) ).
tt(t35_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_random_1 B A (k1_random_1 A)) =>  (? [C:$i] :  ((m2_finseq_1 C k1_numbers) &  (? [D:$i] :  ((m2_finseq_1 D A) &  ( ((k3_finseq_1 C) = (k5_card_1 A))  &  ((v2_funct_1 D) &  ( ((k2_relset_1 A D) = A)  &  ( ((k3_finseq_1 D) = (k5_card_1 A))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_seq_1 C E) = (k1_seq_1 B (k1_funct_1 D E))) ) ) )  &  ((k8_random_1 A (k1_random_1 A) (k2_random_1 A) B) = (k13_complex1 (k18_rvsum_1 C) (k5_card_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_xboole_0 D (k1_vectsp_6 A B C)) =>  ( (D = k1_xboole_0)  |  ((k5_ranknull A B C D) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 1 A))  & (r1_xxreal_0 (k1_rat_1 A) (k2_rat_1 A))) )  &  (~  ( (~ (r1_xxreal_0 (k1_rat_1 A) (k2_rat_1 A)))  & (r1_xxreal_0 1 A)) ) ) ) ) ).
tt(t35_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_polynom4 A (k5_ratfunc1 A B) C) = (k4_struct_0 A)) )  =>  ((k13_ratfunc1 A (k6_ratfunc1 A B) C) = (k13_ratfunc1 A B C)) ) ) ) ) ) ) ) ).
tt(t35_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k4_rcomp_1 A B))  =>  ((r1_xxreal_0 B A) |  ((k2_tops_1 k2_topalg_2 C) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ).
tt(t35_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_int_1 A) = (k5_real_1 A (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers))) ) ) ).
tt(t35_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 C) = (k5_card_1 B)) )  =>  ((r2_classes1 (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A))) &  ( ((k20_rfunct_3 C (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) C) = (k20_rfunct_3 B (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B))  &  ((k21_rfunct_3 C (k19_rfunct_3 C (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A)) C) = (k21_rfunct_3 B (k19_rfunct_3 B (k15_valued_1 B k1_numbers D A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((k2_relat_1 (k3_relat_1 A B)) = (k3_relat_1 (k2_relat_1 B) (k2_relat_1 A))) ) ) ) ) ).
tt(t35_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 D)) => (m1_subset_1 (a_6_0_relset_2 A B C D E F) (k1_zfmisc_1 (k1_zfmisc_1 E)))) ) ) ) ) ) ) ) ).
tt(t35_revrot_1,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (r1_xxreal_0 1 C))  =>  ((r1_xxreal_0 (k4_finseq_4 A B) C) |  ((k5_goboard5 A C) = (k5_goboard5 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A B) (k7_nat_d (k2_nat_1 C (k3_finseq_1 A)) (k4_finseq_4 A B)))) ) ) ) ) ) ) ) ) ).
tt(t35_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( (~ (r2_hidden B (k1_relat_1 A)))  => (r4_rewrite1 A B B)) ) ) ) ).
tt(t35_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r3_rewrite2 A B C D) & (r3_rewrite2 A B D E))  => (r3_rewrite2 A B C E)) ) ) ) ) ) ) ) ) ) ).
tt(t35_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (~  ((r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C D)) (k1_rewrite3 E F G)) &  (! [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 E)) =>  (! [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 E)) =>  (~  ( (H = D)  &  ((r1_rewrite3 F G A I C) &  (B = (k1_flang_1 E I H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k4_rfunct_1 (k1_rfunct_1 A B)) = (k1_rfunct_1 (k5_relat_1 B (k9_xtuple_0 (k4_rfunct_1 B))) A)) ) ) ) ) ).
tt(t35_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_xxreal_0 k6_numbers B))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A)))  &  ( ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_xxreal_0 B k6_numbers))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ) ).
tt(t35_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k8_relset_1 A k1_numbers B (k1_tarski C)) = (k8_relset_1 A k1_numbers (k18_rfunct_3 A B) (k1_tarski C))) ) ) ) ) ) ) ) ).
tt(t35_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v8_valued_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_numbers)) =>  ( (C = (a_2_0_rinfsup1 A B))  =>  ((k4_seq_4 C) = (k1_seq_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t35_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v7_valued_0 A) &  (k1_supinf_1 = (k1_rinfsup2 A)) )  =>  ((v8_mesfunc5 A) &  ((k2_mesfunc5 A) = k1_supinf_1) ) ) ) ) ).
tt(t35_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ((k3_rlaffin1 B (k8_rlvect_2 B A C)) = (k8_real_1 A (k3_rlaffin1 B C))) ) ) ) ) ) ) ).
tt(t35_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v1_rlsub_1 B A) &  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  ((r1_rlsub_2 A C B) & (r1_rlsub_2 A B C)) ) ) ) ) ) ) ).
tt(t35_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k3_rltopsp1 A B)) (k3_rltopsp1 A (k4_algstr_0 A B)))) ) ) ) ).
tt(t35_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((k1_rlvect_1 C D (k6_xcmplx_0 A B)) = (k5_algstr_0 C (k1_rlvect_1 C D A) (k1_rlvect_1 C D B))) ) ) ) ) ) ) ) ) ).
tt(t35_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ( ((k3_rlvect_2 A C) = (k6_domain_1 (u1_struct_0 A) B))  =>  ((k6_rlvect_2 A C) = (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ) ).
tt(t35_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~ (v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) C B) A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  (C = (k1_rlvect_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k2_nat_1 (k1_rlvect_5 (k1_rlsub_2 A B C)) (k1_rlvect_5 (k2_rlsub_2 A B C))) = (k2_nat_1 (k1_rlvect_5 B) (k1_rlvect_5 C))) ) ) ) ) ) ) ).
tt(t35_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v5_relat_1 F k4_numbers) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) )  =>  ( ( (C = (k4_rlvect_1 A E))  &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) D) (k2_rlvect_x A B)) &  ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 F))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 (k3_finseq_1 D))) =>  ((k7_partfun1 (u1_struct_0 A) E G) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) D G) (k1_seq_1 F G))) ) ) ) ) ) ) )  => (r2_hidden C (k2_rlvect_x A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rmod_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C B) & (l1_vectsp_2 C B)) ) ) ) ) )  =>  ((r1_struct_0 (k1_rmod_2 B C) A) <=>  (A = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t35_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( ((m1_rmod_2 C A D) & (m1_rmod_2 E A D))  => (m1_rmod_2 (k1_rmod_3 A B C E) A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ( ((k2_rmod_4 A B D) = (k6_domain_1 (u1_struct_0 B) C))  =>  ((k5_rmod_4 A B D) = (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ((k7_robbins1 A) = (k5_lattices (k8_robbins1 A))) ) ) ).
tt(t35_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k5_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)) C)) = (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A C) C))) ) ) ) ) ) ) ).
tt(t35_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A B (k3_lattices A (k3_robbins1 A B) (k4_lattices A B C))) = (k4_lattices A B C)) ) ) ) ) ) ) ) ).
tt(t35_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A (k4_roughs_1 A B)) = (k4_roughs_1 A B)) ) ) ) ) ).
tt(t35_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  => (r1_xxreal_0 k6_numbers (k2_rpr_1 A C B))) ) ) ) ) ) ) ).
tt(t35_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_bhsp_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  => (m1_rusub_1 A (k2_rusub_1 A))) ) ).
tt(t35_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  ((r1_rusub_2 A C B) & (r1_rusub_2 A B C)) ) ) ) ) ) ) ).
tt(t35_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((r1_struct_0 (k1_rusub_3 A (k8_domain_1 (u1_struct_0 A) B C D)) E) <=>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_rusub_4 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t35_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k4_bhsp_2 A B D)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  & (r1_tarski (k4_bhsp_2 A C E) (k4_bhsp_2 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k6_rvsum_1 (k8_rvsum_1 A B)) = (k8_rvsum_1 B A)) ) ) ) ) ).
tt(t35_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k16_rvsum_1 (k11_finseq_1 A B C)) = (k3_binop_2 (k3_binop_2 A B) C)) ) ) ) ) ) ) ).
tt(t35_scmbsort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k4_sf_mastr (k1_scmbsort A)) = (k1_tarski A)) ) ) ).
tt(t35_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_amistd_1 3 k1_scmfsa_2 B (k12_scmfsa_2 A C)) = (k2_tarski A (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t35_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 6)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  (A = (k11_scmfsa_2 B)) ) ) ) ) ) ) ) ).
tt(t35_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k5_card_1 (k6_scmfsa6a A B)) = 4) ) ) ) ) ).
tt(t35_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A (k1_scmfsa_m B) C) & (r6_scmfsa7b A (k1_scmfsa_m B) C))  =>  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C (k3_scmfsa6a A (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 C A) (k1_funct_4 B (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)))) 1)) ) ) ) ) ) ) ) ).
tt(t35_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ( ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (F = G) )  =>  ((k1_funct_1 C G) = (k1_funct_1 D G)) ) ) )  &  ( (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 C G) = (k18_scmfsa_2 D G)) ) )  & (r5_scmfsa7b E C A)) )  =>  ((r2_scmfsa7b E F) |  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (F = H) )  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A E) (k8_memstr_0 3 k1_scmfsa_2 C) G) H) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B E) (k8_memstr_0 3 k1_scmfsa_2 D) G) H)) ) ) )  &  ( (! [H:$i] :  ((m1_scmfsa_2 H) =>  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A E) (k8_memstr_0 3 k1_scmfsa_2 C) G) H) = (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B E) (k8_memstr_0 3 k1_scmfsa_2 D) G) H)) ) )  &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A E) (k8_memstr_0 3 k1_scmfsa_2 C) G)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B E) (k8_memstr_0 3 k1_scmfsa_2 D) G)))  &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A E) (k8_memstr_0 3 k1_scmfsa_2 C) G)) = (k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 B E) (k8_memstr_0 3 k1_scmfsa_2 D) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k2_scmfsa8b C A B) (k2_nat_1 (k5_card_1 B) 2)) = (k11_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) 3))) ) ) ) ) ) ) ).
tt(t35_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_xxreal_0 (k1_funct_1 B C) k6_numbers))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmfsa_9 A B) 3) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 B) 5))) ) ) ) ) ).
tt(t35_scmfsa_m,ax, (! [A:$i] :  ((r2_hidden A (k9_xtuple_0 k10_scmfsa_m)) <=>  (? [B:$i] :  ((m2_finseq_1 B k4_numbers) &  (A = (k16_funcop_1 (k5_scmfsa_2 k6_numbers) B)) ) ) ) ) ).
tt(t35_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt D B A) & (r2_scm_halt D B A))  =>  ( ((k1_funct_1 B E) = k6_numbers)  |  ((r1_scm_halt (k1_scmfsa8b E C D) B A) & (r2_scm_halt (k1_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k2_scmisort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( (E = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmisort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers)) C))  &  (F = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k2_scmisort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers)) D)) )  => (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 9)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  (A = (k12_scmpds_2 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmpds_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) & (v2_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) &  ((v2_scmpds_4 E) & (v3_scmpds_4 E)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_4 D E) C B) A) = (k1_funct_1 (k6_scmpds_4 E (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 D C B)) B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k2_scmpds_6 A B C D)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)) ) ) ) ) ) ) ) ) ).
tt(t35_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) =>  ((r1_scmpds_6 (k1_scmpds_7 D E F C) B A) & (r2_scmpds_6 (k1_scmpds_7 D E F C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_amistd_1 2 (k1_scmring2 A) B) = (k2_tarski B (k1_ordinal1 B))) ) ) ) ) ).
tt(t35_scmyciel,ax, ((k5_scmyciel k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t35_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) & (r1_semi_af1 A B C E))  =>  ( (B = C)  | (r1_semi_af1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  <=> (v2_relat_1 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t35_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k3_comseq_2 A) = k5_complex1) ) )  =>  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) = k6_numbers) ) ) ) ) ) ).
tt(t35_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 k6_numbers A) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers C D) = (k12_binop_2 B (k9_binop_2 (k4_nat_1 D D) A))) ) ) )  =>  ((v2_comseq_2 C) &  ((k2_seq_2 C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t35_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k5_seqfunc A B) C) (k56_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C))) & (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k4_seqfunc A B) C) (k32_valued_1 k5_numbers k1_numbers (k10_seqfunc A B C)))) ) ) ) ) ) ) ).
tt(t35_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((v5_valued_0 A) & (v3_funct_1 B))  => (v5_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ( ((v6_valued_0 A) & (v3_funct_1 B))  => (v6_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ( ((v7_valued_0 A) & (v3_funct_1 B))  => (v7_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)))  &  ( ((v8_valued_0 A) & (v3_funct_1 B))  => (v8_valued_0 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ).
tt(t35_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_series_1 A) => (v1_series_1 A)) ) ) ).
tt(t35_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k2_nat_1 (k4_nat_1 2 B) 3) (k4_nat_1 (k4_nat_1 B (k2_nat_1 B 1)) (k13_newton 3 B)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 1 (k13_complex1 1 (k4_nat_1 (k2_nat_1 B 1) (k13_newton 3 B))))) ) ) ) ) ) ) ).
tt(t35_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  & (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 B) A))) ) ) ) ) ) ).
tt(t35_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 9 (k3_xcmplx_0 (k6_xcmplx_0 (k13_complex1 1 (k3_square_1 A)) 1) (k6_xcmplx_0 (k13_complex1 1 (k3_square_1 B)) 1)))) ) ) ) ) ).
tt(t35_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden (k3_subset_1 A C) (k7_setfam_1 A B)) <=> (r2_hidden C B)) ) ) ) ) ) ).
tt(t35_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B E) = (k5_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E) (k3_funct_2 k5_numbers (k9_setfam_1 A) D E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A B) E) = (k5_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A C) E) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k3_prob_1 A (k7_setlim_2 A C B)) (k7_subset_1 A B (k3_prob_1 A C)))) ) ) ) ) ).
tt(t35_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v3_binop_1 D A) &  ((v1_binop_1 D A) &  ((v2_binop_1 D A) & (v1_setwiseo D A)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G C A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  ((k7_setwiseo C A D (k8_setwiseo B C F E) G) = (k7_setwiseo B A D E (k1_partfun1 B C C A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_2 D A (k4_finseq_2 C A)) =>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 C A)) =>  ( ((v1_binop_1 B A) &  ((v2_binop_1 B A) & (v1_setwiseo B A)) )  =>  ((k5_binop_1 A B (k1_finsop_1 A D B) (k1_finsop_1 A E B)) = (k1_finsop_1 A (k1_finseqop A A A B D E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) => (r1_tarski (k5_scmfsa_m A B) (k2_sf_mastr (k4_sfmastr3 C A B)))) ) ) ) ) ) ).
tt(t35_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((r2_hidden A (k2_relset_1 (u1_compos_1 k1_scmfsa_2) B)) => (r1_tarski (k3_sf_mastr A) (k4_sf_mastr B))) ) ) ) ) ).
tt(t35_sgraph1,ax, ( ((u1_struct_0 k8_sgraph1) = (k2_finseq_1 3))  &  ((u1_sgraph1 k8_sgraph1) = (k4_setwiseo (k5_finsub_1 k5_numbers) (k3_setwiseo k5_numbers 1 2) (k3_setwiseo k5_numbers 2 3) (k3_setwiseo k5_numbers 3 1))) ) ).
tt(t35_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v11_lattices A)) ) ).
tt(t35_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A (k5_sheffer1 A C B) B)) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t35_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  (! [D:$i] :  ((m2_simplex0 D A C) =>  ( ((v7_simplex0 D A B) & (m2_simplex0 D A B))  => (v7_simplex0 D A C)) ) ) ) ) ) ) ) ).
tt(t35_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  ( ((v1_setfam_1 E) &  ((r1_tarski (k5_setfam_1 (u1_struct_0 B) E) C) & (r1_xxreal_0 (k3_real_1 (k1_xxreal_3 (k5_card_1 E) A) 1) (k5_card_1 C))) )  =>  ( ((m3_simplex0 D (k4_simplex1 B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C))) (k1_xxreal_3 A (k5_card_1 E))) & (r1_tarski (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) E) D))  <=>  (? [F:$i] :  ( ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  &  ((r1_xboole_0 F E) &  ((v6_ordinal1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 B)) F E)) &  ((v1_setfam_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 B)) F E)) &  ( ((k5_card_1 F) = (k3_real_1 A 1))  &  ((r1_tarski (k5_setfam_1 (u1_struct_0 B) F) C) &  (D = (k4_subset_1 (u1_struct_0 B) (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) E) (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_sincos10,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))) => (r2_hidden (k1_seq_1 k2_fdiff_9 A) (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ) ).
tt(t35_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k4_sin_cos2 k1_numbers) &  ((k1_fdiff_1 k4_sin_cos2 A) = (k1_seq_1 k1_sin_cos2 A)) ) ) ) ).
tt(t35_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k3_binop_2 A (k11_binop_2 (k24_binop_2 2 B) k32_sin_cos))) = (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A)) ) ) ) ) ).
tt(t35_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos B)) (k20_sin_cos C)) = (k3_xcmplx_0 (k7_xcmplx_0 1 4) (k2_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 B C) A))) (k17_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 C A) B))) (k17_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C))))) ) ) ) ) ) ) ).
tt(t35_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~  ((k18_sin_cos (k6_real_1 A 2)) = k6_numbers) )  &  ( (~  ((k21_sin_cos (k6_real_1 A 2)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k5_square_1 (k1_sin_cos4 (k6_real_1 A 2)))) = k6_numbers) )  &  ( (~  ((k3_sin_cos4 (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k8_real_1 2 (k4_sin_cos4 A)) (k9_real_1 (k4_sin_cos4 A) 1)))) )  &  (~  ((k3_sin_cos4 (k6_real_1 A 2)) = (k1_real_1 (k7_square_1 (k10_real_1 (k8_real_1 2 (k4_sin_cos4 A)) (k9_real_1 (k4_sin_cos4 A) 1))))) ) ) ) ) ) ) ) ) ).
tt(t35_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 k32_sin_cos A))  & (r1_xxreal_0 (k20_sin_cos A) (k1_real_1 1))) ) ) ) ) ).
tt(t35_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_sin_cos7 A) = (k4_sin_cos7 (k12_binop_2 A (k7_square_1 (k9_binop_2 (k3_square_1 A) 1))))) ) ) ).
tt(t35_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 (k10_real_1 k32_sin_cos 2))))  &  ( (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 2) A))  &  (~  ( ((k5_sin_cos9 (k1_seq_1 k29_sin_cos A)) = A)  &  ((k5_sin_cos9 (k1_sin_cos4 A)) = A) ) ) ) ) ) ) ) ).
tt(t35_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k8_nat_1 k1_numbers (k3_series_1 (k22_sin_cos B)) A) = (k8_nat_1 k1_numbers (k3_series_1 (k8_comseq_3 (k3_sin_cos (k3_xcmplx_0 B k7_complex1)))) (k2_nat_1 (k4_nat_1 2 A) 1)))  &  ((k8_nat_1 k1_numbers (k3_series_1 (k23_sin_cos B)) A) = (k8_nat_1 k1_numbers (k3_series_1 (k7_comseq_3 (k3_sin_cos (k3_xcmplx_0 B k7_complex1)))) (k4_nat_1 2 A))) ) ) ) ) ) ).
tt(t35_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) (k1_rltopsp1 (k15_euclid 2) C D)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B A) (k2_topreal1 2 B (k2_nat_1 A 1)))) &  ( (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) = C) )  &  (~  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v3_topreal1 A) => (v3_topreal1 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A))) ) ) ).
tt(t35_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_sprect_1 A) 1) = (k11_pscomp_1 A)) ) ) ).
tt(t35_sprect_2,ax, ((k15_pscomp_1 k1_topreal1) = (k1_rltopsp1 (k15_euclid 2) (k19_euclid k6_numbers 1) (k19_euclid 1 1))) ).
tt(t35_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((k3_topreal1 2 A) = (a_1_0_sprect_3 A)) ) ) ).
tt(t35_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k21_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t35_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((k3_xcmplx_0 (k6_xcmplx_0 (k6_square_1 A) (k6_square_1 B)) (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B))) = (k6_xcmplx_0 A B)) ) ) ) ) ) ).
tt(t35_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (m1_subset_1 (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B) (u4_struct_0 (k14_stacks_1 A)))) ) ) ) ).
tt(t35_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k23_binop_2 A 1) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) B)))) )  =>  (~  ( (~  (B = k6_numbers) )  &  ( (~  ((k1_stirl2_1 (k23_binop_2 A 1) B C (k1_seq_4 (k2_stirl2_1 (k23_binop_2 A 1) B C A))) = (k1_seq_4 A)) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k1_stirl2_1 (k23_binop_2 A 1) B C (k1_seq_4 (k2_stirl2_1 (k23_binop_2 A 1) B C A)))) &  (~  (D = A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [E:$i] :  ((m1_substut1 E A D) =>  ( ((v3_substut1 B A) &  ((v3_substut1 D A) &  ((k24_substut1 A B C) = (k24_substut1 A D E)) ) )  =>  ( ((k23_substut1 A B) = (k23_substut1 A D))  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k1_enumset1 B C D) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ).
tt(t35_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_substut1 A)) => (m2_subset_1 (k37_substut1 A (k17_substut1 A C D E)) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ) ) ) ) ).
tt(t35_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) &  ((v5_supinf_2 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) ) )  =>  (! [B:$i] :  ((m1_supinf_2 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B C))) ) ) ) ) ) ).
tt(t35_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  (~  ((k2_symsp_1 A B E (k4_vectsp_1 A B G F) D C) = (k8_group_1 A G (k2_symsp_1 A B E F D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ((r1_tarski (k4_relat_1 A) B) &  ((k3_relat_1 (k4_relat_1 A) (k6_subset_1 B (k4_relat_1 A))) = k1_xboole_0) )  =>  ((k5_relat_1 B A) = (k4_relat_1 A)) )  &  ( ((r1_tarski (k4_relat_1 A) B) &  ((k3_relat_1 (k6_subset_1 B (k4_relat_1 A)) (k4_relat_1 A)) = k1_xboole_0) )  =>  ((k6_relat_1 A B) = (k4_relat_1 A)) ) ) ) ) ) ).
tt(t35_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  =>  ((k4_taxonom1 A) = (k2_taxonom1 (u1_struct_0 A) (u1_metric_1 A))) ) ) ).
tt(t35_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (r1_tarski (k9_tdlat_1 A) (k1_tdlat_1 A))) ) ).
tt(t35_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) = (k1_pcomps_1 A (k1_tdlat_2 A B))) ) ) ) ) ).
tt(t35_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ((k1_tops_1 A B) = (k2_pre_topc A B)) ) ) ) ) ) ) ).
tt(t35_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r1_tarski (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)) (k2_polynom1 (k15_pre_poly A) C D))) ) ) ) ) ) ) ) ).
tt(t35_tex_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( (~  ( (~ (v1_xboole_0 (k6_subset_1 A (k6_domain_1 A B))))  & (v3_tdlat_3 (k3_tex_1 A B))) )  &  (~  ( (~ (v3_tdlat_3 (k3_tex_1 A B)))  & (v1_xboole_0 (k6_subset_1 A (k6_domain_1 A B)))) ) ) ) ) ) ) ).
tt(t35_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C B) =>  ((k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A C)) = C) ) ) ) ) ) ) ) ) ).
tt(t35_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v4_tex_3 B A) <=> (v3_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t35_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C (k3_tex_4 A B)) & (r1_tarski B (k3_tex_4 A C)))  =>  ((k3_tex_4 A B) = (k3_tex_4 A C)) ) ) ) ) ) ) ) ).
tt(t35_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( ((r1_tsep_1 (k1_tsep_1 A B C) D) =>  ((r1_tsep_1 B D) & (r1_tsep_1 C D)) )  &  ( ( ((r1_tsep_1 B D) & (r1_tsep_1 C D))  => (r1_tsep_1 (k1_tsep_1 A B C) D))  &  ( ((r1_tsep_1 D (k1_tsep_1 A B C)) =>  ((r1_tsep_1 D B) & (r1_tsep_1 D C)) )  &  ( ((r1_tsep_1 D B) & (r1_tsep_1 D C))  => (r1_tsep_1 D (k1_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((v8_relat_2 B) =>  (! [C:$i] :  ((r2_hidden C A) =>  ((v1_toler_1 (k9_relat_1 B C) A B) & (m1_toler_1 (k9_relat_1 B C) A B)) ) ) ) ) ) ) ).
tt(t35_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) & (r1_borsuk_6 A E F)) ) )  =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r3_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E G (k1_borsuk_2 A C D E H I)) J) (k1_borsuk_2 A B D F (k1_borsuk_2 A B C D G H) (k1_borsuk_2 A D E F I J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ((r1_topalg_6 A B C) =>  ( ((k2_topalg_6 A B) = (k2_topalg_6 A C))  &  ((k3_topalg_6 A B) = (k3_topalg_6 A C)) ) ) ) ) ) ) ) ) ).
tt(t35_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( ((v7_pre_topc A) & (v1_metrizts A))  =>  ( ((v3_topdim_1 A) & (r1_xxreal_0 (k4_topdim_1 A) k6_numbers))  <=>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) => (r2_metrizts A B C (k1_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t35_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((r1_tarski B C) & (r1_topgen_1 A B D))  => (r1_topgen_1 A C D)) ) ) ) ) ) ) ) ).
tt(t35_topgen_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (? [C:$i] :  ( ((v1_tops_2 C (k5_topgen_2 A B)) &  ((v2_cantor_1 C (k5_topgen_2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k5_topgen_2 A B)))))) )  &  (C = (k2_xboole_0 (k7_subset_1 (k1_zfmisc_1 A) (k10_eqrel_1 A) (k1_tarski (k1_tarski B))) (a_1_3_topgen_2 A))) ) ) ) ) ) ).
tt(t35_topgen_3,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~  ((v1_finset_1 B) & (v1_finset_1 (k3_subset_1 A B))) ) ) ) ) ) ).
tt(t35_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v5_topgen_4 (k2_struct_0 A) A)) ) ).
tt(t35_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))) =>  ( (A = k1_topgen_5)  =>  ( ((k2_pre_topc k3_topgen_5 A) = A)  &  ((k1_tops_1 k3_topgen_5 A) = k1_xboole_0) ) ) ) ) ).
tt(t35_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topgrp_1 A) & (l1_pre_topc A)) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (v4_pre_topc (k6_domain_1 (u1_struct_0 A) B) A)) )  => (v7_pre_topc A)) ) ) ).
tt(t35_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k6_topreal1 A) = (a_1_5_topreal1 A)) ) ) ).
tt(t35_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k11_finseq_1 A (k19_euclid (k17_euclid B) (k18_euclid A)) B))  =>  ( ((k17_euclid A) = (k17_euclid B))  |  ( ((k18_euclid A) = (k18_euclid B))  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = A)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = B)  & (v4_topreal1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k12_pscomp_1 A) (k13_pscomp_1 A)) (k3_topreal1 2 (k1_sprect_1 A)))) ) ).
tt(t35_topreal8,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  =>  ((v1_xboole_0 A) |  ((v1_zfmisc_1 B) |  ((k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ).
tt(t35_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden C (k3_topreal9 A D B)) & (r2_hidden E (k3_topreal9 A D B)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) C E) (k3_topreal9 A D B)) = (k2_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)) k2_topreala (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)) k2_topreala (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D)))) (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))) (u1_struct_0 (k1_topreala A B C D))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)) k2_topreala (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D)))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))) (u1_struct_0 (k1_topreala A B C D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k4_int_1 A) = (k10_real_1 1 4))  =>  ((k1_funct_1 k12_toprealb A) = (k19_euclid k6_numbers 1)) ) ) ) ).
tt(t35_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k32_valued_2 A (u1_struct_0 (k15_euclid B)) D C)) &  ((v1_funct_2 (k32_valued_2 A (u1_struct_0 (k15_euclid B)) D C) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k32_valued_2 A (u1_struct_0 (k15_euclid B)) D C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t35_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 E C) & (r1_xxreal_0 D (k12_euclid (k8_nat_1 (u1_struct_0 (k15_euclid A)) B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (r1_tarski (k2_tops_1 A B) B)) ) ) ) ) ).
tt(t35_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k5_setfam_1 (u1_struct_0 (k1_pre_topc A B)) (k1_tops_2 A B C))) => (r1_tarski B (k5_setfam_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t35_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=> (v1_tops_1 (k1_tops_1 A B) A)) ) ) ) ) ).
tt(t35_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v2_transgeo B A) | (v3_transgeo B A))  => (v4_transgeo B A)) ) ) ) ) ).
tt(t35_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k5_card_1 (k1_trees_1 A)) = (k3_finseq_1 A)) ) ) ).
tt(t35_trees_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ( (! [B:$i] :  ((r2_hidden B A) =>  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) ) ) )  & (v6_ordinal1 A))  =>  ((v1_relat_1 (k3_tarski A)) &  ((v1_funct_1 (k3_tarski A)) & (v3_trees_2 (k3_tarski A))) ) ) ) ) ).
tt(t35_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((v5_trees_3 (k2_finseq_2 B A)) <=>  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) ) ) ) ) ) ) ).
tt(t35_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k1_funct_1 A B) = (k1_funct_1 (k5_trees_2 A B) k1_xboole_0)) ) ) ) ) ).
tt(t35_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A) & (r1_connsp_1 A B C))  =>  ((v4_pre_topc B A) & (v4_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t35_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A B D) & (r4_tsep_2 A C E))  =>  ((r1_tsep_1 B C) | (r4_tsep_2 A (k2_tsep_1 A B C) (k1_tsep_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_tsp_2 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) => (v4_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_tsp_2 A B) C) B)) ) ) ) ) ) ) ).
tt(t35_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) => (r3_turing_1 k18_turing_1 (k3_comput_1 A k6_numbers))) ) ) ).
tt(t35_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  => (v1_relat_1 (k3_msafree2 (k40_twoscomp A B)))) ) ) ) ).
tt(t35_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k2_uniroots A) = (a_1_2_uniroots A)) ) ) ).
tt(t35_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  ((k8_group_1 A (k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) (k1_normsp_1 A C (k7_nat_d (k1_algseq_1 A C) 1))) = (k4_struct_0 A)) )  & (r1_xxreal_0 (k1_algseq_1 A (k11_polynom3 A B C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t35_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) => (r1_valuat_1 A B (k8_cqc_lang A D (k8_cqc_lang A (k6_cqc_lang A D) E)) F C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_valued_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) )  =>  ((r2_hidden A (k1_relset_1 k5_numbers B)) => (r1_xxreal_0 (k64_valued_1 B) A)) ) ) ) ) ).
tt(t35_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k24_valued_1 (k14_valued_2 C A) B) = (k14_valued_2 (k24_valued_1 C B) A)) ) ) ) ) ) ) ).
tt(t35_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 C B A) &  ((v1_hahnban1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (D = (k3_vectsp_4 A B E (k9_vectsp10 A B C)))  =>  ((k3_funct_2 (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B C))) (u1_struct_0 A) (k11_vectsp10 A B C) D) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k2_vectsp11 A B C) = (k1_ranknull A B B (k1_vectsp11 B C D)))  => (r1_vectsp_5 A B (k1_ranknull A B B (k1_vectsp11 B C D)) (k3_ranknull A B B (k1_vectsp11 B C D)))) ) ) ) ) ) ) ) ) ).
tt(t35_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_algstr_0 (u1_struct_0 A) (u1_algstr_0 A))))  &  ((v2_group_1 (g3_algstr_0 (u1_struct_0 A) (u1_algstr_0 A))) &  ((v3_group_1 (g3_algstr_0 (u1_struct_0 A) (u1_algstr_0 A))) &  ((v5_group_1 (g3_algstr_0 (u1_struct_0 A) (u1_algstr_0 A))) & (l3_algstr_0 (g3_algstr_0 (u1_struct_0 A) (u1_algstr_0 A)))) ) ) ) ) ) ).
tt(t35_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v3_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k5_vectsp_2 A B C (k5_algstr_0 B D E)) = (k5_algstr_0 B (k5_vectsp_2 A B C D) (k5_vectsp_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_vectsp_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  ((r1_struct_0 (k1_vectsp_4 B C) A) <=>  (A = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t35_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( (~  ( (? [E:$i] :  ((m1_vectsp_4 E A B) &  ((u1_struct_0 E) = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) )  &  ( (~ (m1_vectsp_4 C A D))  &  (~ (m1_vectsp_4 D A C)) ) ) )  &  (~  ( ((m1_vectsp_4 C A D) | (m1_vectsp_4 D A C))  &  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (~  ((u1_struct_0 E) = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) => (r1_vectsp_6 A B (k6_vectsp_6 A B (k5_struct_0 A) C) C)) ) ) ) ) ) ).
tt(t35_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 B (k1_vectsp_9 A C)) <=>  (? [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A C))  &  ((k1_vectsp_9 A D) = B) ) ) ) ) ) ) ) ) ) ).
tt(t35_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k5_vfunct_1 A B C) A)) ) ) ) ) ) ) ).
tt(t35_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k5_vfunct_1 A B C) A)) ) ) ) ) ) ) ).
tt(t35_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_waybel_0 B A) <=> (v2_waybel_0 (k4_waybel_0 A B) A)) ) ) ) ) ).
tt(t35_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ( (D = (k5_yellow_6 A B C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) => (r2_hidden (k2_waybel_0 A D E) C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) &  ((v1_waybel_6 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_tarski (k4_yellow_4 A B C) B) &  ((r2_hidden E B) &  ( (~ (r2_hidden D B))  &  (! [F:$i] :  ( ((v2_waybel_6 F A) & (m1_subset_1 F (u1_struct_0 A)))  =>  (~  ((r3_orders_2 A D F) &  (~ (r2_hidden F (k4_waybel_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) E) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_waybel13,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ( (~  ((v2_waybel_8 A) &  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v7_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  =>  (~  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) ) ) ) ) )  &  ( (? [B:$i] :  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B))) &  ((v7_waybel_1 C (k3_yellow_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_1 B)) (u1_struct_0 (k3_yellow_1 B)))))) ) )  &  ((v22_waybel_0 C (k3_yellow_1 B) (k3_yellow_1 B)) & (r5_waybel_1 A (k1_yellow_2 (k3_yellow_1 B) (k3_yellow_1 B) C))) ) ) )  => (v2_waybel_8 A)) ) ) ) ).
tt(t35_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v3_waybel_3 A) &  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden D C) &  (~  ((v3_pre_topc D A) & (v2_waybel_0 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel16 B A) =>  (B = (k2_yellow_0 A (a_2_0_waybel16 A B))) ) ) ) ) ) ).
tt(t35_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v3_waybel11 B A)) ) ) ) ) ).
tt(t35_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  &  ((v5_orders_3 D A C) &  ((v5_orders_3 E C A) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D E)) & (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k3_struct_0 C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) )  => (v6_waybel_1 B A)) ) ) ) ) ).
tt(t35_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k7_yellow_3 A A (k2_yellow_0 A (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k2_waybel20 A B) C)) C) B)) ) ) ) ) ) ) ).
tt(t35_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k1_yellow_0 A B) (k10_yellow_6 A (k4_waybel17 A B)))) ) ) ) ).
tt(t35_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_waybel23 (k5_waybel_0 A B) A)) ) ) ) ).
tt(t35_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((v8_yellow_0 (k3_waybel24 A B) (k6_yellow_1 (u1_struct_0 A) B)) & (m1_yellow_0 (k3_waybel24 A B) (k6_yellow_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t35_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B))) &  ((v5_pre_topc C (k1_waybel25 A) (k1_waybel25 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel25 A)) (u1_struct_0 (k1_waybel25 B)))))) ) )  => (v22_waybel_0 C (k1_waybel25 A) (k1_waybel25 B))) ) ) ) ) ) ).
tt(t35_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (r5_waybel_1 (k1_waybel26 A (k3_waybel18 B (k7_funcop_1 B k9_waybel18))) (k5_yellow_1 B (k7_funcop_1 B (k1_waybel26 A k9_waybel18))))) ) ) ) ).
tt(t35_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v1_lattice3 D) &  ((v2_lattice3 D) &  ((v3_lattice3 D) & (l1_orders_2 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( ((v23_waybel_0 E A B) & (v23_waybel_0 F C D))  => (v23_waybel_0 (k4_waybel27 A B C D E F) (k2_waybel27 B C) (k2_waybel27 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k5_waybel_2 A) (k6_yellow_3 A A B C)) = (k1_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(t35_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  ((v3_waybel30 A) & (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(t35_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v18_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B)) &  ((v17_waybel_0 (k3_waybel_1 A A B) (k1_yellow_2 A A B) A) &  ((r2_funct_2 (u1_struct_0 (k1_yellow_2 A A B)) (u1_struct_0 A) (k2_waybel34 (k1_yellow_2 A A B) A (k2_waybel_1 A A B)) (k3_waybel_1 A A B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_yellow_2 A A B)) (k1_waybel34 (k1_yellow_2 A A B) A (k3_waybel_1 A A B)) (k2_waybel_1 A A B))) ) ) ) ) ) ) ).
tt(t35_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 D A) &  ((r1_tarski C (k5_setfam_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 D)))  =>  (~ (r1_tarski B (k3_tarski E))) ) ) ) ) ) ) )  => (r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C)) ) ) ) ) ) ) ).
tt(t35_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r2_hidden (k11_waybel_4 A B) (u1_struct_0 (k8_waybel_4 A)))) ) ) ) ).
tt(t35_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_1 A) <=> (v4_waybel_6 (k4_waybel_6 A) A)) ) ) ).
tt(t35_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_waybel_3 A (k2_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A D) A A)) )  &  ((v10_waybel_0 C A) & (r3_waybel_9 A C B)) )  =>  (B = (k1_waybel_2 A C)) ) ) ) ) ) ) ) ).
tt(t35_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((m1_subset_1 B (u1_struct_0 (k1_uniroots A))) => (r1_int_1 (k6_xcmplx_0 (k1_newton (k5_card_1 (u1_struct_0 (k4_weddwitt A))) (k1_vectsp_9 (k4_weddwitt A) (k7_weddwitt A B))) 1) (k6_xcmplx_0 (k1_newton (k5_card_1 (u1_struct_0 (k4_weddwitt A))) (k1_vectsp_9 (k4_weddwitt A) (k6_weddwitt A))) 1))) ) ) ) ) ).
tt(t35_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_wellord1 A) &  ( ((k9_xtuple_0 B) = (k1_relat_1 A))  &  ((r1_tarski (k10_xtuple_0 B) (k1_relat_1 A)) &  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) A) =>  ( (C = D)  |  ((r2_hidden (k4_tarski (k1_funct_1 B C) (k1_funct_1 B D)) A) &  (~  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k1_relat_1 A)) => (r2_hidden (k4_tarski C (k1_funct_1 B C)) A)) ) ) ) ) ) ) ).
tt(t35_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( ((k3_int_2 A B) = 1)  &  ( ((k3_xcmplx_0 A B) = (k1_newton C D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( (A = (k1_newton E D))  &  (B = (k1_newton F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k4_xboole_0 A D) (k4_xboole_0 B C))) ) ) ) ) ).
tt(t35_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k4_xboolean A B)) = (k3_xboolean A)) ) ) ) ) ).
tt(t35_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k2_xcmplx_0 A B) = (k6_xcmplx_0 C D))  =>  ((k2_xcmplx_0 A D) = (k6_xcmplx_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t35_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B C))  => (r1_xxreal_0 (k2_xcmplx_0 B A) C)) ) ) ) ) ) ) ).
tt(t35_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k12_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k12_xtuple_0 A) (k12_xtuple_0 B))) ) ) ).
tt(t35_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k3_xxreal_0 (k4_xxreal_0 A B) B) = B) ) ) ) ) ).
tt(t35_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k2_xxreal_1 B C) (k1_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t35_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  => (v2_xxreal_2 (k3_xxreal_1 A B))) ) ) ) ) ).
tt(t35_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k1_xxreal_3 A C) (k1_xxreal_3 B C))) ) ) ) ) ) ) ).
tt(t35_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B C) &  ((r2_yellow_0 A B) & (r2_yellow_0 A C)) )  => (r1_orders_2 A (k2_yellow_0 A C) (k2_yellow_0 A B))) ) ) ) ) ).
tt(t35_yellow10,ax, (! [A:$i] :  ( ((v3_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((k5_yellow_3 A B (k4_waybel_0 (k3_yellow_3 A B) C)) = (k4_waybel_0 B (k5_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t35_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~ (v1_xboole_0 C)) ) ) ) ) ) ) ).
tt(t35_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B B) B) => (r2_funct_2 (u1_struct_0 (k7_waybel18 A A B)) (u1_struct_0 (k7_waybel18 A A B)) (k1_partfun1 (u1_struct_0 (k7_waybel18 A A B)) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k7_waybel18 A A B)) (k4_tmap_1 A (k7_waybel18 A A B)) (k8_waybel18 A A B)) (k3_struct_0 (k7_waybel18 A A B)))) ) ) ) ) ).
tt(t35_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) &  ((v4_waybel_3 B) & (v5_waybel_3 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_waybel_0 C (k5_yellow_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_1 A B)))))  =>  (! [D:$i] :  ((m1_subset_1 D A) => (v1_waybel_0 (k5_waybel_3 A B D C) (k3_waybel_3 A B D))) ) ) ) ) ) ) ) ).
tt(t35_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ( ((k9_xtuple_0 D) = (k3_yellow18 A B))  & (r1_tarski (k10_xtuple_0 D) (k3_yellow18 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t35_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (? [C:$i] :  ((m2_yellow_6 C A B) & (v3_yellow_6 C A)) ) ) ) ) ) ) ).
tt(t35_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l1_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v11_functor0 C A B) & (l2_functor0 C A B)) )  =>  ((v17_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A D E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A D E)) =>  ( ((k8_functor0 A B C D E F) = (k8_functor0 A B C D E G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((v11_quantal1 B) & (v22_waybel_0 B A A))  =>  ((v4_waybel_0 (k1_yellow_2 A A B) A) &  ((v3_orders_2 (k1_yellow_2 A A B)) &  ((v4_orders_2 (k1_yellow_2 A A B)) &  ((v5_orders_2 (k1_yellow_2 A A B)) &  ((v1_lattice3 (k1_yellow_2 A A B)) &  ((v2_lattice3 (k1_yellow_2 A A B)) &  ((v3_lattice3 (k1_yellow_2 A A B)) & (l1_orders_2 (k1_yellow_2 A A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r1_yellow_0 A C) &  ((r1_yellow_0 B D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_yellow_3 A B))) =>  ((r2_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) G) => (r1_orders_2 (k3_yellow_3 A B) (k7_yellow_3 A B E F) G)) ) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_lattice3 A C G) => (r1_orders_2 A E G)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r2_lattice3 B D G) => (r1_orders_2 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_waybel_0 A (k2_yellow_4 A (k4_waybel_0 A B) (k4_waybel_0 A C))) = (k4_waybel_0 A (k2_yellow_4 A B C))) ) ) ) ) ) ) ).
tt(t35_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A (k1_yellow_5 A B C) D) => (r3_orders_2 A B (k13_lattice3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t35_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k10_yellow_6 A B)) & (r2_hidden D (k10_yellow_6 A B)))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r6_waybel_1 A B C) <=> (r6_waybel_1 (k7_lattice3 A) (k8_lattice3 A B) (k8_lattice3 A C))) ) ) ) ) ) ) ).
tt(t35_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v2_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E C) => (v4_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D (k3_subset_1 (u1_struct_0 B) E)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_zf_lang A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  ((r2_hidden C (k2_zf_model D)) =>  ((k1_funct_1 (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 B) (k4_zf_fund1 (k2_zf_model D))) (k3_zf_fund1 C)) = (k3_funct_2 k1_zf_lang A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t35_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  ((v4_zf_lang A) &  ((v5_zf_lang (k20_zf_lang A)) & (v4_zf_lang (k22_zf_lang (k20_zf_lang A)))) ) ) ) ) ).
tt(t35_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v7_zf_lang A) =>  ( ((k18_zf_lang A) = (k1_funct_1 A 2))  &  ((k19_zf_lang A) = (k1_funct_1 A 3)) ) ) ) ) ).
tt(t35_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~  (A = (k1_tarski B)) )  &  ( (~  (A = k1_xboole_0) )  &  (! [C:$i] :  (~  ((r2_hidden C A) &  (~  (C = B) ) ) ) ) ) ) ) ) ) ).
tt(t35_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_ordinal2 B k4_ordinal1) &  ( (C = (k4_classes1 B))  & (r3_zfrefle1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t35_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) => (r1_struct_0 A (k4_struct_0 B))) ) ) ) ).
tt(t360_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t361_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t362_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t363_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 C B)) = (k2_xboole_0 (k4_xxreal_1 A C) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t364_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k1_xxreal_1 C B)) = (k2_xboole_0 (k2_xxreal_1 A C) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t365_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t366_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t367_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k1_tarski B)) = (k2_xboole_0 (k4_xxreal_1 A B) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t368_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k1_tarski B)) = (k2_xboole_0 (k2_xxreal_1 A B) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t369_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 B k1_xxreal_0)) = (k2_xboole_0 (k1_xxreal_1 A B) (k1_tarski k1_xxreal_0))) ) ) ) ) ).
tt(t36_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((k1_funct_1 (k7_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) (k2_nat_1 (k3_finseq_1 C) 1)) = (k8_abcmiz_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(t36_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) =>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  ((m2_finseq_2 (k11_finseq_1 A B C) k2_abcmiz_1 k4_abcmiz_1) <=>  ( ((k3_abcmiz_1 A) = k1_xboole_0)  &  ( (~  (A = B) )  &  ((r1_tarski (k3_abcmiz_1 B) (k6_domain_1 k2_abcmiz_1 A)) &  ( (~  (A = C) )  &  ( (~  (B = C) )  & (r1_tarski (k3_abcmiz_1 C) (k7_domain_1 k2_abcmiz_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_a B A) & (m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))))  => (r2_hidden (k10_abcmiz_a A B) (k9_abcmiz_a A B))) ) ) ) ).
tt(t36_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_aff_1 A B C) =>  ((v1_aff_1 B A) & (v1_aff_1 C A)) ) ) ) ) ) ) ) ).
tt(t36_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B D) &  ((r1_tarski C D) & (v1_aff_4 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((k1_funct_1 (k1_ordinal4 B (k5_afinsq_1 A)) (k1_afinsq_1 B)) = A) ) ) ) ).
tt(t36_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((k1_afinsq_1 (k5_afinsq_2 A B)) = (k5_card_1 (k3_xboole_0 B (k1_afinsq_1 A))))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 (k5_afinsq_2 A B)) C))  =>  ((k1_funct_1 (k5_afinsq_2 A B) C) = (k1_funct_1 A (k1_recdef_1 (k4_afinsq_2 (k3_xboole_0 B (k1_afinsq_1 A))) C))) ) ) ) ) ) ) ) ).
tt(t36_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k14_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k14_afproj A))) =>  ( ( (D = (k5_afproj A B))  &  ( (E = (k6_afproj A C))  &  ((v1_aff_1 B A) & (v1_aff_4 C A)) ) )  =>  ((r1_incsp_1 (k14_afproj A) D E) <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_afvect0 A B C) = (k1_afvect0 A D C))  <=>  ( (B = D)  | (r1_afvect0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t36_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  ((v1_funct_1 (k1_algspec1 (u1_struct_0 A) B)) &  ((v1_funct_2 (k1_algspec1 (u1_struct_0 A) B) (u1_struct_0 A) (u1_struct_0 (k2_algspec1 A B C))) & (m1_subset_1 (k1_algspec1 (u1_struct_0 A) B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_algspec1 A B C)))))) ) ) ) ) ) ) ) ) ).
tt(t36_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)))) =>  ( (B = (k7_relset_1 (k11_algstr_4 A 1) (u1_struct_0 (k14_algstr_4 A)) (k16_algstr_4 A 1) A))  =>  ((k14_algstr_4 A) = (k9_algstr_4 (k14_algstr_4 A) B)) ) ) ) ) ) ).
tt(t36_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C B) & (m1_altcat_2 C B)) ) )  =>  ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v3_altcat_2 C A) & (m1_altcat_2 C A)) ) ) ) ) ) ) ) ) ).
tt(t36_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_analmetr A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_analmetr A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k3_analmetr A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k3_analmetr A))) =>  ( ( (B = F)  &  ( (C = G)  &  ( (D = H)  &  (E = I) ) ) )  =>  ((r2_analoaf A B C D E) <=> (r2_analoaf (k3_analmetr A) F G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) & (r1_analort A B C D E G H)) )  => (r1_analort A B C D E F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((r2_hidden D (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A B))) &  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A C))) &  ((k1_funct_1 (k2_pua2mss1 A B) D) = (k1_funct_1 (k2_pua2mss1 A C) E)) ) )  =>  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k76_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k76_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G))  &  ( ((r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k77_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k77_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((v1_armstrng (k11_armstrng A B) A) & (v2_finsub_1 (k11_armstrng A B))) ) ) ) ) ).
tt(t36_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ( (~ (r2_hidden A k4_ordinal1))  =>  ( (A = (k4_tarski (k6_arytm_3 A) (k7_arytm_3 A)))  &  (~  ((k7_arytm_3 A) = 1) ) ) ) ) ) ).
tt(t36_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ((k11_asympt_0 A B) = (k3_xboole_0 (k9_asympt_0 A B) (k10_asympt_0 A B))) ) ) ) ).
tt(t36_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B k6_asympt_1) =>  ((k1_seq_1 A B) = B) )  &  ( (~ (r2_hidden B k6_asympt_1))  =>  ((k1_seq_1 A B) = (k5_series_1 2 B)) ) ) ) )  =>  ((r2_hidden A (k11_asympt_0 (k3_asympt_1 1) k6_asympt_1)) &  ( (~ (r2_hidden A (k8_asympt_0 (k3_asympt_1 1))))  &  ((v7_asympt_0 (k3_asympt_1 1)) &  (~ (v6_asympt_0 A)) ) ) ) ) ) ) ).
tt(t36_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  & (r2_hidden (k4_tarski B k1_xboole_0) (k3_tarski (k10_xtuple_0 (k12_bagorder A))))) ) ) ) ) ) ).
tt(t36_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (v11_bcialg_1 A)) ) ).
tt(t36_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((m1_bcialg_2 B A) <=>  ((m3_bcialg_2 B A) & (m2_bcialg_2 B A)) ) ) ) ) ) ).
tt(t36_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A (k4_struct_0 A) C)) = B)  &  ((k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A B C)) = (k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A C B)) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B C) D) E) = (k1_bcialg_1 A B (k7_bcialg_4 A (k3_finseq_4 (u1_struct_0 A) C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((m1_bcialg_5 A B C (k2_nat_1 C D) (k2_nat_1 B D)) =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((r1_bcialg_1 A C D) => (r1_bcialg_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t36_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ((k4_bhsp_1 A B C) = k6_numbers) ) )  &  (~  ( (~  ((k4_bhsp_1 A B C) = k6_numbers) )  &  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t36_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k3_bhsp_2 A (k2_normsp_1 A D E) (k3_rlvect_1 A B C))) &  ((k2_seq_2 (k3_bhsp_2 A (k2_normsp_1 A D E) (k3_rlvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_bhsp_2 B A) =>  ((v1_bhsp_2 (k1_valued_0 (u1_struct_0 A) B C) A) &  ((k1_bhsp_2 A (k1_valued_0 (u1_struct_0 A) B C)) = (k1_bhsp_2 A B)) ) ) ) ) ) ) ) ) ).
tt(t36_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 (k2_bhsp_2 A B)) C))) ) ) ) ) ) ).
tt(t36_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear G A B C) &  ((v3_bilinear G A B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D (k5_algstr_0 C E F)) = (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D E) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) G D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_binari_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ((k1_binari_3 A (k6_binarith A B)) = B) ) ) ) ) ).
tt(t36_binari_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ( ((r1_xxreal_0 (k20_binop_2 A B) (k21_binop_2 (k5_series_1 2 (k7_nat_d C 1)) 1)) &  ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B)) )  =>  ((k3_binari_2 C (k7_binarith C (k2_binari_4 C A) (k2_binari_4 C B))) = (k20_binop_2 A B)) ) ) ) ) ) ) ) ).
tt(t36_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_lattices A (k4_lattices A B C) (k1_boolealg A B C)) B)) ) ) ) ) ) ).
tt(t36_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A (k13_borsuk_1 A B C))) (k12_borsuk_1 A (k13_borsuk_1 A B C)) D) (u1_struct_0 (k11_borsuk_1 B C))) => (r2_hidden D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t36_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~  (B = 1) )  &  (~  ( (~ (v1_xboole_0 (k4_rcomp_1 A B)))  & (m1_subset_1 (k4_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4)))) ) ) ) ) ) ) ) ) ).
tt(t36_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_rcomp_1 B C))  =>  ( (B = C)  |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t36_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ((v5_pre_topc A (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ((v5_pre_topc B (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) => (m1_subset_1 (k3_xcmplx_0 (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A C) (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B C)) (u1_struct_0 k5_topmetr))) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A D) = E)  &  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B D) = F) )  =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) C D) = (k3_xcmplx_0 E F)) ) ) ) ) ) ) )  & (v5_pre_topc C (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (B = k3_numbers)  =>  ((v3_pre_topc (k9_subset_1 k1_numbers k3_numbers (k2_rcomp_1 k2_xxreal_0 A)) (k1_pre_topc k3_topmetr B)) & (m1_subset_1 (k9_subset_1 k1_numbers k3_numbers (k2_rcomp_1 k2_xxreal_0 A)) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k3_topmetr B))))) ) ) ) ) ) ).
tt(t36_bspace,ax, (! [A:$i] : (v1_vectsp_7 (k9_bspace A) k2_bspace (k7_bspace A))) ).
tt(t36_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  ( (B = (k4_enumset1 C D E F G H))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ((k5_bvfunc_2 A H B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k17_bvfunc_1 A B (k6_partit1 A)) (k14_bvfunc_1 A B))) ) ) ) ).
tt(t36_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B C) (k1_bvfunc_1 A (k9_bvfunc_1 A B (k1_bvfunc_1 A C))))) ) ) ) ) ) ).
tt(t36_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k9_bvfunc_1 A C D)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t36_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A C (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t36_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C (k1_bvfunc_1 A D)) B F) (k7_bvfunc_2 A (k2_bvfunc_1 A E D) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E (k1_bvfunc_1 A C)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A B) (k9_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t36_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k1_bvfunc_1 A (k2_bvfunc_1 A B C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t36_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D C)) (k5_bvfunc_1 A B D)) C)) ) ) ) ) ) ) ) ).
tt(t36_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_c0sp1 A)))  &  ((v13_algstr_0 (k11_c0sp1 A)) &  ((v2_rlvect_1 (k11_c0sp1 A)) &  ((v3_rlvect_1 (k11_c0sp1 A)) &  ((v4_rlvect_1 (k11_c0sp1 A)) &  ((v5_rlvect_1 (k11_c0sp1 A)) &  ((v6_rlvect_1 (k11_c0sp1 A)) &  ((v7_rlvect_1 (k11_c0sp1 A)) &  ((v8_rlvect_1 (k11_c0sp1 A)) &  ((v3_normsp_0 (k11_c0sp1 A)) &  ((v4_normsp_0 (k11_c0sp1 A)) &  ((v2_normsp_1 (k11_c0sp1 A)) &  ((v3_lopban_1 (k11_c0sp1 A)) & (l1_normsp_1 (k11_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_c0sp2 A)))  &  ((v13_algstr_0 (k9_c0sp2 A)) &  ((v2_rlvect_1 (k9_c0sp2 A)) &  ((v3_rlvect_1 (k9_c0sp2 A)) &  ((v4_rlvect_1 (k9_c0sp2 A)) &  ((v5_rlvect_1 (k9_c0sp2 A)) &  ((v6_rlvect_1 (k9_c0sp2 A)) &  ((v7_rlvect_1 (k9_c0sp2 A)) &  ((v8_rlvect_1 (k9_c0sp2 A)) &  ((v3_normsp_0 (k9_c0sp2 A)) &  ((v4_normsp_0 (k9_c0sp2 A)) &  ((v2_normsp_1 (k9_c0sp2 A)) & (l1_normsp_1 (k9_c0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B) (k1_calcul_1 (k3_cqc_lang A) C)) &  ( ((k2_calcul_1 A B) = (k2_calcul_1 A C))  & (r4_calcul_1 A B)) )  => (r4_calcul_1 A C)) ) ) ) ) ) ) ).
tt(t36_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  (A = (k1_ordinal1 B)) ) ) ) ) ) ) ) ).
tt(t36_card_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_nat_1 A B) = (k8_ordinal3 A B)) ) ) ) ) ).
tt(t36_card_3,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((k7_card_3 (k7_funcop_1 k1_xboole_0 A)) = 1) ) ) ).
tt(t36_card_5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski B A) =>  ((k2_wellord2 (k1_wellord2 B)) = (k5_card_1 B)) ) ) ) ) ) ).
tt(t36_card_fil,ax, (! [A:$i] :  (! [B:$i] :  ((v1_card_1 B) =>  (~  ((r1_ordinal1 B (k1_card_1 A)) &  (! [C:$i] :  (~  ((r1_tarski C A) &  ((k1_card_1 C) = B) ) ) ) ) ) ) ) ) ).
tt(t36_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((k2_tarski A B) = (k8_relat_1 D (k1_tarski C)))  =>  ((k2_card_fin E D C) = (k3_xboole_0 (k1_funct_1 E A) (k1_funct_1 E B))) ) ) ) ) ) ) ) ) ).
tt(t36_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v6_card_fil A) => (v2_classes1 (k4_classes1 A))) ) ) ).
tt(t36_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((v8_cat_1 D A B C) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A C E) =>  (! [G:$i] :  ((m1_cat_1 G A C E) =>  ( ((k5_cat_1 A B C E D F) = (k5_cat_1 A B C E D G))  =>  ( ((k2_cat_1 A C E) = k1_xboole_0)  |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ((k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k12_cat_2 A B C D E) F) = (k11_cat_2 A B C D (k4_cat_1 A E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((v10_cat_1 B A) &  ( ((k3_graph_1 A D) = C)  &  ((k4_graph_1 A D) = B) ) )  =>  ((k10_cat_3 A C B) = D) ) ) ) ) ) ) ) ) ) ).
tt(t36_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B (k2_cat_4 A C D))) = k1_xboole_0) )  &  (~  ((k2_cat_1 A (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A (k2_cat_4 A B C) D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( (D = (k21_binop_2 A (k24_binop_2 2 (k23_binop_2 C 1))))  &  (E = (k21_binop_2 B (k23_binop_2 C 1))) )  =>  ((k1_card_1 (a_3_0_catalan2 A B C)) = (k24_binop_2 (k5_card_1 (k2_catalan2 (k24_binop_2 2 C) C)) (k5_card_1 (k2_catalan2 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v1_xboole_0 (k6_cc0sp2 A)))  & (m1_subset_1 (k6_cc0sp2 A) (k1_zfmisc_1 (u1_struct_0 (k8_cfuncdom (u1_struct_0 A)))))) ) ) ).
tt(t36_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r1_cfcont_1 B A) =>  ( ((k7_partfun1 k2_numbers B A) = k6_numbers)  | (r1_cfcont_1 (k2_cfunct_1 k2_numbers B) A)) ) ) ) ) ) ).
tt(t36_cfdiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v6_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_numbers)))  =>  ( ((r2_cfdiff_1 B A) & (r1_tarski C A))  => (r2_cfdiff_1 B C)) ) ) ) ) ) ).
tt(t36_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( (~  (C = k6_numbers) )  => (r2_relset_1 A k2_numbers (k2_cfunct_1 A (k25_valued_1 A k2_numbers B C)) (k25_valued_1 A k2_numbers (k2_cfunct_1 A B) (k12_complex1 C)))) ) ) ) ) ) ) ).
tt(t36_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ((r2_hidden A (k8_cgames_1 B)) => (r1_tarski (k10_cgames_1 A) (k11_cgames_1 B))) ) ) ) ) ).
tt(t36_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_chain_1 E B) =>  (~  ((r1_xxreal_0 A B) &  ((r2_hidden (k3_chain_1 B C D) (k4_chain_1 B E A)) &  ( (~  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) => (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 D F))) ) )  &  (? [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) & (r1_xxreal_0 (k1_seq_1 C F) (k1_seq_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_chord B A) => (v5_glib_001 B A)) ) ) ) ) ).
tt(t36_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 D C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 D C) C)))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v3_card_1 F D) & (v1_finseq_1 F)) ) )  =>  (! [G:$i] :  ((m1_circcmb3 G C) =>  ( ( ((k10_xtuple_0 F) = (k2_xboole_0 A B))  &  ((r1_tarski A (u1_struct_0 G)) & (r1_xboole_0 B (k3_msafree2 G))) )  =>  ((r2_hidden (k3_circcmb3 (k4_circcmb3 D C E F)) (k2_msafree2 G)) |  ((k2_msafree2 (k6_circcmb3 C G (k4_circcmb3 D C E F))) = (k2_xboole_0 (k2_msafree2 G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_circcomb,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((u1_msualg_1 (k4_circcomb A C B)) = (k13_funcop_1 C A C))  &  ((u2_msualg_1 (k4_circcomb A C B)) = (k13_funcop_1 C A B)) ) ) ) ) ) ).
tt(t36_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ((r5_circtrm1 A B C D E F) => (r1_circtrm1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) <=> (r2_hidden (k4_classes1 A) (k4_classes1 B))) ) ) ) ) ).
tt(t36_classes2,ax, (! [A:$i] :  (! [B:$i] :  (~  ((v2_classes1 A) &  ((r1_tarski B (k4_classes1 (k1_card_1 A))) &  ( (~ (r2_tarski B (k4_classes1 (k1_card_1 A))))  &  (~ (r2_hidden B (k4_classes1 (k1_card_1 A)))) ) ) ) ) ) ) ).
tt(t36_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_clopban1 A B))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ( ((k1_normsp_0 (k14_clopban1 A B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k14_clopban1 A B))) )  &  ( ( (C = (k4_struct_0 (k14_clopban1 A B)))  =>  ((k1_normsp_0 (k14_clopban1 A B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k14_clopban1 A B) (k1_clvect_1 (k14_clopban1 A B) C E)) = (k8_real_1 (k17_complex1 E) (k1_normsp_0 (k14_clopban1 A B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k14_clopban1 A B) (k1_algstr_0 (k14_clopban1 A B) C D)) (k7_real_1 (k1_normsp_0 (k14_clopban1 A B) C) (k1_normsp_0 (k14_clopban1 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~  ((k1_normsp_1 A B D) = (k4_struct_0 A)) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D))) ) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_clopban3 B A)) ) ) ) ) ) ) ) ).
tt(t36_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k7_clopban4 A (k4_struct_0 A)) = (k5_struct_0 A)) ) ) ).
tt(t36_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v5_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  (! [F:$i] :  ( ((v2_relat_1 F) & (m3_pboole F A (k1_mboolean A B)))  =>  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) & (v1_partfun1 G A)) ) )  =>  ((r1_pboole A G F) <=>  ((r1_pboole A G C) & (r2_pboole A E G)) ) ) )  => (r6_pboole A (k2_closure1 A B D E) (k4_mssubfam A B F))) ) ) ) )  =>  ((v1_closure1 D A B) & (v2_closure1 D A B)) ) ) ) ) ) ) ) ) ).
tt(t36_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((v9_closure2 C A B) &  ((v9_closure2 D A B) & (r2_funct_2 (k6_closure2 A B) (k6_closure2 A B) (k8_closure2 A B D C) (k8_closure2 A B C D))) )  => (v9_closure2 (k8_closure2 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t36_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) => (r1_struct_0 B (k4_struct_0 A))) ) ) ) ).
tt(t36_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k3_clvect_2 A (k16_csspace A D E) (k3_rlvect_1 A B C))) &  ((k2_seq_2 (k3_clvect_2 A (k16_csspace A D E) (k3_rlvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k8_nat_1 k1_numbers (k3_series_1 (k2_clvect_2 A B)) C))) ) ) ) ) ) ).
tt(t36_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v9_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((r1_tarski (k8_cohsp_1 A B C) (k8_cohsp_1 A B D)) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_tarski (k3_funct_2 A B C E) (k3_funct_2 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r2_hidden (k4_tarski (k1_eqrel_1 A) A) (k16_coh_sp B))) ) ) ).
tt(t36_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_complex1 (k5_xcmplx_0 A)) = (k12_complex1 (k15_complex1 A))) ) ) ).
tt(t36_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 A (k8_complex1 B C)) = (k8_complex1 (k1_complex2 A B) (k1_complex2 A C))) ) ) ) ) ) ) ).
tt(t36_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ( ((k3_vectsp_1 k1_complfld C B) = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld C A) (k8_group_1 k1_complfld B A)))  &  ((k3_vectsp_1 k1_complfld C B) = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld A C) (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k45_valued_1 (k45_valued_1 A B) C) = (k45_valued_1 A (k1_valued_1 B C))) ) ) ) ) ) ) ) ).
tt(t36_compl_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v1_finset_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ( (~ (v1_finset_1 C))  &  ((r1_tarski C (k5_setfam_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ((r2_hidden D B) &  (~ (v1_finset_1 (k9_subset_1 A D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r2_hidden k6_numbers (k2_afinsq_1 (k10_compos_1 A B)))) ) ) ) ).
tt(t36_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k1_compos_2 A B C) k6_numbers) = B) ) ) ) ) ) ) ).
tt(t36_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_comptrig A) = k32_sin_cos) ) ) ) ).
tt(t36_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k1_relset_1 (k3_finseq_2 k5_numbers) (k5_comput_1 A B)) = (k4_finseq_2 A k5_numbers))  &  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A))  =>  ((k10_xtuple_0 (k5_comput_1 A B)) = k5_numbers) ) ) ) ) ) ) ).
tt(t36_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A (k51_valued_1 k5_numbers k2_numbers k2_numbers B C)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A C) B))) ) ) ) ) ) ).
tt(t36_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( (~  (k6_complex1 = A) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k10_comseq_3 (k1_comseq_3 A)) B) = (k13_complex1 (k11_complex1 k6_complex1 (k2_comseq_3 A (k2_nat_1 B 1))) (k11_complex1 k6_complex1 A))) ) ) ) ) ) ).
tt(t36_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  ((k1_binop_1 (k10_conlat_1 A) (k1_binop_1 (k9_conlat_1 A) B C) C) = C) ) ) ) ) ) ) ).
tt(t36_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_connsp_1 C A) &  ( (~ (r1_xboole_0 B C))  &  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A B (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t36_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_convex4 C A) =>  (! [D:$i] :  ((m1_convex4 D A) =>  ( ((m2_convex4 C A B) & (m2_convex4 D A B))  => (m2_convex4 (k9_convex4 A C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t36_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k15_cqc_sim1 A (k5_cqc_lang A)) = (k6_domain_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k5_cqc_lang A) (k26_qc_lang1 A) (k1_setwiseo (k3_qc_lang1 A)) (k11_cqc_sim1 (k3_qc_lang1 A))))) ) ) ).
tt(t36_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden C (k1_cqc_the1 A B)) <=>  (? [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (k3_cqc_lang A) k2_cqc_the1)) &  ((r2_cqc_the1 A B D) &  ((k3_cqc_the1 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k7_cqc_lang A B C)) (k7_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C))) A) & (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C)) (k11_cqc_lang A D (k7_cqc_lang A B C))) A)) ) ) ) ) ) ) ) ) ).
tt(t36_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r5_cqc_the3 A (k11_cqc_lang A C B) B)) ) ) ) ) ) ).
tt(t36_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) => (r1_csspace A B (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t36_descip_1,ax,(r2_funct_2 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1) k28_descip_1 (k2_funct_2 (k4_finseq_2 64 k6_margrel1) k26_descip_1))).
tt(t36_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) => (v4_dickson A)) ) ) ).
tt(t36_diff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 E C) A) C) B) D) = (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 E C) (k2_nat_1 A B)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers F G) = (k10_real_1 A G)) ) )  & (r2_zfmisc_1 B C D E))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ( (D = k6_numbers)  |  ( (E = k6_numbers)  |  ((k11_diff_1 F B C D E) = (k1_real_1 (k10_real_1 A (k8_real_1 (k8_real_1 (k8_real_1 B C) D) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k7_square_1 D)) ) )  =>  ( (A = B)  |  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  ((k9_diff_1 C A B) = (k10_real_1 1 (k7_real_1 (k7_square_1 A) (k7_square_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D F) = (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 E A) F)) ) )  =>  ((k9_diff_1 D B C) = (k9_real_1 (k9_diff_1 E (k7_real_1 B A) (k7_real_1 C A)) (k9_diff_1 E B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r5_waybel_4 A (k2_struct_0 A) C) &  ( (C = B)  | (r2_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(t36_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_diraf A B C D)) ) ) ) ) ) ) ) ) ).
tt(t36_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  ((k2_ec_pf_1 A (k8_group_1 (k9_int_3 A) B C)) = (k3_xcmplx_0 (k2_ec_pf_1 A B) (k2_ec_pf_1 A C))) ) ) ) ) ) ) ).
tt(t36_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((r1_ec_pf_1 A (k7_ec_pf_2 A C) C) & (r2_hidden (k7_ec_pf_2 A C) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B)))) ) ) ) ) ) ) ).
tt(t36_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  (! [D:$i] :  ((m1_cat_1 D (k11_ens_1 A) B C) =>  ( (~  ((k2_cat_1 (k11_ens_1 A) B C) = k1_xboole_0) )  =>  ((v7_cat_1 D (k11_ens_1 A) B C) <=> (v2_funct_1 (k2_xtuple_0 (k15_ens_1 A D)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k1_matrprob A C 1) = (k1_matrprob A B 1))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ((k1_matrprob A C (k2_nat_1 D 1)) = (k8_finseq_1 A (k1_matrprob A C D) (k1_matrprob A B (k2_nat_1 D 1)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 B)) =>  ((r2_hidden (k7_real_1 (k8_real_1 (k9_real_1 D 1) (k1_matrix_1 B)) E) (k4_finseq_1 (k1_matrprob A C (k3_finseq_1 B)))) &  ((k3_matrix_1 A B D E) = (k1_funct_1 (k1_matrprob A C (k3_finseq_1 B)) (k7_real_1 (k8_real_1 (k9_real_1 D 1) (k1_matrix_1 B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_enumset1,ax, (! [A:$i] :  ((k1_enumset1 A A A) = (k1_tarski A)) ) ).
tt(t36_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (~  ((r2_hidden A (k7_eqrel_1 B C)) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~  (A = (k6_eqrel_1 B B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t36_equation,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (k4_equation A)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) &  ((v3_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  ((r2_equation A B C) => (r2_equation A (k13_msualg_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t36_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B B) = (k5_square_1 (k12_euclid B))) ) ) ) ) ).
tt(t36_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((k4_euclid_3 A B C) = k6_numbers)  =>  ( ((k3_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)) = (k3_euclid_3 (k5_algstr_0 (k15_euclid 2) C B)))  &  ((k4_euclid_3 C B A) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t36_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k7_real_1 (k5_square_1 (k12_euclid (k7_euclid A B C))) (k5_square_1 (k12_euclid (k8_euclid A B C)))) = (k8_real_1 2 (k7_real_1 (k5_square_1 (k12_euclid B)) (k5_square_1 (k12_euclid C))))) ) ) ) ) ) ) ).
tt(t36_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ((r2_hidden A (k5_jgraph_6 F G H)) &  ((r2_hidden B (k5_jgraph_6 F G H)) &  ((r2_hidden C (k5_jgraph_6 F G H)) &  ((r2_hidden D (k5_jgraph_6 F G H)) &  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) A C)) &  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) B D)) & (r2_zfmisc_1 A B C D)) ) ) ) ) )  =>  ((k4_euclid_3 A D B) = (k4_euclid_3 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlsub_1 B (k10_funcsdom (k2_finseq_1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r2_hidden C (u1_struct_0 B)) & (r2_hidden D (u1_struct_0 B)))  => (r2_hidden (k7_euclid A C D) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t36_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k3_rlvect_1 (k15_euclid A) B (k4_algstr_0 (k15_euclid A) B)) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ).
tt(t36_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid E)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid E)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid E)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid E)) =>  (! [J:$i] :  ((m2_finseq_2 J k1_numbers (k1_euclid E)) =>  (~  ((r3_euclidlp E J F) &  ( (J = (k7_euclid E (k9_euclid E G A) (k9_euclid E H B)))  &  ( (F = (k7_euclid E (k9_euclid E G C) (k9_euclid E H D)))  &  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  (! [M:$i] :  ((m1_subset_1 M k1_numbers) =>  (! [N:$i] :  ((m1_subset_1 N k1_numbers) =>  (~  ( (G = (k7_euclid E (k9_euclid E J K) (k9_euclid E F L)))  &  (H = (k7_euclid E (k9_euclid E J M) (k9_euclid E F N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) )  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((k10_funct_7 (k10_funct_7 C A B) A B) = C) ) ) ) ) ) ).
tt(t36_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  ((r1_extpro_1 A B C D) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k8_extpro_1 A B C D) E) =>  ((k3_extpro_1 A B C (k5_extpro_1 A B C D E)) = (k2_compos_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) &  ((v4_circcomb B A) &  ((v6_circcomb B A) & (l3_msualg_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden (k4_tarski D E) (u4_struct_0 A)) &  (! [F:$i] :  ((r2_hidden F (k10_xtuple_0 D)) => (r1_facirc_1 A B C F)) ) )  => (r1_facirc_1 A B (k6_circuit2 A B C) (k4_tarski D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers E A)) &  ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers F B)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers E C)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers F D))) ) )  => (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers E F) (k3_xboole_0 (k3_xboole_0 (k3_xboole_0 A C) B) D)))) ) ) ) ) ) ) ) ) ).
tt(t36_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k16_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k19_sin_cos (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t36_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 k2_sin_cos9) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t36_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 B (k3_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k3_limfunc1 A)) => (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) ) ) )  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A)))) ) ) ) ) ).
tt(t36_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))) 2))) &  ( (B = (k3_valued_1 k1_numbers k1_numbers k1_numbers C D))  &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ( ((k1_seq_1 C E) = E)  &  (~ (r1_xxreal_0 (k1_seq_1 B E) k6_numbers)) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))) 2) A) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k10_real_1 1 2))) 2) A) E) = (k8_real_1 (k7_real_1 (k8_real_1 2 E) 1) (k10_prepower (k7_real_1 (k2_newton E 2) E) (k1_real_1 (k10_real_1 1 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k24_sin_cos) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) A) C) = (k8_real_1 (k1_seq_1 k24_sin_cos C) (k10_prepower (k7_real_1 1 (k1_seq_1 k24_sin_cos C)) (k10_real_1 1 2)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k24_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k19_sin_cos B)) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t36_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k19_sin_cos (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t36_fib_num2,ax, ((k4_xcmplx_0 (k7_xcmplx_0 1 k1_fib_num)) = k2_fib_num) ).
tt(t36_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_nat_1 (k3_fib_num3 A B (k2_nat_1 C 2)) (k3_fib_num3 A B (k2_nat_1 C 3))) = (k3_fib_num3 A B (k2_nat_1 C 4))) ) ) ) ) ) ) ).
tt(t36_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = 1) )  =>  ((k1_fib_num3 (k2_xcmplx_0 A 1)) = (k13_complex1 (k2_xcmplx_0 (k1_fib_num3 A) (k6_square_1 (k3_xcmplx_0 5 (k6_xcmplx_0 (k1_pepin (k1_fib_num3 A)) (k3_xcmplx_0 4 (k3_power (k4_xcmplx_0 1) A)))))) 2)) ) ) ) ).
tt(t36_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  ( ((r5_finseq_8 A C B) & (r5_finseq_8 A D B))  => (r2_finseq_8 A (k9_finseq_8 A (k1_finseq_8 A C D) B) (k1_finseq_8 A B D) 1)) ) ) ) ) ) ) ) ) ).
tt(t36_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B (k5_filter_0 A B C)) & (r1_tarski C (k5_filter_0 A B C))) ) ) ) ) ) ) ).
tt(t36_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r3_lattices (k7_filter_1 A B) (k9_filter_1 A B C E) (k9_filter_1 A B D F)) <=>  ((r3_lattices A C D) & (r3_lattices B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A)))))  =>  ( ((k3_filter_0 (k1_lattice2 A) (k3_filter_2 A B)) = (k7_filter_2 A B))  &  ( ((k3_filter_0 A B) = (k7_filter_2 (k1_lattice2 A) (k3_filter_2 A B)))  &  ( ((k3_filter_0 A (k4_filter_2 A C)) = (k7_filter_2 (k1_lattice2 A) C))  &  ((k3_filter_0 (k1_lattice2 A) C) = (k7_filter_2 A (k4_filter_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t36_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m2_finseq_1 (k7_finseq_1 A B) C) =>  ((m2_finseq_1 A C) & (m2_finseq_1 B C)) ) ) ) ) ) ) ).
tt(t36_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C D)))) )  =>  ( (E = (k10_finseq_1 A B))  =>  ((k1_partfun1 k5_numbers C C D E F) = (k10_finseq_1 (k1_funct_1 F A) (k1_funct_1 F B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((k9_finseq_1 A) = (k11_finseq_1 B C D)) ) ) ) ) ) ).
tt(t36_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (r2_hidden C (k4_finseq_1 (k5_finseq_4 A B))))  =>  ((k1_funct_1 A C) = (k1_funct_1 (k5_finseq_4 A B) C)) ) ) ) ) ) ) ).
tt(t36_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((k2_rfinseq B (k2_nat_1 (k3_finseq_1 C) A) (k8_finseq_1 B C D)) = (k2_rfinseq B A D)) ) ) ) ) ) ) ) ) ).
tt(t36_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (~ (r2_hidden A (k10_xtuple_0 B)))  =>  ((k4_finseq_4 (k7_finseq_1 (k7_finseq_1 B (k9_finseq_1 A)) C) A) = (k2_nat_1 (k3_finseq_1 B) 1)) ) ) ) ) ) ) ).
tt(t36_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((r6_binop_1 B F G) => (r2_funct_2 A B (k9_funcop_1 B A F E (k5_binop_1 B G C D)) (k6_funcop_1 B A G (k9_funcop_1 B A F E C) (k9_funcop_1 B A F E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  ((v2_fintopo2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k10_fintopo2 A B) B)) ) ) ) ) ).
tt(t36_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski B (k7_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t36_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) & (v4_fin_topo B A)) )  => (v4_fin_topo (k9_fin_topo A B) A)) ) ) ) ) ).
tt(t36_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k2_flang_1 A) B) =>  ((r1_xxreal_0 C D) | (r1_tarski (k7_flang_1 A B D) (k7_flang_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t36_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k1_flang_2 A B C D) B) = (k6_flang_1 A B (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t36_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_3 A (k7_flang_1 A B C) D) (k7_flang_1 A (k1_flang_3 A B D) C))) ) ) ) ) ) ) ).
tt(t36_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D B) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E B) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) )  =>  ((k1_funct_1 (k20_fomodel0 B A C) (k7_finseq_1 D E)) = (k7_finseq_1 (k1_funct_1 (k20_fomodel0 B A C) D) (k1_funct_1 (k20_fomodel0 B A C) E))) ) ) ) ) ) ) ) ) ) ).
tt(t36_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) C) (k2_relset_1 (u1_struct_0 A) B)) &  ((v2_funct_1 C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) &  ((v3_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  (~ (m2_valued_0 (k1_partfun1 k5_numbers k5_numbers k5_numbers (u1_struct_0 A) D C) (u1_struct_0 A) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_frechet,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k10_real_1 1 B)))  &  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t36_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  =>  ((v4_fsm_1 (k7_fsm_1 B C D A) B C D) =>  ((k6_fsm_1 B C D (k2_nat_1 A 1)) = (k6_fsm_1 B C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t36_fsm_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_3 D B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B)))))  =>  ((k3_rewrite3 B (k9_flang_1 B) (k4_fsm_3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D) C (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D (k2_flang_1 B) A))) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) (k3_rewrite3 B (k4_subset_1 (k3_catalan2 B) (k9_flang_1 B) (k4_flang_1 B (k2_flang_1 B))) D C A))) ) ) ) ) ) ) ) ).
tt(t36_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (~  ((r2_hidden A (k2_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden B (k2_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden C (k2_msafree2 (k19_ftacell1 A B C D E))) &  ((r2_hidden D (k2_msafree2 (k19_ftacell1 A B C D E))) & (r2_hidden E (k2_msafree2 (k19_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((v1_funct_1 (k3_funcop_1 C D E)) &  ((v1_funct_2 (k3_funcop_1 C D E) B A) & (m1_subset_1 (k3_funcop_1 C D E) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ( ((k9_xtuple_0 (k3_relat_1 A (k2_funct_1 A))) = (k9_xtuple_0 A))  &  ((k10_xtuple_0 (k3_relat_1 A (k2_funct_1 A))) = (k9_xtuple_0 A)) ) ) ) ) ).
tt(t36_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r1_tarski (k7_relset_1 A B D C) B)) ) ) ) ) ).
tt(t36_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k1_funct_1 (k4_funct_3 B C) A) = 1)  => (r2_hidden A B)) ) ) ) ).
tt(t36_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_partfun1 D A) =>  ((k1_funct_4 C D) = D) ) ) ) ) ) ) ) ).
tt(t36_funct_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((r1_tarski (k10_xtuple_0 (k1_funct_5 A)) (k4_partfun1 (k10_xtuple_0 (k9_xtuple_0 A)) (k10_xtuple_0 A))) & (r1_tarski (k10_xtuple_0 (k3_funct_5 A)) (k4_partfun1 (k9_xtuple_0 (k9_xtuple_0 A)) (k10_xtuple_0 A)))) ) ) ).
tt(t36_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden B (k4_card_3 (k2_funct_6 C))) & (r2_hidden A (k9_xtuple_0 B)))  =>  ((k5_funct_6 (k7_funct_6 C) B A) = (k5_funct_6 C A (k1_funct_1 B A))) ) ) ) ) ) ) ).
tt(t36_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ((k7_partfun1 A (k3_funct_7 A B D C) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t36_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k37_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t36_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_int_1 C))  => (v1_funct_9 (k15_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers k19_sin_cos A) B) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ).
tt(t36_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v21_functor0 C A B) & (v7_functor0 C A B))  => (v6_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t36_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ((m1_functor3 G B C E F) =>  ((r1_functor3 B C E F) =>  ((r1_functor3 A C (k1_functor3 A B C D E) (k1_functor3 A B C D F)) & (m1_functor3 (k6_functor3 A B C E F D G) A C (k1_functor3 A B C D E) (k1_functor3 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) <=> (r1_fuzzy_1 (k3_fuzzy_1 A C) (k3_fuzzy_1 A B))) ) ) ) ) ) ) ).
tt(t36_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_2 A B C) (k3_fuzzy_1 A (k2_fuzzy_2 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C))))) ) ) ) ) ) ).
tt(t36_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (C = (k4_struct_0 A)) )  &  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k3_funct_2 (u1_struct_0 A) k7_numbers B C) = (k4_xxreal_3 D (k1_fvaluat1 (k2_relset_1 k7_numbers B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B C (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) = C) ) ) ) ) ) ) ).
tt(t36_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~ (v1_xboole_0 (k30_gate_1 A B C D E F G H)))  <=>  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r4_gcd_1 A (k5_gcd_1 A B (k8_group_1 A C E) (k8_group_1 A D E)) (k8_group_1 A E (k5_gcd_1 A B C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((r1_xxreal_0 (k3_finseq_1 F) A) &  ((r1_xxreal_0 (k3_finseq_1 F) B) &  ((r1_xxreal_0 (k3_finseq_1 F) C) & (r1_xxreal_0 (k3_finseq_1 F) D)) ) )  =>  ((k10_genealg1 E F G A B C D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((r2_geomtrap A B C D E F G) &  ( (I = (k8_real_1 (k9_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k3_rlvect_1 A D E)) (k8_real_1 2 (k4_geomtrap A B C (k5_algstr_0 A D E) F))) (k2_real_1 (k4_geomtrap A B C (k5_algstr_0 A D E) (k5_algstr_0 A D E)))))  &  (H = (k3_rlvect_1 A F (k1_rlvect_1 A (k5_algstr_0 A D E) I))) ) )  =>  ( (D = E)  |  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k14_twoscomp) C) k14_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp) (u1_struct_0 (k13_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) => (r1_tarski (k21_glib_000 A B) (k21_glib_000 A C))) ) ) ) ) ).
tt(t36_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( ((k2_nat_1 (k3_finseq_1 (k8_glib_001 A B C D)) C) = (k2_nat_1 D 1))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 (k8_glib_001 A B C D)) E))  =>  ( ((k1_funct_1 (k8_glib_001 A B C D) (k2_nat_1 E 1)) = (k1_funct_1 B (k2_nat_1 C E)))  & (r2_hidden (k2_nat_1 C E) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ( (~ (v5_glib_002 B A))  => (v1_glib_002 C)) ) ) ) ) ) ) ).
tt(t36_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k7_glib_003 A) = (k7_glib_003 (k12_glib_003 A B C))) ) ) ) ) ).
tt(t36_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_card_1 (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))) = (k6_nat_1 (k1_nat_1 B 1) (k5_card_1 (k1_glib_002 A (k10_subset_1 (k6_glib_000 A)))))) ) ) ) ) ).
tt(t36_goboard1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ( (~  ((k3_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) = k1_xboole_0) )  &  ( (~  ((k3_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) = k1_xboole_0) )  &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 B)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) &  ((r1_xxreal_0 1 (k3_finseq_1 C)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r2_hidden (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid 1 1)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers k6_numbers)))) ) ).
tt(t36_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k7_nat_d (k1_matrix_1 (k2_goboard2 A)) 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A)))) (k13_complex1 1 2)) (k19_euclid 1 k6_numbers)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) (k1_matrix_1 (k2_goboard2 A))) (k19_euclid 1 1))) (k3_topreal1 2 A))) ) ).
tt(t36_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C)) ) ) ) ) ) )  =>  ((k5_gobrd13 D E A) = (k3_goboard5 E (k2_nat_1 B 1) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k2_jordan2c 2 (k3_topreal1 2 A)) = (k2_goboard9 A)) ) ) ).
tt(t36_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v1_finset_1 (k6_goedelcp A B)) => (v1_finset_1 (k6_goedelcp A (k4_subset_1 (k3_cqc_lang A) B (k6_domain_1 (k3_cqc_lang A) C))))) ) ) ) ) ) ) ).
tt(t36_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  ( ((r2_graph_2 A C) & (r1_graph_2 A B C))  =>  ((k10_xtuple_0 B) = (k2_tarski (k1_funct_1 (u1_graph_1 A) (k1_funct_1 C 1)) (k1_funct_1 (u2_graph_1 A) (k1_funct_1 C 1)))) ) ) ) ) ) ) ) ).
tt(t36_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_graph_1 D A) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k8_graph_3 A B C))) =>  ( ( (F = E)  & (r1_graph_2 A E D))  => (r1_graph_2 (k8_graph_3 A B C) F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ((r3_graph_5 A D B C) => (r1_graph_5 A D B C)) ) ) ) ) ) ) ) ) ).
tt(t36_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ( ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 A (k4_nat_1 3 B)))  |  ((k1_seq_1 (k6_graphsp (k19_graphsp B) C) A) = (k1_seq_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t36_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k25_grcat_1 A))) =>  (! [D:$i] :  ((m3_grcat_1 D (k18_grcat_1 (k17_grcat_1 A))) =>  (! [E:$i] :  ((m3_grcat_1 E (k18_grcat_1 (k17_grcat_1 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ( ( ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B))  =>  ((k19_grcat_1 (k17_grcat_1 A) E) = (k20_grcat_1 (k17_grcat_1 A) D)) )  &  ( ( ((k19_grcat_1 (k17_grcat_1 A) E) = (k20_grcat_1 (k17_grcat_1 A) D))  =>  ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B)) )  &  ( ( ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B))  => (r2_hidden (k4_tarski E D) (k9_xtuple_0 (k24_grcat_1 (k17_grcat_1 A)))))  &  ( ((r2_hidden (k4_tarski E D) (k9_xtuple_0 (k24_grcat_1 (k17_grcat_1 A)))) =>  ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B)) )  &  ( ( ((k3_graph_1 (k25_grcat_1 A) C) = (k4_graph_1 (k25_grcat_1 A) B))  =>  ((k1_cat_1 (k25_grcat_1 A) B C) = (k13_grcat_1 E D)) )  &  ( ( ((k3_graph_1 (k25_grcat_1 A) B) = (k3_graph_1 (k25_grcat_1 A) C))  =>  ((k19_grcat_1 (k17_grcat_1 A) D) = (k19_grcat_1 (k17_grcat_1 A) E)) )  &  ( ( ((k19_grcat_1 (k17_grcat_1 A) D) = (k19_grcat_1 (k17_grcat_1 A) E))  =>  ((k3_graph_1 (k25_grcat_1 A) B) = (k3_graph_1 (k25_grcat_1 A) C)) )  &  ( ( ((k4_graph_1 (k25_grcat_1 A) B) = (k4_graph_1 (k25_grcat_1 A) C))  =>  ((k20_grcat_1 (k17_grcat_1 A) D) = (k20_grcat_1 (k17_grcat_1 A) E)) )  &  ( ((k20_grcat_1 (k17_grcat_1 A) D) = (k20_grcat_1 (k17_grcat_1 A) E))  =>  ((k4_graph_1 (k25_grcat_1 A) B) = (k4_graph_1 (k25_grcat_1 A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k3_int_7 A) = (k1_uniroots (k9_int_3 A))) ) ) ).
tt(t36_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (~  ( (~  (D = (k1_groeb_1 A C (k7_polynom1 A C))) )  &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (~  ((r2_groeb_1 A B C E D) &  (~ (r2_hidden (k7_polynom1 A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  (~  ((r2_groeb_2 A C D E F) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 H A C) &  ((v3_polynom7 H A C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 I A C) &  ((v1_polynom1 I (k15_pre_poly A) C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (~  ((r2_hidden G (k4_finseq_1 F)) &  ((r2_hidden I E) &  ( ((k1_funct_1 F G) = (k9_polynom1 A C H I))  & (r1_termord A B (k3_termord A B C D) (k3_termord A B C (k9_polynom1 A C H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k5_groeb_3 A B C D 1) (k5_termord A B C D)) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_groeb_3 A B C D 1) (k6_termord A B C D))) ) ) ) ) ) ) ) ) ).
tt(t36_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k1_group_11 A (k1_group_11 A B C) C) (k2_group_11 A (k2_group_11 A B C) C))) ) ) ) ) ) ).
tt(t36_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B (k19_binop_2 A) C) = (k2_group_1 B (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(t36_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_group_2 A B (k2_subset_1 (u1_struct_0 A))) = (u1_struct_0 A))  &  ((k4_group_2 A B (k2_subset_1 (u1_struct_0 A))) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t36_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_group_3 A (k1_group_2 A B) C) = (k1_group_2 A (k3_group_3 A B C))) ) ) ) ) ) ) ).
tt(t36_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (~ (v1_group_4 (k1_group_1 A) A)) ) ) ).
tt(t36_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_group_5 A B C) = (k1_group_1 A))  <=>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ) ).
tt(t36_group_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E (k5_group_1 B A D)) = (k5_group_1 C A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k2_group_1 (k2_group_7 (k1_enumset1 1 2 3) (k11_finseq_1 A B C)) (k6_group_7 A B C D E F)) = (k6_group_7 A B C (k2_group_1 A D) (k2_group_1 B E) (k2_group_1 C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  ((m1_group_9 C A D) <=>  ((k19_group_9 A B C D) = D) ) ) ) ) ) ) ) ) ).
tt(t36_groupp_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) ) )  =>  ( ((v2_group_10 B A) &  ((k2_groupp_1 A B) = 1) )  => (v3_groupp_1 B A)) ) ) ) ) ).
tt(t36_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ((k1_hausdorf A B B) = k6_numbers) ) ) ) ) ).
tt(t36_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k13_glib_001 A (k2_helly A B C))) <=>  ((k2_helly A B C) = (k7_glib_001 A (k2_helly A B D) (k2_helly A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t36_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear G k1_complfld A B) &  ((v2_bilinear G k1_complfld A B) &  ((v4_bilinear G k1_complfld A B) &  ((v2_hermitan G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) G (k5_algstr_0 A C D) (k5_algstr_0 B E F)) = (k5_algstr_0 k1_complfld (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) G C E) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) G C F)) (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) G D E) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) G D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k4_yellow_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A))) = (k1_tarski k1_xboole_0)) ) ) ).
tt(t36_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ((r1_xxreal_0 B C) |  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k1_taylor_1 B) D) C) A) = (k8_real_1 (k8_real_1 (k6_newton C B) (k3_newton C)) (k5_prepower A (k9_real_1 B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k3_hilbert1 A B) A) B) k6_hilbert1)) ) ) ) ).
tt(t36_hilbert2,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (~  ((r2_hidden A (k6_trees_2 k1_hilbert1 (k3_hilbert2 B))) &  ( (~  (A = k2_hilbert1) )  &  (~ (v3_hilbert2 A)) ) ) ) ) ) ) ) ).
tt(t36_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_hilbert3 C A) (k3_hilbert3 C A)) &  ((v3_funct_2 E (k3_hilbert3 C A) (k3_hilbert3 C A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C A))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_hilbert3 C B) (k3_hilbert3 C B)) &  ((v3_funct_2 F (k3_hilbert3 C B) (k3_hilbert3 C B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C B) (k3_hilbert3 C B))))) ) )  =>  ( ((r2_funct_2 (k3_hilbert3 C A) (k3_hilbert3 C A) E (k5_hilbert3 C D A)) & (r2_funct_2 (k3_hilbert3 C B) (k3_hilbert3 C B) F (k5_hilbert3 C D B)))  => (r1_funct_2 (k3_hilbert3 C (k3_hilbert1 A B)) (k3_hilbert3 C (k3_hilbert1 A B)) (k9_funct_2 (k3_hilbert3 C A) (k3_hilbert3 C B)) (k9_funct_2 (k3_hilbert3 C A) (k3_hilbert3 C B)) (k5_hilbert3 C D (k3_hilbert1 A B)) (k1_hilbert3 (k3_hilbert3 C A) (k3_hilbert3 C B) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) =>  ( (B = (k9_polynom3 A))  |  ((k2_hurwitz A (k5_hurwitz A B (k3_hurwitz A C 1))) = (k6_xcmplx_0 (k2_hurwitz A B) 1)) ) ) ) ) ) ) ) ) ).
tt(t36_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k17_idea_1 (k2_nat_1 D 1) B A C) = (k7_finseq_1 (k17_idea_1 D B A C) (k9_finseq_1 (k15_idea_1 A (k8_matrix_1 k5_numbers C (k2_nat_1 D 1)))))) ) ) ) ) ) ) ) ) ).
tt(t36_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_ideal_1 D A C) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ((m2_finseq_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (~  ((r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) F C) E) &  ((r1_ideal_1 A C D G) &  (! [H:$i] :  ((m1_ideal_1 H B E) =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 H))  &  (! [I:$i] :  ((r2_hidden I (k1_relset_1 k5_numbers H)) =>  ((k1_funct_1 H I) = (k6_algstr_0 B (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) G I))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) G I)))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A)) G I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A) =>  ( (B = C)  |  ( (B = D)  |  ((k1_incsp_1 A B C) = (k1_incsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) (u1_cat_1 C) (k7_isocat_1 C)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) D) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v11_struct_0 F))  &  ((v2_cat_1 F) &  ((v3_cat_1 F) &  ((v4_cat_1 F) &  ((v5_cat_1 F) &  ((v6_cat_1 F) &  ((v3_cat_5 F) & (l1_cat_1 F)) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m2_cat_1 G E F) =>  ((k16_index_1 A C B (k15_index_1 C D E F G)) = (k15_index_1 A (k16_index_1 A C B D) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 B A D E) =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ( (F = (k1_instalg1 B A C D E))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  ((r1_msualg_6 B G H F I) => (r1_msualg_6 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D H) C I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 (k1_int_1 A) (k2_int_1 A))) ) ).
tt(t36_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_nat_d B (k1_recdef_1 A C))) ) )  => (r1_nat_d B (k2_wsierp_1 A))) ) ) ) ) ).
tt(t36_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (r1_xxreal_0 A 2))  =>  ((k2_int_5 (k4_xcmplx_0 1) A) = (k1_newton (k4_xcmplx_0 1) (k3_nat_d (k7_nat_d A 1) 2))) ) ) ) ).
tt(t36_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k2_int_6 (k8_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) C) (k6_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t36_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (C = (k1_taylor_1 2))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = 1)  &  ( (~  (F = k6_numbers) )  &  ((k1_seq_1 E F) = (k10_real_1 (k8_real_1 2 F) (k5_square_1 (k7_real_1 1 (k5_square_1 F))))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers D C))) = B)  &  ( (B = (k9_xtuple_0 E))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E A))) ) ) ) )  =>  ((k2_integra5 A E) = (k9_real_1 (k1_seq_1 (k3_rfunct_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers D C)) (k4_seq_4 A)) (k1_seq_1 (k3_rfunct_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers D C)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ( ((k1_seq_1 B D) = (k7_binop_2 (k12_binop_2 1 (k11_binop_2 D (k9_binop_2 1 (k5_square_1 (k1_seq_1 k3_taylor_1 D)))))))  &  ( (~ (r1_xxreal_0 (k1_seq_1 k3_taylor_1 D) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k3_taylor_1 D))) ) ) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t36_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 1 (k8_real_1 (k5_square_1 D) (k5_square_1 (k1_seq_1 k16_sin_cos (k10_real_1 1 D)))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t36_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos D) (k1_seq_1 k16_sin_cos (k1_seq_1 k16_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t36_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ((m1_integra1 E B) =>  (! [F:$i] :  ((m2_finseq_1 F (k1_euclid A)) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) &  (F = G) )  =>  ((m3_integr15 F A B C E) <=> (m1_integr18 G (k4_real_ns1 A) B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ((m1_integra1 D C) =>  (~  ((r2_hidden A (k4_finseq_1 D)) &  ((r2_hidden B (k4_finseq_1 D)) &  ((r1_xxreal_0 A B) &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_measure5 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers))) )  =>  (~  ( ((k5_seq_4 E) = (k1_seq_1 (k3_finseq_6 k1_numbers D A B) 1))  &  ( ((k4_seq_4 E) = (k1_seq_1 (k3_finseq_6 k1_numbers D A B) (k3_finseq_1 (k3_finseq_6 k1_numbers D A B))))  & (m1_integra1 (k3_finseq_6 k1_numbers D A B) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (v4_xxreal_2 (k1_rvsum_1 (k9_integra1 A B)))) ) ) ) ) ).
tt(t36_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ((k7_rfunct_1 C C) = (k2_partfun1 k1_numbers k1_numbers (k1_integra8 1) C)) ) ) ) ) ) ) ).
tt(t36_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 (k8_real_1 (k8_real_1 2 A) k32_sin_cos) (k8_real_1 (k7_real_1 (k8_real_1 2 A) 1) k32_sin_cos)))  => (r1_integra9 B k16_sin_cos k19_sin_cos)) ) ) ) ) ).
tt(t36_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  => (r1_interva1 A (k4_interva1 A (k3_interva1 A B C) C) C)) ) ) ) ) ) ).
tt(t36_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 (k4_intpro_1 A B) C) (k3_intpro_1 A (k3_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t36_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 A B) => (v1_int_1 (k13_complex1 (k9_newton B) (k9_newton A)))) ) ) ) ) ).
tt(t36_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  (! [I:$i] :  ((m2_nattra_1 I B C F G) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 B C F G))  => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k6_isocat_1 A B C D E F G H I) (k7_nattra_1 A C (k9_cat_1 A B C D F) (k9_cat_1 A B C D G) (k9_cat_1 A B C E G) (k5_isocat_1 A B C F G D I) (k4_isocat_1 A B C D E H G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 A C F G))  => (r1_nattra_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~ (v3_isomichi B A))  &  ( (~ (v4_isomichi B A))  &  (~ (v5_isomichi B A)) ) ) ) ) ) ) ) ).
tt(t36_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k1_rltopsp1 (k15_euclid A) C D)) =>  ((r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)) (k12_euclid (k5_algstr_0 (k15_euclid A) C D))) & (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B D)) (k12_euclid (k5_algstr_0 (k15_euclid A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_0_jgraph_2) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t36_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) =>  ((k1_funct_1 B C) = (k8_real_1 (k17_euclid C) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid C) (k18_euclid C))))))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) &  ((k18_euclid C) = k6_numbers) ) ) ) ) )  => (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) k3_topmetr)) ) ) ) ) ).
tt(t36_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) B) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  (~  ( (C = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  & (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr (k7_real_1 (k8_real_1 D A) C) (k7_real_1 (k8_real_1 D B) C)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr (k7_real_1 (k8_real_1 D A) C) (k7_real_1 (k8_real_1 D B) C))))))) )  =>  (~  ((v3_tops_2 E (k4_topmetr A B) (k4_topmetr (k7_real_1 (k8_real_1 D A) C) (k7_real_1 (k8_real_1 D B) C))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 A B)) =>  ((k1_funct_1 E F) = (k7_real_1 (k8_real_1 D F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_pscomp_1 (k1_sppol_2 A B C D)) = A) ) ) ) ) ) ) ) ) ) ).
tt(t36_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = H)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid C) F) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid B)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan14,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_jordan1h A B) & (r1_xxreal_0 B C))  => (r1_tarski (k2_goboard9 (k1_jordan13 A C)) (k2_goboard9 (k1_jordan13 A B)))) ) ) ) ) ) ) ).
tt(t36_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D)))) ) )  =>  ( ( (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 D k6_numbers)) ) )  &  (~  ( (B = k6_numbers)  &  (D = k6_numbers) ) ) )  |  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) (k1_jordan1a (k1_jordan8 E B)) A)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) (k1_jordan1a (k1_jordan8 E D)) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  ( (F = (a_4_6_jordan1 A B C D))  &  (G = (a_4_7_jordan1 A B C D)) ) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) E) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) F G))  &  ( (~  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) E) = k1_xboole_0) )  &  ((r1_xboole_0 F G) &  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E))))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E))))) =>  ( ( (H = F)  &  (I = G) )  =>  ((v3_connsp_1 H (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E))) & (v3_connsp_1 I (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1b,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) => (r1_tarski (k3_goboard5 (k1_jordan8 A C) (k3_finseq_1 (k1_jordan8 A C)) B) (k2_jordan2c 2 A))) ) ) ) ) ) ) ).
tt(t36_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))))  =>  ((r1_xxreal_0 B k6_numbers) |  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k1_jordan1a (k1_jordan8 A B)))) = (k7_xcmplx_0 (k2_xcmplx_0 (k9_pscomp_1 A) (k7_pscomp_1 A)) 2)) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan8 D B)))) )  =>  ((r1_xxreal_0 1 (k1_int_1 (k7_real_1 (k10_real_1 (k9_real_1 C 2) (k13_newton 2 (k7_nat_d B A))) 2))) & (r1_xxreal_0 (k3_real_1 (k1_int_1 (k7_real_1 (k10_real_1 (k9_real_1 C 2) (k13_newton 2 (k7_nat_d B A))) 2)) 1) (k3_finseq_1 (k1_jordan8 D A)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ((v2_connsp_1 D (k15_euclid 2)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden B (k3_goboard9 A)) &  ((r2_hidden C (k2_goboard9 A)) &  ((r2_hidden B D) &  ((r2_hidden C D) & (r1_xboole_0 D (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~ (v2_funct_2 (k2_jgraph_2 A B C D) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xxreal_0 (k18_euclid (k1_jordan21 A)) (k18_euclid (k2_jordan21 A)))) ) ) ).
tt(t36_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_tarski (k4_jordan19 A) A)) ) ).
tt(t36_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v3_jordan23 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) &  (B = (k1_funct_1 A (k2_nat_1 (k1_jordan3 A B) 1))) ) ) ) )  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ((k2_nat_1 (k2_nat_1 (k1_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) B) (k1_jordan3 A B)) 1) = (k3_finseq_1 A)) ) ) ) ) ) ) ).
tt(t36_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ((k2_jordan2c A (k1_struct_0 (k15_euclid A))) = (k1_euclid A)) ) ) ) ).
tt(t36_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) )  =>  ( (B = C)  | (r1_jordan3 (k4_jordan3 A B C) B C)) ) ) ) ) ) ) ) ).
tt(t36_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v2_funct_1 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) ) )  =>  ( ( (~  ((k1_funct_1 B C) = (k1_funct_1 B D)) )  &  (~  ((k7_partfun1 A B C) = (k7_partfun1 A B D)) ) )  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k18_euclid D) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) B C)))  & (r2_hidden D (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  ( (A = (k6_subset_1 (u1_struct_0 k17_borsuk_1) (k2_tarski k6_numbers 1)))  =>  ( (~  (A = k1_xboole_0) )  & (v2_connsp_1 A k17_borsuk_1)) ) ) ) ).
tt(t36_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_jordan_a B A) =>  (~ (r1_xxreal_0 (k5_jordan_a A B) k6_numbers)) ) ) ) ) ).
tt(t36_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A C D) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) => (r1_tarski (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D F E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((u1_struct_0 (k8_knaster A B)) = (a_2_3_knaster A B)) ) ) ) ) ).
tt(t36_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) = (k1_tops_1 k3_topmetr k6_kurato_1)) ) ).
tt(t36_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) C D) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B D))) ) )  => (r1_tarski (k2_kurato_2 (k15_euclid 2) C) (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_kurato_2 (k15_euclid 2) A) (k2_kurato_2 (k15_euclid 2) B)))) ) ) ) ) ) ) ).
tt(t36_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k5_matrix_6 A B C))) =>  ((k3_matrix_1 (u1_struct_0 B) (k5_matrix_6 A B C) D E) = (k8_group_1 B (k8_group_1 B (k11_algstr_0 B (k12_matrix_3 A B C)) (k1_laplace B (k4_group_1 B) (k4_algstr_0 B (k1_group_1 B)) (k2_xcmplx_0 D E))) (k5_laplace E D A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 (k1_lattice2 B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k1_lattice2 B)))))) )  =>  ((r1_funct_2 A (u1_struct_0 B) A (u1_struct_0 (k1_lattice2 B)) D E) =>  ( ((k2_lattice2 A B C D) = (k3_lattice2 A (k1_lattice2 B) C E))  &  ((k3_lattice2 A B C D) = (k2_lattice2 A (k1_lattice2 B) C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ((v6_lattice3 A) <=>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_lattices A (k16_lattice3 A (a_3_5_lattice3 A B C)) (k3_lattices A C (k16_lattice3 A B)))) ) ) ) ) ) ).
tt(t36_lattice4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((r2_hidden A (k4_lattice4 B C)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k4_filter_0 B D E))  &  ((r2_hidden D C) & (r2_hidden E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 D A B) &  ((v2_lattice5 D A B) &  ((v3_lattice5 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [E:$i] :  ((m1_lattice5 E A B D) =>  ((r1_ordinal1 C (k7_lattice5 A B D)) =>  ((v1_funct_1 (k12_lattice5 A B D E C)) &  ((v1_funct_2 (k12_lattice5 A B D E C) (k2_zfmisc_1 (k8_lattice5 A C) (k8_lattice5 A C)) (u1_struct_0 B)) &  ((v1_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B) &  ((v2_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B) &  ((v3_lattice5 (k12_lattice5 A B D E C) (k8_lattice5 A C) B) & (m1_subset_1 (k12_lattice5 A B D E C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k8_lattice5 A C) (k8_lattice5 A C)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((r1_lattice8 A 2) <=> (v1_yellow11 A)) ) ) ).
tt(t36_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B))) = (k6_glib_000 A))  <=> (r1_xxreal_0 (k15_glib_000 A) B)) ) ) ) ) ).
tt(t36_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((k4_fuzzy_4 A A A (k5_lfuzzy_1 A B) (k5_lfuzzy_1 A B)) = (k1_yellow_0 (k4_lfuzzy_0 (k2_zfmisc_1 A A)) (a_2_1_lfuzzy_1 A B))) ) ) ) ) ).
tt(t36_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 k6_numbers (k1_seq_1 A C))) ) ) ) )  | (v2_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ) ).
tt(t36_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r6_limfunc2 B A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r6_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t36_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc3 B A) =>  ((r1_limfunc3 (k56_valued_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc3 (k56_valued_1 k1_numbers k1_numbers B) A) = (k18_complex1 (k1_limfunc3 B A))) ) ) ) ) ) ) ).
tt(t36_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc3 B A) &  ((v5_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r3_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t36_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((r1_lmod_6 A B C) => (r1_tarski (k2_struct_0 B) (k2_struct_0 C))) ) ) ) ) ) ) ).
tt(t36_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (D = (k1_rlvect_1 (k16_lopban_1 A B) C E))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k17_lopban_1 A B D F) = (k1_rlvect_1 B (k17_lopban_1 A B C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~  ((k1_normsp_1 A B D) = (k4_struct_0 A)) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D))) ) ) )  & (v2_comseq_2 C))  =>  ((r1_xxreal_0 1 (k2_seq_2 C)) | (v2_lopban_3 B A)) ) ) ) ) ) ) ) ).
tt(t36_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lopban_4 A B C) =>  ((k6_algstr_0 A B (k10_lopban_4 A C)) = (k6_algstr_0 A (k10_lopban_4 A C) B)) ) ) ) ) ) ) ) ).
tt(t36_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) )  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  & (r1_filter_1 A (k6_lopclset B))) ) ) ) ).
tt(t36_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k12_lpspace1 B C D))) =>  ( (E = F)  =>  ((k26_valued_1 B k1_numbers E A) = (k1_rlvect_1 (k12_lpspace1 B C D) F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) & (r1_lpspace1 A B C D E))  => (r2_hidden D (k5_lpspace2 A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ltlaxio1,ax, (! [A:$i] :  ((m2_subset_1 A k1_hilbert1 k13_ltlaxio1) =>  (~  ( (~ (v1_ltlaxio1 A))  &  ( (~ (v3_ltlaxio1 A))  &  ( (~ (v4_ltlaxio1 A))  &  ( (~ (v5_ltlaxio1 A))  &  ( (~ (v6_ltlaxio1 A))  &  ( (~ (v7_ltlaxio1 A))  &  ( (~ (v8_ltlaxio1 A))  &  (~ (v9_ltlaxio1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden B (k4_cqc_the1 A)) <=> (r2_hidden (k6_cqc_lang A (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ) ).
tt(t36_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) (k3_mathmorp A B C) (k3_mathmorp A B D)) (k3_mathmorp A B (k9_subset_1 (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ).
tt(t36_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((v4_matrix10 B) & (v4_matrix10 C))  => (v4_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t36_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) B B) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ( ((k3_finseq_1 D) = B)  &  ((k3_finseq_1 E) = B) ) )  =>  ((k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) F (k3_fvsum_1 C D E))) = (k3_rlvect_1 C (k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) F D)) (k12_matrix_3 B C (k3_matrix11 A B B (u1_struct_0 C) F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 A k5_numbers)) =>  (~  ( ((k10_xtuple_0 D) = (k10_xtuple_0 F))  &  ( ((k10_xtuple_0 E) = (k10_xtuple_0 G))  &  ( (~  ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) C A A D E)) = (k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) C A A F G))) )  &  (~  ((k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) C A A D E)) = (k4_algstr_0 B (k12_matrix_3 A B (k1_matrix13 (u1_struct_0 B) C A A F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C B))  =>  ((k13_fvsum_1 A (k3_matrix14 A B C) (k3_matrix14 A B C)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t36_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k4_matrix15 A C D) = (k4_matrix15 A (k6_matrix_3 A C B) (k6_matrix_3 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v4_matrix16 B (u1_struct_0 A)) =>  ((k2_matrix16 (u1_struct_0 A) (k5_fvsum_1 A B)) = (k1_matrix_6 (k3_finseq_1 B) A (k2_matrix16 (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(t36_matrix_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 D)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 D))) ) )  => (r2_hidden (k4_tarski B C) (k2_matrix_1 D))) ) ) ) ) ) ) ) ).
tt(t36_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k2_matrix_3 A B) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B)))  =>  (B = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ) ).
tt(t36_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (v1_matrix_6 D A B))  =>  ((v1_matrix_6 (k4_matrix_6 A B C D) A B) &  ((k5_matrix_6 A B (k4_matrix_6 A B C D)) = (k4_matrix_6 A B (k5_matrix_6 A B D) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_xxreal_0 1 A) =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B (k5_matrix_1 A (u1_struct_0 B) D)) (k3_matrix_7 A C)) = (k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((r1_matrix_8 A B C D) & (v2_matrix_8 D A B))  =>  ((r1_xxreal_0 A k6_numbers) | (v2_matrix_8 C A B)) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 B (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  => (m2_finseq_1 B (k2_finseq_1 A))) ) ) ) ).
tt(t36_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k17_rvsum_1 (k9_seq_4 A B)) = (k3_binop_2 (k17_rvsum_1 A) (k17_rvsum_1 B))) ) ) ) ) ) ).
tt(t36_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrixj1 C A) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 A))))  =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k13_matrixj1 A B (k3_matrixj1 A C D)) = (k13_matrixj1 A B (k3_matrixj1 A C (k4_matrixj1 A (k13_matrixj1 A B D))))) ) ) ) ) ) ) ) ) ).
tt(t36_matrixr1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 C) = A)  &  ((k1_matrix_1 C) = B) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k3_matrixr1 C (k8_matrixr1 A B)) = C)  &  ((k3_matrixr1 (k8_matrixr1 A B) C) = C) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C A B B) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( (D = (k1_funct_1 C E))  & (r2_hidden E (k2_finseq_1 B)))  =>  ((k3_finseq_1 D) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ((k1_matrlin2 A B C (k4_matrlin2 A B C D E F) D E) = F) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((k3_finseq_1 D) = (k3_finseq_1 C))  =>  (D = (k9_matrlin A B C (k4_rlvect_1 B (k5_matrlin A B D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k6_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) D)))) =>  ((r2_hidden C (k6_matroid0 A B)) | (r2_hidden D (k6_matroid0 A (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C))))) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 k2_vectsp_1)) =>  ( (A = B)  =>  ((k18_rvsum_1 A) = (k4_rlvect_1 k2_vectsp_1 B)) ) ) ) ) ) ).
tt(t36_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 k2_vectsp_1) C B) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v3_card_1 G C) &  ((v1_finseq_1 G) & (v3_valued_0 G)) ) ) )  =>  ((k1_funct_1 (k3_matrtop1 (k2_xcmplx_0 A C) B (k8_matrlin (u1_struct_0 k2_vectsp_1) A C B E F)) (k7_finseq_1 D G)) = (k4_rvsum_1 (k1_funct_1 (k3_matrtop1 A B E) D) (k1_funct_1 (k3_matrtop1 C B F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (~  ((v2_matrtop3 B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 C (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (~  ((v3_matrtop3 C A) & (v1_matrtop3 (k1_partfun1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B C) (k3_matrix13 A))) ) ) ) ) ) ) ) ) ) ).
tt(t36_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v2_finset_1 B)) ) ) ) )  =>  ( (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ((r1_pboole A C B) &  ((r1_pboole A D B) &  ( (~ (r2_pboole A C D))  &  (~ (r2_pboole A D C)) ) ) ) ) ) ) ) )  => (r1_pboole A (k2_mboolean A B) B)) ) ) ) ).
tt(t36_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_zfmisc_1 (k2_tarski A B) (k1_tarski C) (k1_tarski D)) = (k2_tarski (k3_xtuple_0 A C D) (k3_xtuple_0 B C D))) ) ) ) ) ).
tt(t36_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_measure1 E A B C) =>  ((r1_tarski D E) => (m2_measure1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k7_real_1 (k18_complex1 A) (k18_complex1 B)) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ) ) ).
tt(t36_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  ((k5_member_1 (k7_member_1 A)) = (k7_member_1 (k5_member_1 A))) ) ) ).
tt(t36_membered,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_hidden B A) & (v6_membered B))  => (v6_membered (k1_setfam_1 A))) ) ) ).
tt(t36_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_funct_4 (k1_funct_4 C (k7_memstr_0 A B D)) (k7_memstr_0 A B E)) = (k1_funct_4 C (k7_memstr_0 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (~  ((r2_mesfun6c A B C D) &  ((r2_mesfun6c A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k1_mesfun6c A B C (k2_valued_1 A k2_numbers k2_numbers D E)) = (k2_xcmplx_0 (k1_mesfun6c A B C (k2_partfun1 A k2_numbers D F)) (k1_mesfun6c A B C (k2_partfun1 A k2_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (~  ((r2_mesfun6c A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (~  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((k1_funct_1 E F) = (k8_subset_1 A (k1_relset_1 A D) (k14_mesfunc1 (k55_valued_1 A k2_numbers D) (k1_measure6 (k10_real_1 1 (k1_nat_1 F 1)))))) ) )  &  ( ((k7_subset_1 A (k1_relset_1 A D) (k10_relat_1 (k55_valued_1 A k2_numbers D) k6_numbers)) = (k5_setfam_1 A (k4_measure1 A B E)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden (k1_funct_1 E F) B) &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k1_funct_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_mesfunc8 C A k2_numbers) &  ((r1_tarski (k1_relset_1 A D) (k1_relset_1 A (k4_mesfunc5 A k2_numbers C k6_numbers))) &  ((r2_hidden B (k1_relset_1 A D)) &  ((v1_comseq_3 (k9_mesfun7c A C B)) &  ((k1_funct_1 D B) = (k11_comseq_3 (k9_mesfun7c A C B))) ) ) ) )  =>  ((k1_funct_1 D B) = (k3_comseq_2 (k9_mesfun7c A (k3_mesfun9c A C) B))) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc1 A B C E) &  ((r1_mesfunc1 A B D E) & (r1_tarski E (k9_xtuple_0 D))) )  => (r2_hidden (k9_subset_1 A (k9_subset_1 A E (k15_mesfunc1 A C (k1_measure6 F))) (k17_mesfunc1 A D (k1_measure6 F))) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_prob_2 E) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ( ((v1_prob_2 F) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  ( ( ((k1_relset_1 k5_numbers E) = (k1_relset_1 k5_numbers F))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k1_relset_1 k5_numbers E)) =>  ((k1_funct_1 F H) = (k9_subset_1 A (k1_funct_1 E H) D)) ) ) )  & (r1_mesfunc3 A B C E G)) )  => (r1_mesfunc3 A B (k2_partfun1 A k7_numbers C D) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((k1_relset_1 A B) = (k1_relset_1 A (k47_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B))))  &  ((k1_relset_1 A B) = (k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B)))) ) ) ) ) ) ).
tt(t36_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers B D))) )  => (v6_supinf_2 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) ) ) ) ) ) ) ).
tt(t36_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_metric_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k2_metric_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_metric_2 A)) => (r1_xxreal_0 (k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) B D) (k2_xcmplx_0 (k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) B C) (k1_metric_1 (k2_metric_2 A) (k2_metric_2 A) (k10_metric_2 A) C D)))) ) ) ) ) ) ) ) ).
tt(t36_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) =>  ((k8_midsp_1 A B C) = (k8_midsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C C))) =>  ((r2_hidden (k4_tarski A B) (k18_mmlquery C D)) <=>  ( (A = B)  &  ((r2_hidden A C) &  (~ (r2_hidden A (k1_relset_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t36_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v9_mod_4 B A) <=> (v2_mod_4 (k7_mod_4 A A B) A (k2_mod_4 A))) ) ) ) ) ).
tt(t36_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~  ( ((k5_card_1 (k9_xtuple_0 A)) = 1)  &  ( (~  (A = k17_modal_1) )  &  (! [B:$i] :  ((m1_subset_1 B k3_modal_1) =>  (~  (A = (k16_modal_1 B)) ) ) ) ) ) ) ) ) ).
tt(t36_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r3_modelc_1 A B C G E) => (r3_modelc_1 A B C G F)) ) )  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r3_modelc_1 A B C G (k53_modelc_1 A B C D E)) => (r3_modelc_1 A B C G (k53_modelc_1 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((r2_modelc_2 A B) & (r2_modelc_2 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t36_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r5_modelc_3 C B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B))) )  => (r1_xxreal_0 (k21_modelc_3 C (k10_modelc_3 (k1_funct_1 B A) C)) (k3_real_1 (k6_xcmplx_0 (k21_modelc_3 C (k10_modelc_3 (k1_funct_1 B 1) C)) A) 1))) ) ) ) ) ) ) ).
tt(t36_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((v1_moebius1 (k4_nat_1 B A)) |  ((k2_moebius1 (k4_nat_1 B A)) = (k7_binop_2 (k2_moebius1 B))) ) ) ) ) ) ) ).
tt(t36_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B A))  =>  ( ((r2_hidden (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) (u1_struct_0 B)) & (v17_monoid_0 A))  => (v17_monoid_0 B)) ) ) ) ) ).
tt(t36_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k15_monoid_1 A (k20_monoid_1 A (k6_finseq_1 A)) B) = k6_numbers) ) ) ) ) ).
tt(t36_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k1_funct_1 B C) = k1_xboole_0)  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (~  ( ((k2_msualg_1 A D) = C)  &  ((k1_msualg_1 A D) = k1_xboole_0) ) ) ) ) ) ) ) )  => (v4_msualg_1 (k1_msafree3 A B) A)) ) ) ) ) ).
tt(t36_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  & (r1_msaterm A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A C)) => (m3_pboole (k4_pboole A D B) A (k1_mboolean A C))) ) ) ) ) ) ) ).
tt(t36_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  ((k6_lattices (k17_msualg_2 A B)) = (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B))) ) ) ) ) ).
tt(t36_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((r2_pboole (u1_struct_0 A) (k7_msualg_6 A B C) (k8_msualg_6 A B C)) &  ((r2_pboole (u1_struct_0 A) (k6_msualg_6 A B C) (k8_msualg_6 A B C)) & (r2_pboole (u1_struct_0 A) (k7_msualg_6 A B (k6_msualg_6 A B C)) (k8_msualg_6 A B C))) ) ) ) ) ) ) ) ).
tt(t36_msualg_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) =>  (! [E:$i] :  ( ((v2_msualg_4 E A B) &  ((v3_msualg_4 E A B) & (m1_msualg_4 E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  =>  (~  ((r2_pboole (u1_struct_0 A) E (k17_msualg_4 A B C D)) &  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A (k13_msualg_4 A B E)) (u3_msualg_1 A C)) =>  (~  ((r1_msualg_3 A (k13_msualg_4 A B E) C F) & (r8_pboole (u1_struct_0 A) D (k3_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A (k13_msualg_4 A B E)) (u3_msualg_1 A C) (k15_msualg_4 A B E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_mycielsk,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k3_mycielsk (k5_mycielsk A)) = 1) ) ) ).
tt(t36_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 12) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  (~  (A = 12) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k13_pre_poly (k12_nat_3 B))) => (r1_nat_d A B)) ) ) ) ) ).
tt(t36_nat_4,ax,(v1_int_2 317)).
tt(t36_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_nat_5 (k4_nat_5 A))) ) ).
tt(t36_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k7_nat_d A B) = k6_numbers)  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t36_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_nattra_1 F A B C D) =>  (! [G:$i] :  ((m2_nattra_1 G A B D E) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 (k11_nattra_1 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (u4_struct_0 (k11_nattra_1 A B))) =>  ( ( (H = (k4_tarski (k4_tarski C D) F))  &  (I = (k4_tarski (k4_tarski D E) G)) )  =>  ((k1_cat_1 (k11_nattra_1 A B) H I) = (k4_tarski (k4_tarski C E) (k7_nattra_1 A B C D E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_ncfcont1 A B C D) => (r2_ncfcont1 A B (k4_vfunct_1 (u1_struct_0 A) B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 C) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D A)))  => (r2_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t36_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_ndiff_1 B A C E) & (r1_ndiff_1 B A D E))  =>  ((r1_ndiff_1 B A (k2_vfunct_1 (u1_struct_0 B) A C D) E) &  ((k3_ndiff_1 B A (k2_vfunct_1 (u1_struct_0 B) A C D) E) = (k5_algstr_0 (k16_lopban_1 B A) (k3_ndiff_1 B A C E) (k3_ndiff_1 B A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  & (r2_relset_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B F) E)) ) ) )  =>  ((r1_nfcont_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) <=> (r1_nfcont_3 (k4_real_ns1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_prvect_2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_prvect_2 A B))) =>  ((k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) (k5_algstr_0 (k11_prvect_2 A B) C D)) = (k5_algstr_0 (k14_prvect_2 A) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) C) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) D))) ) ) ) ) ) ) ) ) ).
tt(t36_neckla_3,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  ( (A = (k2_neckla_2 B C))  & (r2_hidden (k1_domain_1 (u1_struct_0 B) (u1_struct_0 C) D E) (u1_orders_2 (k3_necklace A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k10_real_1 (k1_nat_1 A 1) A) 1)) ) ) ) ).
tt(t36_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  (D = k1_xboole_0) )  &  ((r1_tarski D (k1_relset_1 (u1_struct_0 B) C)) &  ((v1_nfcont_1 D B) &  ((r3_nfcont_1 B A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r2_hidden E D) &  ((r2_hidden F D) &  ( ((k7_partfun1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) E) = (k4_seq_4 (k7_relset_1 (u1_struct_0 B) k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) D)))  &  ((k7_partfun1 k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) F) = (k5_seq_4 (k7_relset_1 (u1_struct_0 B) k1_numbers (k3_normsp_0 (u1_struct_0 B) A C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (r1_tarski C B))  => (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D C) A)) ) ) ) ) ) ) ).
tt(t36_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  ((r2_hidden B (k9_normform A D)) =>  ((r2_hidden B D) &  ( ((r2_hidden C D) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) C B))  =>  (C = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)))))) )  =>  ((r1_funct_2 (u1_struct_0 (k3_normsp_2 A)) (u1_struct_0 (k3_normsp_2 B)) (u1_struct_0 (k4_normsp_2 A)) (u1_struct_0 (k4_normsp_2 B)) C D) =>  ((v5_pre_topc C (k3_normsp_2 A) (k3_normsp_2 B)) <=> (v5_pre_topc D (k4_normsp_2 A) (k4_normsp_2 B))) ) ) ) ) ) ) ) ) ) ).
tt(t36_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) ) )  => (r3_lattice4 A (k6_openlatt (k17_openlatt A)) (k18_openlatt A))) ) ).
tt(t36_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) D) = (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) (k3_oppcat_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t36_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_orders_1 A B) => (v2_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t36_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) => (m2_orders_2 (k1_tarski (k1_funct_1 B (u1_struct_0 A))) A B)) ) ) ) ).
tt(t36_ordinal1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (? [B:$i] :  ((v3_ordinal1 B) &  ((r2_hidden A B) & (v4_ordinal1 B)) ) ) ) ) ).
tt(t36_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k11_ordinal2 (k1_ordinal1 A) B) = (k10_ordinal2 (k11_ordinal2 A B) B)) ) ) ) ) ).
tt(t36_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (A = k1_xboole_0) )  =>  ((r1_ordinal1 B (k11_ordinal2 B A)) & (r1_ordinal1 B (k11_ordinal2 A B))) ) ) ) ) ) ).
tt(t36_ordinal4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 B) &  ((v3_ordinal2 B) &  ((r2_hidden k4_ordinal1 A) &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C (k9_xtuple_0 B)) &  ((k1_funct_1 B C) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ordinal5,ax, ((k2_ordinal5 k6_numbers) = (k1_ordinal5 k4_ordinal1 k4_ordinal1)) ).
tt(t36_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((v2_ordinal6 B) &  ((r2_hidden (k3_tarski A) (k9_xtuple_0 B)) &  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r1_tarski C D) &  ((r2_hidden D A) & (r1_abian D B)) ) ) ) ) ) ) ) )  =>  ((v1_xboole_0 A) |  ((k3_tarski A) = (k1_funct_1 B (k3_tarski A))) ) ) ) ) ) ).
tt(t36_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t36_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E (k1_funct_1 B C)) &  (D = (k1_trees_4 (k4_tarski E C))) )  =>  ((r2_hidden F (k25_osafree A B (k15_osafree A B) D)) <=>  (F = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  =>  ((k11_msualg_2 A B (k10_osalg_2 A B (k3_osalg_2 A B)) C) = (k10_osalg_2 A B (k3_osalg_2 A B))) ) ) ) ) ) ) ).
tt(t36_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_parsp_2 A B C D E) & (r1_parsp_1 A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_tarski (k3_xboole_0 (k10_xtuple_0 D) (k9_xtuple_0 E)) A) =>  ((k1_partfun1 C A A B (k3_partfun1 D C A) (k3_partfun1 E A B)) = (k3_partfun1 (k3_relat_1 D E) C B)) ) ) ) ) ) ) ) ) ).
tt(t36_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((v3_funct_1 (k2_partfun1 C B D A)) <=>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ( ((r2_hidden E (k9_subset_1 C A (k1_relset_1 C D))) & (r2_hidden F (k9_subset_1 C A (k1_relset_1 C D))))  =>  ((k7_partfun1 B D E) = (k7_partfun1 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ( ((k3_partit1 A (k6_partit1 A) B) = (k6_partit1 A))  &  ((k2_partit1 A (k6_partit1 A) B) = B) ) ) ) ) ) ).
tt(t36_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k2_pboole A (k2_pboole A (k3_pboole A B C) (k3_pboole A C D)) (k3_pboole A D B)) (k3_pboole A (k3_pboole A (k2_pboole A B C) (k2_pboole A C D)) (k2_pboole A D B)))) ) ) ) ) ) ) ).
tt(t36_pcomps_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  (~  ((r1_pcomps_1 A B) & (v2_struct_0 (k4_pcomps_1 A B))) ) ) ) ) ) ).
tt(t36_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k21_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k4_tarski E G))  &  (D = (k4_tarski F H)) )  =>  ((r1_orders_2 (k21_pcs_0 A B) C D) <=>  ((r1_orders_2 A E F) & (r1_orders_2 B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_pdiff_3,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 2)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ((r4_pdiff_3 B A) & (r4_pdiff_3 C A))  => (r3_pdiff_1 2 2 (k20_valued_1 (k1_euclid 2) k1_numbers k1_numbers (k1_pdiff_3 2 2 B) (k1_pdiff_3 2 2 C)) A)) ) ) ) ) ) ) ).
tt(t36_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 B A) &  ((r3_pdiff_1 3 2 B A) &  ((r3_pdiff_1 3 3 B A) &  ((r3_pdiff_1 3 1 C A) &  ((r3_pdiff_1 3 2 C A) & (r3_pdiff_1 3 3 C A)) ) ) ) )  =>  ((k4_pdiff_4 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers B C) A) = (k8_euclid 3 (k4_pdiff_4 B A) (k4_pdiff_4 C A))) ) ) ) ) ) ) ) ).
tt(t36_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r9_pdiff_5 B A) =>  ((k9_pdiff_5 B A) = (k11_pdiff_1 3 3 (k1_pdiff_3 3 3 B) A)) ) ) ) ) ) ).
tt(t36_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r3_pdiff_7 A B C D) <=>  ((r2_hidden D (k1_relset_1 (k1_euclid A) C)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden G (k1_relset_1 (k1_euclid A) C)) &  ( (~ (r1_xxreal_0 F (k12_euclid (k8_euclid A G D))))  & (r1_xxreal_0 E (k12_euclid (k8_euclid B (k7_partfun1 (k1_euclid B) C G) (k7_partfun1 (k1_euclid B) C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r2_nfcont_4 A B C) <=>  ((r2_hidden C (k1_relset_1 (k1_euclid A) B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden F (k1_relset_1 (k1_euclid A) B)) &  ( (~ (r1_xxreal_0 E (k12_euclid (k8_euclid A F C))))  & (r1_xxreal_0 D (k17_complex1 (k10_binop_2 (k7_partfun1 k1_numbers B F) (k7_partfun1 k1_numbers B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k4_nat_d (k1_newton B A) B) = k6_numbers) ) ) ) ) ) ).
tt(t36_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  (! [D:$i] :  ((m3_pnproc_1 D A B) =>  ((k8_pnproc_1 A B (k4_pre_poly B C D)) = (k3_relat_1 (k7_pnproc_1 A C) (k7_pnproc_1 A D))) ) ) ) ) ) ) ) ).
tt(t36_polyeq_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_comptrig B A 1) =>  (B = A) ) ) ) ) ).
tt(t36_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k11_polyform A B) = (k1_vectsp_9 k2_bspace (k17_polyform A B))) ) ) ) ) ).
tt(t36_polynom3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k14_polynom3 A)) = (k10_polynom3 A)) ) ) ).
tt(t36_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k2_polynom5 A (k3_algseq_1 A B) C) (k3_algseq_1 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C)))) ) ) ) ) ) ).
tt(t36_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) B B) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F B) &  ((r1_xxreal_0 1 G) & (r1_xxreal_0 G B)) ) )  =>  ((k3_matrix_1 (u1_struct_0 A) (k4_matrix_3 A C D) F G) = (k8_group_1 A (k1_polynom8 A B) (k3_matrix_1 (u1_struct_0 A) E F G))) ) ) ) ) )  =>  ((k4_matrix_3 A C D) = (k6_matrix_3 A E (k1_polynom8 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r6_polyred A B C D E) <=>  (? [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  &  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C D)) & (r3_pre_poly A (k3_termord A B C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 k6_numbers B))  & (r1_xxreal_0 1 (k3_power A B))) ) ) ) ) ) ) ).
tt(t36_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v4_valued_0 D)) ) ) )  => (r6_pboole A (k12_pre_poly A (k12_pre_poly A B C) D) (k12_pre_poly A B (k11_pre_poly A C D)))) ) ) ) ) ) ) ).
tt(t36_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_prepower A B) = (k1_newton A B)) ) ) ) ) ).
tt(t36_pre_topc,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))) =>  ( (B = C)  =>  ((g1_pre_topc (u1_struct_0 (k1_pre_topc A B)) (u1_pre_topc (k1_pre_topc A B))) = (k1_pre_topc (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) C)) ) ) ) ) ) ) ) ).
tt(t36_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((k1_seq_1 E (k6_prob_1 A B C D)) = (k7_real_1 (k1_seq_1 E C) (k1_seq_1 E (k7_prob_1 A B D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  (~  ( (~ (r1_xxreal_0 (k1_seq_1 E C) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E D) k6_numbers))  &  (~  ((k1_seq_1 (k3_prob_2 A B E D) C) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B E C) D) (k1_seq_1 E C)) (k1_seq_1 E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((k1_kurato_0 A (k3_prob_3 A C)) = (k1_kurato_0 A C)) ) ) ) ) ) ).
tt(t36_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( (! [E:$i] :  ((r2_hidden E D) <=>  (? [F:$i] :  (? [G:$i] :  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r1_tarski F E) &  ((r1_tarski E G) &  ((k1_funct_1 C (k6_subset_1 G F)) = k6_numbers) ) ) ) ) ) ) ) )  =>  (D = (k4_prob_4 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A D C)) (k8_cqc_lang A (k9_cqc_lang A B D) C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t36_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A B (k1_projpl_1 A C D)) &  ( (~  (C = B) )  &  ( (~  (C = D) )  &  (~ (r1_incsp_1 A D (k1_projpl_1 A C B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k18_pscomp_1 A) = (k19_pscomp_1 A))  =>  ((k14_pscomp_1 A) = (k1_tarski (k18_pscomp_1 A))) ) ) ) ).
tt(t36_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r1_pboole A B C) | (r6_pboole A B D))  => (r1_pboole A B (k2_pboole A C (k1_pzfmisc1 A D)))) ) ) ) ) ) ) ) ).
tt(t36_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang2 B A) =>  ((v3_qc_lang1 B A) &  ((v5_qc_lang1 (k18_qc_lang1 A B) A) & (v3_qc_lang1 (k22_qc_lang1 A (k18_qc_lang1 A B)) A)) ) ) ) ) ) ) ).
tt(t36_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v2_qc_lang1 B A) =>  ( ((k4_qc_lang3 A C B) = (k1_qc_lang3 A (k17_qc_lang1 A B) C))  &  ((k4_qc_lang3 A C B) = (a_3_1_qc_lang3 A B C)) ) ) ) ) ) ) ) ) ).
tt(t36_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  ((k4_qc_lang4 A B C) = (a_3_3_qc_lang4 A B C)) ) ) ) ) ) ) ).
tt(t36_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k15_quatern2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k15_quatern2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k15_quatern2)) =>  ( ((k3_rlvect_1 k15_quatern2 A B) = (k3_rlvect_1 k15_quatern2 B A))  &  ( ((k3_rlvect_1 k15_quatern2 (k3_rlvect_1 k15_quatern2 A B) C) = (k3_rlvect_1 k15_quatern2 A (k3_rlvect_1 k15_quatern2 B C)))  &  ((k3_rlvect_1 k15_quatern2 A (k4_struct_0 k15_quatern2)) = A) ) ) ) ) ) ) ) ) ).
tt(t36_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) => (r1_xxreal_0 (k3_quatern2 (k29_quaterni (k26_quaterni A B) C)) (k7_real_1 (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k3_quatern2 C)))) ) ) ) ) ) ).
tt(t36_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k17_quaterni (k26_quaterni A B)) = (k7_real_1 (k17_quaterni A) (k17_quaterni B)))  &  ( ((k18_quaterni (k26_quaterni A B)) = (k7_real_1 (k18_quaterni A) (k18_quaterni B)))  &  ( ((k19_quaterni (k26_quaterni A B)) = (k7_real_1 (k19_quaterni A) (k19_quaterni B)))  &  ((k20_quaterni (k26_quaterni A B)) = (k7_real_1 (k20_quaterni A) (k20_quaterni B))) ) ) ) ) ) ) ) ).
tt(t36_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  ((k4_algstr_0 (k19_quofield A) B) = (k1_funct_1 (k17_quofield A) B)) ) ) ) ) ).
tt(t36_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A C) =>  (! [E:$i] :  ((m1_random_1 E A C) =>  ( ((v6_supinf_2 E) & (r1_random_1 A C E D))  =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 (k1_seq_1 D (a_4_0_random_1 A B C E)) (k13_complex1 (k8_random_1 A C D E) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (~  ((r2_hidden F (k1_vectsp_6 A C (k8_ranknull A B C E D))) & (r1_xboole_0 (k7_ranknull B C D (k6_domain_1 (u1_struct_0 C) F)) (k1_vectsp_6 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((r1_xxreal_0 A 1) <=> (r1_xxreal_0 (k2_rat_1 A) (k1_rat_1 A))) ) ) ).
tt(t36_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_ratfunc1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k2_polynom4 A (k5_ratfunc1 A B) C) = (k4_struct_0 A)) )  &  ( (~ (r1_ratfunc1 A (k4_ratfunc1 A B) (k5_ratfunc1 A B) C))  &  (~  ((k13_ratfunc1 A (k11_ratfunc1 A B) C) = (k13_ratfunc1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k1_rcomp_1 A B))  =>  ((k1_tops_1 k2_topalg_2 C) = (k2_rcomp_1 A B)) ) ) ) ) ) ) ) ).
tt(t36_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 B) (k1_nat_1 A 1)) = (k1_seq_1 (k3_real_3 (k10_real_1 1 (k4_int_1 B))) A)) ) ) ) ) ).
tt(t36_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ( ((k3_finseq_1 (k20_rfunct_3 B (k4_rearran1 A B D C) B)) = (k5_card_1 B))  & (r1_xxreal_0 1 (k3_finseq_1 (k20_rfunct_3 B (k4_rearran1 A B D C) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k3_relat_1 (k3_relat_1 A B) C) = (k3_relat_1 A (k3_relat_1 B C))) ) ) ) ) ) ) ).
tt(t36_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( (D = k1_xboole_0)  =>  ( (C = k1_xboole_0)  |  ((k6_relset_2 A B C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t36_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k2_goboard9 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) = (k2_goboard9 B)) ) ) ) ) ).
tt(t36_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_rewrite1 A B C) =>  ((r5_rewrite1 A B C) &  ((r6_rewrite1 A B C) &  ((r5_rewrite1 A C B) & (r6_rewrite1 A C B)) ) ) ) ) ) ) ) ).
tt(t36_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r3_rewrite2 A B C D) =>  ((r3_rewrite2 A B (k1_flang_1 A C E) (k1_flang_1 A D E)) & (r3_rewrite2 A B (k1_flang_1 A E C) (k1_flang_1 A E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (~  ((r2_hidden (k4_tarski (k4_tarski A D) (k4_tarski B E)) (k1_rewrite3 C F G)) &  (! [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 C)) =>  (~  ((r1_rewrite3 F G A H B) &  (D = (k1_flang_1 C H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k18_valued_1 A (k1_rfunct_1 B C)) = (k1_rfunct_1 (k18_valued_1 A B) C)) ) ) ) ) ) ) ).
tt(t36_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_hidden C (k9_subset_1 k1_numbers (k3_xboole_0 A B) (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E)))) =>  ((r2_hidden C (k9_subset_1 k1_numbers A (k1_relset_1 k1_numbers D))) & (r2_hidden C (k9_subset_1 k1_numbers B (k1_relset_1 k1_numbers E)))) ) ) ) ) ) ) ) ) ) ).
tt(t36_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k8_relset_1 A k1_numbers B (k1_limfunc1 k6_numbers)) = (k8_relset_1 A k1_numbers (k18_rfunct_3 A B) (k1_tarski k6_numbers))) ) ) ) ) ).
tt(t36_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k3_rinfsup1 B) A) = (k2_rinfsup1 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t36_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v8_valued_0 A) =>  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k2_rinfsup2 A)) ) ) ) ) ).
tt(t36_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k3_rlaffin1 A (k10_rlvect_2 A B C)) = (k9_real_1 (k3_rlaffin1 A B) (k3_rlaffin1 A C))) ) ) ) ) ) ) ).
tt(t36_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((k1_rlsub_1 B) = (k1_rlsub_1 A)) ) ) ) ) ).
tt(t36_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  ( ((k1_rlsub_2 A B C) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  &  ((k1_rlsub_2 A C B) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ) ) ).
tt(t36_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k7_rusub_4 A B C) D) => (r1_tarski (k7_rusub_4 A (k1_tops_1 A B) (k1_tops_1 A C)) (k1_tops_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t36_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k1_rlvect_1 B C A) = (k1_rlvect_1 B D A))  =>  ( (A = k6_numbers)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((k3_rlvect_2 A D) = (k7_domain_1 (u1_struct_0 A) B C))  =>  ( (B = C)  |  ((k6_rlvect_2 A D) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_funct_2 (u1_struct_0 A) k1_numbers D B)) (k1_rlvect_1 A C (k3_funct_2 (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) &  ( (~ (v1_rlvect_3 (k8_domain_1 (u1_struct_0 A) D B C) A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  (D = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r1_xxreal_0 (k9_real_1 (k2_nat_1 (k1_rlvect_5 B) (k1_rlvect_5 C)) (k1_rlvect_5 A)) (k1_rlvect_5 (k2_rlsub_2 A B C)))) ) ) ) ) ) ).
tt(t36_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_rlvect_x A (k2_rlvect_x A B)) = (k2_rlvect_x A B)) ) ) ) ) ).
tt(t36_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ((k1_rmod_2 A C) = (k1_rmod_2 A B)) ) ) ) ) ) ) ).
tt(t36_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( (~  ( (? [E:$i] :  ((m1_rmod_2 E A B) &  ((u1_struct_0 E) = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) )  &  ( (~ (m1_rmod_2 C A D))  &  (~ (m1_rmod_2 D A C)) ) ) )  &  (~  ( ((m1_rmod_2 C A D) | (m1_rmod_2 D A C))  &  (! [E:$i] :  ((m1_rmod_2 E A B) =>  (~  ((u1_struct_0 E) = (k2_xboole_0 (u1_struct_0 C) (u1_struct_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ( ((k2_rmod_4 A B E) = (k7_domain_1 (u1_struct_0 B) C D))  =>  ( (C = D)  |  ((k5_rmod_4 A B E) = (k3_rlvect_1 B (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C) C) (k5_vectsp_2 A B (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E D) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_robbins1 A (k5_robbins1 A B C) (k9_robbins1 A B C)) = C) ) ) ) ) ) ) ).
tt(t36_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)) D)) C)) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A C) C)))) = C) ) ) ) ) ) ) ) ) ).
tt(t36_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A B C) = (k3_lattices A (k4_lattices A (k3_lattices A B C) B) (k4_lattices A (k3_lattices A B C) (k3_robbins1 A B)))) ) ) ) ) ) ) ) ).
tt(t36_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A (k4_roughs_1 A B)) = (k3_roughs_1 A (k4_roughs_1 A B))) ) ) ) ) ).
tt(t36_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  =>  ((k2_rpr_1 A C B) = (k9_real_1 1 (k10_real_1 (k1_rpr_1 A (k7_subset_1 A C B)) (k1_rpr_1 A C)))) ) ) ) ) ) ) ) ).
tt(t36_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k4_struct_0 A) (k3_rusub_1 A C B)) <=> (r1_struct_0 B C)) ) ) ) ) ) ) ).
tt(t36_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  ( ((k1_rusub_2 A B C) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)))  &  ((k1_rusub_2 A C B) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ) ) ).
tt(t36_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rusub_3 A (k8_domain_1 (u1_struct_0 A) B C D)) B) &  ((r1_struct_0 (k1_rusub_3 A (k8_domain_1 (u1_struct_0 A) B C D)) C) & (r1_struct_0 (k1_rusub_3 A (k8_domain_1 (u1_struct_0 A) B C D)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t36_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_rusub_4 (k7_rusub_4 A B C) A)) ) ) ) ) ) ).
tt(t36_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden C (k9_subset_1 (u1_struct_0 A) (k4_bhsp_2 A B E) (k4_bhsp_2 A D F))) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_tarski (k4_bhsp_2 A C G) (k4_bhsp_2 A B E)) & (r1_tarski (k4_bhsp_2 A C G) (k4_bhsp_2 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k6_rvsum_1 (k8_rvsum_1 A B)) = (k4_rvsum_1 (k6_rvsum_1 A) B)) ) ) ) ) ).
tt(t36_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k16_rvsum_1 (k2_finseq_2 A B)) = (k5_binop_2 A B)) ) ) ) ) ).
tt(t36_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_amistd_1 3 k1_scmfsa_2 (k12_scmfsa_2 A B)) = (k1_tarski A)) ) ) ) ) ).
tt(t36_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 7)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k12_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) A B) (k1_funct_4 (k1_scmfsa6b C A B) (k7_memstr_0 3 k1_scmfsa_2 (k5_card_1 C))))) ) ) ) ) ) ) ).
tt(t36_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ((r5_scmfsa7b C (k1_funct_4 B (k7_memstr_0 3 k1_scmfsa_2 E)) (k1_funct_4 A C)) & (r6_scmfsa7b C (k1_funct_4 B (k7_memstr_0 3 k1_scmfsa_2 E)) (k1_funct_4 A C))) )  &  ( ((r5_scmfsa7b C (k1_funct_4 B (k7_memstr_0 3 k1_scmfsa_2 E)) (k1_funct_4 A C)) & (r6_scmfsa7b C (k1_funct_4 B (k7_memstr_0 3 k1_scmfsa_2 E)) (k1_funct_4 A C)))  =>  ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa8b B (k1_scmfsa8a 2) A) (k2_nat_1 (k5_card_1 A) 3)) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 A) 5))) ) ) ) ) ).
tt(t36_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r4_scmfsa9a A (k1_scmfsa_m B) C D) =>  ( ( (~ (r3_scmfsa9a A (k1_scmfsa_m B) C D))  &  (~ (v7_amistd_1 D 3 k1_scmfsa_2)) )  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa_9 C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 (k1_scmfsa_m B) D C A) (k2_scmfsa9a A (k1_scmfsa_m B) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmfsa_9 A B) 2) = (k11_scmfsa_2 3)) ) ) ) ) ).
tt(t36_scmfsa_m,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (? [B:$i] :  ((m2_finseq_1 B k1_numbers) &  ((r2_classes1 A B) &  ((v8_valued_0 B) &  ((m2_finseq_1 B k4_numbers) &  ((k1_funct_1 k10_scmfsa_m (k16_funcop_1 (k5_scmfsa_2 k6_numbers) A)) = (k16_funcop_1 (k5_scmfsa_2 k6_numbers) B)) ) ) ) ) ) ) ) ).
tt(t36_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_scm_halt C E A) & (r2_scm_halt C E A))  =>  ( ((k1_funct_1 E D) = k6_numbers)  | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b D B C) E A) (k1_funct_4 (k1_scmfsa6b C E A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmisort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski k3_scmisort C) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ((r1_tarski (k1_scmfsa_m (k16_funcop_1 (k5_scmfsa_2 k6_numbers) D)) B) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 C B A)) (k9_xtuple_0 k3_scmisort))) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 10)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  (A = (k13_scmpds_2 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k2_scmpds_6 A B C D))) & (r2_hidden 1 (k9_xtuple_0 (k2_scmpds_6 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t36_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k6_scmpds_4 (k1_scmpds_7 D F G C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden (k2_nat_1 B 1) (k3_amistd_1 2 (k1_scmring2 A) B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k3_amistd_1 2 (k1_scmring2 A) B)) => (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t36_scmyciel,ax, (! [A:$i] :  ((k5_scmyciel (k1_tarski A)) = (k2_tarski k1_xboole_0 (k1_tarski A))) ) ).
tt(t36_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) =>  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (D = C) )  &  ( (~  (B = E) )  &  ( (~  (C = E) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers A) (k37_valued_1 k5_numbers k1_numbers B)) (k37_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ).
tt(t36_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seqm_3 A) & (v1_comseq_2 A))  => (v2_comseq_2 A)) ) ) ).
tt(t36_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((r2_seqfunc A C D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E D) => (r2_relset_1 k5_numbers k1_numbers (k10_seqfunc A (k2_seqfunc A C B) E) (k26_valued_1 k5_numbers k1_numbers (k10_seqfunc A C E) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_seqm_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 B) =>  ((r1_xxreal_0 A k6_numbers) | (v1_seq_2 (k26_valued_1 k5_numbers k1_numbers B A))) )  &  ( ( (k6_numbers = A)  => (v1_comseq_2 (k26_valued_1 k5_numbers k1_numbers B A)))  &  ((v1_seq_2 B) =>  ((r1_xxreal_0 k6_numbers A) | (v2_seq_2 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ) ) ).
tt(t36_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k3_funct_2 k5_numbers k1_numbers A B))) )  & (v1_series_1 A))  => (v2_series_1 A)) ) ) ).
tt(t36_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) B) (k13_newton 2 (k2_nat_1 B 1))) (k3_xcmplx_0 (k2_xcmplx_0 (k13_newton 2 (k2_nat_1 B 1)) (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 1))) (k2_xcmplx_0 (k13_newton 2 (k2_nat_1 B 2)) (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 2)))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k8_complex1 (k13_complex1 1 3) (k13_complex1 (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 2)) (k3_xcmplx_0 3 (k2_xcmplx_0 (k13_newton 2 (k2_nat_1 B 2)) (k1_newton (k4_xcmplx_0 1) (k2_nat_1 B 2))))))) ) ) ) ) ) ).
tt(t36_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers A (k20_valued_1 k5_numbers k1_numbers k1_numbers B B)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 A) C))) ) ) ) ) ) ) ).
tt(t36_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  ( ((k2_xcmplx_0 A B) = 1)  => (r1_xxreal_0 (k13_complex1 17 4) (k2_xcmplx_0 (k3_xcmplx_0 A B) (k13_complex1 1 (k3_xcmplx_0 A B))))) ) ) ) ) ).
tt(t36_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski (k7_setfam_1 A B) (k7_setfam_1 A C)) => (r1_tarski B C)) ) ) ) ) ) ).
tt(t36_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B E) = (k6_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E) (k3_funct_2 k5_numbers (k9_setfam_1 A) D E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A B) E) = (k6_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A C) E) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_prob_1 A (k8_setlim_2 A C B)) = (k7_subset_1 A (k3_prob_1 A C) B)) ) ) ) ) ) ).
tt(t36_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 C B) &  ((v2_binop_1 C B) &  ((v3_binop_1 C B) & (v1_setwiseo C B)) ) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) D)))) )  =>  ( ((v1_binop_1 E D) &  ((v2_binop_1 E D) &  ((v3_binop_1 E D) & (v1_setwiseo E D)) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G B D) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B D)))) )  =>  ( ( ((k3_funct_2 B D G (k4_binop_1 B C)) = (k4_binop_1 D E))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  ((k3_funct_2 B D G (k5_binop_1 B C H I)) = (k5_binop_1 D E (k3_funct_2 B D G H) (k3_funct_2 B D G I))) ) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 A)) =>  ((k3_funct_2 B D G (k7_setwiseo A B C H F)) = (k7_setwiseo A D E H (k1_partfun1 A B B D F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) & (v1_setwiseo D A)) )  =>  ((k1_finsop_1 A (k5_finseq_2 A E (k5_binop_1 A D B C)) D) = (k5_binop_1 A D (k1_finsop_1 A (k5_finseq_2 A E B) D) (k1_finsop_1 A (k5_finseq_2 A E C) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k4_sf_mastr (k4_sfmastr3 C A B)) = (k1_tarski C)) ) ) ) ) ) ) ).
tt(t36_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  => (r1_tarski (k4_sf_mastr (k1_funct_4 A B)) (k1_finsub_1 (k1_zfmisc_1 k3_scmfsa_2) (k4_sf_mastr A) (k4_sf_mastr B)))) ) ) ) ).
tt(t36_sgraph1,ax, ((r2_hidden (k2_tarski 1 2) (u1_sgraph1 k8_sgraph1)) &  ((r2_hidden (k2_tarski 2 3) (u1_sgraph1 k8_sgraph1)) & (r2_hidden (k2_tarski 3 1) (u1_sgraph1 k8_sgraph1))) ) ).
tt(t36_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  => (v3_sheffer1 A)) ) ).
tt(t36_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C B)) C) = (k5_sheffer1 A C C)) ) ) ) ) ) ) ).
tt(t36_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v7_simplex0 C A B) & (m2_simplex0 C A B))  =>  (! [D:$i] :  ( ((v7_simplex0 D A B) & (m2_simplex0 D A B))  =>  ( ((k2_struct_0 C) = (k2_struct_0 D))  =>  ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D))) ) ) ) ) ) ) ) ) ).
tt(t36_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ((v6_ordinal1 C) &  ((v1_finset_1 C) &  ((v5_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ( ((v1_setfam_1 C) & (r1_tarski (k5_setfam_1 (u1_struct_0 A) C) B))  =>  ((m3_simplex0 (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) C) (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) B))) (k5_real_1 (k5_card_1 (k5_setfam_1 (u1_struct_0 A) C)) 1)) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~ (r1_xxreal_0 D k1_xboole_0))  &  ((r1_xxreal_0 D (k5_card_1 (k5_setfam_1 (u1_struct_0 A) C))) &  (! [E:$i] :  (~  ((r2_hidden E C) &  ((k1_card_1 E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_sincos10,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))) => (r2_hidden (k1_seq_1 k2_fdiff_9 A) (k1_rcomp_1 1 (k7_square_1 2)))) ) ).
tt(t36_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k7_sin_cos2 k1_numbers) &  ((k1_fdiff_1 k7_sin_cos2 A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k4_sin_cos2 A)))) ) ) ) ).
tt(t36_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_sin_cos (k5_binop_2 k7_complex1 A)) = (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A)))) ) ) ).
tt(t36_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) (k20_sin_cos C)) = (k3_xcmplx_0 (k7_xcmplx_0 1 4) (k2_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 A B) C)) (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 B C) A))) (k20_sin_cos (k6_xcmplx_0 (k2_xcmplx_0 C A) B))) (k20_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C))))) ) ) ) ) ) ) ).
tt(t36_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_sin_cos5 A) = (k13_complex1 (k2_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))) (k6_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A)))))  &  ( ((k2_sin_cos5 A) = (k10_real_1 2 (k2_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A)))))  &  ((k3_sin_cos5 A) = (k10_real_1 2 (k6_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))))) ) ) ) ) ).
tt(t36_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k32_sin_cos))  &  ((r1_xxreal_0 A (k8_real_1 2 k32_sin_cos)) & (r1_xxreal_0 (k20_sin_cos A) (k1_real_1 1))) ) ) ) ) ).
tt(t36_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_sin_cos7 A) = (k1_sin_cos7 (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)))) ) ) ) ).
tt(t36_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k32_sin_cos A))  &  (~  ( ((k6_sin_cos9 (k1_seq_1 k30_sin_cos A)) = A)  &  ((k6_sin_cos9 (k2_sin_cos4 A)) = A) ) ) ) ) ) ) ) ).
tt(t36_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v2_comseq_2 (k3_series_1 (k22_sin_cos A))) &  ( ((k4_series_1 (k22_sin_cos A)) = (k4_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 A k7_complex1)))))  &  ((v2_comseq_2 (k3_series_1 (k23_sin_cos A))) &  ((k4_series_1 (k23_sin_cos A)) = (k3_complex1 (k11_comseq_3 (k3_sin_cos (k3_xcmplx_0 A k7_complex1))))) ) ) ) ) ) ).
tt(t36_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B))) ) )  => (r1_sppol_1 2 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B A) (k2_topreal1 2 B (k2_nat_1 A 1))))) ) ) ) ) ).
tt(t36_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v3_topreal1 A) &  ((v3_topreal1 B) &  ((r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 B)) &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 A)))  => (r1_xboole_0 (k2_topreal1 2 A C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)))) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 2 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  => (r1_xboole_0 (k2_topreal1 2 B C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)))) ) ) ) ) ) )  => (v3_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t36_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_sprect_1 A) 2) = (k12_pscomp_1 A)) ) ) ).
tt(t36_sprect_2,ax, ((k20_pscomp_1 k1_topreal1) = (k19_euclid k6_numbers 1)) ).
tt(t36_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ((k2_goboard2 A) = (k6_matrix_2 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 4) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 3) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 2))) ) ) ).
tt(t36_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k24_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t36_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ( (A = B)  |  ((k7_xcmplx_0 1 (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B))) = (k7_xcmplx_0 (k6_xcmplx_0 (k6_square_1 A) (k6_square_1 B)) (k6_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t36_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k14_stacks_1 A))) =>  ( (C = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B))  =>  ((r1_stacks_1 A B) <=> (r1_stacks_1 (k14_stacks_1 A) C)) ) ) ) ) ) ) ) ).
tt(t36_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k23_binop_2 A C) (k23_binop_2 B D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A C) (k23_binop_2 B D))))) )  =>  ( ((v1_stirl2_1 F (k23_binop_2 A C) (k23_binop_2 B D)) &  (E = (k2_partfun1 (k23_binop_2 A C) (k23_binop_2 B D) F A)) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ((r2_hidden G (k2_relset_1 B E)) &  ((r2_hidden H (k2_relset_1 B E)) &  ( (~ (r1_xxreal_0 H G))  & (r1_xxreal_0 (k5_nat_1 (k1_stirl2_1 A B E (k1_seq_4 H))) (k5_nat_1 (k1_stirl2_1 A B E (k1_seq_4 G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ((v1_sublemma B A) & (m1_subset_1 B (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))))  =>  (! [C:$i] :  ((m1_substut1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (k16_substut1 A) (k3_qc_lang1 A))) =>  (! [E:$i] :  ((m1_substut1 E A D) =>  ( ((v3_substut1 B A) &  ((v3_substut1 D A) &  ((k9_sublemma A B C) = (k24_substut1 A D E)) ) )  =>  ( ((k23_substut1 A B) = (k23_substut1 A D))  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k2_enumset1 B C D E) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t36_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  ((m2_subset_1 (k37_substut1 A B) (k9_qc_lang1 A) (k3_cqc_lang A)) => (m2_subset_1 (k37_substut1 A (k20_substut1 A B)) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ).
tt(t36_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) &  ((v5_supinf_2 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) ) )  =>  (! [B:$i] :  ((m1_supinf_2 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k12_supinf_2 (k15_supinf_2 A B) C) (k12_supinf_2 (k15_supinf_2 A B) (k2_nat_1 C 1))) & (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k15_supinf_2 A B) C))) ) ) ) ) ) ) ).
tt(t36_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ( (~  ((k3_rlvect_1 A (k1_group_1 A) (k1_group_1 A)) = (k4_struct_0 A)) )  &  ( (~ (r1_orders_2 B C D))  &  (~  ((k2_symsp_1 A B E (k3_rlvect_1 B F G) D C) = (k3_rlvect_1 A (k2_symsp_1 A B E F D C) (k2_symsp_1 A B E G D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ((k3_relat_1 (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))) (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))))) = k1_xboole_0)  =>  ( ((k5_relat_1 A (k9_xtuple_0 (k1_sysrel A))) = (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))))  &  ((k5_relat_1 A (k10_xtuple_0 (k1_sysrel A))) = (k4_relat_1 (k9_xtuple_0 (k1_sysrel A)))) ) )  &  ( ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k10_xtuple_0 (k1_sysrel A)))) (k4_relat_1 (k10_xtuple_0 (k1_sysrel A)))) = k1_xboole_0)  =>  ( ((k6_relat_1 (k9_xtuple_0 (k1_sysrel A)) A) = (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))))  &  ((k6_relat_1 (k10_xtuple_0 (k1_sysrel A)) A) = (k4_relat_1 (k10_xtuple_0 (k1_sysrel A)))) ) ) ) ) ) ).
tt(t36_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k13_lang1 (u1_struct_0 A) (k3_taxonom1 A k6_numbers))) =>  ((k8_eqrel_1 (u1_struct_0 A) B) = (k10_eqrel_1 (u1_struct_0 A))) ) ) ) ) ) ).
tt(t36_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ((k5_binop_1 (k9_tdlat_1 A) (k10_tdlat_1 A) B C) = (k1_binop_1 (k2_tdlat_1 A) B C)) ) ) ) ) ) ) ).
tt(t36_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))) = (k1_tdlat_2 A (k1_pcomps_1 A B))) ) ) ) ) ).
tt(t36_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tops_1 B A) => (v5_tops_1 B A))  &  ((v5_tops_1 B A) => (v6_tops_1 B A)) ) ) ) ) ) ) ).
tt(t36_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D)) = (k7_subset_1 (k15_pre_poly A) (k2_polynom1 (k15_pre_poly A) C D) (k1_tarski (k3_termord A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t36_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) & (v3_tdlat_3 (k6_tmap_1 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ) ).
tt(t36_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ).
tt(t36_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_tops_1 B A) &  (! [C:$i] :  ( ((v1_pre_topc C) & (m1_pre_topc C A))  =>  (~  ((v4_tex_3 C A) &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_tex_4 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k3_tex_4 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ).
tt(t36_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ( (~ (r1_tsep_1 (k2_tsep_1 A B C) D))  =>  ( (~ (r1_tsep_1 B D))  &  (~ (r1_tsep_1 C D)) ) )  &  ( (~ (r1_tsep_1 D (k2_tsep_1 A B C)))  =>  ( (~ (r1_tsep_1 D B))  &  (~ (r1_tsep_1 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_toler_1 D A B) & (m1_toler_1 D A B))  =>  ((r2_hidden C D) => (r1_tarski D (k9_relat_1 B C))) ) ) ) ) ) ) ).
tt(t36_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_borsuk_2 G A B C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) =>  (! [I:$i] :  ((m1_borsuk_2 I A D E) =>  (! [J:$i] :  ((m1_borsuk_2 J A E F) => (r4_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E G (k1_borsuk_2 A C D E H I)) J) (k1_borsuk_2 A B D F (k1_borsuk_2 A B C D G H) (k1_borsuk_2 A D E F I J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( ( ((k9_xtuple_0 B) = (k9_xtuple_0 C))  &  (D = (k9_xtuple_0 B)) )  =>  ((r2_topalg_6 A B C) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 (k1_pre_topc k2_topalg_2 D) k5_topmetr)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k1_pre_topc k2_topalg_2 D) k5_topmetr)) (u1_struct_0 A))))) )  &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((v5_pre_topc E (k2_borsuk_1 (k1_pre_topc k2_topalg_2 D) k5_topmetr) A) &  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k1_pre_topc k2_topalg_2 D))) =>  ( ((k1_binop_1 E H k6_numbers) = (k1_funct_1 B H))  &  ((k1_binop_1 E H 1) = (k1_funct_1 C H)) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((k1_binop_1 E (k2_xxreal_2 D) H) = F)  &  ((k1_binop_1 E (k1_xxreal_2 D) H) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( ((v12_pre_topc A) & (v1_metrizts A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v2_tops_2 B A) &  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v4_card_3 B) &  ((v2_topdim_1 B A) & (r1_xxreal_0 (k3_topdim_1 A B) k6_numbers)) ) ) ) ) ) )  |  ((v3_topdim_1 A) & (r1_xxreal_0 (k4_topdim_1 A) k6_numbers)) ) ) ) ) ).
tt(t36_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v7_pre_topc A) & (v2_topgen_1 B A))  => (v2_topgen_1 (k2_pre_topc A B) A)) ) ) ) ) ).
tt(t36_topgen_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))))  =>  ( (! [D:$i] :  ((r2_hidden D C) => (v1_finset_1 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B D))) )  =>  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k2_xboole_0 (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)) (k1_setfam_1 (a_3_1_topgen_2 A B C)))) ) ) ) ) ) ) ) ).
tt(t36_topgen_3,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_pre_topc B (k5_topgen_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_topgen_3 A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v3_pre_topc C (k5_topgen_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_topgen_3 A))))) )  =>  (~ (r2_subset_1 B C)) ) ) ) ) ) ) ).
tt(t36_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v6_topgen_4 (k2_struct_0 A) A)) ) ).
tt(t36_topgen_5,ax, ((v1_tops_1 (k8_subset_1 (u1_struct_0 (k15_euclid 2)) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k4_card_3 (k10_finseq_1 k3_numbers k3_numbers))) k3_topgen_5) & (m1_subset_1 (k8_subset_1 (u1_struct_0 (k15_euclid 2)) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k4_card_3 (k10_finseq_1 k3_numbers k3_numbers))) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t36_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_topgrp_1 A) & (l1_pre_topc A)) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B D) &  ((v3_pre_topc D A) & (r1_tarski (k2_pre_topc A D) C)) ) ) ) ) ) ) ) ) ) ) )  => (v9_pre_topc A)) ) ) ).
tt(t36_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k7_topreal1 A) = (a_1_6_topreal1 A)) ) ) ).
tt(t36_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k17_euclid A) = (k17_euclid B))  &  (C = (k11_finseq_1 A (k19_euclid (k17_euclid A) (k10_real_1 (k7_real_1 (k18_euclid A) (k18_euclid B)) 2)) B)) )  =>  ( ((k18_euclid A) = (k18_euclid B))  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = A)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = B)  & (v4_topreal1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)) (k3_topreal1 2 (k1_sprect_1 A)))) ) ).
tt(t36_topreal8,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A D E)) ) ) ) ) ) ) ) ) ) )  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v1_topreal1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 4))  &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v1_topreal1 C) &  ( ((k3_topreal1 2 B) = (k3_topreal1 2 C))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)))  & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden C (k3_topreal9 A D B)) & (r2_hidden E (k3_topreal9 A D B)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A C E) (k3_topreal9 A D B)) = (k2_tarski C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))) (u1_struct_0 (k1_topreala A B C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D))) (u1_struct_0 (k1_topreala A B C D)))))) )  =>  ( (E = (k2_partfun1 (u1_struct_0 (k2_borsuk_1 k3_topmetr k3_topmetr)) (u1_struct_0 (k15_euclid 2)) k2_topreala (u1_struct_0 (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D)))))  => (v3_tops_2 E (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D)) (k1_topreala A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k4_int_1 A) = (k10_real_1 3 4))  =>  ((k1_funct_1 k12_toprealb A) = (k19_euclid k6_numbers (k1_real_1 1))) ) ) ) ).
tt(t36_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k38_valued_2 A (u1_struct_0 (k15_euclid B)) D C)) &  ((v1_funct_2 (k38_valued_2 A (u1_struct_0 (k15_euclid B)) D C) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k38_valued_2 A (u1_struct_0 (k15_euclid B)) D C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t36_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v3_toprns_1 B A) & (v3_toprns_1 C A))  => (v3_toprns_1 (k1_toprns_1 A B C) A)) ) ) ) ) ) ) ).
tt(t36_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_tops_1 A C)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k2_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) (k2_tops_1 A B) (k2_tops_1 A C)))) ) ) ) ) ) ) ).
tt(t36_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_finset_1 C) => (v1_finset_1 (k1_tops_2 A B C))) ) ) ) ) ) ) ).
tt(t36_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v1_tops_1 B A))  => (v1_tops_3 B A)) ) ) ) ) ).
tt(t36_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v4_transgeo B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A))) &  ((v3_funct_2 C (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A)))))) ) )  =>  (~  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A)) B C) & (r3_transgeo (k2_diraf A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v2_trees_1 (k1_tarski A))) ) ).
tt(t36_trees_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (! [C:$i] :  ((r2_hidden C A) =>  ((v1_relat_1 C) &  ((v5_relat_1 C B) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) ) ) )  & (v6_ordinal1 A))  =>  ((v1_relat_1 (k3_tarski A)) &  ((v5_relat_1 (k3_tarski A) B) &  ((v1_funct_1 (k3_tarski A)) & (v3_trees_2 (k3_tarski A))) ) ) ) ) ) ) ) ).
tt(t36_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~  (B = k6_numbers) )  =>  ((v6_trees_3 (k2_finseq_2 B A)) <=>  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) ) ) ) ) ) ) ).
tt(t36_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  ((k2_trees_9 A B) = (k3_relat_1 (k1_trees_9 (k9_xtuple_0 A) B) A)) ) ) ) ) ).
tt(t36_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_xboole_0 B C) & (v3_pre_topc B A))  => (r1_xboole_0 B (k2_pre_topc A C))) ) ) ) ) ) ) ).
tt(t36_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A D B) & (r4_tsep_2 A E C))  =>  ((r1_tsep_1 B C) | (r4_tsep_2 A (k1_tsep_1 A D E) (k2_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_turing_1,ax, ( ((k1_funct_1 k19_turing_1 (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))  &  ( ((k1_funct_1 k19_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 1 k6_numbers 1))  &  ( ((k1_funct_1 k19_turing_1 (k1_domain_1 k5_numbers k5_numbers 1 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 k6_numbers 1))  &  ( ((k1_funct_1 k19_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 1)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 2 k6_numbers 1))  &  ((k1_funct_1 k19_turing_1 (k1_domain_1 k5_numbers k5_numbers 2 k6_numbers)) = (k4_domain_1 k5_numbers k5_numbers k5_numbers 3 k6_numbers k6_numbers)) ) ) ) ) ).
tt(t36_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((r2_hidden A (u1_struct_0 (k40_twoscomp A B))) &  ((r2_hidden B (u1_struct_0 (k40_twoscomp A B))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k15_twoscomp) (u1_struct_0 (k40_twoscomp A B))) & (r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (u1_struct_0 (k40_twoscomp A B)))) ) ) ) ) ) ) ).
tt(t36_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((r2_hidden B (k2_uniroots A)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_uniroots k1_complfld))) &  ( (B = C)  & (r1_nat_d (k6_group_1 (k1_uniroots k1_complfld) C) A)) ) ) ) ) ) ) ).
tt(t36_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 (k1_algseq_1 A B) 1))  &  ( (~ (r1_xxreal_0 (k1_algseq_1 A C) 1))  & (r1_xxreal_0 (k1_algseq_1 A (k11_polynom3 A B C)) (k1_algseq_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t36_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [G:$i] :  ((m1_valuat_1 G A B) => (r1_valuat_1 A B (k8_cqc_lang A (k8_cqc_lang A D E) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A E F)) (k6_cqc_lang A (k7_cqc_lang A D F)))) G C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((k1_relset_1 k5_numbers (k63_valued_1 A)) = (k7_subset_1 k5_numbers (k1_relset_1 k5_numbers A) (k1_tarski (k62_valued_1 A)))) ) ) ).
tt(t36_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k14_valued_2 C A) B) = (k14_valued_2 C (k3_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t36_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_5 D A B (k2_vectsp11 A B C)) => (v2_funct_1 (k8_matrlin2 A B B D C))) ) ) ) ) ) ) ) ).
tt(t36_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t36_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k5_vectsp_2 A C B D) = (k4_struct_0 C))  <=>  ( (B = (k4_struct_0 A))  |  (D = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k1_vectsp_4 A C) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ).
tt(t36_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (r2_hidden B (k3_vectsp_5 A B))) ) ) ) ).
tt(t36_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_vectsp_6 A B D) C) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t36_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 B (k1_vectsp_9 A C)) & (v1_xboole_0 (k2_vectsp_9 A C B))) ) ) ) ) ) ) ) ).
tt(t36_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k3_normsp_0 A B C) A)) ) ) ) ) ) ) ).
tt(t36_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k3_normsp_0 A B C) A)) ) ) ) ) ) ) ).
tt(t36_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattice3 A B C) <=> (r1_lattice3 A (k4_waybel_0 A B) C)) ) ) ) ) ) ) ).
tt(t36_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v3_pre_topc (k2_waybel_3 A B) A)) ) ) ) ).
tt(t36_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_card_3 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A E B))  &  ((r2_hidden D C) & (r3_orders_2 A (k12_lattice3 A E D) B)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D B))  &  (! [E:$i] :  ( ((v2_waybel_6 E A) & (m1_subset_1 E (u1_struct_0 A)))  =>  (~  ((r3_orders_2 A B E) &  (~ (r2_hidden E (k4_waybel_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) D) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) => (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A)))) ) ) ).
tt(t36_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r2_hidden C (u1_struct_0 (k1_waybel_8 A))) & (r3_waybel_4 A (k6_subset_1 (u1_struct_0 A) (k6_waybel_0 A C)) B)) ) )  <=> (v1_waybel16 B A)) ) ) ) ) ).
tt(t36_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v3_waybel11 B A)) ) ) ) ) ).
tt(t36_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v7_waybel_1 B A) => (v3_waybel_1 (k1_waybel_1 (k1_yellow_2 A A B) A (k3_waybel_1 A A B) (k2_waybel_1 A A B)) (k1_yellow_2 A A B) A)) ) ) ) ) ).
tt(t36_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  ((v22_waybel_0 (k3_waybel20 A B) A A) &  (B = (k8_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 (k3_yellow_3 A A)) (k1_waybel20 A A A A (k3_waybel20 A B) (k3_waybel20 A B)) (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t36_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  (! [D:$i] :  ((m2_waybel21 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k2_waybel_0 A C E) = (k2_waybel_0 A B (k2_yellow_6 (u1_struct_0 C) B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel23 (k5_waybel_0 A B) A)) ) ) ) ).
tt(t36_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ((k3_yellow_0 (k3_waybel24 A B)) = (k6_struct_0 A B (k3_yellow_0 B))) ) ) ) ) ).
tt(t36_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v1_waybel25 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) & (l1_pre_topc B)) ) )  =>  ((r1_waybel18 B A) => (v1_waybel25 B)) ) ) ) ) ).
tt(t36_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v2_waybel18 B) & (l1_pre_topc B)) ) ) )  =>  ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B))) ) ) ) ) ) ).
tt(t36_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v1_lattice3 D) &  ((v2_lattice3 D) &  ((v3_lattice3 D) & (l1_orders_2 D)) ) ) ) ) )  =>  ( ((r5_waybel_1 A B) & (r5_waybel_1 C D))  => (r5_waybel_1 (k2_waybel27 B C) (k2_waybel27 A D))) ) ) ) ) ) ) ) ) ).
tt(t36_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B (k3_yellow_3 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((k2_yellow_0 A (k7_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 A) (k5_waybel_2 A) B)) = (k2_yellow_0 A (k2_yellow_4 A (k4_yellow_3 A A B) (k5_yellow_3 A A B)))) ) ) ) ) ).
tt(t36_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v3_waybel_3 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v1_compts_1 A) &  ((v8_pre_topc A) &  ((v2_yellow13 A) & (v3_waybel30 A)) ) ) ) ) ).
tt(t36_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_waybel_0 (k1_yellow_2 A A B) A) <=> (v22_waybel_0 (k3_waybel_1 A A B) (k1_yellow_2 A A B) A)) ) ) ) ) ).
tt(t36_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = C)  =>  ((v1_waybel_3 B (k2_yellow_1 (u1_pre_topc A))) <=> (v2_compts_1 C A)) ) ) ) ) ) ) ) ).
tt(t36_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C) = (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) C)) ) ) ) ) ) ) ).
tt(t36_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v2_waybel_1 A) <=> (v9_waybel_1 A)) ) ) ).
tt(t36_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_waybel_3 A (k2_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r3_orders_2 A D B)) ) ) ) ) ) ) )  =>  ( ( (B = (k4_yellow_0 A))  & (v1_waybel_3 (k4_yellow_0 A) A))  | (r1_subset_1 (k4_waybel_0 A (k12_waybel_0 A (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)))) (k1_waybel_3 A B))) ) ) ) ) ) ).
tt(t36_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A D) A A)) )  &  ((v11_waybel_0 C A) & (r3_waybel_9 A C B)) )  =>  (B = (k1_waybel_9 A C)) ) ) ) ) ) ) ) ).
tt(t36_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((m1_subset_1 B (u1_struct_0 (k1_uniroots A))) => (r1_nat_d (k1_vectsp_9 (k4_weddwitt A) (k7_weddwitt A B)) (k1_vectsp_9 (k4_weddwitt A) (k6_weddwitt A)))) ) ) ) ) ).
tt(t36_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_wellord1 A B C) =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski D E) A) =>  ( (D = E)  |  ((r2_hidden (k4_tarski (k1_funct_1 C D) (k1_funct_1 C E)) B) &  (~  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_wsierp_1,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((k3_int_2 (k1_seq_1 A C) B) = 1) ) ) )  =>  ((k3_int_2 (k3_wsierp_1 A) B) = 1) ) ) ) ) ) ).
tt(t36_xboole_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 A B) A)) ) ).
tt(t36_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k5_xboolean A B)) = (k9_xboolean A B)) ) ) ) ) ).
tt(t36_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A (k2_xcmplx_0 B C)) = (k6_xcmplx_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t36_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 C (k2_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t36_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k12_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k12_xtuple_0 A) (k12_xtuple_0 B)))) ) ).
tt(t36_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k4_xxreal_0 (k3_xxreal_0 A B) B) = B) ) ) ) ) ).
tt(t36_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k3_xxreal_1 B C) (k1_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t36_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (m2_xxreal_2 A k1_xboole_0)) ) ).
tt(t36_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k1_xxreal_3 A C) (k1_xxreal_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t36_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_yellow_0 A B) &  ((r1_yellow_0 A C) & (r1_yellow_0 A (k2_xboole_0 B C))) )  =>  ((k1_yellow_0 A (k2_xboole_0 B C)) = (k10_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ).
tt(t36_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_yellow_3 A B (k5_waybel_0 A C) (k5_waybel_0 B D)) = (k5_waybel_0 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t36_yellow12,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v2_pre_topc C) & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v2_pre_topc D) & (l1_pre_topc D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D)))  &  ( (E = F)  & (v5_pre_topc E A C)) ) )  => (v5_pre_topc F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  => (v3_tops_2 (k8_waybel18 B A (k4_tmap_1 A B)) B (k7_waybel18 B A (k4_tmap_1 A B)))) ) ) ) ).
tt(t36_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v1_yellow_1 C) & (v4_waybel_3 C)) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D A) => (m1_yellow_0 (k3_waybel_3 A C D) (k3_waybel_3 A B D))) )  => (m1_yellow_0 (k5_yellow_1 A C) (k5_yellow_1 A B))) ) ) ) ) ) ) ).
tt(t36_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ((k5_altcat_1 A B C D E F) = (k3_relat_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((v1_yellow19 B A) => (v3_yellow_6 B A)) ) ) ) ) ) ).
tt(t36_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_altcat_1 B))  =>  (! [C:$i] :  ( ((v11_functor0 C A B) & (l2_functor0 C A B))  =>  ((v20_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (~  ((k1_altcat_1 B D E) = k1_xboole_0) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B D E)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  (? [I:$i] :  ((m1_subset_1 I (k1_altcat_1 A G H)) &  ( (E = (k3_functor0 A B C G))  &  ( (D = (k3_functor0 A B C H))  &  ( (~  ((k1_altcat_1 A G H) = k1_xboole_0) )  &  (F = (k8_functor0 A B C G H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_yellow_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v12_waybel_0 C A)) ) )  =>  ((v12_waybel_0 (k6_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t36_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_yellow_0 A C) &  ((r2_yellow_0 B D) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) G) => (r1_orders_2 (k3_yellow_3 A B) G (k7_yellow_3 A B E F))) ) ) ) )  =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_lattice3 A C G) => (r1_orders_2 A G E)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r1_lattice3 B D G) => (r1_orders_2 B G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_yellow_4 A B (k1_struct_0 A)) = k1_xboole_0) ) ) ) ) ).
tt(t36_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k7_waybel_1 A (k13_lattice3 A B C)) = (k12_lattice3 A (k7_waybel_1 A B) (k7_waybel_1 A C)))  &  ((k7_waybel_1 A (k12_lattice3 A B C)) = (k13_lattice3 A (k7_waybel_1 A B) (k7_waybel_1 A C))) ) ) ) ) ) ) ) ).
tt(t36_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v1_yellow_6 B A) & (l1_waybel_0 B A)) ) ) )  =>  ((k11_yellow_6 A B) = (k4_yellow_6 A B)) ) ) ) ) ).
tt(t36_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v10_waybel_1 A) <=> (v10_waybel_1 (k7_lattice3 A))) ) ) ).
tt(t36_yellow_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C B) &  ((v2_cantor_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc D A B) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden E C) => (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_zf_fund1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r2_relset_1 k4_ordinal1 A (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 C) (k4_zf_fund1 (k2_zf_model B))) (k2_partfun1 k4_ordinal1 A (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang A k2_zf_fund1 D) (k4_zf_fund1 (k2_zf_model B)))) & (r2_hidden C (k5_zf_model B A)))  => (r2_hidden D (k5_zf_model B A))) ) ) ) ) ) ) ) ) ).
tt(t36_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  ((v5_zf_lang A) &  ((v9_zf_lang (k21_zf_lang A)) & (v9_zf_lang (k22_zf_lang A))) ) ) ) ) ).
tt(t36_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v2_zf_lang A) =>  (A = (k4_zf_lang (k18_zf_lang A) (k19_zf_lang A))) ) ) ) ).
tt(t36_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_tarski B C)) <=>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (A = (k1_tarski B)) )  &  ( (~  (A = (k1_tarski C)) )  &  (~  (A = (k2_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(t36_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_zf_refle B A)) ) ) ) )  =>  (~  ((r2_hidden k4_ordinal1 A) &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((r2_hidden C D) => (r1_tarski (k5_zf_refle A B C) (k5_zf_refle A B D))) ) ) ) )  &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((v4_ordinal1 C) =>  ( (C = k1_xboole_0)  |  ((k5_zf_refle A B C) = (k3_card_3 (k5_relat_1 B C))) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 C) &  ((v3_ordinal2 C) &  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ( ((k4_ordinal4 A C D) = D)  =>  ( (k1_xboole_0 = D)  | (r2_zfrefle1 (k5_zf_refle A B D) (k4_zf_refle A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t36_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t370_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 B k1_xxreal_0)) = (k2_xboole_0 (k2_xxreal_1 A B) (k1_tarski k1_xxreal_0))) ) ) ) ) ).
tt(t371_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 B k1_xxreal_0) (k4_xxreal_1 A k1_xxreal_0)) = (k2_xboole_0 (k3_xxreal_1 B A) (k1_tarski k1_xxreal_0))) ) ) ) ) ).
tt(t372_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 B k1_xxreal_0) (k2_xxreal_1 A k1_xxreal_0)) = (k2_xboole_0 (k4_xxreal_1 B A) (k1_tarski k1_xxreal_0))) ) ) ) ) ).
tt(t373_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t374_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 A B)) = (k2_xboole_0 (k1_tarski A) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t375_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k4_xxreal_1 A B)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t376_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k2_xxreal_1 A B)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t377_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k2_xxreal_1 A B)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t378_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k3_xxreal_1 A B)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t379_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_xxreal_1 A B)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t37_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((k8_abcmiz_0 A (k8_abcmiz_0 A B C) D) = (k8_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t37_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v2_abcmiz_1 B A) =>  ((k1_msualg_1 A B) = (k2_finseq_2 (k3_finseq_1 (k1_msualg_1 A B)) k8_abcmiz_1)) ) ) ) ) ) ).
tt(t37_abcmiz_a,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( (~  ((v4_abcmiz_a B A) & (v5_abcmiz_a B A)) )  &  ( (~  ((v4_abcmiz_a B A) & (v6_abcmiz_a B A)) )  &  (~  ((v5_abcmiz_a B A) & (v6_abcmiz_a B A)) ) ) ) ) ) ) ) ).
tt(t37_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_aff_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (D = E) )  &  ( (~  (F = G) )  &  ((r2_analoaf A D E F G) &  ( (B = (k2_aff_1 A D E))  &  (C = (k2_aff_1 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ((r2_hidden D E) & (v1_aff_4 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k7_afinsq_1 A B C) = (k1_ordinal4 (k5_afinsq_1 A) (k6_afinsq_1 B C)))  &  ((k7_afinsq_1 A B C) = (k1_ordinal4 (k6_afinsq_1 A B) (k5_afinsq_1 C))) ) ) ) ) ).
tt(t37_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k6_afinsq_2 A (k5_afinsq_1 C) B) = C) ) ) ) ) ) ) ).
tt(t37_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k13_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k14_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  ( ( (C = B)  &  (E = (k4_tarski D 2)) )  =>  ((r1_incsp_1 (k14_afproj A) B D) <=> (r1_incsp_1 (k13_afproj A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_afvect0 A B (k1_afvect0 A C (k1_afvect0 A B D))) = (k1_afvect0 A (k1_afvect0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t37_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k2_algspec1 A B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_algspec1 A B C)))))) )  =>  ((r8_pboole (u1_struct_0 A) D (k1_algspec1 (u1_struct_0 A) B)) =>  (! [E:$i] :  ((m1_algspec1 E (k1_algspec1 (u4_struct_0 A) C)) =>  ((u1_msualg_1 (k2_algspec1 A B C)) = (k3_relat_1 E (k1_partfun1 (u4_struct_0 A) (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 A)) (k3_finseq_2 (u1_struct_0 (k2_algspec1 A B C))) (u1_msualg_1 A) (k12_lang1 (u1_struct_0 A) (u1_struct_0 (k2_algspec1 A B C)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 (k14_algstr_4 A))) &  ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_algstr_4 B (k14_algstr_4 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 A)))))) ) ) )  =>  ((k4_algstr_4 (k14_algstr_4 A) B) = (k9_algstr_4 (k4_algstr_4 (k14_algstr_4 A) B) (k7_relset_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k4_algstr_4 (k14_algstr_4 A) B)) (k5_algstr_4 (k14_algstr_4 A) B) (k7_relset_1 (k11_algstr_4 A 1) (u1_struct_0 (k14_algstr_4 A)) (k16_algstr_4 A 1) A)))) ) ) ) ) ).
tt(t37_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B E F)) =>  ( ( (E = C)  &  ( (F = D)  &  (G = H) ) )  =>  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  ( ((v4_altcat_3 G A C D) => (v4_altcat_3 H B E F))  &  ((v5_altcat_3 G A C D) => (v5_altcat_3 H B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) ) ) ) ).
tt(t37_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) & (r2_analort A B C D E G H)) )  => (r2_analort A B C D E F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m5_margrel1 B (u1_struct_0 A) (k1_unialg_2 A)) =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((r2_hidden D (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) B)) &  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) C)) &  ((k1_funct_1 B D) = (k1_funct_1 C E)) ) )  =>  ((r2_relset_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) B C) &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  &  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F)) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E G F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E G F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B (k10_armstrng A (k11_armstrng A B))) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B C) & (v6_armstrng C A))  => (r1_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) (k10_armstrng A (k11_armstrng A B)) C)) ) ) ) ) ) ) ) ).
tt(t37_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ( (~  ( (~  (A = k1_xboole_0) )  &  ((k6_arytm_3 A) = k1_xboole_0) ) )  &  (~  ( (~  ((k6_arytm_3 A) = k1_xboole_0) )  &  (A = k1_xboole_0) ) ) ) ) ) ).
tt(t37_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r1_xxreal_0 2 B) & (r2_asympt_0 A B)) ) )  => (v7_asympt_0 A)) ) ) ).
tt(t37_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 A C) = (k3_power C (k3_power 2 (k1_int_1 (k6_power 2 C))))) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k5_series_1 C C)) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v4_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers C B) &  ((r2_hidden A (k11_asympt_0 C k6_asympt_1)) &  ( (~ (r2_hidden A (k8_asympt_0 C)))  &  ((v6_asympt_0 A) &  ((v6_asympt_0 C) &  (~ (r2_asympt_0 C 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) => (m1_subset_1 (k6_subset_1 B (k6_domain_1 (u1_struct_0 A) (k11_bagorder A B))) (k5_finsub_1 (u1_struct_0 A)))) ) ) ) ).
tt(t37_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_bcialg_1 A C)) =>  ((k1_bcialg_1 A B D) = (k6_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t37_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m4_bcialg_2 C A B) => (m1_bcialg_2 C A)) ) ) ) ) ) ).
tt(t37_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  ((v7_bcialg_3 A) & (v10_bcialg_3 A)) ) ) ) ) ) ) ).
tt(t37_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k7_bcialg_1 A B)) => (r1_bcialg_1 A E D)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (! [F:$i] :  ((m2_subset_1 F (u1_struct_0 A) (k7_bcialg_1 A C)) => (r1_bcialg_1 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((m1_bcialg_5 A k6_numbers k6_numbers k6_numbers k6_numbers) <=>  ((v8_bcialg_1 A) & (m1_bcialg_5 A k6_numbers k6_numbers k6_numbers k6_numbers)) ) ) ) ).
tt(t37_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v2_funct_1 C) <=>  ((k5_bcialg_6 B A C) = (k1_tarski (k4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t37_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) ) ) ) ) ).
tt(t37_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k4_bhsp_1 A B C))) ) ) ) ) ) ).
tt(t37_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ( ((k1_bhsp_2 A D) = B)  &  ((v1_bhsp_2 E A) &  ((k1_bhsp_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k3_bhsp_2 A (k3_normsp_1 A D E) (k5_algstr_0 A B C))) &  ((k2_seq_2 (k3_bhsp_2 A (k3_normsp_1 A D E) (k5_algstr_0 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  (B = (k1_valued_0 (u1_struct_0 A) C D)) ) ) )  | (v1_bhsp_2 C A)) ) ) ) ) ) ) ) ).
tt(t37_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k1_normsp_1 A (k1_bhsp_4 A B) C)) (k1_seq_1 (k3_series_1 (k2_bhsp_2 A B)) C))) ) ) ) ) ) ).
tt(t37_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear H A B C) &  ((v2_bilinear H A B C) &  ((v3_bilinear H A B C) &  ((v4_bilinear H A B C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H (k5_algstr_0 B D E) (k5_algstr_0 C F G)) = (k5_algstr_0 A (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H D F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H D G)) (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H E F) (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) H E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_binari_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ( ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d (k23_binop_2 C 1) 1))) (k20_binop_2 A B)) &  ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) A) & (r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) B)) )  =>  ((r1_xxreal_0 k6_numbers A) |  ((r1_xxreal_0 k6_numbers B) |  ((k3_binari_2 (k23_binop_2 C 1) (k7_binarith (k23_binop_2 C 1) (k2_binari_4 (k23_binop_2 C 1) A) (k2_binari_4 (k23_binop_2 C 1) B))) = (k20_binop_2 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t37_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k1_boolealg A C D)) (k3_lattices A (k1_boolealg A B C) (k4_lattices A B D)))) ) ) ) ) ) ) ) ).
tt(t37_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_eqrel_1 C (u1_struct_0 B)))  =>  (! [D:$i] :  ((r2_hidden D (u1_struct_0 B)) => (r2_hidden (k1_funct_1 (k12_borsuk_1 A (k13_borsuk_1 A B C)) D) (u1_struct_0 (k11_borsuk_1 B C)))) ) ) ) ) ) ) ) ).
tt(t37_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~  (A = k6_numbers) )  &  (~  ( (~ (v1_xboole_0 (k3_rcomp_1 A B)))  & (m1_subset_1 (k3_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4)))) ) ) ) ) ) ) ) ) ).
tt(t37_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k4_subset_1 k1_numbers (k3_rcomp_1 B C) (k4_rcomp_1 C D)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k2_pre_topc k3_topmetr A) = (k1_rcomp_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ((v5_pre_topc A (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ((v5_pre_topc B (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) => (m1_subset_1 (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A C) (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B C)) (u1_struct_0 k5_topmetr))) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A D) = E)  &  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B D) = F) )  =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) C D) = (k2_xcmplx_0 E F)) ) ) ) ) ) ) )  & (v5_pre_topc C (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (B = k3_numbers)  =>  ((v3_pre_topc (k9_subset_1 k1_numbers k3_numbers (k2_rcomp_1 A k1_xxreal_0)) (k1_pre_topc k3_topmetr B)) & (m1_subset_1 (k9_subset_1 k1_numbers k3_numbers (k2_rcomp_1 A k1_xxreal_0)) (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc k3_topmetr B))))) ) ) ) ) ) ).
tt(t37_bspace,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_bspace A))) =>  ( (? [C:$i] :  ((r2_hidden C A) &  (B = (k1_tarski C)) ) )  => (r2_hidden B (k9_bspace A))) ) ) ) ).
tt(t37_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k1_bvfunc_1 A (k6_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t37_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  ( (G = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B I) (k16_funcop_1 C J)) (k16_funcop_1 D K)) (k16_funcop_1 E L)) (k16_funcop_1 F M)) (k16_funcop_1 A H)))  =>  ( (A = B)  |  ( (A = C)  |  ( (A = D)  |  ( (A = E)  |  ( (A = F)  |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (D = E)  |  ( (D = F)  |  ( (E = F)  |  ( ((k1_funct_1 G A) = H)  &  ( ((k1_funct_1 G B) = I)  &  ( ((k1_funct_1 G C) = J)  &  ( ((k1_funct_1 G D) = K)  &  ( ((k1_funct_1 G E) = L)  &  ((k1_funct_1 G F) = M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k16_bvfunc_1 A B (k10_eqrel_1 A)) B)) ) ) ) ).
tt(t37_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t37_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc26 A C D)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) D))) ) ) ) ) ) ) ) ).
tt(t37_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k9_bvfunc_1 A (k7_bvfunc_2 A C B E) D) (k7_bvfunc_2 A (k9_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ).
tt(t37_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F) (k7_bvfunc_2 A (k2_bvfunc_1 A E (k1_bvfunc_1 A D)) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E (k1_bvfunc_1 A C)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D)) (k5_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t37_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B C))) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t37_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A D C)) (k2_bvfunc_1 A B D)) C)) ) ) ) ) ) ) ) ).
tt(t37_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v2_struct_0 (k11_c0sp1 A)))  &  ((v13_algstr_0 (k11_c0sp1 A)) &  ((v2_rlvect_1 (k11_c0sp1 A)) &  ((v3_rlvect_1 (k11_c0sp1 A)) &  ((v4_rlvect_1 (k11_c0sp1 A)) &  ((v5_rlvect_1 (k11_c0sp1 A)) &  ((v6_rlvect_1 (k11_c0sp1 A)) &  ((v7_rlvect_1 (k11_c0sp1 A)) &  ((v8_rlvect_1 (k11_c0sp1 A)) &  ((v3_normsp_0 (k11_c0sp1 A)) &  ((v4_normsp_0 (k11_c0sp1 A)) &  ((v2_normsp_1 (k11_c0sp1 A)) &  ((v2_funcsdom (k11_c0sp1 A)) &  ((v3_group_1 (k11_c0sp1 A)) &  ((v1_vectsp_1 (k11_c0sp1 A)) &  ((v3_vectsp_1 (k11_c0sp1 A)) &  ((v5_lopban_2 (k11_c0sp1 A)) & (l1_lopban_2 (k11_c0sp1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B)) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C))) &  ( ((k6_cqc_lang A (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) B))) = (k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C)))  &  ( ((k2_calcul_1 A B) = (k2_calcul_1 A C))  &  ((r4_calcul_1 A B) & (r4_calcul_1 A C)) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) 1) |  ((r1_xxreal_0 (k3_finseq_1 C) 1) | (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) (k2_calcul_1 A B))))) ) ) ) ) ) ) ) ) ).
tt(t37_card_1,ax, (! [A:$i] :  ((r2_hidden A k4_ordinal1) => (v1_card_1 A)) ) ).
tt(t37_card_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k4_nat_1 A B) = (k9_ordinal3 A B)) ) ) ) ) ).
tt(t37_card_3,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((k6_card_3 (k16_funcop_1 B A)) = A) ) ) ) ).
tt(t37_card_5,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski (k1_tarski A) B) =>  ((k2_wellord2 (k1_wellord2 (k1_tarski A))) = 1) ) ) ) ) ).
tt(t37_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v2_card_1 A)) ) )  =>  (! [B:$i] :  ((m1_card_fil B A) =>  (~  ((v1_card_fil B A) &  ((v3_card_fil B A) & (r1_card_fil A A B)) ) ) ) ) ) ) ).
tt(t37_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (~ (v1_xboole_0 C))  =>  ((r2_hidden A (k2_card_fin C (k7_funcop_1 (k9_xtuple_0 C) B) B)) <=>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) => (r2_hidden A (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(t37_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~ (v1_xboole_0 (k4_classes1 A))) ) ) ).
tt(t37_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v8_cat_1 E A B C) & (v8_cat_1 F A C D))  => (v8_cat_1 (k5_cat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k7_cat_1 B C (k12_cat_2 A B C D E)) F) = (k1_binop_1 (k7_cat_1 (k8_cat_2 A B) C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v10_cat_1 C A) =>  ((k10_cat_3 A B C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t37_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k5_cat_1 A (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B (k2_cat_4 A C D)) (k17_cat_4 A B C D) (k16_cat_4 A B C D)) = (k4_cat_1 A (k2_cat_4 A B (k2_cat_4 A C D))))  &  ((k5_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B (k2_cat_4 A C D)) (k2_cat_4 A (k2_cat_4 A B C) D) (k16_cat_4 A B C D) (k17_cat_4 A B C D)) = (k4_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t37_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 (k24_binop_2 2 B) A) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k1_card_1 (a_2_0_catalan2 A B)) = (k7_afinsq_2 C))  &  ( ((k1_relset_1 k5_numbers C) = B)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 B D))  =>  ((k1_recdef_1 C D) = (k24_binop_2 (k5_card_1 (k2_catalan2 (k24_binop_2 2 D) D)) (k5_card_1 (k2_catalan2 (k7_nat_d A (k24_binop_2 2 (k23_binop_2 D 1))) (k7_nat_d B (k23_binop_2 D 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k8_cfuncdom (u1_struct_0 A))))))  =>  ( (B = (k6_cc0sp2 A))  => (v1_cc0sp1 B (k8_cfuncdom (u1_struct_0 A)))) ) ) ) ) ).
tt(t37_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_cfcont_1 B A) & (r1_cfcont_1 C A))  =>  ( ((k7_partfun1 k2_numbers B A) = k6_numbers)  | (r1_cfcont_1 (k1_cfunct_1 k2_numbers C B) A)) ) ) ) ) ) ) ) ).
tt(t37_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_cfunct_1 A (k31_valued_1 A k2_numbers B)) (k25_valued_1 A k2_numbers (k2_cfunct_1 A B) (k10_complex1 k6_complex1)))) ) ) ) ).
tt(t37_cgames_1,ax, ((k12_cgames_1 k1_xboole_0 k3_cgames_1) = (k1_tarski k3_cgames_1)) ).
tt(t37_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  ((r2_hidden C (k4_chain_1 A B k6_numbers)) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  ( (C = (k3_chain_1 A D D))  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (r2_hidden (k1_seq_1 D E) (k2_chain_1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_chord B A) => (v5_glib_001 B A)) ) ) ) ) ).
tt(t37_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 1 B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 B) B)))) )  =>  (! [D:$i] :  ((m1_circcmb3 D B) =>  ((r2_hidden A (u1_struct_0 D)) =>  ((r2_hidden (k3_circcmb3 (k4_circcmb3 1 B C (k9_finseq_1 A))) (k2_msafree2 D)) |  ((k2_msafree2 (k6_circcmb3 B D (k4_circcmb3 1 B C (k9_finseq_1 A)))) = (k2_msafree2 D)) ) ) ) ) ) ) ) ) ) ).
tt(t37_circcomb,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k4_circcomb A C B))) =>  ( (D = (k4_tarski C A))  &  ( ((k1_msualg_1 (k4_circcomb A C B) D) = C)  &  ((k2_msualg_1 (k4_circcomb A C B) D) = B) ) ) ) ) ) ) ) ) ).
tt(t37_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ((r5_circtrm1 A B C D E F) <=>  ((r1_circtrm1 A B C D) &  ( ((u3_msualg_1 A E) = (k3_relat_1 C (u3_msualg_1 B F)))  &  ((u4_msualg_1 A E) = (k3_relat_1 D (u4_msualg_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=> (r1_tarski (k4_classes1 A) (k4_classes1 B))) ) ) ) ) ).
tt(t37_classes2,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_tarski A (k4_classes1 (k1_card_1 (k1_classes1 B)))) &  ( (~ (r2_tarski A (k4_classes1 (k1_card_1 (k1_classes1 B)))))  &  (~ (r2_hidden A (k4_classes1 (k1_card_1 (k1_classes1 B))))) ) ) ) ) ) ).
tt(t37_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k14_clopban1 A B)) &  ((v3_normsp_0 (k14_clopban1 A B)) & (v8_clvect_1 (k14_clopban1 A B))) ) ) ) ) ) ).
tt(t37_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D)))) ) ) ) )  & (v2_clopban3 B A)) ) ) ) ) ) ) ).
tt(t37_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k7_clopban4 A B) (k7_clopban4 A (k4_algstr_0 A B))) = (k5_struct_0 A))  &  ((k6_algstr_0 A (k7_clopban4 A (k4_algstr_0 A B)) (k7_clopban4 A B)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t37_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_mssubfam C A B) & (m3_pboole C A (k1_mboolean A B)))  =>  (! [D:$i] :  ((m2_pboole D A (k5_mssubfam A B) (k5_mssubfam A B)) =>  ( (! [E:$i] :  ((m1_pboole E A (k5_mssubfam A B)) =>  (! [F:$i] :  ( ((v2_relat_1 F) & (m3_pboole F A (k1_mboolean A B)))  =>  ( (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) & (v1_partfun1 G A)) ) )  =>  ((r1_pboole A G F) <=>  ((r1_pboole A G C) & (r2_pboole A E G)) ) ) )  => (r6_pboole A (k2_closure1 A B D E) (k4_mssubfam A B F))) ) ) ) )  => (v3_closure1 D A B)) ) ) ) ) ) ) ) ).
tt(t37_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 A B) (k6_closure2 A B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 A B) (k6_closure2 A B))))) )  =>  ( ((v10_closure2 C A B) & (v10_closure2 D A B))  => (v10_closure2 (k8_closure2 A B D C) A B)) ) ) ) ) ) ) ) ).
tt(t37_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) => (r1_struct_0 C (k4_struct_0 B))) ) ) ) ) ) ).
tt(t37_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ( ((k1_clvect_2 A D) = B)  &  ((v1_clvect_2 E A) &  ((k1_clvect_2 A E) = C) ) ) )  =>  ((v2_comseq_2 (k3_clvect_2 A (k3_normsp_1 A D E) (k5_algstr_0 A B C))) &  ((k2_seq_2 (k3_clvect_2 A (k3_normsp_1 A D E) (k5_algstr_0 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k1_normsp_1 A (k1_bhsp_4 A B) C)) (k8_nat_1 k1_numbers (k3_series_1 (k2_clvect_2 A B)) C))) ) ) ) ) ) ).
tt(t37_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v9_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( ((k8_cohsp_1 A B C) = (k8_cohsp_1 A B D))  => (r2_funct_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t37_coh_sp,ax, (! [A:$i] : (r2_hidden (k4_tarski (k6_partfun1 A) A) (k16_coh_sp A))) ).
tt(t37_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k15_complex1 (k13_complex1 A B)) = (k13_complex1 (k15_complex1 A) (k15_complex1 B))) ) ) ) ) ).
tt(t37_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 (k9_complex1 A B) C) = (k9_complex1 A (k1_complex2 B C))) ) ) ) ) ) ) ).
tt(t37_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_vectsp_1 k1_complfld C (k8_group_1 k1_complfld A B)) = (k3_vectsp_1 k1_complfld (k3_vectsp_1 k1_complfld C A) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k1_valued_1 A (k45_valued_1 B C)) = (k45_valued_1 (k1_valued_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t37_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  ((v1_compts_1 (k3_pcomps_1 A)) <=>  ((v1_tbsp_1 A) & (v4_tbsp_1 A)) ) ) ) ).
tt(t37_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k8_compos_1 A (k3_compos_2 A B C) D) k6_numbers) = B) ) ) ) ) ) ) ) ) ).
tt(t37_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_comptrig (k3_xcmplx_0 A k7_complex1)) = (k10_real_1 k32_sin_cos 2)) ) ) ) ).
tt(t37_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k19_margrel1 (k5_comput_1 A B)) = A) ) ) ) ) ).
tt(t37_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (r2_relset_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B C) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers B A) (k19_valued_1 k5_numbers k2_numbers k2_numbers C A)))) ) ) ) ) ) ) ).
tt(t37_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_relat_1 A))  =>  ( ((k3_comseq_2 A) = k5_complex1)  |  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k36_valued_1 k5_numbers k2_numbers A))) = (k12_complex1 (k15_complex1 (k3_comseq_2 A)))) ) ) ) ) ).
tt(t37_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A (k2_nat_1 C 1)) = (k9_complex1 B (k8_nat_1 k2_numbers A C))) ) )  =>  ( (B = k6_complex1)  |  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers (k10_comseq_3 A) C) = (k9_complex1 (k8_nat_1 k2_numbers A k6_numbers) (k13_complex1 (k11_complex1 k6_complex1 (k2_comseq_3 B (k2_nat_1 C 1))) (k11_complex1 k6_complex1 B)))) ) ) ) ) ) ) ) ) ).
tt(t37_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  (! [C:$i] :  ( ((v4_conlat_1 C A) &  ( (~ (v5_conlat_1 C A))  &  ((v7_conlat_1 C A) & (l2_conlat_1 C A)) ) )  =>  ((k1_binop_1 (k9_conlat_1 A) B (k1_binop_1 (k10_conlat_1 A) B C)) = B) ) ) ) ) ) ) ).
tt(t37_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_connsp_1 A) &  ((v2_connsp_1 B A) & (r3_connsp_1 A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) C)) )  => (v2_connsp_1 (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) C) A)) ) ) ) ) ) ) ).
tt(t37_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_convex1 A (k1_convex1 A B D) C) = (k1_convex1 A B (k8_real_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t37_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) => (r1_convex4 A (k9_convex4 A B B) (k2_convex4 A))) ) ) ) ).
tt(t37_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  ((k15_cqc_sim1 A (k4_cqc_lang B A D C)) = (k6_domain_1 (k4_zfmisc_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k1_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) (k4_cqc_lang B A D C) (k13_cqc_sim1 A (k4_cqc_lang B A D C)) (k1_setwiseo (k3_qc_lang1 A)) (k11_cqc_sim1 (k3_qc_lang1 A))))) ) ) ) ) ) ) ) ) ).
tt(t37_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((r2_hidden C (k1_cqc_the1 A B)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  (~  ((r1_tarski D B) &  ((v1_finset_1 D) & (r2_hidden C (k1_cqc_the1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k11_cqc_lang A D (k7_cqc_lang A B C)) (k7_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t37_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r5_cqc_the3 A B C) => (r5_cqc_the3 A (k11_cqc_lang A D B) (k11_cqc_lang A E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) => (r1_csspace A (k4_algstr_0 A B) C)) ) ) ) ) ) ) ).
tt(t37_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 48 k6_margrel1)) =>  (? [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [C:$i] :  ((m2_finseq_2 C k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [D:$i] :  ((m2_finseq_2 D k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [E:$i] :  ((m2_finseq_2 E k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [F:$i] :  ((m2_finseq_2 F k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [G:$i] :  ((m2_finseq_2 G k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [H:$i] :  ((m2_finseq_2 H k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  (? [I:$i] :  ((m2_finseq_2 I k6_margrel1 (k4_finseq_2 6 k6_margrel1)) &  ( (B = (k1_funct_1 (k31_descip_1 A) 1))  &  ( (C = (k1_funct_1 (k31_descip_1 A) 2))  &  ( (D = (k1_funct_1 (k31_descip_1 A) 3))  &  ( (E = (k1_funct_1 (k31_descip_1 A) 4))  &  ( (F = (k1_funct_1 (k31_descip_1 A) 5))  &  ( (G = (k1_funct_1 (k31_descip_1 A) 6))  &  ( (H = (k1_funct_1 (k31_descip_1 A) 7))  &  ( (I = (k1_funct_1 (k31_descip_1 A) 8))  &  (A = (k9_binarith (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 6 6) 6) 6) 6) 6) 6) 6 k6_margrel1 (k9_binarith (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 6 6) 6) 6) 6) 6) 6 k6_margrel1 (k9_binarith (k1_nat_1 (k1_nat_1 (k1_nat_1 (k1_nat_1 6 6) 6) 6) 6) 6 k6_margrel1 (k9_binarith (k1_nat_1 (k1_nat_1 (k1_nat_1 6 6) 6) 6) 6 k6_margrel1 (k9_binarith (k1_nat_1 (k1_nat_1 6 6) 6) 6 k6_margrel1 (k9_binarith (k1_nat_1 6 6) 6 k6_margrel1 (k9_binarith 6 6 k6_margrel1 B C) D) E) F) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((v4_dickson A) &  ((v4_dickson B) &  ((v3_dickson A) & (v3_dickson B)) ) )  =>  ((v3_dickson (k3_yellow_3 A B)) & (v4_dickson (k3_yellow_3 A B))) ) ) ) ) ) ).
tt(t37_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 k1_numbers k1_numbers)) &  ((v1_diff_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 G F) =>  ((k3_funct_2 k5_numbers k1_numbers (k12_diff_1 E F) G) = (k8_real_1 (k8_real_1 (k6_newton G F) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) G) B)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D A) (k7_nat_d F G)) (k7_real_1 B (k8_real_1 G A))))) ) ) ) ) )  =>  ( ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 1) B) = (k6_series_1 (k12_diff_1 E 1) 1))  &  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers C D) A) 2) B) = (k6_series_1 (k12_diff_1 E 2) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k1_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers G H) = (k10_real_1 A H)) ) )  & (r3_zfmisc_1 B C D E F))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ( (D = k6_numbers)  |  ( (E = k6_numbers)  |  ( (F = k6_numbers)  |  ((k1_diff_2 G B C D E F) = (k10_real_1 A (k8_real_1 (k8_real_1 (k8_real_1 (k8_real_1 B C) D) E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k7_square_1 E)) ) )  & (r1_zfmisc_1 A B C))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ((k10_diff_1 D A B C) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k8_real_1 (k7_real_1 (k7_square_1 A) (k7_square_1 B)) (k7_real_1 (k7_square_1 A) (k7_square_1 C))) (k7_real_1 (k7_square_1 B) (k7_square_1 C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k3_diff_1 (k3_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C (k8_real_1 2 A)) B) (k8_real_1 2 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B)))) ) ) ) ) ) ) ).
tt(t37_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) )  =>  ((k4_dilworth A (k5_dilworth A)) = (k2_struct_0 A)) ) ) ).
tt(t37_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_diraf A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t37_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 B))) =>  ( ((k4_nat_d A 2) = k6_numbers)  =>  ( (C = k6_numbers)  |  ((k2_ec_pf_1 B (k2_binom (k9_int_3 B) C A)) = 1) ) ) ) ) ) ) ) ) ).
tt(t37_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k7_ec_pf_2 A D)) = k6_numbers)  =>  ( ((k7_ec_pf_2 A D) = (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers))  &  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  (! [D:$i] :  ((m1_cat_1 D (k11_ens_1 A) B C) =>  ((v8_cat_1 D (k11_ens_1 A) B C) =>  ( ((k2_cat_1 (k11_ens_1 A) B C) = k1_xboole_0)  |  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden F E) &  ((r2_hidden G E) &  (~  (F = G) ) ) ) ) ) ) ) )  | (v1_ens_1 (k15_ens_1 A D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 k1_numbers)) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k1_matrprob k1_numbers B (k2_nat_1 C 1)) = (k8_finseq_1 k1_numbers (k1_matrprob k1_numbers B C) (k1_matrprob k1_numbers A (k2_nat_1 C 1)))) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k18_rvsum_1 (k1_matrprob k1_numbers B (k2_nat_1 C 1))) = (k7_real_1 (k18_rvsum_1 (k1_matrprob k1_numbers B C)) (k18_rvsum_1 (k1_matrprob k1_numbers A (k2_nat_1 C 1))))) ) ) ) ) ) ) ) ) ) ).
tt(t37_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_enumset1 A A A B) = (k2_tarski A B)) ) ) ).
tt(t37_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k10_eqrel_1 A) = (a_1_0_eqrel_1 A)) ) ) ).
tt(t37_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 (k4_equation B) C)) =>  (! [E:$i] :  ((m1_pralg_2 E A B) =>  ( (! [F:$i] :  (~  ((r2_hidden F A) &  (! [G:$i] :  ((l3_msualg_1 G B) =>  (~  ( (G = (k1_funct_1 E F))  & (r1_equation B G C D)) ) ) ) ) ) )  => (r1_equation B (k14_pralg_2 A B E) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t37_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k12_euclid B) = (k7_square_1 (k23_rvsum_1 B B))) ) ) ) ) ).
tt(t37_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~  ((k4_euclid_3 A B C) = k6_numbers) )  =>  ((k4_euclid_3 C B A) = (k9_real_1 (k8_real_1 2 k32_sin_cos) (k4_euclid_3 A B C))) ) ) ) ) ) ) ) ).
tt(t37_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k9_real_1 (k5_square_1 (k12_euclid (k7_euclid A B C))) (k5_square_1 (k12_euclid (k8_euclid A B C)))) = (k8_real_1 4 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t37_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ((r2_hidden A (k5_jgraph_6 D E F)) &  ((r2_hidden B (k5_jgraph_6 D E F)) &  ((r2_hidden C (k5_jgraph_6 D E F)) &  ((k4_euclid_3 A B C) = k6_numbers) ) ) )  =>  ( (A = B)  |  ( (B = C)  |  (A = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_rlsub_1 B (k10_funcsdom (k2_finseq_1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden C (u1_struct_0 B)) & (r2_hidden D (u1_struct_0 B)))  => (r2_hidden (k7_euclid A (k9_euclid A C E) (k9_euclid A D F)) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (A = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k1_seq_1 A 1)) (k9_euclid 3 k3_euclid_8 (k1_seq_1 A 2))) (k9_euclid 3 k4_euclid_8 (k1_seq_1 A 3)))) ) ) ).
tt(t37_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((k3_rlvect_1 (k15_euclid A) B C) = (k4_struct_0 (k15_euclid A)))  =>  (B = (k4_algstr_0 (k15_euclid A) C)) ) ) ) ) ) ) ) ).
tt(t37_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r3_euclidlp A B C) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t37_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  (! [B:$i] :  ((m1_exchsort B A) =>  ( ((k9_xtuple_0 B) = (k9_xtuple_0 A))  &  ((k10_xtuple_0 B) = (k10_xtuple_0 A)) ) ) ) ) ) ).
tt(t37_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) )  =>  ((k3_msafree2 A) = (u4_struct_0 A)) ) ) ).
tt(t37_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A)) & (r1_tarski A (k1_relset_1 k1_numbers C)))  => (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ).
tt(t37_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t37_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t37_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) &  ((r2_fdiff_1 A (k2_subset_1 k1_numbers)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r1_xxreal_0 (k1_fdiff_1 A B) k6_numbers)) ) ) ) )  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers))) & (v2_funct_1 A)) ) ) ) ).
tt(t37_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) C) E) = (k8_real_1 A (k1_seq_1 k19_sin_cos (k7_real_1 (k8_real_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k24_sin_cos)) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 (k6_power k8_power A)))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = 1)  &  ((k1_seq_1 D E) = (k8_real_1 E (k6_power k8_power A))) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (A = 1)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k24_sin_cos)) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 (k6_power k8_power A)))) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k24_sin_cos)) (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 (k8_real_1 3 (k6_power k8_power A)))) B) E) = (k8_real_1 (k10_prepower A E) (k10_prepower (k7_real_1 1 (k10_prepower A E)) (k10_real_1 1 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k24_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t37_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t37_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 (k3_power k1_fib_num A)) (k3_xcmplx_0 2 (k3_power (k4_xcmplx_0 1) A))) (k3_square_1 (k3_power k1_fib_num (k4_xcmplx_0 A)))) = (k3_square_1 (k6_xcmplx_0 (k3_power k1_fib_num A) (k3_power k2_fib_num A)))) ) ) ).
tt(t37_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_fib_num3 k6_numbers 1 A) = (k1_pre_ff A)) ) ) ).
tt(t37_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 4 A) =>  ((k1_fib_num3 (k2_xcmplx_0 A 1)) = (k1_int_1 (k13_complex1 (k2_xcmplx_0 (k2_xcmplx_0 (k1_fib_num3 A) 1) (k6_square_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 5 (k1_pepin (k1_fib_num3 A))) (k3_xcmplx_0 2 (k1_fib_num3 A))) 1))) 2))) ) ) ) ).
tt(t37_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (C = k1_xboole_0)  =>  ((r1_xxreal_0 D k6_numbers) |  ((k8_finseq_8 A B C D) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (k3_filter_0 A (k5_filter_0 A B C))) ) ) ) ) ) ) ).
tt(t37_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((v12_lattices A) & (v12_lattices B))  <=> (v12_lattices (k7_filter_1 A B))) ) ) ) ) ).
tt(t37_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r1_filter_2 (u1_struct_0 A) (k7_filter_2 A B) B)) ) ) ) ).
tt(t37_finseq_1,ax, (! [A:$i] :  ((k9_finseq_1 A) = (k1_tarski (k4_tarski 1 A))) ) ).
tt(t37_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m2_finseq_1 F D) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G D E) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 D E)))) )  =>  ( (F = (k11_finseq_1 A B C))  =>  ((k1_partfun1 k5_numbers D D E F G) = (k11_finseq_1 (k1_funct_1 G A) (k1_funct_1 G B) (k1_funct_1 G C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((k10_finseq_1 A B) = (k11_finseq_1 C D E)) ) ) ) ) ) ) ).
tt(t37_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k10_xtuple_0 A)) & (r2_hidden B (k10_xtuple_0 (k5_finseq_4 A B)))) ) ) ) ) ).
tt(t37_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k2_rfinseq A (k3_finseq_1 B) (k8_finseq_1 A B C)) = C) ) ) ) ) ) ) ).
tt(t37_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_finseq_4 B A) =>  ((k2_nat_1 (k4_finseq_4 B A) (k4_finseq_4 (k3_finseq_5 B) A)) = (k2_nat_1 (k3_finseq_1 B) 1)) ) ) ) ) ).
tt(t37_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C C) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B B) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  ((k3_funct_2 C B F (k5_binop_1 C G I J)) = (k5_binop_1 B H (k3_funct_2 C B F I) (k3_funct_2 C B F J))) ) ) ) )  => (r2_funct_2 A B (k1_partfun1 A C C B (k6_funcop_1 C A G D E) F) (k6_funcop_1 B A H (k1_partfun1 A C C B D F) (k1_partfun1 A C C B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k9_fintopo2 A (k3_subset_1 (u1_struct_0 A) B))) = (k10_fintopo2 A B)) ) ) ) ) ).
tt(t37_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k7_fintopo3 A B C) (k7_fintopo3 A B (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t37_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) &  ((v1_fintopo6 A) &  ((v4_fin_topo B A) &  ( ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) = (k4_subset_1 (u1_struct_0 A) C D))  & (r1_fintopo4 A C D)) ) ) ) )  => (v4_fin_topo (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ) ).
tt(t37_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B C) => (r1_tarski (k7_flang_1 A B D) (k7_flang_1 A C D))) ) ) ) ) ) ) ) ).
tt(t37_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 E F))  =>  ((k6_flang_1 A (k1_flang_2 A B C D) (k1_flang_2 A B E F)) = (k1_flang_2 A B (k2_xcmplx_0 C E) (k2_xcmplx_0 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden C (k1_flang_3 A B E)) & (r2_hidden D (k1_flang_3 A B F)))  => (r2_hidden (k1_flang_1 A C D) (k1_flang_3 A B (k2_xcmplx_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((v5_relat_1 D (k3_finseq_2 B)) =>  ((k1_funct_1 (k20_fomodel0 B A C) (k1_funct_1 (k8_fomodel0 B) D)) = (k1_funct_1 (k8_fomodel0 B) (k3_relat_1 D (k20_fomodel0 B A C)))) ) ) ) ) ) ) ) ) ).
tt(t37_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v3_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_frechet A B D) => (r1_frechet A (k1_partfun1 k5_numbers k5_numbers k5_numbers (u1_struct_0 A) C B) D)) ) ) ) ) ) ) ) ) ).
tt(t37_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B C))  =>  ( ((k7_fsm_1 B C D A) = (k7_fsm_1 B C D (k2_nat_1 A 1)))  => (v4_fsm_1 (k7_fsm_1 B C D A) B C D)) ) ) ) ) ) ) ) ) ).
tt(t37_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_3 C A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  ((k3_rewrite3 A (k9_flang_1 A) (k4_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) C) B (u1_fsm_3 A (k9_flang_1 A) (k4_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) C))) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 C)) (k3_rewrite3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) C B (u1_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) C)))) ) ) ) ) ) ) ).
tt(t37_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  (! [I:$i] :  ((m1_subset_1 I k6_margrel1) =>  ( ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  (I = (k1_funct_1 F C)) ) )  =>  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) (k21_ftacell1 A B C D E)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k9_margrel1 G) (k9_margrel1 H)) (k10_margrel1 (k9_margrel1 H) (k9_margrel1 I))) (k10_margrel1 (k9_margrel1 I) (k9_margrel1 G)))))  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) (k22_ftacell1 A B C D E)) = (k9_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k3_funct_2 B A (k6_funcop_1 A B C D E) F) = (k5_binop_1 A C (k3_funct_2 B A D F) (k3_funct_2 B A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ( ((k9_xtuple_0 (k3_relat_1 (k2_funct_1 A) A)) = (k10_xtuple_0 A))  &  ((k10_xtuple_0 (k3_relat_1 (k2_funct_1 A) A)) = (k10_xtuple_0 A)) ) ) ) ) ).
tt(t37_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k6_subset_1 B C)) =>  ((k1_funct_1 (k4_funct_3 C B) A) = k1_xboole_0) ) ) ) ) ).
tt(t37_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((k1_funct_4 C D) = D) ) ) ) ) ) ) ) ).
tt(t37_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k4_partfun1 A B)) =>  ((r1_tarski (k9_xtuple_0 (k2_funct_5 C)) (k2_zfmisc_1 (k9_xtuple_0 C) A)) & (r1_tarski (k9_xtuple_0 (k4_funct_5 C)) (k2_zfmisc_1 A (k9_xtuple_0 C)))) ) ) ) ) ) ).
tt(t37_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden A (k9_xtuple_0 B)) &  ( (C = (k1_funct_1 B A))  &  ((r2_hidden D (k4_card_3 (k2_funct_6 B))) &  (E = (k1_funct_1 (k7_funct_6 B) D)) ) ) )  =>  ((r2_hidden (k1_funct_1 D A) (k9_xtuple_0 C)) &  ( ((k1_funct_1 E A) = (k1_funct_1 C (k1_funct_1 D A)))  & (r2_hidden E (k4_card_3 (k3_funct_6 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ( (D = E)  |  ((k7_partfun1 A (k3_funct_7 A B D C) E) = (k7_partfun1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k55_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t37_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  => (v1_funct_9 (k7_funcop_1 k1_numbers B) A)) ) ) ) ) ).
tt(t37_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) &  ((v12_functor0 C A B) & (l2_functor0 C A B)) ) )  =>  ( ((v21_functor0 C A B) & (v7_functor0 C A B))  => (v12_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t37_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ( ((v15_functor0 F B C) & (m2_functor0 F B C))  =>  (! [G:$i] :  ( ((v15_functor0 G B C) & (m2_functor0 G B C))  =>  (! [H:$i] :  ((m1_functor3 H A B D E) =>  (! [I:$i] :  ((m1_functor3 I B C F G) =>  ( ((r1_functor3 A B D E) & (r1_functor3 B C F G))  =>  ((r1_functor3 A C (k1_functor3 A B C D F) (k1_functor3 A B C E G)) & (m1_functor3 (k7_functor3 A B C D E F G H I) A C (k1_functor3 A B C D F) (k1_functor3 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B (k3_fuzzy_1 A C)) => (r1_fuzzy_1 C (k3_fuzzy_1 A B))) ) ) ) ) ) ) ).
tt(t37_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k2_fuzzy_2 A B (k4_fuzzy_1 A)) (k4_fuzzy_1 A)) & (r2_funct_2 A k1_numbers (k2_fuzzy_2 A B (k5_fuzzy_1 A)) B)) ) ) ) ) ).
tt(t37_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ( ((k3_funct_2 (u1_struct_0 A) k7_numbers C B) = k6_numbers)  <=>  ((k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t37_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_algstr_1 B) &  ((v2_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)) C) = (k6_fvsum_1 A B C)) ) ) ) ) ) ) ).
tt(t37_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~  ( (~ (v1_xboole_0 (k31_gate_1 A B C D E F G H)))  &  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) & (v1_xboole_0 H)) ) ) ) ) ) ) ) )  &  (~  ( (~  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) & (v1_xboole_0 H)) ) ) ) ) ) ) )  & (v1_xboole_0 (k31_gate_1 A B C D E F G H))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_gcd_1 A B C D) = (k5_struct_0 A))  =>  ((k5_gcd_1 A B C (k8_group_1 A D E)) = (k5_gcd_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G A B D C))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G A C B D))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G A C D B))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G A D C B))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B A C D))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B A D C))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B C A D))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B C D A))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B D A C))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G B D C A))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G C B A D))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G C B D A))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G C D A B))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G C D B A))  &  ( ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G D B C A))  &  ((k10_genealg1 E F G A B C D) = (k10_genealg1 E F G D C B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((r2_geomtrap A B C D E F J) &  ((r2_geomtrap A B C D E G K) &  ((r2_geomtrap A B C D E H L) &  ((r2_geomtrap A B C D E I M) & (r1_analoaf A F G H I)) ) ) )  =>  ( (D = E)  | (r1_analoaf A J K L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k13_gfacirc1 A B C))) &  ((r2_hidden (k12_gfacirc1 A B C) (k3_msafree2 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k3_msafree2 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k3_msafree2 (k13_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k3_msafree2 (k13_gfacirc1 A B C))) & (r2_hidden (k9_gfacirc1 A B C) (k3_msafree2 (k13_gfacirc1 A B C)))) ) ) ) ) ) ) ) ).
tt(t37_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k22_glib_000 A B D) (k22_glib_000 A C E))) ) ) ) ) ) ) ).
tt(t37_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ( ((k3_glib_001 A (k8_glib_001 A B C D)) = (k1_funct_1 B C))  &  ( ((k4_glib_001 A (k8_glib_001 A B C D)) = (k1_funct_1 B D))  & (r1_glib_001 A (k1_funct_1 B C) (k1_funct_1 B D) (k8_glib_001 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v1_glib_002 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) &  ( (~  (B = C) )  &  ( (~ (v5_glib_002 B A))  &  (~ (v5_glib_002 C A)) ) ) ) ) ) ) ) ) ).
tt(t37_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (B = C) )  =>  ((k1_funct_1 (k6_glib_003 (k12_glib_003 A B D)) C) = (k1_funct_1 (k6_glib_003 A) C)) ) ) ) ) ) ) ).
tt(t37_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  ((v13_glib_000 (k16_glib_004 A)) &  ((k2_nat_1 (k39_glib_000 (k16_glib_004 A)) 1) = (k5_card_1 (k1_glib_002 A (k10_subset_1 (k6_glib_000 A))))) ) ) ) ).
tt(t37_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D C) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k3_finseq_1 D)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)))) &  ((r2_hidden B (k4_finseq_1 D)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D B) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C A)))) ) ) )  =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 A E) &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 D)) &  ((r1_xxreal_0 B F) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D F) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C E)))) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  ((r1_xxreal_0 E (k3_finseq_1 C)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 D)) &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) D F) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r2_hidden (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid 1 1)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) (k1_matrix_1 A))))) ) ).
tt(t37_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_goboard8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  => (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k5_goboard5 B A)) (k3_topreal1 2 B))) ) ) ) ) ).
tt(t37_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C)) ) ) ) ) ) )  =>  ((k4_gobrd13 D E A) = (k3_goboard5 E (k2_nat_1 B 1) (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k1_jordan2c 2 (k3_topreal1 2 A)) = (k3_goboard9 A)) ) ) ).
tt(t37_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (~  ((r7_calcul_1 A B C) & (r6_calcul_1 A (k4_subset_1 (k3_cqc_lang A) B (k6_domain_1 (k3_cqc_lang A) (k6_cqc_lang A C))) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  ( ((r2_graph_2 A C) & (r1_graph_2 A B C))  =>  ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) &  ((v1_graph_2 B) & (v2_graph_2 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_graph_1 D A) => (m1_graph_1 D (k8_graph_3 A B C))) ) ) ) ) ) ) ) ).
tt(t37_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k4_graph_5 A B C) (k3_graph_5 A B C))) ) ) ) ) ) ).
tt(t37_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k4_finseq_1 (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C)) = (k4_finseq_1 (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) C))) ) ) ) ) ) ) ).
tt(t37_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden k3_algstr_0 (k26_grcat_1 A))) ) ).
tt(t37_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_uniroots A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (B = C)  =>  ((k2_group_1 (k1_uniroots A) B) = (k11_algstr_0 A C)) ) ) ) ) ) ) ) ).
tt(t37_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden F D) &  ((r2_hidden G D) &  ( ((k5_termord A B C F) = E)  &  ( ((k5_termord A B C G) = E)  &  ( (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 H (k15_pre_poly A) C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r2_hidden H D) &  ((r2_polyred A B C H F) &  ((k5_termord A B C H) = E) ) ) ) ) )  &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 H (k15_pre_poly A) C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r2_hidden H D) &  ((r2_polyred A B C H G) &  ((k5_termord A B C H) = E) ) ) ) ) ) ) ) ) ) )  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [F:$i] :  ((m2_ideal_1 F (k11_polynom1 A C) E) =>  (~  ((r4_groeb_2 A B C D E F) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 H A C) &  ((v3_polynom7 H A C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 I A C) &  ((v1_polynom1 I (k15_pre_poly A) C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (~  ((r2_hidden I E) &  ((r2_hidden G (k4_finseq_1 F)) &  ( ((k7_partfun1 (u1_struct_0 (k11_polynom1 A C)) F G) = (k9_polynom1 A C H I))  & (r6_pboole A (k3_termord A B C D) (k3_termord A B C (k9_polynom1 A C H I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (E = (k6_xcmplx_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) 1))  =>  ((v1_funct_1 (k6_groeb_3 A B C D E)) &  ((v1_funct_2 (k6_groeb_3 A B C D E) (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 (k6_groeb_3 A B C D E) A C) &  ((v3_polynom7 (k6_groeb_3 A B C D E) A C) & (m1_subset_1 (k6_groeb_3 A B C D E) (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k2_group_11 A (k1_group_11 A B C) C) B)) ) ) ) ) ) ).
tt(t37_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k5_group_1 B A (k2_group_1 B C)) = (k2_group_1 B (k5_group_1 B A C))) ) ) ) ) ) ) ).
tt(t37_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_group_2 A (k1_group_1 A) B) = B)  &  ((k5_group_2 A (k1_group_1 A) B) = B) ) ) ) ) ) ).
tt(t37_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_3 A (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) = (k6_domain_1 (u1_struct_0 A) (k2_group_3 A B C))) ) ) ) ) ) ) ).
tt(t37_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v2_group_4 B A) =>  ((r1_struct_0 B C) |  ((k5_group_4 A (k4_subset_1 (u1_struct_0 A) (k8_group_2 A B) (k6_domain_1 (u1_struct_0 A) C))) = A) ) ) ) ) ) ) ) ) ).
tt(t37_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_5 A B C) = (k1_group_1 A)) ) ) ) ) ) ) ) ).
tt(t37_group_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E (k5_group_1 B A D)) = (k5_group_1 C A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))) B C) = (k4_group_7 A C)) ) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)))) &  ((v1_group_6 B A (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))))))) ) ) ) ) ) ) ) ).
tt(t37_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A B) =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ( ((m1_group_9 C A E) & (m1_group_9 D A E))  => (m1_group_9 (k19_group_9 A B C D) A E)) ) ) ) ) ) ) ) ) ) ).
tt(t37_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) &  ((k1_hausdorf A B C) = k6_numbers) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t37_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k13_glib_001 A (k2_helly A B C))) <=> (r1_tarski (k2_helly A B D) (k2_helly A B C))) ) ) ) ) ) ) ) ) ).
tt(t37_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k1_complfld)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k1_complfld)) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear I k1_complfld A B) &  ((v2_bilinear I k1_complfld A B) &  ((v4_bilinear I k1_complfld A B) &  ((v2_hermitan I A B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I (k1_algstr_0 A C (k4_vectsp_1 k1_complfld A G D)) (k1_algstr_0 B E (k4_vectsp_1 k1_complfld B H F))) = (k3_rlvect_1 k1_complfld (k3_rlvect_1 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I C E) (k8_group_1 k1_complfld (k2_complfld H) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I C F))) (k3_rlvect_1 k1_complfld (k8_group_1 k1_complfld G (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I D E)) (k8_group_1 k1_complfld G (k8_group_1 k1_complfld (k2_complfld H) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I D F)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_yellow_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A))) = k1_xboole_0) ) ) ).
tt(t37_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A C) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k1_taylor_1 B) C) B) A) = (k3_newton B)) ) ) ) ) ) ) ) ).
tt(t37_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 (k3_hilbert1 A B) A) C) B) k6_hilbert1)) ) ) ) ) ) ).
tt(t37_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_hilbert3 C A) (k3_hilbert3 C B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B))))) )  =>  ((k1_funct_1 (k5_hilbert3 C D (k3_hilbert1 A B)) E) = (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C B) (k2_funct_2 (k3_hilbert3 C A) (k5_hilbert3 C D A)) (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C B) (k3_hilbert3 C B) (k3_hilbert3 C B) E (k5_hilbert3 C D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_hurwitz,ax, (~ (v1_hurwitz (k9_polynom3 k1_complfld))) ).
tt(t37_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k18_idea_1 (k2_nat_1 D 1) B A C) = (k7_finseq_1 (k9_finseq_1 (k16_idea_1 A (k8_matrix_1 k5_numbers C (k2_nat_1 D 1)))) (k18_idea_1 D B A C))) ) ) ) ) ) ) ) ) ).
tt(t37_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) =>  (? [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (r2_ideal_1 A B C D)) ) ) ) ) ) ) ) ).
tt(t37_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k3_incsp_1 A D (k1_incsp_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t37_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B) (k7_isocat_1 B)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) D) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 E) (u4_struct_0 E) (u1_graph_1 E) (u2_graph_1 E) (u1_cat_1 E) (k7_isocat_1 E)) =>  ((k14_index_1 A B B C (k16_index_1 B E D F)) = (k16_index_1 A E (k14_index_1 A B B C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 B A C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_rewrite1 (k3_msualg_6 B) E F) => (r1_rewrite1 (k3_msualg_6 A) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_int_1 (k2_int_1 A)) = (k2_int_1 A)) ) ) ).
tt(t37_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r2_hidden B (k1_relset_1 k5_numbers A)) & (r2_hidden C (k1_relset_1 k5_numbers A)))  =>  ( (B = C)  |  ((k6_nat_d (k1_recdef_1 A B) (k1_recdef_1 A C)) = 1) ) ) ) ) ) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k1_relset_1 k5_numbers A)) &  ((k1_recdef_1 A B) = k6_numbers) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((v1_int_1 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers A)) =>  ((k6_int_1 (k5_real_1 C (k1_recdef_1 B D)) (k1_recdef_1 A D)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( ((k4_nat_d A 4) = 1)  =>  ((r1_xxreal_0 A 2) | (r1_int_5 (k4_xcmplx_0 1) A)) ) ) ) ).
tt(t37_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) => (r2_int_1 (k2_int_6 (k18_valued_1 (k1_int_6 A C) (k1_int_6 B C)) C) (k3_xcmplx_0 A B) (k1_funct_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t37_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) B) = (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t37_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k12_binop_2 A (k7_square_1 (k10_binop_2 1 (k5_square_1 (k9_binop_2 (k11_binop_2 A G) B))))))  &  ( ((k1_seq_1 E G) = (k9_binop_2 (k11_binop_2 A G) B))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 E G))) ) ) ) ) ) )  &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos6))) &  ( (F = (k1_relset_1 k1_numbers D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D C))) ) ) )  =>  ((k2_integra5 C D) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos6) (k4_seq_4 C)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k1_sin_cos6) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( ((k1_seq_1 B E) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 k1_sin_cos9 E) k6_numbers)) ) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)) k1_sin_cos9))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k3_taylor_1))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t37_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos D) (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t37_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ((m1_integra1 E B) =>  (! [F:$i] :  ((m3_integr15 F A B C E) =>  (! [G:$i] :  ((m1_integr18 G (k4_real_ns1 A) B D E) =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) &  (F = G) )  =>  ((k4_integr15 A B C E F) = (k1_integr18 (k4_real_ns1 A) B D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_measure5 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers))) )  =>  (! [E:$i] :  ((m1_integra1 E C) =>  ( ((r2_hidden A (k4_finseq_1 E)) &  ((r2_hidden B (k4_finseq_1 E)) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 (k5_seq_4 D) (k1_seq_1 E A)) &  ((k1_seq_1 E B) = (k4_seq_4 D)) ) ) ) )  => (m1_integra1 (k3_finseq_6 k1_numbers E A B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ((r1_integra1 B C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 B)) & (r1_tarski (k2_integra1 A C D) (k2_integra1 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( (C = (k1_rcomp_1 A B))  =>  ( ((k4_seq_4 C) = B)  &  ((k5_seq_4 C) = A) ) ) ) ) ) ) ) ) ).
tt(t37_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( (C = (k1_rcomp_1 (k7_real_1 A (k8_real_1 (k8_real_1 2 B) k32_sin_cos)) (k7_real_1 A (k8_real_1 (k7_real_1 (k8_real_1 2 B) 1) k32_sin_cos))))  => (r1_integra9 C k16_sin_cos k19_sin_cos)) ) ) ) ) ) ) ).
tt(t37_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) => (m1_subset_1 (k4_setfam_1 B C) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ).
tt(t37_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A (k3_intpro_1 B C)) (k3_intpro_1 (k4_intpro_1 A B) C)) k8_intpro_1)) ) ) ) ) ) ).
tt(t37_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (v1_int_1 (k3_xcmplx_0 (k9_newton A) (k1_seq_1 (k3_series_1 k5_irrat_1) A)))) ) ).
tt(t37_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_nattra_1 E A B C D) =>  ((r2_nattra_1 A B C D) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k6_isocat_1 A B B C D (k10_cat_1 B) (k10_cat_1 B) E (k6_nattra_1 B B (k10_cat_1 B))) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 A C F G))  =>  (! [H:$i] :  ((m1_nattra_1 H A B D E) =>  (! [I:$i] :  ((m1_nattra_1 I A C F G) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ((k4_nattra_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G) (k13_isocat_2 A B C D E F G H I) J) = (k10_cat_2 B C (k4_nattra_1 A B D E H J) (k4_nattra_1 A C F G I J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_isomichi B A) <=> (v1_xboole_0 (k1_isomichi A B))) ) ) ) ) ).
tt(t37_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  =>  ( (B = k1_xboole_0)  |  ( (C = k1_xboole_0)  | (r1_xxreal_0 k6_numbers (k7_weierstr A B C))) ) ) ) ) ) ) ) ) ).
tt(t37_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_1_jgraph_2) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t37_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k5_relat_1 (k2_funct_1 k1_jgraph_3) A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_0_jgraph_3) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t37_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k3_jgraph_4 A)) & (v5_pre_topc B (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t37_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 k6_numbers D))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr (k7_real_1 (k8_real_1 D B) C) (k7_real_1 (k8_real_1 D A) C)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 (k4_topmetr (k7_real_1 (k8_real_1 D B) C) (k7_real_1 (k8_real_1 D A) C))))))) )  =>  (~  ((v3_tops_2 E (k4_topmetr A B) (k4_topmetr (k7_real_1 (k8_real_1 D B) C) (k7_real_1 (k8_real_1 D A) C))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 A B)) =>  ((k1_funct_1 E F) = (k7_real_1 (k8_real_1 D F) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k7_pscomp_1 (k1_sppol_2 A B C D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t37_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid D)) & (r1_xxreal_0 (k18_euclid C) H)) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)))  & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D)))) ) )  =>  ( ( (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 D k6_numbers)) ) )  &  (~  ( (B = k6_numbers)  &  (D = k6_numbers) ) ) )  |  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) A (k1_jordan1a (k1_jordan8 E B)))) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) C (k1_jordan1a (k1_jordan8 E D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  ( (F = (a_4_6_jordan1 A B C D))  &  (G = (a_4_7_jordan1 A B C D)) ) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ( (E = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) F) F))  &  (E = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) G) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) & (r1_xxreal_0 D 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1g,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) &  ( (~  (B = 1) )  &  (~  (C = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 (k1_jordan8 E B))) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ( (F = (k1_int_1 (k7_real_1 (k10_real_1 (k9_real_1 C 2) (k13_newton 2 (k7_nat_d B A))) 2)))  &  ( (G = (k1_int_1 (k7_real_1 (k10_real_1 (k9_real_1 D 2) (k13_newton 2 (k7_nat_d B A))) 2)))  & (r1_tarski (k3_goboard5 (k1_jordan8 E B) C D) (k3_goboard5 (k1_jordan8 E A) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan1j,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k2_jordan3 A B) = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k4_finseq_4 A B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t37_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  ((v2_connsp_1 (k3_subset_1 (u1_struct_0 (k14_euclid 2)) (k9_metric_1 (k14_euclid 2) B A)) (k15_euclid 2)) & (m1_subset_1 (k3_subset_1 (u1_struct_0 (k14_euclid 2)) (k9_metric_1 (k14_euclid 2) B A)) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ).
tt(t37_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k1_jordan21 A) = (k2_jordan21 A)) ) ) ) ).
tt(t37_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r2_hidden (k2_jordan21 A) (k9_jordan6 A)) & (r2_hidden (k1_jordan21 A) (k8_jordan6 A)))  |  ((r2_hidden (k1_jordan21 A) (k9_jordan6 A)) & (r2_hidden (k2_jordan21 A) (k8_jordan6 A))) ) ) ) ).
tt(t37_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_jordan23 A) & (r1_xxreal_0 2 (k3_finseq_1 A)))  =>  ((k2_jordan3 A (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) = A) ) ) ) ) ) ).
tt(t37_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E)))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E)))))) )  =>  (~  ((v5_pre_topc F k5_topmetr (k1_pre_topc (k15_euclid A) E)) &  ( (B = (k1_funct_1 F k6_numbers))  &  ( (C = (k1_funct_1 F 1))  &  ((v5_pre_topc G k5_topmetr (k1_pre_topc (k15_euclid A) E)) &  ( (C = (k1_funct_1 G k6_numbers))  &  ( (D = (k1_funct_1 G 1))  &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) E)))))) )  =>  (~  ((v5_pre_topc H k5_topmetr (k1_pre_topc (k15_euclid A) E)) &  ( (B = (k1_funct_1 H k6_numbers))  &  (D = (k1_funct_1 H 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) )  =>  ( (B = C)  | (v4_topreal1 (k4_jordan3 A B C))) ) ) ) ) ) ) ) ).
tt(t37_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) =>  ((r1_xxreal_0 B 1) | (v4_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t37_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k6_pscomp_1 (k3_topreal1 2 A)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1))) ) ) ).
tt(t37_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A C D))  =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D E F)) = (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (r1_tarski (u1_struct_0 (k8_knaster A B)) (u1_struct_0 A))) ) ) ) ).
tt(t37_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) = (k2_pre_topc k3_topmetr k6_kurato_1)) ) ).
tt(t37_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) C E) = (k3_borsuk_1 (k15_euclid 2) (k15_euclid 2) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A E) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B E))) ) )  &  ((m2_valued_0 D (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) C) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (~  ((m2_valued_0 E (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A) &  ((m2_valued_0 F (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) D G) = (k3_borsuk_1 (k15_euclid 2) (k15_euclid 2) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) E G) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( ( ((k3_finseq_1 D) = A)  &  ((k4_matrix_3 B C D) = E) )  =>  ( (D = (k4_matrix_3 B (k5_matrix_6 A B C) E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) =>  ((k3_matrix_1 (u1_struct_0 B) D F G) = (k8_group_1 B (k11_algstr_0 B (k12_matrix_3 A B C)) (k12_matrix_3 A B (k3_laplace F A A (u1_struct_0 B) C (k9_matrix_1 (u1_struct_0 B) E G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_lattice2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_lattice2 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ( ((k4_lattices A B C) = (k3_lattices (k1_lattice2 A) D E))  &  ((k3_lattices A B C) = (k4_lattices (k1_lattice2 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((k15_lattice3 A B) = (k16_lattice3 A (a_2_2_lattice3 A B))) ) ) ) ).
tt(t37_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k4_lattice4 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ( (C = (k3_lattices A (k7_lattices A D) E))  &  ((r2_hidden D B) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) (u1_struct_0 B)) &  ((v1_lattice5 E D B) &  ((v2_lattice5 E D B) &  ((v3_lattice5 E D B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) (u1_struct_0 B))))) ) ) ) )  =>  ((r2_lattice5 A B C D E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ((r3_orders_2 B (k3_lattice5 A B C F G) (k13_lattice3 B H I)) &  (! [J:$i] :  ((m1_subset_1 J D) =>  (! [K:$i] :  ((m1_subset_1 K D) =>  (! [L:$i] :  ((m1_subset_1 L D) =>  (~  ( ((k1_binop_1 E F J) = H)  &  ( ((k3_lattice5 D B E K L) = H)  &  ( ((k3_lattice5 D B E J K) = I)  &  ((k1_binop_1 E L G) = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k39_glib_000 (k16_lexbfs A)) = (k15_glib_000 A)) ) ) ).
tt(t37_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v3_lfuzzy_1 B A) =>  ((r1_xxreal_0 C k6_numbers) | (r1_fuzzy_1 (k4_lfuzzy_1 A B C) B)) ) ) ) ) ) ) ) ).
tt(t37_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v7_valued_0 A)) ) )  => (v2_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t37_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_limfunc2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k2_rcomp_1 (k9_real_1 A D) A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 (k9_real_1 A D) A)) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r2_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t37_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  ((k1_seq_1 B E) = k6_numbers) )  &  (~  ((k1_seq_1 B F) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_limfunc3 B A) = k6_numbers)  |  ((r1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k1_limfunc3 B A))) ) ) ) ) ) ) ) ).
tt(t37_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc3 B A) &  ((v7_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t37_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_lmod_6 A C D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C E) => (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_normsp_0 (k16_lopban_1 A B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k16_lopban_1 A B))) )  &  ( ( (C = (k4_struct_0 (k16_lopban_1 A B)))  =>  ((k1_normsp_0 (k16_lopban_1 A B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k16_lopban_1 A B) (k1_rlvect_1 (k16_lopban_1 A B) C E)) = (k8_real_1 (k18_complex1 E) (k1_normsp_0 (k16_lopban_1 A B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 A B) (k1_algstr_0 (k16_lopban_1 A B) C D)) (k7_real_1 (k1_normsp_0 (k16_lopban_1 A B) C) (k1_normsp_0 (k16_lopban_1 A B) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k1_normsp_1 A B C) = (k4_struct_0 A)) ) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k10_real_1 (k1_seq_1 (k4_normsp_0 A B) (k2_nat_1 D 1)) (k1_seq_1 (k4_normsp_0 A B) D)))) ) ) ) )  & (v2_lopban_3 B A)) ) ) ) ) ) ) ).
tt(t37_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k10_lopban_4 A (k4_struct_0 A)) = (k5_struct_0 A)) ) ) ).
tt(t37_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) & (r2_hidden E (k9_lpspace1 A B C)))  =>  ((r1_lpspace1 A B C E D) <=> (r2_hidden E (k13_lpspace1 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ((r2_hidden E (k5_lpspace2 A B C D F)) =>  ( (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A G)) = k6_numbers)  &  ( (G = (k1_relset_1 A D))  & (r1_mesfunc6 A B D G)) ) ) ) )  |  ((r1_lpspace1 A B C E D) & (r2_hidden D (k1_lpspace2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ( (~  ( (~ (v3_ltlaxio1 A))  &  ( (~ (v4_ltlaxio1 A))  &  ( (~ (v5_ltlaxio1 A))  &  ( (~ (v6_ltlaxio1 A))  &  ( (~ (v7_ltlaxio1 A))  &  ( (~ (v8_ltlaxio1 A))  &  (~ (v9_ltlaxio1 A)) ) ) ) ) ) ) )  => (r3_ltlaxio1 B A)) ) ) ) ) ).
tt(t37_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) <=> (r2_hidden (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A C))) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t37_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k3_mathmorp A (k3_subset_1 (u1_struct_0 A) B) C)) = (k6_rusub_4 A B (k2_mathmorp A C))) ) ) ) ) ) ) ).
tt(t37_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 (k2_matrix10 A B) C) => (v4_matrix10 (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t37_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [E:$i] :  ((m1_matrix_1 E C A B) =>  ( ((k2_matrix_1 E) = (k2_matrix_1 (k4_matrix11 A B C D E)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden (k4_tarski F G) (k2_matrix_1 E)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  (~  ( ((k1_funct_1 D F) = H)  &  ((r2_hidden (k4_tarski H G) (k2_matrix_1 E)) &  ((k3_matrix_1 C (k4_matrix11 A B C D E) F G) = (k3_matrix_1 C E H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_matrix_1 F A B C) =>  (! [G:$i] :  ((m2_finseq_1 G A) =>  (! [H:$i] :  ((m2_finseq_1 H A) =>  (! [I:$i] :  ((m2_finseq_2 I k5_numbers (k4_finseq_2 D k5_numbers)) =>  (! [J:$i] :  ((m2_finseq_2 J k5_numbers (k4_finseq_2 E k5_numbers)) =>  ( ( ((k3_finseq_1 G) = (k1_matrix_1 F))  &  ( (H = (k1_partfun1 k5_numbers k5_numbers k5_numbers A J G))  & (r1_tarski (k2_zfmisc_1 (k10_xtuple_0 I) (k10_xtuple_0 J)) (k2_matrix_1 F))) )  =>  (! [K:$i] :  ((v7_ordinal1 K) =>  (! [L:$i] :  ((v7_ordinal1 L) =>  ( ((k8_relat_1 I (k1_tarski L)) = (k1_tarski K))  =>  ((k3_matrix11 K D E A (k1_matrix13 A F D E I J) H) = (k1_matrix13 A (k3_matrix11 L B C A F G) D E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ( ((k3_matrix_1 (u1_struct_0 B) D 1 1) = (k11_algstr_0 B C))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k1_funct_1 D F) = (k3_matrix14 B A F)) ) ) ) )  &  ( ((k3_matrix_1 (u1_struct_0 B) E 1 1) = C)  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k3_matrix_1 (u1_struct_0 B) E 1 F) = (k4_algstr_0 B (k8_group_1 B C (k3_matrix_1 (u1_struct_0 B) D 1 F)))) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k1_funct_1 E F) = (k3_matrix14 B A F)) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (C = (k4_struct_0 B))  |  ((v1_matrix_6 D A B) &  (E = (k5_matrix_6 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))))  =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((r2_hidden B (k4_matrix15 A C D)) &  ((r2_hidden E (k4_matrix15 A C F)) &  ((k1_matrix_1 D) = (k1_matrix_1 F)) ) )  => (r2_hidden (k3_matrix_3 A B E) (k4_matrix15 A C (k3_matrix_3 A D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v4_matrix16 B (u1_struct_0 A)) &  ((v4_matrix16 C (u1_struct_0 A)) &  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) )  => (v4_matrix16 (k3_fvsum_1 A B C) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t37_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_matrix_1 F E A B) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B)) ) )  => (r2_hidden (k4_tarski C D) (k2_matrix_1 F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k3_matrix_3 A B (k2_matrix_3 A C)) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t37_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((v1_matrix_6 D A B) & (r1_matrix_6 A B C D)) )  =>  ((v1_matrix_6 (k4_matrix_6 A B C D) A B) &  ((k5_matrix_6 A B (k4_matrix_6 A B C D)) = (k4_matrix_6 A B (k5_matrix_6 A B C) (k5_matrix_6 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrix_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((r1_xxreal_0 1 A) =>  ((k12_matrix_3 A B C) = (k12_matrix_3 A B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ).
tt(t37_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((r1_matrix_8 A B C D) & (v3_matrix_8 D A B))  => (v3_matrix_8 C A B)) ) ) ) ) ) ) ) ) ).
tt(t37_matrix_9,ax, ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 1 3 2) (k3_finseq_4 k5_numbers 2 1 3)) = (k3_finseq_4 k5_numbers 2 3 1))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 1 3) (k3_finseq_4 k5_numbers 1 3 2)) = (k3_finseq_4 k5_numbers 3 1 2))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 3 2 1) (k3_finseq_4 k5_numbers 2 1 3)) = (k3_finseq_4 k5_numbers 3 1 2))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 1 3) (k3_finseq_4 k5_numbers 3 2 1)) = (k3_finseq_4 k5_numbers 2 3 1))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 3 2 1) (k3_finseq_4 k5_numbers 3 2 1)) = (k3_finseq_4 k5_numbers 1 2 3))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 1 3) (k3_finseq_4 k5_numbers 2 1 3)) = (k3_finseq_4 k5_numbers 1 2 3))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 1 3 2) (k3_finseq_4 k5_numbers 1 3 2)) = (k3_finseq_4 k5_numbers 1 2 3))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 3 1) (k3_finseq_4 k5_numbers 1 3 2)) = (k3_finseq_4 k5_numbers 3 2 1))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 3 1) (k3_finseq_4 k5_numbers 2 3 1)) = (k3_finseq_4 k5_numbers 3 1 2))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 3 1 2) (k3_finseq_4 k5_numbers 2 3 1)) = (k3_finseq_4 k5_numbers 1 2 3))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 2 3 1) (k3_finseq_4 k5_numbers 3 1 2)) = (k3_finseq_4 k5_numbers 1 2 3))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 3 1 2) (k3_finseq_4 k5_numbers 3 1 2)) = (k3_finseq_4 k5_numbers 2 3 1))  &  ( ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 3 2 1) (k3_finseq_4 k5_numbers 1 3 2)) = (k3_finseq_4 k5_numbers 2 3 1))  &  ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k3_finseq_4 k5_numbers 1 3 2) (k3_finseq_4 k5_numbers 3 2 1)) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 A) = (k3_finseq_1 D)) ) )  =>  ((k1_finseqop k2_numbers k2_numbers k2_numbers k29_binop_2 A B) = (k1_finseqop k1_numbers k1_numbers k1_numbers k35_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_matrixj1 E C) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 C))))  =>  ( ((r2_hidden A (k2_finseq_1 (k2_wsierp_1 (k10_matrixj1 C E)))) &  (B = (k1_matrixj1 (k10_matrixj1 C E) A)) )  =>  ((k8_matrix_1 C (k13_matrixj1 C D E) A) = (k8_finseq_1 C (k8_finseq_1 C (k5_finseq_2 C (k2_wsierp_1 (k11_matrixj1 C (k6_matrixj1 C (k7_nat_d B 1) E))) D) (k8_matrix_1 C (k2_matrixj1 C E B) (k7_nat_d A (k2_wsierp_1 (k10_matrixj1 C (k6_matrixj1 C (k7_nat_d B 1) E)))))) (k5_finseq_2 C (k7_nat_d (k2_wsierp_1 (k11_matrixj1 C E)) (k2_wsierp_1 (k11_matrixj1 C (k6_matrixj1 C B E)))) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  (A = (k3_matrixr1 A B)) ) )  =>  (B = (k8_matrixr1 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ) ) ).
tt(t37_matrixr2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_matrix_1 B A 3 3) =>  (B = (k11_finseq_1 (k3_finseq_4 A (k3_matrix_1 A B 1 1) (k3_matrix_1 A B 1 2) (k3_matrix_1 A B 1 3)) (k3_finseq_4 A (k3_matrix_1 A B 2 1) (k3_matrix_1 A B 2 2) (k3_matrix_1 A B 2 3)) (k3_finseq_4 A (k3_matrix_1 A B 3 1) (k3_matrix_1 A B 3 2) (k3_matrix_1 A B 3 3)))) ) ) ) ) ).
tt(t37_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k4_matrlin2 A B C D E (k5_matrlin2 (k3_finseq_1 D) (k3_finseq_1 E) A F G)) (k3_matrlin A B C (k4_matrlin2 A B C D E F) (k4_matrlin2 A B C D E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m2_finseq_1 H (u1_struct_0 A)) =>  ( ((k3_finseq_1 G) = (k3_finseq_1 E))  =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden I (k9_xtuple_0 F)) &  ( ((k3_finseq_1 H) = (k3_finseq_1 E))  &  (! [J:$i] :  ((v7_ordinal1 J) =>  ((r2_hidden J (k9_xtuple_0 E)) =>  ((k1_funct_1 H J) = (k7_partfun1 (u1_struct_0 A) (k9_matrlin A C F (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k7_partfun1 (u1_struct_0 B) E J))) I)) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 E) k6_numbers) |  ((k7_partfun1 (u1_struct_0 A) (k9_matrlin A C F (k4_rlvect_1 C (k5_matrlin A C G (k4_finseqop (u1_struct_0 B) (u1_struct_0 C) E D)))) I) = (k4_rlvect_1 A (k11_fvsum_1 A G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_matroid0 B A) =>  ( (~ (v1_xboole_0 B))  & (v1_finset_1 B)) ) ) ) ) ) ).
tt(t37_matrprob,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 k2_vectsp_1) (k4_finseq_2 A (u1_struct_0 k2_vectsp_1))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 k2_vectsp_1) (k4_finseq_2 A (u1_struct_0 k2_vectsp_1))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k22_rvsum_1 B C) = (k13_fvsum_1 k2_vectsp_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) &  ((v1_finseq_1 D) & (v3_valued_0 D)) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 k2_vectsp_1) A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 k2_vectsp_1) A C) =>  ( ( (A = k6_numbers)  =>  ((k23_binop_2 B C) = k6_numbers) )  =>  ((k1_funct_1 (k3_matrtop1 A (k2_nat_1 (k1_matrix_1 E) (k1_matrix_1 F)) (k1_matrix15 (u1_struct_0 k2_vectsp_1) A B C E F)) D) = (k7_finseq_1 (k1_funct_1 (k3_matrtop1 A B E) D) (k1_funct_1 (k3_matrtop1 A C F) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  ((v2_matrtop3 B A) =>  ( ((k12_matrix_3 A k2_vectsp_1 (k3_matrtop3 A B)) = (k5_struct_0 k2_vectsp_1))  <=> (v3_matrtop3 B A)) ) ) ) ) ) ).
tt(t37_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_zfmisc_1 (k1_tarski A) (k2_tarski B C) (k1_tarski D)) = (k2_tarski (k3_xtuple_0 A B D) (k3_xtuple_0 A C D))) ) ) ) ) ).
tt(t37_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_measure1 D A B C) =>  (! [E:$i] :  ((m2_measure1 E A B C) =>  ((m2_measure1 (k1_measure1 A B D E) A B C) &  ((m2_measure1 (k2_measure1 A B D E) A B C) & (m2_measure1 (k3_measure1 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k7_real_1 (k18_complex1 A) (k18_complex1 C)) (k18_complex1 B))) ) ) ) ) ) ) ) ) ).
tt(t37_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_member_1 (k1_tarski A)) = (k1_tarski (k2_binop_2 A))) ) ) ).
tt(t37_membered,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v3_membered B) =>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r1_xxreal_0 C D)) ) ) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D A) => (r1_xxreal_0 D C)) ) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D B) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  ((k1_funct_4 C (k7_memstr_0 A B (k5_memstr_0 A B C))) = C) ) ) ) ) ) ) ) ).
tt(t37_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ((r3_mesfunc6 A B C D) &  ((r3_mesfunc6 A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k1_mesfunc6 A B C (k47_valued_1 A k1_numbers k1_numbers D E)) = (k3_supinf_2 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D F)) (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers (k32_valued_1 A k1_numbers E) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] : (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers B) C) (k55_valued_1 A k2_numbers (k2_partfun1 A k2_numbers B C)))) ) ) ) ) ).
tt(t37_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfun7c A B (k4_mesfunc5 A k2_numbers D E))) )  => (r1_mesfun7c A B (k4_mesfunc5 A k2_numbers (k3_mesfun9c A D) C))) ) ) ) ) ) ) ) ) ).
tt(t37_mesfunc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_mesfunc1 A B C D) & (r1_tarski D (k9_xtuple_0 C)))  => (r1_mesfunc1 A B (k6_mesfunc1 A C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((r1_mesfunc2 A B D) => (m2_subset_1 (k1_relset_1 A D) (k1_zfmisc_1 A) B)) ) ) ) ) ) ) ) ) ).
tt(t37_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) =>  ( ( ((k1_seq_1 (k18_rfunct_3 A B) C) = (k1_seq_1 B C))  |  ((k1_seq_1 (k18_rfunct_3 A B) C) = k6_numbers) )  &  ( ((k1_seq_1 (k19_rfunct_3 A B) C) = (k1_real_1 (k1_seq_1 B C)))  |  ((k1_seq_1 (k19_rfunct_3 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t37_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((v1_mesfunc8 B A k7_numbers) &  ((r2_hidden E (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) &  ( (! [F:$i] :  ((v7_ordinal1 F) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers B F))) )  & (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C) E) (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_midsp_1 A B C) = (k8_midsp_1 A D E))  =>  ((k3_midsp_1 A B E) = (k3_midsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k18_mmlquery A B) = (k4_relat_1 (k6_subset_1 A (k1_relset_1 A B)))) ) ) ) ).
tt(t37_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v10_mod_4 B A) <=> (v1_ringcat1 (k7_mod_4 A A B) A (k2_mod_4 A))) ) ) ) ) ).
tt(t37_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~  ((r1_xxreal_0 2 (k5_card_1 (k9_xtuple_0 A))) &  ( (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ( (~  (A = (k10_modal_1 B)) )  &  (~  (A = (k11_modal_1 B)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  (~  (A = (k12_modal_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ((r1_tarski E F) => (r1_tarski (k54_modelc_1 A B C D E) (k54_modelc_1 A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_modelc_2 B A) =>  ( ( (~ (v3_modelc_2 A))  &  (~ (v6_modelc_2 A)) )  | (r2_modelc_2 B (k10_modelc_2 A))) ) ) ) ) ) ).
tt(t37_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) &  ((v3_modelc_3 B A) & (l1_modelc_3 B A)) )  =>  (! [C:$i] :  ( ((v1_modelc_3 C A) &  ((v3_modelc_3 C A) & (l1_modelc_3 C A)) )  =>  ((r6_modelc_3 A C B) => (r1_tarski (u3_modelc_3 A C) (u1_modelc_3 A B))) ) ) ) ) ) ) ).
tt(t37_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ( (~ (r1_int_2 A B))  =>  ((k2_moebius1 (k4_nat_1 A B)) = k6_numbers) ) ) ) ) ) ).
tt(t37_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) &  ((v17_monoid_0 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m3_monoid_0 B A))  => (v17_monoid_0 B)) ) ) ) ).
tt(t37_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k20_monoid_1 A (k6_finseq_1 A)) = (k17_monoid_1 A k6_numbers)) ) ) ).
tt(t37_msafree3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_msualg_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) => (r1_tarski (k3_msualg_1 A D C) (k3_msualg_1 A D B))) ) ) ) ) ) ) ) ).
tt(t37_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finset_1 G) & (v3_trees_2 G)) ) )  =>  ( ((r1_msaterm A B C D E F) & (r1_msaterm A B C D E G))  =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) => (m3_pboole (k5_pboole A C D) A (k1_mboolean A B))) ) ) ) ) ) ) ).
tt(t37_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (m1_msualg_2 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A B)) ) ) ) ).
tt(t37_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) => (r8_pboole (u1_struct_0 A) (k6_msualg_6 A B (k7_msualg_6 A B C)) (k8_msualg_6 A B C))) ) ) ) ) ) ).
tt(t37_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 (k6_mycielsk A B)))) ) ) ) ).
tt(t37_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 13) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  (~  (A = 13) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( ((v7_ordinal1 B) & (v1_int_2 B))  & (r1_nat_d B A))  =>  ((v1_xboole_0 A) | (r2_hidden B (k13_pre_poly (k12_nat_3 A)))) ) ) ) ) ) ).
tt(t37_nat_4,ax,(v1_int_2 631)).
tt(t37_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ((r1_int_2 A B) =>  ((k5_nat_5 (k24_binop_2 A B)) = (k24_binop_2 (k5_nat_5 A) (k5_nat_5 B))) ) ) ) ) ) ).
tt(t37_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) =>  ((k7_nat_d (k2_xcmplx_0 B C) A) = (k6_xcmplx_0 (k2_xcmplx_0 B C) A)) ) ) ) ) ) ) ) ).
tt(t37_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v2_nattra_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_cat_1 A B B) = (k1_tarski (k4_cat_1 A B))) ) ) ) ) ).
tt(t37_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((r3_ncfcont1 B A C D) => (r3_ncfcont1 B A (k2_vfunct_2 (u1_struct_0 B) A C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))  => (r3_ncfcont2 A B C D)) ) ) ) ) ) ) ) ).
tt(t37_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_ndiff_1 B A D E) =>  ((r1_ndiff_1 B A (k4_vfunct_1 (u1_struct_0 B) A D C) E) &  ((k3_ndiff_1 B A (k4_vfunct_1 (u1_struct_0 B) A D C) E) = (k1_rlvect_1 (k16_lopban_1 B A) (k3_ndiff_1 B A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_ndiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  =>  ((r1_ndiff_3 (k4_real_ns1 1) B A) &  ((k1_ndiff_3 (k4_real_ns1 1) B A) = (k12_finseq_1 k5_numbers 1)) ) ) ) ) ) ) ).
tt(t37_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) (k5_algstr_0 (k14_prvect_2 A) C D)) = (k5_algstr_0 (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t37_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_necklace A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  (~  ((r1_subset_1 (u1_struct_0 C) (u1_struct_0 D)) &  ( ((k5_yellow_0 A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k6_domain_1 (u1_struct_0 A) B))) = (k1_neckla_2 C D))  &  ((v1_neckla_3 A) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~ (r2_hidden (k1_domain_1 (u1_struct_0 C) (u1_struct_0 A) E B) (u1_orders_2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 1 (k6_real_1 A (k1_nat_1 A 1)))) ) ) ).
tt(t37_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  ((v1_nfcont_1 C A) &  ((r4_nfcont_1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  ( ((k7_partfun1 k1_numbers B D) = (k4_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C)))  &  ((k7_partfun1 k1_numbers B E) = (k5_seq_4 (k7_relset_1 (u1_struct_0 A) k1_numbers B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) E C) A))  => (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k7_integr15 A k1_numbers D E) (k3_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ).
tt(t37_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((r2_hidden B (k9_normform A C)) => (r2_hidden B C)) ) ) ) ) ) ).
tt(t37_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B (k9_oppcat_1 A B C)) (k4_oppcat_1 A D)) = (k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t37_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v3_orders_1 A) => (r3_orders_1 A (k1_relat_1 A))) ) ) ).
tt(t37_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_orders_2 C A B) => (r2_hidden (k1_funct_1 B (u1_struct_0 A)) C)) ) ) ) ) ) ).
tt(t37_ordinal1,ax, (! [A:$i] :  ((k6_subset_1 (k1_ordinal1 A) (k1_tarski A)) = A) ) ).
tt(t37_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k11_ordinal2 D B)) ) ) ) )  =>  ((k11_ordinal2 A B) = (k3_tarski (k4_ordinal2 C))) ) ) ) ) ) ) ) ) ) ).
tt(t37_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((k11_ordinal2 A B) = 1)  =>  ( (A = 1)  &  (B = 1) ) ) ) ) ) ) ).
tt(t37_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_ordinal2 A B) & (r2_ordinal2 B C))  => (r2_ordinal2 A C)) ) ) ) ) ) ) ).
tt(t37_ordinal5,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v4_ordinal5 A))  => (r2_hidden k4_ordinal1 A)) ) ).
tt(t37_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((v2_ordinal6 B) &  ((r2_hidden (k3_tarski A) (k9_xtuple_0 B)) &  (! [C:$i] :  ((r2_hidden C A) => (r1_abian C B)) ) ) )  =>  ((v1_xboole_0 A) |  ((k3_tarski A) = (k1_funct_1 B (k3_tarski A))) ) ) ) ) ) ).
tt(t37_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t37_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v12_osalg_1 C A) &  ((v13_osalg_1 C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (k22_osafree A B) (u3_msualg_1 A C)) =>  (? [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A C)) &  ((r1_msualg_3 A (k8_osafree A B) C E) &  ((v1_osalg_3 E A) & (r8_pboole (u1_struct_0 A) (k1_msafree (u1_struct_0 A) (u3_msualg_1 A (k8_osafree A B)) (u3_msualg_1 A C) (k22_osafree A B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  (! [E:$i] :  ((m2_osalg_2 E A B) =>  ((r8_pboole (u1_struct_0 A) E (k2_pboole (u1_struct_0 A) D (u3_msualg_1 A C))) =>  ((k11_osalg_2 A B (k10_osalg_2 A B D) C) = (k10_osalg_2 A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_parsp_1 A B C B D)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_parsp_2 A B C D E) & (r2_parsp_2 A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v2_funct_1 C) => (v2_funct_1 (k3_partfun1 C A B))) ) ) ) ) ).
tt(t37_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( (~ (r1_xboole_0 A (k1_relset_1 B D)))  =>  ((v3_funct_1 (k2_partfun1 B C D A)) <=>  (? [E:$i] :  ((m1_subset_1 E C) &  ((k2_relset_1 C (k2_partfun1 B C D A)) = (k1_tarski E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ( ((k3_partit1 A (k10_eqrel_1 A) B) = B)  &  ((k2_partit1 A (k10_eqrel_1 A) B) = (k10_eqrel_1 A)) ) ) ) ) ) ).
tt(t37_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A (k2_pboole A B C) D) => (r2_pboole A B D)) ) ) ) ) ) ) ) ).
tt(t37_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k21_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (C = (k4_tarski E G))  &  ( (D = (k4_tarski F H))  &  ((r1_pcs_0 (k21_pcs_0 A B) C D) &  ( (~ (r1_pcs_0 A E F))  &  (~ (r1_pcs_0 B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r1_pdiff_3 A B) => (r1_fcont_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 A) B) (k1_seq_1 (k1_pdiff_1 1 2) B))) ) ) ) ) ).
tt(t37_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 C B) &  ((r3_pdiff_1 3 2 C B) & (r3_pdiff_1 3 3 C B)) )  =>  ((k4_pdiff_4 (k26_valued_1 (k1_euclid 3) k1_numbers C A) B) = (k9_euclid 3 (k4_pdiff_4 C B) A)) ) ) ) ) ) ) ) ).
tt(t37_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 3) B)) =>  ( ((r1_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B))))) &  ((k1_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 1 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [E:$i] :  ( (C = D)  =>  ((r4_pdiff_7 A B C E) <=> (r3_nfcont_1 (k4_real_ns1 A) (k4_real_ns1 B) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r2_nfcont_4 A B C) <=> (r3_pdiff_7 A 1 (k3_pdiff_1 A B) C)) ) ) ) ) ) ) ).
tt(t37_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v1_int_2 B) & (r1_int_2 A B))  =>  ((k4_nat_d (k1_newton A (k7_nat_d B 1)) B) = 1) ) ) ) ) ) ).
tt(t37_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  ( ((k9_xtuple_0 (k8_pnproc_1 A B C)) = (k9_funct_2 A k5_numbers))  & (r1_tarski (k10_xtuple_0 (k8_pnproc_1 A B C)) (k9_funct_2 A k5_numbers))) ) ) ) ) ) ).
tt(t37_polyeq_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_comptrig B k6_numbers A) =>  (B = k6_numbers) ) ) ) ) ).
tt(t37_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A B)) =>  ((k3_bspace (k3_rlvect_1 (k17_polyform A B) C D) E) = (k3_rlvect_1 k2_bspace (k3_bspace C E) (k3_bspace D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_polynom4 A (k3_algseq_1 A B) C) = B) ) ) ) ) ) ) ).
tt(t37_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_polynom8 A B F) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ( ((k3_finseq_1 C) = F)  &  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G F))  =>  ((k7_partfun1 (u1_struct_0 A) C G) = (k3_polynom8 A B (k3_xcmplx_0 (k6_xcmplx_0 D E) (k6_xcmplx_0 G 1)))) ) ) ) ) ) ) ) ) )  =>  ((k3_matrix_1 (u1_struct_0 A) (k4_matrix_3 A (k7_polynom8 A F B) (k7_polynom8 A F (k11_algstr_0 A B))) D E) = (k4_rlvect_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~ (r6_polyred A B C (k7_polynom1 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t37_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 (k3_power B C) (k3_power A C))) ) ) ) ) ) ) ) ) ) ).
tt(t37_pre_poly,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k13_pre_poly A) (k9_xtuple_0 A))) ) ).
tt(t37_prepower,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k5_prepower 1 A) = 1) ) ) ).
tt(t37_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((k1_seq_1 E (k6_prob_1 A B C D)) = (k7_real_1 (k1_seq_1 E C) (k1_seq_1 E (k7_prob_1 A B D (k5_prob_1 A B C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m2_prob_1 F A B) =>  ( (E = (k3_subset_1 A D))  =>  ((r1_xxreal_0 (k1_seq_1 F C) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 F D) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 F E) k6_numbers) |  ( ((k1_seq_1 (k3_prob_2 A B F C) D) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B F D) C) (k1_seq_1 F D)) (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B F D) C) (k1_seq_1 F D)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B F E) C) (k1_seq_1 F E)))))  &  ((k1_seq_1 (k3_prob_2 A B F C) E) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B F E) C) (k1_seq_1 F E)) (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B F D) C) (k1_seq_1 F D)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B F E) C) (k1_seq_1 F E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) => (v7_valued_0 (k8_prob_1 A B (k2_prob_3 A C) D))) ) ) ) ) ) ) ) ).
tt(t37_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) => (r1_funct_2 (k4_prob_4 A B C) k1_numbers (k2_measure3 A B (k2_prob_4 A B C)) k7_numbers (k7_prob_4 A B C) (k4_measure3 A B (k2_prob_4 A B C)))) ) ) ) ) ) ).
tt(t37_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B (k7_cqc_lang A C (k6_cqc_lang A C))) (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t37_projpl_1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) & (l1_incsp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A C H) &  ((r1_incsp_1 A D H) &  ( (~ (r1_incsp_1 A B H))  &  ( (~  (C = D) )  &  ( (~  (E = B) )  &  ( (~  (F = B) )  &  ((r1_incsp_1 A E (k1_projpl_1 A B C)) &  ((r1_incsp_1 A F (k1_projpl_1 A B D)) &  (! [I:$i] :  ((m1_subset_1 I (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A I (k1_projpl_1 A E F)) &  ((r1_incsp_1 A I G) &  (~  (I = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k18_euclid (k11_pscomp_1 A)) = (k18_euclid (k20_pscomp_1 A)))  &  ( ((k18_euclid (k11_pscomp_1 A)) = (k18_euclid (k21_pscomp_1 A)))  &  ( ((k18_euclid (k20_pscomp_1 A)) = (k18_euclid (k21_pscomp_1 A)))  &  ( ((k18_euclid (k20_pscomp_1 A)) = (k18_euclid (k12_pscomp_1 A)))  &  ((k18_euclid (k21_pscomp_1 A)) = (k18_euclid (k12_pscomp_1 A))) ) ) ) ) ) ) ).
tt(t37_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A (k2_pboole A B (k1_pzfmisc1 A C)) D) <=>  ((r1_pboole A C D) & (r2_pboole A B D)) ) ) ) ) ) ) ) ) ).
tt(t37_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v1_qc_lang2 B A) =>  (B = (k3_qc_lang2 A (k10_qc_lang2 A B) (k11_qc_lang2 A B))) ) ) ) ) ) ).
tt(t37_qc_lang3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_qc_lang1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 B))))  =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 B) (k8_qc_lang1 B A)) =>  (! [E:$i] :  ( ((v3_card_1 E A) & (m2_finseq_1 E (k2_qc_lang1 B)))  =>  ( ((k4_qc_lang3 B C (k10_qc_lang1 B D E)) = (k1_qc_lang3 B E C))  &  ((k4_qc_lang3 B C (k10_qc_lang1 B D E)) = (a_4_0_qc_lang3 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) =>  (! [E:$i] :  ((m2_qc_lang4 E A B C) =>  (! [F:$i] :  ((m1_trees_1 F (k9_xtuple_0 (k2_qc_lang4 A C))) =>  ((r2_hidden F (k3_qc_lang4 A C D)) => (m2_qc_lang4 (k8_finseq_1 k5_numbers E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_quatern2,ax, ((k5_struct_0 k16_quatern2) = k2_quatern2) ).
tt(t37_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) => (r1_xxreal_0 (k3_quatern2 (k29_quaterni (k29_quaterni A B) C)) (k7_real_1 (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k3_quatern2 C)))) ) ) ) ) ) ).
tt(t37_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (A = (k26_quaterni (k26_quaterni (k23_quaterni (k17_quaterni A) (k25_quaterni (k18_quaterni A) k1_xcmplx_0)) (k25_quaterni (k19_quaterni A) k11_quaterni)) (k25_quaterni (k20_quaterni A) k12_quaterni))) ) ) ).
tt(t37_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  ((k6_algstr_0 (k19_quofield A) B C) = (k1_binop_1 (k16_quofield A) B C)) ) ) ) ) ) ) ).
tt(t37_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D (k1_vectsp_6 A C E))) & (r2_hidden F (k1_vectsp_6 A C E)))  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_ranknull A C B E D) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D F)) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 k6_numbers (k2_rat_1 A))) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k2_rat_1 A)))  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(t37_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k2_rcomp_1 A B))  =>  ((k1_tops_1 k2_topalg_2 C) = (k2_rcomp_1 A B)) ) ) ) ) ) ) ) ).
tt(t37_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 1)) = (k1_seq_1 (k4_real_3 (k10_real_1 1 (k4_int_1 B))) A)) ) ) ) ) ).
tt(t37_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ( ((k5_card_1 B) = (k5_card_1 C))  & (r2_hidden A (k4_finseq_1 E))) )  =>  ((k17_finseq_1 k1_numbers A (k20_rfunct_3 C (k4_rearran1 B C E D) C)) = (k20_rfunct_3 C (k4_rearran1 B C E D) (k1_funct_1 (k2_rearran1 C E) A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( (! [B:$i] :  (! [C:$i] :  (~ (r2_hidden (k4_tarski B C) A)) ) )  =>  (A = k1_xboole_0) ) ) ) ).
tt(t37_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( (D = (k2_zfmisc_1 A B))  =>  ((k6_relset_2 A B C D) = B) ) ) ) ) ) ) ) ).
tt(t37_revrot_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_goboard9 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) = (k3_goboard9 B)) ) ) ) ) ).
tt(t37_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r5_rewrite1 A B C) | (r6_rewrite1 A B C))  => (r2_rewrite1 A B C)) ) ) ) ) ).
tt(t37_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ((r3_rewrite2 A B C D) => (r3_rewrite2 A B (k1_flang_1 A (k1_flang_1 A E C) F) (k1_flang_1 A (k1_flang_1 A E D) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ((r1_rewrite3 E F A B C) <=> (r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C (k2_flang_1 D))) (k1_rewrite3 D E F))) ) ) ) ) ) ) ) ) ) ).
tt(t37_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k1_rfunct_1 A (k1_rfunct_1 B C)) = (k1_rfunct_1 (k18_valued_1 A (k5_relat_1 C (k9_xtuple_0 (k4_rfunct_1 C)))) B)) ) ) ) ) ) ) ).
tt(t37_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))))  &  ( ( ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))))  &  ( ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))))  &  ( ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t37_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k18_rfunct_3 A B) C))) ) ) ) ) ) ).
tt(t37_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k4_rinfsup1 B) A) = (k1_rinfsup1 (k1_valued_0 k1_numbers B A))) ) ) ) ) ).
tt(t37_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v7_valued_0 A) =>  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k1_rinfsup2 A)) ) ) ) ) ).
tt(t37_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_rlaffin1 A B) = (k3_rlaffin1 A (k1_rlaffin1 A B C))) ) ) ) ) ) ) ).
tt(t37_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k1_rlsub_1 B) = (k1_rlsub_1 C)) ) ) ) ) ) ) ).
tt(t37_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  ( ((k2_rlsub_2 A B C) = (k1_rlsub_1 A))  &  ((k2_rlsub_2 A C B) = (k1_rlsub_1 A)) ) ) ) ) ) ) ) ).
tt(t37_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_rusub_4 A (k1_tops_1 A C) B) = (k1_tops_1 A (k5_rusub_4 A C B))) ) ) ) ) ) ) ).
tt(t37_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( ((k1_rlvect_1 C D A) = (k1_rlvect_1 C D B))  =>  ( (D = (k4_struct_0 C))  |  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) => (r1_tarski (k3_rlvect_2 A (k7_rlvect_2 A B C)) (k4_subset_1 (u1_struct_0 A) (k3_rlvect_2 A B) (k3_rlvect_2 A C)))) ) ) ) ) ) ).
tt(t37_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m2_rlvect_2 D A (k6_domain_1 (u1_struct_0 A) B)) &  ((k3_funct_2 (u1_struct_0 A) k1_numbers D B) = C) ) ) ) ) ) ) ) ) ).
tt(t37_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) =>  ((k1_rlvect_5 A) = (k2_nat_1 (k1_rlvect_5 B) (k1_rlvect_5 C))) ) ) ) ) ) ) ) ).
tt(t37_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k2_rlvect_x A B) = (k2_rlvect_x A C))  =>  ((k1_rlvect_3 A B) = (k1_rlvect_3 A C)) ) ) ) ) ) ) ) ).
tt(t37_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k1_rmod_2 A C) = (k1_rmod_2 A D)) ) ) ) ) ) ) ) ) ).
tt(t37_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  => (r2_hidden B (k3_rmod_3 A B))) ) ) ) ).
tt(t37_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) => (r1_tarski (k2_rmod_4 A B (k6_rmod_4 A B C D)) (k4_subset_1 (u1_struct_0 B) (k2_rmod_4 A B C) (k2_rmod_4 A B D)))) ) ) ) ) ) ) ) ).
tt(t37_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_robbins1 A B C) = C) ) ) ) ) ) ) ).
tt(t37_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A C D)) (k3_robbins1 A (k5_robbins1 A C B))))) = (k5_robbins1 A C B)) ) ) ) ) ) ) ) ) ).
tt(t37_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  =>  ((v1_robbins4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) =>  ((k4_lattices A (k3_lattices A B C) (k3_lattices A C (k3_robbins1 A B))) = (k3_lattices A (k4_lattices A B C) (k4_lattices A C (k3_robbins1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t37_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k4_roughs_1 A B)) & (r2_hidden (k4_tarski C D) (u1_orders_2 A)))  => (r2_hidden D (k4_roughs_1 A B))) ) ) ) ) ) ) ).
tt(t37_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski B C) =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((k2_rpr_1 A C B) = (k10_real_1 (k1_rpr_1 A B) (k1_rpr_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t37_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden C (k3_rusub_1 A C B))) ) ) ) ) ) ).
tt(t37_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  ( ((k2_rusub_2 A B C) = (k1_rusub_1 A))  &  ((k2_rusub_2 A C B) = (k1_rusub_1 A)) ) ) ) ) ) ) ) ).
tt(t37_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((r2_hidden F (k3_rusub_1 A B (k1_rusub_3 A (k8_domain_1 (u1_struct_0 A) C D E)))) <=>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A B (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r2_hidden (k4_bhsp_2 A B C) (k4_rusub_5 A))) ) ) ) ) ) ).
tt(t37_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k9_rvsum_1 A B B) = (k5_finseq_2 k5_numbers A k6_numbers)) ) ) ) ) ).
tt(t37_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k17_rvsum_1 (k5_finseq_2 k2_numbers A k5_complex1)) = k5_complex1) ) ) ).
tt(t37_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_amistd_1 3 k1_scmfsa_2 B (k13_scmfsa_2 A C)) = (k2_tarski A (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t37_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 8)  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k13_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B D A) & (r6_scmfsa7b B D A))  =>  ((r5_scmfsa7b (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2)) D A) & (r6_scmfsa7b (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2)) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ( ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (F = G) )  =>  ((k1_funct_1 C G) = (k1_funct_1 D G)) ) ) )  &  ( (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 C G) = (k18_scmfsa_2 D G)) ) )  &  ((r5_scmfsa7b E C A) & (r6_scmfsa7b E C A)) ) )  =>  ((r2_scmfsa7b E F) |  ((r5_scmfsa7b E D B) & (r6_scmfsa7b E D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  & (r1_scmfsa8a B A (k2_scmfsa6a C)))  =>  ((r6_scmfsa7b (k1_scmfsa8b E C D) B A) &  ((r5_scmfsa7b (k1_scmfsa8b E C D) B A) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8b E C D)) (k8_memstr_0 3 k1_scmfsa_2 B)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) C) k6_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) =>  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k5_card_1 B) 6) C))  => (r2_hidden C (k2_afinsq_1 (k2_scmfsa_9 A B)))) ) ) ) ) ) ) ).
tt(t37_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 (k1_scmfsa_m A) B) = (k1_funct_1 A B)) ) )  &  (! [B:$i] :  ((m1_scmfsa_2 B) =>  ((k18_scmfsa_2 (k1_scmfsa_m A) B) = (k18_scmfsa_2 A B)) ) ) ) ) ) ).
tt(t37_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k1_scmfsa8b E C D)) &  ( ( ((k1_funct_1 B E) = k6_numbers)  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3)))))  &  ( (~  ((k1_funct_1 B E) = k6_numbers) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k1_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (~  ((r1_tarski (k1_funct_4 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) (k16_funcop_1 (k5_scmfsa_2 k6_numbers) B)) A) &  ((r1_tarski k3_scmisort C) &  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (~  ((r2_classes1 B D) &  ((v8_valued_0 D) &  ((m2_finseq_1 D k4_numbers) &  ((k18_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 C A) (k5_scmfsa_2 k6_numbers)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 11)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  (A = (k14_scmpds_2 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k5_relat_1 A (k2_xboole_0 k2_ami_2 (k1_tarski (k4_struct_0 k1_scmpds_2)))) = (k5_relat_1 B (k2_xboole_0 k2_ami_2 (k1_tarski (k4_struct_0 k1_scmpds_2)))))  =>  (A = B) ) ) ) ) ) ).
tt(t37_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmpds_6 A B C D) k6_numbers) = (k7_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2))) ) ) ) ) ) ) ) ) ).
tt(t37_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k1_scmpds_7 D E F C) (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k2_nat_1 (k5_card_1 C) 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_compos_0 (u1_compos_1 (k1_scmring2 A)) (k8_scmring2 A B) C) = (k8_scmring2 A (k2_nat_1 B C))) ) ) ) ) ) ) ).
tt(t37_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((k5_scmyciel (k2_tarski A B)) = (k2_enumset1 k1_xboole_0 (k1_tarski A) (k1_tarski B) (k2_tarski A B))) ) ) ).
tt(t37_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) =>  ( (~ (r1_semi_af1 A B C D))  &  ( (~ (r1_semi_af1 A C B E))  &  ( (~ (r1_semi_af1 A D E B))  &  (~ (r1_semi_af1 A E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers B A) A) B)) ) ) ) ) ).
tt(t37_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (v7_valued_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k2_seq_2 A))) ) ) ) ) ).
tt(t37_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((r1_seqfunc A k1_numbers B D) & (r1_seqfunc A k1_numbers C D))  =>  ((r1_seqfunc A k1_numbers (k6_seqfunc A B C) D) &  ((r1_seqfunc A k1_numbers (k7_seqfunc A B C) D) & (r1_seqfunc A k1_numbers (k8_seqfunc A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t37_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_comseq_2 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (v1_comseq_2 (k26_valued_1 k5_numbers k1_numbers A B))) ) )  &  ( ((v1_comseq_2 A) => (v1_comseq_2 (k32_valued_1 k5_numbers k1_numbers A)))  &  ( ((v1_comseq_2 A) => (v1_comseq_2 (k56_valued_1 k5_numbers k1_numbers A)))  &  ((v1_comseq_2 (k56_valued_1 k5_numbers k1_numbers A)) => (v1_comseq_2 A)) ) ) ) ) ) ).
tt(t37_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~  ((k3_funct_2 k5_numbers k1_numbers A C) = k6_numbers) )  &  ((k3_funct_2 k5_numbers k1_numbers B C) = (k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) (k2_nat_1 C 1)) (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) C))) ) ) )  & (v2_comseq_2 B))  =>  ((r1_xxreal_0 1 (k2_seq_2 B)) | (v2_series_1 A)) ) ) ) ) ) ).
tt(t37_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 (k9_newton B) B)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 (k9_newton (k2_nat_1 B 1)) 1)) ) ) ) ) ) ) ).
tt(t37_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers))  &  (~ (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 B (k5_real_1 C 1)))) ) ) )  & (r1_xxreal_0 (k8_real_1 (k2_nat_1 A 1) (k1_seq_1 B (k2_nat_1 A 1))) (k1_seq_1 (k3_series_1 B) A))) ) ) ) ) ) ).
tt(t37_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 9 (k8_complex1 (k8_complex1 (k13_complex1 1 A) (k13_complex1 1 B)) (k13_complex1 1 C)))) ) ) ) ) ) ) ).
tt(t37_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski (k7_setfam_1 A B) C) <=> (r1_tarski B (k7_setfam_1 A C))) ) ) ) ) ) ).
tt(t37_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) B E) = (k5_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) C E) (k3_funct_2 k5_numbers (k9_setfam_1 A) D E))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A B) E) (k5_prob_1 A (k9_setfam_1 A) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A C) E) (k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A D) E)))) ) ) ) ) ) ) ) ) ) ).
tt(t37_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k3_prob_1 A (k9_setlim_2 A C B)) (k5_subset_1 A B (k3_prob_1 A C)))) ) ) ) ) ).
tt(t37_setwiseo,ax, (! [A:$i] : (v3_binop_1 (k9_setwiseo A) (k5_finsub_1 A))) ).
tt(t37_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m2_finseq_2 E A (k4_finseq_2 D A)) =>  (! [F:$i] :  ((m2_finseq_2 F A (k4_finseq_2 D A)) =>  ( ((v1_binop_1 B A) &  ((v2_binop_1 B A) &  ((v1_setwiseo B A) &  ((v1_finseqop B A) & (r8_binop_1 A A A C (k7_finseqop A B (k6_partfun1 A) (k5_finseqop A B)))) ) ) )  =>  ((k5_binop_1 A C (k1_finsop_1 A E B) (k1_finsop_1 A F B)) = (k1_finsop_1 A (k1_finseqop A A A C E F) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r6_pboole (u1_struct_0 k1_scmfsa_2) D (k1_scmfsa6b (k5_sfmastr3 B) A C)) =>  ((r3_graph_2 (k18_scmfsa_2 D B) 1 (k3_finseq_1 (k18_scmfsa_2 D B))) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_1 (k18_scmfsa_2 A B)) (k4_finseq_1 (k18_scmfsa_2 A B))) &  ((v3_funct_2 E (k4_finseq_1 (k18_scmfsa_2 A B)) (k4_finseq_1 (k18_scmfsa_2 A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 (k18_scmfsa_2 A B)) (k4_finseq_1 (k18_scmfsa_2 A B)))))) ) )  &  ((k18_scmfsa_2 D B) = (k1_partfun1 (k4_finseq_1 (k18_scmfsa_2 A B)) (k4_finseq_1 (k18_scmfsa_2 A B)) k5_numbers k4_numbers E (k18_scmfsa_2 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((r1_xboole_0 (k1_relset_1 k5_numbers A) (k1_relset_1 k5_numbers B)) =>  ((k4_sf_mastr (k1_funct_4 A B)) = (k1_finsub_1 (k1_zfmisc_1 k3_scmfsa_2) (k4_sf_mastr A) (k4_sf_mastr B))) ) ) ) ) ) ).
tt(t37_sgraph1,ax,(r4_sgraph1 k5_numbers k8_sgraph1 (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers 1) (k12_finseq_1 k5_numbers 2)) (k12_finseq_1 k5_numbers 3)) (k12_finseq_1 k5_numbers 1)))).
tt(t37_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v9_sheffer1 A) &  ((v10_sheffer1 A) &  ((v11_sheffer1 A) &  ((v12_sheffer1 A) & (l3_sheffer1 A)) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) ) ) ) ).
tt(t37_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) D) = (k5_sheffer1 A D (k5_sheffer1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t37_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((u1_pre_topc (k7_simplex0 A B C)) = (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 B)) (k9_setfam_1 C) (u1_pre_topc B))) ) ) ) ) ) ).
tt(t37_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( ((v6_ordinal1 B) &  ((v1_setfam_1 B) &  ((k5_card_1 B) = (k1_card_1 (k5_setfam_1 (u1_struct_0 A) B))) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_xboole_0 C (k5_setfam_1 (u1_struct_0 A) B)) &  ((v1_rlaffin1 (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C) A) & (r1_tarski (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C) D)) )  =>  ((v1_xboole_0 C) | (m3_simplex0 (k4_subset_1 (u1_struct_0 A) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) C)))) (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) D))) (k5_card_1 B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t37_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 1 (k1_seq_1 k4_sin_cos2 A))) ) ).
tt(t37_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k15_sin_cos (k1_binop_2 (k5_binop_2 k7_complex1 A))) = (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A)))) ) ) ).
tt(t37_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos A)) (k3_xcmplx_0 (k17_sin_cos B) (k17_sin_cos B)))) ) ) ) ) ).
tt(t37_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k6_xcmplx_0 (k25_sin_cos A) (k25_sin_cos (k4_xcmplx_0 A))) = k6_numbers) )  =>  ((k8_real_1 (k9_sin_cos2 A) (k1_sin_cos5 A)) = 1) ) ) ) ).
tt(t37_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) &  ( (~ (r1_xxreal_0 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 1 (k17_sin_cos A))) ) ) ) ) ) ) ).
tt(t37_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k2_sin_cos7 A) = (k4_sin_cos7 (k12_binop_2 (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)) A))) ) ) ) ).
tt(t37_sin_cos9,ax, ( ((k5_sin_cos9 (k1_real_1 1)) = (k1_real_1 (k10_real_1 k32_sin_cos 4)))  &  ((k1_seq_1 k1_sin_cos9 (k1_real_1 1)) = (k1_real_1 (k10_real_1 k32_sin_cos 4))) ) ).
tt(t37_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k19_sin_cos A) = (k4_series_1 (k23_sin_cos A)))  &  ((k1_seq_1 k16_sin_cos A) = (k4_series_1 (k22_sin_cos A))) ) ) ) ).
tt(t37_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((v1_topreal1 B) &  ((v3_sppol_1 B) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) (k3_finseq_1 B)) &  ( (E = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)))  & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) (k1_rltopsp1 (k15_euclid 2) C D))) ) ) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1)) = D)  |  ((r2_hidden C (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B A) (k2_topreal1 2 B (k2_nat_1 A 1)))) |  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden G (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B A) (k2_topreal1 2 B (k2_nat_1 A 1)))))  &  ((r2_hidden G (k1_rltopsp1 (k15_euclid 2) C D)) & (r2_hidden G (k9_metric_1 (k14_euclid 2) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k2_topreal1 2 A C))) )  =>  ((r2_hidden B (k10_xtuple_0 A)) | (v3_topreal1 (k5_finseq_5 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ) ).
tt(t37_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_sprect_1 A) 3) = (k13_pscomp_1 A)) ) ) ).
tt(t37_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( ( ( (~ (r1_xxreal_0 C 1))  & (r1_xxreal_0 B (k3_finseq_1 A)))  |  ((r1_xxreal_0 1 C) &  (~ (r1_xxreal_0 (k3_finseq_1 A) B)) ) )  &  (~  ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  ( ((k2_goboard9 A) = (a_1_1_sprect_3 A))  &  ((k3_goboard9 A) = (a_1_2_sprect_3 A)) ) ) ) ).
tt(t37_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t37_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B A) |  ((k7_xcmplx_0 1 (k2_xcmplx_0 (k6_square_1 B) (k6_square_1 A))) = (k7_xcmplx_0 (k6_xcmplx_0 (k6_square_1 B) (k6_square_1 A)) (k6_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t37_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k14_stacks_1 A))) =>  ((r1_stacks_1 (k14_stacks_1 A) B) <=>  (B = (u1_stacks_1 A)) ) ) ) ) ) ).
tt(t37_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k23_binop_2 A 1) (k23_binop_2 B 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) (k23_binop_2 B 1))))) )  =>  ( ((v2_funct_2 C (k23_binop_2 B 1)) &  ((v1_stirl2_1 C (k23_binop_2 A 1) (k23_binop_2 B 1)) &  ((k1_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) C (k6_domain_1 (k23_binop_2 B 1) (k2_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) C A))) = (k1_seq_4 A)) ) )  =>  ((r1_tarski (k2_relset_1 k3_numbers (k2_partfun1 (k23_binop_2 A 1) (k23_binop_2 B 1) C A)) B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (D = (k2_partfun1 (k23_binop_2 A 1) (k23_binop_2 B 1) C A))  =>  ((v2_funct_2 D B) & (v1_stirl2_1 D A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ((v3_substut1 (k7_sublemma A C B) A) =>  ((k30_substut1 A (k9_sublemma A (k7_sublemma A C B) D)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t37_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k3_enumset1 B C D E F) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k16_substut1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  ( ( ((k19_substut1 A B) = (k19_substut1 A C))  &  ((m2_subset_1 (k37_substut1 A B) (k9_qc_lang1 A) (k3_cqc_lang A)) & (m2_subset_1 (k37_substut1 A C) (k9_qc_lang1 A) (k3_cqc_lang A))) )  => (m2_subset_1 (k37_substut1 A (k21_substut1 A B C)) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ) ).
tt(t37_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v4_card_3 A) &  ((v5_supinf_2 A) & (m1_subset_1 A (k1_zfmisc_1 k7_numbers))) ) )  =>  (! [B:$i] :  ((m1_supinf_2 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 (k15_supinf_2 A B) C) (k12_supinf_2 (k15_supinf_2 A B) (k2_nat_1 C D)))) ) ) ) ) ) ) ) ).
tt(t37_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ((k3_relat_1 A (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A)))) = k1_xboole_0)  =>  ((k3_relat_1 (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))) (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 (k1_sysrel A))))) = k1_xboole_0) )  &  ( ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A))) A) = k1_xboole_0)  =>  ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 (k1_sysrel A)))) (k4_relat_1 (k9_xtuple_0 (k1_sysrel A)))) = k1_xboole_0) ) ) ) ) ).
tt(t37_taxonom1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v5_tbsp_1 B) & (l1_metric_1 B)) ) ) )  =>  ((r1_xxreal_0 (k3_tbsp_1 B (k2_struct_0 B)) A) => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k3_taxonom1 B A) (k1_eqrel_1 (u1_struct_0 B)))) ) ) ) ) ).
tt(t37_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)) (k9_tdlat_1 A)) =>  ((k5_binop_1 (k9_tdlat_1 A) (k11_tdlat_1 A) B C) = (k1_binop_1 (k3_tdlat_1 A) B C)) ) ) ) ) ) ) ).
tt(t37_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))))) ) ) ) ).
tt(t37_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (C = (u1_struct_0 B))  & (v1_tops_1 C A))  => (v4_tdlat_3 B)) ) ) ) ) ) ) ).
tt(t37_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k2_polynom1 (k15_pre_poly A) C (k4_polynom1 A C (k5_termord A B C D) (k6_termord A B C D))) = (k2_polynom1 (k15_pre_poly A) C D)) ) ) ) ) ) ) ) ) ).
tt(t37_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = (u1_struct_0 A)) )  &  ((v1_tops_1 B A) & (v3_tdlat_3 (k6_tmap_1 A B))) ) ) ) ) ) ) ).
tt(t37_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v2_tex_2 B A)) ) ) ) ).
tt(t37_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r3_tsep_2 A B C) =>  ((v2_tex_3 B A) <=> (v4_tex_3 C A)) ) ) ) ) ) ) ) ).
tt(t37_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_tex_4 A (k9_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) (k3_tex_4 A B) (k3_tex_4 A C)))) ) ) ) ) ) ).
tt(t37_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  ( (~ (r1_tsep_1 B C))  =>  ( ( ((r1_tsep_1 B D) | (r1_tsep_1 C D))  => (r1_tsep_1 (k2_tsep_1 A B C) D))  &  ( ((r1_tsep_1 D B) | (r1_tsep_1 D C))  => (r1_tsep_1 D (k2_tsep_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_tarski (k3_toler_1 A B) (k3_toler_1 A C)) <=> (r1_relset_1 A A B C)) ) ) ) ) ) ).
tt(t37_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) & (r1_borsuk_6 A C E)) )  =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A E C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C D) => (r3_borsuk_2 A B D (k1_borsuk_2 A B C D (k1_borsuk_2 A B E C (k1_borsuk_2 A B C E F (k2_borsuk_2 A E C G)) G) H) (k1_borsuk_2 A B C D F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((m2_subset_1 D (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) &  (? [E:$i] :  ((m2_subset_1 E (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) &  ( (B = (k4_topalg_6 A D E))  &  ( (D = (k5_relat_1 B (k1_rcomp_1 (k2_xxreal_2 (k9_xtuple_0 B)) C)))  &  (E = (k5_relat_1 B (k1_rcomp_1 C (k1_xxreal_2 (k9_xtuple_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_xboole_0 B C) =>  (! [D:$i] :  ( ((v1_topdim_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xxreal_0 (k2_topdim_1 A D) k6_numbers) &  ((v5_waybel23 (k1_pre_topc A D)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_metrizts A B C E) & (r1_xboole_0 E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v4_topgen_1 B A) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) B) (k5_setfam_1 (u1_struct_0 A) (k3_topgen_1 A B)))) ) ) ) ) ).
tt(t37_topgen_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k2_xboole_0 (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)) (k1_setfam_1 (a_2_1_topgen_2 A B)))) ) ) ) ) ).
tt(t37_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_topgen_3 A B)))))  =>  ((k2_pre_topc (k6_topgen_3 A B) C) = (k2_xboole_0 C (k6_domain_1 A B))) ) ) ) ) ) ) ).
tt(t37_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_topgen_4 B A) => (v6_topgen_4 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t37_topgen_5,ax, ((v2_topgen_1 (k8_subset_1 (u1_struct_0 (k15_euclid 2)) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k4_card_3 (k10_finseq_1 k3_numbers k3_numbers))) k3_topgen_5) & (m1_subset_1 (k8_subset_1 (u1_struct_0 (k15_euclid 2)) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k4_card_3 (k10_finseq_1 k3_numbers k3_numbers))) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t37_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k6_algstr_0 A B C)) =>  (? [E:$i] :  ( ((v3_pre_topc E A) & (m1_connsp_2 E A B))  &  (? [F:$i] :  ( ((v3_pre_topc F A) & (m1_connsp_2 F A C))  & (r1_tarski (k2_group_2 A E F) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k7_topreal1 A) = (a_1_7_topreal1 A)) ) ) ).
tt(t37_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k18_euclid A) = (k18_euclid B))  &  (C = (k11_finseq_1 A (k19_euclid (k10_real_1 (k7_real_1 (k17_euclid A) (k17_euclid B)) 2) (k18_euclid A)) B)) )  =>  ( ((k17_euclid A) = (k17_euclid B))  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = A)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = B)  & (v4_topreal1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t37_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A)) (k3_topreal1 2 (k1_sprect_1 A)))) ) ).
tt(t37_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) =>  (~  ( (G = D)  &  ( (H = E)  &  ( (I = F)  &  ( (~  (D = E) )  &  ((r2_hidden D (k1_topreal9 A F B)) &  ( (C = (k10_real_1 (k7_real_1 (k1_real_1 (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid A) E D) (k5_algstr_0 (k15_euclid A) D F)))) (k7_square_1 (k2_quin_1 (k18_rvsum_1 (k11_euclid A (k8_euclid A H G))) (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid A) E D) (k5_algstr_0 (k15_euclid A) D F))) (k9_real_1 (k18_rvsum_1 (k11_euclid A (k8_euclid A G I))) (k3_square_1 B))))) (k8_real_1 2 (k18_rvsum_1 (k11_euclid A (k8_euclid A H G))))))  &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid A))) =>  (~  ( ((k1_tarski J) = (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A D E) (k3_topreal9 A F B)))  &  (J = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k9_real_1 1 C)) (k1_rlvect_1 (k15_euclid A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_t_0topsp (k2_borsuk_1 (k4_topmetr A B) (k4_topmetr C D)) (k1_topreala A B C D))) ) ) ) ) ) ) ) ) ).
tt(t37_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_funct_1 k12_toprealb A) = (k19_euclid (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) k19_sin_cos) A) (k1_funct_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) k16_sin_cos) A))) ) ) ) ) ) ) ).
tt(t37_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k43_valued_2 A (u1_struct_0 (k15_euclid B)) D C)) &  ((v1_funct_2 (k43_valued_2 A (u1_struct_0 (k15_euclid B)) D C) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k43_valued_2 A (u1_struct_0 (k15_euclid B)) D C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t37_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v3_toprns_1 B A) & (v3_toprns_1 C A))  =>  ((k6_toprns_1 A (k1_toprns_1 A B C)) = (k3_rlvect_1 (k15_euclid A) (k6_toprns_1 A B) (k6_toprns_1 A C))) ) ) ) ) ) ) ) ).
tt(t37_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k1_tops_1 A B)) (k2_tops_1 A B))) ) ) ) ).
tt(t37_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 C A) => (v1_tops_2 (k1_tops_2 A B C) (k1_pre_topc A B))) ) ) ) ) ) ) ).
tt(t37_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_3 B A) & (v2_tops_1 B A)) ) ) ) ) ) ).
tt(t37_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A))) &  ((v3_funct_2 B (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A)))))) ) )  =>  (~  ((r3_transgeo (k2_diraf A) B) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((r1_funct_2 (u1_struct_0 (k2_diraf A)) (u1_struct_0 (k2_diraf A)) (u1_struct_0 A) (u1_struct_0 A) B C) & (v4_transgeo C A)) ) ) ) ) ) ) ) ) ) ).
tt(t37_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (~ (r3_xboole_0 A B))  => (v2_trees_1 (k2_tarski A B))) ) ) ) ) ).
tt(t37_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) =>  (! [D:$i] :  ((m1_trees_1 D (k5_trees_1 A C B)) =>  (! [E:$i] :  ((m1_trees_1 E B) =>  ((r2_relset_1 k5_numbers k5_numbers D (k8_finseq_1 k5_numbers C E)) => (r2_tarski (k1_trees_2 (k5_trees_1 A C B) D) (k1_trees_2 B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v6_trees_3 A)) )  =>  ( ((k9_xtuple_0 (k2_funct_6 A)) = (k9_xtuple_0 A))  & (v4_trees_3 (k2_funct_6 A))) ) ) ).
tt(t37_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  ((k1_relset_1 k5_numbers (k3_relat_1 (k1_trees_9 (k9_xtuple_0 A) B) A)) = (k4_finseq_1 (k1_trees_9 (k9_xtuple_0 A) B))) ) ) ) ) ).
tt(t37_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_pre_topc C A))  =>  ((r1_xboole_0 B C) <=> (r1_connsp_1 A B C)) ) ) ) ) ) ) ) ).
tt(t37_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  (! [D:$i] :  ((m1_pre_topc D A) =>  (! [E:$i] :  ((m1_pre_topc E A) =>  ( ((r3_tsep_2 A B D) &  ((r3_tsep_2 A C E) & (r4_tsep_1 A B C)) )  => (r4_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 k20_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k20_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((r1_xxreal_0 3 (k3_finseq_1 D)) &  ( (A = (k4_domain_1 k5_numbers k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)) k6_numbers C B))  & (r2_turing_1 (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers C) D) k20_turing_1 B)) )  =>  ((v2_turing_1 A k20_turing_1) &  ( ((k2_mcart_1 (u2_turing_1 k20_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)) (k11_turing_1 k20_turing_1 A)) = (k2_nat_1 (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) (k7_partfun1 k5_numbers D 2)) 4))  & (r2_turing_1 (k2_finseq_4 k5_numbers (k2_nat_1 (k2_nat_1 (k2_nat_1 C (k7_partfun1 k5_numbers D 1)) (k7_partfun1 k5_numbers D 2)) 4) (k7_partfun1 k5_numbers D 3)) k20_turing_1 (k3_mcart_1 (u2_turing_1 k20_turing_1) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 k20_turing_1)) (k11_turing_1 k20_turing_1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((u1_struct_0 (k40_twoscomp A B)) = (k2_xboole_0 (k2_tarski A B) (k2_tarski (k4_tarski (k10_finseq_1 A B) k15_twoscomp) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)))) ) ) ) ) ).
tt(t37_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  => (m1_group_2 (k3_uniroots A) (k1_uniroots k1_complfld))) ) ).
tt(t37_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_normsp_1 A (k11_polynom3 A (k4_polynom5 A B C) D) k6_numbers) = (k6_algstr_0 A B (k1_normsp_1 A D k6_numbers)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k1_normsp_1 A (k11_polynom3 A (k4_polynom5 A B C) D) (k1_nat_1 E 1)) = (k1_algstr_0 A (k6_algstr_0 A B (k1_normsp_1 A D (k1_nat_1 E 1))) (k6_algstr_0 A C (k8_nat_1 (u1_struct_0 A) D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ( ((r1_valuat_1 A B D F C) & (r1_valuat_1 A B (k8_cqc_lang A D E) F C))  => (r1_valuat_1 A B E F C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((k1_relset_1 k5_numbers A) = (k2_xboole_0 (k1_relset_1 k5_numbers (k63_valued_1 A)) (k1_tarski (k62_valued_1 A)))) ) ) ).
tt(t37_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k1_valued_1 B C) A) = (k1_valued_1 (k14_valued_2 B A) (k14_valued_2 C A))) ) ) ) ) ) ) ).
tt(t37_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_vectsp_5 E A B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) (k4_algstr_0 A D))))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 E) (u1_struct_0 E)) &  ((v13_vectsp_1 F E E) &  ((v1_mod_2 F A E E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 E))))) ) ) )  =>  ((r1_funct_2 (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 E) (u1_struct_0 B) F (k8_matrlin2 A B B E C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  ( ((k3_funct_2 (u1_struct_0 E) (u1_struct_0 E) F G) = (k4_vectsp_1 A E D G))  =>  (G = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  ((v4_vectsp_1 A) =>  ((k5_struct_0 A) = (k1_group_1 A)) ) ) ) ).
tt(t37_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k5_vectsp_2 A C (k11_algstr_0 A B) (k5_vectsp_2 A C B D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t37_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k1_vectsp_4 A C) = (k1_vectsp_4 A D)) ) ) ) ) ) ) ) ) ).
tt(t37_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) => (m1_vectsp_5 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t37_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((r1_vectsp_6 A B (k5_vectsp_6 A B C D) (k2_vectsp_6 A B)) => (r1_vectsp_6 A B D (k7_vectsp_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t37_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 B (k1_vectsp_9 A C)))  =>  ((k2_vectsp_9 A C B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t37_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  ( ((v1_partfun1 D A) & (v1_partfun1 E A))  =>  ( ((k7_partfun1 (u1_struct_0 C) (k6_vfunct_1 A C D E) B) = (k3_rlvect_1 C (k7_partfun1 (u1_struct_0 C) D B) (k7_partfun1 (u1_struct_0 C) E B)))  &  ((k7_partfun1 (u1_struct_0 C) (k2_vfunct_1 A C D E) B) = (k5_algstr_0 C (k7_partfun1 (u1_struct_0 C) D B) (k7_partfun1 (u1_struct_0 C) E B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((v1_partfun1 C A) & (v1_partfun1 D A))  =>  ( ((k7_partfun1 (u1_struct_0 B) (k3_vfunct_2 A B C D) E) = (k3_rlvect_1 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 (u1_struct_0 B) D E)))  &  ((k7_partfun1 (u1_struct_0 B) (k2_vfunct_1 A B C D) E) = (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 (u1_struct_0 B) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_yellow_0 A B) <=> (r2_yellow_0 A (k4_waybel_0 A B))) ) ) ) ) ).
tt(t37_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  ( ((u1_pre_topc A) = (k5_waybel11 A))  => (v4_waybel11 A)) ) ) ).
tt(t37_waybel12,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v2_waybel12 B A) &  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ).
tt(t37_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_yellow_8 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) =>  ((v3_pre_topc E A) & (v2_waybel_0 E A)) ) ) ) ) ) ) )  & (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))))  =>  (B = (k1_yellow_0 A (a_2_4_waybel14 A B))) ) ) ) ) ) ).
tt(t37_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v2_waybel19 B) & (m1_yellow_9 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (D = C)  => (v3_pre_topc D B)) ) ) ) ) ) ) ) ) ) ).
tt(t37_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ((v7_waybel_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 C A D E) C A) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v22_waybel_0 C A A) &  ( (B = (k8_relset_1 (u1_struct_0 (k3_yellow_3 A A)) (u1_struct_0 (k3_yellow_3 A A)) (k1_waybel20 A A A A C C) (k6_partfun1 (u1_struct_0 A))))  &  (! [D:$i] :  ( ((v1_orders_2 D) &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v1_lattice3 D) &  ((v2_lattice3 D) &  ((v3_lattice3 D) &  ((v3_waybel_3 D) & (l1_orders_2 D)) ) ) ) ) ) ) )  =>  (~  ( ((u1_struct_0 D) = (k8_eqrel_1 (u1_struct_0 A) (k2_waybel20 A B)))  &  ( ((u1_orders_2 D) = (a_3_0_waybel20 A B C))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 D) E F) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k2_waybel20 A B) F)) ) )  => (m1_waybel16 E A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) => (r3_orders_2 A (k1_waybel11 A B) (k1_waybel11 A C))) ) ) ) ) ) ).
tt(t37_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_waybel23 (k6_waybel_0 A B) A)) ) ) ) ).
tt(t37_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ((k4_yellow_0 (k3_waybel24 A B)) = (k6_struct_0 A B (k4_yellow_0 B))) ) ) ) ) ).
tt(t37_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k1_waybel25 A)))  =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) ) ) ) ) ).
tt(t37_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) ) )  =>  ( ( ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B)))  =>  ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) & (v3_waybel_3 B)) )  &  ( ((v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))) & (v3_waybel_3 B))  =>  ((v3_lattice3 (k1_waybel26 A B)) & (v3_waybel_3 (k1_waybel26 A B))) ) ) ) ) ) ) ).
tt(t37_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v22_waybel_0 C B B) &  ((v6_waybel_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  ((k1_yellow_2 (k2_waybel27 A B) (k2_waybel27 A B) (k4_waybel27 A A B B (k3_struct_0 A) C)) = (k2_waybel27 A (k1_yellow_2 B B C))) ) ) ) ) ) ) ).
tt(t37_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k11_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_0_waybel_2 A B C))) ) ) ) )  => (v1_waybel_2 A)) ) ) ).
tt(t37_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_yellow13 A) &  ((v3_waybel30 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) ) ) )  => (v2_waybel30 A)) ) ).
tt(t37_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_waybel_0 (k1_yellow_2 A A B) A) <=>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k1_yellow_2 A A B)))  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C))))) )  =>  ((r1_funct_2 (u1_struct_0 D) (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 A) E B) => (v1_t_0topsp E D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( (B = (u1_struct_0 A))  =>  ((v1_waybel_3 B (k2_yellow_1 (u1_pre_topc A))) <=> (v1_compts_1 A)) ) ) ) ) ) ).
tt(t37_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v7_waybel_4 (k11_waybel_4 A B) A)) ) ) ) ).
tt(t37_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k1_yellow_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (v6_waybel_6 D A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (k9_subset_1 (u1_struct_0 (k7_lattice3 A)) (k1_waybel_3 A B) (k4_waybel_6 (k7_lattice3 A))))) ) ) ) ) ) ).
tt(t37_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_waybel_3 (k4_yellow_0 A) A) =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_waybel_3 A (k2_yellow_0 A B) (k4_yellow_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) & (r3_orders_2 A C (k4_yellow_0 A))) ) ) ) ) ) ) )  &  (~ (r2_subset_1 (k4_waybel_0 A (k12_waybel_0 A (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A (k4_yellow_0 A))))) (k1_waybel_3 A (k4_yellow_0 A)))) ) ) ) ) ).
tt(t37_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_waybel_9 A)) ) ) ) ) ) )  =>  ( ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((v10_waybel_0 B A) =>  ((r1_waybel_9 A B) & (r2_hidden (k1_waybel_2 A B) (k10_yellow_6 A B))) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) ) )  => (v2_waybel_2 A)) ) ) ).
tt(t37_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((k5_card_1 (u1_struct_0 (k10_group_5 (k1_uniroots A)))) = (k6_xcmplx_0 (k5_card_1 (u1_struct_0 (k4_weddwitt A))) 1)) ) ) ).
tt(t37_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) => (r3_wellord1 A A (k4_relat_1 (k1_relat_1 A)))) ) ).
tt(t37_wsierp_1,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 2 (k3_finseq_1 A)) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden C (k4_finseq_1 A)))  =>  ( (B = C)  |  ((k3_int_2 (k1_seq_1 A B) (k1_seq_1 A C)) = 1) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (~  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (~  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) =>  ((k7_real_1 (k8_real_1 (k1_seq_1 A D) (k1_seq_1 C D)) (k1_seq_1 B D)) = (k7_real_1 (k8_real_1 (k1_seq_1 A 1) (k1_seq_1 C 1)) (k1_seq_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 A B) = k1_xboole_0)  <=> (r1_tarski A B)) ) ) ).
tt(t37_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k9_xboolean A B)) = (k9_xboolean A B)) ) ) ) ) ).
tt(t37_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A (k6_xcmplx_0 B C)) = (k2_xcmplx_0 (k6_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t37_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k2_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t37_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k12_xtuple_0 A) (k12_xtuple_0 B)) (k12_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t37_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k4_xxreal_0 A (k3_xxreal_0 C B)) = (k3_xxreal_0 (k4_xxreal_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t37_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k4_xxreal_1 B C) (k1_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t37_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (m1_xxreal_2 A k1_xboole_0)) ) ).
tt(t37_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k3_xxreal_3 A D) (k3_xxreal_3 B C))) ) ) ) ) ) ) ) ) ).
tt(t37_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_yellow_0 A B) &  ((r2_yellow_0 A C) & (r2_yellow_0 A (k2_xboole_0 B C))) )  =>  ((k2_yellow_0 A (k2_xboole_0 B C)) = (k11_lattice3 A (k2_yellow_0 A B) (k2_yellow_0 A C))) ) ) ) ) ) ).
tt(t37_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_tarski (k4_yellow_3 A B (k5_waybel_0 (k3_yellow_3 A B) C)) (k5_waybel_0 A (k8_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k5_waybel_0 (k3_yellow_3 A B) C)) (k5_waybel_0 B (k9_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t37_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k6_partfun1 (u1_struct_0 A)) = (a_1_0_yellow12 A)) ) ) ).
tt(t37_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v2_pre_topc (k4_waybel18 A B C)) &  ((v6_pre_topc (k4_waybel18 A B C)) & (l1_pre_topc (k4_waybel18 A B C))) ) ) )  => (v6_pre_topc (k3_waybel18 A B))) ) ) ) ) ).
tt(t37_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_yellow_1 B) & (v4_waybel_3 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v1_yellow_1 C) & (v4_waybel_3 C)) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((v4_yellow_0 (k3_waybel_3 A C D) (k3_waybel_3 A B D)) & (m1_yellow_0 (k3_waybel_3 A C D) (k3_waybel_3 A B D))) ) )  =>  ((v4_yellow_0 (k5_yellow_1 A C) (k5_yellow_1 A B)) & (m1_yellow_0 (k5_yellow_1 A C) (k5_yellow_1 A B))) ) ) ) ) ) ) ) ).
tt(t37_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_hidden (k6_partfun1 (k3_yellow18 A B)) (k1_altcat_1 A B B)) =>  ((k8_altcat_1 A B) = (k6_partfun1 (k3_yellow18 A B))) ) ) ) ) ) ).
tt(t37_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  (! [E:$i] :  ((l2_functor0 E A B) =>  ((r2_yellow20 A B E C D) => (r1_functor0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_yellow_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v13_waybel_0 C A)) ) )  =>  ((v13_waybel_0 (k6_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t37_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_lattice3 A C G) => (r1_orders_2 A E G)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r2_lattice3 B D G) => (r1_orders_2 B F G)) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_yellow_3 A B))) =>  ((r2_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) G) => (r1_orders_2 (k3_yellow_3 A B) (k7_yellow_3 A B E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  => (r2_hidden (k11_lattice3 A D E) (k3_yellow_4 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (r3_orders_2 A (k7_waybel_1 A C) (k7_waybel_1 A B))) ) ) ) ) ) ) ).
tt(t37_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r2_hidden C (k10_yellow_6 A B)))  &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  (? [E:$i] :  ((m2_yellow_6 E A D) & (r2_hidden C (k10_yellow_6 A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_waybel_1 (k7_lattice3 A) (k8_lattice3 A B)) = (k7_waybel_1 A B)) ) ) ) ) ).
tt(t37_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v1_cantor_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E D) &  ((r2_hidden B E) & (r1_xboole_0 E C)) ) ) ) )  => (r2_hidden B (k2_pre_topc A C))) ) ) ) ) ) ) ) ) ).
tt(t37_zf_fund1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k4_ordinal1)))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A (k9_funct_2 B C)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang C)))) )  =>  (~  (A = (k2_partfun1 k4_ordinal1 C (k1_partfun1 k4_ordinal1 k1_zf_lang k1_zf_lang C k2_zf_fund1 D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v11_zf_lang A) =>  ((v4_zf_lang A) &  ((v6_zf_lang (k20_zf_lang A)) & (v4_zf_lang (k24_zf_lang (k20_zf_lang A)))) ) ) ) ) ).
tt(t37_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_zf_lang A) =>  (A = (k5_zf_lang (k18_zf_lang A) (k19_zf_lang A))) ) ) ) ).
tt(t37_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( ((k1_tarski A) = (k2_xboole_0 B C))  &  ( (~  ( (B = (k1_tarski A))  &  (C = (k1_tarski A)) ) )  &  ( (~  ( (B = k1_xboole_0)  &  (C = (k1_tarski A)) ) )  &  (~  ( (B = (k1_tarski A))  &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t37_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) )  =>  (~  ((v2_ordinal2 B) &  ((v3_ordinal2 B) &  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( ( ((k4_ordinal4 A B C) = C)  &  (D = (k4_classes1 C)) )  =>  ( (k1_xboole_0 = C)  | (r2_zfrefle1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t37_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r1_struct_0 D B) => (r1_struct_0 D (k1_zmodul01 A B C))) ) ) ) ) ) ) ) ) ).
tt(t380_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_xxreal_1 A B)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t381_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k4_xxreal_1 A B)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t382_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 k1_numbers (k2_xxreal_1 A B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t383_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k2_xxreal_1 A B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k1_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t384_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k3_xxreal_1 A B)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t385_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k6_subset_1 k1_numbers (k1_xxreal_1 A B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t386_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_xxreal_1 A B)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t387_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_tarski A)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t388_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_tarski A)) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t389_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k6_subset_1 k1_numbers (k1_tarski A)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t38_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r3_abcmiz_0 A B (k6_finseq_1 (u1_abcmiz_0 A)))) ) ) ) ).
tt(t38_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ( ((k1_msualg_1 A (k15_abcmiz_1 A)) = (k3_pre_poly (u1_struct_0 A) (k13_abcmiz_1 A)))  &  ( ((k2_msualg_1 A (k15_abcmiz_1 A)) = (k13_abcmiz_1 A))  &  ( ((k1_msualg_1 A (k16_abcmiz_1 A)) = (k4_pre_poly (u1_struct_0 A) (k13_abcmiz_1 A) (k12_abcmiz_1 A)))  &  ((k2_msualg_1 A (k16_abcmiz_1 A)) = (k12_abcmiz_1 A)) ) ) ) ) ) ).
tt(t38_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v3_abcmiz_1 A) <=>  (? [B:$i] :  ((m2_abcmiz_1 B A (k12_abcmiz_1 A)) &  (? [C:$i] :  ((m2_abcmiz_1 C A (k13_abcmiz_1 A)) &  ((v4_abcmiz_a B A) & (v4_abcmiz_a C A)) ) ) ) ) ) ) ) ).
tt(t38_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_aff_1 F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [G:$i] :  ( ((v1_aff_1 G A) & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D G) & (r2_hidden E G)) ) )  =>  ( (B = C)  |  ( (D = E)  |  ((r3_aff_1 A F G) <=> (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B C) &  ((r2_hidden B D) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C E) &  ((r1_tarski D E) & (v1_aff_4 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ( (C = (k6_afinsq_1 A B))  <=>  ( ((k1_afinsq_1 C) = 2)  &  ( ((k1_funct_1 C k6_numbers) = A)  &  ((k1_funct_1 C 1) = B) ) ) ) ) ) ) ) ).
tt(t38_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k6_afinsq_2 A (k6_afinsq_1 C D) B) = (k5_binop_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t38_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k14_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k14_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k14_afproj A))) =>  (~  ((r1_incsp_1 (k14_afproj A) B D) &  ((r1_incsp_1 (k14_afproj A) B E) &  ((r1_incsp_1 (k14_afproj A) C D) &  ((r1_incsp_1 (k14_afproj A) C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_afvect0 A B (k1_afvect0 A C D)) = (k1_afvect0 A C (k1_afvect0 A B D)))  <=>  (~  ( (~  (B = C) )  &  ( (~ (r1_afvect0 A B C))  &  (~ (r1_afvect0 A C (k1_afvect0 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  (! [D:$i] :  ((m1_algspec1 D (k1_algspec1 (u4_struct_0 A) C)) =>  ((u2_msualg_1 (k2_algspec1 A B C)) = (k3_relat_1 D (k3_relat_1 (u2_msualg_1 A) (k1_algspec1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t38_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_funct_1 (k1_partfun1 A B (k11_algstr_4 B 1) (u1_struct_0 (k14_algstr_4 B)) C (k16_algstr_4 B 1))) &  ((v1_funct_2 (k1_partfun1 A B (k11_algstr_4 B 1) (u1_struct_0 (k14_algstr_4 B)) C (k16_algstr_4 B 1)) A (u1_struct_0 (k14_algstr_4 B))) & (m1_subset_1 (k1_partfun1 A B (k11_algstr_4 B 1) (u1_struct_0 (k14_algstr_4 B)) C (k16_algstr_4 B 1)) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k14_algstr_4 B)))))) ) ) ) ) ) ) ) ).
tt(t38_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 A D C)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_altcat_1 B E F)) =>  (! [J:$i] :  ((m1_subset_1 J (k1_altcat_1 B F E)) =>  ( ( (E = C)  &  ( (F = D)  &  ( (G = I)  &  (H = J) ) ) )  =>  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  ( ((k1_altcat_1 B F E) = k1_xboole_0)  |  ( ((r1_altcat_3 A C D G H) => (r1_altcat_3 B E F I J))  &  ( ((r1_altcat_3 B E F I J) => (r1_altcat_3 A C D G H))  &  ( ((r1_altcat_3 A D C H G) => (r1_altcat_3 B F E J I))  &  ((r1_altcat_3 B F E J I) => (r1_altcat_3 A D C H G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  ( ( (~ (v7_struct_0 (k3_analmetr A)))  &  ((v1_diraf (k3_analmetr A)) &  ((v2_diraf (k3_analmetr A)) & (l1_analoaf (k3_analmetr A))) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) ) ) ) ) ).
tt(t38_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (F = G) )  & (r1_analort A B C F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A B))) =>  (! [D:$i] :  (~  ((r2_hidden D (k10_xtuple_0 C)) &  (D = (k1_funct_1 (k2_pua2mss1 A B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k78_aofa_i00 A B D E F G)) D) = 1) )  &  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k78_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  ( ( (~ (r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k79_aofa_i00 A B D E F G)) D) = 1) )  &  ( ((r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k79_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = D) )  =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k78_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k79_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) => (r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) (k12_armstrng A B) (k10_armstrng A (k11_armstrng A B)))) ) ) ) ).
tt(t38_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((r2_hidden A k4_ordinal1) <=>  ((k7_arytm_3 A) = 1) ) ) ) ).
tt(t38_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) &  ((v6_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v7_asympt_0 A) &  ((r1_xxreal_0 2 C) & (r2_hidden B (k9_asympt_0 A (a_1_3_asympt_0 C)))) )  => (r2_hidden B (k6_asympt_0 A))) ) ) ) ) ) ) ).
tt(t38_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r2_hidden B k6_asympt_1) =>  ((k1_seq_1 A B) = B) )  &  ( (~ (r2_hidden B k6_asympt_1))  =>  ((k1_seq_1 A B) = (k5_series_1 B 2)) ) ) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((r2_hidden (k3_asympt_1 1) (k11_asympt_0 B k6_asympt_1)) &  ( (~ (r2_hidden (k3_asympt_1 1) (k8_asympt_0 B)))  &  ((r2_hidden (k12_asympt_0 B 2) (k6_asympt_0 B)) &  ((v6_asympt_0 (k3_asympt_1 1)) &  (~ (v6_asympt_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_partfun1 (k3_tarski (k10_xtuple_0 (k12_bagorder A))) (k5_finsub_1 (u1_struct_0 A))) &  ((v1_relat_2 (k3_tarski (k10_xtuple_0 (k12_bagorder A)))) &  ((v4_relat_2 (k3_tarski (k10_xtuple_0 (k12_bagorder A)))) &  ((v8_relat_2 (k3_tarski (k10_xtuple_0 (k12_bagorder A)))) & (m1_subset_1 (k3_tarski (k10_xtuple_0 (k12_bagorder A))) (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 (u1_struct_0 A)) (k5_finsub_1 (u1_struct_0 A)))))) ) ) ) ) ) ).
tt(t38_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k4_bcialg_1 A)) =>  ((k1_bcialg_1 A B C) = B) ) ) ) ) ) ) ).
tt(t38_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m4_bcialg_2 C A B) => (r1_tarski (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) C (k4_struct_0 A)) B)) ) ) ) ) ) ).
tt(t38_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C B))) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t38_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B (k1_bcialg_4 A B C)) & (r1_bcialg_1 A C (k1_bcialg_4 A B C))) ) ) ) ) ) ) ).
tt(t38_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=> (m1_bcialg_5 A k6_numbers k6_numbers k6_numbers k6_numbers)) ) ) ).
tt(t38_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ((v3_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  (D = (k2_funct_1 C)) )  => (v3_funct_2 D (u1_struct_0 A) (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t38_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) ) ) ) ) ).
tt(t38_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  & (r1_xxreal_0 (k4_bhsp_1 A B C) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k4_bhsp_1 A B C) k6_numbers))  &  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t38_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k3_bhsp_2 A (k5_normsp_1 A D C) (k1_rlvect_1 A B C))) &  ((k2_seq_2 (k3_bhsp_2 A (k5_normsp_1 A D C) (k1_rlvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_3 B A) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  (B = (k1_valued_0 (u1_struct_0 A) C D)) ) ) )  | (v1_bhsp_3 C A)) ) ) ) ) ) ) ) ).
tt(t38_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k3_bhsp_4 A B C)) (k6_series_1 (k2_bhsp_2 A B) C))) ) ) ) ) ) ).
tt(t38_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear J A B C) &  ((v2_bilinear J A B C) &  ((v3_bilinear J A B C) &  ((v4_bilinear J A B C) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J (k1_algstr_0 B D (k4_vectsp_1 A B H E)) (k1_algstr_0 C F (k4_vectsp_1 A C I G))) = (k1_algstr_0 A (k1_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J D F) (k6_algstr_0 A I (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J D G))) (k1_algstr_0 A (k6_algstr_0 A H (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J E F)) (k6_algstr_0 A H (k6_algstr_0 A I (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J E G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_binari_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ( ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) A) &  ((r1_xxreal_0 A (k21_binop_2 (k5_series_1 2 (k7_nat_d C 1)) 1)) &  ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) B) &  ((r1_xxreal_0 B (k21_binop_2 (k5_series_1 2 (k7_nat_d C 1)) 1)) &  ((r1_xxreal_0 (k19_binop_2 (k5_series_1 2 (k7_nat_d C 1))) (k20_binop_2 A B)) & (r1_xxreal_0 (k20_binop_2 A B) (k21_binop_2 (k5_series_1 2 (k7_nat_d C 1)) 1))) ) ) ) )  =>  ( ( (~  ((r1_xxreal_0 k6_numbers A) &  (~ (r1_xxreal_0 k6_numbers B)) ) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 k6_numbers B)) ) )  |  ((k3_binari_2 C (k7_binarith C (k2_binari_4 C A) (k2_binari_4 C B))) = (k20_binop_2 A B)) ) ) ) ) ) ) ) ) ).
tt(t38_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k1_boolealg A B C)) (k4_lattices A B C))) ) ) ) ) ) ).
tt(t38_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_borsuk_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_borsuk_1 A B))) =>  (! [D:$i] :  ((m2_connsp_2 D A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B) (k6_domain_1 (u1_struct_0 (k11_borsuk_1 A B)) C))) => (m1_connsp_2 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 (k11_borsuk_1 A B)) (k12_borsuk_1 A B) D) (k11_borsuk_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t38_borsuk_4,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_borsuk_3 (k1_pre_topc (k15_euclid 2) k1_topreal1) (k1_pre_topc (k15_euclid 2) A))) ) ).
tt(t38_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k1_seq_4 B))  =>  ((k2_pre_topc k3_topmetr A) = (k1_seq_4 B)) ) ) ) ) ) ).
tt(t38_borsuk_6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ((v5_pre_topc A (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ((v5_pre_topc B (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) => (m1_subset_1 (k6_xcmplx_0 (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A C) (k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B C)) (u1_struct_0 k5_topmetr))) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) A D) = E)  &  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) B D) = F) )  =>  ((k3_funct_2 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (u1_struct_0 k5_topmetr) C D) = (k6_xcmplx_0 E F)) ) ) ) ) ) ) )  & (v5_pre_topc C (k2_borsuk_1 k5_topmetr k5_topmetr) k5_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k3_numbers)  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v1_connsp_1 B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k1_pre_topc k3_topmetr A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k1_pre_topc k3_topmetr A)))))) )  =>  ((v5_pre_topc C B (k1_pre_topc k3_topmetr A)) => (v3_funct_1 C)) ) ) ) ) ) ) ) ).
tt(t38_bspace,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (? [C:$i] :  ((m2_vectsp_6 C k2_bspace (k7_bspace A) (k9_bspace A)) &  ((k4_vectsp_6 k2_bspace (k7_bspace A) C) = B) ) ) ) ) ) ) ).
tt(t38_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  ( (G = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B I) (k16_funcop_1 C J)) (k16_funcop_1 D K)) (k16_funcop_1 E L)) (k16_funcop_1 F M)) (k16_funcop_1 A H)))  =>  ((k9_xtuple_0 G) = (k4_enumset1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k17_bvfunc_1 A B (k10_eqrel_1 A)) B)) ) ) ) ).
tt(t38_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k9_bvfunc_1 A (k9_bvfunc_1 A B C) C))) ) ) ) ) ) ).
tt(t38_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k6_bvfunc26 A C D)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t38_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_1 A C (k7_bvfunc_2 A D B E)) (k7_bvfunc_2 A (k6_bvfunc_1 A C D) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B F) (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A C E) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E D) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t38_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B C) B) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t38_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r1_bvfunc_1 A B C) & (r1_bvfunc_1 A D E))  => (r1_bvfunc_1 A (k5_bvfunc_1 A B D) (k5_bvfunc_1 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) (k1_calcul_1 (k3_cqc_lang A) D)) &  ( ((k2_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) C)) = (k6_cqc_lang A B))  &  ( ((k6_cqc_lang A (k2_calcul_1 A C)) = (k2_calcul_1 A D))  &  ((r4_calcul_1 A C) & (r4_calcul_1 A D)) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) | (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C)) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t38_card_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_wellord2 A B) & (v1_finset_1 A))  => (v1_finset_1 B)) ) ) ).
tt(t38_card_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_card_1 (k2_nat_1 A B)) = (k1_card_2 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t38_card_3,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((k7_card_3 (k16_funcop_1 B A)) = A) ) ) ) ).
tt(t38_card_5,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski (k1_tarski A) B) =>  ((k3_wellord1 (k1_wellord2 (k2_wellord2 (k1_wellord2 (k1_tarski A)))) (k1_wellord2 (k1_tarski A))) = (k16_funcop_1 k6_numbers A)) ) ) ) ) ).
tt(t38_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) => (v2_card_1 A)) ) ) ).
tt(t38_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finset_1 C)) )  =>  ((r2_hidden A (k10_xtuple_0 B)) => (v1_finset_1 (k2_card_fin C B A))) ) ) ) ) ) ).
tt(t38_card_lar,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  &  ((v1_card_1 A) &  (~ (v4_card_3 A)) ) )  =>  ((v6_card_fil A) =>  ( (~ (v1_xboole_0 (k4_classes1 A)))  & (v1_classes2 (k4_classes1 A))) ) ) ) ).
tt(t38_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ((v8_cat_1 (k5_cat_1 A B C D E F) A B D) =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A C D) = k1_xboole_0)  | (v8_cat_1 F A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k13_cat_2 A B C D E) F) = (k11_cat_2 A B C D F (k4_cat_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v11_cat_1 B A) =>  ( ((k3_graph_1 A (k11_cat_3 A B C)) = B)  &  ((k4_graph_1 A (k11_cat_3 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t38_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_cat_1 A (k2_cat_4 A (k2_cat_4 A B C) D) (k2_cat_4 A B (k2_cat_4 A C D)))) ) ) ) ) ) ) ) ).
tt(t38_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k2_catalan2 (k24_binop_2 2 A) A) = (a_1_5_catalan2 A)) ) ) ) ).
tt(t38_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v1_ideal_1 (k6_cc0sp2 A) (k6_cfuncdom (u1_struct_0 A)))) ) ).
tt(t38_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfcont_1 B A) <=>  ((r1_tarski A (k1_relset_1 k2_numbers B)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((r1_tarski (k2_relset_1 k2_numbers C) A) &  ((v2_comseq_2 C) & (r2_hidden (k3_comseq_2 C) A)) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C B)) &  ((k7_partfun1 k2_numbers B (k3_comseq_2 C)) = (k3_comseq_2 (k8_funct_2 k5_numbers k2_numbers k2_numbers C B))) ) ) ) ) ) ) ) ) ) ).
tt(t38_cfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (~  ((r1_cfdiff_1 B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_partfun1 C k2_numbers) &  ((v2_cfdiff_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) ) )  =>  (~  ( ((k10_funct_2 k2_numbers k2_numbers C k5_complex1) = k5_complex1)  & (r1_cfcont_1 C k5_complex1)) ) ) ) ) ) ) ) ) ) ).
tt(t38_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k1_numbers (k6_rfunct_1 A k1_numbers (k55_valued_1 A k2_numbers B)) (k55_valued_1 A k2_numbers (k2_cfunct_1 A B)))) ) ) ) ).
tt(t38_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) => (r2_hidden k3_cgames_1 (k10_cgames_1 A))) ) ).
tt(t38_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_chain_1 D A) =>  ((r2_hidden (k3_chain_1 A B C) (k4_chain_1 A D k6_numbers)) <=>  ( (B = C)  &  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (r2_hidden (k1_seq_1 B E) (k2_chain_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ( (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ((r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A B) C) => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) )  => (v1_chord B A)) ) ) ) ) ).
tt(t38_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ((m1_circcmb3 E C) =>  ((r2_hidden A (u1_struct_0 E)) =>  ((r2_hidden B (k3_msafree2 E)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 2 C D (k10_finseq_1 A B))) (k2_msafree2 E)) |  ((k2_msafree2 (k6_circcmb3 C E (k4_circcmb3 2 C D (k10_finseq_1 A B)))) = (k2_xboole_0 (k2_msafree2 E) (k1_tarski B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_circcomb,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((k2_msafree2 (k4_circcomb A C B)) = (k6_subset_1 (k10_xtuple_0 C) (k1_tarski B)))  &  ((k3_msafree2 (k4_circcomb A C B)) = (k1_tarski B)) ) ) ) ) ) ).
tt(t38_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  => (r5_circtrm1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)) B B)) ) ) ) ).
tt(t38_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_tarski A (k4_classes1 A))) ) ).
tt(t38_classes2,ax, (! [A:$i] :  ((v2_classes1 A) => (v2_classes1 (k4_classes1 (k1_card_1 A)))) ) ).
tt(t38_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_clopban1 A B)))  &  ((v13_algstr_0 (k14_clopban1 A B)) &  ((v2_rlvect_1 (k14_clopban1 A B)) &  ((v3_rlvect_1 (k14_clopban1 A B)) &  ((v4_rlvect_1 (k14_clopban1 A B)) &  ((v3_normsp_0 (k14_clopban1 A B)) &  ((v4_normsp_0 (k14_clopban1 A B)) &  ((v2_clvect_1 (k14_clopban1 A B)) &  ((v3_clvect_1 (k14_clopban1 A B)) &  ((v4_clvect_1 (k14_clopban1 A B)) &  ((v5_clvect_1 (k14_clopban1 A B)) &  ((v8_clvect_1 (k14_clopban1 A B)) & (l2_clvect_1 (k14_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A C B))  &  ( ((k3_rlvect_1 A (k3_rlvect_1 A B C) D) = (k3_rlvect_1 A B (k3_rlvect_1 A C D)))  &  ( ((k3_rlvect_1 A B (k4_struct_0 A)) = B)  &  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((k3_rlvect_1 A B G) = (k4_struct_0 A)) ) )  &  ( ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D)))  &  ( ((k1_clvect_1 A B k6_complex1) = B)  &  ( ((k1_clvect_1 A B k5_complex1) = (k4_struct_0 A))  &  ( ((k1_clvect_1 A (k4_struct_0 A) E) = (k4_struct_0 A))  &  ( ((k1_clvect_1 A B (k10_complex1 k6_complex1)) = (k4_algstr_0 A B))  &  ( ((k6_algstr_0 A B (k5_struct_0 A)) = B)  &  ( ((k6_algstr_0 A (k5_struct_0 A) B) = B)  &  ( ((k6_algstr_0 A B (k3_rlvect_1 A C D)) = (k3_rlvect_1 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ( ((k6_algstr_0 A (k3_rlvect_1 A C D) B) = (k3_rlvect_1 A (k6_algstr_0 A C B) (k6_algstr_0 A D B)))  &  ( ((k1_clvect_1 A (k6_algstr_0 A B C) E) = (k6_algstr_0 A (k1_clvect_1 A B E) C))  &  ( ((k1_clvect_1 A (k3_rlvect_1 A B C) E) = (k3_rlvect_1 A (k1_clvect_1 A B E) (k1_clvect_1 A C E)))  &  ( ((k1_clvect_1 A B (k8_complex1 E F)) = (k3_rlvect_1 A (k1_clvect_1 A B E) (k1_clvect_1 A B F)))  &  ( ((k1_clvect_1 A B (k9_complex1 E F)) = (k1_clvect_1 A (k1_clvect_1 A B F) E))  &  ( ((k1_clvect_1 A (k6_algstr_0 A B C) (k9_complex1 E F)) = (k6_algstr_0 A (k1_clvect_1 A B E) (k1_clvect_1 A C F)))  &  ( ((k1_clvect_1 A (k6_algstr_0 A B C) E) = (k6_algstr_0 A B (k1_clvect_1 A C E)))  &  ( ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A))  &  ( ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A))  &  ( ((k6_algstr_0 A B (k5_algstr_0 A C D)) = (k5_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ( ((k6_algstr_0 A (k5_algstr_0 A C D) B) = (k5_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B)))  &  ( ((k5_algstr_0 A (k3_rlvect_1 A B C) D) = (k3_rlvect_1 A B (k5_algstr_0 A C D)))  &  ( ((k3_rlvect_1 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A B (k5_algstr_0 A C D)))  &  ( ((k5_algstr_0 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A B (k3_rlvect_1 A C D)))  &  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A (k5_algstr_0 A B D) (k3_rlvect_1 A D C)))  &  ( ((k5_algstr_0 A B C) = (k3_rlvect_1 A (k5_algstr_0 A B D) (k5_algstr_0 A D C)))  &  ( (B = (k3_rlvect_1 A (k5_algstr_0 A B C) C))  &  ( (B = (k5_algstr_0 A C (k5_algstr_0 A C B)))  &  ( ( ((k1_normsp_0 A B) = k6_numbers)  =>  (B = (k4_struct_0 A)) )  &  ( ( (B = (k4_struct_0 A))  =>  ((k1_normsp_0 A B) = k6_numbers) )  &  ( ((k1_normsp_0 A (k1_clvect_1 A B E)) = (k8_real_1 (k17_complex1 E) (k1_normsp_0 A B)))  &  ((r1_xxreal_0 (k1_normsp_0 A (k3_rlvect_1 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C))) &  ((r1_xxreal_0 (k1_normsp_0 A (k6_algstr_0 A B C)) (k8_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C))) &  ( ((k1_normsp_0 A (k5_struct_0 A)) = 1)  & (v3_clopban1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v25_algstr_0 (k7_clopban4 A B) A) &  ( ((k9_algstr_0 A (k7_clopban4 A B)) = (k7_clopban4 A (k4_algstr_0 A B)))  &  ((v25_algstr_0 (k7_clopban4 A (k4_algstr_0 A B)) A) &  ((k9_algstr_0 A (k7_clopban4 A (k4_algstr_0 A B))) = (k7_clopban4 A B)) ) ) ) ) ) ) ) ).
tt(t38_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v9_closure1 B A) & (l1_closure1 B A))  =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B))) =>  ( (! [D:$i] :  ((m1_pboole D (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B))) =>  (! [E:$i] :  ( ((v2_relat_1 E) & (m3_pboole E (u1_struct_0 A) (k1_mboolean (u1_struct_0 A) (u3_msualg_1 A B))))  =>  ( (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 A)) &  ((v1_funct_1 F) & (v1_partfun1 F (u1_struct_0 A))) ) )  =>  ((r1_pboole (u1_struct_0 A) F E) <=>  ((r1_pboole (u1_struct_0 A) F (u1_closure1 A B)) & (r2_pboole (u1_struct_0 A) D F)) ) ) )  => (r6_pboole (u1_struct_0 A) (k2_closure1 (u1_struct_0 A) (u3_msualg_1 A B) C D) (k4_mssubfam (u1_struct_0 A) (u3_msualg_1 A B) E))) ) ) ) )  =>  ((v1_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v2_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v3_closure1 C (u1_struct_0 A) (u3_msualg_1 A B)) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)) (k5_mssubfam (u1_struct_0 A) (u3_msualg_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t38_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  (! [C:$i] :  ((m1_closure2 C (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))))) )  =>  ( ((r2_hidden C (u1_closure2 A B)) &  (! [E:$i] :  ((m1_closure2 E (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) => (r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) D E) (k11_closure2 A B E))) ) )  => (r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) D C) C)) ) ) ) ) ) ) ) ) ).
tt(t38_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) => (r1_struct_0 A (k4_struct_0 B))) ) ) ) ).
tt(t38_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k3_clvect_2 A (k6_clvect_1 A D C) (k1_clvect_1 A B C))) &  ((k2_seq_2 (k3_clvect_2 A (k6_clvect_1 A D C) (k1_clvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k2_clvect_3 A B C)) (k6_series_1 (k2_clvect_2 A B) C))) ) ) ) ) ) ).
tt(t38_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k3_tarski B)))) =>  (~  ( (! [D:$i] :  ((r2_hidden D C) => (v1_finset_1 (k1_xtuple_0 D))) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E G) C))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden (k2_xboole_0 D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E F) C))  =>  (D = E) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v9_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  (C = (k8_cohsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_coh_sp,ax, (! [A:$i] : (r2_hidden (k4_tarski (k1_eqrel_1 A) A) (k16_coh_sp A))) ).
tt(t38_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k4_complex1 A) = k6_numbers)  =>  ((k15_complex1 A) = A) ) ) ) ).
tt(t38_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 A (k9_complex1 B C)) = (k9_complex1 (k15_complex1 B) (k1_complex2 A C))) ) ) ) ) ) ) ).
tt(t38_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld C B) A) = (k3_vectsp_1 k1_complfld C (k3_vectsp_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_compl_sp,ax, (! [A:$i] :  (! [B:$i] :  ((l1_metric_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((r2_hidden D (k2_xboole_0 (k2_zfmisc_1 A (k6_subset_1 (u1_struct_0 B) (k1_tarski C))) (k1_tarski (k4_tarski A C)))) <=>  (? [E:$i] :  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (D = (k4_tarski E F))  &  ( ((r2_hidden E A) &  (~  (F = C) ) )  |  ( (E = A)  &  (F = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 A)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) &  ((v1_afinsq_1 E) &  ((v3_compos_1 E A) & (v4_compos_1 E A)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k8_compos_1 A (k2_compos_2 A (k3_compos_2 A B C) D) E) k6_numbers) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_comptrig (k3_xcmplx_0 A k7_complex1)) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) ).
tt(t38_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((k1_recdef_1 (k5_comput_1 A B) C) = (k1_recdef_1 C B)) ) ) ) ) ) ) ).
tt(t38_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 B) =>  ( (A = k5_complex1)  | (v2_relat_1 (k25_valued_1 k5_numbers k2_numbers B A))) ) ) ) ) ) ).
tt(t38_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k3_comseq_2 B) = k5_complex1)  | (v2_comseq_2 (k51_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ) ).
tt(t38_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k3_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers A D))  &  ((k4_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers B D)) ) ) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  <=> (v2_comseq_2 C)) ) ) ) ) ) ) ) ).
tt(t38_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k1_binop_1 (k9_conlat_1 A) B (k5_conlat_1 A)) = B) ) ) ) ) ).
tt(t38_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k1_connsp_1 A B))) ) ) ) ).
tt(t38_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_convex1 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A (k1_convex1 A B D) (k1_convex1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t38_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((k3_rlvect_1 (k15_convex4 A) (k1_rlvect_2 (k15_convex4 A) B) (k1_rlvect_2 (k15_convex4 A) C)) = (k5_convex4 A B C)) ) ) ) ) ) ) ).
tt(t38_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C D E F) (k15_cqc_sim1 A B)) => (r1_tarski (k24_qc_lang1 A C) (k2_xboole_0 (k24_qc_lang1 A B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((v1_cqc_the1 B A) => (r1_tarski (k4_cqc_the1 A) B)) ) ) ) ) ).
tt(t38_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k11_cqc_lang A D (k7_cqc_lang A B C)) A) <=> (v2_cqc_the1 (k7_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t38_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r6_cqc_the3 A B C) => (r5_cqc_the3 A B C)) ) ) ) ) ) ) ).
tt(t38_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) => (r1_csspace A (k4_algstr_0 A B) (k4_algstr_0 A C))) ) ) ) ) ) ) ).
tt(t38_descip_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D (k4_finseq_2 B k6_margrel1) (k4_finseq_2 C (k4_finseq_2 B k6_margrel1))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) (k4_finseq_2 B k6_margrel1)) (k4_finseq_2 A k6_margrel1))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) &  ((v3_funct_2 F (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1) (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1))))) ) )  =>  (! [G:$i] :  ((m2_finseq_2 G k6_margrel1 (k4_finseq_2 (k4_nat_1 2 A) k6_margrel1)) =>  ((k40_descip_1 A B C (k1_descip_1 (k4_finseq_2 B k6_margrel1) C D) E F (k40_descip_1 A B C D E F G)) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((r5_waybel_1 A B) &  ((v4_dickson A) & (v3_dickson A)) )  =>  ((v3_dickson B) & (v4_dickson B)) ) ) ) ) ) ).
tt(t38_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden A (k1_relset_1 k1_numbers C)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers C)))  =>  ((k1_seq_1 (k4_diff_1 C B) A) = (k9_real_1 (k1_seq_1 C A) (k1_seq_1 C (k9_real_1 A B)))) ) ) ) ) ) ) ) ).
tt(t38_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 A D))  &  ( (~  (D = k6_numbers) )  &  (~  ((k7_real_1 D B) = k6_numbers) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k3_diff_1 C B) D) = (k10_real_1 (k1_real_1 (k8_real_1 A B)) (k8_real_1 (k7_real_1 D B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t38_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k7_square_1 F)) ) )  & (r2_zfmisc_1 A B C D))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ((r1_xxreal_0 D k6_numbers) |  ((k11_diff_1 E A B C D) = (k10_real_1 (k7_real_1 (k7_real_1 (k7_real_1 (k7_square_1 A) (k7_square_1 B)) (k7_square_1 C)) (k7_square_1 D)) (k8_real_1 (k8_real_1 (k8_real_1 (k8_real_1 (k8_real_1 (k7_real_1 (k7_square_1 A) (k7_square_1 B)) (k7_real_1 (k7_square_1 A) (k7_square_1 C))) (k7_real_1 (k7_square_1 A) (k7_square_1 D))) (k7_real_1 (k7_square_1 B) (k7_square_1 C))) (k7_real_1 (k7_square_1 B) (k7_square_1 D))) (k7_real_1 (k7_square_1 C) (k7_square_1 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k4_diff_1 (k3_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B))) ) ) ) ) ) ) ).
tt(t38_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((r3_waybel_4 A (k2_struct_0 A) C) &  ( (C = B)  | (r2_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t38_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_analoaf B))  =>  ( (B = (k2_diraf A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 B)) =>  ( ( (C = G)  &  ( (D = H)  &  ( (E = I)  &  (F = J) ) ) )  =>  ((r2_analoaf B G H I J) <=> (r2_diraf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ec_pf_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 B))) =>  ( ((k4_nat_d A 2) = 1)  =>  ((k2_ec_pf_1 B (k2_binom (k9_int_3 B) C A)) = (k2_ec_pf_1 B C)) ) ) ) ) ) ) ) ).
tt(t38_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( (~  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k7_ec_pf_2 A D)) = k6_numbers) )  =>  ( ((k7_ec_pf_2 A D) = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers (k8_group_1 (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) (k11_algstr_0 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D))) (k8_group_1 (k9_int_3 A) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) (k11_algstr_0 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D))) 1))  &  (~  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  ( (~  ((k2_cat_1 (k11_ens_1 A) B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k11_ens_1 A) B C) =>  ((v1_ens_1 (k15_ens_1 A D) A) => (v8_cat_1 D (k11_ens_1 A) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t38_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 k1_numbers)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrprob k1_numbers B 1) = (k1_matrprob k1_numbers A 1))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ((k1_matrprob k1_numbers B (k2_nat_1 C 1)) = (k8_finseq_1 k1_numbers (k1_matrprob k1_numbers B C) (k1_matrprob k1_numbers A (k2_nat_1 C 1)))) ) ) ) ) ) )  =>  ((k5_matrprob A) = (k18_rvsum_1 (k1_matrprob k1_numbers B (k3_finseq_1 A)))) ) ) ) ) ) ).
tt(t38_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_enumset1 A A A B C) = (k1_enumset1 A B C)) ) ) ) ).
tt(t38_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k11_eqrel_1 A D B) = (k11_eqrel_1 A D C)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t38_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 B) (k4_equation B)) =>  (! [D:$i] :  ((m1_pralg_2 D A B) =>  ( (! [E:$i] :  (~  ((r2_hidden E A) &  (! [F:$i] :  ((l3_msualg_1 F B) =>  (~  ( (F = (k1_funct_1 D E))  & (r2_equation B F C)) ) ) ) ) ) )  => (r2_equation B (k14_pralg_2 A B D) C)) ) ) ) ) ) ) ) ).
tt(t38_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 k6_numbers (k12_euclid B))) ) ) ) ).
tt(t38_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (~  ((k4_euclid_3 C B A) = k6_numbers) )  =>  ((k4_euclid_3 C B A) = (k9_real_1 (k8_real_1 2 k32_sin_cos) (k4_euclid_3 A B C))) ) ) ) ) ) ) ) ).
tt(t38_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k18_complex1 (k23_rvsum_1 B C)) (k8_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t38_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ((r2_hidden A (k5_jgraph_6 F G H)) &  ((r2_hidden B (k5_jgraph_6 F G H)) &  ((r2_hidden C (k5_jgraph_6 F G H)) &  ((r2_hidden D (k5_jgraph_6 F G H)) &  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) A C)) & (r2_hidden E (k1_rltopsp1 (k15_euclid 2) B D))) ) ) ) )  =>  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A E)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E C))) = (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B E)) (k12_euclid (k5_algstr_0 (k15_euclid 2) E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((k2_binop_1 (k1_euclid A) (k1_euclid A) k1_numbers (k6_real_ns1 A) B C) = (k23_rvsum_1 B C)) ) ) ) ) ) ) ).
tt(t38_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k9_euclid 3 B A) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k11_binop_2 A (k1_seq_1 B 1))) (k9_euclid 3 k3_euclid_8 (k11_binop_2 A (k1_seq_1 B 2)))) (k9_euclid 3 k4_euclid_8 (k11_binop_2 A (k1_seq_1 B 3))))) ) ) ) ) ).
tt(t38_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k4_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C)) = (k5_algstr_0 (k15_euclid A) (k4_algstr_0 (k15_euclid A) B) C)) ) ) ) ) ) ) ).
tt(t38_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ((r3_euclidlp A (k8_euclid A B C) (k8_euclid A D C)) &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  => (m1_exchsort A A)) ) ).
tt(t38_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (v1_relat_1 (k3_msafree2 (k5_circcomb A B)))) ) ) ).
tt(t38_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A)) =>  ((v2_fcont_1 (k32_valued_1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A))) & (v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k56_valued_1 k1_numbers k1_numbers B) A))) ) ) ) ) ).
tt(t38_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))))) ) ) ) ) ) ) ) ).
tt(t38_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) B) = (k10_real_1 2 (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t38_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) &  ((r2_fdiff_1 A (k2_subset_1 k1_numbers)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_fdiff_1 A B))) ) ) ) )  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers))) & (v2_funct_1 A)) ) ) ) ).
tt(t38_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k19_sin_cos))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k7_real_1 (k8_real_1 A E) B)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k19_sin_cos) C) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k19_sin_cos) C) E) = (k1_real_1 (k8_real_1 A (k1_seq_1 k16_sin_cos (k7_real_1 (k8_real_1 A E) B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k1_real_1 (k10_real_1 1 2))))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = (k8_real_1 2 C)) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k1_real_1 (k10_real_1 1 2))) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k1_real_1 (k10_real_1 1 2))) A) C) = (k18_sin_cos (k8_real_1 2 C))) ) ) ) ) ) ) ) ) ) ).
tt(t38_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k9_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t38_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) B) = (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t38_fib_num2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_xxreal_0 B A) =>  ((k6_xcmplx_0 (k1_pepin (k1_pre_ff A)) (k4_nat_1 (k1_pre_ff (k2_nat_1 A B)) (k1_pre_ff (k7_nat_d A B)))) = (k3_xcmplx_0 (k1_newton (k4_xcmplx_0 1) (k7_nat_d A B)) (k1_pepin (k1_pre_ff B)))) ) ) ) ) ) ).
tt(t38_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k3_fib_num3 2 1 A) = (k1_fib_num3 A)) ) ) ).
tt(t38_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 2))  =>  ((k1_fib_num3 A) = (k1_int_1 (k3_xcmplx_0 (k13_complex1 1 k1_fib_num) (k2_xcmplx_0 (k1_fib_num3 (k2_xcmplx_0 A 1)) (k13_complex1 1 2))))) ) ) ) ).
tt(t38_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 D (k3_finseq_1 B)) =>  ((r1_xxreal_0 D k6_numbers) | (r1_xxreal_0 (k8_finseq_8 A B C D) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t38_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (k5_filter_0 A B C)) ) ) ) ) ) ) ).
tt(t38_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v11_lattices B) & (l3_lattices B)) ) ) )  <=>  ( (~ (v2_struct_0 (k7_filter_1 A B)))  &  ((v10_lattices (k7_filter_1 A B)) &  ((v11_lattices (k7_filter_1 A B)) & (l3_lattices (k7_filter_1 A B))) ) ) ) ) ) ) ) ).
tt(t38_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_tarski C D) => (r1_tarski (k7_filter_2 A C) (k7_filter_2 A D)))  & (r1_tarski (k7_filter_2 A (k7_filter_2 A B)) (k7_filter_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t38_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k9_finseq_1 A))  <=>  ( ((k4_finseq_1 B) = (k2_finseq_1 1))  &  ((k10_xtuple_0 B) = (k1_tarski A)) ) ) ) ) ) ).
tt(t38_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))))) )  =>  ((r1_xxreal_0 B (k3_finseq_1 C)) =>  ( ( (B = k6_numbers)  &  (~  (A = k6_numbers) ) )  |  ((v1_relat_1 (k3_relat_1 D C)) &  ((v1_funct_1 (k3_relat_1 D C)) & (v1_finseq_1 (k3_relat_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ((k3_finseq_1 A) = (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C)))  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 A D) = (k1_funct_1 B D)) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 A (k2_nat_1 (k3_finseq_1 B) D)) = (k1_funct_1 C D)) ) ) ) ) )  =>  (A = (k7_finseq_1 B C)) ) ) ) ) ) ) ) ).
tt(t38_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r1_xboole_0 (k10_xtuple_0 (k5_finseq_4 A B)) (k1_tarski B))) ) ) ) ).
tt(t38_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k7_partfun1 A C (k4_finseq_4 C B)) = B) ) ) ) ) ) ) ) ).
tt(t38_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_finseq_4 B A) =>  ((k3_finseq_5 (k5_finseq_4 B A)) = (k6_finseq_4 (k3_finseq_5 B) A)) ) ) ) ) ).
tt(t38_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C C) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B B) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  ((k3_funct_2 C B F (k5_binop_1 C G I J)) = (k5_binop_1 B H (k3_funct_2 C B F I) (k3_funct_2 C B F J))) ) ) ) )  => (r2_funct_2 A B (k1_partfun1 A C C B (k10_funcop_1 C A G D E) F) (k10_funcop_1 B A H (k3_funct_2 C B F D) (k1_partfun1 A C C B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k10_fintopo2 A (k3_subset_1 (u1_struct_0 A) B))) = (k9_fintopo2 A B)) ) ) ) ) ).
tt(t38_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k9_fintopo3 A B (k2_nat_1 C 1)) = (k1_fintopo3 A (k9_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t38_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_fintopo6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v4_fin_topo C A) <=> (v4_fin_topo D B)) ) ) ) ) ) ) ) ) ) ).
tt(t38_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k4_subset_1 (k3_catalan2 A) (k7_flang_1 A B D) (k7_flang_1 A C D)) (k7_flang_1 A (k4_subset_1 (k3_catalan2 A) B C) D))) ) ) ) ) ) ) ).
tt(t38_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_flang_2 A B (k2_xcmplx_0 C 1) (k2_xcmplx_0 D 1)) = (k6_flang_1 A (k1_flang_2 A B C D) B)) ) ) ) ) ) ) ) ).
tt(t38_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_flang_3 B C D) = (k1_tarski A))  =>  (A = (k2_flang_1 B)) ) ) ) ) ) ) ) ).
tt(t38_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k7_relset_1 (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A) (k11_monoid_0 A) (k6_partfun1 (k4_finseq_2 1 A))) = (a_1_2_fomodel0 A)) ) ) ).
tt(t38_frechet2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k5_numbers B C) = (k2_nat_1 C A)) ) ) ) ) ) ) ).
tt(t38_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D B C)) )  =>  (~  ( ((k2_nat_1 A 1) = (k5_card_1 (u1_struct_0 D)))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 E A) & (v4_fsm_1 (k7_fsm_1 B C D E) B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_fsm_3 B A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  ((k6_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B) = (k6_fsm_3 A (k9_flang_1 A) (k4_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B))) ) ) ) ) ).
tt(t38_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) (k48_gfacirc1 A B C)) = (k9_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I))))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) A) = G)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) B) = H)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) C) = I)  &  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) D) = J)  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 2) E) = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G B) =>  ((k3_funct_2 B A F G) = (k5_binop_1 A C (k3_funct_2 B A D G) (k3_funct_2 B A E G))) ) )  => (r2_funct_2 B A F (k6_funcop_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) &  ( ((k9_xtuple_0 A) = (k10_xtuple_0 B))  &  ( ((k10_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden D (k9_xtuple_0 B)))  =>  ( ((k1_funct_1 A C) = D)  <=>  ((k1_funct_1 B D) = C) ) ) ) ) ) ) )  =>  (B = (k2_funct_1 A)) ) ) ) ) ) ).
tt(t38_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (~  (B = k1_xboole_0) )  =>  (! [E:$i] :  ((r2_hidden E (k8_relset_1 A B D C)) <=>  ((r2_hidden E A) & (r2_hidden (k1_funct_1 D E) C)) ) ) ) ) ) ) ) ) ).
tt(t38_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) &  ((r1_tarski C B) &  ((k4_funct_3 A B) = (k4_funct_3 C B)) ) )  =>  (A = C) ) ) ) ) ).
tt(t38_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((k1_funct_4 B C) = C) ) ) ) ) ) ).
tt(t38_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  ( (D = (k1_funct_1 C A))  & (r2_hidden B (k9_xtuple_0 D))) )  =>  ((r2_hidden (k4_tarski A B) (k9_xtuple_0 (k2_funct_5 C))) &  ( ((k1_binop_1 (k2_funct_5 C) A B) = (k1_funct_1 D B))  & (r2_hidden (k1_funct_1 D B) (k10_xtuple_0 (k2_funct_5 C)))) ) ) ) ) ) ) ) ) ).
tt(t38_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k10_xtuple_0 (k7_funct_6 A)) = (k4_card_3 (k3_funct_6 A))) ) ) ).
tt(t38_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k3_funct_7 A B E (k7_partfun1 A B E)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k55_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t38_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ( ((v21_functor0 C A B) & (v10_functor0 C A B))  => (v10_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t38_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C B A) & (m2_functor0 C B A))  =>  (! [D:$i] :  ( ((v15_functor0 D B A) & (m2_functor0 D B A))  =>  (! [E:$i] :  ((m1_functor3 E B A C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r1_functor3 B A C D) =>  ((k2_functor2 B A D C (k8_functor3 B A C D E) F) = (k1_altcat_3 A (k3_functor0 B A C F) (k3_functor0 B A D F) (k2_functor2 B A C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k3_fuzzy_1 A (k2_fuzzy_1 A B C)) (k3_fuzzy_1 A B))) ) ) ) ) ) ).
tt(t38_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_funct_2 A k1_numbers (k3_fuzzy_2 A B (k4_fuzzy_1 A)) B) & (r2_funct_2 A k1_numbers (k3_fuzzy_2 A B (k5_fuzzy_1 A)) (k5_fuzzy_1 A))) ) ) ) ) ).
tt(t38_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ( ((k3_funct_2 (u1_struct_0 A) k7_numbers C B) = k1_xxreal_0)  <=>  ((k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B) = k1_xxreal_0) ) ) ) ) ) ) ) ) ).
tt(t38_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v1_algstr_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B C (k6_fvsum_1 A B D)) = (k4_fvsum_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t38_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~  ( (~ (v1_xboole_0 (k32_gate_1 A B C D E F G H)))  &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) ) ) )  &  (~  ( (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( (~ (v1_xboole_0 C))  &  ( (~ (v1_xboole_0 D))  &  ( (~ (v1_xboole_0 E))  &  ( (~ (v1_xboole_0 F))  &  ( (~ (v1_xboole_0 G))  &  (~ (v1_xboole_0 H)) ) ) ) ) ) ) ) )  & (v1_xboole_0 (k32_gate_1 A B C D E F G H))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (E = (k5_gcd_1 A B C D))  =>  ( (E = (k4_struct_0 A))  |  ((k5_gcd_1 A B (k1_gcd_1 A C E) (k1_gcd_1 A D E)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v2_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) ) ) )  =>  (! [F:$i] :  ((m1_genealg1 F E) =>  (! [G:$i] :  ((m1_genealg1 G E) =>  ( ((k10_genealg1 E F G A A B C) = (k8_genealg1 E F G B C))  &  ( ((k10_genealg1 E F G A D A C) = (k8_genealg1 E F G D C))  &  ( ((k10_genealg1 E F G A D B A) = (k8_genealg1 E F G D B))  &  ( ((k10_genealg1 E F G A D D C) = (k8_genealg1 E F G A C))  &  ( ((k10_genealg1 E F G A D B D) = (k8_genealg1 E F G A B))  &  ((k10_genealg1 E F G A D B B) = (k8_genealg1 E F G A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_geomtrap A B C D E F I) &  ((r2_geomtrap A B C D E G J) &  ((r2_geomtrap A B C D E H K) &  (H = (k1_geomtrap A F G)) ) ) )  =>  ( (D = E)  |  (K = (k1_geomtrap A I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  ((r2_hidden A (k2_msafree2 (k13_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k13_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k13_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k23_glib_000 A B D) (k23_glib_000 A C E))) ) ) ) ) ) ) ).
tt(t38_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 E (k3_finseq_1 B))) )  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k7_glib_001 A (k8_glib_001 A B C D) (k8_glib_001 A B D E)) (k8_glib_001 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (~  ((v5_glib_002 B A) & (v4_glib_000 A)) ) ) ) ) ) ).
tt(t38_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k6_glib_000 A)) =>  ((k7_glib_003 (k13_glib_003 A B C)) = (k1_funct_4 (k7_glib_003 A) (k16_funcop_1 B C))) ) ) ) ) ) ).
tt(t38_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_glib_000 C A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B))) => (v3_glib_002 C)) ) ) ) ) ) ).
tt(t38_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r2_hidden (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid (k1_real_1 1) 1)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers (k1_matrix_1 A))))) ) ).
tt(t38_goboard7,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) )  =>  ((r1_xxreal_0 B 1) |  (B = (k3_finseq_1 A)) ) ) ) ) ) ) ).
tt(t38_goboard8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 B)))  => (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k4_goboard5 B A)) (k3_topreal1 2 B))) ) ) ) ) ).
tt(t38_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k5_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r2_jordan2c 2 (k3_topreal1 2 A) B) =>  (B = (k2_goboard9 A)) ) ) ) ) ) ).
tt(t38_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v4_card_3 A) &  ((v1_finset_1 (k6_goedelcp A B)) & (r7_calcul_1 A B C)) )  => (r1_henmodel A B C)) ) ) ) ) ) ) ).
tt(t38_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_graph_1 B A) =>  (~  ((r2_graph_2 A B) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (~  ( (~  (C = D) )  &  ((r1_graph_2 A C B) &  ((r1_graph_2 A D B) &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ((r1_graph_2 A E B) &  ( (~  (E = C) )  &  (~  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v2_funct_1 D) & (m2_graph_1 D A))  =>  ((v2_funct_1 D) & (m2_graph_1 D (k8_graph_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t38_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  => (r1_tarski (k6_graph_5 A B) (k7_graph_5 A))) ) ) ) ).
tt(t38_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ( (~  ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C) A) = k1_xboole_0) )  => (r2_xboole_0 (k13_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) C) A) (k13_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C) A))) ) ) ) ) ) ) ).
tt(t38_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((u1_struct_0 (k27_grcat_1 A)) = (k26_grcat_1 A)) ) ) ).
tt(t38_gr_cy_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v8_struct_0 B) & (m1_group_2 B (k1_uniroots A)))  =>  ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v1_gr_cy_1 B) & (l3_algstr_0 B)) ) ) ) ) ) ) ) ).
tt(t38_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 G A C) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ( ((r2_hidden F E) &  ((r2_hidden G E) &  ((r3_pre_poly A (k3_termord A B C G) (k3_termord A B C F)) & (r2_groeb_1 A B C E D)) ) )  =>  ( (F = G)  | (r2_groeb_1 A B C (k7_subset_1 (u1_struct_0 (k11_polynom1 A C)) E (k1_groeb_1 A C F)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r1_rewrite1 (k3_polyred A B C E) D (k7_polynom1 A C)) => (r6_groeb_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  => (r1_termord A B (k3_termord A B C (k6_groeb_3 A B C D (k2_nat_1 E 1))) (k3_termord A B C (k6_groeb_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k1_group_11 A (k2_group_11 A (k1_group_11 A B C) C) C) = (k1_group_11 A B C)) ) ) ) ) ) ) ).
tt(t38_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k6_algstr_0 B C D) = (k6_algstr_0 B D C))  =>  ((k5_group_1 B A (k6_algstr_0 B C D)) = (k6_algstr_0 B (k5_group_1 B A C) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ) ).
tt(t38_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((k4_group_2 A B C) = (k5_group_2 A B C)) ) ) ) ) ) ) ) ).
tt(t38_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_group_3 A (k6_domain_1 (u1_struct_0 A) B) (k7_domain_1 (u1_struct_0 A) C D)) = (k7_domain_1 (u1_struct_0 A) (k2_group_3 A B C) (k2_group_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t38_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  ( (? [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D C))  & (v2_group_4 D C)) )  =>  ((r1_struct_0 (k6_group_4 C) B) <=>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D C))  =>  ((v2_group_4 D C) => (r1_struct_0 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k2_group_5 A B C))) ) ) ) ) ) ) ) ) ).
tt(t38_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v1_group_6 (k6_partfun1 (u1_struct_0 A)) A A)) ) ).
tt(t38_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)))) &  ((v1_group_6 B A (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))))))) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))) B C) = (k4_group_7 A C)) ) )  => (v3_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_group_7 (k1_tarski 1) (k9_finseq_1 A))))) ) ) ) ) ).
tt(t38_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ((m1_group_9 C A D) => (m1_group_9 (k19_group_9 A B C E) A (k19_group_9 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t38_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))))  =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) &  ((v2_compts_1 C (k3_pcomps_1 A)) & (v2_compts_1 D (k3_pcomps_1 A))) )  => (r1_xxreal_0 (k1_hausdorf A B D) (k7_real_1 (k1_hausdorf A B C) (k1_hausdorf A C D)))) ) ) ) ) ) ) ) ) ).
tt(t38_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  ( ( ((k4_glib_001 A B) = (k3_glib_001 A C))  &  ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A B) (k13_glib_001 A C)) = (k1_tarski (k4_glib_001 A B))) )  => (v5_glib_001 (k7_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(t38_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k1_complfld)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k1_complfld)) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear I k1_complfld A B) &  ((v2_bilinear I k1_complfld A B) &  ((v4_bilinear I k1_complfld A B) &  ((v2_hermitan I A B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I (k5_algstr_0 A C (k4_vectsp_1 k1_complfld A G D)) (k5_algstr_0 B E (k4_vectsp_1 k1_complfld B H F))) = (k5_algstr_0 k1_complfld (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I C E) (k8_group_1 k1_complfld (k2_complfld H) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I C F))) (k5_algstr_0 k1_complfld (k8_group_1 k1_complfld G (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I D E)) (k8_group_1 k1_complfld G (k8_group_1 k1_complfld (k2_complfld H) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) I D F)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  ( ((r3_orders_2 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) B C) &  (B = (k1_tarski k1_xboole_0)) )  =>  (C = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(t38_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  => (r1_taylor_1 (k1_taylor_1 A) A B)) ) ) ) ).
tt(t38_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k4_hilbert1 C A) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(t38_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_hilbert3 C A) (k3_hilbert3 C B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B))))) )  =>  ((k1_funct_1 (k2_funct_2 (k3_hilbert3 C (k3_hilbert1 A B)) (k5_hilbert3 C D (k3_hilbert1 A B))) E) = (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C B) (k5_hilbert3 C D A) (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C B) (k3_hilbert3 C B) (k3_hilbert3 C B) E (k2_funct_2 (k3_hilbert3 C B) (k5_hilbert3 C D B))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  => (v1_hurwitz (k3_polynom5 k1_complfld (k10_polynom3 k1_complfld) A))) ) ) ).
tt(t38_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v1_relat_1 (k17_idea_1 D B A C)) &  ((v1_funct_1 (k17_idea_1 D B A C)) &  ((v1_finseq_1 (k17_idea_1 D B A C)) & (v1_funct_7 (k17_idea_1 D B A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m2_ideal_1 D A C) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ((m2_finseq_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (~  ((r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) F C) E) &  ((r2_ideal_1 A C D G) &  (! [H:$i] :  ((m2_ideal_1 H B E) =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 H))  &  (! [I:$i] :  ((r2_hidden I (k1_relset_1 k5_numbers H)) =>  ((k1_funct_1 H I) = (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) G I))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) G I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ((r2_incsp_1 A E (k2_incsp_1 A B C D)) =>  ((v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A) | (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m5_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A) (k7_isocat_1 A)) =>  (! [C:$i] :  ((m4_index_1 C (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) B) =>  (! [D:$i] :  ((m5_index_1 D (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) (u1_cat_1 C) (k7_isocat_1 C)) =>  (! [E:$i] :  ((m4_index_1 E (u1_struct_0 C) (u4_struct_0 C) (u1_graph_1 C) (u2_graph_1 C) D) =>  (! [F:$i] :  ((m5_index_1 F (u1_struct_0 E) (u4_struct_0 E) (u1_graph_1 E) (u2_graph_1 E) (u1_cat_1 E) (k7_isocat_1 E)) =>  ((k16_index_1 A C B (k16_index_1 C E D F)) = (k16_index_1 A E (k16_index_1 A C B D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 B A D E) =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ( (F = (k1_instalg1 B A C D E))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((r1_rewrite1 (k3_msualg_6 B) G H) =>  (! [I:$i] :  ((m2_msualg_6 I B F G H) => (m2_msualg_6 I A C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D G) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_int_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k1_relset_1 k5_numbers A)) & (r2_hidden D (k1_relset_1 k5_numbers A)))  =>  ( (C = D)  |  ((k6_nat_d (k1_recdef_1 A C) (k1_recdef_1 A D)) = 1) ) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_nat_d (k1_recdef_1 A C) B)) ) ) )  => (r1_nat_d (k3_wsierp_1 A) B)) ) ) ) ) ).
tt(t38_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( ((k4_nat_d A 4) = 3)  & (r1_int_5 (k4_xcmplx_0 1) A)) ) ) ) ) ).
tt(t38_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k2_xcmplx_0 A B)) =>  ((r1_xxreal_0 (k19_rvsum_1 C) (k2_xcmplx_0 A B)) |  ((k2_int_6 (k4_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) C) = (k2_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ).
tt(t38_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k16_sin_cos D)))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t38_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C F) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k12_binop_2 A (k7_square_1 (k10_binop_2 1 (k5_square_1 (k9_binop_2 (k11_binop_2 A G) B))))))  &  ( ((k1_seq_1 E G) = (k9_binop_2 (k11_binop_2 A G) B))  &  ( (~ (r1_xxreal_0 (k1_seq_1 E G) (k19_binop_2 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 E G))) ) ) ) ) ) )  &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k4_sin_cos6))) &  ( (F = (k1_relset_1 k1_numbers D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D C))) ) ) )  =>  ((k2_integra5 C D) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k4_sin_cos6)) (k4_seq_4 C)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k4_sin_cos6)) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_integr13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ((r2_relset_1 k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 (k5_real_1 A 1))) (k3_valued_1 k1_numbers k1_numbers k1_numbers D (k1_taylor_1 2))) A)) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = 1) ) ) )  &  ((r1_tarski E (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 A)))) &  ( (E = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 A)) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos D) (k1_seq_1 k19_sin_cos (k1_seq_1 k16_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t38_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_integra1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k3_finseq_2 (k1_euclid A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (k1_euclid A)))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k3_finseq_2 (u1_struct_0 (k4_real_ns1 A)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k3_finseq_2 (u1_struct_0 (k4_real_ns1 A))))))) )  =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) & (r1_funct_2 k5_numbers (k3_finseq_2 (k1_euclid A)) k5_numbers (k3_finseq_2 (u1_struct_0 (k4_real_ns1 A))) F G))  =>  ((m4_integr15 F A B C E) <=> (m2_integr18 G (k4_real_ns1 A) B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((r1_integra1 B C) & (v1_seq_2 (k2_partfun1 A k1_numbers D A)))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  ((r2_hidden E (k4_finseq_1 B)) => (r1_xxreal_0 (k18_rvsum_1 (k17_finseq_1 k1_numbers (k13_integra1 A B C E) (k4_integra1 A D C))) (k18_rvsum_1 (k17_finseq_1 k1_numbers E (k4_integra1 A D B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((r1_tarski A B) => (r1_xxreal_0 (k3_integra1 A) (k3_integra1 B))) ) ) ) ) ).
tt(t38_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 A B) =>  ((k4_integra5 A B (k1_integra8 1)) = (k9_real_1 B A)) ) ) ) ) ) ).
tt(t38_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 (k1_real_1 k32_sin_cos) k32_sin_cos))  => (r1_integra9 A k16_sin_cos k19_sin_cos)) ) ) ).
tt(t38_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_interva1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_interva1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ((k4_setfam_1 B C) = (a_3_1_interva1 A B C)) ) ) ) ) ) ) ).
tt(t38_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k3_intpro_1 A C) (k3_intpro_1 A (k4_intpro_1 B C)))) k8_intpro_1)) ) ) ) ) ) ).
tt(t38_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (C = (k13_complex1 1 (k2_nat_1 A 1)))  => (r1_xxreal_0 (k13_complex1 (k9_newton A) (k9_newton (k2_nat_1 (k2_nat_1 A B) 1))) (k3_power C (k2_nat_1 B 1)))) ) ) ) ) ) ) ).
tt(t38_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  (! [E:$i] :  ((m2_nattra_1 E B A C D) =>  ((r2_nattra_1 B A C D) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) (k6_isocat_1 B B A (k10_cat_1 B) (k10_cat_1 B) C D (k6_nattra_1 B B (k10_cat_1 B)) E) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 A C F G))  => (r2_nattra_1 A (k8_cat_2 B C) (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_isomichi B A) <=> (v3_isomichi (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t38_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( ((v2_compts_1 B (k3_pcomps_1 A)) & (v2_compts_1 C (k3_pcomps_1 A)))  =>  ( (B = k1_xboole_0)  |  ( (C = k1_xboole_0)  |  ((r1_xboole_0 B C) <=>  (~ (r1_xxreal_0 (k7_weierstr A B C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_0_jgraph_2) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t38_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (C = (k5_relat_1 (k2_funct_1 k1_jgraph_3) A))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (A = a_0_1_jgraph_3) ) )  => (v5_pre_topc C (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ).
tt(t38_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~ (v2_funct_1 (k3_jgraph_4 A))) ) ) ) ) ) ).
tt(t38_jgraph_5,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) )  &  ((v3_tops_2 A k5_topmetr (k4_topmetr (k1_real_1 1) 1)) &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k1_rcomp_1 k6_numbers 1)) =>  ((k1_funct_1 A B) = (k7_real_1 (k8_real_1 (k1_real_1 2) B) 1)) ) ) )  &  ( ((k1_funct_1 A k6_numbers) = 1)  &  ((k1_funct_1 A 1) = (k1_real_1 1)) ) ) ) ) ) ).
tt(t38_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k8_pscomp_1 (k1_sppol_2 A B C D)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t38_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid B) F) &  ((r1_xxreal_0 G (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) H) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 B 1))))  =>  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) (k1_jordan1a (k1_jordan8 B 1)) A)) = (k13_complex1 (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2)) ) ) ) ) ) ).
tt(t38_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_9_jordan1 A B C D))  &  (F = (a_4_4_jordan1 A B C D)) )  => (r1_tarski F (k2_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) & (r1_xxreal_0 B 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan1g,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) &  ( (~  (B = (k3_finseq_1 A)) )  &  (~  (C = (k3_finseq_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 (k1_jordan8 E B))) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 (k2_nat_1 F 1) (k3_finseq_1 (k1_jordan8 E A))) &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 (k2_nat_1 G 1) (k1_matrix_1 (k1_jordan8 E A))) & (r1_tarski (k3_goboard5 (k1_jordan8 E B) C D) (k3_goboard5 (k1_jordan8 E A) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k10_xtuple_0 B)) => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 B C) A)) ) ) ) ) ) ) ) ).
tt(t38_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  => (r1_xxreal_0 k6_numbers (k1_jordan1k A B C))) ) ) ) ) ) ).
tt(t38_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xxreal_0 (k18_euclid (k1_jordan21 A)) (k9_pscomp_1 A))) ) ) ).
tt(t38_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k6_pscomp_1 A) = (k6_pscomp_1 (k3_jordan19 A))) ) ) ).
tt(t38_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v3_jordan23 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) ) )  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ((k2_jordan3 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A) B) = (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 A B))) ) ) ) ) ) ) ).
tt(t38_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) C D) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D E) B) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ((v5_pre_topc F k5_topmetr (k1_pre_topc (k15_euclid A) B)) &  ( (C = (k1_funct_1 F k6_numbers))  &  (E = (k1_funct_1 F 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) )  => (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B 2 (k3_finseq_1 B))))) ) ) ) ) ).
tt(t38_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 A) (k2_nat_1 B 1)) | (v4_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t38_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k9_pscomp_1 (k3_topreal1 2 A)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 1))) ) ) ).
tt(t38_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) D E B) &  (C = (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k2_tarski D E))) )  => (v3_pre_topc C (k1_pre_topc (k15_euclid A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  (! [F:$i] :  ((m1_borsuk_2 F A C D) =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B C D E F)) = (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) E) (k2_relset_1 (u1_struct_0 A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (u1_struct_0 (k8_knaster A B))) <=> (r2_abian (u1_struct_0 A) C B)) ) ) ) ) ) ) ).
tt(t38_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) = (k2_pre_topc k3_topmetr k6_kurato_1)) ) ).
tt(t38_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)))) C D) = (k3_borsuk_1 (k15_euclid 2) (k15_euclid 2) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A D) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B D))) ) )  => (r1_tarski (k2_kurato_2 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) C) (k3_borsuk_1 (k15_euclid 2) (k15_euclid 2) (k2_kurato_2 (k15_euclid 2) A) (k2_kurato_2 (k15_euclid 2) B)))) ) ) ) ) ) ) ).
tt(t38_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( ( ((k1_matrix_1 D) = A)  &  ((k4_matrix_3 B D C) = E) )  =>  ( (D = (k4_matrix_3 B E (k5_matrix_6 A B C)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 D)) =>  ((k3_matrix_1 (u1_struct_0 B) D F G) = (k8_group_1 B (k11_algstr_0 B (k12_matrix_3 A B C)) (k12_matrix_3 A B (k3_matrix11 G A A (u1_struct_0 B) C (k8_matrix_1 (u1_struct_0 B) E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_lattice2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_lattice2 A))) =>  ( ( (B = D)  &  (C = E) )  => (r3_lattices (k1_lattice2 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden B C) =>  ((r3_lattices A B (k15_lattice3 A C)) & (r3_lattices A (k16_lattice3 A C) B)) ) ) ) ) ) ) ).
tt(t38_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((k2_lattice2 (u1_struct_0 A) A (k5_setwiseo (u1_struct_0 A) C (k2_setwiseo (u1_struct_0 A) B)) (k5_lattice4 A)) = (k3_lattices A (k2_lattice2 (u1_struct_0 A) A C (k5_lattice4 A)) (k7_lattices A B))) ) ) ) ) ) ) ).
tt(t38_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((m2_lattice5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k1_xtuple_0 (k1_funct_1 D E)) (k1_xtuple_0 (k1_funct_1 D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v3_lexbfs (k15_lexbfs A (k16_lexbfs A)))) ) ).
tt(t38_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ((v3_lfuzzy_1 B A) => (r2_relset_1 (k2_zfmisc_1 A A) k1_numbers B (k5_lfuzzy_1 A B))) ) ) ) ) ).
tt(t38_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v8_valued_0 A)) ) )  => (v1_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t38_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r3_limfunc2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k2_rcomp_1 (k9_real_1 A D) A) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 (k9_real_1 A D) A)) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t38_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k8_real_1 (k1_limfunc3 B A) (k1_limfunc3 C A))) ) ) ) ) ) ) ) ) ).
tt(t38_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc3 B A) &  ((v8_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r3_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t38_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_lmod_6 A C D) <=> (r1_tarski (k2_struct_0 C) (k2_struct_0 D))) ) ) ) ) ) ) ) ) ).
tt(t38_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v4_normsp_0 (k16_lopban_1 A B)) &  ((v3_normsp_0 (k16_lopban_1 A B)) & (v2_normsp_1 (k16_lopban_1 A B))) ) ) ) ) ) ).
tt(t38_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A C B))  &  ( ((k3_rlvect_1 A (k3_rlvect_1 A B C) D) = (k3_rlvect_1 A B (k3_rlvect_1 A C D)))  &  ( ((k3_rlvect_1 A B (k4_struct_0 A)) = B)  &  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((k3_rlvect_1 A B G) = (k4_struct_0 A)) ) )  &  ( ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D)))  &  ( ((k1_rlvect_1 A B 1) = B)  &  ( ((k1_rlvect_1 A B k6_numbers) = (k4_struct_0 A))  &  ( ((k1_rlvect_1 A (k4_struct_0 A) E) = (k4_struct_0 A))  &  ( ((k1_rlvect_1 A B (k1_real_1 1)) = (k4_algstr_0 A B))  &  ( ((k6_algstr_0 A B (k5_struct_0 A)) = B)  &  ( ((k6_algstr_0 A (k5_struct_0 A) B) = B)  &  ( ((k6_algstr_0 A B (k3_rlvect_1 A C D)) = (k3_rlvect_1 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ( ((k6_algstr_0 A (k3_rlvect_1 A C D) B) = (k3_rlvect_1 A (k6_algstr_0 A C B) (k6_algstr_0 A D B)))  &  ( ((k1_rlvect_1 A (k6_algstr_0 A B C) E) = (k6_algstr_0 A (k1_rlvect_1 A B E) C))  &  ( ((k1_rlvect_1 A (k3_rlvect_1 A B C) E) = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C E)))  &  ( ((k1_rlvect_1 A B (k7_real_1 E F)) = (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A B F)))  &  ( ((k1_rlvect_1 A B (k8_real_1 E F)) = (k1_rlvect_1 A (k1_rlvect_1 A B F) E))  &  ( ((k1_rlvect_1 A (k6_algstr_0 A B C) (k8_real_1 E F)) = (k6_algstr_0 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)))  &  ( ((k1_rlvect_1 A (k6_algstr_0 A B C) E) = (k6_algstr_0 A B (k1_rlvect_1 A C E)))  &  ( ((k6_algstr_0 A (k4_struct_0 A) B) = (k4_struct_0 A))  &  ( ((k6_algstr_0 A B (k4_struct_0 A)) = (k4_struct_0 A))  &  ( ((k6_algstr_0 A B (k5_algstr_0 A C D)) = (k5_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ( ((k6_algstr_0 A (k5_algstr_0 A C D) B) = (k5_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B)))  &  ( ((k5_algstr_0 A (k3_rlvect_1 A B C) D) = (k3_rlvect_1 A B (k5_algstr_0 A C D)))  &  ( ((k3_rlvect_1 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A B (k5_algstr_0 A C D)))  &  ( ((k5_algstr_0 A (k5_algstr_0 A B C) D) = (k5_algstr_0 A B (k3_rlvect_1 A C D)))  &  ( ((k3_rlvect_1 A B C) = (k3_rlvect_1 A (k5_algstr_0 A B D) (k3_rlvect_1 A D C)))  &  ( ((k5_algstr_0 A B C) = (k3_rlvect_1 A (k5_algstr_0 A B D) (k5_algstr_0 A D C)))  &  ( (B = (k3_rlvect_1 A (k5_algstr_0 A B C) C))  &  ( (B = (k5_algstr_0 A C (k5_algstr_0 A C B)))  &  ( ( ((k1_normsp_0 A B) = k6_numbers)  =>  (B = (k4_struct_0 A)) )  &  ( ( (B = (k4_struct_0 A))  =>  ((k1_normsp_0 A B) = k6_numbers) )  &  ( ((k1_normsp_0 A (k1_rlvect_1 A B E)) = (k8_real_1 (k18_complex1 E) (k1_normsp_0 A B)))  &  ((r1_xxreal_0 (k1_normsp_0 A (k3_rlvect_1 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C))) &  ((r1_xxreal_0 (k1_normsp_0 A (k6_algstr_0 A B C)) (k8_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C))) &  ( ((k1_normsp_0 A (k5_struct_0 A)) = 1)  & (v3_lopban_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k10_lopban_4 A B) (k10_lopban_4 A (k4_algstr_0 A B))) = (k5_struct_0 A))  &  ((k6_algstr_0 A (k10_lopban_4 A (k4_algstr_0 A B)) (k10_lopban_4 A B)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t38_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_hidden D (k9_lpspace1 A B C)) => (r2_hidden D (k13_lpspace1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t38_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ((r2_hidden D (k1_lpspace2 A B C E)) => (r2_hidden D (k5_lpspace2 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_hilbert1) =>  (! [C:$i] :  ((m2_finseq_1 C k1_hilbert1) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 (k1_nat_1 E (k3_finseq_1 B)) (k3_finseq_1 C)) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 B)))  =>  ((k1_funct_1 B F) = (k1_funct_1 C (k2_xcmplx_0 F E))) ) ) )  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) & (r7_ltlaxio1 D B A)) ) ) )  => (r7_ltlaxio1 (k2_xcmplx_0 D E) C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) <=> (r2_hidden (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t38_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k3_mathmorp A B C)) = (k6_rusub_4 A (k3_subset_1 (u1_struct_0 A) B) (k2_mathmorp A C))) ) ) ) ) ) ) ).
tt(t38_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 B C) => (v4_matrix10 (k4_matrix10 A C B))) ) ) ) ) ) ) ).
tt(t38_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k8_matrix_1 C (k4_matrix11 A B C E D) F) = (k1_funct_1 D (k1_funct_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_matrix_1 F A B C) =>  (! [G:$i] :  ((m2_finseq_2 G k5_numbers (k4_finseq_2 D k5_numbers)) =>  (! [H:$i] :  ((m2_finseq_1 H A) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  (! [J:$i] :  ((m2_finseq_2 J k5_numbers (k4_finseq_2 E k5_numbers)) =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 J) (k10_xtuple_0 G)) (k2_matrix_1 F)) =>  ((r2_hidden I (k10_xtuple_0 J)) |  ((k1_matrix13 A F E D J G) = (k1_matrix13 A (k3_matrix11 I B C A F H) E D J G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ( ((k3_matrix_1 (u1_struct_0 B) D 1 1) = (k11_algstr_0 B C))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E A) =>  ((r1_xxreal_0 E 1) |  ((k1_funct_1 D E) = (k3_matrix14 B A E)) ) ) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ( (C = (k4_struct_0 B))  | (v1_matrix_6 D A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 (u1_struct_0 E))))  =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 E) B A) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 E) B C) =>  ((r2_hidden G (k4_matrix15 E H I)) => (r2_hidden G (k4_matrix15 E (k3_matrix11 D B A (u1_struct_0 E) H (k10_fvsum_1 (k1_matrix_1 H) E (k8_matrix_1 (u1_struct_0 E) H D) F)) (k3_matrix11 D B C (u1_struct_0 E) I (k10_fvsum_1 (k1_matrix_1 I) E (k8_matrix_1 (u1_struct_0 E) I D) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((v4_matrix16 B (u1_struct_0 A)) & (v4_matrix16 C (u1_struct_0 A))) )  =>  ((k2_matrix16 (u1_struct_0 A) (k3_fvsum_1 A B C)) = (k3_matrix_3 A (k2_matrix16 (u1_struct_0 A) B) (k2_matrix16 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t38_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_matrix_1 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) =>  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k3_matrix_3 A (k3_matrix_3 A B C) (k2_matrix_3 A C))) ) ) ) ) ) ) ) ).
tt(t38_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) )  => (r2_matrix_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t38_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_8 A B (k2_matrix_6 A B C (k12_matrix_1 B A)) (k2_matrix_6 A B D (k12_matrix_1 B A)))) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) )  =>  (~  ((v4_matrix_2 A 3) &  ( (~  (A = (k3_finseq_4 k5_numbers 2 1 3)) )  &  ( (~  (A = (k3_finseq_4 k5_numbers 1 3 2)) )  &  (~  (A = (k3_finseq_4 k5_numbers 3 2 1)) ) ) ) ) ) ) ) ).
tt(t38_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k9_matrixc1 (k14_rvsum_1 A B)) = (k5_matrixc1 (k9_matrixc1 A) (k9_matrixc1 B))) ) ) ) ) ) ).
tt(t38_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_matrixj1 E C) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 C))))  =>  ( ((r2_hidden A (k2_finseq_1 (k2_wsierp_1 (k11_matrixj1 C E)))) &  (B = (k1_matrixj1 (k11_matrixj1 C E) A)) )  =>  ((k9_matrix_1 C (k13_matrixj1 C D E) A) = (k8_finseq_1 C (k8_finseq_1 C (k5_finseq_2 C (k2_wsierp_1 (k10_matrixj1 C (k6_matrixj1 C (k7_nat_d B 1) E))) D) (k9_matrix_1 C (k2_matrixj1 C E B) (k7_nat_d A (k2_wsierp_1 (k11_matrixj1 C (k6_matrixj1 C (k7_nat_d B 1) E)))))) (k5_finseq_2 C (k7_nat_d (k2_wsierp_1 (k10_matrixj1 C E)) (k2_wsierp_1 (k10_matrixj1 C (k6_matrixj1 C B E)))) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k3_matrixr1 A B) = (k8_matrixr1 (k3_finseq_1 A) (k1_matrix_1 A))) ) )  =>  (B = (k4_matrixr1 A)) ) ) ) ) ) ).
tt(t38_matrixr2,ax, (! [A:$i] :  ((m1_matrix_1 A k1_numbers 3 3) =>  ((k3_matrixr2 3 A) = (k7_real_1 (k9_real_1 (k7_real_1 (k9_real_1 (k9_real_1 (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 1) (k3_matrix_1 k1_numbers A 2 2)) (k3_matrix_1 k1_numbers A 3 3)) (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 3) (k3_matrix_1 k1_numbers A 2 2)) (k3_matrix_1 k1_numbers A 3 1))) (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 1) (k3_matrix_1 k1_numbers A 2 3)) (k3_matrix_1 k1_numbers A 3 2))) (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 2) (k3_matrix_1 k1_numbers A 2 3)) (k3_matrix_1 k1_numbers A 3 1))) (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 2) (k3_matrix_1 k1_numbers A 2 1)) (k3_matrix_1 k1_numbers A 3 3))) (k8_real_1 (k8_real_1 (k3_matrix_1 k1_numbers A 1 3) (k3_matrix_1 k1_numbers A 2 1)) (k3_matrix_1 k1_numbers A 3 2)))) ) ) ).
tt(t38_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 F)) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin A C D (k4_matrlin2 A C D E F G) B) (k4_matrlin2 A C D E F (k2_matrix13 (k3_finseq_1 E) (k3_finseq_1 F) A G B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ( ((k3_finseq_1 E) = k6_numbers)  =>  ((k10_matrlin A B C D E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_matroid0 B A) <=>  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r1_matroid0 A (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C)) B)) ) ) ) ) ) ) ) ) ).
tt(t38_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 k2_vectsp_1)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 k2_vectsp_1)) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( (A = C)  &  (B = D) ) )  =>  ((k22_rvsum_1 A B) = (k13_fvsum_1 k2_vectsp_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C B) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 k2_vectsp_1) B A) =>  ( (D = (k17_finseq_1 (k3_finseq_2 (u1_struct_0 k2_vectsp_1)) B (k12_matrix_1 k2_vectsp_1 A)))  =>  ((k16_finseq_1 B (k1_funct_1 (k3_matrtop1 B A D) C)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t38_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 B (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (~  ((v2_matrtop3 B A) &  ( (~  ((k12_matrix_3 A k2_vectsp_1 (k3_matrtop3 A B)) = (k5_struct_0 k2_vectsp_1)) )  &  (~  ((k12_matrix_3 A k2_vectsp_1 (k3_matrtop3 A B)) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1))) ) ) ) ) ) ) ) ) ).
tt(t38_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_zfmisc_1 (k1_tarski A) (k1_tarski B) (k2_tarski C D)) = (k2_tarski (k3_xtuple_0 A B C) (k3_xtuple_0 A B D))) ) ) ) ) ).
tt(t38_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m2_measure1 E A B C) =>  ( ((k12_supinf_2 C (k1_measure1 A B D E)) = (k12_supinf_2 C D))  &  ( ((k12_supinf_2 C (k2_measure1 A B D E)) = k1_supinf_2)  &  ((k12_supinf_2 C (k3_measure1 A B D E)) = (k12_supinf_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_measure6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ((v2_relat_1 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v1_comseq_2 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ) ) ) ).
tt(t38_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_member_1 (k2_tarski A B)) = (k2_tarski (k2_binop_2 A) (k2_binop_2 B))) ) ) ) ) ).
tt(t38_memstr_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_memstr_0 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 B C)) & (v1_partfun1 D (u1_struct_0 C))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 C)) &  ((v1_funct_1 E) & (v5_funct_1 E (k2_memstr_0 B C))) ) )  =>  ((r1_tarski (k1_funct_4 E (k7_memstr_0 B C A)) D) =>  ((k5_memstr_0 B C D) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_mesfun6c A B C D) =>  ((r2_mesfun6c A B C (k25_valued_1 A k2_numbers D E)) &  ((k1_mesfun6c A B C (k25_valued_1 A k2_numbers D E)) = (k3_xcmplx_0 E (k1_mesfun6c A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k55_valued_1 A k2_numbers B) (k55_valued_1 A k2_numbers C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  & (r1_tarski (k1_relset_1 A (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C))) (k1_relset_1 A (k55_valued_1 A k2_numbers B)))) ) ) ) ) ) ) ).
tt(t38_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers E F) C)) )  => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers (k3_mesfun9c A E) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B C) & (r1_mesfunc2 A B D))  => (r1_mesfunc2 A B (k3_mesfunc1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t38_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k1_seq_1 (k18_rfunct_3 A B) C) = (k1_seq_1 B C)) )  =>  ((k1_seq_1 (k19_rfunct_3 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t38_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( ((v1_mesfunc8 B A k7_numbers) &  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers))) &  (! [D:$i] :  ((v7_ordinal1 D) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers B D))) ) ) )  =>  ((v7_valued_0 (k3_mesfunc5 A (k4_mesfunc9 A B) C)) & (v10_mesfunc5 (k3_mesfunc5 A (k4_mesfunc9 A B) C))) ) ) ) ) ) ) ) ).
tt(t38_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_midsp_1 A) = (k8_midsp_1 A B B)) ) ) ) ) ).
tt(t38_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_relset_1 A (k18_mmlquery A (k18_mmlquery A B))) = (k1_relset_1 A B)) ) ) ) ).
tt(t38_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v7_mod_4 B A A) <=> (v8_mod_4 (k7_mod_4 A A B) A (k2_mod_4 A))) ) ) ) ) ).
tt(t38_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~ (r1_xxreal_0 (k5_card_1 (k9_xtuple_0 (k10_modal_1 A))) (k5_card_1 (k9_xtuple_0 A)))) ) ) ).
tt(t38_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ((m1_modelc_1 C A B) =>  (! [D:$i] :  ((m1_modelc_1 D A B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((k3_funct_2 k5_numbers A C E) = (k3_funct_2 k5_numbers A D k6_numbers))  => (m1_modelc_1 (k57_modelc_1 A B C D E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (~  ( (~  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) )  &  ((r3_modelc_2 B A) &  ( (~ (r2_modelc_2 B (k11_modelc_2 A)))  &  (~ (r2_modelc_2 B (k12_modelc_2 A))) ) ) ) ) ) ) ) ) ).
tt(t38_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  =>  (~  ((r6_modelc_3 B D C) &  ((r2_hidden A (u1_modelc_3 B C)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 E)) &  ((r5_modelc_3 B E) &  ( ((k1_funct_1 E 1) = (k12_modelc_3 B D))  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = C)  &  ((r1_xxreal_0 1 F) &  ( (~ (r1_xxreal_0 (k3_finseq_1 E) F))  & (r1_modelc_3 B (k10_modelc_3 (k1_funct_1 E F) B) (k10_modelc_3 (k1_funct_1 E (k1_nat_1 F 1)) B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r2_hidden A k1_moebius1) <=>  (~  ((k2_moebius1 A) = k6_numbers) ) ) ) ) ).
tt(t38_monoid_0,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_monoid_0)) <=> (m1_subset_1 A k1_numbers)) ) ).
tt(t38_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k20_monoid_1 A (k12_finseq_1 A B)) = (k18_monoid_1 A B)) ) ) ) ) ).
tt(t38_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_msualg_6 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_2 C A B) => (v1_msualg_6 C A)) ) ) ) ) ) ).
tt(t38_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  ((r1_msaterm A B C D E F) => (r2_hidden (k1_funct_1 F k1_xboole_0) (k1_funct_1 (u3_msualg_1 A B) (k7_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (m3_pboole (k1_pzfmisc1 A B) A (k1_mboolean A C))) ) ) ) ) ) ).
tt(t38_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) => (r2_hidden (u3_msualg_1 A B) (k5_msualg_2 A B C))) ) ) ) ) ) ).
tt(t38_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_hidden (k4_tarski E F) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (k8_msualg_6 A B C) D)) <=>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((r1_rewrite1 (k3_msualg_6 A) G D) &  (? [H:$i] :  ((m1_subset_1 H (k1_funct_1 (u3_msualg_1 A B) G)) &  (? [I:$i] :  ((m1_subset_1 I (k1_funct_1 (u3_msualg_1 A B) G)) &  (? [J:$i] :  ((m1_msualg_6 J A B) &  (? [K:$i] :  ((m2_msualg_6 K A B G D) &  ((r2_hidden (k4_tarski H I) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C G)) &  ( (E = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) D) K (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) G) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) J G) H)))  &  (F = (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) D) K (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) G) (k1_funct_1 (u3_msualg_1 A B) G) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) J G) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden (k4_tarski C D) (u1_orders_2 (k6_mycielsk A B))) &  ( (~  ( (~ (r1_xxreal_0 A C))  &  (~ (r1_xxreal_0 A D)) ) )  &  ( (~  ( (~ (r1_xxreal_0 A C))  &  ((r1_xxreal_0 A D) &  (~ (r1_xxreal_0 (k3_xcmplx_0 2 A) D)) ) ) )  &  ( (~  ((r1_xxreal_0 A C) &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 2 A) C))  &  (~ (r1_xxreal_0 A D)) ) ) )  &  ( (~  ( (C = (k3_xcmplx_0 2 A))  &  ((r1_xxreal_0 A D) &  (~ (r1_xxreal_0 (k3_xcmplx_0 2 A) D)) ) ) )  &  (~  ((r1_xxreal_0 A C) &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 2 A) C))  &  (D = (k3_xcmplx_0 2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k4_card_1 A) = (k1_nat_1 A 1)) ) ) ).
tt(t38_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (~  ((r1_nat_d A B) &  ((k1_seq_1 (k12_nat_3 B) A) = k6_numbers) ) ) ) ) ) ) ).
tt(t38_nat_4,ax,(v1_int_2 1259)).
tt(t38_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  ( ((v1_int_2 (k7_nat_d (k2_newton 2 A) 1)) &  (B = (k24_binop_2 (k13_newton 2 (k7_nat_d A 1)) (k7_nat_d (k2_newton 2 A) 1))) )  => (v2_nat_5 B)) ) ) ) ) ).
tt(t38_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) =>  ((k7_nat_d (k2_xcmplx_0 B C) A) = (k2_nat_1 (k7_nat_d B A) C)) ) ) ) ) ) ) ) ).
tt(t38_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v2_nattra_1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((v1_finset_1 C) &  ( (C = (k2_cat_1 A B B))  &  ((k5_card_1 C) = 1) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  ((k2_cat_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t38_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_ncfcont1 A B C D) =>  ((r5_ncfcont1 A (k3_normsp_0 (u1_struct_0 A) B C) D) & (r1_ncfcont1 A B (k5_vfunct_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t38_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~ (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers))  &  (B = C) ) )  &  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t38_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_nfcont_1 C A) &  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) B)) &  ((k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) = (k6_partfun1 C)) ) )  =>  ((r2_ndiff_1 C A A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A A)) (k4_ndiff_1 A A B C) D) = (k6_partfun1 (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ndiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k1_euclid 1) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 1) k1_numbers)))) )  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 1)) =>  ((r2_funct_2 (k1_euclid 1) k1_numbers A (k1_pdiff_1 1 1)) =>  ((r1_pdiff_7 1 A B) & (r2_funct_2 (k1_euclid 1) k1_numbers (k1_pdiff_7 1 A B) A)) ) ) ) ) ) ).
tt(t38_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_prvect_2 A B))) =>  (~  ( (~  (C = (k4_struct_0 (k11_prvect_2 A B))) )  &  ((k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) C) = (k4_struct_0 (k14_prvect_2 A))) ) ) ) ) ) ) ) ) ).
tt(t38_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (F = (k9_domain_1 (u1_struct_0 A) B C D E))  &  ((r2_zfmisc_1 B C D E) &  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (u1_orders_2 A)) &  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C D) (u1_orders_2 A)) & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E) (u1_orders_2 A))) ) ) )  =>  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B D) (u1_orders_2 A)) |  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B E) (u1_orders_2 A)) |  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C E) (u1_orders_2 A)) | (r1_necklace (k4_necklace 4) (k5_yellow_0 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 A (k9_newton A))) ) ).
tt(t38_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r5_nfcont_1 C D A E) & (r1_tarski B A))  => (r5_nfcont_1 C D B E)) ) ) ) ) ) ) ) ) ).
tt(t38_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) E C) A))  => (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k8_integr15 A k1_numbers D E) (k3_xboole_0 B C)) A)) ) ) ) ) ) ) ) ) ).
tt(t38_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  ( ((r2_hidden B (k9_normform A D)) &  ((r2_hidden C D) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) C B)) )  =>  (C = B) ) ) ) ) ) ) ) ) ).
tt(t38_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C (k2_oppcat_1 A) B) => (m2_cat_1 (k9_oppcat_1 A B C) A B)) ) ) ) ) ) ).
tt(t38_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r3_orders_1 A B) & (r1_tarski C B))  => (r3_orders_1 A C)) ) ) ) ) ).
tt(t38_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_orders_1 D (k1_orders_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m2_orders_2 E A D) =>  ( ((r2_hidden B E) &  (C = (k1_funct_1 D (u1_struct_0 A))) )  => (r3_orders_2 A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k11_ordinal2 A k1_xboole_0) = k1_xboole_0) ) ) ).
tt(t38_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden A (k10_ordinal2 B C)) &  ( (~ (r2_hidden A B))  &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D C) &  (A = (k10_ordinal2 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_ordinal4,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_ordinal2 A B) =>  ((v4_ordinal1 A) <=> (v4_ordinal1 B)) ) ) ) ) ) ).
tt(t38_ordinal5,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v4_ordinal5 A))  =>  ((k12_ordinal2 k4_ordinal1 (k12_ordinal2 A k4_ordinal1)) = (k12_ordinal2 A (k12_ordinal2 A k4_ordinal1))) ) ) ).
tt(t38_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  ((v4_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ((r1_ordinal1 B (k9_xtuple_0 (k3_ordinal6 C))) &  ((r1_abian A C) &  (! [D:$i] :  ((r2_hidden D B) => (r2_hidden (k1_funct_1 (k3_ordinal6 C) D) A)) ) ) )  => (r2_hidden B (k9_xtuple_0 (k3_ordinal6 C)))) ) ) ) ) ) ) ).
tt(t38_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  ((v13_o_ring_1 B A) & (v1_o_ring_1 C A)) )  &  ( (~  ((v13_o_ring_1 B A) & (v3_o_ring_1 C A)) )  &  ( (~  ((v13_o_ring_1 B A) & (v5_o_ring_1 C A)) )  &  ( (~  ((v13_o_ring_1 B A) & (v7_o_ring_1 C A)) )  &  ( (~  ((v13_o_ring_1 B A) & (v9_o_ring_1 C A)) )  &  ( (~  ((v13_o_ring_1 B A) & (v11_o_ring_1 C A)) )  &  (~  ((v13_o_ring_1 B A) & (v13_o_ring_1 C A)) ) ) ) ) ) ) ) )  => (v13_o_ring_1 (k1_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t38_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v1_osafree (k24_osafree A B) A (k16_osafree A B))) ) ) ) ).
tt(t38_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A B)) =>  ((k11_osalg_2 A B (k10_osalg_2 A B D) C) = (k10_osalg_2 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t38_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) & (l1_parsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_parsp_1 A B C B D))  &  ( (~  (E = F) )  &  ((r1_parsp_1 A E F E B) &  ((r1_parsp_1 A E F E C) & (r1_parsp_1 A E F E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_parsp_2 A B C D) &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v2_funct_1 C) =>  ((k2_funct_1 (k3_partfun1 C A B)) = (k3_partfun1 (k2_funct_1 C) B A)) ) ) ) ) ) ).
tt(t38_partfun2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ( ((v3_funct_1 (k2_partfun1 C D E A)) & (r1_tarski B A))  => (v3_funct_1 (k2_partfun1 C D E B))) ) ) ) ) ) ) ) ) ).
tt(t38_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B (k3_pboole A C D)) => (r2_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t38_pcs_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_pcs_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k21_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k21_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k7_yellow_3 A B E G))  &  (D = (k7_yellow_3 A B F H)) )  =>  ( ( (~ (r1_pcs_0 A E F))  &  (~ (r1_pcs_0 B G H)) )  | (r1_pcs_0 (k21_pcs_0 A B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r2_pdiff_3 A B) => (r1_fcont_1 (k1_pdiff_2 2 2 (k1_pdiff_3 1 2 A) B) (k1_seq_1 (k1_pdiff_1 2 2) B))) ) ) ) ) ).
tt(t38_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 D C) &  ((r3_pdiff_1 3 2 D C) &  ((r3_pdiff_1 3 3 D C) &  ((r3_pdiff_1 3 1 E C) &  ((r3_pdiff_1 3 2 E C) & (r3_pdiff_1 3 3 E C)) ) ) ) )  =>  ((k4_pdiff_4 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k26_valued_1 (k1_euclid 3) k1_numbers D A) (k26_valued_1 (k1_euclid 3) k1_numbers E B)) C) = (k7_euclid 3 (k9_euclid 3 (k4_pdiff_4 D C) A) (k9_euclid 3 (k4_pdiff_4 E C) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 3) B)) =>  ( ((r2_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B))))) &  ((k2_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 1 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ((r4_pdiff_7 A B C D) <=>  ((r1_tarski D (k1_relset_1 (k1_euclid A) C)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E D) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden H D) &  ( (~ (r1_xxreal_0 G (k12_euclid (k8_euclid A H E))))  & (r1_xxreal_0 F (k12_euclid (k8_euclid B (k7_partfun1 (k1_euclid B) C H) (k7_partfun1 (k1_euclid B) C E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r2_nfcont_4 A B D) & (r2_nfcont_4 A C D))  =>  ((r2_nfcont_4 A (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D) & (r2_nfcont_4 A (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t38_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v1_int_2 A) & (r1_nat_d B (k1_newton A C)))  =>  ((r1_xxreal_0 B 1) |  ((r1_nat_d B (k3_nat_d (k1_newton A C) A)) |  (B = (k1_newton A C)) ) ) ) ) ) ) ) ) ) ).
tt(t38_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  (! [D:$i] :  ((m2_finseq_2 D B (k3_finseq_2 B)) =>  ((k8_pnproc_1 A B (k1_pre_poly B C D)) = (k3_relat_1 (k8_pnproc_1 A B C) (k8_pnproc_1 A B D))) ) ) ) ) ) ) ) ).
tt(t38_polyeq_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_comptrig C B A) =>  ( (C = k6_numbers)  =>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(t38_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((k19_polyform A B E (k3_rlvect_1 (k17_polyform A B) C D)) = (k3_fvsum_1 k2_bspace (k19_polyform A B E C) (k19_polyform A B E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 k5_numbers (u1_struct_0 A) (k4_polynom5 A B C) k6_numbers) = B)  &  ( ((k3_funct_2 k5_numbers (u1_struct_0 A) (k4_polynom5 A B C) 1) = C)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 2 D) =>  ((k1_funct_1 (k4_polynom5 A B C) D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C B) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D B) & (r1_polynom8 A E B)) ) ) )  =>  ( (C = D)  |  ((k3_matrix_1 (u1_struct_0 A) (k4_matrix_3 A (k7_polynom8 A B E) (k7_polynom8 A B (k11_algstr_0 A E))) C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 F A C) &  ((v3_polynom7 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r4_polyred A B C D E (k6_polynom1 A C D (k10_polynom1 A C F E))) => (r2_hidden (k3_termord A B C (k10_polynom1 A C F E)) (k2_polynom1 (k15_pre_poly A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 k6_numbers C))  & (r1_xxreal_0 (k3_power A C) (k3_power B C))) ) ) ) ) ) ) ) ) ) ).
tt(t38_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) )  =>  ((k13_pre_poly (k11_pre_poly A B C)) = (k2_xboole_0 (k13_pre_poly B) (k13_pre_poly C))) ) ) ) ) ) ).
tt(t38_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ((k4_prepower A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t38_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ((k1_seq_1 E (k6_prob_1 A B C D)) = (k9_real_1 (k7_real_1 (k1_seq_1 E C) (k1_seq_1 E D)) (k1_seq_1 E (k5_prob_1 A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  (! [F:$i] :  ((m1_prob_1 F A B) =>  (! [G:$i] :  ((m2_prob_1 G A B) =>  ( ((r1_xboole_0 D E) &  (F = (k3_subset_1 A (k6_prob_1 A B D E))) )  =>  ((r1_xxreal_0 (k1_seq_1 G C) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 G D) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 G E) k6_numbers) |  ((r1_xxreal_0 (k1_seq_1 G F) k6_numbers) |  ( ((k1_seq_1 (k3_prob_2 A B G C) D) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G D) C) (k1_seq_1 G D)) (k7_real_1 (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G D) C) (k1_seq_1 G D)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G E) C) (k1_seq_1 G E))) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G F) C) (k1_seq_1 G F)))))  &  ( ((k1_seq_1 (k3_prob_2 A B G C) E) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G E) C) (k1_seq_1 G E)) (k7_real_1 (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G D) C) (k1_seq_1 G D)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G E) C) (k1_seq_1 G E))) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G F) C) (k1_seq_1 G F)))))  &  ((k1_seq_1 (k3_prob_2 A B G C) F) = (k10_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G F) C) (k1_seq_1 G F)) (k7_real_1 (k7_real_1 (k8_real_1 (k1_seq_1 (k3_prob_2 A B G D) C) (k1_seq_1 G D)) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G E) C) (k1_seq_1 G E))) (k8_real_1 (k1_seq_1 (k3_prob_2 A B G F) C) (k1_seq_1 G F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) => (v8_valued_0 (k8_prob_1 A B (k1_prob_3 A C) D))) ) ) ) ) ) ) ) ).
tt(t38_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) => (r1_prob_4 A (k4_prob_4 A B C) (k7_prob_4 A B C))) ) ) ) ) ) ).
tt(t38_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k9_cqc_lang A B C) (k9_cqc_lang A B D)) (k9_cqc_lang A B (k7_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t38_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k17_euclid (k11_pscomp_1 A)) (k17_euclid (k20_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k11_pscomp_1 A)) (k17_euclid (k21_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k11_pscomp_1 A)) (k17_euclid (k12_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k20_pscomp_1 A)) (k17_euclid (k21_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k20_pscomp_1 A)) (k17_euclid (k12_pscomp_1 A))) & (r1_xxreal_0 (k17_euclid (k21_pscomp_1 A)) (k17_euclid (k12_pscomp_1 A)))) ) ) ) ) ) ) ).
tt(t38_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) C) C) => (r1_pboole A B C)) ) ) ) ) ) ).
tt(t38_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang2 B A) =>  (B = (k2_qc_lang2 A (k12_qc_lang2 A B) (k11_qc_lang2 A B))) ) ) ) ) ) ).
tt(t38_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v3_qc_lang1 B A) =>  ((k4_qc_lang3 A C B) = (k4_qc_lang3 A C (k18_qc_lang1 A B))) ) ) ) ) ) ) ) ).
tt(t38_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) =>  (! [E:$i] :  ((m2_qc_lang4 E A B D) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  ((m2_qc_lang4 (k7_finseq_1 E F) A B C) => (r2_hidden F (k3_qc_lang4 A D C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_quatern2,ax, ((k1_group_1 k16_quatern2) = k2_quatern2) ).
tt(t38_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k9_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k10_real_1 (k7_real_1 (k3_quatern2 (k26_quaterni A B)) (k3_quatern2 (k29_quaterni A B))) 2))) ) ) ) ).
tt(t38_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ( ((k18_quaterni A) = k6_numbers)  &  ( ((k18_quaterni B) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ( ((k19_quaterni B) = k6_numbers)  &  ( ((k20_quaterni A) = k6_numbers)  &  ((k20_quaterni B) = k6_numbers) ) ) ) ) )  =>  ( ((k17_quaterni (k27_quaterni A B)) = (k8_real_1 (k17_quaterni A) (k17_quaterni B)))  &  ( ((k18_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k19_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k19_quaterni B))))  &  ( ((k19_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k20_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k20_quaterni B))))  &  ((k20_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k18_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k18_quaterni B)))) ) ) ) ) ) ) ) ) ).
tt(t38_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( ((k5_struct_0 (k19_quofield A)) = (k12_quofield A))  &  ((k4_struct_0 (k19_quofield A)) = (k11_quofield A)) ) ) ) ).
tt(t38_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A C) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 C)) =>  ( ( ((k10_xtuple_0 F) = (k1_vectsp_6 A C E))  & (v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D (k1_vectsp_6 A C E))))  =>  ((k4_finseqop (u1_struct_0 C) (u1_struct_0 B) (k3_vectsp_6 A C F E) D) = (k3_vectsp_6 A B (k4_finseqop (u1_struct_0 C) (u1_struct_0 B) F D) (k8_ranknull A C B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((r1_xxreal_0 A k6_numbers) <=> (r1_xxreal_0 (k2_rat_1 A) k6_numbers)) ) ) ).
tt(t38_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k3_rcomp_1 A B))  =>  ((k1_tops_1 k2_topalg_2 C) = (k2_rcomp_1 A B)) ) ) ) ) ) ) ) ).
tt(t38_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 1 A) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k4_real_3 B) A))) ) ) ) ) ).
tt(t38_rearran1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ( ((v1_rearran1 E) &  ((v2_rearran1 E) &  ((v3_rearran1 E (k1_zfmisc_1 C)) & (m2_finseq_1 E (k1_zfmisc_1 C))) ) )  =>  ( ((v1_partfun1 D B) &  ((k5_card_1 B) = (k5_card_1 C)) )  => (r2_relset_1 C k1_numbers (k4_rearran1 B C E (k15_valued_1 B k1_numbers D A)) (k15_valued_1 C k1_numbers (k4_rearran1 B C E D) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_relat_1,ax, ( ((k9_xtuple_0 k1_xboole_0) = k1_xboole_0)  &  ((k10_xtuple_0 k1_xboole_0) = k1_xboole_0) ) ).
tt(t38_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 B A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (E = (a_4_5_relset_2 A B C D))  =>  ((k6_relset_2 B A C (k8_setfam_1 (k2_zfmisc_1 B A) D)) = (k8_setfam_1 A E)) ) ) ) ) ) ) ) ) ) ).
tt(t38_revrot_1,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_sprect_2 A) | (v1_sprect_2 (k1_goboard9 A))) ) ) ).
tt(t38_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r5_rewrite1 A B B) & (r6_rewrite1 A B B)) ) ) ) ).
tt(t38_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ( ((r3_rewrite2 A B C D) & (r3_rewrite2 A B E F))  =>  ((r3_rewrite2 A B (k1_flang_1 A C E) (k1_flang_1 A D F)) & (r3_rewrite2 A B (k1_flang_1 A E C) (k1_flang_1 A F D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ((r1_rewrite3 F G A D B) <=> (r2_hidden (k4_tarski (k4_tarski A (k1_flang_1 C D E)) (k4_tarski B E)) (k1_rewrite3 C F G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ( ((k30_valued_1 (k1_rfunct_1 A B)) = (k1_rfunct_1 (k30_valued_1 A) B))  &  ((k1_rfunct_1 A (k30_valued_1 B)) = (k30_valued_1 (k1_rfunct_1 A B))) ) ) ) ) ) ).
tt(t38_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ( ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B))))  &  ( ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ) ).
tt(t38_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k8_relset_1 A k1_numbers B (k1_tarski (k1_real_1 C))) = (k8_relset_1 A k1_numbers (k19_rfunct_3 A B) (k1_tarski C))) ) ) ) ) ) ) ) ).
tt(t38_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) =>  ((k1_seq_1 (k3_rinfsup1 A) k6_numbers) = (k2_rinfsup1 A)) ) ) ) ).
tt(t38_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v10_mesfunc5 A) &  ((v10_mesfunc5 B) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) ) ) )  => (r1_xxreal_0 (k2_mesfunc5 A) (k2_mesfunc5 B))) ) ) ) ) ).
tt(t38_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ( (~  (A = k6_numbers) )  =>  ((k3_rlaffin1 B C) = (k3_rlaffin1 B (k2_rlaffin1 B C A))) ) ) ) ) ) ) ) ).
tt(t38_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (m1_rlsub_1 (k1_rlsub_1 B) A)) ) ) ) ).
tt(t38_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) => (r1_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(t38_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_rusub_4 A (k2_pre_topc A C) B) = (k2_pre_topc A (k5_rusub_4 A C B))) ) ) ) ) ) ) ).
tt(t38_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k2_nat_1 (k3_finseq_1 D) 1))  &  ( (D = (k5_relat_1 C (k4_finseq_1 D)))  &  (B = (k1_funct_1 C (k3_finseq_1 C))) ) )  =>  ((k4_rlvect_1 A C) = (k1_algstr_0 A (k4_rlvect_1 A D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t38_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((m2_rlvect_2 C A B) & (m2_rlvect_2 D A B))  => (m2_rlvect_2 (k7_rlvect_2 A C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t38_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~  (B = C) )  &  (! [F:$i] :  ((m2_rlvect_2 F A (k7_domain_1 (u1_struct_0 A) B C)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers F B) = D)  &  ((k3_funct_2 (u1_struct_0 A) k1_numbers F C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_rlvect_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_rlvect_5 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_rlvect_5 B)) <=>  (? [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C B))  &  ((k1_rlvect_5 C) = A) ) ) ) ) ) ) ) ).
tt(t38_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) => (m1_rmod_2 (k1_rmod_2 A C) A B)) ) ) ) ) ) ).
tt(t38_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_rmod_3 A B C D) => (r1_rmod_3 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t38_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ( ((m2_rmod_4 D A B C) & (m2_rmod_4 E A B C))  => (m2_rmod_4 (k6_rmod_4 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k9_robbins1 A (k5_robbins1 A (k3_robbins1 A B) C) D) = (k3_robbins1 A (k5_robbins1 A (k9_robbins1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t38_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A C (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A D C)) B))))) = (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A D C)) B)) ) ) ) ) ) ) ) ) ).
tt(t38_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) &  ((v1_robbins4 A) & (l4_robbins1 A)) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A (k1_lattices A B C) D) = (k1_lattices A (k3_robbins1 A (k2_lattices A (k3_robbins1 A D) (k3_robbins1 A C))) B)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A B C) = (k1_lattices A (k2_lattices A (k1_lattices A B C) (k1_lattices A B D)) (k2_lattices A (k1_lattices A B C) (k3_robbins1 A B)))) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k1_lattices A B (k2_lattices A C (k3_robbins1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t38_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C)) & (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C) 1)) ) ) ) ) ) ) ).
tt(t38_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((k2_rpr_1 A C B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t38_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ((k3_rusub_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(t38_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) => (r1_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(t38_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) C)) B) =>  ( (B = (k4_struct_0 A))  |  ((k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) B)) = (k1_rusub_3 A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t38_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (r2_hidden (u1_struct_0 A) (k4_rusub_5 A))) ) ).
tt(t38_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ( ((k9_rvsum_1 A B C) = (k5_finseq_2 k5_numbers A k6_numbers))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t38_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k17_rvsum_1 (k9_rvsum_2 B A)) = (k5_binop_2 A (k16_rvsum_1 B))) ) ) ) ) ).
tt(t38_scmbsort,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  ((k5_card_1 (k1_scmbsort A)) = 63) ) ) ).
tt(t38_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k2_amistd_1 3 k1_scmfsa_2 (k13_scmfsa_2 A B)) = (k1_tarski A)) ) ) ) ) ).
tt(t38_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 9)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~  (A = (k14_scmfsa_2 C B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmfsa8a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_partfun1 D k5_numbers)) ) ) )  =>  ( ((r5_scmfsa7b A C D) & (r6_scmfsa7b A C D))  => (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 D (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a A (k1_scmfsa8a (k2_nat_1 (k5_card_1 B) 1))) B) (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 C))) ) ) ) ) ) ) ) ) ).
tt(t38_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ( ( (! [G:$i] :  ( ((v1_ami_2 G) &  ( (~ (v1_scmfsa_m G))  & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (F = G) )  =>  ((k1_funct_1 C G) = (k1_funct_1 D G)) ) ) )  &  ( (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 C G) = (k18_scmfsa_2 D G)) ) )  &  ((r5_scmfsa7b E (k1_scmfsa_m C) A) & (r6_scmfsa7b E (k1_scmfsa_m C) A)) ) )  =>  ((r2_scmfsa7b E F) |  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (F = G) )  =>  ((k1_funct_1 (k1_scmfsa6b E C A) G) = (k1_funct_1 (k1_scmfsa6b E D B) G)) ) ) )  &  ( (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b E C A) G) = (k18_scmfsa_2 (k1_scmfsa6b E D B) G)) ) )  &  ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E C A)) = (k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b E D B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  &  ( ((k1_funct_1 B E) = k6_numbers)  & (r1_scmfsa8a B A (k2_scmfsa6a C))) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v1_afinsq_1 F)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D))  & (r3_scmfsa9a A C E F))  => (r3_scmfsa9a B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) =>  ((r6_scmfsa7b (k2_scmfsa_9 D C) B A) & (r5_scmfsa7b (k2_scmfsa_9 D C) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t38_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))  &  ( ( ((k1_funct_1 B E) = k6_numbers)  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b C B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b C B A) F)) ) ) ) )  &  ( (~  ((k1_funct_1 B E) = k6_numbers) )  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b D B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b D B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmisort,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) => (v4_extpro_1 (k1_scmfsa_m (k16_funcop_1 (k5_scmfsa_2 k6_numbers) A)) 3 k1_scmfsa_2 k3_scmisort)) ) ).
tt(t38_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 12)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  (A = (k15_scmpds_2 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmpds_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k6_memstr_0 2 k1_scmpds_2 B) = (k6_memstr_0 2 k1_scmpds_2 C))  =>  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 3)  |  ((k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 A B)) = (k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 A C))) ) ) ) ) ) ) ) ) ).
tt(t38_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F)) = k6_numbers)  &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((r1_scmpds_6 (k2_scmpds_6 E F C D) B A) & (r2_scmpds_6 (k2_scmpds_6 E F C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F))) =>  ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_7 D F G C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_compos_0 (u1_compos_1 (k1_scmring2 A)) (k9_scmring2 A C B) D) = (k9_scmring2 A (k2_nat_1 C D) B)) ) ) ) ) ) ) ) ) ).
tt(t38_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k5_scmyciel A) (k5_scmyciel B))) ) ) ).
tt(t38_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) =>  ( (~ (r1_semi_af1 A B C D))  &  ( (~ (r1_semi_af1 A B D C))  &  ( (~ (r1_semi_af1 A B C E))  &  ( (~ (r1_semi_af1 A B E C))  &  ( (~ (r1_semi_af1 A B D E))  &  ( (~ (r1_semi_af1 A B E D))  &  ( (~ (r1_semi_af1 A C B D))  &  ( (~ (r1_semi_af1 A C D B))  &  ( (~ (r1_semi_af1 A C B E))  &  ( (~ (r1_semi_af1 A C E B))  &  ( (~ (r1_semi_af1 A C D E))  &  ( (~ (r1_semi_af1 A C E D))  &  ( (~ (r1_semi_af1 A D B C))  &  ( (~ (r1_semi_af1 A D C B))  &  ( (~ (r1_semi_af1 A D B E))  &  ( (~ (r1_semi_af1 A D E B))  &  ( (~ (r1_semi_af1 A D C E))  &  ( (~ (r1_semi_af1 A D E C))  &  ( (~ (r1_semi_af1 A E B C))  &  ( (~ (r1_semi_af1 A E C B))  &  ( (~ (r1_semi_af1 A E B D))  &  ( (~ (r1_semi_af1 A E D B))  &  ( (~ (r1_semi_af1 A E C D))  &  (~ (r1_semi_af1 A E D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) (k52_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A C) (k20_valued_1 k5_numbers k1_numbers k1_numbers B D)))) ) ) ) ) ) ) ) ).
tt(t38_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (v8_valued_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k2_seq_2 A) (k8_nat_1 k1_numbers A B))) ) ) ) ) ).
tt(t38_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r1_seqfunc A k1_numbers B C) =>  ((r1_seqfunc A k1_numbers (k5_seqfunc A B) C) & (r1_seqfunc A k1_numbers (k4_seqfunc A B) C)) ) ) ) ) ) ) ).
tt(t38_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_seq_2 A) & (v8_valued_0 B))  => (v1_seq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t38_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 A (k18_complex1 (k3_funct_2 k5_numbers k1_numbers B D)))) ) ) ) )  &  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t38_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 B (k9_newton (k2_nat_1 B 1)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 1 (k13_complex1 1 (k9_newton (k2_nat_1 B 1))))) ) ) ) ) ) ) ).
tt(t38_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers))  & (r1_xxreal_0 (k1_seq_1 B (k5_real_1 C 1)) (k1_seq_1 B C))) ) )  => (r1_xxreal_0 (k1_seq_1 (k3_series_1 B) A) (k8_real_1 (k2_nat_1 A 1) (k1_seq_1 B (k2_nat_1 A 1))))) ) ) ) ) ).
tt(t38_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 8 (k3_xcmplx_0 (k3_xcmplx_0 (k6_xcmplx_0 (k13_complex1 1 A) 1) (k6_xcmplx_0 (k13_complex1 1 B) 1)) (k6_xcmplx_0 (k13_complex1 1 C) 1)))) ) ) ) ) ) ) ).
tt(t38_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((k7_setfam_1 A B) = (k7_setfam_1 A C))  =>  (B = C) ) ) ) ) ) ) ).
tt(t38_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A C) D) = B) ) ) ) ) ) ) ) ) ).
tt(t38_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_prob_1 A (k5_setlim_2 A C B)) = (k9_subset_1 A B (k1_prob_1 A C))) ) ) ) ) ) ).
tt(t38_setwiseo,ax, (! [A:$i] : (v1_binop_1 (k9_setwiseo A) (k5_finsub_1 A))) ).
tt(t38_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ((v1_setwiseo D A) &  ( (B = (k4_binop_1 A D))  &  ((r6_binop_1 A E D) &  ((k5_binop_1 A E C B) = B) ) ) ) ) )  =>  ((k5_binop_1 A E C (k1_finsop_1 A F D)) = (k1_finsop_1 A (k3_finseqop A A A E C F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_sf_mastr A) = (k4_sf_mastr (k61_valued_1 A B))) ) ) ) ) ).
tt(t38_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A B C)))) = (k5_sheffer1 A B (k5_sheffer1 A C C))) ) ) ) ) ) ) ) ) ).
tt(t38_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k7_simplex0 A B C)))) =>  ( (E = D)  =>  ((k7_simplex0 A (k7_simplex0 A B C) E) = (k7_simplex0 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_ordinal1 B) &  ((v1_finset_1 B) &  ((v5_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ( ((v1_setfam_1 B) &  ((k5_card_1 B) = (k5_card_1 (k5_setfam_1 (u1_struct_0 A) B))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v1_rlaffin1 (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) A) =>  ((r2_hidden C (k5_setfam_1 (u1_struct_0 A) B)) |  ((a_3_0_simplex1 A B C) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) B) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C))))))) ) ) ) ) ) ) ) ) ) ).
tt(t38_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t38_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_fcont_1 k1_sin_cos2 A)) ) ).
tt(t38_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A) = (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A)) ) ) ).
tt(t38_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos B) (k20_sin_cos B)) (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos A)))) ) ) ) ) ).
tt(t38_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_real_1 (k5_square_1 (k2_sin_cos5 A)) (k5_square_1 (k9_sin_cos2 A))) = 1) ) ) ).
tt(t38_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 (k17_sin_cos A) (k1_real_1 1))) ) ) ) ) ) ) ).
tt(t38_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_sin_cos7 A) = (k11_binop_2 2 (k2_sin_cos7 (k7_square_1 (k12_binop_2 (k9_binop_2 A 1) 2))))) ) ) ) ).
tt(t38_sin_cos9,ax, ( ((k6_sin_cos9 (k1_real_1 1)) = (k8_real_1 (k10_real_1 3 4) k32_sin_cos))  &  ((k1_seq_1 k2_sin_cos9 (k1_real_1 1)) = (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) ) ).
tt(t38_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = B)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 A (k8_nat_1 k1_numbers C D))) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(t38_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_sppol_1 C D B) =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 (k3_finseq_1 C) A) | (r1_sppol_1 2 (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k17_euclid A) = (k17_euclid B))  |  ((k18_euclid A) = (k18_euclid B)) )  => (v1_topreal1 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t38_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_sprect_1 A) 4) = (k10_pscomp_1 A)) ) ) ).
tt(t38_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  &  ( ( ( (~ (r1_xxreal_0 B 1))  & (r1_xxreal_0 C (k3_finseq_1 A)))  |  ((r1_xxreal_0 1 B) &  (~ (r1_xxreal_0 (k3_finseq_1 A) C)) ) )  &  (~  ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k2_goboard9 A)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k3_goboard9 A)) &  ((k2_jordan5c (k3_topreal1 2 B) (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) = (k11_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(t38_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) 1)) ) ) ) ).
tt(t38_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((k7_xcmplx_0 1 (k6_xcmplx_0 (k6_square_1 A) (k6_square_1 B))) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B)) (k6_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t38_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k14_stacks_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_stacks_1 A))) =>  ( ( (D = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B))  &  (E = C) )  =>  ((r2_hidden (k7_stacks_1 A B C) (k7_stacks_1 (k14_stacks_1 A) D E)) &  ((k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) (k7_stacks_1 A B C)) = (k7_stacks_1 (k14_stacks_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k23_binop_2 A 1) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_2 C B) &  ((v1_stirl2_1 C (k23_binop_2 A 1) B) &  ((k2_partfun1 (k23_binop_2 A 1) B C A) = D) ) )  =>  ( ((k1_stirl2_1 (k23_binop_2 A 1) B C (k1_seq_4 (k2_stirl2_1 (k23_binop_2 A 1) B C A))) = (k1_seq_4 A))  |  ((v2_funct_2 D B) & (v1_stirl2_1 D A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ( ((v3_substut1 (k7_sublemma A C B) A) & (r2_hidden B (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))))  =>  ( (~ (r2_hidden (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))))  &  (~ (r2_hidden (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) (k9_substut1 A (k2_sublemma A C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k4_enumset1 B C D E F G) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k25_substut1 A C B)) =>  ( ((m2_subset_1 (k37_substut1 A C) (k9_qc_lang1 A) (k3_cqc_lang A)) & (v3_substut1 (k25_substut1 A C B) A))  => (m2_subset_1 (k37_substut1 A (k24_substut1 A (k25_substut1 A C B) D)) (k9_qc_lang1 A) (k3_cqc_lang A))) ) ) ) ) ) ) ) ) ).
tt(t38_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (~ (v1_xboole_0 (k2_relset_1 k7_numbers A)))  &  ((v4_card_3 (k2_relset_1 k7_numbers A)) & (m1_subset_1 (k2_relset_1 k7_numbers A) (k1_zfmisc_1 k7_numbers))) ) ) ) ).
tt(t38_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ( ((k3_relat_1 A B) = A)  &  ((k3_relat_1 B (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B)))) = k1_xboole_0) )  =>  ((k3_relat_1 A (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B)))) = k1_xboole_0) )  &  ( ( ((k3_relat_1 B A) = A)  &  ((k3_relat_1 (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) B) = k1_xboole_0) )  =>  ((k3_relat_1 (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) A) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t38_taxonom1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v5_tbsp_1 B) & (l1_metric_1 B)) ) ) )  =>  ((r1_xxreal_0 (k3_tbsp_1 B (k2_struct_0 B)) A) => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k3_taxonom1 B A) (k13_lang1 (u1_struct_0 B) (k3_taxonom1 B A)))) ) ) ) ) ).
tt(t38_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ( (~ (v2_struct_0 (g3_lattices (k9_tdlat_1 A) (k10_tdlat_1 A) (k11_tdlat_1 A))))  &  ((v10_lattices (g3_lattices (k9_tdlat_1 A) (k10_tdlat_1 A) (k11_tdlat_1 A))) &  ((v17_lattices (g3_lattices (k9_tdlat_1 A) (k10_tdlat_1 A) (k11_tdlat_1 A))) & (l3_lattices (g3_lattices (k9_tdlat_1 A) (k10_tdlat_1 A) (k11_tdlat_1 A)))) ) ) ) ) ).
tt(t38_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))))) ) ) ) ).
tt(t38_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  => (v4_tdlat_3 B)) )  => (v5_tdlat_3 A)) ) ) ).
tt(t38_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  => (r8_pboole (k15_pre_poly A) (k4_polynom1 A C (k5_termord A B C D) (k6_termord A B C D)) D)) ) ) ) ) ) ) ) ).
tt(t38_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_tex_2 B A) <=> (v1_zfmisc_1 B)) ) ) ) ) ).
tt(t38_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r4_tsep_2 A B C) =>  ((v4_tex_3 B A) <=> (v2_tex_3 C A)) ) ) ) ) ) ) ) ).
tt(t38_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (r1_tarski C B))  => (r1_tarski (k3_tex_4 A C) B)) ) ) ) ) ) ) ).
tt(t38_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  ( (~ (r1_tsep_1 C B))  =>  ((v1_borsuk_1 (k2_tsep_1 A C B) B) & (m1_pre_topc (k2_tsep_1 A C B) B)) ) ) ) ) ) ) ) ).
tt(t38_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r1_tarski (k4_toler_1 A B) (k3_toler_1 A B))) ) ) ).
tt(t38_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D C) =>  (! [H:$i] :  ((m1_borsuk_2 H A C E) => (r4_borsuk_2 A B E (k1_borsuk_2 A B C E (k1_borsuk_2 A B D C (k1_borsuk_2 A B C D F (k2_borsuk_2 A D C G)) G) H) (k1_borsuk_2 A B C E F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ( ( ((k1_xxreal_2 (k9_xtuple_0 B)) = (k2_xxreal_2 (k9_xtuple_0 C)))  &  ((k3_topalg_6 A B) = (k2_topalg_6 A C)) )  =>  ((v7_topalg_6 (k4_topalg_6 A B C) A) &  ( ((k9_xtuple_0 (k4_topalg_6 A B C)) = (k1_rcomp_1 (k2_xxreal_2 (k9_xtuple_0 B)) (k1_xxreal_2 (k9_xtuple_0 C))))  &  ( ((k1_funct_1 (k4_topalg_6 A B C) (k2_xxreal_2 (k9_xtuple_0 B))) = (k2_topalg_6 A B))  &  ((k1_funct_1 (k4_topalg_6 A B C) (k1_xxreal_2 (k9_xtuple_0 C))) = (k3_topalg_6 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_waybel23 (k1_pre_topc A B)) =>  ( ((v1_topdim_1 B A) & (r1_xxreal_0 (k2_topdim_1 A B) k6_numbers))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C D) &  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden C E) &  ((r1_tarski E D) & (r1_xboole_0 B (k2_tops_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v4_topgen_1 B A) => (v2_topgen_1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t38_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A)))) =>  (~  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden C B) =>  ((v2_pre_topc (g1_pre_topc A C)) & (l1_pre_topc (g1_pre_topc A C))) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( (C = (k8_setfam_1 (k9_setfam_1 A) B))  &  ( ((v2_pre_topc (g1_pre_topc A C)) & (l1_pre_topc (g1_pre_topc A C)))  &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden D B) => (m2_yellow_9 (g1_pre_topc A D) (g1_pre_topc A C))) ) )  &  (! [D:$i] :  ( ((v2_pre_topc D) & (l1_pre_topc D))  =>  ( ( ((u1_struct_0 D) = A)  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden E B) => (m2_yellow_9 (g1_pre_topc A E) D)) ) ) )  => (m2_yellow_9 (g1_pre_topc A C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_topgen_3 A B)))))  =>  ((v4_pre_topc C (k6_topgen_3 A B)) <=> (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t38_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_topgen_4 B A) => (v5_topgen_4 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t38_topgen_5,ax, ((v1_tops_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) k3_topgen_5) & (m1_subset_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t38_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_topgrp_1 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k6_algstr_0 A B C)) =>  (? [E:$i] :  ((m1_connsp_2 E A B) &  (? [F:$i] :  ((m1_connsp_2 F A C) & (r1_tarski (k2_group_2 A E F) D)) ) ) ) ) ) ) ) ) )  => (v4_topgrp_1 A)) ) ) ).
tt(t38_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k7_topreal1 A)) &  ((r2_hidden A (k5_topreal1 A)) &  ((r2_hidden A (k4_topreal1 A)) & (r2_hidden A (k6_topreal1 A))) ) ) ) ) ).
tt(t38_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) & (r2_hidden (k2_nat_1 B 1) (k4_finseq_1 A)))  =>  ((k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) (k2_nat_1 B 1) A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A)) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1))))) ) ) ) ) ) ).
tt(t38_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (~ (v1_xboole_0 (a_1_0_topreal6 A)))  &  ((v2_connsp_1 (a_1_0_topreal6 A) (k15_euclid 2)) &  ((v1_convex1 (a_1_0_topreal6 A) (k15_euclid 2)) & (m1_subset_1 (a_1_0_topreal6 A) (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) ).
tt(t38_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) =>  (~  ( (G = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2))))  &  ( (H = E)  &  ( (I = F)  &  ( (~  (D = E) )  &  ((r2_hidden D (k3_topreal9 A F B)) &  ((r2_hidden E (k2_topreal9 A F B)) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (J = D) )  &  ( ((k2_tarski D J) = (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A D E) (k3_topreal9 A F B)))  &  ( ((r2_hidden E (k3_topreal9 A F B)) =>  (J = E) )  &  ( (C = (k10_real_1 (k7_real_1 (k1_real_1 (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid A) E (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2)))) (k5_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2))) F)))) (k7_square_1 (k2_quin_1 (k18_rvsum_1 (k11_euclid A (k8_euclid A H G))) (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid A) E (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2)))) (k5_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2))) F))) (k9_real_1 (k18_rvsum_1 (k11_euclid A (k8_euclid A G I))) (k3_square_1 B))))) (k8_real_1 2 (k18_rvsum_1 (k11_euclid A (k8_euclid A H G))))))  =>  ((r2_hidden E (k3_topreal9 A F B)) |  (J = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) D (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid A) E (k10_real_1 1 2))) (k9_real_1 1 C)) (k1_rlvect_1 (k15_euclid A) E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_topmetr C D)))) => (m1_subset_1 (k4_card_3 (k4_funct_4 1 2 E F)) (k1_zfmisc_1 (u1_struct_0 (k1_topreala A B C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_toprealb,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc k2_topalg_2 A)) (u1_struct_0 (k8_toprealb 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 A)) (u1_struct_0 (k8_toprealb 2)))))) )  =>  ( ((r1_tarski (k3_rcomp_1 k6_numbers 1) A) &  (B = (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb A)) )  => (v2_funct_2 B (u1_struct_0 (k8_toprealb 2)))) ) ) ) ) ).
tt(t38_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k49_valued_2 A (u1_struct_0 (k15_euclid B)) D C)) &  ((v1_funct_2 (k49_valued_2 A (u1_struct_0 (k15_euclid B)) D C) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k49_valued_2 A (u1_struct_0 (k15_euclid B)) D C) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t38_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 C A) => (v3_toprns_1 (k2_toprns_1 B A C) A)) ) ) ) ) ) ) ).
tt(t38_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_tops_1 A (k2_pre_topc A B)) (k2_tops_1 A B))) ) ) ) ).
tt(t38_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 C A) => (v2_tops_2 (k1_tops_2 A B C) (k1_pre_topc A B))) ) ) ) ) ) ) ).
tt(t38_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (r1_tarski B C))  => (v1_tops_3 C A)) ) ) ) ) ) ) ).
tt(t38_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  => (v4_transgeo (k6_partfun1 (u1_struct_0 A)) A)) ) ).
tt(t38_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((m4_trees_1 k1_xboole_0 A) & (m4_trees_1 (k1_tarski k1_xboole_0) A)) ) ) ).
tt(t38_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k2_trees_2 A C) = (k2_trees_2 B C)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t38_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v6_trees_3 A)) ) )  =>  ((k3_finseq_1 (k2_funct_6 A)) = (k3_finseq_1 A)) ) ) ).
tt(t38_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  ((k4_finseq_1 (k2_trees_9 A B)) = (k4_finseq_1 (k1_trees_9 (k9_xtuple_0 A) B))) ) ) ) ) ).
tt(t38_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A) & (r1_connsp_1 A B C))  =>  ((v3_pre_topc B A) & (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t38_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A B D) &  ((r4_tsep_2 A C E) & (r3_tsep_1 A B C)) )  => (r4_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 3 A) => (r3_turing_1 k20_turing_1 (k5_comput_1 A 3))) ) ) ).
tt(t38_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((k3_msafree2 (k40_twoscomp A B)) = (k2_tarski (k4_tarski (k10_finseq_1 A B) k15_twoscomp) (k4_tarski (k10_finseq_1 A B) k3_twoscomp))) ) ) ) ) ).
tt(t38_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ( ((k3_funct_2 k5_numbers (u1_struct_0 A) (k4_uniroots B A) k6_numbers) = (k4_algstr_0 A (k1_group_1 A)))  &  ((k3_funct_2 k5_numbers (u1_struct_0 A) (k4_uniroots B A) B) = (k1_group_1 A)) ) ) ) ) ) ).
tt(t38_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k1_algseq_1 A (k11_polynom3 A (k4_polynom5 A B (k5_struct_0 A)) C)) = (k2_nat_1 (k1_algseq_1 A C) 1)) ) ) ) ) ) ) ).
tt(t38_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) => (r1_valuat_1 A B (k8_cqc_lang A (k11_cqc_lang A C E) E) F D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_finset_1 A)) ) ) )  =>  ((k5_card_1 (k63_valued_1 A)) = (k6_xcmplx_0 (k5_card_1 A) 1)) ) ) ).
tt(t38_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k45_valued_1 B C) A) = (k45_valued_1 (k14_valued_2 B A) (k14_valued_2 C A))) ) ) ) ) ) ) ).
tt(t38_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 D C C) &  ((v1_mod_2 D B C C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((r1_xxreal_0 1 A) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 C)) &  ((v13_vectsp_1 F C C) &  ((v1_mod_2 F B C C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 C))))) ) ) )  =>  (~  ((r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k1_vectsp11 C (k3_matrlin B C C D (k4_matrlin B C C (k3_struct_0 C) E)) A) (k3_matrlin B C C (k6_matrlin2 B C C C F D) (k1_vectsp11 C (k4_matrlin B C C (k3_struct_0 C) E) A))) &  (! [G:$i] :  ((v7_ordinal1 G) => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k6_matrlin2 B C C C F (k1_vectsp11 C D G)) (k6_matrlin2 B C C C (k1_vectsp11 C D G) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (m1_vectsp_4 (k1_vectsp_4 A C) A B)) ) ) ) ) ) ).
tt(t38_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  ((r1_vectsp_5 A B D C) & (r1_vectsp_5 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t38_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ((k1_vectsp_6 A B (k7_vectsp_6 A B C)) = (k1_vectsp_6 A B C)) ) ) ) ) ) ) ).
tt(t38_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_4 D A C) => (r1_tarski (k2_vectsp_9 A D B) (k2_vectsp_9 A C B))) ) ) ) ) ) ) ) ).
tt(t38_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_partfun1 E A) & (v1_partfun1 D A))  =>  ((k7_partfun1 (u1_struct_0 C) (k3_vfunct_1 A C E D) B) = (k1_rlvect_1 C (k7_partfun1 (u1_struct_0 C) D B) (k1_seq_1 E B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((v1_partfun1 D A) & (v1_partfun1 C A))  =>  ((k7_partfun1 (u1_struct_0 B) (k1_vfunct_2 A B D C) E) = (k1_clvect_1 B (k7_partfun1 (u1_struct_0 B) C E) (k7_partfun1 k2_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_yellow_0 A B) =>  ((k2_yellow_0 A B) = (k2_yellow_0 A (k4_waybel_0 A B))) ) ) ) ) ) ).
tt(t38_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r2_hidden C (k6_yellow_6 A)) =>  ((r1_waybel11 A C B) <=> (r2_hidden B (k10_yellow_6 A C))) ) ) ) ) ) ) ) ).
tt(t38_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v3_waybel12 (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A)) A)) ) ).
tt(t38_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (a_2_4_waybel14 A B))) ) )  => (v3_waybel_3 A)) ) ) ).
tt(t38_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_pre_topc (k6_waybel_0 A B) A) &  ((v4_pre_topc (k5_waybel_0 A B) A) & (v4_pre_topc (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ) ) ).
tt(t38_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_orders_3 B A A) =>  ( (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 C A D E) C A) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) E D))) ) ) ) ) ) ) )  | (v7_waybel_1 B A)) ) ) ) ) ) ).
tt(t38_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) &  ((v3_waybel_3 C) & (l1_orders_2 C)) ) ) ) ) ) )  =>  (~  ( ((u1_struct_0 C) = (k8_eqrel_1 (u1_struct_0 A) (k2_waybel20 A B)))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) D E) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k2_waybel20 A B) E)) ) )  => (m1_waybel16 D A C)) ) ) ) ) ) )  |  ( (~ (v2_struct_0 (k5_yellow_0 (k3_yellow_3 A A) B)))  &  ((v4_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) &  ((v7_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) &  ((v4_waybel_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A)) & (m1_yellow_0 (k5_yellow_0 (k3_yellow_3 A A) B) (k3_yellow_3 A A))) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m2_yellow_6 C A B) =>  (! [D:$i] :  ((m2_waybel21 D A B C) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (~  ((r1_orders_2 B (k2_yellow_6 (u1_struct_0 C) B D F) E) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (~  ((r1_orders_2 C F G) & (r1_orders_2 A (k2_waybel_0 A C G) (k2_waybel_0 A B E))) ) ) ) ) ) ) ) ) )  =>  ((k1_waybel11 A B) = (k1_waybel11 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel23 (k6_waybel_0 A B) A)) ) ) ) ).
tt(t38_waybel24,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  ((k2_waybel17 A B) = (k3_waybel24 A B)) ) ) ) ) ).
tt(t38_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  =>  ((v1_compts_1 A) &  ((v6_waybel_3 A) & (v4_yellow_8 A)) ) ) ) ).
tt(t38_waybel26,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) (k5_waybel26 C)) <=>  ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k1_funct_1 C A))) ) ) ) ) ) ).
tt(t38_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C))) &  ((v22_waybel_0 D B (k6_yellow_1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C)))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v1_funct_1 (k1_funct_1 (k10_funct_6 D) E)) &  ((v1_funct_2 (k1_funct_1 (k10_funct_6 D) E) (u1_struct_0 B) (u1_struct_0 C)) &  ((v22_waybel_0 (k1_funct_1 (k10_funct_6 D) E) B C) & (m1_subset_1 (k1_funct_1 (k10_funct_6 D) E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v19_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ) ).
tt(t38_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (a_2_5_waybel30 A B))) ) ) ) ) ).
tt(t38_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_waybel_0 (k1_yellow_2 A A B) A) => (v1_waybel34 (k2_waybel_1 A A B) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t38_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  ( (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B D) &  ((r1_tarski D C) & (v2_compts_1 D A)) ) ) )  => (r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C)) ) ) ) ) ) ) ).
tt(t38_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v2_waybel_2 A)) ) ).
tt(t38_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_waybel_5 A) <=>  ((v3_waybel_3 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (B = (k1_yellow_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) => (v6_waybel_6 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_subset_1 (k4_waybel_0 A (k12_waybel_0 A (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)))) (k1_waybel_3 A B)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r1_waybel_3 A (k2_yellow_0 A C) B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) & (r3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((v10_waybel_0 B A) =>  ((r1_waybel_9 A B) & (r2_hidden (k1_waybel_2 A B) (k10_yellow_6 A B))) ) ) ) ) ) ) ).
tt(t38_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v8_struct_0 A) &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v5_group_1 A)) ) ).
tt(t38_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) => (r4_wellord1 A A)) ) ).
tt(t38_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( ((k3_int_2 A B) = 1)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ( (~  (k6_numbers = C) )  &  ( (~  (k6_numbers = D) )  &  ((r1_xxreal_0 C (k6_square_1 A)) &  ((r1_xxreal_0 D (k6_square_1 A)) &  ((r1_int_1 A (k2_xcmplx_0 (k3_xcmplx_0 B C) D)) | (r1_int_1 A (k6_xcmplx_0 (k3_xcmplx_0 B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A (k4_xboole_0 B A)) =>  (A = k1_xboole_0) ) ) ) ).
tt(t38_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k5_xboolean A (k9_xboolean B C)) = (k4_xboolean (k5_xboolean A (k3_xboolean B)) (k5_xboolean A (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t38_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A (k6_xcmplx_0 B C)) = (k2_xcmplx_0 A (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t38_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 B C))  => (r1_xxreal_0 B (k2_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(t38_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k12_xtuple_0 A) (k12_xtuple_0 B)) (k12_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t38_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k3_xxreal_0 A (k4_xxreal_0 B C)) = (k4_xxreal_0 (k3_xxreal_0 A B) (k3_xxreal_0 A C))) ) ) ) ) ) ) ).
tt(t38_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k2_xxreal_1 B C) (k2_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t38_xxreal_2,ax, ((k2_xxreal_2 k1_xboole_0) = k1_xxreal_0) ).
tt(t38_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) <=> (r1_xxreal_0 (k2_xxreal_3 B) (k2_xxreal_3 A))) ) ) ) ) ).
tt(t38_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_yellow_0 A (k6_domain_1 (u1_struct_0 A) B)) & (r2_yellow_0 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t38_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k4_yellow_3 A B (k5_waybel_0 (k3_yellow_3 A B) C)) = (k5_waybel_0 A (k8_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t38_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_funct_1 (k12_funct_3 (u1_struct_0 A))) &  ((v1_funct_2 (k12_funct_3 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 A A))) &  ((v5_pre_topc (k12_funct_3 (u1_struct_0 A)) A (k2_borsuk_1 A A)) & (m1_subset_1 (k12_funct_3 (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 A A)))))) ) ) ) ) ).
tt(t38_yellow14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v7_pre_topc (k4_waybel18 A B C)) & (v2_pre_topc (k4_waybel18 A B C))) ) )  => (v7_pre_topc (k3_waybel18 A B))) ) ) ) ) ).
tt(t38_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] : (m1_yellow_0 (k6_yellow_1 C B) (k6_yellow_1 C A))) ) ) ) ) ).
tt(t38_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v4_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v1_altcat_3 D A B C) &  (~  ((k10_xtuple_0 D) = (k3_yellow18 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v11_altcat_1 D) &  ((v12_altcat_1 D) & (l2_altcat_1 D)) ) ) )  =>  (! [E:$i] :  ((l2_functor0 E A B) =>  ((r3_yellow20 A B E C D) => (r2_functor0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_yellow_2,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((v12_waybel_0 C A) & (v1_waybel_0 C A)) ) ) )  =>  ((v1_waybel_0 (k6_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t38_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_lattice3 A C G) => (r1_orders_2 A G E)) ) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r2_lattice3 B D G) => (r1_orders_2 B G F)) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_yellow_3 A B))) =>  ((r2_lattice3 (k3_yellow_3 A B) (k6_yellow_3 A B C D) G) => (r1_orders_2 (k3_yellow_3 A B) G (k7_yellow_3 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r2_yellow_4 A (k4_yellow_4 A B C) B)) ) ) ) ) ) ).
tt(t38_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A B C) => (r3_orders_2 A (k1_yellow_5 A D C) (k1_yellow_5 A D B))) ) ) ) ) ) ) ) ) ).
tt(t38_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((r2_hidden B (k6_yellow_6 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~ (r2_hidden C (k10_yellow_6 A B)))  &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  (~  ((r2_hidden D (k6_yellow_6 A)) &  (! [E:$i] :  ((m2_yellow_6 E A D) =>  (~ (r2_hidden C (k10_yellow_6 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v11_waybel_1 A) & (l1_orders_2 A)) ) ) ) ) )  => (r5_waybel_1 A (k7_lattice3 A))) ) ).
tt(t38_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v2_cantor_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (~  ((r1_tarski E D) &  ((r2_hidden B (k8_setfam_1 (u1_struct_0 A) E)) & (r1_xboole_0 (k8_setfam_1 (u1_struct_0 A) E) C)) ) ) ) )  => (r2_hidden B (k2_pre_topc A C))) ) ) ) ) ) ) ) ) ).
tt(t38_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ((v2_zf_lang A) &  (~  ( (~ (v3_zf_lang A))  &  ( (~ (v4_zf_lang A))  &  ( (~ (v5_zf_lang A))  &  (~ (v6_zf_lang A)) ) ) ) ) ) )  &  ( (~  ((v3_zf_lang A) &  (~  ( (~ (v4_zf_lang A))  &  ( (~ (v5_zf_lang A))  &  (~ (v6_zf_lang A)) ) ) ) ) )  &  ( (~  ((v4_zf_lang A) &  ((v5_zf_lang A) | (v6_zf_lang A)) ) )  &  (~  ((v5_zf_lang A) & (v6_zf_lang A)) ) ) ) ) ) ) ).
tt(t38_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v5_zf_lang A) =>  ( (~  ( (B = (k21_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((k7_zf_lang B C) = A) ) ) ) ) )  &  ( ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k7_zf_lang B C) = A) ) )  =>  (B = (k21_zf_lang A)) )  &  ( (~  ( (B = (k22_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((k7_zf_lang C B) = A) ) ) ) ) )  &  ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k7_zf_lang C B) = A) ) )  =>  (B = (k22_zf_lang A)) ) ) ) ) ) ) ) ) ) ).
tt(t38_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( ((k1_tarski A) = (k2_xboole_0 B C))  &  ( (~  (B = C) )  &  ( (~  (B = k1_xboole_0) )  &  (~  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t38_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (~  ((r2_hidden B C) &  ( (D = (k4_classes1 C))  & (r2_zfrefle1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t38_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_struct_0 C B) => (r1_struct_0 C (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t390_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k1_tarski A)) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t391_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t392_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k2_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t393_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k4_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 C B)) = (k2_xboole_0 (k3_xxreal_1 A C) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t394_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 C B)) = (k2_xboole_0 (k1_xxreal_1 A C) (k4_xxreal_1 B k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t395_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((k6_subset_1 (k2_xxreal_1 B k1_xxreal_0) (k3_xxreal_1 B A)) = (k2_xboole_0 (k1_tarski B) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ).
tt(t396_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k4_xxreal_1 B A)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ).
tt(t397_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 k1_xxreal_0) (k3_xxreal_1 B A)) = (k2_xboole_0 (k1_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ).
tt(t398_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 k1_numbers (k4_xxreal_1 B A)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 B) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ).
tt(t399_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 k1_numbers (k3_xxreal_1 B A)) = (k2_xboole_0 (k3_xxreal_1 k2_xxreal_0 B) (k4_xxreal_1 A k1_xxreal_0))) ) ) ) ) ).
tt(t39_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r1_abcmiz_0 A B C) <=> (r3_abcmiz_0 A B (k12_finseq_1 (u1_abcmiz_0 A) C))) ) ) ) ) ) ) ).
tt(t39_abcmiz_1,ax,(r1_subset_1 (k2_tarski k9_abcmiz_1 k10_abcmiz_1) k20_abcmiz_1)).
tt(t39_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_abcmiz_a B A) & (m1_subset_1 B (u4_struct_0 A)))  => (m1_abcmiz_1 (k4_trees_4 (k4_tarski B (u1_struct_0 A)) k1_xboole_0) A (k2_msualg_1 A B))) ) ) ) ).
tt(t39_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D G) &  ((r2_hidden E G) & (r3_aff_1 A F G)) ) ) )  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r5_aff_1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B D) &  ((r1_tarski C D) & (v1_aff_4 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ( (D = (k7_afinsq_1 A B C))  <=>  ( ((k1_afinsq_1 D) = 3)  &  ( ((k1_funct_1 D k6_numbers) = A)  &  ( ((k1_funct_1 D 1) = B)  &  ((k1_funct_1 D 2) = C) ) ) ) ) ) ) ) ) ) ).
tt(t39_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k6_afinsq_2 A (k7_afinsq_1 C D E) B) = (k5_binop_1 A B (k5_binop_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 (k14_afproj A))) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k14_afproj A))) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k14_afproj A))) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k14_afproj A))) &  ((r1_incsp_1 (k14_afproj A) C B) &  ((r1_incsp_1 (k14_afproj A) D B) &  ((r1_incsp_1 (k14_afproj A) E B) &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_afvect0 A B (k1_afvect0 A C (k1_afvect0 A D E))) = (k1_afvect0 A D (k1_afvect0 A C (k1_afvect0 A B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_pua2mss1 A B C D) => (m1_instalg1 (k2_algspec1 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t39_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B))))) )  &  ((v1_group_6 D (k14_algstr_4 A) B) & (r1_algstr_4 D (k3_relat_1 (k2_funct_1 (k16_algstr_4 A 1)) C))) ) ) ) ) ) ) ) ) ).
tt(t39_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v2_altcat_2 B A) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B E F)) =>  ( ( (E = C)  &  ( (F = D)  &  (G = H) ) )  =>  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  ( ((k1_altcat_1 B F E) = k1_xboole_0)  |  ( ((v1_altcat_3 G A C D) => (v1_altcat_3 H B E F))  &  ( ((v2_altcat_3 G A C D) => (v2_altcat_3 H B E F))  &  ((v3_altcat_3 G A C D) => (v3_altcat_3 H B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  ((v3_analmetr A) <=>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ((r2_analoaf A B C D D) &  ( (~  ((r2_analoaf A B C F G) &  ((r2_analoaf A B C H I) &  ( (~ (r2_analoaf A F G H I))  &  (~  (B = C) ) ) ) ) )  &  ( ((r2_analoaf A B C B D) => (r2_analoaf A C B C D))  &  ( (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ((r2_analoaf A B C D J) & (r2_analoaf A B D C J)) ) )  &  ( (~  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) => (r2_analoaf A J K J L)) ) ) ) ) ) )  &  ( (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ((r2_analoaf A B C D J) &  (~  (D = J) ) ) ) )  &  ( (~  ((r2_analoaf A B C C E) &  ( (~  (C = B) )  &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ((r2_analoaf A D C C J) & (r2_analoaf A D B E J)) ) ) ) ) ) )  &  ( ((r4_analmetr A B C B C) =>  (B = C) )  &  ((r4_analmetr A B C D D) &  ( ((r4_analmetr A B C D E) =>  ((r4_analmetr A B C E D) & (r4_analmetr A D E B C)) )  &  ( (~  ((r4_analmetr A B C F G) &  ((r2_analoaf A B C H I) &  ( (~ (r4_analmetr A F G H I))  &  (~  (B = C) ) ) ) ) )  &  ( (~  ((r4_analmetr A B C F G) &  ((r4_analmetr A B C H I) &  ( (~ (r2_analoaf A F G H I))  &  (~  (B = C) ) ) ) ) )  &  ( (? [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) &  ((r4_analmetr A B C D J) &  (~  (D = J) ) ) ) )  &  (~  ( (~ (r2_analoaf A B C D E))  &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B J) & (r2_analoaf A D E D J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (F = G) )  & (r2_analort A B C F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_freealg B A) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  ( (! [D:$i] :  ((m2_subset_1 D k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ((r2_hidden E (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A D))) &  ((r2_hidden (k1_funct_1 (k2_pua2mss1 A D) E) B) &  (D = C) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((r2_hidden D (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A C))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k1_funct_1 (k2_pua2mss1 A C) D) (k9_aofa_000 A B (k1_nat_1 E 1))) => (r1_tarski (k10_xtuple_0 D) (k9_aofa_000 A B E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E F G)) D) = 1) )  &  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E F G)) D) = k6_numbers) )  &  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F)))  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E G F)) D) = 1) )  &  ( ((r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F)) =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E G F)) D) = k6_numbers) )  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = D) )  =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E G F)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (C = (k2_xboole_0 (k1_tarski A) (a_2_7_armstrng A B)))  =>  ((v1_armstrng C A) & (v2_finsub_1 C)) ) ) ) ) ) ) ).
tt(t39_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((k8_arytm_3 (k6_arytm_3 A) (k7_arytm_3 A)) = A) ) ) ).
tt(t39_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) &  ((v6_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v7_asympt_0 A) &  ((r1_xxreal_0 2 C) & (r2_hidden B (k10_asympt_0 A (a_1_3_asympt_0 C)))) )  => (r2_hidden B (k7_asympt_0 A))) ) ) ) ) ) ) ).
tt(t39_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k7_asympt_1 B)) ) )  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v4_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (~  ((r2_funct_2 k5_numbers k1_numbers B A) &  ((v6_asympt_0 A) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 (k3_asympt_1 1) C))) )  &  (~ (v7_asympt_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_bagorder A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_bagorder A))) =>  ((r2_hidden (k1_domain_1 (u1_struct_0 (k14_bagorder A)) (u1_struct_0 (k14_bagorder A)) B C) (u1_orders_2 (k14_bagorder A))) <=>  (? [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k5_finsub_1 (u1_struct_0 A))) &  ( (B = D)  &  ( (C = E)  &  (~  ( (~  (D = k1_xboole_0) )  &  ( (~  ( (~  (D = k1_xboole_0) )  &  ( (~  (E = k1_xboole_0) )  &  ( (~  ((k11_bagorder A D) = (k11_bagorder A E)) )  & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k11_bagorder A D) (k11_bagorder A E)) (u1_orders_2 A))) ) ) )  &  (~  ( (~  (D = k1_xboole_0) )  &  ( (~  (E = k1_xboole_0) )  &  ( ((k11_bagorder A D) = (k11_bagorder A E))  & (r2_hidden (k1_domain_1 (k1_zfmisc_1 D) (k1_zfmisc_1 E) (k6_subset_1 D (k6_domain_1 (u1_struct_0 A) (k11_bagorder A D))) (k6_subset_1 E (k6_domain_1 (u1_struct_0 A) (k11_bagorder A E)))) (k13_bagorder A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_bcialg_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k7_bcialg_1 A C)) => (r2_hidden (k1_bcialg_1 A D E) (k7_bcialg_1 A (k6_bcialg_1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t39_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m4_bcialg_2 C A B) =>  ((v12_bcialg_1 B A) <=>  (B = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) C (k4_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t39_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ).
tt(t39_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_4 A B C) (k1_bcialg_4 A C D)) (k1_bcialg_4 A D B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t39_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_bcialg_1 D) &  ((v4_bcialg_1 D) &  ((v5_bcialg_1 D) &  ((v7_bcialg_1 D) & (l2_bcialg_1 D)) ) ) ) )  =>  ( ( (B = (k4_bcialg_1 D))  &  (C = (k5_bcialg_1 D)) )  =>  ((k9_subset_1 (u1_struct_0 A) B C) = (k1_tarski (k4_struct_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t39_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v2_bcialg_6 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) D E) (u1_struct_0 B) (u1_struct_0 C)) &  ((v2_bcialg_6 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) D E) B C) & (m1_subset_1 (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A C D)) B) =>  ((r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A (k1_bcialg_1 A C D) C))) B) &  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A D (k1_bcialg_1 A D C)) C) B) & (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A D (k1_bcialg_1 A D C)) (k1_bcialg_1 A C D)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_bhsp_1 A B C) = (k7_square_1 (k2_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A B C)))) ) ) ) ) ) ) ).
tt(t39_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 D A) &  ((k1_bhsp_2 A D) = B) )  =>  ((v2_comseq_2 (k3_bhsp_2 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C))) &  ((k2_seq_2 (k3_bhsp_2 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v1_bhsp_3 B A) => (v1_bhsp_3 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t39_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) D) (k1_normsp_1 A (k1_bhsp_4 A B) C))) (k18_complex1 (k9_real_1 (k1_seq_1 (k3_series_1 (k2_bhsp_2 A B)) D) (k1_seq_1 (k3_series_1 (k2_bhsp_2 A B)) C))))) ) ) ) ) ) ) ) ).
tt(t39_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear J A B C) &  ((v2_bilinear J A B C) &  ((v3_bilinear J A B C) &  ((v4_bilinear J A B C) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J (k5_algstr_0 B D (k4_vectsp_1 A B H E)) (k5_algstr_0 C F (k4_vectsp_1 A C I G))) = (k5_algstr_0 A (k5_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J D F) (k6_algstr_0 A I (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J D G))) (k5_algstr_0 A (k6_algstr_0 A H (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J E F)) (k6_algstr_0 A H (k6_algstr_0 A I (k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) J E G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A (k3_lattices A B C) C) (k1_boolealg A B C))) ) ) ) ) ) ).
tt(t39_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_borsuk_1 (k10_borsuk_1 A) A)) ) ).
tt(t39_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_topreal1 (k15_euclid A) C D B) => (r1_borsuk_3 k1_borsuk_4 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k7_domain_1 (u1_struct_0 (k15_euclid A)) C D))))) ) ) ) ) ) ) ) ) ).
tt(t39_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = B)  =>  ((v3_rcomp_1 A) <=> (v3_pre_topc B k3_topmetr)) ) ) ) ) ) ).
tt(t39_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((v5_pre_topc D k5_topmetr A) =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D) (u1_struct_0 k5_topmetr) (u1_struct_0 A)) &  ((v5_pre_topc (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D) k5_topmetr A) & (m1_subset_1 (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc C (k4_topmetr A B) k3_topmetr) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr A B)) (u1_struct_0 k3_topmetr))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_xxreal_0 A B) &  (C = D) )  => (v1_fcont_1 D)) ) ) ) ) ) ) ) ) ).
tt(t39_bspace,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k1_vectsp_7 k2_bspace (k7_bspace A) (k9_bspace A)) = (k7_bspace A)) ) ) ).
tt(t39_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  ( (G = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B I) (k16_funcop_1 C J)) (k16_funcop_1 D K)) (k16_funcop_1 E L)) (k16_funcop_1 F M)) (k16_funcop_1 A H)))  =>  ((k10_xtuple_0 G) = (k4_enumset1 (k1_funct_1 G A) (k1_funct_1 G B) (k1_funct_1 G C) (k1_funct_1 G D) (k1_funct_1 G E) (k1_funct_1 G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_funct_2 A k6_margrel1 (k16_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k2_bvfunc_1 A (k16_bvfunc_1 A B D) (k16_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t39_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t39_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k2_bvfunc_1 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B (k5_bvfunc_1 A B C))))) ) ) ) ) ) ).
tt(t39_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((r3_bvfunc_2 A C B E) => (r1_bvfunc_1 A (k6_bvfunc_1 A (k7_bvfunc_2 A D B E) C) (k7_bvfunc_2 A (k6_bvfunc_1 A D C) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F) (k6_bvfunc_2 A (k9_bvfunc_1 A D (k1_bvfunc_1 A E)) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A E (k1_bvfunc_1 A C)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k2_bvfunc_1 A (k2_bvfunc_1 A C D) E)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A B D)) (k5_bvfunc_1 A B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t39_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B C) (k5_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t39_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A B (k5_bvfunc_1 A B C))) ) ) ) ) ) ).
tt(t39_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B) (k1_calcul_1 (k3_cqc_lang A) C)) &  ((r4_calcul_1 A B) & (r4_calcul_1 A C)) )  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B) (k12_finseq_1 (k3_cqc_lang A) (k7_cqc_lang A (k2_calcul_1 A B) (k2_calcul_1 A C)))))) ) ) ) ) ) ) ).
tt(t39_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_finset_1 A) & (v1_finset_1 (k1_card_1 A))) ) ) ).
tt(t39_card_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k5_card_1 (k4_nat_1 A B)) = (k2_card_2 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t39_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_ordinal1 (k1_card_1 (k3_card_3 A)) (k6_card_3 (k1_card_3 A)))) ) ).
tt(t39_card_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k4_ordinal1)) => (r1_ordinal1 (k1_card_1 A) (k2_wellord2 (k1_wellord2 A)))) ) ).
tt(t39_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) => (v4_card_fil A)) ) ) ).
tt(t39_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  ((v1_finset_1 (k9_xtuple_0 A)) => (v1_finset_1 (k3_tarski (k10_xtuple_0 A)))) ) ) ).
tt(t39_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  (! [E:$i] :  ((m1_cat_1 E A C B) =>  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A C B) = k1_xboole_0)  | (v8_cat_1 D A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D (k8_cat_2 A B) C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k7_cat_1 A C (k13_cat_2 A B C D F)) E) = (k1_binop_1 (k7_cat_1 (k8_cat_2 A B) C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((v11_cat_1 B A) &  ( ((k3_graph_1 A D) = B)  &  ((k4_graph_1 A D) = C) ) )  =>  ((k11_cat_3 A B C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t39_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  ((k2_cat_1 A (k2_cat_4 A B D) (k2_cat_4 A C E)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (~  ( ((k7_afinsq_2 B) = (k1_catalan1 (k23_binop_2 A 1)))  &  ( ((k1_relset_1 k5_numbers B) = A)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 A C))  =>  ((k1_recdef_1 B C) = (k11_binop_2 (k1_catalan1 (k23_binop_2 C 1)) (k1_catalan1 (k7_nat_d A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v6_clvect_1 (k6_cc0sp2 A) (k6_cfuncdom (u1_struct_0 A)))) ) ).
tt(t39_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfcont_1 B A) <=>  ((r1_tarski A (k1_relset_1 k2_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C A) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k2_numbers) =>  (~  ((r2_hidden F A) &  ( (~ (r1_xxreal_0 E (k17_complex1 (k11_complex1 F C))))  & (r1_xxreal_0 D (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers B F) (k7_partfun1 k2_numbers B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k1_cfunct_1 A B C) (k19_valued_1 A k2_numbers k2_numbers B (k2_cfunct_1 A C)))) ) ) ) ) ) ).
tt(t39_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ( (! [B:$i] :  ((r2_hidden B (k6_cgames_1 (k13_cgames_1 A))) <=>  (? [C:$i] :  ((v2_cgames_1 C) &  ((r2_hidden C (k7_cgames_1 A)) &  (B = (k13_cgames_1 C)) ) ) ) ) )  &  (! [B:$i] :  ((r2_hidden B (k7_cgames_1 (k13_cgames_1 A))) <=>  (? [C:$i] :  ((v2_cgames_1 C) &  ((r2_hidden C (k6_cgames_1 A)) &  (B = (k13_cgames_1 C)) ) ) ) ) ) ) ) ) ).
tt(t39_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  ((r2_hidden C (k4_chain_1 A B A)) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ( (C = (k3_chain_1 A D E))  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) => (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 D F) (k1_seq_1 E F)) (k2_chain_1 A B F))) )  &  ( (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 D F))) ) )  |  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (? [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  &  ((r1_glib_001 A (k3_glib_001 A B) (k4_glib_001 A B) C) & (v1_chord C A)) ) ) ) ) ) ) ).
tt(t39_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ((m1_circcmb3 E C) =>  ((r2_hidden B (u1_struct_0 E)) =>  ((r2_hidden A (k3_msafree2 E)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 2 C D (k10_finseq_1 A B))) (k2_msafree2 E)) |  ((k2_msafree2 (k6_circcmb3 C E (k4_circcmb3 2 C D (k10_finseq_1 A B)))) = (k2_xboole_0 (k2_msafree2 E) (k1_tarski A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k5_circcomb A B) = (k4_circcomb A B (k4_tarski B A))) ) ) ) ).
tt(t39_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) & (l3_msualg_1 F B))  =>  ((r5_circtrm1 A B C D E F) => (r5_circtrm1 B A (k2_funct_1 C) (k2_funct_1 D) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r2_hidden B (k4_classes1 A)) =>  ( (~ (r2_tarski B (k4_classes1 A)))  & (r2_hidden (k1_card_1 B) (k1_card_1 (k4_classes1 A)))) ) ) ) ) ).
tt(t39_classes2,ax, (! [A:$i] : (v2_classes1 (k4_classes1 (k1_card_1 (k1_classes1 A))))) ).
tt(t39_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_clopban1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_clopban1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_clopban1 A B))) =>  ( (E = (k5_algstr_0 (k14_clopban1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k15_clopban1 A B E F) = (k5_algstr_0 B (k15_clopban1 A B C F) (k15_clopban1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_clopban3 A B k6_numbers) = (k5_struct_0 A)) ) ) ) ) ).
tt(t39_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) => (r1_lopban_4 A (k1_clvect_1 A B C) (k1_clvect_1 A B D))) ) ) ) ) ) ) ) ).
tt(t39_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_closure1 C (u1_struct_0 A) B) &  ((v2_closure1 C (u1_struct_0 A) B) &  ((v3_closure1 C (u1_struct_0 A) B) & (m2_pboole C (u1_struct_0 A) (k5_mssubfam (u1_struct_0 A) B) (k5_mssubfam (u1_struct_0 A) B))) ) )  => (r6_pboole (u1_struct_0 A) (k7_closure1 A (k6_closure1 A B C)) C)) ) ) ) ) ) ).
tt(t39_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  (! [C:$i] :  ((m1_closure2 C (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))))) )  =>  ( ((r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) D C) C) &  (! [E:$i] :  ((m1_closure2 E (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) => (r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) D E) (k11_closure2 A B E))) ) )  => (r2_hidden C (u1_closure2 A B))) ) ) ) ) ) ) ) ) ).
tt(t39_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k3_rlvect_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t39_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 D A) &  ((k1_clvect_2 A D) = B) )  =>  ((v2_comseq_2 (k3_clvect_2 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C))) &  ((k2_seq_2 (k3_clvect_2 A (k5_bhsp_1 A D C) (k3_rlvect_1 A B C))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A B) D) (k1_normsp_1 A (k1_bhsp_4 A B) C))) (k18_complex1 (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 (k2_clvect_2 A B)) D) (k8_nat_1 k1_numbers (k3_series_1 (k2_clvect_2 A B)) C))))) ) ) ) ) ) ) ) ).
tt(t39_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A B C D) = (k7_relat_1 (k8_cohsp_1 A B C) (k3_cohsp_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t39_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k19_coh_sp B)) <=>  (? [C:$i] :  ((m1_subset_1 C (k16_coh_sp B)) &  (? [D:$i] :  ((m1_subset_1 D (k16_coh_sp B)) &  ( ( ((k17_coh_sp B D) = k1_xboole_0)  =>  ((k17_coh_sp B C) = k1_xboole_0) )  &  ((v1_funct_1 A) &  ((v1_funct_2 A (k17_coh_sp B C) (k17_coh_sp B D)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k17_coh_sp B C) (k17_coh_sp B D))))) ) ) ) ) ) ) ) ) ) ).
tt(t39_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 A) = k6_numbers)  =>  ((k15_complex1 A) = (k4_xcmplx_0 A)) ) ) ) ).
tt(t39_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 (k9_complex1 A B) C) = (k1_complex2 B (k9_complex1 (k15_complex1 A) C))) ) ) ) ) ) ) ).
tt(t39_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  ( (~  (C = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_vectsp_1 k1_complfld (k3_vectsp_1 k1_complfld D A) (k3_vectsp_1 k1_complfld B C)) = (k3_vectsp_1 k1_complfld (k8_group_1 k1_complfld D C) (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k30_valued_1 (k45_valued_1 A B)) = (k1_valued_1 (k30_valued_1 A) B)) ) ) ) ) ) ).
tt(t39_compl_sp,ax, (! [A:$i] :  ((l1_metric_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v2_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) => (v6_metric_1 A))  &  ( ((v4_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) => (v8_metric_1 A))  &  ( ( ((v5_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) & (v2_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))))  => (v9_metric_1 A))  &  ( ((v3_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))) & (v2_metric_1 (k2_compl_sp A B C) (k2_xboole_0 (k2_zfmisc_1 C (k6_subset_1 (u1_struct_0 A) (k1_tarski B))) (k1_tarski (k4_tarski C B)))))  => (v7_metric_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k1_funct_1 (k8_compos_1 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A C D) E) F) B) k6_numbers) = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_comptrig,ax, ((k1_comptrig 1) = k6_numbers) ).
tt(t39_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (k2_comput_1 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (k2_comput_1 C))))) )  =>  (~  ((v1_comput_1 (k10_xtuple_0 D)) &  ( (! [E:$i] :  ((m1_subset_1 E B) => (r1_tarski (k9_xtuple_0 (k3_funct_2 B (k2_comput_1 C) D E)) (k4_finseq_2 A C))) )  &  (! [E:$i] :  ((m2_rfunct_3 E (k3_finseq_2 C) C (k2_comput_1 C)) =>  (~  ( (E = (k3_card_3 D))  & (r1_tarski (k1_relset_1 (k3_finseq_2 C) E) (k4_finseq_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k31_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(t39_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k3_comseq_2 B) = k5_complex1)  |  ((k3_comseq_2 (k51_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k13_complex1 (k3_comseq_2 A) (k3_comseq_2 B))) ) ) ) ) ) ) ).
tt(t39_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_comseq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k3_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers A D))  &  ((k4_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers B D)) ) ) )  =>  ((v2_comseq_2 C) &  ((k3_comseq_2 C) = (k2_xcmplx_0 (k2_seq_2 A) (k3_xcmplx_0 (k2_seq_2 B) k7_complex1))) ) ) ) ) ) ) ) ) ).
tt(t39_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k1_binop_1 (k10_conlat_1 A) B (k5_conlat_1 A)) = (k5_conlat_1 A)) ) ) ) ) ).
tt(t39_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v2_connsp_1 B A) & (r1_tarski (k1_connsp_1 A C) B))  =>  (B = (k1_connsp_1 A C)) ) ) ) ) ) ) ) ).
tt(t39_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_tarski B C) => (r1_tarski (k1_convex1 A B D) (k1_convex1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t39_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((k1_clvect_1 (k15_convex4 A) (k1_rlvect_2 (k15_convex4 A) C) B) = (k7_convex4 A B C)) ) ) ) ) ) ) ).
tt(t39_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 (k3_qc_lang1 A))) =>  ( ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D B G F) (k15_cqc_sim1 A E)) & (r2_hidden (k2_qc_lang3 A C) (k8_setwiseo (k3_qc_lang1 A) (k3_qc_lang1 A) F G)))  => (r2_qc_lang1 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r1_tarski (k4_cqc_the1 A) (k1_cqc_the1 A B))) ) ) ) ).
tt(t39_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A (k11_cqc_lang A D B) (k11_cqc_lang A D C)) (k11_cqc_lang A D (k9_cqc_lang A B C))) A)) ) ) ) ) ) ) ) ).
tt(t39_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) => (r1_cqc_the3 A B C)) ) ) ) ) ) ) ).
tt(t39_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_csspace A B (k4_struct_0 A))) ) ) ) ).
tt(t39_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A (k4_finseq_2 48 k6_margrel1) (k4_finseq_2 16 (k4_finseq_2 48 k6_margrel1))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 32 k6_margrel1) (k4_finseq_2 48 k6_margrel1)) (k4_finseq_2 32 k6_margrel1))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) &  ((v3_funct_2 C (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 64 k6_margrel1) (k4_finseq_2 64 k6_margrel1))))) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k41_descip_1 (k1_descip_1 (k4_finseq_2 48 k6_margrel1) 16 A) B C (k41_descip_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t39_dickson,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A 1) &  ((v1_funct_1 A) &  ((v1_partfun1 A 1) & (v1_yellow_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B 1) => (r5_waybel_1 (k3_waybel_3 1 A B) (k5_yellow_1 1 A))) ) ) ) ).
tt(t39_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_hidden (k7_real_1 A (k10_real_1 B 2)) (k1_relset_1 k1_numbers C)) & (r2_hidden (k9_real_1 A (k10_real_1 B 2)) (k1_relset_1 k1_numbers C)))  =>  ((k1_seq_1 (k5_diff_1 C B) A) = (k9_real_1 (k1_seq_1 C (k7_real_1 A (k10_real_1 B 2))) (k1_seq_1 C (k9_real_1 A (k10_real_1 B 2))))) ) ) ) ) ) ) ) ).
tt(t39_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 A D))  &  ( (~  (D = k6_numbers) )  &  (~  ((k9_real_1 D B) = k6_numbers) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k4_diff_1 C B) D) = (k10_real_1 (k1_real_1 (k8_real_1 A B)) (k8_real_1 (k9_real_1 D B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t39_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k7_square_1 D)) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 (k7_real_1 A B) k6_numbers) |  ((k1_seq_1 (k3_diff_1 C B) A) = (k9_real_1 (k7_square_1 (k7_real_1 A B)) (k7_square_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t39_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k5_diff_1 (k3_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) (k7_real_1 B (k13_complex1 A 2))) (k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B))) ) ) ) ) ) ) ).
tt(t39_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) )  =>  ((k3_dilworth A (k6_dilworth A)) = (k2_struct_0 A)) ) ) ).
tt(t39_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_analoaf B))  =>  ( (B = (k2_diraf A))  =>  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (C = D) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((r2_analoaf B C D D C) &  ((r2_analoaf B C D E E) &  ( ( ((r2_analoaf B C D E F) & (r2_analoaf B C D G H))  =>  ( (C = D)  | (r2_analoaf B E F G H)) )  &  ((r2_analoaf B C D C E) => (r2_analoaf B D C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_analoaf B C D C E)) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r2_analoaf B C E D F) &  (~  (D = F) ) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r2_analoaf B C D E F) & (r2_analoaf B C E D F)) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r2_analoaf B E C C F) &  ( (~  (C = E) )  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (~  ((r2_analoaf B D C C G) & (r2_analoaf B D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  ( (~ (r1_xxreal_0 A 2))  =>  ((k1_card_1 (a_2_0_ec_pf_1 A B)) = (k2_xcmplx_0 1 (k2_ec_pf_1 A B))) ) ) ) ) ) ).
tt(t39_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((r1_ec_pf_1 A C D) <=>  ((k7_ec_pf_2 A C) = (k7_ec_pf_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t39_ens_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_ens_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_ens_1 A))) =>  ( (~  ((k2_cat_1 (k11_ens_1 A) B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_cat_1 D (k11_ens_1 A) B C) =>  ((v8_cat_1 D (k11_ens_1 A) B C) => (v1_ens_1 (k15_ens_1 A D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k3_finseq_1 (k2_entropy1 A B)) = (k4_nat_1 (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ).
tt(t39_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_enumset1 A A A B C D) = (k2_enumset1 A B C D)) ) ) ) ) ).
tt(t39_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_eqrel_1 (k1_tarski A) A)) ) ).
tt(t39_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k12_euclid (k4_struct_0 (k15_euclid A))) = k6_numbers) ) ) ).
tt(t39_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_complex1 (k1_complex2 A B)) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B)))) ) ) ) ) ).
tt(t39_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k12_euclid (k7_euclid A B C)) (k7_real_1 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t39_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( (D = (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)))  &  ( (E = (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)))  &  ( (F = (k12_euclid (k5_algstr_0 (k15_euclid 2) B C)))  &  (G = (k6_real_1 (k2_euclid_6 B A C) 2)) ) ) )  =>  ((k18_complex1 (k1_euclid_6 B A C)) = (k6_square_1 (k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 G (k6_xcmplx_0 G D)) (k6_xcmplx_0 G E)) (k6_xcmplx_0 G F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  (! [F:$i] :  ((m2_rlvect_2 F (k10_funcsdom (k2_finseq_1 A)) D) =>  ( ((v2_funct_1 C) &  ((v1_euclid_7 D) &  ( ((k2_relset_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) C) = (k3_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) F))  &  ((r2_hidden E D) &  ((r2_hidden B (k4_finseq_1 (k5_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) C F))) &  (E = (k1_funct_1 C B)) ) ) ) ) )  =>  ((k1_binop_1 (k6_real_ns1 A) E (k4_rlvect_1 (k10_funcsdom (k2_finseq_1 A)) (k5_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) C F))) = (k1_binop_1 (k6_real_ns1 A) E (k1_rlvect_1 (k10_funcsdom (k2_finseq_1 A)) E (k1_seq_1 F (k7_partfun1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))) C B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_euclid_8 A B C) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 A) (k9_euclid 3 k3_euclid_8 B)) (k9_euclid 3 k4_euclid_8 C))) ) ) ) ) ) ) ).
tt(t39_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k4_algstr_0 (k15_euclid A) B) = (k1_rlvect_1 (k15_euclid A) B (k1_real_1 1))) ) ) ) ) ).
tt(t39_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  ((r3_euclidlp B C D) => (r3_euclidlp B (k7_euclid B C (k9_euclid B D A)) D)) ) ) ) ) ) ) ) ) ).
tt(t39_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_exchsort B)) )  =>  ((m1_exchsort A B) => (m1_exchsort B A)) ) ) ) ) ).
tt(t39_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v2_facirc_1 B)) ) )  =>  (~ (v1_facirc_1 (k2_msafree2 (k5_circcomb A B)))) ) ) ) ).
tt(t39_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (? [B:$i] :  ((v1_xreal_0 B) &  ((k2_relset_1 k1_numbers A) = (k1_seq_4 B)) ) )  => (v1_fcont_1 A)) ) ) ).
tt(t39_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos (k7_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t39_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k8_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) ) ) ) ) ) ) ) ).
tt(t39_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) &  ((r2_fdiff_1 A (k2_subset_1 k1_numbers)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 k6_numbers (k1_fdiff_1 A B))) ) ) )  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers)))) ) ) ).
tt(t39_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k19_sin_cos B) = k6_numbers) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t39_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) 2))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = 1)  &  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos C) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos C)))  &  (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos C) (k1_real_1 1))) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) 2) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) 2) A) C) = (k10_prepower (k7_real_1 1 (k1_seq_1 k19_sin_cos C)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ).
tt(t39_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k7_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t39_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t39_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_nat_1 (k1_pepin (k1_pre_ff A)) (k1_pepin (k1_pre_ff (k1_nat_1 A 1)))) = (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 1))) ) ) ).
tt(t39_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_nat_1 (k3_fib_num3 A B C) (k3_fib_num3 A B (k2_nat_1 C 3))) = (k4_nat_1 2 (k3_fib_num3 A B (k2_nat_1 C 2)))) ) ) ) ) ) ) ).
tt(t39_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 4 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 A B) |  ((v1_abian A) |  ((k1_fib_num3 (k2_xcmplx_0 A B)) = (k1_int_1 (k2_xcmplx_0 (k3_xcmplx_0 (k3_power k1_fib_num B) (k1_fib_num3 A)) 1))) ) ) ) ) ) ) ) ).
tt(t39_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) => (r2_finseq_8 A (k5_finseq_8 A B C) C 1)) ) ) ) ) ) ).
tt(t39_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k3_filter_0 A (k4_subset_1 (u1_struct_0 A) B C)) = (k5_filter_0 A B C)) ) ) ) ) ) ) ).
tt(t39_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((v13_lattices A) & (v13_lattices B))  <=> (v13_lattices (k7_filter_1 A B))) ) ) ) ) ).
tt(t39_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B C) => (r1_tarski (k6_filter_2 A B) (k7_filter_2 A C))) ) ) ) ) ) ) ).
tt(t39_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k9_finseq_1 A))  <=>  ( ((k3_finseq_1 B) = 1)  &  ((k10_xtuple_0 B) = (k1_tarski A)) ) ) ) ) ) ).
tt(t39_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ((v1_relat_1 (k3_relat_1 C B)) &  ((v1_funct_1 (k3_relat_1 C B)) & (v1_finseq_1 (k3_relat_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t39_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski B (k2_finseq_1 A)) =>  ((k3_finseq_1 (k14_finseq_1 B)) = (k5_card_1 B)) ) ) ) ) ) ).
tt(t39_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r1_tarski (k10_xtuple_0 (k5_finseq_4 A B)) (k10_xtuple_0 A))) ) ) ) ).
tt(t39_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ((r2_hidden A (k4_finseq_1 C)) => (r1_xxreal_0 (k4_finseq_4 C (k7_partfun1 B C A)) A)) ) ) ) ) ) ) ).
tt(t39_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_finseq_4 B A) => (r2_finseq_4 (k3_finseq_5 B) A)) ) ) ) ).
tt(t39_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F C B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 C C) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 B B) B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  ((k3_funct_2 C B F (k5_binop_1 C G I J)) = (k5_binop_1 B H (k3_funct_2 C B F I) (k3_funct_2 C B F J))) ) ) ) )  => (r2_funct_2 A B (k1_partfun1 A C C B (k9_funcop_1 C A G E D) F) (k9_funcop_1 B A H (k1_partfun1 A C C B E F) (k3_funct_2 C B F D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (k9_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k9_fintopo2 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t39_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fintopo3 A B k6_numbers) = B) ) ) ) ) ).
tt(t39_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) & (r1_fintopo6 A B)) )  => (v3_fin_topo B A)) ) ) ) ) ).
tt(t39_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k7_flang_1 A (k9_subset_1 (k3_catalan2 A) B C) D) (k9_subset_1 (k3_catalan2 A) (k7_flang_1 A B D) (k7_flang_1 A C D)))) ) ) ) ) ) ) ).
tt(t39_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((k6_flang_1 A (k1_flang_2 A B C D) (k1_flang_2 A B E F)) = (k6_flang_1 A (k1_flang_2 A B E F) (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k1_flang_3 A B D) (k8_flang_1 A C))) ) ) ) ) ) ) ) ).
tt(t39_fomodel0,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( (A = 1)  <=>  (~  (A = k1_xboole_0) ) ) ) ) ).
tt(t39_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_frechet2 A B C) => (r1_frechet2 A (k1_valued_0 (u1_struct_0 A) B D) C)) ) ) ) ) ) ) ) ) ).
tt(t39_fsm_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D B C)) )  =>  ( ((k2_nat_1 A 1) = (k5_card_1 (u1_struct_0 D)))  =>  ((k8_fsm_1 B C D) = (k7_fsm_1 B C D A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_fsm_3 B A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A)))))  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_fsm_3 C A (k9_flang_1 A)) & (l2_fsm_3 C A (k9_flang_1 A))) )  &  ((k6_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B) = (k6_fsm_3 A (k9_flang_1 A) C)) ) ) ) ) ) ) ).
tt(t39_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k49_gfacirc1 A B C))))  &  (? [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  (? [H:$i] :  ((m1_subset_1 H k6_margrel1) &  (? [I:$i] :  ((m1_subset_1 I k6_margrel1) &  (? [J:$i] :  ((m1_subset_1 J k6_margrel1) &  (? [K:$i] :  ((m1_subset_1 K k6_margrel1) &  ( (G = (k1_funct_1 F A))  &  ( (H = (k1_funct_1 F B))  &  ( (I = (k1_funct_1 F C))  &  ( (J = (k1_funct_1 F D))  &  ( (K = (k1_funct_1 F E))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) (k23_ftacell1 A B C D E)) = (k9_margrel1 (k1_binarith (k1_binarith (k10_margrel1 (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)) (k9_margrel1 K)) (k10_margrel1 (k9_margrel1 K) (k9_margrel1 J))) (k10_margrel1 (k9_margrel1 J) (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I))))))  &  ((k1_funct_1 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) (k24_ftacell1 A B C D E)) = (k9_margrel1 (k2_binarith (k2_binarith (k2_binarith (k2_binarith (k9_margrel1 G) (k9_margrel1 H)) (k9_margrel1 I)) (k9_margrel1 J)) (k9_margrel1 K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (r2_funct_2 B A (k1_partfun1 B A A A D (k6_funcop_1 A A C (k6_partfun1 A) E)) (k6_funcop_1 A B C D (k1_partfun1 B A A A D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t39_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ( ((k3_relat_1 A (k2_funct_1 A)) = (k4_relat_1 (k9_xtuple_0 A)))  &  ((k3_relat_1 (k2_funct_1 A) A) = (k4_relat_1 (k10_xtuple_0 A))) ) ) ) ) ).
tt(t39_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  => (r1_tarski (k8_relset_1 A B D C) A)) ) ) ) ) ).
tt(t39_funct_3,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k4_funct_3 A B)) (k2_tarski k1_xboole_0 1))) ) ).
tt(t39_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k1_funct_4 C D) = D) ) ) ) ) ) ) ) ).
tt(t39_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  ( (D = (k1_funct_1 C A))  & (r2_hidden B (k9_xtuple_0 D))) )  =>  ((r2_hidden (k4_tarski B A) (k9_xtuple_0 (k4_funct_5 C))) &  ( ((k1_binop_1 (k4_funct_5 C) B A) = (k1_funct_1 D B))  & (r2_hidden (k1_funct_1 D B) (k10_xtuple_0 (k4_funct_5 C)))) ) ) ) ) ) ) ) ) ).
tt(t39_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (~ (r2_hidden k1_xboole_0 (k10_xtuple_0 A)))  =>  ((v2_funct_1 (k7_funct_6 A)) <=>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden B (k10_xtuple_0 A)) => (v2_funct_1 B)) ) ) ) ) ) ) ).
tt(t39_funct_7,ax, (! [A:$i] :  ((k4_funct_7 A k1_xboole_0) = (k6_partfun1 A)) ) ).
tt(t39_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k41_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t39_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ( ((v21_functor0 C A B) & (v11_functor0 C A B))  => (v11_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t39_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor3 E A B C D) =>  ((r1_functor3 A B C D) => (r8_pboole (u1_struct_0 A) (k5_functor2 A B D C D (k8_functor3 A B C D E) E) (k4_functor2 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k3_fuzzy_1 A B) (k3_fuzzy_1 A (k1_fuzzy_1 A B C)))) ) ) ) ) ) ).
tt(t39_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_2 A B C) (k1_fuzzy_1 A B C))) ) ) ) ) ) ).
tt(t39_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_fvaluat1 D A) =>  ((v3_fvaluat1 A) =>  ( ((k3_funct_2 (u1_struct_0 A) k7_numbers D B) = (k3_funct_2 (u1_struct_0 A) k7_numbers D C))  <=>  ((k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A D) B) = (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k6_fvsum_1 A B (k8_fvsum_1 A B C D)) = (k8_fvsum_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t39_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~ (v1_xboole_0 (k33_gate_1 A B C D E F G H)))  <=>  ((v1_xboole_0 A) &  ((v1_xboole_0 B) &  ((v1_xboole_0 C) &  ((v1_xboole_0 D) &  ((v1_xboole_0 E) &  ((v1_xboole_0 F) &  ((v1_xboole_0 G) & (v1_xboole_0 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_gcd_1 A B (k3_rlvect_1 A C (k8_group_1 A D E)) E) = (k5_gcd_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) ) ) )  =>  (! [E:$i] :  ((m1_genealg1 E D) =>  (! [F:$i] :  ((m1_genealg1 F D) =>  ( ((k10_genealg1 D E F A A B B) = E)  &  ( ((k10_genealg1 D E F A C A C) = E)  &  ((k10_genealg1 D E F A C C A) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r2_geomtrap A B C D E F H) & (r2_geomtrap A B C D E G I))  =>  ( (D = E)  | (r2_geomtrap A B C D E (k1_geomtrap A F G) (k1_geomtrap A H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k13_gfacirc1 A B C) (k14_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_funct_1 (k5_facirc_1 (k13_gfacirc1 A B C) (k14_gfacirc1 A B C) D 2) (k12_gfacirc1 A B C)) = (k2_binarith (k2_binarith E F) G))  &  ((k1_funct_1 (k5_facirc_1 (k13_gfacirc1 A B C) (k14_gfacirc1 A B C) D 2) (k9_gfacirc1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E F) (k10_margrel1 F G)) (k10_margrel1 G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ( ((k26_glib_000 A B) = (k23_glib_000 A (k6_glib_000 A) (k6_domain_1 (k6_glib_000 A) B)))  &  ((k27_glib_000 A B) = (k23_glib_000 A (k6_domain_1 (k6_glib_000 A) B) (k6_glib_000 A))) ) ) ) ) ) ).
tt(t39_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A B 1 (k3_finseq_1 B)) B)) ) ) ) ).
tt(t39_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( ((r5_glib_000 A B) &  ( (C = D)  & (v5_glib_002 C A)) )  => (v5_glib_002 D B)) ) ) ) ) ) ) ) ) ).
tt(t39_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k6_glib_000 A)) =>  ((k1_funct_1 (k7_glib_003 (k13_glib_003 A B C)) B) = C) ) ) ) ) ) ).
tt(t39_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  ((k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k17_glib_004 A)) = (k6_glib_000 A)) ) ) ).
tt(t39_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r2_hidden (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid 1 (k1_real_1 1))) (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) k6_numbers)))) ) ).
tt(t39_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 C))) &  ((r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) (k10_real_1 1 2)) (k3_topreal1 2 C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 C)) &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) = (k2_topreal1 2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski (k2_nat_1 B 1) C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 B 1) C))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k4_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_jordan2c 2 (k3_topreal1 2 A) B) & (r1_xboole_0 B (k3_goboard9 A))) ) ) ) ) ) ).
tt(t39_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  ((r1_graph_2 A B C) =>  ( ( ((k1_card_1 (u1_struct_0 A)) = 1)  |  ( (~  (C = k1_xboole_0) )  &  (~ (r2_graph_2 A C)) ) )  <=>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((r1_graph_2 A D C) =>  (D = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_graph_3 B C D))) =>  ( (E = C)  =>  ( (C = D)  |  ((k2_graph_3 (k8_graph_3 B C D) E A) = (k2_graph_3 B C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_tarski (k4_graph_5 A B C) (k7_graph_5 A))) ) ) ) ) ) ).
tt(t39_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ( (D = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) E))  &  ( (F = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) E))  &  (C = (k15_graphsp (k7_graphsp D A) D A)) ) )  =>  ( ((k7_graphsp D A) = k1_xboole_0)  |  ( ((k14_graphsp F A) = (k4_subset_1 k5_numbers (k14_graphsp D A) (k6_domain_1 k5_numbers C)))  &  (~ (r2_hidden C (k14_graphsp D A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((u1_struct_0 (k29_grcat_1 A)) = (k28_grcat_1 A)) ) ) ).
tt(t39_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (~  ( (~  (D = (k1_groeb_1 A C (k7_polynom1 A C))) )  &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (~  ((r2_groeb_1 A B C E D) & (r4_groeb_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_groeb_2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 D A C) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r6_groeb_2 A B C D E) => (r10_polyred A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  &  (~ (r2_termord A B (k3_termord A B C (k6_groeb_3 A B C D E)) (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_tarski B (k1_group_11 A (k2_group_11 A B C) C)) => (r1_tarski (k2_group_11 A B C) (k2_group_11 A (k1_group_11 A (k2_group_11 A B C) C) C))) ) ) ) ) ) ) ).
tt(t39_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( ((k6_algstr_0 C D E) = (k6_algstr_0 C E D))  =>  ((k6_algstr_0 C (k5_group_1 C A D) (k5_group_1 C B E)) = (k6_algstr_0 C (k5_group_1 C B E) (k5_group_1 C A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((v8_struct_0 A) => (v8_struct_0 B)) ) ) ) ) ).
tt(t39_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_group_3 A (k7_domain_1 (u1_struct_0 A) B C) (k6_domain_1 (u1_struct_0 A) D)) = (k7_domain_1 (u1_struct_0 A) (k2_group_3 A B D) (k2_group_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t39_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (~ (v2_group_4 C A)) ) )  => (r1_struct_0 (k6_group_4 A) B)) ) ) ) ) ).
tt(t39_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_group_5 A B C (k1_group_1 A)) = (k1_group_1 A))  &  ( ((k3_group_5 A B (k1_group_1 A) C) = (k1_group_1 A))  &  ((k3_group_5 A (k1_group_1 A) B C) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ).
tt(t39_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  => (v1_group_6 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t39_group_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (r1_group_6 A (k2_group_7 (k1_tarski 1) (k9_finseq_1 A)))) ) ).
tt(t39_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_group_9 D A C) =>  (! [E:$i] :  ((m1_group_9 E A C) =>  (! [F:$i] :  ((m1_group_9 F A B) =>  (! [G:$i] :  ((m1_group_9 G A B) =>  ( ( (D = F)  &  (E = G) )  =>  ((k17_group_9 A B F G) = (k17_group_9 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_hausdorf,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((v2_compts_1 B (k15_euclid A)) & (v2_compts_1 C (k15_euclid A)))  => (r1_xxreal_0 k6_numbers (k3_hausdorf A B C))) ) ) ) ) ) ) ).
tt(t39_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k13_glib_001 A (k2_helly A B C))) <=>  ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A (k2_helly A B D)) (k13_glib_001 A (k2_helly A D C))) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(t39_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_hermitan B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C (k4_struct_0 A)) = (k4_struct_0 k1_complfld)) ) ) ) ) ) ) ).
tt(t39_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  ( ((r3_orders_2 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) B C) &  (C = k1_xboole_0) )  =>  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t39_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A E) =>  ((r1_xxreal_0 C D) |  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 C) B) E) D) A) = (k8_real_1 (k8_real_1 (k8_real_1 B (k6_newton D C)) (k3_newton D)) (k5_prepower A (k9_real_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k4_hilbert1 A C) B)) k6_hilbert1)) ) ) ) ) ) ).
tt(t39_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_hilbert3 C A) (k3_hilbert3 C B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_hilbert3 C A) (k3_hilbert3 C B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_hilbert3 C A) (k3_hilbert3 C B))))) )  =>  ( (E = (k1_funct_1 (k5_hilbert3 C D (k3_hilbert1 A B)) F))  => (r2_funct_2 (k3_hilbert3 C A) (k3_hilbert3 C B) (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C B) (k3_hilbert3 C B) (k3_hilbert3 C B) F (k5_hilbert3 C D B)) (k1_partfun1 (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C A) (k3_hilbert3 C B) (k5_hilbert3 C D A) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((v1_hurwitz (k3_polynom5 k1_complfld (k3_hurwitz k1_complfld B 1) A)) <=>  (~ (r1_xxreal_0 k6_numbers (k3_complex1 B))) ) ) ) ) ) ) ).
tt(t39_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v1_relat_1 (k18_idea_1 D B A C)) &  ((v1_funct_1 (k18_idea_1 D B A C)) &  ((v1_finseq_1 (k18_idea_1 D B A C)) & (v1_funct_7 (k18_idea_1 D B A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m3_ideal_1 C A B) =>  (? [D:$i] :  ((m2_finseq_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (r3_ideal_1 A B C D)) ) ) ) ) ) ) ) ).
tt(t39_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C D) E) =>  ((r1_incsp_1 A B E) |  ( (C = D)  |  ((k3_incsp_1 A B E) = (k2_incsp_1 A C D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (r1_funct_2 (u1_struct_0 A) (u4_struct_0 A) (u1_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 A)) (k7_isocat_1 A) (k7_isocat_1 (k2_oppcat_1 A)))) ) ).
tt(t39_instalg1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A B) =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((r2_hidden F A) =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ( ( (G = (k1_funct_1 E F))  &  (H = (k1_funct_1 (k1_msafree A B C D E) F)) )  =>  (! [I:$i] :  ((r2_hidden I (k1_funct_1 D F)) =>  ((k1_funct_1 H I) = (k1_funct_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden D (k1_relset_1 k5_numbers C)) & (r2_hidden E (k1_relset_1 k5_numbers C)))  =>  ( (D = E)  |  ((k6_nat_d (k1_recdef_1 C D) (k1_recdef_1 C E)) = 1) ) ) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k5_numbers C)) & (r1_xxreal_0 (k1_recdef_1 C D) k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ((m1_trees_4 D k1_numbers k5_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ( ((k6_int_1 (k5_real_1 A (k1_recdef_1 D E)) (k1_recdef_1 C E)) = k6_numbers)  &  ((k6_int_1 (k5_real_1 B (k1_recdef_1 D E)) (k1_recdef_1 C E)) = k6_numbers) ) ) ) )  => (r2_int_1 A B (k3_wsierp_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t39_int_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((v2_funct_1 B) <=> (v2_funct_1 (k2_finseq_7 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t39_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k6_xcmplx_0 A B)) =>  ((r1_xxreal_0 (k19_rvsum_1 C) (k6_xcmplx_0 A B)) |  ((k2_int_6 (k8_rvsum_1 (k1_int_6 A C) (k1_int_6 B C)) C) = (k6_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ).
tt(t39_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) B) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t39_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A F) &  ((r2_relset_1 k1_numbers k1_numbers B (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 E G) = (k11_binop_2 G (k9_prepower (k10_binop_2 1 (k5_prepower G 2)) (k13_binop_2 (k18_binop_2 1 2)))))  &  ( ((k1_seq_1 C G) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B G) k6_numbers)) ) ) ) ) )  &  ((r1_tarski F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k18_binop_2 1 2))))) &  ( (F = (k1_relset_1 k1_numbers E))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E A))) ) ) ) ) )  =>  ((k2_integra5 A E) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k18_binop_2 1 2)))) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k4_taylor_1 (k18_binop_2 1 2)))) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_integr13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers D (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 (k5_real_1 A 1))) (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2))) A))) &  ((r1_tarski E (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A)))) &  ( (E = (k1_relset_1 k1_numbers D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A)) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos D) (k1_seq_1 k19_sin_cos (k1_seq_1 k19_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t39_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k1_integra1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [F:$i] :  ((m4_integr15 F A B C E) =>  (! [G:$i] :  ((m2_integr18 G (k4_real_ns1 A) B D E) =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) & (r1_funct_2 k5_numbers (k3_finseq_2 (k1_euclid A)) k5_numbers (k3_finseq_2 (u1_struct_0 (k4_real_ns1 A))) F G))  => (r2_funct_2 k5_numbers (u1_struct_0 (k4_real_ns1 A)) (k6_integr15 A B C E F) (k3_integr18 (k4_real_ns1 A) B D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((r1_integra1 B C) & (v2_seq_2 (k2_partfun1 A k1_numbers D A)))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  ((r2_hidden E (k4_finseq_1 B)) => (r1_xxreal_0 (k18_rvsum_1 (k17_finseq_1 k1_numbers E (k5_integra1 A D B))) (k18_rvsum_1 (k17_finseq_1 k1_numbers (k13_integra1 A B C E) (k5_integra1 A D C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_integra2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C (k1_integra2 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D A) &  (C = (k8_real_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A k19_sin_cos) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k5_seq_4 A)))) ) ) ).
tt(t39_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))  => (r1_integra9 A k16_sin_cos k19_sin_cos)) ) ) ).
tt(t39_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r1_tarski B C) & (r1_tarski D E))  =>  ((k4_setfam_1 (k2_interva1 A B C) (k2_interva1 A D E)) = (a_5_2_interva1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k3_intpro_1 A B) A) B) k8_intpro_1)) ) ) ) ).
tt(t39_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (B = (k13_complex1 1 (k2_nat_1 A 1)))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k3_xcmplx_0 (k9_newton A) (k4_series_1 (k1_valued_0 k1_numbers k5_irrat_1 (k2_nat_1 A 1)))) (k13_complex1 B (k6_xcmplx_0 1 B)))) ) ) ) ) ) ).
tt(t39_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_cat_1 H B C) =>  (! [I:$i] :  ((m2_cat_1 I C D) =>  (! [J:$i] :  ((m2_cat_1 J C D) =>  (! [K:$i] :  ((m2_nattra_1 K A B E F) =>  (! [L:$i] :  ((m2_nattra_1 L B C G H) =>  (! [M:$i] :  ((m2_nattra_1 M C D I J) =>  ( ((r2_nattra_1 A B E F) &  ((r2_nattra_1 B C G H) & (r2_nattra_1 C D I J)) )  => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 D) (k6_isocat_1 A C D (k9_cat_1 A B C E G) (k9_cat_1 A B C F H) I J (k6_isocat_1 A B C E F G H K L) M) (k6_isocat_1 A B D E F (k9_cat_1 B C D G I) (k9_cat_1 B C D H J) K (k6_isocat_1 B C D G H I J L M)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A C) =>  (! [G:$i] :  ((m2_cat_1 G A C) =>  ( ((r2_nattra_1 A B D E) & (r2_nattra_1 A C F G))  =>  (! [H:$i] :  ((m2_nattra_1 H A B D E) =>  (! [I:$i] :  ((m2_nattra_1 I A C F G) =>  ((r2_funct_2 (u1_struct_0 A) (u4_struct_0 B) (k11_isocat_2 A B C (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G) (k14_isocat_2 A B C D E F G H I)) H) & (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k12_isocat_2 A B C (k8_isocat_2 A B C D F) (k8_isocat_2 A B C E G) (k14_isocat_2 A B C D E F G H I)) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_isomichi B A) <=> (v4_isomichi (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t39_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 A)) &  ((r1_goboard4 (k1_goboard1 A) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k2_goboard1 A) C D) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) & (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)))))) ) ) ) )  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 E) &  ( ((k1_funct_1 E 1) = (k1_funct_1 A 1))  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = (k1_funct_1 A (k3_finseq_1 A)))  &  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 E)) &  ((r1_goboard4 (k1_goboard1 E) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k2_goboard1 E) C D) &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 A)) &  (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E F) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A G))))) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 (k2_nat_1 F 1) (k3_finseq_1 E)) & (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E F) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 F 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k2_partfun1 (k8_struct_0 (k15_euclid 2)) (k8_struct_0 (k15_euclid 2)) k1_jgraph_2 B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_1_jgraph_2) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t39_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k5_relat_1 (k2_funct_1 k1_jgraph_3) B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_0_jgraph_3) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t39_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( ((v1_funct_1 (k3_jgraph_4 A)) &  ((v1_funct_2 (k3_jgraph_4 A) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 (k3_jgraph_4 A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A)) = (u1_struct_0 (k15_euclid 2))) ) ) ) ) ) ) ) ).
tt(t39_jgraph_5,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)))))) )  &  ((v3_tops_2 A k5_topmetr (k4_topmetr (k1_real_1 1) 1)) &  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k1_rcomp_1 k6_numbers 1)) =>  ((k1_funct_1 A B) = (k9_real_1 (k8_real_1 2 B) 1)) ) ) )  &  ( ((k1_funct_1 A k6_numbers) = (k1_real_1 1))  &  ((k1_funct_1 A 1) = 1) ) ) ) ) ) ).
tt(t39_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_pscomp_1 (k1_sppol_2 A B C D)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t39_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = H)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid B) F) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k3_topreal1 2 (k2_jordan1e B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 B 1))))  =>  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) A (k1_jordan1a (k1_jordan8 B 1)))) = (k13_complex1 (k7_real_1 (k9_pscomp_1 B) (k7_pscomp_1 B)) 2)) ) ) ) ) ) ).
tt(t39_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_9_jordan1 A B C D))  &  (F = (a_4_4_jordan1 A B C D)) )  => (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) & (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A C)) (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan1g,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_tarski (k10_xtuple_0 (k1_jordan1e A B)) (k10_xtuple_0 (k1_jordan9 A B))) & (r1_tarski (k10_xtuple_0 (k2_jordan1e A B)) (k10_xtuple_0 (k1_jordan9 A B)))) ) ) ) ) ).
tt(t39_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((v9_rltopsp1 A (k15_euclid 2)) & (v9_rltopsp1 (k2_jordan2c 2 A) (k15_euclid 2))) ) ) ) ).
tt(t39_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k10_xtuple_0 B)) => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k2_jordan3 B C) A)) ) ) ) ) ) ) ) ).
tt(t39_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( (~ (r1_xboole_0 B C))  =>  ((k1_jordan1k A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t39_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xxreal_0 (k18_euclid (k1_jordan21 A)) (k7_pscomp_1 A))) ) ).
tt(t39_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k8_pscomp_1 A) = (k8_pscomp_1 (k3_jordan19 A))) ) ) ).
tt(t39_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) ) ) )  =>  ( (B = (k1_funct_1 A 1))  | (r1_jordan3 (k3_jordan3 A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) B)) ) ) ) ) ) ).
tt(t39_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) C D) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D E) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) E F) B) &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ((v5_pre_topc G k5_topmetr (k1_pre_topc (k15_euclid A) B)) &  ( (C = (k1_funct_1 G k6_numbers))  &  (F = (k1_funct_1 G 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) )  => (r1_jordan3 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B 2 (k3_finseq_1 B))) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) ).
tt(t39_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)))  =>  ((r1_xxreal_0 C B) | (v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ) ).
tt(t39_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k8_pscomp_1 (k3_topreal1 2 A)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) 1))) ) ) ).
tt(t39_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) F G D) &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid A)) C D) = B)  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid A)) C D) = (k2_tarski F G))  &  (E = (k7_subset_1 (u1_struct_0 (k15_euclid A)) C (k2_tarski F G))) ) ) )  => (v3_pre_topc E (k1_pre_topc (k15_euclid A) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  (! [H:$i] :  ((m1_borsuk_2 H A D E) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) & (r1_borsuk_6 A D E)) )  =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D F G) H)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) F) (k2_relset_1 (u1_struct_0 A) G)) (k2_relset_1 (u1_struct_0 A) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_knaster A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k8_knaster A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((r3_lattices (k8_knaster A B) C D) <=> (r3_lattices A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr k6_kurato_1) = (k2_pre_topc k3_topmetr k6_kurato_1)) ) ).
tt(t39_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_funct_1 B D) = C) ) )  =>  ((k1_kurato_2 A B) = (k2_kurato_2 A B)) ) ) ) ) ) ) ) ).
tt(t39_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = A)  &  ((k11_laplace B C D) = (k4_matrix_1 (u1_struct_0 B) (k10_laplace (u1_struct_0 B) E))) )  =>  ( ((k4_matrix_1 (u1_struct_0 B) (k10_laplace (u1_struct_0 B) D)) = (k11_laplace B (k5_matrix_6 A B C) E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k1_funct_1 D F) = (k8_group_1 B (k11_algstr_0 B (k12_matrix_3 A B C)) (k12_matrix_3 A B (k3_laplace F A A (u1_struct_0 B) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_lattice2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_lattice2 A))) =>  ( ((r3_lattices (k1_lattice2 A) D E) &  ( (B = D)  &  (C = E) ) )  => (r3_lattices A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r3_lattice3 A B C) => (r3_lattices A B (k16_lattice3 A C))) ) ) ) ) ) ).
tt(t39_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  ((k7_lattices A (k1_lattice4 A B)) = (k3_lattice2 (u1_struct_0 A) A B (k5_lattice4 A))) ) ) ) ) ).
tt(t39_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) (u1_struct_0 B)) &  ((v1_lattice5 C A B) &  ((v2_lattice5 C A B) &  ((v3_lattice5 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 B))))) ) ) ) )  =>  (! [D:$i] :  ((m2_lattice5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k2_xtuple_0 (k1_funct_1 D E)) (k2_xtuple_0 (k1_funct_1 D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k39_glib_000 (k15_lexbfs A (k16_lexbfs A))) = (k39_glib_000 (k16_lexbfs A))) ) ) ).
tt(t39_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k4_lfuzzy_1 A B D) (k4_lfuzzy_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t39_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v5_valued_0 A)) ) )  => (v2_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t39_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r5_limfunc2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k2_rcomp_1 A (k7_real_1 A D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 A (k7_real_1 A D))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) )  | (r5_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t39_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_limfunc3 C A) = k6_numbers)  |  ((r1_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers B C) A) &  ((k1_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers B C) A) = (k10_real_1 (k1_limfunc3 B A) (k1_limfunc3 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t39_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r2_limfunc3 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  ((k1_seq_1 B E) = (k1_limfunc3 B A)) ) ) ) ) ) ) ) )  | (r2_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t39_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_lmod_6 A C D) <=> (r1_tarski (k2_lmod_6 A B C (k2_struct_0 C)) (k2_lmod_6 A B D (k2_struct_0 D)))) ) ) ) ) ) ) ) ) ).
tt(t39_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_lopban_1 A B)))  &  ((v13_algstr_0 (k16_lopban_1 A B)) &  ((v2_rlvect_1 (k16_lopban_1 A B)) &  ((v3_rlvect_1 (k16_lopban_1 A B)) &  ((v4_rlvect_1 (k16_lopban_1 A B)) &  ((v5_rlvect_1 (k16_lopban_1 A B)) &  ((v6_rlvect_1 (k16_lopban_1 A B)) &  ((v7_rlvect_1 (k16_lopban_1 A B)) &  ((v8_rlvect_1 (k16_lopban_1 A B)) &  ((v3_normsp_0 (k16_lopban_1 A B)) &  ((v4_normsp_0 (k16_lopban_1 A B)) &  ((v2_normsp_1 (k16_lopban_1 A B)) & (l1_normsp_1 (k16_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_lopban_3 A B k6_numbers) = (k5_struct_0 A)) ) ) ) ) ).
tt(t39_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v25_algstr_0 (k10_lopban_4 A B) A) &  ( ((k9_algstr_0 A (k10_lopban_4 A B)) = (k10_lopban_4 A (k4_algstr_0 A B)))  &  ((v25_algstr_0 (k10_lopban_4 A (k4_algstr_0 A B)) A) &  ((k9_algstr_0 A (k10_lopban_4 A (k4_algstr_0 A B))) = (k10_lopban_4 A B)) ) ) ) ) ) ) ) ).
tt(t39_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) & (r2_hidden E (k9_lpspace1 A B C)))  =>  ( ((k13_lpspace1 A B C D) = (k13_lpspace1 A B C E))  <=> (r1_lpspace1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((k5_lpspace2 A B C E F) = (k5_lpspace2 A B C D F))  =>  ( (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A G)) = k6_numbers)  &  ( (G = (k1_relset_1 A D))  & (r1_mesfunc6 A B D G)) ) ) ) )  |  ( ((k5_lpspace2 A B C E F) = k1_xboole_0)  | (r1_lpspace1 A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m2_finseq_1 B k1_hilbert1) =>  (! [C:$i] :  ((m2_finseq_1 C k1_hilbert1) =>  (! [D:$i] :  ((m2_finseq_1 D k1_hilbert1) =>  ( ( (B = (k8_finseq_1 k1_hilbert1 C D))  &  ((r1_xxreal_0 1 (k3_finseq_1 C)) &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 C)))  => (r7_ltlaxio1 E C A)) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 D)))  => (r7_ltlaxio1 E D A)) ) ) ) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 B)))  => (r7_ltlaxio1 E B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B (k6_cqc_lang A C)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A C (k6_cqc_lang A B)) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t39_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k4_mathmorp A (k3_subset_1 (u1_struct_0 A) B) (k2_mathmorp A C))) = (k5_mathmorp A B C)) ) ) ) ) ) ) ).
tt(t39_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 k6_numbers A) & (v1_matrix10 C))  => (v4_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t39_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C B A) =>  ((k3_relat_1 (k1_finseq_2 B) D) = D) ) ) ) ) ) ) ) ) ).
tt(t39_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((m1_matrix_1 H A B C) =>  (! [I:$i] :  ((m2_finseq_2 I k5_numbers (k4_finseq_2 F k5_numbers)) =>  (! [J:$i] :  ((m2_finseq_2 J k5_numbers (k4_finseq_2 D k5_numbers)) =>  (~  ((r2_hidden E (k10_xtuple_0 I)) &  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 I) (k10_xtuple_0 J)) (k2_matrix_1 H)) &  (! [K:$i] :  ((m2_finseq_2 K k5_numbers (k4_finseq_2 F k5_numbers)) =>  (~  ( ((k10_xtuple_0 K) = (k2_xboole_0 (k6_subset_1 (k10_xtuple_0 I) (k1_tarski E)) (k1_tarski G)))  &  ((k1_matrix13 A (k3_matrix11 E B C A H (k8_matrix_1 A H G)) F D I J) = (k1_matrix13 A H F D K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  ((k3_matrix_1 (u1_struct_0 B) C 1 1) = (k4_struct_0 B)) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ((v1_matrix_6 D A B) &  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C D) 1 1) = (k5_struct_0 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E A) =>  ((r1_xxreal_0 E 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C D) 1 E) = (k4_struct_0 B)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 E A) &  ((k3_matrix_1 (u1_struct_0 B) C E 1) = (k4_struct_0 B)) )  =>  ((r1_xxreal_0 E 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C D) E 1) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v6_struct_0 F))  &  ((v13_algstr_0 F) &  ((v33_algstr_0 F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) =>  (! [H:$i] :  ( ((v1_matrix_1 H) & (m2_finseq_1 H (k3_finseq_2 (u1_struct_0 F))))  =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 F) D A) =>  (! [J:$i] :  ((m1_matrix_1 J (u1_struct_0 F) D B) =>  ( ((r2_hidden H (k4_matrix15 F I J)) & (r2_hidden C (k2_finseq_1 D)))  => (r2_hidden H (k4_matrix15 F (k3_matrix11 E D A (u1_struct_0 F) I (k4_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I E) (k10_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I C) G))) (k3_matrix11 E D B (u1_struct_0 F) J (k4_fvsum_1 (k1_matrix_1 J) F (k8_matrix_1 (u1_struct_0 F) J E) (k10_fvsum_1 (k1_matrix_1 J) F (k8_matrix_1 (u1_struct_0 F) J C) G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v3_matrix16 (k12_matrix_1 B A) (u1_struct_0 B))) ) ) ) ) ).
tt(t39_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_matrix_1 F E A B) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 F)) =>  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C A) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k3_matrix_3 A B (k3_matrix_3 A C (k2_matrix_3 A C)))) ) ) ) ) ) ) ) ).
tt(t39_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) )  => (r2_matrix_6 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t39_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_8 A B (k2_matrix_6 A B C C) (k2_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) => (r2_hidden (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) C B) (k12_matrix_2 A))) ) ) ) ) ) ).
tt(t39_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_complsp2 A B) = (k17_rvsum_1 (k5_matrixc1 A (k1_complsp2 B)))) ) ) ) ) ) ).
tt(t39_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 A)))  =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 A)))  =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 A)))  =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 F))  &  ( ((k1_matrix_1 D) = (k1_matrix_1 F))  &  ( ((k3_finseq_1 E) = (k3_finseq_1 G))  &  ( ((k1_matrix_1 E) = (k1_matrix_1 G))  &  ((k13_matrixj1 A B (k5_matrixj1 A D E)) = (k13_matrixj1 A C (k5_matrixj1 A F G))) ) ) ) )  =>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  &  ((k5_matrixr1 B A) = B) ) )  =>  (A = (k8_matrixr1 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ) ) ).
tt(t39_matrixr2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers)) &  ((v3_funct_2 A (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 k6_numbers) (k2_finseq_1 k6_numbers))))) ) )  =>  (A = (k6_finseq_1 k5_numbers)) ) ) ).
tt(t39_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 C) (k4_matrlin2 A B C D E F) (k4_matrlin2 A B C D E G)) =>  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 E) k6_numbers))  =>  ((k1_matrix_1 (k10_matrlin A B C D E F)) = (k3_finseq_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_matroid0 B A) =>  ((k1_nat_1 (k4_matroid0 A B) 1) = (k1_card_1 B)) ) ) ) ) ) ).
tt(t39_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ( (A = (k6_matrixr1 B C))  <=>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 A)) =>  ((k3_matrix_1 k1_numbers A D E) = (k22_rvsum_1 (k8_matrix_1 k1_numbers B D) (k9_matrix_1 k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  ((v2_funct_1 (k3_matrtop1 B A C)) <=>  ((k8_matrix13 k2_vectsp_1 C) = B) ) ) ) ) ) ) ) ).
tt(t39_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v13_vectsp_1 C (k15_euclid B) (k15_euclid B)) &  ((v1_topreal9 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B))) &  ((v13_vectsp_1 D (k15_euclid B) (k15_euclid B)) &  ((v1_topreal9 D B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)))))) ) ) )  =>  ( ((v2_matrtop3 C B) &  ( ((k12_matrix_3 B k2_vectsp_1 (k3_matrtop3 B C)) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1)))  &  ((r2_hidden A (k2_finseq_1 B)) &  ((k3_matrtop3 B D) = (k1_matrtop3 B A)) ) ) )  => (v3_matrtop3 (k1_partfun1 (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) D C) B)) ) ) ) ) ) ) ) ) ).
tt(t39_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_zfmisc_1 (k2_tarski A B) (k2_tarski C D) (k1_tarski E)) = (k2_enumset1 (k3_xtuple_0 A C E) (k3_xtuple_0 B C E) (k3_xtuple_0 A D E) (k3_xtuple_0 B D E))) ) ) ) ) ) ).
tt(t39_measure6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v5_xxreal_2 (k2_relset_1 k1_numbers A)) <=> (v1_comseq_2 A)) ) ) ).
tt(t39_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k1_xxreal_3 C D) (k8_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t39_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((r1_tarski (k7_memstr_0 A B k6_numbers) C) =>  ((k5_memstr_0 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t39_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) =>  ((r2_mesfun6c A B C (k25_valued_1 A k2_numbers D k7_complex1)) &  ((k1_mesfun6c A B C (k25_valued_1 A k2_numbers D k7_complex1)) = (k3_xcmplx_0 k7_complex1 (k1_mesfun6c A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers B) (k1_relset_1 A (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C)))) (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers C) (k1_relset_1 A (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C))))) (k2_partfun1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k55_valued_1 A k2_numbers B) (k55_valued_1 A k2_numbers C)) (k1_relset_1 A (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C)))))) ) ) ) ) ) ).
tt(t39_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k2_numbers D k6_numbers)) = C)  &  ((v1_mesfunc8 D A k2_numbers) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers (k3_mesfun9c A D) E) C)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) => (v1_comseq_3 (k9_mesfun7c A D E))) ) ) ) ) )  => (r1_mesfun6c A B (k10_mesfun7c A (k3_mesfun9c A D)) C)) ) ) ) ) ) ) ) ) ).
tt(t39_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_mesfunc2 A B D) => (r1_mesfunc2 A B (k6_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k1_seq_1 (k18_rfunct_3 A B) C) = k6_numbers) )  =>  ((k1_seq_1 (k19_rfunct_3 A B) C) = (k1_real_1 (k1_seq_1 B C))) ) ) ) ) ) ) ).
tt(t39_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (v3_mesfunc5 (k4_mesfunc5 A k7_numbers B D))) )  => (v3_mesfunc5 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) ) ) ) ) ) ) ).
tt(t39_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k8_midsp_1 A B C) = (k8_midsp_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t39_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k4_mmlquery A (k18_mmlquery A (k18_mmlquery A C)) B) = (k4_mmlquery A C B)) ) ) ) ) ) ).
tt(t39_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v8_mod_4 B A A) <=> (v7_mod_4 (k7_mod_4 A A B) A (k2_mod_4 A))) ) ) ) ) ).
tt(t39_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~ (r1_xxreal_0 (k5_card_1 (k9_xtuple_0 (k11_modal_1 A))) (k5_card_1 (k9_xtuple_0 A)))) ) ) ).
tt(t39_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r3_modelc_1 A B C E (k26_modelc_1 (k48_modelc_1 A B C) D)) <=> (r3_modelc_1 A B C E (k53_modelc_1 A B C D (k26_modelc_1 (k48_modelc_1 A B C) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_modelc_2 A (k3_modelc_2 B)) => (r2_modelc_2 A B)) ) ) ) ) ).
tt(t39_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  =>  ( ((r6_modelc_3 B D C) &  ((v8_modelc_2 A) & (r2_hidden A (u1_modelc_3 B C))) )  =>  ((r2_hidden (k11_modelc_2 A) (u1_modelc_3 B C)) |  ((r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C)) & (r2_hidden A (u3_modelc_3 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k3_moebius1 A)) <=>  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_nat_d B A)) ) ) ) ) ) ).
tt(t39_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (m2_monoid_0 A k2_monoid_0))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 A B C) = (k9_binop_2 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k20_monoid_1 A (k1_monoid_0 A C (k12_finseq_1 A B))) = (k6_algstr_0 (k13_monoid_1 A) (k20_monoid_1 A C) (k18_monoid_1 A B))) ) ) ) ) ) ) ).
tt(t39_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  ((v1_msualg_6 (k1_msafree3 A B) A) & (v2_msafree (k1_msafree3 A B) A)) ) ) ) ) ).
tt(t39_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  ((r1_msaterm A B C E D F) =>  ((k9_msaterm A B C E D) = (k1_funct_1 F k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D C))  => (m3_pboole (k2_pzfmisc1 A B D) A (k1_mboolean A C))) ) ) ) ) ) ) ) ).
tt(t39_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) => (r1_tarski (k5_msualg_2 A B C) (k6_msualg_2 A B))) ) ) ) ) ) ).
tt(t39_msualg_6,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E A))  =>  ((r2_hidden (k4_tarski D E) C) <=> (r2_rewrite1 B D E)) ) ) )  =>  ((v1_partfun1 C A) &  ((v3_relat_2 C) & (v8_relat_2 C)) ) ) ) ) ) ) ) ).
tt(t39_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) => (r1_relset_1 (u1_struct_0 B) (u1_struct_0 B) (u1_orders_2 B) (u1_orders_2 (k6_mycielsk A B)))) ) ) ) ).
tt(t39_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) <=> (r1_ordinal1 A B)) ) ) ) ) ).
tt(t39_nat_3,ax, ((k12_nat_3 1) = (k16_pre_poly k10_newton)) ).
tt(t39_nat_4,ax,(v1_int_2 2503)).
tt(t39_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  (~  ((v1_abian A) &  ((v2_nat_5 A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_int_2 (k7_nat_d (k2_newton 2 B) 1)) &  (A = (k24_binop_2 (k13_newton 2 (k7_nat_d B 1)) (k7_nat_d (k2_newton 2 B) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t39_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 (k7_nat_d A B)) | (r1_xxreal_0 1 (k6_xcmplx_0 A B)))  =>  ((k7_nat_d A B) = (k6_xcmplx_0 A B)) ) ) ) ) ) ).
tt(t39_nattra_1,ax, (! [A:$i] :  (! [B:$i] : (v2_nattra_1 (k3_cat_1 A B))) ) ).
tt(t39_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_ncfcont1 A B C D) =>  ((r5_ncfcont1 A (k3_normsp_0 (u1_struct_0 A) B C) D) & (r2_ncfcont1 A B (k5_vfunct_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t39_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k5_algstr_0 A C B))) ) ) ) ) ) ) ).
tt(t39_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) (k6_vfunct_1 (u1_struct_0 A) B D E))) &  ((r2_ndiff_1 C A B D) & (r2_ndiff_1 C A B E)) )  =>  ((r2_ndiff_1 C A B (k6_vfunct_1 (u1_struct_0 A) B D E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) (k4_ndiff_1 A B (k6_vfunct_1 (u1_struct_0 A) B D E) C) F) = (k3_rlvect_1 (k16_lopban_1 A B) (k3_ndiff_1 A B D F) (k3_ndiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_ndiff_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers A (k1_pdiff_1 1 1)) =>  ((r3_ndiff_4 1 A B) & (r2_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k3_ndiff_4 1 A B) A)) ) ) ) ) ) ).
tt(t39_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_prvect_2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) (k1_rlvect_1 (k11_prvect_2 A B) C D)) = (k1_rlvect_1 (k14_prvect_2 A) (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B (k4_struct_0 (k14_prvect_2 A))) C) D)) ) ) ) ) ) ) ) ) ).
tt(t39_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  ( ((r1_subset_1 (u1_struct_0 C) (u1_struct_0 D)) &  ( ((k5_yellow_0 A (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k6_domain_1 (u1_struct_0 A) B))) = (k1_neckla_2 C D))  &  ((v1_neckla_3 A) & (v1_neckla_3 (k3_necklace A))) ) )  =>  ((v7_struct_0 A) | (r2_necklace (k4_necklace 4) A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = 1) )  &  ((r1_nat_d A B) & (r1_nat_d A (k1_nat_1 B 1))) ) ) ) ) ) ) ).
tt(t39_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r5_nfcont_1 C D A E) & (r5_nfcont_1 C D B F))  => (r5_nfcont_1 C D (k3_xboole_0 A B) (k6_vfunct_1 (u1_struct_0 C) D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) D B) A) & (r1_tarski B (k1_relset_1 k1_numbers D)))  => (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k9_integr15 A C k1_numbers D) B) A)) ) ) ) ) ) ) ) ).
tt(t39_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ( ((r2_hidden B C) &  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  ( ((r2_hidden D C) & (r1_normform (k5_finsub_1 A) (k5_finsub_1 A) D B))  =>  (D = B) ) ) ) )  => (r2_hidden B (k9_normform A C))) ) ) ) ) ) ).
tt(t39_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B C) (k5_oppcat_1 A D)) = (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)) ) ) ) ) ) ) ) ) ).
tt(t39_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_orders_1 A B) => (v3_orders_1 (k2_wellord1 A B))) ) ) ) ).
tt(t39_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_orders_2 D A C) =>  ( (B = (k1_funct_1 C (u1_struct_0 A)))  =>  ((k3_orders_2 A D B) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t39_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( ((k11_ordinal2 1 A) = A)  &  ((k11_ordinal2 A 1) = A) ) ) ) ).
tt(t39_ordinal3,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden D (k9_xtuple_0 A)) &  (E = (k1_funct_1 A D)) )  =>  ((k1_funct_1 B D) = (k10_ordinal2 C E)) ) ) ) ) ) )  =>  ( (k1_xboole_0 = (k9_xtuple_0 A))  |  ((k4_ordinal2 B) = (k10_ordinal2 C (k4_ordinal2 A))) ) ) ) ) ) ) ) ) ).
tt(t39_ordinal5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v4_ordinal5 B))  =>  ((r2_hidden k6_numbers A) =>  ((k1_ordinal5 B (k1_nat_1 A 2)) = (k12_ordinal2 k4_ordinal1 (k1_ordinal5 B (k1_nat_1 A 1)))) ) ) ) ) ) ).
tt(t39_ordinal6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ((v2_ordinal6 B) & (r2_hidden A (k9_xtuple_0 (k3_ordinal6 B))))  =>  ((k1_funct_1 (k3_ordinal6 B) A) = (k3_card_3 (k5_relat_1 (k3_ordinal6 B) A))) ) ) ) ) ) ).
tt(t39_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v5_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t39_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (v2_osafree (k16_osafree A B) A)) ) ) ) ).
tt(t39_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  =>  (! [D:$i] :  ( ((v12_osalg_1 D A) & (m1_msualg_2 D A B))  =>  ((k11_osalg_2 A B C D) = (k11_osalg_2 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t39_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_parsp_2 A B C D E) & (r2_parsp_2 A B C F G))  => (r1_parsp_1 A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k6_relset_1 B C A (k3_partfun1 D B C)) = (k3_partfun1 D B (k3_xboole_0 A C))) ) ) ) ) ) ).
tt(t39_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r1_xboole_0 A (k1_relset_1 B D)) => (v3_funct_1 (k2_partfun1 B C D A))) ) ) ) ) ) ) ) ).
tt(t39_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k2_pboole A (k2_pboole A B C) D) (k2_pboole A (k2_pboole A B D) (k2_pboole A C D)))) ) ) ) ) ) ) ).
tt(t39_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k22_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k22_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k4_tarski E G))  &  (D = (k4_tarski F H)) )  =>  ((r1_orders_2 (k22_pcs_0 A B) C D) <=>  ((r1_orders_2 A F E) & (r1_orders_2 B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r3_pdiff_3 A B) => (r1_fcont_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 A) B) (k1_seq_1 (k1_pdiff_1 1 2) B))) ) ) ) ) ).
tt(t39_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_1 3 1 D C) &  ((r3_pdiff_1 3 2 D C) &  ((r3_pdiff_1 3 3 D C) &  ((r3_pdiff_1 3 1 E C) &  ((r3_pdiff_1 3 2 E C) & (r3_pdiff_1 3 3 E C)) ) ) ) )  =>  ((k4_pdiff_4 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k26_valued_1 (k1_euclid 3) k1_numbers D A) (k26_valued_1 (k1_euclid 3) k1_numbers E B)) C) = (k8_euclid 3 (k9_euclid 3 (k4_pdiff_4 D C) A) (k9_euclid 3 (k4_pdiff_4 E C) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 3 3) B)) =>  ( ((r3_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 3 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B))))) &  ((k3_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  (C = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A D B) E)) ) )  =>  ((k1_seq_1 (k1_pdiff_1 D A) C) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_nfcont_4 A B C) => (r2_nfcont_4 A (k26_valued_1 (k1_euclid A) k1_numbers B D) C)) ) ) ) ) ) ) ) ) ).
tt(t39_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  ( ((k4_nat_d A B) = 1)  <=> (r2_int_1 A 1 B)) ) ) ) ) ) ).
tt(t39_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  (! [D:$i] :  ((m2_finseq_2 D B (k3_finseq_2 B)) =>  ((k8_pnproc_1 A B (k1_pre_poly B D (k3_pre_poly B C))) = (k3_relat_1 (k8_pnproc_1 A B D) (k7_pnproc_1 A C))) ) ) ) ) ) ) ) ).
tt(t39_polyeq_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (m1_comptrig (k3_binop_2 (k21_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A)) (k5_binop_2 (k18_sin_cos (k12_binop_2 (k11_binop_2 (k11_binop_2 2 k32_sin_cos) B) A)) k7_complex1)) 1 A)) ) ) ) ).
tt(t39_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((k4_rlvect_1 k2_bspace (k3_fvsum_1 k2_bspace (k19_polyform A B E C) (k19_polyform A B E D))) = (k3_rlvect_1 k2_bspace (k4_rlvect_1 k2_bspace (k19_polyform A B E C)) (k4_rlvect_1 k2_bspace (k19_polyform A B E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_algseq_1 A (k4_polynom5 A B C)) 2)) ) ) ) ) ) ).
tt(t39_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom8 A C B) =>  ((k4_matrix_3 A (k7_polynom8 A B C) (k7_polynom8 A B (k11_algstr_0 A C))) = (k6_matrix_3 A (k12_matrix_1 A B) (k1_polynom8 A B))) ) ) ) ) ) ) ) ) ).
tt(t39_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r3_polyred A B C D E F G) & (r2_hidden G (k2_polynom1 (k15_pre_poly A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C 1))  & (r1_xxreal_0 (k3_power C B) (k3_power C A))) ) ) ) ) ) ) ) ) ).
tt(t39_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v4_valued_0 C)) ) ) )  => (r1_tarski (k13_pre_poly (k12_pre_poly A B C)) (k13_pre_poly B))) ) ) ) ) ).
tt(t39_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k4_prepower A B) k6_numbers)) ) ) ) ) ) ).
tt(t39_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) => (r1_xxreal_0 (k1_seq_1 E (k6_prob_1 A B C D)) (k7_real_1 (k1_seq_1 E C) (k1_seq_1 E D)))) ) ) ) ) ) ) ) ) ) ).
tt(t39_prob_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m2_prob_1 E A B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 E D) k6_numbers))  => (r1_xxreal_0 (k9_real_1 1 (k10_real_1 (k1_seq_1 E (k7_prob_1 A B (k4_prob_1 A B) C)) (k1_seq_1 E D))) (k1_seq_1 (k3_prob_2 A B E D) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) => (v7_valued_0 (k3_series_1 (k8_prob_1 A B C D)))) ) ) ) ) ) ) ) ).
tt(t39_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  ((k3_funct_2 B k1_numbers C D) = (k1_funct_1 (k7_prob_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t39_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B (k9_cqc_lang A C D)) (k9_cqc_lang A (k7_cqc_lang A B C) (k7_cqc_lang A B D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t39_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k15_pscomp_1 B)) =>  ( ((k18_euclid A) = (k18_euclid (k20_pscomp_1 B)))  &  ((v2_compts_1 B (k15_euclid 2)) =>  ((r1_xxreal_0 (k17_euclid (k20_pscomp_1 B)) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k17_euclid (k21_pscomp_1 B)))) ) ) ) ) ) ) ) ).
tt(t39_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B C) => (r6_pboole A (k2_pboole A (k1_pzfmisc1 A B) C) C)) ) ) ) ) ) ).
tt(t39_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang2 B A) =>  (B = (k4_qc_lang2 A (k13_qc_lang2 A B) (k14_qc_lang2 A B))) ) ) ) ) ) ).
tt(t39_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A C (k13_qc_lang1 A B)) = (k4_qc_lang3 A C B)) ) ) ) ) ) ) ).
tt(t39_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) =>  ((a_4_1_qc_lang4 A B C D) = (a_4_2_qc_lang4 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t39_quatern2,ax, ((k4_struct_0 k16_quatern2) = k1_quatern2) ).
tt(t39_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k9_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k10_real_1 (k7_real_1 (k3_quatern2 (k26_quaterni A B)) (k3_quatern2 (k29_quaterni B A))) 2))) ) ) ) ).
tt(t39_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ( ((k17_quaterni A) = k6_numbers)  &  ((k17_quaterni B) = k6_numbers) )  =>  ( ((k17_quaterni (k27_quaterni A B)) = (k9_real_1 (k9_real_1 (k1_real_1 (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))))  &  ( ((k18_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k19_quaterni A) (k20_quaterni B)) (k8_real_1 (k20_quaterni A) (k19_quaterni B))))  &  ( ((k19_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k20_quaterni A) (k18_quaterni B)) (k8_real_1 (k18_quaterni A) (k20_quaterni B))))  &  ((k20_quaterni (k27_quaterni A B)) = (k9_real_1 (k8_real_1 (k18_quaterni A) (k19_quaterni B)) (k8_real_1 (k19_quaterni A) (k18_quaterni B)))) ) ) ) ) ) ) ) ) ).
tt(t39_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k19_quofield A))) =>  ((k1_algstr_0 (k19_quofield A) (k1_algstr_0 (k19_quofield A) B C) D) = (k1_algstr_0 (k19_quofield A) B (k1_algstr_0 (k19_quofield A) C D))) ) ) ) ) ) ) ) ) ).
tt(t39_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_vectsp_6 E A C) =>  ((v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D (k1_vectsp_6 A C E))) =>  ((k2_ranknull C B D (k1_vectsp_6 A C E)) = (k1_vectsp_6 A B (k8_ranknull A C B E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_rat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k2_rat_1 B) (k4_real_1 A (k1_rat_1 B)))) )  &  (~  ( (~ (r1_xxreal_0 (k2_rat_1 B) (k4_real_1 A (k1_rat_1 B))))  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t39_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ( (C = (k4_rcomp_1 A B))  =>  ((k1_tops_1 k2_topalg_2 C) = (k2_rcomp_1 A B)) ) ) ) ) ) ) ) ).
tt(t39_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 1 A) => (r2_hidden (k1_seq_1 (k4_real_3 B) A) k5_numbers)) ) ) ) ) ).
tt(t39_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_rearran1 D) &  ((v2_rearran1 D) &  ((v3_rearran1 D (k1_zfmisc_1 B)) & (m2_finseq_1 D (k1_zfmisc_1 B))) ) )  =>  ( ((v1_partfun1 C A) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ((r2_classes1 (k3_rearran1 A B D C) C) &  ((r2_classes1 (k4_rearran1 A B D C) C) &  ( ((k1_rvsum_1 (k3_rearran1 A B D C)) = (k1_rvsum_1 C))  &  ((k1_rvsum_1 (k4_rearran1 A B D C)) = (k1_rvsum_1 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ((k3_relat_1 k1_xboole_0 A) = k1_xboole_0)  &  ((k3_relat_1 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t39_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_relset_1 A B D E) => (r1_tarski (k6_relset_2 A B C D) (k6_relset_2 A B C E))) ) ) ) ) ) ) ) ) ).
tt(t39_rewrite1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r5_rewrite1 k1_xboole_0 A B) | (r6_rewrite1 k1_xboole_0 A B))  =>  (A = B) ) ) ) ).
tt(t39_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( ( ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))))  & (r3_rewrite2 A B C D))  => (r3_rewrite2 A B D C)) ) ) ) ) ) ) ) ).
tt(t39_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  & (l1_rewrite3 H G))  =>  ((r2_hidden (k4_tarski (k4_tarski A D) (k4_tarski B E)) (k1_rewrite3 C G H)) => (r2_hidden (k4_tarski (k4_tarski A (k1_flang_1 C D F)) (k4_tarski B (k1_flang_1 C E F))) (k1_rewrite3 C G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((k1_valued_1 (k1_rfunct_1 A B) (k1_rfunct_1 C B)) = (k1_rfunct_1 (k1_valued_1 A C) B))  &  ((k45_valued_1 (k1_rfunct_1 A B) (k1_rfunct_1 C B)) = (k1_rfunct_1 (k45_valued_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t39_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t39_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k8_relset_1 A k1_numbers B (k2_limfunc1 k6_numbers)) = (k8_relset_1 A k1_numbers (k19_rfunct_3 A B) (k1_tarski k6_numbers))) ) ) ) ) ).
tt(t39_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) =>  ((k1_seq_1 (k4_rinfsup1 A) k6_numbers) = (k1_rinfsup1 A)) ) ) ) ).
tt(t39_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  => (r1_xxreal_0 (k6_rinfsup2 A) (k5_rinfsup2 A))) ) ).
tt(t39_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k6_rlvect_2 A (k1_rlaffin1 A C B)) = (k3_rlvect_1 A (k1_rlvect_1 A B (k3_rlaffin1 A C)) (k6_rlvect_2 A C))) ) ) ) ) ) ) ).
tt(t39_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) => (m1_rlsub_1 (k1_rlsub_1 A) B)) ) ) ) ).
tt(t39_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((r1_rlsub_2 A (k1_rlsub_1 A) (k2_rlsub_1 A)) & (r1_rlsub_2 A (k2_rlsub_1 A) (k1_rlsub_1 A))) ) ) ).
tt(t39_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A B) => (m1_connsp_2 (k5_rusub_4 A D C) A (k3_rlvect_1 A C B))) ) ) ) ) ) ) ) ).
tt(t39_rlvect_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  (F = (k1_funct_1 D E)) )  =>  ((k1_funct_1 C E) = (k1_rlvect_1 B F A)) ) ) ) ) ) )  =>  ((k4_rlvect_1 B C) = (k1_rlvect_1 B (k4_rlvect_1 B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) => (r1_rlvect_2 A (k7_rlvect_2 A B C) (k7_rlvect_2 A C B))) ) ) ) ) ) ).
tt(t39_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [H:$i] :  ((m2_rlvect_2 H A (k8_domain_1 (u1_struct_0 A) B C D)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers H B) = E)  &  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers H C) = F)  &  ((k3_funct_2 (u1_struct_0 A) k1_numbers H D) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_rlvect_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_rlvect_5 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 A (k1_rlvect_5 B)) & (v1_xboole_0 (k2_rlvect_5 B A))) ) ) ) ) ) ).
tt(t39_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) => (m1_rmod_2 (k1_rmod_2 A B) A C)) ) ) ) ) ) ).
tt(t39_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  ((r1_rmod_3 A B (k1_rmod_2 A B) (k2_rmod_2 A B)) & (r1_rmod_3 A B (k2_rmod_2 A B) (k1_rmod_2 A B))) ) ) ) ) ).
tt(t39_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) => (r1_rmod_4 A B (k6_rmod_4 A B C D) (k6_rmod_4 A B D C))) ) ) ) ) ) ) ) ).
tt(t39_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A B B) = (k11_robbins1 A B)) ) ) ) ) ).
tt(t39_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A C B)) (k3_robbins1 A (k5_robbins1 A C D))))) = (k5_robbins1 A C B)) ) ) ) ) ) ) ) ) ).
tt(t39_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) &  ((v1_robbins4 A) & (l4_robbins1 A)) ) ) ) ) )  <=>  ((v1_robbins3 A) &  ((v3_robbins3 A) &  ((v10_robbins1 A) & (v2_robbins4 A)) ) ) ) ) ) ).
tt(t39_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v3_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C) (k1_rcomp_1 k6_numbers 1))) ) ) ) ) ) ).
tt(t39_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ( (~ (r1_xxreal_0 (k1_rpr_1 A B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  &  (~  ((k8_real_1 (k1_rpr_1 A B) (k2_rpr_1 A B C)) = (k8_real_1 (k1_rpr_1 A C) (k2_rpr_1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_rusub_1 A B (k1_rusub_1 A)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t39_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((r1_rusub_2 A (k1_rusub_1 A) (k2_rusub_1 A)) & (r1_rusub_2 A (k2_rusub_1 A) (k1_rusub_1 A))) ) ) ).
tt(t39_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) B C) A) &  ((r1_struct_0 (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) D E)) B) & (r1_struct_0 (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) D E)) C)) )  =>  ( (B = C)  |  ( ((k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) D E)) = (k1_rusub_3 A (k7_domain_1 (u1_struct_0 A) B C)))  &  ((v1_rlvect_3 (k7_domain_1 (u1_struct_0 A) D E) A) &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B (k4_rusub_5 A)) & (r2_hidden C (k4_rusub_5 A)))  => (r2_hidden (k9_subset_1 (u1_struct_0 A) B C) (k4_rusub_5 A))) ) ) ) ) ) ) ).
tt(t39_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k8_rvsum_1 (k8_rvsum_1 A B) C) = (k8_rvsum_1 A (k4_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t39_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k17_rvsum_1 (k5_rvsum_2 A)) = (k1_binop_2 (k16_rvsum_1 A))) ) ) ).
tt(t39_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k2_scmbsort A) =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 63 C))  =>  ((k1_funct_1 k2_scmbsort C) = (k3_compos_1 k1_scmfsa_2 A C)) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k3_amistd_1 3 k1_scmfsa_2 A) = (k2_tarski A (k1_ordinal1 A))) ) ) ).
tt(t39_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 10)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (~  (A = (k15_scmfsa_2 C B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B (k1_scmfsa_m D) A) & (r6_scmfsa7b B (k1_scmfsa_m D) A))  => (r1_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2))) (k1_funct_4 D (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1))))) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ((v1_ami_2 F) &  ( (~ (v1_scmfsa_m F))  & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r2_scmfsa7b C E))  &  ( (~ (r2_scmfsa7b D E))  &  (~  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k4_scmfsa8b E F C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 5))  &  ( ( ((k1_funct_1 B E) = (k1_funct_1 B F))  =>  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (E = G) )  =>  ((k1_funct_1 (k1_scmfsa6b (k4_scmfsa8b E F C D) B A) G) = (k1_funct_1 (k1_scmfsa6b C B A) G)) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa8b E F C D) B A) G) = (k18_scmfsa_2 (k1_scmfsa6b C B A) G)) ) ) ) )  &  ( (~  ((k1_funct_1 B E) = (k1_funct_1 B F)) )  =>  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (E = G) )  =>  ((k1_funct_1 (k1_scmfsa6b (k4_scmfsa8b E F C D) B A) G) = (k1_funct_1 (k1_scmfsa6b D B A) G)) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa8b E F C D) B A) G) = (k18_scmfsa_2 (k1_scmfsa6b D B A) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_scmfsa8a B A (k2_scmfsa6a C)) =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r6_scmfsa7b (k2_scmfsa8b E C D) B A) &  ((r5_scmfsa7b (k2_scmfsa8b E C D) B A) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa8b E C D)) (k8_memstr_0 3 k1_scmfsa_2 B)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r3_scmfsa9a A B C D) & (r4_scmfsa9a A B C D)) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 E (k2_scmfsa9a A B C D)) & (r1_xxreal_0 F (k2_scmfsa9a A B C D)))  =>  ( (E = F)  |  ( (~  ((k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E) = (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F)) )  &  (~  ((k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) E)) = (k6_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r5_scmfsa7b C D A) &  ((r6_scmfsa7b C D A) &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 E))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) E)) 4))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 E))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) E))) ) ) )  =>  ((r1_xxreal_0 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D)) E) |  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k2_nat_1 1 E) 1))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 E 1))) 4))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k2_nat_1 1 E) 1))) = (k6_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_funct_4 D (k7_memstr_0 3 k1_scmfsa_2 k6_numbers)) (k2_nat_1 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((r1_scm_halt (k2_scmfsa8b E C D) B A) & (r2_scm_halt (k2_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmisort,ax,(r2_extpro_1 3 k1_scmfsa_2 k3_scmisort (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) k10_scmfsa_m)).
tt(t39_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmpds_2) A) = 13)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (~  (A = (k16_scmpds_2 B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v4_scmpds_4 C) & (m1_subset_1 C (u1_compos_1 k1_scmpds_2)))  =>  ( ((k6_memstr_0 2 k1_scmpds_2 A) = (k6_memstr_0 2 k1_scmpds_2 B))  =>  ((k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 C A)) = (k6_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 C B))) ) ) ) ) ) ) ) ).
tt(t39_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((r1_scmpds_6 D B A) & (r2_scmpds_6 D B A))  =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F)) = k6_numbers)  |  ((r1_scmpds_6 (k2_scmpds_6 E F C D) B A) & (r2_scmpds_6 (k2_scmpds_6 E F C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 H (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ( ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) D) = (k1_funct_1 H D))  &  ( ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) (k2_scmpds_2 (k1_funct_1 B D) E)) = (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((r2_hidden (k2_scmpds_2 (k1_funct_1 B D) E) G) |  ((r1_xxreal_0 F k6_numbers) |  ( (D = (k2_scmpds_2 (k1_funct_1 B D) E))  |  ((r1_scmpds_6 (k1_scmpds_7 D E F C) B A) & (r2_scmpds_6 (k1_scmpds_7 D E F C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k1_scmring2 A))) => (r1_xxreal_0 (k2_compos_0 (u1_compos_1 (k1_scmring2 A)) B) 7)) ) ) ) ).
tt(t39_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((r2_hidden B (k3_tarski A)) => (r1_tarski (k5_scmyciel (k1_tarski B)) A)) ) ) ) ).
tt(t39_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_semi_af1 A B C D E) &  ((r1_semi_af1 A B C F) & (r1_semi_af1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  => (v2_relat_1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t39_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  & (v1_seqm_3 (k2_valued_0 k1_numbers B A))) ) ) ) ).
tt(t39_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((r1_seqfunc A k1_numbers C D) => (r1_seqfunc A k1_numbers (k2_seqfunc A C B) D)) ) ) ) ) ) ) ) ).
tt(t39_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_seq_2 A) & (v7_valued_0 B))  => (v2_seq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t39_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((k3_funct_2 k5_numbers k1_numbers A B) = k6_numbers) ) ) )  &  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 1 (k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) (k2_nat_1 C 1)) (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) C)))) ) ) ) )  & (v1_series_1 A)) ) ) ) ) ).
tt(t39_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k13_complex1 (k6_xcmplx_0 (k2_nat_1 (k13_newton B 2) B) 1) (k9_newton (k2_nat_1 B 2))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k11_complex1 (k13_complex1 1 2) (k13_complex1 (k2_nat_1 B 1) (k9_newton (k2_nat_1 B 2))))) ) ) ) ) ) ) ).
tt(t39_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers k1_numbers A (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 B D)) & (r1_xxreal_0 k6_numbers (k1_seq_1 C D))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) D) (k8_real_1 (k1_seq_1 (k3_series_1 B) D) (k1_seq_1 (k3_series_1 C) D)))) ) ) ) ) ) ) ) ) ).
tt(t39_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 64 (k3_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 1 (k13_complex1 1 A)) (k2_xcmplx_0 1 (k13_complex1 1 B))) (k2_xcmplx_0 1 (k13_complex1 1 C))))) ) ) ) ) ) ) ).
tt(t39_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k7_setfam_1 A (k4_subset_1 (k1_zfmisc_1 A) B C)) = (k4_subset_1 (k1_zfmisc_1 A) (k7_setfam_1 A B) (k7_setfam_1 A C))) ) ) ) ) ) ).
tt(t39_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A C) D) = B) ) ) ) ) ) ) ) ) ).
tt(t39_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_prob_1 A (k6_setlim_2 A C B)) = (k4_subset_1 A B (k1_prob_1 A C))) ) ) ) ) ) ).
tt(t39_setwiseo,ax, (! [A:$i] : (v2_binop_1 (k9_setwiseo A) (k5_finsub_1 A))) ).
tt(t39_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ((v1_setwiseo D A) &  ( (B = (k4_binop_1 A D))  &  ((r6_binop_1 A E D) &  ((k5_binop_1 A E B C) = B) ) ) ) ) )  =>  ((k5_binop_1 A E (k1_finsop_1 A F D) C) = (k1_finsop_1 A (k2_finseqop A A A E F C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_sf_mastr A) = (k3_sf_mastr (k5_compos_0 (u1_compos_1 k1_scmfsa_2) A B))) ) ) ) ) ).
tt(t39_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B C) C) (k5_sheffer1 A C (k5_sheffer1 A D B))) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D B)) (k5_sheffer1 A C (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t39_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B A)) )  =>  ((k7_simplex0 A B (k2_struct_0 B)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ).
tt(t39_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_ordinal1 B) &  ((v1_finset_1 B) &  ((v5_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ( ((v1_setfam_1 B) &  ( ((k3_real_1 (k5_card_1 B) 1) = (k5_card_1 (k5_setfam_1 (u1_struct_0 A) B)))  & (v1_rlaffin1 (k5_setfam_1 (u1_struct_0 A) B) A)) )  =>  ((k1_card_1 (a_2_0_simplex1 A B)) = 2) ) ) ) ) ) ).
tt(t39_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)))).
tt(t39_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_fcont_1 k4_sin_cos2 A)) ) ).
tt(t39_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) = (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A)) ) ) ).
tt(t39_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k2_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos A)) (k3_xcmplx_0 (k17_sin_cos B) (k20_sin_cos B)))) ) ) ) ) ).
tt(t39_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  =>  ((k9_real_1 (k5_square_1 (k1_sin_cos5 A)) (k5_square_1 (k3_sin_cos5 A))) = 1) ) ) ) ).
tt(t39_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ((r1_xxreal_0 A (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) & (r1_xxreal_0 (k17_sin_cos A) (k1_real_1 1))) ) ) ) ) ) ) ).
tt(t39_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) =>  ((k3_sin_cos7 A) = (k11_binop_2 2 (k3_sin_cos7 (k7_square_1 (k12_binop_2 (k9_binop_2 A 1) 2))))) ) ) ) ).
tt(t39_sin_cos9,ax, ( ((k5_sin_cos9 1) = (k10_real_1 k32_sin_cos 4))  &  ((k1_seq_1 k1_sin_cos9 1) = (k10_real_1 k32_sin_cos 4)) ) ).
tt(t39_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k3_newton A) (k3_newton B))) ) ) ) ) ).
tt(t39_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k4_metric_1 (k14_euclid A) D E) = (k12_euclid (k5_algstr_0 (k15_euclid A) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (v1_topreal1 A))  => (v1_topreal1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t39_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_sprect_1 A) 5) = (k11_pscomp_1 A)) ) ) ).
tt(t39_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k20_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t39_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k2_goboard9 A)) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k3_goboard9 A)) &  ((k2_jordan5c (k3_topreal1 2 B) (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B))) = (k13_pscomp_1 (k3_topreal1 2 A))) ) ) ) ) ) ) ) ).
tt(t39_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k24_pscomp_1 (k3_topreal1 2 A)) = (k23_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t39_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B A) |  ((k7_xcmplx_0 1 (k6_xcmplx_0 (k6_square_1 B) (k6_square_1 A))) = (k7_xcmplx_0 (k2_xcmplx_0 (k6_square_1 B) (k6_square_1 A)) (k6_xcmplx_0 B A))) ) ) ) ) ) ) ).
tt(t39_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k14_stacks_1 A))) =>  ( (C = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B))  =>  ((r1_stacks_1 A B) |  ((r2_hidden (k5_stacks_1 A B) (k5_stacks_1 (k14_stacks_1 A) C)) &  ((k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) (k5_stacks_1 A B)) = (k5_stacks_1 (k14_stacks_1 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t39_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k23_binop_2 A 1) (k23_binop_2 B C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) (k23_binop_2 B C))))) )  =>  ( ((v2_funct_2 D B) &  ((v1_stirl2_1 D A B) &  (D = (k2_partfun1 (k23_binop_2 A 1) (k23_binop_2 B C) E A)) ) )  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden F (k2_relset_1 (k23_binop_2 B C) E)) &  ((r2_hidden G (k2_relset_1 (k23_binop_2 B C) E)) &  ( (~ (r1_xxreal_0 G F))  & (r1_xxreal_0 (k5_nat_1 (k1_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B C) E (k1_seq_4 G))) (k5_nat_1 (k1_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B C) E (k1_seq_4 F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  (~  ((v3_substut1 (k7_sublemma A C B) A) &  ( (~ (r2_hidden B (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))))  & (r2_hidden (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k5_enumset1 B C D E F G H) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_substut1 A)) => (r1_tarski (k2_relset_1 (k3_qc_lang1 A) (k2_substut1 A B)) (k3_qc_lang1 A))) ) ) ) ).
tt(t39_supinf_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 B) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B C))) ) ) ) ) ) ).
tt(t39_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ( ((k3_relat_1 A B) = A)  &  ((k3_relat_1 B (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B)))) = k1_xboole_0) )  => (r1_tarski (k1_sysrel A) (k1_sysrel B)))  &  ( ( ((k3_relat_1 B A) = A)  &  ((k3_relat_1 (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) B) = k1_xboole_0) )  => (r1_tarski (k1_sysrel A) (k1_sysrel B))) ) ) ) ) ) ).
tt(t39_taxonom1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v5_tbsp_1 B) & (l1_metric_1 B)) ) ) )  =>  ((r1_xxreal_0 (k3_tbsp_1 B (k2_struct_0 B)) A) => (r2_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k13_lang1 (u1_struct_0 B) (k3_taxonom1 B A)) (k1_eqrel_1 (u1_struct_0 B)))) ) ) ) ) ).
tt(t39_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k6_tdlat_1 A) = (k1_realset1 (k2_tdlat_1 A) (k5_tdlat_1 A))) ) ) ).
tt(t39_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))))) ) ) ) ).
tt(t39_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((k1_tdlat_1 A) = (k5_tdlat_1 A)) ) ) ).
tt(t39_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((k3_polynom1 A C (k6_termord A B C D) (k3_termord A B C D)) = (k4_struct_0 C)) ) ) ) ) ) ) ) ) ).
tt(t39_tex_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v3_tex_2 C A)) )  => (v3_tex_2 D B)) ) ) ) ) ) ) ) ) ).
tt(t39_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v4_tex_3 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (u1_struct_0 B)) => (v3_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t39_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ((a_2_7_tex_4 A B) = k1_xboole_0) )  => (r1_tarski (k3_tex_4 A B) (k1_setfam_1 (a_2_7_tex_4 A B)))) ) ) ) ) ).
tt(t39_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  ( (~ (r1_tsep_1 C B))  =>  ((v1_tsep_1 (k2_tsep_1 A C B) B) & (m1_pre_topc (k2_tsep_1 A C B) B)) ) ) ) ) ) ) ) ).
tt(t39_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v3_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( (! [D:$i] :  ((r2_hidden D A) => (r1_tarski (k9_relat_1 B D) (k9_relat_1 C D))) )  => (r1_relset_1 A A B C)) ) ) ) ) ) ).
tt(t39_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A B D) & (r1_borsuk_6 A D E)) )  =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H A B D) => (r3_borsuk_2 A B D (k1_borsuk_2 A B E D (k1_borsuk_2 A B D E (k1_borsuk_2 A B B D (k1_borsuk_2 A B C B F (k2_borsuk_2 A B C F)) H) G) (k2_borsuk_2 A D E G)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [D:$i] :  ( ((v7_topalg_6 D A) & (m2_subset_1 D (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [E:$i] :  ( ((v7_topalg_6 E A) & (m2_subset_1 E (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [F:$i] :  ( ((v7_topalg_6 F A) & (m2_subset_1 F (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [G:$i] :  ( ((v7_topalg_6 G A) & (m2_subset_1 G (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ( ((r2_topalg_6 A B C) &  ( ((k9_xtuple_0 B) = (k9_xtuple_0 C))  &  ((r2_topalg_6 A D E) &  ( ((k9_xtuple_0 D) = (k9_xtuple_0 E))  &  ( (F = (k4_topalg_6 A B D))  &  ( (G = (k4_topalg_6 A C E))  &  ( ((k3_topalg_6 A B) = (k2_topalg_6 A D))  &  ((k1_xxreal_2 (k9_xtuple_0 B)) = (k2_xxreal_2 (k9_xtuple_0 D))) ) ) ) ) ) ) )  => (r2_topalg_6 A F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_waybel23 (k1_pre_topc A B)) =>  ( ((v1_topdim_1 B A) & (r1_xxreal_0 (k2_topdim_1 A B) k6_numbers))  <=>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) => (r1_xboole_0 B (k2_tops_1 A D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k2_tops_1 A (k1_struct_0 A)) = k1_xboole_0) ) ) ).
tt(t39_topgen_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ( (C = (k1_cantor_1 A (k2_cantor_1 A (k5_setfam_1 (k9_setfam_1 A) B))))  &  ( ((v2_pre_topc (g1_pre_topc A C)) & (l1_pre_topc (g1_pre_topc A C)))  &  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden D B) => (m2_yellow_9 (g1_pre_topc A C) (g1_pre_topc A D))) ) )  &  (! [D:$i] :  ( ((v2_pre_topc D) & (l1_pre_topc D))  =>  ( ( ((u1_struct_0 D) = A)  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden E B) => (m2_yellow_9 D (g1_pre_topc A E))) ) ) )  => (m2_yellow_9 D (g1_pre_topc A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_subset_1 C (u1_struct_0 (k6_topgen_3 A B))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_topgen_3 A B)))))  =>  ((v3_pre_topc C (k6_topgen_3 A B)) <=>  (~ (r2_hidden B C)) ) ) ) ) ) ) ) ).
tt(t39_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_topgen_4 B A) & (v5_topgen_4 C A))  => (v5_topgen_4 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t39_topgen_5,ax, ((v2_topgen_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) k3_topgen_5) & (m1_subset_1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) k2_topgen_5 k1_topgen_5) (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t39_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A (k2_group_1 A B)) =>  (? [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A B))  & (r1_tarski (k1_group_2 A D) C)) ) ) ) ) ) ) ) ).
tt(t39_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 2 (k3_finseq_1 B)) =>  ((r2_hidden A (k3_topreal1 2 B)) |  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = A)  & (r2_hidden B (k9_metric_1 (k14_euclid 2) C D)))  =>  ( (~ (r1_xxreal_0 (k17_euclid B) (k9_real_1 (k17_euclid A) D)))  &  (~ (r1_xxreal_0 (k7_real_1 (k17_euclid A) D) (k17_euclid B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (~ (v1_xboole_0 (k3_topreal9 A C B)))  => (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ) ).
tt(t39_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  (! [E:$i] :  ( ((v3_pre_topc E (k4_topmetr A B)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))  =>  (! [F:$i] :  ( ((v3_pre_topc F (k4_topmetr C D)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_topmetr C D)))))  =>  ((v3_pre_topc (k4_card_3 (k4_funct_4 1 2 E F)) (k1_topreala A B C D)) & (m1_subset_1 (k4_card_3 (k4_funct_4 1 2 E F)) (k1_zfmisc_1 (u1_struct_0 (k1_topreala A B C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) 1) =>  (! [C:$i] :  ((r2_hidden C (k3_toprealb B A)) => (v2_funct_1 (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb C))) ) ) ) ) ) ) ).
tt(t39_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k74_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k74_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k74_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t39_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 C A) =>  ((k6_toprns_1 A (k2_toprns_1 B A C)) = (k1_rlvect_1 (k15_euclid A) (k6_toprns_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t39_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xboole_0 (k1_tops_1 A B) (k2_tops_1 A B))) ) ) ) ).
tt(t39_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  (~  ((v1_tops_2 C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 D A) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (k2_struct_0 B))  =>  (C = (k1_tops_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=> (v3_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t39_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) => (v4_transgeo (k2_funct_2 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t39_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) => (m4_trees_1 (k1_tarski B) A)) ) ) ) ).
tt(t39_trees_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_trees_2 k8_trees_1 A) = (k1_tarski (k5_finseq_2 k5_numbers A k6_numbers))) ) ) ).
tt(t39_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 C)) =>  ( ((k2_domain_1 A B (k3_trees_2 (k2_zfmisc_1 A B) C D)) = (k1_funct_1 (k8_trees_3 A B C) D))  &  ((k1_funct_1 (k9_trees_3 A B C) D) = (k3_domain_1 A B (k3_trees_2 (k2_zfmisc_1 A B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t39_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers C)) (k9_xtuple_0 A)) <=> (r2_hidden (k2_nat_1 C 1) (k4_finseq_1 (k1_trees_9 (k9_xtuple_0 A) B)))) ) ) ) ) ) ) ).
tt(t39_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) => (r1_connsp_1 A (k9_subset_1 (u1_struct_0 A) B D) (k9_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t39_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A B D) &  ((r4_tsep_2 A C E) &  ((r1_tsep_1 B C) & (r4_tsep_1 A D E)) ) )  => (r3_tsep_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  ((r2_hidden (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u4_turing_1 A) (u4_turing_1 B)) (k21_turing_1 A B)) & (r2_hidden (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) (u5_turing_1 B)) (k21_turing_1 A B))) ) ) ) ) ).
tt(t39_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k15_twoscomp) (k3_msafree2 (k40_twoscomp A B))) & (r2_hidden (k4_tarski (k10_finseq_1 A B) k3_twoscomp) (k3_msafree2 (k40_twoscomp A B)))) ) ) ) ) ).
tt(t39_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_xboole_0 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ( (~  (C = B) )  &  (~  ((k1_funct_1 (k4_uniroots B A) C) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_algseq_1 A (k2_polynom5 A (k4_polynom5 A B (k5_struct_0 A)) C)) = (k2_nat_1 C 1)) ) ) ) ) ) ) ).
tt(t39_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) => (r2_valuat_1 A B C (k5_cqc_lang A))) ) ) ) ) ) ).
tt(t39_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r2_hidden B (k1_relset_1 k5_numbers (k61_valued_1 A C))) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k9_xtuple_0 A)) &  (B = (k2_xcmplx_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k18_valued_1 B C) A) = (k18_valued_1 B (k14_valued_2 C A))) ) ) ) ) ) ) ).
tt(t39_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 B)) &  ((v13_vectsp_1 C B B) &  ((v1_mod_2 C A B B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v1_vectsp11 C A B) & (m1_vectsp11 E A B C))  =>  ( (D = E)  |  (! [F:$i] :  ((m1_vectsp_5 F A B (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) (k4_algstr_0 A D))))) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 F) (u1_struct_0 F)) &  ((v13_vectsp_1 G F F) &  ((v1_mod_2 G A F F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 F) (u1_struct_0 F))))) ) ) )  =>  ((r1_funct_2 (u1_struct_0 F) (u1_struct_0 F) (u1_struct_0 F) (u1_struct_0 B) G (k8_matrlin2 A B B F C)) =>  ((v1_vectsp11 G A F) &  ( (~ (m1_vectsp11 D A F G))  &  ((m1_vectsp11 E A F G) & (m1_vectsp_4 (k2_vectsp11 A B (k3_matrlin A B B C (k4_matrlin A B B (k3_struct_0 B) (k4_algstr_0 A E)))) A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (m1_vectsp_4 (k1_vectsp_4 A B) A C)) ) ) ) ) ) ).
tt(t39_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  ( ((k1_vectsp_5 A B C D) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)))  &  ((k1_vectsp_5 A B D C) = (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t39_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((m2_vectsp_6 D A B C) => (m2_vectsp_6 (k7_vectsp_6 A B D) A B C)) ) ) ) ) ) ) ) ) ).
tt(t39_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((v1_partfun1 D A) =>  ((k7_partfun1 (u1_struct_0 C) (k4_vfunct_1 A C D E) B) = (k1_rlvect_1 C (k7_partfun1 (u1_struct_0 C) D B) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v1_partfun1 C A) =>  ((k7_partfun1 (u1_struct_0 B) (k2_vfunct_2 A B C D) E) = (k1_clvect_1 B (k7_partfun1 (u1_struct_0 B) C E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r2_yellow_0 A (k6_waybel_0 A B)) &  ((k2_yellow_0 A (k6_waybel_0 A B)) = B) ) ) ) ) ) ).
tt(t39_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v7_yellow_6 (k2_waybel11 A) A) => (v3_waybel_3 A)) ) ) ).
tt(t39_waybel12,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v4_card_3 B) &  ((v3_waybel12 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (C = (k3_yellow_0 A)) )  &  (! [D:$i] :  ( ((v2_waybel_6 D A) & (m1_subset_1 D (u1_struct_0 A)))  =>  (~  ( (~  (D = (k4_yellow_0 A)) )  &  (~ (r2_hidden D (k4_waybel_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D C) =>  ((v3_pre_topc D A) & (v2_waybel_0 D A)) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) &  ( (B = (k1_yellow_0 (k2_yellow_1 (k5_waybel11 A)) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ((r2_hidden D C) => (v6_waybel_6 D (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k6_waybel_0 A B)) A) &  ((v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)) A) & (v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) B)) A)) ) ) ) ) ) ).
tt(t39_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v8_waybel_1 B A) => (v3_waybel_1 (k1_waybel_1 A (k1_yellow_2 A A B) (k2_waybel_1 A A B) (k3_waybel_1 A A B)) A (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t39_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v1_partfun1 (k4_waybel20 A B) (u1_struct_0 A)) &  ((v3_relat_2 (k4_waybel20 A B)) &  ((v8_relat_2 (k4_waybel20 A B)) & (m1_subset_1 (k4_waybel20 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t39_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_yellow_6 C A B) & (m1_yellow_6 C A B)) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((r1_orders_2 B D E) & (r2_hidden E (u1_struct_0 C))) ) ) ) )  =>  ((m2_yellow_6 C A B) & (m2_waybel21 (k1_yellow_9 B C) A B C)) ) ) ) ) ) ) ) ).
tt(t39_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_waybel23 (k1_waybel_3 A B) A)) ) ) ) ).
tt(t39_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v6_pre_topc A) &  ((v2_waybel18 A) & (l1_pre_topc A)) ) ) )  => (v1_waybel25 A)) ) ).
tt(t39_waybel26,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_finset_1 (k9_xtuple_0 A)) & (v1_finset_1 (k10_xtuple_0 A))) ) ) ).
tt(t39_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C))) &  ((v22_waybel_0 D B (k6_yellow_1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C)))))) ) )  =>  ((v1_funct_1 (k10_funct_6 D)) &  ((v1_funct_2 (k10_funct_6 D) A (u1_struct_0 (k2_waybel27 B C))) & (m1_subset_1 (k10_funct_6 D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k2_waybel27 B C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t39_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) )  => (v19_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ).
tt(t39_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (B = (k1_yellow_0 A (a_2_4_waybel30 A B))) ) ) ) ) ) ).
tt(t39_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v1_waybel34 (k2_waybel_1 A A B) A (k1_yellow_2 A A B)) => (v4_waybel_0 (k1_yellow_2 A A B) A)) ) ) ) ) ).
tt(t39_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_waybel_3 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (~  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B D) &  ((r1_tarski D C) & (v2_compts_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (v7_waybel_4 (k11_waybel_4 A B) A)) ) ) ) ).
tt(t39_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_waybel_5 A) <=>  ((v2_waybel_1 A) &  ((v3_waybel_3 A) & (v3_waybel_3 (k7_lattice3 A))) ) ) ) ) ).
tt(t39_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_subset_1 (k4_waybel_0 A (k12_waybel_0 A (k3_subset_1 (u1_struct_0 A) (k5_waybel_0 A B)))) (k1_waybel_3 A B)) => (v4_waybel_7 B A)) ) ) ) ) ).
tt(t39_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  ((v11_waybel_0 B A) =>  ((r2_waybel_9 A B) & (r2_hidden (k1_waybel_9 A B) (k10_yellow_6 A B))) ) ) ) ) ) ) ).
tt(t39_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ((k5_struct_0 (k4_weddwitt A)) = (k5_struct_0 A)) ) ) ).
tt(t39_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_wellord1 A B C) => (r3_wellord1 B A (k2_funct_1 C))) ) ) ) ) ) ) ).
tt(t39_wsierp_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 (k2_finseq_3 A B)) (k4_finseq_1 B))) ) ) ) ).
tt(t39_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_xboole_0 A (k4_xboole_0 B A)) = (k2_xboole_0 A B)) ) ) ).
tt(t39_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k9_xboolean A (k9_xboolean B C)) = (k5_xboolean (k4_xboolean (k3_xboolean A) B) (k4_xboolean (k3_xboolean A) C))) ) ) ) ) ) ) ).
tt(t39_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k6_xcmplx_0 A B) = (k2_xcmplx_0 (k6_xcmplx_0 A C) (k6_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t39_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t39_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k13_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k13_xtuple_0 A) (k13_xtuple_0 B))) ) ) ).
tt(t39_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k4_xxreal_0 A (k3_xxreal_0 B C)) = (k3_xxreal_0 (k4_xxreal_0 A B) (k4_xxreal_0 A C))) ) ) ) ) ) ) ).
tt(t39_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) | (r1_tarski (k1_xxreal_1 B C) (k3_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t39_xxreal_2,ax, ((k1_xxreal_2 k1_xboole_0) = k2_xxreal_0) ).
tt(t39_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 B (k1_xxreal_3 B A))) ) ) ) ) ).
tt(t39_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_yellow_0 A (k6_domain_1 (u1_struct_0 A) B)) = B)  &  ((k2_yellow_0 A (k6_domain_1 (u1_struct_0 A) B)) = B) ) ) ) ) ) ).
tt(t39_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k5_yellow_3 A B (k5_waybel_0 (k3_yellow_3 A B) C)) = (k5_waybel_0 B (k9_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t39_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v1_funct_1 (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B))) &  ((v1_funct_2 (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 A)) &  ((v5_pre_topc (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k2_borsuk_1 A B) A) & (m1_subset_1 (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t39_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((v4_yellow_0 (k6_yellow_1 C B) (k6_yellow_1 C A)) & (m1_yellow_0 (k6_yellow_1 C B) (k6_yellow_1 C A))) ) ) ) ) ) ).
tt(t39_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v4_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v2_altcat_3 D A B C) &  (~ (v2_funct_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  ((r2_yellow20 A B C A B) => (v21_functor0 C A B)) ) ) ) ) ) ) ).
tt(t39_yellow_2,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) =>  ((v13_waybel_0 C A) & (v2_waybel_0 C A)) ) ) )  =>  ((v2_waybel_0 (k6_setfam_1 (u1_struct_0 A) B) A) & (m1_subset_1 (k6_setfam_1 (u1_struct_0 A) B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t39_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((r1_yellow_0 A C) & (r1_yellow_0 B D))  <=> (r1_yellow_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t39_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_yellow_4 A (k4_yellow_4 A B C) B)) ) ) ) ) ) ).
tt(t39_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_orders_2 A B C) & (r3_orders_2 A D E))  => (r3_orders_2 A (k1_yellow_5 A B E) (k1_yellow_5 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k10_yellow_6 A B)) =>  (! [D:$i] :  ((m3_yellow_6 D (u1_struct_0 B) A) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r2_hidden (k2_waybel_0 A B E) (k10_yellow_6 A (k7_yellow_6 (u1_struct_0 B) A D E)))) )  => (r2_hidden C (k10_yellow_6 A (k8_yellow_6 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t39_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B))))) ) )  &  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)))))) ) )  &  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  ( ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)))))) ) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)))))) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden E B) & (r2_hidden C E))  => (r1_waybel_0 A D E)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A D)) E) => (r2_hidden C (k2_pre_topc A E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_zf_lang A B) => (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t39_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v8_zf_lang A) =>  ( (~  ( (B = (k21_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((k10_zf_lang B C) = A) ) ) ) ) )  &  ( ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k10_zf_lang B C) = A) ) )  =>  (B = (k21_zf_lang A)) )  &  ( (~  ( (B = (k22_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((k10_zf_lang C B) = A) ) ) ) ) )  &  ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  ((k10_zf_lang C B) = A) ) )  =>  (B = (k22_zf_lang A)) ) ) ) ) ) ) ) ) ) ).
tt(t39_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k2_xboole_0 (k1_tarski A) B) B) => (r2_hidden A B)) ) ) ).
tt(t39_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_ordinal2 B k4_ordinal1) &  ( (C = (k4_classes1 B))  & (r2_zfrefle1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t39_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  (! [B:$i] :  ((l1_abcmiz_0 B) =>  ( ((g1_abcmiz_0 (u1_abcmiz_0 A) (u2_abcmiz_0 A)) = (g1_abcmiz_0 (u1_abcmiz_0 B) (u2_abcmiz_0 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_abcmiz_0 B)) =>  ( (C = D)  =>  ((k1_abcmiz_0 A C) = (k1_abcmiz_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_abcmiz_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( (A = (k4_tarski B C))  =>  (B = C) ) ) ) ) ) ).
tt(t3_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((v5_abcmiz_1 B A (k28_abcmiz_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  (~  (B = (k35_abcmiz_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t3_abian,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A (k1_abian A B k6_numbers) C) = C) ) ) ) ) ) ) ).
tt(t3_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k18_complex1 A) = (k4_xcmplx_0 A))  &  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(t3_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C D D) & (r2_analoaf A D D B C)) ) ) ) ) ) ) ) ) ).
tt(t3_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v7_aff_2 A) => (v8_aff_2 A)) ) ) ).
tt(t3_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) => (v1_aff_3 A)) ) ) ).
tt(t3_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r5_aff_1 A D E) =>  ( ( (~ (r2_aff_1 A B C D))  &  (~ (r2_aff_1 A C B D)) )  |  ((r2_aff_1 A B C E) & (r2_aff_1 A C B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k2_finseq_1 A) (k1_nat_1 A 1))) ) ).
tt(t3_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  (~  ((r2_hidden A (k10_xtuple_0 B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k1_relset_1 k5_numbers B)) &  ((k1_funct_1 B C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t3_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  &  ((v1_aff_4 B A) & (v1_aff_4 C A)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t3_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((k4_finseqop (u1_struct_0 A) (u1_struct_0 A) B (k6_partfun1 (u1_struct_0 A))) = B) ) ) ) ) ).
tt(t3_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden A (k7_card_1 (k1_nat_1 A 1)))) ) ).
tt(t3_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_xboole_0 (k9_xtuple_0 A) (k10_xtuple_0 C)) & (r1_xboole_0 (k7_relat_1 B (k9_xtuple_0 C)) (k9_xtuple_0 A)))  =>  ((k3_relat_1 (k1_funct_4 B C) A) = (k3_relat_1 B A)) ) ) ) ) ) ) ) ).
tt(t3_algstr_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ( ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_0 A B (k4_struct_0 A)) = B) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A B C) = (k4_struct_0 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 A B (k1_algstr_0 A C D))) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k1_algstr_0 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t3_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v3_algstr_1 A) &  ((v2_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_algstr_2 A (k1_algstr_2 A B)) = B) ) ) ) ) ).
tt(t3_algstr_3,ax, (1 = (k5_struct_0 k3_algstr_3)) ).
tt(t3_algstr_4,ax, (! [A:$i] :  ((l3_algstr_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_partfun1 C (u1_struct_0 A)) &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_algstr_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ( (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden D (k9_xtuple_0 B)) &  ((k1_funct_1 B D) = (k4_tarski E F)) )  => (r2_hidden E (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) C F))) ) ) ) ) )  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k6_algstr_4 A B) C)) ) ) ) ) ) ) ).
tt(t3_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden D (k1_funct_2 A B)) & (r2_hidden E (k1_funct_2 B C)))  => (r2_hidden (k3_relat_1 D E) (k1_funct_2 A C))) ) ) ) ) ) ) ) ).
tt(t3_altcat_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k2_funct_4 (k3_relat_1 (k15_funct_3 B C) A)) = (k3_relat_1 (k15_funct_3 C B) (k2_funct_4 A))) ) ) ) ) ) ) ).
tt(t3_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v1_altcat_3 D A B C) &  ((v2_altcat_3 D A B C) &  (~  ((k1_altcat_3 A C B (k1_altcat_3 A B C D)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v3_altcat_3 D A B C) =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C B) = k1_xboole_0)  | (v3_altcat_3 (k1_altcat_3 A B C D) A C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k3_ami_3 A B) C) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 C)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k3_ami_3 A B) C) A) = (k2_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k3_ami_3 A B) C) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A C)) = 1)  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1))) = 2)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 k6_numbers)) = (k5_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 k6_numbers)) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1))))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 1)) = (k6_int_1 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 k6_numbers)) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1))))  &  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 2)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (~  (A = B) ) ) ) ) ) ).
tt(t3_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  ( (A = k6_numbers)  =>  ((k3_compos_0 (u1_compos_1 k1_ami_3) A) = (k1_tarski k6_numbers)) ) ) ) ).
tt(t3_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  ((v3_amistd_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k2_nat_1 C 1) (k3_amistd_1 A B C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k3_amistd_1 A B C)) => (r1_xxreal_0 C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_compos_0 (u1_compos_1 (k4_amistd_1 A)))) =>  ((k3_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = (k1_tarski k6_numbers)) ) ) ) ) ).
tt(t3_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_4 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (r1_tarski (k3_amistd_4 A B C) (k2_amistd_4 A B C))) ) ) ) ) ) ).
tt(t3_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) & (l1_extpro_1 B A)) ) ) )  =>  ((v3_amistd_5 B A) <=>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  (~ (v2_compos_1 C B)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) &  ((v1_finset_1 D) & (v4_extpro_1 D A B C)) ) ) ) )  =>  ( (~  ((k6_memstr_0 A B D) = k1_xboole_0) )  => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ((v3_funct_2 C k5_numbers k5_numbers) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 D E) <=> (r1_ami_wstd A B (k3_funct_2 k5_numbers k5_numbers C D) (k3_funct_2 k5_numbers k5_numbers C E))) ) ) ) )  <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k3_funct_2 k5_numbers k5_numbers C (k2_nat_1 D 1)) (k3_amistd_1 A B (k3_funct_2 k5_numbers k5_numbers C D))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k3_funct_2 k5_numbers k5_numbers C E) (k3_amistd_1 A B (k3_funct_2 k5_numbers k5_numbers C D))) => (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_analmetr,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r1_analmetr A B C)) ) ) ) ) ) ).
tt(t3_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_rlvect_1 A (k5_algstr_0 A B C) D) = (k4_algstr_0 A (k1_rlvect_1 A (k5_algstr_0 A C B) D))) ) ) ) ) ) ) ) ) ).
tt(t3_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k1_analort A B C (k4_struct_0 A)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t3_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_anproj_1 A B (k4_struct_0 A)) <=>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t3_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (E = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H))) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B E) (k1_rlvect_1 A C F)) (k1_rlvect_1 A D G)) = (k4_struct_0 A))  =>  ( (E = k6_numbers)  &  ( (F = k6_numbers)  &  (G = k6_numbers) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ((r2_anproj_1 A B C G) &  ((r2_anproj_1 A E F G) &  (~ (v9_struct_0 G A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k5_trees_3 A)) =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden D (k2_relset_1 (k5_trees_3 A) B)) &  (D = (k4_trees_4 C B)) ) ) ) ) ) ) ) ) ).
tt(t3_aofa_i00,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k9_xtuple_0 B)) =>  ((k3_relat_1 C (k1_funct_4 A B)) = (k3_relat_1 C B)) ) ) ) ) ) ) ) ).
tt(t3_arithm,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 1 A) = A) ) ) ).
tt(t3_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  &  ( (B = (k1_setfam_1 C))  &  (! [D:$i] :  ((r2_hidden D C) => (r1_armstrng D A)) ) ) ) ) ) ) ) ) ).
tt(t3_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k2_arrow A)) => (r1_arrow C B B)) ) ) ) ) ) ).
tt(t3_arytm_0,ax, (! [A:$i] :  (~  ((r2_hidden (k4_tarski k11_arytm_3 A) k1_numbers) &  (A = k11_arytm_3) ) ) ) ).
tt(t3_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  (! [C:$i] :  ((m1_subset_1 C k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 B C))  => (r1_arytm_2 A C)) ) ) ) ) ) ) ).
tt(t3_arytm_2,ax, (! [A:$i] :  (~ (r2_hidden (k4_tarski k11_arytm_3 A) k2_arytm_2)) ) ).
tt(t3_arytm_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r1_arytm_3 k1_xboole_0 A) =>  (A = 1) ) ) ) ).
tt(t3_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v2_comseq_2 A) => (r1_xxreal_0 k6_numbers (k2_seq_2 A))) ) ) ).
tt(t3_asympt_1,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v2_xxreal_0 B) & (m1_subset_1 B k1_numbers))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r2_hidden (k1_asympt_1 B 1 k6_numbers) (k6_asympt_0 (k1_asympt_1 A 1 k6_numbers)))) ) ) ) ) ) ).
tt(t3_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r2_hidden (k6_partfun1 (u1_struct_0 A)) (k1_autalg_1 A))) ) ).
tt(t3_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (m2_funct_2 (k6_partfun1 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A))) ) ).
tt(t3_axioms,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( ((r2_hidden k6_numbers A) &  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B A) => (r2_hidden (k2_xcmplx_0 B 1) A)) ) ) )  => (r1_tarski k5_numbers A)) ) ) ).
tt(t3_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( ((k1_bcialg_1 A B C) = (k4_struct_0 A))  &  ((k1_bcialg_1 A C D) = (k4_struct_0 A)) )  =>  ((k1_bcialg_1 A B D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t3_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_2 A B C 2) = (k1_bcialg_1 A (k1_bcialg_1 A B C) C)) ) ) ) ) ) ) ).
tt(t3_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ) ).
tt(t3_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_4 A B C) B) C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A (k1_bcialg_1 A D B) C) => (r1_bcialg_1 A D (k1_bcialg_4 A B C))) ) ) ) ) ) ) ) )  <=>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) ) ) ).
tt(t3_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v8_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_bcialg_1 B (k1_bcialg_1 B C D) C) & (r1_bcialg_1 B (k1_bcialg_2 B C D (k2_nat_1 A 1)) (k1_bcialg_2 B C D A))) ) ) ) ) ) ) ) ) ).
tt(t3_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_bcialg_6 A k6_numbers B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t3_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A D E))) (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A D F)))) (k1_bcialg_1 A F E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_bhsp_1 B C (k1_rlvect_1 B D A)) = (k8_real_1 A (k2_bhsp_1 B C D))) ) ) ) ) ) ) ) ) ).
tt(t3_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (v1_bhsp_2 C A))  => (v1_bhsp_2 (k2_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t3_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_3 B A) & (v1_bhsp_3 C A))  => (v1_bhsp_3 (k6_bhsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t3_bhsp_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k1_bhsp_4 B (k5_normsp_1 B C A)) (k5_normsp_1 B (k1_bhsp_4 B C) A))) ) ) ) ) ) ).
tt(t3_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (m2_bhsp_5 k1_xboole_0 A)) ) ).
tt(t3_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_bhsp_6 B A) => (v3_bhsp_6 B A)) ) ) ) ) ).
tt(t3_bhsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_bhsp_5 B A))  =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ((r1_tarski B (k9_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers C D) = (k2_bhsp_1 A D D)) ) ) ) )  =>  ((k2_bhsp_1 A (k1_bhsp_6 A B) (k1_bhsp_6 A B)) = (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t3_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k5_bilinear A B C D D) (k1_bilinear A B C))) ) ) ) ) ) ) ) ).
tt(t3_binari_2,ax, (! [A:$i] :  ( ((v3_card_1 A 2) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k9_binarith 1 1 k6_margrel1 (k10_binarith k6_margrel1 k7_margrel1) (k10_binarith k6_margrel1 k8_margrel1)))  =>  ((k3_binari_2 2 A) = (k19_binop_2 2)) ) ) ) ).
tt(t3_binari_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k3_finseq_5 A) = (k3_finseq_5 B))  =>  (A = B) ) ) ) ) ) ).
tt(t3_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_euclid A (k5_euclid A) (k5_euclid A)) = (k5_euclid A)) ) ) ).
tt(t3_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k5_xboolean A k7_margrel1) = A) ) ) ).
tt(t3_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B)) = B) ) ) ) ) ).
tt(t3_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r3_binop_1 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((k3_binop_1 A B C D) = D)  &  ((k3_binop_1 A B D C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t3_binop_2,ax, ((k4_binop_1 k3_numbers k39_binop_2) = k6_numbers) ).
tt(t3_bintree1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( ((k1_trees_2 A B) = k1_xboole_0)  <=> (r2_hidden B (k3_trees_1 A))) ) ) ) ) ).
tt(t3_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (A = (k3_finseq_2 (k7_domain_1 k5_numbers k6_numbers 1)))  => (v1_bintree1 A)) ) ) ).
tt(t3_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k1_boolealg A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t3_boole,ax, (! [A:$i] :  ((k4_xboole_0 A k1_xboole_0) = A) ) ).
tt(t3_boolmark,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((r1_xboole_0 A B) =>  ((k7_relat_1 (k1_funct_4 C (k7_funcop_1 A D)) B) = (k7_relat_1 C B)) ) ) ) ) ) ) ).
tt(t3_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k2_bor_cant (k8_prob_1 A B D C))) E) = (k3_funct_2 k1_numbers k1_numbers k24_sin_cos (k1_real_1 (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B D C)) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_pre_topc D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ((m1_connsp_2 E A C) => (m2_connsp_2 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D E) B (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k5_topmetr) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 A))))) )  &  ((v5_pre_topc C k5_topmetr A) &  ( ((k1_funct_1 C k6_numbers) = B)  &  ((k1_funct_1 C 1) = B) ) ) ) ) ) ) ) ) ).
tt(t3_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((r2_borsuk_3 A B) & (r2_borsuk_3 B C))  => (r2_borsuk_3 A C)) ) ) ) ) ) ) ).
tt(t3_borsuk_4,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_zfmisc_1 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (? [D:$i] :  ((m1_subset_1 D A) &  ((r2_hidden D B) &  (~  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_borsuk_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r4_zfmisc_1 A B C D E F) =>  ((k5_card_1 (k4_enumset1 A B C D E F)) = 6) ) ) ) ) ) ) ) ).
tt(t3_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  ((r1_xxreal_0 A (k10_real_1 1 2)) => (m1_subset_1 (k8_real_1 2 A) (u1_struct_0 k5_topmetr))) ) ) ).
tt(t3_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 (k4_int_1 B) (k4_int_1 A)))  =>  ((k4_int_1 (k6_xcmplx_0 A B)) = (k7_real_1 (k9_real_1 (k4_int_1 A) (k4_int_1 B)) 1)) ) ) ) ) ) ).
tt(t3_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r2_hidden B D) &  ( (~  (B = C) )  &  ((v9_rltopsp1 (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C)) (k15_euclid A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden E (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k2_tops_1 (k15_euclid A) D) (k4_topreal9 A B C))) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden F (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C))) => (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid A) B F)) (k12_euclid (k5_algstr_0 (k15_euclid A) B E)))) ) )  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ( (~ (r1_xxreal_0 F k1_xboole_0))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden G (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C))) &  (~ (r1_xxreal_0 F (k12_euclid (k5_algstr_0 (k15_euclid A) E G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_brouwer,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((u1_struct_0 (k2_brouwer A C B)) = (k2_topreal9 A C B)) ) ) ) ) ) ) ).
tt(t3_bspace,ax, ((k2_struct_0 k2_bspace) = (k2_tarski k1_xboole_0 1)) ).
tt(t3_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k5_bvfunc_1 A C (k1_bvfunc_1 A D))) (k5_bvfunc_1 A D (k1_bvfunc_1 A B))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A C (k1_bvfunc_1 A B)) (k5_bvfunc_1 A D (k1_bvfunc_1 A C))) (k5_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t3_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r1_tarski (k15_bvfunc_1 A B (k2_partit1 A C D)) (k15_bvfunc_1 A B C))) ) ) ) ) ) ) ) ).
tt(t3_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ( (B = (k1_enumset1 C D E))  =>  ( (C = D)  |  ( (D = E)  |  ( (E = C)  |  ((k2_bvfunc_2 A B) = (k2_partit1 A (k2_partit1 A C D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B B) B)) ) ) ) ) ) ).
tt(t3_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A C) (k1_bvfunc_1 A B)))) ) ) ) ) ) ).
tt(t3_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k12_bvfunc_1 A) B) (k1_bvfunc_1 A B))) ) ) ) ).
tt(t3_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_hidden C B) => (r1_setfam_1 (k2_bvfunc_2 A B) C)) ) ) ) ) ) ) ).
tt(t3_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k2_bvfunc_1 A C D) (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k2_bvfunc_1 A B C)) B)) ) ) ) ) ) ).
tt(t3_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 B (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t3_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k5_bvfunc_1 A B C) (k5_bvfunc_1 A C B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t3_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t3_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) E) (k5_bvfunc_1 A (k5_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C E)) (k9_bvfunc_1 A D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k1_bvfunc_1 A C)) (k1_bvfunc_1 A B))) ) ) ) ) ) ).
tt(t3_c0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v5_rlvect_1 F) &  ((v6_rlvect_1 F) &  ((v7_rlvect_1 F) &  ((v2_funcsdom F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v1_vectsp_1 F) &  ((v3_vectsp_1 F) & (l1_funcsdom F)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 F))) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 k1_numbers A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers A) A)))) )  =>  ( ( (G = A)  &  ( (B = (k4_struct_0 F))  &  ( (C = (k5_struct_0 F))  &  ( (D = (k1_realset1 (u1_algstr_0 F) G))  &  ( (E = (k1_realset1 (u2_algstr_0 F) G))  &  ( (H = (k2_partfun1 (k2_zfmisc_1 k1_numbers (u1_struct_0 F)) (u1_struct_0 F) (u1_rlvect_1 F) (k2_zfmisc_1 k1_numbers G)))  & (v1_c0sp1 G F)) ) ) ) ) )  => (m2_c0sp1 (g1_funcsdom A E D H C B) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k3_rlvect_1 (k3_c0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers G H) = (k7_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers E H) (k3_funct_2 (u1_struct_0 A) k1_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((r2_relset_1 k5_numbers (k3_cqc_lang A) B (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B) (k12_finseq_1 (k3_cqc_lang A) (k2_calcul_1 A B)))) &  ((k2_relset_1 (k3_cqc_lang A) B) = (k4_subset_1 (k3_cqc_lang A) (k2_relset_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) B)) (k6_domain_1 (k3_cqc_lang A) (k2_calcul_1 A B)))) ) ) ) ) ) ) ).
tt(t3_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (A = k6_numbers)  | (r2_hidden (k2_xcmplx_0 A B) (k2_calcul_2 B A))) ) ) ) ) ).
tt(t3_cantor_1,ax, (! [A:$i] :  ((l1_pre_topc A) => (v1_tops_2 (u1_pre_topc A) A)) ) ).
tt(t3_card_1,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((r2_hidden A B) <=>  ((r1_ordinal1 A B) &  (~  (A = B) ) ) ) ) ) ) ) ).
tt(t3_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k1_funct_2 B C)) =>  ((r2_wellord2 A B) &  ((k1_card_1 A) = (k1_card_1 B)) ) ) ) ) ) ).
tt(t3_card_3,ax, ((k2_card_3 k1_xboole_0) = k1_xboole_0) ).
tt(t3_card_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~  ( (~  ( (B = k6_numbers)  &  (~  (A = k6_numbers) ) ) )  &  ((k2_newton B A) = k6_numbers) ) )  &  (~  ( (~  ((k2_newton B A) = k6_numbers) )  &  ( (B = k6_numbers)  &  (~  (A = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t3_card_5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~ (v1_finset_1 (k3_card_1 A))) ) ) ).
tt(t3_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) <=>  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  &  ( (~ (r2_hidden k1_xboole_0 B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k9_subset_1 A C D) B))  &  ( ((r2_hidden C B) & (r1_tarski C D))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cardfin2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_cardfin2 A) = A) ) ) ).
tt(t3_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden D B) =>  ((r2_hidden C A) |  ((k5_card_1 (k1_funct_2 A B)) = (k1_card_1 (a_4_1_card_fin A B C D))) ) ) ) ) ) ) ) ) ).
tt(t3_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D B) & (r2_hidden C D)) ) ) ) ) ) ) )  =>  ((v1_xboole_0 B) |  ((v3_ordinal1 (k3_ordinal2 B)) &  ((v4_ordinal1 (k3_ordinal2 B)) &  (~ (v1_finset_1 (k3_ordinal2 B))) ) ) ) ) ) ) ) ) ).
tt(t3_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (~  (A = B) )  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  ( ((k10_funct_2 (k2_tarski A B) C (k5_funct_4 C A B D E) A) = D)  &  ((k10_funct_2 (k2_tarski A B) C (k5_funct_4 C A B D E) B) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_cat_4 A B))) =>  (C = D) ) ) ) ) ) ) ).
tt(t3_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  ((m3_cat_2 A B) =>  ((g1_cat_1 (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A) (u1_cat_1 A)) = (g1_cat_1 (u1_struct_0 B) (u4_struct_0 B) (u1_graph_1 B) (u2_graph_1 B) (u1_cat_1 B))) ) ) ) ) ) ).
tt(t3_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k7_nat_d (k4_nat_1 2 A) 1) A)) ) ) ) ).
tt(t3_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  ((v1_catalan2 A) =>  ((k1_recdef_1 A k6_numbers) = k6_numbers) ) ) ) ).
tt(t3_catalg_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  ( (! [E:$i] :  ((r2_hidden E B) =>  ((r1_tarski (k1_funct_1 C E) (k9_xtuple_0 A)) & (r1_tarski (k7_relat_1 A (k1_funct_1 C E)) (k1_funct_1 D E))) ) )  => (m2_pboole (k1_catalg_1 B C A) B C D)) ) ) ) ) ) ) ) ).
tt(t3_cayley,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_cayley (k2_finseq_1 A)) = (k12_matrix_2 A)) ) ) ).
tt(t3_cc0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v2_cfuncdom A) & (l1_cfuncdom A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_cc0sp1 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k3_rlvect_1 B C D) = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k8_group_1 B C D) = (k8_group_1 A E F)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( (C = D)  =>  ((k1_clvect_1 B C E) = (k1_clvect_1 A D E)) ) ) ) ) ) ) )  &  ( ((k1_group_1 B) = (k1_group_1 A))  &  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t3_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) )  =>  ((v1_cc0sp2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k2_numbers)) =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 A) k2_numbers B C) D) &  ((v6_cfdiff_1 D) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C E) &  ((v3_pre_topc E A) & (r1_tarski (k7_relset_1 (u1_struct_0 A) k2_numbers B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  => (r2_relset_1 k5_numbers k2_numbers (k9_comseq_3 C (k25_valued_1 k5_numbers k2_numbers B A)) (k25_valued_1 k5_numbers k2_numbers (k9_comseq_3 C B) A))) ) ) ) ) ) ).
tt(t3_cfdiff_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_comseq_2 (k1_cfdiff_1 A)) = k6_numbers) ) ) ) ).
tt(t3_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) )  =>  ((v2_comseq_2 (k56_valued_1 k5_numbers k1_numbers A)) &  ((k2_seq_2 (k56_valued_1 k5_numbers k1_numbers A)) = k6_numbers) ) )  &  ( ((v2_comseq_2 (k56_valued_1 k5_numbers k1_numbers A)) &  ((k2_seq_2 (k56_valued_1 k5_numbers k1_numbers A)) = k6_numbers) )  =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) ) ) ) ) ).
tt(t3_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ((k4_cfuncdom A) = (k5_cfuncdom A)) ) ) ) ).
tt(t3_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k1_relset_1 A (k19_valued_1 A k2_numbers k2_numbers B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k19_valued_1 A k2_numbers k2_numbers B C))) =>  ((k7_partfun1 k2_numbers (k19_valued_1 A k2_numbers k2_numbers B C) D) = (k9_complex1 (k7_partfun1 k2_numbers B D) (k7_partfun1 k2_numbers C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cgames_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) => (r1_tarski (k2_cgames_1 A) (k2_cgames_1 B))) ) ) ) ) ).
tt(t3_chain_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_zfmisc_1 (k2_tarski A B)) <=>  (A = B) ) ) ) ).
tt(t3_chord,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  (! [B:$i] :  ( ((v1_int_1 B) &  (~ (v1_abian B)) )  =>  ( (~ (r1_xxreal_0 B A))  => (r1_xxreal_0 A (k6_xcmplx_0 B 2))) ) ) ) ) ).
tt(t3_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((v1_circuit2 C A B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_facirc_1 A B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v1_circuit2 (k5_facirc_1 A B C D) A B) => (r1_xxreal_0 (k2_circcmb3 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t3_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  ( ((r1_circcomb A B) &  ((r1_circcomb B C) & (r1_circcomb C A)) )  => (r1_circcomb (k2_circcomb A B) C)) ) ) ) ) ) ) ).
tt(t3_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((v3_rltopsp1 B A) & (v3_rltopsp1 C A))  => (v3_rltopsp1 (k7_rusub_4 A (k1_convex1 A B D) (k1_convex1 A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ((m3_msaterm C A B) <=>  (~ (v11_struct_0 (k1_circtrm1 A B C))) ) ) ) ) ) ) ) ).
tt(t3_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  ((k1_relset_1 (u1_struct_0 A) C) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t3_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_hidden D (k2_msafree2 A)) =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B C) D) (k1_trees_4 (k4_tarski E D))) = (k1_trees_4 (k4_tarski (k1_funct_1 C D) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A (k1_classes1 B)) & (r1_tarski C A))  => (r2_hidden C (k1_classes1 B))) ) ) ) ).
tt(t3_classes2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v2_classes1 A) &  ((r2_hidden B A) & (r2_hidden C A)) )  => (r2_hidden (k4_tarski B C) A)) ) ) ) ).
tt(t3_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) D C))) ) ) ) ) ) ) ) ).
tt(t3_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_partfun1 (u1_struct_0 A))) &  ((v1_funct_2 (k6_partfun1 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 (k6_partfun1 (u1_struct_0 A)) A A) &  ((v1_clopban1 (k6_partfun1 (u1_struct_0 A)) A A) &  ((v2_clopban1 (k6_partfun1 (u1_struct_0 A)) A A) & (m1_subset_1 (k6_partfun1 (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t3_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k3_rlvect_1 A (k5_algstr_0 A B D) (k5_algstr_0 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t3_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_clvect_1 B A) & (v9_clvect_1 C A))  => (v9_clvect_1 (k4_clopban3 A B C) A)) ) ) ) ) ) ) ).
tt(t3_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B D) =>  ((r1_pboole A C B) => (r1_pboole A (k16_pralg_1 A E C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) => (m1_subset_1 (k4_subset_1 (k1_closure2 A B) C D) (k1_zfmisc_1 (k1_closure2 A B)))) ) ) ) ) ) ) ).
tt(t3_closure3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))) =>  ((r1_tarski C (k6_msualg_2 A B)) =>  (! [D:$i] :  ((m3_pboole D (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) D (k4_mssubfam (u1_struct_0 A) (u3_msualg_1 A B) (k5_closure2 (u1_struct_0 A) (u3_msualg_1 A B) C))) => (v3_msualg_2 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_algstr_0 A B) = (k1_clvect_1 A B (k10_complex1 k6_complex1))) ) ) ) ) ).
tt(t3_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 B A) & (v1_clvect_2 C A))  => (v1_clvect_2 (k16_csspace A B C) A)) ) ) ) ) ) ) ).
tt(t3_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k1_bhsp_4 A (k6_clvect_1 A B C)) = (k6_clvect_1 A (k1_bhsp_4 A B) C)) ) ) ) ) ) ) ).
tt(t3_cohsp_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v1_classes1 A))  =>  ((k2_cohsp_1 A) = A) ) ) ).
tt(t3_coh_sp,ax, ( (~ (v1_xboole_0 (k1_tarski k1_xboole_0)))  &  ((v1_classes1 (k1_tarski k1_xboole_0)) & (v1_coh_sp (k1_tarski k1_xboole_0))) ) ).
tt(t3_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_collsp A B C D) &  ((r1_collsp A B C E) & (r1_collsp A B C F)) )  =>  ( (B = C)  | (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_combgras,ax, (! [A:$i] :  (! [B:$i] :  ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((v2_funct_1 C) &  ((r1_tarski A (k9_xtuple_0 C)) & (r1_tarski (k7_relat_1 C A) B)) ) ) ) ) ) ) ).
tt(t3_commacat,ax, (! [A:$i] :  (! [B:$i] :  ( ((u1_struct_0 (k3_cat_1 B A)) = (k1_tarski B))  &  ((u4_struct_0 (k3_cat_1 B A)) = (k1_tarski A)) ) ) ) ).
tt(t3_compact1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_tarski (k2_struct_0 A) (k2_struct_0 B)) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (C = (k2_struct_0 A))  &  ((u1_pre_topc (k1_pre_topc B C)) = (u1_pre_topc A)) ) ) ) )  | (v6_compact1 (k1_yellow_9 B A) A B)) ) ) ) ) ) ).
tt(t3_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k3_complex1 A) = (k3_complex1 B))  &  ((k4_complex1 A) = (k4_complex1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t3_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k17_sin_cos (k6_xcmplx_0 A B)) = (k6_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos B)) (k3_xcmplx_0 (k20_sin_cos A) (k17_sin_cos B))))  &  ((k20_sin_cos (k6_xcmplx_0 A B)) = (k2_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)))) ) ) ) ) ) ).
tt(t3_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k5_algstr_0 k1_complfld A B) = (k4_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_complsp1 A))) => (m2_finseq_2 B k2_numbers (k14_seq_4 A))) ) ) ) ).
tt(t3_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k3_finseq_1 (k12_seq_4 B A)) = (k3_finseq_1 B)) ) ) ) ) ).
tt(t3_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  =>  ((v3_prob_1 B) => (v7_valued_0 (k1_compl_sp A B))) ) ) ) ) ).
tt(t3_compos_0,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_compos_0 A) &  ((v2_compos_0 A) & (v3_compos_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k5_compos_0 A B k6_numbers) = B) ) ) ) ) ).
tt(t3_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) => (r2_hidden k6_numbers (k2_afinsq_1 (k4_compos_1 A)))) ) ).
tt(t3_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k2_compos_2 A (k2_compos_2 A D B) C) = (k8_compos_1 A D (k3_compos_2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k5_square_1 (k17_complex1 A)) = (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) ) ) ).
tt(t3_compts_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = k1_xboole_0)  =>  ((v2_compts_1 B A) <=> (v1_compts_1 (k1_pre_topc A B))) )  &  ((v2_pre_topc A) =>  ( (B = k1_xboole_0)  |  ((v2_compts_1 B A) <=> (v1_compts_1 (k1_pre_topc A B))) ) ) ) ) ) ) ) ).
tt(t3_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((k2_finseq_3 A (k2_funct_7 C A B)) = (k2_finseq_3 A C)) ) ) ) ) ) ).
tt(t3_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B k5_numbers) &  ((k1_funct_1 A B) = k5_complex1) ) ) ) ) ) ) ).
tt(t3_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k2_comseq_2 k5_numbers A))) ) ) ).
tt(t3_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = k6_numbers) ) )  => (v2_series_1 A)) ) ) ).
tt(t3_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_conaffm A) => (v6_conaffm A)) ) ) ).
tt(t3_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) C) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B))) ) ) ) ) ) ) ).
tt(t3_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)))))  =>  ((k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k5_setfam_1 (u4_struct_0 A) B)) = (k1_setfam_1 (a_2_1_conlat_2 A B))) ) ) ) ) ).
tt(t3_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v5_conmetr1 A) => (v1_conmetr1 A)) ) ) ).
tt(t3_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((v4_analmetr B A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C D) & (r10_analmetr A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ((v3_pre_topc B A) &  ((v3_pre_topc C A) & (r1_xboole_0 B C)) ) )  => (r1_connsp_1 A B C)) ) ) ) ) ) ) ).
tt(t3_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_pre_topc B A) & (r2_hidden C B))  => (m1_connsp_2 B A C)) ) ) ) ) ) ) ).
tt(t3_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k1_connsp_3 A (k1_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t3_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_convex1 B A) & (v1_convex1 C A))  => (v1_convex1 (k1_rusub_5 A B C) A)) ) ) ) ) ) ) ).
tt(t3_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (B = (a_3_1_convex2 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t3_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (! [E:$i] :  ( ((v2_convex1 E A) & (m1_rlvect_2 E A))  =>  (? [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r1_tarski (k8_domain_1 (u1_struct_0 A) B C D) F) &  (~  ((v2_convex1 E A) & (m2_rlvect_2 E A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_convex4 D A B) =>  ((r1_tarski B C) => (m2_convex4 D A C)) ) ) ) ) ) ) ) ) ).
tt(t3_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k3_convfun1 A B))) =>  ( ( ((k3_finseq_1 D) = C)  &  ( ((k3_finseq_1 E) = C)  &  ( ((k3_finseq_1 F) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 C)) =>  ((k1_funct_1 F G) = (k4_tarski (k1_funct_1 D G) (k1_funct_1 E G))) ) ) ) ) ) )  =>  ((k4_rlvect_1 (k3_convfun1 A B) F) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 B) (k4_rlvect_1 A D) (k4_rlvect_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k5_qc_lang1 A) (k2_qc_lang1 A)))))  =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (! [F:$i] :  ((m2_finseq_1 F (k2_qc_lang1 A)) =>  (! [G:$i] :  ((m2_finseq_1 G (k2_qc_lang1 A)) =>  ( ( (C = (k2_cqc_lang A E D))  &  ( (G = (k1_cqc_lang A F C))  &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 F))) ) )  =>  ( ( ((k1_funct_1 F B) = E)  =>  ((k1_funct_1 G B) = D) )  &  ( (~  ((k1_funct_1 F B) = E) )  =>  ((k1_funct_1 G B) = (k1_funct_1 F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cqc_sim1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((k7_relat_1 (k1_funct_4 C (k16_funcop_1 A B)) (k6_subset_1 D (k1_tarski A))) = (k7_relat_1 C (k6_subset_1 D (k1_tarski A)))) ) ) ) ) ) ).
tt(t3_cqc_the1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((v1_finset_1 A) &  ((r1_tarski A (k2_zfmisc_1 B C)) &  (! [D:$i] :  (! [E:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D B) &  ((v1_finset_1 E) &  ((r1_tarski E C) & (r1_tarski A (k2_zfmisc_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) D) A) => (v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A)) ) ) ) ) ) ) ) ) ).
tt(t3_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A D B) & (r3_cqc_the1 A (k6_domain_1 (k3_cqc_lang A) B) C))  => (r3_cqc_the1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t3_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ( ((k8_real_1 (k3_complex1 A) (k4_complex1 B)) = (k8_real_1 (k3_complex1 B) (k4_complex1 A)))  & (r1_xxreal_0 k6_numbers (k7_real_1 (k8_real_1 (k3_complex1 A) (k3_complex1 B)) (k8_real_1 (k4_complex1 A) (k4_complex1 B)))))  =>  ((k17_complex1 (k2_xcmplx_0 A B)) = (k7_real_1 (k17_complex1 A) (k17_complex1 B))) ) ) ) ) ) ).
tt(t3_csspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) )  =>  ((v2_comseq_3 A) &  ((k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)) = k6_numbers) ) ) ) ) ).
tt(t3_csspace4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_csspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_csspace4)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ( ((k1_normsp_0 k3_csspace4 A) = k6_numbers)  =>  (A = (k4_struct_0 k3_csspace4)) )  &  ( ( (A = (k4_struct_0 k3_csspace4))  =>  ((k1_normsp_0 k3_csspace4 A) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_normsp_0 k3_csspace4 A)) &  ((r1_xxreal_0 (k1_normsp_0 k3_csspace4 (k1_algstr_0 k3_csspace4 A B)) (k7_real_1 (k1_normsp_0 k3_csspace4 A) (k1_normsp_0 k3_csspace4 B))) &  ((k1_normsp_0 k3_csspace4 (k1_clvect_1 k3_csspace4 A C)) = (k8_real_1 (k17_complex1 C) (k1_normsp_0 k3_csspace4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  ((k1_clvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) B A) = (k25_valued_1 k5_numbers k2_numbers (k2_csspace B) A)) ) ) ) ) ).
tt(t3_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_decomp_1 B A) <=>  (B = (k1_decomp_1 A B)) ) ) ) ) ) ).
tt(t3_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C A (k4_finseq_2 (k4_nat_1 2 B) A)) =>  ((k9_binarith B B A (k4_descip_1 A B C) (k5_descip_1 A B C)) = C) ) ) ) ) ) ) ).
tt(t3_dickson,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  & (v2_funct_1 B)) ) ) ) ).
tt(t3_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers C (k7_real_1 B A)) (k3_funct_2 k1_numbers k1_numbers C B))) ) ) ) ) ) ) ).
tt(t3_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k9_diff_1 C (k9_real_1 A B) A) = (k6_real_1 (k1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C B) 1) A) B)) ) ) ) ) ) ) ).
tt(t3_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k5_diff_1 C A) B) = (k9_real_1 (k1_seq_1 (k4_diff_1 C (k10_real_1 A 2)) B) (k1_seq_1 (k4_diff_1 C (k1_real_1 (k10_real_1 A 2))) B))) ) ) ) ) ) ) ).
tt(t3_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k6_power k8_power A) = (k1_seq_1 k3_taylor_1 A)) ) ) ) ).
tt(t3_dilworth,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D B) =>  ((r1_xboole_0 A B) => (m1_eqrel_1 (k2_xboole_0 C D) (k2_xboole_0 A B))) ) ) ) ) ) ) ).
tt(t3_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A D E B C) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v2_struct_0 (k6_analort A B C)))  &  ((v1_dirort (k6_analort A B C)) & (l1_analoaf (k6_analort A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_dist_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((k5_card_1 (k9_xtuple_0 B)) = (k3_finseq_1 B)) ) ) ) ).
tt(t3_domain_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ((r2_hidden A (k3_zfmisc_1 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E B) &  (? [F:$i] :  ((m1_subset_1 F C) &  (? [G:$i] :  ((m1_subset_1 G D) &  (A = (k3_xtuple_0 E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_dtconstr,ax, ((k14_trees_3 k1_xboole_0) = k1_xboole_0) ).
tt(t3_dynkin,ax, (! [A:$i] :  (! [B:$i] :  ((k3_card_3 (k13_funct_7 A B k1_xboole_0)) = (k2_xboole_0 A B)) ) ) ).
tt(t3_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((m1_ec_pf_1 A B) =>  (! [C:$i] :  ((r1_struct_0 A C) => (r1_struct_0 B C)) ) ) ) ) ) ) ).
tt(t3_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_group_1 A D (k11_algstr_0 A B)) = (k8_group_1 A E (k11_algstr_0 A C)))  =>  ( (B = (k4_struct_0 A))  |  ( (C = (k4_struct_0 A))  |  ((k8_group_1 A D C) = (k8_group_1 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) =>  (! [C:$i] :  ((m2_funct_2 C (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) => (r2_hidden (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B) (k1_endalg A))) ) ) ) ) ) ).
tt(t3_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  => (r1_tarski (k1_ens_1 B) (k1_ens_1 A))) ) ) ) ).
tt(t3_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((r1_xxreal_0 (k6_power k8_power A) (k9_real_1 A 1)) &  ( ( (A = 1)  =>  ((k6_power k8_power A) = (k9_real_1 A 1)) )  &  ( ( ((k6_power k8_power A) = (k9_real_1 A 1))  =>  (A = 1) )  &  ( (~  ( (~  (A = 1) )  & (r1_xxreal_0 (k9_real_1 A 1) (k6_power k8_power A))) )  &  (~  ( (~ (r1_xxreal_0 (k9_real_1 A 1) (k6_power k8_power A)))  &  (A = 1) ) ) ) ) ) ) ) ) ) ).
tt(t3_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k2_xboole_0 (k2_tarski A B) (k1_tarski C))) ) ) ) ).
tt(t3_eqrel_1,ax, (! [A:$i] :  ((v3_relat_2 (k6_partfun1 A)) &  ((v8_relat_2 (k6_partfun1 A)) &  ((v1_partfun1 (k6_partfun1 A) A) & (m1_subset_1 (k6_partfun1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(t3_equation,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden E (k1_funct_2 A (k1_funct_2 B C))) & (r2_hidden D B))  =>  ( ((k9_xtuple_0 (k1_funct_1 (k10_funct_6 E) D)) = A)  & (r1_tarski (k10_xtuple_0 (k1_funct_1 (k10_funct_6 E) D)) C)) ) ) ) ) ) ) ) ) ) ).
tt(t3_e_siec,ax, (! [A:$i] :  ((v2_e_siec (g1_e_siec A (k4_relat_1 A) (k4_relat_1 A))) &  ((v3_e_siec (g1_e_siec A (k4_relat_1 A) (k4_relat_1 A))) & (l1_e_siec (g1_e_siec A (k4_relat_1 A) (k4_relat_1 A)))) ) ) ).
tt(t3_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v3_valued_0 C)) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ( (D = B)  &  (E = C) )  =>  ((k23_rvsum_1 B C) = (k11_binop_2 (k18_binop_2 1 4) (k10_binop_2 (k5_square_1 (k12_euclid (k7_euclid A D E))) (k5_square_1 (k12_euclid (k8_euclid A D E)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_euclid_3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k1_euclid_3 A) = (k1_euclid_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t3_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  ( ((k9_euclid A B 1) = B)  &  ((k9_euclid A B k6_numbers) = (k5_euclid A)) ) ) ) ) ) ).
tt(t3_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (A = (k4_euclid_5 (k1_euclid_5 A) (k2_euclid_5 A) (k3_euclid_5 A))) ) ) ).
tt(t3_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k21_sin_cos (k4_euclid_3 A B C)) = (k21_sin_cos (k4_euclid_3 C B A))) ) ) ) ) ) ) ).
tt(t3_euclid_7,ax, (! [A:$i] :  ((k3_relat_1 (k12_finseq_1 k5_numbers 1) (k9_finseq_1 A)) = (k9_finseq_1 A)) ) ).
tt(t3_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ( (~ (r3_euclidlp 3 A B))  =>  ((k5_euclid_8 A B) = (k16_euclid 3)) ) ) ) ) ) ).
tt(t3_euclid_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k54_valued_1 (k45_valued_1 A B)) = (k54_valued_1 (k45_valued_1 B A))) ) ) ) ) ).
tt(t3_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  ( ((k6_euclid B (k9_euclid B C A)) = (k9_euclid B C (k1_real_1 A)))  &  ((k6_euclid B (k9_euclid B C A)) = (k9_euclid B (k6_euclid B C) A)) ) ) ) ) ) ) ) ).
tt(t3_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r6_analmetr A B C D) =>  ( (B = C)  |  ( ( (~ (r6_analmetr A B C E))  &  (~ (r6_analmetr A C B E)) )  | (r9_analmetr A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( ((v1_int_2 A) & (r2_hidden B (a_1_0_euler_1 A)))  =>  ((v1_int_2 A) &  ((r2_hidden B A) &  (~ (r2_hidden B (k1_tarski k6_numbers))) ) ) )  &  ( ((v1_int_2 A) & (r2_hidden B A))  =>  ((r2_hidden B (k1_tarski k6_numbers)) |  ((v1_int_2 A) & (r2_hidden B (a_1_0_euler_1 A))) ) ) ) ) ) ) ) ).
tt(t3_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_int_2 A C) & (r1_int_2 B C))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ( (C = k1_xboole_0)  | (r1_int_2 C (k4_nat_d (k3_xcmplx_0 A B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t3_exchsort,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden A B))  =>  ((k6_subset_1 (k2_xboole_0 B (k1_tarski A)) B) = (k1_tarski A)) ) ) ) ).
tt(t3_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m3_pboole E A B) =>  (! [F:$i] :  ((m3_pboole F A B) =>  ((r2_pboole A E F) => (r6_pboole A (k9_pboole A E (k1_msafree A B C F D)) (k9_pboole A E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_extpro_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  (~ (v1_setfam_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) & (v1_funct_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k5_extpro_1 A B C D (k1_nat_1 E 1)) = (k4_extpro_1 A B (k5_extpro_1 A B C D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k3_extreal1 A) = A) ) ) ) ).
tt(t3_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) => (r1_xxreal_0 k6_numbers (k3_extreal1 A))) ) ).
tt(t3_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  ( ((v1_relat_1 (k3_msafree2 A)) & (v1_relat_1 (k3_msafree2 B)))  => (v1_relat_1 (k3_msafree2 (k2_circcomb A B)))) ) ) ) ) ).
tt(t3_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  ((l1_msualg_1 B) => (r1_circcomb (k1_facirc_2 A) B)) ) ) ).
tt(t3_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fcont_1 B A) <=>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((r2_hidden E (k1_relset_1 k1_numbers B)) &  ( (~ (r1_xxreal_0 D (k18_complex1 (k6_xcmplx_0 E A))))  & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 B E) (k1_seq_1 B A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) &  ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers C A)) & (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers D B))) ) )  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t3_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k7_real_1 B C))  =>  ((r1_xxreal_0 D (k18_complex1 C)) |  ( (~ (r1_xxreal_0 D k6_numbers))  & (r2_hidden A (k2_rcomp_1 (k9_real_1 B D) (k7_real_1 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos B)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t3_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k1_sin_cos9) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t3_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v3_fdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k26_valued_1 k1_numbers k1_numbers B A)) &  ((v3_fdiff_1 (k26_valued_1 k1_numbers k1_numbers B A)) & (m1_subset_1 (k26_valued_1 k1_numbers k1_numbers B A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ).
tt(t3_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = (k2_nat_1 (k4_nat_1 2 B) 1)) ) )  =>  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) &  ((v5_valued_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) ) ) ) ) ).
tt(t3_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 C E))) ) ) ) )  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers D A))))) ) ) ) )  & (r1_tarski (k1_tarski B) (k1_relset_1 k1_numbers A)))  =>  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C E)) (k1_relset_1 k1_numbers A)) &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 C F))) ) )  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers A)) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 D F))) ) ) ) ) ) )  =>  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k9_real_1 A D))  &  (~ (r1_xxreal_0 (k1_seq_1 C D) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) B) D) = (k10_real_1 1 (k9_real_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers D E))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ( ((k1_seq_1 D F) = (k9_real_1 F A))  &  ( ((k1_seq_1 E F) = (k9_real_1 F B))  &  (~  ((k1_seq_1 E F) = k6_numbers) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers D E) C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers D E) C) F) = (k10_real_1 (k9_real_1 A B) (k5_square_1 (k9_real_1 F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 C E) = (k5_square_1 A)) ) ) )  &  (D = (k1_taylor_1 2)) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) B) E) = (k1_real_1 (k8_real_1 2 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k10_prepower A (k1_real_1 (k10_real_1 1 2))) = (k10_real_1 1 (k7_square_1 A))) ) ) ) ).
tt(t3_fdiff_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski B (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers C D))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k5_prepower (k1_seq_1 (k3_rfunct_1 k1_numbers k1_numbers C D) E) A) = (k10_real_1 (k5_prepower (k1_seq_1 C E) A) (k5_prepower (k1_seq_1 D E) A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fdiff_9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_prepower (k10_real_1 1 A) B) = (k10_real_1 1 (k5_prepower A B))) ) ) ) ) ).
tt(t3_ff_siec,ax, (! [A:$i] :  ( ((u1_struct_0 (k3_ff_siec A)) = k1_xboole_0)  &  ( ((u4_struct_0 (k3_ff_siec A)) = A)  &  ((k1_net_1 (k3_ff_siec A)) = k1_xboole_0) ) ) ) ).
tt(t3_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k1_fib_fusc A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v5_memstr_0 F 2 k1_ami_3 3) & (m1_scm_1 F (k16_afinsq_1 1 B D E)))  =>  ( ( (D = (k1_pre_ff C))  &  (E = (k1_pre_ff (k2_nat_1 C 1))) )  =>  ((r1_xxreal_0 B k6_numbers) |  ((r1_extpro_1 2 k1_ami_3 A F) &  ( ((k8_extpro_1 2 k1_ami_3 A F) = (k6_xcmplx_0 (k4_nat_1 6 B) 4))  &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ( (G = (k6_xcmplx_0 (k2_nat_1 C B) 1))  &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A F) (k10_ami_3 2)) = (k1_pre_ff G))  &  ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A F) (k10_ami_3 3)) = (k1_pre_ff (k2_nat_1 G 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fib_num2,ax, (! [A:$i] :  ( ((v1_int_1 A) & (v1_abian A))  =>  ((k3_power (k4_xcmplx_0 1) A) = 1) ) ) ).
tt(t3_fib_num3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_power A 2) = (k3_power (k4_xcmplx_0 A) 2)) ) ) ).
tt(t3_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v1_abian A) =>  ( (B = k6_numbers)  |  ((k3_power (k4_xcmplx_0 B) A) = (k3_power B A)) ) ) ) ) ) ) ).
tt(t3_fib_num,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 (k13_complex1 1 B) k6_numbers))  & (r1_xxreal_0 (k13_complex1 1 B) A)) ) ) ) ) ) ) ) ) ).
tt(t3_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k3_finseq_1 B) = k6_numbers)  =>  (C = (k1_finseq_8 A B C)) ) ) ) ) ) ) ) ).
tt(t3_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A B (k3_lattices A D C))) ) ) ) ) ) ) ) ) ).
tt(t3_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m2_filter_1 E A B) =>  ((k1_binop_1 (k3_filter_1 A B E) (k6_eqrel_1 A A B C) (k6_eqrel_1 A A B D)) = (k6_eqrel_1 A A B (k5_binop_1 A E C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ( (E = (k1_realset1 C B))  &  (F = (k1_realset1 D B)) )  =>  ( ((r4_binop_1 A C D) => (r4_binop_1 B E F))  &  ((r5_binop_1 A C D) => (r5_binop_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((m2_subset_1 (k3_rcomp_1 A k1_xxreal_0) (k1_zfmisc_1 k1_numbers) k12_prob_1) & (m2_subset_1 (k2_rcomp_1 k2_xxreal_0 A) (k1_zfmisc_1 k1_numbers) k12_prob_1)) ) ) ).
tt(t3_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (A = k6_numbers)  | (r2_hidden A (k2_finseq_1 A))) ) ) ).
tt(t3_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((k4_xxreal_0 k6_numbers (k6_xcmplx_0 A B)) = k6_numbers) ) ) ) ) ) ).
tt(t3_finseq_3,ax, ((k2_finseq_1 5) = (k3_enumset1 1 2 3 4 5)) ).
tt(t3_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r1_finseq_4 A B) <=>  ((r2_hidden B (k9_xtuple_0 A)) &  (! [C:$i] :  (~  ((r2_hidden C (k9_xtuple_0 A)) &  ( (~  (B = C) )  &  ((k1_funct_1 A B) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t3_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((k8_relat_1 A (k1_tarski C)) = (k1_tarski B))  =>  ((r2_hidden B (k9_xtuple_0 A)) &  ((r2_hidden C (k10_xtuple_0 A)) &  ((k1_funct_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t3_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ((k5_relat_1 (k10_finseq_1 A B) (k2_finseq_1 1)) = (k9_finseq_1 A)) ) ) ).
tt(t3_finseq_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k3_finseq_1 B)))  =>  ((k1_funct_1 B A) = (k1_funct_1 (k7_finseq_1 C B) (k2_nat_1 (k3_finseq_1 C) A))) ) ) ) ) ) ) ) ).
tt(t3_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_finseq_6 A (k6_finseq_1 A) B C) = (k6_finseq_1 A)) ) ) ) ) ) ) ).
tt(t3_finseqop,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k3_funcop_1 A k1_xboole_0 B) = k1_xboole_0)  &  ((k3_funcop_1 A B k1_xboole_0) = k1_xboole_0) ) ) ) ) ) ).
tt(t3_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k3_xboole_0 A B))) ) ) ).
tt(t3_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 C A) & (v1_binop_1 C A))  =>  ( ( (~ (v1_setwiseo C A))  &  (~ (r1_xxreal_0 1 (k3_finseq_1 B))) )  |  ((k1_finsop_1 A B C) = (k7_setwiseo k5_numbers A C (k3_finsop_1 B) (k2_finsop_1 A (k8_funcop_1 A k5_numbers (k4_binop_1 A C)) B))) ) ) ) ) ) ) ) ) ).
tt(t3_finsub_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v4_finsub_1 C))  =>  ( ((m1_subset_1 A C) & (m1_subset_1 B C))  => (m1_subset_1 (k5_xboole_0 A B) C)) ) ) ) ) ).
tt(t3_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_fin_topo A B) = (k7_subset_1 (u1_struct_0 A) (k9_fin_topo A B) (k8_fin_topo A B))) ) ) ) ) ).
tt(t3_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) => (r1_tarski (k1_fintopo3 A B) B)) ) ) ) ) ).
tt(t3_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_tarski (k9_fintopo3 A B D) (k9_fintopo3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_fintopo5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ((v1_fintopo5 C A B) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (~  ( (D = (k2_funct_1 C))  & (v1_fintopo5 D B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = (k4_subset_1 (u1_struct_0 A) C D))  & (r1_xboole_0 C D))  =>  ( (C = k1_xboole_0)  |  ( (D = k1_xboole_0)  |  ( (~ (r1_xboole_0 (k9_fin_topo A C) D))  &  (~ (r1_xboole_0 C (k9_fin_topo A D))) ) ) ) ) ) ) ) )  => (v4_fin_topo B A)) ) ) ) ) ).
tt(t3_fin_topo,ax,(v3_orders_2 k4_fin_topo)).
tt(t3_flang_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k2_xcmplx_0 A B) = 1)  <=>  ( ( (A = 1)  &  (B = k6_numbers) )  |  ( (A = k6_numbers)  &  (B = 1) ) ) ) ) ) ) ) ).
tt(t3_flang_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k2_xcmplx_0 A C) = B)  &  (~ (r1_xxreal_0 C k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k7_flang_1 A B D) (k1_flang_3 A B C))) ) ) ) ) ) ) ) ).
tt(t3_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k4_finseq_2 C (k3_xboole_0 A B)) = (k3_xboole_0 (k4_finseq_2 C A) (k4_finseq_2 C B))) ) ) ) ) ).
tt(t3_fomodel1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v14_fomodel1 C (k2_xcmplx_0 A 1) B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (? [D:$i] :  ((m2_subset_1 D (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k2_fomodel0 (k3_finseq_2 (k15_fomodel1 B)) (k3_funct_2 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 B))) (k28_fomodel1 B) A))) &  ((v3_card_1 D (k1_int_2 (k19_fomodel1 B (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) C)))) &  (C = (k7_finseq_1 (k4_matrix_2 (k15_fomodel1 B) (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) C)) (k3_funct_2 (k3_finseq_2 (k3_finseq_2 (k15_fomodel1 B))) (k3_finseq_2 (k15_fomodel1 B)) (k21_fomodel1 B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v13_fomodel1 E B) & (m2_subset_1 E (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_fomodel2 F B C)) )  =>  ( ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 B) C (k9_funct_2 (k35_fomodel1 B) C) (k8_fomodel2 B C D F) (k1_nat_1 A 1)) E) = (k1_funct_1 (k4_fomodel2 B C F (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) E)) (k3_relat_1 (k33_fomodel1 B E) (k8_nat_1 (k9_funct_2 (k35_fomodel1 B) C) (k8_fomodel2 B C D F) A))))  &  ((v14_fomodel1 E k6_numbers B) =>  ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 B) C (k9_funct_2 (k35_fomodel1 B) C) (k8_fomodel2 B C D F) (k1_nat_1 A 1)) E) = (k1_funct_1 (k4_fomodel2 B C F (k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) E)) k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_fomodel2 D B A) & (v3_fomodel3 D B A C)) ) )  => (r2_funct_2 (k35_fomodel1 B) (k8_eqrel_1 A C) (k10_fomodel2 B (k8_eqrel_1 A C) (k23_fomodel3 B A C D)) (k1_partfun1 (k35_fomodel1 B) A A (k8_eqrel_1 A C) (k10_fomodel2 B A D) (k17_fomodel3 A C)))) ) ) ) ) ) ) ) ).
tt(t3_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ((m2_funct_2 D (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)) (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C)))) =>  ((r2_hidden A (k1_funct_1 D B)) => (v4_fomodel4 A 1 C (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 C)) (k9_setfam_1 (k1_fomodel4 C))) D) B)) ) ) ) ) ) ) ).
tt(t3_fraenkel,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C B) & (r1_tarski D A))  =>  ( ((k1_funct_2 C D) = k1_xboole_0)  |  (! [E:$i] :  ((m1_subset_1 E (k1_funct_2 C D)) =>  ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (! [D:$i] :  ((m2_valued_0 D (u1_struct_0 A) B) =>  (~ (r1_tarski (k2_relset_1 (u1_struct_0 A) D) C)) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r2_hidden (k8_nat_1 (u1_struct_0 A) B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_frechet,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  (C = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t3_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((v1_freealg B) =>  ((k1_lang1 (k3_freealg A B)) = B) ) ) ) ) ).
tt(t3_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D B)) )  =>  ((k1_funct_1 (k6_circuit2 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fscirc_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  =>  ( ((k1_fscirc_2 1 A B) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k8_fscirc_1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ( ((k2_fscirc_2 1 A B) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k8_fscirc_1 (k1_funct_1 A 1) (k1_funct_1 B 1) C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k9_fscirc_1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ((k3_fscirc_2 1 A B) = (k6_fscirc_1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)) ) ) ) ) ) ) ) ) ).
tt(t3_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r2_fsm_1 A B (k6_finseq_1 A) (k12_finseq_1 (u1_struct_0 B) C))) ) ) ) ) ) ).
tt(t3_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_fsm_1 E A))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  ((k2_fsm_1 A E F (k3_finseq_4 A B C D)) = (k9_finseq_4 (u1_struct_0 E) F (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A F B)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A F B)) C)) (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A (k3_funct_2 (k2_zfmisc_1 (u1_struct_0 E) A) (u1_struct_0 E) (u1_fsm_1 A E) (k1_domain_1 (u1_struct_0 E) A F B)) C)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fsm_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden A (k4_finseq_1 B)) &  ((k2_xcmplx_0 (k3_finseq_1 B) 1) = (k3_finseq_1 C)) )  => (r2_hidden (k2_xcmplx_0 A 1) (k4_finseq_1 C))) ) ) ) ) ) ) ).
tt(t3_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  (~  ( (~  (E = (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp)) )  &  ( (~ (r2_hidden E (k3_msafree2 (k13_gfacirc1 A B C))))  &  (~  ((k2_msafree2 (k1_ftacell1 A B C D E)) = (k3_enumset1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((k1_funcop_1 (k5_relat_1 A B)) = (k5_relat_1 (k1_funcop_1 A) B)) ) ) ) ).
tt(t3_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  ((k8_funcsdom A) = (k9_funcsdom A)) ) ) ) ).
tt(t3_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) => (r2_hidden (k1_funct_1 B A) (k10_xtuple_0 B))) ) ) ) ).
tt(t3_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((r2_hidden D A) => (r2_hidden (k1_funct_1 C D) B)) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(t3_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k9_xtuple_0 B)) & (r1_tarski (k7_relat_1 B A) (k9_xtuple_0 C)))  => (r1_tarski A (k9_xtuple_0 (k3_relat_1 B C)))) ) ) ) ) ) ).
tt(t3_funct_4,ax, (! [A:$i] :  (! [B:$i] :  ((r1_relset_1 A A (k6_partfun1 A) (k6_partfun1 B)) <=> (r1_tarski A B)) ) ) ).
tt(t3_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_funct_4 (k7_funcop_1 (k2_zfmisc_1 A B) C)) = (k7_funcop_1 (k2_zfmisc_1 B A) C)) ) ) ) ).
tt(t3_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r2_hidden (k3_funct_2 A B C D) (k7_relset_1 A B C E)) => (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_funct_8 A k1_numbers k1_numbers B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) &  ((k1_funct_1 B C) = k6_numbers) ) ) ) ) )  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k7_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 B (k1_real_1 C))) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ).
tt(t3_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 B A) & (v1_funct_9 C A))  => (v1_funct_9 (k45_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t3_functor0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k7_relat_1 B (k6_partfun1 A)) = (k7_relat_1 (k2_funct_4 B) (k6_partfun1 A))) ) ) ) ).
tt(t3_functor1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (~  ((v3_funct_2 D A B) &  ((v3_funct_2 E B C) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (~  ( (F = (k1_partfun1 A B B C D E))  & (v3_funct_2 F A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  ((r1_functor2 A B C D) =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  (! [F:$i] :  ((m1_functor2 F A B C D) =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k2_functor2 A B C D E G) = (k2_functor2 A B C D F G)) ) )  => (r8_pboole (u1_struct_0 A) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v12_altcat_1 C) & (l2_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) &  ((v11_functor0 D A B) & (l2_functor0 D A B)) )  =>  (! [E:$i] :  ((l2_functor0 E B C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((k4_functor0 A C (k13_functor0 A B C D E) F G) = (k3_relat_1 (k7_functor0 A B D F G) (k4_functor0 B C E (k3_functor0 A B D G) (k3_functor0 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 B B)) ) ) ) ).
tt(t3_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k1_fuzzy_2 A B C)) (k2_fuzzy_1 A (k3_fuzzy_1 A B) C))) ) ) ) ) ) ).
tt(t3_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ((r1_xxreal_0 k6_numbers (k1_seq_1 C D)) & (r1_xxreal_0 (k1_seq_1 C D) 1)) ) ) ) ) ) ) ) ).
tt(t3_fvaluat1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 (k4_xxreal_3 A C) (k4_xxreal_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t3_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  => (v1_binop_1 (u2_algstr_0 A) (u1_struct_0 A))) ) ).
tt(t3_gate_1,ax, (~ (v1_xboole_0 (k1_gate_1 k1_xboole_0))) ).
tt(t3_gate_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ((v1_xboole_0 (k2_gate_1 A B)) & (v1_xboole_0 (k3_gate_1 (k1_gate_1 A) (k1_gate_1 B)))) )  &  ( ( (~ (v1_xboole_0 (k3_gate_1 (k1_gate_1 A) (k1_gate_1 B))))  => (v1_xboole_0 (k2_gate_1 A B)))  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  ( (~ (v1_xboole_0 (k3_gate_1 C B)))  & (v1_xboole_0 (k3_gate_1 (k2_gate_1 A C) B))) ) )  &  ( ( (~ (v1_xboole_0 (k3_gate_1 (k2_gate_1 A C) B)))  =>  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  (~ (v1_xboole_0 (k3_gate_1 C B))) ) )  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  ( (~ (v1_xboole_0 (k3_gate_1 C B)))  &  ( (~ (v1_xboole_0 (k3_gate_1 D B)))  & (v1_xboole_0 (k3_gate_1 (k8_gate_1 A C D) B))) ) ) )  &  ( ( (~ (v1_xboole_0 (k3_gate_1 (k8_gate_1 A C D) B)))  =>  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  ( (~ (v1_xboole_0 (k3_gate_1 C B)))  &  (~ (v1_xboole_0 (k3_gate_1 D B))) ) ) )  &  (~  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 A)) )  & (v1_xboole_0 (k3_gate_1 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gate_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k8_gate_1 S R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R Q)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T))))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k8_gate_1 V U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U T)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k1_gate_1 S))) )  &  ( (~  ( (~ (v1_xboole_0 (k1_gate_1 S)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 Q)) )  &  ( (~  ( (~ (v1_xboole_0 Q))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 R)) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 V)) )  &  (~  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 C)) )  &  (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 N)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (! [W:$i] :  (! [X:$i] :  (! [Y:$i] :  (~  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k2_gate_1 A D))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A D)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 Q))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 Q)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F)))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F)))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F))))  & (v1_xboole_0 R)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 S))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0)))  & (v1_xboole_0 S)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k10_gate_1 O Q k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 O Q k1_xboole_0)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 W))  & (v1_xboole_0 (k11_gate_1 O Q k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 O Q k1_xboole_0)))  & (v1_xboole_0 W)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 (k10_gate_1 P R W))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 P R W)))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 X))  & (v1_xboole_0 (k11_gate_1 P R W))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 P R W)))  & (v1_xboole_0 X)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C F) S X))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C F) S X)))  & (v1_xboole_0 V)) )  &  ( (~  ( (~ (v1_xboole_0 Y))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C F) S X))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C F) S X)))  & (v1_xboole_0 Y)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 V)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 Y)) )  &  ( (~  ( (~ (v1_xboole_0 Y))  & (v1_xboole_0 L)) )  &  (~  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k5_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k5_gate_5 A B C D E)))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k6_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k6_gate_5 A B C D E)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k10_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_5 A B C D E F)))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k11_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_5 A B C D E F)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k12_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k12_gate_5 A B C D E F)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k13_gate_5 A B C D E F))) )  &  (~  ( (~ (v1_xboole_0 (k13_gate_5 A B C D E F)))  & (v1_xboole_0 L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v5_group_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_gcd_1 A C B) & (r1_gcd_1 A E D))  => (r1_gcd_1 A (k8_group_1 A C E) (k8_group_1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_genealg1 C B) =>  (! [D:$i] :  ((m1_genealg1 D B) => (m1_genealg1 (k1_genealg1 B C D A) B)) ) ) ) ) ) ) ) ).
tt(t3_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k2_diraf (k2_analoaf A)))) =>  ( ( (H = D)  &  ( (I = E)  &  ( (J = F)  &  (K = G) ) ) )  =>  ((r2_analoaf (k2_diraf (k2_analoaf A)) H I J K) <=> (r1_geomtrap A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gfacirc1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 A B)) = (k10_margrel1 A (k9_margrel1 B)))  &  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 A B)) = (k1_funct_1 k3_twoscomp (k10_finseq_1 B A)))  &  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 A B)) = (k1_funct_1 k12_twoscomp (k10_finseq_1 A B)))  &  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 k6_numbers k6_numbers)) = k6_numbers)  &  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 1 k6_numbers)) = 1)  &  ((k1_funct_1 k3_gfacirc1 (k10_finseq_1 1 1)) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gfacirc2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  =>  ( ((k1_gfacirc2 1 A B) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k13_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ( ((k2_gfacirc2 1 A B) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k13_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k14_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)))  &  ((k3_gfacirc2 1 A B) = (k9_gfacirc1 (k1_funct_1 A 1) (k1_funct_1 B 1) C)) ) ) ) ) ) ) ) ) ).
tt(t3_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ( ((k6_glib_000 A) = (k1_funct_1 A k1_glib_000))  &  ( ((k7_glib_000 A) = (k1_funct_1 A k2_glib_000))  &  ( ((k8_glib_000 A) = (k1_funct_1 A k3_glib_000))  &  ((k9_glib_000 A) = (k1_funct_1 A k4_glib_000)) ) ) ) ) ) ).
tt(t3_glib_001,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (r1_xxreal_0 (k3_finseq_1 (k15_finseq_1 C)) (k3_finseq_1 B))) ) ) ) ) ).
tt(t3_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ((v1_glib_002 C) =>  ( (! [D:$i] :  (~  ((r2_hidden D (k28_glib_000 A B)) &  (~ (r1_glib_000 A B B D)) ) ) )  | (v1_glib_002 A)) ) ) ) ) ) ) ) ).
tt(t3_glib_003,ax, ( (k2_glib_003 = 5)  &  ( (k3_glib_003 = 6)  &  (k4_glib_003 = 7) ) ) ).
tt(t3_glib_004,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_partfun1 D B) &  ((v3_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (k6_subset_1 A B)) &  ((v1_funct_1 E) &  ((v1_partfun1 E (k6_subset_1 A B)) &  ((v3_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( (C = (k1_funct_4 D E))  =>  ((k3_uproots A C) = (k2_xcmplx_0 (k3_uproots B D) (k3_uproots (k6_subset_1 A B) E))) ) ) ) ) ) ) ) ) ) ).
tt(t3_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  (! [E:$i] :  ((r5_glib_005 A B C) =>  ((r2_hidden E (k13_glib_001 A C)) |  ( ( (~  ((r2_glib_000 A (k4_glib_001 A C) E D) &  (~ (r1_xxreal_0 (k1_funct_1 (k5_glib_003 A) D) (k1_funct_1 B D))) ) )  &  (~  ((r2_glib_000 A E (k4_glib_001 A C) D) &  (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers)) ) ) )  | (r5_glib_005 A B (k10_glib_001 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden B (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))) &  ((r2_hidden B (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A D))) &  ((r2_hidden C (k4_finseq_1 A)) & (r2_hidden D (k4_finseq_1 A))) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t3_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k3_finseq_1 A) = (k2_nat_1 B 1))  =>  ( (B = k6_numbers)  |  ((k3_topreal1 2 A) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A)) (k2_topreal1 2 A B))) ) ) ) ) ) ) ).
tt(t3_goboard4,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k10_xtuple_0 (k8_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1))) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k1_matrix_1 A)))) & (r1_xboole_0 (k3_topreal1 2 B) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((v5_goboard1 D) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k1_matrix_1 D)) &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 C B))  &  ((r1_xxreal_0 C (k3_finseq_1 D)) & (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C A)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D B A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_goboard6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid A))) =>  ( (C = (k9_metric_1 (k14_euclid A) D B))  => (v3_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t3_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((k3_rlvect_1 (k15_euclid A) B C) = (k3_rlvect_1 (k15_euclid A) D C))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t3_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D)) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D)) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_goboard9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski B C) &  ((v2_connsp_1 B A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r3_connsp_1 A C D) & (r1_tarski B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_gobrd10 A C B D) => (r2_gobrd10 (k2_nat_1 A 1) (k2_nat_1 C 1) (k2_nat_1 B 1) (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ).
tt(t3_gobrd11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_connsp_1 B A) & (v3_connsp_1 C A))  => (m1_connsp_3 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t3_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 (k2_goboard2 A))) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))))  =>  ((v2_connsp_1 (k2_pre_topc (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k4_connsp_3 (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) &  ((k4_connsp_3 (k15_euclid 2) (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C)) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) = (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 A) B C))) ) ) ) ) ) ) ) ) ).
tt(t3_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) |  ((k3_goboard5 C A B) = (k4_card_3 (k5_funct_4 (k1_zfmisc_1 k1_numbers) 1 2 (k1_rcomp_1 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A 1)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) 1))) (k1_rcomp_1 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 B)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C 1 (k2_nat_1 B 1))))))) ) ) ) ) ) ) ) ) ) ).
tt(t3_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_goedelcp B A) =>  ((r1_henmodel A B (k12_cqc_lang A D C)) <=>  (? [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) & (r1_henmodel A B (k4_substut2 A C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  ((r2_hidden (k1_funct_1 (u1_graph_1 A) B) (u1_struct_0 A)) & (r2_hidden (k1_funct_1 (u2_graph_1 A) B) (u1_struct_0 A))) ) ) ) ) ).
tt(t3_graph_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_tarski A (k2_finseq_1 C)) & (r1_tarski B (k4_finseq_1 (k14_finseq_1 A))))  =>  ((k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k14_finseq_1 B) (k14_finseq_1 A)) = (k14_finseq_1 (k10_xtuple_0 (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 A) B)))) ) ) ) ) ) ).
tt(t3_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_graph_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (~  ((r1_graph_2 A C B) & (v1_xboole_0 C)) ) ) ) ) ) ) ) ).
tt(t3_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  ( ((k1_graph_4 A k1_xboole_0) = k1_xboole_0)  &  ((k2_graph_4 A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t3_graph_5,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (C = (a_2_1_graph_5 A B))  => (v1_finset_1 C)) ) ) ) ) ) ).
tt(t3_graphsp,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k7_partfun1 A B C) = (k1_funct_1 B C)) ) ) ) ) ) ) ).
tt(t3_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((r2_hidden (k1_tarski k1_xboole_0) A) &  ((r2_hidden (k4_tarski (k1_tarski k1_xboole_0) (k1_tarski k1_xboole_0)) A) &  ((r2_hidden (k2_zfmisc_1 (k1_tarski k1_xboole_0) (k1_tarski k1_xboole_0)) A) &  ((r2_hidden k9_funct_5 A) & (r2_hidden k8_funct_5 A)) ) ) ) ) ) ).
tt(t3_gr_cy_1,ax, ((k1_gr_cy_1 (k6_finseq_1 k4_numbers)) = k6_numbers) ).
tt(t3_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( (C = D)  =>  ((k5_group_4 A (k6_domain_1 (u1_struct_0 A) C)) = (k5_group_4 B (k6_domain_1 (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  ((k4_nat_d A 2) = 1) ) ) ).
tt(t3_grfunc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  & (r1_tarski A B))  =>  (A = B) ) ) ) ) ) ).
tt(t3_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k2_group_5 A B C)) = (k2_group_3 A (k2_group_5 A (k2_group_1 A B) C) B)) ) ) ) ) ) ) ).
tt(t3_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( ((r1_tarski F G) & (r5_polyred A B C D E F))  => (r5_polyred A B C D E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A B (k2_groeb_2 A B C)) & (r3_pre_poly A C (k2_groeb_2 A B C))) ) ) ) ) ) ).
tt(t3_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ( ((r1_termord A B C D) & (r2_termord A B D E))  => (r2_termord A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  => (r2_group_10 A B D C C)) ) ) ) ) ) ) ) ).
tt(t3_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_xboole_0 (k13_group_2 A B D) (k8_group_2 A C)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E (k13_group_2 A B D)) & (r1_struct_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_group_7 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_group_7 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_group_7 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_group_7 A B C))) =>  ( ( (D = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C F))  &  (E = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C G)) )  =>  ((k6_algstr_0 (k2_group_7 A B) D E) = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C (k6_algstr_0 (k1_group_7 A B C) F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_group_1,ax, ((v3_group_1 (g3_algstr_0 k1_numbers k33_binop_2)) & (v2_group_1 (g3_algstr_0 k1_numbers k33_binop_2))) ).
tt(t3_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_group_2 A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) (k2_group_1 A B))) ) ) ) ) ).
tt(t3_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v5_group_1 (k6_group_2 A))) ) ).
tt(t3_group_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r1_struct_0 D C) => (r1_struct_0 D (k5_group_1 B A C))) ) ) ) ) ) ) ) ) ).
tt(t3_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  ((r1_struct_0 D B) => (r1_struct_0 D (k2_group_3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_6 C A B) =>  (! [D:$i] :  ((m1_group_6 D A B) =>  ((k10_group_2 A C D) = (k10_group_2 B C D)) ) ) ) ) ) ) ) ) ).
tt(t3_group_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_group_7 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  ( ((r2_hidden B A) &  ( (D = (k1_funct_1 C B))  & (v3_group_1 (k2_group_7 A C))) )  => (v3_group_1 D)) ) ) ) ) ) ) ).
tt(t3_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k5_group_1 B E C) = (k5_group_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (F = D)  &  (G = E) )  =>  ((k6_algstr_0 C F G) = (k6_algstr_0 B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k5_group_1 A C B) = (k1_group_1 A))  =>  ((k5_group_1 A C (k2_group_1 A B)) = (k1_group_1 A)) ) ) ) ) ) ) ) ).
tt(t3_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D C) & (m1_group_6 D A C)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ((r1_group_2 A E (k10_group_2 A B C)) =>  (! [F:$i] :  ( ((v1_group_3 F E) & (m1_group_6 F A E))  =>  (~  ( (F = (k10_group_2 A B D))  &  (! [G:$i] :  ((m1_group_2 G (k5_group_6 C D)) =>  (~ (r1_group_6 (k5_group_6 E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_hahnban1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k2_xcmplx_0 (k17_complex1 A) (k3_xcmplx_0 k6_numbers k7_complex1)) = (k9_complex1 (k13_complex1 (k15_complex1 A) (k2_xcmplx_0 (k17_complex1 A) (k3_xcmplx_0 k6_numbers k7_complex1))) A)) ) ) ).
tt(t3_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k4_rlsub_2 A D B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F))  =>  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_hallmar1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] : (r1_tarski (k1_hallmar1 A B C) A)) ) ) ) ).
tt(t3_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden k6_numbers (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B))) ) ) ) ) ) ) ).
tt(t3_heine,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_limfunc1 A) => (v1_limfunc1 (k1_heine A 2))) ) ) ).
tt(t3_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_xxreal_0 (k3_finseq_1 (k1_helly A B)) (k3_finseq_1 A))) ) ) ) ).
tt(t3_henmodel,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden E (k1_relset_1 k5_numbers B)) & (r2_hidden D (k1_relset_1 k5_numbers B)))  =>  ((r1_xxreal_0 E D) | (r1_tarski (k3_funct_2 k5_numbers A B D) (k3_funct_2 k5_numbers A B E))) ) ) ) ) )  &  ((r1_tarski C (k3_tarski (k2_relset_1 A B))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~ (r1_tarski C (k3_funct_2 k5_numbers A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (? [B:$i] :  ((m1_subset_1 B k2_numbers) &  ( ((k17_complex1 B) = 1)  &  ( ((k3_complex1 (k9_complex1 B A)) = (k17_complex1 A))  &  ((k4_complex1 (k9_complex1 B A)) = k6_numbers) ) ) ) ) ) ) ).
tt(t3_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_collsp A D E B) &  ((r1_collsp A D E C) & (r1_collsp A B C F)) )  =>  ( (B = C)  | (r1_collsp A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k9_normform A (k10_normform A B B)) = B) ) ) ) ).
tt(t3_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( ((k4_substlat A B C D) = C)  =>  (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k8_mcart_1 k1_numbers k5_numbers k5_numbers (k6_domain_1 k5_numbers A))))) )  =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  & (r1_tarski B (k8_mcart_1 k5_numbers k5_numbers (k1_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 C) (k6_domain_1 k5_numbers k6_numbers)) (k6_domain_1 k5_numbers A)))) ) ) ) ) ) ).
tt(t3_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_xxreal_0 1 A) =>  ( ((k1_relset_1 k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 A))) = (k4_xboole_0 k1_numbers (k1_tarski k6_numbers)))  &  ((k8_relset_1 k1_numbers k1_numbers (k1_taylor_1 A) (k1_tarski k6_numbers)) = (k1_tarski k6_numbers)) ) ) ) ) ).
tt(t3_hilbasis,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r1_xxreal_0 A B) => (m2_subset_1 (k5_relat_1 C A) (k14_pre_poly A) (k15_pre_poly A))) ) ) ) ) ) ) ).
tt(t3_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 B (k3_hilbert1 C D)) (k3_hilbert1 (k3_hilbert1 B C) (k3_hilbert1 B D))) (k5_hilbert1 A))) ) ) ) ) ) ) ) ).
tt(t3_hilbert2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 (k9_finseq_1 A) B) => (r2_hidden A B)) ) ) ).
tt(t3_hilbert3,ax, (! [A:$i] :  ((v1_zfmisc_1 A) =>  (! [B:$i] :  ((r2_hidden B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (r1_abian B C)) ) ) ) ) ) ).
tt(t3_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 B C))  => (r1_xxreal_0 (k4_power B A) (k4_power C A))) ) ) ) ) ) ) ) ).
tt(t3_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ((r1_aff_1 A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v6_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) &  ((v4_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k6_algstr_0 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B C) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B D)) = (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B (k2_nat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t3_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k6_xcmplx_0 A B) A)) ) ) ) ).
tt(t3_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_hidden (k4_struct_0 A) B)) ) ) ) ).
tt(t3_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) <=> (m1_subset_1 B (u1_incsp_1 (k3_incproj A)))) ) ) ) ).
tt(t3_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  ((r5_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D) <=>  ((r2_incsp_1 A B D) & (r2_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_index_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ( ((k3_index_1 (k7_funcop_1 A B)) = (k7_funcop_1 A (u1_struct_0 B)))  &  ((k4_index_1 (k7_funcop_1 A B)) = (k7_funcop_1 A (u4_struct_0 B))) ) ) ) ) ).
tt(t3_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 A))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_msualg_1 A B (k11_msafree A C))) =>  ((k3_funct_2 (k3_msualg_1 A B (k11_msafree A C)) (k4_msualg_1 A B (k11_msafree A C)) (k5_msualg_1 A B (k11_msafree A C)) D) = (k4_trees_4 (k4_tarski B (u1_struct_0 A)) D)) ) ) ) ) ) ) ) ) ).
tt(t3_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_xxreal_0 k6_numbers A) => (r2_hidden A k5_numbers)) ) ) ).
tt(t3_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_int_1 k6_numbers A) <=>  (A = k6_numbers) ) ) ) ).
tt(t3_int_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_int_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_int_3)) =>  ( (~  (B = (k4_struct_0 k1_int_3)) )  =>  (A = (k3_rlvect_1 k1_int_3 (k8_group_1 k1_int_3 (k4_int_3 A B) B) (k5_int_3 A B))) ) ) ) ) ) ).
tt(t3_int_4,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (B = k6_numbers) )  => (r2_tarski A (k1_integra2 A B))) ) ) ) ) ).
tt(t3_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  ( ((k3_finseq_1 A) = 1)  =>  ((k1_int_5 A) = (k7_funcop_1 k4_numbers (k1_funct_1 A 1))) ) ) ) ).
tt(t3_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k3_finseq_1 (k18_valued_1 A B)) = (k6_nat_1 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t3_int_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((k5_relat_1 B (k13_pre_poly B)) = (k5_relat_1 C (k13_pre_poly C)))  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t3_integr10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_real_1 (k1_seq_1 k24_sin_cos A) (k1_seq_1 k24_sin_cos B)) = (k4_integra5 B A k24_sin_cos)) ) ) ) ) ).
tt(t3_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k10_real_1 1 (k7_real_1 A 1))) k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k10_real_1 1 (k7_real_1 A 1))) k1_numbers) B) = (k8_real_1 (k5_prepower (k1_seq_1 k16_sin_cos B) A) (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ).
tt(t3_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( (~ (r1_xxreal_0 1 (k1_seq_1 k24_sin_cos E)))  &  ((k1_seq_1 B E) = 1) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9))) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k41_valued_1 k1_numbers k1_numbers k24_sin_cos))))) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k1_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) 2)) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t3_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k2_fdiff_9)) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k3_taylor_1 B)) (k8_real_1 B (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k3_taylor_1 B)))))) ) ) ) ) ) ) ) ).
tt(t3_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_integr15 E A B C) =>  (~ (r1_xxreal_0 (k1_integr15 A B C E) (k7_real_1 (k7_integra1 A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_integr16,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) => (r2_relset_1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers (k2_partfun1 k1_numbers k2_numbers A B)) (k2_partfun1 k1_numbers k1_numbers (k6_comseq_3 k1_numbers A) B))) ) ) ) ).
tt(t3_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k4_vfunct_1 k5_numbers A B D)) =>  ((k4_rlvect_1 A C) = (k1_rlvect_1 A (k4_rlvect_1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_integr19,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r1_xxreal_0 B C) &  ((r2_hidden D (k3_integra5 B C)) &  ((r2_hidden E (k3_integra5 B C)) & (r1_tarski (k3_integra5 B C) A)) ) )  => (r1_tarski (k3_integra5 (k3_xxreal_0 D E) (k4_xxreal_0 D E)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t3_integr1c,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_integr1c B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_integr1c C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_integr1c D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k2_numbers)))) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_tarski (k2_relset_1 k2_numbers B) (k1_relset_1 k2_numbers A)) &  ((r1_integr1c A B) &  ((r2_integr1c A B) &  ((r1_xxreal_0 E F) &  ( ((k1_relset_1 k1_numbers B) = (k1_rcomp_1 E F))  &  ((r2_hidden G (k1_rcomp_1 E F)) &  ( ((k1_relset_1 k1_numbers C) = (k1_rcomp_1 E G))  &  ( ((k1_relset_1 k1_numbers D) = (k1_rcomp_1 G F))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H (k1_relset_1 k1_numbers C)) =>  ((k1_funct_1 B H) = (k1_funct_1 C H)) ) ) )  &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H (k1_relset_1 k1_numbers D)) =>  ((k1_funct_1 B H) = (k1_funct_1 D H)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k3_integr1c A B) = (k2_xcmplx_0 (k3_integr1c A C) (k3_integr1c A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((v3_xxreal_2 A) & (v4_xxreal_2 A)) ) ) ).
tt(t3_integra2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (? [B:$i] :  ( ((v1_integra2 B) & (m2_finseq_1 B k1_numbers))  & (r2_classes1 A B)) ) ) ) ).
tt(t3_integra3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (~  ((r2_hidden A B) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) & (r2_hidden A (k2_integra1 B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((v1_partfun1 B A) &  ((k1_rvsum_1 B) = (k1_seq_4 C)) )  <=> (r2_relset_1 A k1_numbers B (k26_valued_1 A k1_numbers (k7_rfunct_1 A A) C))) ) ) ) ) ) ) ).
tt(t3_integra5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) )  => (r1_xxreal_0 (k18_rvsum_1 A) (k18_rvsum_1 B))) ) ) ) ) ).
tt(t3_integra6,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski B C) & (r1_tarski B D))  =>  ((k5_relat_1 (k5_relat_1 A C) B) = (k5_relat_1 (k5_relat_1 A D) B)) ) ) ) ) ) ) ).
tt(t3_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B A) A)) => (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t3_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k21_sin_cos (k7_real_1 A (k8_real_1 (k4_nat_1 2 B) k32_sin_cos))) = (k21_sin_cos A)) ) ) ) ) ).
tt(t3_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k2_integra5 B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos)) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos) (k10_real_1 1 A)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k24_sin_cos) (k10_real_1 1 A)) (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t3_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (r1_tarski B C))  =>  ((k1_interva1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t3_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 B C) B) (k7_intpro_1 A))) ) ) ) ) ) ).
tt(t3_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 (k3_irrat_1 A) B) = (k1_seq_1 (k2_irrat_1 B) A)) ) ) ) ) ).
tt(t3_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_cat_1 F B D E) =>  ((v9_cat_1 F B D E) => (v9_cat_1 (k9_cat_3 B D E A C F) A (k8_cat_1 B A C D) (k8_cat_1 B A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v1_isomichi B A)) ) ) ) ) ).
tt(t3_jct_misc,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden A (k2_rcomp_1 B C)) & (r1_xxreal_0 (k4_xxreal_0 (k18_complex1 B) (k18_complex1 C)) (k18_complex1 A))) ) ) ) ) ) ) ) ).
tt(t3_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (m2_finseq_1 B (u1_struct_0 (k1_jgraph_1 A)))) ) ) ) ).
tt(t3_jgraph_2,ax, ( ((k17_euclid (k4_struct_0 (k15_euclid 2))) = k6_numbers)  &  ((k18_euclid (k4_struct_0 (k15_euclid 2))) = k6_numbers) ) ).
tt(t3_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k3_subset_1 (u1_struct_0 A) D) = (k6_domain_1 (u1_struct_0 A) C))  &  ( ((k3_subset_1 (u1_struct_0 B) E) = (k6_domain_1 (u1_struct_0 B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F C)))  &  ((v8_pre_topc A) &  ((v8_pre_topc B) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_pre_topc A D))) =>  (~  ((k1_funct_1 F G) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F C)) ) ) )  &  ( ((v1_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) F D)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) F D) (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B E))) &  ((v5_pre_topc (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) F D) (k1_pre_topc A D) (k1_pre_topc B E)) & (m1_subset_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) F D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A D)) (u1_struct_0 (k1_pre_topc B E)))))) ) )  &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F C) G) &  ((v3_pre_topc G B) &  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C H) &  ((v3_pre_topc H A) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) F H) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v5_pre_topc F A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jgraph_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((v5_pre_topc A (k15_euclid 2) (k15_euclid 2)) &  ((v2_funct_1 A) &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) = (k2_struct_0 (k15_euclid 2)))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (? [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  &  ( (C = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r2_hidden B D) &  ((v3_pre_topc D (k15_euclid 2)) &  ((r1_tarski D C) & (r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A B) D)) ) ) ) ) ) ) ) ) ) ) ) )  => (v3_tops_2 A (k15_euclid 2) (k15_euclid 2))) ) ) ).
tt(t3_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_metric_1 F))  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_metric_1 G))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 F)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 G)) =>  ( ((r1_xxreal_0 C A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B D) &  ( (F = (k2_topmetr A B))  &  ( (G = (k2_topmetr C D))  &  (H = I) ) ) ) ) )  => (r1_tarski (k9_metric_1 F H E) (k9_metric_1 G I E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A B) & (r2_hidden D (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C))))  =>  ( ((k18_euclid D) = C)  &  ((r1_xxreal_0 A (k17_euclid D)) & (r1_xxreal_0 (k17_euclid D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( ((k17_euclid A) = (k17_euclid B))  &  ((r1_xxreal_0 D (k18_euclid A)) & (r1_xxreal_0 (k18_euclid B) E)) )  =>  ((r1_xxreal_0 C (k17_euclid A)) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid A)) | (r1_jordan6 (k1_sppol_2 (k17_euclid A) C D E) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jgraph_8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_borsuk_2 D (k15_euclid A) B C) =>  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid A)) D) (k1_rltopsp1 (k15_euclid A) B C)) =>  ((k2_relset_1 (u1_struct_0 (k15_euclid A)) D) = (k1_rltopsp1 (k15_euclid A) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v2_connsp_1 E (k15_euclid 2)) &  ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k1_jordan9 E B))) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k1_jordan8 E B))) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 (k1_jordan8 E B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) (k2_nat_1 C 1) D))  & (r1_xxreal_0 D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan11,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 A (k1_jordan11 A))) (k2_nat_1 (k2_jordan11 A) 1))) ) ) ).
tt(t3_jordan12,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  =>  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) B C) (k10_xtuple_0 B)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid A)) B (k2_nat_1 C 1)) (k10_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(t3_jordan14,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A)) )  => (v4_pre_topc (k3_gobrd13 B A C) (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t3_jordan15,ax, (! [A:$i] :  ( ((v4_pre_topc A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v9_rltopsp1 A (k15_euclid 2)) => (v2_rcomp_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))) ) ) ).
tt(t3_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) => (r2_hidden B (k3_jordan6 A C D B))) ) ) ) ) ) ) ) ) ).
tt(t3_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B (k22_pscomp_1 A)) => (r2_hidden B (k8_jordan6 A))) ) ) ) ) ).
tt(t3_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v3_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k4_topreal1 A)))) ) ).
tt(t3_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan9 B A))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k1_jordan1e B A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k15_pscomp_1 A)) =>  ((k18_euclid B) = (k7_pscomp_1 A)) ) ) ) ) ) ).
tt(t3_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) & (v2_connsp_1 C A))  =>  ((r1_xboole_0 B C) | (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t3_jordan1b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 A)) & (r2_hidden B (k3_topreal1 2 A)))  =>  ((k1_funct_1 (k3_jordan3 A B) 1) = (k1_funct_1 A 1)) ) ) ) ) ) ).
tt(t3_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v9_rltopsp1 A (k15_euclid 2)) => (v5_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))) ) ) ).
tt(t3_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 2 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 (k1_jordan8 E (k2_nat_1 B 1))))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E B)) A) |  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) A C)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E (k2_nat_1 B 1)) (k7_nat_d (k4_nat_1 2 A) 2) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan1e,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) &  ((k2_jordan3 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t3_jordan1f,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C B)) (k3_topreal1 2 D)))  &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C B) (k2_matrix_1 E)) &  ((r1_xxreal_0 A C) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 A F) &  ((r1_xxreal_0 F C) &  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E F B)) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C B)) (k3_topreal1 2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan1g,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden D (k10_xtuple_0 B)) & (r1_goboard1 A B C))  => (r1_goboard1 A (k2_finseq_5 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t3_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B C) (k2_tarski B C)) A) =>  ( (B = C)  | (r1_tarski (k1_rltopsp1 (k15_euclid 2) B C) (k2_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t3_jordan1i,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan9 B A) (k24_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) 1)) ) ) ) ) ).
tt(t3_jordan1j,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) (k3_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 A B) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))))) = (k2_tarski (k20_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ).
tt(t3_jordan1k,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((v2_funct_2 C B) => (r1_tarski (k3_subset_1 B (k7_relset_1 A B C D)) (k7_relset_1 A B C (k3_subset_1 A D)))) ) ) ) ) ) ) ) ).
tt(t3_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ((r1_xxreal_0 D (k17_euclid A)) & (r1_xxreal_0 D (k17_euclid B))) )  => (r1_xxreal_0 D (k17_euclid C))) ) ) ) ) ) ) ) ) ).
tt(t3_jordan21,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_1_jordan21 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t3_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v2_compts_1 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k1_jordan19 A) B) (k15_euclid 2)) & (v2_connsp_1 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k1_jordan19 A) B) (k15_euclid 2))) ) ) ) ) ).
tt(t3_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_jordan3 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t3_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ((r1_jordan24 2 C A B) => (r1_jordan24 2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 D E D F) C) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 D E D F) A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k2_jgraph_2 D E D F) B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k1_numbers (k1_rlvect_1 (k15_euclid A) C B) D) = (k4_real_1 B (k7_partfun1 k1_numbers C D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ( ( ((k17_euclid A) = (k17_euclid B))  |  ((k18_euclid A) = (k18_euclid B)) )  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (~  ((k17_euclid C) = (k17_euclid D)) )  &  (~  ((k18_euclid C) = (k18_euclid D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_nat_d (k2_xcmplx_0 B B) B) = k6_numbers) ) ) ) ) ).
tt(t3_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C))))))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k1_rcomp_1 k6_numbers 1)) =>  ((k1_funct_1 D E) = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 E)) (k1_rlvect_1 (k15_euclid A) C E))) ) ) )  &  ((v3_tops_2 D k5_topmetr (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C))) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan5b,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  => (r1_xxreal_0 (k2_nat_1 (k7_nat_d B A) 1) B)) ) ) ) ) ).
tt(t3_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C B) &  ((v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) (k15_euclid 2)) & (r1_topreal1 (k15_euclid 2) C D A)) )  =>  ((k1_jordan5c A B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r2_hidden A (k10_xtuple_0 B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)) &  ((k1_funct_1 B C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B C)))))) )  =>  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B C)) E D) & (v5_pre_topc D A (k1_pre_topc B C)))  => (v5_pre_topc E A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r2_hidden B A))  => (r1_jordan6 A (k18_pscomp_1 A) B)) ) ) ) ) ).
tt(t3_jordan8,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_goboard1 B C D) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  (~  ((r2_hidden (k4_tarski E F) (k2_matrix_1 D)) &  ( ((k7_partfun1 B C A) = (k3_matrix_1 B D E F))  &  ((r2_hidden (k4_tarski G H) (k2_matrix_1 D)) &  ( ((k7_partfun1 B C (k2_nat_1 A 1)) = (k3_matrix_1 B D G H))  &  (~  ( (~  ( (E = G)  &  ((k2_nat_1 F 1) = H) ) )  &  ( (~  ( ((k2_nat_1 E 1) = G)  &  (F = H) ) )  &  ( (~  ( (E = (k2_nat_1 G 1))  &  (F = H) ) )  &  (~  ( (E = G)  &  (F = (k2_nat_1 H 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (~  ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 (k4_finseq_5 B C))) &  ( ((k2_nat_1 A D) = (k2_nat_1 (k3_finseq_1 C) 1))  &  ((k7_partfun1 B C A) = (k7_partfun1 B (k4_finseq_5 B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan_a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers) &  ((v1_pscomp_1 D (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid A)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 k1_numbers)) &  ( (G = (a_4_0_jordan_a A C D F))  &  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers E F) = (k5_seq_4 G)) ) ) ) ) )  =>  ((k5_seq_4 (k7_relset_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers D (k3_borsuk_1 (k15_euclid A) (k15_euclid A) B C))) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid A)) k1_numbers E B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A)))  & (r1_xxreal_0 (k18_euclid B) (k18_euclid (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) A B) (k10_real_1 1 2))))) ) ) ) ) ) ).
tt(t3_knaster,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_abian B (k1_abian A C D)) &  (! [E:$i] :  ((r1_abian E (k1_abian A C D)) =>  (B = E) ) ) ) ) )  => (r1_abian B C)) ) ) ) ) ).
tt(t3_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (B = k1_xboole_0)  =>  ((k9_prob_1 A B) = (k2_tarski k1_xboole_0 A)) ) ) ) ) ) ).
tt(t3_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((r2_hidden C (k2_kurato_0 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 A) B D))) ) ) ) ) ) ) ).
tt(t3_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A B) (k2_kurato_1 A B)) &  ((r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)) (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) (k2_kurato_1 A B)) &  ((r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))) (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))))) (k2_kurato_1 A B)) & (r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B)))))) (k2_kurato_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t3_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (B = D)  =>  ((r1_xxreal_0 E (k12_euclid (k5_algstr_0 (k15_euclid A) C D))) | (r2_hidden C (k9_metric_1 (k14_euclid A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r1_lang1 A B C) => (r2_lang1 A (k3_pre_poly (u1_struct_0 A) B) C)) ) ) ) ) ) ) ).
tt(t3_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 C))) =>  ((k1_matrix_1 (k7_matrix_2 A B C)) = (k7_nat_d (k1_matrix_1 C) 1)) ) ) ) ) ) ) ) ).
tt(t3_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ( (B = (u1_struct_0 C))  => (r1_group_2 A (k5_group_4 A B) C)) ) ) ) ) ) ) ).
tt(t3_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((v3_orders_2 A) & (v3_orders_2 B))  => (v3_orders_2 (k1_latsum_1 A B))) ) ) ) ) ).
tt(t3_lattice2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((v1_funct_1 (k7_funct_4 A B C (k2_partfun1 A B D E))) &  ((v1_funct_2 (k7_funct_4 A B C (k2_partfun1 A B D E)) A B) & (m1_subset_1 (k7_funct_4 A B C (k2_partfun1 A B D E)) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_lattice3,ax, (! [A:$i] :  ((v13_lattices (k1_lattice3 A)) &  ((k5_lattices (k1_lattice3 A)) = k1_xboole_0) ) ) ).
tt(t3_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) (k2_filter_0 A D) B))) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) & (r3_lattices A (k4_lattices A D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lattice5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v6_ordinal1 A) =>  ((k2_zfmisc_1 (k3_tarski A) (k3_tarski A)) = (k3_tarski (a_1_0_lattice5 A))) ) ) ) ).
tt(t3_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice6 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r3_lattices A B C) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_lattices A D C) & (r1_lattice6 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r2_orders_2 A C D) <=>  (~ (r1_xxreal_0 (k1_lattice7 A D) (k1_lattice7 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lattice8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_yellow_0 B (k1_lattice5 A)) &  ((v6_yellow_0 B (k1_lattice5 A)) & (m1_yellow_0 B (k1_lattice5 A))) ) )  =>  (~  ( (~ (v7_struct_0 B))  &  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (~  ((r2_hidden C (u1_struct_0 B)) &  (~  (C = (k6_partfun1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_lattices A B (k3_lattices A C D)) = (k3_lattices A (k4_lattices A B C) (k4_lattices A B D))) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_lattices A B (k4_lattices A C D)) = (k4_lattices A (k3_lattices A B C) (k3_lattices A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_lexbfs,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 C) (k2_finseq_1 (k7_nat_d C B)))) <=>  ( (~ (r1_xxreal_0 A (k7_nat_d C B)))  & (r1_xxreal_0 A C)) ) ) ) ) ) ) ) ).
tt(t3_lfuzzy_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_xxreal_0 B C) <=> (r1_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t3_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r2_relset_1 A k1_numbers B C) <=>  ((r1_fuzzy_1 B C) & (r1_fuzzy_1 C B)) ) ) ) ) ) ) ) ).
tt(t3_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((r1_limfunc2 A B) &  ((k1_limfunc2 A B) = C) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 B E))  & (r2_hidden E (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) ) )  &  ( ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 B E))  & (r2_hidden E (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 D) &  ( ((k2_seq_2 D) = B)  & (r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 B)))) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) &  ((k2_seq_2 (k8_funct_2 k5_numbers k1_numbers k1_numbers D A)) = C) ) ) ) ) )  =>  ((r1_limfunc2 A B) &  ((k1_limfunc2 A B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v8_valued_0 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers)) ) ) ) ) ) ).
tt(t3_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski (k2_rcomp_1 (k9_real_1 B A) B) (k1_relset_1 k1_numbers C)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 B E))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  & (r1_tarski (k10_xtuple_0 B) (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 E F) &  (~  ( (~ (r1_xxreal_0 (k18_complex1 (k9_real_1 A (k1_seq_1 B F))) k6_numbers))  &  ( (~ (r1_xxreal_0 D (k18_complex1 (k9_real_1 A (k1_seq_1 B F)))))  & (r2_hidden (k1_seq_1 B F) (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  ((v4_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  => (v4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t3_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (v1_lmod_5 (k1_subset_1 (u1_struct_0 B)) A B)) ) ) ) ).
tt(t3_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v7_vectsp_1 (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)) A) & (m1_vectsp_4 (g1_vectsp_1 A (u1_struct_0 B) (u1_algstr_0 B) (u2_struct_0 B) (u1_vectsp_1 A B)) A B)) ) ) ) ) ).
tt(t3_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v7_struct_0 A) =>  ( (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  ((k1_vectsp_6 A B D) = k1_xboole_0) ) )  & (v7_struct_0 (k1_mod_3 A B C))) ) ) ) ) ) ) ) ).
tt(t3_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) D C))) ) ) ) ) ) ) ) ).
tt(t3_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k6_partfun1 (u1_struct_0 A))) &  ((v1_funct_2 (k6_partfun1 (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 (k6_partfun1 (u1_struct_0 A)) A A) &  ((v1_lopban_1 (k6_partfun1 (u1_struct_0 A)) A A) &  ((v2_lopban_1 (k6_partfun1 (u1_struct_0 A)) A A) & (m1_subset_1 (k6_partfun1 (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t3_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k3_rlvect_1 A (k5_algstr_0 A B D) (k5_algstr_0 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t3_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_normsp_1 B A) & (v3_normsp_1 C A))  => (v3_normsp_1 (k4_lopban_3 A B C) A)) ) ) ) ) ) ) ).
tt(t3_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) )  =>  (~  ( ((k3_tarski (k10_xtuple_0 B)) = (u1_struct_0 A))  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v2_nfcont_1 (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C) A)) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k1_lopban_5 A E D) (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_lopban_5 A (k4_struct_0 A) (k8_real_1 C B)) = (k1_convex1 A (k1_lopban_5 A (k4_struct_0 A) B) C)) ) ) ) ) ) ) ) ).
tt(t3_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc B A))  => (r2_hidden B (k1_lopclset A))) ) ) ) ) ).
tt(t3_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v1_lpspace1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_hidden (k4_struct_0 A) B) =>  ((v2_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) &  ((v3_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) &  ((v4_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) &  ((v5_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) &  ((v6_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) &  ((v7_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B))) & (v8_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k4_power B C) (k4_power A C))) ) ) ) ) ) ) ) ) ) ).
tt(t3_lp_space,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((v1_series_1 (k1_lp_space A C)) & (v1_series_1 (k1_lp_space B C))) )  =>  ((v1_series_1 (k1_lp_space (k1_series_1 k1_numbers A B) C)) & (r1_xxreal_0 (k4_power (k4_series_1 (k1_lp_space (k1_series_1 k1_numbers A B) C)) (k10_real_1 1 C)) (k7_real_1 (k4_power (k4_series_1 (k1_lp_space A C)) (k10_real_1 1 C)) (k4_power (k4_series_1 (k1_lp_space B C)) (k10_real_1 1 C))))) ) ) ) ) ) ) ) ).
tt(t3_ltlaxio1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean (k6_xboolean (k4_xboolean A B) C) (k6_xboolean A (k6_xboolean B C))) = 1) ) ) ) ) ) ) ).
tt(t3_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A C D) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A B D) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t3_margrel1,ax, (! [A:$i] :  ( ((v3_finseq_1 A) & (v2_card_3 A))  =>  ( (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~ (r2_hidden B A)) ) )  =>  (A = k1_xboole_0) ) ) ) ).
tt(t3_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski B C) => (r1_tarski (k1_mathmorp A D B) (k1_mathmorp A D C))) ) ) ) ) ) ) ) ) ).
tt(t3_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  & (r2_hidden (k4_tarski A B) (k2_matrix_1 C))) )  =>  ((k3_matrix_1 k1_numbers (k5_matrixr1 C D) A B) = (k9_real_1 (k3_matrix_1 k1_numbers C A B) (k3_matrix_1 k1_numbers D A B))) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r2_hidden (k2_tarski 1 2) (k2_sgraph1 (k2_finseq_1 A)))) ) ) ).
tt(t3_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 C) B A) =>  ( ((r2_hidden E (k4_finseq_1 G)) & (r2_hidden F (k2_finseq_1 (k1_matrix_1 G))))  =>  ((k1_funct_1 (k10_fvsum_1 (k1_matrix_1 G) C (k8_matrix_1 (u1_struct_0 C) G E) D) F) = (k8_group_1 C D (k3_matrix_1 (u1_struct_0 C) G E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k13_matrix_3 A B C) = (k13_matrix_3 A B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(t3_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k3_finseq_1 (k7_fvsum_1 A B C)) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ).
tt(t3_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) )  =>  ((k3_fvsum_1 A (k8_finseq_1 (u1_struct_0 A) B D) (k8_finseq_1 (u1_struct_0 A) C E)) = (k8_finseq_1 (u1_struct_0 A) (k3_fvsum_1 A B C) (k3_fvsum_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_matrix_1 C B A A) =>  ((v1_matrix16 C B) =>  ((r1_xxreal_0 A k6_numbers) | (v3_matrix16 (k5_matrix_1 A B C) B)) ) ) ) ) ) ) ) ).
tt(t3_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((r1_matrix17 (u1_struct_0 B) E D) => (r1_matrix17 (u1_struct_0 B) (k2_matrix13 A A B E C) (k9_fvsum_1 B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrix_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (v1_matrix_1 (k9_finseq_1 A))) ) ).
tt(t3_matrix_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k3_finseq_1 (k3_matrix_2 A B C D)) = 2)  &  ( ((k1_matrix_1 (k3_matrix_2 A B C D)) = 2)  &  ((k2_matrix_1 (k3_matrix_2 A B C D)) = (k2_zfmisc_1 (k2_finseq_1 2) (k2_finseq_1 2))) ) ) ) ) ) ) ).
tt(t3_matrix_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k3_matrix_3 A (k3_matrix_3 A B C) D) = (k3_matrix_3 A B (k3_matrix_3 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k1_matrix_4 A B B) = (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B))) ) ) ) ) ).
tt(t3_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ((k1_matrix_5 A) = (k1_matrix_5 B))  =>  (A = B) ) ) ) ) ) ).
tt(t3_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) => (r1_matrix_6 A B C (k1_matrix_3 B A A))) ) ) ) ) ) ).
tt(t3_matrix_7,ax, ((k12_matrix_2 2) = (k2_tarski (k10_finseq_1 1 2) (k10_finseq_1 2 1))) ).
tt(t3_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((v1_matrix_8 C A B) <=> (v1_matrix_8 (k5_matrix_1 A (u1_struct_0 B) C) A B)) ) ) ) ) ) ) ) ).
tt(t3_matrix_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_funct_1 A)) )  =>  (~  ( ((k9_xtuple_0 A) = (k2_finseq_1 2))  &  ( ((k10_xtuple_0 A) = (k2_finseq_1 2))  &  ( (~  (A = (k6_partfun1 (k2_finseq_1 2))) )  &  (~  (A = (k3_finseq_5 (k6_partfun1 (k2_finseq_1 2)))) ) ) ) ) ) ) ) ).
tt(t3_matrixc1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ((k3_finseq_1 (k7_matrix_5 A B)) = (k3_finseq_1 B))  &  ((k1_matrix_1 (k7_matrix_5 A B)) = (k1_matrix_1 B)) ) ) ) ) ) ).
tt(t3_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden A (k4_finseq_1 D)) =>  ((k4_wsierp_1 B (k1_nat_1 A (k3_finseq_1 C)) (k8_finseq_1 B C D)) = (k8_finseq_1 B C (k4_wsierp_1 B A D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v1_matrix_6 (k2_matrixj2 B C A) A B) <=>  (~  ( (~  (A = k1_xboole_0) )  &  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k4_rvsum_1 A (k6_rvsum_1 A)) = (k5_euclid (k3_finseq_1 A)))  &  ((k8_rvsum_1 A A) = (k5_euclid (k3_finseq_1 A))) ) ) ) ).
tt(t3_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k1_numbers)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) =>  ((k3_matrix_1 k1_numbers (k7_matrixr1 C D) A B) = (k4_real_1 C (k3_matrix_1 k1_numbers D A B))) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  =>  (! [E:$i] :  ((m1_vectsp_7 E A C) =>  (! [F:$i] :  ((m1_vectsp_7 F A D) => (m1_vectsp_7 (k2_xboole_0 E F) A (k1_vectsp_5 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrlin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C (k1_nat_1 A 1) B) => (m1_matrix_1 (k1_matrlin C (k1_nat_1 A 1) D) C A B)) ) ) ) ) ) ) ) ).
tt(t3_matroid0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  & (l1_pre_topc A))  =>  ((v1_matroid0 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (r1_tarski C B))  => (v3_pre_topc C A)) ) ) ) ) ) ) ) ).
tt(t3_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (k6_numbers = C) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  (~  ((k3_funct_2 k5_numbers k1_numbers B (k23_binop_2 C 1)) = (k9_binop_2 (k1_seq_1 B C) (k1_seq_1 A (k23_binop_2 C 1)))) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k4_finseq_1 A)) &  ((r2_hidden D (k4_finseq_1 A)) & (r1_xxreal_0 C D)) )  => (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrtop1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_partfun3 (k9_finseq_1 A)) = (k9_finseq_1 (k6_square_1 A))) ) ) ).
tt(t3_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) k1_numbers)))) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 k2_vectsp_1)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 k2_vectsp_1))))) )  =>  ( ((r1_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 k2_vectsp_1) C E) &  (B = D) )  =>  ((k5_rlvect_2 (k15_euclid A) B C) = (k3_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_matrtop3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v3_valued_0 B)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k18_rvsum_1 (k12_rvsum_1 (k2_funct_7 B C A))) = (k7_real_1 (k9_real_1 (k18_rvsum_1 (k12_rvsum_1 B)) (k5_square_1 (k1_seq_1 B C))) (k3_square_1 A))) ) ) ) ) ) ) ) ).
tt(t3_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_rlvect_1 A B B) = (k1_rlvect_1 A B 2)) ) ) ) ) ).
tt(t3_mboolean,ax, (! [A:$i] :  (! [B:$i] : (r6_pboole A (k1_mboolean A (k7_funcop_1 A B)) (k7_funcop_1 A (k1_zfmisc_1 B)))) ) ).
tt(t3_measure1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) => (m1_subset_1 (k1_enumset1 B C D) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ) ) ).
tt(t3_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 B D (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  ( ((r1_tarski (k1_measure2 A B (k1_measure3 A B D)) E) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) => (r1_tarski E (k8_nat_1 B D F))) ) )  =>  ((k12_supinf_2 C E) = (k12_supinf_2 C (k1_measure2 A B (k1_measure3 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_measure4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k9_setfam_1 A)))  &  ((v1_prob_1 (k9_setfam_1 A) A) &  ((v4_prob_1 (k9_setfam_1 A) A) & (m1_subset_1 (k9_setfam_1 A) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ).
tt(t3_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  ( (~ (r1_xxreal_0 B D))  &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D k1_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_measure6,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((v6_supinf_2 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 B (k12_supinf_2 A C))) ) )  | (r1_xxreal_0 B (k19_supinf_2 A))) ) ) ) ) ) ).
tt(t3_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v6_supinf_2 B) &  ((v6_supinf_2 C) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k12_supinf_2 A D) = (k3_supinf_2 (k12_supinf_2 B D) (k12_supinf_2 C D))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k12_supinf_2 (k18_supinf_2 A) D) = (k3_supinf_2 (k12_supinf_2 (k18_supinf_2 B) D) (k12_supinf_2 (k18_supinf_2 C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_measure8,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v6_supinf_2 A) &  ((v6_supinf_2 B) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k1_mesfunc9 C D) = (k1_xxreal_3 (k1_mesfunc9 A D) (k1_mesfunc9 B D))) ) ) ) )  =>  ((v6_supinf_2 C) &  ( ((k19_supinf_2 C) = (k1_xxreal_3 (k19_supinf_2 A) (k19_supinf_2 B)))  &  ((k3_mesfunc9 C) = (k1_xxreal_3 (k3_mesfunc9 A) (k3_mesfunc9 B))) ) ) ) ) ) ) ) ) ) ).
tt(t3_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) <=> (r1_tarski (k4_member_1 A) (k4_member_1 B))) ) ) ) ) ).
tt(t3_membered,ax, (! [A:$i] :  ((v3_membered A) => (r1_tarski A k1_numbers)) ) ).
tt(t3_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_memstr_0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (~ (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k6_memstr_0 A B C)))) ) ) ) ) ) ) ).
tt(t3_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k4_algstr_0 (k15_euclid 2) A)) = (k7_binop_2 (k17_euclid A)))  &  ((k18_euclid (k4_algstr_0 (k15_euclid 2) A)) = (k7_binop_2 (k18_euclid A))) ) ) ) ).
tt(t3_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  =>  ((r1_xxreal_0 (k6_rinfsup2 A) (k6_rinfsup2 B)) & (r1_xxreal_0 (k5_rinfsup2 A) (k5_rinfsup2 B))) ) ) ) ) ) ).
tt(t3_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((r2_relset_1 A k1_numbers (k5_comseq_3 A (k25_valued_1 A k2_numbers B C)) (k47_valued_1 A k1_numbers k1_numbers (k26_valued_1 A k1_numbers (k5_comseq_3 A B) (k3_complex1 C)) (k26_valued_1 A k1_numbers (k6_comseq_3 A B) (k4_complex1 C)))) & (r2_relset_1 A k1_numbers (k6_comseq_3 A (k25_valued_1 A k2_numbers B C)) (k3_valued_1 A k1_numbers k1_numbers (k26_valued_1 A k1_numbers (k5_comseq_3 A B) (k4_complex1 C)) (k26_valued_1 A k1_numbers (k6_comseq_3 A B) (k3_complex1 C))))) ) ) ) ) ) ) ).
tt(t3_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k3_mesfun7c A B))) =>  ((k12_supinf_2 (k3_mesfun7c A B) C) = (k8_supinf_2 (k17_supinf_2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B C))))) ) ) ) ) ) ) ) ).
tt(t3_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D C) => (v2_comseq_2 (k10_seqfunc A B D))) ) ) )  => (r2_relset_1 A k7_numbers (k2_partfun1 A k7_numbers (k8_mesfun7c A B) C) (k8_mesfun7c A (k1_mesfun9c A k1_numbers B C)))) ) ) ) ) ) ).
tt(t3_mesfunc1,ax,(r2_tarski k5_numbers k4_numbers)).
tt(t3_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k3_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k3_numbers B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G B) =>  ( ((v3_valued_0 C) &  ((v3_valued_0 D) &  (! [H:$i] :  ((v1_rat_1 H) =>  ((k1_funct_1 E H) = (k9_subset_1 A (k9_subset_1 A G (k15_mesfunc1 A C (k1_measure6 H))) (k9_subset_1 A G (k15_mesfunc1 A D (k1_measure6 (k9_real_1 F H)))))) ) ) ) )  =>  ((k9_subset_1 A G (k15_mesfunc1 A (k3_mesfunc1 A C D) (k1_measure6 F))) = (k3_tarski (k2_relset_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B C) &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k7_numbers) =>  (~  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k12_supinf_2 C G) = (k12_supinf_2 E F)) ) ) ) ) )  &  (! [F:$i] :  (~  ((r2_hidden F (k1_relset_1 A C)) &  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  (~  ( ((k4_finseq_1 G) = (k4_finseq_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k12_supinf_2 E H) (k12_supinf_2 (k3_mesfunc2 (k1_funct_1 D H) A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_prob_2 E) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ((m2_finseq_1 F k7_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  ( ((r1_mesfunc2 A B C) &  ( (! [H:$i] :  ((r2_hidden H (k9_xtuple_0 C)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 C H))) )  &  ((r1_mesfunc3 A B C E F) &  ( ((k4_finseq_1 G) = (k4_finseq_1 E))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k12_supinf_2 F H) (k12_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E D) H))) ) ) ) ) ) ) )  =>  ( ((k9_xtuple_0 C) = k1_xboole_0)  |  ((k1_mesfunc3 A B D C) = (k4_extreal1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C (k3_extreal1 (k4_supinf_2 A B))))  &  ( (~  ( (A = k1_supinf_1)  &  (B = k1_supinf_1) ) )  &  ( (~  ( (A = k2_supinf_1)  &  (B = k2_supinf_1) ) )  &  (~  ( (~  (A = k1_supinf_1) )  &  ( (~  (A = k2_supinf_1) )  &  ( (~  (B = k1_supinf_1) )  &  (~  (B = k2_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((r2_hidden D (k11_mesfunc1 B C)) <=>  ((r2_hidden D (k1_relset_1 A B)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (E = (k1_seq_1 B D))  &  (~ (r1_xxreal_0 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  ((r1_mesfunc5 A B C E) &  ((v6_supinf_2 (k4_mesfunc1 A E D)) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  & (r1_xxreal_0 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)) (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  ((r1_funct_2 k5_numbers B k5_numbers (k9_setfam_1 A) E (k5_setlim_1 A B D)) &  ((k12_supinf_2 C (k3_kurato_0 A D)) = (k8_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) & (v3_mesfunc5 C))  => (v3_mesfunc5 (k3_mesfunc1 A B C))) ) ) ) ) ) ) ).
tt(t3_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_metric_1 A B C) = (k2_metric_1 A C B)) ) ) ) )  => (v8_metric_1 A)) ) ) ).
tt(t3_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k1_metric_2 A B)) & (r2_hidden D (k1_metric_2 A B)))  => (r3_metric_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(t3_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))) => (r1_xxreal_0 (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) C E) (k7_real_1 (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) C D) (k1_metric_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_metric_3 A B) D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_metric_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) <=>  ((v2_metric_1 B A) &  ((v3_metric_1 B A) &  ((v4_metric_1 B A) & (v5_metric_1 B A)) ) ) ) ) ) ) ) ).
tt(t3_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 D A B) => (r1_metrizts A B C (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) ) ) ) ) ) ) ) ) ).
tt(t3_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v3_pre_topc C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ((r2_hidden B C) &  (! [D:$i] :  ( ((v1_mfold_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ((r1_tarski D C) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mfold_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) => (v3_tops_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t3_midsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_midsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_midsp_1)) =>  ((k1_midsp_1 k2_midsp_1 A B) = (k1_binop_1 k9_funct_5 A B)) ) ) ) ) ).
tt(t3_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 D))))) )  =>  ( ((r1_midsp_2 A D E) &  ((k2_binop_1 A A (u1_struct_0 D) E B C) = (k4_struct_0 D)) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ((m2_finseq_1 E B) =>  (! [F:$i] :  ((m2_finseq_1 F B) =>  ( ( (D = (k8_finseq_1 B (k8_finseq_1 B E (k12_finseq_1 B C)) F))  &  (A = (k2_nat_1 (k3_finseq_1 E) 1)) )  =>  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k3_finseq_1 E)))  =>  ((k1_funct_1 D G) = (k1_funct_1 E G)) ) ) )  &  ( ((k1_funct_1 D A) = C)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 A 1) G) & (r1_xxreal_0 G (k3_finseq_1 D)))  =>  ((k1_funct_1 D G) = (k1_funct_1 F (k6_xcmplx_0 G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r2_hidden C (k4_mmlquery A D B)) <=>  ((r2_hidden C B) &  (~  ((k1_mmlquery A D C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((l1_mod_2 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( (D = (g1_mod_2 A B C E))  =>  ( ((k2_mod_2 A D) = B)  &  ( ((k3_mod_2 A D) = C)  & (r1_funct_2 (u1_struct_0 (k2_mod_2 A D)) (u1_struct_0 (k3_mod_2 A D)) (u1_struct_0 B) (u1_struct_0 C) (k4_mod_2 A D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_vectsp_6 A B (k6_vectsp_6 A B D C)) = (k4_vectsp_1 A B D (k4_vectsp_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t3_mod_4,ax, ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  ((k5_struct_0 A) = (k5_struct_0 (k2_mod_4 A))) ) )  &  (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  ( ((k4_struct_0 A) = (k4_struct_0 (k2_mod_4 A)))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_mod_4 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_mod_4 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_mod_4 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_mod_4 A))) =>  ( ( (B = F)  &  ( (C = G)  &  ( (D = H)  &  (E = I) ) ) )  =>  ( ((k1_algstr_0 A B C) = (k1_algstr_0 (k2_mod_4 A) F G))  &  ( ((k6_algstr_0 A B C) = (k6_algstr_0 (k2_mod_4 A) G F))  &  ( ((k4_algstr_0 A B) = (k4_algstr_0 (k2_mod_4 A) F))  &  ( ((k1_algstr_0 A (k1_algstr_0 A B C) D) = (k1_algstr_0 (k2_mod_4 A) (k1_algstr_0 (k2_mod_4 A) F G) H))  &  ( ((k1_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 (k2_mod_4 A) F (k1_algstr_0 (k2_mod_4 A) G H)))  &  ( ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 (k2_mod_4 A) H (k6_algstr_0 (k2_mod_4 A) G F)))  &  ( ((k6_algstr_0 A B (k6_algstr_0 A C D)) = (k6_algstr_0 (k2_mod_4 A) (k6_algstr_0 (k2_mod_4 A) H G) F))  &  ( ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k6_algstr_0 (k2_mod_4 A) (k1_algstr_0 (k2_mod_4 A) G H) F))  &  ( ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k6_algstr_0 (k2_mod_4 A) F (k1_algstr_0 (k2_mod_4 A) G H)))  &  ((k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A D E)) = (k1_algstr_0 (k2_mod_4 A) (k6_algstr_0 (k2_mod_4 A) G F) (k6_algstr_0 (k2_mod_4 A) I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (~  ( (~  (A = B) )  & (r2_xboole_0 (k12_finseq_1 k5_numbers A) (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) C))) ) ) ) ) ) ) ) ).
tt(t3_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v2_mod_2 D A) & (m1_mod_2 D A B C))  => (m5_modcat_1 (k1_tarski D) A B C)) ) ) ) ) ) ) ) ).
tt(t3_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  & (r1_modelc_1 A B C)) ) ) ) ) ) ).
tt(t3_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  => (r1_xxreal_0 1 (k3_finseq_1 A))) ) ).
tt(t3_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  ((k1_modelc_3 A) = (k10_xtuple_0 B)) ) ) ) ) ).
tt(t3_moebius1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_int_2 A B) &  ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) ) ).
tt(t3_monoid_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (k1_tarski A) (k1_tarski A)) (k1_tarski A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) (k1_tarski A)) (k1_tarski A))))) )  =>  ( (B = (k13_funcop_1 A A A))  &  ((v1_setwiseo B (k1_tarski A)) &  ((v1_binop_1 B (k1_tarski A)) &  ((v2_binop_1 B (k1_tarski A)) &  ((v3_binop_1 B (k1_tarski A)) &  ((v5_monoid_0 B (k1_tarski A)) &  ((v8_monoid_0 B (k1_tarski A)) & (v9_monoid_0 B (k1_tarski A))) ) ) ) ) ) ) ) ) ) ).
tt(t3_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_binop_1 C B) => (r2_funct_2 A B (k3_monoid_1 A B B B C D E) (k3_monoid_1 A B B B C E D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 A))  =>  ( (B = k1_xboole_0)  |  ( ((k6_rusub_4 A B C) = C)  &  ((k6_rusub_4 A C B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((r2_hidden (k4_tarski (k4_tarski C (u1_struct_0 A)) D) (k4_msafree A B)) =>  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((r2_hidden (k1_funct_1 D E) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k4_tarski F (u1_struct_0 A)) = (k1_funct_1 D E))  =>  ((k2_msualg_1 A F) = (k1_funct_1 (k1_msualg_1 A C) E)) ) ) ) )  &  ((r2_hidden (k1_funct_1 D E) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) => (r2_hidden (k1_funct_1 D E) (k2_msafree (u1_struct_0 A) B (k1_funct_1 (k1_msualg_1 A C) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (r1_tarski (k1_msafree2 A) (k3_msafree2 A))) ) ).
tt(t3_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 B))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden A (k1_funct_1 D E)) & (r2_hidden A (k1_funct_1 C E)))  <=> (r2_hidden (k1_trees_4 (k4_tarski A E)) (k1_funct_1 (k1_equation (u1_struct_0 B) D (k15_msafree B C)) E))) ) ) ) ) ) ) ) ) ) ).
tt(t3_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((m1_msafree C A B) <=>  ((k12_msualg_2 A B C) = B) ) ) ) ) ) ) ) ).
tt(t3_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ((m2_msalimit D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_orders_2 A F E) =>  ( (E = F)  |  ((k1_binop_1 D F E) = (k1_binop_1 (k2_msalimit A B C D) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A C) B))) =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  (~  ((r2_hidden F (k1_funct_1 (u3_msualg_1 A C) E)) &  ((k1_funct_1 D k1_xboole_0) = (k4_tarski F E)) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 B E)) =>  (~  ((k1_funct_1 D k1_xboole_0) = (k4_tarski F E)) ) ) ) ) )  &  (~ (r2_hidden (k1_funct_1 D k1_xboole_0) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msinst_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (~  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) &  ( (~  ((k3_msualg_1 A B C) = k1_xboole_0) )  &  ((k3_msualg_1 A B D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (r1_tarski (k2_xboole_0 (k10_xtuple_0 (u1_graph_1 A)) (k10_xtuple_0 (u2_graph_1 A))) (u1_struct_0 A))) ) ).
tt(t3_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_struct_0 A) & (l1_msualg_1 A)) )  =>  ((v5_msafree2 A) <=> (v3_msscyc_1 (k4_msscyc_2 A))) ) ) ).
tt(t3_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden k1_xboole_0 B) =>  ((k8_setfam_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(t3_mssublat,ax, (! [A:$i] :  ((k3_funct_2 k5_numbers (k3_finseq_2 (k1_tarski A)) (k7_finseq_2 A) 2) = (k10_finseq_1 A A)) ) ).
tt(t3_msualg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v2_margrel1 B) &  ((v3_margrel1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) )  =>  ((k9_xtuple_0 B) = (k9_funct_2 (k2_finseq_1 (k19_margrel1 B)) A)) ) ) ) ) ).
tt(t3_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) =>  ((v3_msualg_2 C A B) &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_msualg_2 A B D C) = (k5_msualg_1 A D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((k8_pboole (k2_msualg_3 A B) D) = D) ) ) ) ) ) ) ) ).
tt(t3_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v2_msualg_4 C A B) &  ((v3_msualg_4 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) )  => (r2_msualg_3 A B (k13_msualg_4 A B C) (k15_msualg_4 A B C))) ) ) ) ) ) ).
tt(t3_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  => (r8_pboole A (k3_msualg_5 A B C) C)) ) ) ) ) ) ).
tt(t3_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ( (~  ((k3_msualg_1 A B C) = k1_xboole_0) )  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 (k1_msualg_1 A B))) &  ((k1_funct_1 (u3_msualg_1 A C) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A B) D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k5_lattices (k5_msualg_5 A B)) = (k2_msualg_3 A B)) ) ) ) ) ).
tt(t3_msualg_8,ax, (! [A:$i] :  ((k5_lattices (k2_msualg_5 A)) = (k6_partfun1 A)) ) ).
tt(t3_msualg_9,ax, (! [A:$i] : (r1_tarski (k8_eqrel_1 A (k1_eqrel_1 A)) (k1_tarski A))) ).
tt(t3_msuhom_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v1_funcop_1 A) => (v1_funcop_1 (k5_relat_1 A B))) ) ) ) ).
tt(t3_multop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_zfmisc_1 A B C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k3_zfmisc_1 A B C) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k3_zfmisc_1 A B C) D)))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H B) =>  (! [I:$i] :  ((m1_subset_1 I C) =>  ((k2_multop_1 A B C D E G H I) = (k2_multop_1 A B C D F G H I)) ) ) ) ) ) )  => (r2_funct_2 (k3_zfmisc_1 A B C) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_mycielsk,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  ( (~ (r1_tarski F A))  &  ( (~ (r1_tarski F B))  &  ( (~ (r1_tarski F C))  &  ( (~ (r1_tarski F D))  &  (~ (r1_tarski F E)) ) ) ) ) )  => (r1_tarski F (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D) E))) ) ) ) ) ) ) ).
tt(t3_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_nagata_1 B A) => (v1_nagata_1 (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t3_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((v3_pre_topc C (k2_borsuk_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (F = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 A) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k8_subset_1 (u1_struct_0 (k2_borsuk_1 A B)) C (k2_zfmisc_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 B) E)))))  => (v3_pre_topc F A))  &  ( (G = (k7_relset_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k8_subset_1 (u1_struct_0 (k2_borsuk_1 A B)) C (k2_zfmisc_1 (k6_domain_1 (u1_struct_0 A) D) (u1_struct_0 B)))))  => (v3_pre_topc G B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (k6_numbers = A) )  & (r1_xxreal_0 A k6_numbers)) ) ) ) ).
tt(t3_nat_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k3_nat_d A A) = 1) ) ) ).
tt(t3_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  => (r1_nat_d B (k1_newton B A))) ) ) ) ) ).
tt(t3_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k1_newton A B) B)) ) ) ) ) ) ).
tt(t3_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (A = (k2_newton 2 B))  =>  ((v1_abian C) | (r1_int_2 A C)) ) ) ) ) ) ) ) ).
tt(t3_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A B) <=>  (B = (k3_nat_1 A (k3_nat_d B A))) ) ) ) ) ) ).
tt(t3_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ((r1_lattices k3_nat_lat A B) => (r1_nat_d A B)) ) ) ) ) ).
tt(t3_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_ncfcont1 C A B) => (r2_hidden B C)) ) ) ) ) ) ).
tt(t3_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r3_ncfcont2 A C D E) & (r1_tarski B A))  => (r3_ncfcont2 B C D E)) ) ) ) ) ) ) ) ) ).
tt(t3_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (a_3_0_ndiff_1 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_nfcont_1 E A D) =>  ((r1_tarski E (k1_relset_1 (u1_struct_0 A) C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( (! [H:$i] :  ( ((v2_relat_1 H) &  ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k1_numbers) &  ((v1_fdiff_1 H k6_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v3_funct_1 I) &  ((v1_funct_2 I k5_numbers (u1_struct_0 A)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( ((k2_relset_1 (u1_struct_0 A) I) = (k1_tarski D))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A F H) I)) E))  =>  ((v3_normsp_1 (k1_ndiff_1 B (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A F H) I) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) I C)) (k37_valued_1 k5_numbers k1_numbers H)) B) &  (G = (k6_normsp_1 B (k1_ndiff_1 B (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A F H) I) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) I C)) (k37_valued_1 k5_numbers k1_numbers H)))) ) ) ) ) ) )  <=>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 H k6_numbers))  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I k6_numbers))  &  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ( (~ (r1_xxreal_0 I (k18_complex1 J)))  &  ( (~  (J = k6_numbers) )  &  ((r2_hidden (k3_rlvect_1 A (k1_rlvect_1 A F J) D) E) & (r1_xxreal_0 H (k1_normsp_0 B (k5_algstr_0 B (k1_rlvect_1 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 A (k1_rlvect_1 A F J) D)) (k7_partfun1 (u1_struct_0 B) C D)) (k2_real_1 J)) G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ( ((v1_funct_1 (k6_vfunct_1 k1_numbers A B C)) &  ((v1_funct_2 (k6_vfunct_1 k1_numbers A B C) k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 (k6_vfunct_1 k1_numbers A B C) A) & (m1_subset_1 (k6_vfunct_1 k1_numbers A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  &  ((v1_funct_1 (k2_vfunct_1 k1_numbers A B C)) &  ((v1_funct_2 (k2_vfunct_1 k1_numbers A B C) k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 (k2_vfunct_1 k1_numbers A B C) A) & (m1_subset_1 (k2_vfunct_1 k1_numbers A B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t3_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (C = B)  =>  ((k1_ndiff_4 A B D) = (k1_ndiff_3 (k4_real_ns1 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 D A B) &  ((v1_lopban_1 D A B) &  ((v2_lopban_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C D)) &  ((v1_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C D) B) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C D) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t3_neckla_2,ax, (! [A:$i] :  ((r2_hidden A k13_classes2) => (v1_finset_1 A)) ) ).
tt(t3_neckla_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((k2_zfmisc_1 (k2_enumset1 A B C D) (k2_enumset1 E F G H)) = (k2_xboole_0 (k6_enumset1 (k4_tarski A E) (k4_tarski A F) (k4_tarski B E) (k4_tarski B F) (k4_tarski A G) (k4_tarski A H) (k4_tarski B G) (k4_tarski B H)) (k6_enumset1 (k4_tarski C E) (k4_tarski C F) (k4_tarski D E) (k4_tarski D F) (k4_tarski C G) (k4_tarski C H) (k4_tarski D G) (k4_tarski D H)))) ) ) ) ) ) ) ) ) ).
tt(t3_necklace,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A B) => (v7_ordinal1 A)) ) ) ) ).
tt(t3_net_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_petri B) =>  ((m1_subset_1 A (u4_struct_0 B)) =>  ( ((u4_struct_0 B) = k1_xboole_0)  | (m1_subset_1 A (k2_net_1 B))) ) ) ) ) ).
tt(t3_newton,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k4_finseq_1 B) = (k4_finseq_1 (k10_rvsum_1 B A))) ) ) ) ) ).
tt(t3_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (m1_nfcont_1 (a_3_0_nfcont_1 A B C) A B)) ) ) ) ) ) ) ).
tt(t3_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r1_nfcont_2 A C D E) & (r1_nfcont_2 B C D F))  => (r1_nfcont_2 (k3_xboole_0 A B) C D (k2_vfunct_1 (u1_struct_0 C) D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k4_vfunct_1 k5_numbers A B C) (k5_normsp_1 A B C))) ) ) ) ) ) ).
tt(t3_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r1_nfcont_4 A C B) <=>  ((r2_hidden B (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((v1_xreal_0 F) =>  (~  ((r2_hidden F (k1_relset_1 k1_numbers C)) &  ( (~ (r1_xxreal_0 E (k18_complex1 (k10_binop_2 F B))))  & (r1_xxreal_0 D (k12_euclid (k8_euclid A (k7_partfun1 (k1_euclid A) C F) (k7_partfun1 (k1_euclid A) C B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((k1_normform A B (k1_normform A B C D) E) = (k1_normform A B C (k1_normform A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) (k7_real_1 (k1_normsp_0 A B) (k1_normsp_0 A C)))) ) ) ) ) ) ).
tt(t3_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_normsp_2 A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (D = B)  &  ((k10_metric_1 (k2_normsp_2 A) B C) = (a_3_1_normsp_2 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_ntalgo_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 A k6_numbers) => (r1_xxreal_0 (k6_int_1 B A) k6_numbers)) ) ) ) ) ).
tt(t3_numbers,ax,(r2_xboole_0 k3_numbers k2_numbers)).
tt(t3_numeral1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k1_relset_1 k5_numbers A) = (k1_relset_1 k5_numbers B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers A)) =>  ((k1_recdef_1 B D) = (k4_nat_d (k1_recdef_1 A D) C)) ) ) ) )  =>  ((k4_nat_d (k7_afinsq_2 A) C) = (k4_nat_d (k7_afinsq_2 B) C)) ) ) ) ) ) ) ) ).
tt(t3_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (g3_lattices (k1_openlatt A) (k4_openlatt A) (k5_openlatt A))))  &  ((v10_lattices (g3_lattices (k1_openlatt A) (k4_openlatt A) (k5_openlatt A))) & (l3_lattices (g3_lattices (k1_openlatt A) (k4_openlatt A) (k5_openlatt A)))) ) ) ) ).
tt(t3_oposet_1,ax,(v3_orders_2 k1_oposet_1)).
tt(t3_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_oppcat_1 A (k3_oppcat_1 A B)) = B) ) ) ) ) ).
tt(t3_orders_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v4_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ((r2_hidden B A) => (r2_hidden (k4_tarski B B) C)) ) ) ) ) ).
tt(t3_orders_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_orders_2 A B C) & (r1_orders_2 A C D))  => (r1_orders_2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t3_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v3_orders_2 A) &  ((k2_struct_0 A) = (k6_domain_1 (u1_struct_0 A) B)) )  => (v1_orders_3 A)) ) ) ) ) ).
tt(t3_orders_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  => (r1_orders_4 A (k6_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A))) (k6_domain_1 (u1_struct_0 A) (k4_yellow_0 A)))) ) ).
tt(t3_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_tarski (k1_ordinal1 A) (k9_setfam_1 A))) ) ).
tt(t3_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) <=> (r2_hidden (k1_ordinal1 A) (k1_ordinal1 B))) ) ) ) ) ).
tt(t3_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal2 C A) => (r1_ordinal2 C (k1_ordinal4 B A))) ) ) ) ) ) ) ).
tt(t3_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ((r1_tarski (k10_xtuple_0 A) (k10_xtuple_0 (k1_ordinal4 A B))) & (r1_tarski (k10_xtuple_0 B) (k10_xtuple_0 (k1_ordinal4 A B)))) ) ) ) ) ).
tt(t3_ordinal6,ax, (! [A:$i] :  ((v1_ordinal6 A) => (r1_tarski A (k3_ordinal2 A))) ) ).
tt(t3_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_o_ring_1 B A) =>  ((v7_o_ring_1 B A) &  ((v11_o_ring_1 B A) & (v13_o_ring_1 B A)) ) ) ) ) ) ) ).
tt(t3_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ((r1_orders_2 B (k3_rlvect_1 B E C) D) & (r1_orders_2 B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  ( ((k2_lang1 (k2_osafree A B)) = (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))  &  ((k1_lang1 (k2_osafree A B)) = (k3_card_3 (k3_msafree (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(t3_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  ((v6_osalg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((r1_osalg_1 A B C) =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t3_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_msualg_1 A) &  ((v2_msualg_2 A) & (l1_msualg_1 A)) ) ) )  => (v2_msualg_2 (k1_osalg_1 A))) ) ).
tt(t3_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v1_funcop_1 B)) ) ) )  =>  ((v1_osalg_3 B A) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_osalg_1 A C D) => (r1_tarski (k1_funct_1 (k6_finseq_2 (u1_struct_0 A) B) C) (k1_funct_1 (k6_finseq_2 (u1_struct_0 A) B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_osalg_4 A B C) & (r1_osalg_4 A C D))  => (r1_osalg_4 A B D)) ) ) ) ) ) ) ) ) ).
tt(t3_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_analoaf A))) <=> (m1_subset_1 B (u1_struct_0 A))) ) ) ) ).
tt(t3_pardepap,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v11_aff_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) )  =>  ((r2_analoaf A B C B D) |  ((r2_analoaf A B C B F) | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ((k4_parsp_1 A B) = (k4_domain_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (k4_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B)) (k4_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B)) (k4_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t3_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C B D) = (k6_xtuple_0 E F E G))  =>  ((r1_parsp_1 (k9_parsp_1 A) B C B D) |  ( (~  (E = F) )  &  ( (~  (E = G) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (~  ((r2_hidden C (k10_xtuple_0 D)) &  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ((r2_hidden E (k1_relset_1 A D)) &  (C = (k1_funct_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((r2_relset_1 C B F (k1_partfun1 C A A B D E)) <=>  ( (! [G:$i] :  ((m1_subset_1 G C) =>  ((r2_hidden G (k1_relset_1 C F)) <=>  ((r2_hidden G (k1_relset_1 C D)) & (r2_hidden (k7_partfun1 A D G) (k1_relset_1 A E))) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G C) =>  ((r2_hidden G (k1_relset_1 C F)) =>  ((k7_partfun1 B F G) = (k7_partfun1 B E (k7_partfun1 A D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_partfun3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k1_relset_1 A (k3_rfunct_1 A k1_numbers B C)) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) ) ) ) ) ) ) ).
tt(t3_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( ((r1_setfam_1 C B) & (r1_setfam_1 B C))  => (r1_tarski C B)) ) ) ) ) ) ) ).
tt(t3_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r1_relset_1 A A B (k1_eqrel_1 A))) ) ) ) ).
tt(t3_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_diraf A B C B D) &  ( (~  (B = C) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_diraf A B E B F) & (r2_diraf A E C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(t3_pcomps_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_setfam_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden C D) & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_pcomps_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v8_pre_topc A) &  ((v2_pcomps_1 A) &  ((m1_setfam_1 B (u1_struct_0 A)) &  ((v1_tops_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_tops_2 C A) &  ((m1_setfam_1 C (u1_struct_0 A)) &  ((r1_setfam_1 (k1_pcomps_1 A C) B) & (v1_pcomps_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((l1_pcs_0 B) =>  ( ( ((g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A)) = (g1_pcs_0 (u1_struct_0 B) (u1_pcs_0 B)))  & (v4_pcs_0 A))  => (v4_pcs_0 B)) ) ) ) ) ).
tt(t3_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers (k1_euclid 1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 1))))) )  =>  ( (A = (k2_funct_1 (k1_pdiff_1 1 1)))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (B = (k3_funct_2 k1_numbers (k1_euclid 1) A C))  =>  ((k1_normsp_0 (k4_real_ns1 1) B) = (k18_complex1 C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (B = (k3_funct_2 k1_numbers (k1_euclid 1) A D))  &  (C = (k3_funct_2 k1_numbers (k1_euclid 1) A E)) )  =>  ((k3_rlvect_1 (k4_real_ns1 1) B C) = (k3_funct_2 k1_numbers (k1_euclid 1) A (k7_real_1 D E))) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k3_funct_2 k1_numbers (k1_euclid 1) A C))  =>  ((k1_rlvect_1 (k4_real_ns1 1) B D) = (k3_funct_2 k1_numbers (k1_euclid 1) A (k8_real_1 D C))) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (B = (k3_funct_2 k1_numbers (k1_euclid 1) A C))  =>  ((k4_algstr_0 (k4_real_ns1 1) B) = (k3_funct_2 k1_numbers (k1_euclid 1) A (k1_real_1 C))) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (B = (k3_funct_2 k1_numbers (k1_euclid 1) A D))  &  (C = (k3_funct_2 k1_numbers (k1_euclid 1) A E)) )  =>  ((k5_algstr_0 (k4_real_ns1 1) B C) = (k3_funct_2 k1_numbers (k1_euclid 1) A (k9_real_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r3_pdiff_1 2 1 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 1 D C) A)) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r3_pdiff_3 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 1 (k1_pdiff_3 2 2 D) C) A)) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_4,ax, ( ((k1_relset_1 (k1_euclid 3) (k1_pdiff_1 3 3)) = (k1_euclid 3))  &  ( ((k1_rvsum_1 (k1_pdiff_1 3 3)) = k1_numbers)  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_seq_1 (k1_pdiff_1 3 3) (k11_finseq_1 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r3_pdiff_5 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 3 (k1_pdiff_3 1 3 E) D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid B) (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 B))) =>  ( ( (C = D)  &  ( (E = F)  & (r1_pdiff_1 B A C E)) )  =>  ((k8_pdiff_1 B A C E) = (k3_ndiff_1 (k4_real_ns1 B) (k4_real_ns1 A) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_rfinseq k1_numbers B (k5_euclid A)) = (k5_euclid (k7_nat_d A B))) ) ) ) ) ).
tt(t3_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C A) B)) (k1_normsp_0 (k4_real_ns1 A) B))) ) ) ) ) ) ) ).
tt(t3_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((k1_relset_1 (k1_euclid A) (k3_pdiff_1 A B)) = (k1_relset_1 (k1_euclid A) B)) ) ) ) ) ).
tt(t3_pencil_1,ax, (! [A:$i] :  ((r1_ordinal1 2 (k1_card_1 A)) =>  (! [B:$i] :  (? [C:$i] :  ((r2_hidden C A) &  (~  (B = C) ) ) ) ) ) ) ).
tt(t3_pencil_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 B)) &  ((k3_finseq_1 (k1_pencil_2 A B C D)) = k1_xboole_0) ) )  =>  ( (C = 1)  &  (D = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_pencil_3,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v6_pencil_1 A) & (l1_pre_topc A)) )  =>  ((v10_pencil_1 A) => (v8_pencil_1 A)) ) ) ).
tt(t3_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A (k2_vectsp_4 A B)) => (m1_vectsp_4 C A B)) ) ) ) ) ) ).
tt(t3_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A (k3_xcmplx_0 C B)) & (r1_int_2 C A))  => (r1_nat_d A B)) ) ) ) ) ) ) ).
tt(t3_petri_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C A)))) )  =>  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F E A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 E A)))) )  =>  ( ((r1_tarski C B) &  ((r1_tarski E B) &  ((k1_petri_2 A B C D) = (k1_petri_2 A B E F)) ) )  =>  ( (C = E)  & (r1_funct_2 C A E A D F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_petri A B) = (a_2_3_petri A B)) ) ) ) ) ).
tt(t3_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ( (C = (k1_tarski (k4_tarski A B)))  =>  ((k15_finseq_1 C) = (k9_finseq_1 B)) ) ) ) ) ) ) ).
tt(t3_polyalg1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  ((k2_rfinseq A 1 B) = (k1_polynom3 A 1 B)) ) ) ) ) ).
tt(t3_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ((k1_polyeq_1 k6_numbers A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t3_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( (E = (k2_xcmplx_0 D (k13_complex1 1 D)))  &  ((k1_polyeq_2 A B C B A D) = k6_numbers) )  =>  ( (A = k6_numbers)  |  ((r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)) (k3_xcmplx_0 8 (k3_square_1 A))) k6_numbers) |  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  ( ( (F = (k13_complex1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)) (k3_xcmplx_0 8 (k3_square_1 A))))) (k3_xcmplx_0 2 A)))  &  (G = (k13_complex1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 B) (k3_xcmplx_0 (k3_xcmplx_0 4 A) C)) (k3_xcmplx_0 8 (k3_square_1 A))))) (k3_xcmplx_0 2 A))) )  =>  ( (~  (D = k6_numbers) )  &  (~  ( (~  (D = (k13_complex1 (k2_xcmplx_0 F (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 F) 1))) 2)) )  &  ( (~  (D = (k13_complex1 (k2_xcmplx_0 G (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 G) 1))) 2)) )  &  ( (~  (D = (k13_complex1 (k6_xcmplx_0 F (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 F) 1))) 2)) )  &  (~  (D = (k13_complex1 (k6_xcmplx_0 G (k6_square_1 (k1_quin_1 1 (k4_xcmplx_0 G) 1))) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((k2_polyeq_3 k6_numbers A B D) = k6_numbers) ) )  =>  ( (A = k6_numbers)  |  (C = (k7_binop_2 (k12_binop_2 B A))) ) ) ) ) ) ) ) ) ).
tt(t3_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 A B)))  &  ( (~  ( (~ (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 C) (k7_square_1 (k2_quin_1 B C A))) (k3_xcmplx_0 2 B)) k6_numbers))  &  (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 C) (k7_square_1 (k2_quin_1 B C A))) (k3_xcmplx_0 2 B)))) ) )  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k7_xcmplx_0 (k2_xcmplx_0 (k4_xcmplx_0 C) (k7_square_1 (k2_quin_1 B C A))) (k3_xcmplx_0 2 B))))  &  (~ (r1_xxreal_0 (k7_xcmplx_0 (k6_xcmplx_0 (k4_xcmplx_0 C) (k7_square_1 (k2_quin_1 B C A))) (k3_xcmplx_0 2 B)) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 A A) A) A) = (k1_newton A 4)) ) ) ).
tt(t3_polyform,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((r1_xxreal_0 1 A) => (v7_ordinal1 A)) ) ) ).
tt(t3_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))) =>  ((k6_matrlin A (k2_pre_poly (k3_finseq_2 (u1_struct_0 A)))) = (k2_pre_poly (u1_struct_0 A))) ) ) ) ) ).
tt(t3_polynom2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 B)) =>  ( (D = C)  |  ((k7_partfun1 (u1_struct_0 A) B D) = (k4_struct_0 A)) ) ) ) ) )  =>  ((k4_rlvect_1 A B) = (k7_partfun1 (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ).
tt(t3_polynom3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k18_rvsum_1 A) = (k18_rvsum_1 (k4_finseq_5 k1_numbers A))) ) ) ).
tt(t3_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((k1_algseq_1 A (k9_polynom3 A)) = k6_numbers) ) ) ).
tt(t3_polynom5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_xxreal_0 B (k3_xcmplx_0 C A))) ) ) ) ) )  => (r1_xxreal_0 B k6_numbers)) ) ) ) ) ).
tt(t3_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  ( (B = k1_xboole_0)  =>  ((k1_polynom6 A B C D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t3_polynom7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k1_xboole_0) &  ((v1_funct_1 A) &  ((v1_partfun1 A k1_xboole_0) &  ((v4_valued_0 A) & (v2_pre_poly A)) ) ) ) )  =>  (A = (k16_pre_poly k1_xboole_0)) ) ) ).
tt(t3_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (C = (k3_vectsp_1 A (k8_group_1 A C B) B)) ) ) ) ) ) ) ) ).
tt(t3_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  =>  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B (k5_vfunct_1 (k15_pre_poly A) B C) C) (k7_polynom1 A B)) & (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k4_polynom1 A B C (k5_vfunct_1 (k15_pre_poly A) B C)) (k7_polynom1 A B))) ) ) ) ) ) ).
tt(t3_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( (~ (v1_xboole_0 (k1_poset_1 A B (k3_yellow_0 A))))  &  ((v6_orders_2 (k1_poset_1 A B (k3_yellow_0 A)) A) & (m1_subset_1 (k1_poset_1 A B (k3_yellow_0 A)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t3_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) | (v1_abian B))  => (r1_xxreal_0 k6_numbers (k1_newton A B))) ) ) ) ) ).
tt(t3_pralg_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (v2_funct_1 (k6_pralg_1 A B))) ) ) ) ).
tt(t3_pralg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k3_msualg_1 A C B) = (k4_card_3 (k3_relat_1 (k1_msualg_1 A C) (u3_msualg_1 A B))))  &  ( ((k9_xtuple_0 (k3_relat_1 (k1_msualg_1 A C) (u3_msualg_1 A B))) = (k9_xtuple_0 (k1_msualg_1 A C)))  &  ((k4_msualg_1 A C B) = (k1_funct_1 (u3_msualg_1 A B) (k2_msualg_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t3_pralg_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_partfun1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 B) (k8_eqrel_1 B C)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 B) (k8_eqrel_1 B C)) =>  ( ((r2_hidden A D) & (r2_hidden A E))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pre_circ,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (~ (v1_xboole_0 (k3_tarski (k10_xtuple_0 B)))) ) ) ) ) ).
tt(t3_pre_ff,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( ((k5_int_1 A B) = k6_numbers)  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t3_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (~  ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = k6_numbers)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k6_prelamb A (k12_finseq_1 (u1_struct_0 A) D) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 A)) =>  ((k5_pre_poly A (k8_finseq_1 (k3_finseq_2 A) B C)) = (k1_pre_poly A (k5_pre_poly A B) (k5_pre_poly A C))) ) ) ) ) ) ).
tt(t3_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k1_prepower A))  <=>  ( ((k1_seq_1 B k6_numbers) = 1)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_seq_1 B (k2_nat_1 C 1)) = (k8_real_1 (k1_seq_1 B C) A)) ) ) ) ) ) ) ) ) ).
tt(t3_pre_topc,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) = B) ) ) ) ) ).
tt(t3_prgcor_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 B (k4_nat_d A (k4_nat_1 2 B))) =>  ((r1_xxreal_0 B k6_numbers) |  ((k3_nat_d A B) = (k2_nat_1 (k4_nat_1 (k3_nat_d A (k4_nat_1 2 B)) 2) 1)) ) ) ) ) ) ) ).
tt(t3_prgcor_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ( ((k1_seq_1 B k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  =>  ((k1_seq_1 B (k1_nat_1 C 1)) = (k7_real_1 (k1_seq_1 B C) (k1_seq_1 A (k1_nat_1 C 1)))) ) ) ) )  =>  ((k18_rvsum_1 A) = (k1_seq_1 B (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t3_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k2_xboole_0 C D) B)) ) ) ) ) ) ).
tt(t3_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (? [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_prob_2 A B E F) = (k5_prob_1 A B (k1_prob_2 A B C F) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_prob_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (? [C:$i] :  ((v7_ordinal1 C) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((k1_funct_1 B D) = A) ) ) ) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = A) ) ) ) ) ) ) ).
tt(t3_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) => (v1_prob_2 (k13_funct_7 B C k1_xboole_0))) ) ) ) ) ) ).
tt(t3_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k9_cqc_lang A B C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t3_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B C E) &  ( (~  (B = E) )  & (r1_collsp A B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ((v1_projpl_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((r2_projpl_1 A B D E) &  ((r2_projpl_1 A C D E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A D B) &  ( (~ (r1_incsp_1 A D C))  &  ((r1_incsp_1 A E C) &  (~ (r1_incsp_1 A E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B D))  &  ( (~ (r1_incsp_1 A B E))  &  ((r1_incsp_1 A C E) &  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (~  ((r1_incsp_1 A F D) &  ((k1_funct_1 (k1_projred1 A D E B) F) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((r3_binop_1 (u1_struct_0 A) (k4_struct_0 A) (u1_algstr_0 A)) & (r1_finseqop (u1_struct_0 A) (k5_vectsp_1 A) (u1_algstr_0 A))) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) ) ) ) ) ).
tt(t3_prvect_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k1_seq_1 A B) = k6_numbers) ) ) )  =>  ((k18_rvsum_1 A) = k6_numbers) ) ) ) ).
tt(t3_prvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ( ((k9_xtuple_0 C) = (k7_domain_1 k5_numbers 1 2))  &  ( ((k1_funct_1 C 1) = A)  &  ( ((k1_funct_1 C 2) = B)  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) (k4_card_3 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k4_card_3 C))))) )  =>  (~  ((v2_funct_1 D) &  ((v2_funct_2 D (k4_card_3 C)) &  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden E A) & (r2_hidden F B))  =>  ((k1_binop_1 D E F) = (k10_finseq_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_pscomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers)))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_xxreal_0 A (k1_seq_1 C D))) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) => (r1_xxreal_0 D (k1_seq_1 C E))) )  => (r1_xxreal_0 D A)) ) ) )  =>  (A = (k1_pscomp_1 B C)) ) ) ) ) ) ) ) ).
tt(t3_pythtrip,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((v1_abian A) =>  ((k4_nat_d (k1_pepin A) 4) = k6_numbers) ) ) ) ).
tt(t3_pzfmisc1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (~  ((v3_relat_1 B) & (v2_relat_1 B)) ) ) ) ) ) ).
tt(t3_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((r1_tarski k5_numbers (k1_qc_lang1 A)) & (r2_hidden k6_numbers (k1_qc_lang1 A))) ) ) ).
tt(t3_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  (B = (k14_qc_lang1 A (k19_qc_lang1 A B) (k20_qc_lang1 A B))) ) ) ) ) ) ).
tt(t3_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k24_qc_lang1 A (k12_qc_lang1 A)) = k1_xboole_0) ) ) ).
tt(t3_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( ((r2_hidden B (k4_finseq_1 (k1_qc_lang4 A C))) &  (D = (k1_funct_1 (k1_qc_lang4 A C) B)) )  => (r1_qc_lang2 A D C)) ) ) ) ) ) ) ) ) ).
tt(t3_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) => (r3_qmax_1 A B B)) ) ) ) ).
tt(t3_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_quantal1 B A) & (v1_xboole_0 B)) ) ) ) ) ) ).
tt(t3_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k26_quaterni A k1_quatern2) = A) ) ) ).
tt(t3_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((m1_subset_1 A k1_numbers) =>  ((k29_quaterni A B) = (k6_quaterni (k9_real_1 (k17_quaterni A) (k17_quaterni B)) (k1_real_1 (k18_quaterni B)) (k1_real_1 (k19_quaterni B)) (k1_real_1 (k20_quaterni B)))) ) ) ) ) ) ).
tt(t3_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((r2_zfmisc_1 A B C D) =>  ( ((k1_funct_1 (k2_quaterni A B C D E F G H) A) = E)  &  ( ((k1_funct_1 (k2_quaterni A B C D E F G H) B) = F)  &  ( ((k1_funct_1 (k2_quaterni A B C D E F G H) C) = G)  &  ((k1_funct_1 (k2_quaterni A B C D E F G H) D) = H) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 k6_numbers (k1_quin_1 A B C)))  & (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((k2_quofield A B (k2_quofield A C D)) = (k2_quofield A (k2_quofield A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t3_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  (A = k6_numbers) )  =>  ((k4_nat_d (k4_nat_d B (k3_xcmplx_0 A C)) C) = (k4_nat_d B C)) ) ) ) ) ) ) ) ).
tt(t3_radix_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k6_int_1 (k3_xcmplx_0 A B) C) = (k6_int_1 (k3_xcmplx_0 A (k6_int_1 B C)) C)) ) ) ) ) ) ) ) ).
tt(t3_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k1_radix_3 A) (k1_radix_3 (k2_xcmplx_0 A 1)))) ) ).
tt(t3_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 2 A) =>  ((k7_radix_3 (k2_xcmplx_0 C 1) A (k2_xcmplx_0 C 1) (k10_radix_3 C A (k10_radix_1 A C B))) = (k5_radix_3 (k4_radix_1 C A C (k10_radix_1 A C B)) A)) ) ) ) ) ) ) ) ).
tt(t3_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 4 (k1_radix_1 A))) ) ) ).
tt(t3_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 2 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  => (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B C) (k8_radix_1 (k2_xcmplx_0 A 2) B (k4_radix_6 A B C)))) ) ) ) ) ) ) ).
tt(t3_ramsey_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~ (v1_finset_1 A))  & (v1_finset_1 (k2_xboole_0 A B))) ) ) ) ).
tt(t3_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_mesfunc5 A B C D) &  ((r1_tarski E (k1_relset_1 A D)) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G E) => (r1_xxreal_0 (k12_supinf_2 D G) F)) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C E)) | (r1_xxreal_0 (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers D E)) (k1_extreal1 (k1_measure6 F) (k12_supinf_2 C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_funcop_1 k5_numbers A 1) = (k3_mesfunc2 A A)) ) ) ).
tt(t3_ranknull,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~ (r1_xboole_0 B C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) )  &  (~  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) & (r2_hidden D C)) ) )  & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t3_rat_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (v1_rat_1 (k7_xcmplx_0 A B))) ) ) ) ).
tt(t3_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k3_group_4 A B) = (k8_group_1 A (k7_partfun1 (u1_struct_0 A) B C) (k3_group_4 A (k1_polynom3 (u1_struct_0 A) C B)))) ) ) ) ) ) ) ) ).
tt(t3_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden A (k2_rcomp_1 B C)) <=>  (~ (r1_xxreal_0 (k6_xcmplx_0 C B) (k18_complex1 (k5_real_1 (k2_xcmplx_0 B C) (k8_real_1 2 A))))) ) ) ) ) ) ) ) ).
tt(t3_rcomp_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((k6_measure6 (k4_subset_1 k1_numbers A B)) = (k4_subset_1 k1_numbers (k6_measure6 A) (k6_measure6 B))) ) ) ) ) ).
tt(t3_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_int_1 (k13_complex1 A B)) = (k3_nat_d A B)) ) ) ) ) ).
tt(t3_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (v3_xxreal_0 A))  & (v3_xxreal_0 B)) ) ) ) ) ) ) ).
tt(t3_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_real_lat)) =>  ( ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat B C) A))  &  ( ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat A B) C))  &  ( ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat B A) C))  &  ( ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat C A) B))  &  ( ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat C B) A))  &  ((k1_binop_1 k2_real_lat A (k1_binop_1 k2_real_lat B C)) = (k1_binop_1 k2_real_lat (k1_binop_1 k2_real_lat A C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (B = C)  =>  ((k1_rlvect_1 (k4_real_ns1 A) B D) = (k9_euclid A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_realset1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  <=>  (! [B:$i] :  (~ (v1_xboole_0 (k6_subset_1 A (k1_tarski B)))) ) ) ) ).
tt(t3_realset2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( ((k3_rlvect_1 A B C) = (k4_struct_0 A))  &  ((k3_rlvect_1 A C B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t3_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k1_funct_1 (k5_realset2 A) (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B C)) = (k1_binop_1 (k4_realset2 A) (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) B) (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) C))) ) ) ) ) ) ) ).
tt(t3_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_rearran1 B) &  ((v3_rearran1 B (k1_zfmisc_1 A)) & (m2_finseq_1 B (k1_zfmisc_1 A))) )  =>  ((k1_funct_1 B (k3_finseq_1 B)) = A) ) ) ) ) ).
tt(t3_recdef_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (k3_zfmisc_1 B C D)) =>  (A = (k3_xtuple_0 (k4_xtuple_0 A) (k5_xtuple_0 A) (k2_xtuple_0 A))) ) ) ) ) ) ).
tt(t3_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k6_subset_1 (k9_xtuple_0 A) (k9_xtuple_0 B)) (k9_xtuple_0 (k6_subset_1 A B)))) ) ) ) ).
tt(t3_relat_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r4_relat_2 B A) <=> (r5_relat_2 (k4_xboole_0 B (k4_relat_1 A)) A)) ) ) ) ).
tt(t3_reloc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_ami_3)))  =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) (k9_ami_3 B C) A) = (k9_ami_3 (k2_xcmplx_0 B A) C)) ) ) ) ) ) ) ).
tt(t3_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden A B) & (r2_hidden C D))  => (m1_subset_1 (k1_tarski (k4_tarski A C)) (k1_zfmisc_1 (k2_zfmisc_1 B D)))) ) ) ) ) ).
tt(t3_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((k10_eqrel_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k10_eqrel_1 A) (k10_eqrel_1 B))) ) ) ).
tt(t3_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  => (r2_hidden (k7_partfun1 A B (k3_finseq_1 B)) (k10_xtuple_0 B))) ) ) ) ).
tt(t3_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  (! [D:$i] :  ((k1_rewrite1 (k7_finseq_1 A (k9_finseq_1 C)) (k7_finseq_1 (k9_finseq_1 D) B)) = (k7_finseq_1 (k7_finseq_1 A (k9_finseq_1 D)) B)) ) ) ) ) ) ) ).
tt(t3_rewrite2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((m1_rewrite1 C B) =>  ((r1_xxreal_0 1 A) => (m1_rewrite1 (k16_finseq_1 A C) B)) ) ) ) ) ) ) ).
tt(t3_rewrite3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((r2_hidden (k2_xcmplx_0 A 1) (k4_finseq_1 B)) |  ((k3_finseq_1 B) = A) ) ) ) ) ) ) ).
tt(t3_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (k12_finseq_1 k1_numbers B))  =>  ( ((k1_rfinseq2 A) = 1)  &  ((k3_rfinseq2 A) = B) ) ) ) ) ) ) ).
tt(t3_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_classes1 A B) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k4_finseq_1 A) = (k4_finseq_1 B)) ) ) ) ) ) ) ).
tt(t3_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (~  ((r2_hidden B (k9_xtuple_0 (k4_rfunct_1 C))) &  ((k1_funct_1 C B) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t3_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  => (r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers C (k26_valued_1 k5_numbers k1_numbers B A)) (k26_valued_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers C B) A))) ) ) ) ) ) ).
tt(t3_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k8_real_1 2 (k1_rfunct_3 A)) = (k3_real_1 A (k18_complex1 A))) ) ) ).
tt(t3_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ( ( ((k18_rvsum_1 B) = k6_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t3_rinfsup1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_hidden A (k2_relset_1 k1_numbers B)) <=> (r2_hidden (k4_xcmplx_0 A) (k2_relset_1 k1_numbers (k32_valued_1 k5_numbers k1_numbers B)))) ) ) ) ) ).
tt(t3_rinfsup2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ( (A = B)  & (v3_xxreal_2 B))  =>  ((v3_xxreal_2 A) &  ((k7_supinf_2 A) = (k5_seq_4 B)) ) ) ) ) ) ) ).
tt(t3_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_algstr_0 A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) = (k5_algstr_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(t3_ringcat1,ax, (! [A:$i] :  ( ((v2_ringcat1 A) &  ((v3_ringcat1 A) & (l1_ringcat1 A)) )  =>  ((m1_ringcat1 A (k1_ringcat1 A) (k2_ringcat1 A)) & (r1_ringcat1 (k1_ringcat1 A) (k2_ringcat1 A))) ) ) ).
tt(t3_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_convex1 A B) (k3_convex1 A C))) ) ) ) ) ) ) ).
tt(t3_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m2_rlvect_2 D A B) =>  ( ((r1_tarski B (k3_convex1 A C)) &  ((k3_rlaffin1 A D) = 1) )  =>  ((r2_hidden (k6_rlvect_2 A D) (k4_rlaffin1 A C)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m2_finseq_1 F k1_numbers) &  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) &  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers (k5_rlaffin1 A C (k6_rlvect_2 A D)) E) = (k18_rvsum_1 F))  &  ( ((k3_finseq_1 G) = (k3_finseq_1 F))  &  ((v2_funct_1 G) &  ( ((k2_relset_1 (u1_struct_0 A) G) = (k3_rlvect_2 A D))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 F)) =>  ((k1_funct_1 F H) = (k4_real_1 (k1_funct_1 D (k1_funct_1 G H)) (k3_funct_2 (u1_struct_0 A) k1_numbers (k5_rlaffin1 A C (k1_funct_1 G H)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((v1_rlvect_5 A) <=> (v1_rlvect_5 (k2_rlsub_1 A))) ) ) ).
tt(t3_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((r1_struct_0 (k2_rlsub_2 A B C) D) <=>  ((r1_struct_0 B D) & (r1_struct_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t3_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D B) & (r2_hidden E C))  => (r2_hidden (k1_algstr_0 A D E) (k6_rusub_4 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rlvect_1,ax, (! [A:$i] :  ( ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) )  => (v6_algstr_0 A)) ) ).
tt(t3_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 D E) = (k1_rlvect_1 A (k7_partfun1 (u1_struct_0 A) C E) B)) ) ) ) )  =>  ((k4_rlvect_1 A D) = (k1_rlvect_1 A (k4_rlvect_1 A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((k6_rlvect_2 A (k9_rlvect_2 A B)) = (k4_algstr_0 A (k6_rlvect_2 A B))) ) ) ) ) ).
tt(t3_rlvect_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k4_algstr_0 B (k1_rlvect_1 B C A)) = (k1_rlvect_1 B C (k1_real_1 A))) ) ) ) ) ) ) ).
tt(t3_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k3_rlvect_2 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (C = D)  &  (~  ((k3_funct_2 (u1_struct_0 A) k1_numbers B D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_relset_1 k5_numbers (u1_struct_0 A) C (k4_vfunct_1 k5_numbers A B D)) =>  ((k4_rlvect_1 A C) = (k1_rlvect_1 A (k4_rlvect_1 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k5_algstr_0 B D E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((r1_struct_0 (k2_rmod_3 A B C D) E) <=>  ((r1_struct_0 C E) & (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k5_vectsp_2 A B C (k4_rlvect_1 B (k2_finseq_4 (u1_struct_0 B) D E))) = (k3_rlvect_1 B (k5_vectsp_2 A B C D) (k5_vectsp_2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A B)) = B) ) ) ) ) ).
tt(t3_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B (k3_robbins1 A B))) B)) = (k3_robbins1 A B)) ) ) ) ) ).
tt(t3_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((v2_robbins3 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v9_lattices A)) ) )  => (v8_lattices A)) ) ) ).
tt(t3_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_robbins1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_lattices A (k1_lattices A B C) D) = (k1_lattices A (k3_robbins1 A (k2_lattices A (k3_robbins1 A D) (k3_robbins1 A C))) B)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k2_lattices A B (k1_lattices A B C))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k1_lattices A B (k2_lattices A C (k3_robbins1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k2_rcomp_1 A B)) &  ((k1_fdiff_1 C D) = (k10_real_1 (k9_real_1 (k1_seq_1 C B) (k1_seq_1 C A)) (k9_real_1 B A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_roughs_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (r1_relset_1 A A (k6_partfun1 A) B)) ) ) ).
tt(t3_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v3_card_1 D 1) & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (~  ( (D = (k4_subset_1 A B C))  &  ( (~  ( (B = D)  &  (C = D) ) )  &  ( (~  ( (B = D)  &  (C = k1_xboole_0) ) )  &  (~  ( (B = k1_xboole_0)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rsspace2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k3_series_1 A) B))) )  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k1_seq_1 (k3_series_1 A) B))) )  &  ((v1_series_1 A) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k4_series_1 A))) )  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A B) (k4_series_1 A))) ) ) ) ) ) ) ) ) ).
tt(t3_rsspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = k6_numbers) ) )  =>  ((v2_series_1 A) &  ((k4_series_1 (k56_valued_1 k5_numbers k1_numbers A)) = k6_numbers) ) ) ) ) ).
tt(t3_rsspace4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_rsspace4)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_rsspace4)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ( ((k1_normsp_0 k3_rsspace4 A) = k6_numbers)  =>  (A = (k4_struct_0 k3_rsspace4)) )  &  ( ( (A = (k4_struct_0 k3_rsspace4))  =>  ((k1_normsp_0 k3_rsspace4 A) = k6_numbers) )  &  ((r1_xxreal_0 k6_numbers (k1_normsp_0 k3_rsspace4 A)) &  ((r1_xxreal_0 (k1_normsp_0 k3_rsspace4 (k1_algstr_0 k3_rsspace4 A B)) (k7_real_1 (k1_normsp_0 k3_rsspace4 A) (k1_normsp_0 k3_rsspace4 B))) &  ((k1_normsp_0 k3_rsspace4 (k1_rlvect_1 k3_rsspace4 A C)) = (k8_real_1 (k18_complex1 C) (k1_normsp_0 k3_rsspace4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  ((k1_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) B A) = (k26_valued_1 k5_numbers k1_numbers (k2_rsspace B) A)) ) ) ) ) ).
tt(t3_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t3_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((r1_struct_0 (k2_rusub_2 A B C) D) <=>  ((r1_struct_0 B D) & (r1_struct_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t3_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((k1_rusub_3 A (k1_subset_1 (u1_struct_0 A))) = (k1_rusub_1 A)) ) ) ).
tt(t3_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v1_rusub_4 A) =>  (! [B:$i] :  ((m1_rusub_3 B A) => (v1_finset_1 B)) ) ) ) ) ).
tt(t3_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v2_rusub_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r1_rusub_5 A B C) & (r1_rusub_5 A C D))  => (r1_rusub_5 A B D)) ) ) ) ) ) ) ) ) ).
tt(t3_rvsum_1,ax,(r6_binop_1 k1_numbers k35_binop_2 k33_binop_2)).
tt(t3_rvsum_2,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C k2_numbers))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D k2_numbers))  =>  ((k1_funct_1 (k4_rvsum_2 B C D) A) = (k3_binop_2 (k1_funct_1 C A) (k1_funct_1 D A))) ) ) ) ) ) ) ) ).
tt(t3_scheme1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = (k4_nat_1 4 B)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 4 B) 1)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 4 B) 2)) )  &  (~  (A = (k2_nat_1 (k4_nat_1 4 B) 3)) ) ) ) ) ) ) ) ) ) ).
tt(t3_scm_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_ami_3)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski (k1_ordinal4 (k5_afinsq_1 A) (k5_afinsq_1 B)) C) =>  ( ((k3_compos_1 k1_ami_3 C k6_numbers) = A)  &  ((k3_compos_1 k1_ami_3 C 1) = B) ) ) ) ) ) ) ) ) ).
tt(t3_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k15_scmfsa_2 D C B) A) B) = (k2_funct_7 (k18_scmfsa_2 A B) (k18_complex1 (k1_funct_1 A C)) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t3_scm_comp,ax, (! [A:$i] :  ((m1_dtconstr A (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (~  ( (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  (~  (A = (k3_scm_comp B)) ) ) )  &  (! [B:$i] :  ((m1_dtconstr B (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ( (~  (A = (k5_scm_comp B C)) )  &  ( (~  (A = (k6_scm_comp B C)) )  &  ( (~  (A = (k7_scm_comp B C)) )  &  ( (~  (A = (k8_scm_comp B C)) )  &  (~  (A = (k9_scm_comp B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k7_scmfsa_2 A B) = (k3_xtuple_0 2 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(t3_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 (k1_funct_4 A (k7_memstr_0 3 k1_scmfsa_2 B)) C)) ) ) ) ) ) ) ).
tt(t3_scmfsa_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k13_scmfsa_2 B C) A) = (k13_scmfsa_2 (k2_nat_1 B A) C)) ) ) ) ) ) ) ).
tt(t3_scmfsa6a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r2_hidden (k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) (k9_domain_1 k5_numbers k6_numbers 6 7 8)) |  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 A B) (k4_struct_0 k1_scmfsa_2)) = (k1_ordinal1 (k5_memstr_0 3 k1_scmfsa_2 B))) ) ) ) ) ) ).
tt(t3_scmfsa6b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (r2_hidden D (k2_sf_mastr C)))  =>  ((k1_funct_1 (k1_scmfsa6b C A B) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmfsa_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_scmfsa_7 A k6_numbers) = (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 (k6_scmfsa_2 A (k4_scmfsa_2 k6_numbers))) (k5_afinsq_1 (k8_scmfsa_2 A (k4_scmfsa_2 k6_numbers)))) (k5_afinsq_1 (k2_compos_1 k1_scmfsa_2)))) ) ) ).
tt(t3_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa_7 C D) B A) C) = D)  &  ( (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (E = C) )  =>  ((k1_funct_1 (k1_scmfsa6b (k1_scmfsa_7 C D) B A) E) = (k1_funct_1 B E)) ) ) )  &  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k1_scmfsa_7 C D) B A) E) = (k18_scmfsa_2 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D))  & (r5_scmfsa7b E C A))  => (r5_scmfsa7b E D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b C B A) (k1_scmfsa6b C (k1_scmfsa_m B) A))) ) ) ) ) ) ).
tt(t3_scmfsa9a,ax, ((k2_sf_mastr (k4_compos_1 k1_scmfsa_2)) = k1_xboole_0) ).
tt(t3_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k1_scmfsa8b B (k4_compos_1 k1_scmfsa_2) (k2_scmfsa8b B (k4_compos_1 k1_scmfsa_2) (k3_scmfsa6a A (k1_scmfsa8a k6_numbers))))) = (k2_nat_1 (k5_card_1 A) 11)) ) ) ) ) ).
tt(t3_scmfsa_i,ax,(r2_hidden (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0) k2_scmfsa_i)).
tt(t3_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ((k9_xtuple_0 (k1_scmfsa_m A)) = (k2_xboole_0 (k2_xboole_0 (k9_xtuple_0 A) (k6_domain_1 (u1_struct_0 k1_scmfsa_2) (k4_scmfsa_2 k6_numbers))) (k6_domain_1 (u1_struct_0 k1_scmfsa_2) (k4_struct_0 k1_scmfsa_2)))) ) ) ).
tt(t3_scm_inst,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ((r2_hidden A (k7_domain_1 k5_numbers 7 8)) => (r2_hidden (k3_xtuple_0 A (k12_finseq_1 k5_numbers B) (k12_finseq_1 k2_scm_inst C)) k3_scm_inst)) ) ) ) ) ) ).
tt(t3_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmfsa_2)) =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmfsa_2)) =>  (~  ( (D = (k1_funct_1 A B))  &  ((k3_sf_mastr D) = (k3_sf_mastr C)) ) ) ) )  |  ((k4_sf_mastr A) = (k4_sf_mastr (k1_funct_4 A (k16_funcop_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t3_scmpds_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_ami_2 k2_ami_2) => (r2_hidden A (k2_xboole_0 k2_ami_2 k4_numbers))) ) ).
tt(t3_scmpds_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((k6_memstr_0 2 k1_scmpds_2 B) = (k6_memstr_0 2 k1_scmpds_2 C))  =>  ((k1_funct_1 B A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t3_scmpds_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~  (A = B) )  &  ((k2_scmpds_2 A k6_numbers) = (k2_scmpds_2 B k6_numbers)) ) ) ) ) ) ) ).
tt(t3_scmpds_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r1_tarski (k61_valued_1 A (k5_card_1 B)) (k1_scmpds_4 (k1_scmpds_4 B A) C))) ) ) ) ) ) ).
tt(t3_scmpds_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ((r2_hidden (k2_compos_0 (u1_compos_1 k1_scmpds_2) B) (k10_domain_1 k5_numbers k6_numbers 4 5 6 14)) =>  ((k8_memstr_0 2 k1_scmpds_2 A) = (k8_memstr_0 2 k1_scmpds_2 (k2_extpro_1 2 k1_scmpds_2 B A))) ) ) ) ) ) ).
tt(t3_scmpds_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_amistd_1 2 k1_scmpds_2 A (k3_scmpds_2 B)) = (k1_tarski (k1_int_2 (k2_xcmplx_0 B A)))) ) ) ) ) ).
tt(t3_scmpds_i,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 15)) =>  (! [B:$i] :  ((m1_subset_1 B k1_scmpds_i) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ( (B = (k3_xtuple_0 A k1_xboole_0 (k12_finseq_1 k2_scm_inst C)))  =>  ((k3_scmpds_i B) = C) ) ) ) ) ) ) ) ).
tt(t3_scmp_gcd,ax, (~  (k2_scmp_gcd = k3_scmp_gcd) ) ).
tt(t3_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_ami_2) =>  ((r2_hidden B k2_ami_2) =>  ((k1_funct_1 (k3_relat_1 k3_ami_2 (k1_scmring1 A)) B) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t3_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 C))))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 (k1_scmring2 C))))  =>  ((r2_hidden B (k9_domain_1 k5_numbers 1 2 3 4)) => (r2_hidden (k3_xtuple_0 B k1_xboole_0 (k10_finseq_1 D E)) (k1_scmringi A))) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_scmring2 A))) =>  ( (B = (k4_struct_0 (k1_scmring2 A)))  |  ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A)))) ) ) ) ) ) ).
tt(t3_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~  (B = C) )  &  ((k2_scmring3 A B) = (k2_scmring3 A C)) ) ) ) ) ) ) ) ) ).
tt(t3_scmringi,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 8)) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_scmringi B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_scm_inst) =>  ( (C = (k3_xtuple_0 A (k12_finseq_1 k5_numbers D) (k12_finseq_1 k2_scm_inst E)))  =>  ( ((k5_scmringi B C) = D)  &  ((k6_scmringi B C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (~  ((k4_tarski A B) = A) ) ) ) ).
tt(t3_scpinvar,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_xxreal_0 k6_numbers (k1_funct_1 C A)) =>  ((k1_funct_1 B C) = k6_numbers) )  &  ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 C A)))  =>  ((k1_funct_1 B C) = (k4_xcmplx_0 (k1_funct_1 C A))) ) ) ) ) ) ) ) ) ).
tt(t3_scpisort,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_funct_1 A C) = (k1_funct_1 B D))  &  ( ((k1_funct_1 A D) = (k1_funct_1 B C))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 A)))  =>  ( (E = C)  |  ( (E = D)  |  ((k1_funct_1 A E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_classes1 A B)) ) ) ) ) ) ) ) ) ).
tt(t3_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 D 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((k6_memstr_0 2 k1_scmpds_2 D) = (k6_memstr_0 2 k1_scmpds_2 B))  => (r2_scmpds_6 C D E)) ) ) ) )  => (r1_scmpds_6 C B A)) ) ) ) ) ) ) ).
tt(t3_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B B C D)) ) ) ) ) ) ) ) ).
tt(t3_seq_1,ax, (! [A:$i] :  ( ((v2_relat_1 A) &  ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r1_tarski (k2_relset_1 k1_numbers A) (k6_subset_1 k1_numbers (k1_tarski k6_numbers)))) ) ).
tt(t3_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 B (k18_complex1 (k1_seq_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(t3_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 B A)) ) ) ) ) ).
tt(t3_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) B (k7_seqfunc A C D)) <=>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r2_relset_1 A k1_numbers (k1_seqfunc A k1_numbers B E) (k47_valued_1 A k1_numbers k1_numbers (k1_seqfunc A k1_numbers C E) (k1_seqfunc A k1_numbers D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 (k2_nat_1 B 1) C)))) ) ) ) ) ) ) ) ).
tt(t3_series_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers B C) = (k3_power A (k2_nat_1 C 1))) ) )  =>  ((r1_xxreal_0 1 (k18_complex1 A)) |  ((v2_comseq_2 B) &  ((k2_seq_2 B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t3_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = B) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_complex1 (k4_nat_1 B (k2_nat_1 B 1)) 2)) ) ) ) ) ) ).
tt(t3_series_3,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  => (r1_xxreal_0 2 (k8_complex1 (k13_complex1 A B) (k13_complex1 B A)))) ) ) ) ).
tt(t3_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_newton (k2_xcmplx_0 (k6_xcmplx_0 A B) C) 2) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k1_newton B 2)) (k1_newton C 2)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) C)) (k3_xcmplx_0 (k3_xcmplx_0 2 B) C))) ) ) ) ) ) ) ).
tt(t3_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k13_complex1 (k2_xcmplx_0 B C) (k2_xcmplx_0 A C)) 1)) ) ) ) ) ) ) ) ).
tt(t3_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (r1_tarski (k1_setfam_1 B) A)) ) ) ).
tt(t3_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden C (k3_funct_2 k5_numbers B D (k2_nat_1 A E)))) )  <=>  (! [E:$i] :  ((r2_hidden E (a_3_0_setlim_1 A B D)) => (r2_hidden C E)) ) ) ) ) ) ) ) ) ).
tt(t3_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k4_setlim_2 A B C) = (k2_setlim_2 A (k3_setlim_2 A B C) (k3_setlim_2 A C B))) ) ) ) ) ) ).
tt(t3_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 F B) & (v2_binop_1 F B))  =>  ( (C = D)  |  ( (C = E)  |  ( (D = E)  |  ((k7_setwiseo A B F (k4_setwiseo A C D E) G) = (k5_binop_1 B F (k5_binop_1 B F (k3_funct_2 A B G C) (k3_funct_2 A B G D)) (k3_funct_2 A B G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((r6_scmfsa7b C (k1_scmfsa_m B) A) &  ((r6_scmfsa7b D (k1_scmfsa6b C B A) A) &  ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b D (k1_scmfsa6b C B A) A)) ) )  => (r6_scmfsa7b (k3_scmfsa6a C D) (k1_scmfsa_m B) A)) ) ) ) ) ) ) ) ) ).
tt(t3_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (~  ( ( ((r5_scmfsa7b D (k1_scmfsa_m A) B) & (r6_scmfsa7b D (k1_scmfsa_m A) B))  | (v7_amistd_1 D 3 k1_scmfsa_2))  &  ( (~  ( (~  ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1) )  & (v1_scmfsa_m C)) )  &  ( (~ (r2_hidden C (k2_sf_mastr D)))  &  (~  ((k1_funct_1 (k1_scmfsa6b D A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r2_scmfsa7b (k4_compos_1 k1_scmfsa_2) A)) ) ) ).
tt(t3_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k8_scmfsa_2 A B) = (k8_scmfsa_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k1_sgraph1 1 A) = (k2_finseq_1 A)) ) ) ).
tt(t3_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v1_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattices A B (k3_sheffer1 A B)) = (k2_sheffer1 A)) ) ) ) ) ).
tt(t3_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C B) B)) (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A B D) D)))) = C) ) ) ) ) ) ) ) ) ).
tt(t3_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A B) & (v1_classes1 B))  => (r1_tarski (k1_simplex0 A) B)) ) ) ).
tt(t3_simplex1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_matroid0 B) & (m1_simplex0 B (u1_struct_0 A)))  =>  ((v6_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v3_pre_topc C B) => (m2_simplex0 (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_simplex1 A B C))) (u1_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t3_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B (k3_pcomps_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A))))))  =>  (! [C:$i] :  ((m1_simplex2 C A B) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ( ((v1_compts_1 (k3_pcomps_1 A)) &  ((m1_setfam_1 B (u1_struct_0 (k3_pcomps_1 A))) & (r1_xxreal_0 D C)) )  => (m1_simplex2 D A B)) ) ) ) ) ) ) ) ) ).
tt(t3_sincos10,ax,(r1_tarski (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers) (k1_relset_1 k1_numbers k2_fdiff_9))).
tt(t3_sin_cos2,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t3_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) = (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k1_binop_2 A))) ) ) ).
tt(t3_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_sin_cos4 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k2_sin_cos4 A))) ) ) ).
tt(t3_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  ( (~  ((k17_sin_cos C) = k6_numbers) )  &  (~  ((k17_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k4_real_1 (k3_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k17_sin_cos C)) (k9_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k2_sin_cos4 B) (k2_sin_cos4 C)) (k8_real_1 (k2_sin_cos4 A) (k2_sin_cos4 C))) (k8_real_1 (k2_sin_cos4 A) (k2_sin_cos4 B))) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 (k1_real_1 1) (k17_sin_cos A))) ) ).
tt(t3_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 1 (k5_square_1 (k12_binop_2 A (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)))))) ) ) ).
tt(t3_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k2_sin_cos5 A) 1) &  ( (~ (r1_xxreal_0 (k2_sin_cos5 A) k6_numbers))  &  ((k2_sin_cos5 k6_numbers) = 1) ) ) ) ) ).
tt(t3_sin_cos9,ax, ((r2_fdiff_1 k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) =>  ((k1_fdiff_1 k29_sin_cos A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos A)))) ) ) ) ) ).
tt(t3_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k8_nat_1 k2_numbers (k3_sin_cos B) (k2_nat_1 A 1)) = (k13_complex1 (k3_xcmplx_0 (k8_nat_1 k2_numbers (k3_sin_cos B) A) B) (k2_xcmplx_0 (k2_nat_1 A 1) (k3_xcmplx_0 k6_numbers k7_complex1))))  &  ( ((k8_nat_1 k2_numbers (k3_sin_cos B) k6_numbers) = 1)  &  ((k17_complex1 (k8_nat_1 k2_numbers (k3_sin_cos B) A)) = (k8_nat_1 k1_numbers (k4_sin_cos (k17_complex1 B)) A)) ) ) ) ) ) ) ).
tt(t3_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_euclid A)) => (r1_xxreal_0 (k9_real_1 (k12_euclid (k8_euclid A B C)) (k12_euclid (k8_euclid A C D))) (k12_euclid (k8_euclid A B D)))) ) ) ) ) ) ) ) ).
tt(t3_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k1_nat_1 B 1) (k3_finseq_1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A))) =>  ((k2_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) C A) B) = (k2_topreal1 2 A B)) ) ) ) ) ) ) ) ).
tt(t3_sprect_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_funct_1 (k11_finseq_1 A B C)) =>  ( (A = B)  &  ( (B = C)  &  (C = A) ) ) ) ) ) ) ).
tt(t3_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( ((r1_xxreal_0 A B) &  ((r2_hidden A (k4_finseq_1 E)) &  ((r2_hidden B (k4_finseq_1 E)) & (r2_hidden C (k4_finseq_1 (k3_finseq_6 D E A B)))) ) )  =>  ((k7_partfun1 D (k3_finseq_6 D E A B) C) = (k7_partfun1 D E (k7_nat_d (k2_nat_1 C A) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid A) C D)))  =>  ((r1_xxreal_0 D k1_xboole_0) |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sprect_4,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r2_hidden B (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A C (k3_finseq_1 A)))))  =>  ((r1_xxreal_0 (k3_finseq_1 A) C) | (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) B)) ) ) ) ) ) ) ) ).
tt(t3_sprect_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C (k10_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 B)) & (r1_xxreal_0 (k4_finseq_4 B C) (k4_finseq_4 B D))) )  =>  ((k4_finseq_4 (k1_finseq_5 A B D) C) = (k4_finseq_4 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t3_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_square_1 A) = (k3_square_1 (k4_xcmplx_0 A))) ) ) ).
tt(t3_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((k7_stacks_1 A B D) = (k7_stacks_1 A C E)) ) )  =>  ( (D = E)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) => (r1_xxreal_0 (k6_nat_1 (k5_nat_1 A) (k5_nat_1 B)) (k5_nat_1 (k4_subset_1 k5_numbers A B)))) ) ) ) ).
tt(t3_struct_0,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (~ (r2_hidden (k4_struct_0 A) (k8_struct_0 A))) ) ) ).
tt(t3_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k16_substut1 A) (k38_substut1 A)) =>  ((v2_substut1 B A) =>  ((k39_substut1 A B) = (k5_cqc_lang A)) ) ) ) ) ) ).
tt(t3_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D B) <=> (r2_hidden D C)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(t3_subset,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)) ) ) ).
tt(t3_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ((k4_substlat A B C D) = (k4_substlat A B D C)) ) ) ) ) ) ) ).
tt(t3_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) =>  ((k9_substut1 A B) = (k8_substut1 A (k17_qc_lang1 A B))) ) ) ) ) ) ).
tt(t3_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A D)) & (m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A E)))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  =>  ( ((k1_xxreal_2 A) = (k2_xxreal_2 (k3_supinf_1 A)))  &  ((k2_xxreal_2 A) = (k1_xxreal_2 (k4_supinf_1 A))) ) ) ) ).
tt(t3_supinf_2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k4_supinf_2 A B) = (k9_real_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t3_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ((r1_orders_2 B (k3_rlvect_1 B E C) D) & (r1_orders_2 B E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski C (k2_zfmisc_1 A B)) =>  ((r1_tarski (k9_xtuple_0 C) A) & (r1_tarski (k10_xtuple_0 C) B)) ) ) ) ) ) ).
tt(t3_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_t_0topsp A))) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_t_0topsp A) C)) ) ) ) ) ) ) ).
tt(t3_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_eqrel_1 (a_1_0_t_1topsp A) (u1_struct_0 A)) & (m1_subset_1 (a_1_0_t_1topsp A) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 (u1_struct_0 A)))))) ) ) ).
tt(t3_tarski,ax, (! [A:$i] :  (? [B:$i] :  ((r2_hidden A B) &  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r1_tarski D C))  => (r2_hidden D B)) ) )  &  ( (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  ((r1_tarski E C) => (r2_hidden E D)) ) ) ) ) ) ) )  &  (! [C:$i] :  (~  ((r1_tarski C B) &  ( (~ (r2_tarski C B))  &  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_taxonom1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) =>  ((k1_relset_1 A B) = A) ) ) ) ) ).
tt(t3_taylor_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 C B) =>  ((r1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k1_taylor_1 A)) B) &  ((k1_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k1_taylor_1 A)) B) = (k8_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 C B) (k5_real_1 A 1))) (k1_fdiff_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t3_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_tarski (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D)) (k9_xtuple_0 B)) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))))  =>  ((r1_xxreal_0 D k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  ( (~ (r1_xxreal_0 1 F))  &  ((k18_complex1 (k9_real_1 (k1_seq_1 B E) (k1_seq_1 (k3_series_1 (k6_taylor_1 B (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D)) C E)) A))) = (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 (k9_real_1 C D) (k7_real_1 C D))) (k2_nat_1 A 1)) (k7_real_1 C (k8_real_1 F (k9_real_1 E C)))) (k2_newton (k9_real_1 E C) (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_tbsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 B (k4_power A C))) ) ) ) ) ) ) ) ) ) ).
tt(t3_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  <=>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k3_rlvect_1 A C C) = B) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t3_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))) (k2_pre_topc A B))) ) ) ) ).
tt(t3_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc C A) &  ((k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) = B) )  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t3_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A (k3_subset_1 (u1_struct_0 A) B)) = (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A B))) ) ) ) ) ).
tt(t3_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v9_struct_0 E B))  & (m1_subset_1 E (u1_struct_0 B)))  =>  (! [F:$i] :  ( ( (~ (v9_struct_0 F B))  & (m1_subset_1 F (u1_struct_0 B)))  => (r8_pboole (k15_pre_poly A) (k1_polynom7 A B (k6_algstr_0 B E F) (k11_pre_poly A C D)) (k9_polynom1 A B (k1_polynom7 A B E C) (k1_polynom7 A B F D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_tmap_1 A (k3_subset_1 (u1_struct_0 A) B))))) =>  ( (C = B)  => (v4_pre_topc C (k6_tmap_1 A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(t3_tex_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (~  ((v1_subset_1 (k6_domain_1 A B) A) & (v1_zfmisc_1 A)) ) ) ) ) ) ).
tt(t3_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v2_tops_1 B A) <=> (v1_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t3_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k3_tarski (a_2_2_tex_4 A B))) ) ) ) ) ).
tt(t3_tietze,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ((r1_tarski A B) => (r1_tarski (k45_valued_1 A C) (k45_valued_1 B C))) ) ) ) ) ) ) ).
tt(t3_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ( ((k2_partfun1 C B E (k9_subset_1 A C D)) = (k2_partfun1 D B F (k9_subset_1 A C D)))  => (r1_funct_2 (k4_subset_1 A C D) B (k4_subset_1 A D C) B (k1_tmap_1 A B C D E F) (k1_tmap_1 A B D C F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_toler_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k1_relat_1 (k1_eqrel_1 A))) & (r2_hidden C (k1_relat_1 (k1_eqrel_1 A))))  => (r2_hidden (k4_tarski B C) (k1_eqrel_1 A))) ) ) ) ).
tt(t3_topalg_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k17_borsuk_1)) =>  ( (A = (k3_rcomp_1 k6_numbers B))  =>  ((k3_subset_1 (u1_struct_0 k17_borsuk_1) A) = (k1_rcomp_1 B 1)) ) ) ) ) ) ).
tt(t3_topalg_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_topalg_2 B A) & (m1_pre_topc B (k15_euclid A))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_borsuk_2 D B C C) =>  ((u1_struct_0 (k5_topalg_1 B C)) = (k1_tarski (k6_eqrel_1 (k2_topalg_1 B C) (k2_topalg_1 B C) (k4_topalg_1 B C) D))) ) ) ) ) ) ) ) ) ).
tt(t3_topalg_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_tarski B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_tarski B C))))) )  =>  (A = (k4_subset_1 A (k8_relset_1 A (k2_tarski B C) D (k1_tarski B)) (k8_relset_1 A (k2_tarski B C) D (k1_tarski C)))) ) ) ) ) ) ).
tt(t3_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v2_funct_1 E) & (v2_funct_1 F))  => (v2_funct_1 (k1_topalg_4 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topalg_5,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r1_tarski (k6_connsp_3 A B C) B)) ) ) ) ) ) ) ).
tt(t3_topalg_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1)) => (r2_hidden (k4_algstr_0 (k15_euclid A) B) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k3_topreal9 A (k4_struct_0 (k15_euclid A)) 1) (k1_tarski B)))) ) ) ) ) ).
tt(t3_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  ( (E = C)  =>  ((r2_hidden E (k13_prob_1 (u1_struct_0 (k1_pre_topc A B)) k5_numbers (k9_setfam_1 (u1_struct_0 (k1_pre_topc A B))) (k1_topdim_1 (k1_pre_topc A B)) D)) <=> (r2_hidden C (k13_prob_1 (u1_struct_0 A) k5_numbers (k9_setfam_1 (u1_struct_0 A)) (k1_topdim_1 A) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B))) =>  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 B))))  =>  ((r1_tarski D C) =>  ((r1_xxreal_0 (k5_card_1 D) (k1_nat_1 A 1)) | (v1_xboole_0 (k6_setfam_1 B D))) ) ) )  => (r1_xxreal_0 (k1_topdim_2 B C) A)) ) ) ) ) ) ).
tt(t3_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t3_topgen_2,ax, (! [A:$i] :  ( (! [B:$i] :  ((r2_hidden B A) => (v1_card_1 B)) )  => (v1_card_1 (k3_tarski A))) ) ).
tt(t3_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (~  ((r1_tarski (k10_xtuple_0 B) (k9_setfam_1 (k9_setfam_1 A))) &  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) & (r2_hidden D (k1_funct_1 B C)))  => (r2_hidden C D)) ) )  &  ( (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden C E) &  ((r2_hidden E (k1_funct_1 B D)) &  ((r2_hidden D A) &  (! [F:$i] :  (~  ((r2_hidden F (k1_funct_1 B C)) & (r1_tarski F E)) ) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden C A) &  ((r2_hidden D (k1_funct_1 B C)) &  ((r2_hidden E (k1_funct_1 B C)) &  (! [F:$i] :  (~  ((r2_hidden F (k1_funct_1 B C)) & (r1_tarski F (k3_xboole_0 D E))) ) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( (C = (k3_card_3 B))  &  (! [D:$i] :  ((l1_pre_topc D) =>  ( ( ((u1_struct_0 D) = A)  &  ((u1_pre_topc D) = (k1_cantor_1 A C)) )  =>  ( ((v2_pre_topc D) & (l1_pre_topc D))  &  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_pre_topc E) & (l1_pre_topc E)) )  =>  ( (E = D)  => (m1_topgen_2 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=> (r1_tarski (k2_topgen_1 A B) B)) ) ) ) ) ).
tt(t3_topgen_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden B (k9_xtuple_0 C)) =>  ((k1_funct_1 (k10_funct_6 (k16_funcop_1 A C)) B) = (k16_funcop_1 A (k1_funct_1 C B))) ) ) ) ) ) ).
tt(t3_topgrp_1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_struct_0 A) B) = B) ) ) ) ) ).
tt(t3_topmetr2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A B)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A C))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A C)))))) )  =>  (~  ( ((k9_subset_1 (u1_struct_0 A) B C) = (k1_tarski D))  &  ((v3_tops_2 E k5_topmetr (k1_pre_topc A B)) &  ( ((k1_funct_1 E 1) = D)  &  ((v3_tops_2 F k5_topmetr (k1_pre_topc A C)) &  ( ((k1_funct_1 F k6_numbers) = D)  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C)))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))))))) )  =>  (~  ((v3_tops_2 G k5_topmetr (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) &  ( ((k1_funct_1 G k6_numbers) = (k1_funct_1 E k6_numbers))  &  ((k1_funct_1 G 1) = (k1_funct_1 F 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topmetr3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v2_tbsp_1 D A) &  ( (E = (k1_partfun1 k5_numbers (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) D C))  & (v5_pre_topc C (k3_pcomps_1 A) (k3_pcomps_1 B))) )  => (v2_tbsp_1 E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topmetr,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_pre_topc B C)) ) ) ) ) ) ) ).
tt(t3_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ((r1_xxreal_0 (k17_euclid A) (k17_euclid C)) & (r1_xxreal_0 (k17_euclid C) (k17_euclid B))) ) ) ) ) ) ) ) ).
tt(t3_topreal2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) D)))))) )  =>  ( ((v3_tops_2 E (k1_pre_topc (k15_euclid 2) C) (k1_pre_topc (k15_euclid 2) D)) & (r1_topreal1 (k15_euclid 2) A B C))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ( ( (F = (k1_funct_1 E A))  &  (G = (k1_funct_1 E B)) )  => (r1_topreal1 (k15_euclid 2) F G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(t3_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal4 A B C) =>  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) ) ) ) ).
tt(t3_topreal5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r2_hidden B A))  &  ( (? [C:$i] :  ((v1_xreal_0 C) &  (? [D:$i] :  ((v1_xreal_0 D) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ( (~ (r1_xxreal_0 B C))  &  (~ (r1_xxreal_0 D B)) ) ) ) ) ) ) )  & (v2_connsp_1 A k3_topmetr)) ) ) ) ) ) ) ).
tt(t3_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k18_complex1 B) (k18_complex1 A))) ) ) ) ) ).
tt(t3_topreal7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k4_finseq_1 B) (k4_finseq_1 (k7_finseq_1 A B)))) ) ) ) ).
tt(t3_topreal8,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ( ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B A) & (m2_finseq_1 B A)) )  =>  (~ (r1_xxreal_0 (k3_finseq_1 B) 2)) ) ) ) ) ).
tt(t3_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (v1_xboole_0 A))  &  (B = (k3_rlvect_1 (k15_euclid A) B (k22_euclid A))) ) ) ) ) ) ) ).
tt(t3_topreala,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r2_hidden E (k4_card_3 (k4_funct_4 A B C D))) =>  ( (A = B)  |  ((r2_hidden (k1_funct_1 E A) C) & (r2_hidden (k1_funct_1 E B) D)) ) ) ) ) ) ) ) ) ).
tt(t3_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((r2_hidden C (k1_toprealb A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k4_numbers) &  (C = (k2_rcomp_1 (k2_xcmplx_0 A D) (k2_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t3_toprealc,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k24_valued_1 C (k6_xcmplx_0 A B)) = (k45_valued_1 (k24_valued_1 C A) (k24_valued_1 C B))) ) ) ) ) ) ) ).
tt(t3_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_toprns_1 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((k8_nat_1 (u1_struct_0 (k15_euclid A)) B C) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t3_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=> (v3_pre_topc (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t3_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((m1_setfam_1 B (u1_struct_0 A)) &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t3_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k9_subset_1 (u1_struct_0 A) (k1_tops_1 A B) (k2_pre_topc A C)) (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ).
tt(t3_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_t_0topsp C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden D E) &  (! [F:$i] :  ( ((v3_pre_topc F B) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) F) & (r1_tarski F (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k3_funct_2 A A C (k3_funct_2 A A (k2_funct_2 A C) B)) = B)  &  ((k3_funct_2 A A (k2_funct_2 A C) (k3_funct_2 A A C B)) = B) ) ) ) ) ) ) ) ).
tt(t3_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v7_transgeo E A) &  ((r2_analoaf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) C D) & (r2_analoaf A B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) D)) )  =>  ((r1_aff_1 A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) C) |  (D = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B C)) )  =>  ((v1_borsuk_1 (k4_topmetr B C) (k4_topmetr A D)) & (m1_pre_topc (k4_topmetr B C) (k4_topmetr A D))) ) ) ) ) ) ) ) ) ) ).
tt(t3_trees_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k9_finseq_1 A) (k9_finseq_1 B)) <=>  (A = B) ) ) ) ).
tt(t3_trees_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ( ((k3_finseq_1 B) = (k2_nat_1 A 1))  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  (~  ( (B = (k7_finseq_1 C (k9_finseq_1 D)))  &  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_trees_3 A) & (v1_trees_3 B))  <=> (v1_trees_3 (k2_xboole_0 A B))) ) ) ).
tt(t3_trees_4,ax, (! [A:$i] :  ( ((k9_xtuple_0 (k1_trees_4 A)) = (k2_trees_1 k6_numbers))  &  ((k1_funct_1 (k1_trees_4 A) k1_xboole_0) = A) ) ) ).
tt(t3_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden (k8_finseq_1 k5_numbers B C) (k9_xtuple_0 A)) =>  ((k5_trees_2 A (k8_finseq_1 k5_numbers B C)) = (k5_trees_2 (k5_trees_2 A B) C)) ) ) ) ) ) ) ) ).
tt(t3_trees_a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m4_trees_1 B A) => (r1_tarski (a_2_1_trees_a A B) (a_2_0_trees_a A B))) ) ) ) ).
tt(t3_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k6_domain_1 (u1_struct_0 A) B) (k1_triang_1 A))) ) ) ) ).
tt(t3_tsep_1,ax, (! [A:$i] :  ( ((v1_pre_topc A) & (l1_pre_topc A))  =>  ((k1_pre_topc A (k2_struct_0 A)) = A) ) ) ).
tt(t3_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tsep_2 A B C) =>  ( (B = (k3_subset_1 (u1_struct_0 A) C))  &  (C = (k3_subset_1 (u1_struct_0 A) B)) ) ) ) ) ) ) ) ) ).
tt(t3_tsp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v1_tsp_1 C A)) )  => (v1_tsp_1 D B)) ) ) ) ) ) ) ) ) ).
tt(t3_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((v3_pre_topc B A) | (v4_pre_topc B A))  &  ((v1_tsp_2 B A) & (v1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t3_turing_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~  (F = C) )  =>  ((k1_funct_1 (k1_funct_4 A (k16_funcop_1 (k4_tarski B C) D)) (k4_tarski E F)) = (k1_funct_1 A (k4_tarski E F))) ) ) ) ) ) ) ) ) ).
tt(t3_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k8_twoscomp (k10_finseq_1 A B)) = (k1_binarith A B))  &  ( ((k1_funct_1 k9_twoscomp (k10_finseq_1 A B)) = (k1_binarith (k9_margrel1 A) B))  &  ((k1_funct_1 k10_twoscomp (k10_finseq_1 A B)) = (k1_binarith (k9_margrel1 A) (k9_margrel1 B))) ) ) ) ) ) ) ).
tt(t3_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ( (~ (v1_xboole_0 (k10_xtuple_0 (u1_unialg_1 A))))  & (m1_subset_1 (k10_xtuple_0 (u1_unialg_1 A)) (k1_zfmisc_1 (k4_partfun1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A))))) ) ) ).
tt(t3_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_unialg_2 B A) => (r1_tarski (u1_struct_0 B) (u1_struct_0 A))) ) ) ) ).
tt(t3_uniform1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (F = (k1_funct_1 C E))  &  (! [G:$i] :  ((v1_xreal_0 G) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ( (I = (k1_funct_1 C H))  &  ( (~ (r1_xxreal_0 G (k4_metric_1 A E H)))  & (r1_xxreal_0 D (k4_metric_1 B F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (v5_pre_topc C (k3_pcomps_1 A) (k3_pcomps_1 B))) ) ) ) ) ) ) ).
tt(t3_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k1_complfld)))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ( ((k3_finseq_1 C) = (k5_card_1 A))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_complfld)) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  (E = (k1_funct_1 (k1_uproots A) D)) )  =>  ((k1_funct_1 C D) = (k17_complex1 (k5_algstr_0 k1_complfld B E))) ) ) ) ) ) )  =>  ((k17_complex1 (k2_polynom4 k1_complfld (k10_uproots k1_complfld (k2_uproots (u1_struct_0 k1_complfld) A 1)) B)) = (k21_rvsum_1 C)) ) ) ) ) ) ) ) ).
tt(t3_uproots,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k3_finseq_1 (k1_uproots A)) = (k5_card_1 A)) ) ) ).
tt(t3_urysohn1,ax, ((k1_urysohn1 1) = (k8_domain_1 k1_numbers k6_numbers (k10_real_1 1 2) 1)) ).
tt(t3_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ( (~  (A = k1_xboole_0) )  =>  ((k1_integra2 A k6_numbers) = (k1_seq_4 k6_numbers)) ) ) ) ).
tt(t3_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_urysohn3 E A B C D) => (m1_subset_1 E (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t3_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [E:$i] :  ((m2_funct_2 E (k2_valuat_1 A B) k6_margrel1 (k9_funct_2 (k2_valuat_1 A B) k6_margrel1)) =>  ( ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k3_valuat_1 A B C E) D) = k8_margrel1)  <=>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ( (! [G:$i] :  ((m2_subset_1 G (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~  (C = G) )  =>  ((k3_funct_2 (k3_qc_lang1 A) B F G) = (k3_funct_2 (k3_qc_lang1 A) B D G)) ) ) )  =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 E F) = k8_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v3_valued_0 B))  =>  ((r1_tarski A B) => (v3_valued_0 A)) ) ) ) ) ).
tt(t3_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k9_xtuple_0 (k13_valued_1 A B)) = (k9_xtuple_0 A))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 (k13_valued_1 A B) C) = (k6_xcmplx_0 (k1_funct_1 A C) B)) ) ) ) ) ) ) ) ).
tt(t3_valued_2,ax, (! [A:$i] : (m1_subset_1 (k7_valued_2 A) (k1_zfmisc_1 (k6_valued_2 A)))) ).
tt(t3_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v3_vectmetr B A) => (v2_funct_1 B)) ) ) ) ) ).
tt(t3_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_struct_0 (k1_vectsp_7 A B (k6_domain_1 (u1_struct_0 B) D)) C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (C = (k4_vectsp_1 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 D E) (k2_matrix_1 B)) =>  ((k6_matrix13 (u1_struct_0 A) (k3_matrix_3 A B C) D E) = (k5_matrlin2 (k5_card_1 D) (k5_card_1 E) A (k6_matrix13 (u1_struct_0 A) B D E) (k6_matrix13 (u1_struct_0 A) C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_vectsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_vectsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_vectsp_1)) =>  ( ((k3_rlvect_1 k2_vectsp_1 A B) = (k3_rlvect_1 k2_vectsp_1 B A))  &  ( ((k3_rlvect_1 k2_vectsp_1 (k3_rlvect_1 k2_vectsp_1 A B) C) = (k3_rlvect_1 k2_vectsp_1 A (k3_rlvect_1 k2_vectsp_1 B C)))  &  ( ((k3_rlvect_1 k2_vectsp_1 A (k4_struct_0 k2_vectsp_1)) = A)  &  ( ((k3_rlvect_1 k2_vectsp_1 A (k4_algstr_0 k2_vectsp_1 A)) = (k4_struct_0 k2_vectsp_1))  &  ( ((k8_group_1 k2_vectsp_1 A B) = (k8_group_1 k2_vectsp_1 B A))  &  ( ((k8_group_1 k2_vectsp_1 (k8_group_1 k2_vectsp_1 A B) C) = (k8_group_1 k2_vectsp_1 A (k8_group_1 k2_vectsp_1 B C)))  &  ( ((k8_group_1 k2_vectsp_1 (k5_struct_0 k2_vectsp_1) A) = A)  &  ( (~  ( (~  (A = (k4_struct_0 k2_vectsp_1)) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_vectsp_1)) =>  (~  ((k8_group_1 k2_vectsp_1 D A) = (k5_struct_0 k2_vectsp_1)) ) ) ) ) )  &  ( ((k8_group_1 k2_vectsp_1 A (k3_rlvect_1 k2_vectsp_1 B C)) = (k3_rlvect_1 k2_vectsp_1 (k8_group_1 k2_vectsp_1 A B) (k8_group_1 k2_vectsp_1 A C)))  &  ((k8_group_1 k2_vectsp_1 (k3_rlvect_1 k2_vectsp_1 B C) A) = (k3_rlvect_1 k2_vectsp_1 (k8_group_1 k2_vectsp_1 B A) (k8_group_1 k2_vectsp_1 C A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k4_struct_0 A))  <=>  ((k4_algstr_0 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t3_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r2_hidden D C) & (r2_hidden E C))  => (r2_hidden (k5_algstr_0 B D E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((r1_struct_0 (k2_vectsp_5 A B C D) E) <=>  ((r1_struct_0 C E) & (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k2_vectsp_6 A B) C) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t3_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v1_vectsp_7 (k6_domain_1 (u1_struct_0 B) C) A B) <=>  (~  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t3_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((k2_vectsp_8 A B) = (u1_struct_0 (k1_vectsp_8 A B))) ) ) ) ) ).
tt(t3_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  ((v2_funct_1 C) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((r1_tarski (k1_vectsp_6 A B D) (k10_xtuple_0 C)) =>  ((k4_rlvect_1 B (k3_vectsp_6 A B C D)) = (k4_vectsp_6 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~  (D = k6_numbers) )  =>  ((k8_relset_1 A (u1_struct_0 B) (k4_vfunct_1 A B C D) (k1_tarski (k4_struct_0 B))) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ( (~  (D = k5_complex1) )  =>  ((k8_relset_1 A (u1_struct_0 B) (k2_vfunct_2 A B C D) (k1_tarski (k4_struct_0 B))) = (k8_relset_1 A (u1_struct_0 B) C (k1_tarski (k4_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v1_waybel_0 C A))  => (v1_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  ((v4_yellow_0 (k7_lattice3 B) (k7_lattice3 A)) & (m1_yellow_0 (k7_lattice3 B) (k7_lattice3 A))) )  &  ( ( ((v4_yellow_0 (k7_lattice3 B) (k7_lattice3 A)) & (m1_yellow_0 (k7_lattice3 B) (k7_lattice3 A)))  =>  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  &  ( ( ((v4_yellow_0 (k7_lattice3 B) A) & (m1_yellow_0 (k7_lattice3 B) A))  =>  ((v4_yellow_0 B (k7_lattice3 A)) & (m1_yellow_0 B (k7_lattice3 A))) )  &  ( ((v4_yellow_0 B (k7_lattice3 A)) & (m1_yellow_0 B (k7_lattice3 A)))  =>  ((v4_yellow_0 (k7_lattice3 B) A) & (m1_yellow_0 (k7_lattice3 B) A)) ) ) ) ) ) ) ) ) ).
tt(t3_waybel11,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t3_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_4 A B C) => (r1_tarski (k3_waybel_0 A B) (k3_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t3_waybel13,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t3_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_waybel_0 A (k12_lattice3 A B C)) = (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k5_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t3_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_orders_2 A (k4_yellow_0 A) B) =>  (B = (k4_yellow_0 A)) ) ) ) ) ) ).
tt(t3_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_4 A (k6_subset_1 (u1_struct_0 A) (k6_waybel_0 A C)) B) =>  ((k7_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)) = (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_waybel_0 A C))) ) ) ) ) ) ) ) ).
tt(t3_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v22_waybel_0 C A B) => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t3_waybel18,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (v2_pre_topc (g1_pre_topc A (k1_cantor_1 A (k2_cantor_1 A B))))) ) ) ).
tt(t3_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k1_waybel19 A) = (k1_waybel19 B)) ) ) ) ) ) ).
tt(t3_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v2_lattice3 A) =>  ((k11_lattice3 A (k3_yellow_0 A) B) = (k3_yellow_0 A)) )  &  ( ((v1_lattice3 A) &  ((v3_orders_2 A) & (v4_orders_2 A)) )  =>  ((k10_lattice3 A (k3_yellow_0 A) B) = B) ) ) ) ) ) ) ).
tt(t3_waybel20,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski (k9_xtuple_0 (k7_relat_1 (k15_funct_3 A B) C)) (k7_relat_1 A (k9_xtuple_0 C))) & (r1_tarski (k10_xtuple_0 (k7_relat_1 (k15_funct_3 A B) C)) (k7_relat_1 B (k10_xtuple_0 C)))) ) ) ) ) ) ).
tt(t3_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_yellow_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_yellow_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v19_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ((k2_yellow_6 (u1_struct_0 A) B C (k4_yellow_0 A)) = (k4_yellow_0 B))  => (m1_waybel21 C A B)) ) ) ) ) ) ) ).
tt(t3_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v17_waybel_0 (k3_struct_0 A) A A)) ) ).
tt(t3_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v8_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  => (r1_tarski (k11_waybel_0 A C) (k11_waybel_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t3_waybel24,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v2_yellow_0 B) & (l1_orders_2 B)) ) ) )  =>  ((k4_yellow_0 (k7_yellow_1 A B)) = (k6_struct_0 A B (k4_yellow_0 B))) ) ) ) ) ).
tt(t3_waybel25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B (k5_yellow_1 A (k7_funcop_1 A (k3_yellow_1 1)))))  =>  ((u1_struct_0 B) = (u1_struct_0 (k3_waybel18 A (k7_funcop_1 A k9_waybel18)))) ) ) ) ) ).
tt(t3_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_waybel26 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_waybel26 A B))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  =>  ( ( (C = E)  &  (D = F) )  =>  ((r3_orders_2 (k1_waybel26 A B) C D) <=> (r1_yellow_2 (u1_struct_0 A) (k1_waybel25 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_waybel27 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_waybel27 E)) )  =>  ( ((r1_tarski (k9_xtuple_0 D) (k1_funct_2 A (k1_funct_2 B C))) & (r1_tarski (k10_xtuple_0 D) (k9_xtuple_0 E)))  =>  ((k3_relat_1 D E) = (k6_partfun1 (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel28,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_hidden B (k6_yellow_6 A)) &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ((r2_hidden D (k6_yellow_6 A)) =>  (C = (k1_waybel11 A D)) ) ) ) )  =>  ( (C = (k1_waybel11 A B))  &  (! [D:$i] :  ((m2_yellow_6 D A B) =>  ((r2_hidden D (k6_yellow_6 A)) => (r1_orders_2 A (k1_waybel_9 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C)) & (m1_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C))) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C))) & (m1_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( ((v2_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 E))) )  => (v23_waybel_0 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_lattice3 A B (k1_yellow_0 A (k2_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t3_waybel30,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k7_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))))) )  =>  ((k1_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) B) = (k3_tarski B)) ) ) ) ) ).
tt(t3_waybel31,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((k1_waybel31 A) = (k1_card_1 (u1_struct_0 (k1_waybel_8 A)))) ) ) ).
tt(t3_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (? [B:$i] :  ((m1_yellow_9 B A) & (v4_waybel11 B)) ) ) ) ).
tt(t3_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((l1_waybel_0 C A) =>  (~  ((r2_hidden C (k6_yellow_6 A)) &  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v6_waybel_0 D B) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) ) )  =>  (~  ((r2_hidden D (k6_yellow_6 B)) &  ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v18_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k2_waybel34 A B C) D) = (k1_yellow_0 B (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) C (k5_waybel_0 A D)))) ) ) ) ) ) ) ) ) ).
tt(t3_waybel35,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden (k4_tarski C D) B) & (r2_hidden (k4_tarski D C) B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ( ((v1_lattice3 A) | (v25_waybel_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_waybel_3 A B D) & (r1_waybel_3 A C D))  =>  ((r1_yellow_0 A (k7_domain_1 (u1_struct_0 A) B C)) & (r1_waybel_3 A (k10_lattice3 A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k4_yellow_0 (k2_yellow_1 (k3_waybel_4 A))) = (k2_waybel_4 A)) ) ) ).
tt(t3_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  => (v4_waybel_1 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ).
tt(t3_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_waybel_1 B) &  ((v19_waybel_0 C A B) &  ((v20_waybel_0 C A B) & (v2_funct_1 C)) ) )  => (v2_waybel_1 A)) ) ) ) ) ) ) ).
tt(t3_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ((v7_struct_0 A) <=>  ((k4_yellow_0 A) = (k3_yellow_0 A)) ) ) ) ).
tt(t3_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v6_yellow_0 (k1_waybel_8 A) A) & (r2_hidden (k3_yellow_0 A) (u1_struct_0 (k1_waybel_8 A)))) ) ) ).
tt(t3_waybel_9,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ( (C = D)  & (m1_setfam_1 C (u1_struct_0 A))) )  => (m1_setfam_1 D (u1_struct_0 B))) ) ) ) ) ) ) ) ) ).
tt(t3_weddwitt,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_nat_d (k7_nat_d (k13_newton A B) 1) (k7_nat_d (k13_newton A C) 1)) =>  ((r1_xxreal_0 B k6_numbers) |  ((r1_xxreal_0 A 1) | (r1_nat_d B C)) ) ) ) ) ) ) ) ) ).
tt(t3_weierstr,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v1_finset_1 B) &  ((v1_topmetr B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~ (r1_tarski (k5_setfam_1 (u1_struct_0 A) B) (k9_metric_1 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] : (r1_tarski (k1_wellord1 (u1_orders_2 A) B) (u1_struct_0 A))) ) ) ).
tt(t3_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v1_wellord1 A) <=> (r1_wellord1 A (k1_relat_1 A))) ) ) ).
tt(t3_wellset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r2_hidden A (k1_relat_1 C)) &  ((r2_hidden B (k1_relat_1 C)) & (v2_wellord1 C)) )  =>  ((r2_hidden A (k1_wellord1 C B)) | (r2_hidden (k4_tarski B A) C)) ) ) ) ) ) ).
tt(t3_wsierp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((k1_newton A C) = (k1_newton B C)) ) )  =>  ((r1_xxreal_0 C k6_numbers) |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t3_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~ (r1_xboole_0 A B))  &  (! [C:$i] :  (~  ((r2_hidden C A) & (r2_hidden C B)) ) ) ) )  &  (~  ( (? [C:$i] :  ((r2_hidden C A) & (r2_hidden C B)) )  & (r1_xboole_0 A B)) ) ) ) ) ).
tt(t3_xboole_1,ax, (! [A:$i] :  ((r1_tarski A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ).
tt(t3_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k5_xboolean A A) = A) ) ) ).
tt(t3_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (A = (k2_xcmplx_0 A B))  =>  (B = k6_numbers) ) ) ) ) ) ).
tt(t3_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ).
tt(t3_xregular,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C D) & (r2_hidden D B))  => (r1_xboole_0 C A)) ) ) ) ) ) ) ).
tt(t3_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k3_xtuple_0 A B C) = (k3_xtuple_0 D E F))  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ) ) ) ).
tt(t3_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (r1_xxreal_0 A k1_xxreal_0)) ) ).
tt(t3_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k2_xxreal_1 B C)) <=>  ((r1_xxreal_0 B A) &  (~ (r1_xxreal_0 C A)) ) ) ) ) ) ) ) ) ).
tt(t3_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r2_hidden A B) => (r1_xxreal_0 (k2_xxreal_2 B) A)) ) ) ) ) ).
tt(t3_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v3_lattice3 A))  => (v3_lattice3 B)) ) ) ) ) ).
tt(t3_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v2_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((k4_yellow_0 (k3_yellow_3 A B)) = (k7_yellow_3 A B (k4_yellow_0 A) (k4_yellow_0 B))) ) ) ) ) ).
tt(t3_yellow11,ax, ((k6_subset_1 3 1) = (k7_domain_1 k5_numbers 1 2)) ).
tt(t3_yellow12,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k8_relset_1 A (k2_zfmisc_1 A A) (k12_funct_3 A) (k8_mcart_1 A A B B)) = B) ) ) ) ).
tt(t3_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  => (v9_pre_topc A)) ) ).
tt(t3_yellow14,ax, (! [A:$i] :  ( ((v2_struct_0 A) & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  => (v2_struct_0 B)) ) ) ) ) ) ) ).
tt(t3_yellow16,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C B) & (m1_yellow_0 C B)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ( ((r1_funct_2 A (u1_struct_0 B) A (u1_struct_0 C) F D) &  ((r1_funct_2 A (u1_struct_0 B) A (u1_struct_0 C) G E) & (r1_yellow_2 A B F G)) )  => (r1_yellow_2 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((r1_tarski (k10_xtuple_0 (k12_card_3 A B)) (k1_funct_1 A B)) &  ( (~  ((k4_card_3 A) = k1_xboole_0) )  =>  ((k10_xtuple_0 (k12_card_3 A B)) = (k1_funct_1 A B)) ) ) ) ) ) ) ).
tt(t3_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l1_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (l1_altcat_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_altcat_2 C) & (l1_altcat_1 C)) )  =>  (! [D:$i] :  ( ((v8_functor0 D A B) & (l2_functor0 D A B))  =>  (! [E:$i] :  ( ((v8_functor0 E A B) & (l2_functor0 E A B))  =>  (! [F:$i] :  ((l2_functor0 F B C) =>  (! [G:$i] :  ((l2_functor0 G B C) =>  ( ( ((g2_functor0 A B (u1_functor0 A B D) (u2_functor0 A B D)) = (g2_functor0 A B (u1_functor0 A B E) (u2_functor0 A B E)))  &  ((g2_functor0 B C (u1_functor0 B C F) (u2_functor0 B C F)) = (g2_functor0 B C (u1_functor0 B C G) (u2_functor0 B C G))) )  =>  ((k13_functor0 A B C D F) = (k13_functor0 A B C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v13_waybel_0 C (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A))))))  =>  ((r2_waybel_7 A C B) <=> (r1_tarski (k1_yellow19 A B) C)) ) ) ) ) ) ) ).
tt(t3_yellow_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 A))) =>  ((r3_orders_2 (k2_yellow_1 A) B C) <=> (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t3_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) &  ((v11_functor0 C A B) & (l2_functor0 C A B)) )  =>  (! [D:$i] :  ( ((v8_functor0 D B A) &  ((v11_functor0 D B A) & (l2_functor0 D B A)) )  =>  ( ((v21_functor0 C A B) &  (D = (k15_functor0 A B C)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A E F) = k1_xboole_0) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A E F)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B (k3_functor0 A B C F) (k3_functor0 A B C E))) =>  ( ((k8_functor0 A B C E F G) = H)  <=>  ((k8_functor0 B A D (k3_functor0 A B C F) (k3_functor0 A B C E) H) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A B C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C D)) =>  ((k5_altcat_1 A B C D E F) = (k1_partfun1 (u1_struct_0 (k3_yellow21 A B)) (u1_struct_0 (k3_yellow21 A C)) (u1_struct_0 (k3_yellow21 A C)) (u1_struct_0 (k3_yellow21 A D)) (k5_yellow21 A B C E) (k5_yellow21 A C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_yellow_0 A B) & (r1_yellow_0 A C))  =>  ((r1_yellow_0 A (k2_xboole_0 B C)) &  ((k1_yellow_0 A (k2_xboole_0 B C)) = (k13_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t3_yellow_3,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_orders_2 A B D) & (r1_orders_2 A C E))  => (r1_orders_2 A (k13_lattice3 A B C) (k13_lattice3 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_yellow_4 A (k1_struct_0 A) B)) ) ) ) ).
tt(t3_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A (k13_lattice3 A B C) D) => (r1_orders_2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t3_yellow_6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((u1_struct_0 A) = (u1_struct_0 (k7_lattice3 A))) ) ) ).
tt(t3_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v2_struct_0 A) <=> (v2_struct_0 (k7_lattice3 A))) ) ) ).
tt(t3_yellow_8,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r2_tarski B (k7_setfam_1 A B))) ) ) ).
tt(t3_yellow_9,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((k7_setfam_1 (u1_struct_0 A) B) = (a_2_0_yellow_9 A B)) ) ) ) ) ).
tt(t3_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (m1_subset_1 (k4_tarski (k4_tarski (k2_yoneda_1 A (k4_graph_1 A B)) (k2_yoneda_1 A (k3_graph_1 A B))) (k3_yoneda_1 A B)) (u4_struct_0 (k11_nattra_1 A (k1_yoneda_1 A))))) ) ) ) ).
tt(t3_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r1_tarski (k3_xboole_0 C A) (k1_zf_colla A B)) <=> (r2_hidden C (k1_zf_colla A (k1_ordinal1 B)))) ) ) ) ) ) ) ).
tt(t3_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v8_zf_fund1 B A) => (r2_hidden k1_xboole_0 B)) ) ) ) ) ).
tt(t3_zf_fund2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_zf_refle B A)) ) ) ) )  =>  ( ((r2_hidden k4_ordinal1 A) &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (m1_subset_1 D A))  =>  ((r2_hidden C D) => (r1_tarski (k5_zf_refle A B C) (k5_zf_refle A B D))) ) ) ) )  &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((v4_ordinal1 C) =>  ( (C = k1_xboole_0)  |  ((k5_zf_refle A B C) = (k3_card_3 (k5_relat_1 B C))) ) ) ) )  &  ( (! [C:$i] :  ( ((v3_ordinal1 C) & (m1_subset_1 C A))  =>  ((r2_hidden (k5_zf_refle A B C) (k4_zf_refle A B)) & (v1_ordinal1 (k5_zf_refle A B C))) ) )  & (v1_zf_fund2 (k4_zf_refle A B))) ) ) )  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model C)) => (r2_zf_model (k4_zf_refle A B) (k11_zf_model C))) ) ) ) ) ) ) ) ).
tt(t3_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((k20_zf_lang (k6_zf_lang A)) = A) ) ) ).
tt(t3_zf_lang,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  ( ((k8_zf_lang C A) = (k8_zf_lang D B))  =>  ( (C = D)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t3_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski (k1_tarski A) (k1_tarski B)) =>  (A = B) ) ) ) ).
tt(t3_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ((r2_zf_model A k7_zf_model) <=>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B A) & (r2_hidden C A))  => (r2_hidden (k2_tarski B C) A)) ) ) ) ) ) ) ).
tt(t3_zfmodel2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden (k2_zf_lang C) (k4_zf_lang1 A)) & (r1_xxreal_0 B C)) ) ) ) ) )  &  (~  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) => (r2_hidden B (k4_zf_lang1 A))) ) ) ) ) ) ).
tt(t3_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ((r2_hidden (k3_funct_2 k1_zf_lang A D B) (k3_funct_2 k1_zf_lang A D C)) <=> (r2_hidden D (k5_zf_model (k5_zf_lang B C) A))) ) ) ) ) ) ) ) ) ).
tt(t3_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k9_zf_lang)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k9_zf_lang)) =>  ( ((r1_zfrefle1 A B) & (r1_zfrefle1 A C))  => (r1_zfrefle1 A (k4_subset_1 k9_zf_lang B C))) ) ) ) ) ) ) ).
tt(t3_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ((r2_hidden k4_ordinal1 A) => (r2_zf_model A k9_zf_model)) ) ) ).
tt(t3_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v6_zmodul01 A) &  (B = (k4_algstr_0 A B)) )  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t400_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) =>  ((k6_subset_1 (k2_xxreal_1 B k1_xxreal_0) (k4_xxreal_1 B A)) = (k2_xboole_0 (k1_tarski B) (k2_xxreal_1 A k1_xxreal_0))) ) ) ) ) ) ).
tt(t401_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k1_xxreal_1 A B) (k2_xxreal_1 A B)) = (k1_tarski B)) ) ) ) ) ) ).
tt(t402_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k3_xxreal_1 A B) (k4_xxreal_1 A B)) = (k1_tarski B)) ) ) ) ) ) ).
tt(t403_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k1_xxreal_1 A B) (k3_xxreal_1 A B)) = (k1_tarski A)) ) ) ) ) ) ).
tt(t404_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k6_subset_1 (k2_xxreal_1 A B) (k4_xxreal_1 A B)) = (k1_tarski A)) ) ) ) ) ) ).
tt(t405_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k2_xxreal_1 k2_xxreal_0 A)) = (k1_tarski A)) ) ) ).
tt(t406_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k3_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 k2_xxreal_0 A)) = (k1_tarski A)) ) ) ).
tt(t407_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k1_xxreal_1 k2_xxreal_0 A) (k3_xxreal_1 k2_xxreal_0 A)) = (k1_tarski k2_xxreal_0)) ) ) ).
tt(t408_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k2_xxreal_1 k2_xxreal_0 A) (k4_xxreal_1 k2_xxreal_0 A)) = (k1_tarski k2_xxreal_0)) ) ) ).
tt(t409_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k2_xxreal_1 A k1_xxreal_0)) = (k1_tarski k1_xxreal_0)) ) ) ).
tt(t40_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l2_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) =>  ((r3_abcmiz_0 A B C) & (r3_abcmiz_0 A (k8_abcmiz_0 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t40_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k20_abcmiz_1) =>  ( ( ((k23_abcmiz_1 A) = k6_abcmiz_1)  => (r2_hidden A k17_abcmiz_1))  &  ( ((r2_hidden A k17_abcmiz_1) =>  ((k23_abcmiz_1 A) = k6_abcmiz_1) )  &  ( ( ((k23_abcmiz_1 A) = k7_abcmiz_1)  => (r2_hidden A k18_abcmiz_1))  &  ( ((r2_hidden A k18_abcmiz_1) =>  ((k23_abcmiz_1 A) = k7_abcmiz_1) )  &  ( ( ((k23_abcmiz_1 A) = k8_abcmiz_1)  => (r2_hidden A k19_abcmiz_1))  &  ((r2_hidden A k19_abcmiz_1) =>  ((k23_abcmiz_1 A) = k8_abcmiz_1) ) ) ) ) ) ) ) ) ).
tt(t40_abcmiz_a,ax, ((k1_msualg_1 k27_abcmiz_1 (k14_abcmiz_a k8_abcmiz_a)) = k1_xboole_0) ).
tt(t40_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) &  ((r2_hidden C D) & (r3_aff_1 A D E)) )  => (r2_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) & (v1_aff_1 C A))  =>  ((r5_aff_1 A B C) <=> (r1_aff_4 A B C)) ) ) ) ) ) ) ) ).
tt(t40_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  (~  (A = (k1_ordinal4 B (k5_afinsq_1 C))) ) ) ) ) ) ) ) ) ).
tt(t40_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  ( (~ (v1_setwiseo C A))  & (r1_xxreal_0 (k1_afinsq_1 B) k6_numbers)) )  =>  ((k6_afinsq_2 A (k1_ordinal4 B (k5_afinsq_1 D)) C) = (k5_binop_1 A C (k6_afinsq_2 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t40_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k14_afproj A))) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k14_afproj A))) &  ((r1_incsp_1 (k14_afproj A) B D) & (r1_incsp_1 (k14_afproj A) C D)) ) ) ) ) ) ) ) ) ).
tt(t40_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k1_afvect0 A B (k1_afvect0 A C (k1_afvect0 A D E))) = (k1_afvect0 A F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) <=> (r3_pua2mss1 A (k2_algspec1 A B C) (k1_algspec1 (u1_struct_0 A) B) (k1_algspec1 (u4_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t40_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B))))) )  =>  ( ((v1_group_6 D (k14_algstr_4 A) B) &  ((r1_algstr_4 D (k3_relat_1 (k2_funct_1 (k16_algstr_4 A 1)) C)) &  ((v1_group_6 E (k14_algstr_4 A) B) & (r1_algstr_4 E (k3_relat_1 (k2_funct_1 (k16_algstr_4 A 1)) C))) ) )  => (r2_relset_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 B) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A C D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_altcat_1 B E F)) =>  ( ( (E = C)  &  ( (F = D)  &  (G = H) ) )  =>  ( ((k1_altcat_1 B E F) = k1_xboole_0)  |  ( ((k1_altcat_1 B F E) = k1_xboole_0)  |  ( ((v1_altcat_3 H B E F) => (v1_altcat_3 G A C D))  &  ( ((v2_altcat_3 H B E F) => (v2_altcat_3 G A C D))  &  ((v3_altcat_3 H B E F) => (v3_altcat_3 G A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_analmetr A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k3_analmetr A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k3_analmetr A))) =>  ( ( (B = E)  &  ( (C = F)  &  (D = G) ) )  =>  ((r5_analmetr A B C D) <=> (r1_aff_1 (k3_analmetr A) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (F = G) )  & (r1_analort A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_freealg A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden C (k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k1_funct_1 (k2_pua2mss1 A B) C) (k9_aofa_000 A (k11_aofa_000 A) (k1_nat_1 D 1))) => (r1_tarski (k10_xtuple_0 C) (k9_aofa_000 A (k11_aofa_000 A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k78_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k78_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) G)) )  &  ( ( (~ (r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F)))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k79_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k79_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (r1_xxreal_0 G (k21_aofa_i00 B k4_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (B = (a_2_8_armstrng A C))  =>  ((k2_xboole_0 (k1_tarski A) (a_2_9_armstrng A C)) = (k9_armstrng A B)) ) ) ) ) ) ) ) ).
tt(t40_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( ((k8_arytm_3 k1_xboole_0 A) = k1_xboole_0)  &  ((k8_arytm_3 B 1) = B) ) ) ) ) ) ).
tt(t40_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) &  ((v6_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((v7_asympt_0 A) &  ((r1_xxreal_0 2 C) & (r2_hidden B (k11_asympt_0 A (a_1_3_asympt_0 C)))) )  => (r2_hidden B (k8_asympt_0 A))) ) ) ) ) ) ) ).
tt(t40_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_funct_2 k5_numbers k1_numbers A (k47_valued_1 k5_numbers k1_numbers k1_numbers (k3_asympt_1 1) (k4_asympt_1 1))) =>  ((k13_asympt_0 k5_numbers (k8_asympt_0 A) (k8_asympt_0 (k3_asympt_1 1))) = (k8_asympt_0 (k3_asympt_1 1))) ) ) ) ).
tt(t40_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((v3_wellfnd1 B A) => (v3_wellfnd1 (k10_nat_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t40_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k7_bcialg_1 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_bcialg_1 A B)) => (r2_hidden (k1_bcialg_1 A C D) (k4_bcialg_1 A))) ) ) ) ) ) ) ) ).
tt(t40_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_bcialg_2 D A) =>  ((r2_hidden (k4_tarski B C) D) =>  ((r2_hidden (k1_bcialg_1 A B C) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) D (k4_struct_0 A))) & (r2_hidden (k1_bcialg_1 A C B) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) D (k4_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A B C)) = (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A (k1_bcialg_1 A C B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_4 A (k1_bcialg_1 A B C) (k1_bcialg_1 A C B)) (k1_bcialg_4 A B C))) ) ) ) ) ) ).
tt(t40_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) )  =>  ( (B = (k5_bcialg_1 C))  =>  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) &  ((v8_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) ) )  <=>  (B = (k1_tarski (k4_struct_0 C))) ) ) ) ) ) ) ) ) ).
tt(t40_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_bcialg_1 D A) =>  ( ((u1_struct_0 D) = (k2_relset_1 (u1_struct_0 A) C))  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 D)) &  ((v2_bcialg_6 C B D) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ).
tt(t40_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k4_bhsp_1 A (k3_rlvect_1 A B C) (k3_rlvect_1 A D E)) (k7_real_1 (k4_bhsp_1 A B D) (k4_bhsp_1 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_bhsp_2 A C D)) <=>  (~ (r1_xxreal_0 D (k3_bhsp_1 A (k5_algstr_0 A C B)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_bhsp_3 A B C) => (r2_bhsp_3 A (k1_valued_0 (u1_struct_0 A) B D) (k1_valued_0 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t40_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k5_algstr_0 A (k3_bhsp_4 A B D) (k3_bhsp_4 A B C))) (k18_complex1 (k9_real_1 (k6_series_1 (k2_bhsp_2 A B) D) (k6_series_1 (k2_bhsp_2 A B) C))))) ) ) ) ) ) ) ) ).
tt(t40_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  ( ((v1_bilinear D A B C) | (v2_bilinear D A B C))  =>  ((v3_funct_1 D) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 A) D E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k4_lattices A B C) (k5_lattices A)) <=> (r1_boolealg A (k1_boolealg A B C) B)) ) ) ) ) ) ) ).
tt(t40_borsuk_1,ax, ((u1_struct_0 k17_borsuk_1) = (k1_rcomp_1 k6_numbers 1)) ).
tt(t40_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_topreal1 (k15_euclid A) C D B) => (r1_borsuk_3 k5_topmetr (k1_pre_topc (k15_euclid A) B))) ) ) ) ) ) ) ) ) ).
tt(t40_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( (A = (k2_rcomp_1 B C))  => (v3_pre_topc A k3_topmetr)) ) ) ) ) ) ) ).
tt(t40_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ( ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) )  =>  ( ((k1_funct_1 (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D) k6_numbers) = C)  &  ((k1_funct_1 (k1_partfun1 (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 (k4_topmetr k6_numbers 1)) (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k3_treal_1 k6_numbers 1 (k2_treal_1 k6_numbers 1) (k1_treal_1 k6_numbers 1)) D) 1) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_borsuk_7,ax, ((k30_valued_1 k8_borsuk_7) = k9_borsuk_7) ).
tt(t40_bspace,ax, (! [A:$i] :  ((v1_finset_1 A) => (m1_vectsp_7 (k9_bspace A) k2_bspace (k7_bspace A))) ) ).
tt(t40_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ( ((v1_relat_1 K) & (v1_funct_1 K))  =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k4_enumset1 C D E F G H))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (G = H) )  & (r1_xboole_0 (k15_bvfunc_1 A J (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H)) (k15_bvfunc_1 A I C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_funct_2 A k6_margrel1 (k17_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k5_bvfunc_1 A (k17_bvfunc_1 A B D) (k17_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t40_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A (k9_bvfunc_1 A E C) (k9_bvfunc_1 A B (k9_bvfunc_1 A E D)))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc_1 A B C)) (k1_bvfunc_1 A (k5_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t40_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B F) (k6_bvfunc_2 A (k9_bvfunc_1 A C D) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A D E) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E C) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k5_bvfunc_1 A (k5_bvfunc_1 A C D) E)) (k5_bvfunc_1 A (k5_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A B D)) (k2_bvfunc_1 A B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B C) C) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t40_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A B C) (k5_bvfunc_1 A B C))) ) ) ) ) ) ).
tt(t40_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ( ((k7_cqc_lang A B C) = (k2_calcul_1 A D))  & (r4_calcul_1 A D))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) D) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t40_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k1_card_1 A) = (k1_card_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t40_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_xboole_0 A B) =>  ((k5_card_1 (k2_xboole_0 A B)) = (k2_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ).
tt(t40_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  => (r1_ordinal1 (k1_card_1 (k3_card_3 A)) (k6_card_3 A))) ) ).
tt(t40_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) => (v5_card_fil A)) ) ) ).
tt(t40_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k1_card_fin B C 1 k6_numbers)) <=>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  &  ( (D = A)  &  ( ((k1_relset_1 k5_numbers D) = B)  &  ((r1_tarski (k2_relset_1 k5_numbers D) (k7_domain_1 k5_numbers k6_numbers 1)) &  ((k7_afinsq_2 D) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v8_cat_1 (k4_cat_1 A B) A B B)) ) ) ) ).
tt(t40_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k4_cat_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k4_cat_2 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (k4_cat_2 A C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (k4_cat_2 A C))))) )  =>  (~  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E G) (k4_cat_1 A F)) = (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D F) (k4_cat_1 B G))) ) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  ((k1_cat_1 C (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D (k3_graph_1 A G)) F) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E (k4_graph_1 B F)) G)) = (k1_cat_1 C (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E (k3_graph_1 B F)) G) (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D (k4_graph_1 A G)) F))) ) ) ) )  &  (! [F:$i] :  ((m2_cat_1 F (k8_cat_2 B A) C) =>  (~  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  ((k11_cat_2 B A C F G H) = (k1_cat_1 C (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E (k3_graph_1 B G)) H) (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D (k4_graph_1 A H)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v11_cat_1 B A) =>  ((k11_cat_3 A B C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t40_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k18_cat_4 A B B C C (k4_cat_1 A B) (k4_cat_1 A C)) = (k4_cat_1 A (k2_cat_4 A B C))) ) ) ) ) ) ) ).
tt(t40_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_card_1 (a_2_1_catalan2 A B)) = (k5_card_1 (k2_catalan2 A B))) ) ) ) ) ).
tt(t40_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_clvect_1 B A) =>  ((v1_xboole_0 B) | (m1_clvect_1 (g1_clvect_1 B (k10_csspace A B) (k1_c0sp1 A B) (k9_csspace A B)) A)) ) ) ) ) ) ).
tt(t40_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfcont_1 B A) <=> (r2_cfcont_1 (k5_relset_1 k2_numbers k2_numbers B A) A)) ) ) ) ).
tt(t40_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 A k2_numbers (k25_valued_1 A k2_numbers (k1_cfunct_1 A B C) D) (k1_cfunct_1 A (k25_valued_1 A k2_numbers B D) C))) ) ) ) ) ) ) ) ).
tt(t40_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((k13_cgames_1 (k13_cgames_1 A)) = A) ) ) ).
tt(t40_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_chain_1 D A) =>  ((r2_hidden (k3_chain_1 A B C) (k4_chain_1 A D A)) <=>  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) => (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 B E) (k1_seq_1 C E)) (k2_chain_1 A D E))) )  &  ( (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) )  |  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_chord B A) =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  ((r1_xxreal_0 D (k3_finseq_1 B)) =>  ((r1_xxreal_0 D (k1_nat_1 C 2)) |  (! [E:$i] :  (~ (r1_glib_000 A (k1_funct_1 B C) (k1_funct_1 B D) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ((m1_circcmb3 E C) =>  ( ((r2_hidden A (u1_struct_0 E)) & (r2_hidden B (u1_struct_0 E)))  =>  ((r2_hidden (k3_circcmb3 (k4_circcmb3 2 C D (k10_finseq_1 A B))) (k2_msafree2 E)) |  ((k2_msafree2 (k6_circcmb3 C E (k4_circcmb3 2 C D (k10_finseq_1 A B)))) = (k2_msafree2 E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((u1_msualg_1 (k5_circcomb A B)) = (k13_funcop_1 B A B))  &  ((u2_msualg_1 (k5_circcomb A B)) = (k13_funcop_1 B A (k4_tarski B A))) ) ) ) ) ).
tt(t40_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v4_msualg_1 H A) & (l3_msualg_1 H A))  =>  (! [I:$i] :  ( ((v4_msualg_1 I B) & (l3_msualg_1 I B))  =>  (! [J:$i] :  ( ((v4_msualg_1 J C) & (l3_msualg_1 J C))  =>  ( ((r5_circtrm1 A B D E H I) & (r5_circtrm1 B C F G I J))  => (r5_circtrm1 A C (k3_relat_1 D F) (k3_relat_1 E G) H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski A (k4_classes1 B)) <=> (r1_tarski (k9_setfam_1 A) (k4_classes1 (k1_ordinal1 B)))) ) ) ) ).
tt(t40_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  (~  ((v1_ordinal1 B) &  ((r2_hidden A (k6_classes1 B)) &  (! [C:$i] :  (~  ((r2_hidden C B) &  ((k6_classes1 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t40_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) =>  ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = (k1_normsp_0 A (k7_clvect_1 A B))) ) ) ) ) ) ) ).
tt(t40_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A B)))  =>  ((v1_clopban3 (k5_clopban3 A B) A) & (v2_clopban3 (k5_clopban3 A B) A)) ) ) ) ) ) ).
tt(t40_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((k6_algstr_0 A (k7_clopban4 A (k1_clvect_1 A B C)) (k7_clopban4 A (k1_clvect_1 A B D))) = (k7_clopban4 A (k1_clvect_1 A B (k2_xcmplx_0 C D))))  &  ( ((k6_algstr_0 A (k7_clopban4 A (k1_clvect_1 A B D)) (k7_clopban4 A (k1_clvect_1 A B C))) = (k7_clopban4 A (k1_clvect_1 A B (k2_xcmplx_0 D C))))  &  ( ((k7_clopban4 A (k1_clvect_1 A B (k2_xcmplx_0 C D))) = (k7_clopban4 A (k1_clvect_1 A B (k2_xcmplx_0 D C))))  & (r1_lopban_4 A (k7_clopban4 A (k1_clvect_1 A B C)) (k7_clopban4 A (k1_clvect_1 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_closure1,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v9_closure1 B A) & (l1_closure1 B A))  =>  ((k6_closure1 A (u3_msualg_1 A B) (k7_closure1 A B)) = (g1_closure1 A (u3_msualg_1 A B) (u1_closure1 A B))) ) ) ) ) ).
tt(t40_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B)))))) )  =>  ( (! [D:$i] :  ((m1_closure2 D (u1_struct_0 A) (u3_msualg_1 A B) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A B))) => (r6_pboole (u1_struct_0 A) (k7_closure2 (u1_struct_0 A) (u3_msualg_1 A B) C D) (k11_closure2 A B D))) )  =>  ((v7_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) &  ((v8_closure2 C (u1_struct_0 A) (u3_msualg_1 A B)) & (v9_closure2 C (u1_struct_0 A) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t40_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  ((r1_struct_0 D B) => (r1_struct_0 D (k1_clvect_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t40_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_clvect_2 A C D)) <=>  (~ (r1_xxreal_0 D (k13_csspace A (k5_algstr_0 A C B)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k5_algstr_0 A (k2_clvect_3 A B D) (k2_clvect_3 A B C))) (k18_complex1 (k9_real_1 (k6_series_1 (k2_clvect_2 A B) D) (k6_series_1 (k2_clvect_2 A B) C))))) ) ) ) ) ) ) ) ).
tt(t40_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((r2_hidden E (k3_funct_2 A B C D)) <=>  (? [F:$i] :  ((m1_subset_1 F A) &  ((r2_hidden (k4_tarski F E) (k8_cohsp_1 A B C)) & (r1_tarski F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (? [C:$i] :  ((m1_subset_1 C (k19_coh_sp A)) &  (? [D:$i] :  ((m1_subset_1 D (k16_coh_sp A)) &  (? [E:$i] :  ((m1_subset_1 E (k16_coh_sp A)) &  ( (B = (k4_tarski (k4_tarski D E) C))  &  ( ( ((k17_coh_sp A E) = k1_xboole_0)  =>  ((k17_coh_sp A D) = k1_xboole_0) )  &  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k17_coh_sp A D) (k17_coh_sp A E)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k17_coh_sp A D) (k17_coh_sp A E))))) )  &  (! [F:$i] :  (! [G:$i] :  ((r2_hidden (k4_tarski F G) (k18_coh_sp A D)) => (r2_hidden (k4_tarski (k1_funct_1 C F) (k1_funct_1 C G)) (k18_coh_sp A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k3_xcmplx_0 A (k15_complex1 A))) = (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))))  &  ((k4_complex1 (k3_xcmplx_0 A (k15_complex1 A))) = k6_numbers) ) ) ) ).
tt(t40_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ((k1_complex2 (k8_complex1 (k9_complex1 A B) (k9_complex1 C D)) E) = (k8_complex1 (k9_complex1 A (k1_complex2 B E)) (k9_complex1 C (k1_complex2 D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k3_rlvect_1 k1_complfld (k3_vectsp_1 k1_complfld C A) (k3_vectsp_1 k1_complfld D B)) = (k3_vectsp_1 k1_complfld (k3_rlvect_1 k1_complfld (k8_group_1 k1_complfld C B) (k8_group_1 k1_complfld D A)) (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k45_valued_1 A (k45_valued_1 B C)) = (k1_valued_1 (k45_valued_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t40_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v4_tbsp_1 (k3_compl_sp A B C)) => (v4_tbsp_1 A)) ) ) ) ) ) ) ).
tt(t40_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k8_compos_1 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A C D) E) F) G) B) k6_numbers) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_comptrig,ax, ((k1_comptrig k7_complex1) = (k10_real_1 k32_sin_cos 2)) ).
tt(t40_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k2_comput_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k2_comput_1 A))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k8_nat_1 (k2_comput_1 A) B C) (k8_nat_1 (k2_comput_1 A) B (k2_nat_1 C 1)))) )  => (r2_hidden (k3_card_3 B) (k2_comput_1 A))) ) ) ) ) ).
tt(t40_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A)) (k25_valued_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers B) (k12_complex1 A)))) ) ) ) ).
tt(t40_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) &  ((v2_comseq_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k3_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers A D))  &  ((k4_complex1 (k8_nat_1 k2_numbers C D)) = (k8_nat_1 k1_numbers B D)) ) ) )  =>  ((v2_comseq_2 A) &  ((v2_comseq_2 B) &  ( ((k2_seq_2 A) = (k3_complex1 (k3_comseq_2 C)))  &  ((k2_seq_2 B) = (k4_complex1 (k3_comseq_2 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k1_binop_1 (k10_conlat_1 A) B (k6_conlat_1 A)) = B) ) ) ) ) ).
tt(t40_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_connsp_1 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k1_connsp_1 A C)) ) ) ) ) ) ) ) ).
tt(t40_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t40_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  ((k4_algstr_0 (k15_convex4 A) (k1_rlvect_2 (k15_convex4 A) B)) = (k8_convex4 A B)) ) ) ) ) ).
tt(t40_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (~  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C B F E) (k15_cqc_sim1 A D)) & (r2_hidden (k2_qc_lang3 A B) (k8_setwiseo (k3_qc_lang1 A) (k3_qc_lang1 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (v1_cqc_the1 (k4_cqc_the1 A) A)) ) ).
tt(t40_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A D (k9_cqc_lang A B C)) (k9_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C))) A) & (v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C)) (k12_cqc_lang A D (k9_cqc_lang A B C))) A)) ) ) ) ) ) ) ) ) ).
tt(t40_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D (k8_cqc_lang A B C)) => (r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) D (k6_domain_1 (k3_cqc_lang A) B)) C)) ) ) ) ) ) ) ) ) ).
tt(t40_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) =>  ((k12_csspace A (k3_rlvect_1 A B C) (k3_rlvect_1 A B C)) = (k2_xcmplx_0 (k12_csspace A B B) (k12_csspace A C C))) ) ) ) ) ) ) ) ).
tt(t40_descip_1,ax, (! [A:$i] :  ((m2_finseq_2 A k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 64 k6_margrel1)) =>  ((k43_descip_1 (k42_descip_1 A B) B) = A) ) ) ) ) ).
tt(t40_dickson,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  ( (~ (v2_struct_0 (k5_yellow_1 A B)))  <=> (v4_waybel_3 B)) ) ) ) ) ).
tt(t40_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 A D))  &  ( (~  ((k7_real_1 D (k10_real_1 B 2)) = k6_numbers) )  &  (~  ((k9_real_1 D (k10_real_1 B 2)) = k6_numbers) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k1_funct_1 (k5_diff_1 C B) D) = (k10_real_1 (k1_real_1 (k8_real_1 A B)) (k8_real_1 (k9_real_1 D (k10_real_1 B 2)) (k7_real_1 D (k10_real_1 B 2))))) ) ) ) ) ) ) ) ) ) ).
tt(t40_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k7_square_1 D)) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 (k9_real_1 A B) k6_numbers) |  ((k1_seq_1 (k4_diff_1 C B) A) = (k9_real_1 (k7_square_1 A) (k7_square_1 (k9_real_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) 1) B) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) k6_numbers) (k7_real_1 B A)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 C A) k6_numbers) B))) ) ) ) ) ) ) ).
tt(t40_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski (k5_dilworth A) B) =>  (B = (k5_dilworth A)) ) ) ) ) ) ).
tt(t40_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ((r2_analoaf A B C D D) &  ( ( ((r2_analoaf A B C D E) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) )  &  ((r2_analoaf A B C B D) => (r2_analoaf A C B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A D B B E) &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k3_ec_pf_1 (k9_int_3 A)) = (k6_subset_1 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k6_domain_1 (k3_zfmisc_1 k5_numbers k5_numbers k5_numbers) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers k6_numbers k6_numbers)))) ) ) ).
tt(t40_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ( (C = (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers))  => (r1_ec_pf_1 A (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C) C)) ) ) ) ) ) ) ).
tt(t40_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ((v1_cat_2 (k11_ens_1 B) (k11_ens_1 A)) & (m3_cat_2 (k11_ens_1 B) (k11_ens_1 A))) ) ) ) ) ).
tt(t40_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  ((r2_hidden (k7_real_1 (k8_real_1 (k9_real_1 C 1) (k1_matrix_1 B)) D) (k4_finseq_1 (k2_entropy1 A B))) &  ((k3_matrix_1 A B C D) = (k1_funct_1 (k2_entropy1 A B) (k7_real_1 (k8_real_1 (k9_real_1 C 1) (k1_matrix_1 B)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k5_enumset1 A A A B C D E) = (k3_enumset1 A B C D E)) ) ) ) ) ) ).
tt(t40_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  ((v1_eqrel_1 (k6_domain_1 (k1_zfmisc_1 (k1_zfmisc_1 A)) B) A) & (m1_subset_1 (k6_domain_1 (k1_zfmisc_1 (k1_zfmisc_1 A)) B) (k1_zfmisc_1 (k1_zfmisc_1 (k9_setfam_1 A))))) ) ) ) ).
tt(t40_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k23_rvsum_1 B B) = k6_numbers)  <=>  ((k12_euclid B) = k6_numbers) ) ) ) ) ) ).
tt(t40_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k4_complex1 (k1_complex2 A B)) = (k7_real_1 (k1_real_1 (k8_real_1 (k3_complex1 A) (k4_complex1 B))) (k8_real_1 (k4_complex1 A) (k3_complex1 B)))) ) ) ) ) ).
tt(t40_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ( (B = (a_4_0_euclid_4 A C D E))  &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden F (k2_euclid_4 A C D)) &  ( ((k12_euclid (k8_euclid A E F)) = (k5_seq_4 B))  & (r1_rvsum_1 (k8_euclid A C D) (k8_euclid A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ((r2_hidden A (k5_jgraph_6 F G H)) &  ((r2_hidden B (k5_jgraph_6 F G H)) &  ((r2_hidden C (k5_jgraph_6 F G H)) &  ((r2_hidden D (k5_jgraph_6 F G H)) &  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) A C)) & (r2_hidden E (k1_rltopsp1 (k15_euclid 2) B D))) ) ) ) )  =>  ((k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D B))) = (k7_real_1 (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) B A)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D C))) (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) D A))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((v1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A))) &  ((r2_hidden C B) &  ((r2_hidden D B) &  (D = (k9_euclid A C E)) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k9_euclid 3 (k1_euclid_8 B C D) A) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k11_binop_2 A B)) (k9_euclid 3 k3_euclid_8 (k11_binop_2 A C))) (k9_euclid 3 k4_euclid_8 (k11_binop_2 A D)))) ) ) ) ) ) ) ) ) ).
tt(t40_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k4_algstr_0 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B C)) = (k1_rlvect_1 (k15_euclid A) B (k7_binop_2 C)))  &  ((k4_algstr_0 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B C)) = (k1_rlvect_1 (k15_euclid A) (k4_algstr_0 (k15_euclid A) B) C)) ) ) ) ) ) ) ) ).
tt(t40_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid A)) =>  ( ((r3_euclidlp A (k8_euclid A B C) (k8_euclid A D E)) &  ((r2_hidden F (k2_euclid_4 A C B)) &  ((r2_hidden G (k2_euclid_4 A C B)) &  ((r2_hidden H (k2_euclid_4 A E D)) & (r2_hidden I (k2_euclid_4 A E D))) ) ) )  =>  ( (F = G)  |  ( (H = I)  | (r3_euclidlp A (k8_euclid A G F) (k8_euclid A I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_exchsort A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_exchsort B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) )  =>  ( ((m1_exchsort A B) & (m1_exchsort B C))  => (m1_exchsort A C)) ) ) ) ) ) ) ).
tt(t40_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_msafree2 (k5_circcomb A (k10_finseq_1 B C))) = (k2_tarski B C)) ) ) ) ).
tt(t40_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k1_relset_1 k1_numbers A)) =>  ((k1_seq_1 A B) = B) ) ) )  => (v1_fcont_1 A)) ) ) ).
tt(t40_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos (k9_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k30_sin_cos B))) (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t40_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos B) (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t40_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) &  ((r2_fdiff_1 A (k2_subset_1 k1_numbers)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 (k1_fdiff_1 A B) k6_numbers)) ) ) )  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k2_subset_1 k1_numbers)))) ) ) ).
tt(t40_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k16_sin_cos B) = k6_numbers) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t40_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = 1)  &  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos C) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos C)))  &  (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos C) (k1_real_1 1))) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B k19_sin_cos) (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) A) C) = (k10_prepower (k9_real_1 1 (k1_seq_1 k19_sin_cos C)) (k10_real_1 1 2))) ) ) ) ) ) ) ) ) ) ).
tt(t40_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos B)) (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t40_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) A) B) = (k1_real_1 (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos B)))))) ) ) ) ) ) ) ) ).
tt(t40_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((k1_pre_ff (k1_nat_1 A B)) = (k2_nat_1 (k4_nat_1 (k1_pre_ff B) (k1_pre_ff (k1_nat_1 A 1))) (k4_nat_1 (k1_pre_ff (k7_nat_d B 1)) (k1_pre_ff A)))) ) ) ) ) ).
tt(t40_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k2_nat_1 (k3_fib_num3 A B C) (k3_fib_num3 A B (k2_nat_1 C 4))) = (k4_nat_1 3 (k3_fib_num3 A B (k2_nat_1 C 2)))) ) ) ) ) ) ) ).
tt(t40_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) => (r2_finseq_8 A (k9_finseq_8 A B C) C 1)) ) ) ) ) ) ).
tt(t40_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B (k3_filter_0 A (k4_subset_1 (u1_struct_0 A) D (k6_domain_1 (u1_struct_0 A) C)))) => (r2_hidden (k4_filter_0 A C B) (k3_filter_0 A D))) ) ) ) ) ) ) ) ) ).
tt(t40_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((v14_lattices A) & (v14_lattices B))  <=> (v14_lattices (k7_filter_1 A B))) ) ) ) ) ).
tt(t40_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_filter_2 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B)) => (r1_filter_2 (u1_struct_0 A) (k7_filter_2 A C) (k6_filter_2 A B))) ) ) ) ) ) ) ).
tt(t40_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( (B = (k9_finseq_1 A))  <=>  ( ((k3_finseq_1 B) = 1)  &  ((k1_funct_1 B 1) = A) ) ) ) ) ) ).
tt(t40_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) )  =>  ((v1_relat_1 (k3_relat_1 B A)) &  ((v1_funct_1 (k3_relat_1 B A)) & (v1_finseq_1 (k3_relat_1 B A))) ) ) ) ) ) ).
tt(t40_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski B (k2_finseq_1 A)) =>  ((k1_relset_1 k5_numbers (k14_finseq_1 B)) = (k2_finseq_1 (k5_card_1 B))) ) ) ) ) ) ).
tt(t40_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( ((k4_finseq_4 A B) = 1)  <=>  ((k5_finseq_4 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t40_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden C (k10_xtuple_0 (k17_finseq_1 B A D))) =>  ((k4_finseq_4 (k17_finseq_1 B A D) C) = (k4_finseq_4 D C)) ) ) ) ) ) ) ) ) ) ).
tt(t40_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k1_finseq_5 A C B) = (k7_finseq_1 (k5_finseq_4 C B) (k12_finseq_1 A B))) ) ) ) ) ) ) ) ).
tt(t40_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((r7_binop_1 B F E) => (r2_funct_2 A B (k1_partfun1 A B B B (k6_funcop_1 B A E C D) F) (k6_funcop_1 B A E (k1_partfun1 A B B B C F) (k1_partfun1 A B B B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (k9_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k3_subset_1 (u1_struct_0 A) (k10_fintopo2 A B)))) ) ) ) ) ).
tt(t40_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fintopo3 A B 1) = (k1_fintopo3 A B)) ) ) ) ) ).
tt(t40_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_fin_topo A) &  ((r1_fintopo6 A B) &  ((r1_fintopo6 A C) &  ( (~  (B = C) )  &  (~ (r1_fintopo4 A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_catalan2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_catalan2 A)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden C (k7_flang_1 A B E)) & (r2_hidden D (k7_flang_1 A B F)))  => (r2_hidden (k1_flang_1 A C D) (k7_flang_1 A B (k2_xcmplx_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k7_flang_1 A (k1_flang_2 A B C D) E) = (k1_flang_2 A B (k3_xcmplx_0 C E) (k3_xcmplx_0 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t40_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_tarski (k2_flang_2 A B) (k1_flang_3 A B C)) <=>  ( (C = k6_numbers)  | (r2_hidden (k2_flang_1 A) B)) ) ) ) ) ) ) ).
tt(t40_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v5_relat_1 C (k3_finseq_2 A)) => (r2_hidden (k1_funct_1 C B) (k3_finseq_2 A))) ) ) ) ) ).
tt(t40_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_frechet2 A B C) => (r2_hidden C (k2_pre_topc A (k2_relset_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(t40_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v8_struct_0 E) & (l2_fsm_1 E A B)) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ( (D = (k11_fsm_1 A B E))  & (r2_hidden F G))  =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((r2_hidden H (k2_finseq_1 (k2_nat_1 (k3_finseq_1 C) 1))) => (r2_hidden (k1_funct_1 (k2_fsm_1 A E F C) H) (k1_funct_1 (k2_fsm_1 A D G C) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v8_struct_0 B) & (l2_fsm_3 B A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))))) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v4_fsm_3 C A (k9_flang_1 A)) & (l2_fsm_3 C A (k9_flang_1 A))) ) )  &  ((k6_fsm_3 A (k4_subset_1 (k3_catalan2 A) (k9_flang_1 A) (k4_flang_1 A (k2_flang_1 A))) B) = (k6_fsm_3 A (k9_flang_1 A) C)) ) ) ) ) ) ) ).
tt(t40_ftacell1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (! [E:$i] :  ( (~  (E = (k4_tarski (k10_finseq_1 D (k48_gfacirc1 A B C)) k4_twoscomp)) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E)))) => (v1_circuit2 (k5_facirc_1 (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E) F 4) (k19_ftacell1 A B C D E) (k20_ftacell1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  => (r2_funct_2 B A (k1_partfun1 B A A A D (k6_funcop_1 A A C E (k6_partfun1 A))) (k6_funcop_1 A B C (k1_partfun1 B A A A D E) D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) => (v2_funct_1 (k2_funct_1 A))) ) ) ).
tt(t40_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((k8_relset_1 A B C B) = A) ) ) ) ) ) ).
tt(t40_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k2_tarski k1_xboole_0 1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k2_tarski k1_xboole_0 1))))) )  =>  (B = (k4_funct_3 (k8_relat_1 B (k1_tarski 1)) A)) ) ) ) ).
tt(t40_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_funct_1 (k1_funct_4 C D)) & (m1_subset_1 (k1_funct_4 C D) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(t40_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k4_partfun1 A B)) =>  ((r1_tarski (k10_xtuple_0 (k2_funct_5 C)) B) & (r1_tarski (k10_xtuple_0 (k4_funct_5 C)) B)) ) ) ) ) ) ).
tt(t40_funct_6,ax, ( ((k6_funct_6 k1_xboole_0) = k1_xboole_0)  &  ((k7_funct_6 k1_xboole_0) = (k16_funcop_1 k1_xboole_0 k1_xboole_0)) ) ).
tt(t40_funct_7,ax, (! [A:$i] :  ((k5_funct_7 k1_xboole_0 A) = (k9_finseq_1 A)) ) ).
tt(t40_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 A k1_numbers k1_numbers) => (v4_funct_8 (k41_valued_1 k1_numbers k1_numbers A) k1_numbers k1_numbers)) ) ) ).
tt(t40_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v21_functor0 C A B) &  ((v7_functor0 C A B) & (v10_functor0 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B D E)) =>  ( (~  ((k1_altcat_1 B D E) = k1_xboole_0) )  =>  ((k1_funct_1 (k4_functor0 A B C (k3_functor0 B A (k15_functor0 A B C) D) (k3_functor0 B A (k15_functor0 A B C) E)) (k1_funct_1 (k4_functor0 B A (k15_functor0 A B C) D E) F)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor3 E A B C D) =>  ((r1_functor3 A B C D) => (r8_pboole (u1_struct_0 A) (k5_functor2 A B C D C E (k8_functor3 A B C D E)) (k4_functor2 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k4_fuzzy_1 A)) (k5_fuzzy_1 A)) & (r2_funct_2 A k1_numbers (k3_fuzzy_1 A (k5_fuzzy_1 A)) (k4_fuzzy_1 A))) ) ) ).
tt(t40_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A B C) (k3_fuzzy_2 A B C))) ) ) ) ) ) ).
tt(t40_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ((v2_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers C B)) <=> (v2_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B))) ) ) ) ) ) ) ) ).
tt(t40_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k6_fvsum_1 A B (k8_fvsum_1 A B C D)) = (k4_fvsum_1 A B (k6_fvsum_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t40_gate_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (~  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 B F A)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 C G J)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 D H K)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 E I L)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k3_gate_1 B F))) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k3_gate_1 C G))) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k3_gate_1 D H))) )  &  ( (~  ( (~ (v1_xboole_0 Q))  & (v1_xboole_0 (k3_gate_1 E I))) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 (k18_gate_1 A N O P Q))) )  &  ( (~  ( (~ (v1_xboole_0 S))  & (v1_xboole_0 (k3_gate_1 M R))) )  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 M R)))  & (v1_xboole_0 S)) )  &  (~  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 S)) )  &  (~  ( (~ (v1_xboole_0 S))  & (v1_xboole_0 M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((k5_gcd_1 A B C D) = (k5_struct_0 A))  &  ((k5_gcd_1 A B E F) = (k5_struct_0 A)) )  =>  ( (D = (k4_struct_0 A))  |  ((k5_gcd_1 A B (k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) (k8_group_1 A D (k1_gcd_1 A F (k5_gcd_1 A B D F)))) = (k5_gcd_1 A B (k3_rlvect_1 A (k8_group_1 A C (k1_gcd_1 A F (k5_gcd_1 A B D F))) (k8_group_1 A E (k1_gcd_1 A D (k5_gcd_1 A B D F)))) (k5_gcd_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) => (m1_genealg1 (k5_genealg1 F G H A B C D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((r2_geomtrap A B C D E F J) &  ((r2_geomtrap A B C D E G K) &  ((r2_geomtrap A B C D E H L) &  ((r2_geomtrap A B C D E I M) & (r3_analmetr A F G H I B C)) ) ) )  =>  ( (D = E)  | (r3_analmetr A J K L M B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k14_twoscomp)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k2_twoscomp)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k13_gfacirc1 A B C) (k14_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k13_gfacirc1 A B C) (k14_gfacirc1 A B C) D 2) (k13_gfacirc1 A B C) (k14_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  => (m1_glib_000 A A)) ) ).
tt(t40_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k2_glib_001 A (k1_funct_1 B C) (k1_funct_1 B (k2_nat_1 C 2)) (k1_funct_1 B (k2_nat_1 C 1))) (k8_glib_001 A B C (k2_nat_1 C 2)))) ) ) ) ) ) ) ).
tt(t40_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v1_glib_002 A)) ) ) ) ) )  => (r1_xxreal_0 (k15_glib_000 A) (k2_nat_1 (k17_glib_000 A) 1))) ) ).
tt(t40_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] : (r5_glib_000 A (k13_glib_003 A B C))) ) ) ) ).
tt(t40_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) &  ((v2_glib_000 B) &  ((v1_glib_002 B) &  ((v1_glib_003 B) & (v7_glib_003 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_glib_003 C) &  ((v4_glib_003 C A) & (m1_glib_000 C A)) )  =>  ( ( ((v9_glib_000 C A) &  ((v3_glib_002 C) &  ((v1_glib_003 C) &  ((v4_glib_003 C A) &  ((v1_glib_004 C A) & (m1_glib_000 C A)) ) ) ) )  &  ((r5_glib_000 A B) &  ((k5_glib_003 A) = (k5_glib_003 B)) ) )  =>  ((v9_glib_000 C B) &  ((v3_glib_002 C) &  ((v1_glib_003 C) &  ((v4_glib_003 C B) &  ((v1_glib_004 C B) & (m1_glib_000 C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t40_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 C))) &  ((r2_hidden (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) (k10_real_1 1 2)) (k3_topreal1 2 C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 1) (k3_finseq_1 C)) &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) = (k2_topreal1 2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k5_gobrd13 D E A) = (k3_goboard5 E B (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((r1_jordan2c 2 (k3_topreal1 2 A) B) =>  (B = (k1_jordan2c 2 (k3_topreal1 2 A))) ) ) ) ) ) ).
tt(t40_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_graph_1 E B) =>  (! [F:$i] :  ((m2_graph_1 F B) =>  ( ((r1_graph_2 B C E) &  ( (F = (k2_partfun1 k5_numbers (u4_struct_0 B) E (k2_finseq_1 A)))  &  (D = (k2_partfun1 k5_numbers (u1_struct_0 B) C (k2_finseq_1 (k2_nat_1 A 1)))) ) )  => (r1_graph_2 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_graph_3 B D C))) =>  ( (E = C)  =>  ( (D = C)  |  ((k3_graph_3 (k8_graph_3 B D C) E A) = (k3_graph_3 B C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ((r1_graph_5 A D B C) => (r1_tarski (k6_graph_5 A D) (k4_graph_5 A B C))) ) ) ) ) ) ) ) ) ).
tt(t40_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 C A) &  ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) C) B) A) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t40_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden k3_algstr_0 (k28_grcat_1 A))) ) ).
tt(t40_groeb_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_ideal_1 D (k11_polynom1 A C)) &  ((v2_ideal_1 D (k11_polynom1 A C)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C))))) )  =>  ( ((r2_groeb_1 A B C E D) &  ((r4_groeb_1 A B C E) &  ((r2_groeb_1 A B C F D) & (r4_groeb_1 A B C F)) ) )  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_groeb_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  ((r1_groeb_1 A B C D) <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D)) => (r6_groeb_2 A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v3_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r2_hidden (k11_pre_poly A (k2_polynom7 A C E) G) (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C (k9_polynom1 A C E D) F))) <=> (r2_hidden G (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k2_group_11 A (k1_group_11 A (k2_group_11 A B C) C) C) = (k2_group_11 A B C)) ) ) ) ) ) ) ).
tt(t40_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((k6_algstr_0 B C D) = (k6_algstr_0 B D C))  =>  ((k6_algstr_0 B C (k5_group_1 B A D)) = (k6_algstr_0 B (k5_group_1 B A D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t40_group_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  ((r1_struct_0 C A) => (r1_struct_0 B A)) ) ) ) ) ) ).
tt(t40_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_group_3 A (k7_domain_1 (u1_struct_0 A) B C) (k7_domain_1 (u1_struct_0 A) D E)) = (k9_domain_1 (u1_struct_0 A) (k2_group_3 A B D) (k2_group_3 A B E) (k2_group_3 A C D) (k2_group_3 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ((v2_group_4 B A) => (m1_group_2 (k6_group_4 A) B)) ) ) ) ) ).
tt(t40_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_5 A B B C) = (k1_group_1 A)) ) ) ) ) ) ) ).
tt(t40_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k7_group_6 A B) E) (k7_group_6 A C)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D (k7_group_6 B C)) (k7_group_6 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ((m1_group_9 C A D) =>  ((v4_group_9 C A D) & (m1_group_9 C A D)) ) ) ) ) ) ) ) ) ).
tt(t40_hausdorf,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ((k3_hausdorf A B B) = k6_numbers) ) ) ) ) ).
tt(t40_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (! [F:$i] :  ( ((v5_glib_001 F A) & (m3_glib_001 F A))  =>  (! [G:$i] :  ( ((v5_glib_001 G A) & (m3_glib_001 G A))  =>  ( ( (F = (k2_helly A B C))  &  ( (G = (k2_helly A B D))  &  (E = (k1_funct_1 F (k3_finseq_1 (k1_helly F G)))) ) )  =>  ((r1_tarski F G) |  ((r1_tarski G F) |  ((k9_subset_1 (k6_glib_000 A) (k13_glib_001 A (k2_helly A E C)) (k13_glib_001 A (k2_helly A E D))) = (k1_tarski E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear D k1_complfld A A) &  ((v4_bilinear D k1_complfld A A) &  ((v3_hermitan D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  ((k3_rlvect_1 k1_complfld (k3_rlvect_1 k1_complfld (k3_rlvect_1 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C)) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C)) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C)) = (k5_algstr_0 k1_complfld (k3_rlvect_1 k1_complfld (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k3_rlvect_1 A B C) (k3_rlvect_1 A B C)) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k5_algstr_0 A B C) (k5_algstr_0 A B C))) (k8_group_1 k1_complfld k2_hahnban1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k3_rlvect_1 A B (k4_vectsp_1 k1_complfld A k2_hahnban1 C)) (k3_rlvect_1 A B (k4_vectsp_1 k1_complfld A k2_hahnban1 C))))) (k8_group_1 k1_complfld k2_hahnban1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A k2_hahnban1 C)) (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A k2_hahnban1 C)))))) ) ) ) ) ) ) ) ) ).
tt(t40_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)))) =>  (~  ((r1_lattice3 (k1_heyting3 k5_numbers (k6_domain_1 k5_numbers A)) (k5_heyting3 A) B) &  (B = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ).
tt(t40_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A D) =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k26_valued_1 k1_numbers k1_numbers (k1_taylor_1 C) B) D) C) A) = (k8_real_1 B (k3_newton C))) ) ) ) ) ) ) ) ) ) ).
tt(t40_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 (k4_hilbert1 A B) C) (k3_hilbert1 (k4_hilbert1 A B) (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(t40_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (! [E:$i] :  ((r1_abian E (k5_hilbert3 C D A)) =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r1_abian F (k5_hilbert3 C D (k3_hilbert1 A B))) => (r1_abian (k1_funct_1 F E) (k5_hilbert3 C D B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (B = (k4_struct_0 k1_complfld)) )  =>  ((v1_hurwitz A) <=> (v1_hurwitz (k3_polynom5 k1_complfld A B))) ) ) ) ) ) ).
tt(t40_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~  (D = k6_numbers) )  => (m1_funct_7 (k17_idea_1 D B A C) k14_idea_1 k14_idea_1)) ) ) ) ) ) ) ) ) ).
tt(t40_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l4_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m3_ideal_1 D A C) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [G:$i] :  ((m2_finseq_1 G (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  (~  ((r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) F C) E) &  ((r3_ideal_1 A C D G) &  (! [H:$i] :  ((m3_ideal_1 H B E) =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 H))  &  (! [I:$i] :  ((r2_hidden I (k1_relset_1 k5_numbers H)) =>  ((k1_funct_1 H I) = (k6_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) G I))) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) F (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k7_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) G I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  =>  ((k2_incsp_1 A B C D) = (k4_incsp_1 A (k1_incsp_1 A B C) (k1_incsp_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k3_msualg_1 A F (k11_msafree A (k3_relat_1 D C)))) =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v1_funct_1 H) & (v1_finseq_1 H)) )  =>  ( (H = (k5_msualg_3 A (k11_msafree A (k3_relat_1 D C)) (k1_instalg1 A B (k11_msafree B C) D E) F (k3_instalg1 A B C D E) G))  =>  ((k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k3_relat_1 D C))) (u3_msualg_1 A (k1_instalg1 A B (k11_msafree B C) D E)) (k3_instalg1 A B C D E) (k2_msualg_1 A F)) (k4_trees_4 (k4_tarski F (u1_struct_0 A)) G)) = (k4_trees_4 (k4_tarski (k1_funct_1 E F) (u1_struct_0 B)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_int_1 (k1_int_1 A)) = (k1_int_1 A)) ) ) ).
tt(t40_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((r1_int_2 A B) &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (! [F:$i] :  ((v1_int_1 F) =>  ( ( ((k6_int_1 (k6_xcmplx_0 F C) A) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 F D) B) = k6_numbers) )  => (r2_int_1 F (k2_xcmplx_0 C (k3_xcmplx_0 A E)) (k3_xcmplx_0 A B))) ) )  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 A E) (k6_xcmplx_0 D C)) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( ( ((k3_finseq_1 B) = A)  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ( (~ (r1_xxreal_0 (k1_recdef_1 B C) k6_numbers))  & (r1_xxreal_0 (k1_recdef_1 B C) A)) ) ) )  & (v2_funct_1 B)) )  =>  ((k2_relset_1 k5_numbers B) = (k2_finseq_1 A)) ) ) ) ) ) ).
tt(t40_int_6,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_1 C) &  ((v1_partfun3 C) & (v1_int_6 C)) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k3_xcmplx_0 A B)) =>  ((r1_xxreal_0 (k19_rvsum_1 C) (k3_xcmplx_0 A B)) |  ((k2_int_6 (k18_valued_1 (k1_int_6 A C) (k1_int_6 B C)) C) = (k3_xcmplx_0 A B)) ) ) ) ) ) ) ) ) ).
tt(t40_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k16_sin_cos D)))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t40_integr12,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B G) &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers D E)) &  ((r2_relset_1 k1_numbers k1_numbers E (k1_taylor_1 2)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 F H) = (k11_binop_2 H (k9_prepower (k10_binop_2 (k5_square_1 A) (k5_prepower H 2)) (k13_binop_2 (k18_binop_2 1 2)))))  &  ( ((k1_seq_1 D H) = (k5_square_1 A))  &  (~ (r1_xxreal_0 (k1_seq_1 C H) k6_numbers)) ) ) ) ) )  &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k18_binop_2 1 2))))) &  ( (G = (k1_relset_1 k1_numbers F))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F B))) ) ) ) ) )  =>  ((k2_integra5 B F) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k18_binop_2 1 2)))) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k18_binop_2 1 2)))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_integr13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A)))) & (r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A))) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A))) B) C) = (k10_real_1 (k4_real_1 A (k5_prepower (k1_seq_1 k2_sin_cos9 C) (k5_real_1 A 1))) (k7_real_1 1 (k5_square_1 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t40_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) &  (E = F) )  =>  ( (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k1_integra1 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [H:$i] :  ((m4_integr15 H A B C G) =>  ( ((v2_comseq_2 (k2_integra3 B G)) &  ((k2_seq_2 (k2_integra3 B G)) = k6_numbers) )  =>  ((v3_normsp_1 (k6_integr15 A B C G H) (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) (k6_integr15 A B C G H)) = E) ) ) ) ) ) )  <=>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k1_integra1 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 B))))) )  =>  (! [H:$i] :  ((m2_integr18 H (k4_real_ns1 A) B D G) =>  ( ((v2_comseq_2 (k2_integra3 B G)) &  ((k2_seq_2 (k2_integra3 B G)) = k6_numbers) )  =>  ((v3_normsp_1 (k3_integr18 (k4_real_ns1 A) B D G H) (k4_real_ns1 A)) &  ((k6_normsp_1 (k4_real_ns1 A) (k3_integr18 (k4_real_ns1 A) B D G H)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r1_integra1 C D) &  ((r2_hidden A (k4_finseq_1 C)) & (v1_seq_2 (k2_partfun1 B k1_numbers E B))) )  => (r1_xxreal_0 (k1_seq_1 (k14_integra1 (k4_integra1 B E D)) (k13_integra1 B C D A)) (k1_seq_1 (k14_integra1 (k4_integra1 B E C)) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_integra2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v2_membered A))  =>  ((k22_member_1 A k6_numbers) = (k1_seq_4 k6_numbers)) ) ) ).
tt(t40_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))  =>  ((k2_integra5 A k19_sin_cos) = 1) ) ) ) ).
tt(t40_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 (k1_real_1 (k8_real_1 2 k32_sin_cos)) (k8_real_1 2 k32_sin_cos)))  => (r1_integra9 A k16_sin_cos k19_sin_cos)) ) ) ).
tt(t40_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  ((k9_interva1 A B C) = (k2_interva1 A (k7_subset_1 A (k5_interva1 A B) (k6_interva1 A C)) (k7_subset_1 A (k6_interva1 A B) (k5_interva1 A C)))) ) ) ) ) ) ) ).
tt(t40_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 (k3_intpro_1 A B) A) C) B) k8_intpro_1)) ) ) ) ) ) ).
tt(t40_irrat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 2 B) &  ( (A = (k13_complex1 1 (k2_xcmplx_0 B 1)))  & (r1_xxreal_0 1 (k13_complex1 A (k6_xcmplx_0 1 A)))) ) ) ) ) ) ) ).
tt(t40_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_nattra_1 G B C E F) =>  ((r2_nattra_1 B C E F) => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k5_isocat_1 A B C E F D G) (k6_isocat_1 A B C D D E F (k6_nattra_1 A B D) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  => (r1_isocat_1 (k11_nattra_1 A (k8_cat_2 B C)) (k8_cat_2 (k11_nattra_1 A B) (k11_nattra_1 A C)))) ) ) ) ) ) ).
tt(t40_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_isomichi B A) <=> (v5_isomichi (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t40_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 A)) &  ((r1_goboard4 (k2_goboard1 A) (k1_seq_1 (k2_goboard1 A) 1) (k1_seq_1 (k2_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k1_goboard1 A) C D) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 (k2_nat_1 E 1) (k3_finseq_1 A)) & (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A E) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 E 1)))))) ) ) ) )  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal1 E) &  ( ((k1_funct_1 E 1) = (k1_funct_1 A 1))  &  ( ((k1_funct_1 E (k3_finseq_1 E)) = (k1_funct_1 A (k3_finseq_1 A)))  &  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 E)) &  ((r1_goboard4 (k2_goboard1 E) (k1_seq_1 (k2_goboard1 A) 1) (k1_seq_1 (k2_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k1_goboard1 E) C D) &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (~  ((r2_hidden G (k4_finseq_1 A)) &  (~ (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E F) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A G))))) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 (k2_nat_1 F 1) (k3_finseq_1 E)) & (r1_xxreal_0 B (k12_euclid (k5_algstr_0 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E F) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k2_nat_1 F 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jgraph_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~  ( (B = k1_jgraph_2)  & (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t40_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  ( ( (C = (k5_relat_1 (k2_funct_1 k1_jgraph_3) B))  &  ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_1_jgraph_3) ) )  =>  ((v5_pre_topc C (k1_pre_topc (k1_pre_topc (k15_euclid 2) A) B) (k1_pre_topc (k15_euclid 2) A)) & (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t40_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  ((r2_hidden B D) &  ((v3_pre_topc D (k15_euclid 2)) &  ((r1_tarski D C) & (r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (A = a_0_6_jgraph_5)  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))))))) )  =>  (~  ((v3_tops_2 B (k4_topmetr (k1_real_1 1) 1) (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k9_jordan6 A)) =>  ((k1_funct_1 B (k17_euclid C)) = C) ) ) )  &  ( ((k1_funct_1 B (k1_real_1 1)) = (k18_pscomp_1 A))  &  ((k1_funct_1 B 1) = (k22_pscomp_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k11_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid A D)) ) ) ) ) ) ) ) ) ) ).
tt(t40_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) & (r1_xxreal_0 G (k18_euclid D))) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D))) & (r1_xxreal_0 D B)) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) A (k3_finseq_1 (k1_jordan8 E B)))) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) C (k3_finseq_1 (k1_jordan8 E D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_9_jordan1 A B C D))  &  (F = (a_4_5_jordan1 A B C D)) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (r1_tarski F (k2_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 B (k3_finseq_1 (k1_jordan8 A C))) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A C))) &  ((r1_tarski (k3_goboard5 (k1_jordan8 A C) B D) (k1_jordan2c 2 A)) & (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 A C)) (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r2_sprect_2 (k1_jordan9 B A) (k1_jordan1e B A))) ) ) ) ).
tt(t40_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ( (~ (v3_funct_1 B))  &  ((v1_finseq_6 B (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 B) &  ((v2_topreal1 B) &  ((v1_goboard5 B) &  ((v2_goboard5 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((v1_sprect_2 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) B A)) => (v1_sprect_2 B)) ) ) ) ) ).
tt(t40_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 A)) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D) (k3_topreal1 2 B))) ) ) )  => (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D) (k10_xtuple_0 B))) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r1_xxreal_0 B (k1_topreal6 A E F))) ) ) ) )  => (r1_xxreal_0 B (k1_jordan1k A C D))) ) ) ) ) ) ) ) ) ).
tt(t40_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xxreal_0 (k9_pscomp_1 A) (k18_euclid (k2_jordan21 A)))) ) ).
tt(t40_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k6_pscomp_1 A) = (k6_pscomp_1 (k4_jordan19 A))) ) ) ).
tt(t40_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) ) ) )  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ( (B = (k1_funct_1 A 1))  | (r1_jordan3 (k2_jordan3 A B) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) ) ) ) ) ).
tt(t40_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden H B) &  ((r2_hidden I B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) C D) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D E) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) E F) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) F G) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) G H) B) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) H I) B) &  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ((v5_pre_topc J k5_topmetr (k1_pre_topc (k15_euclid A) B)) &  ( (C = (k1_funct_1 J k6_numbers))  &  (I = (k1_funct_1 J 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_tarski (k3_topreal1 2 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A)) (k3_topreal1 2 A))) ) ) ) ).
tt(t40_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 C (k3_finseq_1 A)) =>  ((r1_xxreal_0 B 1) |  ((r1_xxreal_0 C B) | (v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ) ) ).
tt(t40_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k7_pscomp_1 (k3_topreal1 2 A)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 (k1_matrix_1 (k2_goboard2 A))))) ) ) ).
tt(t40_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) D E B) &  (C = (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k2_tarski D E))) )  => (v2_connsp_1 C (k1_pre_topc (k15_euclid A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  (! [H:$i] :  ((m1_borsuk_2 H A D E) =>  ((k2_relset_1 (u1_struct_0 A) (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D F G) H)) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) F) (k2_relset_1 (u1_struct_0 A) G)) (k2_relset_1 (u1_struct_0 A) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  => (v4_lattice3 (k8_knaster A B))) ) ) ) ).
tt(t40_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr k6_kurato_1) = k6_kurato_1) ) ).
tt(t40_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_funct_1 A C) = B) ) )  =>  ((k2_kurato_2 (k15_euclid 2) A) = (k2_pre_topc (k15_euclid 2) B)) ) ) ) ) ) ).
tt(t40_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ((k12_matrix_3 A B C) = (k4_struct_0 B)) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 D) = A)  &  ((k12_laplace B C D) = (k10_laplace (u1_struct_0 B) E)) )  =>  ( ((k10_laplace (u1_struct_0 B) D) = (k12_laplace B (k5_matrix_6 A B C) E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k1_funct_1 D F) = (k8_group_1 B (k11_algstr_0 B (k12_matrix_3 A B C)) (k12_matrix_3 A B (k3_matrix11 F A A (u1_struct_0 B) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((r2_hidden C D) => (r3_lattices A (k3_lattice2 B A D E) (k3_funct_2 B (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((r2_hidden B C) & (r4_lattice3 A B C))  =>  ((k15_lattice3 A C) = B) ) ) ) ) ) ) ).
tt(t40_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  ((k3_lattice2 (u1_struct_0 A) A (k5_setwiseo (u1_struct_0 A) C (k2_setwiseo (u1_struct_0 A) B)) (k5_lattice4 A)) = (k4_lattices A (k3_lattice2 (u1_struct_0 A) A C (k5_lattice4 A)) (k7_lattices A B))) ) ) ) ) ) ) ).
tt(t40_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  => (v2_funct_2 (k16_lattice5 A) (u1_struct_0 A))) ) ).
tt(t40_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k40_glib_000 (k15_lexbfs A (k16_lexbfs A))) = (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k14_lexbfs A (k16_lexbfs A)))) ) ) ).
tt(t40_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) ) )  =>  ( ((v3_lfuzzy_1 C A) & (r1_fuzzy_1 B C))  => (r1_fuzzy_1 (k5_lfuzzy_1 A B) C)) ) ) ) ) ) ) ).
tt(t40_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) &  ((v2_comseq_2 A) &  ( ((k2_seq_2 A) = k6_numbers)  & (v6_valued_0 A)) ) )  => (v1_limfunc1 (k37_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t40_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r6_limfunc2 B A) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ((r1_tarski (k2_rcomp_1 A (k7_real_1 A D)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k2_rcomp_1 A (k7_real_1 A D))) => (r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r6_limfunc2 C A)) ) ) ) ) ) ) ) ).
tt(t40_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ( ((k1_limfunc3 B A) = k6_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))))) ) ) )  |  ((r1_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc3 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t40_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r3_limfunc3 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  ((k1_seq_1 B E) = (k1_limfunc3 B A)) ) ) ) ) ) ) ) )  | (r3_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t40_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_lmod_6 A (k1_vectsp_4 A C) B) &  ((r1_lmod_6 A (k1_vectsp_4 A B) C) & (r1_lmod_6 A (k1_vectsp_4 A D) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k16_lopban_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k16_lopban_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 A B))) =>  ( (E = (k5_algstr_0 (k16_lopban_1 A B) C D))  <=>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k17_lopban_1 A B E F) = (k5_algstr_0 B (k17_lopban_1 A B C F) (k17_lopban_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A B)))  =>  ((v1_lopban_3 (k5_lopban_3 A B) A) & (v2_lopban_3 (k5_lopban_3 A B) A)) ) ) ) ) ) ).
tt(t40_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r1_lopban_4 A (k1_rlvect_1 A B C) (k1_rlvect_1 A B D))) ) ) ) ) ) ) ) ).
tt(t40_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) & (r2_hidden E (k9_lpspace1 A B C)))  =>  ( ((k13_lpspace1 A B C D) = (k13_lpspace1 A B C E))  <=> (r2_hidden E (k13_lpspace1 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) &  ((k5_lpspace2 A B C D F) = (k5_lpspace2 A B C E F)) )  =>  ( (! [G:$i] :  ((m2_subset_1 G (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A G)) = k6_numbers)  &  ( (G = (k1_relset_1 A E))  & (r1_mesfunc6 A B E G)) ) ) ) )  | (r1_lpspace1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_hilbert1) =>  (! [D:$i] :  ((m2_finseq_1 D k1_hilbert1) =>  ( ( (C = (k8_finseq_1 k1_hilbert1 D (k12_finseq_1 k1_hilbert1 A)))  &  ((r1_xxreal_0 1 (k3_finseq_1 D)) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 D)))  => (r7_ltlaxio1 E D B)) ) )  & (r7_ltlaxio1 (k3_finseq_1 C) C B)) ) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 C)))  => (r7_ltlaxio1 E C B)) ) )  & (r8_ltlaxio1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t40_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A (k6_cqc_lang A B) C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k6_cqc_lang A C) B) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t40_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_subset_1 (u1_struct_0 A) (k5_mathmorp A (k3_subset_1 (u1_struct_0 A) B) (k2_mathmorp A C))) = (k4_mathmorp A B C)) ) ) ) ) ) ) ).
tt(t40_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 A k6_numbers) & (v2_matrix10 C))  => (v4_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t40_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  ( (F = (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_funct_2 (k2_finseq_1 A) E) D))  =>  ((k10_matrix_3 A B (k4_matrix11 A A (u1_struct_0 B) E C) D) = (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers (u1_struct_0 B) E (k10_matrix_3 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E A B C) =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  ( (~ (r2_hidden D (k2_finseq_1 (k3_finseq_1 E))))  =>  ((k3_matrix11 D B C A E F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  ((k3_matrix_1 (u1_struct_0 B) C 1 1) = (k4_struct_0 B)) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ((v1_matrix_6 D A B) &  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B D C) 1 1) = (k5_struct_0 B))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E A) =>  ((r1_xxreal_0 E 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B D C) E 1) = (k4_struct_0 B)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 E A) &  ((k3_matrix_1 (u1_struct_0 B) C 1 E) = (k4_struct_0 B)) )  =>  ((r1_xxreal_0 E 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B D C) 1 E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v6_struct_0 F))  &  ((v13_algstr_0 F) &  ((v33_algstr_0 F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 F) D A) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 F) D B) =>  ((r2_hidden C (k2_finseq_1 D)) =>  ( ( (E = C)  &  (G = (k4_algstr_0 F (k1_group_1 F))) )  |  ((k4_matrix15 F H I) = (k4_matrix15 F (k3_matrix11 E D A (u1_struct_0 F) H (k4_fvsum_1 (k1_matrix_1 H) F (k8_matrix_1 (u1_struct_0 F) H E) (k10_fvsum_1 (k1_matrix_1 H) F (k8_matrix_1 (u1_struct_0 F) H C) G))) (k3_matrix11 E D B (u1_struct_0 F) I (k4_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I E) (k10_fvsum_1 (k1_matrix_1 I) F (k8_matrix_1 (u1_struct_0 F) I C) G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (v1_matrix16 (k12_matrix_1 B A) (u1_struct_0 B))) ) ) ) ) ).
tt(t40_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 B)) => (m2_finseq_1 (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t40_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k3_matrix_3 A (k3_matrix_3 A (k2_matrix_3 A C) B) C)) ) ) ) ) ) ) ) ).
tt(t40_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (r1_matrix_6 A B C D))  => (r1_matrix_6 A B (k5_matrix_6 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t40_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_8 A B (k2_matrix_6 A B (k2_matrix_6 A B C C) C) (k2_matrix_6 A B (k2_matrix_6 A B D D) D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k13_matrix_2 A))) =>  ( ( ((k4_nat_d (k3_finseq_1 B) 2) = k6_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (~  ( ((k1_funct_1 B C) = D)  & (v4_matrix_2 D (k11_matrix_2 (k12_matrix_2 A)))) ) ) ) ) ) ) ) )  =>  ((v1_funct_1 (k3_group_4 (k13_matrix_2 A) B)) &  ((v1_funct_2 (k3_group_4 (k13_matrix_2 A) B) (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 (k3_group_4 (k13_matrix_2 A) B) (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v5_matrix_2 (k3_group_4 (k13_matrix_2 A) B) A) & (m1_subset_1 (k3_group_4 (k13_matrix_2 A) B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ) ) ) ) ) ) ) ).
tt(t40_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k2_numbers)))  =>  ( ( ((k1_matrix_1 C) = (k1_matrix_1 D))  & (r2_hidden B (k2_finseq_1 (k3_finseq_1 C))))  =>  ((k8_matrix_1 k2_numbers (k3_matrix_5 C D) B) = (k9_seq_4 (k8_matrix_1 k2_numbers C B) (k8_matrix_1 k2_numbers D B))) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_matrixj1 D A) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 A))))  =>  ( (C = k1_xboole_0)  =>  ( ((k13_matrixj1 A B (k3_matrixj1 A D (k4_matrixj1 A C))) = (k13_matrixj1 A B D))  &  ((k13_matrixj1 A B (k3_matrixj1 A (k4_matrixj1 A C) D)) = (k13_matrixj1 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ((k6_matrixr1 B (k7_matrixr1 A C)) = (k7_matrixr1 A (k6_matrixr1 B C))) ) ) ) ) ) ) ) ).
tt(t40_matrixr2,ax, ((k12_matrix_2 k6_numbers) = (k1_tarski (k6_finseq_1 k5_numbers))) ).
tt(t40_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_matrlin F A C) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 D)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 F)) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 A) (k3_finseq_1 F) (k3_finseq_1 G)) =>  ( ((k1_matrix_1 H) = (k3_finseq_1 I))  =>  (! [J:$i] :  ((m1_matrix_1 J (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 G)) =>  ( (J = (k4_matrix_3 A H I))  => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 D) (k4_matrlin2 A B D E G J) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) (k4_matrlin2 A B C E F H) (k4_matrlin2 A C D F G I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ((m1_matrlin F A B) =>  (! [G:$i] :  ((m1_matrlin G A C) =>  ( ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) &  ((k10_matrlin A B C D F G) = (k10_matrlin A B C E F G)) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 F) k6_numbers) | (r2_funct_2 (u1_struct_0 B) (u1_struct_0 C) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_matroid0 B A) & (r2_hidden C B))  => (r2_matroid0 A C (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(t40_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 (k12_matrixr1 A B)))) =>  ((k1_seq_1 (k12_matrixr1 A B) C) = (k22_rvsum_1 B (k9_matrix_1 k1_numbers A C))) ) ) ) ) ) ) ) ) ).
tt(t40_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A) =>  ((v2_funct_1 (k3_matrtop1 A A B)) <=>  (~  ((k12_matrix_3 A k2_vectsp_1 B) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ).
tt(t40_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (A = 1)  &  ( ((k12_euclid B) = (k12_euclid C))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 D (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (~  ((v2_matrtop3 D A) &  ( ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) D B) = C)  &  ( ((k3_matrtop3 A D) = (k1_matrtop3 A A))  |  ((k3_matrtop3 A D) = (k12_matrix_1 k2_vectsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_zfmisc_1 (k2_tarski A B) (k1_tarski C) (k2_tarski D E)) = (k2_enumset1 (k3_xtuple_0 A C D) (k3_xtuple_0 B C D) (k3_xtuple_0 A C E) (k3_xtuple_0 B C E))) ) ) ) ) ) ).
tt(t40_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden A B) <=> (r2_hidden (k4_xcmplx_0 A) (k4_measure6 B))) ) ) ) ) ).
tt(t40_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  (! [D:$i] :  ((v2_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k8_member_1 A C) (k8_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t40_memstr_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_memstr_0 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 B C))) ) )  =>  ((r1_tarski (k7_memstr_0 B C A) D) =>  ((k5_memstr_0 B C D) = A) ) ) ) ) ) ) ) ) ) ).
tt(t40_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((r2_mesfun6c A B C D) =>  ((r2_mesfun6c A B C (k25_valued_1 A k2_numbers D E)) &  ((k1_mesfun6c A B C (k25_valued_1 A k2_numbers D E)) = (k3_xcmplx_0 E (k1_mesfun6c A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((r2_hidden D (k1_relset_1 A (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C)))) => (r1_xxreal_0 (k1_seq_1 (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers B C)) D) (k1_seq_1 (k3_valued_1 A k1_numbers k1_numbers (k55_valued_1 A k2_numbers B) (k55_valued_1 A k2_numbers C)) D))) ) ) ) ) ) ) ) ).
tt(t40_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k2_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r2_mesfun6c A B C (k4_mesfunc5 A k2_numbers D E))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (r2_mesfun6c A B C (k4_mesfunc5 A k2_numbers (k3_mesfun9c A D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  ((r1_mesfunc2 A B E) &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 A (k4_mesfunc1 A D E))) => (r1_xxreal_0 (k12_supinf_2 E F) (k12_supinf_2 D F))) ) ) )  => (v6_supinf_2 (k4_mesfunc1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k1_seq_1 (k19_rfunct_3 A B) C) = (k1_real_1 (k1_seq_1 B C))) )  =>  ((k1_seq_1 (k18_rfunct_3 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t40_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (v4_mesfunc5 (k4_mesfunc5 A k7_numbers B D))) )  => (v4_mesfunc5 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) C))) ) ) ) ) ) ) ).
tt(t40_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_midsp_1 A (k8_midsp_1 A B C) (k8_midsp_1 A C D)) = (k8_midsp_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t40_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k10_mmlquery A B C k6_numbers) = (k4_mmlquery A (k18_mmlquery A C) B)) ) ) ) ) ) ).
tt(t40_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_algstr_0 A D)) = (k4_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k5_algstr_0 A D E)) = (k5_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  ( (~ (r1_xxreal_0 (k5_card_1 (k9_xtuple_0 (k12_modal_1 A B))) (k5_card_1 (k9_xtuple_0 A))))  &  (~ (r1_xxreal_0 (k5_card_1 (k9_xtuple_0 (k12_modal_1 A B))) (k5_card_1 (k9_xtuple_0 B)))) ) ) ) ) ) ).
tt(t40_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ((r3_modelc_1 A B C E D) &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F D) => (r3_modelc_1 A B C F (k25_modelc_1 (k48_modelc_1 A B C) D))) ) )  &  (! [F:$i] :  ((m1_modelc_1 F A B) =>  (~  ( ((k3_funct_2 k5_numbers A F k6_numbers) = E)  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) => (r3_modelc_1 A B C (k3_funct_2 k5_numbers A F G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_modelc_2 A (k6_modelc_2 B)) => (r2_modelc_2 A B)) ) ) ) ) ).
tt(t40_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  =>  ( ((r6_modelc_3 B D C) &  ((v8_modelc_2 A) & (r2_hidden A (u3_modelc_3 B D))) )  =>  ((r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C)) & (r2_hidden A (u1_modelc_3 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t40_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  => (r1_tarski (k3_moebius1 A) (k2_finseq_1 A))) ) ).
tt(t40_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (m2_monoid_0 A k2_monoid_0)) )  =>  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = k6_numbers) ) ) ).
tt(t40_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k20_monoid_1 A (k1_monoid_0 A B C)) = (k6_algstr_0 (k13_monoid_1 A) (k20_monoid_1 A B) (k20_monoid_1 A C))) ) ) ) ) ) ) ).
tt(t40_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_dtconstr E (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finset_1 F) & (v3_trees_2 F)) ) )  =>  ((r1_msaterm A B C E D F) =>  (! [G:$i] :  ((m1_trees_1 G (k9_xtuple_0 E)) =>  ((k1_funct_1 F G) = (k9_msaterm A B C (k8_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E G) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) => (r2_pboole A (k2_mboolean A C) B)) ) ) ) ) ).
tt(t40_msualg_6,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_relset_1 A A B C) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_rewrite1 B D E))  => (r2_hidden (k4_tarski D E) C)) ) ) ) ) ) ) ) ) ).
tt(t40_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) &  ((r2_hidden D A) & (r2_hidden (k4_tarski C D) (u1_orders_2 (k6_mycielsk A B)))) )  => (r2_hidden (k4_tarski C D) (u1_orders_2 B))) ) ) ) ) ) ) ).
tt(t40_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_ordinal1 (k5_card_1 A) (k5_card_1 B)) <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t40_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ((k1_seq_1 (k12_nat_3 (k1_newton B A)) B) = A) ) ) ) ) ).
tt(t40_nat_4,ax,(v1_int_2 4001)).
tt(t40_nat_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_xboole_0 A)) )  =>  ((k3_uproots (k3_moebius1 A) (k1_nat_5 k5_numbers k6_nat_5 (k3_moebius1 A))) = A) ) ) ).
tt(t40_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_nat_d A k6_numbers) = A) ) ) ).
tt(t40_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v2_nattra_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) => (v2_nattra_1 B)) ) ) ) ).
tt(t40_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r3_ncfcont1 B A C D) =>  ((r2_nfcont_1 B (k3_normsp_0 (u1_struct_0 B) A C) D) & (r3_ncfcont1 B A (k5_vfunct_1 (u1_struct_0 B) A C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t40_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_ncfcont2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) (k2_vfunct_1 (u1_struct_0 A) B D E))) &  ((r2_ndiff_1 C A B D) & (r2_ndiff_1 C A B E)) )  =>  ((r2_ndiff_1 C A B (k2_vfunct_1 (u1_struct_0 A) B D E)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) (k4_ndiff_1 A B (k2_vfunct_1 (u1_struct_0 A) B D E) C) F) = (k5_algstr_0 (k16_lopban_1 A B) (k3_ndiff_1 A B D F) (k3_ndiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_ndiff_1 C (k4_real_ns1 1) (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C)) &  ((v1_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 A)) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))) &  ((v13_vectsp_1 C (k4_real_ns1 1) (k4_real_ns1 A)) &  ((v1_lopban_1 C (k4_real_ns1 1) (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) ) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C)) &  ((v1_funct_2 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C) k1_numbers (u1_struct_0 (k4_real_ns1 A))) &  ((v2_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 A)) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B C) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) (k1_rlvect_1 (k14_prvect_2 A) C D)) = (k1_rlvect_1 (k11_prvect_2 A B) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t40_neckla_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v1_orders_2 A) &  ((v1_necklace A) &  ((v3_necklace A) & (l1_orders_2 A)) ) ) ) )  =>  ( ((v1_neckla_2 A) & (r2_hidden (u1_struct_0 A) k13_classes2))  => (r2_hidden (g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) k4_neckla_2)) ) ) ).
tt(t40_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  (A = k6_numbers) )  => (r1_nat_d A (k9_newton (k2_xcmplx_0 A B)))) ) ) ) ) ).
tt(t40_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r5_nfcont_1 C D A E) & (r5_nfcont_1 C D B F))  => (r5_nfcont_1 C D (k3_xboole_0 A B) (k2_vfunct_1 (u1_struct_0 C) D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) =>  ((v2_nfcont_4 (k2_nfcont_4 A k1_numbers (k2_partfun1 k1_numbers (k1_euclid A) C B)) A) &  ((v2_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_nfcont_4 A k1_numbers C) B)) & (v2_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) (k2_nfcont_4 A k1_numbers C) B) A)) ) ) ) ) ) ) ) ).
tt(t40_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) => (r1_tarski (k9_normform A B) B)) ) ) ).
tt(t40_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k4_oppcat_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t40_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_orders_1 A B) => (r1_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t40_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_orders_2 C A B) =>  (! [D:$i] :  ((m2_orders_2 D A B) =>  (~ (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t40_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden B C) =>  ( (A = k1_xboole_0)  | (r2_hidden (k11_ordinal2 B A) (k11_ordinal2 C A))) ) ) ) ) ) ) ) ).
tt(t40_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) => (v4_ordinal1 (k11_ordinal2 A B))) ) ) ) ) ).
tt(t40_ordinal5,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v4_ordinal5 A))  =>  ((k2_ordinal5 A) = (k1_ordinal5 A k4_ordinal1)) ) ) ).
tt(t40_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((r1_tarski A B) => (r1_tarski (k3_ordinal6 A) (k3_ordinal6 B))) ) ) ) ) ).
tt(t40_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v5_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t40_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_hidden (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C) (k25_osafree A B (k20_osafree A B) C)) &  ((r3_orders_2 A (k10_osafree A B (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C)) (k10_osafree A B C)) &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((r2_hidden E (k1_funct_1 B D)) &  (C = (k1_trees_4 (k4_tarski E D))) )  =>  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C) = C) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_trees_4 E (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ( ((r1_lang1 (k2_osafree A B) (k9_osafree A B D) (k1_dtconstr (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) E)) &  (C = (k8_trees_4 (u1_struct_0 (k2_osafree A B)) (k9_osafree A B D) E)) )  =>  ((r2_osalg_1 A (k11_osafree A B (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B))) (k1_msualg_1 A D)) &  ((r1_lang1 (k2_osafree A B) (k9_osafree A B D) (k14_trees_3 (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B)))) &  ((r1_lang1 (k2_osafree A B) (k9_osafree A B (k2_osalg_1 A D (k11_osafree A B (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B))))) (k14_trees_3 (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B)))) &  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C) = (k4_trees_4 (k9_osafree A B (k2_osalg_1 A D (k11_osafree A B (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B))))) (k11_lang1 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) E (k29_osafree A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v12_osalg_1 C A) & (m1_msualg_2 C A B)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) )  =>  ((k11_msualg_2 A B C (k11_osalg_2 A B C D)) = C) ) ) ) ) ) ) ) ) ).
tt(t40_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_parsp_2 A E F B C) & (r2_parsp_2 A E F D G))  =>  ((r1_parsp_2 A B C D) | (r2_parsp_2 A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_partfun1 (k3_partfun1 C A B) A) => (r1_tarski A (k9_xtuple_0 C))) ) ) ) ) ).
tt(t40_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r2_relset_1 A B (k2_partfun1 A B E C) (k4_partfun2 A B (k1_relset_1 A (k2_partfun1 A B E C)) D)) => (v3_funct_1 (k2_partfun1 A B E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k3_pboole A (k3_pboole A B C) D) (k3_pboole A (k3_pboole A B D) (k3_pboole A C D)))) ) ) ) ) ) ) ).
tt(t40_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((l2_pcs_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k22_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k22_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ( (C = (k4_tarski E G))  &  ( (D = (k4_tarski F H))  &  ((r1_pcs_0 (k22_pcs_0 A B) C D) &  ((r1_pcs_0 A E F) &  (~ (r1_pcs_0 B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_pdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ((r4_pdiff_3 A B) => (r1_fcont_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 A) B) (k1_seq_1 (k1_pdiff_1 2 2) B))) ) ) ) ) ).
tt(t40_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((v1_partfun1 B (k1_euclid 3)) & (v3_funct_1 B))  =>  ((k4_pdiff_4 B A) = (k16_euclid 3)) ) ) ) ) ) ).
tt(t40_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 3) B)) =>  ( ((r4_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B))))) &  ((k4_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  (D = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E C) F)) ) )  => (r2_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A E C) (k6_pdiff_1 A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r2_nfcont_4 A B C) => (r2_nfcont_4 A (k55_valued_1 (k1_euclid A) k1_numbers B) C)) ) ) ) ) ) ) ).
tt(t40_pepin,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r2_int_1 A B C) & (r2_int_1 A D C))  => (r2_int_1 B D C)) ) ) ) ) ) ) ) ) ).
tt(t40_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k10_pnproc_1 A B (k4_subset_1 (k3_finseq_2 B) C D) E) = (k4_subset_1 (k3_finseq_2 B) (k10_pnproc_1 A B C E) (k10_pnproc_1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t40_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((k1_newton B C) = (k1_newton A C)) )  =>  ( (B = k6_numbers)  |  ( (A = k6_numbers)  |  ((k17_complex1 B) = (k17_complex1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t40_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((k4_rlvect_1 k2_bspace (k19_polyform A B E (k3_rlvect_1 (k17_polyform A B) C D))) = (k3_rlvect_1 k2_bspace (k4_rlvect_1 k2_bspace (k19_polyform A B E C)) (k4_rlvect_1 k2_bspace (k19_polyform A B E D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k4_polynom5 A B C)) = 2) ) ) ) ) ) ) ) ).
tt(t40_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom8 A C B) =>  ((r1_xxreal_0 B k6_numbers) |  ((k4_matrix_3 A (k7_polynom8 A B C) (k7_polynom8 A B (k11_algstr_0 A C))) = (k4_matrix_3 A (k7_polynom8 A B (k11_algstr_0 A C)) (k7_polynom8 A B C))) ) ) ) ) ) ) ) ) ).
tt(t40_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  ( ((r2_termord A B G H) & (r3_polyred A B C D E F G))  =>  ((r2_hidden H (k2_polynom1 (k15_pre_poly A) C F)) <=> (r2_hidden H (k2_polynom1 (k15_pre_poly A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  & (r1_xxreal_0 (k3_power C A) (k3_power C B))) ) ) ) ) ) ) ) ) ) ).
tt(t40_pre_poly,ax, (! [A:$i] :  ((v1_relat_1 (k8_funcop_1 k5_numbers A k6_numbers)) &  ((v4_relat_1 (k8_funcop_1 k5_numbers A k6_numbers) A) &  ((v1_funct_1 (k8_funcop_1 k5_numbers A k6_numbers)) &  ((v1_partfun1 (k8_funcop_1 k5_numbers A k6_numbers) A) &  ((v4_valued_0 (k8_funcop_1 k5_numbers A k6_numbers)) & (v2_pre_poly (k8_funcop_1 k5_numbers A k6_numbers))) ) ) ) ) ) ).
tt(t40_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k4_prepower (k3_xcmplx_0 A B) C) = (k3_xcmplx_0 (k4_prepower A C) (k4_prepower B C))) ) ) ) ) ) ) ).
tt(t40_prob_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 (k9_setfam_1 A)))  &  ((v1_prob_1 (k9_setfam_1 A) A) &  ((v4_prob_1 (k9_setfam_1 A) A) & (m1_subset_1 (k9_setfam_1 A) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ).
tt(t40_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((k3_funct_2 k5_numbers k1_numbers (k8_prob_1 A B (k2_prob_3 A C) D) k6_numbers) = (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B C D)) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t40_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_prob_4 D A B C) =>  ((k3_funct_2 (k4_prob_4 A B C) k1_numbers (k7_prob_4 A B C) D) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t40_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k9_cqc_lang A B C) (k9_cqc_lang A D C)) (k9_cqc_lang A (k7_cqc_lang A B D) C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t40_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k15_pscomp_1 A) (k1_rltopsp1 (k15_euclid 2) (k20_pscomp_1 A) (k21_pscomp_1 A)))) ) ).
tt(t40_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k2_pboole A (k2_pzfmisc1 A B C) D) D) <=>  ((r1_pboole A B D) & (r1_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t40_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang2 B A) =>  (B = (k5_qc_lang2 A (k21_qc_lang1 A (k18_qc_lang1 A B)) (k18_qc_lang1 A (k22_qc_lang1 A (k18_qc_lang1 A B))))) ) ) ) ) ) ).
tt(t40_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A B (k1_qc_lang2 A)) = k1_xboole_0) ) ) ) ) ).
tt(t40_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) => (r1_tarski (a_4_1_qc_lang4 A B C D) (k4_qc_lang4 A B D))) ) ) ) ) ) ) ) ).
tt(t40_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) =>  ((k4_algstr_0 k16_quatern2 A) = (k6_algstr_0 k16_quatern2 (k4_algstr_0 k16_quatern2 (k1_group_1 k16_quatern2)) A)) ) ) ).
tt(t40_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k17_complex1 (k9_real_1 (k3_quatern2 A) (k3_quatern2 B))) (k3_quatern2 (k29_quaterni B A)))) ) ) ) ).
tt(t40_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k27_quaterni A A)) = (k9_real_1 (k9_real_1 (k9_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A))))  &  ( ((k18_quaterni (k27_quaterni A A)) = (k8_real_1 2 (k8_real_1 (k17_quaterni A) (k18_quaterni A))))  &  ( ((k19_quaterni (k27_quaterni A A)) = (k8_real_1 2 (k8_real_1 (k17_quaterni A) (k19_quaterni A))))  &  ((k20_quaterni (k27_quaterni A A)) = (k8_real_1 2 (k8_real_1 (k17_quaterni A) (k20_quaterni A)))) ) ) ) ) ) ).
tt(t40_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  ((k1_algstr_0 (k19_quofield A) B C) = (k1_algstr_0 (k19_quofield A) C B)) ) ) ) ) ) ) ).
tt(t40_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m1_vectsp_7 F A C) =>  (! [G:$i] :  ((m2_vectsp_6 G A C (k7_subset_1 (u1_struct_0 C) F E)) =>  ( ((m1_vectsp_7 E A (k1_ranknull A C B D)) & (r1_tarski E F))  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D (k4_vectsp_6 A C G)) = (k4_vectsp_6 A B (k8_ranknull A C B G D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_rat_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ((r1_xxreal_0 A B) <=> (r1_xxreal_0 (k4_real_1 A (k1_rat_1 B)) (k2_rat_1 B))) ) ) ) ) ).
tt(t40_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  ((v5_xxreal_2 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) ) ) ) ) ) ) ) ).
tt(t40_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 1 A) =>  ( ((k1_seq_1 (k4_real_3 B) A) = k6_numbers)  | (r1_xxreal_0 1 (k1_seq_1 (k4_real_3 B) A))) ) ) ) ) ) ).
tt(t40_relat_1,ax, ((k1_relat_1 k1_xboole_0) = k1_xboole_0) ).
tt(t40_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r1_tarski (k4_subset_1 B (k6_relset_2 A B C D) (k6_relset_2 A B C E)) (k6_relset_2 A B C (k4_subset_1 (k2_zfmisc_1 A B) D E)))) ) ) ) ) ) ) ) ).
tt(t40_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r5_rewrite1 A B C) => (r5_rewrite1 A C B)) ) ) ) ) ).
tt(t40_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B C) & (r3_rewrite2 A B D E))  => (r3_rewrite2 A C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t40_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ((r2_hidden (k4_tarski (k4_tarski A D) (k4_tarski B E)) (k1_rewrite3 C F G)) => (r1_xxreal_0 (k1_afinsq_1 E) (k1_afinsq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k1_valued_1 (k1_rfunct_1 A B) (k1_rfunct_1 C D)) = (k1_rfunct_1 (k1_valued_1 (k18_valued_1 A D) (k18_valued_1 C B)) (k18_valued_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t40_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t40_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k19_rfunct_3 A B) C))) ) ) ) ) ) ).
tt(t40_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 C) =>  ( (B = (k1_seq_1 (k3_rinfsup1 C) A))  <=>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 B (k1_seq_1 C (k2_nat_1 A D)))) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_xxreal_0 (k2_xcmplx_0 B D) (k1_seq_1 C (k2_nat_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 A) <=>  ((k6_rinfsup2 A) = (k5_rinfsup2 A)) ) ) ) ).
tt(t40_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ((k6_rlvect_2 B (k2_rlaffin1 B C A)) = (k1_rlvect_1 B (k6_rlvect_2 B C) A)) ) ) ) ) ) ) ).
tt(t40_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (m1_rlsub_1 (k1_rlsub_1 B) C)) ) ) ) ) ) ).
tt(t40_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) => (m1_rlsub_2 B A C)) ) ) ) ) ) ).
tt(t40_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A B) => (m1_connsp_2 (k5_rusub_4 A C (k4_algstr_0 A B)) A (k4_struct_0 A))) ) ) ) ) ) ).
tt(t40_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D (k4_finseq_1 B)) &  (E = (k1_funct_1 C D)) )  =>  ((k1_funct_1 B D) = (k4_algstr_0 A E)) ) ) ) ) ) )  =>  ((k4_rlvect_1 A B) = (k4_algstr_0 A (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ).
tt(t40_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) => (r1_rlvect_2 A (k7_rlvect_2 A B (k7_rlvect_2 A C D)) (k7_rlvect_2 A (k7_rlvect_2 A B C) D))) ) ) ) ) ) ) ) ).
tt(t40_rlvect_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_rlvect_5 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 A (k1_rlvect_5 B)))  =>  ((k2_rlvect_5 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t40_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (m1_rmod_2 (k1_rmod_2 A C) A D)) ) ) ) ) ) ) ) ).
tt(t40_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m2_rmod_2 E A B C) =>  (! [F:$i] :  ((m2_rmod_2 F A B D) =>  ( (~ (r1_xboole_0 E F))  => (m2_rmod_2 (k9_subset_1 (u1_struct_0 B) E F) A B (k2_rmod_3 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) => (r1_rmod_4 A B (k6_rmod_4 A B C (k6_rmod_4 A B D E)) (k6_rmod_4 A B (k6_rmod_4 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t40_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k12_robbins1 A B) (k11_robbins1 A B)) = B) ) ) ) ) ).
tt(t40_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) (k3_robbins1 A (k5_robbins1 A B D)))))) C) = C) ) ) ) ) ) ) ) ) ).
tt(t40_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C) = 1)  <=> (r2_hidden C (k3_roughs_1 A B))) ) ) ) ) ) ) ).
tt(t40_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  =>  ( ((k2_rpr_1 A C B) = (k9_real_1 1 (k2_rpr_1 A C (k3_subset_1 A B))))  &  ((k2_rpr_1 A C (k3_subset_1 A B)) = (k9_real_1 1 (k2_rpr_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t40_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_rusub_1 A B (k2_rusub_1 A)) = (u1_struct_0 A)) ) ) ) ) ).
tt(t40_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) => (m1_rusub_2 B A C)) ) ) ) ) ) ).
tt(t40_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((r1_struct_0 (k1_rusub_1 A) B) <=>  (B = (k4_struct_0 A)) ) ) ) ) ).
tt(t40_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k4_rusub_5 A)) => (r2_hidden (k5_setfam_1 (u1_struct_0 A) B) (k4_rusub_5 A))) ) ) ) ) ).
tt(t40_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k4_rvsum_1 A (k8_rvsum_1 B C)) = (k8_rvsum_1 (k4_rvsum_1 A B) C)) ) ) ) ) ) ) ).
tt(t40_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ((k17_rvsum_1 (k4_rvsum_2 A B C)) = (k3_binop_2 (k17_rvsum_1 B) (k17_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t40_scmbsort,ax, ((v3_scm_halt (k1_scmbsort (k5_scmfsa_2 k6_numbers))) & (v2_scm_halt (k1_scmbsort (k5_scmfsa_2 k6_numbers)))) ).
tt(t40_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_hidden (k2_nat_1 A 1) (k3_amistd_1 3 k1_scmfsa_2 A)) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k3_amistd_1 3 k1_scmfsa_2 A)) => (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t40_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 11)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (~  (A = (k16_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B (k1_scmfsa_m D) A) & (r6_scmfsa7b B (k1_scmfsa_m D) A))  =>  ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2)) D A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ((v1_ami_2 F) &  ( (~ (v1_scmfsa_m F))  & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r2_scmfsa7b C E))  &  ( (~ (r2_scmfsa7b D E))  &  (~  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k5_scmfsa8b E F C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 5))  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B E) (k1_funct_1 B F)))  =>  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (E = G) )  =>  ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa8b E F C D) B A) G) = (k1_funct_1 (k1_scmfsa6b C B A) G)) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa8b E F C D) B A) G) = (k18_scmfsa_2 (k1_scmfsa6b C B A) G)) ) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B E) (k1_funct_1 B F)) =>  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (E = G) )  =>  ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa8b E F C D) B A) G) = (k1_funct_1 (k1_scmfsa6b D B A) G)) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k5_scmfsa8b E F C D) B A) G) = (k18_scmfsa_2 (k1_scmfsa6b D B A) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_scmfsa8a B A (k2_scmfsa6a C)))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a C (k4_compos_1 k1_scmfsa_2)) B A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  (~  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r3_scmfsa9a A B C D) &  ((r4_scmfsa9a A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  =>  (~  ((v7_memstr_0 E 3 k1_scmfsa_2) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) (k2_nat_1 F 1)))) &  (~ (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 B D C A) F) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b C D A) &  ((r6_scmfsa7b C D A) &  ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D))))) = (k2_nat_1 (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D)))) 4)) ) )  =>  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 B C)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 D))))) = (k11_scmfsa_2 (k2_nat_1 (k5_card_1 C) 4))) ) ) ) ) ) ) ) ) ) ).
tt(t40_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  => (r2_hidden B (k9_xtuple_0 A))) ) ) ) ).
tt(t40_scmpds_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_scmpds_5 C) & (m1_subset_1 C (u1_compos_1 k1_scmpds_2)))  =>  ((k2_extpro_1 2 k1_scmpds_2 C B) = (k6_scmpds_4 (k9_compos_1 k1_scmpds_2 C) B A)) ) ) ) ) ) ) ).
tt(t40_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F)) = k6_numbers)  &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((k6_scmpds_4 (k2_scmpds_6 E F C D) B A) = (k1_funct_4 (k6_scmpds_4 C B A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 H (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ( ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) D) = (k1_funct_1 H D))  &  ( ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) (k2_scmpds_2 (k1_funct_1 B D) E)) = (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 H) I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E))) |  ((r2_hidden (k2_scmpds_2 (k1_funct_1 B D) E) G) |  ((r1_xxreal_0 F k6_numbers) |  ( (D = (k2_scmpds_2 (k1_funct_1 B D) E))  |  ((k6_scmpds_4 (k1_scmpds_7 D E F C) B A) = (k6_scmpds_4 (k1_scmpds_7 D E F C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D E F)) B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ((k3_tarski A) = (k3_tarski (k6_scmyciel A))) ) ) ).
tt(t40_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) => (r2_semi_af1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers B A))) ) ) ) ).
tt(t40_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v1_comseq_2 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((m2_valued_0 B k1_numbers A) & (v2_comseq_2 B)) ) ) ) ) ) ) ) ).
tt(t40_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((r2_seqfunc A B D) & (r2_seqfunc A C D))  =>  ((r2_seqfunc A (k6_seqfunc A B C) D) &  ((r2_relset_1 A k1_numbers (k11_seqfunc A (k6_seqfunc A B C) D) (k3_valued_1 A k1_numbers k1_numbers (k11_seqfunc A B D) (k11_seqfunc A C D))) &  ((r2_seqfunc A (k7_seqfunc A B C) D) &  ((r2_relset_1 A k1_numbers (k11_seqfunc A (k7_seqfunc A B C) D) (k47_valued_1 A k1_numbers k1_numbers (k11_seqfunc A B D) (k11_seqfunc A C D))) &  ((r2_seqfunc A (k8_seqfunc A B C) D) & (r2_relset_1 A k1_numbers (k11_seqfunc A (k8_seqfunc A B C) D) (k20_valued_1 A k1_numbers k1_numbers (k11_seqfunc A B D) (k11_seqfunc A C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_seqm_3,ax, ((v5_valued_0 (k6_funct_3 k1_numbers k5_numbers)) & (v4_valued_0 (k6_funct_3 k1_numbers k5_numbers))) ).
tt(t40_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers A C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers B) C))) ) )  & (v2_comseq_2 A))  =>  ((r1_xxreal_0 1 (k2_seq_2 A)) | (v2_series_1 B)) ) ) ) ) ) ).
tt(t40_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 (k4_nat_1 B (k13_newton 2 B)) (k9_newton (k2_nat_1 B 2)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ((k1_seq_1 (k3_series_1 A) B) = (k6_xcmplx_0 1 (k13_complex1 (k13_newton 2 (k2_nat_1 B 1)) (k9_newton (k2_nat_1 B 2))))) ) ) ) ) ) ) ).
tt(t40_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers k1_numbers B (k20_valued_1 k5_numbers k1_numbers k1_numbers C D)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers (k1_seq_1 C E)))  &  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 D E))) ) ) ) )  => (r1_xxreal_0 (k1_seq_1 (k3_series_1 B) A) (k8_real_1 (k1_seq_1 (k3_series_1 C) A) (k1_seq_1 (k3_series_1 D) A)))) ) ) ) ) ) ) ) ) ).
tt(t40_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 (k13_complex1 1 3) (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) (k3_square_1 C)))) ) ) ) ) ) ) ).
tt(t40_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (B = (k1_tarski A))  =>  ((k7_setfam_1 A B) = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t40_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v3_prob_1 C) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 B) C A) (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) (k2_nat_1 A 1)))) ) ) ) ) ) ).
tt(t40_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k7_subset_1 A B (k1_prob_1 A C)) (k1_prob_1 A (k7_setlim_2 A C B)))) ) ) ) ) ).
tt(t40_setwiseo,ax, (! [A:$i] : (r3_binop_1 (k5_finsub_1 A) (k1_setwiseo A) (k9_setwiseo A))) ).
tt(t40_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ((v1_finseqop C A) & (r6_binop_1 A D C)) ) ) )  =>  ((k5_binop_1 A D B (k1_finsop_1 A E C)) = (k1_finsop_1 A (k3_finseqop A A A D B E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_sf_mastr A) = (k4_sf_mastr (k5_compos_1 k1_scmfsa_2 A B))) ) ) ) ) ).
tt(t40_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A D E)) = (k5_sheffer1 A (k5_sheffer1 A E D) (k5_sheffer1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) &  ((v3_matroid0 B) & (m1_simplex0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (m2_simplex0 (k7_simplex0 A B C) A (k7_simplex0 A B D))) ) ) ) ) ) ) ) ).
tt(t40_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((v3_pre_topc D (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) C)))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_simplex1 A (k5_simplex0 (u1_struct_0 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) C)))))))  <=>  ( ((v3_pre_topc D (k4_simplex1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_simplex1 A B)))))  & (r1_tarski (k3_convex1 A D) (k3_convex1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_sincos10,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t40_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_fcont_1 k7_sin_cos2 A)) ) ).
tt(t40_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) = (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A)) ) ) ).
tt(t40_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k20_sin_cos A)) (k3_xcmplx_0 (k17_sin_cos B) (k20_sin_cos B)))) ) ) ) ) ).
tt(t40_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  &  ( (~  ((k3_sin_cos2 B) = k6_numbers) )  &  (~  ((k1_sin_cos5 (k2_xcmplx_0 A B)) = (k10_real_1 (k7_real_1 1 (k8_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B))) (k7_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B)))) ) ) ) ) ) ) ) ) ).
tt(t40_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ((r1_xxreal_0 A (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) & (r1_xxreal_0 1 (k17_sin_cos A))) ) ) ) ) ) ) ).
tt(t40_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_sin_cos7 A) = (k11_binop_2 2 (k1_sin_cos7 (k7_square_1 (k12_binop_2 (k10_binop_2 A 1) 2))))) ) ) ) ).
tt(t40_sin_cos9,ax, ( ((k6_sin_cos9 1) = (k10_real_1 k32_sin_cos 4))  &  ((k1_seq_1 k2_sin_cos9 1) = (k10_real_1 k32_sin_cos 4)) ) ).
tt(t40_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 C 1) & (r1_xxreal_0 A B)) )  => (r1_xxreal_0 (k1_newton C B) (k1_newton C A))) ) ) ) ) ) ) ).
tt(t40_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ((k18_euclid A) = (k18_euclid C)) ) ) ) ) ) ) ) ).
tt(t40_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_topreal1 A) => (v1_topreal1 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) A))) ) ) ).
tt(t40_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k3_finseq_1 (k1_sprect_1 A)) = 5) ) ) ).
tt(t40_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k21_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t40_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (~  ((r1_xxreal_0 (k6_pscomp_1 (k3_topreal1 2 A)) (k17_euclid B)) &  ((r1_xxreal_0 (k17_euclid B) (k8_pscomp_1 (k3_topreal1 2 A))) &  ((r1_xxreal_0 (k9_pscomp_1 (k3_topreal1 2 A)) (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k7_pscomp_1 (k3_topreal1 2 A)))) ) ) )  => (r2_hidden B (k2_goboard9 A))) ) ) ) ) ).
tt(t40_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t40_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( ((k3_square_1 A) = (k3_square_1 B))  &  ( (~  (A = B) )  &  (~  (A = (k4_xcmplx_0 B)) ) ) ) ) ) ) ) ) ).
tt(t40_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k14_stacks_1 A))) =>  ( (C = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B))  =>  ((r1_stacks_1 A B) |  ((k6_stacks_1 (k14_stacks_1 A) C) = (k6_stacks_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t40_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k23_binop_2 A 1) (k23_binop_2 B 1)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) (k23_binop_2 B 1))))) )  =>  ( ((v2_funct_2 C B) &  ((v1_stirl2_1 C A B) &  ( (C = (k2_partfun1 (k23_binop_2 A 1) (k23_binop_2 B 1) D A))  &  ((k2_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) D A) = B) ) ) )  =>  ((v2_funct_2 D (k23_binop_2 B 1)) &  ((v1_stirl2_1 D (k23_binop_2 A 1) (k23_binop_2 B 1)) &  ((k1_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) D (k6_domain_1 (k23_binop_2 B 1) (k2_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1) D A))) = (k1_seq_4 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  (~  ((v3_substut1 (k7_sublemma A C B) A) & (r2_hidden (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  ( (~  (A = k1_xboole_0) )  => (m1_subset_1 (k6_enumset1 B C D E F G H I) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v6_supinf_2 A) =>  ((r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 A) B) (k12_supinf_2 (k18_supinf_2 A) (k2_nat_1 B 1))) & (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k18_supinf_2 A) B))) ) ) ) ) ) ).
tt(t40_sysrel,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ( ( ((k3_relat_1 A B) = A)  &  ( ((k3_relat_1 B (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B)))) = k1_xboole_0)  &  ( ((k3_relat_1 B A) = B)  &  ((k3_relat_1 A (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A)))) = k1_xboole_0) ) ) )  =>  ((k1_sysrel A) = (k1_sysrel B)) )  &  ( ( ((k3_relat_1 B A) = A)  &  ( ((k3_relat_1 (k6_subset_1 B (k4_relat_1 (k9_xtuple_0 B))) B) = k1_xboole_0)  &  ( ((k3_relat_1 A B) = B)  &  ((k3_relat_1 (k6_subset_1 A (k4_relat_1 (k9_xtuple_0 A))) A) = k1_xboole_0) ) ) )  =>  ((k1_sysrel A) = (k1_sysrel B)) ) ) ) ) ) ) ).
tt(t40_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v5_tbsp_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (u1_struct_0 A)) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ( (~ (v3_xxreal_0 C))  & (v1_xreal_0 C))  =>  ( ((r1_xxreal_0 (k3_tbsp_1 A (k2_struct_0 A)) C) & (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k13_lang1 (u1_struct_0 A) (k3_taxonom1 A C))))  =>  ((k8_eqrel_1 (u1_struct_0 A) B) = (k1_tarski (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t40_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k7_tdlat_1 A) = (k1_realset1 (k3_tdlat_1 A) (k5_tdlat_1 A))) ) ) ).
tt(t40_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))))) ) ) ) ).
tt(t40_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ( ((k2_tdlat_1 A) = (k6_tdlat_1 A))  &  ((k3_tdlat_1 A) = (k7_tdlat_1 A)) ) ) ) ).
tt(t40_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_hidden E (k2_polynom1 (k15_pre_poly A) C D)) =>  ( (E = (k3_termord A B C D))  |  ((k3_polynom1 A C (k6_termord A B C D) E) = (k3_polynom1 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v3_tex_2 B A)) ) ) ) ) ).
tt(t40_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ( ((v4_tex_3 B A) & (m1_pre_topc C B))  => (v4_tex_3 C A)) ) ) ) ) ) ) ).
tt(t40_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (r1_tarski C B))  => (r1_tarski (k3_tex_4 A C) B)) ) ) ) ) ) ) ).
tt(t40_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_borsuk_1 D A) & (m1_pre_topc D A)) )  =>  ( ((m1_pre_topc B D) & (r1_tsep_1 D C))  =>  ( ((v1_borsuk_1 B (k1_tsep_1 A B C)) & (m1_pre_topc B (k1_tsep_1 A B C)))  &  ((v1_borsuk_1 B (k1_tsep_1 A C B)) & (m1_pre_topc B (k1_tsep_1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_toler_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v3_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r1_relset_1 A A B (k4_relset_1 A A A A B B))) ) ) ).
tt(t40_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H A B D) => (r4_borsuk_2 A B D (k1_borsuk_2 A B E D (k1_borsuk_2 A B D E (k1_borsuk_2 A B B D (k1_borsuk_2 A B C B F (k2_borsuk_2 A B C F)) H) G) (k2_borsuk_2 A D E G)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  ((k6_topalg_6 A (k12_finseq_1 (k1_topalg_6 A) B)) = B) ) ) ) ) ).
tt(t40_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_waybel23 (k1_pre_topc A B)) &  ((v1_topdim_1 B A) &  ((v1_topdim_1 C A) & (r1_xxreal_0 (k2_topdim_1 A B) k6_numbers)) ) )  =>  ((v1_topdim_1 (k4_subset_1 (u1_struct_0 A) C B) A) & (r1_xxreal_0 (k2_topdim_1 A (k4_subset_1 (u1_struct_0 A) C B)) (k3_real_1 (k2_topdim_1 A C) 1))) ) ) ) ) ) ) ) ).
tt(t40_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k2_topgen_1 A (k1_struct_0 A)) = (k1_struct_0 A)) ) ) ).
tt(t40_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B A) =>  ( ((v4_pre_topc (k1_tarski C) (k6_topgen_3 A B)) & (m1_subset_1 (k1_tarski C) (k1_zfmisc_1 (u1_struct_0 (k6_topgen_3 A B)))))  <=>  (C = B) ) ) ) ) ) ).
tt(t40_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_topgen_4 B A) & (v5_topgen_4 C A))  => (v5_topgen_4 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t40_topgen_5,ax, ((v3_tops_1 k1_topgen_5 k3_topgen_5) & (m1_subset_1 k1_topgen_5 (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ).
tt(t40_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l1_topgrp_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A (k2_group_1 A B)) =>  (? [D:$i] :  ((m1_connsp_2 D A B) & (r1_tarski (k1_group_2 A D) C)) ) ) ) ) )  => (v3_topgrp_1 A)) ) ) ).
tt(t40_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k3_topreal1 2 C)) = (k1_tarski A))  & (r2_hidden B (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ).
tt(t40_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = A)  & (r2_hidden B (k9_metric_1 (k14_euclid 2) C D)))  =>  ( (~ (r1_xxreal_0 (k18_euclid B) (k9_real_1 (k18_euclid A) D)))  &  (~ (r1_xxreal_0 (k7_real_1 (k18_euclid A) D) (k18_euclid B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~ (v1_xboole_0 A))  &  ((v1_xboole_0 (k3_topreal9 A C B)) & (r1_xxreal_0 k6_numbers B)) ) ) ) ) ) ) ) ) ).
tt(t40_topreala,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  (! [E:$i] :  ( ((v4_pre_topc E (k4_topmetr A B)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))))  =>  (! [F:$i] :  ( ((v4_pre_topc F (k4_topmetr C D)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k4_topmetr C D)))))  =>  ((v4_pre_topc (k4_card_3 (k4_funct_4 1 2 E F)) (k1_topreala A B C D)) & (m1_subset_1 (k4_card_3 (k4_funct_4 1 2 E F)) (k1_zfmisc_1 (u1_struct_0 (k1_topreala A B C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((r2_hidden C (k3_toprealb A B)) =>  ((k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb C) = (k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k5_setfam_1 (u1_struct_0 k2_topalg_2) (k3_toprealb A B)))) ) ) ) ) ) ) ).
tt(t40_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k80_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k80_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k80_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t40_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 B A) => (v3_toprns_1 (k3_toprns_1 A B) A)) ) ) ) ) ).
tt(t40_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) B (k2_tops_1 A B))) ) ) ) ) ).
tt(t40_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( ((k9_xtuple_0 D) = C)  &  ( ((k10_xtuple_0 D) = (k1_tops_2 A B C))  &  (! [E:$i] :  ((r2_hidden E C) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (F = E)  =>  ((k1_funct_1 D E) = (k9_subset_1 (u1_struct_0 A) F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) <=> (v1_tops_3 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t40_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo B A) & (v4_transgeo C A))  => (v4_transgeo (k1_transgeo (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t40_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (! [C:$i] :  ((m1_trees_1 C A) =>  ( (~ (r3_xboole_0 B C))  => (m4_trees_1 (k2_tarski B C) A)) ) ) ) ) ) ) ).
tt(t40_trees_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v6_ordinal1 C) & (m1_subset_1 C (k1_zfmisc_1 (k4_partfun1 A B))))  => (r2_hidden (k3_tarski C) (k4_partfun1 A B))) ) ) ) ).
tt(t40_trees_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 A B)) &  ((v1_funct_1 C) & (v3_trees_2 C)) ) )  =>  ((k13_funct_3 (k8_trees_3 A B C) (k9_trees_3 A B C)) = C) ) ) ) ) ) ) ).
tt(t40_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k7_finseq_1 B (k12_finseq_1 k5_numbers C)) (k9_xtuple_0 A)) =>  ((k1_funct_1 A (k7_finseq_1 B (k12_finseq_1 k5_numbers C))) = (k1_funct_1 (k2_trees_9 A B) (k2_nat_1 C 1))) ) ) ) ) ) ) ) ).
tt(t40_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_connsp_1 A B D) | (r1_connsp_1 A C D))  => (r1_connsp_1 A (k9_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t40_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((r4_tsep_2 A B D) &  ((r4_tsep_2 A C E) &  ( ((k1_tsep_1 A D E) = (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))  & (r4_tsep_1 A D E)) ) )  => (r3_tsep_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u2_turing_1 A)) => (r2_hidden (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) C (u4_turing_1 B)) (k21_turing_1 A B))) ) ) ) ) ) ).
tt(t40_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((k2_msafree2 (k40_twoscomp A B)) = (k2_tarski A B)) ) ) ) ) ).
tt(t40_uniroots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((k1_algseq_1 A (k4_uniroots B A)) = (k23_binop_2 B 1)) ) ) ) ) ).
tt(t40_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_algseq_1 A (k13_polynom3 A (k2_polynom5 A (k4_polynom5 A B (k5_struct_0 A)) D) C)) = (k2_nat_1 D (k1_algseq_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t40_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r2_valuat_1 A B E (k8_cqc_lang A (k7_cqc_lang A C D) (k7_cqc_lang A D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t40_valued_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k14_valued_2 (k50_valued_1 B C) A) = (k50_valued_1 B (k24_valued_1 C A))) ) ) ) ) ) ) ).
tt(t40_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v1_vectsp_7 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D C) =>  (! [E:$i] :  ((m2_vectsp_6 E A B (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D))) =>  ( ((k5_card_1 C) = (k5_card_1 (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) (k6_domain_1 (u1_struct_0 B) (k3_rlvect_1 B D (k4_vectsp_6 A B E))))))  & (v1_vectsp_7 (k4_subset_1 (u1_struct_0 B) (k7_subset_1 (u1_struct_0 B) C (k6_domain_1 (u1_struct_0 B) D)) (k6_domain_1 (u1_struct_0 B) (k3_rlvect_1 B D (k4_vectsp_6 A B E)))) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (m1_vectsp_4 (k1_vectsp_4 A C) A D)) ) ) ) ) ) ) ) ).
tt(t40_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  ( ((k2_vectsp_5 A B C D) = (k1_vectsp_4 A B))  &  ((k2_vectsp_5 A B D C) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t40_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_vectsp_6 A B D E) C) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C)))))  =>  ((v1_partfun1 D A) =>  ( ((k7_partfun1 (u1_struct_0 C) (k5_vfunct_1 A C D) B) = (k4_algstr_0 C (k7_partfun1 (u1_struct_0 C) D B)))  &  ((k1_seq_1 (k3_normsp_0 A C D) B) = (k1_normsp_0 C (k7_partfun1 (u1_struct_0 C) D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((v1_partfun1 C A) =>  ( ((k7_partfun1 (u1_struct_0 B) (k5_vfunct_1 A B C) D) = (k4_algstr_0 B (k7_partfun1 (u1_struct_0 B) C D)))  &  ((k1_funct_1 (k3_normsp_0 A B C) D) = (k1_normsp_0 B (k7_partfun1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k13_lattice3 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  ((k12_yellow_6 A) = (k2_waybel11 A)) ) ) ) ).
tt(t40_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = C)  & (v3_yellow_8 (k3_subset_1 (u1_struct_0 A) C) A))  => (v2_waybel_6 B (k2_yellow_1 (u1_pre_topc A)))) ) ) ) ) ) ) ).
tt(t40_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) &  ( (B = (k1_yellow_0 (k2_yellow_1 (k5_waybel11 A)) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ((r2_hidden D C) => (v6_waybel_6 D (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) )  & (v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))))  <=> (v1_waybel_5 (k2_yellow_1 (k5_waybel11 A)))) ) ) ).
tt(t40_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_pre_topc (k2_waybel_3 A B) A) & (v4_pre_topc (k3_subset_1 (u1_struct_0 A) (k2_waybel_3 A B)) A)) ) ) ) ) ).
tt(t40_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ((v8_waybel_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 A C D E) A C) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v22_waybel_0 B A A) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  => (v1_waybel20 (k4_waybel20 A B) A)) ) ) ) ).
tt(t40_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((m2_yellow_6 (k5_waybel_9 A B C) A B) & (m2_waybel21 (k1_yellow_9 B (k5_waybel_9 A B C)) A B (k5_waybel_9 A B C))) ) ) ) ) ) ) ).
tt(t40_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_waybel23 (k1_waybel_3 A B) A)) ) ) ) ).
tt(t40_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  =>  ( ( (D = (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C))))  &  ((r1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C))) & (r2_hidden E (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C)))) )  => (r1_yellow_2 (u1_struct_0 A) (k1_waybel25 B) E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((v3_pre_topc (k5_waybel26 D) (k2_borsuk_1 A B)) & (m1_subset_1 (k5_waybel26 D) (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  => (v5_pre_topc D A C)) ) ) ) ) ) ) ) ) ).
tt(t40_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k2_waybel27 B C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k2_waybel27 B C)))))) )  =>  ((v1_funct_1 (k10_funct_6 D)) &  ((v1_funct_2 (k10_funct_6 D) (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C))) &  ((v22_waybel_0 (k10_funct_6 D) B (k6_yellow_1 A C)) & (m1_subset_1 (k10_funct_6 D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_yellow_1 A C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ) ).
tt(t40_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) &  ((v2_waybel_2 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v2_waybel_8 A) <=>  ((v3_waybel30 A) & (v2_waybel_8 (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ).
tt(t40_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r4_waybel_0 A B (k6_struct_0 A B C) D) & (r3_waybel_0 A B (k6_struct_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t40_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v6_waybel_3 A) & (v8_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (~  ((r1_waybel_3 (k2_yellow_1 (u1_pre_topc A)) B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (D = B)  &  ((r1_tarski (k2_pre_topc A D) C) & (v2_compts_1 (k2_pre_topc A D) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_waybel_4 A B (k1_waybel_4 A)) = (k1_waybel_3 A B)) ) ) ) ) ).
tt(t40_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((v5_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v2_waybel_0 (k6_waybel_4 A C B) A)) ) ) ) ) ) ) ).
tt(t40_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) )  => (v3_yellow_0 A)) ) ) ).
tt(t40_weddwitt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_struct_0 (k5_weddwitt A B)) = (k5_struct_0 A)) ) ) ) ) ).
tt(t40_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r4_wellord1 A B) => (r4_wellord1 B A)) ) ) ) ) ).
tt(t40_wsierp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k2_finseq_3 1 (k7_finseq_1 (k9_finseq_1 B) A)) = A)  &  ((k2_finseq_3 (k2_nat_1 (k3_finseq_1 A) 1) (k7_finseq_1 A (k9_finseq_1 B))) = A) ) ) ) ) ).
tt(t40_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 (k2_xboole_0 A B) B) = (k4_xboole_0 A B)) ) ) ).
tt(t40_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k9_xboolean A (k4_xboolean B C)) = (k5_xboolean (k3_xboolean (k5_xboolean A B)) (k3_xboolean (k5_xboolean A C)))) ) ) ) ) ) ) ).
tt(t40_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 A (k6_xcmplx_0 B C)) = (k6_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(t40_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t40_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k13_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k13_xtuple_0 A) (k13_xtuple_0 B)))) ) ).
tt(t40_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k4_xxreal_0 (k4_xxreal_0 (k3_xxreal_0 A B) (k3_xxreal_0 B C)) (k3_xxreal_0 C A)) = (k3_xxreal_0 (k3_xxreal_0 (k4_xxreal_0 A B) (k4_xxreal_0 B C)) (k4_xxreal_0 C A))) ) ) ) ) ) ) ).
tt(t40_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) | (r1_tarski (k2_xxreal_1 B C) (k3_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t40_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ( (~ (v1_xboole_0 A))  <=> (r1_xxreal_0 (k2_xxreal_2 A) (k1_xxreal_2 A))) ) ) ).
tt(t40_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 k6_numbers (k3_xxreal_3 B A))) ) ) ) ) ).
tt(t40_yellow_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_yellow_0 A (k7_domain_1 (u1_struct_0 A) B C)) = (k12_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t40_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_yellow_3 A B (k6_waybel_0 A C) (k6_waybel_0 B D)) = (k6_waybel_0 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t40_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v1_funct_1 (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B))) &  ((v1_funct_2 (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 B)) &  ((v5_pre_topc (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k2_borsuk_1 A B) B) & (m1_subset_1 (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(t40_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r5_yellow16 B A C) <=>  ((r1_yellow_0 A C) =>  ((r1_yellow_0 B C) &  ((k1_yellow_0 B C) = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t40_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v4_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v3_altcat_3 D A B C) &  (~  ((v2_funct_1 D) &  ((k10_xtuple_0 D) = (k3_yellow18 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  ((r3_yellow20 A B C A B) => (v21_functor0 C A B)) ) ) ) ) ) ) ).
tt(t40_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( (~ (v1_xboole_0 (k9_subset_1 (u1_struct_0 A) B C)))  &  ((v1_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A) &  ((v12_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A) & (m1_subset_1 (k9_subset_1 (u1_struct_0 A) B C) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t40_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((r2_yellow_0 A C) & (r2_yellow_0 B D))  <=> (r2_yellow_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t40_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k4_yellow_4 A B B))) ) ) ) ).
tt(t40_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_orders_2 A B (k13_lattice3 A C D)) =>  ((r3_orders_2 A (k1_yellow_5 A B C) D) & (r3_orders_2 A (k1_yellow_5 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t40_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) => (r1_tarski B (k12_yellow_6 (k13_yellow_6 A B)))) ) ) ) ).
tt(t40_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)) C D) =>  ( ((v5_orders_3 C A B) => (v5_waybel_0 D A (k7_lattice3 B)))  &  ( ((v5_waybel_0 D A (k7_lattice3 B)) => (v5_orders_3 C A B))  &  ( ((v5_waybel_0 C A B) => (v5_orders_3 D A (k7_lattice3 B)))  &  ((v5_orders_3 D A (k7_lattice3 B)) => (v5_waybel_0 C A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_tops_2 D B) &  ((v1_cantor_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ((v1_tops_2 (a_4_0_yellow_9 A B C D) (k2_borsuk_1 A B)) &  ((v1_cantor_1 (a_4_0_yellow_9 A B C D) (k2_borsuk_1 A B)) & (m1_subset_1 (a_4_0_yellow_9 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t40_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( (~  ( (~  ((r3_zf_lang A B) & (r2_zf_lang B C)) )  &  ( (~  ((r2_zf_lang A B) & (r3_zf_lang B C)) )  &  ( (~  ((r2_zf_lang A B) & (r1_zf_lang B C)) )  &  ( (~  ((r1_zf_lang A B) & (r2_zf_lang B C)) )  &  ( (~  ((r3_zf_lang A B) & (r1_zf_lang B C)) )  &  (~  ((r1_zf_lang A B) & (r3_zf_lang B C)) ) ) ) ) ) ) )  => (r3_zf_lang A C)) ) ) ) ) ) ) ).
tt(t40_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_zf_lang A) =>  (A = (k7_zf_lang (k21_zf_lang A) (k22_zf_lang A))) ) ) ) ).
tt(t40_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k2_xboole_0 (k1_tarski A) B) = B) ) ) ) ).
tt(t40_zfrefle1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (~  ((r2_hidden k4_ordinal1 A) &  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B A))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_ordinal2 B k4_ordinal1) &  ( (C = (k4_classes1 B))  & (v1_zf_model C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t40_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 k4_numbers C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k4_numbers C) C)))) )  =>  ( ( (B = C)  &  ( (D = (k4_struct_0 A))  &  ( (E = (k1_realset1 (u1_algstr_0 A) B))  &  (F = (k2_partfun1 (k2_zfmisc_1 k4_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_zmodul01 A) (k2_zfmisc_1 k4_numbers B))) ) ) )  => (m1_zmodul01 (g1_zmodul01 C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t410_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k3_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 A k1_xxreal_0)) = (k1_tarski k1_xxreal_0)) ) ) ).
tt(t411_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k1_xxreal_1 A k1_xxreal_0) (k3_xxreal_1 A k1_xxreal_0)) = (k1_tarski A)) ) ) ).
tt(t412_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_subset_1 (k2_xxreal_1 A k1_xxreal_0) (k4_xxreal_1 A k1_xxreal_0)) = (k1_tarski A)) ) ) ).
tt(t413_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C B) |  ((k2_xboole_0 (k1_xxreal_1 A B) (k2_xxreal_1 B C)) = (k2_xxreal_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t414_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B A) |  ((k2_xboole_0 (k3_xxreal_1 A B) (k1_xxreal_1 B C)) = (k3_xxreal_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t415_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~  ((k2_xboole_0 (k3_xxreal_1 A B) (k2_xxreal_1 B C)) = (k4_xxreal_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t416_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C B) |  ((k3_xboole_0 (k1_xxreal_1 A B) (k2_xxreal_1 B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t417_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 B C) =>  ((r1_xxreal_0 B A) |  ((k3_xboole_0 (k3_xxreal_1 A B) (k1_xxreal_1 B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t418_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 B C))  =>  ((k3_xboole_0 (k1_xxreal_1 A B) (k1_xxreal_1 B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t419_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 k2_xxreal_0 A) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k2_tarski k2_xxreal_0 A))) ) ) ).
tt(t41_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 E (k2_nat_1 (k3_finseq_1 C) 1))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( (F = (k1_funct_1 (k7_abcmiz_0 A B C) D))  &  (G = (k1_funct_1 (k7_abcmiz_0 A B C) E)) )  => (r3_orders_2 A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((m1_abcmiz_1 A B C) <=> (r2_hidden A (k1_funct_1 (u3_msualg_1 B (k1_msafree3 B (k28_abcmiz_1 B))) C))) ) ) ) ) ) ).
tt(t41_abcmiz_a,ax, ( ((k41_abcmiz_1 k27_abcmiz_1 k15_abcmiz_a) = k1_xboole_0)  &  ((k42_abcmiz_1 k27_abcmiz_1 k15_abcmiz_a) = (k12_abcmiz_a k27_abcmiz_1 (k14_abcmiz_a k8_abcmiz_a))) ) ).
tt(t41_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_aff_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_aff_1 A B B)) ) ) ) ).
tt(t41_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) & (v1_aff_4 C A))  =>  ((r1_aff_4 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski D C) &  ((r5_aff_1 A B D) | (r5_aff_1 A D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  (~  ( ((k1_ordinal4 A B) = (k1_ordinal4 C D))  &  ((r1_xxreal_0 (k1_afinsq_1 A) (k1_afinsq_1 C)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_ordinal1 E) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) )  =>  (~  ((k1_ordinal4 A E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 D A) =>  ( ( (~ (v1_setwiseo D A))  &  (~  ((r1_xxreal_0 1 (k1_afinsq_1 B)) & (r1_xxreal_0 1 (k1_afinsq_1 C))) ) )  |  ((k6_afinsq_2 A (k1_ordinal4 B C) D) = (k5_binop_1 A D (k6_afinsq_2 A B D) (k6_afinsq_2 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k14_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 (k13_afproj A))) =>  (~  ( (~  (B = C) )  &  ((r2_hidden (k1_domain_1 (u1_incsp_1 (k14_afproj A)) (u2_incsp_1 (k13_afproj A)) B D) (u3_incsp_1 (k13_afproj A))) &  ((r2_hidden (k1_domain_1 (u1_incsp_1 (k14_afproj A)) (u2_incsp_1 (k13_afproj A)) C D) (u3_incsp_1 (k13_afproj A))) &  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k14_afproj A))) =>  (~  (D = (k4_tarski E 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k1_afvect0 A B (k1_afvect0 A E C)) = (k1_afvect0 A E (k1_afvect0 A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski (k9_xtuple_0 B) (u1_struct_0 A)) &  ((r1_tarski (k9_xtuple_0 C) (u4_struct_0 A)) & (r1_algspec1 A B C)) )  => (r3_pua2mss1 A (k2_algspec1 A B C) (k1_funct_4 (k6_partfun1 (u1_struct_0 A)) B) (k1_funct_4 (k6_partfun1 (u4_struct_0 A)) C))) ) ) ) ) ) ) ).
tt(t41_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_algstr_4 D A))  =>  (! [E:$i] :  ( ((v1_partfun1 E (u1_struct_0 B)) &  ((v3_relat_2 E) &  ((v8_relat_2 E) &  ((v1_algstr_4 E B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))))) ) ) )  =>  (~  ((v1_group_6 C B A) &  ( ((u1_struct_0 D) = (k2_relset_1 (u1_struct_0 A) C))  &  ((r2_relset_1 (u1_struct_0 B) (u1_struct_0 B) E (k7_algstr_4 (u1_struct_0 B) (u1_struct_0 A) C)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k4_algstr_4 B E)) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_algstr_4 B E)) (u1_struct_0 D))))) )  =>  (~  ((r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 D) C (k1_partfun1 (u1_struct_0 B) (u1_struct_0 (k4_algstr_4 B E)) (u1_struct_0 (k4_algstr_4 B E)) (u1_struct_0 D) (k5_algstr_4 B E) F)) &  ((v3_funct_2 F (u1_struct_0 (k4_algstr_4 B E)) (u1_struct_0 D)) & (v1_group_6 F (k4_algstr_4 B E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_altcat_4 A)))  &  ((v2_altcat_1 (k5_altcat_4 A)) &  ((v3_altcat_2 (k5_altcat_4 A) (k3_altcat_4 A)) & (m1_altcat_2 (k5_altcat_4 A) (k3_altcat_4 A))) ) ) ) ) ).
tt(t41_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_analmetr A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_analmetr A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k4_analmetr A B C) = (k2_aff_1 (k3_analmetr A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (F = G) )  & (r2_analort A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_aofa_000,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v2_margrel1 C) &  ((v3_margrel1 C A) &  ((v8_comput_1 C 2) &  ((v1_aofa_000 C) &  ((v2_aofa_000 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) ) ) ) )  =>  ((r1_aofa_000 C B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v2_margrel1 D) &  ((v3_margrel1 D A) &  ((v8_comput_1 D 3) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_funct_1 E) &  ((v2_margrel1 E) &  ((v3_margrel1 E A) &  ((v8_comput_1 E 2) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)))) ) ) ) )  =>  (? [F:$i] :  ( ((v1_unialg_1 F) &  ((v4_unialg_1 F) & (l1_unialg_1 F)) )  &  ( ((u1_struct_0 F) = A)  &  ( ((u1_unialg_1 F) = (k8_finseq_1 (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)) (k2_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)) (k1_aofa_000 A A (k4_finseq_2 k6_numbers A) B) C) (k2_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 A) A)) D E)))  &  ((v3_aofa_000 F) &  ((v4_aofa_000 F) &  ((v8_aofa_000 F) &  ((v7_aofa_000 F) &  ((v5_aofa_000 F) &  ((v6_aofa_000 F) &  ((v3_unialg_1 F) & (v2_unialg_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E F G)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G))) )  &  ( ( (~ (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F)))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E G F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k75_aofa_i00 A B D E G F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (r1_xxreal_0 (k21_aofa_i00 B k4_numbers C G) (k21_aofa_i00 B k4_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (B = (a_2_2_armstrng A C))  =>  ((k2_xboole_0 (k1_tarski A) (a_2_10_armstrng A C)) = (k9_armstrng A B)) ) ) ) ) ) ) ) ).
tt(t41_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  ( (~  (A = k1_xboole_0) )  =>  ((k8_arytm_3 A A) = 1) ) ) ) ).
tt(t41_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k13_asympt_0 k5_numbers (k6_asympt_0 A) (k6_asympt_0 B)) = (k6_asympt_0 (k1_asympt_0 A B))) ) ) ) ) ).
tt(t41_asympt_1,ax, (? [A:$i] :  ((m1_funct_2 A k5_numbers k1_numbers) &  ( (A = (k1_tarski (k3_asympt_1 1)))  &  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_asympt_1 (k1_real_1 1)) B) (k1_seq_1 (k3_asympt_1 1) B))) )  &  (~ (r2_hidden (k3_asympt_1 (k1_real_1 1)) (k15_asympt_0 A (k6_asympt_0 (k4_asympt_1 1))))) ) ) ) ) ).
tt(t41_bagorder,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v1_wellfnd1 A) => (v1_wellfnd1 (k14_bagorder A))) ) ) ).
tt(t41_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k7_bcialg_1 A B)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k7_bcialg_1 A C)) =>  (~  ( (~  (B = C) )  & (r2_hidden (k1_bcialg_1 A D E) (k4_bcialg_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  (! [D:$i] :  ((m5_bcialg_2 D A B) =>  (! [E:$i] :  ((m5_bcialg_2 E A C) =>  ( ((k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) D (k4_struct_0 A)) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) E (k4_struct_0 A)))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B (k1_bcialg_1 A C D))) = (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A B D)))) ) ) ) ) ) ) ) ) ) ).
tt(t41_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bcialg_4 A (k1_bcialg_1 A B (k4_struct_0 A)) (k1_bcialg_1 A (k4_struct_0 A) B)) = B) ) ) ) ) ).
tt(t41_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) )  =>  ( (B = (k4_bcialg_1 C))  =>  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) &  ((v19_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) ) )  <=>  (B = (k1_tarski (k4_struct_0 C))) ) ) ) ) ) ) ) ) ).
tt(t41_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v12_bcialg_1 (k5_bcialg_6 B A C) B) & (m2_bcialg_1 (k5_bcialg_6 B A C) B)) ) ) ) ) ) ) ).
tt(t41_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ) ).
tt(t41_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k4_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) (k7_real_1 (k4_bhsp_1 A B D) (k4_bhsp_1 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t41_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_bhsp_2 A C D)) <=>  (~ (r1_xxreal_0 D (k4_bhsp_1 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t41_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v2_bhsp_3 B A) => (v2_bhsp_3 (k1_valued_0 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t41_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k3_bhsp_1 A (k4_bhsp_4 A B D C)) (k18_complex1 (k7_series_1 (k2_bhsp_2 A B) D C)))) ) ) ) ) ) ) ) ).
tt(t41_bilinear,ax, (! [A:$i] :  ((l2_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) )  =>  ((r1_tarski (k10_bilinear A B B C) (k12_bilinear A B C)) & (r1_tarski (k11_bilinear A B B C) (k12_bilinear A B C))) ) ) ) ) ) ) ).
tt(t41_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k3_lattices A C D)) (k4_lattices A (k1_boolealg A B C) (k1_boolealg A B D)))) ) ) ) ) ) ) ) ).
tt(t41_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v2_borsuk_1 C B) & (m1_borsuk_1 C B))  =>  ((r1_borsuk_1 A B) => (r1_borsuk_1 (k11_borsuk_1 A (k15_borsuk_1 A B C)) (k16_borsuk_1 A B C))) ) ) ) ) ) ) ).
tt(t41_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (~  (B = C) )  => (r1_borsuk_3 k5_topmetr (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C)))) ) ) ) ) ) ) ).
tt(t41_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k4_rcomp_1 k2_xxreal_0 B))  => (v4_pre_topc A k3_topmetr)) ) ) ) ) ).
tt(t41_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ( ((v5_pre_topc D k5_topmetr A) &  ( ((k1_funct_1 D k6_numbers) = B)  &  ((k1_funct_1 D 1) = C) ) )  =>  ((v5_pre_topc (k2_borsuk_2 A B C D) k5_topmetr A) &  ( ((k1_funct_1 (k2_borsuk_2 A B C D) k6_numbers) = C)  &  ((k1_funct_1 (k2_borsuk_2 A B C D) 1) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_borsuk_7,ax, ((k30_valued_1 k9_borsuk_7) = k8_borsuk_7) ).
tt(t41_bspace,ax, (! [A:$i] :  ((k1_card_1 (k9_bspace A)) = (k1_card_1 A)) ) ).
tt(t41_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ( ((v1_relat_1 K) & (v1_funct_1 K))  =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k4_enumset1 C D E F G H))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (G = H) )  &  ( ((k15_bvfunc_1 A I (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H)) = (k15_bvfunc_1 A J (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H)))  & (r1_xboole_0 (k15_bvfunc_1 A J (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A I (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_bvfunc_1 A B (k18_bvfunc_1 A B))) ) ) ) ).
tt(t41_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) B) D) C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t41_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k10_bvfunc_1 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t41_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [F:$i] :  ((m1_eqrel_1 F A) => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B F) (k6_bvfunc_2 A (k9_bvfunc_1 A D (k1_bvfunc_1 A C)) B F)) (k6_bvfunc_2 A (k9_bvfunc_1 A C E) B F)) (k7_bvfunc_2 A (k2_bvfunc_1 A E (k1_bvfunc_1 A D)) B F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k2_bvfunc_1 A B B)) (k12_bvfunc_1 A))) ) ) ) ).
tt(t41_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ( ((k7_cqc_lang A B C) = (k2_calcul_1 A D))  & (r4_calcul_1 A D))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) D) (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t41_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) <=> (r1_ordinal1 A B)) ) ) ) ) ).
tt(t41_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  ( (~ (r2_hidden A B))  =>  ((k5_card_1 (k2_xboole_0 B (k1_tarski A))) = (k2_nat_1 (k5_card_1 B) 1)) ) ) ) ) ).
tt(t41_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_card_3 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_card_3 B)) )  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r2_hidden (k1_funct_1 A C) (k1_funct_1 B C))) ) )  => (r2_hidden (k6_card_3 A) (k7_card_3 B))) ) ) ) ) ).
tt(t41_card_fil,ax, (! [A:$i] :  ( ( (~ (v1_finset_1 A))  & (v1_card_1 A))  =>  ((v7_card_fil A) => (v6_card_fil A)) ) ) ).
tt(t41_card_fin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finset_1 B)) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((v1_finset_1 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k5_card_1 (k1_card_fin E A C D)) (k1_card_fin E A C D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k5_card_1 (k1_card_fin E A C D)) (k1_card_fin E A C D))))) )  =>  ( ( ((k9_xtuple_0 B) = E)  & (v2_funct_1 F))  =>  ( (C = D)  |  (! [G:$i] :  ( ((v5_ordinal1 G) &  ((v1_relat_1 G) &  ((v5_relat_1 G k5_numbers) &  ((v1_funct_1 G) & (v1_finset_1 G)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers G) = (k1_relset_1 (k5_card_1 (k1_card_fin E A C D)) F))  &  (! [H:$i] :  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  ( ((r2_hidden H (k1_relset_1 k5_numbers G)) &  (I = (k1_funct_1 F H)) )  =>  ((k1_recdef_1 G H) = (k1_card_1 (k2_card_fin B I C))) ) ) ) ) )  =>  ((k3_card_fin A B) = (k7_afinsq_2 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ((v9_cat_1 D A B C) <=>  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (k4_cat_2 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k4_cat_2 B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (k4_cat_2 A C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (k4_cat_2 A C))))) )  =>  ( (? [F:$i] :  ((m2_cat_1 F (k8_cat_2 B A) C) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((r2_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k13_cat_2 B A C F G) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D G)) & (r2_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k12_cat_2 B A C F H) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E H))) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  ((k1_cat_1 C (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D (k3_graph_1 A G)) F) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E (k4_graph_1 B F)) G)) = (k1_cat_1 C (k3_funct_2 (u4_struct_0 A) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 B) A C (k4_cat_2 A C) E (k3_graph_1 B F)) G) (k3_funct_2 (u4_struct_0 B) (u4_struct_0 C) (k3_cat_2 (u1_struct_0 A) B C (k4_cat_2 B C) D (k4_graph_1 A G)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_cat_3 E C D A) =>  ((r2_hidden B A) =>  ((k3_graph_1 C (k7_partfun1 (u4_struct_0 C) E B)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t41_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_cat_1 G A B C) =>  (! [H:$i] :  ((m1_cat_1 H A D E) =>  (! [I:$i] :  ((m1_cat_1 I A F B) =>  (! [J:$i] :  ((m1_cat_1 J A F D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A F B) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A F D) = k1_xboole_0) )  &  (~  ((k5_cat_1 A F (k2_cat_4 A B D) (k2_cat_4 A C E) (k9_cat_4 A B D F I J) (k18_cat_4 A B C D E G H)) = (k9_cat_4 A C E F (k5_cat_1 A F B C I G) (k5_cat_1 A F D E J H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 (k24_binop_2 2 B) A) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k5_card_1 (k2_catalan2 A B)) = (k23_binop_2 (k7_afinsq_2 C) (k5_card_1 (k2_catalan2 (k7_nat_d A 1) B))))  &  ( ((k1_relset_1 k5_numbers C) = B)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 B D))  =>  ((k1_recdef_1 C D) = (k24_binop_2 (k5_card_1 (k2_catalan2 (k24_binop_2 2 D) D)) (k5_card_1 (k2_catalan2 (k7_nat_d A (k24_binop_2 2 (k23_binop_2 D 1))) (k7_nat_d B (k23_binop_2 D 1)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (m1_clvect_1 (g1_clvect_1 (k6_cc0sp2 A) (k10_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k1_c0sp1 (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A)) (k9_csspace (k6_cfuncdom (u1_struct_0 A)) (k6_cc0sp2 A))) (k6_cfuncdom (u1_struct_0 A)))) ) ).
tt(t41_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 C A) & (r1_tarski B A))  => (r2_cfcont_1 C B)) ) ) ) ) ).
tt(t41_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) C) (k2_partfun1 A k2_numbers B (k1_relset_1 A (k2_cfunct_1 A C))))) ) ) ) ) ) ).
tt(t41_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ( ((r2_hidden A (k6_cgames_1 (k13_cgames_1 B))) => (r2_hidden (k13_cgames_1 A) (k7_cgames_1 B)))  &  ( ((r2_hidden (k13_cgames_1 A) (k7_cgames_1 B)) => (r2_hidden A (k6_cgames_1 (k13_cgames_1 B))))  &  ( ((r2_hidden A (k6_cgames_1 B)) => (r2_hidden (k13_cgames_1 A) (k7_cgames_1 (k13_cgames_1 B))))  &  ( ((r2_hidden (k13_cgames_1 A) (k7_cgames_1 (k13_cgames_1 B))) => (r2_hidden A (k6_cgames_1 B)))  &  ( ((r2_hidden A (k7_cgames_1 (k13_cgames_1 B))) => (r2_hidden (k13_cgames_1 A) (k6_cgames_1 B)))  &  ( ((r2_hidden (k13_cgames_1 A) (k6_cgames_1 B)) => (r2_hidden A (k7_cgames_1 (k13_cgames_1 B))))  &  ( ((r2_hidden A (k7_cgames_1 B)) => (r2_hidden (k13_cgames_1 A) (k6_cgames_1 (k13_cgames_1 B))))  &  ((r2_hidden (k13_cgames_1 A) (k6_cgames_1 (k13_cgames_1 B))) => (r2_hidden A (k7_cgames_1 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ( (B = (k2_nat_1 A 1))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_euclid B))) =>  ((r2_hidden D (k4_chain_1 B C A)) <=>  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid B)) &  (? [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid B)) &  (? [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 B)) &  ( (D = (k3_chain_1 B E F))  &  ( ((k1_seq_1 E G) = (k1_seq_1 F G))  &  ((r2_hidden (k1_seq_1 E G) (k2_chain_1 B C G)) &  (! [H:$i] :  ((m2_subset_1 H k5_numbers (k2_finseq_1 B)) =>  ( (~  (H = G) )  =>  ( (~ (r1_xxreal_0 (k1_seq_1 F H) (k1_seq_1 E H)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 E H) (k1_seq_1 F H)) (k2_chain_1 B C H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m3_glib_001 D C) =>  ((v1_chord D C) =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (! [F:$i] :  ( ((v7_ordinal1 F) &  (~ (v1_abian F)) )  =>  ((r1_xxreal_0 F (k3_finseq_1 D)) =>  ((r1_xxreal_0 F (k1_nat_1 E 2)) |  (! [G:$i] :  (~ (r1_glib_000 A (k1_funct_1 D E) (k1_funct_1 D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ((r2_hidden A (u1_struct_0 F)) =>  ((r2_hidden B (k3_msafree2 F)) |  ((r2_hidden C (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k2_tarski B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k5_circcomb A B))) =>  ( (C = (k4_tarski B A))  &  ( ((k1_msualg_1 (k5_circcomb A B) C) = B)  &  ((k2_msualg_1 (k5_circcomb A B) C) = C) ) ) ) ) ) ) ) ).
tt(t41_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r4_circtrm1 A B C D E F) =>  ( ((k9_xtuple_0 C) = (u1_struct_0 A))  &  ((r1_tarski (k10_xtuple_0 C) (u1_struct_0 B)) &  ( ((k9_xtuple_0 D) = (u4_struct_0 A))  & (r1_tarski (k10_xtuple_0 D) (u4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r1_tarski A B) & (r2_hidden B (k4_classes1 C)))  => (r2_hidden A (k4_classes1 C))) ) ) ) ) ).
tt(t41_classes2,ax, (! [A:$i] :  ((v1_ordinal1 A) => (r1_ordinal1 (k1_card_1 (k6_classes1 A)) (k1_card_1 A))) ) ).
tt(t41_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_clopban1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k14_clopban1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k14_clopban1 A B)))))) )  =>  ((v1_csspace3 C (k14_clopban1 A B)) => (v9_clvect_1 C (k14_clopban1 A B))) ) ) ) ) ) ) ) ).
tt(t41_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A (k5_algstr_0 A (k5_struct_0 A) B))))  =>  ((v1_clopban3 (k5_clopban3 A (k5_algstr_0 A (k5_struct_0 A) B)) A) & (v2_clopban3 (k5_clopban3 A (k5_algstr_0 A (k5_struct_0 A) B)) A)) ) ) ) ) ) ).
tt(t41_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B)) &  ((v7_closure2 C (u1_struct_0 A) B) &  ((v8_closure2 C (u1_struct_0 A) B) &  ((v9_closure2 C (u1_struct_0 A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B))))) ) ) ) )  => (r1_funct_2 (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A (k10_closure2 A B C))) (k6_closure2 (u1_struct_0 A) (u3_msualg_1 A (k10_closure2 A B C))) (k6_closure2 (u1_struct_0 A) B) (k6_closure2 (u1_struct_0 A) B) (k12_closure2 A (k10_closure2 A B C)) C)) ) ) ) ) ) ).
tt(t41_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r1_struct_0 C B) => (r1_struct_0 C (k4_algstr_0 A B))) ) ) ) ) ) ) ).
tt(t41_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_clvect_2 A C D)) <=>  (~ (r1_xxreal_0 D (k15_csspace A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t41_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k13_csspace A (k3_clvect_3 A B D C)) (k18_complex1 (k7_series_1 (k2_clvect_2 A B) D C)))) ) ) ) ) ) ) ) ).
tt(t41_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  ((k8_cohsp_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t41_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k16_coh_sp A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k17_coh_sp A B) (k17_coh_sp A C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k17_coh_sp A B) (k17_coh_sp A C))))) )  =>  ( (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski E F) (k18_coh_sp A B)) => (r2_hidden (k4_tarski (k1_funct_1 D E) (k1_funct_1 D F)) (k18_coh_sp A C))) ) )  =>  ( ( ((k17_coh_sp A C) = k1_xboole_0)  &  (~  ((k17_coh_sp A B) = k1_xboole_0) ) )  | (r2_hidden (k4_tarski (k4_tarski B C) D) (k20_coh_sp A))) ) ) ) ) ) ) ) ) ).
tt(t41_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k2_xcmplx_0 A (k15_complex1 A))) = (k8_real_1 2 (k3_complex1 A)))  &  ((k4_complex1 (k2_xcmplx_0 A (k15_complex1 A))) = k6_numbers) ) ) ) ).
tt(t41_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ((k1_complex2 A (k8_complex1 (k9_complex1 B C) (k9_complex1 D E))) = (k8_complex1 (k9_complex1 (k15_complex1 B) (k1_complex2 A C)) (k9_complex1 (k15_complex1 D) (k1_complex2 A E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k3_rlvect_1 k1_complfld (k3_vectsp_1 k1_complfld B A) (k3_vectsp_1 k1_complfld C A)) = (k3_vectsp_1 k1_complfld (k3_rlvect_1 k1_complfld B C) A)) ) ) ) ) ) ) ) ).
tt(t41_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k12_seq_4 (k17_seq_4 (k3_finseq_1 A)) B) = (k17_seq_4 (k3_finseq_1 A))) ) ) ) ) ).
tt(t41_compl_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k3_compl_sp B C A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k3_compl_sp B C A)))))) )  =>  (~  ((v3_tbsp_1 D (k3_compl_sp B C A)) &  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k3_compl_sp B C A))) &  ( (E = (k4_tarski A C))  &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (? [H:$i] :  ((v7_ordinal1 H) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k4_metric_1 (k3_compl_sp B C A) (k8_nat_1 (u1_struct_0 (k3_compl_sp B C A)) D H) E))) ) ) ) ) ) ) ) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  (? [G:$i] :  ((v7_ordinal1 G) &  ((r1_xxreal_0 E G) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ((k8_nat_1 (u1_struct_0 (k3_compl_sp B C A)) D G) = (k4_tarski F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ((k5_compos_1 B (k1_funct_4 C D) A) = (k1_funct_4 (k5_compos_1 B C A) (k5_compos_1 B D A))) ) ) ) ) ) ) ) ) ).
tt(t41_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  (! [H:$i] :  ( ((v6_compos_0 H (u1_compos_1 A)) & (m1_subset_1 H (u1_compos_1 A)))  =>  ((k1_funct_1 (k8_compos_1 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A C D) E) F) G) H) B) k6_numbers) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r2_hidden (k1_comptrig A) (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) <=>  ( (~ (r1_xxreal_0 (k3_complex1 A) k6_numbers))  &  (~ (r1_xxreal_0 (k4_complex1 A) k6_numbers)) ) ) ) ) ).
tt(t41_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_comput_1 B) & (m2_finseq_1 B (k2_comput_1 A)))  => (r1_tarski (k9_xtuple_0 (k6_funct_6 B)) (k4_finseq_2 (k1_comput_1 B) A))) ) ) ) ).
tt(t41_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (r2_relset_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers A)) (k25_valued_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers A) (k10_complex1 k6_complex1)))) ) ) ).
tt(t41_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (v2_relat_1 B)) )  =>  ( ((k3_comseq_2 B) = k5_complex1)  |  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B))) = (k13_complex1 (k15_complex1 (k3_comseq_2 A)) (k15_complex1 (k3_comseq_2 B)))) ) ) ) ) ) ) ).
tt(t41_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) &  ((v2_comseq_2 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  =>  ((v2_comseq_2 (k7_comseq_3 A)) &  ((v2_comseq_2 (k8_comseq_3 A)) &  ( ((k2_seq_2 (k7_comseq_3 A)) = (k3_complex1 (k3_comseq_2 A)))  &  ((k2_seq_2 (k8_comseq_3 A)) = (k4_complex1 (k3_comseq_2 A))) ) ) ) ) ) ).
tt(t41_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ( ((v4_conlat_1 B A) &  ( (~ (v5_conlat_1 B A))  &  ((v7_conlat_1 B A) & (l2_conlat_1 B A)) ) )  =>  ((k1_binop_1 (k9_conlat_1 A) B (k6_conlat_1 A)) = (k6_conlat_1 A)) ) ) ) ) ).
tt(t41_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_connsp_1 B A) & (r2_hidden C B))  =>  (B = (k1_connsp_1 A C)) ) ) ) ) ) ) ) ).
tt(t41_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_convex1 A B))) ) ) ) ).
tt(t41_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_convex4 B A) =>  (! [C:$i] :  ((m1_convex4 C A) =>  ((k5_algstr_0 (k15_convex4 A) (k1_rlvect_2 (k15_convex4 A) B) (k1_rlvect_2 (k15_convex4 A) C)) = (k9_convex4 A B C)) ) ) ) ) ) ) ).
tt(t41_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 (k3_qc_lang1 A))) =>  ( ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D B G F) (k15_cqc_sim1 A E)) & (r2_hidden (k2_qc_lang3 A C) (k7_relat_1 F (k24_qc_lang1 A E))))  => (r2_qc_lang1 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r2_hidden (k5_cqc_lang A) (k4_cqc_the1 A))) ) ).
tt(t41_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k12_cqc_lang A D (k9_cqc_lang A B C)) (k9_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t41_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v6_qc_lang1 B A) & (r1_cqc_the3 A B C))  => (v2_cqc_the1 (k8_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(t41_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_csspace A B C) =>  ((k12_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A B C)) = (k2_xcmplx_0 (k12_csspace A B B) (k12_csspace A C C))) ) ) ) ) ) ) ) ).
tt(t41_dickson,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k1_nat_1 A 1)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k1_nat_1 A 1)) & (v1_yellow_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_nat_1 A 1))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_nat_1 A 1)) =>  ( ( (C = A)  &  (D = A) )  => (r5_waybel_1 (k3_yellow_3 (k5_yellow_1 C (k5_relat_1 B C)) (k3_waybel_3 (k1_nat_1 A 1) B D)) (k5_yellow_1 (k1_nat_1 A 1) B))) ) ) ) ) ) ) ) ) ).
tt(t41_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 k16_sin_cos A B) = (k10_real_1 (k8_real_1 (k8_real_1 2 (k21_sin_cos (k10_real_1 (k7_real_1 A B) 2))) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))) (k9_real_1 A B))) ) ) ) ) ).
tt(t41_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k7_square_1 D)) ) )  =>  ((r1_xxreal_0 (k7_real_1 A (k10_real_1 B 2)) k6_numbers) |  ((r1_xxreal_0 (k9_real_1 A (k10_real_1 B 2)) k6_numbers) |  ((k1_seq_1 (k5_diff_1 C B) A) = (k9_real_1 (k7_square_1 (k7_real_1 A (k10_real_1 B 2))) (k7_square_1 (k9_real_1 A (k10_real_1 B 2))))) ) ) ) ) ) ) ) ) ) ).
tt(t41_diff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) (k2_nat_1 A 1)) C) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) A) (k7_real_1 C B)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 D B) A) C))) ) ) ) ) ) ) ) ) ).
tt(t41_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski (k6_dilworth A) B) =>  (B = (k6_dilworth A)) ) ) ) ) ) ).
tt(t41_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ( (~ (v7_struct_0 (k2_diraf A)))  &  ((v1_diraf (k2_diraf A)) & (l1_analoaf (k2_diraf A))) ) ) ) ).
tt(t41_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  ((k3_funct_2 (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (u1_struct_0 (k9_int_3 A)) (k5_ec_pf_1 A B C) (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D E F)) = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) F) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 3) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) B D) (k2_binom (k9_int_3 A) F 2))) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) F 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((k9_ec_pf_2 A B (k8_ec_pf_2 A B) (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C)) = C) ) ) ) ) ) ) ).
tt(t41_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden (k2_cat_1 A B C) (k16_ens_1 A))) ) ) ) ) ) ).
tt(t41_entropy1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 (k2_entropy1 A B))) &  (D = (k9_real_1 C 1)) )  =>  ((r2_hidden (k4_tarski (k2_nat_1 (k3_nat_d D (k1_matrix_1 B)) 1) (k2_nat_1 (k4_nat_d D (k1_matrix_1 B)) 1)) (k2_matrix_1 B)) &  ((k1_funct_1 (k2_entropy1 A B) C) = (k3_matrix_1 A B (k2_nat_1 (k3_nat_d D (k1_matrix_1 B)) 1) (k2_nat_1 (k4_nat_d D (k1_matrix_1 B)) 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k6_enumset1 A A A B C D E F) = (k4_enumset1 A B C D E F)) ) ) ) ) ) ) ).
tt(t41_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~ (r1_xboole_0 (k11_eqrel_1 A C B) (k11_eqrel_1 A D B)))  =>  ((k11_eqrel_1 A C B) = (k11_eqrel_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k23_rvsum_1 B B) = k6_numbers)  <=>  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t41_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k23_rvsum_1 A B) = (k7_real_1 (k8_real_1 (k17_euclid A) (k17_euclid B)) (k8_real_1 (k18_euclid A) (k18_euclid B)))) ) ) ) ) ).
tt(t41_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k4_euclid_4 A B C)) & (r2_hidden C (k4_euclid_4 A B C))) ) ) ) ) ) ) ).
tt(t41_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k17_euclid A) (k17_euclid B)))  &  ((k18_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k9_real_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(t41_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k8_euclid_7 A)) = A) ) ) ).
tt(t41_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k6_euclid 3 A) = (k8_euclid 3 (k8_euclid 3 (k6_euclid 3 (k9_euclid 3 k2_euclid_8 (k1_seq_1 A 1))) (k9_euclid 3 k3_euclid_8 (k1_seq_1 A 2))) (k9_euclid 3 k4_euclid_8 (k1_seq_1 A 3)))) ) ) ).
tt(t41_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k5_algstr_0 (k15_euclid A) B C) = (k3_rlvect_1 (k15_euclid A) B (k4_algstr_0 (k15_euclid A) C))) ) ) ) ) ) ) ).
tt(t41_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r2_euclidlp A B C) =>  ( (~ (r3_euclidlp A B C))  &  ( (~  (B = (k5_euclid A)) )  &  (~  (C = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v2_funct_1 (k10_funct_7 (k6_partfun1 A) B C))) ) ) ).
tt(t41_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k5_circcomb A (k10_finseq_1 B C))))) ) ) ) ) ) ).
tt(t41_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [E:$i] :  ((v1_xreal_0 E) =>  ((r2_hidden E A) =>  ((k1_seq_1 D E) = (k2_xcmplx_0 (k3_xcmplx_0 B E) C)) ) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D A))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) B) = (k10_real_1 (k7_real_1 (k9_real_1 (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k1_seq_1 k29_sin_cos B)) (k1_seq_1 k30_sin_cos B)) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B))))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (r2_fdiff_1 C (k2_rcomp_1 A B)))  =>  ( ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_xxreal_0 (k1_fdiff_1 C D) k6_numbers)) ) )  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 C D))) ) ) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k21_sin_cos (k8_real_1 2 B))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)))) &  ( (B = (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers k16_sin_cos 2)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k10_real_1 1 2)) A) D) = (k10_real_1 (k1_seq_1 k19_sin_cos D) (k7_real_1 1 (k8_real_1 2 (k1_seq_1 k16_sin_cos D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) B) = (k8_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos B)) (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t41_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) A) B) = (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t41_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  => (r1_nat_d (k1_pre_ff B) (k1_pre_ff (k4_nat_1 B A)))) ) ) ) ).
tt(t41_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k6_xcmplx_0 (k3_fib_num3 A B (k2_nat_1 C 3)) (k3_fib_num3 A B C)) = (k4_nat_1 2 (k3_fib_num3 A B (k2_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t41_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_finseq_8 A (k17_finseq_1 A D B) C 1) =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) | (r2_finseq_8 A B C 1)) ) ) ) ) ) ) ) ) ) ).
tt(t41_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v19_lattices E A) &  ((v20_lattices E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((r2_hidden (k4_filter_0 A B C) E) & (r2_hidden (k4_filter_0 A C D) E))  => (r2_hidden (k4_filter_0 A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((v15_lattices A) & (v15_lattices B))  <=> (v15_lattices (k7_filter_1 A B))) ) ) ) ) ).
tt(t41_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v14_lattices A) & (r2_hidden (k6_lattices A) B))  =>  ((r1_filter_2 (u1_struct_0 A) (k7_filter_2 A B) (k5_filter_2 A)) &  ((k7_filter_2 A B) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t41_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k1_funct_1 (k7_finseq_1 (k9_finseq_1 A) B) 1) = A) ) ) ) ).
tt(t41_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  ( ( ((k10_xtuple_0 D) = (k2_finseq_1 A))  &  ((r1_xxreal_0 A (k3_finseq_1 B)) &  (C = (k3_relat_1 D B)) ) )  =>  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t41_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_tarski A (k2_finseq_1 B)) &  ( (~ (r1_xxreal_0 D C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 F (k3_finseq_1 (k14_finseq_1 A))) &  ( ((k1_funct_1 (k14_finseq_1 A) F) = C)  &  ( ((k1_funct_1 (k14_finseq_1 A) E) = D)  & (r1_xxreal_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (m2_finseq_1 A C))  => (m2_finseq_1 (k5_finseq_4 A B) C)) ) ) ) ) ) ).
tt(t41_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((r2_hidden A (k4_finseq_1 C)) & (v2_funct_1 C))  =>  ((k4_finseq_4 C (k7_partfun1 B C A)) = A) ) ) ) ) ) ) ) ).
tt(t41_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k2_finseq_5 A C B) = (k7_finseq_1 (k12_finseq_1 A B) (k6_finseq_4 C B))) ) ) ) ) ) ) ) ).
tt(t41_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((r7_binop_1 B F E) => (r2_funct_2 A B (k1_partfun1 A B B B (k10_funcop_1 B A E C D) F) (k10_funcop_1 B A E (k3_funct_2 B B F C) (k1_partfun1 A B B B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (k8_fintopo2 A (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t41_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k9_fintopo3 A B 2) = (k1_fintopo3 A (k1_fintopo3 A B))) ) ) ) ) ).
tt(t41_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_orders_2 A) &  ((v1_fin_topo A) &  ((r1_fintopo6 A B) &  ((r1_fintopo6 A C) &  ( (~  (B = C) )  &  (~ (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_flang_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r2_hidden B (k8_flang_1 A C)) <=>  (? [D:$i] :  ((v7_ordinal1 D) & (r2_hidden B (k7_flang_1 A C D))) ) ) ) ) ) ) ).
tt(t41_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k1_flang_2 A (k7_flang_1 A B (k2_xcmplx_0 C 1)) D E) (k6_flang_1 A (k1_flang_2 A (k7_flang_1 A B C) D E) (k1_flang_2 A B D E)))) ) ) ) ) ) ) ) ) ).
tt(t41_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k2_flang_2 A B)) = (k1_flang_3 A B C)) ) ) ) ) ) ).
tt(t41_fomodel0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((v3_card_1 B A) & (v3_card_1 D A))  =>  ( ( (~  ((k7_finseq_1 B C) = (k7_finseq_1 D E)) )  &  (~  ((k7_finseq_1 C B) = (k7_finseq_1 E D)) ) )  |  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((v3_frechet A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_frechet2 A B C) &  (! [D:$i] :  ((m2_valued_0 D (u1_struct_0 A) B) =>  (~ (r1_frechet A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  => (r4_fsm_1 A B C (k11_fsm_1 A B C))) ) ) ) ) ) ).
tt(t41_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  => (r2_funct_2 B A (k1_partfun1 B A A A D (k6_funcop_1 A A C (k6_partfun1 A) (k6_partfun1 A))) (k6_funcop_1 A B C D D))) ) ) ) ) ) ) ) ).
tt(t41_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) &  ( ((k10_xtuple_0 A) = (k9_xtuple_0 B))  &  ((k3_relat_1 A B) = (k4_relat_1 (k9_xtuple_0 A))) ) )  =>  (B = (k2_funct_1 A)) ) ) ) ) ) ).
tt(t41_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [D:$i] :  (~  ((r2_hidden D B) &  ((k8_relset_1 A B C (k1_tarski D)) = k1_xboole_0) ) ) )  <=>  ((k2_relset_1 B C) = B) ) ) ) ) ) ).
tt(t41_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k6_funct_3 A B) = (k5_relat_1 (k4_relat_1 A) B)) ) ) ) ).
tt(t41_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k10_xtuple_0 (k2_funct_4 A)) (k10_xtuple_0 A))) ) ).
tt(t41_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k1_funct_2 A B)) =>  ((r1_tarski (k10_xtuple_0 (k2_funct_5 C)) B) & (r1_tarski (k10_xtuple_0 (k4_funct_5 C)) B)) ) ) ) ) ) ).
tt(t41_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (~  (A = k1_xboole_0) )  =>  ( ((k9_xtuple_0 (k6_funct_6 (k7_funcop_1 A B))) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 (k6_funct_6 (k7_funcop_1 A B)) C) = (k7_funcop_1 A (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(t41_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k4_funct_7 A (k7_finseq_1 B (k9_finseq_1 C))) = (k3_relat_1 (k4_funct_7 A B) C)) ) ) ) ) ) ).
tt(t41_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 B k1_numbers k1_numbers) => (v4_funct_8 (k9_valued_1 k1_numbers k1_numbers B A) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t41_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v21_functor0 C A B) &  ((v7_functor0 C A B) & (v11_functor0 C A B)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 B D E)) =>  ( (~  ((k1_altcat_1 B D E) = k1_xboole_0) )  =>  ((k1_funct_1 (k4_functor0 A B C (k3_functor0 B A (k15_functor0 A B C) E) (k3_functor0 B A (k15_functor0 A B C) D)) (k1_funct_1 (k4_functor0 B A (k15_functor0 A B C) D E) F)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ((m1_functor3 E A B C D) =>  ((r1_functor3 A B C D) => (r8_pboole (u1_struct_0 A) (k8_functor3 A B D C (k8_functor3 A B C D E)) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k6_fuzzy_1 A B (k4_fuzzy_1 A)) B)) ) ) ) ).
tt(t41_fuzzy_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ( ((k8_real_1 C (k2_square_1 A B)) = (k2_square_1 (k8_real_1 C A) (k8_real_1 C B)))  &  ((k8_real_1 C (k1_square_1 A B)) = (k1_square_1 (k8_real_1 C A) (k8_real_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t41_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C B)) <=> (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B))) ) ) ) ) ) ) ) ).
tt(t41_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B C C) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ) ) ).
tt(t41_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 (k34_gate_1 A B)))  <=>  ( (~  ((v1_xboole_0 A) & (v1_xboole_0 B)) )  &  (~  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) ) ) ) ) ) ).
tt(t41_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( ((k5_gcd_1 A B C D) = (k5_struct_0 A))  &  ((k5_gcd_1 A B E F) = (k5_struct_0 A)) )  =>  ( (D = (k4_struct_0 A))  |  ( (F = (k4_struct_0 A))  |  ((k5_gcd_1 A B (k8_group_1 A (k1_gcd_1 A C (k5_gcd_1 A B C F)) (k1_gcd_1 A E (k5_gcd_1 A B E D))) (k8_group_1 A (k1_gcd_1 A D (k5_gcd_1 A B E D)) (k1_gcd_1 A F (k5_gcd_1 A B C F)))) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H k6_numbers A B C D) = (k10_genealg1 F H G A B C D))  &  ( ((k11_genealg1 F G H E k6_numbers B C D) = (k10_genealg1 F H G E B C D))  &  ( ((k11_genealg1 F G H E A k6_numbers C D) = (k10_genealg1 F H G E A C D))  &  ( ((k11_genealg1 F G H E A B k6_numbers D) = (k10_genealg1 F H G E A B D))  &  ((k11_genealg1 F G H E A B C k6_numbers) = (k10_genealg1 F H G E A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (! [L:$i] :  ((m1_subset_1 L (u1_struct_0 A)) =>  (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 A)) =>  ( ((r1_analmetr A B C) &  ((r2_geomtrap A B C D E F J) &  ((r2_geomtrap A B C D E G K) &  ((r2_geomtrap A B C D E H L) &  ((r2_geomtrap A B C D E I M) & (r2_geomtrap A B C F G H I)) ) ) ) )  =>  ( (D = E)  | (r2_geomtrap A B C J K L M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k17_gfacirc1 A B C)) = (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) ) ) ) ).
tt(t41_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ( ( ((m1_glib_000 A B) & (m1_glib_000 B A))  =>  ( ((k6_glib_000 A) = (k6_glib_000 B))  &  ( ((k7_glib_000 A) = (k7_glib_000 B))  &  ((r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k10_glib_000 A) (k10_glib_000 B)) & (r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k11_glib_000 A) (k11_glib_000 B))) ) ) )  &  ( ( ((k6_glib_000 A) = (k6_glib_000 B))  &  ( ((k7_glib_000 A) = (k7_glib_000 B))  &  ((r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k10_glib_000 A) (k10_glib_000 B)) & (r1_funct_2 (k7_glib_000 A) (k6_glib_000 A) (k7_glib_000 B) (k6_glib_000 B) (k11_glib_000 A) (k11_glib_000 B))) ) )  =>  ((m1_glib_000 A B) & (m1_glib_000 B A)) ) ) ) ) ) ) ).
tt(t41_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 (k3_finseq_1 B) D) | (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k10_glib_001 A (k8_glib_001 A B C D) (k1_funct_1 B (k2_nat_1 D 1))) (k8_glib_001 A B C (k2_nat_1 D 2)))) ) ) ) ) ) ) ) ) ) ).
tt(t41_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_002 A)) ) ) ) )  => (v7_glib_000 A)) ) ).
tt(t41_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k5_glib_003 A) = (k5_glib_003 (k13_glib_003 A B C))) ) ) ) ) ).
tt(t41_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_glib_000 B A) &  ((v3_glib_002 B) &  ((v1_glib_003 B) &  ((v4_glib_003 B A) &  ((v1_glib_004 B A) & (m1_glib_000 B A)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_glib_000 C) & (v1_glib_003 C)) ) ) ) )  =>  ( ((r5_glib_000 B C) &  ((k5_glib_003 B) = (k5_glib_003 C)) )  =>  ((v9_glib_000 C A) &  ((v3_glib_002 C) &  ((v1_glib_003 C) &  ((v4_glib_003 C A) &  ((v1_glib_004 C A) & (m1_glib_000 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t41_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ((r2_hidden (k4_tarski B (k2_nat_1 C 1)) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski B C) (k2_matrix_1 E)) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B (k2_nat_1 C 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E B C)) ) ) ) ) ) )  =>  ((k4_gobrd13 D E A) = (k3_goboard5 E (k7_nat_d B 1) (k7_nat_d C 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k6_pscomp_1 (k3_topreal1 2 A)) = (k6_pscomp_1 (k3_goboard9 A))) ) ) ).
tt(t41_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_graph_1 D))  =>  (! [E:$i] :  ((m2_graph_1 E D) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C (k3_finseq_1 E)) &  (A = (k2_graph_2 (u4_struct_0 D) E B C)) ) ) )  => (m2_graph_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_graph_3 B D C))) =>  ( ( (E = D)  & (r2_hidden (u4_struct_0 B) A))  =>  ( ((k3_graph_3 (k8_graph_3 B D C) E A) = (k2_xboole_0 (k3_graph_3 B D A) (k1_tarski (u4_struct_0 B))))  & (r1_xboole_0 (k3_graph_3 B D A) (k1_tarski (u4_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v7_graph_1 E B) & (m2_graph_1 E B))  =>  ((r2_graph_5 B C D E A) => (r1_tarski (k6_graph_5 B E) (k5_graph_5 B C D A))) ) ) ) ) ) ) ) ) ) ).
tt(t41_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  ((k4_finseq_1 C) = (k4_finseq_1 (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C))) ) ) ) ) ) ) ).
tt(t41_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v2_funct_1 C) & (v2_funct_2 C (u1_struct_0 B)))  =>  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) C) (k3_struct_0 B)) &  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) (k3_struct_0 A)) &  ((v2_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) & (v2_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t41_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  => (r1_tarski (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D (k2_nat_1 E 1))) (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_group_11 A (k1_group_11 A B C) C)) => (r1_tarski (k13_group_2 A C D) (k1_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t41_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_group_1 A (k6_group_1 A B) B) = (k1_group_1 A)) ) ) ) ) ).
tt(t41_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_struct_0 A C)) ) ) ) ) ) ).
tt(t41_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A (k4_group_3 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k2_group_3 B E C))  & (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((u1_struct_0 (k6_group_4 A)) = (a_1_1_group_4 A)) ) ) ).
tt(t41_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_5 A B C B) = (k2_group_5 A (k2_group_3 A B C) B)) ) ) ) ) ) ) ).
tt(t41_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((r1_struct_0 (k9_group_6 A B D) C) <=>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D C) = (k1_group_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  (! [D:$i] :  ((m1_group_9 D A B) =>  ( ((v4_group_9 (k17_group_9 A B D C) A D) & (m1_group_9 (k17_group_9 A B D C) A D))  &  ((v4_group_9 (k17_group_9 A B C D) A D) & (m1_group_9 (k17_group_9 A B C D) A D)) ) ) ) ) ) ) ) ) ).
tt(t41_hausdorf,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((v2_compts_1 B (k15_euclid A)) &  ((v2_compts_1 C (k15_euclid A)) &  ((k3_hausdorf A B C) = k6_numbers) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t41_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((k3_helly A B C D) = (k3_helly A B D C)) ) ) ) ) ) ) ) ) ).
tt(t41_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v4_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)) = (k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)))  &  ((k4_hermitan A B C) = (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C))) ) ) ) ) ) ) ) ).
tt(t41_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A E) =>  ((r1_xxreal_0 C D) |  ( ((k1_seq_1 (k6_taylor_1 (k1_taylor_1 C) E A B) D) = (k8_real_1 (k8_real_1 (k6_newton D C) (k5_prepower A (k9_real_1 C D))) (k2_newton (k9_real_1 B A) D)))  &  ((k1_seq_1 (k6_taylor_1 (k1_taylor_1 C) E A B) C) = (k2_newton (k9_real_1 B A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k4_hilbert1 A C) (k4_hilbert1 B C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t41_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( ((v1_hilbert3 A) & (v1_hilbert3 (k3_hilbert1 A B)))  => (v1_hilbert3 B)) ) ) ) ) ).
tt(t41_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_hurwitz (k13_polynom3 k1_complfld A B)) <=>  ((v1_hurwitz A) & (v1_hurwitz B)) ) ) ) ) ) ).
tt(t41_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~  (D = k6_numbers) )  => (m1_funct_7 (k18_idea_1 D B A C) k14_idea_1 k14_idea_1)) ) ) ) ) ) ) ) ) ).
tt(t41_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_ideal_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (m1_ideal_1 (k2_partfun1 k5_numbers (u1_struct_0 A) C (k2_finseq_1 D)) A B)) ) ) ) ) ) ) ) ).
tt(t41_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D E) B) &  (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r3_pua2mss1 A B D E) =>  (! [F:$i] :  ((m1_dtconstr F (u1_struct_0 (k5_msafree A (k3_relat_1 D C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k3_relat_1 D C)))) (k1_msaterm A (k3_relat_1 D C))) =>  ((m2_msaterm (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A (k3_relat_1 D C))) (u3_msualg_1 A (k1_instalg1 A B (k11_msafree B C) D E)) (k3_instalg1 A B C D E) (k7_msaterm A (k3_relat_1 D C) F)) F) B C) <=> (m2_msaterm F A (k3_relat_1 D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_int_1 A) = (k2_int_1 A))  <=>  (~  ((k3_real_1 (k1_int_1 A) 1) = (k2_int_1 A)) ) ) ) ) ).
tt(t41_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ( (~ (r1_int_1 (k3_int_2 A B) (k6_xcmplx_0 C D)))  &  (? [E:$i] :  ((v1_int_1 E) &  ( ((k6_int_1 (k6_xcmplx_0 E C) A) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 E D) B) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ( ((k3_int_2 B A) = 1)  &  ( (D = (k10_rvsum_1 (k1_finseq_2 (k3_nat_d (k7_nat_d A 1) 2)) B))  &  (C = (k1_card_1 (a_2_0_int_5 A D))) ) )  =>  ((r1_xxreal_0 A 2) |  ((k2_int_5 B A) = (k1_newton (k4_xcmplx_0 1) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  (~  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((r1_xxreal_0 k6_numbers C) &  ( (~ (r1_xxreal_0 (k19_rvsum_1 B) C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 A)) => (r2_int_1 C (k1_funct_1 A D) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) A) B) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t41_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( ((k1_seq_1 C E) = (k12_binop_2 (k1_seq_1 k19_sin_cos E) (k5_prepower (k1_seq_1 k16_sin_cos E) (k23_binop_2 A 1))))  &  (~  ((k1_seq_1 k16_sin_cos E) = k6_numbers) ) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)) (k13_binop_2 (k18_binop_2 1 A))) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) (k1_taylor_1 A)) (k13_binop_2 (k18_binop_2 1 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_integr13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 C F) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers D (k26_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 (k5_real_1 A 1))) (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2))) A)) &  ((r1_tarski E (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A)))) &  ( (E = (k1_relset_1 k1_numbers D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A))) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k10_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t41_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) & (v1_integr15 C A B))  =>  ((v2_integr15 C A B) <=> (v1_integr18 D (k4_real_ns1 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ((m1_integra1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r1_integra1 C D) &  ((r2_hidden A (k4_finseq_1 C)) & (v2_seq_2 (k2_partfun1 B k1_numbers E B))) )  => (r1_xxreal_0 (k1_seq_1 (k14_integra1 (k5_integra1 B E C)) A) (k1_seq_1 (k14_integra1 (k5_integra1 B E D)) (k13_integra1 B C D A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers k32_sin_cos))  =>  ((k2_integra5 A k19_sin_cos) = k6_numbers) ) ) ) ).
tt(t41_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (B = (k1_rcomp_1 (k1_real_1 (k8_real_1 (k8_real_1 2 A) k32_sin_cos)) (k8_real_1 (k8_real_1 2 A) k32_sin_cos)))  => (r1_integra9 B k16_sin_cos k19_sin_cos)) ) ) ) ) ).
tt(t41_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( (B = (k2_interva1 A D E))  =>  ((k9_interva1 A B C) = (k2_interva1 A (k7_subset_1 A D (k6_interva1 A C)) (k7_subset_1 A E (k5_interva1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k4_intpro_1 C A) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(t41_irrat_1,ax, (~ (v1_rat_1 k7_power)) ).
tt(t41_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D B C) =>  (! [E:$i] :  ((m2_cat_1 E B C) =>  (! [F:$i] :  ((m2_cat_1 F C A) =>  (! [G:$i] :  ((m2_nattra_1 G B C D E) =>  ((r2_nattra_1 B C D E) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) (k4_isocat_1 B C A D E G F) (k6_isocat_1 B C A D E F F G (k6_nattra_1 C A F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_isomichi B A) =>  ( ((k1_tops_1 A (k2_pre_topc A B)) = (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))  &  ((k2_pre_topc A (k1_tops_1 A B)) = (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B)))) ) ) ) ) ) ) ).
tt(t41_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( ((k3_finseq_1 (k1_goboard1 A)) = (k3_finseq_1 A))  &  ( ((k1_seq_1 (k1_goboard1 A) 1) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)))  &  ((k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A)) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) ) ) ) ).
tt(t41_jgraph_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ( (A = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  ( (B = a_0_2_jgraph_2)  &  ( (C = a_0_3_jgraph_2)  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))))) )  =>  (~  ((v5_pre_topc D (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A)) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) &  ((v2_funct_1 D) &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden E B) &  ( (~  (E = (k4_struct_0 (k15_euclid 2))) )  & (r2_hidden (k1_funct_1 D E) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( (~ (r2_hidden E (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C)))  => (r2_hidden (k1_funct_1 D E) B)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E C) =>  ((k1_funct_1 D E) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k4_struct_0 (k15_euclid 2))))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (~  ( (B = (k5_relat_1 (k2_funct_1 k1_jgraph_3) A))  & (v5_pre_topc B (k1_pre_topc (k15_euclid 2) A) (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ).
tt(t41_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B (k3_jgraph_4 A)) & (v3_tops_2 B (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t41_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (A = a_0_6_jgraph_5)  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_topmetr (k1_real_1 1) 1)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))))))) )  =>  (~  ((v3_tops_2 B (k4_topmetr (k1_real_1 1) 1) (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k8_jordan6 A)) =>  ((k1_funct_1 B (k17_euclid C)) = C) ) ) )  &  ( ((k1_funct_1 B (k1_real_1 1)) = (k18_pscomp_1 A))  &  ((k1_funct_1 B 1) = (k22_pscomp_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k12_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid B D)) ) ) ) ) ) ) ) ) ) ).
tt(t41_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 (k18_euclid B) H) &  ((r1_xxreal_0 G (k18_euclid C)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) E))  &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) E C)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D))) & (r1_xxreal_0 D B)) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) (k3_finseq_1 (k1_jordan8 E B)) A)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) (k3_finseq_1 (k1_jordan8 E D)) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_9_jordan1 A B C D))  &  (F = (a_4_5_jordan1 A B C D)) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan1b,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A B))) & (r1_tarski (k3_goboard5 (k1_jordan8 A B) C D) (k1_jordan2c 2 A))) ) ) ) ) )  => (r1_xxreal_0 1 B)) ) ) ) ) ).
tt(t41_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  => (r2_sprect_2 (k1_jordan9 B A) (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e B A)))) ) ) ) ).
tt(t41_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((k2_goboard9 A) = (k2_jordan2c 2 (k3_topreal1 2 A)))  => (v1_sprect_2 A)) ) ) ).
tt(t41_jordan1j,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 B) &  ((v3_topreal1 B) &  ((v2_funct_1 B) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))  &  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 A)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) = k1_xboole_0) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 2 C) & (r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 B)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 B C) (k1_rltopsp1 (k15_euclid 2) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) = k1_xboole_0) ) ) ) ) ) ) ) ) )  => (v1_goboard5 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t41_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ((r1_tarski D B) => (r1_xxreal_0 (k1_jordan1k A C B) (k1_jordan1k A C D))) ) ) ) ) ) ) ) ) ).
tt(t41_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xxreal_0 (k7_pscomp_1 A) (k18_euclid (k2_jordan21 A)))) ) ) ).
tt(t41_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k8_pscomp_1 A) = (k8_pscomp_1 (k4_jordan19 A))) ) ) ).
tt(t41_jordan23,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) ) ) )  =>  ( (B = (k1_funct_1 A 1))  | (v4_topreal1 (k3_jordan3 A B))) ) ) ) ) ) ).
tt(t41_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 (k14_euclid A))))) =>  (~  ( (D = (k1_rltopsp1 (k15_euclid A) B C))  &  ( (~ (r2_hidden (k4_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) B C)))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden E (k1_rltopsp1 (k15_euclid A) B C)) &  ( (~ (r1_xxreal_0 (k12_euclid E) k6_numbers))  &  ((k12_euclid E) = (k1_seq_1 (k6_weierstr (k14_euclid A) D) (k4_struct_0 (k15_euclid A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (r1_tarski (k3_topreal1 2 (k3_jordan3 A B)) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t41_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B D)) &  ( (~  (B = A) )  &  ( (~ (r2_hidden C (k1_rltopsp1 (k15_euclid 2) B D)))  &  (~ (r2_hidden D (k1_rltopsp1 (k15_euclid 2) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 A))) &  ( (E = (a_2_0_jordan5d A C))  &  ( ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C 1)))  &  (D = (k6_seq_4 E)) ) ) ) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D)) (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan6,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))) =>  ( ((r1_tarski B C) &  ( (E = D)  & (v2_connsp_1 D (k1_pre_topc A B))) )  => (v2_connsp_1 E (k1_pre_topc A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_jordan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m1_borsuk_2 (k6_struct_0 k5_topmetr A B) A B B)) ) ) ) ).
tt(t41_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r2_abian (u1_struct_0 A) (k9_knaster A B) B) &  (? [C:$i] :  ((v3_ordinal1 C) &  ((r1_ordinal1 (k1_card_1 C) (k1_card_1 (u1_struct_0 A))) &  ((k5_knaster A B (k5_lattices A) C) = (k9_knaster A B)) ) ) ) ) ) ) ) ) ).
tt(t41_kurato_1,ax, (~  (k6_kurato_1 = (k1_tops_1 k3_topmetr k6_kurato_1)) ) ).
tt(t41_kurato_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) B C) = (k2_pre_topc (k15_euclid 2) (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) A C))) ) )  =>  ((k2_kurato_2 (k15_euclid 2) B) = (k2_kurato_2 (k15_euclid 2) A)) ) ) ) ) ) ).
tt(t41_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (? [F:$i] :  ((m1_subset_1 F C) &  ((r2_hidden F D) & (r3_lattices A (k3_funct_2 C (u1_struct_0 A) E F) B)) ) )  => (r3_lattices A (k3_lattice2 C A D E) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((r2_hidden B C) & (r3_lattice3 A B C))  =>  ((k16_lattice3 A C) = B) ) ) ) ) ) ) ).
tt(t41_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (u1_struct_0 A))) =>  ((k7_lattices A (k2_lattice4 A B)) = (k2_lattice2 (u1_struct_0 A) A B (k5_lattice4 A))) ) ) ) ) ).
tt(t41_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_lattice5 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (C = (k3_tarski (a_2_1_lattice5 A B)))  =>  ((v1_funct_1 (k3_tarski (a_2_2_lattice5 A B))) &  ((v1_funct_2 (k3_tarski (a_2_2_lattice5 A B)) (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 (k3_tarski (a_2_2_lattice5 A B)) C A) &  ((v2_lattice5 (k3_tarski (a_2_2_lattice5 A B)) C A) &  ((v3_lattice5 (k3_tarski (a_2_2_lattice5 A B)) C A) & (m1_subset_1 (k3_tarski (a_2_2_lattice5 A B)) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k15_glib_000 A) B))  =>  ((k6_lexbfs A (k15_lexbfs A (k16_lexbfs A)) B) = (k10_lexbfs A (k13_lexbfs A (k16_lexbfs A) B))) ) ) ) ) ) ).
tt(t41_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  ( ( (~ (v1_limfunc1 B))  &  (~ (v2_limfunc1 B)) )  |  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t41_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc2 C A) =>  ( ((k1_limfunc2 C A) = B)  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A E))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers C)) & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 C F) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  ( ((k1_limfunc3 B A) = (k1_limfunc3 C A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A E))  &  ( (~ (r1_xxreal_0 F A))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G E))  &  ( (~ (r1_xxreal_0 A G))  &  ((r2_hidden G (k9_xtuple_0 D)) &  ( (~ (r1_xxreal_0 F H))  &  ( (~ (r1_xxreal_0 H A))  & (r2_hidden H (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k9_xtuple_0 D) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E))))) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) )  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))) (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E))))) & (r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 D) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))) (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E))))))  |  ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))) (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E))))) & (r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 D) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))) (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))))) ) ) ) ) ) )  |  ((r1_limfunc3 D A) &  ((k1_limfunc3 D A) = (k1_limfunc3 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r5_limfunc2 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) & (r1_xxreal_0 (k1_seq_1 B E) (k1_limfunc3 B A))) ) ) ) ) ) ) )  | (r2_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t41_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) =>  ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = (k1_normsp_0 A (k6_normsp_1 A B))) ) ) ) ) ) ) ).
tt(t41_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A (k5_algstr_0 A (k5_struct_0 A) B))))  =>  ((v1_lopban_3 (k5_lopban_3 A (k5_algstr_0 A (k5_struct_0 A) B)) A) & (v2_lopban_3 (k5_lopban_3 A (k5_algstr_0 A (k5_struct_0 A) B)) A)) ) ) ) ) ) ).
tt(t41_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k6_algstr_0 A (k10_lopban_4 A (k1_rlvect_1 A B C)) (k10_lopban_4 A (k1_rlvect_1 A B D))) = (k10_lopban_4 A (k1_rlvect_1 A B (k7_real_1 C D))))  &  ( ((k6_algstr_0 A (k10_lopban_4 A (k1_rlvect_1 A B D)) (k10_lopban_4 A (k1_rlvect_1 A B C))) = (k10_lopban_4 A (k1_rlvect_1 A B (k7_real_1 D C))))  &  ( ((k10_lopban_4 A (k1_rlvect_1 A B (k7_real_1 C D))) = (k10_lopban_4 A (k1_rlvect_1 A B (k7_real_1 D C))))  & (r1_lopban_4 A (k10_lopban_4 A (k1_rlvect_1 A B C)) (k10_lopban_4 A (k1_rlvect_1 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) &  ((r2_hidden E (k9_lpspace1 A B C)) &  ((r2_hidden F (k9_lpspace1 A B C)) &  ((r2_hidden G (k9_lpspace1 A B C)) &  ( ((k13_lpspace1 A B C D) = (k13_lpspace1 A B C E))  &  ((k13_lpspace1 A B C F) = (k13_lpspace1 A B C G)) ) ) ) ) )  =>  ((k13_lpspace1 A B C (k3_valued_1 A k1_numbers k1_numbers D F)) = (k13_lpspace1 A B C (k3_valued_1 A k1_numbers k1_numbers E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ((r1_lpspace1 A B C D E) =>  ((k5_lpspace2 A B C D F) = (k5_lpspace2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 B A) => (r3_ltlaxio1 B A)) ) ) ) ) ).
tt(t41_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A B D)) A)) ) ) ) ) ) ) ) ) ).
tt(t41_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k4_mathmorp A B C) B) & (r1_tarski B (k5_mathmorp A B C))) ) ) ) ) ) ) ).
tt(t41_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 A k6_numbers) & (v3_matrix10 C))  => (v4_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t41_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  ( (F = (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_funct_2 (k2_finseq_1 A) E) D))  =>  ((k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B (k4_matrix11 A A (u1_struct_0 B) E C) D) (u2_algstr_0 B)) = (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B C F) (u2_algstr_0 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [G:$i] :  ( ((v1_matrix_1 G) & (m2_finseq_1 G (k3_finseq_2 (u1_struct_0 C))))  =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 E) (k10_xtuple_0 F)) (k2_matrix_1 G)) =>  ((k2_matrix13 A B C (k1_matrix13 (u1_struct_0 C) G A B E F) D) = (k1_matrix13 (u1_struct_0 C) (k6_matrix_3 C G D) A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  ((k3_matrix_1 (u1_struct_0 B) C 1 1) = (k4_struct_0 B)) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (~  ((v1_matrix_6 D A B) &  ((v1_matrix_6 E A B) &  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) 1 1) = (k5_struct_0 B))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) F 1) = (k4_struct_0 B)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) 1 F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((r2_hidden C (k4_matrix15 B D E)) &  ((r2_hidden A (k4_finseq_1 D)) &  ((k8_matrix_1 (u1_struct_0 B) D A) = (k5_finseq_2 (u1_struct_0 B) (k1_matrix_1 D) (k4_struct_0 B))) ) )  =>  ((k8_matrix_1 (u1_struct_0 B) E A) = (k5_finseq_2 (u1_struct_0 B) (k1_matrix_1 E) (k4_struct_0 B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v2_matrix16 C (u1_struct_0 A)) => (v2_matrix16 (k9_fvsum_1 A C B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t41_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 A)) =>  ((k16_matrix_1 B) = (k3_tarski (a_2_0_matrix_1 A B))) ) ) ) ) ).
tt(t41_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k2_matrix_3 A (k3_matrix_3 A (k2_matrix_3 A B) C)) = (k3_matrix_3 A B (k2_matrix_3 A C))) ) ) ) ) ) ) ) ).
tt(t41_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ( ((k4_matrix_6 A B C (k5_matrix_1 A (u1_struct_0 B) C)) = (k12_matrix_1 B A))  & (v1_matrix_6 C A B))  <=> (v4_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t41_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((v1_matrix_6 C A B) => (r1_matrix_8 A B (k4_matrix_6 A B D C) (k4_matrix_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t41_matrix_9,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k13_matrix_2 3))) =>  (~  ( ((k4_nat_d (k3_finseq_1 A) 2) = k6_numbers)  &  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 3)) =>  (~  ( ((k1_funct_1 A B) = C)  & (v4_matrix_2 C (k11_matrix_2 (k12_matrix_2 3)))) ) ) ) ) ) ) )  &  ( (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 1 2 3)) )  &  ( (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 2 3 1)) )  &  (~  ((k3_group_4 (k13_matrix_2 3) A) = (k3_finseq_4 k5_numbers 3 1 2)) ) ) ) ) ) ) ) ) ).
tt(t41_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((r2_hidden A (k2_finseq_1 (k3_finseq_1 B))) =>  ((k8_matrix_1 k2_numbers B A) = (k1_complsp2 (k8_matrix_1 k2_numbers (k1_matrixc1 B) A))) ) ) ) ) ) ).
tt(t41_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E (u1_struct_0 B)) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ( ((r2_hidden A (k4_finseq_1 D)) &  ((k1_matrix_1 D) = (k1_matrix_1 (k8_matrix_2 B A D))) )  =>  ((k8_matrix_2 B A (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) (k4_matrixj1 (u1_struct_0 B) D) E))) = (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) (k4_matrixj1 (u1_struct_0 B) (k8_matrix_2 B A D)) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k1_matrix_1 C) k6_numbers) |  ((k6_matrixr1 (k7_matrixr1 A B) C) = (k7_matrixr1 A (k6_matrixr1 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 A) k6_numbers k6_numbers) =>  ((k12_matrix_3 k6_numbers A B) = (k5_struct_0 A)) ) ) ) ) ).
tt(t41_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A C) =>  (! [E:$i] :  ((m1_matrlin E A B) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 D) k1_xboole_0))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 E) k1_xboole_0))  &  (~  ((r1_struct_0 (k1_ranknull A C B (k4_matrlin2 A C B D E G)) F) <=> (r1_struct_0 (k7_matrix15 A (k4_matrix_1 (u1_struct_0 A) G)) (k9_matrlin A C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  (! [G:$i] :  ((m1_matrlin G A B) =>  (! [H:$i] :  ((m1_matrlin H A C) =>  (! [I:$i] :  ((m1_matrlin I A D) =>  ( ((v13_vectsp_1 F C D) & (v1_mod_2 F A C D))  =>  ((r1_xxreal_0 (k3_finseq_1 G) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 H) k6_numbers) |  ((k10_matrlin A B D (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 D) E F) G I) = (k4_matrix_3 A (k10_matrlin A B C E G H) (k10_matrlin A C D F H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_matroid0 B A) &  ((v5_matroid0 C A) & (r1_tarski B C)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t41_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k1_matrix_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k1_matrix_1 A) k6_numbers) |  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 (k11_matrixr1 A B)))) =>  ((k1_seq_1 (k11_matrixr1 A B) C) = (k22_rvsum_1 (k8_matrix_1 k1_numbers A C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) =>  ((v2_funct_2 (k3_matrtop1 A B C) (u1_struct_0 (k15_euclid B))) <=>  ((k8_matrix13 k2_vectsp_1 C) = B) ) ) ) ) ) ) ) ).
tt(t41_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (A = 1) )  &  ( ((k12_euclid B) = (k12_euclid C))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A))) &  ((v13_vectsp_1 D (k15_euclid A) (k15_euclid A)) &  ((v1_topreal9 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)))))) ) ) )  =>  (~  ((v3_matrtop3 D A) &  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) D B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k3_zfmisc_1 (k1_tarski A) (k2_tarski B C) (k2_tarski D E)) = (k2_enumset1 (k3_xtuple_0 A B D) (k3_xtuple_0 A C D) (k3_xtuple_0 A B E) (k3_xtuple_0 A C E))) ) ) ) ) ) ).
tt(t41_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v4_xxreal_2 A) <=> (v3_xxreal_2 (k4_measure6 A))) ) ) ).
tt(t41_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k8_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k8_member_1 A B) (k8_member_1 A C))) ) ) ) ) ) ) ).
tt(t41_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) ) )  =>  (~ (r2_subset_1 (k9_xtuple_0 C) (k4_subset_1 (u1_struct_0 B) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) (k8_struct_0 B)))) ) ) ) ) ) ) ).
tt(t41_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D k1_numbers) => (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k26_valued_1 A k1_numbers B D) C) (k26_valued_1 A k1_numbers (k2_partfun1 A k1_numbers B C) D))) ) ) ) ) ) ) ).
tt(t41_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [D:$i] :  ((r2_hidden D (k1_relset_1 A B)) => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 C D))) )  => (v6_supinf_2 (k47_valued_1 A k1_numbers k1_numbers C B))) ) ) ) ) ) ) ).
tt(t41_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((r1_mesfun7c A B C) => (r1_mesfun6c A B C D)) ) ) ) ) ) ) ) ) ).
tt(t41_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ((m1_subset_1 E k7_numbers) =>  (~  ( (~  (E = k1_supinf_1) )  &  ( (~  (E = k2_supinf_1) )  &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc2 A B F) &  ( ((k1_relset_1 A F) = D)  &  (! [G:$i] :  ((r2_hidden G D) =>  ((k12_supinf_2 F G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((r2_hidden C (k1_relset_1 A B)) &  ((k1_seq_1 (k19_rfunct_3 A B) C) = k6_numbers) )  =>  ((k1_seq_1 (k18_rfunct_3 A B) C) = (k1_seq_1 B C)) ) ) ) ) ) ) ).
tt(t41_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers D F) C) & (v3_mesfunc5 (k4_mesfunc5 A k7_numbers D F))) ) )  => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A D) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_midsp_1 A (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B (k3_midsp_1 A B C)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k3_midsp_1 A B C) C))) ) ) ) ) ) ).
tt(t41_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r2_relset_1 A A (k18_mmlquery A (k18_mmlquery A (k18_mmlquery A B))) (k18_mmlquery A B))) ) ) ).
tt(t41_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v13_algstr_0 E) &  ((v8_vectsp_1 E B) &  ((v9_vectsp_1 E B) &  ((v10_vectsp_1 E B) &  ((v11_vectsp_1 E B) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l1_vectsp_1 E B)) ) ) ) ) ) ) ) )  => (m1_mod_4 (k6_grcat_1 D E) A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t41_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~  ( (~  (A = k17_modal_1) )  &  ( (~  ((v1_modal_1 A) & (m1_subset_1 A k6_modal_1)) )  &  ( (~  ((v2_modal_1 A) & (m1_subset_1 A k6_modal_1)) )  &  ( (~  ((v3_modal_1 A) & (m1_subset_1 A k6_modal_1)) )  &  (~  ((v4_modal_1 A) & (m1_subset_1 A k6_modal_1)) ) ) ) ) ) ) ) ) ).
tt(t41_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F E) <=> (r3_modelc_1 A B C F (k53_modelc_1 A B C D E))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F E) => (r3_modelc_1 A B C F (k26_modelc_1 (k48_modelc_1 A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r3_modelc_2 A (k4_modelc_2 B C)) &  ( (~ (r2_modelc_2 A B))  &  (~ (r2_modelc_2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t41_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  =>  ( ((r6_modelc_3 B D C) & (r2_hidden A (u1_modelc_3 B C)))  =>  ( ((v4_modelc_2 A) =>  ((r2_hidden (k11_modelc_2 A) (u1_modelc_3 B C)) & (r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C))) )  &  ( (~  ( ((v5_modelc_2 A) | (v7_modelc_2 A))  &  ( (~ (r2_hidden (k11_modelc_2 A) (u1_modelc_3 B C)))  &  (~ (r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C))) ) ) )  &  ( ((v6_modelc_2 A) => (r2_hidden (k10_modelc_2 A) (u3_modelc_3 B C)))  &  ((v8_modelc_2 A) => (r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_moebius1,ax, ((k3_moebius1 1) = (k6_domain_1 k5_numbers 1)) ).
tt(t41_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) & (m2_monoid_0 A k2_monoid_0)) )  =>  ( (A = k3_monoid_0)  <=>  ((u1_struct_0 A) = k4_numbers) ) ) ) ).
tt(t41_monoid_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ( ((k15_monoid_1 B (k20_monoid_1 B (k4_monoid_1 B A C)) C) = A)  &  (! [D:$i] :  ((m1_subset_1 D B) =>  ( (~  (D = C) )  =>  ((k15_monoid_1 B (k20_monoid_1 B (k4_monoid_1 B A C)) D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((k9_msaterm A B C (k4_msaterm A B C E F) D) = F) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((r6_pboole A C (k1_pboole A)) => (r6_pboole A (k4_mssubfam A B C) B)) ) ) ) ) ) ).
tt(t41_msualg_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden (k4_tarski C D) (k1_msualg_5 A B)) <=> (r2_rewrite1 B C D)) ) ) ) ) ) ) ) ) ).
tt(t41_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_tarski C D) (u1_orders_2 B)) =>  ((r2_hidden (k4_tarski C (k2_xcmplx_0 D A)) (u1_orders_2 (k6_mycielsk A B))) & (r2_hidden (k4_tarski (k2_xcmplx_0 C A) D) (u1_orders_2 (k6_mycielsk A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t41_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden (k5_card_1 A) (k5_card_1 B)) <=>  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(t41_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k1_seq_1 (k12_nat_3 A) A) = 1) ) ) ).
tt(t41_nat_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( (A = (k4_rvsum_1 B C))  =>  ((k4_finseq_1 A) = (k3_xboole_0 (k4_finseq_1 B) (k4_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t41_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k7_nat_d C B) (k7_nat_d C A))) ) ) ) ) ) ) ).
tt(t41_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ( ((v2_nattra_1 A) & (v2_nattra_1 B))  => (v2_nattra_1 (k8_cat_2 A B))) ) ) ) ) ).
tt(t41_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r7_ncfcont1 A B D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) C) &  ((v9_clvect_1 E A) & (r2_hidden (k7_clvect_1 A E) C)) )  =>  ((v9_clvect_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D) B) &  ((k7_partfun1 (u1_struct_0 B) D (k7_clvect_1 A E)) = (k7_clvect_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ncfcont2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_clopban1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((v1_funct_1 (k9_funct_7 B C)) &  ((v1_funct_2 (k9_funct_7 B C) (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_ncfcont2 (k9_funct_7 B C) A) & (m1_subset_1 (k9_funct_7 B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = D)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_nfcont_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r1_tarski C (k1_relset_1 (u1_struct_0 A) (k4_vfunct_1 (u1_struct_0 A) B E D))) & (r2_ndiff_1 C A B E))  =>  ((r2_ndiff_1 C A B (k4_vfunct_1 (u1_struct_0 A) B E D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) (k4_ndiff_1 A B (k4_vfunct_1 (u1_struct_0 A) B E D) C) F) = (k1_rlvect_1 (k16_lopban_1 A B) (k3_ndiff_1 A B E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers B (k1_pdiff_1 1 1)) =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C)) &  ((v2_ndiff_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 1) (k4_real_ns1 A)) & (m1_subset_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers (u1_struct_0 (k4_real_ns1 A))) &  ((v2_ndiff_3 C (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) )  =>  ((v1_funct_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C)) &  ((v1_funct_2 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))) &  ((v13_vectsp_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 1) (k4_real_ns1 A)) &  ((v1_lopban_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 1) (k4_real_ns1 A)) &  ((v2_lopban_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k4_real_ns1 1) (k4_real_ns1 A)) & (m1_subset_1 (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((r1_ndiff_1 (k14_prvect_2 A) B C D) =>  ((r1_ndiff_5 A B E C D) &  ((k6_ndiff_5 A B E C D) = (k3_relat_1 (k4_ndiff_5 A (k5_ndiff_5 A E) (k4_struct_0 (k14_prvect_2 A))) (k3_ndiff_1 (k14_prvect_2 A) B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ( (A = k6_numbers)  | (r1_nat_d A (k9_newton B))) ) ) ) ) ) ).
tt(t41_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ((r5_nfcont_1 C D A E) => (r5_nfcont_1 C D A (k4_vfunct_1 (u1_struct_0 C) D E B))) ) ) ) ) ) ) ) ) ) ).
tt(t41_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_euclid A)) =>  ( (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F B) =>  ((k7_partfun1 (k1_euclid A) C F) = (k7_euclid A (k9_euclid A D F) E)) ) ) )  => (v1_nfcont_4 (k2_partfun1 k1_numbers (k1_euclid A) C B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t41_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (~  ((r2_hidden B C) &  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (k5_finsub_1 A) (k5_finsub_1 A)) (k7_normform A)) =>  (~  ((r1_normform (k5_finsub_1 A) (k5_finsub_1 A) D B) & (r2_hidden D (k9_normform A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k3_oppcat_1 A D)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t41_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_orders_1 A B) => (r2_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t41_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_orders_2 C A B) =>  (! [D:$i] :  ((m2_orders_2 D A B) =>  ( (~  (C = D) )  =>  ((m1_orders_2 C A D) <=>  (~ (m1_orders_2 D A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k11_ordinal2 A C) (k11_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t41_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden A (k11_ordinal2 B C)) &  ((v4_ordinal1 B) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D B) & (r2_hidden A (k11_ordinal2 D C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_ordinal5,ax, ((k3_ordinal5 k6_numbers) = (k1_ordinal5 k4_ordinal1 k4_ordinal1)) ).
tt(t41_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ((r2_hidden A B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k2_ordinal1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k2_ordinal1 B))))) )  => (r2_hidden (k3_card_3 C) B)) ) ) ) ) ) ) ).
tt(t41_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t41_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_hidden D (k25_osafree A B (k20_osafree A B) C)) =>  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) D) = (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t41_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ( ((v3_msualg_1 C A) &  ((v12_osalg_1 C A) & (m1_msualg_2 C A B)) )  =>  (! [D:$i] :  ( ((v3_msualg_1 D A) &  ((v12_osalg_1 D A) & (m1_msualg_2 D A B)) )  =>  ((k11_osalg_2 A B (k11_msualg_2 A B C D) D) = D) ) ) ) ) ) ) ) ) ).
tt(t41_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_parsp_2 A B C D) &  ((r2_parsp_2 A B E C F) & (r2_parsp_2 A B E D G)) )  =>  ( (C = D)  | (r2_parsp_2 A C F D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_partfun1 (k3_partfun1 k1_xboole_0 A B) A) =>  (A = k1_xboole_0) ) ) ) ).
tt(t41_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C))))  => (v3_funct_1 (k2_partfun1 B C D (k1_tarski A)))) ) ) ) ) ) ) ).
tt(t41_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A B (k2_pboole A B C)) (k2_pboole A B C))) ) ) ) ) ).
tt(t41_pcs_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_pcs_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_pcs_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k22_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k22_pcs_0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ( ( (C = (k7_yellow_3 A B E G))  &  (D = (k7_yellow_3 A B F H)) )  =>  ( ((r1_pcs_0 A E F) &  (~ (r1_pcs_0 B G H)) )  | (r1_pcs_0 (k22_pcs_0 A B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid 3)) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( (D = (k11_finseq_1 A B C))  =>  ((k6_pdiff_4 F E D) = (k7_real_1 (k7_real_1 (k10_real_1 (k8_real_1 (k11_pdiff_1 3 1 F E) A) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 A) (k5_square_1 B)) (k5_square_1 C)))) (k10_real_1 (k8_real_1 (k11_pdiff_1 3 2 F E) B) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 A) (k5_square_1 B)) (k5_square_1 C))))) (k10_real_1 (k8_real_1 (k11_pdiff_1 3 3 F E) C) (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 A) (k5_square_1 B)) (k5_square_1 C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 3) B)) =>  ( ((r5_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B))))) &  ((k5_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F A) &  ( (E = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F D) G))  & (r2_relset_1 k1_numbers k1_numbers C (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers (k6_pdiff_1 A F D) B))) ) )  =>  ((k1_fdiff_1 C G) = (k11_pdiff_1 A F B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r2_nfcont_4 A B D) & (r2_nfcont_4 A C D))  => (r2_nfcont_4 A (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D)) ) ) ) ) ) ) ) ) ).
tt(t41_pepin,ax,(v1_int_2 3)).
tt(t41_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k10_pnproc_1 A B C (k4_subset_1 (k3_finseq_2 B) D E)) = (k4_subset_1 (k3_finseq_2 B) (k10_pnproc_1 A B C D) (k10_pnproc_1 A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t41_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_bspace)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A B)) =>  ((k3_bspace (k4_vectsp_1 k2_bspace (k17_polyform A B) D C) E) = (k8_group_1 k2_bspace D (k3_bspace C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k1_algseq_1 A (k4_polynom5 A B (k4_struct_0 A))) = 1) ) ) ) ) ) ).
tt(t41_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 (k1_algseq_1 A B) C) =>  ((r1_xxreal_0 C k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 C E))  =>  ((k8_nat_1 (u1_struct_0 A) (k6_polynom8 C A B D) E) = (k3_matrix_1 (u1_struct_0 A) (k4_matrix_3 A (k7_polynom8 A C D) (k4_polynom8 C A B)) (k2_nat_1 E 1) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  ( ((r2_termord A B G H) & (r3_polyred A B C D E F G))  =>  ((k3_polynom1 A C D H) = (k3_polynom1 A C F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_power A B) = (k1_newton A B)) ) ) ) ) ).
tt(t41_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r1_pre_poly A B C) & (r1_pre_poly A C D))  => (r1_pre_poly A B D)) ) ) ) ) ) ) ) ) ).
tt(t41_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k4_prepower A (k4_xcmplx_0 B)) = (k10_real_1 1 (k4_prepower A B))) ) ) ) ) ).
tt(t41_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) => (r2_funct_2 k5_numbers (k1_zfmisc_1 A) (k2_prob_1 A (k12_funct_7 (k1_zfmisc_1 A) B C)) (k12_funct_7 (k1_zfmisc_1 A) (k3_subset_1 A B) (k3_subset_1 A C)))) ) ) ) ) ).
tt(t41_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((v2_comseq_2 (k8_prob_1 A B (k2_prob_3 A C) D)) &  ( ((k2_seq_2 (k8_prob_1 A B (k2_prob_3 A C) D)) = (k1_rinfsup1 (k8_prob_1 A B (k2_prob_3 A C) D)))  &  ((k2_seq_2 (k8_prob_1 A B (k2_prob_3 A C) D)) = (k1_funct_1 D (k1_kurato_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) (k4_prob_4 A B C)) =>  (! [E:$i] :  ((r2_hidden E (k6_prob_4 A B C D)) =>  ((k1_funct_1 C E) = (k3_funct_2 (k4_prob_4 A B C) k1_numbers (k7_prob_4 A B C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A (k9_cqc_lang A B C) D) (k9_cqc_lang A (k7_cqc_lang A B D) (k7_cqc_lang A C D))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t41_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k20_pscomp_1 A) (k21_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(t41_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((k2_pboole A (k1_pzfmisc1 A B) C) = (k1_pboole A)) ) ) ) ) ) ) ) ).
tt(t41_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (~ (r1_qc_lang2 A B (k12_qc_lang1 A))) ) ) ) ) ).
tt(t41_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v4_qc_lang1 B A) =>  ((k4_qc_lang3 A C B) = (k4_subset_1 C (k4_qc_lang3 A C (k19_qc_lang1 A B)) (k4_qc_lang3 A C (k20_qc_lang1 A B)))) ) ) ) ) ) ) ) ).
tt(t41_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) =>  ( (? [E:$i] :  ((m2_qc_lang4 E A B C) &  (? [F:$i] :  ((m2_qc_lang4 F A B D) & (r1_tarski E F)) ) ) )  => (r2_qc_lang2 A D C)) ) ) ) ) ) ) ) ) ).
tt(t41_quatern2,ax, ((k17_quatern2 (k4_struct_0 k16_quatern2)) = (k4_struct_0 k16_quatern2)) ).
tt(t41_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k17_complex1 (k9_real_1 (k3_quatern2 A) (k3_quatern2 B))) (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)))) ) ) ) ).
tt(t41_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k28_quaterni A)) = (k1_real_1 (k17_quaterni A)))  &  ( ((k18_quaterni (k28_quaterni A)) = (k1_real_1 (k18_quaterni A)))  &  ( ((k19_quaterni (k28_quaterni A)) = (k1_real_1 (k19_quaterni A)))  &  ((k20_quaterni (k28_quaterni A)) = (k1_real_1 (k20_quaterni A))) ) ) ) ) ) ).
tt(t41_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  ((k1_algstr_0 (k19_quofield A) B (k4_struct_0 (k19_quofield A))) = B) ) ) ) ) ).
tt(t41_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~ (v1_vectsp_7 C A B))  &  (! [D:$i] :  ((m2_vectsp_6 D A B C) =>  (~  ( (~  ((k1_vectsp_6 A B D) = k1_xboole_0) )  &  ((k4_vectsp_6 A B D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ( ((k1_rat_1 A) = (k1_rat_1 B))  &  ((k2_rat_1 A) = (k2_rat_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t41_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  ( ( (E = (k3_rcomp_1 C D))  & (r1_xxreal_0 D B))  =>  ((r1_xxreal_0 C A) |  ((k1_tops_1 (k4_topmetr A B) E) = (k2_rcomp_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_seq_1 (k4_real_3 (k13_complex1 A B)) C) = (k1_seq_1 (k2_real_3 A B) C))  &  ( ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k13_complex1 A B)) 1) = (k13_complex1 B (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) k6_numbers)))  &  ((k3_funct_2 k5_numbers k1_numbers (k3_real_3 (k13_complex1 A B)) (k1_nat_1 C 2)) = (k10_real_1 (k1_seq_1 (k1_real_3 A B) C) (k3_funct_2 k5_numbers k5_numbers (k1_real_3 A B) (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ).
tt(t41_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ( ((k9_xtuple_0 A) = k1_xboole_0)  |  ((k10_xtuple_0 A) = k1_xboole_0) )  =>  (A = k1_xboole_0) ) ) ) ).
tt(t41_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))) =>  ((r2_hidden A (k1_relset_2 C D (k3_subset_1 (k2_zfmisc_1 C D) E) B)) <=>  ( (~ (r2_hidden (k4_tarski B A) E))  &  ((r2_hidden B C) & (r2_hidden A D)) ) ) ) ) ) ) ) ) ).
tt(t41_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r6_rewrite1 A B C) => (r6_rewrite1 A C B)) ) ) ) ) ).
tt(t41_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r3_rewrite2 A B C D) <=> (r3_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k6_rewrite2 (k8_afinsq_1 A))) C D)) ) ) ) ) ) ) ) ).
tt(t41_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 E))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ( ( ((v1_relat_1 (u1_rewrite3 F G)) & (v1_funct_1 (u1_rewrite3 F G)))  &  ((r2_hidden (k4_tarski A (k4_tarski B C)) (k1_rewrite3 E F G)) & (r2_hidden (k4_tarski A (k4_tarski D C)) (k1_rewrite3 E F G))) )  =>  (B = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k1_rfunct_1 (k1_rfunct_1 A B) (k1_rfunct_1 C D)) = (k1_rfunct_1 (k18_valued_1 A (k5_relat_1 D (k9_xtuple_0 (k4_rfunct_1 D)))) (k18_valued_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t41_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t41_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_classes1 C D) => (r2_classes1 (k18_rfunct_3 A C) (k18_rfunct_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t41_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 C) =>  ( (B = (k1_seq_1 (k4_rinfsup1 C) A))  <=>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 C (k2_nat_1 A D)) B)) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 C (k2_nat_1 A E)) (k6_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v10_mesfunc5 A) =>  ( ((k2_mesfunc5 A) = (k6_rinfsup2 A))  &  ((k2_mesfunc5 A) = (k5_rinfsup2 A)) ) ) ) ) ).
tt(t41_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (v1_rlvect_3 (k7_subset_1 (u1_struct_0 A) (k5_rusub_4 A B (k4_algstr_0 A C)) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) A)) ) ) ) ) ) ) ) ).
tt(t41_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_rlvect_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  => (m1_rlsub_1 A (k2_rlsub_1 A))) ) ).
tt(t41_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((m1_rlsub_2 (k1_rlsub_1 A) A (k2_rlsub_1 A)) & (m1_rlsub_2 (k2_rlsub_1 A) A (k1_rlsub_1 A))) ) ) ).
tt(t41_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v9_rltopsp1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v9_rltopsp1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ).
tt(t41_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k8_finseq_1 (u1_struct_0 A) B C)) = (k1_algstr_0 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ).
tt(t41_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((r1_rlvect_2 A (k7_rlvect_2 A B (k4_rlvect_2 A)) B) & (r1_rlvect_2 A (k7_rlvect_2 A (k4_rlvect_2 A) B) B)) ) ) ) ) ).
tt(t41_rlvect_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v1_rlvect_5 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlsub_1 C B) => (r1_tarski (k2_rlvect_5 C A) (k2_rlvect_5 B A))) ) ) ) ) ) ).
tt(t41_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  => (m1_rmod_2 B A (k2_rmod_2 A B))) ) ) ) ).
tt(t41_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_rmod_3 A B C D) <=>  (! [E:$i] :  ((m2_rmod_2 E A B C) =>  (! [F:$i] :  ((m2_rmod_2 F A B D) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((k9_subset_1 (u1_struct_0 B) E F) = (k6_domain_1 (u1_struct_0 B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ((r1_rmod_4 A B (k6_rmod_4 A B C (k3_rmod_4 A B)) C) & (r1_rmod_4 A B (k6_rmod_4 A B (k3_rmod_4 A B) C) C)) ) ) ) ) ) ) ).
tt(t41_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k14_robbins1 A B) B) = (k11_robbins1 A B)) ) ) ) ) ).
tt(t41_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A B (k3_robbins1 A C)) D)) C))) = C) ) ) ) ) ) ) ) ) ).
tt(t41_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C) = k6_numbers)  <=> (r2_hidden C (k3_subset_1 (u1_struct_0 A) (k4_roughs_1 A B)))) ) ) ) ) ) ) ).
tt(t41_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_tarski C B) =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((k2_rpr_1 A C B) = 1) ) ) ) ) ) ) ) ) ).
tt(t41_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k4_struct_0 A) (k3_rusub_1 A C B)) <=>  ((k3_rusub_1 A C B) = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t41_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((m1_rusub_2 (k1_rusub_1 A) A (k2_rusub_1 A)) & (m1_rusub_2 (k2_rusub_1 A) A (k1_rusub_1 A))) ) ) ).
tt(t41_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B D) => (m1_rusub_1 (k2_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t41_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ((v2_pre_topc (g1_pre_topc (u1_struct_0 A) (k4_rusub_5 A))) & (l1_pre_topc (g1_pre_topc (u1_struct_0 A) (k4_rusub_5 A)))) ) ) ).
tt(t41_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k8_rvsum_1 A (k8_rvsum_1 B C)) = (k4_rvsum_1 (k8_rvsum_1 A B) C)) ) ) ) ) ) ) ).
tt(t41_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ((k17_rvsum_1 (k8_rvsum_2 A B C)) = (k4_binop_2 (k17_rvsum_1 B) (k17_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t41_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((r2_classes1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)) (k18_scmfsa_2 (k1_scmfsa6b (k1_scmbsort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers))) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 D (k3_finseq_1 (k18_scmfsa_2 B (k5_scmfsa_2 k6_numbers)))))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ( (E = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k1_scmbsort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers)) C))  &  (F = (k1_funct_1 (k18_scmfsa_2 (k1_scmfsa6b (k1_scmbsort (k5_scmfsa_2 k6_numbers)) B A) (k5_scmfsa_2 k6_numbers)) D)) )  => (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k11_scmfsa_2 A) B) = (k11_scmfsa_2 (k2_nat_1 A B))) ) ) ) ) ).
tt(t41_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (~  ( ((k2_compos_0 (u1_compos_1 k1_scmfsa_2) A) = 12)  &  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (~  (A = (k17_scmfsa_2 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmfsa8a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r5_scmfsa7b B (k1_scmfsa_m D) A) & (r6_scmfsa7b B (k1_scmfsa_m D) A))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa6a (k3_scmfsa6a (k3_scmfsa6a B (k1_scmfsa8a (k2_nat_1 (k5_card_1 C) 1))) C) (k4_compos_1 k1_scmfsa_2)) D A) (k1_funct_4 (k1_scmfsa6b B D A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 1))))) ) ) ) ) ) ) ) ) ).
tt(t41_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_scmfsa8a B A (k2_scmfsa6a D)) =>  ( ((k1_funct_1 B E) = k6_numbers)  |  ((r6_scmfsa7b (k1_scmfsa8b E C D) B A) &  ((r5_scmfsa7b (k1_scmfsa8b E C D) B A) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8b E C D)) (k8_memstr_0 3 k1_scmfsa_2 B)) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a D (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B)) 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) &  ((v1_finset_1 F) &  ((v1_afinsq_1 F) & (v1_scmfsa7b F)) ) ) ) ) ) )  =>  ( ( ((k1_funct_1 C (k4_scmfsa_2 k6_numbers)) = 1)  &  ( ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D))  &  ((r3_scmfsa9a A C E F) & (r4_scmfsa9a A C E F)) ) )  => (r4_scmfsa9a B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmfsa_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k1_funct_1 (k2_scmfsa_9 A B) (k2_nat_1 (k5_card_1 B) 4)) = (k11_scmfsa_2 k6_numbers)) ) ) ) ) ).
tt(t41_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) &  ((r1_scm_halt D B A) & (r2_scm_halt D B A)) )  =>  ((r1_scm_halt (k2_scmfsa8b E C D) B A) & (r2_scm_halt (k2_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  => (r1_tarski k2_ami_2 (k9_xtuple_0 A))) ) ).
tt(t41_scmpds_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) & (v2_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v4_scmpds_4 E) &  ((v1_scmpds_5 E) & (m1_subset_1 E (u1_compos_1 k1_scmpds_2))) )  =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_4 D E) C B) A) = (k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 E (k6_scmpds_4 D C B)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) & (v3_scmpds_4 D)) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((r1_scmpds_6 D B A) & (r2_scmpds_6 D B A))  =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) F)) = k6_numbers)  |  ((k6_scmpds_4 (k2_scmpds_6 E F C D) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k2_scmpds_7 A B C D)) = (k2_nat_1 (k5_card_1 D) 3)) ) ) ) ) ) ) ) ) ).
tt(t41_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  =>  ( (B = C)  |  ((r2_hidden (k2_tarski B C) (k1_scmyciel A)) <=>  (~ (r2_hidden (k2_tarski B C) (k1_scmyciel (k6_scmyciel A)))) ) ) ) ) ) ) ) ).
tt(t41_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) => (r2_semi_af1 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A (k52_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B) C))) ) ) ) ) ) ).
tt(t41_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) <=>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B (k18_complex1 (k10_binop_2 (k8_nat_1 k1_numbers A D) (k8_nat_1 k1_numbers A C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r2_seqfunc A B C) =>  ((r2_seqfunc A (k5_seqfunc A B) C) &  ((r2_relset_1 A k1_numbers (k11_seqfunc A (k5_seqfunc A B) C) (k56_valued_1 A k1_numbers (k11_seqfunc A B C))) &  ((r2_seqfunc A (k4_seqfunc A B) C) & (r2_relset_1 A k1_numbers (k11_seqfunc A (k4_seqfunc A B) C) (k32_valued_1 A k1_numbers (k11_seqfunc A B C)))) ) ) ) ) ) ) ) ) ).
tt(t41_seqm_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k18_complex1 (k9_real_1 A B)) = 1)  <=>  ( ( (~ (r1_xxreal_0 A B))  &  (A = (k7_real_1 B 1)) )  |  ( (~ (r1_xxreal_0 B A))  &  (B = (k7_real_1 A 1)) ) ) ) ) ) ) ) ).
tt(t41_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers A C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers B) C))) ) )  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 1 (k3_funct_2 k5_numbers k1_numbers A D))) ) ) ) )  & (v1_series_1 B)) ) ) ) ) ) ) ).
tt(t41_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 C D) = (k2_xcmplx_0 (k3_xcmplx_0 A D) B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 (k3_series_1 C) D) = (k2_xcmplx_0 (k2_xcmplx_0 (k13_complex1 (k3_xcmplx_0 (k3_xcmplx_0 A (k2_nat_1 D 1)) D) 2) (k3_xcmplx_0 D B)) B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k18_complex1 (k1_seq_1 (k3_series_1 A) B)) (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers A)) B))) ) ) ) ).
tt(t41_series_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((k2_xcmplx_0 (k2_xcmplx_0 A B) C) = 1)  => (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A B) (k3_xcmplx_0 B C)) (k3_xcmplx_0 C A)) (k13_complex1 1 3))) ) ) ) ) ) ) ).
tt(t41_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski (k3_tarski A) B) & (r2_hidden C A))  => (r1_tarski C B)) ) ) ) ).
tt(t41_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v3_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) (k2_nat_1 A 1))) ) ) ) ) ) ) ).
tt(t41_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k1_prob_1 A (k8_setlim_2 A C B)) = (k7_subset_1 A (k1_prob_1 A C) B)) ) ) ) ) ) ).
tt(t41_setwiseo,ax, (! [A:$i] : (v1_setwiseo (k9_setwiseo A) (k5_finsub_1 A))) ).
tt(t41_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ((m2_finseq_1 E A) =>  ( ((v1_binop_1 C A) &  ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ((v1_finseqop C A) & (r6_binop_1 A D C)) ) ) )  =>  ((k5_binop_1 A D (k1_finsop_1 A E C) B) = (k1_finsop_1 A (k2_finseqop A A A D E B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k4_sf_mastr A) = (k4_sf_mastr (k6_compos_1 k1_scmfsa_2 A B))) ) ) ) ) ).
tt(t41_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A C B) D))) = (k5_sheffer1 A B (k5_sheffer1 A C C))) ) ) ) ) ) ) ) ) ).
tt(t41_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_simplex0 D A) =>  ( ((r1_xxreal_0 (k2_xxreal_3 1) B) & (r1_xxreal_0 B C))  => (m2_simplex0 (k8_simplex0 A D B) A (k8_simplex0 A D C))) ) ) ) ) ) ) ) ).
tt(t41_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v6_simplex0 C (u1_struct_0 B)) &  ((v1_simplex1 C B) &  ((v2_simplex1 C B) & (m1_simplex0 C (u1_struct_0 B))) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_tops_2 E C) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) )  =>  ( ((v1_setfam_1 E) & (r1_xxreal_0 (k1_xxreal_3 (k5_card_1 E) A) (k6_simplex0 C)))  =>  ( ((m3_simplex0 D (k4_simplex1 B C) (k1_xxreal_3 A (k5_card_1 E))) & (r1_tarski (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) E) D))  <=>  (? [F:$i] :  ( ((v1_finset_1 F) &  ((v1_tops_2 F C) & (m1_subset_1 F (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) )  &  ((r1_xboole_0 F E) &  ((v6_ordinal1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 C)) F E)) &  ((v1_setfam_1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 C)) F E)) &  ( ((k5_card_1 F) = (k3_real_1 A 1))  &  (D = (k4_subset_1 (u1_struct_0 B) (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) E) (k7_relset_1 (k1_orders_1 (u1_struct_0 B)) (u1_struct_0 B) (k2_rlaffin2 B) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_sincos10,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)))) = (k1_rcomp_1 1 (k7_square_1 2))) ).
tt(t41_sin_cos2,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos2 k1_numbers))).
tt(t41_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) = (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A)) ) ) ).
tt(t41_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos A)) (k3_xcmplx_0 (k17_sin_cos B) (k17_sin_cos B)))) ) ) ) ) ).
tt(t41_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  &  ( (~  ((k3_sin_cos2 B) = k6_numbers) )  &  (~  ((k1_sin_cos5 (k6_xcmplx_0 A B)) = (k10_real_1 (k9_real_1 1 (k8_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B))) (k9_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B)))) ) ) ) ) ) ) ) ) ).
tt(t41_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k8_real_1 (k8_real_1 2 k32_sin_cos) B)))  &  ( (~ (r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 1 (k20_sin_cos A))) ) ) ) ) ) ) ).
tt(t41_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  =>  ((k4_sin_cos7 A) = (k1_sin_cos7 (k12_binop_2 A (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))))) ) ) ) ).
tt(t41_sin_cos9,ax, ( ((k1_seq_1 k29_sin_cos k6_numbers) = k6_numbers)  &  ((k1_sin_cos4 k6_numbers) = k6_numbers) ) ).
tt(t41_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_real_1 (k2_newton B A) (k3_newton A)) = (k10_real_1 (k2_newton B A) (k3_newton A))) ) ) ) ) ).
tt(t41_sppol_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ((k17_euclid A) = (k17_euclid C)) ) ) ) ) ) ) ) ).
tt(t41_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((v1_topreal1 A) & (r2_hidden B (k2_topreal1 2 A C)))  => (v1_topreal1 (k5_finseq_5 (u1_struct_0 (k15_euclid 2)) A B C))) ) ) ) ) ) ) ).
tt(t41_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k3_topreal1 2 (k1_sprect_1 A)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k12_pscomp_1 A) (k13_pscomp_1 A))) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k10_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A))))) ) ) ).
tt(t41_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k25_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t41_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k20_pscomp_1 (k3_topreal1 2 A)))  => (r1_tarski (k2_goboard9 (k1_sprect_1 (k3_topreal1 2 A))) (k2_goboard9 A))) ) ) ).
tt(t41_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t41_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( ((k3_square_1 A) = 1)  &  ( (~  (A = 1) )  &  (~  (A = (k4_xcmplx_0 1)) ) ) ) ) ) ) ).
tt(t41_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k14_stacks_1 A))) =>  ( (C = (k6_eqrel_1 (u4_struct_0 A) (u4_struct_0 A) (k10_stacks_1 A) B))  =>  ((k9_stacks_1 (k14_stacks_1 A) C) = (k9_stacks_1 A B)) ) ) ) ) ) ) ) ).
tt(t41_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k23_binop_2 A 1) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k23_binop_2 A 1) B)))) )  =>  ( ((v2_funct_2 C B) &  ((v1_stirl2_1 C A B) &  (C = (k2_partfun1 (k23_binop_2 A 1) B D A)) ) )  =>  ((r1_xxreal_0 B (k2_stirl2_1 (k23_binop_2 A 1) B D A)) |  ((v2_funct_2 D B) &  ((v1_stirl2_1 D (k23_binop_2 A 1) B) &  (~  ((k1_stirl2_1 (k23_binop_2 A 1) B D (k1_seq_4 (k2_stirl2_1 (k23_binop_2 A 1) B D A))) = (k1_seq_4 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ((v3_substut1 (k7_sublemma A C B) A) =>  ((k19_substut1 A C) = (k14_substut1 A B (k2_sublemma A C) (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))) ) ) ) ) ) ) ) ) ) ).
tt(t41_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 B))) ) ) ).
tt(t41_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 A) B) (k12_supinf_2 (k18_supinf_2 A) (k2_nat_1 B C)))) ) ) ) ) ) ) ).
tt(t41_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) &  ((v5_tbsp_1 A) & (l1_metric_1 A)) ) ) ) ) )  => (r2_hidden (k1_tarski (u1_struct_0 A)) (k4_taxonom1 A))) ) ).
tt(t41_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m2_nat_lat (k8_tdlat_1 A) (k4_tdlat_1 A))) ) ).
tt(t41_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))))) ) ) ) ).
tt(t41_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((k4_tdlat_1 A) = (k8_tdlat_1 A)) ) ) ).
tt(t41_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_tex_2 B A))  => (v1_tops_1 B A)) ) ) ) ) ).
tt(t41_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) &  ((v4_pre_topc B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) ) )  =>  (~  ((v3_tex_3 C A) &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ((a_2_8_tex_4 A B) = k1_xboole_0) )  => (r1_tarski (k3_tex_4 A B) (k1_setfam_1 (a_2_8_tex_4 A B)))) ) ) ) ) ).
tt(t41_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D A) & (m1_pre_topc D A)) )  =>  ( ((m1_pre_topc B D) & (r1_tsep_1 D C))  =>  ( ((v1_tsep_1 B (k1_tsep_1 A B C)) & (m1_pre_topc B (k1_tsep_1 A B C)))  &  ((v1_tsep_1 B (k1_tsep_1 A C B)) & (m1_pre_topc B (k1_tsep_1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A B D) & (r1_borsuk_6 A E D)) )  =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H A B D) => (r3_borsuk_2 A B D (k1_borsuk_2 A B E D (k1_borsuk_2 A B C E F (k1_borsuk_2 A C D E (k1_borsuk_2 A C B D (k2_borsuk_2 A B C F) H) G)) (k2_borsuk_2 A D E G)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_topalg_6 A)) =>  ((k6_topalg_6 A (k8_finseq_1 (k1_topalg_6 A) C (k12_finseq_1 (k1_topalg_6 A) B))) = (k4_topalg_6 A (k6_topalg_6 A C) B)) ) ) ) ) ) ) ).
tt(t41_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_topgen_1 B A) <=>  ((k2_topgen_1 A B) = B) ) ) ) ) ) ).
tt(t41_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_xboole_0 (k1_tarski B) A) =>  ( ((v3_pre_topc (k1_tarski C) (k6_topgen_3 A B)) & (m1_subset_1 (k1_tarski C) (k1_zfmisc_1 (u1_struct_0 (k6_topgen_3 A B)))))  <=>  ((r2_hidden C A) &  (~  (C = B) ) ) ) ) ) ) ) ).
tt(t41_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_topgen_4 B A) & (v6_topgen_4 C A))  => (v6_topgen_4 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t41_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5))) =>  ( (A = k1_topgen_5)  => (v1_xboole_0 (k2_topgen_1 k3_topgen_5 A))) ) ) ).
tt(t41_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k6_algstr_0 A B (k2_group_1 A C))) =>  (? [E:$i] :  ( ((v3_pre_topc E A) & (m1_connsp_2 E A B))  &  (? [F:$i] :  ( ((v3_pre_topc F A) & (m1_connsp_2 F A C))  & (r1_tarski (k2_group_2 A E (k1_group_2 A F)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_topreal3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((v4_topreal1 A) &  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) (k2_topreal1 2 A B)) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A))) ) )  =>  ((k2_nat_1 B 1) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t41_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = B)  => (r1_tarski (k4_card_3 (k5_funct_4 (k1_zfmisc_1 k1_numbers) 1 2 (k2_rcomp_1 (k9_real_1 (k17_euclid A) (k6_real_1 C (k7_square_1 2))) (k7_real_1 (k17_euclid A) (k6_real_1 C (k7_square_1 2)))) (k2_rcomp_1 (k9_real_1 (k18_euclid A) (k6_real_1 C (k7_square_1 2))) (k7_real_1 (k18_euclid A) (k6_real_1 C (k7_square_1 2)))))) (k9_metric_1 (k14_euclid 2) B C))) ) ) ) ) ) ) ).
tt(t41_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((k17_euclid (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C A) (k1_rlvect_1 (k15_euclid 2) D B))) = (k7_real_1 (k4_real_1 A (k17_euclid C)) (k4_real_1 B (k17_euclid D)))) ) ) ) ) ) ) ) ) ).
tt(t41_toprealb,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k13_toprealb (k4_toprealb (k2_xcmplx_0 B A))) = (k1_partfun1 k1_numbers k1_numbers (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb B) (k3_real_1 (k4_toprealb B) 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb B)))) (k2_partfun1 k1_numbers k1_numbers (k1_fcont_1 1 (k4_xcmplx_0 A)) (k2_rcomp_1 (k2_xcmplx_0 B A) (k3_real_1 (k2_xcmplx_0 B A) 1))) (k13_toprealb (k4_toprealb B)))) ) ) ) ) ).
tt(t41_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k85_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k85_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k85_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t41_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 B A) =>  ((k6_toprns_1 A (k3_toprns_1 A B)) = (k4_algstr_0 (k15_euclid A) (k6_toprns_1 A B))) ) ) ) ) ) ).
tt(t41_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_tops_1 A (k2_tops_1 A (k2_tops_1 A B))) = (k2_tops_1 A (k2_tops_1 A B))) ) ) ) ) ).
tt(t41_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_struct_0 B) = k1_xboole_0)  =>  ((k2_struct_0 A) = k1_xboole_0) )  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_struct_0 B)) = (k2_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t41_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski C B) &  ((v3_pre_topc C A) & (v1_tops_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t41_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_diraf A C D E F) <=> (r2_diraf A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  => (r1_xxreal_0 1 (k7_trees_1 A))) ) ).
tt(t41_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (m4_trees_3 A (k2_trees_1 k6_numbers))) ) ).
tt(t41_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  ((r2_hidden B (k1_trees_2 (k9_xtuple_0 A) C)) => (r2_hidden (k1_funct_1 A B) (k10_xtuple_0 (k2_trees_9 A C)))) ) ) ) ) ) ) ).
tt(t41_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_connsp_1 A B D) & (r1_connsp_1 A C D))  <=> (r1_connsp_1 A (k4_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t41_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r4_tsep_2 A B C) =>  ((r4_tsep_1 A B C) <=> (r3_tsep_1 A B C)) ) ) ) ) ) ) ) ).
tt(t41_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u2_turing_1 B)) => (r2_hidden (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) C) (k21_turing_1 A B))) ) ) ) ) ) ).
tt(t41_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  ((r2_hidden A (k2_msafree2 (k40_twoscomp A B))) & (r2_hidden B (k2_msafree2 (k40_twoscomp A B)))) ) ) ) ) ).
tt(t41_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k2_polynom4 k1_complfld (k4_uniroots A k1_complfld) B) = (k4_binop_2 (k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) B A) 1)) ) ) ) ) ).
tt(t41_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((r2_funct_2 k5_numbers (u1_struct_0 A) C (k11_polynom3 A (k4_polynom5 A B (k5_struct_0 A)) D)) &  ((k1_normsp_1 A C (k7_nat_d (k1_algseq_1 A C) 1)) = (k5_struct_0 A)) )  =>  ((k1_normsp_1 A D (k7_nat_d (k1_algseq_1 A D) 1)) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t41_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) => (r2_valuat_1 A B D (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C))) ) ) ) ) ) ) ) ).
tt(t41_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k16_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k16_valued_2 A B C)) = C) ) ) ) ) ) ).
tt(t41_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_vectsp_6 E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 F B C) &  ((v1_mod_2 F A B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (~  ((r1_tarski (k1_vectsp_6 A C E) (k2_ranknull B C F D)) &  (! [G:$i] :  ((m2_vectsp_6 G A B D) =>  (~  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) F (k4_vectsp_6 A B G)) = (k4_vectsp_6 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (m1_vectsp_4 B A (k2_vectsp_4 A B))) ) ) ) ).
tt(t41_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) => (r1_vectsp_5 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t41_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) => (r1_tarski (k1_vectsp_6 A B (k8_vectsp_6 A B C D)) (k4_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B C) (k1_vectsp_6 A B D)))) ) ) ) ) ) ) ) ).
tt(t41_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_tarski A B) & (r1_vfunct_1 C D E B))  => (r1_vfunct_1 C D E A)) ) ) ) ) ) ) ) ) ).
tt(t41_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((r1_tarski D E) & (r1_vfunct_2 A B C E))  => (r1_vfunct_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t41_waybel_0,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v2_waybel_0 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k12_lattice3 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t41_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_waybel_6 B A) => (v3_pre_topc B A)) ) ) ) ) ).
tt(t41_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = C)  =>  ( (B = (k4_yellow_0 (k2_yellow_1 (u1_pre_topc A))))  |  ((v2_waybel_6 B (k2_yellow_1 (u1_pre_topc A))) <=> (v3_yellow_8 (k3_subset_1 (u1_struct_0 A) C) A)) ) ) ) ) ) ) ) ) ).
tt(t41_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ((v1_waybel_5 (k2_yellow_1 (k5_waybel11 A))) <=>  ((v3_waybel_3 (k2_yellow_1 (k5_waybel11 A))) & (v3_waybel_3 (k7_lattice3 (k2_yellow_1 (k5_waybel11 A))))) ) ) ) ).
tt(t41_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v2_waybel19 B) & (m1_yellow_9 B A)) )  =>  (! [C:$i] :  ( ((v13_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ((v3_pre_topc C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = C)  => (v3_pre_topc D A)) ) ) ) ) ) ) ) ) ) ).
tt(t41_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_orders_3 B A A) =>  ( (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (~  ((v3_waybel_1 (k1_waybel_1 A C D E) A C) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D E))) ) ) ) ) ) ) )  | (v8_waybel_1 B A)) ) ) ) ) ) ).
tt(t41_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_waybel20 A B))) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (C = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k2_waybel20 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t41_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_waybel11 A (k5_waybel_9 A B C)) = (k1_waybel11 A B)) ) ) ) ) ) ) ).
tt(t41_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v2_waybel23 (k2_waybel_3 A B) A)) ) ) ) ).
tt(t41_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_waybel25 B)))))) )  =>  ( ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (v10_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C F) (k1_waybel25 B))) )  &  (E = (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C)))) )  =>  ((k2_yellow_6 (u1_struct_0 A) (k1_waybel25 B) E D) = (k1_waybel_2 (k1_waybel25 B) (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_waybel26,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r1_tarski (k9_xtuple_0 A) B) =>  ((k5_waybel26 (k6_waybel26 A B)) = A) ) ) ) ) ).
tt(t41_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_waybel27 B (k6_yellow_1 A C))) (u1_struct_0 (k6_yellow_1 A (k2_waybel27 B C)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel27 B (k6_yellow_1 A C))) (u1_struct_0 (k6_yellow_1 A (k2_waybel27 B C))))))) )  &  ((v3_waybel27 D) & (v23_waybel_0 D (k2_waybel27 B (k6_yellow_1 A C)) (k6_yellow_1 A (k2_waybel27 B C)))) ) ) ) ) ) ) ) ) ).
tt(t41_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ((v1_waybel_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) )  =>  ((v10_waybel_0 C A) =>  ((k11_lattice3 A B (k1_waybel_2 A C)) = (k1_yellow_0 A (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A C))))) ) ) ) ) ) ) ) ) ).
tt(t41_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) ) )  => (v18_waybel_0 (k6_struct_0 A B (k3_yellow_0 B)) A B)) ) ) ) ).
tt(t41_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v9_pre_topc A) & (v3_waybel_3 (k2_yellow_1 (u1_pre_topc A))))  => (v6_waybel_3 A)) ) ) ).
tt(t41_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (v6_waybel_4 (k2_waybel_4 A) A)) ) ).
tt(t41_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((v5_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k7_yellow_3 A A C E) B) & (r2_hidden (k7_yellow_3 A A D F) B))  => (r2_hidden (k7_yellow_3 A A (k12_lattice3 A C D) (k12_lattice3 A E F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_waybel_9,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v8_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_compts_1 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_pre_topc (k4_waybel_1 A B) A A)) )  => (v2_waybel_2 A)) ) ) ).
tt(t41_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r3_wellord1 A B D) & (r3_wellord1 B C E))  => (r3_wellord1 A C (k3_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~  ((k6_int_1 A B) = k6_numbers) )  &  (~  ((k4_xcmplx_0 (k5_int_1 A B)) = (k3_real_1 (k5_int_1 (k4_xcmplx_0 A) B) 1)) ) ) ) ) ) ) ) ) ).
tt(t41_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 (k4_xboole_0 A B) C) = (k4_xboole_0 A (k2_xboole_0 B C))) ) ) ) ).
tt(t41_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k4_xboolean A (k9_xboolean B C)) = (k4_xboolean (k4_xboolean A (k3_xboolean B)) (k3_xboolean C))) ) ) ) ) ) ) ).
tt(t41_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 C D)) = (k3_xcmplx_0 (k6_xcmplx_0 B A) (k6_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ).
tt(t41_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 A (k2_xcmplx_0 B C))) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t41_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k13_xtuple_0 A) (k13_xtuple_0 B)) (k13_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t41_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_0 A k1_xxreal_0) = k1_xxreal_0) ) ) ).
tt(t41_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k4_xxreal_1 B C) (k3_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t41_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) => (m1_xxreal_2 k1_xxreal_0 A)) ) ).
tt(t41_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 (k3_xxreal_3 C B) A) =>  ( ( (A = k2_xxreal_0)  &  ( (B = k1_xxreal_0)  &  (~ (r1_xxreal_0 C k6_numbers)) ) )  |  ( ( (A = k1_xxreal_0)  &  ( (B = k2_xxreal_0)  &  (~ (r1_xxreal_0 C k6_numbers)) ) )  | (r1_xxreal_0 C (k1_xxreal_3 A B))) ) ) ) ) ) ) ) ) ).
tt(t41_yellow_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_0 A (k7_domain_1 (u1_struct_0 A) B C)) = (k13_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t41_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_tarski (k4_yellow_3 A B (k6_waybel_0 (k3_yellow_3 A B) C)) (k6_waybel_0 A (k8_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k6_waybel_0 (k3_yellow_3 A B) C)) (k6_waybel_0 B (k9_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t41_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  =>  ((v1_funct_1 (k14_funct_3 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) D E)) &  ((v1_funct_2 (k14_funct_3 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) D E) (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 B C))) &  ((v5_pre_topc (k14_funct_3 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) D E) A (k2_borsuk_1 B C)) & (m1_subset_1 (k14_funct_3 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_borsuk_1 B C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r6_yellow16 B A C) <=>  ((r2_yellow_0 A C) =>  ((r2_yellow_0 B C) &  ((k2_yellow_0 B C) = (k2_yellow_0 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t41_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v9_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow18 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ( ((v2_funct_1 D) & (r2_hidden (k2_funct_1 D) (k1_altcat_1 A C B)))  => (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t41_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  ((v21_functor0 C A B) => (r2_yellow20 A B C A B)) ) ) ) ) ) ) ).
tt(t41_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) & (l1_orders_2 B)) ) )  =>  ((m1_subset_1 A (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B)))) <=>  ( (~ (v1_xboole_0 A))  &  ((v1_waybel_0 A B) &  ((v12_waybel_0 A B) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ).
tt(t41_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ( ((r1_yellow_0 A (k4_yellow_3 A B C)) & (r1_yellow_0 B (k5_yellow_3 A B C)))  <=> (r1_yellow_0 (k3_yellow_3 A B) C)) ) ) ) ) ) ) ).
tt(t41_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_yellow_4 A (k4_yellow_4 A B C) D) = (k4_yellow_4 A B (k4_yellow_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t41_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A (k7_waybel_1 A B) (k7_waybel_1 A (k12_lattice3 A B C))) & (r3_orders_2 A (k7_waybel_1 A C) (k7_waybel_1 A (k12_lattice3 A B C)))) ) ) ) ) ) ) ).
tt(t41_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v8_yellow_6 B A) & (m4_yellow_6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k13_yellow_6 A B)))) =>  ((v3_pre_topc C (k13_yellow_6 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E A)) ) )  =>  ((r2_hidden (k4_tarski E D) B) => (r1_waybel_0 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B) C D) =>  ( ((v5_orders_3 C A (k7_lattice3 B)) => (v5_orders_3 D (k7_lattice3 A) B))  &  ( ((v5_orders_3 D (k7_lattice3 A) B) => (v5_orders_3 C A (k7_lattice3 B)))  &  ( ((v5_waybel_0 C A (k7_lattice3 B)) => (v5_waybel_0 D (k7_lattice3 A) B))  &  ((v5_waybel_0 D (k7_lattice3 A) B) => (v5_waybel_0 C A (k7_lattice3 B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_tops_2 D B) &  ((v2_cantor_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ((v1_tops_2 (k2_xboole_0 (a_3_0_yellow_9 A B D) (a_3_1_yellow_9 A B C)) (k2_borsuk_1 A B)) &  ((v2_cantor_1 (k2_xboole_0 (a_3_0_yellow_9 A B D) (a_3_1_yellow_9 A B C)) (k2_borsuk_1 A B)) & (m1_subset_1 (k2_xboole_0 (a_3_0_yellow_9 A B D) (a_3_1_yellow_9 A B C)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t41_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (~ (r1_zf_lang A A)) ) ) ).
tt(t41_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v8_zf_lang A) =>  (A = (k10_zf_lang (k21_zf_lang A) (k22_zf_lang A))) ) ) ) ).
tt(t41_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_xboole_0 (k2_tarski A B) C) C) => (r2_hidden A C)) ) ) ) ).
tt(t41_zfrefle1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (~  ((r2_hidden k4_ordinal1 B) &  ((r2_hidden A B) &  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (~  ((r2_hidden A C) &  ((r2_hidden C B) & (v1_zf_model C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t41_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_zmodul01 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) ) )  =>  ( ((m1_zmodul01 A B) & (m1_zmodul01 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t420_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 k2_xxreal_0 A) = (k2_xboole_0 (k2_xxreal_1 k2_xxreal_0 A) (k1_tarski A))) ) ) ).
tt(t421_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 k2_xxreal_0 A) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k3_xxreal_1 k2_xxreal_0 A))) ) ) ).
tt(t422_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_xxreal_1 k2_xxreal_0 A) = (k2_xboole_0 (k1_tarski k2_xxreal_0) (k4_xxreal_1 k2_xxreal_0 A))) ) ) ).
tt(t423_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_xxreal_1 k2_xxreal_0 A) = (k2_xboole_0 (k4_xxreal_1 k2_xxreal_0 A) (k1_tarski A))) ) ) ).
tt(t424_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 A k1_xxreal_0) = (k2_xboole_0 (k4_xxreal_1 A k1_xxreal_0) (k2_tarski A k1_xxreal_0))) ) ) ).
tt(t425_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 A k1_xxreal_0) = (k2_xboole_0 (k2_xxreal_1 A k1_xxreal_0) (k1_tarski k1_xxreal_0))) ) ) ).
tt(t426_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_1 A k1_xxreal_0) = (k2_xboole_0 (k1_tarski A) (k3_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t427_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k2_xxreal_1 A k1_xxreal_0) = (k2_xboole_0 (k1_tarski A) (k4_xxreal_1 A k1_xxreal_0))) ) ) ).
tt(t428_xxreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_xxreal_1 A k1_xxreal_0) = (k2_xboole_0 (k4_xxreal_1 A k1_xxreal_0) (k1_tarski k1_xxreal_0))) ) ) ).
tt(t42_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k2_relset_1 (u1_struct_0 A) (k7_abcmiz_0 A B C))) =>  ((r3_orders_2 A (k8_abcmiz_0 A B C) D) & (r3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 (k1_msualg_1 A B)) = 1)  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (D = (k1_funct_1 (k1_msualg_1 A B) 1))  & (m1_abcmiz_1 C A D)) ) )  => (m1_abcmiz_1 (k4_trees_4 (k4_tarski B (u1_struct_0 A)) (k3_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C)) A (k2_msualg_1 A B))) ) ) ) ) ) ) ) ).
tt(t42_abcmiz_a,ax, (! [A:$i] :  ((m1_subset_1 A (u4_struct_0 k27_abcmiz_1)) =>  ((v2_abcmiz_1 A k27_abcmiz_1) <=> (r2_hidden A k20_abcmiz_1)) ) ) ).
tt(t42_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_aff_1 A B C) => (r3_aff_1 A C B)) ) ) ) ) ) ) ).
tt(t42_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_4 C A) & (r1_tarski B C)) )  => (r1_aff_4 A B C)) ) ) ) ) ) ) ).
tt(t42_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k8_afinsq_1 B)) <=>  ((v1_relat_1 A) &  ((v5_relat_1 A B) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) ) ) ) ) ).
tt(t42_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 D A) =>  ( ( (~ (v1_setwiseo D A))  &  (~  ((r1_xxreal_0 1 (k1_afinsq_1 B)) & (r1_xxreal_0 1 (k1_afinsq_1 C))) ) )  |  ((k6_afinsq_2 A (k1_ordinal4 B C) D) = (k5_binop_1 A D (k6_afinsq_2 A B D) (k6_afinsq_2 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k13_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k14_afproj A))) =>  ((r2_hidden (k4_tarski B (k4_tarski C 2)) (u3_incsp_1 (k13_afproj A))) => (m1_subset_1 B (u1_incsp_1 (k14_afproj A)))) ) ) ) ) ) ) ).
tt(t42_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((u1_struct_0 (k5_afvect0 A B)) = (u1_struct_0 A))  &  ( ((u1_algstr_0 (k5_afvect0 A B)) = (k3_afvect0 A B))  &  ((k4_struct_0 (k5_afvect0 A B)) = B) ) ) ) ) ) ) ).
tt(t42_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = (u1_struct_0 A))  &  ( ((k9_xtuple_0 C) = (u4_struct_0 A))  & (r1_algspec1 A B C)) )  => (r3_pua2mss1 A (k2_algspec1 A B C) B C)) ) ) ) ) ) ) ).
tt(t42_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_partfun1 C (u1_struct_0 A)) &  ((v3_relat_2 C) &  ((v8_relat_2 C) &  ((v1_algstr_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B))))) )  =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B) (k5_algstr_4 A C) D) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B) (k5_algstr_4 A C) E)) => (r2_relset_1 (u1_struct_0 (k4_algstr_4 A C)) (u1_struct_0 B) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k5_altcat_4 A)))  &  ((v2_altcat_1 (k5_altcat_4 A)) &  ((v3_altcat_2 (k5_altcat_4 A) (k4_altcat_4 A)) & (m1_altcat_2 (k5_altcat_4 A) (k4_altcat_4 A))) ) ) ) ) ).
tt(t42_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) <=> (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_analmetr A))))) ) ) ) ).
tt(t42_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) &  ((r1_analort A B C H I F G) &  ((r1_analort A B C H I J K) &  ( (~  (H = I) )  &  ( (~  (F = G) )  &  (~ (r1_analort A B C D E J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) & (l1_unialg_1 A)) )  =>  ((k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A (k1_funct_7 1 (k4_finseq_1 (u1_unialg_1 A))))) = (k1_tarski k1_xboole_0)) ) ) ).
tt(t42_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k59_aofa_i00 A B D E G F)) G) = (k6_int_1 (k21_aofa_i00 B k4_numbers C G) F))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = G) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k59_aofa_i00 A B D E G F)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r5_armstrng A B (k9_armstrng A (k10_armstrng A B)))) ) ) ) ).
tt(t42_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ( (~  (A = k1_xboole_0) )  =>  ( ((k6_arytm_3 (k8_arytm_3 B A)) = (k4_arytm_3 B A))  &  ((k7_arytm_3 (k8_arytm_3 B A)) = (k4_arytm_3 A B)) ) ) ) ) ) ) ).
tt(t42_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((k14_asympt_0 k5_numbers (k6_asympt_0 A) (k6_asympt_0 B)) = (k6_asympt_0 (k5_asympt_0 A B))) ) ) ) ) ).
tt(t42_asympt_1,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v2_asympt_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((r2_hidden B (k6_asympt_0 (k3_asympt_0 C A))) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_xxreal_0 D (k1_seq_1 C F))) ) ) ) ) ) ) ) )  | (r2_hidden B (k6_asympt_0 C))) ) ) ) ) ) ) ) ).
tt(t42_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k5_bcialg_1 A)) =>  ( (~  (B = C) )  =>  ((k9_subset_1 (u1_struct_0 A) (k7_bcialg_1 A B) (k7_bcialg_1 A C)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t42_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_bcialg_2 F A) =>  ( ((r2_hidden (k4_tarski B C) F) & (r2_hidden D (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) F (k4_struct_0 A))))  => (r2_hidden (k4_tarski B (k1_bcialg_2 A C D E)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A (k1_bcialg_1 A C (k1_bcialg_1 A C B)) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ).
tt(t42_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v3_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A (k4_struct_0 A) C)) = B)  &  ( ((k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A B C)) = (k1_bcialg_1 A (k1_bcialg_1 A C D) (k1_bcialg_1 A C B)))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B C) D) = (k1_bcialg_1 A B (k1_bcialg_4 A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v19_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A k6_numbers 1 k6_numbers k6_numbers)) ) ) ).
tt(t42_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v2_funct_2 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (D = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ).
tt(t42_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) = (k4_bhsp_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t42_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r2_hidden B (k4_bhsp_2 A B C))) ) ) ) ) ) ) ).
tt(t42_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((v3_funct_1 B) => (v3_funct_1 (k1_valued_0 (u1_struct_0 A) B C))) ) ) ) ) ) ) ).
tt(t42_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) &  ((v3_bhsp_3 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_bhsp_4 B A) => (v1_bhsp_4 B A)) ) ) ) ) ).
tt(t42_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  => (v1_vectsp_4 (k10_bilinear A B C D) A B)) ) ) ) ) ) ) ) ).
tt(t42_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k4_lattices A C D)) (k3_lattices A (k1_boolealg A B C) (k1_boolealg A B D)))) ) ) ) ) ) ) ) ).
tt(t42_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ((v2_borsuk_1 C B) & (m1_borsuk_1 C B))  =>  ((r2_borsuk_1 A B) => (r2_borsuk_1 (k11_borsuk_1 A (k15_borsuk_1 A B C)) (k16_borsuk_1 A B C))) ) ) ) ) ) ) ).
tt(t42_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))) =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) &  ( (~ (r1_xxreal_0 C B))  &  (A = (k1_rcomp_1 B C)) ) ) ) ) )  => (r1_borsuk_3 k5_topmetr (k1_pre_topc k1_borsuk_4 A))) ) ) ).
tt(t42_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k3_rcomp_1 B k1_xxreal_0))  => (v4_pre_topc A k3_topmetr)) ) ) ) ) ).
tt(t42_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) & (r1_borsuk_6 A C D))  => (r1_borsuk_6 A B D)) ) ) ) ) ) ) ) ) ).
tt(t42_borsuk_7,ax, ((k45_valued_1 k8_borsuk_7 k9_borsuk_7) = (k4_euclid_5 2 k6_numbers k6_numbers)) ).
tt(t42_bspace,ax, (! [A:$i] :  ((k1_card_1 (k2_struct_0 (k7_bspace A))) = (k3_card_2 2 (k1_card_1 A))) ) ).
tt(t42_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_bvfunc_1 A B C) => (r1_setfam_1 C (k18_bvfunc_1 A B))) ) ) ) ) ) ) ).
tt(t42_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k2_bvfunc_1 A D B) C)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t42_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k9_bvfunc_1 A B C)) (k11_bvfunc_1 A))) ) ) ) ) ) ).
tt(t42_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k10_bvfunc_1 A B C) (k9_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t42_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ( ((k2_calcul_1 A E) = (k11_cqc_lang A C B))  & (r4_calcul_1 A E))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) (k4_substut2 A B C D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) <=> (r2_hidden A B)) ) ) ) ) ).
tt(t42_card_2,ax, (! [A:$i] :  ( ((k1_card_1 A) = 1)  <=>  (? [B:$i] :  (A = (k1_tarski B)) ) ) ) ).
tt(t42_card_3,ax, (! [A:$i] :  ((v1_finset_1 A) => (r2_hidden (k1_card_1 A) (k1_card_1 k4_ordinal1))) ) ).
tt(t42_card_fin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finset_1 B)) )  =>  ( ((v1_finset_1 (k9_xtuple_0 B)) &  (A = k6_numbers) )  =>  ((k3_card_fin A B) = (k1_card_1 (k3_tarski (k10_xtuple_0 B)))) ) ) ) ) ) ).
tt(t42_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [E:$i] :  ((m1_cat_1 E A C B) &  (? [F:$i] :  ((m1_cat_1 F A C B) &  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ( ((k5_cat_1 A B C B D F) = (k4_cat_1 A B))  &  (~  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 (u4_struct_0 A))))) )  => (m1_cat_3 C A B k1_xboole_0)) ) ) ) ) ) ).
tt(t42_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A B D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  (~  ((k9_cat_4 A C D B E F) = (k5_cat_1 A B (k2_cat_4 A B B) (k2_cat_4 A C D) (k15_cat_4 A B) (k18_cat_4 A B C B D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  &  ( ((k7_afinsq_2 C) = (k5_card_1 (k2_catalan2 (k23_binop_2 (k23_binop_2 (k24_binop_2 2 A) 2) B) (k23_binop_2 A 1))))  &  ( ((k1_relset_1 k5_numbers C) = (k23_binop_2 B 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D B) =>  ((k1_recdef_1 C D) = (k5_card_1 (k2_catalan2 (k23_binop_2 (k23_binop_2 (k24_binop_2 2 A) 1) D) A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((r2_hidden B (k6_cc0sp2 A)) => (r2_hidden B (k2_cc0sp1 (u1_struct_0 A)))) ) ) ) ).
tt(t42_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_hidden A (k1_relset_1 k2_numbers B)) => (r2_cfcont_1 B (k1_tarski A))) ) ) ) ) ).
tt(t42_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) (k1_cfunct_1 A D E)) (k1_cfunct_1 A (k19_valued_1 A k2_numbers k2_numbers B D) (k19_valued_1 A k2_numbers k2_numbers C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t42_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (~  ( (~ (v7_cgames_1 A))  &  ( (~ (v9_cgames_1 A))  &  ( (~ (v10_cgames_1 A))  &  (~ (v8_cgames_1 A)) ) ) ) ) ) ) ).
tt(t42_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid B)) =>  (! [E:$i] :  ((m1_chain_1 E B) =>  ( (B = (k2_nat_1 A 1))  =>  ((r2_hidden (k3_chain_1 B C D) (k4_chain_1 B E A)) <=>  (? [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 B)) &  ( ((k1_seq_1 C F) = (k1_seq_1 D F))  &  ((r2_hidden (k1_seq_1 C F) (k2_chain_1 B E F)) &  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 B)) =>  ( (~  (G = F) )  =>  ( (~ (r1_xxreal_0 (k1_seq_1 D G) (k1_seq_1 C G)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 C G) (k1_seq_1 D G)) (k2_chain_1 B E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  ((v1_chord B A) =>  (! [C:$i] :  ( ((v7_ordinal1 C) &  (~ (v1_abian C)) )  =>  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  ( ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 B)))  => (v1_chord (k8_glib_001 A B C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t42_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ((r2_hidden B (u1_struct_0 F)) =>  ((r2_hidden A (k3_msafree2 F)) |  ((r2_hidden C (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k2_tarski A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k2_msafree2 (k5_circcomb A B)) = (k10_xtuple_0 B))  &  ((k3_msafree2 (k5_circcomb A B)) = (k1_tarski (k4_tarski B A))) ) ) ) ) ).
tt(t42_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r4_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 B)) =>  ( (H = (k1_funct_1 D G))  => (r1_funct_2 (k3_msualg_1 B H F) (k4_msualg_1 B H F) (k3_msualg_1 A G E) (k4_msualg_1 A G E) (k5_msualg_1 B H F) (k5_msualg_1 A G E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k4_classes1 B)) <=> (r2_hidden (k9_setfam_1 A) (k4_classes1 (k1_ordinal1 B)))) ) ) ) ).
tt(t42_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_classes1 A) &  ((v1_ordinal1 B) & (r2_hidden B A)) )  => (r2_hidden B (k4_classes1 (k1_card_1 A)))) ) ) ).
tt(t42_clopban1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) &  ((v3_clopban1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k14_clopban1 A B)))  &  ((v13_algstr_0 (k14_clopban1 A B)) &  ((v2_rlvect_1 (k14_clopban1 A B)) &  ((v3_rlvect_1 (k14_clopban1 A B)) &  ((v4_rlvect_1 (k14_clopban1 A B)) &  ((v3_normsp_0 (k14_clopban1 A B)) &  ((v4_normsp_0 (k14_clopban1 A B)) &  ((v2_clvect_1 (k14_clopban1 A B)) &  ((v3_clvect_1 (k14_clopban1 A B)) &  ((v4_clvect_1 (k14_clopban1 A B)) &  ((v5_clvect_1 (k14_clopban1 A B)) &  ((v8_clvect_1 (k14_clopban1 A B)) &  ((v3_clopban1 (k14_clopban1 A B)) & (l2_clvect_1 (k14_clopban1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A (k5_algstr_0 A (k5_struct_0 A) B))))  =>  ((v25_algstr_0 B A) &  ((k9_algstr_0 A B) = (k1_clopban3 A (k5_clopban3 A (k5_algstr_0 A (k5_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(t42_closure2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v15_closure2 B A) & (l1_closure2 B A))  =>  ((k10_closure2 A (u3_msualg_1 A B) (k12_closure2 A B)) = (g1_closure2 A (u3_msualg_1 A B) (u1_closure2 A B))) ) ) ) ) ).
tt(t42_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t42_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r2_hidden B (k4_clvect_2 A B C))) ) ) ) ) ) ) ).
tt(t42_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) &  ((v4_clvect_2 A) & (l1_csspace A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_3 B A) => (v1_clvect_3 B A)) ) ) ) ) ).
tt(t42_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  (~  ((r2_hidden D (k3_tarski B)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v9_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k8_cohsp_1 A B E) = (k1_tarski (k4_tarski C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (B = (k4_tarski (k4_tarski (k21_coh_sp A B) (k22_coh_sp A B)) (k2_xtuple_0 B))) ) ) ) ).
tt(t42_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 (k6_xcmplx_0 A (k15_complex1 A))) = k6_numbers)  &  ((k4_complex1 (k6_xcmplx_0 A (k15_complex1 A))) = (k8_real_1 2 (k4_complex1 A))) ) ) ) ).
tt(t42_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 (k10_complex1 A) B) = (k1_complex2 A (k10_complex1 B))) ) ) ) ) ).
tt(t42_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ( ((k4_algstr_0 k1_complfld (k3_vectsp_1 k1_complfld B A)) = (k3_vectsp_1 k1_complfld (k4_algstr_0 k1_complfld B) A))  &  ((k4_algstr_0 k1_complfld (k3_vectsp_1 k1_complfld B A)) = (k3_vectsp_1 k1_complfld B (k4_algstr_0 k1_complfld A))) ) ) ) ) ) ) ).
tt(t42_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k11_seq_4 (k12_seq_4 A B)) = (k12_seq_4 (k11_seq_4 A) B)) ) ) ) ) ).
tt(t42_compl_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((v4_tbsp_1 B) => (v4_tbsp_1 (k3_compl_sp B C A))) ) ) ) ) ) ).
tt(t42_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_compos_1 A (k1_funct_4 B C) D) = (k1_funct_4 (k6_compos_1 A B D) (k6_compos_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t42_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xxreal_0 (k62_valued_1 B) D))  =>  ((k1_funct_1 (k8_compos_1 A B C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t42_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r2_hidden (k1_comptrig A) (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) <=>  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 A)))  &  (~ (r1_xxreal_0 (k4_complex1 A) k6_numbers)) ) ) ) ) ).
tt(t42_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_rfunct_3 B (k3_finseq_2 A) A (k2_comput_1 A)) =>  (! [C:$i] :  ( ((v3_comput_1 C) & (m2_finseq_1 C (k2_comput_1 A)))  =>  ((r1_tarski (k9_xtuple_0 (k3_relat_1 (k6_funct_6 C) B)) (k4_finseq_2 (k1_comput_1 C) A)) &  ((r1_tarski (k10_xtuple_0 (k3_relat_1 (k6_funct_6 C) B)) A) & (r2_hidden (k3_relat_1 (k6_funct_6 C) B) (k2_comput_1 A))) ) ) ) ) ) ) ) ).
tt(t42_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) =>  ((r2_relset_1 k5_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B A)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k31_valued_1 k5_numbers k2_numbers B) A)) & (r2_relset_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B (k31_valued_1 k5_numbers k2_numbers A)) (k31_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers B A)))) ) ) ) ) ) ).
tt(t42_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k3_comseq_2 A) = k5_complex1) ) )  => (v2_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) ) ) ) ) ).
tt(t42_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 (k7_comseq_3 A)) & (v2_comseq_2 (k8_comseq_3 A)))  =>  ((v2_comseq_2 A) &  ( ((k3_complex1 (k3_comseq_2 A)) = (k2_seq_2 (k7_comseq_3 A)))  &  ((k4_complex1 (k3_comseq_2 A)) = (k2_seq_2 (k8_comseq_3 A))) ) ) ) ) ) ).
tt(t42_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v10_lattices (k11_conlat_1 A)) & (l3_lattices (k11_conlat_1 A))) ) ) ) ).
tt(t42_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_connsp_1 A B)) =>  ((k1_connsp_1 A C) = (k1_connsp_1 A B)) ) ) ) ) ) ) ) ).
tt(t42_convex4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_complex1 (k3_xcmplx_0 A B)) = (k4_real_1 A (k3_complex1 B))) ) ) ) ) ).
tt(t42_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 (k3_qc_lang1 A))) =>  ( ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) D B G F) (k15_cqc_sim1 A E)) & (r2_hidden (k2_qc_lang3 A C) (k7_relat_1 F (k24_qc_lang1 A D))))  => (r2_qc_lang1 A C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) B) B) (k4_cqc_the1 A))) ) ) ) ).
tt(t42_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k12_cqc_lang A D (k9_cqc_lang A B C)) A) <=> (v2_cqc_the1 (k9_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t42_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r6_cqc_the3 A B C) =>  ((r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) E (k6_domain_1 (k3_cqc_lang A) C)) D) <=> (r3_cqc_the1 A E (k8_cqc_lang A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k13_csspace A B) = k6_numbers)  <=>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t42_dickson,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_yellow_1 B)) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((v4_dickson (k3_waybel_3 A B C)) & (v3_dickson (k3_waybel_3 A B C))) ) )  =>  ((v3_dickson (k5_yellow_1 A B)) & (v4_dickson (k5_yellow_1 A B))) ) ) ) ) ) ).
tt(t42_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 k16_sin_cos A) B) = (k8_real_1 2 (k8_real_1 (k21_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2))))) ) ) ) ) ).
tt(t42_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k5_square_1 D)) ) )  =>  ( (A = B)  |  ((k9_diff_1 C A B) = (k7_real_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t42_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers C B) (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k1_real_1 A)) B))) ) ) ) ) ) ) ).
tt(t42_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xxreal_0 (k1_dilworth (k5_yellow_0 A B)) (k1_dilworth A))) ) ) ) ).
tt(t42_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ((r2_analoaf A B C D D) &  ( ( ((r2_analoaf A B C D E) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) )  &  ((r2_analoaf A B C B D) => (r2_analoaf A C B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A D B B E) &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  <=>  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) ) ) ) ) ).
tt(t42_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) => (m2_subset_1 (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers) (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C))) ) ) ) ) ) ).
tt(t42_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  =>  ((k7_ec_pf_2 A (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C)) = (k1_funct_1 (k8_ec_pf_2 A B) (k7_ec_pf_2 A C))) ) ) ) ) ) ) ) ).
tt(t42_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ( ((k2_cat_1 A B (k4_graph_1 A C)) = k1_xboole_0)  =>  ((k2_cat_1 A B (k3_graph_1 A C)) = k1_xboole_0) )  &  ( ((k2_cat_1 A (k3_graph_1 A C) B) = k1_xboole_0)  =>  ((k2_cat_1 A (k4_graph_1 A C) B) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t42_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k5_matrprob A) = (k18_rvsum_1 (k2_entropy1 k1_numbers A))) ) ) ).
tt(t42_enumset1,ax, (! [A:$i] :  ((k2_enumset1 A A A A) = (k1_tarski A)) ) ).
tt(t42_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_eqrel_1 C B) =>  (~  ((r2_hidden A C) &  (! [D:$i] :  ((m1_subset_1 D B) =>  (~  (A = (k11_eqrel_1 B D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( ((k12_euclid B) = k6_numbers)  <=>  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t42_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k23_rvsum_1 A B) = (k3_complex1 (k1_complex2 (k2_euclid_3 A) (k2_euclid_3 B)))) ) ) ) ) ).
tt(t42_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden B (k4_euclid_4 A C D)) & (r2_hidden E (k4_euclid_4 A C D)))  => (r1_tarski (k4_euclid_4 A B E) (k4_euclid_4 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t42_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  ( (B = C)  =>  ((k5_euclid_7 A B) = (k4_rlvect_1 (k10_funcsdom (k2_finseq_1 A)) C)) ) ) ) ) ) ) ) ).
tt(t42_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k6_euclid 3 (k1_euclid_8 A B C)) = (k8_euclid 3 (k8_euclid 3 (k6_euclid 3 (k9_euclid 3 k2_euclid_8 A)) (k9_euclid 3 k3_euclid_8 B)) (k9_euclid 3 k4_euclid_8 C))) ) ) ) ) ) ) ).
tt(t42_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((k5_algstr_0 (k15_euclid A) B B) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ).
tt(t42_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ( (~ (r3_euclidlp A B C))  &  ( (~  (B = (k5_euclid A)) )  &  ( (~  (C = (k5_euclid A)) )  &  (~ (r2_euclidlp A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_exchsort E)) )  =>  ( ((r2_hidden A B) &  ((r2_hidden C B) &  ( (D = (k10_funct_7 (k6_partfun1 B) A C))  &  (B = (k9_xtuple_0 E)) ) ) )  =>  ((k10_funct_7 E A C) = (k3_relat_1 D E)) ) ) ) ) ) ) ) ) ).
tt(t42_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_msafree2 (k5_circcomb A (k11_finseq_1 B C D))) = (k1_enumset1 B C D)) ) ) ) ) ).
tt(t42_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k1_relset_1 k1_numbers A)) =>  ((k1_seq_1 A B) = (k3_square_1 B)) ) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A (k1_relset_1 k1_numbers A)))) ) ) ).
tt(t42_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) k24_sin_cos) A) B) = (k10_real_1 (k9_real_1 (k9_real_1 (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k1_seq_1 k29_sin_cos B)) (k1_seq_1 k30_sin_cos B)) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t42_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k1_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos B) (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k19_sin_cos B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t42_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) & (r2_fdiff_1 B (k10_prob_1 A)))  =>  ( ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))) ) ) ) ) ) ).
tt(t42_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k3_taylor_1))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 (k1_seq_1 k19_sin_cos B) k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k3_taylor_1) A) B) = (k1_real_1 (k1_sin_cos4 B))) ) ) ) ) ) ) ) ).
tt(t42_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k1_real_1 (k10_real_1 1 2))))) &  ( (B = (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers k19_sin_cos 2)))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ( ((k1_seq_1 C D) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k1_real_1 (k10_real_1 1 2))) A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B k3_taylor_1) (k1_real_1 (k10_real_1 1 2))) A) D) = (k10_real_1 (k1_seq_1 k16_sin_cos D) (k7_real_1 1 (k8_real_1 2 (k1_seq_1 k19_sin_cos D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k1_seq_1 k24_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t42_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) A) B) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k1_seq_1 k19_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t42_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_nat_d B A) => (r1_nat_d (k1_pre_ff B) (k1_pre_ff A))) ) ) ) ) ).
tt(t42_fib_num3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  =>  ((k3_fib_num3 A B C) = (k2_nat_1 (k4_nat_1 (k3_fib_num3 A B k6_numbers) (k1_pre_ff (k7_nat_d C 1))) (k4_nat_1 (k3_fib_num3 A B 1) (k1_pre_ff C)))) ) ) ) ) ) ) ).
tt(t42_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (? [D:$i] :  ((m1_finseq_1 D A) & (r1_filerec1 A D B C)) ) ) ) ) ) ) ) ).
tt(t42_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_filter_0 A B C) = (k3_lattices A (k7_lattices A B) C)) ) ) ) ) ) ) ).
tt(t42_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v13_lattices B) & (l3_lattices B)) ) ) )  =>  ((k5_lattices (k7_filter_1 A B)) = (k9_filter_1 A B (k5_lattices A) (k5_lattices B))) ) ) ) ) ) ).
tt(t42_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((v14_lattices A) & (r2_hidden (k6_lattices A) B))  =>  ((r1_filter_2 (u1_struct_0 A) B (k5_filter_2 A)) &  (B = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t42_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k1_funct_1 (k7_finseq_1 B (k9_finseq_1 A)) (k2_nat_1 (k3_finseq_1 B) 1)) = A) ) ) ) ).
tt(t42_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) )  =>  ( ( ((k10_xtuple_0 C) = (k4_finseq_1 A))  &  (B = (k3_relat_1 C A)) )  =>  ((k3_finseq_1 B) = (k3_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(t42_finseq_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_tarski A (k2_finseq_1 C)) & (r1_tarski B (k2_finseq_1 D)))  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden E A) &  ((r2_hidden F B) & (r1_xxreal_0 F E)) ) ) ) ) ) )  <=> (r2_relset_1 k5_numbers k5_numbers (k14_finseq_1 (k2_xboole_0 A B)) (k8_finseq_1 k5_numbers (k14_finseq_1 A) (k14_finseq_1 B)))) ) ) ) ) ) ) ) ).
tt(t42_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  (C = (k6_xcmplx_0 (k3_finseq_1 A) (k4_finseq_4 A B))) )  =>  ((k4_finseq_1 (k6_finseq_4 A B)) = (k2_finseq_1 C)) ) ) ) ) ) ) ).
tt(t42_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k3_finseq_1 (k1_finseq_5 A C B)) = (k4_finseq_4 C B)) ) ) ) ) ) ) ) ).
tt(t42_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~  (B = k1_xboole_0) )  => (r2_hidden (k7_partfun1 A B 1) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t42_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B B)))) )  =>  ((r7_binop_1 B F E) => (r2_funct_2 A B (k1_partfun1 A B B B (k9_funcop_1 B A E D C) F) (k9_funcop_1 B A E (k1_partfun1 A B B B D F) (k3_funct_2 B B F C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (k7_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k10_fintopo2 A B))) ) ) ) ) ).
tt(t42_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k9_fintopo3 A (k9_subset_1 (u1_struct_0 A) B C) D) = (k9_subset_1 (u1_struct_0 A) (k9_fintopo3 A B D) (k9_fintopo3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t42_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) & (v4_fin_topo B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_fintopo6 A C) &  ( (~ (r1_xboole_0 B C))  &  (~ (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k7_flang_1 A B C) (k8_flang_1 A B))) ) ) ) ) ).
tt(t42_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k1_flang_2 A (k7_flang_1 A B C) D E) (k1_flang_2 A B (k3_xcmplx_0 C D) (k3_xcmplx_0 C E)))) ) ) ) ) ) ) ) ) ).
tt(t42_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k1_flang_3 A B C) (k2_flang_2 A B)) = (k6_flang_1 A (k2_flang_2 A B) (k1_flang_3 A B C))) ) ) ) ) ) ).
tt(t42_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((v5_relat_1 (k1_funct_1 (k8_fomodel0 B) A) C) & (r2_hidden A (k3_finseq_2 (k3_finseq_2 B))))  => (m2_finseq_1 A (k3_finseq_2 C))) ) ) ) ) ) ).
tt(t42_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_frechet A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_yellow_8 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ( ((k9_xtuple_0 D) = k5_numbers)  &  ( ((k10_xtuple_0 D) = C)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 E F) => (r1_tarski (k1_funct_1 D F) (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  ( ((r7_fsm_1 A B C D) & (r7_fsm_1 A B D E))  => (r7_fsm_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((k3_funct_2 A A (k6_funcop_1 A A B (k6_partfun1 A) D) C) = (k5_binop_1 A B C (k3_funct_2 A A D C))) ) ) ) ) ) ) ) ) ).
tt(t42_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) &  ( ((k10_xtuple_0 B) = (k9_xtuple_0 A))  &  ((k3_relat_1 B A) = (k4_relat_1 (k10_xtuple_0 A))) ) )  =>  (B = (k2_funct_1 A)) ) ) ) ) ) ).
tt(t42_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r1_tarski C A) =>  ( ( (B = k1_xboole_0)  &  (~  (A = k1_xboole_0) ) )  | (r1_tarski C (k8_relset_1 A B D (k7_relset_1 A B D C)))) ) ) ) ) ) ) ).
tt(t42_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((r2_hidden A C) => (r2_hidden (k1_funct_1 (k6_funct_3 B C) A) B)) ) ) ) ) ).
tt(t42_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) (k9_xtuple_0 C)) <=> (r2_hidden (k4_tarski B A) (k9_xtuple_0 (k2_funct_4 C)))) ) ) ) ) ).
tt(t42_funct_5,ax, ( ((k1_funct_5 k1_xboole_0) = k1_xboole_0)  &  ((k3_funct_5 k1_xboole_0) = k1_xboole_0) ) ).
tt(t42_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 (k7_funct_6 (k7_funcop_1 A B))) = (k1_funct_2 A (k9_xtuple_0 B)))  &  ( ((k10_xtuple_0 (k7_funct_6 (k7_funcop_1 A B))) = (k1_funct_2 A (k10_xtuple_0 B)))  &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden C (k1_funct_2 A (k9_xtuple_0 B))) =>  ((k1_funct_1 (k7_funct_6 (k7_funcop_1 A B)) C) = (k3_relat_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t42_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k5_funct_7 (k7_finseq_1 B (k9_finseq_1 C)) A) = (k7_finseq_1 (k5_funct_7 B A) (k9_finseq_1 (k1_funct_1 C (k1_funct_1 (k5_funct_7 B A) (k2_nat_1 (k3_finseq_1 B) 1)))))) ) ) ) ) ) ).
tt(t42_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 B k1_numbers k1_numbers) => (v4_funct_8 (k15_valued_1 k1_numbers k1_numbers B A) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t42_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v21_functor0 C A B) &  ((v13_functor0 C A B) &  ((v10_functor0 C A B) & (v7_functor0 C A B)) ) )  => (v13_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t42_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E A B) & (m2_functor0 E A B))  =>  (! [F:$i] :  ((m1_functor3 F A B C E) =>  (! [G:$i] :  ((m1_functor3 G A B E D) =>  (! [H:$i] :  ((m1_functor3 H A B C D) =>  ( ((r8_pboole (u1_struct_0 A) H (k5_functor2 A B C E D F G)) &  ((r1_functor3 A B C E) & (r1_functor3 A B E D)) )  => (r8_pboole (u1_struct_0 A) (k8_functor3 A B C D H) (k5_functor2 A B D E C (k8_functor3 A B E D G) (k8_functor3 A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k6_fuzzy_1 A B (k5_fuzzy_1 A)) (k3_fuzzy_1 A B))) ) ) ) ).
tt(t42_fuzzy_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k7_real_1 C (k2_square_1 A B)) = (k2_square_1 (k7_real_1 C A) (k7_real_1 C B)))  &  ((k7_real_1 C (k1_square_1 A B)) = (k1_square_1 (k7_real_1 C A) (k7_real_1 C B))) ) ) ) ) ) ) ) ).
tt(t42_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ( (~  ( (~ (v3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers C B)))  & (v3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B))) )  &  (~  ( (~ (v3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B)))  & (v3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers C B))) ) ) ) ) ) ) ) ) ) ).
tt(t42_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k8_fvsum_1 A B C D) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B)))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t42_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m2_gcd_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r5_gcd_1 A B D E) => (r5_gcd_1 A C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H k6_numbers k6_numbers A B C) = (k9_genealg1 F G H A B C))  &  ( ((k11_genealg1 F G H k6_numbers D k6_numbers B C) = (k9_genealg1 F G H D B C))  &  ( ((k11_genealg1 F G H k6_numbers D A k6_numbers C) = (k9_genealg1 F G H D A C))  &  ( ((k11_genealg1 F G H k6_numbers D A B k6_numbers) = (k9_genealg1 F G H D A B))  &  ( ((k11_genealg1 F G H E k6_numbers k6_numbers B C) = (k9_genealg1 F G H E B C))  &  ( ((k11_genealg1 F G H E k6_numbers A k6_numbers C) = (k9_genealg1 F G H E A C))  &  ( ((k11_genealg1 F G H E k6_numbers A B k6_numbers) = (k9_genealg1 F G H E A B))  &  ( ((k11_genealg1 F G H E D k6_numbers k6_numbers C) = (k9_genealg1 F G H E D C))  &  ( ((k11_genealg1 F G H E D k6_numbers B k6_numbers) = (k9_genealg1 F G H E D B))  &  ((k11_genealg1 F G H E D A k6_numbers k6_numbers) = (k9_genealg1 F G H E D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden (k1_domain_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) D E)) (k5_geomtrap A F G)) <=> (r2_geomtrap A F G B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k19_gfacirc1 A B C)) = (k2_xboole_0 (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) (k1_tarski (k21_gfacirc1 A B C)))) ) ) ) ).
tt(t42_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ( ((r2_hidden C (k24_glib_000 A B)) => (r2_hidden C (k6_glib_000 A)))  &  ((r2_hidden C (k25_glib_000 A B)) => (r2_hidden C (k7_glib_000 A))) ) ) ) ) ) ) ).
tt(t42_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k8_glib_001 A B C C) = (k12_finseq_1 (k6_glib_000 A) (k5_glib_001 A B C))) ) ) ) ) ) ) ) ).
tt(t42_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ((r2_hidden C (k28_glib_000 A (k4_glib_001 A B))) =>  ((r2_hidden C (k14_glib_001 A B)) | (v5_glib_001 (k10_glib_001 A B C) A)) ) ) ) ) ) ) ).
tt(t42_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k6_glib_003 A) = (k6_glib_003 (k13_glib_003 A B C))) ) ) ) ) ).
tt(t42_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k15_glib_004 A (k16_glib_004 A) B)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k17_glib_004 A)))) ) ) ) ).
tt(t42_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t42_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 2))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 (k2_goboard2 D)) (k2_nat_1 B 1)) |  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 2)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C D) & (r1_xxreal_0 (k2_nat_1 A 1) B)) ) )  =>  ( ((k5_gobrd13 C D A) = (k5_gobrd13 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) D A))  &  ((k4_gobrd13 C D A) = (k4_gobrd13 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k8_pscomp_1 (k3_topreal1 2 A)) = (k8_pscomp_1 (k3_goboard9 A))) ) ) ).
tt(t42_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_graph_1 F C) =>  (! [G:$i] :  ((m2_graph_1 G C) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k3_finseq_1 F)) &  ( (G = (k2_graph_2 (u4_struct_0 C) F A B))  &  ((r1_graph_2 C D F) &  (E = (k2_graph_2 (u1_struct_0 C) D A (k2_nat_1 B 1))) ) ) ) ) )  => (r1_graph_2 C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k8_graph_3 B C D))) =>  ( ( (E = D)  & (r2_hidden (u4_struct_0 B) A))  =>  ( ((k2_graph_3 (k8_graph_3 B C D) E A) = (k2_xboole_0 (k2_graph_3 B D A) (k1_tarski (u4_struct_0 B))))  & (r1_xboole_0 (k2_graph_3 B D A) (k1_tarski (u4_struct_0 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v7_graph_1 B A) & (m2_graph_1 B A))  =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  ((r2_hidden B (k6_graph_5 A C)) => (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t42_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) => (r2_graphsp C C A B)) ) ) ) ) ) ).
tt(t42_grcat_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k25_grcat_1 A))) =>  (! [C:$i] :  ((m2_grcat_1 C (k17_grcat_1 A)) =>  ( (B = C)  =>  ((k4_cat_1 (k25_grcat_1 A) B) = (k21_grcat_1 (k17_grcat_1 A) C)) ) ) ) ) ) ) ) ).
tt(t42_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  =>  ((k4_xboole_0 (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D E)) (k2_polynom1 (k15_pre_poly A) C (k6_groeb_3 A B C D (k2_nat_1 E 1)))) = (k1_tarski (k3_termord A B C (k6_groeb_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k1_group_11 A (k1_group_11 A B C) C) = (k2_group_11 A (k1_group_11 A B C) C)) ) ) ) ) ) ) ).
tt(t42_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k6_group_1 A (k1_group_1 A)) = 1) ) ) ).
tt(t42_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t42_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A (k5_group_3 B D C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k2_group_3 B C E))  & (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r1_struct_0 (k6_group_4 A) B) <=>  (~ (v1_group_4 B A)) ) ) ) ) ) ).
tt(t42_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_5 A B C C) = (k2_group_3 A (k6_algstr_0 A (k2_group_5 A B (k2_group_1 A C)) (k2_group_5 A B C)) C)) ) ) ) ) ) ) ).
tt(t42_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((k9_group_6 A B (k7_group_6 A B)) = A) ) ) ) ) ).
tt(t42_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_9 B A) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) ) )  =>  ((v7_struct_0 B) =>  ((k4_group_9 A B) = B) ) ) ) ) ).
tt(t42_hausdorf,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ( ((v2_compts_1 B (k15_euclid A)) &  ((v2_compts_1 C (k15_euclid A)) & (v2_compts_1 D (k15_euclid A))) )  => (r1_xxreal_0 (k3_hausdorf A B D) (k7_real_1 (k3_hausdorf A B C) (k3_hausdorf A C D)))) ) ) ) ) ) ) ) ) ).
tt(t42_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((k3_helly A B C D) = (k3_helly A C B D)) ) ) ) ) ) ) ) ) ).
tt(t42_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear D k1_complfld A A) &  ((v2_bilinear D k1_complfld A A) &  ((v4_bilinear D k1_complfld A A) &  ((v2_hermitan D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k1_complfld)) =>  ( ((k17_complex1 F) = 1)  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) F) C)) (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) F) C))) = (k3_rlvect_1 k1_complfld (k5_algstr_0 k1_complfld (k5_algstr_0 k1_complfld (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B B) (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) (k8_group_1 k1_complfld F (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B)))) (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) (k8_group_1 k1_complfld (k2_complfld F) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C)))) (k8_group_1 k1_complfld (k1_hahnban1 (k3_square_1 E) k6_numbers) (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ( ((k1_seq_1 (k1_taylor_2 (k1_taylor_1 A) (k2_rcomp_1 (k1_real_1 C) C) D) B) = k6_numbers)  &  ((k1_seq_1 (k1_taylor_2 (k1_taylor_1 A) (k2_rcomp_1 (k1_real_1 C) C) D) A) = (k2_newton D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k3_hilbert1 A B) (k4_hilbert1 A C)) (k4_hilbert1 B C)) k6_hilbert1)) ) ) ) ) ) ).
tt(t42_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  ((r2_hidden A k6_hilbert1) => (v1_hilbert3 A)) ) ) ).
tt(t42_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((k2_hurwitz k1_complfld (k7_hurwitz A)) = (k2_hurwitz k1_complfld A)) ) ) ).
tt(t42_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ( (B = (k1_funct_1 (k15_idea_1 A D) C))  & (r1_xxreal_0 4 (k3_finseq_1 C)))  =>  ((r1_xxreal_0 4 (k3_finseq_1 B)) &  ((r1_idea_1 A (k1_recdef_1 B 1)) &  ((r1_idea_1 A (k1_recdef_1 B 2)) &  ((r1_idea_1 A (k1_recdef_1 B 3)) & (r1_idea_1 A (k1_recdef_1 B 4))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_ideal_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (m2_ideal_1 (k2_partfun1 k5_numbers (u1_struct_0 A) C (k2_finseq_1 D)) A B)) ) ) ) ) ) ) ) ).
tt(t42_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) &  ((r2_incsp_1 A C B) &  (~ (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v2_funct_1 E)) )  =>  ((r3_pua2mss1 A B D E) => (r3_msualg_3 A (k11_msafree A (k3_relat_1 D C)) (k1_instalg1 A B (k11_msafree B C) D E) (k3_instalg1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (A = (k3_real_1 (k1_int_1 A) (k4_int_1 A))) ) ) ).
tt(t42_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((r1_int_1 (k3_int_2 A B) (k6_xcmplx_0 C D)) &  (! [E:$i] :  ((v1_int_1 E) =>  (~  ( (! [F:$i] :  ((v1_int_1 F) =>  ( ( ((k6_int_1 (k6_xcmplx_0 F D) A) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 F C) B) = k6_numbers) )  => (r2_int_1 F (k2_xcmplx_0 D (k3_xcmplx_0 A E)) (k2_int_2 A B))) ) )  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k5_int_1 A (k3_int_2 A B)) E) (k5_int_1 (k6_xcmplx_0 C D) (k3_int_2 A B))) (k5_int_1 B (k3_int_2 A B))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ( (~ (r1_xxreal_0 A 2))  =>  ((k2_int_5 2 A) = (k1_newton (k4_xcmplx_0 1) (k3_nat_d (k7_nat_d (k1_pepin A) 1) 8))) ) ) ) ).
tt(t42_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_relat_1 A k4_numbers) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finseq_1 B) &  ((v1_partfun3 B) & (v1_int_6 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( ((r1_xxreal_0 k6_numbers C) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) => (r2_int_1 C (k1_funct_1 A E) (k1_funct_1 B E))) ) )  &  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) => (r2_int_1 D (k1_funct_1 A E) (k1_funct_1 B E))) ) ) ) ) )  =>  ((r1_xxreal_0 (k19_rvsum_1 B) C) |  ((r1_xxreal_0 (k19_rvsum_1 B) D) |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k19_sin_cos D)))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t42_integr12,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( ((k1_seq_1 C E) = (k12_binop_2 (k1_seq_1 k16_sin_cos E) (k5_prepower (k1_seq_1 k19_sin_cos E) (k23_binop_2 A 1))))  &  (~  ((k1_seq_1 k19_sin_cos E) = k6_numbers) ) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) )  =>  ((r1_xxreal_0 A k6_numbers) |  ((k2_integra5 B C) = (k10_binop_2 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)) (k18_binop_2 1 A)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) (k1_taylor_1 A)) (k18_binop_2 1 A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos9 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 2)))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t42_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t42_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (k1_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((r1_funct_2 B (k1_euclid A) B (u1_struct_0 (k4_real_ns1 A)) C D) &  ((v1_integr15 C A B) & (v2_integr15 C A B)) )  =>  ((v1_integr18 D (k4_real_ns1 A) B) &  ((k10_integr15 A B C) = (k4_integr18 (k4_real_ns1 A) B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k1_seq_1 (k14_integra1 (k4_integra1 A C B)) (k3_finseq_1 B)) = (k6_integra1 A C B)) ) ) ) ) ) ) ).
tt(t42_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k10_real_1 (k8_real_1 k32_sin_cos 3) 2)))  =>  ((k2_integra5 A k19_sin_cos) = (k1_real_1 1)) ) ) ) ).
tt(t42_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( (C = (k1_rcomp_1 (k9_real_1 A (k8_real_1 (k8_real_1 2 B) k32_sin_cos)) (k7_real_1 A (k8_real_1 (k8_real_1 2 B) k32_sin_cos))))  => (r1_integra9 C k16_sin_cos k19_sin_cos)) ) ) ) ) ) ) ).
tt(t42_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_interva1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ( ( (B = (k2_interva1 A D E))  &  (C = (k2_interva1 A F G)) )  =>  ((k9_interva1 A B C) = (k2_interva1 A (k7_subset_1 A D G) (k7_subset_1 A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k4_intpro_1 A C) B)) k8_intpro_1)) ) ) ) ) ) ).
tt(t42_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F A B) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_cat_1 H B C) =>  (! [I:$i] :  ((m2_cat_1 I B C) =>  (! [J:$i] :  ((m2_nattra_1 J A B D E) =>  (! [K:$i] :  ((m2_nattra_1 K A B E F) =>  (! [L:$i] :  ((m2_nattra_1 L B C G H) =>  (! [M:$i] :  ((m2_nattra_1 M B C H I) =>  ( ((r2_nattra_1 A B D E) &  ((r2_nattra_1 A B E F) &  ((r2_nattra_1 B C G H) & (r2_nattra_1 B C H I)) ) )  => (r2_funct_2 (u1_struct_0 A) (u4_struct_0 C) (k6_isocat_1 A B C D F G I (k7_nattra_1 A B D E F J K) (k7_nattra_1 B C G H I L M)) (k7_nattra_1 A C (k9_cat_1 A B C D G) (k9_cat_1 A B C E H) (k9_cat_1 A B C F I) (k6_isocat_1 A B C D E G H J L) (k6_isocat_1 A B C E F H I K M)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k1_tops_1 A (k2_pre_topc A B)) = (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))  |  ((k2_pre_topc A (k1_tops_1 A B)) = (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B)))) )  => (v3_isomichi B A)) ) ) ) ) ).
tt(t42_jgraph_1,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ( ((k3_finseq_1 (k2_goboard1 A)) = (k3_finseq_1 A))  &  ( ((k1_seq_1 (k2_goboard1 A) 1) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)))  &  ((k1_seq_1 (k2_goboard1 A) (k3_finseq_1 A)) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) ) ) ) ) ).
tt(t42_jgraph_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) =>  (~  ( (D = k6_numbers)  &  ( (E = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_2_jgraph_2)  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A D)) = (k1_real_1 1))  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A E)) = 1)  &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A D))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A D)) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A E))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A E)) 1) &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B D)) = (k1_real_1 1))  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B E)) = 1)  &  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B D))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B D)) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B E))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B E)) 1) &  ((r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jgraph_3,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ( (A = (k2_funct_1 k1_jgraph_3))  & (v5_pre_topc A (k15_euclid 2) (k15_euclid 2))) ) ) ).
tt(t42_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  & (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (A = a_0_6_jgraph_5)  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))))))) )  =>  (~  ((v3_tops_2 B k5_topmetr (k1_pre_topc (k15_euclid 2) (k9_jordan6 A))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( ((k1_funct_1 B E) = C)  &  ( ((k1_funct_1 B F) = D)  &  ((r2_hidden E (k1_rcomp_1 k6_numbers 1)) & (r2_hidden F (k1_rcomp_1 k6_numbers 1))) ) )  =>  ( (~  ( (~ (r1_xxreal_0 F E))  & (r1_xxreal_0 (k17_euclid C) (k17_euclid D))) )  &  (~  ( (~ (r1_xxreal_0 (k17_euclid C) (k17_euclid D)))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k1_funct_1 B k6_numbers) = (k22_pscomp_1 A))  &  ((k1_funct_1 B 1) = (k18_pscomp_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k10_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid A C)) ) ) ) ) ) ) ) ) ) ).
tt(t42_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) &  ((r1_xxreal_0 G (k18_euclid B)) &  ((r1_xxreal_0 (k18_euclid B) H) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D))) & (r1_xxreal_0 D B)) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) 1 C)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) 1 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_jordan1 A) =>  ( (~  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = k1_xboole_0) )  &  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) &  ( ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) A) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  &  ((r1_xboole_0 B C) &  ( ((k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) B) B) = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) C) C))  &  ( (D = B)  &  ( (E = C)  &  ((v3_connsp_1 D (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) &  ((v3_connsp_1 E (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  (~  ((v3_connsp_1 F (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) &  ( (~  (F = D) )  &  (~  (F = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k10_xtuple_0 (k1_jordan1e B A)))) ) ) ) ) ) ) ) ) ).
tt(t42_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) (k2_goboard9 A))) = (k3_goboard9 A)) ) ) ).
tt(t42_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k1_jordan8 B A))) &  ((r2_hidden (k18_pscomp_1 B) (k3_goboard5 (k1_jordan8 B A) 1 C)) &  (~  ((k18_pscomp_1 B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 2 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) &  ((r2_hidden D B) &  ((r2_hidden E C) &  ((k4_jordan1k A B C) = (k1_topreal6 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k1_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k7_pscomp_1 A))) (k1_rltopsp1 (k15_euclid 2) (k2_jordan21 A) (k19_euclid (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2) (k9_pscomp_1 A))))) ) ).
tt(t42_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) & (r2_hidden B (k3_topreal1 2 A))) ) ) )  =>  ( (B = (k1_funct_1 A (k3_finseq_1 A)))  |  ( (B = (k1_funct_1 A 1))  | (v4_topreal1 (k2_jordan3 A B))) ) ) ) ) ) ) ).
tt(t42_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (C = (a_2_2_jordan2c A B))  &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (~  (D = (k1_rlvect_1 (k15_euclid A) E F)) )  &  (~  (E = (k1_rlvect_1 (k15_euclid A) D F)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden F C) &  ((r2_hidden G C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D F) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) F G) C) & (r1_tarski (k1_rltopsp1 (k15_euclid A) G E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) => (r1_tarski (k3_topreal1 2 (k2_jordan3 A B)) (k3_topreal1 2 A))) ) ) ) ) ).
tt(t42_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal1 2 A 1) (k2_topreal1 2 A (k7_nat_d (k3_finseq_1 A) 1))) = (k1_tarski (k1_funct_1 A 1))) ) ) ).
tt(t42_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  ( (E = (a_2_1_jordan5d A C))  &  ( ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C)))  &  (D = (k6_seq_4 E)) ) ) ) ) ) )  => (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C)) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden E B) &  ( (~  (E = C) )  &  (~  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r1_topreal1 (k15_euclid A) B C D) &  (! [E:$i] :  ((m1_borsuk_2 E (k15_euclid A) B C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) D)))))) )  =>  (~  ( ((k2_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) D)) F) = D)  &  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r2_abian (u1_struct_0 A) (k10_knaster A B) B) &  (? [C:$i] :  ((v3_ordinal1 C) &  ((r1_ordinal1 (k1_card_1 C) (k1_card_1 (u1_struct_0 A))) &  ((k6_knaster A B (k6_lattices A) C) = (k10_knaster A B)) ) ) ) ) ) ) ) ) ).
tt(t42_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) = (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)))) ) ).
tt(t42_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) =>  ((k3_funct_2 C (u1_struct_0 A) E F) = B) ) ) )  =>  ( (D = k1_xboole_0)  |  ((k3_lattice2 C A D E) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k15_lattice3 A (k6_domain_1 (u1_struct_0 A) B)) = B)  &  ((k16_lattice3 A (k6_domain_1 (u1_struct_0 A) B)) = B) ) ) ) ) ) ).
tt(t42_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((r2_hidden (k5_lattices A) B) & (r2_hidden (k6_lattices A) B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C (k4_lattice4 A B)) &  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (u1_struct_0 A))) =>  (~  ((r1_tarski D (k4_lattice4 A B)) &  ((k2_lattice2 (u1_struct_0 A) A C (k5_lattice4 A)) = (k2_lattice4 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_lattice5 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 D C A) &  ((v2_lattice5 D C A) &  ((v3_lattice5 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ( (C = (k3_tarski (a_2_1_lattice5 A B)))  &  ( (D = (k3_tarski (a_2_2_lattice5 A B)))  &  ((r3_orders_2 A (k3_lattice5 C A D E F) (k13_lattice3 A G H)) &  (! [I:$i] :  ((m1_subset_1 I C) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  (! [K:$i] :  ((m1_subset_1 K C) =>  (~  ( ((k3_lattice5 C A D E I) = G)  &  ( ((k3_lattice5 C A D J K) = G)  &  ( ((k3_lattice5 C A D I J) = H)  &  ((k3_lattice5 C A D K F) = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 (k15_glib_000 A) B))  &  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (C = (k10_lexbfs A (k13_lexbfs A (k16_lexbfs A) B)))  &  (! [D:$i] :  ( ((r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) =>  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))) |  ((k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) (k1_nat_1 B 1))) D) = (k1_finsub_1 (k1_zfmisc_1 k5_numbers) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) D) (k6_domain_1 k5_numbers (k7_nat_d (k15_glib_000 A) B)))) ) )  &  ( (~  ((r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) &  (~ (r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B))))) ) )  =>  ((k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) (k1_nat_1 B 1))) D) = (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v1_limfunc1 A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 B C))) ) )  => (v1_limfunc1 B)) ) ) ) ) ).
tt(t42_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_limfunc2 C A) =>  ( ((k2_limfunc2 C A) = B)  <=>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k1_relset_1 k1_numbers C)) & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 C F) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r1_limfunc3 C A) &  ((k1_limfunc3 B A) = (k1_limfunc3 C A)) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((r1_tarski (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E))) (k3_xboole_0 (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C)) (k9_xtuple_0 D))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A E) A) (k2_rcomp_1 A (k7_real_1 A E)))) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) ) ) ) ) ) )  |  ((r1_limfunc3 D A) &  ((k1_limfunc3 D A) = (k1_limfunc3 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r6_limfunc2 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) & (r1_xxreal_0 (k1_seq_1 B E) (k1_limfunc3 B A))) ) ) ) ) ) ) )  | (r3_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t42_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ((v3_lopban_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k16_lopban_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k16_lopban_1 A B)))))) )  =>  ((v1_rsspace3 C (k16_lopban_1 A B)) => (v3_normsp_1 C (k16_lopban_1 A B))) ) ) ) ) ) ) ) ).
tt(t42_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (r1_xxreal_0 1 (k1_normsp_0 A (k5_algstr_0 A (k5_struct_0 A) B))))  =>  ((v25_algstr_0 B A) &  ((k9_algstr_0 A B) = (k1_lopban_3 A (k5_lopban_3 A (k5_algstr_0 A (k5_struct_0 A) B)))) ) ) ) ) ) ) ).
tt(t42_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( ((r2_hidden E (k9_lpspace1 B C D)) &  ((r2_hidden F (k9_lpspace1 B C D)) &  ((k13_lpspace1 B C D E) = (k13_lpspace1 B C D F)) ) )  =>  ((k13_lpspace1 B C D (k26_valued_1 B k1_numbers E A)) = (k13_lpspace1 B C D (k26_valued_1 B k1_numbers F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ((r1_lpspace1 A B C D E) =>  ((k5_lpspace2 A B C D F) = (k5_lpspace2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r2_hidden A k13_ltlaxio1) | (r2_hidden A B))  => (r8_ltlaxio1 B A)) ) ) ) ) ).
tt(t42_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A C D) A))  => (v2_cqc_the1 (k8_cqc_lang A B D) A)) ) ) ) ) ) ) ) ) ).
tt(t42_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_mathmorp A B B) = B) ) ) ) ) ).
tt(t42_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers B B) =>  ( ((r1_xxreal_0 k6_numbers A) & (v4_matrix10 C))  => (v4_matrix10 (k5_matrix10 B A C))) ) ) ) ) ) ) ).
tt(t42_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  ((r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) D (k2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) C)) =>  ((k2_matrix11 A B C) = (k2_matrix11 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 B k5_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k5_numbers (k4_finseq_2 C k5_numbers)) =>  ( ( (E = (k1_finseq_2 (k3_finseq_1 D)))  &  (F = (k1_finseq_2 (k1_matrix_1 D))) )  =>  ((k1_matrix13 A D B C E F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrix14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_matrix_1 F A B C) => (m1_matrix_1 (k2_finseq_7 (k3_finseq_2 A) F D E) A B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  ((r1_tarski (k10_xtuple_0 E) (k4_finseq_1 C)) =>  ((r1_xxreal_0 A k1_xboole_0) | (r1_tarski (k4_matrix15 B C D) (k4_matrix15 B (k1_matrix13 (u1_struct_0 B) C A (k5_card_1 (k2_finseq_1 (k1_matrix_1 C))) E (k5_matrix13 (k2_finseq_1 (k1_matrix_1 C)))) (k1_matrix13 (u1_struct_0 B) D A (k5_card_1 (k2_finseq_1 (k1_matrix_1 D))) E (k5_matrix13 (k2_finseq_1 (k1_matrix_1 D))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v2_matrix16 C (u1_struct_0 A)) =>  ((k1_matrix16 (u1_struct_0 A) (k9_fvsum_1 A C B)) = (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k1_matrix16 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(t42_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 B)))  =>  ( ((r2_hidden A (k4_finseq_1 D)) &  ((k1_funct_1 D A) = C) )  =>  ((k3_finseq_1 C) = (k1_matrix_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k3_matrix_3 A B C) = (k2_matrix_3 A (k3_matrix_3 A (k2_matrix_3 A B) (k2_matrix_3 A C)))) ) ) ) ) ) ) ) ).
tt(t42_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) C) = (k12_matrix_1 B A)) )  <=> (v4_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t42_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (r1_matrix_8 A B D C))  => (v1_matrix_6 D A B)) ) ) ) ) ) ) ) ) ).
tt(t42_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 3 2 1)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 3 2 1) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 3 2 1) (k2_finseq_1 3) (k2_finseq_1 3)) &  ( (~ (v5_matrix_2 (k3_finseq_4 k5_numbers 3 2 1) 3))  & (m1_subset_1 (k3_finseq_4 k5_numbers 3 2 1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(t42_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ((k3_finseq_1 B) = (k1_matrix_1 C))  =>  ((k5_matrixc1 B (k1_complsp2 (k8_matrix_1 k2_numbers (k1_matrixc1 C) A))) = (k1_complsp2 (k5_matrixc1 (k8_matrix_1 k2_numbers (k1_matrixc1 C) A) (k1_complsp2 B)))) ) ) ) ) ) ) ) ).
tt(t42_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E (u1_struct_0 B)) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ( ((r2_hidden A (k4_finseq_1 D)) &  ((k1_matrix_1 D) = (k1_matrix_1 (k8_matrix_2 B A D))) )  =>  ((k8_matrix_2 B (k2_nat_1 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 B) E)) A) (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) E (k4_matrixj1 (u1_struct_0 B) D)))) = (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) E (k4_matrixj1 (u1_struct_0 B) (k8_matrix_2 B A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((k3_matrixr1 A (k8_matrixr1 (k3_finseq_1 A) (k1_matrix_1 A))) = A) ) ) ).
tt(t42_matrixr2,ax, (! [A:$i] :  ((m1_matrix_1 A k1_numbers k6_numbers k6_numbers) =>  ((k3_matrixr2 k6_numbers A) = 1) ) ) ).
tt(t42_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ((v7_struct_0 B) <=>  ((k1_vectsp_9 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t42_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ((m1_matrlin F A B) =>  (! [G:$i] :  ((m1_matrlin G A C) =>  ((k10_matrlin A B C (k3_matrlin A B C D E) F G) = (k3_matrix_3 A (k10_matrlin A B C D F G) (k10_matrlin A B C E F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C B) & (v5_matroid0 C A)) ) ) )  => (v3_pre_topc B A)) ) ) ) ) ).
tt(t42_matrprob,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ( (A = (k6_matrixr1 B C))  <=>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 A) = (k1_matrix_1 C))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 A))) =>  ((k8_matrix_1 k1_numbers A D) = (k12_matrixr1 C (k8_matrix_1 k1_numbers B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A) =>  ((v2_funct_2 (k3_matrtop1 A A B) (u1_struct_0 (k15_euclid A))) <=>  (~  ((k12_matrix_3 A k2_vectsp_1 B) = (k4_struct_0 k2_vectsp_1)) ) ) ) ) ) ) ).
tt(t42_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((k3_zfmisc_1 (k2_tarski A B) (k2_tarski C D) (k2_tarski E F)) = (k6_enumset1 (k3_xtuple_0 A C E) (k3_xtuple_0 A D E) (k3_xtuple_0 A C F) (k3_xtuple_0 A D F) (k3_xtuple_0 B C E) (k3_xtuple_0 B D E) (k3_xtuple_0 B C F) (k3_xtuple_0 B D F))) ) ) ) ) ) ) ).
tt(t42_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v3_xxreal_2 A) <=> (v4_xxreal_2 (k4_measure6 A))) ) ) ).
tt(t42_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) => (r1_tarski (k8_member_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k8_member_1 A B) (k8_member_1 A C)))) ) ) ) ) ) ).
tt(t42_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k9_xtuple_0 (k8_memstr_0 A B C)) = (k2_xboole_0 (k9_xtuple_0 C) (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)))) ) ) ) ) ) ) ).
tt(t42_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ( (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((r1_mesfunc6 A B D F) & (r1_mesfunc6 A B E F)) ) ) )  &  ((r3_mesfunc6 A B C D) &  ((r3_mesfunc6 A B C E) &  ((v6_supinf_2 (k47_valued_1 A k1_numbers k1_numbers E D)) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  & (r1_xxreal_0 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D F)) (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (~  ((r2_mesfun6c A B C D) &  ((r2_mesfun6c A B C E) &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers D E)))  & (r1_xxreal_0 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers D E)) F)) (k3_supinf_2 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers D) F)) (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers (k55_valued_1 A k2_numbers E) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((r1_mesfun7c A B C) => (r1_mesfun7c A B (k2_partfun1 A k2_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(t42_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc1 A B D E) &  (F = (k9_subset_1 A (k1_relset_1 A D) E)) )  => (r1_mesfunc1 A B (k2_partfun1 A k7_numbers D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers B (k47_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B)))) ) ) ) ).
tt(t42_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((v2_mesfunc9 B A) &  ((v1_mesfunc8 B A k7_numbers) &  ((v2_mesfunc9 C A) &  ((v1_mesfunc8 C A k7_numbers) &  ((r2_hidden E (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)) (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)))) &  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G (k9_subset_1 A (k1_relset_1 A (k4_mesfunc5 A k7_numbers B k6_numbers)) (k1_relset_1 A (k4_mesfunc5 A k7_numbers C k6_numbers)))) => (r1_xxreal_0 (k1_mesfunc9 (k4_mesfunc5 A k7_numbers B F) G) (k1_mesfunc9 (k4_mesfunc5 A k7_numbers C F) G))) ) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A B) D) E) (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A C) D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_midsp_1 A (k8_midsp_1 A B (k3_midsp_1 A B C)) (k8_midsp_1 A B (k3_midsp_1 A B C))) = (k8_midsp_1 A B C)) ) ) ) ) ) ) ).
tt(t42_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r1_relset_1 A A (k20_mmlquery A (k18_mmlquery A B) (k18_mmlquery A C)) (k18_mmlquery A (k19_mmlquery A B C)))) ) ) ) ) ).
tt(t42_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((m1_mod_4 D A A (k3_struct_0 A) B C) <=>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k3_rlvect_1 B E F)) = (k3_rlvect_1 C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D E) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F))) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k4_vectsp_1 A B E F)) = (k4_vectsp_1 A C E (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (~  ( (~  (A = k17_modal_1) )  &  ( (! [B:$i] :  ((m1_subset_1 B k3_modal_1) =>  (~  (A = (k16_modal_1 B)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (~  (A = (k10_modal_1 B)) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (~  (A = (k11_modal_1 B)) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  (~  (A = (k12_modal_1 B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F E) <=> (r3_modelc_1 A B C F (k53_modelc_1 A B C D E))) ) )  <=> (r2_abian (k1_zfmisc_1 A) (k51_modelc_1 A B C E) (k58_modelc_1 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r3_modelc_2 A (k5_modelc_2 B C)) &  ( (~ (r2_modelc_2 A B))  &  (~ (r2_modelc_2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t42_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  =>  (! [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  =>  (! [E:$i] :  ( ((v1_modelc_3 E B) &  ((v3_modelc_3 E B) & (l1_modelc_3 E B)) )  =>  (~  ((r6_modelc_3 B D C) &  ((r6_modelc_3 B C E) &  ((r2_hidden A (u1_modelc_3 B C)) &  ((v7_modelc_2 A) &  ( (~ (r2_hidden (k12_modelc_2 A) (u1_modelc_3 B C)))  &  (~  ((r2_hidden (k11_modelc_2 A) (u1_modelc_3 B C)) & (r2_hidden A (u1_modelc_3 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_moebius1,ax, ((k3_uproots k5_numbers (k4_moebius1 (k3_moebius1 1))) = 1) ).
tt(t42_monoid_0,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_monoid_0)) <=> (v1_int_1 A)) ) ).
tt(t42_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (m1_subset_1 (k20_monoid_1 A B) (u1_struct_0 (k19_monoid_1 A)))) ) ) ) ).
tt(t42_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 C E)) =>  ((k9_msaterm A B C (k5_msaterm A B C E F) D) = (k3_funct_2 (k1_funct_1 C E) (k1_funct_1 (u3_msualg_1 A B) E) (k1_msualg_3 (u1_struct_0 A) C (u3_msualg_1 A B) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v2_relat_1 C) & (m3_pboole C A (k1_mboolean A B)))  => (r2_pboole A (k4_mssubfam A B C) (k2_mboolean A C))) ) ) ) ) ).
tt(t42_msualg_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C A B B) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 B D)) =>  ((r2_hidden (k4_tarski E F) (k1_msualg_4 A B B (k3_msualg_5 A B C) D)) <=> (r2_rewrite1 (k1_msualg_4 A B B C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C A) & (r2_hidden (k4_tarski C (k2_xcmplx_0 D A)) (u1_orders_2 (k6_mycielsk A B))))  => (r2_hidden (k4_tarski C D) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ).
tt(t42_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_card_1 (k5_card_1 A)) = (k5_card_1 (k1_nat_1 A 1))) ) ) ).
tt(t42_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (~  (A = k6_numbers) )  =>  ((k1_polynom2 k10_newton (k12_nat_3 (k1_newton B A))) = (k1_tarski B)) ) ) ) ) ) ).
tt(t42_nat_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) & (r1_xxreal_0 (k1_funct_1 A B) k6_numbers)) ) ) )  & (r1_xxreal_0 (k21_rvsum_1 A) k6_numbers)) ) ) ) ).
tt(t42_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k7_nat_d A C) (k7_nat_d B C))) ) ) ) ) ) ) ).
tt(t42_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v2_nattra_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  ((r1_nattra_1 B A C D) => (r2_funct_2 (u4_struct_0 B) (u4_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(t42_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r8_ncfcont1 A B D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) C) &  ((v9_clvect_1 E A) & (r2_hidden (k7_clvect_1 A E) C)) )  =>  ((v3_normsp_1 (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D) B) &  ((k7_partfun1 (u1_struct_0 B) D (k7_clvect_1 A E)) = (k6_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_nfcont_1 D A) &  ((r1_tarski D (k1_relset_1 (u1_struct_0 A) C)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C D))) )  =>  ((r2_ndiff_1 D A B C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E D) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A B)) (k4_ndiff_1 A B C D) E) = (k4_struct_0 (k16_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  &  ((r2_relset_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B F) E) & (r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C)) ) ) ) )  =>  ((r1_ndiff_3 (k4_real_ns1 A) E D) &  ( ((k1_ndiff_3 (k4_real_ns1 A) E D) = (k1_funct_1 (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) (k12_finseq_1 k5_numbers 1)))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k1_funct_1 (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) (k12_finseq_1 k1_numbers G)) = (k1_rlvect_1 (k4_real_ns1 A) (k1_ndiff_3 (k4_real_ns1 A) E D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k23_binop_2 (k3_finseq_1 C) 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k7_partfun1 (u1_struct_0 A) C D) = (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) B (k23_binop_2 D 1)))) ) ) ) )  =>  ((k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B 1) (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B))) = (k4_rlvect_1 A C)) ) ) ) ) ) ) ) ).
tt(t42_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = 1) )  &  ( (~  (A = k6_numbers) )  &  ((r1_nat_d A (k2_nat_1 (k9_newton B) 1)) & (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ).
tt(t42_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r5_nfcont_1 B C A D) =>  ((r5_nfcont_1 B C A (k5_vfunct_1 (u1_struct_0 B) C D)) & (r6_nfcont_1 B A (k3_normsp_0 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t42_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_euclid A)) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A))  => (r2_nfcont_4 A (k1_pdiff_1 B A) C)) ) ) ) ) ) ) ).
tt(t42_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k9_normform A B) = B) ) ) ) ).
tt(t42_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) D) = (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t42_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_orders_1 A B) => (r3_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t42_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_orders_2 C A B) =>  (! [D:$i] :  ((m2_orders_2 D A B) =>  ((r2_xboole_0 C D) <=> (m1_orders_2 C A D)) ) ) ) ) ) ) ) ) ).
tt(t42_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k11_ordinal2 C A) (k11_ordinal2 C B))) ) ) ) ) ) ) ).
tt(t42_ordinal3,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_ordinal2 B)) ) )  =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ((v4_ordinal1 (k4_ordinal2 A)) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ((r2_hidden D (k9_xtuple_0 A)) &  (E = (k1_funct_1 A D)) )  =>  ((k1_funct_1 B D) = (k11_ordinal2 E C)) ) ) ) ) ) ) )  =>  ( (C = k1_xboole_0)  |  ((k4_ordinal2 B) = (k11_ordinal2 (k4_ordinal2 A) C)) ) ) ) ) ) ) ) ) ).
tt(t42_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k3_ordinal5 (k1_ordinal1 A)) = (k1_ordinal5 (k3_ordinal5 A) k4_ordinal1)) ) ) ).
tt(t42_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ((r2_hidden A B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k2_ordinal1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k2_ordinal1 B))))) )  => (r2_hidden (k4_ordinal2 C) B)) ) ) ) ) ) ) ).
tt(t42_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t42_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((r2_hidden D (k25_osafree A B (k20_osafree A B) C)) <=>  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) D) = (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t42_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  => (r1_tarski (k12_osalg_2 A B) (k14_msualg_2 A B))) ) ) ) ).
tt(t42_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r2_parsp_2 A B C D E) &  ((r2_parsp_2 A B C F G) & (r2_parsp_2 A D E H I)) )  => (r1_parsp_1 A F H G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k9_xtuple_0 C)) & (r1_tarski (k10_xtuple_0 C) B))  => (v1_partfun1 (k3_partfun1 C A B) A)) ) ) ) ) ).
tt(t42_partfun2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ( ((v3_funct_1 (k2_partfun1 C D E A)) & (v3_funct_1 (k2_partfun1 C D E B)))  =>  ((r1_xboole_0 (k3_xboole_0 A B) (k1_relset_1 C E)) | (v3_funct_1 (k2_partfun1 C D E (k2_xboole_0 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t42_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k3_pboole A B (k3_pboole A B C)) (k3_pboole A B C))) ) ) ) ) ).
tt(t42_pcs_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k23_pcs_0 A B)) <=>  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F D) & (r1_orders_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((k6_pdiff_4 C A B) = (k23_rvsum_1 (k4_pdiff_4 C A) (k5_pdiff_4 B))) ) ) ) ) ) ) ).
tt(t42_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 3 3) B)) =>  ( ((r6_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 3 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B))))) &  ((k6_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 2 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F A) &  ( (~ (r1_xxreal_0 D C))  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k1_rcomp_1 C D)) => (r2_hidden (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G) (k1_relset_1 (k1_euclid A) B))) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k1_rcomp_1 C D)) => (r3_pdiff_1 A F B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G))) ) )  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden G (k2_rcomp_1 C D)) &  ( (H = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G))  &  ((k10_binop_2 (k7_partfun1 k1_numbers B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) D)) (k7_partfun1 k1_numbers B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) C))) = (k11_binop_2 (k10_binop_2 D C) (k11_pdiff_1 A F B H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  ( (C = D)  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_pdiff_9 A B C))  <=> (r4_nfcont_1 (k4_real_ns1 A) D B)) ) ) ) ) ) ) ) ) ).
tt(t42_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = k6_numbers) )  &  ((k1_euler_1 A) = k6_numbers) ) ) ) ) ).
tt(t42_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  (! [D:$i] :  ((m2_finseq_2 D B (k3_finseq_2 B)) =>  ((k10_pnproc_1 A B (k6_domain_1 (k3_finseq_2 B) C) (k6_domain_1 (k3_finseq_2 B) D)) = (k6_domain_1 (k3_finseq_2 B) (k1_pre_poly B C D))) ) ) ) ) ) ) ) ).
tt(t42_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_bspace)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((k19_polyform A B E (k4_vectsp_1 k2_bspace (k17_polyform A B) D C)) = (k9_fvsum_1 k2_bspace (k19_polyform A B E C) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k4_polynom5 A (k4_struct_0 A) (k4_struct_0 A)) (k9_polynom3 A))) ) ).
tt(t42_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k1_algseq_1 A B) C) =>  ((r1_xxreal_0 C k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k6_polynom8 C A B D) (k5_polynom8 A (k4_matrix_3 A (k7_polynom8 A C D) (k4_polynom8 C A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t42_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r4_polyred A B C D E F) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  ((r2_hidden G (k2_polynom1 (k15_pre_poly A) C F)) => (r1_termord A B G (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_power,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_power k6_numbers A) = k6_numbers) ) ) ) ).
tt(t42_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r2_pre_poly A B C) & (r2_pre_poly A C D))  => (r2_pre_poly A B D)) ) ) ) ) ) ) ) ) ).
tt(t42_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k5_prepower (k10_real_1 1 A) B) = (k10_real_1 1 (k4_prepower A B))) ) ) ) ) ).
tt(t42_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((v1_prob_2 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 E D))  => (r1_xboole_0 (k1_funct_1 (k2_prob_3 A C) D) (k1_funct_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden B (k4_cqc_the1 A)) => (r2_hidden (k9_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t42_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k20_pscomp_1 A) (k15_pscomp_1 A)) & (r2_hidden (k21_pscomp_1 A) (k15_pscomp_1 A))) ) ) ).
tt(t42_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((k2_pboole A (k2_pzfmisc1 A B C) D) = (k1_pboole A)) ) ) ) ) ) ) ) ) ) ).
tt(t42_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  =>  (~ (r1_qc_lang2 A B (k10_qc_lang1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k14_qc_lang1 A B C)) = (k4_subset_1 D (k4_qc_lang3 A D B) (k4_qc_lang3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t42_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_qc_lang4 C A B) =>  (! [D:$i] :  ((m1_qc_lang4 D A B) =>  ((r2_qc_lang2 A C D) =>  (! [E:$i] :  ((m2_qc_lang4 E A B D) =>  (? [F:$i] :  ((m2_qc_lang4 F A B C) & (r1_tarski E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) =>  ( ((k17_quatern2 A) = (k4_struct_0 k16_quatern2))  =>  (A = (k4_struct_0 k16_quatern2)) ) ) ) ).
tt(t42_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) => (r1_xxreal_0 (k9_real_1 (k3_quatern2 A) (k3_quatern2 B)) (k7_real_1 (k3_quatern2 (k29_quaterni A C)) (k3_quatern2 (k29_quaterni C B))))) ) ) ) ) ) ).
tt(t42_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k17_quaterni (k29_quaterni A B)) = (k9_real_1 (k17_quaterni A) (k17_quaterni B)))  &  ( ((k18_quaterni (k29_quaterni A B)) = (k9_real_1 (k18_quaterni A) (k18_quaterni B)))  &  ( ((k19_quaterni (k29_quaterni A B)) = (k9_real_1 (k19_quaterni A) (k19_quaterni B)))  &  ((k20_quaterni (k29_quaterni A B)) = (k9_real_1 (k20_quaterni A) (k20_quaterni B))) ) ) ) ) ) ) ) ).
tt(t42_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  ((k8_group_1 (k19_quofield A) (k5_struct_0 (k19_quofield A)) B) = B) ) ) ) ) ).
tt(t42_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m2_vectsp_6 F A B (k2_ranknull C B D E)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ((r2_hidden G E) & (v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D E)))  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k9_ranknull A C B E D F) G) = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) F (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k4_real_1 (k2_rat_1 B) (k1_rat_1 A)) (k4_real_1 (k2_rat_1 A) (k1_rat_1 B)))) )  &  (~  ( (~ (r1_xxreal_0 (k4_real_1 (k2_rat_1 B) (k1_rat_1 A)) (k4_real_1 (k2_rat_1 A) (k1_rat_1 B))))  & (r1_xxreal_0 B A)) ) ) ) ) ) ) ).
tt(t42_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  ( ( (E = (k4_rcomp_1 C D))  & (r1_xxreal_0 A C))  =>  ((r1_xxreal_0 B D) |  ((k1_tops_1 (k4_topmetr A B) E) = (k2_rcomp_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_rat_1 A) <=>  (? [B:$i] :  ((v7_ordinal1 B) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B C) =>  ((k1_seq_1 (k4_real_3 A) C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t42_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( ((k9_xtuple_0 A) = k1_xboole_0)  <=>  ((k10_xtuple_0 A) = k1_xboole_0) ) ) ) ).
tt(t42_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( (~  (C = k1_xboole_0) )  => (r1_tarski (k6_relset_2 A B C D) (k7_relset_1 A B D C))) ) ) ) ) ) ) ).
tt(t42_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( ((r1_rewrite1 A B C) & (r5_rewrite1 A C D))  |  ((r5_rewrite1 A B C) & (r1_rewrite1 A D C)) )  => (r5_rewrite1 A B D)) ) ) ) ) ) ).
tt(t42_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ((r3_rewrite2 A (k1_partit_2 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C) =>  (B = C) ) ) ) ) ) ) ).
tt(t42_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (~  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 F G)))))  &  ((r2_hidden (k4_tarski (k4_tarski A D) (k4_tarski B E)) (k1_rewrite3 C F G)) & (r1_xxreal_0 (k1_afinsq_1 D) (k1_afinsq_1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k45_valued_1 (k1_rfunct_1 A B) (k1_rfunct_1 C D)) = (k1_rfunct_1 (k45_valued_1 (k18_valued_1 A D) (k18_valued_1 C B)) (k18_valued_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t42_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers C A)) & (v3_funct_1 (k2_partfun1 k1_numbers k1_numbers D B)))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t42_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_classes1 C D) => (r2_classes1 (k19_rfunct_3 A C) (k19_rfunct_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t42_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 B (k1_seq_1 C (k2_nat_1 A D)))) )  <=> (r1_xxreal_0 B (k1_seq_1 (k3_rinfsup1 C) A))) ) ) ) ) ) ) ) ).
tt(t42_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) <=>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  ( ( ((k6_rlvect_2 A C) = (k4_struct_0 A))  &  ((k3_rlaffin1 A C) = k6_numbers) )  =>  ((k3_rlvect_2 A C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t42_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r2_hidden (k4_struct_0 A) (k3_rlsub_1 A B C)) <=> (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t42_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m2_rlsub_1 D A B) =>  (! [E:$i] :  ((m2_rlsub_1 E A C) =>  ( (~ (r1_xboole_0 D E))  => (m2_rlsub_1 (k9_subset_1 (u1_struct_0 A) D E) A (k2_rlsub_2 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v9_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C B) => (v9_rltopsp1 C A)) ) ) ) ) ) ) ).
tt(t42_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k10_xtuple_0 B) = (k10_xtuple_0 C))  &  ((v2_funct_1 B) & (v2_funct_1 C)) )  =>  ((k4_rlvect_1 A B) = (k4_rlvect_1 A C)) ) ) ) ) ) ) ) ).
tt(t42_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ( (~  (B = k6_numbers) )  =>  ((k3_rlvect_2 A (k8_rlvect_2 A B C)) = (k3_rlvect_2 A C)) ) ) ) ) ) ) ) ).
tt(t42_rmod_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C B) & (l1_vectsp_2 C B)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rmod_2 E B C) =>  ((r2_hidden A (k3_rmod_2 B C D E)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) &  ((r1_struct_0 E F) &  (A = (k3_rlvect_1 C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_vectsp_2 B A) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( ((k1_rmod_3 A B C D) = B)  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) => (r1_tarski (k2_rmod_4 A B (k7_rmod_4 A B C D)) (k2_rmod_4 A B D))) ) ) ) ) ) ) ) ).
tt(t42_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A (k16_robbins1 A B) (k11_robbins1 A B)) = (k5_robbins1 A (k15_robbins1 A B) (k13_robbins1 A B))) ) ) ) ) ).
tt(t42_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A C (k3_robbins1 A B)) D))) = B) ) ) ) ) ) ) ) ) ).
tt(t42_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~ (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C) k6_numbers))  &  (~ (r1_xxreal_0 1 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C))) )  <=> (r2_hidden C (k5_roughs_1 A B))) ) ) ) ) ) ) ).
tt(t42_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (~ (r1_xxreal_0 (k1_rpr_1 A B) k6_numbers))  =>  ((k2_rpr_1 A B (k2_subset_1 A)) = 1) ) ) ) ) ) ).
tt(t42_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=>  ((k3_rusub_1 A C B) = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t42_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m2_rusub_1 D A B) =>  (! [E:$i] :  ((m2_rusub_1 E A C) =>  ( (~ (r1_xboole_0 D E))  => (m2_rusub_1 (k9_subset_1 (u1_struct_0 A) D E) A (k2_rusub_2 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ( ((m1_rusub_1 B C) & (m1_rusub_1 B D))  => (m1_rusub_1 B (k2_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t42_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  ( (B = (k2_struct_0 A))  =>  ((v3_pre_topc B (k5_rusub_5 A)) & (v4_pre_topc B (k5_rusub_5 A))) ) ) ) ) ) ).
tt(t42_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (B = (k9_rvsum_1 A (k5_rvsum_1 A B C) C)) ) ) ) ) ) ) ).
tt(t42_rvsum_2,ax, ((k20_rvsum_1 (k6_finseq_1 k2_numbers)) = 1) ).
tt(t42_scmbsort,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  ((r1_tarski k2_scmbsort C) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ((r1_tarski (k1_scmfsa_m (k16_funcop_1 (k5_scmfsa_2 k6_numbers) D)) B) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 C B A)) (k9_xtuple_0 k2_scmbsort))) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k12_scmfsa_2 A C) B) = (k12_scmfsa_2 (k2_nat_1 A B) C)) ) ) ) ) ) ) ).
tt(t42_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  => (r2_hidden B (k1_relset_1 (u1_struct_0 k1_scmfsa_2) A))) ) ) ) ).
tt(t42_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_scmfsa8a B A (k2_scmfsa6a D)))  =>  ( ((k1_funct_1 B E) = k6_numbers)  |  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k1_scmfsa8b E C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a D (k4_compos_1 k1_scmfsa_2)) B A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmfsa9a,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (C = D) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (E = (k1_funct_1 B C))  =>  ( ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa9a C D) B A) D) = (k3_pre_ff E))  &  ((k1_funct_1 (k1_scmfsa6b (k3_scmfsa9a C D) B A) C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 C))  &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r5_scmfsa7b C B A) & (r6_scmfsa7b C B A))  =>  ((r1_xxreal_0 (k1_funct_1 B D) k6_numbers) |  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B)) 3))) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B)) 3)) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 D C)) (k8_memstr_0 3 k1_scmfsa_2 B) E)) (k2_afinsq_1 (k2_scmfsa_9 D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_xxreal_0 (k1_funct_1 E D) k6_numbers) &  ((r1_scm_halt C E A) & (r2_scm_halt C E A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b D B C) E A) (k1_funct_4 (k1_scmfsa6b C E A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 B) (k5_card_1 C)) 3))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((k9_xtuple_0 (k6_memstr_0 2 k1_scmpds_2 A)) = k2_ami_2) ) ) ).
tt(t42_scmpds_5,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 C 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 k1_scmpds_2)) &  ((v1_scmpds_5 D) & (m1_subset_1 D (u1_compos_1 k1_scmpds_2))) )  =>  (! [E:$i] :  ( ((v4_scmpds_4 E) &  ((v1_scmpds_5 E) & (m1_subset_1 E (u1_compos_1 k1_scmpds_2))) )  =>  ((k1_funct_1 (k6_scmpds_4 (k4_scmpds_4 D E) C B) A) = (k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 E (k2_extpro_1 2 k1_scmpds_2 D C)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k2_scmpds_6 E F C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( (~ (r1_xxreal_0 (k2_nat_1 (k5_card_1 E) 3) D))  <=> (r2_hidden D (k2_afinsq_1 (k2_scmpds_7 A B C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (A = (k7_scmyciel A (k3_tarski A))) ) ) ).
tt(t42_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) => (r2_semi_af1 A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A (k52_valued_1 k5_numbers k1_numbers k1_numbers B C)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A C) B))) ) ) ) ) ) ).
tt(t42_seq_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v3_funct_1 A) & (v2_comseq_2 B))  =>  ( ((k2_seq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k9_binop_2 (k8_nat_1 k1_numbers A k6_numbers) (k2_seq_2 B)))  &  ( ((k2_seq_2 (k47_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k10_binop_2 (k8_nat_1 k1_numbers A k6_numbers) (k2_seq_2 B)))  &  ( ((k2_seq_2 (k47_valued_1 k5_numbers k1_numbers k1_numbers B A)) = (k10_binop_2 (k2_seq_2 B) (k8_nat_1 k1_numbers A k6_numbers)))  &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) = (k11_binop_2 (k8_nat_1 k1_numbers A k6_numbers) (k2_seq_2 B))) ) ) ) ) ) ) ) ) ).
tt(t42_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ((r2_seqfunc A C D) =>  ((r2_seqfunc A (k2_seqfunc A C B) D) & (r2_relset_1 A k1_numbers (k11_seqfunc A (k2_seqfunc A C B) D) (k26_valued_1 A k1_numbers (k11_seqfunc A C D) B))) ) ) ) ) ) ) ) ) ).
tt(t42_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((k7_real_1 (k18_complex1 (k9_real_1 A B)) (k18_complex1 (k9_real_1 C D))) = 1)  <=>  ( ( ((k18_complex1 (k9_real_1 A B)) = 1)  &  (C = D) )  |  ( ((k18_complex1 (k9_real_1 C D)) = 1)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k1_numbers A C) = (k2_power C (k3_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers B) C))) ) )  &  ((v2_comseq_2 A) &  ( (~ (r1_xxreal_0 (k2_seq_2 A) 1))  & (v1_series_1 B)) ) ) ) ) ) ) ) ).
tt(t42_series_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 C D) = (k2_xcmplx_0 (k3_xcmplx_0 A D) B)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_seq_1 (k3_series_1 C) D) = (k13_complex1 (k3_xcmplx_0 (k2_nat_1 D 1) (k2_xcmplx_0 (k1_seq_1 C k6_numbers) (k1_seq_1 C D))) 2)) ) ) ) ) ) ) ) ) ) ).
tt(t42_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r1_xxreal_0 (k1_seq_1 (k3_series_1 B) A) (k1_seq_1 (k3_series_1 (k56_valued_1 k5_numbers k1_numbers B)) A))) ) ) ) ).
tt(t42_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 (k3_power A (k3_xcmplx_0 2 A)) (k3_power B (k3_xcmplx_0 2 B))) (k3_power C (k3_xcmplx_0 2 C))) (k3_xcmplx_0 (k3_xcmplx_0 (k3_power A (k2_xcmplx_0 B C)) (k3_power B (k2_xcmplx_0 A C))) (k3_power C (k2_xcmplx_0 A B))))) ) ) ) ) ) ) ) ) ).
tt(t42_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski C (k3_tarski (k2_xboole_0 A B))) &  (! [D:$i] :  ((r2_hidden D B) => (r1_xboole_0 D C)) ) )  => (r1_tarski C (k3_tarski A))) ) ) ) ).
tt(t42_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v3_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k1_kurato_0 B C)) ) ) ) ) ) ) ).
tt(t42_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k5_subset_1 A B (k1_prob_1 A C)) (k1_prob_1 A (k9_setlim_2 A C B)))) ) ) ) ) ).
tt(t42_setwiseo,ax, (! [A:$i] : (r3_binop_1 (k5_finsub_1 A) (k4_binop_1 (k5_finsub_1 A) (k9_setwiseo A)) (k9_setwiseo A))) ).
tt(t42_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((k4_sf_mastr A) = (k4_sf_mastr (k2_scmfsa6a A))) ) ) ).
tt(t42_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C B)) = (k5_sheffer1 A B (k5_sheffer1 A C C))) ) ) ) ) ) ) ).
tt(t42_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  (~  ((v1_matroid0 C) &  ((v4_simplex0 (k8_simplex0 A C B)) &  ( (~ (v4_simplex0 C))  &  (~  (B = (k2_xxreal_3 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_tops_2 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v3_pre_topc D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((v6_ordinal1 C) &  ((v1_setfam_1 C) &  ( ((k5_card_1 C) = (k5_card_1 (k5_setfam_1 (u1_struct_0 B) C)))  &  ((r1_tarski (k5_setfam_1 (u1_struct_0 B) C) D) &  ((k5_card_1 D) = (k3_real_1 (k5_card_1 C) 1)) ) ) ) )  =>  ((a_4_0_simplex1 A B C D) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k4_subset_1 (u1_struct_0 A) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) C) (k7_relset_1 (k1_orders_1 (u1_struct_0 A)) (u1_struct_0 A) (k2_rlaffin2 A) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) D))))) ) ) ) ) ) ) ) ) ) ).
tt(t42_sincos10,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos))) = (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) ).
tt(t42_sin_cos2,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k4_sin_cos2 k1_numbers))).
tt(t42_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 B)) (k5_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 B)) k7_complex1))) ) ) ) ) ).
tt(t42_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k3_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k6_xcmplx_0 (k3_xcmplx_0 (k20_sin_cos B) (k20_sin_cos B)) (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos A)))) ) ) ) ) ).
tt(t42_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  &  ( (~  ((k3_sin_cos2 B) = k6_numbers) )  &  (~  ( ((k7_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B)) = (k10_real_1 (k3_sin_cos2 (k2_xcmplx_0 A B)) (k8_real_1 (k3_sin_cos2 A) (k3_sin_cos2 B))))  &  ((k9_real_1 (k1_sin_cos5 A) (k1_sin_cos5 B)) = (k1_real_1 (k10_real_1 (k3_sin_cos2 (k6_xcmplx_0 A B)) (k8_real_1 (k3_sin_cos2 A) (k3_sin_cos2 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t42_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) B) A) &  ( (~ (r1_xxreal_0 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B)) A))  & (r1_xxreal_0 (k20_sin_cos A) (k1_real_1 1))) ) ) ) ) ) ) ).
tt(t42_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ((k4_sin_cos7 A) = (k2_sin_cos7 (k12_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))))) ) ) ) ) ) ) ).
tt(t42_sin_cos9,ax, ( ((k1_seq_1 k30_sin_cos (k10_real_1 k32_sin_cos 2)) = k6_numbers)  &  ((k2_sin_cos4 (k10_real_1 k32_sin_cos 2)) = k6_numbers) ) ).
tt(t42_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_complex1 (k11_comseq_3 (k3_sin_cos A))) = k6_numbers) ) ) ).
tt(t42_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k10_xtuple_0 A)) &  ((v2_topreal1 A) & (v3_topreal1 A)) )  =>  ( (1 = (k4_finseq_4 A B))  |  ( ((k4_finseq_4 A B) = (k3_finseq_1 A))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) A B)) (k3_topreal1 2 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) A B))) = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t42_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k3_topreal1 2 (k1_sprect_1 A)) = (k1_sppol_2 (k6_pscomp_1 A) (k8_pscomp_1 A) (k9_pscomp_1 A) (k7_pscomp_1 A))) ) ) ).
tt(t42_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k24_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t42_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) B C)) <=>  ((r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) B)) & (r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) C))) ) ) ) ) ) ) ) ).
tt(t42_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t42_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  => (r1_xxreal_0 (k3_square_1 A) A)) ) ) ).
tt(t42_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  => (r3_stacks_1 A A (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A)))) ) ).
tt(t42_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_card_1 (a_2_1_stirl2_1 A B)) = (k1_card_1 (a_2_0_stirl2_1 A B))) ) ) ) ) ).
tt(t42_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r1_tarski (k24_qc_lang1 A (k5_cqc_lang A)) (k9_substut1 A (k5_cqc_lang A)))) ) ).
tt(t42_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((k3_subset_1 A B) = (k3_subset_1 A C))  =>  (B = C) ) ) ) ) ) ) ).
tt(t42_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 A) C) (k12_supinf_2 (k18_supinf_2 B) C))) ) ) ) ) ) ) ).
tt(t42_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) & (l1_metric_1 A)) ) )  => (m1_taxonom1 (k4_taxonom1 A) (u1_struct_0 A))) ) ).
tt(t42_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k10_tdlat_1 A) = (k1_realset1 (k2_tdlat_1 A) (k9_tdlat_1 A))) ) ) ).
tt(t42_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))))) ) ) ) ).
tt(t42_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((k1_tdlat_1 A) = (k9_tdlat_1 A)) ) ) ).
tt(t42_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_1 B A) & (v2_tex_2 B A))  => (v3_tex_2 B A)) ) ) ) ) ).
tt(t42_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((v4_tex_3 B A) <=>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) ) )  &  ((v3_tex_3 C A) & (m1_pre_topc B C)) ) ) ) ) ) ) ) ).
tt(t42_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tex_4 C A) & (r1_tarski (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) C))  =>  (C = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ) ).
tt(t42_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tmap_1 B A C D) <=>  (! [E:$i] :  ((m1_connsp_2 E A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D)) => (m1_connsp_2 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) C E) B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A D E) =>  (! [H:$i] :  ((m1_borsuk_2 H A B D) => (r4_borsuk_2 A B D (k1_borsuk_2 A B E D (k1_borsuk_2 A B C E F (k1_borsuk_2 A C D E (k1_borsuk_2 A C B D (k2_borsuk_2 A B C F) H) G)) (k2_borsuk_2 A D E G)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k1_topalg_6 A)) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 C)))  => (r1_tarski (k10_xtuple_0 (k7_partfun1 (k1_topalg_6 A) C D)) B)) ) )  => (r1_tarski (k10_xtuple_0 (k6_topalg_6 A C)) B)) ) ) ) ) ) ).
tt(t42_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v5_topgen_1 (k1_struct_0 A) A)) ) ).
tt(t42_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_subset_1 C (u1_struct_0 (k7_topgen_3 A B))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_topgen_3 A B)))))  =>  ((k1_tops_1 (k7_topgen_3 A B) C) = (k8_subset_1 (u1_struct_0 (k7_topgen_3 A B)) C B)) ) ) ) ) ) ).
tt(t42_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_topgen_4 B A) & (v6_topgen_4 C A))  => (v6_topgen_4 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t42_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_topgen_5)) =>  ((v4_pre_topc A k3_topgen_5) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topgen_5)))) ) ) ).
tt(t42_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l1_topgrp_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_connsp_2 D A (k6_algstr_0 A B (k2_group_1 A C))) =>  (? [E:$i] :  ((m1_connsp_2 E A B) &  (? [F:$i] :  ((m1_connsp_2 F A C) & (r1_tarski (k2_group_2 A E (k1_group_2 A F)) D)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) ) ) ) ) ) ).
tt(t42_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden B (k9_metric_1 (k14_euclid 2) E D)) & (r2_hidden C (k9_metric_1 (k14_euclid 2) E D)))  =>  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) |  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) |  ( ( (~  ( ((k17_euclid B) = (k17_euclid C))  &  (~  ((k18_euclid B) = (k18_euclid C)) ) ) )  &  (~  ( (~  ((k17_euclid B) = (k17_euclid C)) )  &  ((k18_euclid B) = (k18_euclid C)) ) ) )  |  ( ( (~  ((k17_euclid A) = (k17_euclid B)) )  &  (~  ((k18_euclid A) = (k18_euclid B)) ) )  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k1_rltopsp1 (k15_euclid 2) B C)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = B)  => (r1_tarski (k9_metric_1 (k14_euclid 2) B C) (k4_card_3 (k5_funct_4 (k1_zfmisc_1 k1_numbers) 1 2 (k2_rcomp_1 (k9_real_1 (k17_euclid A) C) (k7_real_1 (k17_euclid A) C)) (k2_rcomp_1 (k9_real_1 (k18_euclid A) C) (k7_real_1 (k18_euclid A) C)))))) ) ) ) ) ) ) ).
tt(t42_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((k18_euclid (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) C A) (k1_rlvect_1 (k15_euclid 2) D B))) = (k7_real_1 (k4_real_1 A (k18_euclid C)) (k4_real_1 B (k18_euclid D)))) ) ) ) ) ) ) ) ) ).
tt(t42_toprealb,ax,(r1_funct_2 (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb k6_numbers)))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb k6_numbers) (k3_real_1 (k4_toprealb k6_numbers) 1))))) (u1_struct_0 (k11_toprealb k9_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 k6_numbers 1)))) (k2_tops_2 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb k6_numbers) (k3_real_1 (k4_toprealb k6_numbers) 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb k6_numbers)))) (k13_toprealb (k4_toprealb k6_numbers))) k14_toprealb)).
tt(t42_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  ((v1_funct_1 (k91_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k91_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k91_valued_2 A A (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t42_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v3_toprns_1 B A) & (v3_toprns_1 C A))  => (v3_toprns_1 (k4_toprns_1 A B C) A)) ) ) ) ) ) ) ).
tt(t42_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  ((k2_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A B) B)) ) ) ) ) ) ).
tt(t42_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) => (m1_subset_1 (k7_relat_1 (k3_funct_3 C) D) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t42_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = (u1_struct_0 A)) )  &  ((v4_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski C D) &  ( (~  (D = (u1_struct_0 A)) )  &  ((v4_pre_topc D A) &  ((k4_subset_1 (u1_struct_0 A) B D) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_diraf A C D E) <=> (r3_diraf A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_trees_1,ax, ((k6_trees_1 (k2_trees_1 k6_numbers)) = k6_numbers) ).
tt(t42_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( ((r1_tarski (k2_trees_2 A 1) (k2_trees_2 B 1)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k12_finseq_1 k5_numbers C) A) =>  ((k4_trees_1 A (k12_finseq_1 k5_numbers C)) = (k4_trees_1 B (k12_finseq_1 k5_numbers C))) ) ) ) )  => (r1_tarski A B)) ) ) ) ) ).
tt(t42_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_trees_2 A) & (v3_trees_9 A)) ) )  =>  (! [B:$i] :  ((m1_trees_1 B (k9_xtuple_0 A)) =>  (! [C:$i] :  (~  ((r2_hidden C (k10_xtuple_0 (k2_trees_9 A B))) &  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 A)) =>  (~  ( (C = (k1_funct_1 A D))  & (r2_hidden D (k1_trees_2 (k9_xtuple_0 A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B D) &  ((r1_tarski C E) &  ((r1_xboole_0 D C) &  ((r1_xboole_0 E B) &  ((v4_pre_topc D A) & (v4_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc D B) &  ((m1_pre_topc E C) &  ( ((k1_tsep_1 A D E) = (k1_tsep_1 A B C))  & (r4_tsep_1 A D E)) ) )  => (r4_tsep_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k21_turing_1 A B)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_turing_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u2_turing_1 B)) &  (C = (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (~ (v1_facirc_1 (k2_msafree2 (k40_twoscomp A B)))) ) ) ) ) ).
tt(t42_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k6_polynom5 k1_complfld (k4_uniroots A k1_complfld)) = (k2_uniroots A)) ) ) ).
tt(t42_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_uproots A B k6_numbers) B)) ) ) ) ).
tt(t42_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r2_valuat_1 A B E (k8_cqc_lang A C (k8_cqc_lang A (k6_cqc_lang A C) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t42_valued_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ((v1_valued_2 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D))))  =>  ( ((k16_valued_2 A C E) = (k16_valued_2 B D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((k2_ranknull B C D E) = F)  =>  ((k7_relat_1 D (u1_struct_0 (k1_vectsp_7 A B E))) = (u1_struct_0 (k1_vectsp_7 A C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_vectsp_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_vectsp_4 E B C) =>  ((r2_hidden A (k3_vectsp_4 B C D E)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) &  ((r1_struct_0 E F) &  (A = (k3_rlvect_1 C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((r1_vectsp_5 A B (k1_vectsp_4 A B) (k2_vectsp_4 A B)) & (r1_vectsp_5 A B (k2_vectsp_4 A B) (k1_vectsp_4 A B))) ) ) ) ) ).
tt(t42_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_vectsp_6 E A B) =>  ( ((m2_vectsp_6 D A B C) & (m2_vectsp_6 E A B C))  => (m2_vectsp_6 (k8_vectsp_6 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((r1_xboole_0 A (k1_relset_1 B D)) => (r1_vfunct_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t42_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r1_xboole_0 D (k1_relset_1 A C)) => (r1_vfunct_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t42_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v1_waybel_0 B A) <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ( (~  (C = k1_xboole_0) )  => (r2_hidden (k1_yellow_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t42_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r1_tarski (k6_waybel_0 A C) B)) ) ) ) ) ) ) ).
tt(t42_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = C)  =>  ((v2_waybel12 B (k2_yellow_1 (u1_pre_topc A))) <=> (v1_tops_3 C A)) ) ) ) ) ) ) ) ).
tt(t42_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (~  ((v2_waybel_8 A) &  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  (B = (a_1_0_waybel14 A)) ) ) ) ) ) ) ) ).
tt(t42_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v4_pre_topc B A) <=> (v2_waybel11 B A)) ) ) ) ) ).
tt(t42_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  ((k2_relset_1 (u1_struct_0 A) B) = (k3_xboole_0 (a_2_0_waybel_1 A B) (a_2_1_waybel_1 A B))) ) ) ) ) ) ).
tt(t42_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))))  =>  ((v1_waybel20 B A) =>  (B = (k4_waybel20 A (k3_waybel20 A B))) ) ) ) ) ) ).
tt(t42_waybel21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) & (l1_waybel_0 B A)) ) )  =>  (! [C:$i] :  (~  ((r1_waybel_0 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((r2_hidden (k2_waybel_0 A B D) C) & (r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A (k5_waybel_9 A B D))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_yellow_0 (k5_yellow_0 A B))) ) ) ) ).
tt(t42_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C (k3_waybel24 A (k1_waybel25 B)))) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v10_waybel_0 (k2_waybel25 (u1_struct_0 A) (k1_waybel25 B) (k3_waybel24 A (k1_waybel25 B)) C D) (k1_waybel25 B))) )  =>  ((v1_funct_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C)))) &  ((v1_funct_2 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C))) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C))) A B) & (m1_subset_1 (k1_yellow_0 (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)) (k2_relset_1 (u1_struct_0 (k3_waybel24 A (k1_waybel25 B))) (u1_waybel_0 (k3_waybel24 A (k1_waybel25 B)) C))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t42_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v3_pre_topc C (k2_borsuk_1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v3_pre_topc (k9_relat_1 C D) B) & (m1_subset_1 (k9_relat_1 C D) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t42_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  => (r5_waybel_1 (k2_waybel27 B (k6_yellow_1 A C)) (k6_yellow_1 A (k2_waybel27 B C)))) ) ) ) ) ) ).
tt(t42_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) )  =>  ((v10_waybel_0 C A) =>  ((k11_lattice3 A B (k1_waybel_2 A C)) = (k1_yellow_0 A (k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A C))))) ) ) ) ) )  => (v1_waybel_2 A)) ) ) ).
tt(t42_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v2_yellow_0 B) & (l1_orders_2 B)) ) ) )  => (v17_waybel_0 (k6_struct_0 A B (k4_yellow_0 B)) A B)) ) ) ) ).
tt(t42_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_waybel_3 A) => (v3_waybel_3 (k2_yellow_1 (u1_pre_topc A)))) ) ) ).
tt(t42_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))) )  =>  (~  ((v7_waybel_4 B A) &  ((r2_hidden B (u1_struct_0 (k8_waybel_4 A))) &  (! [C:$i] :  ( ((v5_waybel_4 C A) &  ((v6_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  (C = (k1_funct_1 (k10_waybel_4 A) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((v5_waybel_7 B A) <=>  (! [C:$i] :  ( ((v4_yellow_0 C (k3_yellow_3 A A)) & (m1_yellow_0 C (k3_yellow_3 A A)))  =>  ( ((u1_struct_0 C) = B)  => (v5_yellow_0 C (k3_yellow_3 A A))) ) ) ) ) ) ) ) ).
tt(t42_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r4_wellord1 A B) & (r4_wellord1 B C))  => (r4_wellord1 A C)) ) ) ) ) ) ) ).
tt(t42_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k6_int_1 A B) = k6_numbers)  =>  ((r1_xxreal_0 B k6_numbers) |  ((k4_xcmplx_0 (k5_int_1 A B)) = (k5_int_1 (k4_xcmplx_0 A) B)) ) ) ) ) ) ) ).
tt(t42_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 (k2_xboole_0 A B) C) = (k2_xboole_0 (k4_xboole_0 A C) (k4_xboole_0 B C))) ) ) ) ).
tt(t42_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k9_xboolean A B)) = (k3_xboolean A)) ) ) ) ) ).
tt(t42_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 A B) C) D) = (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 B D)) (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t42_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 k6_numbers C))  => (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t42_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k13_xtuple_0 A) (k13_xtuple_0 B)) (k13_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t42_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_0 A k1_xxreal_0) = A) ) ) ).
tt(t42_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k3_xxreal_1 B C) (k3_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t42_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) => (m2_xxreal_2 k2_xxreal_0 A)) ) ).
tt(t42_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A (k1_xxreal_3 C B)) =>  ( ( (A = k1_xxreal_0)  &  ( (B = k1_xxreal_0)  &  (~ (r1_xxreal_0 k6_numbers C)) ) )  |  ( ( (A = k2_xxreal_0)  &  ( (B = k2_xxreal_0)  &  (~ (r1_xxreal_0 k6_numbers C)) ) )  | (r1_xxreal_0 (k3_xxreal_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t42_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ((r1_yellow_0 A k1_xboole_0) & (r2_yellow_0 A (u1_struct_0 A))) ) ) ).
tt(t42_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k4_yellow_3 A B (k6_waybel_0 (k3_yellow_3 A B) C)) = (k6_waybel_0 A (k8_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t42_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((v1_funct_1 (k14_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_struct_0 A) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)))) &  ((v1_funct_2 (k14_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_struct_0 A) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B))) (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 B A))) &  ((v5_pre_topc (k14_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_struct_0 A) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B))) (k2_borsuk_1 A B) (k2_borsuk_1 B A)) & (m1_subset_1 (k14_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_struct_0 A) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 B A)))))) ) ) ) ) ) ) ).
tt(t42_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v4_waybel_0 (k6_yellow_1 C B) (k6_yellow_1 C A)) & (m1_yellow_0 (k6_yellow_1 C B) (k6_yellow_1 C A))) ) ) ) ) ) ) ).
tt(t42_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v4_yellow18 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v3_altcat_3 D A B C) &  (~  ((k1_altcat_3 A B C D) = (k2_funct_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  ((v21_functor0 C A B) => (r3_yellow20 A B C A B)) ) ) ) ) ) ) ).
tt(t42_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B)))) =>  ((r2_hidden A C) => (m1_subset_1 A (u1_struct_0 B))) ) ) ) ) ) ).
tt(t42_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ( ((r2_yellow_0 A (k4_yellow_3 A B C)) & (r2_yellow_0 B (k5_yellow_3 A B C)))  <=> (r2_yellow_0 (k3_yellow_3 A B) C)) ) ) ) ) ) ) ).
tt(t42_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) = (a_3_3_yellow_4 A B C)) ) ) ) ) ) ) ).
tt(t42_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A (k7_waybel_1 A (k13_lattice3 A B C)) (k7_waybel_1 A B)) & (r3_orders_2 A (k7_waybel_1 A (k13_lattice3 A B C)) (k7_waybel_1 A C))) ) ) ) ) ) ) ).
tt(t42_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v8_yellow_6 B A) & (m4_yellow_6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k13_yellow_6 A B)))) =>  ((v4_pre_topc C (k13_yellow_6 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E A)) ) )  =>  ( ((r2_hidden (k4_tarski E D) B) & (r2_waybel_0 A E C))  => (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)) C D) =>  ( ((v5_orders_3 C A B) => (v5_orders_3 D (k7_lattice3 A) (k7_lattice3 B)))  &  ( ((v5_orders_3 D (k7_lattice3 A) (k7_lattice3 B)) => (v5_orders_3 C A B))  &  ( ((v5_waybel_0 C A B) => (v5_waybel_0 D (k7_lattice3 A) (k7_lattice3 B)))  &  ((v5_waybel_0 D (k7_lattice3 A) (k7_lattice3 B)) => (v5_waybel_0 C A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_yellow_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 B))))  =>  ( (C = (a_4_1_yellow_9 A B D E))  => (r2_relset_1 A B (k8_setfam_1 (k2_zfmisc_1 A B) C) (k8_mcart_1 A B (k8_setfam_1 A D) (k8_setfam_1 B E)))) ) ) ) ) ) ) ) ) ).
tt(t42_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_zf_lang A B) & (r2_zf_lang B A)) ) ) ) ) ) ).
tt(t42_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((v6_zf_lang B) =>  ( (~  ( (A = (k23_zf_lang B))  &  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (~  ((k8_zf_lang A D) = B) ) ) ) ) )  &  ( ( (? [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  &  ((k8_zf_lang A D) = B) ) )  =>  (A = (k23_zf_lang B)) )  &  ( (~  ( (C = (k24_zf_lang B))  &  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (~  ((k8_zf_lang D C) = B) ) ) ) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) &  ((k8_zf_lang D C) = B) ) )  =>  (C = (k24_zf_lang B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t42_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (r2_hidden C B))  =>  ((k2_xboole_0 (k2_tarski A C) B) = B) ) ) ) ) ).
tt(t42_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_zmodul01 C) &  ((v3_zmodul01 C) &  ((v4_zmodul01 C) &  ((v5_zmodul01 C) & (l1_zmodul01 C)) ) ) ) ) ) ) ) )  =>  ( ((m1_zmodul01 A B) & (m1_zmodul01 B C))  => (m1_zmodul01 A C)) ) ) ) ) ) ) ).
tt(t43_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) => (r3_orders_2 A (k8_abcmiz_0 A B C) B)) ) ) ) ) ) ) ).
tt(t43_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  ((m1_abcmiz_1 (k30_abcmiz_1 A (k15_abcmiz_1 A) B) A (k13_abcmiz_1 A)) &  ((k30_abcmiz_1 A (k15_abcmiz_1 A) B) = (k4_trees_4 (k4_tarski k10_abcmiz_1 (u1_struct_0 A)) (k3_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) B))) ) ) ) ) ) ).
tt(t43_abcmiz_a,ax, (! [A:$i] :  ( ((v4_abcmiz_a A k27_abcmiz_1) & (m1_subset_1 A (u4_struct_0 k27_abcmiz_1)))  =>  ((k10_abcmiz_a k27_abcmiz_1 (k29_abcmiz_1 k27_abcmiz_1 A)) = A) ) ) ).
tt(t43_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C D) & (r5_aff_1 A D E))  => (r2_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 C A) &  ((v1_aff_4 D A) &  ((r2_hidden B C) &  ((r2_hidden B D) & (r1_aff_4 A C D)) ) ) )  => (r1_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t43_afinsq_1,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k8_afinsq_1 A))) ).
tt(t43_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((r2_hidden A (k1_relset_1 k5_numbers C)) =>  ( ( (~ (v1_setwiseo D B))  &  (A = k6_numbers) )  |  ((k1_binop_1 D (k6_afinsq_2 B (k5_relat_1 C A) D) (k1_funct_1 C A)) = (k6_afinsq_2 B (k5_relat_1 C (k23_binop_2 A 1)) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 (k13_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 (k13_afproj A))) =>  (~  ((v1_aff_4 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r1_tarski C B) &  ((r1_tarski D B) &  ( (E = (k4_tarski C 1))  &  ( (F = (k4_tarski D 1))  &  (! [G:$i] :  ((m1_subset_1 G (u1_incsp_1 (k13_afproj A))) =>  (~  ((r1_incsp_1 (k13_afproj A) G E) & (r1_incsp_1 (k13_afproj A) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_afvect0 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = E)  &  (D = F) )  =>  ((k1_algstr_0 (k5_afvect0 A B) C D) = (k5_binop_1 (u1_struct_0 A) (k3_afvect0 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  ((k2_algspec1 A (k1_algspec1 (u1_struct_0 A) B) C) = (k2_algspec1 A B C)) ) ) ) ) ) ) ) ).
tt(t43_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (? [B:$i] :  ( (~ (v1_xboole_0 B))  &  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k2_zfmisc_1 (u1_struct_0 (k14_algstr_4 B)) (u1_struct_0 (k14_algstr_4 B)))) & (v1_funct_1 C)) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_algstr_4 (k14_algstr_4 B) (k6_algstr_4 (k14_algstr_4 B) C))) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_algstr_4 (k14_algstr_4 B) (k6_algstr_4 (k14_algstr_4 B) C))) (u1_struct_0 A))))) )  &  ((v3_funct_2 D (u1_struct_0 (k4_algstr_4 (k14_algstr_4 B) (k6_algstr_4 (k14_algstr_4 B) C))) (u1_struct_0 A)) & (v1_group_6 D (k4_algstr_4 (k14_algstr_4 B) (k6_algstr_4 (k14_algstr_4 B) C)) A)) ) ) ) ) ) ) ) ) ).
tt(t43_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k4_altcat_4 A)))  &  ((v2_altcat_1 (k4_altcat_4 A)) &  ((v3_altcat_2 (k4_altcat_4 A) (k1_altcat_4 A)) & (m1_altcat_2 (k4_altcat_4 A) (k1_altcat_4 A))) ) ) ) ) ).
tt(t43_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_analmetr A)))) =>  ( (B = C)  =>  ((v4_analmetr B A) <=> (v1_aff_1 C (k3_analmetr A))) ) ) ) ) ) ) ) ).
tt(t43_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) &  ((r2_analort A B C H I F G) &  ((r2_analort A B C H I J K) &  ( (~  (H = I) )  &  ( (~  (F = G) )  &  (~ (r2_analort A B C D E J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) & (l1_unialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m5_margrel1 B (u1_struct_0 A) (k1_unialg_2 A)) =>  ((r2_relset_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A) B (k2_pua2mss1 A (k1_funct_7 1 (k4_finseq_1 (u1_unialg_1 A))))) =>  ( ((k19_margrel1 B) = k6_numbers)  & (r2_hidden (k12_aofa_000 A) (k2_relset_1 (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(t43_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k55_aofa_i00 A B D E F G)) F) = (k6_int_1 (k21_aofa_i00 B k4_numbers C F) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k55_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v6_armstrng B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) &  ((r5_armstrng A C (k9_armstrng A B)) & (r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) B (k10_armstrng A C))) ) ) ) ) ) ) ).
tt(t43_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k4_ordinal1) =>  (! [B:$i] :  ((m1_subset_1 B k4_ordinal1) =>  ((r1_arytm_3 A B) =>  ( (B = k1_xboole_0)  |  ( ((k6_arytm_3 (k8_arytm_3 A B)) = A)  &  ((k7_arytm_3 (k8_arytm_3 A B)) = B) ) ) ) ) ) ) ) ).
tt(t43_asympt_1,ax, ((k5_series_1 2 12) = 4096) ).
tt(t43_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v12_bcialg_1 (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A)) ) ) ).
tt(t43_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  (? [H:$i] :  ((m1_subset_1 H k5_numbers) &  ((k1_bcialg_2 B (k1_bcialg_2 B C (k1_bcialg_1 B C D) E) (k1_bcialg_1 B D C) F) = (k1_bcialg_2 B (k1_bcialg_2 B D (k1_bcialg_1 B D C) G) (k1_bcialg_1 B C D) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_2 B A) =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  ( (C = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)))  => (m5_bcialg_2 B A C)) ) ) ) ) ) ) ) ).
tt(t43_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A (k1_bcialg_1 A B C) C)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t43_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v3_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_bcialg_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_4 A C D) = (k1_bcialg_1 A B (k1_bcialg_1 A (k1_bcialg_1 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t43_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v19_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A (k2_nat_1 B C) B D (k2_nat_1 (k2_nat_1 D C) 1))) ) ) ) ) ) ) ) ) ).
tt(t43_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v10_bcialg_1 D B) => (v10_bcialg_1 (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t43_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  (B = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t43_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k4_bhsp_1 A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) (k7_real_1 (k4_bhsp_1 A C B) (k4_bhsp_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t43_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden B (k4_bhsp_2 A C E)) &  ((r2_hidden D (k4_bhsp_2 A C E)) & (r1_xxreal_0 (k8_real_1 2 E) (k4_bhsp_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_bhsp_3 A) & (v1_bhsp_3 B A))  => (v2_bhsp_3 B A)) ) ) ) ) ).
tt(t43_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_bhsp_4 B (k6_bhsp_1 B C D) A) (k6_bhsp_1 B (k5_bhsp_4 B C A) (k5_bhsp_4 B D A)))) ) ) ) ) ) ) ) ).
tt(t43_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  => (v1_vectsp_4 (k11_bilinear A B C D) A C)) ) ) ) ) ) ) ) ).
tt(t43_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k4_lattices A B (k1_boolealg A C D)) (k1_boolealg A (k4_lattices A B C) (k4_lattices A B D)))) ) ) ) ) ) ) ) ).
tt(t43_borsuk_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 A 1))  <=> (r2_hidden A (u1_struct_0 k17_borsuk_1))) ) ) ).
tt(t43_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  ( (~ (r1_xxreal_0 F E))  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 k5_topmetr))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k1_pre_topc k5_topmetr G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) B))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k5_topmetr G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) B)))))) )  =>  (~  ( (G = (k1_rcomp_1 E F))  &  ((v3_tops_2 H (k1_pre_topc k5_topmetr G) (k1_pre_topc (k15_euclid A) B)) &  ( ((k1_funct_1 H E) = C)  &  ((k1_funct_1 H F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_rcomp_1 A k1_xxreal_0) = (k4_subset_1 k1_numbers (k1_seq_4 A) (k2_rcomp_1 A k1_xxreal_0))) ) ) ).
tt(t43_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) D (k2_borsuk_2 A C B (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t43_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( ((k17_euclid A) = (k8_real_1 (k12_euclid A) (k21_sin_cos (k3_euclid_3 A))))  &  ((k18_euclid A) = (k8_real_1 (k12_euclid A) (k18_sin_cos (k3_euclid_3 A)))) ) ) ) ).
tt(t43_bspace,ax, ((k1_vectsp_9 k2_bspace (k7_bspace k1_xboole_0)) = k1_xboole_0) ).
tt(t43_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t43_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C E) F) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k8_xboolean k8_margrel1 A) = (k3_xboolean A)) ) ) ).
tt(t43_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k9_bvfunc_1 A (k2_bvfunc_1 A B C) (k2_bvfunc_1 A D C))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t43_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc26 A B C)) (k11_bvfunc_1 A))) ) ) ) ) ) ).
tt(t43_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k10_bvfunc_1 A B C) (k9_bvfunc_1 A C B)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t43_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ( ((k2_calcul_1 A E) = (k4_substut2 A B C D))  & (r4_calcul_1 A E))  =>  ((r2_hidden D (k3_calcul_1 A (k1_calcul_1 (k3_cqc_lang A) E))) |  ((r2_hidden D (k24_qc_lang1 A (k11_cqc_lang A C B))) | (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) E) (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C B))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_card_1,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r2_wellord2 A B)) ) ) ) ) ) ).
tt(t43_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) => (r1_xxreal_0 (k5_card_1 (k2_xboole_0 A B)) (k2_nat_1 (k5_card_1 A) (k5_card_1 B)))) ) ) ) ).
tt(t43_card_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) => (r2_hidden A B)) ) ) ) ) ).
tt(t43_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finset_1 C)) )  =>  ( ((k9_xtuple_0 C) = A)  =>  ((r1_xxreal_0 B (k5_card_1 A)) |  ((k3_card_fin B C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t43_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 D A B C) =>  ((v7_cat_1 D A B C) & (v8_cat_1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( ((k3_graph_1 B D) = C)  => (m1_cat_3 (k1_cat_3 (u4_struct_0 B) A D) B C (k1_tarski A))) ) ) ) ) ) ) ) ).
tt(t43_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v3_cat_4 A) & (l1_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_cat_1 H A B C) =>  (! [I:$i] :  ((m1_cat_1 I A D E) =>  (! [J:$i] :  ((m1_cat_1 J A F B) =>  (! [K:$i] :  ((m1_cat_1 K A G D) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D E) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A F B) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A G D) = k1_xboole_0) )  &  (~  ((k5_cat_1 A (k2_cat_4 A F G) (k2_cat_4 A B D) (k2_cat_4 A C E) (k18_cat_4 A F B G D J K) (k18_cat_4 A B C D E H I)) = (k18_cat_4 A F C G E (k5_cat_1 A F B C J H) (k5_cat_1 A G D E K I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers A) = (k1_relset_1 k5_numbers B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_afinsq_1 A)) =>  ((k1_seq_1 A C) = (k1_seq_1 B (k7_nat_d (k1_afinsq_1 A) (k23_binop_2 1 C)))) ) ) ) )  =>  ((k7_afinsq_2 A) = (k7_afinsq_2 B)) ) ) ) ) ) ).
tt(t43_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((r2_hidden B (k6_cc0sp2 A)) => (r2_hidden B (k2_cc0sp2 A))) ) ) ) ).
tt(t43_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 B A) & (r2_cfcont_1 C A))  =>  ((r2_cfcont_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers B C) A) &  ((r2_cfcont_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers B C) A) & (r2_cfcont_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t43_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_cfunct_1 A (k1_cfunct_1 A B C)) (k1_cfunct_1 A (k2_partfun1 A k2_numbers C (k1_relset_1 A (k2_cfunct_1 A C))) B))) ) ) ) ) ) ).
tt(t43_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v5_cgames_1 A) <=>  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k7_cgames_1 A)) &  (! [C:$i] :  ((v2_cgames_1 C) =>  (~  ((r2_hidden C (k6_cgames_1 B)) & (v5_cgames_1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  ((r2_hidden C (k4_chain_1 A B 1)) <=>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  (? [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) &  ( (C = (k3_chain_1 A D E))  &  ( (~  ((r1_xxreal_0 (k1_seq_1 E F) (k1_seq_1 D F)) &  (~  ( (A = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 E F))) ) ) ) )  &  ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 D F) (k1_seq_1 E F)) (k2_chain_1 A B F)) &  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k2_finseq_1 A)) =>  ( (~  (G = F) )  =>  ( ((k1_seq_1 D G) = (k1_seq_1 E G))  & (r2_hidden (k1_seq_1 D G) (k2_chain_1 A B G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v1_glib_002 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  (~  ((r1_subset_1 B C) &  (! [D:$i] :  ( ((v5_glib_001 D A) & (m3_glib_001 D A))  =>  (~  ((v1_chord D A) &  ( (~ (v3_glib_001 D A))  &  ((r2_hidden (k3_glib_001 A D) B) &  ((r2_hidden (k4_glib_001 A D) C) &  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (~  ( (~ (r1_xxreal_0 E 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  (~  ( (~ (r2_hidden (k1_funct_1 D E) B))  &  (~ (r2_hidden (k1_funct_1 D E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ((r2_hidden C (u1_struct_0 F)) =>  ((r2_hidden A (k3_msafree2 F)) |  ((r2_hidden B (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k2_tarski A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  => (r1_circcomb (k5_circcomb A B) (k5_circcomb A C))) ) ) ) ) ).
tt(t43_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r4_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 B)) =>  ( (H = (k1_funct_1 D G))  =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 A E))) =>  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 B F))) =>  ( (I = (k3_relat_1 C J))  =>  ((k3_circuit1 B F J H) = (k3_circuit1 A E I G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k4_classes1 B)) <=> (r2_hidden (k1_tarski A) (k4_classes1 (k1_ordinal1 B)))) ) ) ) ).
tt(t43_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_ordinal1 A) & (r2_hidden A (k1_classes1 B)))  => (r2_hidden A (k4_classes1 (k1_card_1 (k1_classes1 B))))) ) ) ).
tt(t43_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 k2_numbers C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers C) C)))) )  =>  ( ( (B = C)  &  ( (D = (k4_struct_0 A))  &  ( (E = (k1_realset1 (u1_algstr_0 A) B))  &  (F = (k2_partfun1 (k2_zfmisc_1 k2_numbers (u1_struct_0 A)) (u1_struct_0 A) (u1_clvect_1 A) (k2_zfmisc_1 k2_numbers B))) ) ) )  => (m1_clvect_1 (g1_clvect_1 C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden B (k4_clvect_2 A C E)) &  ((r2_hidden D (k4_clvect_2 A C E)) & (r1_xxreal_0 (k8_real_1 2 E) (k15_csspace A B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k6_clvect_3 A (k16_csspace A B C) D) = (k16_csspace A (k6_clvect_3 A B D) (k6_clvect_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t43_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v9_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( ((k8_cohsp_1 A B E) = (k1_tarski (k4_tarski C D)))  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((r1_tarski C F) =>  ((k3_funct_2 A B E F) = (k1_tarski D)) )  &  ( (~ (r1_tarski C F))  =>  ((k3_funct_2 A B E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  ( (~  ( ((k17_coh_sp A (k22_coh_sp A B)) = k1_xboole_0)  &  (~  ((k17_coh_sp A (k21_coh_sp A B)) = k1_xboole_0) ) ) )  &  ( ((v1_funct_1 (k2_xtuple_0 B)) &  ((v1_funct_2 (k2_xtuple_0 B) (k17_coh_sp A (k21_coh_sp A B)) (k17_coh_sp A (k22_coh_sp A B))) & (m1_subset_1 (k2_xtuple_0 B) (k1_zfmisc_1 (k2_zfmisc_1 (k17_coh_sp A (k21_coh_sp A B)) (k17_coh_sp A (k22_coh_sp A B)))))) )  &  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k18_coh_sp A (k21_coh_sp A B))) => (r2_hidden (k4_tarski (k1_funct_1 (k2_xtuple_0 B) C) (k1_funct_1 (k2_xtuple_0 B) D)) (k18_coh_sp A (k22_coh_sp A B)))) ) ) ) ) ) ) ) ).
tt(t43_complex1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k17_complex1 A) = A) ) ) ) ).
tt(t43_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 (k10_complex1 A) B) = (k10_complex1 (k1_complex2 A B))) ) ) ) ) ).
tt(t43_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k3_vectsp_1 k1_complfld B A) = (k3_vectsp_1 k1_complfld (k4_algstr_0 k1_complfld B) (k4_algstr_0 k1_complfld A))) ) ) ) ) ) ).
tt(t43_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k12_seq_4 (k10_seq_4 B C) A) = (k10_seq_4 (k12_seq_4 B A) (k12_seq_4 C A))) ) ) ) ) ) ) ) ).
tt(t43_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  ((v4_tbsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_metric_1 A B C) = k6_numbers) ) ) )  =>  (! [C:$i] :  ( (~ (v1_finset_1 C))  =>  ((v4_tbsp_1 (k3_compl_sp A B C)) &  (? [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 (u1_struct_0 (k3_compl_sp A B C)))) &  ((v1_compl_sp D (k3_compl_sp A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 (k3_compl_sp A B C))))))) ) ) )  &  ((v7_compl_sp D (k3_compl_sp A B C)) &  ((v2_prob_1 D) & (v1_xboole_0 (k2_kurato_0 (u1_struct_0 (k3_compl_sp A B C)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_compos_1 A (k6_compos_1 A B C) D) = (k6_compos_1 A B (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t43_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k62_valued_1 (k8_compos_1 A B C)) = (k2_xcmplx_0 (k62_valued_1 B) (k62_valued_1 C))) ) ) ) ) ) ) ).
tt(t43_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r2_hidden (k1_comptrig A) (k2_rcomp_1 k32_sin_cos (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) <=>  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 A)))  &  (~ (r1_xxreal_0 k6_numbers (k4_complex1 A))) ) ) ) ) ).
tt(t43_comput_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) & (v2_margrel1 A)) ) ) )  =>  ((k1_comput_1 (k9_finseq_1 A)) = (k19_margrel1 A)) ) ) ).
tt(t43_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((r2_relset_1 k5_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B) (k51_valued_1 k5_numbers k2_numbers k2_numbers C B)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers A C) B)) & (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B) (k51_valued_1 k5_numbers k2_numbers k2_numbers C B)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers A C) B))) ) ) ) ) ) ) ).
tt(t43_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k3_comseq_2 A) = k5_complex1) ) )  =>  ((k3_comseq_2 (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) = k5_complex1) ) ) ) ) ) ).
tt(t43_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ( ((k8_nat_1 k2_numbers A k6_numbers) = B)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A (k2_nat_1 C 1)) = (k9_complex1 (k8_nat_1 k2_numbers A C) B)) ) ) )  =>  ((r1_xxreal_0 (k17_complex1 B) k6_numbers) |  ((r1_xxreal_0 1 (k17_complex1 B)) |  ((v2_comseq_2 A) &  ((k3_comseq_2 A) = k5_complex1) ) ) ) ) ) ) ) ) ).
tt(t43_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_conlat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_conlat_1 A))) =>  ((r3_lattices (k11_conlat_1 A) B C) <=> (r2_conlat_1 A (k12_conlat_1 A B) (k12_conlat_1 A C))) ) ) ) ) ) ) ).
tt(t43_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) <=> (v3_connsp_1 C A)) ) )  => (m1_setfam_1 B (u1_struct_0 A))) ) ) ) ) ).
tt(t43_convex4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k4_complex1 (k3_xcmplx_0 A B)) = (k4_real_1 A (k4_complex1 B))) ) ) ) ) ).
tt(t43_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) (k3_qc_lang1 A) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 (k3_qc_lang1 A))) =>  (~  ((r2_hidden (k5_domain_1 (k3_cqc_lang A) (k1_qc_lang1 A) (k5_finsub_1 (k3_qc_lang1 A)) (k9_funct_2 (k3_qc_lang1 A) (k3_qc_lang1 A)) C B F E) (k15_cqc_sim1 A D)) & (r2_hidden (k2_qc_lang3 A B) (k7_relat_1 E (k24_qc_lang1 A C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A (k6_cqc_lang A B) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t43_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A D (k7_cqc_lang A B C)) (k7_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t43_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v6_qc_lang1 B A) & (r1_cqc_the3 A B C))  => (r1_cqc_the3 A (k6_cqc_lang A C) (k6_cqc_lang A B))) ) ) ) ) ) ) ).
tt(t43_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) & (l1_csspace B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k13_csspace B (k1_clvect_1 B C A)) = (k8_real_1 (k17_complex1 A) (k13_csspace B C))) ) ) ) ) ) ) ).
tt(t43_dickson,ax,(r1_relat_2 k10_dickson k5_numbers)).
tt(t43_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 k16_sin_cos A) B) = (k8_real_1 2 (k8_real_1 (k21_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2))))) ) ) ) ) ).
tt(t43_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k5_square_1 E)) ) )  & (r1_zfmisc_1 A B C))  =>  ((k10_diff_1 D A B C) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t43_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D F) = (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 E A) F)) ) )  =>  ((k9_diff_1 D B C) = (k9_real_1 (k9_diff_1 E B C) (k9_diff_1 E (k9_real_1 B A) (k9_real_1 C A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_dilworth,ax, (! [A:$i] :  ( ((v3_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v1_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k5_card_1 B) = (k1_dilworth A))  & (r1_tarski B C))  =>  ((k1_dilworth (k5_yellow_0 A C)) = (k1_dilworth A)) ) ) ) ) ) ) ) ).
tt(t43_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) &  ((v3_analoaf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_diraf A B C D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_diraf A B C B F) & (r2_diraf A D E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  ( ((k2_binom (k9_int_3 A) E 2) = (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 3) (k8_group_1 (k9_int_3 A) B D)) C))  <=> (m2_subset_1 (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers D E 1) (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ( (C = D)  <=>  ((k9_ec_pf_2 A B (k8_ec_pf_2 A B) C) = (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t43_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k17_ens_1 A B (k4_cat_1 A C)) = (k6_partfun1 (k2_cat_1 A B C))) ) ) ) ) ) ) ).
tt(t43_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v2_matrprob A) <=> (v4_partfun3 (k2_entropy1 k1_numbers A))) ) ) ).
tt(t43_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k3_enumset1 A A A A B) = (k2_tarski A B)) ) ) ).
tt(t43_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((k7_subset_1 A (k5_setfam_1 A B) (k3_tarski C)) = (k5_setfam_1 A (k7_subset_1 (k1_zfmisc_1 A) B C))) ) ) ) ) ) ) ).
tt(t43_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( (~  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  & (r1_xxreal_0 (k23_rvsum_1 B B) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k23_rvsum_1 B B) k6_numbers))  &  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ).
tt(t43_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  &  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  &  (~  ( ((k23_rvsum_1 A B) = k6_numbers)  <=>  ( ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k10_real_1 k32_sin_cos 2))  |  ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r2_hidden B (k4_euclid_4 A C D)) & (r2_hidden E (k4_euclid_4 A C D)))  =>  ( (B = E)  | (r1_tarski (k4_euclid_4 A C D) (k4_euclid_4 A B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k12_euclid (k5_algstr_0 (k15_euclid 2) B A))) ) ) ) ) ).
tt(t43_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k10_funcsdom (k2_finseq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  (~  ( (C = (k8_euclid_7 A))  &  (! [D:$i] :  ((m2_rlvect_2 D (k10_funcsdom (k2_finseq_1 A)) C) =>  (~  (B = (k6_rlvect_2 (k10_funcsdom (k2_finseq_1 A)) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 A B) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k9_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1))) (k9_euclid 3 k3_euclid_8 (k9_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)))) (k9_euclid 3 k4_euclid_8 (k9_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3))))) ) ) ) ) ).
tt(t43_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((k5_algstr_0 (k15_euclid A) B C) = (k4_struct_0 (k15_euclid A)))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t43_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (? [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) &  ((r2_hidden E (k2_euclid_4 A B C)) & (r1_rvsum_1 (k8_euclid A B C) (k8_euclid A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) )  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((m1_exchsort (k10_funct_7 C A B) C) & (m1_exchsort C (k10_funct_7 C A B))) ) ) ) ) ) ).
tt(t43_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k5_circcomb C (k10_finseq_1 A B)))) &  ((r2_hidden B (u1_struct_0 (k5_circcomb C (k10_finseq_1 A B)))) & (r2_hidden (k4_tarski (k10_finseq_1 A B) C) (u1_struct_0 (k5_circcomb C (k10_finseq_1 A B))))) ) ) ) ) ).
tt(t43_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = (k3_square_1 C)) ) ) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t43_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k16_sin_cos) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k1_fdiff_9 B)) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t43_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k29_sin_cos)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k10_real_1 (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t43_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) & (r2_fdiff_1 B (k3_limfunc1 A)))  =>  ( ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))) ) ) ) ) ) ).
tt(t43_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1) A) B) = (k2_sin_cos4 B)) ) ) ) ) ) ) ) ).
tt(t43_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k8_real_1 (k8_real_1 2 A) D)) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A))) B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A))) B) D) = (k8_real_1 (k10_real_1 1 2) (k21_sin_cos (k8_real_1 (k8_real_1 2 A) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos))) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k24_sin_cos) A) B) = (k10_real_1 (k8_real_1 2 (k1_seq_1 k19_sin_cos B)) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t43_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k1_seq_1 k19_sin_cos B))) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos B) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t43_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_xxreal_0 (k1_pre_ff A) (k1_pre_ff (k1_nat_1 A 1)))) ) ).
tt(t43_fib_num3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_nat_1 (k4_nat_1 (k1_pre_ff B) (k1_fib_num3 A)) (k4_nat_1 (k1_fib_num3 B) (k1_pre_ff A))) = (k3_fib_num3 (k1_pre_ff k6_numbers) (k1_fib_num3 k6_numbers) (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t43_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  ((r1_filerec1 A D B C) => (r1_filerec1 A D D C)) ) ) ) ) ) ) ) ) ).
tt(t43_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) <=>  ((k4_lattices A B (k7_lattices A C)) = (k5_lattices A)) ) ) ) ) ) ) ) ).
tt(t43_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v14_lattices B) & (l3_lattices B)) ) ) )  =>  ((k6_lattices (k7_filter_1 A B)) = (k9_filter_1 A B (k6_lattices A) (k6_lattices B))) ) ) ) ) ) ).
tt(t43_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_2 B A) <=> (v2_filter_0 (k3_filter_2 A B) (k1_lattice2 A))) ) ) ) ) ).
tt(t43_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k11_finseq_1 A B C) = (k7_finseq_1 (k9_finseq_1 A) (k10_finseq_1 B C)))  &  ((k11_finseq_1 A B C) = (k7_finseq_1 (k10_finseq_1 A B) (k9_finseq_1 C))) ) ) ) ) ).
tt(t43_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ( ((r1_xxreal_0 A (k3_finseq_1 B)) &  (C = (k3_relat_1 D B)) )  =>  ((k3_finseq_1 C) = A) ) ) ) ) ) ) ) ) ) ).
tt(t43_finseq_3,ax, ((k14_finseq_1 k1_xboole_0) = k1_xboole_0) ).
tt(t43_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (r2_hidden C (k4_finseq_1 (k6_finseq_4 A B))))  => (r2_hidden (k1_nat_1 C (k4_finseq_4 A B)) (k4_finseq_1 A))) ) ) ) ) ) ).
tt(t43_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) & (r2_hidden A (k2_finseq_1 (k4_finseq_4 D C))))  =>  ((k7_partfun1 B (k1_finseq_5 B D C) A) = (k7_partfun1 B D A)) ) ) ) ) ) ) ) ) ) ).
tt(t43_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~  (B = k1_xboole_0) )  =>  ((k4_finseq_4 B (k7_partfun1 A B 1)) = 1) ) ) ) ) ) ).
tt(t43_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo D A) =>  ((r2_funct_2 B A (k6_funcop_1 A B D (k8_funcop_1 A B (k4_binop_1 A D)) C) C) & (r2_funct_2 B A (k6_funcop_1 A B D C (k8_funcop_1 A B (k4_binop_1 A D))) C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k8_fintopo2 A B) = (k4_subset_1 (u1_struct_0 A) (k13_fintopo2 A B) (k14_fintopo2 A B))) ) ) ) ) ).
tt(t43_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k9_fintopo3 A B C) B)) ) ) ) ) ) ) ).
tt(t43_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v3_orders_2 A) &  ((v1_fin_topo A) &  ( (D = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B))  &  ((v1_fintopo6 A) &  ((v4_fin_topo B A) & (r2_fintopo6 A D C)) ) ) ) )  => (v4_fin_topo (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) C) A)) ) ) ) ) ) ) ) ) ).
tt(t43_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) => (r1_tarski B (k8_flang_1 A B))) ) ) ).
tt(t43_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k1_flang_2 A (k7_flang_1 A B C) D E) (k7_flang_1 A (k1_flang_2 A B D E) C))) ) ) ) ) ) ) ) ) ).
tt(t43_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B (k8_flang_1 A C)) =>  ((r1_tarski (k6_flang_1 A (k1_flang_3 A C D) B) (k1_flang_3 A C D)) & (r1_tarski (k6_flang_1 A B (k1_flang_3 A C D)) (k1_flang_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t43_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( (A = B)  =>  ((k1_funct_4 (k1_funct_4 E (k16_funcop_1 A C)) (k16_funcop_1 B D)) = (k1_funct_4 E (k16_funcop_1 B D))) )  &  ( (~  (A = B) )  =>  ((k1_funct_4 (k1_funct_4 E (k16_funcop_1 A C)) (k16_funcop_1 B D)) = (k1_funct_4 (k1_funct_4 E (k16_funcop_1 B D)) (k16_funcop_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t43_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) B)) ) )  => (v7_pre_topc A)) ) ) ).
tt(t43_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E B A))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) G (k2_binop_1 (u1_struct_0 D) B (u1_struct_0 D) (u1_fsm_1 B D) H I)) = (k2_binop_1 (u1_struct_0 E) B (u1_struct_0 E) (u1_fsm_1 B E) (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) G H) I)) ) ) ) )  =>  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ( ((r1_xxreal_0 1 H) & (r1_xxreal_0 H (k2_nat_1 (k3_finseq_1 C) 1)))  =>  ((k1_funct_1 G (k1_funct_1 (k2_fsm_1 B D F C) H)) = (k1_funct_1 (k2_fsm_1 B E (k3_funct_2 (u1_struct_0 D) (u1_struct_0 E) G F) C) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((k3_funct_2 A A (k6_funcop_1 A A B D (k6_partfun1 A)) C) = (k5_binop_1 A B (k3_funct_2 A A D C) C)) ) ) ) ) ) ) ) ) ).
tt(t43_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) =>  ((k2_funct_1 (k2_funct_1 A)) = A) ) ) ) ).
tt(t43_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  =>  ((k8_relset_1 A B C (k7_relset_1 A B C A)) = A) ) ) ) ) ) ).
tt(t43_funct_3,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k7_funct_3 A B)) A)) ) ).
tt(t43_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden (k4_tarski A B) (k9_xtuple_0 (k2_funct_4 C))) =>  ((k1_binop_1 (k2_funct_4 C) A B) = (k1_binop_1 C B A)) ) ) ) ) ) ).
tt(t43_funct_5,ax, ( ((k2_funct_5 k1_xboole_0) = k1_xboole_0)  &  ((k4_funct_5 k1_xboole_0) = k1_xboole_0) ) ).
tt(t43_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = A)  &  ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((r2_hidden D A) => (r2_wellord2 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) )  => (r2_wellord2 (k4_card_3 B) (k4_card_3 C))) ) ) ) ) ) ).
tt(t43_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k4_funct_7 A (k7_finseq_1 (k9_finseq_1 C) B)) = (k3_relat_1 (k5_relat_1 C A) (k4_funct_7 (k7_relat_1 C A) B))) ) ) ) ) ) ).
tt(t43_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_funct_8 B k1_numbers k1_numbers) => (v6_funct_8 (k26_valued_1 k1_numbers k1_numbers B A) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t43_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v6_functor0 C A B) &  ((v8_functor0 C A B) & (l2_functor0 C A B)) )  =>  ( ((v21_functor0 C A B) &  ((v14_functor0 C A B) &  ((v11_functor0 C A B) & (v7_functor0 C A B)) ) )  => (v14_functor0 (k15_functor0 A B C) B A)) ) ) ) ) ) ) ).
tt(t43_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  => (r8_pboole (u1_struct_0 A) (k8_functor3 A B C C (k9_functor3 A B C)) (k9_functor3 A B C))) ) ) ) ) ) ).
tt(t43_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k1_fuzzy_1 A (k1_fuzzy_1 A (k2_fuzzy_1 A B C) (k2_fuzzy_1 A C D)) (k2_fuzzy_1 A D B)) (k2_fuzzy_1 A (k2_fuzzy_1 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A C D)) (k1_fuzzy_1 A D B)))) ) ) ) ) ) ) ) ).
tt(t43_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k2_fuzzy_2 A B (k2_fuzzy_1 A C D)) (k2_fuzzy_1 A (k2_fuzzy_2 A B C) (k2_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t43_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A B) (k4_fvaluat1 A B)) = 1) ) ) ) ) ) ).
tt(t43_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B (k8_fvsum_1 A B C D) E) = (k8_fvsum_1 A B C (k4_fvsum_1 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r7_gcd_1 A C D) =>  ((k5_gcd_1 A B C D) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t43_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H k6_numbers k6_numbers k6_numbers A B) = (k8_genealg1 F H G A B))  &  ( ((k11_genealg1 F G H k6_numbers k6_numbers C k6_numbers B) = (k8_genealg1 F H G C B))  &  ( ((k11_genealg1 F G H k6_numbers k6_numbers C A k6_numbers) = (k8_genealg1 F H G C A))  &  ( ((k11_genealg1 F G H k6_numbers D k6_numbers k6_numbers B) = (k8_genealg1 F H G D B))  &  ( ((k11_genealg1 F G H k6_numbers D k6_numbers A k6_numbers) = (k8_genealg1 F H G D A))  &  ( ((k11_genealg1 F G H k6_numbers D C k6_numbers k6_numbers) = (k8_genealg1 F H G D C))  &  ( ((k11_genealg1 F G H E k6_numbers k6_numbers k6_numbers B) = (k8_genealg1 F H G E B))  &  ( ((k11_genealg1 F G H E k6_numbers k6_numbers A k6_numbers) = (k8_genealg1 F H G E A))  &  ( ((k11_genealg1 F G H E k6_numbers C k6_numbers k6_numbers) = (k8_genealg1 F H G E C))  &  ((k11_genealg1 F G H E D k6_numbers k6_numbers k6_numbers) = (k8_genealg1 F H G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_geomtrap A B C))) <=> (m1_subset_1 D (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t43_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k19_gfacirc1 A B C)))) ) ) ).
tt(t43_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m1_glib_000 C B) => (m1_glib_000 C A)) ) ) ) ) ) ).
tt(t43_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) =>  ((v1_abian C) | (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A (k8_glib_001 A B 1 D) 1 C) (k8_glib_001 A B 1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t43_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v2_glib_002 A)) ) ) ) ) ) )  =>  (~  ( (~  ((k7_glib_000 A) = k1_xboole_0) )  &  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ((v11_glib_000 B A) &  ((v11_glib_000 C A) & (r2_hidden C (k1_glib_002 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (B = C) )  =>  ((k1_funct_1 (k7_glib_003 (k13_glib_003 A B D)) C) = (k1_funct_1 (k7_glib_003 A) C)) ) ) ) ) ) ) ).
tt(t43_glib_004,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ((v1_glib_002 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_glib_003 B) &  ((v4_glib_003 B A) & (m2_glib_000 B A (k2_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k17_glib_004 A)) (k3_domain_1 (k1_zfmisc_1 (k6_glib_000 A)) (k1_zfmisc_1 (k7_glib_000 A)) (k17_glib_004 A)))) )  =>  ((v9_glib_000 B A) &  ((v3_glib_002 B) &  ((v1_glib_003 B) &  ((v4_glib_003 B A) &  ((v1_glib_004 B A) & (m1_glib_000 B A)) ) ) ) ) ) ) ) ) ).
tt(t43_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) B)) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t43_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) B) & (r1_gobrd13 C (k17_finseq_1 C B D) E A)) )  => (r1_gobrd13 C D E A)) ) ) ) ) ) ) ) ) ) ).
tt(t43_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k7_pscomp_1 (k3_topreal1 2 A)) = (k7_pscomp_1 (k3_goboard9 A))) ) ) ).
tt(t43_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_graph_1 D A) =>  (! [E:$i] :  ((m2_graph_1 E A) =>  ( ((r1_graph_2 A B D) &  ((r1_graph_2 A C E) &  ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 C 1)) ) )  => (m2_graph_1 (k8_finseq_1 (u4_struct_0 A) D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_graph_3 B C E))) =>  ( (F = D)  =>  ( (D = E)  |  ((k2_graph_3 (k8_graph_3 B C E) F A) = (k2_graph_3 B D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ((r1_graph_5 A D B C) =>  ( (~  ((k6_graph_5 A D) = k1_xboole_0) )  &  (~  ((k4_graph_5 A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ((r2_graphsp C D A B) & (r2_graphsp D E A B))  => (r2_graphsp C E A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l2_algstr_0 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( (~ (r1_xxreal_0 (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D)) E))  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_groeb_3 A B C D (k2_nat_1 E 1)) (k6_termord A B C (k6_groeb_3 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k2_group_11 A (k2_group_11 A B C) C) = (k1_group_11 A (k2_group_11 A B C) C)) ) ) ) ) ) ) ).
tt(t43_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_group_1 A B) = 1)  =>  (B = (k1_group_1 A)) ) ) ) ) ) ).
tt(t43_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = B)  &  (F = C) )  =>  ((k6_algstr_0 D E F) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k5_group_3 A C B) (k2_group_2 A (k5_group_2 A B (k1_group_2 A C)) C))) ) ) ) ) ) ).
tt(t43_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ((k7_group_4 A B C) = (k2_group_2 A (k8_group_2 A B) (k8_group_2 A C)))  &  ( ((k7_group_4 A B C) = (k12_group_2 A B (k8_group_2 A C)))  &  ((k7_group_4 A B C) = (k11_group_2 A C (k8_group_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t43_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_group_5 A B C (k2_group_3 A C B)) = (k2_group_5 A C (k2_group_5 A C B))) ) ) ) ) ) ) ).
tt(t43_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  => (r1_group_2 A (k9_group_6 A (k5_group_6 A B) (k8_group_6 A B)) B)) ) ) ) ).
tt(t43_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  ((k1_group_1 (k10_group_9 A B C)) = (k15_group_9 A B C)) ) ) ) ) ) ).
tt(t43_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((k3_helly A B C D) = (k3_helly A C D B)) ) ) ) ) ) ) ) ) ).
tt(t43_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear D k1_complfld A A) &  ((v4_bilinear D k1_complfld A A) &  ((v3_hermitan D A) &  ((v5_hermitan D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k1_complfld)) =>  ( ( ((k17_complex1 F) = 1)  &  ((k3_complex1 (k8_group_1 k1_complfld F (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B))) = (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B))) )  =>  ( ((k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) F) C)) (k5_algstr_0 A B (k4_vectsp_1 k1_complfld A (k8_group_1 k1_complfld (k1_hahnban1 E k6_numbers) F) C)))) = (k7_real_1 (k5_real_1 (k4_hermitan A D B) (k8_real_1 (k8_real_1 2 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B))) E)) (k3_xcmplx_0 (k4_hermitan A D C) (k3_square_1 E))))  & (r1_xxreal_0 k6_numbers (k7_real_1 (k5_real_1 (k4_hermitan A D B) (k8_real_1 (k8_real_1 2 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B))) E)) (k3_xcmplx_0 (k4_hermitan A D C) (k3_square_1 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers B))  => (r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 A)) B)) ) ) ) ) ).
tt(t43_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A B) (k4_hilbert1 B A)) k6_hilbert1)) ) ) ) ).
tt(t43_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  ( ((v2_hilbert3 A) & (v2_hilbert3 (k3_hilbert1 A B)))  => (v2_hilbert3 B)) ) ) ) ) ).
tt(t43_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_tarski (k10_xtuple_0 (k4_funct_7 k14_idea_1 (k17_idea_1 D B A C))) k14_idea_1) &  ((k9_xtuple_0 (k4_funct_7 k14_idea_1 (k17_idea_1 D B A C))) = k14_idea_1) ) ) ) ) ) ) ) ) ) ).
tt(t43_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m3_ideal_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (m3_ideal_1 (k2_partfun1 k5_numbers (u1_struct_0 A) C (k2_finseq_1 D)) A B)) ) ) ) ) ) ) ) ).
tt(t43_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ( (~  (B = D) )  & (r1_incsp_1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t43_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (r8_pboole (u1_struct_0 A) (k3_instalg1 A A B (k6_partfun1 (u1_struct_0 A)) (k6_partfun1 (u4_struct_0 A))) (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k11_msafree A B))))) ) ) ) ).
tt(t43_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k4_int_1 A)))  & (r1_xxreal_0 k6_numbers (k4_int_1 A))) ) ) ).
tt(t43_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((r1_int_1 (k3_int_2 C A) D) &  ((r1_int_1 (k3_int_2 E B) F) &  ((r1_int_2 A B) &  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  (! [I:$i] :  ((v1_int_1 I) =>  (~  ( (! [J:$i] :  ((v1_int_1 J) =>  ( ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 C J) D) A) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 E J) F) B) = k6_numbers) )  => (r2_int_1 J (k2_xcmplx_0 H (k3_xcmplx_0 (k5_int_1 A (k3_int_2 C A)) G)) (k3_xcmplx_0 (k5_int_1 A (k3_int_2 C A)) (k5_int_1 B (k3_int_2 E B))))) ) )  &  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k5_int_1 C (k3_int_2 C A)) H) (k5_int_1 D (k3_int_2 C A))) (k5_int_1 A (k3_int_2 C A))) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k5_int_1 E (k3_int_2 E B)) I) (k5_int_1 F (k3_int_2 E B))) (k5_int_1 B (k3_int_2 E B))) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k5_int_1 A (k3_int_2 C A)) G) (k6_xcmplx_0 I H)) (k5_int_1 B (k3_int_2 E B))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( ( ((k4_nat_d A 8) = 1)  |  ((k4_nat_d A 8) = 7) )  &  (~ (r1_int_5 2 A)) ) ) ) ) ) ).
tt(t43_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) A) B) = (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t43_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A F) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D)) E)) &  ((r2_relset_1 k1_numbers k1_numbers E k2_sin_cos9) &  ((r1_tarski F (k2_rcomp_1 (k19_binop_2 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_taylor_1 2)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 B G) = (k12_binop_2 1 (k11_binop_2 (k9_binop_2 1 (k5_square_1 G)) (k1_seq_1 k2_sin_cos9 G))))  &  ( ((k1_seq_1 C G) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 E G) k6_numbers)) ) ) ) ) )  &  (F = (k1_relset_1 k1_numbers B)) ) ) ) ) ) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k3_taylor_1)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k3_taylor_1)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k2_sin_cos9 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2))))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t43_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k10_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t43_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (C = D)  &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) & (r1_tarski B (k1_relset_1 k1_numbers C))) )  =>  ((r1_integr15 A B C) <=> (r1_integr18 (k4_real_ns1 A) B D)) ) ) ) ) ) ) ) ) ) ).
tt(t43_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k1_seq_1 (k14_integra1 (k5_integra1 A C B)) (k3_finseq_1 B)) = (k7_integra1 A C B)) ) ) ) ) ) ) ).
tt(t43_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k8_real_1 k32_sin_cos 2)))  =>  ((k2_integra5 A k19_sin_cos) = k6_numbers) ) ) ) ).
tt(t43_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) B) &  ((v1_comseq_2 (k2_partfun1 B k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) B) C))) ) ) ) )  => (r1_xxreal_0 k6_numbers (k2_integra9 B A))) ) ) ) ) ).
tt(t43_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A))))  & (m1_interva1 (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A)) A)) ) ) ).
tt(t43_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 (k4_intpro_1 A B) C) (k3_intpro_1 (k4_intpro_1 A B) (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t43_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  (! [H:$i] :  ((m2_cat_1 H B C) =>  ((r3_nattra_1 B C G H) =>  ((r3_nattra_1 B D (k9_cat_1 B C D G F) (k9_cat_1 B C D H F)) & (r3_nattra_1 A C (k9_cat_1 A B C E G) (k9_cat_1 A B C E H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_isomichi B A) & (v3_isomichi C A))  =>  ( ((k9_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A B)) (k1_tops_1 A (k2_pre_topc A C))) = (k1_tops_1 A (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) B C))))  &  ((k4_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A B)) (k2_pre_topc A (k1_tops_1 A C))) = (k2_pre_topc A (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ) ) ).
tt(t43_jgraph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden A (k4_finseq_1 B)) =>  ( ((k1_seq_1 (k1_goboard1 B) A) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A)))  &  ((k1_seq_1 (k2_goboard1 B) A) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ) ).
tt(t43_jgraph_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E F) = (k19_euclid (k7_real_1 (k4_real_1 A (k17_euclid F)) B) (k7_real_1 (k4_real_1 C (k18_euclid F)) D))) ) )  => (v5_pre_topc E (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jgraph_3,ax, ( ((v1_funct_1 k1_jgraph_3) &  ((v1_funct_2 k1_jgraph_3 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 k1_jgraph_3 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) k1_jgraph_3) = (u1_struct_0 (k15_euclid 2)))  &  (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) A k1_jgraph_3) => (v3_tops_2 A (k15_euclid 2) (k15_euclid 2))) ) ) ) ) ).
tt(t43_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  (~  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  (~ (r1_xxreal_0 k6_numbers (k18_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jgraph_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (A = a_0_6_jgraph_5)  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A)))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))))))) )  =>  (~  ((v3_tops_2 B k5_topmetr (k1_pre_topc (k15_euclid 2) (k8_jordan6 A))) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ( ((k1_funct_1 B E) = C)  &  ( ((k1_funct_1 B F) = D)  &  ((r2_hidden E (k1_rcomp_1 k6_numbers 1)) & (r2_hidden F (k1_rcomp_1 k6_numbers 1))) ) )  =>  ( (~  ( (~ (r1_xxreal_0 F E))  & (r1_xxreal_0 (k17_euclid D) (k17_euclid C))) )  &  (~  ( (~ (r1_xxreal_0 (k17_euclid D) (k17_euclid C)))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) )  &  ( ((k1_funct_1 B k6_numbers) = (k18_pscomp_1 A))  &  ((k1_funct_1 B 1) = (k22_pscomp_1 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k13_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid B C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = H)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 E (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) F) & (r1_xxreal_0 (k17_euclid B) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid D) E) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1)))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E D))) & (r1_xxreal_0 D B)) ) ) )  => (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E D) C 1)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) A 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (E = (a_4_9_jordan1 A B C D))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (v1_jordan1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A))) (k10_xtuple_0 (k2_jordan1e B A)))) ) ) ) ) ) ) ) ) ).
tt(t43_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_pre_topc (k15_euclid 2) (k3_goboard9 A))) = (k2_goboard9 A)) ) ) ).
tt(t43_jordan1j,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden (k1_funct_1 A (k3_finseq_1 A)) (k3_topreal1 2 (k3_jordan3 A B))))  =>  ((k1_funct_1 A (k3_finseq_1 A)) = B) ) ) ) ) ) ).
tt(t43_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k4_jordan1k A (k6_domain_1 (u1_struct_0 (k15_euclid A)) B) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)) = (k1_topreal6 A B C)) ) ) ) ) ) ) ).
tt(t43_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_tarski A B) &  ( ((k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) = (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)))  & (v4_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) )  =>  ((v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) | (r1_xxreal_0 (k18_euclid (k1_jordan21 A)) (k18_euclid (k1_jordan21 B)))) ) ) ) ) ) ).
tt(t43_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) ) ) ) )  =>  ( ((k3_finseq_1 A) = 2)  |  ( (B = C)  |  ( (B = (k1_funct_1 A 1))  |  ( (C = (k1_funct_1 A 1))  | (r1_jordan3 (k4_jordan3 A B C) B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (C = (k6_subset_1 (k1_euclid A) (a_2_3_jordan2c A B)))  &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (~  (D = (k1_rlvect_1 (k15_euclid A) E F)) )  &  (~  (E = (k1_rlvect_1 (k15_euclid A) D F)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden F C) &  ((r2_hidden G C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D F) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) F G) C) & (r1_tarski (k1_rltopsp1 (k15_euclid A) G E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((r2_hidden C (k3_topreal1 2 A)) &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) ) )  =>  ( (C = (k1_funct_1 A (k3_finseq_1 A)))  | (r1_jordan3 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan3 A C) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B 2 (k3_finseq_1 B))) C (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) ) ) ) ).
tt(t43_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 1 B) &  ( (D = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))  &  (E = (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B 1) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k7_nat_d (k3_finseq_1 A) 1) C))) ) )  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 (k3_finseq_1 A) C) |  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E)) = (k2_tarski (k1_funct_1 A B) (k1_funct_1 A C)))  &  ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E)) = (k3_topreal1 2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A))) &  ( (E = (a_2_1_jordan5d A C))  &  ( ((k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C)))  &  (D = (k1_xxreal_2 E)) ) ) ) ) ) )  => (r1_xxreal_0 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  ((k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k2_tarski C D)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_jordan,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (? [D:$i] :  ((m1_borsuk_2 D (k15_euclid A) B C) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C)))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C))))))) )  &  ( ((k2_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k1_rltopsp1 (k15_euclid A) B C))) E) = (k1_rltopsp1 (k15_euclid A) B C))  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_abian (u1_struct_0 A) C B) =>  ((r3_lattices A (k9_knaster A B) C) & (r3_lattices A C (k10_knaster A B))) ) ) ) ) ) ) ) ).
tt(t43_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) = (k1_tops_1 k3_topmetr k6_kurato_1)) ) ).
tt(t43_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (~  (D = k1_xboole_0) )  =>  ((k4_lattices A B (k3_lattice2 C A D E)) = (k3_lattice2 C A D (k10_funcop_1 (u1_struct_0 A) C (u1_lattices A) B E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_lattices A B C) = (k15_lattice3 A (k7_domain_1 (u1_struct_0 A) B C)))  &  ((k4_lattices A B C) = (k16_lattice3 A (k7_domain_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t43_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((r2_hidden (k5_lattices A) B) & (r2_hidden (k6_lattices A) B))  =>  ((a_2_1_lattice4 A B) = (k3_lattice4 A B)) ) ) ) ) ) ).
tt(t43_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_lattice5 B (u1_struct_0 A) A (k16_lattice5 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) (u1_struct_0 A)) &  ((v1_lattice5 D C A) &  ((v2_lattice5 D C A) &  ((v3_lattice5 D C A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) (u1_struct_0 A))))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C))) &  ((v19_waybel_0 E A (k1_lattice5 C)) &  ((v20_waybel_0 E A (k1_lattice5 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C)))))) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F C) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ( ((v1_partfun1 H C) &  ((v3_relat_2 H) &  ((v8_relat_2 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  =>  (! [I:$i] :  ( ((v1_partfun1 I C) &  ((v3_relat_2 I) &  ((v8_relat_2 I) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 C C)))) ) )  =>  (! [J:$i] :  (! [K:$i] :  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 C)) E (k4_lattice5 C A D)) &  ( (C = (k3_tarski (a_2_1_lattice5 A B)))  &  ( (D = (k3_tarski (a_2_2_lattice5 A B)))  &  ((r2_hidden H (u1_struct_0 (k1_yellow_2 A (k1_lattice5 C) E))) &  ((r2_hidden I (u1_struct_0 (k1_yellow_2 A (k1_lattice5 C) E))) &  ((r2_hidden (k4_tarski J K) (k5_eqrel_1 C H I)) &  (! [L:$i] :  ( ( (~ (v1_xboole_0 L))  & (m2_finseq_1 L C))  =>  (~  ( ((k3_finseq_1 L) = (k2_nat_1 3 2))  & (r1_lattice5 C L J K H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] : (r1_tarski (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) C) (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 (k15_glib_000 A)) (k2_finseq_1 (k7_nat_d (k15_glib_000 A) B))))) ) ) ) ) ).
tt(t43_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_limfunc1 A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 B C) (k1_seq_1 A C))) ) )  => (v2_limfunc1 B)) ) ) ) ) ).
tt(t43_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc2 C A) =>  ((r1_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A) &  ((k1_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A) = (k8_real_1 B (k1_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t43_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) & (r1_limfunc3 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) )  |  ((r1_tarski (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D)))) (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k9_xtuple_0 C) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) )  | (r1_xxreal_0 (k1_limfunc3 B A) (k1_limfunc3 C A))) ) ) ) ) ) ) ) ).
tt(t43_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r2_limfunc3 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) &  ((k1_seq_1 B E) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) )  | (r5_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t43_lopban_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) &  ((v3_lopban_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k16_lopban_1 A B)))  &  ((v13_algstr_0 (k16_lopban_1 A B)) &  ((v2_rlvect_1 (k16_lopban_1 A B)) &  ((v3_rlvect_1 (k16_lopban_1 A B)) &  ((v4_rlvect_1 (k16_lopban_1 A B)) &  ((v5_rlvect_1 (k16_lopban_1 A B)) &  ((v6_rlvect_1 (k16_lopban_1 A B)) &  ((v7_rlvect_1 (k16_lopban_1 A B)) &  ((v8_rlvect_1 (k16_lopban_1 A B)) &  ((v3_normsp_0 (k16_lopban_1 A B)) &  ((v4_normsp_0 (k16_lopban_1 A B)) &  ((v2_normsp_1 (k16_lopban_1 A B)) &  ((v3_lopban_1 (k16_lopban_1 A B)) & (l1_normsp_1 (k16_lopban_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) &  ((r2_hidden E (k9_lpspace1 A B C)) & (r1_lpspace1 A B C D E)) )  =>  ((k1_mesfunc6 A B C D) = (k1_mesfunc6 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) & (r2_hidden E (k5_lpspace2 A B C D F)))  =>  ((k5_lpspace2 A B C D F) = (k5_lpspace2 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r8_ltlaxio1 C A) & (r8_ltlaxio1 C (k3_hilbert1 A B)))  => (r8_ltlaxio1 C B)) ) ) ) ) ) ) ).
tt(t43_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 B A) => (v2_cqc_the1 (k8_cqc_lang A C B) A)) ) ) ) ) ) ) ).
tt(t43_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k3_mathmorp A (k4_mathmorp A B C) C) (k3_mathmorp A B C)) & (r1_tarski (k6_rusub_4 A (k4_mathmorp A B C) C) (k6_rusub_4 A B C))) ) ) ) ) ) ) ).
tt(t43_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers C C) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers C C) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ((v4_matrix10 D) & (v4_matrix10 E)) ) )  => (v4_matrix10 (k3_matrix10 C (k5_matrix10 C A D) (k5_matrix10 C B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) (k1_nat_1 A 2) (k1_nat_1 A 2)) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2))) &  ((v3_funct_2 E (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2)))))) ) )  =>  ( (D = E)  =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [G:$i] :  ((m1_matrix_2 G (k12_matrix_2 (k1_nat_1 A 2))) =>  ( (G = (k1_partfun1 (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 (k1_nat_1 A 2)))) (k2_funct_2 (k2_finseq_1 (k1_nat_1 A 2)) E) F))  =>  ((k3_funct_2 (k12_matrix_2 (k1_nat_1 A 2)) (u1_struct_0 B) (k11_matrix_3 (k1_nat_1 A 2) B C) G) = (k8_group_1 B (k2_matrix11 A B D) (k3_funct_2 (k12_matrix_2 (k1_nat_1 A 2)) (u1_struct_0 B) (k11_matrix_3 (k1_nat_1 A 2) B (k4_matrix11 (k1_nat_1 A 2) (k1_nat_1 A 2) (u1_struct_0 B) E C)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix13,ax, (! [A:$i] :  ( ((v1_finset_1 A) &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers))) )  =>  (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski A (k2_finseq_1 B))) ) ) ) ).
tt(t43_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C B) &  (D = (k4_matrix14 A B C)) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B)) ) )  =>  ( (C = 1)  |  ( ( ( (E = 1)  &  (F = C) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( ( ( (E = C)  &  (F = 1) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( ( ( (E = 1)  &  (F = 1) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) )  &  ( ( ( (E = C)  &  (F = C) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) )  &  ( (~  ( ( (E = 1)  |  (E = C) )  &  ( (F = 1)  |  (F = C) ) ) )  =>  ( ( (E = F)  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( (~  (E = F) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 A k5_numbers)) =>  ( ((r1_tarski (k10_xtuple_0 E) (k4_finseq_1 C)) &  ( ((k4_finseq_1 C) = (k4_finseq_1 D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k7_subset_1 k5_numbers (k4_finseq_1 C) (k10_xtuple_0 E))) =>  ( ((k8_matrix_1 (u1_struct_0 B) C F) = (k5_finseq_2 (u1_struct_0 B) (k1_matrix_1 C) (k4_struct_0 B)))  &  ((k8_matrix_1 (u1_struct_0 B) D F) = (k5_finseq_2 (u1_struct_0 B) (k1_matrix_1 D) (k4_struct_0 B))) ) ) ) ) ) )  =>  ((r1_xxreal_0 A k1_xboole_0) |  ((k4_matrix15 B C D) = (k4_matrix15 B (k1_matrix13 (u1_struct_0 B) C A (k5_card_1 (k2_finseq_1 (k1_matrix_1 C))) E (k5_matrix13 (k2_finseq_1 (k1_matrix_1 C)))) (k1_matrix13 (u1_struct_0 B) D A (k5_card_1 (k2_finseq_1 (k1_matrix_1 D))) E (k5_matrix13 (k2_finseq_1 (k1_matrix_1 D)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((v2_matrix16 D (u1_struct_0 A)) =>  ((k2_matrix_6 (k3_finseq_1 D) A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix16 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix16 (u1_struct_0 A) D) C)) = (k1_matrix16 (u1_struct_0 A) (k9_fvsum_1 A D (k1_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ((r2_hidden A (k4_finseq_1 E)) &  ( ((k1_funct_1 E A) = D)  & (r2_hidden B (k4_finseq_1 D))) )  => (r2_hidden (k4_tarski A B) (k2_matrix_1 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k2_matrix_3 A (k1_matrix_4 A B C)) = (k1_matrix_4 A C B)) ) ) ) ) ) ) ) ).
tt(t43_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v4_matrix_6 C A B) =>  ((k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) C) = (k4_matrix_6 A B C (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ) ).
tt(t43_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (r1_matrix_8 A B D C))  => (r1_matrix_8 A B (k5_matrix_6 A B D) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t43_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 2 1 3)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 2 1 3) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 2 1 3) (k2_finseq_1 3) (k2_finseq_1 3)) &  ( (~ (v5_matrix_2 (k3_finseq_4 k5_numbers 2 1 3) 3))  & (m1_subset_1 (k3_finseq_4 k5_numbers 2 1 3) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(t43_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 B))  & (r1_xxreal_0 1 (k3_finseq_1 A)))  =>  ((k1_complsp2 (k6_matrixc1 B A)) = (k6_matrixc1 (k1_matrixc1 B) (k1_complsp2 A))) ) ) ) ) ) ).
tt(t43_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E (u1_struct_0 B)) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) =>  ((k7_matrix_2 A B (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) (k4_matrixj1 (u1_struct_0 B) D) E))) = (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) (k4_matrixj1 (u1_struct_0 B) (k7_matrix_2 A B D)) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrixr1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k7_matrixr1 A (k3_matrixr1 B C)) = (k3_matrixr1 (k7_matrixr1 A B) (k7_matrixr1 A C))) ) ) ) ) ) ) ) ).
tt(t43_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  ((k12_matrix_3 B A C) = (k12_matrix_3 B A (k5_matrix_1 B (u1_struct_0 A) C))) ) ) ) ) ) ) ).
tt(t43_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v2_funct_1 D) <=>  ((k1_ranknull A B C D) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  (! [F:$i] :  ((m1_matrlin F A C) =>  (! [G:$i] :  ((m1_matrlin G A D) =>  ( (~  (B = (k4_struct_0 A)) )  =>  ((k10_matrlin A C D (k4_matrlin A C D E B) F G) = (k6_matrix_3 A (k10_matrlin A C D E F G) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((v5_matroid0 B A) &  ((v5_matroid0 C A) &  ( (~  (B = C) )  &  ((r2_hidden D (k9_subset_1 (u1_struct_0 A) B C)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v5_matroid0 E A) & (r1_tarski E (k7_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) (k6_domain_1 (u1_struct_0 A) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_1 k1_numbers (k6_matrprob A B C)) = (k6_matrprob B A (k4_matrix_1 k1_numbers C))) ) ) ) ) ) ) ) ) ).
tt(t43_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B (u1_struct_0 k2_vectsp_1) A A) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A A) =>  ( (~  ((k12_matrix_3 A k2_vectsp_1 B) = (k4_struct_0 k2_vectsp_1)) )  =>  ( ((k2_funct_1 (k3_matrtop1 A A B)) = (k3_matrtop1 A A C))  <=>  ((k5_matrix_6 A k2_vectsp_1 B) = C) ) ) ) ) ) ) ) ) ).
tt(t43_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((v3_xxreal_2 A) =>  ((k5_seq_4 A) = (k1_real_1 (k4_seq_4 (k4_measure6 A)))) ) ) ) ).
tt(t43_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k8_member_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k1_xxreal_3 A B))) ) ) ) ) ).
tt(t43_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  (~  ((r2_hidden D (k9_xtuple_0 (k8_memstr_0 A B C))) &  ( (~ (r2_hidden D (k9_xtuple_0 C)))  &  (~  (D = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_mesfun6c A B C D) =>  ( (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (~  ( (E = (k1_relset_1 A D))  & (r1_mesfun6c A B D E)) ) ) )  | (r1_xxreal_0 (k17_complex1 (k1_mesfun6c A B C D)) (k1_mesfunc6 A B C (k55_valued_1 A k2_numbers D)))) ) ) ) ) ) ) ) ) ) ).
tt(t43_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_mesfun7c A B C) <=>  ((r2_mesfunc6 A B (k5_comseq_3 A C)) & (r2_mesfunc6 A B (k6_comseq_3 A C))) ) ) ) ) ) ) ) ).
tt(t43_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_mesfun7c A B C) => (m1_subset_1 (k1_relset_1 A C) B)) ) ) ) ) ) ) ).
tt(t43_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_tarski D (k1_relset_1 A E)) &  ((r1_mesfunc1 A B E D) &  ((r1_mesfunc1 A B F D) &  ((v3_mesfunc5 E) & (v3_mesfunc5 F)) ) ) )  => (r1_mesfunc1 A B (k3_mesfunc1 A (k1_mesfunc2 A (k3_mesfunc1 A E F)) (k2_mesfunc2 A E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_mesfunc6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k17_complex1 A) = (k3_extreal1 (k1_measure6 A))) ) ) ).
tt(t43_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( ((v2_mesfunc9 B A) & (v1_mesfunc8 B A k7_numbers))  => (v1_mesfunc8 (k4_mesfunc9 A B) A k7_numbers)) ) ) ) ) ).
tt(t43_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (! [D:$i] :  ((m1_midsp_1 D A) =>  ((k7_midsp_1 A (k7_midsp_1 A B C) D) = (k7_midsp_1 A B (k7_midsp_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t43_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r2_relset_1 A A (k18_mmlquery A (k20_mmlquery A B C)) (k19_mmlquery A (k18_mmlquery A B) (k18_mmlquery A C)))) ) ) ) ) ).
tt(t43_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  ( (~  ((k16_modal_1 A) = (k10_modal_1 B)) )  &  ( (~  ((k16_modal_1 A) = (k11_modal_1 B)) )  &  (~  ((k16_modal_1 A) = (k12_modal_1 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k51_modelc_1 A B C (k26_modelc_1 (k48_modelc_1 A B C) D)) = (k2_knaster A (k58_modelc_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t43_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r3_modelc_2 A (k7_modelc_2 B C)) &  ( (~ (r2_modelc_2 A B))  &  (~ (r2_modelc_2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  => (m1_subset_1 (k11_modelc_3 A) (k23_modelc_3 A))) ) ).
tt(t43_moebius1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ((r1_xboole_0 A B) =>  ((k2_xboole_0 (k13_pre_poly (k4_moebius1 A)) (k13_pre_poly (k4_moebius1 B))) = (k13_pre_poly (k11_pre_poly k5_numbers (k4_moebius1 A) (k4_moebius1 B)))) ) ) ) ) ) ).
tt(t43_monoid_0,ax, (k4_monoid_0 = (g3_algstr_0 k5_numbers k47_binop_2)) ).
tt(t43_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (~  ((m1_subset_1 A (u1_struct_0 (k19_monoid_1 B))) &  (! [C:$i] :  ((m2_finseq_1 C B) =>  (~  (A = (k20_monoid_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t43_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) C (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_msaterm F A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E)) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ( ((k3_finseq_1 G) = (k3_finseq_1 F))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 F)) =>  (! [I:$i] :  ((m1_dtconstr I (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) (k5_trees_3 (u1_struct_0 (k5_msafree A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C)))) (k1_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C))) =>  ( (I = (k1_funct_1 F H))  =>  ((k1_funct_1 G H) = (k9_msaterm A B C I D)) ) ) ) ) ) ) )  =>  ((k9_msaterm A B C (k6_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) (k2_msaterm A (k2_pboole (u1_struct_0 A) (u3_msualg_1 A B) C) E) F) D) = (k1_funct_1 (k5_msualg_1 A E B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  ((r1_pboole A C D) => (r2_pboole A (k4_mssubfam A B D) C)) ) ) ) ) ) ) ) ).
tt(t43_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) => (r2_pboole (u1_struct_0 A) C (k9_msualg_6 A B C))) ) ) ) ) ) ).
tt(t43_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D A) & (r2_hidden (k4_tarski (k2_xcmplx_0 C A) D) (u1_orders_2 (k6_mycielsk A B))))  => (r2_hidden (k4_tarski C D) (u1_orders_2 B))) ) ) ) ) ) ) ) ) ).
tt(t43_nat_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski A B) => (r1_xxreal_0 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t43_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k1_polynom2 k10_newton (k12_nat_3 A)) = (k1_tarski A)) ) ) ).
tt(t43_nat_4,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((r1_tarski A B) & (r1_tarski B k5_numbers))  =>  ((r2_hidden k1_xboole_0 B) | (r1_xxreal_0 (k3_wsierp_1 (k14_finseq_1 A)) (k3_wsierp_1 (k14_finseq_1 B)))) ) ) ) ) ).
tt(t43_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 (k7_nat_d A B)) | (r1_xxreal_0 1 (k6_xcmplx_0 A B)))  =>  ((k2_nat_1 (k7_nat_d A B) B) = A) ) ) ) ) ) ).
tt(t43_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v2_nattra_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C B A) =>  (! [D:$i] :  ((m1_nattra_1 D B A C C) => (r2_funct_2 (u1_struct_0 B) (u4_struct_0 A) D (k6_nattra_1 B A C))) ) ) ) ) ) ) ) ).
tt(t43_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r9_ncfcont1 B A D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 B) E) C) &  ((v3_normsp_1 E B) & (r2_hidden (k6_normsp_1 B E) C)) )  =>  ((v9_clvect_1 (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D) A) &  ((k7_partfun1 (u1_struct_0 A) D (k6_normsp_1 B E)) = (k7_clvect_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_nfcont_1 E A) &  ((r1_tarski E (k1_relset_1 (u1_struct_0 A) B)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F E) =>  ((k7_partfun1 (u1_struct_0 A) B F) = (k3_rlvect_1 A (k1_rlvect_1 A F C) D)) ) ) ) ) )  =>  ((r2_ndiff_1 E A A B) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F E) =>  ((k7_partfun1 (u1_struct_0 (k16_lopban_1 A A)) (k4_ndiff_1 A A B E) F) = (k4_lopban_2 A (k6_lopban_2 A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers (u1_struct_0 (k4_real_ns1 1))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 1)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (B = (k2_funct_1 (k1_pdiff_1 1 1)))  &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  & (r2_relset_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) B F) E)) ) ) )  =>  ((r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) <=> (r1_ndiff_3 (k4_real_ns1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k4_card_3 (k4_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (k4_prvect_2 A))) =>  (! [D:$i] : (m1_subset_1 (k1_funct_4 B (k11_card_3 (k4_prvect_2 A) C D)) (k4_card_3 (k4_prvect_2 A)))) ) ) ) ) ) ) ).
tt(t43_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k5_nat_d A (k5_nat_d B C)) = (k5_nat_d (k5_nat_d A B) C)) ) ) ) ) ) ) ).
tt(t43_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))  => (r5_nfcont_1 B C A D)) ) ) ) ) ) ) ) ).
tt(t43_nfcont_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ((r1_nfcont_4 B C A) <=>  ((r2_hidden A (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 B)) => (r1_fcont_1 (k1_partfun1 k1_numbers (k1_euclid B) (k1_euclid B) k1_numbers C (k1_pdiff_1 D B)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) => (r1_tarski (k9_normform A (k5_setwiseo (k7_normform A) B C)) (k5_setwiseo (k7_normform A) (k9_normform A B) C))) ) ) ) ) ).
tt(t43_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) D) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) (k4_oppcat_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t43_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  => (r1_orders_1 B A)) ) ) ).
tt(t43_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) =>  (~  ((k3_tarski (k4_orders_2 A B)) = k1_xboole_0) ) ) ) ) ) ).
tt(t43_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k12_ordinal2 A k1_xboole_0) = 1) ) ) ).
tt(t43_ordinal3,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (k1_xboole_0 = (k9_xtuple_0 A)) )  =>  ((k4_ordinal2 (k1_ordinal3 B A)) = (k10_ordinal2 B (k4_ordinal2 A))) ) ) ) ) ) ).
tt(t43_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k3_ordinal5 C)) ) ) ) )  =>  ((k3_ordinal5 A) = (k8_ordinal2 B)) ) ) ) ) ) ) ) ).
tt(t43_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) )  =>  (~  ((r2_hidden k4_ordinal1 B) &  ((r2_hidden A B) &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden A D) & (r1_abian D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t43_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) =>  ((k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C)) = (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) C)) ) ) ) ) ) ) ).
tt(t43_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_subset_1 C (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_msualg_2 A B) (k13_osalg_2 A B)) =>  ((k5_binop_1 (k13_osalg_2 A B) (k15_osalg_2 A B) C D) = (k5_binop_1 (k14_msualg_2 A B) (k16_msualg_2 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(t43_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_parsp_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_partfun1 (k3_partfun1 C A B) A) => (r1_tarski (k7_relat_1 C A) B)) ) ) ) ) ).
tt(t43_partfun2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C D))))  =>  ((v3_funct_1 (k2_partfun1 C D E A)) => (v3_funct_1 (k2_partfun1 C D (k2_partfun1 C D E B) A))) ) ) ) ) ) ) ) ) ).
tt(t43_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r2_pboole A (k1_pboole A) B)) ) ) ).
tt(t43_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k24_pcs_0 A B)) <=>  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r1_pcs_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_pdiff_4,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((k7_pdiff_4 B C D A) = (k1_euclid_8 (k9_real_1 (k11_pdiff_1 3 2 D A) (k11_pdiff_1 3 3 C A)) (k9_real_1 (k11_pdiff_1 3 3 B A) (k11_pdiff_1 3 1 D A)) (k9_real_1 (k11_pdiff_1 3 1 C A) (k11_pdiff_1 3 2 B A)))) ) ) ) ) ) ) ) ) ).
tt(t43_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 1 3) B)) =>  ( ((r7_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 1 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B))))) &  ((k7_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 1 (k1_pdiff_3 3 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F A) &  ((r1_xxreal_0 C D) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k1_rcomp_1 C D)) => (r2_hidden (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G) (k1_relset_1 (k1_euclid A) B))) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G (k1_rcomp_1 C D)) => (r3_pdiff_1 A F B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G))) ) )  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden G (k1_rcomp_1 C D)) &  ( (H = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) G))  &  ((k10_binop_2 (k7_partfun1 k1_numbers B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) D)) (k7_partfun1 k1_numbers B (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F E) C))) = (k11_binop_2 (k10_binop_2 D C) (k11_pdiff_1 A F B H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  ( ( (C = D)  & (r1_tarski B (k1_relset_1 (k1_euclid A) C)))  =>  ((r1_pdiff_9 A B C) <=>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 (k4_real_ns1 A))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((r1_tarski (k2_relset_1 (u1_struct_0 (k4_real_ns1 A)) E) B) &  ((v3_normsp_1 E (k4_real_ns1 A)) & (r2_hidden (k6_normsp_1 (k4_real_ns1 A) E) B)) )  =>  ((v2_comseq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) E D)) &  ((k7_partfun1 k1_numbers D (k6_normsp_1 (k4_real_ns1 A) E)) = (k2_seq_2 (k8_funct_2 k5_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 A (k4_xcmplx_0 A))) ) ) ) ).
tt(t43_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  (! [D:$i] :  ((m2_finseq_2 D B (k3_finseq_2 B)) =>  (! [E:$i] :  ((m2_finseq_2 E B (k3_finseq_2 B)) =>  ((k10_pnproc_1 A B (k7_domain_1 (k3_finseq_2 B) C D) (k6_domain_1 (k3_finseq_2 B) E)) = (k7_domain_1 (k3_finseq_2 B) (k1_pre_poly B C E) (k1_pre_poly B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t43_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  ( (C = D)  <=>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A B)) =>  ((k3_bspace C E) = (k3_bspace D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k4_polynom5 A B (k4_struct_0 A)) (k3_algseq_1 A B))) ) ) ) ).
tt(t43_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 (k1_algseq_1 A B) D) & (r1_xxreal_0 (k1_algseq_1 A C) D))  =>  ((r1_xxreal_0 D k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_polynom8 A E (k4_nat_1 2 D)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k6_polynom8 (k4_nat_1 2 D) A (k6_polynom8 (k4_nat_1 2 D) A (k13_polynom3 A B C) E) (k11_algstr_0 A E)) (k3_polynom5 A (k13_polynom3 A B C) (k1_polynom8 A (k4_nat_1 2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r4_polyred A B C D E F) => (r2_polyred A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_power A B) = (k4_prepower A B)) ) ) ) ) ).
tt(t43_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r1_pre_poly A B C) & (r2_pre_poly A C D))  => (r1_pre_poly A B D)) ) ) ) ) ) ) ) ) ).
tt(t43_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  (A = k6_numbers) )  =>  ((k4_prepower A (k6_xcmplx_0 B C)) = (k13_complex1 (k1_newton A B) (k1_newton A C))) ) ) ) ) ) ) ) ).
tt(t43_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  (! [E:$i] :  ((m2_prob_1 E B C) =>  ((v1_prob_2 D) =>  ((k1_funct_1 (k8_prob_1 B C (k2_prob_3 B D) E) A) = (k1_funct_1 (k3_series_1 (k8_prob_1 B C D E)) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden B (k4_cqc_the1 A)) => (r2_hidden (k9_cqc_lang A C B) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t43_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k20_pscomp_1 A)) A) = (k1_tarski (k20_pscomp_1 A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k21_pscomp_1 A) (k12_pscomp_1 A)) A) = (k1_tarski (k21_pscomp_1 A))) ) ) ) ).
tt(t43_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k3_pboole A B (k1_pzfmisc1 A C)) (k1_pzfmisc1 A C)) => (r1_pboole A C B)) ) ) ) ) ) ).
tt(t43_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B (k13_qc_lang1 A C)) <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t43_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v5_qc_lang1 B A) =>  ((k4_qc_lang3 A C B) = (k4_qc_lang3 A C (k22_qc_lang1 A B))) ) ) ) ) ) ) ) ).
tt(t43_quatern2,ax, ((k17_quatern2 (k5_struct_0 k16_quatern2)) = (k5_struct_0 k16_quatern2)) ).
tt(t43_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (~  ( (~  ((k9_real_1 (k3_quatern2 A) (k3_quatern2 B)) = k6_numbers) )  & (r1_xxreal_0 (k9_real_1 (k7_real_1 (k5_square_1 (k3_quatern2 A)) (k5_square_1 (k3_quatern2 B))) (k8_real_1 (k8_real_1 2 (k3_quatern2 A)) (k3_quatern2 B))) k6_numbers)) ) ) ) ) ) ).
tt(t43_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k31_quaterni A) = (k6_quaterni (k17_quaterni A) (k1_real_1 (k18_quaterni A)) (k1_real_1 (k19_quaterni A)) (k1_real_1 (k20_quaterni A)))) ) ) ).
tt(t43_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  ((k8_group_1 (k19_quofield A) B C) = (k8_group_1 (k19_quofield A) C B)) ) ) ) ) ) ) ).
tt(t43_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v13_vectsp_1 D C B) &  ((v1_mod_2 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [F:$i] :  ((m2_vectsp_6 F A B (k2_ranknull C B D E)) =>  ((v2_funct_1 (k2_partfun1 (u1_struct_0 C) (u1_struct_0 B) D E)) => (r1_vectsp_6 A B (k8_ranknull A C B (k9_ranknull A C B E D F) D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ( ((k1_rat_1 (k4_xcmplx_0 A)) = (k1_rat_1 A))  &  ((k2_rat_1 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k2_rat_1 A))) ) ) ) ).
tt(t43_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_numbers)) =>  ( (C = D)  =>  ((v2_connsp_1 C (k4_topmetr A B)) <=> (v6_xxreal_2 D)) ) ) ) ) ) ) ) ) ) ).
tt(t43_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) ) )  & (v1_rat_1 A)) ) ) ) ).
tt(t43_relat_1,ax, ((k2_relat_1 k1_xboole_0) = k1_xboole_0) ).
tt(t43_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  (! [E:$i] :  ( (~  ( (~ (r1_xboole_0 D (k7_relset_1 B A (k3_relset_1 A B C) E)))  &  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden F D) &  ((r2_hidden G E) & (r2_hidden F (k1_relset_2 B A (k3_relset_1 A B C) G))) ) ) ) ) ) )  &  (~  ( (? [F:$i] :  (? [G:$i] :  ((r2_hidden F D) &  ((r2_hidden G E) & (r2_hidden F (k1_relset_2 B A (k3_relset_1 A B C) G))) ) ) )  & (r1_xboole_0 D (k7_relset_1 B A (k3_relset_1 A B C) E))) ) ) ) ) ) ) ) ) ).
tt(t43_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( ((r1_rewrite1 A C B) & (r6_rewrite1 A C D))  |  ((r6_rewrite1 A B C) & (r1_rewrite1 A C D)) )  => (r6_rewrite1 A B D)) ) ) ) ) ) ).
tt(t43_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r3_rewrite2 A (k7_rewrite2 A B) C D) => (r3_rewrite2 A B C D)) ) ) ) ) ) ) ) ).
tt(t43_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  (~  ( (~ (r2_hidden (k2_flang_1 D) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))))  & (r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C B)) (k1_rewrite3 D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ((k54_valued_1 (k1_rfunct_1 A B)) = (k1_rfunct_1 (k54_valued_1 A) (k54_valued_1 B))) ) ) ) ) ).
tt(t43_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_tarski A)))) ) ) ).
tt(t43_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_classes1 (k18_rfunct_3 A C) (k18_rfunct_3 B D)) & (r2_classes1 (k19_rfunct_3 A C) (k19_rfunct_3 B D)))  => (r2_classes1 C D)) ) ) ) ) ) ) ) ) ).
tt(t43_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 A D) => (r1_xxreal_0 B (k1_seq_1 C D))) ) )  <=> (r1_xxreal_0 B (k1_seq_1 (k3_rinfsup1 C) A))) ) ) ) ) ) ) ) ).
tt(t43_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_rlaffin1 B A) & (r1_tarski C B))  => (v1_rlaffin1 C A)) ) ) ) ) ) ) ).
tt(t43_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) => (r2_hidden B (k3_rlsub_1 A B C))) ) ) ) ) ) ).
tt(t43_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) <=>  (! [D:$i] :  ((m2_rlsub_1 D A B) =>  (! [E:$i] :  ((m2_rlsub_1 E A C) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k9_subset_1 (u1_struct_0 A) D E) = (k6_domain_1 (u1_struct_0 A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_finset_1 B) &  (B = (a_1_0_rltopsp1 A)) )  => (v9_rltopsp1 (k5_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t43_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  ((k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) = (k4_struct_0 A)) ) ) ).
tt(t43_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k8_rlvect_2 A k6_numbers B) (k4_rlvect_2 A))) ) ) ) ).
tt(t43_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r2_hidden (k4_struct_0 B) (k3_rmod_2 A B C D)) <=> (r1_struct_0 D C)) ) ) ) ) ) ) ) ) ).
tt(t43_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ( ((r1_rmod_3 A B C D) &  ( (E = (k3_rlvect_1 B F G))  &  ( (E = (k3_rlvect_1 B H I))  &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  ((r1_struct_0 D G) & (r1_struct_0 D I)) ) ) ) ) )  =>  ( (F = H)  &  (G = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (D = (k4_struct_0 A)) )  =>  ((k2_rmod_4 A B (k7_rmod_4 A B D C)) = (k2_rmod_4 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t43_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A (k15_robbins1 A B) (k11_robbins1 A B)) = (k5_robbins1 A (k14_robbins1 A B) (k13_robbins1 A B))) ) ) ) ) ).
tt(t43_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A C B) D))) = (k3_robbins1 A B)) ) ) ) ) ) ) ) ) ).
tt(t43_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_3 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~ (v4_roughs_1 B A)) ) ) ) ) ).
tt(t43_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_rpr_1 A B (k3_subset_1 A B)) = k6_numbers) ) ) ) ) ).
tt(t43_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_struct_0 B C) =>  ((k3_rusub_1 A (k1_rlvect_1 A C D) B) = (u1_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t43_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((r1_rusub_2 A B C) <=>  (! [D:$i] :  ((m2_rusub_1 D A B) =>  (! [E:$i] :  ((m2_rusub_1 E A C) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((k9_subset_1 (u1_struct_0 A) D E) = (k6_domain_1 (u1_struct_0 A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ( ((m1_rusub_1 B D) & (m1_rusub_1 C D))  => (m1_rusub_1 (k1_rusub_2 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t43_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  ( (B = (k1_struct_0 A))  =>  ((v3_pre_topc B (k5_rusub_5 A)) & (v4_pre_topc B (k5_rusub_5 A))) ) ) ) ) ) ).
tt(t43_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  (B = (k5_rvsum_1 A (k9_rvsum_1 A B C) C)) ) ) ) ) ) ) ).
tt(t43_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k19_rvsum_1 (k7_finseq_1 (k9_finseq_1 A) B)) = (k5_binop_2 A (k19_rvsum_1 B))) ) ) ) ) ).
tt(t43_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  (~  ((r1_tarski (k1_funct_4 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) (k16_funcop_1 (k5_scmfsa_2 k6_numbers) C)) B) &  ((r1_tarski k2_scmbsort A) &  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (~  ((r2_classes1 C D) &  ((v8_valued_0 D) &  ((m2_finseq_1 D k4_numbers) &  ((k18_scmfsa_2 (k6_extpro_1 3 k1_scmfsa_2 A B) (k5_scmfsa_2 k6_numbers)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_scmfsa10,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) (k13_scmfsa_2 A C) B) = (k13_scmfsa_2 (k2_nat_1 A B) C)) ) ) ) ) ) ) ).
tt(t43_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r2_hidden A (k1_relset_1 (u1_struct_0 k1_scmfsa_2) B))) ) ) ) ).
tt(t43_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) & (r1_scmfsa8a B A (k2_scmfsa6a D)))  =>  ((r6_scmfsa7b (k2_scmfsa8b E C D) B A) &  ((r5_scmfsa7b (k2_scmfsa8b E C D) B A) &  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa8b E C D)) (k1_funct_4 B (k7_memstr_0 3 k1_scmfsa_2 k6_numbers))) = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a D (k4_compos_1 k1_scmfsa_2))) (k8_memstr_0 3 k1_scmfsa_2 B)) 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 C D E A) (k2_nat_1 B 1)) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 C D E A) B) D E A) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t43_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k2_scmfsa8b E C D)) &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B E) k6_numbers))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3)))))  &  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k2_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (~  (A = (k4_struct_0 k1_scmpds_2)) ) ) ) ).
tt(t43_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v3_scmpds_4 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) G)) = k6_numbers)  =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_6 E G C D) B A) F) = (k1_funct_1 (k6_scmpds_4 C B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_scmpds_7,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((k1_funct_1 (k2_scmpds_7 A B C D) k6_numbers) = (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 D) 3)))  &  ( ((k1_funct_1 (k2_scmpds_7 A B C D) (k2_nat_1 (k5_card_1 D) 1)) = (k11_scmpds_2 A B (k4_xcmplx_0 C)))  &  ((k1_funct_1 (k2_scmpds_7 A B C D) (k2_nat_1 (k5_card_1 D) 2)) = (k3_scmpds_2 (k4_xcmplx_0 (k2_nat_1 (k5_card_1 D) 2)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((k7_scmyciel A B) = (k7_scmyciel A (k3_xboole_0 B (k3_tarski A)))) ) ) ) ).
tt(t43_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) =>  ((r2_semi_af1 A B D C E) &  ((r2_semi_af1 A D E B C) &  ((r2_semi_af1 A C B E D) &  ((r2_semi_af1 A D B E C) &  ((r2_semi_af1 A E C D B) & (r2_semi_af1 A C E B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) => (r2_funct_2 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers B C) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers B A) (k20_valued_1 k5_numbers k1_numbers k1_numbers C A)))) ) ) ) ) ) ) ).
tt(t43_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 B C)) ) )  => (r1_xxreal_0 B (k3_seq_4 A))) ) ) ) ) ).
tt(t43_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((r3_seqfunc A B C) <=>  ((r1_seqfunc A k1_numbers B C) &  ((r2_seqfunc A B C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  (? [G:$i] :  ((m1_subset_1 G A) &  ((r1_xxreal_0 E F) &  ((r2_hidden G C) & (r1_xxreal_0 D (k18_complex1 (k9_real_1 (k1_seq_1 (k1_seqfunc A k1_numbers B F) G) (k1_seq_1 (k11_seqfunc A B C) G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_seqm_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~  ( (~ (r1_xxreal_0 A 1))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (A = (k2_nat_1 B 1))  &  (~ (r1_xxreal_0 B k6_numbers)) ) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ( (A = (k2_nat_1 B 1))  &  (~ (r1_xxreal_0 B k6_numbers)) ) ) )  & (r1_xxreal_0 A 1)) ) ) ) ) ).
tt(t43_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers)) ) )  & (r1_xxreal_0 (k1_seq_1 (k1_series_3 B) A) k6_numbers)) ) ) ) ) ) ).
tt(t43_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) => (r1_xxreal_0 (k2_xcmplx_0 (k3_xcmplx_0 (k1_newton A C) B) (k3_xcmplx_0 A (k1_newton B C))) (k2_xcmplx_0 (k1_newton A (k2_nat_1 C 1)) (k1_newton B (k2_nat_1 C 1))))) ) ) ) ) ) ) ).
tt(t43_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r2_hidden B A) =>  ((r2_hidden B (k8_setfam_1 A C)) <=>  (! [D:$i] :  ((r2_hidden D C) => (r2_hidden B D)) ) ) ) ) ) ) ) ).
tt(t43_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ((k3_prob_1 A (k4_setlim_1 A B)) = (k1_kurato_0 A B)) ) ) ) ) ).
tt(t43_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k1_setlim_2 B C D)) A) = (k9_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t43_setwiseo,ax, (! [A:$i] :  ((k4_binop_1 (k5_finsub_1 A) (k9_setwiseo A)) = k1_xboole_0) ) ).
tt(t43_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k3_scmfsa6a A B)) = (k1_finsub_1 (k1_zfmisc_1 k3_scmfsa_2) (k4_sf_mastr A) (k4_sf_mastr B))) ) ) ) ) ).
tt(t43_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B C) C) = (k5_sheffer1 A C (k5_sheffer1 A B B))) ) ) ) ) ) ) ).
tt(t43_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) => (r1_xxreal_0 (k6_simplex0 (k8_simplex0 A C B)) (k6_simplex0 C))) ) ) ) ) ).
tt(t43_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) &  ((v3_matroid0 B) &  ((v6_simplex0 B (u1_struct_0 A)) &  ((v1_simplex1 B A) &  ((v2_simplex1 B A) & (m1_simplex0 B (u1_struct_0 A))) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_tops_2 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ( ((v6_ordinal1 C) &  ((v1_setfam_1 C) &  ((k3_real_1 (k5_card_1 C) 1) = (k5_card_1 (k5_setfam_1 (u1_struct_0 B) C))) ) )  =>  ((k1_card_1 (a_3_1_simplex1 A B C)) = 2) ) ) ) ) ) ) ) ).
tt(t43_sincos10,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))))) = (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) ).
tt(t43_sin_cos2,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k7_sin_cos2 k1_numbers))).
tt(t43_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 B)) (k5_binop_2 (k7_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 B))) k7_complex1))) ) ) ) ) ).
tt(t43_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  (~  ((k7_xcmplx_0 (k17_sin_cos (k2_xcmplx_0 A B)) (k17_sin_cos (k6_xcmplx_0 A B))) = (k7_xcmplx_0 (k2_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)) (k6_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B)))) ) ) ) ) ) ) ) ) ).
tt(t43_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_sin_cos2 (k8_real_1 3 A)) = (k7_real_1 (k8_real_1 3 (k3_sin_cos2 A)) (k8_real_1 4 (k2_newton (k3_sin_cos2 A) 3)))) ) ) ).
tt(t43_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) B))))  &  ((r1_xxreal_0 A (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) B))) & (r1_xxreal_0 (k20_sin_cos A) (k1_real_1 1))) ) ) ) ) ) ) ).
tt(t43_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  =>  ((k4_sin_cos7 A) = (k11_binop_2 (k18_binop_2 1 2) (k1_sin_cos7 (k12_binop_2 (k11_binop_2 2 A) (k10_binop_2 1 (k3_square_1 A)))))) ) ) ) ).
tt(t43_sin_cos9,ax, ( ((k5_sin_cos9 k6_numbers) = k6_numbers)  &  ((k1_seq_1 k1_sin_cos9 k6_numbers) = k6_numbers) ) ).
tt(t43_sin_cos,ax, ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos 1) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos 1) k6_numbers))  &  (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos 1) (k1_seq_1 k19_sin_cos 1))) ) ) ).
tt(t43_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( ( ((k17_euclid A) = (k17_euclid B))  |  ((k18_euclid A) = (k18_euclid B)) )  &  (~ (v4_topreal1 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ) ) ) ).
tt(t43_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k6_pscomp_1 A) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))) ) ) ).
tt(t43_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k18_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t43_sprect_3,ax, (! [A:$i] :  ( ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) B)) =>  ( ( (~  ((k17_euclid B) = (k6_pscomp_1 (k3_topreal1 2 A))) )  &  ( (~  ((k17_euclid B) = (k8_pscomp_1 (k3_topreal1 2 A))) )  &  ( (~  ((k18_euclid B) = (k9_pscomp_1 (k3_topreal1 2 A))) )  &  (~  ((k18_euclid B) = (k7_pscomp_1 (k3_topreal1 2 A))) ) ) ) )  | (r2_hidden B (k3_topreal1 2 A))) ) ) ) ) ) ).
tt(t43_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t43_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k6_xcmplx_0 (k3_square_1 A) 1) k6_numbers) =>  ((r1_xxreal_0 (k4_xcmplx_0 1) A) & (r1_xxreal_0 A 1)) ) ) ) ).
tt(t43_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_stacks_1 A B C D) => (r3_stacks_1 B A (k2_funct_1 C) (k2_funct_1 D))) ) ) ) ) ) ) ) ) ).
tt(t43_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 A C))  =>  ((k1_card_1 (a_3_0_stirl2_1 A B C)) = (k1_card_1 (a_2_2_stirl2_1 A B))) ) ) ) ) ) ) ) ).
tt(t43_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  ((k24_qc_lang1 A (k4_cqc_lang B A C D)) = (k9_substut1 A (k4_cqc_lang B A C D))) ) ) ) ) ) ) ) ) ).
tt(t43_subset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden D C) &  ((r1_tarski C (k2_zfmisc_1 A B)) &  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (~  (D = (k4_tarski E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  => (r1_xxreal_0 (k19_supinf_2 A) (k19_supinf_2 B))) ) ) ) ) ).
tt(t43_taxonom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) &  ((v5_tbsp_1 A) & (l1_metric_1 A)) ) ) ) ) )  => (m2_taxonom1 (k4_taxonom1 A) (u1_struct_0 A))) ) ).
tt(t43_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((k11_tdlat_1 A) = (k1_realset1 (k3_tdlat_1 A) (k9_tdlat_1 A))) ) ) ).
tt(t43_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))))) ) ) ) ).
tt(t43_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ( ((k2_tdlat_1 A) = (k10_tdlat_1 A))  &  ((k3_tdlat_1 A) = (k11_tdlat_1 A)) ) ) ) ).
tt(t43_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_2 B A) <=>  (~ (v1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ).
tt(t43_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (~  ( ((v3_tex_3 B A) | (v3_tex_3 C A))  &  ( (~ (r1_tsep_1 B C))  &  (~ (v3_tex_3 (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t43_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tex_4 B A) & (v4_pre_topc B A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  (B = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t43_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tmap_1 A B C D) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_pre_topc E B) &  ((r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) E) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc F A) &  ((r2_hidden D F) & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) &  ((r1_borsuk_6 A D E) &  ((r1_borsuk_6 A E F) & (r1_borsuk_6 A B G)) ) ) )  =>  (! [H:$i] :  ((m1_borsuk_2 H A B C) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A D E) =>  (! [K:$i] :  ((m1_borsuk_2 K A E F) =>  (! [L:$i] :  ((m1_borsuk_2 L A G D) => (r3_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E H (k1_borsuk_2 A C D E I J)) K) (k1_borsuk_2 A B G F (k1_borsuk_2 A B D G (k1_borsuk_2 A B C D H I) (k2_borsuk_2 A G D L)) (k1_borsuk_2 A G E F (k1_borsuk_2 A G D E L J) K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_topalg_6 A)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) |  ( ((k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B C) (k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B C)))) = (k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 C 1)) (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 C 1))))))  &  ((k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B C))) = (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 C 1))))) ) ) ) ) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  => (v7_topalg_6 (k7_partfun1 (k1_topalg_6 A) B C) A)) ) )  &  (! [C:$i] :  ( ((v7_topalg_6 C A) & (m2_subset_1 C (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (~  ( ((k6_topalg_6 A B) = C)  &  ( ((k9_xtuple_0 C) = (k1_xxreal_1 (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B 1))) (k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k3_finseq_1 B))))))  &  ( ((k2_topalg_6 A C) = (k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B 1) (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B 1)))))  &  ((k3_topalg_6 A C) = (k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B (k3_finseq_1 B)) (k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k3_finseq_1 B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (v6_topgen_1 (k1_struct_0 A) A)) ) ).
tt(t43_topgen_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_subset_1 C (u1_struct_0 (k7_topgen_3 A B))) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_topgen_3 A B)))))  =>  ((v3_pre_topc C (k7_topgen_3 A B)) <=> (r1_tarski C B)) ) ) ) ) ) ).
tt(t43_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v5_topgen_4 B A)) ) ) ) ) ).
tt(t43_topgen_5,ax, ((v1_tops_1 k3_numbers k2_topgen_3) & (m1_subset_1 k3_numbers (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ).
tt(t43_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m3_topgrp_1 (k1_topgrp_1 A B) A)) ) ) ) ).
tt(t43_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden B (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden (k19_euclid (k17_euclid B) (k18_euclid C)) (k9_metric_1 (k14_euclid 2) E D)) &  ((k17_euclid A) = (k17_euclid B)) ) )  =>  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) |  ((r2_hidden (k19_euclid (k17_euclid B) (k18_euclid C)) (k1_rltopsp1 (k15_euclid 2) A B)) |  ( ((k17_euclid B) = (k17_euclid C))  |  ( ((k18_euclid B) = (k18_euclid C))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k19_euclid (k17_euclid B) (k18_euclid C))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid B) (k18_euclid C)) C)) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 C) = (k2_rcomp_1 (k9_real_1 (k17_euclid A) D) (k7_real_1 (k17_euclid A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t43_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k5_jgraph_6 A B C)) <=>  ((k12_euclid (k5_algstr_0 (k15_euclid 2) D (k19_euclid A B))) = C) ) ) ) ) ) ) ) ) ) ).
tt(t43_toprealb,ax,(r1_funct_2 (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k10_real_1 1 2))))) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k10_real_1 1 2)) (k3_real_1 (k4_toprealb (k10_real_1 1 2)) 1))))) (u1_struct_0 (k11_toprealb k10_toprealb)) (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))) (k2_tops_2 (u1_struct_0 (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k10_real_1 1 2)) (k3_real_1 (k4_toprealb (k10_real_1 1 2)) 1))))) (u1_struct_0 (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k10_real_1 1 2))))) (k13_toprealb (k4_toprealb (k10_real_1 1 2)))) k15_toprealb)).
tt(t43_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  =>  ((v1_funct_1 (k53_valued_2 A (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k53_valued_2 A (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k53_valued_2 A (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t43_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ( ((v3_toprns_1 B A) & (v3_toprns_1 C A))  =>  ((k6_toprns_1 A (k4_toprns_1 A B C)) = (k5_algstr_0 (k15_euclid A) (k6_toprns_1 A B) (k6_toprns_1 A C))) ) ) ) ) ) ) ) ).
tt(t43_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) <=>  ((k2_tops_1 A B) = (k7_subset_1 (u1_struct_0 A) B (k1_tops_1 A B))) ) ) ) ) ) ).
tt(t43_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_struct_0 B) = k1_xboole_0)  =>  ((k2_struct_0 A) = k1_xboole_0) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc D B) => (v3_pre_topc (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_3 B A) => (v1_tops_3 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t43_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo D A) & (r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C))  => (r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t43_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  ( ((k6_trees_1 A) = k6_numbers)  =>  (A = (k2_trees_1 k6_numbers)) ) ) ) ).
tt(t43_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C (k3_trees_1 A)) => (r1_tarski A (k5_trees_1 A C B))) ) ) ) ) ) ) ).
tt(t43_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((v1_finset_1 (k1_trees_1 B)) & (m1_trees_2 (k1_trees_1 B) A)) ) ) ) ) ).
tt(t43_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B D) &  ((r1_tarski C E) &  ((r1_xboole_0 (k9_subset_1 (u1_struct_0 A) D E) (k4_subset_1 (u1_struct_0 A) B C)) &  ((v4_pre_topc D A) & (v4_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (m1_pre_topc E A))  =>  ( ((m1_pre_topc D B) &  ((m1_pre_topc E C) &  ( ((k2_tsep_1 A D E) = (k2_tsep_1 A B C))  & (r4_tsep_1 A B C)) ) )  =>  ((r1_tsep_1 D E) | (r4_tsep_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_turing_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_turing_1 A)) =>  ( (C = (k3_funct_2 (k2_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A)) (k3_zfmisc_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 A) (k1_domain_1 (u2_turing_1 A) (u1_turing_1 A) D E)))  =>  ( (D = (u5_turing_1 A))  |  ((k1_funct_1 (u3_turing_1 (k32_turing_1 A B)) (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 A) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) D (u4_turing_1 B)) E)) = (k4_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (k1_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (u4_turing_1 B)) (k2_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (k3_mcart_1 (u2_turing_1 A) (u1_turing_1 A) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k34_twoscomp A B) (k35_twoscomp A B)))) =>  ( ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) (k36_twoscomp A B)) = (k1_funct_1 k15_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) A) = (k1_funct_1 C A))  &  ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t43_uniroots,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (C = B)  &  ((k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) B A) = (k2_newton C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_xxreal_0 (k1_algseq_1 A C) B) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_uproots A C B) (k9_polynom3 A))) ) ) ) ) ) ) ).
tt(t43_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) => (r2_valuat_1 A B F (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A D E)) (k6_cqc_lang A (k7_cqc_lang A C E)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k22_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k22_valued_2 A B C)) = C) ) ) ) ) ) ).
tt(t43_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 F B C) &  ((v1_mod_2 F A B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (~  ((v2_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) F (k8_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B D) (k10_xtuple_0 E)))) &  ((r1_tarski (k10_xtuple_0 E) (k1_vectsp_6 A B D)) &  (! [G:$i] :  ((m1_vectsp_6 G A C) =>  (~  ( ((k1_vectsp_6 A C G) = (k2_ranknull B C F (k8_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B D) (k10_xtuple_0 E))))  &  ( ((k4_finseqop (u1_struct_0 B) (u1_struct_0 C) (k3_vectsp_6 A B E D) F) = (k3_vectsp_6 A C (k4_finseqop (u1_struct_0 B) (u1_struct_0 C) E F) G))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  ((r2_hidden H (k8_subset_1 (u1_struct_0 B) (k1_vectsp_6 A B D) (k10_xtuple_0 E))) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D H) = (k3_funct_2 (u1_struct_0 C) (u1_struct_0 A) G (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r2_hidden (k4_struct_0 B) (k3_vectsp_4 A B C D)) <=> (r1_struct_0 D C)) ) ) ) ) ) ) ) ) ).
tt(t43_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) => (m1_vectsp_5 C A B D)) ) ) ) ) ) ) ) ).
tt(t43_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) => (r1_vectsp_6 A B (k8_vectsp_6 A B C C) (k2_vectsp_6 A B))) ) ) ) ) ) ).
tt(t43_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  => (r1_vfunct_1 B C (k4_vfunct_1 B C D k6_numbers) A)) ) ) ) ) ) ) ).
tt(t43_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] : (r1_vfunct_2 A B (k2_vfunct_2 A B C k5_complex1) D)) ) ) ) ) ) ) ).
tt(t43_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((v2_waybel_0 B A) <=>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 B)))  =>  ( (~  (C = k1_xboole_0) )  => (r2_hidden (k2_yellow_0 A C) B)) ) ) ) ) ) ) ) ).
tt(t43_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((r2_hidden B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v6_waybel_3 A) =>  (! [B:$i] :  ( ((v4_card_3 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  ( ((v1_waybel12 B A) & (v1_tops_2 B A))  =>  ((v1_xboole_0 B) |  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc C A) &  (! [D:$i] :  ( ((v3_yellow_8 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden E B) & (r1_xboole_0 (k3_finsub_1 (k1_zfmisc_1 (u1_struct_0 A)) D C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (B = (a_1_0_waybel14 A)) ) )  =>  ((v2_waybel_8 (k2_yellow_1 (k5_waybel11 A))) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) &  ( (B = (k1_yellow_0 (k2_yellow_1 (k5_waybel11 A)) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ((r2_hidden D C) => (v6_waybel_6 D (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_waybel19,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k10_yellow_6 A (k3_yellow_9 A B)) = (k6_domain_1 (u1_struct_0 A) (k2_yellow_0 A B))) ) ) ) ) ).
tt(t43_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  ( ( (~ (v1_xboole_0 (a_2_0_waybel_1 A B)))  & (m1_subset_1 (a_2_0_waybel_1 A B) (k1_zfmisc_1 (u1_struct_0 A))))  &  ( (~ (v1_xboole_0 (a_2_1_waybel_1 A B)))  & (m1_subset_1 (a_2_1_waybel_1 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t43_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v22_waybel_0 B A A) &  ((v8_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k3_waybel20 A (k4_waybel20 A B)))) ) ) ) ).
tt(t43_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v11_waybel_0 B A) & (l1_waybel_0 B A)) ) ) )  =>  ( (~ (v1_xboole_0 (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B))))  &  ((v2_waybel_0 (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) A) & (m1_subset_1 (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t43_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ((v2_waybel23 (u1_struct_0 (k1_waybel_8 A)) A) & (m1_subset_1 (u1_struct_0 (k1_waybel_8 A)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(t43_waybel25,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v6_pre_topc B) &  ((v1_waybel25 B) & (l1_pre_topc B)) ) ) )  =>  ((v4_waybel_0 (k3_waybel24 A (k1_waybel25 B)) (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B))) & (m1_yellow_0 (k3_waybel24 A (k1_waybel25 B)) (k6_yellow_1 (u1_struct_0 A) (k1_waybel25 B)))) ) ) ) ) ).
tt(t43_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc B))))  =>  (! [D:$i] :  ( ((v3_pre_topc D (k2_borsuk_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  ((v1_funct_1 (k6_waybel26 D (u1_struct_0 A))) &  ((v1_funct_2 (k6_waybel26 D (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc (k6_waybel26 D (u1_struct_0 A)) A C) & (m1_subset_1 (k6_waybel26 D (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (v3_waybel_3 (k2_waybel27 A B))) ) ) ) ).
tt(t43_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  ((v22_waybel_0 (k4_waybel_2 A) (k3_yellow_3 A A) A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k11_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k3_yellow_4 A B C))) ) ) ) ) ) ) ) ).
tt(t43_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((m1_subset_1 B (u1_struct_0 (k8_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (r2_hidden (u1_struct_0 B) A)) ) ) ) ) ) ) ).
tt(t43_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_setfam_1 (a_2_1_waybel_4 A B)) = (k1_waybel_3 A B)) ) ) ) ) ).
tt(t43_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v5_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((v5_waybel_7 B A) <=> (v19_waybel_0 (k7_waybel_4 A B) A (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ) ).
tt(t43_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_wellord1 A B C) =>  ( ((v1_relat_2 A) => (v1_relat_2 B))  &  ( ((v8_relat_2 A) => (v8_relat_2 B))  &  ( ((v6_relat_2 A) => (v6_relat_2 B))  &  ( ((v4_relat_2 A) => (v4_relat_2 B))  &  ((v1_wellord1 A) => (v1_wellord1 B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_xboole_0 B C)) => (r1_tarski (k4_xboole_0 A B) C)) ) ) ) ).
tt(t43_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean A (k9_xboolean B C)) = (k4_xboolean (k6_xboolean A (k3_xboolean B)) (k6_xboolean A (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t43_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 A B) C) D) = (k6_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 B D)) (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t43_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 (k6_xcmplx_0 B A) B)) ) ) ) ) ).
tt(t43_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  ((k14_xtuple_0 (k2_xboole_0 A B)) = (k2_xboole_0 (k14_xtuple_0 A) (k14_xtuple_0 B))) ) ) ).
tt(t43_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k4_xxreal_0 A k2_xxreal_0) = A) ) ) ).
tt(t43_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 D C) | (r1_tarski (k1_xxreal_1 B C) (k2_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t43_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( ((r1_tarski A B) & (v4_xxreal_2 B))  => (v4_xxreal_2 A)) ) ) ) ) ).
tt(t43_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A k1_numbers) =>  ((r1_xxreal_0 C B) |  ( (~ (r1_xxreal_0 (k1_xxreal_3 C A) (k1_xxreal_3 B A)))  &  (~ (r1_xxreal_0 (k3_xxreal_3 C A) (k3_xxreal_3 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t43_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  ((r2_yellow_0 A k1_xboole_0) & (r1_yellow_0 A (u1_struct_0 A))) ) ) ).
tt(t43_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k5_yellow_3 A B (k6_waybel_0 (k3_yellow_3 A B) C)) = (k6_waybel_0 B (k9_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t43_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 B A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 B A)))))) )  =>  ((r1_funct_2 (u1_struct_0 (k2_borsuk_1 A B)) (u1_struct_0 (k2_borsuk_1 B A)) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)) C (k14_funct_3 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 B) (u1_struct_0 A) (k10_funct_3 (u1_struct_0 A) (u1_struct_0 B)) (k9_funct_3 (u1_struct_0 A) (u1_struct_0 B)))) => (v3_tops_2 C (k2_borsuk_1 A B) (k2_borsuk_1 B A))) ) ) ) ) ) ) ).
tt(t43_yellow16,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  => (v24_waybel_0 (k6_yellow_1 A B))) ) ) ) ).
tt(t43_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (k3_yellow18 (k4_yellow18 A) B)) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A D B)) &  ( (~  ((k1_altcat_1 A D B) = k1_xboole_0) )  &  (C = (k4_tarski E (k4_tarski D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  => (r2_yellow20 A A (k12_functor0 A) B B)) ) ) ) ).
tt(t43_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ((k11_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t43_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((r1_yellow_0 A C) & (r1_yellow_0 B D))  =>  ((k1_yellow_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D)) = (k7_yellow_3 A B (k1_yellow_0 A C) (k1_yellow_0 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t43_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_yellow_4 A B (k4_subset_1 (u1_struct_0 A) C D)) = (k4_subset_1 (u1_struct_0 A) (k3_yellow_4 A B C) (k3_yellow_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t43_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B (k1_yellow_5 A C B)) =>  (B = (k3_yellow_0 A)) ) ) ) ) ) ) ) ).
tt(t43_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v8_yellow_6 B A) & (m4_yellow_6 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k13_yellow_6 A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k13_yellow_6 A B))) =>  (~  ((r2_hidden D (k2_pre_topc (k13_yellow_6 A B) C)) &  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_orders_2 E) &  ((v7_waybel_0 E) & (l1_waybel_0 E (k13_yellow_6 A B))) ) )  =>  (~  ((r2_hidden (k4_tarski E D) B) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k13_yellow_6 A B)) (u1_waybel_0 (k13_yellow_6 A B) E)) C) & (r2_hidden D (k10_yellow_6 (k13_yellow_6 A B) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((m1_waybel_1 C A B) => (m1_waybel_1 C (k7_lattice3 A) B))  &  ( ((m1_waybel_1 C (k7_lattice3 A) B) => (m1_waybel_1 C A B))  &  ( ((m1_waybel_1 C A B) => (m1_waybel_1 C A (k7_lattice3 B)))  &  ( ((m1_waybel_1 C A (k7_lattice3 B)) => (m1_waybel_1 C A B))  &  ( ((m1_waybel_1 C A B) => (m1_waybel_1 C (k7_lattice3 A) (k7_lattice3 B)))  &  ((m1_waybel_1 C (k7_lattice3 A) (k7_lattice3 B)) => (m1_waybel_1 C A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v2_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_tops_2 D B) &  ((v2_cantor_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ( ( ((k5_setfam_1 (u1_struct_0 A) C) = (u1_struct_0 A))  &  ((k5_setfam_1 (u1_struct_0 B) D) = (u1_struct_0 B)) )  =>  ((v1_tops_2 (a_4_2_yellow_9 A B C D) (k2_borsuk_1 A B)) &  ((v2_cantor_1 (a_4_2_yellow_9 A B C D) (k2_borsuk_1 A B)) & (m1_subset_1 (a_4_2_yellow_9 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_zf_lang A B) & (r3_zf_lang B A)) ) ) ) ) ) ).
tt(t43_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((v11_zf_lang B) =>  ( (~  ( (A = (k23_zf_lang B))  &  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (~  ((k13_zf_lang A D) = B) ) ) ) ) )  &  ( ( (? [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  &  ((k13_zf_lang A D) = B) ) )  =>  (A = (k23_zf_lang B)) )  &  ( (~  ( (C = (k24_zf_lang B))  &  (! [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) =>  (~  ((k13_zf_lang D C) = B) ) ) ) ) )  &  ( (? [D:$i] :  ((m2_subset_1 D k5_numbers k1_zf_lang) &  ((k13_zf_lang D C) = B) ) )  =>  (C = (k24_zf_lang B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t43_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((k2_xboole_0 (k1_tarski A) B) = k1_xboole_0) ) ) ) ).
tt(t43_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_zmodul01 B C)) ) ) ) ) ) ) ).
tt(t44_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) => (r1_tarski (k2_relset_1 (u1_abcmiz_0 A) C) (k2_abcmiz_0 A (k8_abcmiz_0 A B C)))) ) ) ) ) ) ) ).
tt(t44_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  ( ((k30_abcmiz_1 A (k15_abcmiz_1 A) B) = (k30_abcmiz_1 A (k15_abcmiz_1 A) C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t44_abcmiz_a,ax, (! [A:$i] :  ( ((v2_abcmiz_1 A k27_abcmiz_1) &  ((v5_abcmiz_a A k27_abcmiz_1) & (m1_subset_1 A (u4_struct_0 k27_abcmiz_1))) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B k27_abcmiz_1 (k14_abcmiz_1 k27_abcmiz_1)) =>  ((k10_abcmiz_a k27_abcmiz_1 (k30_abcmiz_1 k27_abcmiz_1 A B)) = A) ) ) ) ) ).
tt(t44_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~  ((r5_aff_1 A B C) & (r5_aff_1 A C D)) )  &  ( (~  ((r5_aff_1 A B C) & (r5_aff_1 A D C)) )  &  ( (~  ((r5_aff_1 A C B) & (r5_aff_1 A C D)) )  &  (~  ((r5_aff_1 A C B) & (r5_aff_1 A D C)) ) ) ) ) )  => (r5_aff_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t44_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_aff_4 A B C D) =>  ((r2_aff_4 A B D C) &  ((r2_aff_4 A C B D) &  ((r2_aff_4 A C D B) &  ((r2_aff_4 A D B C) & (r2_aff_4 A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((k1_afinsq_1 (k2_funct_7 A B C)) = (k1_afinsq_1 A))  &  ( ( (~ (r1_xxreal_0 (k1_afinsq_1 A) B))  =>  ((k1_funct_1 (k2_funct_7 A B C) B) = C) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~  (D = B) )  =>  ((k1_funct_1 (k2_funct_7 A B C) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo C A) | (r1_xxreal_0 1 (k1_afinsq_1 B)))  =>  ((k6_afinsq_2 A B C) = (k1_finsop_1 A (k10_afinsq_1 A B) C)) ) ) ) ) ) ) ) ).
tt(t44_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k14_afproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 (k14_afproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 (k14_afproj A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 (k14_afproj A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 (k14_afproj A))) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 (k14_afproj A))) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 (k14_afproj A))) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 (k14_afproj A))) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 (k14_afproj A))) =>  (~  ((r1_incsp_1 (k14_afproj A) B G) &  ((r1_incsp_1 (k14_afproj A) C G) &  ((r1_incsp_1 (k14_afproj A) D H) &  ((r1_incsp_1 (k14_afproj A) E H) &  ((r1_incsp_1 (k14_afproj A) F G) &  ((r1_incsp_1 (k14_afproj A) F H) &  ((r1_incsp_1 (k14_afproj A) B I) &  ((r1_incsp_1 (k14_afproj A) D I) &  ((r1_incsp_1 (k14_afproj A) C J) &  ((r1_incsp_1 (k14_afproj A) E J) &  ( (~ (r1_incsp_1 (k14_afproj A) F I))  &  ( (~ (r1_incsp_1 (k14_afproj A) F J))  &  ( (~  (G = H) )  &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 (k14_afproj A))) =>  (~  ((r1_incsp_1 (k14_afproj A) K I) & (r1_incsp_1 (k14_afproj A) K J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  =>  ((k4_algstr_0 (k5_afvect0 A B) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k4_afvect0 A B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t44_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_algspec1 A B C) =>  ((k2_algspec1 A B (k1_algspec1 (u4_struct_0 A) C)) = (k2_algspec1 A B C)) ) ) ) ) ) ) ) ).
tt(t44_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  => (r2_relset_1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 C)) (k18_algstr_4 A C (k1_partfun1 A B B C D E)) (k1_partfun1 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B)) (u1_struct_0 (k14_algstr_4 B)) (u1_struct_0 (k14_algstr_4 C)) (k18_algstr_4 A B D) (k18_algstr_4 B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t44_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (~ (v2_struct_0 (k3_altcat_4 A)))  &  ((v2_altcat_1 (k3_altcat_4 A)) &  ((v3_altcat_2 (k3_altcat_4 A) (k2_altcat_4 A)) & (m1_altcat_2 (k3_altcat_4 A) (k2_altcat_4 A))) ) ) ) ) ).
tt(t44_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r6_analmetr A B C D) => (v4_analmetr D A))  &  ((r7_analmetr A D E) =>  ((v4_analmetr D A) & (v4_analmetr E A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) &  ((r1_analort A B C F G H I) &  ((r1_analort A B C J K H I) &  ( (~ (r1_analort A B C D E J K))  &  ( (~  (F = G) )  &  (~  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v4_aofa_000 A) & (l1_unialg_1 A)) )  =>  ((k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A (k1_funct_7 2 (k4_finseq_1 (u1_unialg_1 A))))) = (k4_finseq_2 2 (u1_struct_0 A))) ) ) ).
tt(t44_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k83_aofa_i00 A B D E F G)) F) = (k6_int_1 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k83_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( ((v1_armstrng B A) & (v2_finsub_1 B))  => (r5_armstrng A (k2_armstrng B) B)) ) ) ) ).
tt(t44_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  ( (~  (A = k1_xboole_0) )  =>  ((k8_arytm_3 (k9_ordinal3 B A) (k9_ordinal3 C A)) = (k8_arytm_3 B C)) ) ) ) ) ) ) ) ).
tt(t44_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 3 A) & (r1_xxreal_0 (k5_square_1 A) (k2_nat_1 (k4_nat_1 2 A) 1))) ) ) ) ).
tt(t44_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v12_bcialg_1 (u1_struct_0 A) A) & (m2_bcialg_1 (u1_struct_0 A) A)) ) ) ).
tt(t44_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (r1_tarski (k3_bcialg_2 A) (k4_bcialg_2 A))) ) ).
tt(t44_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A B C)) = C) ) ) ) ) ) ) ) ) ).
tt(t44_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v3_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski (k3_bcialg_4 A B C) (k8_bcialg_4 A D)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k3_bcialg_4 A B C)) => (r1_bcialg_1 A E (k1_bcialg_1 A D (k1_bcialg_1 A (k1_bcialg_1 A D B) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v13_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ((m1_bcialg_5 A k6_numbers 1 k6_numbers k6_numbers) & (m1_bcialg_5 A 1 k6_numbers k6_numbers k6_numbers)) ) ) ) ).
tt(t44_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k5_bcialg_1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 B) (k5_bcialg_1 B)) =>  ( (E = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))  => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k7_bcialg_1 A D)) (k7_bcialg_1 B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ((v3_bciideal (k1_tarski (k4_struct_0 A)) A) & (m2_bcialg_1 (k1_tarski (k4_struct_0 A)) A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = B)  <=>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = (k4_struct_0 A)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = B)  =>  ((k1_bcialg_1 A C B) = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A C D) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D B) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A C B)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))) = (k1_bcialg_1 A B C))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A (k1_bcialg_1 A B C) B)) = (k1_bcialg_1 A B C)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A B D) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B))) = (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bhsp_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((k1_normsp_1 B (k5_vfunct_1 k5_numbers B C) A) = (k4_algstr_0 B (k1_normsp_1 B C A))) ) ) ) ) ) ) ).
tt(t44_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden B (k4_bhsp_2 A C E)) => (r2_hidden (k5_algstr_0 A B D) (k4_bhsp_2 A (k5_algstr_0 A C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k5_bhsp_4 C D (k1_series_1 k1_numbers A B)) (k6_bhsp_1 C (k5_bhsp_4 C D A) (k5_bhsp_4 C D B)))) ) ) ) ) ) ) ) ).
tt(t44_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v2_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ((k11_bilinear A B C D) = (k11_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) ) ) ) ) ) ) ) ) ).
tt(t44_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A (k3_lattices A B C) (k4_lattices A B C)) (k3_lattices A (k1_boolealg A B C) (k1_boolealg A C B)))) ) ) ) ) ) ).
tt(t44_borsuk_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v2_pre_topc D) & (l1_pre_topc D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_pre_topc C A B) & (m1_pre_topc D B))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k1_pre_topc A E)) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A E)) (u1_struct_0 D))))) )  =>  ( (F = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C E))  => (v5_pre_topc F (k1_pre_topc A E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_rcomp_1 k2_xxreal_0 A) = (k4_subset_1 k1_numbers (k1_seq_4 A) (k2_rcomp_1 k2_xxreal_0 A))) ) ) ).
tt(t44_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) D (k2_borsuk_2 A C B (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ).
tt(t44_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (A = (k1_euclid_3 (k2_xcmplx_0 (k8_real_1 (k12_euclid A) (k21_sin_cos (k3_euclid_3 A))) (k3_xcmplx_0 (k8_real_1 (k12_euclid A) (k18_sin_cos (k3_euclid_3 A))) k7_complex1)))) ) ) ).
tt(t44_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A E B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) F) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k8_xboolean k7_margrel1 A) = k8_margrel1) ) ) ).
tt(t44_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k2_bvfunc_1 A B D) (k2_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t44_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k6_bvfunc26 A B C)) (k2_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t44_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k5_bvfunc_1 A B (k5_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t44_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A C) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A (k2_calcul_1 A C))))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ).
tt(t44_card_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_card_1 (k1_card_1 A)) = (k1_card_1 (k1_ordinal1 A))) ) ) ).
tt(t44_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_tarski B A) =>  ((k5_card_1 (k6_subset_1 A B)) = (k6_xcmplx_0 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ).
tt(t44_card_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((r2_hidden (k1_card_1 A) B) => (r2_hidden A B)) ) ) ) ) ).
tt(t44_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((k9_xtuple_0 A) = B)  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k5_card_1 B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k5_card_1 B) B)))) )  =>  (~  ((v2_funct_1 C) &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k5_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers D) = (k5_card_1 B))  &  ( (! [E:$i] :  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k1_recdef_1 D E) = (k5_card_1 (k1_funct_1 (k3_relat_1 C A) E))) ) )  &  ((k3_card_fin 1 A) = (k7_afinsq_2 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v9_cat_1 (k4_cat_1 A B) A B B)) ) ) ) ).
tt(t44_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_binop_1 (k7_cat_1 (k8_cat_2 A B) A (k14_cat_2 A B)) C D) = C) ) ) ) ) ) ) ) ) ).
tt(t44_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  ( ( ((k3_graph_1 C E) = D)  &  ((k3_graph_1 C F) = D) )  => (m1_cat_3 (k5_funct_4 (u4_struct_0 C) A B E F) C D (k2_tarski A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((v4_cat_4 A) <=>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) & (v11_cat_1 B A)) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) &  ( ((k3_graph_1 A E) = B)  &  ( ((k3_graph_1 A F) = C)  &  ( ((k4_graph_1 A E) = D)  &  ( ((k4_graph_1 A F) = D)  & (r4_cat_3 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_catalan2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k1_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers B) = (k1_relset_1 k5_numbers C))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_afinsq_1 B)) =>  ((k1_seq_1 B D) = (k11_binop_2 A (k1_seq_1 C D))) ) ) ) )  =>  ((k7_afinsq_2 B) = (k11_binop_2 A (k7_afinsq_2 C))) ) ) ) ) ) ) ) ).
tt(t44_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_struct_0 (k7_cc0sp2 A)) = (k1_cc0sp2 A k6_numbers)) ) ) ).
tt(t44_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 C A) & (r2_cfcont_1 D B))  =>  ((r2_cfcont_1 (k2_valued_1 k2_numbers k2_numbers k2_numbers C D) (k3_xboole_0 A B)) &  ((r2_cfcont_1 (k46_valued_1 k2_numbers k2_numbers k2_numbers C D) (k3_xboole_0 A B)) & (r2_cfcont_1 (k19_valued_1 k2_numbers k2_numbers k2_numbers C D) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t44_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k19_valued_1 A k2_numbers k2_numbers B (k1_cfunct_1 A C D)) (k1_cfunct_1 A (k19_valued_1 A k2_numbers k2_numbers B C) D))) ) ) ) ) ) ) ) ).
tt(t44_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v6_cgames_1 A) <=>  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k6_cgames_1 A)) &  (! [C:$i] :  ((v2_cgames_1 C) =>  (~  ((r2_hidden C (k7_cgames_1 B)) & (v6_cgames_1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_chain_1 D A) =>  ((r2_hidden (k3_chain_1 A B C) (k4_chain_1 A D 1)) <=>  (? [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) &  ( (~  ((r1_xxreal_0 (k1_seq_1 C E) (k1_seq_1 B E)) &  (~  ( (A = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) )  &  ((m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 B E) (k1_seq_1 C E)) (k2_chain_1 A D E)) &  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k2_finseq_1 A)) =>  ( (~  (F = E) )  =>  ( ((k1_seq_1 B F) = (k1_seq_1 C F))  & (r2_hidden (k1_seq_1 B F) (k2_chain_1 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r1_chord A C D) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 B)) =>  ( ( (C = E)  &  (D = F) )  => (r1_chord B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ( ((r2_hidden A (u1_struct_0 F)) & (r2_hidden B (u1_struct_0 F)))  =>  ((r2_hidden C (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k1_tarski C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v1_circcomb A) <=>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  ((k1_funct_1 (u2_msualg_1 A) B) = B) ) ) ) ) ) ).
tt(t44_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r4_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) => (m1_subset_1 (k3_relat_1 C G) (k4_card_3 (u3_msualg_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden A (k4_classes1 C)) & (r2_hidden B (k4_classes1 C)))  <=> (r2_hidden (k2_tarski A B) (k4_classes1 (k1_ordinal1 C)))) ) ) ) ) ).
tt(t44_classes2,ax, (! [A:$i] :  ((v1_ordinal1 A) => (r1_classes1 A (k4_classes1 (k1_card_1 (k1_classes1 A))))) ) ).
tt(t44_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  => (m1_clvect_1 A A)) ) ).
tt(t44_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden B (k4_clvect_2 A C E)) => (r2_hidden (k5_algstr_0 A B D) (k4_clvect_2 A (k5_algstr_0 A C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k6_clvect_3 A B (k1_series_1 k2_numbers C D)) = (k16_csspace A (k6_clvect_3 A B C) (k6_clvect_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t44_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_cohsp_1 A B C))) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v9_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  ((k8_cohsp_1 A B E) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  ( ((k21_coh_sp A B) = (k22_coh_sp A C))  =>  ( ((k2_xtuple_0 (k24_coh_sp A C B)) = (k3_relat_1 (k2_xtuple_0 C) (k2_xtuple_0 B)))  &  ( ((k21_coh_sp A (k24_coh_sp A C B)) = (k21_coh_sp A C))  &  ((k22_coh_sp A (k24_coh_sp A C B)) = (k22_coh_sp A B)) ) ) ) ) ) ) ) ) ).
tt(t44_complex1,ax, ((k17_complex1 k6_numbers) = k6_numbers) ).
tt(t44_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_complex1 (k1_complex2 A B)) = (k1_complex2 A (k10_complex1 B))) ) ) ) ) ).
tt(t44_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( (~  (B = (k4_struct_0 k1_complfld)) )  &  (~  ((k5_algstr_0 k1_complfld (k3_vectsp_1 k1_complfld C A) (k3_vectsp_1 k1_complfld D B)) = (k3_vectsp_1 k1_complfld (k5_algstr_0 k1_complfld (k8_group_1 k1_complfld C B) (k8_group_1 k1_complfld D A)) (k8_group_1 k1_complfld A B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (A = C)  &  (B = D) )  =>  ((k5_binop_1 k2_numbers k27_binop_2 A B) = (k5_binop_1 k1_numbers k33_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t44_compl_sp,ax, (? [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  &  ((v4_tbsp_1 A) &  (? [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) ) )  &  ((v7_compl_sp B A) &  ((v2_prob_1 B) & (v1_xboole_0 (k2_kurato_0 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t44_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B C) => (r1_tarski (k6_compos_1 A B D) (k6_compos_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t44_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) &  ((v3_compos_1 B A) & (v4_compos_1 B A)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 D (k62_valued_1 B)) =>  ((k1_funct_1 (k8_compos_1 A C B) (k2_xcmplx_0 (k62_valued_1 C) D)) = (k5_compos_0 (u1_compos_1 A) (k7_partfun1 (u1_compos_1 A) B D) (k62_valued_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t44_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r2_hidden (k1_comptrig A) (k2_rcomp_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 2 k32_sin_cos))) <=>  ( (~ (r1_xxreal_0 (k3_complex1 A) k6_numbers))  &  (~ (r1_xxreal_0 k6_numbers (k4_complex1 A))) ) ) ) ) ).
tt(t44_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_rfunct_3 A (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_rfunct_3 B (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)))  =>  (! [C:$i] :  ( ((v3_comput_1 C) & (m2_finseq_1 C (k2_comput_1 k5_numbers)))  =>  ( (B = (k3_relat_1 (k6_funct_6 C) A))  =>  ((k19_margrel1 B) = (k1_comput_1 C)) ) ) ) ) ) ) ) ).
tt(t44_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  =>  ((r2_relset_1 k5_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers C A) (k51_valued_1 k5_numbers k2_numbers k2_numbers D B)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k2_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers C B) (k19_valued_1 k5_numbers k2_numbers k2_numbers D A)) (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) & (r2_relset_1 k5_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers C A) (k51_valued_1 k5_numbers k2_numbers k2_numbers D B)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k46_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers C B) (k19_valued_1 k5_numbers k2_numbers k2_numbers D A)) (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t44_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A C) = (k2_comseq_3 B (k2_nat_1 C 1))) ) )  =>  ((r1_xxreal_0 1 (k17_complex1 B)) |  ((v2_comseq_2 A) &  ((k3_comseq_2 A) = k5_complex1) ) ) ) ) ) ) ) ).
tt(t44_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( (~ (v2_struct_0 (k11_conlat_1 A)))  &  ((v10_lattices (k11_conlat_1 A)) &  ((v4_lattice3 (k11_conlat_1 A)) & (l3_lattices (k11_conlat_1 A))) ) ) ) ) ).
tt(t44_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_connsp_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v2_connsp_1 B (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))))) ) ) ) ) ).
tt(t44_convex4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((r1_xxreal_0 k1_xboole_0 A) & (r1_xxreal_0 A 1))  =>  ( ((k17_complex1 (k3_xcmplx_0 A B)) = (k4_real_1 A (k17_complex1 B)))  &  ((k17_complex1 (k3_xcmplx_0 (k6_xcmplx_0 k6_complex1 A) B)) = (k3_xcmplx_0 (k6_xcmplx_0 k6_complex1 A) (k17_complex1 B))) ) ) ) ) ) ) ).
tt(t44_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k24_qc_lang1 A B) = (k24_qc_lang1 A (k14_cqc_sim1 A B))) ) ) ) ) ).
tt(t44_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A C D)) (k6_cqc_lang A (k7_cqc_lang A B D)))) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ).
tt(t44_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k12_cqc_lang A D (k7_cqc_lang A B C)) A) => (v2_cqc_the1 (k7_cqc_lang A (k12_cqc_lang A D B) (k12_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t44_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((v6_qc_lang1 B A) & (r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) D (k6_domain_1 (k3_cqc_lang A) B)) C))  => (r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) D (k6_domain_1 (k3_cqc_lang A) (k6_cqc_lang A C))) (k6_cqc_lang A B))) ) ) ) ) ) ) ) ) ).
tt(t44_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k13_csspace A B))) ) ) ) ).
tt(t44_dickson,ax,(r4_relat_2 k10_dickson k5_numbers)).
tt(t44_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 k16_sin_cos A) B) = (k8_real_1 2 (k8_real_1 (k21_sin_cos B) (k18_sin_cos (k10_real_1 A 2))))) ) ) ) ) ).
tt(t44_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k5_square_1 F)) ) )  & (r2_zfmisc_1 A B C D))  =>  ((k11_diff_1 E A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k3_diff_1 (k4_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B))) ) ) ) ) ) ) ).
tt(t44_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xxreal_0 (k2_dilworth (k5_yellow_0 A B)) (k2_dilworth A))) ) ) ) ).
tt(t44_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) &  ((v3_analoaf B) & (l1_analoaf B)) ) )  =>  ( (A = (k2_diraf B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A C D E F))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_analoaf A C D C G) & (r2_analoaf A E F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [C:$i] :  ((m2_subset_1 C (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( ((r1_ec_pf_1 A B C) & (r1_ec_pf_1 A C D))  => (r1_ec_pf_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t44_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  =>  ((r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C)) <=>  ((k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t44_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k18_ens_1 A C (k4_cat_1 A B)) = (k6_partfun1 (k2_cat_1 A B C))) ) ) ) ) ) ) ).
tt(t44_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ((v4_matrprob A) <=> (v1_matrprob (k2_entropy1 k1_numbers A))) ) ) ).
tt(t44_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_enumset1 A A A A B C) = (k1_enumset1 A B C)) ) ) ) ).
tt(t44_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_hidden B C) =>  ((k5_setfam_1 A (k7_subset_1 (k1_zfmisc_1 A) C (k6_domain_1 (k1_zfmisc_1 A) B))) = (k6_subset_1 A B)) ) ) ) ) ) ) ) ).
tt(t44_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( (~  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  & (r1_xxreal_0 (k12_euclid B) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k12_euclid B) k6_numbers))  &  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ).
tt(t44_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  &  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  &  (~  ( (~  ( ( ((k7_real_1 (k1_real_1 (k8_real_1 (k17_euclid A) (k18_euclid B))) (k8_real_1 (k18_euclid A) (k17_euclid B))) = (k8_real_1 (k12_euclid A) (k12_euclid B)))  |  ((k7_real_1 (k1_real_1 (k8_real_1 (k17_euclid A) (k18_euclid B))) (k8_real_1 (k18_euclid A) (k17_euclid B))) = (k1_real_1 (k8_real_1 (k12_euclid A) (k12_euclid B)))) )  &  ( (~  ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k10_real_1 k32_sin_cos 2)) )  &  (~  ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) )  &  (~  ( ( ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k10_real_1 k32_sin_cos 2))  |  ((k4_euclid_3 A (k4_struct_0 (k15_euclid 2)) B) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) )  &  ( (~  ((k7_real_1 (k1_real_1 (k8_real_1 (k17_euclid A) (k18_euclid B))) (k8_real_1 (k18_euclid A) (k17_euclid B))) = (k8_real_1 (k12_euclid A) (k12_euclid B))) )  &  (~  ((k7_real_1 (k1_real_1 (k8_real_1 (k17_euclid A) (k18_euclid B))) (k8_real_1 (k18_euclid A) (k17_euclid B))) = (k1_real_1 (k8_real_1 (k12_euclid A) (k12_euclid B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((v2_euclid_4 D A) &  ((v2_euclid_4 E A) &  ((r2_hidden B D) &  ((r2_hidden C D) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k7_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 2 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_euclid_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_real_ns1 A)))) =>  (~  ( (C = (k8_euclid_7 A))  &  (! [D:$i] :  ((m2_rlvect_2 D (k7_real_ns1 A) C) =>  (~  (B = (k6_rlvect_2 (k7_real_ns1 A) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k8_euclid 3 A B) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k10_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1))) (k9_euclid 3 k3_euclid_8 (k10_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)))) (k9_euclid 3 k4_euclid_8 (k10_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3))))) ) ) ) ) ).
tt(t44_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( ((k4_algstr_0 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C)) = (k5_algstr_0 (k15_euclid A) C B))  &  ((k4_algstr_0 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C)) = (k3_rlvect_1 (k15_euclid A) (k4_algstr_0 (k15_euclid A) B) C)) ) ) ) ) ) ) ) ).
tt(t44_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r4_euclidlp A B C) & (r2_euclidlp A C D))  => (r4_euclidlp A B D)) ) ) ) ) ) ) ) ) ).
tt(t44_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_exchsort C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_exchsort D)) )  =>  ( ((r2_hidden A (k9_xtuple_0 C)) &  ((r2_hidden B (k9_xtuple_0 C)) & (m1_exchsort C D)) )  =>  ((m1_exchsort (k10_funct_7 C A B) D) & (m1_exchsort C (k10_funct_7 D A B))) ) ) ) ) ) ) ) ).
tt(t44_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden A (u1_struct_0 (k5_circcomb D (k11_finseq_1 A B C)))) &  ((r2_hidden B (u1_struct_0 (k5_circcomb D (k11_finseq_1 A B C)))) & (r2_hidden C (u1_struct_0 (k5_circcomb D (k11_finseq_1 A B C))))) ) ) ) ) ) ).
tt(t44_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((v1_xreal_0 B) =>  ((r2_hidden B (k1_relset_1 k1_numbers A)) =>  ((k1_seq_1 A B) = (k18_complex1 B)) ) ) )  => (v1_fcont_1 A)) ) ) ).
tt(t44_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_fdiff_9 k19_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k1_fdiff_9 B)) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t44_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k29_sin_cos)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k10_real_1 (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k29_sin_cos B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t44_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) & (r2_fdiff_1 A (k2_subset_1 k1_numbers)))  =>  ( ( (? [B:$i] :  ((m1_subset_1 B k1_numbers) & (r1_xxreal_0 (k1_fdiff_1 A B) k6_numbers)) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 A B))) ) )  | (v3_rcomp_1 (k2_relset_1 k1_numbers A))) ) ) ) ).
tt(t44_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) A) B) = (k7_real_1 (k1_real_1 (k1_seq_1 k19_sin_cos B)) (k8_real_1 B (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t44_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k10_real_1 E 2))  &  ((k1_seq_1 D E) = (k8_real_1 (k8_real_1 2 A) E)) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))) B) E) = (k5_square_1 (k18_sin_cos (k8_real_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t44_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) A) B) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k1_seq_1 k16_sin_cos B)) (k10_real_1 (k8_real_1 (k1_seq_1 k29_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t44_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k1_pre_ff (k2_nat_1 A 1)) (k1_pre_ff A))) ) ) ) ).
tt(t44_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_nat_1 (k1_fib_num3 A) (k1_fib_num3 (k2_nat_1 A 3))) = (k4_nat_1 2 (k1_fib_num3 (k2_nat_1 A 2)))) ) ) ).
tt(t44_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_finseq_1 B A) =>  (! [C:$i] :  ((m1_finseq_1 C A) =>  (! [D:$i] :  ((m1_finseq_1 D A) =>  (! [E:$i] :  ((m1_finseq_1 E A) =>  ( ((r5_finseq_8 A C B) &  ((r5_finseq_8 A D B) &  (E = (k1_finseq_8 A C D)) ) )  =>  ((r1_filerec1 A C E B) & (r1_filerec1 A D E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_0 B A) <=>  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) | (r2_hidden (k7_lattices A C) B)) ) ) ) ) ) ) ) ) ).
tt(t44_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v15_lattices B) & (l3_lattices B)) ) ) )  =>  ( ((r2_lattices A C D) & (r2_lattices B E F))  <=> (r2_lattices (k7_filter_1 A B) (k9_filter_1 A B C E) (k9_filter_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k1_lattice2 A)))))  =>  ( ((k8_filter_2 A B C) = (k5_filter_0 (k1_lattice2 A) (k3_filter_2 A B) (k3_filter_2 A C)))  &  ( ((k8_filter_2 (k1_lattice2 A) (k3_filter_2 A B) (k3_filter_2 A C)) = (k5_filter_0 A B C))  &  ( ((k8_filter_2 (k1_lattice2 A) D E) = (k5_filter_0 A (k4_filter_2 A D) (k4_filter_2 A E)))  &  ((k8_filter_2 A (k4_filter_2 A D) (k4_filter_2 A E)) = (k5_filter_0 (k1_lattice2 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( (C = (k10_finseq_1 A B))  <=>  ( ((k3_finseq_1 C) = 2)  &  ( ((k1_funct_1 C 1) = A)  &  ((k1_funct_1 C 2) = B) ) ) ) ) ) ) ) ).
tt(t44_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 A) (k4_finseq_1 A)) &  ((v3_funct_2 C (k4_finseq_1 A) (k4_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 A) (k4_finseq_1 A))))) ) )  =>  ( (B = (k3_relat_1 C A))  =>  ((k3_finseq_1 B) = (k3_finseq_1 A)) ) ) ) ) ) ) ) ).
tt(t44_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (k6_numbers = A) )  =>  ((k14_finseq_1 (k1_tarski A)) = (k9_finseq_1 A)) ) ) ) ).
tt(t44_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (r1_tarski (k10_xtuple_0 (k6_finseq_4 A B)) (k10_xtuple_0 A))) ) ) ) ).
tt(t44_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k7_partfun1 A (k1_finseq_5 A C B) 1) = (k7_partfun1 A C 1)) ) ) ) ) ) ) ) ).
tt(t44_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((k7_partfun1 A C 1) = B)  =>  ( (C = k1_xboole_0)  |  ( ((k1_finseq_5 A C B) = (k12_finseq_1 A B))  &  ((k2_finseq_5 A C B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t44_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v1_setwiseo D B) => (r2_funct_2 A B (k10_funcop_1 B A D (k4_binop_1 B D) C) C)) ) ) ) ) ) ) ) ) ).
tt(t44_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fintopo2 (k3_subset_1 (u1_struct_0 A) B) A) => (v4_fintopo2 B A)) ) ) ) ) ).
tt(t44_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_2 A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_tarski (k9_fintopo3 A B (k2_nat_1 C 1)) (k9_fintopo3 A B C))) ) ) ) ) ) ) ).
tt(t44_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((v2_fintopo6 B A) &  ( (D = (k1_funct_1 B (k3_finseq_1 B)))  & (r2_hidden C (k1_fin_topo A D))) )  => (v2_fintopo6 (k8_finseq_1 (u1_struct_0 A) B (k12_finseq_1 (u1_struct_0 A) C)) A)) ) ) ) ) ) ) ) ) ).
tt(t44_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) => (r1_tarski (k6_flang_1 A B B) (k8_flang_1 A B))) ) ) ).
tt(t44_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) => (r1_tarski (k1_flang_2 A (k7_flang_1 A B (k2_xcmplx_0 C D)) E F) (k6_flang_1 A (k1_flang_2 A (k7_flang_1 A B C) E F) (k1_flang_2 A (k7_flang_1 A B D) E F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_3 A (k9_subset_1 (k8_afinsq_1 A) B C) D) (k9_subset_1 (k8_afinsq_1 A) (k1_flang_3 A B D) (k1_flang_3 A C D)))) ) ) ) ) ) ) ).
tt(t44_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ((v5_relat_1 (k7_finseq_1 (k7_finseq_1 B C) D) A) =>  ((v5_relat_1 D A) &  ((v5_relat_1 C A) & (v5_relat_1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t44_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) => (v7_pre_topc A)) ) ) ).
tt(t44_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C B A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D B A))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  ( ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) G (k2_binop_1 (u1_struct_0 C) B (u1_struct_0 C) (u1_fsm_1 B C) H I)) = (k2_binop_1 (u1_struct_0 D) B (u1_struct_0 D) (u1_fsm_1 B D) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) G H) I))  &  ((k2_binop_1 (u1_struct_0 C) B A (u3_fsm_1 B A C) H I) = (k2_binop_1 (u1_struct_0 D) B A (u3_fsm_1 B A D) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) G H) I)) ) ) ) ) )  =>  ((r5_fsm_1 B A C E F) <=> (r5_fsm_1 B A D (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) G E) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A (k6_funcop_1 A A B (k6_partfun1 A) (k6_partfun1 A)) C) = (k5_binop_1 A B C C)) ) ) ) ) ) ) ).
tt(t44_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 A) & (v2_funct_1 B))  =>  ((k2_funct_1 (k3_relat_1 A B)) = (k3_relat_1 (k2_funct_1 B) (k2_funct_1 A))) ) ) ) ) ) ).
tt(t44_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = k1_xboole_0)  =>  (B = k1_xboole_0) )  => (r1_tarski (k8_relset_1 A B E D) (k8_relset_1 A C (k1_partfun1 A B B C E F) (k7_relset_1 B C F D)))) ) ) ) ) ) ) ) ) ).
tt(t44_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = k1_xboole_0) )  =>  ((k10_xtuple_0 (k7_funct_3 B A)) = B) ) ) ) ).
tt(t44_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (? [B:$i] :  (? [C:$i] : (r1_tarski (k9_xtuple_0 (k2_funct_4 A)) (k2_zfmisc_1 B C))) ) ) ) ).
tt(t44_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  &  ( ((k9_xtuple_0 D) = (k2_zfmisc_1 A B))  &  ((k1_funct_5 C) = (k1_funct_5 D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t44_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ( ((k9_xtuple_0 C) = (k10_xtuple_0 B))  &  ((v2_funct_1 B) &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) => (r2_wellord2 (k1_funct_1 A D) (k1_funct_1 C (k1_funct_1 B D)))) ) ) ) )  => (r2_wellord2 (k4_card_3 A) (k4_card_3 C))) ) ) ) ) ) ) ).
tt(t44_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k5_funct_7 (k7_finseq_1 (k9_finseq_1 C) B) A) = (k7_finseq_1 (k9_finseq_1 A) (k5_funct_7 B (k1_funct_1 C A)))) ) ) ) ) ) ).
tt(t44_funct_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_funct_8 B k1_numbers k1_numbers) => (v4_funct_8 (k26_valued_1 k1_numbers k1_numbers B A) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t44_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ( ((v10_functor0 C A B) & (v5_functor0 C A B))  => (v7_functor0 C A B)) ) ) ) ) ) ) ).
tt(t44_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A (k3_fuzzy_1 A B) (k3_fuzzy_1 A C))) (k3_fuzzy_1 A (k6_fuzzy_1 A B C)))) ) ) ) ) ) ).
tt(t44_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k2_fuzzy_2 A B (k1_fuzzy_1 A C D)) (k1_fuzzy_1 A (k2_fuzzy_2 A B C) (k2_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t44_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( ((v3_fvaluat1 A) & (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C B)))  => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) B) (k3_funct_2 (u1_struct_0 A) k7_numbers C B))) ) ) ) ) ) ) ).
tt(t44_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k4_fvsum_1 A B C (k8_fvsum_1 A B D E)) = (k8_fvsum_1 A B (k4_fvsum_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((v2_gcd_1 B A) &  ((r8_gcd_1 A B C D) & (r8_gcd_1 A B E F)) )  => (r8_gcd_1 A B (k6_gcd_1 A B C D E F) (k7_gcd_1 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H k6_numbers k6_numbers k6_numbers k6_numbers A) = (k7_genealg1 F G H A))  &  ( ((k11_genealg1 F G H k6_numbers k6_numbers k6_numbers B k6_numbers) = (k7_genealg1 F G H B))  &  ( ((k11_genealg1 F G H k6_numbers k6_numbers C k6_numbers k6_numbers) = (k7_genealg1 F G H C))  &  ( ((k11_genealg1 F G H k6_numbers D k6_numbers k6_numbers k6_numbers) = (k7_genealg1 F G H D))  &  ((k11_genealg1 F G H E k6_numbers k6_numbers k6_numbers k6_numbers) = (k7_genealg1 F G H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k7_geomtrap A F G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k7_geomtrap A F G))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k7_geomtrap A F G))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k7_geomtrap A F G))) =>  ( ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  (E = K) ) ) )  =>  ((r2_analoaf (k7_geomtrap A F G) H I J K) <=> (r2_geomtrap A F G B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (~  ((k2_msafree2 (k17_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t44_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ((m1_glib_000 C A) =>  ( ((r1_tarski (k24_glib_000 A B) (k24_glib_000 A C)) & (r1_tarski (k25_glib_000 A B) (k25_glib_000 A C)))  => (m1_glib_000 B C)) ) ) ) ) ) ) ).
tt(t44_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ( ( (~ (v1_abian E))  & (m1_subset_1 E k5_numbers))  =>  ( ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k4_glib_001 A B) = (k3_glib_001 A C)) ) )  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k8_glib_001 A (k7_glib_001 A B C) D E) (k8_glib_001 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ( ((r5_glib_000 A B) & (v2_glib_002 A))  => (v2_glib_002 B)) ) ) ) ) ).
tt(t44_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) & (v2_glib_003 B)) ) ) ) )  =>  ( ((k6_glib_003 A) = (k6_glib_003 B))  =>  ((k11_glib_003 A) = (k11_glib_003 B)) ) ) ) ) ) ).
tt(t44_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ).
tt(t44_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) B) & (r2_gobrd13 C (k17_finseq_1 C B D) E A)) )  => (r2_gobrd13 C D E A)) ) ) ) ) ) ) ) ) ) ).
tt(t44_gobrd14,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  ((k9_pscomp_1 (k3_topreal1 2 A)) = (k9_pscomp_1 (k3_goboard9 A))) ) ) ).
tt(t44_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_graph_1 E A) =>  (! [F:$i] :  ((m2_graph_1 F A) =>  (! [G:$i] :  ((m2_graph_1 G A) =>  ( ((r1_graph_2 A B E) &  ((r1_graph_2 A C F) &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 C 1))  &  ( (G = (k8_finseq_1 (u4_struct_0 A) E F))  &  (D = (k4_graph_2 (u1_struct_0 A) B C)) ) ) ) )  => (r1_graph_2 A D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_graph_3 B E C))) =>  ( (F = D)  =>  ( (D = E)  |  ((k3_graph_3 (k8_graph_3 B E C) F A) = (k3_graph_3 B D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v7_graph_1 E B) & (m2_graph_1 E B))  =>  ((r2_graph_5 B C D E A) =>  ( (~  ((k6_graph_5 B E) = k1_xboole_0) )  &  (~  ((k5_graph_5 B C D A) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) => (r2_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C) (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) (k2_nat_1 B 1)) C) (k2_nat_1 (k4_nat_1 3 A) 1) (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)))) ) ) ) ) ) ).
tt(t44_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_vectsp_2 C) & (l6_algstr_0 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 E A C) &  ((v3_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F (k5_card_1 (k2_polynom1 (k15_pre_poly A) C D))) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_groeb_3 A B C (k9_polynom1 A C E D) F) (k9_polynom1 A C E (k6_groeb_3 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( (C = (k10_group_2 A D E))  => (r1_tarski (k2_group_11 A B C) (k9_subset_1 (u1_struct_0 A) (k2_group_11 A B D) (k2_group_11 A B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_group_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k5_group_1 B A C) = (k1_group_1 B))  => (r1_int_1 (k6_group_1 B C) A)) ) ) ) ) ) ) ).
tt(t44_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k1_group_1 B) = (k1_group_1 A)) ) ) ) ) ).
tt(t44_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_3 A (k3_group_3 A C D) B) = (k3_group_3 A C (k5_group_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t44_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k11_group_2 A D (k7_group_4 A B C)) = (k12_group_2 A B (k7_group_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t44_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_5 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A (k6_algstr_0 A (k2_group_5 A B D) (k3_group_5 A B D C)) (k2_group_5 A C D))) ) ) ) ) ) ) ) ) ).
tt(t44_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 (k10_group_6 A B C))) ) ) ) ) ) ) ).
tt(t44_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  (! [D:$i] :  ( ((v2_group_9 D A) &  ((v4_group_9 D A B) & (m1_group_9 D A B)) )  =>  (! [E:$i] :  ( ((v4_group_9 E A D) & (m1_group_9 E A D))  =>  ( ( (E = C)  & (m1_group_9 C A D))  =>  ((v4_group_9 (k10_group_9 A D E) A (k10_group_9 A B C)) & (m1_group_9 (k10_group_9 A D E) A (k10_group_9 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((k3_helly A B C D) = (k3_helly A D B C)) ) ) ) ) ) ) ) ) ).
tt(t44_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear D k1_complfld A A) &  ((v4_bilinear D k1_complfld A A) &  ((v3_hermitan D A) &  ((v5_hermitan D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ( ((k4_hermitan A D C) = k6_numbers)  =>  ((k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D C B)) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t44_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ((r2_hidden A C) =>  ((r2_hidden k6_numbers C) |  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 B)) C) A) = (k1_real_1 (k10_real_1 B (k1_seq_1 (k1_taylor_1 (k2_nat_1 B 1)) A)))) ) ) ) ) ) ) ) ) ).
tt(t44_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k3_hilbert1 A B) (k4_hilbert1 A C)) (k4_hilbert1 C B)) k6_hilbert1)) ) ) ) ) ) ).
tt(t44_hilbert3,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ((m1_hilbert3 D C) =>  (~  ( (? [E:$i] : (r1_abian E (k5_hilbert3 C D A)))  &  ( (! [E:$i] :  (~ (r1_abian E (k5_hilbert3 C D B))) )  & (v2_hilbert3 (k3_hilbert1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) => (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k7_hurwitz (k3_polynom5 k1_complfld A B)) (k3_polynom5 k1_complfld (k7_hurwitz A) (k2_complfld B)))) ) ) ) ).
tt(t44_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_tarski (k10_xtuple_0 (k4_funct_7 k14_idea_1 (k18_idea_1 D B A C))) k14_idea_1) &  ((k9_xtuple_0 (k4_funct_7 k14_idea_1 (k18_idea_1 D B A C))) = k14_idea_1) ) ) ) ) ) ) ) ) ) ).
tt(t44_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  ((k7_ideal_1 A B) = B) ) ) ) ) ).
tt(t44_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (~  ((r2_incsp_1 A E D) &  (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  & (l1_msualg_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v1_partfun1 D (u1_struct_0 C))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r3_pua2mss1 A B E F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ((r3_pua2mss1 B C G H) =>  ((k3_instalg1 A C D (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) E G) (k3_relat_1 F H)) = (k8_pboole (k3_instalg1 A B (k3_relat_1 G D) E F) (k3_relat_1 E (k3_instalg1 B C D G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_int_1 (k4_int_1 A)) = k6_numbers) ) ) ).
tt(t44_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ( (~  (C = k6_numbers) )  &  ((r1_int_2 A B) &  ((r1_int_2 A C) &  ((r1_int_2 B C) &  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  (? [I:$i] :  ((v1_int_1 I) &  ( ((k6_int_1 (k6_xcmplx_0 I D) A) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 I E) B) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 I F) C) = k6_numbers)  &  (~  ((r2_int_1 I (k2_xcmplx_0 (k2_xcmplx_0 D (k3_xcmplx_0 A G)) (k3_xcmplx_0 (k3_xcmplx_0 A B) H)) (k3_xcmplx_0 (k3_xcmplx_0 A B) C)) &  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 A G) (k6_xcmplx_0 E D)) B) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 A B) H) (k6_xcmplx_0 (k6_xcmplx_0 F D) (k3_xcmplx_0 A G))) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( ( ((k4_nat_d A 8) = 3)  |  ((k4_nat_d A 8) = 5) )  & (r1_int_5 2 A)) ) ) ) ) ).
tt(t44_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k19_sin_cos D)))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t44_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r1_tarski D (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k1_sin_cos6 E) k6_numbers))  &  ((k1_seq_1 B E) = 1) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 k3_taylor_1))) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))) k1_sin_cos6)))) ) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t44_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2))) A) B) = (k10_real_1 (k1_seq_1 k2_sin_cos9 B) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t44_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k1_seq_1 k19_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k29_sin_cos D) (k1_seq_1 k16_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t44_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (C = D)  &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) C B) A) &  ((r1_tarski B (k1_relset_1 k1_numbers C)) & (r1_integr15 A B C)) ) )  =>  ((r1_integr18 (k4_real_ns1 A) B D) &  ((k11_integr15 A B C) = (k5_integr18 (k4_real_ns1 A) B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ((r1_integra1 B C) =>  ((k13_integra1 A B C (k3_finseq_1 B)) = (k3_finseq_1 C)) ) ) ) ) ) ) ) ).
tt(t44_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (A = (k1_rcomp_1 (k8_real_1 (k4_nat_1 2 B) k32_sin_cos) (k8_real_1 (k2_nat_1 (k4_nat_1 2 B) 1) k32_sin_cos)))  =>  ((k2_integra5 A k19_sin_cos) = k6_numbers) ) ) ) ) ) ).
tt(t44_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra9 B (k26_valued_1 k1_numbers k1_numbers A 1)) = (k2_integra9 B A)) ) ) ) ) ).
tt(t44_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (~ (v1_xboole_0 (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A))))  & (m1_interva1 (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A)) A)) ) ) ).
tt(t44_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k4_intpro_1 A C) (k4_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t44_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  (! [E:$i] :  ((m2_cat_1 E A A) =>  ((r3_nattra_1 A A E (k10_cat_1 A)) =>  ((r3_nattra_1 A B (k9_cat_1 A A B E C) C) & (r3_nattra_1 B A (k9_cat_1 B A A D E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_isomichi B A) & (v3_isomichi C A))  =>  ((v3_isomichi (k4_subset_1 (u1_struct_0 A) B C) A) & (v3_isomichi (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t44_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) C D A) &  ((r1_topreal1 (k15_euclid 2) E F B) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden G A) =>  ((r1_xxreal_0 (k17_euclid C) (k17_euclid G)) & (r1_xxreal_0 (k17_euclid G) (k17_euclid D))) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden G B) =>  ((r1_xxreal_0 (k17_euclid C) (k17_euclid G)) & (r1_xxreal_0 (k17_euclid G) (k17_euclid D))) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden G A) =>  ((r1_xxreal_0 (k18_euclid E) (k18_euclid G)) & (r1_xxreal_0 (k18_euclid G) (k18_euclid F))) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden G B) =>  ((r1_xxreal_0 (k18_euclid E) (k18_euclid G)) & (r1_xxreal_0 (k18_euclid G) (k18_euclid F))) ) ) )  & (r2_subset_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jgraph_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~ (v2_funct_1 (k2_jgraph_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jgraph_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (H = k6_numbers)  &  ( (I = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( (C = a_0_5_jgraph_3)  &  ( (D = a_0_6_jgraph_3)  &  ( (E = a_0_7_jgraph_3)  &  ( (F = a_0_8_jgraph_3)  &  ( (G = a_0_9_jgraph_3)  &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H) E) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I) D) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H) G) &  ((r2_hidden (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) C) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B) C) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))) & (r1_xxreal_0 A (k13_complex1 (k18_euclid C) (k12_euclid C))))  =>  ((r1_xxreal_0 1 A) |  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  ((r1_xxreal_0 k6_numbers (k17_euclid C)) |  ((r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden B (k8_jordan6 C)) & (r1_jordan6 C A B)) )  => (r2_hidden A (k8_jordan6 C))) ) ) ) ) ) ) ).
tt(t44_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k14_pscomp_1 (k1_sppol_2 A B C D)) = (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))) ) ) ) ) ) ) ) ) ) ).
tt(t44_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k17_euclid D) = F)  &  ((r1_xxreal_0 (k18_euclid A) H) & (r1_xxreal_0 G (k18_euclid D))) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) (k1_jordan1a (k1_jordan8 C B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C B) (k1_jordan1a (k1_jordan8 C B)) (k3_finseq_1 (k1_jordan8 C B)))) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) (k1_jordan1a (k1_jordan8 C A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 C A) (k1_jordan1a (k1_jordan8 C A)) (k3_finseq_1 (k1_jordan8 C A)))))) ) ) ) ) ) ) ).
tt(t44_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  (F = (a_4_7_jordan1 A B C D)) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ((k2_pre_topc (k15_euclid 2) F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_topreal1 2 (k1_jordan1e B A)))) ) ) ) ) ) ) ) ) ).
tt(t44_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((v2_connsp_1 B (k15_euclid 2)) =>  ((k2_goboard2 (k1_jordan9 B A)) = (k1_jordan8 B A)) ) ) ) ) ) ).
tt(t44_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((k3_jordan3 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t44_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 k6_numbers (k5_jordan1k A C B))) ) ) ) ) ) ).
tt(t44_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_tarski A B) &  ( ((k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) = (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)))  & (v3_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))))) )  =>  ((v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) | (r1_xxreal_0 (k18_euclid (k2_jordan21 B)) (k18_euclid (k2_jordan21 A)))) ) ) ) ) ) ).
tt(t44_jordan23,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_jordan23 A) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden C (k3_topreal1 2 A))) ) ) ) )  =>  ( ((k3_finseq_1 A) = 2)  |  ( (B = C)  |  ( (B = (k1_funct_1 A 1))  |  ( (C = (k1_funct_1 A 1))  | (v4_topreal1 (k4_jordan3 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan2c,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((m2_finseq_2 A k1_numbers (k1_euclid (k3_finseq_1 A))) & (m1_subset_1 A (u1_struct_0 (k15_euclid (k3_finseq_1 A))))) ) ) ).
tt(t44_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((r2_hidden C (k3_topreal1 2 A)) &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) ) )  =>  ( (C = (k1_funct_1 A (k3_finseq_1 A)))  | (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k2_jordan3 A C) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) B 2 (k3_finseq_1 B))))) ) ) ) ) ) ) ) ).
tt(t44_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) =>  ((r1_xxreal_0 D C) | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k2_goboard2 A))) &  ( (E = (a_2_0_jordan5d A C))  &  ( ((k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) = (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C 1)))  &  (D = (k1_xxreal_2 E)) ) ) ) ) ) )  => (r1_xxreal_0 (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid A) C)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) E F B) &  ((r1_tarski B C) &  (D = (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k2_tarski E F))) ) )  => (v2_connsp_1 D (k1_pre_topc (k15_euclid A) C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ((r2_hidden D A) &  ((r2_hidden E A) &  ( (~  (D = B) )  &  ( (~  (D = C) )  &  ( (~  (E = B) )  &  ( (~  (E = C) )  &  (! [F:$i] :  ((m1_borsuk_2 F (k15_euclid 2) D E) =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) A) & (r1_subset_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) (k7_domain_1 (u1_struct_0 (k15_euclid 2)) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) C) => (r3_lattices A (k9_knaster A B) C)) ) ) ) ) ) ) ).
tt(t44_kurato_1,ax, (~  ((k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) = (k1_tops_1 k3_topmetr k6_kurato_1)) ) ).
tt(t44_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ((r3_lattices A B (k3_lattice2 C A D E)) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) => (r3_lattices A B (k3_funct_2 C (u1_struct_0 A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k15_lattice3 A (a_2_3_lattice3 A B)))  &  (B = (k16_lattice3 A (a_2_4_lattice3 A B))) ) ) ) ) ) ).
tt(t44_lattice5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (? [B:$i] :  ( (~ (v1_xboole_0 B))  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k1_lattice5 B))) &  ((v19_waybel_0 C A (k1_lattice5 B)) &  ((v20_waybel_0 C A (k1_lattice5 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_lattice5 B)))))) ) ) )  &  ((v2_funct_1 C) & (r1_xxreal_0 (k2_lattice5 B (k1_yellow_2 A (k1_lattice5 B) C)) 3)) ) ) ) ) ) ) ).
tt(t44_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) C)) B) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) D)) B))) ) ) ) ) ) ) ) ).
tt(t44_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v3_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 E D))  &  ((r2_hidden E (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc2 B A) =>  ((r1_limfunc2 (k32_valued_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc2 (k32_valued_1 k1_numbers k1_numbers B) A) = (k1_real_1 (k1_limfunc2 B A))) ) ) ) ) ) ) ).
tt(t44_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  ((k1_seq_1 B E) = k6_numbers) )  &  (~  ((k1_seq_1 B F) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (~ (r2_limfunc3 B A))  &  (~ (r3_limfunc3 B A)) )  |  ((r1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t44_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r3_limfunc3 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) &  ((k1_seq_1 B E) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) )  | (r6_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t44_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r3_mesfunc6 A B C D) =>  ((r2_hidden (k1_mesfunc6 A B C D) k1_numbers) &  ((r2_hidden (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D)) k1_numbers) & (r3_mesfunc6 A B C (k56_valued_1 A k1_numbers D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [H:$i] :  ( ((v2_xxreal_0 H) & (m1_subset_1 H k1_numbers))  =>  ( ( ((k5_lpspace2 A B C D H) = (k5_lpspace2 A B C E H))  &  ((k5_lpspace2 A B C F H) = (k5_lpspace2 A B C G H)) )  =>  ( (! [I:$i] :  ((m2_subset_1 I (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A I)) = k6_numbers)  &  ( (I = (k1_relset_1 A D))  & (r1_mesfunc6 A B D I)) ) ) ) )  |  ( (! [I:$i] :  ((m2_subset_1 I (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A I)) = k6_numbers)  &  ( (I = (k1_relset_1 A E))  & (r1_mesfunc6 A B E I)) ) ) ) )  |  ( (! [I:$i] :  ((m2_subset_1 I (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A I)) = k6_numbers)  &  ( (I = (k1_relset_1 A F))  & (r1_mesfunc6 A B F I)) ) ) ) )  |  ( (! [I:$i] :  ((m2_subset_1 I (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A I)) = k6_numbers)  &  ( (I = (k1_relset_1 A G))  & (r1_mesfunc6 A B G I)) ) ) ) )  |  ((v1_xboole_0 (k5_lpspace2 A B C D H)) |  ((v1_xboole_0 (k5_lpspace2 A B C F H)) |  ((k5_lpspace2 A B C (k3_valued_1 A k1_numbers k1_numbers D F) H) = (k5_lpspace2 A B C (k3_valued_1 A k1_numbers k1_numbers E G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 B A) => (r8_ltlaxio1 B (k2_ltlaxio1 A))) ) ) ) ) ).
tt(t44_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) => (v2_cqc_the1 (k8_cqc_lang A C (k8_cqc_lang A B D)) A)) ) ) ) ) ) ) ) ) ).
tt(t44_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k3_mathmorp A B C) (k3_mathmorp A (k5_mathmorp A B C) C)) & (r1_tarski (k6_rusub_4 A B C) (k6_rusub_4 A (k5_mathmorp A B C) C))) ) ) ) ) ) ) ).
tt(t44_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r1_matrix10 B C) => (r2_matrix10 B C)) ) ) ) ) ) ) ).
tt(t44_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k12_matrix_2 A) (k12_matrix_2 A)) &  ((v3_funct_2 C (k12_matrix_2 A) (k12_matrix_2 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (k12_matrix_2 A))))) ) )  &  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  ((k3_funct_2 (k12_matrix_2 A) (k12_matrix_2 A) C D) = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) B D)) ) ) ) ) ) ) ) ) ).
tt(t44_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  ((k6_matrix13 A D (k3_matrix13 B) (k3_matrix13 C)) = (k2_matrlin A (k4_matrix_2 A (k3_matrix_1 A D B C)))) ) ) ) ) ) ) ) ) ).
tt(t44_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  =>  ((k3_matrix_1 (u1_struct_0 A) (k4_matrix14 A B 1) D D) = (k5_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski D (k4_finseq_1 B)) =>  ((v1_xboole_0 D) | (r1_tarski (k4_matrix15 A B C) (k4_matrix15 A (k6_matrix13 (u1_struct_0 A) B D (k2_finseq_1 (k1_matrix_1 B))) (k6_matrix13 (u1_struct_0 A) C D (k2_finseq_1 (k1_matrix_1 C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((v2_matrix16 C (u1_struct_0 A)) &  ((v2_matrix16 D (u1_struct_0 A)) &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k1_matrix16 (u1_struct_0 A) C) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix16 (u1_struct_0 A) D) B)) = (k1_matrix16 (u1_struct_0 A) (k9_fvsum_1 A (k3_fvsum_1 A C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((k1_funct_1 E A) = D) )  =>  ( ((k3_finseq_1 D) = (k1_matrix_1 E))  & (r2_hidden B (k4_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k1_matrix_4 A (k2_matrix_3 A B) C) = (k1_matrix_4 A (k2_matrix_3 A C) B)) ) ) ) ) ) ) ) ).
tt(t44_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v4_matrix_6 C A B) & (r1_matrix_6 A B C D))  => (r1_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t44_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_8 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrix_9,ax, ((v1_funct_1 (k3_finseq_4 k5_numbers 1 3 2)) &  ((v1_funct_2 (k3_finseq_4 k5_numbers 1 3 2) (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 (k3_finseq_4 k5_numbers 1 3 2) (k2_finseq_1 3) (k2_finseq_1 3)) &  ( (~ (v5_matrix_2 (k3_finseq_4 k5_numbers 1 3 2) 3))  & (m1_subset_1 (k3_finseq_4 k5_numbers 1 3 2) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) ) ).
tt(t44_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k5_matrixc1 A (k5_matrixc1 B C)) = (k5_matrixc1 (k5_matrixc1 A B) C)) ) ) ) ) ) ) ) ).
tt(t44_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E (u1_struct_0 B)) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) =>  ((k7_matrix_2 (k1_nat_1 A (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 B) E))) B (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) E (k4_matrixj1 (u1_struct_0 B) D)))) = (k13_matrixj1 (u1_struct_0 B) C (k3_matrixj1 (u1_struct_0 B) E (k4_matrixj1 (u1_struct_0 B) (k7_matrix_2 A B D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((k7_matrixr1 k6_numbers A) = (k8_matrixr1 (k3_finseq_1 A) (k1_matrix_1 A))) ) ) ) ).
tt(t44_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((k3_matrixr2 A B) = (k3_matrixr2 A (k5_matrix_1 A k1_numbers B))) ) ) ) ) ).
tt(t44_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ( ((k8_matrix13 A F) = (k3_finseq_1 D))  => (v2_funct_1 (k4_matrlin2 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) &  ((v2_matroid0 A) &  ((v4_matroid0 A) & (l1_pre_topc A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((v3_pre_topc B A) &  ((v5_matroid0 C A) &  ((v5_matroid0 D A) &  ((r1_tarski C (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) E))) & (r1_tarski D (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) E)))) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k23_rvsum_1 A (k11_matrixr1 C B)) = (k5_matrprob (k6_matrprob A B C))) ) ) ) ) ) ) ) ) ).
tt(t44_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (? [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D k1_numbers))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k12_euclid (k2_matrtop1 (k9_matrix_1 (u1_struct_0 k2_vectsp_1) C E)))) ) ) )  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E B) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  => (r1_xxreal_0 (k12_euclid (k1_funct_1 (k3_matrtop1 B A C) E)) (k11_binop_2 (k18_rvsum_1 D) (k12_euclid E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  (D = (k3_xtuple_0 (k1_mcart_1 A B C D) (k2_mcart_1 A B C D) (k3_mcart_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t44_measure6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((v4_xxreal_2 A) =>  ((k4_seq_4 A) = (k1_real_1 (k5_seq_4 (k4_measure6 A)))) ) ) ) ).
tt(t44_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k8_member_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k1_xxreal_3 A B) (k1_xxreal_3 A C))) ) ) ) ) ) ) ).
tt(t44_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v5_memstr_0 C A B k6_numbers)) ) ) )  =>  ((k8_memstr_0 A B C) = C) ) ) ) ) ) ) ).
tt(t44_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r2_mesfun6c A B C D) &  ((r2_mesfun6c A B C E) & (r1_tarski F (k1_relset_1 A (k2_valued_1 A k2_numbers k2_numbers D E)))) )  =>  ((r2_mesfun6c A B C (k2_valued_1 A k2_numbers k2_numbers D E)) &  ((k3_mesfun6c A B C (k2_valued_1 A k2_numbers k2_numbers D E) F) = (k2_xcmplx_0 (k3_mesfun6c A B C D F) (k3_mesfun6c A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (~  ((r1_mesfun7c A B C) &  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k2_numbers) =>  (~  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_funct_1 C G) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((r1_mesfun7c A B C) & (r1_mesfun7c A B D))  => (r1_mesfun7c A B (k2_valued_1 A k2_numbers k2_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(t44_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_tarski D (k9_subset_1 A (k1_relset_1 A E) (k1_relset_1 A F))) &  ((r1_mesfunc1 A B E D) &  ((r1_mesfunc1 A B F D) &  ((v3_mesfunc5 E) & (v3_mesfunc5 F)) ) ) )  => (r1_mesfunc1 A B (k3_mesfunc1 A (k2_mesfunc2 A (k3_mesfunc1 A E F)) (k1_mesfunc2 A E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k7_numbers (k1_mesfunc5 A (k56_valued_1 A k1_numbers B)) (k10_mesfunc1 A (k1_mesfunc5 A B)))) ) ) ) ).
tt(t44_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers)) = C)  &  ((v2_mesfunc9 D A) &  ((v1_mesfunc8 D A k7_numbers) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A D) E) C)) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E C) => (v1_mesfunc9 (k3_mesfunc5 A D E))) ) ) ) ) ) )  => (r1_mesfunc1 A B (k7_mesfunc8 A (k4_mesfunc9 A D)) C)) ) ) ) ) ) ) ) ) ).
tt(t44_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  ((k7_midsp_1 A B (k6_midsp_1 A)) = B) ) ) ) ) ).
tt(t44_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ( ((k1_relset_1 A B) = A)  &  ((k1_relset_1 A C) = A) )  => (r2_relset_1 A A (k23_mmlquery A (k20_mmlquery A B C) D) (k19_mmlquery A (k23_mmlquery A B D) (k23_mmlquery A C D)))) ) ) ) ) ) ) ) ).
tt(t44_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  ( (~  ((k10_modal_1 A) = (k11_modal_1 B)) )  &  (~  ((k10_modal_1 A) = (k12_modal_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t44_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r3_modelc_1 A B C H F) => (r3_modelc_1 A B C H G)) ) )  =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r3_modelc_1 A B C H (k59_modelc_1 A B C D E F)) => (r3_modelc_1 A B C H (k59_modelc_1 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (~  ((r3_modelc_2 A (k8_modelc_2 B C)) &  ( (~ (r2_modelc_2 A B))  &  (~ (r2_modelc_2 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t44_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) &  ((v3_modelc_3 B A) & (l1_modelc_3 B A)) )  => (m1_subset_1 B (k23_modelc_3 A))) ) ) ) ).
tt(t44_moebius1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ((r1_xboole_0 A B) =>  ((k4_moebius1 (k4_subset_1 k5_numbers A B)) = (k11_pre_poly k5_numbers (k4_moebius1 A) (k4_moebius1 B))) ) ) ) ) ) ).
tt(t44_monoid_0,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_monoid_0)) <=> (m2_subset_1 A k1_numbers k5_numbers)) ) ).
tt(t44_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((k2_binop_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) (k1_zfmisc_1 C) (k21_monoid_1 A B C D) E F) = (k7_relset_1 (k2_zfmisc_1 A B) C D (k2_zfmisc_1 E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  ((r1_pboole A (k1_pboole A) C) => (r6_pboole A (k4_mssubfam A B C) (k1_pboole A))) ) ) ) ) ) ).
tt(t44_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ( ((v2_msualg_4 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  ((r2_pboole (u1_struct_0 A) C D) => (r2_pboole (u1_struct_0 A) (k9_msualg_6 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t44_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A C) =>  ((r1_xxreal_0 (k3_xcmplx_0 2 A) C) |  ((r2_hidden (k4_tarski C (k3_xcmplx_0 2 A)) (u1_orders_2 (k6_mycielsk A B))) & (r2_hidden (k4_tarski (k3_xcmplx_0 2 A) C) (u1_orders_2 (k6_mycielsk A B)))) ) ) ) ) ) ) ) ) ).
tt(t44_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A B) <=>  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ).
tt(t44_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_int_2 A B) => (r1_xboole_0 (k1_polynom2 k10_newton (k12_nat_3 A)) (k1_polynom2 k10_newton (k12_nat_3 B)))) ) ) ) ) ).
tt(t44_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m1_trees_4 D k5_numbers k10_newton) =>  (! [E:$i] :  ( ((v7_ordinal1 E) & (v1_int_2 E))  =>  ( ((r1_tarski C k10_newton) &  ((r1_tarski C (k2_finseq_1 B)) &  ( (D = (k14_finseq_1 C))  &  (A = (k3_wsierp_1 D)) ) ) )  =>  ( ((r2_hidden E (k1_rvsum_1 D)) =>  ((k11_nat_3 A E) = 1) )  &  ( (~ (r2_hidden E (k1_rvsum_1 D)))  =>  ((k11_nat_3 A E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k7_nat_d A 1) B)) ) ) ) ) ).
tt(t44_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((v2_nattra_1 A) => (v2_nattra_1 (k11_nattra_1 B A))) ) ) ) ) ).
tt(t44_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r7_ncfcont1 A B D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E C) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_hidden H C) &  ( (~ (r1_xxreal_0 G (k1_normsp_0 A (k5_algstr_0 A H E))))  & (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D H) (k7_partfun1 (u1_struct_0 B) D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_ndiff_1 B A C D) => (r1_nfcont_1 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t44_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers B (k1_pdiff_1 1 1)) &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  & (r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) F (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B E))) ) ) )  =>  ((r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) <=> (r1_ndiff_3 (k4_real_ns1 A) E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (k4_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  (! [F:$i] :  ( ( (D = (k4_struct_0 (k14_prvect_2 A)))  &  ( (E = B)  &  (C = (k1_funct_4 D (k11_card_3 (k4_prvect_2 A) E F))) ) )  => (r1_xxreal_0 (k1_normsp_0 (k14_prvect_2 A) C) (k1_normsp_0 (k14_prvect_2 A) B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A B) <=>  ((k5_nat_d A B) = B) ) ) ) ) ) ).
tt(t44_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r5_nfcont_1 A A B (k1_partfun2 (u1_struct_0 A) B))) ) ) ) ).
tt(t44_nfcont_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((v1_nfcont_4 B A) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) => (v1_fcont_1 (k1_partfun1 k1_numbers (k1_euclid A) (k1_euclid A) k1_numbers B (k1_pdiff_1 C A)))) ) ) ) ) ) ) ) ).
tt(t44_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k9_normform A (k5_setwiseo (k7_normform A) (k9_normform A B) C)) = (k9_normform A (k5_setwiseo (k7_normform A) B C))) ) ) ) ) ) ).
tt(t44_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 B) (k7_cat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k3_oppcat_1 A D)) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t44_orders_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  => (r2_orders_1 B A)) ) ) ).
tt(t44_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_orders_2 D A C) =>  ( (B = (k3_tarski (k4_orders_2 A C)))  =>  ( (D = (k3_tarski (k4_orders_2 A C)))  | (m1_orders_2 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t44_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k12_ordinal2 A (k1_ordinal1 B)) = (k11_ordinal2 A (k12_ordinal2 A B))) ) ) ) ) ).
tt(t44_ordinal3,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 (k4_ordinal2 A)) =>  ( (k1_xboole_0 = (k9_xtuple_0 A))  |  ( (B = k1_xboole_0)  |  ((k4_ordinal2 (k4_ordinal3 B A)) = (k11_ordinal2 (k4_ordinal2 A) B)) ) ) ) ) ) ) ) ).
tt(t44_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) => (r2_hidden (k3_ordinal5 A) (k3_ordinal5 B))) ) ) ) ) ).
tt(t44_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_ordinal1 A) (k2_ordinal1 A)) &  ((v2_ordinal6 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) )  =>  ((r2_hidden k4_ordinal1 A) =>  ((v1_funct_1 (k3_ordinal6 B)) &  ((v1_funct_2 (k3_ordinal6 B) (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 (k3_ordinal6 B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ) ) ) ).
tt(t44_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t44_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_osalg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 (k2_osafree A B)) (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B))) => (r2_hidden (k4_tarski D (k3_funct_2 (k4_dtconstr (k2_osafree A B)) (k4_dtconstr (k2_osafree A B)) (k29_osafree A B) D)) (k2_msualg_4 A (k8_osafree A B) C (k10_osafree A B D)))) ) ) ) ) ) ) ) ).
tt(t44_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (v1_binop_1 (k14_osalg_2 A B) (k13_osalg_2 A B))) ) ) ) ).
tt(t44_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_parsp_2 A B D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k9_xtuple_0 C)) & (r1_tarski (k7_relat_1 C A) B))  => (v1_partfun1 (k3_partfun1 C A B) A)) ) ) ) ) ).
tt(t44_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D B) => (v3_funct_1 (k2_partfun1 A B (k4_partfun2 A B C D) C))) ) ) ) ) ) ) ) ).
tt(t44_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((r2_pboole A B (k1_pboole A)) => (r6_pboole A B (k1_pboole A))) ) ) ) ).
tt(t44_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k25_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k25_pcs_0 A B))) =>  ((r1_orders_2 (k25_pcs_0 A B) C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F D) & (r1_orders_2 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 2 3) B)) =>  ( ((r8_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 2 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B))))) &  ((k8_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 2 (k1_pdiff_3 3 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F A) &  ( (~ (r1_xxreal_0 G (k12_euclid (k8_euclid A C B))))  &  ( (~ (r1_xxreal_0 G (k12_euclid (k8_euclid A D B))))  &  ( (H = (k1_seq_1 (k1_pdiff_1 F A) C))  &  ( (D = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F C) I))  &  ((r2_hidden J (k1_rcomp_1 H I)) &  ( (E = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A F C) J))  & (r1_xxreal_0 G (k12_euclid (k8_euclid A E B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A C) D) =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_pdiff_9 A B C))  <=> (r4_pdiff_7 A 1 D B)) ) ) ) ) ) ) ) ) ).
tt(t44_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k3_nat_d A A) = 1) ) ) ) ).
tt(t44_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m2_finseq_2 C B (k3_finseq_2 B)) =>  (! [D:$i] :  ((m2_finseq_2 D B (k3_finseq_2 B)) =>  (! [E:$i] :  ((m2_finseq_2 E B (k3_finseq_2 B)) =>  ((k10_pnproc_1 A B (k6_domain_1 (k3_finseq_2 B) C) (k7_domain_1 (k3_finseq_2 B) D E)) = (k7_domain_1 (k3_finseq_2 B) (k1_pre_poly B C D) (k1_pre_poly B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t44_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  ( (C = D)  <=>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A B)) =>  ((r2_hidden E C) <=> (r2_hidden E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k4_polynom5 A B C) D) = (k1_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t44_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 (k1_algseq_1 A B) D) & (r1_xxreal_0 (k1_algseq_1 A C) D))  =>  ((r1_xxreal_0 D k6_numbers) |  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_polynom8 A E (k4_nat_1 2 D)) =>  ( ((k1_polynom8 A (k4_nat_1 2 D)) = (k4_struct_0 A))  | (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_polynom5 A (k6_polynom8 (k4_nat_1 2 D) A (k2_polynom8 A (k6_polynom8 (k4_nat_1 2 D) A B E) (k6_polynom8 (k4_nat_1 2 D) A C E)) (k11_algstr_0 A E)) (k11_algstr_0 A (k1_polynom8 A (k4_nat_1 2 D)))) (k13_polynom3 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_rewrite1 (k3_polyred A B C F) D E) =>  ((r1_polyred A B C E D) &  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) E (k7_polynom1 A C)) | (r1_termord A B (k3_termord A B C E) (k3_termord A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power A B) = (k6_prepower A B)) ) ) ) ) ) ).
tt(t44_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r2_pre_poly A B C) & (r1_pre_poly A C D))  => (r1_pre_poly A B D)) ) ) ) ) ) ) ) ) ).
tt(t44_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~  (A = k6_numbers) )  =>  ((k4_prepower A (k2_xcmplx_0 B C)) = (k3_xcmplx_0 (k4_prepower A B) (k4_prepower A C))) ) ) ) ) ) ) ) ).
tt(t44_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((v1_prob_2 C) => (r2_funct_2 k5_numbers k1_numbers (k8_prob_1 A B (k2_prob_3 A C) D) (k3_series_1 (k8_prob_1 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t44_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k7_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden B (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t44_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k20_pscomp_1 A) = (k21_pscomp_1 A))  =>  ((k15_pscomp_1 A) = (k1_tarski (k20_pscomp_1 A))) ) ) ) ).
tt(t44_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pboole A B C) => (r6_pboole A (k3_pboole A C (k1_pzfmisc1 A B)) (k1_pzfmisc1 A B))) ) ) ) ) ) ).
tt(t44_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B (k1_qc_lang2 A)) <=>  (B = (k12_qc_lang1 A)) ) ) ) ) ) ).
tt(t44_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k15_qc_lang1 A B C)) = (k4_qc_lang3 A D C)) ) ) ) ) ) ) ) ) ).
tt(t44_quatern2,ax, ((k3_quatern2 (k4_struct_0 k16_quatern2)) = k6_numbers) ).
tt(t44_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k10_real_1 (k7_real_1 (k3_quatern2 (k26_quaterni A B)) (k3_quatern2 (k29_quaterni B A))) 2) (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)))) ) ) ) ).
tt(t44_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k31_quaterni A)) = (k17_quaterni A))  &  ( ((k18_quaterni (k31_quaterni A)) = (k1_real_1 (k18_quaterni A)))  &  ( ((k19_quaterni (k31_quaterni A)) = (k1_real_1 (k19_quaterni A)))  &  ((k20_quaterni (k31_quaterni A)) = (k1_real_1 (k20_quaterni A))) ) ) ) ) ) ).
tt(t44_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k19_quofield A))) =>  ((k8_group_1 (k19_quofield A) (k8_group_1 (k19_quofield A) B C) D) = (k8_group_1 (k19_quofield A) B (k8_group_1 (k19_quofield A) C D))) ) ) ) ) ) ) ) ) ).
tt(t44_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k1_vectsp_9 A B) = (k2_xcmplx_0 (k10_ranknull A B C D) (k11_ranknull A B C D))) ) ) ) ) ) ) ) ) ).
tt(t44_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ( (B = (k10_real_1 1 A))  =>  ((r1_xxreal_0 A k6_numbers) |  ( ((k2_rat_1 B) = (k1_rat_1 A))  &  ((k1_rat_1 B) = (k2_rat_1 A)) ) ) )  &  ( ( ((k2_rat_1 B) = (k1_rat_1 A))  &  ((k1_rat_1 B) = (k2_rat_1 A)) )  =>  ( (~ (r1_xxreal_0 A k6_numbers))  &  (B = (k10_real_1 1 A)) ) ) ) ) ) ) ) ).
tt(t44_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ((v3_pre_topc C (k4_topmetr A B)) &  ((v2_connsp_1 C (k4_topmetr A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) )  =>  (~  ( (~ (v1_xboole_0 C))  &  ( (~  (C = (k1_rcomp_1 A B)) )  &  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 D A))  &  ((r1_xxreal_0 D B) &  (C = (k3_rcomp_1 A D)) ) ) ) ) )  &  ( (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 A D) &  ( (~ (r1_xxreal_0 B D))  &  (C = (k4_rcomp_1 D B)) ) ) ) ) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((r1_xxreal_0 A D) &  ( (~ (r1_xxreal_0 E D))  &  ((r1_xxreal_0 E B) &  (C = (k2_rcomp_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers) k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_hidden (k1_seq_1 (k5_real_3 A) B) k5_numbers)) ) ) ) ) ).
tt(t44_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_xboole_0 (k10_xtuple_0 A) (k9_xtuple_0 B)) =>  ((k3_relat_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t44_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  (! [E:$i] :  ( (~  ( (? [F:$i] :  (? [G:$i] :  ((r2_hidden F D) &  ((r2_hidden G E) & (r2_hidden F (k1_relset_2 B A (k3_relset_1 A B C) G))) ) ) )  & (r1_xboole_0 E (k7_relset_1 A B C D))) )  &  (~  ( (~ (r1_xboole_0 E (k7_relset_1 A B C D)))  &  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden F D) &  ((r2_hidden G E) & (r2_hidden F (k1_relset_2 B A (k3_relset_1 A B C) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r7_rewrite1 A B C) => (r5_rewrite1 A B C)) ) ) ) ) ).
tt(t44_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ( ((r3_rewrite2 A B C D) & (r2_rewrite2 A (k4_lang1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) C D)) E F))  => (r3_rewrite2 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ( ((v2_rewrite3 F D E) &  ((r2_hidden (k4_tarski A B) (k1_rewrite3 D E F)) & (r2_hidden (k4_tarski A C) (k1_rewrite3 D E F))) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((k5_relat_1 (k1_valued_1 B C) A) = (k1_valued_1 (k5_relat_1 B A) (k5_relat_1 C A)))  &  ( ((k5_relat_1 (k1_valued_1 B C) A) = (k1_valued_1 (k5_relat_1 B A) C))  &  ((k5_relat_1 (k1_valued_1 B C) A) = (k1_valued_1 B (k5_relat_1 C A))) ) ) ) ) ) ) ) ).
tt(t44_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_tarski A)))) ) ) ).
tt(t44_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] : (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k18_rfunct_3 A B) C) (k18_rfunct_3 A (k2_partfun1 A k1_numbers B C)))) ) ) ) ) ).
tt(t44_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 C (k2_nat_1 A D)) B)) )  <=> (r1_xxreal_0 (k1_seq_1 (k4_rinfsup1 C) A) B)) ) ) ) ) ) ) ) ).
tt(t44_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 (k5_rusub_4 A C B) A) => (v1_rlaffin1 C A)) ) ) ) ) ) ) ).
tt(t44_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  ((k3_rlsub_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(t44_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( ((k1_rlsub_2 A B C) = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = (a_1_1_rltopsp1 A))  => (m1_yellow13 B A (k4_struct_0 A))) ) ) ) ) ).
tt(t44_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B)) = B) ) ) ) ) ).
tt(t44_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ((m2_rlvect_2 D A C) => (m2_rlvect_2 (k8_rlvect_2 A B D) A C)) ) ) ) ) ) ) ) ) ).
tt(t44_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) => (r2_hidden C (k3_rmod_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t44_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ( (B = (k1_rmod_3 A B C D))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) &  ( (E = (k3_rlvect_1 B F G))  &  ( (E = (k3_rlvect_1 B H I))  &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  ((r1_struct_0 D G) &  ((r1_struct_0 D I) &  (~  ( (F = H)  &  (G = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  | (r1_rmod_3 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t44_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) => (r1_rmod_4 A B (k7_rmod_4 A B (k4_struct_0 A) C) (k3_rmod_4 A B))) ) ) ) ) ) ).
tt(t44_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_robbins1 A (k15_robbins1 A B) B) = (k16_robbins1 A B)) ) ) ) ) ).
tt(t44_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) B) = (k5_robbins1 A B (k3_robbins1 A C))) ) ) ) ) ) ) ).
tt(t44_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v1_orders_3 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_funct_2 (u1_struct_0 A) k1_numbers (u1_struct_0 A) (k2_tarski k1_xboole_0 1) (k6_roughs_1 A B) (k5_funct_3 B (u1_struct_0 A)))) ) ) ) ).
tt(t44_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((k2_rpr_1 A (k3_subset_1 A B) B) = k6_numbers) ) ) ) ) ).
tt(t44_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k3_rusub_1 A (k1_rlvect_1 A C D) B) = (u1_struct_0 B))  =>  ( (D = k6_numbers)  | (r1_struct_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t44_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ( ((k1_rusub_2 A B C) = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A)))  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ((r1_struct_0 B E) &  ((r1_struct_0 C F) &  (D = (k3_rlvect_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((m1_rusub_1 B C) => (m1_rusub_1 B (k1_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t44_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))  =>  ( (C = k6_numbers)  | (v1_xboole_0 (k6_bhsp_2 A B C))) ) ) ) ) ) ) ) ).
tt(t44_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k1_seq_1 (k24_valued_1 C B) A) = (k11_binop_2 B (k1_seq_1 C A))) ) ) ) ) ) ).
tt(t44_rvsum_2,ax, (! [A:$i] :  ((m2_finseq_2 A k2_numbers (k4_finseq_2 k6_numbers k2_numbers)) =>  ((k20_rvsum_1 A) = 1) ) ) ).
tt(t44_scmbsort,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) => (v4_extpro_1 (k1_scmfsa_m (k16_funcop_1 (k5_scmfsa_2 k6_numbers) A)) 3 k1_scmfsa_2 k2_scmbsort)) ) ).
tt(t44_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  (~ (r2_hidden A (k1_relset_1 (u1_struct_0 k1_ami_3) B))) ) ) ) ) ).
tt(t44_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  &  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) & (r1_scmfsa8a B A (k2_scmfsa6a D))) )  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k3_scmfsa6a D (k4_compos_1 k1_scmfsa_2)) B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) (k2_nat_1 k6_numbers 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k2_scmfsa_9 C B)) B) (k8_memstr_0 3 k1_scmfsa_2 D)) 3)))) ) ) ) ) ) ) ) ).
tt(t44_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 3))  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 B E) k6_numbers))  =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b C B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b C B A) F)) ) ) ) )  &  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) =>  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k1_funct_1 (k1_scmfsa6b D B A) F)) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8b E C D) B A) F) = (k18_scmfsa_2 (k1_scmfsa6b D B A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ( ((k5_memstr_0 2 k1_scmpds_2 A) = (k5_memstr_0 2 k1_scmpds_2 B))  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t44_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v2_compos_1 D k1_scmpds_2) &  ((v2_scmpds_4 D) & (v3_scmpds_4 D)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B E) G)) = k6_numbers) )  =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_6 E G C D) (k8_memstr_0 2 k1_scmpds_2 B) A) F) = (k1_funct_1 (k6_scmpds_4 D (k8_memstr_0 2 k1_scmpds_2 B) A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) =>  ((r1_scmpds_6 (k2_scmpds_7 D E F C) B A) & (r2_scmpds_6 (k2_scmpds_7 D E F C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((v4_scmyciel B) =>  ((r1_tarski A B) => (r1_tarski A (k7_scmyciel B (k3_tarski A)))) ) ) ) ) ).
tt(t44_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r1_semi_af1 A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_semi_af1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 B) =>  ( (A = k6_numbers)  | (v2_relat_1 (k26_valued_1 k5_numbers k1_numbers B A))) ) ) ) ) ) ).
tt(t44_seq_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v3_membered B))  =>  ( ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C B) => (r1_xxreal_0 A C)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D B) => (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 C A)) ) ) )  =>  (A = (k3_seq_4 B)) ) ) ) ) ) ).
tt(t44_seqfunc,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 k1_numbers k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k1_numbers k1_numbers))))) )  =>  ( ((r3_seqfunc k1_numbers B A) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers B C) A))) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k11_seqfunc k1_numbers B A) A))) ) ) ) ).
tt(t44_seqm_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( ((k3_finseq_1 A) = (k2_nat_1 C 1))  &  ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden D (k2_finseq_1 C)) &  ( (~  ((k1_funct_1 (k2_finseq_3 B A) D) = (k1_funct_1 A D)) )  &  (~  ((k1_funct_1 (k2_finseq_3 B A) D) = (k1_funct_1 A (k2_nat_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) )  => (r1_xxreal_0 k6_numbers (k1_seq_1 (k1_series_3 B) A))) ) ) ) ) ).
tt(t44_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( ((k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) = (k3_square_1 C))  &  ((r1_xxreal_0 3 D) & (r1_xxreal_0 (k1_newton C (k2_nat_1 D 2)) (k2_xcmplx_0 (k1_newton A (k2_nat_1 D 2)) (k1_newton B (k2_nat_1 D 2))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski B C) => (r1_tarski (k8_setfam_1 A C) (k8_setfam_1 A B))) ) ) ) ) ) ).
tt(t44_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v3_prob_1 C) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 B) C A) (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) (k2_nat_1 A 1)))) ) ) ) ) ) ).
tt(t44_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k4_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A)) (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k2_setlim_2 B C D)) A))) ) ) ) ) ) ) ).
tt(t44_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k10_setwiseo A B (k2_setwiseo A D) C) = (k3_funct_2 A (k5_finsub_1 B) C D)) ) ) ) ) ) ) ) ).
tt(t44_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  ((k4_sf_mastr (k11_compos_1 k1_scmfsa_2 A)) = (k3_sf_mastr A)) ) ) ).
tt(t44_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C C)) = (k5_sheffer1 A B (k5_sheffer1 A B C))) ) ) ) ) ) ) ).
tt(t44_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  ((r1_xxreal_0 (k2_xxreal_3 1) B) => (r1_xxreal_0 (k6_simplex0 (k8_simplex0 A C B)) B)) ) ) ) ) ) ).
tt(t44_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) &  ((v3_matroid0 C) &  ((v6_simplex0 C (u1_struct_0 B)) &  ((v1_simplex1 C B) &  ((v2_simplex1 C B) & (m1_simplex0 C (u1_struct_0 B))) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ( ((v1_matroid0 C) &  ((v3_matroid0 C) & (m1_simplex1 C B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) D)))) )  &  ( ((k5_card_1 D) = (k3_real_1 A 1))  &  ( ((k6_simplex0 C) = A)  &  (! [E:$i] :  ((m3_simplex0 E C (k5_real_1 A 1)) =>  (! [F:$i] :  ( (F = (a_4_1_simplex1 A B C E))  =>  ( ( (~ (r1_xboole_0 (k3_convex1 B (k1_simplex1 B C E)) (k1_rlaffin2 B D)))  =>  ((k1_card_1 F) = 2) )  &  ((r1_xboole_0 (k3_convex1 B (k1_simplex1 B C E)) (k1_rlaffin2 B D)) =>  ((k1_card_1 F) = 1) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m3_simplex0 E (k4_simplex1 B C) (k5_real_1 A 1)) =>  (! [F:$i] :  ( (F = (a_4_2_simplex1 A B C E))  =>  ( ( (~ (r1_xboole_0 (k3_convex1 B (k1_simplex1 B (k4_simplex1 B C) E)) (k1_rlaffin2 B D)))  =>  ((k1_card_1 F) = 2) )  &  ((r1_xboole_0 (k3_convex1 B (k1_simplex1 B (k4_simplex1 B C) E)) (k1_rlaffin2 B D)) =>  ((k1_card_1 F) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_sincos10,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)))) = (k1_rcomp_1 1 (k7_square_1 2))) ).
tt(t44_sin_cos2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k1_seq_1 k7_sin_cos2 A)))  &  (~ (r1_xxreal_0 (k1_seq_1 k7_sin_cos2 A) (k1_real_1 1))) ) ) ) ).
tt(t44_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 B)) (k5_binop_2 (k7_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 B))) k7_complex1))) ) ) ) ) ).
tt(t44_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  ((k20_sin_cos A) = k6_numbers) )  &  ( (~  ((k20_sin_cos B) = k6_numbers) )  &  (~  ((k7_xcmplx_0 (k20_sin_cos (k2_xcmplx_0 A B)) (k20_sin_cos (k6_xcmplx_0 A B))) = (k7_xcmplx_0 (k6_xcmplx_0 1 (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B))) (k2_xcmplx_0 1 (k3_xcmplx_0 (k1_sin_cos4 A) (k1_sin_cos4 B))))) ) ) ) ) ) ) ) ) ).
tt(t44_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_sin_cos2 (k8_real_1 3 A)) = (k9_real_1 (k8_real_1 4 (k2_newton (k6_sin_cos2 A) 3)) (k8_real_1 3 (k6_sin_cos2 A)))) ) ) ).
tt(t44_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k21_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) = 1)  => (r2_hidden A k4_numbers)) ) ) ).
tt(t44_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ((k4_sin_cos7 A) = (k11_binop_2 (k18_binop_2 1 2) (k2_sin_cos7 (k12_binop_2 (k9_binop_2 1 (k3_square_1 A)) (k10_binop_2 1 (k3_square_1 A)))))) ) ) ) ) ) ) ).
tt(t44_sin_cos9,ax, ( ((k6_sin_cos9 k6_numbers) = (k10_real_1 k32_sin_cos 2))  &  ((k1_seq_1 k2_sin_cos9 k6_numbers) = (k10_real_1 k32_sin_cos 2)) ) ).
tt(t44_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r2_funct_2 k5_numbers k1_numbers (k4_sin_cos A) (k7_comseq_3 (k3_sin_cos A)))) ) ).
tt(t44_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r2_hidden A (k4_finseq_1 B)) => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B A) (k3_topreal1 2 B))) ) ) ) ) ).
tt(t44_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k9_pscomp_1 A) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A))) ) ) ).
tt(t44_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k19_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t44_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k1_xboole_0 D) &  ((r1_xxreal_0 D 1) & (r1_sprect_2 A (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) B C))) )  => (r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) B (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid 2) C D))))) ) ) ) ) ) ) ) ) ).
tt(t44_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k22_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k21_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t44_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k3_square_1 B) (k3_square_1 A))) ) ) ) ) ) ) ).
tt(t44_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_stacks_1 C) &  ((v3_stacks_1 C) &  ((v4_stacks_1 C) &  ((v5_stacks_1 C) &  ((v6_stacks_1 C) & (l1_stacks_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ((r3_stacks_1 A B D E) & (r3_stacks_1 B C F G))  => (r3_stacks_1 A C (k3_relat_1 D F) (k3_relat_1 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_stirl2_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_xboole_0 (k3_tarski (k10_xtuple_0 (k5_relat_1 A B))) (k1_funct_1 A B)) = (k3_tarski (k10_xtuple_0 (k5_relat_1 A (k23_binop_2 B 1))))) ) ) ) ) ).
tt(t44_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r1_tarski (k24_qc_lang1 A B) (k9_substut1 A B)) => (r1_tarski (k24_qc_lang1 A (k6_cqc_lang A B)) (k9_substut1 A (k6_cqc_lang A B)))) ) ) ) ) ).
tt(t44_subset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (~  ((r2_xboole_0 B C) &  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_hidden D C) & (r1_tarski B (k7_subset_1 A C (k1_tarski D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((k12_supinf_2 (k18_supinf_2 A) k6_numbers) = (k12_supinf_2 A k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( (C = (k12_supinf_2 (k18_supinf_2 A) B))  =>  ((k12_supinf_2 (k18_supinf_2 A) (k2_nat_1 B 1)) = (k3_supinf_2 C (k12_supinf_2 A (k2_nat_1 B 1)))) ) ) ) ) ) ) ) ) ).
tt(t44_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  => (m2_nat_lat (k12_tdlat_1 A) (k4_tdlat_1 A))) ) ).
tt(t44_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))))) ) ) ) ).
tt(t44_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  ((k4_tdlat_1 A) = (k12_tdlat_1 A)) ) ) ).
tt(t44_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_tex_2 B A) <=> (v1_zfmisc_1 B)) ) ) ) ) ).
tt(t44_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ((v4_tex_3 B A) & (v4_tex_3 C A))  => (v4_tex_3 (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ).
tt(t44_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tex_4 B A) =>  ((v3_pre_topc B A) | (v2_tops_1 B A)) ) ) ) ) ) ).
tt(t44_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ((v5_pre_topc C B A) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_tmap_1 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t44_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_borsuk_2 H A B C) =>  (! [I:$i] :  ((m1_borsuk_2 I A C D) =>  (! [J:$i] :  ((m1_borsuk_2 J A D E) =>  (! [K:$i] :  ((m1_borsuk_2 K A E F) =>  (! [L:$i] :  ((m1_borsuk_2 L A G D) => (r4_borsuk_2 A B F (k1_borsuk_2 A B E F (k1_borsuk_2 A B C E H (k1_borsuk_2 A C D E I J)) K) (k1_borsuk_2 A B G F (k1_borsuk_2 A B D G (k1_borsuk_2 A B C D H I) (k2_borsuk_2 A G D L)) (k1_borsuk_2 A G E F (k1_borsuk_2 A G D E L J) K)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_topalg_6 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_topalg_6 A)) =>  (! [D:$i] :  ( ((v7_topalg_6 D A) & (m2_subset_1 D (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [E:$i] :  ( ((v7_topalg_6 E A) & (m2_subset_1 E (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k6_topalg_6 A B) = D)  &  ( ((k6_topalg_6 A C) = E)  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 B) F) |  ( ((k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B F) (k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B F)))) = (k1_funct_1 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 F 1)) (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 F 1))))))  &  ((k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B F))) = (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) B (k1_nat_1 F 1))))) ) ) ) ) )  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 1 F) =>  ((r1_xxreal_0 (k3_finseq_1 C) F) |  ( ((k1_funct_1 (k7_partfun1 (k1_topalg_6 A) C F) (k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) C F)))) = (k1_funct_1 (k7_partfun1 (k1_topalg_6 A) C (k1_nat_1 F 1)) (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) C (k1_nat_1 F 1))))))  &  ((k1_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) C F))) = (k2_xxreal_2 (k9_xtuple_0 (k7_partfun1 (k1_topalg_6 A) C (k1_nat_1 F 1))))) ) ) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F (k3_finseq_1 B)) &  (! [G:$i] :  ( ((v7_topalg_6 G A) & (m2_subset_1 G (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [H:$i] :  ( ((v7_topalg_6 H A) & (m2_subset_1 H (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (~  ( (G = (k7_partfun1 (k1_topalg_6 A) B F))  &  ( (H = (k7_partfun1 (k1_topalg_6 A) C F))  &  ((r2_topalg_6 A G H) &  ((k9_xtuple_0 G) = (k9_xtuple_0 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) | (r2_topalg_6 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_topgen_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ((v7_pre_topc A) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k2_struct_0 A))  &  ((r1_xboole_0 B C) &  ((v5_topgen_1 B A) & (v6_topgen_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ((u1_pre_topc (k7_topgen_3 A B)) = (k2_xboole_0 (k1_tarski A) (k9_setfam_1 B))) ) ) ) ).
tt(t44_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v6_topgen_4 B A)) ) ) ) ) ).
tt(t44_topgen_5,ax,(v7_topgen_1 k2_topgen_3)).
tt(t44_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m3_topgrp_1 (k2_topgrp_1 A B) A)) ) ) ) ).
tt(t44_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_euclid 2))) =>  ( ((r2_hidden B (k9_metric_1 (k14_euclid 2) E D)) &  ((r2_hidden (k19_euclid (k17_euclid C) (k18_euclid B)) (k9_metric_1 (k14_euclid 2) E D)) &  ((k18_euclid A) = (k18_euclid B)) ) )  =>  ((r2_hidden A (k9_metric_1 (k14_euclid 2) E D)) |  ((r2_hidden (k19_euclid (k17_euclid C) (k18_euclid B)) (k1_rltopsp1 (k15_euclid 2) A B)) |  ( ((k17_euclid B) = (k17_euclid C))  |  ( ((k18_euclid B) = (k18_euclid C))  |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k19_euclid (k17_euclid C) (k18_euclid B))) (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k17_euclid C) (k18_euclid B)) C)) (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 C) = (k2_rcomp_1 (k9_real_1 (k18_euclid A) D) (k7_real_1 (k18_euclid A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t44_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k7_jgraph_6 A B C)) <=> (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid 2) D (k19_euclid A B))) C)) ) ) ) ) ) ) ) ) ).
tt(t44_toprealb,ax,(v3_tops_2 (k13_toprealb (k4_toprealb (k10_real_1 1 2))) (k1_pre_topc k2_topalg_2 (k5_toprealb (k2_rcomp_1 (k4_toprealb (k10_real_1 1 2)) (k3_real_1 (k4_toprealb (k10_real_1 1 2)) 1)))) (k11_toprealb (k3_funct_2 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k4_toprealb (k10_real_1 1 2)))))).
tt(t44_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  =>  ((v1_funct_1 (k59_valued_2 A (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k59_valued_2 A (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k59_valued_2 A (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t44_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((v3_toprns_1 B A) => (v2_toprns_1 B A)) ) ) ) ) ).
tt(t44_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_1 B A) & (r1_tarski B C))  => (v1_tops_1 C A)) ) ) ) ) ) ) ).
tt(t44_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => (r1_tarski (k2_pre_topc A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)) (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_pre_topc B D)))) ) ) ) ) ) ) ) ) ).
tt(t44_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (v1_tops_3 C A))  => (v1_tops_3 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t44_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_diraf A B C D E) &  ( (~ (r2_diraf A B D C E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r3_diraf A B D F) & (r3_diraf A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k6_trees_1 (k2_trees_1 (k2_nat_1 A 1))) = 1) ) ) ).
tt(t44_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  ((k1_funct_1 (k7_trees_2 A C B) C) = (k1_funct_1 B k1_xboole_0)) ) ) ) ) ) ) ).
tt(t44_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k2_trees_2 A k6_numbers) = (k1_tarski k1_xboole_0)) ) ) ).
tt(t44_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B D) &  ((r1_tarski C E) &  ((r1_xboole_0 D C) &  ((r1_xboole_0 E B) &  ((v3_pre_topc D A) & (v3_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  (! [D:$i] :  ((m1_pre_topc D A) =>  (! [E:$i] :  ((m1_pre_topc E B) =>  (! [F:$i] :  ((m1_pre_topc F B) =>  ( ( ((u1_struct_0 C) = (u1_struct_0 E))  &  ((u1_struct_0 D) = (u1_struct_0 F)) )  =>  ((r3_tsep_1 A C D) <=> (r3_tsep_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1))) =>  (! [D:$i] :  ((m1_subset_1 D (u2_turing_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_turing_1 B)) =>  ( (C = (k3_funct_2 (k2_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B)) (k3_zfmisc_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1)) (u3_turing_1 B) (k1_domain_1 (u2_turing_1 B) (u1_turing_1 B) D E)))  =>  ((k1_funct_1 (u3_turing_1 (k32_turing_1 A B)) (k1_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 B) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) D) E)) = (k4_domain_1 (k2_zfmisc_1 (u2_turing_1 A) (u2_turing_1 B)) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) (k1_domain_1 (u2_turing_1 A) (u2_turing_1 B) (u5_turing_1 A) (k1_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C)) (k2_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C) (k3_mcart_1 (u2_turing_1 B) (u1_turing_1 B) (k8_domain_1 k1_numbers (k1_real_1 1) k6_numbers 1) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k34_twoscomp A B) (k35_twoscomp A B)))) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( ( (D = (k1_funct_1 C A))  &  (E = (k1_funct_1 C B)) )  =>  ( ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) (k36_twoscomp A B)) = (k2_binarith (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) A) = D)  &  ((k1_funct_1 (k6_circuit2 (k34_twoscomp A B) (k35_twoscomp A B) C) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) &  ( (C = B)  &  ((k2_polynom4 k1_complfld (k4_uniroots A k1_complfld) C) = (k10_binop_2 (k2_newton B A) 1)) ) ) ) ) ) ) ) ).
tt(t44_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_xxreal_0 B (k1_algseq_1 A C)) =>  ((k2_nat_1 (k1_algseq_1 A (k5_uproots A C B)) B) = (k1_algseq_1 A C)) ) ) ) ) ) ) ) ).
tt(t44_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) =>  ( ((r2_valuat_1 A B E C) & (r2_valuat_1 A B E (k8_cqc_lang A C D)))  => (r2_valuat_1 A B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k26_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k26_valued_2 A B C)) = (k26_valued_2 A B C)) ) ) ) ) ) ).
tt(t44_vectsp11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_vectsp_6 F A B) =>  ( ((r1_tarski (k1_vectsp_6 A B F) (k4_subset_1 (u1_struct_0 B) D E)) &  ((k4_vectsp_6 A B F) = (k4_struct_0 B)) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 G B C) &  ((v1_mod_2 G A B C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ( ((v2_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) G E)) &  ( ((v1_vectsp_7 (k2_ranknull B C G E) A C) & (m1_subset_1 (k2_ranknull B C G E) (k1_zfmisc_1 (u1_struct_0 C))))  & (r1_tarski (k2_ranknull B C G D) (k6_domain_1 (u1_struct_0 C) (k4_struct_0 C)))) )  => (r1_tarski (k1_vectsp_6 A B F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) => (r2_hidden C (k3_vectsp_4 A B C D))) ) ) ) ) ) ) ) ).
tt(t44_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((m1_vectsp_5 (k1_vectsp_4 A B) A B (k2_vectsp_4 A B)) & (m1_vectsp_5 (k2_vectsp_4 A B) A B (k1_vectsp_4 A B))) ) ) ) ) ).
tt(t44_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((k4_vectsp_6 A B (k5_vectsp_6 A B C D)) = (k3_rlvect_1 B (k4_vectsp_6 A B C) (k4_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ).
tt(t44_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_vfunct_1 B C D A) => (r1_vfunct_1 B C (k4_vfunct_1 B C D E) A)) ) ) ) ) ) ) ) ) ) ).
tt(t44_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((r1_vfunct_2 A B C E) => (r1_vfunct_2 A B (k2_vfunct_2 A B C D) E)) ) ) ) ) ) ) ) ) ) ).
tt(t44_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  ( ((v1_lattice3 A) | (v2_lattice3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v12_waybel_0 B A) &  ((v1_waybel_0 B A) &  ((v12_waybel_0 C A) & (v1_waybel_0 C A)) ) )  => (v1_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t44_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_yellow_8 (a_2_3_waybel11 A B) A B) &  ((v1_tops_2 (a_2_3_waybel11 A B) A) & (m1_subset_1 (a_2_3_waybel11 A B) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ).
tt(t44_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((v4_yellow_8 A) & (v6_waybel_3 A))  => (v2_yellow_8 A)) ) ) ).
tt(t44_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (~  ((v2_waybel_8 (k2_yellow_1 (k5_waybel11 A))) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k5_waybel11 A))))) &  ( (B = (k1_yellow_0 (k2_yellow_1 (k5_waybel11 A)) C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_yellow_1 (k5_waybel11 A)))) =>  ((r2_hidden D C) => (v6_waybel_6 D (k2_yellow_1 (k5_waybel11 A)))) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~  (B = (a_1_0_waybel14 A)) ) ) ) ) ) ) ) ) ).
tt(t44_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  ( ((k2_relset_1 (u1_struct_0 A) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B (a_2_0_waybel_1 A B))) = (k2_relset_1 (u1_struct_0 A) B))  &  ((k2_relset_1 (u1_struct_0 A) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B (a_2_1_waybel_1 A B))) = (k2_relset_1 (u1_struct_0 A) B)) ) ) ) ) ) ) ).
tt(t44_waybel20,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v6_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v17_waybel_0 B A A) =>  ( ((v3_orders_2 (k1_yellow_2 A A B)) &  ((v4_orders_2 (k1_yellow_2 A A B)) &  ((v5_orders_2 (k1_yellow_2 A A B)) &  ((v1_lattice3 (k1_yellow_2 A A B)) &  ((v2_lattice3 (k1_yellow_2 A A B)) &  ((v3_waybel_3 (k1_yellow_2 A A B)) & (l1_orders_2 (k1_yellow_2 A A B))) ) ) ) ) )  & (v7_yellow_0 (k1_yellow_2 A A B) A)) ) ) ) ) ) ).
tt(t44_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_orders_2 B) &  ((v7_waybel_0 B) &  ((v11_waybel_0 B A) & (l1_waybel_0 B A)) ) ) )  =>  ((k10_yellow_6 A B) = (k6_domain_1 (u1_struct_0 A) (k1_waybel_9 A B))) ) ) ) ) ).
tt(t44_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_waybel_8 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v6_waybel23 (u1_struct_0 (k1_waybel_8 A)) A) & (m1_waybel23 (u1_struct_0 (k1_waybel_8 A)) A)) ) ) ).
tt(t44_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc B))))  =>  (! [D:$i] :  ( ((v3_pre_topc D (k2_borsuk_1 A B)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  (! [E:$i] :  ( ((v3_pre_topc E (k2_borsuk_1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  ((r1_tarski D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k1_waybel26 A C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k1_waybel26 A C))) =>  ( ( (F = (k6_waybel26 D (u1_struct_0 A)))  &  (G = (k6_waybel26 E (u1_struct_0 A))) )  => (r3_orders_2 (k1_waybel26 A C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel_8 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v2_waybel_8 B) & (l1_orders_2 B)) ) ) ) ) ) )  => (v2_waybel_8 (k2_waybel27 A B))) ) ) ) ).
tt(t44_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  ( (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k11_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k3_yellow_4 A B C))) ) ) ) )  => (v1_waybel_2 A)) ) ) ).
tt(t44_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k8_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k8_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k8_waybel34 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k8_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k8_waybel34 A) C))) &  ((v17_waybel_0 D (k4_yellow21 (k8_waybel34 A) B) (k4_yellow21 (k8_waybel34 A) C)) &  ((v22_waybel_0 D (k4_yellow21 (k8_waybel34 A) B) (k4_yellow21 (k8_waybel34 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k8_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k8_waybel34 A) C)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v2_waybel_2 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_setfam_1 (a_2_2_waybel_4 A B)) = (k1_waybel_3 A B)) ) ) ) ) ).
tt(t44_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v5_waybel_7 (k1_waybel_4 A) A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A (k12_lattice3 A C D) B) &  ( (~ (r3_orders_2 A C B))  &  (~ (r3_orders_2 A D B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_wellord1 A) & (r3_wellord1 A B C))  => (v2_wellord1 B)) ) ) ) ) ) ) ).
tt(t44_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k4_xboole_0 A B) C) => (r1_tarski A (k2_xboole_0 B C))) ) ) ) ).
tt(t44_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k9_xboolean A B)) = (k6_xboolean B A)) ) ) ) ) ).
tt(t44_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 A B) C) D) = (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A D) (k3_xcmplx_0 B D)) (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t44_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 B (k6_xcmplx_0 B A))) ) ) ) ) ) ).
tt(t44_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k14_xtuple_0 (k3_xboole_0 A B)) (k3_xboole_0 (k14_xtuple_0 A) (k14_xtuple_0 B)))) ) ).
tt(t44_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k3_xxreal_0 A k2_xxreal_0) = k2_xxreal_0) ) ) ).
tt(t44_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 D C) | (r1_tarski (k3_xxreal_1 B C) (k2_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t44_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( ((r1_tarski A B) & (v3_xxreal_2 B))  => (v3_xxreal_2 A)) ) ) ) ) ).
tt(t44_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) & (r1_xxreal_0 k6_numbers C)) )  =>  ((k1_xxreal_3 (k1_xxreal_3 A B) C) = (k1_xxreal_3 A (k1_xxreal_3 B C))) ) ) ) ) ) ) ) ).
tt(t44_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_orders_2 A (k3_yellow_0 A) B)) ) ) ) ).
tt(t44_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k13_yellow_3 A B (k1_waybel_3 A C) (k1_waybel_3 B D)) = (k1_waybel_3 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t44_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  => (r1_t_0topsp (k2_borsuk_1 A B) (k2_borsuk_1 B A))) ) ) ) ).
tt(t44_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_borsuk_1 C A B) =>  ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t44_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k3_yellow18 (k4_yellow18 A) B) (k3_yellow18 (k4_yellow18 A) C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k3_yellow18 (k4_yellow18 A) B) (k3_yellow18 (k4_yellow18 A) C))))) )  &  ((r2_hidden E (k1_binop_1 (u1_altcat_1 (k4_yellow18 A)) B C)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_altcat_1 A F B)) =>  ( (~  ((k1_altcat_1 A F B) = k1_xboole_0) )  =>  ((k1_funct_1 E (k4_tarski G (k4_tarski F B))) = (k4_tarski (k5_altcat_1 A F B C G D) (k4_tarski F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_yellow20,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) => (r1_tarski (k2_funct_4 A) (k2_funct_4 B))) ) ) ) ) ).
tt(t44_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ( (D = (a_3_0_yellow_2 A B C))  &  ((r1_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) (k7_domain_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) B C)) &  ((k10_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B C) = (k3_waybel_0 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((r2_yellow_0 A C) & (r2_yellow_0 B D))  =>  ((k2_yellow_0 (k3_yellow_3 A B) (k6_yellow_3 A B C D)) = (k7_yellow_3 A B (k2_yellow_0 A C) (k2_yellow_0 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t44_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) B (k4_yellow_4 A C D)) (k4_yellow_4 A (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) B D)))) ) ) ) ) ) ) ) ).
tt(t44_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  (C = (k13_lattice3 A B (k1_yellow_5 A C B))) ) ) ) ) ) ) ) ).
tt(t44_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m4_yellow_6 B A) =>  ( ((k12_yellow_6 (k13_yellow_6 A B)) = B)  <=> (v8_yellow_6 B A)) ) ) ) ) ).
tt(t44_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A)))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 (k7_lattice3 B)) C E) & (r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A)) D F))  =>  ((v3_waybel_1 (k1_waybel_1 A B C D) A B) <=> (v3_waybel_1 (k1_waybel_1 (k7_lattice3 B) (k7_lattice3 A) F E) (k7_lattice3 B) (k7_lattice3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t44_yellow_9,ax, (! [A:$i] :  ((l1_waybel_9 A) => (m1_yellow_9 A A)) ) ).
tt(t44_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r2_zf_lang A B) & (r1_zf_lang B A)) ) ) ) ) ) ).
tt(t44_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_zf_lang A) =>  (A = (k8_zf_lang (k23_zf_lang A) (k24_zf_lang A))) ) ) ) ).
tt(t44_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((k2_xboole_0 (k2_tarski A B) C) = k1_xboole_0) ) ) ) ) ).
tt(t44_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 C D)) ) )  => (m1_zmodul01 B C)) ) ) ) ) ) ) ).
tt(t45_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ( (D = (k2_relset_1 (u1_abcmiz_0 A) C))  => (r2_abcmiz_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t45_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ( ((k3_finseq_1 (k1_msualg_1 A B)) = 2)  =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  ( (E = (k1_funct_1 (k1_msualg_1 A B) 1))  &  ( (F = (k1_funct_1 (k1_msualg_1 A B) 2))  &  ((m1_abcmiz_1 C A E) & (m1_abcmiz_1 D A F)) ) ) ) ) ) )  => (m1_abcmiz_1 (k4_trees_4 (k4_tarski B (u1_struct_0 A)) (k4_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) C D)) A (k2_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t45_abcmiz_a,ax, (! [A:$i] :  ( ((v8_abcmiz_1 A k27_abcmiz_1) & (m1_abcmiz_1 A k27_abcmiz_1 (k13_abcmiz_1 k27_abcmiz_1)))  =>  ((k10_abcmiz_a k27_abcmiz_1 (k30_abcmiz_1 k27_abcmiz_1 (k32_abcmiz_1 k27_abcmiz_1) A)) = k10_abcmiz_1) ) ) ).
tt(t45_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A C D) &  ((r2_hidden B C) & (r2_hidden B D)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t45_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_aff_4 A B C D) & (r2_aff_4 A B C E)) ) )  =>  ( (B = C)  | (r2_aff_4 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)))  =>  ( ((k1_afinsq_1 A) = 4)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ((k1_funct_1 A 3) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) &  ((v3_funct_2 E (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_relset_1 k5_numbers B) (k1_relset_1 k5_numbers B))))) ) )  =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  (C = (k3_relat_1 E B)) ) )  =>  ( ( (~ (v1_setwiseo D A))  &  (~ (r1_xxreal_0 1 (k1_afinsq_1 B))) )  |  ((k6_afinsq_2 A B D) = (k6_afinsq_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v5_incproj (k13_afproj A)) =>  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) ) ) ) ).
tt(t45_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_struct_0 (k5_afvect0 A B)) = B) ) ) ) ) ).
tt(t45_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  => (m2_algspec1 A A)) ) ).
tt(t45_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((r1_tarski C B) & (r1_funct_2 A C A B D E))  => (r1_funct_2 (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 C)) (u1_struct_0 (k14_algstr_4 A)) (u1_struct_0 (k14_algstr_4 B)) (k18_algstr_4 A C D) (k18_algstr_4 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) => (v4_altcat_3 D A B C)) ) ) ) ) )  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (k1_altcat_4 A)) ) ) ) ).
tt(t45_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analmetr A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r7_analmetr A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  ( (~  (D = E) )  &  ( (~  (F = G) )  &  ( (B = (k4_analmetr A D E))  &  ( (C = (k4_analmetr A F G))  & (r4_analmetr A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) &  ((r2_analort A B C F G H I) &  ((r2_analort A B C J K H I) &  ( (~ (r2_analort A B C D E J K))  &  ( (~  (F = G) )  &  (~  (H = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v8_aofa_000 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k13_aofa_000 A (k12_aofa_000 A) B) = B)  &  ((k13_aofa_000 A B (k12_aofa_000 A)) = B) ) ) ) ) ) ).
tt(t45_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k60_aofa_i00 A B D E G F)) G) = (k5_int_1 (k21_aofa_i00 B k4_numbers C G) F))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = G) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k60_aofa_i00 A B D E G F)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  ( ((v1_armstrng C A) &  ((v2_finsub_1 C) & (r5_armstrng A B C)) )  => (r1_tarski (k2_armstrng C) (k2_xboole_0 B (k1_tarski A)))) ) ) ) ) ).
tt(t45_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (A = k1_xboole_0) )  &  (~  ( ((k8_arytm_3 C B) = (k8_arytm_3 D A))  <=>  ((k9_ordinal3 C A) = (k9_ordinal3 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 10 A) & (r1_xxreal_0 (k4_power 2 (k9_real_1 A 1)) (k5_square_1 (k4_nat_1 2 A)))) ) ) ) ).
tt(t45_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v12_bcialg_1 (k4_bcialg_1 A) A) & (m2_bcialg_1 (k4_bcialg_1 A) A)) ) ) ).
tt(t45_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (r1_tarski (k4_bcialg_2 A) (k5_bcialg_2 A))) ) ).
tt(t45_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) C) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t45_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v4_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_bcialg_4 A B B) = B) ) ) ) ) ) ).
tt(t45_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v16_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A k6_numbers 1 1 1)) ) ) ).
tt(t45_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((m2_bcialg_1 C A) => (m2_bcialg_1 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D C) B)) ) ) ) ) ) ) ) ) ).
tt(t45_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A B (k1_bcialg_1 A B C)) (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ).
tt(t45_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k6_bhsp_1 A B (k6_bhsp_1 A C D)) (k6_bhsp_1 A (k6_bhsp_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t45_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_bhsp_2 A C D)) => (r2_hidden (k5_algstr_0 A B C) (k4_bhsp_2 A (k4_struct_0 A) D))) ) ) ) ) ) ) ) ) ).
tt(t45_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k5_bhsp_4 C D (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k5_bhsp_4 C (k5_bhsp_4 C D B) A))) ) ) ) ) ) ) ) ).
tt(t45_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v3_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) )  =>  ((k10_bilinear A B C D) = (k10_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) ) ) ) ) ) ) ) ) ).
tt(t45_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A (k1_boolealg A B C) D) (k1_boolealg A B (k3_lattices A C D)))) ) ) ) ) ) ) ) ).
tt(t45_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  ( (A = (k2_rcomp_1 B C))  => (v3_pre_topc A k5_topmetr)) ) ) ) ) ) ) ).
tt(t45_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k2_rcomp_1 A k1_xxreal_0) = k1_numbers) ) ) ) ).
tt(t45_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E k5_topmetr k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) )  =>  ( ( ((k1_funct_1 E k6_numbers) = k6_numbers)  &  ( ((k1_funct_1 E 1) = 1)  & (r1_borsuk_6 A B C)) )  => (r3_borsuk_2 A B C (k2_borsuk_6 A B C D E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k12_euclid B) = (k12_euclid C))  &  ((k3_euclid_3 B) = (k7_real_1 (k3_euclid_3 C) (k8_real_1 (k8_real_1 2 k32_sin_cos) A))) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t45_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A F B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k8_xboolean A A) = (k3_xboolean A))  &  ((k3_xboolean (k8_xboolean A A)) = A) ) ) ) ).
tt(t45_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k2_bvfunc_1 A B D)) (k2_bvfunc_1 A C D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t45_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k11_bvfunc_1 A) (k11_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ).
tt(t45_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k2_bvfunc_1 A B (k2_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t45_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 C)) &  ((r4_calcul_1 A C) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B)))) )  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) C) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ).
tt(t45_card_1,ax, (! [A:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k2_card_1 A))) ) ).
tt(t45_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((k5_card_1 (k2_xboole_0 A B)) = (k6_xcmplx_0 (k2_nat_1 (k5_card_1 A) (k5_card_1 B)) (k5_card_1 (k3_xboole_0 A B)))) ) ) ) ) ).
tt(t45_card_3,ax, (! [A:$i] :  (~  ((v6_ordinal1 A) &  (! [B:$i] :  (~  ((r1_tarski B A) &  ( ((k3_tarski B) = (k3_tarski A))  &  (! [C:$i] :  (~  ((r1_tarski C B) &  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  (~  ((r2_hidden D C) &  (! [E:$i] :  ((r2_hidden E C) => (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finset_1 C)) )  =>  ( ((k9_xtuple_0 C) = B)  =>  ((k3_card_fin (k5_card_1 B) C) = (k1_card_1 (k2_card_fin C (k7_funcop_1 B A) A))) ) ) ) ) ) ) ).
tt(t45_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v9_cat_1 E A B C) & (v9_cat_1 F A C D))  => (v9_cat_1 (k5_cat_1 A B C D E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_binop_1 (k7_cat_1 (k8_cat_2 A B) B (k15_cat_2 A B)) C D) = D) ) ) ) ) ) ) ) ) ).
tt(t45_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m1_cat_3 E B C A) =>  ( ((k4_graph_1 B D) = C)  => (m1_cat_3 (k6_cat_3 B A E D) B (k3_graph_1 B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t45_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) => (r2_funct_2 k5_numbers k1_numbers (k4_catalan2 A (k26_valued_1 k5_numbers k1_numbers B C)) (k26_valued_1 k5_numbers k1_numbers (k4_catalan2 A B) C))) ) ) ) ) ) ).
tt(t45_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k4_struct_0 (k9_cc0sp2 A)) = (k1_cc0sp2 A k6_numbers)) ) ) ).
tt(t45_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfcont_1 C B) => (r2_cfcont_1 (k25_valued_1 k2_numbers k2_numbers C A) B)) ) ) ) ) ) ).
tt(t45_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k1_cfunct_1 A B (k1_cfunct_1 A C D)) (k1_cfunct_1 A (k19_valued_1 A k2_numbers k2_numbers B (k2_partfun1 A k2_numbers D (k1_relset_1 A (k2_cfunct_1 A D)))) C))) ) ) ) ) ) ) ) ).
tt(t45_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ( ((v5_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k7_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v9_cgames_1 B)) ) ) ) ) ) )  &  ( ( (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k7_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v9_cgames_1 B)) ) ) ) ) )  => (v5_cgames_1 A))  &  ( ((v6_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k6_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v10_cgames_1 B)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k6_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v10_cgames_1 B)) ) ) ) ) )  => (v6_cgames_1 A)) ) ) ) ) ) ).
tt(t45_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid C)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid C)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid C)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid C)) =>  (! [H:$i] :  ((m1_chain_1 H C) =>  ( ((r1_xxreal_0 A C) &  ((r1_xxreal_0 B C) &  ((r2_hidden (k3_chain_1 C D E) (k4_chain_1 C H A)) &  ((r2_hidden (k3_chain_1 C F G) (k4_chain_1 C H B)) & (r1_tarski (k3_chain_1 C D E) (k3_chain_1 C F G))) ) ) )  =>  (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 C)) =>  (~  ( (~  ( ((k1_seq_1 D I) = (k1_seq_1 F I))  &  ((k1_seq_1 E I) = (k1_seq_1 G I)) ) )  &  ( (~  ( ((k1_seq_1 D I) = (k1_seq_1 F I))  &  ((k1_seq_1 E I) = (k1_seq_1 F I)) ) )  &  ( (~  ( ((k1_seq_1 D I) = (k1_seq_1 G I))  &  ((k1_seq_1 E I) = (k1_seq_1 G I)) ) )  &  (~  ((r1_xxreal_0 (k1_seq_1 D I) (k1_seq_1 E I)) &  ( (~ (r1_xxreal_0 (k1_seq_1 F I) (k1_seq_1 G I)))  &  ((r1_xxreal_0 (k1_seq_1 G I) (k1_seq_1 D I)) & (r1_xxreal_0 (k1_seq_1 E I) (k1_seq_1 F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k6_glib_000 C)) =>  ( ( (D = F)  &  (E = G) )  =>  ((r1_chord A D E) <=> (r1_chord C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ( ((r2_hidden A (u1_struct_0 F)) & (r2_hidden C (u1_struct_0 F)))  =>  ((r2_hidden B (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k1_tarski B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v1_circcomb A) => (r1_tarski (u4_struct_0 A) (u1_struct_0 A))) ) ) ).
tt(t45_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F A) &  ((v4_msafree2 F A) & (l3_msualg_1 F A)) )  =>  ((r4_circtrm1 B A C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B E))) =>  ( ( (H = (k3_relat_1 C G))  &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ((r2_hidden I (k2_msafree2 B)) => (r1_facirc_1 A F G (k1_funct_1 C I))) ) ) )  =>  ((k6_circuit2 B E H) = (k3_relat_1 C (k6_circuit2 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_classes1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden A (k4_classes1 C)) & (r2_hidden B (k4_classes1 C)))  <=> (r2_hidden (k4_tarski A B) (k4_classes1 (k1_ordinal1 (k1_ordinal1 C))))) ) ) ) ) ).
tt(t45_classes2,ax, (! [A:$i] :  ((v1_ordinal1 A) =>  ((k4_classes1 (k1_card_1 (k1_classes1 A))) = (k1_classes1 A)) ) ) ).
tt(t45_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_clvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_clvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) ) )  =>  ( ((m1_clvect_1 A B) & (m1_clvect_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t45_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_clvect_2 A C D)) => (r2_hidden (k5_algstr_0 A B C) (k4_clvect_2 A (k4_struct_0 A) D))) ) ) ) ) ) ) ) ) ).
tt(t45_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k6_clvect_3 A B (k19_valued_1 k5_numbers k2_numbers k2_numbers C D)) = (k6_clvect_3 A (k6_clvect_3 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t45_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  (~  ( (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) &  ((v9_cohsp_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k2_xboole_0 D E) = (k8_cohsp_1 A B F)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v9_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k3_tarski C) = (k8_cohsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  (! [C:$i] :  ((m1_subset_1 C (k20_coh_sp A)) =>  (! [D:$i] :  ((m1_subset_1 D (k20_coh_sp A)) =>  ( ( ((k21_coh_sp A B) = (k22_coh_sp A C))  &  ((k21_coh_sp A D) = (k22_coh_sp A B)) )  =>  ((k24_coh_sp A (k24_coh_sp A C B) D) = (k24_coh_sp A C (k24_coh_sp A B D))) ) ) ) ) ) ) ) ) ).
tt(t45_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k17_complex1 A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t45_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 (k10_complex1 A) (k10_complex1 B)) = (k1_complex2 A B)) ) ) ) ) ).
tt(t45_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k5_algstr_0 k1_complfld (k3_vectsp_1 k1_complfld B A) (k3_vectsp_1 k1_complfld C A)) = (k3_vectsp_1 k1_complfld (k5_algstr_0 k1_complfld B C) A)) ) ) ) ) ) ) ) ).
tt(t45_complsp2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers) k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers) k1_numbers)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k2_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k1_numbers) =>  ( ( (C = E)  &  ( (D = F)  &  ( ((k3_finseq_1 C) = (k3_finseq_1 F))  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k4_finseq_1 C)) =>  ((k5_binop_1 k2_numbers A (k9_matrix_5 C G) (k9_matrix_5 D G)) = (k5_binop_1 k1_numbers B (k1_seq_1 E G) (k1_seq_1 F G))) ) ) ) ) ) )  =>  ((k1_finseqop k2_numbers k2_numbers k2_numbers A C D) = (k1_finseqop k1_numbers k1_numbers k1_numbers B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ((k6_compos_1 A B k6_numbers) = B) ) ) ) ) ).
tt(t45_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  ((k1_funct_1 (k3_compos_2 A B C) 1) = (k5_compos_0 (u1_compos_1 A) C 1)) ) ) ) ) ) ) ).
tt(t45_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~ (r1_xxreal_0 (k4_complex1 A) k6_numbers))  & (r1_xxreal_0 (k18_sin_cos (k1_comptrig A)) k6_numbers)) ) ) ) ).
tt(t45_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_margrel1 B A) & (m2_rfunct_3 B (k3_finseq_2 A) A (k2_comput_1 A))) )  =>  (! [C:$i] :  ( ((v3_comput_1 C) & (m2_finseq_1 C (k2_comput_1 A)))  =>  ( ( ((k19_margrel1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 A) A (k2_comput_1 A)) =>  ((r2_hidden D (k10_xtuple_0 C)) =>  ((v3_margrel1 D A) &  (~ (v1_xboole_0 D)) ) ) ) ) )  =>  ((v1_xboole_0 C) |  ( ( (~ (v1_xboole_0 (k3_relat_1 (k6_funct_6 C) B)))  &  ((v3_margrel1 (k3_relat_1 (k6_funct_6 C) B) A) & (m2_rfunct_3 (k3_relat_1 (k6_funct_6 C) B) (k3_finseq_2 A) A (k2_comput_1 A))) )  &  ((k9_xtuple_0 (k3_relat_1 (k6_funct_6 C) B)) = (k4_finseq_2 (k1_comput_1 C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t45_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k2_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B) (k51_valued_1 k5_numbers k2_numbers k2_numbers C D)) (k51_valued_1 k5_numbers k2_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A D) (k19_valued_1 k5_numbers k2_numbers k2_numbers B C)))) ) ) ) ) ) ) ) ).
tt(t45_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v1_comseq_2 B) &  ((k3_comseq_2 A) = k5_complex1) ) )  =>  ((k3_comseq_2 (k2_comseq_2 k5_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B))) = k5_complex1) ) ) ) ) ) ).
tt(t45_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 B (k17_complex1 (k8_nat_1 k2_numbers A D)))) ) ) ) )  &  ((v2_comseq_2 (k55_valued_1 k5_numbers k2_numbers A)) &  ((k2_seq_2 (k55_valued_1 k5_numbers k2_numbers A)) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t45_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A))))) =>  ( (B = C)  =>  ((v3_connsp_1 B A) <=> (v3_connsp_1 C (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ) ) ) ) ) ).
tt(t45_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((v2_convex4 B A) => (v2_convex4 (k19_convex4 A B C) A)) ) ) ) ) ) ) ).
tt(t45_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k13_cqc_sim1 A B) = (k13_cqc_sim1 A (k14_cqc_sim1 A B))) ) ) ) ) ).
tt(t45_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B C) (k7_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t45_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B))) (k11_cqc_lang A C B)) A) & (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C B) (k11_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B)))) A)) ) ) ) ) ) ) ).
tt(t45_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v6_qc_lang1 B A) & (r1_cqc_the3 A (k6_cqc_lang A B) (k6_cqc_lang A C)))  => (r1_cqc_the3 A C B)) ) ) ) ) ) ) ).
tt(t45_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k17_complex1 (k12_csspace A B C)) (k8_real_1 (k13_csspace A B) (k13_csspace A C)))) ) ) ) ) ) ).
tt(t45_dickson,ax,(r7_relat_2 k10_dickson k5_numbers)).
tt(t45_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 k19_sin_cos A B) = (k1_real_1 (k10_real_1 (k8_real_1 (k8_real_1 2 (k18_sin_cos (k10_real_1 (k7_real_1 A B) 2))) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))) (k9_real_1 A B)))) ) ) ) ) ).
tt(t45_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k5_square_1 D)) ) )  =>  ((k1_seq_1 (k3_diff_1 C A) B) = (k7_real_1 (k8_real_1 (k8_real_1 2 B) A) (k5_square_1 A))) ) ) ) ) ) ) ) ).
tt(t45_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k4_diff_1 (k4_diff_1 C A) A) B) = (k9_real_1 (k8_real_1 2 (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B)) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C (k8_real_1 2 A)) B))) ) ) ) ) ) ) ).
tt(t45_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k5_card_1 B) = (k2_dilworth A))  & (r1_tarski B C))  =>  ((k2_dilworth (k5_yellow_0 A C)) = (k2_dilworth A)) ) ) ) ) ) ) ) ).
tt(t45_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) &  ((v3_analoaf A) & (l1_analoaf A)) ) )  =>  ( (~ (v7_struct_0 (k2_diraf A)))  &  ((v1_diraf (k2_diraf A)) &  ((v2_diraf (k2_diraf A)) & (l1_analoaf (k2_diraf A))) ) ) ) ) ).
tt(t45_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  ( ((r2_hidden D (k6_ec_pf_1 A B C)) &  ( ((k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = (k8_group_1 (k9_int_3 A) F (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D)))  &  ( ((k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = (k8_group_1 (k9_int_3 A) F (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D)))  &  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = (k8_group_1 (k9_int_3 A) F (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D))) ) ) )  =>  ((r1_xxreal_0 A 3) |  ( ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A)))  |  ( (F = (k4_struct_0 (k9_int_3 A)))  | (r2_hidden E (k6_ec_pf_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  =>  ( ( ((k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D))  &  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) )  <=>  ( (C = D)  |  (C = (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A D))  =>  ((k17_ens_1 A B (k1_cat_1 A D C)) = (k1_partfun1 (k2_cat_1 A B (k3_graph_1 A D)) (k2_cat_1 A B (k4_graph_1 A D)) (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C)) (k17_ens_1 A B D) (k17_ens_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t45_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  => (v1_matrprob (k2_entropy1 k1_numbers (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B))))) ) ) ) ).
tt(t45_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k5_enumset1 A A A A B C D) = (k2_enumset1 A B C D)) ) ) ) ) ).
tt(t45_eqrel_1,ax,(m1_eqrel_1 k1_xboole_0 k1_xboole_0)).
tt(t45_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k5_square_1 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C))) = (k9_binop_2 (k9_binop_2 (k5_square_1 (k12_euclid B)) (k11_binop_2 2 (k23_rvsum_1 C B))) (k5_square_1 (k12_euclid C)))) ) ) ) ) ) ) ).
tt(t45_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  (~  ( ((k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) A B) (k5_algstr_0 (k15_euclid 2) C B)) = k6_numbers)  <=>  ( ((k4_euclid_3 A B C) = (k10_real_1 k32_sin_cos 2))  |  ((k4_euclid_3 A B C) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((v2_euclid_4 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k7_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 4 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  ( (B = (k8_euclid_7 A))  => (m1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A)))) ) ) ) ) ).
tt(t45_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k7_euclid 3 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k9_binop_2 A D)) (k9_euclid 3 k3_euclid_8 (k9_binop_2 B E))) (k9_euclid 3 k4_euclid_8 (k9_binop_2 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k3_rlvect_1 (k15_euclid A) B (k5_algstr_0 (k15_euclid A) C D)) = (k5_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t45_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ((r4_euclidlp A B C) => (r3_euclidlp A B C)) ) ) ) ) ) ) ).
tt(t45_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_orders_2 A C B) <=>  (~ (r3_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t45_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden B (u1_struct_0 (k4_circcomb A C B))) &  (! [D:$i] :  ((r2_hidden D (k10_xtuple_0 C)) => (r2_hidden D (u1_struct_0 (k4_circcomb A C B)))) ) ) ) ) ) ) ).
tt(t45_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = (k18_complex1 C)) ) ) )  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ).
tt(t45_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k16_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k2_fdiff_9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t45_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k30_sin_cos)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k1_real_1 (k10_real_1 (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t45_fdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_subset_1 k1_numbers) (k1_relset_1 k1_numbers A)) & (r2_fdiff_1 A (k2_subset_1 k1_numbers)))  =>  ( ( (? [B:$i] :  ((m1_subset_1 B k1_numbers) & (r1_xxreal_0 (k1_fdiff_1 A B) k6_numbers)) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 A B))) ) )  |  ((v2_funct_1 A) &  ((r2_fdiff_1 (k2_partfun2 k1_numbers k1_numbers A) (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers A))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers A))) =>  ((k1_fdiff_1 (k2_partfun2 k1_numbers k1_numbers A) B) = (k10_real_1 1 (k1_fdiff_1 A (k1_seq_1 (k2_partfun2 k1_numbers k1_numbers A) B)))) ) ) ) ) ) ) ) ) ) ).
tt(t45_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos) A) B) = (k7_real_1 (k1_seq_1 k16_sin_cos B) (k8_real_1 B (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t45_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k10_real_1 E 2))  &  ((k1_seq_1 D E) = (k8_real_1 (k8_real_1 2 A) E)) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k16_sin_cos) (k10_real_1 1 (k8_real_1 4 A)))) B) E) = (k5_square_1 (k21_sin_cos (k8_real_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos B) (k9_real_1 (k1_seq_1 k19_sin_cos B) (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t45_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9))) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9) A) B) = (k9_real_1 (k1_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))) (k1_seq_1 k16_sin_cos B))) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos B) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t45_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k1_pre_ff B) (k1_pre_ff A))) ) ) ) ) ).
tt(t45_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_fib_num3 A A B) = (k3_xcmplx_0 (k7_xcmplx_0 (k3_fib_num3 A A k6_numbers) 2) (k2_nat_1 (k1_pre_ff B) (k1_fib_num3 B)))) ) ) ) ) ).
tt(t45_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~  (B = (k1_filter_0 A)) )  & (v2_filter_0 B A))  <=> (v1_filter_0 B A)) ) ) ) ) ).
tt(t45_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v15_lattices B) &  ((v16_lattices B) & (l3_lattices B)) ) ) ) )  <=>  ( (~ (v2_struct_0 (k7_filter_1 A B)))  &  ((v10_lattices (k7_filter_1 A B)) &  ((v15_lattices (k7_filter_1 A B)) &  ((v16_lattices (k7_filter_1 A B)) & (l3_lattices (k7_filter_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t45_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_hidden B D) & (r2_hidden C E))  =>  ((r2_hidden (k3_lattices A B C) (k8_filter_2 A D E)) & (r2_hidden (k3_lattices A C B) (k8_filter_2 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( (D = (k11_finseq_1 A B C))  <=>  ( ((k3_finseq_1 D) = 3)  &  ( ((k1_funct_1 D 1) = A)  &  ( ((k1_funct_1 D 2) = B)  &  ((k1_funct_1 D 3) = C) ) ) ) ) ) ) ) ) ) ).
tt(t45_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 A) (k2_finseq_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 B))))) )  =>  ((r1_xxreal_0 B (k3_finseq_1 D)) =>  ( ( (B = k6_numbers)  &  (~  (A = k6_numbers) ) )  | (m2_finseq_1 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 B) k5_numbers C E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  &  (~  ((k14_finseq_1 (k2_tarski A B)) = (k10_finseq_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t45_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((r2_hidden B (k10_xtuple_0 A)) &  (~ (r2_hidden B (k10_xtuple_0 (k6_finseq_4 A B)))) ) ) ) ) ) ).
tt(t45_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k7_partfun1 A (k1_finseq_5 A C B) (k4_finseq_4 C B)) = B) ) ) ) ) ) ) ) ).
tt(t45_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k2_rfinseq A 1 (k8_finseq_1 A (k12_finseq_1 A B) C)) = C) ) ) ) ) ) ) ).
tt(t45_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ((v1_setwiseo D B) => (r2_funct_2 A B (k9_funcop_1 B A D C (k4_binop_1 B D)) C)) ) ) ) ) ) ) ) ) ).
tt(t45_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_fintopo2 (k3_subset_1 (u1_struct_0 A) B) A) => (v3_fintopo2 B A)) ) ) ) ) ).
tt(t45_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k9_fintopo3 A B C) = (k3_subset_1 (u1_struct_0 A) (k7_fintopo3 A (k3_subset_1 (u1_struct_0 A) B) C))) ) ) ) ) ) ) ).
tt(t45_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v2_fintopo6 B A) &  ((v2_fintopo6 C A) & (r2_hidden (k1_funct_1 C 1) (k1_fin_topo A (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B))))) )  => (v2_fintopo6 (k8_finseq_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t45_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_catalan2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_catalan2 A)) =>  ( ((r2_hidden C (k8_flang_1 A B)) & (r2_hidden D (k8_flang_1 A B)))  => (r2_hidden (k1_flang_1 A C D) (k8_flang_1 A B))) ) ) ) ) ) ) ) ).
tt(t45_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B k6_numbers k6_numbers) = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ).
tt(t45_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k4_subset_1 (k8_afinsq_1 A) (k1_flang_3 A B D) (k1_flang_3 A C D)) (k1_flang_3 A (k4_subset_1 (k8_afinsq_1 A) B C) D))) ) ) ) ) ) ) ).
tt(t45_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k21_fomodel0 (k1_tarski A)) = (k10_xtuple_0 A)) ) ) ).
tt(t45_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (~ (v7_pre_topc A))  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((r2_funct_2 k5_numbers (u1_struct_0 A) D (k8_funcop_1 (u1_struct_0 A) k5_numbers B)) &  ( (~  (B = C) )  & (r1_frechet A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (~  ( (C = (k11_fsm_1 A B D))  &  ( (~  (E = F) )  & (r5_fsm_1 A B C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C B) =>  ((v1_funct_1 (k2_funcop_1 A C)) &  ((v1_funct_2 (k2_funcop_1 A C) A B) & (m1_subset_1 (k2_funcop_1 A C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ).
tt(t45_funct_1,ax, (! [A:$i] :  ((k2_funct_1 (k4_relat_1 A)) = (k4_relat_1 A)) ) ).
tt(t45_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 A)))) )  =>  ((k7_relset_1 k1_xboole_0 A C B) = k1_xboole_0) ) ) ) ) ).
tt(t45_funct_3,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k8_funct_3 A B)) B)) ) ).
tt(t45_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) => (r1_tarski (k9_xtuple_0 (k2_funct_4 C)) (k2_zfmisc_1 B A))) ) ) ) ) ).
tt(t45_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  &  ( ((k9_xtuple_0 D) = (k2_zfmisc_1 A B))  &  ((k3_funct_5 C) = (k3_funct_5 D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t45_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((k9_xtuple_0 B) = A)  => (r2_wellord2 (k4_card_3 B) (k4_card_3 (k3_relat_1 C B)))) ) ) ) ) ) ).
tt(t45_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k4_funct_7 A (k9_finseq_1 B)) = (k3_relat_1 (k6_partfun1 A) B)) ) ) ) ).
tt(t45_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v6_funct_8 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t45_functor0,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ((l1_functor0 C A B) =>  ( ((v11_functor0 C A B) & (v5_functor0 C A B))  => (v7_functor0 C A B)) ) ) ) ) ) ) ).
tt(t45_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A (k6_fuzzy_1 A B C) (k1_fuzzy_1 A B C)) (k2_fuzzy_1 A B C))) ) ) ) ) ) ).
tt(t45_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_2 A B (k2_fuzzy_1 A C D)) (k2_fuzzy_1 A (k3_fuzzy_2 A B C) (k3_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t45_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ( ((v3_fvaluat1 A) &  ((k3_funct_2 (u1_struct_0 A) k7_numbers C B) = 1) )  => (r2_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A C) C)) ) ) ) ) ) ) ).
tt(t45_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k8_fvsum_1 A B C (k8_fvsum_1 A B D E)) = (k4_fvsum_1 A B (k8_fvsum_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r8_gcd_1 A B C D) & (r8_gcd_1 A B E F))  =>  ((k8_group_1 A (k6_gcd_1 A B C D E F) (k8_group_1 A D F)) = (k8_group_1 A (k7_gcd_1 A B C D E F) (k3_rlvect_1 A (k8_group_1 A C F) (k8_group_1 A E D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_genealg1 B A) =>  (! [C:$i] :  ((m1_genealg1 C A) =>  ((k11_genealg1 A B C k6_numbers k6_numbers k6_numbers k6_numbers k6_numbers) = C) ) ) ) ) ) ) ).
tt(t45_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_geomtrap A B C))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_geomtrap A B C))) =>  ( ((r1_analmetr A B C) &  ( (D = F)  &  (E = G) ) )  =>  ((k1_geomtrap A D E) = (k9_geomtrap (k7_geomtrap A B C) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (~  ((k2_msafree2 (k19_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t45_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  ( ((k10_glib_000 B) = (k5_relset_1 (k7_glib_000 A) (k6_glib_000 A) (k10_glib_000 A) (k25_glib_000 A B)))  &  ((k11_glib_000 B) = (k5_relset_1 (k7_glib_000 A) (k6_glib_000 A) (k11_glib_000 A) (k25_glib_000 A B))) ) ) ) ) ) ).
tt(t45_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ((k3_finseq_1 (k8_glib_001 A B 1 C)) = C) ) ) ) ) ) ) ) ).
tt(t45_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v3_glib_002 A)) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) &  (? [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) &  ( (~  (B = C) )  &  ((v11_glib_000 B A) & (v11_glib_000 C A)) ) ) ) ) ) ) ) ).
tt(t45_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) =>  ((k11_glib_003 (k12_glib_003 A B C)) = (k2_xboole_0 (k11_glib_003 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t45_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B (k3_finseq_1 B) A)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ).
tt(t45_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 2) B)) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 (k2_goboard2 D)) (k2_nat_1 A 1)) |  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 2) B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  (! [D:$i] :  ((m2_finseq_1 D C) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 C)))  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 2) B) & (r3_gobrd13 C (k17_finseq_1 C B D) E A)) )  => (r3_gobrd13 C D E A)) ) ) ) ) ) ) ) ) ) ).
tt(t45_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ( ((v3_graph_2 C B) & (m2_graph_1 C B))  =>  ((v3_graph_2 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B) & (m2_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B)) ) ) ) ) ) ) ).
tt(t45_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v2_funct_1 D) & (m2_graph_1 D (k8_graph_3 A B C)))  =>  ( (~ (r2_hidden (u4_struct_0 A) (k10_xtuple_0 D)))  =>  ((v2_funct_1 D) & (m2_graph_1 D A)) ) ) ) ) ) ) ) ) ) ).
tt(t45_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r1_tarski (k5_graph_5 B C D A) (k7_graph_5 B))) ) ) ) ) ) ) ).
tt(t45_graphsp,ax, (! [A:$i] :  ((m2_funct_2 A (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers) (k9_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers))) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 (k8_graphsp A B C) D))  &  ((k7_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) A) D) B) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r4_polyred A B C D F E) => (r4_polyred A B C (k5_vfunct_1 (k15_pre_poly A) C D) F (k5_vfunct_1 (k15_pre_poly A) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( (C = (k10_group_2 A D E))  => (r1_tarski (k9_subset_1 (u1_struct_0 A) (k1_group_11 A B D) (k1_group_11 A B E)) (k1_group_11 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) & (l1_struct_0 A)) )  => (r1_xxreal_0 1 (k7_group_1 A))) ) ).
tt(t45_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k1_group_1 B) = (k1_group_1 C)) ) ) ) ) ) ) ).
tt(t45_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_group_3 A (k4_group_3 A C B) D) = (k3_group_3 A C (k4_group_2 A B D))) ) ) ) ) ) ) ) ) ).
tt(t45_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k11_group_2 A D (k13_group_2 A C B)) = (k4_group_2 A B (k7_group_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t45_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_5 A B (k6_algstr_0 A C D)) = (k6_algstr_0 A (k6_algstr_0 A (k2_group_5 A B D) (k2_group_5 A B C)) (k3_group_5 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t45_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((r1_struct_0 (k10_group_6 B A D) C) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (C = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D (k1_group_1 B)) = (k1_group_1 C)) ) ) ) ) ) ) ) ).
tt(t45_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((k3_helly A B C D) = (k3_helly A D C B)) ) ) ) ) ) ) ) ) ).
tt(t45_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear D k1_complfld A A) &  ((v4_bilinear D k1_complfld A A) &  ((v3_hermitan D A) &  ((v5_hermitan D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  => (r1_xxreal_0 (k5_square_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) D B C))) (k3_xcmplx_0 (k4_hermitan A D B) (k4_hermitan A D C)))) ) ) ) ) ) ) ) ).
tt(t45_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((r1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k6_partfun1 k1_numbers)) A) &  ((k1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k6_partfun1 k1_numbers)) A) = (k1_real_1 (k10_real_1 1 (k5_square_1 A)))) ) ) ) ) ).
tt(t45_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k4_hilbert1 A C) (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(t45_hilbert3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~  (A = B) )  & (v2_hilbert3 (k3_hilbert1 (k3_hilbert1 (k3_hilbert1 (k1_hilbert2 A) (k1_hilbert2 B)) (k1_hilbert2 A)) (k1_hilbert2 A)))) ) ) ) ) ) ).
tt(t45_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k7_hurwitz (k5_vfunct_1 k5_numbers k1_complfld A)) (k5_vfunct_1 k5_numbers k1_complfld (k7_hurwitz A)))) ) ).
tt(t45_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  ( ( (E = (k1_funct_1 (k4_funct_7 k14_idea_1 (k17_idea_1 D B A C)) F))  &  ((r1_xxreal_0 4 (k3_finseq_1 F)) &  ((r1_idea_1 A (k1_recdef_1 F 1)) &  ((r1_idea_1 A (k1_recdef_1 F 2)) &  ((r1_idea_1 A (k1_recdef_1 F 3)) & (r1_idea_1 A (k1_recdef_1 F 4))) ) ) ) )  =>  ((r1_xxreal_0 4 (k3_finseq_1 E)) &  ((r1_idea_1 A (k1_recdef_1 E 1)) &  ((r1_idea_1 A (k1_recdef_1 E 2)) &  ((r1_idea_1 A (k1_recdef_1 E 3)) & (r1_idea_1 A (k1_recdef_1 E 4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k8_ideal_1 A B) = B) ) ) ) ) ).
tt(t45_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (~  ( (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B C D) A))  &  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k4_int_1 A) = k6_numbers)  <=> (v1_int_1 A)) ) ) ).
tt(t45_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ( (~  (C = k6_numbers) )  &  ( (~  ((r1_int_1 (k3_int_2 A B) (k6_xcmplx_0 D E)) &  ((r1_int_1 (k3_int_2 A C) (k6_xcmplx_0 D F)) & (r1_int_1 (k3_int_2 B C) (k6_xcmplx_0 E F))) ) )  &  (? [G:$i] :  ((v1_int_1 G) &  ( ((k6_int_1 (k6_xcmplx_0 G D) A) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 G E) B) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 G F) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k4_nat_d A 2) = (k4_nat_d B 2))  =>  ((k1_newton (k4_xcmplx_0 1) A) = (k1_newton (k4_xcmplx_0 1) B)) ) ) ) ) ) ).
tt(t45_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k10_real_1 1 (k7_real_1 1 (k5_square_1 D)))) ) ) )  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 k1_sin_cos9 (k4_seq_4 A)) (k1_seq_1 k1_sin_cos9 (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t45_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r1_tarski D (k2_rcomp_1 (k19_binop_2 1) 1)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( ((k1_seq_1 B E) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 k4_sin_cos6 E) k6_numbers)) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 k3_taylor_1))) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)) (k4_taylor_1 (k18_binop_2 1 2))) k4_sin_cos6)))) ) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 k3_taylor_1)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 k3_taylor_1)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t45_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers k2_sin_cos9 (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)))) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2))) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k10_real_1 1 2))) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t45_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))) (k1_seq_1 k19_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos D) (k1_seq_1 k16_sin_cos D)) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k1_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t45_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ( (D = E)  &  ((r1_xxreal_0 B C) &  ((v3_integr15 (k2_partfun1 k1_numbers (k1_euclid A) D (k3_integra5 B C)) A) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers D)) & (r1_integr15 A (k3_integra5 B C) D)) ) ) )  =>  ((k12_integr15 B C A D) = (k6_integr18 (k4_real_ns1 A) E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((r1_integra1 B C) & (v1_seq_2 (k2_partfun1 A k1_numbers D A)))  => (r1_xxreal_0 (k6_integra1 A D C) (k6_integra1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t45_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (A = (k1_rcomp_1 (k7_real_1 B (k8_real_1 (k4_nat_1 2 C) k32_sin_cos)) (k7_real_1 B (k8_real_1 (k2_nat_1 (k4_nat_1 2 C) 1) k32_sin_cos))))  =>  ((k2_integra5 A k19_sin_cos) = (k1_real_1 (k8_real_1 2 (k18_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t45_integra9,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  ( ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C) &  ((v1_partfun1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C) C)) &  ((v1_comseq_2 (k2_partfun1 C k1_numbers (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) C)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A A)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((r1_integra5 C (k20_valued_1 k1_numbers k1_numbers k1_numbers B B)) &  ((r1_integra9 C A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A A) C) D))) ) )  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers B B) C) D))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k5_square_1 (k2_integra9 C (k3_valued_1 k1_numbers k1_numbers k1_numbers A B))) = (k7_real_1 (k5_square_1 (k2_integra9 C A)) (k5_square_1 (k2_integra9 C B)))) ) ) ) ) ) ) ) ).
tt(t45_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ((k10_interva1 A B) = (k2_interva1 A (k3_subset_1 A (k6_interva1 A B)) (k3_subset_1 A (k5_interva1 A B)))) ) ) ) ) ).
tt(t45_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k3_intpro_1 A B) (k4_intpro_1 A C)) (k4_intpro_1 B C)) k8_intpro_1)) ) ) ) ) ) ).
tt(t45_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r1_isocat_1 A B) => (r2_isocat_1 A B)) ) ) ) ) ).
tt(t45_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)) C E) & (v5_pre_topc C A B))  => (v5_pre_topc E A (k1_pre_topc B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jgraph_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (~  ( (G = k6_numbers)  &  ( (H = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G)) = C)  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H)) = D)  &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G)) F) &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H)) F) &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G)) = E)  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H)) = F)  &  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G)) D) &  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H)) D) &  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 F E))  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) C))  &  ( (~ (r1_xxreal_0 D (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I))))  &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) E))  &  (~ (r1_xxreal_0 F (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)))) ) ) ) ) ) )  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  (~  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) C))  &  ( (~ (r1_xxreal_0 D (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I))))  &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) E))  &  (~ (r1_xxreal_0 F (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)))) ) ) ) ) ) )  & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ( (~ (r1_xxreal_0 A (k13_complex1 (k18_euclid C) (k12_euclid C))))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  & (r1_jordan6 C A B))  =>  ( (A = B)  |  ((r1_xxreal_0 k6_numbers (k17_euclid A)) |  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  ( (~ (r1_xxreal_0 (k17_euclid A) (k17_euclid B)))  &  (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k16_pscomp_1 (k1_sppol_2 A B C D)) = (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k17_euclid C) = F)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid C)) & (r1_xxreal_0 (k17_euclid D) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) |  ((r1_xxreal_0 (k18_euclid B) (k18_euclid C)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 D B)))) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) (k1_jordan1a (k1_jordan8 D B)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) (k1_jordan1a (k1_jordan8 D B)) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) (k1_jordan1a (k1_jordan8 D B)) C)))) ) ) ) ) ) ) ) ) ).
tt(t45_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = (a_4_8_jordan1 A B C D))  &  (F = (a_4_6_jordan1 A B C D)) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 D B) |  ((k2_pre_topc (k15_euclid 2) F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  & (r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C (k1_matrix_1 (k1_jordan8 B A))) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ) ) ) ) ).
tt(t45_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((v2_connsp_1 B (k15_euclid 2)) => (r2_hidden (k20_pscomp_1 B) (k4_goboard5 (k1_jordan9 B A) 1))) ) ) ) ) ).
tt(t45_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal1 2 A)) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k3_jordan3 A B) (k3_finseq_1 (k3_jordan3 A B))) = B) ) ) ) ) ) ).
tt(t45_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden C B) =>  ((k5_jordan1k A C B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t45_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_tarski A B) &  ((r2_hidden (k1_jordan21 B) A) &  ((v4_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2))))) &  ((k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) = (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B))) ) ) )  =>  ((v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) |  ((k1_jordan21 A) = (k1_jordan21 B)) ) ) ) ) ) ) ).
tt(t45_jordan23,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (k1_jordan2c 2 (k3_topreal1 2 (k1_jordan9 B A)))) &  (! [E:$i] :  ( ((v4_topreal1 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2))))  =>  (~  ( (E = (k4_jordan3 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) (k7_nat_d (k3_finseq_1 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k1_jordan3 (k1_jordan9 B A) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))))) 1) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k1_jordan3 (k1_jordan9 B A) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))))) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))) (k1_jordan18 C (k3_topreal1 2 (k1_jordan9 B A)))))  &  (? [F:$i] :  ( ((v4_topreal1 F) & (m2_finseq_1 F (u1_struct_0 (k15_euclid 2))))  &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) F (k2_goboard2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) E (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k1_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))))) &  ( ((k3_topreal1 2 (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k1_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))) = (k3_topreal1 2 F))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) F 1) = (k1_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) F (k3_finseq_1 F)) = (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))  &  ((r1_xxreal_0 2 (k3_finseq_1 F)) &  (? [G:$i] :  ( ((v4_topreal1 G) & (m2_finseq_1 G (u1_struct_0 (k15_euclid 2))))  &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) G (k2_goboard2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) E (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) (k1_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))) (k2_jordan18 C (k3_topreal1 2 (k1_jordan9 B A))))))) &  ( ((k3_topreal1 2 E) = (k3_topreal1 2 G))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) E 1) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) G 1))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k3_finseq_1 E)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) G (k3_finseq_1 G)))  &  ((r1_xxreal_0 (k3_finseq_1 E) (k3_finseq_1 G)) &  (? [H:$i] :  ( ( (~ (v1_xboole_0 H))  &  ( (~ (v3_funct_1 H))  &  ((v1_finseq_6 H (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 H) &  ((v2_topreal1 H) &  ((v1_goboard5 H) &  ((v2_goboard5 H) & (m2_finseq_1 H (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  &  (H = (k4_graph_2 (u1_struct_0 (k15_euclid 2)) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (C = B)  &  (D = (k9_euclid A B E)) )  =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 C)))  =>  ((k7_partfun1 k1_numbers D F) = (k8_real_1 E (k7_partfun1 k1_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) )  => (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k7_nat_d (k3_finseq_1 A) 1)) B))) ) ) ) ) ).
tt(t45_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_jordan4 A B C D) =>  ((r1_xxreal_0 C D) | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 (k7_jordan5d A)) &  ((r1_xxreal_0 (k7_jordan5d A) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k8_jordan5d A)) &  ((r1_xxreal_0 (k8_jordan5d A) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k5_jordan5d A)) &  ((r1_xxreal_0 (k5_jordan5d A) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k6_jordan5d A)) & (r1_xxreal_0 (k6_jordan5d A) (k3_finseq_1 (k2_goboard2 A)))) ) ) ) ) ) ) ) ) ).
tt(t45_jordan6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k1_pre_topc B E)) (u1_struct_0 C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc B E)) (u1_struct_0 C))))) )  =>  (~  ((r1_tarski D E) &  ((v5_pre_topc F A (k1_pre_topc B D)) &  ((v5_pre_topc G (k1_pre_topc B E) C) &  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (~  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 C) H (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)) (u1_struct_0 (k1_pre_topc B E)) (u1_struct_0 C) F G)) & (v5_pre_topc H A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k1_sppol_2 A B C D) (k2_jgraph_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t45_knaster,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v14_quantal1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C)) => (r3_lattices A C (k10_knaster A B))) ) ) ) ) ) ) ).
tt(t45_kurato_1,ax, (~  ((k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) = (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))) ) ).
tt(t45_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((k2_partfun1 B (u1_struct_0 A) D C) = (k2_partfun1 B (u1_struct_0 A) E C))  =>  ( (C = k1_xboole_0)  |  ((k3_lattice2 B A C D) = (k3_lattice2 B A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) =>  ((r3_lattices A (k15_lattice3 A B) (k15_lattice3 A C)) & (r3_lattices A (k16_lattice3 A C) (k16_lattice3 A B))) ) ) ) ) ) ).
tt(t45_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  (! [E:$i] :  ( ( (E = (k10_lexbfs A (k13_lexbfs A (k16_lexbfs A) C)))  & (r2_hidden D (k2_chord A (k1_tarski E))))  =>  ((r1_xxreal_0 (k15_glib_000 A) C) |  ((r1_xxreal_0 B C) |  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) C)))) | (r2_hidden (k7_nat_d (k15_glib_000 A) C) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v6_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (~ (r1_xxreal_0 D E))  &  ((r2_hidden E (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 C (k18_complex1 (k9_real_1 (k1_seq_1 A E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k7_real_1 (k1_limfunc2 B A) (k1_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t45_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ( ((k1_limfunc3 B A) = k6_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  ((k1_seq_1 B E) = k6_numbers) )  &  (~  ((k1_seq_1 B F) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A C) A) (k2_rcomp_1 A (k7_real_1 A C))))) => (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) ) ) ) ) ) )  | (r2_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A)) ) ) ) ) ) ).
tt(t45_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r2_limfunc3 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) &  ((k1_seq_1 A D) = (k4_limfunc1 A)) ) ) ) ) )  | (v4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t45_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) &  ((r2_hidden E (k9_lpspace1 A B C)) & (r1_lpspace1 A B C D E)) )  =>  ((r1_lpspace1 A B C (k56_valued_1 A k1_numbers D) (k56_valued_1 A k1_numbers E)) &  ((k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D)) = (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [H:$i] :  ( ((v2_xxreal_0 H) & (m1_subset_1 H k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C H)) &  ((r2_hidden E (k1_lpspace2 A B C H)) &  ((r2_hidden F (k1_lpspace2 A B C H)) &  ((r2_hidden G (k1_lpspace2 A B C H)) &  ( ((k5_lpspace2 A B C D H) = (k5_lpspace2 A B C E H))  &  ((k5_lpspace2 A B C F H) = (k5_lpspace2 A B C G H)) ) ) ) ) )  =>  ((k5_lpspace2 A B C (k3_valued_1 A k1_numbers k1_numbers D F) H) = (k5_lpspace2 A B C (k3_valued_1 A k1_numbers k1_numbers E G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r8_ltlaxio1 C (k3_hilbert1 A B)) & (r8_ltlaxio1 C (k3_hilbert1 A (k2_ltlaxio1 A))))  => (r8_ltlaxio1 C (k3_hilbert1 A (k6_ltlaxio1 B)))) ) ) ) ) ) ) ).
tt(t45_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) & (v2_cqc_the1 C A))  => (v2_cqc_the1 (k8_cqc_lang A B D) A)) ) ) ) ) ) ) ) ) ).
tt(t45_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) =>  ((r1_tarski (k4_mathmorp A B D) (k4_mathmorp A C D)) & (r1_tarski (k5_mathmorp A B D) (k5_mathmorp A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ( ((r1_matrix10 B C) & (r1_matrix10 C D))  => (r1_matrix10 B D)) ) ) ) ) ) ) ) ) ).
tt(t45_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) (k1_nat_1 A 2) (k1_nat_1 A 2)) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2))) &  ((v3_funct_2 E (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 (k1_nat_1 A 2)) (k2_finseq_1 (k1_nat_1 A 2)))))) ) )  =>  ( (D = E)  =>  ((k12_matrix_3 (k1_nat_1 A 2) B (k4_matrix11 (k1_nat_1 A 2) (k1_nat_1 A 2) (u1_struct_0 B) E C)) = (k8_group_1 B (k2_matrix11 A B D) (k12_matrix_3 (k1_nat_1 A 2) B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (v7_ordinal1 E))  =>  (! [F:$i] :  ( ((v1_matrix_1 F) & (m2_finseq_1 F (k3_finseq_2 A)))  =>  (~  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 E D))  &  (~  ((k6_matrix13 A F (k4_matrix13 B C) (k4_matrix13 D E)) = (k6_matrix_2 A (k3_matrix_1 A F B D) (k3_matrix_1 A F B E) (k3_matrix_1 A F C D) (k3_matrix_1 A F C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 A) B B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D B) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E B)) ) )  =>  ( (D = E)  |  ((k3_matrix_1 (u1_struct_0 A) (k4_matrix14 A B 1) D E) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski D (k4_finseq_1 B)) &  ( ((k4_finseq_1 B) = (k4_finseq_1 C))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k7_subset_1 k5_numbers (k4_finseq_1 B) D)) =>  ( ((k8_matrix_1 (u1_struct_0 A) B E) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 B) (k4_struct_0 A)))  &  ((k8_matrix_1 (u1_struct_0 A) C E) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 C) (k4_struct_0 A))) ) ) ) ) ) )  =>  ((v1_xboole_0 D) |  ((k4_matrix15 A B C) = (k4_matrix15 A (k6_matrix13 (u1_struct_0 A) B D (k2_finseq_1 (k1_matrix_1 B))) (k6_matrix13 (u1_struct_0 A) C D (k2_finseq_1 (k1_matrix_1 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ((v2_matrix16 D (u1_struct_0 A)) &  ((v2_matrix16 E (u1_struct_0 A)) &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k1_matrix16 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 E) (k3_finseq_1 E) A (k1_matrix16 (u1_struct_0 A) E) C)) = (k1_matrix16 (u1_struct_0 A) (k3_fvsum_1 A (k9_fvsum_1 A D B) (k9_fvsum_1 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k16_matrix_1 B) = (a_2_1_matrix_1 A B)) ) ) ) ) ).
tt(t45_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k1_matrix_4 A (k2_matrix_3 A C) (k1_matrix_4 A (k2_matrix_3 A B) C))) ) ) ) ) ) ) ) ).
tt(t45_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (v1_matrix_6 D A B))  =>  ((v1_matrix_6 (k4_matrix_6 A B C D) A B) &  ((k5_matrix_6 A B (k4_matrix_6 A B C D)) = (k4_matrix_6 A B (k5_matrix_6 A B D) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((r2_matrix_8 A B C D) & (r2_matrix_8 A B D E))  =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_8 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_matrix_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ((v3_funct_2 A (k2_finseq_1 3) (k2_finseq_1 3)) &  ( (~ (v5_matrix_2 A 3))  & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 3) (k2_finseq_1 3))))) ) ) )  =>  (~  ( (~  (A = (k3_finseq_4 k5_numbers 3 2 1)) )  &  ( (~  (A = (k3_finseq_4 k5_numbers 1 3 2)) )  &  (~  (A = (k3_finseq_4 k5_numbers 2 1 3)) ) ) ) ) ) ) ).
tt(t45_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ((k17_rvsum_1 (k11_seq_4 A)) = (k1_binop_2 (k17_rvsum_1 A))) ) ) ).
tt(t45_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v2_matrixj1 k1_xboole_0 A) & (m2_finseq_1 k1_xboole_0 (k3_finseq_2 (k3_finseq_2 A)))) ) ) ).
tt(t45_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ( (B = (k9_matrixr1 A))  <=>  ( ((k9_matrix_1 k1_numbers B 1) = A)  &  ((k1_matrix_1 B) = 1) ) ) ) ) ) ) ) ).
tt(t45_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k12_matrix_3 A B (k4_matrix_6 A B C D)) = (k8_group_1 B (k12_matrix_3 A B C) (k12_matrix_3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t45_matrlin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  => (m1_matrlin (k11_matrix13 B A A (k12_matrix_1 B A)) B (k6_prvect_1 B A))) ) ) ) ).
tt(t45_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k23_rvsum_1 A (k5_finseq_2 k5_numbers (k3_finseq_1 A) 1)) = (k18_rvsum_1 A)) ) ) ).
tt(t45_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E B) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  => (r1_xxreal_0 (k12_euclid (k1_funct_1 (k3_matrtop1 B A C) E)) (k11_binop_2 D (k12_euclid E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ( (~ (r1_tarski A (k3_zfmisc_1 A B C)))  &  ( (~ (r1_tarski A (k3_zfmisc_1 B C A)))  &  (~ (r1_tarski A (k3_zfmisc_1 C A B))) ) ) )  =>  (A = k1_xboole_0) ) ) ) ) ).
tt(t45_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 A) <=> (v2_rcomp_1 (k4_measure6 A))) ) ) ).
tt(t45_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k8_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k1_xxreal_3 A C) (k1_xxreal_3 A D) (k1_xxreal_3 B C) (k1_xxreal_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t45_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  ((k6_memstr_0 A B (k8_memstr_0 A B C)) = (k6_memstr_0 A B C)) ) ) ) ) ) ) ).
tt(t45_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ((r2_mesfun6c A B C D) =>  ((k3_mesfun6c A B C (k25_valued_1 A k2_numbers D E) F) = (k3_xcmplx_0 E (k3_mesfun6c A B C D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_mesfun7c A B C) <=>  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  (? [E:$i] :  ((m2_finseq_1 E k2_numbers) & (r3_mesfun7c A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((r1_mesfun7c A B C) => (r1_mesfun7c A B (k25_valued_1 A k2_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(t45_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((r2_hidden D B) => (r1_xxreal_0 k6_numbers (k12_supinf_2 C D))) ) ) ) ) ) ) ) ).
tt(t45_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k56_valued_1 A k1_numbers B) (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A B) (k19_rfunct_3 A B)))) ) ) ) ).
tt(t45_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc5 A B C (k4_mesfunc5 A k7_numbers D E))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_mesfunc5 A B C (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (? [C:$i] :  ((m1_midsp_1 C A) &  ((k7_midsp_1 A B C) = (k6_midsp_1 A)) ) ) ) ) ) ) ).
tt(t45_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((v1_mmlquery B A) <=>  (B = (k4_relat_1 (k1_relset_1 A B))) ) ) ) ) ).
tt(t45_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k6_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  (~  ((k11_modal_1 A) = (k12_modal_1 B C)) ) ) ) ) ) ) ) ).
tt(t45_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 A)) =>  ((r1_tarski F G) => (r1_tarski (k60_modelc_1 A B C D E F) (k60_modelc_1 A B C D E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden A (k13_modelc_2 B)) <=> (r2_modelc_2 A B)) ) ) ) ) ).
tt(t45_modelc_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((m1_subset_1 A (k23_modelc_3 B)) <=>  (? [C:$i] :  ( ((v1_modelc_3 C B) &  ((v3_modelc_3 C B) & (l1_modelc_3 C B)) )  &  (C = A) ) ) ) ) ) ) ).
tt(t45_moebius1,ax, ((k5_moebius1 1) = (k16_pre_poly k10_newton)) ).
tt(t45_monoid_0,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_monoid_0)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_monoid_0)) =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_algstr_0 k5_monoid_0 C D) = (k23_binop_2 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t45_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G E) & (r2_hidden H F))  => (r2_hidden (k1_binop_1 D G H) (k2_binop_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) (k1_zfmisc_1 C) (k21_monoid_1 A B C D) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v2_relat_1 D) & (m3_pboole D A (k1_mboolean A C)))  =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E D) => (r2_pboole A B E)) ) )  => (r2_pboole A B (k4_mssubfam A C D))) ) ) ) ) ) ) ) ).
tt(t45_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D) E F) =>  (! [G:$i] :  ((m1_msualg_6 G A B) => (r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D) (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) G D) E) (k3_funct_2 (k1_funct_1 (u3_msualg_1 A B) D) (k1_funct_1 (u3_msualg_1 A B) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) G D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_mycielsk B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_mycielsk A B)))) =>  ( (C = A)  =>  (B = (k5_yellow_0 (k6_mycielsk A B) C)) ) ) ) ) ) ) ) ).
tt(t45_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden A (k1_nat_1 A 1))) ) ).
tt(t45_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  => (r1_tarski (k1_polynom2 k10_newton (k12_nat_3 A)) (k1_polynom2 k10_newton (k12_nat_3 (k24_binop_2 A B))))) ) ) ) ).
tt(t45_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (r1_xxreal_0 (k3_wsierp_1 (k14_finseq_1 (a_1_0_nat_4 A))) (k4_power 4 A))) ) ).
tt(t45_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_nat_d A 2) = (k7_nat_d (k7_nat_d A 1) 1)) ) ) ).
tt(t45_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_cat_1 A) &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) ) )  =>  ((v2_nattra_1 A) =>  ((k12_nattra_1 A) = A) ) ) ) ).
tt(t45_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r8_ncfcont1 A B D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 A) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E C) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_hidden H C) &  ( (~ (r1_xxreal_0 G (k1_normsp_0 A (k5_algstr_0 A H E))))  & (r1_xxreal_0 F (k1_normsp_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) D H) (k7_partfun1 (u1_struct_0 B) D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ndiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r2_ndiff_1 A B C D) => (r3_nfcont_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t45_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k4_real_ns1 1)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_funct_2 (u1_struct_0 (k4_real_ns1 1)) k1_numbers (k1_euclid 1) k1_numbers B (k1_pdiff_1 1 1)) &  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k4_real_ns1 1)) F)) &  ((r2_hidden D (k1_relset_1 k1_numbers E)) &  ( (C = (k12_finseq_1 k1_numbers D))  &  ((r2_relset_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 A)) F (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) k1_numbers k1_numbers (u1_struct_0 (k4_real_ns1 A)) B E)) & (r1_ndiff_3 (k4_real_ns1 A) E D)) ) ) ) )  =>  ((r1_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) &  ( ((k1_ndiff_3 (k4_real_ns1 A) E D) = (k1_funct_1 (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) (k12_finseq_1 k5_numbers 1)))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k1_funct_1 (k3_ndiff_1 (k4_real_ns1 1) (k4_real_ns1 A) F C) (k12_finseq_1 k1_numbers G)) = (k1_rlvect_1 (k4_real_ns1 A) (k1_ndiff_3 (k4_real_ns1 A) E D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (? [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k14_prvect_2 A))) &  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (k4_card_3 (k4_prvect_2 A))) &  (? [I:$i] :  ((m1_subset_1 I (k4_card_3 (k4_prvect_2 A))) &  ( (I = E)  &  ( (H = (k4_struct_0 (k14_prvect_2 A)))  &  ( ((k3_finseq_1 F) = (k23_binop_2 (k3_finseq_1 A) 1))  &  ( ((k3_finseq_1 G) = (k3_finseq_1 A))  &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  ((r2_hidden J (k4_finseq_1 F)) =>  ((k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) F J) = (k1_funct_4 H (k11_card_3 (k4_prvect_2 A) I (k2_finseq_1 (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) J))))) ) ) )  &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  ((r2_hidden J (k4_finseq_1 G)) =>  ((k7_partfun1 (u1_struct_0 B) G J) = (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 (k14_prvect_2 A) D (k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) F J))) (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 (k14_prvect_2 A) D (k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) F (k23_binop_2 J 1)))))) ) ) )  &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k14_prvect_2 A))) =>  ( ((r2_hidden J (k4_finseq_1 F)) &  ((k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) F J) = K) )  => (r1_xxreal_0 (k1_normsp_0 (k14_prvect_2 A) K) (k1_normsp_0 (k14_prvect_2 A) E))) ) ) ) )  &  ((k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_rlvect_1 (k14_prvect_2 A) D E)) (k7_partfun1 (u1_struct_0 B) C D)) = (k4_rlvect_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d C B))  <=> (r1_nat_d (k5_nat_d A C) B)) ) ) ) ) ) ) ).
tt(t45_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r5_nfcont_1 B C A D) => (r3_nfcont_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t45_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A))  => (r1_nfcont_1 (k4_real_ns1 A) (k4_real_ns1 1) (k4_pdiff_1 B A) C)) ) ) ) ) ) ) ).
tt(t45_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k9_normform A (k5_setwiseo (k7_normform A) B (k9_normform A C))) = (k9_normform A (k5_setwiseo (k7_normform A) B C))) ) ) ) ) ) ).
tt(t45_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) D) = (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t45_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_orders_1 A B) =>  ((v1_relat_2 (k2_wellord1 A B)) &  ((v4_relat_2 (k2_wellord1 A B)) &  ((v8_relat_2 (k2_wellord1 A B)) &  ((v1_partfun1 (k2_wellord1 A B) B) & (m1_subset_1 (k2_wellord1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) ) ) ) ).
tt(t45_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_orders_1 B (k1_orders_1 (u1_struct_0 A))) => (m2_orders_2 (k3_tarski (k4_orders_2 A B)) A B)) ) ) ) ).
tt(t45_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = A)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D A) =>  ((k1_funct_1 C D) = (k12_ordinal2 B D)) ) ) ) )  =>  ((k12_ordinal2 B A) = (k8_ordinal2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t45_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (A = k1_xboole_0) )  =>  ((k3_tarski (k10_ordinal2 B A)) = (k10_ordinal2 B (k3_tarski A))) ) ) ) ) ) ).
tt(t45_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = (k3_ordinal5 B)) ) ) )  => (v2_ordinal2 A)) ) ) ).
tt(t45_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  ((v2_ordinal6 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 (k3_ordinal6 A))) => (r1_ordinal1 (k1_funct_1 A B) (k1_funct_1 (k3_ordinal6 A) B))) ) ) ) ) ) ).
tt(t45_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t45_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ((v2_msualg_4 C A (k8_osafree A B)) &  ((v3_osalg_4 C A (k8_osafree A B)) & (m1_osalg_4 C A (k8_osafree A B))) )  => (r2_pboole (u1_struct_0 A) (k20_osafree A B) C)) ) ) ) ) ) ).
tt(t45_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (v2_binop_1 (k14_osalg_2 A B) (k13_osalg_2 A B))) ) ) ) ).
tt(t45_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_parsp_2 A B B C D) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t45_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  => (r2_hidden C (k4_partfun1 A B))) ) ) ) ).
tt(t45_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A))))  =>  ( ((r1_tarski (k1_relset_1 B C) (k1_relset_1 B D)) &  (! [E:$i] :  ((m1_subset_1 E B) =>  ((r2_hidden E (k1_relset_1 B C)) =>  ((k7_partfun1 A C E) = (k7_partfun1 A D E)) ) ) ) )  => (r1_relset_1 B A C D)) ) ) ) ) ) ) ) ) ).
tt(t45_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) &  ((r2_pboole A B D) & (r6_pboole A (k3_pboole A C D) (k1_pboole A))) )  => (r6_pboole A B (k1_pboole A))) ) ) ) ) ) ) ) ).
tt(t45_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k25_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k25_pcs_0 A B))) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E C) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_hidden F D) & (r1_orders_2 A E F)) ) ) ) ) ) ) )  => (r1_orders_2 (k25_pcs_0 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(t45_pdiff_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 (k1_pdiff_1 3 3) B)) =>  ( ((r9_pdiff_5 A B) & (r1_tarski C (k1_relset_1 k1_numbers (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B))))  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski (k1_seq_1 (k1_pdiff_1 3 3) B)))  & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) C))  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B))))) &  ((k9_pdiff_5 A B) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers E (k1_pdiff_2 3 3 (k1_pdiff_3 3 3 A) B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G A) &  ((v1_pdiff_7 C A) &  ((r2_hidden D C) &  ( (~ (r1_xxreal_0 H (k12_euclid (k8_euclid A E D))))  &  ( (~ (r1_xxreal_0 H (k12_euclid (k8_euclid A F D))))  &  ((r1_tarski C (k1_relset_1 (k1_euclid A) B)) &  ( (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid A)) =>  ((r2_hidden K C) => (r3_pdiff_1 A G B K)) ) )  &  ( (~ (r1_xxreal_0 H k6_numbers))  &  ( (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid A)) =>  ( (~ (r1_xxreal_0 H (k12_euclid (k8_euclid A K D))))  => (r2_hidden K C)) ) )  &  ( (F = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A G E) I))  &  ( (J = (k1_seq_1 (k1_pdiff_1 G A) E))  &  (! [K:$i] :  ((m2_finseq_2 K k1_numbers (k1_euclid A)) =>  (~  ( (~ (r1_xxreal_0 H (k12_euclid (k8_euclid A K D))))  &  ((r3_pdiff_1 A G B K) &  ((k10_binop_2 (k7_partfun1 k1_numbers B F) (k7_partfun1 k1_numbers B E)) = (k11_binop_2 (k10_binop_2 I J) (k11_pdiff_1 A G B K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) =>  ((r1_pdiff_9 A B C) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden G B) &  ( (~ (r1_xxreal_0 F (k12_euclid (k8_euclid A G D))))  & (r1_xxreal_0 E (k17_complex1 (k10_binop_2 (k7_partfun1 k1_numbers C G) (k7_partfun1 k1_numbers C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_int_2 A) &  ((v1_int_2 B) &  ( (C = (k3_xcmplx_0 A B))  &  ((r1_int_2 D (k1_euler_1 C)) &  ((k4_nat_d (k3_xcmplx_0 D E) (k1_euler_1 C)) = 1) ) ) ) )  =>  ( (A = B)  |  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (~ (r1_xxreal_0 C F))  =>  ((k2_pepin E (k2_pepin D F C) C) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k11_pnproc_1 A B (k4_subset_1 (k3_finseq_2 B) C D) E) = (k4_subset_1 (k3_finseq_2 B) (k11_pnproc_1 A B C E) (k11_pnproc_1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t45_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_polyform A (k6_xcmplx_0 B 1))) =>  ((k3_bspace (k20_polyform A B C) D) = (k4_rlvect_1 k2_bspace (k19_polyform A B D C))) ) ) ) ) ) ) ) ) ).
tt(t45_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k4_polynom5 A B (k4_struct_0 A)) D) = B) ) ) ) ) ) ) ) ) ).
tt(t45_polyred,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_algstr_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r2_hidden E D) => (r1_rewrite1 (k3_polyred A B C D) (k10_polynom1 A C F E) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 1 B))  =>  ((k3_power A (k10_real_1 1 B)) = (k1_power B A)) ) ) ) ) ) ).
tt(t45_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r2_pre_poly A B C) | (r2_pre_poly A C B)) ) ) ) ) ) ) ).
tt(t45_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k4_prepower (k4_prepower A B) C) = (k4_prepower A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t45_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((v1_prob_2 C) =>  ((v2_comseq_2 (k3_series_1 (k8_prob_1 A B C D))) &  ( ((k2_seq_2 (k3_series_1 (k8_prob_1 A B C D))) = (k1_rinfsup1 (k3_series_1 (k8_prob_1 A B C D))))  &  ((k2_seq_2 (k3_series_1 (k8_prob_1 A B C D))) = (k1_funct_1 D (k1_kurato_0 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k7_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden C (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t45_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k17_euclid (k13_pscomp_1 A)) = (k17_euclid (k23_pscomp_1 A)))  &  ( ((k17_euclid (k13_pscomp_1 A)) = (k17_euclid (k22_pscomp_1 A)))  &  ( ((k17_euclid (k23_pscomp_1 A)) = (k17_euclid (k22_pscomp_1 A)))  &  ( ((k17_euclid (k23_pscomp_1 A)) = (k17_euclid (k12_pscomp_1 A)))  &  ((k17_euclid (k22_pscomp_1 A)) = (k17_euclid (k12_pscomp_1 A))) ) ) ) ) ) ) ).
tt(t45_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r1_pboole A B C) & (r1_pboole A D C))  <=> (r6_pboole A (k3_pboole A (k2_pzfmisc1 A B D) C) (k2_pzfmisc1 A B D))) ) ) ) ) ) ) ) ).
tt(t45_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B (k14_qc_lang1 A C D)) <=>  ( (B = C)  |  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v1_qc_lang2 B A) =>  ((k4_qc_lang3 A C B) = (k4_subset_1 C (k4_qc_lang3 A C (k10_qc_lang2 A B)) (k4_qc_lang3 A C (k11_qc_lang2 A B)))) ) ) ) ) ) ) ) ).
tt(t45_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k16_quatern2)) =>  ( ((k3_quatern2 A) = k6_numbers)  =>  (A = (k4_struct_0 k16_quatern2)) ) ) ) ).
tt(t45_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) => (r1_xxreal_0 (k10_real_1 (k7_real_1 (k3_quatern2 (k26_quaterni A B)) (k3_quatern2 (k29_quaterni A B))) 2) (k7_real_1 (k3_quatern2 A) (k3_quatern2 B)))) ) ) ) ).
tt(t45_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( (A = k6_numbers)  =>  ((k31_quaterni A) = k6_numbers) ) ) ) ).
tt(t45_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  (~  ( (~  (B = (k4_struct_0 (k19_quofield A))) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k19_quofield A))) =>  (~  ((k8_group_1 (k19_quofield A) B C) = (k5_struct_0 (k19_quofield A))) ) ) ) ) ) ) ) ) ) ).
tt(t45_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 D B C) &  ((v1_mod_2 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v2_funct_1 D) =>  ((k1_vectsp_9 A B) = (k10_ranknull A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t45_rat_1,ax, (! [A:$i] :  ((v1_rat_1 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ( (B = (k10_real_1 1 A))  =>  ((r1_xxreal_0 k6_numbers A) |  ( ((k2_rat_1 B) = (k1_real_1 (k1_rat_1 A)))  &  ((k1_rat_1 B) = (k4_xcmplx_0 (k2_rat_1 A))) ) ) )  &  ( ( ((k2_rat_1 B) = (k1_real_1 (k1_rat_1 A)))  &  ((k1_rat_1 B) = (k4_xcmplx_0 (k2_rat_1 A))) )  =>  ( (~ (r1_xxreal_0 k6_numbers A))  &  (B = (k10_real_1 1 A)) ) ) ) ) ) ) ) ).
tt(t45_rcomp_3,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((m1_setfam_1 B (u1_struct_0 A)) &  (C = (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B (a_2_0_rcomp_3 A B))) )  => (m1_setfam_1 C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t45_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers) k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_seq_1 (k5_real_3 A) B) k6_numbers)) ) ) ) ) ) ).
tt(t45_relat_1,ax, (! [A:$i] :  ( ((k9_xtuple_0 (k4_relat_1 A)) = A)  &  ((k10_xtuple_0 (k4_relat_1 A)) = A) ) ) ).
tt(t45_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_xboole_0 C (k7_relset_1 B A (k3_relset_1 A B E) D)) <=> (r1_xboole_0 D (k7_relset_1 A B E C))) ) ) ) ) ) ) ) ) ).
tt(t45_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r8_rewrite1 A B C) => (r6_rewrite1 A B C)) ) ) ) ) ).
tt(t45_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  ( ((r3_rewrite2 A B C D) & (r3_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k4_lang1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) C D))) E F))  => (r3_rewrite2 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k8_afinsq_1 F))) =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  & (l1_rewrite3 H G))  =>  ( ((v2_rewrite3 H F G) &  ((r2_hidden (k4_tarski A (k4_tarski B C)) (k1_rewrite3 F G H)) & (r2_hidden (k4_tarski A (k4_tarski D E)) (k1_rewrite3 F G H))) )  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((k5_relat_1 (k18_valued_1 B C) A) = (k18_valued_1 (k5_relat_1 B A) (k5_relat_1 C A)))  &  ( ((k5_relat_1 (k18_valued_1 B C) A) = (k18_valued_1 (k5_relat_1 B A) C))  &  ((k5_relat_1 (k18_valued_1 B C) A) = (k18_valued_1 B (k5_relat_1 C A))) ) ) ) ) ) ) ) ).
tt(t45_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_tarski A)))) ) ) ).
tt(t45_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] : (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k19_rfunct_3 A B) C) (k19_rfunct_3 A (k2_partfun1 A k1_numbers B C)))) ) ) ) ) ).
tt(t45_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 A D) => (r1_xxreal_0 (k1_seq_1 C D) B)) ) )  <=> (r1_xxreal_0 (k1_seq_1 (k4_rinfsup1 C) A) B)) ) ) ) ) ) ) ) ).
tt(t45_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v1_rlaffin1 (k1_convex1 B C A) B) =>  ( (A = k6_numbers)  | (v1_rlaffin1 C B)) ) ) ) ) ) ) ) ).
tt(t45_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_rlsub_1 A B (k1_rlsub_1 A)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t45_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_rlsub_2 A B C) &  ( (D = (k3_rlvect_1 A E F))  &  ( (D = (k3_rlvect_1 A G H))  &  ((r1_struct_0 B E) &  ((r1_struct_0 B G) &  ((r1_struct_0 C F) & (r1_struct_0 C H)) ) ) ) ) )  =>  ( (E = G)  &  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow13 B A (k4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (C = (a_2_0_rltopsp1 A B))  => (m2_yellow13 C A)) ) ) ) ) ) ) ).
tt(t45_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k1_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t45_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlvect_2 D A) => (r1_rlvect_2 A (k8_rlvect_2 A (k7_real_1 B C) D) (k7_rlvect_2 A (k8_rlvect_2 A B D) (k8_rlvect_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t45_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  ((k3_rmod_2 A B (k4_struct_0 B) C) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(t45_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_rmod_3 A B C D) =>  ((k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_rmod_3 A B E C D)) = (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_rmod_3 A B E D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ((m2_rmod_4 E A B D) => (m2_rmod_4 (k7_rmod_4 A B C E) A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k15_robbins1 A B) (k11_robbins1 A B)) = B) ) ) ) ) ).
tt(t45_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A (k5_robbins1 A B (k3_robbins1 A C))))) = (k3_robbins1 A (k5_robbins1 A B C))) ) ) ) ) ) ) ).
tt(t45_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (u1_orders_2 A)) =>  ((k1_funct_1 (k6_roughs_1 A B) C) = (k1_funct_1 (k6_roughs_1 A B) D)) ) ) ) ) ) ) ) ).
tt(t45_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((k2_rpr_1 A C (k3_subset_1 A B)) = 1) ) ) ) ) ) ) ) ) ).
tt(t45_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=>  ((k3_rusub_1 A (k4_algstr_0 A C) B) = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t45_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r1_rusub_2 A B C) &  ( (D = (k3_rlvect_1 A E F))  &  ( (D = (k3_rlvect_1 A G H))  &  ((r1_struct_0 B E) &  ((r1_struct_0 B G) &  ((r1_struct_0 C F) & (r1_struct_0 C H)) ) ) ) ) )  =>  ( (E = G)  &  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((m1_rusub_1 B C) => (r1_tarski (k3_rusub_1 A D B) (k3_rusub_1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t45_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) )  &  ( (~ (r1_xxreal_0 C k6_numbers))  & (v1_xboole_0 (k6_bhsp_2 A B C))) ) ) ) ) ) ) ) ) ).
tt(t45_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k1_seq_1 (k10_rvsum_1 C B) A) = (k11_binop_2 B (k1_seq_1 C A))) ) ) ) ) ) ).
tt(t45_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_rvsum_1 (k2_finseq_2 (k23_binop_2 A B) C)) = (k5_binop_2 (k19_rvsum_1 (k2_finseq_2 A C)) (k19_rvsum_1 (k2_finseq_2 B C)))) ) ) ) ) ) ) ).
tt(t45_scmbsort,ax,(r2_extpro_1 3 k1_scmfsa_2 k2_scmbsort (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) k10_scmfsa_m)).
tt(t45_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r1_tarski k2_scmfsa_2 (k1_relset_1 (u1_struct_0 k1_scmfsa_2) A))) ) ).
tt(t45_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scmfsa8a B A (k2_scmfsa6a C)) & (r1_scmfsa8a B A (k2_scmfsa6a D)))  =>  ((r5_scmfsa7b (k1_scmfsa8b E C D) B A) & (r6_scmfsa7b (k1_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ( ((k5_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E)) = k6_numbers)  & (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) F)))  =>  ((r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E) (k8_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E))) & (r6_pboole (u1_struct_0 k1_scmfsa_2) (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) (k2_nat_1 E 1)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k2_scmfsa_9 C B)) (k8_memstr_0 3 k1_scmfsa_2 D) (k2_nat_1 F (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A (k2_scmfsa_9 C B)) B) (k8_memstr_0 3 k1_scmfsa_2 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E))) 3))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k5_scmpds_2 C B) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k5_scmpds_2 C B) A) C) = B)  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (D = C) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k5_scmpds_2 C B) A) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k5_scmpds_6 A B C)) = (k2_nat_1 (k5_card_1 C) 1)) ) ) ) ) ) ) ).
tt(t45_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) k6_numbers) =>  ((k6_scmpds_4 (k2_scmpds_7 D F G C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 3)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((k3_tarski (k7_scmyciel A B)) = (k3_xboole_0 (k3_tarski A) B)) ) ) ) ).
tt(t45_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_semi_af1 A B C D E) & (r2_semi_af1 A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k32_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t45_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D A) => (r1_xxreal_0 D C)) ) )  => (r1_xxreal_0 (k2_seq_4 A) C)) ) ) ) ) ) ) ).
tt(t45_seqm_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_tarski (k10_xtuple_0 A) (k2_finseq_1 B)) &  ( ((k1_seq_1 A (k3_finseq_1 A)) = B)  &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k9_real_1 (k3_finseq_1 A) 1)))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (F = (k1_seq_1 A E))  &  ( (G = (k1_seq_1 A (k2_nat_1 E 1)))  &  ( (~  ((k18_complex1 (k9_real_1 F G)) = 1) )  &  (~  (F = G) ) ) ) ) ) ) ) ) ) ) ) )  &  ((r2_hidden C (k2_finseq_1 B)) &  ((r2_hidden (k2_nat_1 C 1) (k2_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 A)) &  ( ((k1_seq_1 A D) = C)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden E (k4_finseq_1 A)) &  ((k1_seq_1 A E) = C) )  => (r1_xxreal_0 E D)) ) ) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ((r2_hidden (k2_nat_1 D 1) (k4_finseq_1 A)) &  ((k1_seq_1 A (k2_nat_1 D 1)) = (k2_nat_1 C 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers))  &  (~ (r1_xxreal_0 1 (k1_seq_1 A B))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k1_series_3 A) B) k6_numbers))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k1_series_3 A) B))) ) ) ) ) ) ) ).
tt(t45_series_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 (k1_newton (k2_xcmplx_0 1 (k13_complex1 1 A)) (k2_nat_1 A 1)) (k1_newton (k2_xcmplx_0 1 (k13_complex1 1 (k2_nat_1 A 1))) A))) ) ) ) ).
tt(t45_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((m1_setfam_1 B A) <=>  ((k5_setfam_1 A B) = A) ) ) ) ) ).
tt(t45_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v3_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k3_funct_2 k5_numbers (k9_setfam_1 B) C A)) ) ) ) ) ) ) ).
tt(t45_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k3_setlim_2 B C D)) A) (k7_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A)))) ) ) ) ) ) ) ).
tt(t45_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k10_setwiseo A B (k3_setwiseo A D E) C) = (k5_setwiseo B (k3_funct_2 A (k5_finsub_1 B) C D) (k3_funct_2 A (k5_finsub_1 B) C E))) ) ) ) ) ) ) ) ) ) ).
tt(t45_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k4_scmfsa6a A B)) = (k2_xboole_0 (k3_sf_mastr A) (k4_sf_mastr B))) ) ) ) ) ).
tt(t45_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C C)) (k5_sheffer1 A B (k5_sheffer1 A D C))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D C)) (k5_sheffer1 A B (k5_sheffer1 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t45_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  ( ((r1_xxreal_0 (k2_xxreal_3 1) B) &  ((k8_simplex0 A C B) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) )  => (r1_xxreal_0 (k6_simplex0 C) B)) ) ) ) ) ) ).
tt(t45_simplex1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) & (l1_rlvect_1 D)) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_rlaffin1 E D) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 D)))) )  =>  (! [F:$i] :  ((m3_simplex0 F (k5_simplex1 C D (k5_simplex0 (u1_struct_0 D) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) E))) (k5_real_1 B 1)) =>  ( ( ((k5_card_1 E) = (k3_real_1 B 1))  &  (A = (a_5_0_simplex1 B C D E F)) )  =>  ( ( (~ (r1_xboole_0 (k3_convex1 D (k1_simplex1 D (k5_simplex1 C D (k5_simplex0 (u1_struct_0 D) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) E))) F)) (k1_rlaffin2 D E)))  =>  ((k1_card_1 A) = 2) )  &  ((r1_xboole_0 (k3_convex1 D (k1_simplex1 D (k5_simplex1 C D (k5_simplex0 (u1_struct_0 D) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 D)) E))) F)) (k1_rlaffin2 D E)) =>  ((k1_card_1 A) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_sincos10,ax,(r1_tarski (k1_rcomp_1 1 (k7_square_1 2)) (k1_relset_1 k1_numbers k1_sincos10))).
tt(t45_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 B)) (k5_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 B)) k7_complex1))) ) ) ) ) ).
tt(t45_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k6_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B))) = (k3_xcmplx_0 (k1_sin_cos4 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k2_sin_cos4 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)))) ) ) ) ) ).
tt(t45_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k3_sin_cos2 A) = k6_numbers) )  =>  ((k1_sin_cos5 (k8_real_1 2 A)) = (k10_real_1 (k7_real_1 1 (k5_square_1 (k1_sin_cos5 A))) (k8_real_1 2 (k1_sin_cos5 A)))) ) ) ) ).
tt(t45_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t45_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  =>  ((k4_sin_cos7 A) = (k11_binop_2 (k18_binop_2 1 2) (k4_sin_cos7 (k12_binop_2 (k11_binop_2 2 A) (k9_binop_2 1 (k3_square_1 A)))))) ) ) ) ).
tt(t45_sin_cos9,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k7_relset_1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))))).
tt(t45_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((v1_series_1 (k4_sin_cos A)) &  ((k4_series_1 (k4_sin_cos A)) = (k3_complex1 (k11_comseq_3 (k3_sin_cos A)))) ) ) ) ).
tt(t45_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( ( ((k17_euclid A) = (k17_euclid B))  |  ((k18_euclid A) = (k18_euclid B)) )  &  (~ (v5_topreal1 (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ).
tt(t45_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k7_pscomp_1 A) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 A))) ) ) ).
tt(t45_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k23_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t45_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sprect_2 B C) & (r2_hidden A (k4_finseq_1 C)))  => (r1_sprect_2 B (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) C A)))) ) ) ) ) ) ) ).
tt(t45_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k21_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t45_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A (k4_xcmplx_0 1)) => (r1_xxreal_0 (k4_xcmplx_0 A) (k3_square_1 A))) ) ) ).
tt(t45_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r3_stacks_1 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 B)) =>  ( (F = (k1_funct_1 D E))  =>  ((k9_stacks_1 B F) = (k3_relat_1 (k9_stacks_1 A E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k24_binop_2 A (k3_stirl2_1 B A)) = (k1_card_1 (a_2_3_stirl2_1 A B))) ) ) ) ) ).
tt(t45_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r1_tarski (k24_qc_lang1 A B) (k9_substut1 A B)) & (r1_tarski (k24_qc_lang1 A C) (k9_substut1 A C)))  => (r1_tarski (k24_qc_lang1 A (k7_cqc_lang A B C)) (k9_substut1 A (k7_cqc_lang A B C)))) ) ) ) ) ) ) ).
tt(t45_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~  ( (~ (v1_zfmisc_1 B))  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((k12_supinf_2 A B) = k1_supinf_1) ) ) )  |  ((k19_supinf_2 A) = k1_supinf_1) ) ) ) ) ).
tt(t45_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))) (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ).
tt(t45_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_tdlat_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_tdlat_1 A)) =>  ( ((k5_binop_1 (k1_tdlat_1 A) (k2_tdlat_1 A) B C) = (k2_xboole_0 B C))  &  ((k5_binop_1 (k1_tdlat_1 A) (k3_tdlat_1 A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(t45_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((v3_tex_2 C A) <=> (v4_tex_2 B A)) ) ) ) ) ) ) ) ).
tt(t45_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ( ((v4_tex_3 B A) & (v3_tex_3 C A))  |  ((v3_tex_3 B A) & (v4_tex_3 C A)) )  => (v3_tex_3 (k1_tsep_1 A B C) A)) ) ) ) ) ) ) ).
tt(t45_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k6_domain_1 (u1_struct_0 A) B))  => (v3_tex_4 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t45_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 C))  & (r1_tarski (u1_pre_topc C) (u1_pre_topc B)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 C) D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_tmap_1 A B D F) => (r1_tmap_1 A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ((r2_hidden E (k6_eqrel_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C) (k3_topalg_1 A B C) D)) <=> (r3_borsuk_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v7_topalg_6 B A) & (m2_subset_1 B (k4_partfun1 k1_numbers (k2_struct_0 A)) (k1_topalg_6 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 C)) &  ( ((k1_funct_1 C 1) = (k2_xxreal_2 (k9_xtuple_0 B)))  &  ( ((k1_funct_1 C (k3_finseq_1 C)) = (k1_xxreal_2 (k9_xtuple_0 B)))  &  ((v5_valued_0 C) &  (! [D:$i] :  ((m2_finseq_1 D (k1_topalg_6 A)) =>  (~  ( ((k3_finseq_1 D) = (k6_xcmplx_0 (k3_finseq_1 C) 1))  &  ( (B = (k6_topalg_6 A D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k3_finseq_1 D)))  =>  ((k7_partfun1 (k1_topalg_6 A) D E) = (k5_relat_1 B (k1_rcomp_1 (k7_partfun1 k1_numbers C E) (k7_partfun1 k1_numbers C (k1_nat_1 E 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_topgen_1 A B) = k1_xboole_0) ) ) ) ) ).
tt(t45_topgen_3,ax, (! [A:$i] :  ((k2_tex_1 A) = (k7_topgen_3 A k11_arytm_3)) ) ).
tt(t45_topgen_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k3_numbers)  => (v5_topgen_4 A k3_topmetr)) ) ) ).
tt(t45_topgen_5,ax,(v7_topgen_1 k3_topgen_5)).
tt(t45_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  => (m3_topgrp_1 (k3_group_1 A) A)) ) ).
tt(t45_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 B) = A)  => (r2_hidden B (u1_struct_0 (k14_euclid A)))) ) ) ) ) ).
tt(t45_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k6_pscomp_1 C) = (k9_real_1 (k17_euclid A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t45_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (k6_jgraph_6 A B C)) <=>  (~ (r1_xxreal_0 C (k12_euclid (k5_algstr_0 (k15_euclid 2) D (k19_euclid A B))))) ) ) ) ) ) ) ) ) ) ).
tt(t45_toprealb,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2))))) &  ( (A = (k7_domain_1 (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2))) (k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k2_rcomp_1 k6_numbers 1)) (k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2)))))  &  ((m1_setfam_1 A (u1_struct_0 (k8_toprealb 2))) &  ((v1_tops_2 A (k8_toprealb 2)) &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k8_toprealb 2)))) =>  ( ( (B = (k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k2_rcomp_1 k6_numbers 1)))  =>  ( ((k5_setfam_1 (u1_struct_0 k2_topalg_2) (k3_toprealb k6_numbers 1)) = (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((r2_hidden C (k3_toprealb k6_numbers 1)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc k2_topalg_2 C)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 C)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B)))))) )  =>  ( (D = (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb C))  => (v3_tops_2 D (k1_pre_topc k2_topalg_2 C) (k1_pre_topc (k8_toprealb 2) B))) ) ) ) ) ) ) )  &  ( (B = (k7_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb (k2_rcomp_1 (k10_real_1 1 2) (k10_real_1 3 2))))  =>  ( ((k5_setfam_1 (u1_struct_0 k2_topalg_2) (k3_toprealb (k10_real_1 1 2) (k10_real_1 3 2))) = (k8_relset_1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb B))  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k2_topalg_2))) =>  ((r2_hidden C (k3_toprealb (k10_real_1 1 2) (k10_real_1 3 2))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc k2_topalg_2 C)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k2_topalg_2 C)) (u1_struct_0 (k1_pre_topc (k8_toprealb 2) B)))))) )  =>  ( (D = (k2_partfun1 (u1_struct_0 k2_topalg_2) (u1_struct_0 (k8_toprealb 2)) k12_toprealb C))  => (v3_tops_2 D (k1_pre_topc k2_topalg_2 C) (k1_pre_topc (k8_toprealb 2) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  =>  ((v1_funct_1 (k64_valued_2 A (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k64_valued_2 A (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k64_valued_2 A (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t45_toprns_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ((v3_toprns_1 B A) &  ( (~  ((k6_toprns_1 A B) = (k4_struct_0 (k15_euclid A))) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 (k12_euclid (k8_nat_1 (u1_struct_0 (k15_euclid A)) B D)) (k10_real_1 (k12_euclid (k6_toprns_1 A B)) 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v3_pre_topc C A) & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t45_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_pre_topc A D)) (k2_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ).
tt(t45_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (v1_tops_1 C A))  => (v1_tops_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t45_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) =>  ( ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k6_partfun1 (u1_struct_0 A))) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) = C) ) ) ) )  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_diraf A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_trees_1,ax, ((k7_trees_1 (k2_trees_1 k6_numbers)) = 1) ).
tt(t45_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 A)) =>  ( (~ (r1_tarski C D))  =>  ((k1_funct_1 (k7_trees_2 A C B) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t45_trees_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((k2_trees_2 B (k2_nat_1 A 1)) = (k3_tarski (a_2_3_trees_9 A B))) ) ) ) ) ).
tt(t45_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski B D) &  ((r1_tarski C E) &  ((r1_xboole_0 (k9_subset_1 (u1_struct_0 A) D E) (k4_subset_1 (u1_struct_0 A) B C)) &  ((v3_pre_topc D A) & (v3_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (~  ( (~ (r1_tsep_1 C B))  &  ( (~ (r1_tsep_1 D B))  &  (? [E:$i] :  ((m1_pre_topc E B) &  (? [F:$i] :  ((m1_pre_topc F B) &  ( (E = (k2_tsep_1 A C B))  &  ( (F = (k2_tsep_1 A D B))  &  ((r3_tsep_1 A C D) &  (~ (r3_tsep_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k3_zfmisc_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)))) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_funct_2 E k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u2_turing_1 B) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 B)))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u2_turing_1 (k32_turing_1 A B)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 A B))))) =>  ( ((v2_turing_1 C A) &  ( (C = (k4_domain_1 (u2_turing_1 A) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (u4_turing_1 A) D E))  &  ((v2_turing_1 F B) &  ( (F = (k4_domain_1 (u2_turing_1 B) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (u4_turing_1 B) (k2_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k11_turing_1 A C)) (k3_mcart_1 (u2_turing_1 A) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (k11_turing_1 A C))))  &  (G = (k4_domain_1 (u2_turing_1 (k32_turing_1 A B)) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 A)) (u4_turing_1 (k32_turing_1 A B)) D E)) ) ) ) )  =>  ((v2_turing_1 G (k32_turing_1 A B)) &  ( ((k2_mcart_1 (u2_turing_1 (k32_turing_1 A B)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 A B))) (k11_turing_1 (k32_turing_1 A B) G)) = (k2_mcart_1 (u2_turing_1 B) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 B)) (k11_turing_1 B F)))  &  ((k3_mcart_1 (u2_turing_1 (k32_turing_1 A B)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 A B))) (k11_turing_1 (k32_turing_1 A B) G)) = (k3_mcart_1 (u2_turing_1 B) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 B)) (k11_turing_1 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k36_twoscomp A B)) = (k1_funct_1 k15_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = (k1_funct_1 C A))  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t45_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ((k8_uproots k1_complfld (k4_uniroots A k1_complfld)) = (k2_uproots (u1_struct_0 k1_complfld) (k2_uniroots A) 1)) ) ) ).
tt(t45_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~ (r1_xxreal_0 (k1_algseq_1 A D) C))  =>  ((k2_polynom4 A (k5_uproots A D C) B) = (k3_rlvect_1 A (k8_group_1 A B (k2_polynom4 A (k5_uproots A D (k2_nat_1 C 1)) B)) (k1_normsp_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t45_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_valuat_1 E A B) => (r2_valuat_1 A B E (k8_cqc_lang A (k11_cqc_lang A C D) D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k31_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k31_valued_2 A B E C) D) = (k31_valued_2 A B E (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t45_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  ((k3_vectsp_4 A B (k4_struct_0 B) C) = (u1_struct_0 C)) ) ) ) ) ) ) ).
tt(t45_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m2_vectsp_4 E A B C) =>  (! [F:$i] :  ((m2_vectsp_4 F A B D) =>  ( (~ (r1_xboole_0 E F))  => (m2_vectsp_4 (k9_subset_1 (u1_struct_0 B) E F) A B (k2_vectsp_5 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_vectsp_6 A B (k6_vectsp_6 A B D C)) = (k4_vectsp_1 A B D (k4_vectsp_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t45_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((r1_vfunct_1 B C D A) =>  ((v1_comseq_2 (k2_partfun1 B k1_numbers (k3_normsp_0 B C D) A)) & (r1_vfunct_1 B C (k5_vfunct_1 B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t45_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((r1_vfunct_2 A B C D) =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers (k3_normsp_0 A B C) D)) & (r1_vfunct_2 A B (k5_vfunct_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t45_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  ( ((v1_lattice3 A) | (v2_lattice3 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v13_waybel_0 B A) &  ((v2_waybel_0 B A) &  ((v13_waybel_0 C A) & (v2_waybel_0 C A)) ) )  => (v2_waybel_0 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ) ).
tt(t45_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  ((v1_cantor_1 (a_1_1_waybel11 A) A) &  ((v1_tops_2 (a_1_1_waybel11 A) A) & (m1_subset_1 (a_1_1_waybel11 A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ).
tt(t45_waybel14,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  ( (? [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  &  (B = (a_1_0_waybel14 A)) ) )  => (v2_waybel_8 A)) ) ) ).
tt(t45_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_0_waybel_1 A B))  =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v2_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v19_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v5_pre_topc C A B) <=>  ((v22_waybel_0 C A B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t45_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((m1_waybel23 (u1_struct_0 (k1_waybel_8 A)) A) => (v2_waybel_8 A)) ) ) ).
tt(t45_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C (k2_yellow_1 (u1_pre_topc B))))  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k1_waybel26 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B)))) (u1_struct_0 (k1_waybel26 A C)))))) )  &  ((v5_orders_3 D (k2_yellow_1 (u1_pre_topc (k2_borsuk_1 A B))) (k1_waybel26 A C)) &  (! [E:$i] :  ( ((v3_pre_topc E (k2_borsuk_1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))))  =>  ((k1_funct_1 D E) = (k6_waybel26 E (u1_struct_0 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 (k2_waybel27 B C))) &  ((v22_waybel_0 D A (k2_waybel27 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_waybel27 B C)))))) ) )  =>  ((v1_funct_1 (k2_funct_5 D)) &  ((v1_funct_2 (k2_funct_5 D) (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v22_waybel_0 (k2_funct_5 D) (k3_yellow_3 A B) C) & (m1_subset_1 (k2_funct_5 D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v1_waybel_2 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) =>  (B = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C))) ) ) ) ) ) ) ) ).
tt(t45_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((m1_subset_1 B (u1_struct_0 (k9_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (r2_hidden (u1_struct_0 B) A)) ) ) ) ) ) ) ).
tt(t45_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  (! [B:$i] :  ( ((v5_waybel_4 B A) &  ((v6_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k1_waybel_4 A) B) & (v6_waybel_4 (k1_waybel_4 A) A)) ) ) ) ) ) ).
tt(t45_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v5_waybel_7 (k1_waybel_4 A) A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) => (v5_waybel_6 B A)) ) ) ) ) ) ).
tt(t45_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((v2_wellord1 A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r3_wellord1 A B C) & (r3_wellord1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) =>  (B = (k2_xboole_0 A (k4_xboole_0 B A))) ) ) ) ).
tt(t45_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k5_xboolean A (k9_xboolean B C)) = (k4_xboolean (k6_xboolean B A) (k6_xboolean C A))) ) ) ) ) ) ) ).
tt(t45_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k2_xcmplx_0 A B) (k6_xcmplx_0 C D)) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 A D)) (k3_xcmplx_0 B C)) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t45_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A k6_numbers) => (r1_xxreal_0 B (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t45_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k4_xboole_0 (k14_xtuple_0 A) (k14_xtuple_0 B)) (k14_xtuple_0 (k4_xboole_0 A B)))) ) ).
tt(t45_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden A k1_numbers) &  ((r2_hidden B k1_numbers) &  ((r1_xxreal_0 A C) & (r1_xxreal_0 C B)) ) )  => (r2_hidden C k1_numbers)) ) ) ) ) ) ) ).
tt(t45_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k4_xxreal_1 B C) (k2_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t45_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( ((r1_tarski A B) & (v5_xxreal_2 B))  => (v5_xxreal_2 A)) ) ) ) ) ).
tt(t45_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k1_xxreal_3 B A) C) <=> (r1_xxreal_0 B (k3_xxreal_3 C A))) ) ) ) ) ) ) ) ).
tt(t45_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_orders_2 A B (k4_yellow_0 A))) ) ) ) ).
tt(t45_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_tarski (k4_yellow_3 A B (k1_waybel_3 (k3_yellow_3 A B) C)) (k1_waybel_3 A (k8_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k1_waybel_3 (k3_yellow_3 A B) C)) (k1_waybel_3 B (k9_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t45_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v8_pre_topc B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_0_yellow12 A B C D))  => (v3_pre_topc E A)) ) )  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (E = (a_4_1_yellow12 A B C D))  => (v4_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) => (v11_quantal1 C)) ) ) ) ) ) ) ).
tt(t45_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r2_hidden D (k1_binop_1 (u1_altcat_1 (k4_yellow18 A)) B C)) &  ((r2_hidden E (k1_binop_1 (u1_altcat_1 (k4_yellow18 A)) B C)) &  ((k1_funct_1 D (k4_tarski (k8_altcat_1 A B) (k4_tarski B B))) = (k1_funct_1 E (k4_tarski (k8_altcat_1 A B) (k4_tarski B B)))) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t45_yellow20,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v1_relat_1 (k9_xtuple_0 A)) & (r1_tarski (k2_funct_4 A) (k2_funct_4 B)))  => (r1_tarski A B)) ) ) ) ) ).
tt(t45_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k7_waybel_0 A))))  =>  ( (~ (v1_xboole_0 (k1_setfam_1 B)))  &  ((v1_waybel_0 (k1_setfam_1 B) A) &  ((v12_waybel_0 (k1_setfam_1 B) A) & (m1_subset_1 (k1_setfam_1 B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ).
tt(t45_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((v3_lattice3 (k3_yellow_3 A B)) =>  ((v3_lattice3 A) & (v3_lattice3 B)) ) ) ) ) ) ).
tt(t45_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_yellow_4 A (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) B D)) (k4_subset_1 (u1_struct_0 A) B (k4_yellow_4 A C D)))) ) ) ) ) ) ) ) ).
tt(t45_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_yellow_5 A B C) = (k3_yellow_0 A))  <=> (r3_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t45_yellow_7,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A C (k7_funcop_1 A B)) =>  ((k2_funct_6 D) = C) ) ) ) ) ) ) ) ).
tt(t45_yellow_9,ax, (! [A:$i] :  ((l1_waybel_9 A) =>  (! [B:$i] :  ((m1_yellow_9 B A) => (m1_yellow_9 A B)) ) ) ) ).
tt(t45_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_zf_lang A B) & (r1_zf_lang B A)) ) ) ) ) ) ).
tt(t45_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v11_zf_lang A) =>  (A = (k13_zf_lang (k23_zf_lang A) (k24_zf_lang A))) ) ) ) ).
tt(t45_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k3_xboole_0 A (k1_tarski B)) = (k1_tarski B))  => (r2_hidden B A)) ) ) ).
tt(t45_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t46_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ( ((r3_abcmiz_0 A B C) & (r1_tarski (k2_relset_1 (u1_abcmiz_0 A) D) (k2_relset_1 (u1_abcmiz_0 A) C)))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E (k2_relset_1 (u1_struct_0 A) (k7_abcmiz_0 A B D))) => (r3_orders_2 A (k8_abcmiz_0 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k12_abcmiz_1 A)) =>  ((m1_abcmiz_1 (k31_abcmiz_1 A (k16_abcmiz_1 A) B C) A (k12_abcmiz_1 A)) &  ((k31_abcmiz_1 A (k16_abcmiz_1 A) B C) = (k4_trees_4 (k4_tarski k9_abcmiz_1 (u1_struct_0 A)) (k4_pre_poly (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) B C))) ) ) ) ) ) ) ) ).
tt(t46_abcmiz_a,ax, (! [A:$i] :  ( ((v2_abcmiz_1 A k27_abcmiz_1) &  ((v6_abcmiz_a A k27_abcmiz_1) & (m1_subset_1 A (u4_struct_0 k27_abcmiz_1))) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B k27_abcmiz_1 (k14_abcmiz_1 k27_abcmiz_1)) =>  (! [C:$i] :  ((m1_abcmiz_1 C k27_abcmiz_1 (k14_abcmiz_1 k27_abcmiz_1)) =>  ((k10_abcmiz_a k27_abcmiz_1 (k31_abcmiz_1 k27_abcmiz_1 A B C)) = A) ) ) ) ) ) ) ).
tt(t46_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B E) &  ( (~ (r2_hidden C E))  &  ((r2_aff_1 A C D E) &  ( (~  (C = D) )  & (r1_aff_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_4 D A) &  ((r1_tarski B D) & (r1_tarski C D)) ) ) )  =>  ( (B = C)  |  ((r2_aff_4 A B C E) <=> (r1_tarski E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)))  =>  ( ((k1_afinsq_1 A) = 5)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ( ((k1_funct_1 A 3) = E)  &  ((k1_funct_1 A 4) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_finset_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E A) &  ((v1_funct_1 E) &  ((v5_ordinal1 E) & (v1_finset_1 E)) ) ) )  =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) &  ( ((k1_afinsq_1 B) = (k1_afinsq_1 C))  &  ( ((k1_afinsq_1 B) = (k1_afinsq_1 E))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k1_relset_1 k5_numbers E)) =>  ((k1_funct_1 E F) = (k1_binop_1 D (k1_funct_1 B F) (k1_funct_1 C F))) ) ) ) ) ) ) )  =>  ( ( (~ (v1_setwiseo D A))  &  (~ (r1_xxreal_0 1 (k1_afinsq_1 B))) )  |  ((k6_afinsq_2 A (k1_ordinal4 B C) D) = (k6_afinsq_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( (~  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) )  =>  ((v6_incsp_1 (k14_afproj A)) &  ((v1_incproj (k14_afproj A)) &  ((v2_incproj (k14_afproj A)) &  ((v3_incproj (k14_afproj A)) &  ((v4_incproj (k14_afproj A)) & (l1_incsp_1 (k14_afproj A))) ) ) ) ) ) ) ) ).
tt(t46_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_afvect0 A B))) &  ((k3_rlvect_1 (k5_afvect0 A B) D D) = C) ) ) ) ) ) ) ) ) ).
tt(t46_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m2_algspec1 B A) =>  (! [C:$i] :  ((m2_algspec1 C B) => (m2_algspec1 C A)) ) ) ) ) ) ).
tt(t46_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  => (r1_funct_2 (u1_struct_0 (k14_algstr_4 B)) (u1_struct_0 (k14_algstr_4 B)) (k1_relset_1 (u1_struct_0 (k14_algstr_4 B)) (k18_algstr_4 B A C)) (k1_relset_1 (u1_struct_0 (k14_algstr_4 B)) (k18_algstr_4 B A C)) (k18_algstr_4 B B (k6_partfun1 B)) (k6_partfun1 (k1_relset_1 (u1_struct_0 (k14_algstr_4 B)) (k18_algstr_4 B A C))))) ) ) ) ) ) ).
tt(t46_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) => (v5_altcat_3 D A B C)) ) ) ) ) )  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (k2_altcat_4 A)) ) ) ) ).
tt(t46_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_analmetr A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k3_analmetr A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((r8_analmetr A B C) <=> (r5_aff_1 (k3_analmetr A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r1_analort A B C D E F G) &  ((r1_analort A B C F G H I) &  ((r1_analort A B C D E J K) &  ( (~ (r1_analort A B C J K H I))  &  ( (~  (F = G) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v4_aofa_000 A) &  ((v7_aofa_000 A) & (l1_unialg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k13_aofa_000 A (k13_aofa_000 A B C) D) = (k13_aofa_000 A B (k13_aofa_000 A C D))) ) ) ) ) ) ) ) ) ).
tt(t46_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m3_aofa_i00 G A B D E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k56_aofa_i00 A B D E F G)) F) = (k5_int_1 (k21_aofa_i00 B k4_numbers C F) (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers G C)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k56_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v6_armstrng B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  (? [C:$i] :  ((l1_armstrng C) &  ( ((u1_armstrng C) = A)  &  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k1_funct_1 (u2_armstrng C) D) = k4_numbers) ) )  &  (B = (k5_armstrng C)) ) ) ) ) ) ) ) ) ).
tt(t46_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (A = k1_xboole_0) )  &  (~  ((k9_arytm_3 (k8_arytm_3 C B) (k8_arytm_3 D A)) = (k8_arytm_3 (k8_ordinal3 (k9_ordinal3 C A) (k9_ordinal3 B D)) (k9_ordinal3 B A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 9 A) & (r1_xxreal_0 (k4_nat_1 2 (k5_series_1 A 6)) (k5_series_1 (k2_nat_1 A 1) 6))) ) ) ) ).
tt(t46_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r1_bcialg_1 A D C))  => (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ).
tt(t46_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  => (r1_tarski (k4_bcialg_2 A) (k6_bcialg_2 A))) ) ).
tt(t46_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A (k1_bcialg_1 A B D) C)) = (k1_bcialg_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v4_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  ((k1_bcialg_4 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(t46_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v15_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A k6_numbers 1 1 1)) ) ) ).
tt(t46_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  ((v12_bcialg_1 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D C) B) & (m2_bcialg_1 (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t46_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B)))) ) ) ) ) ) ) ) ).
tt(t46_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 B) & (v3_funct_1 C))  => (v3_funct_1 (k6_bhsp_1 A B C))) ) ) ) ) ) ) ).
tt(t46_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden B (k4_bhsp_2 A C D)) & (r1_xxreal_0 D E))  => (r2_hidden B (k4_bhsp_2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_bhsp_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k5_bhsp_4 C D (k26_valued_1 k5_numbers k1_numbers B A)) (k5_normsp_1 C (k5_bhsp_4 C D B) A))) ) ) ) ) ) ) ) ).
tt(t46_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k14_bilinear A B C D) = (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) ) ) ) ) ) ) ) ) ).
tt(t46_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k1_boolealg A B C) (k1_boolealg A C B)) => (r1_boolealg A B C)) ) ) ) ) ) ) ).
tt(t46_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  ( (A = (k2_rcomp_1 B C))  => (v3_pre_topc A k1_borsuk_4)) ) ) ) ) ) ) ).
tt(t46_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k3_rcomp_1 A k1_xxreal_0) = k1_numbers) ) ) ) ).
tt(t46_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E k5_topmetr k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 k5_topmetr))))) ) )  =>  ( ( ((k1_funct_1 E k6_numbers) = k6_numbers)  &  ((k1_funct_1 E 1) = 1) )  => (r4_borsuk_2 A B C (k2_borsuk_6 A B C D E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( (B = (k1_funct_1 k12_toprealb A))  =>  ((k3_euclid_3 B) = (k8_real_1 (k8_real_1 2 k32_sin_cos) (k4_int_1 A))) ) ) ) ) ) ).
tt(t46_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A G B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k3_xboolean (k8_xboolean A B)) = (k4_xboolean A B)) ) ) ) ) ).
tt(t46_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B (k9_bvfunc_1 A B C)) (k9_bvfunc_1 A C D)) D)) ) ) ) ) ) ) ) ).
tt(t46_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k11_bvfunc_1 A) (k12_bvfunc_1 A)) (k11_bvfunc_1 A))) ) ).
tt(t46_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B (k5_bvfunc_1 A C D)) (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t46_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A C))) (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B))))) ) ) ) ) ) ) ) ) ).
tt(t46_card_1,ax, ((k3_card_1 k1_xboole_0) = k4_ordinal1) ).
tt(t46_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((k5_card_1 (k2_zfmisc_1 A B)) = (k4_nat_1 (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ).
tt(t46_card_3,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ( ( (! [C:$i] :  ((r2_hidden C B) => (r2_hidden (k1_card_1 C) A)) )  & (v6_ordinal1 B))  => (r1_ordinal1 (k1_card_1 (k3_tarski B)) A)) ) ) ) ).
tt(t46_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finset_1 C)) )  =>  ( (C = (k16_funcop_1 A B))  =>  ((k3_card_fin 1 C) = (k5_card_1 B)) ) ) ) ) ) ) ).
tt(t46_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v9_cat_1 D A B C) => (v9_cat_1 (k6_cat_1 A B C D) A C B)) ) ) ) ) ) ) ) ) ).
tt(t46_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_cat_3 E B C A) =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A D) (k3_cat_3 B A E)) => (m1_cat_3 (k8_cat_3 B A D E) B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t46_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k23_cat_4 A B))) =>  (C = D) ) ) ) ) ) ) ).
tt(t46_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k4_catalan2 A (k1_series_1 k1_numbers B C)) (k1_series_1 k1_numbers (k4_catalan2 A B) (k4_catalan2 A C)))) ) ) ) ) ) ).
tt(t46_cc0sp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_cc0sp2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_cc0sp2 B))) =>  ( ( ((k1_normsp_0 (k9_cc0sp2 B) C) = k6_numbers)  =>  (C = (k4_struct_0 (k9_cc0sp2 B))) )  &  ( ( (C = (k4_struct_0 (k9_cc0sp2 B)))  =>  ((k1_normsp_0 (k9_cc0sp2 B) C) = k6_numbers) )  &  ( ((k1_normsp_0 (k9_cc0sp2 B) (k1_clvect_1 (k9_cc0sp2 B) C A)) = (k8_real_1 (k18_complex1 A) (k1_normsp_0 (k9_cc0sp2 B) C)))  & (r1_xxreal_0 (k1_normsp_0 (k9_cc0sp2 B) (k1_algstr_0 (k9_cc0sp2 B) C D)) (k7_real_1 (k1_normsp_0 (k9_cc0sp2 B) C) (k1_normsp_0 (k9_cc0sp2 B) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ((r2_cfcont_1 B A) => (r2_cfcont_1 (k31_valued_1 k2_numbers k2_numbers B) A)) ) ) ) ).
tt(t46_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A k2_numbers (k31_valued_1 A k2_numbers (k1_cfunct_1 A B C)) (k1_cfunct_1 A (k31_valued_1 A k2_numbers B) C)) & (r2_relset_1 A k2_numbers (k1_cfunct_1 A B (k31_valued_1 A k2_numbers C)) (k31_valued_1 A k2_numbers (k1_cfunct_1 A B C)))) ) ) ) ) ) ) ).
tt(t46_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v8_cgames_1 A) <=>  ( (? [B:$i] :  ((v2_cgames_1 B) &  ((r2_hidden B (k6_cgames_1 A)) & (v5_cgames_1 B)) ) )  &  (? [B:$i] :  ((v2_cgames_1 B) &  ((r2_hidden B (k7_cgames_1 A)) & (v6_cgames_1 B)) ) ) ) ) ) ) ).
tt(t46_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid C)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid C)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid C)) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid C)) =>  (! [H:$i] :  ((m1_chain_1 H C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 B C) &  ((r2_hidden (k3_chain_1 C D E) (k4_chain_1 C H A)) &  ((r2_hidden (k3_chain_1 C F G) (k4_chain_1 C H B)) &  ((r1_tarski (k3_chain_1 C D E) (k3_chain_1 C F G)) &  (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 C)) =>  ( (~  ( ((k1_seq_1 D I) = (k1_seq_1 F I))  &  ((k1_seq_1 E I) = (k1_seq_1 F I)) ) )  &  (~  ( ((k1_seq_1 D I) = (k1_seq_1 G I))  &  ((k1_seq_1 E I) = (k1_seq_1 G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (~  ( (~  ((k3_glib_001 A B) = (k4_glib_001 A B)) )  &  ( (~ (r1_chord A (k3_glib_001 A B) (k4_glib_001 A B)))  &  (~ (r1_xxreal_0 2 (k15_glib_001 A B))) ) ) ) ) ) ) ) ).
tt(t46_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ( ((r2_hidden B (u1_struct_0 F)) & (r2_hidden C (u1_struct_0 F)))  =>  ((r2_hidden A (k3_msafree2 F)) |  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_xboole_0 (k2_msafree2 F) (k1_tarski A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_circcomb,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_circcomb (k5_circcomb A B)) & (v2_circcomb (k5_circcomb A B))) ) ) ) ).
tt(t46_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ( ((r4_circtrm1 A B C D E F) & (r3_circtrm1 A B C))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A E))) =>  ( (H = (k3_relat_1 C G))  =>  ((k6_circuit2 A E H) = (k3_relat_1 C (k6_circuit2 B F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((v1_ordinal1 A) &  ((k3_xboole_0 (k4_classes1 B) (k1_classes1 A)) = (k3_xboole_0 (k4_classes1 (k1_ordinal1 B)) (k1_classes1 A))) )  => (r1_tarski (k1_classes1 A) (k4_classes1 B))) ) ) ) ).
tt(t46_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (v3_ordinal1 (k2_ordinal1 A))) ) ).
tt(t46_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) & (l1_clvect_1 C)) ) ) ) ) ) ) ) )  =>  ( ((m1_clvect_1 A B) & (m1_clvect_1 B C))  => (m1_clvect_1 A C)) ) ) ) ) ) ) ).
tt(t46_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r2_hidden B (k4_clvect_2 A C D)) & (r1_xxreal_0 D E))  => (r2_hidden B (k4_clvect_2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k6_clvect_3 A B (k25_valued_1 k5_numbers k2_numbers C D)) = (k6_clvect_1 A (k6_clvect_3 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t46_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  => (r1_tarski (k8_cohsp_1 A B C) (k2_zfmisc_1 (k2_cohsp_1 A) (k3_tarski B)))) ) ) ) ) ) ).
tt(t46_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k16_coh_sp A)) =>  ( ((k2_xtuple_0 (k23_coh_sp A B)) = (k6_partfun1 (k17_coh_sp A B)))  &  ( ((k21_coh_sp A (k23_coh_sp A B)) = B)  &  ((k22_coh_sp A (k23_coh_sp A B)) = B) ) ) ) ) ) ).
tt(t46_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r1_xxreal_0 k6_numbers (k17_complex1 A))) ) ).
tt(t46_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 (k11_complex1 A B) C) = (k11_complex1 (k1_complex2 A C) (k1_complex2 B C))) ) ) ) ) ) ) ).
tt(t46_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  &  ( ( ((k8_group_1 k1_complfld B A) = C)  |  ((k8_group_1 k1_complfld A B) = C) )  &  (~  (B = (k3_vectsp_1 k1_complfld C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 A) = (k3_finseq_1 D)) ) )  =>  ((k1_finseqop k2_numbers k2_numbers k2_numbers k27_binop_2 A B) = (k1_finseqop k1_numbers k1_numbers k1_numbers k33_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 B)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ((r2_hidden A (k9_xtuple_0 D)) <=> (r2_hidden (k2_xcmplx_0 A C) (k9_xtuple_0 (k6_compos_1 B D C)))) ) ) ) ) ) ) ) ) ).
tt(t46_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k3_compos_2 A B C) D) 1) = (k5_compos_0 (u1_compos_1 A) C 1)) ) ) ) ) ) ) ) ) ).
tt(t46_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k4_complex1 A)))  & (r1_xxreal_0 k6_numbers (k18_sin_cos (k1_comptrig A)))) ) ) ) ).
tt(t46_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_margrel1 B A) & (m2_rfunct_3 B (k3_finseq_2 A) A (k2_comput_1 A)))  =>  (! [C:$i] :  ( ((v3_comput_1 C) & (m2_finseq_1 C (k2_comput_1 A)))  =>  ( ( ((k19_margrel1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 A) A (k2_comput_1 A)) =>  ((r2_hidden D (k10_xtuple_0 C)) => (v3_margrel1 D A)) ) ) )  =>  ((v3_margrel1 (k3_relat_1 (k6_funct_6 C) B) A) & (m2_rfunct_3 (k3_relat_1 (k6_funct_6 C) B) (k3_finseq_2 A) A (k2_comput_1 A))) ) ) ) ) ) ) ) ).
tt(t46_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers A) (k55_valued_1 k5_numbers k2_numbers B)))) ) ) ) ).
tt(t46_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers A D) (k8_nat_1 k2_numbers A C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_connsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))) =>  ( ( (B = D)  & (v2_connsp_1 B A))  => (v2_connsp_1 D (k1_pre_topc A C))) ) ) ) ) ) ) ) ) ).
tt(t46_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_convex4 B A) & (v2_convex4 C A))  => (v2_convex4 (k7_rusub_4 A B C) A)) ) ) ) ) ) ) ).
tt(t46_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_cqc_sim1 A B C) & (r2_cqc_sim1 A C D))  => (r2_cqc_sim1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t46_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden B (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)))  => (r2_hidden C (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t46_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k11_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B))) (k11_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t46_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((v6_qc_lang1 B A) & (r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) D (k6_domain_1 (k3_cqc_lang A) (k6_cqc_lang A B))) (k6_cqc_lang A C)))  => (r3_cqc_the1 A (k4_subset_1 (k3_cqc_lang A) D (k6_domain_1 (k3_cqc_lang A) C)) B)) ) ) ) ) ) ) ) ) ).
tt(t46_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k13_csspace A (k3_rlvect_1 A B C)) (k7_real_1 (k13_csspace A B) (k13_csspace A C)))) ) ) ) ) ) ).
tt(t46_dickson,ax,(r8_relat_2 k10_dickson k5_numbers)).
tt(t46_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 k19_sin_cos A) B) = (k1_real_1 (k8_real_1 2 (k8_real_1 (k18_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2)))))) ) ) ) ) ).
tt(t46_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k5_square_1 D)) ) )  =>  ((k1_seq_1 (k4_diff_1 C A) B) = (k8_real_1 A (k9_real_1 (k8_real_1 2 B) A))) ) ) ) ) ) ) ) ).
tt(t46_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k5_diff_1 (k4_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) (k9_real_1 B (k13_complex1 A 2))))) ) ) ) ) ) ) ).
tt(t46_dilworth,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v5_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  => (r1_xxreal_0 (k2_dilworth A) (k5_card_1 B))) ) ) ) ).
tt(t46_diraf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_analoaf A))  =>  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  <=>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B C C B) &  ((r2_analoaf A B C D D) &  ( ( ((r2_analoaf A B C D E) & (r2_analoaf A B C F G))  =>  ( (B = C)  | (r2_analoaf A D E F G)) )  &  ((r2_analoaf A B C B D) => (r2_analoaf A C B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B C B D)) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B D C E) &  (~  (C = E) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A B C D E) & (r2_analoaf A B D C E)) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A D B B E) &  ( (~  (B = D) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A C B B F) & (r2_analoaf A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C B F) & (r2_analoaf A D E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m2_subset_1 B (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [C:$i] :  ((m2_subset_1 C (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ((r1_ec_pf_1 A B C) <=> (r2_hidden (k1_domain_1 (k3_ec_pf_1 (k9_int_3 A)) (k3_ec_pf_1 (k9_int_3 A)) B C) (k7_ec_pf_1 A))) ) ) ) ) ) ) ).
tt(t46_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((r1_ec_pf_1 A C D) <=> (r1_ec_pf_1 A (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C) (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t46_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_graph_1 A C) = (k4_graph_1 A D))  =>  ((k18_ens_1 A B (k1_cat_1 A D C)) = (k1_partfun1 (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B) (k2_cat_1 A (k4_graph_1 A D) B) (k2_cat_1 A (k3_graph_1 A D) B) (k18_ens_1 A B C) (k18_ens_1 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  => (v1_matrprob (k2_entropy1 k1_numbers (k6_matrixr1 (k1_entropy1 A) B)))) ) ) ) ) ).
tt(t46_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((k6_enumset1 A A A A B C D E) = (k3_enumset1 A B C D E)) ) ) ) ) ) ).
tt(t46_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A (k8_relat_1 C B)) => (r1_tarski (k7_relat_1 C A) B)) ) ) ) ) ).
tt(t46_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B C))) = (k9_binop_2 (k10_binop_2 (k5_square_1 (k12_euclid B)) (k11_binop_2 2 (k23_rvsum_1 C B))) (k5_square_1 (k12_euclid C)))) ) ) ) ) ) ) ).
tt(t46_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ( (~  (C = B) )  &  ( ( ((k4_euclid_3 A B C) = (k10_real_1 k32_sin_cos 2))  |  ((k4_euclid_3 A B C) = (k8_real_1 (k10_real_1 3 2) k32_sin_cos)) )  &  (~  ((k7_real_1 (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B))) (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) C B)))) = (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((v2_euclid_4 C A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (B = D) )  & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k9_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 4 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_rlvect_5 (k10_funcsdom (k2_finseq_1 A))) = A) ) ) ).
tt(t46_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k8_euclid 3 (k1_euclid_8 A B C) (k1_euclid_8 D E F)) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k10_binop_2 A D)) (k9_euclid 3 k3_euclid_8 (k10_binop_2 B E))) (k9_euclid 3 k4_euclid_8 (k10_binop_2 C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k5_algstr_0 (k15_euclid A) B (k3_rlvect_1 (k15_euclid A) C D)) = (k5_algstr_0 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t46_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  ((r2_euclidlp A B C) & (r4_euclidlp A B C)) ) ) ) ) ) ) ) ).
tt(t46_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v16_waybel_0 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v1_exchsort D)) ) )  =>  ((r2_hidden (k4_tarski A B) (k6_exchsort C D)) <=>  ((r2_hidden A (k9_xtuple_0 D)) &  ((r2_hidden B (k9_xtuple_0 D)) &  ((r2_hidden A B) & (r2_orders_2 C (k7_partfun1 (u1_struct_0 C) D B) (k7_partfun1 (u1_struct_0 C) D A))) ) ) ) ) ) ) ) ) ) ).
tt(t46_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((v2_circcomb (k4_circcomb A C B)) & (v2_msafree2 (k4_circcomb A C B))) ) ) ) ) ).
tt(t46_fcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v1_rfunct_2 (k2_partfun1 k1_numbers k1_numbers B A)) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 C D) &  ((k7_relset_1 k1_numbers k1_numbers B A) = (k1_rcomp_1 C D)) ) ) ) ) ) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) ) ).
tt(t46_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k19_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k19_sin_cos) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k2_fdiff_9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t46_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k30_sin_cos)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k30_sin_cos B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t46_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k10_prob_1 A) (k1_relset_1 k1_numbers B)) & (r2_fdiff_1 B (k10_prob_1 A)))  =>  ( ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k10_prob_1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) )  |  ((v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) &  ((r2_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))))) =>  ((k1_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) C) = (k10_real_1 1 (k1_fdiff_1 B (k1_seq_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 A))) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) k16_sin_cos))) =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k19_sin_cos) k16_sin_cos) A) B) = (k8_real_1 B (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t46_fdiff_6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)))) =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)) B) C) = (k1_real_1 (k8_real_1 (k5_prepower (k1_seq_1 k19_sin_cos C) (k9_real_1 A 1)) (k1_seq_1 k16_sin_cos C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k19_sin_cos A) = k6_numbers) )  =>  ((r1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) &  ((k1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos A)))) ) ) ) ) ).
tt(t46_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k1_pre_ff A) (k1_pre_ff B))) ) ) ) ) ) ) ).
tt(t46_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_fib_num3 B (k2_nat_1 A B) C) = (k3_fib_num3 A B (k2_nat_1 C 1))) ) ) ) ) ) ) ).
tt(t46_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_filter_0 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=>  (~ (r2_hidden (k7_lattices A C) B)) ) ) ) ) ) ) ) ) ).
tt(t46_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  &  ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v17_lattices B) & (l3_lattices B)) ) ) )  <=>  ( (~ (v2_struct_0 (k7_filter_1 A B)))  &  ((v10_lattices (k7_filter_1 A B)) &  ((v17_lattices (k7_filter_1 A B)) & (l3_lattices (k7_filter_1 A B))) ) ) ) ) ) ) ) ).
tt(t46_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r2_hidden B (k8_filter_2 A C D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (B = (k3_lattices A E F))  &  ((r2_hidden E C) & (r2_hidden F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  (~  (A = (k7_finseq_1 B (k9_finseq_1 C))) ) ) ) ) ) ) ) ) ).
tt(t46_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  ((r1_xxreal_0 A (k3_finseq_1 C)) => (m2_finseq_1 (k1_partfun1 (k2_finseq_1 A) (k2_finseq_1 A) k5_numbers B D C) B)) ) ) ) ) ) ) ) ) ).
tt(t46_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_finseq_1 (k14_finseq_1 (k2_finseq_1 A))) = A) ) ) ).
tt(t46_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (~  ((r2_hidden B (k10_xtuple_0 A)) &  ((v2_funct_1 A) & (r2_hidden B (k10_xtuple_0 (k6_finseq_4 A B)))) ) ) ) ) ) ).
tt(t46_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((r2_hidden D (k10_xtuple_0 C)) &  ((r2_hidden B (k10_xtuple_0 C)) & (r1_xxreal_0 (k4_finseq_4 C D) (k4_finseq_4 C B))) )  => (r2_hidden D (k10_xtuple_0 (k1_finseq_5 A C B)))) ) ) ) ) ) ) ) ).
tt(t46_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k2_rfinseq A 1 (k2_finseq_4 A B C)) = (k12_finseq_1 A C)) ) ) ) ) ) ) ).
tt(t46_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r6_binop_1 A F G) => (r2_relset_1 k5_numbers A (k3_finseqop A A A F (k5_binop_1 A G B C) E) (k1_finseqop A A A G (k3_finseqop A A A F B E) (k3_finseqop A A A F C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_fintopo2 A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k6_domain_1 (u1_struct_0 A) D) (k6_fintopo2 A D))) ) )  =>  ((k9_fintopo2 A (k9_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k9_fintopo2 A B) (k9_fintopo2 A C))) ) ) ) ) ) ) ) ).
tt(t46_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k9_subset_1 (u1_struct_0 A) (k9_fintopo3 A B D) (k9_fintopo3 A C D)) = (k3_subset_1 (u1_struct_0 A) (k7_fintopo3 A (k3_subset_1 (u1_struct_0 A) (k9_subset_1 (u1_struct_0 A) B C)) D))) ) ) ) ) ) ) ) ) ).
tt(t46_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_fin_topo A) =>  ((v4_fin_topo B A) <=> (v3_fintopo6 B A)) ) ) ) ) ) ).
tt(t46_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((r1_tarski B (k8_flang_1 A C)) & (r1_tarski D (k8_flang_1 A C)))  => (r1_tarski (k6_flang_1 A B D) (k8_flang_1 A C))) ) ) ) ) ) ) ) ).
tt(t46_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B k6_numbers 1) = (k4_subset_1 (k8_afinsq_1 A) (k4_flang_1 A (k2_flang_1 A)) B)) ) ) ) ).
tt(t46_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k5_afinsq_1 A) (k1_flang_3 B C D)) <=>  ((r2_hidden (k5_afinsq_1 A) C) &  ((r2_hidden (k2_flang_1 B) C) | (r1_xxreal_0 D 1)) ) ) ) ) ) ) ) ) ).
tt(t46_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) => (r1_tarski (k21_fomodel0 B) (k21_fomodel0 A))) ) ) ) ).
tt(t46_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v5_fsm_1 C A B) & (l2_fsm_1 C A B)) ) )  => (r7_fsm_1 A B C (k11_fsm_1 A B C))) ) ) ) ) ) ).
tt(t46_funcop_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v1_funct_1 (k8_funcop_1 B A C)) &  ((v1_funct_2 (k8_funcop_1 B A C) A B) & (m1_subset_1 (k8_funcop_1 B A C) (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(t46_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = (k3_xboole_0 (k9_xtuple_0 C) A))  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) )  =>  (B = (k5_relat_1 C A)) ) ) ) ) ) ) ).
tt(t46_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 A)))) )  =>  ((k8_relset_1 k1_xboole_0 A C B) = k1_xboole_0) ) ) ) ) ).
tt(t46_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = k1_xboole_0) )  =>  ((k10_xtuple_0 (k8_funct_3 A B)) = B) ) ) ) ).
tt(t46_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  =>  ((k9_xtuple_0 (k2_funct_4 C)) = (k2_zfmisc_1 B A)) ) ) ) ) ) ).
tt(t46_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k10_xtuple_0 C) (k1_funct_2 A B)) &  ((r1_tarski (k10_xtuple_0 D) (k1_funct_2 A B)) &  ((k2_funct_5 C) = (k2_funct_5 D)) ) )  =>  ( (A = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ).
tt(t46_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (~ (r2_hidden k1_xboole_0 (k10_xtuple_0 A)))  =>  ((k8_funct_6 A k1_xboole_0) = (k7_funcop_1 (k9_xtuple_0 A) k1_xboole_0)) ) ) ) ).
tt(t46_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k9_xtuple_0 B) A) =>  ((k4_funct_7 A (k9_finseq_1 B)) = B) ) ) ) ) ).
tt(t46_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v4_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t46_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ( ((v15_functor0 C A B) & (v5_functor0 C A B))  => (v7_functor0 C A B)) ) ) ) ) ) ) ).
tt(t46_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k6_fuzzy_1 A B B) (k1_fuzzy_1 A B (k3_fuzzy_1 A B)))) ) ) ) ).
tt(t46_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r2_funct_2 A k1_numbers (k3_fuzzy_2 A B (k1_fuzzy_1 A C D)) (k1_fuzzy_1 A (k3_fuzzy_2 A B C) (k3_fuzzy_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t46_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_funct_2 (u1_struct_0 A) k7_numbers (k5_fvaluat1 A (k5_fvaluat1 A B)) (k5_fvaluat1 A B))) ) ) ) ) ).
tt(t46_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (C = (k8_fvsum_1 A B (k4_fvsum_1 A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t46_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((v2_gcd_1 B A) &  ((r8_gcd_1 A B C D) & (r8_gcd_1 A B E F)) )  => (r8_gcd_1 A B (k8_gcd_1 A B C D E F) (k9_gcd_1 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((r1_xxreal_0 (k3_finseq_1 G) A) =>  ((k11_genealg1 F G H A B C D E) = (k10_genealg1 F G H B C D E)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) B) =>  ((k11_genealg1 F G H A B C D E) = (k10_genealg1 F G H A C D E)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) C) =>  ((k11_genealg1 F G H A B C D E) = (k10_genealg1 F G H A B D E)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) D) =>  ((k11_genealg1 F G H A B C D E) = (k10_genealg1 F G H A B C E)) )  &  ((r1_xxreal_0 (k3_finseq_1 G) E) =>  ((k11_genealg1 F G H A B C D E) = (k10_genealg1 F G H A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v2_struct_0 (k7_geomtrap A B C)))  &  ((v2_geomtrap (k7_geomtrap A B C)) & (l1_geomtrap (k7_geomtrap A B C))) ) ) ) ) ) ) ) ) ).
tt(t46_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k19_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t46_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((m2_glib_000 F A B D) =>  (! [G:$i] :  ((m2_glib_000 G A C E) =>  ( ((r1_tarski C B) &  ((r1_tarski E D) &  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  & (r1_tarski E (k21_glib_000 A C))) ) )  => (m1_glib_000 G F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden D (k1_relset_1 k5_numbers (k8_glib_001 A B 1 C))) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k1_funct_1 (k8_glib_001 A B 1 C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((v3_glib_002 A) <=>  ((v2_glib_002 A) &  ((k15_glib_000 A) = (k2_nat_1 (k17_glib_000 A) 1)) ) ) ) ) ).
tt(t46_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) => (r1_tarski (k11_glib_003 A) (k11_glib_003 (k12_glib_003 A B C)))) ) ) ) ) ).
tt(t46_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)))))) ) ) ) ) ) ).
tt(t46_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 B)))  =>  ( ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 B C E) &  ( ((k17_finseq_1 B A C) = (k17_finseq_1 B A D))  &  ((r1_gobrd13 B C E (k7_nat_d A 1)) & (r1_gobrd13 B D E (k7_nat_d A 1))) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((k17_finseq_1 B (k2_nat_1 A 1) C) = (k17_finseq_1 B (k2_nat_1 A 1) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_graph_2 D A) & (m2_graph_1 D A))  =>  ( ((r1_graph_2 A B D) & (r1_graph_2 A C D))  =>  ((r1_xxreal_0 (k3_finseq_1 D) 2) |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v2_funct_1 E) & (m2_graph_1 E (k8_graph_3 A B C)))  =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k8_graph_3 A B C))) =>  ( ( (D = F)  & (r1_graph_2 (k8_graph_3 A B C) F E))  =>  ((r2_hidden (u4_struct_0 A) (k10_xtuple_0 E)) | (r1_graph_2 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ((r5_graph_5 B A) => (r6_graph_5 B A)) ) ) ) ) ).
tt(t46_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) => (r2_graphsp C (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) C) (k2_nat_1 (k4_nat_1 3 A) 1) (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 3 A)))) ) ) ) ) ) ).
tt(t46_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r5_polyred A B C D E (k1_groeb_1 A C G)) &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  (~  ((r2_hidden H (k2_polynom1 (k15_pre_poly A) C F)) & (r3_pre_poly A (k3_termord A B C G) H)) ) ) ) )  => (r5_polyred A B C (k5_polynom1 A C D F) (k5_polynom1 A C E F) (k1_groeb_1 A C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k1_group_11 A B E) (k9_subset_1 (u1_struct_0 A) (k1_group_11 A B C) (k1_group_11 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_group_1,ax, ( (~ (v2_struct_0 (g3_algstr_0 k1_numbers k33_binop_2)))  &  ((v2_group_1 (g3_algstr_0 k1_numbers k33_binop_2)) &  ((v3_group_1 (g3_algstr_0 k1_numbers k33_binop_2)) &  ((v5_group_1 (g3_algstr_0 k1_numbers k33_binop_2)) & (l3_algstr_0 (g3_algstr_0 k1_numbers k33_binop_2))) ) ) ) ).
tt(t46_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (r1_struct_0 B (k1_group_1 A))) ) ) ) ).
tt(t46_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_group_3 A (k5_group_3 A C B) D) = (k5_group_3 A (k2_group_2 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t46_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k5_group_2 A B (k7_group_4 A C D)) = (k12_group_2 A C (k14_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t46_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A (k2_group_3 A (k3_group_5 A B (k2_group_1 A C) D) C) (k2_group_3 A (k3_group_5 A C (k2_group_1 A D) B) D)) (k2_group_3 A (k3_group_5 A D (k2_group_1 A B) C) B)) = (k1_group_1 A)) ) ) ) ) ) ) ) ) ).
tt(t46_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r1_group_2 B (k10_group_6 A B C) (k5_group_4 B (k2_relset_1 (u1_struct_0 B) C)))) ) ) ) ) ) ).
tt(t46_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E (k2_group_1 B D)) = (k2_group_1 C (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r2_hidden D (k13_glib_001 A (k2_helly A B C))) =>  ((k3_helly A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t46_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k5_square_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C D))) (k8_real_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)) (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B D D))))) ) ) ) ) ) ) ) ).
tt(t46_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers A))  => (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k6_partfun1 k1_numbers)) A) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 2)) (k1_real_1 1)) A))) ) ) ).
tt(t46_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 (k4_hilbert1 C A) (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(t46_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k7_hurwitz (k8_polynom3 k1_complfld A B)) (k8_polynom3 k1_complfld (k7_hurwitz A) (k7_hurwitz B)))) ) ) ) ).
tt(t46_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_matrix_1 D k5_numbers B 6) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  ( ((r1_xxreal_0 E B) &  ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 F)) &  ((r1_idea_1 A (k1_recdef_1 F 1)) &  ((r1_idea_1 A (k1_recdef_1 F 2)) &  ((r1_idea_1 A (k1_recdef_1 F 3)) &  ((r1_idea_1 A (k1_recdef_1 F 4)) &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r1_xxreal_0 G E) =>  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 1)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 2)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 3)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 4)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 5)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C G 6)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 1)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 2)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 3)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 4)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 5)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D G 6)) &  ( ((k3_matrix_1 k5_numbers D G 1) = (k10_idea_1 A (k3_matrix_1 k5_numbers C G 1)))  &  ( ((k3_matrix_1 k5_numbers D G 2) = (k6_idea_1 A (k3_matrix_1 k5_numbers C G 3)))  &  ( ((k3_matrix_1 k5_numbers D G 3) = (k6_idea_1 A (k3_matrix_1 k5_numbers C G 2)))  &  ( ((k3_matrix_1 k5_numbers D G 4) = (k10_idea_1 A (k3_matrix_1 k5_numbers C G 4)))  &  ( ((k3_matrix_1 k5_numbers C G 5) = (k3_matrix_1 k5_numbers D G 5))  &  ((k3_matrix_1 k5_numbers C G 6) = (k3_matrix_1 k5_numbers D G 6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k4_funct_7 k14_idea_1 (k7_finseq_1 (k17_idea_1 E B A C) (k18_idea_1 E B A D))) F) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k9_ideal_1 A B) = B) ) ) ) ) ).
tt(t46_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r5_incsp_1 A (k7_domain_1 (u1_incsp_1 A) D E) C) &  (~ (v3_incsp_1 (k8_domain_1 (u1_incsp_1 A) B D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 (k4_int_1 A) k6_numbers))  & (v1_int_1 A)) )  &  (~  ( (~ (v1_int_1 A))  & (r1_xxreal_0 (k4_int_1 A) k6_numbers)) ) ) ) ) ).
tt(t46_int_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v7_ordinal1 C))  =>  ((k5_nat_d (k6_nat_d A C) (k6_nat_d B C)) = (k6_nat_d (k5_nat_d A B) C)) ) ) ) ) ) ) ).
tt(t46_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k8_rvsum_1 (k8_finseq_1 k1_numbers A C) (k8_finseq_1 k1_numbers B D)) = (k8_finseq_1 k1_numbers (k8_rvsum_1 A B) (k8_rvsum_1 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_integr11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B C) &  ((r1_tarski C (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k10_real_1 A (k7_real_1 1 (k5_square_1 E)))) ) ) )  &  ( (C = (k9_xtuple_0 D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers k1_sin_cos9 A) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers k1_sin_cos9 A) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t46_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2))))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k1_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k1_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t46_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k1_seq_1 k16_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k29_sin_cos D) (k1_seq_1 k19_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t46_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) D) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) E) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers D)) & (r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers E))) ) ) )  =>  ( ((k6_integr18 (k4_real_ns1 A) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) D E) B C) = (k3_rlvect_1 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) D B C) (k6_integr18 (k4_real_ns1 A) E B C)))  &  ((k6_integr18 (k4_real_ns1 A) (k2_vfunct_1 k1_numbers (k4_real_ns1 A) D E) B C) = (k5_algstr_0 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) D B C) (k6_integr18 (k4_real_ns1 A) E B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((r1_integra1 B C) & (v2_seq_2 (k2_partfun1 A k1_numbers D A)))  => (r1_xxreal_0 (k7_integra1 A D B) (k7_integra1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t46_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k5_seq_4 A)))) ) ) ).
tt(t46_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (~ (r2_hidden (k1_real_1 A) B))  => (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_fcont_1 1 A)) B))) ) ) ) ) ).
tt(t46_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( (B = (k2_interva1 A C D))  & (r1_tarski C D))  =>  ((k10_interva1 A B) = (k2_interva1 A (k3_subset_1 A D) (k3_subset_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t46_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A B) (k4_intpro_1 B A)) k8_intpro_1)) ) ) ) ).
tt(t46_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( ((r2_isocat_1 A B) & (r2_isocat_1 B C))  => (r2_isocat_1 A C)) ) ) ) ) ) ) ).
tt(t46_jgraph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  (~  ((v1_compts_1 A) &  ((v8_pre_topc B) &  ((v5_pre_topc C A B) &  ((v2_funct_1 C) &  ( (D = (k2_relset_1 (u1_struct_0 B) C))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)))))) )  =>  (~  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k1_pre_topc B D)) C E) & (v3_tops_2 E A (k1_pre_topc B D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jgraph_2,ax, ( ((v4_pre_topc a_0_4_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_4_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((v4_pre_topc a_0_5_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_5_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(t46_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ( (~ (r1_xxreal_0 (k13_complex1 (k18_euclid C) (k12_euclid C)) (k13_complex1 (k18_euclid B) (k12_euclid B))))  &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  &  ( (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) C))  & (r1_xxreal_0 (k13_complex1 (k18_euclid E) (k12_euclid E)) (k13_complex1 (k18_euclid D) (k12_euclid D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r1_jordan6 C A B) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) & (r1_xxreal_0 k6_numbers (k18_euclid B))) ) )  =>  ( (A = B)  |  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ( ((k18_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid A C))  &  ((k22_pscomp_1 (k1_sppol_2 A B C D)) = (k19_euclid B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = F)  &  ( ((k17_euclid B) = F)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 (k18_euclid A) H) &  ((r1_xxreal_0 G (k18_euclid B)) & (r1_xxreal_0 (k17_euclid C) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 D B)))) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) (k1_jordan1a (k1_jordan8 D B)) C)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D A) (k1_jordan1a (k1_jordan8 D A)) (k3_finseq_1 (k1_jordan8 D A)))))) ) ) ) ) ) ) ) ) ).
tt(t46_jordan1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) => (v1_convex1 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) A B) (k2_tarski A B)) (k15_euclid 2))) ) ) ) ).
tt(t46_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 B A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k1_jordan9 B A))) & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)) (k3_topreal1 2 (k2_jordan1e B A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((v2_connsp_1 C (k15_euclid 2)) & (r1_xxreal_0 A B))  => (r1_tarski (k3_topreal1 2 (k1_jordan9 C B)) (k2_pre_topc (k15_euclid 2) (k3_goboard9 (k1_jordan9 C A))))) ) ) ) ) ) ) ).
tt(t46_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k3_topreal1 2 (k1_jordan1e B A))) &  ((k17_euclid C) = (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) )  =>  (C = (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t46_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) &  ((r2_hidden D B) &  ((k5_jordan1k A C B) = (k1_topreal6 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan21,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r1_tarski A B) &  ((r2_hidden (k2_jordan21 B) A) &  ((v3_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B)) 2))))) &  ((k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) = (k7_real_1 (k6_pscomp_1 B) (k8_pscomp_1 B))) ) ) )  =>  ((v1_xboole_0 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) |  ((k2_jordan21 A) = (k2_jordan21 B)) ) ) ) ) ) ) ).
tt(t46_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (~  (B = (k5_euclid A)) )  &  ( (B = C)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  (~  ((k1_funct_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) )  => (r1_jordan3 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k7_nat_d (k3_finseq_1 A) 1)) B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))) ) ) ) ) ).
tt(t46_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_jordan4 A B C D) =>  ( (C = D)  | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 (k4_jordan5d A)) &  ((r1_xxreal_0 (k4_jordan5d A) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k3_jordan5d A)) &  ((r1_xxreal_0 (k3_jordan5d A) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k2_jordan5d A)) &  ((r1_xxreal_0 (k2_jordan5d A) (k1_matrix_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 (k1_jordan5d A)) & (r1_xxreal_0 (k1_jordan5d A) (k1_matrix_1 (k2_goboard2 A)))) ) ) ) ) ) ) ) ) ).
tt(t46_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) D E B) &  ((r1_topreal1 (k15_euclid A) D E C) & (r1_tarski B C)) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_tarski (k1_jgraph_6 A B C D) (k2_jgraph_6 A B C D))) ) ) ) ) ) ) ) ).
tt(t46_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A)))))) )  =>  ((v14_quantal1 B (k1_lattice3 A)) <=> (v6_cohsp_1 B)) ) ) ) ) ).
tt(t46_kurato_1,ax,(r1_zfmisc_1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))))).
tt(t46_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 C)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F D) => (r3_lattices A B (k3_funct_2 C (u1_struct_0 A) E F))) ) )  =>  ( (D = k1_xboole_0)  | (r3_lattices A B (k3_lattice2 C A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ((k15_lattice3 A B) = (k15_lattice3 A (a_2_5_lattice3 A B)))  &  ((k16_lattice3 A B) = (k16_lattice3 A (a_2_6_lattice3 A B))) ) ) ) ) ).
tt(t46_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C B))  =>  (! [D:$i] :  (~  ( (~ (r2_hidden (k7_nat_d (k15_glib_000 A) B) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) (k1_nat_1 B 1))) D)))  & (r2_hidden (k7_nat_d (k15_glib_000 A) B) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) C)) D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v4_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ((r2_hidden D (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 (k1_seq_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc2 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k9_real_1 (k1_limfunc2 B A) (k1_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t46_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ( ((k1_limfunc3 B A) = k6_numbers)  &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 A E))  &  ((r2_hidden E (k9_xtuple_0 B)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F A))  &  ((r2_hidden F (k9_xtuple_0 B)) &  ( (~  ((k1_seq_1 B E) = k6_numbers) )  &  (~  ((k1_seq_1 B F) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A C) A) (k2_rcomp_1 A (k7_real_1 A C))))) => (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) )  | (r3_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A)) ) ) ) ) ) ).
tt(t46_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r3_limfunc3 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) &  ((k1_seq_1 A D) = (k4_limfunc1 A)) ) ) ) ) )  | (v5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t46_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k18_lpspace1 A B C))) &  ((r2_hidden D F) & (r2_hidden E F)) ) )  =>  ((r1_lpspace1 A B C D E) &  ((r2_hidden D (k9_lpspace1 A B C)) & (r2_hidden E (k9_lpspace1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  ( ((k5_lpspace2 A B C D G) = (k5_lpspace2 A B C E G))  =>  ( (! [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A H)) = k6_numbers)  &  ( ((k1_relset_1 A D) = H)  & (r1_mesfunc6 A B D H)) ) ) ) )  |  ( (! [H:$i] :  ((m2_subset_1 H (k1_zfmisc_1 A) B) =>  (~  ( ((k1_funct_1 C (k3_subset_1 A H)) = k6_numbers)  &  ( ((k1_relset_1 A E) = H)  & (r1_mesfunc6 A B E H)) ) ) ) )  |  ((v1_xboole_0 (k5_lpspace2 A B C D G)) |  ((k5_lpspace2 A B C (k26_valued_1 A k1_numbers D F) G) = (k5_lpspace2 A B C (k26_valued_1 A k1_numbers E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 D (k3_hilbert1 A (k4_ltlaxio1 B C))) =>  ((r8_ltlaxio1 D (k3_hilbert1 A B)) & (r8_ltlaxio1 D (k3_hilbert1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t46_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k5_cqc_lang A)) A) & (v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A (k5_cqc_lang A)) B) A)) ) ) ) ) ).
tt(t46_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_mathmorp A (k1_mathmorp A D B) C) = (k1_mathmorp A D (k4_mathmorp A B C))) ) ) ) ) ) ) ) ) ).
tt(t46_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ( ((r1_matrix10 B C) & (r1_matrix10 D E))  => (r1_matrix10 (k3_matrix10 A B D) (k3_matrix10 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 E (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) )  =>  ( (D = E)  =>  ((k12_matrix_3 A B (k4_matrix11 A A (u1_struct_0 B) E C)) = (k14_matrix_2 B A (k12_matrix_3 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ((k6_matrix13 A B (k2_finseq_1 (k3_finseq_1 B)) (k2_finseq_1 (k1_matrix_1 B))) = B) ) ) ) ) ).
tt(t46_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ( (C = 1)  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B)) ) )  =>  ( ( (E = F)  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( (~  (E = F) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) )  =>  (D = (k4_matrix14 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) | (r1_tarski (k4_matrix15 B C D) (k4_matrix15 B (k8_matrix_2 B A C) (k8_matrix_2 B A D)))) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v4_matrix16 C (u1_struct_0 A)) => (v4_matrix16 (k9_fvsum_1 A C B) (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t46_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  => (r1_xxreal_0 (k5_card_1 (k16_matrix_1 B)) (k4_nat_1 (k3_finseq_1 B) (k1_matrix_1 B)))) ) ) ) ).
tt(t46_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A B) C) D) = (k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A B) D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v4_matrix_6 C A B) & (v4_matrix_6 D A B))  =>  ((r1_xxreal_0 A k6_numbers) | (v4_matrix_6 (k4_matrix_6 A B C D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_8 A B (k2_matrix_6 A B C C) (k2_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  ((k12_matrix_3 3 A K) = (k1_algstr_0 A (k5_algstr_0 A (k1_algstr_0 A (k5_algstr_0 A (k5_algstr_0 A (k8_group_1 A (k8_group_1 A B F) J) (k8_group_1 A (k8_group_1 A D F) H)) (k8_group_1 A (k8_group_1 A B G) I)) (k8_group_1 A (k8_group_1 A C G) H)) (k8_group_1 A (k8_group_1 A C E) J)) (k8_group_1 A (k8_group_1 A D E) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ((k17_rvsum_1 (k8_finseq_1 k2_numbers A B)) = (k3_binop_2 (k17_rvsum_1 A) (k17_rvsum_1 B))) ) ) ) ) ).
tt(t46_matrixj1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v2_matrixj1 B A) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 A))))  =>  ((k10_matrixj1 A B) = (k11_matrixj1 A B)) ) ) ) ) ).
tt(t46_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k9_matrixr1 (k4_rvsum_1 A B)) = (k3_matrixr1 (k9_matrixr1 A) (k9_matrixr1 B))) ) ) ) ) ) ) ).
tt(t46_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((k3_matrixr2 A (k1_matrixr2 A B C)) = (k8_real_1 (k3_matrixr2 A B) (k3_matrixr2 A C))) ) ) ) ) ) ) ).
tt(t46_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A B) =>  (! [D:$i] :  ((m1_matrlin D A (k6_prvect_1 A (k3_finseq_1 C))) =>  ( (D = (k11_matrix13 A (k3_finseq_1 C) (k3_finseq_1 C) (k12_matrix_1 A (k3_finseq_1 C))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_prvect_1 A (k3_finseq_1 C)))) =>  ((k9_matrlin A (k6_prvect_1 A (k3_finseq_1 C)) D E) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((k23_rvsum_1 (k12_matrixr1 C A) B) = (k5_matrprob (k6_matrprob A B C))) ) ) ) ) ) ) ) ).
tt(t46_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) B A) =>  (~  ( ((k8_matrix13 k2_vectsp_1 C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E B) &  ((v1_finseq_1 E) & (v3_valued_0 E)) ) ) )  => (r1_xxreal_0 (k12_euclid E) (k11_binop_2 D (k12_euclid (k1_funct_1 (k3_matrtop1 B A C) E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden A B) <=> (r2_hidden (k7_real_1 C A) (k2_measure6 B C))) ) ) ) ) ) ) ).
tt(t46_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k3_binop_2 C D) (k9_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t46_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  ( ((k5_memstr_0 A B C) = k6_numbers)  =>  ((k8_memstr_0 A B C) = C) ) ) ) ) ) ) ) ).
tt(t46_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski C (k1_relset_1 A D)) =>  ((k8_subset_1 A C (k14_mesfunc1 D E)) = (k7_subset_1 A C (k8_subset_1 A C (k11_mesfunc1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_mesfun7c,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 (k6_complsp2 A))) =>  ((k1_seq_1 (k6_complsp2 A) B) = (k3_complex1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t46_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) &  ((v1_mesfunc8 E A k7_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers)))  &  ( (D = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E G) D)) )  &  ((r1_mesfunc5 A B C F) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G D) => (r1_xxreal_0 (k1_mesfunc9 (k10_mesfunc1 A (k4_mesfunc5 A k7_numbers E H)) G) (k1_mesfunc9 F G))) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) => (v10_mesfunc5 (k3_mesfunc5 A E G))) ) ) ) ) ) ) )  => (r1_mesfunc5 A B C (k7_mesfunc8 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r2_hidden (k8_relset_1 A k7_numbers D (k1_tarski k1_supinf_1)) B) &  ((r2_hidden (k8_relset_1 A k7_numbers D (k1_tarski k2_supinf_1)) B) &  ((r2_hidden (k8_relset_1 A k7_numbers E (k1_tarski k1_supinf_1)) B) & (r2_hidden (k8_relset_1 A k7_numbers E (k1_tarski k2_supinf_1)) B)) ) )  =>  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A D))  & (r1_mesfunc1 A B D F)) ) ) )  |  ( (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A E))  & (r1_mesfunc1 A B E F)) ) ) )  | (r2_hidden (k1_relset_1 A (k3_mesfunc1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r1_mesfunc6 A B C D) => (r1_mesfunc6 A B (k18_rfunct_3 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t46_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers)))  &  ((v2_mesfunc9 E A) &  ((v1_mesfunc8 E A k7_numbers) &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E H) D) &  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers E H)) &  ((k1_mesfunc9 F H) = (k7_mesfunc5 A B C (k4_mesfunc5 A k7_numbers E H))) ) ) ) ) ) ) )  =>  ((k7_mesfunc5 A B C (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A E) G)) = (k1_mesfunc9 (k2_mesfunc9 F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  ((k7_midsp_1 A B C) = (k7_midsp_1 A C B)) ) ) ) ) ) ) ).
tt(t46_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_mmlquery D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((r2_hidden B (k1_mmlquery A D C)) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t46_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k3_modal_1) =>  (! [B:$i] :  ((m1_subset_1 B k6_modal_1) =>  (! [C:$i] :  ((m1_subset_1 C k6_modal_1) =>  ( (~  (k17_modal_1 = (k16_modal_1 A)) )  &  ( (~  (k17_modal_1 = (k10_modal_1 B)) )  &  ( (~  (k17_modal_1 = (k11_modal_1 B)) )  &  (~  (k17_modal_1 = (k12_modal_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r3_modelc_1 A B C F (k27_modelc_1 (k48_modelc_1 A B C) D E)) <=> (r3_modelc_1 A B C F (k59_modelc_1 A B C D E (k27_modelc_1 (k48_modelc_1 A B C) D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_modelc_2 A B) => (r1_tarski (k13_modelc_2 A) (k13_modelc_2 B))) ) ) ) ) ).
tt(t46_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r7_modelc_3 A B C) => (r8_modelc_3 A B C)) ) ) ) ) ) ) ).
tt(t46_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  ((k3_relat_1 (k9_finseq_1 A) (k5_moebius1 A)) = (k9_finseq_1 A)) ) ) ).
tt(t46_monoid_0,ax, (k5_monoid_0 = (g4_algstr_0 k5_numbers k47_binop_2 k6_numbers)) ).
tt(t46_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((k2_binop_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) (k1_zfmisc_1 C) (k21_monoid_1 A B C D) E F) = (a_6_0_monoid_1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  ((r2_pboole A C D) => (r2_pboole A (k4_mssubfam A B D) (k4_mssubfam A B C))) ) ) ) ) ) ) ) ).
tt(t46_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  => (v4_msualg_6 (k9_msualg_6 A B C) A B)) ) ) ) ) ) ).
tt(t46_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_necklace B) & (m1_mycielsk B A))  =>  ((r1_xxreal_0 2 (k1_dilworth B)) =>  ((k1_dilworth B) = (k1_dilworth (k6_mycielsk A B))) ) ) ) ) ) ).
tt(t46_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  (A = (k3_xboole_0 A B)) ) ) ) ) ) ).
tt(t46_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k1_polynom2 k10_newton (k12_nat_3 (k24_binop_2 A B))) = (k4_subset_1 k10_newton (k1_polynom2 k10_newton (k12_nat_3 A)) (k1_polynom2 k10_newton (k12_nat_3 B)))) ) ) ) ) ).
tt(t46_nat_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 2 A) => (r1_xxreal_0 (k3_wsierp_1 (k14_finseq_1 (a_1_1_nat_4 A))) (k4_power 4 (k9_real_1 A 1)))) ) ) ).
tt(t46_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k1_nat_1 A 1) B) =>  ( (~ (r1_xxreal_0 B (k7_nat_d A 1)))  &  ( (~ (r1_xxreal_0 B (k7_nat_d A 2)))  & (r1_xxreal_0 A B)) ) ) ) ) ) ) ).
tt(t46_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  ((k12_nattra_1 (k12_nattra_1 A)) = (k12_nattra_1 A)) ) ) ).
tt(t46_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r9_ncfcont1 B A D C) <=>  ((r1_tarski C (k1_relset_1 (u1_struct_0 B) D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden E C) &  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (~  ((r2_hidden H C) &  ( (~ (r1_xxreal_0 G (k1_normsp_0 B (k5_algstr_0 B H E))))  & (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) D H) (k7_partfun1 (u1_struct_0 A) D E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_ndiff_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B)))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 C))) =>  ( ((v3_nfcont_1 E C) &  ((r2_ndiff_1 A C B D) & (r1_tarski E A)) )  => (r2_ndiff_1 E C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_ndiff_3 B (k4_real_ns1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) B k6_numbers) = (k4_struct_0 (k4_real_ns1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (~ (r1_xxreal_0 D (k17_complex1 E)))  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 A) (k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) B E)) (k11_binop_2 C (k17_complex1 E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A B))) =>  ( (D = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) E))  =>  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_nat_d A 1) = A) ) ) ).
tt(t46_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ((r6_nfcont_1 B A C) => (r4_nfcont_1 B C A)) ) ) ) ) ) ).
tt(t46_nfcont_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B))))))  =>  ((r1_nfcont_3 (k4_real_ns1 B) C A) <=>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k2_finseq_1 B)) => (r1_nfcont_3 (k4_real_ns1 1) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 B)) (u1_struct_0 (k4_real_ns1 1)) C (k4_pdiff_1 D B)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t46_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  ((r1_tarski B C) => (r1_tarski (k10_normform A B D) (k10_normform A C D))) ) ) ) ) ) ) ) ).
tt(t46_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k5_oppcat_1 A D)) = (k5_oppcat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t46_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r3_orders_1 A B) =>  ((v1_relat_2 (k2_wellord1 A B)) &  ((v4_relat_2 (k2_wellord1 A B)) &  ((v8_relat_2 (k2_wellord1 A B)) &  ((v1_partfun1 (k2_wellord1 A B) B) & (m1_subset_1 (k2_wellord1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) ) ) ) ).
tt(t46_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_relat_1 (k2_wellord1 (u1_orders_2 A) B)) = B) ) ) ) ) ).
tt(t46_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( ((k12_ordinal2 A 1) = A)  &  ((k12_ordinal2 1 A) = 1) ) ) ) ).
tt(t46_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k11_ordinal2 (k10_ordinal2 A B) C) = (k10_ordinal2 (k11_ordinal2 A C) (k11_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t46_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v4_ordinal1 A) =>  ( (A = k1_xboole_0)  |  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ( ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k3_ordinal5 C)) ) ) ) )  =>  ((k3_ordinal5 A) = (k3_card_3 B)) ) ) ) ) ) ) ) ).
tt(t46_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  => (v1_ordinal6 (a_1_1_ordinal6 A))) ) ).
tt(t46_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t46_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  => (r8_pboole (u1_struct_0 A) (k15_osafree A B) (k20_osafree A B))) ) ) ) ).
tt(t46_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (v1_binop_1 (k15_osalg_2 A B) (k13_osalg_2 A B))) ) ) ) ).
tt(t46_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D D) =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t46_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k4_partfun1 A B)) =>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(t46_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden C (k1_relset_1 A E)) &  (D = (k7_partfun1 B E C)) )  <=> (r2_hidden (k4_tarski C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B C) & (r6_pboole A (k3_pboole A C D) (k1_pboole A)))  => (r6_pboole A (k3_pboole A B D) (k1_pboole A))) ) ) ) ) ) ) ) ).
tt(t46_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k25_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k25_pcs_0 A B))) =>  ((r1_pcs_0 (k25_pcs_0 A B) C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r1_pcs_0 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r1_pdiff_5 B A) & (r1_pdiff_5 C A))  =>  ((r3_pdiff_1 3 1 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 1 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k7_real_1 (k1_pdiff_5 B A) (k1_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t46_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ( ((k3_finseq_1 B) = (k23_binop_2 A 1))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 B)) =>  ((k7_partfun1 (k1_euclid A) B F) = (k8_finseq_1 k1_numbers (k17_finseq_1 k1_numbers (k7_nat_d (k23_binop_2 A 1) F) C) (k5_euclid (k7_nat_d F 1)))) ) ) ) ) ) )  =>  ((k7_euclid A D (k7_partfun1 (k1_euclid A) B E)) = (k3_funct_2 k1_numbers (k1_euclid A) (k6_pdiff_1 A (k7_nat_d (k23_binop_2 A 1) E) (k7_euclid A D (k7_partfun1 (k1_euclid A) B (k23_binop_2 E 1)))) (k1_seq_1 (k1_pdiff_1 (k7_nat_d (k23_binop_2 A 1) E) A) (k7_euclid A D C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_pdiff_9 A B C) &  ((r1_pdiff_9 A B D) &  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_tarski B (k1_relset_1 (k1_euclid A) D))) ) )  =>  ((r1_pdiff_9 A B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)) & (r1_pdiff_9 A B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers C D))) ) ) ) ) ) ) ) ) ).
tt(t46_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k3_pepin 1 A) = 1) ) ) ) ).
tt(t46_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  (! [D:$i] :  ((m3_pnproc_1 D A B) =>  ((k11_pnproc_1 A B (k6_domain_1 (k3_finseq_2 B) (k3_pre_poly B C)) (k6_domain_1 (k3_finseq_2 B) (k3_pre_poly B D))) = (k7_domain_1 (k3_finseq_2 B) (k4_pre_poly B C D) (k4_pre_poly B D C))) ) ) ) ) ) ) ) ).
tt(t46_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k17_polyform A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  ((k20_polyform A B (k3_rlvect_1 (k17_polyform A B) C D)) = (k3_rlvect_1 (k17_polyform A (k6_xcmplx_0 B 1)) (k20_polyform A B C) (k20_polyform A B D))) ) ) ) ) ) ) ) ) ).
tt(t46_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_group_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k4_polynom5 A (k4_struct_0 A) C) D) = (k6_algstr_0 A C D)) ) ) ) ) ) ) ) ) ).
tt(t46_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom7 G A C) &  ((v3_polynom7 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ((r5_polyred A B C E F D) => (r5_polyred A B C (k10_polynom1 A C G E) (k10_polynom1 A C G F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_power A 2) = (k3_square_1 A)) ) ) ).
tt(t46_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (! [D:$i] :  ((r2_hidden D A) => (r1_xxreal_0 (k1_funct_1 B D) (k1_funct_1 C D))) )  => (r3_pre_poly A B C)) ) ) ) ) ) ).
tt(t46_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 A k6_numbers) |  ((k4_prepower (k2_prepower B A) C) = (k2_prepower B (k4_prepower A C))) ) ) ) ) ) ) ) ) ).
tt(t46_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ((m2_prob_1 D A B) =>  ((v1_prob_2 C) =>  ((k1_funct_1 D (k1_kurato_0 A C)) = (k4_series_1 (k8_prob_1 A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t46_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k7_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k9_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t46_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k18_euclid (k13_pscomp_1 A)) (k18_euclid (k23_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k13_pscomp_1 A)) (k18_euclid (k22_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k13_pscomp_1 A)) (k18_euclid (k12_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k23_pscomp_1 A)) (k18_euclid (k22_pscomp_1 A))) &  ((r1_xxreal_0 (k18_euclid (k23_pscomp_1 A)) (k18_euclid (k12_pscomp_1 A))) & (r1_xxreal_0 (k18_euclid (k22_pscomp_1 A)) (k18_euclid (k12_pscomp_1 A)))) ) ) ) ) ) ) ).
tt(t46_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k3_pboole A (k1_pzfmisc1 A B) C) (k1_pboole A)) & (r1_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t46_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r1_qc_lang2 A B (k15_qc_lang1 A D C)) <=>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t46_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k3_qc_lang2 A B C)) = (k4_subset_1 D (k4_qc_lang3 A D B) (k4_qc_lang3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t46_quatern2,ax, ((k3_quatern2 (k5_struct_0 k16_quatern2)) = 1) ).
tt(t46_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k8_quatern2 (k27_quaterni A B)) = (k27_quaterni (k8_quatern2 B) (k8_quatern2 A))) ) ) ) ) ).
tt(t46_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k31_quaterni A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t46_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k19_quofield A)))  &  ( (~ (v6_struct_0 (k19_quofield A)))  &  ((v13_algstr_0 (k19_quofield A)) &  ((v33_algstr_0 (k19_quofield A)) &  ((v2_rlvect_1 (k19_quofield A)) &  ((v3_rlvect_1 (k19_quofield A)) &  ((v4_rlvect_1 (k19_quofield A)) &  ((v1_group_1 (k19_quofield A)) &  ((v3_group_1 (k19_quofield A)) &  ((v5_vectsp_1 (k19_quofield A)) & (l6_algstr_0 (k19_quofield A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_rcomp_3,ax, (! [A:$i] :  ( ((v13_struct_0 A 1) & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((m1_setfam_1 C (u1_struct_0 A)) => (r2_hidden (k1_tarski B) C)) ) ) ) ) ) ) ).
tt(t46_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers) k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 A) (k1_nat_1 B 2)) (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 2)) (k3_funct_2 k5_numbers k1_numbers (k5_real_3 A) (k1_nat_1 B 1))))) ) ) ) ) ) ).
tt(t46_relat_1,ax, (! [A:$i] :  ((k2_relat_1 (k4_relat_1 A)) = (k4_relat_1 A)) ) ).
tt(t46_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((k7_relset_1 A B C D) = (k7_relset_1 A B C (k3_xboole_0 D (k9_xtuple_0 C)))) ) ) ) ) ) ).
tt(t46_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( (~ (r2_hidden B (k1_relat_1 A)))  => (r9_rewrite1 A B)) ) ) ) ).
tt(t46_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r2_hidden C (k8_rewrite2 A B D)) <=> (r3_rewrite2 A B D C)) ) ) ) ) ) ) ) ).
tt(t46_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ((v2_rewrite3 C A B) => (v1_funct_1 (k1_rewrite3 A B C))) ) ) ) ) ) ) ).
tt(t46_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  ( ((k5_relat_1 (k30_valued_1 B) A) = (k30_valued_1 (k5_relat_1 B A)))  &  ( ((k5_relat_1 (k4_rfunct_1 B) A) = (k4_rfunct_1 (k5_relat_1 B A)))  &  ((k5_relat_1 (k54_valued_1 B) A) = (k54_valued_1 (k5_relat_1 B A))) ) ) ) ) ) ).
tt(t46_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers B (k1_tarski A)))) ) ) ).
tt(t46_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  => (r2_relset_1 A k1_numbers (k18_rfunct_3 A B) B)) ) ) ) ) ).
tt(t46_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 B) =>  ((k1_seq_1 (k3_rinfsup1 B) A) = (k3_xxreal_0 (k1_seq_1 (k3_rinfsup1 B) (k2_nat_1 A 1)) (k1_seq_1 B A))) ) ) ) ) ) ).
tt(t46_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden (k4_struct_0 A) B) =>  ((v1_rlaffin1 B A) <=> (v1_rlvect_3 (k7_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) A)) ) ) ) ) ) ).
tt(t46_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_rlsub_1 A B (k2_rlsub_1 A)) = (u1_struct_0 A)) ) ) ) ) ).
tt(t46_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( (A = (k1_rlsub_2 A B C))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (D = (k3_rlvect_1 A E F))  &  ( (D = (k3_rlvect_1 A G H))  &  ((r1_struct_0 B E) &  ((r1_struct_0 B G) &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  (~  ( (E = G)  &  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  | (r1_rlsub_2 A B C)) ) ) ) ) ) ) ) ).
tt(t46_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rltopsp1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rltopsp1 A C) B) = (k1_convex1 A B C)) ) ) ) ) ) ) ).
tt(t46_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k1_algstr_0 A (k1_algstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t46_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) => (r1_rlvect_2 A (k8_rlvect_2 A B (k7_rlvect_2 A C D)) (k7_rlvect_2 A (k8_rlvect_2 A B C) (k8_rlvect_2 A B D)))) ) ) ) ) ) ) ) ).
tt(t46_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_rmod_2 A B C (k1_rmod_2 A B)) = (k6_domain_1 (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(t46_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_rmod_3 A B C D) =>  ((k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_rmod_3 A B E C D)) = (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_rmod_3 A B E D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rmod_4 E A B) => (r1_rmod_4 A B (k7_rmod_4 A B (k3_rlvect_1 A C D) E) (k6_rmod_4 A B (k7_rmod_4 A B C E) (k7_rmod_4 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t46_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_robbins1 A B) = (k3_robbins1 A C))  =>  ((k9_robbins1 A B D) = (k9_robbins1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) (k5_robbins1 A B D))) C) = C) ) ) ) ) ) ) ) ) ).
tt(t46_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k3_subset_1 (u1_struct_0 A) B)) C) = (k6_xcmplx_0 1 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) C))) ) ) ) ) ) ) ).
tt(t46_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((r1_xxreal_0 (k1_rpr_1 A B) k6_numbers) |  ((r1_xxreal_0 1 (k1_rpr_1 A C)) |  ((k2_rpr_1 A (k3_subset_1 A C) B) = (k10_real_1 (k1_rpr_1 A B) (k9_real_1 1 (k1_rpr_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t46_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=>  ((k3_rusub_1 A D B) = (k3_rusub_1 A (k3_rlvect_1 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t46_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ( (A = (k1_rusub_2 A B C))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) &  ( (D = (k3_rlvect_1 A E F))  &  ( (D = (k3_rlvect_1 A G H))  &  ((r1_struct_0 B E) &  ((r1_struct_0 B G) &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  (~  ( (E = G)  &  (F = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  | (r1_rusub_2 A B C)) ) ) ) ) ) ) ) ).
tt(t46_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (C = k6_numbers)  => (v1_xboole_0 (k4_bhsp_2 A B C))) ) ) ) ) ) ) ).
tt(t46_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k10_rvsum_1 (k6_finseq_1 k1_numbers) A) = (k6_finseq_1 k1_numbers)) ) ) ).
tt(t46_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_rvsum_1 (k2_finseq_2 (k24_binop_2 A B) C)) = (k19_rvsum_1 (k2_finseq_2 B (k19_rvsum_1 (k2_finseq_2 A C))))) ) ) ) ) ) ) ).
tt(t46_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  => (r1_tarski k3_scmfsa_2 (k1_relset_1 (u1_struct_0 k1_scmfsa_2) A))) ) ).
tt(t46_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scmfsa8a B A (k2_scmfsa6a C)) & (r1_scmfsa8a B A (k2_scmfsa6a D)))  =>  ((r5_scmfsa7b (k2_scmfsa8b E C D) B A) & (r6_scmfsa7b (k2_scmfsa8b E C D) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r5_scmfsa7b B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E) (k1_funct_4 A (k2_scmfsa_9 C B))) & (r6_scmfsa7b B (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) E) (k1_funct_4 A (k2_scmfsa_9 C B)))) ) )  =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  =>  (~  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) (k1_nat_1 F 1)))) &  (~  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers) ) ) )  &  ( ( ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F) C) k6_numbers))  &  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F) C) k6_numbers) =>  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers) ) ) ) ) ) ) ) )  |  ((r6_scmfsa7b (k2_scmfsa_9 C B) D A) & (r5_scmfsa7b (k2_scmfsa_9 C B) D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B E) = k6_numbers)  &  ((r1_scm_halt D B A) & (r2_scm_halt D B A)) )  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k10_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k10_scmpds_2 D B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = C)  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (E = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k10_scmpds_2 D B C) A) E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r2_hidden k6_numbers (k9_xtuple_0 (k5_scmpds_6 A B C)))) ) ) ) ) ) ).
tt(t46_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k2_scmpds_7 D E F C) (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k2_nat_1 (k5_card_1 C) 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((r2_hidden B (k3_tarski A)) =>  ((k7_scmyciel A (k1_tarski B)) = (k2_tarski k1_xboole_0 (k1_tarski B))) ) ) ) ) ).
tt(t46_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_semi_af1 A B C D E) & (r2_analoaf A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A)) (k26_valued_1 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers B) (k5_xcmplx_0 A)))) ) ) ) ).
tt(t46_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D A) => (r1_xxreal_0 D C)) ) )  => (r1_xxreal_0 B C)) ) ) )  =>  (B = (k2_seq_4 A)) ) ) ) ) ) ).
tt(t46_seqm_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_tarski (k10_xtuple_0 A) (k2_finseq_1 B)) &  ( ((k1_seq_1 A 1) = 1)  &  ( ((k1_seq_1 A (k3_finseq_1 A)) = B)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k9_real_1 (k3_finseq_1 A) 1)))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (D = (k1_seq_1 A C))  &  ( (E = (k1_seq_1 A (k2_nat_1 C 1)))  &  ( (~  ((k18_complex1 (k9_real_1 D E)) = 1) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k2_finseq_1 B)) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 A)) &  ((k1_seq_1 A D) = C) ) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ( ((k1_seq_1 A C) = E)  &  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r2_hidden G (k4_finseq_1 A)) &  ((k1_seq_1 A G) = E) )  => (r1_xxreal_0 G C)) ) )  &  ( (~ (r1_xxreal_0 D C))  &  ((r2_hidden D (k4_finseq_1 A)) &  ( (F = (k1_seq_1 A D))  & (r1_xxreal_0 F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 1 (k1_seq_1 A B))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 1 (k1_seq_1 (k1_series_3 A) B))) ) ) ) ) ).
tt(t46_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 1 D))  => (r1_xxreal_0 (k3_xcmplx_0 (k2_xcmplx_0 (k1_newton A D) (k1_newton B D)) (k2_xcmplx_0 (k1_newton A C) (k1_newton B C))) (k3_xcmplx_0 2 (k2_xcmplx_0 (k1_newton A (k2_nat_1 D C)) (k1_newton B (k2_nat_1 D C)))))) ) ) ) ) ) ) ) ) ).
tt(t46_setfam_1,ax, (! [A:$i] : (m1_subset_1 (k1_tarski k1_xboole_0) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ).
tt(t46_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k2_setlim_1 A B) B)) ) ) ) ).
tt(t46_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k1_setlim_2 B C D)) A) (k9_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A)))) ) ) ) ) ) ) ).
tt(t46_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k10_setwiseo A B (k4_setwiseo A D E F) C) = (k5_setwiseo B (k5_setwiseo B (k3_funct_2 A (k5_finsub_1 B) C D) (k3_funct_2 A (k5_finsub_1 B) C E)) (k3_funct_2 A (k5_finsub_1 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k4_sf_mastr (k5_scmfsa6a B A)) = (k2_xboole_0 (k4_sf_mastr B) (k3_sf_mastr A))) ) ) ) ) ).
tt(t46_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A C C))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t46_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  ( ((v1_matroid0 C) & (r1_xxreal_0 (k6_simplex0 C) B))  =>  ((k8_simplex0 A C B) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) ) ) ) ) ) ) ).
tt(t46_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C)))) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C)))) C)))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C))))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski F C) & (r2_hidden E (k3_convex1 B F)))  => (r2_hidden (k1_funct_1 D E) F)) ) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((k1_card_1 (a_4_3_simplex1 A B C D)) = (k7_real_1 (k8_real_1 2 E) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_sincos10,ax,(r1_tarski (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)) (k1_relset_1 k1_numbers k2_sincos10))).
tt(t46_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k5_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B)) k7_complex1))) ) ) ) ) ).
tt(t46_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k20_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)) = k6_numbers) )  =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k2_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B))) = (k1_sin_cos4 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2))) ) ) ) ) ) ).
tt(t46_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k3_sin_cos2 A))) ) ) ).
tt(t46_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) = (k2_rcomp_1 (k1_real_1 1) 1)) ).
tt(t46_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_square_1 A) 1))  =>  ((k5_sin_cos7 A) = (k4_sin_cos7 (k12_binop_2 1 A))) ) ) ) ).
tt(t46_sin_cos9,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k7_relset_1 k1_numbers k1_numbers k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos))))).
tt(t46_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_series_1 (k4_sin_cos (k2_xcmplx_0 A B))) = (k8_real_1 (k4_series_1 (k4_sin_cos A)) (k4_series_1 (k4_sin_cos B)))) ) ) ) ) ).
tt(t46_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r2_hidden A (k10_xtuple_0 B)) =>  ( ((k4_finseq_4 B A) = 1)  | (v4_topreal1 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t46_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((k8_pscomp_1 A) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))) ) ) ).
tt(t46_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_zfmisc_1 A))  & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  => (r2_hidden (k22_pscomp_1 (k3_topreal1 2 A)) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A))) ) ).
tt(t46_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sprect_2 A B) & (r2_hidden C (k3_topreal1 2 B)))  => (r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) C))) ) ) ) ) ) ) ).
tt(t46_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t46_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 1) A))  & (r1_xxreal_0 (k3_square_1 A) (k4_xcmplx_0 A))) ) ) ) ).
tt(t46_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_stacks_1 C) &  ((v3_stacks_1 C) &  ((v4_stacks_1 C) &  ((v5_stacks_1 C) &  ((v6_stacks_1 C) & (l1_stacks_1 C)) ) ) ) ) ) )  =>  ( ((r4_stacks_1 A B) & (r4_stacks_1 B C))  => (r4_stacks_1 A C)) ) ) ) ) ) ) ).
tt(t46_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k3_stirl2_1 (k23_binop_2 A 1) (k23_binop_2 B 1)) = (k23_binop_2 (k24_binop_2 (k23_binop_2 B 1) (k3_stirl2_1 A (k23_binop_2 B 1))) (k3_stirl2_1 A B))) ) ) ) ) ).
tt(t46_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r1_tarski (k24_qc_lang1 A B) (k9_substut1 A B)) => (r1_tarski (k24_qc_lang1 A (k11_cqc_lang A C B)) (k9_substut1 A (k11_cqc_lang A C B)))) ) ) ) ) ) ) ).
tt(t46_subset_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_zfmisc_1 A))  =>  (? [B:$i] :  ((m1_subset_1 B A) &  (A = (k1_tarski B)) ) ) ) ) ).
tt(t46_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ((v6_supinf_2 A) &  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((k12_supinf_2 A B) = k1_supinf_1) ) )  & (v7_supinf_2 A)) ) ) ) ) ).
tt(t46_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A B)))) ) ) ) ).
tt(t46_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_tdlat_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_tdlat_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_tdlat_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_tdlat_1 A)) =>  ( ( (B = D)  &  (C = E) )  =>  ( ((k3_lattices (k4_tdlat_1 A) B C) = (k2_xboole_0 D E))  &  ((k4_lattices (k4_tdlat_1 A) B C) = (k3_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((v4_tex_2 B A) <=>  ((v1_tdlat_3 B) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tdlat_3 C) & (m1_pre_topc C A)) )  =>  ((m1_pre_topc B C) =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) ) ) ) ) ) ) ) ) ) ).
tt(t46_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (~  ( ((v4_tex_3 B A) | (v4_tex_3 C A))  &  ( (~ (r1_tsep_1 B C))  &  (~ (v4_tex_3 (k2_tsep_1 A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t46_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k2_tex_4 A B) (k1_setfam_1 (a_2_9_tex_4 A B)))) ) ) ) ).
tt(t46_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  & (r1_tarski (u1_pre_topc B) (u1_pre_topc A)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 C) D E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ( (F = G)  & (r1_tmap_1 B C E G))  => (r1_tmap_1 A C D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ( ((k6_eqrel_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C) (k3_topalg_1 A B C) D) = (k6_eqrel_1 (k1_topalg_1 A B C) (k1_topalg_1 A B C) (k3_topalg_1 A B C) E))  <=> (r3_borsuk_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_topalg_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (v1_topalg_6 (k4_mfold_2 A))) ) ) ).
tt(t46_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_orders_4 A) & (l1_pre_topc A)) )  => (v7_topgen_1 A)) ) ).
tt(t46_topgen_3,ax, (! [A:$i] :  ((k1_compts_1 A) = (k7_topgen_3 A A)) ) ).
tt(t46_topgen_4,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  ((v7_pre_topc A) => (v7_topgen_4 A)) ) ) ).
tt(t46_topgen_5,ax,(v7_pre_topc k3_topgen_5)).
tt(t46_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v4_pre_topc (k5_group_2 A C B) A)) ) ) ) ) ) ).
tt(t46_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 B) = A)  => (r2_hidden B (u1_struct_0 (k15_euclid A)))) ) ) ) ) ).
tt(t46_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k8_pscomp_1 C) = (k7_real_1 (k17_euclid A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t46_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_tarski (k5_jgraph_6 A B C) (k7_jgraph_6 A B C))) ) ) ) ) ) ).
tt(t46_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 k3_topmetr))))) )  =>  ((v1_funct_1 (k70_valued_2 A (u1_struct_0 (k15_euclid B)) C D)) &  ((v1_funct_2 (k70_valued_2 A (u1_struct_0 (k15_euclid B)) C D) A (u1_struct_0 (k15_euclid B))) & (m1_subset_1 (k70_valued_2 A (u1_struct_0 (k15_euclid B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ).
tt(t46_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tops_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) =>  ((k2_pre_topc A C) = (k2_pre_topc A (k9_subset_1 (u1_struct_0 A) C B))) ) ) ) ) ) ) ) ) ).
tt(t46_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ( ((v5_pre_topc D A C) & (v5_pre_topc E C B))  => (v5_pre_topc (k1_partfun1 (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 B) D E) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_1 B A) & (v3_tops_1 C A))  => (v1_tops_1 (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t46_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C) = C) ) )  =>  ((r3_diraf A B C D) |  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E D) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k7_trees_1 (k2_trees_1 (k2_nat_1 A 1))) = (k2_nat_1 A 1)) ) ) ).
tt(t46_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_trees_2 B)) )  =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 A)) =>  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) =>  ((k1_funct_1 (k7_trees_2 A C B) (k8_finseq_1 k5_numbers C D)) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ).
tt(t46_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (v1_finset_1 (k2_trees_2 A B))) ) ) ) ).
tt(t46_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_xboole_0 B C) & (r2_tsep_1 A B C))  <=> (r1_connsp_1 A B C)) ) ) ) ) ) ) ).
tt(t46_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_pre_topc C A) =>  (! [D:$i] :  ((m1_pre_topc D A) =>  (! [E:$i] :  ((m1_pre_topc E B) =>  (! [F:$i] :  ((m1_pre_topc F B) =>  ( ( ((u1_struct_0 C) = (u1_struct_0 E))  &  ((u1_struct_0 D) = (u1_struct_0 F)) )  =>  ((r4_tsep_1 A C D) <=> (r4_tsep_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m2_funct_2 C k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) =>  ( ((u1_turing_1 A) = (u1_turing_1 B))  => (m2_funct_2 C k4_numbers (u1_turing_1 (k32_turing_1 A B)) (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 A B))))) ) ) ) ) ) ) ).
tt(t46_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( ( (D = (k1_funct_1 C A))  &  (E = (k1_funct_1 C B)) )  =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k36_twoscomp A B)) = (k2_binarith (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = D)  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  => (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k4_uniroots A k1_complfld) (k10_uproots k1_complfld (k2_uproots (u1_struct_0 k1_complfld) (k2_uniroots A) 1)))) ) ).
tt(t46_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_algseq_1 A B) = 1)  =>  ((k6_polynom5 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t46_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m1_valuat_1 F A B) =>  ((r2_valuat_1 A B F (k8_cqc_lang A D E)) =>  ((r2_hidden C (k24_qc_lang1 A D)) | (r2_valuat_1 A B F (k8_cqc_lang A D (k11_cqc_lang A C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v2_relat_1 E) & (r2_relset_1 A (k2_valued_2 (k1_valued_2 B)) (k31_valued_2 A B E C) (k31_valued_2 A B E D)))  =>  ( (E = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_vectsp_4 A B C (k1_vectsp_4 A B)) = (k6_domain_1 (u1_struct_0 B) C)) ) ) ) ) ) ) ).
tt(t46_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) <=>  (! [E:$i] :  ((m2_vectsp_4 E A B C) =>  (! [F:$i] :  ((m2_vectsp_4 F A B D) =>  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((k9_subset_1 (u1_struct_0 B) E F) = (k6_domain_1 (u1_struct_0 B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  ((k4_vectsp_6 A B (k7_vectsp_6 A B C)) = (k4_algstr_0 B (k4_vectsp_6 A B C))) ) ) ) ) ) ) ).
tt(t46_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_vfunct_1 C D E A) & (r1_vfunct_1 C D F B))  => (r1_vfunct_1 C D (k6_vfunct_1 C D E F) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r1_vfunct_2 A B C E) & (r1_vfunct_2 A B D F))  => (r1_vfunct_2 A B (k3_vfunct_2 A B C D) (k3_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v1_waybel_0 C A)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E B) & (r1_tarski (k4_subset_1 (u1_struct_0 A) C D) E)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k5_setfam_1 (u1_struct_0 A) B))  => (v1_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(t46_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v3_pre_topc B A) <=> (v1_waybel_6 B A)) ) ) ) ) ).
tt(t46_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_1_waybel_1 A B))  =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C)) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C))) & (m1_subset_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t46_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v2_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel21 C A B) =>  ((v5_pre_topc C A B) <=>  ((v17_waybel_0 C A B) & (v22_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(t46_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((m1_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r1_waybel_3 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C)) &  ((v22_waybel_0 D (k3_yellow_3 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)) (u1_struct_0 C))))) ) )  =>  ((v1_funct_1 (k1_funct_5 D)) &  ((v1_funct_2 (k1_funct_5 D) (u1_struct_0 A) (u1_struct_0 (k2_waybel27 B C))) &  ((v22_waybel_0 (k1_funct_5 D) A (k2_waybel27 B C)) & (m1_subset_1 (k1_funct_5 D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k2_waybel27 B C)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) => (r3_orders_2 A B (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C)))) ) ) ) )  => (v22_waybel_0 (k4_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ).
tt(t46_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k9_waybel34 A) B C)) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_yellow21 (k9_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k9_waybel34 A) C))) &  ((v18_waybel_0 E (k4_yellow21 (k9_waybel34 A) B) (k4_yellow21 (k9_waybel34 A) C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k9_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k9_waybel34 A) C)))))) ) )  &  ( (E = D)  & (v22_waybel_0 (k2_waybel34 (k4_yellow21 (k9_waybel34 A) C) (k4_yellow21 (k9_waybel34 A) B) E) (k4_yellow21 (k9_waybel34 A) C) (k4_yellow21 (k9_waybel34 A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t46_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v3_waybel_3 A) <=>  ((v2_waybel_2 A) &  (? [B:$i] :  ( ((v5_waybel_4 B A) &  ((v6_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  &  (! [C:$i] :  ( ((v5_waybel_4 C A) &  ((v6_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ).
tt(t46_waybel_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v2_waybel_1 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v4_waybel_7 B A) => (v5_waybel_6 B A)) ) )  => (v5_waybel_7 (k1_waybel_4 A) A)) ) ) ).
tt(t46_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v2_wellord1 A) =>  (! [B:$i] :  (~  ((r2_hidden B (k1_relat_1 A)) & (r4_wellord1 A (k2_wellord1 A (k1_wellord1 A B)))) ) ) ) ) ) ).
tt(t46_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 A (k2_xboole_0 A B)) = k1_xboole_0) ) ) ).
tt(t46_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k6_xboolean A (k9_xboolean B C)) = (k4_xboolean (k5_xboolean (k3_xboolean A) (k3_xboolean B)) (k5_xboolean (k3_xboolean A) (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t46_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) (k2_xcmplx_0 C D)) = (k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 A D)) (k3_xcmplx_0 B C)) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t46_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 (k6_xcmplx_0 B A) B)) ) ) ) ) ) ).
tt(t46_xtuple_0,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_xboole_0 (k14_xtuple_0 A) (k14_xtuple_0 B)) (k14_xtuple_0 (k5_xboole_0 A B)))) ) ).
tt(t46_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden A k1_numbers) & (r1_xxreal_0 A B))  =>  ((r1_xxreal_0 C B) | (r2_hidden B k1_numbers)) ) ) ) ) ) ) ) ).
tt(t46_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  => (r1_tarski (k4_xxreal_1 B C) (k4_xxreal_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t46_xxreal_2,ax, ( (~ (v3_xxreal_2 k1_numbers))  &  (~ (v4_xxreal_2 k1_numbers)) ) ).
tt(t46_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k3_xxreal_3 B A) k6_numbers)) ) ) ) ) ) ) ).
tt(t46_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) <=> (r2_lattice3 A C D)) ) )  & (r1_yellow_0 A B))  => (r1_yellow_0 A C)) ) ) ) ) ).
tt(t46_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k4_yellow_3 A B (k1_waybel_3 (k3_yellow_3 A B) C)) = (k1_waybel_3 A (k8_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t46_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v8_pre_topc A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)))) =>  ( (B = (k6_partfun1 (u1_struct_0 A)))  => (v4_pre_topc B (k2_borsuk_1 A A))) ) ) ) ) ) ).
tt(t46_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_funct_1 (k5_funct_3 B (u1_struct_0 A))) &  ((v1_funct_2 (k5_funct_3 B (u1_struct_0 A)) (u1_struct_0 A) (u1_struct_0 k9_waybel18)) &  ((v5_pre_topc (k5_funct_3 B (u1_struct_0 A)) A k9_waybel18) & (m1_subset_1 (k5_funct_3 B (u1_struct_0 A)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k9_waybel18))))) ) ) ) ) ) ) ).
tt(t46_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  => (r1_functor0 A (k4_yellow18 A))) ) ).
tt(t46_yellow20,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 A A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 A A))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (k2_zfmisc_1 B B)) &  ((v1_funct_1 D) & (v1_partfun1 D (k2_zfmisc_1 B B))) ) )  =>  ((r2_altcat_2 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) C D) => (r2_altcat_2 (k2_zfmisc_1 A A) (k2_zfmisc_1 B B) (k2_funct_4 C) (k2_funct_4 D))) ) ) ) ) ) ) ).
tt(t46_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))))))  =>  ((r2_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) B) &  ((k2_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) B) = (k1_setfam_1 B)) ) ) ) ) ) ).
tt(t46_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))))  =>  ( ((v3_lattice3 (k3_yellow_3 A B)) | (r1_yellow_0 (k3_yellow_3 A B) C))  =>  ((k1_yellow_0 (k3_yellow_3 A B) C) = (k7_yellow_3 A B (k1_yellow_0 A (k4_yellow_3 A B C)) (k1_yellow_0 B (k5_yellow_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t46_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) = (k6_domain_1 (u1_struct_0 A) (k11_lattice3 A B C))) ) ) ) ) ) ) ).
tt(t46_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A B (k13_lattice3 A C D)) &  ((k12_lattice3 A B D) = (k3_yellow_0 A)) )  => (r3_orders_2 A B C)) ) ) ) ) ) ) ) ) ).
tt(t46_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) <=> (m2_pboole D B C (k7_funcop_1 B (u1_struct_0 (k7_lattice3 A))))) ) ) ) ) ) ) ).
tt(t46_yellow_9,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  (! [C:$i] :  ((m1_yellow_9 C B) => (m1_yellow_9 C A)) ) ) ) ) ) ).
tt(t46_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_zf_lang (k6_zf_lang A) B) => (r3_zf_lang A B)) ) ) ) ) ).
tt(t46_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v9_zf_lang A) =>  ( (~  ( (B = (k25_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k11_zf_lang B C)) ) ) ) ) )  &  ( ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_zf_lang B C)) ) )  =>  (B = (k25_zf_lang A)) )  &  ( (~  ( (B = (k26_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k11_zf_lang C B)) ) ) ) ) )  &  ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k11_zf_lang C B)) ) )  =>  (B = (k26_zf_lang A)) ) ) ) ) ) ) ) ) ) ).
tt(t46_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) =>  ((k3_xboole_0 B (k1_tarski A)) = (k1_tarski A)) ) ) ) ).
tt(t46_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t47_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) => (r3_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t47_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (! [E:$i] :  ((m1_abcmiz_1 E A (k12_abcmiz_1 A)) =>  ( ((k31_abcmiz_1 A (k16_abcmiz_1 A) B D) = (k31_abcmiz_1 A (k16_abcmiz_1 A) C E))  =>  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_abcmiz_a,ax, (! [A:$i] :  ((m1_abcmiz_1 A k27_abcmiz_1 (k12_abcmiz_1 k27_abcmiz_1)) =>  (! [B:$i] :  ( ((v8_abcmiz_1 B k27_abcmiz_1) & (m1_abcmiz_1 B k27_abcmiz_1 (k13_abcmiz_1 k27_abcmiz_1)))  =>  ((k10_abcmiz_a k27_abcmiz_1 (k31_abcmiz_1 k27_abcmiz_1 (k33_abcmiz_1 k27_abcmiz_1) B A)) = k9_abcmiz_1) ) ) ) ) ).
tt(t47_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C G) &  ((r1_aff_1 A D E B) &  ((r1_aff_1 A D F C) &  ((r2_hidden D G) &  (E = F) ) ) ) )  =>  ((r2_hidden E G) |  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B C) &  ((r2_hidden B D) &  ((v1_aff_1 C A) & (v1_aff_1 D A)) ) )  =>  ((r2_aff_4 A C D D) &  ((r2_aff_4 A D C D) & (r2_aff_4 A D D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)) (k5_afinsq_1 G)))  =>  ( ((k1_afinsq_1 A) = 6)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ( ((k1_funct_1 A 3) = E)  &  ( ((k1_funct_1 A 4) = F)  &  ((k1_funct_1 A 5) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_afinsq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 C C) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 D D) D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) D)))) )  =>  ( ((r1_xxreal_0 1 (k1_afinsq_1 B)) &  ((r1_tarski A (k3_xboole_0 C D)) &  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) & (r2_hidden H A))  =>  ( ((k1_binop_1 E G H) = (k1_binop_1 F G H))  & (r2_hidden (k1_binop_1 E G H) A)) ) ) ) ) )  =>  ((k6_afinsq_2 C B E) = (k6_afinsq_2 D B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (~  ( ((v6_incsp_1 (k14_afproj A)) &  ((v1_incproj (k14_afproj A)) &  ((v2_incproj (k14_afproj A)) &  ((v3_incproj (k14_afproj A)) &  ((v4_incproj (k14_afproj A)) & (l1_incsp_1 (k14_afproj A))) ) ) ) )  &  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) ) ) ) ) ).
tt(t47_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_afvect0 A B))) =>  ( ((k3_rlvect_1 (k5_afvect0 A B) C C) = (k4_struct_0 (k5_afvect0 A B)))  =>  (C = (k4_struct_0 (k5_afvect0 A B))) ) ) ) ) ) ) ) ).
tt(t47_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  ((r1_circcomb A B) => (m2_algspec1 (k2_circcomb A B) A)) ) ) ) ) ).
tt(t47_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) => (v2_funct_1 (k18_algstr_4 A B C))) ) ) ) ) ) ) ).
tt(t47_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v1_altcat_3 D A B C) &  (~  ((k1_altcat_1 A C B) = k1_xboole_0) ) ) ) ) ) ) ) )  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (k3_altcat_4 A)) ) ) ) ).
tt(t47_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v4_analmetr B A) => (r6_analmetr A C C B)) ) ) ) ) ) ) ).
tt(t47_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  ((r2_analort A B C D E F G) &  ((r2_analort A B C F G H I) &  ((r2_analort A B C D E J K) &  ( (~ (r2_analort A B C J K H I))  &  ( (~  (F = G) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v5_aofa_000 A) & (l1_unialg_1 A)) )  =>  ((k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A (k1_funct_7 3 (k4_finseq_1 (u1_unialg_1 A))))) = (k4_finseq_2 3 (u1_struct_0 A))) ) ) ).
tt(t47_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B D) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) D))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k84_aofa_i00 A B D E F G)) F) = (k5_int_1 (k21_aofa_i00 B k4_numbers C F) (k21_aofa_i00 B k4_numbers C G)))  &  (! [H:$i] :  ((m1_subset_1 H B) =>  ( (~  (H = F) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k84_aofa_i00 A B D E F G)) H) = (k21_aofa_i00 B k4_numbers C H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (B = (a_2_2_armstrng A C))  =>  ((k13_armstrng A B) = (k1_tarski C)) ) ) ) ) ) ) ) ).
tt(t47_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  ( (~  (A = k1_xboole_0) )  =>  ((k9_arytm_3 (k8_arytm_3 B A) (k8_arytm_3 C A)) = (k8_arytm_3 (k8_ordinal3 B C) A)) ) ) ) ) ) ) ) ).
tt(t47_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 30 A) & (r1_xxreal_0 (k5_series_1 2 A) (k5_series_1 A 6))) ) ) ) ).
tt(t47_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v13_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A B) = B) ) ) ) ) ) ).
tt(t47_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((k4_bcialg_2 A) = (k3_xboole_0 (k5_bcialg_2 A) (k6_bcialg_2 A))) ) ) ).
tt(t47_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A D (k1_bcialg_1 A D C)) = (k1_bcialg_1 A C (k1_bcialg_1 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v4_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_4 A B C) D) = (k1_bcialg_4 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t47_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v17_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A k6_numbers 1 k6_numbers k6_numbers)) ) ) ).
tt(t47_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_2 D (u1_struct_0 B)) => (m2_bcialg_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B)) ) ) ) ) ) ) ) ) ).
tt(t47_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ).
tt(t47_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 B) & (v3_funct_1 C))  => (v3_funct_1 (k3_normsp_1 A B C))) ) ) ) ) ) ) ).
tt(t47_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k5_bhsp_2 A C D)) <=> (r1_xxreal_0 (k3_bhsp_1 A (k5_algstr_0 A C B)) D)) ) ) ) ) ) ) ) ) ).
tt(t47_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_bhsp_4 B (k5_vfunct_1 k5_numbers B C) A) (k5_bhsp_4 B C (k32_valued_1 k5_numbers k1_numbers A)))) ) ) ) ) ) ).
tt(t47_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((k13_bilinear A B C D) = (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) ) ) ) ) ) ) ) ) ).
tt(t47_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k5_lattices A)) B)) ) ) ) ).
tt(t47_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ( (A = (k4_rcomp_1 k6_numbers B))  => (v4_pre_topc A k1_borsuk_4)) ) ) ) ) ).
tt(t47_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k4_rcomp_1 k2_xxreal_0 A) = k1_numbers) ) ) ) ).
tt(t47_borsuk_6,ax, ( ((k1_funct_1 k3_borsuk_6 k6_numbers) = k6_numbers)  &  ((k1_funct_1 k3_borsuk_6 1) = 1) ) ).
tt(t47_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 3))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 3))) =>  ( ( (C = A)  &  (D = B) )  =>  ((k1_binop_1 (k13_euclid 3) C D) = (k7_square_1 (k7_real_1 (k7_real_1 (k5_square_1 (k9_real_1 (k1_euclid_5 A) (k1_euclid_5 B))) (k5_square_1 (k9_real_1 (k2_euclid_5 A) (k2_euclid_5 B)))) (k5_square_1 (k9_real_1 (k3_euclid_5 A) (k3_euclid_5 B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t47_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A H B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k8_xboolean A (k3_xboolean A)) = k8_margrel1)  &  ((k3_xboolean (k8_xboolean A (k3_xboolean A))) = k7_margrel1) ) ) ) ).
tt(t47_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k9_bvfunc_1 A B D)) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A (k1_bvfunc_1 A B) (k5_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t47_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A (k12_bvfunc_1 A) (k12_bvfunc_1 A)) (k12_bvfunc_1 A))) ) ).
tt(t47_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B))) (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A C)))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t47_card_1,ax, ((k1_card_1 k4_ordinal1) = k4_ordinal1) ).
tt(t47_card_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) )  => (r1_xxreal_0 (k5_card_1 (k10_xtuple_0 A)) (k5_card_1 (k9_xtuple_0 A)))) ) ).
tt(t47_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  =>  ((k4_card_3 (k4_funct_4 A B (k1_tarski C) (k1_tarski D))) = (k1_tarski (k4_funct_4 A B C D))) ) ) ) ) ) ).
tt(t47_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  ((v1_finset_1 D) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v2_finset_1 E)) )  =>  ( (E = (k4_funct_4 A B C D))  =>  ( (A = B)  |  ( ((k3_card_fin 1 E) = (k23_binop_2 (k5_card_1 C) (k5_card_1 D)))  &  ((k3_card_fin 2 E) = (k5_card_1 (k3_xboole_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A C D) =>  ( ((v9_cat_1 E A B C) & (v9_cat_1 F A C D))  =>  ((k6_cat_1 A B D (k5_cat_1 A B C D E F)) = (k5_cat_1 A D C B (k6_cat_1 A C D F) (k6_cat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A C) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k8_cat_2 B C)) (k7_cat_1 A (k8_cat_2 B C) (k16_cat_2 A B C D E)) F) = (k9_cat_2 B C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B D) F) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 C) (k7_cat_1 A C E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_cat_3 D B (k4_graph_1 B C) A) => (r2_funct_2 A (u4_struct_0 (k2_oppcat_1 B)) (k7_cat_3 (k2_oppcat_1 B) A (k4_cat_3 B A D) (k5_oppcat_1 B C)) (k4_cat_3 B A (k6_cat_3 B A D C)))) ) ) ) ) ) ) ).
tt(t47_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k23_cat_4 A B))) =>  (C = D) ) ) ) ) ) ) ).
tt(t47_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k3_funct_2 k5_numbers k1_numbers (k4_catalan2 A B) k6_numbers) = (k11_binop_2 (k3_funct_2 k5_numbers k1_numbers A k6_numbers) (k3_funct_2 k5_numbers k1_numbers B k6_numbers))) ) ) ) ) ).
tt(t47_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (~ (v2_struct_0 (k9_cc0sp2 A)))  &  ((v13_algstr_0 (k9_cc0sp2 A)) &  ((v2_rlvect_1 (k9_cc0sp2 A)) &  ((v3_rlvect_1 (k9_cc0sp2 A)) &  ((v4_rlvect_1 (k9_cc0sp2 A)) &  ((v3_normsp_0 (k9_cc0sp2 A)) &  ((v4_normsp_0 (k9_cc0sp2 A)) &  ((v2_clvect_1 (k9_cc0sp2 A)) &  ((v3_clvect_1 (k9_cc0sp2 A)) &  ((v4_clvect_1 (k9_cc0sp2 A)) &  ((v5_clvect_1 (k9_cc0sp2 A)) &  ((v8_clvect_1 (k9_cc0sp2 A)) & (l2_clvect_1 (k9_cc0sp2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 B A) &  ((k8_relset_1 k2_numbers k2_numbers B (k1_tarski k6_numbers)) = k1_xboole_0) )  => (r2_cfcont_1 (k2_cfunct_1 k2_numbers B) A)) ) ) ) ).
tt(t47_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) (k1_cfunct_1 A D C)) (k1_cfunct_1 A (k2_valued_1 A k2_numbers k2_numbers B D) C)) & (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) (k1_cfunct_1 A D C)) (k1_cfunct_1 A (k46_valued_1 A k2_numbers k2_numbers B D) C))) ) ) ) ) ) ) ) ) ).
tt(t47_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v7_cgames_1 A) <=>  ( (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k6_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v10_cgames_1 B)) ) ) ) ) )  &  (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k7_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v9_cgames_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(t47_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (! [F:$i] :  ((m1_chain_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k2_finseq_1 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k2_finseq_1 A))) =>  ( ((r1_tarski (k3_chain_1 A B C) (k3_chain_1 A D E)) &  ( (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 A)) =>  ( ((r2_hidden I G) &  ( (~ (r1_xxreal_0 (k1_seq_1 C I) (k1_seq_1 B I)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 B I) (k1_seq_1 C I)) (k2_chain_1 A F I))) )  |  ( (~ (r2_hidden I G))  &  ( ((k1_seq_1 B I) = (k1_seq_1 C I))  & (r2_hidden (k1_seq_1 B I) (k2_chain_1 A F I))) ) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 A)) =>  ( ((r2_hidden I H) &  ( (~ (r1_xxreal_0 (k1_seq_1 E I) (k1_seq_1 D I)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 D I) (k1_seq_1 E I)) (k2_chain_1 A F I))) )  |  ( (~ (r2_hidden I H))  &  ( ((k1_seq_1 D I) = (k1_seq_1 E I))  & (r2_hidden (k1_seq_1 D I) (k2_chain_1 A F I))) ) ) ) ) ) )  =>  ((r1_tarski G H) &  ( (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 A)) =>  ( (~  ( (~ (r2_hidden I G))  & (r2_hidden I H)) )  =>  ( ((k1_seq_1 B I) = (k1_seq_1 D I))  &  ((k1_seq_1 C I) = (k1_seq_1 E I)) ) ) ) )  &  (! [I:$i] :  ((m2_subset_1 I k5_numbers (k2_finseq_1 A)) =>  (~  ( (~ (r2_hidden I G))  &  ((r2_hidden I H) &  ( (~  ( ((k1_seq_1 B I) = (k1_seq_1 D I))  &  ((k1_seq_1 C I) = (k1_seq_1 D I)) ) )  &  (~  ( ((k1_seq_1 B I) = (k1_seq_1 E I))  &  ((k1_seq_1 C I) = (k1_seq_1 E I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ((r1_chord A B C) &  ((r1_chord A C D) &  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  (! [F:$i] :  (! [G:$i] :  (~  ( (~ (v1_glib_001 E A))  &  ( ((k3_finseq_1 E) = 5)  &  ( ((k15_glib_001 A E) = 2)  &  ((r1_glib_000 A B C F) &  ((r1_glib_000 A C D G) &  ( ((k14_glib_001 A E) = (k2_tarski F G))  &  ( ((k13_glib_001 A E) = (k1_enumset1 B C D))  &  ( ((k1_funct_1 E 1) = B)  &  ( ((k1_funct_1 E 3) = C)  &  ((k1_funct_1 E 5) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_circcmb3 F D) =>  ( ((r2_hidden A (u1_struct_0 F)) &  ((r2_hidden B (u1_struct_0 F)) & (r2_hidden C (u1_struct_0 F))) )  =>  ((r2_hidden (k3_circcmb3 (k4_circcmb3 3 D E (k11_finseq_1 A B C))) (k2_msafree2 F)) |  ((k2_msafree2 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C)))) = (k2_msafree2 F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  => (r1_circcomb A B)) ) ) ) ).
tt(t47_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ( ((r4_circtrm1 A B C D E F) & (r3_circtrm1 A B C))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A E))) =>  ( (H = (k3_relat_1 C G))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ((k5_facirc_1 A E H I) = (k3_relat_1 C (k5_facirc_1 B F G I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_classes1,ax, (! [A:$i] :  (~  ((v1_ordinal1 A) &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~ (r1_tarski (k1_classes1 A) (k4_classes1 B))) ) ) ) ) ) ).
tt(t47_classes2,ax, (! [A:$i] :  ((v1_ordinal1 A) => (v1_classes2 (k1_classes1 A))) ) ).
tt(t47_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_clvect_1 B C)) ) ) ) ) ) ) ).
tt(t47_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k5_clvect_2 A C D)) <=> (r1_xxreal_0 (k13_csspace A (k5_algstr_0 A C B)) D)) ) ) ) ) ) ) ) ) ).
tt(t47_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k6_clvect_3 A (k5_vfunct_1 k5_numbers A B) C) = (k6_clvect_3 A B (k31_valued_1 k5_numbers k2_numbers C))) ) ) ) ) ) ) ).
tt(t47_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((k3_tarski (k9_cohsp_1 A B)) = (k2_zfmisc_1 (k2_cohsp_1 A) (k3_tarski B))) ) ) ) ) ).
tt(t47_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k20_coh_sp A)) =>  ( ((k24_coh_sp A (k23_coh_sp A (k21_coh_sp A B)) B) = B)  &  ((k24_coh_sp A B (k23_coh_sp A (k22_coh_sp A B))) = B) ) ) ) ) ).
tt(t47_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k17_complex1 A) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k17_complex1 A) k6_numbers))  &  (A = k6_numbers) ) ) ) ) ) ).
tt(t47_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k1_complex2 A (k11_complex1 B C)) = (k11_complex1 (k1_complex2 A B) (k1_complex2 A C))) ) ) ) ) ) ) ).
tt(t47_complfld,ax, ((k2_complfld (k4_struct_0 k1_complfld)) = (k4_struct_0 k1_complfld)) ).
tt(t47_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 A) = (k3_finseq_1 D)) ) )  =>  ((k9_seq_4 A B) = (k4_rvsum_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t47_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_compos_1 B) (u1_compos_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_compos_1 B) (u1_compos_1 B))))) )  =>  ( (D = (k1_funct_4 (k6_partfun1 (u1_compos_1 B)) (k16_funcop_1 (k2_compos_1 B) C)))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 B)) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) ) )  =>  ((k5_compos_1 B (k3_relat_1 E D) A) = (k3_relat_1 (k5_compos_1 B E A) (k1_funct_4 (k6_partfun1 (u1_compos_1 B)) (k16_funcop_1 (k2_compos_1 B) (k5_compos_0 (u1_compos_1 B) C A))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) 1) = (k5_compos_0 (u1_compos_1 A) C 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 k6_numbers (k4_complex1 A)) => (r1_xxreal_0 k6_numbers (k18_sin_cos (k1_comptrig A)))) ) ) ).
tt(t47_comput_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_margrel1 B A) & (m2_rfunct_3 B (k3_finseq_2 A) A (k2_comput_1 A))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v3_margrel1 C A) & (m2_rfunct_3 C (k3_finseq_2 A) A (k2_comput_1 A))) )  =>  ( ( ((k19_margrel1 B) = k6_numbers)  &  ( ((k19_margrel1 C) = k6_numbers)  &  ((k1_funct_1 B k1_xboole_0) = (k1_funct_1 C k1_xboole_0)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t47_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k55_valued_1 k5_numbers k2_numbers A))) ) ) ).
tt(t47_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_2 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 C E) & (r1_xxreal_0 B (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers A D) (k8_nat_1 k2_numbers A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_convex4 B A) & (v2_convex4 C A))  => (v2_convex4 (k1_rusub_5 A B C) A)) ) ) ) ) ) ) ).
tt(t47_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_hidden (k8_cqc_lang A (k11_cqc_lang A C B) B) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t47_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B))) (k12_cqc_lang A C B)) A) & (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C B) (k12_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B)))) A)) ) ) ) ) ) ) ).
tt(t47_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v6_qc_lang1 B A) & (v6_qc_lang1 C A))  =>  ((r1_cqc_the3 A B C) <=> (r1_cqc_the3 A (k6_cqc_lang A C) (k6_cqc_lang A B))) ) ) ) ) ) ) ) ).
tt(t47_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k13_csspace A (k4_algstr_0 A B)) = (k13_csspace A B)) ) ) ) ) ).
tt(t47_dickson,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ( ((v4_dickson A) & (v3_dickson A))  =>  ((v3_dickson (k3_yellow_3 A k11_dickson)) & (v4_dickson (k3_yellow_3 A k11_dickson))) ) ) ) ).
tt(t47_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 k19_sin_cos A) B) = (k1_real_1 (k8_real_1 2 (k8_real_1 (k18_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2)))))) ) ) ) ) ).
tt(t47_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k5_square_1 D)) ) )  =>  ((k1_seq_1 (k5_diff_1 C A) B) = (k8_real_1 (k8_real_1 2 A) B)) ) ) ) ) ) ) ) ).
tt(t47_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) 1) B) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) k6_numbers) B) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) k6_numbers) (k9_real_1 B A)))) ) ) ) ) ) ) ).
tt(t47_dilworth,ax, (! [A:$i] :  ( ((v4_dilworth A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v5_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A)))  =>  (~  ( ((k1_card_1 C) = (k5_card_1 B))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (~  ((v3_funct_2 D B C) &  (! [E:$i] :  ((r2_hidden E B) => (r2_hidden E (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  ( ((r2_hidden D (k6_ec_pf_1 A B C)) & (r2_hidden E (k6_ec_pf_1 A B C)))  =>  ( ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A)))  |  ((r1_ec_pf_1 A D E) <=> (r2_hidden (k1_domain_1 (k3_ec_pf_1 (k9_int_3 A)) (k3_ec_pf_1 (k9_int_3 A)) D E) (k8_ec_pf_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)) <=> (r1_ec_pf_1 A (k9_ec_pf_2 A B (k8_ec_pf_2 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t47_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m1_subset_1 (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A B (k3_graph_1 A C)) (k2_cat_1 A B (k4_graph_1 A C))) (k17_ens_1 A B C)) (k2_ens_1 (k16_ens_1 A)))) ) ) ) ) ) ).
tt(t47_entropy1,ax, (! [A:$i] :  ( ((v4_partfun3 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k4_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k8_real_1 (k1_seq_1 A C) (k6_power 2 (k1_seq_1 A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t47_enumset1,ax, (! [A:$i] :  ((k3_enumset1 A A A A A) = (k1_tarski A)) ) ).
tt(t47_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_zfmisc_1 B C)) =>  ((k1_funct_1 (k1_funct_3 (k9_funct_3 B C)) A) = (k7_relset_1 (k2_zfmisc_1 B C) B (k9_funct_3 B C) A)) ) ) ) ) ).
tt(t47_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k9_binop_2 (k5_square_1 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C))) (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)))) = (k11_binop_2 2 (k9_binop_2 (k5_square_1 (k12_euclid B)) (k5_square_1 (k12_euclid C))))) ) ) ) ) ) ) ).
tt(t47_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = A) )  &  ( (~  (A = C) )  &  ( (~  (C = B) )  &  ( (~ (r1_xxreal_0 k32_sin_cos (k4_euclid_3 B A C)))  &  (~  ((k7_real_1 (k7_real_1 (k4_euclid_3 B A C) (k4_euclid_3 A C B)) (k4_euclid_3 C B A)) = k32_sin_cos) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_euclid_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (B = (a_4_1_euclid_4 A C D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden F (k4_euclid_4 A C D)) &  ( ((k12_euclid (k5_algstr_0 (k15_euclid A) E F)) = (k5_seq_4 B))  & (r1_rvsum_1 (k5_algstr_0 (k15_euclid A) C D) (k5_algstr_0 (k15_euclid A) E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((k4_euclid_3 A B C) = (k9_real_1 (k8_real_1 2 (k4_euclid_3 D E F)) (k8_real_1 6 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k10_funcsdom (k2_finseq_1 A))))) =>  ((m1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A))) =>  ((k1_card_1 B) = A) ) ) ) ) ) ).
tt(t47_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ( ((k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k1_seq_1 A 1)) (k9_euclid 3 k3_euclid_8 (k1_seq_1 A 2))) (k9_euclid 3 k4_euclid_8 (k1_seq_1 A 3))) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k9_binop_2 (k1_seq_1 B 1) (k1_seq_1 C 1))) (k9_euclid 3 k3_euclid_8 (k9_binop_2 (k1_seq_1 B 2) (k1_seq_1 C 2)))) (k9_euclid 3 k4_euclid_8 (k9_binop_2 (k1_seq_1 B 3) (k1_seq_1 C 3)))))  <=>  ((k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k1_seq_1 B 1)) (k9_euclid 3 k3_euclid_8 (k1_seq_1 B 2))) (k9_euclid 3 k4_euclid_8 (k1_seq_1 B 3))) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k10_binop_2 (k1_seq_1 A 1) (k1_seq_1 C 1))) (k9_euclid 3 k3_euclid_8 (k10_binop_2 (k1_seq_1 A 2) (k1_seq_1 C 2)))) (k9_euclid 3 k4_euclid_8 (k10_binop_2 (k1_seq_1 A 3) (k1_seq_1 C 3))))) ) ) ) ) ) ) ) ).
tt(t47_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k5_algstr_0 (k15_euclid A) B (k5_algstr_0 (k15_euclid A) C D)) = (k3_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t47_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) => (r2_hidden (k2_euclid_4 A B C) (k1_euclidlp A))) ) ) ) ) ) ).
tt(t47_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  => (r1_tarski (k6_exchsort A B) (k2_zfmisc_1 (k9_xtuple_0 B) (k9_xtuple_0 B)))) ) ) ) ).
tt(t47_facirc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] : (r2_hidden (k4_tarski A B) (k3_msafree2 (k5_circcomb B A)))) ) ) ).
tt(t47_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_xxreal_0 A B) & (r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)))  =>  ( ( (~ (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))  &  (~ (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) )  | (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))) ) ) ) ) ) ) ) ).
tt(t47_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k1_fdiff_9)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k10_real_1 (k8_real_1 (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t47_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k3_limfunc1 A) (k1_relset_1 k1_numbers B)) & (r2_fdiff_1 B (k3_limfunc1 A)))  =>  ( ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 (k1_fdiff_1 B C) k6_numbers)) ) )  &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ((r2_hidden C (k3_limfunc1 A)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 B C))) ) ) )  |  ((v2_funct_1 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) &  ((r2_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))))) =>  ((k1_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) C) = (k10_real_1 1 (k1_fdiff_1 B (k1_seq_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 A))) C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos) k19_sin_cos))) =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k16_sin_cos) k19_sin_cos) A) B) = (k8_real_1 B (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t47_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3)) k19_sin_cos))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3)) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3)) k19_sin_cos) A) B) = (k2_newton (k1_seq_1 k16_sin_cos B) 3)) ) ) ) ) ) ) ) ).
tt(t47_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  ((k1_seq_1 k16_sin_cos A) = k6_numbers) )  =>  ((r1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) A) &  ((k1_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) A) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos A))))) ) ) ) ) ).
tt(t47_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k1_pre_ff A) = 1)  <=>  ( (A = 1)  |  (A = 2) ) ) ) ) ).
tt(t47_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k6_xcmplx_0 (k4_nat_1 (k3_fib_num3 A B (k2_nat_1 C 2)) (k3_fib_num3 A B C)) (k13_newton (k3_fib_num3 A B (k2_nat_1 C 1)) 2)) = (k3_xcmplx_0 (k3_power (k4_xcmplx_0 1) C) (k6_xcmplx_0 (k13_newton (k3_fib_num3 A B 2) 2) (k4_nat_1 (k3_fib_num3 A B 1) (k3_fib_num3 A B 3))))) ) ) ) ) ) ) ).
tt(t47_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((v1_filter_0 D A) &  ( ((r2_hidden B D) &  (~ (r2_hidden C D)) )  |  ( (~ (r2_hidden B D))  & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ( ((v3_filter_0 A) & (v3_filter_0 B))  <=> (v3_filter_0 (k7_filter_1 A B))) ) ) ) ) ).
tt(t47_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_filter_2 (u1_struct_0 A) (k8_filter_2 A B C) (k8_filter_2 A C B))) ) ) ) ) ) ).
tt(t47_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (~  ( ((k7_finseq_1 A B) = (k7_finseq_1 C D))  &  ((r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 C)) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (~  ((k7_finseq_1 A E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_finseq_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) )  => (m2_finseq_1 (k1_partfun1 (k4_finseq_1 B) (k4_finseq_1 B) k5_numbers A C B) A)) ) ) ) ) ) ).
tt(t47_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r2_relset_1 k5_numbers k5_numbers (k2_partfun1 k5_numbers k5_numbers (k14_finseq_1 (k2_finseq_1 (k2_xcmplx_0 A B))) (k2_finseq_1 A)) (k14_finseq_1 (k2_finseq_1 A)))) ) ) ) ).
tt(t47_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((r2_hidden B (k10_xtuple_0 A)) & (r1_xboole_0 (k10_xtuple_0 (k6_finseq_4 A B)) (k1_tarski B))) ) ) ) ) ).
tt(t47_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (~  ((r2_hidden B (k10_xtuple_0 C)) & (v1_xboole_0 (k1_finseq_5 A C B))) ) ) ) ) ) ) ) ).
tt(t47_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k2_rfinseq A 1 (k3_finseq_4 A B C D)) = (k2_finseq_4 A C D)) ) ) ) ) ) ) ) ) ).
tt(t47_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v3_card_1 E D) & (m2_finseq_1 E A))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 A A) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((r6_binop_1 A F G) => (r2_relset_1 k5_numbers A (k2_finseqop A A A F E (k5_binop_1 A G B C)) (k1_finseqop A A A G (k2_finseqop A A A F E B) (k2_finseqop A A A F E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_fintopo2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_fintopo2 A) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k6_domain_1 (u1_struct_0 A) D) (k6_fintopo2 A D))) ) )  =>  ((k4_subset_1 (u1_struct_0 A) (k10_fintopo2 A B) (k10_fintopo2 A C)) = (k10_fintopo2 A (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t47_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_fintopo3 A k6_numbers B) = (k1_fin_topo A B)) ) ) ) ) ).
tt(t47_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((v2_fintopo6 B A) & (r1_xxreal_0 1 C))  => (v2_fintopo6 (k17_finseq_1 (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t47_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k8_flang_1 A B) = (k4_flang_1 A (k2_flang_1 A)))  <=>  ( (B = k1_xboole_0)  |  (B = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ) ) ).
tt(t47_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B 1 1) = B) ) ) ) ).
tt(t47_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B (k1_flang_3 A C D)) =>  ((k1_flang_3 A C D) = (k1_flang_3 A (k4_subset_1 (k8_afinsq_1 A) C B) D)) ) ) ) ) ) ) ) ) ).
tt(t47_fomodel0,ax, (! [A:$i] :  ((v4_funct_1 A) =>  (! [B:$i] :  ((v4_funct_1 B) =>  ((k21_fomodel0 (k2_xboole_0 A B)) = (k2_xboole_0 (k21_fomodel0 A) (k21_fomodel0 B))) ) ) ) ) ).
tt(t47_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  ((v5_fsm_1 C A B) <=>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) )  & (r7_fsm_1 A B C (k11_fsm_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t47_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v1_funct_1 (k4_funcop_1 C D E)) &  ((v1_funct_2 (k4_funcop_1 C D E) B A) & (m1_subset_1 (k4_funcop_1 C D E) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k5_relat_1 C B))) =>  ((k1_funct_1 (k5_relat_1 C B) A) = (k1_funct_1 C A)) ) ) ) ) ) ).
tt(t47_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_tarski A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B)))) )  =>  ( (~  (B = k1_xboole_0) )  => (r2_hidden (k1_funct_1 C A) B)) ) ) ) ) ).
tt(t47_funct_3,ax, (! [A:$i] : (r1_tarski (k10_xtuple_0 (k11_funct_3 A)) (k2_zfmisc_1 A A))) ).
tt(t47_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) =>  ((k10_xtuple_0 (k2_funct_4 C)) = (k10_xtuple_0 C)) ) ) ) ) ) ).
tt(t47_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k10_xtuple_0 C) (k1_funct_2 A B)) &  ((r1_tarski (k10_xtuple_0 D) (k1_funct_2 A B)) &  ((k4_funct_5 C) = (k4_funct_5 D)) ) )  =>  ( (A = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ).
tt(t47_funct_6,ax, (! [A:$i] :  ((k8_funct_6 k1_xboole_0 A) = k1_xboole_0) ) ).
tt(t47_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k5_funct_7 (k9_finseq_1 B) A) = (k10_finseq_1 A (k1_funct_1 B A))) ) ) ) ).
tt(t47_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v6_funct_8 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t47_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ( ((v16_functor0 C A B) & (v5_functor0 C A B))  => (v7_functor0 C A B)) ) ) ) ) ) ) ).
tt(t47_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_2 A (k2_fuzzy_1 A B C) (k2_fuzzy_1 A B D)) (k2_fuzzy_1 A B (k2_fuzzy_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t47_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k6_fvaluat1 A B)) <=> (r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers B C))) ) ) ) ) ) ) ).
tt(t47_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (C = (k4_fvsum_1 A B (k8_fvsum_1 A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t47_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_gcd_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r8_gcd_1 A B C D) & (r8_gcd_1 A B E F))  =>  ((k8_group_1 A (k8_gcd_1 A B C D E F) (k8_group_1 A D F)) = (k8_group_1 A (k9_gcd_1 A B C D E F) (k8_group_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) & (r1_xxreal_0 (k3_finseq_1 G) B))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H C D E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) & (r1_xxreal_0 (k3_finseq_1 G) C))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H B D E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) & (r1_xxreal_0 (k3_finseq_1 G) D))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H B C E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) & (r1_xxreal_0 (k3_finseq_1 G) E))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H B C D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) C))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A D E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) D))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A C E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) E))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A C D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) D))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A B E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) E))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A B D)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E))  =>  ((k11_genealg1 F G H A B C D E) = (k9_genealg1 F G H A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) <=> (m1_subset_1 B (u1_struct_0 (k2_diraf A)))) ) ) ) ).
tt(t47_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k19_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k19_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k19_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (u1_struct_0 (k19_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (u1_struct_0 (k19_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k19_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp) (u1_struct_0 (k19_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t47_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ( ((k24_glib_000 A C) = (k6_subset_1 (k6_glib_000 A) (k6_domain_1 (k6_glib_000 A) B)))  &  ((k25_glib_000 A C) = (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k6_domain_1 (k6_glib_000 A) B)))) ) ) ) ) ) ) ) ).
tt(t47_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) & (r2_hidden E (k1_relset_1 k5_numbers (k8_glib_001 A B C D)))) )  =>  ( ((k1_funct_1 (k8_glib_001 A B C D) E) = (k1_funct_1 B (k6_xcmplx_0 (k2_nat_1 C E) 1)))  & (r2_hidden (k6_xcmplx_0 (k2_nat_1 C E) 1) (k1_relset_1 k5_numbers B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((v3_glib_002 A) <=>  ((v1_glib_002 A) &  ((k15_glib_000 A) = (k2_nat_1 (k17_glib_000 A) 1)) ) ) ) ) ).
tt(t47_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v2_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) =>  ((r2_hidden B (k11_glib_003 A)) |  ((k5_card_1 (k11_glib_003 (k12_glib_003 A B C))) = (k2_nat_1 (k5_card_1 (k11_glib_003 A)) 1)) ) ) ) ) ) ) ).
tt(t47_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)))))) ) ) ) ) ) ).
tt(t47_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 B)))  =>  ( ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 B C E) &  ( ((k17_finseq_1 B A C) = (k17_finseq_1 B A D))  &  ((r2_gobrd13 B C E (k7_nat_d A 1)) & (r2_gobrd13 B D E (k7_nat_d A 1))) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((k17_finseq_1 B (k2_nat_1 A 1) C) = (k17_finseq_1 B (k2_nat_1 A 1) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v3_graph_2 C A) & (m2_graph_1 C A))  =>  ((r1_graph_2 A B C) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ((k1_funct_1 B D) = (k1_funct_1 B E)) ) )  =>  ((r1_xxreal_0 E D) |  ( (D = 1)  &  (E = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_graph_3 B D E))) =>  ( ( (F = C)  & (r2_hidden (u4_struct_0 B) A))  =>  ( (D = E)  |  ( ( (~  (C = D) )  &  (~  (C = E) ) )  |  ((k7_graph_3 (k8_graph_3 B D E) F A) = (k2_nat_1 (k7_graph_3 B C A) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ((r5_graph_5 B A) &  (D = (k9_graph_5 B C A)) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) => (r1_xxreal_0 k6_numbers (k1_seq_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ((r1_xxreal_0 1 A) &  ((r2_hidden 1 (k4_finseq_1 B)) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((k1_seq_1 B C) = 1) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 2 C) & (r1_xxreal_0 C A))  =>  ((k1_seq_1 B (k2_nat_1 A C)) = (k1_real_1 1)) ) ) ) ) ) )  =>  ( ((k1_seq_1 B (k2_nat_1 A 1)) = (k1_real_1 1))  |  ( (1 = (k15_graphsp (k7_graphsp B A) B A))  &  ( ((k14_graphsp B A) = k1_xboole_0)  &  ((k6_domain_1 k5_numbers 1) = (k14_graphsp (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) 1) B) A)) ) ) ) ) ) ) ) ) ).
tt(t47_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) &  ((v1_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r5_polyred A B C (k10_polynom1 A C D E) (k10_polynom1 A C (k6_termord A B C D) E) (k1_groeb_1 A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t47_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k4_subset_1 (u1_struct_0 A) (k2_group_11 A B C) (k2_group_11 A B D)) (k2_group_11 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k8_group_1 A B C)) = (k8_group_1 A (k2_group_1 A B) (k2_group_1 A C))) ) ) ) ) ) ) ).
tt(t47_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_struct_0 C (k1_group_1 B))) ) ) ) ) ) ).
tt(t47_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_3 A (k4_group_3 A D B) C) = (k4_group_3 A D (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t47_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k11_group_2 A D (k11_group_2 A C B)) = (k2_group_2 A B (k7_group_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t47_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden A (k4_group_5 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (A = (k2_group_5 B E F))  &  ((r2_hidden E C) & (r2_hidden F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  => (r1_group_2 B (k10_group_6 A B (k7_group_6 A B)) (k6_group_2 B))) ) ) ) ).
tt(t47_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 E B C) &  ((v7_group_9 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((r1_struct_0 (k13_group_9 A B C E) D) <=>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) E D) = (k1_group_1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k3_helly A B B B) = B) ) ) ) ) ).
tt(t47_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k4_hermitan A B (k3_rlvect_1 A C D)) (k3_square_1 (k2_xcmplx_0 (k6_square_1 (k4_hermitan A B C)) (k6_square_1 (k4_hermitan A B D)))))) ) ) ) ) ) ) ) ).
tt(t47_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((r1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 2)) A) &  ((k1_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 2)) A) = (k1_real_1 (k10_real_1 (k8_real_1 2 A) (k5_square_1 (k5_prepower A 2))))) ) ) ) ) ).
tt(t47_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 A (k4_hilbert1 C B))) k6_hilbert1)) ) ) ) ) ) ).
tt(t47_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 B k1_complfld) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k7_hurwitz (k13_polynom3 k1_complfld A B)) (k13_polynom3 k1_complfld (k7_hurwitz A) (k7_hurwitz B)))) ) ) ) ).
tt(t47_idea_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_1 C k5_numbers B 6) =>  (! [D:$i] :  ((m1_matrix_1 D k5_numbers B 6) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m2_finseq_1 F k5_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k5_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k5_numbers) =>  (! [I:$i] :  ((m2_finseq_1 I k5_numbers) =>  (! [J:$i] :  ((m2_finseq_1 J k5_numbers) =>  ( ((r1_xxreal_0 E B) &  ((v1_int_2 (k2_nat_1 (k5_series_1 2 A) 1)) &  ((r1_xxreal_0 4 (k3_finseq_1 J)) &  ((r1_idea_1 A (k1_recdef_1 J 1)) &  ((r1_idea_1 A (k1_recdef_1 J 2)) &  ((r1_idea_1 A (k1_recdef_1 J 3)) &  ((r1_idea_1 A (k1_recdef_1 J 4)) &  ( (! [K:$i] :  ((m1_subset_1 K k5_numbers) =>  ((r1_xxreal_0 K E) =>  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 1)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 2)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 3)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 4)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 5)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers C K 6)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 1)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 2)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 3)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 4)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 5)) &  ((r1_idea_1 A (k3_matrix_1 k5_numbers D K 6)) &  ( ((k3_matrix_1 k5_numbers D K 1) = (k10_idea_1 A (k3_matrix_1 k5_numbers C K 1)))  &  ( ((k3_matrix_1 k5_numbers D K 2) = (k6_idea_1 A (k3_matrix_1 k5_numbers C K 3)))  &  ( ((k3_matrix_1 k5_numbers D K 3) = (k6_idea_1 A (k3_matrix_1 k5_numbers C K 2)))  &  ( ((k3_matrix_1 k5_numbers D K 4) = (k10_idea_1 A (k3_matrix_1 k5_numbers C K 4)))  &  ( ((k3_matrix_1 k5_numbers C K 5) = (k3_matrix_1 k5_numbers D K 5))  &  ((k3_matrix_1 k5_numbers C K 6) = (k3_matrix_1 k5_numbers D K 6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ((r1_idea_1 A (k1_recdef_1 F 1)) &  ((r1_idea_1 A (k1_recdef_1 F 2)) &  ((r1_idea_1 A (k1_recdef_1 F 3)) &  ((r1_idea_1 A (k1_recdef_1 F 4)) &  ( ((k1_recdef_1 G 1) = (k10_idea_1 A (k1_recdef_1 F 1)))  &  ( ((k1_recdef_1 G 2) = (k6_idea_1 A (k1_recdef_1 F 2)))  &  ( ((k1_recdef_1 G 3) = (k6_idea_1 A (k1_recdef_1 F 3)))  &  ( ((k1_recdef_1 G 4) = (k10_idea_1 A (k1_recdef_1 F 4)))  &  ((r1_idea_1 A (k1_recdef_1 H 1)) &  ((r1_idea_1 A (k1_recdef_1 H 2)) &  ((r1_idea_1 A (k1_recdef_1 H 3)) &  ((r1_idea_1 A (k1_recdef_1 H 4)) &  ( ((k1_recdef_1 I 1) = (k10_idea_1 A (k1_recdef_1 H 1)))  &  ( ((k1_recdef_1 I 2) = (k6_idea_1 A (k1_recdef_1 H 2)))  &  ( ((k1_recdef_1 I 3) = (k6_idea_1 A (k1_recdef_1 H 3)))  &  ( ((k1_recdef_1 I 4) = (k10_idea_1 A (k1_recdef_1 H 4)))  &  ( ((k1_recdef_1 I 5) = (k1_recdef_1 H 5))  &  ((k1_recdef_1 I 6) = (k1_recdef_1 H 6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k3_relat_1 (k3_relat_1 (k3_relat_1 (k3_relat_1 (k3_relat_1 (k19_idea_1 F A) (k4_funct_7 k14_idea_1 (k17_idea_1 E B A C))) (k21_idea_1 A H)) (k22_idea_1 A I)) (k4_funct_7 k14_idea_1 (k18_idea_1 E B A D))) (k20_idea_1 G A)) J) = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ((k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ).
tt(t47_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k1_int_1 (k7_xcmplx_0 A A)) = 1) ) ) ) ).
tt(t47_int_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v7_ordinal1 D))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (v7_ordinal1 E))  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (v7_ordinal1 F))  =>  (~  ((r1_int_1 (k6_nat_d D E) (k6_xcmplx_0 A B)) &  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  (? [I:$i] :  ((v1_int_1 I) &  ( ((k6_int_1 (k6_xcmplx_0 I A) D) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 I B) E) = k6_numbers)  &  ( ((k6_int_1 (k6_xcmplx_0 I C) F) = k6_numbers)  &  (~  ((r2_int_1 I (k2_xcmplx_0 (k2_xcmplx_0 A (k3_xcmplx_0 D G)) (k3_xcmplx_0 (k5_nat_d D E) H)) (k5_nat_d (k5_nat_d D E) F)) &  ( ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k3_nat_d D (k6_nat_d D E)) G) (k5_int_1 (k6_xcmplx_0 B A) (k6_nat_d D E))) (k3_nat_d E (k6_nat_d D E))) = k6_numbers)  &  ((k6_int_1 (k6_xcmplx_0 (k3_xcmplx_0 (k3_nat_d (k5_nat_d D E) (k6_nat_d (k5_nat_d D E) F)) H) (k5_int_1 (k6_xcmplx_0 C (k2_xcmplx_0 A (k3_xcmplx_0 D G))) (k6_nat_d (k5_nat_d D E) F))) (k3_nat_d F (k6_nat_d (k5_nat_d D E) F))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k18_rvsum_1 (k8_rvsum_1 (k5_finseq_2 k1_numbers (k3_finseq_1 A) B) A)) = (k6_xcmplx_0 (k3_xcmplx_0 (k3_finseq_1 A) B) (k18_rvsum_1 A))) ) ) ) ) ).
tt(t47_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k1_real_1 (k10_real_1 1 (k7_real_1 1 (k5_square_1 D))))) ) ) )  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 k2_sin_cos9 (k4_seq_4 A)) (k1_seq_1 k2_sin_cos9 (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t47_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers k2_sin_cos9 (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2))))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k2_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) k2_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t47_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))) (k1_seq_1 k16_sin_cos D)) (k10_real_1 (k8_real_1 (k1_seq_1 k30_sin_cos D) (k1_seq_1 k19_sin_cos D)) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k2_fdiff_9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t47_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) & (r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers D)))  =>  ((k6_integr18 (k4_real_ns1 A) D C B) = (k4_algstr_0 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) D B C))) ) ) ) ) ) ) ) ) ) ).
tt(t47_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (? [D:$i] :  ((m1_integra1 D A) &  ((r1_integra1 B D) & (r1_integra1 C D)) ) ) ) ) ) ) ) ) ).
tt(t47_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k1_real_1 1)) ) ) ) ).
tt(t47_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k7_real_1 A F))  &  (~  ((k1_seq_1 C F) = k6_numbers) ) ) ) ) )  &  ( (E = (k1_relset_1 k1_numbers C))  &  ( ((k1_relset_1 k1_numbers C) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k7_real_1 A F))))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers C) (k4_seq_4 B)) (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers C) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_interva1 A (k10_interva1 A (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A))) (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A)))) ) ).
tt(t47_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k3_intpro_1 A B) (k4_intpro_1 A C)) (k4_intpro_1 C B)) k8_intpro_1)) ) ) ) ) ) ).
tt(t47_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  => (m1_isocat_1 (k10_cat_1 A) A A)) ) ).
tt(t47_jgraph_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  (~  ( (G = k6_numbers)  &  ( (H = 1)  &  ((v5_pre_topc A k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 A) &  ((v5_pre_topc B k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 B) &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A G)) = C)  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A H)) = D)  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B G)) = E)  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B H)) = F)  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k5_topmetr)) =>  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) D) &  ((r1_xxreal_0 C (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) D) &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) A I)) F) &  ((r1_xxreal_0 E (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) B I)) F)) ) ) ) ) ) ) ) )  & (r2_subset_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jgraph_2,ax, ( ((v4_pre_topc a_0_6_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_6_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((v4_pre_topc a_0_7_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_7_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(t47_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k13_complex1 (k18_euclid B) (k12_euclid B)) = A)  =>  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) B))  =>  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ((k18_euclid C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = a_0_6_jgraph_5)  &  ((r1_jordan6 C A B) &  ( (~  (A = B) )  &  ((r1_xxreal_0 k6_numbers (k18_euclid B)) & (r1_xxreal_0 (k17_euclid B) (k17_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 (k1_sppol_2 A B C D)) (k22_pscomp_1 (k1_sppol_2 A B C D)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D)))) & (r1_topreal1 (k15_euclid 2) (k22_pscomp_1 (k1_sppol_2 A B C D)) (k18_pscomp_1 (k1_sppol_2 A B C D)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k17_euclid A) = F)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) H) & (r1_xxreal_0 (k17_euclid B) F)) ) ) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 D 1))  &  ((r1_xxreal_0 D C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 C 1) |  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E A)) (k2_nat_1 C 1)) |  ((r1_xxreal_0 D 1) |  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 E A)) (k2_nat_1 D 1)) |  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2) F) & (r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 D 2)) 2) G))  =>  ((r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 1)) 2) F) |  ((r1_xxreal_0 (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 D 1)) 2) G) | (r1_tarski (k3_goboard5 (k1_jordan8 E B) F G) (k3_goboard5 (k1_jordan8 E A) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r2_hidden (k1_jordan5c (k3_topreal1 2 (k1_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) (k10_xtuple_0 (k1_jordan1e A B)))) ) ) ) ) ).
tt(t47_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((v2_connsp_1 C (k15_euclid 2)) & (r1_xxreal_0 A B))  => (r1_tarski (k2_goboard9 (k1_jordan9 C A)) (k2_goboard9 (k1_jordan9 C B)))) ) ) ) ) ) ) ).
tt(t47_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k3_topreal1 2 (k2_jordan1e B A))) &  ((k17_euclid C) = (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) )  =>  (C = (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t47_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r1_tarski B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k5_jordan1k A D C) (k5_jordan1k A D B))) ) ) ) ) ) ) ) ) ).
tt(t47_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xxreal_0 (k18_euclid (k1_jordan21 (k8_jordan6 A))) (k7_pscomp_1 A))) ) ).
tt(t47_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (~  ((r1_xxreal_0 2 A) &  ( (~  (B = (k5_euclid A)) )  &  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (~  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (~  (C = (k9_euclid A B D)) )  &  (~  (B = (k9_euclid A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((r2_hidden C (k3_topreal1 2 B)) &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) ) )  =>  ( (C = (k1_funct_1 B 1))  | (r1_jordan3 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k7_nat_d (k3_finseq_1 A) 1)) (k3_jordan3 B C)) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) C)) ) ) ) ) ) ) ) ).
tt(t47_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_jordan4 A B C D) =>  ( (C = D)  | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k15_jordan5d A) = (k13_jordan5d A)) ) ) ) ).
tt(t47_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal2 A) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ( (~  (C = D) )  &  ( (B = (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k2_tarski C D)))  & (v2_connsp_1 B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k2_jgraph_6 A B C D) = (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_jgraph_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t47_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A))) &  ((v14_quantal1 B (k1_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A)))))) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  &  ((k1_knaster A C) = (k9_knaster (k1_lattice3 A) B)) ) ) ) ) ) ) ).
tt(t47_kurato_1,ax,(r1_zfmisc_1 (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))))).
tt(t47_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  ((r2_hidden F C) => (r3_lattices A (k3_funct_2 B (u1_struct_0 A) D F) (k3_funct_2 B (u1_struct_0 A) E F))) ) )  =>  ( (C = k1_xboole_0)  | (r3_lattices A (k3_lattice2 B A C D) (k3_lattice2 B A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r3_lattices A D E) & (r2_hidden E C)) ) ) ) ) ) ) )  => (r3_lattices A (k15_lattice3 A B) (k15_lattice3 A C))) ) ) ) ) ).
tt(t47_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C B) =>  ((r1_xxreal_0 C D) |  (! [E:$i] :  (~  ( (~ (r2_hidden (k7_nat_d (k15_glib_000 A) D) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) C)) E)))  & (r2_hidden (k7_nat_d (k15_glib_000 A) D) (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v5_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ((r2_hidden D (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 B (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((k8_relset_1 k1_numbers k1_numbers B (k1_tarski k6_numbers)) = k1_xboole_0) )  =>  ( ((k1_limfunc2 B A) = k6_numbers)  |  ((r1_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k1_limfunc2 B A))) ) ) ) ) ) ) ) ).
tt(t47_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((k1_limfunc3 B A) = k6_numbers) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A C) A) (k2_rcomp_1 A (k7_real_1 A C))))) & (r1_xxreal_0 (k1_seq_1 B D) k6_numbers)) ) ) ) ) ) ) )  | (r2_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A)) ) ) ) ) ) ).
tt(t47_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r2_limfunc3 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) &  ((k1_seq_1 A D) = (k5_limfunc1 A)) ) ) ) ) )  | (v7_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t47_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k18_lpspace1 A B C))) =>  ((r2_hidden D E) =>  ((r3_mesfunc6 A B C D) &  ((r2_hidden D (k9_lpspace1 A B C)) & (r3_mesfunc6 A B C (k56_valued_1 A k1_numbers D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C G)) &  ((r2_hidden E (k1_lpspace2 A B C G)) &  ((k5_lpspace2 A B C D G) = (k5_lpspace2 A B C E G)) ) )  =>  ((k5_lpspace2 A B C (k26_valued_1 A k1_numbers D F) G) = (k5_lpspace2 A B C (k26_valued_1 A k1_numbers E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r8_ltlaxio1 D (k3_hilbert1 A B)) & (r8_ltlaxio1 D (k3_hilbert1 B C)))  => (r8_ltlaxio1 D (k3_hilbert1 A C))) ) ) ) ) ) ) ) ) ).
tt(t47_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A B C)) A) => (v2_cqc_the1 (k8_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(t47_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_mathmorp A (k1_mathmorp A D B) C) = (k1_mathmorp A D (k5_mathmorp A B C))) ) ) ) ) ) ) ) ) ).
tt(t47_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r1_matrix10 B C) => (r1_matrix10 (k3_matrix10 A B D) (k3_matrix10 A C D))) ) ) ) ) ) ) ) ) ).
tt(t47_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k12_matrix_2 A) (k12_matrix_2 A)) &  ((v3_funct_2 B (k12_matrix_2 A) (k12_matrix_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (k12_matrix_2 A))))) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  ( (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  ((k3_funct_2 (k12_matrix_2 A) (k12_matrix_2 A) B D) = (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) C D)) ) )  =>  ((v5_matrix_2 C (k11_matrix_2 (k12_matrix_2 A))) |  ((k7_relat_1 B (a_1_0_matrix11 A)) = (a_1_1_matrix11 A)) ) ) ) ) ) ) ) ) ).
tt(t47_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r2_hidden B (k2_finseq_1 (k5_card_1 D))) & (r1_tarski E (k2_finseq_1 (k1_matrix_1 C))))  =>  ((k8_matrix_1 A (k6_matrix13 A C D E) B) = (k1_partfun1 k5_numbers k5_numbers k5_numbers A (k5_matrix13 E) (k8_matrix_1 A C (k1_funct_1 (k5_matrix13 D) B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 A) B B) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C B) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E B) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F B)) ) )  =>  ( ( ( (E = 1)  &  (F = C) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( ( ( (E = C)  &  (F = 1) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( ( ( (E = 1)  &  (F = 1) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) )  &  ( ( ( (E = C)  &  (F = C) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) )  &  ( (~  ( ( (E = 1)  |  (E = C) )  &  ( (F = 1)  |  (F = C) ) ) )  =>  ( ( (E = F)  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k5_struct_0 A)) )  &  ( (~  (E = F) )  =>  ((k3_matrix_1 (u1_struct_0 A) D E F) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (C = 1)  |  (D = (k4_matrix14 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 B)) &  ( ((k8_matrix_1 (u1_struct_0 A) B D) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 B) (k4_struct_0 A)))  &  ((r2_hidden D (k4_finseq_1 C)) &  ((k8_matrix_1 (u1_struct_0 A) C D) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 C) (k4_struct_0 A))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) 1) |  ((k4_matrix15 A B C) = (k4_matrix15 A (k8_matrix_2 A D B) (k8_matrix_2 A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v4_matrix16 C (u1_struct_0 A)) =>  ((k2_matrix16 (u1_struct_0 A) (k9_fvsum_1 A C B)) = (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k2_matrix16 (u1_struct_0 A) C) B)) ) ) ) ) ) ) ) ).
tt(t47_matrix_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 A)))  =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 D)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 D))) ) )  => (r2_hidden (k3_matrix_1 A D B C) (k16_matrix_1 D))) ) ) ) ) ) ) ) ) ).
tt(t47_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A B) C) D) = (k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A C) D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v4_matrix_6 C A B) & (r1_matrix_6 A B C D))  => (r1_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t47_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_8 A B (k2_matrix_6 A B (k2_matrix_6 A B C C) C) (k2_matrix_6 A B (k2_matrix_6 A B D D) D))) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrix_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_matrix_1 K (u1_struct_0 A) 3 3) =>  ( (K = (k3_finseq_4 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k3_finseq_4 (u1_struct_0 A) B C D) (k3_finseq_4 (u1_struct_0 A) E F G) (k3_finseq_4 (u1_struct_0 A) H I J)))  =>  ((k2_matrix_9 3 A K) = (k1_algstr_0 A (k1_algstr_0 A (k1_algstr_0 A (k1_algstr_0 A (k1_algstr_0 A (k8_group_1 A (k8_group_1 A B F) J) (k8_group_1 A (k8_group_1 A D F) H)) (k8_group_1 A (k8_group_1 A B G) I)) (k8_group_1 A (k8_group_1 A C G) H)) (k8_group_1 A (k8_group_1 A C E) J)) (k8_group_1 A (k8_group_1 A D E) I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ( ((k3_finseq_1 A) = 1)  =>  ((k17_rvsum_1 A) = (k9_matrix_5 A 1)) ) ) ) ).
tt(t47_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ( ((v2_matrixj1 F (u1_struct_0 D)) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 (u1_struct_0 D)))))  =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 D) A A) =>  ( ((r2_hidden B (k4_finseq_1 G)) & (r2_hidden C (k2_finseq_1 A)))  =>  ((k9_matrix_2 B C (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 D) (k15_matrixj1 (u1_struct_0 D) (k16_matrixj1 (u1_struct_0 D) A G) F))) D (k20_matrixj1 (u1_struct_0 D) E (k15_matrixj1 (u1_struct_0 D) (k16_matrixj1 (u1_struct_0 D) A G) F))) = (k13_matrixj1 (u1_struct_0 D) E (k3_matrixj1 (u1_struct_0 D) (k4_matrixj1 (u1_struct_0 D) (k9_matrix_2 B C A D G)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  ((k9_matrixr1 (k10_rvsum_1 B A)) = (k7_matrixr1 A (k9_matrixr1 B))) ) ) ) ) ) ).
tt(t47_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 A)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k12_matrixr1 C (k8_rvsum_1 A B)) = (k8_rvsum_1 (k12_matrixr1 C A) (k12_matrixr1 C B))) ) ) ) ) ) ) ) ) ).
tt(t47_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrlin F A B) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_matrlin H A (k6_prvect_1 A (k3_finseq_1 F))) =>  ( (H = (k11_matrix13 A (k3_finseq_1 F) (k3_finseq_1 F) (k12_matrix_1 A (k3_finseq_1 F))))  =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 A) (k3_finseq_1 E) (k3_finseq_1 H)) =>  ( ( (I = (k1_matrlin2 A C B D E F))  &  ((v13_vectsp_1 D C B) & (v1_mod_2 D A C B)) )  =>  ((k3_funct_2 (u1_struct_0 C) (u1_struct_0 (k6_prvect_1 A (k3_finseq_1 F))) (k4_matrlin2 A C (k6_prvect_1 A (k3_finseq_1 F)) E H I) G) = (k9_matrlin A B F (k3_funct_2 (u1_struct_0 C) (u1_struct_0 B) D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k23_rvsum_1 (k12_matrixr1 C A) B) = (k23_rvsum_1 A (k11_matrixr1 C B))) ) ) ) ) ) ) ) ) ).
tt(t47_matrtop1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 k2_vectsp_1) A B) => (v5_pre_topc (k3_matrtop1 A B C) (k15_euclid A) (k15_euclid B))) ) ) ) ) ) ).
tt(t47_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  ( (~  (D = (k1_mcart_1 A B C D)) )  &  ( (~  (D = (k2_mcart_1 A B C D)) )  &  (~  (D = (k3_mcart_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (A = (k2_measure6 A k6_numbers)) ) ) ).
tt(t47_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  (! [D:$i] :  ((v1_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k9_member_1 A C) (k9_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t47_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((r1_tarski (k8_memstr_0 A B D) C) =>  ((k5_memstr_0 A B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t47_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski C (k1_relset_1 A D)) =>  ((k8_subset_1 A C (k13_mesfunc1 D E)) = (k7_subset_1 A C (k8_subset_1 A C (k12_mesfunc1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_mesfun7c,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 (k7_complsp2 A))) =>  ((k1_seq_1 (k7_complsp2 A) B) = (k4_complex1 (k1_funct_1 A B))) ) ) ) ) ) ).
tt(t47_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k1_numbers E k6_numbers)))  &  ( (D = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers E G) D)) )  &  ((r3_mesfunc6 A B C F) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G D) => (r1_xxreal_0 (k1_seq_1 (k55_valued_1 A k1_numbers (k4_mesfunc5 A k1_numbers E H)) G) (k1_seq_1 F G))) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) => (v2_comseq_2 (k10_seqfunc A E G))) ) ) ) ) ) ) )  => (r1_mesfunc5 A B C (k8_mesfun7c A E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ( (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( (F = (k1_relset_1 A D))  & (r1_mesfunc1 A B D F)) ) )  &  ( (? [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) &  ( (F = (k1_relset_1 A E))  & (r1_mesfunc1 A B E F)) ) )  &  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  (~  ( (F = (k1_relset_1 A (k3_mesfunc1 A D E)))  & (r1_mesfunc1 A B (k3_mesfunc1 A D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc6 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r1_mesfunc6 A B (k19_rfunct_3 A C) D)) ) ) ) ) ) ) ) ) ).
tt(t47_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_tarski D (k1_relset_1 A F)) &  ((v6_supinf_2 F) &  ((r1_mesfunc1 A B F D) &  ((v2_mesfunc9 E A) &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers E G)) &  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers E G)) & (r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k7_numbers E G)))) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) =>  ((v1_mesfunc9 (k3_mesfunc5 A E G)) &  ((k1_mesfunc9 F G) = (k3_mesfunc9 (k3_mesfunc5 A E G))) ) ) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_mesfunc9 G H) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers E H) D))) ) )  &  ((v1_mesfunc9 G) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers F D)) = (k3_mesfunc9 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) =>  (! [C:$i] :  ((m1_midsp_1 C A) =>  (! [D:$i] :  ((m1_midsp_1 D A) =>  ( ((k7_midsp_1 A B C) = (k7_midsp_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t47_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_mmlquery C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k2_mmlquery A C B) = (k4_mmlquery A C B)) ) ) ) ) ) ).
tt(t47_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r3_modelc_1 A B C G F) <=> (r3_modelc_1 A B C G (k59_modelc_1 A B C D E F))) ) )  =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r3_modelc_1 A B C G (k27_modelc_1 (k48_modelc_1 A B C) D E)) => (r3_modelc_1 A B C G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_modelc_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((m1_subset_1 A (k1_zfmisc_1 (k13_modelc_2 B))) => (m1_subset_1 A (k1_zfmisc_1 k9_modelc_2))) ) ) ) ).
tt(t47_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r8_modelc_3 A B C) =>  (! [D:$i] :  ( ((r2_hidden D (k22_modelc_3 A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))))  =>  ((v3_modelc_3 (k10_modelc_3 D A) A) |  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 F E) & (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A) A)) ) ) )  => (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k3_relat_1 (k9_finseq_1 A) (k5_moebius1 (k1_newton A B))) = (k9_finseq_1 A)) ) ) ) ) ).
tt(t47_monoid_0,ax, ( (k47_binop_2 = (k1_realset1 k33_binop_2 k5_numbers))  &  (k47_binop_2 = (k1_realset1 k44_binop_2 k5_numbers)) ) ).
tt(t47_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 C C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  ((v1_binop_1 D C) =>  ((k7_relset_1 (k2_zfmisc_1 C C) C D (k2_zfmisc_1 A B)) = (k7_relset_1 (k2_zfmisc_1 C C) C D (k2_zfmisc_1 B A))) ) ) ) ) ) ) ) ).
tt(t47_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m3_pboole E A (k1_mboolean A B)) =>  ( ((r1_pboole A C E) & (r2_pboole A C D))  => (r2_pboole A (k4_mssubfam A B E) D)) ) ) ) ) ) ) ) ) ) ).
tt(t47_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C D) F G) =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ((r1_msualg_6 A D E B H) => (r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) C E) (k1_funct_1 H F) (k1_funct_1 H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_mycielsk,ax, (! [A:$i] :  ( ((v1_mycielsk A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_xxreal_0 (k2_mycielsk (k5_yellow_0 A B)) (k2_mycielsk A))) ) ) ) ).
tt(t47_nat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  => (r2_funct_2 k5_numbers A (k10_nat_1 A B k6_numbers) B)) ) ) ) ).
tt(t47_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_int_2 A B) =>  ((k5_card_1 (k1_polynom2 k10_newton (k12_nat_3 (k24_binop_2 A B)))) = (k23_binop_2 (k5_card_1 (k1_polynom2 k10_newton (k12_nat_3 A))) (k5_card_1 (k1_polynom2 k10_newton (k12_nat_3 B))))) ) ) ) ) ) ).
tt(t47_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~  (A = k6_numbers) )  &  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  (~  ( ((k3_finseq_1 C) = A)  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ( ( ((k1_recdef_1 C D) = 1)  => (r1_nat_d (k1_newton B D) A))  &  ( ((r1_nat_d (k1_newton B D) A) =>  ((k1_recdef_1 C D) = 1) )  &  ( (~  ( ((k1_recdef_1 C D) = k6_numbers)  & (r1_nat_d (k1_newton B D) A)) )  &  ( (~ (r1_nat_d (k1_newton B D) A))  =>  ((k1_recdef_1 C D) = k6_numbers) ) ) ) ) ) ) )  &  ((k11_nat_3 A B) = (k2_wsierp_1 C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 (k1_nat_1 A 2) B) | (r1_xxreal_0 (k2_nat_1 (k1_nat_1 A 1) 1) B))  =>  ( (~ (r1_xxreal_0 B (k1_nat_1 A 1)))  &  ( (~ (r1_xxreal_0 B (k7_nat_d (k1_nat_1 A 1) 1)))  &  ( (~ (r1_xxreal_0 B (k7_nat_d (k1_nat_1 A 1) 2)))  &  ((r1_xxreal_0 (k1_nat_1 A 1) B) &  ( (~ (r1_xxreal_0 B (k2_nat_1 (k7_nat_d A 1) 1)))  &  ( (~ (r1_xxreal_0 B (k7_nat_d (k2_nat_1 (k7_nat_d A 1) 1) 1)))  &  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B (k7_nat_d A 1)))  &  ( (~ (r1_xxreal_0 B (k7_nat_d A 2)))  & (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_nattra_1,ax, (! [A:$i] :  (! [B:$i] :  ((k12_nattra_1 (k3_cat_1 A B)) = (k3_cat_1 A B)) ) ) ).
tt(t47_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r10_ncfcont1 A C B) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_hidden G B) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A G D))))  & (r1_xxreal_0 E (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C G) (k7_partfun1 k2_numbers C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((r1_ndiff_1 B A C D) &  (! [E:$i] :  ((m1_nfcont_1 E B D) =>  (~  ((r1_tarski E (k1_relset_1 (u1_struct_0 B) C)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v2_ndiff_1 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ( ((k7_partfun1 (u1_struct_0 A) F (k4_struct_0 B)) = (k4_struct_0 A))  &  ((r1_nfcont_1 B A F (k4_struct_0 B)) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r2_hidden G E) =>  ((k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) C G) (k7_partfun1 (u1_struct_0 A) C D)) = (k3_rlvect_1 A (k17_lopban_1 B A (k3_ndiff_1 B A C D) (k5_algstr_0 B G D)) (k7_partfun1 (u1_struct_0 A) F (k5_algstr_0 B G D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 D (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v1_lopban_1 D (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v2_lopban_1 D (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C D)) &  ((v1_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C D) (k4_real_ns1 B)) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C D) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t47_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k11_prvect_2 A B))) =>  ( (D = (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A B)) (k3_ndiff_5 A B) C))  =>  (C = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t47_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_nat_d (k5_nat_d A B) (k3_xcmplx_0 A B))) ) ) ) ).
tt(t47_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k2_relset_1 (u1_struct_0 A) C) = (k1_tarski D)) ) )  => (r3_nfcont_1 B A C (k1_relset_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(t47_nfcont_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ((v1_nfcont_3 B (k4_real_ns1 A)) <=>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) => (v1_nfcont_3 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) B (k4_pdiff_1 C A)) (k4_real_ns1 1))) ) ) ) ) ) ) ) ).
tt(t47_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) => (r1_tarski (k9_normform A (k10_normform A B C)) (k10_normform A (k9_normform A B) C))) ) ) ) ) ).
tt(t47_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 B) (k9_oppcat_1 A B (k10_oppcat_1 A B C)) C)) ) ) ) ) ) ).
tt(t47_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r2_wellord1 A B) =>  ((v1_relat_2 (k2_wellord1 A B)) &  ((v4_relat_2 (k2_wellord1 A B)) &  ((v8_relat_2 (k2_wellord1 A B)) &  ((v1_partfun1 (k2_wellord1 A B) B) & (m1_subset_1 (k2_wellord1 A B) (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ) ) ) ) ).
tt(t47_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_orders_1 (k2_wellord1 (u1_orders_2 A) B)) =>  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t47_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (? [B:$i] :  ((v3_ordinal1 B) &  (? [C:$i] :  ((v3_ordinal1 C) &  ((v4_ordinal1 B) &  ((v7_ordinal1 C) &  (A = (k10_ordinal2 B C)) ) ) ) ) ) ) ) ) ).
tt(t47_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ( (B = (k10_ordinal2 (k11_ordinal2 C A) D))  & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v4_ordinal1 A) =>  ((v1_xboole_0 A) |  ((r2_hidden B (k3_ordinal5 A)) <=>  (? [C:$i] :  ((v3_ordinal1 C) &  ((r2_hidden C A) & (r2_hidden B (k3_ordinal5 C))) ) ) ) ) ) ) ) ) ).
tt(t47_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v3_ordinal6 C)) ) )  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 (k7_ordinal6 C))))  => (r1_abian (k1_funct_1 (k7_ordinal6 C) B) (k1_funct_1 C A))) ) ) ) ) ) ) ).
tt(t47_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v9_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v9_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t47_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) &  ((v8_osalg_1 A) &  ((v10_osalg_1 A) &  ((v2_osalg_4 A) & (l3_osalg_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m2_osafree C A B) <=> (r2_hidden C (k30_osafree A B))) ) ) ) ) ) ).
tt(t47_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (v2_binop_1 (k15_osalg_2 A B) (k13_osalg_2 A B))) ) ) ) ).
tt(t47_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_parsp_2 A B C C B) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t47_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k4_partfun1 A B)) =>  ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(t47_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ((r2_hidden (k4_tarski D E) (k1_partfun1 A B B C F G)) =>  ((r2_hidden (k4_tarski D (k7_partfun1 B F D)) F) & (r2_hidden (k4_tarski (k7_partfun1 B F D) E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((r6_pboole A (k2_pboole A B (k1_pboole A)) B) & (r6_pboole A (k2_pboole A (k1_pboole A) B) B)) ) ) ) ).
tt(t47_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k25_pcs_0 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k25_pcs_0 A B))) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E C) & (r2_hidden F D))  => (r1_pcs_0 A E F)) ) ) ) )  => (r1_pcs_0 (k25_pcs_0 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(t47_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r2_pdiff_5 B A) & (r2_pdiff_5 C A))  =>  ((r3_pdiff_1 3 2 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 2 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k7_real_1 (k2_pdiff_5 B A) (k2_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t47_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((v1_pdiff_7 C A) &  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ((r2_pdiff_7 A 1 E B C) & (r4_pdiff_7 A 1 (k2_pdiff_7 A 1 E B C) C)) ) ) ) ) )  =>  ((r1_pdiff_1 A 1 B D) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (? [F:$i] :  ((m2_finseq_1 F (k1_euclid 1)) &  ( ((k4_finseq_1 F) = (k2_finseq_1 A))  &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ((k1_funct_1 F G) = (k9_euclid 1 (k12_pdiff_1 A 1 G B D) (k1_seq_1 (k1_pdiff_1 G A) E))) ) ) )  &  ((k1_pdiff_6 A 1 (k8_pdiff_1 A 1 B D) E) = (k5_euclid_7 1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_pdiff_9 A B C))  => (r1_pdiff_9 A B (k26_valued_1 (k1_euclid A) k1_numbers C D))) ) ) ) ) ) ) ) ).
tt(t47_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k4_nat_d (k1_newton B C) A) = 1)  & (r1_int_2 B A))  =>  ((r1_xxreal_0 A 1) | (r1_nat_d (k3_pepin B A) C)) ) ) ) ) ) ) ) ).
tt(t47_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m3_pnproc_1 C A B) =>  (! [D:$i] :  ((m3_pnproc_1 D A B) =>  (! [E:$i] :  ((m3_pnproc_1 E A B) =>  ((k11_pnproc_1 A B (k7_domain_1 (k3_finseq_2 B) (k3_pre_poly B C) (k3_pre_poly B D)) (k6_domain_1 (k3_finseq_2 B) (k3_pre_poly B E))) = (k9_domain_1 (k3_finseq_2 B) (k4_pre_poly B C E) (k4_pre_poly B D E) (k4_pre_poly B E C) (k4_pre_poly B E D))) ) ) ) ) ) ) ) ) ) ).
tt(t47_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_bspace)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  ((k20_polyform A B (k4_vectsp_1 k2_bspace (k17_polyform A B) C D)) = (k4_vectsp_1 k2_bspace (k17_polyform A (k6_xcmplx_0 B 1)) C (k20_polyform A B D))) ) ) ) ) ) ) ) ) ).
tt(t47_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k4_polynom5 A B (k5_struct_0 A)) D) = (k1_algstr_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(t47_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) E F) => (r1_rewrite1 (k3_polyred A B C D) (k10_polynom1 A C G E) (k10_polynom1 A C G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((v1_abian B) =>  ((k3_power (k4_xcmplx_0 A) B) = (k3_power A B)) ) ) ) ) ) ).
tt(t47_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A B C) => (r6_pboole A (k11_pre_poly A (k12_pre_poly A C B) B) C)) ) ) ) ) ) ) ).
tt(t47_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (B = k6_numbers)  =>  ((k6_prepower A B) = 1) ) ) ) ) ) ).
tt(t47_prob_3,ax, (! [A:$i] :  (? [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) =>  ((k4_prob_3 A B C) = A) ) ) ) ) ) ) ).
tt(t47_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden B (k4_cqc_the1 A)) & (r2_hidden C (k4_cqc_the1 A)))  => (r2_hidden (k7_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t47_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k16_pscomp_1 B)) =>  ( ((k17_euclid A) = (k17_euclid (k23_pscomp_1 B)))  &  ((v2_compts_1 B (k15_euclid 2)) =>  ((r1_xxreal_0 (k18_euclid (k23_pscomp_1 B)) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k18_euclid (k22_pscomp_1 B)))) ) ) ) ) ) ) ) ).
tt(t47_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k3_pboole A (k2_pzfmisc1 A B C) D) (k1_pboole A)) =>  ((v1_xboole_0 A) |  ( (~ (r1_pboole A B D))  &  (~ (r1_pboole A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((v2_qc_lang1 B A) & (r1_qc_lang2 A C B)) ) ) ) ) ) ) ) ).
tt(t47_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v2_qc_lang2 B A) =>  ((k4_qc_lang3 A C B) = (k4_subset_1 C (k4_qc_lang3 A C (k12_qc_lang2 A B)) (k4_qc_lang3 A C (k11_qc_lang2 A B)))) ) ) ) ) ) ) ) ).
tt(t47_quatern2,ax, ((k8_quatern2 (k5_struct_0 k16_quatern2)) = (k5_struct_0 k16_quatern2)) ).
tt(t47_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k8_quatern2 (k31_quaterni A)) = (k31_quaterni (k8_quatern2 A))) ) ) ).
tt(t47_quaterni,ax, ((k31_quaterni k22_quaterni) = k22_quaterni) ).
tt(t47_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k19_quofield A))) =>  ( (~  (B = (k4_struct_0 (k19_quofield A))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (C = (k4_struct_0 A)) )  =>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ( ( (B = (k10_quofield A D))  &  (D = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C (k5_struct_0 A))) )  =>  (! [E:$i] :  ((m2_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ( (E = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k5_struct_0 A) C))  =>  ((k11_algstr_0 (k19_quofield A) B) = (k10_quofield A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_rcomp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((m1_setfam_1 B (u1_struct_0 A)) & (v1_finset_1 B))  =>  (! [D:$i] :  ( ( (C = (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B (a_2_1_rcomp_3 A B)))  &  (D = (a_2_2_rcomp_3 A C)) )  => (r5_orders_1 (k1_wellord2 D) D)) ) ) ) ) ) ) ) ) ).
tt(t47_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers) k6_numbers))  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (B = (k3_funct_2 k5_numbers k1_numbers (k5_real_3 A) (k1_nat_1 D 1)))  &  (C = (k1_seq_1 (k5_real_3 A) D)) )  =>  ((k6_nat_d B C) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( (! [C:$i] :  ((r2_hidden C A) => (r2_hidden (k4_tarski C C) B)) )  => (r1_tarski (k4_relat_1 A) B)) ) ) ) ).
tt(t47_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((k7_relset_1 B A (k3_relset_1 A B C) D) = (k7_relset_1 B A (k3_relset_1 A B C) (k3_xboole_0 D (k10_xtuple_0 C)))) ) ) ) ) ) ).
tt(t47_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_rewrite1 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski B A) => (v1_rewrite1 B)) ) ) ) ) ).
tt(t47_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) => (r2_hidden C (k8_rewrite2 A B C))) ) ) ) ) ).
tt(t47_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden (k2_xcmplx_0 E 1) (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  (! [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 A)) =>  (~  ( ((k1_funct_1 D E) = (k4_tarski F G))  &  ((k1_funct_1 D (k2_xcmplx_0 E 1)) = (k4_tarski H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((k5_relat_1 (k45_valued_1 B C) A) = (k45_valued_1 (k5_relat_1 B A) (k5_relat_1 C A)))  &  ( ((k5_relat_1 (k45_valued_1 B C) A) = (k45_valued_1 (k5_relat_1 B A) C))  &  ((k5_relat_1 (k45_valued_1 B C) A) = (k45_valued_1 B (k5_relat_1 C A))) ) ) ) ) ) ) ) ).
tt(t47_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A) A))) ) ).
tt(t47_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 (k1_seq_1 B C) k6_numbers)) ) )  => (r2_relset_1 A k1_numbers (k19_rfunct_3 A B) (k32_valued_1 A k1_numbers B))) ) ) ) ) ).
tt(t47_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 B) =>  ((k1_seq_1 (k4_rinfsup1 B) A) = (k4_xxreal_0 (k1_seq_1 (k4_rinfsup1 B) (k2_nat_1 A 1)) (k1_seq_1 B A))) ) ) ) ) ) ).
tt(t47_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_rlaffin1 B A) & (v2_rlaffin1 C A))  => (v2_rlaffin1 (k4_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t47_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r2_hidden (k4_struct_0 A) (k3_rlsub_1 A B C)) <=>  ((k3_rlsub_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t47_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_rlsub_2 A B C) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D C B))) ) ) ) ) ) ) ) ) ) ).
tt(t47_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k1_numbers))  =>  ((k2_relset_1 (u1_struct_0 A) (k4_rltopsp1 A B)) = (k2_struct_0 A)) ) ) ) ) ).
tt(t47_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_rlvect_1 A (k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A))) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t47_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlvect_2 D A) => (r1_rlvect_2 A (k8_rlvect_2 A B (k8_rlvect_2 A C D)) (k8_rlvect_2 A (k8_real_1 B C) D))) ) ) ) ) ) ) ) ).
tt(t47_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_rmod_2 A B C (k2_rmod_2 A B)) = (u1_struct_0 B)) ) ) ) ) ) ) ).
tt(t47_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))))  &  ((v10_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) & (l3_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B)))) ) ) ) ) ) ).
tt(t47_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) => (r1_rmod_4 A B (k7_rmod_4 A B C (k6_rmod_4 A B D E)) (k6_rmod_4 A B (k7_rmod_4 A B C D) (k7_rmod_4 A B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t47_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_robbins1 A B (k3_robbins1 A C)) = (k9_robbins1 A C (k3_robbins1 A B))) ) ) ) ) ) ) ).
tt(t47_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) D)) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) C)))) C) = (k3_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) C)))) ) ) ) ) ) ) ) ) ).
tt(t47_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski B C) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A C) D))) ) ) ) ) ) ) ) ) ).
tt(t47_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_xboole_0 B C) =>  ((r1_xxreal_0 (k1_rpr_1 A B) k6_numbers) |  ((r1_xxreal_0 1 (k1_rpr_1 A C)) |  ((k2_rpr_1 A (k3_subset_1 A C) (k3_subset_1 A B)) = (k9_real_1 1 (k10_real_1 (k1_rpr_1 A B) (k9_real_1 1 (k1_rpr_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(t47_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=>  ((k3_rusub_1 A D B) = (k3_rusub_1 A (k5_algstr_0 A D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t47_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((r1_rusub_2 A C D) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A B C D)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t47_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)))  =>  ((r1_xxreal_0 C k6_numbers) |  ((k4_bhsp_2 A B C) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t47_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k10_rvsum_1 (k9_finseq_1 B) A) = (k12_finseq_1 k1_numbers (k11_binop_2 A B))) ) ) ) ) ).
tt(t47_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k20_rvsum_1 (k5_finseq_2 k2_numbers A (k5_binop_2 B C))) = (k5_binop_2 (k19_rvsum_1 (k2_finseq_2 A B)) (k19_rvsum_1 (k2_finseq_2 A C)))) ) ) ) ) ) ) ).
tt(t47_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k1_relset_1 k2_scmfsa_2 (k5_relat_1 A k2_scmfsa_2)) = k2_scmfsa_2) ) ) ).
tt(t47_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A B))  & (r4_scmfsa7b (k2_scmfsa6a A) B)) ) ) ) ) ) ).
tt(t47_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 B))  &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_afinsq_1 B) & (v7_amistd_1 B 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) &  ( (~ (v1_scmfsa_m C))  & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~  ((r1_xxreal_0 (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) (k1_nat_1 F 1)))) &  (~  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers) ) ) )  &  ( ( ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F) C) k6_numbers))  &  ((r1_xxreal_0 (k1_funct_1 (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F) C) k6_numbers) =>  ((k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers E (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D B C A) F)) = k6_numbers) ) ) ) ) ) ) )  =>  ((r6_scmfsa7b (k2_scmfsa_9 C B) D A) & (r5_scmfsa7b (k2_scmfsa_9 C B) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t47_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((r1_scm_halt D B A) & (r2_scm_halt D B A))  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) | (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k16_scmpds_2 D E B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k16_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C)))  &  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k16_scmpds_2 D E B C) A) F) = (k1_funct_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_funct_1 (k5_scmpds_6 A B C) k6_numbers) = (k7_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 1))) ) ) ) ) ) ) ).
tt(t47_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) k6_numbers) =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_7 D F G C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  ( (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  =>  ( (B = C)  | (r2_hidden (k2_tarski B C) (k1_scmyciel A))) ) ) )  => (v5_scmyciel A)) ) ) ).
tt(t47_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_semi_af1 A B C D E) & (r2_semi_af1 A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers A)) (k26_valued_1 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers A) (k1_real_1 1)))) ) ).
tt(t47_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v3_membered B) =>  ( ((r1_tarski A B) & (v3_xxreal_2 B))  => (r1_xxreal_0 (k3_seq_4 B) (k3_seq_4 A))) ) ) ) ) ).
tt(t47_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 A C)) & (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 (k7_real_1 (k1_seq_1 (k1_series_3 A) C) (k1_seq_1 (k1_series_3 B) C)) (k1_seq_1 (k1_series_3 (k1_series_1 k1_numbers A B)) C))) ) ) ) ) ) ) ).
tt(t47_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 1 (k7_square_1 (k2_nat_1 B 1)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_xxreal_0 (k3_xcmplx_0 2 (k7_square_1 (k2_nat_1 B 1))) (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ) ).
tt(t47_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((v3_setfam_1 B A) & (r1_tarski C B))  => (v3_setfam_1 C A)) ) ) ) ) ) ).
tt(t47_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v2_prob_1 C) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) (k2_nat_1 A 1)) (k3_funct_2 k5_numbers (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t47_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k2_setlim_2 B C D)) A) = (k4_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t47_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  ((k10_setwiseo A B (k1_setwiseo A) C) = k1_xboole_0) ) ) ) ) ) ).
tt(t47_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ((k4_sf_mastr (k6_scmfsa6a A B)) = (k5_setwiseo k3_scmfsa_2 (k3_sf_mastr A) (k3_sf_mastr B))) ) ) ) ) ).
tt(t47_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A D (k5_sheffer1 A B (k5_sheffer1 A B C))))) = (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A C C)))) ) ) ) ) ) ) ) ) ).
tt(t47_simplex0,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m3_simplex0 C B A) =>  ( (~ (v1_xboole_0 C))  => (v7_ordinal1 A)) ) ) ) ) ) ) ).
tt(t47_simplex1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_rlaffin1 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C)))) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C)))) C)))) )  =>  (~  ( (! [E:$i] :  ((m1_subset_1 E (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C))))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski F C) & (r2_hidden E (k3_convex1 B F)))  => (r2_hidden (k1_funct_1 D E) F)) ) ) ) )  &  (! [E:$i] :  ((m3_simplex0 E (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C))) (k5_real_1 (k5_card_1 C) 1)) =>  (~  ((k7_relset_1 (k4_simplex0 (k5_simplex1 A B (k5_simplex0 (u1_struct_0 B) (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 B)) C)))) C D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_sincos10,ax,(r1_tarski (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)) (k1_relset_1 k1_numbers k3_sincos10))).
tt(t47_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k5_binop_2 (k7_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B))) k7_complex1))) ) ) ) ) ).
tt(t47_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k20_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) = k6_numbers) )  =>  ((k7_xcmplx_0 (k6_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k2_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B))) = (k1_sin_cos4 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2))) ) ) ) ) ) ).
tt(t47_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A k6_numbers) => (r1_xxreal_0 (k3_sin_cos2 A) k6_numbers)) ) ) ).
tt(t47_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t47_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A 1) =>  ((r1_xxreal_0 A k6_numbers) |  ((k6_sin_cos7 A) = (k2_sin_cos7 (k12_binop_2 1 A))) ) ) ) ) ).
tt(t47_sin_cos9,ax,(v5_valued_0 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t47_sin_cos,ax, ((k1_relset_1 k1_numbers k24_sin_cos) = k1_numbers) ).
tt(t47_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r2_hidden A (k10_xtuple_0 B)) =>  ( ((k4_finseq_4 B A) = (k3_finseq_1 B))  | (v4_topreal1 (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ) ).
tt(t47_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  =>  ((k6_pscomp_1 A) = (k3_xxreal_0 (k6_pscomp_1 B) (k6_pscomp_1 C))) ) ) ) ) ) ) ) ).
tt(t47_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ( (~ (v3_funct_1 E))  &  ((v1_finseq_6 E (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 E) &  ((v2_topreal1 E) &  ((v1_goboard5 E) &  ((v2_goboard5 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 E))) ) )  =>  ((r1_xxreal_0 C B) |  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k3_finseq_1 E) D))  | (r1_xboole_0 (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E A B)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_sprect_3,ax, (! [A:$i] :  ( ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) B C)) =>  ((r2_hidden C (k3_topreal1 2 A)) | (r1_tarski (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B C) (k3_topreal1 2 A)) (k1_tarski B))) ) ) ) ) ) ) ) ).
tt(t47_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t47_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k3_square_1 A) (k3_square_1 B)) & (r1_xxreal_0 k6_numbers B))  =>  ((r1_xxreal_0 (k4_xcmplx_0 B) A) & (r1_xxreal_0 A B)) ) ) ) ) ) ).
tt(t47_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_stacks_1 B) &  ((v3_stacks_1 B) &  ((v4_stacks_1 B) &  ((v5_stacks_1 B) &  ((v6_stacks_1 B) & (l1_stacks_1 B)) ) ) ) ) ) )  =>  ( ((r4_stacks_1 A B) & (v7_stacks_1 A))  => (v7_stacks_1 B)) ) ) ) ) ).
tt(t47_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k3_stirl2_1 A 2) = (k11_binop_2 (k18_binop_2 1 2) (k10_binop_2 (k2_newton 2 A) 2))) ) ) ) ).
tt(t47_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r1_tarski (k24_qc_lang1 A B) (k9_substut1 A B))) ) ) ) ).
tt(t47_subset_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (~  ((v1_zfmisc_1 B) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k1_tarski C)) ) ) ) ) ) ) ) ) ) ).
tt(t47_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ((v6_supinf_2 A) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  & (v7_supinf_2 B)) )  => (v7_supinf_2 A)) ) ) ) ) ).
tt(t47_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))))) ) ) ) ).
tt(t47_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_tdlat_1 A)))) =>  ( (C = B)  =>  ((k15_lattice3 (k4_tdlat_1 A) C) = (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ) ) ).
tt(t47_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_tex_2 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) & (m1_pre_topc C A)) )  =>  (~  ((v4_tex_2 C A) &  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_pre_topc B A) =>  (~ (v3_tex_3 B A)) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t47_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k2_tex_4 A B) (k1_setfam_1 (a_2_1_tex_4 A B)))) ) ) ) ).
tt(t47_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ( (G = (k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F))  &  ((r1_tmap_1 B C D F) & (r1_tmap_1 C A E G)) )  => (r1_tmap_1 B A (k1_partfun1 (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 C) (u1_struct_0 A) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((r2_hidden C (u1_struct_0 (k5_topalg_1 A B))) <=>  (? [D:$i] :  ((m1_borsuk_2 D A B B) &  (C = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) D)) ) ) ) ) ) ) ) ) ).
tt(t47_topalg_6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r1_xxreal_0 3 A) => (v1_topalg_6 (k7_toprealb A C B))) ) ) ) ) ) ) ).
tt(t47_topgen_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k3_numbers)  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = k1_borsuk_5) ) ) ) ).
tt(t47_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v7_topgen_4 A) => (v6_pre_topc A)) ) ) ).
tt(t47_topgen_5,ax, (~ (v10_pre_topc k3_topgen_5)) ).
tt(t47_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v4_pre_topc (k4_group_2 A C B) A)) ) ) ) ) ) ).
tt(t47_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k9_pscomp_1 C) = (k9_real_1 (k18_euclid A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t47_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  ( (D = (k19_euclid A B))  =>  ((k10_metric_1 (k14_euclid 2) D C) = (k7_jgraph_6 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t47_toprealc,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((v3_membered D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) D)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k4_toprealc B (k3_funct_2 (u1_struct_0 C) (u1_struct_0 (k15_euclid B)) (k15_toprealc B (u1_struct_0 C) D E) F) A) = (k3_funct_2 (u1_struct_0 C) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_1 B A) &  ((v1_tops_1 C A) & (v3_pre_topc C A)) )  => (v1_tops_1 (k9_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t47_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ((v5_pre_topc C A B) & (v1_tops_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (E = (k7_relat_1 (k3_funct_3 C) D))  => (v1_tops_2 E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (v2_tops_1 C A))  => (v1_tops_1 (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t47_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo D A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C) = C) ) )  =>  ( (B = C)  | (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t47_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) => (r1_xxreal_0 (k6_trees_1 (k4_trees_1 A B)) (k6_trees_1 A))) ) ) ) ).
tt(t47_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ((m1_trees_1 C (k2_xboole_0 A B)) =>  ( ( ((r2_hidden C A) & (r2_hidden C B))  =>  ((k4_trees_1 (k2_xboole_0 A B) C) = (k2_xboole_0 (k4_trees_1 A C) (k4_trees_1 B C))) )  &  ( ( (~ (r2_hidden C A))  =>  ((k4_trees_1 (k2_xboole_0 A B) C) = (k4_trees_1 B C)) )  &  ( (~ (r2_hidden C B))  =>  ((k4_trees_1 (k2_xboole_0 A B) C) = (k4_trees_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t47_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  =>  ((v1_finset_1 A) <=>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  ((k2_trees_2 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t47_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r2_tsep_1 A B C)) ) ) ) ) ) ) ).
tt(t47_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (~  ( (~ (r1_tsep_1 C B))  &  ( (~ (r1_tsep_1 D B))  &  (? [E:$i] :  ((m1_pre_topc E B) &  (? [F:$i] :  ((m1_pre_topc F B) &  ( (E = (k2_tsep_1 A C B))  &  ( (F = (k2_tsep_1 A D B))  &  ((r4_tsep_1 A C D) &  (~ (r4_tsep_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_turing_1,ax, (! [A:$i] :  ((l1_turing_1 A) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((m2_funct_2 C k4_numbers (u1_turing_1 (k32_turing_1 A B)) (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 A B)))) =>  ( ((u1_turing_1 A) = (u1_turing_1 B))  =>  ((m2_funct_2 C k4_numbers (u1_turing_1 A) (k9_funct_2 k4_numbers (u1_turing_1 A))) & (m2_funct_2 C k4_numbers (u1_turing_1 B) (k9_funct_2 k4_numbers (u1_turing_1 B)))) ) ) ) ) ) ) ) ).
tt(t47_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k37_twoscomp A B) (k38_twoscomp A B)))) =>  ( ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) (k39_twoscomp A B)) = (k1_funct_1 k3_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) A) = (k1_funct_1 C A))  &  ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t47_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((v1_int_1 B) => (v1_int_1 (k2_polynom4 k1_complfld (k4_uniroots A k1_complfld) B))) ) ) ) ) ).
tt(t47_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (~  ((r1_polynom5 A C B) & (r1_xxreal_0 (k1_algseq_1 A (k6_uproots A B C)) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t47_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [F:$i] :  ((m2_subset_1 F (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [G:$i] :  ((m1_valuat_1 G A B) =>  (! [H:$i] :  ((m1_subset_1 H (k9_qc_lang1 A)) =>  ( ( (E = (k13_cqc_lang A H C))  &  ( (F = (k13_cqc_lang A H D))  & (r2_valuat_1 A B G E)) )  =>  ((r2_hidden C (k24_qc_lang1 A H)) | (r2_valuat_1 A B G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k9_xtuple_0 (k36_valued_2 B D C)) = (k1_relset_1 A D)) ) ) ) ) ) ) ) ).
tt(t47_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_vectsp_4 A B C (k2_vectsp_4 A B)) = (u1_struct_0 B)) ) ) ) ) ) ) ).
tt(t47_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( ((k1_vectsp_5 A B C D) = B)  <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  ((k4_vectsp_6 A B (k8_vectsp_6 A B C D)) = (k5_algstr_0 B (k4_vectsp_6 A B C) (k4_vectsp_6 A B D))) ) ) ) ) ) ) ) ) ).
tt(t47_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers))))  =>  ( ((v1_comseq_2 (k2_partfun1 C k1_numbers F A)) & (r1_vfunct_1 C D E B))  => (r1_vfunct_1 C D (k3_vfunct_1 C D F E) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_comseq_2 (k2_partfun1 A k2_numbers F D)) & (r1_vfunct_2 A B C E))  => (r1_vfunct_2 A B (k1_vfunct_2 A B F C) (k3_xboole_0 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_waybel_0 C A)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden E B) & (r1_tarski (k4_subset_1 (u1_struct_0 A) C D) E)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k5_setfam_1 (u1_struct_0 A) B))  => (v2_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(t47_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_tops_1 A (k6_waybel_0 A B)) = (k2_waybel_3 A B)) ) ) ) ) ).
tt(t47_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_0_waybel_1 A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C)))))) )  =>  ( (D = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C))  => (v7_waybel_1 D (k5_yellow_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) &  ((v2_waybel19 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_waybel21 C A B) =>  ((v5_pre_topc C A B) <=> (v1_waybel21 C A B)) ) ) ) ) ) ) ).
tt(t47_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k3_yellow_0 A) B) =>  ((m1_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A C D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ((r3_orders_2 A C E) & (r1_waybel_3 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_waybel27,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v1_lattice3 C) &  ((v2_lattice3 C) &  ((v3_lattice3 C) & (l1_orders_2 C)) ) ) ) ) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_waybel27 A (k2_waybel27 B C))) (u1_struct_0 (k2_waybel27 (k3_yellow_3 A B) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_waybel27 A (k2_waybel27 B C))) (u1_struct_0 (k2_waybel27 (k3_yellow_3 A B) C)))))) )  &  ((v1_waybel27 D) & (v23_waybel_0 D (k2_waybel27 A (k2_waybel27 B C)) (k2_waybel27 (k3_yellow_3 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t47_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) )  =>  ((v10_waybel_0 C A) =>  ((k12_lattice3 A B (k1_waybel_2 A C)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A C))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ((k12_lattice3 A B (k4_yellow_2 A D)) = (k1_waybel_2 A (k3_waybel_2 A B (k2_waybel_2 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t47_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  ((k8_waybel34 A) = (k2_yellow20 (k4_waybel34 A) (k6_yellow21 A))) ) ) ).
tt(t47_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v8_waybel_4 B A) => (v9_waybel_4 B A)) ) ) ) ) ).
tt(t47_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  (~  ((v2_wellord1 C) &  ((r2_hidden A (k1_relat_1 C)) &  ((r2_hidden B (k1_relat_1 C)) &  ( (~  (A = B) )  & (r4_wellord1 (k2_wellord1 C (k1_wellord1 C A)) (k2_wellord1 C (k1_wellord1 C B)))) ) ) ) ) ) ) ) ) ).
tt(t47_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 A (k3_xboole_0 A B)) = (k4_xboole_0 A B)) ) ) ).
tt(t47_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k9_xboolean A (k7_xboolean A B)) = (k4_xboolean (k3_xboolean A) B)) ) ) ) ) ).
tt(t47_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k3_xcmplx_0 (k6_xcmplx_0 A B) (k6_xcmplx_0 C D)) = (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 A D)) (k3_xcmplx_0 B C)) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t47_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k6_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(t47_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r2_hidden A k1_numbers) & (r1_xxreal_0 C A))  =>  ((r1_xxreal_0 C B) | (r2_hidden C k1_numbers)) ) ) ) ) ) ) ) ).
tt(t47_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~ (r1_tarski (k1_xxreal_1 B C) (k4_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t47_xxreal_2,ax,(v3_xxreal_2 (k1_tarski k1_xxreal_0))).
tt(t47_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 k6_numbers B) &  ( (~ (r1_xxreal_0 C (k1_xxreal_3 B A)))  & (r1_xxreal_0 (k3_xxreal_3 C A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t47_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_yellow_0 A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) <=> (r2_lattice3 A C D)) ) ) )  =>  ((k1_yellow_0 A B) = (k1_yellow_0 A C)) ) ) ) ) ) ).
tt(t47_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k5_yellow_3 A B (k1_waybel_3 (k3_yellow_3 A B) C)) = (k1_waybel_3 B (k9_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t47_yellow12,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((l1_pre_topc C) =>  ((m3_yellow_9 A B C) <=> (m3_yellow_9 (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) B C)) ) ) ) ) ) ) ).
tt(t47_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden C D) => (r2_hidden B D)) ) )  =>  ((v1_funct_1 (k5_funct_4 (u1_struct_0 A) k6_numbers 1 C B)) &  ((v1_funct_2 (k5_funct_4 (u1_struct_0 A) k6_numbers 1 C B) (u1_struct_0 k9_waybel18) (u1_struct_0 A)) &  ((v5_pre_topc (k5_funct_4 (u1_struct_0 A) k6_numbers 1 C B) k9_waybel18 A) & (m1_subset_1 (k5_funct_4 (u1_struct_0 A) k6_numbers 1 C B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k9_waybel18) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t47_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) & (m1_altcat_2 B A)) )  => (m1_altcat_2 (k1_yellow18 B) (k1_yellow18 A))) ) ) ) ).
tt(t47_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ((r2_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) k1_xboole_0) &  ((k2_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) k1_xboole_0) = (k2_struct_0 A)) ) ) ) ).
tt(t47_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))))  =>  ( ((v3_lattice3 (k3_yellow_3 A B)) | (r2_yellow_0 (k3_yellow_3 A B) C))  =>  ((k2_yellow_0 (k3_yellow_3 A B) C) = (k7_yellow_3 A B (k2_yellow_0 A (k4_yellow_3 A B C)) (k2_yellow_0 B (k5_yellow_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t47_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k7_domain_1 (u1_struct_0 A) C D)) = (k7_domain_1 (u1_struct_0 A) (k11_lattice3 A B C) (k11_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t47_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A B C) = (k13_lattice3 A (k1_yellow_5 A B C) C)) ) ) ) ) ) ) ).
tt(t47_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) => (r3_orders_2 A (k4_yellow_2 A (k5_waybel_5 A D)) (k5_yellow_2 A (k4_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D))))) ) ) ) ) ) ) ) ).
tt(t47_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v1_waybel11 C A))  => (v1_waybel11 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t47_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r2_zf_lang (k7_zf_lang A B) C) =>  ((r3_zf_lang A C) & (r3_zf_lang B C)) ) ) ) ) ) ) ) ).
tt(t47_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v9_zf_lang A) =>  (A = (k11_zf_lang (k25_zf_lang A) (k26_zf_lang A))) ) ) ) ).
tt(t47_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (r2_hidden C B))  =>  ((k3_xboole_0 (k2_tarski A C) B) = (k2_tarski A C)) ) ) ) ) ).
tt(t47_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  =>  (B = A) ) ) ) ) ) ).
tt(t48_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) =>  ((k8_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) = (k8_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) D C))) ) ) ) ) ) ) ) ) ) ).
tt(t48_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  =>  (! [D:$i] :  ((m1_abcmiz_1 D A B) =>  (! [E:$i] :  ((m1_abcmiz_1 E A C) =>  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_abcmiz_a,ax, (! [A:$i] :  ( ((v9_abcmiz_1 A k27_abcmiz_1) & (m1_abcmiz_1 A k27_abcmiz_1 (k12_abcmiz_1 k27_abcmiz_1)))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 k27_abcmiz_1))))  =>  ((k18_abcmiz_a (k40_abcmiz_1 k27_abcmiz_1 B A)) = (k2_xboole_0 (k9_abcmiz_a k27_abcmiz_1 A) (k3_tarski (a_1_2_abcmiz_a B)))) ) ) ) ) ).
tt(t48_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_aff_1 F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D F) & (r2_analoaf A B C D E)) ) )  =>  ( (B = C)  | (r2_hidden E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) )  &  ((v1_aff_4 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t48_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)) (k5_afinsq_1 G)) (k5_afinsq_1 H)))  =>  ( ((k1_afinsq_1 A) = 7)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ( ((k1_funct_1 A 3) = E)  &  ( ((k1_funct_1 A 4) = F)  &  ( ((k1_funct_1 A 5) = G)  &  ((k1_funct_1 A 6) = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v3_valued_0 A) =>  ((k7_afinsq_2 A) = (k6_afinsq_2 k1_numbers A k33_binop_2)) ) ) ) ).
tt(t48_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((r2_hidden D B) &  ((r2_hidden D C) &  ((r2_hidden F B) &  ((r2_hidden G B) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden J C) &  ((r2_analoaf A E I F H) & (r2_analoaf A F J G I)) ) ) ) ) ) ) ) ) )  =>  ( (B = C)  |  ( (D = F)  |  ( (D = I)  |  ( (D = J)  |  ( ( (~  (E = F) )  &  ( (~  (F = G) )  &  (~  (E = G) ) ) )  | (r2_analoaf A E J G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v2_struct_0 (k5_afvect0 A B)))  &  ( (~ (v7_struct_0 (k5_afvect0 A B)))  &  ((v13_algstr_0 (k5_afvect0 A B)) &  ((v2_rlvect_1 (k5_afvect0 A B)) &  ((v3_rlvect_1 (k5_afvect0 A B)) &  ((v4_rlvect_1 (k5_afvect0 A B)) &  ((v12_vectsp_1 (k5_afvect0 A B)) &  ((v1_tdgroup (k5_afvect0 A B)) & (l2_algstr_0 (k5_afvect0 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  => (m2_algspec1 (k2_circcomb A B) B)) ) ) ) ).
tt(t48_algstr_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) => (v2_funct_2 (k18_algstr_4 A B C) (u1_struct_0 (k14_algstr_4 B)))) ) ) ) ) ) ) ).
tt(t48_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v2_altcat_3 D A B C) &  (~  ((k1_altcat_1 A C B) = k1_xboole_0) ) ) ) ) ) ) ) )  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (k4_altcat_4 A)) ) ) ) ).
tt(t48_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r6_analmetr A C D B) =>  ( ( (~ (r2_analoaf A C D E F))  &  (~ (r2_analoaf A E F C D)) )  |  ( (C = D)  | (r6_analmetr A E F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ( (~ (r1_analort A B C D G E F))  &  ( (~ (r1_analort A B C D G F E))  &  ((r1_analort A B C F H F E) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( ((r1_analort A B C D G D I) | (r1_analort A B C D G I D))  &  ((r1_analort A B C F H F I) | (r1_analort A B C F H I F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_aofa_000,ax, (! [A:$i] :  ( ((v4_unialg_1 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) )  =>  ((k1_relset_1 (k3_finseq_2 (u1_struct_0 A)) (k2_pua2mss1 A (k1_funct_7 4 (k4_finseq_1 (u1_unialg_1 A))))) = (k4_finseq_2 2 (u1_struct_0 A))) ) ) ).
tt(t48_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k65_aofa_i00 A B D E F)) D) = (k6_int_1 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C) 2))  &  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k66_aofa_i00 A B D E F)) D) = (k6_int_1 (k2_xcmplx_0 (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C) 1) 2))  &  (! [G:$i] :  ((m1_subset_1 G B) =>  ( (~  (G = D) )  =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k65_aofa_i00 A B D E F)) G) = (k21_aofa_i00 B k4_numbers C G))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k66_aofa_i00 A B D E F)) G) = (k21_aofa_i00 B k4_numbers C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_armstrng,ax, (! [A:$i] :  ((l1_armstrng A) =>  ( (~ (v1_xboole_0 (k13_armstrng (u1_armstrng A) (k5_armstrng A))))  & (v11_armstrng (k13_armstrng (u1_armstrng A) (k5_armstrng A)))) ) ) ).
tt(t48_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((k10_arytm_3 A k11_arytm_3) = k11_arytm_3) ) ) ).
tt(t48_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 9))  & (r1_xxreal_0 (k4_power 2 A) (k5_square_1 (k8_real_1 2 A)))) ) ) ) ).
tt(t48_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C B) = (k1_bcialg_1 A B C)) ) ) ) )  <=> (v13_bcialg_1 A)) ) ) ).
tt(t48_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m4_bcialg_2 C A B) =>  (! [D:$i] :  ((m1_bcialg_2 D A) =>  ( (! [E:$i] :  ((m2_bcialg_2 E A) => (m5_bcialg_2 E A B)) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(t48_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) &  ((v6_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v2_bcialg_3 B A) =>  ((v11_bcialg_3 A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_bcialg_1 A (k1_bcialg_1 A (k1_bcialg_1 A C (k1_bcialg_1 A D E)) (k1_bcialg_1 A C D)) (k1_bcialg_1 A C (k1_bcialg_1 A B E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v4_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_4 A B C) = (k1_bcialg_4 A B (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ).
tt(t48_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v20_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  => (m1_bcialg_5 A k6_numbers 1 k6_numbers k6_numbers)) ) ) ).
tt(t48_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_2 D (u1_struct_0 B)) =>  ((v12_bcialg_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B) & (m2_bcialg_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t48_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  (B = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t48_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ((v3_funct_1 C) => (v3_funct_1 (k5_normsp_1 B C A))) ) ) ) ) ) ) ).
tt(t48_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k5_bhsp_2 A C D)) <=> (r1_xxreal_0 (k4_bhsp_1 A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t48_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v2_comseq_2 A) & (v1_bhsp_2 C B))  => (v1_bhsp_2 (k5_bhsp_4 B C A) B)) ) ) ) ) ) ) ).
tt(t48_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))))) (u1_struct_0 A) (k17_bilinear A B C D) (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C D))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C D)))) (u1_struct_0 A) (k17_bilinear A B C D) (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t48_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k7_lattices A (k1_boolealg A B C)) (k3_lattices A (k7_lattices A B) C))) ) ) ) ) ) ).
tt(t48_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  ( (A = (k3_rcomp_1 B 1))  => (v4_pre_topc A k1_borsuk_4)) ) ) ) ) ).
tt(t48_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ((k2_rcomp_1 k2_xxreal_0 A) = k1_numbers) ) ) ) ).
tt(t48_borsuk_6,ax, ( ((k1_funct_1 k4_borsuk_6 k6_numbers) = k6_numbers)  &  ((k1_funct_1 k4_borsuk_6 1) = 1) ) ).
tt(t48_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 3))) =>  ( ( (B = C)  &  ((k3_euclid_5 B) = k6_numbers) )  => (r1_tarski (k4_card_3 (k1_borsuk_7 1 2 3 (k2_rcomp_1 (k9_real_1 (k1_euclid_5 B) (k13_complex1 A (k7_square_1 2))) (k7_real_1 (k1_euclid_5 B) (k13_complex1 A (k7_square_1 2)))) (k2_rcomp_1 (k9_real_1 (k2_euclid_5 B) (k13_complex1 A (k7_square_1 2))) (k7_real_1 (k2_euclid_5 B) (k13_complex1 A (k7_square_1 2)))) (k1_tarski k6_numbers))) (k9_metric_1 (k14_euclid 3) C A))) ) ) ) ) ) ) ).
tt(t48_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  ( (B = (k5_enumset1 C D E F G H I))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (G = H)  |  ( (G = I)  |  ( (H = I)  |  ((k5_bvfunc_2 A I B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k4_xboolean B C)) = (k3_xboolean (k4_xboolean (k4_xboolean A B) C))) ) ) ) ) ) ) ).
tt(t48_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B B) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k10_bvfunc_1 A B B)) (k11_bvfunc_1 A))) ) ) ) ) ).
tt(t48_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B))) (k12_finseq_1 (k3_cqc_lang A) C))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A C))) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t48_card_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (v1_card_1 A))  =>  (? [B:$i] :  ((v7_ordinal1 B) &  (A = (k1_card_1 B)) ) ) ) ) ).
tt(t48_card_2,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r2_xboole_0 A B) =>  ( (~ (r1_xxreal_0 (k5_card_1 B) (k5_card_1 A)))  & (r2_hidden (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ).
tt(t48_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k4_card_3 B)) =>  ((v1_relat_1 A) & (v1_funct_1 A)) ) ) ) ) ).
tt(t48_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ( ((v1_finset_1 (k9_xtuple_0 A)) & (r2_hidden B (k9_xtuple_0 A)))  =>  ((k3_card_fin 1 A) = (k23_binop_2 (k3_card_fin 1 (k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k1_tarski B)))) (k5_card_1 (k1_funct_1 A B)))) ) ) ) ) ).
tt(t48_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_cat_1 A B C) <=>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_cat_1 D A B C) &  (? [E:$i] :  ((m1_cat_1 E A C B) &  ( ((k5_cat_1 A C B C E D) = (k4_cat_1 A C))  &  ((k5_cat_1 A B C B D E) = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F C D) => (r1_funct_2 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 C)) (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 D)) (u4_struct_0 (k8_cat_2 A C)) (u4_struct_0 (k8_cat_2 B D)) (k6_cat_2 (u4_struct_0 A) (u4_struct_0 C) (u4_struct_0 B) (u4_struct_0 D) E F) (k16_cat_2 (k8_cat_2 A C) B D (k9_cat_1 (k8_cat_2 A C) A B (k14_cat_2 A C) E) (k9_cat_1 (k8_cat_2 A C) C D (k15_cat_2 A C) F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_cat_3 E B C A) =>  (! [F:$i] :  ((m1_cat_3 F B D A) =>  ( ((r1_cat_3 B C A E) &  ((r1_cat_3 B D A F) & (r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A E) (k3_cat_3 B A F))) )  => (r1_cat_1 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k23_cat_4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k23_cat_4 A B))) => (r2_hidden E (k2_cat_1 (k23_cat_4 A B) C D))) ) ) ) ) ) ) ) ).
tt(t48_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (? [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k1_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  &  ( ((k1_seq_1 (k3_series_1 (k4_catalan2 A B)) C) = (k7_afinsq_2 D))  &  ( ((k1_relset_1 k5_numbers D) = (k23_binop_2 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k23_binop_2 C 1)) =>  ((k1_seq_1 D E) = (k11_binop_2 (k1_seq_1 A E) (k3_funct_2 k5_numbers k1_numbers (k3_series_1 B) (k7_nat_d C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 B A) &  ((k8_relset_1 k2_numbers k2_numbers (k5_relset_1 k2_numbers k2_numbers B A) (k1_tarski k6_numbers)) = k1_xboole_0) )  => (r2_cfcont_1 (k2_cfunct_1 k2_numbers B) A)) ) ) ) ).
tt(t48_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k2_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) (k1_cfunct_1 A D E)) (k1_cfunct_1 A (k2_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B E) (k19_valued_1 A k2_numbers k2_numbers D C)) (k19_valued_1 A k2_numbers k2_numbers C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t48_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v9_cgames_1 A) <=>  ( (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k7_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v9_cgames_1 B)) ) ) ) ) )  &  (? [B:$i] :  ((v2_cgames_1 B) &  ((r2_hidden B (k6_cgames_1 A)) & (v5_cgames_1 B)) ) ) ) ) ) ) ).
tt(t48_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_chain_1 D A) =>  ((m2_subset_1 (k3_chain_1 A B C) (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A D A)) =>  ( ((k3_chain_1 A B C) = (k8_chain_1 A D))  <=>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (D = E) )  &  ((r1_chord A B C) &  ((r1_chord A C D) &  ((r1_chord A D E) &  (! [F:$i] :  ( ((v5_glib_001 F A) & (m3_glib_001 F A))  =>  (~  ( ((k3_finseq_1 F) = 7)  &  ( ((k15_glib_001 A F) = 3)  &  ( ((k13_glib_001 A F) = (k2_enumset1 B C D E))  &  ( ((k1_funct_1 F 1) = B)  &  ( ((k1_funct_1 F 3) = C)  &  ( ((k1_funct_1 F 5) = D)  &  ((k1_funct_1 F 7) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_circcmb3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v8_struct_0 B) & (m1_circcmb3 B A))  =>  (! [C:$i] :  ((m2_circcmb3 C A B) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 D A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 D A) A)))) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v3_card_1 F D) & (v1_finseq_1 F)) ) )  =>  ( (~ (r2_hidden (k3_circcmb3 (k4_circcmb3 D A E F)) (k2_msafree2 B)))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 (k6_circcmb3 A B (k4_circcmb3 D A E F)) (k7_circcmb3 A B (k4_circcmb3 D A E F) C (k5_circcmb3 D A E F))))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B C))) =>  ( (H = (k5_relat_1 G (u1_struct_0 B)))  => (r1_xxreal_0 (k2_circcmb3 (k6_circcmb3 A B (k4_circcmb3 D A E F)) (k7_circcmb3 A B (k4_circcmb3 D A E F) C (k5_circcmb3 D A E F)) G) (k2_nat_1 1 (k2_circcmb3 B C H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ( ((v4_circcomb C A) & (v4_circcomb D B))  => (r1_partfun1 (u4_msualg_1 A C) (u4_msualg_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t48_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ( ((r4_circtrm1 A B C D E F) & (r3_circtrm1 A B C))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A E))) =>  ( ( (H = (k3_relat_1 C G))  & (v1_circuit2 G B F))  => (v1_circuit2 H A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_classes1,ax, (! [A:$i] :  ((v1_ordinal1 A) => (r1_tarski (k3_tarski A) A)) ) ).
tt(t48_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v1_xboole_0 (k1_classes1 A)))  & (v1_classes2 (k1_classes1 A))) ) ) ).
tt(t48_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 C D)) ) )  => (m1_clvect_1 B C)) ) ) ) ) ) ) ).
tt(t48_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k5_clvect_2 A C D)) <=> (r1_xxreal_0 (k15_csspace A C B) D)) ) ) ) ) ) ) ) ) ).
tt(t48_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v1_clvect_2 B A))  => (v1_clvect_2 (k6_clvect_3 A B C) A)) ) ) ) ) ) ) ).
tt(t48_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C A))  =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D A))  =>  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski (k4_tarski C E) (k4_tarski D F)) (k1_coh_sp (k9_cohsp_1 A B))) <=>  ( ( (~ (r2_hidden (k2_xboole_0 C D) A))  &  ((r2_hidden E (k3_tarski B)) & (r2_hidden F (k3_tarski B))) )  |  ((r2_hidden (k4_tarski E F) (k1_coh_sp B)) &  ( (E = F)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_complex1,ax, ((k17_complex1 k6_complex1) = 1) ).
tt(t48_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 (k8_complex1 A B) (k8_complex1 A B)) = (k8_complex1 (k8_complex1 (k8_complex1 (k1_complex2 A A) (k1_complex2 A B)) (k1_complex2 B A)) (k1_complex2 B B))) ) ) ) ) ).
tt(t48_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( ((k2_complfld A) = (k4_struct_0 k1_complfld))  =>  (A = (k4_struct_0 k1_complfld)) ) ) ) ).
tt(t48_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ( ((k3_finseq_1 (k6_complsp2 A)) = (k3_finseq_1 A))  &  ((k3_finseq_1 (k7_complsp2 A)) = (k3_finseq_1 A)) ) ) ) ).
tt(t48_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  => (r1_xboole_0 (k2_afinsq_1 B) (k9_xtuple_0 (k6_compos_1 A C (k5_card_1 B))))) ) ) ) ) ) ).
tt(t48_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) 1) = (k5_compos_0 (u1_compos_1 A) C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 (k4_complex1 A) k6_numbers) => (r1_xxreal_0 (k18_sin_cos (k1_comptrig A)) k6_numbers)) ) ) ).
tt(t48_comput_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 A) &  ((v4_valued_0 A) &  ((v2_margrel1 A) & (v2_comput_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) &  ((v2_margrel1 B) & (v2_comput_1 B)) ) ) ) ) )  =>  ( ( ((k19_margrel1 A) = k6_numbers)  &  ( ((k19_margrel1 B) = k6_numbers)  &  ((k1_recdef_1 A k1_xboole_0) = (k1_recdef_1 B k1_xboole_0)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t48_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers A)) (k55_valued_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers A)))) ) ).
tt(t48_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers B C)) (k8_nat_1 k1_numbers A C))) )  &  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) )  =>  ((v2_comseq_2 B) &  ((k3_comseq_2 B) = k5_complex1) ) ) ) ) ) ) ).
tt(t48_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_convex4 B A) <=>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (C = D)  &  ( (~ (r1_xxreal_0 D k1_xboole_0))  &  (~ (r1_xxreal_0 1 D)) ) ) ) )  => (r1_tarski (k6_rusub_4 A (k19_convex4 A B C) (k19_convex4 A B (k6_xcmplx_0 k6_complex1 C))) B)) ) ) ) ) ) ) ) ).
tt(t48_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) =>  ((r2_hidden D (k24_qc_lang1 A B)) | (r2_hidden (k8_cqc_lang A B (k11_cqc_lang A D C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t48_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B))) (k12_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t48_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r6_cqc_the3 A B C) & (r6_cqc_the3 A D E))  =>  ((r1_cqc_the3 A C E) <=> (r1_cqc_the3 A (k6_cqc_lang A D) (k6_cqc_lang A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k9_real_1 (k13_csspace A B) (k13_csspace A C)) (k13_csspace A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t48_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((v4_dickson A) &  ((v3_dickson B) &  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 B)) &  ((u1_struct_0 A) = (u1_struct_0 B)) ) ) )  => (v1_wellfnd1 (k5_dickson B))) ) ) ) ) ).
tt(t48_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 k19_sin_cos A) B) = (k1_real_1 (k8_real_1 2 (k8_real_1 (k18_sin_cos B) (k18_sin_cos (k10_real_1 A 2)))))) ) ) ) ) ).
tt(t48_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k10_real_1 A (k5_square_1 E))) ) )  =>  ( (B = C)  |  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ((k9_diff_1 D B C) = (k1_real_1 (k8_real_1 (k10_real_1 A (k8_real_1 B C)) (k7_real_1 (k10_real_1 1 B) (k10_real_1 1 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_diff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) (k2_nat_1 A 1)) C) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) A) C) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 D B) A) (k9_real_1 C B)))) ) ) ) ) ) ) ) ) ).
tt(t48_dilworth,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v5_dilworth C A) & (m1_eqrel_1 C (u1_struct_0 A)))  =>  ( ((k5_card_1 C) = (k5_card_1 B))  =>  (! [D:$i] :  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E B) =>  (~  ((k9_subset_1 (u1_struct_0 A) D B) = (k1_tarski E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  ((r2_hidden D (k6_ec_pf_1 A B C)) &  ( (~  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) = k6_numbers) )  &  (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (~  ((r2_hidden E (k6_ec_pf_1 A B C)) &  ((r1_ec_pf_1 A E D) &  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (~  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  &  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) = k6_numbers) )  &  (~  ( ((k7_ec_pf_2 A C) = (k1_funct_1 (k8_ec_pf_2 A B) (k7_ec_pf_2 A D)))  <=> (r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m1_subset_1 (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A (k4_graph_1 A C) B) (k2_cat_1 A (k3_graph_1 A C) B)) (k18_ens_1 A B C)) (k2_ens_1 (k16_ens_1 A)))) ) ) ) ) ) ).
tt(t48_entropy1,ax, (! [A:$i] :  ( ((v4_partfun3 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ( ( ((k1_seq_1 A B) = k6_numbers)  =>  ((k1_seq_1 (k4_entropy1 A) B) = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers))  =>  ((k1_seq_1 (k4_entropy1 A) B) = (k8_real_1 (k1_seq_1 A B) (k6_power 2 (k1_seq_1 A B)))) ) ) ) ) ) ) ) ).
tt(t48_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_enumset1 A A A A A B) = (k2_tarski A B)) ) ) ).
tt(t48_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A (k2_zfmisc_1 B C)) =>  ((k1_funct_1 (k1_funct_3 (k10_funct_3 B C)) A) = (k7_relset_1 (k2_zfmisc_1 B C) C (k10_funct_3 B C) A)) ) ) ) ) ).
tt(t48_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k10_binop_2 (k5_square_1 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C))) (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)))) = (k11_binop_2 4 (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t48_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden E (k9_euclid_3 A B C D)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( ((k7_real_1 (k7_real_1 F G) H) = 1)  &  (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B F) (k1_rlvect_1 (k15_euclid A) C G)) (k1_rlvect_1 (k15_euclid A) D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ( (D = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)))  &  (E = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) C B))) )  =>  ((k4_euclid_3 A B C) = (k3_complex2 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_euclid_7,ax,(m1_rlvect_3 k1_xboole_0 (k10_funcsdom (k2_finseq_1 k6_numbers)))).
tt(t48_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 A B C) D) = (k7_euclid 3 (k7_euclid 3 (k9_euclid 3 k2_euclid_8 (k1_seq_1 A D)) (k9_euclid 3 k3_euclid_8 (k1_seq_1 B D))) (k9_euclid 3 k4_euclid_8 (k1_seq_1 C D)))) ) ) ) ) ) ) ) ) ).
tt(t48_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (B = (k5_algstr_0 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) C))  &  (B = (k3_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C) C)) ) ) ) ) ) ) ) ).
tt(t48_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((r2_hidden B D) & (r2_hidden C D))  => (r1_tarski (k2_euclid_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t48_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) )  =>  ((v5_exchsort B A) <=>  ((k6_exchsort A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t48_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B))))) =>  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B)) E) (k4_tarski (k10_finseq_1 A B) D)) = (k1_funct_1 D (k10_finseq_1 (k1_funct_1 E A) (k1_funct_1 E B))))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B)) E) A) = (k1_funct_1 E A))  &  ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B)) E) B) = (k1_funct_1 E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 (k1_fcont_1 A B) k6_numbers) = B) ) ) ) ) ).
tt(t48_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k1_fdiff_9)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k10_real_1 (k8_real_1 (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k16_sin_cos B)) (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k1_fdiff_9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t48_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers C)) & (r2_fdiff_1 C (k2_rcomp_1 A B)))  =>  ( ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_xxreal_0 (k1_fdiff_1 C D) k6_numbers)) ) )  &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k2_rcomp_1 A B)) & (r1_xxreal_0 k6_numbers (k1_fdiff_1 C D))) ) ) )  |  ((v2_funct_1 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))) &  ((r2_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))) (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D (k1_relset_1 k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))))) =>  ((k1_fdiff_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))) D) = (k10_real_1 1 (k1_fdiff_1 C (k1_seq_1 (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A B))) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))) 2))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) & (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers)) ) ) ) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))) 2) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k4_taylor_1 (k10_real_1 1 2))) 2) A) B) = (k8_real_1 (k1_seq_1 k19_sin_cos B) (k10_prepower (k1_seq_1 k16_sin_cos B) (k1_real_1 (k10_real_1 1 2))))) ) ) ) ) ) ) ) ).
tt(t48_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3))))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 3)) (k10_real_1 1 3))) A) B) = (k2_newton (k1_seq_1 k19_sin_cos B) 3)) ) ) ) ) ) ) ) ).
tt(t48_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k1_taylor_1 2)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k19_sin_cos B) = k6_numbers) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k1_taylor_1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k1_taylor_1 2)) A) B) = (k10_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos B)) (k5_prepower (k1_seq_1 k19_sin_cos B) 3))) ) ) ) ) ) ) ) ).
tt(t48_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  (~  ( ((k1_pre_ff A) = (k1_pre_ff B))  <=>  (A = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_fib_num3 (k3_fib_num3 A B C) (k3_fib_num3 A B (k2_nat_1 C 1)) D) = (k3_fib_num3 A B (k2_nat_1 D C))) ) ) ) ) ) ) ) ) ).
tt(t48_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_lattices A) &  ((v10_lattices A) & (l3_lattices A)) ) )  =>  ((k6_filter_0 A (k1_filter_0 A)) = A) ) ) ).
tt(t48_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  ((k1_lattice2 (k7_filter_1 A B)) = (k7_filter_1 (k1_lattice2 A) (k1_lattice2 B))) ) ) ) ) ).
tt(t48_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_filter_2 (u1_struct_0 A) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B C)) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) (k7_filter_2 A B) C))) & (r1_filter_2 (u1_struct_0 A) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B C)) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B (k7_filter_2 A C))))) ) ) ) ) ) ) ).
tt(t48_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ((v2_funct_1 A) & (v2_funct_1 B)) )  =>  ((k3_finseq_1 A) = (k3_finseq_1 B)) ) ) ) ) ) ).
tt(t48_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (m2_finseq_1 (k6_partfun1 (k2_finseq_1 A)) k5_numbers)) ) ).
tt(t48_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k14_finseq_1 (k2_finseq_1 A)) = (k1_finseq_2 A)) ) ) ).
tt(t48_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_funct_1 A))  => (r1_xboole_0 (k10_xtuple_0 (k6_finseq_4 A B)) (k1_tarski B))) ) ) ) ).
tt(t48_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) => (r1_tarski (k10_xtuple_0 (k1_finseq_5 A C B)) (k10_xtuple_0 C))) ) ) ) ) ) ).
tt(t48_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  ( ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 A D))  &  ((k7_partfun1 B C D) = (k7_partfun1 B C A)) ) ) ) ) ) )  =>  ((k4_finseq_4 C (k7_partfun1 B C A)) = A) ) ) ) ) ) ) ) ).
tt(t48_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ( ((v3_card_1 F C) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J B) =>  ((k3_funct_2 B A D (k5_binop_1 B G I J)) = (k5_binop_1 A H (k3_funct_2 B A D I) (k3_funct_2 B A D J))) ) ) ) )  => (r2_relset_1 k5_numbers A (k4_finseqop B A (k1_finseqop B B B G E F) D) (k1_finseqop A A A H (k4_finseqop B A E D) (k4_finseqop B A F D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k10_fintopo3 A (k2_nat_1 C 1) B) = (k12_fin_topo A (k10_fintopo3 A C B))) ) ) ) ) ) ) ).
tt(t48_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((v2_fintopo6 B A) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) | (v2_fintopo6 (k2_rfinseq (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ) ).
tt(t48_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) => (r2_hidden (k2_flang_1 A) (k8_flang_1 A B))) ) ) ).
tt(t48_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B k6_numbers 2) = (k4_subset_1 (k3_catalan2 A) (k4_subset_1 (k8_afinsq_1 A) (k4_flang_1 A (k2_flang_1 A)) B) (k6_flang_1 A B B))) ) ) ) ).
tt(t48_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r2_hidden B (k2_flang_3 A C)) <=>  (? [D:$i] :  ((v7_ordinal1 D) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r2_hidden B (k7_flang_1 A C D))) ) ) ) ) ) ) ) ).
tt(t48_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (A = (k2_xboole_0 (k6_subset_1 A B) (k3_xboole_0 A B))) ) ) ).
tt(t48_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C B A)) )  =>  ((r1_tarski (k12_fsm_1 B A C) (u1_struct_0 C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((r2_hidden D (k12_fsm_1 B A C)) <=> (v6_fsm_1 D B A C)) ) ) ) ) ) ) ) ) ) ).
tt(t48_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k3_funct_2 B A (k9_funcop_1 A B C D E) F) = (k5_binop_1 A C (k3_funct_2 B A D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k3_xboole_0 (k9_xtuple_0 C) B)) =>  ((k1_funct_1 (k5_relat_1 C B) A) = (k1_funct_1 C A)) ) ) ) ) ) ).
tt(t48_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k1_tarski A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B)))) )  =>  ( (~  (B = k1_xboole_0) )  =>  ((k2_relset_1 B C) = (k1_tarski (k1_funct_1 C A))) ) ) ) ) ) ).
tt(t48_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k3_xboole_0 (k9_xtuple_0 B) (k9_xtuple_0 C))) =>  ((k1_funct_1 (k13_funct_3 B C) A) = (k4_tarski (k1_funct_1 B A) (k1_funct_1 C A))) ) ) ) ) ) ) ).
tt(t48_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))))  =>  ((v1_funct_1 (k2_funct_4 D)) & (m1_subset_1 (k2_funct_4 D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ) ) ) ).
tt(t48_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k1_funct_2 A B)) =>  ( (A = k1_xboole_0)  |  ( ((k1_funct_5 (k2_funct_5 C)) = C)  &  ((k3_funct_5 (k4_funct_5 C)) = C) ) ) ) ) ) ) ) ).
tt(t48_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k8_funct_6 (k7_funcop_1 A B) C) = (k7_funcop_1 A (k1_funct_2 B C))) ) ) ) ).
tt(t48_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funcop_1 D) & (v1_finseq_1 D)) ) )  =>  ((r1_tarski (k10_xtuple_0 (k4_funct_7 A C)) B) =>  ((k4_funct_7 A (k7_finseq_1 C D)) = (k3_relat_1 (k4_funct_7 A C) (k4_funct_7 B D))) ) ) ) ) ) ) ) ).
tt(t48_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v4_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t48_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (~  ((v21_functor0 C A B) &  (! [D:$i] :  ((m2_functor0 D B A) =>  (~  ( (D = (k15_functor0 A B C))  &  ((v21_functor0 D B A) & (v15_functor0 D B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_2 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A B D)) (k1_fuzzy_1 A B (k2_fuzzy_2 A C D)))) ) ) ) ) ) ) ) ).
tt(t48_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_fvaluat1 B A) => (r1_tarski (k6_fvaluat1 A B) (u1_struct_0 A))) ) ) ) ).
tt(t48_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k10_funcop_1 (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A) B (k6_partfun1 (u1_struct_0 A))) C) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t48_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k4_algstr_0 A B) C) = (k4_algstr_0 A (k6_algstr_0 A B C)))  &  ((k6_algstr_0 A B (k4_algstr_0 A C)) = (k4_algstr_0 A (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ).
tt(t48_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) C)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H D E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) D)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H C E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H C D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) D)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H B E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H B D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H B C)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) D)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H A E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H A D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H A C)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) C) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) )  =>  ((k11_genealg1 F G H A B C D E) = (k8_genealg1 F G H A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_geomtrap A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_diraf A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k2_diraf A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_diraf A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_diraf A))) =>  ( ( (B = F)  &  ( (C = G)  &  ( (D = H)  &  (E = I) ) ) )  =>  ((r2_analoaf (k2_diraf A) F G H I) <=>  ((r2_analoaf A B C D E) | (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k3_msafree2 (k19_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k3_msafree2 (k19_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k3_msafree2 (k19_gfacirc1 A B C))) & (r2_hidden (k21_gfacirc1 A B C) (k3_msafree2 (k19_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t48_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) &  (~ (v4_glib_000 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ( ((k2_nat_1 (k15_glib_000 C) 1) = (k15_glib_000 A))  &  ((k2_nat_1 (k17_glib_000 C) (k5_card_1 (k28_glib_000 A B))) = (k17_glib_000 A)) ) ) ) ) ) ) ) ).
tt(t48_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (C = D)  =>  ((k8_glib_001 A C E F) = (k8_glib_001 B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ( ((r5_glib_000 A B) & (v3_glib_002 A))  => (v3_glib_002 B)) ) ) ) ) ).
tt(t48_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k11_glib_003 (k12_glib_003 A B D))) =>  ((r2_hidden C (k11_glib_003 A)) |  ( (B = C)  & (r2_hidden B (k7_glib_000 A))) ) ) ) ) ) ) ) ).
tt(t48_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k19_euclid 1 k6_numbers)))))) ) ) ) ) ) ).
tt(t48_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 2))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 (k2_goboard2 D)) (k2_nat_1 B 1)) |  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_gobrd13,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 B)))  =>  ( ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 C)) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 D)) &  ((r1_goboard1 B C E) &  ( ((k17_finseq_1 B A C) = (k17_finseq_1 B A D))  &  ((r3_gobrd13 B C E (k7_nat_d A 1)) & (r3_gobrd13 B D E (k7_nat_d A 1))) ) ) ) )  =>  ((r1_xxreal_0 A 1) |  ((k17_finseq_1 B (k2_nat_1 A 1) C) = (k17_finseq_1 B (k2_nat_1 A 1) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  (~  ( (~  ((v3_graph_2 C A) & (m2_graph_1 C A)) )  &  ((r1_graph_2 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ((m2_graph_1 F A) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 F)))  &  ((r1_graph_2 A G F) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 G)))  &  ( ((k1_funct_1 B 1) = (k1_funct_1 G 1))  &  ( ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 G (k3_finseq_1 G)))  &  ( ((k15_finseq_1 D) = F)  &  ((k15_finseq_1 E) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k8_graph_3 B D E))) =>  ( (F = C)  =>  ( (C = D)  |  ( (C = E)  |  ((k7_graph_3 (k8_graph_3 B D E) F A) = (k7_graph_3 B C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_graph_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u4_struct_0 C)) =>  (~  ((r1_tarski (k10_xtuple_0 D) (k10_xtuple_0 E)) &  ((r6_graph_5 C B) &  ((r2_hidden A (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r2_hidden F (k4_finseq_1 E)) &  ((k1_seq_1 (k9_graph_5 C E B) F) = (k1_seq_1 (k9_graph_5 C D B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k3_finseq_2 k1_numbers)) =>  ( ( (D = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) 1) E))  &  ( (F = (k6_graphsp (k8_nat_1 (k1_funct_2 (k3_finseq_2 k1_numbers) (k3_finseq_2 k1_numbers)) (k5_graphsp (k3_finseq_2 k1_numbers) (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A))) B) E))  &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k8_graphsp (k3_graphsp (k3_finseq_2 k1_numbers) (k16_graphsp A) (k19_graphsp A)) E A)) & (r2_hidden C (k14_graphsp D A))) ) ) )  => (r2_hidden C (k14_graphsp F A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) &  ((v1_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((k3_polynom1 A C F (k3_termord A B C (k10_polynom1 A C D E))) = (k4_struct_0 C))  => (r5_polyred A B C (k5_polynom1 A C (k10_polynom1 A C D E) F) (k5_polynom1 A C (k10_polynom1 A C (k6_termord A B C D) E) F) (k1_groeb_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k2_group_11 A B E) (k9_subset_1 (u1_struct_0 A) (k11_group_2 A D (k2_group_11 A B C)) (k11_group_2 A C (k2_group_11 A B D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_group_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k5_group_1 B A (k8_group_1 B C D)) = (k8_group_1 B (k5_group_1 B A C) (k5_group_1 B A D))) ) ) ) ) ) ) ) ) ).
tt(t48_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ( (D = B)  =>  ((k2_group_1 C D) = (k2_group_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t48_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_3 A (k5_group_3 A D B) C) = (k5_group_3 A (k5_group_2 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t48_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((k2_group_2 A (k7_group_4 A C D) B) = (k12_group_2 A C (k12_group_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t48_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_group_5 A (k1_subset_1 (u1_struct_0 A)) B) = k1_xboole_0)  &  ((k4_group_5 A B (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ) ) ) ).
tt(t48_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  =>  ((k10_group_6 A (k5_group_6 A B) (k8_group_6 A B)) = (k5_group_6 A B)) ) ) ) ) ).
tt(t48_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) &  ((v4_group_9 C A B) & (m1_group_9 C A B)) )  =>  ((k13_group_9 A B (k10_group_9 A B C) (k12_group_9 A B C)) = C) ) ) ) ) ) ).
tt(t48_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k3_helly A B B C) = B) ) ) ) ) ) ) ).
tt(t48_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B (k3_rlvect_1 A C D) (k3_rlvect_1 A C D))) (k5_square_1 (k7_real_1 (k7_square_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C))) (k7_square_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B D D))))))) ) ) ) ) ) ) ) ).
tt(t48_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers A))  => (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 2)) A) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 3)) (k1_real_1 2)) A))) ) ) ).
tt(t48_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k3_hilbert1 A B) (k3_hilbert1 A C)) (k3_hilbert1 A (k4_hilbert1 B C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t48_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k2_polynom4 k1_complfld (k7_hurwitz (k3_hurwitz k1_complfld B 1)) A) = (k5_algstr_0 k1_complfld (k4_algstr_0 k1_complfld A) (k2_complfld B))) ) ) ) ) ).
tt(t48_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ((k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ).
tt(t48_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) => (v4_incsp_1 (k9_domain_1 (u1_incsp_1 A) B C D E) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k5_int_1 A k6_numbers) = k6_numbers) ) ) ).
tt(t48_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (r1_int_4 A (a_1_0_int_4 A))) ) ).
tt(t48_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((m2_finseq_1 C (k1_zfmisc_1 B)) =>  ( ( ((k3_finseq_1 C) = A)  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k4_finseq_1 C)) & (r2_hidden E (k4_finseq_1 C)))  =>  ( (D = E)  | (r1_xboole_0 (k1_funct_1 C D) (k1_funct_1 C E))) ) ) ) ) ) )  =>  ((k5_card_1 (k3_tarski (k2_relset_1 (k1_zfmisc_1 B) C))) = (k2_wsierp_1 (k3_int_5 B C))) ) ) ) ) ) ) ) ).
tt(t48_integr11,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B C) &  ((r1_tarski C (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E C) =>  ((k1_seq_1 D E) = (k1_real_1 (k10_real_1 A (k7_real_1 1 (k5_square_1 E))))) ) ) )  &  ( (C = (k9_xtuple_0 D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers k2_sin_cos9 A) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers k2_sin_cos9 A) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t48_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos) (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = 1) ) ) )  &  ( (D = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos9 k24_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t48_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k30_sin_cos D)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k29_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t48_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ( (F = G)  &  ((r1_xxreal_0 B C) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) F (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) F) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) ) )  =>  ((k6_integr18 (k4_real_ns1 A) F D E) = (k12_integr15 D E A G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers D A)) => (r1_xxreal_0 (k7_integra1 A D B) (k6_integra1 A D C))) ) ) ) ) ) ) ) ) ).
tt(t48_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers k32_sin_cos))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k1_real_1 2)) ) ) ) ).
tt(t48_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k7_real_1 A F))  &  (~  ((k1_seq_1 C F) = k6_numbers) ) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1))) = E)  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1))) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_real_1 1 (k5_square_1 (k7_real_1 A F)))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers C) (k1_real_1 1)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (r1_interva1 A (k10_interva1 A (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A))) (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A)))) ) ).
tt(t48_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k4_intpro_1 A C) (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t48_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  ( ((r2_isocat_1 A B) & (r2_isocat_1 B C))  =>  (! [D:$i] :  ((m1_isocat_1 D A B) =>  (! [E:$i] :  ((m1_isocat_1 E B C) => (m1_isocat_1 (k9_cat_1 A B C D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jgraph_2,ax, ( ((v4_pre_topc a_0_8_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_8_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  &  ((v4_pre_topc a_0_9_jgraph_2 (k15_euclid 2)) & (m1_subset_1 a_0_9_jgraph_2 (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ).
tt(t48_jgraph_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k4_struct_0 (k15_euclid 2)) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k3_jgraph_4 A) (k4_struct_0 (k15_euclid 2)))) ) ) ).
tt(t48_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = a_0_6_jgraph_5)  &  ((r1_jordan6 C A B) &  ( (~  (A = B) )  &  ((r1_xxreal_0 (k18_euclid A) k6_numbers) &  ( (~  (A = (k18_pscomp_1 C)) )  & (r1_xxreal_0 (k17_euclid A) (k17_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  ( ( (G = (k19_euclid A C))  &  ( (H = (k19_euclid B D))  &  ( (I = (k19_euclid A D))  &  ( (J = (k19_euclid B C))  &  ( (E = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) G I H))  &  (F = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) G J H)) ) ) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((v4_topreal1 E) &  ( ((k3_topreal1 2 E) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) G I) (k1_rltopsp1 (k15_euclid 2) I H)))  &  ((v4_topreal1 F) &  ( ((k3_topreal1 2 F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) G J) (k1_rltopsp1 (k15_euclid 2) J H)))  &  ( ((k1_sppol_2 A B C D) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 E) (k3_topreal1 2 F)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 E) (k3_topreal1 2 F)) = (k2_tarski G H))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) E 1) = G)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) E (k3_finseq_1 E)) = H)  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) F 1) = G)  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) F (k3_finseq_1 F)) = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  ( ( ((k18_euclid A) = G)  &  ( ((k18_euclid B) = G)  &  ( ((k18_euclid C) = G)  &  ( ((k18_euclid D) = G)  & (r1_xxreal_0 (k17_euclid A) F)) ) ) )  =>  ((r1_xxreal_0 F E) |  ((r1_xxreal_0 H G) |  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) |  ((r1_xxreal_0 (k17_euclid B) (k17_euclid C)) |  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) |  ((r1_xxreal_0 (k17_euclid D) E) | (r1_jordan17 (k1_sppol_2 E F G H) A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 3 C))  =>  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E A)) C) |  ((r1_xxreal_0 D 1) |  ((r1_xxreal_0 (k1_matrix_1 (k1_jordan8 E A)) (k2_nat_1 D 1)) |  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (F = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 C 2)) 2))  &  (G = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d B A)) (k9_real_1 D 2)) 2)) )  => (r1_tarski (k3_goboard5 (k1_jordan8 E B) (k7_nat_d F 1) G) (k3_goboard5 (k1_jordan8 E A) (k7_nat_d C 1) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  => (r2_hidden (k2_jordan5c (k3_topreal1 2 (k2_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) (k10_xtuple_0 (k2_jordan1e A B)))) ) ) ) ) ).
tt(t48_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((v2_connsp_1 C (k15_euclid 2)) & (r1_xxreal_0 A B))  => (r1_tarski (k3_goboard9 (k1_jordan9 C B)) (k3_goboard9 (k1_jordan9 C A)))) ) ) ) ) ) ) ).
tt(t48_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) A))  =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ( ((k3_gobrd13 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k3_gobrd13 B A D))  &  ((k2_gobrd13 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k2_gobrd13 B A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden E C) => (r1_xxreal_0 B (k1_topreal6 A D E))) ) )  => (r1_xxreal_0 B (k5_jordan1k A D C))) ) ) ) ) ) ) ) ) ).
tt(t48_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r1_xxreal_0 (k9_pscomp_1 A) (k18_euclid (k2_jordan21 (k9_jordan6 A))))) ) ).
tt(t48_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_xxreal_0 2 A) &  ( (C = (a_2_2_jordan2c A B))  &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (~  (D = (k1_rlvect_1 (k15_euclid A) E F)) )  &  (~  (E = (k1_rlvect_1 (k15_euclid A) D F)) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden F C) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden J C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D F) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) F G) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) G H) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) H I) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) I J) C) & (r1_tarski (k1_rltopsp1 (k15_euclid A) J E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ( ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 B 1))  &  ((r2_hidden C (k3_topreal1 2 B)) &  ((v4_topreal1 A) &  ((v4_topreal1 B) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k1_funct_1 B 1))) ) ) ) )  =>  ( (C = (k1_funct_1 B 1))  | (v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k7_nat_d (k3_finseq_1 A) 1)) (k3_jordan3 B C)))) ) ) ) ) ) ) ) ).
tt(t48_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r3_jordan4 A B C D) =>  ( (C = D)  | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k9_jordan5d A) = (k11_jordan5d A)) ) ) ) ).
tt(t48_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (~  ((v1_topreal2 A) &  ((r1_topreal1 (k15_euclid 2) F G B) &  ((r1_topreal1 (k15_euclid 2) F G C) &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C) = A)  &  ((r1_topreal1 (k15_euclid 2) F G D) &  ((r1_topreal1 (k15_euclid 2) F G E) &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) D E) = A)  &  ( (~  ( (B = D)  &  (C = E) ) )  &  (~  ( (B = E)  &  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) => (r1_xboole_0 (k2_jgraph_6 A B C D) (k3_jgraph_6 A B C D))) ) ) ) ) ) ) ) ).
tt(t48_knaster,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A))) &  ((v14_quantal1 B (k1_lattice3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_lattice3 A)) (u1_struct_0 (k1_lattice3 A)))))) ) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  &  ((k2_knaster A C) = (k10_knaster (k1_lattice3 A) B)) ) ) ) ) ) ) ).
tt(t48_kurato_1,ax, (! [A:$i] :  ((r2_hidden A (k1_enumset1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))))) =>  ( (~ (v1_xboole_0 A))  &  ((v3_pre_topc A k3_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ) ) ) ).
tt(t48_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v13_lattices A) <=> (v14_lattices (k1_lattice2 A))) ) ) ).
tt(t48_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((r1_tarski B (k9_setfam_1 (u1_struct_0 A))) =>  ((k15_lattice3 A (k3_tarski B)) = (k15_lattice3 A (a_2_7_lattice3 A B))) ) ) ) ) ).
tt(t48_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (~  ((r2_hidden C (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) D)) &  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ( ((k10_lexbfs A (k13_lexbfs A (k16_lexbfs A) (k7_nat_d (k15_glib_000 A) C))) = E)  &  ( (~ (r2_hidden E (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) (k7_nat_d (k15_glib_000 A) C))))))  & (r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ((r2_hidden D (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 (k1_seq_1 A D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_limfunc2 B A) =>  ((r1_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A) = (k18_complex1 (k1_limfunc2 B A))) ) ) ) ) ) ) ).
tt(t48_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((k1_limfunc3 B A) = k6_numbers) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k9_subset_1 k1_numbers (k9_xtuple_0 B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A C) A) (k2_rcomp_1 A (k7_real_1 A C))))) & (r1_xxreal_0 k6_numbers (k1_seq_1 B D))) ) ) ) ) ) ) )  | (r3_limfunc3 (k6_rfunct_1 k1_numbers k1_numbers B) A)) ) ) ) ) ) ).
tt(t48_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r3_limfunc3 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) &  ((k1_seq_1 A D) = (k5_limfunc1 A)) ) ) ) ) )  | (v8_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t48_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k18_lpspace1 A B C))) =>  ( ((r2_hidden D F) & (r2_hidden E F))  =>  ((r1_lpspace1 A B C D E) &  ( ((k1_mesfunc6 A B C D) = (k1_mesfunc6 A B C E))  &  ((k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D)) = (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C F)) &  ((r2_hidden E (k1_lpspace2 A B C F)) & (r1_lpspace1 A B C D E)) )  =>  ((k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers D))) = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 D (k3_hilbert1 A (k3_hilbert1 B C))) => (r8_ltlaxio1 D (k3_hilbert1 (k4_ltlaxio1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t48_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B D)) A)) ) ) ) ) ) ) ) ) ).
tt(t48_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k4_mathmorp A D C) (k6_rusub_4 A (k3_mathmorp A D B) C))) ) ) ) ) ) ) ) ) ).
tt(t48_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r1_matrix10 B C) => (r1_matrix10 (k4_matrix10 A D C) (k4_matrix10 A D B))) ) ) ) ) ) ) ) ) ).
tt(t48_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 2 A) &  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((v1_finset_1 C) =>  (~  ( (C = (a_1_0_matrix11 A))  &  ( (B = (a_1_1_matrix11 A))  &  ( ((k3_xboole_0 C B) = k1_xboole_0)  &  ( ((k2_xboole_0 C B) = (k12_matrix_2 A))  &  ((k5_card_1 C) = (k5_card_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ((r2_hidden B (k2_finseq_1 (k5_card_1 D))) =>  ((k8_matrix_1 A (k6_matrix13 A C D (k2_finseq_1 (k1_matrix_1 C))) B) = (k8_matrix_1 A C (k1_funct_1 (k5_matrix13 D) B))) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix14 B A D) C) D E) = (k3_matrix_1 (u1_struct_0 B) C 1 E))  &  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix14 B A D) C) 1 E) = (k3_matrix_1 (u1_struct_0 B) C D E)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F A)) ) )  =>  ( (E = 1)  |  ( (E = D)  |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix14 B A D) C) E F) = (k3_matrix_1 (u1_struct_0 B) C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) A C) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  ((r1_tarski (k4_matrix15 D E F) (k4_matrix15 D (k4_matrix11 A B (u1_struct_0 D) G E) (k4_matrix11 A C (u1_struct_0 D) G F))) &  ((v2_funct_1 G) =>  ((k4_matrix15 D E F) = (k4_matrix15 D (k4_matrix11 A B (u1_struct_0 D) G E) (k4_matrix11 A C (u1_struct_0 D) G F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((v4_matrix16 D (u1_struct_0 A)) =>  ((k2_matrix_6 (k3_finseq_1 D) A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k2_matrix16 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k2_matrix16 (u1_struct_0 A) D) C)) = (k2_matrix16 (u1_struct_0 A) (k9_fvsum_1 A D (k1_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A B) C) D) = (k1_matrix_4 A (k1_matrix_4 A (k2_matrix_3 A D) C) B)) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B (k2_matrix_6 A B C C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((v4_matrix_6 C A B) => (r2_matrix_8 A B (k4_matrix_6 A B D C) (k4_matrix_6 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t48_matrix_9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 B)) =>  (~  ((r2_hidden A (k2_finseq_1 B)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k2_finseq_1 B)) &  (A = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k3_finseq_1 A) = (k23_binop_2 C 1))  &  (B = (k17_finseq_1 k2_numbers C A)) )  =>  ((k17_rvsum_1 A) = (k3_binop_2 (k17_rvsum_1 B) (k7_partfun1 k2_numbers A (k3_finseq_1 A)))) ) ) ) ) ) ) ) ).
tt(t48_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ( ((v2_matrixj1 F (u1_struct_0 D)) & (m2_finseq_1 F (k3_finseq_2 (k3_finseq_2 (u1_struct_0 D)))))  =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 D) A A) =>  ( ((r2_hidden B (k4_finseq_1 G)) & (r2_hidden C (k2_finseq_1 A)))  =>  ((k9_matrix_2 (k1_nat_1 B (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 D) F))) (k1_nat_1 C (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 D) F))) (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 D) (k15_matrixj1 (u1_struct_0 D) F (k16_matrixj1 (u1_struct_0 D) A G)))) D (k20_matrixj1 (u1_struct_0 D) E (k15_matrixj1 (u1_struct_0 D) F (k16_matrixj1 (u1_struct_0 D) A G)))) = (k13_matrixj1 (u1_struct_0 D) E (k3_matrixj1 (u1_struct_0 D) F (k4_matrixj1 (u1_struct_0 D) (k9_matrix_2 B C A D G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k10_matrixr1 A))  <=>  ( ((k8_matrix_1 k1_numbers B 1) = A)  &  ((k3_finseq_1 B) = 1) ) ) ) ) ) ) ).
tt(t48_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 A)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k11_matrixr1 C (k8_rvsum_1 A B)) = (k8_rvsum_1 (k11_matrixr1 C A) (k11_matrixr1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 F B C) &  ((v1_mod_2 F A B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k10_ranknull A B C F) = (k8_matrix13 A (k1_matrlin2 A B C F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 A) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k23_rvsum_1 (k11_matrixr1 C A) B) = (k23_rvsum_1 A (k11_matrixr1 (k4_matrix_1 k1_numbers C) B))) ) ) ) ) ) ) ) ) ) ).
tt(t48_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( (~ (r1_xboole_0 (k3_zfmisc_1 A B C) (k3_zfmisc_1 D E F)))  =>  ( (~ (r1_xboole_0 A D))  &  ( (~ (r1_xboole_0 B E))  &  (~ (r1_xboole_0 C F)) ) ) ) ) ) ) ) ) ) ).
tt(t48_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_measure6 (k2_measure6 A C) B) = (k2_measure6 A (k7_real_1 B C))) ) ) ) ) ) ) ).
tt(t48_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k9_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k9_member_1 A B) (k9_member_1 A C))) ) ) ) ) ) ) ).
tt(t48_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k8_memstr_0 A B C)))) ) ) ) ) ) ).
tt(t48_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r1_tarski C (k1_relset_1 A D)) =>  ((k8_subset_1 A C (k12_mesfunc1 D E)) = (k7_subset_1 A C (k8_subset_1 A C (k13_mesfunc1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  =>  (! [E:$i] :  ((m2_finseq_1 E k2_numbers) =>  ((r3_mesfun7c A B C D E) <=>  ((r2_mesfun7c A B (k5_comseq_3 A C) D (k6_complsp2 E)) & (r2_mesfun7c A B (k6_comseq_3 A C) D (k7_complsp2 E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ( (D = (k1_relset_1 A (k4_mesfunc5 A k1_numbers E k6_numbers)))  &  ( (D = (k1_relset_1 A F))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers E G) D)) )  &  ((r3_mesfunc6 A B C F) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G D) => (r1_xxreal_0 (k1_seq_1 (k55_valued_1 A k1_numbers (k4_mesfunc5 A k1_numbers E H)) G) (k1_seq_1 F G))) ) ) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_seq_1 G H) = (k1_mesfunc6 A B C (k4_mesfunc5 A k1_numbers E H))) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H D) => (v2_comseq_2 (k10_seqfunc A E H))) ) )  =>  ((v2_comseq_2 G) &  ((k2_seq_2 G) = (k7_mesfunc5 A B C (k8_mesfun7c A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((k1_relset_1 A D) = E)  =>  ((r1_mesfunc1 A B D F) <=> (r1_mesfunc1 A B D (k5_prob_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc6 A B C D) & (r1_tarski D (k1_relset_1 A C)))  => (r1_mesfunc6 A B (k56_valued_1 A k1_numbers C) D)) ) ) ) ) ) ) ) ) ).
tt(t48_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_tarski D (k1_relset_1 A E)) &  ((v6_supinf_2 E) &  ((r1_mesfunc1 A B E D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ((v2_mesfunc9 F A) &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers F G)) &  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers F G)) & (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers F G) D)) ) ) )  &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) =>  ((v1_mesfunc9 (k3_mesfunc5 A F G)) &  ((k1_mesfunc9 E G) = (k3_mesfunc9 (k3_mesfunc5 A F G))) ) ) ) )  &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_mesfunc9 G H) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers F H) D))) ) )  &  ((v1_mesfunc9 G) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers E D)) = (k3_mesfunc9 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_midsp_1 B A) <=> (r2_hidden B (k10_midsp_1 A))) ) ) ) ).
tt(t48_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (r2_relset_1 A A (k18_mmlquery A (k18_mmlquery A B)) B)) ) ) ).
tt(t48_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k48_modelc_1 A B C))) =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r3_modelc_1 A B C G F) <=> (r3_modelc_1 A B C G (k59_modelc_1 A B C D E F))) ) )  <=> (r2_abian (k1_zfmisc_1 A) (k51_modelc_1 A B C F) (k61_modelc_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  & (r4_modelc_2 A B C)) ) ) ) ) ) ).
tt(t48_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r7_modelc_3 A B C) =>  (! [D:$i] :  ( ((r2_hidden D (k22_modelc_3 A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))))  =>  ((v3_modelc_3 (k10_modelc_3 D A) A) |  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r1_xxreal_0 F E) & (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A) A)) ) ) )  =>  ((r4_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A) (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C (k1_nat_1 E 1)) D) A)) & (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( ((k11_nat_3 B A) = k6_numbers)  =>  ((k1_recdef_1 (k5_moebius1 B) A) = k6_numbers) ) ) ) ) ) ).
tt(t48_monoid_0,ax, ((r3_binop_1 k5_numbers k6_numbers k47_binop_2) & (v9_monoid_0 k47_binop_2 k5_numbers)) ).
tt(t48_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 D D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D D) D)))) )  =>  ((v2_binop_1 E D) =>  ((k7_relset_1 (k2_zfmisc_1 D D) D E (k2_zfmisc_1 (k7_relset_1 (k2_zfmisc_1 D D) D E (k2_zfmisc_1 A B)) C)) = (k7_relset_1 (k2_zfmisc_1 D D) D E (k2_zfmisc_1 A (k7_relset_1 (k2_zfmisc_1 D D) D E (k2_zfmisc_1 B C))))) ) ) ) ) ) ) ) ) ).
tt(t48_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ((m3_pboole E A (k1_mboolean A B)) =>  ( ((r1_pboole A C E) & (r6_pboole A (k3_pboole A C D) (k1_pboole A)))  => (r6_pboole A (k3_pboole A (k4_mssubfam A B E) D) (k1_pboole A))) ) ) ) ) ) ) ) ) ) ).
tt(t48_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v3_msualg_6 C A B) & (m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)))  => (v3_msualg_6 (k9_msualg_6 A B C) A B)) ) ) ) ) ) ).
tt(t48_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_necklace B) & (m1_mycielsk B A))  =>  ((k2_mycielsk (k6_mycielsk A B)) = (k2_xcmplx_0 1 (k2_mycielsk B))) ) ) ) ) ).
tt(t48_nat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_funct_2 k5_numbers A (k10_nat_1 A (k10_nat_1 A B C) D) (k10_nat_1 A B (k2_xcmplx_0 C D)))) ) ) ) ) ) ) ) ).
tt(t48_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k1_polynom2 k10_newton (k12_nat_3 A)) = (k1_polynom2 k10_newton (k12_nat_3 (k1_newton A B)))) ) ) ) ) ).
tt(t48_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (? [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) &  ( ((k3_finseq_1 C) = A)  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_recdef_1 C D) = (k1_int_1 (k10_real_1 A (k1_newton B D)))) ) ) )  &  ((k11_nat_3 (k9_newton A) B) = (k2_wsierp_1 C)) ) ) ) ) ) ) ) ) ).
tt(t48_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 A B) | (r1_xxreal_0 A (k7_nat_d B 1)))  =>  ( (~ (r1_xxreal_0 (k1_nat_1 B 1) A))  &  ((r1_xxreal_0 A (k1_nat_1 B 1)) &  ( (~ (r1_xxreal_0 (k2_nat_1 (k1_nat_1 B 1) 1) A))  &  ((r1_xxreal_0 A (k2_nat_1 (k1_nat_1 B 1) 1)) &  ( (~ (r1_xxreal_0 (k1_nat_1 B 2) A))  & (r1_xxreal_0 A (k1_nat_1 B 2))) ) ) ) ) ) ) ) ) ) ).
tt(t48_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((k12_nattra_1 (k8_cat_2 A B)) = (k8_cat_2 (k12_nattra_1 A) (k12_nattra_1 B))) ) ) ) ) ).
tt(t48_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ((r11_ncfcont1 A C B) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_hidden G B) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A G D))))  & (r1_xxreal_0 E (k18_complex1 (k9_real_1 (k7_partfun1 k1_numbers C G) (k7_partfun1 k1_numbers C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) C k6_numbers) = (k4_struct_0 (k4_real_ns1 A)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k4_real_ns1 B)) D (k4_struct_0 (k4_real_ns1 A))) = (k4_struct_0 (k4_real_ns1 B)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers (u1_struct_0 (k4_real_ns1 A))) &  ((v2_ndiff_3 E (k4_real_ns1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D)) &  ((v1_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D) (k4_real_ns1 B)) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A B))) =>  ( (D = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) E))  => (r2_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B C) (k4_ndiff_5 A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_nat_d A (k6_nat_d B C)) = (k6_nat_d (k6_nat_d A B) C)) ) ) ) ) ) ) ).
tt(t48_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) D)) & (v3_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 C) D A)))  => (r3_nfcont_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t48_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k10_normform A B C) = (k10_normform A C B)) ) ) ) ) ) ).
tt(t48_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B))))) )  => (r2_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (k10_oppcat_1 A B (k9_oppcat_1 A B C)) C)) ) ) ) ) ) ).
tt(t48_orders_1,ax, (! [A:$i] :  ((r1_orders_1 (k6_partfun1 A) A) & (r2_orders_1 (k6_partfun1 A) A)) ) ).
tt(t48_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_orders_1 (k2_wellord1 (u1_orders_2 A) B))) ) ) ) ).
tt(t48_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) => (v3_ordinal1 B)) ) ) ) ).
tt(t48_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  (! [E:$i] :  ((v3_ordinal1 E) =>  ( ( ((k10_ordinal2 (k11_ordinal2 B A) C) = (k10_ordinal2 (k11_ordinal2 D A) E))  &  ((r2_hidden C A) & (r2_hidden E A)) )  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_ordinal1 A (k3_ordinal5 A))) ) ).
tt(t48_ordinal6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ((r2_hidden A (k9_xtuple_0 (k7_ordinal6 B))) => (r1_tarski A (k1_funct_1 (k7_ordinal6 B) A))) ) ) ) ).
tt(t48_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t48_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  => (v15_lattices (k16_osalg_2 A B))) ) ) ) ).
tt(t48_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) => (r1_parsp_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_partfun1,ax, (! [A:$i] :  ((k4_partfun1 k1_xboole_0 A) = (k1_tarski k1_xboole_0)) ) ).
tt(t48_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( (E = (k1_tarski (k4_tarski C D)))  =>  ((k7_partfun1 B E C) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k2_pboole A B C) (k1_pboole A)) => (r6_pboole A B (k1_pboole A))) ) ) ) ) ) ).
tt(t48_pcs_0,ax, (! [A:$i] :  ((l2_pcs_0 A) =>  (! [B:$i] :  ((r2_hidden B (k26_pcs_0 A)) =>  ((v21_pcs_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t48_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_5 B A) & (r3_pdiff_5 C A))  =>  ((r3_pdiff_1 3 3 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 3 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k7_real_1 (k3_pdiff_5 B A) (k3_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t48_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  ( ((v3_nfcont_1 C (k4_real_ns1 A)) &  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ((r7_pdiff_1 A 1 E B C) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 1)) (k15_pdiff_1 A 1 E B C) C)) ) ) ) ) )  =>  ((r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) B D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k4_real_ns1 A))) =>  (? [F:$i] :  ((m2_finseq_1 F (k1_euclid 1)) &  ( ((k4_finseq_1 F) = (k2_finseq_1 A))  &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ((k1_funct_1 F G) = (k1_funct_1 (k9_pdiff_1 A 1 G B D) (k12_finseq_1 k1_numbers (k1_seq_1 (k1_pdiff_1 G A) E)))) ) ) )  &  ((k17_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1) (k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) B D) E) = (k5_euclid_7 1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_pdiff_9 A B C) &  ((r1_pdiff_9 A B D) &  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_tarski B (k1_relset_1 (k1_euclid A) D))) ) )  => (r1_pdiff_9 A B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers C D))) ) ) ) ) ) ) ) ).
tt(t48_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_int_2 B A) & (r1_nat_d (k3_pepin B A) C))  =>  ((r1_xxreal_0 A 1) |  ((k4_nat_d (k1_newton B C) A) = 1) ) ) ) ) ) ) ) ) ).
tt(t48_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k10_pnproc_1 A B (k10_pnproc_1 A B C D) E) = (k10_pnproc_1 A B C (k10_pnproc_1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t48_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((v1_funct_1 (k21_polyform A B)) &  ((v1_funct_2 (k21_polyform A B) (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1)))) &  ((v13_vectsp_1 (k21_polyform A B) (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1))) &  ((v1_mod_2 (k21_polyform A B) k2_bspace (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1))) & (m1_subset_1 (k21_polyform A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k17_polyform A B)) (u1_struct_0 (k17_polyform A (k6_xcmplx_0 B 1))))))) ) ) ) ) ) ) ) ).
tt(t48_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k4_polynom5 A (k4_struct_0 A) (k5_struct_0 A)) D) = D) ) ) ) ) ) ) ) ) ).
tt(t48_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v3_polynom7 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) E (k7_polynom1 A C)) => (r1_rewrite1 (k3_polyred A B C D) (k10_polynom1 A C F E) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (v1_abian B))  =>  ((k3_power (k4_xcmplx_0 A) B) = (k4_xcmplx_0 (k3_power A B))) ) ) ) ) ) ).
tt(t48_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r6_pboole A (k12_pre_poly A (k11_pre_poly A C B) B) C)) ) ) ) ) ).
tt(t48_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (B = 1)  =>  ((r1_xxreal_0 A k6_numbers) |  ((k6_prepower A B) = A) ) ) ) ) ) ) ).
tt(t48_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) => (m1_subset_1 (k5_setfam_1 A (k2_relset_1 (k9_setfam_1 A) B)) (k1_zfmisc_1 A))) ) ) ).
tt(t48_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B D) (k9_cqc_lang A C D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t48_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k16_pscomp_1 A) (k1_rltopsp1 (k15_euclid 2) (k23_pscomp_1 A) (k22_pscomp_1 A)))) ) ).
tt(t48_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A B (k4_pboole A C (k1_pzfmisc1 A D))) => (r1_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t48_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v3_qc_lang1 B A) =>  ((r1_qc_lang2 A C B) <=>  (C = (k18_qc_lang1 A B)) ) ) ) ) ) ) ) ) ).
tt(t48_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k2_qc_lang2 A B C)) = (k4_subset_1 D (k4_qc_lang3 A D B) (k4_qc_lang3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t48_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 A B) = (k6_quaterni (k7_real_1 (k7_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k18_quaterni A) (k18_quaterni B))) (k8_real_1 (k19_quaterni A) (k19_quaterni B))) (k8_real_1 (k20_quaterni A) (k20_quaterni B))) (k7_real_1 (k9_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k1_real_1 (k18_quaterni B))) (k8_real_1 (k18_quaterni A) (k17_quaterni B))) (k8_real_1 (k19_quaterni A) (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k19_quaterni B))) (k7_real_1 (k9_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k1_real_1 (k19_quaterni B))) (k8_real_1 (k17_quaterni B) (k19_quaterni A))) (k8_real_1 (k18_quaterni B) (k20_quaterni A))) (k8_real_1 (k20_quaterni B) (k18_quaterni A))) (k7_real_1 (k9_real_1 (k7_real_1 (k8_real_1 (k17_quaterni A) (k1_real_1 (k20_quaterni B))) (k8_real_1 (k20_quaterni A) (k17_quaterni B))) (k8_real_1 (k18_quaterni A) (k19_quaterni B))) (k8_real_1 (k19_quaterni A) (k18_quaterni B))))) ) ) ) ) ).
tt(t48_quatern3,ax, ((k8_quatern2 k2_quatern2) = k2_quatern2) ).
tt(t48_quaterni,ax, ( ((k17_quaterni (k31_quaterni k1_xcmplx_0)) = k6_numbers)  &  ( ((k18_quaterni (k31_quaterni k1_xcmplx_0)) = (k1_real_1 1))  &  ( ((k19_quaterni (k31_quaterni k1_xcmplx_0)) = k6_numbers)  &  ((k20_quaterni (k31_quaterni k1_xcmplx_0)) = k6_numbers) ) ) ) ).
tt(t48_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  (~  ((k8_group_1 A (k20_quofield A B C) (k20_quofield A D E)) = (k20_quofield A (k8_group_1 A B D) (k8_group_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_rcomp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  (! [C:$i] :  ( (C = (a_2_3_rcomp_3 A B))  =>  (! [D:$i] :  ( ((r7_orders_1 (k1_wellord2 C) D) & (r2_hidden D (k1_relat_1 (k1_wellord2 C))))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden E D) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden F D) &  ((r2_hidden G D) &  ((r1_tarski E (k4_subset_1 (u1_struct_0 A) F G)) &  ( (~  (E = F) )  &  (~  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) ) )  =>  ((r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) k6_numbers) k6_numbers) |  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k1_newton k1_fib_num B) (k1_seq_1 (k5_real_3 A) B))) ) ) ) ) ) ).
tt(t48_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_relat_1 D) =>  ((r2_hidden (k4_tarski A B) (k3_relat_1 (k4_relat_1 C) D)) <=>  ((r2_hidden A C) & (r2_hidden (k4_tarski A B) D)) ) ) ) ) ) ) ).
tt(t48_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k3_subset_1 B (k6_relset_2 A B C D)) = (k7_relset_1 A B (k3_subset_1 (k2_zfmisc_1 A B) D) C)) ) ) ) ) ) ) ).
tt(t48_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ((r11_rewrite1 A B) => (r10_rewrite1 A B)) ) ) ) ) ).
tt(t48_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B C) => (r1_tarski (k8_rewrite2 A B D) (k8_rewrite2 A C D))) ) ) ) ) ) ) ) ).
tt(t48_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k2_xcmplx_0 E 1) (k4_finseq_1 D)))  =>  ( ((k1_funct_1 D E) = (k4_tarski (k1_xtuple_0 (k1_funct_1 D E)) (k2_xtuple_0 (k1_funct_1 D E))))  &  ((k1_funct_1 D (k2_xcmplx_0 E 1)) = (k4_tarski (k1_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1))) (k2_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ( ((k5_relat_1 (k1_rfunct_1 B C) A) = (k1_rfunct_1 (k5_relat_1 B A) (k5_relat_1 C A)))  &  ( ((k5_relat_1 (k1_rfunct_1 B C) A) = (k1_rfunct_1 (k5_relat_1 B A) C))  &  ((k5_relat_1 (k1_rfunct_1 B C) A) = (k1_rfunct_1 B (k5_relat_1 C A))) ) ) ) ) ) ) ) ).
tt(t48_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers B) A))) ) ) ) ).
tt(t48_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k15_valued_1 A k1_numbers B k6_numbers) B)) ) ) ) ).
tt(t48_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 B) => (r1_xxreal_0 (k1_seq_1 (k3_rinfsup1 B) A) (k1_seq_1 (k3_rinfsup1 B) (k2_nat_1 A 1)))) ) ) ) ) ).
tt(t48_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r1_tarski B C) & (v2_rlaffin1 C A))  => (v2_rlaffin1 B A)) ) ) ) ) ) ) ).
tt(t48_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_struct_0 C B) <=>  ((k3_rlsub_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t48_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_rlsub_2 A B C) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D C B))) ) ) ) ) ) ) ) ) ) ).
tt(t48_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B k1_numbers))  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) (k4_rltopsp1 A B)) (k4_rltopsp1 A (k2_real_1 B)))) ) ) ) ).
tt(t48_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_rlvect_1 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) C D)) B) = (k3_rlvect_1 A (k1_rlvect_1 A C B) (k1_rlvect_1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t48_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k8_rlvect_2 A 1 B) B)) ) ) ) ).
tt(t48_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r2_hidden (k4_struct_0 B) (k3_rmod_2 A B C D)) <=>  ((k3_rmod_2 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t48_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))))  &  ((v10_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) &  ((v13_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) & (l3_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B)))) ) ) ) ) ) ) ).
tt(t48_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rmod_4 E A B) => (r1_rmod_4 A B (k7_rmod_4 A B D (k7_rmod_4 A B C E)) (k7_rmod_4 A B (k6_algstr_0 A C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t48_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k15_robbins1 A B) B) = (k11_robbins1 A B)) ) ) ) ) ).
tt(t48_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k5_robbins1 A B C)) D)) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) C)))) C) = (k5_robbins1 A (k3_robbins1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t48_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k4_subset_1 (u1_struct_0 A) B C)) D))) ) ) ) ) ) ) ) ).
tt(t48_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ( (~ (r1_xxreal_0 (k1_rpr_1 A (k9_subset_1 A C D)) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_rpr_1 A D) k6_numbers))  &  (~  ((k1_rpr_1 A (k9_subset_1 A (k9_subset_1 A B C) D)) = (k8_real_1 (k8_real_1 (k2_rpr_1 A (k9_subset_1 A C D) B) (k2_rpr_1 A D C)) (k1_rpr_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k3_rusub_1 A C B)) <=>  ((k3_rusub_1 A C B) = (k3_rusub_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t48_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  (! [D:$i] :  ((m1_rusub_1 D A) =>  ((r1_rusub_2 A C D) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A B C D)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A B D C))) ) ) ) ) ) ) ) ) ) ).
tt(t48_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  ((u1_struct_0 A) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) )  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (D = B) )  & (r2_hidden D (k4_bhsp_2 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k10_rvsum_1 (k2_finseq_2 A C) B) = (k5_finseq_2 k1_numbers A (k11_binop_2 B C))) ) ) ) ) ) ) ).
tt(t48_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k2_numbers))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ((k20_rvsum_1 (k12_rvsum_2 A B C)) = (k5_binop_2 (k20_rvsum_1 B) (k20_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t48_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ((k1_relset_1 k3_scmfsa_2 (k5_relat_1 A k3_scmfsa_2)) = k3_scmfsa_2) ) ) ).
tt(t48_scmfsa8c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r3_scmfsa7b A B))  & (r4_scmfsa7b (k11_compos_1 k1_scmfsa_2 A) B)) ) ) ) ) ) ).
tt(t48_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) & (v7_amistd_1 A 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers)))) )  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( (~  ((r1_xxreal_0 (k1_funct_1 C D) (k3_funct_2 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) k5_numbers C (k8_nat_1 (k4_card_3 (k2_memstr_0 3 k1_scmfsa_2)) (k5_scmfsa_9 D A B E) 1))) &  (~  ((k1_funct_1 C D) = k6_numbers) ) ) )  &  ( ( ((k1_funct_1 C D) = k6_numbers)  => (r1_xxreal_0 (k1_funct_1 D B) k6_numbers))  &  ((r1_xxreal_0 (k1_funct_1 D B) k6_numbers) =>  ((k1_funct_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) )  => (v7_amistd_1 (k2_scmfsa_9 B A) 3 k1_scmfsa_2)) ) ) ) ) ).
tt(t48_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v2_scm_halt D)) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((v2_scm_halt (k3_scmfsa8b E C D)) &  ( ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 B E)))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b C B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7)))))  &  ((r1_xxreal_0 k6_numbers (k1_funct_1 B E)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k1_scmfsa6b (k3_scmfsa8b E C D) B A) (k1_funct_4 (k1_scmfsa6b D B A) (k7_memstr_0 3 k1_scmfsa_2 (k2_nat_1 (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) (k5_card_1 D)) 7))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k11_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k11_scmpds_2 D B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k2_xcmplx_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) C))  &  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (E = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k11_scmpds_2 D B C) A) E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((r1_scmpds_6 (k5_scmpds_6 D E C) B A) & (r2_scmpds_6 (k5_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ( ((k1_funct_1 (k6_scmpds_4 C H I) (k2_scmpds_2 (k1_funct_1 B D) E)) = (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 (k6_scmpds_4 C H I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ((r2_hidden (k2_scmpds_2 (k1_funct_1 B D) E) G) |  ((r1_xxreal_0 F k6_numbers) |  ( (D = (k2_scmpds_2 (k1_funct_1 B D) E))  |  ((r1_scmpds_6 (k2_scmpds_7 D E F C) B A) & (r2_scmpds_6 (k2_scmpds_7 D E F C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_scmyciel,ax,(v5_scmyciel (k1_tarski k1_xboole_0))).
tt(t48_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_semi_af1 A B C D) &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers A) B)) & (r2_funct_2 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A (k32_valued_1 k5_numbers k1_numbers B)) (k32_valued_1 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ).
tt(t48_seq_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v3_membered A))  =>  (! [B:$i] :  ((v3_membered B) =>  ( ((r1_tarski A B) & (v4_xxreal_2 B))  => (r1_xxreal_0 (k2_seq_4 A) (k2_seq_4 B))) ) ) ) ) ).
tt(t48_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k13_complex1 (k2_nat_1 (k4_nat_1 2 C) 1) (k2_nat_1 (k4_nat_1 2 C) 2))) ) )  => (r1_xxreal_0 (k1_seq_1 (k1_series_3 B) A) (k13_complex1 1 (k7_square_1 (k2_nat_1 (k4_nat_1 3 A) 4))))) ) ) ) ) ).
tt(t48_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k13_complex1 1 (k5_square_1 (k2_nat_1 B 1)))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k6_xcmplx_0 2 (k13_complex1 1 (k2_nat_1 B 1))))) ) ) ) ) ).
tt(t48_setfam_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_setfam_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v3_setfam_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))))  => (v3_setfam_1 (k4_subset_1 (k1_zfmisc_1 A) B C) A)) ) ) ) ) ) ).
tt(t48_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v2_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k4_setlim_1 B C) A) = (k3_funct_2 k5_numbers (k9_setfam_1 B) C A)) ) ) ) ) ) ) ).
tt(t48_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k7_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A)) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k3_setlim_2 B C D)) A))) ) ) ) ) ) ) ).
tt(t48_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 A)) =>  ((k10_setwiseo A B (k5_setwiseo A E (k2_setwiseo A D)) C) = (k5_setwiseo B (k10_setwiseo A B E C) (k3_funct_2 A (k5_finsub_1 B) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t48_sf_mastr,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_scmfsa_2)))  =>  (~ (r2_hidden (k2_scmfsa_m A) A)) ) ) ).
tt(t48_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C D)) (k5_sheffer1 A B (k5_sheffer1 A C D))) (k5_sheffer1 A C C)) = (k5_sheffer1 A B (k5_sheffer1 A C C))) ) ) ) ) ) ) ) ) ).
tt(t48_simplex0,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ((v1_matroid0 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m3_simplex0 B A (k3_xxreal_3 (k5_card_1 B) 1))) ) ) ) ).
tt(t48_sincos10,ax,(r1_tarski (k1_rcomp_1 1 (k7_square_1 2)) (k1_relset_1 k1_numbers k4_sincos10))).
tt(t48_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k5_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B)) k7_complex1))) ) ) ) ) ).
tt(t48_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k17_sin_cos (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) = k6_numbers) )  =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k6_xcmplx_0 (k20_sin_cos B) (k20_sin_cos A))) = (k2_sin_cos4 (k7_xcmplx_0 (k6_xcmplx_0 A B) 2))) ) ) ) ) ) ).
tt(t48_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_sin_cos2 (k6_real_1 A 2)) = (k7_square_1 (k10_real_1 (k7_real_1 (k6_sin_cos2 A) 1) 2))) ) ) ).
tt(t48_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k16_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k10_real_1 3 2) k32_sin_cos))) = (k2_rcomp_1 (k1_real_1 1) 1)) ).
tt(t48_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 A 1) =>  ((r1_xxreal_0 A k6_numbers) |  ((k7_sin_cos7 A) = (k3_sin_cos7 (k12_binop_2 1 A))) ) ) ) ) ).
tt(t48_sin_cos9,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t48_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_seq_1 k24_sin_cos A) = (k3_complex1 (k11_comseq_3 (k3_sin_cos A)))) ) ) ).
tt(t48_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v4_topreal1 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2))))  =>  ((r2_hidden A (k2_topreal1 2 C B)) =>  ((r2_hidden A (k10_xtuple_0 C)) | (v4_topreal1 (k5_finseq_5 (u1_struct_0 (k15_euclid 2)) C A B))) ) ) ) ) ) ) ) ).
tt(t48_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  =>  ((k9_pscomp_1 A) = (k3_xxreal_0 (k9_pscomp_1 B) (k9_pscomp_1 C))) ) ) ) ) ) ) ) ).
tt(t48_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ( (~ (v3_funct_1 E))  &  ((v1_finseq_6 E (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 E) &  ((v2_topreal1 E) &  ((v1_goboard5 E) &  ((v2_goboard5 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 E))) ) )  =>  ((r1_xxreal_0 C B) |  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k3_finseq_1 E) D))  | (r1_xboole_0 (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E A B)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_sprect_3,ax, (! [A:$i] :  ( ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) C)))  =>  ((r2_hidden C (k3_topreal1 2 A)) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B C) (k3_topreal1 2 A)) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t48_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t48_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers B) =>  ((r1_xxreal_0 (k3_square_1 B) (k3_square_1 A)) |  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 B)))  &  (~ (r1_xxreal_0 B A)) ) ) ) ) ) ) ) ).
tt(t48_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) &  ((v7_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  &  ( (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k1_funct_1 B C) = (k9_stacks_1 A C)) ) )  & (r3_stacks_1 A (k8_stacks_1 (u1_struct_0 A)) (k6_partfun1 (u1_struct_0 A)) B)) ) ) ) ) ).
tt(t48_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) =>  ((k3_stirl2_1 A 3) = (k11_binop_2 (k18_binop_2 1 6) (k9_binop_2 (k10_binop_2 (k2_newton 3 A) (k11_binop_2 3 (k2_newton 2 A))) 3))) ) ) ) ).
tt(t48_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [F:$i] :  ((m1_subset_1 F D) =>  ( (~  (C = B) )  =>  ((k1_funct_1 (k1_sublemma A D E (k12_sublemma A D C F)) B) = (k1_funct_1 E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_subset_1,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (? [C:$i] :  ((r2_hidden C A) &  (~  (B = C) ) ) ) ) ) ) ) ).
tt(t48_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) =>  ((k12_supinf_2 A C) = k1_supinf_2) ) ) )  =>  ((k19_supinf_2 A) = (k12_supinf_2 (k18_supinf_2 A) B)) ) ) ) ) ) ) ).
tt(t48_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A B)) (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))))) ) ) ) ).
tt(t48_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v4_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tdlat_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_tdlat_1 A)))) =>  ( (C = B)  =>  ( ( (~  (C = k1_xboole_0) )  =>  ((k16_lattice3 (k4_tdlat_1 A) C) = (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B))) )  &  ( (C = k1_xboole_0)  =>  ((k16_lattice3 (k4_tdlat_1 A) C) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k3_tarski (a_2_0_tex_2 A B))) ) ) ) ) ).
tt(t48_tex_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ((v1_tex_2 B A) & (m1_pre_topc B A))  =>  (~ (v1_tex_3 B A)) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t48_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_tarski (k2_tex_4 A B) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t48_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((v5_pre_topc D C B) & (r1_tmap_1 B A E F))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ((r2_hidden G (k8_relset_1 (u1_struct_0 C) (u1_struct_0 B) D (k6_domain_1 (u1_struct_0 B) F))) => (r1_tmap_1 C A (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) D E) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ( ((r1_borsuk_6 A B C) & (r3_borsuk_2 A B C D E))  => (r2_funct_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)) (k6_topalg_1 A B C D) (k6_topalg_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_topgen_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k1_borsuk_5)  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = k3_numbers) ) ) ) ).
tt(t48_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_topgen_4 A B D) & (r1_tarski B C))  => (r1_topgen_4 A C D)) ) ) ) ) ) ) ) ) ).
tt(t48_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_topgen_5 A) =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C D) &  ((r2_hidden D B) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E A k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr))))) ) )  =>  (~  ( ((k1_funct_1 E C) = k6_numbers)  & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr) E (k3_subset_1 (u1_struct_0 A) D)) (k6_domain_1 k1_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v4_pre_topc (k1_group_2 A B) A)) ) ) ) ).
tt(t48_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ( (C = (k9_metric_1 (k14_euclid 2) B D))  &  (A = B) )  =>  ((k7_pscomp_1 C) = (k7_real_1 (k18_euclid A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t48_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  ( (D = (k19_euclid A B))  =>  ((k9_metric_1 (k14_euclid 2) D C) = (k6_jgraph_6 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t48_toprealc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_membered B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  => (r1_funct_2 A (u1_struct_0 (k15_euclid k6_numbers)) A k1_numbers (k15_toprealc k6_numbers A B C) (k8_funcop_1 k1_numbers A k6_numbers))) ) ) ) ) ) ).
tt(t48_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  ((k1_tops_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t48_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ((v5_pre_topc C A B) & (v2_tops_2 D B))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (E = (k7_relat_1 (k3_funct_3 C) D))  => (v2_tops_2 E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_tops_3 B A) & (v3_tops_1 C A))  => (v1_tops_3 (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t48_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v4_transgeo D A) &  ((v4_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C))  &  ( (~  (B = C) )  &  (~ (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_trees_1 A)) )  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  (~  ( (~  (B = k1_xboole_0) )  & (r1_xxreal_0 (k6_trees_1 A) (k6_trees_1 (k4_trees_1 A B)))) ) ) ) ) ) ).
tt(t48_trees_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((v4_trees_3 B) =>  ((r2_hidden (k7_finseq_1 (k12_finseq_1 k5_numbers A) C) (k11_trees_3 B)) <=>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) A))  & (r2_hidden C (k1_funct_1 B (k2_nat_1 A 1)))) ) ) ) ) ) ) ) ) ).
tt(t48_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  =>  (~  ( (~ (v1_finset_1 A))  &  (! [B:$i] :  ((m1_trees_2 B A) => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t48_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v4_pre_topc C A))  => (r2_tsep_1 A B C)) ) ) ) ) ) ) ).
tt(t48_turing_1,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((l1_turing_1 B) =>  (! [C:$i] :  ((l1_turing_1 C) =>  (! [D:$i] :  ((m2_funct_2 D k4_numbers (u1_turing_1 B) (k9_funct_2 k4_numbers (u1_turing_1 B))) =>  (! [E:$i] :  ((m2_funct_2 E k4_numbers (u1_turing_1 C) (k9_funct_2 k4_numbers (u1_turing_1 C))) =>  ( ((r1_funct_2 k4_numbers (u1_turing_1 B) k4_numbers (u1_turing_1 C) D E) & (r2_turing_1 A B D))  => (r2_turing_1 A C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k37_twoscomp A B) (k38_twoscomp A B)))) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( ( (D = (k1_funct_1 C A))  &  (E = (k1_funct_1 C B)) )  =>  ( ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) (k39_twoscomp A B)) = (k10_margrel1 (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) A) = D)  &  ((k1_funct_1 (k6_circuit2 (k37_twoscomp A B) (k38_twoscomp A B) C) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_uniroots,ax,(r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k5_uniroots 1) (k4_polynom5 k1_complfld (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld)) (k1_group_1 k1_complfld)))).
tt(t48_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_polynom5 A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t48_valued_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((r2_hidden B (k9_xtuple_0 (k36_valued_2 C E D))) =>  ((k1_funct_1 (k36_valued_2 C E D) B) = (k13_valued_1 (k1_funct_1 E B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t48_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r2_hidden (k4_struct_0 B) (k3_vectsp_4 A B C D)) <=>  ((k3_vectsp_4 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t48_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ( ((r1_vectsp_5 A B C D) &  ( (E = (k3_rlvect_1 B F G))  &  ( (E = (k3_rlvect_1 B H I))  &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  ((r1_struct_0 D G) & (r1_struct_0 D I)) ) ) ) ) )  =>  ( (F = H)  &  (G = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_algstr_0 A (k4_algstr_0 A (k5_struct_0 A)) B) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(t48_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_vfunct_1 C D E A) & (r1_vfunct_1 C D F B))  => (r1_vfunct_1 C D (k2_vfunct_1 C D E F) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r1_vfunct_2 A B C E) & (r1_vfunct_2 A B D F))  => (r1_vfunct_2 A B (k2_vfunct_1 A B C D) (k3_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v14_waybel_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k5_waybel_0 A C)) ) ) ) ) ) ) ) ).
tt(t48_waybel11,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v3_waybel_3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A B) = (k3_tarski (a_2_4_waybel11 A B))) ) ) ) ) ).
tt(t48_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_1_waybel_1 A B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 A C)))))) )  =>  ( (D = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) B C))  => (v8_waybel_1 D (k5_yellow_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((r2_hidden (k4_yellow_0 A) (u1_struct_0 B)) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (C = (u1_struct_0 B))  & (v4_pre_topc C A)) ) ) )  | (v7_yellow_0 B A)) ) ) ) ) ) ).
tt(t48_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k3_yellow_0 A) B) =>  ((m1_waybel23 B A) <=>  ((r1_tarski (u1_struct_0 (k1_waybel_8 A)) B) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r3_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ((k12_lattice3 A B (k4_yellow_2 A D)) = (k1_waybel_2 A (k3_waybel_2 A B (k2_waybel_2 A C D)))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) )  =>  ((v10_waybel_0 C A) =>  ((k12_lattice3 A B (k1_waybel_2 A C)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A C))))) ) ) ) ) ) ) ) ) ).
tt(t48_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r2_hidden (u1_struct_0 B) A) =>  ((m1_subset_1 B (u1_struct_0 (k10_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (v3_waybel_3 B)) ) ) ) ) ) ) ) ).
tt(t48_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v6_waybel_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (~  ( (~ (r3_orders_2 A B C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E B) D) &  (~ (r3_orders_2 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((v2_wellord1 B) &  ((r1_tarski A (k1_relat_1 B)) & (r3_wellord1 B C D)) )  =>  ((r3_wellord1 (k2_wellord1 B A) (k2_wellord1 C (k7_relat_1 D A)) (k5_relat_1 D A)) & (r4_wellord1 (k2_wellord1 B A) (k2_wellord1 C (k7_relat_1 D A)))) ) ) ) ) ) ) ) ) ).
tt(t48_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 A (k4_xboole_0 A B)) = (k3_xboole_0 A B)) ) ) ).
tt(t48_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k7_xboolean A B)) = (k9_xboolean A B)) ) ) ) ) ).
tt(t48_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k7_xcmplx_0 (k7_xcmplx_0 A B) C) = (k7_xcmplx_0 (k7_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t48_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 k6_numbers (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t48_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 C B))  &  (~ (r2_hidden B k1_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t48_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 B A) | (r1_tarski (k2_xxreal_1 B C) (k4_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t48_xxreal_2,ax,(v4_xxreal_2 (k1_tarski k2_xxreal_0))).
tt(t48_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((r1_xxreal_0 C (k1_xxreal_3 B A)) | (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t48_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) <=> (r1_lattice3 A C D)) ) )  & (r2_yellow_0 A B))  => (r2_yellow_0 A C)) ) ) ) ) ).
tt(t48_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k12_yellow_3 A B (k2_waybel_3 A C) (k2_waybel_3 B D)) = (k2_waybel_3 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t48_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ((m3_yellow_9 E (k2_borsuk_1 A C) (k2_borsuk_1 B D)) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u1_struct_0 C) = (u1_struct_0 D)) )  =>  ((v1_tops_2 (a_4_2_yellow12 A B C D) E) &  ((v1_cantor_1 (a_4_2_yellow12 A B C D) E) & (m1_subset_1 (a_4_2_yellow12 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v3_pre_topc D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B D) =>  ((r2_hidden C D) | (r1_funct_2 (k2_tarski k6_numbers 1) (k2_tarski k1_xboole_0 1) (u1_struct_0 k9_waybel18) (u1_struct_0 k9_waybel18) (k1_partfun1 (k2_tarski k6_numbers 1) (u1_struct_0 A) (u1_struct_0 A) (k2_tarski k1_xboole_0 1) (k5_funct_4 (u1_struct_0 A) k6_numbers 1 C B) (k5_funct_3 D (u1_struct_0 A))) (k3_struct_0 k9_waybel18))) ) ) ) ) ) ) ) ) ) ).
tt(t48_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  =>  ((v2_altcat_1 (k1_yellow18 B)) &  ((v3_altcat_2 (k1_yellow18 B) (k1_yellow18 A)) & (m1_altcat_2 (k1_yellow18 B) (k1_yellow18 A))) ) ) ) ) ) ).
tt(t48_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  => (v3_lattice3 (k2_yellow_1 (k7_waybel_0 A)))) ) ).
tt(t48_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  => (r1_tarski (k6_yellow_3 A B (k4_yellow_3 A B C) (k5_yellow_3 A B C)) (k3_waybel_0 (k3_yellow_3 A B) C))) ) ) ) ) ) ).
tt(t48_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B D) & (r1_tarski C E))  => (r1_tarski (k3_yellow_4 A B C) (k3_yellow_4 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t48_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k13_lattice3 A B C)) = (k3_yellow_0 A)) ) ) ) ) ) ) ).
tt(t48_yellow_7,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v1_waybel_5 A) <=>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) & (v1_partfun1 C B)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D B C (k7_funcop_1 B (u1_struct_0 A))) =>  ((k4_yellow_2 A (k5_waybel_5 A D)) = (k5_yellow_2 A (k4_waybel_5 A (k2_waybel_5 B (u1_struct_0 A) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t48_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ( ((u1_pre_topc B) = (k5_waybel11 A))  => (v2_pre_topc B)) ) ) ) ) ).
tt(t48_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((r2_zf_lang (k8_zf_lang C A) B) => (r3_zf_lang A B)) ) ) ) ) ) ) ).
tt(t48_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v10_zf_lang A) =>  ( (~  ( (B = (k27_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k12_zf_lang B C)) ) ) ) ) )  &  ( ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k12_zf_lang B C)) ) )  =>  (B = (k27_zf_lang A)) )  &  ( (~  ( (B = (k28_zf_lang A))  &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k12_zf_lang C B)) ) ) ) ) )  &  ( (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k12_zf_lang C B)) ) )  =>  (B = (k28_zf_lang A)) ) ) ) ) ) ) ) ) ) ).
tt(t48_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_xboole_0 (k1_tarski A) B) & (r2_hidden A B)) ) ) ) ).
tt(t48_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_zmodul01 B) & (m1_zmodul01 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=> (r1_struct_0 A C)) ) )  =>  (B = A) ) ) ) ) ) ).
tt(t49_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r2_abcmiz_0 A B C) => (r3_orders_2 A (k6_abcmiz_0 A B C) B)) ) ) ) ) ) ) ).
tt(t49_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  ((m1_abcmiz_1 A B (k14_abcmiz_1 B)) <=> (r2_hidden A (k34_abcmiz_1 B))) ) ) ) ).
tt(t49_abcmiz_a,ax, (! [A:$i] :  ( ((v8_abcmiz_1 A k27_abcmiz_1) & (m1_abcmiz_1 A k27_abcmiz_1 (k13_abcmiz_1 k27_abcmiz_1)))  =>  (! [B:$i] :  ((m3_abcmiz_1 B k27_abcmiz_1) =>  ((k18_abcmiz_a (k43_abcmiz_1 k27_abcmiz_1 B A)) = (k2_xboole_0 (k9_abcmiz_a k27_abcmiz_1 A) (k18_abcmiz_a B))) ) ) ) ) ).
tt(t49_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_aff_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_hidden B D) & (r5_aff_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t49_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [K:$i] :  ((m1_subset_1 K (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B I) &  ((r2_hidden B J) &  ((r2_hidden B K) &  ((r2_hidden C I) &  ((r2_hidden F I) &  ((r2_hidden D J) &  ((r2_hidden G J) &  ((r2_hidden E K) &  ((r2_hidden H K) &  ((v1_aff_1 I A) &  ((v1_aff_1 J A) &  ((v1_aff_1 K A) &  ((r2_analoaf A C D F G) & (r2_analoaf A C E F H)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (I = J)  |  ( (I = K)  | (r2_analoaf A D E G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)) (k5_afinsq_1 G)) (k5_afinsq_1 H)) (k5_afinsq_1 I)))  =>  ( ((k1_afinsq_1 A) = 8)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ( ((k1_funct_1 A 3) = E)  &  ( ((k1_funct_1 A 4) = F)  &  ( ((k1_funct_1 A 5) = G)  &  ( ((k1_funct_1 A 6) = H)  &  ((k1_funct_1 A 7) = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v5_relat_1 A k3_numbers) =>  ((k7_afinsq_2 A) = (k6_afinsq_2 k3_numbers A k39_binop_2)) ) ) ) ).
tt(t49_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v10_incproj (k13_afproj A)) => (v2_aff_2 A)) ) ) ).
tt(t49_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 (k2_tdgroup A)))  &  ((v2_tdgroup (k2_tdgroup A)) & (l1_analoaf (k2_tdgroup A))) ) ) ) ).
tt(t49_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ( ((r1_partfun1 D F) &  ((r3_pua2mss1 A C D E) & (r3_pua2mss1 B C F G)) )  => (r3_pua2mss1 (k2_circcomb A B) C (k1_funct_4 D F) (k1_funct_4 E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v3_altcat_3 D A B C) &  (~  ((k1_altcat_1 A C B) = k1_xboole_0) ) ) ) ) ) ) ) )  =>  ((g2_altcat_1 (u1_struct_0 A) (u1_altcat_1 A) (u2_altcat_1 A)) = (k5_altcat_4 A)) ) ) ) ).
tt(t49_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r6_analmetr A C D B) => (r6_analmetr A D C B)) ) ) ) ) ) ) ) ) ).
tt(t49_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_analort A B C D E D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r1_analort A B C G H D E) &  ( (~  ( (~ (r1_analort A B C G H D F))  &  (~ (r1_analort A B C G H F D)) ) )  &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (~ (r2_hidden (k12_aofa_000 A) (k18_aofa_000 A))) ) ) ).
tt(t49_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k72_aofa_i00 A B D E F)) D) = (k6_int_1 (k21_aofa_i00 B k4_numbers C F) 2))  &  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k73_aofa_i00 A B D E F)) D) = (k6_int_1 (k2_xcmplx_0 (k21_aofa_i00 B k4_numbers C F) 1) 2))  &  (! [G:$i] :  ((m1_subset_1 G B) =>  ( (~  (G = D) )  =>  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k72_aofa_i00 A B D E F)) G) = (k21_aofa_i00 B k4_numbers C G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( (~ (v1_xboole_0 B))  &  ((v11_armstrng B) &  (! [C:$i] :  ( ((v6_armstrng C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))))  =>  (~  (B = (k13_armstrng A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  ((k10_arytm_3 (k8_arytm_3 B C) (k8_arytm_3 D A)) = (k8_arytm_3 (k9_ordinal3 B D) (k9_ordinal3 C A))) ) ) ) ) ) ) ) ) ).
tt(t49_asympt_1,ax, (? [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 A B) & (r1_xxreal_0 (k9_real_1 (k7_square_1 B) (k6_power 2 B)) 1)) ) ) ) ) ) ).
tt(t49_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v13_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A C B) (k1_bcialg_1 A D B)) = (k1_bcialg_1 A D C))  &  ((k1_bcialg_1 A B (k4_struct_0 A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m4_bcialg_2 C A B) =>  (! [D:$i] :  ((m1_bcialg_2 D A) =>  ( (! [E:$i] :  ((m3_bcialg_2 E A) => (m5_bcialg_2 E A B)) )  =>  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(t49_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v4_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = (k1_bcialg_4 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B (k1_bcialg_1 A B C)))) ) ) ) ) ) ) ).
tt(t49_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v10_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  ((v8_bcialg_1 A) & (m1_bcialg_5 A k6_numbers 1 k6_numbers 1)) ) ) ) ).
tt(t49_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m5_bcialg_2 C A B) => (v2_funct_2 (k6_bcialg_6 A B C) (u1_struct_0 (k9_bcialg_2 A C)))) ) ) ) ) ) ).
tt(t49_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((v3_bciideal B A) & (m2_bcialg_1 B A)) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = B)  <=>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = (k4_struct_0 A)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = B)  =>  ((k1_bcialg_1 A C B) = C) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A C D) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D B) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A C B)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B (k1_bcialg_1 A C (k1_bcialg_1 A C B))) = (k1_bcialg_1 A B C))  &  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A (k1_bcialg_1 A B C) B)) = (k1_bcialg_1 A B C)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A B D) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B))) = (k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k6_bhsp_1 A B (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ).
tt(t49_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) => (r2_hidden B (k5_bhsp_2 A B C))) ) ) ) ) ) ) ).
tt(t49_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v1_comseq_2 A) & (v2_bhsp_3 C B))  => (v2_bhsp_3 (k5_bhsp_4 B C A) B)) ) ) ) ) ) ) ).
tt(t49_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) &  ((v1_bilinear D A B C) &  ((v2_bilinear D A B C) &  ((v3_bilinear D A B C) &  ((v4_bilinear D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) ) ) ) ) )  =>  ( ((k10_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D)) (k17_bilinear A B C D)) = (k10_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))))  &  ( ((k11_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D)) (k17_bilinear A B C D)) = (k11_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))) (k16_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) C (k15_bilinear A B C D))))  &  ( ((k10_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D)) (k17_bilinear A B C D)) = (k10_bilinear A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D)) (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))))  &  ((k11_bilinear A (k6_vectsp10 A B (k13_bilinear A B C D)) (k6_vectsp10 A C (k14_bilinear A B C D)) (k17_bilinear A B C D)) = (k11_bilinear A (k6_vectsp10 A B (k13_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D))) (k6_vectsp10 A C (k14_bilinear A B C D)) (k15_bilinear A B (k6_vectsp10 A C (k14_bilinear A B C D)) (k16_bilinear A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_boolealg A B (k3_lattices A C D)) <=>  ((r3_boolealg A B C) | (r3_boolealg A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  ( (~ (r1_xxreal_0 F E))  &  ( (~  (F = 1) )  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k1_pre_topc k1_borsuk_4 G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) C))))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k1_borsuk_4 G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))))))) )  =>  (~  ( (G = (k4_rcomp_1 E F))  &  ((v3_tops_2 H (k1_pre_topc k1_borsuk_4 G) (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) &  ((k1_funct_1 H F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k2_rcomp_1 B k1_xxreal_0))  =>  ((k2_pre_topc k3_topmetr A) = (k3_rcomp_1 B k1_xxreal_0)) ) ) ) ) ) ).
tt(t49_borsuk_6,ax, ( ((k1_funct_1 k5_borsuk_6 k6_numbers) = k6_numbers)  &  ((k1_funct_1 k5_borsuk_6 1) = 1) ) ).
tt(t49_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_complex2 B C) = (k2_complex2 B (k7_real_1 C (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))) ) ) ) ) ) ) ).
tt(t49_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k7_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t49_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  ( (H = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B J) (k16_funcop_1 C K)) (k16_funcop_1 D L)) (k16_funcop_1 E M)) (k16_funcop_1 F N)) (k16_funcop_1 G O)) (k16_funcop_1 A I)))  =>  ( (A = B)  |  ( (A = C)  |  ( (A = D)  |  ( (A = E)  |  ( (A = F)  |  ( (A = G)  |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (E = F)  |  ( (E = G)  |  ( (F = G)  |  ( ((k1_funct_1 H A) = I)  &  ( ((k1_funct_1 H B) = J)  &  ( ((k1_funct_1 H C) = K)  &  ( ((k1_funct_1 H D) = L)  &  ( ((k1_funct_1 H E) = M)  &  ( ((k1_funct_1 H F) = N)  &  ((k1_funct_1 H G) = O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k4_xboolean B C)) = (k8_xboolean (k4_xboolean A B) C)) ) ) ) ) ) ) ).
tt(t49_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k5_bvfunc_1 A B C)) (k5_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t49_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A C)))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)) (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A B))))) ) ) ) ) ) ) ) ) ).
tt(t49_card_1,ax, (1 = (k1_tarski k1_xboole_0)) ).
tt(t49_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 B) =>  ( ( (~ (r1_ordinal1 (k1_card_1 A) (k1_card_1 B)))  &  (~ (r2_hidden (k1_card_1 A) (k1_card_1 B))) )  | (v1_finset_1 A)) ) ) ) ).
tt(t49_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k8_card_3 B)) =>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) => (r2_hidden (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ) ) ).
tt(t49_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 (k1_yellow20 B (k7_funcop_1 (k9_xtuple_0 B) A))) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((k1_funct_1 (k1_yellow20 B (k7_funcop_1 (k9_xtuple_0 B) A)) C) = (k3_xboole_0 (k1_funct_1 B C) A)) ) ) ) ) ) ) ).
tt(t49_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_cat_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_cat_1 D A B C) &  ((k2_cat_1 A B C) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_cat_3 D B C A) =>  ( ((r1_cat_3 B C A D) &  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden E A) &  ((r2_hidden F A) &  ((k2_cat_1 B (k4_graph_1 B (k7_partfun1 (u4_struct_0 B) D E)) (k4_graph_1 B (k7_partfun1 (u4_struct_0 B) D F))) = k1_xboole_0) ) ) ) ) ) )  =>  (! [E:$i] :  ((r2_hidden E A) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( (F = (k4_graph_1 B (k7_partfun1 (u4_struct_0 B) D E)))  =>  ( ((k2_cat_1 B C F) = k1_xboole_0)  |  (! [G:$i] :  ((m1_cat_1 G B C F) =>  ( (G = (k7_partfun1 (u4_struct_0 B) D E))  => (v1_cat_3 G B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k23_cat_4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k23_cat_4 A B))) => (m1_cat_1 E (k23_cat_4 A B) C D)) ) ) ) ) ) ) ) ).
tt(t49_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((v1_series_1 B) &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k1_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((k1_seq_1 (k3_series_1 (k4_catalan2 A B)) C) = (k10_binop_2 (k11_binop_2 (k4_series_1 B) (k1_seq_1 (k3_series_1 A) C)) (k7_afinsq_2 D)))  &  ( ((k1_relset_1 k5_numbers D) = (k23_binop_2 C 1))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k23_binop_2 C 1)) =>  ((k1_seq_1 D E) = (k11_binop_2 (k1_seq_1 A E) (k4_series_1 (k10_nat_1 k1_numbers B (k23_binop_2 (k7_nat_d C E) 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_cfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r2_cfcont_1 B A) &  ( ((k8_relset_1 k2_numbers k2_numbers B (k1_tarski k6_numbers)) = k1_xboole_0)  & (r2_cfcont_1 C A)) )  => (r2_cfcont_1 (k1_cfunct_1 k2_numbers C B) A)) ) ) ) ) ) ).
tt(t49_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k1_cfunct_1 A (k1_cfunct_1 A B C) (k1_cfunct_1 A D E)) (k1_cfunct_1 A (k19_valued_1 A k2_numbers k2_numbers B (k2_partfun1 A k2_numbers E (k1_relset_1 A (k2_cfunct_1 A E)))) (k19_valued_1 A k2_numbers k2_numbers C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v10_cgames_1 A) <=>  ( (! [B:$i] :  ((v2_cgames_1 B) =>  (~  ((r2_hidden B (k6_cgames_1 A)) &  ( (~ (v8_cgames_1 B))  &  (~ (v10_cgames_1 B)) ) ) ) ) )  &  (? [B:$i] :  ((v2_cgames_1 B) &  ((r2_hidden B (k7_cgames_1 A)) & (v6_cgames_1 B)) ) ) ) ) ) ) ).
tt(t49_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m1_chain_1 D A) =>  ( ((k3_chain_1 A B C) = (k8_chain_1 A D))  <=>  (! [E:$i] :  ((m2_subset_1 E k5_numbers (k2_finseq_1 A)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E)))  & (m2_chain_1 (k1_domain_1 k1_numbers k1_numbers (k1_seq_1 B E) (k1_seq_1 C E)) (k2_chain_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden C (k2_chord A B)) & (r2_hidden C B)) ) ) ) ) ) ).
tt(t49_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_circcmb3 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_xtuple_0 B) => (r2_hidden B (k3_msafree2 A))) ) ) ) ) ).
tt(t49_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) & (l1_msualg_1 B)) )  => (v1_circcomb (k2_circcomb A B))) ) ) ) ).
tt(t49_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ( ((r4_circtrm1 A B C D E F) & (r3_circtrm1 A B C))  =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A E))) =>  ( (H = (k3_relat_1 C G))  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r1_facirc_1 A E H I) <=> (r1_facirc_1 B F G (k1_funct_1 C I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_ordinal1 A) & (v1_ordinal1 B))  => (v1_ordinal1 (k2_xboole_0 A B))) ) ) ).
tt(t49_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) => (v1_classes2 (k1_classes1 A))) ) ).
tt(t49_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_clvect_1 B) & (m1_clvect_1 B A))  =>  (! [C:$i] :  ( ((v1_clvect_1 C) & (m1_clvect_1 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t49_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) => (r2_hidden B (k5_clvect_2 A B C))) ) ) ) ) ) ) ).
tt(t49_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_2 C) & (v3_clvect_2 B A))  => (v3_clvect_2 (k6_clvect_3 A B C) A)) ) ) ) ) ) ) ).
tt(t49_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v9_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ((v10_cohsp_1 C) <=>  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden (k4_tarski D E) (k8_cohsp_1 A B C)) &  (! [F:$i] :  (~  (D = (k1_tarski F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_complex1,ax, ((k17_complex1 k7_complex1) = 1) ).
tt(t49_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_complex2 (k11_complex1 A B) (k11_complex1 A B)) = (k8_complex1 (k11_complex1 (k11_complex1 (k1_complex2 A A) (k1_complex2 A B)) (k1_complex2 B A)) (k1_complex2 B B))) ) ) ) ) ).
tt(t49_complfld,ax, ((k2_complfld (k5_struct_0 k1_complfld)) = (k5_struct_0 k1_complfld)) ).
tt(t49_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( ((k6_complsp2 (k9_seq_4 A B)) = (k4_rvsum_1 (k6_complsp2 A) (k6_complsp2 B)))  &  ((k7_complsp2 (k9_seq_4 A B)) = (k4_rvsum_1 (k7_complsp2 A) (k7_complsp2 B))) ) ) ) ) ) ) ).
tt(t49_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ((k5_card_1 (k6_compos_1 B C A)) = (k5_card_1 C)) ) ) ) ) ) ) ).
tt(t49_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G) 1) = (k5_compos_0 (u1_compos_1 A) C 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~ (r1_xxreal_0 (k3_complex1 A) k6_numbers))  & (r1_xxreal_0 (k21_sin_cos (k1_comptrig A)) k6_numbers)) ) ) ) ).
tt(t49_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) =>  (~  ((r2_hidden E (k1_relset_1 (k3_finseq_2 k5_numbers) (k6_comput_1 B C A D))) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  (E = (k3_funct_7 k5_numbers D A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k51_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers A) (k55_valued_1 k5_numbers k2_numbers B)))) ) ) ) ).
tt(t49_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((m2_valued_0 A k2_numbers B) =>  ((m2_valued_0 (k7_comseq_3 A) k1_numbers (k7_comseq_3 B)) & (m2_valued_0 (k8_comseq_3 A) k1_numbers (k8_comseq_3 B))) ) ) ) ) ) ).
tt(t49_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l1_clvect_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_convex4 B A) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (C = D)  &  ( (~ (r1_xxreal_0 D k1_xboole_0))  &  (~ (r1_xxreal_0 1 D)) ) ) ) )  => (r1_tarski (k7_rusub_4 A (k19_convex4 A B (k6_xcmplx_0 k6_complex1 C)) (k19_convex4 A B C)) B)) ) ) ) ) ) ) ) ).
tt(t49_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((r2_hidden (k13_cqc_lang A B C) (k3_cqc_lang A)) &  ((r2_hidden (k13_cqc_lang A B D) (k3_cqc_lang A)) & (r2_hidden (k13_cqc_lang A B C) (k4_cqc_the1 A))) )  =>  ((r2_hidden C (k24_qc_lang1 A B)) | (r2_hidden (k13_cqc_lang A B D) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t49_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B))) (k11_cqc_lang A C B)) A) & (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C B) (k6_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B)))) A)) ) ) ) ) ) ) ).
tt(t49_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r6_cqc_the3 A B C) & (r6_cqc_the3 A D E))  =>  ((r5_cqc_the3 A C E) <=> (r5_cqc_the3 A (k6_cqc_lang A B) (k6_cqc_lang A D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k18_complex1 (k9_real_1 (k13_csspace A B) (k13_csspace A C))) (k13_csspace A (k5_algstr_0 A B C)))) ) ) ) ) ) ).
tt(t49_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v3_dickson A) =>  ((v4_dickson A) <=>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  ( ((v3_dickson B) &  ((r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (u1_orders_2 A) (u1_orders_2 B)) &  ((u1_struct_0 A) = (u1_struct_0 B)) ) )  => (v1_wellfnd1 (k5_dickson B))) ) ) ) ) ) ) ).
tt(t49_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) A B) = (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 B)) (k21_sin_cos (k8_real_1 2 A)))) (k9_real_1 A B))) ) ) ) ) ).
tt(t49_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers E F) = (k10_real_1 A (k5_square_1 F))) ) )  & (r1_zfmisc_1 B C D))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ( (D = k6_numbers)  |  ((k10_diff_1 E B C D) = (k8_real_1 (k10_real_1 A (k8_real_1 (k8_real_1 B C) D)) (k7_real_1 (k7_real_1 (k10_real_1 1 B) (k10_real_1 1 C)) (k10_real_1 1 D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k13_complex1 A 2)) B) (k3_funct_2 k1_numbers k1_numbers (k2_diff_1 C (k10_complex1 (k13_complex1 A 2))) B))) ) ) ) ) ) ) ).
tt(t49_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v2_dilworth B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v5_dilworth C (k5_yellow_0 A (k4_dilworth A B))) & (m1_eqrel_1 C (u1_struct_0 (k5_yellow_0 A (k4_dilworth A B)))))  =>  (! [D:$i] :  ( ((v5_dilworth D (k5_yellow_0 A (k3_dilworth A B))) & (m1_eqrel_1 D (u1_struct_0 (k5_yellow_0 A (k3_dilworth A B)))))  =>  (~  ( ((k5_card_1 B) = (k2_dilworth A))  &  ( ((k1_card_1 C) = (k2_dilworth A))  &  ( ((k1_card_1 D) = (k2_dilworth A))  &  (! [E:$i] :  ( ((v5_dilworth E A) & (m1_eqrel_1 E (u1_struct_0 A)))  =>  (~  ((k1_card_1 E) = (k2_dilworth A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  ((r2_hidden D (k6_ec_pf_1 A B C)) &  ( ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) D) = k6_numbers)  &  (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (~  ((r2_hidden E (k6_ec_pf_1 A B C)) &  ((r1_ec_pf_1 A E D) &  ( ((k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = k6_numbers)  &  ( ((k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = 1)  &  ((k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) E) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  ((r1_ec_pf_1 A C D) =>  ((k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t49_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) => (m2_cat_1 (k19_ens_1 B C) B (k11_ens_1 A))) ) ) ) ) ) ) ).
tt(t49_entropy1,ax, (! [A:$i] :  ( ((v4_partfun3 A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k6_rvsum_1 (k4_entropy1 A)))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k8_real_1 (k1_seq_1 A C) (k6_power 2 (k10_real_1 1 (k1_seq_1 A C))))) ) ) ) ) ) ) ) ) ) ).
tt(t49_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_enumset1 A A A A A B C) = (k1_enumset1 A B C)) ) ) ) ).
tt(t49_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( (~  ((k8_mcart_1 A B C D) = k1_xboole_0) )  =>  ( ((k7_relset_1 (k2_zfmisc_1 A B) A (k9_funct_3 A B) (k8_mcart_1 A B C D)) = C)  &  ((k7_relset_1 (k2_zfmisc_1 A B) B (k10_funct_3 A B) (k8_mcart_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t49_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k23_rvsum_1 B C) = (k11_binop_2 (k18_binop_2 1 4) (k10_binop_2 (k5_square_1 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C))) (k5_square_1 (k12_euclid (k5_algstr_0 (k15_euclid A) B C)))))) ) ) ) ) ) ) ).
tt(t49_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) => (r1_tarski (k5_euclid_3 A B C D) (k6_euclid_3 A B C D))) ) ) ) ) ) ) ) ).
tt(t49_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k7_real_1 (k3_complex2 A B) (k3_complex2 B C)) = (k3_complex2 A C))  |  ((k7_real_1 (k3_complex2 A B) (k3_complex2 B C)) = (k7_real_1 (k3_complex2 A C) (k8_real_1 2 k32_sin_cos))) ) ) ) ) ) ) ) ).
tt(t49_euclid_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (m1_rusub_3 (k8_euclid_7 A) (k7_real_ns1 A))) ) ).
tt(t49_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( (A = (k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 B C D) E))  <=>  ( ((k1_seq_1 A 1) = (k1_seq_1 B E))  &  ( ((k1_seq_1 A 2) = (k1_seq_1 C E))  &  ((k1_seq_1 A 3) = (k1_seq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_rlvect_1 (k15_euclid A) (k5_algstr_0 (k15_euclid A) B C) D) = (k5_algstr_0 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B D) (k1_rlvect_1 (k15_euclid A) C D))) ) ) ) ) ) ) ) ) ).
tt(t49_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( (~  ( (~ (r1_xboole_0 B C))  &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) )  &  (~  ( (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  ((r2_hidden D B) & (r2_hidden D C)) ) )  & (r1_xboole_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t49_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v16_waybel_0 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v1_exchsort D)) ) )  =>  (~  ((r2_hidden (k4_tarski A B) (k6_exchsort C D)) & (r2_hidden (k4_tarski B A) (k6_exchsort C D))) ) ) ) ) ) ) ) ).
tt(t49_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B))))) => (v1_circuit2 (k6_circuit2 (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B)) E) (k5_circcomb D (k10_finseq_1 A B)) (k7_circcomb 2 C D (k10_finseq_1 A B)))) ) ) ) ) ) ) ) ).
tt(t49_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 (k1_fcont_1 A B) 1) = (k2_xcmplx_0 A B)) ) ) ) ) ).
tt(t49_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k2_fdiff_9)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t49_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_fdiff_1 B A) =>  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski A))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers B)) & (r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k32_valued_1 k5_numbers k1_numbers C) D)) (k1_relset_1 k1_numbers B))) )  =>  ((v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers C 2)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D C) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers D C) B)))) &  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers C 2)) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D C) B) (k8_funct_2 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers D C) B)))) = (k1_fdiff_1 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)))) =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)) A) B) = (k8_real_1 (k1_seq_1 k16_sin_cos B) (k1_seq_1 k19_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t49_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k16_sin_cos) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos (k6_power k8_power B)) B)) ) ) ) ) ) ) ) ).
tt(t49_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) (k1_taylor_1 2)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k16_sin_cos B) = k6_numbers) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) (k1_taylor_1 2)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos) (k1_taylor_1 2)) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 2 (k1_seq_1 k19_sin_cos B)) (k5_prepower (k1_seq_1 k16_sin_cos B) 3)))) ) ) ) ) ) ) ) ).
tt(t49_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~  (A = 4) )  &  ( (~ (v1_int_2 A))  &  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (~  ( (~  (B = 1) )  &  ( (~  (B = 2) )  &  ( (~  (B = A) )  & (r1_nat_d B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_fib_num3 A B (k2_nat_1 C 1)) = (k2_nat_1 (k4_nat_1 A (k1_pre_ff C)) (k4_nat_1 B (k1_pre_ff (k2_nat_1 C 1))))) ) ) ) ) ) ) ).
tt(t49_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((u1_struct_0 (k6_filter_0 A B)) = B)  &  ( ((u2_lattices (k6_filter_0 A B)) = (k1_realset1 (u2_lattices A) B))  &  ((u1_lattices (k6_filter_0 A B)) = (k1_realset1 (u1_lattices A) B)) ) ) ) ) ) ) ).
tt(t49_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  => (r1_filter_1 (k7_filter_1 A B) (k7_filter_1 B A))) ) ) ) ).
tt(t49_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B C)) = (a_3_1_filter_2 A B C)) ) ) ) ) ) ) ).
tt(t49_finseq_1,ax, (! [A:$i] : (r2_hidden k1_xboole_0 (k13_finseq_1 A))) ).
tt(t49_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k2_finseq_1 A)) =>  ((k1_funct_1 (k1_finseq_2 A) B) = B) ) ) ) ) ).
tt(t49_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k5_relat_1 A (k2_finseq_1 B)) = A)  <=> (r1_xxreal_0 (k3_finseq_1 A) B)) ) ) ) ) ).
tt(t49_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  ( ((k4_finseq_4 A B) = (k3_finseq_1 A))  <=>  ((k6_finseq_4 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t49_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (~  ((r2_hidden B (k10_xtuple_0 C)) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ( ((k2_nat_1 D 1) = (k4_finseq_4 C B))  &  ((k2_finseq_5 A C B) = (k2_rfinseq A D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~  (B = C) )  =>  ((k1_finseq_5 A (k2_finseq_4 A B C) C) = (k2_finseq_4 A B C)) ) ) ) ) ) ) ) ).
tt(t49_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J B) =>  ((k3_funct_2 B A E (k5_binop_1 B G I J)) = (k5_binop_1 A H (k3_funct_2 B A E I) (k3_funct_2 B A E J))) ) ) ) )  => (r2_relset_1 k5_numbers A (k4_finseqop B A (k3_finseqop B B B G C F) E) (k3_finseqop A A A H (k3_funct_2 B A E C) (k4_finseqop B A F E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r3_fintopo6 A (k12_finseq_1 (u1_struct_0 A) C) B C C)) ) ) ) ) ) ) ).
tt(t49_flang_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 B))) =>  ( ((k8_flang_1 B C) = (k1_tarski A))  =>  (A = (k2_flang_1 B)) ) ) ) ) ) ).
tt(t49_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B 1 2) = (k4_subset_1 (k3_catalan2 A) B (k6_flang_1 A B B))) ) ) ) ).
tt(t49_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_tarski (k7_flang_1 A B C) (k2_flang_3 A B))) ) ) ) ) ) ).
tt(t49_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r1_xboole_0 (k4_finseq_2 C A) (k4_finseq_2 D B)))  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t49_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C B A)) )  =>  ((v1_funct_1 (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k2_zfmisc_1 (k12_fsm_1 B A C) B))) &  ((v1_funct_2 (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k2_zfmisc_1 (k12_fsm_1 B A C) B)) (k2_zfmisc_1 (k12_fsm_1 B A C) B) (k12_fsm_1 B A C)) & (m1_subset_1 (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k2_zfmisc_1 (k12_fsm_1 B A C) B)) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k12_fsm_1 B A C) B) (k12_fsm_1 B A C))))) ) ) ) ) ) ) ) ).
tt(t49_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (! [G:$i] :  ((m1_subset_1 G B) =>  ((k3_funct_2 B A D G) = (k5_binop_1 A C (k3_funct_2 B A E G) F)) ) )  => (r2_funct_2 B A D (k9_funcop_1 A B C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A B) =>  ((k1_funct_1 (k5_relat_1 C B) A) = (k1_funct_1 C A)) ) ) ) ) ) ).
tt(t49_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k1_tarski A) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski A) B)))) )  =>  ( (~  (B = k1_xboole_0) )  => (r1_tarski (k7_relset_1 (k1_tarski A) B D C) (k1_tarski (k1_funct_1 D A)))) ) ) ) ) ) ).
tt(t49_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = B)  &  ( ((k9_xtuple_0 D) = B)  & (r2_hidden A B)) )  =>  ((k1_funct_1 (k13_funct_3 C D) A) = (k4_tarski (k1_funct_1 C A) (k1_funct_1 D A))) ) ) ) ) ) ) ) ).
tt(t49_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ( (~  (C = k1_xboole_0) )  =>  ((v1_funct_1 (k2_funct_4 D)) &  ((v1_funct_2 (k2_funct_4 D) (k2_zfmisc_1 B A) C) & (m1_subset_1 (k2_funct_4 D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ) ) ) ) ) ).
tt(t49_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((k9_xtuple_0 C) = (k2_zfmisc_1 A B))  =>  ( ((k2_funct_5 (k1_funct_5 C)) = C)  &  ((k4_funct_5 (k3_funct_5 C)) = C) ) ) ) ) ) ) ).
tt(t49_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r2_wellord2 (k1_funct_2 (k3_card_3 (k2_card_3 B)) A) (k4_card_3 (k8_funct_6 B A)))) ) ) ).
tt(t49_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_finseq_1 C)) ) )  =>  ((k1_funct_1 (k5_funct_7 (k7_finseq_1 B C) A) (k2_nat_1 (k3_finseq_1 (k7_finseq_1 B C)) 1)) = (k1_funct_1 (k5_funct_7 C (k1_funct_1 (k5_funct_7 B A) (k2_nat_1 (k3_finseq_1 B) 1))) (k2_nat_1 (k3_finseq_1 C) 1))) ) ) ) ) ) ).
tt(t49_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t49_functor0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (~  ((v21_functor0 C A B) &  (! [D:$i] :  ((m2_functor0 D B A) =>  (~  ( (D = (k15_functor0 A B C))  &  ((v21_functor0 D B A) & (v16_functor0 D B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((k1_seq_1 (k3_fuzzy_2 A C D) B) = (k9_real_1 1 (k8_real_1 (k9_real_1 1 (k1_seq_1 C B)) (k9_real_1 1 (k1_seq_1 D B))))) ) ) ) ) ) ) ) ) ).
tt(t49_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k4_struct_0 A) (k6_fvaluat1 A B))) ) ) ) ) ).
tt(t49_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_fvsum_1 A B) C) = (k6_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t49_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k4_struct_0 A)) )  &  ( (~  (C = (k4_struct_0 A)) )  &  (~  ((k8_group_1 A (k11_algstr_0 A B) (k11_algstr_0 A C)) = (k11_algstr_0 A (k8_group_1 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) D)) ) )  =>  ((k11_genealg1 F G H A B C D E) = (k7_genealg1 F G H E)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) & (r1_xxreal_0 (k3_finseq_1 G) E)) ) )  =>  ((k11_genealg1 F G H A B C D E) = (k7_genealg1 F G H D)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) ) )  =>  ((k11_genealg1 F G H A B C D E) = (k7_genealg1 F G H C)) )  &  ( ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) C) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) ) )  =>  ((k11_genealg1 F G H A B C D E) = (k7_genealg1 F G H B)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) ) )  =>  ((k11_genealg1 F G H A B C D E) = (k7_genealg1 F G H A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (~  ((r2_hidden A (k2_msafree2 (k19_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k19_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k19_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) B) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) B))) =>  ((r2_xboole_0 B (k6_glib_000 A)) =>  ( ((k24_glib_000 A C) = (k6_subset_1 (k6_glib_000 A) B))  &  ((k25_glib_000 A C) = (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) B))) ) ) ) ) ) ) ) ).
tt(t49_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k2_nat_1 (k3_finseq_1 (k20_glib_001 A B C D)) D) = (k2_nat_1 (k3_finseq_1 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t49_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((r1_glib_002 A B) => (m1_subset_1 B (k6_glib_000 A))) ) ) ) ).
tt(t49_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k11_glib_003 A) = (k11_glib_003 (k13_glib_003 A B C))) ) ) ) ) ).
tt(t49_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1)) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1)) (k19_euclid 1 k6_numbers)))))) ) ) ) ) ) ).
tt(t49_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_graph_1 C A) =>  (~  ((r1_graph_2 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  ( ((v3_graph_2 F A) & (m2_graph_1 F A))  =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 A)) =>  (~  ( ((k15_finseq_1 D) = F)  &  ( ((k15_finseq_1 E) = G)  &  ((r1_graph_2 A G F) &  ( ((k1_funct_1 B 1) = (k1_funct_1 G 1))  &  ((k1_funct_1 B (k3_finseq_1 B)) = (k1_funct_1 G (k3_finseq_1 G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v2_funct_1 C) &  ((v1_msscyc_1 C A) & (m2_graph_1 C A)) )  => (v1_abian (k7_graph_3 A B (k10_xtuple_0 C)))) ) ) ) ) ) ).
tt(t49_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 B)) =>  ( ( ((k3_finseq_1 C) = 1)  &  ((r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 D)) & (r5_graph_5 B A)) )  => (r1_xxreal_0 (k10_graph_5 B C A) (k10_graph_5 B D A))) ) ) ) ) ) ) ) ) ).
tt(t49_graphsp,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r4_graphsp A C D E) & (r4_graphsp B C D E))  =>  (A = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) E F) => (r1_rewrite1 (k3_polyred A B C D) (k5_vfunct_1 (k15_pre_poly A) C E) (k5_vfunct_1 (k15_pre_poly A) C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k3_group_11 A C B)) => (r1_tarski (k13_group_2 A B D) (k8_group_2 A C))) ) ) ) ) ) ) ) ) ).
tt(t49_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((v2_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (k1_group_1 A))) &  ((v3_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (k1_group_1 A))) &  ((v4_rlvect_1 (g2_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (k1_group_1 A))) & (v13_algstr_0 (g2_algstr_0 (u1_struct_0 A) (u2_algstr_0 A) (k1_group_1 A)))) ) ) ) ) ).
tt(t49_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k3_group_1 B) = (k5_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k3_group_1 A) (u1_struct_0 B))) ) ) ) ) ).
tt(t49_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_group_3 A D (k2_group_3 A B C)) = (k5_group_3 A (k4_group_2 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t49_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((r1_struct_0 (k8_group_4 A C D) B) <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  ( ((k3_finseq_1 E) = (k3_finseq_1 F))  &  ((r1_tarski (k10_xtuple_0 E) (k4_subset_1 (u1_struct_0 A) (k8_group_2 A C) (k8_group_2 A D))) &  (B = (k3_group_4 A (k4_group_4 A F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_group_5 A (k6_domain_1 (u1_struct_0 A) B) (k6_domain_1 (u1_struct_0 A) C)) = (k6_domain_1 (u1_struct_0 A) (k2_group_5 A B C))) ) ) ) ) ) ) ).
tt(t49_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k10_group_6 B A C))) &  ((v1_group_6 C B (k10_group_6 B A C)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k10_group_6 B A C)))))) ) ) ) ) ) ) ) ) ).
tt(t49_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((k2_relset_1 (u1_struct_0 C) D) = (u1_struct_0 (k14_group_9 A B C D))) ) ) ) ) ) ) ) ).
tt(t49_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k3_helly A B C B) = B) ) ) ) ) ) ) ).
tt(t49_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_xcmplx_0 (k4_hermitan A B (k3_rlvect_1 A C D)) (k4_hermitan A B (k5_algstr_0 A C D))) = (k7_real_1 (k8_real_1 2 (k4_hermitan A B C)) (k8_real_1 2 (k4_hermitan A B D)))) ) ) ) ) ) ) ) ) ).
tt(t49_hfdiff_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_xxreal_0 1 A) =>  ((r2_hidden k6_numbers B) | (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 A)) B) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 (k2_nat_1 A 1))) (k1_real_1 A)) B))) ) ) ) ) ) ).
tt(t49_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 (k4_hilbert1 A B) C) (k4_hilbert1 A (k4_hilbert1 B C))) k6_hilbert1)) ) ) ) ) ) ).
tt(t49_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((v1_hurwitz A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ((r1_xxreal_0 k6_numbers (k3_complex1 B)) & (r1_xxreal_0 (k17_complex1 (k2_polynom4 k1_complfld A B)) k6_numbers)) ) ) ) ) ) ) ).
tt(t49_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  ((k8_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ).
tt(t49_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  ( (~ (r1_incsp_1 A B D))  & (r3_incsp_1 A D C)) ) ) ) ) ) ) ) ) ).
tt(t49_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~  (A = k6_numbers) )  =>  ((k5_int_1 A A) = 1) ) ) ) ).
tt(t49_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ((r1_int_4 A B) =>  ( ((k5_card_1 B) = A)  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  & (r2_hidden (k4_tarski C D) (k1_int_4 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( (~ (r1_xxreal_0 B 2))  &  ( (~  (A = B) )  &  (~  ((k3_xcmplx_0 (k2_int_5 A B) (k2_int_5 B A)) = (k1_newton (k4_xcmplx_0 1) (k4_nat_1 (k3_nat_d (k7_nat_d A 1) 2) (k3_nat_d (k7_nat_d B 1) 2)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos B) (k7_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t49_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers B (k32_valued_1 k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2))))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = 1) ) ) )  &  ( (D = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k29_sin_cos D)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t49_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) F) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) G) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) F (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) G (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) ) ) ) )  =>  ((k6_integr18 (k4_real_ns1 A) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) F G) D E) = (k3_rlvect_1 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) F D E) (k6_integr18 (k4_real_ns1 A) G D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) => (r1_xxreal_0 (k11_integra1 A B) (k10_integra1 A B))) ) ) ) ) ).
tt(t49_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k10_real_1 (k8_real_1 k32_sin_cos 3) 2)))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k1_real_1 1)) ) ) ) ).
tt(t49_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k9_real_1 A F))  &  (~  ((k1_seq_1 C F) = k6_numbers) ) ) ) ) )  &  ( ((k1_relset_1 k1_numbers C) = E)  &  ( ((k1_relset_1 k1_numbers C) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_real_1 1 (k5_square_1 (k9_real_1 A F)))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers C) (k4_seq_4 B)) (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers C) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ((k10_interva1 A (k3_interva1 A B B)) = (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A))) ) ) ) ) ) ).
tt(t49_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k4_intpro_1 C A) (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t49_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r2_isocat_1 A B) =>  (! [C:$i] :  ((m1_isocat_1 C A B) =>  (? [D:$i] :  ((m1_isocat_1 D B A) &  ((r3_nattra_1 A A (k9_cat_1 A B A C D) (k10_cat_1 A)) & (r3_nattra_1 B B (k9_cat_1 B A B D C) (k10_cat_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t49_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 B (k13_complex1 (k17_euclid A) (k12_euclid A))) =>  ((r1_xxreal_0 (k18_euclid A) k6_numbers) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))) (k8_real_1 (k12_euclid A) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k6_xcmplx_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B)))))))) ) )  &  ((r1_xxreal_0 (k18_euclid A) k6_numbers) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 B) A) = A) ) ) ) ) ) ) ).
tt(t49_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = a_0_6_jgraph_5)  &  ( ((r1_xxreal_0 k6_numbers (k18_euclid B)) | (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ((r1_jordan6 C A B) &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid A)))  &  (~ (r1_xxreal_0 k6_numbers (k17_euclid A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m2_finseq_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  ( ( (I = (k19_euclid C E))  &  ( (J = (k19_euclid D F))  &  ( (G = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k19_euclid C E) (k19_euclid C F) (k19_euclid D F)))  &  ( (H = (k3_finseq_4 (u1_struct_0 (k15_euclid 2)) (k19_euclid C E) (k19_euclid D E) (k19_euclid D F)))  &  ( (A = (k3_topreal1 2 G))  &  (B = (k3_topreal1 2 H)) ) ) ) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 F E) |  ((r1_topreal1 (k15_euclid 2) I J A) &  ((r1_topreal1 (k15_euclid 2) I J B) &  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  ( ((k1_sppol_2 C D E F) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) A B) = (k2_tarski I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 A B C D)) & (r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F (k2_jgraph_2 (k10_real_1 1 A) (k4_xcmplx_0 (k7_xcmplx_0 B A)) (k10_real_1 1 C) (k4_xcmplx_0 (k7_xcmplx_0 D C)))))  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ( (F = (k2_funct_1 E))  &  (E = (k2_funct_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ( (~ (r1_xxreal_0 D 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) D))  &  ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) D F) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C F))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))) => (r1_tarski (k3_goboard5 (k1_jordan8 C B) A k6_numbers) (k2_jordan2c 2 C))) ) ) ) ) ) ) ).
tt(t49_jordan1g,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k10_xtuple_0 A)) =>  ((k3_jordan3 A B) = (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k4_finseq_4 A B))) ) ) ) ) ) ).
tt(t49_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( (~ (r1_xxreal_0 (k3_jordan1h B A) 2))  &  (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) (k3_jordan1h B A))) ) ) ) ) ) ).
tt(t49_jordan1j,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 D (k3_finseq_1 B)) =>  ((k17_finseq_1 A D (k4_graph_2 A B C)) = (k17_finseq_1 A D B)) ) ) ) ) ) ) ) ) ).
tt(t49_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((k5_jordan1k A B (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)) = (k1_topreal6 A B C)) ) ) ) ) ) ) ).
tt(t49_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden (k2_jordan21 A) (k9_jordan6 A)) & (r2_hidden (k1_jordan21 A) (k9_jordan6 A))) ) ) ) ).
tt(t49_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_xxreal_0 2 A) &  ( (C = (k6_subset_1 (k1_euclid A) (a_2_3_jordan2c A B)))  &  ((r2_hidden D C) &  ((r2_hidden E C) &  ( (~  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( (~  (D = (k1_rlvect_1 (k15_euclid A) E F)) )  &  (~  (E = (k1_rlvect_1 (k15_euclid A) D F)) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid A))) =>  (~  ((r2_hidden F C) &  ((r2_hidden G C) &  ((r2_hidden H C) &  ((r2_hidden I C) &  ((r2_hidden J C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) D F) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) F G) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) G H) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) H I) C) &  ((r1_tarski (k1_rltopsp1 (k15_euclid A) I J) C) & (r1_tarski (k1_rltopsp1 (k15_euclid A) J E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r3_jordan4 A B C D) =>  ( ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B)))  | (r1_topreal4 (k3_topreal1 2 B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A D))) ) ) ) ) ) ) ) ) ) ).
tt(t49_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k16_jordan5d A) = (k14_jordan5d A)) ) ) ) ).
tt(t49_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 (k17_euclid C) B) &  ((r1_xxreal_0 B (k17_euclid D)) & (r1_topreal1 (k15_euclid 2) C D A)) )  =>  ( (~ (r1_xboole_0 A (k6_jordan6 B)))  & (v4_pre_topc (k9_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_jordan6 B)) (k15_euclid 2))) ) ) ) ) ) ) ) ) ) ).
tt(t49_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jgraph_6 A B C D) (k1_jgraph_6 A B C D)) = (k1_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t49_kurato_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k1_enumset1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))))) &  (A = k1_numbers) ) ) ) ).
tt(t49_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v14_lattices A) <=> (v13_lattices (k1_lattice2 A))) ) ) ).
tt(t49_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  &  ((k5_lattices A) = (k15_lattice3 A k1_xboole_0)) ) ) ) ).
tt(t49_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k14_lexbfs A (k16_lexbfs A)))) = (k6_glib_000 A)) ) ) ).
tt(t49_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v8_limfunc1 A) <=>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ((r2_hidden D (k1_relset_1 k1_numbers A)) & (r1_xxreal_0 B (k1_seq_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A C))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D C))  &  ( (~ (r1_xxreal_0 A D))  &  ((r2_hidden D (k1_relset_1 k1_numbers B)) &  (~  ((k1_seq_1 B D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_limfunc2 B A) = k6_numbers)  |  ((r1_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k1_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k1_limfunc2 B A))) ) ) ) ) ) ) ) ).
tt(t49_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r2_limfunc2 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) & (r1_xxreal_0 (k1_limfunc3 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r2_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t49_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k20_lpspace1 A B C))) =>  ( (? [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden E (k9_lpspace1 A B C)) &  ( (D = (k13_lpspace1 A B C E))  &  ((k1_normsp_0 (k20_lpspace1 A B C) D) = (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers E))) ) ) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_hidden E D) =>  ((k1_mesfunc6 A B C (k56_valued_1 A k1_numbers E)) = (k1_normsp_0 (k20_lpspace1 A B C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ((r2_hidden D (k1_lpspace2 A B C E)) =>  ((r2_hidden (k1_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D))) k1_numbers) & (r1_xxreal_0 k6_numbers (k1_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 D (k3_hilbert1 (k4_ltlaxio1 A B) C)) => (r8_ltlaxio1 D (k3_hilbert1 A (k3_hilbert1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t49_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A C D)) A) & (v2_cqc_the1 (k8_cqc_lang A B C) A))  => (v2_cqc_the1 (k8_cqc_lang A B D) A)) ) ) ) ) ) ) ) ) ).
tt(t49_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k5_mathmorp A D B) (k3_mathmorp A (k6_rusub_4 A D C) B))) ) ) ) ) ) ) ) ) ).
tt(t49_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) => (r2_matrix10 (k1_matrix10 (k3_matrix10 A B C)) (k3_matrixr1 (k1_matrix10 B) (k1_matrix10 C)))) ) ) ) ) ) ).
tt(t49_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_finseq_1 A)) & (r2_hidden D (k2_finseq_1 A)))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((k8_matrix_1 (u1_struct_0 B) E C) = (k8_matrix_1 (u1_struct_0 B) E D))  =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  (! [G:$i] :  ((m1_matrix_2 G (k12_matrix_2 A)) =>  (! [H:$i] :  ((m1_matrix_2 H (k12_matrix_2 A)) =>  ( ((r2_funct_2 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) G (k1_partfun1 (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) (k2_finseq_1 (k11_matrix_2 (k12_matrix_2 A))) H F)) &  ((v4_matrix_2 H (k11_matrix_2 (k12_matrix_2 A))) &  ((k1_funct_1 H C) = D) ) )  =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B E) G) = (k4_algstr_0 B (k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r2_hidden B (k2_finseq_1 (k5_card_1 D))) & (r1_tarski E (k2_finseq_1 (k3_finseq_1 C))))  =>  ((k9_matrix_1 A (k6_matrix13 A C E D) B) = (k1_partfun1 k5_numbers k5_numbers k5_numbers A (k5_matrix13 E) (k9_matrix_1 A C (k1_funct_1 (k5_matrix13 D) B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((v1_matrix_6 (k4_matrix14 B A C) A B) &  ((k5_matrix_6 A B (k4_matrix14 B A C)) = (k4_matrix14 B A C)) ) ) ) ) ) ) ) ) ).
tt(t49_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ((k5_card_1 E) = A)  &  ((r1_tarski E (k2_finseq_1 B)) &  ( ((k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 A) E) = (k12_matrix_1 C A))  &  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) (k7_nat_d B A) B) =>  (~  ( ((k6_matrix13 (u1_struct_0 C) F (k2_finseq_1 (k7_nat_d B A)) (k7_subset_1 k5_numbers (k2_finseq_1 B) E)) = (k12_matrix_1 C (k7_nat_d B A)))  &  ( ((k6_matrix13 (u1_struct_0 C) F (k2_finseq_1 (k7_nat_d B A)) E) = (k2_matrix_3 C (k4_matrix_1 (u1_struct_0 C) (k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 A) (k7_subset_1 k5_numbers (k2_finseq_1 B) E)))))  &  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 C) B G) =>  ( (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ((r2_hidden I (k2_finseq_1 G)) &  ( (! [J:$i] :  ((v7_ordinal1 J) =>  (~  ((r2_hidden J (k2_finseq_1 (k7_nat_d B A))) &  ((k9_matrix_1 (u1_struct_0 C) H I) = (k8_matrix_1 (u1_struct_0 C) F J)) ) ) ) )  &  (~  ((k9_matrix_1 (u1_struct_0 C) H I) = (k5_finseq_2 (u1_struct_0 C) B (k4_struct_0 C))) ) ) ) ) ) )  => (r2_hidden H (k4_matrix15 C D (k1_matrix_3 C A G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((v4_matrix16 C (u1_struct_0 A)) &  ((v4_matrix16 D (u1_struct_0 A)) &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k2_matrix16 (u1_struct_0 A) C) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k2_matrix16 (u1_struct_0 A) D) B)) = (k2_matrix16 (u1_struct_0 A) (k9_fvsum_1 A (k3_fvsum_1 A C D) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 C) = (k1_matrix_1 D)) ) ) )  =>  ((k1_matrix_4 A (k1_matrix_4 A D B) (k1_matrix_4 A D C)) = (k2_matrix_3 A (k1_matrix_4 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B (k2_matrix_6 A B C D) D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) & (r2_matrix_8 A B D C))  =>  ((r1_xxreal_0 A k6_numbers) | (v1_matrix_6 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) C D) E) = (k4_struct_0 B)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r2_hidden E (k2_finseq_1 A)) &  ((k1_funct_1 (k10_matrix_3 A B C D) E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((k17_rvsum_1 (k10_matrixc1 A)) = (k17_rvsum_1 (k11_matrixc1 A))) ) ) ) ).
tt(t49_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k22_matrixj1 B (k16_matrixj1 (u1_struct_0 B) A C)) = (k4_matrix_2 (u1_struct_0 B) (k12_matrix_3 A B C))) ) ) ) ) ) ) ).
tt(t49_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ( ((k4_matrix_1 k1_numbers (k10_matrixr1 A)) = (k9_matrixr1 A))  &  ((k4_matrix_1 k1_numbers (k9_matrixr1 A)) = (k10_matrixr1 A)) ) ) ) ) ).
tt(t49_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k1_matrix_1 B) k6_numbers) |  ((k12_matrixr1 B (k6_rvsum_1 A)) = (k6_rvsum_1 (k12_matrixr1 B A))) ) ) ) ) ) ) ) ).
tt(t49_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) (k3_finseq_1 D) (k3_finseq_1 E)) =>  ((k10_ranknull A B C (k4_matrlin2 A B C D E F)) = (k8_matrix13 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 A) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k23_rvsum_1 A (k12_matrixr1 C B)) = (k23_rvsum_1 (k12_matrixr1 (k4_matrix_1 k1_numbers C) A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t49_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_zfmisc_1 A B C D) = (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C) D)) ) ) ) ) ).
tt(t49_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v4_xxreal_2 A) <=> (v4_xxreal_2 (k2_measure6 A B))) ) ) ) ) ).
tt(t49_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) => (r1_tarski (k9_member_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k9_member_1 A B) (k9_member_1 A C)))) ) ) ) ) ) ).
tt(t49_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k1_funct_4 C (k8_memstr_0 A B D))))) ) ) ) ) ) ) ) ).
tt(t49_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k8_subset_1 A C (k10_relat_1 D E)) = (k8_subset_1 A (k8_subset_1 A C (k14_mesfunc1 D E)) (k12_mesfunc1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r1_mesfun7c A B C) <=>  (? [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D B))  &  (? [E:$i] :  ((m2_finseq_1 E k2_numbers) &  ( ((k1_relset_1 A C) = (k3_tarski (k2_relset_1 B D)))  &  ( ((k4_finseq_1 D) = (k4_finseq_1 E))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_seq_1 (k5_comseq_3 A C) G) = (k1_seq_1 (k6_complsp2 E) F)) ) ) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 D)) =>  (! [G:$i] :  ((r2_hidden G (k1_funct_1 D F)) =>  ((k1_seq_1 (k6_comseq_3 A C) G) = (k1_seq_1 (k7_complsp2 E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k1_numbers E k6_numbers)))  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers E F) D)) )  &  ((v1_mesfun9c E A) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F D) => (v2_comseq_2 (k10_seqfunc A E F))) ) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k1_mesfunc9 C D)) |  ( (! [F:$i] :  ((v7_ordinal1 F) => (r3_mesfunc6 A B C (k4_mesfunc5 A k1_numbers E F))) )  &  ((r1_mesfunc5 A B C (k8_mesfun7c A E)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_mesfunc9 F G) = (k1_mesfunc6 A B C (k4_mesfunc5 A k1_numbers E G))) ) )  &  ((v10_mesfunc5 F) &  ((k2_mesfunc5 F) = (k7_mesfunc5 A B C (k8_mesfun7c A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (? [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) &  ((k1_relset_1 A D) = E) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ((r1_mesfunc1 A B D F) => (r1_mesfunc1 A B (k6_mesfunc1 A D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_mesfunc6 A B C) <=> (r1_mesfunc2 A B (k1_mesfunc5 A C))) ) ) ) ) ) ) ).
tt(t49_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ( (C = (k1_relset_1 A (k4_mesfunc5 A k7_numbers D k6_numbers)))  &  ((v1_mesfunc8 D A k7_numbers) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers D E)) & (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers D E) C)) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_funct_2 k5_numbers (k4_partfun1 A k7_numbers)))))) )  =>  (~  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers (k10_mesfunc9 A E F) G)) &  ((k1_relset_1 A (k4_mesfunc5 A k7_numbers (k10_mesfunc9 A E F) G)) = (k1_relset_1 A (k4_mesfunc5 A k7_numbers D F))) ) ) )  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers (k10_mesfunc9 A E F) G))) )  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r1_xxreal_0 G H) =>  (! [I:$i] :  ((m1_subset_1 I A) =>  ((r2_hidden I (k1_relset_1 A (k4_mesfunc5 A k7_numbers D F))) => (r1_xxreal_0 (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k10_mesfunc9 A E F) G) I) (k1_mesfunc9 (k4_mesfunc5 A k7_numbers (k10_mesfunc9 A E F) H) I))) ) ) ) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G (k1_relset_1 A (k4_mesfunc5 A k7_numbers D F))) =>  ((v10_mesfunc5 (k3_mesfunc5 A (k10_mesfunc9 A E F) G)) &  ((k2_mesfunc5 (k3_mesfunc5 A (k10_mesfunc9 A E F) G)) = (k1_mesfunc9 (k4_mesfunc5 A k7_numbers D F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k10_midsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  ((k11_midsp_1 A B C) = (k11_midsp_1 A C B)) ) ) ) ) ) ) ).
tt(t49_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ((v1_mmlquery C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))))  => (r2_relset_1 A A (k18_mmlquery A (k19_mmlquery A B C)) (k20_mmlquery A (k18_mmlquery A B) (k18_mmlquery A C)))) ) ) ) ) ).
tt(t49_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k51_modelc_1 A B C (k27_modelc_1 (k48_modelc_1 A B C) D E)) = (k1_knaster A (k61_modelc_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_modelc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_2 A) & (l1_modelc_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k15_modelc_2 (u1_modelc_2 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k9_modelc_2 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k9_modelc_2 (u1_struct_0 A))))) )  =>  ( ((r4_modelc_2 A B C) & (r4_modelc_2 A B D))  => (r2_funct_2 k9_modelc_2 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(t49_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r7_modelc_3 A B C) =>  (! [D:$i] :  (~  ((r2_hidden D (k22_modelc_3 A)) &  ( (~ (v3_modelc_3 (k10_modelc_3 D A) A))  &  ((r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( (~ (r1_xxreal_0 E F))  & (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A) A)) ) ) )  & (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (~  ((k11_nat_3 A B) = k6_numbers) )  =>  ((k1_recdef_1 (k5_moebius1 A) B) = B) ) ) ) ) ) ).
tt(t49_monoid_0,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k6_monoid_0)) <=> (m1_subset_1 A k1_numbers)) ) ).
tt(t49_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_binop_1 B A) => (v1_binop_1 (k21_monoid_1 A A A B) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(t49_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  (! [E:$i] :  ((m3_pboole E A (k1_mboolean A B)) =>  ((r6_pboole A C (k2_pboole A D E)) => (r6_pboole A (k4_mssubfam A B C) (k3_pboole A (k4_mssubfam A B D) (k4_mssubfam A B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_msualg_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C A B B) =>  (! [D:$i] :  ((m1_msualg_4 D A B B) =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 B E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 B E)) =>  ((r2_hidden (k4_tarski F G) (k1_msualg_4 A B B D E)) <=> (r2_rewrite1 (k1_msualg_4 A B B C E) F G)) ) ) ) ) ) )  => (v1_msualg_4 D A B)) ) ) ) ) ) ) ) ) ).
tt(t49_mycielsk,ax, ( ((k7_mycielsk k6_numbers) = (k5_mycielsk 2))  &  (! [A:$i] :  ((v7_ordinal1 A) =>  ((k7_mycielsk (k2_xcmplx_0 A 1)) = (k6_mycielsk (k7_nat_d (k3_xcmplx_0 3 (k2_newton 2 A)) 1) (k7_mycielsk A))) ) ) ) ).
tt(t49_nat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_funct_2 k5_numbers A (k10_nat_1 A (k10_nat_1 A B C) D) (k10_nat_1 A (k10_nat_1 A B D) C))) ) ) ) ) ) ) ) ).
tt(t49_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k12_nat_3 (k24_binop_2 A B)) = (k11_pre_poly k10_newton (k12_nat_3 A) (k12_nat_3 B))) ) ) ) ) ).
tt(t49_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (? [C:$i] :  ((m2_finseq_1 C k1_numbers) &  ( ((k3_finseq_1 C) = (k4_nat_1 2 A))  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k4_finseq_1 C)) =>  ((k1_funct_1 C D) = (k5_real_1 (k1_int_1 (k10_real_1 (k4_nat_1 2 A) (k1_newton B D))) (k8_real_1 2 (k1_int_1 (k10_real_1 A (k1_newton B D)))))) ) ) )  &  ((k11_nat_3 (k6_newton A (k4_nat_1 2 A)) B) = (k18_rvsum_1 C)) ) ) ) ) ) ) ) ) ).
tt(t49_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  ((r1_xxreal_0 B A) &  (~ (r1_xxreal_0 (k1_nat_1 A 1) B)) ) )  => (r1_xxreal_0 A (k7_nat_d B 1))) ) ) ) ) ).
tt(t49_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r12_ncfcont1 A C B) <=>  ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_hidden G B) &  ( (~ (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A G D))))  & (r1_xxreal_0 E (k17_complex1 (k11_complex1 (k7_partfun1 k2_numbers C G) (k7_partfun1 k2_numbers C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C (k4_real_ns1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) C k6_numbers) = (k4_struct_0 (k4_real_ns1 A)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) )  =>  ( ((k7_partfun1 (u1_struct_0 (k4_real_ns1 B)) D (k4_struct_0 (k4_real_ns1 A))) = (k4_struct_0 (k4_real_ns1 B)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers (u1_struct_0 (k4_real_ns1 A))) &  ((v2_ndiff_3 E (k4_real_ns1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A)))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))) &  ((v13_vectsp_1 F (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v1_lopban_1 F (k4_real_ns1 A) (k4_real_ns1 B)) &  ((v2_lopban_1 F (k4_real_ns1 A) (k4_real_ns1 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) )  =>  ((v1_funct_1 (k6_vfunct_1 k1_numbers (k4_real_ns1 B) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C F) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D))) &  ((v1_ndiff_3 (k6_vfunct_1 k1_numbers (k4_real_ns1 B) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C F) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D)) (k4_real_ns1 B)) & (m1_subset_1 (k6_vfunct_1 k1_numbers (k4_real_ns1 B) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) C F) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) (k6_vfunct_1 k1_numbers (k4_real_ns1 A) E C) D)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 A)) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_prvect_2 A B))) =>  ( (E = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A B)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A B D) F))  =>  ( (B = C)  |  ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A C)) (k3_ndiff_5 A C) D) = (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A C)) (k3_ndiff_5 A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_nat_d A B) =>  ((k6_nat_d A B) = A) ) ) ) ) ) ).
tt(t49_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) =>  ((k7_partfun1 (u1_struct_0 A) B C) = C) ) ) )  => (r3_nfcont_1 A A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t49_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k7_normform A))) =>  ((r1_tarski B C) => (r1_tarski (k10_normform A D B) (k10_normform A D C))) ) ) ) ) ) ) ) ).
tt(t49_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  => (r2_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 B)) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k10_oppcat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)))) ) ) ) ) ) ).
tt(t49_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (~  ((r4_orders_1 A B) &  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t49_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_orders_1 (u1_orders_2 A) B) =>  ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ).
tt(t49_ordinal2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  => (r1_tarski (k10_xtuple_0 A) (k4_ordinal2 A))) ) ).
tt(t49_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( ((r2_hidden 1 A) & (v4_ordinal1 B))  =>  ( (B = k1_xboole_0)  |  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_ordinal2 C)) ) )  =>  ( ( ((k9_xtuple_0 C) = B)  &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) =>  ((k1_funct_1 C D) = (k11_ordinal2 D A)) ) ) ) )  =>  ((k11_ordinal2 B A) = (k4_ordinal2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t49_ordinal5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  ((r2_hidden B A) =>  ( ((v3_ordinal1 B) & (v4_ordinal5 B))  &  (? [C:$i] :  ( ((v3_ordinal1 C) & (v4_ordinal5 C))  &  ((r2_hidden B C) & (r2_hidden C A)) ) ) ) ) )  =>  ((v3_ordinal1 (k3_tarski A)) & (v4_ordinal5 (k3_tarski A))) ) ) ) ).
tt(t49_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ((r2_hidden A (k10_xtuple_0 B)) => (r1_ordinal1 (k9_xtuple_0 (k7_ordinal6 B)) (k9_xtuple_0 A))) ) ) ) ) ).
tt(t49_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t49_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  ((k5_lattices (k16_osalg_2 A B)) = (k10_osalg_2 A B (k3_osalg_2 A B))) ) ) ) ) ).
tt(t49_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) => (r1_parsp_1 A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_partfun1,ax, (! [A:$i] :  ((k4_partfun1 A k1_xboole_0) = (k1_tarski k1_xboole_0)) ) ).
tt(t49_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((k1_relset_1 A D) = (k1_tarski C))  =>  (D = (k1_tarski (k4_tarski C (k7_partfun1 B D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t49_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k3_pboole A B (k1_pboole A)) (k1_pboole A))) ) ) ).
tt(t49_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r4_pdiff_5 B A) & (r4_pdiff_5 C A))  =>  ((r3_pdiff_1 3 1 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 1 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k7_real_1 (k4_pdiff_5 B A) (k4_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t49_pdiff_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1))))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)))) =>  ((v3_nfcont_1 C (k4_real_ns1 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((r7_pdiff_1 A 1 D B C) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 1) (k4_real_ns1 1)) (k15_pdiff_1 A 1 D B C) C)) ) ) )  <=>  ((r2_ndiff_1 C (k4_real_ns1 A) (k4_real_ns1 1) B) & (r3_nfcont_1 (k4_real_ns1 A) (k16_lopban_1 (k4_real_ns1 A) (k4_real_ns1 1)) (k4_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 1) B C) C)) ) ) ) ) ) ) ) ) ).
tt(t49_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) k1_numbers))))  =>  ( (C = D)  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r1_pdiff_9 A B C))  <=> (r4_nfcont_1 (k4_real_ns1 A) D B)) ) ) ) ) ) ) ) ) ).
tt(t49_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((v1_int_2 A) & (r1_int_2 B A))  => (r1_nat_d (k3_pepin B A) (k7_nat_d A 1))) ) ) ) ) ).
tt(t49_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((k12_pnproc_1 A k6_numbers) = A) ) ) ).
tt(t49_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k1_vectsp_9 k2_bspace (k17_polyform A B)) = (k2_xcmplx_0 (k10_ranknull k2_bspace (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1)) (k21_polyform A B)) (k11_ranknull k2_bspace (k17_polyform A B) (k17_polyform A (k6_xcmplx_0 B 1)) (k21_polyform A B)))) ) ) ) ) ).
tt(t49_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_polynom5 A (k9_polynom3 A) B) (k9_polynom3 A))) ) ) ) ).
tt(t49_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 H (k15_pre_poly A) C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_polynom1 A C E F) G) &  ((r1_rewrite1 (k3_polyred A B C D) G H) &  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 I (k15_pre_poly A) C) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 J (k15_pre_poly A) C) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (~  ((r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k6_polynom1 A C I J) H) &  ((r1_rewrite1 (k3_polyred A B C D) E I) & (r1_rewrite1 (k3_polyred A B C D) F J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  => (r1_xxreal_0 (k7_real_1 1 (k3_xcmplx_0 B A)) (k3_power (k7_real_1 1 A) B))) ) ) ) ) ).
tt(t49_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r3_pre_poly A B C) => (r2_pre_poly A B C)) ) ) ) ) ) ) ).
tt(t49_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k6_prepower A B) = (k1_newton A B)) ) ) ) ) ) ).
tt(t49_prob_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k9_setfam_1 A)) =>  ((r2_hidden B (k5_prob_3 A C)) <=>  (? [D:$i] :  ((v7_ordinal1 D) &  ((r2_hidden D (k1_relset_1 k5_numbers C)) & (r2_hidden B (k4_prob_3 A C D))) ) ) ) ) ) ) ) ).
tt(t49_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A D B) (k9_cqc_lang A D C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t49_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k23_pscomp_1 A) (k22_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k12_pscomp_1 A)))) ) ).
tt(t49_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r1_pboole A B (k4_pboole A C (k1_pzfmisc1 A D))) &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  ((r1_qc_lang2 A C B) <=>  ( (C = (k19_qc_lang1 A B))  |  (C = (k20_qc_lang1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t49_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v3_qc_lang2 B A) =>  ((k4_qc_lang3 A C B) = (k4_subset_1 C (k4_qc_lang3 A C (k13_qc_lang2 A B)) (k4_qc_lang3 A C (k14_qc_lang2 A B)))) ) ) ) ) ) ) ) ).
tt(t49_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k18_quatern2 A A) = (k5_square_1 (k3_quatern2 A))) ) ) ).
tt(t49_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ( ((k3_quatern2 A) = (k3_quatern2 B))  &  ((k8_quatern2 A) = (k8_quatern2 B)) )  =>  ( ((k3_quatern2 A) = k6_numbers)  |  (A = B) ) ) ) ) ) ) ).
tt(t49_quaterni,ax, ( ((k17_quaterni (k31_quaterni k11_quaterni)) = k6_numbers)  &  ( ((k18_quaterni (k31_quaterni k11_quaterni)) = k6_numbers)  &  ( ((k19_quaterni (k31_quaterni k11_quaterni)) = (k1_real_1 1))  &  ((k20_quaterni (k31_quaterni k11_quaterni)) = k6_numbers) ) ) ) ).
tt(t49_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~  (C = (k4_struct_0 A)) )  &  ( (~  (E = (k4_struct_0 A)) )  &  (~  ((k3_rlvect_1 A (k20_quofield A B C) (k20_quofield A D E)) = (k20_quofield A (k3_rlvect_1 A (k8_group_1 A B E) (k8_group_1 A D C)) (k8_group_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) &  ((r1_xxreal_0 A B) & (r2_hidden (k1_rcomp_1 A B) C)) ) ) )  => (m1_rcomp_3 (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B)) A B C)) ) ) ) ) ) ) ).
tt(t49_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k1_seq_1 (k4_real_3 B) C) A)) )  =>  ((r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) k6_numbers) k6_numbers) |  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k1_seq_1 (k5_real_3 B) C) (k2_newton (k10_real_1 (k3_real_1 A (k7_square_1 (k3_real_1 (k3_square_1 A) 4))) 2) (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(t49_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_relat_1 D) =>  ((r2_hidden (k4_tarski A B) (k3_relat_1 D (k4_relat_1 C))) <=>  ((r2_hidden B C) & (r2_hidden (k4_tarski A B) D)) ) ) ) ) ) ) ).
tt(t49_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k3_subset_1 B (k7_relset_1 A B D C)) = (k6_relset_2 A B C (k3_subset_1 (k2_zfmisc_1 A B) D))) ) ) ) ) ) ) ).
tt(t49_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v6_rewrite1 A) =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_rewrite1 A B C) & (r2_hidden (k4_tarski B D) A))  => (r5_rewrite1 A C D)) ) ) ) ) ) ) ).
tt(t49_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ((k8_rewrite2 A B C) = (k8_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k6_rewrite2 (k8_afinsq_1 A))) C)) ) ) ) ) ) ).
tt(t49_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden E (k4_finseq_1 D)) & (r2_hidden (k2_xcmplx_0 E 1) (k4_finseq_1 D)))  =>  ((r1_struct_0 C (k1_xtuple_0 (k1_funct_1 D E))) &  ((r2_hidden (k2_xtuple_0 (k1_funct_1 D E)) (k8_afinsq_1 A)) &  ((r1_struct_0 C (k1_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1)))) &  ((r2_hidden (k2_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1))) (k8_afinsq_1 A)) &  ((r2_hidden (k1_xtuple_0 (k1_funct_1 D E)) (k9_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))) & (r2_hidden (k1_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1))) (k10_xtuple_0 (u1_rewrite3 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k5_relat_1 (k24_valued_1 B C) A) = (k24_valued_1 (k5_relat_1 B A) C)) ) ) ) ) ) ).
tt(t49_rfunct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers B A)) => (v8_valued_0 (k2_partfun1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers B) A))) ) ) ) ).
tt(t49_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] : (r2_relset_1 A k1_numbers (k15_valued_1 A k1_numbers (k2_partfun1 A k1_numbers B D) C) (k2_partfun1 A k1_numbers (k15_valued_1 A k1_numbers B C) D))) ) ) ) ) ) ) ).
tt(t49_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 B) => (r1_xxreal_0 (k1_seq_1 (k4_rinfsup1 B) (k2_nat_1 A 1)) (k1_seq_1 (k4_rinfsup1 B) A))) ) ) ) ) ).
tt(t49_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k4_rlaffin1 A B))) ) ) ) ).
tt(t49_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_struct_0 D B) =>  ((k3_rlsub_1 A (k1_rlvect_1 A B C) D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ( ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) = D)  &  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) )  =>  (E = (k4_rlsub_2 A D B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  => (v3_pre_topc (k1_convex1 A B C) A)) ) ) ) ) ) ).
tt(t49_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_rlvect_1 A (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C D E)) B) = (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A C B) (k1_rlvect_1 A D B)) (k1_rlvect_1 A E B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k9_rlvect_2 A C) B) = (k1_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers C B))) ) ) ) ) ) ) ).
tt(t49_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_struct_0 D C) <=>  ((k3_rmod_2 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))))  &  ((v10_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) &  ((v14_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) & (l3_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B)))) ) ) ) ) ) ) ).
tt(t49_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) => (r1_rmod_4 A B (k7_rmod_4 A B (k1_group_1 A) C) C)) ) ) ) ) ) ).
tt(t49_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k5_robbins1 A (k13_robbins1 A B) (k15_robbins1 A B)) B) = (k11_robbins1 A B)) ) ) ) ) ).
tt(t49_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A (k3_robbins1 A (k5_robbins1 A C B))) (k5_robbins1 A C D))))) (k5_robbins1 A C D)) = (k5_robbins1 A (k3_robbins1 A (k3_robbins1 A (k5_robbins1 A C B))) (k5_robbins1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t49_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k9_subset_1 (u1_struct_0 A) B C)) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D))) ) ) ) ) ) ) ) ).
tt(t49_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ( (~ (r1_xxreal_0 (k1_rpr_1 A C) k6_numbers))  &  ( (~ (r1_xxreal_0 1 (k1_rpr_1 A C)))  &  (~  ((k1_rpr_1 A B) = (k7_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k8_real_1 (k2_rpr_1 A (k3_subset_1 A C) B) (k1_rpr_1 A (k3_subset_1 A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_rusub_1 A C B) = (k3_rusub_1 A (k4_algstr_0 A C) B))  <=> (r1_struct_0 B C)) ) ) ) ) ) ) ).
tt(t49_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))) =>  ( ( ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) = D)  &  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) E)) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) E))) )  =>  (E = (k4_rusub_2 A D B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 (k5_rusub_5 A)))  &  ((u1_pre_topc (k5_rusub_5 A)) = (k4_rusub_5 A)) ) ) ) ).
tt(t49_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k10_rvsum_1 C (k11_binop_2 A B)) = (k10_rvsum_1 (k10_rvsum_1 C B) A)) ) ) ) ) ) ) ).
tt(t49_rvsum_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k2_numbers))  =>  ((k20_rvsum_1 (k10_rvsum_2 A C B)) = (k5_binop_2 (k19_rvsum_1 (k2_finseq_2 A B)) (k20_rvsum_1 C))) ) ) ) ) ) ) ).
tt(t49_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_ami_3)) =>  ((v1_relat_1 (k5_relat_1 A k1_ami_2)) &  ((v4_relat_1 (k5_relat_1 A k1_ami_2) (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 (k5_relat_1 A k1_ami_2)) &  ((v5_funct_1 (k5_relat_1 A k1_ami_2) (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 (k5_relat_1 A k1_ami_2) (u1_struct_0 k1_ami_3))) ) ) ) ) ) ) ) ).
tt(t49_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r1_scmfsa7b (k2_compos_1 k1_scmfsa_2) A)) ) ) ).
tt(t49_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v2_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r6_scmfsa7b A (k1_scmfsa_m B) C)) ) ) ) ) ) ) ).
tt(t49_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k12_scmpds_2 D E B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k12_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k2_xcmplx_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C))))  &  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k12_scmpds_2 D E B C) A) F) = (k1_funct_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers) )  =>  ((r1_scmpds_6 (k5_scmpds_6 D E C) B A) & (r2_scmpds_6 (k5_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ( (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 H) &  ((v5_funct_1 H (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 H (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 H 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I k5_numbers) &  ((v5_relat_1 I (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 I) & (v1_partfun1 I k5_numbers)) ) ) )  =>  ( ( (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 H J) = (k1_funct_1 B J)) ) ) )  &  ((k1_funct_1 H D) = (k1_funct_1 B D)) )  =>  ( ((k1_funct_1 (k6_scmpds_4 C H I) D) = (k1_funct_1 H D))  &  ( ((k1_funct_1 (k6_scmpds_4 C H I) (k2_scmpds_2 (k1_funct_1 B D) E)) = (k1_funct_1 H (k2_scmpds_2 (k1_funct_1 B D) E)))  &  ((r1_scmpds_6 C H I) &  ((r2_scmpds_6 C H I) &  (! [J:$i] :  ( ((v1_ami_2 J) & (m1_subset_1 J (u1_struct_0 k1_scmpds_2)))  =>  ((r2_hidden J G) =>  ((k1_funct_1 (k6_scmpds_4 C H I) J) = (k1_funct_1 H J)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) k6_numbers) |  ((r2_hidden (k2_scmpds_2 (k1_funct_1 B D) E) G) |  ((r1_xxreal_0 F k6_numbers) |  ( (D = (k2_scmpds_2 (k1_funct_1 B D) E))  |  ((k6_scmpds_4 (k2_scmpds_7 D E F C) B A) = (k6_scmpds_4 (k2_scmpds_7 D E F C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k3_scmpds_4 C (k11_scmpds_2 D E (k4_xcmplx_0 F))) B A)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_scmyciel,ax, (! [A:$i] : (v5_scmyciel (k5_scmyciel A))) ).
tt(t49_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_semi_af1 A B C D E) & (r2_semi_af1 A B C F G))  => (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r2_funct_2 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) (k52_valued_1 k5_numbers k1_numbers k1_numbers C B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers A C) B)) & (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) (k52_valued_1 k5_numbers k1_numbers k1_numbers C B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers A C) B))) ) ) ) ) ) ) ).
tt(t49_seq_4,ax,(r3_binop_1 k2_numbers k5_complex1 k27_binop_2)).
tt(t49_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k1_seq_1 A C) = (k7_real_1 1 (k1_seq_1 B C)))  &  ( (~ (r1_xxreal_0 (k1_seq_1 B C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 (k7_real_1 1 (k1_seq_1 (k3_series_1 B) C)) (k1_seq_1 (k1_series_3 A) C))) ) ) ) ) ) ) ).
tt(t49_series_5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_seq_1 B C) = (k13_complex1 1 (k5_square_1 (k2_nat_1 C 1)))) ) )  & (r1_xxreal_0 2 (k1_seq_1 (k3_series_1 B) A))) ) ) ) ) ) ).
tt(t49_setfam_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (~  ( (~  (A = (k1_tarski B)) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (C = B) ) ) ) ) ) ) ) ).
tt(t49_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) => (r2_funct_2 k5_numbers (k9_setfam_1 A) (k4_setlim_1 A B) B)) ) ) ) ).
tt(t49_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k5_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B C) A) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A)) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k4_setlim_2 B C D)) A))) ) ) ) ) ) ) ).
tt(t49_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  ((k10_setwiseo A B D C) = (k3_tarski (k8_setwiseo A (k5_finsub_1 B) C D))) ) ) ) ) ) ) ) ).
tt(t49_sf_mastr,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k2_scmfsa_2)))  =>  ( ((k2_scmfsa_m C) = (k4_scmfsa_2 A))  =>  ((r2_hidden (k4_scmfsa_2 B) C) | (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ).
tt(t49_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C C) (k5_sheffer1 A D (k5_sheffer1 A B (k5_sheffer1 A B C))))) = (k5_sheffer1 A B C)) ) ) ) ) ) ) ) ) ).
tt(t49_simplex0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v3_pencil_1 B))  &  ((v1_matroid0 B) & (m1_simplex0 B A)) )  =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  & (m2_simplex0 C A B))  =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((m3_simplex0 E C D) =>  ( (~  ((v1_xboole_0 E) &  ( (~ (r1_xxreal_0 D (k6_simplex0 C)))  &  (~  ((k6_simplex0 C) = (k6_simplex0 B)) ) ) ) )  => (m3_simplex0 E B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_sincos10,ax, ((k2_partfun1 k1_numbers k1_numbers k1_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4))))) ).
tt(t49_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))) = (k3_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k5_binop_2 (k7_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B))) k7_complex1))) ) ) ) ) ).
tt(t49_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k17_sin_cos (k7_xcmplx_0 (k6_xcmplx_0 A B) 2)) = k6_numbers) )  =>  ((k7_xcmplx_0 (k6_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k6_xcmplx_0 (k20_sin_cos B) (k20_sin_cos A))) = (k2_sin_cos4 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2))) ) ) ) ) ) ).
tt(t49_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k3_sin_cos2 (k6_real_1 A 2)) = k6_numbers) )  =>  ((k9_sin_cos2 (k6_real_1 A 2)) = (k10_real_1 (k9_real_1 (k6_sin_cos2 A) 1) (k3_sin_cos2 A))) ) ) ) ).
tt(t49_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k6_numbers k32_sin_cos)) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t49_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k8_sin_cos7 A) = (k1_sin_cos7 (k12_binop_2 1 A))) ) ) ) ).
tt(t49_sin_cos9,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k1_real_1 1) 1)) => (r2_hidden (k1_seq_1 k1_sin_cos9 A) (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4)))) ) ).
tt(t49_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k15_sin_cos A) = (k26_sin_cos A)) ) ) ).
tt(t49_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_topreal4 A B C) => (r1_topreal4 A C B)) ) ) ) ) ) ) ).
tt(t49_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  =>  ((k7_pscomp_1 A) = (k4_xxreal_0 (k7_pscomp_1 B) (k7_pscomp_1 C))) ) ) ) ) ) ) ) ).
tt(t49_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ( (~ (v3_funct_1 E))  &  ((v1_finseq_6 E (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 E) &  ((v2_topreal1 E) &  ((v1_goboard5 E) &  ((v2_goboard5 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 E))) ) )  =>  ((r1_xxreal_0 C B) |  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k3_finseq_1 E) D))  | (r1_xboole_0 (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E B A)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 C)))) ) )  => (r1_sprect_2 C (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)))) ) ) ) ) ) ) ).
tt(t49_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t49_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 A) B) & (r1_xxreal_0 B A))  => (r1_xxreal_0 (k3_square_1 B) (k3_square_1 A))) ) ) ) ) ).
tt(t49_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) &  ((v7_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) ) )  => (r4_stacks_1 A (k8_stacks_1 (u1_struct_0 A)))) ) ).
tt(t49_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 3 A) =>  ((k3_stirl2_1 A 4) = (k11_binop_2 (k18_binop_2 1 24) (k10_binop_2 (k9_binop_2 (k10_binop_2 (k2_newton 4 A) (k11_binop_2 4 (k2_newton 3 A))) (k11_binop_2 6 (k2_newton 2 A))) 4))) ) ) ) ).
tt(t49_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [F:$i] :  ((m1_subset_1 F D) =>  ( (B = C)  =>  ((k3_funct_2 (k3_qc_lang1 A) D (k1_sublemma A D E (k12_sublemma A D B F)) C) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r2_hidden (k12_supinf_2 A B) k1_numbers)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r2_hidden (k12_supinf_2 (k18_supinf_2 A) B) k1_numbers)) ) ) ) ) ).
tt(t49_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))) (k2_pre_topc A (k1_tops_1 A (k5_setfam_1 (u1_struct_0 A) B))))) ) ) ) ).
tt(t49_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  ( (~ (v2_struct_0 (k4_tdlat_1 A)))  &  ((v10_lattices (k4_tdlat_1 A)) &  ((v12_lattices (k4_tdlat_1 A)) & (l3_lattices (k4_tdlat_1 A))) ) ) ) ) ) ).
tt(t49_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t49_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  & (v3_tex_3 B A)) )  & (v1_tdlat_3 A)) ) ) ) ).
tt(t49_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k2_tex_4 A B) = (k2_tex_4 A C))  <=>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t49_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((r1_tmap_1 C A D F) & (v5_pre_topc E A B))  => (r1_tmap_1 C B (k1_partfun1 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ((m1_borsuk_2 E A B C) =>  ((r4_borsuk_2 A B C D E) => (r2_funct_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)) (k6_topalg_1 A B C D) (k6_topalg_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_topgen_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k3_numbers)  =>  ((k1_tops_1 k3_topmetr A) = k1_xboole_0) ) ) ) ).
tt(t49_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_topgen_4 A B C) => (r1_topgen_1 A B C)) ) ) ) ) ) ) ).
tt(t49_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B k3_topmetr))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_hidden F E) <=> (r1_xxreal_0 (k1_funct_1 C F) (k1_funct_1 D F))) ) )  => (v4_pre_topc E A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v3_pre_topc (k5_group_2 A C B) A)) ) ) ) ) ) ).
tt(t49_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (B = (k9_metric_1 (k14_euclid 2) A C))  & (v1_sppol_1 B)) ) ) ) ) ) ) ) ).
tt(t49_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_euclid 2))) =>  ( (D = (k19_euclid A B))  =>  ((k11_metric_1 (k14_euclid 2) D C) = (k5_jgraph_6 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t49_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) )  =>  ((k53_valued_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C D) = (k74_valued_2 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C (k15_toprealc A (u1_struct_0 B) (u1_struct_0 k3_topmetr) D))) ) ) ) ) ) ) ) ) ).
tt(t49_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_tops_1 B A) &  ((v2_tops_1 C A) & (v4_pre_topc C A)) )  => (v2_tops_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t49_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  =>  ( ((k1_relset_1 (u1_struct_0 B) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) = (k2_struct_0 B))  &  ((k2_relset_1 (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t49_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_3 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((v1_tops_1 C A) &  ((v3_tops_1 D A) &  ( ((k4_subset_1 (u1_struct_0 A) C D) = B)  & (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v4_transgeo B A) =>  ((v5_transgeo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_diraf A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t49_trees_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_xboole_0 (k7_finseq_1 A B) (k7_finseq_1 A C)) => (r2_xboole_0 B C)) ) ) ) ) ) ) ).
tt(t49_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v4_trees_3 A) =>  ( ((k2_trees_2 (k11_trees_3 A) 1) = (a_1_0_trees_3 A))  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) B))  =>  ((k4_trees_1 (k11_trees_3 A) (k12_finseq_1 k5_numbers B)) = (k1_funct_1 A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ).
tt(t49_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_trees_9 A)) )  =>  (~  ( (~ (v1_finset_1 A))  &  (! [B:$i] :  ( ((v2_trees_2 B A) & (m1_trees_2 B A))  => (v1_finset_1 B)) ) ) ) ) ) ).
tt(t49_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_pre_topc C A))  => (r2_tsep_1 A B C)) ) ) ) ) ) ) ).
tt(t49_turing_1,ax, (! [A:$i] :  ((m1_subset_1 A (k3_zfmisc_1 (u2_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1))))) =>  (! [B:$i] :  ((m2_funct_2 B k4_numbers (u1_turing_1 k18_turing_1) (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ( (A = (k4_domain_1 (k2_zfmisc_1 k5_numbers k5_numbers) k5_numbers (k9_funct_2 k4_numbers (u1_turing_1 k18_turing_1)) (k1_domain_1 k5_numbers k5_numbers k6_numbers k6_numbers) C B))  & (r2_turing_1 (k2_finseq_4 k5_numbers C D) k18_turing_1 B))  =>  ((v2_turing_1 A (k32_turing_1 k18_turing_1 k16_turing_1)) &  ( ((k2_mcart_1 (u2_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1))) (k11_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1) A)) = C)  & (r2_turing_1 (k2_finseq_4 k5_numbers C 1) (k32_turing_1 k18_turing_1 k16_turing_1) (k3_mcart_1 (u2_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1)) k4_numbers (k9_funct_2 k4_numbers (u1_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1))) (k11_turing_1 (k32_turing_1 k18_turing_1 k16_turing_1) A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k39_twoscomp A B)) = (k1_funct_1 k3_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = (k1_funct_1 C A))  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ).
tt(t49_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_polynom3 k1_complfld))) =>  ( ( ((k3_finseq_1 B) = A)  &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  ((r2_hidden C (k4_finseq_1 B)) =>  ( ( (~ (r1_nat_d C A))  =>  ((k1_funct_1 B C) = (k3_algseq_1 k1_complfld (k1_group_1 k1_complfld))) )  &  ((r1_nat_d C A) =>  ((k1_funct_1 B C) = (k5_uniroots C)) ) ) ) ) ) )  =>  ((k4_uniroots A k1_complfld) = (k3_group_4 (k14_polynom3 k1_complfld) B)) ) ) ) ) ) ).
tt(t49_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) C (k13_polynom3 A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A)) D)) => (r1_polynom5 A C B)) ) ) ) ) ) ) ) ) ).
tt(t49_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v2_relat_1 E) & (r2_relset_1 A (k2_valued_2 (k1_valued_2 B)) (k37_valued_2 A B E C) (k37_valued_2 A B E D)))  =>  ( (E = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_struct_0 D C) <=>  ((k3_vectsp_4 A B C D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ( (B = (k1_vectsp_5 A B C D))  =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (? [H:$i] :  ((m1_subset_1 H (u1_struct_0 B)) &  (? [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) &  ( (E = (k3_rlvect_1 B F G))  &  ( (E = (k3_rlvect_1 B H I))  &  ((r1_struct_0 C F) &  ((r1_struct_0 C H) &  ((r1_struct_0 D G) &  ((r1_struct_0 D I) &  (~  ( (F = H)  &  (G = I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  | (r1_vectsp_5 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t49_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (~  ((k4_algstr_0 A (k5_struct_0 A)) = (k4_struct_0 A)) ) ) ) ).
tt(t49_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_vfunct_1 C D E A) & (r1_vfunct_1 C D E B))  => (r1_vfunct_1 C D E (k2_xboole_0 A B))) ) ) ) ) ) ) ) ) ).
tt(t49_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  ( ((r1_vfunct_2 A B C D) & (r1_vfunct_2 A B C E))  => (r1_vfunct_2 A B C (k2_xboole_0 D E))) ) ) ) ) ) ) ) ) ).
tt(t49_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v15_waybel_0 B A) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (B = (k6_waybel_0 A C)) ) ) ) ) ) ) ) ).
tt(t49_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_orders_3 B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (a_2_0_waybel_1 A B))  => (v8_yellow_0 (k5_yellow_0 A C) A)) ) ) ) ) ) ) ) ).
tt(t49_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (C = (u1_struct_0 B))  & (v4_pre_topc C A)) ) )  => (v4_waybel_0 B A)) ) ) ) ) ).
tt(t49_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel23 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k3_yellow_0 A) B) =>  ((m1_waybel23 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r3_orders_2 A D C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E B) &  ( (~ (r3_orders_2 A E C))  & (r3_orders_2 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_2 A) <=>  ((v19_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) & (v20_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ) ).
tt(t49_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k10_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k10_waybel34 A) B C)) <=>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k4_yellow21 (k10_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k10_waybel34 A) C))) &  ((v17_waybel_0 D (k4_yellow21 (k10_waybel34 A) B) (k4_yellow21 (k10_waybel34 A) C)) &  ((v22_waybel_0 D (k4_yellow21 (k10_waybel34 A) B) (k4_yellow21 (k10_waybel34 A) C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k10_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k10_waybel34 A) C)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_waybel_4 D A) &  ((v3_waybel_4 D A) &  ((v6_waybel_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) D) &  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r3_orders_2 A B E) &  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E C) D) &  (~  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r3_wellord1 A B C) =>  (! [D:$i] :  (~  ((r2_hidden D (k1_relat_1 A)) &  (! [E:$i] :  (~  ((r2_hidden E (k1_relat_1 B)) &  ((k7_relat_1 C (k1_wellord1 A D)) = (k1_wellord1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 A (k4_xboole_0 B C)) = (k4_xboole_0 (k3_xboole_0 A B) C)) ) ) ) ).
tt(t49_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k9_xboolean A (k7_xboolean B C)) = (k3_xboolean (k4_xboolean (k5_xboolean (k5_xboolean A (k3_xboolean B)) C) (k5_xboolean (k5_xboolean A (k3_xboolean C)) B)))) ) ) ) ) ) ) ).
tt(t49_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 A k6_numbers) = k6_numbers) ) ) ).
tt(t49_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 k6_numbers (k6_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t49_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 (k4_xxreal_0 A B) A) =>  ((k4_xxreal_0 A B) = A) ) ) ) ) ) ).
tt(t49_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 D C) | (r1_tarski (k3_xxreal_1 B C) (k4_xxreal_1 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t49_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  ( (~ (v1_xboole_0 A))  & (v4_xxreal_2 A)) )  =>  (~  ( (~  (A = (k1_tarski k2_xxreal_0)) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r2_hidden B A)) ) ) ) ) ) ) ).
tt(t49_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~ (r1_xxreal_0 B (k1_xxreal_3 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_yellow_0 A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) <=> (r1_lattice3 A C D)) ) ) )  =>  ((k2_yellow_0 A B) = (k2_yellow_0 A C)) ) ) ) ) ) ).
tt(t49_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_tarski (k4_yellow_3 A B (k2_waybel_3 (k3_yellow_3 A B) C)) (k2_waybel_3 A (k8_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k2_waybel_3 (k3_yellow_3 A B) C)) (k2_waybel_3 B (k9_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t49_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ((m3_yellow_9 E (k2_borsuk_1 A C) (k2_borsuk_1 B D)) =>  (! [F:$i] :  ((m3_yellow_9 F A B) =>  (! [G:$i] :  ((m3_yellow_9 G C D) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u1_struct_0 C) = (u1_struct_0 D)) )  =>  ( ((u1_struct_0 (k2_borsuk_1 F G)) = (u1_struct_0 E))  &  ((u1_pre_topc (k2_borsuk_1 F G)) = (u1_pre_topc E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_yellow_9 D (k3_yellow_1 1)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 D))))) )  =>  ( ( (E = (k5_funct_3 B (u1_struct_0 A)))  &  (F = (k5_funct_3 C (u1_struct_0 A))) )  =>  ((r1_tarski B C) <=> (r1_yellow_2 (u1_struct_0 A) D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t49_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v3_altcat_2 B A) & (m1_altcat_2 B A)) ) )  => (r3_yellow20 A (k1_yellow18 A) (k2_yellow18 A (k1_yellow18 A)) B (k1_yellow18 B))) ) ) ) ).
tt(t49_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ( ((k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k2_yellow_2 A)) = (k7_waybel_0 A))  & (m1_subset_1 (k2_relset_1 (u1_struct_0 A) (k2_yellow_2 A)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ).
tt(t49_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C (k3_yellow_3 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B))))) )  => (r1_tarski (k6_yellow_3 A B (k4_yellow_3 A B C) (k5_yellow_3 A B C)) (k4_waybel_0 (k3_yellow_3 A B) C))) ) ) ) ) ) ).
tt(t49_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k9_subset_1 (u1_struct_0 A) B C) (k4_yellow_4 A B C))) ) ) ) ) ) ).
tt(t49_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k12_lattice3 A B C)) = (k1_yellow_5 A B C)) ) ) ) ) ) ) ).
tt(t49_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k4_yellow_2 A B) = (k5_yellow_2 (k7_lattice3 A) B))  &  ((k5_yellow_2 A B) = (k4_yellow_2 (k7_lattice3 A) B)) ) ) ) ) ) ).
tt(t49_yellow_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ( ((u1_pre_topc B) = (k5_waybel11 A))  => (v4_waybel11 B)) ) ) ) ) ).
tt(t49_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_zf_lang (k7_zf_lang A (k6_zf_lang B)) (k11_zf_lang A B)) &  ((r3_zf_lang A (k11_zf_lang A B)) &  ((r3_zf_lang (k6_zf_lang B) (k11_zf_lang A B)) & (r3_zf_lang B (k11_zf_lang A B))) ) ) ) ) ) ) ).
tt(t49_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((v10_zf_lang A) =>  (A = (k12_zf_lang (k27_zf_lang A) (k28_zf_lang A))) ) ) ) ).
tt(t49_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r1_xboole_0 (k2_tarski A B) C) & (r2_hidden A C)) ) ) ) ) ).
tt(t49_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ( ((u1_struct_0 C) = B)  => (v7_zmodul01 B A)) ) ) ) ) ) ) ).
tt(t4_abcmiz_0,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  (! [C:$i] :  ((l1_abcmiz_0 C) =>  ( ( ((u1_abcmiz_0 C) = (k2_tarski A B))  &  ( ((k1_funct_1 (u2_abcmiz_0 C) A) = B)  &  ((k1_funct_1 (u2_abcmiz_0 C) B) = A) ) )  =>  ( (~ (v4_abcmiz_0 C))  &  ((v5_abcmiz_0 C) & (v6_abcmiz_0 C)) ) ) ) ) ) ) ) ).
tt(t4_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k7_relset_1 A A (k6_partfun1 A) B) B)) ) ).
tt(t4_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) & (l1_msualg_1 A)) )  =>  ((v1_abcmiz_a A) =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((v2_abcmiz_1 B A) <=> (r2_hidden B k20_abcmiz_1)) ) ) ) ) ) ).
tt(t4_abian,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_abian B (k1_zfmisc_1 (k1_zfmisc_1 A))) <=>  ((k5_setfam_1 A B) = A) ) ) ) ) ).
tt(t4_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k1_real_1 (k18_complex1 A)) A) & (r1_xxreal_0 A (k18_complex1 A))) ) ) ).
tt(t4_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) =>  ((r2_analoaf A B C E D) &  ((r2_analoaf A C B D E) &  ((r2_analoaf A C B E D) &  ((r2_analoaf A D E B C) &  ((r2_analoaf A D E C B) &  ((r2_analoaf A E D B C) & (r2_analoaf A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v8_aff_2 A) => (v9_aff_2 A)) ) ) ).
tt(t4_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) => (v3_aff_3 A)) ) ) ).
tt(t4_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((r2_aff_1 A B C F) | (r2_aff_1 A C B F))  &  ( ((r2_analoaf A B C D E) | (r2_analoaf A D E B C))  &  ( (~  (B = C) )  &  (~  ((r2_aff_1 A D E F) & (r2_aff_1 A E D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_nat_1 A 1) = (k2_xboole_0 (k1_tarski k6_numbers) (k2_finseq_1 A))) ) ) ).
tt(t4_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) => (r2_hidden (k1_funct_1 B C) A)) ) )  =>  ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_finset_1 B)) ) ) ) ) ) ) ) ).
tt(t4_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = (u1_struct_0 A))  & (v1_aff_4 B A))  =>  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) ) ) ) ) ) ).
tt(t4_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B C B D) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t4_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_unialg_1 C) &  ((v3_unialg_1 C) &  ((v4_unialg_1 C) & (l1_unialg_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 A)) =>  ((k4_finseqop (u1_struct_0 B) (u1_struct_0 C) (k4_finseqop (u1_struct_0 A) (u1_struct_0 B) F D) E) = (k4_finseqop (u1_struct_0 A) (u1_struct_0 C) F (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) <=> (r1_tarski (k7_card_1 A) (k7_card_1 B))) ) ) ) ) ).
tt(t4_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_partfun1 A B) & (r1_partfun1 C D))  => (r1_partfun1 (k3_relat_1 C A) (k3_relat_1 D B))) ) ) ) ) ) ) ) ) ).
tt(t4_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  (A = B) ) ) ) ) ).
tt(t4_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ((k6_algstr_0 A (k1_algstr_2 A (k5_struct_0 A)) (k1_algstr_2 A (k5_struct_0 A))) = (k5_struct_0 A)) ) ) ).
tt(t4_algstr_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_algstr_3 A) & (l1_algstr_3 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ( ((k1_algstr_3 A D B E) = (k1_algstr_3 A F B G))  &  ((k1_algstr_3 A D C E) = (k1_algstr_3 A F C G)) )  =>  ( (B = C)  |  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_group_6 C A B) => (v1_algstr_4 (k7_algstr_4 (u1_struct_0 A) (u1_struct_0 B) C) A)) ) ) ) ) ) ) ).
tt(t4_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  ((k1_funct_2 A B) = k1_xboole_0) )  &  ( (~  ((k1_funct_2 B C) = k1_xboole_0) )  &  ((k1_funct_2 A C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t4_altcat_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) => (m2_pboole (k8_pboole E F) A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_altcat_3 A B B (k8_altcat_1 A B)) = (k8_altcat_1 A B)) ) ) ) ) ).
tt(t4_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v12_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_altcat_3 (k8_altcat_1 A B) A B B) & (v4_altcat_3 (k8_altcat_1 A B) A B B)) ) ) ) ) ).
tt(t4_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k4_ami_3 A B) C) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 C)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k4_ami_3 A B) C) A) = (k6_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k4_ami_3 A B) C) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A C)) = 2)  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1))) = 3)  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 k6_numbers)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 2)))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 1)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 2)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 2))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ami_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  => (r2_hidden B (k9_xtuple_0 A))) ) ) ) ).
tt(t4_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  ( (A = 1)  =>  ((k3_compos_0 (u1_compos_1 k1_ami_3) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t4_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = k6_numbers)  => (v2_extpro_1 B A (k4_amistd_1 A))) ) ) ) ) ).
tt(t4_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v2_extpro_1 C A B) => (v1_xboole_0 (k2_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(t4_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) => (r1_tarski (k2_amistd_4 A B C) (k4_amistd_4 A B C))) ) ) ) ) ) ).
tt(t4_amistd_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) &  ((v3_extpro_1 C B) &  ((v2_amistd_5 C B) & (l1_extpro_1 C B)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 C)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 C)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 B C)) & (v1_partfun1 E (u1_struct_0 C))) ) ) )  => (r8_pboole (u1_struct_0 C) (k2_extpro_1 B C (k5_compos_0 (u1_compos_1 C) D A) (k9_memstr_0 B C E A)) (k9_memstr_0 B C (k2_extpro_1 B C D E) A))) ) ) ) ) ) ) ) ) ) ).
tt(t4_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_extpro_1 B A)) ) )  =>  ((v2_ami_wstd B A) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  &  ((v3_funct_2 C k5_numbers k5_numbers) &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k3_funct_2 k5_numbers k5_numbers C (k2_nat_1 D 1)) (k3_amistd_1 A B (k3_funct_2 k5_numbers k5_numbers C D))) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k3_funct_2 k5_numbers k5_numbers C E) (k3_amistd_1 A B (k3_funct_2 k5_numbers k5_numbers C D))) => (r1_xxreal_0 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analmetr A B C D E) => (r2_analmetr A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k1_rlvect_1 A (k5_algstr_0 A B C) (k9_real_1 D E)) = (k1_rlvect_1 A (k5_algstr_0 A C B) (k9_real_1 E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k1_analort A B C (k4_algstr_0 A D)) = (k4_algstr_0 A (k1_analort A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t4_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_anproj_1 A B C) &  ((r1_anproj_1 A D E) &  ((r1_anproj_1 A F G) & (r2_anproj_1 A B D F)) ) )  => (r2_anproj_1 A C E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  (? [J:$i] :  ((m1_subset_1 J k1_numbers) &  (F = (k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B G) (k1_rlvect_1 A C H)) (k1_rlvect_1 A D I)) (k1_rlvect_1 A E J))) ) ) ) ) ) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 F A))  &  ( (~ (v9_struct_0 G A))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r2_anproj_1 A F G I) &  ((r2_anproj_1 A C D H) &  ((r2_anproj_1 A B I H) &  ( (~ (v9_struct_0 H A))  &  (~ (v9_struct_0 I A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C D) & (r1_tarski D (k9_xtuple_0 A)))  =>  ((k1_funct_1 (k2_aofa_000 A B D) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t4_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 E) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((v1_funct_1 (k1_funct_4 (k8_funcop_1 C B F) (k3_relat_1 (k2_funct_1 E) D))) &  ((v1_funct_2 (k1_funct_4 (k8_funcop_1 C B F) (k3_relat_1 (k2_funct_1 E) D)) B C) & (m1_subset_1 (k1_funct_4 (k8_funcop_1 C B F) (k3_relat_1 (k2_funct_1 E) D)) (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_arithm,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k6_xcmplx_0 A k6_numbers) = A) ) ) ).
tt(t4_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ((v2_finsub_1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  ((r1_armstrng C B) =>  ( (C = A)  |  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((r1_tarski D B) &  (C = (k8_setfam_1 A D)) )  => (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k2_arrow A)) =>  ((r1_arrow D B C) | (r1_arrow D C B)) ) ) ) ) ) ) ) ) ).
tt(t4_arytm_0,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) => (r2_hidden (k2_arytm_1 A B) k1_numbers)) ) ) ) ).
tt(t4_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r1_arytm_2 A B) & (r1_arytm_2 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t4_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( (A = k11_arytm_3)  =>  ((k8_arytm_2 A B) = k11_arytm_3) ) ) ) ) ) ).
tt(t4_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  (~  ( (~  ( (A = k1_xboole_0)  &  (B = k1_xboole_0) ) )  &  (! [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  =>  (! [D:$i] :  ( ((v3_ordinal1 D) & (v7_ordinal1 D))  =>  (! [E:$i] :  ( ((v3_ordinal1 E) & (v7_ordinal1 E))  =>  (~  ((r1_arytm_3 D E) &  ( (A = (k9_ordinal3 C D))  &  (B = (k9_ordinal3 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) &  ((v2_comseq_2 B) & (r1_asympt_0 A B)) )  => (r1_xxreal_0 (k2_seq_2 A) (k2_seq_2 B))) ) ) ) ) ).
tt(t4_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r1_tarski (k6_asympt_0 A) (k6_asympt_0 B)) =>  ( ((k6_asympt_0 A) = (k6_asympt_0 B))  |  ((r2_hidden A (k6_asympt_0 B)) &  (~ (r2_hidden A (k7_asympt_0 B))) ) ) )  &  ((r2_hidden A (k6_asympt_0 B)) =>  ((r2_hidden A (k7_asympt_0 B)) |  ((r1_tarski (k6_asympt_0 A) (k6_asympt_0 B)) &  (~  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t4_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) &  (C = (k2_funct_1 B)) )  => (r4_alg_1 A A C)) ) ) ) ) ) ) ).
tt(t4_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_group_6 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r2_hidden B (k1_autgroup A)) <=> (v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A))) ) ) ) ) ).
tt(t4_axioms,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (A = (a_1_0_axioms A)) ) ) ).
tt(t4_bagorder,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  ( ((k2_wsierp_1 A) = k6_numbers)  <=>  (A = (k5_finseq_2 k5_numbers (k3_finseq_1 A) k6_numbers)) ) ) ) ).
tt(t4_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = (k4_struct_0 A))  =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D)) = (k4_struct_0 A))  &  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k1_bcialg_2 A B C (k2_nat_1 D 1)) = (k1_bcialg_1 A (k1_bcialg_2 A B C D) C)) ) ) ) ) ) ) ) ) ).
tt(t4_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A B C)) = (k1_bcialg_1 A C (k1_bcialg_1 A C (k1_bcialg_1 A B (k1_bcialg_1 A B C))))) ) ) ) ) ) ) ) ).
tt(t4_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k3_bcialg_4 A B C)) &  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k3_bcialg_4 A B C)) => (r1_bcialg_1 A E D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v8_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_bcialg_2 B (k4_struct_0 B) C A) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t4_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_bcialg_6 A 1 B) = B) ) ) ) ) ).
tt(t4_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A (k4_struct_0 A) (k1_bcialg_1 A B C)) (k1_bcialg_1 A C B)) = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t4_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k2_bhsp_1 B (k1_rlvect_1 B C A) D) = (k2_bhsp_1 B C (k1_rlvect_1 B D A))) ) ) ) ) ) ) ) ) ).
tt(t4_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_2 B A) & (v1_bhsp_2 C A))  => (v1_bhsp_2 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t4_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_bhsp_3 B A) & (v1_bhsp_3 C A))  => (v1_bhsp_3 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t4_bhsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k1_bhsp_4 A (k5_vfunct_1 k5_numbers A B)) (k5_vfunct_1 k5_numbers A (k1_bhsp_4 A B)))) ) ) ) ).
tt(t4_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k4_struct_0 A))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bhsp_1 A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t4_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v2_hahnban B A) &  ((v3_hahnban B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k4_finseq_1 C) = (k4_finseq_1 D))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k1_funct_1 D E) = (k1_funct_1 B (k1_funct_1 C E))) ) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers B (k1_finsop_1 (u1_struct_0 A) C (u1_algstr_0 A))) = (k1_finsop_1 k1_numbers D k33_binop_2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_bhsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_bhsp_5 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_subset_1 C (k1_zfmisc_1 B)) => (m1_bhsp_5 C A)) ) ) ) ) ) ) ).
tt(t4_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k3_bilinear A B C (k2_bilinear A B C E F) D) (k2_bilinear A B C (k3_bilinear A B C E D) (k3_bilinear A B C F D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_binari_2,ax, (! [A:$i] :  ( ((v3_card_1 A 2) & (m2_finseq_1 A k6_margrel1))  =>  ( (A = (k9_binarith 1 1 k6_margrel1 (k10_binarith k6_margrel1 k8_margrel1) (k10_binarith k6_margrel1 k8_margrel1)))  =>  ((k3_binari_2 2 A) = (k19_binop_2 1)) ) ) ) ).
tt(t4_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden (k5_euclid A) (k3_finseq_2 k6_margrel1))) ) ).
tt(t4_binari_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 A C) &  ((r1_xxreal_0 C B) &  ( (~  (A = C) )  &  (~  ((r1_xxreal_0 (k23_binop_2 A 1) C) & (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k3_xboolean (k4_xboolean A B)) = (k5_xboolean (k3_xboolean A) (k3_xboolean B))) ) ) ) ) ).
tt(t4_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_algstr_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k9_fvsum_1 A C B)) = (k6_algstr_0 A B (k4_rlvect_1 A C))) ) ) ) ) ) ) ).
tt(t4_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((v1_binop_1 B A) =>  ((r3_binop_1 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t4_binop_2,ax, ((k4_binop_1 k4_numbers k44_binop_2) = k6_numbers) ).
tt(t4_bintree1,ax,(v1_bintree1 (k2_trees_1 k6_numbers))).
tt(t4_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ( (A = (k3_finseq_2 (k7_domain_1 k5_numbers k6_numbers 1)))  =>  ((k3_trees_1 A) = k1_xboole_0) ) ) ) ).
tt(t4_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_lattices A (k1_boolealg A B C) D) & (r3_lattices A (k1_boolealg A C B) D))  => (r3_lattices A (k2_boolealg A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t4_boole,ax, (! [A:$i] :  ((k4_xboole_0 k1_xboole_0 A) = k1_xboole_0) ) ).
tt(t4_boolmark,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k7_relat_1 (k1_funct_4 C (k7_funcop_1 A B)) A) = (k1_tarski B)) ) ) ) ) ) ).
tt(t4_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B (k2_prob_1 A D) C)) E) (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k2_bor_cant (k8_prob_1 A B D C))) E))) ) ) ) ) ) ) ) ) ) ).
tt(t4_borsuk_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_connsp_2 D A C) =>  ((r1_tarski B C) => (m2_connsp_2 D A B)) ) ) ) ) ) ) ) ) ).
tt(t4_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) (u1_struct_0 B))))) )  =>  ((r1_funct_2 (u1_struct_0 (k2_borsuk_1 B (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)))) (u1_struct_0 B) (k2_zfmisc_1 (u1_struct_0 B) (k6_domain_1 (u1_struct_0 A) C)) (u1_struct_0 B) D (k9_funct_3 (u1_struct_0 B) (k6_domain_1 (u1_struct_0 A) C))) => (v2_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t4_borsuk_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v2_funct_1 A) &  ((v2_funct_1 B) &  ( ((k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) = (k1_tarski C))  &  ((k3_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) = (k1_tarski (k1_funct_1 A C))) ) ) )  => (v2_funct_1 (k1_funct_4 A B))) ) ) ) ) ) ).
tt(t4_borsuk_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ((r5_zfmisc_1 A B C D E F G) =>  ((k5_card_1 (k5_enumset1 A B C D E F G)) = 7) ) ) ) ) ) ) ) ) ).
tt(t4_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  ((r1_xxreal_0 (k10_real_1 1 2) A) => (m1_subset_1 (k9_real_1 (k8_real_1 2 A) 1) (u1_struct_0 k5_topmetr))) ) ) ).
tt(t4_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (? [C:$i] :  ((v1_int_1 C) &  ( ((k4_int_1 (k6_xcmplx_0 A B)) = (k7_real_1 (k9_real_1 (k4_int_1 A) (k4_int_1 B)) C))  &  ( (C = k6_numbers)  |  (C = 1) ) ) ) ) ) ) ) ) ).
tt(t4_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_convex1 D (k15_euclid A)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (~  ((v4_pre_topc D (k15_euclid A)) &  ((r2_hidden B (k1_tops_1 (k15_euclid A) D)) &  ( (~  (B = C) )  &  ((v9_rltopsp1 (k9_subset_1 (u1_struct_0 (k15_euclid A)) D (k4_topreal9 A B C)) (k15_euclid A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) (k2_tops_1 (k15_euclid A) D) (k4_topreal9 A B C)) = (k6_domain_1 (u1_struct_0 (k15_euclid A)) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_brouwer,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (C = D) )  &  ((m1_subset_1 C (u1_struct_0 (k2_brouwer A E B))) &  ( (~ (m1_subset_1 C (u1_struct_0 (k7_toprealb A E B))))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_toprealb A E B))) =>  (~  ((k1_tarski F) = (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A C D) (k3_topreal9 A E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_bspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_bspace)) =>  ( (A = k1_xboole_0)  |  (A = 1) ) ) ) ).
tt(t4_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D B) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D C) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A D (k5_bvfunc_1 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t4_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r1_tarski (k15_bvfunc_1 A B C) (k15_bvfunc_1 A B (k6_partit1 A))) & (r1_tarski (k15_bvfunc_1 A B (k10_eqrel_1 A)) (k15_bvfunc_1 A B C))) ) ) ) ) ) ) ).
tt(t4_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ( (B = (k1_enumset1 C D E))  =>  ( (C = D)  |  ( (E = C)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k2_bvfunc_1 A B (k2_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t4_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B C) (k10_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t4_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k11_bvfunc_1 A) B) (k12_bvfunc_1 A))) ) ) ) ).
tt(t4_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r2_hidden C B) => (r1_setfam_1 C (k3_bvfunc_2 A B))) ) ) ) ) ) ) ).
tt(t4_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k2_bvfunc_1 A (k6_bvfunc_2 A C B E) (k6_bvfunc_2 A D B E))) (k5_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A C) B E) (k7_bvfunc_2 A (k1_bvfunc_1 A D) B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t4_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k5_bvfunc_1 A B C)) B)) ) ) ) ) ) ).
tt(t4_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 C (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t4_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k9_bvfunc_1 A B (k9_bvfunc_1 A C D))) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t4_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k2_bvfunc_1 A C D)) (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t4_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k6_margrel1) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D) E) (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B E) (k9_bvfunc_1 A C E)) (k9_bvfunc_1 A D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t4_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k5_bvfunc_1 A B C) (k1_bvfunc_1 A B)) C)) ) ) ) ) ) ).
tt(t4_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) & (l1_funcsdom A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_rlvect_1 A (k4_struct_0 A) B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t4_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ( (E = B)  &  (F = C) )  =>  ( (C = (k1_rlvect_1 (k3_c0sp2 A) B H))  <=>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers F I) = (k8_real_1 H (k3_funct_2 (u1_struct_0 A) k1_numbers E I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 1))  & (r1_xxreal_0 (k3_finseq_1 (k1_calcul_1 (k3_cqc_lang A) B)) k6_numbers)) ) ) ) ) ) ).
tt(t4_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) <=> (r1_tarski (k2_calcul_2 C A) (k2_calcul_2 C B))) ) ) ) ) ) ) ).
tt(t4_cantor_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (r1_tarski B (k2_cantor_1 A B))) ) ) ).
tt(t4_card_1,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((r2_hidden A B) <=>  (~ (r1_ordinal1 B A)) ) ) ) ) ) ).
tt(t4_card_2,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 (k2_zfmisc_1 A B) (k2_zfmisc_1 B A)) &  ((k1_card_1 (k2_zfmisc_1 A B)) = (k1_card_1 (k2_zfmisc_1 B A))) ) ) ) ).
tt(t4_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((k2_card_3 (k16_funcop_1 A B)) = (k16_funcop_1 A (k2_zfmisc_1 B (k1_tarski A)))) ) ) ).
tt(t4_card_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k3_xcmplx_0 (k2_newton 2 A) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k3_xcmplx_0 (k2_newton 2 C) (k2_nat_1 (k4_nat_1 2 D) 1)))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_card_5,ax, (! [A:$i] :  ((v1_card_1 A) =>  (~  ( (~ (v1_finset_1 A))  &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  (A = (k3_card_1 B)) ) ) ) ) ) ) ) ).
tt(t4_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_card_fil (k1_tarski A) A)) ) ).
tt(t4_cardfin2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 (k18_binop_2 1 2) (k17_complex1 (k10_binop_2 A B))))  =>  (A = (k1_cardfin2 B)) ) ) ) ) ) ).
tt(t4_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ( (A = k1_xboole_0)  =>  (B = k1_xboole_0) )  =>  ((k5_card_1 (k1_funct_2 B A)) = (k13_newton (k5_card_1 A) (k5_card_1 B))) ) ) ) ) ) ).
tt(t4_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  ( (~  ( (~ (v1_card_lar B A))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C A) & (r1_tarski B C)) ) ) ) ) )  &  (~  ( (? [C:$i] :  ((v3_ordinal1 C) &  ((r2_hidden C A) & (r1_tarski B C)) ) )  & (v1_card_lar B A)) ) ) ) ) ) ) ).
tt(t4_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) => (m1_cat_1 B A (k3_graph_1 A B) (k4_graph_1 A B))) ) ) ) ).
tt(t4_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) => (r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A (k8_funcop_1 (u4_struct_0 B) A C)) (k8_funcop_1 (u1_struct_0 B) A (k3_graph_1 B C)))) ) ) ) ) ).
tt(t4_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k5_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k5_cat_4 A B))) =>  (C = D) ) ) ) ) ) ) ).
tt(t4_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m3_cat_2 C B) => (m3_cat_2 C A)) ) ) ) ) ) ).
tt(t4_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k2_nat_1 (k7_nat_d A 2) 1) = (k7_nat_d A 1)) ) ) ) ).
tt(t4_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_catalan2 (k8_funcop_1 k5_numbers A k6_numbers))) ) ).
tt(t4_catalg_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_catalg_1 C A) =>  ((m1_catalg_1 C B) =>  (A = B) ) ) ) ) ) ).
tt(t4_cayley,ax, ((k1_cayley k1_xboole_0) = 1) ).
tt(t4_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  => (m1_cc0sp1 (k3_cc0sp1 A) (k8_cfuncdom A))) ) ).
tt(t4_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k2_numbers) &  ((v1_cc0sp2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) &  ((v1_cc0sp2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) )  =>  ((v1_funct_1 (k11_pre_poly (u1_struct_0 A) B C)) &  ((v1_funct_2 (k11_pre_poly (u1_struct_0 A) B C) (u1_struct_0 A) k2_numbers) &  ((v1_cc0sp2 (k11_pre_poly (u1_struct_0 A) B C) A) & (m1_subset_1 (k11_pre_poly (u1_struct_0 A) B C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) ) ) ) ) ) ) ) ).
tt(t4_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r2_relset_1 k5_numbers k2_numbers (k9_comseq_3 B (k31_valued_1 k5_numbers k2_numbers A)) (k31_valued_1 k5_numbers k2_numbers (k9_comseq_3 B A))) & (r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B (k55_valued_1 k5_numbers k2_numbers A)) (k55_valued_1 k5_numbers k2_numbers (k9_comseq_3 B A)))) ) ) ) ) ).
tt(t4_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v3_funct_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = (k3_funct_2 k5_numbers k2_numbers A C)) ) ) ) ) ) ) ) ).
tt(t4_cfdiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ( ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = (k4_struct_0 A)) )  =>  ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = k6_numbers) ) )  &  ( ((v2_comseq_2 (k4_normsp_0 A B)) &  ((k2_seq_2 (k4_normsp_0 A B)) = k6_numbers) )  =>  ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t4_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((r2_funct_2 A k2_numbers B (k2_funcsdom A k2_numbers k2_numbers (k9_funct_2 A k2_numbers) (k3_cfuncdom A) (k1_domain_1 k2_numbers (k9_funct_2 A k2_numbers) D C))) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers B E) = (k9_complex1 D (k3_funct_2 A k2_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ( ((k1_relset_1 A (k25_valued_1 A k2_numbers B C)) = (k1_relset_1 A B))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k25_valued_1 A k2_numbers B C))) =>  ((k7_partfun1 k2_numbers (k25_valued_1 A k2_numbers B C) D) = (k9_complex1 C (k7_partfun1 k2_numbers B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  ((v1_cgames_1 A) & (l1_cgames_1 A)) ) ) ).
tt(t4_chain_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((v1_zfmisc_1 A) &  ( (~ (v1_zfmisc_1 (k2_xboole_0 A (k1_tarski B))))  &  (! [C:$i] :  (~  (A = (k1_tarski C)) ) ) ) ) ) ) ) ).
tt(t4_chord,ax, (! [A:$i] :  ( ((v1_int_1 A) &  (~ (v1_abian A)) )  =>  (! [B:$i] :  ( ((v1_int_1 B) &  (~ (v1_abian B)) )  =>  ( (~ (r1_xxreal_0 A B))  => (r1_xxreal_0 (k2_xcmplx_0 B 2) A)) ) ) ) ) ).
tt(t4_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_circuit2 (k5_facirc_1 A B C D) A B) & (r1_xxreal_0 D E))  =>  ((k5_facirc_1 A B C E) = (k5_facirc_1 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v1_circuit2 (k5_facirc_1 A B C D) A B) => (r8_pboole (u1_struct_0 A) (k1_circcmb3 A B C) (k5_facirc_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t4_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((k2_circcomb A A) = (g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A))) ) ) ).
tt(t4_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((v3_rltopsp1 B A) &  ((v3_rltopsp1 C A) & (v3_rltopsp1 D A)) )  => (v3_rltopsp1 (k7_rusub_4 A (k7_rusub_4 A (k1_convex1 A B E) (k1_convex1 A C F)) (k1_convex1 A D G)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) => (m1_dtconstr D (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) )  &  (! [D:$i] :  ((r2_hidden D (u4_struct_0 (k1_circtrm1 A B C))) => (m2_msaterm D A B)) ) ) ) ) ) ) ) ) ).
tt(t4_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_hidden (k1_funct_1 C D) (k1_funct_1 (u3_msualg_1 A B) D))) ) ) ) ) ) ) ) ).
tt(t4_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) &  ((v1_finseq_1 G) & (v6_trees_3 G)) ) )  =>  ( ((r2_hidden D (k3_msafree2 A)) &  ( (E = (k4_trees_4 (k4_tarski (k4_msafree2 A D) (u1_struct_0 A)) F))  &  ( ((k4_finseq_1 F) = (k4_finseq_1 G))  &  (! [H:$i] :  ((m1_subset_1 H k5_numbers) =>  ((r2_hidden H (k4_finseq_1 F)) =>  ((k1_funct_1 G H) = (k1_funct_1 (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B C) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A D)) H)) (k1_funct_1 F H))) ) ) ) ) ) )  =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B C) D) E) = (k4_trees_4 (k4_tarski (k4_msafree2 A D) (u1_struct_0 A)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A (k1_classes1 B)) => (r2_hidden (k9_setfam_1 A) (k1_classes1 B))) ) ) ).
tt(t4_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v2_classes1 A) & (r2_hidden B A))  => (r1_tarski (k1_classes1 B) A)) ) ) ).
tt(t4_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) D E)) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t4_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_clopban1 B A A) &  ((v2_clopban1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_clopban1 C A A) &  ((v2_clopban1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 D A A) &  ((v1_clopban1 D A A) &  ((v2_clopban1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D (k1_clopban2 A C B)) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D E) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 C A) => (v9_clvect_1 (k2_clopban3 A C B) A)) ) ) ) ) ) ) ).
tt(t4_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_funcop_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D (k2_funct_6 C)) =>  ((k16_pralg_1 A B (k16_pralg_1 A C D)) = (k15_pralg_1 (k8_pboole C B) D)) ) ) ) ) ) ) ) ) ).
tt(t4_closure2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A B))) => (m1_subset_1 (k9_subset_1 (k1_closure2 A B) C D) (k1_zfmisc_1 (k1_closure2 A B)))) ) ) ) ) ) ) ).
tt(t4_closure3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_setfam_1 B A) & (r2_setfam_1 C B))  => (r2_setfam_1 C A)) ) ) ) ).
tt(t4_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (B = (k4_algstr_0 A B))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t4_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v1_clvect_2 B A) & (v1_clvect_2 C A))  => (v1_clvect_2 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t4_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((k1_bhsp_4 A (k5_vfunct_1 k5_numbers A B)) = (k5_vfunct_1 k5_numbers A (k1_bhsp_4 A B))) ) ) ) ) ).
tt(t4_cohsp_1,ax, ((k1_coh_sp (k1_tarski k1_xboole_0)) = k1_xboole_0) ).
tt(t4_coh_sp,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((r2_hidden A (k3_tarski B)) => (r2_hidden (k1_tarski A) B)) ) ) ) ).
tt(t4_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_collsp A B C D) =>  ((r1_collsp A C B D) & (r1_collsp A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_combgras,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v2_funct_1 B) & (r1_tarski A (k9_xtuple_0 B)))  =>  ((k1_card_1 (k7_relat_1 B A)) = (k1_card_1 A)) ) ) ) ) ).
tt(t4_commacat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cat_1 B A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cat_1 B A))) =>  ((k2_cat_1 (k3_cat_1 B A) C D) = (k1_tarski A)) ) ) ) ) ) ) ).
tt(t4_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) => (r1_tarski (k2_struct_0 A) (k2_struct_0 (k1_compact1 A)))) ) ).
tt(t4_complex1,ax, ( ((k3_complex1 k6_numbers) = k6_numbers)  &  ((k4_complex1 k6_numbers) = k6_numbers) ) ).
tt(t4_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_seq_1 k16_sin_cos (k5_real_1 A k32_sin_cos)) = (k1_real_1 (k1_seq_1 k16_sin_cos A)))  &  ((k1_seq_1 k19_sin_cos (k5_real_1 A k32_sin_cos)) = (k1_real_1 (k1_seq_1 k19_sin_cos A))) ) ) ) ).
tt(t4_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ( (A = C)  &  (B = D) )  =>  ((k8_group_1 k1_complfld A B) = (k5_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_complsp1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (C = B)  =>  ((v1_seq_4 C A) <=> (v3_pre_topc B (k1_complsp1 A))) ) ) ) ) ) ) ) ).
tt(t4_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k4_finseq_1 A) = (k4_finseq_1 (k30_valued_1 A))) ) ) ).
tt(t4_compl_sp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 (u1_struct_0 A))) &  ((v1_compl_sp B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 (u1_struct_0 A)))))) ) )  =>  ( ((v2_prob_1 B) &  ((k2_seq_2 (k1_compl_sp A B)) = k6_numbers) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k8_nat_1 (u1_struct_0 A) C D) (k8_nat_1 (k9_setfam_1 (u1_struct_0 A)) B D))) )  => (v3_tbsp_1 C A)) ) ) ) ) ) ) ) ).
tt(t4_compos_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_compos_0 B) &  ((v2_compos_0 B) & (v3_compos_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((v4_compos_0 C B) =>  ((k5_compos_0 B C A) = C) ) ) ) ) ) ) ) ).
tt(t4_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  ((k5_card_1 (k4_compos_1 A)) = 1) ) ) ).
tt(t4_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k8_compos_1 A (k1_compos_2 A B C) D) = (k1_compos_2 A B (k8_compos_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t4_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ( (B = k6_numbers)  |  ((k1_newton (k1_power B A) B) = A) ) ) ) ) ) ) ).
tt(t4_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ((v3_finset_1 B) &  ((v2_tops_2 B A) &  ((k6_setfam_1 (u1_struct_0 A) B) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t4_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((k2_funct_7 C A B) = (k2_funct_7 D A B))  =>  ((k2_finseq_3 A C) = (k2_finseq_3 A D)) ) ) ) ) ) ) ) ) ).
tt(t4_comseq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((k8_nat_1 k2_numbers A B) = k5_complex1) ) ) ) ) ) ) ).
tt(t4_comseq_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k2_comseq_2 k5_numbers (k25_valued_1 k5_numbers k2_numbers B A)) (k25_valued_1 k5_numbers k2_numbers (k2_comseq_2 k5_numbers B) (k15_complex1 A)))) ) ) ) ).
tt(t4_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 C E) & (r1_xxreal_0 B (k18_complex1 (k9_real_1 (k8_nat_1 k1_numbers A D) (k8_nat_1 k1_numbers A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v6_conaffm A) => (v7_conaffm A)) ) ) ).
tt(t4_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u4_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) C) (k3_funct_2 (k1_zfmisc_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) B))) ) ) ) ) ) ) ).
tt(t4_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k11_conlat_1 A)))) =>  ( ( (~ (v5_conlat_1 (k16_lattice3 (k11_conlat_1 A) B) A))  &  ((v7_conlat_1 (k16_lattice3 (k11_conlat_1 A) B) A) & (l2_conlat_1 (k16_lattice3 (k11_conlat_1 A) B) A)) )  &  ( (~ (v5_conlat_1 (k15_lattice3 (k11_conlat_1 A) B) A))  &  ((v7_conlat_1 (k15_lattice3 (k11_conlat_1 A) B) A) & (l2_conlat_1 (k15_lattice3 (k11_conlat_1 A) B) A)) ) ) ) ) ) ) ).
tt(t4_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v6_conmetr1 A) => (v2_conmetr1 A)) ) ) ).
tt(t4_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_analmetr E A) &  ((r2_hidden B E) &  ((r2_hidden C E) & (r2_hidden D E)) ) )  => (r5_analmetr A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  & (r1_connsp_1 A B C))  =>  ((v3_pre_topc B A) &  ((v4_pre_topc B A) &  ((v3_pre_topc C A) & (v4_pre_topc C A)) ) ) ) ) ) ) ) ) ) ).
tt(t4_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((m1_connsp_2 B A C) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t4_connsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_connsp_1 B A) &  ((k1_connsp_3 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t4_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_tarski (k6_rusub_4 A (k1_convex1 A B C) (k1_convex1 A B (k9_real_1 1 C))) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (B = (a_3_2_convex2 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t4_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_convex1 B A) <=> (r1_tarski (a_2_0_convex3 A B) B)) ) ) ) ) ).
tt(t4_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (m2_convex4 (k2_convex4 A) A B)) ) ) ) ).
tt(t4_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k12_supinf_2 B C) = k2_supinf_1) ) ) )  =>  ((v1_convfun1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 1 E))  &  (~ (r1_xxreal_0 (k12_supinf_2 B (k1_algstr_0 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D (k10_binop_2 1 E)))) (k3_supinf_2 (k1_extreal1 (k1_measure6 E) (k12_supinf_2 B C)) (k1_extreal1 (k1_measure6 (k10_binop_2 1 E)) (k12_supinf_2 B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) <=>  ( ((k6_qc_lang3 A B) = k1_xboole_0)  &  ((k5_qc_lang3 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t4_cqc_sim1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( (~ (r2_hidden B (k7_relat_1 C (k6_subset_1 D (k1_tarski A)))))  =>  ((k7_relat_1 (k1_funct_4 C (k16_funcop_1 A B)) (k6_subset_1 D (k1_tarski A))) = (k6_subset_1 (k7_relat_1 (k1_funct_4 C (k16_funcop_1 A B)) D) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t4_cqc_the1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((v1_finset_1 A) &  ((v1_finset_1 B) &  ((r1_tarski A (k2_zfmisc_1 C B)) &  (! [D:$i] :  (~  ((v1_finset_1 D) &  ((r1_tarski D C) & (r1_tarski A (k2_zfmisc_1 D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) D) A) => (v2_cqc_the1 (k8_cqc_lang A C (k8_cqc_lang A B D)) A)) ) ) ) ) ) ) ) ) ).
tt(t4_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A C B) & (r1_tarski C D))  => (r3_cqc_the1 A D B)) ) ) ) ) ) ) ) ) ).
tt(t4_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k8_real_1 2 (k17_complex1 (k3_xcmplx_0 A B))) (k7_real_1 (k5_square_1 (k17_complex1 A)) (k5_square_1 (k17_complex1 B))))) ) ) ) ).
tt(t4_csspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_3 A) &  ((k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)) = k6_numbers) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers A B) = k5_complex1) ) ) ) ) ) ).
tt(t4_csspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k3_csspace4)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k3_csspace4))))) )  =>  ((v1_csspace3 A k3_csspace4) => (v9_clvect_1 A k3_csspace4)) ) ) ).
tt(t4_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  ((k3_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) (k3_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) A B) C) = (k3_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) A (k3_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) B C))) ) ) ) ) ) ) ).
tt(t4_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_decomp_1 B A) <=>  (B = (k2_decomp_1 A B)) ) ) ) ) ) ).
tt(t4_descip_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 A)) =>  ((k3_finseq_1 (k6_descip_1 A)) = (k3_finseq_1 A)) ) ) ) ).
tt(t4_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_dickson B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( (~ (r1_xxreal_0 D C))  => (r1_orders_2 A (k8_nat_1 (u1_struct_0 A) B C) (k8_nat_1 (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t4_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers C B) (k3_funct_2 k1_numbers k1_numbers C (k9_real_1 B A)))) ) ) ) ) ) ) ).
tt(t4_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k10_diff_1 C (k9_real_1 B (k8_real_1 2 A)) (k9_real_1 B A) B) = (k6_real_1 (k1_funct_1 (k1_seqfunc k1_numbers k1_numbers (k7_diff_1 C A) 2) B) (k8_real_1 2 (k5_square_1 A)))) ) ) ) ) ) ) ) ).
tt(t4_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers E B) F) C) (k2_nat_1 A 1)) D) = (k7_real_1 (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 E C) (k2_nat_1 A 1)) D)) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 F C) (k2_nat_1 A 1)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k9_real_1 (k1_seq_1 k3_taylor_1 A) (k1_seq_1 k3_taylor_1 B)) = (k1_seq_1 k3_taylor_1 (k13_complex1 A B))) ) ) ) ) ) ) ) ) ).
tt(t4_dilworth,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_eqrel_1 C B) =>  ((r2_xboole_0 B A) => (m1_eqrel_1 (k2_xboole_0 C (k6_domain_1 (k1_zfmisc_1 A) (k6_subset_1 A B))) A)) ) ) ) ) ).
tt(t4_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_analoaf A B B C D) & (r2_analoaf A C D B B)) ) ) ) ) ) ) ) ) ).
tt(t4_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ( (~ (v2_struct_0 (k5_analort A B C)))  &  ((v1_dirort (k5_analort A B C)) & (l1_analoaf (k5_analort A B C))) ) ) ) ) ) ) ) ) ).
tt(t4_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((k2_dist_1 A B C) = (k11_binop_2 (k3_finseq_1 B) (k3_dist_1 A B C))) ) ) ) ) ) ).
tt(t4_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( (! [E:$i] :  ((r2_hidden E A) <=>  (? [F:$i] :  ((m1_subset_1 F B) &  (? [G:$i] :  ((m1_subset_1 G C) &  (? [H:$i] :  ((m1_subset_1 H D) &  (E = (k3_xtuple_0 F G H)) ) ) ) ) ) ) ) )  =>  (A = (k3_zfmisc_1 B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_dtconstr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((k14_trees_3 (k9_finseq_1 A)) = (k9_finseq_1 (k1_funct_1 A k1_xboole_0))) ) ) ).
tt(t4_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((r1_tarski B (k1_setfam_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C A) => (r1_tarski B C)) ) ) ) ) ) ).
tt(t4_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v36_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v36_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((m1_ec_pf_1 A B) & (m1_ec_pf_1 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t4_ec_pf_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k8_group_1 A D C) = (k8_group_1 A B E))  =>  ( (B = (k4_struct_0 A))  |  ( (C = (k4_struct_0 A))  |  ((k8_group_1 A D (k11_algstr_0 A B)) = (k8_group_1 A E (k11_algstr_0 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_endalg A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_endalg A))) =>  (! [D:$i] :  ((m2_funct_2 D (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) =>  (! [E:$i] :  ((m2_funct_2 E (u1_struct_0 A) (u1_struct_0 A) (k1_endalg A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 (k3_endalg A) B C) = (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k2_ens_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k1_ens_1 A)) &  (? [D:$i] :  ((m1_subset_1 D A) &  (? [E:$i] :  ((m1_subset_1 E A) &  ( (B = (k1_domain_1 (k2_zfmisc_1 A A) (k1_ens_1 A) (k1_domain_1 A A D E) C))  &  ( ( (E = k1_xboole_0)  =>  (D = k1_xboole_0) )  &  ((v1_funct_1 C) &  ((v1_funct_2 C D E) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B 1))  & (r1_xxreal_0 (k6_power A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t4_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_xboole_0 (k1_tarski A) (k1_enumset1 B C D))) ) ) ) ) ).
tt(t4_eqrel_1,ax, (! [A:$i] :  ((v3_relat_2 (k1_eqrel_1 A)) &  ((v8_relat_2 (k1_eqrel_1 A)) &  ((v1_partfun1 (k1_eqrel_1 A) A) & (m1_subset_1 (k1_eqrel_1 A) (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ).
tt(t4_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) & (v1_funcop_1 D)) ) ) )  =>  ( ((r6_pboole A (k2_funct_6 D) B) & (r2_pboole A (k3_funct_6 D) C))  => (m2_pboole D A B C)) ) ) ) ) ) ) ) ) ).
tt(t4_e_siec,ax, ((v2_e_siec (g1_e_siec k1_xboole_0 k1_xboole_0 k1_xboole_0)) &  ((v3_e_siec (g1_e_siec k1_xboole_0 k1_xboole_0 k1_xboole_0)) & (l1_e_siec (g1_e_siec k1_xboole_0 k1_xboole_0 k1_xboole_0))) ) ).
tt(t4_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k5_square_1 (k12_euclid A)) = (k23_rvsum_1 A A)) ) ) ).
tt(t4_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k2_euclid_3 A) = (k2_euclid_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t4_euclid_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid C)) =>  ((k9_euclid C D (k8_real_1 A B)) = (k9_euclid C (k9_euclid C D B) A)) ) ) ) ) ) ) ) ) ).
tt(t4_euclid_5,ax, ((k4_struct_0 (k15_euclid 3)) = (k4_euclid_5 k6_numbers k6_numbers k6_numbers)) ).
tt(t4_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((k7_real_1 (k4_euclid_3 A B C) (k4_euclid_3 C B D)) = (k4_euclid_3 A B D))  |  ((k7_real_1 (k4_euclid_3 A B C) (k4_euclid_3 C B D)) = (k7_real_1 (k4_euclid_3 A B D) (k8_real_1 2 k32_sin_cos))) ) ) ) ) ) ) ) ) ) ).
tt(t4_euclid_7,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid k6_numbers)) =>  (A = (k6_finseq_1 k1_numbers)) ) ) ).
tt(t4_euclid_8,ax, ((k12_euclid k2_euclid_8) = 1) ).
tt(t4_euclid_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) ) )  =>  ( (~  (A = k6_numbers) )  => (r2_hidden (k1_euclid_9 A B C) (k4_finseq_1 B))) ) ) ) ) ) ) ).
tt(t4_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k10_euclid A (k5_euclid A)) = (k5_finseq_2 k1_numbers A k6_numbers)) ) ) ).
tt(t4_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k8_euclid A B (k8_euclid A C D)) = (k7_euclid A (k8_euclid A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t4_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r5_analmetr A B C D) =>  ((r5_analmetr A B D C) &  ((r5_analmetr A C B D) &  ((r5_analmetr A C D B) &  ((r5_analmetr A D B C) & (r5_analmetr A D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_euler_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((r2_hidden B A) =>  ((k5_card_1 (k6_subset_1 A (k1_tarski B))) = (k6_xcmplx_0 (k5_card_1 A) (k5_card_1 (k1_tarski B)))) ) ) ) ) ).
tt(t4_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_int_2 A B) &  (B = (k4_nat_d (k3_xcmplx_0 C D) A)) )  =>  ((r1_xxreal_0 A 1) | (r1_int_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_exchsort,ax, (! [A:$i] :  ((k6_subset_1 (k1_ordinal1 A) A) = (k1_tarski A)) ) ).
tt(t4_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) ) )  =>  (! [E:$i] :  ((m2_pboole E A B C) =>  (! [F:$i] :  ((m2_pboole F A C D) =>  (! [G:$i] :  ((m3_pboole G A B) => (r6_pboole A (k1_msafree A B D G (k3_msualg_3 A B C D E F)) (k3_msualg_3 A G C D (k1_msafree A B C G E) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_extpro_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  (~ (v1_setfam_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_extpro_1 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 B C)) & (v1_partfun1 D (u1_struct_0 C))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 C)) & (v1_funct_1 E)) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k5_extpro_1 B C E D (k2_nat_1 A F)) = (k5_extpro_1 B C E (k5_extpro_1 B C E D A) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k3_extreal1 A) = (k2_supinf_2 A)) ) ) ) ).
tt(t4_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (~  ( (~  (A = k6_numbers) )  & (r1_xxreal_0 (k3_extreal1 A) k6_numbers)) ) ) ) ).
tt(t4_facirc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ( ((r1_circcomb A B) & (r1_xboole_0 (k3_msafree2 B) (k2_msafree2 A)))  =>  ((r1_tarski (k2_msafree2 A) (k2_msafree2 (k2_circcomb A B))) &  ((k2_msafree2 (k2_circcomb A B)) = (k2_xboole_0 (k2_msafree2 A) (k7_subset_1 (u1_struct_0 B) (k2_msafree2 B) (k3_msafree2 A)))) ) ) ) ) ) ) ).
tt(t4_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r2_hidden A (u1_struct_0 B)) =>  ((k2_circcomb (k1_facirc_2 A) B) = (g1_msualg_1 (u1_struct_0 B) (u4_struct_0 B) (u1_msualg_1 B) (u2_msualg_1 B))) ) ) ) ) ).
tt(t4_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fcont_1 A B) <=>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 A B)) =>  (? [D:$i] :  ((m1_rcomp_1 D B) &  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((r2_hidden E (k1_relset_1 k1_numbers A)) & (r2_hidden E D))  => (r2_hidden (k1_seq_1 A E) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) &  ((r1_tarski B (k1_relset_1 k1_numbers D)) &  ((v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers C A)) & (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers D B))) ) )  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) (k3_xboole_0 A B)))) ) ) ) ) ) ) ).
tt(t4_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden (k9_real_1 A B) (k2_rcomp_1 (k4_xcmplx_0 C) C)) =>  ( (~ (r1_xxreal_0 C k6_numbers))  & (r2_hidden A (k2_rcomp_1 (k9_real_1 B C) (k7_real_1 B C)))) ) ) ) ) ) ) ) ).
tt(t4_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) A) B) = (k8_real_1 (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos B))))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t4_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k2_sin_cos9) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t4_fdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v2_fdiff_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_fdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ((v1_funct_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((v2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (m1_subset_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ( ((v1_funct_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((v2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (m1_subset_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  &  ((v1_funct_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) &  ((v2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (m1_subset_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ) ).
tt(t4_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v2_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v1_fdiff_1 B k6_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v3_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((k2_relset_1 k1_numbers C) = (k1_tarski A))  =>  ((v2_comseq_2 C) &  ( ((k2_seq_2 C) = A)  &  ((v2_comseq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers B C)) &  ((k2_seq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers B C)) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ( (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v3_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers D) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k1_relset_1 k1_numbers A)) &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 C E) k6_numbers)) ) ) ) )  => (v2_comseq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C D) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers D A))))) ) ) ) )  & (r1_tarski (k1_tarski B) (k1_relset_1 k1_numbers A)))  =>  (! [C:$i] :  ( ((v2_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) &  ((v1_fdiff_1 C k6_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [D:$i] :  ( ((v2_relat_1 D) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) &  ((v1_fdiff_1 D k6_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v3_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ( ((k2_relset_1 k1_numbers E) = (k1_tarski B))  &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C E)) (k1_relset_1 k1_numbers A)) &  ((r1_tarski (k2_relset_1 k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E)) (k1_relset_1 k1_numbers A)) &  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) )  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 D F) k6_numbers)) ) ) ) ) ) )  =>  ((k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers C E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A)))) = (k2_seq_2 (k20_valued_1 k5_numbers k1_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers D) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k8_funct_2 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers D E) A) (k8_funct_2 k5_numbers k1_numbers k1_numbers E A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k26_valued_1 k1_numbers k1_numbers C A)))) &  ( (C = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 D E) = (k7_real_1 A E))  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k26_valued_1 k1_numbers k1_numbers C A)) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) (k26_valued_1 k1_numbers k1_numbers C A)) B) E) = (k10_real_1 E (k7_real_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers A))  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) A) B) = (k1_real_1 (k10_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t4_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)))) &  ( (D = (k1_taylor_1 2))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 C E) = (k5_square_1 A))  &  (~  ((k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers C D) E) = k6_numbers) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) (k47_valued_1 k1_numbers k1_numbers k1_numbers C D)) B) E) = (k10_real_1 (k8_real_1 (k8_real_1 4 (k5_square_1 A)) E) (k5_square_1 (k9_real_1 (k5_square_1 A) (k2_newton E 2))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) & (r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers k1_sin_cos6 A))))  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers k1_sin_cos6 A) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers k1_sin_cos6 A) B) C) = (k10_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 C))))) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski C (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers D E))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ( ((k1_seq_1 D F) = (k7_real_1 F A))  &  ((k1_seq_1 E F) = (k9_real_1 F B)) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers D E) C) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F C) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers D E) C) F) = (k10_real_1 (k9_real_1 (k1_real_1 A) B) (k5_square_1 (k9_real_1 F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k1_fdiff_9)) =>  ((r2_fdiff_1 k1_fdiff_9 A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 k1_fdiff_9 A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k5_square_1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t4_ff_siec,ax, (! [A:$i] :  ( ((u1_struct_0 (k4_ff_siec A)) = k1_xboole_0)  &  ( ((u4_struct_0 (k4_ff_siec A)) = (k1_tarski A))  &  ((k1_net_1 (k4_ff_siec A)) = k1_xboole_0) ) ) ) ).
tt(t4_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k3_fib_fusc A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ((v5_memstr_0 F 2 k1_ami_3 k6_numbers) & (m1_scm_1 F (k16_afinsq_1 2 B D E)))  =>  ( ((k3_pre_ff C) = (k2_nat_1 (k4_nat_1 D (k3_pre_ff B)) (k4_nat_1 E (k3_pre_ff (k2_nat_1 B 1)))))  =>  ((r1_xxreal_0 C k6_numbers) |  ((r1_extpro_1 2 k1_ami_3 A F) &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A F) (k10_ami_3 3)) = (k3_pre_ff C))  &  ( ( (B = k6_numbers)  =>  ((k8_extpro_1 2 k1_ami_3 A F) = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k8_extpro_1 2 k1_ami_3 A F) = (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 B)) 1)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fib_num2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k3_power (k3_xcmplx_0 (k4_xcmplx_0 1) A) B) = (k3_xcmplx_0 (k3_power (k4_xcmplx_0 1) B) (k3_power A B))) ) ) ) ) ).
tt(t4_fib_num3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k2_nat_1 (k7_nat_d A 1) 2) = (k7_nat_d (k1_nat_1 A 2) 1)) ) ) ).
tt(t4_fib_num4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (v1_abian A))  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_power (k4_xcmplx_0 B) A) = (k4_xcmplx_0 (k3_power B A))) ) ) ) ) ) ) ) ) ).
tt(t4_fib_num,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_pre_ff (k1_nat_1 A (k1_nat_1 B 1))) = (k2_nat_1 (k4_nat_1 (k1_pre_ff B) (k1_pre_ff A)) (k4_nat_1 (k1_pre_ff (k1_nat_1 B 1)) (k1_pre_ff (k1_nat_1 A 1))))) ) ) ) ) ).
tt(t4_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_xxreal_0 (k3_finseq_1 (k2_rfinseq A D B)) (k3_finseq_1 (k2_rfinseq A C B)))) ) ) ) ) ) ) ) ) ).
tt(t4_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_lattices A B C) & (r1_lattices A D E))  => (r1_lattices A (k3_lattices A B D) (k3_lattices A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  ((v1_binop_1 C A) => (v1_binop_1 (k3_filter_1 A B C) (k8_eqrel_1 A B))) ) ) ) ) ) ) ).
tt(t4_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ( (E = (k1_realset1 C B))  &  ( (F = (k1_realset1 D B))  & (r6_binop_1 A C D)) )  => (r6_binop_1 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (m2_subset_1 (k3_rcomp_1 B A) (k1_zfmisc_1 k1_numbers) k12_prob_1)) ) ) ) ).
tt(t4_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden (k1_nat_1 A 1) (k2_finseq_1 (k1_nat_1 A 1)))) ) ).
tt(t4_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((k4_xxreal_0 k6_numbers (k6_xcmplx_0 B A)) = (k6_xcmplx_0 B A)) ) ) ) ) ) ).
tt(t4_finseq_3,ax, ((k2_finseq_1 6) = (k4_enumset1 1 2 3 4 5 6)) ).
tt(t4_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) => (r1_finseq_4 A B)) )  <=> (v2_funct_1 A)) ) ) ).
tt(t4_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((v2_funct_1 A) <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k8_relat_1 A (k1_tarski (k1_funct_1 A B))) = (k1_tarski B)) ) ) ) ) ) ).
tt(t4_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_relat_1 (k11_finseq_1 A B C) (k2_finseq_1 1)) = (k9_finseq_1 A)) ) ) ) ).
tt(t4_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden C (k4_finseq_1 (k2_rfinseq A D B))) =>  ((k1_funct_1 (k2_rfinseq A D B) C) = (k1_funct_1 B (k2_xcmplx_0 D C))) ) ) ) ) ) ) ) ) ) ).
tt(t4_finseq_8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B C) =>  ((k2_finseq_8 A B C) = (k2_finseq_6 A B C)) ) ) ) ) ) ) ) ).
tt(t4_finseqop,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k4_funcop_1 B k1_xboole_0 A) = k1_xboole_0) ) ) ) ).
tt(t4_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_finset_1 A) => (v1_finset_1 (k6_subset_1 A B))) ) ) ).
tt(t4_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo D A) | (r1_xxreal_0 1 (k3_finseq_1 C)))  =>  ((k1_finsop_1 A (k8_finseq_1 A C (k12_finseq_1 A B)) D) = (k5_binop_1 A D (k1_finsop_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t4_finsub_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden (k5_xboole_0 B C) A) & (r2_hidden (k6_subset_1 B C) A)) ) ) ) )  => (v4_finsub_1 A)) ) ) ).
tt(t4_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_fin_topo (k3_subset_1 (u1_struct_0 A) B) A) => (v3_fin_topo B A)) ) ) ) ) ).
tt(t4_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_fintopo3 A B) = (k3_subset_1 (u1_struct_0 A) (k12_fin_topo A (k3_subset_1 (u1_struct_0 A) B)))) ) ) ) ) ).
tt(t4_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_xxreal_0 C D) => (r1_tarski (k5_fintopo3 A B D) (k5_fintopo3 A B C))) ) ) ) ) ) ) ) ) ).
tt(t4_fintopo5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((v1_fintopo5 C A B) &  (F = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_hidden G (k10_fintopo3 A D E)) <=> (r2_hidden (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C G) (k10_fintopo3 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_fin_topo B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (B = (k4_subset_1 (u1_struct_0 A) C D))  &  ((r1_xboole_0 C D) &  ((r1_fintopo4 A C D) &  ( (~  (C = (k1_struct_0 A)) )  &  (~  (D = (k1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (m1_setfam_1 (a_1_0_fin_topo A) (u1_struct_0 A))) ) ).
tt(t4_flang_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k3_catalan2 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k3_catalan2 B)) =>  ( ((k1_flang_1 B C D) = (k5_afinsq_1 A))  <=>  ( ( (C = (k2_flang_1 B))  &  (D = (k5_afinsq_1 A)) )  |  ( (D = (k2_flang_1 B))  &  (C = (k5_afinsq_1 A)) ) ) ) ) ) ) ) ) ) ).
tt(t4_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  ( ( ((k1_flang_1 A B C) = B)  |  ((k1_flang_1 A C B) = B) )  =>  (C = k1_xboole_0) ) ) ) ) ) ) ).
tt(t4_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_flang_3 A B C) = k1_xboole_0)  <=>  ( (~ (r1_xxreal_0 C k6_numbers))  &  (B = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t4_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((v5_relat_1 B A) & (v5_relat_1 C A))  =>  ((k1_binop_1 (k11_monoid_0 A) B C) = (k7_finseq_1 B C)) ) ) ) ) ) ) ) ).
tt(t4_fomodel1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  => (r1_tarski (k1_funct_1 (k28_fomodel1 C) A) (k1_funct_1 (k28_fomodel1 C) (k2_xcmplx_0 A B)))) ) ) ) ) ) ).
tt(t4_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ((v11_fomodel1 C) & (l1_fomodel1 C)) )  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E D) =>  (! [F:$i] :  ((m1_subset_1 F D) =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_fomodel2 G C D)) )  =>  (! [H:$i] :  ( ((v14_fomodel1 H A C) & (m2_subset_1 H (k3_finseq_2 (k15_fomodel1 C)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 C)) (k1_tarski k1_xboole_0))))  =>  ((k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 C) D (k9_funct_2 (k35_fomodel1 C) D) (k8_fomodel2 C D E G) (k1_nat_1 A 1)) H) = (k1_funct_1 (k10_funct_5 k5_numbers (k35_fomodel1 C) D (k9_funct_2 (k35_fomodel1 C) D) (k8_fomodel2 C D F G) (k2_nat_1 (k1_nat_1 A 1) B)) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fomodel3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  => (r2_funct_2 (k35_fomodel1 B) (k35_fomodel1 B) (k10_fomodel2 B (k35_fomodel1 B) (k7_fomodel3 B A)) (k3_fomodel2 (k35_fomodel1 B)))) ) ) ).
tt(t4_fomodel4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v4_fomodel2 C B) & (m2_subset_1 C (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  ((r2_hidden C A) => (v8_fomodel4 C B (k6_domain_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 B)) (k9_setfam_1 (k1_fomodel4 B))) (k22_fomodel4 B)) A)) ) ) ) ) ) ).
tt(t4_fraenkel,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski C B) & (r1_tarski D A))  =>  ( ((k1_funct_2 C D) = k1_xboole_0)  |  (! [E:$i] :  ((m1_subset_1 E (k1_funct_2 C D)) =>  (? [F:$i] :  ((m2_funct_2 F B A (k9_funct_2 B A)) &  ((k2_partfun1 B A F C) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 A) B) (k4_subset_1 (u1_struct_0 A) C D)) &  (! [E:$i] :  ((m2_valued_0 E (u1_struct_0 A) B) =>  ( (~ (r1_tarski (k2_relset_1 (u1_struct_0 A) E) C))  &  (~ (r1_tarski (k2_relset_1 (u1_struct_0 A) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_frechet,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc C A))  => (v3_pre_topc (k7_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t4_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  ((k1_unialg_1 (k7_freealg A B)) = A) ) ) ) ) ).
tt(t4_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k6_circuit2 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 B C) k2_twoscomp)) = (k10_margrel1 E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fscirc_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1)))  =>  ( ((k1_fscirc_2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k8_fscirc_1 A B C)))  &  ( ((k2_fscirc_2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k8_fscirc_1 A B C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k8_margrel1) k1_xboole_0) (k9_fscirc_1 A B C)))  &  ((k3_fscirc_2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k6_fscirc_1 A B C)) ) ) ) ) ) ) ).
tt(t4_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k1_funct_1 (k2_fsm_1 A B D C) (k3_finseq_1 (k2_fsm_1 A B D C))) = E)  <=> (r1_fsm_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ((v1_fsm_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((k1_funct_1 C 1) = (k1_funct_1 D 1))  => (r3_xboole_0 (k2_fsm_1 A B (u2_fsm_1 A B) C) (k2_fsm_1 A B (u2_fsm_1 A B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t4_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (~  ( ((k1_afinsq_1 B) = 1)  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  ( ((k3_flang_1 A C) = B)  &  (C = (k1_funct_1 B k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden B (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden C (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden D (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden E (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k12_gfacirc1 A B C) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k9_gfacirc1 A B C) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k12_gfacirc1 (k12_gfacirc1 A B C) E D) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp) (u1_struct_0 (k1_ftacell1 A B C D E))) & (r2_hidden (k9_gfacirc1 (k12_gfacirc1 A B C) E D) (u1_struct_0 (k1_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_funcop_1,ax, (! [A:$i] :  ((k1_funcop_1 (k12_funct_3 A)) = (k12_funct_3 A)) ) ).
tt(t4_funcsdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_funct_2 A k1_numbers B (k2_funcsdom A k1_numbers k1_numbers (k9_funct_2 A k1_numbers) (k7_funcsdom A) (k1_domain_1 k1_numbers (k9_funct_2 A k1_numbers) D C))) <=>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k1_numbers B E) = (k8_real_1 D (k3_funct_2 A k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((k9_xtuple_0 B) = (k1_tarski A))  =>  ((k10_xtuple_0 B) = (k1_tarski (k1_funct_1 B A))) ) ) ) ) ).
tt(t4_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden C A) =>  ( (B = k1_xboole_0)  | (r2_hidden (k1_funct_1 D C) (k2_relset_1 B D))) ) ) ) ) ) ) ).
tt(t4_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k10_xtuple_0 (k3_relat_1 B C))) & (v2_funct_1 C))  => (r1_tarski (k8_relat_1 C A) (k10_xtuple_0 B))) ) ) ) ) ) ).
tt(t4_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_relset_1 A (k1_tarski C) (k7_funcop_1 A C) (k7_funcop_1 B C))) ) ) ) ).
tt(t4_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k1_funct_5 A) = (k3_funct_5 (k2_funct_4 A)))  &  ((k2_funct_5 A) = (k2_funct_4 (k4_funct_5 A))) ) ) ) ).
tt(t4_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((r2_hidden (k3_funct_2 A B C D) (k7_subset_1 B (k7_relset_1 A B C E) F)) => (r2_hidden D (k7_subset_1 A E (k8_relset_1 A B C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k7_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 B (k1_real_1 C))) = (k1_real_1 1)) ) ) ) )  => (r2_funct_8 A k1_numbers k1_numbers B)) ) ) ) ) ).
tt(t4_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 B A) & (v1_funct_9 C A))  => (v1_funct_9 (k18_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t4_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) <=> (v2_funct_2 (k16_funct_3 A A B B C C) (k2_zfmisc_1 B B))) ) ) ) ) ).
tt(t4_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_altcat_2 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_altcat_2 B) & (m1_altcat_2 B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_altcat_2 C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_altcat_2 D B))  =>  ( (C = D)  =>  ((k10_functor0 A C) = (k13_functor0 D B A (k10_functor0 B D) (k10_functor0 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t4_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_functor2 A B C C (k1_functor2 A B C) D) = (k8_altcat_1 B (k3_functor0 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t4_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) & (l2_altcat_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((k13_functor0 A B B C (k11_functor0 B)) = (g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C))) ) ) ) ) ) ) ).
tt(t4_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 C D))  => (r1_fuzzy_1 C D)) ) ) ) ) ) ) ) ) ).
tt(t4_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k1_fuzzy_2 A B D) (k1_fuzzy_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t4_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  (! [E:$i] :  ((r1_xxreal_0 k6_numbers (k1_fuzzy_4 A B C D E)) & (r1_xxreal_0 (k1_fuzzy_4 A B C D E) 1)) ) ) ) ) ) ) ) ) ).
tt(t4_fvaluat1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~  (A = k1_xxreal_0) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k6_xxreal_3 B A) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t4_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v6_vectsp_1 A) & (l4_algstr_0 A)) ) )  => (r3_binop_1 (u1_struct_0 A) (k5_struct_0 A) (u2_algstr_0 A))) ) ).
tt(t4_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 (k2_gate_1 A B)))  <=>  ( (~ (v1_xboole_0 A))  &  (~ (v1_xboole_0 B)) ) ) ) ) ).
tt(t4_gate_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (! [W:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k8_gate_1 S R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R Q)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T))))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k8_gate_1 V U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U T)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 Q) W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 Q) W)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 (k2_gate_1 (k4_gate_1 Q R) W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k4_gate_1 Q R) W)))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 (k2_gate_1 (k3_gate_1 (k2_gate_1 S (k1_gate_1 Q)) (k2_gate_1 Q (k4_gate_1 R S))) W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k3_gate_1 (k2_gate_1 S (k1_gate_1 Q)) (k2_gate_1 Q (k4_gate_1 R S))) W)))  & (v1_xboole_0 V)) )  &  (~  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k2_gate_1 A W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A W)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k2_gate_1 B W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 B W)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k2_gate_1 C W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 C W)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k2_gate_1 D W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 D W)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k2_gate_1 E W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 E W)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k2_gate_1 F W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 F W)))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k2_gate_1 G W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 G W)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k3_gate_1 H (k1_gate_1 W)))) )  &  (~  ( (~ (v1_xboole_0 (k3_gate_1 H (k1_gate_1 W))))  & (v1_xboole_0 I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gate_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (! [T:$i] :  (! [U:$i] :  (! [V:$i] :  (! [W:$i] :  (~  ( (~  ( (~ (v1_xboole_0 A))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 A)) )  &  ( (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) (k1_gate_1 R) Q)))  & (v1_xboole_0 B)) )  &  ( (~  ( (~ (v1_xboole_0 C))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R (k1_gate_1 Q))))  & (v1_xboole_0 C)) )  &  ( (~  ( (~ (v1_xboole_0 D))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 S) R Q)))  & (v1_xboole_0 D)) )  &  ( (~  ( (~ (v1_xboole_0 E))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) (k1_gate_1 Q))))  & (v1_xboole_0 E)) )  &  ( (~  ( (~ (v1_xboole_0 F))  & (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S (k1_gate_1 R) Q)))  & (v1_xboole_0 F)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R (k1_gate_1 Q))))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k8_gate_1 S R Q))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 S R Q)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) (k1_gate_1 U) T)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U (k1_gate_1 T))))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 (k1_gate_1 V) U T)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) (k1_gate_1 T))))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V (k1_gate_1 U) T)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T)))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U (k1_gate_1 T))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k8_gate_1 V U T))) )  &  ( (~  ( (~ (v1_xboole_0 (k8_gate_1 V U T)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 T))  & (v1_xboole_0 (k2_gate_1 (k1_gate_1 S) W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 (k1_gate_1 S) W)))  & (v1_xboole_0 T)) )  &  ( (~  ( (~ (v1_xboole_0 U))  & (v1_xboole_0 (k2_gate_1 Q W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 Q W)))  & (v1_xboole_0 U)) )  &  ( (~  ( (~ (v1_xboole_0 V))  & (v1_xboole_0 (k2_gate_1 R W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 R W)))  & (v1_xboole_0 V)) )  &  (~  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k2_gate_1 A W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A W)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k2_gate_1 B W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 B W)))  & (v1_xboole_0 L)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k2_gate_1 D W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 D W)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k2_gate_1 H W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 H W)))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k2_gate_1 G W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 G W)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k3_gate_1 (k2_gate_1 E W) (k1_gate_1 W)))) )  &  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 (k2_gate_1 E W) (k1_gate_1 W))))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k2_gate_1 F W))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 F W)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k2_gate_1 C W))) )  &  (~  ( (~ (v1_xboole_0 (k2_gate_1 C W)))  & (v1_xboole_0 N)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gate_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  (! [R:$i] :  (! [S:$i] :  (~  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 (k2_gate_1 A D))) )  &  ( (~  ( (~ (v1_xboole_0 (k2_gate_1 A D)))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 Q))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 B D) (k2_gate_1 A E) k1_xboole_0)))  & (v1_xboole_0 Q)) )  &  ( (~  ( (~ (v1_xboole_0 O))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F)))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F))))  & (v1_xboole_0 O)) )  &  ( (~  ( (~ (v1_xboole_0 R))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F)))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C D) (k2_gate_1 B E) (k2_gate_1 A F))))  & (v1_xboole_0 R)) )  &  ( (~  ( (~ (v1_xboole_0 P))  & (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0)))  & (v1_xboole_0 P)) )  &  ( (~  ( (~ (v1_xboole_0 S))  & (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_1 (k2_gate_1 C E) (k2_gate_1 B F) k1_xboole_0)))  & (v1_xboole_0 S)) )  &  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 M)) )  &  ( (~  ( (~ (v1_xboole_0 M))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 N)) )  &  ( (~  ( (~ (v1_xboole_0 N))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k10_gate_1 O Q k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_1 O Q k1_xboole_0)))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k14_gate_5 O Q P R k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k14_gate_5 O Q P R k1_xboole_0)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k16_gate_5 O Q P R (k2_gate_1 C F) S k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k16_gate_5 O Q P R (k2_gate_1 C F) S k1_xboole_0)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k17_gate_5 O Q P R (k2_gate_1 C F) S k1_xboole_0))) )  &  ( (~  ( (~ (v1_xboole_0 (k17_gate_5 O Q P R (k2_gate_1 C F) S k1_xboole_0)))  & (v1_xboole_0 L)) )  &  (~  ( (~  ( (~ (v1_xboole_0 G))  & (v1_xboole_0 (k5_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k5_gate_5 A B C D E)))  & (v1_xboole_0 G)) )  &  ( (~  ( (~ (v1_xboole_0 H))  & (v1_xboole_0 (k6_gate_5 A B C D E))) )  &  ( (~  ( (~ (v1_xboole_0 (k6_gate_5 A B C D E)))  & (v1_xboole_0 H)) )  &  ( (~  ( (~ (v1_xboole_0 I))  & (v1_xboole_0 (k10_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k10_gate_5 A B C D E F)))  & (v1_xboole_0 I)) )  &  ( (~  ( (~ (v1_xboole_0 J))  & (v1_xboole_0 (k11_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k11_gate_5 A B C D E F)))  & (v1_xboole_0 J)) )  &  ( (~  ( (~ (v1_xboole_0 K))  & (v1_xboole_0 (k12_gate_5 A B C D E F))) )  &  ( (~  ( (~ (v1_xboole_0 (k12_gate_5 A B C D E F)))  & (v1_xboole_0 K)) )  &  ( (~  ( (~ (v1_xboole_0 L))  & (v1_xboole_0 (k13_gate_5 A B C D E F))) )  &  (~  ( (~ (v1_xboole_0 (k13_gate_5 A B C D E F)))  & (v1_xboole_0 L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_gcd_1 A B C) & (r3_gcd_1 A C D))  => (r3_gcd_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t4_genealg1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_genealg1 B A) =>  (! [C:$i] :  ((m1_genealg1 C A) =>  ((k7_genealg1 A B C k6_numbers) = C) ) ) ) ) ) ) ).
tt(t4_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k2_analmetr A B C))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k2_analmetr A B C))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k2_analmetr A B C))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k2_analmetr A B C))) =>  ( ( (H = D)  &  ( (I = E)  &  ( (J = F)  &  (K = G) ) ) )  =>  ((r2_analoaf (k2_analmetr A B C) H I J K) <=> (r1_geomtrap A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gfacirc1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 A B)) = (k2_binarith A (k9_margrel1 B)))  &  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 A B)) = (k1_funct_1 k15_twoscomp (k10_finseq_1 A B)))  &  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 A B)) = (k1_funct_1 k8_twoscomp (k10_finseq_1 (k1_funct_1 k4_twoscomp (k10_finseq_1 A B)) (k1_funct_1 k2_twoscomp (k10_finseq_1 A B)))))  &  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 k6_numbers k6_numbers)) = 1)  &  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 k6_numbers 1)) = k6_numbers)  &  ( ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 1 k6_numbers)) = k6_numbers)  &  ((k1_funct_1 k4_gfacirc1 (k10_finseq_1 1 1)) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gfacirc2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (C = (k4_tarski k1_xboole_0 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1)))  =>  ( ((k1_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k2_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k13_gfacirc1 A B C)))  &  ( ((k2_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k3_circcomb (k5_circcomb (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k13_gfacirc1 A B C) (k7_circcomb k1_xboole_0 k6_margrel1 (k1_margrel1 k6_margrel1 (k4_finseq_2 k6_numbers k6_margrel1) k7_margrel1) k1_xboole_0) (k14_gfacirc1 A B C)))  &  ((k3_gfacirc2 1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k9_gfacirc1 A B C)) ) ) ) ) ) ) ).
tt(t4_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ( ((k1_relset_1 (k7_glib_000 A) (k10_glib_000 A)) = (k7_glib_000 A))  &  ( ((k1_relset_1 (k7_glib_000 A) (k11_glib_000 A)) = (k7_glib_000 A))  &  ((r1_tarski (k2_relset_1 (k6_glib_000 A) (k10_glib_000 A)) (k6_glib_000 A)) & (r1_tarski (k2_relset_1 (k6_glib_000 A) (k11_glib_000 A)) (k6_glib_000 A))) ) ) ) ) ).
tt(t4_glib_001,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k1_relset_1 k5_numbers (k15_finseq_1 C))) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden E (k1_relset_1 k5_numbers B)) &  ((r1_xxreal_0 D E) &  ((k1_funct_1 (k15_finseq_1 C) D) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ( (~ (v4_glib_000 A))  & (v1_glib_002 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) (k1_tarski B)))) =>  ((v11_glib_000 B A) => (v1_glib_002 C)) ) ) ) ) ) ) ).
tt(t4_glib_003,ax, ( (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_003 A)) ) ) ) )  =>  ((k5_glib_003 A) = (k1_funct_1 A k2_glib_003)) ) )  &  ( (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  ((k6_glib_003 A) = (k1_funct_1 A k3_glib_003)) ) )  &  (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  ((k7_glib_003 A) = (k1_funct_1 A k4_glib_003)) ) ) ) ) ).
tt(t4_glib_004,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ((k1_relset_1 A C) = (k1_tarski B))  =>  ((k3_uproots A C) = (k1_seq_1 C B)) ) ) ) ) ) ).
tt(t4_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k1_relset_1 (k6_glib_000 A) (k4_glib_005 A B (k5_glib_005 A B C) k6_numbers)) = (k6_domain_1 (k6_glib_000 A) C)) ) ) ) ) ) ) ).
tt(t4_goboard1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden B (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A C))) &  ((r2_hidden B (k10_xtuple_0 (k9_matrix_1 (u1_struct_0 (k15_euclid 2)) A D))) &  ((r2_hidden C (k2_finseq_1 (k1_matrix_1 A))) & (r2_hidden D (k2_finseq_1 (k1_matrix_1 A)))) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t4_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ( ((k3_finseq_1 A) = (k2_nat_1 B 1))  &  ((v2_topreal1 A) & (v3_topreal1 A)) )  =>  ((r1_xxreal_0 B 1) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A)) (k2_topreal1 2 A B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ) ) ).
tt(t4_goboard4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((v1_topreal1 A) &  ((v1_topreal1 B) &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 A)) &  ((r2_hidden (k2_nat_1 C 1) (k4_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1))) ) ) ) ) )  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden (k2_nat_1 C 1) (k4_finseq_1 B)) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) B C) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 C 1))) ) ) ) ) )  &  ((r1_goboard4 (k1_goboard1 A) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k1_goboard1 B) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k2_goboard1 A) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) &  ((r1_goboard4 (k2_goboard1 B) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) & (r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((v4_goboard1 D) &  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 B A))  &  ((r1_xxreal_0 B (k1_matrix_1 D)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 D)) & (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C B)) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D C A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_goboard6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ((r2_hidden B (k1_tops_1 (k3_pcomps_1 A) C)) <=>  (? [D:$i] :  ((v1_xreal_0 D) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k9_metric_1 A B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ( ((k3_rlvect_1 (k15_euclid A) C B) = (k3_rlvect_1 (k15_euclid A) C D))  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t4_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 2))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 2))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_goboard9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 C A) &  ((r3_connsp_1 A E D) &  ((r1_tarski B D) & (r1_tarski C E)) ) )  =>  ((r1_xboole_0 B C) | (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_gobrd10 A C B D) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 1 D)) ) ) )  => (r2_gobrd10 (k7_nat_d A 1) (k7_nat_d C 1) (k7_nat_d B 1) (k7_nat_d D 1))) ) ) ) ) ) ) ) ) ).
tt(t4_gobrd11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_connsp_3 A (k4_subset_1 (u1_struct_0 A) B C) D) = (k4_subset_1 (u1_struct_0 (k1_pre_topc A D)) (k4_connsp_3 A B D) (k4_connsp_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t4_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)) = (k3_tarski (a_1_0_gobrd12 A))) ) ) ).
tt(t4_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) B) | (v2_compts_1 (k3_goboard5 C A B) (k15_euclid 2))) ) ) ) ) ) ) ) ) ).
tt(t4_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( ((v1_henmodel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))))  =>  (! [D:$i] :  ((m1_henmodel D A C) =>  ( ((v1_goedelcp C A) & (v2_goedelcp C A))  =>  ( ((v1_goedelcp C A) &  ((v2_goedelcp C A) &  (~  ((r1_valuat_1 A (k1_henmodel A) B D (k3_henmodel A)) <=> (r1_henmodel A C B)) ) ) )  |  ((r1_valuat_1 A (k1_henmodel A) (k6_cqc_lang A B) D (k3_henmodel A)) <=> (r1_henmodel A C (k6_cqc_lang A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_graph_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_graph_1 C B) => (m2_graph_1 (k2_partfun1 k5_numbers (u4_struct_0 B) C (k2_finseq_1 A)) B)) ) ) ) ) ) ).
tt(t4_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_card_1 (a_2_0_graph_2 A B)) = (k2_nat_1 B 1)) ) ) ) ) ).
tt(t4_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  ((v2_funct_1 (k9_finseq_1 B)) & (m2_graph_1 (k9_finseq_1 B) A)) ) ) ) ) ).
tt(t4_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  ((r3_graph_4 A B C) => (r1_graph_2 A B C)) ) ) ) ) ) ) ).
tt(t4_graph_5,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( ((k5_card_1 A) = (k2_nat_1 B 1))  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (~  ( (A = (k2_xboole_0 D (k1_tarski C)))  &  ((k5_card_1 D) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r6_graph_5 A C) &  ((k3_finseq_1 B) = 1) )  =>  ((k10_graph_5 A B C) = (k1_funct_1 C (k1_funct_1 B 1))) ) ) ) ) ) ) ) ).
tt(t4_grcat_1,ax, ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (A = k1_xboole_0) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  ((k3_rlvect_1 k3_algstr_0 A B) = k1_xboole_0) ) ) ) )  &  ( (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  ((k4_algstr_0 k3_algstr_0 A) = k1_xboole_0) ) )  &  ((k4_struct_0 k3_algstr_0) = k1_xboole_0) ) ) ) ).
tt(t4_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k4_numbers) =>  ((k3_group_4 A (k4_group_4 A C (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 C) B))) = (k5_group_1 A (k1_gr_cy_1 C) B)) ) ) ) ) ) ) ).
tt(t4_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~ (v2_struct_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))))  &  ((v2_group_1 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))) &  ((v3_group_1 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))) &  ((v1_gr_cy_1 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))) & (l3_algstr_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ) ) ) ) ).
tt(t4_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  ( (~  (A = 7) )  =>  ((k4_nat_d A 3) = 2) ) ) ) ).
tt(t4_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden (k4_tarski A B) (k3_relat_1 D C)) =>  ((r2_hidden (k4_tarski A (k1_funct_1 D A)) D) & (r2_hidden (k4_tarski (k1_funct_1 D A) B) C)) ) ) ) ) ) ) ) ).
tt(t4_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_group_1 A (k2_group_3 A (k2_group_5 A B (k2_group_1 A C)) C)) = (k2_group_3 A (k2_group_5 A (k2_group_1 A C) B) C)) ) ) ) ) ) ) ).
tt(t4_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_tarski D E) => (r1_relset_1 (k8_struct_0 (k11_polynom1 A C)) (u1_struct_0 (k11_polynom1 A C)) (k3_polyred A B C D) (k3_polyred A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ( ((r3_pre_poly A B D) & (r3_pre_poly A C D))  => (r3_pre_poly A (k2_groeb_2 A B C) D)) ) ) ) ) ) ) ) ).
tt(t4_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  ((r2_termord A B C D) => (r2_termord A B (k11_pre_poly A C E) (k11_pre_poly A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  ((r2_group_10 A B E C D) => (r2_group_10 A B E D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  =>  ((r1_struct_0 D C) => (r1_struct_0 D (k6_algstr_0 A (k6_algstr_0 A B C) (k2_group_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t4_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_group_7 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_group_7 A B C))) =>  ( (D = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C E))  =>  ((k2_group_1 (k2_group_7 A B) D) = (k2_funct_7 (k1_group_1 (k2_group_7 A B)) C (k2_group_1 (k1_group_7 A B C) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A C B) = C)  &  ((k6_algstr_0 A B C) = C) ) ) )  =>  (B = (k1_group_1 A)) ) ) ) ) ) ).
tt(t4_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_group_2 A (k7_domain_1 (u1_struct_0 A) B C)) = (k7_domain_1 (u1_struct_0 A) (k2_group_1 A B) (k2_group_1 A C))) ) ) ) ) ) ) ).
tt(t4_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k2_group_2 A B D) (k2_group_2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_4,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r1_struct_0 D C) => (r1_struct_0 D (k5_group_1 B A C))) ) ) ) ) ) ) ) ) ).
tt(t4_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r2_hidden A (k7_group_4 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B E F))  &  ((r1_struct_0 C E) & (r1_struct_0 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k6_algstr_0 A B C) (k2_group_1 A B)) = (k2_group_3 A C (k2_group_1 A B)))  &  ((k6_algstr_0 A B (k6_algstr_0 A C (k2_group_1 A B))) = (k2_group_3 A C (k2_group_1 A B))) ) ) ) ) ) ) ) ).
tt(t4_group_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) & (v1_group_7 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  ( ((r2_hidden B A) &  ( (D = (k1_funct_1 C B))  & (v5_group_1 (k2_group_7 A C))) )  => (v5_group_1 D)) ) ) ) ) ) ) ).
tt(t4_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (C = D)  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k5_group_1 B E C) = (k5_group_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((k1_group_1 B) = (k1_group_1 C)) ) ) ) ) ) ).
tt(t4_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k5_group_1 A C (k2_group_1 A B)) = (k1_group_1 A))  =>  ((k5_group_1 A C B) = (k1_group_1 A)) ) ) ) ) ) ) ) ).
tt(t4_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D C) & (m1_group_6 D A C)) )  =>  (! [E:$i] :  ( ((v15_algstr_0 E) & (m1_group_2 E A))  =>  ((r1_group_2 A E (k10_group_2 A C B)) =>  (! [F:$i] :  ( ((v1_group_3 F E) & (m1_group_6 F A E))  =>  (~  ( (F = (k10_group_2 A D B))  &  (! [G:$i] :  ((m1_group_2 G (k5_group_6 C D)) =>  (~ (r1_group_6 (k5_group_6 E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_hahnban1,ax, ((k8_group_1 k1_complfld k2_hahnban1 k2_hahnban1) = (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld))) ).
tt(t4_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k4_rlsub_2 A D B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F))  =>  ((r1_struct_0 B E) & (r1_struct_0 C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  (! [D:$i] :  ((r1_tarski C D) => (r1_tarski (k1_hallmar1 A B C) (k1_hallmar1 A B D))) ) ) ) ) ) ) ).
tt(t4_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r2_hidden D (k7_relset_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 k3_topmetr) (k4_weierstr A C) B)) => (r1_xxreal_0 k6_numbers D)) ) ) ) ) ) ) ) ) ).
tt(t4_heine,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (v1_compts_1 (k4_topmetr A B))) ) ) ) ) ).
tt(t4_helly,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  => (r1_tarski (k9_finseq_1 (k1_funct_1 A 1)) A)) ) ).
tt(t4_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((v1_henmodel B A) & (r1_tarski (k2_relset_1 (k3_cqc_lang A) C) B))  => (v2_henmodel C A)) ) ) ) ) ) ) ).
tt(t4_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k9_complex1 A (k15_complex1 A)) = (k2_xcmplx_0 (k5_square_1 (k17_complex1 A)) (k3_xcmplx_0 k6_numbers k7_complex1))) ) ) ).
tt(t4_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((r1_tarski C B) => (r2_hidden C (k8_normform A))) ) ) ) ) ).
tt(t4_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( ((k3_substlat A B (k4_substlat A B C D)) = C)  =>  (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k8_mcart_1 k1_numbers k5_numbers k5_numbers (k6_domain_1 k5_numbers A))))) )  =>  (~  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k5_numbers))  => (r2_hidden (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 C) 1) A) B)) ) ) ) ) ) ) ).
tt(t4_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r2_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 C)) (k8_real_1 A B)) (k26_valued_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 C)) B) A))) ) ) ) ) ) ).
tt(t4_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_partfun1 D B) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ( ( (E = (k5_relat_1 C A))  &  ( (F = (k5_relat_1 D A))  & (r3_pre_poly B C D)) )  => (r3_pre_poly A E F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 B (k3_hilbert1 C B)) (k5_hilbert1 A))) ) ) ) ) ) ).
tt(t4_hilbert2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  (B = (k7_finseq_1 C (k9_finseq_1 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_hilbert3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((k1_funct_6 (k10_xtuple_0 A)) = (k10_xtuple_0 A)) ) ) ).
tt(t4_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k7_real_1 (k10_real_1 1 A) (k10_real_1 1 B)) = 1)  =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 C k6_numbers) |  ((r1_xxreal_0 D k6_numbers) |  ((r1_xxreal_0 (k8_real_1 C D) (k7_real_1 (k10_real_1 (k10_prepower C A) A) (k10_real_1 (k10_prepower D B) B))) &  ( ( ((k8_real_1 C D) = (k7_real_1 (k10_real_1 (k10_prepower C A) A) (k10_real_1 (k10_prepower D B) B)))  =>  ((k10_prepower C A) = (k10_prepower D B)) )  &  ( ((k10_prepower C A) = (k10_prepower D B))  =>  ((k8_real_1 C D) = (k7_real_1 (k10_real_1 (k10_prepower C A) A) (k10_real_1 (k10_prepower D B) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ((r1_aff_1 A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v6_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_hurwitz,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k4_algstr_0 A (k1_group_1 A)) (k4_nat_1 2 B)) = (k1_group_1 A))  &  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k4_algstr_0 A (k1_group_1 A)) (k2_nat_1 (k4_nat_1 2 B) 1)) = (k4_algstr_0 A (k1_group_1 A))) ) ) ) ) ) ).
tt(t4_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k6_xcmplx_0 B A) C)) ) ) ) ) ) ) ).
tt(t4_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  => (v1_ideal_1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t4_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_incproj B A) <=> (m1_subset_1 B (u2_incsp_1 (k3_incproj A)))) ) ) ) ).
tt(t4_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ((r5_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C D) E) <=>  ((r2_incsp_1 A B E) &  ((r2_incsp_1 A C E) & (r2_incsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_index_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m3_index_1 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F B) => (m2_cat_1 (k1_funct_1 (k2_xtuple_0 E) F) (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A C F)) (k2_index_1 A (k1_xtuple_0 E) (k3_funct_2 B A D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ( ((g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C)))  =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((k5_msualg_1 A D B) = (k5_msualg_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v1_int_1 A) =>  ((v1_int_1 (k3_real_1 A 1)) & (v1_int_1 (k5_real_1 A 1))) ) ) ) ).
tt(t4_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ( (A = k6_numbers)  |  (B = k6_numbers) )  <=>  ((k2_int_2 A B) = k6_numbers) ) ) ) ) ) ).
tt(t4_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) &  ((v1_int_3 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) &  ((v3_gcd_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_int_4,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ( (B = k6_numbers)  =>  ((v1_xboole_0 A) |  ((k1_integra2 A B) = (k1_tarski k6_numbers)) ) )  &  (~  ( ((k1_integra2 A B) = (k1_tarski k6_numbers))  &  ( (~  (B = k6_numbers) )  &  (~  (A = (k1_tarski k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t4_int_5,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  ( ((k3_finseq_1 A) = 1)  =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  ((k3_funct_2 k4_numbers k4_numbers (k1_int_5 A) B) = (k1_funct_1 A 1)) ) ) ) ) ) ).
tt(t4_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 C (k3_finseq_1 A)) =>  ((k16_finseq_1 C (k18_valued_1 A B)) = (k18_valued_1 (k16_finseq_1 C A) (k16_finseq_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t4_int_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ( ((k1_polynom2 A B) = k1_xboole_0)  &  ((k1_polynom2 A C) = k1_xboole_0) )  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t4_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_tarski (k3_integra5 C D) (k1_relset_1 k1_numbers A)) &  ((r1_tarski (k3_integra5 C D) (k1_relset_1 k1_numbers B)) &  ((r1_integr10 A C D) & (r1_integr10 B C D)) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_integr10 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C D) &  ((k1_integr10 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C D) = (k7_real_1 (k1_integr10 A C D) (k1_integr10 B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k1_real_1 (k10_real_1 1 (k7_real_1 A 1)))) k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos (k1_taylor_1 (k7_real_1 A 1))) (k1_real_1 (k10_real_1 1 (k7_real_1 A 1)))) k1_numbers) B) = (k8_real_1 (k5_prepower (k1_seq_1 k19_sin_cos B) A) (k1_seq_1 k16_sin_cos B))) ) ) ) ) ) ).
tt(t4_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ( (~ (r1_xxreal_0 1 (k1_seq_1 k24_sin_cos E)))  &  ((k1_seq_1 B E) = 1) ) ) ) )  &  ((r1_tarski D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9))) &  ( (D = (k1_relset_1 k1_numbers C))  & (r2_relset_1 k1_numbers k1_numbers C (k3_rfunct_1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k24_sin_cos) (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k41_valued_1 k1_numbers k1_numbers k24_sin_cos))))) ) ) )  =>  ((k2_integra5 A C) = (k10_binop_2 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k24_sin_cos k2_sin_cos9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t4_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ((r2_relset_1 k1_numbers k1_numbers B (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) 2)) &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t4_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k24_sin_cos)) A) B) = (k10_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k2_fdiff_9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t4_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((v1_seq_2 (k2_partfun1 A k1_numbers B A)) &  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_integr15 E A B C) =>  (~ (r1_xxreal_0 (k9_real_1 (k6_integra1 A B C) D) (k1_integr15 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integr16,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [C:$i] :  ((m1_integra1 C A) =>  (! [D:$i] :  ((m1_integr16 D A B C) =>  ((m1_integr15 (k1_integr16 D) A (k5_comseq_3 A B) C) & (m1_integr15 (k2_integr16 D) A (k6_comseq_3 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t4_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((r2_relset_1 B (u1_struct_0 A) E (k4_vfunct_1 B A D C)) & (v1_integr18 D A B))  =>  ((v1_integr18 E A B) &  ((k4_integr18 A B E) = (k1_rlvect_1 A (k4_integr18 A B D) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers F)) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers G))) ) ) )  => (r1_tarski (k3_integra5 C D) (k1_relset_1 k1_numbers (k7_integr15 A k1_numbers F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (A = (k1_rcomp_1 (k5_seq_4 A) (k4_seq_4 A))) ) ) ).
tt(t4_integra2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 E (k3_finseq_1 B)) & (r1_xxreal_0 C D)) )  =>  ((r1_xxreal_0 E D) |  ((k8_finseq_1 A (k3_finseq_6 A B C D) (k3_finseq_6 A B (k2_nat_1 D 1) E)) = (k3_finseq_6 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  (? [D:$i] :  ((m1_integra1 D A) &  ((r1_integra1 B D) &  ((r1_integra1 C D) &  ((k1_rvsum_1 D) = (k4_subset_1 k1_numbers (k1_rvsum_1 B) (k1_rvsum_1 C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k1_rvsum_1 B) = (k1_seq_4 C))  =>  ((v3_integra1 B A) &  ((k12_integra1 A B) = (k8_real_1 C (k3_integra1 A))) ) ) ) ) ) ) ) ) ).
tt(t4_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 C k1_numbers (k20_valued_1 C k1_numbers k1_numbers (k1_integra5 A C) (k1_integra5 B C)) (k1_integra5 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) C))) ) ) ) ) ) ).
tt(t4_integra6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r1_tarski A C))  =>  ((k2_partfun1 B k1_numbers (k7_rfunct_1 B B) A) = (k2_partfun1 C k1_numbers (k7_rfunct_1 C C) A)) ) ) ) ) ).
tt(t4_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r2_hidden C A) & (r1_fdiff_1 (k2_partfun1 k1_numbers k1_numbers B A) C))  => (r1_fdiff_1 B C)) ) ) ) ) ) ).
tt(t4_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k21_sin_cos (k7_real_1 A (k8_real_1 (k2_nat_1 (k4_nat_1 2 B) 1) k32_sin_cos))) = (k1_real_1 (k21_sin_cos A))) ) ) ) ) ).
tt(t4_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ( (~  (A = k6_numbers) )  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k1_real_1 (k10_real_1 1 A))) k1_numbers) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k1_real_1 (k10_real_1 1 A))) k1_numbers) B) = (k18_sin_cos (k8_real_1 A B))) ) ) ) ) ) ) ).
tt(t4_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ( ((k1_interva1 A B C) = k1_xboole_0)  & (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t4_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 B C) C) (k7_intpro_1 A))) ) ) ) ) ) ).
tt(t4_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_power A (k4_xcmplx_0 (k2_nat_1 B 1))) = (k13_complex1 (k3_power A (k4_xcmplx_0 B)) A)) ) ) ) ) ) ).
tt(t4_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  ((r1_nattra_1 A B C D) =>  (! [E:$i] :  ((m1_nattra_1 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) => (r2_hidden (k4_nattra_1 A B C D E F) (k2_cat_1 B (k8_cat_1 A B C F) (k8_cat_1 A B D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v2_isomichi B A)) ) ) ) ) ).
tt(t4_jct_misc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_borsuk_1 A B))) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_pre_topc E A) &  ((v3_pre_topc F B) &  ((r2_hidden D (k3_borsuk_1 A B E F)) & (r1_tarski (k3_borsuk_1 A B E F) C)) ) ) ) ) ) ) ) ) ) ) )  => (v3_pre_topc C (k2_borsuk_1 A B))) ) ) ) ) ) ) ).
tt(t4_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) => (m2_finseq_1 (k2_jgraph_1 B) (u4_struct_0 (k1_jgraph_1 A)))) ) ) ) ).
tt(t4_jgraph_2,ax, ((k22_euclid 2) = (k10_finseq_1 1 1)) ).
tt(t4_jgraph_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ( (~  (A = (k4_struct_0 (k15_euclid 2))) )  =>  ( ( ( ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A)))  |  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = (k19_euclid (k10_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))) (k10_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k17_euclid A) (k18_euclid A)))))))) )  &  (~  ( (~  ((r1_xxreal_0 (k17_euclid A) (k18_euclid A)) & (r1_xxreal_0 (k1_real_1 (k18_euclid A)) (k17_euclid A))) )  &  ( (~  ((r1_xxreal_0 (k18_euclid A) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k1_real_1 (k18_euclid A)))) )  &  (~  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) k1_jgraph_3 A) = (k19_euclid (k10_real_1 (k17_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))) (k10_real_1 (k18_euclid A) (k7_square_1 (k7_real_1 1 (k5_square_1 (k10_real_1 (k18_euclid A) (k17_euclid A)))))))) ) ) ) ) ) ) ) ) ).
tt(t4_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (~  (E = k6_numbers) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C F) = k6_numbers) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ((v1_xreal_0 I) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B G) = H)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C G) = I) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) F G) = (k13_complex1 (k6_xcmplx_0 (k13_complex1 H I) D) E)) ) ) ) ) ) ) )  & (v5_pre_topc F A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jgraph_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B 1) &  (C = (k1_rcomp_1 A B)) ) ) )  =>  ((k4_topmetr A B) = (k1_pre_topc k5_topmetr C)) ) ) ) ) ) ) ) ).
tt(t4_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k5_topmetr))) =>  ( (C = (k1_rcomp_1 A B))  => (v4_pre_topc C k5_topmetr)) ) ) ) ) ) ) ).
tt(t4_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 D (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) &  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) & (r1_xxreal_0 (k17_euclid B) C)) ) )  =>  ((r1_xxreal_0 C (k17_euclid A)) |  ((r1_xxreal_0 (k18_euclid B) D) | (r1_jordan6 (k1_sppol_2 (k17_euclid A) C D (k18_euclid B)) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jgraph_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_borsuk_2 G (k15_euclid 2) C D) =>  (! [H:$i] :  ((m1_borsuk_2 H (k15_euclid 2) E F) =>  (~  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) = A)  &  ( ((k2_relset_1 (u1_struct_0 (k15_euclid 2)) H) = B)  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden I A) =>  ((r1_xxreal_0 (k17_euclid C) (k17_euclid I)) & (r1_xxreal_0 (k17_euclid I) (k17_euclid D))) ) ) )  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden I B) =>  ((r1_xxreal_0 (k17_euclid C) (k17_euclid I)) & (r1_xxreal_0 (k17_euclid I) (k17_euclid D))) ) ) )  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden I A) =>  ((r1_xxreal_0 (k18_euclid E) (k18_euclid I)) & (r1_xxreal_0 (k18_euclid I) (k18_euclid F))) ) ) )  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden I B) =>  ((r1_xxreal_0 (k18_euclid E) (k18_euclid I)) & (r1_xxreal_0 (k18_euclid I) (k18_euclid F))) ) ) )  & (r2_subset_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ((v2_connsp_1 E (k15_euclid 2)) &  ((v2_compts_1 E (k15_euclid 2)) &  ( (~ (v1_sppol_1 E))  &  ( (~ (v2_sppol_1 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k1_jordan9 E B))) &  ((r2_hidden (k4_tarski C D) (k2_matrix_1 (k1_jordan8 E B))) &  ((r2_hidden (k4_tarski (k2_nat_1 C 1) D) (k2_matrix_1 (k1_jordan8 E B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) (k2_nat_1 C 1) D))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 E B) (k2_nat_1 A 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C D))  & (r1_xxreal_0 (k1_matrix_1 (k1_jordan8 E B)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan1h B A) =>  ((k3_jordan1h B A) = (k7_real_1 (k8_real_1 (k13_newton 2 (k7_nat_d A (k1_jordan11 B))) (k9_real_1 (k3_jordan1h B (k1_jordan11 B)) 2)) 2)) ) ) ) ) ) ).
tt(t4_jordan12,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) &  ((v1_goboard5 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)) & (r1_xxreal_0 2 (k3_finseq_1 B))) )  =>  ((v2_topreal1 A) & (v3_topreal1 A)) ) ) ) ) ) ).
tt(t4_jordan14,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 (k2_nat_1 D 1) (k1_matrix_1 A))) ) )  =>  ((r2_hidden B (k1_tops_1 (k15_euclid 2) (k3_goboard5 A C D))) <=>  ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D))))  &  ( (~ (r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 C 1) D)) (k17_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C D))))  &  (~ (r1_xxreal_0 (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A C (k2_nat_1 D 1))) (k18_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan15,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_rcomp_1 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 A))) ) ).
tt(t4_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) => (r2_hidden B (k4_jordan6 A C D B))) ) ) ) ) ) ) ) ) ).
tt(t4_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A (k22_pscomp_1 A) B) => (r2_hidden B (k9_jordan6 A))) ) ) ) ) ).
tt(t4_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k6_topreal1 A)))) ) ).
tt(t4_jordan19,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A B))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C D) (k3_topreal1 2 (k1_jordan9 A B))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C (k1_matrix_1 (k1_jordan8 A B))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C D)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k16_pscomp_1 A)) =>  ((k17_euclid B) = (k8_pscomp_1 A)) ) ) ) ) ) ).
tt(t4_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((v2_connsp_1 C A) & (v2_connsp_1 D A)) )  =>  ((r1_xboole_0 B C) |  ((r1_xboole_0 C D) | (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan1b,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k3_topreal1 2 A)))  =>  ((k1_funct_1 (k2_jordan3 A B) (k3_finseq_1 (k2_jordan3 A B))) = (k1_funct_1 A (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t4_jordan1c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ( (C = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) A B))  & (v3_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B)))  =>  ((v1_xboole_0 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 B)) |  ((k6_pscomp_1 C) = (k3_xxreal_0 (k6_pscomp_1 A) (k6_pscomp_1 B))) ) ) ) ) ) ) ) ) ).
tt(t4_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((r1_xxreal_0 2 A) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 E B))) &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 (k1_jordan8 E (k2_nat_1 B 1))))) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 E B)) A) |  ((k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E B) C A)) = (k18_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 E (k2_nat_1 B 1)) D (k7_nat_d (k4_nat_1 2 A) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan1e,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B (k3_topreal1 2 A)) & (r1_xxreal_0 2 (k3_finseq_1 (k3_jordan3 A B))))  => (r2_hidden (k1_funct_1 A 1) (k3_topreal1 2 (k3_jordan3 A B)))) ) ) ) ) ).
tt(t4_jordan1f,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v3_relat_1 E))  &  ((v1_matrix_1 E) &  ((v2_goboard1 E) &  ((v3_goboard1 E) &  ((v4_goboard1 E) &  ((v5_goboard1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (~  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) D E) &  ( (~ (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C B)) (k3_topreal1 2 D)))  &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 E)) &  ((r2_hidden (k4_tarski C B) (k2_matrix_1 E)) &  ((r1_xxreal_0 A C) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~  ((r1_xxreal_0 A F) &  ((r1_xxreal_0 F C) &  ((k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E F B)) = (k4_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) E C B)) (k3_topreal1 2 D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e B A) (k1_jordan8 B A))) ) ) ) ).
tt(t4_jordan1h,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden (k4_tarski A B) k1_jordan1h) => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t4_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) =>  ((k5_goboard5 A (k4_finseq_4 A B)) = (k5_goboard5 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A B) 1)) ) ) ) ) ) ).
tt(t4_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k1_jordan1e B A) = (k2_finseq_5 (u1_struct_0 (k15_euclid 2)) (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A)))) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))))) ) ) ) ) ).
tt(t4_jordan1k,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((v2_funct_1 C) => (r1_tarski (k7_relset_1 A B C (k3_subset_1 A D)) (k3_subset_1 B (k7_relset_1 A B C D)))) ) ) ) ) ) ) ) ).
tt(t4_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (~ (r1_xxreal_0 D (k17_euclid A)))  &  ( (~ (r1_xxreal_0 D (k17_euclid B)))  & (r1_xxreal_0 D (k17_euclid C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan21,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_2_jordan21 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t4_jordan22,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((v2_compts_1 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k2_jordan19 A) B) (k15_euclid 2)) & (v2_connsp_1 (k3_funct_2 k5_numbers (k9_setfam_1 (u1_struct_0 (k15_euclid 2))) (k2_jordan19 A) B) (k15_euclid 2))) ) ) ) ) ).
tt(t4_jordan23,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_jordan23 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 B)) &  ((k7_partfun1 A B C) = (k7_partfun1 A B D)) ) )  =>  ( ( (C = 1)  &  (D = (k3_finseq_1 B)) )  |  ( ( (C = (k3_finseq_1 B))  &  (D = 1) )  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan24,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_jordan24 2 C A B) => (r1_jordan24 2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 D) C) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 D) A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 D) B))) ) ) ) ) ) ) ) ) ).
tt(t4_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k2_finseq_1 A)) =>  ((k7_partfun1 k1_numbers (k4_algstr_0 (k15_euclid A) B) C) = (k1_real_1 (k7_partfun1 k1_numbers B C))) ) ) ) ) ) ) ) ).
tt(t4_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 2 B) & (v4_topreal1 A))  => (v4_topreal1 (k17_finseq_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(t4_jordan4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 B A) &  ((k4_nat_d B A) = k6_numbers) )  =>  ((r1_xxreal_0 B k6_numbers) |  (B = A) ) ) ) ) ) ) ).
tt(t4_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_borsuk_2 C (k15_euclid 2) A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_compts_1 D) & (m1_pre_topc D (k15_euclid 2))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 D))))) )  =>  ( ((v2_funct_1 C) &  ((r1_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 D) (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) E C) &  ((k2_struct_0 D) = (k2_relset_1 (u1_struct_0 (k15_euclid 2)) C)) ) )  => (v3_tops_2 E k5_topmetr D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan5b,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_hidden A (u1_struct_0 k17_borsuk_1)) => (r2_hidden (k9_real_1 1 A) (u1_struct_0 k17_borsuk_1))) ) ) ).
tt(t4_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ( ((r2_hidden E A) &  ( ((k1_funct_1 F G) = E)  &  ((v3_tops_2 F k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 F k6_numbers) = C)  &  ( ((k1_funct_1 F 1) = D)  &  ((r1_xxreal_0 k6_numbers G) &  ((r1_xxreal_0 G 1) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ((r1_xxreal_0 H 1) &  ( (~ (r1_xxreal_0 H G))  & (r2_hidden (k1_funct_1 F H) B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))))) )  =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((v3_tops_2 H k5_topmetr (k1_pre_topc (k15_euclid 2) A)) &  ( ((k1_funct_1 H k6_numbers) = C)  &  ( ((k1_funct_1 H 1) = D)  &  ( ((k1_funct_1 H I) = E)  &  ((r1_xxreal_0 k6_numbers I) & (r1_xxreal_0 I 1)) ) ) ) )  =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (~  ((r1_xxreal_0 J 1) &  ( (~ (r1_xxreal_0 J I))  & (r2_hidden (k1_funct_1 H J) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan5d,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((r2_hidden A (k10_xtuple_0 B)) =>  ((r1_xxreal_0 (k1_funct_1 (k28_seq_4 B) 1) A) & (r1_xxreal_0 A (k1_funct_1 (k28_seq_4 B) (k3_finseq_1 (k28_seq_4 B))))) ) ) ) ) ) ).
tt(t4_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_0_jordan6 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t4_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((v1_topreal2 A) =>  ( ((k1_jordan7 A (k18_pscomp_1 A) (k22_pscomp_1 A)) = (k8_jordan6 A))  &  ((k1_jordan7 A (k22_pscomp_1 A) (k18_pscomp_1 A)) = (k9_jordan6 A)) ) ) ) ) ).
tt(t4_jordan8,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) =>  ((v2_goboard5 B) & (v1_topreal1 B)) ) ) ) ) ) ).
tt(t4_jordan9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (~  ((r2_hidden A (k4_finseq_1 (k4_finseq_5 B C))) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden D (k4_finseq_1 C)) &  ( ((k2_nat_1 A D) = (k2_nat_1 (k3_finseq_1 C) 1))  &  ((k7_partfun1 B (k4_finseq_5 B C) A) = (k7_partfun1 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan_a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers) &  ((v1_pscomp_1 D (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers)))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid A)) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 k1_numbers)) &  ( (G = (a_4_1_jordan_a A B D F))  &  ((k3_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers E F) = (k5_seq_4 G)) ) ) ) ) )  =>  ((k5_seq_4 (k7_relset_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid A) (k15_euclid A))) k1_numbers D (k3_borsuk_1 (k15_euclid A) (k15_euclid A) B C))) = (k5_seq_4 (k7_relset_1 (u1_struct_0 (k15_euclid A)) k1_numbers E C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ((v2_sppol_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v2_sppol_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ).
tt(t4_knaster,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  => (r2_abian (k9_setfam_1 A) (k1_knaster A B) B)) ) ) ).
tt(t4_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  (! [E:$i] :  ((m2_subset_1 E B D) =>  (! [F:$i] :  ( ((v5_relat_1 F B) &  ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k9_setfam_1 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ( ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H B D) =>  ((k3_funct_2 B k1_numbers C (k5_prob_1 A B (k1_prob_2 A B F G) H)) = (k3_xcmplx_0 (k3_funct_2 B k1_numbers C (k1_prob_2 A B F G)) (k3_funct_2 B k1_numbers C H))) ) ) ) )  & (v1_prob_2 F))  =>  ((k1_funct_1 C (k9_subset_1 A E (k1_prob_1 A F))) = (k3_xcmplx_0 (k3_funct_2 B k1_numbers C E) (k1_funct_1 C (k1_prob_1 A F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((r2_hidden C (k3_kurato_0 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) => (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 A) B (k2_nat_1 D E)))) ) ) ) ) ) ) ) ) ).
tt(t4_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden (k3_subset_1 (u1_struct_0 A) B) (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)) (k2_kurato_1 A B)) &  ((r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))) (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))) (k2_kurato_1 A B)) &  ((r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))) (k2_kurato_1 A B)) &  ((r2_hidden (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B)))))) (k2_kurato_1 A B)) & (r2_hidden (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) (k2_pre_topc A (k3_subset_1 (u1_struct_0 A) B))))))) (k2_kurato_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t4_kurato_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r2_hidden B (k2_pre_topc (k15_euclid A) C)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (~  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid A)) D) C) &  ((v3_toprns_1 D A) &  ((k6_toprns_1 A D) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_lang1 A (k3_pre_poly (u1_struct_0 A) B) C) => (r1_lang1 A B C)) ) ) ) ) ) ) ).
tt(t4_laplace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 1))  =>  ((k1_matrix_1 B) = (k1_matrix_1 (k8_matrix_2 A C B))) ) ) ) ) ) ) ) ).
tt(t4_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (D = (k2_xboole_0 (u1_struct_0 B) (u1_struct_0 C)))  => (r1_group_2 A (k8_group_4 A B C) (k5_group_4 A D))) ) ) ) ) ) ) ) ) ).
tt(t4_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) &  ((r2_hidden C (u1_struct_0 A)) &  ((r2_hidden D (u1_struct_0 A)) &  ((r1_latsum_1 A B) & (v4_orders_2 A)) ) ) )  => (r2_hidden (k4_tarski C D) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(t4_lattice2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k7_funct_4 A B (k2_partfun1 A B D C) E) = E) ) ) ) ) ) ) ) ) ) ).
tt(t4_lattice3,ax, (! [A:$i] :  ((v14_lattices (k1_lattice3 A)) &  ((k6_lattices (k1_lattice3 A)) = A) ) ) ).
tt(t4_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_lattice4 E A B) =>  ((r3_lattices A C D) => (r3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lattice5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden B (u1_struct_0 (k1_lattice5 A))) <=>  ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(t4_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v2_lattice6 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r3_lattices A C B) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r3_lattices A C D) & (r1_lattice6 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ( (C = D)  <=>  ((k1_lattice7 A C) = (k1_lattice7 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v17_waybel_0 C A B) & (v18_waybel_0 C A B))  =>  ((v19_waybel_0 C A B) & (v20_waybel_0 C A B)) ) ) ) ) ) ) ) ).
tt(t4_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_lattices A B C) <=>  ((k2_lattices A B C) = B) ) ) ) ) ) ) ) ).
tt(t4_lexbfs,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A C) => (r1_tarski (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 B) (k2_finseq_1 (k7_nat_d B A))) (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 B) (k2_finseq_1 (k7_nat_d B C))))) ) ) ) ) ) ) ).
tt(t4_lfuzzy_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A B C) = (k2_lfuzzy_0 A B C)) ) ) ) ) ) ) ).
tt(t4_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 B B)) ) ) ) ).
tt(t4_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (? [C:$i] :  ((m1_rcomp_1 C B) & (r1_tarski (k7_subset_1 k1_numbers C (k1_tarski B)) (k1_relset_1 k1_numbers A))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B C))  &  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E C))  &  ( (~ (r1_xxreal_0 B E))  &  ((r2_hidden E (k1_relset_1 k1_numbers A)) &  ( (~ (r1_xxreal_0 D F))  &  ( (~ (r1_xxreal_0 F B))  & (r2_hidden F (k1_relset_1 k1_numbers A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~ (r1_xxreal_0 (k2_seq_2 A) k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k1_seq_1 A C) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t4_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski (k2_rcomp_1 B (k7_real_1 B A)) (k1_relset_1 k1_numbers C)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D B))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E B))  & (r2_hidden E (k1_relset_1 k1_numbers C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 B A) (k7_real_1 B A)) (k1_tarski B)) = (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 B A) B) (k2_rcomp_1 B (k7_real_1 B A)))) ) ) ) ) ) ).
tt(t4_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  ((v5_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  => (v5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t4_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v1_lmod_5 (k7_domain_1 (u1_struct_0 B) C D) A B) =>  ( ((k4_struct_0 A) = (k5_struct_0 A))  |  ( (~  (C = (k4_struct_0 B)) )  &  (~  (D = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (m1_vectsp_4 B A (k2_vectsp_4 A B))) ) ) ) ).
tt(t4_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v7_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v1_mod_3 C A B) &  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_funct_2 D A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_funct_2 E A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) D E)) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_lopban_1 B A A) &  ((v2_lopban_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_lopban_1 C A A) &  ((v2_lopban_1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 D A A) &  ((v1_lopban_1 D A A) &  ((v2_lopban_1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) D (k1_lopban_2 A C B)) <=>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D E) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 C A) => (v3_normsp_1 (k2_lopban_3 A C B) A)) ) ) ) ) ) ) ).
tt(t4_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) &  ((v2_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((r5_nfcont_1 A B (u1_struct_0 A) C) &  ((r3_nfcont_1 A B C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_nfcont_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k7_rusub_4 A D E)) = (k7_rusub_4 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)))) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k1_lattices (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)) B C) = (k2_lopclset A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v1_lpspace1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)))) =>  ( ( (E = C)  &  (F = D) )  =>  ((k1_algstr_0 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)) E F) = (k1_algstr_0 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B k6_numbers) | (r1_xxreal_0 k6_numbers (k4_power A B))) ) ) ) ) ) ).
tt(t4_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) => (v1_rlsub_1 (k2_lp_space A) k7_rsspace)) ) ) ).
tt(t4_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (~  ( (~  (A = k2_hilbert1) )  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~  (A = (k1_hilbert2 B)) )  &  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  ( (~  (A = (k3_hilbert1 C D)) )  &  (! [E:$i] :  ((m1_subset_1 E k1_hilbert1) =>  (! [F:$i] :  ((m1_subset_1 F k1_hilbert1) =>  (~  (A = (k4_hilbert1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B B) (k4_cqc_the1 A))) ) ) ) ).
tt(t4_margrel1,ax, (! [A:$i] : (m2_margrel1 k1_xboole_0 A)) ).
tt(t4_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = k1_xboole_0)  =>  ((k1_mathmorp A B C) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t4_matrix10,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k1_numbers)))  =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 D)) =>  ((k3_matrix_1 k1_numbers (k7_matrixr1 A D) B C) = (k8_real_1 A (k3_matrix_1 k1_numbers D B C))) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))))) =>  ( (! [E:$i] :  ((r2_hidden E D) =>  ((k1_funct_1 (k1_matrix11 A B C) E) = (k1_group_1 B)) ) )  =>  ((k7_setwiseo (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B) (u2_algstr_0 B) D (k1_matrix11 A B C)) = (k1_group_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) A B) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 E) A B) =>  ( ((r2_hidden C (k4_finseq_1 G)) &  ((r2_hidden D (k4_finseq_1 G)) &  (H = (k2_matrix12 A B E G C F)) ) )  =>  ( ( (D = C)  =>  ((k8_matrix_1 (u1_struct_0 E) H D) = (k10_fvsum_1 (k1_matrix_1 G) E (k8_matrix_1 (u1_struct_0 E) G C) F)) )  &  ( (~  (D = C) )  =>  ((k8_matrix_1 (u1_struct_0 E) H D) = (k8_matrix_1 (u1_struct_0 E) G D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_2 B (k12_matrix_2 A)) =>  ( (~  (B = (k1_finseq_2 A)) )  =>  ( (? [C:$i] :  ((v7_ordinal1 C) &  ((r2_hidden C (k2_finseq_1 A)) &  (~ (r1_xxreal_0 (k1_funct_1 B C) C)) ) ) )  &  (? [C:$i] :  ((v7_ordinal1 C) &  ((r2_hidden C (k2_finseq_1 A)) &  (~ (r1_xxreal_0 C (k1_funct_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l4_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k4_finseq_1 (k11_fvsum_1 A B C))) =>  ( ((k1_funct_1 (k11_fvsum_1 A B C) D) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) C D)))  &  ((k7_partfun1 (u1_struct_0 A) (k11_fvsum_1 A B C) D) = (k6_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k9_fvsum_1 A (k8_finseq_1 (u1_struct_0 A) B C) D) = (k8_finseq_1 (u1_struct_0 A) (k9_fvsum_1 A B D) (k9_fvsum_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t4_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m1_matrix_1 D B A A) =>  ((r1_matrix16 B D C) =>  ((r1_xxreal_0 A k6_numbers) |  (C = (k8_matrix_1 B D 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix17 (u1_struct_0 B) D C) => (r1_matrix17 (u1_struct_0 B) (k1_matrix_6 A B D) (k5_fvsum_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t4_matrix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ( ((k3_finseq_1 B) = A)  &  ((k3_finseq_1 C) = A) )  => (v1_matrix_1 (k10_finseq_1 B C))) ) ) ) ) ) ) ).
tt(t4_matrix_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski 1 1) (k2_matrix_1 (k3_matrix_2 A B C D))) &  ((r2_hidden (k4_tarski 1 2) (k2_matrix_1 (k3_matrix_2 A B C D))) &  ((r2_hidden (k4_tarski 2 1) (k2_matrix_1 (k3_matrix_2 A B C D))) & (r2_hidden (k4_tarski 2 2) (k2_matrix_1 (k3_matrix_2 A B C D)))) ) ) ) ) ) ) ).
tt(t4_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  ((k3_matrix_3 C D (k1_matrix_3 C A B)) = D) ) ) ) ) ) ) ) ) ).
tt(t4_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k3_matrix_3 A B D) = (k3_matrix_3 A C D)) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 k1_complfld))))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 k1_complfld))))  =>  ( ((k2_matrix_5 A) = (k2_matrix_5 B))  =>  (A = B) ) ) ) ) ) ).
tt(t4_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((r1_matrix_6 A B C D) &  ((r1_matrix_6 A B D E) & (r1_matrix_6 A B C E)) )  => (r1_matrix_6 A B C (k4_matrix_6 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrix_7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) &  ((v3_funct_2 A (k2_finseq_1 2) (k2_finseq_1 2)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 2) (k2_finseq_1 2))))) ) )  =>  ((v4_matrix_2 A 2) =>  (A = (k10_finseq_1 2 1)) ) ) ) ).
tt(t4_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v3_matrix_8 C A B) => (v1_matrix_6 C A B)) ) ) ) ) ) ) ).
tt(t4_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_hidden (k3_finseq_5 (k1_finseq_2 A)) (k12_matrix_2 A))) ) ).
tt(t4_matrixc1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 k2_numbers)))  =>  ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) =>  ((k3_matrix_1 k2_numbers (k7_matrix_5 C D) A B) = (k5_binop_2 C (k3_matrix_1 k2_numbers D A B))) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  ((r2_hidden A (k2_finseq_1 (k1_nat_1 B 1))) =>  ((k4_wsierp_1 C A (k5_finseq_2 C (k1_nat_1 B 1) D)) = (k5_finseq_2 C B D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ( (A = B)  |  ((k8_matrix_1 (u1_struct_0 C) (k2_matrixj2 C D B) A) = (k4_fvsum_1 (k1_matrix_1 (k12_matrix_1 C B)) C (k10_fvsum_1 (k1_matrix_1 (k12_matrix_1 C B)) C (k8_matrix_1 (u1_struct_0 C) (k12_matrix_1 C B) A) D) (k8_matrix_1 (u1_struct_0 C) (k12_matrix_1 C B) (k1_nat_1 A 1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_rvsum_1 A B) = (k4_rvsum_1 A (k6_rvsum_1 B))) ) ) ) ) ) ).
tt(t4_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( ((k3_finseq_1 (k6_matrixr1 B C)) = (k3_finseq_1 B))  &  ( ((k1_matrix_1 (k6_matrixr1 B C)) = (k1_matrix_1 C))  &  ( ((k3_finseq_1 (k6_matrixr1 B C)) = A)  &  ((k1_matrix_1 (k6_matrixr1 B C)) = A) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrlin C A (k2_vectsp_4 A B)) => (m1_matrlin C A B)) ) ) ) ) ) ).
tt(t4_matrlin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( (~  (A = k1_xboole_0) )  =>  (A = (k7_finseq_1 (k2_finseq_3 (k3_finseq_1 A) A) (k9_finseq_1 (k1_funct_1 A (k3_finseq_1 A))))) ) ) ) ).
tt(t4_matroid0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  & (l1_pre_topc A)) )  =>  ((v2_matroid0 A) <=>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc B A) &  ((v3_pre_topc C A) &  ( ((k5_card_1 C) = (k2_nat_1 (k5_card_1 B) 1))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k7_subset_1 (u1_struct_0 A) C B)) & (v3_pre_topc (k4_subset_1 (u1_struct_0 A) B (k6_domain_1 (u1_struct_0 A) D)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((r1_xxreal_0 1 (k3_finseq_1 A)) &  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((k3_funct_2 k5_numbers k1_numbers B 1) = (k1_seq_1 A 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (k6_numbers = C) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  (~  ((k3_funct_2 k5_numbers k1_numbers B (k23_binop_2 C 1)) = (k9_binop_2 (k1_seq_1 B C) (k1_seq_1 A (k23_binop_2 C 1)))) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 A C) (k1_seq_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t4_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k1_partfun3 (k39_valued_1 A)) = (k3_euclid A)) ) ) ).
tt(t4_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A))) =>  ( (C = B)  =>  ((k4_rlvect_1 (k15_euclid A) B) = (k4_rlvect_1 (k6_prvect_1 k2_vectsp_1 A) C)) ) ) ) ) ) ) ) ).
tt(t4_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k12_matrix_3 B k2_vectsp_1 (k1_matrtop3 B A)) = (k4_algstr_0 k2_vectsp_1 (k5_struct_0 k2_vectsp_1))) ) ) ) ) ) ).
tt(t4_mazurulm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_algstr_0 A (k3_rlvect_1 A B C) C) = B) ) ) ) ) ) ) ).
tt(t4_mboolean,ax, (! [A:$i] :  (! [B:$i] : (r6_pboole A (k1_mboolean A (k7_funcop_1 A (k1_tarski B))) (k7_funcop_1 A (k2_tarski k1_xboole_0 (k1_tarski B))))) ) ).
tt(t4_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  ( ((k6_setfam_1 A B) = (k6_subset_1 A (k5_setfam_1 A (k7_setfam_1 A B))))  &  ((k5_setfam_1 A B) = (k6_subset_1 A (k6_setfam_1 A (k7_setfam_1 A B)))) ) ) ) ) ).
tt(t4_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  &  ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 B D (k2_nat_1 E 1)) = (k1_measure1 A B (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B C k6_numbers) = k1_xboole_0)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B C (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B D k6_numbers) (k8_nat_1 B D E)))  & (r1_tarski (k8_nat_1 B D (k2_nat_1 E 1)) (k8_nat_1 B D E))) ) ) )  =>  ((k2_measure2 A B (k1_measure3 A B C)) = (k3_measure1 A B (k8_nat_1 B D k6_numbers) (k1_measure2 A B (k1_measure3 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t4_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) => (r1_xxreal_0 (k12_supinf_2 B (k4_subset_1 A C D)) (k3_supinf_2 (k12_supinf_2 B C) (k12_supinf_2 B D)))) ) ) ) ) ) ) ).
tt(t4_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((m1_subset_1 D k7_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  ( (~ (r1_xxreal_0 D B))  &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D k1_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_measure6,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (~  ( (~ (r1_xxreal_0 A k1_supinf_2))  &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k12_supinf_2 B C) k1_supinf_2)) ) )  &  (~ (r1_xxreal_0 A (k19_supinf_2 B))) ) ) ) ) ) ) ) ) ).
tt(t4_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k12_supinf_2 A D) = (k3_supinf_2 (k12_supinf_2 B D) (k12_supinf_2 C D))) ) )  &  ((v6_supinf_2 B) & (v6_supinf_2 C)) )  => (r1_xxreal_0 (k19_supinf_2 A) (k3_supinf_2 (k19_supinf_2 B) (k19_supinf_2 C)))) ) ) ) ) ) ) ).
tt(t4_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_measure8 D A B) => (v6_supinf_2 (k2_measure8 A B C D))) ) ) ) ) ) ) ).
tt(t4_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( ((k4_member_1 A) = (k4_member_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t4_membered,ax, (! [A:$i] :  ((v4_membered A) => (r1_tarski A k3_numbers)) ) ).
tt(t4_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((l1_memstr_0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  => (r1_xboole_0 (k1_tarski (k4_struct_0 B)) (k9_xtuple_0 (k6_memstr_0 A B C)))) ) ) ) ) ) ).
tt(t4_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k17_euclid (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A C) (k1_rlvect_1 (k15_euclid 2) B D))) = (k9_binop_2 (k11_binop_2 C (k17_euclid A)) (k11_binop_2 D (k17_euclid B))))  &  ((k18_euclid (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) A C) (k1_rlvect_1 (k15_euclid 2) B D))) = (k9_binop_2 (k11_binop_2 C (k18_euclid A)) (k11_binop_2 D (k18_euclid B)))) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 B (k12_supinf_2 A C))) )  => (r1_xxreal_0 B (k2_rinfsup2 A))) ) ) ) ) ).
tt(t4_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A k1_numbers (k32_valued_1 A k1_numbers (k6_comseq_3 A B)) (k5_comseq_3 A (k25_valued_1 A k2_numbers B k7_complex1))) & (r2_relset_1 A k1_numbers (k5_comseq_3 A B) (k6_comseq_3 A (k25_valued_1 A k2_numbers B k7_complex1)))) ) ) ) ) ).
tt(t4_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfun7c A B) C)) = (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k4_mesfun7c A B) C))) =>  ((k12_supinf_2 (k4_mesfunc5 A k7_numbers (k4_mesfun7c A B) C) D) = (k12_supinf_2 (k3_rinfsup2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B D))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_mesfunc8 D A k1_numbers) &  ((r1_tarski C (k1_relset_1 A (k4_mesfunc5 A k1_numbers D k6_numbers))) &  (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers D F) C)) ) ) )  => (r1_mesfunc6 A B (k4_mesfunc5 A k1_numbers (k1_mesfun9c A k1_numbers D C) E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_tarski k4_numbers (k2_mesfunc1 (k1_nat_1 A 1)))) ) ).
tt(t4_mesfunc2,ax, (? [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k3_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k3_numbers)))) )  &  ((v2_funct_1 A) &  ( ((k1_relset_1 k5_numbers A) = k5_numbers)  &  ((k2_relset_1 k3_numbers A) = k3_numbers) ) ) ) ) ).
tt(t4_mesfunc3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v1_prob_2 B) <=>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k4_finseq_1 B)) & (r2_hidden D (k4_finseq_1 B)))  =>  ( (C = D)  | (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (~  ((r1_mesfunc2 A B C) &  ( (~  ((k9_xtuple_0 C) = k1_xboole_0) )  &  ( (! [E:$i] :  ((r2_hidden E (k9_xtuple_0 C)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 C E))) )  &  (! [E:$i] :  ( ((v1_prob_2 E) & (m2_finseq_1 E B))  =>  (! [F:$i] :  ((m2_finseq_1 F k7_numbers) =>  (! [G:$i] :  ((m2_finseq_1 G k7_numbers) =>  (~  ((r1_mesfunc3 A B C E F) &  ( ((k4_finseq_1 G) = (k4_finseq_1 E))  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k12_supinf_2 G H) = (k1_extreal1 (k12_supinf_2 F H) (k12_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E D) H))) ) ) )  &  ((k1_mesfunc3 A B D C) = (k4_extreal1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ((r1_xxreal_0 k6_numbers B) &  ( (~ (r1_xxreal_0 A B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k8_real_1 (k2_newton 2 A) A)) &  ((r1_xxreal_0 (k10_real_1 (k5_real_1 C 1) (k2_newton 2 A)) B) &  (~ (r1_xxreal_0 (k6_real_1 C (k2_newton 2 A)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((r2_hidden D (k12_mesfunc1 B C)) <=>  ((r2_hidden D (k1_relset_1 A B)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (E = (k1_seq_1 B D))  & (r1_xxreal_0 E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ((r1_mesfunc5 A B C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (~  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers B E F) = (k9_subset_1 A (k1_relset_1 A D) (k18_mesfunc1 A (k10_mesfunc1 A D) (k1_measure6 (k10_real_1 1 (k2_nat_1 F 1)))))) ) )  &  ( ((k7_subset_1 A (k1_relset_1 A D) (k19_mesfunc1 A D k1_supinf_2)) = (k3_tarski (k2_relset_1 B E)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden (k3_funct_2 k5_numbers B E F) B) &  (~ (r1_xxreal_0 k1_supinf_1 (k12_supinf_2 C (k3_funct_2 k5_numbers B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (~  ( (~ (r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C (k3_card_3 D))))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (~  ((r1_funct_2 k5_numbers B k5_numbers (k9_setfam_1 A) E (k6_setlim_1 A B D)) &  ((k12_supinf_2 C (k4_kurato_0 A D)) = (k7_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v4_mesfunc5 B) & (v4_mesfunc5 C))  => (v4_mesfunc5 (k3_mesfunc1 A B C))) ) ) ) ) ) ) ).
tt(t4_metric_1,ax, (! [A:$i] :  ((l1_metric_1 A) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k2_metric_1 A B D) (k7_real_1 (k2_metric_1 A B C) (k2_metric_1 A C D)))) ) ) ) ) )  <=> (v9_metric_1 A)) ) ) ).
tt(t4_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k1_metric_2 A B))) ) ) ) ).
tt(t4_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ( ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k4_metric_3 A B C) D E) = k6_numbers)  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_metric_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_metric_1 A) &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) ) )  =>  ((v2_metric_1 (u1_metric_1 A) (u1_struct_0 A)) &  ((v3_metric_1 (u1_metric_1 A) (u1_struct_0 A)) &  ((v4_metric_1 (u1_metric_1 A) (u1_struct_0 A)) & (v5_metric_1 (u1_metric_1 A) (u1_struct_0 A))) ) ) ) ) ).
tt(t4_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ((r1_borsuk_3 A B) =>  ((k2_waybel23 A) = (k2_waybel23 B)) ) ) ) ) ) ).
tt(t4_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((u1_struct_0 (k1_mfold_1 A B C)) = (k1_topreal9 A B C)) ) ) ) ) ) ) ).
tt(t4_mfold_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k1_pre_topc A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) (u1_struct_0 (k1_pre_topc B C))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C))) (u1_struct_0 (k1_pre_topc B C)))))) )  =>  ( (E = (k6_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))  => (v3_tops_2 E (k1_pre_topc A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C)) (k1_pre_topc B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_midsp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k2_midsp_1)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k2_midsp_1)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k2_midsp_1)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_midsp_1)) =>  ( ((k1_midsp_1 k2_midsp_1 A A) = A)  &  ( ((k1_midsp_1 k2_midsp_1 A B) = (k1_midsp_1 k2_midsp_1 B A))  &  ( ((k1_midsp_1 k2_midsp_1 (k1_midsp_1 k2_midsp_1 A B) (k1_midsp_1 k2_midsp_1 C D)) = (k1_midsp_1 k2_midsp_1 (k1_midsp_1 k2_midsp_1 A C) (k1_midsp_1 k2_midsp_1 B D)))  &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 k2_midsp_1)) &  ((k1_midsp_1 k2_midsp_1 E A) = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l2_algstr_0 D)) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) (u1_struct_0 D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 D))))) )  =>  ((r1_midsp_2 A D E) =>  ((k2_binop_1 A A (u1_struct_0 D) E B C) = (k4_algstr_0 D (k2_binop_1 A A (u1_struct_0 D) E C B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A B))  &  ( (~  (A = (k2_nat_1 B 1)) )  &  (~ (r1_xxreal_0 (k2_nat_1 B 2) A)) ) ) ) ) ) ) ) ).
tt(t4_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r1_tarski (k4_mmlquery A C B) B)) ) ) ) ) ).
tt(t4_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_mod_2 B A) & (l1_mod_2 B A))  =>  ((v13_vectsp_1 (u3_mod_2 A B) (u1_mod_2 A B) (u2_mod_2 A B)) & (v1_mod_2 (u3_mod_2 A B) A (u1_mod_2 A B) (u2_mod_2 A B))) ) ) ) ) ).
tt(t4_mod_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r1_struct_0 (k1_mod_3 B C D) A) <=>  (? [E:$i] :  ((m2_vectsp_6 E B C D) &  (A = (k4_vectsp_6 B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_mod_4 A)))  &  ((v13_algstr_0 (k2_mod_4 A)) &  ((v36_algstr_0 (k2_mod_4 A)) &  ((v3_group_1 (k2_mod_4 A)) &  ((v4_vectsp_1 (k2_mod_4 A)) &  ((v5_vectsp_1 (k2_mod_4 A)) &  ((v2_rlvect_1 (k2_mod_4 A)) &  ((v3_rlvect_1 (k2_mod_4 A)) &  ((v4_rlvect_1 (k2_mod_4 A)) & (l6_algstr_0 (k2_mod_4 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  (~  ( (~  (A = B) )  & (r1_tarski (k12_finseq_1 k5_numbers A) (k8_finseq_1 k5_numbers (k12_finseq_1 k5_numbers B) C))) ) ) ) ) ) ) ) ).
tt(t4_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_modcat_1 B C A) & (r1_modcat_1 B D A))  =>  (C = D) ) ) ) ) ) ) ).
tt(t4_modelc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_modelc_1 A) & (l2_modelc_1 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k18_modelc_1 (u3_modelc_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k12_modelc_1 (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k12_modelc_1 (u1_struct_0 A))))) )  =>  ( ((r1_modelc_1 A B C) & (r1_modelc_1 A B D))  => (r2_funct_2 k12_modelc_1 (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(t4_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v3_modelc_2 A) =>  (A = (k3_modelc_2 (k10_modelc_2 A))) ) ) ) ).
tt(t4_modelc_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ((k17_modelc_3 B (k7_modelc_3 B) A) = k6_numbers) ) ) ) ) ).
tt(t4_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_int_2 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (~  ( (~  (A = 1) )  &  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ((r1_nat_d B A) &  (~  (B = A) ) ) ) ) ) ) ) ) ) ).
tt(t4_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_group_1 A) => (r3_binop_1 (u1_struct_0 A) (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) (u2_algstr_0 A))) ) ) ).
tt(t4_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_binop_1 C B) => (r2_funct_2 A B (k3_monoid_1 A B B B C (k3_monoid_1 A B B B C D E) F) (k3_monoid_1 A B B B C D (k3_monoid_1 A B B B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 A))  =>  ((k1_morph_01 A C B) = C) ) ) ) ) ) ) ) ).
tt(t4_msafree1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_prob_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m2_pboole E A B C) =>  ((r2_funct_2 (k3_card_3 B) (k3_card_3 C) (k1_msafree1 A B C D) (k1_msafree1 A B C E)) => (r8_pboole A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  => (r1_xboole_0 (k2_msafree2 A) (k1_msafree2 A))) ) ).
tt(t4_msafree3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_partfun1 C (u1_struct_0 B))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden A (k1_funct_1 C D)) => (r2_hidden (k1_trees_4 (k4_tarski A D)) (k1_funct_1 (u3_msualg_1 B (k1_msafree3 B C)) D))) ) ) ) ) ) ) ) ).
tt(t4_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  => (r1_xboole_0 (k3_card_3 (k3_msafree (u1_struct_0 A) B)) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))))) ) ) ) ).
tt(t4_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ( ((v1_msalimit D A B C) & (m2_msalimit D A B C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r1_orders_2 A F E) =>  ((k1_binop_1 (k2_msalimit A B C D) F E) = (k1_binop_1 D F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_funct_1 B C)) => (m1_dtconstr (k1_trees_4 (k4_tarski D C)) (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B))) ) ) ) ) ) ) ) ).
tt(t4_msinst_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v1_msualg_6 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_msualg_6 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ( ((v1_msualg_6 E A) & (l3_msualg_1 E A))  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A E)) =>  (! [H:$i] :  ((m1_subset_1 H (k3_msualg_1 A B C)) =>  (~  ( (~  ((k3_msualg_1 A B C) = k1_xboole_0) )  &  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) &  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A E)) &  (! [I:$i] :  ((m2_pboole I (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A E)) =>  (~  ( (I = (k8_pboole F G))  &  ((k5_msualg_3 A C E B I H) = (k5_msualg_3 A D E B G (k5_msualg_3 A C D B F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = (k1_funct_1 (u1_graph_1 A) B))  &  (D = (k1_funct_1 (u2_graph_1 A) B)) )  => (r1_graph_2 A (k4_pre_poly (u1_struct_0 A) C D) (k9_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t4_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v5_msafree2 A) => (v3_msscyc_1 (k4_msscyc_2 A))) ) ) ).
tt(t4_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (! [D:$i] :  ((r2_hidden D B) => (r1_tarski C D)) )  => (r1_tarski C (k8_setfam_1 A B))) ) ) ) ) ) ).
tt(t4_mssublat,ax, (! [A:$i] :  ((k3_funct_2 k5_numbers (k3_finseq_2 (k1_tarski A)) (k7_finseq_2 A) 3) = (k11_finseq_1 A A A)) ) ).
tt(t4_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (~ (v1_xboole_0 (k1_unialg_1 A))) ) ) ).
tt(t4_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m3_pboole C (u1_struct_0 A) (u3_msualg_1 A B)) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) => (r8_pboole (u4_struct_0 A) (k4_msualg_2 A B C) (u4_msualg_1 A B))) ) ) ) ) ) ) ).
tt(t4_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  ((k8_pboole D (k2_msualg_3 A C)) = D) ) ) ) ) ) ) ) ).
tt(t4_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r1_msualg_3 A B C D) => (r3_msualg_3 A (k13_msualg_4 A B (k17_msualg_4 A B C D)) C (k19_msualg_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t4_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  => (r2_pboole A (k2_pboole A C D) (k4_msualg_5 A B C D))) ) ) ) ) ) ) ) ).
tt(t4_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) => (m1_msualg_6 (k2_msualg_3 (u1_struct_0 A) (u3_msualg_1 A B)) A B)) ) ) ) ).
tt(t4_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  ((k6_lattices (k5_msualg_5 A B)) = (k6_pboole A B B)) ) ) ) ) ).
tt(t4_msualg_8,ax, (! [A:$i] :  ((k6_lattices (k2_msualg_5 A)) = (k1_eqrel_1 A)) ) ).
tt(t4_msualg_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k8_eqrel_1 A (k1_eqrel_1 A)) = (k1_tarski A)) ) ) ).
tt(t4_msuhom_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((k6_finseq_2 B (k5_relat_1 C B)) = (k5_relat_1 (k6_finseq_2 A C) (k3_finseq_2 B))) ) ) ) ) ) ).
tt(t4_multop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_zfmisc_1 B C D E) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 B C D E) A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_zfmisc_1 B C D E) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 B C D E) A)))) )  =>  ( (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  ( ((r2_hidden H B) &  ((r2_hidden I C) &  ((r2_hidden J D) & (r2_hidden K E)) ) )  =>  ((k1_funct_1 F (k6_xtuple_0 H I J K)) = (k1_funct_1 G (k6_xtuple_0 H I J K))) ) ) ) ) )  => (r2_funct_2 (k4_zfmisc_1 B C D E) A F G)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_mycielsk,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r2_hidden F (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 A B) C) D) E)) <=>  (~  ( (~ (r2_hidden F A))  &  ( (~ (r2_hidden F B))  &  ( (~ (r2_hidden F C))  &  ( (~ (r2_hidden F D))  &  (~ (r2_hidden F E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_nagata_1 B A) => (v1_nagata_1 (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C) A)) ) ) ) ) ) ) ).
tt(t4_nagata_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers)))) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers (u1_struct_0 (k2_borsuk_1 A A)) k1_numbers B C) => (v1_pscomp_1 C (k2_borsuk_1 A A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v1_pscomp_1 (k2_nagata_2 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t4_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t4_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_nat_d A 1) = A) ) ) ).
tt(t4_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_nat_d (k1_newton C B) D) =>  ((r1_xxreal_0 B A) | (r1_nat_d (k1_newton C (k23_binop_2 A 1)) D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 B A) &  (C = (k1_int_1 (k6_real_1 A 2))) )  => (r1_xxreal_0 (k6_newton B A) (k6_newton C A))) ) ) ) ) ) ) ).
tt(t4_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_finset_1 (k1_tarski A)) & (m1_subset_1 (k1_tarski A) (k1_zfmisc_1 k5_numbers))) ) ) ).
tt(t4_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d B C))  => (r1_nat_d A C)) ) ) ) ) ) ) ).
tt(t4_nat_lat,ax, (k4_nat_lat = 1) ).
tt(t4_nattra_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 (k3_cat_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k3_cat_1 A B))) =>  (C = D) ) ) ) ) ) ) ).
tt(t4_ncfcont1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) (k1_relset_1 (u1_struct_0 B) E)) => (r2_hidden (k1_normsp_1 B D A) (k1_relset_1 (u1_struct_0 B) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ( ((r1_ncfcont2 A C D E) & (r1_ncfcont2 B C D F))  => (r1_ncfcont2 (k3_xboole_0 A B) C D (k3_vfunct_2 (u1_struct_0 C) D E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_nfcont_1 D A C) =>  (~ (r1_tarski D B)) ) ) ) ) ) )  => (v3_nfcont_1 B A)) ) ) ) ) ).
tt(t4_ndiff_2,ax, ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~ (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers))  &  (B = C) ) )  &  (~  ( (~  (B = C) )  & (r1_xxreal_0 (k1_normsp_0 A (k5_algstr_0 A B C)) k6_numbers)) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_normsp_0 A (k5_algstr_0 A B C)) = (k1_normsp_0 A (k5_algstr_0 A C B))) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers)  <=>  (B = C) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) )  &  (B = C) ) )  &  (~  ( (~  (B = C) )  &  ((k1_normsp_0 A (k5_algstr_0 A B C)) = k6_numbers) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A D C))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A B D))))  &  ( (~ (r1_xxreal_0 (k10_real_1 E 2) (k1_normsp_0 A (k5_algstr_0 A C D))))  & (r1_xxreal_0 E (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 C (k1_normsp_0 A B))) ) ) )  =>  (B = (k4_struct_0 A)) ) ) ) ) )  &  (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_xxreal_0 D (k1_normsp_0 A (k5_algstr_0 A B C)))) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k4_vfunct_1 k1_numbers A C B)) &  ((v1_funct_2 (k4_vfunct_1 k1_numbers A C B) k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 (k4_vfunct_1 k1_numbers A C B) A) & (m1_subset_1 (k4_vfunct_1 k1_numbers A C B) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(t4_ndiff_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid B)))))  =>  ((r2_ndiff_4 B C A) => (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) ) ) ) ) ) ).
tt(t4_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ( ((k7_partfun1 (u1_struct_0 A) C k6_numbers) = (k4_struct_0 A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k7_partfun1 (u1_struct_0 B) D (k4_struct_0 A)) = (k4_struct_0 B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D)) &  ((v1_ndiff_3 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D) B) & (m1_subset_1 (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_neckla_2,ax, (! [A:$i] :  ((r2_hidden A k4_neckla_2) =>  ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v1_orders_2 A) & (l1_orders_2 A)) ) ) ) ) ).
tt(t4_neckla_3,ax, (! [A:$i] :  ((v1_zfmisc_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (~  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  (~  (B = (k1_tarski (k4_tarski C C))) ) ) ) ) ) ) ) ) ).
tt(t4_necklace,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  => (r2_hidden k6_numbers A)) ) ).
tt(t4_net_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_net_1 B) & (l1_petri B))  =>  (~  ((r2_hidden A (u1_struct_0 B)) & (r2_hidden A (u4_struct_0 B))) ) ) ) ) ).
tt(t4_newton,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_newton A k6_numbers) = 1) ) ) ).
tt(t4_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_nfcont_1 C A B) => (r2_hidden B C)) ) ) ) ) ) ).
tt(t4_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D)))))  =>  ((r1_nfcont_2 A C D E) => (r1_nfcont_2 A C D (k4_vfunct_1 (u1_struct_0 C) D E B))) ) ) ) ) ) ) ) ) ) ).
tt(t4_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C (k4_vfunct_1 k1_numbers A B D)) (k5_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C B) D))) ) ) ) ) ) ) ) ) ).
tt(t4_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  ( (C = D)  =>  ((a_3_0_nfcont_4 A B C) = (a_3_1_nfcont_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((k2_normform A B (k2_normform A B C D) E) = (k2_normform A B C (k2_normform A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_normsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k1_normsp_0 A B))) ) ) ) ).
tt(t4_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k2_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k2_normsp_2 A)))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_normsp_2 A))) =>  ( ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k2_normsp_2 A)) B C) &  (D = E) )  =>  ((r1_metric_6 (k2_normsp_2 A) C E) <=>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (? [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) &  ((r1_xxreal_0 G H) & (r1_xxreal_0 F (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B H) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ntalgo_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 (k4_xcmplx_0 A) (k4_xcmplx_0 (k6_int_1 B A)))) ) ) ) ) ) ).
tt(t4_numbers,ax,(r2_xboole_0 k4_numbers k3_numbers)).
tt(t4_numeral1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B 1))  => (r1_xxreal_0 1 (k1_afinsq_1 (k2_numeral1 A B)))) ) ) ) ) ).
tt(t4_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((u1_struct_0 (k6_openlatt A)) = (k1_openlatt A)) ) ) ).
tt(t4_oposet_1,ax,(v3_necklace k2_oposet_1)).
tt(t4_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_oppcat_1 A (k4_oppcat_1 A B)) = B) ) ) ) ) ).
tt(t4_orders_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_2 D) &  ((v4_relat_2 D) &  ((v8_relat_2 D) &  ((v1_partfun1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden (k4_tarski B C) D) & (r2_hidden (k4_tarski C B) D)) ) )  =>  (B = C) ) ) ) ) ) ) ).
tt(t4_orders_2,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_orders_2 A B C) & (r2_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(t4_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (~  ( ((k2_struct_0 A) = (k1_tarski B))  & (v3_orders_3 A)) ) ) ) ) ).
tt(t4_orders_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  ( (~  ( (~  ((u1_struct_0 A) = k1_xboole_0) )  &  ((u1_struct_0 B) = k1_xboole_0) ) )  &  ( (~  ( (~  ((u1_struct_0 B) = k1_xboole_0) )  &  ((u1_struct_0 A) = k1_xboole_0) ) )  &  ( (~  ( ((u1_struct_0 B) = k1_xboole_0)  &  (~  ((u1_struct_0 A) = k1_xboole_0) ) ) )  &  ( ( ((u1_struct_0 A) = k1_xboole_0)  =>  ((u1_struct_0 B) = k1_xboole_0) )  &  ( ((u1_struct_0 B) = k1_xboole_0)  =>  ((u1_struct_0 A) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_ordinal2,ax,(v4_ordinal1 k1_xboole_0)).
tt(t4_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((r1_tarski B A) => (v3_ordinal1 (k3_tarski B))) ) ) ) ).
tt(t4_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal2 B A) => (r1_ordinal2 (k10_ordinal2 C B) (k1_ordinal3 C A))) ) ) ) ) ) ) ).
tt(t4_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v5_ordinal1 B)) )  =>  ((v1_ordinal2 (k1_ordinal4 A B)) =>  ((v1_ordinal2 A) & (v1_ordinal2 B)) ) ) ) ) ) ).
tt(t4_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_ordinal1 A B) <=>  (~ (r2_hidden B A)) ) ) ) ) ) ).
tt(t4_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v5_o_ring_1 B A) =>  ((v7_o_ring_1 B A) &  ((v9_o_ring_1 B A) &  ((v11_o_ring_1 B A) & (v13_o_ring_1 B A)) ) ) ) ) ) ) ) ).
tt(t4_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ((r1_orders_2 B E D) & (r1_orders_2 B (k3_rlvect_1 B C E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((r2_hidden C (k6_dtconstr (k2_osafree A B))) <=>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (? [E:$i] :  ((r2_hidden E (k1_funct_1 B D)) &  (C = (k4_tarski E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_osalg_1 A)) )  =>  ((v6_osalg_1 A) => (v5_osalg_1 A)) ) ) ).
tt(t4_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  => (v12_osalg_1 (g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) A)) ) ) ) ).
tt(t4_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) )  => (v1_osalg_3 (k2_msualg_3 (u1_struct_0 A) B) A)) ) ) ) ).
tt(t4_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_orders_2 A B C) =>  ((k3_osalg_4 A B) = (k3_osalg_4 A C)) ) ) ) ) ) ) ) ).
tt(t4_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  ( (B = (k2_analoaf A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  ( ( (C = G)  &  ( (D = H)  &  ( (E = I)  &  (F = J) ) ) )  =>  ((r2_diraf B C D E F) <=> (r1_geomtrap A G H I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pardepap,ax, (? [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A B E B F) &  ((r2_analoaf A B G B H) &  ((r2_analoaf A C E D F) & (r2_analoaf A C G D H)) ) ) )  =>  ((r2_analoaf A B C B E) |  ((r2_analoaf A B C B G) | (r2_analoaf A E G F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) &  ((r2_analoaf A B C F G) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) )  =>  ((r2_analoaf A B C B D) |  ((r2_analoaf A B C B F) | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C B D) &  ((r2_analoaf A E F E G) &  ((r2_analoaf A B F C E) & (r2_analoaf A C G D F)) ) )  => (r2_analoaf A D E B G)) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C B D))  &  ((r2_analoaf A B C D E) &  ((r2_analoaf A B D C E) & (r2_analoaf A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r1_tarski (k7_parsp_1 A) (k4_zfmisc_1 (k5_parsp_1 A) (k5_parsp_1 A) (k5_parsp_1 A) (k5_parsp_1 A)))) ) ).
tt(t4_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ( ((k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C B D) = (k6_xtuple_0 E F E G))  &  ( ((k8_group_1 A H (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F))) = (k8_group_1 A I (k5_algstr_0 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))))  &  ( ((k8_group_1 A H (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F))) = (k8_group_1 A I (k5_algstr_0 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G))))  &  ((k8_group_1 A H (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F))) = (k8_group_1 A I (k5_algstr_0 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) E) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G)))) ) ) )  =>  ((r1_parsp_1 (k9_parsp_1 A) B C B D) |  ( (H = (k4_struct_0 A))  &  (I = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  ((r2_hidden B (k9_xtuple_0 C)) => (r2_hidden (k1_funct_1 C B) A)) ) ) ) ) ).
tt(t4_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( ((r2_hidden D (k1_relset_1 A E)) & (r2_hidden (k7_partfun1 B E D) (k1_relset_1 B F)))  =>  ((k7_partfun1 C (k1_partfun1 A B B C E F) D) = (k7_partfun1 C F (k7_partfun1 B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ( ((r1_setfam_1 C B) & (r1_setfam_1 B C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t4_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A (k4_relset_1 A A A A (k1_eqrel_1 A) B) (k1_eqrel_1 A)) & (r2_relset_1 A A (k4_relset_1 A A A A B (k1_eqrel_1 A)) (k1_eqrel_1 A))) ) ) ) ) ).
tt(t4_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r3_diraf A B D E) &  ((r3_diraf A B C F) &  ((r3_diraf A B C G) &  ((r2_diraf A C D E F) & (r2_diraf A C D E G)) ) ) )  =>  ((r3_diraf A B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((r2_hidden D A) =>  ((k1_funct_1 (k5_pboole A B C) D) = (k5_xboole_0 (k1_funct_1 B D) (k1_funct_1 C D))) ) ) ) ) ) ) ) ).
tt(t4_pcomps_1,ax, (! [A:$i] :  ((u1_pre_topc (k1_compts_1 A)) = (k9_setfam_1 A)) ) ).
tt(t4_pcomps_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( ((r1_pcomps_1 (u1_struct_0 A) C) &  (B = (k4_pcomps_1 (u1_struct_0 A) C)) )  =>  ((u1_struct_0 B) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t4_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((l1_pcs_0 B) =>  ( ( ((g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A)) = (g1_pcs_0 (u1_struct_0 B) (u1_pcs_0 B)))  & (v5_pcs_0 A))  => (v5_pcs_0 B)) ) ) ) ) ).
tt(t4_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k1_euclid 1) k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 1) k1_numbers)))) )  =>  ((r2_funct_2 (k1_euclid 1) k1_numbers A (k1_pdiff_1 1 1)) =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k1_seq_1 A B) = C)  =>  ((k1_normsp_0 (k4_real_ns1 1) B) = (k18_complex1 C)) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_seq_1 A B) = D)  &  ((k1_seq_1 A C) = E) )  =>  ((k1_seq_1 A (k3_rlvect_1 (k4_real_ns1 1) B C)) = (k7_real_1 D E)) ) ) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_seq_1 A B) = C)  =>  ((k1_seq_1 A (k1_rlvect_1 (k4_real_ns1 1) B D)) = (k8_real_1 D C)) ) ) ) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((k1_seq_1 A B) = C)  =>  ((k1_seq_1 A (k4_algstr_0 (k4_real_ns1 1) B)) = (k1_real_1 C)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 1))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( ((k1_seq_1 A B) = D)  &  ((k1_seq_1 A C) = E) )  =>  ((k1_seq_1 A (k5_algstr_0 (k4_real_ns1 1) B C)) = (k9_real_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r3_pdiff_1 2 2 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 2 D C) B)) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r4_pdiff_3 D C))  => (r1_fdiff_1 (k1_pdiff_2 2 2 (k1_pdiff_3 2 2 D) C) B)) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 1 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 1 E D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r4_pdiff_5 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 1 (k1_pdiff_3 2 3 E) D) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k7_integr15 B (k1_euclid A) C D) = (k6_vfunct_1 (u1_struct_0 (k4_real_ns1 A)) (k4_real_ns1 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 A B) =>  ((k17_finseq_1 k1_numbers (k7_nat_d A 1) (k5_euclid B)) = (k5_euclid (k7_nat_d A 1))) )  &  ((k2_rfinseq k1_numbers A (k5_euclid B)) = (k5_euclid (k7_nat_d B A))) ) ) ) ) ) ).
tt(t4_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_normsp_0 (k4_real_ns1 1) (k3_funct_2 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 1)) (k4_pdiff_1 C A) B)) = (k17_complex1 (k1_seq_1 (k1_pdiff_1 C A) B))) ) ) ) ) ) ) ).
tt(t4_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) =>  ((k1_relset_1 (k1_euclid A) (k2_partfun1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A C) B)) = B) ) ) ) ) ) ) ).
tt(t4_pencil_1,ax, (! [A:$i] :  ((r1_ordinal1 2 (k1_card_1 A)) <=>  (~ (v1_zfmisc_1 A)) ) ) ).
tt(t4_pencil_2,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r2_hidden C (k4_finseq_1 B)) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E (k6_xcmplx_0 C 1))) )  =>  ((k1_funct_1 (k1_pencil_2 A B C D) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pencil_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v3_pencil_1 A))  &  ((v6_pencil_1 A) & (l1_pre_topc A)) ) )  =>  ((v10_pencil_1 A) => (v9_pencil_1 A)) ) ) ).
tt(t4_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) => (m1_vectsp_4 (k2_vectsp_4 A C) A B)) ) ) ) ) ) ).
tt(t4_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) &  ((r1_nat_d C B) & (r1_int_2 A C)) )  => (r1_nat_d (k3_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t4_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r1_tarski A B) &  ((r1_tarski C D) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_petri_2 A C) (k2_petri_2 B D)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_petri_2 A C) (k2_petri_2 B D))))) )  =>  (? [F:$i] :  ((r2_hidden F (k2_petri_2 A C)) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 C)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H G A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 G A)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I G B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 G B)))) )  =>  (~  ((v1_finset_1 G) &  ((r1_funct_2 G A G B H I) &  ( (F = (k1_petri_2 A C G H))  &  ((k1_funct_1 E F) = (k1_petri_2 B D G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((r2_hidden C (k7_petri A B)) <=>  (? [D:$i] :  ((m1_petri D (u1_struct_0 A) (u4_struct_0 A) (u1_petri A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_hidden E B) &  (D = (k4_tarski E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  (~  ( ((k15_finseq_1 B) = (k9_finseq_1 A))  &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (B = (k1_tarski (k4_tarski C A))) ) ) ) ) ) ) ) ) ).
tt(t4_polyalg1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (B = (k7_finseq_1 (k9_finseq_1 (k1_funct_1 B 1)) (k1_polynom3 A 1 B))) ) ) ) ) ).
tt(t4_polyeq_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( (! [G:$i] :  ((v1_xreal_0 G) =>  ((k3_polyeq_1 A B C G) = (k3_polyeq_1 D E F G)) ) )  =>  ( (A = D)  &  ( (B = E)  &  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k1_newton A 3) = (k3_xcmplx_0 (k3_square_1 A) A))  &  ( ((k3_xcmplx_0 (k1_newton A 3) A) = (k1_newton A 4))  &  ((k3_xcmplx_0 (k3_square_1 A) (k3_square_1 A)) = (k1_newton A 4)) ) ) ) ) ).
tt(t4_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  ( (! [G:$i] :  ((v1_xcmplx_0 G) =>  ((k3_polyeq_1 A B C G) = (k5_polyeq_1 A G E F)) ) )  =>  ( (A = k6_numbers)  |  ( ((k12_binop_2 B A) = (k1_binop_2 (k3_binop_2 E F)))  &  ((k12_binop_2 C A) = (k5_binop_2 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ((v1_abian C) &  ((r1_xxreal_0 1 C) &  ( ((k2_newton B C) = A)  &  ( (~  (B = (k2_power C A)) )  &  (~  (B = (k4_xcmplx_0 (k2_power C A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_newton (k6_xcmplx_0 A B) 2) = (k2_xcmplx_0 (k6_xcmplx_0 (k1_newton A 2) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k1_newton B 2))) ) ) ) ) ).
tt(t4_polyform,ax, (~ (v1_abian 1)) ).
tt(t4_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((k3_pre_poly (u1_struct_0 A) (k4_rlvect_1 A B)) = (k6_matrlin A (k3_pre_poly (k3_finseq_2 (u1_struct_0 A)) B))) ) ) ) ) ).
tt(t4_polynom2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ( (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r2_hidden C (k4_finseq_1 B)) &  ((k7_partfun1 (u1_struct_0 A) B C) = (k4_struct_0 A)) ) ) )  =>  ((k3_group_4 A B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t4_polynom3,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 (k1_funct_1 A B) (k2_wsierp_1 A))) ) ) ) ) ).
tt(t4_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  & (l5_algstr_0 A)) )  =>  ((k1_algseq_1 A (k10_polynom3 A)) = 1) ) ) ).
tt(t4_polynom5,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 A B) (k18_rvsum_1 A))) ) ) ) ) ) ).
tt(t4_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  ( (A = k1_xboole_0)  =>  ((k1_polynom6 A B C D) = D) ) ) ) ) ) ) ) ) ) ).
tt(t4_polynom7,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k15_pre_poly k1_xboole_0) (u1_struct_0 A)) &  ((v1_polynom1 B (k15_pre_poly k1_xboole_0) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly k1_xboole_0) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 (u1_struct_0 A))))) )  =>  ((k5_polynom2 k1_xboole_0 A B C) = (k3_polynom1 k1_xboole_0 A B (k16_pre_poly k1_xboole_0))) ) ) ) ) ) ) ).
tt(t4_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = B)  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D B))  =>  ((k7_partfun1 (u1_struct_0 A) C D) = (k5_struct_0 A)) ) ) ) )  =>  ((k4_rlvect_1 A C) = (k5_binom A (k5_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t4_polyred,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l2_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k6_polynom1 A B C (k7_polynom1 A B)) C)) ) ) ) ) ).
tt(t4_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((k1_yellow_0 A (k2_poset_1 A B)) = (k1_yellow_0 A (k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k2_poset_1 A B)))) ) ) ) ) ).
tt(t4_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  ( (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 k6_numbers A)) )  & (v1_abian B)) )  =>  ( ((k1_newton (k1_power B A) B) = A)  &  ((k1_power B (k1_newton A B)) = A) ) ) ) ) ) ) ).
tt(t4_pralg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  ((v1_funct_1 (k6_pralg_1 (u1_struct_0 A) (u1_struct_0 B))) &  ((v1_funct_2 (k6_pralg_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 (k5_pralg_1 A B)) (u1_struct_0 (k5_pralg_1 B A))) & (m1_subset_1 (k6_pralg_1 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_pralg_1 A B)) (u1_struct_0 (k5_pralg_1 B A)))))) ) ) ) ) ) ) ).
tt(t4_pralg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k1_msualg_1 A C) = k1_xboole_0)  =>  ((k3_msualg_1 A C B) = (k1_tarski k1_xboole_0)) ) ) ) ) ) ) ) ).
tt(t4_pralg_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v4_funct_1 C) & (v2_card_3 C)) )  =>  ( (C = (k10_xtuple_0 B))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((r2_hidden E (k9_card_3 C)) =>  ((k1_funct_1 (k1_funct_1 B D) E) = (k1_funct_1 (k1_funct_1 (k10_funct_6 B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pre_circ,ax, (! [A:$i] :  ((k2_funct_5 (k7_funcop_1 A k1_xboole_0)) = k1_xboole_0) ) ).
tt(t4_pre_ff,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 B A) |  ((k5_int_1 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t4_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (~  ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 1)  &  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (D = (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))  &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k6_prelamb A E (k2_prelamb A F G)))  &  ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B D)) = (k6_prelamb A (k8_finseq_1 (u1_struct_0 A) E (k12_finseq_1 (u1_struct_0 A) G)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_2 B A (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_finseq_2 C A (k3_finseq_2 A)) =>  ((k5_pre_poly A (k4_pre_poly (k3_finseq_2 A) B C)) = (k1_pre_poly A B C)) ) ) ) ) ) ).
tt(t4_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  (A = k6_numbers) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((k1_seq_1 (k1_prepower A) B) = k6_numbers) ) ) ) ) ) ) ).
tt(t4_pre_topc,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  ( (~  (B = (k2_struct_0 A)) )  &  ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) = k1_xboole_0) ) )  &  (~  ( (~  ((k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B) = k1_xboole_0) )  &  (B = (k2_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t4_prgcor_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 B (k4_nat_d A (k4_nat_1 2 B))))  &  (~  ((k4_nat_d A (k4_nat_1 2 B)) = (k4_nat_d A B)) ) ) ) ) ) ) ) ) ).
tt(t4_prgcor_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (? [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  &  ( ((k1_afinsq_1 B) = (k2_nat_1 (k3_finseq_1 A) 1))  &  ( ((k1_seq_1 B k6_numbers) = k6_numbers)  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  =>  ((k1_seq_1 B (k1_nat_1 C 1)) = (k7_real_1 (k1_seq_1 B C) (k1_seq_1 A (k1_nat_1 C 1)))) ) ) )  &  ((k18_rvsum_1 A) = (k1_seq_1 B (k3_finseq_1 A))) ) ) ) ) ) ) ) ).
tt(t4_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (r2_hidden k1_xboole_0 B)) ) ) ).
tt(t4_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( ((v2_prob_1 C) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_prob_2 A B D F) = (k5_prob_1 A B (k1_prob_2 A B C F) E)) ) ) )  => (v2_prob_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  (! [E:$i] :  ((m2_prob_1 E B C) => (r1_xxreal_0 k6_numbers (k1_funct_1 (k8_prob_1 B C D E) A))) ) ) ) ) ) ) ) ) ) ).
tt(t4_prob_4,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  <=>  ((r1_tarski B (k1_zfmisc_1 A)) &  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((r1_tarski (k4_measure1 A (k9_setfam_1 A) C) B) => (r2_hidden (k1_prob_1 A C) B)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C B) => (r2_hidden (k3_subset_1 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t4_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k9_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t4_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r1_collsp A B C E) & (r1_collsp A B D E))  =>  ((r1_collsp A B C D) |  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  <=>  ((v1_projpl_1 A) &  ( (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) & (r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D)) ) ) ) ) )  &  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) => (r1_incsp_1 A B C)) ) ) ) )  &  ( (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) &  ((r1_zfmisc_1 C D E) & (r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) C D E) B)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_incsp_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u2_incsp_1 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u2_incsp_1 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u2_incsp_1 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u2_incsp_1 A)) =>  (~  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) B C F) G) &  ((r4_incsp_1 A (k8_domain_1 (u1_incsp_1 A) D E F) H) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B D) I) &  ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) C E) J) &  ( (~ (r1_incsp_1 A F I))  &  ( (~ (r1_incsp_1 A F J))  &  ( (~  (G = H) )  &  (! [K:$i] :  ((m1_subset_1 K (u1_incsp_1 A)) =>  (~ (r2_projpl_1 A K I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (~  ((r1_incsp_1 A B D) &  ( (~ (r1_incsp_1 A B E))  &  ((r1_incsp_1 A C E) &  (~ (r1_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B C))  &  ( (~ (r1_incsp_1 A B D))  &  (~  ((k1_relset_1 (u1_incsp_1 A) (k1_projred1 A C D B)) = (k1_projred2 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r3_binop_1 (u1_struct_0 A) (k4_struct_0 A) (u1_algstr_0 A))) ) ).
tt(t4_prvect_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((m1_prvect_2 C B A) <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  (! [D:$i] :  ((r2_hidden D (k4_finseq_1 B)) =>  ((v1_funct_1 (k1_funct_1 C D)) &  ((v1_funct_2 (k1_funct_1 C D) (k2_zfmisc_1 A (k1_funct_1 B D)) (k1_funct_1 B D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A (k1_funct_1 B D)) (k1_funct_1 B D))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_prvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k4_card_3 (k9_finseq_1 A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k4_card_3 (k9_finseq_1 A)))))) )  &  ((v2_funct_1 B) &  ((v2_funct_2 B (k4_card_3 (k9_finseq_1 A))) &  (! [C:$i] :  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k9_finseq_1 C)) ) ) ) ) ) ) ) ) ).
tt(t4_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_seq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_seq_1 B C) (k2_pscomp_1 A B))) ) ) ) ) ) ).
tt(t4_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_setfam_1 A B) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (? [D:$i] :  ((m2_finseq_1 D B) & (r1_tarski (k4_card_3 C) (k4_card_3 D))) ) ) ) ) ) ) ).
tt(t4_pythtrip,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (v1_abian A))  =>  ((k4_nat_d (k1_pepin A) 4) = 1) ) ) ) ).
tt(t4_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A B (k1_pzfmisc1 A C)) <=>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r1_pboole A D B) <=> (r6_pboole A D C)) ) ) ) ) ) ) ) ) ).
tt(t4_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (r1_tarski (k2_qc_lang1 A) (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A)))) ) ).
tt(t4_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((k19_qc_lang1 A (k14_qc_lang1 A B C)) = B)  &  ((k20_qc_lang1 A (k14_qc_lang1 A B C)) = C) ) ) ) ) ) ) ) ).
tt(t4_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v2_qc_lang1 B A) =>  ((k24_qc_lang1 A B) = (k23_qc_lang1 A (k17_qc_lang1 A B))) ) ) ) ) ) ).
tt(t4_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k10_xtuple_0 (k1_qc_lang4 A B)) = (a_2_0_qc_lang4 A B)) ) ) ) ) ).
tt(t4_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k5_qmax_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_qmax_1 A)) =>  ( ((r3_qmax_1 A B C) & (r3_qmax_1 A C D))  => (r3_qmax_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t4_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_quantal1 A))  =>  ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (k1_lattice3 k1_xboole_0))  =>  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_group_1 A) &  ((v6_quantal1 A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (v10_lattices A)) ) ) ) ) ) ) ) ) ) ).
tt(t4_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k28_quaterni (k6_quaterni A B C D)) = (k6_quaterni (k1_real_1 A) (k1_real_1 B) (k1_real_1 C) (k1_real_1 D))) ) ) ) ) ) ) ) ) ).
tt(t4_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((m1_subset_1 A k1_numbers) =>  ((k27_quaterni A B) = (k6_quaterni (k8_real_1 (k17_quaterni A) (k17_quaterni B)) (k8_real_1 (k17_quaterni A) (k18_quaterni B)) (k8_real_1 (k17_quaterni A) (k19_quaterni B)) (k8_real_1 (k17_quaterni A) (k20_quaterni B)))) ) ) ) ) ) ).
tt(t4_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ((r2_zfmisc_1 A B C D) =>  ((k10_xtuple_0 (k2_quaterni A B C D E F G H)) = (k2_enumset1 E F G H)) ) ) ) ) ) ) ) ) ) ).
tt(t4_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((r1_xxreal_0 (k1_quin_1 A B C) k6_numbers) =>  ((r1_xxreal_0 k6_numbers A) | (r1_xxreal_0 (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t4_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) =>  ((k3_quofield A B (k3_quofield A C D)) = (k3_quofield A (k3_quofield A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t4_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  ((k4_nat_d (k2_xcmplx_0 B 1) A) = k6_numbers) )  &  (~  ((k4_nat_d (k2_xcmplx_0 B 1) A) = (k2_xcmplx_0 (k4_nat_d B A) 1)) ) ) ) ) ) ) ) ) ).
tt(t4_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 B k6_numbers) |  ((k3_nat_d (k4_nat_d A (k1_newton B C)) (k1_newton B (k7_nat_d C 1))) = (k4_nat_d (k3_nat_d A (k1_newton B (k7_nat_d C 1))) B)) ) ) ) ) ) ) ) ) ).
tt(t4_radix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 2 A) => (r1_tarski (k2_radix_3 A) (k3_radix_1 A))) ) ) ).
tt(t4_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 2 A) & (r1_radix_1 1 B A))  =>  ((k7_radix_3 (k2_xcmplx_0 1 1) A (k2_xcmplx_0 1 1) (k10_radix_3 1 A (k10_radix_1 A 1 B))) = (k5_radix_3 B A)) ) ) ) ) ) ).
tt(t4_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m2_finseq_1 B (k3_radix_1 A)))  =>  ((k8_radix_1 1 A B) = (k4_radix_1 1 A 1 B)) ) ) ) ) ).
tt(t4_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 2 B) =>  (! [C:$i] :  ( ((v3_card_1 C (k2_xcmplx_0 A 2)) & (m2_finseq_1 C (k3_radix_1 B)))  => (r1_xxreal_0 (k8_radix_1 (k2_xcmplx_0 A 2) B (k6_radix_6 A B C)) (k8_radix_1 (k2_xcmplx_0 A 2) B C))) ) ) ) ) ) ) ).
tt(t4_ramsey_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( (~ (v1_finset_1 A))  &  ((v1_finset_1 B) & (v1_finset_1 (k6_subset_1 A B))) ) ) ) ) ).
tt(t4_random_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r3_mesfunc6 A B C D) &  ((r1_tarski E (k1_relset_1 A D)) &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G E) => (r1_xxreal_0 (k1_seq_1 D G) F)) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k12_supinf_2 C E)) | (r1_xxreal_0 (k1_mesfunc6 A B C (k2_partfun1 A k1_numbers D E)) (k1_extreal1 (k1_measure6 F) (k12_supinf_2 C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (m1_random_1 (k8_funcop_1 k1_numbers A B) A C)) ) ) ) ) ) ).
tt(t4_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v1_finset_1 (k2_struct_0 B)) => (v1_matrlin B A)) ) ) ) ) ).
tt(t4_ratfunc1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k4_xxreal_0 (k2_xcmplx_0 A B) (k2_xcmplx_0 A C)) = (k2_xcmplx_0 A (k4_xxreal_0 B C))) ) ) ) ) ) ) ).
tt(t4_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k10_xtuple_0 C) (k1_rcomp_1 A B)) => (v1_comseq_2 C)) ) ) ) ) ) ) ).
tt(t4_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k5_seq_4 (k3_rcomp_1 A B)) = A) ) ) ) ) ) ).
tt(t4_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k4_nat_d A B) = k6_numbers)  =>  ((k13_complex1 A B) = (k3_nat_d A B)) ) ) ) ) ) ).
tt(t4_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (v2_xxreal_0 B))  & (v2_xxreal_0 A)) ) ) ) ) ) ) ).
tt(t4_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k3_real_lat)) =>  ( ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat B C) A))  &  ( ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat A B) C))  &  ( ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat B A) C))  &  ( ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat C A) B))  &  ( ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat C B) A))  &  ((k1_binop_1 k1_real_lat A (k1_binop_1 k1_real_lat B C)) = (k1_binop_1 k1_real_lat (k1_binop_1 k1_real_lat A C) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  ( (B = C)  =>  ((k4_algstr_0 (k4_real_ns1 A) B) = (k6_euclid A C)) ) ) ) ) ) ) ) ).
tt(t4_realset1,ax, (? [A:$i] :  ( (~ (v1_xboole_0 A))  &  (! [B:$i] :  ((m1_subset_1 B A) =>  (~ (v1_xboole_0 (k6_subset_1 A (k6_domain_1 A B)))) ) ) ) ) ).
tt(t4_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  ((k6_algstr_0 A (k6_algstr_0 A B C) D) = (k6_algstr_0 A B (k6_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t4_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k5_algstr_0 A B C) = (k5_algstr_0 A D E))  <=>  ((k3_rlvect_1 A B E) = (k3_rlvect_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v3_rearran1 B (k1_zfmisc_1 A)) & (m2_finseq_1 B (k1_zfmisc_1 A)))  =>  (~  ((k3_finseq_1 B) = k6_numbers) ) ) ) ) ) ).
tt(t4_recdef_2,ax, (! [A:$i] :  ( (? [B:$i] :  (? [C:$i] :  (? [D:$i] :  (? [E:$i] :  (A = (k6_xtuple_0 B C D E)) ) ) ) )  =>  (A = (k6_xtuple_0 (k7_xtuple_0 A) (k8_xtuple_0 A) (k5_xtuple_0 A) (k2_xtuple_0 A))) ) ) ).
tt(t4_relat_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r5_relat_2 B A) => (r4_relat_2 (k2_xboole_0 B (k4_relat_1 A)) A)) ) ) ) ).
tt(t4_reloc,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = k6_numbers) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 1) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 2) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 3) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 4) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) A) = 5) ) ) ) ) ) ) )  =>  ((k5_compos_0 (u1_compos_1 k1_ami_3) A B) = A) ) ) ) ) ) ).
tt(t4_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ( ((r1_tarski (k9_xtuple_0 C) A) & (r1_tarski (k10_xtuple_0 C) B))  => (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ).
tt(t4_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((k10_eqrel_1 (k3_xboole_0 A B)) = (k9_subset_1 (k1_zfmisc_1 B) (k10_eqrel_1 A) (k10_eqrel_1 B))) ) ) ).
tt(t4_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_revrot_1 A B (k7_partfun1 A B (k3_finseq_1 B))) =>  ((k1_finseq_5 A B (k7_partfun1 A B (k3_finseq_1 B))) = B) ) ) ) ) ) ).
tt(t4_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( (~  (A = k1_xboole_0) )  =>  ((k1_rewrite1 (k9_finseq_1 B) A) = A) ) ) ) ) ).
tt(t4_rewrite2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((m1_rewrite1 C B) =>  (~  ((r2_hidden A (k4_finseq_1 C)) &  (! [D:$i] :  ((m1_rewrite1 D B) =>  (~  ( ((k3_finseq_1 D) = A)  &  ( ((k1_funct_1 D 1) = (k1_funct_1 C 1))  &  ((k1_funct_1 D (k3_finseq_1 D)) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rewrite3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_rewrite1 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( (B = (k7_finseq_1 C D))  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 D) k6_numbers) |  ((m1_rewrite1 C A) & (m1_rewrite1 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (A = (k12_finseq_1 k1_numbers B))  =>  ( ((k2_rfinseq2 A) = 1)  &  ((k4_rfinseq2 A) = B) ) ) ) ) ) ) ).
tt(t4_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_classes1 A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) &  ((v3_funct_2 C (k4_finseq_1 B) (k4_finseq_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 B) (k4_finseq_1 B))))) ) )  &  (A = (k3_relat_1 C B)) ) ) ) ) ) ) ) ).
tt(t4_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k8_relat_1 (k4_rfunct_1 A) (k1_tarski k6_numbers)) = k1_xboole_0) ) ) ).
tt(t4_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  ((r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B (k32_valued_1 k5_numbers k1_numbers A)) (k32_valued_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B A))) & (r2_relset_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B (k56_valued_1 k5_numbers k1_numbers A)) (k56_valued_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B A)))) ) ) ) ) ).
tt(t4_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k1_rfunct_3 (k3_xcmplx_0 A B)) = (k4_real_1 A (k1_rfunct_3 B))) ) ) ) ) ) ).
tt(t4_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  (k6_numbers = (k1_seq_1 B C)) ) ) )  =>  (B = (k5_finseq_2 k1_numbers A k6_numbers)) ) ) ) ) ) ).
tt(t4_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((k2_relset_1 k1_numbers (k32_valued_1 k5_numbers k1_numbers A)) = (k5_member_1 (k2_relset_1 k1_numbers A))) ) ) ).
tt(t4_rinfsup2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ( (A = B)  & (v3_xxreal_2 A))  =>  ((v3_xxreal_2 B) &  ((k7_supinf_2 A) = (k5_seq_4 B)) ) ) ) ) ) ) ).
tt(t4_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v2_ring_1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t4_ringcat1,ax, (! [A:$i] :  ( ((v2_ringcat1 A) &  ((v3_ringcat1 A) & (l1_ringcat1 A)) )  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  &  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  &  ((m1_ringcat1 A B C) &  ( (A = (g1_ringcat1 B C D))  & (v1_ringcat1 D B C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C (k3_convex1 A B)) =>  ((k3_convex1 A B) = (k3_convex1 A (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ).
tt(t4_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_rusub_4 E A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) (k3_convex1 A C) (k3_convex1 A D)) E) & (r1_tarski (k3_convex1 A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) E)) )  =>  ((r2_hidden B E) |  ((k9_subset_1 (u1_struct_0 A) (k3_convex1 A (k7_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) B))) (k3_convex1 A D)) = (k9_subset_1 (u1_struct_0 A) (k3_convex1 A C) (k3_convex1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rlaffin3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_rlvect_5 (k15_euclid A)) = A) ) ) ).
tt(t4_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v1_rlsub_1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t4_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ((k1_rlsub_2 A B B) = B) ) ) ) ) ).
tt(t4_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (D = (a_3_0_rltopsp1 A B C))  =>  ((k6_rusub_4 A B C) = (k5_setfam_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B (k4_struct_0 A)) = B)  &  ((k1_algstr_0 A (k4_struct_0 A) B) = B) ) ) ) ) ) ).
tt(t4_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 C D) = (k4_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D))) ) ) ) )  =>  ((k4_rlvect_1 A C) = (k4_algstr_0 A (k4_rlvect_1 A B))) ) ) ) ) ) ) ) ).
tt(t4_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k6_rlvect_2 A (k10_rlvect_2 A B C)) = (k5_algstr_0 A (k6_rlvect_2 A B) (k6_rlvect_2 A C))) ) ) ) ) ) ) ).
tt(t4_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((m1_rlsub_1 C D) => (r1_tarski (k3_rlsub_1 A B C) (k3_rlsub_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t4_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_1 C) (k4_finseq_1 C)) &  ((v3_funct_2 E (k4_finseq_1 C) (k4_finseq_1 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_1 C) (k4_finseq_1 C))))) ) )  =>  ( (D = (k1_partfun1 (k4_finseq_1 C) (k4_finseq_1 C) k5_numbers (u1_struct_0 A) E C))  =>  ((k4_rlvect_1 A (k5_rlvect_2 A C B)) = (k4_rlvect_1 A (k5_rlvect_2 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rlvect_x,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) & (l1_rlvect_1 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  (! [E:$i] :  ((m2_rlvect_2 E C D) =>  ( (A = B)  => (r1_rlvect_2 C (k8_rlvect_2 C A E) (k1_rlvect_x C B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  => (v1_rmod_2 (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) A B)) ) ) ) ).
tt(t4_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  ((k1_rmod_3 A B C C) = C) ) ) ) ) ) ) ).
tt(t4_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((k5_vectsp_2 A B C (k4_rlvect_1 B (k3_finseq_4 (u1_struct_0 B) D E F))) = (k3_rlvect_1 B (k3_rlvect_1 B (k5_vectsp_2 A B C D) (k5_vectsp_2 A B C E)) (k5_vectsp_2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_robbins1 A B (k3_robbins1 A B)) = (k5_robbins1 A C (k3_robbins1 A C))) ) ) ) ) ) ) ).
tt(t4_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A D B)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A C (k3_robbins1 A C))) C)) (k3_robbins1 A (k1_lattices A C E)))))))) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ( ((v2_robbins3 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v9_lattices A)) ) )  =>  ((v7_lattices A) & (v5_lattices A)) ) ) ) ).
tt(t4_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v8_robbins3 A) & (l4_robbins1 A)) ) )  =>  ((v10_robbins1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) => (r3_lattices A (k3_robbins1 A C) (k3_robbins1 A B))) ) ) ) ) ) ) ) ).
tt(t4_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k1_rcomp_1 A (k7_real_1 A B)) (k1_relset_1 k1_numbers C)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A (k7_real_1 A B)))) &  ((r2_fdiff_1 C (k2_rcomp_1 A (k7_real_1 A B))) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (~ (r1_xxreal_0 1 D))  &  ((k1_seq_1 C (k7_real_1 A B)) = (k7_real_1 (k1_seq_1 C A) (k8_real_1 B (k1_fdiff_1 C (k7_real_1 A (k8_real_1 D B)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v1_roughs_1 A))  & (l1_orders_2 A)) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  & (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B C) (u1_orders_2 A))) ) ) ) ) ) ) ).
tt(t4_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((v3_card_1 (k6_domain_1 A B) 1) & (m1_subset_1 (k6_domain_1 A B) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(t4_rsspace2,ax, ( (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 (k8_real_1 (k7_real_1 A B) (k7_real_1 A B)) (k7_real_1 (k8_real_1 (k8_real_1 2 A) A) (k8_real_1 (k8_real_1 2 B) B)))) ) ) )  &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r1_xxreal_0 (k8_real_1 A A) (k7_real_1 (k8_real_1 (k8_real_1 2 (k9_real_1 A B)) (k9_real_1 A B)) (k8_real_1 (k8_real_1 2 B) B)))) ) ) ) ) ).
tt(t4_rsspace3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_series_1 A) &  ((k4_series_1 (k56_valued_1 k5_numbers k1_numbers A)) = k6_numbers) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ).
tt(t4_rsspace4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k3_rsspace4)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k3_rsspace4))))) )  =>  ((v1_rsspace3 A k3_rsspace4) => (v3_normsp_1 A k3_rsspace4)) ) ) ).
tt(t4_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  ((k3_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) (k3_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) A B) C) = (k3_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) A (k3_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) B C))) ) ) ) ) ) ) ).
tt(t4_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  ((k4_struct_0 B) = (k4_struct_0 A)) ) ) ) ) ).
tt(t4_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ((k1_rusub_2 A B B) = B) ) ) ) ) ).
tt(t4_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k1_rusub_3 A B) = (k1_rusub_1 A))  &  ( (~  (B = k1_xboole_0) )  &  (~  (B = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ) ) ) ) ).
tt(t4_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_rusub_4 A) & (v1_rlvect_3 B A))  => (v1_finset_1 B)) ) ) ) ) ).
tt(t4_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v2_rusub_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (v2_rusub_4 (k1_rusub_5 A B C) A)) ) ) ) ) ) ).
tt(t4_rvsum_1,ax,(r7_binop_1 k1_numbers k2_rvsum_1 k35_binop_2)).
tt(t4_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k3_rvsum_2 (k6_finseq_1 k2_numbers) A) = (k6_finseq_1 k2_numbers)) ) ) ).
tt(t4_scheme1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~  (A = (k4_nat_1 5 B)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 5 B) 1)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 5 B) 2)) )  &  ( (~  (A = (k2_nat_1 (k4_nat_1 5 B) 3)) )  &  (~  (A = (k2_nat_1 (k4_nat_1 5 B) 4)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_ami_3)))  =>  ( ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D B)) = C)  &  ((k3_compos_1 k1_ami_3 A C) = (k2_ami_3 E F)) )  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = (k2_nat_1 C 1))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) E) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) F))  &  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_ami_3)))  =>  ( (~  (G = E) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) G) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (C = (k2_nat_1 D 1)) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k14_scmfsa_2 (k4_scmfsa_2 C) E B) (k1_scmfsa_m A)) (k4_scmfsa_2 (k2_nat_1 D 1))) = (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scm_comp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k6_dtconstr k1_scm_comp)) =>  ((k12_scm_comp A (k3_scm_comp B)) = (k1_funct_1 A B)) ) ) ) ) ).
tt(t4_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k8_scmfsa_2 A B) = (k3_xtuple_0 3 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(t4_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  ((k18_scmfsa_2 A C) = (k18_scmfsa_2 (k1_funct_4 A (k7_memstr_0 3 k1_scmfsa_2 B)) C)) ) ) ) ) ) ) ).
tt(t4_scmfsa_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  ( (~ (r2_hidden (k2_compos_0 (u1_compos_1 k1_scmfsa_2) B) (k1_enumset1 6 7 8)))  =>  ((k5_compos_0 (u1_compos_1 k1_scmfsa_2) B A) = B) ) ) ) ) ) ).
tt(t4_scmfsa6b,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 D))  &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v7_amistd_1 D 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  ( (~ (r2_hidden A (k4_sf_mastr D)))  =>  ((k18_scmfsa_2 (k1_scmfsa6b D B C) A) = (k18_scmfsa_2 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t4_scmfsa6c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k6_memstr_0 3 k1_scmfsa_2 B) = (k6_memstr_0 3 k1_scmfsa_2 C))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 A B)) = (k6_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 A C))) ) ) ) ) ) ) ) ).
tt(t4_scmfsa_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 C (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 C 3 k1_scmfsa_2 B)) ) ) ) )  =>  ( ((k1_funct_1 C (k4_scmfsa_2 k6_numbers)) = 1)  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k2_afinsq_1 (k2_scmfsa_7 D E))) =>  ((k1_funct_1 (k2_scmfsa_7 D E) F) = (k3_compos_1 k1_scmfsa_2 A (k2_nat_1 B F))) ) ) )  =>  ( (D = (k4_scmfsa_2 k6_numbers))  |  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F (k1_afinsq_1 (k2_scmfsa_7 D E))) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C F)) = (k2_nat_1 B F))  &  ( (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (G = D) )  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A C F) G) = (k1_funct_1 C G)) ) ) )  &  (! [G:$i] :  ((m1_scmfsa_2 G) =>  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A C F) G) = (k18_scmfsa_2 C G)) ) ) ) ) ) ) )  &  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A C (k1_afinsq_1 (k2_scmfsa_7 D E))) D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scmfsa7b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  ( ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa_7 C D) B A) C) = D)  &  ( (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~  (E = (k4_scmfsa_2 1)) )  &  ( (~  (E = (k4_scmfsa_2 2)) )  &  (~  ((k1_funct_1 (k1_scmfsa6b (k4_scmfsa_7 C D) B A) E) = (k1_funct_1 B E)) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_scmfsa_2 E) =>  ( (~  (E = C) )  =>  ((k18_scmfsa_2 (k1_scmfsa6b (k4_scmfsa_7 C D) B A) E) = (k18_scmfsa_2 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ( ((k6_memstr_0 3 k1_scmfsa_2 A) = (k6_memstr_0 3 k1_scmfsa_2 B))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k8_memstr_0 3 k1_scmfsa_2 A) (k8_memstr_0 3 k1_scmfsa_2 B))) ) ) ) ) ) ) ) ) ).
tt(t4_scmfsa9a,ax, ((k4_sf_mastr (k4_compos_1 k1_scmfsa_2)) = k1_xboole_0) ).
tt(t4_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k1_scmfsa_9 B A)) = (k2_nat_1 (k5_card_1 A) 6)) ) ) ) ) ).
tt(t4_scmfsa_i,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  (! [D:$i] :  ((m1_subset_1 D k1_scmfsa_i) =>  ((r2_hidden A (k2_tarski 9 10)) => (r2_hidden (k3_xtuple_0 A k1_xboole_0 (k11_finseq_1 B D C)) k2_scmfsa_i)) ) ) ) ) ) ) ) ).
tt(t4_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  => (r2_hidden (k4_scmfsa_2 k6_numbers) (k9_xtuple_0 (k1_scmfsa_m A)))) ) ).
tt(t4_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (r2_hidden D (k2_sf_mastr C)))  =>  ((k1_funct_1 (k1_scmfsa6b C A B) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_scm_inst,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  ((r2_hidden A (k10_domain_1 k5_numbers 1 2 3 4 5)) => (r2_hidden (k3_xtuple_0 A k1_xboole_0 (k2_finseq_4 k2_scm_inst B C)) k3_scm_inst)) ) ) ) ) ) ).
tt(t4_scmisort,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  & (r4_scmfsa7b (k2_scmfsa_9 B A) C)) ) ) ) ) ) ) ) ).
tt(t4_scmpds_3,ax, (~ (r2_hidden (k4_struct_0 k1_scmpds_2) k2_ami_2)) ).
tt(t4_scmpds_4,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (? [B:$i] :  ((m1_subset_1 B k5_numbers) &  (A = (k2_scmpds_2 B k6_numbers)) ) ) ) ) ).
tt(t4_scmpds_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  => (r1_tarski A (k10_compos_1 k1_scmpds_2 (k1_scmpds_4 A B)))) ) ) ) ).
tt(t4_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_amistd_1 2 k1_scmpds_2 B (k4_scmpds_2 A)) = a_0_0_scmpds_9) ) ) ) ) ).
tt(t4_scmpds_i,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 15)) =>  (! [B:$i] :  ((m1_subset_1 B k1_scmpds_i) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (B = (k3_xtuple_0 A k1_xboole_0 (k9_finseq_1 C)))  =>  ((k4_scmpds_i B) = C) ) ) ) ) ) ) ) ).
tt(t4_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k3_scmpds_4 B A)) = (k2_nat_1 (k5_card_1 B) 1)) ) ) ) ) ).
tt(t4_scmring1,ax, (! [A:$i] :  ((m2_subset_1 A k1_ami_2 k2_ami_2) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ((k1_funct_1 (k3_relat_1 k3_ami_2 (k1_scmring1 B)) A) = (u1_struct_0 B)) ) ) ) ) ).
tt(t4_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 (k1_scmring2 C))))  => (r2_hidden (k3_xtuple_0 5 k1_xboole_0 (k10_finseq_1 D B)) (k1_scmringi A))) ) ) ) ) ) ) ) ).
tt(t4_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 B (u1_struct_0 (k1_scmring2 A)))) ) ) )  => (r1_tarski (k8_struct_0 k1_ami_3) (k9_xtuple_0 B))) ) ) ) ).
tt(t4_scmringi,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 8)) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_scmringi B)) =>  (! [D:$i] :  ((m1_subset_1 D k2_scm_inst) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (C = (k3_xtuple_0 A k1_xboole_0 (k7_scmringi B D E)))  =>  ( ((k8_scmringi B C) = D)  &  ((k9_scmringi B C) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden A E) &  ((r2_hidden C E) &  ((k2_tarski A (k4_tarski B E)) = (k2_tarski C (k4_tarski D E))) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ).
tt(t4_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_finseq_1 J k4_numbers) =>  ( ((r1_scpisort J B I) &  ( ((k3_finseq_1 J) = G)  &  ( ((k1_funct_1 B E) = k6_numbers)  &  ( ((k1_funct_1 B D) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd H)) = (k4_xcmplx_0 G))  &  ( ((k1_funct_1 B F) = (k2_nat_1 I 1))  &  (! [K:$i] :  ( ((v1_relat_1 K) &  ((v4_relat_1 K (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 K) &  ((v5_funct_1 K (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 K (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 K 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [L:$i] :  ( ((v1_relat_1 L) &  ((v4_relat_1 L k5_numbers) &  ((v5_relat_1 L (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 L) & (v1_partfun1 L k5_numbers)) ) ) )  =>  ( ( ((k1_funct_1 K D) = k6_numbers)  &  (! [M:$i] :  ((m2_subset_1 M k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 M I))  =>  ((k1_funct_1 K (k1_scmp_gcd M)) = (k1_funct_1 B (k1_scmp_gcd M))) ) ) ) )  =>  ( (! [M:$i] :  ((m2_finseq_1 M k4_numbers) =>  (~  ((r1_scpisort M B I) &  ( ((k3_finseq_1 M) = (k2_xcmplx_0 (k1_funct_1 K (k1_scmp_gcd H)) G))  &  ( ((k1_funct_1 K E) = (k1_gr_cy_1 M))  &  ((k1_funct_1 K F) = (k2_nat_1 (k2_nat_1 I 1) (k3_finseq_1 M))) ) ) ) ) ) )  |  ((r1_xxreal_0 k6_numbers (k1_funct_1 K (k1_scmp_gcd H))) |  ( ((k1_funct_1 (k6_scmpds_4 C K L) D) = k6_numbers)  &  ((r1_scmpds_6 C K L) &  ((r2_scmpds_6 C K L) &  ( ((k1_funct_1 (k6_scmpds_4 C K L) (k1_scmp_gcd H)) = (k2_xcmplx_0 (k1_funct_1 K (k1_scmp_gcd H)) 1))  &  ( (? [M:$i] :  ((m2_finseq_1 M k4_numbers) &  ((r1_scpisort M B I) &  ( ((k3_finseq_1 M) = (k2_xcmplx_0 (k2_xcmplx_0 (k1_funct_1 K (k1_scmp_gcd H)) G) 1))  &  ( ((k1_funct_1 (k6_scmpds_4 C K L) F) = (k2_nat_1 (k2_nat_1 I 1) (k3_finseq_1 M)))  &  ((k1_funct_1 (k6_scmpds_4 C K L) E) = (k1_gr_cy_1 M)) ) ) ) ) )  &  (! [M:$i] :  ((m2_subset_1 M k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 M I))  =>  ((k1_funct_1 (k6_scmpds_4 C K L) (k1_scmp_gcd M)) = (k1_funct_1 B (k1_scmp_gcd M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scmpds_8 D H C) B A) E) = (k1_gr_cy_1 J))  &  ((r1_scmpds_6 (k1_scmpds_8 D H C) B A) & (r2_scmpds_6 (k1_scmpds_8 D H C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  =>  ((k8_memstr_0 2 k1_scmpds_2 A) = (k8_memstr_0 2 k1_scmpds_2 B)) ) ) ) ) ) ).
tt(t4_scpqsort,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 k1_scmpds_2)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_compos_1 k1_scmpds_2)) =>  ((k5_card_1 (k3_scmpds_4 (k3_scmpds_4 (k4_scmpds_4 A B) C) D)) = 4) ) ) ) ) ) ) ) ) ).
tt(t4_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A C B D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  (~  ((r2_hidden B k5_numbers) &  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t4_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D B) & (r1_xxreal_0 C (k18_complex1 (k1_seq_1 A D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v5_xxreal_2 A) <=>  (? [B:$i] :  ((v1_xreal_0 B) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r2_hidden C A) & (r1_xxreal_0 B (k18_complex1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t4_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k6_seqfunc A B C) (k6_seqfunc A C B)) & (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k6_seqfunc A (k6_seqfunc A B C) D) (k6_seqfunc A B (k6_seqfunc A C D)))) ) ) ) ) ) ) ) ) ).
tt(t4_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v6_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A C))) ) ) ) ) ) ) ) ) ).
tt(t4_series_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_series_1 A) =>  ((v2_comseq_2 A) &  ((k2_seq_2 A) = k6_numbers) ) ) ) ) ).
tt(t4_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k4_nat_1 2 B)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k4_nat_1 B (k2_nat_1 B 1))) ) ) ) ) ) ).
tt(t4_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k3_xcmplx_0 A B) (k4_square_1 (k13_complex1 (k2_xcmplx_0 A B) 2)))) ) ) ) ).
tt(t4_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_newton (k6_xcmplx_0 (k6_xcmplx_0 A B) C) 2) = (k2_xcmplx_0 (k6_xcmplx_0 (k6_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 2) (k1_newton B 2)) (k1_newton C 2)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_xcmplx_0 (k3_xcmplx_0 2 A) C)) (k3_xcmplx_0 (k3_xcmplx_0 2 B) C))) ) ) ) ) ) ) ).
tt(t4_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_square_1 (k13_complex1 A B)) (k13_complex1 A B))) ) ) ) ) ) ).
tt(t4_setfam_1,ax, (! [A:$i] :  ((r2_hidden k1_xboole_0 A) =>  ((k1_setfam_1 A) = k1_xboole_0) ) ) ).
tt(t4_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ((r2_hidden A (k2_relset_1 B C)) <=>  (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  (A = (k3_funct_2 k5_numbers B C D)) ) ) ) ) ) ) ) ) ).
tt(t4_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k1_setlim_2 B C D) A) = (k1_setlim_2 B (k10_nat_1 (k9_setfam_1 B) C A) (k10_nat_1 (k9_setfam_1 B) D A))) ) ) ) ) ) ) ) ).
tt(t4_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v1_binop_1 E B) &  ((v2_binop_1 E B) & (r1_xboole_0 C D)) )  =>  ( ( (~  ( (~  (C = k1_xboole_0) )  &  (~  (D = k1_xboole_0) ) ) )  &  (~ (v1_setwiseo E B)) )  |  ((k7_setwiseo A B E (k5_setwiseo A C D) F) = (k5_binop_1 B E (k7_setwiseo A B E C F) (k7_setwiseo A B E D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 D (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 D 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  ( ((r5_scmfsa7b B D A) &  ((r1_tarski B A) & (r1_extpro_1 3 k1_scmfsa_2 A D)) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E (k8_extpro_1 3 k1_scmfsa_2 A D)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 A D E) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a B C)) D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r5_scmfsa7b C A B) <=> (r5_scmfsa7b C (k1_scmfsa_m A) B)) ) ) ) ) ) ) ) ).
tt(t4_sfmastr3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~  (A = B) )  & (r1_scmfsa7b (k6_scmfsa_2 C B) A)) ) ) ) ) ) ) ) ).
tt(t4_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k9_scmfsa_2 A B) = (k9_scmfsa_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 A) => (r1_tarski (k1_sgraph1 A B) (k2_finseq_1 B))) ) ) ) ) ).
tt(t4_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_lattices A B (k1_sheffer1 A)) = (k1_sheffer1 A)) ) ) ) ) ).
tt(t4_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B B) B)) (k5_sheffer1 A C (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B B) B))))) = (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B B) B))) ) ) ) ) ) ) ).
tt(t4_simplex0,ax, (! [A:$i] :  ((k1_simplex0 (k1_tarski A)) = (k9_setfam_1 A)) ) ).
tt(t4_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_simplex0 C (u1_struct_0 A)) =>  ((r1_tarski (u1_pre_topc B) (u1_pre_topc C)) => (r1_tarski (k3_simplex1 A B) (k3_simplex1 A C))) ) ) ) ) ) ) ).
tt(t4_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden C B) &  ((r2_hidden D B) &  ((k2_metric_1 A C D) = (k3_tbsp_1 A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sincos10,ax,(r1_tarski (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)) (k1_relset_1 k1_numbers k2_fdiff_9))).
tt(t4_sin_cos2,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))))).
tt(t4_sin_cos3,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k3_binop_2 A B)) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B)))) ) ) ) ) ).
tt(t4_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos A)) = (k6_xcmplx_0 1 (k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos A)))) ) ) ).
tt(t4_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~  ((k17_sin_cos A) = k6_numbers) )  &  ( (~  ((k17_sin_cos B) = k6_numbers) )  &  ( (~  ((k17_sin_cos C) = k6_numbers) )  &  (~  ((k20_sin_cos (k2_xcmplx_0 (k2_xcmplx_0 A B) C)) = (k1_real_1 (k4_real_1 (k3_xcmplx_0 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos B)) (k17_sin_cos C)) (k9_real_1 (k7_real_1 (k7_real_1 (k2_sin_cos4 A) (k2_sin_cos4 B)) (k2_sin_cos4 C)) (k8_real_1 (k8_real_1 (k2_sin_cos4 A) (k2_sin_cos4 B)) (k2_sin_cos4 C)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 (k17_sin_cos A) 1)) ) ).
tt(t4_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)) k6_numbers)) ) ) ).
tt(t4_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k9_sin_cos2 A))) ) ) ).
tt(t4_sin_cos9,ax, ((r2_fdiff_1 k30_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (k2_rcomp_1 k6_numbers k32_sin_cos)) =>  ((k1_fdiff_1 k30_sin_cos A) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos A))))) ) ) ) ) ).
tt(t4_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k8_nat_1 k2_numbers (k7_sin_cos B) A) = (k8_nat_1 k2_numbers B (k7_nat_d A 1))) ) ) ) ) ) ).
tt(t4_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_euclid A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_euclid A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_euclid A)) => (r1_xxreal_0 (k9_real_1 (k12_euclid (k8_euclid A C B)) (k12_euclid (k8_euclid A C D))) (k12_euclid (k8_euclid A D B)))) ) ) ) ) ) ) ) ).
tt(t4_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 C (k3_finseq_1 A)) & (r1_xxreal_0 1 B))  =>  ((k2_topreal1 2 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) C A) B) = (k2_topreal1 2 A (k2_xcmplx_0 C B))) ) ) ) ) ) ) ) ).
tt(t4_sprect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r3_connsp_1 A C B) &  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t4_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_finseq_1 E D) =>  ( ((r2_hidden A (k4_finseq_1 E)) &  ((r2_hidden B (k4_finseq_1 E)) & (r2_hidden C (k4_finseq_1 (k3_finseq_6 D E A B)))) )  =>  ((r1_xxreal_0 A B) |  ((k7_partfun1 D (k3_finseq_6 D E A B) C) = (k7_partfun1 D E (k2_nat_1 (k7_nat_d A C) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) C (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid A) B D)))  =>  ((r1_xxreal_0 1 D) |  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sprect_4,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r2_hidden B (k2_topreal1 2 A D)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 D 1))))) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) D) | (r1_jordan5c (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_sprect_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden C (k10_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 B)) & (r1_xxreal_0 (k4_finseq_4 B C) (k4_finseq_4 B D))) )  =>  ((k4_finseq_4 (k1_finseq_6 A B C) D) = (k2_xcmplx_0 (k6_xcmplx_0 (k4_finseq_4 B D) (k4_finseq_4 B C)) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t4_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_square_1 (k2_xcmplx_0 A B)) = (k2_xcmplx_0 (k2_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_square_1 B))) ) ) ) ) ).
tt(t4_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_stacks_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((v3_stacks_1 A) &  ( ((k5_stacks_1 A B) = (k5_stacks_1 A C))  &  ((k6_stacks_1 A B) = (k6_stacks_1 A C)) ) )  =>  ((r1_stacks_1 A B) |  ((r1_stacks_1 A C) |  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t4_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  ( (~ (r2_hidden (k5_nat_1 A) (k9_subset_1 k5_numbers A B)))  =>  ((k5_nat_1 A) = (k5_nat_1 (k7_subset_1 k5_numbers A B))) ) ) ) ) ) ).
tt(t4_struct_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) (k8_struct_0 A))) ) ) ).
tt(t4_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) =>  ((v2_substut1 D A) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  ((r1_valuat_1 A B (k39_substut1 A D) C E) <=> (r1_sublemma A D B (k1_sublemma A B E (k3_sublemma A D B E)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~ (r2_hidden C B)) ) ) ) ) ) ) ) ).
tt(t4_subset,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden A B) & (m1_subset_1 B (k1_zfmisc_1 C)))  => (m1_subset_1 A C)) ) ) ) ).
tt(t4_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 (k4_partfun1 A B))) =>  ( (C = (k1_tarski k1_xboole_0))  =>  ((k4_substlat A B D C) = D) ) ) ) ) ) ) ) ).
tt(t4_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v3_qc_lang1 B A) =>  ((k9_substut1 A B) = (k9_substut1 A (k18_qc_lang1 A B))) ) ) ) ) ) ).
tt(t4_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (? [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A D) = B)  &  ((k19_substut1 A D) = C) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_substut1 A)) =>  (? [D:$i] :  ((m2_subset_1 D (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A D) = (k6_cqc_lang A B))  &  ((k19_substut1 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v2_membered B))  =>  ( (B = (k5_setfam_1 k7_numbers A))  => (m1_xxreal_2 (k1_xxreal_2 B) (k5_supinf_1 A))) ) ) ) ) ).
tt(t4_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ((r1_orders_2 B E D) & (r1_orders_2 B (k3_rlvect_1 B C E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_sysrel,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r1_tarski C (k2_zfmisc_1 A B)) => (r1_tarski (k2_relat_1 C) (k2_zfmisc_1 B A))) ) ) ) ) ).
tt(t4_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A)) (k4_t_0topsp A) B) = (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_t_0topsp A) B)) ) ) ) ) ).
tt(t4_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v7_pre_topc (k2_t_1topsp A))) ) ).
tt(t4_taxonom1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) =>  ((k2_relset_1 A B) = A) ) ) ) ) ).
tt(t4_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((m1_taxonom1 B A) & (r2_hidden C (k3_tarski B)))  => (r1_tarski C A)) ) ) ) ) ).
tt(t4_taylor_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k25_sin_cos (k4_xcmplx_0 A)) = (k10_real_1 1 (k25_sin_cos A))) ) ) ).
tt(t4_taylor_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_tarski (k2_rcomp_1 (k1_real_1 C) C) (k9_xtuple_0 B)) & (r1_taylor_1 B (k2_nat_1 A 1) (k2_rcomp_1 (k1_real_1 C) C)))  =>  ((r1_xxreal_0 C k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden D (k2_rcomp_1 (k1_real_1 C) C)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (~ (r1_xxreal_0 1 E))  &  ((k18_complex1 (k9_real_1 (k1_seq_1 B D) (k1_seq_1 (k3_series_1 (k1_taylor_2 B (k2_rcomp_1 (k1_real_1 C) C) D)) A))) = (k18_complex1 (k10_real_1 (k8_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B (k2_rcomp_1 (k1_real_1 C) C)) (k2_nat_1 A 1)) (k8_real_1 E D)) (k2_newton D (k2_nat_1 A 1))) (k3_newton (k2_nat_1 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  <=>  ( ((k9_xtuple_0 B) = k5_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (m1_subset_1 (k1_funct_1 B C) (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t4_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  ( ((u1_struct_0 (k2_tdgroup A)) = (u1_struct_0 A))  &  ((u1_analoaf (k2_tdgroup A)) = (k1_tdgroup A)) ) ) ) ).
tt(t4_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_tops_1 A B) (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A B))))) ) ) ) ).
tt(t4_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) &  ((k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) = C) )  => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t4_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  & (v4_pre_topc B A))  =>  ((k4_subset_1 (u1_struct_0 A) B (k1_tops_1 A C)) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t4_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (r8_pboole (k15_pre_poly A) (k4_polynom7 A B (k6_algstr_0 B C D)) (k9_polynom1 A B (k4_polynom7 A B C) (k4_polynom7 A B D)))) ) ) ) ) ) ) ) ).
tt(t4_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_tmap_1 A B)))) =>  ( ( (C = B)  & (v1_tops_1 B A))  =>  ((v1_tops_1 C (k6_tmap_1 A B)) & (v3_pre_topc C (k6_tmap_1 A B))) ) ) ) ) ) ) ) ).
tt(t4_tex_2,ax, (! [A:$i] :  ( (~ (v1_zfmisc_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) => (v1_subset_1 (k6_domain_1 A B) A)) ) ) ) ).
tt(t4_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v1_tops_3 B A) <=> (v3_tops_1 C A)) ) ) ) ) ) ) ) ).
tt(t4_tex_4,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = D)  & (v1_tex_4 C A)) )  => (v1_tex_4 D B)) ) ) ) ) ) ) ) ) ).
tt(t4_tietze,ax, (! [A:$i] :  ( ((v2_struct_0 A) &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v5_pre_topc C A B)) ) ) ) ) ) ).
tt(t4_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 A)))  =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 A)))  =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 A)))  =>  ( ( (F = (k4_subset_1 A C D))  &  (G = (k4_subset_1 A D E)) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H C B) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I D B) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J E B) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 E B)))) )  =>  ( ( ((k2_partfun1 C B H (k9_subset_1 A C D)) = (k2_partfun1 D B I (k9_subset_1 A C D)))  &  ( ((k2_partfun1 D B I (k9_subset_1 A D E)) = (k2_partfun1 E B J (k9_subset_1 A D E)))  &  ((k2_partfun1 C B H (k9_subset_1 A C E)) = (k2_partfun1 E B J (k9_subset_1 A C E))) ) )  =>  (! [K:$i] :  ( ((v1_funct_1 K) &  ((v1_funct_2 K F B) & (m1_subset_1 K (k1_zfmisc_1 (k2_zfmisc_1 F B)))) )  =>  (! [L:$i] :  ( ((v1_funct_1 L) &  ((v1_funct_2 L G B) & (m1_subset_1 L (k1_zfmisc_1 (k2_zfmisc_1 G B)))) )  =>  ( ((r1_funct_2 F B (k4_subset_1 A C D) B K (k1_tmap_1 A B C D H I)) & (r1_funct_2 G B (k4_subset_1 A D E) B L (k1_tmap_1 A B D E I J)))  => (r1_funct_2 (k4_subset_1 A F E) B (k4_subset_1 A C G) B (k1_tmap_1 A B F E K J) (k1_tmap_1 A B C G H L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_toler_1,ax, (! [A:$i] : (v7_relat_2 (k1_eqrel_1 A))) ).
tt(t4_topalg_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k17_borsuk_1)) =>  ( (A = (k4_rcomp_1 B 1))  => (v3_pre_topc A k17_borsuk_1)) ) ) ) ) ).
tt(t4_topalg_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k7_partfun1 k1_numbers (k1_jordan2b A) 1) = A) ) ) ).
tt(t4_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k6_struct_0 A B D) C) = D) ) ) ) ) ) ) ) ) ).
tt(t4_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l3_algstr_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( ((v2_funct_2 E (u1_struct_0 C)) & (v2_funct_2 F (u1_struct_0 D)))  => (v2_funct_2 (k1_topalg_4 A B C D E F) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topalg_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_pre_topc A C) = (k1_pre_topc B D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ( ((k2_xxreal_2 (k1_relset_1 (u1_struct_0 k5_topmetr) D)) = k6_numbers)  &  ((k1_xxreal_2 (k1_relset_1 (u1_struct_0 k5_topmetr) D)) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t4_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((r2_hidden B C) & (v2_topdim_1 C A))  => (v1_topdim_1 B A)) ) ) ) ) ) ) ).
tt(t4_topdim_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_pcomps_1 B) & (l1_pre_topc B)) )  =>  ((v5_waybel23 B) =>  ( (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))))  =>  (~  ((v2_tops_2 C B) &  ((m1_setfam_1 C (u1_struct_0 B)) &  ((v4_card_3 C) &  ((v2_topdim_1 C B) & (r1_xxreal_0 (k3_topdim_1 B C) A)) ) ) ) ) ) )  |  ((v3_topdim_1 B) & (r1_xxreal_0 (k4_topdim_1 B) A)) ) ) ) ) ) ) ).
tt(t4_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (B = k1_xboole_0)  =>  ((k1_topgen_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t4_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  ((k2_topgen_2 A) = (k3_tarski (a_1_0_topgen_2 A))) ) ) ).
tt(t4_topgen_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((r2_hidden k11_arytm_3 B) &  ( (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k2_xboole_0 C D) B)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((r1_tarski C B) => (r2_hidden (k8_setfam_1 A C) B)) ) ) ) )  =>  (! [C:$i] :  ((l1_pre_topc C) =>  ( ( ((u1_struct_0 C) = A)  &  ((u1_pre_topc C) = (k7_setfam_1 A B)) )  =>  ( ((v2_pre_topc C) & (l1_pre_topc C))  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((v4_pre_topc D C) <=> (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden D B) &  ((r1_tarski D C) &  (~  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topgen_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 (k10_funct_6 B))) <=>  (? [C:$i] :  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ((r2_hidden C (k9_xtuple_0 B)) &  ( (D = (k1_funct_1 B C))  & (r2_hidden A (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ).
tt(t4_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k2_group_2 A B D) (k2_group_2 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topmetr3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 k8_metric_1)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k8_metric_1))))) )  =>  ((r1_funct_2 k5_numbers k1_numbers k5_numbers (u1_struct_0 k8_metric_1) A B) =>  ( ((v2_comseq_2 A) => (v2_tbsp_1 B k8_metric_1))  &  ( ((v2_tbsp_1 B k8_metric_1) => (v2_comseq_2 A))  &  ((v2_comseq_2 A) =>  ((k2_seq_2 A) = (k1_tbsp_1 k8_metric_1 B)) ) ) ) ) ) ) ) ) ).
tt(t4_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_pre_topc (k1_pre_topc A B) (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) & (m1_pre_topc (k1_pre_topc A C) (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t4_topreal1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) & (r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)))  =>  ((r1_xxreal_0 (k18_euclid A) (k18_euclid C)) & (r1_xxreal_0 (k18_euclid C) (k18_euclid B))) ) ) ) ) ) ) ) ).
tt(t4_topreal2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((v1_topreal2 A) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k17_euclid (k1_rlvect_1 (k15_euclid 2) A B)) = (k4_real_1 B (k17_euclid A)))  &  ((k18_euclid (k1_rlvect_1 (k15_euclid 2) A B)) = (k4_real_1 B (k18_euclid A))) ) ) ) ) ) ).
tt(t4_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal4 A B C) &  (B = C) ) ) ) ) ) ) ) ) ).
tt(t4_topreal5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc G A k3_topmetr) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  =>  (~  ((v1_connsp_1 A) &  ( ((k1_funct_1 G B) = D)  &  ( ((k1_funct_1 G C) = E)  &  ((r1_xxreal_0 D F) &  ((r1_xxreal_0 F E) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((k1_funct_1 G H) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k21_rvsum_1 (k5_finseq_2 k1_numbers k6_numbers A)) = 1) ) ) ).
tt(t4_topreal7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r1_xxreal_0 A (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) =>  ((r1_xxreal_0 A (k3_finseq_1 B)) | (r2_hidden (k5_real_1 A (k3_finseq_1 B)) (k4_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t4_topreal8,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) |  ((k4_finseq_4 A B) = k6_numbers) ) ) ) ) ).
tt(t4_topreal9,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ( (E = (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) C (k9_real_1 1 B)) (k1_rlvect_1 (k15_euclid A) D B)))  =>  ( (~  ( (E = C)  &  ( (~  (B = k6_numbers) )  &  (~  (C = D) ) ) ) )  &  ( ( ( (B = k6_numbers)  |  (C = D) )  =>  (E = C) )  &  ( (~  ( (E = D)  &  ( (~  (B = 1) )  &  (~  (C = D) ) ) ) )  &  ( ( (B = 1)  |  (C = D) )  =>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_topreala,ax, (! [A:$i] :  (! [B:$i] :  ((k10_finseq_1 A B) = (k4_funct_4 1 2 A B)) ) ) ).
tt(t4_toprealb,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k6_xcmplx_0 A B) 1) => (v4_taxonom2 (k1_toprealb B A))) ) ) ) ) ).
tt(t4_toprealc,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k1_valued_1 (k14_valued_2 B A) (k14_valued_2 C A)) = (k14_valued_2 (k1_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t4_toprns_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid A)))))) )  =>  ((k8_nat_1 (u1_struct_0 (k15_euclid A)) (k1_toprns_1 A C D) B) = (k3_rlvect_1 (k15_euclid A) (k8_nat_1 (u1_struct_0 (k15_euclid A)) C B) (k8_nat_1 (u1_struct_0 (k15_euclid A)) D B))) ) ) ) ) ) ) ) ) ).
tt(t4_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=> (v4_pre_topc (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t4_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k7_subset_1 (u1_struct_0 A) (k5_setfam_1 (u1_struct_0 A) B) (k5_setfam_1 (u1_struct_0 A) C)) (k5_setfam_1 (u1_struct_0 A) (k7_subset_1 (k1_zfmisc_1 (u1_struct_0 A)) B C)))) ) ) ) ) ) ).
tt(t4_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) B C)) (k4_subset_1 (u1_struct_0 A) (k2_pre_topc A B) (k1_tops_1 A C)))) ) ) ) ) ) ).
tt(t4_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ((v1_t_0topsp C A (k3_pcomps_1 B)) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (F = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C D))  &  ((r2_hidden D E) &  (! [G:$i] :  ( ((v1_xreal_0 G) & (v2_xxreal_0 G))  =>  (~ (r1_tarski (k9_metric_1 B F G) (k7_relset_1 (u1_struct_0 A) (u1_struct_0 (k3_pcomps_1 B)) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  => (r2_funct_2 A A (k1_transgeo A (k6_partfun1 A) B) (k1_transgeo A B (k6_partfun1 A)))) ) ) ) ).
tt(t4_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v11_aff_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D F) &  ((r2_analoaf A B C E G) &  ((r2_analoaf A B D C F) & (r2_analoaf A B E C G)) ) )  =>  ((r1_aff_1 A B C D) |  ((r1_aff_1 A B C E) | (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_treal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B C)) )  =>  ( ((k4_topmetr A D) = (k1_tsep_1 k3_topmetr (k4_topmetr A C) (k4_topmetr B D)))  &  ((k4_topmetr B C) = (k2_tsep_1 k3_topmetr (k4_topmetr A C) (k4_topmetr B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_trees_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((r3_xboole_0 A B) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  (A = B) ) ) ) ) ) ).
tt(t4_trees_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k1_trees_1 (k7_finseq_1 B (k9_finseq_1 A))) = (k2_xboole_0 (k1_trees_1 B) (k1_tarski B))) ) ) ) ).
tt(t4_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_trees_3 A) & (v1_trees_3 B))  => (v1_trees_3 (k5_xboole_0 A B))) ) ) ).
tt(t4_trees_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((k1_trees_4 A) = (k1_trees_4 B))  =>  (A = B) ) ) ) ).
tt(t4_trees_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ((v1_zfmisc_1 A) <=> (r2_hidden k1_xboole_0 (k3_trees_1 (k9_xtuple_0 A)))) ) ) ).
tt(t4_trees_a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m4_trees_1 B A) => (r1_tarski B (a_2_0_trees_a A B))) ) ) ) ).
tt(t4_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  => (r2_hidden k1_xboole_0 (k1_triang_1 A))) ) ).
tt(t4_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) <=> (m1_pre_topc B C)) ) ) ) ) ) ) ).
tt(t4_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = (k3_subset_1 (u1_struct_0 A) C))  |  (C = (k3_subset_1 (u1_struct_0 A) B)) )  => (r1_tsep_2 A B C)) ) ) ) ) ) ) ).
tt(t4_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (u1_struct_0 A))  =>  ((v1_tsp_1 B A) <=> (v6_pre_topc A)) ) ) ) ) ) ).
tt(t4_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (v1_tsp_2 B A)) ) ) ) ) ).
tt(t4_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((k1_gr_cy_1 (k4_turing_1 1 (k2_finseq_4 k5_numbers A B))) = A)  &  ((k1_gr_cy_1 (k4_turing_1 2 (k2_finseq_4 k5_numbers A B))) = (k2_nat_1 A B)) ) ) ) ) ) ).
tt(t4_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k11_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k1_binarith A B)))  &  ( ((k1_funct_1 k12_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k1_binarith (k9_margrel1 A) B)))  &  ((k1_funct_1 k13_twoscomp (k10_finseq_1 A B)) = (k9_margrel1 (k1_binarith (k9_margrel1 A) (k9_margrel1 B)))) ) ) ) ) ) ) ).
tt(t4_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (B = (u1_struct_0 A))  =>  ((v1_unialg_2 B A) &  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ((k2_unialg_2 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(t4_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ( ((r2_unialg_2 A B C) &  ((k19_margrel1 C) = k6_numbers) )  =>  ((k2_unialg_2 A B C) = C) ) ) ) ) ) ) ) ).
tt(t4_uniform1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ((v5_pre_topc C (k3_pcomps_1 A) (k3_pcomps_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( (F = (k1_funct_1 C E))  &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 G k6_numbers))  &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  (~  ( (I = (k1_funct_1 C H))  &  ( (~ (r1_xxreal_0 G (k4_metric_1 A E H)))  & (r1_xxreal_0 D (k4_metric_1 B F I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_uniroots,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 k1_complfld)) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (v1_int_1 (k1_funct_1 A B))) ) )  => (v1_int_1 (k4_rlvect_1 k1_complfld A))) ) ) ).
tt(t4_uproots,ax, (! [A:$i] :  ((k1_uproots (k1_tarski A)) = (k9_finseq_1 A)) ) ).
tt(t4_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( ((k4_finseq_1 (k5_urysohn1 A)) = (k2_finseq_1 (k2_nat_1 (k13_newton 2 A) 1)))  &  ((k10_xtuple_0 (k5_urysohn1 A)) = (k1_urysohn1 A)) ) ) ) ).
tt(t4_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k1_integra2 k1_xboole_0 A) = k1_xboole_0) ) ) ).
tt(t4_urysohn3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v10_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( (~  (B = k1_xboole_0) )  &  ((r1_xboole_0 B C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A))))))) )  =>  (~  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((m1_urysohn3 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E) A B C E) &  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E))) =>  ((k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D E) F) = (k1_funct_1 (k1_urysohn3 k2_urysohn1 (k9_setfam_1 (u1_struct_0 A)) D (k2_nat_1 E 1)) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_valuat_1 C A B) => (r2_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B C (k5_cqc_lang A)) (k1_margrel1 k6_margrel1 (k2_valuat_1 A B) k8_margrel1))) ) ) ) ) ) ).
tt(t4_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B k3_numbers))  =>  ((r1_tarski A B) => (v5_relat_1 A k3_numbers)) ) ) ) ) ).
tt(t4_valued_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_membered B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k3_funct_2 A k2_numbers (k14_valued_1 A B C D) E) = (k6_xcmplx_0 (k3_funct_2 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_valued_2,ax, (! [A:$i] : (m1_subset_1 (k9_valued_2 A) (k1_zfmisc_1 (k8_valued_2 A)))) ).
tt(t4_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 B (u1_struct_0 A)) &  ((v3_vectmetr B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v2_funct_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) (u1_struct_0 A)) & (v3_vectmetr (k2_tops_2 (u1_struct_0 A) (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t4_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k4_vectsp_1 A B D C) = (k4_vectsp_1 A B E C))  =>  ( (C = (k4_struct_0 B))  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) A A) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) A A) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k2_finseq_1 A)))  =>  ((k2_laplace B C A D (k5_matrlin2 A A D E F)) = (k5_matrlin2 (k7_nat_d A 1) (k7_nat_d A 1) D (k2_laplace B C A D E) (k2_laplace B C A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  ( (~  (B = (k4_struct_0 A)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((k6_algstr_0 A E B) = (k5_struct_0 A)) ) ) ) ) )  &  ( ((k6_algstr_0 A B (k1_algstr_0 A C D)) = (k1_algstr_0 A (k6_algstr_0 A B C) (k6_algstr_0 A B D)))  &  ((k6_algstr_0 A (k1_algstr_0 A C D) B) = (k1_algstr_0 A (k6_algstr_0 A C B) (k6_algstr_0 A D B))) ) ) ) ) ) ) ) )  <=>  ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ).
tt(t4_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ( (B = (k3_rlvect_1 A C D))  &  (B = (k3_rlvect_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  => (v1_vectsp_4 (k6_domain_1 (u1_struct_0 B) (k4_struct_0 B)) A B)) ) ) ) ).
tt(t4_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v7_vectsp_1 C A) & (m1_vectsp_4 C A B))  =>  ((k1_vectsp_5 A B C C) = C) ) ) ) ) ) ) ).
tt(t4_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_vectsp_6 E A B C) =>  ((r1_tarski C D) => (m2_vectsp_6 E A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ((v1_vectsp_7 (k7_domain_1 (u1_struct_0 B) C D) A B) &  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A B))) (u1_struct_0 (k1_vectsp_8 A B)) (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B) (u1_lattices (k1_vectsp_8 A B)) (k6_vectsp_5 A B))) ) ) ) ).
tt(t4_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_vectsp_6 E A B) &  ( ((k1_vectsp_6 A B E) = (k9_subset_1 (u1_struct_0 B) (k10_xtuple_0 D) (k1_vectsp_6 A B C)))  &  ((k3_vectsp_6 A B D C) = (k3_vectsp_6 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k1_vfunct_1 A B C D) (k1_vfunct_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t4_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k1_vfunct_1 A B C D) (k1_vfunct_1 A B D C))) ) ) ) ) ) ) ) ).
tt(t4_waybel_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v2_waybel_0 C A))  => (v2_waybel_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel10,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_funct_1 (k4_relat_1 B)) &  ((v1_funct_2 (k4_relat_1 B) (u1_struct_0 (k5_yellow_0 A B)) (u1_struct_0 A)) & (m1_subset_1 (k4_relat_1 B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)) (u1_struct_0 A))))) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k5_yellow_0 A B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B)) (u1_struct_0 A))))) )  =>  ( (C = (k4_relat_1 B))  => (v5_orders_3 C (k5_yellow_0 A B) A)) ) ) ) ) ) ) ) ).
tt(t4_waybel11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r2_hidden (k1_yellow_0 A B) B)) ) ) ) ).
tt(t4_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_yellow_4 A C B) => (r1_tarski (k4_waybel_0 A B) (k4_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t4_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ( (~ (v1_xboole_0 (u1_struct_0 A)))  &  ((v1_waybel_0 (u1_struct_0 A) A) &  ((v12_waybel_0 (u1_struct_0 A) A) & (m1_subset_1 (u1_struct_0 A) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t4_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k6_waybel_0 A (k13_lattice3 A B C)) = (k9_subset_1 (u1_struct_0 A) (k6_waybel_0 A B) (k6_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t4_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((v2_funct_2 C (u1_struct_0 B)) & (v3_waybel_1 (k1_waybel_1 A B C D) A B))  => (r5_waybel_1 B (k1_yellow_2 B A D))) ) ) ) ) ) ) ) ) ).
tt(t4_waybel16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_waybel_4 A (k6_subset_1 (u1_struct_0 A) (k5_waybel_0 A C)) B) =>  ((k7_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k6_domain_1 (u1_struct_0 A) B)) = (k9_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (k5_waybel_0 A C))) ) ) ) ) ) ) ) ).
tt(t4_waybel17,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v24_waybel_0 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v5_pre_topc C A B) => (v5_orders_3 C A B)) ) ) ) ) ) ) ).
tt(t4_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k4_waybel18 A B C)))) =>  ((k8_relset_1 (u1_struct_0 (k3_waybel18 A B)) (u1_struct_0 (k4_waybel18 A B C)) (k6_waybel18 A B C) D) = (k4_card_3 (k2_funct_7 (k12_pralg_1 A B) C D))) ) ) ) ) ) ) ) ) ).
tt(t4_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_waybel19 A) & (l1_waybel_9 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v3_pre_topc (k3_subset_1 (u1_struct_0 A) (k6_waybel_0 A B)) A) & (v4_pre_topc (k6_waybel_0 A B) A)) ) ) ) ) ).
tt(t4_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v2_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( ((v2_lattice3 A) &  ((v4_orders_2 A) & (v3_orders_2 A)) )  =>  ((k11_lattice3 A (k4_yellow_0 A) B) = B) )  &  ((v1_lattice3 A) =>  ((k10_lattice3 A (k4_yellow_0 A) B) = (k4_yellow_0 A)) ) ) ) ) ) ) ).
tt(t4_waybel20,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r1_tarski C (k2_zfmisc_1 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ( ((k9_xtuple_0 (k7_relat_1 (k15_funct_3 A B) C)) = (k7_relat_1 A (k9_xtuple_0 C)))  &  ((k10_xtuple_0 (k7_relat_1 (k15_funct_3 A B) C)) = (k7_relat_1 B (k10_xtuple_0 C))) ) ) ) ) ) ) ) ).
tt(t4_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v19_waybel_0 C A B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r3_waybel_0 A B C D)) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_waybel_0 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t4_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  => (v22_waybel_0 (k3_struct_0 A) A A)) ) ).
tt(t4_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v8_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k11_waybel_0 A C) = (k11_waybel_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k5_waybel_0 A D)))) ) ) ) ) ) ) ) ) ).
tt(t4_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C A))  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D) E F) & (v23_waybel_0 E A B))  => (v3_tops_2 F C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel26,ax,(m1_yellow_9 (k1_waybel25 k9_waybel18) (k3_yellow_1 1))).
tt(t4_waybel27,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_waybel27 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v2_waybel27 E)) )  =>  ( ((r1_tarski (k9_xtuple_0 D) (k1_funct_2 B (k1_funct_2 A C))) & (r1_tarski (k10_xtuple_0 D) (k9_xtuple_0 E)))  =>  ((k3_relat_1 D E) = (k6_partfun1 (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  => (v1_waybel28 (k3_struct_0 A) A)) ) ).
tt(t4_waybel29,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C)) & (m1_yellow_0 D (k6_yellow_1 (k2_zfmisc_1 A B) C))) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C))) & (m1_yellow_0 E (k6_yellow_1 A (k6_yellow_1 B C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 E) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 E) (u1_struct_0 D))))) )  =>  ( ((v1_waybel27 F) &  ((v2_funct_1 F) & (v2_funct_2 F (u1_struct_0 D))) )  => (v23_waybel_0 F E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k1_yellow_0 A (k2_yellow_4 A B C)) = (k13_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t4_waybel30,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k2_yellow_1 (k7_waybel_0 A))) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  ((k1_yellow_0 (k2_yellow_1 (k7_waybel_0 A)) (k4_yellow_4 (k2_yellow_1 (k7_waybel_0 A)) (k6_domain_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) C) B)) = (k3_tarski (a_3_0_waybel30 A B C))) ) ) ) ) ) ) ).
tt(t4_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) )  =>  ( ((k2_yellow_1 (u1_pre_topc A)) = B)  =>  (! [C:$i] :  ( ((v6_waybel23 C B) & (m1_waybel23 C B))  =>  ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ).
tt(t4_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow_9 B A) =>  ((v4_waybel11 B) => (v2_pre_topc B)) ) ) ) ) ).
tt(t4_waybel33,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v25_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) &  ((v25_waybel_0 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D)))  =>  ((k1_waybel11 A C) = (k1_waybel11 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A)) (k1_waybel34 A B C) (k2_waybel34 (k7_lattice3 B) (k7_lattice3 A) (k3_waybel34 A B C)))) ) ) ) ) ) ).
tt(t4_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v4_waybel_4 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (m1_waybel35 (k7_domain_1 (u1_struct_0 A) (k3_yellow_0 A) B) A C)) ) ) ) ) ) ).
tt(t4_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_waybel_3 A (k3_yellow_0 A) B)) ) ) ) ).
tt(t4_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k4_waybel_4 A) B)) ) ) ) ).
tt(t4_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  ((v4_waybel_1 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) => (v3_waybel_3 A)) ) ) ).
tt(t4_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v18_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ((v2_waybel_2 B) &  ((v19_waybel_0 C A B) & (v2_funct_1 C)) )  => (v2_waybel_2 A)) ) ) ) ) ) ) ).
tt(t4_waybel_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v1_subset_1 B (u1_struct_0 A)) <=>  (~ (r2_hidden (k3_yellow_0 A) B)) ) ) ) ) ) ).
tt(t4_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k2_waybel_8 A B)) <=>  ((r1_orders_2 A C B) & (v1_waybel_3 C A)) ) ) ) ) ) ) ) ).
tt(t4_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_waybel_0 A B) = (k2_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_struct_0 A))) ) ) ) ) ).
tt(t4_weddwitt,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k1_card_1 (k1_funct_2 A B)) = (k1_newton B A)) ) ) ) ) ) ).
tt(t4_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ( ((v5_pre_topc C A B) & (v1_tops_2 D B))  => (v1_tops_2 (k6_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t4_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v12_waybel_0 B A) & (r2_hidden C B))  => (r1_tarski (k1_wellord1 (u1_orders_2 A) C) B)) ) ) ) ) ) ).
tt(t4_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((r2_wellord1 A (k1_relat_1 A)) <=> (v2_wellord1 A)) ) ) ).
tt(t4_wellset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  (~  ((r2_hidden A (k1_relat_1 C)) &  ((r2_hidden B (k1_relat_1 C)) &  ((v2_wellord1 C) &  ((r2_hidden A (k1_wellord1 C B)) & (r2_hidden (k4_tarski B A) C)) ) ) ) ) ) ) ) ) ).
tt(t4_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_int_1 A B) & (r1_int_1 A C))  => (r1_int_1 A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t4_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~ (r1_xboole_0 A B))  &  (! [C:$i] :  (~ (r2_hidden C (k3_xboole_0 A B))) ) ) )  &  (~  ( (? [C:$i] : (r2_hidden C (k3_xboole_0 A B)))  & (r1_xboole_0 A B)) ) ) ) ) ).
tt(t4_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_xboole_0 (k2_xboole_0 A B) C) = (k2_xboole_0 A (k2_xboole_0 B C))) ) ) ) ).
tt(t4_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k5_xboolean A B)) = (k5_xboolean A B)) ) ) ) ) ).
tt(t4_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k3_xcmplx_0 A (k3_xcmplx_0 B C)) = (k3_xcmplx_0 (k3_xcmplx_0 A B) C)) ) ) ) ) ) ) ).
tt(t4_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (? [C:$i] :  ((v1_xreal_0 C) &  ( (~ (r1_xxreal_0 A C))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ).
tt(t4_xregular,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C D) &  ((r2_hidden D E) & (r2_hidden E B)) )  => (r1_xboole_0 C A)) ) ) ) ) ) ) ) ).
tt(t4_xtuple_0,ax, (! [A:$i] :  ((v2_xtuple_0 A) =>  (! [B:$i] :  ((v2_xtuple_0 B) =>  ( ( ((k4_xtuple_0 A) = (k4_xtuple_0 B))  &  ( ((k5_xtuple_0 A) = (k5_xtuple_0 B))  &  ((k2_xtuple_0 A) = (k2_xtuple_0 B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t4_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((r1_xxreal_0 k1_xxreal_0 A) =>  (A = k1_xxreal_0) ) ) ) ).
tt(t4_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r2_hidden A (k4_xxreal_1 B C)) <=>  ( (~ (r1_xxreal_0 A B))  &  (~ (r1_xxreal_0 C A)) ) ) ) ) ) ) ) ) ).
tt(t4_xxreal_2,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r2_hidden A B) => (r1_xxreal_0 A (k1_xxreal_2 B))) ) ) ) ) ).
tt(t4_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  ((k1_xxreal_3 A k6_numbers) = A) ) ) ).
tt(t4_yellow_0,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_orders_2 A B C) =>  (! [D:$i] :  ( ((r1_lattice3 A D C) => (r1_lattice3 A D B))  &  ((r2_lattice3 A D B) => (r2_lattice3 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t4_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  ((k3_yellow_0 (k3_yellow_3 A B)) = (k7_yellow_3 A B (k3_yellow_0 A) (k3_yellow_0 B))) ) ) ) ) ).
tt(t4_yellow11,ax, ((k6_subset_1 3 2) = (k6_domain_1 k5_numbers 2)) ).
tt(t4_yellow12,ax, (! [A:$i] :  (! [B:$i] :  ( ((k9_xtuple_0 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B))) = (k2_zfmisc_1 A B))  &  ((k10_xtuple_0 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B))) = (k2_zfmisc_1 B A)) ) ) ) ).
tt(t4_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  => (v8_pre_topc A)) ) ).
tt(t4_yellow14,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ((v2_struct_0 B) & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  => (v2_struct_0 A)) ) ) ) ) ) ) ).
tt(t4_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k6_margrel1) =>  ((k4_finseq_1 (k1_yellow15 A B C)) = (k4_finseq_1 B)) ) ) ) ) ) ).
tt(t4_yellow16,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ((v11_quantal1 A) &  ((r1_tarski (k10_xtuple_0 B) (k10_xtuple_0 A)) & (r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A))) )  =>  ((k3_relat_1 B A) = B) ) ) ) ) ) ).
tt(t4_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k8_relat_1 (k12_card_3 A B) (k1_funct_1 A B)) = (k4_card_3 A)) ) ) ) ) ).
tt(t4_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  ( ((r1_yellow18 A B) & (r1_yellow18 B C))  => (r1_yellow18 A C)) ) ) ) ) ) ) ).
tt(t4_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_waybel_7 A (k1_yellow19 A B) B)) ) ) ) ).
tt(t4_yellow_1,ax, (! [A:$i] :  ((k3_yellow_1 A) = (k2_yellow_1 (k9_setfam_1 A))) ) ).
tt(t4_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D B A) =>  ( ((k13_functor0 B A B D C) = (k12_functor0 B))  =>  ((g2_functor0 B A (u1_functor0 B A D) (u2_functor0 B A D)) = (k15_functor0 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t4_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) &  ((v4_yellow21 A) & (l2_altcat_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v23_waybel_0 (k5_yellow21 A B C D) (k3_yellow21 A B) (k3_yellow21 A C)) => (v3_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t4_yellow_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_yellow_0 A B) & (r2_yellow_0 A C))  =>  ((r2_yellow_0 A (k2_xboole_0 B C)) &  ((k2_yellow_0 A (k2_xboole_0 B C)) = (k12_lattice3 A (k2_yellow_0 A B) (k2_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t4_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k12_lattice3 A (k1_yellow_0 A B) C) = C) ) ) ) ) ) ) ) ).
tt(t4_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_yellow_4 A B C) & (r1_yellow_4 A C D))  => (r1_yellow_4 A B D)) ) ) ) ) ) ) ) ) ).
tt(t4_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A D (k12_lattice3 A B C)) => (r1_orders_2 A D B)) ) ) ) ) ) ) ) ) ).
tt(t4_yellow_6,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((u1_struct_0 (k3_yellow_6 A B C)) = (u1_struct_0 A)) ) ) ) ) ) ) ).
tt(t4_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v3_orders_2 A) <=> (v3_orders_2 (k7_lattice3 A))) ) ) ).
tt(t4_yellow_8,ax, (! [A:$i] :  (! [B:$i] :  ( ((r2_tarski A B) & (v4_card_3 A))  => (v4_card_3 B)) ) ) ).
tt(t4_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_waybel_0 A B) = (k3_tarski (a_2_1_yellow_9 A B)))  &  ((k3_waybel_0 A B) = (k3_tarski (a_2_2_yellow_9 A B))) ) ) ) ) ) ).
tt(t4_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_cat_1 B A (k11_nattra_1 A (k1_yoneda_1 A))) =>  ( ((v2_funct_1 (k7_cat_1 A (k11_nattra_1 A (k1_yoneda_1 A)) B)) & (v14_cat_1 B A (k11_nattra_1 A (k1_yoneda_1 A))))  => (v2_funct_1 B)) ) ) ) ) ).
tt(t4_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 B C) => (r1_tarski (k1_zf_colla A B) (k1_zf_colla A C))) ) ) ) ) ) ) ).
tt(t4_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v8_zf_fund1 B A) &  ((r2_hidden C B) & (r2_hidden D B)) )  =>  ((r2_hidden (k2_xboole_0 C D) B) &  ((r2_hidden (k6_subset_1 C D) B) & (r2_hidden (k3_relat_1 C D) B)) ) ) ) ) ) ) ) ) ).
tt(t4_zf_fund2,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ((k1_zf_fund2 A B C) = (a_3_1_zf_fund2 A B C)) ) ) ) ) ) ) ).
tt(t4_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((k21_zf_lang (k7_zf_lang A B)) = A)  &  ((k22_zf_lang (k7_zf_lang A B)) = B) ) ) ) ) ) ).
tt(t4_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  <=> (r2_hidden A k9_zf_lang)) ) ).
tt(t4_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k1_tarski A) = (k2_tarski B C))  =>  (A = B) ) ) ) ) ).
tt(t4_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ((r2_zf_model A k8_zf_model) <=>  (! [B:$i] :  ((m1_subset_1 B A) => (r2_hidden (k3_tarski B) A)) ) ) ) ) ) ).
tt(t4_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( (~ (r2_hidden A (k4_zf_lang1 C)))  =>  ((r1_zf_model B D C) <=> (r1_zf_model B D (k8_zf_lang A C))) ) ) ) ) ) ) ) ) ) ).
tt(t4_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_zf_lang A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( (~ (r2_hidden C (k5_zf_model B A)))  <=> (r2_hidden C (k5_zf_model (k6_zf_lang B) A))) ) ) ) ) ) ) ).
tt(t4_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_zf_model A) => (r1_zfrefle1 A k2_zfrefle1)) ) ) ).
tt(t4_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_zf_model A k10_zf_model)) ) ).
tt(t4_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((v6_zmodul01 A) &  ((k3_rlvect_1 A B B) = (k4_struct_0 A)) )  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t50_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r2_abcmiz_0 A B C) => (r1_tarski C (k2_abcmiz_0 A (k6_abcmiz_0 A B C)))) ) ) ) ) ) ) ).
tt(t50_abcmiz_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_abcmiz_1) =>  (! [B:$i] :  ((m1_subset_1 B k2_abcmiz_1) =>  (! [C:$i] :  ( ((v1_instalg1 C) &  ((v1_abcmiz_1 C) &  ((v3_abcmiz_1 C) & (l1_msualg_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_instalg1 D) &  ((v1_abcmiz_1 D) &  ((v3_abcmiz_1 D) & (l1_msualg_1 D)) ) )  =>  ( ((k35_abcmiz_1 A C) = (k35_abcmiz_1 B D))  =>  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t50_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ( ((r1_abcmiz_a A B C) & (r1_abcmiz_a A C D))  => (r1_abcmiz_a A B D)) ) ) ) ) ) ) ) ) ).
tt(t50_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A C D) &  ((r5_aff_1 A C E) &  ((r2_hidden B D) & (r2_hidden B E)) ) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( (~  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) )  => (v4_aff_2 A)) ) ) ).
tt(t50_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  (! [J:$i] :  ( (A = (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k1_ordinal4 (k5_afinsq_1 B) (k5_afinsq_1 C)) (k5_afinsq_1 D)) (k5_afinsq_1 E)) (k5_afinsq_1 F)) (k5_afinsq_1 G)) (k5_afinsq_1 H)) (k5_afinsq_1 I)) (k5_afinsq_1 J)))  =>  ( ((k1_afinsq_1 A) = 9)  &  ( ((k1_funct_1 A k6_numbers) = B)  &  ( ((k1_funct_1 A 1) = C)  &  ( ((k1_funct_1 A 2) = D)  &  ( ((k1_funct_1 A 3) = E)  &  ( ((k1_funct_1 A 4) = F)  &  ( ((k1_funct_1 A 5) = G)  &  ( ((k1_funct_1 A 6) = H)  &  ( ((k1_funct_1 A 7) = I)  &  ((k1_funct_1 A 8) = J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v5_relat_1 A k4_numbers) =>  ((k7_afinsq_2 A) = (k6_afinsq_2 k4_numbers A k44_binop_2)) ) ) ) ).
tt(t50_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 A)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 A)) =>  ( ((r2_hidden E B) &  ((r2_hidden E C) &  ((r2_hidden E D) &  ((r2_hidden F B) &  ((r2_hidden G C) &  ((r2_hidden J C) &  ((r2_hidden H D) &  ((r2_hidden K D) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_1 D A) &  ((r2_analoaf A F G I J) & (r2_analoaf A F H I K)) ) ) ) ) ) ) ) ) ) ) )  =>  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (B = C)  |  ( (B = D)  |  ( ( (~  (E = I) )  &  (~  (F = I) ) )  | (r2_analoaf A G H J K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_analoaf A) &  ((v2_tdgroup A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (A = (k2_tdgroup (k5_afvect0 A B))) ) ) ) ) ).
tt(t50_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_instalg1 C) & (l1_msualg_1 C)) )  =>  ( ( ((m2_algspec1 C A) & (m2_algspec1 C B))  =>  ((r1_circcomb A B) & (m2_algspec1 C (k2_circcomb A B))) )  &  ( ((r1_circcomb A B) & (m2_algspec1 C (k2_circcomb A B)))  =>  ((m2_algspec1 C A) & (m2_algspec1 C B)) ) ) ) ) ) ) ) ) ).
tt(t50_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_altcat_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_altcat_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 (k1_altcat_4 A) B C)) =>  ( (~  ((k1_altcat_1 (k1_altcat_4 A) B C) = k1_xboole_0) )  => (v4_altcat_3 D (k1_altcat_4 A) B C)) ) ) ) ) ) ) ) ) ).
tt(t50_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r6_analmetr A D E B) & (r9_analmetr A B C))  => (r6_analmetr A D E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ( (~ (r2_analort A B C D G E F))  &  ( (~ (r2_analort A B C D G F E))  &  ((r2_analort A B C F H F E) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ( ((r2_analort A B C D G D I) | (r2_analort A B C D G I D))  &  ((r2_analort A B C F H F I) | (r2_analort A B C F H I F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = (k13_aofa_000 A B C)) )  &  ( (~  (C = (k13_aofa_000 A B C)) )  & (r2_hidden (k13_aofa_000 A B C) (k18_aofa_000 A))) ) ) ) ) ) ) ) ) ).
tt(t50_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m3_aofa_i00 F A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E) =>  ( ( (~ (v1_abian (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C)))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k65_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k65_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (v1_abian (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C))) )  &  ( ((v1_abian (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C)) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k66_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k66_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (v1_abian (k3_funct_2 (k9_funct_2 B k4_numbers) k4_numbers F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_armstrng,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ( ((v11_armstrng B) &  (C = (a_2_13_armstrng A B)) )  =>  ((v1_xboole_0 B) |  (B = (k13_armstrng A (k10_armstrng A C))) ) ) ) ) ) ) ) ).
tt(t50_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((k9_arytm_3 A k11_arytm_3) = A) ) ) ).
tt(t50_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~  (C = 1) )  &  (~  ((k4_power A B) = (k4_power C (k8_real_1 B (k6_power C A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v13_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B D)) = (k1_bcialg_1 A D C))  &  ((k2_bcialg_1 A B) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_2 B A) =>  ((v12_bcialg_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)) A) & (m2_bcialg_1 (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)) A)) ) ) ) ) ).
tt(t50_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_bcialg_4 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v4_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) )  <=>  ( (~ (v2_struct_0 A))  &  ((v5_bcialg_1 A) &  ((v2_bcialg_4 A) &  ((v5_bcialg_4 A) &  ((v6_bcialg_4 A) &  ((v7_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) ) ) ) ).
tt(t50_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v11_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  ((v8_bcialg_1 A) & (m1_bcialg_5 A 1 k6_numbers k6_numbers k6_numbers)) ) ) ) ).
tt(t50_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (~  ( (C = (k5_bcialg_6 A B E))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B)) &  ((v2_bcialg_6 F (k9_bcialg_2 A D) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B))))) ) )  =>  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B) (k6_bcialg_6 A C D) F)) & (v2_funct_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m3_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A C (k1_bcialg_1 A D C)) B) => (r2_hidden C B)) ) ) ) ) ) ) ) ) ) ).
tt(t50_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k5_bhsp_1 A B (k4_struct_0 A)))) ) ) ) ).
tt(t50_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_bhsp_2 A C D)) => (r2_hidden B (k5_bhsp_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v2_comseq_2 A) & (v1_bhsp_2 C B))  =>  ((v1_bhsp_2 (k5_bhsp_4 B C A) B) &  ((k1_bhsp_2 B (k5_bhsp_4 B C A)) = (k1_rlvect_1 B (k1_bhsp_2 B C) (k2_seq_2 A))) ) ) ) ) ) ) ) ) ).
tt(t50_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  => (r1_tarski (k8_vectsp10 A B D) (k10_bilinear A B C (k9_bilinear A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t50_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r4_boolealg A (k4_lattices A B C) (k1_boolealg A B C))) ) ) ) ) ) ) ).
tt(t50_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 k5_topmetr)) =>  (~  ((r1_topreal1 (k15_euclid A) C D B) &  ( (~ (r1_xxreal_0 F E))  &  ( (~  (E = k6_numbers) )  &  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  & (m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k1_pre_topc k1_borsuk_4 G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) D))))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc k1_borsuk_4 G)) (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) D)))))))) )  =>  (~  ( (G = (k3_rcomp_1 E F))  &  ((v3_tops_2 H (k1_pre_topc k1_borsuk_4 G) (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) D)))) &  ((k1_funct_1 H E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_measure6 (k2_rcomp_1 A k1_xxreal_0)) = (k3_rcomp_1 A k1_xxreal_0)) ) ) ).
tt(t50_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ( ((v3_funct_1 E) & (m1_borsuk_2 E A C C))  =>  ((r1_borsuk_6 A B C) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k2_borsuk_6 A B C D k3_borsuk_6) (k1_borsuk_2 A B C C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) => (r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 B) (k1_jordan24 (k7_real_1 B (k8_real_1 (k8_real_1 2 k32_sin_cos) A))))) ) ) ) ).
tt(t50_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C D) C E)) (k6_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  ( (H = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B J) (k16_funcop_1 C K)) (k16_funcop_1 D L)) (k16_funcop_1 E M)) (k16_funcop_1 F N)) (k16_funcop_1 G O)) (k16_funcop_1 A I)))  =>  ((k9_xtuple_0 H) = (k5_enumset1 A B C D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k9_xboolean k8_margrel1 A) = k7_margrel1) ) ) ).
tt(t50_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k5_bvfunc26 A C D)) (k5_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) (k2_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t50_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) D)) (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) (k9_cqc_lang A B D))) (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_card_1,ax, (2 = (k2_tarski k1_xboole_0 1)) ).
tt(t50_card_2,ax, (! [A:$i] :  (! [B:$i] : (r1_xxreal_0 (k5_card_1 (k2_tarski A B)) 2)) ) ).
tt(t50_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r2_hidden k1_xboole_0 (k8_card_3 A))) ) ).
tt(t50_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k3_xboole_0 (k3_tarski (k10_xtuple_0 B)) A) = (k3_tarski (k10_xtuple_0 (k1_yellow20 B (k7_funcop_1 (k9_xtuple_0 B) A))))) ) ) ) ).
tt(t50_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v11_cat_1 B A) =>  (! [C:$i] :  ((m1_cat_1 C A B B) =>  ((k4_cat_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t50_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v11_struct_0 D))  &  ((v2_cat_1 D) &  ((v3_cat_1 D) &  ((v4_cat_1 D) &  ((v5_cat_1 D) &  ((v6_cat_1 D) & (l1_cat_1 D)) ) ) ) ) ) )  =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F C D) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((k1_binop_1 (k7_cat_1 (k8_cat_2 A C) (k8_cat_2 B D) (k17_cat_2 A C B D E F)) G H) = (k9_cat_2 B D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B E) G) (k3_funct_2 (u1_struct_0 C) (u1_struct_0 D) (k7_cat_1 C D F) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 (u4_struct_0 A))))) )  =>  ((r1_cat_3 A B k1_xboole_0 C) <=> (v10_cat_1 B A)) ) ) ) ) ) ) ).
tt(t50_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k23_cat_4 A B))) =>  (~  ((k2_cat_1 (k23_cat_4 A B) C D) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t50_catalan2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v5_relat_1 A k1_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (? [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k1_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  &  ( ((k1_relset_1 k5_numbers B) = (k1_relset_1 k5_numbers A))  &  ((r1_xxreal_0 (k18_complex1 (k7_afinsq_2 A)) (k7_afinsq_2 B)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) =>  ((k1_seq_1 B C) = (k18_complex1 (k1_seq_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t50_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((v1_partfun1 A k2_numbers) &  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((k7_partfun1 k2_numbers A (k8_complex1 B C)) = (k8_complex1 (k7_partfun1 k2_numbers A B) (k7_partfun1 k2_numbers A C))) ) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~ (r1_cfcont_1 A B)) ) )  | (r2_cfcont_1 A k2_numbers)) ) ) ) ).
tt(t50_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k2_numbers (k46_valued_1 A k2_numbers k2_numbers (k1_cfunct_1 A B C) (k1_cfunct_1 A D E)) (k1_cfunct_1 A (k46_valued_1 A k2_numbers k2_numbers (k19_valued_1 A k2_numbers k2_numbers B E) (k19_valued_1 A k2_numbers k2_numbers D C)) (k19_valued_1 A k2_numbers k2_numbers C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t50_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C (k2_nat_1 A 1))) =>  ((r2_hidden E (k9_chain_1 B C A D)) <=> (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden C (k2_chord A B)) <=>  ( (~ (r2_hidden C B))  &  (? [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) &  ((r2_hidden D B) & (r1_chord A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t50_circcmb3,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  (~ (r2_hidden A B)) ) ) ) ) ).
tt(t50_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_circcomb A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_circcomb B) & (l1_msualg_1 B)) )  => (v2_circcomb (k2_circcomb A B))) ) ) ) ).
tt(t50_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B F))) => (m1_subset_1 (k3_relat_1 C G) (k4_card_3 (u3_msualg_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_ordinal1 A) & (v1_ordinal1 B))  => (v1_ordinal1 (k3_xboole_0 A B))) ) ) ).
tt(t50_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (A = (k4_classes1 (k2_ordinal1 A))) ) ) ).
tt(t50_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_clvect_1 B) & (m1_clvect_1 B A))  =>  (! [C:$i] :  ( ((v1_clvect_1 C) & (m1_clvect_1 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t50_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k4_clvect_2 A C D)) => (r2_hidden B (k5_clvect_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v2_comseq_2 C) & (v1_clvect_2 B A))  =>  ((v1_clvect_2 (k6_clvect_3 A B C) A) &  ((k1_clvect_2 A (k6_clvect_3 A B C)) = (k1_clvect_1 A (k1_clvect_2 A B) (k3_comseq_2 C))) ) ) ) ) ) ) ) ) ).
tt(t50_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k10_cohsp_1 A)) <=> (r2_hidden (k4_tarski (k1_tarski B) C) (k7_cohsp_1 A))) ) ) ) ) ).
tt(t50_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k4_complex1 A) = k6_numbers)  =>  ((k17_complex1 A) = (k17_complex1 (k3_complex1 A))) ) ) ) ).
tt(t50_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k3_complex1 (k1_complex2 A B)) = k6_numbers)  <=>  ( ((k4_complex1 (k1_complex2 A B)) = (k8_real_1 (k17_complex1 A) (k17_complex1 B)))  |  ((k4_complex1 (k1_complex2 A B)) = (k1_real_1 (k8_real_1 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ) ) ) ).
tt(t50_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k2_complfld A)) = A) ) ) ).
tt(t50_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 A) = (k3_finseq_1 D)) ) )  =>  ((k1_finseqop k2_numbers k2_numbers k2_numbers k28_binop_2 A B) = (k1_finseqop k1_numbers k1_numbers k1_numbers k34_binop_2 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t50_compos_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((r2_hidden A (k2_afinsq_1 (k9_compos_1 B C))) <=>  (A = k6_numbers) ) ) ) ) ) ) ).
tt(t50_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v3_compos_1 C A) & (v4_compos_1 C A)) ) ) ) ) ) ) )  =>  ((k1_funct_1 (k2_compos_2 A C B) (k62_valued_1 C)) = (k5_compos_0 (u1_compos_1 A) B (k62_valued_1 C))) ) ) ) ) ) ) ).
tt(t50_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 A)))  & (r1_xxreal_0 k6_numbers (k21_sin_cos (k1_comptrig A)))) ) ) ) ).
tt(t50_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( (~ (r2_hidden A (k4_finseq_1 D)))  =>  ((k6_comput_1 B C A D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t50_comseq_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_relset_1 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers (k25_valued_1 k5_numbers k2_numbers B A)) (k26_valued_1 k5_numbers k1_numbers (k55_valued_1 k5_numbers k2_numbers B) (k17_complex1 A)))) ) ) ) ).
tt(t50_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((v1_comseq_2 A) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ((m2_valued_0 B k2_numbers A) & (v2_comseq_2 B)) ) ) ) ) ) ) ) ).
tt(t50_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_convex4 B A) & (v2_convex4 C A))  =>  (! [D:$i] :  ((v1_xcmplx_0 D) => (v2_convex4 (k7_rusub_4 A (k19_convex4 A B D) (k19_convex4 A C (k6_xcmplx_0 k6_complex1 D))) A)) ) ) ) ) ) ) ) ) ).
tt(t50_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) => (r3_cqc_the1 A B (k5_cqc_lang A))) ) ) ) ).
tt(t50_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k6_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B))) (k11_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t50_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A B C) <=>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) & (v2_cqc_the1 (k8_cqc_lang A C B) A)) ) ) ) ) ) ) ) ).
tt(t50_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k15_csspace A B B) = k6_numbers) ) ) ) ) ).
tt(t50_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 B)) (k21_sin_cos (k8_real_1 2 (k7_real_1 B A)))))) ) ) ) ) ).
tt(t50_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k10_real_1 A (k5_square_1 E))) ) )  =>  ( (B = k6_numbers)  |  ( ((k7_real_1 B C) = k6_numbers)  |  ((k1_seq_1 (k3_diff_1 D C) B) = (k10_real_1 (k8_real_1 (k8_real_1 (k1_real_1 A) C) (k7_real_1 (k8_real_1 2 B) C)) (k5_square_1 (k7_real_1 (k5_square_1 B) (k8_real_1 C B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D F) = (k3_funct_2 k1_numbers k1_numbers (k5_diff_1 E A) F)) ) )  =>  ((k9_diff_1 D B C) = (k9_real_1 (k9_diff_1 E (k7_real_1 B (k13_complex1 A 2)) (k7_real_1 C (k13_complex1 A 2))) (k9_diff_1 E (k9_real_1 B (k13_complex1 A 2)) (k9_real_1 C (k13_complex1 A 2))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_dilworth,ax, (! [A:$i] :  ( ((v8_struct_0 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  => (r1_xxreal_0 (k1_dilworth A) (k5_card_1 B))) ) ) ) ).
tt(t50_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  ((r2_hidden D (k8_eqrel_1 (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C))) &  ( (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (~  ((r2_hidden E (k6_ec_pf_1 A B C)) &  ( (E = (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers))  &  (D = (k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) E)) ) ) ) ) )  &  (! [E:$i] :  ((m2_subset_1 E (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k3_ec_pf_1 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (~  ((r2_hidden E (k6_ec_pf_1 A B C)) &  ( (E = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers F G 1))  &  (D = (k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (~  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  &  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) = k6_numbers) )  &  (~  ( ((r1_ec_pf_1 A C D) | (r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)))  <=>  ((k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) = (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) => (m1_oppcat_1 (k20_ens_1 B C) B (k11_ens_1 A))) ) ) ) ) ) ) ).
tt(t50_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v4_partfun3 C) & (m2_finseq_1 C k1_numbers))  =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ((k1_seq_1 C D) = (k8_real_1 A B)) )  =>  ((k1_seq_1 (k4_entropy1 C) D) = (k7_real_1 (k8_real_1 (k8_real_1 A B) (k6_power 2 A)) (k8_real_1 (k8_real_1 A B) (k6_power 2 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k6_enumset1 A A A A A B C D) = (k2_enumset1 A B C D)) ) ) ) ) ).
tt(t50_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ( (~  ((k8_mcart_1 A B C D) = k1_xboole_0) )  =>  ( ((k1_funct_1 (k1_funct_3 (k9_funct_3 A B)) (k8_mcart_1 A B C D)) = C)  &  ((k1_funct_1 (k1_funct_3 (k10_funct_3 A B)) (k8_mcart_1 A B C D)) = D) ) ) ) ) ) ) ) ) ).
tt(t50_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k23_rvsum_1 B C) (k9_binop_2 (k23_rvsum_1 B B) (k23_rvsum_1 C C)))) ) ) ) ) ) ).
tt(t50_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((r1_euclid_3 A B C) =>  ( (~  (B = C) )  &  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  &  (~  (C = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k2_numbers) =>  ( ( (D = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) A B)))  &  (E = (k2_euclid_3 (k5_algstr_0 (k15_euclid 2) C B))) )  =>  ( ((k3_complex1 (k1_complex2 D E)) = (k7_real_1 (k8_real_1 (k9_real_1 (k17_euclid A) (k17_euclid B)) (k9_real_1 (k17_euclid C) (k17_euclid B))) (k8_real_1 (k9_real_1 (k18_euclid A) (k18_euclid B)) (k9_real_1 (k18_euclid C) (k18_euclid B)))))  &  ( ((k4_complex1 (k1_complex2 D E)) = (k7_real_1 (k1_real_1 (k8_real_1 (k9_real_1 (k17_euclid A) (k17_euclid B)) (k9_real_1 (k18_euclid C) (k18_euclid B)))) (k8_real_1 (k9_real_1 (k18_euclid A) (k18_euclid B)) (k9_real_1 (k17_euclid C) (k17_euclid B)))))  &  ( ((k17_complex1 D) = (k7_square_1 (k7_real_1 (k5_square_1 (k9_real_1 (k17_euclid A) (k17_euclid B))) (k5_square_1 (k9_real_1 (k18_euclid A) (k18_euclid B))))))  &  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) = (k17_complex1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_euclid_7 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))))  => (m1_rlvect_3 B (k10_funcsdom (k2_finseq_1 A)))) ) ) ) ).
tt(t50_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ( ((k3_finseq_1 A) = 3)  &  ((k4_finseq_1 A) = (k2_finseq_1 3)) ) ) ) ).
tt(t50_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k1_rlvect_1 (k15_euclid A) B (k10_binop_2 C D)) = (k5_algstr_0 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B C) (k1_rlvect_1 (k15_euclid A) B D))) ) ) ) ) ) ) ) ) ).
tt(t50_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r1_xboole_0 C D) &  ((r2_hidden B C) & (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) & (r2_hidden (k4_tarski B C) (k6_exchsort D E)))  => (r2_hidden (k4_tarski A C) (k6_exchsort D E))) ) ) ) ) ) ) ) ).
tt(t50_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C)))) =>  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C) D) (k4_tarski (k10_finseq_1 A B) C)) = (k1_funct_1 C (k10_finseq_1 (k1_funct_1 D A) (k1_funct_1 D B))))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C) D) A) = (k1_funct_1 D A))  &  ((k1_funct_1 (k6_circuit2 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C) D) B) = (k1_funct_1 D B)) ) ) ) ) ) ) ) ) ).
tt(t50_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  => (v2_funct_1 (k1_fcont_1 A B))) ) ) ) ) ).
tt(t50_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k2_fdiff_9)) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k2_fdiff_9 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k1_real_1 (k10_real_1 (k8_real_1 (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k19_sin_cos B)) (k5_square_1 (k1_seq_1 k16_sin_cos B)))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k2_fdiff_9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t50_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k16_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) B) = (k10_real_1 (k2_newton (k1_seq_1 k19_sin_cos B) 3) (k9_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t50_fdiff_6,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos)))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k3_taylor_1 k19_sin_cos)) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos (k6_power k8_power B)) B)) ) ) ) ) ) ) ) ).
tt(t50_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = (k10_real_1 C 2))  &  (~  ((k1_seq_1 k19_sin_cos (k1_seq_1 B C)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) A) C) = (k10_real_1 1 (k7_real_1 1 (k1_seq_1 k19_sin_cos C)))) ) ) ) ) ) ) ) ) ) ).
tt(t50_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((v1_int_2 (k1_pre_ff A)) =>  ((r1_xxreal_0 A 1) |  ( (A = 4)  | (v1_int_2 A)) ) ) ) ) ).
tt(t50_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_fib_num3 k6_numbers A B) = (k4_nat_1 A (k1_pre_ff B))) ) ) ) ) ).
tt(t50_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_filter_0 A D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_filter_0 A D))) =>  ( ( (B = E)  &  (C = F) )  =>  ( ((k3_lattices A B C) = (k3_lattices (k6_filter_0 A D) E F))  &  ((k4_lattices A B C) = (k4_lattices (k6_filter_0 A D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_filter_0 A B C) = (k3_lattices A (k4_lattices A B C) (k4_lattices A (k7_lattices A B) (k7_lattices A C)))) ) ) ) ) ) ) ).
tt(t50_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B (k8_filter_2 A B C)) & (r1_tarski C (k8_filter_2 A B C))) ) ) ) ) ) ) ).
tt(t50_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finseq_1 A)) )  =>  ((k10_xtuple_0 (k14_finseq_1 (k9_xtuple_0 A))) = (k9_xtuple_0 A)) ) ) ).
tt(t50_finseq_2,ax, ((k1_finseq_2 1) = (k12_finseq_1 k5_numbers 1)) ).
tt(t50_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_relat_1 (k1_finseq_2 (k2_xcmplx_0 A B)) (k2_finseq_1 A)) = (k1_finseq_2 A)) ) ) ) ) ).
tt(t50_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( ((r2_hidden B (k10_xtuple_0 A)) & (m2_finseq_1 A C))  => (m2_finseq_1 (k6_finseq_4 A B) C)) ) ) ) ) ) ).
tt(t50_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k3_finseq_1 (k2_finseq_5 A C B)) = (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 C) (k4_finseq_4 C B)) 1)) ) ) ) ) ) ) ) ).
tt(t50_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  (B = C) )  =>  ((k1_finseq_5 A (k3_finseq_4 A B C D) C) = (k2_finseq_4 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t50_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ( ((v3_card_1 F D) & (m2_finseq_1 F B))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 B B) B) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 A A) A) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J B) =>  ((k3_funct_2 B A E (k5_binop_1 B G I J)) = (k5_binop_1 A H (k3_funct_2 B A E I) (k3_funct_2 B A E J))) ) ) ) )  => (r2_relset_1 k5_numbers A (k4_finseqop B A (k2_finseqop B B B G F C) E) (k2_finseqop A A A H (k4_finseqop B A F E) (k3_funct_2 B A E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fintopo6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~ (r3_fintopo6 A E B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_flang_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden B (k7_flang_1 A C (k2_xcmplx_0 D 1))) =>  ((r2_hidden B (k6_flang_1 A (k8_flang_1 A C) C)) & (r2_hidden B (k6_flang_1 A C (k8_flang_1 A C)))) ) ) ) ) ) ) ) ).
tt(t50_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k1_flang_2 A B 2 2) = (k6_flang_1 A B B)) ) ) ) ).
tt(t50_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_3 A B) = (k1_flang_3 A B 1)) ) ) ) ).
tt(t50_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v3_fomodel0 B A) & (r1_tarski C B))  => (v3_fomodel0 C A)) ) ) ) ) ).
tt(t50_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k12_fsm_1 A B C) A) (k12_fsm_1 A B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k12_fsm_1 A B C) A) (k12_fsm_1 A B C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 (k12_fsm_1 A B C) A) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k12_fsm_1 A B C) A) B)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k12_fsm_1 A B C)) =>  ( ( (D = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) A) (u1_struct_0 C) (u1_fsm_1 A C) (k2_zfmisc_1 (k12_fsm_1 A B C) A)))  &  ( (E = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) A) B (u3_fsm_1 A B C) (k2_zfmisc_1 (k12_fsm_1 A B C) A)))  &  (F = (u2_fsm_1 A C)) ) )  => (r4_fsm_1 A B C (g2_fsm_1 A B (k12_fsm_1 A B C) D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_funct_2 B A (k1_partfun1 B A A A D (k9_funcop_1 A A C (k6_partfun1 A) E)) (k9_funcop_1 A B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t50_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden A B))  => (r2_hidden (k1_funct_1 C A) (k10_xtuple_0 (k5_relat_1 C B)))) ) ) ) ) ).
tt(t50_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_tarski B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))))) )  =>  ((r2_hidden C A) =>  ((k1_funct_1 D C) = B) ) ) ) ) ) ) ).
tt(t50_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = A)  &  ((k9_xtuple_0 C) = A) )  =>  ((k9_xtuple_0 (k13_funct_3 B C)) = A) ) ) ) ) ) ) ).
tt(t50_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ((v1_funct_1 (k2_funct_4 D)) &  ((v1_funct_2 (k2_funct_4 D) (k2_zfmisc_1 B A) C) & (m1_subset_1 (k2_funct_4 D) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) ) ) ) ) ) ) ) ).
tt(t50_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) =>  ( ((k2_funct_5 (k1_funct_5 C)) = C)  &  ((k4_funct_5 (k3_funct_5 C)) = C) ) ) ) ) ) ) ).
tt(t50_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k9_funct_6 k1_xboole_0 A) = (k7_funcop_1 (k9_xtuple_0 A) (k1_tarski k1_xboole_0))) ) ) ).
tt(t50_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_funcop_1 C) & (v1_finseq_1 C)) ) )  =>  ((k5_funct_7 (k7_finseq_1 B C) A) = (k1_rewrite1 (k5_funct_7 B A) (k5_funct_7 C (k1_funct_1 (k5_funct_7 B A) (k2_nat_1 (k3_finseq_1 B) 1))))) ) ) ) ) ) ).
tt(t50_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v4_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t50_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k2_fuzzy_1 A B (k3_fuzzy_2 A C D)) (k3_fuzzy_2 A (k2_fuzzy_1 A B C) (k2_fuzzy_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t50_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k5_struct_0 A) (k6_fvaluat1 A B))) ) ) ) ) ).
tt(t50_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ((r2_hidden A (k4_finseq_1 (k9_fvsum_1 B E C))) &  (D = (k1_funct_1 E A)) )  =>  ((k1_funct_1 (k9_fvsum_1 B E C) A) = (k6_algstr_0 B C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((r1_xxreal_0 (k3_finseq_1 G) A) &  ((r1_xxreal_0 (k3_finseq_1 G) B) &  ((r1_xxreal_0 (k3_finseq_1 G) C) &  ((r1_xxreal_0 (k3_finseq_1 G) D) & (r1_xxreal_0 (k3_finseq_1 G) E)) ) ) )  =>  ((k11_genealg1 F G H A B C D E) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k19_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t50_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_subset_1 (k6_glib_000 A) B) (k21_glib_000 A (k6_subset_1 (k6_glib_000 A) B))) =>  ( (~  (B = (k6_glib_000 A)) )  =>  ( ((k2_nat_1 (k15_glib_000 C) (k5_card_1 B)) = (k15_glib_000 A))  &  ((k2_nat_1 (k17_glib_000 C) (k5_card_1 (k20_glib_000 A B))) = (k17_glib_000 A)) ) ) ) ) ) ) ) ) ).
tt(t50_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_glib_001 A C D B) => (r1_glib_001 A C D (k20_glib_001 A B E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ( ((r5_glib_000 A B) & (r1_glib_002 A C))  => (r1_glib_002 B C)) ) ) ) ) ) ).
tt(t50_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k7_glib_000 A)) => (r2_hidden B (k11_glib_003 (k12_glib_003 A B C)))) ) ) ) ) ).
tt(t50_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B (k3_finseq_1 B) A)) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k19_euclid 1 k6_numbers)))))) ) ) ) ) ) ).
tt(t50_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A (k2_nat_1 B 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  ( ((v2_funct_1 A) & (m2_graph_1 A C))  =>  ((v2_funct_1 (k5_relat_1 A (k2_finseq_1 B))) & (m2_graph_1 (k5_relat_1 A (k2_finseq_1 B)) C)) ) ) ) ) ) ) ) ).
tt(t50_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v2_funct_1 D) & (m2_graph_1 D A))  =>  ((r1_graph_2 A C D) =>  ((v1_msscyc_1 D A) |  ((v1_abian (k7_graph_3 A B (k10_xtuple_0 D))) <=>  ( (~  (B = (k1_funct_1 C 1)) )  &  (~  (B = (k1_funct_1 C (k3_finseq_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  ((r5_graph_5 B A) => (r1_xxreal_0 k6_numbers (k10_graph_5 B C A))) ) ) ) ) ) ) ).
tt(t50_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ( ((r5_graphsp A C B) & (r5_graphsp A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t50_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r1_rewrite1 (k3_polyred A B C (k1_groeb_1 A C G)) D E) &  (! [H:$i] :  ( ((v1_relat_1 H) &  ((v4_relat_1 H A) &  ((v1_funct_1 H) &  ((v1_partfun1 H A) &  ((v4_valued_0 H) & (v2_pre_poly H)) ) ) ) )  =>  (~  ((r2_hidden H (k2_polynom1 (k15_pre_poly A) C F)) & (r3_pre_poly A (k3_termord A B C G) H)) ) ) ) )  => (r1_rewrite1 (k3_polyred A B C (k1_groeb_1 A C G)) (k5_polynom1 A C D F) (k5_polynom1 A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski (k13_group_2 A B D) (k8_group_2 A C)) => (r2_hidden D (k3_group_11 A C B))) ) ) ) ) ) ) ) ) ).
tt(t50_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B 1) = B) ) ) ) ) ).
tt(t50_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 D C))  => (r1_struct_0 D (k6_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t50_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_3 A C B) = (k5_group_2 A B (k4_group_2 A (k2_group_1 A B) C))) ) ) ) ) ) ) ).
tt(t50_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_group_2 A (k8_group_4 A B C) (k5_group_4 A (k7_group_4 A B C)))) ) ) ) ) ) ).
tt(t50_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (r1_tarski D E))  => (r1_tarski (k4_group_5 A B D) (k4_group_5 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v8_struct_0 B) => (v8_struct_0 (k10_group_6 B A C))) ) ) ) ) ) ) ).
tt(t50_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  =>  ((k14_group_9 A B (k10_group_9 A B C) (k12_group_9 A B C)) = (k10_group_9 A B C)) ) ) ) ) ) ).
tt(t50_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((k3_helly A B C C) = C) ) ) ) ) ) ) ).
tt(t50_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k7_real_1 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B (k3_rlvect_1 A C D) (k3_rlvect_1 A C D))) (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B (k5_algstr_0 A C D) (k5_algstr_0 A C D)))) = (k7_real_1 (k8_real_1 2 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C))) (k8_real_1 2 (k17_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B D D))))) ) ) ) ) ) ) ) ) ).
tt(t50_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 B 2 A) & (r1_taylor_1 C 2 A))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) 2) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 2) C) (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) (k2_fdiff_1 C A)) 2)) (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C A) 2))))) ) ) ) ) ) ) ).
tt(t50_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 A (k4_hilbert1 B C)) (k4_hilbert1 (k4_hilbert1 A B) C)) k6_hilbert1)) ) ) ) ) ) ).
tt(t50_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ( ((r1_xxreal_0 1 (k2_hurwitz k1_complfld A)) & (v1_hurwitz A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 B)))  & (r1_xxreal_0 (k17_complex1 (k2_polynom4 k1_complfld (k7_hurwitz A) B)) (k17_complex1 (k2_polynom4 k1_complfld A B)))) )  &  ( (~  ( (~ (r1_xxreal_0 (k3_complex1 B) k6_numbers))  & (r1_xxreal_0 (k17_complex1 (k2_polynom4 k1_complfld A B)) (k17_complex1 (k2_polynom4 k1_complfld (k7_hurwitz A) B)))) )  &  ( ((k3_complex1 B) = k6_numbers)  =>  ((k17_complex1 (k2_polynom4 k1_complfld A B)) = (k17_complex1 (k2_polynom4 k1_complfld (k7_hurwitz A) B))) ) ) ) ) ) ) ) ) ).
tt(t50_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v4_rlvect_1 A) &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) ) ) )  =>  ((k9_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ).
tt(t50_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (~  ((r2_incsp_1 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u2_incsp_1 A)) =>  (~  ( (~  (E = F) )  &  ((r3_incsp_1 A E C) &  ((r3_incsp_1 A F C) &  ( (~ (r3_incsp_1 A D C))  &  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A B E) & (r1_incsp_1 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k6_int_1 A A) = k6_numbers) ) ) ).
tt(t50_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r1_int_4 A k1_xboole_0) <=>  (A = k6_numbers) ) ) ) ).
tt(t50_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( ( ((k4_nat_d A 4) = 3)  &  ((k4_nat_d B 4) = 3) )  =>  ((r1_xxreal_0 A 2) |  ((r1_xxreal_0 B 2) |  ( (A = B)  |  ((k2_int_5 A B) = (k4_xcmplx_0 (k2_int_5 B A))) ) ) ) ) ) ) ) ) ).
tt(t50_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 k19_sin_cos D) (k7_real_1 1 (k1_seq_1 k19_sin_cos D)))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t50_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos)) A) B) = (k10_real_1 (k1_seq_1 k24_sin_cos (k1_seq_1 k2_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t50_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k30_sin_cos D)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t50_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) F) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) G) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) F (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) G (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) ) ) ) )  =>  ((k6_integr18 (k4_real_ns1 A) (k2_vfunct_1 k1_numbers (k4_real_ns1 A) F G) D E) = (k5_algstr_0 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) F D E) (k6_integr18 (k4_real_ns1 A) G D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((k9_member_1 (k4_measure6 A) (k4_measure6 B)) = (k5_member_1 (k9_member_1 A B))) ) ) ) ) ).
tt(t50_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers (k8_real_1 k32_sin_cos 2)))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = k6_numbers) ) ) ) ).
tt(t50_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k7_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) = E)  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_real_1 1 (k7_real_1 A F))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ((k10_interva1 A (k4_interva1 A B B)) = (k2_interva1 A (k2_subset_1 A) (k2_subset_1 A))) ) ) ) ) ) ).
tt(t50_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 A (k4_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t50_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m2_cat_1 D B A) =>  ((r3_nattra_1 A A (k9_cat_1 A B A C D) (k10_cat_1 A)) => (v14_cat_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t50_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r1_xxreal_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) =>  ((r1_xxreal_0 (k18_euclid A) k6_numbers) |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))) (k8_real_1 (k12_euclid A) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B)))))))) ) ) ) ) ) ) ).
tt(t50_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (C = a_0_6_jgraph_5)  &  ((r1_jordan6 C A B) &  ( (~  (A = B) )  &  ((r1_xxreal_0 k6_numbers (k17_euclid A)) &  ((r1_xxreal_0 k6_numbers (k17_euclid B)) & (r1_xxreal_0 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~ (v1_topreal2 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 A B C D)) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ((v3_tops_2 E (k15_euclid 2) (k15_euclid 2)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 (k17_euclid G) (k17_euclid F)))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E G)) (k17_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) E)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C E))) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan8 C B))) => (r1_tarski (k3_goboard5 (k1_jordan8 C B) A (k1_matrix_1 (k1_jordan8 C B))) (k2_jordan2c 2 C))) ) ) ) ) ) ) ) ) ).
tt(t50_jordan1g,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ((v4_pre_topc B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k10_xtuple_0 A)) =>  ((r1_xboole_0 (k3_topreal1 2 A) B) |  ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) B) |  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A 1 (k4_finseq_4 A (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))))) B) = (k1_tarski (k1_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ) ).
tt(t50_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r1_xxreal_0 1 (k7_nat_d (k3_jordan1h B A) 1)) &  (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) (k7_nat_d (k3_jordan1h B A) 1))) ) ) ) ) ) ).
tt(t50_jordan1j,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k17_finseq_1 A (k3_finseq_1 B) (k4_graph_2 A B C)) = B) ) ) ) ) ) ).
tt(t50_jordan1k,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden D B) => (r1_xxreal_0 (k5_jordan1k A C B) (k1_topreal6 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_jordan21,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_hidden (k2_jordan21 A) (k8_jordan6 A)) & (r2_hidden (k1_jordan21 A) (k8_jordan6 A))) ) ) ) ).
tt(t50_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ((a_2_2_jordan2c A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t50_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ((r3_jordan4 A D B C) &  ((r3_jordan4 A E B C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E)) = (k2_tarski (k1_funct_1 A B) (k1_funct_1 A C)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 D) (k3_topreal1 2 E)) = (k3_topreal1 2 A))  &  ((r1_topreal4 (k3_topreal1 2 D) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) &  ((r1_topreal4 (k3_topreal1 2 E) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C)) &  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 (k15_euclid 2))) =>  (~  ((r3_jordan4 A F B C) &  ( (~  (F = D) )  &  (~  (F = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k10_jordan5d A) = (k12_jordan5d A)) ) ) ) ).
tt(t50_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) (k8_jordan6 A)) &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) (k8_jordan6 A)) &  ((r1_topreal1 (k15_euclid 2) (k22_pscomp_1 A) (k18_pscomp_1 A) (k9_jordan6 A)) &  ((r1_topreal1 (k15_euclid 2) (k18_pscomp_1 A) (k22_pscomp_1 A) (k9_jordan6 A)) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) (k9_jordan6 A)) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ( ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k8_jordan6 A) (k9_jordan6 A)) = A)  &  (~ (r1_xxreal_0 (k18_euclid (k1_jordan5c (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k18_pscomp_1 A) (k22_pscomp_1 A))) (k18_euclid (k2_jordan5c (k9_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) (k22_pscomp_1 A) (k18_pscomp_1 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t50_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k1_tops_1 (k15_euclid 2) (k2_jgraph_6 A B C D)) = (k1_jgraph_6 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_kurato_1,ax, (! [A:$i] :  (~  ((r2_hidden A (k1_enumset1 (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))))) &  (A = k1_numbers) ) ) ) ).
tt(t50_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) & (l3_lattices A)) ) )  <=>  ( (~ (v2_struct_0 (k1_lattice2 A)))  &  ((v10_lattices (k1_lattice2 A)) &  ((v11_lattices (k1_lattice2 A)) & (l3_lattices (k1_lattice2 A))) ) ) ) ) ) ).
tt(t50_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  &  ((k6_lattices A) = (k15_lattice3 A (u1_struct_0 A))) ) ) ) ).
tt(t50_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (m3_chord (k2_funct_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k14_lexbfs A (k16_lexbfs A)))) A)) ) ).
tt(t50_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  ((v4_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) ) ) ) ) ) )  =>  ((v4_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (v4_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t50_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k8_real_1 (k1_limfunc2 B A) (k1_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t50_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc3 B A) &  ((r3_limfunc2 C (k1_limfunc3 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 A F))  &  ((r2_hidden F (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C))) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G A))  & (r2_hidden G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 A D) A) (k2_rcomp_1 A (k7_real_1 A D))))) & (r1_xxreal_0 (k1_limfunc3 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  | (r3_limfunc3 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t50_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k20_lpspace1 A B C))) =>  ((r2_hidden D E) =>  ( (E = (k13_lpspace1 A B C D))  &  ((k1_normsp_0 (k20_lpspace1 A B C) E) = (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  ( (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k10_lpspace2 A B C F))) &  ((r2_hidden D G) & (r2_hidden E G)) ) )  =>  ((r1_lpspace1 A B C D E) &  ((r2_hidden D (k1_lpspace2 A B C F)) & (r2_hidden E (k1_lpspace2 A B C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r8_ltlaxio1 E (k3_hilbert1 (k4_ltlaxio1 A B) C)) & (r8_ltlaxio1 E (k3_hilbert1 A D)))  => (r8_ltlaxio1 E (k3_hilbert1 (k4_ltlaxio1 A B) (k4_ltlaxio1 D C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A B C) D) A) => (v2_cqc_the1 (k8_cqc_lang A C D) A)) ) ) ) ) ) ) ) ) ).
tt(t50_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k6_rusub_4 A B C) = (k6_rusub_4 A (k5_mathmorp A B C) C))  &  ((k3_mathmorp A B C) = (k3_mathmorp A (k4_mathmorp A B C) C)) ) ) ) ) ) ) ) ).
tt(t50_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r2_matrix10 B C) => (r2_matrix10 (k4_matrix10 A B D) (k4_matrix10 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_finseq_1 A)) & (r2_hidden D (k2_finseq_1 A)))  =>  ((r1_xxreal_0 D C) |  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((k8_matrix_1 (u1_struct_0 B) E C) = (k8_matrix_1 (u1_struct_0 B) E D))  =>  ((k12_matrix_3 A B E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ((r2_hidden B (k2_finseq_1 (k5_card_1 D))) =>  ((k9_matrix_1 A (k6_matrix13 A C (k2_finseq_1 (k3_finseq_1 C)) D) B) = (k9_matrix_1 A C (k1_funct_1 (k5_matrix13 D) B))) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((k5_matrix_1 A (u1_struct_0 B) (k4_matrix14 B A C)) = (k4_matrix14 B A C)) ) ) ) ) ) ) ) ).
tt(t50_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) A B) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) A C) =>  (! [G:$i] :  ( ((v1_finset_1 G) &  ((v1_setfam_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ((k5_card_1 G) = A)  &  ((r1_tarski G (k2_finseq_1 B)) &  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  ( ((k6_matrix13 (u1_struct_0 D) E (k2_finseq_1 A) G) = (k12_matrix_1 D A))  &  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 D) B C) =>  (~  ( ((k6_matrix13 (u1_struct_0 D) H (k7_subset_1 k5_numbers (k2_finseq_1 B) G) (k2_finseq_1 C)) = (k1_matrix_3 D (k7_nat_d B A) C))  &  ( ((k6_matrix13 (u1_struct_0 D) H G (k2_finseq_1 C)) = F)  & (r2_hidden H (k4_matrix15 D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ((v4_matrix16 D (u1_struct_0 A)) &  ((v4_matrix16 E (u1_struct_0 A)) &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k2_matrix16 (u1_struct_0 A) D) B) (k2_matrix13 (k3_finseq_1 E) (k3_finseq_1 E) A (k2_matrix16 (u1_struct_0 A) E) C)) = (k2_matrix16 (u1_struct_0 A) (k3_fvsum_1 A (k9_fvsum_1 A D B) (k9_fvsum_1 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k1_matrix_4 A (k1_matrix_3 A (k3_finseq_1 B) (k1_matrix_1 B)) B) = (k2_matrix_3 A B)) ) ) ) ) ).
tt(t50_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B (k2_matrix_6 A B C C) (k2_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r2_matrix_8 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r2_matrix_8 A B (k5_matrix_1 A (u1_struct_0 B) C) (k5_matrix_1 A (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) D E) F) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B D) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ((k11_matrixc1 A) = (k10_matrixc1 (k4_matrix_1 k2_numbers A))) ) ) ).
tt(t50_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v2_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ((k22_matrixj1 A (k15_matrixj1 (u1_struct_0 A) B C)) = (k8_finseq_1 (u1_struct_0 A) (k22_matrixj1 A B) (k22_matrixj1 A C))) ) ) ) ) ) ) ).
tt(t50_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k10_matrixr1 (k4_rvsum_1 A B)) = (k3_matrixr1 (k10_matrixr1 A) (k10_matrixr1 B))) ) ) ) ) ) ).
tt(t50_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k1_matrix_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k11_matrixr1 B (k6_rvsum_1 A)) = (k6_rvsum_1 (k11_matrixr1 B A))) ) ) ) ) ) ) ).
tt(t50_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrlin D A B) =>  (! [E:$i] :  ((m1_matrlin E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 F B C) &  ((v1_mod_2 F A B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ( ((k1_vectsp_9 A B) = (k1_vectsp_9 A C))  =>  ( (~ (v7_struct_0 (k1_ranknull A B C F)))  <=>  ((k12_matrix_3 (k3_finseq_1 D) A (k3_matrlin2 A B C F D E)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (A = (k5_finseq_2 k5_numbers (k3_finseq_1 A) 1)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 (k12_matrixr1 B A)))) =>  ((k1_seq_1 (k12_matrixr1 B A) C) = (k18_rvsum_1 (k9_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t50_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k3_zfmisc_1 (k2_zfmisc_1 A B) C D) = (k4_zfmisc_1 A B C D)) ) ) ) ) ).
tt(t50_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v3_xxreal_2 A) <=> (v3_xxreal_2 (k2_measure6 A B))) ) ) ) ) ).
tt(t50_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k9_member_1 (k9_member_1 A B) C) = (k9_member_1 A (k9_member_1 B C))) ) ) ) ) ) ) ).
tt(t50_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((r1_tarski (k8_memstr_0 A B C) D) => (r1_tarski (k7_memstr_0 A B k6_numbers) D)) ) ) ) ) ) ) ) ) ).
tt(t50_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 E A k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k1_numbers E k6_numbers)))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r3_mesfunc6 A B C (k4_mesfunc5 A k1_numbers E G))) )  & (r1_mesfun9c A E F)) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k1_mesfunc9 C D)) |  ((r3_mesfunc6 A B C F) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k7_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k1_mesfunc9 G H) = (k1_mesfunc6 A B C (k4_mesfunc5 A k1_numbers E H))) ) )  &  ((v10_mesfunc5 G) &  ((k2_mesfunc5 G) = (k1_mesfunc6 A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v8_mesfunc5 A) =>  ( (~ (v9_mesfunc5 A))  &  (~ (v7_mesfunc5 A)) ) ) ) ) ).
tt(t50_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r2_mesfunc6 A B C) => (r1_mesfunc6 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t50_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ( (D = (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers)))  &  ((v2_mesfunc9 E A) &  ((v1_mesfunc8 E A k7_numbers) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E F) D) & (v6_supinf_2 (k4_mesfunc5 A k7_numbers E F))) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ((k1_mesfunc9 F G) = (k7_mesfunc5 A B C (k4_mesfunc5 A k7_numbers E G)))  &  ((k7_mesfunc5 A B C (k4_mesfunc5 A k7_numbers (k4_mesfunc9 A E) G)) = (k1_mesfunc9 (k2_mesfunc9 F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k10_midsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k10_midsp_1 A)) =>  ((k11_midsp_1 A (k11_midsp_1 A B C) D) = (k11_midsp_1 A B (k11_midsp_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k1_relset_1 A (k20_mmlquery A B (k18_mmlquery A B))) = A) ) ) ) ).
tt(t50_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  ((k51_modelc_1 A B C (k25_modelc_1 (k48_modelc_1 A B C) D)) = (k50_modelc_1 A B (k51_modelc_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t50_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  =>  ((k21_modelc_2 B C (k3_modelc_2 A)) = (k3_robbins1 B (k21_modelc_2 B C A))) ) ) ) ) ) ) ).
tt(t50_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r8_modelc_3 A B C) =>  (! [D:$i] :  ((r2_hidden D (k22_modelc_3 A)) =>  ((v3_modelc_3 (k10_modelc_3 D A) A) |  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A))) =>  ((v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A) A) | (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C (k1_nat_1 E 1)) D) A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((r1_int_2 A B) =>  ((k5_moebius1 (k4_nat_1 A B)) = (k11_pre_poly k10_newton (k5_moebius1 A) (k5_moebius1 B))) ) ) ) ) ) ).
tt(t50_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (m2_monoid_0 A k6_monoid_0))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ( (B = D)  &  (C = E) )  =>  ((k6_algstr_0 A B C) = (k11_binop_2 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 B A) => (v2_binop_1 (k21_monoid_1 A A A B) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(t50_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A B) =>  ((r6_pboole A C (k1_pzfmisc1 A D)) => (r6_pboole A (k4_mssubfam A B C) D)) ) ) ) ) ) ) ) ).
tt(t50_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 (u3_msualg_1 A B) E)) =>  ((r2_hidden (k4_tarski F G) (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) D E)) <=> (r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (k8_msualg_6 A B C) E) F G)) ) ) ) ) ) )  =>  ((v2_msualg_4 D A B) &  ((v3_msualg_6 D A B) &  ((v4_msualg_6 D A B) & (m1_msualg_4 D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k1_dilworth (k7_mycielsk A)) = 2)  &  ((k2_mycielsk (k7_mycielsk A)) = (k2_xcmplx_0 A 2)) ) ) ) ).
tt(t50_nat_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k5_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  => (r2_funct_2 k5_numbers A (k10_nat_1 A (k1_partfun1 k5_numbers k5_numbers k5_numbers A D B) C) (k1_partfun1 k5_numbers k5_numbers k5_numbers A (k10_nat_1 k5_numbers D C) B))) ) ) ) ) ) ) ) ).
tt(t50_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_nat_d A B) =>  ((k12_nat_3 (k3_nat_d B A)) = (k12_pre_poly k10_newton (k12_nat_3 B) (k12_nat_3 A))) ) ) ) ) ) ).
tt(t50_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  ( (B = k1_xboole_0)  =>  ((k1_nat_4 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t50_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k7_nat_d B C) A)) ) ) ) ) ) ) ).
tt(t50_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r7_ncfcont1 A B D C) <=> (r7_ncfcont1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C) C)) ) ) ) ) ) ) ) ).
tt(t50_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ((r1_ndiff_3 (k4_real_ns1 A) D C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  ((r1_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) E (k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) D C)) =>  ((r1_ndiff_3 (k4_real_ns1 B) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) D E) C) &  ((k1_ndiff_3 (k4_real_ns1 B) (k1_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B)) D E) C) = (k17_lopban_1 (k4_real_ns1 A) (k4_real_ns1 B) (k3_ndiff_1 (k4_real_ns1 A) (k4_real_ns1 B) E (k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) D C)) (k1_ndiff_3 (k4_real_ns1 A) D C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers (k4_finseq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_prvect_2 A C))) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k11_prvect_2 A C)) (u1_struct_0 B)))))  =>  ( ( ((k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A C)) (k3_ndiff_5 A C) D) = E)  & (r2_relset_1 (u1_struct_0 (k11_prvect_2 A C)) (u1_struct_0 B) G (k1_partfun1 (u1_struct_0 (k11_prvect_2 A C)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B) (k4_ndiff_5 A C D) F)))  =>  ((k3_ndiff_1 (k11_prvect_2 A C) B G E) = (k6_ndiff_5 A B C F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_nat_d A B) & (r1_nat_d A C))  <=> (r1_nat_d A (k6_nat_d B C))) ) ) ) ) ) ) ).
tt(t50_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ((r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) B (k1_partfun2 (u1_struct_0 A) (k1_relset_1 (u1_struct_0 A) B))) => (r3_nfcont_1 A A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t50_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k9_normform A (k10_normform A (k9_normform A B) C)) = (k9_normform A (k10_normform A B C))) ) ) ) ) ) ).
tt(t50_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_cat_1 B) &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  => (r1_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 (k2_oppcat_1 B))) (u4_struct_0 A) (u4_struct_0 B) (k11_oppcat_1 A (k2_oppcat_1 B) (k11_oppcat_1 A B C)) C)) ) ) ) ) ) ).
tt(t50_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (~  ((r5_orders_1 A B) &  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t50_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r3_orders_1 (u1_orders_2 A) B)) ) ) ) ).
tt(t50_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((r2_ordinal2 A k1_xboole_0) =>  (A = k1_xboole_0) ) ) ) ).
tt(t50_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k11_ordinal2 (k11_ordinal2 A B) C) = (k11_ordinal2 A (k11_ordinal2 B C))) ) ) ) ) ) ) ).
tt(t50_ordinal5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ( (! [B:$i] :  ((r2_hidden B A) =>  ((v3_ordinal1 B) & (v4_ordinal5 B)) ) )  &  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B A) => (r2_hidden (k2_ordinal5 B) A)) ) ) )  =>  ((v3_ordinal1 (k3_tarski A)) & (v4_ordinal5 (k3_tarski A))) ) ) ) ).
tt(t50_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  (~  ( (~  ((k9_xtuple_0 B) = k1_xboole_0) )  &  ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) => (r1_abian A (k1_funct_1 B C))) ) )  &  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ((r2_hidden C (k9_xtuple_0 (k7_ordinal6 B))) &  (A = (k1_funct_1 (k7_ordinal6 B) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t50_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m2_osalg_2 C A B) =>  ((r8_pboole (u1_struct_0 A) C (u3_msualg_1 A B)) =>  ((k6_lattices (k16_osalg_2 A B)) = (k10_osalg_2 A B C)) ) ) ) ) ) ) ) ).
tt(t50_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) =>  ((r1_parsp_2 A B C D) | (r2_parsp_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k4_partfun1 A C) (k4_partfun1 B D))) ) ) ) ) ).
tt(t50_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_relset_1 A B D (k9_subset_1 (k2_zfmisc_1 A B) E F)) & (r2_hidden C (k1_relset_1 A D)))  =>  ( ((k7_partfun1 B D C) = (k7_partfun1 B E C))  &  ((k7_partfun1 B D C) = (k7_partfun1 B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r2_pboole A B (k2_pboole A C D)) & (r6_pboole A (k3_pboole A B D) (k1_pboole A)))  => (r2_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t50_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r5_pdiff_5 B A) & (r5_pdiff_5 C A))  =>  ((r3_pdiff_1 3 2 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 2 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k7_real_1 (k5_pdiff_5 B A) (k5_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t50_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  ((r4_pdiff_7 A B D C) => (r1_pdiff_9 A C (k1_nfcont_4 B (k1_euclid A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t50_pepin,ax, ((k4_pepin k6_numbers) = 3) ).
tt(t50_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((k12_pnproc_1 C (k2_nat_1 A B)) = (k12_pnproc_1 (k12_pnproc_1 C B) A)) ) ) ) ) ) ) ).
tt(t50_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((v5_polyform A) <=>  (! [B:$i] :  ((v1_int_1 B) =>  ((k22_polyform A B) = (k24_polyform A B)) ) ) ) ) ) ).
tt(t50_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_polynom5 A B (k9_polynom3 A)) (k3_algseq_1 A (k3_funct_2 k5_numbers (u1_struct_0 A) B k6_numbers)))) ) ) ) ).
tt(t50_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) (k6_polynom1 A C E F) (k7_polynom1 A C)) => (r5_rewrite1 (k3_polyred A B C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~  (B = C) )  &  ((k3_power A B) = (k3_power A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r6_pboole A B (k11_pre_poly A C D)) => (r3_pre_poly A C B)) ) ) ) ) ) ) ) ).
tt(t50_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) &  (B = (k5_xcmplx_0 C)) )  =>  ((k6_prepower A B) = (k2_prepower C A)) ) ) ) ) ) ) ) ).
tt(t50_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ((k1_relset_1 k5_numbers (k6_prob_3 A B)) = (k1_relset_1 k5_numbers B)) ) ) ) ).
tt(t50_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A D B) (k7_cqc_lang A D C)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t50_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k23_pscomp_1 A) (k16_pscomp_1 A)) & (r2_hidden (k22_pscomp_1 A) (k16_pscomp_1 A))) ) ) ).
tt(t50_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k4_pboole A B (k1_pzfmisc1 A C)) B) & (r1_pboole A C B)) ) ) ) ) ) ) ) ).
tt(t50_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((v5_qc_lang1 B A) =>  ((r1_qc_lang2 A C B) <=>  (C = (k22_qc_lang1 A B)) ) ) ) ) ) ) ) ) ).
tt(t50_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k4_qc_lang2 A B C)) = (k4_subset_1 D (k4_qc_lang3 A D B) (k4_qc_lang3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t50_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k18_quatern2 A A)) = (k5_square_1 (k3_quatern2 A)))  &  ( ((k18_quaterni (k18_quatern2 A A)) = k6_numbers)  &  ( ((k19_quaterni (k18_quatern2 A A)) = k6_numbers)  &  ((k19_quaterni (k18_quatern2 A A)) = k6_numbers) ) ) ) ) ) ).
tt(t50_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k29_quaterni A B) (k26_quaterni C D)) = (k29_quaterni (k26_quaterni (k29_quaterni (k27_quaterni A C) (k27_quaterni B C)) (k27_quaterni A D)) (k27_quaterni B D))) ) ) ) ) ) ) ) ) ).
tt(t50_quaterni,ax, ( ((k17_quaterni (k31_quaterni k12_quaterni)) = k6_numbers)  &  ( ((k18_quaterni (k31_quaterni k12_quaterni)) = k6_numbers)  &  ( ((k19_quaterni (k31_quaterni k12_quaterni)) = k6_numbers)  &  ((k20_quaterni (k31_quaterni k12_quaterni)) = (k1_real_1 1)) ) ) ) ).
tt(t50_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield C A B) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k4_struct_0 A)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t50_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A A))))) =>  (! [C:$i] :  ((m1_rcomp_3 C A A B) =>  ( ((m1_setfam_1 B (u1_struct_0 (k4_topmetr A A))) &  ((v1_tops_2 B (k4_topmetr A A)) & (v1_rcomp_3 B (k4_topmetr A A))) )  =>  (C = (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A A))) ) ) ) ) ) ) ) ).
tt(t50_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r2_hidden (k1_seq_1 (k6_real_3 B) A) k5_numbers)) ) ) ) ).
tt(t50_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k3_relat_1 B (k4_relat_1 A)) B) & (r1_tarski (k3_relat_1 (k4_relat_1 A) B) B)) ) ) ) ).
tt(t50_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ( ((k9_xtuple_0 C) = (k7_relset_1 A B (k3_relset_1 B A C) A))  &  ((k10_xtuple_0 C) = (k7_relset_1 B A C B)) ) ) ) ) ) ).
tt(t50_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_rewrite1 A) <=> (r11_rewrite1 A A)) ) ) ).
tt(t50_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  ((k8_rewrite2 A (k1_partit_2 (k8_afinsq_1 A) (k8_afinsq_1 A)) B) = (k4_flang_1 A B)) ) ) ) ).
tt(t50_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_rewrite3 D B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E C))  =>  ( ( ((u1_struct_0 D) = (u1_struct_0 E))  &  ((u1_rewrite3 B D) = (u1_rewrite3 C E)) )  =>  (! [F:$i] :  ((m1_rewrite1 F (k1_rewrite3 A B D)) => (m1_rewrite1 F (k1_rewrite3 A C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k3_valued_1 A k1_numbers k1_numbers B C) A))  &  ( ((v1_partfun1 (k3_valued_1 A k1_numbers k1_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) )  &  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k47_valued_1 A k1_numbers k1_numbers B C) A))  &  ( ((v1_partfun1 (k47_valued_1 A k1_numbers k1_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) )  &  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k20_valued_1 A k1_numbers k1_numbers B C) A))  &  ((v1_partfun1 (k20_valued_1 A k1_numbers k1_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) | (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))  => (v2_funct_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B)))) ) ) ) ) ) ) ).
tt(t50_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k8_relset_1 A k1_numbers B (k1_tarski (k7_real_1 D C))) = (k8_relset_1 A k1_numbers (k15_valued_1 A k1_numbers B C) (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t50_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) => (v7_valued_0 (k3_rinfsup1 A))) ) ) ).
tt(t50_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ((v2_rusub_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (B = (k4_rlaffin1 A B)) ) ) ) ) ).
tt(t50_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((k3_rlsub_1 A (k1_rlvect_1 A B C) D) = (u1_struct_0 D))  =>  ( (C = k6_numbers)  | (r1_struct_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t50_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C))) = D) ) ) ) ) ) ) ) ) ).
tt(t50_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  => (v4_pre_topc (k1_convex1 A B C) A)) ) ) ) ) ) ).
tt(t50_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  ((k4_algstr_0 A (k4_rlvect_1 A (k6_finseq_1 (u1_struct_0 A)))) = (k4_struct_0 A)) ) ) ).
tt(t50_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((r1_rlvect_2 A (k7_rlvect_2 A B C) (k4_rlvect_2 A)) => (r1_rlvect_2 A C (k9_rlvect_2 A B))) ) ) ) ) ) ) ).
tt(t50_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rmod_2 E A C) =>  ((r1_struct_0 E D) =>  ((k3_rmod_2 A C (k5_vectsp_2 A C B D) E) = (u1_struct_0 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))))  &  ((v10_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) &  ((v15_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) & (l3_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B)))) ) ) ) ) ) ) ).
tt(t50_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k8_rmod_4 A B D) C) = (k4_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t50_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k5_robbins1 A (k13_robbins1 A B) (k14_robbins1 A B)) B) = (k11_robbins1 A B)) ) ) ) ) ).
tt(t50_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A C B) (k5_robbins1 A C D))))) (k5_robbins1 A C D)) = (k5_robbins1 A (k3_robbins1 A (k3_robbins1 A (k5_robbins1 A C B))) (k5_robbins1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t50_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k4_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A C) D)) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k4_subset_1 (u1_struct_0 A) B C)) D))) ) ) ) ) ) ) ) ).
tt(t50_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( ((k4_subset_1 A C D) = A)  & (r1_xboole_0 C D))  =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A D) k6_numbers) |  ((k1_rpr_1 A B) = (k7_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k8_real_1 (k2_rpr_1 A D B) (k1_rpr_1 A D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden C (k3_rusub_1 A D B)) & (r2_hidden C (k3_rusub_1 A E B)))  =>  ((k3_rusub_1 A D B) = (k3_rusub_1 A E B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_rlvect_1 A (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C)) (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C))) = D) ) ) ) ) ) ) ) ) ).
tt(t50_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (B = (k4_bhsp_2 A D C))  => (v3_pre_topc B (k5_rusub_5 A))) ) ) ) ) ) ) ) ) ).
tt(t50_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k10_rvsum_1 C (k9_binop_2 A B)) = (k4_rvsum_1 (k10_rvsum_1 C A) (k10_rvsum_1 C B))) ) ) ) ) ) ) ).
tt(t50_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k3_finseq_1 (k5_rvsum_2 A)) = (k3_finseq_1 A)) ) ) ).
tt(t50_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 B (u1_struct_0 k1_ami_3))) ) ) )  =>  ((v1_relat_1 (k1_funct_4 A B)) &  ((v4_relat_1 (k1_funct_4 A B) (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 (k1_funct_4 A B)) &  ((v5_funct_1 (k1_funct_4 A B) (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 (k1_funct_4 A B) (u1_struct_0 k1_scmfsa_2))) ) ) ) ) ) ) ) ).
tt(t50_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~  (A = B) )  & (r1_scmfsa7b (k7_scmfsa_2 C B) A)) ) ) ) ) ) ) ) ).
tt(t50_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ((v1_scm_halt A) <=>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r5_scmfsa7b A (k1_scmfsa_m B) C)) ) ) ) ) ) ) ).
tt(t50_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k13_scmpds_2 D E B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k13_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k6_xcmplx_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C))))  &  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k13_scmpds_2 D E B C) A) F) = (k1_funct_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  &  ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A)) )  =>  ((k6_scmpds_4 (k5_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  =>  ((r1_scmpds_6 (k2_scmpds_7 k2_scmp_gcd 2 1 (k9_compos_1 k1_scmpds_2 (k11_scmpds_2 k2_scmp_gcd 3 1))) B A) & (r2_scmpds_6 (k2_scmpds_7 k2_scmp_gcd 2 1 (k9_compos_1 k1_scmpds_2 (k11_scmpds_2 k2_scmp_gcd 3 1))) B A)) ) ) ) ) ) ).
tt(t50_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((r2_hidden B (k3_tarski A)) =>  ((v4_scmyciel (k2_tarski k1_xboole_0 (k1_tarski B))) &  ((v5_scmyciel (k2_tarski k1_xboole_0 (k1_tarski B))) & (m1_subset_1 (k2_tarski k1_xboole_0 (k1_tarski B)) (k1_zfmisc_1 A))) ) ) ) ) ) ).
tt(t50_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_semi_af1 A E F B C) & (r2_semi_af1 A E F D G))  =>  ((r1_semi_af1 A B C D) | (r2_semi_af1 A B C D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_relat_1 A) & (v2_relat_1 B))  =>  ((r2_funct_2 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers C A) (k52_valued_1 k5_numbers k1_numbers k1_numbers D B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers C B) (k20_valued_1 k5_numbers k1_numbers k1_numbers D A)) (k20_valued_1 k5_numbers k1_numbers k1_numbers A B))) & (r2_funct_2 k5_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers C A) (k52_valued_1 k5_numbers k1_numbers k1_numbers D B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k47_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers C B) (k20_valued_1 k5_numbers k1_numbers k1_numbers D A)) (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t50_seq_4,ax,(r1_finseqop k2_numbers k25_binop_2 k27_binop_2)).
tt(t50_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k1_seq_1 A C) = (k7_real_1 1 (k1_seq_1 B C)))  & (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 (k7_real_1 1 (k1_seq_1 (k3_series_1 B) C)) (k1_seq_1 (k1_series_3 A) C))) ) ) ) ) ) ) ).
tt(t50_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_xxreal_0 1 (k1_seq_1 A B))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r1_xxreal_0 (k2_nat_1 B 1) (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ) ).
tt(t50_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v2_prob_1 C) => (r1_tarski (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) (k2_nat_1 A 1)) (k3_funct_2 k5_numbers (k9_setfam_1 B) C A))) ) ) ) ) ) ).
tt(t50_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k5_setlim_2 B D C)) A) = (k9_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t50_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 A)) =>  ((k10_setwiseo A B (k5_setwiseo A D E) C) = (k5_setwiseo B (k10_setwiseo A B D C) (k10_setwiseo A B E C))) ) ) ) ) ) ) ) ) ) ).
tt(t50_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (~ (r2_hidden (k5_sf_mastr A) (k2_sf_mastr A))) ) ) ).
tt(t50_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B C) (k5_sheffer1 A B C)) (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A B C) D)) (k5_sheffer1 A B C))) (k5_sheffer1 A B B)) = (k5_sheffer1 A (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A B C) D)) (k5_sheffer1 A B B))) ) ) ) ) ) ) ) ) ).
tt(t50_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  &  ((v1_matroid0 C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ((m3_simplex0 D C B) =>  ((r1_xxreal_0 B (k6_simplex0 C)) =>  ((m4_simplex0 A C B D) <=>  (? [E:$i] :  ((r2_hidden E D) &  ((k7_subset_1 (u1_struct_0 C) D (k1_tarski E)) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_sincos10,ax, ((k2_partfun1 k1_numbers k1_numbers k2_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos)))) ).
tt(t50_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k2_comseq_3 (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B))) A) = (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k5_binop_2 A B)) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k5_binop_2 A B))))) ) ) ) ) ).
tt(t50_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B)) (k6_xcmplx_0 (k20_sin_cos A) (k20_sin_cos B))) = (k3_xcmplx_0 (k2_sin_cos4 (k7_xcmplx_0 (k2_xcmplx_0 A B) 2)) (k2_sin_cos4 (k7_xcmplx_0 (k6_xcmplx_0 B A) 2)))) ) ) ) ) ).
tt(t50_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k6_sin_cos2 (k6_real_1 A 2)) = k6_numbers) )  =>  ((k9_sin_cos2 (k6_real_1 A 2)) = (k10_real_1 (k3_sin_cos2 A) (k7_real_1 (k6_sin_cos2 A) 1))) ) ) ) ).
tt(t50_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 k6_numbers k32_sin_cos)) = (k2_rcomp_1 (k1_real_1 1) 1)) ).
tt(t50_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers (k9_binop_2 (k11_binop_2 A B) (k11_binop_2 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)) (k7_square_1 (k9_binop_2 (k3_square_1 B) 1))))) =>  ((k9_binop_2 (k1_sin_cos7 A) (k1_sin_cos7 B)) = (k1_sin_cos7 (k9_binop_2 (k11_binop_2 A (k7_square_1 (k9_binop_2 1 (k3_square_1 B)))) (k11_binop_2 B (k7_square_1 (k9_binop_2 1 (k3_square_1 A))))))) ) ) ) ) ) ).
tt(t50_sin_cos9,ax, (! [A:$i] :  ((r2_hidden A (k1_rcomp_1 (k1_real_1 1) 1)) => (r2_hidden (k1_seq_1 k2_sin_cos9 A) (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos)))) ) ).
tt(t50_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k25_sin_cos (k2_xcmplx_0 A B)) = (k3_xcmplx_0 (k25_sin_cos A) (k25_sin_cos B))) ) ) ) ) ).
tt(t50_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_sppol_2 B C A) => (r1_sppol_2 C B A)) ) ) ) ) ) ) ).
tt(t50_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) B C))  =>  ((k8_pscomp_1 A) = (k4_xxreal_0 (k8_pscomp_1 B) (k8_pscomp_1 C))) ) ) ) ) ) ) ) ).
tt(t50_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ( (~ (v3_funct_1 E))  &  ((v1_finseq_6 E (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 E) &  ((v2_topreal1 E) &  ((v1_goboard5 E) &  ((v2_goboard5 E) & (m2_finseq_1 E (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 D (k3_finseq_1 E))) ) )  =>  ((r1_xxreal_0 C B) |  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 (k3_finseq_1 E) D))  | (r1_xboole_0 (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E B A)) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) E C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A (k2_finseq_4 (u1_struct_0 (k15_euclid 2)) B C)) => (r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) B C) (k10_real_1 1 2))))) ) ) ) ) ) ) ).
tt(t50_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t50_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 A)))  &  ( (~ (r1_xxreal_0 A B))  & (r1_xxreal_0 (k3_square_1 A) (k3_square_1 B))) ) ) ) ) ) ) ).
tt(t50_stirl2_1,ax, ( ((k9_newton 3) = 6)  &  ((k9_newton 4) = 24) ) ).
tt(t50_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r1_valuat_1 A D (k11_cqc_lang A C B) E F) <=>  (! [G:$i] :  ((m1_subset_1 G D) => (r1_valuat_1 A D B E (k1_sublemma A D F (k12_sublemma A D C G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_supinf_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v6_supinf_2 A) =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) =>  ((k12_supinf_2 A C) = k1_supinf_2) ) ) )  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 C B) &  ((k12_supinf_2 A C) = k1_supinf_1) ) ) ) ) ) ) ) )  | (v7_supinf_2 A)) ) ) ) ).
tt(t50_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A B))))) ) ) ) ).
tt(t50_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((k4_tdlat_1 A) = (k8_tdlat_1 A))  => (v4_tdlat_3 A)) ) ) ).
tt(t50_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_xboole_0 (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) |  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ).
tt(t50_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ((v1_tex_3 B A) & (v1_tex_2 B A)) ) )  & (v1_tdlat_3 A)) ) ) ) ).
tt(t50_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_subset_1 (k2_tex_4 A B) (k2_tex_4 A C)) <=>  (~  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t50_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_tmap_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t50_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) =>  ((v1_funct_1 (k6_topalg_1 A B C D)) &  ((v1_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) &  ((v1_group_6 (k6_topalg_1 A B C D) (k5_topalg_1 A C) (k5_topalg_1 A B)) & (m1_subset_1 (k6_topalg_1 A B C D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_topgen_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = k1_borsuk_5)  =>  ((k1_tops_1 k3_topmetr A) = k1_xboole_0) ) ) ) ).
tt(t50_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_topgen_4 A B) (k2_topgen_1 A B))) ) ) ) ).
tt(t50_topgen_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B k3_topmetr))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((k1_funct_1 E F) = (k4_xxreal_0 (k1_funct_1 C F) (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v3_pre_topc (k4_group_2 A C B) A)) ) ) ) ) ) ).
tt(t50_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k14_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (B = (k9_metric_1 (k14_euclid 2) A C))  & (v2_sppol_1 B)) ) ) ) ) ) ) ) ).
tt(t50_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_topreal9 2 (k19_euclid A B) C) = (k6_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(t50_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) )  =>  ((k59_valued_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C D) = (k80_valued_2 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C (k15_toprealc A (u1_struct_0 B) (u1_struct_0 k3_topmetr) D))) ) ) ) ) ) ) ) ) ).
tt(t50_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C B) & (v3_pre_topc C A))  =>  (C = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t50_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  => (v2_funct_1 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(t50_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_tops_3 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc C A) &  ((v1_tops_1 C A) &  ((v4_pre_topc D A) &  ((v2_tops_1 D A) &  ( ((k4_subset_1 (u1_struct_0 A) C (k9_subset_1 (u1_struct_0 A) B D)) = B)  &  ((r1_xboole_0 C D) &  ((k4_subset_1 (u1_struct_0 A) C D) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo D A) &  ((v5_transgeo E A) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B)) ) )  =>  ((r3_diraf A B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) C) |  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (~  (A = B) )  & (r1_tarski (k12_finseq_1 k5_numbers A) (k7_finseq_1 (k12_finseq_1 k5_numbers B) C))) ) ) ) ) ) ) ) ).
tt(t50_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) )  =>  ( ((k11_trees_3 A) = (k11_trees_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t50_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_2 B A) =>  (! [C:$i] :  ((m1_trees_1 C A) =>  (~  ((r2_hidden C B) &  ( (~ (v1_finset_1 B))  &  (! [D:$i] :  ((m1_trees_1 D A) =>  (~  ((r2_hidden D B) & (r2_xboole_0 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) => (r2_tsep_1 A (k4_subset_1 (u1_struct_0 A) B D) (k4_subset_1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t50_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( ( (D = (k1_funct_1 C A))  &  (E = (k1_funct_1 C B)) )  =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k39_twoscomp A B)) = (k10_margrel1 (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = D)  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (? [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_polynom3 k1_complfld))) &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 C k1_complfld) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  &  ( (C = (k3_group_4 (k14_polynom3 k1_complfld) B))  &  ( ((k4_finseq_1 B) = (k2_finseq_1 A))  &  ( (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_subset_1 D k1_numbers k5_numbers))  =>  ((r2_hidden D (k2_finseq_1 A)) =>  ( ( (~  ((r1_nat_d D A) &  (~  (D = A) ) ) )  =>  ((k1_funct_1 B D) = (k3_algseq_1 k1_complfld (k1_group_1 k1_complfld))) )  &  ((r1_nat_d D A) =>  ( (D = A)  |  ((k1_funct_1 B D) = (k5_uniroots D)) ) ) ) ) ) )  & (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k4_uniroots A k1_complfld) (k13_polynom3 k1_complfld (k5_uniroots A) C))) ) ) ) ) ) ) ) ) ).
tt(t50_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r1_polynom5 A C B) => (r2_funct_2 k5_numbers (u1_struct_0 A) C (k13_polynom3 A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A)) (k6_uproots A B C)))) ) ) ) ) ) ) ).
tt(t50_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k37_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k31_valued_2 A B E C) D) = (k31_valued_2 A B E (k6_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t50_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_struct_0 E D) =>  ((k3_vectsp_4 A B (k4_vectsp_1 A B C D) E) = (u1_struct_0 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_vectsp_5 A B C D) =>  ((k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)) = (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((v3_funct_1 (k2_partfun1 C (u1_struct_0 D) E A)) & (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) F B)))  =>  ((v3_funct_1 (k2_partfun1 C (u1_struct_0 D) (k6_vfunct_1 C D E F) (k3_xboole_0 A B))) & (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) (k2_vfunct_1 C D E F) (k3_xboole_0 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  (! [F:$i] :  ( ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C E)) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) D F)))  =>  ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) (k3_vfunct_2 A B C D) (k3_xboole_0 E F))) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_1 A B C D) (k3_xboole_0 E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k11_waybel_0 A B)) & (r1_tarski B (k12_waybel_0 A B))) ) ) ) ) ).
tt(t50_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v5_orders_3 B A A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (a_2_1_waybel_1 A B))  => (v7_yellow_0 (k5_yellow_0 A C) A)) ) ) ) ) ) ) ) ).
tt(t50_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) ) )  =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  ( (C = (u1_struct_0 B))  & (v4_pre_topc C A)) ) ) ) ) ) ) ).
tt(t50_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( ((r2_hidden (k3_yellow_0 A) (u1_struct_0 B)) &  ((v2_waybel23 (u1_struct_0 B) A) & (m1_subset_1 (u1_struct_0 B) (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k8_subset_1 (u1_struct_0 A) (k1_waybel_3 A C) (u1_struct_0 B))))  &  ((v1_waybel_0 (k8_subset_1 (u1_struct_0 A) (k1_waybel_3 A C) (u1_struct_0 B)) B) &  ((v12_waybel_0 (k8_subset_1 (u1_struct_0 A) (k1_waybel_3 A C) (u1_struct_0 B)) B) & (m1_subset_1 (k8_subset_1 (u1_struct_0 A) (k1_waybel_3 A C) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t50_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_2 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ) ).
tt(t50_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  ((r2_hidden (u1_struct_0 B) A) =>  ((m1_subset_1 B (u1_struct_0 (k11_waybel34 A))) <=>  ((v1_orders_2 B) &  ((v3_lattice3 B) & (v3_waybel_3 B)) ) ) ) ) ) ) ) ).
tt(t50_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v5_waybel_4 D A) &  ((v6_waybel_4 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (~  ((r1_waybel_3 A B C) &  ( (~  (B = C) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) B E) D) &  ((r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E C) D) &  (~  (B = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v2_wellord1 A) & (r3_wellord1 A B C))  =>  (! [D:$i] :  (~  ((r2_hidden D (k1_relat_1 A)) &  (! [E:$i] :  (~  ((r2_hidden E (k1_relat_1 B)) & (r4_wellord1 (k2_wellord1 A (k1_wellord1 A D)) (k2_wellord1 B (k1_wellord1 B E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_xboole_0 A (k4_xboole_0 B C)) = (k4_xboole_0 (k3_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(t50_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k7_xboolean A B) = (k5_xboolean (k4_xboolean A B) (k9_xboolean A B))) ) ) ) ) ).
tt(t50_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  ((k7_xcmplx_0 A B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t50_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_xcmplx_0 B A) k6_numbers)) ) ) ) ) ) ).
tt(t50_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((r1_xxreal_0 A (k3_xxreal_0 A B)) =>  ((k3_xxreal_0 A B) = A) ) ) ) ) ) ).
tt(t50_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_tarski (k1_xxreal_1 A B) (k1_xxreal_1 C D)))  =>  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t50_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  ( (~ (v1_xboole_0 A))  & (v3_xxreal_2 A)) )  =>  (~  ( (~  (A = (k1_tarski k1_xxreal_0)) )  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~ (r2_hidden B A)) ) ) ) ) ) ) ).
tt(t50_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~ (r1_xxreal_0 A (k1_xxreal_3 B B))) ) ) ) ) ) ) ) ) ).
tt(t50_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((r1_yellow_0 A B) => (r1_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))))  &  ( ((r1_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))) => (r1_yellow_0 A B))  &  ( ((r2_yellow_0 A B) => (r2_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))))  &  ((r2_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))) => (r2_yellow_0 A B)) ) ) ) ) ) ) ).
tt(t50_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_yellow_3 A B (k2_waybel_8 A C) (k2_waybel_8 B D)) = (k2_waybel_8 (k3_yellow_3 A B) (k7_yellow_3 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t50_yellow12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  =>  (! [E:$i] :  ((m3_yellow_9 E A B) =>  (! [F:$i] :  ((m3_yellow_9 F C D) =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u1_struct_0 C) = (u1_struct_0 D)) )  => (m3_yellow_9 (k2_borsuk_1 E F) (k2_borsuk_1 A C) (k2_borsuk_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_yellow_0 C (k6_yellow_1 B A)) & (m1_yellow_0 C (k6_yellow_1 B A))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  (D = (k8_funcop_1 (u1_struct_0 A) B E)) ) ) ) )  => (r5_waybel_1 A C)) ) ) ) ) ) ) ).
tt(t50_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) ) )  =>  ((r2_yellow20 A B C D E) => (r2_yellow20 B A (k15_functor0 A B C) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t50_yellow_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  ((r2_hidden A (k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (k2_yellow_2 B))) <=>  ( (~ (v1_xboole_0 A))  &  ((v1_waybel_0 A B) &  ((v12_waybel_0 A B) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ).
tt(t50_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k4_yellow_4 A B C) = (k9_subset_1 (u1_struct_0 A) B C)) ) ) ) ) ) ) ).
tt(t50_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A (k1_yellow_5 A B C) C) = (k3_yellow_0 A)) ) ) ) ) ) ) ).
tt(t50_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_funcop_1 B)) )  =>  ((r1_funct_2 (k9_xtuple_0 B) (u1_struct_0 A) (k9_xtuple_0 B) (u1_struct_0 (k7_lattice3 A)) (k4_waybel_5 A B) (k5_waybel_5 (k7_lattice3 A) B)) & (r1_funct_2 (k9_xtuple_0 B) (u1_struct_0 A) (k9_xtuple_0 B) (u1_struct_0 (k7_lattice3 A)) (k5_waybel_5 A B) (k4_waybel_5 (k7_lattice3 A) B))) ) ) ) ) ).
tt(t50_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v3_lattice3 B) &  ((v4_waybel11 B) & (l1_waybel_9 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  & (v3_pre_topc C A))  => (v3_pre_topc D B)) ) ) ) ) ) ) ) ) ) ).
tt(t50_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r3_zf_lang (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k10_zf_lang A B)) &  ((r3_zf_lang (k6_zf_lang A) (k10_zf_lang A B)) &  ((r3_zf_lang (k6_zf_lang B) (k10_zf_lang A B)) &  ((r3_zf_lang A (k10_zf_lang A B)) & (r3_zf_lang B (k10_zf_lang A B))) ) ) ) ) ) ) ) ).
tt(t50_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~ (r1_zf_lang C (k4_zf_lang A B))) ) ) ) ) ) ) ).
tt(t50_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (r2_hidden A B))  => (r1_xboole_0 (k1_tarski A) B)) ) ) ).
tt(t50_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v7_zmodul01 B A) &  (! [C:$i] :  ( ((v1_zmodul01 C) & (m1_zmodul01 C A))  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r2_abcmiz_0 A B C) => (r2_hidden (k6_abcmiz_0 A B C) (k4_abcmiz_0 A C))) ) ) ) ) ) ) ).
tt(t51_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v6_trees_3 C)) ) )  =>  ((m1_subset_1 (k4_trees_4 (k4_tarski B (u1_struct_0 A)) C) (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) <=>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k1_msualg_1 A B)))  & (r2_hidden C (k3_finseq_2 (k34_abcmiz_1 A)))) ) ) ) ) ) ) ) ).
tt(t51_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k38_abcmiz_1 A))) =>  ( ((r2_abcmiz_a A B C) & (r2_abcmiz_a A C D))  => (r2_abcmiz_a A B D)) ) ) ) ) ) ) ) ) ).
tt(t51_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 F A) &  ((r2_hidden B F) &  ((r2_hidden C F) &  ((r2_hidden D F) & (r2_hidden E F)) ) ) )  => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [J:$i] :  ((m1_subset_1 J (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A H I) &  ((r5_aff_1 A H J) &  ((r2_hidden B H) &  ((r2_hidden C H) &  ((r2_hidden D I) &  ((r2_hidden E I) &  ((r2_hidden F J) &  ((r2_hidden G J) &  ((v1_aff_1 H A) &  ((v1_aff_1 I A) &  ((v1_aff_1 J A) &  ((r2_analoaf A B D C E) & (r2_analoaf A B F C G)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  |  ( (H = I)  |  ( (H = J)  | (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ( (~ (r1_xxreal_0 (k1_afinsq_1 B) A))  =>  ((k1_funct_1 (k1_ordinal4 B C) A) = (k1_funct_1 B A)) ) ) ) ) ) ) ) ).
tt(t51_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ((v4_valued_0 A) =>  ((k7_afinsq_2 A) = (k6_afinsq_2 k5_numbers A k47_binop_2)) ) ) ) ).
tt(t51_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v9_incproj (k13_afproj A)) => (v4_aff_2 A)) ) ) ).
tt(t51_afvect0,ax, (! [A:$i] :  ( ((v1_analoaf A) & (l1_analoaf A))  =>  ( ( (~ (v7_struct_0 A))  &  ((v2_tdgroup A) & (l1_analoaf A)) )  <=>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v12_vectsp_1 B) &  ((v1_tdgroup B) & (l2_algstr_0 B)) ) ) ) ) ) ) )  &  (A = (k2_tdgroup B)) ) ) ) ) ) ).
tt(t51_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ((v1_instalg1 B) & (l1_msualg_1 B))  =>  ((v2_struct_0 A) => (m2_algspec1 B A)) ) ) ) ) ).
tt(t51_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_altcat_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_altcat_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 (k2_altcat_4 A) B C)) =>  ( (~  ((k1_altcat_1 (k2_altcat_4 A) B C) = k1_xboole_0) )  => (v5_altcat_3 D (k2_altcat_4 A) B C)) ) ) ) ) ) ) ) ) ).
tt(t51_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r6_analmetr A C D B)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t51_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_analmetr A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r2_analort A B C D E D F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (~  ((r2_analort A B C G H D E) &  ( (~  ( (~ (r2_analort A B C G H D F))  &  (~ (r2_analort A B C G H F D)) ) )  &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~ (r2_hidden (k14_aofa_000 A B C D) (k18_aofa_000 A))) ) ) ) ) ) ) ) ) ).
tt(t51_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ( (~ (v1_abian (k21_aofa_i00 B k4_numbers C F)))  => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k72_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ( (~  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k72_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (v1_abian (k21_aofa_i00 B k4_numbers C F))) )  &  ( ((v1_abian (k21_aofa_i00 B k4_numbers C F)) => (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k73_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k73_aofa_i00 A B D E F)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) => (v1_abian (k21_aofa_i00 B k4_numbers C F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (~  ( (~ (v1_xboole_0 B))  &  ((v11_armstrng B) &  (! [C:$i] :  ((l1_armstrng C) =>  (~  ( ((u1_armstrng C) = A)  &  (B = (k13_armstrng (u1_armstrng C) (k5_armstrng C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ((k9_arytm_3 (k9_arytm_3 A B) C) = (k9_arytm_3 A (k9_arytm_3 B C))) ) ) ) ) ) ) ).
tt(t51_asympt_1,ax, ((k9_newton 5) = 120) ).
tt(t51_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_bcialg_1 A))  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v13_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A B D)) = (k1_bcialg_1 A C D))  &  ((k1_bcialg_1 A B (k4_struct_0 A)) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m5_bcialg_2 C A B) =>  ( (~ (v2_struct_0 (k9_bcialg_2 A C)))  &  ((v3_bcialg_1 (k9_bcialg_2 A C)) &  ((v4_bcialg_1 (k9_bcialg_2 A C)) &  ((v5_bcialg_1 (k9_bcialg_2 A C)) &  ((v7_bcialg_1 (k9_bcialg_2 A C)) & (l2_bcialg_1 (k9_bcialg_2 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v8_bcialg_4 A) <=>  ((v3_bcialg_4 A) & (v4_bcialg_4 A)) ) ) ) ).
tt(t51_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ( ((v8_bcialg_1 A) & (m1_bcialg_5 A 1 k6_numbers k6_numbers k6_numbers))  <=>  ( ((v8_bcialg_1 A) & (m1_bcialg_5 A k6_numbers k6_numbers k6_numbers k6_numbers))  &  ((v8_bcialg_1 A) & (m1_bcialg_5 A k6_numbers 1 k6_numbers 1)) ) ) ) ) ).
tt(t51_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (~  ( (C = (k5_bcialg_6 A B E))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B)) &  ((v2_bcialg_6 F (k9_bcialg_2 A D) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B))))) ) )  =>  (~  ((r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) E (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 (k9_bcialg_2 A D)) (u1_struct_0 B) (k6_bcialg_6 A C D) F)) & (v2_funct_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m4_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) D) B) => (r2_hidden (k1_bcialg_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t51_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_normsp_1 B (k6_bhsp_1 B C D) A) (k6_bhsp_1 B (k5_normsp_1 B C A) (k5_normsp_1 B D A)))) ) ) ) ) ) ) ) ).
tt(t51_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_bhsp_2 A C D)) <=>  ((k3_bhsp_1 A (k5_algstr_0 A C B)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t51_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) &  ((v3_bhsp_3 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v1_bhsp_3 C B) & (v3_bhsp_4 A))  => (v1_bhsp_3 (k5_bhsp_4 B C A) B)) ) ) ) ) ) ) ).
tt(t51_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  ( (~  (E = (k7_hahnban1 A C)) )  =>  ((k10_bilinear A B C (k9_bilinear A B C D E)) = (k8_vectsp10 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r4_boolealg A B (k3_lattices A C D)))  <=>  ( (~ (r4_boolealg A B C))  &  (~ (r4_boolealg A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( ((r1_topreal1 (k15_euclid A) D E B) &  ((r1_topreal1 (k15_euclid A) E D C) &  ((k9_subset_1 (u1_struct_0 (k15_euclid A)) B C) = (k7_domain_1 (u1_struct_0 (k15_euclid A)) D E)) ) )  =>  ( (D = E)  | (r1_borsuk_3 k1_borsuk_4 (k1_pre_topc (k15_euclid A) (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k7_subset_1 (u1_struct_0 (k15_euclid A)) B (k6_domain_1 (u1_struct_0 (k15_euclid A)) D)) (k7_subset_1 (u1_struct_0 (k15_euclid A)) C (k6_domain_1 (u1_struct_0 (k15_euclid A)) D)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k2_rcomp_1 k2_xxreal_0 B))  =>  ((k2_pre_topc k3_topmetr A) = (k4_rcomp_1 k2_xxreal_0 B)) ) ) ) ) ) ).
tt(t51_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  (! [E:$i] :  ( ((v3_funct_1 E) & (m1_borsuk_2 E A B B))  =>  ((r1_borsuk_6 A B C) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k2_borsuk_6 A B C D k4_borsuk_6) (k1_borsuk_2 A B B C E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) B)) = (k12_euclid B)) ) ) ) ) ).
tt(t51_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  (! [I:$i] :  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  ( (H = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B J) (k16_funcop_1 C K)) (k16_funcop_1 D L)) (k16_funcop_1 E M)) (k16_funcop_1 F N)) (k16_funcop_1 G O)) (k16_funcop_1 A I)))  =>  ((k10_xtuple_0 H) = (k5_enumset1 (k1_funct_1 H A) (k1_funct_1 H B) (k1_funct_1 H C) (k1_funct_1 H D) (k1_funct_1 H E) (k1_funct_1 H F) (k1_funct_1 H G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k9_xboolean k7_margrel1 A) = (k3_xboolean A)) ) ) ).
tt(t51_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k5_bvfunc26 A C D)) (k5_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t51_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k9_cqc_lang A B C))))) ) ) ) ) ) ) ) ) ).
tt(t51_card_1,ax, (3 = (k1_enumset1 k1_xboole_0 1 2)) ).
tt(t51_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (r1_xxreal_0 (k5_card_1 (k1_enumset1 A B C)) 3)) ) ) ).
tt(t51_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k4_card_3 A) (k8_card_3 A))) ) ).
tt(t51_card_fin,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k8_subset_1 (k3_tarski (k10_xtuple_0 C)) (k2_card_fin C D A) B) = (k2_card_fin (k1_yellow20 C (k7_funcop_1 (k9_xtuple_0 C) B)) D A)) ) ) ) ) ) ) ).
tt(t51_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_cat_1 B A) & (v11_cat_1 C A))  => (r1_cat_1 A B C)) ) ) ) ) ) ) ).
tt(t51_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_cat_3 E B C A) =>  ((r1_cat_3 B C A E) =>  (! [F:$i] :  ((m1_cat_1 F B D C) =>  ( ( ((k3_graph_1 B F) = D)  &  ( ((k4_graph_1 B F) = C)  & (v9_cat_1 F B D C)) )  => (r1_cat_3 B D A (k6_cat_3 B A E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) => (v11_cat_1 C (k23_cat_4 A B))) ) ) ) ).
tt(t51_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v1_series_1 A) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (~ (r1_xxreal_0 B (k18_complex1 (k4_series_1 (k10_nat_1 k1_numbers A C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((v1_cfcont_1 (k1_relset_1 k2_numbers A)) & (r2_cfcont_1 A (k1_relset_1 k2_numbers A)))  => (v1_cfcont_1 (k2_relset_1 k2_numbers A))) ) ) ).
tt(t51_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  => (r2_relset_1 A k1_numbers (k55_valued_1 A k2_numbers (k1_cfunct_1 A B C)) (k3_rfunct_1 A k1_numbers (k55_valued_1 A k2_numbers B) (k55_valued_1 A k2_numbers C)))) ) ) ) ) ) ).
tt(t51_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 A 1)))) =>  ((r2_hidden D (k10_chain_1 B C A E)) <=>  ((r1_xxreal_0 (k2_nat_1 A 1) B) &  (~ (v1_abian (k5_card_1 (k9_subset_1 (k4_chain_1 B C (k2_nat_1 A 1)) (k9_chain_1 B C A D) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  (! [C:$i] :  ((k2_chord A C) = (k2_chord B C)) ) ) ) ) ) ) ).
tt(t51_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 1 B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 1 B) B)))) )  =>  (! [D:$i] :  ( ((v6_circcmb3 D) & (m1_circcmb3 D B))  =>  ( (~  ( (~ (r2_hidden A (u1_struct_0 D)))  & (v1_xtuple_0 A)) )  => (v6_circcmb3 (k6_circcmb3 B D (k4_circcmb3 1 B C (k9_finseq_1 A))))) ) ) ) ) ) ) ) ).
tt(t51_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ( ((v3_circcomb A) & (v3_circcomb B))  => (v3_circcomb (k2_circcomb A B))) ) ) ) ) ).
tt(t51_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A E))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B F))) =>  ( (G = (k3_relat_1 C H))  <=>  (H = (k3_relat_1 (k2_funct_1 C) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_classes1,ax, (! [A:$i] : (v1_ordinal1 (k5_classes1 A))) ).
tt(t51_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~  ((k2_ordinal1 A) = k1_xboole_0) )  & (v4_ordinal1 (k2_ordinal1 A))) ) ) ).
tt(t51_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_clvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_clvect_1 B) & (m1_clvect_1 B A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 A))  =>  (B = A) ) ) ) ) ) ).
tt(t51_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_clvect_2 A C D)) <=>  ((k13_csspace A (k5_algstr_0 A C B)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t51_clvect_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) &  ((v4_clvect_2 B) & (l1_csspace B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v2_clvect_2 C B) & (v3_clvect_3 A))  => (v2_clvect_2 (k6_clvect_3 B C A) B)) ) ) ) ) ) ) ).
tt(t51_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k1_funct_1 A k1_xboole_0) = k1_xboole_0)  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden (k1_tarski B) (k9_xtuple_0 A)) & (r2_hidden C (k1_funct_1 A (k1_tarski B))))  => (r2_hidden (k4_tarski B C) (k10_cohsp_1 A))) ) ) ) ) ) ).
tt(t51_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( ((k3_complex1 A) = k6_numbers)  =>  ((k17_complex1 A) = (k17_complex1 (k4_complex1 A))) ) ) ) ).
tt(t51_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k2_complex2 A k6_numbers) = A) ) ) ).
tt(t51_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k3_rlvect_1 k1_complfld A B)) = (k3_rlvect_1 k1_complfld (k2_complfld A) (k2_complfld B))) ) ) ) ) ).
tt(t51_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 A) = (k3_finseq_1 D)) ) )  =>  ((k10_seq_4 A B) = (k8_rvsum_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t51_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_afinsq_1 (k10_compos_1 A B))) =>  ( ((k1_funct_1 (k10_compos_1 A B) C) = (k2_compos_1 A))  | (r2_hidden C (k2_afinsq_1 B))) ) ) ) ) ) ) ) ).
tt(t51_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k3_compos_2 A B C) D) 2) = (k5_compos_0 (u1_compos_1 A) D 2)) ) ) ) ) ) ) ) ) ).
tt(t51_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 k6_numbers (k3_complex1 A)) => (r1_xxreal_0 k6_numbers (k21_sin_cos (k1_comptrig A)))) ) ) ).
tt(t51_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k5_numbers) => (r1_partfun1 (k6_comput_1 B C A D) (k6_comput_1 B C A E))) ) ) ) ) ) ) ) ) ) ).
tt(t51_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A B) = k5_complex1) ) )  => (v2_comseq_3 A)) ) ) ).
tt(t51_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k19_convex4 A B k6_complex1) = B) ) ) ) ) ).
tt(t51_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r3_cqc_the1 A B (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A C) C) C))) ) ) ) ) ) ).
tt(t51_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A (k11_cqc_lang A C B)) (k12_cqc_lang A C (k6_cqc_lang A B))) A) & (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B)) (k6_cqc_lang A (k11_cqc_lang A C B))) A)) ) ) ) ) ) ) ).
tt(t51_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r7_cqc_the3 A B C) & (r7_cqc_the3 A C D))  => (r7_cqc_the3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t51_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k15_csspace A B C) (k7_real_1 (k15_csspace A B D) (k15_csspace A D C)))) ) ) ) ) ) ) ) ).
tt(t51_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 (k9_real_1 B A))) (k21_sin_cos (k8_real_1 2 B))))) ) ) ) ) ).
tt(t51_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k10_real_1 A (k5_square_1 E))) ) )  =>  ( (B = k6_numbers)  |  ( ((k9_real_1 B C) = k6_numbers)  |  ((k1_seq_1 (k4_diff_1 D C) B) = (k10_real_1 (k8_real_1 (k8_real_1 (k1_real_1 A) C) (k9_real_1 (k8_real_1 2 B) C)) (k5_square_1 (k9_real_1 (k5_square_1 B) (k8_real_1 B C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k3_diff_1 (k5_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) (k7_real_1 B (k13_complex1 A 2))) (k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B))) ) ) ) ) ) ) ).
tt(t51_dilworth,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (? [B:$i] :  ( ((v5_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  &  ((k5_card_1 B) = (k2_dilworth A)) ) ) ) ) ).
tt(t51_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  (~  ((k8_eqrel_1 (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C)) = (k2_xboole_0 (k6_domain_1 (k1_zfmisc_1 (k6_ec_pf_1 A B C)) (k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers))) (a_3_1_ec_pf_1 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (~  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  &  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) = k6_numbers) )  &  ( (~  ((k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) = k6_numbers) )  &  ((r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)) &  ((k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C)) = k1_xboole_0)  =>  ((k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t51_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v4_partfun3 B) & (m2_finseq_1 B k1_numbers))  =>  ((r1_xxreal_0 k6_numbers A) =>  ((k4_entropy1 (k10_rvsum_1 B A)) = (k4_rvsum_1 (k10_rvsum_1 B (k8_real_1 A (k6_power 2 A))) (k10_rvsum_1 (k14_rvsum_1 B (k3_entropy1 2 B)) A))) ) ) ) ) ) ).
tt(t51_enumset1,ax, (! [A:$i] :  ((k4_enumset1 A A A A A A) = (k1_tarski A)) ) ).
tt(t51_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) =>  ( (! [E:$i] :  ((r2_hidden E D) =>  ((r1_tarski E C) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 B)) &  (E = (k8_mcart_1 A B F G)) ) ) ) ) ) ) )  => (r1_tarski (k2_zfmisc_1 (k3_tarski (k7_relat_1 (k1_funct_3 (k9_funct_3 A B)) D)) (k1_setfam_1 (k7_relat_1 (k1_funct_3 (k10_funct_3 A B)) D))) C)) ) ) ) ) ) ) ).
tt(t51_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k18_complex1 (k23_rvsum_1 B C)) (k11_binop_2 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t51_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ((r1_euclid_3 A (k5_algstr_0 (k15_euclid A) C B) (k5_algstr_0 (k15_euclid A) D B)) &  ((r2_hidden E (k9_euclid_3 A B C D)) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B F) (k1_rlvect_1 (k15_euclid A) C G)) (k1_rlvect_1 (k15_euclid A) D H)))  &  ( ((k7_real_1 (k7_real_1 F G) H) = 1)  &  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  ( ( (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B I) (k1_rlvect_1 (k15_euclid A) C J)) (k1_rlvect_1 (k15_euclid A) D K)))  &  ((k7_real_1 (k7_real_1 I J) K) = 1) )  =>  ( (I = F)  &  ( (J = G)  &  (K = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k1_funct_1 C D) = (k12_euclid (k5_algstr_0 (k15_euclid A) D B))) ) )  => (v5_pre_topc C (k15_euclid A) k3_topmetr)) ) ) ) ) ) ) ).
tt(t51_euclid_7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k1_rusub_4 (k7_real_ns1 A)) = A) ) ) ).
tt(t51_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k14_rvsum_1 A B) = (k11_finseq_1 (k11_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k11_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k11_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(t51_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (? [B:$i] :  ((m1_subset_1 B k1_numbers) &  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (A = (k10_finseq_1 B C)) ) ) ) ) ) ) ).
tt(t51_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (? [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) &  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  (B = (k2_euclid_4 A C D)) ) ) ) ) ) ) ) ) ).
tt(t51_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) &  ((v16_waybel_0 C) & (l1_orders_2 C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v1_exchsort D)) ) )  =>  (~  ((r2_hidden (k4_tarski A B) (k6_exchsort C D)) & (r2_hidden (k4_tarski A B) (k6_exchsort C (k10_funct_7 D A B)))) ) ) ) ) ) ) ) ).
tt(t51_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C)))) => (v1_circuit2 (k6_circuit2 (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C) D) (k5_circcomb C (k10_finseq_1 A B)) (k6_facirc_1 A B C))) ) ) ) ) ) ).
tt(t51_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k1_seq_1 (k1_fcont_1 A B) D) (k1_seq_1 (k1_fcont_1 A B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k8_real_1 (k1_seq_1 k24_sin_cos B) (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) ) ) ) ) ) ) ) ).
tt(t51_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)) k19_sin_cos))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k19_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2)) k19_sin_cos) A) B) = (k10_real_1 (k2_newton (k1_seq_1 k16_sin_cos B) 3) (k9_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t51_fdiff_7,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos)))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = (k10_real_1 C 2))  &  (~  ((k1_seq_1 k16_sin_cos (k1_seq_1 B C)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) A) C) = (k1_real_1 (k10_real_1 1 (k9_real_1 1 (k1_seq_1 k19_sin_cos C))))) ) ) ) ) ) ) ) ) ) ).
tt(t51_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_hidden (k4_nat_1 2 A) k3_fib_num2) &  (~ (r2_hidden (k2_nat_1 (k4_nat_1 2 A) 1) k3_fib_num2)) ) ) ) ).
tt(t51_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_fib_num3 A k6_numbers (k2_nat_1 B 1)) = (k4_nat_1 A (k1_pre_ff B))) ) ) ) ) ).
tt(t51_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D A) &  ((v20_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k6_filter_0 A D))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k6_filter_0 A D))) =>  ( ( (B = E)  &  (C = F) )  =>  ((r3_lattices A B C) <=> (r3_lattices (k6_filter_0 A D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k7_lattices A (k4_filter_0 A B C)) = (k4_lattices A B (k7_lattices A C)))  &  ( ((k7_lattices A (k7_filter_0 A B C)) = (k3_lattices A (k4_lattices A B (k7_lattices A C)) (k4_lattices A (k7_lattices A B) C)))  &  ( ((k7_lattices A (k7_filter_0 A B C)) = (k7_filter_0 A B (k7_lattices A C)))  &  ((k7_lattices A (k7_filter_0 A B C)) = (k7_filter_0 A (k7_lattices A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t51_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r1_filter_2 (u1_struct_0 A) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B C)) (k7_filter_2 A (k8_filter_2 A B C)))) ) ) ) ) ) ).
tt(t51_finseq_1,ax, (! [A:$i] :  ( (? [B:$i] :  ((v7_ordinal1 B) & (r1_tarski A (k2_finseq_1 B))) )  =>  ( ((k14_finseq_1 A) = k1_xboole_0)  <=>  (A = k1_xboole_0) ) ) ) ).
tt(t51_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_finseq_2 (k1_nat_1 A 1)) = (k7_finseq_1 (k1_finseq_2 A) (k12_finseq_1 k5_numbers (k1_nat_1 A 1)))) ) ) ).
tt(t51_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k5_relat_1 (k1_finseq_2 A) (k2_finseq_1 B)) = (k1_finseq_2 B))  <=> (r1_xxreal_0 B A)) ) ) ) ) ).
tt(t51_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_hidden B (k10_xtuple_0 A)) =>  (A = (k7_finseq_1 (k7_finseq_1 (k5_finseq_4 A B) (k9_finseq_1 B)) (k6_finseq_4 A B))) ) ) ) ) ).
tt(t51_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) & (r2_hidden (k1_nat_1 A 1) (k4_finseq_1 (k2_finseq_5 B D C))))  => (r2_hidden (k1_nat_1 A (k4_finseq_4 D C)) (k4_finseq_1 D))) ) ) ) ) ) ) ) ) ).
tt(t51_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~  (B = C) )  &  ( (~  (D = C) )  &  (~  ((k1_finseq_5 A (k3_finseq_4 A B D C) C) = (k3_finseq_4 A B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v3_card_1 D B) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r7_binop_1 A F E) => (r2_relset_1 k5_numbers A (k4_finseqop A A (k1_finseqop A A A E C D) F) (k1_finseqop A A A E (k4_finseqop A A C F) (k4_finseqop A A D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) &  ((v2_fintopo6 E A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) E) B) &  ( ((k1_funct_1 E 1) = C)  &  ((k1_funct_1 E (k3_finseq_1 E)) = D) ) ) ) ) )  &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~ (r3_fintopo6 A E B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_tarski (k7_flang_1 A B (k2_xcmplx_0 C 1)) (k6_flang_1 A (k8_flang_1 A B) B)) & (r1_tarski (k7_flang_1 A B (k2_xcmplx_0 C 1)) (k6_flang_1 A B (k8_flang_1 A B)))) ) ) ) ) ) ).
tt(t51_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((k1_flang_2 A C D E) = (k1_tarski B))  =>  ((r1_xxreal_0 D k6_numbers) |  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 D F) & (r1_xxreal_0 F E))  =>  ((k7_flang_1 A C F) = (k1_tarski B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((k2_flang_3 A B) = k1_xboole_0)  <=>  (B = k1_xboole_0) ) ) ) ) ).
tt(t51_fomodel0,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) <=>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((r2_hidden C (k9_xtuple_0 B)) &  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t51_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C B A)) )  =>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v7_fsm_1 D B A) & (l2_fsm_1 D B A)) ) )  &  ( ((u1_fsm_1 B D) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) B) (u1_struct_0 C) (u1_fsm_1 B C) (k2_zfmisc_1 (k12_fsm_1 B A C) B)))  &  ( ((u3_fsm_1 B A D) = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 C) B) A (u3_fsm_1 B A C) (k2_zfmisc_1 (k12_fsm_1 B A C) B)))  &  ( ((u2_fsm_1 B D) = (u2_fsm_1 B C))  & (r4_fsm_1 B A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A (k9_funcop_1 A A B (k6_partfun1 A) C) C) = (k5_binop_1 A B C C)) ) ) ) ) ) ) ).
tt(t51_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A B) =>  ( ((k5_relat_1 (k5_relat_1 C A) B) = (k5_relat_1 C A))  &  ((k5_relat_1 (k5_relat_1 C B) A) = (k5_relat_1 C A)) ) ) ) ) ) ) ).
tt(t51_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_tarski B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_tarski B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))))) )  => (r2_relset_1 A (k1_tarski B) C D)) ) ) ) ) ) ).
tt(t51_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k10_xtuple_0 (k13_funct_3 A B)) (k2_zfmisc_1 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t51_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k2_funct_4 (k2_funct_4 A)) A)) ) ).
tt(t51_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k10_xtuple_0 C) (k4_partfun1 A B)) =>  ((r2_hidden k1_xboole_0 (k10_xtuple_0 C)) |  ( ((k1_funct_5 (k2_funct_5 C)) = C)  &  ((k3_funct_5 (k4_funct_5 C)) = C) ) ) ) ) ) ) ) ).
tt(t51_funct_6,ax, (! [A:$i] :  ((k9_funct_6 A k1_xboole_0) = k1_xboole_0) ) ).
tt(t51_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k4_funct_7 A (k10_finseq_1 B C)) = (k3_relat_1 (k6_partfun1 A) (k3_relat_1 B C))) ) ) ) ) ) ).
tt(t51_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v6_funct_8 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t51_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  => (r1_fuzzy_1 (k1_fuzzy_1 A B (k3_fuzzy_2 A C D)) (k3_fuzzy_2 A (k1_fuzzy_1 A B C) (k1_fuzzy_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t51_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_fvaluat1 A B))) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t51_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  (D = (k1_funct_1 F A)) )  =>  ((k1_funct_1 (k10_fvsum_1 B C F E) A) = (k6_algstr_0 C E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H A B C D E) = (k11_genealg1 F G H B A C D E))  &  ( ((k11_genealg1 F G H A B C D E) = (k11_genealg1 F G H C B A D E))  &  ( ((k11_genealg1 F G H A B C D E) = (k11_genealg1 F G H D B C A E))  &  ((k11_genealg1 F G H A B C D E) = (k11_genealg1 F G H E B C D A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) = (k10_margrel1 E (k9_margrel1 F)))  &  ( ((k1_funct_1 (k6_circuit2 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 F) G))  &  ((k1_funct_1 (k6_circuit2 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski B))) =>  ( ((k24_glib_000 A C) = (k6_glib_000 A))  &  ((k25_glib_000 A C) = (k6_subset_1 (k7_glib_000 A) (k1_tarski B))) ) ) ) ) ) ) ).
tt(t51_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) => (r1_xxreal_0 (k3_finseq_1 (k20_glib_001 A B C D)) (k3_finseq_1 B))) ) ) ) ) ) ) ) ).
tt(t51_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) &  ((v1_glib_000 B) & (v3_glib_003 B)) ) ) ) )  =>  ( ((k7_glib_003 A) = (k7_glib_003 B))  =>  ((k14_glib_003 A) = (k14_glib_003 B)) ) ) ) ) ) ).
tt(t51_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1)) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B (k3_finseq_1 B) A)) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B) (k2_nat_1 A 1)) (k19_euclid 1 k6_numbers)))))) ) ) ) ) ) ).
tt(t51_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 2) B)) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 (k2_goboard2 D)) (k2_nat_1 A 1)) |  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 2) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v3_graph_2 B A) & (m2_graph_1 B A))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 2))  =>  ((v2_funct_1 B) & (m2_graph_1 B A)) ) ) ) ) ) ).
tt(t51_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  => (r2_hidden k1_xboole_0 (k9_graph_3 A))) ) ).
tt(t51_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  ( ( (C = k1_xboole_0)  & (r6_graph_5 B A))  =>  ((k10_graph_5 B C A) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t51_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v7_graph_1 D A) & (m2_graph_1 D A))  =>  ( ((r5_graphsp A D B) &  ((r5_graphsp A D C) & (r1_xxreal_0 1 (k3_finseq_1 D))) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t51_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) &  ((v1_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  => (r1_rewrite1 (k3_polyred A B C (k1_groeb_1 A C E)) (k10_polynom1 A C D E) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t51_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D (k4_group_11 A C B)) & (r1_xboole_0 (k13_group_2 A B D) (k8_group_2 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t51_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B 2) = (k6_algstr_0 A B B)) ) ) ) ) ).
tt(t51_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_struct_0 C B) => (r1_struct_0 C (k2_group_1 A B))) ) ) ) ) ) ) ).
tt(t51_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_group_3 A (k2_group_2 A C D) B) (k2_group_2 A (k4_group_3 A C B) (k4_group_3 A D B)))) ) ) ) ) ) ) ) ).
tt(t51_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ((k7_group_4 A B C) = (k7_group_4 A C B))  =>  ((u1_struct_0 (k8_group_4 A B C)) = (k7_group_4 A B C)) ) ) ) ) ) ) ) ).
tt(t51_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  (~  ((k4_group_5 A B C) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) ) )  => (v5_group_1 (k10_group_6 B A C))) ) ) ) ) ) ) ).
tt(t51_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v2_group_9 C A) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v2_funct_2 D (u1_struct_0 C)) <=>  ((k14_group_9 A B C D) = C) ) ) ) ) ) ) ) ) ).
tt(t51_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 A)) =>  ( ( (B = (k2_helly A D E))  &  (C = (k2_helly A D F)) )  =>  ((r2_hidden E (k13_glib_001 A C)) |  ((r2_hidden F (k13_glib_001 A B)) |  ((k3_helly A D E F) = (k1_funct_1 B (k3_finseq_1 (k1_helly B C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  => (v1_vectsp_4 (k12_bilinear k1_complfld A B) k1_complfld A)) ) ) ) ).
tt(t51_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers k3_taylor_1)) & (r1_tarski A (k1_relset_1 k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k6_partfun1 k1_numbers)))))  => (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 k3_taylor_1 A) (k5_relset_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k6_partfun1 k1_numbers)) A))) ) ) ).
tt(t51_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~ (r1_xxreal_0 (k17_complex1 A) (k17_complex1 B)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 C k1_complfld) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((r1_xxreal_0 1 (k2_hurwitz k1_complfld C)) =>  ((v1_hurwitz C) <=> (v1_hurwitz (k3_normsp_1 k1_complfld (k3_polynom5 k1_complfld C A) (k3_polynom5 k1_complfld (k7_hurwitz C) B)))) ) ) ) ) ) ) ) ) ).
tt(t51_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) )  =>  ((k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k5_struct_0 A))) = (u1_struct_0 A)) ) ) ).
tt(t51_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) &  ((r1_incsp_1 A B C) &  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A B E) &  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A C F) &  ((r3_incsp_1 A D F) & (r3_incsp_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~  ( (C = (k6_xcmplx_0 B A))  & (r1_xxreal_0 1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t51_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( ((k5_card_1 B) = A)  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( ((k3_finseq_1 C) = A)  &  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r2_hidden (k1_funct_1 C D) B)) ) )  & (v2_funct_1 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_int_5,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~ (r1_xxreal_0 A 2))  &  ( (~ (r1_xxreal_0 B 2))  &  ( (~  (A = B) )  &  ( ( ((k4_nat_d A 4) = 1)  |  ((k4_nat_d B 4) = 1) )  &  (~  ((k2_int_5 A B) = (k2_int_5 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k30_sin_cos) k2_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k19_sin_cos B) (k9_real_1 (k1_seq_1 k19_sin_cos B) 1))) ) ) ) ) ) ) ) ).
tt(t51_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ((r2_relset_1 k1_numbers k1_numbers B (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos) (k3_valued_1 k1_numbers k1_numbers k1_numbers C (k1_taylor_1 2)))) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = 1) ) ) )  &  ( (D = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_sin_cos9 k24_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t51_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k29_sin_cos D)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t51_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k4_real_ns1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers E)) &  (! [F:$i] :  ((v1_xreal_0 F) =>  ((r2_hidden F (k3_integra5 B C)) =>  ((k1_funct_1 E F) = D) ) ) ) ) )  =>  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) E) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) E (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((k6_integr18 (k4_real_ns1 A) E B C) = (k1_rlvect_1 (k4_real_ns1 A) D (k10_binop_2 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_integra1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ( ((v4_xxreal_2 A) & (v4_xxreal_2 B))  => (v4_xxreal_2 (k9_member_1 A B))) ) ) ) ) ).
tt(t51_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (A = (k1_rcomp_1 (k8_real_1 (k4_nat_1 2 B) k32_sin_cos) (k8_real_1 (k2_nat_1 (k4_nat_1 2 B) 1) k32_sin_cos)))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k1_real_1 2)) ) ) ) ) ) ).
tt(t51_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k9_real_1 F A))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) = E)  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_real_1 1 (k9_real_1 F A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (~  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  =>  ((k9_interva1 A B B) = (k2_interva1 A (k1_subset_1 A) (k1_subset_1 A))) ) ) ) ) ) ).
tt(t51_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 A C)) (k3_intpro_1 A (k4_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t51_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r2_isocat_1 A B) =>  (! [C:$i] :  ((m1_isocat_1 C A B) =>  ((v13_cat_1 C A B) &  ((v14_cat_1 C A B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r1_cat_1 B D (k8_cat_1 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 B))  &  (~  ( ( ((r1_xxreal_0 B (k13_complex1 (k17_euclid A) (k12_euclid A))) & (r1_xxreal_0 k6_numbers (k18_euclid A)))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B))) (k8_real_1 (k12_euclid A) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k9_real_1 1 B)))))))) ) )  &  ( ((r1_xxreal_0 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) & (r1_xxreal_0 k6_numbers (k18_euclid A)))  =>  ( (A = (k4_struct_0 (k15_euclid 2)))  |  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 B) A) = (k19_euclid (k8_real_1 (k12_euclid A) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B))) (k8_real_1 (k12_euclid A) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid A) (k12_euclid A)) B) (k7_real_1 1 B)))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) & (r2_hidden B C)) )  =>  ((r1_xxreal_0 k6_numbers (k17_euclid A)) |  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  ( ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B))) )  | (r1_jordan6 C A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k8_jordan6 (k1_sppol_2 A B C D)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 A B C D)) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 C k6_numbers) |  ((v3_tops_2 E (k15_euclid 2) (k15_euclid 2)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r1_xxreal_0 (k18_euclid G) (k18_euclid F)))  & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E G)) (k18_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jordan15,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B (k2_nat_1 A 1))) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C E) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) & (r2_subset_1 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) E)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) C E))) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xboole_0 (k4_topreal1 C) (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t51_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k4_finseq_4 (k1_jordan1e A B) (k1_jordan5c (k3_topreal1 2 (k1_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) C))  & (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t51_jordan1h,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r1_jordan1h B A) => (r1_xxreal_0 1 A)) ) ) ) ) ).
tt(t51_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) A))  =>  ((r1_xxreal_0 (k3_finseq_1 B) D) |  ( ((k3_gobrd13 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k3_gobrd13 B A D))  &  ((k2_gobrd13 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k2_gobrd13 B A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_jordan1k,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ((v3_pre_topc B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_tarski A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~ (r2_hidden C B))  & (r1_xxreal_0 (k5_jordan1k 2 C A) (k5_jordan1k 2 C B))) ) ) ) ) ) ) ) ) ).
tt(t51_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r1_xxreal_0 2 A) &  (C = (a_2_2_jordan2c A B)) )  => (v2_connsp_1 C (k15_euclid A))) ) ) ) ) ) ) ).
tt(t51_jordan4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ( (B = (k3_topreal1 2 A))  => (v1_topreal2 B)) ) ) ) ) ).
tt(t51_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal2 A) =>  ( ((k9_jordan6 A) = (k2_xboole_0 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k8_jordan6 A)) (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A))))  &  ((k8_jordan6 A) = (k2_xboole_0 (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k9_jordan6 A)) (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))) ) ) ) ) ).
tt(t51_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_jgraph_6 A B C D) (k1_jgraph_6 A B C D)) = (k1_sppol_2 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t51_kurato_1,ax,(r1_subset_1 (k1_enumset1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)))) (k1_enumset1 (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)))))).
tt(t51_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  => (r3_binop_1 (u1_struct_0 A) (k5_lattices A) (u2_lattices A))) ) ).
tt(t51_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  ((k4_filter_0 A B C) = (k15_lattice3 A (a_3_6_lattice3 A B C))) ) ) ) ) ) ) ) ).
tt(t51_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  ( ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))) &  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))) &  (C = (k7_nat_d (k15_glib_000 A) (k1_recdef_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) E))) ) )  =>  ((r1_xxreal_0 (k1_recdef_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) E) (k1_recdef_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) D)) | (r1_termord k5_numbers (k4_bagorder k5_numbers) (k2_uproots k5_numbers (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) C)) D) 1) (k2_uproots k5_numbers (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) C)) E) 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_limfunc1 A) &  ((v5_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) ) ) ) ) ) )  =>  ((v5_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (v4_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t51_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( ((k1_limfunc2 C A) = k6_numbers)  |  ((r1_limfunc2 (k3_rfunct_1 k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k3_rfunct_1 k1_numbers k1_numbers B C) A) = (k10_real_1 (k1_limfunc2 B A) (k1_limfunc2 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t51_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r2_limfunc3 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) &  ((k1_seq_1 B E) = (k1_limfunc2 B A)) ) ) ) ) ) ) ) )  | (r2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t51_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C k7_numbers) &  ((v10_valued_0 D) &  ((v6_supinf_2 D) &  ((v4_measure1 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C k7_numbers)))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k20_lpspace1 B C D))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k20_lpspace1 B C D))) =>  ( ( ((r2_hidden E G) & (r2_hidden F H))  => (r2_hidden (k3_valued_1 B k1_numbers k1_numbers E F) (k1_algstr_0 (k20_lpspace1 B C D) G H)))  &  ((r2_hidden E G) => (r2_hidden (k26_valued_1 B k1_numbers E A) (k1_rlvect_1 (k20_lpspace1 B C D) G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k10_lpspace2 A B C E))) =>  ((r2_hidden D F) =>  ((r3_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D))) & (r2_hidden D (k1_lpspace2 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) =>  (! [D:$i] :  ((m1_subset_1 D k1_hilbert1) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 k1_hilbert1)) =>  ( ((r8_ltlaxio1 E (k3_hilbert1 A (k3_hilbert1 B C))) & (r8_ltlaxio1 E (k3_hilbert1 C D)))  => (r8_ltlaxio1 E (k3_hilbert1 A (k3_hilbert1 B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A D B) (k8_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t51_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k6_rusub_4 A B C) = (k4_mathmorp A (k6_rusub_4 A B C) C))  &  ((k3_mathmorp A B C) = (k5_mathmorp A (k3_mathmorp A B C) C)) ) ) ) ) ) ) ) ).
tt(t51_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) (k4_matrix10 A D C)) => (r2_matrix10 B D)) ) ) ) ) ) ) ) ) ).
tt(t51_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r2_hidden D (k2_finseq_1 A)) & (r2_hidden E (k2_finseq_1 A)))  =>  ( (D = E)  |  ((k12_matrix_3 A B (k3_matrix11 D A A (u1_struct_0 B) C (k8_matrix_1 (u1_struct_0 B) C E))) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ((k6_matrix13 A C (k7_subset_1 k5_numbers (k2_finseq_1 (k3_finseq_1 C)) (k3_matrix13 B)) (k2_finseq_1 (k1_matrix_1 C))) = (k1_matrlin A B C)) ) ) ) ) ) ) ).
tt(t51_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A))  =>  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C (k4_matrix14 B A D)) E D) = (k3_matrix_1 (u1_struct_0 B) C E 1))  &  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C (k4_matrix14 B A D)) E 1) = (k3_matrix_1 (u1_struct_0 B) C E D)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E A) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F A)) ) )  =>  ( (F = 1)  |  ( (F = D)  |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C (k4_matrix14 B A D)) E F) = (k3_matrix_1 (u1_struct_0 B) C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) k1_xboole_0 A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) k1_xboole_0 B) =>  ((k4_matrix15 C D E) = (k3_matrix13 k1_xboole_0)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((v5_matrix16 D B) => (v5_matrix16 (k2_matrix13 A A B D C) B)) ) ) ) ) ) ) ) ) ).
tt(t51_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k3_matrix_3 A B C) = (k1_matrix_4 A B (k2_matrix_3 A C))) ) ) ) ) ) ) ) ).
tt(t51_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B (k2_matrix_6 A B C D) (k2_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ) ).
tt(t51_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((v4_matrix_6 C A B) => (r1_matrix_8 A B (k4_matrix_6 A B (k4_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) D) C) D)) ) ) ) ) ) ) ) ) ).
tt(t51_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) C D) E) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k12_matrix_2 A)) (k11_matrix_3 A B C)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t51_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 A) k6_numbers))  =>  ((k12_matrixc1 A) = (k12_matrixc1 (k4_matrix_1 k2_numbers A))) ) ) ) ).
tt(t51_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_matrixj1 C (u1_struct_0 B)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ((k22_matrixj1 B (k18_matrixj1 (u1_struct_0 B) A C)) = (k17_finseq_1 (u1_struct_0 B) A (k22_matrixj1 B C))) ) ) ) ) ) ) ).
tt(t51_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ((k10_matrixr1 (k10_rvsum_1 B A)) = (k7_matrixr1 A (k10_matrixr1 B))) ) ) ) ) ).
tt(t51_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k12_matrixr1 (k4_matrixr1 B) A) = (k6_rvsum_1 (k12_matrixr1 B A))) ) ) ) ) ) ) ).
tt(t51_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v1_matrlin C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v8_vectsp_1 D A) &  ((v9_vectsp_1 D A) &  ((v10_vectsp_1 D A) &  ((v11_vectsp_1 D A) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v1_matrlin D A) & (l1_vectsp_1 D A)) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v13_vectsp_1 E B C) &  ((v1_mod_2 E A B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) &  ((v13_vectsp_1 F C D) &  ((v1_mod_2 F A C D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) ) ) )  =>  ((v2_funct_1 (k8_matrlin2 A C D (k3_ranknull A B C E) F)) =>  ( ((k10_ranknull A B D (k6_matrlin2 A B C D E F)) = (k10_ranknull A B C E))  &  ((k11_ranknull A B D (k6_matrlin2 A B C D E F)) = (k11_ranknull A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 B))  &  (A = (k5_finseq_2 k5_numbers (k3_finseq_1 A) 1)) )  =>  ((r1_xxreal_0 (k1_matrix_1 B) k6_numbers) |  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k2_finseq_1 (k3_finseq_1 (k11_matrixr1 B A)))) =>  ((k1_seq_1 (k11_matrixr1 B A) C) = (k18_rvsum_1 (k8_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ) ).
tt(t51_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~  (A = k1_xboole_0) )  &  ( (~  (B = k1_xboole_0) )  &  ( (~  (C = k1_xboole_0) )  &  (~  (D = k1_xboole_0) ) ) ) )  <=>  (~  ((k4_zfmisc_1 A B C D) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t51_measure6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((v3_xxreal_2 B) =>  ((k5_seq_4 (k2_measure6 B A)) = (k7_real_1 A (k5_seq_4 B))) ) ) ) ) ) ).
tt(t51_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k9_member_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k3_binop_2 A B))) ) ) ) ) ).
tt(t51_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_memstr_0 A B (k9_memstr_0 A B C D)) = (k6_memstr_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(t51_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 F A k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k2_numbers F k6_numbers)))  &  ( (D = (k1_relset_1 A E))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers F G) D)) )  &  ((r3_mesfunc6 A B C E) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G D) => (r1_xxreal_0 (k1_seq_1 (k55_valued_1 A k2_numbers (k4_mesfunc5 A k2_numbers F H)) G) (k1_seq_1 E G))) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G D) => (v2_comseq_2 (k9_mesfun7c A F G))) ) ) ) ) ) ) )  => (r2_mesfun6c A B C (k10_mesfun7c A F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v9_mesfunc5 A) =>  ( (~ (v8_mesfunc5 A))  &  (~ (v7_mesfunc5 A)) ) ) ) ) ).
tt(t51_mesfunc6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v6_supinf_2 B) <=>  (! [C:$i] : (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) ) ) ).
tt(t51_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ((r1_tarski D (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers))) &  ((v2_mesfunc9 E A) &  ((v1_mesfunc8 E A k7_numbers) &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers E F)) & (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E F) D)) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F D) => (v1_mesfunc9 (k3_mesfunc5 A E F))) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_mesfunc9 F G) = (k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k4_mesfunc5 A k7_numbers E G) D))) ) )  &  ((v1_mesfunc9 F) &  ((k7_mesfunc5 A B C (k2_partfun1 A k7_numbers (k7_mesfunc8 A (k4_mesfunc9 A E)) D)) = (k3_mesfunc9 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k10_midsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) &  ((k11_midsp_1 A B C) = (k6_midsp_1 A)) ) ) ) ) ) ) ).
tt(t51_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_mmlquery B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  ((k20_mmlquery A B (k18_mmlquery A B)) = (k4_relat_1 A)) ) ) ) ).
tt(t51_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((k3_funct_2 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k58_modelc_1 A B C D) E) = (k9_subset_1 A (k51_modelc_1 A B C D) (k50_modelc_1 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_modelc_2 C) & (l1_modelc_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k15_modelc_2 (u1_modelc_2 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 C))))) )  =>  ((k21_modelc_2 C D (k4_modelc_2 A B)) = (k2_lattices C (k21_modelc_2 C D A) (k21_modelc_2 C D B))) ) ) ) ) ) ) ) ) ).
tt(t51_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k22_modelc_3 A) (k22_modelc_3 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k22_modelc_3 A) (k22_modelc_3 A))))) )  =>  ((r7_modelc_3 A B C) =>  (! [D:$i] :  (~  ((r2_hidden D (k22_modelc_3 A)) &  ( (~ (v3_modelc_3 (k10_modelc_3 D A) A))  &  ((r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 D A))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r1_xxreal_0 E F))  =>  ( (~ (v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A) A))  & (r4_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A) (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C (k1_nat_1 F 1)) D) A))) ) ) )  &  ((v3_modelc_3 (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C E) D) A) A) &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 F E) => (r8_modelc_2 B (k14_modelc_3 A (k10_modelc_3 (k1_funct_1 (k29_modelc_1 (k22_modelc_3 A) C F) D) A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers)))  =>  ( (B = (a_1_1_moebius1 A))  =>  ((k4_moebius1 B) = (k16_pre_poly k5_numbers)) ) ) ) ) ) ).
tt(t51_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (m2_monoid_0 A k6_monoid_0)) )  =>  ( ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = k6_numbers)  |  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = 1) ) ) ) ).
tt(t51_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  ((r3_binop_1 B D C) =>  ( ((k7_relset_1 (k2_zfmisc_1 B B) B C (k2_zfmisc_1 (k6_domain_1 B D) A)) = (k3_xboole_0 B A))  &  ((k7_relset_1 (k2_zfmisc_1 B B) B C (k2_zfmisc_1 A (k6_domain_1 B D))) = (k3_xboole_0 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t51_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m3_pboole C A (k1_mboolean A B)) =>  (! [D:$i] :  ((m3_pboole D A B) =>  (! [E:$i] :  ((m3_pboole E A B) =>  ((r6_pboole A C (k2_pzfmisc1 A D E)) => (r6_pboole A (k4_mssubfam A B C) (k3_pboole A D E))) ) ) ) ) ) ) ) ) ) ).
tt(t51_msualg_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_msualg_4 C A B B) =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  ((r2_pboole A C D) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 B E)) =>  (! [G:$i] :  ((m1_subset_1 G (k1_funct_1 B E)) =>  ((r2_rewrite1 (k1_msualg_4 A B B C E) F G) => (r2_hidden (k4_tarski F G) (k1_msualg_4 A B B D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ((v8_struct_0 B) & (l1_orders_2 B))  &  ( ((k1_dilworth B) = 2)  &  (~ (r1_xxreal_0 (k2_mycielsk B) A)) ) ) ) ) ) ).
tt(t51_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  => (r2_hidden (k8_nat_1 B C A) (k10_xtuple_0 C))) ) ) ) ) ) ).
tt(t51_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k12_nat_3 (k1_newton B A)) = (k4_nat_3 k10_newton (k12_nat_3 B) A)) ) ) ) ) ).
tt(t51_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_trees_4 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_trees_4 C k1_numbers k5_numbers) =>  ((k1_nat_4 (k1_wsierp_1 k1_numbers k5_numbers B C) A) = (k1_wsierp_1 k1_numbers k5_numbers (k1_nat_4 B A) (k1_nat_4 C A))) ) ) ) ) ) ) ).
tt(t51_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 (k7_nat_d B A)) & (r1_xxreal_0 B (k7_nat_d B A))) ) ) ) ) ) ) ).
tt(t51_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ((r8_ncfcont1 A B D C) <=> (r8_ncfcont1 A B (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) D C) C)) ) ) ) ) ) ) ) ).
tt(t51_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A E)) B))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E)))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E)))) =>  ( ((r2_hidden E (k4_finseq_1 A)) &  ( (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E)))) =>  ((r2_hidden J (k2_ndiff_5 (k11_prvect_2 A (k5_ndiff_5 A E)) H I)) => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A E)) B) (k5_algstr_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A E)) B) (k6_ndiff_5 A B E C (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A E) D) J)) G)) F)) ) )  &  ( (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E)))) =>  ((r2_hidden J (k1_rltopsp1 (k11_prvect_2 A (k5_ndiff_5 A E)) H I)) => (r2_hidden (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A E) D) J) (k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) C))) ) )  &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E)))) =>  ((r2_hidden J (k1_rltopsp1 (k11_prvect_2 A (k5_ndiff_5 A E)) H I)) => (r1_ndiff_5 A B E C (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A E) D) J))) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A E) D) I)) (k7_partfun1 (u1_struct_0 B) C (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A E))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A E) D) H))) (k17_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A E)) B G (k5_algstr_0 (k11_prvect_2 A (k5_ndiff_5 A E)) I H)))) (k11_binop_2 F (k1_normsp_0 (k11_prvect_2 A (k5_ndiff_5 A E)) (k5_algstr_0 (k11_prvect_2 A (k5_ndiff_5 A E)) I H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_nat_d A 1) = 1) ) ) ).
tt(t51_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  ( ((r1_tarski B (k1_relset_1 (u1_struct_0 A) C)) & (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k2_partfun1 (u1_struct_0 A) (u1_struct_0 A) C B) (k1_partfun2 (u1_struct_0 A) B)))  => (r3_nfcont_1 A A C B)) ) ) ) ) ) ) ).
tt(t51_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) =>  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k7_normform A))) =>  ((k9_normform A (k10_normform A B (k9_normform A C))) = (k9_normform A (k10_normform A B C))) ) ) ) ) ) ).
tt(t51_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_cat_1 B) &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 B) (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 A))))) )  => (r1_funct_2 (u4_struct_0 (k2_oppcat_1 (k2_oppcat_1 B))) (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 A) (k10_oppcat_1 (k2_oppcat_1 B) A (k10_oppcat_1 B A C)) C)) ) ) ) ) ) ).
tt(t51_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_orders_1 A B) <=> (r5_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t51_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r7_orders_1 (u1_orders_2 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r2_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(t51_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) =>  (B = (k10_ordinal2 A (k5_ordinal3 B A))) ) ) ) ) ) ).
tt(t51_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~  ((v4_ordinal5 A) &  (! [B:$i] :  ((v3_ordinal1 B) =>  (~  (A = (k3_ordinal5 B)) ) ) ) ) ) ) ) ).
tt(t51_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  ((v4_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v3_ordinal6 C)) ) )  =>  ( ((r1_ordinal1 B (k9_xtuple_0 (k7_ordinal6 C))) &  ( (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v5_ordinal1 D) & (v1_ordinal2 D)) ) )  =>  ((r2_hidden D (k10_xtuple_0 C)) => (r1_abian A D)) ) )  &  (! [D:$i] :  ((r2_hidden D B) => (r2_hidden (k1_funct_1 (k7_ordinal6 C) D) A)) ) ) )  =>  ( ((k9_xtuple_0 C) = k1_xboole_0)  | (r2_hidden B (k9_xtuple_0 (k7_ordinal6 C)))) ) ) ) ) ) ) ) ).
tt(t51_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v1_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t51_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_msualg_1 B A) &  ((v4_msualg_1 B A) &  ((v12_osalg_1 B A) & (l3_msualg_1 B A)) ) )  =>  ((k6_lattices (k16_osalg_2 A B)) = B) ) ) ) ) ).
tt(t51_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_parsp_2 A B C D E) => (r3_parsp_2 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((k2_xboole_0 A B) = C) ) ) ) ) ) ) ) ).
tt(t51_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden C (k1_relset_1 A D)) & (r2_relset_1 A B E (k4_subset_1 (k2_zfmisc_1 A B) D F)))  =>  ((k7_partfun1 B E C) = (k7_partfun1 B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r2_pboole A B C) & (r6_pboole A (k3_pboole A C B) (k1_pboole A)))  => (r6_pboole A B (k1_pboole A))) ) ) ) ) ) ).
tt(t51_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r6_pdiff_5 B A) & (r6_pdiff_5 C A))  =>  ((r3_pdiff_1 3 3 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 3 (k3_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k7_real_1 (k6_pdiff_5 B A) (k6_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t51_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ( ((r1_pdiff_7 A B D) & (r1_pdiff_7 A C D))  =>  ((r1_pdiff_7 A (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D) &  ((r2_funct_2 (k1_euclid A) k1_numbers (k1_pdiff_7 A (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D) (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers (k1_pdiff_7 A B D) (k1_pdiff_7 A C D))) &  ((r1_pdiff_7 A (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D) & (r2_funct_2 (k1_euclid A) k1_numbers (k1_pdiff_7 A (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers B C) D) (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers (k1_pdiff_7 A B D) (k1_pdiff_7 A C D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_pepin,ax, ((k4_pepin 1) = 5) ).
tt(t51_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k9_xtuple_0 (k12_pnproc_1 B A)) = (a_2_1_pnproc_1 A B)) ) ) ) ) ).
tt(t51_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 (k29_polyform A))))  =>  ((k1_funct_1 (k29_polyform A) B) = (k2_xcmplx_0 (k1_polyform (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 B 1)) (k1_vectsp_9 k2_bspace (k24_polyform A (k6_xcmplx_0 B 2)))) (k1_polyform (k2_polyform (k4_xcmplx_0 1) (k2_xcmplx_0 B 1)) (k1_vectsp_9 k2_bspace (k22_polyform A (k6_xcmplx_0 B 1)))))) ) ) ) ) ) ).
tt(t51_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 (k1_algseq_1 A (k5_polynom5 A B (k3_algseq_1 A C))) 1)) ) ) ) ) ) ).
tt(t51_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) (k6_polynom1 A C E F) (k7_polynom1 A C)) => (r2_rewrite1 (k3_polyred A B C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  (~  ((k5_power A 1) = k6_numbers) ) ) ) ) ) ) ).
tt(t51_pre_poly,ax, ((k15_pre_poly k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t51_prepower,ax, (! [A:$i] :  ((v1_rat_1 A) =>  ((k7_prepower 1 A) = 1) ) ) ).
tt(t51_prob_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k9_setfam_1 A)) =>  ( (~  (C = k1_xboole_0) )  =>  ((r2_hidden B (k7_prob_3 A C)) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r2_hidden B (k4_prob_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t51_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B D) (k7_cqc_lang A C D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t51_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k13_pscomp_1 A) (k23_pscomp_1 A)) A) = (k1_tarski (k23_pscomp_1 A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k22_pscomp_1 A) (k12_pscomp_1 A)) A) = (k1_tarski (k22_pscomp_1 A))) ) ) ) ).
tt(t51_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k4_pboole A (k1_pzfmisc1 A B) C) (k1_pzfmisc1 A B)) & (r1_pboole A B C)) ) ) ) ) ) ) ) ).
tt(t51_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r1_qc_lang2 A B C) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A C)) (k3_finseq_1 (k11_qc_lang1 A B)))) ) ) ) ) ) ) ) ).
tt(t51_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((v4_qc_lang2 B A) =>  ((k4_qc_lang3 A C B) = (k4_qc_lang3 A C (k18_qc_lang1 A (k22_qc_lang1 A (k18_qc_lang1 A B))))) ) ) ) ) ) ) ) ).
tt(t51_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k3_quatern2 (k18_quatern2 A B)) = (k8_real_1 (k3_quatern2 A) (k3_quatern2 B))) ) ) ) ) ).
tt(t51_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k26_quaterni A B) (k26_quaterni C D)) = (k26_quaterni (k26_quaterni (k26_quaterni (k27_quaterni A C) (k27_quaterni B C)) (k27_quaterni A D)) (k27_quaterni B D))) ) ) ) ) ) ) ) ) ).
tt(t51_quaterni,ax, ((k31_quaterni k1_xcmplx_0) = (k28_quaterni k1_xcmplx_0)) ).
tt(t51_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_quofield C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k4_struct_0 B))  <=>  (D = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  => (r1_xxreal_0 1 (k3_finseq_1 D))) ) ) ) ) ) ) ) ) ).
tt(t51_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 k6_numbers (k1_seq_1 (k6_real_3 B) A))) ) ) ) ).
tt(t51_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k9_xtuple_0 B) A) =>  ((k3_relat_1 (k4_relat_1 A) B) = B) ) ) ) ) ).
tt(t51_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ( ((k9_xtuple_0 (k7_relset_2 A B C D E)) = (k7_relset_1 B A (k3_relset_1 A B D) (k9_xtuple_0 E)))  & (r1_tarski (k9_xtuple_0 (k7_relset_2 A B C D E)) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(t51_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_rewrite1 A) <=>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_rewrite1 A B C) & (r2_hidden (k4_tarski B D) A))  => (r5_rewrite1 A C D)) ) ) ) ) ) ) ).
tt(t51_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  ((k8_rewrite2 A (k6_rewrite2 (k8_afinsq_1 A)) B) = (k4_flang_1 A B)) ) ) ) ).
tt(t51_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  ( (? [E:$i] :  (? [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) &  ((k1_funct_1 D 1) = (k4_tarski E F)) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 D)) =>  ((k2_rewrite3 (k1_funct_1 D E) A) = (k2_xtuple_0 (k1_funct_1 D E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 C A) <=> (v1_partfun1 (k26_valued_1 A k1_numbers C B) A)) ) ) ) ) ) ) ).
tt(t51_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) => (v5_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))) ) ) ) ) ) ) ).
tt(t51_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_classes1 C D) <=> (r2_classes1 (k15_valued_1 A k1_numbers C E) (k15_valued_1 B k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) => (v8_valued_0 (k4_rinfsup1 A))) ) ) ).
tt(t51_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (v2_rusub_4 C A))  => (r1_tarski (k4_rlaffin1 A B) C)) ) ) ) ) ) ) ).
tt(t51_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_struct_0 C B) <=>  ((k3_rlsub_1 A (k4_algstr_0 A B) C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t51_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C))) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)))) ) ) ) ) ) ) ) ) ).
tt(t51_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  =>  ((k1_convex1 A (k1_tops_1 A B) C) = (k1_tops_1 A (k1_convex1 A B C))) ) ) ) ) ) ) ).
tt(t51_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_algstr_0 A (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B))) = (k4_algstr_0 A B)) ) ) ) ) ).
tt(t51_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((k3_rlvect_2 A (k9_rlvect_2 A B)) = (k3_rlvect_2 A B)) ) ) ) ) ).
tt(t51_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r1_struct_0 E C) <=>  ((k3_rmod_2 A B D E) = (k3_rmod_2 A B (k3_rlvect_1 B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))))  &  ((v10_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) &  ((v12_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B))) & (l3_lattices (g3_lattices (k3_rmod_3 A B) (k5_rmod_3 A B) (k6_rmod_3 A B)))) ) ) ) ) ) ) ).
tt(t51_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((r1_rmod_4 A B (k6_rmod_4 A B C D) (k3_rmod_4 A B)) => (r1_rmod_4 A B D (k8_rmod_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t51_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k5_robbins1 A (k13_robbins1 A B) (k15_robbins1 A B)) (k11_robbins1 A B)) = B) ) ) ) ) ).
tt(t51_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k5_robbins1 A (k3_robbins1 A B) (k3_robbins1 A (k5_robbins1 A (k5_robbins1 A C B) (k5_robbins1 A C D))))) (k5_robbins1 A C D)) = (k5_robbins1 A (k5_robbins1 A C B) (k5_robbins1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t51_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_xboole_0 B C) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k4_subset_1 (u1_struct_0 A) B C)) D) = (k2_xcmplx_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t51_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ( ((k4_subset_1 A (k4_subset_1 A C D) E) = A)  &  ((r1_xboole_0 C D) &  ((r1_xboole_0 C E) & (r1_xboole_0 D E)) ) )  =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A D) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A E) k6_numbers) |  ((k1_rpr_1 A B) = (k7_real_1 (k7_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k8_real_1 (k2_rpr_1 A D B) (k1_rpr_1 A D))) (k8_real_1 (k2_rpr_1 A E B) (k1_rpr_1 A E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k3_rusub_1 A D B)) & (r2_hidden C (k3_rusub_1 A (k4_algstr_0 A D) B)))  => (r1_struct_0 B D)) ) ) ) ) ) ) ) ) ).
tt(t51_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C))) & (r1_struct_0 C (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C)))) ) ) ) ) ) ) ) ) ).
tt(t51_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  ((v3_pre_topc B (k5_rusub_5 A)) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k4_bhsp_2 A C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k10_rvsum_1 (k4_rvsum_1 B C) A) = (k4_rvsum_1 (k10_rvsum_1 B A) (k10_rvsum_1 C A))) ) ) ) ) ) ) ).
tt(t51_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k3_rvsum_2 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t51_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (A = B)  &  (C = (k5_relat_1 D k1_ami_2)) )  =>  ((k2_extpro_1 3 k1_scmfsa_2 B D) = (k1_funct_4 D (k2_extpro_1 2 k1_ami_3 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t51_scmfsa8c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r1_scmfsa7b A B))  & (r2_scmfsa7b (k11_compos_1 k1_scmfsa_2 A) B)) ) ) ) ) ) ).
tt(t51_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D)) ) ) ) ) ) ) ) ) ).
tt(t51_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k14_scmpds_2 D E B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k14_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k3_xcmplx_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C))))  &  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A D) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k14_scmpds_2 D E B C) A) F) = (k1_funct_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers) )  =>  ((k6_scmpds_4 (k5_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ( ((k1_funct_1 B k2_scmp_gcd) = k6_numbers)  &  ( ((k1_funct_1 B (k1_scmp_gcd 2)) = C)  &  ((k1_funct_1 B (k1_scmp_gcd 3)) = k6_numbers) ) )  =>  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_7 k2_scmp_gcd 2 1 (k9_compos_1 k1_scmpds_2 (k11_scmpds_2 k2_scmp_gcd 3 1))) B A) (k1_scmp_gcd 3)) = C) ) ) ) ) ) ) ) ).
tt(t51_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) &  ((r2_hidden C (k3_tarski A)) & (r2_hidden (k2_tarski B C) A)) )  =>  ((v4_scmyciel (k2_enumset1 k1_xboole_0 (k1_tarski B) (k1_tarski C) (k2_tarski B C))) &  ((v5_scmyciel (k2_enumset1 k1_xboole_0 (k1_tarski B) (k1_tarski C) (k2_tarski B C))) & (m1_subset_1 (k2_enumset1 k1_xboole_0 (k1_tarski B) (k1_tarski C) (k2_tarski B C)) (k1_zfmisc_1 A))) ) ) ) ) ) ) ).
tt(t51_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_semi_af1 A B C D) &  ((r2_semi_af1 A B E C F) & (r2_semi_af1 A B E D G)) )  =>  ( (C = D)  | (r2_semi_af1 A C F D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B) (k52_valued_1 k5_numbers k1_numbers k1_numbers C D)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A D) (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ).
tt(t51_seq_4,ax,(v1_finseqop k27_binop_2 k2_numbers)).
tt(t51_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers k1_numbers A (k20_valued_1 k5_numbers k1_numbers k1_numbers B C)) &  ((r2_funct_2 k5_numbers k1_numbers D (k20_valued_1 k5_numbers k1_numbers k1_numbers B B)) & (r2_funct_2 k5_numbers k1_numbers E (k20_valued_1 k5_numbers k1_numbers k1_numbers C C))) )  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) => (r1_xxreal_0 (k5_square_1 (k1_seq_1 (k3_series_1 A) F)) (k8_real_1 (k1_seq_1 (k3_series_1 D) F) (k1_seq_1 (k3_series_1 E) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A B) k6_numbers))  &  (~ (r1_xxreal_0 1 (k1_seq_1 A B))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k6_xcmplx_0 (k1_seq_1 (k3_series_1 A) B) B) (k1_seq_1 (k1_series_3 A) B))) ) ) ) ) ).
tt(t51_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v2_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) (k2_nat_1 A 1))) ) ) ) ) ) ) ).
tt(t51_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k6_setlim_2 B D C)) A) = (k4_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t51_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B (k5_finsub_1 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (k5_finsub_1 C))))) )  =>  ((k10_setwiseo B C (k8_setwiseo A B E D) F) = (k10_setwiseo A C D (k1_partfun1 A B B (k5_finsub_1 C) E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( (~  ( (~ (r2_hidden (k6_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ( (~ (r2_hidden (k7_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ( (~ (r2_hidden (k8_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ( (~ (r2_hidden (k9_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  (~ (r2_hidden (k10_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C))) ) ) ) ) )  =>  ( (~  ((k5_sf_mastr C) = A) )  &  (~  ((k5_sf_mastr C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t51_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C D) B)) (k5_sheffer1 A C C)) = (k5_sheffer1 A (k5_sheffer1 A C D) (k5_sheffer1 A C C))) ) ) ) ) ) ) ) ) ).
tt(t51_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_xxreal_0 (k6_simplex0 (k10_simplex0 A B C)) (k1_xxreal_3 (k6_simplex0 B) 1))) ) ) ) ) ).
tt(t51_sincos10,ax, ((k2_partfun1 k1_numbers k1_numbers k3_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4)))))) ).
tt(t51_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k2_comseq_3 (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B))) A) = (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 (k5_binop_2 A B)) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k5_binop_2 A B))))) ) ) ) ) ).
tt(t51_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k3_sin_cos2 (k6_real_1 A 2)) = k6_numbers) )  =>  ((k1_sin_cos5 (k6_real_1 A 2)) = (k10_real_1 (k3_sin_cos2 A) (k9_real_1 (k6_sin_cos2 A) 1))) ) ) ) ).
tt(t51_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t51_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k10_binop_2 (k1_sin_cos7 A) (k1_sin_cos7 B)) = (k1_sin_cos7 (k10_binop_2 (k11_binop_2 A (k7_square_1 (k9_binop_2 1 (k3_square_1 B)))) (k11_binop_2 B (k7_square_1 (k9_binop_2 1 (k3_square_1 A))))))) ) ) ) ) ).
tt(t51_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k1_sin_cos4 (k5_sin_cos9 A)) = A) ) ) ) ).
tt(t51_sin_cos,ax, ((k26_sin_cos k6_numbers) = 1) ).
tt(t51_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sppol_2 B C A) & (r2_hidden D A))  =>  ( (D = B)  | (r1_sppol_2 B D A)) ) ) ) ) ) ) ) ) ) ).
tt(t51_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 A B) =>  ((r2_hidden C (k1_rcomp_1 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r1_xxreal_0 k6_numbers D) &  ((r1_xxreal_0 D 1) &  (C = (k7_real_1 (k8_real_1 D A) (k8_real_1 (k9_real_1 1 D) B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k17_euclid (k21_pscomp_1 (k3_topreal1 2 A))) (k17_euclid (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t51_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A B) => (r1_sprect_2 A (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) B))) ) ) ) ) ).
tt(t51_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k21_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k20_pscomp_1 (k3_topreal1 2 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t51_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 (k3_square_1 A) 1) =>  ((r1_xxreal_0 (k4_xcmplx_0 1) A) & (r1_xxreal_0 A 1)) ) ) ) ).
tt(t51_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( ((k6_newton 1 A) = A)  &  ( ((k6_newton 2 A) = (k18_binop_2 (k22_binop_2 A (k21_binop_2 A 1)) 2))  &  ( ((k6_newton 3 A) = (k18_binop_2 (k22_binop_2 (k22_binop_2 A (k21_binop_2 A 1)) (k21_binop_2 A 2)) 6))  &  ((k6_newton 4 A) = (k18_binop_2 (k22_binop_2 (k22_binop_2 (k22_binop_2 A (k21_binop_2 A 1)) (k21_binop_2 A 2)) (k21_binop_2 A 3)) 24)) ) ) ) ) ) ).
tt(t51_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ( ((v3_substut1 (k7_sublemma A C B) A) & (r2_hidden B (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))))  =>  ((k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) = (k2_qc_lang3 A (k13_substut1 A (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D) (k2_sublemma A C)))) ) ) ) ) ) ) ) ) ) ).
tt(t51_supinf_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ((v6_supinf_2 B) <=>  (! [C:$i] : (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B C))) ) ) ) ) ).
tt(t51_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))) (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B))))) ) ) ) ).
tt(t51_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( ((k4_tdlat_1 A) = (k12_tdlat_1 A))  => (v4_tdlat_3 A)) ) ) ).
tt(t51_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((k9_subset_1 (u1_struct_0 A) B D) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) )  => (v2_tex_2 B A)) ) ) ) ) ).
tt(t51_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) &  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v3_tex_3 C A) & (m1_pre_topc C A)) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t51_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tarski (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) <=> (r1_tarski (k1_setfam_1 (a_2_9_tex_4 A C)) (k1_setfam_1 (a_2_9_tex_4 A B)))) ) ) ) ) ) ) ).
tt(t51_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ( ((u1_struct_0 B) = (u1_struct_0 C))  & (r1_tarski (u1_pre_topc C) (u1_pre_topc B)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) => (v2_funct_1 (k6_topalg_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t51_topgen_1,ax, ((v1_tops_1 k3_numbers k3_topmetr) & (m1_subset_1 k3_numbers (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ).
tt(t51_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_topgen_4 A B) = (k2_pre_topc A (k4_topgen_4 A B))) ) ) ) ) ).
tt(t51_topgen_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B k3_topmetr))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_partfun1 D C) & (v1_funcop_1 D)) ) ) )  =>  (~  ( (! [E:$i] :  ((r2_hidden E C) =>  ((v1_funct_1 (k1_funct_1 D E)) &  ((v1_funct_2 (k1_funct_1 D E) (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc (k1_funct_1 D E) A B) & (m1_subset_1 (k1_funct_1 D E) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_finset_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers))) )  &  ( (G = (k10_xtuple_0 (k1_funct_1 (k10_funct_6 D) F)))  &  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E F) = (k1_xxreal_2 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_pre_topc B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v3_pre_topc (k1_group_2 A B) A)) ) ) ) ).
tt(t51_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C (k9_metric_1 (k14_euclid 2) B A)) & (r2_hidden (k19_euclid (k9_real_1 (k17_euclid C) (k8_real_1 2 A)) (k18_euclid C)) (k9_metric_1 (k14_euclid 2) B A))) ) ) ) ) ) ) ) ).
tt(t51_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k2_topreal9 2 (k19_euclid A B) C) = (k7_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(t51_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) )  =>  ((k64_valued_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C D) = (k85_valued_2 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C (k15_toprealc A (u1_struct_0 B) (u1_struct_0 k3_topmetr) D))) ) ) ) ) ) ) ) ) ).
tt(t51_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  ((v2_tops_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((v3_pre_topc C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski D C) &  ( (~  (D = k1_xboole_0) )  &  ((v3_pre_topc D A) & (r1_xboole_0 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k2_tops_2 (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) C)) ) ) ) ) ) ) ).
tt(t51_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_tops_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  ((v2_tops_1 C A) &  ((v1_tops_3 D A) &  ( ((k9_subset_1 (u1_struct_0 A) C D) = B)  &  ((k4_subset_1 (u1_struct_0 A) C D) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo C A) &  ((v5_transgeo D A) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C B) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B)) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D)) ) ) ) ) ) ) ) ) ).
tt(t51_trees_1,ax, ((k2_trees_1 1) = (k2_tarski k1_xboole_0 (k12_finseq_1 k5_numbers k6_numbers))) ).
tt(t51_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v4_trees_3 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_trees_1 D))  =>  ((r2_hidden A D) <=> (r2_hidden (k7_finseq_1 (k12_finseq_1 k5_numbers (k3_finseq_1 B)) A) (k11_trees_3 (k7_finseq_1 (k7_finseq_1 B (k9_finseq_1 D)) C)))) ) ) ) ) ) ) ) ) ).
tt(t51_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v2_trees_2 B A) & (m1_trees_2 B A))  =>  (! [C:$i] :  ((m1_trees_1 C A) =>  (~  ((r2_hidden C B) &  ( (~ (v1_finset_1 B))  &  (! [D:$i] :  ((m1_trees_1 D A) =>  (~  ((r2_hidden D B) & (r2_hidden D (k1_trees_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski D B) &  ((r1_tarski E C) & (r2_tsep_1 A C B)) )  => (r2_tsep_1 A (k4_subset_1 (u1_struct_0 A) C D) (k4_subset_1 (u1_struct_0 A) B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k36_twoscomp A B)) = (k1_funct_1 k15_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k39_twoscomp A B)) = (k1_funct_1 k3_twoscomp (k10_finseq_1 (k1_funct_1 C A) (k1_funct_1 C B))))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = (k1_funct_1 C A))  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t51_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ( ((k3_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k5_uniroots A) k6_numbers) = 1)  |  ((k3_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k5_uniroots A) k6_numbers) = (k19_binop_2 1)) )  & (v1_int_1 (k3_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k5_uniroots A) B))) ) ) ) ) ).
tt(t51_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) C (k13_polynom3 A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A)) D)) => (r1_polynom5 A C B)) ) ) ) ) ) ) ) ) ).
tt(t51_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k31_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k37_valued_2 A B E C) D) = (k37_valued_2 A B E (k6_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t51_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( ((k3_vectsp_4 A B (k4_vectsp_1 A B C D) E) = (u1_struct_0 E))  =>  ( (C = (k4_struct_0 A))  | (r1_struct_0 E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_vectsp_5 A B C D) =>  ((k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)) = (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E D C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C k1_numbers))))  =>  ( ((v3_funct_1 (k2_partfun1 C k1_numbers F A)) & (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) E B)))  => (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) (k3_vfunct_1 C D F E) (k3_xboole_0 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v3_funct_1 (k2_partfun1 A k2_numbers F D)) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C E)))  => (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) (k1_vfunct_2 A B F C) (k3_xboole_0 D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r1_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r1_yellow_0 A E) &  (D = (k1_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k1_yellow_0 A D) C)) ) ) ) )  => (v1_waybel_0 C A)) ) ) ) ) ) ) ).
tt(t51_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_0_waybel_1 A B))  =>  ( ((v17_waybel_0 B A A) =>  ((v7_yellow_0 (k5_yellow_0 A C) A) & (v7_yellow_0 (k1_yellow_2 A A B) A)) )  &  ((v21_waybel_0 B A A) =>  ((v3_waybel_0 (k5_yellow_0 A C) A) & (v3_waybel_0 (k1_yellow_2 A A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v7_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r1_waybel_0 A C (u1_struct_0 B)) => (r2_hidden (k1_waybel11 A C) (u1_struct_0 B))) ) ) ) ) ) ) ).
tt(t51_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( ((k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (k3_waybel23 A B)) = (k7_waybel_0 B))  & (m1_subset_1 (k2_relset_1 (u1_struct_0 A) (k3_waybel23 A B)) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ).
tt(t51_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_2 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((k12_lattice3 A (k1_yellow_0 A B) (k1_yellow_0 A C)) = (k1_yellow_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ) ).
tt(t51_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k11_waybel34 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k11_waybel34 A))) =>  (! [D:$i] :  ((r2_hidden D (k1_altcat_1 (k11_waybel34 A) B C)) <=>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k4_yellow21 (k11_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k11_waybel34 A) C))) &  ((v18_waybel_0 E (k4_yellow21 (k11_waybel34 A) B) (k4_yellow21 (k11_waybel34 A) C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_yellow21 (k11_waybel34 A) B)) (u1_struct_0 (k4_yellow21 (k11_waybel34 A) C)))))) ) )  &  ( (E = D)  & (v22_waybel_0 (k2_waybel34 (k4_yellow21 (k11_waybel34 A) C) (k4_yellow21 (k11_waybel34 A) B) E) (k4_yellow21 (k11_waybel34 A) C) (k4_yellow21 (k11_waybel34 A) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  => (v8_waybel_4 (k1_waybel_4 A) A)) ) ).
tt(t51_wellord1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((v1_relat_1 D) =>  (! [E:$i] :  ((v1_relat_1 E) =>  ( ((v2_wellord1 D) &  ((v2_wellord1 E) &  ((r2_hidden A (k1_relat_1 D)) &  ((r2_hidden B (k1_relat_1 E)) &  ((r2_hidden C (k1_relat_1 E)) &  ((r4_wellord1 D (k2_wellord1 E (k1_wellord1 E B))) & (r4_wellord1 (k2_wellord1 D (k1_wellord1 D A)) (k2_wellord1 E (k1_wellord1 E C)))) ) ) ) ) )  =>  ((r1_tarski (k1_wellord1 E C) (k1_wellord1 E B)) & (r2_hidden (k4_tarski C B) E)) ) ) ) ) ) ) ) ) ).
tt(t51_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k2_xboole_0 (k3_xboole_0 A B) (k4_xboole_0 A B)) = A) ) ) ).
tt(t51_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k8_xboolean A A) = (k3_xboolean A)) ) ) ).
tt(t51_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k7_xcmplx_0 B (k7_xcmplx_0 A A))) ) ) ) ) ) ).
tt(t51_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 k6_numbers A) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 C (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ).
tt(t51_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k4_xxreal_1 A B) (k1_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((m1_xxreal_2 k2_xxreal_0 A) => (r1_tarski A (k1_tarski k2_xxreal_0))) ) ) ).
tt(t51_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 k1_xxreal_0 A))  &  ( (~ (r1_xxreal_0 B k2_xxreal_0))  & (r1_xxreal_0 (k3_xxreal_3 B A) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t51_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((r1_yellow_0 A B) | (r1_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))))  =>  ((k1_yellow_0 A B) = (k1_yellow_0 A (k3_xboole_0 B (u1_struct_0 A)))) ) ) ) ) ).
tt(t51_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((r1_tarski (k4_yellow_3 A B (k2_waybel_8 (k3_yellow_3 A B) C)) (k2_waybel_8 A (k8_yellow_3 A B C))) & (r1_tarski (k5_yellow_3 A B (k2_waybel_8 (k3_yellow_3 A B) C)) (k2_waybel_8 B (k9_yellow_3 A B C)))) ) ) ) ) ) ) ).
tt(t51_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((r1_t_0topsp A B) <=>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  &  (? [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v5_pre_topc D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  &  ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) D C) (k3_struct_0 B)) & (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D) (k3_struct_0 A))) ) ) ) ) ) ) ) ) ) ).
tt(t51_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) ) )  =>  ((r3_yellow20 A B C D E) => (r3_yellow20 B A (k15_functor0 A B C) E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t51_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  => (v5_orders_3 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ).
tt(t51_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_lattice3 A B C) =>  ((k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) = B) ) ) ) ) ) ) ) ).
tt(t51_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A B (k1_yellow_5 A C B)) = (k13_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t51_yellow_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_waybel_5 A) <=> (v1_waybel_5 (k7_lattice3 A))) ) ) ).
tt(t51_yellow_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_waybel11 B) & (m1_yellow_9 B A))  =>  ((u1_pre_topc B) = (k5_waybel11 A)) ) ) ) ) ).
tt(t51_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((r3_zf_lang (k8_zf_lang B (k6_zf_lang A)) (k13_zf_lang B A)) & (r3_zf_lang (k6_zf_lang A) (k13_zf_lang B A))) ) ) ) ) ).
tt(t51_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~ (r1_zf_lang C (k5_zf_lang A B))) ) ) ) ) ) ) ).
tt(t51_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~ (r2_hidden A B))  &  ( (~ (r2_hidden C B))  &  (~ (r1_xboole_0 (k2_tarski A C) B)) ) ) ) ) ) ) ).
tt(t51_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k3_zmodul01 B) = (k3_zmodul01 A)) ) ) ) ) ).
tt(t52_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r3_orders_2 A D B) & (r1_tarski C (k2_abcmiz_0 A D)))  =>  ((r2_abcmiz_0 A B C) & (r3_orders_2 A D (k6_abcmiz_0 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t52_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_trees_4 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 (k1_msualg_1 A B)))  => (m1_abcmiz_1 (k36_abcmiz_1 A B C) A (k2_msualg_1 A B))) ) ) ) ) ) ) ).
tt(t52_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m3_abcmiz_1 B A) =>  (! [C:$i] :  ((m3_abcmiz_1 C A) =>  (! [D:$i] :  ((m3_abcmiz_1 D A) =>  ( ((r3_abcmiz_a A B C) & (r3_abcmiz_a A C D))  => (r3_abcmiz_a A B D)) ) ) ) ) ) ) ) ) ).
tt(t52_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  => (r2_aff_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t52_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ( (~  ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) ) )  => (v11_aff_2 A)) ) ) ).
tt(t52_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((r1_xxreal_0 (k1_afinsq_1 B) A) =>  ((k5_relat_1 B A) = B) ) ) ) ) ) ).
tt(t52_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  ( (A = k1_xboole_0)  =>  ((k7_afinsq_2 A) = k6_numbers) ) ) ) ).
tt(t52_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  ((v8_incproj (k13_afproj A)) => (v1_translac A)) ) ) ).
tt(t52_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E) = (k3_rlvect_1 A C E)) ) )  &  (D = C) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k3_rlvect_1 A E F)) = (k1_binop_1 (k3_afvect0 (k2_tdgroup A) D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B F)))  &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k4_struct_0 A)) = (k4_struct_0 (k5_afvect0 (k2_tdgroup A) D)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k4_algstr_0 A E)) = (k1_funct_1 (k4_afvect0 (k2_tdgroup A) D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v11_struct_0 C))  &  ((v1_instalg1 C) & (l1_msualg_1 C)) )  =>  (! [D:$i] :  ((m2_algspec1 D C) =>  ((r1_algspec1 D A B) => (r1_algspec1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t52_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k5_altcat_4 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_altcat_4 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 (k5_altcat_4 A) B C)) =>  ( (~  ((k1_altcat_1 (k5_altcat_4 A) B C) = k1_xboole_0) )  =>  ((v3_altcat_3 D (k5_altcat_4 A) B C) & (r2_hidden (k1_altcat_3 (k5_altcat_4 A) B C D) (k1_altcat_1 (k5_altcat_4 A) C B))) ) ) ) ) ) ) ) ) ) ).
tt(t52_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r10_analmetr A B C) & (r9_analmetr A B D))  => (r10_analmetr A D C)) ) ) ) ) ) ) ) ) ).
tt(t52_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_analort A B C))) <=> (m1_subset_1 D (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t52_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r2_hidden (k16_aofa_000 A B C) (k18_aofa_000 A))) ) ) ) ) ) ) ).
tt(t52_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( (! [I:$i] :  ((m2_funct_2 I B k4_numbers (k9_funct_2 B k4_numbers)) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E I F) H) = (k21_aofa_i00 B k4_numbers I H))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E I F) G) = (k21_aofa_i00 B k4_numbers I G)) ) ) )  =>  ( (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (~  ( ((k1_funct_1 I D) = k6_numbers)  &  ( ((k1_funct_1 I H) = 1)  &  ((k1_funct_1 I G) = 2) ) ) ) ) )  | (r4_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A F (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E G 1)) (k74_aofa_i00 A B D E G H)) (k9_funct_2 B k4_numbers) (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E G H)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ( ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) )  =>  ((v8_relat_2 B) &  ((v7_armstrng B A) & (v5_armstrng B A)) ) )  &  ( ((v8_relat_2 B) &  ((v7_armstrng B A) & (v5_armstrng B A)) )  =>  ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) ) ) ) ) ) ) ).
tt(t52_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ((k10_arytm_3 (k10_arytm_3 A B) C) = (k10_arytm_3 A (k10_arytm_3 B C))) ) ) ) ) ) ) ).
tt(t52_asympt_1,ax, ((k5_series_1 5 5) = 3125) ).
tt(t52_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v10_bcialg_1 B A)) ) ) ) ) ).
tt(t52_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (B = (k4_bcialg_1 A))  =>  (! [C:$i] :  ((m5_bcialg_2 C A B) =>  ( (~ (v2_struct_0 (k9_bcialg_2 A C)))  &  ((v3_bcialg_1 (k9_bcialg_2 A C)) &  ((v4_bcialg_1 (k9_bcialg_2 A C)) &  ((v5_bcialg_1 (k9_bcialg_2 A C)) &  ((v7_bcialg_1 (k9_bcialg_2 A C)) &  ((v19_bcialg_1 (k9_bcialg_2 A C)) & (l2_bcialg_1 (k9_bcialg_2 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v2_bcialg_4 A) & (l1_bcialg_4 A)) ) ) ) ) ) )  =>  ((v8_bcialg_4 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A C D)) = (k1_bcialg_4 A (k1_bcialg_1 A (k1_bcialg_1 A B C) D) (k1_bcialg_1 A D (k1_bcialg_1 A D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t52_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_5 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  =>  ( ((v8_bcialg_1 A) & (m1_bcialg_5 A k6_numbers 1 k6_numbers 1))  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B C) = (k1_bcialg_1 A (k1_bcialg_1 A B C) C)) ) ) ) ) ) ) ) ).
tt(t52_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v12_bcialg_1 B A) & (m2_bcialg_1 B A))  =>  (! [C:$i] :  ((m5_bcialg_2 C A B) =>  ((k5_bcialg_6 A (k9_bcialg_2 A C) (k6_bcialg_6 A B C)) = B) ) ) ) ) ) ) ).
tt(t52_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden (k1_bcialg_1 A D E) B))  => (r2_hidden (k1_bcialg_1 A C E) B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k5_normsp_1 C D (k7_real_1 A B)) (k6_bhsp_1 C (k5_normsp_1 C D A) (k5_normsp_1 C D B)))) ) ) ) ) ) ) ) ).
tt(t52_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_bhsp_2 A C D)) <=>  ((k4_bhsp_1 A C B) = D) ) ) ) ) ) ) ) ) ) ).
tt(t52_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 B (k1_bhsp_4 B (k5_bhsp_4 B (k1_bhsp_4 B C) (k47_valued_1 k5_numbers k1_numbers k1_numbers A (k1_valued_0 k1_numbers A 1)))) D) = (k5_algstr_0 B (k1_normsp_1 B (k1_bhsp_4 B (k5_bhsp_4 B C A)) (k2_nat_1 D 1)) (k1_normsp_1 B (k5_bhsp_4 B (k1_bhsp_4 B C) A) (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ).
tt(t52_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  => (r1_tarski (k8_vectsp10 A C E) (k11_bilinear A B C (k9_bilinear A B C D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t52_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r4_boolealg A (k1_boolealg A B C) C)) ) ) ) ) ) ) ).
tt(t52_borsuk_4,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B A) => (r1_borsuk_3 (k1_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_domain_1 (u1_struct_0 (k15_euclid 2)) B))) k1_borsuk_4)) ) ) ) ) ).
tt(t52_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k6_measure6 (k2_rcomp_1 k2_xxreal_0 A)) = (k4_rcomp_1 k2_xxreal_0 A)) ) ) ).
tt(t52_borsuk_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_borsuk_2 F A B C) =>  (! [G:$i] :  ((m1_borsuk_2 G A C D) =>  (! [H:$i] :  ((m1_borsuk_2 H A D E) =>  ( ((r1_borsuk_6 A B C) &  ((r1_borsuk_6 A C D) & (r1_borsuk_6 A D E)) )  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) (k2_borsuk_6 A B E (k1_borsuk_2 A B D E (k1_borsuk_2 A B C D F G) H) k5_borsuk_6) (k1_borsuk_2 A B C E F (k1_borsuk_2 A C D E G H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_euclid_3 (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) B)) = (k1_comptrig (k2_complex2 (k2_euclid_3 B) A))) ) ) ) ) ).
tt(t52_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k7_bvfunc_2 A (k6_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t52_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k5_enumset1 C D E F G H I))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (C = I) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (D = I) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (E = I) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (F = I) )  &  ( (~  (G = H) )  &  ( (~  (G = I) )  &  ( (~  (H = I) )  & (r1_xboole_0 (k15_bvfunc_1 A K (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H) I)) (k15_bvfunc_1 A J C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k9_xboolean A A) = (k3_xboolean A))  &  ((k3_xboolean (k9_xboolean A A)) = A) ) ) ) ).
tt(t52_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k5_bvfunc26 A C D)) (k5_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A (k2_bvfunc_1 A C D))) (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D)))) ) ) ) ) ) ) ) ).
tt(t52_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k9_cqc_lang A C B))))) ) ) ) ) ) ) ) ) ).
tt(t52_card_1,ax, (4 = (k2_enumset1 k1_xboole_0 1 2 3)) ).
tt(t52_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] : (r1_xxreal_0 (k5_card_1 (k2_enumset1 A B C D)) 4)) ) ) ) ).
tt(t52_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k8_card_3 B)) =>  ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k9_xtuple_0 B) (k3_tarski (k10_xtuple_0 B)))))) ) ) ) ) ).
tt(t52_card_fin,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( ((v2_funct_1 A) &  ((v2_funct_1 B) & (r1_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B))) )  => (v2_funct_1 (k1_ordinal4 A B))) ) ) ) ) ).
tt(t52_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v11_cat_1 B A) & (r1_cat_1 A B C))  => (v11_cat_1 C A)) ) ) ) ) ) ) ).
tt(t52_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (r1_cat_3 B C (k1_tarski A) (k1_cat_3 (u4_struct_0 B) A (k4_cat_1 B C)))) ) ) ) ) ).
tt(t52_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k23_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 (k23_cat_4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k23_cat_4 A B))) => (r4_cat_3 (k23_cat_4 A B) C D E)) ) ) ) ) ) ) ) ).
tt(t52_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 B C) &  (! [D:$i] :  ((v7_ordinal1 D) => (r1_xxreal_0 k6_numbers (k1_seq_1 A D))) ) )  => (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k1_seq_1 (k3_series_1 A) C))) ) ) ) ) ) ) ).
tt(t52_cfcont_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k2_numbers)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k2_numbers B)) &  ((v1_cfcont_1 A) & (r2_cfcont_1 B A)) )  => (v1_cfcont_1 (k7_relset_1 k2_numbers k2_numbers B A))) ) ) ) ) ).
tt(t52_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k2_valued_1 B k2_numbers k2_numbers C D) A) (k2_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) (k2_partfun1 B k2_numbers D A))) &  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k2_valued_1 B k2_numbers k2_numbers C D) A) (k2_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) D)) & (r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k2_valued_1 B k2_numbers k2_numbers C D) A) (k2_valued_1 B k2_numbers k2_numbers C (k2_partfun1 B k2_numbers D A)))) ) ) ) ) ) ) ) ) ).
tt(t52_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ( (~ (r1_xxreal_0 (k2_nat_1 A 1) B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 A 1)))) =>  ((k10_chain_1 B C A D) = (k5_chain_1 B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t52_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) <=>  ( (~  (B = C) )  & (r1_chord A C B)) ) ) ) ) ) ) ) ).
tt(t52_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 C) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 C) C)))) )  =>  (! [E:$i] :  ( ((v6_circcmb3 E) & (m1_circcmb3 E C))  =>  (~  ( (~  ( (~ (r2_hidden A (u1_struct_0 E)))  & (v1_xtuple_0 A)) )  &  ( (~  ( (~ (r2_hidden B (u1_struct_0 E)))  & (v1_xtuple_0 B)) )  &  (~ (v6_circcmb3 (k6_circcmb3 C E (k4_circcmb3 2 C D (k10_finseq_1 A B))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  ((v4_circcomb (k7_circcomb A B C D) (k5_circcomb C D)) & (v5_circcomb (k5_circcomb C D))) ) ) ) ) ) ) ) ) ).
tt(t52_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  ( ((k7_relat_1 C (k2_msafree2 A)) = (k2_msafree2 B))  &  ((k7_relat_1 C (k3_msafree2 A)) = (k3_msafree2 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_classes1,ax, (! [A:$i] : (r1_tarski A (k5_classes1 A))) ).
tt(t52_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (~  ( (~ (r2_hidden A B))  &  ( (~  (A = B) )  &  (~ (r2_hidden B A)) ) ) ) ) ) ) ) ).
tt(t52_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_clvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_clvect_1 B) & (m1_clvect_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 B C) <=> (r1_struct_0 A C)) ) )  =>  (B = A) ) ) ) ) ) ).
tt(t52_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_clvect_2 A C D)) <=>  ((k15_csspace A C B) = D) ) ) ) ) ) ) ) ) ) ).
tt(t52_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_bhsp_4 A (k6_clvect_3 A (k1_bhsp_4 A B) (k46_valued_1 k5_numbers k2_numbers k2_numbers C (k1_valued_0 k2_numbers C 1)))) D) = (k5_algstr_0 A (k1_normsp_1 A (k1_bhsp_4 A (k6_clvect_3 A B C)) (k2_nat_1 D 1)) (k1_normsp_1 A (k6_clvect_3 A (k1_bhsp_4 A B) C) (k2_nat_1 D 1)))) ) ) ) ) ) ) ) ) ).
tt(t52_cohsp_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski B C) (k10_cohsp_1 A)) =>  ((r2_hidden (k1_tarski B) (k9_xtuple_0 A)) & (r2_hidden C (k1_funct_1 A (k1_tarski B)))) ) ) ) ) ) ).
tt(t52_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k4_xcmplx_0 A)) = (k17_complex1 A)) ) ) ).
tt(t52_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k2_complex2 B A) = k6_numbers)  <=>  (B = k6_numbers) ) ) ) ) ) ).
tt(t52_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k4_algstr_0 k1_complfld A)) = (k4_algstr_0 k1_complfld (k2_complfld A))) ) ) ).
tt(t52_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( ((k6_complsp2 (k10_seq_4 A B)) = (k8_rvsum_1 (k6_complsp2 A) (k6_complsp2 B)))  &  ((k7_complsp2 (k10_seq_4 A B)) = (k8_rvsum_1 (k7_complsp2 A) (k7_complsp2 B))) ) ) ) ) ) ) ).
tt(t52_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ( ((k2_afinsq_1 (k9_compos_1 A B)) = (k6_domain_1 k5_numbers k6_numbers))  &  ((k1_funct_1 (k9_compos_1 A B) k6_numbers) = B) ) ) ) ) ) ).
tt(t52_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) 2) = (k5_compos_0 (u1_compos_1 A) D 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((r1_xxreal_0 (k3_complex1 A) k6_numbers) =>  ( (A = k6_numbers)  | (r1_xxreal_0 (k21_sin_cos (k1_comptrig A)) k6_numbers)) ) ) ) ).
tt(t52_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) => (r1_tarski (k1_relset_1 (k3_finseq_2 k5_numbers) (k6_comput_1 B C A D)) (k4_finseq_2 (k2_nat_1 1 (k19_margrel1 B)) k5_numbers))) ) ) ) ) ) ) ) ).
tt(t52_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  ((v2_comseq_2 A) &  ((k3_comseq_2 A) = k5_complex1) ) ) ) ) ).
tt(t52_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k19_convex4 A B k5_complex1) = (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) ) ) ) ) ).
tt(t52_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r3_cqc_the1 A B (k8_cqc_lang A C (k8_cqc_lang A (k6_cqc_lang A C) D)))) ) ) ) ) ) ) ) ).
tt(t52_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k6_cqc_lang A (k11_cqc_lang A C B)) (k12_cqc_lang A C (k6_cqc_lang A B))) A)) ) ) ) ) ) ).
tt(t52_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A B C) => (r5_cqc_the3 A B C)) ) ) ) ) ) ) ).
tt(t52_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  &  ((k15_csspace A B C) = k6_numbers) ) )  &  (~  ( (~  ((k15_csspace A B C) = k6_numbers) )  &  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t52_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 B) A)) (k21_sin_cos (k7_real_1 (k8_real_1 2 B) A))))) ) ) ) ) ).
tt(t52_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers D E) = (k10_real_1 A (k5_square_1 E))) ) )  =>  ( ((k7_real_1 B (k10_real_1 C 2)) = k6_numbers)  |  ( ((k9_real_1 B (k10_real_1 C 2)) = k6_numbers)  |  ((k1_seq_1 (k5_diff_1 D C) B) = (k10_real_1 (k1_real_1 (k8_real_1 (k8_real_1 (k8_real_1 2 C) A) B)) (k5_square_1 (k9_real_1 (k5_square_1 B) (k5_square_1 (k10_real_1 C 2)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k4_diff_1 (k5_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) (k9_real_1 B (k13_complex1 A 2))))) ) ) ) ) ) ) ).
tt(t52_dilworth,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_dilworth A) & (l1_orders_2 A)) ) ) )  =>  (? [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  &  ((v7_dilworth B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v7_dilworth C A) & (r2_xboole_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t52_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  ( ((r2_hidden (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers D E 1) (k6_ec_pf_1 A B C)) & (r2_hidden (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers F G 1) (k6_ec_pf_1 A B C)))  =>  ((r1_xxreal_0 A 3) |  ( ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A)))  |  ( ((k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers D E 1)) = (k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) k5_numbers F G 1)))  <=>  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (~  ( (~ (r1_ec_pf_1 A C D))  &  ((r1_ec_pf_1 A C (k9_ec_pf_2 A B (k8_ec_pf_2 A B) D)) &  ((k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D)) = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m1_subset_1 (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 A)) (k1_zfmisc_1 (u4_struct_0 A)) (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C))) (k21_ens_1 A B C)) (k2_ens_1 (k16_ens_1 A)))) ) ) ) ) ) ).
tt(t52_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 (k4_entropy1 A) B) k6_numbers)) ) ) ) ) ).
tt(t52_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k5_enumset1 A A A A A A B) = (k2_tarski A B)) ) ) ).
tt(t52_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (k2_zfmisc_1 A B)))) =>  ( (! [E:$i] :  ((r2_hidden E D) =>  ((r1_tarski E C) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 B)) &  (E = (k8_mcart_1 A B F G)) ) ) ) ) ) ) )  => (r1_tarski (k2_zfmisc_1 (k1_setfam_1 (k7_relat_1 (k1_funct_3 (k9_funct_3 A B)) D)) (k3_tarski (k7_relat_1 (k1_funct_3 (k10_funct_3 A B)) D))) C)) ) ) ) ) ) ) ).
tt(t52_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_xxreal_0 (k12_euclid (k3_rlvect_1 (k15_euclid A) B C)) (k9_binop_2 (k12_euclid B) (k12_euclid C)))) ) ) ) ) ) ).
tt(t52_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  ( (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( (E = (k3_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) (k1_rlvect_1 (k15_euclid A) B F) (k1_rlvect_1 (k15_euclid A) C G)) (k1_rlvect_1 (k15_euclid A) D H)))  &  ((k7_real_1 (k7_real_1 F G) H) = 1) ) ) ) ) ) ) )  => (r2_hidden E (k9_euclid_3 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr))))) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k1_funct_1 C D) = (k12_euclid (k5_algstr_0 (k15_euclid A) D B))) ) )  & (v5_pre_topc C (k15_euclid A) k3_topmetr)) ) ) ) ) ) ) ).
tt(t52_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v5_euclid_7 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))))  =>  ((k1_card_1 B) = A) ) ) ) ) ).
tt(t52_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k9_euclid 3 B A) = (k1_euclid_8 (k11_binop_2 A (k1_seq_1 B 1)) (k11_binop_2 A (k1_seq_1 B 2)) (k11_binop_2 A (k1_seq_1 B 3)))) ) ) ) ) ).
tt(t52_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k17_euclid (k19_euclid A B)) = A)  &  ((k18_euclid (k19_euclid A B)) = B) ) ) ) ) ) ).
tt(t52_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (? [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) & (r2_hidden C B)) ) ) ) ) ) ).
tt(t52_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v3_orders_2 E) &  ((v4_orders_2 E) &  ((v5_orders_2 E) &  ((v16_waybel_0 E) & (l1_orders_2 E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v5_relat_1 F (u1_struct_0 E)) &  ((v1_funct_1 F) & (v1_exchsort F)) ) )  =>  ( ((r2_hidden A (k9_xtuple_0 F)) & (r2_hidden B (k9_xtuple_0 F)))  =>  ( (C = A)  |  ( (C = B)  |  ( (D = A)  |  ( (D = B)  |  ((r2_hidden (k4_tarski C D) (k6_exchsort E F)) <=> (r2_hidden (k4_tarski C D) (k6_exchsort E (k10_funct_7 F A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C))))) =>  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)) F) (k4_tarski (k11_finseq_1 A B C) E)) = (k1_funct_1 E (k11_finseq_1 (k1_funct_1 F A) (k1_funct_1 F B) (k1_funct_1 F C))))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)) F) A) = (k1_funct_1 F A))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)) F) B) = (k1_funct_1 F B))  &  ((k1_funct_1 (k6_circuit2 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)) F) C) = (k1_funct_1 F C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k1_seq_1 (k1_fcont_1 A B) C) (k1_seq_1 (k1_fcont_1 A B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9)) A) B) = (k7_real_1 (k8_real_1 (k1_seq_1 k24_sin_cos B) (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B))) (k10_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t52_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers))  &  (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) (k1_real_1 1))) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) B) = (k10_real_1 (k2_newton (k1_seq_1 k19_sin_cos B) 3) (k7_real_1 1 (k1_seq_1 k16_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t52_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((r2_hidden (k2_nat_1 (k4_nat_1 2 A) 1) k4_fib_num2) &  (~ (r2_hidden (k4_nat_1 2 A) k4_fib_num2)) ) ) ) ).
tt(t52_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k2_nat_1 (k3_fib_num3 A B E) (k3_fib_num3 C D E)) = (k3_fib_num3 (k2_nat_1 A C) (k2_nat_1 B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v14_lattices A) => (v14_lattices (k6_filter_0 A B))) ) ) ) ) ).
tt(t52_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k7_filter_0 A B C) = (k7_filter_0 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t52_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  <=>  ( (~ (v2_struct_0 (k1_lattice2 A)))  &  ((v10_lattices (k1_lattice2 A)) &  ((v15_lattices (k1_lattice2 A)) &  ((v16_lattices (k1_lattice2 A)) & (l3_lattices (k1_lattice2 A))) ) ) ) ) ) ) ).
tt(t52_finseq_1,ax, (! [A:$i] :  ((v1_finset_1 A) <=>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  &  (A = (k10_xtuple_0 B)) ) ) ) ) ).
tt(t52_finseq_2,ax, ((k1_finseq_2 2) = (k10_finseq_1 1 2)) ).
tt(t52_finseq_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k5_relat_1 (k1_finseq_2 A) (k2_finseq_1 B)) = (k1_finseq_2 A))  <=> (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t52_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_funct_1 A))  => (v2_funct_1 (k5_finseq_4 A B))) ) ) ) ).
tt(t52_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) & (r2_hidden (k1_nat_1 A 1) (k4_finseq_1 (k2_finseq_5 B D C))))  =>  ((k7_partfun1 B (k2_finseq_5 B D C) (k1_nat_1 A 1)) = (k7_partfun1 B D (k1_nat_1 A (k4_finseq_4 D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t52_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ( ((k2_finseq_5 A (k12_finseq_1 A B) B) = (k12_finseq_1 A B))  &  ((k1_finseq_5 A (k12_finseq_1 A B) B) = (k12_finseq_1 A B)) ) ) ) ) ) ).
tt(t52_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r7_binop_1 A F E) => (r2_relset_1 k5_numbers A (k4_finseqop A A (k3_finseqop A A A E B D) F) (k3_finseqop A A A E (k3_funct_2 A A F B) (k4_finseqop A A D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r3_fintopo6 A B C D E) &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 B))) )  =>  ((v2_fintopo6 (k17_finseq_1 (u1_struct_0 A) F B) A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (k17_finseq_1 (u1_struct_0 A) F B)) C) &  ( ((k1_funct_1 (k17_finseq_1 (u1_struct_0 A) F B) 1) = D)  &  ((k1_funct_1 (k17_finseq_1 (u1_struct_0 A) F B) (k3_finseq_1 (k17_finseq_1 (u1_struct_0 A) F B))) = (k7_partfun1 (u1_struct_0 A) B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_flang_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((r2_hidden B (k6_flang_1 A (k8_flang_1 A C) C)) | (r2_hidden B (k6_flang_1 A C (k8_flang_1 A C))))  => (r2_hidden B (k8_flang_1 A C))) ) ) ) ) ).
tt(t52_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((k1_flang_2 B C D E) = (k1_tarski A))  =>  ( (D = E)  |  (A = (k2_flang_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_3 A B) = (k6_flang_1 A (k8_flang_1 A B) B)) ) ) ) ).
tt(t52_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( (~  ( (~  ((k1_funct_1 (k8_fomodel0 B) A) = k1_xboole_0) )  &  ( (~  ((k1_funct_1 (k8_fomodel0 C) A) = k1_xboole_0) )  &  (~  ((k1_funct_1 (k8_fomodel0 B) A) = (k1_funct_1 (k8_fomodel0 C) A)) ) ) ) )  &  ( ((v5_relat_1 D (k3_finseq_2 k1_xboole_0)) =>  ((k1_funct_1 (k8_fomodel0 B) D) = k1_xboole_0) )  &  ( ( ((k1_funct_1 (k8_fomodel0 B) D) = k1_xboole_0)  & (v5_relat_1 D (k3_finseq_2 B)))  => (v5_relat_1 D (k3_finseq_2 k1_xboole_0))) ) ) ) ) ) ) ) ) ) ).
tt(t52_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v8_struct_0 G) & (l2_fsm_1 G A B)) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 G)) =>  ( ( (G = (k13_fsm_1 A B D E))  &  ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  (F = H) ) )  =>  ((k2_fsm_1 A D F C) = (k2_fsm_1 A G H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v1_funct_1 (k5_funcop_1 C E D)) &  ((v1_funct_2 (k5_funcop_1 C E D) B A) & (m1_subset_1 (k5_funcop_1 C E D) (k1_zfmisc_1 (k2_zfmisc_1 B A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v2_funct_1 B) => (v2_funct_1 (k5_relat_1 B A))) ) ) ) ).
tt(t52_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((k1_relset_1 A B) = A) ) ) ) ).
tt(t52_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 C) = (k9_xtuple_0 D))  &  ((r1_tarski (k10_xtuple_0 C) A) & (r1_tarski (k10_xtuple_0 D) B)) )  =>  ( ((k3_relat_1 (k13_funct_3 C D) (k9_funct_3 A B)) = C)  &  ((k3_relat_1 (k13_funct_3 C D) (k10_funct_3 A B)) = D) ) ) ) ) ) ) ) ) ).
tt(t52_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) =>  ((k2_funct_4 (k2_funct_4 C)) = C) ) ) ) ) ) ).
tt(t52_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) &  ((r1_tarski (k9_xtuple_0 D) (k2_zfmisc_1 A B)) &  ((k1_funct_5 C) = (k1_funct_5 D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t52_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k9_funct_6 A (k7_funcop_1 B C)) = (k7_funcop_1 B (k1_funct_2 A C))) ) ) ) ).
tt(t52_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski (k9_xtuple_0 B) A) | (r1_tarski (k9_xtuple_0 (k3_relat_1 B C)) A))  =>  ((k4_funct_7 A (k10_finseq_1 B C)) = (k3_relat_1 B C)) ) ) ) ) ) ) ).
tt(t52_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k52_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t52_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r1_xxreal_0 (k1_seq_1 (k4_fuzzy_2 A B) C) (k1_seq_1 D C)) & (r1_xxreal_0 (k1_seq_1 D C) (k1_seq_1 (k5_fuzzy_2 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t52_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ((r1_xxreal_0 k6_numbers (k3_funct_2 (u1_struct_0 A) k7_numbers C B)) <=> (m1_subset_1 B (u1_struct_0 (k7_fvaluat1 A C)))) ) ) ) ) ) ) ) ).
tt(t52_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k10_fvsum_1 1 A (k4_matrix_2 (u1_struct_0 A) C) B) = (k4_matrix_2 (u1_struct_0 A) (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t52_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_relat_1 F) &  ((v2_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) ) ) )  =>  (! [G:$i] :  ((m1_genealg1 G F) =>  (! [H:$i] :  ((m1_genealg1 H F) =>  ( ((k11_genealg1 F G H A A B C D) = (k9_genealg1 F G H B C D))  &  ( ((k11_genealg1 F G H A E A C D) = (k9_genealg1 F G H E C D))  &  ( ((k11_genealg1 F G H A E B A D) = (k9_genealg1 F G H E B D))  &  ((k11_genealg1 F G H A E B C A) = (k9_genealg1 F G H E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)))  &  ( (F = (k1_funct_1 D (k4_tarski (k10_finseq_1 B C) k3_twoscomp)))  &  (G = (k1_funct_1 D (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) ) )  =>  ((k1_twoscomp (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) (k6_circuit2 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D) (k21_gfacirc1 A B C)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski B))) =>  ( ((k15_glib_000 A) = (k15_glib_000 C))  &  ((r2_hidden B (k7_glib_000 A)) =>  ((k2_nat_1 (k17_glib_000 C) 1) = (k17_glib_000 A)) ) ) ) ) ) ) ) ).
tt(t52_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k20_glib_001 A B C C) B)) ) ) ) ) ) ).
tt(t52_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k6_glib_000 A)) =>  ((k14_glib_003 (k13_glib_003 A B C)) = (k2_xboole_0 (k14_glib_003 A) (k1_tarski B))) ) ) ) ) ) ).
tt(t52_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k19_euclid k6_numbers 1)))))) ) ) ) ) ) ).
tt(t52_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_funct_1 D))  &  ( (~ (v1_xboole_0 D))  &  ((v1_finseq_6 D (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 D) &  ((v2_topreal1 D) &  ((v1_goboard5 D) &  ((v2_goboard5 D) & (m2_finseq_1 D (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 D))) &  ((r1_xxreal_0 1 C) &  ( ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B)) = (k2_topreal1 2 D C))  &  ((k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) = (k2_topreal1 2 D (k2_nat_1 C 1))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 D) (k2_nat_1 C 1)) |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) A B))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 C 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 D) (k2_nat_1 A 1) (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_graph_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v3_graph_2 B A) & (m2_graph_1 B A))  =>  ( ((v2_funct_1 B) & (m2_graph_1 B A))  <=>  (~  ( (~  ((k3_finseq_1 B) = k6_numbers) )  &  ( (~  ((k3_finseq_1 B) = 1) )  &  ((k1_funct_1 B 1) = (k1_funct_1 B 2)) ) ) ) ) ) ) ) ) ).
tt(t52_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u4_struct_0 A) (k9_graph_3 A)) =>  ((r2_hidden B (k1_graph_3 A (k10_xtuple_0 C))) =>  ( (~ (v1_xboole_0 (a_3_0_graph_3 A B C)))  & (m1_subset_1 (a_3_0_graph_3 A B C) (k1_zfmisc_1 (k9_graph_3 A)))) ) ) ) ) ) ) ) ).
tt(t52_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 B))))) )  =>  (~  ( (E = (k4_graph_5 B C D))  &  (! [F:$i] :  ((m2_finseq_1 F (u4_struct_0 B)) =>  (~  ((r2_hidden F E) &  (! [G:$i] :  ((m2_finseq_1 G (u4_struct_0 B)) =>  ((r2_hidden G E) => (r1_xxreal_0 (k10_graph_5 B F A) (k10_graph_5 B G A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_graphsp,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k3_finseq_2 k1_numbers)) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_graph_1 E) &  ((v6_graph_1 E) & (l1_graph_1 E)) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u4_struct_0 E) k8_graph_5) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 E) k8_graph_5)))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 E)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  ( ((r6_graphsp C E A F) &  ( (G = 1)  &  ( (H = B)  &  ((r1_xxreal_0 1 A) &  (D = (k6_graphsp (k20_graphsp A) C)) ) ) ) )  =>  ( (1 = H)  |  ( ((u1_struct_0 E) = (k4_subset_1 k5_numbers (k14_graphsp D A) (k13_graphsp D A)))  &  ( (~  ((r2_hidden H (k14_graphsp D A)) &  (! [I:$i] :  ((m2_finseq_1 I k5_numbers) =>  (! [J:$i] :  ( ((v7_graph_1 J E) & (m2_graph_1 J E))  =>  (~  ((r4_graphsp I D B A) &  ((r5_graphsp E J I) &  ((r7_graph_5 E G H J F) &  ((k10_graph_5 E J F) = (k1_seq_1 D (k2_nat_1 (k4_nat_1 2 A) B))) ) ) ) ) ) ) ) ) ) )  &  ((r2_hidden H (k13_graphsp D A)) =>  (! [I:$i] :  ( ((v7_graph_1 I E) & (m2_graph_1 I E))  =>  (~ (r1_graph_5 E I G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v4_relat_1 G A) &  ((v1_funct_1 G) &  ((v1_partfun1 G A) &  ((v4_valued_0 G) & (v2_pre_poly G)) ) ) ) )  =>  (~  ((r2_hidden F (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C D))) &  ((r2_hidden G (k2_polynom1 (k15_pre_poly A) C (k6_termord A B C E))) &  ((k11_pre_poly A (k3_termord A B C D) G) = (k11_pre_poly A (k3_termord A B C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~ (r1_xboole_0 (k13_group_2 A B D) (k8_group_2 A C)))  => (r2_hidden D (k4_group_11 A C B))) ) ) ) ) ) ) ) ) ).
tt(t52_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) (k8_group_1 A B C) D) = (k8_group_1 A (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) B D) (k2_binop_1 (u1_struct_0 A) k5_numbers (u1_struct_0 A) (k4_group_1 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t52_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r2_hidden (k6_algstr_0 A C D) B)) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) => (r2_hidden (k2_group_1 A C) B)) ) )  &  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (~  ((u1_struct_0 C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_group_3 A B (k1_group_1 A)) = B) ) ) ) ) ).
tt(t52_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  ((u1_struct_0 (k8_group_4 A B C)) = (k7_group_4 A B C)) ) ) ) ) ) ) ) ).
tt(t52_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r2_hidden A (k5_group_5 B C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (A = (k2_group_5 B E F))  &  ((r1_struct_0 C E) & (r1_struct_0 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  => (r1_tarski (k7_struct_0 (k10_group_6 B A C)) (k7_struct_0 B))) ) ) ) ) ) ).
tt(t52_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v2_group_9 C A) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v1_group_6 D B C) &  ((v7_group_9 D A B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) ) )  =>  ((v2_funct_2 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 C) D F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  (! [C:$i] :  ( ((v5_glib_001 C A) & (m3_glib_001 C A))  =>  (! [D:$i] :  ( ((v5_glib_001 D A) & (m3_glib_001 D A))  =>  (! [E:$i] :  ( ((v5_glib_001 E A) & (m3_glib_001 E A))  =>  (! [F:$i] :  ((m1_subset_1 F (k6_glib_000 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k6_glib_000 A)) =>  (! [H:$i] :  ((m1_subset_1 H (k6_glib_000 A)) =>  ( ( (B = (k2_helly A F G))  &  ( (C = (k2_helly A F H))  &  ( (D = (k2_helly A G F))  &  (E = (k2_helly A G H)) ) ) )  =>  ((r2_hidden G (k13_glib_001 A C)) |  ((r2_hidden H (k13_glib_001 A B)) |  ((r2_hidden F (k13_glib_001 A E)) |  ((k1_funct_1 B (k3_finseq_1 (k1_helly B C))) = (k1_funct_1 D (k3_finseq_1 (k1_helly D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k12_bilinear k1_complfld A B) = (k10_bilinear k1_complfld A A B)) ) ) ) ) ).
tt(t52_hfdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_xxreal_0 1 B) & (r2_hidden A C))  =>  ((r2_hidden k6_numbers C) |  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 B)) C) 2) A) = (k8_real_1 (k4_nat_1 B (k2_nat_1 B 1)) (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_taylor_1 (k2_nat_1 B 2))) A))) ) ) ) ) ) ) ) ) ).
tt(t52_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((r1_xxreal_0 1 (k2_hurwitz k1_complfld A)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((v1_hurwitz A) =>  ((r1_xxreal_0 k6_numbers (k3_complex1 B)) | (v1_hurwitz (k5_hurwitz k1_complfld (k8_hurwitz A B) (k3_hurwitz k1_complfld B 1)))) ) ) ) ) ) ) ).
tt(t52_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_vectsp_1 A) & (l6_algstr_0 A)) )  =>  ((k8_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k5_struct_0 A))) = (u1_struct_0 A)) ) ) ).
tt(t52_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) &  ((r2_incsp_1 A B D) &  (~ (r3_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t52_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xxreal_0 A (k5_real_1 B 1))) ) ) ) ) ).
tt(t52_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 k4_numbers)))  =>  ( ( ((k5_card_1 B) = A)  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((r2_hidden C B) &  ((r2_hidden D B) &  ( (~  (C = D) )  & (r2_hidden (k4_tarski C D) (k1_int_4 A))) ) ) ) ) ) ) ) )  => (r1_int_4 A B)) ) ) ) ) ).
tt(t52_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k19_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 k19_sin_cos D) (k9_real_1 (k1_seq_1 k19_sin_cos D) 1))) ) ) ) ) )  &  ( ((k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9)) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k30_sin_cos) k2_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t52_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A E) &  ((r1_tarski E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1))) &  ((r2_relset_1 k1_numbers k1_numbers D (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers E) (k3_valued_1 k1_numbers k1_numbers k1_numbers B C))) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_taylor_1 2)) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 B F) = 1) ) ) )  &  ( (E = (k1_relset_1 k1_numbers D))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D A))) ) ) ) ) )  =>  ((k2_integra5 A D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) k3_taylor_1) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t52_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k4_real_ns1 A))) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ( (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 B C)) =>  ((k1_funct_1 G H) = F) ) ) )  &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) )  =>  ((k6_integr18 (k4_real_ns1 A) G D E) = (k1_rlvect_1 (k4_real_ns1 A) F (k10_binop_2 E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((v4_xxreal_2 A) & (v4_xxreal_2 B))  =>  ((k2_seq_4 (k9_member_1 A B)) = (k7_real_1 (k4_seq_4 A) (k4_seq_4 B))) ) ) ) ) ) ).
tt(t52_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (A = (k1_rcomp_1 (k7_real_1 B (k8_real_1 (k4_nat_1 2 C) k32_sin_cos)) (k7_real_1 B (k8_real_1 (k2_nat_1 (k4_nat_1 2 C) 1) k32_sin_cos))))  =>  ((k2_integra5 A (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) = (k1_real_1 (k8_real_1 2 (k21_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t52_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k9_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1))) = E)  &  ( ((k1_relset_1 k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1))) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_real_1 1 (k9_real_1 A F))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) (k4_seq_4 B)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C k3_taylor_1)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r2_hidden A (k4_interva1 A B (k10_interva1 A B)))) ) ) ) ).
tt(t52_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 (k4_intpro_1 A B) C) (k4_intpro_1 A (k4_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t52_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k9_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid D)) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t52_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) & (r2_hidden B C)) )  =>  ((r1_xxreal_0 (k17_euclid A) k6_numbers) |  ((r1_xxreal_0 (k17_euclid B) k6_numbers) |  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ((r1_xxreal_0 k6_numbers (k18_euclid B)) |  ( ( (~ (r1_xxreal_0 (k17_euclid B) (k17_euclid A)))  &  (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A))) )  | (r1_jordan6 C A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k9_jordan6 (k1_sppol_2 A B C D)) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C)) (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) & (r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F) (k2_jgraph_6 A B C D)))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) | (r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E)) (k2_jgraph_6 (k1_real_1 1) 1 (k1_real_1 1) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xboole_0 (k5_topreal1 C) (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t52_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k4_finseq_4 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e A B)) (k1_jordan5c (k3_topreal1 2 (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e A B))) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) C))  & (r1_xxreal_0 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k4_finseq_5 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e A B)) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t52_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1))) ) ) )  =>  ((r1_xboole_0 (k3_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k7_nat_d D 1) (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) & (r2_hidden C (k10_xtuple_0 B))) )  =>  ((r1_xxreal_0 (k4_finseq_4 B C) D) |  ( ((k3_gobrd13 (k3_jordan3 B C) A D) = (k3_gobrd13 B A D))  &  ((k2_gobrd13 (k3_jordan3 B C) A D) = (k2_gobrd13 B A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r1_xxreal_0 1 A) &  ((k6_subset_1 (k1_euclid A) (a_2_3_jordan2c A B)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t52_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_jordan4 C D A B) & (r1_jordan4 C E A B))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ((v1_topreal2 A) &  ( ((k9_subset_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (k8_jordan6 A) B) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ((k2_xboole_0 (k8_jordan6 A) B) = A) ) )  =>  (B = (k9_jordan6 A)) ) ) ) ) ) ).
tt(t52_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (~  ((k2_tops_1 (k15_euclid 2) (k2_jgraph_6 A B C D)) = (k1_sppol_2 A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_kurato_1,ax,(r4_zfmisc_1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))))).
tt(t52_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((k5_lattices A) = (k4_binop_1 (u1_struct_0 A) (u2_lattices A))) ) ) ).
tt(t52_lattice3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) & (l3_lattices A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  => (v5_lattice3 A)) ) ) ).
tt(t52_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (~  ((r2_hidden C (k17_lexbfs (k6_glib_000 A) k5_numbers (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k5_finsub_1 k5_numbers) (k6_glib_000 A) (k13_lexbfs A (k16_lexbfs A) B)) D)) &  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ((r2_hidden E (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)))) &  ( ((k1_recdef_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) E) = C)  & (r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_limfunc1 A) &  ((v7_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) ) ) ) ) ) )  =>  ((v7_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (v7_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t52_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_limfunc2 C A) =>  ((r4_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A) &  ((k2_limfunc2 (k26_valued_1 k1_numbers k1_numbers C B) A) = (k8_real_1 B (k2_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t52_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r3_limfunc3 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) &  ((k1_seq_1 B E) = (k1_limfunc2 B A)) ) ) ) ) ) ) ) )  | (r3_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t52_lpspace1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 B) C) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ( ( (D = (k1_relset_1 B E))  &  (! [F:$i] :  ((r2_hidden F (k1_relset_1 B E)) =>  ((k1_funct_1 E F) = A) ) ) )  => (r1_mesfunc6 B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k10_lpspace2 A B C F))) =>  ( ((r2_hidden D G) & (r2_hidden E G))  =>  ((r1_lpspace1 A B C D E) &  ((k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers D))) = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 C (k3_hilbert1 A B)) => (r8_ltlaxio1 C (k3_hilbert1 (k1_ltlaxio1 B) (k1_ltlaxio1 A)))) ) ) ) ) ) ) ).
tt(t52_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A B) (k6_cqc_lang A C)) A) <=> (v2_cqc_the1 (k8_cqc_lang A C B) A)) ) ) ) ) ) ) ).
tt(t52_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_mathmorp A (k4_mathmorp A B C) C) = (k4_mathmorp A B C)) ) ) ) ) ) ) ).
tt(t52_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r2_matrix10 B (k4_matrix10 A C D)) => (r2_matrix10 D (k4_matrix10 A C B))) ) ) ) ) ) ) ) ) ).
tt(t52_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 A)) & (r2_hidden F (k2_finseq_1 A)))  =>  ( (E = F)  |  ((k12_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) D (k10_fvsum_1 (k1_matrix_1 D) B (k8_matrix_1 (u1_struct_0 B) D F) C))) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  ((k6_matrix13 (u1_struct_0 B) C (k2_finseq_1 (k3_finseq_1 C)) (k7_subset_1 k5_numbers (k2_finseq_1 (k1_matrix_1 C)) (k3_matrix13 A))) = (k7_matrix_2 A B C)) ) ) ) ) ) ) ).
tt(t52_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (C = (k11_matrix_1 B A))  <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D A) &  ((r1_xxreal_0 1 E) & (r1_xxreal_0 E A)) ) )  =>  ((k3_matrix_1 (u1_struct_0 B) C D E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 C))))  =>  ( (~ (v1_xboole_0 (k4_matrix15 C (k1_matrix_3 C A B) D)))  =>  (D = (k1_matrix_3 C A (k1_matrix_1 D))) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v5_matrix16 C B) & (v5_matrix16 D B))  => (v5_matrix16 (k2_matrix_6 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t52_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  (B = (k1_matrix_4 A B (k3_matrix_3 A C (k2_matrix_3 A C)))) ) ) ) ) ) ) ) ).
tt(t52_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) => (r1_matrix_6 A B (k4_matrix_6 A B C D) D)) ) ) ) ) ) ) ) ) ).
tt(t52_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B C) = (k1_matrix_8 A B (k5_matrix_1 A (u1_struct_0 B) C))) ) ) ) ) ) ) ).
tt(t52_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 A)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) D E) F) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k1_matrix_9 A B D) C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_1 k2_numbers (k13_matrixc1 A B C)) = (k1_matrixc1 (k13_matrixc1 B A (k2_matrixc1 C)))) ) ) ) ) ) ) ) ) ).
tt(t52_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) B B) =>  ((k12_matrix_3 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 C) (k17_matrixj1 (u1_struct_0 C) A B D E))) C (k20_matrixj1 (u1_struct_0 C) (k4_struct_0 C) (k17_matrixj1 (u1_struct_0 C) A B D E))) = (k8_group_1 C (k12_matrix_3 A C D) (k12_matrix_3 B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  &  ( ( ((k3_finseq_1 B) = (k3_finseq_1 A))  |  ((k1_matrix_1 (k4_matrix_1 k1_numbers B)) = (k3_finseq_1 A)) )  &  (~  ((k11_matrixr1 (k4_matrix_1 k1_numbers B) A) = (k12_matrixr1 B A)) ) ) ) ) ) ) ) ) ) ).
tt(t52_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k1_matrix_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k11_matrixr1 (k4_matrixr1 B) A) = (k6_rvsum_1 (k11_matrixr1 B A))) ) ) ) ) ) ) ) ).
tt(t52_matrprob,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (? [B:$i] :  ((m2_finseq_1 B k1_numbers) &  ( ((k3_finseq_1 B) = A)  &  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) )  &  ((k18_rvsum_1 B) = 1) ) ) ) ) ) ) ).
tt(t52_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((k4_zfmisc_1 A B C D) = (k4_zfmisc_1 E F G H))  =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ( (C = k1_xboole_0)  |  ( (D = k1_xboole_0)  |  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_measure6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((v4_xxreal_2 B) =>  ((k4_seq_4 (k2_measure6 B A)) = (k7_real_1 A (k4_seq_4 B))) ) ) ) ) ) ).
tt(t52_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k9_member_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k3_binop_2 A B) (k3_binop_2 A C))) ) ) ) ) ) ) ).
tt(t52_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k9_memstr_0 A B C D)))) ) ) ) ) ) ) ) ).
tt(t52_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 F A k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  (~  ( (D = (k1_relset_1 A (k4_mesfunc5 A k2_numbers F k6_numbers)))  &  ( (D = (k1_relset_1 A E))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers F G) D)) )  &  ((r3_mesfunc6 A B C E) &  ( (! [G:$i] :  ((m1_subset_1 G A) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden G D) => (r1_xxreal_0 (k1_seq_1 (k55_valued_1 A k2_numbers (k4_mesfunc5 A k2_numbers F H)) G) (k1_seq_1 E G))) ) ) ) )  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k2_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k8_nat_1 k2_numbers G H) = (k1_mesfun6c A B C (k4_mesfunc5 A k2_numbers F H))) ) )  &  ( (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H D) => (v2_comseq_2 (k9_mesfun7c A F H))) ) )  =>  ((v2_comseq_2 G) &  ((k3_comseq_2 G) = (k1_mesfun6c A B C (k10_mesfun7c A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_nat_1 k7_numbers A C) = B) ) )  =>  ((v7_mesfunc5 A) &  ((k2_mesfunc5 A) = B) ) ) ) ) ) ) ).
tt(t52_mesfunc6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) )  => (v6_supinf_2 B)) ) ) ) ).
tt(t52_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ( (D = (k1_relset_1 A (k4_mesfunc5 A k7_numbers E k6_numbers)))  &  ((v6_supinf_2 (k4_mesfunc5 A k7_numbers E k6_numbers)) &  ((v1_mesfunc8 E A k7_numbers) &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfunc1 A B (k4_mesfunc5 A k7_numbers E F) D)) )  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r1_xxreal_0 F G) =>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((r2_hidden H D) => (r1_xxreal_0 (k1_mesfunc9 (k4_mesfunc5 A k7_numbers E F) H) (k1_mesfunc9 (k4_mesfunc5 A k7_numbers E G) H))) ) ) ) ) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F D) => (v10_mesfunc5 (k3_mesfunc5 A E F))) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k7_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (~  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k1_mesfunc9 F G) = (k7_mesfunc5 A B C (k4_mesfunc5 A k7_numbers E G))) ) )  &  ((v10_mesfunc5 F) &  ((k7_mesfunc5 A B C (k7_mesfunc8 A E)) = (k2_mesfunc5 F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k10_midsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k10_midsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k10_midsp_1 A)) =>  ( ( ((k11_midsp_1 A B C) = (k6_midsp_1 A))  &  ((k11_midsp_1 A B D) = (k6_midsp_1 A)) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t52_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((k19_mmlquery A B (k18_mmlquery A B)) = k1_xboole_0) ) ) ) ).
tt(t52_modelc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k30_modelc_1 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k48_modelc_1 A B C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 A)) =>  ((k3_funct_2 (k1_zfmisc_1 A) (k1_zfmisc_1 A) (k61_modelc_1 A B C D E) F) = (k4_subset_1 A (k51_modelc_1 A B C E) (k9_subset_1 A (k51_modelc_1 A B C D) (k50_modelc_1 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_modelc_2 C) & (l1_modelc_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k15_modelc_2 (u1_modelc_2 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 C))))) )  =>  ((k21_modelc_2 C D (k5_modelc_2 A B)) = (k1_lattices C (k21_modelc_2 C D A) (k21_modelc_2 C D B))) ) ) ) ) ) ) ) ) ).
tt(t52_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k23_modelc_3 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 B))))) )  =>  (? [D:$i] :  ( ((v1_modelc_3 D B) &  ((v3_modelc_3 D B) & (l1_modelc_3 D B)) )  &  (D = (k10_modelc_3 (k1_funct_1 C A) B)) ) ) ) ) ) ) ) ) ).
tt(t52_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (~ (r1_xxreal_0 (k6_moebius1 A) k6_numbers)) ) ) ).
tt(t52_monoid_0,ax, (k7_monoid_0 = (g3_algstr_0 k5_numbers k48_binop_2)) ).
tt(t52_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r3_binop_1 A C B) =>  ((r3_binop_1 (k1_zfmisc_1 A) (k6_domain_1 A C) (k21_monoid_1 A A A B)) &  ((v1_setwiseo (k21_monoid_1 A A A B) (k1_zfmisc_1 A)) &  ((k4_binop_1 (k1_zfmisc_1 A) (k21_monoid_1 A A A B)) = (k6_domain_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t52_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m3_pboole D A (k1_mboolean A B)) =>  ((r1_pboole A C (k4_mssubfam A B D)) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E D) => (r1_pboole A C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  ((r2_pboole (u1_struct_0 A) (k9_msualg_6 A B C) (k10_msualg_6 A B C)) &  ((r2_pboole (u1_struct_0 A) (k6_msualg_6 A B C) (k10_msualg_6 A B C)) &  ((r2_pboole (u1_struct_0 A) (k7_msualg_6 A B C) (k10_msualg_6 A B C)) & (r2_pboole (u1_struct_0 A) (k8_msualg_6 A B C) (k10_msualg_6 A B C))) ) ) ) ) ) ) ) ) ).
tt(t52_mycielsk,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (? [B:$i] :  ( ((v8_struct_0 B) & (l1_orders_2 B))  &  ( ((k2_dilworth B) = 2)  &  (~ (r1_xxreal_0 (k3_mycielsk B) A)) ) ) ) ) ) ).
tt(t52_nat_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k8_nat_1 B C D) A)) )  => (r1_tarski (k10_xtuple_0 C) A)) ) ) ) ) ) ).
tt(t52_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( ((k1_polynom2 k10_newton (k12_nat_3 A)) = k1_xboole_0)  =>  (A = 1) ) ) ) ).
tt(t52_nat_4,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((k1_nat_4 (k3_pre_poly k5_numbers B) A) = (k3_pre_poly k5_numbers (k11_nat_3 B A))) ) ) ) ) ).
tt(t52_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k7_nat_d A B) C) => (r1_xxreal_0 A (k2_xcmplx_0 C B))) ) ) ) ) ) ) ).
tt(t52_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ((r9_ncfcont1 B A D C) <=> (r9_ncfcont1 B A (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) D C) C)) ) ) ) ) ) ) ) ).
tt(t52_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ((m2_subset_1 F k5_numbers (k4_finseq_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k11_prvect_2 A F))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k11_prvect_2 A F))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k11_prvect_2 A F))) =>  (~  ( (~ (r1_xxreal_0 G (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) C B))))  &  ( (~ (r1_xxreal_0 G (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) D B))))  &  ( (H = (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A F)) (k3_ndiff_5 A F) C))  &  ( (D = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A F)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A F C) I))  &  ((r2_hidden J (k1_rltopsp1 (k11_prvect_2 A F) H I)) &  ( (E = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A F)) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A F C) J))  & (r1_xxreal_0 G (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) E B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_nat_d A k6_numbers) = A) ) ) ).
tt(t52_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r2_hidden F A) =>  ((k7_partfun1 (u1_struct_0 B) C F) = (k3_rlvect_1 B (k1_rlvect_1 B F D) E)) ) ) ) )  => (r3_nfcont_1 B B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t52_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k10_normform A B (k10_normform A C D)) = (k10_normform A (k10_normform A B C) D)) ) ) ) ) ) ) ) ).
tt(t52_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 B) (u4_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C))))) )  => (r2_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 C) (k10_oppcat_1 A C (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E)) (k1_partfun1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) (k10_oppcat_1 A B D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t52_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r4_orders_1 (k2_relat_1 A) B) <=> (r5_orders_1 A B)) ) ) ) ).
tt(t52_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r6_orders_1 (u1_orders_2 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r2_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t52_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((k5_ordinal3 (k10_ordinal2 A B) A) = B) ) ) ) ) ).
tt(t52_ordinal5,ax, ((k4_ordinal5 k1_xboole_0) = k6_numbers) ).
tt(t52_ordinal6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ( ( (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) => (v2_ordinal6 (k1_funct_1 B C))) ) )  & (r2_hidden A (k9_xtuple_0 (k7_ordinal6 B))))  =>  ( ((k9_xtuple_0 B) = k1_xboole_0)  |  ((k1_funct_1 (k7_ordinal6 B) A) = (k3_card_3 (k5_relat_1 (k7_ordinal6 B) A))) ) ) ) ) ) ) ).
tt(t52_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t52_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r3_parsp_2 A B C D E) &  ((r1_parsp_2 A B C D) & (r2_parsp_2 A F G B C)) )  => (r2_parsp_2 A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_partfun1 A B) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((r1_tarski A C) & (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(t52_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden C (k1_relset_1 A D)) & (r2_relset_1 A B E (k4_subset_1 (k2_zfmisc_1 A B) F D)))  =>  ((k7_partfun1 B E C) = (k7_partfun1 B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k4_pboole A B C) (k1_pboole A)) <=> (r2_pboole A B C)) ) ) ) ) ) ).
tt(t52_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r1_pdiff_5 B A) & (r1_pdiff_5 C A))  =>  ((r3_pdiff_1 3 1 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 1 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k9_real_1 (k1_pdiff_5 B A) (k1_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t52_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r1_pdiff_7 A B D) =>  ((r1_pdiff_7 A (k26_valued_1 (k1_euclid A) k1_numbers B C) D) & (r2_funct_2 (k1_euclid A) k1_numbers (k1_pdiff_7 A (k26_valued_1 (k1_euclid A) k1_numbers B C) D) (k26_valued_1 (k1_euclid A) k1_numbers (k1_pdiff_7 A B D) C))) ) ) ) ) ) ) ) ) ) ).
tt(t52_pepin,ax, ((k4_pepin 2) = 17) ).
tt(t52_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  ( (B = k1_xboole_0)  <=>  ((k12_pnproc_1 B A) = k1_xboole_0) ) ) ) ) ) ).
tt(t52_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k30_polyform A) = (k6_polyform (k29_polyform A) (k3_polyform (k2_polyform (k4_xcmplx_0 1) (k7_polyform A))))) ) ) ).
tt(t52_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (~  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_algseq_1 A C) 1))  &  (~  ((k1_algseq_1 A (k5_polynom5 A B C)) = (k7_real_1 (k9_real_1 (k9_real_1 (k4_nat_1 (k1_algseq_1 A B) (k1_algseq_1 A C)) (k1_algseq_1 A B)) (k1_algseq_1 A C)) 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r11_polyred A B C C)) ) ) ) ) ) ).
tt(t52_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  (~  ((k5_power A A) = 1) ) ) ) ) ) ) ).
tt(t52_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((k1_funct_1 (k16_pre_poly A) B) = k6_numbers) ) ) ).
tt(t52_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k6_prepower A B) k6_numbers)) ) ) ) ) ) ).
tt(t52_prob_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C (k9_setfam_1 A)) =>  ( (~  (C = k1_xboole_0) )  =>  ((r2_hidden B (k6_setfam_1 A (k2_relset_1 (k9_setfam_1 A) C))) <=>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) => (r2_hidden B (k4_prob_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t52_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A B D) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A B (k7_cqc_lang A C D)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t52_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k23_pscomp_1 A) = (k22_pscomp_1 A))  =>  ((k16_pscomp_1 A) = (k1_tarski (k23_pscomp_1 A))) ) ) ) ).
tt(t52_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k4_pboole A (k1_pzfmisc1 A B) C) (k1_pboole A)) <=> (r1_pboole A B C)) ) ) ) ) ) ).
tt(t52_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B C) => (r2_qc_lang2 A B C)) ) ) ) ) ) ) ).
tt(t52_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (k2_qc_lang1 A))))  =>  ((k4_qc_lang3 A D (k5_qc_lang2 A B C)) = (k4_qc_lang3 A D C)) ) ) ) ) ) ) ) ) ).
tt(t52_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k18_quatern2 A A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t52_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k28_quaterni (k26_quaterni A B)) = (k29_quaterni (k28_quaterni A) B)) ) ) ) ) ).
tt(t52_quaterni,ax, ((k31_quaterni k11_quaterni) = (k28_quaterni k11_quaterni)) ).
tt(t52_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (~  (D = (k4_struct_0 A)) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k11_algstr_0 A D)) = (k11_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((k3_finseq_1 D) = 1) ) ) ) )  =>  (D = (k12_finseq_1 (k1_zfmisc_1 k1_numbers) (k1_rcomp_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t52_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) 1) k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_seq_1 (k6_real_3 A) B) k6_numbers)) ) ) ) ) ) ).
tt(t52_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k3_relat_1 (k4_relat_1 (k9_xtuple_0 A)) A) = A) ) ) ).
tt(t52_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ( ((k10_xtuple_0 (k7_relset_2 A B C D E)) = (k7_relset_1 B C E (k10_xtuple_0 D)))  & (r1_tarski (k10_xtuple_0 (k7_relset_2 A B C D E)) (k10_xtuple_0 E))) ) ) ) ) ) ) ) ).
tt(t52_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v9_rewrite1 A) <=> (r10_rewrite1 A A)) ) ) ).
tt(t52_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) => (r4_rewrite2 A B B C)) ) ) ) ) ).
tt(t52_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l1_rewrite3 E D))  =>  (! [F:$i] :  ((m1_rewrite1 F (k1_rewrite3 B D E)) =>  ( ((k1_funct_1 F (k3_finseq_1 F)) = (k4_tarski A C))  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (~  ((r2_hidden G (k4_finseq_1 F)) &  (! [H:$i] :  ((m1_subset_1 H (k8_afinsq_1 B)) =>  (~  ((k2_xtuple_0 (k1_funct_1 F G)) = (k1_flang_1 B H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 B A) <=> (v1_partfun1 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(t52_rfunct_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) => (v6_valued_0 (k2_partfun1 k1_numbers k1_numbers (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) (k7_relset_1 k1_numbers k1_numbers C (k1_rcomp_1 A B))))) ) ) ) ) ) ) ).
tt(t52_rfunct_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_rfunct_3 C (k1_rcomp_1 A B)) <=>  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers D) & (r1_xxreal_0 D 1))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden E (k1_rcomp_1 A B)) & (r2_hidden F (k1_rcomp_1 A B)))  => (r1_xxreal_0 (k1_seq_1 C (k7_real_1 (k8_real_1 D E) (k8_real_1 (k9_real_1 1 D) F))) (k7_real_1 (k8_real_1 D (k1_seq_1 C E)) (k8_real_1 (k9_real_1 1 D) (k1_seq_1 C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 B) => (r1_xxreal_0 (k1_seq_1 (k3_rinfsup1 B) A) (k1_seq_1 (k4_rinfsup1 B) A))) ) ) ) ) ).
tt(t52_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k4_rlaffin1 A B) (k4_rlaffin1 A C))) ) ) ) ) ) ) ).
tt(t52_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_struct_0 D B) <=>  ((k3_rlsub_1 A C D) = (k3_rlsub_1 A (k3_rlvect_1 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t52_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t52_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  =>  ((k1_convex1 A (k2_pre_topc A B) C) = (k2_pre_topc A (k1_convex1 A B C))) ) ) ) ) ) ) ).
tt(t52_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_algstr_0 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C))) = (k5_algstr_0 A (k4_algstr_0 A B) C)) ) ) ) ) ) ) ).
tt(t52_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((m2_rlvect_2 C A B) => (m2_rlvect_2 (k9_rlvect_2 A C) A B)) ) ) ) ) ) ) ).
tt(t52_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r1_struct_0 E C) <=>  ((k3_rmod_2 A B D E) = (k3_rmod_2 A B (k5_algstr_0 B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ((k2_rmod_4 A B (k8_rmod_4 A B C)) = (k2_rmod_4 A B C)) ) ) ) ) ) ) ).
tt(t52_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k17_robbins1 A B) B) = (k3_robbins1 A (k15_robbins1 A B))) ) ) ) ) ).
tt(t52_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k3_robbins1 A (k3_robbins1 A B)) (k5_robbins1 A C D)) = (k5_robbins1 A (k5_robbins1 A C B) (k5_robbins1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t52_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k9_subset_1 (u1_struct_0 A) B C)) D) (k3_xxreal_0 (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A B) D) (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A C) D)))) ) ) ) ) ) ) ) ).
tt(t52_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( ( ((k4_subset_1 A C D) = A)  & (r1_xboole_0 C D))  =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A D) k6_numbers) |  ((k2_rpr_1 A B C) = (k10_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k7_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k8_real_1 (k2_rpr_1 A D B) (k1_rpr_1 A D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden (k1_rlvect_1 A C D) (k3_rusub_1 A C B)) =>  ( (D = 1)  | (r1_struct_0 B C)) ) ) ) ) ) ) ) ) ) ).
tt(t52_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C)) = (k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t52_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) & (r1_tarski (k4_subset_1 (u1_struct_0 A) (k4_bhsp_2 A B D) (k4_bhsp_2 A C E)) (k4_bhsp_2 A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k10_rvsum_1 A 1) = A) ) ) ).
tt(t52_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k3_finseq_1 (k7_rvsum_2 A B)) = (k3_finseq_1 A)) ) ) ) ) ) ).
tt(t52_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (A = (k5_relat_1 B k1_ami_2))  =>  (B = (k1_funct_4 B A)) ) ) ) ) ) ).
tt(t52_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  &  ( (~ (r4_scmfsa7b B C))  & (r4_scmfsa7b (k3_scmfsa6a A B) C)) ) ) ) ) ) ) ) ) ).
tt(t52_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r4_scmfsa7b C D))  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 D E B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ( (~  ((k2_scmpds_2 (k1_funct_1 A D) B) = (k2_scmpds_2 (k1_funct_1 A E) C)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A D) B)) = (k5_int_1 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C)))) )  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 D E B C) A) (k2_scmpds_2 (k1_funct_1 A E) C)) = (k6_int_1 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A E) C))))  &  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (~  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A D) B)) )  &  ( (~  (F = (k2_scmpds_2 (k1_funct_1 A E) C)) )  &  (~  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 D E B C) A) F) = (k1_funct_1 A F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k5_scmpds_6 D E C) B A)) = (k2_nat_1 (k5_card_1 C) 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k1_funct_1 (k6_scmpds_4 (k3_scmpds_7 C) B A) (k1_scmp_gcd 3)) = C) ) ) ) ) ) ) ).
tt(t52_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (~  ((r2_hidden B (k3_tarski A)) &  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v4_scmyciel C) &  ((v5_scmyciel C) & (m1_subset_1 C (k1_zfmisc_1 A))) ) )  =>  (~  ((k3_tarski C) = (k1_tarski B)) ) ) ) ) ) ) ) ) ).
tt(t52_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ( ((r2_semi_af1 A B C D E) &  ((r2_semi_af1 A B C F G) & (r2_semi_af1 A D E H I)) )  => (r2_analoaf A F H G I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers (k20_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k20_valued_1 k5_numbers k1_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) (k56_valued_1 k5_numbers k1_numbers B)))) ) ) ) ).
tt(t52_seq_4,ax,(r2_funct_2 k2_numbers k2_numbers (k5_finseqop k2_numbers k27_binop_2) k25_binop_2)).
tt(t52_series_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers k1_numbers A (k20_valued_1 k5_numbers k1_numbers k1_numbers B B)) &  ((r2_funct_2 k5_numbers k1_numbers C (k20_valued_1 k5_numbers k1_numbers k1_numbers D D)) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k1_seq_1 B F)) &  ((r1_xxreal_0 k6_numbers (k1_seq_1 D F)) &  ((k1_seq_1 E F) = (k5_square_1 (k7_real_1 (k1_seq_1 B F) (k1_seq_1 D F)))) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) => (r1_xxreal_0 (k7_square_1 (k1_seq_1 (k3_series_1 E) F)) (k7_real_1 (k7_square_1 (k1_seq_1 (k3_series_1 A) F)) (k7_square_1 (k1_seq_1 (k3_series_1 C) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A C) k6_numbers))  &  ((k1_seq_1 B C) = (k13_complex1 1 (k1_seq_1 A C))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r1_xxreal_0 (k1_seq_1 (k3_series_1 B) C) k6_numbers)) ) ) ) ) ) ) ) ).
tt(t52_setlim_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((v2_prob_1 C) =>  ((k3_funct_2 k5_numbers (k9_setfam_1 B) (k2_setlim_1 B C) A) = (k3_prob_1 B C)) ) ) ) ) ) ) ).
tt(t52_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k7_setlim_2 B D C)) A) (k7_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A)))) ) ) ) ) ) ) ).
tt(t52_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_binop_1 D A) &  ((v2_binop_1 D A) & (v3_binop_1 D A)) )  =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  ( (~  (E = k1_xboole_0) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B (k5_finsub_1 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (k5_finsub_1 C))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k5_finsub_1 C) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 C) A)))) )  =>  ( (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 C)) =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 C)) =>  ((k3_funct_2 (k5_finsub_1 C) A G (k5_setwiseo C H I)) = (k5_binop_1 A D (k3_funct_2 (k5_finsub_1 C) A G H) (k3_funct_2 (k5_finsub_1 C) A G I))) ) ) ) )  =>  ((k3_funct_2 (k5_finsub_1 C) A G (k10_setwiseo B C E F)) = (k7_setwiseo B A D E (k1_partfun1 B (k5_finsub_1 C) (k5_finsub_1 C) A F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((r2_hidden (k12_scmfsa_2 B A) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)) | (r2_hidden (k13_scmfsa_2 B A) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ((k5_sf_mastr C) = A) ) ) ) ) ) ) ) ) ).
tt(t52_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C D) B)) (k5_sheffer1 A C C)) = C) ) ) ) ) ) ) ) ) ).
tt(t52_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v1_setfam_1 (k9_xtuple_0 C)) => (r1_xxreal_0 (k6_simplex0 (k10_simplex0 A B C)) (k6_simplex0 B))) ) ) ) ) ) ).
tt(t52_sincos10,ax, ((k2_partfun1 k1_numbers k1_numbers k4_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) = (k2_partfun2 k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2))))) ).
tt(t52_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k15_sin_cos (k5_binop_2 (k5_binop_2 k7_complex1 A) B)) = (k2_comseq_3 (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B))) A)) ) ) ) ) ).
tt(t52_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ((k6_sin_cos2 (k6_real_1 A 2)) = k6_numbers) )  =>  ((k1_sin_cos5 (k6_real_1 A 2)) = (k10_real_1 (k7_real_1 (k6_sin_cos2 A) 1) (k3_sin_cos2 A))) ) ) ) ).
tt(t52_sin_cos6,ax, ((k7_relset_1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 k32_sin_cos (k8_real_1 2 k32_sin_cos))) = (k2_rcomp_1 (k1_real_1 1) 1)) ).
tt(t52_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((k9_binop_2 (k2_sin_cos7 A) (k2_sin_cos7 B)) = (k2_sin_cos7 (k9_binop_2 (k11_binop_2 A B) (k7_square_1 (k11_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 B) 1)))))) ) ) ) ) ) ).
tt(t52_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k2_sin_cos4 (k6_sin_cos9 A)) = A) ) ) ) ).
tt(t52_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  => (r1_xxreal_0 1 (k1_seq_1 k24_sin_cos A))) ) ) ).
tt(t52_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sppol_2 B C A) & (r2_hidden D A))  =>  ( (D = C)  | (r1_sppol_2 D C A)) ) ) ) ) ) ) ) ) ) ).
tt(t52_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_rcomp_1 (k17_euclid A) (k17_euclid B))) ) ) ) ) ) ).
tt(t52_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k20_pscomp_1 (k3_topreal1 2 A)) = (k21_pscomp_1 (k3_topreal1 2 A))) ) ) ) ).
tt(t52_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sprect_2 A B) &  ((r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) C)) &  ((v4_topreal1 B) & (r2_hidden C (k3_topreal1 2 B))) ) )  => (r1_sprect_2 A (k3_jordan3 B C))) ) ) ) ) ) ) ).
tt(t52_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t52_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  =>  ( (~ (r1_xxreal_0 A (k4_xcmplx_0 1)))  &  (~ (r1_xxreal_0 1 A)) ) ) ) ) ).
tt(t52_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_stirl2_1 (k23_binop_2 A 1) A) = (k6_newton 2 (k23_binop_2 A 1))) ) ) ).
tt(t52_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k16_substut1 A) (k38_substut1 A)) =>  (! [D:$i] :  ((m1_substut1 D A (k7_sublemma A C B)) =>  ((v3_substut1 (k7_sublemma A C B) A) =>  ((r2_hidden B (k10_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A C)) D))) |  ((k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A C B) D))) = B) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_supinf_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 B C))) )  => (v6_supinf_2 B)) ) ) ) ).
tt(t52_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k1_tops_1 A (k2_pre_topc A (k6_setfam_1 (u1_struct_0 A) B))) (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A B))))) ) ) ) ).
tt(t52_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (v4_tdlat_3 A)) ) ).
tt(t52_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) = (k6_domain_1 (u1_struct_0 A) C)) ) ) )  => (v2_tex_2 B A)) ) ) ) ) ).
tt(t52_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((v1_tops_1 B A) &  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v1_tex_2 C A) &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t52_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_tarski (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) <=> (r1_tarski (k4_tex_4 A C) (k1_setfam_1 (a_2_9_tex_4 A B)))) ) ) ) ) ) ) ).
tt(t52_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ( ((u1_struct_0 A) = (u1_struct_0 B))  & (r1_tarski (u1_pre_topc B) (u1_pre_topc A)))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 C)) &  ((v5_pre_topc D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) => (v2_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A B)))) ) ) ) ) ) ) ) ) ).
tt(t52_topgen_1,ax, ((v1_tops_1 k1_borsuk_5 k3_topmetr) & (m1_subset_1 k1_borsuk_5 (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ).
tt(t52_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k4_topgen_4 A B) (k4_topgen_4 A C))) ) ) ) ) ) ) ).
tt(t52_topgen_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v7_pre_topc A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v2_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden C D) &  ((r2_hidden D B) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc E A k5_topmetr) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr))))) ) )  =>  (~  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k5_topmetr) E C) = k6_numbers)  & (r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 k5_topmetr) E (k3_subset_1 (u1_struct_0 A) D)) (k6_domain_1 k1_numbers 1))) ) ) ) ) ) ) ) ) ) )  => (v1_topgen_5 A)) ) ) ) ) ).
tt(t52_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) => (v3_pre_topc (k2_group_2 A C B) A)) ) ) ) ) ) ) ).
tt(t52_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid 2))) =>  ( (C = (k4_struct_0 (k15_euclid 2)))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_tarski B (k9_metric_1 (k14_euclid 2) C (k7_real_1 (k7_real_1 (k7_real_1 (k7_real_1 (k18_complex1 (k8_pscomp_1 B)) (k18_complex1 (k7_pscomp_1 B))) (k18_complex1 (k6_pscomp_1 B))) (k18_complex1 (k9_pscomp_1 B))) A)))) ) ) ) ) ) ) ) ).
tt(t52_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_topreal9 2 (k19_euclid A B) C) = (k5_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(t52_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 k3_topmetr)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 k3_topmetr))))) )  =>  ((k70_valued_2 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) C D) = (k91_valued_2 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C (k15_toprealc A (u1_struct_0 B) (u1_struct_0 k3_topmetr) D))) ) ) ) ) ) ) ) ) ).
tt(t52_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tops_1 B A) <=> (r1_tarski B (k2_tops_1 A B))) ) ) ) ) ).
tt(t52_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  =>  ( ((k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C)) = (k6_partfun1 (k1_relset_1 (u1_struct_0 A) C)))  &  ((k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) C) = (k6_partfun1 (k2_relset_1 (u1_struct_0 B) C))) ) ) ) ) ) ) ) ) ).
tt(t52_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_tops_1 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc C A) &  ((v2_tops_1 C A) &  ((v3_pre_topc D A) &  ((v1_tops_1 D A) &  ( ((k9_subset_1 (u1_struct_0 A) C (k4_subset_1 (u1_struct_0 A) B D)) = B)  &  ((r1_xboole_0 C D) &  ((k4_subset_1 (u1_struct_0 A) C D) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v5_transgeo B A) => (v5_transgeo (k2_funct_2 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t52_trees_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r2_xboole_0 (k12_finseq_1 k5_numbers A) (k12_finseq_1 k5_numbers B))) ) ) ) ) ).
tt(t52_trees_3,ax, ((k11_trees_3 k1_xboole_0) = (k2_trees_1 k6_numbers)) ).
tt(t52_trees_9,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k5_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r1_xxreal_0 (k8_nat_1 k5_numbers A (k2_nat_1 B 1)) (k8_nat_1 k5_numbers A B))) )  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((r1_xxreal_0 B C) &  (~  ((k8_nat_1 k5_numbers A C) = (k8_nat_1 k5_numbers A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_1 A B D) & (r2_tsep_1 A C D))  => (r2_tsep_1 A (k9_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t52_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) =>  (! [D:$i] :  ((m1_subset_1 D k6_margrel1) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  ( ( (D = (k1_funct_1 C A))  &  (E = (k1_funct_1 C B)) )  =>  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k36_twoscomp A B)) = (k2_binarith (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k39_twoscomp A B)) = (k10_margrel1 (k9_margrel1 D) E))  &  ( ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) A) = D)  &  ((k1_funct_1 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) B) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((v1_int_1 B) => (v1_int_1 (k2_polynom4 k1_complfld (k5_uniroots A) B))) ) ) ) ) ).
tt(t52_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) <=> (r1_xxreal_0 1 (k7_uproots A C B))) ) ) ) ) ) ) ).
tt(t52_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k37_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k37_valued_2 A B E C) D) = (k37_valued_2 A B E (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t52_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_struct_0 D C) <=>  ((k3_vectsp_4 A B (k4_algstr_0 B C) D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t52_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) =>  ( ( ((k3_rlvect_1 B (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F) (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)) = E)  &  ((r1_struct_0 C (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) F)) & (r1_struct_0 D (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) F))) )  =>  (F = (k4_vectsp_5 A B E C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((v3_funct_1 (k2_partfun1 B (u1_struct_0 C) D A)) => (v3_funct_1 (k2_partfun1 B (u1_struct_0 C) (k4_vfunct_1 B C D E) A))) ) ) ) ) ) ) ) ) ) ).
tt(t52_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C E)) => (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) (k2_vfunct_2 A B C D) E))) ) ) ) ) ) ) ) ) ) ).
tt(t52_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r1_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r1_yellow_0 A E) &  (D = (k1_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k1_yellow_0 A D) C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_lattice3 A B D) <=> (r2_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t52_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (C = (a_2_1_waybel_1 A B))  =>  ( ((v18_waybel_0 B A A) =>  ((v8_yellow_0 (k5_yellow_0 A C) A) & (v8_yellow_0 (k1_yellow_2 A A B) A)) )  &  ((v22_waybel_0 B A A) =>  ((v4_waybel_0 (k5_yellow_0 A C) A) & (v4_waybel_0 (k1_yellow_2 A A B) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ( ((r2_hidden (k4_yellow_0 A) (u1_struct_0 B)) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A C)) (u1_struct_0 B)) => (r2_hidden (k1_waybel11 A C) (u1_struct_0 B))) ) ) )  => (v7_yellow_0 B A)) ) ) ) ) ).
tt(t52_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (k3_waybel23 A B))) <=>  ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C B) &  ((v12_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t52_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  ((v2_waybel_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ((r3_orders_2 A B (k1_yellow_0 A C)) =>  (B = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) C))) ) ) ) ) ) ) ) ) ).
tt(t52_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r3_yellow20 (k4_waybel34 A) (k5_waybel34 A) (k6_waybel34 A) (k8_waybel34 A) (k9_waybel34 A))) ) ).
tt(t52_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_waybel_3 A B D) & (r1_waybel_3 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ((v2_wellord1 A) &  ((v2_wellord1 B) &  ( (~ (r4_wellord1 A B))  &  ( (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 A)) & (r4_wellord1 (k2_wellord1 A (k1_wellord1 A C)) B)) ) )  &  (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 B)) & (r4_wellord1 A (k2_wellord1 B (k1_wellord1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 A (k4_xboole_0 B C)) = (k2_xboole_0 (k4_xboole_0 A B) (k3_xboole_0 A C))) ) ) ) ).
tt(t52_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean A (k8_xboolean A B)) = (k4_xboolean A (k3_xboolean B))) ) ) ) ) ).
tt(t52_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 A (k7_xcmplx_0 A B)) = B) ) ) ) ) ) ).
tt(t52_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B C))  => (r1_xxreal_0 B (k6_xcmplx_0 C A))) ) ) ) ) ) ) ).
tt(t52_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k2_xxreal_1 A B) (k1_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  ((m2_xxreal_2 k1_xxreal_0 A) => (r1_tarski A (k1_tarski k1_xxreal_0))) ) ) ).
tt(t52_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~ (r1_xxreal_0 C (k1_xxreal_3 A B)))  &  (~  ( (~  (A = k1_xxreal_0) )  &  ( (~  (B = k1_xxreal_0) )  &  ( (~  (C = k2_xxreal_0) )  &  (~ (r1_xxreal_0 (k3_xxreal_3 C B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((r2_yellow_0 A B) | (r2_yellow_0 A (k3_xboole_0 B (u1_struct_0 A))))  =>  ((k2_yellow_0 A B) = (k2_yellow_0 A (k3_xboole_0 B (u1_struct_0 A)))) ) ) ) ) ).
tt(t52_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k4_yellow_3 A B (k2_waybel_8 (k3_yellow_3 A B) C)) = (k2_waybel_8 A (k8_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t52_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) E D) (k3_struct_0 B)) & (v3_tops_2 F B C))  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 B) (u1_struct_0 C) F) E) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D F)) (k3_struct_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_altcat_1 F) &  ((v3_altcat_2 F A) & (m1_altcat_2 F A)) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v2_altcat_1 G) &  ((v3_altcat_2 G B) & (m1_altcat_2 G B)) ) )  =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  &  ((v2_altcat_1 H) &  ((v3_altcat_2 H C) & (m1_altcat_2 H C)) ) )  =>  ( ((r2_yellow20 A B D F G) & (r2_yellow20 B C E G H))  => (r2_yellow20 A C (k1_functor3 A B C D E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t52_yellow_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  => (v5_orders_3 (k3_yellow_2 A) A (k2_yellow_1 (k7_waybel_0 A)))) ) ).
tt(t52_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_lattice3 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B) C)) ) ) ) ) ) ).
tt(t52_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k13_lattice3 A (k12_lattice3 A B C) (k1_yellow_5 A B C)) = B) ) ) ) ) ) ) ).
tt(t52_yellow_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((k5_waybel11 A) = (k5_waybel11 B)) ) ) ) ) ) ).
tt(t52_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_zf_lang A B) <=> (r2_hidden A (k29_zf_lang B))) ) ) ) ) ).
tt(t52_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_zf_lang A (k6_zf_lang B)) <=>  (A = B) ) ) ) ) ) ).
tt(t52_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_xboole_0 (k1_tarski A) B) |  ((k3_xboole_0 (k1_tarski A) B) = (k1_tarski A)) ) ) ) ).
tt(t52_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((k3_zmodul01 B) = (k3_zmodul01 C)) ) ) ) ) ) ) ).
tt(t53_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r1_tarski C (k2_abcmiz_0 A B)) =>  ((r2_abcmiz_0 A B C) &  ((k6_abcmiz_0 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(t53_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( (! [C:$i] :  ((m1_subset_1 C k2_abcmiz_1) =>  (~  (B = (k35_abcmiz_1 C A)) ) ) )  &  ( (! [C:$i] :  ( ((v2_abcmiz_1 C A) & (m1_subset_1 C (u4_struct_0 A)))  =>  (! [D:$i] :  ((m1_trees_4 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (B = (k36_abcmiz_1 A C D)) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (~  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) )  &  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (~  (B = (k31_abcmiz_1 A (k33_abcmiz_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k2_abcmiz_1 (k34_abcmiz_1 A)))))  =>  ((r4_abcmiz_a A B C D) => (r4_abcmiz_a A C B D)) ) ) ) ) ) ) ) ) ).
tt(t53_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_aff_1 A B C D) & (r2_aff_1 A B C E))  =>  ( (B = C)  | (r5_aff_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  &  ( (~ (r1_aff_1 A B C D))  &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_analoaf A B D E G) & (r2_analoaf A C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ( ((r1_xxreal_0 A (k1_afinsq_1 C)) & (r2_hidden B A))  =>  ( ((k1_funct_1 (k5_relat_1 C A) B) = (k1_funct_1 C B))  & (r2_hidden B (k2_afinsq_1 C))) ) ) ) ) ) ) ) ).
tt(t53_afinsq_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_afinsq_2 (k5_afinsq_1 A)) = A) ) ) ).
tt(t53_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D) = (k3_rlvect_1 A C D)) ) )  => (v2_funct_1 B)) ) ) ) ) ) ) ).
tt(t53_algspec1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v11_struct_0 C))  &  ((v1_instalg1 C) & (l1_msualg_1 C)) )  =>  (! [D:$i] :  ((m2_algspec1 D C) =>  ((r1_algspec1 D A B) => (m2_algspec1 (k2_algspec1 D A B) (k2_algspec1 C A B))) ) ) ) ) ) ) ) ) ).
tt(t53_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k1_altcat_4 (k1_altcat_4 A)) = (k1_altcat_4 A)) ) ) ).
tt(t53_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (r6_analmetr A E F B)) )  =>  ((r4_analmetr A E F C D) & (r4_analmetr A C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_analort A B C))) <=> (m1_subset_1 D (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t53_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) & (l1_unialg_1 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ( (~ (r2_hidden B (k18_aofa_000 A)))  &  ( (~  (B = (k12_aofa_000 A)) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (B = (k13_aofa_000 A C D))  &  ( (~  (C = (k13_aofa_000 A C D)) )  &  (~  (D = (k13_aofa_000 A C D)) ) ) ) ) ) ) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (B = (k14_aofa_000 A C D E)) ) ) ) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  (B = (k16_aofa_000 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m2_funct_2 C B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_aofa_i00 E A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)) & (m1_aofa_000 E A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers)))  =>  (! [F:$i] :  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  (! [I:$i] :  ((m1_aofa_i00 I B (u1_struct_0 A) (k9_funct_2 B k4_numbers) E) =>  ( ( (! [J:$i] :  ((m2_funct_2 J B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((r2_hidden J F) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E J G) I) = (k21_aofa_i00 B k4_numbers J I))  &  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E J G) H) = (k21_aofa_i00 B k4_numbers J H))  &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E J G) F) &  ((r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E J (k74_aofa_i00 A B D E H I)) F) & (r2_hidden (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E J (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E H 1)) F)) ) ) ) ) ) )  & (r2_hidden C F))  =>  ( (! [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  =>  (~  ( ((k1_funct_1 J D) = k6_numbers)  &  ( ((k1_funct_1 J I) = 1)  &  ((k1_funct_1 J H) = 2) ) ) ) ) )  | (r4_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A G (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E H 1)) (k74_aofa_i00 A B D E H I)) (k9_funct_2 B k4_numbers) (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) E C (k74_aofa_i00 A B D E H I)) (k1_aofa_i00 (k9_funct_2 B k4_numbers) D k6_numbers) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ( ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) )  =>  ((v8_relat_2 B) &  ((v7_armstrng B A) & (v12_armstrng B A)) ) )  &  ( ((v8_relat_2 B) &  ((v7_armstrng B A) & (v12_armstrng B A)) )  =>  ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) ) ) ) ) ) ) ).
tt(t53_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((k10_arytm_3 A k12_arytm_3) = A) ) ) ).
tt(t53_asympt_1,ax, ((k5_series_1 4 4) = 256) ).
tt(t53_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) =>  ((k4_bcialg_1 A) = (k1_tarski (k4_struct_0 A))) ) ) ) ).
tt(t53_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) &  ((v8_bcialg_1 B) &  ((v1_bcialg_5 B) & (l2_bcialg_1 B)) ) ) ) ) ) )  =>  ( ((v8_bcialg_1 B) & (m1_bcialg_5 B A (k2_nat_1 A 1) A (k2_nat_1 A 1)))  <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k1_bcialg_2 B C D (k2_nat_1 A 1)) = (k1_bcialg_2 B C D (k2_nat_1 A 2))) ) ) ) ) ) ) ) ) ) ).
tt(t53_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_bcialg_1 C A) =>  (! [D:$i] :  ((m2_bcialg_1 D B) =>  (! [E:$i] :  ((m5_bcialg_2 E B D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) &  ((v2_bcialg_6 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ( ( (D = (k5_bcialg_6 B A F))  &  ((u1_struct_0 C) = (k2_relset_1 (u1_struct_0 A) F)) )  => (r1_bcialg_6 (k9_bcialg_2 B E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B)) ) ) ) ) ) )  => (m4_bciideal B A)) ) ) ) ) ).
tt(t53_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k5_normsp_1 C D (k8_real_1 A B)) (k5_normsp_1 C (k5_normsp_1 C D B) A))) ) ) ) ) ) ) ) ).
tt(t53_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_bhsp_2 A C D)) => (r2_hidden B (k5_bhsp_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t53_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 B (k1_bhsp_4 B (k5_bhsp_4 B C A)) (k2_nat_1 D 1)) = (k5_algstr_0 B (k1_normsp_1 B (k5_bhsp_4 B (k1_bhsp_4 B C) A) (k2_nat_1 D 1)) (k1_normsp_1 B (k1_bhsp_4 B (k5_bhsp_4 B (k1_bhsp_4 B C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers A 1) A))) D))) ) ) ) ) ) ) ) ) ).
tt(t53_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  ( (~  (D = (k7_hahnban1 A B)) )  =>  ((k11_bilinear A B C (k9_bilinear A B C D E)) = (k8_vectsp10 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~ (r4_boolealg A B C))  => (r1_boolealg A (k1_boolealg A (k3_lattices A B C) C) B)) ) ) ) ) ) ) ).
tt(t53_borsuk_4,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) & (r2_hidden C A))  => (r1_borsuk_3 (k1_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_domain_1 (u1_struct_0 (k15_euclid 2)) B))) (k1_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) A (k6_domain_1 (u1_struct_0 (k15_euclid 2)) C))))) ) ) ) ) ) ) ).
tt(t53_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ( (A = (k2_rcomp_1 k2_xxreal_0 C))  &  (B = (k2_rcomp_1 C k1_xxreal_0)) )  => (r1_connsp_1 k3_topmetr A B)) ) ) ) ) ) ) ).
tt(t53_borsuk_6,ax, (k6_borsuk_6 = a_0_12_borsuk_6) ).
tt(t53_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = (k4_struct_0 (k15_euclid 2))) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k3_euclid_3 (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) B)) = (k7_real_1 (k7_real_1 A (k3_euclid_3 B)) (k8_real_1 (k8_real_1 2 k32_sin_cos) C))) ) ) ) ) ) ) ) ) ) ).
tt(t53_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k6_bvfunc_2 A (k7_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t53_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_subset_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k5_enumset1 C D E F G H I))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (C = I) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (D = I) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (E = I) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (F = I) )  &  ( (~  (G = H) )  &  ( (~  (G = I) )  &  ( (~  (H = I) )  &  ( ((k15_bvfunc_1 A J (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H) I)) = (k15_bvfunc_1 A K (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H) I)))  & (r1_xboole_0 (k15_bvfunc_1 A K (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A J (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k3_xboolean (k9_xboolean A B)) = (k5_xboolean A B)) ) ) ) ) ).
tt(t53_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k5_bvfunc26 A C D)) (k5_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A (k2_bvfunc_1 A C D))) (k2_bvfunc_1 A (k2_bvfunc_1 A (k1_bvfunc_1 A B) C) D)))) ) ) ) ) ) ) ) ).
tt(t53_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_finseq_1 E (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) B)) (k12_finseq_1 (k3_cqc_lang A) C))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) D)) (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) E (k12_finseq_1 (k3_cqc_lang A) (k9_cqc_lang A B D))) (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_card_1,ax, (5 = (k3_enumset1 k1_xboole_0 1 2 3 4)) ).
tt(t53_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] : (r1_xxreal_0 (k5_card_1 (k3_enumset1 A B C D E)) 5)) ) ) ) ) ).
tt(t53_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k4_card_3 B)) & (r2_hidden C (k8_card_3 B)))  => (r2_hidden (k1_funct_4 A C) (k4_card_3 B))) ) ) ) ) ) ) ).
tt(t53_card_fin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finset_1 B)) )  =>  (! [C:$i] :  ((v1_finset_1 C) =>  (! [D:$i] :  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ( ((k9_xtuple_0 B) = C)  & (r2_hidden D (k9_xtuple_0 B)))  =>  ((r1_xxreal_0 A k6_numbers) |  ((k3_card_fin (k23_binop_2 A 1) B) = (k23_binop_2 (k3_card_fin (k23_binop_2 A 1) (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) (k1_tarski D)))) (k3_card_fin A (k1_yellow20 (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) (k1_tarski D))) (k7_funcop_1 (k6_subset_1 (k9_xtuple_0 B) (k1_tarski D)) (k1_funct_1 B D)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_cat_1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_cat_1 D A C B) &  ((k2_cat_1 A C B) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_cat_3 D B C A) =>  ( ((r1_cat_3 B C A D) &  (! [E:$i] :  ((r2_hidden E A) => (v10_cat_1 (k4_graph_1 B (k7_partfun1 (u4_struct_0 B) D E)) B)) ) )  => (v10_cat_1 C B)) ) ) ) ) ) ) ) ).
tt(t53_cat_4,ax, (! [A:$i] :  (! [B:$i] : (v6_cat_4 (k23_cat_4 A B))) ) ).
tt(t53_catalan2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_series_1 A) & (v1_series_1 B))  =>  ((v1_series_1 (k4_catalan2 A B)) &  ((k4_series_1 (k4_catalan2 A B)) = (k11_binop_2 (k4_series_1 A) (k4_series_1 B))) ) ) ) ) ) ) ).
tt(t53_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k19_valued_1 B k2_numbers k2_numbers C D) A) (k19_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) (k2_partfun1 B k2_numbers D A))) &  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k19_valued_1 B k2_numbers k2_numbers C D) A) (k19_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) D)) & (r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k19_valued_1 B k2_numbers k2_numbers C D) A) (k19_valued_1 B k2_numbers k2_numbers C (k2_partfun1 B k2_numbers D A)))) ) ) ) ) ) ) ) ) ).
tt(t53_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ((r1_xxreal_0 (k2_nat_1 A 1) B) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C (k2_nat_1 A 1))) =>  ((r2_hidden D (k10_chain_1 B C A (k6_domain_1 (k4_chain_1 B C (k2_nat_1 A 1)) E))) <=> (r1_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k2_chord A (k1_tarski C))) <=> (r2_hidden C (k2_chord A (k1_tarski B)))) ) ) ) ) ).
tt(t53_circcmb3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ( ((v6_circcmb3 F) & (m1_circcmb3 F D))  =>  (~  ( (~  ( (~ (r2_hidden A (u1_struct_0 F)))  & (v1_xtuple_0 A)) )  &  ( (~  ( (~ (r2_hidden B (u1_struct_0 F)))  & (v1_xtuple_0 B)) )  &  ( (~  ( (~ (r2_hidden C (u1_struct_0 F)))  & (v1_xtuple_0 C)) )  &  (~ (v6_circcmb3 (k6_circcmb3 D F (k4_circcmb3 3 D E (k11_finseq_1 A B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A k6_margrel1) k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) k6_margrel1)))) )  => (v3_circcomb (k5_circcomb C B))) ) ) ) ) ) ).
tt(t53_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) => (r3_circtrm1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( ((r1_tarski A B) & (v1_ordinal1 B))  => (r1_tarski (k5_classes1 A) B)) ) ) ).
tt(t53_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ((r1_tarski A B) | (r2_hidden B A)) ) ) ) ) ).
tt(t53_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ( ((u1_struct_0 C) = B)  => (v6_clvect_1 B A)) ) ) ) ) ) ) ).
tt(t53_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden B (k6_clvect_2 A C D)) => (r2_hidden B (k5_clvect_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t53_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_normsp_1 A (k1_bhsp_4 A (k6_clvect_3 A B C)) (k2_nat_1 D 1)) = (k5_algstr_0 A (k1_normsp_1 A (k6_clvect_3 A (k1_bhsp_4 A B) C) (k2_nat_1 D 1)) (k1_normsp_1 A (k1_bhsp_4 A (k6_clvect_3 A (k1_bhsp_4 A B) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers C 1) C))) D))) ) ) ) ) ) ) ) ) ).
tt(t53_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v6_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) (k11_cohsp_1 A B C)) & (r2_hidden (k4_tarski E G) (k11_cohsp_1 A B C)))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k15_complex1 A)) = (k17_complex1 A)) ) ) ).
tt(t53_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k17_complex1 (k2_complex2 B A)) = (k17_complex1 B)) ) ) ) ) ).
tt(t53_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k5_algstr_0 k1_complfld A B)) = (k5_algstr_0 k1_complfld (k2_complfld A) (k2_complfld B))) ) ) ) ) ).
tt(t53_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k12_seq_4 (k12_seq_4 A C) B) = (k12_seq_4 A (k5_binop_2 B C))) ) ) ) ) ) ) ).
tt(t53_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) => (r2_hidden k6_numbers (k2_afinsq_1 (k9_compos_1 A B)))) ) ) ) ).
tt(t53_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) 2) = (k5_compos_0 (u1_compos_1 A) D 2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_newton (k2_xcmplx_0 (k20_sin_cos A) (k3_xcmplx_0 (k17_sin_cos A) k7_complex1)) B) = (k2_xcmplx_0 (k20_sin_cos (k3_xcmplx_0 B A)) (k3_xcmplx_0 (k17_sin_cos (k3_xcmplx_0 B A)) k7_complex1))) ) ) ) ) ).
tt(t53_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ((v1_xboole_0 B) => (v1_xboole_0 (k6_comput_1 B C A D))) ) ) ) ) ) ) ) ) ).
tt(t53_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  ((v1_series_1 (k7_comseq_3 A)) &  ((v1_series_1 (k8_comseq_3 A)) &  ((k11_comseq_3 A) = (k2_xcmplx_0 (k4_series_1 (k7_comseq_3 A)) (k3_xcmplx_0 (k4_series_1 (k8_comseq_3 A)) k7_complex1))) ) ) ) ) ) ).
tt(t53_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A B (k6_rusub_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t53_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) => (r3_cqc_the1 A B (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A D E)) (k6_cqc_lang A (k7_cqc_lang A C E)))))) ) ) ) ) ) ) ) ) ) ).
tt(t53_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A (k12_cqc_lang A C B)) (k11_cqc_lang A C (k6_cqc_lang A B))) A) & (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C (k6_cqc_lang A B)) (k6_cqc_lang A (k12_cqc_lang A C B))) A)) ) ) ) ) ) ) ).
tt(t53_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r7_cqc_the3 A B C) <=> (r7_cqc_the3 A (k6_cqc_lang A B) (k6_cqc_lang A C))) ) ) ) ) ) ) ).
tt(t53_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k15_csspace A B C))) ) ) ) ) ) ).
tt(t53_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A B) = (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k18_sin_cos (k8_real_1 2 A)) (k18_sin_cos (k8_real_1 2 B)))) (k9_real_1 A B))) ) ) ) ) ).
tt(t53_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k16_sin_cos) A B) = (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k8_real_1 (k8_real_1 3 (k21_sin_cos (k10_real_1 (k7_real_1 A B) 2))) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k8_real_1 3 (k7_real_1 A B)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 (k9_real_1 A B)) 2))))) (k9_real_1 A B))) ) ) ) ) ).
tt(t53_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k5_diff_1 (k5_diff_1 C A) A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers (k3_diff_1 C A) B) (k3_funct_2 k1_numbers k1_numbers (k4_diff_1 C A) B))) ) ) ) ) ) ) ).
tt(t53_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v4_dilworth A) & (l1_orders_2 A)) ) )  =>  (? [B:$i] :  ( ((v5_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  &  ((k1_card_1 B) = (k2_dilworth A)) ) ) ) ) ).
tt(t53_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  (! [E:$i] :  ( ( (D = (k6_domain_1 (k1_zfmisc_1 (k6_ec_pf_1 A B C)) (k6_eqrel_1 (k6_ec_pf_1 A B C) (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C) (k4_domain_1 k5_numbers k5_numbers k5_numbers k6_numbers 1 k6_numbers))))  &  (E = (a_3_1_ec_pf_1 A B C)) )  =>  ((r1_xxreal_0 A 3) |  ( ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A)))  | (r1_xboole_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m2_subset_1 D (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (~  ( (C = (k6_int_1 3 A))  &  ( ((k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) = k6_numbers)  &  ( (~  ((k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) = k6_numbers) )  &  ((k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) 2)) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) D) 2))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k21_ens_1 A (k4_cat_1 A B) C) = (k17_ens_1 A B C))  &  ((k21_ens_1 A C (k4_cat_1 A B)) = (k18_ens_1 A B C)) ) ) ) ) ) ) ) ).
tt(t53_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v2_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k8_matrix_1 k1_numbers (k5_entropy1 A) B) = (k4_entropy1 (k8_matrix_1 k1_numbers A B))) ) ) ) ) ) ).
tt(t53_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k6_enumset1 A A A A A A B C) = (k1_enumset1 A B C)) ) ) ) ).
tt(t53_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k5_setfam_1 B (k7_relset_1 (k1_zfmisc_1 A) (k1_zfmisc_1 B) (k2_funct_3 A B C) D)) = (k7_relset_1 A B C (k5_setfam_1 A D))) ) ) ) ) ) ) ) ).
tt(t53_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_rvsum_1 B (k4_struct_0 (k15_euclid A)))) ) ) ) ).
tt(t53_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((k9_euclid_3 A B C D) = (a_4_2_euclid_3 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t53_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k6_euclid 3 A) = (k1_euclid_8 (k7_binop_2 (k1_seq_1 A 1)) (k7_binop_2 (k1_seq_1 A 2)) (k7_binop_2 (k1_seq_1 A 3)))) ) ) ).
tt(t53_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (A = (k19_euclid (k17_euclid A) (k18_euclid A))) ) ) ).
tt(t53_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ( (~  (D = B) )  & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) =>  ( ((r2_hidden (k4_tarski C B) (k6_exchsort D E)) & (r2_hidden C A))  <=> (r2_hidden (k4_tarski C A) (k6_exchsort D (k10_funct_7 E A B)))) ) ) ) ) ) ) ) ) ).
tt(t53_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_finset_1 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k4_finseq_2 3 D) D) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 D) D)))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (u3_msualg_1 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C))))) => (v1_circuit2 (k6_circuit2 (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)) F) (k5_circcomb E (k11_finseq_1 A B C)) (k7_circcomb 3 D E (k11_finseq_1 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t53_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k1_seq_1 (k1_fcont_1 A B) C) (k1_seq_1 (k1_fcont_1 A B) D))) ) ) ) ) ) ) ) ) ).
tt(t53_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k7_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k24_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t53_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos B) k6_numbers))  &  (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos B) (k1_real_1 1))) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k19_sin_cos) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 2)) (k10_real_1 1 2))) A) B) = (k10_real_1 (k2_newton (k1_seq_1 k16_sin_cos B) 3) (k7_real_1 1 (k1_seq_1 k19_sin_cos B)))) ) ) ) ) ) ) ) ).
tt(t53_fib_num2,ax, ((k5_fib_num2 k6_numbers) = k1_xboole_0) ).
tt(t53_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((k3_fib_num3 (k4_nat_1 C A) (k4_nat_1 C B) D) = (k4_nat_1 C (k3_fib_num3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t53_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v12_lattices A) => (v12_lattices (k6_filter_0 A B))) ) ) ) ) ).
tt(t53_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_filter_0 A B (k7_filter_0 A B C)) = C) ) ) ) ) ) ) ).
tt(t53_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  <=>  ( (~ (v2_struct_0 (k1_lattice2 A)))  &  ((v10_lattices (k1_lattice2 A)) &  ((v17_lattices (k1_lattice2 A)) & (l3_lattices (k1_lattice2 A))) ) ) ) ) ) ).
tt(t53_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_wellord2 (k2_finseq_1 A) (k2_finseq_1 B)) =>  (A = B) ) ) ) ) ) ).
tt(t53_finseq_2,ax, ((k1_finseq_2 3) = (k11_finseq_1 1 2 3)) ).
tt(t53_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k3_finseq_1 A) = (k2_xcmplx_0 C D))  &  (B = (k5_relat_1 A (k2_finseq_1 C))) )  =>  ((k3_finseq_1 B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t53_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_funct_1 A))  => (v2_funct_1 (k6_finseq_4 A B))) ) ) ) ).
tt(t53_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k7_partfun1 A (k2_finseq_5 A C B) 1) = B) ) ) ) ) ) ) ).
tt(t53_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ( (~  (B = C) )  =>  ((k2_finseq_5 A (k2_finseq_4 A B C) C) = (k12_finseq_1 A C)) ) ) ) ) ) ) ) ).
tt(t53_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v3_card_1 D C) & (m2_finseq_1 D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r7_binop_1 A F E) => (r2_relset_1 k5_numbers A (k4_finseqop A A (k2_finseqop A A A E D B) F) (k2_finseqop A A A E (k4_finseqop A A D F) (k3_funct_2 A A F B)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r3_fintopo6 A B C D E) =>  ((r1_xxreal_0 (k3_finseq_1 B) F) |  ((v2_fintopo6 (k2_rfinseq (u1_struct_0 A) F B) A) &  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (k2_rfinseq (u1_struct_0 A) F B)) C) &  ( ((k1_funct_1 (k2_rfinseq (u1_struct_0 A) F B) 1) = (k7_partfun1 (u1_struct_0 A) B (k2_nat_1 1 F)))  &  ((k1_funct_1 (k2_rfinseq (u1_struct_0 A) F B) (k3_finseq_1 (k2_rfinseq (u1_struct_0 A) F B))) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski (k6_flang_1 A (k8_flang_1 A B) B) (k8_flang_1 A B)) & (r1_tarski (k6_flang_1 A B (k8_flang_1 A B)) (k8_flang_1 A B))) ) ) ) ).
tt(t53_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k5_afinsq_1 A) (k1_flang_2 B C D E)) <=>  ((r2_hidden (k5_afinsq_1 A) C) &  ((r1_xxreal_0 D E) &  ( ((r2_hidden (k2_flang_1 B) C) &  (~ (r1_xxreal_0 E k6_numbers)) )  |  ((r1_xxreal_0 D 1) & (r1_xxreal_0 1 E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k8_flang_1 A B) = (k4_subset_1 (k8_afinsq_1 A) (k4_flang_1 A (k2_flang_1 A)) (k2_flang_3 A B))) ) ) ) ).
tt(t53_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ((r1_tarski B C) &  ((r1_tarski A (k3_finseq_2 B)) &  ((v5_relat_1 D A) & (v1_setfam_1 A)) ) )  =>  ( (D = k1_xboole_0)  |  ((k1_funct_1 (k8_fomodel0 B) D) = (k1_funct_1 (k8_fomodel0 C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v8_struct_0 G) & (l2_fsm_1 G A B)) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 G)) =>  ( ( (G = (k13_fsm_1 A B D E))  &  ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  (F = H) ) )  =>  ((k4_fsm_1 A B D F C) = (k4_fsm_1 A B G H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  ((k3_funct_2 B A (k10_funcop_1 A B C E D) F) = (k5_binop_1 A C E (k3_funct_2 B A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (B = (k6_relat_1 A C))  <=>  ( (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) <=>  ((r2_hidden D (k9_xtuple_0 C)) & (r2_hidden (k1_funct_1 C D) A)) ) )  &  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 B D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ( ( ((k2_relset_1 A B) = A)  &  ((k2_relset_1 A C) = A) )  =>  ((k2_relset_1 A (k4_relset_1 A A A A C B)) = A) ) ) ) ) ) ) ).
tt(t53_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ((k13_funct_3 (k9_funct_3 A B) (k10_funct_3 A B)) = (k4_relat_1 (k2_zfmisc_1 A B))) ) ) ).
tt(t53_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))))  =>  ((k2_funct_4 (k2_funct_4 D)) = D) ) ) ) ) ) ).
tt(t53_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k9_xtuple_0 C) (k2_zfmisc_1 A B)) &  ((r1_tarski (k9_xtuple_0 D) (k2_zfmisc_1 A B)) &  ((k3_funct_5 C) = (k3_funct_5 D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t53_funct_6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r2_wellord2 (k4_card_3 (k9_funct_6 A B)) (k1_funct_2 A (k4_card_3 B)))) ) ) ).
tt(t53_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k5_funct_7 (k10_finseq_1 B C) A) = (k11_finseq_1 A (k1_funct_1 B A) (k1_funct_1 C (k1_funct_1 B A)))) ) ) ) ) ) ).
tt(t53_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v4_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v4_funct_8 (k52_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t53_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k2_fuzzy_1 (k2_zfmisc_1 A B) C (k5_fuzzy_2 A B)) (k5_fuzzy_2 A B)) &  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k1_fuzzy_1 (k2_zfmisc_1 A B) C (k5_fuzzy_2 A B)) C) &  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k2_fuzzy_1 (k2_zfmisc_1 A B) C (k4_fuzzy_2 A B)) C) & (r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k1_fuzzy_1 (k2_zfmisc_1 A B) C (k4_fuzzy_2 A B)) (k4_fuzzy_2 A B))) ) ) ) ) ) ) ) ) ).
tt(t53_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B)))) => (m2_xxreal_2 k6_numbers (k7_relset_1 (u1_struct_0 A) k7_numbers B C))) ) ) ) ) ) ) ).
tt(t53_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k10_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A D) C) = (k5_finseq_2 (u1_struct_0 B) A (k6_algstr_0 B C D))) ) ) ) ) ) ) ) ) ).
tt(t53_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) ) ) )  =>  (! [H:$i] :  ((m1_genealg1 H G) =>  (! [I:$i] :  ((m1_genealg1 I G) => (m1_genealg1 (k6_genealg1 G H I A B C D E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (? [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C)))) &  (? [E:$i] :  ((m1_subset_1 E k6_margrel1) &  (? [F:$i] :  ((m1_subset_1 F k6_margrel1) &  (? [G:$i] :  ((m1_subset_1 G k6_margrel1) &  ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  ( (G = (k1_funct_1 D C))  &  (~  ( ((k1_twoscomp (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) (k5_facirc_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D 2) (k21_gfacirc1 A B C)) = (k1_binarith (k1_binarith (k10_margrel1 E (k9_margrel1 F)) (k10_margrel1 (k9_margrel1 F) G)) (k10_margrel1 G E)))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) = (k10_margrel1 E (k9_margrel1 F)))  &  ( ((k1_funct_1 (k5_facirc_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 F) G))  &  ((k1_funct_1 (k5_facirc_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) = (k10_margrel1 G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) B)) =>  ( ((k24_glib_000 A C) = (k6_glib_000 A))  &  ((k25_glib_000 A C) = (k6_subset_1 (k7_glib_000 A) B)) ) ) ) ) ) ) ).
tt(t53_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k4_glib_001 A (k8_glib_001 A B 1 C)) = (k3_glib_001 A (k8_glib_001 A B D (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t53_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k6_glib_000 A)) => (r1_tarski (k14_glib_003 A) (k14_glib_003 (k13_glib_003 A B C)))) ) ) ) ) ).
tt(t53_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1) (k19_euclid k6_numbers 1)))))) ) ) ) ) ) ).
tt(t53_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) (k2_nat_1 B 1)))  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2))) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_graph_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k7_partfun1 A (k4_graph_2 A B C) 1) = (k7_partfun1 A B 1)) ) ) ) ) ) ) ).
tt(t53_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  (! [C:$i] :  ((m2_finseq_2 C (u4_struct_0 A) (k9_graph_3 A)) =>  (~  ( (~ (r1_xboole_0 (k1_graph_3 A (k10_xtuple_0 B)) (k1_graph_3 A (k10_xtuple_0 C))))  &  ((r1_xboole_0 (k10_xtuple_0 B) (k10_xtuple_0 C)) &  ( (~  ( (B = k1_xboole_0)  &  (C = k1_xboole_0) ) )  & (v1_xboole_0 (k11_graph_3 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t53_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_graph_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v1_finset_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k3_finseq_2 (u4_struct_0 C))))) )  =>  (~  ( (F = (k5_graph_5 C D E A))  &  (! [G:$i] :  ((m2_finseq_1 G (u4_struct_0 C)) =>  (~  ((r2_hidden G F) &  (! [H:$i] :  ((m2_finseq_1 H (u4_struct_0 C)) =>  ((r2_hidden H F) => (r1_xxreal_0 (k10_graph_5 C G B) (k10_graph_5 C H B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k3_groeb_2 A B C D E) (k6_polynom1 A C (k10_polynom1 A C (k5_termord A B C E) (k6_termord A B C D)) (k10_polynom1 A C (k5_termord A B C D) (k6_termord A B C E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k3_group_11 A C B) (k8_group_2 A C))) ) ) ) ) ) ).
tt(t53_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  => (v5_group_1 B)) ) ) ) ) ).
tt(t53_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (B = k1_xboole_0) )  =>  ((k5_group_3 A B (k1_group_1 A)) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ) ) ).
tt(t53_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((u1_struct_0 (k8_group_4 A B C)) = (k7_group_4 A B C)) ) ) ) ) ) ) ).
tt(t53_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r2_hidden (k1_group_1 A) (k5_group_5 A B C))) ) ) ) ) ) ).
tt(t53_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r1_xxreal_0 (k7_group_1 (k10_group_6 A B C)) (k7_group_1 A))) ) ) ) ) ) ).
tt(t53_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v4_group_9 C A B) & (m1_group_9 C A B))  => (v2_funct_2 (k12_group_9 A B C) (u1_struct_0 (k10_group_9 A B C)))) ) ) ) ) ).
tt(t53_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (~  ( (! [F:$i] :  ((r2_hidden F E) =>  ( (? [G:$i] :  ( ((v3_glib_002 G) & (m1_glib_000 G A))  &  (F = (k24_glib_000 A G)) ) )  &  (~  ( (~  ((r2_hidden B F) & (r2_hidden C F)) )  &  ( (~  ((r2_hidden B F) & (r2_hidden D F)) )  &  (~  ((r2_hidden C F) & (r2_hidden D F)) ) ) ) ) ) ) )  &  ((k1_setfam_1 E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k12_bilinear k1_complfld A B) = (k11_bilinear k1_complfld A A B)) ) ) ) ) ).
tt(t53_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) A) 2) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) A) (k1_real_1 2))))) ) ).
tt(t53_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (~  ((r1_xxreal_0 1 (k2_hurwitz k1_complfld A)) &  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) &  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 B)))  & (r1_xxreal_0 (k17_complex1 (k2_polynom4 k1_complfld (k7_hurwitz A) B)) (k17_complex1 (k2_polynom4 k1_complfld A B)))) ) )  & (v1_hurwitz A)) ) ) ) ) ).
tt(t53_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_vectsp_1 A) & (l6_algstr_0 A)) )  =>  ((k9_ideal_1 A (k6_domain_1 (u1_struct_0 A) (k5_struct_0 A))) = (u1_struct_0 A)) ) ) ).
tt(t53_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r2_incsp_1 A D C) &  (~ (r1_incsp_1 A D B)) ) ) ) ) ) ) ) ) ) ).
tt(t53_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((r1_xxreal_0 k6_numbers (k2_int_1 A)) &  ((r1_xxreal_0 k6_numbers (k1_int_1 A)) &  ((m2_subset_1 (k2_int_1 A) k1_numbers k5_numbers) & (m2_subset_1 (k1_int_1 A) k1_numbers k5_numbers)) ) ) ) ) ) ).
tt(t53_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k4_numbers)))  =>  ((r1_int_4 A C) => (r1_int_4 A (k2_measure6 C B))) ) ) ) ) ) ) ).
tt(t53_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k7_real_1 (k1_seq_1 k16_sin_cos B) 1))) ) ) ) ) ) ) ) ).
tt(t53_integr13,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B G) &  ((r1_tarski G (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1))) &  ((r2_relset_1 k1_numbers k1_numbers E (k3_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) A))) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 F H) = (k10_real_1 H A))  &  ((k1_seq_1 C H) = 1) ) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers F (k1_taylor_1 2))) &  ( (G = (k1_relset_1 k1_numbers E))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B))) ) ) ) ) )  =>  ( (A = k6_numbers)  |  ((k2_integra5 B E) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k10_real_1 A 2)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers C D) k3_taylor_1) (k10_real_1 A 2)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k9_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t53_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) F) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) F (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers F)) &  ((r2_hidden D (k3_integra5 B C)) & (r2_hidden E (k3_integra5 B C))) ) ) ) )  =>  ((k6_integr18 (k4_real_ns1 A) F B E) = (k3_rlvect_1 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) F B D) (k6_integr18 (k4_real_ns1 A) F D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((v1_seq_2 (k2_partfun1 B k1_numbers D B)) & (v1_seq_2 (k2_partfun1 B k1_numbers E B))) )  => (r1_xxreal_0 (k1_seq_1 (k4_integra1 B (k3_valued_1 B k1_numbers k1_numbers D E) C) A) (k7_real_1 (k1_seq_1 (k4_integra1 B D C) A) (k1_seq_1 (k4_integra1 B E C) A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A k24_sin_cos) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k24_sin_cos (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers k24_sin_cos (k5_seq_4 A)))) ) ) ).
tt(t53_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k7_real_1 A G))  &  (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C A))) = F)  &  ( (F = (k1_relset_1 k1_numbers E))  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 E G) = (k10_real_1 G (k7_real_1 A G))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B))) ) ) ) ) )  =>  ((k2_integra5 B E) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C A)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C A)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r2_hidden k1_xboole_0 (k3_interva1 A B (k10_interva1 A B)))) ) ) ) ).
tt(t53_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k4_intpro_1 A (k4_intpro_1 B C)) (k4_intpro_1 (k4_intpro_1 A B) C)) k8_intpro_1)) ) ) ) ) ) ).
tt(t53_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k7_real_1 1 A)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid D)) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t53_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) &  ((r2_hidden B C) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) & (r1_xxreal_0 k6_numbers (k18_euclid B))) ) ) )  =>  ((r1_xxreal_0 k6_numbers (k17_euclid A)) |  ((r1_xxreal_0 k6_numbers (k17_euclid B)) |  ( ( (~ (r1_xxreal_0 (k17_euclid A) (k17_euclid B)))  &  (~ (r1_xxreal_0 (k18_euclid A) (k18_euclid B))) )  | (r1_jordan6 C A B)) ) ) ) ) ) ) ) ) ) ).
tt(t53_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 (k1_sppol_2 A B C D))))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 (k1_sppol_2 A B C D)))))))) )  =>  (~  ((v3_tops_2 E k5_topmetr (k1_pre_topc (k15_euclid 2) (k8_jordan6 (k1_sppol_2 A B C D)))) &  ( ((k1_funct_1 E k6_numbers) = (k18_pscomp_1 (k1_sppol_2 A B C D)))  &  ( ((k1_funct_1 E 1) = (k22_pscomp_1 (k1_sppol_2 A B C D)))  &  ( ((k2_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k8_jordan6 (k1_sppol_2 A B C D)))) E) = (k8_jordan6 (k1_sppol_2 A B C D)))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 k6_numbers (k10_real_1 1 2))) =>  ((k1_funct_1 E F) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k19_euclid A C) (k9_real_1 1 (k8_real_1 2 F))) (k1_rlvect_1 (k15_euclid 2) (k19_euclid A D) (k8_real_1 2 F)))) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 (k10_real_1 1 2) 1)) =>  ((k1_funct_1 E F) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k19_euclid A D) (k9_real_1 1 (k9_real_1 (k8_real_1 2 F) 1))) (k1_rlvect_1 (k15_euclid 2) (k19_euclid B D) (k9_real_1 (k8_real_1 2 F) 1)))) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))) =>  ((r1_xxreal_0 k6_numbers (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) C) (k6_xcmplx_0 D C)) 2)) &  ((r1_xxreal_0 (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) C) (k6_xcmplx_0 D C)) 2) 1) &  ((k1_funct_1 E (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) C) (k6_xcmplx_0 D C)) 2)) = F) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) =>  ((r1_xxreal_0 k6_numbers (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) A) (k6_xcmplx_0 B A)) 2) (k10_real_1 1 2))) &  ((r1_xxreal_0 (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) A) (k6_xcmplx_0 B A)) 2) (k10_real_1 1 2)) 1) &  ((k1_funct_1 E (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) A) (k6_xcmplx_0 B A)) 2) (k10_real_1 1 2))) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((v5_pre_topc F k5_topmetr (k15_euclid 2)) & (v2_funct_1 F)) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((v5_pre_topc (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) k5_topmetr (k15_euclid 2)) & (v2_funct_1 (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xboole_0 (k6_topreal1 C) (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t53_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k10_xtuple_0 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) 2 (k4_finseq_4 (k1_jordan1e A B) (k1_jordan5c (k3_topreal1 2 (k1_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))))))) => (r1_xxreal_0 (k17_euclid C) (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2))) ) ) ) ) ) ) ) ).
tt(t53_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 D 1) E)) ) ) )  =>  ((r1_xboole_0 (k3_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k2_nat_1 D 1) (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_jordan1j,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A))  =>  ((r1_xxreal_0 (k4_finseq_4 B C) D) |  ( ((k3_gobrd13 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k3_gobrd13 B A D))  &  ((k2_gobrd13 (k1_finseq_5 (u1_struct_0 (k15_euclid 2)) B C) A D) = (k2_gobrd13 B A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r1_xxreal_0 2 A) &  (C = (k6_subset_1 (k1_euclid A) (a_2_3_jordan2c A B))) )  => (v2_connsp_1 C (k15_euclid A))) ) ) ) ) ) ) ).
tt(t53_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_jordan4 C D A B) & (r2_jordan4 C E A B))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ((v1_topreal2 A) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) B (k9_jordan6 A)) = (k2_tarski (k18_pscomp_1 A) (k22_pscomp_1 A)))  &  ((k2_xboole_0 B (k9_jordan6 A)) = A) ) )  =>  (B = (k8_jordan6 A)) ) ) ) ) ) ).
tt(t53_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k6_pscomp_1 (k2_jgraph_6 A B C D)) = A) ) ) ) ) ) ) ) ) ) ).
tt(t53_kurato_1,ax,(r1_subset_1 (k4_enumset1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)))) (k1_tarski k6_kurato_1))).
tt(t53_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  ( ((k2_partfun1 A (u1_struct_0 C) D B) = (k2_partfun1 A (u1_struct_0 C) E B))  =>  ((k2_lattice2 A C B D) = (k2_lattice2 A C B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v4_lattice3 B) &  ((v5_lattice3 B) & (l3_lattices B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k4_lattices B C (k15_lattice3 B A)) = (k15_lattice3 B (a_3_7_lattice3 A B C)))  &  ((k4_lattices B (k15_lattice3 B A) C) = (k15_lattice3 B (a_3_8_lattice3 A B C))) ) ) ) ) ) ) ).
tt(t53_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (v5_lexbfs (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k13_lexbfs A (k16_lexbfs A) B)) A)) ) ) ) ).
tt(t53_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v8_limfunc1 A) &  ((v8_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) ) ) ) ) ) )  =>  ((v8_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)) & (v7_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t53_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_limfunc2 B A) =>  ((r4_limfunc2 (k32_valued_1 k1_numbers k1_numbers B) A) &  ((k2_limfunc2 (k32_valued_1 k1_numbers k1_numbers B) A) = (k1_real_1 (k2_limfunc2 B A))) ) ) ) ) ) ) ).
tt(t53_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  ((v3_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ((v3_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k4_limfunc1 B)) ) ) ) ) ) ) ).
tt(t53_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r2_hidden D (k9_lpspace1 A B C)) &  ((k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D)) = k6_numbers) )  => (r1_lpspace1 A B C D (k8_lpspace1 A k6_numbers))) ) ) ) ) ) ) ) ) ).
tt(t53_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k12_lpspace2 A B C D))) =>  ( (? [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  &  ((r2_hidden F (k1_lpspace2 A B C D)) &  (E = (k5_lpspace2 A B C F D)) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (~  ((r2_hidden F E) &  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ((r1_xxreal_0 k6_numbers G) &  ( (G = (k1_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers F))))  &  ((k1_normsp_0 (k12_lpspace2 A B C D) E) = (k4_power G (k10_real_1 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) => (r8_ltlaxio1 C (k3_hilbert1 (k4_ltlaxio1 (k2_ltlaxio1 A) (k2_ltlaxio1 B)) (k2_ltlaxio1 (k4_ltlaxio1 A B))))) ) ) ) ) ) ).
tt(t53_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k6_cqc_lang A (k6_cqc_lang A B)) A) <=> (v2_cqc_the1 B A)) ) ) ) ) ).
tt(t53_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_mathmorp A (k5_mathmorp A B C) C) = (k5_mathmorp A B C)) ) ) ) ) ) ) ).
tt(t53_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) D) => (r2_matrix10 (k4_matrix10 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t53_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 A)) & (r2_hidden F (k2_finseq_1 A)))  =>  ( (E = F)  |  ((k12_matrix_3 A B D) = (k12_matrix_3 A B (k3_matrix11 E A A (u1_struct_0 B) D (k4_fvsum_1 (k1_matrix_1 D) B (k8_matrix_1 (u1_struct_0 B) D E) (k10_fvsum_1 (k1_matrix_1 D) B (k8_matrix_1 (u1_struct_0 B) D F) C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrix13,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_setfam_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers))) )  =>  ((v1_finset_1 (k8_relat_1 (k5_matrix13 B) A)) &  ((v1_setfam_1 (k8_relat_1 (k5_matrix13 B) A)) & (m1_subset_1 (k8_relat_1 (k5_matrix13 B) A) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ).
tt(t53_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (~  ( (~  (C = (k11_matrix_1 B A)) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (~  ((v1_matrix_6 D A B) &  ((v1_matrix_6 E A B) &  ( ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) 1 1) = (k5_struct_0 B))  &  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) F 1) = (k4_struct_0 B)) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 F 1) |  ((k3_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B (k4_matrix_6 A B D C) E) 1 F) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrix15,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v6_struct_0 E))  &  ((v13_algstr_0 E) &  ((v33_algstr_0 E) &  ((v3_group_1 E) &  ((v5_group_1 E) &  ((v4_vectsp_1 E) &  ((v5_vectsp_1 E) &  ((v2_rlvect_1 E) &  ((v3_rlvect_1 E) &  ((v4_rlvect_1 E) & (l6_algstr_0 E)) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 E) B C) =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 E) B D) =>  ((r2_hidden A (k4_matrix15 E F G)) =>  ((r1_xxreal_0 B k1_xboole_0) | (m1_matrix_1 A (u1_struct_0 E) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v12_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) B B) =>  ( ((r2_hidden (k4_tarski C D) (k2_matrix_1 E)) &  ( (C = D)  & (v5_matrix16 E A)) )  =>  ((k3_matrix_1 (u1_struct_0 A) E C D) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k1_matrix_4 A B D) = (k3_matrix_3 A C (k2_matrix_3 A D))) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) => (r1_matrix_6 A B (k4_matrix_6 A B C C) D)) ) ) ) ) ) ) ) ) ).
tt(t53_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k2_matrix_6 A B C D)) = (k3_rlvect_1 B (k1_matrix_8 A B C) (k1_matrix_8 A B D))) ) ) ) ) ) ) ) ) ).
tt(t53_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) C D) E) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k12_matrix_3 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t53_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((k1_matrixc1 (k13_matrixc1 A B C)) = (k13_matrixc1 (k1_complsp2 A) (k1_complsp2 B) (k1_matrixc1 C))) ) ) ) ) ) ) ) ).
tt(t53_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ((k12_matrix_3 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) B)) A (k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) B)) = (k3_group_4 A (k22_matrixj1 A B))) ) ) ) ) ).
tt(t53_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_matrix_1 B) k6_numbers))  &  ( ( ((k1_matrix_1 B) = (k3_finseq_1 A))  |  ((k3_finseq_1 (k4_matrix_1 k1_numbers B)) = (k3_finseq_1 A)) )  &  (~  ((k11_matrixr1 B A) = (k12_matrixr1 (k4_matrix_1 k1_numbers B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t53_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 C) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k11_matrixr1 C (k10_rvsum_1 B A)) = (k10_rvsum_1 (k11_matrixr1 C B) A)) ) ) ) ) ) ) ) ) ).
tt(t53_matrprob,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 A B) 1)) ) ) ) ) ).
tt(t53_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((k4_zfmisc_1 A B C D) = (k4_zfmisc_1 E F G H))  =>  ( ((k4_zfmisc_1 A B C D) = k1_xboole_0)  |  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((v2_rcomp_1 A) <=> (v2_rcomp_1 (k2_measure6 A B))) ) ) ) ) ).
tt(t53_member_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k9_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k3_binop_2 A C) (k3_binop_2 A D) (k3_binop_2 B C) (k3_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t53_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_memstr_0 A B (k9_memstr_0 A B C D)) = (k2_nat_1 (k5_memstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t53_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 E A k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k2_numbers E k6_numbers)))  &  ( (! [F:$i] :  ((v7_ordinal1 F) => (r1_mesfun6c A B (k4_mesfunc5 A k2_numbers E F) D)) )  &  ((v2_mesfun9c E A) &  (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F D) => (v2_comseq_2 (k9_mesfun7c A E F))) ) ) ) ) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k1_mesfunc9 C D)) |  ( (! [F:$i] :  ((v7_ordinal1 F) => (r2_mesfun6c A B C (k4_mesfunc5 A k2_numbers E F))) )  &  ((r2_mesfun6c A B C (k10_mesfun7c A E)) &  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ((k8_nat_1 k2_numbers F G) = (k1_mesfun6c A B C (k4_mesfunc5 A k2_numbers E G))) ) )  &  ((v2_comseq_2 F) &  ((k3_comseq_2 F) = (k1_mesfun6c A B C (k10_mesfun7c A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_mesfunc5,ax, (! [A:$i] :  ((m2_finseq_1 A k7_numbers) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 k6_numbers (k12_supinf_2 A B))) ) )  => (r1_xxreal_0 k6_numbers (k4_extreal1 A))) ) ) ).
tt(t53_mesfunc6,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v2_mesfunc5 B) <=>  (! [C:$i] : (r1_xxreal_0 (k1_seq_1 B C) k6_numbers)) ) ) ) ) ).
tt(t53_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((u1_struct_0 (k15_midsp_1 A)) = (k10_midsp_1 A)) ) ) ).
tt(t53_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r1_relset_1 A A (k19_mmlquery A (k20_mmlquery A B C) (k18_mmlquery A B)) C)) ) ) ) ) ).
tt(t53_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_2 B) & (l1_modelc_2 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k15_modelc_2 (u1_modelc_2 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 B))))) )  =>  ((k21_modelc_2 B C (k6_modelc_2 A)) = (k22_modelc_2 B (k21_modelc_2 B C A))) ) ) ) ) ) ) ).
tt(t53_modelc_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k23_modelc_3 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 C))))) )  =>  ( ((v7_modelc_2 B) &  ((r2_hidden B (u1_modelc_3 C (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 C) D 1) C))) &  ( (! [E:$i] :  ((v7_ordinal1 E) => (r6_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C) (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 C) D (k1_nat_1 E 1)) C))) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden (k12_modelc_2 B) (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C)))) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 A E) |  ((r2_hidden (k11_modelc_2 B) (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C))) & (r2_hidden B (u1_modelc_3 C (k10_modelc_3 (k1_funct_1 D E) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (A = (k6_moebius1 A)) ) ) ).
tt(t53_monoid_0,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k7_monoid_0)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k7_monoid_0)) =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_algstr_0 k7_monoid_0 C D) = (k24_binop_2 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t53_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo B A) =>  ((v1_setwiseo (k21_monoid_1 A A A B) (k1_zfmisc_1 A)) &  ((r3_binop_1 (k1_zfmisc_1 A) (k6_domain_1 A (k4_binop_1 A B)) (k21_monoid_1 A A A B)) &  ((k4_binop_1 (k1_zfmisc_1 A) (k21_monoid_1 A A A B)) = (k6_domain_1 A (k4_binop_1 A B))) ) ) ) ) ) ) ) ).
tt(t53_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v2_relat_1 D) & (m3_pboole D A (k1_mboolean A C)))  =>  ( ((r1_pboole A B C) &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E D) => (r1_pboole A B E)) ) ) )  => (r1_pboole A B (k4_mssubfam A C D))) ) ) ) ) ) ) ) ).
tt(t53_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A B) D)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_funct_1 (u3_msualg_1 A B) D)) =>  ((r2_hidden (k4_tarski E F) (k2_msualg_4 A B (k10_msualg_6 A B C) D)) <=> (r2_rewrite1 (k1_msualg_4 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B) (k8_msualg_6 A B C) D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (v1_xboole_0 A))  &  ( (~  (A = 1) )  & (r1_xxreal_0 A 1)) ) ) ) ) ).
tt(t53_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k12_nat_3 (k3_int_2 B A)) = (k5_nat_3 k10_newton (k12_nat_3 B) (k12_nat_3 A))) ) ) ) ) ).
tt(t53_nat_4,ax, (! [A:$i] :  ((m1_trees_4 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  ( (~  ((k3_wsierp_1 A) = k6_numbers) )  =>  ((k11_nat_3 (k3_wsierp_1 A) B) = (k2_wsierp_1 (k1_nat_4 A B))) ) ) ) ) ) ).
tt(t53_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 A (k2_xcmplx_0 B C)) => (r1_xxreal_0 (k7_nat_d A C) B)) ) ) ) ) ) ) ).
tt(t53_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r10_ncfcont1 A C B) <=> (r10_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k2_numbers C B) B)) ) ) ) ) ) ).
tt(t53_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k14_prvect_2 A))) =>  (! [H:$i] :  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H)))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H)))) =>  (! [K:$i] :  ((m1_subset_1 K k1_numbers) =>  (! [L:$i] :  ((m1_subset_1 L k1_numbers) =>  ( ((r2_hidden H (k4_finseq_1 A)) &  ((v3_nfcont_1 D (k14_prvect_2 A)) &  ((r2_hidden E D) &  ((r1_tarski D (k1_relset_1 (u1_struct_0 (k14_prvect_2 A)) C)) &  ( (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k14_prvect_2 A))) =>  ((r2_hidden M D) => (r1_ndiff_5 A B H C M)) ) )  &  ( (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k14_prvect_2 A))) =>  ( (~ (r1_xxreal_0 K (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) M E))))  => (r2_hidden M D)) ) )  &  ( (! [M:$i] :  ((m1_subset_1 M (u1_struct_0 (k14_prvect_2 A))) =>  ( (~ (r1_xxreal_0 K (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) M E))))  => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A H)) B) (k5_algstr_0 (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A H)) B) (k6_ndiff_5 A B H C M) (k6_ndiff_5 A B H C E))) L)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A H) F) I))  &  (J = (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H))) (k3_ndiff_5 A (k5_ndiff_5 A H)) F)) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 K (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) F E))) |  ((r1_xxreal_0 K (k1_normsp_0 (k14_prvect_2 A) (k5_algstr_0 (k14_prvect_2 A) G E))) | (r1_xxreal_0 (k1_normsp_0 B (k5_algstr_0 B (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C G) (k7_partfun1 (u1_struct_0 B) C F)) (k17_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A H)) B (k6_ndiff_5 A B H C E) (k5_algstr_0 (k11_prvect_2 A (k5_ndiff_5 A H)) I J)))) (k11_binop_2 (k1_normsp_0 (k11_prvect_2 A (k5_ndiff_5 A H)) (k5_algstr_0 (k11_prvect_2 A (k5_ndiff_5 A H)) I J)) L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k5_nat_d (k6_nat_d A B) B) = B) ) ) ) ) ).
tt(t53_nfcont_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k1_relset_1 (u1_struct_0 A) B)) =>  ((k7_partfun1 k1_numbers B C) = (k1_normsp_0 A C)) ) ) )  => (r4_nfcont_1 A B (k1_relset_1 (u1_struct_0 A) B))) ) ) ) ) ).
tt(t53_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k10_normform A B (k5_setwiseo (k7_normform A) C D)) = (k5_setwiseo (k7_normform A) (k10_normform A B C) (k10_normform A B D))) ) ) ) ) ) ) ) ).
tt(t53_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 B) (u4_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C))))) )  => (r2_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 C)) (k11_oppcat_1 A C (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E)) (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 (k2_oppcat_1 C)) D (k11_oppcat_1 B C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t53_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((r9_orders_1 A B) & (v4_relat_2 A))  => (r7_orders_1 A B)) ) ) ) ).
tt(t53_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r8_orders_1 (u1_orders_2 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  => (r2_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(t53_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A B) =>  ( ( (~ (r1_ordinal1 C A))  &  (~ (r2_hidden C A)) )  | (r2_hidden (k5_ordinal3 A C) (k5_ordinal3 B C))) ) ) ) ) ) ) ) ).
tt(t53_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k4_ordinal5 (k5_afinsq_1 A)) = A) ) ) ).
tt(t53_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) => (v2_ordinal6 (k1_funct_1 A B))) ) )  =>  ( ((k9_xtuple_0 A) = k1_xboole_0)  | (v3_ordinal2 (k7_ordinal6 A))) ) ) ) ).
tt(t53_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t53_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r3_parsp_2 A B C D E) & (r3_parsp_2 A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k9_xtuple_0 A) (k9_xtuple_0 B)) =>  ((r1_partfun1 A B) <=>  (! [C:$i] :  ((r2_hidden C (k9_xtuple_0 A)) =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t53_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (~  ((r2_hidden C (k1_relset_1 A D)) &  ((r2_relset_1 A B D (k4_subset_1 (k2_zfmisc_1 A B) E F)) &  ( (~  ((k7_partfun1 B D C) = (k7_partfun1 B E C)) )  &  (~  ((k7_partfun1 B D C) = (k7_partfun1 B F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k4_pboole A B D) (k4_pboole A C D))) ) ) ) ) ) ) ) ).
tt(t53_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r2_pdiff_5 B A) & (r2_pdiff_5 C A))  =>  ((r3_pdiff_1 3 2 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 2 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k9_real_1 (k2_pdiff_5 B A) (k2_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t53_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A C) D) =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r2_pdiff_9 B A C))  <=> (r1_pdiff_6 B 1 A D)) ) ) ) ) ) ) ) ) ).
tt(t53_pepin,ax, ((k4_pepin 3) = 257) ).
tt(t53_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  &  ( ((k9_xtuple_0 C) = (k9_xtuple_0 B))  &  ( ((k10_xtuple_0 C) = (k9_xtuple_0 (k12_pnproc_1 B A)))  &  ( (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k1_funct_1 C D) = (k2_nat_1 A D)) ) ) )  & (v2_funct_1 C)) ) ) ) ) ) ) ) ) ).
tt(t53_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k28_polyform A) = (k6_polyform (k3_polyform (k4_xcmplx_0 1)) (k30_polyform A))) ) ) ).
tt(t53_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_polynom4 A (k5_polynom5 A B C) D) = (k2_polynom4 A B (k2_polynom4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t53_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r11_polyred A B C D) => (r11_polyred A B D C)) ) ) ) ) ) ) ) ) ).
tt(t53_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ((k2_xcmplx_0 (k5_power A B) (k5_power A C)) = (k5_power A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r6_pboole A (k11_pre_poly A B (k16_pre_poly A)) B)) ) ) ).
tt(t53_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_xcmplx_0 (k6_prepower A B) (k6_prepower A C)) = (k6_prepower A (k2_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t53_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ((k7_prob_3 A B) = (k6_setfam_1 A (k2_relset_1 (k9_setfam_1 A) B))) ) ) ) ).
tt(t53_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A D C) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B D) C) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ).
tt(t53_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k18_euclid (k10_pscomp_1 A)) = (k18_euclid (k25_pscomp_1 A)))  &  ( ((k18_euclid (k10_pscomp_1 A)) = (k18_euclid (k24_pscomp_1 A)))  &  ( ((k18_euclid (k25_pscomp_1 A)) = (k18_euclid (k24_pscomp_1 A)))  &  ( ((k18_euclid (k25_pscomp_1 A)) = (k18_euclid (k13_pscomp_1 A)))  &  ((k18_euclid (k24_pscomp_1 A)) = (k18_euclid (k13_pscomp_1 A))) ) ) ) ) ) ) ).
tt(t53_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (~  ( (~ (v1_xboole_0 A))  &  ((r6_pboole A (k4_pboole A (k2_pzfmisc1 A B C) D) (k1_pzfmisc1 A B)) & (r1_pboole A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r1_qc_lang2 A B C) => (r3_qc_lang2 A B C)) ) ) ) ) ) ) ).
tt(t53_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k5_qc_lang3 A (k12_qc_lang1 A)) = k1_xboole_0) ) ) ).
tt(t53_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k18_quatern2 (k26_quaterni A B) C) = (k26_quaterni (k18_quatern2 A C) (k18_quatern2 B C))) ) ) ) ) ) ) ).
tt(t53_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k28_quaterni (k29_quaterni A B)) = (k26_quaterni (k28_quaterni A) B)) ) ) ) ) ).
tt(t53_quaterni,ax, ((k31_quaterni k12_quaterni) = (k28_quaterni k12_quaterni)) ).
tt(t53_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (~  (E = (k4_struct_0 A)) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C (k8_group_1 A D (k11_algstr_0 A E))) = (k8_group_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k11_algstr_0 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [F:$i] :  ((m1_rcomp_3 F A B E) =>  ( ((m1_setfam_1 E (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 E (k4_topmetr A B)) &  ((v1_rcomp_3 E (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((r2_hidden C (k4_finseq_1 F)) & (r2_hidden D (k4_finseq_1 F))) ) ) ) )  =>  ((r1_xxreal_0 D C) | (r1_xxreal_0 (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) F C)) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) F D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 2)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1))) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 2)))) ) ) ) ).
tt(t53_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k10_xtuple_0 B) A) =>  ((k3_relat_1 B (k4_relat_1 A)) = B) ) ) ) ) ).
tt(t53_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski C (k9_xtuple_0 D)) <=> (r1_tarski C (k7_relset_1 A A (k7_relset_2 A B A D (k3_relset_1 A B D)) C))) ) ) ) ) ) ) ).
tt(t53_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v4_rewrite1 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r4_rewrite1 A B C) & (r4_rewrite1 A B D))  =>  (C = D) ) ) ) ) ) ) ).
tt(t53_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r4_rewrite2 A B C D) => (r4_rewrite2 A C B D)) ) ) ) ) ) ) ) ).
tt(t53_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (! [H:$i] :  ((m1_rewrite1 H (k1_rewrite3 C F G)) =>  (~  ( ((k1_funct_1 H 1) = (k4_tarski A D))  &  ( ((k1_funct_1 H (k3_finseq_1 H)) = (k4_tarski B E))  &  (! [I:$i] :  ((m1_subset_1 I (k8_afinsq_1 C)) =>  (~  (D = (k1_flang_1 C I E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 B A) <=> (v1_partfun1 (k56_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(t53_rfunct_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_rfunct_3 C (k1_rcomp_1 A B)) <=>  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ( ((r2_hidden D (k1_rcomp_1 A B)) &  ((r2_hidden E (k1_rcomp_1 A B)) & (r2_hidden F (k1_rcomp_1 A B))) )  =>  ((r1_xxreal_0 E D) |  ((r1_xxreal_0 F E) | (r1_xxreal_0 (k10_real_1 (k9_real_1 (k1_seq_1 C D) (k1_seq_1 C E)) (k9_real_1 D E)) (k10_real_1 (k9_real_1 (k1_seq_1 C E) (k1_seq_1 C F)) (k9_real_1 E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 B) => (r1_xxreal_0 (k1_seq_1 (k3_rinfsup1 B) A) (k2_rinfsup1 (k4_rinfsup1 B)))) ) ) ) ) ).
tt(t53_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_rlaffin1 A (k5_rusub_4 A C B)) = (k5_rusub_4 A (k4_rlaffin1 A C) B)) ) ) ) ) ) ) ).
tt(t53_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_struct_0 D B) <=>  ((k3_rlsub_1 A C D) = (k3_rlsub_1 A (k5_algstr_0 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D B C)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rlsub_2 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t53_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v7_pre_topc A) =>  ((k1_convex1 A (k2_pre_topc A B) k6_numbers) = (k2_pre_topc A (k1_convex1 A B k6_numbers))) ) ) ) ) ) ).
tt(t53_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_algstr_0 A (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D))) = (k5_algstr_0 A (k5_algstr_0 A (k4_algstr_0 A B) C) D)) ) ) ) ) ) ) ) ) ).
tt(t53_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k9_rlvect_2 A (k9_rlvect_2 A B)) B)) ) ) ) ).
tt(t53_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r2_hidden C (k3_rmod_2 A B D E)) <=>  ((k3_rmod_2 A B D E) = (k3_rmod_2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((m2_rmod_4 D A B C) => (m2_rmod_4 (k8_rmod_4 A B D) A B C)) ) ) ) ) ) ) ) ) ).
tt(t53_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k9_robbins1 A (k17_robbins1 A B) B) = (k3_robbins1 A (k5_robbins1 A (k13_robbins1 A B) (k15_robbins1 A B)))) ) ) ) ) ).
tt(t53_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k5_robbins1 A B C) (k5_robbins1 A B D)) = (k5_robbins1 A C (k5_robbins1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t53_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r2_relset_1 k5_numbers k1_numbers (k7_roughs_1 A (k8_finseq_1 (k1_zfmisc_1 (u1_struct_0 A)) B (k12_finseq_1 (k1_zfmisc_1 (u1_struct_0 A)) D)) C) (k8_finseq_1 k1_numbers (k7_roughs_1 A B C) (k12_finseq_1 k1_numbers (k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A D) C))))) ) ) ) ) ) ) ) ).
tt(t53_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ( ((k4_subset_1 A (k4_subset_1 A C D) E) = A)  &  ((r1_xboole_0 C D) &  ((r1_xboole_0 C E) & (r1_xboole_0 D E)) ) )  =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A D) k6_numbers) |  ((r1_xxreal_0 (k1_rpr_1 A E) k6_numbers) |  ((k2_rpr_1 A B C) = (k10_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k7_real_1 (k7_real_1 (k8_real_1 (k2_rpr_1 A C B) (k1_rpr_1 A C)) (k8_real_1 (k2_rpr_1 A D B) (k1_rpr_1 A D))) (k8_real_1 (k2_rpr_1 A E B) (k1_rpr_1 A E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_struct_0 B C) => (r2_hidden (k1_rlvect_1 A C D) (k3_rusub_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t53_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D B C)) = (k2_domain_1 (u1_struct_0 A) (u1_struct_0 A) (k4_rusub_2 A D C B))) ) ) ) ) ) ) ) ) ).
tt(t53_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k5_bhsp_2 A C D))  => (v4_pre_topc B (k5_rusub_5 A))) ) ) ) ) ) ) ) ) ).
tt(t53_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k11_rvsum_1 A B k6_numbers) = (k5_finseq_2 k5_numbers A k6_numbers)) ) ) ) ) ).
tt(t53_rvsum_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  ((k3_finseq_1 (k9_rvsum_2 B A)) = (k3_finseq_1 B)) ) ) ) ) ).
tt(t53_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (B = (k1_funct_4 C A))  =>  ((k1_funct_1 B (k4_struct_0 k1_scmfsa_2)) = (k1_funct_1 A (k4_struct_0 k1_ami_3))) ) ) ) ) ) ) ) ).
tt(t53_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r3_scmfsa7b B C))  &  ( (~ (r4_scmfsa7b A C))  & (r4_scmfsa7b (k4_scmfsa6a B A) C)) ) ) ) ) ) ) ) ) ).
tt(t53_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~ (r4_scmfsa7b C D))  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k1_scmfsa_m B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t53_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 C C B B) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 C C B B) A) (k2_scmpds_2 (k1_funct_1 A C) B)) = (k6_int_1 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A C) B)) (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A C) B))))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (D = (k2_scmpds_2 (k1_funct_1 A C) B)) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k15_scmpds_2 C C B B) A) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers)  =>  ((k1_funct_1 (k6_scmpds_4 (k5_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((k1_funct_1 B (k1_scmp_gcd F)) = G)  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd C)) C) |  ((r1_xxreal_0 E D) |  ((r1_xxreal_0 F (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd C)) E)) |  ((r1_xxreal_0 G F) |  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd G)) G) |  ((r1_scmpds_6 (k2_scmpds_7 (k1_scmp_gcd C) D 1 (k4_scmpds_4 (k12_scmpds_2 (k1_scmp_gcd C) (k1_scmp_gcd G) E k6_numbers) (k11_scmpds_2 (k1_scmp_gcd F) k6_numbers 1))) B A) & (r2_scmpds_6 (k2_scmpds_7 (k1_scmp_gcd C) D 1 (k4_scmpds_4 (k12_scmpds_2 (k1_scmp_gcd C) (k1_scmp_gcd G) E k6_numbers) (k11_scmpds_2 (k1_scmp_gcd F) k6_numbers 1))) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v5_scmyciel A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  => (r2_hidden (k2_tarski B C) A)) ) ) ) ) ).
tt(t53_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~ (r2_semi_af1 A B D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) => (v2_relat_1 (k56_valued_1 k5_numbers k1_numbers A))) ) ) ).
tt(t53_seq_4,ax,(r3_binop_1 k2_numbers k6_complex1 k29_binop_2)).
tt(t53_series_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B C) k6_numbers))  & (r1_xxreal_0 (k1_seq_1 B (k5_real_1 C 1)) (k1_seq_1 B C))) ) )  => (r1_xxreal_0 (k8_real_1 (k2_nat_1 A 1) (k2_power (k2_nat_1 A 1) (k1_seq_1 (k1_series_3 B) A))) (k1_seq_1 (k3_series_1 B) A))) ) ) ) ) ).
tt(t53_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A C) k6_numbers))  &  ((k1_seq_1 B C) = (k13_complex1 1 (k1_seq_1 A C))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) => (r1_xxreal_0 (k5_square_1 (k2_nat_1 C 1)) (k3_xcmplx_0 (k1_seq_1 (k3_series_1 A) C) (k1_seq_1 (k3_series_1 B) C)))) ) ) ) ) ) ) ).
tt(t53_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  ((k1_kurato_0 A (k2_setlim_1 A B)) = (k3_prob_1 A B)) ) ) ) ) ).
tt(t53_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k8_setlim_2 B D C)) A) = (k7_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A) C)) ) ) ) ) ) ) ) ).
tt(t53_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ((v1_binop_1 D B) &  ((v2_binop_1 D B) &  ((v3_binop_1 D B) & (v1_setwiseo D B)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k5_finsub_1 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k5_finsub_1 C) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 C) B)))) )  =>  ( ( ((k3_funct_2 (k5_finsub_1 C) B F (k1_setwiseo C)) = (k4_binop_1 B D))  &  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 C)) =>  (! [H:$i] :  ((m1_subset_1 H (k5_finsub_1 C)) =>  ((k3_funct_2 (k5_finsub_1 C) B F (k5_setwiseo C G H)) = (k5_binop_1 B D (k3_funct_2 (k5_finsub_1 C) B F G) (k3_funct_2 (k5_finsub_1 C) B F H))) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 A)) =>  ((k3_funct_2 (k5_finsub_1 C) B F (k10_setwiseo A C G E)) = (k7_setwiseo A B D G (k1_partfun1 A (k5_finsub_1 C) (k5_finsub_1 C) B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  ( ((r2_hidden (k14_scmfsa_2 A B C) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) D)) | (r2_hidden (k15_scmfsa_2 A B C) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) D)))  =>  ( (~  ((k5_sf_mastr D) = B) )  &  (~  ((k5_sf_mastr D) = A) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A B D) C)) B)) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A B D) C))) ) ) ) ) ) ) ) ) ).
tt(t53_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matroid0 B) & (m1_simplex0 B A))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((v1_setfam_1 (k9_xtuple_0 C)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 D (k6_simplex0 B)) &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ((v3_pre_topc E B) &  ( ((k1_card_1 E) = (k1_nat_1 D 1))  &  ((r1_tarski (k1_orders_1 E) (k9_xtuple_0 C)) &  ((m1_subset_1 (k7_relat_1 C (k1_orders_1 E)) (k1_zfmisc_1 (u1_struct_0 B))) & (v2_funct_1 (k5_relat_1 C (k1_orders_1 E)))) ) ) ) ) ) ) ) ) ) ) )  =>  ((k6_simplex0 (k10_simplex0 A B C)) = (k6_simplex0 B)) ) ) ) ) ) ) ).
tt(t53_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k1_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 1 (k7_square_1 2)))) ).
tt(t53_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k15_sin_cos (k1_binop_2 (k5_binop_2 (k5_binop_2 k7_complex1 A) B))) = (k2_comseq_3 (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B) (k5_binop_2 k7_complex1 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B))) A)) ) ) ) ) ).
tt(t53_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v5_valued_0 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k7_real_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t53_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((k9_binop_2 (k3_sin_cos7 A) (k3_sin_cos7 B)) = (k3_sin_cos7 (k9_binop_2 (k11_binop_2 A B) (k7_square_1 (k11_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 B) 1)))))) ) ) ) ) ) ).
tt(t53_sin_cos9,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t53_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ( (~ (r1_xxreal_0 (k1_seq_1 k24_sin_cos A) k6_numbers))  & (r1_xxreal_0 (k1_seq_1 k24_sin_cos A) 1)) ) ) ) ).
tt(t53_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sppol_2 B C A) &  ((r2_hidden D A) & (r2_hidden E A)) )  =>  ( (D = E)  | (r1_sppol_2 D E A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k5_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k1_rcomp_1 (k18_euclid A) (k18_euclid B))) ) ) ) ) ) ).
tt(t53_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k18_euclid (k22_pscomp_1 (k3_topreal1 2 A))) (k18_euclid (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t53_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_sprect_2 A B) <=> (r1_sprect_2 (k1_sprect_1 (k3_topreal1 2 A)) B)) ) ) ) ) ).
tt(t53_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t53_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B 1)) ) )  => (r1_xxreal_0 (k3_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 1)) ) ) ) ) ).
tt(t53_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k3_stirl2_1 (k23_binop_2 A 2) A) = (k23_binop_2 (k24_binop_2 3 (k6_newton 4 (k23_binop_2 A 2))) (k6_newton 3 (k23_binop_2 A 2)))) ) ) ).
tt(t53_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  (! [F:$i] :  ((m1_substut1 F A (k7_sublemma A E B)) =>  ((v3_substut1 (k7_sublemma A E B) A) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  ((r2_relset_1 (k3_qc_lang1 A) C (k3_sublemma A E C (k1_sublemma A C D (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A E B) F))) G))) (k14_sublemma A C (k13_sublemma A E B F C (k1_sublemma A C D (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A E B) F))) G))) (k12_sublemma A C B G))) & (r1_xboole_0 (k9_xtuple_0 (k7_substut1 A B (k11_cqc_lang A B (k2_sublemma A E)) F)) (k6_domain_1 (k3_qc_lang1 A) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))) (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)))))) ) ) ) ).
tt(t53_tdlat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v4_tdlat_3 A) <=>  ( (~ (v2_struct_0 (k4_tdlat_1 A)))  &  ((v10_lattices (k4_tdlat_1 A)) &  ((v17_lattices (k4_tdlat_1 A)) & (l3_lattices (k4_tdlat_1 A))) ) ) ) ) ) ).
tt(t53_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ( (C = D)  | (r1_xboole_0 (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_tex_3 B A) & (m1_pre_topc B A)) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tex_2 C A) &  ((v1_tex_3 C A) & (m1_pre_topc C A)) ) ) )  & (r4_tsep_2 A B C)) ) ) ) ) ) ).
tt(t53_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_subset_1 (k4_tex_4 A B) (k4_tex_4 A C)) <=>  (~  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r1_tarski (k4_tex_4 A B) D) & (r1_xboole_0 D (k4_tex_4 A C))) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v3_pre_topc D A) &  ((r1_xboole_0 D (k4_tex_4 A B)) & (r1_tarski (k4_tex_4 A C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ((r2_hidden F (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D F) = (k1_funct_1 E F)) ) ) )  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k2_tmap_1 B A D C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) => (r2_funct_2 (u1_struct_0 (k5_topalg_1 A B)) (u1_struct_0 (k5_topalg_1 A C)) (k2_tops_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)) (k6_topalg_1 A B C D)) (k6_topalg_1 A C B (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t53_topgen_1,ax, ((v2_tops_1 k3_numbers k3_topmetr) & (m1_subset_1 k3_numbers (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ).
tt(t53_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r1_topgen_4 A (k4_subset_1 (u1_struct_0 A) B C) D) &  ( (~ (r1_topgen_4 A B D))  &  (~ (r1_topgen_4 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_topgen_5,ax,(v7_pre_topc k2_topgen_3)).
tt(t53_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc C A) => (v3_pre_topc (k2_group_2 A B C) A)) ) ) ) ) ) ) ).
tt(t53_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k11_metric_1 B C A) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t53_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_tarski (k6_jgraph_6 A B C) (k7_jgraph_6 A B C))) ) ) ) ) ) ).
tt(t53_toprealc,ax,(r2_funct_2 (u1_struct_0 (k2_borsuk_1 (k15_euclid k6_numbers) (k15_euclid k6_numbers))) (u1_struct_0 (k15_euclid k6_numbers)) (k16_toprealc k6_numbers) (k6_struct_0 (k2_borsuk_1 (k15_euclid k6_numbers) (k15_euclid k6_numbers)) (k15_euclid k6_numbers) (k4_struct_0 (k15_euclid k6_numbers))))).
tt(t53_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_tops_1 B A) & (v3_tops_1 C A))  => (v3_tops_1 (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) ) ) ) ).
tt(t53_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_struct_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ( ((k2_relset_1 (u1_struct_0 B) D) = (k2_struct_0 B))  &  ((v2_funct_1 D) &  ( ((k1_relset_1 (u1_struct_0 B) E) = (k2_struct_0 B))  &  ( ((k2_relset_1 (u1_struct_0 C) E) = (k2_struct_0 C))  & (v2_funct_1 E)) ) ) )  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 C) (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E)) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 B) (u1_struct_0 C) E) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski D C) => (r1_tarski (k2_pre_topc B D) (k2_pre_topc A C))) ) ) ) ) ) ) ) ) ).
tt(t53_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v5_transgeo B A) & (v5_transgeo C A))  => (v5_transgeo (k1_transgeo (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t53_trees_1,ax, ((k2_trees_1 2) = (k1_enumset1 k1_xboole_0 (k12_finseq_1 k5_numbers k6_numbers) (k12_finseq_1 k5_numbers 1))) ).
tt(t53_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v4_trees_3 A) => (r1_tarski (k2_trees_1 (k3_finseq_1 A)) (k11_trees_3 A))) ) ) ).
tt(t53_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_tsep_1 A B D) & (r2_tsep_1 A C D))  => (r2_tsep_1 A (k4_subset_1 (u1_struct_0 A) B C) D)) ) ) ) ) ) ) ) ) ).
tt(t53_twoscomp,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 (k40_twoscomp A B) (k41_twoscomp A B)))) => (v1_circuit2 (k6_circuit2 (k40_twoscomp A B) (k41_twoscomp A B) C) (k40_twoscomp A B) (k41_twoscomp A B))) ) ) ) ) ) ).
tt(t53_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k14_polynom3 k1_complfld))) =>  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 k1_complfld))))  =>  ( ( (D = (a_2_0_uniroots A B))  &  ( ((k4_finseq_1 C) = (k2_finseq_1 A))  &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  ((r2_hidden E (k4_finseq_1 C)) =>  ( ( (~  ((r1_nat_d E A) &  ( (~ (r1_nat_d E B))  &  (~  (E = A) ) ) ) )  =>  ((k1_funct_1 C E) = (k3_algseq_1 k1_complfld (k1_group_1 k1_complfld))) )  &  ((r1_nat_d E A) =>  ((r1_nat_d E B) |  ( (E = A)  |  ((k1_funct_1 C E) = (k5_uniroots E)) ) ) ) ) ) ) ) ) )  =>  ((k3_group_4 (k14_polynom3 k1_complfld) C) = (k10_uproots k1_complfld (k2_uproots (u1_struct_0 k1_complfld) D 1))) ) ) ) ) ) ) ) ) ) ).
tt(t53_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_uproots A B (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A))) = 1) ) ) ) ) ).
tt(t53_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k42_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k42_valued_2 A B E C) D) = (k42_valued_2 A B E (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t53_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_struct_0 E C) <=>  ((k3_vectsp_4 A B D E) = (k3_vectsp_4 A B (k3_rlvect_1 B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_rlvect_1 B (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)) (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D))) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((v3_funct_1 (k2_partfun1 B (u1_struct_0 C) D A)) =>  ((v3_funct_1 (k2_partfun1 B k1_numbers (k3_normsp_0 B C D) A)) & (v3_funct_1 (k2_partfun1 B (u1_struct_0 C) (k5_vfunct_1 B C D) A))) ) ) ) ) ) ) ) ) ).
tt(t53_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C D)) =>  ((v3_funct_1 (k2_partfun1 A k1_numbers (k3_normsp_0 A B C) D)) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) (k5_vfunct_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t53_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r1_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r1_yellow_0 A E) &  (D = (k1_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k1_yellow_0 A D) C)) ) ) ) )  =>  ((r1_yellow_0 A B) <=> (r1_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(t53_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ( ((v7_waybel_1 B A) => (v7_yellow_0 (k1_yellow_2 A A B) A))  &  ((v8_waybel_1 B A) => (v8_yellow_0 (k1_yellow_2 A A B) A)) ) ) ) ) ) ).
tt(t53_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 A) (u1_waybel_0 A C)) (u1_struct_0 B)) => (r2_hidden (k1_waybel11 A C) (u1_struct_0 B))) ) )  => (v4_waybel_0 B A)) ) ) ) ) ).
tt(t53_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  ( ((k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (k4_waybel23 A B)) = (k7_waybel_0 B))  & (m1_subset_1 (k2_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k4_waybel23 A B)) (k1_zfmisc_1 (k7_waybel_0 A)))) ) ) ) ) ).
tt(t53_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_2 A) <=> (v22_waybel_0 (k4_waybel_2 A) (k3_yellow_3 A A) A)) ) ) ).
tt(t53_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r3_yellow20 (k5_waybel34 A) (k4_waybel34 A) (k7_waybel34 A) (k9_waybel34 A) (k8_waybel34 A))) ) ).
tt(t53_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_waybel_3 A B C) <=>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_waybel_0 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((r3_orders_2 A C (k1_yellow_0 A D)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E D) & (r1_waybel_3 A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (~  ((r1_tarski A (k1_relat_1 B)) &  ((v2_wellord1 B) &  ( (~ (r4_wellord1 B (k2_wellord1 B A)))  &  (! [C:$i] :  (~  ((r2_hidden C (k1_relat_1 B)) & (r4_wellord1 (k2_wellord1 B (k1_wellord1 B C)) (k2_wellord1 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t53_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 A (k2_xboole_0 B C)) = (k3_xboole_0 (k4_xboole_0 A B) (k4_xboole_0 A C))) ) ) ) ).
tt(t53_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A (k4_xboolean A B)) = (k3_xboolean (k4_xboolean A B))) ) ) ) ) ).
tt(t53_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k7_xcmplx_0 B A) = (k7_xcmplx_0 C A))  =>  ( (A = k6_numbers)  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t53_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ((r1_xxreal_0 A k6_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k6_xcmplx_0 C A) B)) ) ) ) ) ) ) ) ) ).
tt(t53_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k3_xxreal_1 A B) (k1_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  ( (~  (! [B:$i] :  ((m1_xxreal_2 B A) =>  (B = k1_xxreal_0) ) ) )  => (v4_xxreal_2 A)) ) ) ).
tt(t53_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~ (r1_xxreal_0 (k3_xxreal_3 A B) C))  &  (~  ( (~  (C = k1_xxreal_0) )  &  ( (~  (B = k1_xxreal_0) )  &  ( (~  (A = k2_xxreal_0) )  &  (~ (r1_xxreal_0 A (k1_xxreal_3 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_yellow_0 A B)) )  => (v3_lattice3 A)) ) ) ).
tt(t53_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_yellow_3 A B))) =>  ((k5_yellow_3 A B (k2_waybel_8 (k3_yellow_3 A B) C)) = (k2_waybel_8 B (k9_yellow_3 A B C))) ) ) ) ) ) ) ).
tt(t53_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( ((r1_waybel18 B A) & (r1_t_0topsp B C))  => (r1_waybel18 C A)) ) ) ) ) ) ) ).
tt(t53_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v15_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_altcat_1 F) &  ((v3_altcat_2 F A) & (m1_altcat_2 F A)) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v2_altcat_1 G) &  ((v3_altcat_2 G B) & (m1_altcat_2 G B)) ) )  =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  &  ((v2_altcat_1 H) &  ((v3_altcat_2 H C) & (m1_altcat_2 H C)) ) )  =>  ( ((r3_yellow20 A B D F G) & (r2_yellow20 B C E G H))  => (r3_yellow20 A C (k4_functor3 A B C D E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t53_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ((r3_orders_2 A (k3_funct_2 B (u1_struct_0 A) D C) (k4_yellow_2 A D)) & (r3_orders_2 A (k5_yellow_2 A D) (k3_funct_2 B (u1_struct_0 A) D C))) ) ) ) ) ) ) ) ) ).
tt(t53_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B)) & (r1_yellow_0 A B))  => (r3_orders_2 A (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) C) B)) (k12_lattice3 A C (k1_yellow_0 A B)))) ) ) ) ) ) ) ).
tt(t53_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k1_yellow_5 A C D)) = (k13_lattice3 A (k1_yellow_5 A B C) (k12_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t53_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (? [B:$i] :  ((m2_yellow_9 B A) &  ((v1_pre_topc B) &  ((v1_tops_2 (u1_pre_topc A) B) &  ((v2_cantor_1 (u1_pre_topc A) B) & (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ).
tt(t53_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r2_hidden A (k29_zf_lang B)) => (r1_tarski (k29_zf_lang A) (k29_zf_lang B))) ) ) ) ) ).
tt(t53_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_zf_lang A (k7_zf_lang B C)) <=>  ( (A = B)  |  (A = C) ) ) ) ) ) ) ) ) ).
tt(t53_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( ((k3_xboole_0 (k2_tarski A B) C) = (k1_tarski A))  &  ((r2_hidden B C) &  (~  (A = B) ) ) ) ) ) ) ) ).
tt(t53_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) => (m1_zmodul01 (k3_zmodul01 B) A)) ) ) ) ).
tt(t54_abcmiz_0,ax, (! [A:$i] :  ((l2_abcmiz_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ( ((r2_abcmiz_0 A B C) & (r1_tarski D C))  => (r2_abcmiz_0 A B D)) ) ) ) ) ) ) ) ) ).
tt(t54_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_trees_4 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (~  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A B)))  &  ((k36_abcmiz_1 A B D) = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r5_abcmiz_a A B C) => (r6_abcmiz_a A B C)) ) ) ) ) ) ) ).
tt(t54_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C E) &  ((r1_aff_1 A B D F) &  (E = F) ) )  =>  ((r1_aff_1 A B C D) |  ( (E = B)  &  (F = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (r1_aff_1 A B C D))  &  ( (~  (E = F) )  &  ((r2_analoaf A B C E F) &  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ((r2_analoaf A B D E G) & (r2_analoaf A C D F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((r1_xxreal_0 A (k1_afinsq_1 B)) =>  ((k1_afinsq_1 (k5_relat_1 B A)) = A) ) ) ) ) ) ).
tt(t54_afinsq_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_afinsq_2 (k6_afinsq_1 A B)) = (k3_binop_2 A B)) ) ) ) ) ).
tt(t54_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_tdgroup A))) =>  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B E) = (k3_rlvect_1 A C E)) ) )  =>  ((k10_xtuple_0 B) = (u1_struct_0 (k5_afvect0 (k2_tdgroup A) D))) ) ) ) ) ) ) ) ) ) ).
tt(t54_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  ((r1_circcomb A B) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_algspec1 (k2_circcomb A B) C D) =>  ((k2_algspec1 (k2_circcomb A B) C D) = (k2_circcomb (k2_algspec1 A C D) (k2_algspec1 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k2_altcat_4 (k2_altcat_4 A)) = (k2_altcat_4 A)) ) ) ).
tt(t54_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (v4_analmetr B A)) )  =>  ( (C = D)  |  (B = (k4_analmetr A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k5_analort A F G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k5_analort A F G))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k5_analort A F G))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k5_analort A F G))) =>  ( ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  (E = K) ) ) )  =>  ((r2_analoaf (k5_analort A F G) H I J K) <=> (r1_analort A F G B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_aofa_000,ax, ( ((k3_finseq_1 k19_aofa_000) = 4)  &  ( ((k4_finseq_1 k19_aofa_000) = (k2_finseq_1 4))  &  ( ((k1_recdef_1 k19_aofa_000 1) = k6_numbers)  &  ( ((k1_recdef_1 k19_aofa_000 2) = 2)  &  ( ((k1_recdef_1 k19_aofa_000 3) = 3)  &  ((k1_recdef_1 k19_aofa_000 4) = 2) ) ) ) ) ) ).
tt(t54_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ( ((v1_aofa_i00 G A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers)) & (m1_aofa_000 G A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers)))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((r5_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) H G) =>  (! [I:$i] :  ((m1_aofa_i00 I B (u1_struct_0 A) (k9_funct_2 B k4_numbers) G) =>  (! [J:$i] :  ((m1_aofa_i00 J B (u1_struct_0 A) (k9_funct_2 B k4_numbers) G) =>  ( (! [K:$i] :  ((m2_funct_2 K B k4_numbers (k9_funct_2 B k4_numbers)) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) G K H) J) = (k21_aofa_i00 B k4_numbers K J))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) G K H) I) = (k21_aofa_i00 B k4_numbers K I)) ) ) )  =>  ( (! [K:$i] :  ( ((v1_relat_1 K) & (v1_funct_1 K))  =>  (~  ( ((k1_funct_1 K F) = k6_numbers)  &  ( ((k1_funct_1 K J) = 1)  &  ((k1_funct_1 K I) = 2) ) ) ) ) )  | (r5_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) (k17_aofa_000 A (k47_aofa_i00 A B C D I E) (k74_aofa_i00 A B F G I J) H (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) G I 1)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ( ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) )  =>  ((v3_armstrng B A) &  ((v13_armstrng B A) & (v14_armstrng B A)) ) )  &  ( ((v3_armstrng B A) &  ((v13_armstrng B A) & (v14_armstrng B A)) )  =>  ((v3_armstrng B A) &  ((v8_relat_2 B) &  ((v4_armstrng B A) & (v5_armstrng B A)) ) ) ) ) ) ) ) ).
tt(t54_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (~  ( (~  (A = k11_arytm_3) )  &  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (~  ((k10_arytm_3 A B) = 1) ) ) ) ) ) ) ) ).
tt(t54_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k7_real_1 (k9_real_1 (k5_square_1 A) A) 1) k6_numbers)) ) ) ).
tt(t54_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A B)) = B) ) ) ) ) ) ).
tt(t54_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((m1_bcialg_5 A k6_numbers 1 k6_numbers k6_numbers) =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v4_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ).
tt(t54_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_bcialg_1 B) &  ((v4_bcialg_1 B) &  ((v5_bcialg_1 B) &  ((v7_bcialg_1 B) & (l2_bcialg_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) &  ((v2_bcialg_6 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ( (C = (k5_bcialg_6 A B E))  & (v2_funct_2 E (u1_struct_0 B)))  => (r1_bcialg_6 (k9_bcialg_2 A D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m4_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) & (r2_hidden (k1_bcialg_1 A D E) B))  => (r2_hidden (k1_bcialg_1 A C E) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_normsp_1 A B 1) B)) ) ) ) ).
tt(t54_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_tarski (k4_bhsp_2 A B C) (k5_bhsp_2 A B C))) ) ) ) ) ) ).
tt(t54_bhsp_4,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k3_bhsp_4 B (k5_bhsp_4 B C A) (k2_nat_1 D 1)) = (k5_algstr_0 B (k1_normsp_1 B (k5_bhsp_4 B (k1_bhsp_4 B C) A) (k2_nat_1 D 1)) (k3_bhsp_4 B (k5_bhsp_4 B (k1_bhsp_4 B C) (k47_valued_1 k5_numbers k1_numbers k1_numbers (k1_valued_0 k1_numbers A 1) A)) D))) ) ) ) ) ) ) ) ) ).
tt(t54_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) &  ((v1_hahnban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  ( (~  (E = (k7_hahnban1 A C)) )  =>  ( ((k13_bilinear A B C (k9_bilinear A B C D E)) = (k9_vectsp10 A B D))  & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C (k9_bilinear A B C D E)))) (u1_struct_0 C)) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B D))) (u1_struct_0 C)) (u1_struct_0 A) (k15_bilinear A B C (k9_bilinear A B C D E)) (k9_bilinear A (k6_vectsp10 A B (k9_vectsp10 A B D)) C (k11_vectsp10 A B D) E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k3_lattices A (k7_lattices A B) (k7_lattices A C)) (k3_lattices A B C)) =>  ((r4_boolealg A B (k7_lattices A B)) |  ((r4_boolealg A C (k7_lattices A C)) |  ((r1_boolealg A B (k7_lattices A C)) & (r1_boolealg A C (k7_lattices A B))) ) ) ) ) ) ) ) ) ) ).
tt(t54_borsuk_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 k1_borsuk_4))) =>  (~  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) &  ( (~ (r1_xxreal_0 E D))  &  (C = (k1_rcomp_1 D E)) ) ) ) ) )  &  ((r1_borsuk_3 (k1_pre_topc k1_borsuk_4 C) (k1_pre_topc (k15_euclid A) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~ (r1_topreal1 (k15_euclid A) D E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_subset_1 k1_numbers (k3_rcomp_1 B C) (k2_rcomp_1 C k1_xxreal_0)))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k3_rcomp_1 B k1_xxreal_0)) ) ) ) ) ) ) ) ) ).
tt(t54_borsuk_6,ax, (k7_borsuk_6 = a_0_13_borsuk_6) ).
tt(t54_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) (k4_struct_0 (k15_euclid 2))) = (k4_struct_0 (k15_euclid 2))) ) ) ).
tt(t54_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k1_bvfunc_1 A (k7_bvfunc_2 A (k7_bvfunc_2 A B C E) C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k9_xboolean A (k3_xboolean A)) = k7_margrel1)  &  ((k3_xboolean (k9_xboolean A (k3_xboolean A))) = k8_margrel1) ) ) ) ).
tt(t54_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k5_bvfunc26 A C D)) (k1_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A B C) D)))) ) ) ) ) ) ) ) ).
tt(t54_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A (k6_cqc_lang A B)))))) ) ) ) ) ) ) ).
tt(t54_card_1,ax, (6 = (k4_enumset1 k1_xboole_0 1 2 3 4 5)) ).
tt(t54_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] : (r1_xxreal_0 (k5_card_1 (k4_enumset1 A B C D E F)) 6)) ) ) ) ) ) ).
tt(t54_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( (~  ((k4_card_3 A) = k1_xboole_0) )  =>  ((r2_hidden B (k8_card_3 A)) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ((r2_hidden C (k4_card_3 A)) & (r1_tarski B C)) ) ) ) ) ) ) ) ) ).
tt(t54_card_fin,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k3_tarski (k10_xtuple_0 B)) = (k2_xboole_0 (k3_tarski (k10_xtuple_0 (k5_relat_1 B (k6_subset_1 (k9_xtuple_0 B) (k1_tarski A))))) (k1_funct_1 B A))) ) ) ) ) ).
tt(t54_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v10_cat_1 B A) =>  (! [C:$i] :  ((m1_cat_1 C A B B) =>  ((k4_cat_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t54_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  ( (~  (A = B) )  =>  ((r2_cat_3 C D E F) <=> (r1_cat_3 C D (k2_tarski A B) (k5_funct_4 (u4_struct_0 C) A B E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  => (v11_cat_1 (k19_cat_4 A) A)) ) ).
tt(t54_catalan2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k1_seq_1 B C) = (k11_binop_2 (k1_catalan1 (k23_binop_2 C 1)) (k1_newton A C))) ) )  &  ( (~ (r1_xxreal_0 (k13_complex1 1 4) (k18_complex1 A)))  =>  ((v2_series_1 B) &  ( ((k4_series_1 B) = (k9_binop_2 1 (k11_binop_2 A (k2_newton (k4_series_1 B) 2))))  &  ( ((k4_series_1 B) = (k13_complex1 2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k11_binop_2 4 A))))))  &  ( (~  (A = k6_numbers) )  =>  ((k4_series_1 B) = (k13_complex1 (k10_binop_2 1 (k7_square_1 (k10_binop_2 1 (k11_binop_2 4 A)))) (k11_binop_2 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k31_valued_1 B k2_numbers C) A) (k31_valued_1 B k2_numbers (k2_partfun1 B k2_numbers C A))) &  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k2_cfunct_1 B C) A) (k2_cfunct_1 B (k2_partfun1 B k2_numbers C A))) & (r2_relset_1 B k1_numbers (k2_partfun1 B k1_numbers (k55_valued_1 B k2_numbers C) A) (k55_valued_1 B k2_numbers (k2_partfun1 B k2_numbers C A)))) ) ) ) ) ) ) ).
tt(t54_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ( (B = (k2_nat_1 A 1))  =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid B)) (k4_chain_1 B C A)) =>  ((k5_card_1 (k9_chain_1 B C A D)) = 2) ) ) ) ) ) ) ) ) ) ).
tt(t54_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  ((v8_glib_001 B A) =>  ((r1_xxreal_0 (k15_glib_001 A B) 3) |  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ((r2_hidden C (k13_glib_001 A B)) &  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (~  ( (~ (r1_xxreal_0 E (k1_nat_1 D 2)))  &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ( (~  ( (D = 1)  &  (E = (k3_finseq_1 B)) ) )  &  ( (~  ( (D = 1)  &  (E = (k6_xcmplx_0 (k3_finseq_1 B) 2)) ) )  &  ( (~  ( (D = 3)  &  (E = (k3_finseq_1 B)) ) )  &  ( (~  ((k1_funct_1 B D) = (k1_funct_1 B E)) )  &  ((r2_hidden (k1_funct_1 B D) (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) & (r2_hidden (k1_funct_1 B E) (k2_chord A (k6_domain_1 (k6_glib_000 A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  ( ((u4_msualg_1 (k5_circcomb C D) (k7_circcomb A B C D)) = (k13_funcop_1 D C C))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k5_circcomb C D))) =>  ((k1_funct_1 (u3_msualg_1 (k5_circcomb C D) (k7_circcomb A B C D)) E) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A E))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B F))) =>  ( (G = (k3_relat_1 C H))  =>  ((k6_circuit2 A E G) = (k3_relat_1 C (k6_circuit2 B F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_classes1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (! [C:$i] :  ( ((r1_tarski A C) & (v1_ordinal1 C))  => (r1_tarski B C)) )  &  ((r1_tarski A B) & (v1_ordinal1 B)) )  =>  ((k5_classes1 A) = B) ) ) ) ).
tt(t54_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  => (r3_xboole_0 A B)) ) ) ) ).
tt(t54_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v6_clvect_1 B A) &  (! [C:$i] :  ( ((v1_clvect_1 C) & (m1_clvect_1 C A))  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_tarski (k4_clvect_2 A B C) (k5_clvect_2 A B C))) ) ) ) ) ) ).
tt(t54_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k2_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k2_clvect_3 A (k6_clvect_3 A B C) (k2_nat_1 D 1)) = (k5_algstr_0 A (k1_normsp_1 A (k6_clvect_3 A (k1_bhsp_4 A B) C) (k2_nat_1 D 1)) (k2_clvect_3 A (k6_clvect_3 A (k1_bhsp_4 A B) (k46_valued_1 k5_numbers k2_numbers k2_numbers (k1_valued_0 k2_numbers C 1) C)) D))) ) ) ) ) ) ) ) ) ).
tt(t54_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v7_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) (k11_cohsp_1 A B C)) & (r2_hidden (k4_tarski E F) (k11_cohsp_1 A B C)))  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r1_xxreal_0 (k3_complex1 A) (k17_complex1 A))) ) ).
tt(t54_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (~  ( (~  (B = k6_numbers) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (~  ((k1_comptrig (k2_complex2 B A)) = (k7_real_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) C) (k7_real_1 A (k1_comptrig B)))) ) ) ) ) ) ) ) ) ) ).
tt(t54_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k2_complfld (k8_group_1 k1_complfld A B)) = (k8_group_1 k1_complfld (k2_complfld A) (k2_complfld B))) ) ) ) ) ).
tt(t54_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k12_seq_4 A (k1_binop_2 B)) = (k11_seq_4 (k12_seq_4 A B))) ) ) ) ) ).
tt(t54_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k5_card_1 (k9_compos_1 A B)) = 1) ) ) ) ) ).
tt(t54_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G) 2) = (k5_compos_0 (u1_compos_1 A) D 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~  ( (A = k6_numbers)  &  (B = k6_numbers) ) )  =>  ((k1_newton A B) = (k2_xcmplx_0 (k8_real_1 (k2_newton (k17_complex1 A) B) (k21_sin_cos (k4_real_1 B (k1_comptrig A)))) (k3_xcmplx_0 (k8_real_1 (k2_newton (k17_complex1 A) B) (k18_sin_cos (k4_real_1 B (k1_comptrig A)))) k7_complex1))) ) ) ) ) ) ).
tt(t54_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers)) =>  ( ((v2_comput_1 B) &  ((v2_comput_1 C) &  ( ((k2_nat_1 (k19_margrel1 B) 2) = (k19_margrel1 C))  &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 1 (k19_margrel1 B)))) ) ) )  => (r2_hidden D (k1_relset_1 (k3_finseq_2 k5_numbers) (k6_comput_1 B C A D)))) ) ) ) ) ) ) ) ) ).
tt(t54_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_3 A) & (v1_comseq_3 B))  =>  ((v1_comseq_3 (k1_series_1 k2_numbers A B)) &  ((k11_comseq_3 (k1_series_1 k2_numbers A B)) = (k8_complex1 (k11_comseq_3 A) (k11_comseq_3 B))) ) ) ) ) ) ) ).
tt(t54_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k19_convex4 A (k19_convex4 A B D) C) = (k19_convex4 A B (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t54_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (r3_cqc_the1 A B (k8_cqc_lang A (k7_cqc_lang A C D) (k7_cqc_lang A D C)))) ) ) ) ) ) ) ) ).
tt(t54_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k11_cqc_lang A C (k6_cqc_lang A B)) (k6_cqc_lang A (k12_cqc_lang A C B))) A)) ) ) ) ) ) ).
tt(t54_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r7_cqc_the3 A B C) & (r7_cqc_the3 A D E))  => (r7_cqc_the3 A (k7_cqc_lang A B D) (k7_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ( (~  (B = C) )  & (r1_xxreal_0 (k15_csspace A B C) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k15_csspace A B C) k6_numbers))  &  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t54_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k18_sin_cos (k8_real_1 2 (k7_real_1 B A))) (k18_sin_cos (k8_real_1 2 B))))) ) ) ) ) ).
tt(t54_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k8_real_1 (k8_real_1 3 (k21_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2))) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k8_real_1 3 (k7_real_1 (k8_real_1 2 B) A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t54_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) 1) B) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) k6_numbers) (k7_real_1 B (k13_complex1 A 2))) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 C A) k6_numbers) (k9_real_1 B (k13_complex1 A 2))))) ) ) ) ) ) ) ).
tt(t54_dilworth,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_dilworth A) & (l1_orders_2 A)) ) )  =>  (? [B:$i] :  ( ((v6_dilworth B A) & (m1_eqrel_1 B (u1_struct_0 A)))  &  ((k1_card_1 B) = (k1_dilworth A)) ) ) ) ) ).
tt(t54_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k8_eqrel_1 A B)) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 C)) =>  ((v1_finset_1 (k1_funct_1 C D)) & (m1_subset_1 (k1_funct_1 C D) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t54_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [H:$i] :  ((m2_subset_1 H (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (E = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (F = (k5_algstr_0 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k2_binom (k9_int_3 A) E 3)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) E 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  (I = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) E F) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) F)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)))) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) = (k4_algstr_0 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k21_ens_1 A (k4_cat_1 A B) (k4_cat_1 A C)) = (k6_partfun1 (k2_cat_1 A B C))) ) ) ) ) ) ) ).
tt(t54_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v2_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( (B = (k5_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski C D) (k2_matrix_1 B)) =>  ((k3_matrix_1 k1_numbers B C D) = (k8_real_1 (k3_matrix_1 k1_numbers A C D) (k6_power 2 (k3_matrix_1 k1_numbers A C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_enumset1,ax, (! [A:$i] :  ((k5_enumset1 A A A A A A A) = (k1_tarski A)) ) ).
tt(t54_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k3_tarski (k5_setfam_1 A B)) = (k3_tarski (a_2_0_eqrel_1 A B))) ) ) ) ).
tt(t54_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) => (r1_rvsum_1 (k4_struct_0 (k15_euclid A)) B)) ) ) ) ).
tt(t54_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) =>  ((k9_euclid_3 2 A B C) = (k1_euclid 2)) ) ) ) ) ) ) ) ).
tt(t54_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k3_finseq_1 (k6_euclid 3 A)) = (k3_finseq_1 A)) ) ) ).
tt(t54_euclid,ax, ((k4_struct_0 (k15_euclid 2)) = (k19_euclid k6_numbers k6_numbers)) ).
tt(t54_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ( (~ (r2_hidden B C))  &  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ( (C = (k2_euclid_4 A D E))  & (r4_euclidlp A (k8_euclid A B D) (k8_euclid A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) =>  ((r2_hidden (k4_tarski C A) (k6_exchsort D E)) <=>  ((r2_hidden C A) & (r2_hidden (k4_tarski C B) (k6_exchsort D (k10_funct_7 E A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t54_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D)))) =>  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D) E) (k4_tarski (k11_finseq_1 A B C) D)) = (k1_funct_1 D (k11_finseq_1 (k1_funct_1 E A) (k1_funct_1 E B) (k1_funct_1 E C))))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D) E) A) = (k1_funct_1 E A))  &  ( ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D) E) B) = (k1_funct_1 E B))  &  ((k1_funct_1 (k6_circuit2 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D) E) C) = (k1_funct_1 E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 C D))  => (r1_xxreal_0 (k1_seq_1 (k1_fcont_1 A B) D) (k1_seq_1 (k1_fcont_1 A B) C))) ) ) ) ) ) ) ) ) ).
tt(t54_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) B) = (k10_real_1 (k7_real_1 (k9_real_1 (k10_real_1 2 (k7_real_1 1 (k5_square_1 B))) (k1_seq_1 k1_sin_cos9 B)) (k1_seq_1 k2_sin_cos9 B)) (k1_seq_1 k24_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t54_fdiff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)))) =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos (k1_taylor_1 A)) (k10_real_1 1 A)) B) C) = (k8_real_1 (k5_prepower (k1_seq_1 k16_sin_cos C) (k9_real_1 A 1)) (k1_seq_1 k19_sin_cos C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_fib_num2,ax, ((k15_finseq_1 (k5_relat_1 k2_fib_num2 (k6_domain_1 k5_numbers 2))) = (k12_finseq_1 k5_numbers 1)) ).
tt(t54_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_fib_num3 A B C) = (k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k4_xcmplx_0 k2_fib_num)) B) (k3_power k1_fib_num C)) (k3_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 A k1_fib_num) B) (k3_power k2_fib_num C))) (k7_square_1 5))) ) ) ) ) ) ) ).
tt(t54_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((v11_lattices A) => (v11_lattices (k6_filter_0 A B))) ) ) ) ) ).
tt(t54_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_filter_0 A (k3_lattices A B C) B) = (k4_filter_0 A C B))  &  ((k4_filter_0 A B (k4_lattices A B C)) = (k4_filter_0 A B C)) ) ) ) ) ) ) ) ).
tt(t54_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k1_lattice2 A))) =>  ( ((k7_lattices (k1_lattice2 A) (k1_filter_2 A B)) = (k7_lattices A B))  &  ((k7_lattices A (k2_filter_2 A C)) = (k7_lattices (k1_lattice2 A) C)) ) ) ) ) ) ) ) ).
tt(t54_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r2_wellord2 (k2_finseq_1 A) A)) ) ).
tt(t54_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) =>  ((k3_relat_1 (k1_finseq_2 A) B) = B) ) ) ) ) ) ).
tt(t54_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k3_finseq_1 A) = (k2_xcmplx_0 C D))  &  (B = (k5_relat_1 A (k2_finseq_1 C))) )  =>  ((k1_relset_1 k5_numbers B) = (k2_finseq_1 C)) ) ) ) ) ) ) ) ) ) ).
tt(t54_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((r2_finseq_4 A B) <=>  ((r2_hidden B (k10_xtuple_0 A)) &  ((k1_finseq_3 A (k1_tarski B)) = (k7_finseq_1 (k5_finseq_4 A B) (k6_finseq_4 A B))) ) ) ) ) ) ).
tt(t54_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k7_partfun1 A (k2_finseq_5 A C B) (k3_finseq_1 (k2_finseq_5 A C B))) = (k7_partfun1 A C (k3_finseq_1 C))) ) ) ) ) ) ) ) ).
tt(t54_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( (~  (B = C) )  =>  ((k2_finseq_5 A (k3_finseq_4 A B C D) C) = (k2_finseq_4 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t54_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((r6_binop_1 A C D) & (r2_funct_2 A A E (k10_funcop_1 A A C B (k6_partfun1 A))))  => (r7_binop_1 A E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_fintopo6 A B C D E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 B)))  => (r3_fintopo6 A (k17_finseq_1 (u1_struct_0 A) F B) C D (k7_partfun1 (u1_struct_0 A) B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r2_hidden (k2_flang_1 A) B) =>  ( ((k8_flang_1 A B) = (k6_flang_1 A (k8_flang_1 A B) B))  &  ((k8_flang_1 A B) = (k6_flang_1 A B (k8_flang_1 A B))) ) ) ) ) ) ).
tt(t54_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k1_flang_2 A (k9_subset_1 (k8_afinsq_1 A) B C) D E) (k9_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B D E) (k1_flang_2 A C D E)))) ) ) ) ) ) ) ) ) ).
tt(t54_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k2_flang_3 A B) = (k4_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B 1 C) (k1_flang_3 A B (k2_xcmplx_0 C 1)))) ) ) ) ) ) ).
tt(t54_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ( (? [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  &  ( (A = D)  & (v5_relat_1 D (k3_finseq_2 B))) ) )  => (v5_relat_1 (k1_funct_1 (k8_fomodel0 C) A) B)) ) ) ) ) ).
tt(t54_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v8_struct_0 G) & (l2_fsm_1 G A B)) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 G)) =>  ( ( (G = (k13_fsm_1 A B D E))  &  (F = H) )  =>  ((k2_fsm_1 A E F C) = (k2_fsm_1 A G H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( (! [G:$i] :  ((m1_subset_1 G B) =>  ((k3_funct_2 B A D G) = (k5_binop_1 A C F (k3_funct_2 B A E G))) ) )  => (r2_funct_2 B A D (k10_funcop_1 A B C F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k6_relat_1 B C))) <=>  ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden (k1_funct_1 C A) B)) ) ) ) ) ) ).
tt(t54_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((r2_relset_1 A A (k1_partfun1 A A A A B C) B) &  ((k2_relset_1 A B) = A) )  => (r2_relset_1 A A C (k6_partfun1 A))) ) ) ) ) ) ).
tt(t54_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  ( ((k9_xtuple_0 D) = (k9_xtuple_0 C))  &  ((k13_funct_3 A B) = (k13_funct_3 D C)) ) )  =>  ( (A = D)  &  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C D)) (k9_xtuple_0 (k3_funct_4 E F))) <=>  ((r2_hidden (k4_tarski A C) (k9_xtuple_0 E)) & (r2_hidden (k4_tarski B D) (k9_xtuple_0 F))) ) ) ) ) ) ) ) ) ) ).
tt(t54_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k10_xtuple_0 C) (k4_partfun1 A B)) &  ((r1_tarski (k10_xtuple_0 D) (k4_partfun1 A B)) &  ((k2_funct_5 C) = (k2_funct_5 D)) ) )  =>  ((r2_hidden k1_xboole_0 (k10_xtuple_0 C)) |  ((r2_hidden k1_xboole_0 (k10_xtuple_0 D)) |  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t54_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 (k10_funct_6 A))) =>  ((v1_relat_1 (k1_funct_1 (k10_funct_6 A) B)) & (v1_funct_1 (k1_funct_1 (k10_funct_6 A) B))) ) ) ) ) ).
tt(t54_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k4_funct_7 A (k11_finseq_1 B C D)) = (k3_relat_1 (k6_partfun1 A) (k3_relat_1 B (k3_relat_1 C D)))) ) ) ) ) ) ) ) ).
tt(t54_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_funct_8 A k1_numbers k1_numbers) &  ((v4_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v6_funct_8 (k52_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t54_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k3_fuzzy_1 (k2_zfmisc_1 A B) (k4_fuzzy_2 A B)) (k5_fuzzy_2 A B)) & (r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k3_fuzzy_1 (k2_zfmisc_1 A B) (k5_fuzzy_2 A B)) (k4_fuzzy_2 A B))) ) ) ) ) ).
tt(t54_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_fvaluat1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_fvaluat1 A B))) =>  ( ( (C = E)  &  (D = F) )  =>  ((k3_rlvect_1 A C D) = (k3_rlvect_1 (k7_fvaluat1 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B E (k6_algstr_0 B C D)) = (k10_fvsum_1 A B (k10_fvsum_1 A B E D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) ) ) )  =>  (! [H:$i] :  ((m1_genealg1 H G) =>  (! [I:$i] :  ((m1_genealg1 I G) =>  ( ((k12_genealg1 G H I k6_numbers A B C D E) = (k11_genealg1 G I H A B C D E))  &  ( ((k12_genealg1 G H I F k6_numbers B C D E) = (k11_genealg1 G I H F B C D E))  &  ( ((k12_genealg1 G H I F A k6_numbers C D E) = (k11_genealg1 G I H F A C D E))  &  ( ((k12_genealg1 G H I F A B k6_numbers D E) = (k11_genealg1 G I H F A B D E))  &  ( ((k12_genealg1 G H I F A B C k6_numbers E) = (k11_genealg1 G I H F A B C E))  &  ((k12_genealg1 G H I F A B C D k6_numbers) = (k11_genealg1 G I H F A B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (~  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C)))) => (v1_circuit2 (k5_facirc_1 (k19_gfacirc1 A B C) (k20_gfacirc1 A B C) D 2) (k19_gfacirc1 A B C) (k20_gfacirc1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t54_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) B)) =>  ((k15_glib_000 A) = (k15_glib_000 C)) ) ) ) ) ) ).
tt(t54_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 C)) =>  ((k1_funct_1 (k20_glib_001 A B C D) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden B (k6_glib_000 A)) =>  ((r2_hidden B (k14_glib_003 A)) |  ((k5_card_1 (k14_glib_003 (k13_glib_003 A B C))) = (k2_nat_1 (k5_card_1 (k14_glib_003 A)) 1)) ) ) ) ) ) ) ).
tt(t54_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B))) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k19_euclid k6_numbers 1)))))) ) ) ) ) ) ).
tt(t54_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 C))) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_graph_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ( ( (~ (v1_zfmisc_1 C))  & (m2_finseq_1 C A))  =>  ((k7_partfun1 A (k4_graph_2 A B C) (k3_finseq_1 (k4_graph_2 A B C))) = (k7_partfun1 A C (k3_finseq_1 C))) ) ) ) ) ) ) ).
tt(t54_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u4_struct_0 B) (k12_graph_3 B C A)) =>  (! [E:$i] :  ((v1_finset_1 E) =>  ( (E = (u4_struct_0 B))  =>  ( ((k7_graph_3 B C A) = k6_numbers)  | (r1_xxreal_0 (k3_finseq_1 D) (k5_card_1 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 B)) =>  ((r6_graph_5 B A) =>  ((k10_graph_5 B (k8_finseq_1 (u4_struct_0 B) C D) A) = (k2_xcmplx_0 (k10_graph_5 B C A) (k10_graph_5 B D A))) ) ) ) ) ) ) ) ) ) ).
tt(t54_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) (k3_groeb_2 A B C D E) (k6_polynom1 A C (k10_polynom1 A C (k6_termord A B C D) E) (k10_polynom1 A C (k6_termord A B C E) D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k8_group_2 A B) (k4_group_11 A B C))) ) ) ) ) ) ).
tt(t54_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (m1_group_2 A A)) ) ).
tt(t54_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_group_3 A (k4_group_3 A C B) (k2_group_1 A B)) = C)  &  ((k4_group_3 A (k4_group_3 A C (k2_group_1 A B)) B) = C) ) ) ) ) ) ) ) ).
tt(t54_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((v1_group_3 (k8_group_4 A B C) A) & (m1_group_2 (k8_group_4 A B C) A)) ) ) ) ) ) ) ).
tt(t54_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( ((k5_group_5 A (k6_group_2 A) B) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A)))  &  ((k5_group_5 A B (k6_group_2 A)) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ) ) ).
tt(t54_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ( ((v2_funct_1 D) & (r1_struct_0 (k10_group_6 A B D) C))  =>  ((k1_funct_1 D (k1_funct_1 (k2_funct_1 D) C)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t54_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  => (v3_funct_2 (k12_group_9 A B (k4_group_9 A B)) (u1_struct_0 B) (u1_struct_0 (k10_group_9 A B (k4_group_9 A B))))) ) ) ).
tt(t54_helly,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( (! [C:$i] :  (~  ((r2_hidden C B) &  (! [D:$i] :  ( ((v3_glib_002 D) & (m1_glib_000 D A))  =>  (~  (C = (k24_glib_000 A D)) ) ) ) ) ) )  => (v1_helly B)) ) ) ) ) ).
tt(t54_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) )  =>  ((k12_bilinear k1_complfld A B) = (k12_bilinear k1_complfld A (k3_hermitan A A B))) ) ) ) ) ).
tt(t54_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) A) 2) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers k19_sin_cos) A) (k1_real_1 2))))) ) ).
tt(t54_hurwitz,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 A k1_complfld) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ((r1_xxreal_0 1 (k2_hurwitz k1_complfld A)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (~  ( (~ (r1_xxreal_0 k6_numbers (k3_complex1 B)))  &  ( (~ (r1_xxreal_0 (k17_complex1 (k2_polynom4 k1_complfld (k7_hurwitz A) B)) (k17_complex1 (k2_polynom4 k1_complfld A B))))  &  (~  ((v1_hurwitz A) <=> (v1_hurwitz (k5_hurwitz k1_complfld (k8_hurwitz A B) (k3_hurwitz k1_complfld B 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t54_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((k7_ideal_1 A (k2_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t54_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) &  (! [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) =>  (~  ((r3_incsp_1 A B D) & (r3_incsp_1 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t54_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) => (r1_xxreal_0 A (k1_int_1 B))) ) ) ) ) ).
tt(t54_int_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k4_numbers)))  =>  ( ((r1_int_2 B A) & (r1_int_4 A C))  => (r1_int_4 A (k1_integra2 C B))) ) ) ) ) ) ) ).
tt(t54_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 k16_sin_cos D) (k7_real_1 1 (k1_seq_1 k16_sin_cos D)))) ) ) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t54_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) B) = (k9_real_1 (k10_real_1 (k1_seq_1 k1_sin_cos9 B) (k5_square_1 B)) (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t54_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k16_sin_cos D)) (k1_seq_1 k19_sin_cos D))) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t54_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 A))))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_integr18 (k4_real_ns1 A) (k3_integra5 B C) G) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 A)) G (k3_integra5 B C)) (k4_real_ns1 A) k1_numbers) &  ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers G)) &  ((r2_hidden D (k3_integra5 B C)) &  ((r2_hidden E (k3_integra5 B C)) &  (! [H:$i] :  ((v1_xreal_0 H) =>  ((r2_hidden H (k3_integra5 (k3_xxreal_0 D E) (k4_xxreal_0 D E))) => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 A) (k7_partfun1 (u1_struct_0 (k4_real_ns1 A)) G H)) F)) ) ) ) ) ) ) ) )  => (r1_xxreal_0 (k1_normsp_0 (k4_real_ns1 A) (k6_integr18 (k4_real_ns1 A) G D E)) (k11_binop_2 (k11_binop_2 A F) (k18_complex1 (k10_binop_2 E D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_integra1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers)))) )  =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((v2_seq_2 (k2_partfun1 B k1_numbers D B)) & (v2_seq_2 (k2_partfun1 B k1_numbers E B))) )  => (r1_xxreal_0 (k7_real_1 (k1_seq_1 (k5_integra1 B D C) A) (k1_seq_1 (k5_integra1 B E C) A)) (k1_seq_1 (k5_integra1 B (k3_valued_1 B k1_numbers k1_numbers D E) C) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers 1))  =>  ((k2_integra5 A k24_sin_cos) = (k9_real_1 k8_power 1)) ) ) ) ).
tt(t54_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k7_real_1 A G))  &  (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers F))) = F)  &  ( (F = (k1_relset_1 k1_numbers E))  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 E G) = (k10_real_1 (k9_real_1 A G) (k7_real_1 A G))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B))) ) ) ) ) )  =>  ((k2_integra5 B E) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers F)) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers F)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_interva1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_interva1 B A))  => (r2_hidden k1_xboole_0 (k9_interva1 A B B))) ) ) ) ).
tt(t54_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 A A) A) k8_intpro_1)) ) ).
tt(t54_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k9_real_1 1 A))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid D)) &  ((r1_xxreal_0 A (k13_complex1 (k17_euclid D) (k12_euclid D))) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t54_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) &  ((r2_hidden B C) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ((r1_xxreal_0 k6_numbers (k18_euclid B)) & (r1_xxreal_0 (k17_euclid A) (k17_euclid B))) ) ) ) )  => (r1_jordan6 C A B)) ) ) ) ) ) ) ).
tt(t54_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 (k1_sppol_2 A B C D))))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 (k1_sppol_2 A B C D)))))))) )  =>  (~  ((v3_tops_2 E k5_topmetr (k1_pre_topc (k15_euclid 2) (k9_jordan6 (k1_sppol_2 A B C D)))) &  ( ((k1_funct_1 E k6_numbers) = (k22_pscomp_1 (k1_sppol_2 A B C D)))  &  ( ((k1_funct_1 E 1) = (k18_pscomp_1 (k1_sppol_2 A B C D)))  &  ( ((k2_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k9_jordan6 (k1_sppol_2 A B C D)))) E) = (k9_jordan6 (k1_sppol_2 A B C D)))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 k6_numbers (k10_real_1 1 2))) =>  ((k1_funct_1 E F) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k19_euclid B D) (k9_real_1 1 (k8_real_1 2 F))) (k1_rlvect_1 (k15_euclid 2) (k19_euclid B C) (k8_real_1 2 F)))) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k1_rcomp_1 (k10_real_1 1 2) 1)) =>  ((k1_funct_1 E F) = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k19_euclid B C) (k9_real_1 1 (k9_real_1 (k8_real_1 2 F) 1))) (k1_rlvect_1 (k15_euclid 2) (k19_euclid A C) (k9_real_1 (k8_real_1 2 F) 1)))) ) ) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C))) =>  ((r1_xxreal_0 k6_numbers (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) D) (k6_xcmplx_0 C D)) 2)) &  ((r1_xxreal_0 (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) D) (k6_xcmplx_0 C D)) 2) 1) &  ((k1_funct_1 E (k10_real_1 (k10_real_1 (k9_real_1 (k18_euclid F) D) (k6_xcmplx_0 C D)) 2)) = F) ) ) ) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) =>  ((r1_xxreal_0 k6_numbers (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) B) (k6_xcmplx_0 A B)) 2) (k10_real_1 1 2))) &  ((r1_xxreal_0 (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) B) (k6_xcmplx_0 A B)) 2) (k10_real_1 1 2)) 1) &  ((k1_funct_1 E (k7_real_1 (k10_real_1 (k10_real_1 (k9_real_1 (k17_euclid F) B) (k6_xcmplx_0 A B)) 2) (k10_real_1 1 2))) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) = A) )  =>  ((r1_xxreal_0 B A) |  ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden C B) & (r1_xboole_0 (k7_topreal1 C) (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ) ) ) ) ).
tt(t54_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k18_euclid (k1_jordan5c (k3_topreal1 2 (k1_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))) (k18_euclid (k2_jordan5c (k3_topreal1 2 (k2_jordan1e A B)) (k6_jordan6 (k7_xcmplx_0 (k2_xcmplx_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) 2)) (k22_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))) (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B))))))) ) ) ) ) ) ).
tt(t54_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski (k2_nat_1 E 1) D) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 E 1) D))  &  ((r2_hidden (k4_tarski E D) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) E D)) ) ) )  =>  ((r1_xboole_0 (k3_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski E (k7_nat_d D 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_topreal1 A) &  ((v3_topreal1 A) &  ((v2_funct_1 A) &  ((v2_topreal1 B) &  ((v3_topreal1 B) &  ((v2_funct_1 B) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A) (k3_topreal1 2 B)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1))) ) ) ) ) ) ) )  => (v3_topreal1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t54_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (~  ((r1_xxreal_0 1 B) &  ( (C = (k6_subset_1 (k1_euclid B) (a_2_4_jordan2c A B)))  & (v9_rltopsp1 C (k15_euclid B))) ) ) ) ) ) ) ) ) ).
tt(t54_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (A = B) )  &  ((r1_jordan4 C D A B) &  ((r2_jordan4 C E A B) &  ((k1_funct_1 D 2) = (k1_funct_1 E 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r1_jordan5c A B C D B))  =>  (D = B) ) ) ) ) ) ) ) ) ) ).
tt(t54_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k9_pscomp_1 (k2_jgraph_6 A B C D)) = C) ) ) ) ) ) ) ) ) ) ).
tt(t54_kurato_1,ax,(r5_zfmisc_1 k6_kurato_1 (k1_tops_1 k3_topmetr k6_kurato_1) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1)) (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1))) (k2_pre_topc k3_topmetr k6_kurato_1) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr k6_kurato_1)) (k2_pre_topc k3_topmetr (k1_tops_1 k3_topmetr (k2_pre_topc k3_topmetr k6_kurato_1))))).
tt(t54_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F B) => (r3_lattices C (k3_funct_2 A (u1_struct_0 C) D F) E)) ) )  => (r3_lattices C (k2_lattice2 A C B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) &  ((v4_lattice3 B) &  ((v6_lattice3 B) & (l3_lattices B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( ((k3_lattices B C (k16_lattice3 B A)) = (k16_lattice3 B (a_3_9_lattice3 A B C)))  &  ((k3_lattices B (k16_lattice3 B A) C) = (k16_lattice3 B (a_3_10_lattice3 A B C))) ) ) ) ) ) ) ).
tt(t54_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k6_glib_000 A) k5_numbers))))  =>  ( ((v5_lexbfs B A) &  ((k1_relset_1 (k6_glib_000 A) B) = (k6_glib_000 A)) )  =>  (! [C:$i] :  ((m3_chord C A) =>  ( ((k2_funct_1 C) = B)  => (v7_chord C A)) ) ) ) ) ) ) ) ).
tt(t54_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k3_limfunc1 C)))) ) )  | (v4_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t54_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r4_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k3_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k7_real_1 (k2_limfunc2 B A) (k2_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t54_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_limfunc1 A) &  ((v6_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ((v3_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k5_limfunc1 B)) ) ) ) ) ) ) ).
tt(t54_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  ((k1_mesfunc6 A B C (k56_valued_1 A k1_numbers (k8_lpspace1 A k6_numbers))) = k6_numbers) ) ) ) ) ) ) ).
tt(t54_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k12_lpspace2 A B C G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k12_lpspace2 A B C G))) =>  ( ( ((r2_hidden D H) & (r2_hidden E I))  => (r2_hidden (k3_valued_1 A k1_numbers k1_numbers D E) (k1_algstr_0 (k12_lpspace2 A B C G) H I)))  &  ((r2_hidden D H) => (r2_hidden (k26_valued_1 A k1_numbers D F) (k1_rlvect_1 (k12_lpspace2 A B C G) H F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 B A) => (r8_ltlaxio1 B (k6_ltlaxio1 A))) ) ) ) ) ).
tt(t54_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A (k6_cqc_lang A B)) C) A) <=> (v2_cqc_the1 (k8_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(t54_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_mathmorp A B C) (k4_mathmorp A (k4_subset_1 (u1_struct_0 A) B D) C))) ) ) ) ) ) ) ) ).
tt(t54_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ( ((r1_matrix10 B C) & (r2_matrix10 D E))  => (r1_matrix10 (k4_matrix10 A B E) (k4_matrix10 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (~ (r2_hidden C (k12_matrix_2 A)))  =>  ((k12_matrix_3 A B (k4_matrix11 A A (u1_struct_0 B) C D)) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix13,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_finset_1 B) &  ((v1_setfam_1 B) & (m1_subset_1 B (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski A B) =>  ((k14_finseq_1 A) = (k1_partfun1 k5_numbers k5_numbers k5_numbers k5_numbers (k14_finseq_1 (k8_relat_1 (k5_matrix13 B) A)) (k5_matrix13 B))) ) ) ) ) ).
tt(t54_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ( ((k4_matrix_6 A B D C) = (k12_matrix_1 B A))  &  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (~  ((k4_matrix_6 A B C E) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  ( (~ (r1_xxreal_0 B k1_xboole_0))  &  (~  ((k4_matrix15 D (k1_matrix_3 D A B) (k1_matrix_3 D A C)) = (a_3_1_matrix15 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v6_struct_0 F))  &  ((v13_algstr_0 F) &  ((v33_algstr_0 F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_matrix_1 G (u1_struct_0 F) C C) =>  ( ((v5_matrix16 G F) &  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))) &  ( (D = (k2_xcmplx_0 A 1))  &  (E = (k2_xcmplx_0 B 1)) ) ) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 C B) |  ((k3_matrix_1 (u1_struct_0 F) G D E) = (k3_matrix_1 (u1_struct_0 F) G A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k1_matrix_4 A D B) = (k3_matrix_3 A D (k2_matrix_3 A C))) ) ) ) )  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) => (r1_matrix_6 A B (k4_matrix_6 A B C C) (k4_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ).
tt(t54_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k2_matrix_6 A B (k2_matrix_6 A B C D) E)) = (k3_rlvect_1 B (k3_rlvect_1 B (k1_matrix_8 A B C) (k1_matrix_8 A B D)) (k1_matrix_8 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (? [D:$i] :  ((m1_subset_1 D k5_numbers) &  ((r2_hidden D (k2_finseq_1 A)) &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) C D) E) = (k4_struct_0 B)) ) ) ) ) ) )  =>  ((k2_matrix_9 A B C) = (k4_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t54_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k8_complsp2 A B) = (k15_complex1 (k8_complsp2 B A))) ) ) ) ) ) ) ).
tt(t54_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 B))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( (E = (k13_matrixj1 (u1_struct_0 B) (k4_struct_0 B) (k5_matrixj1 (u1_struct_0 B) C D)))  =>  ( ((k3_finseq_1 C) = (k1_matrix_1 C))  |  ((k12_matrix_3 A B E) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 A)))  =>  ((k9_matrix_1 k1_numbers (k3_matrixr1 A B) C) = (k4_rvsum_1 (k9_matrix_1 k1_numbers A C) (k9_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t54_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k12_matrixr1 (k5_matrixr1 B C) A) = (k8_rvsum_1 (k12_matrixr1 B A) (k12_matrixr1 C A))) ) ) ) ) ) ) ) ) ).
tt(t54_matrprob,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A))) )  =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) & (r1_xxreal_0 1 (k1_matrix_1 B))) ) ) ) ) ).
tt(t54_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_zfmisc_1 A A A A) = (k4_zfmisc_1 B B B B))  =>  (A = B) ) ) ) ).
tt(t54_measure6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden A B) <=> (r2_hidden (k10_real_1 1 A) (k5_measure6 B))) ) ) ) ) ).
tt(t54_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k10_member_1 A B) = (a_2_2_member_1 A B)) ) ) ) ) ).
tt(t54_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v4_memstr_0 D A B)) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k9_memstr_0 A B (k1_funct_4 C D) E) = (k1_funct_4 (k9_memstr_0 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_mesfun9c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k2_numbers)) &  ((v1_mesfunc8 E A k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k2_numbers))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ( (D = (k1_relset_1 A (k4_mesfunc5 A k2_numbers E k6_numbers)))  &  ( (! [G:$i] :  ((v7_ordinal1 G) => (r2_mesfun6c A B C (k4_mesfunc5 A k2_numbers E G))) )  & (r2_mesfun9c A E F)) )  =>  ((r1_xxreal_0 k1_xxreal_0 (k1_mesfunc9 C D)) |  ((r2_mesfun6c A B C F) &  (? [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers k2_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  ((k8_nat_1 k2_numbers G H) = (k1_mesfun6c A B C (k4_mesfunc5 A k2_numbers E H))) ) )  &  ((v2_comseq_2 G) &  ((k3_comseq_2 G) = (k1_mesfun6c A B C F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A B) (k8_nat_1 k7_numbers A C))) ) ) ) )  =>  ((v10_mesfunc5 A) &  ((k2_mesfunc5 A) = (k8_supinf_2 (k17_supinf_2 A))) ) ) ) ) ).
tt(t54_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [C:$i] :  ((r2_hidden C (k1_relset_1 A B)) => (r1_xxreal_0 (k1_seq_1 B C) k6_numbers)) )  => (v2_mesfunc5 B)) ) ) ) ) ).
tt(t54_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k15_midsp_1 A)) (u1_struct_0 (k15_midsp_1 A))) (u1_struct_0 (k15_midsp_1 A)) (k2_zfmisc_1 (k10_midsp_1 A) (k10_midsp_1 A)) (k10_midsp_1 A) (u1_algstr_0 (k15_midsp_1 A)) (k12_midsp_1 A))) ) ).
tt(t54_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] : (r1_xxreal_0 (k24_mmlquery A B) (k3_finseq_1 A))) ) ) ).
tt(t54_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_modelc_2 C) & (l1_modelc_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k15_modelc_2 (u1_modelc_2 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 C))))) )  =>  ((k21_modelc_2 C D (k7_modelc_2 A B)) = (k23_modelc_2 C (k21_modelc_2 C D A) (k21_modelc_2 C D B))) ) ) ) ) ) ) ) ) ).
tt(t54_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k23_modelc_3 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k23_modelc_3 B))))) )  =>  (~  ((v7_modelc_2 A) &  ((r2_hidden A (u1_modelc_3 B (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 B) C 1) B))) &  ( (! [D:$i] :  ((v7_ordinal1 D) => (r6_modelc_3 B (k10_modelc_3 (k1_funct_1 C D) B) (k10_modelc_3 (k3_funct_2 k5_numbers (k23_modelc_3 B) C (k1_nat_1 D 1)) B))) )  &  ( (? [D:$i] :  ((v7_ordinal1 D) &  ((r1_xxreal_0 1 D) &  (~  ((r2_hidden A (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C D) B))) &  ((r2_hidden (k11_modelc_2 A) (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C D) B))) &  (~ (r2_hidden (k12_modelc_2 A) (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C D) B)))) ) ) ) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r1_xxreal_0 1 D) &  ((r2_hidden (k12_modelc_2 A) (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C D) B))) &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 1 E) =>  ((r1_xxreal_0 D E) |  ((r2_hidden A (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C E) B))) & (r2_hidden (k11_modelc_2 A) (u1_modelc_3 B (k10_modelc_3 (k1_funct_1 C E) B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  ((k6_moebius1 (k1_newton A B)) = A) ) ) ) ) ).
tt(t54_monoid_0,ax, ((k4_binop_1 (u1_struct_0 k7_monoid_0) (u2_algstr_0 k7_monoid_0)) = 1) ).
tt(t54_monoid_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v9_monoid_0 B A) => (v9_monoid_0 (k21_monoid_1 A A A B) (k1_zfmisc_1 A))) ) ) ) ) ).
tt(t54_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_msualg_4 C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) => (r8_pboole (u1_struct_0 A) (k10_msualg_6 A B C) (k9_msualg_6 A B (k8_msualg_6 A B C)))) ) ) ) ) ) ).
tt(t54_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k1_ordinal1 A) = (a_1_0_nat_1 A)) ) ) ).
tt(t54_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k12_nat_3 (k2_int_2 B A)) = (k6_nat_3 k10_newton (k12_nat_3 B) (k12_nat_3 A))) ) ) ) ) ).
tt(t54_nat_4,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) =>  ((r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 B C)) &  (~ (r1_xxreal_0 (k1_funct_1 A C) k6_numbers)) ) ) ) ) )  => (r1_xxreal_0 (k21_rvsum_1 A) (k21_rvsum_1 B))) ) ) ) ) ).
tt(t54_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 A (k7_nat_d B C)) & (r1_xxreal_0 C B))  => (r1_xxreal_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t54_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers))))  =>  ((r11_ncfcont1 A C B) <=> (r11_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k1_numbers C B) B)) ) ) ) ) ) ).
tt(t54_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k4_prvect_2 A))) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (C = E)  &  ( (F = (k4_struct_0 (k14_prvect_2 A)))  &  ( ((k3_finseq_1 B) = (k23_binop_2 (k3_finseq_1 A) 1))  &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k3_finseq_1 A)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 B)) =>  ((k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) B H) = (k1_funct_4 F (k11_card_3 (k4_prvect_2 A) E (k2_finseq_1 (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) H))))) ) ) ) ) ) ) ) )  =>  ((k3_rlvect_1 (k14_prvect_2 A) D (k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) B G)) = (k3_funct_2 (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)))) (u1_struct_0 (k14_prvect_2 A)) (k4_ndiff_5 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)) (k3_rlvect_1 (k14_prvect_2 A) D (k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) B (k23_binop_2 G 1)))) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)))) (k3_ndiff_5 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G))) (k3_rlvect_1 (k14_prvect_2 A) D C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_nat_d A (k5_nat_d A B)) = A) ) ) ) ) ).
tt(t54_nfcont_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 (u1_struct_0 B) C)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D A) =>  ((k7_partfun1 k1_numbers C D) = (k1_normsp_0 B D)) ) ) ) )  => (r4_nfcont_1 B C A)) ) ) ) ) ) ).
tt(t54_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 (k7_normform A))) => (r1_tarski B (k10_normform A B B))) ) ) ).
tt(t54_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u4_struct_0 B) (u4_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 B) (u4_struct_0 C))))) )  => (r2_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 C)) (k11_oppcat_1 (k2_oppcat_1 A) C (k10_oppcat_1 A C (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E))) (k1_partfun1 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 (k2_oppcat_1 B)) (u4_struct_0 (k2_oppcat_1 B)) (u4_struct_0 (k2_oppcat_1 C)) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B D)) (k11_oppcat_1 (k2_oppcat_1 B) C (k10_oppcat_1 B C E))))) ) ) ) ) ) ) ) ) ) ).
tt(t54_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((r8_orders_1 A B) & (v4_relat_2 A))  => (r6_orders_1 A B)) ) ) ) ).
tt(t54_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((r9_orders_1 (u1_orders_2 A) B) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = C) )  => (r2_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t54_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k5_ordinal3 A A) = k1_xboole_0) ) ) ).
tt(t54_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v1_finset_1 B) & (v1_ordinal2 B)) ) ) )  =>  ((k4_ordinal5 (k1_ordinal4 B (k5_afinsq_1 A))) = (k10_ordinal2 (k4_ordinal5 B) A)) ) ) ) ) ).
tt(t54_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  ( (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden B (k9_xtuple_0 A)) => (v2_ordinal6 (k1_funct_1 A B))) ) )  =>  ( ((k9_xtuple_0 A) = k1_xboole_0)  |  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  ( ((r2_hidden B (k9_xtuple_0 (k7_ordinal6 A))) & (r2_hidden C (k10_xtuple_0 A)))  => (r1_ordinal1 (k1_funct_1 C B) (k1_funct_1 (k7_ordinal6 A) B))) ) ) ) ) ) ) ) ) ).
tt(t54_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t54_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r3_parsp_2 A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t54_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) => (r1_partfun1 A B)) ) ) ) ) ).
tt(t54_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden D (k1_relset_1 A E)) & (r2_hidden D C))  <=> (r2_hidden (k4_tarski D (k7_partfun1 B E D)) (k2_partfun1 A B E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) => (r2_pboole A (k4_pboole A D C) (k4_pboole A D B))) ) ) ) ) ) ) ) ).
tt(t54_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r3_pdiff_5 B A) & (r3_pdiff_5 C A))  =>  ((r3_pdiff_1 3 3 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) &  ((k11_pdiff_1 3 3 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A) = (k9_real_1 (k3_pdiff_5 B A) (k3_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t54_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (v1_pdiff_7 B A))  =>  ((r2_pdiff_9 B A C) <=>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((r2_hidden D B) => (r1_pdiff_7 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_pepin,ax, ((k4_pepin 4) = (k2_nat_1 (k4_nat_1 256 256) 1)) ).
tt(t54_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  ((k5_card_1 B) = (k5_card_1 (k12_pnproc_1 B A))) ) ) ) ) ).
tt(t54_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (~ (v1_xboole_0 (k8_polyform A k6_numbers))) ) ) ).
tt(t54_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  => (v1_polynom5 (k9_polynom3 A) A)) ) ).
tt(t54_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r11_polyred A B C D) & (r11_polyred A B D E))  => (r11_polyred A B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ((k6_xcmplx_0 (k5_power A B) (k5_power A C)) = (k5_power A (k13_complex1 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r6_pboole A (k12_pre_poly A B (k16_pre_poly A)) B)) ) ) ).
tt(t54_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k10_real_1 1 (k6_prepower A B)) = (k6_prepower A (k4_xcmplx_0 B))) ) ) ) ) ) ).
tt(t54_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 C D) = (k4_prob_3 A B D)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r2_hidden D (k1_relset_1 k5_numbers B)))  =>  ((k1_funct_1 C D) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t54_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k9_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k6_cqc_lang A B) (k4_cqc_the1 A)))  => (r2_hidden C (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t54_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_xxreal_0 (k17_euclid (k10_pscomp_1 A)) (k17_euclid (k25_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k10_pscomp_1 A)) (k17_euclid (k24_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k10_pscomp_1 A)) (k17_euclid (k13_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k25_pscomp_1 A)) (k17_euclid (k24_pscomp_1 A))) &  ((r1_xxreal_0 (k17_euclid (k25_pscomp_1 A)) (k17_euclid (k13_pscomp_1 A))) & (r1_xxreal_0 (k17_euclid (k24_pscomp_1 A)) (k17_euclid (k13_pscomp_1 A)))) ) ) ) ) ) ) ).
tt(t54_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k4_pboole A (k2_pzfmisc1 A B C) D) (k2_pzfmisc1 A B C)) =>  ((v1_xboole_0 A) |  ( (~ (r1_pboole A B D))  &  (~ (r1_pboole A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r3_qc_lang2 A B C) & (r1_xxreal_0 (k3_finseq_1 (k11_qc_lang1 A C)) (k3_finseq_1 (k11_qc_lang1 A B)))) ) ) ) ) ) ) ) ).
tt(t54_qc_lang3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_qc_lang1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 B) (k8_qc_lang1 B A)) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k2_qc_lang1 B)))  =>  ((k5_qc_lang3 B (k10_qc_lang1 B C D)) = (a_3_2_qc_lang3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t54_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k18_quatern2 A (k26_quaterni B C)) = (k26_quaterni (k18_quatern2 A B) (k18_quatern2 A C))) ) ) ) ) ) ) ).
tt(t54_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k29_quaterni A (k26_quaterni B C)) = (k29_quaterni (k29_quaterni A B) C)) ) ) ) ) ) ) ).
tt(t54_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k31_quaterni (k26_quaterni A B)) = (k26_quaterni (k31_quaterni A) (k31_quaterni B))) ) ) ) ) ).
tt(t54_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v1_quofield D A B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ((v1_quofield E B C) => (v1_quofield (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [F:$i] :  ((m1_rcomp_3 F A B E) =>  ( ((m1_setfam_1 E (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 E (k4_topmetr A B)) &  ((v1_rcomp_3 E (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((r2_hidden C (k4_finseq_1 F)) & (r2_hidden D (k4_finseq_1 F))) ) ) ) )  =>  ((r1_xxreal_0 D C) | (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) F C)) (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) F D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) 1) k6_numbers))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 2)) (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 2)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1))))) ) ) ) ) ) ).
tt(t54_relat_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k3_relat_1 A (k4_relat_1 (k10_xtuple_0 A))) = A) ) ) ).
tt(t54_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski C (k10_xtuple_0 D)) <=> (r1_tarski C (k7_relset_1 B B (k7_relset_2 B A B (k3_relset_1 A B D) D) C))) ) ) ) ) ) ) ).
tt(t54_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_rewrite1 A) & (v4_rewrite1 A)) )  =>  (! [B:$i] : (r4_rewrite1 A B (k2_rewrite1 A B))) ) ) ).
tt(t54_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r4_rewrite2 A B C E) & (r4_rewrite2 A C D E))  => (r4_rewrite2 A B D E)) ) ) ) ) ) ) ) ) ) ).
tt(t54_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  (! [G:$i] :  ((m1_rewrite1 G (k1_rewrite3 C E F)) =>  ( ( ((k1_funct_1 G 1) = (k4_tarski A D))  &  ((k1_funct_1 G (k3_finseq_1 G)) = (k4_tarski B D)) )  =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 G)) =>  ((k2_xtuple_0 (k1_funct_1 G H)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 (k6_rfunct_1 A k1_numbers B) A) <=>  ( ((k8_relset_1 A k1_numbers B (k1_tarski k6_numbers)) = k1_xboole_0)  & (v1_partfun1 B A)) ) ) ) ) ) ).
tt(t54_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_rfunct_3 A B) & (r1_tarski C B))  => (r2_rfunct_3 A C)) ) ) ) ) ).
tt(t54_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 B) => (r1_xxreal_0 (k1_rinfsup1 (k3_rinfsup1 B)) (k1_seq_1 (k4_rinfsup1 B) A))) ) ) ) ) ).
tt(t54_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v2_rusub_4 C B) => (v2_rusub_4 (k1_convex1 B C A) B)) ) ) ) ) ) ) ).
tt(t54_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden B (k3_rlsub_1 A C D)) <=>  ((k3_rlsub_1 A C D) = (k3_rlsub_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t54_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))))  &  ((v10_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) & (l3_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ) ) ).
tt(t54_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D k1_numbers))  => (m1_connsp_2 (k1_convex1 A C D) A (k1_rlvect_1 A B D))) ) ) ) ) ) ) ) ).
tt(t54_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) C B))) ) ) ) ) ) ) ).
tt(t54_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k10_rlvect_2 A C D) B) = (k9_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers C B) (k3_funct_2 (u1_struct_0 A) k1_numbers D B))) ) ) ) ) ) ) ) ) ).
tt(t54_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_rmod_2 F A B) =>  ( ((r2_hidden C (k3_rmod_2 A B D F)) & (r2_hidden C (k3_rmod_2 A B E F)))  =>  ((k3_rmod_2 A B D F) = (k3_rmod_2 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k9_rmod_4 A B D E) C) = (k5_algstr_0 A (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) D C) (k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k3_robbins1 A (k5_robbins1 A B C)) = (k3_robbins1 A C)) ) ) ) ) ) ) ).
tt(t54_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k5_robbins1 A B C) (k5_robbins1 A B D)) = (k5_robbins1 A D (k5_robbins1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t54_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k1_struct_0 A)) B) = k6_numbers) ) ) ) ) ).
tt(t54_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_rpr_1 A B C) =>  ((r1_xxreal_0 (k1_rpr_1 A C) k6_numbers) |  ((k2_rpr_1 A C B) = (k1_rpr_1 A B)) ) ) ) ) ) ) ) ) ).
tt(t54_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k4_algstr_0 A C) (k3_rusub_1 A C B)) <=> (r1_struct_0 B C)) ) ) ) ) ) ) ).
tt(t54_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))))  &  ((v10_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) & (l3_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ) ) ).
tt(t54_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k5_rusub_5 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( (B = (k6_bhsp_2 A C D))  => (v4_pre_topc B (k5_rusub_5 A))) ) ) ) ) ) ) ) ) ).
tt(t54_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k10_rvsum_1 A (k19_binop_2 1)) = (k6_rvsum_1 A)) ) ) ).
tt(t54_rvsum_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_valued_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_valued_0 C)) ) )  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k11_rvsum_2 (k3_rvsum_2 A B) C) = (k3_rvsum_2 (k11_rvsum_2 A C) (k11_rvsum_2 B C))) ) ) ) ) ) ) ) ).
tt(t54_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (D = (k1_funct_4 E C))  &  (A = B) )  =>  ((k1_funct_1 C A) = (k1_funct_1 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r4_scmfsa7b A C))  &  ( (~ (r3_scmfsa7b B C))  & (r4_scmfsa7b (k5_scmfsa6a A B) C)) ) ) ) ) ) ) ) ) ).
tt(t54_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_scm_halt C) & (v3_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (r4_scmfsa7b C D))  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers)))) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers)))) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D) = (k6_xcmplx_0 (k1_funct_1 B D) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t54_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k3_scmpds_2 B) A) (k4_struct_0 k1_scmpds_2)) = (k17_scmpds_2 A B))  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k3_scmpds_2 B) A) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t54_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers) )  =>  ((k1_funct_1 (k6_scmpds_4 (k5_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k5_numbers) =>  ( ( ((k1_funct_1 B (k1_scmp_gcd F)) = G)  &  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd C)) E)) = k6_numbers)  &  ( ((k3_finseq_1 H) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd C)) D)))  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 H) I))  =>  ((k1_funct_1 H (k2_nat_1 I 1)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd G)) I))) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd C)) C) |  ((r1_xxreal_0 E D) |  ((r1_xxreal_0 F (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd C)) E)) |  ((r1_xxreal_0 G F) |  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd G)) G) |  ((k1_funct_1 (k6_scmpds_4 (k2_scmpds_7 (k1_scmp_gcd C) D 1 (k4_scmpds_4 (k12_scmpds_2 (k1_scmp_gcd C) (k1_scmp_gcd G) E k6_numbers) (k11_scmpds_2 (k1_scmp_gcd F) k6_numbers 1))) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd C)) E)) = (k2_wsierp_1 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ( ((k8_scmyciel A) = k6_numbers)  =>  ((k3_tarski A) = k1_xboole_0) ) ) ) ).
tt(t54_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_semi_af1 A B B C D) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t54_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A)) (k56_valued_1 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers A)))) ) ).
tt(t54_seq_4,ax,(r6_binop_1 k2_numbers k29_binop_2 k27_binop_2)).
tt(t54_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k6_square_1 B))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k3_xcmplx_0 (k3_xcmplx_0 (k13_complex1 1 6) (k2_nat_1 (k4_nat_1 4 B) 3)) (k6_square_1 B)) (k1_seq_1 (k3_series_1 A) B))) ) ) ) ) ) ) ).
tt(t54_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k3_prob_1 A B) (k3_kurato_0 A B))) ) ) ).
tt(t54_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B (k9_setlim_2 B D C)) A) (k5_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k2_setlim_1 B D) A)))) ) ) ) ) ) ) ).
tt(t54_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k5_finsub_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 A))))) )  =>  ((r2_funct_2 A (k5_finsub_1 A) B (k11_setwiseo A)) <=>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A (k5_finsub_1 A) B C) = (k1_tarski C)) ) ) ) ) ) ) ) ).
tt(t54_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((r2_hidden (k16_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)) | (r2_hidden (k17_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ((k5_sf_mastr C) = A) ) ) ) ) ) ) ) ) ).
tt(t54_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A C (k5_sheffer1 A D B))) B)) = (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B D))) C))) ) ) ) ) ) ) ) ) ).
tt(t54_simplex0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_simplex0 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_tarski B C) => (m2_simplex0 (k10_simplex0 A D (k5_relat_1 E B)) A (k10_simplex0 A D (k5_relat_1 E C)))) ) ) ) ) ) ) ) ).
tt(t54_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k2_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ).
tt(t54_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_binop_2 (k5_binop_2 (k6_binop_2 (k3_binop_2 1 (k5_binop_2 (k19_binop_2 1) k7_complex1)) 2) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1)))) (k5_binop_2 (k6_binop_2 (k3_binop_2 1 k7_complex1) 2) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))))) = (k9_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)) (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B)))) ) ) ) ) ).
tt(t54_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v6_valued_0 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t54_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k18_complex1 B) (k18_complex1 A))) )  =>  ((k10_binop_2 (k2_sin_cos7 A) (k2_sin_cos7 B)) = (k2_sin_cos7 (k10_binop_2 (k11_binop_2 A B) (k7_square_1 (k11_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 B) 1)))))) ) ) ) ) ) ).
tt(t54_sin_cos9,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1)))).
tt(t54_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k1_seq_1 k24_sin_cos A) k6_numbers)) ) ) ).
tt(t54_sppol_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k1_sppol_2 A B C D) = (a_4_0_sppol_2 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t54_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) =>  ((k6_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k17_euclid A)) ) ) ) ) ) ).
tt(t54_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k23_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) ) ).
tt(t54_sprect_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v1_sprect_1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) )  =>  (! [B:$i] :  ( ((v4_topreal1 B) & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  ( ((r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k2_goboard9 A)) & (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)) (k3_goboard9 A)))  => (r1_sprect_2 A (k2_jordan3 B (k2_jordan5c (k3_topreal1 2 B) (k3_topreal1 2 A) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B (k3_finseq_1 B)))))) ) ) ) ) ).
tt(t54_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t54_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((k3_xcmplx_0 A (k6_square_1 B)) = (k6_square_1 (k3_xcmplx_0 (k3_square_1 A) B))) ) ) ) ) ) ).
tt(t54_stirl2_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((k10_xtuple_0 (k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski B))))) = (k6_subset_1 (k10_xtuple_0 A) (k1_tarski B)))  &  (! [C:$i] :  ( (~  (C = B) )  =>  ((k8_relat_1 (k5_relat_1 A (k6_subset_1 (k9_xtuple_0 A) (k8_relat_1 A (k1_tarski B)))) (k1_tarski C)) = (k8_relat_1 A (k1_tarski C))) ) ) ) ) ) ) ).
tt(t54_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [F:$i] :  ((m2_subset_1 F (k16_substut1 A) (k38_substut1 A)) =>  (! [G:$i] :  ((m1_substut1 G A (k7_sublemma A F B)) =>  ((v3_substut1 (k7_sublemma A F B) A) =>  ( (! [H:$i] :  ((m1_subset_1 H C) => (r1_sublemma A F C (k1_sublemma A C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H)) (k3_sublemma A F C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H)))) D)) )  <=>  (! [H:$i] :  ((m1_subset_1 H C) => (r1_sublemma A F C (k1_sublemma A C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H)) (k14_sublemma A C (k13_sublemma A F B G C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H))) (k12_sublemma A C B H))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k6_setfam_1 (u1_struct_0 A) B)))) (k6_setfam_1 (u1_struct_0 A) (k1_pcomps_1 A (k1_tdlat_2 A (k1_pcomps_1 A B)))))) ) ) ) ).
tt(t54_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C (k2_pre_topc A B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) &  ((k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) = (k6_domain_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tex_2 B A) &  ((v1_tex_3 B A) & (m1_pre_topc B A)) ) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v3_tex_3 C A) & (m1_pre_topc C A)) ) )  & (r4_tsep_2 A B C)) ) ) ) ) ) ).
tt(t54_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_subset_1 (k4_tex_4 A B) (k4_tex_4 A C)) <=>  (~  ( (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((r1_tarski (k4_tex_4 A B) D) & (r1_xboole_0 D (k4_tex_4 A C))) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_pre_topc D A) &  ((r1_xboole_0 D (k4_tex_4 A B)) & (r1_tarski (k4_tex_4 A C) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  => (r1_funct_2 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 C) (u1_struct_0 A) D (k2_tmap_1 B A D C))) ) ) ) ) ) ) ) ) ).
tt(t54_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) => (r2_funct_2 (u1_struct_0 (k5_topalg_1 A B)) (u1_struct_0 (k5_topalg_1 A C)) (k2_tops_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)) (k6_topalg_1 A B C D)) (k6_topalg_1 A C B (k2_borsuk_2 A B C D)))) ) ) ) ) ) ) ) ).
tt(t54_topgen_1,ax, ((v2_tops_1 k1_borsuk_5 k3_topmetr) & (m1_subset_1 k1_borsuk_5 (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ).
tt(t54_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_topgen_4 A (k4_subset_1 (u1_struct_0 A) B C)) = (k4_subset_1 (u1_struct_0 A) (k4_topgen_4 A B) (k4_topgen_4 A C))) ) ) ) ) ) ) ).
tt(t54_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v4_pre_topc (k10_prob_1 A) k2_topgen_3) & (m1_subset_1 (k10_prob_1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t54_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A B) => (m1_connsp_2 (k1_group_2 A C) A (k2_group_1 A B))) ) ) ) ) ) ).
tt(t54_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k11_metric_1 A B k6_numbers) = (k1_tarski B)) ) ) ) ) ).
tt(t54_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) => (r1_xboole_0 (k6_jgraph_6 A B C) (k5_jgraph_6 A B C))) ) ) ) ) ) ).
tt(t54_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k15_euclid A)))))) )  =>  ((k85_valued_2 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) C D) = (k3_funcop_1 (k16_toprealc A) C D)) ) ) ) ) ) ) ) ) ).
tt(t54_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) => (v1_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t54_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) = (k8_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t54_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v4_pre_topc C A) &  ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  (D = E) ) ) )  =>  ((k2_pre_topc A D) = (k2_pre_topc B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v5_transgeo B A) => (v2_transgeo B A)) ) ) ) ) ).
tt(t54_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((r2_hidden B (k3_trees_1 A)) <=>  (~ (r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers k6_numbers)) A)) ) ) ) ) ) ).
tt(t54_trees_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k2_trees_1 A) = (k11_trees_3 (k2_finseq_2 A (k2_trees_1 k6_numbers)))) ) ) ).
tt(t54_tsep_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) D (k4_subset_1 (u1_struct_0 A) B C)) B) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) E (k4_subset_1 (u1_struct_0 A) B C)) C) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) F (k4_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) B C)) &  ( ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((v4_pre_topc D A) &  ((v4_pre_topc E A) & (v3_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (~  ( (~ (r1_xxreal_0 A B))  &  ((r1_nat_d B A) &  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k14_polynom3 k1_complfld))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 D k1_complfld) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  (~  ( (D = (k3_group_4 (k14_polynom3 k1_complfld) C))  &  ( ((k4_finseq_1 C) = (k2_finseq_1 A))  &  ( (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  ((r2_hidden E (k2_finseq_1 A)) =>  ( ( (~  ((r1_nat_d E A) &  ( (~ (r1_nat_d E B))  &  (~  (E = A) ) ) ) )  =>  ((k1_funct_1 C E) = (k3_algseq_1 k1_complfld (k1_group_1 k1_complfld))) )  &  ((r1_nat_d E A) =>  ((r1_nat_d E B) |  ( (E = A)  |  ((k1_funct_1 C E) = (k5_uniroots E)) ) ) ) ) ) ) )  & (r2_funct_2 k5_numbers (u1_struct_0 k1_complfld) (k4_uniroots A k1_complfld) (k13_polynom3 k1_complfld (k13_polynom3 k1_complfld (k4_uniroots B k1_complfld) (k5_uniroots A)) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k8_uproots A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A))) = (k2_uproots (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) B) 1)) ) ) ) ) ).
tt(t54_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v2_relat_1 E) &  ( (! [F:$i] :  ((r2_hidden F (k1_relset_1 A E)) => (v2_relat_1 (k1_funct_1 E F))) )  & (r2_relset_1 A (k2_valued_2 (k1_valued_2 B)) (k42_valued_2 A B E C) (k42_valued_2 A B E D))) )  =>  ( (E = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_struct_0 E C) <=>  ((k3_vectsp_4 A B D E) = (k3_vectsp_4 A B (k5_algstr_0 B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((r1_struct_0 C (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D))) & (r1_struct_0 D (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((v3_funct_1 (k2_partfun1 B (u1_struct_0 C) D A)) => (r1_vfunct_1 B C D A)) ) ) ) ) ) ) ) ).
tt(t54_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C D)) => (r1_vfunct_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t54_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r1_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r1_yellow_0 A E) &  (D = (k1_yellow_0 A E)) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k1_yellow_0 A D) C)) ) )  & (r1_yellow_0 A B)) ) )  =>  ((k1_yellow_0 A C) = (k1_yellow_0 A B)) ) ) ) ) ) ) ) ).
tt(t54_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v6_waybel_1 B A) => (v3_lattice3 (k1_yellow_2 A A B))) ) ) ) ) ).
tt(t54_waybel21,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_waybel_3 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v2_waybel19 A) & (l1_waybel_9 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v5_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (C = (u1_struct_0 B))  & (r2_hidden (k4_yellow_0 A) C))  =>  ((v4_pre_topc C A) <=>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D A)) ) )  =>  ((r1_waybel_0 A D C) => (r2_hidden (k1_waybel11 A D) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((r2_hidden C (k1_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (k4_waybel23 A B))) <=>  ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C B) &  ((v12_waybel_0 C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t54_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) )  =>  ((v10_waybel_0 C A) =>  ((k12_lattice3 A B (k1_waybel_2 A C)) = (k1_yellow_0 A (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_relset_1 (u1_struct_0 A) (k1_waybel_0 A C))))) ) ) ) ) ) ) ) ) ).
tt(t54_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r3_yellow20 (k4_waybel34 A) (k5_waybel34 A) (k6_waybel34 A) (k10_waybel34 A) (k11_waybel34 A))) ) ).
tt(t54_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_waybel_4 A B (u1_orders_2 A)) => (v1_waybel_0 B A)) ) ) ) ) ).
tt(t54_wellord1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((r4_wellord1 A B) & (v2_wellord1 A))  => (v2_wellord1 B)) ) ) ) ) ).
tt(t54_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_xboole_0 A (k3_xboole_0 B C)) = (k2_xboole_0 (k4_xboole_0 A B) (k4_xboole_0 A C))) ) ) ) ).
tt(t54_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k8_xboolean B C)) = (k4_xboolean (k5_xboolean (k3_xboolean A) B) (k5_xboolean (k3_xboolean A) C))) ) ) ) ) ) ) ).
tt(t54_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  ((k7_xcmplx_0 A B) = k6_numbers) )  =>  (B = (k7_xcmplx_0 A (k7_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t54_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k6_xcmplx_0 C A) B)) ) ) ) ) ) ) ) ) ).
tt(t54_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_tarski (k1_xxreal_1 A B) (k2_xxreal_1 C D)))  =>  ((r1_xxreal_0 C A) &  (~ (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  ( (~  (! [B:$i] :  ((m2_xxreal_2 B A) =>  (B = k2_xxreal_0) ) ) )  => (v3_xxreal_2 A)) ) ) ).
tt(t54_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~ (r1_xxreal_0 C (k3_xxreal_3 A B)))  &  (~  ( (~  (A = k1_xxreal_0) )  &  ( (~  (B = k2_xxreal_0) )  &  ( (~  (C = k2_xxreal_0) )  &  (~ (r1_xxreal_0 (k1_xxreal_3 C B) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v1_lattice3 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r1_yellow_0 A B)) ) ) ) ) ).
tt(t54_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((v1_waybel_6 C (k3_yellow_3 A B)) =>  ((v1_waybel_6 (k4_yellow_3 A B C) A) & (v1_waybel_6 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ) ).
tt(t54_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  => (v5_pre_topc (k1_yellow_9 A B) B A)) ) ) ) ).
tt(t54_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v15_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v16_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_altcat_1 F) &  ((v3_altcat_2 F A) & (m1_altcat_2 F A)) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v2_altcat_1 G) &  ((v3_altcat_2 G B) & (m1_altcat_2 G B)) ) )  =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  &  ((v2_altcat_1 H) &  ((v3_altcat_2 H C) & (m1_altcat_2 H C)) ) )  =>  ( ((r2_yellow20 A B D F G) & (r3_yellow20 B C E G H))  => (r3_yellow20 A C (k3_functor3 A B C D E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t54_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E C) => (r3_orders_2 A (k3_funct_2 C (u1_struct_0 A) D E) B)) )  => (r3_orders_2 A (k4_yellow_2 A D) B)) ) ) ) ) ) ) ) ) ).
tt(t54_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_lattice3 A B (k2_yellow_0 A (k4_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t54_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k1_yellow_5 A B C)) = (k12_lattice3 A B C)) ) ) ) ) ) ) ).
tt(t54_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ((m3_yellow_9 D A B) =>  ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D))) ) ) ) ) ) ) ) ) ).
tt(t54_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  => (r2_hidden A (k29_zf_lang A))) ) ).
tt(t54_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ((r1_zf_lang B (k8_zf_lang A C)) <=>  (B = C) ) ) ) ) ) ) ) ).
tt(t54_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A B) =>  ( ((r2_hidden C B) &  (~  (A = C) ) )  |  ((k3_xboole_0 (k2_tarski A C) B) = (k1_tarski A)) ) ) ) ) ) ).
tt(t54_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) => (m1_zmodul01 (k3_zmodul01 A) B)) ) ) ) ).
tt(t55_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ( ( (E = (k1_finsub_1 (k1_zfmisc_1 (u1_abcmiz_0 A)) D (k6_domain_1 (u1_abcmiz_0 A) C)))  & (r2_abcmiz_0 A B E))  =>  ((k5_abcmiz_0 A (k6_abcmiz_0 A B D) C) = (k6_abcmiz_0 A B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v2_abcmiz_1 B A) & (m1_subset_1 B (u4_struct_0 A)))  =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (! [E:$i] :  ((m1_trees_4 E (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (~  ( ((k3_finseq_1 E) = (k3_finseq_1 (k1_msualg_1 A B)))  &  ((k36_abcmiz_1 A B E) = (k31_abcmiz_1 A (k33_abcmiz_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r7_abcmiz_a A D B C) => (r7_abcmiz_a A D C B)) ) ) ) ) ) ) ) ) ).
tt(t55_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r1_aff_1 A B D E) &  ((r2_analoaf A C D F E) &  (F = B) ) )  =>  ((r1_aff_1 A B C D) |  (E = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) & (v1_aff_4 C A))  =>  ((r1_aff_4 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  (? [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) &  ( (~ (r5_aff_1 A D E))  &  ((r1_tarski D B) &  ((r1_tarski E B) &  ((r1_tarski F C) &  ((r1_tarski G C) &  ( ((r5_aff_1 A D F) | (r5_aff_1 A F D))  &  ((r5_aff_1 A E G) | (r5_aff_1 A G E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  => (r1_xxreal_0 (k1_afinsq_1 (k5_relat_1 B A)) A)) ) ) ) ).
tt(t55_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v1_valued_0 B) & (v1_finset_1 B)) ) ) )  =>  ((k7_afinsq_2 (k1_ordinal4 A B)) = (k3_binop_2 (k7_afinsq_2 A) (k7_afinsq_2 B))) ) ) ) ) ).
tt(t55_afvect0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_tdgroup A))) =>  ( (C = B)  => (r4_afvect0 A (k5_afvect0 (k2_tdgroup A) C))) ) ) ) ) ) ) ).
tt(t55_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_msualg_6 B A) & (l3_msualg_1 B A))  => (m4_algspec1 B A)) ) ) ) ).
tt(t55_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k5_altcat_4 (k5_altcat_4 A)) = (k5_altcat_4 A)) ) ) ).
tt(t55_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden C B) &  ((r2_hidden D B) & (v4_analmetr B A)) )  =>  ( (C = D)  |  ( ( (~ (r4_analmetr A C D E F))  &  (~ (r4_analmetr A E F C D)) )  | (r6_analmetr A E F B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k6_analort A F G))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k6_analort A F G))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k6_analort A F G))) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k6_analort A F G))) =>  ( ( (B = H)  &  ( (C = I)  &  ( (D = J)  &  (E = K) ) ) )  =>  ((r2_analoaf (k6_analort A F G) H I J K) <=> (r2_analort A F G B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_aofa_000,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) )  =>  ((v12_aofa_000 A) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers (k4_finseq_1 (u1_unialg_1 A))) =>  (~  ( (~  (B = 1) )  &  ( (~  (B = 2) )  &  ( (~  (B = 3) )  &  (~  (B = 4) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k9_funct_2 B k4_numbers))) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B C) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) C))  =>  (! [E:$i] :  ((m3_aofa_i00 E A B C D) =>  (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ( ((v1_aofa_i00 G A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers)) & (m1_aofa_000 G A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers)))  =>  (! [H:$i] :  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  ((r6_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) I G H) =>  (! [J:$i] :  ((m1_aofa_i00 J B (u1_struct_0 A) (k9_funct_2 B k4_numbers) G) =>  (! [K:$i] :  ((m1_aofa_i00 K B (u1_struct_0 A) (k9_funct_2 B k4_numbers) G) =>  ( ( (! [L:$i] :  ((m2_funct_2 L B k4_numbers (k9_funct_2 B k4_numbers)) =>  ((r2_hidden L H) =>  ( ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) G L I) K) = (k21_aofa_i00 B k4_numbers L K))  &  ((k21_aofa_i00 B k4_numbers (k2_binop_1 (k9_funct_2 B k4_numbers) (u1_struct_0 A) (k9_funct_2 B k4_numbers) G L I) J) = (k21_aofa_i00 B k4_numbers L J)) ) ) ) )  &  ((r7_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) (k47_aofa_i00 A B C D J E) G H) &  ((r7_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) I G H) &  ((r7_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) (k74_aofa_i00 A B F G J K) G H) & (r7_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) G J 1) G H)) ) ) )  =>  ( (! [L:$i] :  ( ((v1_relat_1 L) & (v1_funct_1 L))  =>  (~  ( ((k1_funct_1 L F) = k6_numbers)  &  ( ((k1_funct_1 L K) = 1)  &  ((k1_funct_1 L J) = 2) ) ) ) ) )  | (r6_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) (k17_aofa_000 A (k47_aofa_i00 A B C D J E) (k74_aofa_i00 A B F G J K) I (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) F k6_numbers) G J 1)) G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_armstrng,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((r2_hidden B (k14_armstrng A C)) =>  ((m1_subset_1 B (k1_zfmisc_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((r2_hidden (k6_armstrng A D E) C) &  ((r1_tarski D B) &  (~ (r1_tarski E B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (~  ( (~  (A = k11_arytm_3) )  &  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  (~  (B = (k10_arytm_3 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t55_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k9_newton A) 1)) ) ) ) ).
tt(t55_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A C (k1_bcialg_1 A C B)) = B) ) ) ) ) ) ) ) ).
tt(t55_bcialg_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((m1_bcialg_5 A B k6_numbers C C) =>  ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v4_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  ( (~ (v2_struct_0 (k10_bcialg_6 A B C D)))  &  ((v3_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v4_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v5_bcialg_1 (k10_bcialg_6 A B C D)) &  ((v7_bcialg_1 (k10_bcialg_6 A B C D)) & (l2_bcialg_1 (k10_bcialg_6 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m4_bciideal B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C D) E) B) => (r2_hidden (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D E)) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_normsp_1 A B (k1_real_1 1)) (k5_vfunct_1 k5_numbers A B))) ) ) ) ).
tt(t55_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_tarski (k6_bhsp_2 A B C) (k5_bhsp_2 A B C))) ) ) ) ) ) ).
tt(t55_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) &  ((v13_vectsp_1 E C A) &  ((v1_hahnban1 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) )  =>  ( (~  (D = (k7_hahnban1 A B)) )  =>  ( ((k14_bilinear A B C (k9_bilinear A B C D E)) = (k9_vectsp10 A C E))  & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C (k9_bilinear A B C D E))))) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 (k6_vectsp10 A C (k9_vectsp10 A C E)))) (u1_struct_0 A) (k16_bilinear A B C (k9_bilinear A B C D E)) (k9_bilinear A B (k6_vectsp10 A C (k9_vectsp10 A C E)) D (k11_vectsp10 A C E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_boolealg A (k3_lattices A (k7_lattices A B) (k7_lattices A C)) (k3_lattices A B C)) =>  ((r4_boolealg A C (k7_lattices A B)) |  ((r4_boolealg A B (k7_lattices A C)) |  ((r1_boolealg A B (k7_lattices A B)) & (r1_boolealg A C (k7_lattices A C))) ) ) ) ) ) ) ) ) ) ).
tt(t55_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k1_borsuk_4)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k1_borsuk_4))))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((v3_tops_2 B (k1_pre_topc (k15_euclid 2) A) k1_borsuk_4) &  ((r1_tarski C A) &  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 k5_topmetr)) &  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 k5_topmetr)) &  ( (~ (r1_xxreal_0 E D))  &  ((k7_relset_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)) (u1_struct_0 k1_borsuk_4) B C) = (k1_rcomp_1 D E)) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~ (r1_topreal1 (k15_euclid 2) D E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_subset_1 k1_numbers (k2_rcomp_1 B C) (k2_rcomp_1 C k1_xxreal_0)))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k3_rcomp_1 B k1_xxreal_0)) ) ) ) ) ) ) ) ) ).
tt(t55_borsuk_6,ax, (k8_borsuk_6 = a_0_14_borsuk_6) ).
tt(t55_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) B) = (k4_struct_0 (k15_euclid 2)))  =>  (B = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ).
tt(t55_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C E) F) G) H) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k9_xboolean A (k5_xboolean B C)) = (k3_xboolean (k5_xboolean (k5_xboolean A B) C))) ) ) ) ) ) ) ).
tt(t55_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc26 A C D)) (k1_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t55_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A (k6_cqc_lang A B))))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ).
tt(t55_card_1,ax, (7 = (k5_enumset1 k1_xboole_0 1 2 3 4 5 6)) ).
tt(t55_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] : (r1_xxreal_0 (k5_card_1 (k5_enumset1 A B C D E F G)) 7)) ) ) ) ) ) ) ).
tt(t55_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_tarski (k8_card_3 A) (k4_partfun1 (k9_xtuple_0 A) (k3_tarski (k10_xtuple_0 A))))) ) ).
tt(t55_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  (? [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  &  ( ((k1_relset_1 k5_numbers C) = (k5_card_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k3_card_fin (k23_binop_2 D 1) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v10_cat_1 B A) & (v10_cat_1 C A))  => (r1_cat_1 A B C)) ) ) ) ) ) ) ).
tt(t55_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A B D) = k1_xboole_0) )  &  (~  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A B D) =>  ((r2_cat_3 A B E F) <=>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A G C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A G D) = k1_xboole_0) )  &  (~  ( (~  ((k2_cat_1 A G B) = k1_xboole_0) )  &  (! [H:$i] :  ((m1_cat_1 H A G C) =>  (! [I:$i] :  ((m1_cat_1 I A G D) =>  (? [J:$i] :  ((m1_cat_1 J A G B) &  (! [K:$i] :  ((m1_cat_1 K A G B) =>  ( ( ((k5_cat_1 A G B C K E) = H)  &  ((k5_cat_1 A G B D K F) = I) )  <=>  (J = K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_cat_1 C A (k19_cat_4 A) B) =>  (! [D:$i] :  ((m1_cat_1 D A (k19_cat_4 A) B) =>  (C = D) ) ) ) ) ) ) ) ) ).
tt(t55_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k46_valued_1 B k2_numbers k2_numbers C D) A) (k46_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) (k2_partfun1 B k2_numbers D A))) &  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k46_valued_1 B k2_numbers k2_numbers C D) A) (k46_valued_1 B k2_numbers k2_numbers (k2_partfun1 B k2_numbers C A) D)) & (r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k46_valued_1 B k2_numbers k2_numbers C D) A) (k46_valued_1 B k2_numbers k2_numbers C (k2_partfun1 B k2_numbers D A)))) ) ) ) ) ) ) ) ) ).
tt(t55_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k4_chain_1 A B (k2_nat_1 k6_numbers 1))) =>  ((k5_card_1 (k10_chain_1 A B k6_numbers (k6_domain_1 (k4_chain_1 A B (k2_nat_1 k6_numbers 1)) C))) = 2) ) ) ) ) ) ) ).
tt(t55_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_glib_001 B A) & (m3_glib_001 B A))  =>  ((v8_glib_001 B A) =>  ((r1_xxreal_0 (k15_glib_001 A B) 3) |  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (~  ((r2_hidden C (k13_glib_001 A B)) &  (! [D:$i] :  ( ((v7_ordinal1 D) &  (~ (v1_abian D)) )  =>  (! [E:$i] :  ( ((v7_ordinal1 E) &  (~ (v1_abian E)) )  =>  (~  ( (~ (r1_xxreal_0 E (k1_nat_1 D 2)))  &  ((r1_xxreal_0 E (k3_finseq_1 B)) &  ( (~  ((k1_funct_1 B D) = (k1_funct_1 B E)) )  &  ((r2_hidden (k1_funct_1 B D) (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) &  ((r2_hidden (k1_funct_1 B E) (k2_chord A (k6_domain_1 (k6_glib_000 A) C))) &  (! [F:$i] :  (~  ((r2_hidden F (k14_glib_001 A B)) & (r1_glib_000 A (k1_funct_1 B D) (k1_funct_1 B E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v3_card_1 E A) & (v1_finseq_1 E)) ) )  => (r2_circcomb (k5_circcomb C D) (k5_circcomb C E) (k7_circcomb A B C D) (k7_circcomb A B C E))) ) ) ) ) ) ) ) ) ) ).
tt(t55_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A E))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B F))) =>  ( (G = (k3_relat_1 C H))  =>  (! [I:$i] :  ((m1_subset_1 I k5_numbers) =>  ((k5_facirc_1 A E G I) = (k3_relat_1 C (k5_facirc_1 B F H I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_classes1,ax, (! [A:$i] :  ((v1_ordinal1 A) =>  ((k5_classes1 A) = A) ) ) ).
tt(t55_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ( (~ (v1_xboole_0 (k2_xboole_0 A B)))  & (v1_classes2 (k2_xboole_0 A B)))  &  ( (~ (v1_xboole_0 (k3_xboole_0 A B)))  & (v1_classes2 (k3_xboole_0 A B))) ) ) ) ) ) ).
tt(t55_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ((k3_clvect_1 B) = (k3_clvect_1 A)) ) ) ) ) ).
tt(t55_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r1_tarski (k6_clvect_2 A B C) (k5_clvect_2 A B C))) ) ) ) ) ) ).
tt(t55_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v10_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v10_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( ((k11_cohsp_1 A B C) = (k11_cohsp_1 A B D))  => (r2_funct_2 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t55_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (r1_xxreal_0 (k4_complex1 A) (k17_complex1 A))) ) ).
tt(t55_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k2_complex2 A (k1_real_1 (k1_comptrig A))) = (k17_complex1 A)) ) ) ).
tt(t55_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k2_complfld (k11_algstr_0 k1_complfld A)) = (k11_algstr_0 k1_complfld (k2_complfld A))) ) ) ) ).
tt(t55_complsp2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k2_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k2_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k1_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k9_matrix_5 A (k9_matrix_5 C E)) = (k1_seq_1 B (k1_seq_1 D E))) ) ) ) )  =>  ((k4_finseqop k2_numbers k2_numbers C A) = (k4_finseqop k1_numbers k1_numbers D B)) ) ) ) ) ) ) ) ) ) ).
tt(t55_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((k5_card_1 (k10_compos_1 A B)) = (k2_nat_1 (k5_card_1 B) 1)) ) ) ) ) ).
tt(t55_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) 3) = (k5_compos_0 (u1_compos_1 A) E 3)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  (B = k6_numbers) )  =>  ((k1_newton (k2_xcmplx_0 (k21_sin_cos (k10_real_1 (k7_real_1 A (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B)) (k3_xcmplx_0 (k18_sin_cos (k10_real_1 (k7_real_1 A (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B)) k7_complex1)) B) = (k2_xcmplx_0 (k21_sin_cos A) (k3_xcmplx_0 (k18_sin_cos A) k7_complex1))) ) ) ) ) ) ) ) ).
tt(t55_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  ((v1_xboole_0 B) => (v1_xboole_0 (k7_comput_1 B C A))) ) ) ) ) ) ) ).
tt(t55_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_comseq_3 A) & (v1_comseq_3 B))  =>  ((v1_comseq_3 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) &  ((k11_comseq_3 (k46_valued_1 k5_numbers k2_numbers k2_numbers A B)) = (k11_complex1 (k11_comseq_3 A) (k11_comseq_3 B))) ) ) ) ) ) ) ).
tt(t55_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k19_convex4 A (k6_rusub_4 A B C) D) = (k6_rusub_4 A (k19_convex4 A B D) (k19_convex4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t55_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r3_cqc_the1 A B C) & (r3_cqc_the1 A B (k8_cqc_lang A C D)))  => (r3_cqc_the1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t55_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C (k11_cqc_lang A D B)) (k11_cqc_lang A D (k11_cqc_lang A C B))) A) & (v2_cqc_the1 (k2_qc_lang2 A (k6_qc_lang2 A C D B) (k6_qc_lang2 A D C B)) A)) ) ) ) ) ) ) ) ) ).
tt(t55_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r7_cqc_the3 A B C) & (r7_cqc_the3 A D E))  => (r7_cqc_the3 A (k8_cqc_lang A B D) (k8_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k15_csspace A B C) = (k7_square_1 (k17_complex1 (k12_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A B C))))) ) ) ) ) ) ) ).
tt(t55_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k18_sin_cos (k8_real_1 2 B)) (k18_sin_cos (k8_real_1 2 (k9_real_1 B A)))))) ) ) ) ) ).
tt(t55_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k8_real_1 (k8_real_1 3 (k21_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2))) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k8_real_1 3 (k9_real_1 (k8_real_1 2 B) A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t55_diff_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) (k2_nat_1 A 1)) C) = (k9_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k7_real_1 C (k13_complex1 B 2))) (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k8_diff_1 D B) A) (k9_real_1 C (k13_complex1 B 2))))) ) ) ) ) ) ) ) ) ).
tt(t55_dilworth,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( ((k7_struct_0 A) = (k2_xcmplx_0 (k3_xcmplx_0 B C) 1))  &  ( (! [D:$i] :  ( ((v1_dilworth D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (r1_xxreal_0 (k2_xcmplx_0 B 1) (k5_card_1 D))) ) )  &  (! [D:$i] :  ( ((v2_dilworth D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~ (r1_xxreal_0 (k2_xcmplx_0 C 1) (k5_card_1 D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_ec_pf_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k8_eqrel_1 A B)) & (v1_funct_1 C)) )  =>  ((v2_funct_1 C) => (v1_prob_2 C)) ) ) ) ) ) ) ).
tt(t55_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [H:$i] :  ((m2_subset_1 H (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (E = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (F = (k5_algstr_0 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k2_binom (k9_int_3 A) E 3)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) E 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  (I = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) E F) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) F)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)))) ) ) ) )  =>  ((k3_rlvect_1 (k9_int_3 A) (k4_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I))))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k2_binom (k9_int_3 A) D 2))) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ((k21_ens_1 A B C) = (k1_partfun1 (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k3_graph_1 A C)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A C)) (k18_ens_1 A (k3_graph_1 A C) B) (k17_ens_1 A (k3_graph_1 A B) C))) ) ) ) ) ) ) ).
tt(t55_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  => (r1_xxreal_0 k6_numbers (k6_entropy1 A))) ) ).
tt(t55_enumset1,ax, (! [A:$i] :  (! [B:$i] :  ((k6_enumset1 A A A A A A A B) = (k2_tarski A B)) ) ) ).
tt(t55_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( ((k5_setfam_1 A B) = A)  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (D = (k3_tarski C))  => (r1_tarski (k3_subset_1 A D) (k3_tarski (k3_subset_1 B C)))) ) ) ) ) ) ) ) ) ).
tt(t55_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ((r1_rvsum_1 B B) <=>  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t55_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) =>  ((r2_hidden D (k8_euclid_3 2 A B C)) <=>  (~  ((r1_xxreal_0 k6_numbers (k10_euclid_3 2 A B C D)) &  ((r1_xxreal_0 k6_numbers (k11_euclid_3 2 A B C D)) & (r1_xxreal_0 k6_numbers (k12_euclid_3 2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 A B) = (k1_euclid_8 (k9_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k9_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k9_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(t55_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_rlvect_1 (k15_euclid 2) A B) = (k19_euclid (k7_real_1 (k17_euclid A) (k17_euclid B)) (k7_real_1 (k18_euclid A) (k18_euclid B)))) ) ) ) ) ).
tt(t55_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ( (~ (r2_hidden B C))  &  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  (~  ( (C = (k2_euclid_4 A D E))  & (r3_euclidlp A (k8_euclid A B D) (k8_euclid A E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) &  ((r2_hidden C B) & (r2_hidden (k4_tarski A C) (k6_exchsort D (k10_funct_7 E A B)))) )  => (r2_hidden (k4_tarski A C) (k6_exchsort D E))) ) ) ) ) ) ) ) ).
tt(t55_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 3 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 3 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D)))) => (v1_circuit2 (k6_circuit2 (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D) E) (k5_circcomb D (k11_finseq_1 A B C)) (k7_facirc_1 A B C D))) ) ) ) ) ) ) ).
tt(t55_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k2_relset_1 k1_numbers (k1_fcont_1 A B)) = k1_numbers) ) ) ) ) ) ).
tt(t55_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t55_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = (k9_real_1 C 1)) ) ) ) )  =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) A) C) = (k8_real_1 C (k1_seq_1 k24_sin_cos C))) ) ) ) ) ) ) ) ) ) ).
tt(t55_fib_num2,ax, ((k5_fib_num2 2) = (k12_finseq_1 k5_numbers 1)) ).
tt(t55_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_fib_num3 (k2_nat_1 (k4_nat_1 2 A) 1) (k2_nat_1 (k4_nat_1 2 A) 1) (k2_nat_1 B 1)) = (k4_nat_1 (k2_nat_1 (k4_nat_1 2 A) 1) (k1_pre_ff (k2_nat_1 B 2)))) ) ) ) ) ).
tt(t55_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  => (v3_filter_0 (k6_filter_0 A B))) ) ) ) ) ).
tt(t55_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A (k4_filter_0 A B C) (k4_filter_0 A B (k3_lattices A C D))) &  ((r3_lattices A (k4_filter_0 A B C) (k4_filter_0 A (k4_lattices A B D) C)) &  ((r3_lattices A (k4_filter_0 A B C) (k4_filter_0 A B (k3_lattices A D C))) & (r3_lattices A (k4_filter_0 A B C) (k4_filter_0 A (k4_lattices A D B) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v18_lattices C A) &  ((v21_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r1_filter_2 (u1_struct_0 A) (k7_filter_2 A (k4_subset_1 (u1_struct_0 A) B C)) (k8_filter_2 A B C))) ) ) ) ) ) ).
tt(t55_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_finseq_1 A)) = (k5_card_1 A)) ) ) ).
tt(t55_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((v1_funct_1 (k1_finseq_2 A)) &  ((v1_funct_2 (k1_finseq_2 A) (k2_finseq_1 A) (k2_finseq_1 A)) &  ((v3_funct_2 (k1_finseq_2 A) (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 (k1_finseq_2 A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) ) ) ) ) ).
tt(t55_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ( ((k3_finseq_1 A) = (k1_nat_1 C 1))  &  (B = (k5_relat_1 A (k2_finseq_1 C))) )  =>  (A = (k7_finseq_1 B (k9_finseq_1 (k1_funct_1 A (k1_nat_1 C 1))))) ) ) ) ) ) ) ) ).
tt(t55_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_funct_1 A))  =>  ((k1_finseq_3 A (k1_tarski B)) = (k7_finseq_1 (k5_finseq_4 A B) (k6_finseq_4 A B))) ) ) ) ) ).
tt(t55_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) => (r1_tarski (k10_xtuple_0 (k2_finseq_5 A C B)) (k10_xtuple_0 C))) ) ) ) ) ) ) ).
tt(t55_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (~  ( (~  (B = C) )  &  ( (~  (D = C) )  &  (~  ((k2_finseq_5 A (k3_finseq_4 A B D C) C) = (k12_finseq_1 A C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((r6_binop_1 A C D) & (r2_funct_2 A A E (k9_funcop_1 A A C (k6_partfun1 A) B)))  => (r7_binop_1 A E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_fintopo6 A B C D E) => (v2_funct_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_flang_1 A) B) =>  ( ((k8_flang_1 A B) = (k6_flang_1 A (k8_flang_1 A B) (k7_flang_1 A B C)))  &  ((k8_flang_1 A B) = (k6_flang_1 A (k7_flang_1 A B C) (k8_flang_1 A B))) ) ) ) ) ) ) ) ).
tt(t55_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k4_subset_1 (k8_afinsq_1 A) (k1_flang_2 A B D E) (k1_flang_2 A C D E)) (k1_flang_2 A (k4_subset_1 (k8_afinsq_1 A) B C) D E))) ) ) ) ) ) ) ) ) ).
tt(t55_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) => (r1_tarski (k2_flang_3 A B) (k8_flang_1 A B))) ) ) ).
tt(t55_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((k3_finseq_2 (k3_xboole_0 A B)) = (k3_xboole_0 (k3_finseq_2 A) (k3_finseq_2 B))) ) ) ).
tt(t55_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  & (l2_fsm_1 E A B))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 E)) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v8_struct_0 G) & (l2_fsm_1 G A B)) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 G)) =>  ( ( (G = (k13_fsm_1 A B D E))  &  (F = H) )  =>  ((k4_fsm_1 A B E F C) = (k4_fsm_1 A B G H C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) => (r2_funct_2 B A (k1_partfun1 B A A A D (k10_funcop_1 A A C E (k6_partfun1 A))) (k10_funcop_1 A B C E D))) ) ) ) ) ) ) ) ) ).
tt(t55_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k6_relat_1 B C))) =>  ((k1_funct_1 (k6_relat_1 B C) A) = (k1_funct_1 C A)) ) ) ) ) ) ).
tt(t55_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((r2_relset_1 A A (k1_partfun1 A A A A C B) B) & (v2_funct_1 B))  => (r2_relset_1 A A C (k6_partfun1 A))) ) ) ) ) ) ).
tt(t55_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k13_funct_3 (k3_relat_1 C A) (k3_relat_1 C B)) = (k3_relat_1 C (k13_funct_3 A B))) ) ) ) ) ) ) ).
tt(t55_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ((r2_hidden (k4_tarski (k4_tarski A B) (k4_tarski C D)) (k9_xtuple_0 (k3_funct_4 E F))) =>  ((k1_binop_1 (k3_funct_4 E F) (k4_tarski A B) (k4_tarski C D)) = (k4_tarski (k1_binop_1 E A C) (k1_binop_1 F B D))) ) ) ) ) ) ) ) ) ) ).
tt(t55_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k10_xtuple_0 C) (k4_partfun1 A B)) &  ((r1_tarski (k10_xtuple_0 D) (k4_partfun1 A B)) &  ((k4_funct_5 C) = (k4_funct_5 D)) ) )  =>  ((r2_hidden k1_xboole_0 (k10_xtuple_0 C)) |  ((r2_hidden k1_xboole_0 (k10_xtuple_0 D)) |  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t55_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_funct_2 A (k1_funct_2 B C))) =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  | (r2_hidden (k10_funct_6 D) (k1_funct_2 B (k1_funct_2 A C)))) ) ) ) ) ) ) ) ).
tt(t55_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( (~  ( (~ (r1_tarski (k9_xtuple_0 B) A))  &  ( (~ (r1_tarski (k9_xtuple_0 (k3_relat_1 B C)) A))  &  (~ (r1_tarski (k9_xtuple_0 (k3_relat_1 B (k3_relat_1 C D))) A)) ) ) )  =>  ((k4_funct_7 A (k11_finseq_1 B C D)) = (k3_relat_1 B (k3_relat_1 C D))) ) ) ) ) ) ) ) ) ).
tt(t55_funct_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_funct_8 A k1_numbers k1_numbers) &  ((v6_funct_8 B k1_numbers k1_numbers) & (v1_funct_8 (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k1_relset_1 k1_numbers B)))) )  => (v6_funct_8 (k52_valued_1 k1_numbers k1_numbers k1_numbers A B) k1_numbers k1_numbers)) ) ) ) ) ).
tt(t55_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k1_fuzzy_2 (k2_zfmisc_1 A B) C D) (k4_fuzzy_2 A B)) => (r1_fuzzy_1 C D)) ) ) ) ) ) ) ) ) ).
tt(t55_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_fvaluat1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_fvaluat1 A B))) =>  ( ( (C = E)  &  (D = F) )  =>  ((k8_group_1 A C D) = (k8_group_1 (k7_fvaluat1 A B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B E (k1_algstr_0 B C D)) = (k4_fvsum_1 A B (k10_fvsum_1 A B E C) (k10_fvsum_1 A B E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) ) ) )  =>  (! [H:$i] :  ((m1_genealg1 H G) =>  (! [I:$i] :  ((m1_genealg1 I G) =>  ( ((r1_xxreal_0 (k3_finseq_1 H) A) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I B C D E F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 H) B) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I A C D E F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 H) C) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I A B D E F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 H) D) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I A B C E F)) )  &  ( ((r1_xxreal_0 (k3_finseq_1 H) E) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I A B C D F)) )  &  ((r1_xxreal_0 (k3_finseq_1 H) F) =>  ((k12_genealg1 G H I A B C D E F) = (k11_genealg1 G H I A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k22_gfacirc1 A B C)) = (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) (k1_tarski (k24_gfacirc1 A B C)))) ) ) ) ).
tt(t55_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k7_glib_000 A))) =>  (! [C:$i] :  ((m2_glib_000 C A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) B)) =>  ((k2_nat_1 (k17_glib_000 C) (k5_card_1 B)) = (k17_glib_000 A)) ) ) ) ) ) ) ).
tt(t55_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ( ((r1_xxreal_0 C E) & (r1_xxreal_0 E (k3_finseq_1 (k20_glib_001 A B C D))))  =>  ( ((k1_funct_1 (k20_glib_001 A B C D) E) = (k1_funct_1 B (k2_xcmplx_0 (k6_xcmplx_0 E C) D)))  &  ((m1_subset_1 (k2_xcmplx_0 (k6_xcmplx_0 E C) D) k5_numbers) & (r1_xxreal_0 (k2_xcmplx_0 (k6_xcmplx_0 E C) D) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k14_glib_003 (k13_glib_003 A B D))) =>  ((r2_hidden C (k14_glib_003 A)) |  ( (B = C)  & (r2_hidden B (k6_glib_000 A))) ) ) ) ) ) ) ) ).
tt(t55_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B)) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B))) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B)) (k19_euclid k6_numbers 1)))))) ) ) ) ) ) ).
tt(t55_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 C))) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_graph_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((k3_graph_2 A k1_xboole_0) = A) ) ) ).
tt(t55_graph_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) => (v1_abian (k7_graph_3 B D A))) )  =>  ( ((k7_graph_3 B C A) = k6_numbers)  |  (! [D:$i] :  ((m1_graph_3 D (u4_struct_0 B) (k9_graph_3 B) (k13_graph_3 B C A)) =>  ( (~ (v1_xboole_0 D))  &  ((r1_tarski (k10_xtuple_0 D) A) & (r2_hidden C (k1_graph_3 B (k10_xtuple_0 D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u4_struct_0 B)) =>  ( ((v2_funct_1 C) &  ((r1_tarski (k10_xtuple_0 C) (k10_xtuple_0 D)) & (r5_graph_5 B A)) )  => (r1_xxreal_0 (k10_graph_5 B C A) (k10_graph_5 B D A))) ) ) ) ) ) ) ) ) ).
tt(t55_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) &  ((v1_polynom7 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) &  ((v1_polynom7 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) ) )  =>  ( ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) &  ((v1_polynom7 (k6_termord A B C D) A C) & (v1_polynom7 (k6_termord A B C E) A C)) )  => (r1_rewrite1 (k3_polyred A B C (k1_groeb_1 A C D)) (k6_polynom1 A C (k10_polynom1 A C (k5_termord A B C E) (k6_termord A B C D)) (k10_polynom1 A C (k5_termord A B C D) (k6_termord A B C E))) (k10_polynom1 A C E (k6_termord A B C D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_tarski (k3_group_11 A C B) (k4_group_11 A C B))) ) ) ) ) ) ).
tt(t55_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ( ((m1_group_2 A B) & (m1_group_2 B A))  =>  ((g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A)) = (g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B))) ) ) ) ) ) ).
tt(t55_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (~  (C = k1_xboole_0) )  =>  ((k3_group_3 A B C) = B) ) ) ) ) ) ) ) ) ).
tt(t55_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r1_group_2 A (k8_group_4 A B B) B)) ) ) ) ).
tt(t55_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((r1_tarski (k5_group_5 A B C) (k8_group_2 A C)) & (r1_tarski (k5_group_5 A C B) (k8_group_2 A C))) ) ) ) ) ) ) ).
tt(t55_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v2_funct_1 C) =>  ((v1_funct_1 (k2_funct_1 C)) &  ((v1_funct_2 (k2_funct_1 C) (u1_struct_0 (k10_group_6 B A C)) (u1_struct_0 B)) &  ((v1_group_6 (k2_funct_1 C) (k10_group_6 B A C) B) & (m1_subset_1 (k2_funct_1 C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k10_group_6 B A C)) (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t55_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) &  ((v3_group_9 D A) & (l1_group_9 D A)) ) ) )  =>  ( ((r3_group_9 A B C) & (r3_group_9 A C D))  => (r3_group_9 A B D)) ) ) ) ) ) ) ) ).
tt(t55_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B k1_complfld))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) )  =>  ( ((k10_bilinear k1_complfld A B C) = (k10_bilinear k1_complfld A B (k3_hermitan A B C)))  &  ((k11_bilinear k1_complfld A B C) = (k11_bilinear k1_complfld A B (k3_hermitan A B C))) ) ) ) ) ) ) ) ).
tt(t55_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) k19_sin_cos) A) 4))) ) ).
tt(t55_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((k8_ideal_1 A (k2_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t55_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u2_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u4_incsp_1 A)) &  ( (~  (C = D) )  &  ((r3_incsp_1 A B C) & (r3_incsp_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t55_int_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 k6_numbers (k5_int_1 A B))) ) ) ) ).
tt(t55_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) )  &  (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos B)) = k6_numbers) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) k29_sin_cos) k1_fdiff_9) A) B) = (k10_real_1 (k1_seq_1 k16_sin_cos B) (k9_real_1 (k1_seq_1 k16_sin_cos B) 1))) ) ) ) ) ) ) ) ).
tt(t55_integr13,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) B) = (k7_real_1 (k10_real_1 (k1_seq_1 k2_sin_cos9 B) (k5_square_1 B)) (k10_real_1 1 (k8_real_1 B (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t55_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k1_seq_1 k19_sin_cos (k1_seq_1 k19_sin_cos D)) (k1_seq_1 k16_sin_cos D))) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t55_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_subset_1 D k1_numbers k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 D))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 D))))))  =>  ( ((r1_xxreal_0 A B) &  ((r1_integr18 (k4_real_ns1 D) (k3_integra5 A B) F) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 D)) F (k3_integra5 A B)) (k4_real_ns1 D) k1_numbers) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers F)) &  ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers E)) &  ( (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k2_rcomp_1 A B)) =>  ((k1_funct_1 E G) = (k6_integr18 (k4_real_ns1 D) F A G)) ) ) )  &  ((r2_hidden C (k2_rcomp_1 A B)) & (r1_nfcont_3 (k4_real_ns1 D) F C)) ) ) ) ) ) )  =>  ((r1_ndiff_3 (k4_real_ns1 D) E C) &  ((k1_ndiff_3 (k4_real_ns1 D) E C) = (k7_partfun1 (u1_struct_0 (k4_real_ns1 D)) F C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_seq_2 (k2_partfun1 A k1_numbers C A)) & (v1_seq_2 (k2_partfun1 A k1_numbers D A)))  => (r1_xxreal_0 (k6_integra1 A (k3_valued_1 A k1_numbers k1_numbers C D) B) (k7_real_1 (k6_integra1 A C B) (k6_integra1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t55_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A k1_sin_cos2) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 (k5_seq_4 A)))) ) ) ).
tt(t55_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k7_real_1 G A))  &  (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)))) = F)  &  ( (F = (k1_relset_1 k1_numbers E))  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 E G) = (k10_real_1 (k9_real_1 G A) (k7_real_1 G A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B))) ) ) ) ) )  =>  ((k2_integra5 B E) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A))) (k4_seq_4 B)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) &  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (B = (k4_tarski C D)) ) ) ) ) ) ) ) ) ).
tt(t55_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ( ((r2_hidden A k8_intpro_1) | (r2_hidden B k8_intpro_1))  => (r2_hidden (k5_intpro_1 A B) k8_intpro_1)) ) ) ) ) ).
tt(t55_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 k3_topmetr))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((k1_funct_1 C D) = (k8_real_1 (k12_euclid D) (k7_square_1 (k9_real_1 1 (k4_square_1 (k13_complex1 (k5_real_1 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) (k7_real_1 1 A))))))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid D)) &  ((r1_xxreal_0 (k13_complex1 (k17_euclid D) (k12_euclid D)) A) &  (~  (D = (k4_struct_0 (k15_euclid 2))) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) | (v5_pre_topc C (k1_pre_topc (k15_euclid 2) B) k3_topmetr)) ) ) ) ) ) ) ) ).
tt(t55_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) &  ((r2_hidden B C) &  ((r1_xxreal_0 k6_numbers (k17_euclid A)) &  ((r1_xxreal_0 k6_numbers (k17_euclid B)) & (r1_xxreal_0 (k18_euclid B) (k18_euclid A))) ) ) ) )  => (r1_jordan6 C A B)) ) ) ) ) ) ) ).
tt(t55_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=> (r1_xxreal_0 (k18_euclid E) (k18_euclid F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) = D) )  =>  ((r1_xxreal_0 D C) |  ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) 1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k3_topreal1 2 (k1_jordan1e A B)) = (k8_jordan6 (k3_topreal1 2 (k1_jordan9 A B)))) ) ) ) ) ) ).
tt(t55_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1)))  &  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E)) ) ) )  =>  ((r1_xboole_0 (k3_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_funct_1 A) &  ((v2_funct_1 B) & (r1_tarski (k3_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) B 1)))) )  => (v2_funct_1 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B))) ) ) ) ) ).
tt(t55_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 1)))) =>  ( (B = (a_1_0_jordan2c A))  => (v1_convex1 B (k15_euclid 1))) ) ) ) ) ).
tt(t55_jordan4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r3_jordan4 C D A B) &  ((r3_jordan4 C E A B) &  ((k1_funct_1 D 2) = (k1_funct_1 E 2)) ) )  =>  ( (A = B)  |  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_topreal1 (k15_euclid 2) B C A) & (r1_jordan5c A B C C D))  =>  (D = C) ) ) ) ) ) ) ) ) ) ).
tt(t55_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k8_pscomp_1 (k2_jgraph_6 A B C D)) = B) ) ) ) ) ) ) ) ) ) ).
tt(t55_kurato_1,ax, ((k5_card_1 (k5_kurato_1 k3_topmetr k6_kurato_1)) = 7) ).
tt(t55_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F B) => (r3_lattices C (k3_funct_2 A (u1_struct_0 C) D F) (k3_funct_2 A (u1_struct_0 C) E F))) ) )  => (r3_lattices C (k2_lattice2 A C B D) (k2_lattice2 A C B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_lattice3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) A)))) )  =>  (~  ( (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 (k1_zfmisc_1 A) A B (k6_domain_1 A C)) = C) ) )  &  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((k3_funct_2 (k1_zfmisc_1 A) A B (k7_relset_1 (k9_setfam_1 A) A B C)) = (k3_funct_2 (k1_zfmisc_1 A) A B (k5_setfam_1 A C))) ) )  &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_lattices C) &  ((v10_lattices C) &  ((v4_lattice3 C) & (l3_lattices C)) ) ) )  =>  (~  ( ((u1_struct_0 C) = A)  &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((k15_lattice3 C D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_000 A) & (v6_chord A)) ) ) ) ) )  =>  ((v7_chord (k2_funct_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k14_lexbfs A (k16_lexbfs A)))) A) & (m3_chord (k2_funct_1 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) (k5_finsub_1 k5_numbers)) (k14_lexbfs A (k16_lexbfs A)))) A)) ) ) ).
tt(t55_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k3_limfunc1 D))) => (r1_xxreal_0 C (k1_seq_1 B E))) ) ) ) ) ) ) ) )  | (v4_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t55_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r4_limfunc2 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k47_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k9_real_1 (k2_limfunc2 B A) (k2_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t55_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_limfunc1 A) &  ((v3_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ((v6_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k4_limfunc1 B)) ) ) ) ) ) ) ).
tt(t55_lpspace1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((r3_mesfunc6 A B C D) & (r3_mesfunc6 A B C E))  => (r1_xxreal_0 (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers D E))) (k3_supinf_2 (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers D)) (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers E))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k12_lpspace2 A B C E))) =>  ((r2_hidden D F) =>  ( (F = (k5_lpspace2 A B C D E))  &  (? [G:$i] :  ((m1_subset_1 G k1_numbers) &  ((r1_xxreal_0 k6_numbers G) &  ( (G = (k1_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D))))  &  ((k1_normsp_0 (k12_lpspace2 A B C E) F) = (k4_power G (k10_real_1 1 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r2_hidden (k3_hilbert1 A B) C) => (r8_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 A)) (k6_ltlaxio1 B))) ) ) ) ) ) ) ).
tt(t55_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k6_cqc_lang A (k6_cqc_lang A C))) A) <=> (v2_cqc_the1 (k8_cqc_lang A B C) A)) ) ) ) ) ) ) ).
tt(t55_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k4_mathmorp A B C))  => (r1_tarski (k4_mathmorp A D B) (k4_mathmorp A D C))) ) ) ) ) ) ) ) ) ).
tt(t55_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ( ((r2_matrix10 B C) & (r1_matrix10 D E))  => (r1_matrix10 (k4_matrix10 A B E) (k4_matrix10 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 C))  =>  ((r1_xxreal_0 (k3_finseq_1 C) k1_xboole_0) |  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k2_finseq_1 (k3_finseq_1 B))) &  (! [E:$i] :  ((m2_finseq_1 E (k3_finseq_2 (u1_struct_0 A))) =>  (~  ( ((k3_finseq_1 E) = (k3_finseq_1 C))  &  ( ((k8_matrix_1 (u1_struct_0 A) (k4_matrix_3 A B C) D) = (k1_finsop_1 (k3_finseq_2 (u1_struct_0 A)) E (k5_matrix11 A)))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k2_finseq_1 (k3_finseq_1 C))) =>  ((k1_funct_1 E F) = (k10_fvsum_1 (k1_matrix_1 C) A (k8_matrix_1 (u1_struct_0 A) C F) (k3_matrix_1 (u1_struct_0 A) B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix13,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 C)))  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  => (r1_tarski (k2_zfmisc_1 (k8_relat_1 (k5_matrix13 E) A) (k8_relat_1 (k5_matrix13 F) B)) (k2_matrix_1 (k6_matrix13 C D E F)))) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ( (~  ( (? [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) &  ((k4_matrix_6 A B D C) = (k12_matrix_1 B A)) ) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) ) ) ) ) )  &  (~  ( (? [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) &  ((k4_matrix_6 A B C D) = (k12_matrix_1 B A)) ) )  &  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ((k4_matrix_6 A B D C) = (k12_matrix_1 B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  ( (~ (v1_xboole_0 (k4_matrix15 C (k1_matrix_3 C A k1_xboole_0) (k1_matrix_3 C A B))))  &  (~  (B = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((v5_matrix16 C B) => (v5_matrix16 (k1_matrix_6 A B C) B)) ) ) ) ) ) ) ).
tt(t55_matrix_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 A)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) )  =>  ((k2_matrix_1 B) = (k2_matrix_1 C)) ) ) ) ) ) ) ).
tt(t55_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r1_matrix_6 A B C D) =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B (k5_matrix_1 A (u1_struct_0 B) C) (k5_matrix_1 A (u1_struct_0 B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k1_matrix_8 A B (k11_matrix_1 B A)) = (k4_struct_0 B)) ) ) ) ) ).
tt(t55_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A A) =>  ((r2_hidden B (k2_finseq_1 A)) =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ((r2_hidden G (k2_finseq_1 A)) &  ( (B = (k1_funct_1 F G))  &  ((k7_partfun1 (u1_struct_0 C) (k9_matrix_1 (u1_struct_0 C) E B) G) = (k7_partfun1 (u1_struct_0 C) (k10_matrix_3 A C E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k15_complex1 (k8_complsp2 A B)) = (k8_complsp2 (k1_complsp2 A) (k1_complsp2 B))) ) ) ) ) ) ) ).
tt(t55_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 B)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 B)))))  =>  ( (~  ((k10_matrixj1 (u1_struct_0 B) C) = (k11_matrixj1 (u1_struct_0 B) C)) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (D = (k13_matrixj1 (u1_struct_0 B) (k4_struct_0 B) C))  =>  ((k12_matrix_3 A B D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrixr1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 A) = (k1_matrix_1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k8_matrix_1 k1_numbers (k3_matrixr1 A B) C) = (k4_rvsum_1 (k8_matrix_1 k1_numbers A C) (k8_matrix_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t55_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 B))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k1_matrix_1 B) = (k1_matrix_1 C)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k11_matrixr1 (k5_matrixr1 B C) A) = (k8_rvsum_1 (k11_matrixr1 B A) (k11_matrixr1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t55_matrprob,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (? [C:$i] :  ((m1_matrix_1 C k1_numbers A B) &  ((v2_matrprob C) &  ((k5_matrprob C) = 1) ) ) ) ) ) ) ) ).
tt(t55_measure6,ax, (! [A:$i] :  ( ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((v2_rcomp_1 A) & (v5_xxreal_2 A))  => (v2_rcomp_1 (k5_measure6 A))) ) ) ).
tt(t55_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k3_xxreal_3 C D) (k10_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t55_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k7_memstr_0 A B (k2_nat_1 (k5_memstr_0 A B C) D)) (k9_memstr_0 A B C D))) ) ) ) ) ) ) ) ).
tt(t55_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A C) (k8_nat_1 k7_numbers B C))) )  => (r1_xxreal_0 (k8_supinf_2 (k17_supinf_2 A)) (k8_supinf_2 (k17_supinf_2 B)))) ) ) ) ) ).
tt(t55_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v6_supinf_2 C) => (v6_supinf_2 (k2_partfun1 A k1_numbers C B))) ) ) ) ) ) ).
tt(t55_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((k4_struct_0 (k15_midsp_1 A)) = (k14_midsp_1 A)) ) ) ).
tt(t55_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ( (~  (A = k1_xboole_0) )  &  ((k24_mmlquery A B) = (k3_finseq_1 A)) )  <=> (r2_hidden B (k1_setfam_1 (k10_xtuple_0 A)))) ) ) ) ).
tt(t55_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_modelc_2 C) & (l1_modelc_2 C)) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k15_modelc_2 (u1_modelc_2 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k15_modelc_2 (u1_modelc_2 C))))) )  =>  ((k21_modelc_2 C D (k8_modelc_2 A B)) = (k24_modelc_2 C (k21_modelc_2 C D A) (k21_modelc_2 C D B))) ) ) ) ) ) ) ) ) ).
tt(t55_modelc_3,ax, (! [A:$i] :  ((k3_tarski (k1_orders_1 A)) = A) ) ).
tt(t55_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  => (r1_nat_d (k6_moebius1 A) A)) ) ).
tt(t55_monoid_0,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k8_monoid_0)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k8_monoid_0)) =>  ( ( (A = C)  &  (B = D) )  =>  ((k6_algstr_0 k8_monoid_0 C D) = (k24_binop_2 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t55_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( ((u1_struct_0 (k22_monoid_1 A)) = (k1_zfmisc_1 (u1_struct_0 A)))  & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k22_monoid_1 A)) (u1_struct_0 (k22_monoid_1 A))) (u1_struct_0 (k22_monoid_1 A)) (k2_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)) (k1_zfmisc_1 (u1_struct_0 A))) (k1_zfmisc_1 (u1_struct_0 A)) (u2_algstr_0 (k22_monoid_1 A)) (k21_monoid_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u2_algstr_0 A)))) ) ) ).
tt(t55_nat_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_tarski (k10_xtuple_0 (k9_nat_1 A B)) (k10_xtuple_0 A))) ) ) ) ).
tt(t55_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( ((k11_nat_3 B A) = k6_numbers)  =>  ((k1_seq_1 (k13_nat_3 B) A) = k6_numbers) ) ) ) ) ) ).
tt(t55_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k21_rvsum_1 (k5_finseq_2 k1_numbers A B)) = (k4_power B A)) ) ) ) ) ) ).
tt(t55_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_xxreal_0 (k2_xcmplx_0 A B) C) => (r1_xxreal_0 B (k7_nat_d C A))) ) ) ) ) ) ) ).
tt(t55_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers))))  =>  ((r12_ncfcont1 A C B) <=> (r12_ncfcont1 A (k2_partfun1 (u1_struct_0 A) k2_numbers C B) B)) ) ) ) ) ) ).
tt(t55_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k14_prvect_2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_prvect_2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k14_prvect_2 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (k4_prvect_2 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 (k4_prvect_2 A))) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ( (C = E)  &  ( (F = (k4_struct_0 (k14_prvect_2 A)))  &  ( ((k3_finseq_1 B) = (k23_binop_2 (k3_finseq_1 A) 1))  &  ((r1_xxreal_0 1 G) &  ((r1_xxreal_0 G (k3_finseq_1 A)) &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k4_finseq_1 B)) =>  ((k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) B H) = (k1_funct_4 F (k11_card_3 (k4_prvect_2 A) E (k2_finseq_1 (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) H))))) ) ) ) ) ) ) ) )  =>  ((k5_algstr_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G))) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)))) (k3_ndiff_5 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G))) (k3_rlvect_1 (k14_prvect_2 A) D C)) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)))) (k3_ndiff_5 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G))) (k3_rlvect_1 (k14_prvect_2 A) D (k7_partfun1 (u1_struct_0 (k14_prvect_2 A)) B (k23_binop_2 G 1))))) = (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G)))) (k3_ndiff_5 A (k5_ndiff_5 A (k7_nat_d (k23_binop_2 (k3_finseq_1 A) 1) G))) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k6_nat_d A (k5_nat_d A B)) = (k5_nat_d (k6_nat_d B A) A)) ) ) ) ) ).
tt(t55_normform,ax, (! [A:$i] :  (! [B:$i] :  ((m2_subset_1 B (k5_finsub_1 (k7_normform A)) (k8_normform A)) =>  ((k9_normform A (k10_normform A B B)) = (k9_normform A B)) ) ) ) ).
tt(t55_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) => (m2_cat_1 (k10_oppcat_1 A B C) (k2_oppcat_1 A) B)) ) ) ) ) ) ).
tt(t55_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((r7_orders_1 A B) & (v6_relat_2 A))  => (r9_orders_1 A B)) ) ) ) ).
tt(t55_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (~  ( (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r3_orders_2 A D C)) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_orders_2 A B C)) ) ) ) ) ) ) ) ).
tt(t55_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A B) =>  ( (~  ((k5_ordinal3 B A) = k1_xboole_0) )  & (r2_hidden k1_xboole_0 (k5_ordinal3 B A))) ) ) ) ) ) ).
tt(t55_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v1_finset_1 B) & (v1_ordinal2 B)) ) ) )  =>  ((k4_ordinal5 (k1_ordinal4 (k5_afinsq_1 A) B)) = (k10_ordinal2 A (k4_ordinal5 B))) ) ) ) ) ).
tt(t55_ordinal6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v3_ordinal6 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 A)) => (r1_tarski (k1_funct_1 A C) (k1_funct_1 B C))) ) ) )  =>  ( ((k9_xtuple_0 A) = k1_xboole_0)  | (r1_tarski (k7_ordinal6 A) (k7_ordinal6 B))) ) ) ) ) ) ).
tt(t55_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t55_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_parsp_2 A B C B C)) ) ) ) ) ) ).
tt(t55_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ( ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  & (r1_partfun1 A B))  =>  (A = B) ) ) ) ) ) ).
tt(t55_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r2_hidden D (k1_relset_1 A E)) & (r2_hidden (k7_partfun1 B E D) C))  <=> (r2_hidden (k4_tarski D (k7_partfun1 B E D)) (k3_partfun2 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D E))  => (r2_pboole A (k4_pboole A B E) (k4_pboole A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t55_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r4_pdiff_5 B A) & (r4_pdiff_5 C A))  =>  ((r3_pdiff_1 3 1 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 1 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k9_real_1 (k4_pdiff_5 B A) (k4_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t55_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r2_pdiff_9 B A C))  => (v1_pdiff_7 B A)) ) ) ) ) ) ) ).
tt(t55_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k4_pepin A) 2)) ) ) ).
tt(t55_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k4_finseq_1 B) = (k4_finseq_1 (k15_finseq_1 (k12_pnproc_1 B A)))) ) ) ) ) ).
tt(t55_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k1_card_1 (k2_struct_0 (k17_polyform A (k4_xcmplx_0 1)))) = 2) ) ) ).
tt(t55_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_polynom5 A (k9_polynom3 A) B)) ) ) ) ).
tt(t55_polyred,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r11_polyred A B C D) & (r11_polyred A B E F))  => (r11_polyred A B (k3_rlvect_1 A C E) (k3_rlvect_1 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k5_power A (k3_power B C)) = (k3_xcmplx_0 C (k5_power A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r6_pboole A (k12_pre_poly A (k16_pre_poly A) B) (k16_pre_poly A))) ) ) ).
tt(t55_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k13_complex1 (k6_prepower A B) (k6_prepower A C)) = (k6_prepower A (k6_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t55_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 C D) = (k4_prob_3 A B D)) ) ) )  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ( (~ (r2_hidden D (k1_relset_1 k5_numbers B)))  =>  ((k1_funct_1 C D) = k1_xboole_0) ) ) ) )  =>  ( ((k1_prob_2 A (k9_setfam_1 A) C k6_numbers) = k1_xboole_0)  &  ((k1_kurato_0 A C) = (k5_prob_3 A B)) ) ) ) ) ) ) ) ).
tt(t55_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k9_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k6_cqc_lang A C) (k4_cqc_the1 A)))  => (r2_hidden B (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t55_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r2_hidden A (k17_pscomp_1 B)) =>  ( ((k18_euclid A) = (k18_euclid (k25_pscomp_1 B)))  &  ((v2_compts_1 B (k15_euclid 2)) =>  ((r1_xxreal_0 (k17_euclid (k25_pscomp_1 B)) (k17_euclid A)) & (r1_xxreal_0 (k17_euclid A) (k17_euclid (k24_pscomp_1 B)))) ) ) ) ) ) ) ) ).
tt(t55_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k4_pboole A (k2_pzfmisc1 A B C) D) (k1_pboole A)) <=>  ((r1_pboole A B D) & (r1_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t55_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r3_qc_lang2 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (~ (r1_qc_lang2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k13_qc_lang1 A B)) = (k5_qc_lang3 A B)) ) ) ) ) ).
tt(t55_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 (k28_quaterni A) B) = (k28_quaterni (k18_quatern2 A B))) ) ) ) ) ).
tt(t55_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k29_quaterni A (k29_quaterni B C)) = (k26_quaterni (k29_quaterni A B) C)) ) ) ) ) ) ) ).
tt(t55_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k31_quaterni (k28_quaterni A)) = (k28_quaterni (k31_quaterni A))) ) ) ).
tt(t55_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  => (v1_quofield (k3_struct_0 A) A A)) ) ).
tt(t55_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [E:$i] :  ((m1_rcomp_3 E A B D) =>  (~  ((m1_setfam_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 D (k4_topmetr A B)) &  ((v1_rcomp_3 D (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k1_nat_1 C 1) (k3_finseq_1 E)) & (v1_xboole_0 (k2_rcomp_1 (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) E (k1_nat_1 C 1))) (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) E C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_seq_1 (k4_real_3 A) B) k6_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k10_real_1 1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 1)) (k5_square_1 (k1_seq_1 (k6_real_3 A) B)))) (k10_real_1 1 (k8_real_1 (k1_seq_1 (k6_real_3 A) B) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1)))))) ) ) ) ) ) ) ).
tt(t55_relat_1,ax, ((k4_relat_1 k1_xboole_0) = k1_xboole_0) ).
tt(t55_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ( ((k9_xtuple_0 C) = (k7_relset_1 A B (k3_relset_1 B A C) A))  &  ((k7_relset_1 A B (k3_relset_1 B A C) (k7_relset_1 B A C B)) = (k7_relset_1 A B (k3_relset_1 B A C) (k10_xtuple_0 C))) ) ) ) ) ) ).
tt(t55_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v2_rewrite1 A) & (v4_rewrite1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((r2_rewrite1 A B C) =>  ((k2_rewrite1 A B) = (k2_rewrite1 A C)) ) ) ) ) ) ).
tt(t55_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) => (r4_rewrite2 A B (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k6_rewrite2 (k8_afinsq_1 A))) C)) ) ) ) ) ).
tt(t55_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden (k2_xcmplx_0 E 1) (k4_finseq_1 D)) &  (! [F:$i] :  ((m1_subset_1 F (k8_afinsq_1 A)) =>  (! [G:$i] :  ((m1_subset_1 G (k8_afinsq_1 A)) =>  (~  ( (F = (k2_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1))))  &  ((r1_rewrite3 B C (k1_xtuple_0 (k1_funct_1 D E)) G (k1_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1)))) &  ((k2_xtuple_0 (k1_funct_1 D E)) = (k1_flang_1 A G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_partfun1 B A) &  ( ((k8_relset_1 A k1_numbers C (k1_tarski k6_numbers)) = k1_xboole_0)  & (v1_partfun1 C A)) )  <=> (v1_partfun1 (k3_rfunct_1 A k1_numbers B C) A)) ) ) ) ) ) ) ).
tt(t55_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_rfunct_3 A B) <=> (r2_rfunct_3 (k15_valued_1 k1_numbers k1_numbers A C) B)) ) ) ) ) ) ).
tt(t55_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) => (r1_xxreal_0 (k1_rinfsup1 (k3_rinfsup1 A)) (k2_rinfsup1 (k4_rinfsup1 A)))) ) ) ).
tt(t55_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (~  (A = k6_numbers) )  =>  ((k4_rlaffin1 B (k1_convex1 B C A)) = (k1_convex1 B (k4_rlaffin1 B C) A)) ) ) ) ) ) ) ) ).
tt(t55_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ( ((k3_rlsub_1 A B C) = (k3_rlsub_1 A (k4_algstr_0 A B) C))  <=> (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t55_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v13_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ).
tt(t55_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C k1_numbers))  => (m1_connsp_2 (k1_convex1 A B C) A (k4_struct_0 A))) ) ) ) ) ) ).
tt(t55_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) = (k1_algstr_0 A (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B)) (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) C)))) ) ) ) ) ) ) ).
tt(t55_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) => (r1_tarski (k3_rlvect_2 A (k10_rlvect_2 A B C)) (k4_subset_1 (u1_struct_0 A) (k3_rlvect_2 A B) (k3_rlvect_2 A C)))) ) ) ) ) ) ).
tt(t55_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C A) & (l1_vectsp_2 C A)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_rmod_2 E A C) =>  ((r1_struct_0 E D) => (r2_hidden (k5_vectsp_2 A C B D) (k3_rmod_2 A C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) => (r1_tarski (k2_rmod_4 A B (k9_rmod_4 A B C D)) (k4_subset_1 (u1_struct_0 B) (k2_rmod_4 A B C) (k2_rmod_4 A B D)))) ) ) ) ) ) ) ) ).
tt(t55_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_robbins1 A (k3_robbins1 A B)) = B) ) )  => (v6_robbins1 A)) ) ) ).
tt(t55_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k5_robbins1 A C D)) = (k5_robbins1 A D (k5_robbins1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t55_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_prob_2 C) & (m2_finseq_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers (k6_roughs_1 A (k2_roughs_1 (u1_struct_0 A) C)) B) = (k18_rvsum_1 (k7_roughs_1 A C B))) ) ) ) ) ) ) ).
tt(t55_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( ((k1_rpr_1 A C) = k6_numbers)  => (r1_rpr_1 A B C)) ) ) ) ) ) ) ).
tt(t55_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k3_rlvect_1 A C D) (k3_rusub_1 A D B)) <=> (r1_struct_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t55_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (v13_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ).
tt(t55_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k12_rvsum_1 (k9_finseq_1 A)) = (k9_finseq_1 (k3_square_1 A))) ) ) ).
tt(t55_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( (C = (k5_relat_1 D k1_ami_2))  &  (A = B) )  =>  ((k1_funct_1 C A) = (k1_funct_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t55_scmfsa8c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~ (r3_scmfsa7b A C))  &  ( (~ (r3_scmfsa7b B C))  & (r4_scmfsa7b (k6_scmfsa6a A B) C)) ) ) ) ) ) ) ) ) ).
tt(t55_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scm_halt C)) ) ) ) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) &  ((r1_tarski C A) & (r1_extpro_1 3 k1_scmfsa_2 A B)) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 A B)) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 A B D) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t55_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ( (~  ((k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) = k6_numbers) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k7_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k17_scmpds_2 A C)) )  &  ( ( ((k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) = k6_numbers)  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k7_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A))) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k7_scmpds_2 D B C) A) E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k5_card_1 (k6_scmpds_6 A B C)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ).
tt(t55_scmpds_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (! [H:$i] :  ((m2_finseq_1 H k5_numbers) =>  ( ( ((k3_finseq_1 H) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd C)) D)))  &  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 H) I))  =>  ((k1_funct_1 H (k2_nat_1 I 1)) = (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd G)) I))) ) ) ) )  =>  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd C)) C) |  ((r1_xxreal_0 E D) |  ((r1_xxreal_0 F (k2_xcmplx_0 (k1_funct_1 B (k1_scmp_gcd C)) E)) |  ((r1_xxreal_0 G F) |  ((r1_xxreal_0 (k1_funct_1 B (k1_scmp_gcd G)) G) |  ((k1_funct_1 (k6_scmpds_4 (k4_scmpds_7 C D E F G) B A) (k2_scmpds_2 (k1_funct_1 B (k1_scmp_gcd C)) E)) = (k2_wsierp_1 H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_scmyciel,ax, (! [A:$i] :  ( ((v1_scmyciel A) & (v4_scmyciel A))  =>  ((k8_scmyciel A) = k6_numbers) ) ) ).
tt(t55_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D D) =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t55_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) (k52_valued_1 k5_numbers k1_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers A) (k56_valued_1 k5_numbers k1_numbers B)))) ) ) ) ).
tt(t55_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k3_funct_2 k2_numbers k2_numbers (k7_seq_4 A) B) = (k5_binop_2 A B)) ) ) ) ) ).
tt(t55_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k6_square_1 B))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k3_xcmplx_0 (k3_xcmplx_0 (k13_complex1 2 3) B) (k6_square_1 B)))) ) ) ) ) ) ) ).
tt(t55_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_kurato_0 A B) = (k4_kurato_0 A (k2_setlim_1 A B))) ) ) ) ).
tt(t55_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k5_setlim_2 B D C)) A) = (k9_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t55_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden B (k3_funct_2 A (k5_finsub_1 A) (k11_setwiseo A) C)) <=>  (B = C) ) ) ) ) ) ) ).
tt(t55_sf_mastr,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k3_scmfsa_2)))  =>  (~ (r2_hidden (k3_scmfsa_m A) A)) ) ) ).
tt(t55_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A C (k5_sheffer1 A D B))) B)) = (k5_sheffer1 A C (k5_sheffer1 A C (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t55_simplex0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_simplex0 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_tarski (k9_subset_1 (k1_zfmisc_1 (u1_struct_0 C)) (k9_xtuple_0 D) (u1_pre_topc C)) B) =>  ((k10_simplex0 A C (k5_relat_1 D B)) = (k10_simplex0 A C D)) ) ) ) ) ) ) ) ).
tt(t55_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k3_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ).
tt(t55_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k3_binop_2 (k5_binop_2 (k6_binop_2 (k3_binop_2 1 (k5_binop_2 (k19_binop_2 1) k7_complex1)) 2) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A (k5_binop_2 B k7_complex1)))) (k5_binop_2 (k6_binop_2 (k3_binop_2 1 k7_complex1) 2) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A (k5_binop_2 (k7_binop_2 B) k7_complex1))))) = (k9_binop_2 (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k16_sin_cos B)) (k11_binop_2 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 A) (k3_funct_2 k1_numbers k1_numbers k19_sin_cos B)))) ) ) ) ) ).
tt(t55_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v6_valued_0 (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t55_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k18_complex1 B) (k18_complex1 A))) )  =>  ((k10_binop_2 (k3_sin_cos7 A) (k3_sin_cos7 B)) = (k3_sin_cos7 (k10_binop_2 (k11_binop_2 A B) (k7_square_1 (k11_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k10_binop_2 (k3_square_1 B) 1)))))) ) ) ) ) ) ).
tt(t55_sin_cos9,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1))) = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k10_real_1 k32_sin_cos 4))) ).
tt(t55_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k25_sin_cos A) k6_numbers)) ) ) ).
tt(t55_sppol_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~  (A = B) )  &  ( (~  (C = D) )  &  (~ (v1_topreal4 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) =>  ((k9_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k18_euclid A)) ) ) ) ) ) ).
tt(t55_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k17_euclid (k24_pscomp_1 (k3_topreal1 2 A))) (k17_euclid (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t55_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ( (~ (v3_funct_1 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) A) |  ((r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) B) | (r1_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 (k2_goboard2 C) A B)) (k3_topreal1 2 (k1_sprect_1 (k3_topreal1 2 C))))) ) ) ) ) ) ) ) ) ).
tt(t55_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t55_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B 1)) ) )  =>  ((r1_xxreal_0 (k3_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))) (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))) & (r1_xxreal_0 (k4_xcmplx_0 (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))) (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))))) ) ) ) ) ) ).
tt(t55_stirl2_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ( ((k1_card_1 B) = (k23_binop_2 A 1))  & (r2_hidden C B))  =>  ((k1_card_1 (k6_subset_1 B (k1_tarski C))) = A) ) ) ) ) ) ).
tt(t55_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) =>  (! [F:$i] :  ((m1_substut1 F A (k7_sublemma A E B)) =>  ((v3_substut1 (k7_sublemma A E B) A) =>  (! [G:$i] :  ((m1_subset_1 G C) => (r2_relset_1 (k3_qc_lang1 A) C (k13_sublemma A E B F C (k1_sublemma A C D (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A E B) F))) G))) (k13_sublemma A E B F C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k5_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))) (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k5_setfam_1 (u1_struct_0 A) B)))))) ) ) ) ).
tt(t55_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((v3_pre_topc B A) | (v4_pre_topc B A))  &  ((v3_tex_2 B A) & (v1_subset_1 B (u1_struct_0 A))) ) ) ) ) ) ) ).
tt(t55_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v1_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ( ((v3_tex_3 B A) & (m1_pre_topc B A))  <=>  ((v3_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t55_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_tex_4 A B) (k1_setfam_1 (a_2_10_tex_4 A B)))) ) ) ) ).
tt(t55_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski E (u1_struct_0 C)) =>  ((k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) D E) = (k7_relset_1 (u1_struct_0 C) (u1_struct_0 A) (k2_tmap_1 B A D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) =>  ((r1_borsuk_6 A B C) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B))) &  ((v1_group_6 E (k5_topalg_1 A C) (k5_topalg_1 A B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))))) ) )  =>  ((r2_funct_2 (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)) E (k6_topalg_1 A B C D)) => (v3_funct_2 E (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_topgen_1,ax, ( (~ (v2_tops_1 k1_numbers k3_topmetr))  & (m1_subset_1 k1_numbers (k1_zfmisc_1 (u1_struct_0 k3_topmetr)))) ).
tt(t55_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_card_3 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r1_topgen_4 A B C)) ) ) ) ) ) ) ) ).
tt(t55_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v4_pre_topc (k1_limfunc1 A) k2_topgen_3) & (m1_subset_1 (k1_limfunc1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t55_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A (k6_algstr_0 A B (k2_group_1 A B))) =>  (? [D:$i] :  ( ((v3_pre_topc D A) & (m1_connsp_2 D A B))  & (r1_tarski (k2_group_2 A D (k1_group_2 A D)) C)) ) ) ) ) ) ) ) ).
tt(t55_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k10_metric_1 B C A) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t55_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k6_jgraph_6 A B C) (k5_jgraph_6 A B C)) = (k7_jgraph_6 A B C)) ) ) ) ) ) ) ).
tt(t55_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k4_finseq_1 D)) =>  ((k7_relset_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) (k17_toprealc A B) (k1_topreal9 A D C)) = (k2_rcomp_1 (k6_xcmplx_0 (k7_partfun1 k1_numbers D B) C) (k2_xcmplx_0 (k7_partfun1 k1_numbers D B) C))) ) ) ) ) ) ) ) ) ) ).
tt(t55_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tops_1 B A) => (v2_tops_1 B A)) ) ) ) ) ).
tt(t55_tops_2,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  & (v2_funct_1 C))  =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) = (k7_relset_1 (u1_struct_0 B) (u1_struct_0 A) (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t55_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k2_pre_topc A C) = (k2_pre_topc B D)) ) ) ) ) ) ) ) ) ) ).
tt(t55_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  & (r1_diraf A C B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C))) )  =>  ((r3_diraf A B C D) | (r1_diraf A D B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_trees_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ((r2_hidden B (k3_trees_1 A)) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~ (r2_hidden (k8_finseq_1 k5_numbers B (k12_finseq_1 k5_numbers C)) A)) ) ) ) ) ) ) ) ).
tt(t55_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) )  =>  ((k11_trees_3 (k7_finseq_1 B (k9_finseq_1 A))) = (k5_trees_1 (k2_xboole_0 (k11_trees_3 B) (k2_trees_1 (k2_nat_1 (k3_finseq_1 B) 1))) (k12_finseq_1 k5_numbers (k3_finseq_1 B)) A)) ) ) ) ) ).
tt(t55_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_tsep_1 A B C) &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_pre_topc D A) &  ((v4_pre_topc E A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) D (k4_subset_1 (u1_struct_0 A) B C)) B) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) E (k4_subset_1 (u1_struct_0 A) B C)) C) &  (~  ( (~ (r1_tarski (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) D E)))  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc F A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) F (k4_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) B C)) &  ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_uniroots,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k14_polynom3 k1_complfld))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 k1_complfld)) &  ((v1_algseq_1 D k1_complfld) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 k1_complfld))))) ) )  =>  ( ( (D = (k3_group_4 (k14_polynom3 k1_complfld) C))  &  ( (B = A)  &  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m2_subset_1 E k1_numbers k5_numbers))  =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  ( (~  ((k1_funct_1 C E) = (k3_algseq_1 k1_complfld (k1_group_1 k1_complfld))) )  &  (~  ((k1_funct_1 C E) = (k5_uniroots E)) ) ) ) ) ) ) ) )  => (v1_int_1 (k2_polynom4 k1_complfld D B))) ) ) ) ) ) ) ) ) ).
tt(t55_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 D A) &  ((v1_uproots D A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k7_uproots A B (k13_polynom3 A C D)) = (k2_nat_1 (k7_uproots A B C) (k7_uproots A B D))) ) ) ) ) ) ) ) ) ).
tt(t55_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k9_xtuple_0 (k47_valued_2 B D C)) = (k1_relset_1 A D)) ) ) ) ) ) ) ) ).
tt(t55_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden C (k3_vectsp_4 A B D E)) <=>  ((k3_vectsp_4 A B D E) = (k3_vectsp_4 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)) = (k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 C)))))  =>  ((v3_funct_1 (k2_partfun1 B (u1_struct_0 C) D A)) =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) => (r1_vfunct_1 B C (k4_vfunct_1 B C D E) A)) )  &  ((r1_vfunct_1 B C (k5_vfunct_1 B C D) A) & (v1_comseq_2 (k2_partfun1 B k1_numbers (k3_normsp_0 B C D) A))) ) ) ) ) ) ) ) ) ) ).
tt(t55_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ((v3_funct_1 (k2_partfun1 A (u1_struct_0 B) C D)) =>  ( (! [E:$i] :  ((m1_subset_1 E k2_numbers) => (r1_vfunct_2 A B (k2_vfunct_2 A B C E) D)) )  &  ((r1_vfunct_2 A B (k5_vfunct_1 A B C) D) & (v1_comseq_2 (k2_partfun1 A k1_numbers (k3_normsp_0 A B C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t55_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_yellow_0 A B) | (v3_lattice3 A))  =>  ((k1_yellow_0 A B) = (k1_yellow_0 A (k11_waybel_0 A B))) ) ) ) ) ) ).
tt(t55_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v7_waybel_1 B A) =>  ((v18_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C (u1_struct_0 (k1_yellow_2 A A B))) & (r1_yellow_0 A C))  =>  ((r1_yellow_0 (k1_yellow_2 A A B) C) &  ((k1_yellow_0 (k1_yellow_2 A A B) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k1_yellow_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((r2_hidden C (k2_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k4_waybel23 A B))) =>  ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t55_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_2 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ((k12_lattice3 A B (k4_yellow_2 A D)) = (k1_waybel_2 A (k3_waybel_2 A B (k2_waybel_2 A C D)))) ) ) ) ) ) ) ) ) ).
tt(t55_waybel34,ax, (! [A:$i] :  ( (~ (v2_setfam_1 A))  => (r3_yellow20 (k5_waybel34 A) (k4_waybel34 A) (k7_waybel34 A) (k11_waybel34 A) (k10_waybel34 A))) ) ).
tt(t55_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_waybel_4 A B C) <=>  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  ((k4_xboole_0 (k2_xboole_0 A B) (k3_xboole_0 A B)) = (k2_xboole_0 (k4_xboole_0 A B) (k4_xboole_0 B A))) ) ) ).
tt(t55_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k5_xboolean B C)) = (k4_xboolean (k3_xboolean (k4_xboolean A B)) (k3_xboolean (k4_xboolean A C)))) ) ) ) ) ) ) ).
tt(t55_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 B C) = (k7_xcmplx_0 (k7_xcmplx_0 B A) (k7_xcmplx_0 C A))) ) ) ) ) ) ) ) ).
tt(t55_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~  (A = B) )  &  ((r1_xxreal_0 (k6_xcmplx_0 A B) k6_numbers) & (r1_xxreal_0 (k6_xcmplx_0 B A) k6_numbers)) ) ) ) ) ) ) ).
tt(t55_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k2_xxreal_1 A B) (k2_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ((m1_xxreal_2 B A) =>  ((r2_hidden B A) =>  (B = (k1_xxreal_2 A)) ) ) ) ) ) ).
tt(t55_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~ (r1_xxreal_0 (k1_xxreal_3 A B) C))  &  (~  ( (~  (C = k1_xxreal_0) )  &  ( (~  (B = k2_xxreal_0) )  &  ( (~  (A = k2_xxreal_0) )  &  (~ (r1_xxreal_0 A (k3_xxreal_3 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  ((v2_lattice3 A) <=>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (r2_yellow_0 A B)) ) ) ) ) ).
tt(t55_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_waybel_6 C A) & (v1_waybel_6 D B))  => (v1_waybel_6 (k6_yellow_3 A B C D) (k3_yellow_3 A B))) ) ) ) ) ) ) ) ) ).
tt(t55_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_borsuk_1 C A B) => (r2_funct_2 (u1_struct_0 B) (u1_struct_0 B) (k1_partfun1 (u1_struct_0 B) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k1_yellow_9 A B) C) (k3_struct_0 B))) ) ) ) ) ) ) ).
tt(t55_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_altcat_1 C) &  ((v11_altcat_1 C) &  ((v12_altcat_1 C) & (l2_altcat_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v16_functor0 D A B) & (m2_functor0 D A B))  =>  (! [E:$i] :  ( ((v16_functor0 E B C) & (m2_functor0 E B C))  =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v2_altcat_1 F) &  ((v3_altcat_2 F A) & (m1_altcat_2 F A)) ) )  =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  &  ((v2_altcat_1 G) &  ((v3_altcat_2 G B) & (m1_altcat_2 G B)) ) )  =>  (! [H:$i] :  ( ( (~ (v2_struct_0 H))  &  ((v2_altcat_1 H) &  ((v3_altcat_2 H C) & (m1_altcat_2 H C)) ) )  =>  ( ((r3_yellow20 A B D F G) & (r3_yellow20 B C E G H))  => (r2_yellow20 A C (k2_functor3 A B C D E) F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_yellow_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D C (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 A))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E C) => (r3_orders_2 A B (k3_funct_2 C (u1_struct_0 A) D E))) )  => (r3_orders_2 A B (k5_yellow_2 A D))) ) ) ) ) ) ) ) ) ).
tt(t55_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_lattice3 A D B) & (r1_lattice3 A E C))  => (r1_lattice3 A (k4_yellow_4 A D E) (k12_lattice3 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t55_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A (k13_lattice3 A B C) C) = (k1_yellow_5 A B C)) ) ) ) ) ) ) ).
tt(t55_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m3_yellow_9 C A B) => (m3_yellow_9 C B A)) ) ) ) ) ) ).
tt(t55_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k29_zf_lang (k11_zf_lang A B)) = (k2_xboole_0 (k2_xboole_0 (k29_zf_lang A) (k29_zf_lang B)) (k1_enumset1 (k6_zf_lang B) (k7_zf_lang A (k6_zf_lang B)) (k11_zf_lang A B)))) ) ) ) ) ).
tt(t55_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((v7_zf_lang A) & (r1_zf_lang B A)) ) ) ) ) ) ).
tt(t55_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k3_xboole_0 (k2_tarski A B) C) = (k2_tarski A B))  => (r2_hidden A C)) ) ) ) ).
tt(t55_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (m1_zmodul01 (k3_zmodul01 B) C)) ) ) ) ) ) ).
tt(t56_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l2_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r3_abcmiz_0 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ( (D = (k2_relset_1 (u1_abcmiz_0 A) C))  =>  ((k8_abcmiz_0 A B C) = (k6_abcmiz_0 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_abcmiz_1 B A (k13_abcmiz_1 A)) =>  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (~  ((k30_abcmiz_1 A (k32_abcmiz_1 A) B) = (k31_abcmiz_1 A (k33_abcmiz_1 A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t56_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  ((r7_abcmiz_a A D B C) =>  ((r1_abcmiz_a A D B) & (r1_abcmiz_a A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t56_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r1_aff_1 A B C E) &  ((r1_aff_1 A B D F) &  ((r1_aff_1 A B D G) &  ((r2_analoaf A C D E F) & (r2_analoaf A C D E G)) ) ) )  =>  ((r1_aff_1 A B C D) |  (F = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r5_aff_1 A B C) & (r1_aff_4 A C D))  => (r1_aff_4 A B D)) ) ) ) ) ) ) ) ) ).
tt(t56_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ( ((k1_afinsq_1 B) = (k1_nat_1 A 1))  =>  (B = (k1_ordinal4 (k5_relat_1 B A) (k5_afinsq_1 (k1_funct_1 B A)))) ) ) ) ) ) ).
tt(t56_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v3_valued_0 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (B = (k2_partfun1 k5_numbers k1_numbers C (k23_binop_2 A 1)))  =>  ((k7_afinsq_2 B) = (k8_nat_1 k1_numbers (k3_series_1 C) A)) ) ) ) ) ) ) ) ).
tt(t56_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ((m2_algspec1 B A) =>  (! [C:$i] :  ((m4_algspec1 C B) => (m4_algspec1 C A)) ) ) ) ) ) ).
tt(t56_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k5_altcat_4 (k1_altcat_4 A)) = (k5_altcat_4 A)) ) ) ).
tt(t56_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden D B) &  ((r2_hidden E B) &  ((r2_hidden F C) &  ((r2_hidden G C) & (r10_analmetr A B C)) ) ) )  => (r4_analmetr A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ( (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k2_trees_4 A C)) ) ) )  &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ((r2_hidden C (k2_finseq_1 4)) &  ( (B = (k4_trees_4 C D))  &  ((k3_finseq_1 D) = (k1_recdef_1 k19_aofa_000 C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ( ((k1_funct_1 H G) = 3)  &  ((k1_funct_1 H C) = 4) ) ) ) ) )  => (r5_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F 1) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 2) (k74_aofa_i00 A B C D G E) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_armstrng,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) &  ((r2_hidden (k6_armstrng A D E) C) &  ((r1_tarski D B) &  (~ (r1_tarski E B)) ) ) ) ) ) )  => (r2_hidden B (k14_armstrng A C))) ) ) ) ) ) ).
tt(t56_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ( ((k10_arytm_3 A B) = (k10_arytm_3 A C))  =>  ( (A = k11_arytm_3)  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t56_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k9_newton B) (k9_newton A))) ) ) ) ) ).
tt(t56_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t56_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (B = k6_numbers)  =>  ((r1_xxreal_0 C k6_numbers) |  ((v8_bcialg_1 E) & (m1_bcialg_5 E k6_numbers k6_numbers k6_numbers k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) => (m1_bcialg_1 (k10_bcialg_6 A B C D) A)) ) ) ) ) ) ) ) ).
tt(t56_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m2_bcialg_1 C A) =>  ( ((r1_tarski B C) & (m4_bciideal B A))  => (m4_bciideal C A)) ) ) ) ) ) ) ).
tt(t56_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k4_normsp_1 A C B) (k5_bhsp_1 A C (k4_algstr_0 A B)))) ) ) ) ) ) ).
tt(t56_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_subset_1 (u1_struct_0 A) (k4_bhsp_2 A B C) (k6_bhsp_2 A B C)) = (k5_bhsp_2 A B C)) ) ) ) ) ) ) ).
tt(t56_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ( (~ (v3_funct_1 D))  &  ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) &  ((v13_vectsp_1 D B A) &  ((v1_hahnban1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ( (~ (v3_funct_1 E))  &  ((v1_funct_2 E (u1_struct_0 C) (u1_struct_0 A)) &  ((v13_vectsp_1 E C A) &  ((v1_hahnban1 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) ) ) ) )  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k13_bilinear A B C (k9_bilinear A B C D E)))) (u1_struct_0 (k6_vectsp10 A C (k14_bilinear A B C (k9_bilinear A B C D E))))) (u1_struct_0 A) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 A B (k9_vectsp10 A B D))) (u1_struct_0 (k6_vectsp10 A C (k9_vectsp10 A C E)))) (u1_struct_0 A) (k17_bilinear A B C (k9_bilinear A B C D E)) (k9_bilinear A (k6_vectsp10 A B (k9_vectsp10 A B D)) (k6_vectsp10 A C (k9_vectsp10 A C E)) (k11_vectsp10 A B D) (k11_vectsp10 A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t56_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A B (k5_lattices A)) B)) ) ) ) ).
tt(t56_borsuk_4,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (~  ((r1_tarski B A) &  ( (~  (B = A) )  &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~ (r1_topreal1 (k15_euclid 2) C D B)) ) ) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  (B = (k6_domain_1 (u1_struct_0 (k15_euclid 2)) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_borsuk_5 B C) (k2_rcomp_1 C D)) (k2_rcomp_1 D k1_xxreal_0)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k2_pre_topc k3_topmetr A) = (k3_rcomp_1 B k1_xxreal_0)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_borsuk_6,ax, ((k4_subset_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) (k4_subset_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) k6_borsuk_6 k7_borsuk_6) k8_borsuk_6) = (k8_mcart_1 k1_numbers k1_numbers (k1_rcomp_1 k6_numbers 1) (k1_rcomp_1 k6_numbers 1))) ).
tt(t56_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 (k1_real_1 A)) B)) = B) ) ) ) ) ).
tt(t56_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A E B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) F) G) H) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k7_xboolean k8_margrel1 A) = A) ) ) ).
tt(t56_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k5_bvfunc26 A B C)) (k2_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t56_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k8_cqc_lang A B C)))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ).
tt(t56_card_1,ax, (8 = (k6_enumset1 k1_xboole_0 1 2 3 4 5 6 7)) ).
tt(t56_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] : (r1_xxreal_0 (k5_card_1 (k6_enumset1 A B C D E F G H)) 8)) ) ) ) ) ) ) ) ).
tt(t56_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski A B) => (r1_tarski (k8_card_3 A) (k8_card_3 B))) ) ) ) ) ).
tt(t56_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((k9_xtuple_0 A) = B)  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  ( ( ((k1_relset_1 k5_numbers C) = (k5_card_1 B))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k3_card_fin (k23_binop_2 D 1) A))) ) ) ) )  =>  ((k1_card_1 (k3_tarski (k10_xtuple_0 A))) = (k7_afinsq_2 C)) ) ) ) ) ) ) ) ) ).
tt(t56_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v10_cat_1 B A) & (r1_cat_1 A C B))  => (v10_cat_1 C A)) ) ) ) ) ) ) ).
tt(t56_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u4_struct_0 A)) =>  ( ((r2_cat_3 A B D E) &  ((r2_cat_3 A C F G) &  ( ((k4_graph_1 A D) = (k4_graph_1 A F))  &  ((k4_graph_1 A E) = (k4_graph_1 A G)) ) ) )  => (r1_cat_1 A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((k2_cat_1 A (k19_cat_4 A) B) = k1_xboole_0) ) ) ) ) ) ).
tt(t56_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k1_cfunct_1 B C D) A) (k1_cfunct_1 B (k2_partfun1 B k2_numbers C A) (k2_partfun1 B k2_numbers D A))) &  ((r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k1_cfunct_1 B C D) A) (k1_cfunct_1 B (k2_partfun1 B k2_numbers C A) D)) & (r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k1_cfunct_1 B C D) A) (k1_cfunct_1 B C (k2_partfun1 B k2_numbers D A)))) ) ) ) ) ) ) ) ) ).
tt(t56_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  ( ((k6_chain_1 A B) = (k3_subset_1 (k4_chain_1 A B A) (k5_chain_1 A B A)))  &  ((k5_chain_1 A B A) = (k3_subset_1 (k4_chain_1 A B A) (k6_chain_1 A B))) ) ) ) ) ) ).
tt(t56_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ( ((k2_chord A (k6_domain_1 (k6_glib_000 A) B)) = k1_xboole_0)  <=> (v10_glib_000 B A)) ) ) ) ) ).
tt(t56_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_finset_1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k4_finseq_2 A B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A B) B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_card_1 D A) & (v1_finseq_1 D)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k5_circcomb C D) (k7_circcomb A B C D)))) =>  ((k1_funct_1 (k6_circuit2 (k5_circcomb C D) (k7_circcomb A B C D) E) (k4_tarski D C)) = (k1_funct_1 C (k3_relat_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E A) &  ((v4_msafree2 E A) & (l3_msualg_1 E A)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F B) &  ((v4_msafree2 F B) & (l3_msualg_1 F B)) )  =>  ((r5_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A E))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 B F))) =>  ( (G = (k3_relat_1 C H))  =>  ((v1_circuit2 G A E) <=> (v1_circuit2 H B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_classes1,ax, ((k5_classes1 k1_xboole_0) = k1_xboole_0) ).
tt(t56_classes2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  => (r2_hidden k1_xboole_0 A)) ) ).
tt(t56_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((k3_clvect_1 B) = (k3_clvect_1 C)) ) ) ) ) ) ) ).
tt(t56_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k4_subset_1 (u1_struct_0 A) (k4_clvect_2 A B C) (k6_clvect_2 A B C)) = (k5_clvect_2 A B C)) ) ) ) ) ) ) ).
tt(t56_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski B)))) =>  (~  ( (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E G) C))  => (r2_hidden (k2_tarski F G) B)) ) ) ) ) )  &  ( (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k2_tarski D E) A) =>  (! [F:$i] :  ( ((r2_hidden (k4_tarski D F) C) & (r2_hidden (k4_tarski E F) C))  =>  (D = E) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v10_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  (C = (k11_cohsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k17_complex1 (k2_xcmplx_0 A B)) (k7_real_1 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ).
tt(t56_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k3_complex1 (k2_complex2 A B)) = (k9_real_1 (k8_real_1 (k3_complex1 A) (k21_sin_cos B)) (k8_real_1 (k4_complex1 A) (k18_sin_cos B))))  &  ((k4_complex1 (k2_complex2 A B)) = (k7_real_1 (k8_real_1 (k3_complex1 A) (k18_sin_cos B)) (k8_real_1 (k4_complex1 A) (k21_sin_cos B)))) ) ) ) ) ) ).
tt(t56_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  (A = (k4_struct_0 k1_complfld)) )  =>  ((k2_complfld (k3_vectsp_1 k1_complfld B A)) = (k3_vectsp_1 k1_complfld (k2_complfld B) (k2_complfld A))) ) ) ) ) ) ).
tt(t56_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( (A = B)  &  ((k3_finseq_1 A) = (k3_finseq_1 B)) )  =>  ((k4_finseqop k2_numbers k2_numbers A k25_binop_2) = (k4_finseqop k1_numbers k1_numbers B k31_binop_2)) ) ) ) ) ) ).
tt(t56_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k5_card_1 (k11_compos_1 A B)) = 2) ) ) ) ) ).
tt(t56_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) 3) = (k5_compos_0 (u1_compos_1 A) E 3)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~  (B = k6_numbers) )  =>  (A = (k1_newton (k2_xcmplx_0 (k8_real_1 (k2_power B (k17_complex1 A)) (k21_sin_cos (k10_real_1 (k7_real_1 (k1_comptrig A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B))) (k3_xcmplx_0 (k8_real_1 (k2_power B (k17_complex1 A)) (k18_sin_cos (k10_real_1 (k7_real_1 (k1_comptrig A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B))) k7_complex1)) B)) ) ) ) ) ) ) ) ).
tt(t56_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  => (r1_tarski (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 B C A)) (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers))) ) ) ) ) ) ).
tt(t56_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((v1_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)) &  ((k11_comseq_3 (k25_valued_1 k5_numbers k2_numbers A B)) = (k3_xcmplx_0 B (k11_comseq_3 A))) ) ) ) ) ) ) ).
tt(t56_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((v2_convex4 B A) <=> (v2_convex4 (k5_rusub_4 A B C) A)) ) ) ) ) ) ) ).
tt(t56_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r3_cqc_the1 A B (k8_cqc_lang A (k11_cqc_lang A D C) C))) ) ) ) ) ) ) ) ).
tt(t56_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden F (k24_qc_lang1 A D)) | (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A E (k11_cqc_lang A F C)) (k11_cqc_lang A E B)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r7_cqc_the3 A B C) & (r7_cqc_the3 A D E))  => (r7_cqc_the3 A (k9_cqc_lang A B D) (k9_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k15_csspace A (k3_rlvect_1 A B C) (k3_rlvect_1 A D E)) (k7_real_1 (k15_csspace A B D) (k15_csspace A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t56_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k18_sin_cos (k7_real_1 (k8_real_1 2 B) A)) (k18_sin_cos (k9_real_1 (k8_real_1 2 B) A))))) ) ) ) ) ).
tt(t56_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k16_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k8_real_1 (k8_real_1 3 (k21_sin_cos B)) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k8_real_1 3 B)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t56_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden B (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k16_sin_cos) A B) = (k13_complex1 (k9_real_1 (k8_real_1 (k2_newton (k18_sin_cos A) 3) (k5_square_1 (k21_sin_cos B))) (k8_real_1 (k2_newton (k18_sin_cos B) 3) (k5_square_1 (k21_sin_cos A)))) (k8_real_1 (k8_real_1 (k5_square_1 (k21_sin_cos A)) (k5_square_1 (k21_sin_cos B))) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t56_dilworth,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( ((k5_card_1 A) = (k2_xcmplx_0 (k3_square_1 B) 1))  &  ((v2_funct_1 A) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v2_finseq_1 C) & (v3_valued_0 C)) ) )  =>  (~  ((r1_tarski C A) &  ((r1_xxreal_0 (k2_xcmplx_0 B 1) (k5_card_1 C)) &  ((v5_valued_0 C) | (v6_valued_0 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_ec_pf_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k8_eqrel_1 A B)) & (v1_funct_1 C)) )  =>  ((v2_funct_2 C (k8_eqrel_1 A B)) =>  ((k3_card_3 C) = A) ) ) ) ) ) ) ) ).
tt(t56_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [H:$i] :  ((m2_subset_1 H (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (E = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (F = (k5_algstr_0 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k2_binom (k9_int_3 A) E 3)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) E 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  (I = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) E F) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) F)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)))) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k3_ec_pf_2 A B) (k2_binom (k9_int_3 A) E 2)) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) 2)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) = (k3_rlvect_1 (k9_int_3 A) (k4_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) D (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G))) 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ( ((k4_graph_1 A B) = (k3_graph_1 A C))  &  ((k3_graph_1 A D) = (k4_graph_1 A E)) )  =>  ((k21_ens_1 A (k1_cat_1 A B C) (k1_cat_1 A E D)) = (k1_partfun1 (k2_cat_1 A (k4_graph_1 A C) (k3_graph_1 A E)) (k2_cat_1 A (k3_graph_1 A C) (k4_graph_1 A E)) (k2_cat_1 A (k4_graph_1 A B) (k3_graph_1 A D)) (k2_cat_1 A (k3_graph_1 A B) (k4_graph_1 A D)) (k21_ens_1 A C E) (k21_ens_1 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r2_hidden B (k4_finseq_1 A)) &  ((k1_seq_1 A B) = 1) ) ) )  =>  ((k6_entropy1 A) = k6_numbers) ) ) ) ).
tt(t56_enumset1,ax, (! [A:$i] :  ((k6_enumset1 A A A A A A A A) = (k1_tarski A)) ) ).
tt(t56_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (~  ( (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((k3_funct_2 A B D F) = (k3_funct_2 A B D G))  =>  ((k3_funct_2 A C E F) = (k3_funct_2 A C E G)) ) ) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (~ (r2_funct_2 A C (k1_partfun1 A B B C D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_rvsum_1 C D) => (r1_rvsum_1 (k1_rlvect_1 (k15_euclid A) C B) D)) ) ) ) ) ) ) ) ) ).
tt(t56_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) =>  ((r2_hidden D (k5_euclid_3 2 A B C)) <=>  ((r1_xxreal_0 k6_numbers (k10_euclid_3 2 A B C D)) &  ((r1_xxreal_0 k6_numbers (k11_euclid_3 2 A B C D)) &  ((r1_xxreal_0 k6_numbers (k12_euclid_3 2 A B C D)) &  (~  ( (~  ((k10_euclid_3 2 A B C D) = k6_numbers) )  &  ( (~  ((k11_euclid_3 2 A B C D) = k6_numbers) )  &  (~  ((k12_euclid_3 2 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  (! [J:$i] :  ((m1_subset_1 J k1_numbers) =>  ( ( (A = (k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 C D E) I))  &  ( (B = (k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 F G H) J))  &  (A = B) ) )  =>  ( ((k1_seq_1 C I) = (k1_seq_1 F J))  &  ( ((k1_seq_1 D I) = (k1_seq_1 G J))  &  ((k1_seq_1 E I) = (k1_seq_1 H J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k3_rlvect_1 (k15_euclid 2) (k19_euclid A B) (k19_euclid C D)) = (k19_euclid (k9_binop_2 A C) (k9_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t56_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( (E = (k2_euclid_4 A B C))  =>  ((a_4_0_euclidlp A B C D) = (k2_euclidlp A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) &  ((r2_hidden A C) & (r2_hidden (k4_tarski C B) (k6_exchsort D (k10_funct_7 E A B)))) )  => (r2_hidden (k4_tarski C B) (k6_exchsort D E))) ) ) ) ) ) ) ) ).
tt(t56_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((k3_msafree2 (k8_facirc_1 A B C D)) = (k2_tarski (k4_tarski (k10_finseq_1 A B) D) (k9_facirc_1 A B C D))) ) ) ) ) ) ).
tt(t56_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (A = k6_numbers) )  =>  ((k2_funct_1 (k1_fcont_1 A B)) = (k1_fcont_1 (k5_xcmplx_0 A) (k10_complex1 (k13_complex1 B A)))) ) ) ) ) ) ).
tt(t56_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k24_sin_cos) A) B) = (k10_real_1 (k8_real_1 2 (k1_seq_1 k24_sin_cos (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t56_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B)) k3_taylor_1))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 B C) = 1) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B)) k3_taylor_1) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B)) k3_taylor_1) A) C) = (k10_real_1 1 (k7_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t56_fib_num2,ax, ((k5_fib_num2 4) = (k10_finseq_1 1 3)) ).
tt(t56_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_lattices (k6_filter_0 A (k2_filter_0 A B))) = B) ) ) ) ) ).
tt(t56_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_lattices A (k4_lattices A (k4_filter_0 A B C) (k4_filter_0 A D C)) (k4_filter_0 A (k3_lattices A B D) C))) ) ) ) ) ) ) ) ).
tt(t56_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_filter_2 A B) <=>  ( (~  (B = (u1_struct_0 A)) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) | (r2_hidden (k7_lattices A C) B)) ) ) ) ) ) ) ) ) ).
tt(t56_finseq_1,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r2_wellord2 A (k2_finseq_1 B))) ) ) ) ) ) ).
tt(t56_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_relat_1 (k7_funcop_1 (k2_finseq_1 A) B)) &  ((v1_funct_1 (k7_funcop_1 (k2_finseq_1 A) B)) & (v1_finseq_1 (k7_funcop_1 (k2_finseq_1 A) B))) ) ) ) ) ).
tt(t56_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 (k5_relat_1 A B)) &  ((v1_funct_1 (k5_relat_1 A B)) & (v1_finseq_1 (k5_relat_1 A B))) )  <=>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  ((k9_subset_1 k5_numbers B (k1_relset_1 k5_numbers A)) = (k2_finseq_1 C)) ) ) ) ) ) ) ).
tt(t56_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) &  ((v2_funct_1 (k1_finseq_3 A (k1_tarski B))) &  ((k1_finseq_3 A (k1_tarski B)) = (k7_finseq_1 (k5_finseq_4 A B) (k6_finseq_4 A B))) ) )  => (v2_funct_1 A)) ) ) ) ).
tt(t56_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((r2_hidden B (k10_xtuple_0 C)) & (v2_funct_1 C))  => (v2_funct_1 (k2_finseq_5 A C B))) ) ) ) ) ) ) ).
tt(t56_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden C (k10_xtuple_0 D)) =>  ((r1_xxreal_0 (k4_finseq_4 D C) A) |  ((k4_finseq_4 D C) = (k1_nat_1 A (k4_finseq_4 (k2_rfinseq B A D) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo D A) =>  ((r2_relset_1 k5_numbers A (k1_finseqop A A A D (k5_finseq_2 A B (k4_binop_1 A D)) C) C) & (r2_relset_1 k5_numbers A (k1_finseqop A A A D C (k5_finseq_2 A B (k4_binop_1 A D))) C)) ) ) ) ) ) ) ) ) ) ).
tt(t56_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_fintopo6 A B C D E) & (v1_fin_topo A))  => (v4_fintopo6 B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ( ((k8_flang_1 A B) = (k4_subset_1 (k3_catalan2 A) (k4_flang_1 A (k2_flang_1 A)) (k6_flang_1 A B (k8_flang_1 A B))))  &  ((k8_flang_1 A B) = (k4_subset_1 (k3_catalan2 A) (k4_flang_1 A (k2_flang_1 A)) (k6_flang_1 A (k8_flang_1 A B) B))) ) ) ) ) ).
tt(t56_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) => (r1_tarski (k1_flang_2 A (k1_flang_2 A B C D) E F) (k1_flang_2 A B (k3_xcmplx_0 C E) (k3_xcmplx_0 D F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r2_hidden (k2_flang_1 A) (k2_flang_3 A B)) <=> (r2_hidden (k2_flang_1 A) B)) ) ) ) ).
tt(t56_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  ((k5_relat_1 (k2_xboole_0 B C) A) = (k2_xboole_0 (k5_relat_1 B A) (k5_relat_1 C A))) ) ) ) ) ) ).
tt(t56_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v5_fsm_1 D A B) & (l2_fsm_1 D A B)) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v5_fsm_1 E A B) & (l2_fsm_1 E A B)) )  =>  (~  ( (C = (k13_fsm_1 A B D E))  &  ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  ((r4_fsm_1 A B D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_fsm_1 A B C))) =>  (~  ((r2_hidden (u2_fsm_1 A D) F) &  ((r2_hidden (u2_fsm_1 A E) F) &  (F = (u2_fsm_1 A (k11_fsm_1 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k3_funct_2 A A (k10_funcop_1 A A B C (k6_partfun1 A)) C) = (k5_binop_1 A B C C)) ) ) ) ) ) ) ).
tt(t56_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k9_xtuple_0 (k6_relat_1 A B)) (k9_xtuple_0 B))) ) ) ).
tt(t56_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v2_funct_1 B) <=>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) &  ((r2_hidden D A) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t56_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_tarski (k7_relat_1 (k13_funct_3 B C) A) (k2_zfmisc_1 (k7_relat_1 B A) (k7_relat_1 C A)))) ) ) ) ) ).
tt(t56_funct_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_tarski (k10_xtuple_0 (k3_funct_4 A B)) (k2_zfmisc_1 (k10_xtuple_0 A) (k10_xtuple_0 B)))) ) ) ) ).
tt(t56_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_tarski A B) => (r1_tarski (k1_funct_2 C A) (k1_funct_2 C B))) ) ) ) ).
tt(t56_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_funct_2 A (k1_funct_2 B C))) =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  (! [G:$i] :  (! [H:$i] :  ( ((r2_hidden G A) &  ((r2_hidden H B) &  ( ((k1_funct_1 D G) = E)  &  ((k1_funct_1 (k10_funct_6 D) H) = F) ) ) )  =>  ( ((k1_funct_1 F G) = (k1_funct_1 E H))  &  ( ((k9_xtuple_0 F) = A)  &  ( ((k9_xtuple_0 E) = B)  &  ((r1_tarski (k10_xtuple_0 F) C) & (r1_tarski (k10_xtuple_0 E) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k5_funct_7 (k11_finseq_1 B C D) A) = (k7_finseq_1 (k9_finseq_1 A) (k11_finseq_1 (k1_funct_1 B A) (k1_funct_1 C (k1_funct_1 B A)) (k1_funct_1 D (k1_funct_1 C (k1_funct_1 B A)))))) ) ) ) ) ) ) ) ).
tt(t56_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k1_funct_1 k1_funct_8 A) = 1) ) ) ) ).
tt(t56_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  =>  ((r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k1_fuzzy_1 (k2_zfmisc_1 A B) C D) (k4_fuzzy_2 A B)) => (r2_funct_2 (k2_zfmisc_1 A B) k1_numbers (k1_fuzzy_2 (k2_zfmisc_1 A B) C D) C)) ) ) ) ) ) ) ) ) ).
tt(t56_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k4_struct_0 (k7_fvaluat1 A B)) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t56_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B (k4_fvsum_1 A B D E) C) = (k4_fvsum_1 A B (k10_fvsum_1 A B D C) (k10_fvsum_1 A B E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) ) ) )  =>  (! [H:$i] :  ((m1_genealg1 H G) =>  (! [I:$i] :  ((m1_genealg1 I G) =>  ( ((k12_genealg1 G H I A B C D E F) = (k12_genealg1 G H I B A C D E F))  &  ( ((k12_genealg1 G H I A B C D E F) = (k12_genealg1 G H I C B A D E F))  &  ( ((k12_genealg1 G H I A B C D E F) = (k12_genealg1 G H I D B C A E F))  &  ( ((k12_genealg1 G H I A B C D E F) = (k12_genealg1 G H I E B C D A F))  &  ((k12_genealg1 G H I A B C D E F) = (k12_genealg1 G H I F B C D E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k22_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k22_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k22_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (u1_struct_0 (k22_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) C) k4_gfacirc1) (u1_struct_0 (k22_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t56_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k26_glib_000 A C)) <=>  ((r2_hidden B (k7_glib_000 A)) &  ((k1_funct_1 (k11_glib_000 A) B) = C) ) ) ) ) ) ) ) ).
tt(t56_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  ( ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  ((k3_finseq_1 (k20_glib_001 A B C D)) = (k6_xcmplx_0 (k2_nat_1 (k3_finseq_1 B) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t56_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v2_glib_003 A) & (v3_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k14_glib_003 A) = (k14_glib_003 (k12_glib_003 A B C))) ) ) ) ) ).
tt(t56_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid 1 1)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers k6_numbers)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid 1 k6_numbers)))))) ) ).
tt(t56_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) (k2_nat_1 A 1)))  &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k1_matrix_1 (k2_goboard2 C))) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 2) B)) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 2) B)) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 2) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 2) B)) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 2) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_graph_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_graph_2 B (k9_finseq_1 A)) = B) ) ) ) ).
tt(t56_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  (~  ( (~  ((k10_xtuple_0 B) = (u4_struct_0 A)) )  &  ( (~ (v1_xboole_0 B))  &  (~  ( (~ (v1_xboole_0 (a_2_0_graph_3 A B)))  & (m1_subset_1 (a_2_0_graph_3 A B) (k1_zfmisc_1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ).
tt(t56_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  (! [C:$i] :  ((m2_finseq_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ( ((v7_graph_1 D B) & (m2_graph_1 D B))  =>  ( ((r2_hidden C (k6_graph_5 B D)) & (r5_graph_5 B A))  => (r1_xxreal_0 (k10_graph_5 B C A) (k10_graph_5 B D A))) ) ) ) ) ) ) ) ) ).
tt(t56_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 D (k15_pre_poly A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_groeb_2 A (k3_termord A B C D) (k3_termord A B C E)) => (r1_rewrite1 (k3_polyred A B C (k1_groeb_3 A C D E)) (k3_groeb_2 A B C D E) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 B C) => (r1_tarski (k4_group_11 A B D) (k4_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t56_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  ( ((m1_group_2 A B) & (m1_group_2 B C))  => (m1_group_2 A C)) ) ) ) ) ) ) ).
tt(t56_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_group_3 A B C) = B) ) ) ) ) ) ) ) ).
tt(t56_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_group_2 A (k8_group_4 A B C) (k8_group_4 A C B))) ) ) ) ) ) ).
tt(t56_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( ((m1_group_2 B C) & (m1_group_2 D E))  => (r1_tarski (k5_group_5 A B D) (k5_group_5 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v2_funct_1 C) <=> (r1_group_2 B (k9_group_6 B A C) (k6_group_2 B))) ) ) ) ) ) ) ).
tt(t56_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_9 B A) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) ) )  => (r3_group_9 A B (k10_group_9 A B (k4_group_9 A B)))) ) ) ).
tt(t56_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k13_bilinear k1_complfld A A B) = (k14_bilinear k1_complfld A A (k3_hermitan A A B))) ) ) ) ) ).
tt(t56_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k29_sin_cos)) =>  ((r2_fdiff_1 k29_sin_cos A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 k29_sin_cos A) (k5_relset_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A))) ) ) ) ).
tt(t56_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  ((k9_ideal_1 A (k2_struct_0 A)) = (u1_struct_0 A)) ) ) ).
tt(t56_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_incsp_1 A)) =>  ( ((r4_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) D) & (r5_incsp_1 A (k7_domain_1 (u1_incsp_1 A) B C) E))  =>  ((r3_incsp_1 A D E) |  (B = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B 1))  & (r1_xxreal_0 A (k5_int_1 A B))) ) ) ) ) ) ) ).
tt(t56_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~  ((k7_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ( (~  ((k9_real_1 1 (k1_seq_1 k16_sin_cos D)) = k6_numbers) )  &  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 k16_sin_cos D) (k9_real_1 (k1_seq_1 k16_sin_cos D) 1))) ) ) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k29_sin_cos) k1_fdiff_9) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t56_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k47_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k1_sin_cos9 (k1_taylor_1 2)) (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)))))) &  ((r1_tarski D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k1_sin_cos9))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k1_sin_cos9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k1_sin_cos9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t56_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k16_sin_cos D)) (k1_seq_1 k19_sin_cos D))) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t56_integr19,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m2_subset_1 D k1_numbers k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 D))))))  =>  (~  ((r1_xxreal_0 A B) &  ((r1_integr18 (k4_real_ns1 D) (k3_integra5 A B) E) &  ((v1_integr19 (k2_partfun1 k1_numbers (u1_struct_0 (k4_real_ns1 D)) E (k3_integra5 A B)) (k4_real_ns1 D) k1_numbers) &  ((r1_tarski (k3_integra5 A B) (k1_relset_1 k1_numbers E)) &  ((r2_hidden C (k2_rcomp_1 A B)) &  ((r1_nfcont_3 (k4_real_ns1 D) E C) &  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k4_real_ns1 D))))))  =>  (~  ((r1_tarski (k2_rcomp_1 A B) (k1_relset_1 k1_numbers F)) &  ( (! [G:$i] :  ((v1_xreal_0 G) =>  ((r2_hidden G (k2_rcomp_1 A B)) =>  ((k1_funct_1 F G) = (k6_integr18 (k4_real_ns1 D) E A G)) ) ) )  &  ((r1_ndiff_3 (k4_real_ns1 D) F C) &  ((k1_ndiff_3 (k4_real_ns1 D) F C) = (k7_partfun1 (u1_struct_0 (k4_real_ns1 D)) E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v2_seq_2 (k2_partfun1 A k1_numbers C A)) & (v2_seq_2 (k2_partfun1 A k1_numbers D A)))  => (r1_xxreal_0 (k7_real_1 (k7_integra1 A C B) (k7_integra1 A D B)) (k7_integra1 A (k3_valued_1 A k1_numbers k1_numbers C D) B))) ) ) ) ) ) ) ) ) ).
tt(t56_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers 1))  =>  ((k2_integra5 A k1_sin_cos2) = (k10_real_1 (k5_square_1 (k9_real_1 k8_power 1)) (k8_real_1 2 k8_power))) ) ) ) ).
tt(t56_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v3_rcomp_1 F) & (m1_subset_1 F (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B F) &  ((r2_relset_1 k1_numbers k1_numbers C (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1)) &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ( ((k1_seq_1 D G) = (k9_real_1 G A))  &  (~ (r1_xxreal_0 (k1_seq_1 D G) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)))) = F)  &  ( (F = (k1_relset_1 k1_numbers E))  &  ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((r2_hidden G F) =>  ((k1_seq_1 E G) = (k10_real_1 (k7_real_1 G A) (k9_real_1 G A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers E B))) ) ) ) ) )  =>  ((k2_integra5 B E) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A))) (k4_seq_4 B)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers F) (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k14_interva1 A (k16_interva1 A B C)) = (k4_subset_1 (u1_struct_0 A) (k14_interva1 A B) (k14_interva1 A C))) ) ) ) ) ) ) ).
tt(t56_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 A B) (k5_intpro_1 B A)) k8_intpro_1)) ) ) ) ).
tt(t56_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  &  ( (C = a_0_2_jgraph_4)  &  (B = (a_1_4_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (C = a_0_6_jgraph_5)  &  ((r2_hidden A C) &  ((r2_hidden B C) &  ((r1_xxreal_0 (k18_euclid A) k6_numbers) &  ((r1_xxreal_0 (k18_euclid B) k6_numbers) & (r1_xxreal_0 (k17_euclid B) (k17_euclid A))) ) ) ) )  =>  ( (B = (k18_pscomp_1 C))  | (r1_jordan6 C A B)) ) ) ) ) ) ) ) ).
tt(t56_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=> (r1_xxreal_0 (k17_euclid E) (k17_euclid F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) = B) )  =>  ((r1_xxreal_0 B A) |  ((k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) = 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k3_finseq_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) D 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k3_topreal1 2 (k2_jordan1e A B)) = (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A B)))) ) ) ) ) ) ).
tt(t56_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1))) ) ) )  =>  ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski D (k2_nat_1 E 2)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_jordan1j,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) & (r2_hidden B (k10_xtuple_0 A)))  =>  ( (B = (k1_funct_1 A 1))  |  ((k2_nat_1 (k1_jordan3 A B) 1) = (k4_finseq_4 A B)) ) ) ) ) ) ) ).
tt(t56_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 1)))) =>  ( (B = (a_1_1_jordan2c A))  => (v1_convex1 B (k15_euclid 1))) ) ) ) ) ).
tt(t56_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r2_hidden B A))  => (r1_jordan6 A B B)) ) ) ) ) ).
tt(t56_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C D))  =>  ((k7_pscomp_1 (k2_jgraph_6 A B C D)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t56_kurato_1,ax, (! [A:$i] :  ((v1_setfam_1 A) =>  (! [B:$i] :  ((r1_tarski B A) => (v1_setfam_1 B)) ) ) ) ).
tt(t56_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  => (r3_binop_1 (u1_struct_0 A) (k6_lattices A) (u1_lattices A))) ) ).
tt(t56_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v2_lexbfs (k26_lexbfs A))) ) ).
tt(t56_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_limfunc1 A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers B (k10_prob_1 C)))) ) )  | (v7_limfunc1 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t56_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((k8_relset_1 k1_numbers k1_numbers B (k1_tarski k6_numbers)) = k1_xboole_0) )  =>  ( ((k2_limfunc2 B A) = k6_numbers)  |  ((r4_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k2_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k2_limfunc2 B A))) ) ) ) ) ) ) ) ).
tt(t56_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v8_limfunc1 A) &  ((v6_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ((v6_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k5_limfunc1 B)) ) ) ) ) ) ) ).
tt(t56_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  => (r2_hidden (k8_lpspace1 A k6_numbers) (k9_lpspace1 A B C))) ) ) ) ) ) ).
tt(t56_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 C A) => (r8_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 B)) A)) ) ) ) ) ) ) ).
tt(t56_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B (k6_cqc_lang A C)) A) => (v2_cqc_the1 (k8_cqc_lang A C (k6_cqc_lang A B)) A)) ) ) ) ) ) ) ).
tt(t56_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = k1_xboole_0)  =>  ((k6_mathmorp k6_numbers A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t56_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) (k4_matrix10 A D E)) => (r2_matrix10 (k4_matrix10 A B D) (k4_matrix10 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden F (k2_finseq_1 A)) &  (! [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) =>  (~  ( ((k3_finseq_1 G) = A)  &  ( ((k12_matrix_3 A B (k3_matrix11 F A A (u1_struct_0 B) E (k8_matrix_1 (u1_struct_0 B) (k4_matrix_6 A B C D) F))) = (k1_finsop_1 (u1_struct_0 B) G (u1_algstr_0 B)))  &  (! [H:$i] :  ((v7_ordinal1 H) =>  ((r2_hidden H (k2_finseq_1 A)) =>  ((k1_funct_1 G H) = (k8_group_1 B (k3_matrix_1 (u1_struct_0 B) C F H) (k12_matrix_3 A B (k3_matrix11 F A A (u1_struct_0 B) E (k8_matrix_1 (u1_struct_0 B) D H))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (! [G:$i] :  ( ((v1_finset_1 G) &  ((v1_setfam_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers))) )  =>  (! [H:$i] :  ( ((v1_finset_1 H) &  ((v1_setfam_1 H) & (m1_subset_1 H (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski C D) &  ((r1_tarski E F) &  ( (G = (k8_relat_1 (k5_matrix13 D) C))  &  (H = (k8_relat_1 (k5_matrix13 F) E)) ) ) )  =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 (k5_matrix13 G)) (k10_xtuple_0 (k5_matrix13 H))) (k2_matrix_1 (k6_matrix13 A B D F))) &  ((k6_matrix13 A (k6_matrix13 A B D F) G H) = (k6_matrix13 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((k4_matrix_6 A B C D) = (k12_matrix_1 B A))  =>  ((v1_matrix_6 C A B) & (v1_matrix_6 D A B)) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  ((k4_matrix15 B (k1_matrix_3 B A k1_xboole_0) (k1_matrix_3 B A k1_xboole_0)) = (k3_matrix13 k1_xboole_0)) ) ) ) ) ).
tt(t56_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v5_matrix16 C B) & (v5_matrix16 D B))  => (v5_matrix16 (k3_matrix_6 A B C D) B)) ) ) ) ) ) ) ) ) ).
tt(t56_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k11_fvsum_1 A (k3_fvsum_1 A B C) D) = (k3_fvsum_1 A (k11_fvsum_1 A B D) (k11_fvsum_1 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((v1_matrix_6 C A B) &  ((v1_matrix_6 D A B) & (v1_matrix_6 E A B)) )  =>  ((v1_matrix_6 (k4_matrix_6 A B (k4_matrix_6 A B C D) E) A B) &  ((k5_matrix_6 A B (k4_matrix_6 A B (k4_matrix_6 A B C D) E)) = (k4_matrix_6 A B (k4_matrix_6 A B (k5_matrix_6 A B E) (k5_matrix_6 A B D)) (k5_matrix_6 A B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k1_matrix_6 A B C)) = (k4_algstr_0 B (k1_matrix_8 A B C))) ) ) ) ) ) ) ).
tt(t56_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( (? [F:$i] :  ((m1_subset_1 F k5_numbers) &  ((r2_hidden F (k2_finseq_1 A)) &  ( (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ((k1_funct_1 (k9_matrix_1 (u1_struct_0 B) D F) G) = (k8_group_1 B C (k7_partfun1 (u1_struct_0 B) (k9_matrix_1 (u1_struct_0 B) E F) G))) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ( (G = F)  |  ((k9_matrix_1 (u1_struct_0 B) D G) = (k9_matrix_1 (u1_struct_0 B) E G)) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  (? [G:$i] :  ((m1_subset_1 G k5_numbers) &  ((r2_hidden G (k2_finseq_1 A)) &  ((k7_partfun1 (u1_struct_0 B) (k10_matrix_3 A B D F) G) = (k8_group_1 B C (k7_partfun1 (u1_struct_0 B) (k10_matrix_3 A B E F) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_matrixc1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  ( (~ (r1_xxreal_0 (k1_matrix_1 A) k6_numbers))  =>  ((k1_matrixc1 (k4_matrix_1 k2_numbers A)) = (k4_matrix_1 k2_numbers (k1_matrixc1 A))) ) ) ) ).
tt(t56_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ( ((k10_matrixj1 (u1_struct_0 A) (k23_matrixj1 A B)) = B)  &  ((k11_matrixj1 (u1_struct_0 A) (k23_matrixj1 A B)) = B) ) ) ) ) ) ).
tt(t56_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 B)))  =>  ((k9_matrix_1 k1_numbers (k7_matrixr1 A B) C) = (k11_rvsum_1 (k3_finseq_1 B) (k9_matrix_1 k1_numbers B C) A)) ) ) ) ) ) ) ) ).
tt(t56_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  ((k6_matrixr1 (k10_matrixr1 A) B) = (k10_matrixr1 (k12_matrixr1 B A))) ) ) ) ) ) ).
tt(t56_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v4_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  ( (~ (v3_relat_1 (k4_matrix_1 k1_numbers A)))  &  ((v1_matrix_1 (k4_matrix_1 k1_numbers A)) &  ((v4_matrprob (k4_matrix_1 k1_numbers A)) & (m2_finseq_1 (k4_matrix_1 k1_numbers A) (k3_finseq_2 k1_numbers))) ) ) ) ) ).
tt(t56_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  (E = (k6_xtuple_0 (k4_mcart_1 A B C D E) (k5_mcart_1 A B C D E) (k6_mcart_1 A B C D E) (k7_mcart_1 A B C D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k1_numbers))) =>  ((v2_measure6 A) => (v2_rcomp_1 (k6_setfam_1 k1_numbers A))) ) ) ).
tt(t56_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  (! [D:$i] :  ((v2_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k10_member_1 A C) (k10_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t56_memstr_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_setfam_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_memstr_0 C B) &  ((v3_memstr_0 C B) & (l1_memstr_0 C B)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 C)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 B C))) ) )  =>  ((r2_hidden (k4_struct_0 C) (k9_xtuple_0 D)) =>  ((k9_memstr_0 B C D A) = (k1_funct_4 (k6_memstr_0 B C D) (k7_memstr_0 B C (k2_nat_1 (k5_memstr_0 B C D) A)))) ) ) ) ) ) ) ) ) ) ).
tt(t56_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k8_nat_1 k7_numbers A B) (k8_supinf_2 (k17_supinf_2 A)))) ) ) ) ).
tt(t56_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v6_supinf_2 B) & (v6_supinf_2 C))  => (v6_supinf_2 (k3_valued_1 A k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t56_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  ((v3_rlvect_1 (k15_midsp_1 A)) &  ((v4_rlvect_1 (k15_midsp_1 A)) &  ((v13_algstr_0 (k15_midsp_1 A)) & (v2_rlvect_1 (k15_midsp_1 A))) ) ) ) ) ).
tt(t56_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  => (r1_xxreal_0 (k25_mmlquery A) (k3_finseq_1 A))) ) ).
tt(t56_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k42_modelc_2 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  ( ((k1_lattices (k42_modelc_2 A B) C D) = (k3_robbins1 (k42_modelc_2 A B) (k2_lattices (k42_modelc_2 A B) (k3_robbins1 (k42_modelc_2 A B) C) (k3_robbins1 (k42_modelc_2 A B) D))))  &  ((k24_modelc_2 (k42_modelc_2 A B) C D) = (k3_robbins1 (k42_modelc_2 A B) (k23_modelc_2 (k42_modelc_2 A B) (k3_robbins1 (k42_modelc_2 A B) C) (k3_robbins1 (k42_modelc_2 A B) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t56_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  ( (~ (v3_modelc_3 B A))  =>  ( (~  ((u2_modelc_3 A B) = k1_xboole_0) )  & (r2_hidden (u2_modelc_3 A B) (k1_orders_1 (k1_modelc_3 A)))) ) ) ) ) ) ).
tt(t56_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_nat_d A B) <=> (r1_nat_d A (k6_moebius1 B))) ) ) ) ) ).
tt(t56_monoid_0,ax, (k8_monoid_0 = (g4_algstr_0 k5_numbers k48_binop_2 1)) ).
tt(t56_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  ((k5_struct_0 (k23_monoid_1 A)) = (k6_domain_1 (u1_struct_0 A) (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)))) ) ) ).
tt(t56_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 2)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  (~  (B = (k1_nat_1 A 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( (~  ((k11_nat_3 B A) = k6_numbers) )  =>  ((k1_seq_1 (k13_nat_3 B) A) = (k1_newton A (k11_nat_3 B A))) ) ) ) ) ) ).
tt(t56_nat_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 B (k4_nat_1 2 A))) ) ) ) ) ) ) ) ).
tt(t56_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k7_nat_d C A) (k7_nat_d B A))) ) ) ) ) ) ) ) ) ).
tt(t56_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r7_ncfcont1 A B E C) & (r1_tarski D C))  => (r7_ncfcont1 A B E D)) ) ) ) ) ) ) ) ) ).
tt(t56_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k14_prvect_2 A))) =>  ( ((v3_nfcont_1 D (k14_prvect_2 A)) &  ((r2_hidden E D) &  (! [F:$i] :  ((r2_hidden F (k4_finseq_1 A)) =>  ((r2_ndiff_5 A B F C D) & (r3_nfcont_1 (k14_prvect_2 A) (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A F)) B) (k7_ndiff_5 A B F C D) D)) ) ) ) )  =>  ((r1_ndiff_1 (k14_prvect_2 A) B C E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k14_prvect_2 A))) =>  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) &  ( ((k4_finseq_1 G) = (k4_finseq_1 A))  &  ( (! [H:$i] :  ((r2_hidden H (k4_finseq_1 A)) =>  ((k1_funct_1 G H) = (k17_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A H)) B (k6_ndiff_5 A B H C E) (k3_funct_2 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 (k11_prvect_2 A (k5_ndiff_5 A H))) (k3_ndiff_5 A (k5_ndiff_5 A H)) F))) ) )  &  ((k17_lopban_1 (k14_prvect_2 A) B (k3_ndiff_1 (k14_prvect_2 A) B C E) F) = (k4_rlvect_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_nat_d A B) => (r1_nat_d (k6_nat_d A C) (k6_nat_d B C))) ) ) ) ) ) ) ).
tt(t56_normform,ax, (! [A:$i] : (m1_subset_1 k1_xboole_0 (u1_struct_0 (k12_normform A)))) ).
tt(t56_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) => (m2_cat_1 (k11_oppcat_1 A B C) A (k2_oppcat_1 B))) ) ) ) ) ) ).
tt(t56_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((r6_orders_1 A B) & (v6_relat_2 A))  => (r8_orders_1 A B)) ) ) ) ).
tt(t56_orders_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (~  ( (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D B) => (r3_orders_2 A C D)) ) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) & (r2_orders_2 A C B)) ) ) ) ) ) ) ) ).
tt(t56_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ( ((k5_ordinal3 A k1_xboole_0) = A)  &  ((k5_ordinal3 k1_xboole_0 A) = k1_xboole_0) ) ) ) ).
tt(t56_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_finset_1 A) & (v1_ordinal2 A)) ) ) )  => (r1_ordinal1 (k1_funct_1 A k6_numbers) (k4_ordinal5 A))) ) ).
tt(t56_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v3_ordinal6 B)) ) )  =>  ( ((r2_hidden (k9_xtuple_0 B) A) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C (k9_xtuple_0 B)) =>  ((v1_funct_1 (k1_funct_1 B C)) &  ((v1_funct_2 (k1_funct_1 B C) (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 (k1_funct_1 B C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ) )  =>  ( ((k9_xtuple_0 B) = k1_xboole_0)  |  ((v1_funct_1 (k8_ordinal6 B)) &  ((v1_funct_2 (k8_ordinal6 B) (k2_ordinal1 A) (k2_ordinal1 A)) & (m1_subset_1 (k8_ordinal6 B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 A) (k2_ordinal1 A))))) ) ) ) ) ) ) ) ).
tt(t56_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t56_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r3_parsp_2 A B C D E) & (r3_parsp_2 A B C F G))  => (r3_parsp_2 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) => (r1_partfun1 A B)) ) ) ) ) ).
tt(t56_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((r2_hidden D (k8_relset_1 A B E C)) <=>  ((r2_hidden (k4_tarski D (k7_partfun1 B E D)) E) & (r2_hidden (k7_partfun1 B E D) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r2_pboole A (k4_pboole A B C) B)) ) ) ) ) ).
tt(t56_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r5_pdiff_5 B A) & (r5_pdiff_5 C A))  =>  ((r3_pdiff_1 3 2 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 2 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k9_real_1 (k5_pdiff_5 B A) (k5_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t56_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ( ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A C) D) &  ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r2_pdiff_9 B A C)) )  =>  ((r1_pdiff_6 B 1 A D) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B C) E) = (k3_relat_1 (k7_partfun1 (k9_funct_2 (k1_euclid A) (k1_euclid 1)) (k1_pdiff_9 A 1 B D) E) (k1_pdiff_1 1 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((v1_int_2 A) &  ( (~ (r1_xxreal_0 A 2))  &  ((r1_nat_d A (k4_pepin B)) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  (A = (k2_nat_1 (k4_nat_1 C (k13_newton 2 (k1_nat_1 B 1))) 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k1_funct_1 (k14_finseq_1 (k9_xtuple_0 (k12_pnproc_1 C B))) A) = (k2_nat_1 B A)) ) ) ) ) ) ) ) ).
tt(t56_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k2_struct_0 (k17_polyform A (k4_xcmplx_0 1))) = (k2_tarski k1_xboole_0 (k1_tarski k1_xboole_0))) ) ) ).
tt(t56_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  ((k3_funct_2 k5_numbers (u1_struct_0 A) (k7_polynom5 A B) (k7_nat_d (k1_algseq_1 A B) 1)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t56_polyred,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r11_polyred A B C D) & (r11_polyred A B E F))  => (r11_polyred A B (k8_group_1 A C E) (k8_group_1 A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~  (B = 1) )  &  ( (~ (r1_xxreal_0 C k6_numbers))  &  (~  ((k5_power A C) = (k3_xcmplx_0 (k5_power A B) (k5_power B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r6_pboole A (k12_pre_poly A B B) (k16_pre_poly A))) ) ) ).
tt(t56_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k6_prepower (k3_xcmplx_0 A B) C) = (k3_xcmplx_0 (k6_prepower A C) (k6_prepower B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_3 C A B) =>  (? [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 D E) = (k8_prob_3 A B C E)) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r2_hidden E (k1_relset_1 k5_numbers C)))  =>  ((k1_funct_1 D E) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A D E) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A (k7_cqc_lang A B D) (k7_cqc_lang A C E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k17_pscomp_1 A) (k1_rltopsp1 (k15_euclid 2) (k25_pscomp_1 A) (k24_pscomp_1 A)))) ) ).
tt(t56_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (~  ( (~ (r6_pboole A B (k1_pboole A)))  &  ( (~ (r6_pboole A B (k1_pzfmisc1 A C)))  &  ( (~ (r6_pboole A B (k1_pzfmisc1 A D)))  &  (~ (r6_pboole A B (k2_pzfmisc1 A C D))) ) ) ) )  => (r6_pboole A (k4_pboole A B (k2_pzfmisc1 A C D)) (k1_pboole A))) ) ) ) ) ) ) ) ).
tt(t56_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( ((r3_qc_lang2 A B C) & (r3_qc_lang2 A C D))  => (r3_qc_lang2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t56_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k5_qc_lang3 A (k1_qc_lang2 A)) = k1_xboole_0) ) ) ).
tt(t56_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k28_quaterni (k18_quatern2 A B)) = (k18_quatern2 A (k28_quaterni B))) ) ) ) ) ).
tt(t56_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k26_quaterni A B) (k29_quaterni C D)) = (k29_quaterni (k29_quaterni (k26_quaterni (k27_quaterni A C) (k27_quaterni B C)) (k27_quaterni A D)) (k27_quaterni B D))) ) ) ) ) ) ) ) ) ).
tt(t56_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k31_quaterni (k29_quaterni A B)) = (k29_quaterni (k31_quaterni A) (k31_quaterni B))) ) ) ) ) ).
tt(t56_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v1_quofield (k22_quofield A) A (k19_quofield A))) ) ).
tt(t56_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  =>  ((k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D 1)) = A) ) ) ) ) ) ) ) ) ) ).
tt(t56_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k1_seq_1 (k4_real_3 B) C) A)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 C 1)) (k2_newton (k10_real_1 (k3_real_1 A (k7_square_1 (k3_real_1 (k3_square_1 A) 4))) 2) (k1_nat_1 C 1)))) ) ) ) ) ) ) ).
tt(t56_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) =>  (! [D:$i] :  ((v1_relat_1 D) =>  ( ((r1_tarski (k10_xtuple_0 B) A) &  ( ((k3_relat_1 B C) = (k4_relat_1 (k9_xtuple_0 D)))  &  ((k3_relat_1 C D) = (k4_relat_1 A)) ) )  =>  (D = B) ) ) ) ) ) ) ) ) ).
tt(t56_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A))) =>  ((k7_relset_1 A B (k3_relset_1 B A C) A) = (k7_relset_1 B B (k7_relset_2 B A B C (k3_relset_1 B A C)) B)) ) ) ) ) ).
tt(t56_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v8_rewrite1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v8_rewrite1 B))  =>  ((r11_rewrite1 A B) => (v8_rewrite1 (k2_xboole_0 A B))) ) ) ) ) ).
tt(t56_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r4_rewrite2 A B C E) &  ((r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) B D) & (r1_relset_1 (k8_afinsq_1 A) (k8_afinsq_1 A) D C)) )  =>  ((r4_rewrite2 A B D E) & (r4_rewrite2 A D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (! [H:$i] :  ((m1_rewrite1 H (k1_rewrite3 C F G)) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  (~  ((r2_hidden I (k4_finseq_1 H)) &  ((r2_hidden (k2_xcmplx_0 I 1) (k4_finseq_1 H)) &  ( ((k1_funct_1 H I) = (k4_tarski A D))  &  ( ((k1_funct_1 H (k2_xcmplx_0 I 1)) = (k4_tarski B E))  &  (! [J:$i] :  ((m1_subset_1 J (k8_afinsq_1 C)) =>  (~  ((r1_rewrite3 F G A J B) &  (D = (k1_flang_1 C J E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_partfun1 C A) & (v1_partfun1 D A))  =>  ( ((k1_funct_1 (k3_valued_1 A k1_numbers k1_numbers C D) B) = (k2_xcmplx_0 (k1_funct_1 C B) (k1_funct_1 D B)))  &  ( ((k1_funct_1 (k47_valued_1 A k1_numbers k1_numbers C D) B) = (k6_xcmplx_0 (k1_funct_1 C B) (k1_funct_1 D B)))  &  ((k1_funct_1 (k20_valued_1 A k1_numbers k1_numbers C D) B) = (k3_xcmplx_0 (k1_funct_1 C B) (k1_funct_1 D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((r2_rfunct_3 A B) <=> (r2_rfunct_3 (k26_valued_1 k1_numbers k1_numbers A C) B)) ) ) ) ) ) ) ).
tt(t56_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  ((v1_comseq_2 (k4_rinfsup1 A)) & (v1_comseq_2 (k3_rinfsup1 A))) ) ) ) ).
tt(t56_rlaffin1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k4_rlaffin1 B (k1_convex1 B C A)) = (k1_convex1 B (k4_rlaffin1 B C) A)) ) ) ) ) ) ) ).
tt(t56_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_rlsub_1 E A) =>  ( ((r2_hidden B (k3_rlsub_1 A C E)) & (r2_hidden B (k3_rlsub_1 A D E)))  =>  ((k3_rlsub_1 A C E) = (k3_rlsub_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v14_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ).
tt(t56_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (? [C:$i] :  ( ((v3_pre_topc C A) & (m1_connsp_2 C A (k4_struct_0 A)))  &  ((v2_rltopsp1 C A) & (r1_tarski (k7_rusub_4 A C C) B)) ) ) ) ) ) ) ).
tt(t56_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  (! [D:$i] :  ((m1_rlvect_2 D A) =>  ( ((m2_rlvect_2 C A B) & (m2_rlvect_2 D A B))  => (m2_rlvect_2 (k10_rlvect_2 A C D) A B)) ) ) ) ) ) ) ) ) ).
tt(t56_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((r1_struct_0 D C) => (r2_hidden (k4_algstr_0 B C) (k3_rmod_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t56_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  (! [E:$i] :  ((m1_rmod_4 E A B) =>  ( ((m2_rmod_4 D A B C) & (m2_rmod_4 E A B C))  => (m2_rmod_4 (k9_rmod_4 A B D E) A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ((v9_robbins1 A) => (v6_robbins1 A)) ) ) ).
tt(t56_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A B (k5_robbins1 A C D)) = (k5_robbins1 A C (k5_robbins1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t56_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_roughs_1 A B) = (a_2_2_roughs_1 A B)) ) ) ) ) ).
tt(t56_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r1_rpr_1 A B C) => (r1_rpr_1 A (k3_subset_1 A B) C)) ) ) ) ) ) ) ).
tt(t56_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden (k5_algstr_0 A D C) (k3_rusub_1 A D B)) <=> (r1_struct_0 B C)) ) ) ) ) ) ) ) ) ).
tt(t56_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (v14_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ).
tt(t56_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k12_rvsum_1 (k2_finseq_2 A B)) = (k2_finseq_2 A (k3_square_1 B))) ) ) ) ) ).
tt(t56_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = (k4_struct_0 k1_scmfsa_2)) ) ) ) ).
tt(t56_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r4_scmfsa7b (k4_compos_1 k1_scmfsa_2) A)) ) ) ).
tt(t56_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  ( ((r1_tarski (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) B) & (r1_tarski C A))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 A B)) &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) B D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((r1_xxreal_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) k6_numbers) =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k8_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k17_scmpds_2 A C)) )  &  ( ( (~ (r1_xxreal_0 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B)) k6_numbers))  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k8_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A))) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k8_scmpds_2 D B C) A) E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k6_scmpds_6 A B C))) & (r2_hidden 1 (k9_xtuple_0 (k6_scmpds_6 A B C)))) ) ) ) ) ) ) ).
tt(t56_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k2_tarski B C) A) =>  ((v4_scmyciel (k7_scmyciel A (k2_tarski B C))) &  ((v5_scmyciel (k7_scmyciel A (k2_tarski B C))) & (m1_subset_1 (k7_scmyciel A (k2_tarski B C)) (k1_zfmisc_1 A))) ) ) ) ) ) ) ).
tt(t56_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_semi_af1 A B C C B) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t56_seq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers (k26_valued_1 k5_numbers k1_numbers B A)) (k26_valued_1 k5_numbers k1_numbers (k56_valued_1 k5_numbers k1_numbers B) (k18_complex1 A)))) ) ) ) ).
tt(t56_seq_4,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (r7_binop_1 k2_numbers (k7_seq_4 A) k27_binop_2)) ) ).
tt(t56_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k2_xcmplx_0 1 (k13_complex1 1 (k2_nat_1 (k4_nat_1 2 B) 1))))  &  ((k1_seq_1 A k6_numbers) = 1) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_seq_1 (k1_series_3 A) B) (k3_xcmplx_0 (k13_complex1 1 2) (k7_square_1 (k2_nat_1 (k4_nat_1 2 B) 3))))) ) ) ) ) ) ) ).
tt(t56_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k4_kurato_0 A B) = (k4_kurato_0 A (k4_setlim_1 A B))) ) ) ) ).
tt(t56_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k6_setlim_2 B D C)) A) = (k4_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A))) ) ) ) ) ) ) ) ).
tt(t56_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ( ((r2_hidden B (k3_funct_2 A (k5_finsub_1 A) (k11_setwiseo A) D)) & (r2_hidden C (k3_funct_2 A (k5_finsub_1 A) (k11_setwiseo A) D)))  =>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t56_sf_mastr,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 k3_scmfsa_2)))  =>  ( ((k3_scmfsa_m C) = (k5_scmfsa_2 A))  =>  ((r2_hidden (k5_scmfsa_2 B) C) | (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ).
tt(t56_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A D (k5_sheffer1 A E (k5_sheffer1 A C B)))))) = (k5_sheffer1 A B (k5_sheffer1 A C C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_simplex0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_simplex0 D A) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ((r1_tarski B C) => (m2_simplex0 (k10_simplex0 A D (k6_relat_1 B E)) A (k10_simplex0 A D (k6_relat_1 C E)))) ) ) ) ) ) ) ) ).
tt(t56_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k4_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 1 (k7_square_1 2)))) ).
tt(t56_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) = (k6_binop_2 (k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 A)) 1) 2)) ) ) ).
tt(t56_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v5_valued_0 (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t56_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  &  ( (~ (r1_xxreal_0 1 (k3_square_1 B)))  &  (~  ((k9_binop_2 (k4_sin_cos7 A) (k4_sin_cos7 B)) = (k4_sin_cos7 (k12_binop_2 (k9_binop_2 A B) (k9_binop_2 1 (k11_binop_2 A B))))) ) ) ) ) ) ) ) ) ).
tt(t56_sin_cos9,ax, ((k2_relset_1 k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_sin_cos9 (k1_rcomp_1 (k1_real_1 1) 1))) = (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))) ).
tt(t56_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) => (v2_comseq_3 (k27_sin_cos A))) ) ).
tt(t56_sppol_2,ax, (k1_topreal1 = (k1_sppol_2 k6_numbers 1 k6_numbers 1)) ).
tt(t56_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_euclid A) (k18_euclid B)) =>  ((k7_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k18_euclid B)) ) ) ) ) ) ).
tt(t56_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) ) ).
tt(t56_sprect_3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r1_sprect_2 A B) &  ((r1_sprect_2 A (k4_matrix_2 (u1_struct_0 (k15_euclid 2)) C)) &  ((v4_topreal1 B) & (r2_hidden C (k3_topreal1 2 B))) ) )  => (r1_sprect_2 A (k2_jordan3 B C))) ) ) ) ) ) ) ).
tt(t56_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t56_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 1) A) &  ((r1_xxreal_0 A 1) &  ((r1_xxreal_0 (k4_xcmplx_0 1) B) & (r1_xxreal_0 B 1)) ) )  => (r1_xxreal_0 (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))) (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B))))) ) ) ) ) ).
tt(t56_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (~  ((v1_finset_1 A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (? [C:$i] :  ((v7_ordinal1 C) &  ((r2_hidden C A) &  (~ (r1_xxreal_0 C B)) ) ) ) ) ) ) ) ) ) ).
tt(t56_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [F:$i] :  ((m2_subset_1 F (k16_substut1 A) (k38_substut1 A)) =>  (! [G:$i] :  ((m1_substut1 G A (k7_sublemma A F B)) =>  ((v3_substut1 (k7_sublemma A F B) A) =>  ( (! [H:$i] :  ((m1_subset_1 H C) => (r1_sublemma A F C (k1_sublemma A C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H)) (k14_sublemma A C (k13_sublemma A F B G C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H))) (k12_sublemma A C B H))) D)) )  <=>  (! [H:$i] :  ((m1_subset_1 H C) => (r1_sublemma A F C (k1_sublemma A C (k1_sublemma A C E (k12_sublemma A C (k35_substut1 A (k32_substut1 A (k9_sublemma A (k7_sublemma A F B) G))) H)) (k14_sublemma A C (k13_sublemma A F B G C E) (k12_sublemma A C B H))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) => (r1_tarski (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)))) (k6_setfam_1 (u1_struct_0 A) (k1_tdlat_2 A (k1_pcomps_1 A (k1_tdlat_2 A B)))))) ) ) ) ).
tt(t56_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_2 B A) => (v1_tops_1 B A)) ) ) ) ) ).
tt(t56_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_pre_topc B A) =>  (~ (v4_tex_3 B A)) ) )  => (v3_tdlat_3 A)) ) ) ).
tt(t56_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) =>  ((k3_tex_4 A B) = B) ) ) ) ) ) ).
tt(t56_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D E) (u1_struct_0 C)) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D E) = (k8_relset_1 (u1_struct_0 C) (u1_struct_0 B) (k2_tmap_1 A B D C) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_borsuk_2 D A B C) => (v3_funct_2 (k6_topalg_1 A B C D) (u1_struct_0 (k5_topalg_1 A C)) (u1_struct_0 (k5_topalg_1 A B)))) ) ) ) ) ) ) ) ).
tt(t56_topgen_1,ax, (? [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) &  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) &  ((v2_tops_1 A k3_topmetr) &  ((v2_tops_1 B k3_topmetr) &  (~ (v2_tops_1 (k4_subset_1 (u1_struct_0 k3_topmetr) A B) k3_topmetr)) ) ) ) ) ) ) ).
tt(t56_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_card_3 B) =>  ((k4_topgen_4 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t56_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((v4_pre_topc (k2_limfunc1 A) k2_topgen_3) & (m1_subset_1 (k2_limfunc1 A) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ).
tt(t56_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (v1_tops_1 (k1_group_2 A B) A)) ) ) ) ).
tt(t56_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k10_metric_1 A B k6_numbers) = (k1_tarski B)) ) ) ) ) ).
tt(t56_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k3_topreal9 2 (k4_struct_0 (k15_euclid 2)) A)) =>  ((k7_real_1 (k5_square_1 (k17_euclid B)) (k5_square_1 (k18_euclid B))) = (k3_square_1 A)) ) ) ) ) ) ).
tt(t56_toprealc,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 (k15_euclid B)) (u1_struct_0 (k15_euclid B)) (u1_struct_0 k3_topmetr) (k15_toprealc B (u1_struct_0 A) (u1_struct_0 k3_topmetr) C) (k17_toprealc B B)))) ) ) ) ) ) ).
tt(t56_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_tops_1 B A) & (v4_pre_topc B A))  => (v3_tops_1 B A)) ) ) ) ) ).
tt(t56_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) => (v3_tops_2 (k2_tops_2 (u1_struct_0 A) (u1_struct_0 B) C) B A)) ) ) ) ) ) ) ).
tt(t56_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_tarski C D) => (r1_tarski (k1_tops_1 A C) (k1_tops_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t56_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo E A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E B) = B)  & (r1_diraf A C B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E C))) )  =>  ( (C = B)  | (r1_diraf A D B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_trees_1,ax,(r2_tarski k5_numbers k8_trees_1)).
tt(t56_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  =>  ((k11_trees_3 (k7_finseq_1 A (k9_finseq_1 (k2_trees_1 k6_numbers)))) = (k2_xboole_0 (k11_trees_3 A) (k2_trees_1 (k2_nat_1 (k3_finseq_1 A) 1)))) ) ) ).
tt(t56_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  =>  ((r2_tsep_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((r1_tarski D B) &  ((r1_tarski E C) &  ((r1_tarski F (k9_subset_1 (u1_struct_0 A) B C)) &  ((v4_pre_topc D A) &  ((v4_pre_topc E A) & (v3_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 k1_complfld)) =>  ( ( (E = D)  &  ( (B = (k2_polynom4 k1_complfld (k5_uniroots A) E))  &  (C = (k2_polynom4 k1_complfld (k4_uniroots A k1_complfld) E)) ) )  => (r1_int_1 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) &  ((v1_uproots C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k8_uproots A (k13_polynom3 A B C)) = (k11_pre_poly (u1_struct_0 A) (k8_uproots A B) (k8_uproots A C))) ) ) ) ) ) ) ).
tt(t56_valued_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  ((r2_hidden B (k9_xtuple_0 (k47_valued_2 C E D))) =>  ((k1_funct_1 (k47_valued_2 C E D) B) = (k24_valued_1 (k1_funct_1 E B) (k5_xcmplx_0 D))) ) ) ) ) ) ) ) ) ) ).
tt(t56_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_vectsp_4 F A B) =>  ( ((r2_hidden C (k3_vectsp_4 A B D F)) & (r2_hidden C (k3_vectsp_4 A B E F)))  =>  ((k3_vectsp_4 A B D F) = (k3_vectsp_4 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_5 D A B C) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k3_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E C D)) = (k2_domain_1 (u1_struct_0 B) (u1_struct_0 B) (k4_vectsp_5 A B E D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_vfunct_1 C D E A) & (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) F B)))  => (r1_vfunct_1 C D (k6_vfunct_1 C D E F) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r1_vfunct_2 A B C E) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) D F)))  => (r1_vfunct_2 A B (k3_vfunct_2 A B C D) (k3_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r2_yellow_0 A E) &  (D = (k2_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k2_yellow_0 A D) C)) ) ) ) )  => (v2_waybel_0 C A)) ) ) ) ) ) ) ).
tt(t56_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v8_waybel_1 B A) =>  ((v17_waybel_0 (k2_waybel_1 A A B) A (k1_yellow_2 A A B)) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C (u1_struct_0 (k1_yellow_2 A A B))) & (r2_yellow_0 A C))  =>  ((r2_yellow_0 (k1_yellow_2 A A B) C) &  ((k2_yellow_0 (k1_yellow_2 A A B) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B (k2_yellow_0 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ( ((k1_relset_1 (u1_struct_0 A) (k5_waybel23 A B)) = (u1_struct_0 A))  & (m1_subset_1 (k2_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))) (k5_waybel23 A B)) (k1_zfmisc_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ) ).
tt(t56_waybel_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v9_waybel_1 A) <=>  ((v2_waybel_2 A) & (v2_waybel_1 A)) ) ) ) ).
tt(t56_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v18_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v1_waybel34 C B A) => (v3_waybel34 C B A)) ) ) ) ) ) ) ).
tt(t56_waybel_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r5_waybel_4 A B C) <=>  ((r2_hidden C B) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_orders_2 A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_xboole_0 A B) & (r2_xboole_0 B C))  => (r2_xboole_0 A C)) ) ) ) ).
tt(t56_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A (k8_xboolean A B)) = (k8_xboolean A B)) ) ) ) ) ).
tt(t56_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 1 (k7_xcmplx_0 1 A)) = A) ) ) ).
tt(t56_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 k6_numbers C))  => (r1_xxreal_0 A (k6_xcmplx_0 B C))) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t56_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k4_xxreal_1 A B) (k2_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  (! [B:$i] :  ((m2_xxreal_2 B A) =>  ((r2_hidden B A) =>  (B = (k2_xxreal_2 A)) ) ) ) ) ) ).
tt(t56_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ((r1_xxreal_0 (k1_xxreal_3 A B) C) &  (~  ( (~  (B = k1_xxreal_0) )  & (r1_xxreal_0 A (k3_xxreal_3 C B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_yellow_0 (g1_orders_2 B (k1_toler_1 (u1_orders_2 A) B)) A) & (m1_yellow_0 (g1_orders_2 B (k1_toler_1 (u1_orders_2 A) B)) A)) ) ) ) ) ).
tt(t56_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((v1_waybel11 C (k3_yellow_3 A B)) =>  ((v1_waybel11 (k4_yellow_3 A B C) A) & (v1_waybel11 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ) ).
tt(t56_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  ((r1_borsuk_1 A B) => (r1_waybel18 B A)) ) ) ) ) ).
tt(t56_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v15_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) ) )  =>  ( ((v21_functor0 C A B) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((m1_subset_1 F (u1_struct_0 D)) <=> (m1_subset_1 (k3_functor0 A B C F) (u1_struct_0 E))) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  ( ( (H = F)  &  (I = G) )  =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 E)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 E)) =>  ( ( (J = (k3_functor0 A B C F))  &  (K = (k3_functor0 A B C G)) )  =>  (! [L:$i] :  ((m1_subset_1 L (k1_altcat_1 A F G)) =>  ((r2_hidden L (k1_altcat_1 D H I)) <=> (r2_hidden (k6_functor0 A B C F G L) (k1_altcat_1 E J K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r2_yellow20 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_lattice3 A D B) & (r2_lattice3 A E C))  => (r2_lattice3 A (k4_yellow_4 A D E) (k12_lattice3 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t56_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k12_lattice3 A B C) = (k3_yellow_0 A))  <=>  ((k1_yellow_5 A B C) = B) ) ) ) ) ) ) ) ).
tt(t56_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C)))) =>  ( (D = (k2_xboole_0 (u1_pre_topc A) (u1_pre_topc B)))  =>  ((u1_pre_topc C) = (k1_cantor_1 (u1_struct_0 C) (k2_cantor_1 (u1_struct_0 C) D))) ) ) ) ) ) ) ) ) ) ).
tt(t56_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k29_zf_lang (k10_zf_lang A B)) = (k2_xboole_0 (k2_xboole_0 (k29_zf_lang A) (k29_zf_lang B)) (k2_enumset1 (k6_zf_lang B) (k6_zf_lang A) (k7_zf_lang (k6_zf_lang A) (k6_zf_lang B)) (k10_zf_lang A B)))) ) ) ) ) ).
tt(t56_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v4_zf_lang A) =>  ((r1_zf_lang B A) <=>  (B = (k20_zf_lang A)) ) ) ) ) ) ) ).
tt(t56_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k4_xboole_0 B (k1_tarski C))) <=>  ((r2_hidden A B) &  (~  (A = C) ) ) ) ) ) ) ).
tt(t56_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_zmodul01 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) ) )  => (m1_zmodul01 A (k4_zmodul01 A))) ) ).
tt(t57_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  ((r5_abcmiz_0 A B C) => (r3_abcmiz_0 A B C)) ) ) ) ) ) ) ).
tt(t57_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( ((k1_funct_1 B k1_xboole_0) = (k4_tarski k10_abcmiz_1 (u1_struct_0 A)))  &  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (~  (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t57_abcmiz_a,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k27_abcmiz_1)) =>  (? [C:$i] :  ( ((v2_abcmiz_1 C k27_abcmiz_1) & (m2_abcmiz_1 C k27_abcmiz_1 B))  &  ((k3_finseq_1 (k1_msualg_1 k27_abcmiz_1 C)) = A) ) ) ) ) ) ) ).
tt(t57_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 D A) &  ((r2_hidden B D) & (r2_hidden C D)) )  =>  ( (B = C)  |  (D = (k2_aff_1 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 B A) => (r1_aff_4 A B B)) ) ) ) ) ).
tt(t57_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  ((k5_relat_1 (k1_ordinal4 A B) (k2_afinsq_1 A)) = A) ) ) ) ) ).
tt(t57_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v3_valued_0 B) & (v1_finset_1 B)) ) ) )  =>  ( ( ((k1_afinsq_1 A) = (k1_afinsq_1 B))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) )  => (r1_xxreal_0 (k7_afinsq_2 A) (k7_afinsq_2 B))) ) ) ) ) ).
tt(t57_algspec1,ax, (! [A:$i] :  ( ((v1_instalg1 A) & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  ((m4_algspec1 C A) =>  ((r1_tarski (u1_struct_0 A) (u1_struct_0 B)) & (r1_tarski (u4_struct_0 A) (u4_struct_0 B))) ) ) ) ) ) ) ) ).
tt(t57_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k5_altcat_4 (k2_altcat_4 A)) = (k5_altcat_4 A)) ) ) ).
tt(t57_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ( ((r2_hidden F B) &  ((r2_hidden F C) &  ((r2_hidden G B) &  ((r2_hidden H C) &  ((r2_hidden G D) &  ((r2_hidden H D) &  ((r10_analmetr A E B) &  ((r10_analmetr A E C) & (v4_analmetr D A)) ) ) ) ) ) ) )  =>  ( (G = H)  | (r10_analmetr A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  ((k12_aofa_000 (k7_freealg k19_aofa_000 A)) = (k4_trees_4 1 k1_xboole_0)) ) ) ).
tt(t57_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ( ((k1_funct_1 H G) = 3)  &  ((k1_funct_1 H C) = 4) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( (I = (k21_aofa_i00 B k4_numbers H E))  =>  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F 1) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 2) (k74_aofa_i00 A B C D G E) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1)))) F) = (k9_newton I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((r2_hidden (k6_armstrng A C D) (k12_armstrng A B)) <=>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ((r1_tarski C E) =>  ((r1_tarski D E) | (r2_hidden E (k14_armstrng A B))) ) ) ) ) ) ) ) )  &  ((k9_armstrng A (k12_armstrng A B)) = (k7_subset_1 (k1_zfmisc_1 A) (k9_setfam_1 A) (k14_armstrng A B))) ) ) ) ) ) ).
tt(t57_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ((k10_arytm_3 A (k9_arytm_3 B C)) = (k9_arytm_3 (k10_arytm_3 A B) (k10_arytm_3 A C))) ) ) ) ) ) ) ).
tt(t57_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 A) &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 (k9_newton B) A) &  ( (~ (r1_xxreal_0 (k9_newton (k2_nat_1 B 1)) A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 (k9_newton C) A) =>  ((r1_xxreal_0 (k9_newton (k2_nat_1 C 1)) A) |  (C = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A D C)) = (k1_bcialg_1 A C (k1_bcialg_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t57_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (C = k6_numbers)  =>  ((r1_xxreal_0 B k6_numbers) |  ((v8_bcialg_1 E) & (m1_bcialg_5 E k6_numbers 1 k6_numbers 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  ((v12_bcialg_1 (k9_subset_1 (u1_struct_0 A) (u1_struct_0 B) C) B) & (m2_bcialg_1 (k9_subset_1 (u1_struct_0 A) (u1_struct_0 B) C) B)) ) ) ) ) ) ) ).
tt(t57_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  ((m3_bciideal B A) =>  ( ((v3_bciideal B A) & (m2_bcialg_1 B A))  & (m4_bciideal B A)) ) ) ) ) ) ).
tt(t57_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k5_vfunct_1 k5_numbers A (k3_normsp_1 A C B)))) ) ) ) ) ) ).
tt(t57_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v1_bilinear C A B B) &  ((v2_bilinear C A B B) &  ((v3_bilinear C A B B) &  ((v4_bilinear C A B B) &  ((v7_bilinear C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((k10_bilinear A B B C) = (k11_bilinear A B B C)) ) ) ) ) ) ) ).
tt(t57_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A B B) (k5_lattices A))) ) ) ) ).
tt(t57_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) )  =>  (~  ((r1_tarski A (k2_rcomp_1 k6_numbers 1)) &  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (~  ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 k6_numbers 1)) &  ( ((k3_seq_4 A) = (k5_seq_4 B))  &  ((k2_seq_4 A) = (k4_seq_4 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xboole_0 (k3_borsuk_5 A B) (k2_borsuk_5 A B))) ) ) ) ).
tt(t57_borsuk_6,ax, ((k9_subset_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) k6_borsuk_6 k7_borsuk_6) = a_0_15_borsuk_6) ).
tt(t57_borsuk_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 (k1_real_1 A)) (k1_jordan24 A)) (k3_struct_0 (k15_euclid 2)))) ) ).
tt(t57_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A F B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) G) H) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ((k7_xboolean k7_margrel1 A) = (k3_xboolean A)) ) ) ).
tt(t57_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k5_bvfunc26 A B C)) (k12_bvfunc_1 A))) ) ) ) ) ) ).
tt(t57_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((k4_substut2 A (k6_cqc_lang A B) C D) = (k6_cqc_lang A (k4_substut2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t57_card_1,ax, (9 = (k7_enumset1 k1_xboole_0 1 2 3 4 5 6 7 8)) ).
tt(t57_card_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~  (A = B) )  =>  ((k5_card_1 (k2_tarski A B)) = 2) ) ) ) ).
tt(t57_card_3,ax, ((k8_card_3 k1_xboole_0) = (k1_tarski k1_xboole_0)) ).
tt(t57_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k9_xtuple_0 A) = B)  =>  ( (! [E:$i] :  (! [F:$i] :  (~  ( (~  (E = F) )  &  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ((r2_hidden G (k1_card_fin B D E F)) =>  ((k1_card_1 (k2_card_fin A G E)) = C) ) ) ) ) ) ) )  |  ((k3_card_fin D A) = (k24_binop_2 C (k6_newton D (k5_card_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ((v10_cat_1 B A) =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  | (v7_cat_1 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t57_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_cat_1 E A B C) =>  (! [F:$i] :  ((m1_cat_1 F A B D) =>  ((r2_cat_3 A B E F) =>  ( ((k2_cat_1 A B C) = k1_xboole_0)  |  ( ((k2_cat_1 A B D) = k1_xboole_0)  |  ( ((k2_cat_1 A C D) = k1_xboole_0)  |  ( ((k2_cat_1 A D C) = k1_xboole_0)  |  ((v1_cat_3 E A B C) & (v1_cat_3 F A B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k24_cat_4 A B) = (k11_cat_3 A (k19_cat_4 A) B)) ) ) ) ) ).
tt(t57_cfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) => (r2_relset_1 B k2_numbers (k2_partfun1 B k2_numbers (k25_valued_1 B k2_numbers C D) A) (k25_valued_1 B k2_numbers (k2_partfun1 B k2_numbers C A) D))) ) ) ) ) ) ) ).
tt(t57_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C A))) =>  ((k7_chain_1 B C A D (k5_chain_1 B C A)) = D) ) ) ) ) ) ) ) ) ).
tt(t57_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_glib_000 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (! [E:$i] :  ((m2_glib_000 E A C (k21_glib_000 A C)) =>  (! [F:$i] :  ((m2_glib_000 F A (k4_subset_1 (k6_glib_000 A) C (k6_domain_1 (k6_glib_000 A) D)) (k21_glib_000 A (k4_subset_1 (k6_glib_000 A) C (k6_domain_1 (k6_glib_000 A) D)))) =>  ( ((v1_glib_002 E) & (r2_hidden D (k2_chord A (k24_glib_000 A E))))  => (v1_glib_002 F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v6_circcomb B A) <=> (r8_pboole (u1_struct_0 A) (u3_msualg_1 A B) (k7_funcop_1 (u1_struct_0 A) k6_margrel1))) ) ) ) ) ).
tt(t57_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_msafree2 B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v4_msualg_1 E B) &  ((v4_msafree2 E B) & (l3_msualg_1 E B)) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F A) &  ((v4_msafree2 F A) & (l3_msualg_1 F A)) )  =>  ((r5_circtrm1 B A C D E F) =>  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B E))) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 A F))) =>  ( (G = (k3_relat_1 C H))  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 B)) =>  ((r1_facirc_1 B E G I) <=> (r1_facirc_1 A F H (k1_funct_1 C I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k5_classes1 A) = A) ) ) ).
tt(t57_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ((r2_hidden A B) => (r2_hidden (k1_tarski A) B)) ) ) ) ).
tt(t57_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) => (m1_clvect_1 (k3_clvect_1 B) A)) ) ) ) ).
tt(t57_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_funct_1 B) => (v2_clvect_2 B A)) ) ) ) ) ).
tt(t57_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v10_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A B C D) = (k7_relat_1 (k11_cohsp_1 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t57_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k17_complex1 (k6_xcmplx_0 A B)) (k7_real_1 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ).
tt(t57_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_complex2 (k8_complex1 A B) C) = (k8_complex1 (k2_complex2 A C) (k2_complex2 B C))) ) ) ) ) ) ) ).
tt(t57_complfld,ax, ((k17_complex1 (k4_struct_0 k1_complfld)) = k6_numbers) ).
tt(t57_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( ( (A = B)  &  ((k3_finseq_1 A) = (k3_finseq_1 B)) )  =>  ((k11_seq_4 A) = (k6_rvsum_1 B)) ) ) ) ) ) ).
tt(t57_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((r2_hidden k6_numbers (k2_afinsq_1 (k11_compos_1 A B))) & (r2_hidden 1 (k2_afinsq_1 (k11_compos_1 A B)))) ) ) ) ) ).
tt(t57_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G) 3) = (k5_compos_0 (u1_compos_1 A) E 3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) => (m1_comptrig (k2_xcmplx_0 (k8_real_1 (k2_power B (k17_complex1 A)) (k21_sin_cos (k10_real_1 (k7_real_1 (k1_comptrig A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B))) (k3_xcmplx_0 (k8_real_1 (k2_power B (k17_complex1 A)) (k18_sin_cos (k10_real_1 (k7_real_1 (k1_comptrig A) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B))) k7_complex1)) A B)) ) ) ) ) ) ).
tt(t57_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  ( ((v2_comput_1 B) &  ((v2_comput_1 C) &  ( ((k2_nat_1 (k19_margrel1 B) 2) = (k19_margrel1 C))  &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 1 (k19_margrel1 B)))) ) ) )  =>  ( ((k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 B C A)) = (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers))  &  ((k19_margrel1 (k7_comput_1 B C A)) = (k2_nat_1 (k19_margrel1 B) 1)) ) ) ) ) ) ) ) ) ).
tt(t57_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ((v1_series_1 (k7_comseq_3 A)) & (v1_series_1 (k8_comseq_3 A)))  =>  ((v1_comseq_3 A) &  ((k11_comseq_3 A) = (k2_xcmplx_0 (k4_series_1 (k7_comseq_3 A)) (k3_xcmplx_0 (k4_series_1 (k8_comseq_3 A)) k7_complex1))) ) ) ) ) ).
tt(t57_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  => (v2_convex4 (k17_convex4 A (k3_clvect_1 A)) A)) ) ).
tt(t57_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r3_cqc_the1 A B (k8_cqc_lang A C D)) =>  ((r2_hidden E (k24_qc_lang1 A C)) | (r3_cqc_the1 A B (k8_cqc_lang A C (k11_cqc_lang A E D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C (k12_cqc_lang A D B)) (k12_cqc_lang A D (k12_cqc_lang A C B))) A) & (v2_cqc_the1 (k2_qc_lang2 A (k7_qc_lang2 A C D B) (k7_qc_lang2 A D C B)) A)) ) ) ) ) ) ) ) ) ).
tt(t57_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r7_cqc_the3 A B C) & (r7_cqc_the3 A D E))  => (r7_cqc_the3 A (k10_cqc_lang A B D) (k10_cqc_lang A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r1_xxreal_0 (k15_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A D E)) (k7_real_1 (k15_csspace A B D) (k15_csspace A C E)))) ) ) ) ) ) ) ) ) ) ).
tt(t57_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A B) = (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 A)) (k21_sin_cos (k8_real_1 2 B)))) (k9_real_1 A B))) ) ) ) ) ).
tt(t57_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) k19_sin_cos) A B) = (k1_real_1 (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k8_real_1 3 (k18_sin_cos (k10_real_1 (k7_real_1 A B) 2))) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))) (k8_real_1 (k18_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 3 A) (k8_real_1 3 B)) 2)) (k18_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 3 A) (k8_real_1 3 B)) 2))))) (k9_real_1 A B)))) ) ) ) ) ).
tt(t57_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k7_real_1 A B)) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k7_real_1 A B))) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A)) 2)))) ) ) ) ) ) ).
tt(t57_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C (k8_eqrel_1 A B)) & (v1_funct_1 C)) )  =>  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  ( ((v2_funct_1 C) &  ((v2_funct_2 C (k8_eqrel_1 A B)) &  ( ((k9_xtuple_0 C) = (k4_finseq_1 D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k9_xtuple_0 C)) =>  ((k1_funct_1 D E) = (k1_card_1 (k1_funct_1 C E))) ) ) ) ) ) )  =>  ((k5_card_1 A) = (k2_wsierp_1 D)) ) ) ) ) ) ) ) ) ) ).
tt(t57_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [H:$i] :  ((m2_subset_1 H (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (E = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (F = (k5_algstr_0 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k2_binom (k9_int_3 A) E 3)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) E 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  (I = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) E F) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) F)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)))) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) E 2)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C D) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) D (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_ens_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k19_ens_1 A B) = (k1_funct_1 (k1_funct_5 (k22_ens_1 A)) (k4_cat_1 A B)))  &  ((k20_ens_1 A B) = (k1_funct_1 (k3_funct_5 (k22_ens_1 A)) (k4_cat_1 A B))) ) ) ) ) ) ).
tt(t57_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_matrprob B) & (m2_finseq_1 B k1_numbers)) )  =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 A))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 A)) =>  ( (~ (r1_xxreal_0 (k1_seq_1 A E) k6_numbers))  &  ( (~ (r1_xxreal_0 (k1_seq_1 B E) k6_numbers))  &  ( ((k1_seq_1 C E) = (k1_real_1 (k8_real_1 (k1_seq_1 A E) (k6_power 2 (k1_seq_1 A E)))))  &  ((k1_seq_1 D E) = (k1_real_1 (k8_real_1 (k1_seq_1 A E) (k6_power 2 (k1_seq_1 B E))))) ) ) ) ) ) ) ) ) )  =>  ((r1_xxreal_0 (k18_rvsum_1 C) (k18_rvsum_1 D)) &  ( ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 A)) =>  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) )  =>  ((k18_rvsum_1 C) = (k18_rvsum_1 D)) )  &  ( ( ((k18_rvsum_1 C) = (k18_rvsum_1 D))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 A)) =>  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) ) )  &  ( (~  ( (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r2_hidden E (k4_finseq_1 A)) &  (~  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) ) )  & (r1_xxreal_0 (k18_rvsum_1 D) (k18_rvsum_1 C))) )  &  (~  ( (~ (r1_xxreal_0 (k18_rvsum_1 D) (k18_rvsum_1 C)))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 A)) &  (~  ((k1_seq_1 A E) = (k1_seq_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k1_enumset1 A C B)) ) ) ) ).
tt(t57_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  => (r1_tarski (k8_relset_1 A B E (k6_domain_1 B D)) (k8_relset_1 A C (k1_partfun1 A B B C E F) (k6_domain_1 C (k3_funct_2 B C F D))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r1_rvsum_1 C D) => (r1_rvsum_1 C (k1_rlvect_1 (k15_euclid A) D B))) ) ) ) ) ) ) ) ) ).
tt(t57_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) =>  ((r2_hidden D (k5_euclid_3 2 A B C)) <=>  (~  ( (~  ( ((k10_euclid_3 2 A B C D) = k6_numbers)  &  ((r1_xxreal_0 k6_numbers (k11_euclid_3 2 A B C D)) & (r1_xxreal_0 k6_numbers (k12_euclid_3 2 A B C D))) ) )  &  ( (~  ((r1_xxreal_0 k6_numbers (k10_euclid_3 2 A B C D)) &  ( ((k11_euclid_3 2 A B C D) = k6_numbers)  & (r1_xxreal_0 k6_numbers (k12_euclid_3 2 A B C D))) ) )  &  (~  ((r1_xxreal_0 k6_numbers (k10_euclid_3 2 A B C D)) &  ((r1_xxreal_0 k6_numbers (k11_euclid_3 2 A B C D)) &  ((k12_euclid_3 2 A B C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_euclid_8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ( ( ((k1_seq_1 A G) = (k1_seq_1 B H))  &  ( ((k1_seq_1 C G) = (k1_seq_1 D H))  &  ((k1_seq_1 E G) = (k1_seq_1 F H)) ) )  =>  ((k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 A C E) G) = (k3_funct_2 k1_numbers (k1_euclid 3) (k6_euclid_8 B D F) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k1_rlvect_1 (k15_euclid 2) B A) = (k19_euclid (k4_real_1 A (k17_euclid B)) (k4_real_1 A (k18_euclid B)))) ) ) ) ) ).
tt(t57_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (? [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) &  ((r2_hidden D C) &  ((k12_euclid (k8_euclid A B D)) = (k3_euclidlp A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t57_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) &  ((r2_hidden B C) & (r2_hidden (k4_tarski A C) (k6_exchsort D (k10_funct_7 E A B)))) )  => (r2_hidden (k4_tarski B C) (k6_exchsort D E))) ) ) ) ) ) ) ) ).
tt(t57_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ( (~  (A = (k4_tarski (k10_finseq_1 B C) D)) )  =>  ((k2_msafree2 (k8_facirc_1 B C A D)) = (k1_enumset1 B C A)) ) ) ) ) ) ) ).
tt(t57_fcont_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_relset_1 k1_numbers k1_numbers (k1_fcont_1 A B) (k1_rcomp_1 k6_numbers 1)) = (k1_rcomp_1 B (k2_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t57_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos) A) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t57_fdiff_4,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k24_sin_cos) k3_taylor_1))) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( ((k1_seq_1 B C) = 1)  &  (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) C) k6_numbers)) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k24_sin_cos) k3_taylor_1) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos B) k24_sin_cos) k3_taylor_1) A) C) = (k10_real_1 1 (k9_real_1 (k1_seq_1 k24_sin_cos C) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t57_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_xboole_0 (k3_xboole_0 k3_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 2))) (k6_domain_1 k5_numbers (k2_nat_1 (k4_nat_1 2 A) 4))) = (k3_xboole_0 k3_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 4)))) ) ) ).
tt(t57_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v14_lattices A) =>  ((k6_lattices (k6_filter_0 A (k2_filter_0 A B))) = (k6_lattices A)) ) ) ) ) ) ).
tt(t57_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r3_lattices A (k4_lattices A (k4_filter_0 A B C) (k4_filter_0 A B D)) (k4_filter_0 A B (k4_lattices A C D)))) ) ) ) ) ) ) ) ).
tt(t57_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~  (B = (k5_filter_2 A)) )  & (v1_filter_2 B A))  <=> (r2_filter_2 A B)) ) ) ) ) ).
tt(t57_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k5_card_1 (k2_finseq_1 A)) = A) ) ) ).
tt(t57_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k2_finseq_1 A)) =>  ((k1_funct_1 (k2_finseq_2 A B) C) = B) ) ) ) ) ) ).
tt(t57_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((k5_card_1 (k8_relat_1 (k7_finseq_1 A B) C)) = (k2_nat_1 (k5_card_1 (k8_relat_1 A C)) (k5_card_1 (k8_relat_1 B C)))) ) ) ) ) ) ).
tt(t57_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((r2_hidden B (k10_xtuple_0 A)) & (v2_funct_1 A))  => (r1_xboole_0 (k10_xtuple_0 (k5_finseq_4 A B)) (k10_xtuple_0 (k6_finseq_4 A B)))) ) ) ) ).
tt(t57_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k4_finseq_1 A) = (k4_finseq_1 (k3_finseq_5 A)))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 (k3_finseq_5 A))) ) ) ) ).
tt(t57_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden C (k10_xtuple_0 D)) =>  ((r1_xxreal_0 (k4_finseq_4 D C) A) | (r2_hidden C (k10_xtuple_0 (k2_rfinseq B A D)))) ) ) ) ) ) ) ) ) ) ).
tt(t57_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo D A) => (r2_relset_1 k5_numbers A (k3_finseqop A A A D (k4_binop_1 A D) C) C)) ) ) ) ) ) ) ) ) ).
tt(t57_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_fintopo6 A B C D E) &  ((v3_orders_2 A) & (v1_fin_topo A)) )  =>  ( (D = E)  |  ( (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ( (~ (r1_xxreal_0 F 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) F))  &  (~  ((k9_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) B) (k1_fin_topo A (k7_partfun1 (u1_struct_0 A) B F))) = (k1_enumset1 (k1_funct_1 B (k7_nat_d F 1)) (k1_funct_1 B F) (k1_funct_1 B (k1_nat_1 F 1)))) ) ) ) ) ) )  &  ( ((k9_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) B) (k1_fin_topo A (k7_partfun1 (u1_struct_0 A) B 1))) = (k2_tarski (k1_funct_1 B 1) (k1_funct_1 B 2)))  &  ((k9_subset_1 (u1_struct_0 A) (k2_relset_1 (u1_struct_0 A) B) (k1_fin_topo A (k7_partfun1 (u1_struct_0 A) B (k3_finseq_1 B)))) = (k2_tarski (k1_funct_1 B (k7_nat_d (k3_finseq_1 B) 1)) (k1_funct_1 B (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k6_flang_1 A B (k8_flang_1 A B)) = (k6_flang_1 A (k8_flang_1 A B) B)) ) ) ) ).
tt(t57_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((r1_xxreal_0 D E) & (r2_hidden (k2_flang_1 A) B))  =>  ((r1_tarski C (k6_flang_1 A C (k1_flang_2 A B D E))) & (r1_tarski C (k6_flang_1 A (k1_flang_2 A B D E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((k2_flang_3 A B) = (k8_flang_1 A B))  <=> (r2_hidden (k2_flang_1 A) B)) ) ) ) ).
tt(t57_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k1_funct_4 (k5_relat_1 B A) C) = (k2_xboole_0 (k5_relat_1 B (k6_subset_1 A (k9_xtuple_0 C))) C)) ) ) ) ) ) ).
tt(t57_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v5_fsm_1 E A B) &  ((v7_fsm_1 E A B) & (l2_fsm_1 E A B)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (~  ( (H = F)  &  ( (I = G)  &  ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  ( (C = (k13_fsm_1 A B D E))  &  ( (~ (r5_fsm_1 A B D H I))  & (r5_fsm_1 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 (k1_funcop_1 D) E) = (k4_tarski (k2_xtuple_0 (k3_funct_2 A (k2_zfmisc_1 B C) D E)) (k1_xtuple_0 (k3_funct_2 A (k2_zfmisc_1 B C) D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski A B) =>  ( ((k6_relat_1 B (k6_relat_1 A C)) = (k6_relat_1 A C))  &  ((k6_relat_1 A (k6_relat_1 B C)) = (k6_relat_1 A C)) ) ) ) ) ) ) ).
tt(t57_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((v2_funct_1 B) &  ((k2_relset_1 A B) = A) )  =>  ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ) ).
tt(t57_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k8_relat_1 (k13_funct_3 C D) (k2_zfmisc_1 A B)) = (k3_xboole_0 (k8_relat_1 C A) (k8_relat_1 D B))) ) ) ) ) ) ) ) ).
tt(t57_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ((r1_tarski (k9_xtuple_0 E) (k2_zfmisc_1 A B)) & (r1_tarski (k9_xtuple_0 F) (k2_zfmisc_1 C D)))  => (r1_tarski (k9_xtuple_0 (k3_funct_4 E F)) (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)))) ) ) ) ) ) ) ) ) ).
tt(t57_funct_5,ax, (! [A:$i] :  ((k1_funct_2 k1_xboole_0 A) = (k1_tarski k1_xboole_0)) ) ).
tt(t57_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r2_hidden D (k1_funct_2 A (k1_funct_2 B C))) =>  ( (A = k1_xboole_0)  |  ( (B = k1_xboole_0)  |  ((k10_funct_6 (k10_funct_6 D)) = D) ) ) ) ) ) ) ) ) ).
tt(t57_funct_7,ax, ( ((k6_funct_7 k1_xboole_0) = k1_xboole_0)  &  ((k7_funct_7 k1_xboole_0) = k1_xboole_0) ) ).
tt(t57_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_funct_1 k1_funct_8 A) = (k1_real_1 1)) ) ) ) ).
tt(t57_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  ((k5_struct_0 (k7_fvaluat1 A B)) = (k5_struct_0 A)) ) ) ) ) ) ).
tt(t57_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) &  ((v5_vectsp_1 B) &  ((v6_vectsp_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B C (k5_struct_0 B)) = C) ) ) ) ) ) ) ).
tt(t57_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ( ( (~ (v1_xboole_0 G))  &  ((v1_relat_1 G) &  ((v2_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) ) ) )  =>  (! [H:$i] :  ((m1_genealg1 H G) =>  (! [I:$i] :  ((m1_genealg1 I G) =>  ( ((k12_genealg1 G H I A A B C D E) = (k10_genealg1 G H I B C D E))  &  ( ((k12_genealg1 G H I A F A C D E) = (k10_genealg1 G H I F C D E))  &  ( ((k12_genealg1 G H I A F B A D E) = (k10_genealg1 G H I F B D E))  &  ( ((k12_genealg1 G H I A F B C A E) = (k10_genealg1 G H I F B C E))  &  ((k12_genealg1 G H I A F B C D A) = (k10_genealg1 G H I F B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (k3_msafree2 (k22_gfacirc1 A B C))) & (r2_hidden (k24_gfacirc1 A B C) (k3_msafree2 (k22_gfacirc1 A B C)))) ) ) ) ).
tt(t57_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k26_glib_000 A C)) <=>  (? [D:$i] : (r2_glib_000 A D C B)) ) ) ) ) ) ) ).
tt(t57_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k1_funct_1 B C) = (k4_glib_001 A B))  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k20_glib_001 A B C (k3_finseq_1 B)) (k8_glib_001 A B 1 C))) ) ) ) ) ) ) ).
tt(t57_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v3_glib_003 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  (! [C:$i] : (r2_hidden B (k14_glib_003 (k13_glib_003 A B C)))) ) ) ) ) ).
tt(t57_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid 1 (k1_real_1 1))) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) k6_numbers)) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid 1 k6_numbers)))))) ) ).
tt(t57_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 C))) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_graph_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C)))  =>  ((k7_partfun1 A (k4_graph_2 A C D) B) = (k7_partfun1 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t57_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_2 B (u4_struct_0 A) (k9_graph_3 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v1_abian (k10_graph_1 A C))) )  =>  ( ((k10_xtuple_0 B) = (u4_struct_0 A))  |  ((v1_xboole_0 B) |  ( (~ (v1_xboole_0 (k14_graph_3 A B)))  &  (~ (r1_xxreal_0 (k5_card_1 (k10_xtuple_0 (k14_graph_3 A B))) (k5_card_1 (k10_xtuple_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t57_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  => (r1_xxreal_0 (k3_finseq_1 B) (k6_graph_1 A))) ) ) ) ).
tt(t57_groeb_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ((r1_groeb_1 A B C D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  =>  ((r1_groeb_2 A (k3_termord A B C E) (k3_termord A B C F)) | (r1_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 C D) => (r1_tarski (k4_group_11 A B C) (k4_group_11 A B D))) ) ) ) ) ) ) ) ) ).
tt(t57_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((r1_tarski (u1_struct_0 B) (u1_struct_0 C)) => (m1_group_2 B C)) ) ) ) ) ) ) ).
tt(t57_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  (B = k1_xboole_0) )  =>  ((k5_group_3 A B C) = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ).
tt(t57_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_group_2 A (k8_group_4 A (k8_group_4 A B C) D) (k8_group_4 A B (k8_group_4 A C D)))) ) ) ) ) ) ) ) ).
tt(t57_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k5_group_5 A B C) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ) ) ) ) ).
tt(t57_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v2_funct_2 C (u1_struct_0 B)) <=>  ((k10_group_6 A B C) = B) ) ) ) ) ) ) ) ).
tt(t57_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_9 B A) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) ) )  => (v7_struct_0 (k10_group_9 A B (k5_group_9 A B)))) ) ) ).
tt(t57_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v4_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)) = k6_numbers)  =>  ((k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C) = (k4_struct_0 k1_complfld)) ) ) ) ) ) ) ) ).
tt(t57_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k29_sin_cos)) =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) A) (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos) k29_sin_cos) A))) ) ) ) ).
tt(t57_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k7_ideal_1 A B) (k7_ideal_1 A C))) ) ) ) ) ) ) ).
tt(t57_incsp_1,ax, (! [A:$i] :  ( ((v15_incsp_1 A) & (l2_incsp_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u4_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_incsp_1 A)) =>  (~  ( (~  (B = C) )  &  ( (? [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) &  ((r2_incsp_1 A D B) & (r2_incsp_1 A D C)) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (~  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  ( ((r2_incsp_1 A E B) & (r2_incsp_1 A E C))  <=> (r1_incsp_1 A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k6_int_1 B A))) ) ) ) ) ).
tt(t57_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers A)) A) B) = (k5_square_1 (k1_seq_1 k29_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t57_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 B E) = 1) ) ) )  &  ((r2_relset_1 k1_numbers k1_numbers C (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers k2_sin_cos9 (k1_taylor_1 2)) (k6_rfunct_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers D) (k3_valued_1 k1_numbers k1_numbers k1_numbers B (k1_taylor_1 2)))))) &  ((r1_tarski D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k2_sin_cos9))) &  ((r1_tarski D (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (D = (k1_relset_1 k1_numbers C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k2_sin_cos9)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers D)) k2_sin_cos9)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t57_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 (k1_seq_1 k16_sin_cos (k1_seq_1 k19_sin_cos D)) (k1_seq_1 k16_sin_cos D))) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t57_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ( ((v1_comseq_2 (k2_partfun1 A k1_numbers B A)) &  ((v1_comseq_2 (k2_partfun1 A k1_numbers C A)) &  ((v3_integra1 B A) & (v3_integra1 C A)) ) )  =>  ((v3_integra1 (k3_valued_1 A k1_numbers k1_numbers B C) A) &  ((k12_integra1 A (k3_valued_1 A k1_numbers k1_numbers B C)) = (k7_real_1 (k12_integra1 A B) (k12_integra1 A C))) ) ) ) ) ) ) ) ) ).
tt(t57_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ((k2_integra5 A k4_sin_cos2) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 (k4_seq_4 A)) (k3_funct_2 k1_numbers k1_numbers k1_sin_cos2 (k5_seq_4 A)))) ) ) ).
tt(t57_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k7_real_1 H A))  &  (~ (r1_xxreal_0 (k1_seq_1 E H) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 B A)))) = G)  &  ( (G = (k1_relset_1 k1_numbers F))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ((k1_seq_1 F H) = (k10_real_1 (k7_real_1 H B) (k7_real_1 H A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F C))) ) ) ) ) )  =>  ((k2_integra5 C F) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 B A))) (k4_seq_4 C)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 B A))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k15_interva1 A (k16_interva1 A B C)) = (k4_subset_1 (u1_struct_0 A) (k15_interva1 A B) (k15_interva1 A C))) ) ) ) ) ) ) ).
tt(t57_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  ((r2_hidden (k5_intpro_1 A B) k8_intpro_1) <=> (r2_hidden (k5_intpro_1 B A) k8_intpro_1)) ) ) ) ) ).
tt(t57_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  &  ( (C = a_0_2_jgraph_4)  &  (B = (a_1_5_jgraph_4 A)) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k18_euclid B) k6_numbers) =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) |  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  => (r1_xxreal_0 (k18_euclid C) k6_numbers)) ) ) ) ) ) ) ) ) ) ).
tt(t57_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid B D))))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=> (r1_xxreal_0 (k18_euclid F) (k18_euclid E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) = C) )  =>  ((r1_xxreal_0 D C) |  ((k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) = (k1_real_1 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan9 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 B A) C) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) (k3_finseq_1 (k1_jordan8 B A)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jordan1g,ax, (! [A:$i] :  ( ((v2_connsp_1 A (k15_euclid 2)) &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 A B))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 A B))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C D) (k3_topreal1 2 (k1_jordan9 A B))) & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) C D)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 A B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 D 1) E)) ) ) )  =>  ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k2_nat_1 D 2) E) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E) (k3_topreal1 2 (k1_jordan1e B A))) &  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_topreal1 2 (k2_jordan1e B A))) &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) &  ((r1_jordan6 A B C) & (r1_jordan6 A C B)) )  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t57_jordan,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r2_hidden E (k2_jgraph_6 A B C D)) & (r1_topreal1 (k15_euclid 2) E F G))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r2_hidden F (k2_jgraph_6 A B C D)) | (r1_tarski (k5_jordan6 G E F E (k1_jordan5c G (k1_sppol_2 A B C D) E F)) (k2_jgraph_6 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_kurato_1,ax, (! [A:$i] :  ( ((v1_setfam_1 A) &  ((v3_setfam_1 A (u1_struct_0 k3_topmetr)) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 k3_topmetr))))) )  =>  (! [B:$i] :  ( ((v1_setfam_1 B) &  ((v3_setfam_1 B (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 k3_topmetr))))) )  =>  ( ((v1_tops_2 A k3_topmetr) & (v2_tops_2 B k3_topmetr))  => (r1_xboole_0 A B)) ) ) ) ) ).
tt(t57_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ((k6_lattices A) = (k4_binop_1 (u1_struct_0 A) (u1_lattices A))) ) ) ).
tt(t57_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) (k18_lexbfs A)) B) = k6_numbers) ) ) ) ).
tt(t57_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_limfunc1 A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k10_prob_1 D))) => (r1_xxreal_0 C (k1_seq_1 B E))) ) ) ) ) ) ) ) )  | (v7_limfunc1 (k20_valued_1 k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ) ).
tt(t57_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r4_limfunc2 B A) =>  ((r4_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A) &  ((k2_limfunc2 (k56_valued_1 k1_numbers k1_numbers B) A) = (k18_complex1 (k2_limfunc2 B A))) ) ) ) ) ) ) ).
tt(t57_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r2_limfunc2 B A) &  ((v3_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k4_limfunc1 C)) ) ) ) ) ) ) ) ) ).
tt(t57_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v2_xxreal_0 E) & (m1_subset_1 E k1_numbers))  =>  ( ((r2_hidden D (k1_lpspace2 A B C E)) &  ((k1_mesfunc6 A B C (k2_mesfun6c E A (k56_valued_1 A k1_numbers D))) = k6_numbers) )  => (r1_lpspace1 A B C D (k8_lpspace1 A k6_numbers))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 A)) B) => (r8_ltlaxio1 C (k3_hilbert1 (k6_ltlaxio1 A) B))) ) ) ) ) ) ) ).
tt(t57_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A B) C) A) => (v2_cqc_the1 (k8_cqc_lang A (k6_cqc_lang A C) B) A)) ) ) ) ) ) ) ).
tt(t57_mathmorp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))))  =>  ((k6_mathmorp k6_numbers (k15_euclid A) B) = (k6_domain_1 (u1_struct_0 (k15_euclid A)) (k4_struct_0 (k15_euclid A)))) ) ) ) ) ).
tt(t57_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) (k4_matrix10 A D E)) => (r2_matrix10 (k4_matrix10 A E C) (k4_matrix10 A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix11,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (~  ( (~ (r2_hidden C A))  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (k9_funct_2 A B) B) (k9_funct_2 (k2_xboole_0 A (k1_tarski C)) B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 A B) B) (k9_funct_2 (k2_xboole_0 A (k1_tarski C)) B))))) )  =>  (~  ((v3_funct_2 D (k2_zfmisc_1 (k9_funct_2 A B) B) (k9_funct_2 (k2_xboole_0 A (k1_tarski C)) B)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_xboole_0 A (k1_tarski C)) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski C)) B)))) )  =>  ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski C)) B F A) = E)  =>  ((k1_binop_1 D E (k1_funct_1 F C)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ( (C = k1_xboole_0)  =>  (D = k1_xboole_0) )  &  ( ( (D = k1_xboole_0)  =>  (C = k1_xboole_0) )  &  ((r1_tarski (k2_zfmisc_1 C D) (k2_matrix_1 (k6_matrix13 A B E F))) &  (! [G:$i] :  ( ((v1_finset_1 G) &  ((v1_setfam_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers))) )  =>  (! [H:$i] :  ( ((v1_finset_1 H) &  ((v1_setfam_1 H) & (m1_subset_1 H (k1_zfmisc_1 k5_numbers))) )  =>  (~  ((r1_tarski G E) &  ((r1_tarski H F) &  ( (G = (k7_relat_1 (k5_matrix13 E) C))  &  ( (H = (k7_relat_1 (k5_matrix13 F) D))  &  ( ((k5_card_1 G) = (k5_card_1 C))  &  ( ((k5_card_1 H) = (k5_card_1 D))  &  ((k6_matrix13 A (k6_matrix13 A B E F) C D) = (k6_matrix13 A B G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ( ( ((k1_matrix_1 B) = k1_xboole_0)  &  (~  ((k1_matrix_1 C) = k1_xboole_0) ) )  |  ( ((k8_matrix13 A B) = (k8_matrix13 A (k7_matrlin (u1_struct_0 A) B C)))  <=>  (~ (v1_xboole_0 (k4_matrix15 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((r3_matrix16 B D C) =>  ((r1_xxreal_0 A k6_numbers) |  (C = (k8_matrix_1 (u1_struct_0 B) D 1)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 C) = (k3_finseq_1 D)) )  =>  ((k11_fvsum_1 A D (k3_fvsum_1 A B C)) = (k3_fvsum_1 A (k11_fvsum_1 A D B) (k11_fvsum_1 A D C))) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((v4_matrix_6 C A B) &  ((v4_matrix_6 D A B) & (v4_matrix_6 E A B)) )  =>  ((r1_xxreal_0 A k6_numbers) | (v4_matrix_6 (k4_matrix_6 A B (k4_matrix_6 A B C D) E) A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k4_algstr_0 B (k1_matrix_8 A B (k1_matrix_6 A B C))) = (k1_matrix_8 A B C)) ) ) ) ) ) ) ).
tt(t57_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k8_complsp2 A (k6_matrixc1 (k2_matrixc1 C) B)) = (k12_matrixc1 (k13_matrixc1 A B (k4_matrix_1 k2_numbers C)))) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k23_matrixj1 A (k4_matrix_2 k5_numbers B)) = (k16_matrixj1 (u1_struct_0 A) B (k12_matrix_1 A B))) ) ) ) ) ).
tt(t57_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 C) = (k3_finseq_1 A)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k11_matrixr1 C (k4_rvsum_1 A B)) = (k4_rvsum_1 (k11_matrixr1 C A) (k11_matrixr1 C B))) ) ) ) ) ) ) ) ) ) ).
tt(t57_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k1_matrix_1 B) = (k3_finseq_1 C)) )  =>  ((k12_matrixr1 (k6_matrixr1 B C) A) = (k12_matrixr1 C (k12_matrixr1 B A))) ) ) ) ) ) ) ) ).
tt(t57_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v4_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) => (r1_xxreal_0 (k3_matrix_1 k1_numbers A B C) 1)) ) ) ) ) ) ) ).
tt(t57_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ( ((v2_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A B) => (r1_tarski (k6_measure6 A) B)) ) ) ) ) ).
tt(t57_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) =>  ((k10_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k10_member_1 A B) (k10_member_1 A C))) ) ) ) ) ) ) ).
tt(t57_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k9_memstr_0 A B (k9_memstr_0 A B C D) E) = (k9_memstr_0 A B C (k2_xcmplx_0 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A C) B)) )  => (r1_xxreal_0 (k8_supinf_2 (k17_supinf_2 A)) B)) ) ) ) ) ).
tt(t57_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((v6_supinf_2 B) =>  ( ((r1_xxreal_0 k6_numbers C) => (v6_supinf_2 (k26_valued_1 A k1_numbers B C)))  &  ((r1_xxreal_0 C k6_numbers) => (v2_mesfunc5 (k26_valued_1 A k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t57_mmlquery,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k24_mmlquery A B) = (k3_finseq_1 A))  =>  ((k25_mmlquery A) = (k3_finseq_1 A)) ) ) ) ) ).
tt(t57_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k3_robbins1 (k42_modelc_2 A B) D)) <=>  (~ (r6_modelc_2 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t57_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (? [B:$i] :  ((m1_orders_1 B (k1_orders_1 (k1_modelc_3 A))) &  ((v1_funct_1 B) &  ((v1_funct_2 B (k1_orders_1 (k1_modelc_3 A)) (k1_modelc_3 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_orders_1 (k1_modelc_3 A)) (k1_modelc_3 A))))) ) ) ) ) ) ).
tt(t57_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( (~ (v1_moebius1 A))  =>  ((k6_moebius1 A) = A) ) ) ) ).
tt(t57_monoid_0,ax, (k48_binop_2 = (k1_realset1 k35_binop_2 k5_numbers)) ).
tt(t57_monoid_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ( ((v5_group_1 A) => (v5_group_1 (k22_monoid_1 A)))  &  ( ((v3_group_1 A) => (v3_group_1 (k22_monoid_1 A)))  &  ((v17_monoid_0 A) => (v17_monoid_0 (k22_monoid_1 A))) ) ) ) ) ).
tt(t57_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 3)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  (~  (B = (k1_nat_1 A 3)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( ((k1_polynom2 k10_newton (k13_nat_3 A)) = k1_xboole_0)  =>  (A = 1) ) ) ) ).
tt(t57_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k7_nat_d B C) (k7_nat_d A C))) ) ) ) ) ) ) ) ) ).
tt(t57_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r8_ncfcont1 A B E C) & (r1_tarski D C))  => (r8_ncfcont1 A B E D)) ) ) ) ) ) ) ) ) ).
tt(t57_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) &  ((v2_prvect_2 A) & (v1_ndiff_5 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k14_prvect_2 A)))) =>  ((v3_nfcont_1 D (k14_prvect_2 A)) =>  ( (! [E:$i] :  ((r2_hidden E (k4_finseq_1 A)) =>  ((r2_ndiff_5 A B E C D) & (r3_nfcont_1 (k14_prvect_2 A) (k16_lopban_1 (k11_prvect_2 A (k5_ndiff_5 A E)) B) (k7_ndiff_5 A B E C D) D)) ) )  <=>  ((r2_ndiff_1 D (k14_prvect_2 A) B C) & (r3_nfcont_1 (k14_prvect_2 A) (k16_lopban_1 (k14_prvect_2 A) B) (k4_ndiff_1 (k14_prvect_2 A) B C D) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_nat_d A B) => (r1_nat_d (k6_nat_d C A) (k6_nat_d C B))) ) ) ) ) ) ) ).
tt(t57_normform,ax, (! [A:$i] :  ((k5_lattices (k12_normform A)) = k1_xboole_0) ) ).
tt(t57_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m1_oppcat_1 (k10_oppcat_1 A B C) (k2_oppcat_1 A) B)) ) ) ) ) ) ).
tt(t57_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  ((r8_orders_1 A B) &  ((r1_tarski C (k1_relat_1 A)) & (v1_relat_2 A)) ) )  => (r4_orders_1 A C)) ) ) ) ) ).
tt(t57_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k5_ordinal3 A (k10_ordinal2 B C)) = (k5_ordinal3 (k5_ordinal3 A B) C)) ) ) ) ) ) ) ).
tt(t57_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden 1 A) => (r2_hidden B (k12_ordinal2 A (k1_ordinal1 (k5_ordinal5 B A))))) ) ) ) ) ).
tt(t57_ordinal6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  ( (~ (v4_card_3 A))  <=> (r2_hidden k4_ordinal1 A)) ) ) ).
tt(t57_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t57_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) => (r3_parsp_2 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A C) & (r1_tarski B C))  => (r1_partfun1 A B)) ) ) ) ) ) ) ).
tt(t57_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((v3_funct_1 (k2_partfun1 C B D A)) <=>  (? [E:$i] :  ((m1_subset_1 E B) &  (! [F:$i] :  ((m1_subset_1 F C) =>  ((r2_hidden F (k9_subset_1 C A (k1_relset_1 C D))) =>  ((k1_funct_1 D F) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B (k4_pboole A C B)) => (r6_pboole A B (k1_pboole A))) ) ) ) ) ) ).
tt(t57_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r6_pdiff_5 B A) & (r6_pdiff_5 C A))  =>  ((r3_pdiff_1 3 3 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) &  ((k11_pdiff_1 3 3 (k47_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 2 3 B) (k1_pdiff_3 2 3 C)) A) = (k9_real_1 (k6_pdiff_5 B A) (k6_pdiff_5 C A))) ) ) ) ) ) ) ) ) ).
tt(t57_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) &  ((r1_tarski B (k1_relset_1 (k1_euclid A) D)) &  ((r2_pdiff_9 B A C) & (r2_pdiff_9 B A D)) ) )  =>  ((r2_pdiff_9 B A (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)) E) = (k1_valued_1 (k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B C) E) (k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~  (A = k6_numbers) )  => (r1_int_2 3 (k4_pepin A))) ) ) ).
tt(t57_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k1_funct_1 (k15_finseq_1 (k12_pnproc_1 C B)) A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t57_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_polyform A (k6_xcmplx_0 B 1))) =>  ( ( (B = k6_numbers)  &  (D = k1_xboole_0) )  =>  ((k16_polyform A B D C) = (k5_struct_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ).
tt(t57_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  ((k1_algseq_1 A (k7_polynom5 A B)) = (k1_algseq_1 A B)) ) ) ) ) ) ).
tt(t57_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_polynom1 A C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  ((r2_rewrite1 (k3_polyred A B C D) E F) => (r11_polyred (k11_polynom1 A C) (k7_ideal_1 (k11_polynom1 A C) D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k5_power A C) (k5_power A B))) ) ) ) ) ) ) ) ) ) ).
tt(t57_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( ((r3_pre_poly A B C) & (r6_pboole A (k12_pre_poly A C B) (k16_pre_poly A)))  => (r6_pboole A C B)) ) ) ) ) ) ).
tt(t57_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_prepower (k10_real_1 1 A) B) = (k10_real_1 1 (k6_prepower A B))) ) ) ) ) ) ).
tt(t57_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_3 C A B) => (r2_hidden (k5_prob_3 A C) B)) ) ) ) ) ).
tt(t57_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m2_subset_1 E (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A)) & (r2_hidden (k8_cqc_lang A D E) (k4_cqc_the1 A)))  => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B D) (k9_cqc_lang A C E)) (k4_cqc_the1 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k25_pscomp_1 A) (k24_pscomp_1 A)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k13_pscomp_1 A)))) ) ).
tt(t57_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((r6_pboole A B (k1_pboole A)) | (r6_pboole A C (k1_pboole A)))  => (r6_pboole A (k6_pboole A B C) (k1_pboole A))) ) ) ) ) ) ).
tt(t57_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( ((r2_qc_lang2 A B C) & (r2_qc_lang2 A C D))  => (r2_qc_lang2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t57_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k14_qc_lang1 A B C)) = (k4_subset_1 (k5_qc_lang1 A) (k5_qc_lang3 A B) (k5_qc_lang3 A C))) ) ) ) ) ) ) ).
tt(t57_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 (k28_quaterni A) (k28_quaterni B)) = (k18_quatern2 A B)) ) ) ) ) ).
tt(t57_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k29_quaterni A B) (k29_quaterni C D)) = (k26_quaterni (k29_quaterni (k29_quaterni (k27_quaterni A C) (k27_quaterni B C)) (k27_quaterni A D)) (k27_quaterni B D))) ) ) ) ) ) ) ) ) ).
tt(t57_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ( ((k31_quaterni (k27_quaterni A B)) = (k27_quaterni (k31_quaterni A) (k31_quaterni B)))  =>  ((k8_real_1 (k19_quaterni A) (k20_quaterni B)) = (k8_real_1 (k20_quaterni A) (k19_quaterni B))) ) ) ) ) ) ).
tt(t57_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (v3_quofield (k22_quofield A) A (k19_quofield A))) ) ).
tt(t57_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  => (r2_hidden A (k7_partfun1 (k9_setfam_1 k1_numbers) D 1))) ) ) ) ) ) ) ) ) ).
tt(t57_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( (C = (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1)))  &  (D = (k1_seq_1 (k6_real_3 B) A)) )  =>  ((k6_nat_d C D) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t57_relat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_relat_1 C) =>  ((r2_hidden A (k9_xtuple_0 (k5_relat_1 C B))) <=>  ((r2_hidden A B) & (r2_hidden A (k9_xtuple_0 C))) ) ) ) ) ) ).
tt(t57_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k7_relset_1 A B C A) = (k7_relset_1 B B (k7_relset_2 B A B (k3_relset_1 A B C) C) B)) ) ) ) ) ).
tt(t57_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_rewrite1 A) <=> (v9_rewrite1 (k18_finseq_1 A))) ) ) ).
tt(t57_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) => (r4_rewrite2 A B (k7_rewrite2 A B) C)) ) ) ) ) ).
tt(t57_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 D))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ((r1_rewrite3 E F A B C) <=> (m1_rewrite1 (k10_finseq_1 (k4_tarski A B) (k4_tarski C (k2_flang_1 D))) (k1_rewrite3 D E F))) ) ) ) ) ) ) ) ) ) ).
tt(t57_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 D A) =>  ((k1_funct_1 (k26_valued_1 A k1_numbers D C) B) = (k3_xcmplx_0 C (k1_funct_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(t57_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r1_tarski B (k1_relset_1 k1_numbers A)) => (r2_rfunct_3 (k26_valued_1 k1_numbers k1_numbers A k6_numbers) B)) ) ) ) ).
tt(t57_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  ((v2_comseq_2 (k3_rinfsup1 A)) &  ((k2_seq_2 (k3_rinfsup1 A)) = (k1_rinfsup1 (k3_rinfsup1 A))) ) ) ) ) ).
tt(t57_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k4_rlaffin1 A C)) =>  ((k4_rlaffin1 A C) = (k5_rusub_4 A (k3_rusub_4 A (k1_rlvect_3 A (k5_rusub_4 A C (k4_algstr_0 A B)))) B)) ) ) ) ) ) ) ) ).
tt(t57_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( ((r2_hidden B (k3_rlsub_1 A C D)) & (r2_hidden B (k3_rlsub_1 A (k4_algstr_0 A C) D)))  => (r1_struct_0 D C)) ) ) ) ) ) ) ) ) ).
tt(t57_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))))  &  ((v10_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) &  ((v15_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A))) & (l3_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ) ) ) ).
tt(t57_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_compts_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v4_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ((m1_connsp_2 D A (k4_struct_0 A)) =>  (~ (r1_xboole_0 (k7_rusub_4 A B D) (k7_rusub_4 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) (k4_struct_0 A) B)) = B)  &  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B (k4_struct_0 A))) = B) ) ) ) ) ) ).
tt(t57_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) => (r1_rlvect_2 A (k10_rlvect_2 A B B) (k4_rlvect_2 A))) ) ) ) ).
tt(t57_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r2_hidden (k3_rlvect_1 B C D) (k3_rmod_2 A B D E)) <=> (r1_struct_0 E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) => (r1_rmod_4 A B (k9_rmod_4 A B C C) (k3_rmod_4 A B))) ) ) ) ) ) ).
tt(t57_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k5_robbins1 A B C) = B) ) ) ) )  => (v6_robbins1 A)) ) ) ).
tt(t57_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_robbins1 A (k5_robbins1 A B C) D) = (k5_robbins1 A B (k5_robbins1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t57_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_roughs_1 A B) = (a_2_3_roughs_1 A B)) ) ) ) ) ).
tt(t57_rpr_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ((r1_xboole_0 B C) &  ((r1_rpr_1 A B C) &  ( (~  ((k1_rpr_1 A B) = k6_numbers) )  &  (~  ((k1_rpr_1 A C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k3_rusub_1 A D B)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 B E) &  (C = (k3_rlvect_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))))  &  ((v10_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) &  ((v15_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A))) & (l3_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ) ) ) ).
tt(t57_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k12_rvsum_1 (k6_rvsum_1 A)) = (k12_rvsum_1 A)) ) ) ).
tt(t57_scmfsa_2,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (~  (A = (k4_struct_0 k1_scmfsa_2)) ) ) ) ).
tt(t57_scmfsa8c,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r4_scmfsa7b (k1_scmfsa8a B) A)) ) ) ) ) ).
tt(t57_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B))) => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B) D) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k1_scmfsa_m B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t57_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  ( ((r1_xxreal_0 k6_numbers (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B))) =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k9_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k17_scmpds_2 A C)) )  &  ( ( (~ (r1_xxreal_0 k6_numbers (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A D) B))))  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k9_scmpds_2 D B C) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A))) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k9_scmpds_2 D B C) A) E) = (k1_funct_1 A E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 (k6_scmpds_6 A B C) k6_numbers) = (k7_scmpds_2 A B 2))  &  ((k1_funct_1 (k6_scmpds_6 A B C) 1) = (k3_scmpds_2 (k2_nat_1 (k5_card_1 C) 1))) ) ) ) ) ) ) ) ).
tt(t57_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ( (~  ((k1_scmyciel A) = k1_xboole_0) )  => (r1_xxreal_0 2 (k8_scmyciel A))) ) ) ).
tt(t57_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) => (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 B)) =>  ((r2_hidden A (k2_finseq_1 B)) => (r2_hidden (k1_funct_1 C A) k2_numbers)) ) ) ) ) ) ) ).
tt(t57_series_5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r1_xxreal_0 1 B) =>  ( ((k1_seq_1 A B) = (k7_square_1 (k4_nat_1 B (k2_nat_1 B 1))))  &  ((k1_seq_1 A k6_numbers) = k6_numbers) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_seq_1 (k3_series_1 A) B) (k13_complex1 (k4_nat_1 B (k2_nat_1 B 1)) 2))) ) ) ) ) ) ) ).
tt(t57_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k4_kurato_0 A B) = (k3_subset_1 A (k3_kurato_0 A (k2_prob_1 A B)))) ) ) ) ).
tt(t57_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k7_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A)) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k7_setlim_2 B D C)) A))) ) ) ) ) ) ) ).
tt(t57_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k5_finsub_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ((r2_hidden E (k10_setwiseo A B D C)) <=>  (? [F:$i] :  ((m1_subset_1 F A) &  ((r2_hidden F D) & (r2_hidden E (k3_funct_2 A (k5_finsub_1 B) C F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) ) )  =>  (~ (r2_hidden (k6_sf_mastr A) (k4_sf_mastr A))) ) ) ).
tt(t57_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A B C))))) = (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A B B)))) ) ) ) ) ) ) ) ) ).
tt(t57_simplex0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_simplex0 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((r1_tarski (k7_relat_1 D (u1_pre_topc C)) B) =>  ((k10_simplex0 A C (k6_relat_1 B D)) = (k10_simplex0 A C D)) ) ) ) ) ) ) ) ).
tt(t57_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 4)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 1 (k7_square_1 2)))) ).
tt(t57_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) = (k6_binop_2 (k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 A)) 1) 2)) ) ) ).
tt(t57_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v2_funct_1 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k7_real_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t57_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 1 (k3_square_1 A)))  &  ( (~ (r1_xxreal_0 1 (k3_square_1 B)))  &  (~  ((k10_binop_2 (k4_sin_cos7 A) (k4_sin_cos7 B)) = (k4_sin_cos7 (k12_binop_2 (k10_binop_2 A B) (k10_binop_2 1 (k11_binop_2 A B))))) ) ) ) ) ) ) ) ) ).
tt(t57_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k5_sin_cos9 A) = (k1_real_1 (k10_real_1 k32_sin_cos 4))) ) )  =>  (A = (k1_real_1 1)) ) ) ) ).
tt(t57_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k3_xcmplx_0 A (k11_comseq_3 (k27_sin_cos A))) = (k6_xcmplx_0 (k11_complex1 (k11_comseq_3 (k3_sin_cos A)) k6_complex1) A)) ) ) ).
tt(t57_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v5_topreal1 A) => (v2_compts_1 A (k15_euclid 2))) ) ) ).
tt(t57_sprect_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 (k17_euclid A) (k17_euclid B)) =>  ((k8_pscomp_1 (k1_rltopsp1 (k15_euclid 2) A B)) = (k17_euclid B)) ) ) ) ) ) ).
tt(t57_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~ (r1_xxreal_0 (k18_euclid (k19_pscomp_1 (k3_topreal1 2 A))) (k18_euclid (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ).
tt(t57_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t57_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k3_xcmplx_0 B (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 A)))) (k3_xcmplx_0 A (k6_square_1 (k2_xcmplx_0 1 (k3_square_1 B)))))) ) ) ) ) ).
tt(t57_stirl2_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( ((v1_xboole_0 B) => (v1_xboole_0 A))  &  ( (~ (r2_hidden C A))  &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D)))))) )  =>  (~  ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D)) F A) = E)  &  ((k1_funct_1 F C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k2_qc_lang1 A)) =>  ((r1_tarski (k2_relset_1 (k2_qc_lang1 A) B) (k3_qc_lang1 A)) =>  ((k23_qc_lang1 A B) = (k2_relset_1 (k2_qc_lang1 A) B)) ) ) ) ) ) ).
tt(t57_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (r1_tarski C (k2_pre_topc A (k1_tops_1 A C)))) ) )  =>  ((r1_tarski (k5_setfam_1 (u1_struct_0 A) B) (k2_pre_topc A (k1_tops_1 A (k5_setfam_1 (u1_struct_0 A) B)))) &  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ).
tt(t57_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_2 B A) =>  ((k3_tarski (a_2_0_tex_2 A B)) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t57_tex_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ((v1_tex_2 B A) & (m1_pre_topc B A))  =>  (~ (v2_tex_3 B A)) ) )  => (v3_tdlat_3 A)) ) ) ).
tt(t57_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_tex_4 A (k1_tops_1 A B)) = (k1_tops_1 A B)) ) ) ) ) ).
tt(t57_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 A))))) )  =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  & (r2_funct_2 (u1_struct_0 C) (u1_struct_0 A) (k2_tmap_1 B A E C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t57_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) => (r2_group_6 (k5_topalg_1 A B) (k5_topalg_1 A C))) ) ) ) ) ) ) ).
tt(t57_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ((v5_waybel23 A) &  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_cantor_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (~ (v4_card_3 B)) ) ) ) ) ) ) ).
tt(t57_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v4_pre_topc (k3_rcomp_1 A B) k2_topgen_3) & (m1_subset_1 (k3_rcomp_1 A B) (k1_zfmisc_1 (u1_struct_0 k2_topgen_3)))) ) ) ) ) ).
tt(t57_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v1_tops_1 (k4_group_2 A C B) A)) ) ) ) ) ) ).
tt(t57_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( (D = (k10_metric_1 A B C))  => (v4_pre_topc D (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(t57_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (D = E) )  &  ((r2_hidden D (k7_jgraph_6 A B C)) &  ((r2_hidden E (k7_jgraph_6 A B C)) & (r1_xxreal_0 C k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (v5_pre_topc (k17_toprealc B A) (k15_euclid B) k3_topmetr)) ) ) ) ) ).
tt(t57_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  ((v3_tops_1 B A) <=>  (B = (k2_tops_1 A B)) ) ) ) ) ) ) ).
tt(t57_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v3_tops_2 D A B) & (v3_tops_2 E B C))  => (v3_tops_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C A) &  ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  (D = E) ) ) )  =>  ((k1_tops_1 A D) = (k1_tops_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 F (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo F A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F B) = B)  & (r1_diraf A C B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F C))) )  =>  ( (C = B)  |  ((r3_diraf A B D E) | (r2_analoaf A D E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_trees_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v4_trees_3 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v4_trees_3 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_trees_1 D))  =>  ((k11_trees_3 (k7_finseq_1 (k7_finseq_1 A (k9_finseq_1 C)) B)) = (k5_trees_1 (k11_trees_3 (k7_finseq_1 (k7_finseq_1 A (k9_finseq_1 D)) B)) (k12_finseq_1 k5_numbers (k3_finseq_1 A)) C)) ) ) ) ) ) ) ) ) ).
tt(t57_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  &  ((r2_tsep_1 A B C) &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_pre_topc D A) &  ((v4_pre_topc E A) &  ((r1_tarski D B) &  ((r1_tarski E C) &  (~  ( (~  ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) D E)) )  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((r1_tarski F (k9_subset_1 (u1_struct_0 A) B C)) & (v3_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((v1_int_1 C) =>  ((r1_nat_d B A) =>  ((r1_xxreal_0 A B) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ( (D = C)  =>  (! [E:$i] :  ((v1_int_1 E) =>  (! [F:$i] :  ((v1_int_1 F) =>  (! [G:$i] :  ((v1_int_1 G) =>  ( ( (E = (k2_polynom4 k1_complfld (k5_uniroots A) D))  &  ( (F = (k2_polynom4 k1_complfld (k4_uniroots A k1_complfld) D))  &  (G = (k2_polynom4 k1_complfld (k4_uniroots B k1_complfld) D)) ) )  => (r1_int_1 E (k5_int_1 F G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ((k1_algseq_1 A B) = 1)  =>  ((k4_uproots (u1_struct_0 A) (k8_uproots A B)) = k6_numbers) ) ) ) ) ) ).
tt(t57_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((k48_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k48_valued_2 A B E C) D) = (k48_valued_2 A B E (k3_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ).
tt(t57_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden (k4_vectsp_1 A B C D) (k3_vectsp_4 A B D E)) =>  ( (C = (k1_group_1 A))  | (r1_struct_0 E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ).
tt(t57_vfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v5_rlvect_1 D) &  ((v6_rlvect_1 D) &  ((v7_rlvect_1 D) &  ((v8_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_normsp_1 D) & (l1_normsp_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 C (u1_struct_0 D)))))  =>  ( ((r1_vfunct_1 C D E A) & (v3_funct_1 (k2_partfun1 C (u1_struct_0 D) F B)))  =>  ((r1_vfunct_1 C D (k2_vfunct_1 C D E F) (k3_xboole_0 A B)) & (r1_vfunct_1 C D (k2_vfunct_1 C D F E) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  (! [F:$i] :  ( ((r1_vfunct_2 A B C E) & (v3_funct_1 (k2_partfun1 A (u1_struct_0 B) D F)))  =>  ((r1_vfunct_2 A B (k2_vfunct_1 A B C D) (k3_xboole_0 E F)) & (r1_vfunct_2 A B (k2_vfunct_1 A B D C) (k3_xboole_0 E F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r2_yellow_0 A E) &  (D = (k2_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k2_yellow_0 A D) C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_lattice3 A B D) <=> (r1_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ).
tt(t57_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v3_waybel_1 (k1_waybel_1 A (k2_yellow_1 (k7_waybel_0 A)) (k3_yellow_2 A) (k2_yellow_2 A)) A (k2_yellow_1 (k7_waybel_0 A))) & (v18_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ).
tt(t57_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  (! [C:$i] :  ((r2_hidden C (k2_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B)))) (k5_waybel23 A B))) =>  ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C (k5_yellow_0 A B)) &  ((v12_waybel_0 C (k5_yellow_0 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_yellow_0 A B))))) ) ) ) ) ) ) ) ) ).
tt(t57_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v18_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ( ((v2_waybel_8 B) & (v3_waybel34 C B A))  => (v1_waybel34 C B A)) ) ) ) ) ) ) ).
tt(t57_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ((v8_waybel_4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_waybel_4 (k5_waybel_4 A C B) D B)) )  => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C C) B)) ) ) ) ) ) ) ) ).
tt(t57_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_xboole_0 A B) & (r2_xboole_0 B A)) ) ) ) ).
tt(t57_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A (k8_xboolean A B)) = (k6_xboolean A B)) ) ) ) ) ).
tt(t57_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_xcmplx_0 1 (k7_xcmplx_0 A B)) = (k7_xcmplx_0 B A)) ) ) ) ) ).
tt(t57_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k6_xcmplx_0 A C) B)) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t57_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k3_xxreal_1 A B) (k2_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) &  (~ (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  ((v4_xxreal_2 A) =>  ( (A = (k1_tarski k2_xxreal_0))  | (r2_hidden (k1_xxreal_2 A) k1_numbers)) ) ) ) ).
tt(t57_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((r1_xxreal_0 A (k3_xxreal_3 C B)) =>  ( ( (A = k1_xxreal_0)  &  (B = k2_xxreal_0) )  |  ( ( (A = k2_xxreal_0)  &  (B = k1_xxreal_0) )  |  ( ( (B = k1_xxreal_0)  &  (C = k1_xxreal_0) )  |  ( (~  (B = k1_xxreal_0) )  & (r1_xxreal_0 (k1_xxreal_3 A B) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ( ((v4_yellow_0 C A) & (m1_yellow_0 C A))  =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C))) ) ) ) ) ) ) ) ).
tt(t57_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v13_waybel_0 D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((v1_waybel11 C A) & (v1_waybel11 D B))  => (v1_waybel11 (k12_yellow_3 A B C D) (k3_yellow_3 A B))) ) ) ) ) ) ) ) ) ).
tt(t57_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ((r1_waybel18 A B) <=>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C B))  &  ((r1_borsuk_1 B C) & (r1_t_0topsp C A)) ) ) ) ) ) ) ) ).
tt(t57_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v16_functor0 C A B) & (m2_functor0 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_altcat_1 D) &  ((v3_altcat_2 D A) & (m1_altcat_2 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_altcat_1 E) &  ((v3_altcat_2 E B) & (m1_altcat_2 E B)) ) )  =>  ( ((v21_functor0 C A B) &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((m1_subset_1 F (u1_struct_0 D)) <=> (m1_subset_1 (k3_functor0 A B C F) (u1_struct_0 E))) ) )  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( (~  ((k1_altcat_1 A F G) = k1_xboole_0) )  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  ( ( (H = F)  &  (I = G) )  =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 E)) =>  (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 E)) =>  ( ( (J = (k3_functor0 A B C F))  &  (K = (k3_functor0 A B C G)) )  =>  (! [L:$i] :  ((m1_subset_1 L (k1_altcat_1 A F G)) =>  ((r2_hidden L (k1_altcat_1 D H I)) <=> (r2_hidden (k8_functor0 A B C F G L) (k1_altcat_1 E K J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  => (r3_yellow20 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t57_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k2_yellow_0 A (k4_yellow_4 A B C)) = (k12_lattice3 A (k2_yellow_0 A B) (k2_yellow_0 A C))) ) ) ) ) ) ) ).
tt(t57_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k13_lattice3 A C D)) = (k12_lattice3 A (k1_yellow_5 A B C) (k1_yellow_5 A B D))) ) ) ) ) ) ) ) ) ).
tt(t57_yellow_9,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((l1_pre_topc B) =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  ((m2_yellow_9 C A) & (m2_yellow_9 C B)) ) ) ) ) ) ) ) ).
tt(t57_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k29_zf_lang (k12_zf_lang A B)) = (k2_xboole_0 (k2_xboole_0 (k29_zf_lang A) (k29_zf_lang B)) (k5_enumset1 (k6_zf_lang B) (k7_zf_lang A (k6_zf_lang B)) (k11_zf_lang A B) (k6_zf_lang A) (k7_zf_lang B (k6_zf_lang A)) (k11_zf_lang B A) (k12_zf_lang A B)))) ) ) ) ) ).
tt(t57_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v5_zf_lang A) =>  ((r1_zf_lang B A) <=>  ( (B = (k21_zf_lang A))  |  (B = (k22_zf_lang A)) ) ) ) ) ) ) ) ).
tt(t57_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 A (k1_tarski B)) = A)  <=>  (~ (r2_hidden B A)) ) ) ) ).
tt(t57_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r2_hidden (k4_struct_0 A) (k5_zmodul01 A B C)) <=> (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t58_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r5_abcmiz_0 A B (k6_finseq_1 (u1_abcmiz_0 A)))) ) ) ) ).
tt(t58_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A))))) =>  (~  ( ((k1_funct_1 B k1_xboole_0) = (k4_tarski k9_abcmiz_1 (u1_struct_0 A)))  &  (! [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) =>  (! [D:$i] :  ((m1_abcmiz_1 D A (k12_abcmiz_1 A)) =>  (~  (B = (k31_abcmiz_1 A (k33_abcmiz_1 A) C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_abcmiz_a,ax, (! [A:$i] :  ((m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k27_abcmiz_1)) =>  (! [C:$i] :  ( ((v2_abcmiz_1 C k27_abcmiz_1) & (m2_abcmiz_1 C k27_abcmiz_1 B))  =>  ( ((k3_finseq_1 (k1_msualg_1 k27_abcmiz_1 C)) = (k3_finseq_1 A))  =>  ((k45_abcmiz_1 k27_abcmiz_1 (k36_abcmiz_1 k27_abcmiz_1 C (k16_abcmiz_a A))) = (k2_relset_1 k2_abcmiz_1 A)) ) ) ) ) ) ) ) ).
tt(t58_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ( (~ (r5_aff_1 A B C))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) &  ((v1_aff_4 C A) & (r1_aff_4 A B C)) )  => (r1_aff_4 A C B)) ) ) ) ) ) ) ).
tt(t58_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  ((r1_xxreal_0 A (k2_afinsq_1 B)) =>  ((k5_relat_1 (k1_ordinal4 B C) A) = (k5_relat_1 B A)) ) ) ) ) ) ) ) ).
tt(t58_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k7_afinsq_2 (k7_funcop_1 A B)) = (k5_binop_2 A B)) ) ) ) ) ).
tt(t58_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C B) =>  ((m4_algspec1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ((v1_funct_1 (k1_funct_1 (u4_msualg_1 B C) D)) &  ((v1_funct_2 (k1_funct_1 (u4_msualg_1 B C) D) (k1_funct_1 (k6_finseq_2 (u1_struct_0 B) (u3_msualg_1 B C)) (k1_msualg_1 A D)) (k1_funct_1 (u3_msualg_1 B C) (k2_msualg_1 A D))) & (m1_subset_1 (k1_funct_1 (u4_msualg_1 B C) D) (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_1 (k6_finseq_2 (u1_struct_0 B) (u3_msualg_1 B C)) (k1_msualg_1 A D)) (k1_funct_1 (u3_msualg_1 B C) (k2_msualg_1 A D)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k5_altcat_4 (k3_altcat_4 A)) = (k5_altcat_4 A)) ) ) ).
tt(t58_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r4_analmetr A B C D D) &  ((r4_analmetr A D D B C) &  ((r2_analoaf A B C D D) & (r2_analoaf A D D B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ((m1_subset_1 (k4_trees_4 1 B) (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t58_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  &  ( ((k1_funct_1 I F) = 1)  &  ( ((k1_funct_1 I G) = 2)  &  ( ((k1_funct_1 I H) = 3)  &  ((k1_funct_1 I C) = 4) ) ) ) ) )  => (r5_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H 1) (k74_aofa_i00 A B C D H F) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H 1))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ( ((k14_armstrng A B) = (k14_armstrng A C))  => (r2_relset_1 (k9_setfam_1 A) (k9_setfam_1 A) (k12_armstrng A B) (k12_armstrng A C))) ) ) ) ) ) ) ).
tt(t58_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 A k5_arytm_3))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B k5_arytm_3))  =>  ((k9_arytm_3 A B) = (k8_ordinal3 A B)) ) ) ) ) ).
tt(t58_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 A (k2_int_1 (k10_real_1 A 2)))) ) ) ) ).
tt(t58_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B E) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A (k1_bcialg_1 A C E) (k1_bcialg_1 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (D = k6_numbers)  =>  ( (A = k6_numbers)  |  ((v8_bcialg_1 E) & (m1_bcialg_5 E k6_numbers k6_numbers k6_numbers k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_bcialg_1 B A) =>  (! [C:$i] :  ( ((v12_bcialg_1 C A) & (m2_bcialg_1 C A))  =>  (! [D:$i] :  ((m5_bcialg_2 D A C) =>  (! [E:$i] :  ((m2_bcialg_1 E (k10_bcialg_6 A B C D)) =>  (! [F:$i] :  ((m5_bcialg_2 F (k10_bcialg_6 A B C D) E) =>  (! [G:$i] :  ((m2_bcialg_1 G B) =>  (! [H:$i] :  ((m5_bcialg_2 H B G) =>  ( ( (F = D)  &  (G = (k9_subset_1 (u1_struct_0 A) (u1_struct_0 B) C)) )  => (r1_bcialg_6 (k9_bcialg_2 B H) (k9_bcialg_2 (k10_bcialg_6 A B C D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k4_normsp_1 A B (k4_struct_0 A)))) ) ) ) ).
tt(t58_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v1_bilinear C A B B) &  ((v2_bilinear C A B B) &  ((v8_bilinear C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C D E) = (k4_algstr_0 A (k2_binop_1 (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) C E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r4_boolealg A (k4_lattices A B C) (k3_boolealg A B C))) ) ) ) ) ) ) ).
tt(t58_borsuk_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A k5_topmetr) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k5_topmetr)))) )  =>  (~  ((r1_tarski A (k2_rcomp_1 k6_numbers 1)) &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k5_topmetr)) =>  (~  ((r1_xxreal_0 B C) &  ((r1_tarski A (k1_rcomp_1 B C)) & (r1_tarski (k1_rcomp_1 B C) (k2_rcomp_1 k6_numbers 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k6_subset_1 k1_numbers (k2_borsuk_5 A B)) = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 A) (k3_borsuk_5 A B)) (k3_rcomp_1 B k1_xxreal_0))) ) ) ) ) ).
tt(t58_borsuk_6,ax, ((k9_subset_1 (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr)) k8_borsuk_6 k7_borsuk_6) = a_0_16_borsuk_6) ).
tt(t58_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden C (k3_topreal9 2 (k4_struct_0 (k15_euclid 2)) A)) <=> (r2_hidden (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 B) C) (k3_topreal9 2 (k4_struct_0 (k15_euclid 2)) A))) ) ) ) ) ) ) ).
tt(t58_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t58_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A G B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) H) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k7_xboolean A A) = k8_margrel1)  &  ((k3_xboolean (k7_xboolean A A)) = k7_margrel1) ) ) ) ).
tt(t58_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k5_bvfunc26 A B C)) (k5_bvfunc_1 A (k1_bvfunc_1 A B) C))) ) ) ) ) ) ).
tt(t58_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( (? [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k4_substut2 A B C E))))) )  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k12_cqc_lang A C B))))) ) ) ) ) ) ) ) ) ).
tt(t58_card_1,ax, (10 = (k8_enumset1 k1_xboole_0 1 2 3 4 5 6 7 8 9)) ).
tt(t58_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (B = C) )  &  (~  ((k5_card_1 (k1_enumset1 A B C)) = 3) ) ) ) ) ) ) ) ) ).
tt(t58_card_3,ax, (! [A:$i] :  (! [B:$i] :  ((k4_partfun1 A B) = (k8_card_3 (k7_funcop_1 A B))) ) ) ).
tt(t58_card_fin,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v2_finset_1 A)) )  =>  (! [B:$i] :  ((v1_finset_1 B) =>  ( ((k9_xtuple_0 A) = B)  =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers C) = (k5_card_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden D (k1_relset_1 k5_numbers C)) &  (! [E:$i] :  (! [F:$i] :  (~  ( (~  (E = F) )  &  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  ((r2_hidden G (k1_card_fin B (k23_binop_2 D 1) E F)) =>  ((k1_card_1 (k2_card_fin A G E)) = (k1_recdef_1 C D)) ) ) ) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v5_relat_1 D k4_numbers) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers D) = (k5_card_1 B))  &  ( ((k1_card_1 (k3_tarski (k10_xtuple_0 A))) = (k7_afinsq_2 D))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 D E) = (k22_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) E) (k1_recdef_1 C E)) (k6_newton (k23_binop_2 E 1) (k5_card_1 B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k4_cat_1 A B)) = B)  &  ((k4_graph_1 A (k4_cat_1 A B)) = B) ) ) ) ) ) ).
tt(t58_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((r2_cat_3 A B C D) &  ((r2_hidden E (k2_cat_1 A B B)) &  ( ((k1_cat_1 A E C) = C)  &  ((k1_cat_1 A E D) = D) ) ) )  =>  (E = (k4_cat_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k24_cat_4 A B)) = (k19_cat_4 A))  &  ((k4_graph_1 A (k24_cat_4 A B)) = B) ) ) ) ) ) ).
tt(t58_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k2_valued_1 A k2_numbers k2_numbers B C) A))  &  ( ((v1_partfun1 (k2_valued_1 A k2_numbers k2_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) )  &  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k46_valued_1 A k2_numbers k2_numbers B C) A))  &  ( ((v1_partfun1 (k46_valued_1 A k2_numbers k2_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) )  &  ( ( ((v1_partfun1 B A) & (v1_partfun1 C A))  => (v1_partfun1 (k19_valued_1 A k2_numbers k2_numbers B C) A))  &  ((v1_partfun1 (k19_valued_1 A k2_numbers k2_numbers B C) A) =>  ((v1_partfun1 B A) & (v1_partfun1 C A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k4_chain_1 A B A))) =>  ((k3_subset_1 (k4_chain_1 A B A) C) = (k7_chain_1 A B A C (k6_chain_1 A B))) ) ) ) ) ) ) ).
tt(t58_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ( ((r2_hidden D B) & (r1_tarski (k2_chord A (k6_domain_1 (k6_glib_000 A) D)) B))  =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 C)) =>  ( (D = E)  =>  ((k2_chord A (k6_domain_1 (k6_glib_000 A) D)) = (k2_chord C (k6_domain_1 (k6_glib_000 C) E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  ((v6_circcomb B A) <=> (r1_tarski (k10_xtuple_0 (u3_msualg_1 A B)) (k1_tarski k6_margrel1))) ) ) ) ) ).
tt(t58_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r8_circtrm1 A B C D E F) => (r7_circtrm1 A B C D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k5_classes1 A) (k5_classes1 B))) ) ) ).
tt(t58_classes2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden A C) & (r2_hidden B C))  =>  ((r2_hidden (k2_tarski A B) C) & (r2_hidden (k4_tarski A B) C)) ) ) ) ) ) ).
tt(t58_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) => (m1_clvect_1 (k3_clvect_1 A) B)) ) ) ) ).
tt(t58_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  (? [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 D F) & (r1_xxreal_0 C (k13_csspace A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v10_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  ((k11_cohsp_1 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t58_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k9_real_1 (k17_complex1 A) (k17_complex1 B)) (k17_complex1 (k2_xcmplx_0 A B)))) ) ) ) ).
tt(t58_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_complex2 (k10_complex1 A) B) = (k10_complex1 (k2_complex2 A B))) ) ) ) ) ).
tt(t58_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( ((k17_complex1 A) = k6_numbers)  =>  (A = (k4_struct_0 k1_complfld)) ) ) ) ).
tt(t58_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  ( ((k6_complsp2 (k12_seq_4 A k7_complex1)) = (k6_rvsum_1 (k7_complsp2 A)))  &  ((k7_complsp2 (k12_seq_4 A k7_complex1)) = (k6_complsp2 A)) ) ) ) ).
tt(t58_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k1_funct_1 (k11_compos_1 A B) k6_numbers) = B) ) ) ) ) ).
tt(t58_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) 4) = (k5_compos_0 (u1_compos_1 A) F 4)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_comptrig,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_comptrig B A 1) =>  (B = A) ) ) ) ) ).
tt(t58_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers)) =>  ((r2_hidden A (k4_finseq_1 D)) =>  ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 B) 1) D A k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 B C A))) <=> (r2_hidden (k2_finseq_3 A D) (k1_relset_1 (k3_finseq_2 k5_numbers) B))) ) ) ) ) ) ) ) ) ) ).
tt(t58_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (v1_comseq_3 (k1_valued_0 k2_numbers A B))) ) ) ) ) ).
tt(t58_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  => (v2_convex4 (k17_convex4 A (k18_convex4 A)) A)) ) ).
tt(t58_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((r2_hidden (k13_cqc_lang A C D) (k3_cqc_lang A)) & (r3_cqc_the1 A B (k13_cqc_lang A C E)))  =>  ((r2_hidden E (k24_qc_lang1 A C)) | (r3_cqc_the1 A B (k13_cqc_lang A C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden F (k24_qc_lang1 A D)) | (v2_cqc_the1 (k2_qc_lang2 A (k12_cqc_lang A E B) (k7_qc_lang2 A E F C)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r7_cqc_the3 A B C) => (r7_cqc_the3 A (k11_cqc_lang A D B) (k11_cqc_lang A D C))) ) ) ) ) ) ) ) ) ).
tt(t58_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k15_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) = (k15_csspace A B D)) ) ) ) ) ) ) ) ) ).
tt(t58_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 (k7_real_1 B A))) (k21_sin_cos (k8_real_1 2 B))))) ) ) ) ) ).
tt(t58_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k8_real_1 3 (k18_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2))) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k18_sin_cos (k10_real_1 (k8_real_1 3 (k7_real_1 (k8_real_1 2 B) A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2))))))) ) ) ) ) ).
tt(t58_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A)) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k9_real_1 A B)) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k9_real_1 A B))) 2)))) ) ) ) ) ) ).
tt(t58_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  (! [F:$i] :  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  ( (E = (a_4_0_ec_pf_1 A B C D))  &  ( (~  (E = k1_xboole_0) )  &  ( (F = (a_4_1_ec_pf_1 A B C D))  &  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G E F) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 E F)))) )  =>  (~  ((v2_funct_2 G F) & (v2_funct_1 G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m2_subset_1 G (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [H:$i] :  ((m2_subset_1 H (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (E = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  ( (F = (k5_algstr_0 (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k2_binom (k9_int_3 A) E 3)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) E 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))))  &  (I = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) E F) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) D (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) F)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 3) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)))) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) E 2) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) G) 2)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) H)) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I) 2) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I) 3) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I)) (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I) 2))) (k8_group_1 (k9_int_3 A) (k3_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) I) 3))))) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  ((r1_tarski (k16_ens_1 B) A) => (m2_cat_1 (k22_ens_1 B) (k8_cat_2 (k2_oppcat_1 B) B) (k11_ens_1 A))) ) ) ) ) ).
tt(t58_entropy1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) & (r1_xxreal_0 (k1_seq_1 A B) k6_numbers)) ) ) )  =>  ((r1_xxreal_0 (k6_entropy1 A) (k6_power 2 (k3_finseq_1 A))) &  ( ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k1_seq_1 A B) = (k10_real_1 1 (k3_finseq_1 A))) ) ) )  =>  ((k6_entropy1 A) = (k6_power 2 (k3_finseq_1 A))) )  &  ( ( ((k6_entropy1 A) = (k6_power 2 (k3_finseq_1 A)))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ((k1_seq_1 A B) = (k10_real_1 1 (k3_finseq_1 A))) ) ) ) )  &  ( (~  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  ((r2_hidden B (k4_finseq_1 A)) &  (~  ((k1_seq_1 A B) = (k10_real_1 1 (k3_finseq_1 A))) ) ) ) )  & (r1_xxreal_0 (k6_power 2 (k3_finseq_1 A)) (k6_entropy1 A))) )  &  (~  ( (~ (r1_xxreal_0 (k6_power 2 (k3_finseq_1 A)) (k6_entropy1 A)))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((r2_hidden B (k4_finseq_1 A)) &  (~  ((k1_seq_1 A B) = (k10_real_1 1 (k3_finseq_1 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k1_enumset1 B A C)) ) ) ) ).
tt(t58_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ((k2_binop_1 A C (k2_zfmisc_1 B C) (k16_funct_3 A C B C D (k6_partfun1 C)) E F) = (k1_domain_1 B C (k3_funct_2 A B D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_euclid_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) => (r1_rvsum_1 B C)) )  =>  (B = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ).
tt(t58_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) =>  ((r2_hidden D (k7_euclid_3 2 A B C)) <=>  ( (~ (r1_xxreal_0 (k10_euclid_3 2 A B C D) k6_numbers))  &  ( (~ (r1_xxreal_0 (k11_euclid_3 2 A B C D) k6_numbers))  &  (~ (r1_xxreal_0 (k12_euclid_3 2 A B C D) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_euclid 3 A B) = (k1_euclid_8 (k11_binop_2 B (k1_seq_1 A 1)) (k11_binop_2 B (k1_seq_1 A 2)) (k11_binop_2 B (k1_seq_1 A 3)))) ) ) ) ) ).
tt(t58_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k1_rlvect_1 (k15_euclid 2) (k19_euclid B C) A) = (k19_euclid (k11_binop_2 A B) (k11_binop_2 A C))) ) ) ) ) ) ) ).
tt(t58_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) => (r1_xxreal_0 k6_numbers (k3_euclidlp A B C))) ) ) ) ) ) ).
tt(t58_exchsort,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v3_orders_2 D) &  ((v4_orders_2 D) &  ((v5_orders_2 D) &  ((v16_waybel_0 D) & (l1_orders_2 D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_relat_1 E (u1_struct_0 D)) &  ((v1_funct_1 E) & (v1_exchsort E)) ) )  =>  ((r2_hidden (k4_tarski A B) (k6_exchsort D E)) =>  ( ((r2_hidden B C) & (r2_hidden (k4_tarski A C) (k6_exchsort D E)))  <=> (r2_hidden (k4_tarski B C) (k6_exchsort D (k10_funct_7 E A B)))) ) ) ) ) ) ) ) ) ).
tt(t58_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  => (v1_relat_1 (k3_msafree2 (k8_facirc_1 A B C D)))) ) ) ) ) ).
tt(t58_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k16_sin_cos) A) B) = (k10_real_1 (k8_real_1 2 (k1_seq_1 k19_sin_cos (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t58_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_xboole_0 (k5_relat_1 k2_fib_num2 (k3_xboole_0 k3_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 2)))) (k1_tarski (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 A) 4) (k3_funct_2 k5_numbers k5_numbers k2_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 4))))) = (k5_relat_1 k2_fib_num2 (k3_xboole_0 k3_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 4))))) ) ) ).
tt(t58_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  => (v15_lattices (k6_filter_0 A (k2_filter_0 A B)))) ) ) ) ) ).
tt(t58_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden (k7_filter_0 A C D) B) & (r2_hidden (k7_filter_0 A E F) B))  =>  ((r2_hidden (k7_filter_0 A (k3_lattices A C E) (k3_lattices A D F)) B) & (r2_hidden (k7_filter_0 A (k4_lattices A C E) (k4_lattices A D F)) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v18_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_filter_2 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) <=>  (~ (r2_hidden (k7_lattices A C) B)) ) ) ) ) ) ) ) ) ).
tt(t58_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) =>  ((k16_finseq_1 A B) = B) ) ) ) ) ) ).
tt(t58_finseq_2,ax, (! [A:$i] :  ((k2_finseq_2 k6_numbers A) = k1_xboole_0) ) ).
tt(t58_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] : (r1_tarski (k8_relat_1 A C) (k8_relat_1 (k7_finseq_1 A B) C))) ) ) ) ) ).
tt(t58_finseq_4,ax, (! [A:$i] :  (~  ((v1_finset_1 A) &  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (~  ( ((k10_xtuple_0 B) = A)  & (v2_funct_1 B)) ) ) ) ) ) ) ).
tt(t58_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden A (k4_finseq_1 B)) =>  ((k1_funct_1 (k3_finseq_5 B) A) = (k1_funct_1 B (k2_xcmplx_0 (k6_xcmplx_0 (k3_finseq_1 B) A) 1))) ) ) ) ) ) ).
tt(t58_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ((r2_hidden B (k4_finseq_1 D)) =>  ((r1_xxreal_0 B A) | (r2_hidden (k7_partfun1 C D B) (k10_xtuple_0 (k2_rfinseq C A D)))) ) ) ) ) ) ) ) ) ) ).
tt(t58_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v1_setwiseo D A) => (r2_relset_1 k5_numbers A (k2_finseqop A A A D C (k4_binop_1 A D)) C)) ) ) ) ) ) ) ) ) ).
tt(t58_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_fintopo6 A C)))) =>  ( ((r3_fintopo6 A B C D E) &  ((v3_orders_2 A) &  ((v1_fin_topo A) &  (F = (k6_domain_1 (u1_struct_0 A) D)) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) G))  =>  ((r2_hidden (k1_funct_1 B (k2_nat_1 G 1)) (k7_fintopo3 (k1_fintopo6 A C) F G)) &  (~  ((r1_xxreal_0 1 G) & (r2_hidden (k1_funct_1 B (k2_nat_1 G 1)) (k7_fintopo3 (k1_fintopo6 A C) F (k7_nat_d G 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k6_flang_1 A (k7_flang_1 A B C) (k8_flang_1 A B)) = (k6_flang_1 A (k8_flang_1 A B) (k7_flang_1 A B C))) ) ) ) ) ) ).
tt(t58_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ((v7_ordinal1 H) =>  ( ((r1_xxreal_0 E F) &  ((r1_xxreal_0 G H) &  ((r1_tarski B (k1_flang_2 A C E F)) & (r1_tarski D (k1_flang_2 A C G H))) ) )  => (r1_tarski (k6_flang_1 A B D) (k1_flang_2 A C (k2_xcmplx_0 E G) (k2_xcmplx_0 F H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B C) => (r1_tarski (k2_flang_3 A B) (k2_flang_3 A C))) ) ) ) ) ) ).
tt(t58_fomodel0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (r2_hidden A (k10_xtuple_0 B)))  => (r1_xboole_0 (k2_zfmisc_1 C (k1_tarski A)) B)) ) ) ) ).
tt(t58_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v5_fsm_1 E A B) &  ((v7_fsm_1 E A B) & (l2_fsm_1 E A B)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (~  ( (H = F)  &  ( (I = G)  &  ( (C = (k13_fsm_1 A B E D))  &  ( (~ (r5_fsm_1 A B D H I))  & (r5_fsm_1 A B C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k2_zfmisc_1 B C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) )  => (r2_relset_1 C B (k11_funcop_1 A C B (k12_funcop_1 A B C D)) (k3_relset_1 B C (k11_funcop_1 A B C D)))) ) ) ) ) ) ) ) ).
tt(t58_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v2_funct_1 B) => (v2_funct_1 (k6_relat_1 A B))) ) ) ) ).
tt(t58_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((v2_funct_1 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden C A) &  ((r2_hidden D A) &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t58_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (~  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  ( ( (C = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  (~  ((v1_funct_1 (k13_funct_3 D E)) &  ((v1_funct_2 (k13_funct_3 D E) A (k2_zfmisc_1 B C)) & (m1_subset_1 (k13_funct_3 D E) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (! [F:$i] :  ( ((v1_relat_1 F) & (v1_funct_1 F))  =>  ( ( ((k9_xtuple_0 E) = (k2_zfmisc_1 A B))  &  ((k9_xtuple_0 F) = (k2_zfmisc_1 C D)) )  =>  ((k9_xtuple_0 (k3_funct_4 E F)) = (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D))) ) ) ) ) ) ) ) ) ) ).
tt(t58_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 A (k1_funct_2 (k1_tarski B) A)) &  ((k1_card_1 A) = (k1_card_1 (k1_funct_2 (k1_tarski B) A))) ) ) ) ).
tt(t58_funct_6,ax, ((k10_funct_6 k1_xboole_0) = k1_xboole_0) ).
tt(t58_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ((k6_funct_7 (k7_finseq_1 (k9_finseq_1 A) B)) = (k9_xtuple_0 A))  &  ((k7_funct_7 (k7_finseq_1 B (k9_finseq_1 A))) = (k10_xtuple_0 A)) ) ) ) ) ) ).
tt(t58_funct_8,ax, ((k3_funct_2 k1_numbers k1_numbers k1_funct_8 k6_numbers) = k6_numbers) ).
tt(t58_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_fvaluat1 A B))) =>  ( (C = D)  =>  ((k4_algstr_0 A C) = (k4_algstr_0 (k7_fvaluat1 A B) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B C (k4_struct_0 B)) = (k5_finseq_2 (u1_struct_0 B) A (k4_struct_0 B))) ) ) ) ) ) ) ).
tt(t58_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  =>  ((r2_hidden A (k2_msafree2 (k22_gfacirc1 A B C))) &  ((r2_hidden B (k2_msafree2 (k22_gfacirc1 A B C))) & (r2_hidden C (k2_msafree2 (k22_gfacirc1 A B C)))) ) ) ) ) ) ).
tt(t58_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k27_glib_000 A C)) <=>  ((r2_hidden B (k7_glib_000 A)) &  ((k1_funct_1 (k10_glib_000 A) B) = C) ) ) ) ) ) ) ) ).
tt(t58_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k3_glib_001 A B) = (k1_funct_1 B C))  => (r2_relset_1 k5_numbers (k2_xboole_0 (k6_glib_000 A) (k7_glib_000 A)) (k20_glib_001 A B 1 C) (k8_glib_001 A B C (k3_finseq_1 B)))) ) ) ) ) ) ) ).
tt(t58_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid (k1_real_1 1) 1)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers (k1_matrix_1 A))) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid 1 k6_numbers)))))) ) ).
tt(t58_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 (k2_nat_1 A 1) (k3_finseq_1 (k2_goboard2 C))) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 (k2_nat_1 B 1) (k1_matrix_1 (k2_goboard2 C))) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 1) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C 2) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) ) ) ) )  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 1 D) &  ( (~ (r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 D 1)))  &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)))  &  ( ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) )  |  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C D) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 D 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_graph_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r1_xxreal_0 1 B) =>  ((r1_xxreal_0 (k3_finseq_1 D) B) |  ((k7_partfun1 A (k4_graph_2 A C D) (k2_nat_1 (k3_finseq_1 C) B)) = (k7_partfun1 A D (k2_nat_1 B 1))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v1_graph_3 B A) & (r1_graph_2 A C B))  =>  ((k10_xtuple_0 C) = (u1_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t58_graph_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_graph_1 A) & (l1_graph_1 A)) )  =>  (! [B:$i] :  ( ((v7_graph_1 B A) &  ((v1_graph_4 B A) & (m2_graph_1 B A)) )  => (r1_xxreal_0 (k3_finseq_1 B) (k7_graph_1 A))) ) ) ) ).
tt(t58_groeb_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v6_struct_0 C))  &  ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) & (r2_hidden F D))  =>  ((r1_groeb_2 A (k3_termord A B C E) (k3_termord A B C F)) | (r1_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) (k7_polynom1 A C))) ) ) ) ) )  =>  ((r2_hidden (k7_polynom1 A C) D) |  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) &  ((r2_hidden F D) & (r4_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) G)) )  =>  ((r1_groeb_2 A (k3_termord A B C E) (k3_termord A B C F)) | (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) G (k7_polynom1 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_2 B C) => (r1_tarski (k4_group_11 A B B) (k4_group_11 A C C))) ) ) ) ) ) ) ).
tt(t58_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 C D)) ) )  => (m1_group_2 B C)) ) ) ) ) ) ) ).
tt(t58_group_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r1_struct_0 (k6_group_3 B D C) A) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ( (A = (k2_group_3 B E C))  & (r1_struct_0 D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  ((r1_group_2 A (k8_group_4 A (k6_group_2 A) B) B) & (r1_group_2 A (k8_group_4 A B (k6_group_2 A)) B)) ) ) ) ) ).
tt(t58_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  ((r2_hidden A (k6_group_5 B)) <=>  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) &  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) &  (A = (k2_group_5 B C D)) ) ) ) ) ) ) ) ) ).
tt(t58_group_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_2 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (? [E:$i] :  ((m1_subset_1 E A) &  ((k3_funct_2 A B C E) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v2_group_9 B A) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v2_group_9 C A) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  =>  ( ((r3_group_9 A B C) & (v7_struct_0 B))  => (v7_struct_0 C)) ) ) ) ) ) ).
tt(t58_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_complex1 (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B C C)) = k6_numbers)  =>  ( ((v5_bilinear B k1_complfld A A) & (v6_bilinear B k1_complfld A A))  |  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t58_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k29_sin_cos)) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k29_sin_cos A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) (k6_rfunct_1 k1_numbers k1_numbers k19_sin_cos)) A) 2))) ) ) ).
tt(t58_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k8_ideal_1 A B) (k8_ideal_1 A C))) ) ) ) ) ) ) ).
tt(t58_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k6_int_1 B A))) ) ) ) ) ) ).
tt(t58_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k19_sin_cos D) k6_numbers))  &  ((k1_seq_1 C D) = (k5_square_1 (k1_seq_1 k29_sin_cos D))) ) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers B)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers B)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos (k1_partfun2 k1_numbers B)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t58_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k1_seq_1 k19_sin_cos D) (k10_real_1 (k1_seq_1 k19_sin_cos D) (k5_square_1 (k1_seq_1 k16_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos)) (k4_seq_4 A)) (k1_seq_1 (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k30_sin_cos)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t58_integra1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  ( ((r2_hidden A (k4_finseq_1 C)) &  ((r2_hidden B (k4_finseq_1 C)) & (r1_xxreal_0 A B)) )  =>  ((k3_finseq_1 (k2_finseq_6 C A B)) = (k7_real_1 (k9_real_1 B A) 1)) ) ) ) ) ) ) ) ).
tt(t58_integra8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  ( (A = (k1_rcomp_1 k6_numbers 1))  =>  ((k2_integra5 A k4_sin_cos2) = (k10_real_1 (k9_real_1 (k5_square_1 k8_power) 1) (k8_real_1 2 k8_power))) ) ) ) ).
tt(t58_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k9_real_1 H A))  &  (~ (r1_xxreal_0 (k1_seq_1 E H) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A)))) = G)  &  ( (G = (k1_relset_1 k1_numbers F))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ((k1_seq_1 F H) = (k10_real_1 (k7_real_1 H B) (k9_real_1 H A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F C))) ) ) ) ) )  =>  ((k2_integra5 C F) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A))) (k4_seq_4 C)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k14_interva1 A (k17_interva1 A B C)) = (k9_subset_1 (u1_struct_0 A) (k14_interva1 A B) (k14_interva1 A C))) ) ) ) ) ) ) ).
tt(t58_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 A (k5_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t58_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_6_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t58_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  &  ((v2_compts_1 F (k15_euclid 2)) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ( (F = a_0_6_jgraph_5)  &  ((r1_jordan6 F B C) &  ( (D = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) B))  &  (E = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k9_jgraph_4 A) C)) ) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r1_jordan6 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C))) & (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid B C))))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ( ((r1_jordan6 (k1_sppol_2 A B C D) E F) =>  ( (E = (k18_pscomp_1 (k1_sppol_2 A B C D)))  |  ((r1_xxreal_0 (k17_euclid F) (k17_euclid E)) &  (~  (F = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) )  &  ((r1_xxreal_0 (k17_euclid F) (k17_euclid E)) =>  ( (F = (k18_pscomp_1 (k1_sppol_2 A B C D)))  |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) &  (~  (E = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) D)) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) |  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))))  & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_connsp_1 D (k15_euclid 2)) &  ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan9 D B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 D B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) C (k1_matrix_1 (k1_jordan8 D B)))) ) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) (k15_pscomp_1 (k3_topreal1 2 (k1_jordan9 D B))))) ) ) ) ) ) ) ) ) ).
tt(t58_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski (k2_nat_1 E 1) D) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 E 1) D))  &  ((r2_hidden (k4_tarski E D) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) E D)) ) ) )  =>  ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k7_nat_d E 1) D) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) &  ((r1_jordan6 A B C) & (r1_jordan6 A C D)) )  => (r1_jordan6 A B D)) ) ) ) ) ) ) ) ) ).
tt(t58_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k3_jordan A)) &  ((v1_funct_2 (k3_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k3_jordan A) (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 (k3_jordan A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ) ) ).
tt(t58_kurato_1,ax,(r1_xboole_0 (k3_kurato_1 k3_topmetr k6_kurato_1) (k4_kurato_1 k3_topmetr k6_kurato_1))).
tt(t58_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v14_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  ( ((k2_partfun1 A (u1_struct_0 C) D B) = (k2_partfun1 A (u1_struct_0 C) E B))  =>  ((k3_lattice2 A C B D) = (k3_lattice2 A C B E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  (~  ( (~ (r2_hidden C (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B))))  &  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)) = (k6_glib_000 A)) )  &  (~ (r1_xxreal_0 (k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) C) (k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) (k19_lexbfs A B)))) ) ) ) ) ) ) ) ) ).
tt(t58_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v4_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v4_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ( ((v4_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v5_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ( ((v5_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v5_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ((v5_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v4_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ) ).
tt(t58_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C D))  &  ( (~ (r1_xxreal_0 D A))  &  ((r2_hidden D (k1_relset_1 k1_numbers B)) &  (~  ((k1_seq_1 B D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((k2_limfunc2 B A) = k6_numbers)  |  ((r4_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) &  ((k2_limfunc2 (k6_rfunct_1 k1_numbers k1_numbers B) A) = (k2_real_1 (k2_limfunc2 B A))) ) ) ) ) ) ) ) ).
tt(t58_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r3_limfunc2 B A) &  ((v6_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k5_limfunc1 C)) ) ) ) ) ) ) ) ) ).
tt(t58_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  ((k1_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers (k8_lpspace1 A k6_numbers)))) = k6_numbers) ) ) ) ) ) ) ) ) ).
tt(t58_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 C (k3_hilbert1 A B)) => (r8_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 A)) B)) ) ) ) ) ) ) ).
tt(t58_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A E (k8_cqc_lang A B C)) => (r3_cqc_the1 A E (k8_cqc_lang A (k8_cqc_lang A C D) (k8_cqc_lang A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_mathmorp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((k6_mathmorp 1 (k15_euclid A) B) = B) ) ) ) ) ).
tt(t58_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) (k4_matrix10 A D E)) => (r2_matrix10 (k4_matrix10 A E D) (k4_matrix10 A C B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_matrix11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_finset_1 C))  =>  (! [D:$i] :  ( (~ (r2_hidden D B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo E A) &  ((v1_binop_1 E A) & (v2_binop_1 E A)) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k9_funct_2 B C) A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 B C) A)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C) A) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C) A)))) )  =>  ( (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H B C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (! [I:$i] :  ((m1_subset_1 I (k5_finsub_1 (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C))) =>  ( (I = (a_4_0_matrix11 B C D H))  =>  ((k7_setwiseo (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C) A E I G) = (k1_funct_1 F H)) ) ) ) ) )  =>  ((k7_setwiseo (k9_funct_2 B C) A E (k15_matrix_2 (k9_funct_2 B C)) F) = (k7_setwiseo (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C) A E (k15_matrix_2 (k9_funct_2 (k2_xboole_0 B (k1_tarski D)) C)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 D) A A) =>  ((k6_matrix13 (u1_struct_0 D) E (k7_subset_1 k5_numbers (k2_finseq_1 A) (k3_matrix13 B)) (k7_subset_1 k5_numbers (k2_finseq_1 A) (k3_matrix13 C))) = (k9_matrix_2 B C A D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  (~  ((r2_hidden D (k4_matrix15 A B (k3_matrix15 (u1_struct_0 A) C))) &  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (~  ( (D = (k3_matrix15 (u1_struct_0 A) E))  &  ((k3_finseq_1 E) = (k1_matrix_1 B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_matrix16 B A) => (v6_matrix16 (k5_fvsum_1 A B) A)) ) ) ) ) ).
tt(t58_matrix_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  ( (~ (r1_xxreal_0 (k3_finseq_1 B) k6_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((m1_matrix_1 B A C (k1_matrix_1 B)) <=>  (C = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ).
tt(t58_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  => (v4_matrix_6 (k12_matrix_1 B A) A B)) ) ) ) ).
tt(t58_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k2_matrix_6 A B C (k1_matrix_6 A B C))) = (k4_struct_0 B)) ) ) ) ) ) ) ).
tt(t58_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((k3_finseq_1 A) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k8_complsp2 (k6_matrixc1 C A) B) = (k12_matrixc1 (k13_matrixc1 A B (k4_matrix_1 k2_numbers C)))) ) ) ) ) ) ) ) ) ) ).
tt(t58_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((k23_matrixj1 A (k8_finseq_1 k5_numbers B C)) = (k15_matrixj1 (u1_struct_0 A) (k23_matrixj1 A B) (k23_matrixj1 A C))) ) ) ) ) ) ) ).
tt(t58_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 C) = (k3_finseq_1 A)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k12_matrixr1 C (k4_rvsum_1 A B)) = (k4_rvsum_1 (k12_matrixr1 C A) (k12_matrixr1 C B))) ) ) ) ) ) ) ) ) ).
tt(t58_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k6_matrixr1 B (k9_matrixr1 A)) = (k9_matrixr1 (k11_matrixr1 B A))) ) ) ) ) ) ) ) ).
tt(t58_matrprob,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (? [C:$i] :  ((m1_matrix_1 C k1_numbers A B) &  ((v2_matrprob C) & (v5_matrprob C)) ) ) ) ) ) ) ).
tt(t58_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k4_zfmisc_1 A B C D)) =>  ( (~  (E = (k4_mcart_1 A B C D E)) )  &  ( (~  (E = (k5_mcart_1 A B C D E)) )  &  ( (~  (E = (k6_mcart_1 A B C D E)) )  &  (~  (E = (k7_mcart_1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) => (r1_tarski A (k6_measure6 A))) ) ).
tt(t58_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((v2_membered C) => (r1_tarski (k10_member_1 A (k3_xboole_0 B C)) (k3_xboole_0 (k10_member_1 A B) (k10_member_1 A C)))) ) ) ) ) ) ).
tt(t58_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k9_memstr_0 A B (k1_funct_4 C (k7_memstr_0 A B D)) E) = (k1_funct_4 C (k7_memstr_0 A B (k2_xcmplx_0 D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ( (~  (B = k1_supinf_1) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A C) B)) )  & (r1_xxreal_0 k1_supinf_1 (k8_supinf_2 (k17_supinf_2 A)))) ) ) ) ) ) ) ).
tt(t58_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( (! [D:$i] :  ((r2_hidden D (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C))) => (r1_xxreal_0 (k1_seq_1 C D) (k1_seq_1 B D))) )  => (v6_supinf_2 (k47_valued_1 A k1_numbers k1_numbers B C))) ) ) ) ) ) ) ).
tt(t58_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_1 C (k9_setfam_1 A)) =>  ((k27_mmlquery A C B (k3_finseq_1 C)) = (k26_mmlquery A C B)) ) ) ) ) ) ).
tt(t58_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k2_lattices (k42_modelc_2 A B) D E)) <=>  ((r6_modelc_2 A B C D) & (r6_modelc_2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 A))) =>  ( (~ (v3_modelc_3 B A))  => (r2_hidden (k24_modelc_3 A C B) (u2_modelc_3 A B))) ) ) ) ) ) ) ).
tt(t58_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  => (r1_xxreal_0 (k6_moebius1 A) A)) ) ).
tt(t58_monoid_0,ax, ((r3_binop_1 k5_numbers 1 k48_binop_2) & (v9_monoid_0 k48_binop_2 k5_numbers)) ).
tt(t58_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 B (k1_nat_1 A 4)) &  ( (~  (B = A) )  &  ( (~  (B = (k1_nat_1 A 1)) )  &  ( (~  (B = (k1_nat_1 A 2)) )  &  ( (~  (B = (k1_nat_1 A 3)) )  &  (~  (B = (k1_nat_1 A 4)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((r1_int_2 A B) =>  ((k13_nat_3 (k24_binop_2 A B)) = (k11_pre_poly k10_newton (k13_nat_3 A) (k13_nat_3 B))) ) ) ) ) ) ).
tt(t58_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) =>  ((k7_nat_d B (k7_nat_d B A)) = A) ) ) ) ) ) ).
tt(t58_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r9_ncfcont1 B A E C) & (r1_tarski D C))  => (r9_ncfcont1 B A E D)) ) ) ) ) ) ) ) ) ).
tt(t58_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 (k6_nat_d A B) k6_numbers)) ) ) ) ) ) ).
tt(t58_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m1_oppcat_1 (k11_oppcat_1 A B C) A (k2_oppcat_1 B))) ) ) ) ) ) ).
tt(t58_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  ((r9_orders_1 A B) &  ((r1_tarski C (k1_relat_1 A)) & (v1_relat_2 A)) ) )  => (r5_orders_1 A C)) ) ) ) ) ).
tt(t58_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k5_ordinal3 C B) (k5_ordinal3 C A))) ) ) ) ) ) ) ).
tt(t58_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden k6_numbers C) & (r2_hidden C A))  =>  ((k5_ordinal5 (k11_ordinal2 C (k12_ordinal2 A B)) A) = B) ) ) ) ) ) ) ) ).
tt(t58_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_classes2 D))  =>  ( ((r2_hidden A B) &  ((r2_hidden B D) &  ((r2_hidden k4_ordinal1 D) & (r2_hidden C (k9_xtuple_0 (k1_funct_1 (k11_ordinal6 D) B)))) ) )  => (r1_abian (k1_funct_1 (k1_funct_1 (k11_ordinal6 D) B) C) (k1_funct_1 (k11_ordinal6 D) A))) ) ) ) ) ) ) ) ) ).
tt(t58_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v3_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t58_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_parsp_1 A) &  ((v1_parsp_2 A) & (l1_parsp_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_parsp_2 A B C D E) => (r3_parsp_2 A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ((r1_partfun1 C E) & (r1_relset_1 A B D C))  => (r1_partfun1 D E)) ) ) ) ) ) ) ) ) ).
tt(t58_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  ((v3_funct_1 (k2_partfun1 C B D A)) <=>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((m1_subset_1 F C) =>  ( ((r2_hidden E (k9_subset_1 C A (k1_relset_1 C D))) & (r2_hidden F (k9_subset_1 C A (k1_relset_1 C D))))  =>  ((k1_funct_1 D E) = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k4_pboole A B B) (k1_pboole A))) ) ) ).
tt(t58_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r1_pdiff_5 C B) =>  ((r3_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) &  ((k11_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) = (k8_real_1 A (k1_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t58_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) &  ((r1_tarski B (k1_relset_1 (k1_euclid A) D)) &  ((r2_pdiff_9 B A C) & (r2_pdiff_9 B A D)) ) )  =>  ((r2_pdiff_9 B A (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers C D)) E) = (k45_valued_1 (k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B C) E) (k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B D) E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r2_int_1 (k13_newton 3 (k3_nat_d (k7_nat_d (k4_pepin A) 1) 2)) (k4_xcmplx_0 1) (k4_pepin A)) => (v1_int_2 (k4_pepin A))) ) ) ).
tt(t58_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k15_finseq_1 (k12_pnproc_1 B A)) = B) ) ) ) ) ).
tt(t58_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ( (B = k6_numbers)  &  ( (D = (k1_tarski C))  &  ( (E = k1_xboole_0)  &  ( (C = (k15_polyform A B F))  &  ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k11_polyform A B))) ) ) ) )  =>  ((k1_funct_1 (k19_polyform A B E D) F) = (k5_struct_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_polynom4 A (k7_polynom5 A B) C) = (k3_vectsp_1 A (k2_polynom4 A B C) (k3_funct_2 k5_numbers (u1_struct_0 A) B (k7_nat_d (k1_algseq_1 A B) 1)))) ) ) ) ) ) ) ) ).
tt(t58_polyred,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k11_polynom1 A C))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_polynom1 A C))) =>  ((r11_polyred (k11_polynom1 A C) (k7_ideal_1 (k11_polynom1 A C) D) E F) => (r2_rewrite1 (k3_polyred A B C D) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_power,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C B))  & (r1_xxreal_0 (k5_power A B) (k5_power A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((r3_pre_poly A B (k16_pre_poly A)) => (r6_pboole A (k16_pre_poly A) B)) ) ) ) ).
tt(t58_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k6_prepower (k13_complex1 A B) C) = (k13_complex1 (k6_prepower A C) (k6_prepower B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m1_prob_3 C A B) => (r2_hidden (k7_prob_3 A C) B)) ) ) ) ) ).
tt(t58_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((r2_hidden (k8_cqc_lang A (k7_cqc_lang A B (k6_cqc_lang A C)) (k6_cqc_lang A B)) (k4_cqc_the1 A)) => (r2_hidden (k8_cqc_lang A B C) (k4_cqc_the1 A))) ) ) ) ) ) ) ).
tt(t58_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r2_hidden (k25_pscomp_1 A) (k17_pscomp_1 A)) & (r2_hidden (k24_pscomp_1 A) (k17_pscomp_1 A))) ) ) ).
tt(t58_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ( ((v2_relat_1 B) &  ((v2_relat_1 C) & (r6_pboole A (k6_pboole A B C) (k6_pboole A C B))) )  => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t58_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ( ((r2_qc_lang2 A B C) & (r2_qc_lang2 A C B))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t58_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k15_qc_lang1 A B C)) = (k5_qc_lang3 A C)) ) ) ) ) ) ) ).
tt(t58_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k18_quatern2 (k29_quaterni A B) C) = (k29_quaterni (k18_quatern2 A C) (k18_quatern2 B C))) ) ) ) ) ) ) ).
tt(t58_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k28_quaterni (k26_quaterni (k26_quaterni A B) C)) = (k29_quaterni (k29_quaterni (k28_quaterni A) B) C)) ) ) ) ) ) ) ).
tt(t58_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ( ((k18_quaterni A) = k6_numbers)  &  ( ((k19_quaterni A) = k6_numbers)  &  ((k20_quaterni A) = k6_numbers) ) )  =>  ((k31_quaterni A) = A) ) ) ) ).
tt(t58_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r1_quofield A (k19_quofield A))) ) ).
tt(t58_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  =>  ((k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) D (k3_finseq_1 D))) = B) ) ) ) ) ) ) ) ) ) ).
tt(t58_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_seq_1 (k4_real_3 A) B) k6_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k10_real_1 1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 2))) (k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1)) (k1_seq_1 (k6_real_3 A) B)))) ) ) ) ) ).
tt(t58_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k5_relat_1 B A)) A)) ) ) ).
tt(t58_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))) =>  ((k6_relset_2 B C (k7_relset_1 A B E D) F) = (k6_relset_2 A C D (k3_subset_1 (k2_zfmisc_1 A C) (k7_relset_2 A B C E (k3_subset_1 (k2_zfmisc_1 B C) F))))) ) ) ) ) ) ) ) ) ) ).
tt(t58_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((v7_rewrite1 A) <=> (v6_rewrite1 (k18_finseq_1 A))) ) ) ).
tt(t58_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r4_rewrite2 A B C D) & (r1_rewrite1 (k7_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C)) D E))  => (r1_rewrite1 (k7_rewrite2 A B) D E)) ) ) ) ) ) ) ) ) ) ).
tt(t58_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ((r1_rewrite3 F G A D B) <=> (m1_rewrite1 (k10_finseq_1 (k4_tarski A (k1_flang_1 C D E)) (k4_tarski B E)) (k1_rewrite3 C F G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 C A) =>  ( ((k1_funct_1 (k32_valued_1 A k1_numbers C) B) = (k4_xcmplx_0 (k1_funct_1 C B)))  &  ((k1_funct_1 (k56_valued_1 A k1_numbers C) B) = (k18_complex1 (k1_funct_1 C B))) ) ) ) ) ) ) ) ) ).
tt(t58_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((r2_rfunct_3 A C) & (r2_rfunct_3 B C))  => (r2_rfunct_3 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C)) ) ) ) ) ) ).
tt(t58_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_comseq_2 A) =>  ((v2_comseq_2 (k4_rinfsup1 A)) &  ((k2_seq_2 (k4_rinfsup1 A)) = (k2_rinfsup1 (k4_rinfsup1 A))) ) ) ) ) ).
tt(t58_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_rlaffin1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C B) &  ((k4_rlaffin1 A B) = (k4_rlaffin1 A C)) )  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t58_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden (k1_rlvect_1 A B C) (k3_rlsub_1 A B D)) =>  ( (C = 1)  | (r1_struct_0 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t58_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v12_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ).
tt(t58_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_yellow13 B A (k4_struct_0 A)) =>  (! [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) =>  (? [D:$i] :  ((m1_connsp_2 D A (k4_struct_0 A)) &  ((r2_hidden D B) & (r1_tarski (k2_pre_topc A D) C)) ) ) ) ) ) ) ) ) ).
tt(t58_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B (k4_algstr_0 A B))) = (k4_struct_0 A))  &  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) (k4_algstr_0 A B) B)) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t58_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 (k16_rlvect_2 A)) = (k11_rlvect_2 A)) ) ) ).
tt(t58_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r2_hidden (k5_algstr_0 B C D) (k3_rmod_2 A B C E)) <=> (r1_struct_0 E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((k5_rmod_4 A B (k6_rmod_4 A B C D)) = (k3_rlvect_1 B (k5_rmod_4 A B C) (k5_rmod_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t58_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v5_robbins1 A) & (l2_robbins1 A)) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ((k5_robbins1 A B C) = C) ) ) ) ) ) ) ).
tt(t58_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_robbins1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v4_lattices A) &  ((v5_lattices A) & (v6_robbins1 A)) )  =>  ((k4_robbins1 A (k1_lattices A C B) (k1_lattices A C (k3_robbins1 A B))) = C) ) ) ) ) ) ) ) ).
tt(t58_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v8_struct_0 A) &  ((v2_roughs_1 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_roughs_1 A B) = (a_2_4_roughs_1 A B)) ) ) ) ) ).
tt(t58_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k3_rusub_1 A D B)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 B E) &  (C = (k5_algstr_0 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (v12_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ).
tt(t58_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k12_rvsum_1 (k10_rvsum_1 B A)) = (k10_rvsum_1 (k12_rvsum_1 B) (k3_square_1 A))) ) ) ) ) ).
tt(t58_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (~  (A = B) ) ) ) ) ) ).
tt(t58_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r6_scmfsa7b C (k1_scmfsa_m B) A) =>  ( (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D)) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ((k18_scmfsa_2 (k1_scmfsa6b C B A) D) = (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)) D))  =>  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B) D)) = (k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k1_scmfsa_m B) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k4_scmpds_2 B) A) (k4_struct_0 k1_scmpds_2)) = (k2_nat_1 (k1_int_2 (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A B) k15_scmpds_i))) 2))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k4_scmpds_2 B) A) B) = (k1_funct_1 A (k2_scmpds_2 (k1_funct_1 A B) k14_scmpds_i)))  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ( (~  (B = C) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k4_scmpds_2 B) A) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ) ) ).
tt(t58_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v3_scmpds_4 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  |  ((r1_scmpds_6 (k6_scmpds_6 D E C) B A) & (r2_scmpds_6 (k6_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  (! [B:$i] :  ( ((v4_scmyciel B) & (v6_scmyciel B))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k8_scmyciel A) (k8_scmyciel B))) ) ) ) ) ).
tt(t58_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) => (r2_analoaf A B D C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  (! [E:$i] :  ((m2_finseq_2 E k2_numbers (k14_seq_4 B)) =>  (! [F:$i] :  ((m2_finseq_2 F k2_numbers (k14_seq_4 B)) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ( (C = (k1_funct_1 E A))  &  (D = (k1_funct_1 F A)) ) )  =>  ((k1_funct_1 (k15_seq_4 B E F) A) = (k3_binop_2 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_funct_1 C) &  ((k3_funct_1 C) = B) )  =>  ((v3_kurato_0 C A) &  ( ((k4_kurato_0 A C) = B)  &  ( ((k3_kurato_0 A C) = B)  &  ((k4_kurato_0 A C) = B) ) ) ) ) ) ) ) ) ) ).
tt(t58_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k8_setlim_2 B D C)) A) = (k7_subset_1 B (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A) C)) ) ) ) ) ) ) ) ).
tt(t58_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  ((k10_setwiseo A A B (k11_setwiseo A)) = B) ) ) ) ) ).
tt(t58_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ((m1_scmfsa_2 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) ) )  =>  (~  ( ((r2_hidden (k14_scmfsa_2 A B C) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) D)) | (r2_hidden (k15_scmfsa_2 A B C) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) D)))  &  ((k6_sf_mastr D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A C (k5_sheffer1 A D (k5_sheffer1 A B C))))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ) ) ).
tt(t58_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  => (m2_simplex0 (k10_simplex0 A C D) A (k10_simplex0 A B D))) ) ) ) ) ) ) ).
tt(t58_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k1_rcomp_1 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) k32_sin_cos))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ).
tt(t58_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 2 A)) = (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)))  &  ((k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 A)) = (k4_binop_2 (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) 1)) ) ) ) ).
tt(t58_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v2_funct_1 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k7_real_1 (k10_real_1 k32_sin_cos 2) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t58_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k5_power k8_power A) = (k11_binop_2 2 (k4_sin_cos7 (k12_binop_2 (k10_binop_2 A 1) (k9_binop_2 A 1))))) ) ) ) ).
tt(t58_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k6_sin_cos9 A) = (k8_real_1 (k10_real_1 3 4) k32_sin_cos)) ) )  =>  (A = (k1_real_1 1)) ) ) ) ).
tt(t58_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (~  ( (~ (r1_xxreal_0 B (k17_complex1 C)))  & (r1_xxreal_0 A (k17_complex1 (k11_comseq_3 (k27_sin_cos C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden B A) & (r2_hidden C A))  =>  ( (B = C)  | (r1_sppol_2 B C A)) ) ) ) ) ) ) ) ) ).
tt(t58_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k6_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k6_pscomp_1 A)) ) ) ).
tt(t58_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((k18_pscomp_1 (k3_topreal1 2 A)) = (k19_pscomp_1 (k3_topreal1 2 A))) ) ) ) ).
tt(t58_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k23_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k22_pscomp_1 (k3_topreal1 2 A)) = (k21_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t58_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 B (k6_square_1 (k2_xcmplx_0 A (k3_square_1 B))))) ) ) ) ) ).
tt(t58_stirl2_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_xboole_0 B) => (v1_xboole_0 A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D)))))) )  =>  ( ( ((k2_partfun1 (k2_xboole_0 A (k1_tarski C)) (k2_xboole_0 B (k1_tarski D)) F A) = E)  &  ((k1_funct_1 F C) = D) )  =>  ( ((v2_funct_2 E B) => (v2_funct_2 F (k2_xboole_0 B (k1_tarski D))))  &  ((v2_funct_1 E) =>  ((r2_hidden D B) | (v2_funct_1 F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  ( ((k1_relset_1 (k3_qc_lang1 A) D) = (k3_qc_lang1 A))  &  ((k1_relset_1 (k1_tarski B) (k12_sublemma A C B E)) = (k6_domain_1 (k3_qc_lang1 A) B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (r1_tarski (k1_tops_1 A (k2_pre_topc A C)) C)) ) )  =>  ((r1_tarski (k1_tops_1 A (k2_pre_topc A (k6_setfam_1 (u1_struct_0 A) B))) (k6_setfam_1 (u1_struct_0 A) B)) &  ((k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)))) = (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t58_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_tex_2 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r2_hidden D B) &  ((k9_subset_1 (u1_struct_0 A) B (k2_pre_topc A (k6_domain_1 (u1_struct_0 A) C))) = (k6_domain_1 (u1_struct_0 A) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  & (v4_tex_3 B A)) )  & (v3_tdlat_3 A)) ) ) ) ).
tt(t58_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_tex_4 A B) (k1_setfam_1 (a_2_0_tex_4 A B)))) ) ) ) ).
tt(t58_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D B))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( ( (E = F)  & (r1_tmap_1 B A C E))  => (r1_tmap_1 D A (k2_tmap_1 B A C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_borsuk_2 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_group_6 (k5_topalg_1 A B) (k5_topalg_1 A C))) ) ) ) ) ) ).
tt(t58_topgen_4,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( (~ (v1_xboole_0 (k1_topgen_3 k5_numbers A B)))  &  ((v4_card_3 (k1_topgen_3 k5_numbers A B)) & (m1_subset_1 (k1_topgen_3 k5_numbers A B) (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) ) ) ) ).
tt(t58_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 k2_topgen_3) (u1_struct_0 k5_topmetr)) &  ((v5_pre_topc C k2_topgen_3 k5_topmetr) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k2_topgen_3) (u1_struct_0 k5_topmetr))))) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k2_topgen_3)) =>  ( ((r2_hidden D (k3_rcomp_1 A B)) =>  ((k3_funct_2 (u1_struct_0 k2_topgen_3) (u1_struct_0 k5_topmetr) C D) = k6_numbers) )  &  ( (~ (r2_hidden D (k3_rcomp_1 A B)))  =>  ((k3_funct_2 (u1_struct_0 k2_topgen_3) (u1_struct_0 k5_topmetr) C D) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (v1_tops_1 (k5_group_2 A C B) A)) ) ) ) ) ) ).
tt(t58_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (C = (k10_metric_1 (k14_euclid A) B D))  => (v4_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t58_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid 2)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid 2)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid 2)) =>  (~  ( (G = E)  &  ( (H = F)  &  ( (I = (k19_euclid A B))  &  ( (C = (k10_real_1 (k7_real_1 (k1_real_1 (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) F E) (k5_algstr_0 (k15_euclid 2) E (k19_euclid A B))))) (k7_square_1 (k2_quin_1 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 H G))) (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) F E) (k5_algstr_0 (k15_euclid 2) E (k19_euclid A B)))) (k9_real_1 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 G I))) (k3_square_1 D))))) (k8_real_1 2 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 H G))))))  &  ( (~  (E = F) )  &  ((r2_hidden E (k6_jgraph_6 A B D)) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ( ((k1_tarski J) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_topreal9 2 E F) (k5_jgraph_6 A B D)))  &  (J = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k9_real_1 1 C)) (k1_rlvect_1 (k15_euclid 2) F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (v1_t_0topsp (k17_toprealc B A) (k15_euclid B) k3_topmetr)) ) ) ) ) ).
tt(t58_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v3_tops_1 (k2_tops_1 A B) A)) ) ) ) ) ).
tt(t58_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc D A) <=> (v4_pre_topc (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((k1_tops_1 A C) = (k1_tops_1 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t58_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 F (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo F A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F B) = B)  &  ((r1_diraf A C B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F C)) & (r3_diraf A B D E)) ) )  =>  ( (C = B)  | (r2_analoaf A D E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F E) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k12_trees_3 A) = (k5_trees_1 (k2_trees_1 1) (k12_finseq_1 k5_numbers k6_numbers) A)) ) ) ).
tt(t58_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) D (k4_subset_1 (u1_struct_0 A) B C)) B) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) E (k4_subset_1 (u1_struct_0 A) B C)) C) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) F (k4_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) B C)) &  ( ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((v3_pre_topc D A) &  ((v3_pre_topc E A) & (v4_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ( (C = B)  =>  (! [D:$i] :  ((v1_int_1 D) =>  ( (D = (k2_polynom4 k1_complfld (k5_uniroots A) C))  => (r1_int_1 D (k21_binop_2 (k13_newton B A) 1))) ) ) ) ) ) ) ) ) ) ).
tt(t58_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k4_uproots (u1_struct_0 A) (k8_uproots A (k2_polynom5 A (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A)) C))) = C) ) ) ) ) ) ) ).
tt(t58_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v2_relat_1 E) &  ( (! [F:$i] :  ((r2_hidden F (k1_relset_1 A E)) => (v2_relat_1 (k1_funct_1 E F))) )  & (r2_relset_1 A (k2_valued_2 (k1_valued_2 B)) (k48_valued_2 A B E C) (k48_valued_2 A B E D))) )  =>  ( (E = k1_xboole_0)  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r1_struct_0 E D) => (r2_hidden (k4_vectsp_1 A B C D) (k3_vectsp_4 A B D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v13_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ) ).
tt(t58_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r2_yellow_0 A E) &  (D = (k2_yellow_0 A E)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k2_yellow_0 A D) C)) ) ) ) )  =>  ((r2_yellow_0 A B) <=> (r2_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(t58_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v7_waybel_1 (k1_partfun1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k2_yellow_2 A) (k3_yellow_2 A)) (k2_yellow_1 (k7_waybel_0 A))) & (r5_waybel_1 (k1_yellow_2 (k2_yellow_1 (k7_waybel_0 A)) (k2_yellow_1 (k7_waybel_0 A)) (k1_partfun1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (k2_yellow_2 A) (k3_yellow_2 A))) A)) ) ) ).
tt(t58_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  => (v5_orders_3 (k3_waybel23 A B) (k2_yellow_1 (k7_waybel_0 B)) A)) ) ) ) ).
tt(t58_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((r4_waybel_0 A B E D) & (r4_waybel_0 B C F (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) E D)))  => (r4_waybel_0 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) E F) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) & (r2_waybel_4 (k5_waybel_4 A C B) D B)) )  => (r2_hidden (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) C C) B)) ) )  => (v8_waybel_4 B A)) ) ) ) ) ).
tt(t58_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r2_xboole_0 A B) & (r1_tarski B C))  => (r2_xboole_0 A C)) ) ) ) ).
tt(t58_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k8_xboolean B C)) = (k4_xboolean (k6_xboolean A B) (k6_xboolean A C))) ) ) ) ) ) ) ).
tt(t58_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 A B) = 1)  =>  (A = B) ) ) ) ) ) ).
tt(t58_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~  ( (~ (r1_xxreal_0 k6_numbers A))  & (r1_xxreal_0 (k4_xcmplx_0 A) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 A) k6_numbers))  & (r1_xxreal_0 k6_numbers A)) ) ) ) ) ).
tt(t58_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_tarski (k1_xxreal_1 A B) (k3_xxreal_1 C D)))  =>  ( (~ (r1_xxreal_0 A C))  & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t58_xxreal_2,ax, (! [A:$i] :  ( ((v2_membered A) &  (~ (v1_xboole_0 A)) )  =>  ((v3_xxreal_2 A) =>  ( (A = (k1_tarski k1_xxreal_0))  | (r2_hidden (k2_xxreal_2 A) k1_numbers)) ) ) ) ).
tt(t58_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k1_xxreal_0)  &  (B = k1_xxreal_0) ) )  &  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (B = k1_xxreal_0)  &  (C = k2_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ((r1_xxreal_0 (k3_xxreal_3 A B) C) &  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t58_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v2_waybel11 (k6_yellow_3 A B C D) (k3_yellow_3 A B)) =>  ( ( (~  (D = k1_xboole_0) )  => (v2_waybel11 C A))  &  ( (~  (C = k1_xboole_0) )  => (v2_waybel11 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k12_lattice3 (k2_yellow_1 (k7_waybel_0 A)) B C) = (k4_yellow_4 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k12_lattice3 A C D)) = (k13_lattice3 A (k1_yellow_5 A B C) (k1_yellow_5 A B D))) ) ) ) ) ) ) ) ) ).
tt(t58_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  (! [D:$i] :  ( ((v1_tops_2 D A) &  ((v2_cantor_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [E:$i] :  ( ((v1_tops_2 E B) &  ((v2_cantor_1 E B) & (m1_subset_1 E (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  ((v1_tops_2 (k2_xboole_0 (k2_xboole_0 D E) (k2_tarski (u1_struct_0 A) (u1_struct_0 B))) C) &  ((v2_cantor_1 (k2_xboole_0 (k2_xboole_0 D E) (k2_tarski (u1_struct_0 A) (u1_struct_0 B))) C) & (m1_subset_1 (k2_xboole_0 (k2_xboole_0 D E) (k2_tarski (u1_struct_0 A) (u1_struct_0 B))) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t58_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k2_zf_model (k4_zf_lang A B)) = (k2_tarski A B)) ) ) ) ) ).
tt(t58_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((v6_zf_lang A) =>  ((r1_zf_lang B A) <=>  (B = (k24_zf_lang A)) ) ) ) ) ) ) ).
tt(t58_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ( ((k4_xboole_0 A (k1_tarski B)) = k1_xboole_0)  &  ( (~  (A = k1_xboole_0) )  &  (~  (A = (k1_tarski B)) ) ) ) ) ) ) ).
tt(t58_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) => (r2_hidden B (k5_zmodul01 A B C))) ) ) ) ) ) ).
tt(t59_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_abcmiz_0 A)) =>  ((r4_abcmiz_0 A B C) <=> (r5_abcmiz_0 A B (k12_finseq_1 (u1_abcmiz_0 A) C))) ) ) ) ) ) ) ).
tt(t59_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v6_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  ((k37_abcmiz_1 A B) = (k30_abcmiz_1 A (k32_abcmiz_1 A) B)) ) ) ) ) ).
tt(t59_abcmiz_a,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k2_abcmiz_1)))  =>  ( ((k1_abcmiz_1 A) = A)  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k27_abcmiz_1)) =>  (? [C:$i] :  ( ((v2_abcmiz_1 C k27_abcmiz_1) & (m2_abcmiz_1 C k27_abcmiz_1 B))  &  (? [D:$i] :  ((m1_trees_4 D (k3_card_3 (u3_msualg_1 k27_abcmiz_1 (k1_msafree3 k27_abcmiz_1 (k28_abcmiz_1 k27_abcmiz_1)))) (k34_abcmiz_1 k27_abcmiz_1)) &  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 k27_abcmiz_1 C)))  &  ((k46_abcmiz_1 k27_abcmiz_1 (k36_abcmiz_1 k27_abcmiz_1 C D)) = A) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_1 D A) &  ( (~ (r2_aff_1 A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_hidden E D) & (r1_aff_1 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_4 B A) &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t59_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ( (A = (k2_xcmplx_0 (k2_afinsq_1 C) B))  =>  ((k5_relat_1 (k1_ordinal4 C D) A) = (k1_ordinal4 C (k5_relat_1 D B))) ) ) ) ) ) ) ) ) ) ).
tt(t59_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 (k1_funct_1 A C) B)) ) )  => (r1_xxreal_0 (k7_afinsq_2 A) (k11_binop_2 (k1_afinsq_1 A) B))) ) ) ) ) ).
tt(t59_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m4_algspec1 B A) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  ((l3_msualg_1 B C) => (l3_msualg_1 B (k2_circcomb C A))) ) ) ) ) ) ) ).
tt(t59_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  ((k5_altcat_4 (k4_altcat_4 A)) = (k5_altcat_4 A)) ) ) ).
tt(t59_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) =>  ((r2_analoaf A B C E D) &  ((r2_analoaf A C B D E) &  ((r2_analoaf A C B E D) &  ((r2_analoaf A D E B C) &  ((r2_analoaf A D E C B) &  ((r2_analoaf A E D B C) & (r2_analoaf A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ((k13_aofa_000 (k7_freealg k19_aofa_000 A) B C) = (k6_trees_4 2 B C)) ) ) ) ) ) ) ).
tt(t59_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  &  ( ((k1_funct_1 I E) = k6_numbers)  &  ( ((k1_funct_1 I F) = 1)  &  ( ((k1_funct_1 I G) = 2)  &  ( ((k1_funct_1 I H) = 3)  &  ((k1_funct_1 I C) = 4) ) ) ) ) ) )  =>  (! [I:$i] :  ((m2_funct_2 I B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [J:$i] :  ((v7_ordinal1 J) =>  ( (J = (k21_aofa_i00 B k4_numbers I F))  =>  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D I (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H 1) (k74_aofa_i00 A B C D H F) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H 1)))) G) = (k1_newton (k21_aofa_i00 B k4_numbers I E) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  ((k14_armstrng A B) = (k14_armstrng A (k12_armstrng A B))) ) ) ) ) ).
tt(t59_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (m1_subset_1 A k5_arytm_3))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (m1_subset_1 B k5_arytm_3))  =>  ((k10_arytm_3 A B) = (k9_ordinal3 A B)) ) ) ) ) ).
tt(t59_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 3 A) & (r1_xxreal_0 (k9_newton A) A)) ) ) ) ).
tt(t59_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k2_bcialg_1 A C) (k2_bcialg_1 A B)) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(t59_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ( ((v8_bcialg_1 E) & (m1_bcialg_5 E A B C D))  =>  ( (A = k6_numbers)  =>  ( (D = k6_numbers)  |  ((v8_bcialg_1 E) & (m1_bcialg_5 E k6_numbers 1 k6_numbers 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k5_vfunct_1 k5_numbers A (k5_vfunct_1 k5_numbers A B)))) ) ) ) ).
tt(t59_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A)) &  ((v1_bilinear C A B B) &  ((v2_bilinear C A B B) &  ((v3_bilinear C A B B) &  ((v4_bilinear C A B B) &  ((v8_bilinear C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B)) (u1_struct_0 A))))) ) ) ) ) ) )  =>  ((k10_bilinear A B B C) = (k11_bilinear A B B C)) ) ) ) ) ) ) ).
tt(t59_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_lattices A B C) (k3_boolealg A B (k1_boolealg A C B)))) ) ) ) ) ) ).
tt(t59_borsuk_4,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v4_pre_topc B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r2_xboole_0 B A) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal1 (k15_euclid 2) C D E) &  ((r1_tarski B E) & (r1_tarski E A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_borsuk_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k7_subset_1 k1_numbers (k3_rcomp_1 A k1_xxreal_0) (k4_subset_1 k1_numbers (k2_rcomp_1 A B) (k2_rcomp_1 B k1_xxreal_0))) = (k4_subset_1 k1_numbers (k1_seq_4 A) (k1_seq_4 B))) ) ) ) ) ) ).
tt(t59_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) =>  ((r2_hidden A k6_borsuk_6) => (r1_xxreal_0 (k1_xtuple_0 A) (k10_real_1 1 2))) ) ) ).
tt(t59_borsuk_7,ax, (! [A:$i] :  ( ((v1_xreal_0 A) &  (~ (v3_xxreal_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k7_relset_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k1_jordan24 B) (k3_topreal9 2 (k4_struct_0 (k15_euclid 2)) A)) = (k3_topreal9 2 (k4_struct_0 (k15_euclid 2)) A)) ) ) ) ) ).
tt(t59_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A H B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G) I) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k3_xboolean (k7_xboolean A B)) = (k10_xboolean A B)) ) ) ) ) ).
tt(t59_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k5_bvfunc26 A B C)) (k2_bvfunc_1 A B (k1_bvfunc_1 A C)))) ) ) ) ) ) ).
tt(t59_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ((k3_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) B C)) = (k4_subset_1 (k3_qc_lang1 A) (k3_calcul_1 A B) (k3_calcul_1 A C))) ) ) ) ) ) ) ).
tt(t59_card_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (~  ( (~ (v1_finset_1 (k9_xtuple_0 A)))  &  ((v2_funct_1 A) & (v1_finset_1 (k10_xtuple_0 A))) ) ) ) ) ).
tt(t59_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (A = B) )  &  ( (~  (A = C) )  &  ( (~  (A = D) )  &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  ( (~  (C = D) )  &  (~  ((k5_card_1 (k2_enumset1 A B C D)) = 4) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_card_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((k8_card_3 C) = (k8_card_3 (k2_partfun1 A B C (a_3_0_card_3 A B C)))) ) ) ) ) ) ) ).
tt(t59_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( (~ (v1_xboole_0 A))  &  ( (~ (v1_xboole_0 B))  &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k1_relset_1 k5_numbers C) = (k23_binop_2 (k5_card_1 B) 1))  &  ( ((k7_afinsq_2 C) = (k1_card_1 (a_2_1_card_fin A B)))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k22_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k6_newton D (k5_card_1 B))) (k1_newton (k21_binop_2 (k5_card_1 B) D) (k5_card_1 A)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k4_cat_1 A B) = (k4_cat_1 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t59_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  ( ((r2_cat_3 A C D E) &  ( ((k3_graph_1 A F) = B)  &  ( ((k4_graph_1 A F) = C)  & (v9_cat_1 F A B C)) ) )  => (r2_cat_3 A B (k1_cat_1 A F D) (k1_cat_1 A F E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_cat_1 A (k19_cat_4 A) B) = (k1_tarski (k24_cat_4 A B))) ) ) ) ) ).
tt(t59_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  ((v1_partfun1 B A) <=> (v1_partfun1 (k25_valued_1 A k2_numbers B C) A)) ) ) ) ) ) ) ).
tt(t59_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ((k10_chain_1 B C A (k5_chain_1 B C (k2_nat_1 A 1))) = (k5_chain_1 B C A)) ) ) ) ) ) ) ).
tt(t59_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( (C = D)  =>  (! [E:$i] :  ((m1_chord E A (k6_domain_1 (k6_glib_000 A) C)) =>  (! [F:$i] :  ((m1_chord F B (k6_domain_1 (k6_glib_000 B) D)) => (r5_glib_000 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ( ((v6_circcomb C A) & (v6_circcomb D B))  => (r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t59_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r7_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m2_circtrm1 G A C B D E F) =>  (! [H:$i] :  ((m1_dtconstr H (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ((r2_hidden H (k9_trees_9 D)) =>  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 E F))) =>  ((r1_facirc_1 E F (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 H)))) (k1_funct_1 G H)) &  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  ( (J = (k3_relat_1 G I))  =>  (! [K:$i] :  ((m1_circtrm1 K A C D B J) =>  ((k1_funct_1 (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 H)))) (k1_funct_1 G H)) = (k7_circtrm1 A B C H K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_classes1,ax, (! [A:$i] :  ((k5_classes1 (k5_classes1 A)) = (k5_classes1 A)) ) ).
tt(t59_classes2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ((r2_hidden A B) =>  ((r2_hidden (k9_setfam_1 A) B) &  ((r2_hidden (k3_tarski A) B) & (r2_hidden (k1_setfam_1 A) B)) ) ) ) ) ) ).
tt(t59_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  (! [C:$i] :  ((m1_clvect_1 C A) => (m1_clvect_1 (k3_clvect_1 B) C)) ) ) ) ) ) ).
tt(t59_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_clvect_2 B A) & (v2_clvect_2 C A))  => (v2_clvect_2 (k16_csspace A B C) A)) ) ) ) ) ) ) ).
tt(t59_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C (k3_tarski A)) &  ((r2_hidden D (k3_tarski B)) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v10_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k11_cohsp_1 A B E) = (k1_tarski (k4_tarski C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k9_real_1 (k17_complex1 A) (k17_complex1 B)) (k17_complex1 (k6_xcmplx_0 A B)))) ) ) ) ).
tt(t59_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k2_complex2 (k11_complex1 A B) C) = (k11_complex1 (k2_complex2 A C) (k2_complex2 B C))) ) ) ) ) ) ) ).
tt(t59_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (~  ( (~  (A = (k4_struct_0 k1_complfld)) )  & (r1_xxreal_0 (k17_complex1 A) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k17_complex1 A) k6_numbers))  &  (A = (k4_struct_0 k1_complfld)) ) ) ) ) ) ).
tt(t59_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_complsp2 (k12_seq_4 A k7_complex1) B) = (k5_binop_2 k7_complex1 (k8_complsp2 A B))) ) ) ) ) ) ).
tt(t59_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k1_funct_1 (k11_compos_1 A B) 1) = (k2_compos_1 A)) ) ) ) ) ).
tt(t59_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G) 4) = (k5_compos_0 (u1_compos_1 A) F 4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_comptrig,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_comptrig B k6_numbers A) =>  (B = k6_numbers) ) ) ) ) ).
tt(t59_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers)) =>  ( ((r2_hidden A (k4_finseq_1 D)) & (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 B) 1) D A k6_numbers) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 B C A))))  =>  ((k1_recdef_1 (k7_comput_1 B C A) (k8_comput_1 (k2_nat_1 (k19_margrel1 B) 1) D A k6_numbers)) = (k1_recdef_1 B (k2_finseq_3 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t59_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) & (v1_comseq_3 (k1_valued_0 k2_numbers A B))) )  => (v1_comseq_3 A)) ) ) ).
tt(t59_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = k1_xboole_0)  => (v2_convex4 B A)) ) ) ) ) ).
tt(t59_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((v2_cqc_the1 C A) => (r3_cqc_the1 A B C)) ) ) ) ) ) ) ).
tt(t59_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A C (k11_cqc_lang A D B)) (k11_cqc_lang A D (k12_cqc_lang A C B))) A)) ) ) ) ) ) ) ) ).
tt(t59_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r7_cqc_the3 A B C) => (r7_cqc_the3 A (k12_cqc_lang A D B) (k12_cqc_lang A D C))) ) ) ) ) ) ) ) ) ).
tt(t59_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k15_csspace A (k5_algstr_0 A B C) (k5_algstr_0 A D C)) (k7_real_1 (k15_csspace A C B) (k15_csspace A C D)))) ) ) ) ) ) ) ) ).
tt(t59_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k8_real_1 2 B)) (k21_sin_cos (k8_real_1 2 (k9_real_1 B A)))))) ) ) ) ) ).
tt(t59_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k8_real_1 3 (k18_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2))) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k18_sin_cos (k10_real_1 (k8_real_1 3 (k9_real_1 (k8_real_1 2 B) A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2))))))) ) ) ) ) ).
tt(t59_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k29_sin_cos)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k29_sin_cos)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k29_sin_cos) k16_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k7_real_1 A (k13_complex1 B 2))) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k7_real_1 A (k13_complex1 B 2)))) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k9_real_1 A (k13_complex1 B 2))) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k9_real_1 A (k13_complex1 B 2)))) 2)))) ) ) ) ) ) ).
tt(t59_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  (~  ((k1_card_1 (a_4_1_ec_pf_1 A B C D)) = (k2_xcmplx_0 1 (k2_ec_pf_1 A (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) D 3) (k8_group_1 (k9_int_3 A) B D)) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k9_int_3 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k9_int_3 A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k9_int_3 A))) =>  (! [K:$i] :  ((m2_subset_1 K (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k6_int_1 3 A))  &  ( (E = (k6_int_1 4 A))  &  ( (F = (k6_int_1 8 A))  &  ( (G = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) D (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2))))  &  ( (H = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))  &  ( (I = (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) H))  &  ( (J = (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k8_group_1 (k9_int_3 A) F I)))  &  (L = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C J) H) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E I) J)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k2_binom (k9_int_3 A) H 2))) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 3)))) ) ) ) ) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C H) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) = (k4_algstr_0 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)))) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C H) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A)) (k23_ens_1 A B C) D) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 B C (k3_graph_1 B D)) (k2_cat_1 B C (k4_graph_1 B D)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B)) (k2_cat_1 B C (k3_graph_1 B D)) (k2_cat_1 B C (k4_graph_1 B D))) (k17_ens_1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t59_entropy1,ax, (! [A:$i] :  ( ((v1_matrix_1 A) &  ((v2_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) )  =>  ((k2_entropy1 k1_numbers (k5_entropy1 A)) = (k4_entropy1 (k2_entropy1 k1_numbers A))) ) ) ).
tt(t59_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k1_enumset1 B C A)) ) ) ) ).
tt(t59_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 C)) => (r2_relset_1 B C (k7_relset_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B C) (k16_funct_3 A C B C D (k6_partfun1 C)) (k8_mcart_1 A C E F)) (k8_mcart_1 B C (k7_relset_1 A B D E) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_euclid_3 2 (k5_algstr_0 (k15_euclid 2) B A) (k5_algstr_0 (k15_euclid 2) C A)) & (v1_xboole_0 (k7_euclid_3 2 A B C))) ) ) ) ) ) ) ) ).
tt(t59_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k9_euclid 3 (k1_euclid_8 A B C) D) = (k1_euclid_8 (k11_binop_2 D A) (k11_binop_2 D B) (k11_binop_2 D C))) ) ) ) ) ) ) ) ) ).
tt(t59_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((k4_algstr_0 (k15_euclid 2) A) = (k19_euclid (k1_real_1 (k17_euclid A)) (k1_real_1 (k18_euclid A)))) ) ) ).
tt(t59_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r2_hidden B C) <=>  ((k3_euclidlp A B C) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t59_exchsort,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A (k6_subset_1 (k1_ordinal1 B) C)) <=>  ((r1_ordinal1 C A) & (r1_ordinal1 A B)) ) ) ) ) ) ) ) ).
tt(t59_facirc_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (! [D:$i] :  ( (~ (v1_xtuple_0 D))  =>  (~ (v1_facirc_1 (k2_msafree2 (k8_facirc_1 B C D A)))) ) ) ) ) ) ) ) ) ).
tt(t59_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos) A) B) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t59_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k5_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 2)) = (k8_finseq_1 k5_numbers (k5_fib_num2 (k4_nat_1 2 A)) (k12_finseq_1 k5_numbers (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 2))))) ) ) ).
tt(t59_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v15_lattices A) &  ((v16_lattices A) & (l3_lattices A)) ) ) )  &  ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v12_lattices A) & (l3_lattices A)) ) ) )  =>  ( (~ (v2_struct_0 (k6_filter_0 A (k2_filter_0 A B))))  &  ((v10_lattices (k6_filter_0 A (k2_filter_0 A B))) &  ((v15_lattices (k6_filter_0 A (k2_filter_0 A B))) &  ((v16_lattices (k6_filter_0 A (k2_filter_0 A B))) & (l3_lattices (k6_filter_0 A (k2_filter_0 A B)))) ) ) ) ) ) ) ) ) ).
tt(t59_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden C (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k9_filter_0 A B) D)) & (r2_hidden E (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k9_filter_0 A B) D)))  =>  ((r2_hidden (k3_lattices A C E) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k9_filter_0 A B) D)) & (r2_hidden (k4_lattices A C E) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k9_filter_0 A B) D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v18_lattices D A) &  ((v21_lattices D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (~  ((r2_filter_2 A D) &  ( ((r2_hidden B D) &  (~ (r2_hidden C D)) )  |  ( (~ (r2_hidden B D))  & (r2_hidden C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_xxreal_0 A (k3_finseq_1 B)) =>  ((k3_finseq_1 (k16_finseq_1 A B)) = A) ) ) ) ) ) ).
tt(t59_finseq_2,ax, (! [A:$i] :  ((k2_finseq_2 1 A) = (k9_finseq_1 A)) ) ).
tt(t59_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k3_finseq_1 (k1_finseq_3 A B)) = (k6_xcmplx_0 (k3_finseq_1 A) (k5_card_1 (k8_relat_1 A B)))) ) ) ) ).
tt(t59_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((r1_tarski (k10_xtuple_0 A) (k4_finseq_1 A)) & (v2_funct_1 A))  =>  ((k10_xtuple_0 A) = (k4_finseq_1 A)) ) ) ) ).
tt(t59_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((k2_xcmplx_0 B C) = (k2_nat_1 (k3_finseq_1 A) 1)) )  => (r2_hidden C (k4_finseq_1 (k3_finseq_5 A)))) ) ) ) ) ) ) ).
tt(t59_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden C (k10_xtuple_0 D)) =>  ((r1_xxreal_0 (k4_finseq_4 D C) A) |  ((k1_finseq_5 B (k2_rfinseq B A D) C) = (k2_rfinseq B A (k1_finseq_5 B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo C A) &  ((v2_binop_1 C A) & (v1_finseqop C A)) )  =>  ( ((k5_binop_1 A C (k3_funct_2 A A (k5_finseqop A C) B) B) = (k4_binop_1 A C))  &  ((k5_binop_1 A C B (k3_funct_2 A A (k5_finseqop A C) B)) = (k4_binop_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t59_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k7_flang_1 A B D) (k8_flang_1 A C))) ) ) ) ) ) ) ) ).
tt(t59_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k8_flang_1 A (k1_flang_2 A B C D)) (k8_flang_1 A B))) ) ) ) ) ) ) ).
tt(t59_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) => (r1_tarski B (k2_flang_3 A B))) ) ) ).
tt(t59_fomodel0,ax, (! [A:$i] :  ( ((k3_xboole_0 (k23_fomodel0 A) A) = k1_xboole_0)  &  (~ (v1_finset_1 (k23_fomodel0 A))) ) ) ).
tt(t59_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v8_struct_0 E) &  ((v5_fsm_1 E A B) &  ((v7_fsm_1 E A B) & (l2_fsm_1 E A B)) ) ) )  =>  ( ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  (C = (k13_fsm_1 A B D E)) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_fsm_1 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G F) =>  (! [H:$i] :  ((m1_subset_1 H F) =>  (~  ((r2_hidden G (u1_struct_0 D)) &  ((r2_hidden H (u1_struct_0 D)) &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((v2_binop_1 C A) => (r2_funct_2 B A (k9_funcop_1 A B C (k10_funcop_1 A B C E D) F) (k10_funcop_1 A B C E (k9_funcop_1 A B C D F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_funct_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r2_hidden A (k9_xtuple_0 B)) =>  ((k9_relat_1 B A) = (k1_tarski (k1_funct_1 B A))) ) ) ) ) ).
tt(t59_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A (k1_partfun1 A A A A B C) C) => (r2_relset_1 A A B (k6_partfun1 A))) ) ) ) ) ) ).
tt(t59_funct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((k3_funct_2 A (k2_zfmisc_1 B C) (k14_funct_3 A B C D E) F) = (k4_tarski (k3_funct_2 A B D F) (k3_funct_2 A C E F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C))))  =>  (! [H:$i] :  ( ((v1_funct_1 H) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D E) F))))  =>  ((v1_funct_1 (k3_funct_4 G H)) & (m1_subset_1 (k3_funct_4 G H) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A D) (k2_zfmisc_1 B E)) (k2_zfmisc_1 C F))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_funct_5,ax, (! [A:$i] :  (! [B:$i] :  ((k9_funct_2 A (k1_tarski B)) = (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B))) (k7_funcop_1 A B))) ) ) ).
tt(t59_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((k9_xtuple_0 (k2_funct_6 A)) = (k9_xtuple_0 A)) ) ) ).
tt(t59_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_funcop_1 B) & (v1_finseq_1 B)) ) )  =>  ( (~  (B = k1_xboole_0) )  => (r1_tarski (k10_xtuple_0 (k4_funct_7 A B)) (k7_funct_7 B))) ) ) ) ).
tt(t59_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_funct_1 k1_funct_8 (k4_xcmplx_0 A)) = (k4_xcmplx_0 (k1_funct_1 k1_funct_8 A))) ) ) ).
tt(t59_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (v1_vectsp_2 (k7_fvaluat1 A B))) ) ) ) ) ).
tt(t59_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v5_group_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_vectsp_1 B) &  ((v6_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B C (k4_algstr_0 B (k5_struct_0 B))) = (k6_fvsum_1 A B C)) ) ) ) ) ) ) ).
tt(t59_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_funct_1 (k6_circuit2 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D) (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) = (k2_binarith E (k9_margrel1 F)))  &  ( ((k1_funct_1 (k6_circuit2 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D) A) = E)  &  ( ((k1_funct_1 (k6_circuit2 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D) B) = F)  &  ((k1_funct_1 (k6_circuit2 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k27_glib_000 A C)) <=>  (? [D:$i] : (r2_glib_000 A C D B)) ) ) ) ) ) ) ).
tt(t59_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((k3_glib_001 A (k20_glib_001 A B C D)) = (k3_glib_001 A B))  &  ((k4_glib_001 A (k20_glib_001 A B C D)) = (k4_glib_001 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t59_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid 1 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid 1 k6_numbers))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) (k1_matrix_1 A))) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid 1 k6_numbers)))))) ) ).
tt(t59_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) A))  &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) (k2_nat_1 B 1)))  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 2))) (k3_topreal1 2 C)) & (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 C (k3_finseq_1 A))) )  =>  ( (D = (k8_graph_2 A B C))  <=>  ((r1_xxreal_0 B D) &  ((r1_xxreal_0 D C) &  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 B E) & (r1_xxreal_0 E C))  => (r1_xxreal_0 (k1_funct_1 A D) (k1_funct_1 A E))) ) )  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 B E) &  ( (~ (r1_xxreal_0 D E))  & (r1_xxreal_0 (k1_funct_1 A E) (k1_funct_1 A D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  =>  ( (? [B:$i] :  ( ((v2_funct_1 B) &  ((v1_msscyc_1 B A) & (m2_graph_1 B A)) )  & (v1_graph_3 B A)) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v1_abian (k10_graph_1 A B))) ) ) ) ) ).
tt(t59_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (~  ( (~  ((k4_graph_5 B C D) = k1_xboole_0) )  &  (! [E:$i] :  ((m2_finseq_1 E (u4_struct_0 B)) =>  (~  ((r2_hidden E (k4_graph_5 B C D)) &  (! [F:$i] :  ((m2_finseq_1 F (u4_struct_0 B)) =>  ((r2_hidden F (k4_graph_5 B C D)) => (r1_xxreal_0 (k10_graph_5 B E A) (k10_graph_5 B F A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_groeb_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  ( (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 G (k15_pre_poly A) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ( ((r2_hidden E D) &  ((r2_hidden F D) & (r4_rewrite1 (k3_polyred A B C D) (k3_groeb_2 A B C E F) G)) )  =>  ((r1_groeb_2 A (k3_termord A B C E) (k3_termord A B C F)) | (r2_funct_2 (k15_pre_poly A) (u1_struct_0 C) G (k7_polynom1 A C))) ) ) ) ) ) ) )  =>  ((r2_hidden (k7_polynom1 A C) D) | (r1_groeb_1 A B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t59_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 B C) => (r1_tarski (k3_group_11 A B D) (k3_group_11 A C D))) ) ) ) ) ) ) ) ) ).
tt(t59_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ).
tt(t59_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((u1_struct_0 (k6_group_3 A C B)) = (k5_group_2 A B (k13_group_2 A C (k2_group_1 A B)))) ) ) ) ) ) ) ).
tt(t59_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((r1_group_2 A (k8_group_4 A (k7_group_2 A) B) (k7_group_2 A)) & (r1_group_2 A (k8_group_4 A B (k7_group_2 A)) (k7_group_2 A))) ) ) ) ) ).
tt(t59_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) & (l3_algstr_0 A)) ) ) )  <=>  ((k6_group_5 A) = (k6_domain_1 (u1_struct_0 A) (k1_group_1 A))) ) ) ) ).
tt(t59_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v1_group_3 B A) & (m1_group_2 B A))  => (v2_funct_2 (k8_group_6 A B) (u1_struct_0 (k5_group_6 A B)))) ) ) ) ).
tt(t59_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) &  ((v1_group_6 D C B) &  ((v7_group_9 D A C B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) ) ) )  => (r3_group_9 A (k10_group_9 A C (k13_group_9 A C B D)) (k14_group_9 A C B D))) ) ) ) ) ) ) ).
tt(t59_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ((k1_binop_1 (k6_hermitan A B C) D (k3_vectsp_4 k1_complfld B E (k14_bilinear k1_complfld A B (k3_hermitan A B C)))) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 k1_complfld) C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k30_sin_cos)) =>  ((r2_fdiff_1 k30_sin_cos A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 k30_sin_cos A) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos)) (k1_real_1 1)) A))) ) ) ) ).
tt(t59_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r1_tarski B C) => (r1_tarski (k9_ideal_1 A B) (k9_ideal_1 A C))) ) ) ) ) ) ) ).
tt(t59_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k2_xcmplx_0 (k3_xcmplx_0 (k5_int_1 B A) A) (k6_int_1 B A))) ) ) ) ) ) ).
tt(t59_integr11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers A)) A) B) = (k5_square_1 (k1_seq_1 k30_sin_cos B))) ) ) ) ) ) ) ) ).
tt(t59_integr14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k7_real_1 (k1_seq_1 k16_sin_cos D) (k10_real_1 (k1_seq_1 k16_sin_cos D) (k5_square_1 (k1_seq_1 k19_sin_cos D))))) ) ) )  &  ((r1_tarski C (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos))) &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t59_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B C) &  ( ((k9_xtuple_0 k29_sin_cos) = C)  &  ( ((k9_xtuple_0 k29_sin_cos) = (k9_xtuple_0 A))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ( ((k1_seq_1 A D) = (k10_real_1 1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k19_sin_cos D))))  &  (~  ((k3_funct_2 k1_numbers k1_numbers k19_sin_cos D) = k6_numbers) ) ) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) ) )  =>  ((k2_integra5 B A) = (k9_real_1 (k1_seq_1 k29_sin_cos (k4_seq_4 B)) (k1_seq_1 k29_sin_cos (k5_seq_4 B)))) ) ) ) ) ) ) ) ).
tt(t59_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k7_real_1 H A))  &  (~ (r1_xxreal_0 (k1_seq_1 E H) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A)))) = G)  &  ( (G = (k1_relset_1 k1_numbers F))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ((k1_seq_1 F H) = (k10_real_1 (k9_real_1 H B) (k7_real_1 H A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F C))) ) ) ) ) )  =>  ((k2_integra5 C F) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A))) (k4_seq_4 C)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k7_real_1 B A))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  ((k15_interva1 A (k17_interva1 A B C)) = (k9_subset_1 (u1_struct_0 A) (k15_interva1 A B) (k15_interva1 A C))) ) ) ) ) ) ) ).
tt(t59_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 A (k5_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t59_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_7_jgraph_4 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t59_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid A)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid B)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid C)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid D)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid D)) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid J)))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=>  (~  ( (~  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A C) (k19_euclid A D))) & (r1_xxreal_0 (k18_euclid E) (k18_euclid F))) )  &  ( (~ (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))))  &  ( (~ (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C))))  &  (~  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) &  (~  (F = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) D) &  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H))) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) B)) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H))) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_connsp_1 D (k15_euclid 2)) &  ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan9 D B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 D B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) 1 C)) ) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) (k14_pscomp_1 (k3_topreal1 2 (k1_jordan9 D B))))) ) ) ) ) ) ) ) ) ).
tt(t59_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1)))  &  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E)) ) ) )  =>  ((r1_xboole_0 (k5_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski D (k7_nat_d E 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k3_topreal1 2 (k1_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k3_topreal1 2 (k2_jordan1e B A))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k14_euclid 1)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (A = (a_1_0_jordan2c B))  & (v6_tbsp_1 A (k14_euclid 1))) ) ) ) ) ) ).
tt(t59_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ( (~  (D = C) )  & (r2_hidden C (k3_jordan6 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v1_funct_1 (k4_jordan A)) &  ((v1_funct_2 (k4_jordan A) (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc (k4_jordan A) (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 (k4_jordan A) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ) ) ).
tt(t59_kurato_1,ax, ((k5_card_1 (k3_kurato_1 k3_topmetr k6_kurato_1)) = 6) ).
tt(t59_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v14_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F B) => (r3_lattices C E (k3_funct_2 A (u1_struct_0 C) D F))) ) )  => (r3_lattices C E (k3_lattice2 A C B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (~  ( (~  ((k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)) = (k6_glib_000 A)) )  & (r2_hidden (k19_lexbfs A B) (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B)))) ) ) ) ) ) ).
tt(t59_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((v7_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v7_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ( ((v7_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v8_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ( ((v8_limfunc1 A) =>  ((r1_xxreal_0 B k6_numbers) | (v8_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) )  &  ((v8_limfunc1 A) =>  ((r1_xxreal_0 k6_numbers B) | (v7_limfunc1 (k26_valued_1 k1_numbers k1_numbers A B))) ) ) ) ) ) ) ) ) ).
tt(t59_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r4_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = (k8_real_1 (k2_limfunc2 B A) (k2_limfunc2 C A))) ) ) ) ) ) ) ) ) ).
tt(t59_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r5_limfunc2 B A) &  ((v3_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r4_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k4_limfunc1 C)) ) ) ) ) ) ) ) ) ).
tt(t59_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  ( ( ((k7_real_1 (k10_real_1 1 F) (k10_real_1 1 G)) = 1)  &  ((r2_hidden D (k1_lpspace2 A B C F)) & (r2_hidden E (k1_lpspace2 A B C G))) )  =>  ((r2_hidden (k20_valued_1 A k1_numbers k1_numbers D E) (k9_lpspace1 A B C)) & (r3_mesfunc6 A B C (k20_valued_1 A k1_numbers k1_numbers D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) =>  ((r8_ltlaxio1 C (k3_hilbert1 (k6_ltlaxio1 A) B)) => (r8_ltlaxio1 (k4_subset_1 k1_hilbert1 C (k6_domain_1 k1_hilbert1 A)) B)) ) ) ) ) ) ) ).
tt(t59_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A E (k8_cqc_lang A B C)) & (r3_cqc_the1 A E (k8_cqc_lang A C D)))  => (r3_cqc_the1 A E (k8_cqc_lang A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_mathmorp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) => (r1_tarski (k6_mathmorp 2 (k15_euclid A) B) (k6_rusub_4 (k15_euclid A) B B))) ) ) ) ).
tt(t59_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  ((r2_matrix10 (k3_matrix10 A B C) D) => (r2_matrix10 B (k4_matrix10 A D C))) ) ) ) ) ) ) ) ) ).
tt(t59_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_matrix_1 D C A B) =>  (! [E:$i] :  ((m1_matrix_1 E C A B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 F A) =>  ((r1_xxreal_0 A k1_xboole_0) |  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_finseq_1 F) (k2_finseq_1 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 F) (k2_finseq_1 A))))) )  =>  (? [H:$i] :  ((m1_matrix_1 H C A B) &  ( (H = (k1_funct_4 D (k5_relat_1 (k3_relat_1 (k1_funct_4 (k1_finseq_2 A) G) E) (k2_finseq_1 F))))  &  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden I (k2_finseq_1 F)) =>  ((k1_funct_1 H I) = (k1_funct_1 E (k1_funct_1 G I))) )  &  ( (~ (r2_hidden I (k2_finseq_1 F)))  =>  ((k1_funct_1 H I) = (k1_funct_1 D I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((m1_matrix_1 E A B C) =>  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (! [G:$i] :  ( ((v1_finset_1 G) &  ((v1_setfam_1 G) & (m1_subset_1 G (k1_zfmisc_1 k5_numbers))) )  =>  (! [H:$i] :  ((m2_finseq_1 H A) =>  (! [I:$i] :  ((m2_finseq_1 I A) =>  ( ( ((k3_finseq_1 H) = (k1_matrix_1 E))  &  ( (I = (k1_partfun1 k5_numbers k5_numbers k5_numbers A (k5_matrix13 F) H))  & (r1_tarski (k2_zfmisc_1 G F) (k2_matrix_1 E))) )  =>  ((k3_matrix11 D (k5_card_1 G) (k5_card_1 F) A (k6_matrix13 A E G F) I) = (k6_matrix13 A (k3_matrix11 (k1_funct_1 (k5_matrix13 G) D) B C A E H) G F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((r2_hidden (k3_matrix15 (u1_struct_0 A) D) (k4_matrix15 A B (k3_matrix15 (u1_struct_0 A) C))) =>  ((k3_finseq_1 D) = (k1_matrix_1 B)) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  ((v6_matrix16 B A) =>  ((k3_matrix16 A (k5_fvsum_1 A B)) = (k1_matrix_6 (k3_finseq_1 B) A (k3_matrix16 A B))) ) ) ) ) ) ).
tt(t59_matrix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 B))))  =>  (! [E:$i] :  ( ((v1_matrix_1 E) & (m2_finseq_1 E (k3_finseq_2 (u1_struct_0 B))))  =>  ( ((k1_matrix_1 D) = (k1_matrix_1 E))  =>  ( (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (~ (r2_hidden (k4_tarski A F) (k2_matrix_1 D))) ) )  |  ((k8_matrix_1 (u1_struct_0 B) (k3_matrix_3 B D E) A) = (k3_fvsum_1 B (k8_matrix_1 (u1_struct_0 B) D A) (k8_matrix_1 (u1_struct_0 B) E A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v4_matrix_6 C A B) & (v4_matrix_6 D A B))  =>  ((r1_xxreal_0 A k6_numbers) | (v4_matrix_6 (k4_matrix_6 A B (k5_matrix_6 A B C) D) A B)) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k3_matrix_6 A B C D)) = (k5_algstr_0 B (k1_matrix_8 A B C) (k1_matrix_8 A B D))) ) ) ) ) ) ) ) ) ).
tt(t59_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((r1_xxreal_0 (k1_matrix_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k8_complsp2 (k6_matrixc1 C A) B) = (k8_complsp2 A (k6_matrixc1 (k2_matrixc1 C) B))) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((k23_matrixj1 B (k17_finseq_1 k5_numbers A C)) = (k18_matrixj1 (u1_struct_0 B) A (k23_matrixj1 B C))) ) ) ) ) ) ) ).
tt(t59_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 C) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k11_matrixr1 C (k10_rvsum_1 B A)) = (k10_rvsum_1 (k11_matrixr1 C B) A)) ) ) ) ) ) ) ) ) ).
tt(t59_matrixr2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k1_matrix_1 C))  &  ((k1_matrix_1 B) = (k3_finseq_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k11_matrixr1 (k6_matrixr1 B C) A) = (k11_matrixr1 B (k11_matrixr1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t59_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v6_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 A)) => (r1_xxreal_0 (k3_matrix_1 k1_numbers A B C) 1)) ) ) ) ) ) ) ).
tt(t59_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  ( (~ (r1_tarski A (k4_zfmisc_1 A B C D)))  &  ( (~ (r1_tarski A (k4_zfmisc_1 B C D A)))  &  ( (~ (r1_tarski A (k4_zfmisc_1 C D A B)))  &  (~ (r1_tarski A (k4_zfmisc_1 D A B C))) ) ) ) )  =>  (A = k1_xboole_0) ) ) ) ) ) ).
tt(t59_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((v2_rcomp_1 A) <=>  (A = (k6_measure6 A)) ) ) ) ).
tt(t59_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k4_member_1 (k8_member_1 A B)) = (k10_member_1 (k4_member_1 A) B)) ) ) ) ) ).
tt(t59_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v1_partfun1 C (u1_struct_0 B))) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k7_nat_d (k5_memstr_0 A B (k9_memstr_0 A B C D)) D) = (k5_memstr_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(t59_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ((v3_mesfunc5 A) =>  ( (~  ( (~  ((k8_supinf_2 (k17_supinf_2 A)) = k1_supinf_1) )  &  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A C) B)) ) ) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((v1_xreal_0 B) &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k8_nat_1 k7_numbers A C) B)) ) ) ) )  &  ((k8_supinf_2 (k17_supinf_2 A)) = k1_supinf_1) ) ) ) ) ) ) ).
tt(t59_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v6_supinf_2 B) &  ((v6_supinf_2 C) & (v6_supinf_2 D)) )  => (v6_supinf_2 (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers B C) D))) ) ) ) ) ) ) ) ) ).
tt(t59_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 A)) =>  ((r1_xxreal_0 B C) => (r1_tarski (k26_mmlquery A D C) (k26_mmlquery A D B))) ) ) ) ) ) ) ) ).
tt(t59_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k22_modelc_2 (k42_modelc_2 A B) D)) <=> (r6_modelc_2 A B (k29_modelc_2 A C 1) D)) ) ) ) ) ) ) ) ) ).
tt(t59_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  (! [D:$i] :  ((m1_orders_1 D (k1_orders_1 (k1_modelc_3 A))) =>  ((r8_modelc_2 C (k14_modelc_3 A B)) =>  ((v3_modelc_3 B A) |  ((r8_modelc_2 C (k14_modelc_3 A (k25_modelc_3 C A D B))) & (r4_modelc_3 A B (k25_modelc_3 C A D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  => (r1_xxreal_0 (k11_nat_3 (k6_moebius1 B) A) (k11_nat_3 B A))) ) ) ) ).
tt(t59_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k9_monoid_0 A) = (g3_algstr_0 (k3_finseq_2 A) (k11_monoid_0 A))) ) ) ).
tt(t59_nat_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (~  ( (~ (r1_xxreal_0 (k5_card_1 A) 1))  &  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  (~  (B = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_nat_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k1_seq_1 (k13_nat_3 (k1_newton A B)) A) = (k1_newton A B)) ) ) ) ) ).
tt(t59_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k2_nat_1 (k7_nat_d B (k1_nat_1 A 1)) 1) = (k7_nat_d B A)) ) ) ) ) ) ).
tt(t59_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) => (r7_ncfcont1 A B C (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t59_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k5_nat_d A B) k6_numbers)) ) ) ) ) ) ) ).
tt(t59_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_oppcat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E B C) => (m1_oppcat_1 (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t59_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r7_orders_1 A B) <=> (r6_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t59_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal1 A B) => (r1_ordinal1 (k5_ordinal3 A C) (k5_ordinal3 B C))) ) ) ) ) ) ) ).
tt(t59_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden k6_numbers A) &  ((r2_hidden 1 B) &  (C = (k5_ordinal5 A B)) ) )  => (r2_hidden (k6_ordinal3 A (k12_ordinal2 B C)) B)) ) ) ) ) ) ) ).
tt(t59_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  ((v4_ordinal1 B) &  (~ (v1_xboole_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden B C) &  (! [D:$i] :  ((v3_ordinal1 D) =>  ((r2_hidden D B) => (r1_abian A (k1_funct_1 (k11_ordinal6 C) D))) ) ) )  => (r1_abian A (k8_ordinal6 (k5_relat_1 (k11_ordinal6 C) B)))) ) ) ) ) ) ) ).
tt(t59_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t59_partfun1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_partfun1 k1_xboole_0 A)) ) ).
tt(t59_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B))))  =>  (~  ((r2_hidden D (k7_relset_1 C B E A)) &  (! [F:$i] :  ((m1_subset_1 F C) =>  (~  ((r2_hidden F (k1_relset_1 C E)) &  ((r2_hidden F A) &  (D = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k4_pboole A B (k1_pboole A)) B)) ) ) ).
tt(t59_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r2_pdiff_5 C B) =>  ((r3_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) &  ((k11_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) = (k8_real_1 A (k2_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t59_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((r1_tarski B (k1_relset_1 (k1_euclid A) C)) & (r2_pdiff_9 B A C))  =>  ((r2_pdiff_9 B A (k26_valued_1 (k1_euclid A) k1_numbers C D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E B) =>  ((k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B (k26_valued_1 (k1_euclid A) k1_numbers C D)) E) = (k24_valued_1 (k7_partfun1 (k9_funct_2 (k1_euclid A) k1_numbers) (k2_pdiff_9 A B C) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_pepin,ax,(v1_int_2 5)).
tt(t59_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k9_xtuple_0 (k2_xboole_0 A (k12_pnproc_1 B (k3_finseq_1 A)))) = (k2_finseq_1 (k2_nat_1 (k3_finseq_1 A) (k3_finseq_1 B)))) ) ) ) ) ).
tt(t59_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_polyform A (k6_xcmplx_0 B 1))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k17_polyform A B))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ( ( (B = k6_numbers)  &  ( (E = (k1_tarski C))  &  ( (C = (k15_polyform A B G))  &  ((r1_xxreal_0 1 F) &  ((r1_xxreal_0 F (k11_polyform A B)) &  ((r1_xxreal_0 1 G) & (r1_xxreal_0 G (k11_polyform A B))) ) ) ) ) )  =>  ( (F = G)  |  ((k1_funct_1 (k19_polyform A B D E) F) = (k4_struct_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_polynom5 A B C) <=> (r1_polynom5 A (k7_polynom5 A B) C)) ) ) ) ) ) ) ) ).
tt(t59_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 F (k15_pre_poly A) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) E F) => (r2_hidden (k6_polynom1 A C E F) (k7_ideal_1 (k11_polynom1 A C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_power,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k8_nat_1 k1_numbers A B) = (k4_power (k7_real_1 1 (k10_real_1 1 (k2_nat_1 B 1))) (k2_nat_1 B 1))) ) )  => (v2_comseq_2 A)) ) ) ).
tt(t59_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r3_pre_poly A (k16_pre_poly A) B)) ) ) ).
tt(t59_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k6_prepower (k6_prepower A B) C) = (k6_prepower A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t59_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_3 D A B) =>  ((k1_relset_1 k5_numbers (k1_partfun1 k5_numbers (k9_setfam_1 A) B k1_numbers D C)) = (k1_relset_1 k5_numbers D)) ) ) ) ) ) ) ) ) ).
tt(t59_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k25_pscomp_1 A)) A) = (k1_tarski (k25_pscomp_1 A)))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k24_pscomp_1 A) (k13_pscomp_1 A)) A) = (k1_tarski (k24_pscomp_1 A))) ) ) ) ).
tt(t59_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r6_pboole A (k6_pboole A B B) (k6_pboole A C C)) => (r6_pboole A B C)) ) ) ) ) ) ).
tt(t59_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r3_qc_lang2 A B C) & (r2_qc_lang2 A C B)) ) ) ) ) ) ) ) ).
tt(t59_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k3_qc_lang2 A B C)) = (k4_subset_1 (k5_qc_lang1 A) (k5_qc_lang3 A B) (k5_qc_lang3 A C))) ) ) ) ) ) ) ).
tt(t59_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k18_quatern2 A (k29_quaterni B C)) = (k29_quaterni (k18_quatern2 A B) (k18_quatern2 A C))) ) ) ) ) ) ) ).
tt(t59_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k28_quaterni (k29_quaterni (k29_quaterni A B) C)) = (k26_quaterni (k26_quaterni (k28_quaterni A) B) C)) ) ) ) ) ) ) ).
tt(t59_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni A) = k6_numbers)  =>  ((k31_quaterni A) = (k28_quaterni A)) ) ) ) ).
tt(t59_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  => (r2_quofield A (k19_quofield A))) ) ).
tt(t59_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  => (r2_hidden B (k7_partfun1 (k9_setfam_1 k1_numbers) D (k3_finseq_1 D)))) ) ) ) ) ) ) ) ) ).
tt(t59_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~ (r1_xxreal_0 (k1_seq_1 (k4_real_3 A) B) k6_numbers)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 2)) (k8_real_1 (k8_real_1 2 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 2))) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1))))) ) ) ) ) ).
tt(t59_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k5_relat_1 B A) B)) ) ) ).
tt(t59_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) => (r2_relset_1 B A (k3_relset_1 A B (k3_subset_1 (k2_zfmisc_1 A B) C)) (k3_subset_1 (k2_zfmisc_1 B A) (k3_relset_1 A B C)))) ) ) ) ).
tt(t59_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r13_rewrite1 A B C) => (r2_rewrite1 A B C)) ) ) ) ) ).
tt(t59_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ( ((r4_rewrite2 A B C D) & (r3_rewrite2 A (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C) D E))  => (r3_rewrite2 A B D E)) ) ) ) ) ) ) ) ) ) ).
tt(t59_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  (! [H:$i] :  ((m1_rewrite1 H (k1_rewrite3 C F G)) =>  ( ( ((k1_funct_1 H 1) = (k4_tarski A D))  &  ((k1_funct_1 H (k3_finseq_1 H)) = (k4_tarski B E)) )  => (r1_xxreal_0 (k1_afinsq_1 E) (k1_afinsq_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v1_partfun1 (k6_rfunct_1 A k1_numbers C) A) =>  ((k1_funct_1 (k6_rfunct_1 A k1_numbers C) B) = (k5_xcmplx_0 (k1_funct_1 C B))) ) ) ) ) ) ) ) ).
tt(t59_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_rfunct_3 A B) => (r2_rfunct_3 (k18_rfunct_3 k1_numbers (k15_valued_1 k1_numbers k1_numbers A C)) B)) ) ) ) ) ) ).
tt(t59_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 B) =>  ((k1_seq_1 (k3_rinfsup1 B) A) = (k1_real_1 (k1_seq_1 (k4_rinfsup1 (k32_valued_1 k5_numbers k1_numbers B)) A))) ) ) ) ) ) ).
tt(t59_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_rlaffin1 A B) = (a_2_1_rlaffin1 A B)) ) ) ) ) ).
tt(t59_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r1_struct_0 D B) => (r2_hidden (k1_rlvect_1 A B C) (k3_rlsub_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t59_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v16_lattices (g3_lattices (k3_rlsub_2 A) (k5_rlsub_2 A) (k6_rlsub_2 A)))) ) ).
tt(t59_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (? [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) & (r1_tarski (k2_pre_topc A C) B)) ) ) ) ) ) ).
tt(t59_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B (k4_algstr_0 A C))) = (k5_algstr_0 A B C)) ) ) ) ) ) ) ).
tt(t59_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  ((k4_struct_0 (k16_rlvect_2 A)) = (k4_rlvect_2 A)) ) ) ).
tt(t59_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ((r2_hidden C (k3_rmod_2 A B D E)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r1_struct_0 E F) &  (C = (k5_algstr_0 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_rmod_4 A B (k7_rmod_4 A B D C)) = (k5_vectsp_2 A B D (k5_rmod_4 A B C))) ) ) ) ) ) ) ) ) ).
tt(t59_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v8_robbins1 A) & (l4_robbins1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k5_robbins1 A B (k3_robbins1 A B)) = (k6_lattices A))  &  ((k4_lattices A B (k3_robbins1 A B)) = (k5_lattices A)) ) ) ) ) ) ).
tt(t59_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) & (l2_robbins1 A)) ) )  =>  ((v5_robbins1 A) => (v1_robbins2 A)) ) ) ).
tt(t59_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_roughs_1 A B C) & (r1_roughs_1 A C D))  => (r1_roughs_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t59_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_hidden C (k3_rusub_1 A E B)) & (r2_hidden D (k3_rusub_1 A E B))) ) )  <=> (r1_struct_0 B (k5_algstr_0 A C D))) ) ) ) ) ) ) ) ) ).
tt(t59_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  => (v16_lattices (g3_lattices (k3_rusub_2 A) (k5_rusub_2 A) (k6_rusub_2 A)))) ) ).
tt(t59_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k1_seq_1 (k14_rvsum_1 B C) A) = (k11_binop_2 (k1_seq_1 B A) (k1_seq_1 C A))) ) ) ) ) ) ).
tt(t59_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (~  (A = B) ) ) ) ) ) ).
tt(t59_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D)) ) ) ) ) ) ) ) ) ).
tt(t59_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((r1_scm_halt C B A) & (r2_scm_halt C B A))  =>  ( ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k1_scmfsa_m B) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B)))) = (k11_scmfsa_2 k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 D (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k1_scmfsa_m B))) &  ((k3_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8c C)) (k1_scmfsa_m B) D)) = (k2_compos_1 k1_scmfsa_2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_scmpds_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k6_scmpds_2 C B) A) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 A)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k6_scmpds_2 C B) A) (k2_scmpds_2 (k1_funct_1 A C) B)) = (k5_memstr_0 2 k1_scmpds_2 A))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ( (~  ((k2_scmpds_2 (k1_funct_1 A C) B) = D) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 (k6_scmpds_2 C B) A) D) = (k1_funct_1 A D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  =>  ((r1_scmpds_6 (k6_scmpds_6 D E C) B A) & (r2_scmpds_6 (k6_scmpds_6 D E C) B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_scmyciel,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((k8_scmyciel (k5_scmyciel A)) = (k5_card_1 A)) ) ) ).
tt(t59_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) =>  ((r1_semi_af1 A B C D) | (r2_semi_af1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  ( ((k15_seq_4 A B (k17_seq_4 A)) = B)  &  (B = (k15_seq_4 A (k17_seq_4 A) B)) ) ) ) ) ) ).
tt(t59_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ((k4_kurato_0 A B) = (k1_kurato_0 A B)) ) ) ) ) ).
tt(t59_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  => (r1_tarski (k5_subset_1 B C (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B D) A)) (k8_nat_1 (k9_setfam_1 B) (k4_setlim_1 B (k9_setlim_2 B D C)) A))) ) ) ) ) ) ) ).
tt(t59_setwiseo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k5_finsub_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k5_finsub_1 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k5_finsub_1 B) (k5_finsub_1 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k5_finsub_1 B) (k5_finsub_1 C))))) )  =>  ( ( ((k3_funct_2 (k5_finsub_1 B) (k5_finsub_1 C) E (k1_setwiseo B)) = (k1_setwiseo C))  &  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 B)) =>  (! [G:$i] :  ((m1_subset_1 G (k5_finsub_1 B)) =>  ((k3_funct_2 (k5_finsub_1 B) (k5_finsub_1 C) E (k5_setwiseo B F G)) = (k5_setwiseo C (k3_funct_2 (k5_finsub_1 B) (k5_finsub_1 C) E F) (k3_funct_2 (k5_finsub_1 B) (k5_finsub_1 C) E G))) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (k5_finsub_1 A)) =>  ((k3_funct_2 (k5_finsub_1 B) (k5_finsub_1 C) E (k10_setwiseo A B F D)) = (k10_setwiseo A C F (k1_partfun1 A (k5_finsub_1 B) (k5_finsub_1 B) (k5_finsub_1 C) D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((r2_hidden (k16_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)) | (r2_hidden (k17_scmfsa_2 A B) (k2_relset_1 (u1_compos_1 k1_scmfsa_2) C)))  &  ((k6_sf_mastr C) = B) ) ) ) ) ) ) ) ) ).
tt(t59_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A C C))) = (k5_sheffer1 A B B)) ) ) ) ) ) ) ).
tt(t59_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ((m2_simplex0 C A B) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k10_simplex0 A B D)))) =>  ( ((r1_tarski (k9_xtuple_0 D) (u1_pre_topc C)) &  (E = (k2_struct_0 C)) )  =>  ((k10_simplex0 A C D) = (k7_simplex0 A (k10_simplex0 A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k3_sincos10 (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1))) (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k1_real_1 (k10_real_1 k32_sin_cos 4))))) = (k1_partfun2 k1_numbers (k1_rcomp_1 (k1_real_1 (k7_square_1 2)) (k1_real_1 1)))) ).
tt(t59_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B))) = (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A B)) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k4_binop_2 A B))))  &  ( ((k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B))) = (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A B)) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k4_binop_2 A B))))  &  ((k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B))) = (k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B)))) ) ) ) ) ) ) ).
tt(t59_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v2_funct_1 (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 (k8_real_1 (k8_real_1 2 k32_sin_cos) A) (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t59_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k5_power k8_power A) = (k4_sin_cos7 (k12_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k9_binop_2 (k3_square_1 A) 1)))) ) ) ) ).
tt(t59_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k5_sin_cos9 A) = k6_numbers) ) )  =>  (A = k6_numbers) ) ) ) ).
tt(t59_sin_cos,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k11_complex1 (k11_comseq_3 (k3_sin_cos (k2_xcmplx_0 B A))) (k11_comseq_3 (k3_sin_cos B))) = (k2_xcmplx_0 (k3_xcmplx_0 (k11_comseq_3 (k3_sin_cos B)) A) (k3_xcmplx_0 (k3_xcmplx_0 A (k11_comseq_3 (k27_sin_cos A))) (k11_comseq_3 (k3_sin_cos B))))) ) ) ) ) ).
tt(t59_sppol_2,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r2_hidden B A) &  ((r2_hidden C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (~  ((r1_topreal4 D B C) &  ((r1_topreal4 E B C) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) D E) = (k2_tarski B C))  &  (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k9_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k9_pscomp_1 A)) ) ) ).
tt(t59_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (r1_subset_1 (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 (k3_topreal1 2 A)) (k20_pscomp_1 (k3_topreal1 2 A))) (k1_rltopsp1 (k15_euclid 2) (k21_pscomp_1 (k3_topreal1 2 A)) (k12_pscomp_1 (k3_topreal1 2 A))))) ) ).
tt(t59_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k25_pscomp_1 (k3_topreal1 2 A)) = (k18_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k25_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t59_square_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 (k6_square_1 (k2_xcmplx_0 A B)) (k2_xcmplx_0 (k6_square_1 A) (k6_square_1 B)))) ) ) ) ) ).
tt(t59_stirl2_1,ax, (! [A:$i] :  ( ((v1_finset_1 A) & (m1_subset_1 A (k1_zfmisc_1 k5_numbers)))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A (k5_card_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A (k5_card_1 A))))) )  &  ((v3_funct_2 B A (k5_card_1 A)) &  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (~  ((r2_hidden C (k1_relset_1 A B)) &  ((r2_hidden D (k1_relset_1 A B)) &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k2_stirl2_1 A (k5_card_1 A) B D) (k2_stirl2_1 A (k5_card_1 A) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ( ((v5_relat_1 E (k3_qc_lang1 A)) &  ((v3_card_1 E B) & (m2_finseq_1 E (k2_qc_lang1 A))) )  => (r2_relset_1 k5_numbers C (k4_valuat_1 A C B E D) (k4_relset_1 k5_numbers (k2_qc_lang1 A) (k3_qc_lang1 A) C E (k5_relset_1 (k3_qc_lang1 A) C D (k23_qc_lang1 A E))))) ) ) ) ) ) ) ) ) ) ).
tt(t59_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 C A) =>  ( ((k4_subset_1 (u1_struct_0 A) (k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) (k4_subset_1 (u1_struct_0 A) B C)) = C)  <=> (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(t59_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v2_tex_2 B A) &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r1_tarski B C) & (v3_tex_2 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t59_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ((v3_tex_3 B A) & (v1_borsuk_1 B A)) ) )  & (v3_tdlat_3 A)) ) ) ) ).
tt(t59_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_tex_4 A B) (k2_pre_topc A B))) ) ) ) ).
tt(t59_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D B))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r1_tarski E (u1_struct_0 D)) &  ((m1_connsp_2 E B F) &  (F = G) ) )  =>  ((r1_tmap_1 B A C F) <=> (r1_tmap_1 D A (k2_tmap_1 B A C D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_borsuk_2 D (k15_euclid A) B C) =>  (! [E:$i] :  ((m1_borsuk_2 E (k15_euclid A) B C) => (r3_borsuk_2 (k15_euclid A) B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t59_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_topgen_4 B A) & (r1_tarski B C))  => (v1_topgen_4 C A)) ) ) ) ) ) ) ).
tt(t59_topgen_5,ax,(v1_topgen_5 k2_topgen_3)).
tt(t59_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) &  ((v1_yellow_8 B A (k1_group_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_tops_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_tops_2 (a_3_0_topgrp_1 A B C) A) &  ((v1_cantor_1 (a_3_0_topgrp_1 A B C) A) & (m1_subset_1 (a_3_0_topgrp_1 A B C) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t59_topreal6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (v6_tbsp_1 (k10_metric_1 B C A) B)) ) ) ) ) ) ).
tt(t59_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (k5_jgraph_6 A B C)) & (r2_hidden E (k6_jgraph_6 A B C)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) D E) (k5_jgraph_6 A B C)) = (k1_tarski D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) )  =>  ((v5_pre_topc C (k15_euclid A) (k15_euclid B)) =>  ((v1_funct_1 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C)) &  ((v1_funct_2 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B))) &  ((v5_pre_topc (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C) (k15_euclid A) (k15_euclid B)) & (m1_subset_1 (k20_valued_2 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t59_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) => (v3_tops_1 (k2_tops_1 A B) A)) ) ) ) ) ).
tt(t59_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_pre_topc B D)) = (k2_pre_topc A (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v1_tops_1 C A))  => (v1_tops_1 D B)) ) ) ) ) ) ) ) ) ).
tt(t59_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo D A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = B)  & (r1_diraf A C B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D C))) )  =>  ( (C = B)  | (v3_transgeo D A)) ) ) ) ) ) ) ) ) ) ).
tt(t59_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((k13_trees_3 A B) = (k5_trees_1 (k5_trees_1 (k2_trees_1 2) (k12_finseq_1 k5_numbers k6_numbers) A) (k12_finseq_1 k5_numbers 1) B)) ) ) ) ) ).
tt(t59_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_tsep_1 A B C) &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) D (k4_subset_1 (u1_struct_0 A) B C)) B) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) E (k4_subset_1 (u1_struct_0 A) B C)) C) &  (~  ( (~ (r1_tarski (k4_subset_1 (u1_struct_0 A) B C) (k4_subset_1 (u1_struct_0 A) D E)))  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v4_pre_topc F A) &  ((r1_tarski (k9_subset_1 (u1_struct_0 A) F (k4_subset_1 (u1_struct_0 A) B C)) (k9_subset_1 (u1_struct_0 A) B C)) &  ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_subset_1 C k1_numbers k5_numbers))  =>  ((r1_nat_d B A) =>  ((r1_xxreal_0 A B) |  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 k1_complfld)) =>  ( (D = C)  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( (E = (k2_polynom4 k1_complfld (k5_uniroots A) D))  => (r1_int_1 E (k5_int_1 (k21_binop_2 (k13_newton C A) 1) (k21_binop_2 (k13_newton C B) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v2_polynom5 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ((k4_uproots (u1_struct_0 A) (k8_uproots A B)) = (k7_nat_d (k1_algseq_1 A B) 1)) ) ) ) ) ).
tt(t59_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((k52_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k52_valued_2 A B C D) E) = (k52_valued_2 A B C (k1_valued_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t59_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_struct_0 D C) => (r2_hidden (k4_algstr_0 B C) (k3_vectsp_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t59_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v14_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ) ).
tt(t59_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_yellow_0 A D)) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D C) &  (! [E:$i] :  ( ((v1_finset_1 E) & (m1_subset_1 E (k1_zfmisc_1 B)))  =>  (~  ((r2_yellow_0 A E) &  (D = (k2_yellow_0 A E)) ) ) ) ) ) ) ) )  &  ( (! [D:$i] :  ( ((v1_finset_1 D) & (m1_subset_1 D (k1_zfmisc_1 B)))  =>  ( (~  (D = k1_xboole_0) )  => (r2_hidden (k2_yellow_0 A D) C)) ) )  & (r2_yellow_0 A B)) ) )  =>  ((k2_yellow_0 A C) = (k2_yellow_0 A B)) ) ) ) ) ) ) ) ).
tt(t59_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((a_3_0_waybel_1 A B C) = (k8_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k4_waybel_1 A B) (k5_waybel_0 A C))) ) ) ) ) ) ) ).
tt(t59_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  => (v5_orders_3 (k4_waybel23 A B) (k2_yellow_1 (k7_waybel_0 B)) (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(t59_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v4_waybel34 D A B) & (v4_waybel34 E B C))  => (v4_waybel34 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v9_waybel_4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_waybel_4 A (k5_waybel_4 A C B) B)) ) ) ) ) ) ) ).
tt(t59_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r2_xboole_0 B C))  => (r2_xboole_0 A C)) ) ) ) ).
tt(t59_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A (k6_xboolean A B)) = (k3_xboolean (k4_xboolean A B))) ) ) ) ) ).
tt(t59_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 1 A) = (k7_xcmplx_0 1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t59_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A (k4_xcmplx_0 B)) => (r1_xxreal_0 (k2_xcmplx_0 A B) k6_numbers)) ) ) ) ) ).
tt(t59_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k4_xxreal_1 A B) (k3_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) => (r1_xxreal_0 (k1_xxreal_2 A) (k1_xxreal_2 B))) ) ) ) ) ).
tt(t59_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  ( (A = k2_xxreal_0)  &  (B = k2_xxreal_0) ) )  &  ( (~  ( (B = k2_xxreal_0)  &  (C = k1_xxreal_0) ) )  &  ((r1_xxreal_0 A (k1_xxreal_3 C B)) &  (B = k2_xxreal_0) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_yellow_0 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  ( (F = D)  & (r1_orders_2 B E F)) )  => (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v2_waybel11 C A) & (v2_waybel11 D B))  => (v2_waybel11 (k6_yellow_3 A B C D) (k3_yellow_3 A B))) ) ) ) ) ) ) ) ) ).
tt(t59_yellow_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_tarski B (k4_waybel_0 A (k4_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t59_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k12_lattice3 A B (k1_yellow_5 A C D)) = (k1_yellow_5 A (k12_lattice3 A B C) (k12_lattice3 A B D))) ) ) ) ) ) ) ) ) ).
tt(t59_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_tops_2 D B) &  ((v1_cantor_1 D B) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) )  =>  (! [E:$i] :  ((m3_yellow_9 E A B) =>  ((v1_tops_2 (k2_xboole_0 (k2_xboole_0 C D) (k3_setfam_1 C D)) E) &  ((v1_cantor_1 (k2_xboole_0 (k2_xboole_0 C D) (k3_setfam_1 C D)) E) & (m1_subset_1 (k2_xboole_0 (k2_xboole_0 C D) (k3_setfam_1 C D)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 E))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t59_zf_lang1,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k2_zf_model (k5_zf_lang A B)) = (k2_tarski A B)) ) ) ) ) ).
tt(t59_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  => (r2_zf_lang A A)) ) ).
tt(t59_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) B) = (k1_tarski A))  <=>  (~ (r2_hidden A B)) ) ) ) ).
tt(t59_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_zmodul01 B A) =>  ((k5_zmodul01 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(t5_abcmiz_0,ax, (! [A:$i] :  ((l1_abcmiz_0 A) =>  (! [B:$i] :  ((l1_abcmiz_0 B) =>  ( ( ((g1_abcmiz_0 (u1_abcmiz_0 A) (u2_abcmiz_0 A)) = (g1_abcmiz_0 (u1_abcmiz_0 B) (u2_abcmiz_0 B)))  & (v5_abcmiz_0 A))  => (v5_abcmiz_0 B)) ) ) ) ) ).
tt(t5_abcmiz_1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (~ (v1_xtuple_0 C)) ) ) ) ) ) ) ).
tt(t5_abcmiz_a,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v1_abcmiz_a A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v1_abcmiz_a B) & (l1_msualg_1 B)) ) )  =>  ( ((u4_struct_0 A) = (u4_struct_0 B))  =>  ((g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A)) = (g1_msualg_1 (u1_struct_0 B) (u4_struct_0 B) (u1_msualg_1 B) (u2_msualg_1 B))) ) ) ) ) ) ).
tt(t5_abian,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v3_abian C (k1_zfmisc_1 (k1_zfmisc_1 A))) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) )  =>  (~  ( (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) C) => (r1_xboole_0 D (k7_relat_1 B D))) )  & (v2_abian B)) ) ) ) ) ) ) ).
tt(t5_absvalue,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((r1_xxreal_0 (k4_xcmplx_0 A) B) & (r1_xxreal_0 B A))  <=> (r1_xxreal_0 (k18_complex1 B) A)) ) ) ) ) ).
tt(t5_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  ( (~  ((r2_analoaf A B C D E) & (r2_analoaf A B C F G)) )  &  ( (~  ((r2_analoaf A B C D E) & (r2_analoaf A F G B C)) )  &  ( (~  ((r2_analoaf A D E B C) & (r2_analoaf A F G B C)) )  &  (~  ((r2_analoaf A D E B C) & (r2_analoaf A B C F G)) ) ) ) ) )  &  (~ (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_aff_2,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v9_aff_2 A) => (v10_aff_2 A)) ) ) ).
tt(t5_aff_3,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v3_aff_3 A) => (v4_aff_3 A)) ) ) ).
tt(t5_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((r2_aff_1 A B C D) | (r2_aff_1 A C B D))  &  ( ((r2_aff_1 A B C E) | (r2_aff_1 A C B E))  &  ( (~  (B = C) )  &  (~ (r5_aff_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((v1_finset_1 A) & (v5_ordinal1 A))  <=>  (? [B:$i] :  ((v7_ordinal1 B) &  ((k9_xtuple_0 A) = B) ) ) ) ) ) ).
tt(t5_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_finset_1 A)) ) )  =>  ( ((k1_relset_1 k5_numbers A) = (k1_relset_1 k5_numbers (k1_afinsq_2 A)))  &  ((k10_xtuple_0 A) = (k10_xtuple_0 (k1_afinsq_2 A))) ) ) ) ).
tt(t5_afproj,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_aff_4 A B D) &  ((r1_aff_4 A B E) &  ((r1_aff_4 A C D) &  ((r1_aff_4 A C E) &  ((v1_aff_1 B A) &  ((v1_aff_1 C A) &  ((v1_aff_4 D A) & (v1_aff_4 E A)) ) ) ) ) ) )  =>  ((r5_aff_1 A B C) | (r1_aff_4 A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_afvect01,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect01 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_analoaf A B B C C)) ) ) ) ) ) ).
tt(t5_afvect0,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_afvect0 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_analoaf A B C D E) & (r2_analoaf A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_alg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  => (r1_alg_1 A A (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t5_algseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k7_card_1 A) = (k7_card_1 B))  =>  (A = B) ) ) ) ) ) ).
tt(t5_algspec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B D)))) )  =>  ((r1_relset_1 A C E F) => (r1_relset_1 (k3_finseq_2 A) (k3_finseq_2 C) (k12_lang1 A C E) (k12_lang1 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_algstr_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_algstr_0)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_algstr_0)) =>  ((k1_algstr_0 k3_algstr_0 A B) = (k4_struct_0 k3_algstr_0)) ) ) ) ) ).
tt(t5_algstr_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_algstr_1 A) &  ((v4_algstr_1 A) &  ((v7_algstr_1 A) &  ((v2_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k6_algstr_0 A B (k2_algstr_2 A C D)) = (k2_algstr_2 A (k6_algstr_0 A B C) (k6_algstr_0 A B D))) ) ) ) ) ) ) ) ) ).
tt(t5_algstr_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_algstr_3 A) & (l1_algstr_3 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (~  (B = (k4_struct_0 A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((k1_algstr_3 A B E C) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_algstr_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (~  ((v1_group_6 C B A) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_relat_1 D (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) & (v1_funct_1 D)) )  =>  (~ (r2_relset_1 (u1_struct_0 B) (u1_struct_0 B) (k7_algstr_4 (u1_struct_0 B) (u1_struct_0 A) C) (k6_algstr_4 B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_altcat_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k2_zfmisc_1 B A)) &  ((v1_funct_1 C) & (v1_partfun1 C (k2_zfmisc_1 B A))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  (! [F:$i] :  (! [G:$i] :  ( ((r2_hidden F D) & (r2_hidden G E))  =>  ((k1_binop_1 C G F) = (k1_binop_1 (k5_relat_1 C (k8_mcart_1 B A E D)) G F)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_altcat_2,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) & (v1_partfun1 D B)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E B) &  ((v1_funct_1 E) & (v1_partfun1 E B)) ) )  =>  (! [F:$i] :  ((m2_pboole F B D E) => (m2_pboole (k3_relat_1 C F) A (k3_relat_1 C D) (k3_relat_1 C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_altcat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  ((v3_altcat_3 D A B C) =>  ((v1_altcat_3 D A B C) & (v2_altcat_3 D A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t5_altcat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_altcat_1 A C B)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_altcat_1 A C B)) =>  ( ( ((k5_altcat_1 A B C B D F) = (k8_altcat_1 A B))  &  ((k5_altcat_1 A C B C E D) = (k8_altcat_1 A C)) )  =>  ( ((k1_altcat_1 A B C) = k1_xboole_0)  |  ( ((k1_altcat_1 A C B) = k1_xboole_0)  |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ami_3,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_ami_3)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_ami_3)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 C (u1_struct_0 k1_ami_3))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k5_ami_3 A B) C) (k4_struct_0 k1_ami_3)) = (k4_card_1 (k5_memstr_0 2 k1_ami_3 C)))  &  ( ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k5_ami_3 A B) C) A) = (k3_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_ami_3)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 2 k1_ami_3 (k5_ami_3 A B) C) D) = (k1_funct_1 C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ami_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  ((r1_tarski k1_ami_4 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A C)) = 3)  =>  ( ( (~ (r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1)) k6_numbers))  =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1))) = k6_numbers) )  &  ( ((r1_xxreal_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1)) k6_numbers) =>  ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1))) = 4) )  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 k6_numbers)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 k6_numbers)))  &  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A (k2_nat_1 C 1)) (k10_ami_3 1)) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 B A C) (k10_ami_3 1))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ami_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) => (r1_xxreal_0 (k2_compos_0 (u1_compos_1 k1_ami_3) A) 8)) ) ).
tt(t5_ami_6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_compos_0 (u1_compos_1 k1_ami_3))) =>  ( (A = 2)  =>  ((k3_compos_0 (u1_compos_1 k1_ami_3) A) = (k1_tarski k1_xboole_0)) ) ) ) ).
tt(t5_amistd_1,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 (k4_amistd_1 A))) =>  (~  ( ((k2_compos_0 (u1_compos_1 (k4_amistd_1 A)) B) = 1)  & (v2_extpro_1 B A (k4_amistd_1 A))) ) ) ) ) ) ).
tt(t5_amistd_2,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_2 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((v4_compos_0 C (u1_compos_1 B)) => (v1_xboole_0 (k2_amistd_1 A B C))) ) ) ) ) ) ) ).
tt(t5_amistd_4,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_amistd_4 B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((k3_amistd_4 A B C) = (k7_subset_1 (u1_struct_0 B) (k2_amistd_4 A B C) (k5_amistd_4 A B C))) ) ) ) ) ) ) ).
tt(t5_amistd_5,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v3_extpro_1 B A) &  ((v2_amistd_5 B A) & (l1_extpro_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v1_partfun1 D (u1_struct_0 B))) ) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((k5_memstr_0 A B D) = (k2_nat_1 E F))  => (r8_pboole (u1_struct_0 B) (k2_extpro_1 A B C (k10_memstr_0 A B D F)) (k10_memstr_0 A B (k2_extpro_1 A B (k5_compos_0 (u1_compos_1 B) C F) D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ami_wstd,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) &  ((v2_ami_wstd B A) & (l1_extpro_1 B A)) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_ami_wstd A B C) = (k1_ami_wstd A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t5_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analmetr A D (k4_struct_0 A) B C) & (r2_analmetr A (k4_struct_0 A) E B C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_analoaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ((k1_rlvect_1 A B D) = C)  =>  ( (D = k6_numbers)  |  (B = (k1_rlvect_1 A C (k2_real_1 D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_analort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_analmetr A B C) =>  ((k1_analort A B C (k5_algstr_0 A D E)) = (k5_algstr_0 A (k1_analort A B C D) (k1_analort A B C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_anproj_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_anproj_1 A B C D) =>  ((r2_anproj_1 A B D C) &  ((r2_anproj_1 A C B D) &  ((r2_anproj_1 A D C B) &  ((r2_anproj_1 A D B C) & (r2_anproj_1 A C D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_anproj_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((k3_rlvect_1 A (k3_rlvect_1 A (k3_rlvect_1 A (k1_rlvect_1 A B F) (k1_rlvect_1 A C G)) (k1_rlvect_1 A D H)) (k1_rlvect_1 A E I)) = (k4_struct_0 A))  =>  ( (F = k6_numbers)  &  ( (G = k6_numbers)  &  ( (H = k6_numbers)  &  (I = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ( (~ (v9_struct_0 F A))  &  ((r2_anproj_1 A B C F) & (r2_anproj_1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_aofa_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k9_xtuple_0 B)) =>  ((r2_hidden C D) |  ((k1_funct_1 (k2_aofa_000 A B D) C) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ) ).
tt(t5_aofa_i00,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k9_xtuple_0 D) = (k9_xtuple_0 E))  &  ((k9_xtuple_0 D) = (k9_funct_2 B C)) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v2_funct_1 F) &  ((k17_aofa_i00 A D F) = (k17_aofa_i00 A E F)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_arithm,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 k6_numbers A) = k6_numbers) ) ) ).
tt(t5_armstrng,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k6_margrel1 (k4_finseq_2 A k6_margrel1)) =>  ((k3_armstrng A (k1_binari_3 A k6_numbers) B) = (k1_binari_3 A k6_numbers)) ) ) ) ) ).
tt(t5_arrow,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k2_arrow A)) =>  (~  ( (~  ( (~ (r1_arrow E B C))  & (r1_arrow E C B)) )  &  ( (~  ( (~ (r1_arrow E C D))  & (r1_arrow E D C)) )  &  (~ (r1_arrow E B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_arytm_0,ax,(r1_xboole_0 k2_arytm_2 (k2_zfmisc_1 (k1_tarski k11_arytm_3) k2_arytm_2))).
tt(t5_arytm_1,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((r1_arytm_2 A B) &  (B = k11_arytm_3) )  =>  (A = k11_arytm_3) ) ) ) ) ) ).
tt(t5_arytm_2,ax, (! [A:$i] :  ((m1_subset_1 A k2_arytm_2) =>  (! [B:$i] :  ((m1_subset_1 B k2_arytm_2) =>  ( ((k7_arytm_2 A B) = k11_arytm_3)  =>  (A = k11_arytm_3) ) ) ) ) ) ).
tt(t5_arytm_3,ax, (! [A:$i] :  ( ((v3_ordinal1 A) & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v7_ordinal1 B))  =>  ((r2_arytm_3 A B) <=>  (? [C:$i] :  ( ((v3_ordinal1 C) & (v7_ordinal1 C))  &  (B = (k9_ordinal3 A C)) ) ) ) ) ) ) ) ).
tt(t5_asympt_0,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v5_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ((v1_limfunc1 (k52_valued_1 k5_numbers k1_numbers k1_numbers A B)) =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B A)) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B A)) = k6_numbers) ) ) ) ) ) ) ).
tt(t5_asympt_1,ax, ((r1_tarski (k6_asympt_0 k2_asympt_1) (k6_asympt_0 (k3_asympt_1 (k10_real_1 1 2)))) &  (~  ((k6_asympt_0 k2_asympt_1) = (k6_asympt_0 (k3_asympt_1 (k10_real_1 1 2)))) ) ) ).
tt(t5_autalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autalg_1 A)) => (r2_hidden (k2_funct_1 B) (k1_autalg_1 A))) ) ) ) ).
tt(t5_autgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) (u1_struct_0 A) (k1_autgroup A)) =>  ((v1_funct_1 (k2_funct_1 B)) &  ((v1_funct_2 (k2_funct_1 B) (u1_struct_0 A) (u1_struct_0 A)) &  ((v1_group_6 (k2_funct_1 B) A A) & (m1_subset_1 (k2_funct_1 B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ).
tt(t5_bagorder,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (C = D)  <=>  ( ((k1_bagorder A k6_numbers (k1_nat_1 B 1) C) = (k1_bagorder A k6_numbers (k1_nat_1 B 1) D))  &  ((k1_bagorder A (k1_nat_1 B 1) A C) = (k1_bagorder A (k1_nat_1 B 1) A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  ((r1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C D)) & (r1_bcialg_1 A (k1_bcialg_1 A D C) (k1_bcialg_1 A D B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_bcialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k1_bcialg_2 A B (k4_struct_0 A) (k2_nat_1 C 1)) = B) ) ) ) ) ) ) ).
tt(t5_bcialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) &  ((v8_bcialg_1 A) &  ((v1_bcialg_3 A) & (l2_bcialg_1 A)) ) ) ) ) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_bcialg_1 A B C) =>  (B = (k1_bcialg_1 A C (k1_bcialg_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t5_bcialg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = (k4_struct_0 A))  =>  (B = C) ) ) ) ) ) ) ) ) ).
tt(t5_bcialg_5,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_bcialg_1 C) &  ((v4_bcialg_1 C) &  ((v5_bcialg_1 C) &  ((v7_bcialg_1 C) &  ((v8_bcialg_1 C) & (l2_bcialg_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((r1_xxreal_0 B A) => (r1_bcialg_1 C (k1_bcialg_2 C D E A) (k1_bcialg_2 C D E B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bcialg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_bcialg_6 A (k19_binop_2 1) B) = (k2_bcialg_1 A B)) ) ) ) ) ).
tt(t5_bciideal,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_bcialg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) B) =>  ((r1_bcialg_1 A C D) => (r2_hidden C B)) ) ) ) ) ) ) ) ) ).
tt(t5_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ((k2_bhsp_1 C (k3_rlvect_1 C (k1_rlvect_1 C D A) (k1_rlvect_1 C E B)) F) = (k7_real_1 (k8_real_1 A (k2_bhsp_1 C D F)) (k8_real_1 B (k2_bhsp_1 C E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bhsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_2 C A) => (v1_bhsp_2 (k5_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t5_bhsp_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_bhsp_3 C A) => (v1_bhsp_3 (k5_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t5_bhsp_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v2_bhsp_1 C) & (l1_bhsp_1 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k6_bhsp_1 C (k5_normsp_1 C (k1_bhsp_4 C D) A) (k5_normsp_1 C (k1_bhsp_4 C E) B)) (k1_bhsp_4 C (k6_bhsp_1 C (k5_normsp_1 C D A) (k5_normsp_1 C E B))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_bhsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k9_binop_2 (k5_square_1 (k3_bhsp_1 A (k3_rlvect_1 A B C))) (k5_square_1 (k3_bhsp_1 A (k5_algstr_0 A B C)))) = (k9_binop_2 (k11_binop_2 2 (k5_square_1 (k3_bhsp_1 A B))) (k11_binop_2 2 (k5_square_1 (k3_bhsp_1 A C))))) ) ) ) ) ) ) ).
tt(t5_bhsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  ( ((v1_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) &  ((v2_binop_1 (u1_algstr_0 A) (u1_struct_0 A)) & (v1_setwiseo (u1_algstr_0 A) (u1_struct_0 A))) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k1_numbers) &  ((v2_hahnban C A) &  ((v3_hahnban C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) ) )  =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers C (k1_bhsp_6 A B)) = (k5_bhsp_5 k1_numbers (u1_struct_0 A) k33_binop_2 B C)) ) ) ) ) ) ) ) ) ).
tt(t5_bhsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_bhsp_5 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((m1_subset_1 C (k1_zfmisc_1 B)) => (m2_bhsp_5 C A)) ) ) ) ) ) ) ).
tt(t5_bilinear,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_vectsp_1 A) & (l6_algstr_0 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_vectsp_1 B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_vectsp_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A))))) )  => (r2_funct_2 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)) (u1_struct_0 A) (k3_bilinear A B C F (k1_algstr_0 A D E)) (k2_bilinear A B C (k3_bilinear A B C F D) (k3_bilinear A B C F E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_binari_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r2_hidden B (k2_finseq_1 A)) &  (B = 1) )  =>  ((k7_partfun1 k6_margrel1 (k1_binari_2 A) B) = k8_margrel1) ) ) ) ) ) ).
tt(t5_binari_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  ( (B = (k5_euclid A))  =>  ((k3_binarith A B) = (k5_finseq_2 k5_numbers A 1)) ) ) ) ) ) ).
tt(t5_binari_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v3_card_1 B A) & (m2_finseq_1 B k6_margrel1))  =>  (! [C:$i] :  ( ((v3_card_1 C A) & (m2_finseq_1 C k6_margrel1))  =>  ( ( (B = (k5_euclid A))  &  (C = (k5_euclid A)) )  =>  ((k4_binarith A B C) = (k5_euclid A)) ) ) ) ) ) ) ) ).
tt(t5_binarith,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k3_xboolean (k5_xboolean A B)) = (k4_xboolean (k3_xboolean A) (k3_xboolean B))) ) ) ) ) ).
tt(t5_binom,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k1_polynom1 A C B)) = (k6_algstr_0 A (k4_rlvect_1 A C) B)) ) ) ) ) ) ) ).
tt(t5_binop_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((v1_binop_1 B A) =>  ((r3_binop_1 A C B) <=>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_binop_1 A B D C) = D) ) ) ) ) ) ) ) ) ) ).
tt(t5_binop_2,ax, ((k4_binop_1 k5_numbers k47_binop_2) = k6_numbers) ).
tt(t5_bintree1,ax,(v1_bintree1 (k2_trees_1 2))).
tt(t5_bintree2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_trees_1 A) & (v1_bintree1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_bintree2 C A) =>  ((r2_hidden C (k2_trees_2 A B)) => (m2_finseq_2 C k6_margrel1 (k4_finseq_2 B k6_margrel1))) ) ) ) ) ) ) ).
tt(t5_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_boolealg A B (k3_lattices A C D)) <=>  ((r3_lattices A C B) &  ((r3_lattices A D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_lattices A C E) & (r3_lattices A D E))  => (r3_lattices A B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_boole,ax, (! [A:$i] :  ((k5_xboole_0 A k1_xboole_0) = A) ) ).
tt(t5_boolmark,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_2 B (u1_struct_0 A) k6_margrel1 (k1_boolmark A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k9_petri A (k6_domain_1 (u4_struct_0 A) C))) =>  ((k3_funct_2 (u1_struct_0 A) k6_margrel1 (k2_boolmark A B C) D) = k8_margrel1) ) ) ) ) ) ) ) ) ) ).
tt(t5_bor_cant,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (! [G:$i] :  ( ((v5_relat_1 G B) &  ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k9_setfam_1 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [H:$i] :  ( ((v5_relat_1 H B) &  ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers (k9_setfam_1 A)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_funct_2 k5_numbers (k9_setfam_1 A) H (k1_partfun1 k5_numbers k5_numbers k5_numbers (k9_setfam_1 A) (k3_bor_cant E F) G)) =>  ((r1_xxreal_0 D E) |  ((k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B H C)) D) = (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k1_series_3 (k8_prob_1 A B G C)) E) (k1_funct_1 (k1_series_3 (k8_prob_1 A B (k1_valued_0 (k9_setfam_1 A) G (k2_nat_1 (k2_nat_1 E F) 1)) C)) (k9_real_1 (k9_real_1 D E) 1)))) ) ) ) ) ) )  &  (! [G:$i] :  ( ((v5_relat_1 G B) &  ((v1_funct_1 G) &  ((v1_funct_2 G k5_numbers (k9_setfam_1 A)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [H:$i] :  ( ((v5_relat_1 H B) &  ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers (k9_setfam_1 A)) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [I:$i] :  ( ((v5_relat_1 I B) &  ((v1_funct_1 I) &  ((v1_funct_2 I k5_numbers (k9_setfam_1 A)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J k5_numbers k5_numbers) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) )  =>  ( ((r2_funct_2 k5_numbers (k9_setfam_1 A) I (k1_partfun1 k5_numbers k5_numbers k5_numbers (k9_setfam_1 A) J G)) & (r2_funct_2 k5_numbers (k9_setfam_1 A) H (k1_partfun1 k5_numbers k5_numbers k5_numbers (k9_setfam_1 A) (k3_bor_cant E F) I)))  =>  ((r1_xxreal_0 D E) |  ((k1_prob_2 A B (k1_prob_3 A H) D) = (k8_subset_1 A (k1_prob_2 A B (k1_prob_3 A I) E) (k1_funct_1 (k1_prob_3 A (k1_valued_0 (k9_setfam_1 A) I (k2_nat_1 (k2_nat_1 E F) 1))) (k9_real_1 (k9_real_1 D E) 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_borsuk_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B)))) =>  ((v3_pre_topc C (k2_borsuk_1 A B)) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k2_borsuk_1 A B))))) &  ( (C = (k5_setfam_1 (u1_struct_0 (k2_borsuk_1 A B)) D))  &  (! [E:$i] :  (~  ((r2_hidden E D) &  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (E = (k8_mcart_1 (u1_struct_0 A) (u1_struct_0 B) F G))  &  ((v3_pre_topc F A) & (v3_pre_topc G B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_borsuk_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v3_funct_1 C) & (m1_borsuk_2 C A B B))  => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 A) C (k6_struct_0 k5_topmetr A B))) ) ) ) ) ) ).
tt(t5_borsuk_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k2_borsuk_1 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) B)) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) B)) (u1_struct_0 B))))) )  =>  ((r1_funct_2 (u1_struct_0 (k2_borsuk_1 (k1_pre_topc A (k6_domain_1 (u1_struct_0 A) C)) B)) (u1_struct_0 B) (k2_zfmisc_1 (k6_domain_1 (u1_struct_0 A) C) (u1_struct_0 B)) (u1_struct_0 B) D (k10_funct_3 (k6_domain_1 (u1_struct_0 A) C) (u1_struct_0 B))) => (v2_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t5_borsuk_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v2_funct_1 A) &  ((v2_funct_1 B) &  ( ((k3_xboole_0 (k9_xtuple_0 A) (k9_xtuple_0 B)) = (k1_tarski C))  &  ( ((k3_xboole_0 (k10_xtuple_0 A) (k10_xtuple_0 B)) = (k1_tarski (k1_funct_1 A C)))  &  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) ) ) )  =>  ((k2_funct_1 (k1_funct_4 A B)) = (k1_funct_4 (k2_funct_1 A) (k2_funct_1 B))) ) ) ) ) ) ) ).
tt(t5_borsuk_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r1_subset_1 (k1_enumset1 A B C) (k1_enumset1 D E F)) =>  ( (~  (A = D) )  &  ( (~  (A = E) )  &  ( (~  (A = F) )  &  ( (~  (B = D) )  &  ( (~  (B = E) )  &  ( (~  (B = F) )  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  (~  (C = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k5_topmetr)) => (m1_subset_1 (k3_xcmplx_0 A B) (u1_struct_0 k5_topmetr))) ) ) ) ).
tt(t5_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~  ( ((k17_sin_cos A) = k6_numbers)  &  ( (~  (A = (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k13_complex1 A (k8_real_1 2 k32_sin_cos))))) )  &  (~  (A = (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) (k1_int_1 (k13_complex1 A (k8_real_1 2 k32_sin_cos)))))) ) ) ) ) ) ) ).
tt(t5_brouwer2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (~ (r1_xxreal_0 C k1_xboole_0))  =>  ((k2_tops_1 (k15_euclid A) (k2_topreal9 A B C)) = (k3_topreal9 A B C)) ) ) ) ) ) ) ) ).
tt(t5_brouwer,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (C = D) )  &  ((r2_hidden C (u1_struct_0 (k7_toprealb A E B))) &  ((m1_subset_1 D (u1_struct_0 (k2_brouwer A E B))) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_toprealb A E B))) =>  (~  ( (~  (F = C) )  &  ((k2_tarski C F) = (k9_subset_1 (u1_struct_0 (k15_euclid A)) (k4_topreal9 A C D) (k3_topreal9 A E B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bspace,ax, ((k4_struct_0 k2_bspace) = k1_xboole_0) ).
tt(t5_bvfunc10,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ( ((r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B D) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A C D) (k12_bvfunc_1 A)))  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k2_bvfunc_1 A B C) D) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ) ).
tt(t5_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  ( ((v2_bvfunc_2 B A) &  (B = (k2_tarski C D)) )  =>  ( (C = D)  |  (! [E:$i] :  (! [F:$i] :  (~  ((r2_hidden E C) &  ((r2_hidden F D) & (r1_xboole_0 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ( (B = (k1_enumset1 C D E))  =>  ( (C = D)  |  ( (D = E)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A E C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k11_bvfunc_1 A)) (k11_bvfunc_1 A))) ) ) ) ).
tt(t5_bvfunc25,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k9_bvfunc_1 A B (k2_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t5_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k11_bvfunc_1 A) (k11_bvfunc_1 A)) (k12_bvfunc_1 A)) &  ((r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k11_bvfunc_1 A) (k12_bvfunc_1 A)) (k12_bvfunc_1 A)) & (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A (k12_bvfunc_1 A) (k12_bvfunc_1 A)) (k11_bvfunc_1 A))) ) ) ) ).
tt(t5_bvfunc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_partit1 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ((m1_eqrel_1 D A) => (r2_bvfunc_1 A (k6_bvfunc_2 A C B D) (k5_bvfunc_2 A D B))) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A (k2_bvfunc_1 A (k7_bvfunc_2 A C B E) (k7_bvfunc_2 A D B E))) (k5_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A C) B E) (k6_bvfunc_2 A (k1_bvfunc_1 A D) B E)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k1_bvfunc_1 A B)) (k11_bvfunc_1 A))) ) ) ) ).
tt(t5_bvfunc_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  ((r2_funct_2 A k6_margrel1 (k1_bvfunc_1 A B) (k12_bvfunc_1 A)) => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B C) (k12_bvfunc_1 A))) ) ) ) ) ) ) ).
tt(t5_bvfunc_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k9_bvfunc_1 A B (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A (k2_bvfunc_1 A B C) D)) (k12_bvfunc_1 A))) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k2_bvfunc_1 A (k9_bvfunc_1 A B D) (k9_bvfunc_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A D B)) (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A C D)) (k9_bvfunc_1 A D B)) (k9_bvfunc_1 A C B)) (k9_bvfunc_1 A B D)))) ) ) ) ) ) ) ) ).
tt(t5_bvfunc_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r1_bvfunc_1 A (k2_bvfunc_1 A (k9_bvfunc_1 A B C) (k9_bvfunc_1 A (k1_bvfunc_1 A B) C)) C)) ) ) ) ) ) ).
tt(t5_c0sp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v2_funcsdom A) & (l1_funcsdom A)) ) ) ) ) ) ) ) )  =>  ((v5_c0sp1 A) =>  ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_c0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_c0sp2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_c0sp2 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_c0sp2 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 A) k1_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k8_group_1 (k3_c0sp2 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) k1_numbers G H) = (k8_real_1 (k3_funct_2 (u1_struct_0 A) k1_numbers E H) (k3_funct_2 (u1_struct_0 A) k1_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  ( ((k2_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) = B)  & (r2_relset_1 k5_numbers (k3_cqc_lang A) (k1_calcul_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) C)) ) ) ) ) ) ) ).
tt(t5_calcul_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k2_xboole_0 (k2_calcul_2 A B) (k1_tarski (k1_nat_1 (k2_xcmplx_0 A B) 1))) = (k2_calcul_2 A (k1_nat_1 B 1))) ) ) ) ) ).
tt(t5_cantor_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((u1_pre_topc A) = (k2_cantor_1 (u1_struct_0 A) (u1_pre_topc A))) ) ) ).
tt(t5_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_wellord2 A B) <=>  ((k1_card_1 A) = (k1_card_1 B)) ) ) ) ).
tt(t5_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_wellord2 (k2_zfmisc_1 (k2_zfmisc_1 A B) C) (k2_zfmisc_1 A (k2_zfmisc_1 B C))) &  ((k1_card_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)) = (k1_card_1 (k2_zfmisc_1 A (k2_zfmisc_1 B C)))) ) ) ) ) ).
tt(t5_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ( (A = B)  | (r1_xboole_0 (k1_funct_1 (k2_card_3 C) A) (k1_funct_1 (k2_card_3 C) B))) ) ) ) ) ) ).
tt(t5_card_4,ax, ((r2_wellord2 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers) k5_numbers) &  ((k1_card_1 k5_numbers) = (k1_card_1 (k8_mcart_1 k1_numbers k1_numbers k5_numbers k5_numbers))) ) ).
tt(t5_card_5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  (~  ((r1_tarski B A) &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) & (v1_ordinal2 C)) ) )  =>  (~  ( (C = (k3_wellord1 (k1_wellord2 (k2_wellord2 (k1_wellord2 B))) (k1_wellord2 B)))  &  ((v2_ordinal2 C) &  ( ((k9_xtuple_0 C) = (k2_wellord2 (k1_wellord2 B)))  &  ((k10_xtuple_0 C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_card_fil,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_card_fil B A) => (r2_hidden A B)) ) ) ) ).
tt(t5_cardfin2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C B))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden D (k2_rcomp_1 B C)) &  ((k25_sin_cos B) = (k9_binop_2 (k8_nat_1 k1_numbers (k3_series_1 (k6_taylor_1 k24_sin_cos (k2_subset_1 k1_numbers) C B)) A) (k12_binop_2 (k11_binop_2 (k25_sin_cos D) (k2_newton (k10_binop_2 B C) (k23_binop_2 A 1))) (k3_newton (k23_binop_2 A 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  (! [D:$i] :  (~  ( ((v1_xboole_0 B) => (v1_xboole_0 A))  &  ( (~ (r2_hidden C A))  &  ( (~ (r2_hidden D B))  &  (~  ((k1_card_1 (a_2_0_card_fin A B)) = (k1_card_1 (a_4_2_card_fin A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_card_lar,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v3_ordinal1 B) &  ((v4_ordinal1 B) &  (~ (v1_finset_1 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (~  ( (~  ((k3_ordinal2 (k8_subset_1 A C B)) = B) )  &  (! [D:$i] :  ((v3_ordinal1 D) =>  (~  ((r2_hidden D B) & (r1_tarski (k8_subset_1 A C B) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_cat_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_cat_1 D A B C) =>  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  =>  ( ((k3_graph_1 A D) = B)  &  ((k4_graph_1 A D) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 A) (k7_cat_1 B A (k1_cat_2 B A C)) D) = C) ) ) ) ) ) ) ) ) ).
tt(t5_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) => (r2_funct_2 A (u1_struct_0 B) (k3_cat_3 B A (k8_funcop_1 (u4_struct_0 B) A C)) (k8_funcop_1 (u1_struct_0 B) A (k4_graph_1 B C)))) ) ) ) ) ).
tt(t5_cat_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_cat_4 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_cat_4 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 (k5_cat_4 A B))) => (r2_hidden E (k2_cat_1 (k5_cat_4 A B) C D))) ) ) ) ) ) ) ) ).
tt(t5_cat_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_cat_2 B A) =>  (! [C:$i] :  ((m3_cat_2 C A) =>  ( (~ (r2_subset_1 (u1_struct_0 B) (u1_struct_0 C)))  =>  ((k3_cat_5 B C) = (k3_cat_5 C B)) ) ) ) ) ) ) ) ).
tt(t5_catalan1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k10_real_1 (k9_real_1 (k4_nat_1 (k4_nat_1 4 A) A) (k4_nat_1 2 A)) (k1_nat_1 A 1)) 1)) ) ) ) ).
tt(t5_catalan2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B A) => (v1_catalan2 (k1_catalan2 (k8_funcop_1 k5_numbers A k6_numbers) (k8_funcop_1 k5_numbers B 1)))) ) ) ) ) ).
tt(t5_catalg_1,ax, (! [A:$i] :  ((k4_catalg_1 (k3_catalg_1 A)) = A) ) ).
tt(t5_cayley,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_cayley A))) =>  ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) ) ) ) ).
tt(t5_cc0sp1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_cc0sp1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k3_cc0sp1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_cc0sp1 A))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A k2_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A k2_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A k2_numbers) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers)))) )  =>  ( ( (E = B)  &  ( (F = C)  &  (G = D) ) )  =>  ( (D = (k3_rlvect_1 (k3_cc0sp1 A) B C))  <=>  (! [H:$i] :  ((m1_subset_1 H A) =>  ((k3_funct_2 A k2_numbers G H) = (k3_binop_2 (k3_funct_2 A k2_numbers E H) (k3_funct_2 A k2_numbers F H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cc0sp2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) k2_numbers) &  ((v1_cc0sp2 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) )  =>  ((v1_funct_1 (k25_valued_1 (u1_struct_0 A) k2_numbers C B)) &  ((v1_funct_2 (k25_valued_1 (u1_struct_0 A) k2_numbers C B) (u1_struct_0 A) k2_numbers) &  ((v1_cc0sp2 (k25_valued_1 (u1_struct_0 A) k2_numbers C B) A) & (m1_subset_1 (k25_valued_1 (u1_struct_0 A) k2_numbers C B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k2_numbers)))) ) ) ) ) ) ) ) ) ).
tt(t5_cfcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  => (r2_relset_1 k5_numbers k2_numbers (k36_valued_1 k5_numbers k2_numbers (k9_comseq_3 B A)) (k9_comseq_3 B (k36_valued_1 k5_numbers k2_numbers A)))) ) ) ) ).
tt(t5_cfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k3_funct_2 k5_numbers k2_numbers (k9_comseq_3 B A) C) = (k8_nat_1 k2_numbers A (k1_seq_1 B C))) ) ) ) ) ) ) ).
tt(t5_cfdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 2)) =>  ( ( (D = (k10_finseq_1 B C))  & (r1_pdiff_1 2 1 (k3_pdiff_1 2 A) D))  =>  ((r3_pdiff_1 2 1 A D) &  ((r3_pdiff_1 2 2 A D) &  ( ((k12_finseq_1 k1_numbers (k11_pdiff_1 2 1 A D)) = (k1_funct_1 (k8_pdiff_1 2 1 (k3_pdiff_1 2 A) D) (k10_finseq_1 1 k6_numbers)))  &  ((k12_finseq_1 k1_numbers (k11_pdiff_1 2 2 A D)) = (k1_funct_1 (k8_pdiff_1 2 1 (k3_pdiff_1 2 A) D) (k10_finseq_1 k6_numbers 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cfuncdom,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_funct_2 B A k2_numbers (k9_funct_2 A k2_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k2_numbers (k9_funct_2 A k2_numbers)) => (r2_funct_2 A k2_numbers (k1_funcsdom A k2_numbers (k1_cfuncdom A) B C) (k1_funcsdom A k2_numbers (k1_cfuncdom A) C B))) ) ) ) ) ) ).
tt(t5_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((k1_relset_1 A (k31_valued_1 A k2_numbers B)) = (k1_relset_1 A B))  &  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden C (k1_relset_1 A (k31_valued_1 A k2_numbers B))) =>  ((k7_partfun1 k2_numbers (k31_valued_1 A k2_numbers B) C) = (k10_complex1 (k7_partfun1 k2_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t5_cgames_1,ax, (! [A:$i] :  ((v2_cgames_1 A) =>  (! [B:$i] :  ((v2_cgames_1 B) =>  ( (A = B)  <=>  ( ((k6_cgames_1 A) = (k6_cgames_1 B))  &  ((k7_cgames_1 A) = (k7_cgames_1 B)) ) ) ) ) ) ) ).
tt(t5_chain_1,ax, (! [A:$i] :  ( ((k1_card_1 A) = 2)  <=>  (? [B:$i] :  (? [C:$i] :  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~  (B = C) )  &  (! [D:$i] :  (~  ((r2_hidden D A) &  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_chord,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  (~ (v1_abian A)) )  =>  (~  ( (~  (1 = A) )  &  (! [B:$i] :  ( ((v7_ordinal1 B) &  (~ (v1_abian B)) )  =>  (~  ((k1_nat_1 B 2) = A) ) ) ) ) ) ) ) ).
tt(t5_circcmb2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_circcomb A B) =>  ((k2_msafree2 (k2_circcomb A B)) = (k2_xboole_0 (k4_xboole_0 (k2_msafree2 A) (k3_msafree2 B)) (k4_xboole_0 (k2_msafree2 B) (k3_msafree2 A)))) ) ) ) ) ) ).
tt(t5_circcmb3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k4_card_3 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((v1_circcmb3 C A B) & (r1_xxreal_0 (k2_circcmb3 A B C) D))  => (r8_pboole (u1_struct_0 A) (k1_circcmb3 A B C) (k5_facirc_1 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t5_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  ((r1_circcomb A B) =>  ((k2_circcomb A B) = (k2_circcomb B A)) ) ) ) ) ) ).
tt(t5_circled1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (v3_rltopsp1 (k3_rusub_4 A (k1_rlsub_1 A)) A)) ) ).
tt(t5_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (k1_msaterm A B))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k1_circtrm1 A B C))) =>  ((r2_hidden D (u4_struct_0 (k1_circtrm1 A B C))) <=> (m2_msaterm D A B)) ) ) ) ) ) ) ) ) ).
tt(t5_circuit1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) C)) =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) &  ((v1_finseq_1 F) & (v6_trees_3 F)) ) )  =>  ( ((r2_hidden C (k3_msafree2 A)) &  (E = (k4_trees_4 (k4_tarski (k4_msafree2 A C) (u1_struct_0 A)) F)) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( ((r2_hidden G (k1_relset_1 k5_numbers F)) & (r2_hidden (k1_funct_1 F G) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D)))  =>  (D = (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A (k4_msafree2 A C)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_circuit2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_msafree2 A) &  ((v5_msafree2 A) & (l1_msualg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m1_msafree2 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D)) =>  ((r2_hidden D (k1_msafree2 A)) =>  ((k3_funct_2 (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_funct_1 (u3_msualg_1 A (k5_msafree2 A B)) D) (k1_msualg_3 (u1_struct_0 A) (u3_msualg_1 A (k5_msafree2 A B)) (u3_msualg_1 A (k5_msafree2 A B)) (k3_circuit2 A B C) D) E) = (k1_trees_4 (k4_tarski (k4_msafree2 A D) (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_classes1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_tarski A (k1_classes1 B)) &  ( (~ (r2_tarski A (k1_classes1 B)))  &  (~ (r2_hidden A (k1_classes1 B))) ) ) ) ) ) ).
tt(t5_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v2_classes1 B) & (r2_hidden A B))  =>  ((r2_hidden (k1_ordinal1 A) B) & (r1_tarski A B)) ) ) ) ) ).
tt(t5_clopban1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) & (l1_clvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) (k4_lopban_1 A B) C) C)) ) ) ) ) ) ).
tt(t5_clopban2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_clopban1 B A A) &  ((v2_clopban1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_clopban1 C A A) &  ((v2_clopban1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 D A A) &  ((v1_clopban1 D A A) &  ((v2_clopban1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_clopban2 A (k1_clopban2 A D C) B) (k1_clopban2 A D (k1_clopban2 A C B)))) ) ) ) ) ) ) ) ).
tt(t5_clopban3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_csspace3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_clopban4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) &  ((v2_cfuncdom A) &  ((v5_clopban2 A) & (l1_clopban2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v9_clvect_1 C A) => (v9_clvect_1 (k3_clopban3 A C B) A)) ) ) ) ) ) ) ).
tt(t5_closure1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) & (v1_funcop_1 B)) ) ) )  =>  ((v1_msualg_3 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( ((r1_pboole A C (k2_funct_6 B)) &  ((r1_pboole A D (k2_funct_6 B)) & (r6_pboole A (k16_pralg_1 A B C) (k16_pralg_1 A B D))) )  => (r6_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t5_closure2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_closure2 A C))) => (m1_subset_1 (k7_subset_1 (k1_closure2 A C) D B) (k1_zfmisc_1 (k1_closure2 A C)))) ) ) ) ) ) ).
tt(t5_closure3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (B = (k1_funct_4 (k1_pboole A) (k5_relat_1 B (k1_closure3 A B)))) ) ) ) ) ).
tt(t5_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k3_rlvect_1 A B B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t5_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 C A) => (v1_clvect_2 (k6_clvect_1 A C B) A)) ) ) ) ) ) ) ).
tt(t5_clvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ((k16_csspace A (k6_clvect_1 A (k1_bhsp_4 A B) D) (k6_clvect_1 A (k1_bhsp_4 A C) E)) = (k1_bhsp_4 A (k16_csspace A (k6_clvect_1 A B D) (k6_clvect_1 A C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cohsp_1,ax, (! [A:$i] :  ((v1_cohsp_1 A) =>  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  (! [D:$i] :  (~  ((r1_tarski (k2_xboole_0 B C) D) & (r2_hidden D A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_coh_sp,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ((v1_partfun1 B (k3_tarski A)) &  ((v1_relat_2 B) &  ((v3_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k3_tarski A) (k3_tarski A))))) ) )  =>  ((r2_relset_1 (k3_tarski A) (k3_tarski A) B (k1_coh_sp A)) <=>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) <=> (r2_hidden (k2_tarski C D) A)) ) ) ) ) ) ) ) ).
tt(t5_collsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) & (l1_collsp A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_collsp A B C B)) ) ) ) ) ) ).
tt(t5_combgras,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( ((k6_subset_1 A B) = (k6_subset_1 A C))  &  ((r1_tarski B A) & (r1_tarski C A)) )  =>  (B = C) ) ) ) ) ).
tt(t5_compact1,ax, (! [A:$i] :  ((l1_pre_topc A) => (m1_pre_topc A (k1_compact1 A))) ) ).
tt(t5_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (A = k6_numbers)  <=>  ((k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A))) = k6_numbers) ) ) ) ).
tt(t5_complex2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k18_sin_cos (k5_real_1 A k32_sin_cos)) = (k4_xcmplx_0 (k17_sin_cos A)))  &  ((k21_sin_cos (k5_real_1 A k32_sin_cos)) = (k4_xcmplx_0 (k20_sin_cos A))) ) ) ) ).
tt(t5_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (A = B)  =>  ( (A = (k4_struct_0 k1_complfld))  |  ((k11_algstr_0 k1_complfld A) = (k2_binop_2 B)) ) ) ) ) ) ) ).
tt(t5_complsp1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_complsp1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k14_seq_4 A))) =>  ( (C = B)  =>  ((v2_seq_4 C A) <=> (v4_pre_topc B (k1_complsp1 A))) ) ) ) ) ) ) ) ).
tt(t5_complsp2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  ((k3_finseq_1 (k30_valued_1 A)) = (k3_finseq_1 A)) ) ) ).
tt(t5_compl_sp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 (k3_tbsp_1 B (k10_metric_1 B C A)) (k8_real_1 2 A))) ) ) ) ) ) ) ).
tt(t5_compos_0,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_compos_0 B) &  ((v2_compos_0 B) & (v3_compos_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((k3_compos_0 B (k2_compos_0 B C)) = (k3_compos_0 B (k2_compos_0 B (k5_compos_0 B C A)))) ) ) ) ) ) ) ).
tt(t5_compos_1,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_compos_1)) =>  ((k5_xtuple_0 A) = k6_numbers) ) ) ).
tt(t5_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 A)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) &  ((v3_compos_1 D A) & (v4_compos_1 D A)) ) ) ) ) ) ) )  =>  ((k2_compos_2 A (k1_compos_2 A B D) C) = (k1_compos_2 A B (k2_compos_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t5_comptrig,ax, ( (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 2) k6_numbers))  &  ( (~ (r1_xxreal_0 k32_sin_cos (k10_real_1 k32_sin_cos 2)))  &  ( (~ (r1_xxreal_0 k32_sin_cos k6_numbers))  &  ( (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 2) (k1_real_1 (k10_real_1 k32_sin_cos 2))))  &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) k32_sin_cos))  &  ( (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) (k10_real_1 k32_sin_cos 2)))  &  ( (~ (r1_xxreal_0 k6_numbers (k1_real_1 (k10_real_1 k32_sin_cos 2))))  &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) k6_numbers))  &  ( (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) k32_sin_cos))  &  ( (~ (r1_xxreal_0 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k10_real_1 3 2) k32_sin_cos)))  &  (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 2) k32_sin_cos) k6_numbers)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_compts_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_compts_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ( (~  (B = k1_xboole_0) )  &  ((v2_tops_2 B A) &  ( ((k6_setfam_1 (u1_struct_0 A) B) = k1_xboole_0)  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (~  ( (~  (C = k1_xboole_0) )  &  ((r1_tarski C B) &  ((v1_finset_1 C) &  ((k6_setfam_1 (u1_struct_0 A) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_comput_1,ax, (! [A:$i] :  ((k4_finseq_2 k6_numbers A) = (k1_tarski k1_xboole_0)) ) ).
tt(t5_comseq_1,ax, (! [A:$i] :  ( ((v2_relat_1 A) &  ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) ) )  => (r1_tarski (k2_relset_1 k2_numbers A) (k6_subset_1 k2_numbers (k1_tarski k5_complex1)))) ) ).
tt(t5_comseq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  => (r2_funct_2 k5_numbers k2_numbers (k2_comseq_2 k5_numbers (k19_valued_1 k5_numbers k2_numbers k2_numbers A B)) (k19_valued_1 k5_numbers k2_numbers k2_numbers (k2_comseq_2 k5_numbers A) (k2_comseq_2 k5_numbers B)))) ) ) ) ).
tt(t5_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A C) B)) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_xxreal_0 (k9_real_1 (k8_nat_1 k1_numbers (k3_series_1 A) (k2_nat_1 C D)) (k8_nat_1 k1_numbers (k3_series_1 A) C)) (k8_real_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t5_conaffm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  ((v5_conaffm A) => (v4_conaffm A)) ) ) ).
tt(t5_conlat_1,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski B (k3_funct_2 (k9_setfam_1 (u4_struct_0 A)) (k9_setfam_1 (u1_struct_0 A)) (k2_conlat_1 A) (k3_funct_2 (k1_zfmisc_1 (u1_struct_0 A)) (k9_setfam_1 (u4_struct_0 A)) (k1_conlat_1 A) B)))) ) ) ) ).
tt(t5_conlat_2,ax, (! [A:$i] :  ( ( (~ (v1_conlat_1 A))  & (l1_conlat_1 A))  =>  ( ((k3_conlat_2 A (k1_struct_0 (k11_conlat_1 A))) = (k6_conlat_1 A))  &  ((k2_conlat_2 A (k1_struct_0 (k11_conlat_1 A))) = (k5_conlat_1 A)) ) ) ) ).
tt(t5_conmetr1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  ((v4_conmetr1 A) => (v3_conmetr1 A)) ) ) ).
tt(t5_conmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v4_analmetr D A) &  ((v4_analmetr E A) &  ((r2_hidden B D) &  ((r2_hidden C D) &  ((r2_hidden B E) &  ((r2_hidden C E) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_connsp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (E = C)  &  ( (F = D)  & (r1_connsp_1 B E F)) )  => (r1_connsp_1 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_connsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((m1_connsp_2 C A B) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((m1_connsp_2 D A B) &  ((v3_pre_topc D A) & (r1_tarski D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_connsp_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v2_connsp_1 B A) =>  ( (B = k1_xboole_0)  | (v2_connsp_1 (k1_connsp_3 A B) A)) ) ) ) ) ) ).
tt(t5_convex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) & (l1_rlvect_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_convex1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  ( (~ (r1_xxreal_0 1 C))  &  (~ (r1_tarski (k7_rusub_4 A (k1_convex1 A B (k9_real_1 1 C)) (k1_convex1 A B C)) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_convex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( (B = (a_3_3_convex2 A C D))  => (v1_convex1 B A)) ) ) ) ) ) ) ) ) ).
tt(t5_convex3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k3_convex1 A B) = (a_2_0_convex3 A B)) ) ) ) ) ).
tt(t5_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_convex4 B A (k1_subset_1 (u1_struct_0 A))) => (r2_funct_2 (u1_struct_0 A) k2_numbers B (k2_convex4 A))) ) ) ) ).
tt(t5_convfun1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k7_numbers)))) )  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((k12_supinf_2 B C) = k2_supinf_1) ) ) )  =>  ((v1_convfun1 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers E) & (r1_xxreal_0 E 1))  => (r1_xxreal_0 (k12_supinf_2 B (k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D (k10_binop_2 1 E)))) (k3_supinf_2 (k1_extreal1 (k1_measure6 E) (k12_supinf_2 B C)) (k1_extreal1 (k1_measure6 (k10_binop_2 1 E)) (k12_supinf_2 B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cqc_lang,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A)))  =>  ( ((v5_relat_1 C (k3_qc_lang1 A)) &  ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A))) )  <=>  ( ((a_3_0_cqc_lang A B C) = k1_xboole_0)  &  ((a_3_1_cqc_lang A B C) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t5_cqc_sim1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (~  ((v2_qc_lang1 B A) &  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v5_relat_1 E (k3_qc_lang1 A)) &  ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A))) )  =>  (~  (B = (k4_cqc_lang C A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_cqc_lang A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((v1_cqc_the1 B A) & (v1_cqc_the1 C A))  => (v1_cqc_the1 (k9_subset_1 (k3_cqc_lang A) B C) A)) ) ) ) ) ) ) ).
tt(t5_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((r2_hidden C (k24_qc_lang1 A (k15_qc_lang1 A D B))) <=>  ((r2_hidden C (k24_qc_lang1 A B)) &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (r1_cqc_the3 A B B)) ) ) ) ).
tt(t5_csspace2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_xxreal_0 (k8_real_1 (k17_complex1 (k2_xcmplx_0 A B)) (k17_complex1 (k2_xcmplx_0 A B))) (k7_real_1 (k8_real_1 (k8_real_1 2 (k17_complex1 A)) (k17_complex1 A)) (k8_real_1 (k8_real_1 2 (k17_complex1 B)) (k17_complex1 B)))) & (r1_xxreal_0 (k8_real_1 (k17_complex1 A) (k17_complex1 A)) (k7_real_1 (k8_real_1 (k8_real_1 2 (k17_complex1 (k6_xcmplx_0 A B))) (k17_complex1 (k6_xcmplx_0 A B))) (k8_real_1 (k8_real_1 2 (k17_complex1 B)) (k17_complex1 B))))) ) ) ) ) ).
tt(t5_csspace3,ax, ( (~ (v2_struct_0 k3_csspace3))  &  ((v13_algstr_0 k3_csspace3) &  ((v2_rlvect_1 k3_csspace3) &  ((v3_rlvect_1 k3_csspace3) &  ((v4_rlvect_1 k3_csspace3) &  ((v2_clvect_1 k3_csspace3) &  ((v3_clvect_1 k3_csspace3) &  ((v4_clvect_1 k3_csspace3) &  ((v5_clvect_1 k3_csspace3) & (l1_clvect_1 k3_csspace3)) ) ) ) ) ) ) ) ) ).
tt(t5_csspace4,ax, ( (~ (v2_struct_0 k3_csspace4))  &  ((v13_algstr_0 k3_csspace4) &  ((v2_rlvect_1 k3_csspace4) &  ((v3_rlvect_1 k3_csspace4) &  ((v4_rlvect_1 k3_csspace4) &  ((v3_normsp_0 k3_csspace4) &  ((v4_normsp_0 k3_csspace4) &  ((v2_clvect_1 k3_csspace4) &  ((v3_clvect_1 k3_csspace4) &  ((v4_clvect_1 k3_csspace4) &  ((v5_clvect_1 k3_csspace4) &  ((v8_clvect_1 k3_csspace4) &  ((v3_clopban1 k3_csspace4) & (l2_clvect_1 k3_csspace4)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_csspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) =>  ((k3_rlvect_1 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace) A (k4_struct_0 (g1_clvect_1 k1_csspace k6_csspace k4_csspace k5_csspace))) = A) ) ) ).
tt(t5_decomp_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_decomp_1 B A) <=>  (B = (k4_decomp_1 A B)) ) ) ) ) ) ).
tt(t5_descip_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_xxreal_0 1 (k3_finseq_1 B)) =>  ((m2_finseq_1 (k6_descip_1 B) A) &  ((k3_finseq_1 (k6_descip_1 B)) = (k3_finseq_1 B)) ) ) ) ) ) ) ).
tt(t5_dickson,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v16_waybel_0 A) <=> (r7_relat_2 (u1_orders_2 A) (u1_struct_0 A))) ) ) ).
tt(t5_diff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k3_funct_2 k1_numbers k1_numbers (k5_diff_1 C A) B) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers C (k7_real_1 B (k10_real_1 A 2))) (k3_funct_2 k1_numbers k1_numbers C (k9_real_1 B (k10_real_1 A 2))))) ) ) ) ) ) ) ).
tt(t5_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k10_diff_1 (k26_valued_1 k1_numbers k1_numbers E A) B C D) = (k8_real_1 A (k10_diff_1 E B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers k1_numbers) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers E (k26_valued_1 k1_numbers k1_numbers F B)) C) (k2_nat_1 A 1)) D) = (k7_real_1 (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 E C) (k2_nat_1 A 1)) D) (k8_real_1 B (k1_seq_1 (k1_seqfunc k1_numbers k1_numbers (k6_diff_1 F C) (k2_nat_1 A 1)) D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k1_numbers k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( ( (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers F G) = (k13_complex1 A (k5_square_1 G))) ) )  & (r2_zfmisc_1 B C D E))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ( (D = k6_numbers)  |  ( (E = k6_numbers)  |  ((k11_diff_1 F B C D E) = (k13_complex1 (k8_real_1 A (k11_complex1 (k9_complex1 (k13_complex1 1 (k8_real_1 (k8_real_1 C D) B)) (k8_complex1 (k8_complex1 (k13_complex1 1 B) (k13_complex1 1 D)) (k13_complex1 1 C))) (k9_complex1 (k13_complex1 1 (k8_real_1 (k8_real_1 D C) E)) (k8_complex1 (k8_complex1 (k13_complex1 1 E) (k13_complex1 1 C)) (k13_complex1 1 D))))) (k9_real_1 B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_dilworth,ax, (! [A:$i] :  ( (~ (v1_finset_1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 A)))  => (r1_xxreal_0 (k5_card_1 C) B)) ) ) ) ) ) ) ).
tt(t5_diraf,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r2_analoaf A B C D E) &  ((r2_analoaf A B C E D) &  ( (~  (B = C) )  &  (~  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_dirort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_dirort A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_analoaf A E D B C) &  (~  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_dist_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((k3_dist_1 A B C) = (k1_rpr_1 (k9_xtuple_0 B) (k1_dist_1 A B C))) ) ) ) ) ) ).
tt(t5_domain_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  ( (A = (k3_zfmisc_1 B C D))  <=>  (! [E:$i] :  ((r2_hidden E A) <=>  (? [F:$i] :  ((m1_subset_1 F B) &  (? [G:$i] :  ((m1_subset_1 G C) &  (? [H:$i] :  ((m1_subset_1 H D) &  (E = (k3_xtuple_0 F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_dtconstr,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k5_trees_3 A))) =>  (! [C:$i] :  ((m1_trees_4 C (k5_trees_3 A) B) =>  (~  ( ((k3_finseq_1 (k1_dtconstr A (k5_trees_3 A) C)) = 1)  &  (! [D:$i] :  ((m1_subset_1 D (k5_trees_3 A)) =>  (~  ( (C = (k3_pre_poly (k5_trees_3 A) D))  & (r2_hidden D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_dynkin,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_nat_1 (k9_setfam_1 A) (k4_dynkin A B) C) = (k7_subset_1 A (k8_nat_1 (k9_setfam_1 A) B C) (k3_tarski (k10_xtuple_0 (k5_relat_1 B C))))) ) ) ) ) ) ) ).
tt(t5_ec_pf_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v36_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v36_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v36_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ((m1_ec_pf_1 A B) & (m1_ec_pf_1 B C))  => (m1_ec_pf_1 A C)) ) ) ) ) ) ) ).
tt(t5_ec_pf_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (C = (k4_struct_0 B))  =>  ((r1_xxreal_0 A 1) |  ((k2_binom B C A) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t5_endalg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k6_partfun1 (u1_struct_0 A)) = (k1_group_1 (k3_endalg A))) ) ) ).
tt(t5_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ( (C = k1_xboole_0)  =>  (B = k1_xboole_0) )  => (r2_hidden (k1_domain_1 (k2_zfmisc_1 A A) (k1_zfmisc_1 (k2_zfmisc_1 B C)) (k1_domain_1 A A B C) D) (k2_ens_1 A))) ) ) ) ) ) ) ) ) ).
tt(t5_entropy1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~  (A = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  (~  ((k1_real_1 (k6_power A B)) = (k6_power A (k10_real_1 1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_xboole_0 (k2_tarski A B) (k2_tarski C D))) ) ) ) ) ).
tt(t5_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_2 C) &  ((v1_partfun1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ((r2_hidden B A) => (r2_hidden (k4_tarski B B) C)) ) ) ) ) ).
tt(t5_equation,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m3_pboole E A B) =>  (! [F:$i] :  ((m3_pboole F A B) =>  (! [G:$i] :  ((m3_pboole G A E) =>  ((r6_pboole A F G) => (r6_pboole A (k1_msafree A E C G (k1_msafree A B C E D)) (k1_msafree A B C F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_e_siec,ax, (! [A:$i] :  (! [B:$i] :  ((v2_e_siec (g1_e_siec A (k4_relat_1 (k4_xboole_0 A B)) (k4_relat_1 (k4_xboole_0 A B)))) &  ((v3_e_siec (g1_e_siec A (k4_relat_1 (k4_xboole_0 A B)) (k4_relat_1 (k4_xboole_0 A B)))) & (l1_e_siec (g1_e_siec A (k4_relat_1 (k4_xboole_0 A B)) (k4_relat_1 (k4_xboole_0 A B))))) ) ) ) ).
tt(t5_euclid_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k12_euclid A) = (k7_square_1 (k23_rvsum_1 A A))) ) ) ).
tt(t5_euclid_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_euclid_3 (k2_xcmplx_0 A (k3_xcmplx_0 B k7_complex1))) = (k19_euclid A B)) ) ) ) ) ).
tt(t5_euclid_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (~  ( ((k9_euclid B C A) = (k5_euclid B))  &  ( (~  (A = k6_numbers) )  &  (~  (C = (k5_euclid B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_euclid_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 3))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 3))) =>  ((k3_rlvect_1 (k15_euclid 3) A B) = (k4_euclid_5 (k7_real_1 (k1_euclid_5 A) (k1_euclid_5 B)) (k7_real_1 (k2_euclid_5 A) (k2_euclid_5 B)) (k7_real_1 (k3_euclid_5 A) (k3_euclid_5 B)))) ) ) ) ) ).
tt(t5_euclid_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ((k1_euclid_6 A B C) = (k10_real_1 (k8_real_1 (k8_real_1 (k12_euclid (k5_algstr_0 (k15_euclid 2) A B)) (k12_euclid (k5_algstr_0 (k15_euclid 2) C B))) (k18_sin_cos (k4_euclid_3 C B A))) 2)) ) ) ) ) ) ) ).
tt(t5_euclid_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k7_euclid A (k7_euclid A (k8_euclid A B C) D) C) = (k7_euclid A B D)) ) ) ) ) ) ) ) ) ).
tt(t5_euclid_8,ax, ((k12_euclid k3_euclid_8) = 1) ).
tt(t5_euclid_9,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) &  ((v3_card_1 C B) & (v1_finseq_1 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) &  ((v3_valued_0 D) &  ((v3_card_1 D B) & (v1_finseq_1 D)) ) ) )  => (r1_xxreal_0 (k1_funct_1 (k3_euclid (k8_rvsum_1 C D)) A) (k1_funct_1 (k3_euclid (k8_rvsum_1 C D)) (k1_euclid_9 B C D)))) ) ) ) ) ) ) ).
tt(t5_euclid,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ((k54_valued_1 (k30_valued_1 A)) = (k54_valued_1 A)) ) ) ).
tt(t5_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  ((k7_euclid A B (k8_euclid A C D)) = (k8_euclid A (k7_euclid A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t5_euclmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~ (r5_analmetr A B C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r4_analmetr A E B C D) & (r4_analmetr A E C B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_euler_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k3_int_2 A B) = 1)  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((k3_int_2 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C)) = C) ) ) ) ) ) ) ) ).
tt(t5_euler_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k4_nat_d (k4_nat_d A B) B) = (k4_nat_d A B)) ) ) ) ) ).
tt(t5_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((r2_hidden C (k7_relat_1 A B)) <=>  (? [D:$i] :  (? [E:$i] :  ((r2_hidden (k4_tarski D E) B) &  ((r2_hidden (k4_tarski D E) (k9_xtuple_0 A)) &  ((k1_binop_1 A D E) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_extens_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r1_pzfmisc1 A B C) =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((m3_pboole C A E) => (m2_pboole D A B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_extpro_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r1_xxreal_0 A B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  (~ (v1_setfam_1 C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_memstr_0 D C) &  ((v3_memstr_0 D C) &  ((v3_extpro_1 D C) & (l1_extpro_1 D C)) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 D)) & (v1_funct_1 E)) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 D)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 C D)) & (v1_partfun1 F (u1_struct_0 D))) ) ) )  =>  ( ((k3_extpro_1 C D E (k5_extpro_1 C D E F A)) = (k2_compos_1 D))  =>  ((k5_extpro_1 C D E F B) = (k5_extpro_1 C D E F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_extreal1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k11_binop_2 A B) = (k1_extreal1 (k1_measure6 A) (k1_measure6 B))) ) ) ) ) ).
tt(t5_extreal2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  ( (A = k6_numbers)  <=>  ((k3_extreal1 A) = k6_numbers) ) ) ) ).
tt(t5_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((v1_facirc_1 A) | (r1_xboole_0 A B)) ) ) ) ).
tt(t5_facirc_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_msualg_1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v6_circcomb C B) & (l3_msualg_1 C B))  =>  ((r2_hidden A (u1_struct_0 B)) =>  ((k3_circcomb (k1_facirc_2 A) B (k2_facirc_2 A) C) = (g3_msualg_1 B (u3_msualg_1 B C) (u4_msualg_1 B C))) ) ) ) ) ) ) ).
tt(t5_fcont_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_fcont_1 A B) <=>  (! [C:$i] :  ((m1_rcomp_1 C (k1_seq_1 A B)) =>  (? [D:$i] :  ((m1_rcomp_1 D B) & (r1_tarski (k7_relset_1 k1_numbers k1_numbers A D) C)) ) ) ) ) ) ) ) ) ).
tt(t5_fcont_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers C)) & (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers C A)))  => (v1_fcont_2 (k2_partfun1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C B) A))) ) ) ) ) ) ).
tt(t5_fcont_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_seq_1 B D) = (k5_real_1 C (k10_real_1 A (k7_real_1 D 1)))) ) )  =>  ((v2_comseq_2 B) &  ((k2_seq_2 B) = C) ) ) ) ) ) ) ) ) ).
tt(t5_fdiff_10,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos))) =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k29_sin_cos k30_sin_cos) A) B) = (k7_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos B))) (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t5_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k29_sin_cos B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 k29_sin_cos B))) ) ) ) ) )  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k29_sin_cos k1_sin_cos9) A) B) = 1) ) ) ) ) ) ) ) ).
tt(t5_fdiff_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v2_fdiff_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ((v1_funct_1 (k26_valued_1 k1_numbers k1_numbers B A)) &  ((v2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers B A)) & (m1_subset_1 (k26_valued_1 k1_numbers k1_numbers B A) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ).
tt(t5_fdiff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((k2_relset_1 k1_numbers B) = (k1_tarski A))  &  ((k2_relset_1 k1_numbers C) = (k1_tarski A)) )  => (r2_relset_1 k5_numbers k1_numbers B C)) ) ) ) ) ) ) ).
tt(t5_fdiff_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r4_fdiff_3 A B) => (r1_fdiff_3 A B)) ) ) ) ) ).
tt(t5_fdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers B)))) &  ( (C = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers D k3_taylor_1))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ( ((k1_seq_1 D E) = (k7_real_1 A E))  &  (~ (r1_xxreal_0 (k1_seq_1 D E) k6_numbers)) ) ) ) ) ) )  =>  ((r2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers B)) B) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E B) =>  ((k1_seq_1 (k2_fdiff_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers C (k8_real_1 2 A)) (k1_partfun2 k1_numbers B)) B) E) = (k10_real_1 (k9_real_1 A E) (k7_real_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fdiff_5,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( (~ (r2_hidden k6_numbers A))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k16_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k10_real_1 1 (k5_square_1 B)) (k1_seq_1 k19_sin_cos (k10_real_1 1 B))))) ) ) ) ) ) ) ) ).
tt(t5_fdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski B (k9_xtuple_0 C)) &  ( (C = (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers D E) (k47_valued_1 k1_numbers k1_numbers k1_numbers D E)) k3_taylor_1))  &  ( (E = (k1_taylor_1 2))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = (k5_square_1 A))  &  ( (~ (r1_xxreal_0 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers D E) F) k6_numbers))  &  (~  (A = k6_numbers) ) ) ) ) ) ) ) ) )  =>  ((r2_fdiff_1 C B) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ((k1_seq_1 (k2_fdiff_1 C B) F) = (k10_real_1 (k8_real_1 (k8_real_1 4 (k5_square_1 A)) F) (k9_real_1 (k2_newton A 4) (k2_newton F 4)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) & (r1_tarski B (k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers k4_sin_cos6 A))))  =>  ((r2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers k4_sin_cos6 A) B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C B) =>  ((k1_seq_1 (k2_fdiff_1 (k26_valued_1 k1_numbers k1_numbers k4_sin_cos6 A) B) C) = (k1_real_1 (k10_real_1 A (k7_square_1 (k9_real_1 1 (k5_square_1 C)))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_fdiff_8,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1))) =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k3_taylor_1) A) B) = (k1_real_1 (k10_real_1 1 B))) ) ) ) ) ) ) ) ) ).
tt(t5_fdiff_9,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k2_fdiff_9)) =>  ((r2_fdiff_1 k2_fdiff_9 A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 k2_fdiff_9 A) B) = (k1_real_1 (k10_real_1 (k1_seq_1 k19_sin_cos B) (k5_square_1 (k1_seq_1 k16_sin_cos B))))) ) ) ) ) ) ) ) ).
tt(t5_ff_siec,ax, (! [A:$i] :  ( ((u1_struct_0 (k5_ff_siec A)) = (k1_tarski A))  &  ( ((u4_struct_0 (k5_ff_siec A)) = k1_xboole_0)  &  ((k1_net_1 (k5_ff_siec A)) = k1_xboole_0) ) ) ) ).
tt(t5_fib_fusc,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  ((r1_tarski k3_fib_fusc A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  (! [C:$i] :  ( ((v5_memstr_0 C 2 k1_ami_3 k6_numbers) & (m1_scm_1 C (k16_afinsq_1 2 B 1 k6_numbers)))  =>  ((r1_extpro_1 2 k1_ami_3 A C) &  ( ((k1_funct_1 (k6_extpro_1 2 k1_ami_3 A C) (k10_ami_3 3)) = (k3_pre_ff B))  &  ( ( (B = k6_numbers)  =>  ((k8_extpro_1 2 k1_ami_3 A C) = 1) )  &  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k8_extpro_1 2 k1_ami_3 A C) = (k2_xcmplx_0 (k3_xcmplx_0 6 (k2_xcmplx_0 (k1_int_1 (k5_power 2 B)) 1)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k3_power C (k2_xcmplx_0 A B)) = (k3_xcmplx_0 (k3_power C A) (k3_power C B))) ) ) ) ) ) ) ).
tt(t5_fib_num3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k13_newton (k2_nat_1 A B) 2) = (k2_nat_1 (k2_nat_1 (k2_nat_1 (k4_nat_1 A A) (k4_nat_1 A B)) (k4_nat_1 A B)) (k4_nat_1 B B))) ) ) ) ) ).
tt(t5_fib_num4,ax, (~ (r1_xxreal_0 1 (k18_complex1 k2_fib_num))) ).
tt(t5_fib_num,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k3_int_2 (k1_pre_ff A) (k1_pre_ff B)) = (k1_pre_ff (k3_int_2 A B))) ) ) ) ) ).
tt(t5_filerec1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_xxreal_0 1 (k3_finseq_1 C)) =>  ((k3_finseq_6 A (k1_finseq_8 A B C) (k2_nat_1 (k3_finseq_1 B) 1) (k2_nat_1 (k3_finseq_1 B) (k3_finseq_1 C))) = C) ) ) ) ) ) ) ) ).
tt(t5_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_lattices A) &  ((v7_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r3_lattices A B C) & (r3_lattices A D E))  => (r3_lattices A (k4_lattices A B D) (k4_lattices A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_filter_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_partfun1 B A) &  ((v3_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ((m2_filter_1 C A B) =>  ((v2_binop_1 C A) => (v2_binop_1 (k3_filter_1 A B C) (k8_eqrel_1 A B))) ) ) ) ) ) ) ).
tt(t5_filter_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 B B) B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B B) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ( (E = (k1_realset1 C B))  &  ( (F = (k1_realset1 D B))  & (r1_lattice2 A C D)) )  => (r1_lattice2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_finance1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (m2_subset_1 (k3_prob_1 k1_numbers (k2_finance1 A B)) (k1_zfmisc_1 k1_numbers) k12_prob_1)) ) ) ) ).
tt(t5_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 A B) <=> (r1_tarski (k2_finseq_1 A) (k2_finseq_1 B))) ) ) ) ) ).
tt(t5_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (m1_subset_1 (k4_xxreal_0 k6_numbers (k6_xcmplx_0 A B)) k5_numbers)) ) ) ) ).
tt(t5_finseq_3,ax, ((k2_finseq_1 7) = (k5_enumset1 1 2 3 4 5 6 7)) ).
tt(t5_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((r2_finseq_4 A B) => (r2_hidden B (k10_xtuple_0 A))) ) ) ) ).
tt(t5_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v2_funct_1 A) &  ((r2_hidden B (k10_xtuple_0 A)) &  ((k8_relat_1 A (k1_tarski B)) = (k8_relat_1 A (k1_tarski C))) ) )  =>  (B = C) ) ) ) ) ) ).
tt(t5_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k5_relat_1 (k11_finseq_1 A B C) (k2_finseq_1 2)) = (k10_finseq_1 A B)) ) ) ) ).
tt(t5_finseq_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_finseq_1 (k1_finseq_7 A B D C)) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ).
tt(t5_finseq_8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((k3_finseq_8 A B 1 C) = (k17_finseq_1 A C B)) ) ) ) ) ) ) ).
tt(t5_finseqop,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k5_funcop_1 B A k1_xboole_0) = k1_xboole_0) ) ) ) ).
tt(t5_finset_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((v1_finset_1 A) => (v1_finset_1 (k7_relat_1 B A))) ) ) ) ).
tt(t5_finsop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ((v2_binop_1 D A) =>  ( ( (~ (v1_setwiseo D A))  &  (~  ((r1_xxreal_0 1 (k3_finseq_1 B)) & (r1_xxreal_0 1 (k3_finseq_1 C))) ) )  |  ((k1_finsop_1 A (k8_finseq_1 A B C) D) = (k5_binop_1 A D (k1_finsop_1 A B D) (k1_finsop_1 A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_finsub_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((r2_hidden (k5_xboole_0 B C) A) & (r2_hidden (k3_xboole_0 B C) A)) ) ) ) )  => (v4_finsub_1 A)) ) ) ).
tt(t5_fintopo2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_fin_topo (k3_subset_1 (u1_struct_0 A) B) A) => (v2_fin_topo B A)) ) ) ) ) ).
tt(t5_fintopo3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B C) => (r1_tarski (k12_fin_topo A B) (k12_fin_topo A C))) ) ) ) ) ) ) ).
tt(t5_fintopo4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_fintopo4 A B C) => (r1_fintopo4 A C B)) ) ) ) ) ) ) ).
tt(t5_fintopo5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ((v1_fintopo5 C A B) &  (F = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E)) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ((r2_hidden (k1_funct_1 (k2_funct_1 C) G) (k10_fintopo3 A D E)) <=> (r2_hidden G (k10_fintopo3 B D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fintopo6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v1_fintopo6 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ((r1_xboole_0 B C) &  ((r1_fintopo4 A B C) &  ( (~  (B = (k1_struct_0 A)) )  &  (~  (C = (k1_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fin_topo,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden B (k5_fin_topo A C)) <=>  ( (~ (r1_xboole_0 (k1_fin_topo A B) C))  &  (~ (r1_xboole_0 (k1_fin_topo A B) (k3_subset_1 (u1_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t5_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k3_catalan2 A)) =>  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v5_ordinal1 D) &  ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ( (B = (k1_ordinal4 C D))  =>  ((m1_subset_1 C (k3_catalan2 A)) & (m1_subset_1 D (k3_catalan2 A))) ) ) ) ) ) ) ) ) ).
tt(t5_flang_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (~  ( ((r2_hidden A C) | (r2_hidden A D))  &  ( (~  (A = (k2_flang_1 B)) )  &  ((k6_flang_1 B C D) = (k4_flang_1 B (k2_flang_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) => (r1_tarski (k1_flang_3 A B D) (k1_flang_3 A B C))) ) ) ) ) ) ) ) ).
tt(t5_fomodel0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B A))  <=> (r2_hidden B (k6_subset_1 (k3_finseq_2 A) (k1_tarski k1_xboole_0)))) ) ) ) ).
tt(t5_fomodel1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (~  ((r2_hidden A (k35_fomodel1 B)) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (~ (r2_hidden A (k3_funct_2 k5_numbers (k9_setfam_1 (k3_finseq_2 (k15_fomodel1 B))) (k28_fomodel1 B) C))) ) ) ) ) ) ) ) ).
tt(t5_fomodel2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((v1_funct_1 (k1_funct_5 (k23_fomodel2 B A C))) &  ((v1_funct_2 (k1_funct_5 (k23_fomodel2 B A C)) (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1)) & (m1_subset_1 (k1_funct_5 (k23_fomodel2 B A C)) (k1_zfmisc_1 (k2_zfmisc_1 (k16_fomodel2 B C) (k3_rfunct_3 (k6_subset_1 (k3_finseq_2 (k1_fomodel1 B)) (k1_tarski k1_xboole_0)) k6_margrel1))))) ) ) ) ) ) ) ) ).
tt(t5_fomodel3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v6_struct_0 B))  &  ((v11_fomodel1 B) & (l1_fomodel1 B)) )  =>  (! [C:$i] :  ( ((v1_partfun1 C A) &  ((v3_relat_2 C) &  ((v8_relat_2 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v15_fomodel1 D B) & (m2_subset_1 D (k3_finseq_2 (k15_fomodel1 B)) (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) &  ((v1_fomodel2 E B A) & (v3_fomodel3 E B A C)) ) )  =>  ( (~  ((k3_funct_2 (k6_subset_1 (k3_finseq_2 (k15_fomodel1 B)) (k1_tarski k1_xboole_0)) (k15_fomodel1 B) (k22_fomodel1 B) D) = (k34_fomodel2 B)) )  =>  ((k14_fomodel2 B (k8_eqrel_1 A C) (k23_fomodel3 B A C E) D) = (k14_fomodel2 B A E D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fomodel4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ( (~ (v6_struct_0 F))  &  ((v11_fomodel1 F) & (l1_fomodel1 F)) )  =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [I:$i] :  ((m1_subset_1 I (k1_zfmisc_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))))) =>  (! [J:$i] :  ((v2_fomodel4 J F) =>  (! [K:$i] :  ((v2_fomodel4 K F) =>  ( ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) F) &  ((v6_fomodel4 (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) I) F) &  ((v4_fomodel4 C A F G J) &  ((v4_fomodel4 D A F H K) & (v4_fomodel4 E B F I (k2_tarski C D))) ) ) )  => (v4_fomodel4 E (k2_xcmplx_0 A B) F (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) (k4_subset_1 (k9_funct_2 (k9_setfam_1 (k1_fomodel4 F)) (k9_setfam_1 (k1_fomodel4 F))) G H) I) (k2_xboole_0 J K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fraenkel,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m2_funct_2 D C A (k9_funct_2 C A)) => (r2_relset_1 C A (k2_partfun1 C A D B) (k2_partfun1 C A D (k3_xboole_0 C B)))) ) ) ) ) ) ).
tt(t5_frechet2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C (k2_frechet A B)) & (r2_hidden D (k2_frechet A B)))  =>  (C = D) ) ) ) ) ) ) )  => (v7_pre_topc A)) ) ) ).
tt(t5_frechet,ax, (! [A:$i] :  ((l1_pre_topc A) =>  ( ((v4_pre_topc (k1_struct_0 A) A) &  ((v4_pre_topc (k2_struct_0 A) A) &  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (v4_pre_topc C A))  => (v4_pre_topc (k4_subset_1 (u1_struct_0 A) B C) A)) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) => (v4_pre_topc (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) )  =>  ((v2_pre_topc A) & (l1_pre_topc A)) ) ) ) ).
tt(t5_freealg,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_freealg B))  =>  (~ (v1_xboole_0 (k8_freealg A B))) ) ) ) ) ).
tt(t5_fscirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  (F = (k1_funct_1 D C)) )  =>  ((k1_funct_1 (k6_circuit2 (k3_fscirc_1 A B C) (k5_fscirc_1 A B C) D) (k4_tarski (k10_finseq_1 A C) k3_twoscomp)) = (k10_margrel1 (k9_margrel1 E) F)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fscirc_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ((k1_fscirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k1_fscirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ( ((k2_fscirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k2_fscirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ((k3_fscirc_2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k3_fscirc_2 A (k7_finseq_1 B E) (k7_finseq_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 F) & (r1_xxreal_0 F (k3_finseq_1 C)))  =>  ((k1_funct_1 (k2_fsm_1 A B E (k8_finseq_1 A C D)) F) = (k1_funct_1 (k2_fsm_1 A B E C) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_fsm_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_fsm_1 B A))  =>  ( (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ( ((k1_funct_1 C 1) = (k1_funct_1 D 1))  => (r3_xboole_0 (k2_fsm_1 A B (u2_fsm_1 A B) C) (k2_fsm_1 A B (u2_fsm_1 A B) D))) ) ) ) )  => (v1_fsm_2 B A)) ) ) ) ) ).
tt(t5_fsm_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k8_afinsq_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (C = k6_numbers) )  &  ((r1_xxreal_0 (k1_afinsq_1 B) (k2_xcmplx_0 C 1)) &  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  (~  ((r1_xxreal_0 (k1_afinsq_1 D) C) &  ((r1_xxreal_0 (k1_afinsq_1 E) C) &  (B = (k1_flang_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ftacell1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k14_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k12_gfacirc1 A B C) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k9_gfacirc1 A B C) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k14_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k12_gfacirc1 (k12_gfacirc1 A B C) E D) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k12_gfacirc1 A B C) E) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 E D) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) &  ((r2_hidden (k4_tarski (k10_finseq_1 D (k12_gfacirc1 A B C)) k2_twoscomp) (k3_msafree2 (k1_ftacell1 A B C D E))) & (r2_hidden (k9_gfacirc1 (k12_gfacirc1 A B C) E D) (k3_msafree2 (k1_ftacell1 A B C D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_funcop_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((k5_relat_1 (k13_funct_3 A B) C) = (k13_funct_3 (k5_relat_1 A C) B)) ) ) ) ) ) ).
tt(t5_funcsdom,ax, (! [A:$i] :  (! [B:$i] :  ((m2_funct_2 B A k1_numbers (k9_funct_2 A k1_numbers)) =>  (! [C:$i] :  ((m2_funct_2 C A k1_numbers (k9_funct_2 A k1_numbers)) => (r2_funct_2 A k1_numbers (k1_funcsdom A k1_numbers (k5_funcsdom A) B C) (k1_funcsdom A k1_numbers (k5_funcsdom A) C B))) ) ) ) ) ).
tt(t5_funct_1,ax, (! [A:$i] :  ( (~  (A = k1_xboole_0) )  =>  (! [B:$i] :  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  &  ( ((k9_xtuple_0 C) = A)  &  ((k10_xtuple_0 C) = (k1_tarski B)) ) ) ) ) ) ) ).
tt(t5_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r2_hidden C A) =>  ( (B = k1_xboole_0)  | (r2_hidden (k1_funct_1 D C) B)) ) ) ) ) ) ) ).
tt(t5_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A (k10_xtuple_0 C)) & (r1_tarski (k8_relat_1 C A) (k10_xtuple_0 B)))  => (r1_tarski A (k10_xtuple_0 (k3_relat_1 B C)))) ) ) ) ) ) ).
tt(t5_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((r1_relset_1 A (k1_tarski B) (k7_funcop_1 A B) (k7_funcop_1 C D)) => (r1_tarski A C)) ) ) ) ) ).
tt(t5_funct_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  ((k2_zfmisc_1 A B) = k1_xboole_0) )  =>  ( ((k1_funct_5 (k7_funcop_1 (k2_zfmisc_1 A B) C)) = (k7_funcop_1 A (k7_funcop_1 B C)))  &  ((k3_funct_5 (k7_funcop_1 (k2_zfmisc_1 A B) C)) = (k7_funcop_1 B (k7_funcop_1 A C))) ) ) ) ) ) ).
tt(t5_funct_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_funct_1 C) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 B)) =>  ((r2_hidden D (k7_subset_1 B (k7_relset_1 A B C E) F)) => (r2_hidden (k1_funct_1 (k2_funct_1 C) D) (k7_subset_1 A E (k8_relset_1 A B C F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k2_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_funct_8 A k1_numbers k1_numbers B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) &  ((k1_funct_1 B C) = k6_numbers) ) ) ) ) )  =>  ((r1_tarski A (k1_relset_1 k1_numbers B)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k7_xcmplx_0 (k1_funct_1 B C) (k1_funct_1 B (k1_real_1 C))) = 1) ) ) ) ) ) ) ) ) ) ).
tt(t5_funct_9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v3_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( ((v1_funct_9 B A) & (v1_funct_9 C A))  => (v1_funct_9 (k50_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t5_functor0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_funct_4 (k7_funcop_1 (k2_zfmisc_1 A B) C)) = (k7_funcop_1 (k2_zfmisc_1 B A) C)) ) ) ) ).
tt(t5_functor1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_altcat_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l2_altcat_1 B))  =>  (! [C:$i] :  ((l2_functor0 C A B) =>  ((v21_functor0 C A B) =>  ((v3_funct_2 (u1_functor0 A B C) (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 B))) & (v1_msualg_3 (u2_functor0 A B C))) ) ) ) ) ) ) ) ).
tt(t5_functor2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D A B) =>  ((r1_functor2 A B C D) =>  (! [E:$i] :  ((m1_functor2 E A B C D) =>  ((r8_pboole (u1_struct_0 A) (k3_functor2 A B C D D E (k1_functor2 A B D)) E) & (r8_pboole (u1_struct_0 A) (k3_functor2 A B C C D (k1_functor2 A B C) E) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_functor3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v12_altcat_1 B) & (l2_altcat_1 B)) )  =>  (! [C:$i] :  ( ((v8_functor0 C A B) & (l2_functor0 C A B))  =>  ((k13_functor0 A A B (k12_functor0 A) C) = (g2_functor0 A B (u1_functor0 A B C) (u2_functor0 A B C))) ) ) ) ) ) ) ).
tt(t5_fuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((k1_square_1 (k1_seq_1 C B) (k1_seq_1 D B)) = (k1_seq_1 (k1_fuzzy_1 A C D) B))  &  ((k2_square_1 (k1_seq_1 C B) (k1_seq_1 D B)) = (k1_seq_1 (k2_fuzzy_1 A C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t5_fuzzy_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ((r1_fuzzy_1 B C) => (r1_fuzzy_1 (k1_fuzzy_2 A D C) (k1_fuzzy_2 A D B))) ) ) ) ) ) ) ) ) ).
tt(t5_fuzzy_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) k1_numbers)))) ) )  => (r2_relset_1 (k2_zfmisc_1 A B) k1_numbers (k2_fuzzy_4 A B (k2_fuzzy_4 B A C)) C)) ) ) ) ) ) ).
tt(t5_fvaluat1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (~  ( (~  (A = k1_xxreal_0) )  &  ( (~ (r1_xxreal_0 k6_numbers B))  &  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 k6_numbers (k6_xxreal_3 B A))) ) ) ) ) ) ) ) ).
tt(t5_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) &  ((v6_vectsp_1 A) & (l4_algstr_0 A)) ) )  =>  ((k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) = (k5_struct_0 A)) ) ) ).
tt(t5_gate_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ( (~ (v1_xboole_0 (k3_gate_1 A B)))  &  ((v1_xboole_0 A) & (v1_xboole_0 B)) ) )  &  (~  ( (~  ((v1_xboole_0 A) & (v1_xboole_0 B)) )  & (v1_xboole_0 (k3_gate_1 A B))) ) ) ) ) ).
tt(t5_gcd_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_group_1 A) & (l4_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_gcd_1 A B C) => (r1_gcd_1 A (k6_algstr_0 A D B) (k6_algstr_0 A D C))) ) ) ) ) ) ) ) ) ).
tt(t5_genealg1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_genealg1 C B) =>  (! [D:$i] :  ((m1_genealg1 D B) =>  ((r1_xxreal_0 (k3_finseq_1 C) A) =>  ((k7_genealg1 B C D A) = C) ) ) ) ) ) ) ) ) ) ).
tt(t5_geomtrap,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((k1_geomtrap A B D) = C) ) ) ) ) ) ) ) ) ).
tt(t5_gfacirc1,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k1_gfacirc1 (k9_finseq_1 (k1_funct_1 k14_twoscomp (k10_finseq_1 A B)))) = (k1_funct_1 k15_twoscomp (k10_finseq_1 A B)))  &  ( ((k1_funct_1 k1_gfacirc1 (k9_finseq_1 (k1_funct_1 k14_twoscomp (k10_finseq_1 A B)))) = (k1_funct_1 k4_gfacirc1 (k10_finseq_1 A B)))  &  ((k1_funct_1 k14_twoscomp (k10_finseq_1 (k1_funct_1 k1_gfacirc1 (k10_binarith k6_margrel1 A)) (k1_funct_1 k1_gfacirc1 (k10_binarith k6_margrel1 B)))) = (k1_funct_1 k14_twoscomp (k10_finseq_1 A B))) ) ) ) ) ) ) ).
tt(t5_gfacirc2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_card_1 B A) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( ((k1_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k1_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ( ((k2_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k2_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G)))  &  ((k3_gfacirc2 A (k7_finseq_1 B D) (k7_finseq_1 C F)) = (k3_gfacirc2 A (k7_finseq_1 B E) (k7_finseq_1 C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  ((v1_glib_000 A) <=>  ((r1_tarski k5_glib_000 (k1_relset_1 k5_numbers A)) &  ( (~ (v1_xboole_0 (k6_glib_000 A)))  &  ( ((v1_funct_1 (k8_glib_000 A)) &  ((v1_funct_2 (k8_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k8_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) )  &  ((v1_funct_1 (k9_glib_000 A)) &  ((v1_funct_2 (k9_glib_000 A) (k7_glib_000 A) (k6_glib_000 A)) & (m1_subset_1 (k9_glib_000 A) (k1_zfmisc_1 (k2_zfmisc_1 (k7_glib_000 A) (k6_glib_000 A))))) ) ) ) ) ) ) ) ).
tt(t5_glib_001,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((k3_finseq_1 (k15_finseq_1 C)) = (k5_card_1 C)) ) ) ) ) ) ).
tt(t5_glib_002,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v1_glib_002 A)) ) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((m2_glib_000 D A (k6_glib_000 A) (k6_subset_1 (k7_glib_000 A) (k1_tarski C))) =>  ( ((v8_glib_001 B A) & (r2_hidden C (k14_glib_001 A B)))  => (v1_glib_002 D)) ) ) ) ) ) ) ) ).
tt(t5_glib_003,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_003 A)) ) ) ) )  => (r1_tarski (k9_xtuple_0 (k6_glib_003 A)) (k7_glib_000 A))) ) ).
tt(t5_glib_004,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v3_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v3_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ( (! [D:$i] :  ((r2_hidden D A) => (r1_xxreal_0 (k1_seq_1 B D) (k1_seq_1 C D))) )  => (r1_xxreal_0 (k3_uproots A B) (k3_uproots A C))) ) ) ) ) ) ).
tt(t5_glib_005,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) &  ((v1_glib_003 A) & (v7_glib_003 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k7_glib_000 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (k7_glib_000 A)) & (v4_valued_0 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 D E) => (r1_tarski (k1_relset_1 (k6_glib_000 A) (k4_glib_005 A B (k5_glib_005 A B C) D)) (k1_relset_1 (k6_glib_000 A) (k4_glib_005 A B (k5_glib_005 A B C) E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_goboard1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  (! [F:$i] :  ( ( (~ (v3_relat_1 F))  &  ((v1_matrix_1 F) &  ((v2_goboard1 F) &  ((v3_goboard1 F) &  ((v4_goboard1 F) &  ((v5_goboard1 F) & (m2_finseq_1 F (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ( (E = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F A B))  &  ( (E = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) F C D))  &  ((r2_hidden (k4_tarski A B) (k2_matrix_1 F)) & (r2_hidden (k4_tarski C D) (k2_matrix_1 F))) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_goboard2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B))) &  ((k2_nat_1 D (k3_finseq_1 A)) = C) )  =>  ((r1_xxreal_0 C (k3_finseq_1 A)) |  ((k2_topreal1 2 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A B) C) = (k2_topreal1 2 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_goboard4,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((v2_funct_1 A) &  ((v1_topreal1 A) &  ((r1_xxreal_0 2 (k3_finseq_1 A)) &  ((v2_funct_1 B) &  ((v1_topreal1 B) &  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_goboard4 (k1_goboard1 A) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k1_goboard1 B) (k1_seq_1 (k1_goboard1 A) 1) (k1_seq_1 (k1_goboard1 A) (k3_finseq_1 A))) &  ((r1_goboard4 (k2_goboard1 A) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) &  ((r1_goboard4 (k2_goboard1 B) (k1_seq_1 (k2_goboard1 B) 1) (k1_seq_1 (k2_goboard1 B) (k3_finseq_1 B))) & (r1_xboole_0 (k3_topreal1 2 A) (k3_topreal1 2 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_goboard5,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2)))))  =>  ( ((v3_goboard1 C) &  ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 C))) ) )  =>  ((r1_xxreal_0 (k1_matrix_1 C) A) |  ((k2_goboard5 C A) = (a_3_0_goboard5 A B C)) ) ) ) ) ) ) ) ) ).
tt(t5_goboard6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((r2_hidden B (k1_tops_1 (k15_euclid A) C)) <=>  (? [D:$i] :  ((v1_xreal_0 D) &  ( (~ (r1_xxreal_0 D k6_numbers))  & (r1_tarski (k9_metric_1 (k14_euclid A) B D) C)) ) ) ) ) ) ) ) ) ) ).
tt(t5_goboard7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) B C)) &  ((k17_euclid B) = (k17_euclid C)) )  =>  ((k17_euclid A) = (k17_euclid C)) ) ) ) ) ) ) ) ).
tt(t5_goboard8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k2_nat_1 B 2) (k3_finseq_1 A)))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 (k2_nat_1 C 2) (k3_finseq_1 (k2_goboard2 A))) &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 (k2_nat_1 D 2) (k1_matrix_1 (k2_goboard2 A))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1))) ) ) ) )  =>  ( ( (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) )  &  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 B 2)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) C (k2_nat_1 D 1)))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 2))) ) ) )  | (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 1))) (k13_complex1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 1) (k2_nat_1 D 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k2_nat_1 C 2) (k2_nat_1 D 2))) (k13_complex1 1 2))) (k3_topreal1 2 A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_gobrd10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 B A) &  ((r1_xxreal_0 C A) &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ( ((k1_funct_1 D 1) = B)  &  ( ((k1_funct_1 D (k3_finseq_1 D)) = C)  &  ( ((k3_finseq_1 D) = (k2_nat_1 (k2_nat_1 (k7_nat_d B C) (k7_nat_d C B)) 1))  &  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 E) &  ((r1_xxreal_0 E (k3_finseq_1 D)) &  (F = (k1_funct_1 D E)) ) )  => (r1_xxreal_0 F A)) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 1 E) &  ( (~ (r1_xxreal_0 (k3_finseq_1 D) E))  &  ( (~  ((k1_funct_1 D (k2_nat_1 E 1)) = (k2_nat_1 (k7_partfun1 k5_numbers D E) 1)) )  &  (~  ((k1_funct_1 D E) = (k2_nat_1 (k7_partfun1 k5_numbers D (k2_nat_1 E 1)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_gobrd11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_connsp_3 A (k9_subset_1 (u1_struct_0 A) B C) D) = (k9_subset_1 (u1_struct_0 (k1_pre_topc A D)) (k4_connsp_3 A B D) (k4_connsp_3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t5_gobrd12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  ((m1_connsp_3 (k4_subset_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) (k4_connsp_3 (k15_euclid 2) (k2_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) (k4_connsp_3 (k15_euclid 2) (k3_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A)))) &  ( ((k4_connsp_3 (k15_euclid 2) (k2_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) = (k2_goboard9 A))  &  ((k4_connsp_3 (k15_euclid 2) (k3_goboard9 A) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 A))) = (k3_goboard9 A)) ) ) ) ) ).
tt(t5_gobrd14,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ( (~ (v3_relat_1 D))  &  ((v1_matrix_1 D) &  ((v2_goboard1 D) &  ((v3_goboard1 D) &  ((v4_goboard1 D) &  ((v5_goboard1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r2_hidden (k4_tarski A B) (k2_matrix_1 D)) & (r2_hidden (k4_tarski (k2_nat_1 A C) B) (k2_matrix_1 D)))  =>  ((k1_topreal6 2 (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A C) B)) = (k9_real_1 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D (k2_nat_1 A C) B)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) D A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_goedelcp,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ( ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) B))) & (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) C))))  => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k7_cqc_lang A B C))))) ) ) ) ) ) ) ) ) ).
tt(t5_graph_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_graph_1 B))  =>  ((r4_graph_1 A B) =>  ((r1_relset_1 (u4_struct_0 A) (u1_struct_0 A) (u1_graph_1 A) (u1_graph_1 B)) & (r1_relset_1 (u4_struct_0 A) (u1_struct_0 A) (u2_graph_1 A) (u2_graph_1 B))) ) ) ) ) ) ).
tt(t5_graph_2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  =>  ((k1_recdef_1 (k14_finseq_1 (a_2_1_graph_2 A B)) C) = (k2_nat_1 B C)) ) ) ) ) ) ) ) ).
tt(t5_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((v2_funct_1 (k2_graph_2 (u4_struct_0 A) B C D)) & (m2_graph_1 (k2_graph_2 (u4_struct_0 A) B C D) A)) ) ) ) ) ) ) ) ) ).
tt(t5_graph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v7_graph_1 C A) & (m2_graph_1 C A))  =>  ((r3_graph_4 A B C) => (r1_tarski (k1_graph_4 A (k10_xtuple_0 C)) (k10_xtuple_0 B))) ) ) ) ) ) ) ).
tt(t5_graph_5,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (~  ( ((k5_card_1 A) = 1)  &  (! [B:$i] :  ((m1_subset_1 B A) =>  (~  (A = (k1_tarski B)) ) ) ) ) ) ) ) ).
tt(t5_graphsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  ((v7_graph_1 (k9_finseq_1 B) A) &  ((v1_graph_4 (k9_finseq_1 B) A) & (m2_graph_1 (k9_finseq_1 B) A)) ) ) ) ) ) ).
tt(t5_grcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((u1_struct_0 (k5_grcat_1 A B)) = B) ) ) ) ) ).
tt(t5_gr_cy_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_struct_0 (k5_group_4 A (k6_domain_1 (u1_struct_0 A) C)) B) <=>  (? [D:$i] :  ((v1_int_1 D) &  (B = (k5_group_1 A D C)) ) ) ) ) ) ) ) ) ) ).
tt(t5_gr_cy_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((v1_int_1 D) &  (C = (k5_group_1 A D B)) ) ) ) )  <=>  (A = (k5_group_4 A (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ) ) ).
tt(t5_gr_cy_3,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_gr_cy_3 A)) )  =>  ( (~  (A = 5) )  =>  ((k4_nat_d A 4) = 3) ) ) ) ).
tt(t5_grfunc_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 (k1_tarski (k4_tarski A B))) & (v1_funct_1 (k1_tarski (k4_tarski A B)))) ) ) ).
tt(t5_grnilp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k2_group_3 A (k3_group_5 A B (k2_group_1 A C) D) C) = (k2_group_5 A (k2_group_3 A (k2_group_5 A B (k2_group_1 A C)) C) (k2_group_3 A D C))) ) ) ) ) ) ) ) ) ).
tt(t5_groeb_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) &  ((v1_polynom1 C (k15_pre_poly A) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) ) )  =>  ((k2_polynom1 (k15_pre_poly A) B (k5_vfunct_1 (k15_pre_poly A) B C)) = (k2_polynom1 (k15_pre_poly A) B C)) ) ) ) ) ) ) ).
tt(t5_groeb_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r1_groeb_2 A B C) <=> (r6_pboole A (k2_groeb_2 A B C) (k11_pre_poly A B C))) ) ) ) ) ) ).
tt(t5_groeb_3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v8_relat_2 B) &  ((v2_bagorder B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ( ((r2_termord A B C D) & (r1_termord A B E F))  => (r2_termord A B (k11_pre_poly A C E) (k11_pre_poly A D F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (k1_funct_2 B B)) &  ((v1_group_10 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (k1_funct_2 B B))))) ) )  =>  ( ((r2_group_10 A B F C D) & (r2_group_10 A B F D E))  => (r2_group_10 A B F C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) => (r1_struct_0 B (k6_algstr_0 A (k6_algstr_0 A C D) (k2_group_1 A C)))) ) ) ) )  => (v1_group_3 B A)) ) ) ) ) ).
tt(t5_group_12,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v1_group_7 B) &  ((v2_group_7 B A) & (v3_group_7 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k2_group_7 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k2_group_7 A B))) =>  ( ((r2_hidden D (k1_group_12 A B C)) & (r2_hidden E (k1_group_12 A B C)))  => (r2_hidden (k6_algstr_0 (k2_group_7 A B) D E) (k1_group_12 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ( ((k6_algstr_0 A B C) = (k1_group_1 A))  &  ((k6_algstr_0 A C B) = (k1_group_1 A)) )  =>  (C = (k2_group_1 A B)) ) ) ) ) ) ) ) ).
tt(t5_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  ((k1_group_2 A (k1_subset_1 (u1_struct_0 A))) = k1_xboole_0) ) ) ).
tt(t5_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski C D) =>  ((r1_tarski (k4_group_2 A B C) (k4_group_2 A B D)) & (r1_tarski (k5_group_2 A B C) (k5_group_2 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k3_group_4 A (k8_finseq_1 (u1_struct_0 A) B C)) = (k6_algstr_0 A (k3_group_4 A B) (k3_group_4 A C))) ) ) ) ) ) ) ).
tt(t5_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ( ((k7_group_4 B C D) = (k7_group_4 B D C))  =>  ((r1_struct_0 (k8_group_4 B C D) A) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ( (A = (k6_algstr_0 B E F))  &  ((r1_struct_0 C E) & (r1_struct_0 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k11_group_2 A B (k13_group_2 A B C)) = (k13_group_2 A B C))  &  ( ((k4_group_2 A C (k7_group_4 A B B)) = (k13_group_2 A B C))  &  ( ((k5_group_2 A C (k7_group_4 A B B)) = (k14_group_2 A B C))  &  ((k12_group_2 A B (k14_group_2 A B C)) = (k14_group_2 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v1_group_7 C) & (v2_group_7 C A)) ) ) ) )  =>  ( (! [D:$i] :  (~  ((r2_hidden D A) &  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v2_group_1 E) & (l3_algstr_0 E)) )  =>  (~  ( (E = (k1_funct_1 C D))  &  ((k1_funct_1 B D) = (k1_group_1 E)) ) ) ) ) ) ) )  =>  (B = (k1_group_1 (k2_group_7 A C))) ) ) ) ) ) ) ).
tt(t5_group_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ( (C = D)  & (v8_struct_0 A))  =>  ((k6_group_1 B C) = (k6_group_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) => (r1_struct_0 C (k1_group_1 B))) ) ) ) ) ).
tt(t5_groupp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k6_group_1 A (k2_group_1 A B)) = (k6_group_1 A B)) ) ) ) ) ).
tt(t5_grsolv_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v1_grsolv_1 A) & (l3_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (v1_grsolv_1 B)) ) ) ) ).
tt(t5_hahnban1,ax, ((k8_group_1 k1_complfld (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld)) (k4_algstr_0 k1_complfld (k1_group_1 k1_complfld))) = (k1_group_1 k1_complfld)) ).
tt(t5_hahnban,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r1_rlsub_2 A B C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((k4_rlsub_2 A D B C) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) E F))  =>  ((k4_rlsub_2 A D C B) = (k1_domain_1 (u1_struct_0 A) (u1_struct_0 A) F E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_hallmar1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_hallmar1 A B (k1_tarski C)) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(t5_hausdorf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  (! [C:$i] :  ((r2_hidden C B) =>  ((k1_funct_1 (k6_weierstr A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t5_helly,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) ) )  =>  ( ((k1_funct_1 A 1) = (k1_funct_1 B 1))  => (r1_xxreal_0 1 (k3_finseq_1 (k1_helly A B)))) ) ) ) ) ).
tt(t5_henmodel,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) C (k12_finseq_1 (k3_cqc_lang A) B))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) C D) (k12_finseq_1 (k3_cqc_lang A) B)))) ) ) ) ) ) ) ) ) ).
tt(t5_hermitan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ( (A = (k2_complfld A))  =>  ((k4_complex1 A) = k6_numbers) ) ) ) ).
tt(t5_hessenbe,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) & (l1_collsp A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_collsp A B C D)) ) ) ) ) ) ) ) ) ).
tt(t5_heyting1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k12_normform A))) =>  (! [C:$i] :  ((r1_tarski C B) => (m1_subset_1 C (u1_struct_0 (k12_normform A)))) ) ) ) ) ).
tt(t5_heyting2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m2_subset_1 C (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  (! [D:$i] :  ((m2_subset_1 D (k5_finsub_1 (k4_partfun1 A B)) (k1_substlat A B)) =>  ( (! [E:$i] :  (~  ((r2_hidden E C) &  (! [F:$i] :  (~  ((r2_hidden F D) & (r1_tarski F E)) ) ) ) ) )  =>  ((k3_substlat A B (k4_substlat A B C D)) = C) ) ) ) ) ) ) ) ).
tt(t5_heyting3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k8_mcart_1 k1_numbers k5_numbers k5_numbers (k6_domain_1 k5_numbers A)))))  =>  (? [C:$i] :  ((m1_subset_1 C k5_numbers) &  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 C D) & (r2_hidden (k1_domain_1 k5_numbers k5_numbers D A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t5_hfdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) => (r2_relset_1 k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers A B) (k26_valued_1 k1_numbers k1_numbers A C)) (k26_valued_1 k1_numbers k1_numbers A (k7_real_1 B C)))) ) ) ) ) ) ).
tt(t5_hilbasis,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_partfun1 C B) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_partfun1 D B) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F A) &  ((v1_funct_1 F) &  ((v1_partfun1 F A) &  ((v4_valued_0 F) & (v2_pre_poly F)) ) ) ) )  =>  ( ( (E = (k5_relat_1 C A))  &  (F = (k5_relat_1 D A)) )  =>  ( ((k5_relat_1 (k12_pre_poly B C D) A) = (k12_pre_poly A E F))  &  ((k5_relat_1 (k11_pre_poly B C D) A) = (k11_pre_poly A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_hilbert1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_hilbert1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C k1_hilbert1) => (r2_hidden (k3_hilbert1 (k4_hilbert1 B C) B) (k5_hilbert1 A))) ) ) ) ) ) ).
tt(t5_hilbert2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_trees_1 C))  =>  ((r2_hidden (k9_finseq_1 A) (k13_trees_3 B C)) <=>  ( (A = k6_numbers)  |  (A = 1) ) ) ) ) ) ) ) ).
tt(t5_hilbert3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden C A) & (r2_hidden D (k1_funct_2 A B)))  => (r2_hidden (k1_funct_1 D C) B)) ) ) ) ) ) ).
tt(t5_holder_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( ((k7_real_1 (k10_real_1 1 A) (k10_real_1 1 B)) = 1)  &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 k6_numbers D)) )  =>  ((r1_xxreal_0 A 1) |  ((r1_xxreal_0 (k8_real_1 C D) (k7_real_1 (k10_real_1 (k4_power C A) A) (k10_real_1 (k4_power D B) B))) &  ( ( ((k8_real_1 C D) = (k7_real_1 (k10_real_1 (k4_power C A) A) (k10_real_1 (k4_power D B) B)))  =>  ((k4_power C A) = (k4_power D B)) )  &  ( ((k4_power C A) = (k4_power D B))  =>  ((k8_real_1 C D) = (k7_real_1 (k10_real_1 (k4_power C A) A) (k10_real_1 (k4_power D B) B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_homothet,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((r1_homothet A D C) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) D B) = B) )  =>  ((r2_hidden B C) | (r2_relset_1 (u1_struct_0 A) (u1_struct_0 A) D (k6_partfun1 (u1_struct_0 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_hurwitz,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k2_complfld (k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) A B)) = (k2_binop_1 (u1_struct_0 k1_complfld) k5_numbers (u1_struct_0 k1_complfld) (k4_group_1 k1_complfld) (k2_complfld A) B)) ) ) ) ) ).
tt(t5_idea_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 C A))  &  ( (~ (r1_xxreal_0 C B))  &  ((v1_int_2 C) &  ((k4_nat_d (k4_nat_1 A B) C) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_algstr_0 A) &  ((v1_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) )  => (v2_ideal_1 (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A)) A)) ) ).
tt(t5_incproj,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) & (l1_collsp A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 (k3_incproj A))) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 (k3_incproj A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_incproj E A) =>  ( ( (B = D)  &  (C = E) )  =>  ((r1_incsp_1 (k3_incproj A) B C) <=> (r2_hidden D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_incsp_1,ax, (! [A:$i] :  ((l2_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_incsp_1 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_incsp_1 A)) =>  ((r5_incsp_1 A (k9_domain_1 (u1_incsp_1 A) B C D E) F) <=>  ((r2_incsp_1 A B F) &  ((r2_incsp_1 A C F) &  ((r2_incsp_1 A D F) & (r2_incsp_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_index_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m3_index_1 B (u1_struct_0 A) (u4_struct_0 A) (u1_graph_1 A) (u2_graph_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) => (m2_cat_1 (k1_funct_1 (k2_xtuple_0 B) C) (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) (k3_graph_1 A C)) (k2_index_1 (u1_struct_0 A) (k1_xtuple_0 B) (k4_graph_1 A C)))) ) ) ) ) ) ).
tt(t5_instalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D A) =>  (! [E:$i] :  ((l3_msualg_1 E A) =>  ( ( ((g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) = (g3_msualg_1 A (u3_msualg_1 A D) (u4_msualg_1 A D)))  &  ((g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C)) = (g3_msualg_1 A (u3_msualg_1 A E) (u4_msualg_1 A E))) )  =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A D) (u3_msualg_1 A E)) =>  ((r8_pboole (u1_struct_0 A) F G) =>  (! [H:$i] :  ((m1_subset_1 H (u4_struct_0 A)) =>  (~  ( (~  ((k3_msualg_1 A H B) = k1_xboole_0) )  &  ( (~  ((k3_msualg_1 A H C) = k1_xboole_0) )  &  (? [I:$i] :  ((m1_subset_1 I (k3_msualg_1 A H B)) &  (? [J:$i] :  ((m1_subset_1 J (k3_msualg_1 A H D)) &  ( (I = J)  &  (~  ((k5_msualg_3 A B C H F I) = (k5_msualg_3 A D E H G J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 A B) => (r2_hidden (k6_xcmplx_0 B A) k5_numbers)) ) ) ) ) ).
tt(t5_int_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ( (A = k6_numbers)  &  (B = k6_numbers) )  <=>  ((k3_int_2 A B) = k6_numbers) ) ) ) ) ) ).
tt(t5_int_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  => (v1_int_3 A)) ) ).
tt(t5_int_4,ax, (! [A:$i] :  ((v3_membered A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  (B = k6_numbers) )  =>  ((k1_card_1 A) = (k1_card_1 (k1_integra2 A B))) ) ) ) ) ) ).
tt(t5_int_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  (~  ( ((k3_finseq_1 B) = (k1_nat_1 A 1))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  &  ( ((k3_finseq_1 D) = (k3_finseq_1 B))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 B)) =>  ((k1_funct_1 B E) = (k6_xcmplx_0 (k1_funct_1 C E) (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((m2_finseq_1 E k1_numbers) =>  (~  ( ((k3_finseq_1 E) = (k6_xcmplx_0 (k3_finseq_1 B) 1))  &  ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k6_xcmplx_0 (k1_funct_1 C F) (k1_funct_1 D (k1_nat_1 F 1)))) ) ) )  &  ((k18_rvsum_1 B) = (k6_xcmplx_0 (k2_xcmplx_0 (k18_rvsum_1 E) (k1_funct_1 C (k1_nat_1 A 1))) (k1_funct_1 D 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_int_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_valued_0 A)) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k1_nat_1 B 1) (k3_finseq_1 A)) =>  ((k7_finseq_1 (k16_finseq_1 B A) (k9_finseq_1 (k1_funct_1 A (k1_nat_1 B 1)))) = (k16_finseq_1 (k1_nat_1 B 1) A)) ) ) ) ) ) ).
tt(t5_int_7,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_int_1 A (k3_xcmplx_0 D (k1_newton B C))) =>  ( (A = B)  | (r1_int_1 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_integr10,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_tarski (k3_integra5 B C) (k1_relset_1 k1_numbers A)) & (r1_integr10 A B C))  =>  ((r1_xxreal_0 C B) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r1_integr10 (k26_valued_1 k1_numbers k1_numbers A D) B C) &  ((k1_integr10 (k26_valued_1 k1_numbers k1_numbers A D) B C) = (k8_real_1 D (k1_integr10 A B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integr11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ( (~  ((k7_real_1 A B) = k6_numbers) )  &  ( (~  ((k9_real_1 A B) = k6_numbers) )  &  (~  ((r2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) k1_numbers) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k1_seq_1 (k2_fdiff_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k7_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k7_real_1 A B)))) (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 (k9_real_1 A B) k6_numbers) k16_sin_cos) (k10_real_1 1 (k8_real_1 2 (k9_real_1 A B))))) k1_numbers) C) = (k8_real_1 (k1_seq_1 k19_sin_cos (k8_real_1 A C)) (k1_seq_1 k19_sin_cos (k8_real_1 B C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integr12,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( (C = (k1_relset_1 k1_numbers B))  & (r2_relset_1 k1_numbers k1_numbers B (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_rfunct_1 k1_numbers k1_numbers k16_sin_cos k19_sin_cos)) (k3_rfunct_1 k1_numbers k1_numbers k24_sin_cos (k41_valued_1 k1_numbers k1_numbers k19_sin_cos))))) )  =>  ((k2_integra5 A B) = (k10_binop_2 (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k29_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t5_integr13,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ( (B = (k1_relset_1 k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos)))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos) A))) )  =>  ((k2_integra5 A (k47_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos)) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t5_integr14,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1))) =>  ((r2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k32_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k2_fdiff_9 k3_taylor_1)) A) B) = (k1_seq_1 k30_sin_cos B)) ) ) ) ) ) ) ) ).
tt(t5_integr15,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_integra1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_integra1 A))))) )  =>  (! [D:$i] :  ((m2_integr15 D A B C) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((v2_seq_2 (k2_partfun1 A k1_numbers B A)) => (r1_xxreal_0 (k1_seq_1 (k4_integra2 A B C) E) (k1_seq_1 (k3_integr15 A B C D) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integr16,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k1_integr16 (k8_finseq_1 k2_numbers A (k12_finseq_1 k2_numbers B))) = (k8_finseq_1 k1_numbers (k1_integr16 A) (k12_finseq_1 k1_numbers (k3_complex1 B)))) ) ) ) ) ).
tt(t5_integr18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A))))) )  =>  ( ((r2_relset_1 B (u1_struct_0 A) D (k5_vfunct_1 B A C)) & (v1_integr18 C A B))  =>  ((v1_integr18 D A B) &  ((k4_integr18 A B D) = (k4_algstr_0 A (k4_integr18 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integr19,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  (! [G:$i] :  ( ((v1_funct_1 G) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ( ((r1_xxreal_0 B C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D E) &  ((r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers F)) & (r1_tarski (k3_integra5 B E) (k1_relset_1 k1_numbers G))) ) ) )  => (r1_tarski (k3_integra5 C D) (k1_relset_1 k1_numbers (k8_integr15 A k1_numbers F G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integra1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ( (A = (k1_rcomp_1 B D))  &  (A = (k1_rcomp_1 C E)) )  =>  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integra2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_seq_2 (k2_partfun1 A k1_numbers C A)) & (r1_tarski B A))  => (v1_seq_2 (k2_partfun1 A k1_numbers (k2_partfun1 A k1_numbers C B) B))) ) ) ) ) ) ) ).
tt(t5_integra3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_integra1 B A) =>  (! [C:$i] :  ((m1_integra1 C A) =>  ( (~ (r1_xxreal_0 (k2_xxreal_2 (k1_rvsum_1 (k4_integra1 A (k7_rfunct_1 A A) C))) (k1_integra3 A B)))  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( ((r2_hidden F (k4_finseq_1 B)) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_rvsum_1 C) (k2_integra1 A B F))) & (r2_hidden E (k9_subset_1 k1_numbers (k1_rvsum_1 C) (k2_integra1 A B F)))) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_integra4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  &  ( ((k1_rvsum_1 C) = (k1_seq_4 B))  & (v1_comseq_2 (k2_partfun1 A k1_numbers C A))) ) ) ) ) ) ) ).
tt(t5_integra5,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 C k1_numbers (k1_integra5 (k3_valued_1 k1_numbers k1_numbers k1_numbers A B) C) (k3_valued_1 C k1_numbers k1_numbers (k1_integra5 A C) (k1_integra5 B C)))) ) ) ) ) ) ).
tt(t5_integra6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k3_integra1 (k3_integra5 A B)) = (k6_xcmplx_0 B A)) ) ) ) ) ) ).
tt(t5_integra7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r2_fdiff_1 (k2_partfun1 k1_numbers k1_numbers B A) A) => (r2_fdiff_1 B A)) ) ) ) ).
tt(t5_integra8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 k6_numbers (k18_sin_cos (k10_real_1 A 2))) =>  ((k18_sin_cos (k10_real_1 A 2)) = (k7_square_1 (k10_real_1 (k9_real_1 1 (k21_sin_cos A)) 2))) ) ) ) ).
tt(t5_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( (~  (A = k6_numbers) )  =>  ((k2_integra5 B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k16_sin_cos)) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k1_real_1 (k10_real_1 1 A))) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_fcont_1 A k6_numbers) k19_sin_cos) (k1_real_1 (k10_real_1 1 A))) (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t5_interva1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ( (~  ((k1_interva1 A B C) = k1_xboole_0) )  => (r1_tarski B C)) ) ) ) ) ) ).
tt(t5_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 B (k3_intpro_1 C (k4_intpro_1 B C))) (k7_intpro_1 A))) ) ) ) ) ) ).
tt(t5_irrat_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k6_newton (k2_nat_1 B 1) A) = (k3_xcmplx_0 (k13_complex1 (k6_xcmplx_0 A B) (k2_nat_1 B 1)) (k6_newton B A))) ) ) ) ) ).
tt(t5_isocat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m2_cat_1 E A B) =>  (! [F:$i] :  ((m2_cat_1 F B C) =>  (! [G:$i] :  ((m2_cat_1 G B C) =>  ( ((r1_nattra_1 A B D E) & (r1_nattra_1 B C F G))  => (r1_nattra_1 A C (k9_cat_1 A B C D F) (k9_cat_1 A B C E G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_isocat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k1_cat_1 A B (k4_cat_1 A (k4_graph_1 A B))) = B) ) ) ) ) ).
tt(t5_isomichi,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) <=>  ((v2_isomichi B A) & (v1_isomichi B A)) ) ) ) ) ) ).
tt(t5_jct_misc,ax, (! [A:$i] :  ( ((v1_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  => (v1_rcomp_1 (k9_subset_1 k1_numbers A B))) ) ) ) ).
tt(t5_jgraph_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 (k3_jgraph_1 A C))))  => (r2_hidden (k1_funct_1 (k3_jgraph_1 A C) B) (u4_struct_0 (k1_jgraph_1 A)))) ) ) ) ) ) ) ).
tt(t5_jgraph_2,ax, ( ((k17_euclid (k22_euclid 2)) = 1)  &  ((k18_euclid (k22_euclid 2)) = 1) ) ).
tt(t5_jgraph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ((v5_pre_topc B A k3_topmetr) &  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((v1_xreal_0 D) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B C) = D)  & (r1_xxreal_0 k6_numbers D)) ) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B D) = E)  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C D) = (k6_square_1 E)) ) ) ) ) )  & (v5_pre_topc C A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jgraph_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((v5_pre_topc B A k3_topmetr) &  ((v5_pre_topc C A k3_topmetr) &  ( (~  (E = k6_numbers) )  &  ( (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C F) = k6_numbers) ) ) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 k3_topmetr)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) )  =>  (~  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) B G) = H)  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) C G) = I) )  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 k3_topmetr) F G) = (k8_real_1 I (k13_complex1 (k5_real_1 (k13_complex1 H I) D) E))) ) ) ) ) ) ) )  & (v5_pre_topc F A k3_topmetr)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jgraph_5,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  ( ((v3_tops_2 E B C) & (v5_pre_topc D A B))  => (v5_pre_topc (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jgraph_6,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_pre_topc B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_pre_topc C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((k1_relset_1 (u1_struct_0 A) D) = (k1_relset_1 (u1_struct_0 A) E))  &  ( ((k1_relset_1 (u1_struct_0 A) D) = (u1_struct_0 A))  &  ((k1_relset_1 (u1_struct_0 A) D) = (k2_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 C (k18_euclid A)) &  ((r1_xxreal_0 (k18_euclid A) D) &  ((r1_xxreal_0 C (k18_euclid B)) & (r1_xxreal_0 (k18_euclid B) D)) ) )  =>  ((r1_xxreal_0 (k17_euclid B) (k17_euclid A)) |  ((r1_xxreal_0 D C) | (r1_jordan6 (k1_sppol_2 (k17_euclid A) (k17_euclid B) C D) A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jgraph_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2))) &  ((v5_pre_topc E k17_borsuk_1 (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2))) &  ((v5_pre_topc F k17_borsuk_1 (k15_euclid 2)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)))))) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k17_borsuk_1)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k17_borsuk_1)) =>  (~  ( (G = k6_numbers)  &  ( (H = 1)  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E G)) = A)  &  ( ((k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E H)) = B)  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F G)) = C)  &  ( ((k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F H)) = D)  &  ( (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 k17_borsuk_1)) =>  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E I))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E I)) B) &  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F I))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F I)) B) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E I))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) E I)) D) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F I))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k17_borsuk_1) (u1_struct_0 (k15_euclid 2)) F I)) D)) ) ) ) ) ) ) ) )  & (r2_subset_1 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) E) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan10,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_subset_1 B (k3_topreal1 2 (k1_jordan9 B A)))) ) ) ) ).
tt(t5_jordan11,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_jordan1h B A) => (r1_xxreal_0 (k3_jordan11 B A) (k2_nat_1 (k4_nat_1 (k13_newton 2 (k7_nat_d A (k1_jordan11 B))) (k7_nat_d (k2_jordan11 B) 2)) 2))) ) ) ) ) ).
tt(t5_jordan12,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k15_euclid 2))) => (r1_tarski (k3_topreal1 2 A) (k3_topreal1 2 (k4_graph_2 (u1_struct_0 (k15_euclid 2)) A B)))) ) ) ) ).
tt(t5_jordan14,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  => (v2_connsp_1 (k1_jordan2c 2 (k3_topreal1 2 A)) (k15_euclid 2))) ) ).
tt(t5_jordan15,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C E) &  ((r1_xxreal_0 E F) &  ((r1_xxreal_0 F D) & (r1_xxreal_0 D (k1_matrix_1 A))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B E) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B F)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan16,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan5c A D E B C) =>  ((r2_hidden B (k5_jordan6 A D E B C)) & (r2_hidden C (k5_jordan6 A D E B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan17,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r1_jordan6 A B (k18_pscomp_1 A)) => (r2_hidden B (k9_jordan6 A))) ) ) ) ) ).
tt(t5_jordan18,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) => (v4_xxreal_2 (k7_relset_1 (u1_struct_0 (k15_euclid 2)) k1_numbers k4_pscomp_1 (k7_topreal1 A)))) ) ).
tt(t5_jordan19,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) & (r2_subset_1 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) (k1_jordan1a (k1_jordan8 B 1)) (k1_matrix_1 (k1_jordan8 B 1))) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1)))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan1a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k17_pscomp_1 A)) =>  ((k18_euclid B) = (k9_pscomp_1 A)) ) ) ) ) ) ).
tt(t5_jordan1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v2_connsp_1 B A) &  ((v2_connsp_1 C A) &  ((v2_connsp_1 D A) & (v2_connsp_1 E A)) ) )  =>  ((r1_xboole_0 B C) |  ((r1_xboole_0 C D) |  ((r1_xboole_0 D E) | (v2_connsp_1 (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) B C) D) E) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan1b,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((k19_pscomp_1 A) = (k22_pscomp_1 A)) ) ) ) ).
tt(t5_jordan1c,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((r2_hidden A B) & (v9_rltopsp1 B (k15_euclid 2)))  =>  ((r1_xxreal_0 (k6_pscomp_1 B) (k17_euclid A)) &  ((r1_xxreal_0 (k17_euclid A) (k8_pscomp_1 B)) &  ((r1_xxreal_0 (k9_pscomp_1 B) (k18_euclid A)) & (r1_xxreal_0 (k18_euclid A) (k7_pscomp_1 B))) ) ) ) ) ) ) ) ).
tt(t5_jordan1d,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ( ((r1_xxreal_0 2 A) & (r1_xxreal_0 2 C))  =>  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 D B)) (k2_nat_1 A 1)) |  ((r1_xxreal_0 (k3_finseq_1 (k1_jordan8 D B)) (k2_nat_1 C 1)) |  ((k3_goboard5 (k1_jordan8 D B) A C) = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_goboard5 (k1_jordan8 D (k2_nat_1 B 1)) (k7_nat_d (k4_nat_1 2 A) 2) (k7_nat_d (k4_nat_1 2 C) 2)) (k3_goboard5 (k1_jordan8 D (k2_nat_1 B 1)) (k7_nat_d (k4_nat_1 2 A) 1) (k7_nat_d (k4_nat_1 2 C) 2))) (k3_goboard5 (k1_jordan8 D (k2_nat_1 B 1)) (k7_nat_d (k4_nat_1 2 A) 2) (k7_nat_d (k4_nat_1 2 C) 1))) (k3_goboard5 (k1_jordan8 D (k2_nat_1 B 1)) (k7_nat_d (k4_nat_1 2 A) 1) (k7_nat_d (k4_nat_1 2 C) 1)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan1e,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  ((v4_topreal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r2_hidden B (k3_topreal1 2 A)) & (r2_hidden (k1_funct_1 A 1) (k3_topreal1 2 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A (k2_nat_1 (k1_jordan3 A B) 1) (k3_finseq_1 A))))) ) ) ) ) ) ) ).
tt(t5_jordan1f,ax, (! [A:$i] :  ( ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan1e A B) 1) = (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 A B)))) ) ) ) ) ).
tt(t5_jordan1g,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  => (r1_goboard1 (u1_struct_0 (k15_euclid 2)) (k2_jordan1e B A) (k1_jordan8 B A))) ) ) ) ).
tt(t5_jordan1h,ax, ((k1_relat_1 k1_jordan1h) = k1_numbers) ).
tt(t5_jordan1i,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k2_relset_1 (u1_struct_0 (k15_euclid 2)) A)) =>  ((k4_goboard5 A (k4_finseq_4 A B)) = (k4_goboard5 (k1_finseq_6 (u1_struct_0 (k15_euclid 2)) A B) 1)) ) ) ) ) ) ).
tt(t5_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) )  =>  ((r2_hidden (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k10_xtuple_0 (k1_jordan1e B A))) & (r2_hidden (k18_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) (k3_topreal1 2 (k1_jordan1e B A)))) ) ) ) ) ).
tt(t5_jordan1k,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ((v3_funct_2 C A B) =>  ((k3_subset_1 B (k7_relset_1 A B C D)) = (k7_relset_1 A B C (k3_subset_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t5_jordan20,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ( (~ (r1_xxreal_0 (k17_euclid A) D))  &  ( (~ (r1_xxreal_0 (k17_euclid B) D))  & (r1_xxreal_0 (k17_euclid C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan21,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (C = (a_2_3_jordan21 A B))  => (v1_convex1 C (k15_euclid 2))) ) ) ) ) ) ) ).
tt(t5_jordan22,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) => (r2_hidden (k1_domain_1 k5_numbers k5_numbers 1 1) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ).
tt(t5_jordan23,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((v2_jordan23 B) <=>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 B) C))  &  ((k7_partfun1 A B C) = (k7_partfun1 A B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan24,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k2_complex2 A (k1_real_1 B)) = (k2_complex2 A (k9_real_1 (k8_real_1 2 k32_sin_cos) B))) ) ) ) ) ).
tt(t5_jordan2b,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r2_hidden D (k2_finseq_1 A)) =>  ((k7_partfun1 k1_numbers (k3_rlvect_1 (k15_euclid A) B C) D) = (k7_real_1 (k7_partfun1 k1_numbers B D) (k7_partfun1 k1_numbers C D))) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan3,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 2 (k7_nat_d (k3_finseq_1 A) B)) & (v4_topreal1 A)) )  => (v4_topreal1 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ) ).
tt(t5_jordan4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( ((v1_finseq_6 B A) & (r1_xxreal_0 1 (k3_finseq_1 B)))  =>  ((k1_funct_1 B 1) = (k1_funct_1 B (k3_finseq_1 B))) ) ) ) ) ) ).
tt(t5_jordan5a,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  ((r2_hidden A (k2_pcomps_1 k8_metric_1)) <=> (v3_rcomp_1 A)) ) ) ).
tt(t5_jordan5b,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C (k1_rltopsp1 (k15_euclid 2) A B)) &  ((k18_euclid C) = (k18_euclid A)) )  =>  ( ((k18_euclid A) = (k18_euclid B))  |  (C = A) ) ) ) ) ) ) ) ) ).
tt(t5_jordan5c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden C A) &  ((r1_topreal1 (k15_euclid 2) D E A) &  (B = (k1_tarski C)) ) )  =>  ((k2_jordan5c A B D E) = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_jordan5d,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B (k3_finseq_1 A)) &  ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k1_matrix_1 (k2_goboard2 A)))) ) )  =>  ((r1_xxreal_0 (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) 1 C)) (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B))) & (r1_xxreal_0 (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B)) (k17_euclid (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 A) (k3_finseq_1 (k2_goboard2 A)) C)))) ) ) ) ) ) ) ) ).
tt(t5_jordan6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( (B = (a_1_1_jordan6 A))  => (v4_pre_topc B (k15_euclid 2))) ) ) ) ) ).
tt(t5_jordan7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_topreal2 A) & (r1_jordan6 A B C))  =>  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) ) ) ) ).
tt(t5_jordan8,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_finseq_1 B (u1_struct_0 (k15_euclid 2))))  =>  (~  ((r1_xxreal_0 2 (k3_finseq_1 B)) &  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) B A) & (v3_funct_1 B)) ) ) ) ) ) ) ).
tt(t5_jordan9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r1_goboard1 A C B) <=> (r1_goboard1 A (k4_finseq_5 A C) B)) ) ) ) ) ) ) ).
tt(t5_jordan_a,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden B (k9_jordan6 A)) =>  ( (B = (k18_pscomp_1 A))  | (r1_jordan6 A (k22_pscomp_1 A) B)) ) ) ) ) ) ).
tt(t5_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ( ((v1_sppol_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (v1_sppol_1 (k9_subset_1 (u1_struct_0 (k15_euclid 2)) B A))) ) ) ) ).
tt(t5_knaster,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k9_setfam_1 A) (k9_setfam_1 A)) &  ((v6_cohsp_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A))))) ) )  => (r2_abian (k9_setfam_1 A) (k2_knaster A B) B)) ) ) ).
tt(t5_kolmog01,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 B)))  => (m1_dynkin (k1_kolmog01 A B D C) A)) ) ) ) ) ) ) ) ).
tt(t5_kurato_0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ((r2_hidden C (k4_kurato_0 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) & (r2_hidden C (k3_funct_2 k5_numbers (k9_setfam_1 A) B (k2_nat_1 D E)))) ) ) ) ) ) ) ) ) ).
tt(t5_kurato_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_kurato_1 A B) = (k2_xboole_0 (k2_xboole_0 (k2_tarski B (k3_subset_1 (u1_struct_0 A) B)) (k3_kurato_1 A B)) (k4_kurato_1 A B))) ) ) ) ) ).
tt(t5_kurato_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_frechet A) <=> (v1_frechet (g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)))) ) ) ).
tt(t5_lang1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_lang1 A))  =>  (! [B:$i] :  ((m2_finseq_2 B (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 A) (k3_finseq_2 (u1_struct_0 A))) =>  ((r2_lang1 A C D) =>  ((r2_lang1 A (k1_pre_poly (u1_struct_0 A) B C) (k1_pre_poly (u1_struct_0 A) B D)) & (r2_lang1 A (k1_pre_poly (u1_struct_0 A) C B) (k1_pre_poly (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_laplace,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B B) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden A (k2_finseq_1 (k1_matrix_1 D))) =>  ((k1_matrix_1 (k9_matrix_2 E A B C D)) = (k7_nat_d B 1)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_latsubgr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_struct_0 B D) | (r1_struct_0 C D))  => (r1_struct_0 (k8_group_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t5_latsum_1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden (k4_tarski C D) (u1_orders_2 (k1_latsum_1 A B))) &  ((r2_hidden C (u1_struct_0 B)) &  ((r2_hidden D (u1_struct_0 B)) &  ((r1_latsum_1 A B) & (v4_orders_2 B)) ) ) )  => (r2_hidden (k4_tarski C D) (u1_orders_2 B))) ) ) ) ) ) ) ).
tt(t5_lattice2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski B A) =>  ((k1_funct_4 A B) = A) ) ) ) ) ) ).
tt(t5_lattice3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k1_lattice3 A))) =>  ((k7_lattices (k1_lattice3 A) B) = (k6_subset_1 A B)) ) ) ) ).
tt(t5_lattice4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_lattice4 E A B) =>  ((v2_funct_1 E) =>  ((r3_lattices A C D) <=> (r3_lattices B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lattice5,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_msualg_5 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k2_msualg_5 A))) =>  ((r3_lattices (k2_msualg_5 A) B C) <=> (r1_tarski B C)) ) ) ) ) ) ).
tt(t5_lattice6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~ (r1_lattice6 A B (k6_lattices A))) ) ) ) ) ).
tt(t5_lattice7,ax, (! [A:$i] :  ( ((v8_struct_0 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_orders_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_hidden C B) & (r2_hidden D B))  =>  ((r3_orders_2 A C D) <=> (r1_xxreal_0 (k1_lattice7 A C) (k1_lattice7 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t5_lattice8,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ( ((r5_waybel_1 A B) & (v1_yellow11 A))  => (v1_yellow11 B)) ) ) ) ) ).
tt(t5_lattices,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_lattices A) &  ((v6_lattices A) &  ((v8_lattices A) &  ((v9_lattices A) & (l3_lattices A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_lattices A B (k1_lattices A B C))) ) ) ) ) ) ).
tt(t5_lexbfs,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k1_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 B) (k2_finseq_1 (k7_nat_d B A))) (k6_domain_1 k5_numbers (k7_nat_d B A))) = (k2_finsub_1 (k1_zfmisc_1 k5_numbers) (k2_finseq_1 B) (k2_finseq_1 (k7_nat_d B (k1_nat_1 A 1))))) ) ) ) ) ) ).
tt(t5_lfuzzy_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_lfuzzy_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A B C) = (k3_lfuzzy_0 A B C)) ) ) ) ) ) ) ).
tt(t5_lfuzzy_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v5_relat_1 B (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D (k1_rcomp_1 k6_numbers 1)) &  ((v1_funct_1 D) &  ((v1_funct_2 D A k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) ) )  =>  ( ((r1_fuzzy_1 B C) & (r1_fuzzy_1 C D))  => (r1_fuzzy_1 B D)) ) ) ) ) ) ) ) ) ).
tt(t5_l_hospit,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (? [D:$i] :  ((m1_rcomp_1 D C) &  ((r1_tarski D (k1_relset_1 k1_numbers A)) &  ((r1_tarski D (k1_relset_1 k1_numbers B)) &  ((r2_fdiff_1 A D) &  ((r2_fdiff_1 B D) &  ((r1_tarski (k7_subset_1 k1_numbers D (k1_tarski C)) (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers A B))) &  ((r1_tarski D (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D)))) &  ( ((k1_seq_1 A C) = k6_numbers)  &  ( ((k1_seq_1 B C) = k6_numbers)  & (r2_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D)) C)) ) ) ) ) ) ) ) ) )  => (r2_limfunc3 (k3_rfunct_1 k1_numbers k1_numbers A B) C)) ) ) ) ) ) ) ).
tt(t5_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((v2_comseq_2 A) &  ( (~ (r1_xxreal_0 (k2_seq_2 A) k6_numbers))  &  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (? [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) &  ((r1_xxreal_0 B C) & (r1_xxreal_0 (k1_seq_1 A C) (k10_real_1 (k2_seq_2 A) 2))) ) ) ) ) ) ) ) ) ) ).
tt(t5_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 (k1_seq_1 B D) (k9_real_1 A (k10_real_1 1 (k2_nat_1 D 1)))))  &  ( (~ (r1_xxreal_0 A (k1_seq_1 B D)))  & (r2_hidden (k1_seq_1 B D) (k1_relset_1 k1_numbers C))) ) ) )  =>  ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  &  ((r1_tarski (k2_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)) & (r1_tarski (k2_relset_1 k1_numbers B) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k10_prob_1 A)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_limfunc3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_tarski (k4_subset_1 k1_numbers (k2_rcomp_1 (k9_real_1 B A) B) (k2_rcomp_1 B (k7_real_1 B A))) (k9_xtuple_0 C)) =>  ((r1_xxreal_0 A k6_numbers) |  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B D))  &  ( (~ (r1_xxreal_0 E B))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F D))  &  ( (~ (r1_xxreal_0 B F))  &  ((r2_hidden F (k9_xtuple_0 C)) &  ( (~ (r1_xxreal_0 E G))  &  ( (~ (r1_xxreal_0 G B))  & (r2_hidden G (k9_xtuple_0 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v5_limfunc1 A) &  ((v7_limfunc1 B) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  => (v4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t5_lmod_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k4_struct_0 A) = (k5_struct_0 A)) )  =>  ( (~ (v1_lmod_5 (k7_domain_1 (u1_struct_0 B) C (k4_struct_0 B)) A B))  &  (~ (v1_lmod_5 (k7_domain_1 (u1_struct_0 B) (k4_struct_0 B) C) A B)) ) ) ) ) ) ) ) ) ).
tt(t5_lmod_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ((v7_struct_0 A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (C = (k4_struct_0 A)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (C = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t5_lmod_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_lmod_5 (k4_subset_1 (u1_struct_0 B) C D) A B) & (r1_xboole_0 C D))  =>  ((k2_vectsp_5 A B (k1_mod_3 A B C) (k1_mod_3 A B D)) = (k1_vectsp_4 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t5_lopban_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_funct_2 C A (u1_struct_0 B) (k9_funct_2 A (u1_struct_0 B))) => (r2_funct_2 A (u1_struct_0 B) (k1_funcsdom A (u1_struct_0 B) (k2_lopban_1 A B) (k4_lopban_1 A B) C) C)) ) ) ) ) ) ).
tt(t5_lopban_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 B A A) &  ((v1_lopban_1 B A A) &  ((v2_lopban_1 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 C A A) &  ((v1_lopban_1 C A A) &  ((v2_lopban_1 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 A)) &  ((v13_vectsp_1 D A A) &  ((v1_lopban_1 D A A) &  ((v2_lopban_1 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k1_lopban_2 A (k1_lopban_2 A D C) B) (k1_lopban_2 A D (k1_lopban_2 A C B)))) ) ) ) ) ) ) ) ).
tt(t5_lopban_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_rsspace3 B A) <=>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 D E) & (r1_xxreal_0 C (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lopban_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v2_funcsdom A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_vectsp_1 A) &  ((v5_lopban_2 A) & (l1_lopban_2 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v3_normsp_1 C A) => (v3_normsp_1 (k3_lopban_3 A C B) A)) ) ) ) ) ) ) ).
tt(t5_lopban_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) &  ((v3_lopban_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k16_lopban_1 A B)))) =>  (~  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((v1_xreal_0 E) &  ((r1_xxreal_0 k6_numbers E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k16_lopban_1 A B))) =>  ((r2_hidden F C) => (r1_xxreal_0 (k1_normsp_0 B (k17_lopban_1 A B F D)) E)) ) ) ) ) ) ) )  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r1_xxreal_0 k6_numbers D) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k16_lopban_1 A B))) =>  ((r2_hidden E C) => (r1_xxreal_0 (k1_normsp_0 (k16_lopban_1 A B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lopban_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 C A B) &  ((v1_lopban_1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k1_convex1 A D E)) = (k1_convex1 B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lopclset,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)))) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)) (k1_lopclset A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k2_lattices (g3_lattices (k1_lopclset A) (k4_lopclset A) (k5_lopclset A)) B C) = (k3_lopclset A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lpspace1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v1_lpspace1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)))) =>  ( (E = D)  =>  ((k1_rlvect_1 (g1_rlvect_1 B (k1_funct_7 (k4_struct_0 A) B) (k1_ideal_1 A B) (k1_lpspace1 A B)) E C) = (k1_rlvect_1 A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_lpspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  =>  ((r1_xxreal_0 C k6_numbers) |  ((k4_power (k8_real_1 A B) C) = (k8_real_1 (k4_power A C) (k4_power B C))) ) ) ) ) ) ) ) ) ).
tt(t5_lp_space,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r1_xxreal_0 1 A) => (m1_rlsub_1 (g1_rlvect_1 (k2_lp_space A) (k10_rsspace k7_rsspace (k2_lp_space A)) (k8_rsspace k7_rsspace (k2_lp_space A)) (k9_rsspace k7_rsspace (k2_lp_space A))) k7_rsspace)) ) ) ).
tt(t5_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k1_zfmisc_1 k10_ltlaxio1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k1_zfmisc_1 k10_ltlaxio1))))) )  =>  ( ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B (k1_ltlaxio1 A))) = 1)  <=>  ((k3_funct_2 (k2_zfmisc_1 k5_numbers k1_hilbert1) k6_margrel1 (k11_ltlaxio1 C) (k1_domain_1 k5_numbers k1_hilbert1 B A)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t5_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A B (k8_cqc_lang A C B)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t5_margrel1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (m1_margrel1 k1_xboole_0 A)) ) ).
tt(t5_mathmorp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_mathmorp A B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = B) ) ) ) ) ).
tt(t5_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  ((k2_matrix_1 B) = (k2_matrix_1 (k1_matrix10 B))) ) ) ) ) ).
tt(t5_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_2 C (k12_matrix_2 (k1_nat_1 A 2))) =>  (! [D:$i] :  ((m1_subset_1 D (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2)))) =>  ( ((k3_funct_2 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B) (k1_matrix11 A B C) D) = (k1_group_1 B))  |  ((k3_funct_2 (k2_sgraph1 (k2_finseq_1 (k1_nat_1 A 2))) (u1_struct_0 B) (k1_matrix11 A B C) D) = (k4_algstr_0 B (k1_group_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix12,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ( (~ (v6_struct_0 F))  &  ((v13_algstr_0 F) &  ((v33_algstr_0 F) &  ((v3_group_1 F) &  ((v5_group_1 F) &  ((v2_rlvect_1 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) &  ((v4_vectsp_1 F) &  ((v5_vectsp_1 F) & (l6_algstr_0 F)) ) ) ) ) ) ) ) ) ) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 F)) =>  (! [H:$i] :  ((m1_matrix_1 H (u1_struct_0 F) A B) =>  (! [I:$i] :  ((m1_matrix_1 I (u1_struct_0 F) A B) =>  ( ((r2_hidden C (k4_finseq_1 H)) &  ((r2_hidden D (k4_finseq_1 H)) &  ((r2_hidden E (k4_finseq_1 H)) &  (I = (k3_matrix12 A B F H C D G)) ) ) )  =>  ( ( (E = C)  =>  ((k8_matrix_1 (u1_struct_0 F) I E) = (k4_fvsum_1 (k1_matrix_1 H) F (k10_fvsum_1 (k1_matrix_1 H) F (k8_matrix_1 (u1_struct_0 F) H D) G) (k8_matrix_1 (u1_struct_0 F) H C))) )  &  ( (~  (E = C) )  =>  ((k8_matrix_1 (u1_struct_0 F) I E) = (k8_matrix_1 (u1_struct_0 F) H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_2 D (k12_matrix_2 A)) =>  (~  ( (~  (D = (k1_finseq_2 A)) )  &  ( ( ((v2_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A))  |  ((v1_matrix_2 C A B) & (m1_matrix_1 C (u1_struct_0 B) A A)) )  &  (~  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) (k11_matrix_3 A B C) D) = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B))) )  =>  ( ((k1_funct_1 (k3_fvsum_1 A B C) D) = (k1_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) C D)))  &  ((k1_funct_1 (k7_fvsum_1 A B C) D) = (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B D) (k7_partfun1 (u1_struct_0 A) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix15,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( ((r1_tarski (k10_xtuple_0 B) (k9_xtuple_0 A)) &  ((r1_tarski (k10_xtuple_0 C) (k9_xtuple_0 A)) &  ( (D = (k3_relat_1 B A))  &  (E = (k3_relat_1 C A)) ) ) )  =>  ((k3_relat_1 (k7_finseq_1 B C) A) = (k7_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix16,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ((m1_matrix_1 G F C C) =>  ( ((v1_matrix16 G F) &  ((r2_hidden (k4_tarski A B) (k2_zfmisc_1 (k2_finseq_1 C) (k2_finseq_1 C))) &  ( (D = (k2_xcmplx_0 A 1))  &  (E = (k2_xcmplx_0 B 1)) ) ) )  =>  ((r1_xxreal_0 C A) |  ((r1_xxreal_0 C B) |  ((k3_matrix_1 F G A B) = (k3_matrix_1 F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix17,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 B) A A) =>  ( ((r1_matrix17 (u1_struct_0 B) E C) & (r1_matrix17 (u1_struct_0 B) F D))  => (r1_matrix17 (u1_struct_0 B) (k2_matrix_6 A B E F) (k3_fvsum_1 B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix_1,ax,(v1_matrix_1 k1_xboole_0)).
tt(t5_matrix_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((r2_hidden (k4_tarski 1 1) (k2_matrix_1 (k5_matrix_2 A 1 (k4_matrix_2 A B)))) &  ((k3_matrix_1 A (k5_matrix_2 A 1 (k4_matrix_2 A B)) 1 1) = B) ) ) ) ) ) ).
tt(t5_matrix_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  ((k3_matrix_3 C D (k2_matrix_3 C D)) = (k1_matrix_3 C A B)) ) ) ) ) ) ) ) ) ).
tt(t5_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  ((k1_matrix_4 A B (k2_matrix_3 A C)) = (k3_matrix_3 A B C)) ) ) ) ) ) ) ).
tt(t5_matrix_5,ax, (! [A:$i] :  ( ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k2_numbers)))  =>  (A = (k2_matrix_5 (k1_matrix_5 A))) ) ) ).
tt(t5_matrix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ( ((r1_matrix_6 A B C D) & (r1_matrix_6 A B C E))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_matrix_6 A B C (k2_matrix_6 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matrix_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 1 C) =>  ((r1_xxreal_0 (k3_finseq_1 B) C) |  (B = (k8_finseq_1 A (k3_finseq_6 A B 1 C) (k3_finseq_6 A B (k2_nat_1 C 1) (k3_finseq_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t5_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( ((v1_matrix_8 C A B) &  ((v1_matrix_8 D A B) & (r1_matrix_6 A B C D)) )  => (r1_matrix_6 A B (k4_matrix_6 A B C C) (k4_matrix_6 A B D D))) ) ) ) ) ) ) ) ) ).
tt(t5_matrix_9,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden B (k12_matrix_2 A)) =>  ( (A = k6_numbers)  | (r2_hidden (k3_finseq_5 B) (k12_matrix_2 A))) ) ) ) ) ) ).
tt(t5_matrixc1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k2_numbers)))  =>  ((k1_matrixc1 (k7_matrix_5 A B)) = (k7_matrix_5 (k15_complex1 A) (k1_matrixc1 B))) ) ) ) ) ).
tt(t5_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k3_group_4 B (k5_finseq_2 (u1_struct_0 B) A C)) = (k1_laplace B (k4_group_1 B) C A)) ) ) ) ) ) ) ).
tt(t5_matrixj2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k8_matrix_1 (u1_struct_0 B) (k2_matrixj2 B C A) A) = (k10_fvsum_1 (k1_matrix_1 (k12_matrix_1 B A)) B (k8_matrix_1 (u1_struct_0 B) (k12_matrix_1 B A) A) C)) ) ) ) ) ) ) ).
tt(t5_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ((k8_rvsum_1 A (k5_euclid (k3_finseq_1 A))) = A) ) ) ).
tt(t5_matrixr2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 (k7_matrixr1 A B)) = (k3_finseq_1 B))  &  ((k1_matrix_1 (k7_matrixr1 A B)) = (k1_matrix_1 B)) ) ) ) ) ) ).
tt(t5_matrlin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))))  =>  ( ((k1_vectsp_9 A (k1_vectsp_7 A B C)) = (k5_card_1 C))  => (v1_vectsp_7 C A B)) ) ) ) ) ) ) ).
tt(t5_matrlin,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_vectsp_6 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v1_vectsp_7 E A B) &  ((r1_tarski (k1_vectsp_6 A B C) E) &  ((r1_tarski (k1_vectsp_6 A B D) E) &  ((k4_vectsp_6 A B C) = (k4_vectsp_6 A B D)) ) ) )  => (r1_vectsp_6 A B C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_matroid0,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (~  ( (~ (r1_xxreal_0 (k5_card_1 B) (k5_card_1 A)))  &  (! [C:$i] :  (~ (r2_hidden C (k6_subset_1 B A))) ) ) ) ) ) ) ) ).
tt(t5_matrprob,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 A B))) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k4_finseq_1 A)) => (r1_xxreal_0 (k1_seq_1 A B) (k18_rvsum_1 A))) ) ) ) ) ) ).
tt(t5_matrtop1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((v4_partfun3 A) => (r1_xxreal_0 (k6_square_1 (k16_rvsum_1 A)) (k16_rvsum_1 (k1_partfun3 A)))) ) ) ).
tt(t5_matrtop2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_vectsp_6 B k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A)) =>  (! [C:$i] :  ((m1_rlvect_2 C (k15_euclid A)) =>  ((r1_funct_2 (u1_struct_0 (k15_euclid A)) k1_numbers (u1_struct_0 (k6_prvect_1 k2_vectsp_1 A)) (u1_struct_0 k2_vectsp_1) C B) =>  ((k6_rlvect_2 (k15_euclid A) C) = (k4_vectsp_6 k2_vectsp_1 (k6_prvect_1 k2_vectsp_1 A) B)) ) ) ) ) ) ) ) ).
tt(t5_matrtop3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  ( ((r2_hidden A (k2_finseq_1 B)) & (r2_hidden C (k2_finseq_1 B)))  =>  ( (A = C)  |  ((k13_fvsum_1 k2_vectsp_1 (k1_matrtop1 D) (k9_matrix_1 (u1_struct_0 k2_vectsp_1) (k1_matrtop3 B A) C)) = (k1_seq_1 D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mazurulm,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k1_numbers (k3_valued_1 k5_numbers k1_numbers (k1_tarski A) B (k7_funcop_1 k5_numbers A)) (k9_valued_1 k5_numbers k1_numbers B A))) ) ) ) ).
tt(t5_mboolean,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r2_pboole A (k1_pboole A) B)) ) ) ).
tt(t5_measure1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (B = (k7_setfam_1 A B)) ) ) ) ).
tt(t5_measure2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B D k6_numbers) = (k8_nat_1 B C k6_numbers))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((k8_nat_1 B D (k2_nat_1 E 1)) = (k2_xboole_0 (k8_nat_1 B C (k2_nat_1 E 1)) (k8_nat_1 B D E))) ) ) )  =>  (! [E:$i] :  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden E (k8_nat_1 B D F)) <=>  (? [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) &  ((r1_xxreal_0 G F) & (r2_hidden E (k8_nat_1 B C G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_measure3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  ( ( ((k8_nat_1 B C k6_numbers) = k1_xboole_0)  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((k8_nat_1 B C (k2_nat_1 E 1)) = (k3_measure1 A B (k8_nat_1 B D k6_numbers) (k8_nat_1 B D E)))  & (r1_tarski (k8_nat_1 B D (k2_nat_1 E 1)) (k8_nat_1 B D E))) ) ) )  =>  ((k1_measure2 A B (k1_measure3 A B D)) = (k3_measure1 A B (k8_nat_1 B D k6_numbers) (k2_measure2 A B (k1_measure3 A B C)))) ) ) ) ) ) ) ) ) ).
tt(t5_measure4,ax, (! [A:$i] :  (! [B:$i] :  ((m1_measure4 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C (k1_measure4 A B)) <=>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 A)) =>  ( ((r1_tarski D C) & (r1_tarski E (k6_subset_1 A C)))  =>  ((k3_supinf_2 (k12_supinf_2 B D) (k12_supinf_2 B E)) = (k12_supinf_2 B (k4_subset_1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_measure5,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( ( (~ (r1_xxreal_0 B A))  =>  ((k2_measure5 (k1_measure5 A B)) = (k4_supinf_2 B A)) )  &  ((r1_xxreal_0 B A) =>  ((k2_measure5 (k1_measure5 A B)) = k1_supinf_2) ) ) ) ) ) ) ).
tt(t5_measure6,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 k7_numbers)))  =>  (~  ( (~ (r1_xxreal_0 A k1_supinf_2))  &  ((m1_subset_1 (k7_supinf_2 B) k1_numbers) &  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden C B) &  (~ (r1_xxreal_0 (k3_supinf_2 (k7_supinf_2 B) A) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_measure7,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 A C) (k12_supinf_2 B C))) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k12_supinf_2 (k18_supinf_2 A) C) (k19_supinf_2 B))) ) ) ) ) ) ) ).
tt(t5_measure8,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v2_finsub_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v2_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m4_measure8 F A B D) => (r1_xxreal_0 k6_numbers (k1_mesfunc9 (k4_measure8 A B D C F) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k4_member_1 (k2_xboole_0 A B)) = (k2_xboole_0 (k4_member_1 A) (k4_member_1 B))) ) ) ) ) ).
tt(t5_membered,ax, (! [A:$i] :  ((v5_membered A) => (r1_tarski A k4_numbers)) ) ).
tt(t5_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 A B)) & (v4_memstr_0 C A B)) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  ((r1_tarski C D) <=> (r1_tarski C (k6_memstr_0 A B D))) ) ) ) ) ) ) ) ) ).
tt(t5_menelaus,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((k17_euclid (k1_rlvect_1 (k15_euclid 2) A (k7_binop_2 B))) = (k7_binop_2 (k11_binop_2 B (k17_euclid A))))  &  ((k18_euclid (k1_rlvect_1 (k15_euclid 2) A (k7_binop_2 B))) = (k7_binop_2 (k11_binop_2 B (k18_euclid A)))) ) ) ) ) ) ).
tt(t5_mesfun10,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k12_supinf_2 A C) B)) )  => (r1_xxreal_0 (k1_rinfsup2 A) B)) ) ) ) ) ).
tt(t5_mesfun6c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((r2_relset_1 A k1_numbers (k5_comseq_3 A (k2_valued_1 A k2_numbers k2_numbers B C)) (k3_valued_1 A k1_numbers k1_numbers (k5_comseq_3 A B) (k5_comseq_3 A C))) & (r2_relset_1 A k1_numbers (k6_comseq_3 A (k2_valued_1 A k2_numbers k2_numbers B C)) (k3_valued_1 A k1_numbers k1_numbers (k6_comseq_3 A B) (k6_comseq_3 A C)))) ) ) ) ) ) ) ).
tt(t5_mesfun7c,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k1_relset_1 A (k4_mesfunc5 A k7_numbers (k5_mesfun7c A B) C)) = (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers)))  &  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden D (k1_relset_1 A (k4_mesfunc5 A k7_numbers (k5_mesfun7c A B) C))) =>  ((k12_supinf_2 (k4_mesfunc5 A k7_numbers (k5_mesfun7c A B) C) D) = (k12_supinf_2 (k4_rinfsup2 (k1_mesfunc5 k5_numbers (k10_seqfunc A B D))) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfun9c,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  => (r2_funct_2 k5_numbers k7_numbers (k2_mesfunc9 (k1_mesfunc5 k5_numbers A)) (k1_mesfunc5 k5_numbers (k3_series_1 A)))) ) ).
tt(t5_mesfunc1,ax,(r2_tarski k5_numbers k3_numbers)).
tt(t5_mesfunc2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (~  ((r2_wellord2 A B) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  (~  ((k2_relset_1 C D) = (k2_relset_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfunc3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v1_prob_2 D) & (m2_finseq_1 D C))  =>  (! [E:$i] :  ((m2_finseq_1 E C) =>  ( ( ((k4_finseq_1 E) = (k4_finseq_1 D))  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k4_finseq_1 E)) =>  ((k1_funct_1 E F) = (k3_xboole_0 B (k1_funct_1 D F))) ) ) ) )  =>  ((v1_prob_2 E) & (m2_finseq_1 E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfunc4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  ( (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 D)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 D F))) )  &  ((r1_mesfunc2 A B E) &  ( ((k9_xtuple_0 E) = (k9_xtuple_0 D))  &  (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 E)) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 E F))) ) ) ) ) )  =>  ( ((k9_xtuple_0 D) = k1_xboole_0)  |  ((r1_mesfunc2 A B (k3_mesfunc1 A D E)) &  ( (~  ((k9_xtuple_0 (k3_mesfunc1 A D E)) = k1_xboole_0) )  &  ( (! [F:$i] :  ((r2_hidden F (k9_xtuple_0 (k3_mesfunc1 A D E))) => (r1_xxreal_0 k1_supinf_2 (k12_supinf_2 (k3_mesfunc1 A D E) F))) )  &  ((k1_mesfunc3 A B C (k3_mesfunc1 A D E)) = (k3_supinf_2 (k1_mesfunc3 A B C D) (k1_mesfunc3 A B C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfunc5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_subset_1 C k7_numbers) =>  ( ((r1_xxreal_0 B (k8_real_1 (k2_newton 2 A) A)) & (r1_xxreal_0 A C))  => (r1_xxreal_0 (k6_real_1 B (k2_newton 2 A)) C)) ) ) ) ) ) ) ).
tt(t5_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((r2_hidden D (k13_mesfunc1 B C)) <=>  ((r2_hidden D (k1_relset_1 A B)) &  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  ( (E = (k1_seq_1 B D))  &  (~ (r1_xxreal_0 E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfunc7,ax, ((k4_binop_1 k7_numbers k1_mesfunc7) = 1) ).
tt(t5_mesfunc8,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (~  ((v3_kurato_0 D A) &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers B)))) )  =>  (~  ((r1_funct_2 k5_numbers B k5_numbers (k9_setfam_1 A) E (k5_setlim_1 A B D)) &  ((k12_supinf_2 C (k4_kurato_0 A D)) = (k8_supinf_2 (k17_supinf_2 (k1_partfun1 k5_numbers B B k7_numbers E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mesfunc9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((v3_mesfunc5 B) & (v4_mesfunc5 C))  => (v3_mesfunc5 (k4_mesfunc1 A B C))) ) ) ) ) ) ) ).
tt(t5_metric_1,ax, (! [A:$i] :  ( ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k4_metric_1 A B C))) ) ) ) ) ) ).
tt(t5_metric_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k1_metric_2 A C)) => (r2_hidden C (k1_metric_2 A B))) ) ) ) ) ) ) ).
tt(t5_metric_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_metric_1 C) &  ((v7_metric_1 C) &  ((v8_metric_1 C) &  ((v9_metric_1 C) & (l1_metric_1 C)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C))) =>  ((k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k4_metric_3 A B C) D E) = (k1_metric_1 (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C)) (k4_metric_3 A B C) E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_metric_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_pcomps_1 A B) <=>  ((v2_metric_1 B A) &  ((v3_metric_1 B A) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) => (r1_xxreal_0 (k1_metric_1 A A B D E) (k7_real_1 (k1_metric_1 A A B C D) (k1_metric_1 A A B C E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_metrizts,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  => (r1_ordinal1 (k2_waybel23 (k2_borsuk_1 A B)) (k2_card_2 (k2_waybel23 A) (k2_waybel23 B)))) ) ) ) ).
tt(t5_mfold_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (~  ( (~  (A = k1_xboole_0) )  &  ((m1_subset_1 B (u1_struct_0 (k2_mfold_1 A))) & (r1_xxreal_0 1 (k12_euclid B))) ) ) ) ) ) ) ).
tt(t5_mfold_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 D A B) => (r1_metrizts A B (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) D C) C)) ) ) ) ) ) ) ) ) ).
tt(t5_midsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_midsp_1 A) & (l1_midsp_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_midsp_1 A (k3_midsp_1 A B C) D) = (k3_midsp_1 A (k3_midsp_1 A B D) (k3_midsp_1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t5_midsp_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v13_algstr_0 F) &  ((v3_rlvect_1 F) &  ((v4_rlvect_1 F) & (l2_algstr_0 F)) ) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A A) (u1_struct_0 F)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) (u1_struct_0 F))))) )  =>  ( ((r1_midsp_2 A F G) &  ((k2_binop_1 A A (u1_struct_0 F) G B C) = (k2_binop_1 A A (u1_struct_0 F) G D E)) )  =>  ((k2_binop_1 A A (u1_struct_0 F) G C B) = (k2_binop_1 A A (u1_struct_0 F) G E D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_midsp_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden A (k7_subset_1 k5_numbers (k2_finseq_1 B) (k1_tarski C))) &  ( (C = (k2_nat_1 D 1))  &  ( (~  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A D)) )  &  (~  ((r1_xxreal_0 (k2_nat_1 C 1) A) & (r1_xxreal_0 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_tarski B (k1_relset_1 A C)) =>  ((k4_mmlquery A C B) = B) ) ) ) ) ) ) ).
tt(t5_mod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((l1_mod_2 D A) =>  ( ( ((k2_mod_2 A D) = B)  &  ( ((k3_mod_2 A D) = C)  &  ((v13_vectsp_1 (k4_mod_2 A D) (k2_mod_2 A D) (k3_mod_2 A D)) & (v1_mod_2 (k4_mod_2 A D) A (k2_mod_2 A D) (k3_mod_2 A D))) ) )  => (m1_mod_2 D A B C)) ) ) ) ) ) ) ) ) ).
tt(t5_mod_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C B) &  ((v9_vectsp_1 C B) &  ((v10_vectsp_1 C B) &  ((v11_vectsp_1 C B) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C B)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r2_hidden A D) => (r1_struct_0 (k1_mod_3 B C D) A)) ) ) ) ) ) ) ) ).
tt(t5_mod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (k2_mod_4 A)))  &  ( (~ (v6_struct_0 (k2_mod_4 A)))  &  ((v13_algstr_0 (k2_mod_4 A)) &  ((v33_algstr_0 (k2_mod_4 A)) &  ((v3_group_1 (k2_mod_4 A)) &  ((v4_vectsp_1 (k2_mod_4 A)) &  ((v5_vectsp_1 (k2_mod_4 A)) &  ((v2_rlvect_1 (k2_mod_4 A)) &  ((v3_rlvect_1 (k2_mod_4 A)) &  ((v4_rlvect_1 (k2_mod_4 A)) & (l6_algstr_0 (k2_mod_4 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_modal_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~ (r2_xboole_0 (k12_finseq_1 k5_numbers A) (k12_finseq_1 k5_numbers B))) ) ) ) ) ).
tt(t5_modcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (? [C:$i] :  ((r2_hidden C (a_2_0_modcat_1 A B)) & (r1_modcat_1 C (k1_mod_2 A) A)) ) ) ) ) ) ).
tt(t5_modelc_1,ax, (! [A:$i] :  ( ((v1_modelc_1 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_modelc_1 B) & (l2_modelc_1 B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k18_modelc_1 (u3_modelc_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k18_modelc_1 (u3_modelc_1 B))))) )  =>  ((k24_modelc_1 B C (k7_modelc_1 A)) = (k3_robbins1 B (k24_modelc_1 B C A))) ) ) ) ) ) ) ).
tt(t5_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_2 A) =>  (A = (k6_modelc_2 (k10_modelc_2 A))) ) ) ) ).
tt(t5_modelc_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_modelc_2 C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k13_modelc_2 B))) =>  ( (~ (r2_hidden C D))  =>  ((k17_modelc_3 B (k7_subset_1 (k13_modelc_2 B) D (k1_tarski C)) A) = (k17_modelc_3 B D A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_moebius1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ( (~  (A = 1) )  &  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  =>  (~ (r1_nat_d B A)) ) ) ) ) ) ) ).
tt(t5_monoid_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  ((v1_group_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k6_algstr_0 A (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A)) B) = B)  &  ((k6_algstr_0 A B (k4_binop_1 (u1_struct_0 A) (u2_algstr_0 A))) = B) ) ) ) ) ) ) ).
tt(t5_monoid_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((r3_binop_1 B C D) =>  ((r2_funct_2 A B (k6_monoid_1 A B B B D C E) E) & (r2_funct_2 A B (k7_monoid_1 A B B B D E C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_morph_01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = (k3_tarski (a_3_1_morph_01 A B C))) ) ) ) ) ) ) ).
tt(t5_msafree1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v1_msafree1 C A) & (l3_msualg_1 C A)) )  =>  (! [D:$i] :  ( ((v4_msualg_1 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A B C)) =>  ((k3_relat_1 F (k1_msafree1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D) E)) = (k5_msualg_3 A C D B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msafree2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k1_relset_1 k5_numbers D)) => (r2_hidden (k1_funct_1 D E) (k1_funct_1 (u3_msualg_1 A B) (k7_partfun1 (u1_struct_0 A) (k1_msualg_1 A C) E)))) ) ) )  => (r2_hidden D (k3_msualg_1 A C B))) ) ) ) ) ) ) ) ) ).
tt(t5_msafree3,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k1_msualg_1 A C) = k1_xboole_0)  => (r2_hidden (k1_trees_4 (k4_tarski C (u1_struct_0 A))) (k1_funct_1 (u3_msualg_1 A (k1_msafree3 A B)) (k2_msualg_1 A C)))) ) ) ) ) ) ) ).
tt(t5_msafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_2 D (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) (k3_finseq_2 (k2_xboole_0 (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A))) (k3_card_3 (k3_msafree (u1_struct_0 A) B))))) =>  ((r2_hidden (k4_tarski (k4_tarski C (u1_struct_0 A)) D) (k4_msafree A B)) <=>  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (! [E:$i] :  ((r2_hidden E (k4_finseq_1 D)) =>  ( ((r2_hidden (k1_funct_1 D E) (k2_zfmisc_1 (u4_struct_0 A) (k1_tarski (u1_struct_0 A)))) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k4_tarski F (u1_struct_0 A)) = (k1_funct_1 D E))  =>  ((k2_msualg_1 A F) = (k1_funct_1 (k1_msualg_1 A C) E)) ) ) ) )  &  ((r2_hidden (k1_funct_1 D E) (k3_card_3 (k3_msafree (u1_struct_0 A) B))) => (r2_hidden (k1_funct_1 D E) (k2_msafree (u1_struct_0 A) B (k1_funct_1 (k1_msualg_1 A C) E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msalimit,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_orders_3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((m1_msalimit C A B) =>  (! [D:$i] :  ( ((v1_msalimit D A B C) & (m2_msalimit D A B C))  =>  ((k3_msalimit A B C D) = (k14_pralg_2 (u1_struct_0 A) B C)) ) ) ) ) ) ) ) ) ).
tt(t5_msaterm,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 (k5_msafree A B)) (k5_trees_3 (u1_struct_0 (k5_msafree A B))) (k1_msaterm A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_funct_1 B D)) =>  ( ((k1_funct_1 C k1_xboole_0) = (k4_tarski E D))  =>  (C = (k1_trees_4 (k4_tarski E D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msinst_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_msualg_6 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v1_msualg_6 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v1_msualg_6 D A) & (l3_msualg_1 D A))  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) =>  (~  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) &  ((r1_pzfmisc1 (u1_struct_0 A) (u3_msualg_1 A C) (u3_msualg_1 A D)) &  ((r1_msualg_3 A B C E) &  ((r1_msualg_3 A C D F) &  (! [G:$i] :  ((m2_pboole G (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A D)) =>  (~  ( (G = (k8_pboole E F))  & (r1_msualg_3 A B D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msscyc_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_graph_1 A))  =>  (! [B:$i] :  ((r2_hidden B (u4_struct_0 A)) =>  ((v7_graph_1 (k9_finseq_1 B) A) & (m1_graph_1 (k9_finseq_1 B) A)) ) ) ) ) ).
tt(t5_msscyc_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v2_finset_1 B)) ) ) ) )  =>  ((v4_msscyc_1 A) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (v1_finset_1 (a_4_0_msscyc_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t5_mssubfam,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (! [D:$i] :  ((r2_hidden D C) => (r1_tarski B D)) )  =>  ( (C = k1_xboole_0)  | (r1_tarski B (k8_setfam_1 A C))) ) ) ) ) ) ).
tt(t5_mssublat,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k1_tarski k6_numbers)) =>  ( (B = (k5_finseq_2 k5_numbers A k6_numbers))  <=>  ((k3_finseq_1 B) = A) ) ) ) ) ) ).
tt(t5_msualg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  ((v7_struct_0 A) =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k10_xtuple_0 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k10_xtuple_0 (u3_msualg_1 A B))) =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t5_msualg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ( ((g3_msualg_1 A (u3_msualg_1 A B) (u4_msualg_1 A B)) = (g3_msualg_1 A (u3_msualg_1 A C) (u4_msualg_1 A C)))  => (m1_msualg_2 B A C)) ) ) ) ) ) ) ).
tt(t5_msualg_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A B C) =>  (! [E:$i] :  ((m2_pboole E A C B) =>  ( ((v1_msualg_3 D) &  ((v2_msualg_3 D A B C) & (r6_pboole A E (k4_msualg_3 A B C D))) )  =>  ((r6_pboole A (k3_msualg_3 A C B C E D) (k2_msualg_3 A C)) & (r6_pboole A (k3_msualg_3 A B C B D E) (k2_msualg_3 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msualg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A C)) =>  ((r2_msualg_3 A B C D) => (r4_msualg_3 A (k13_msualg_4 A B (k17_msualg_4 A B C D)) C (k19_msualg_4 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t5_msualg_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_msualg_4 C A B) & (m1_msualg_4 C A B B))  =>  (! [D:$i] :  ( ((v1_msualg_4 D A B) & (m1_msualg_4 D A B B))  =>  (! [E:$i] :  ( ((v1_msualg_4 E A B) & (m1_msualg_4 E A B B))  =>  ((r2_pboole A (k2_pboole A C D) E) => (r2_pboole A (k4_msualg_5 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msualg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m2_pboole C (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [D:$i] :  ((m2_pboole D (u1_struct_0 A) (u3_msualg_1 A B) (u3_msualg_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k3_msualg_1 A E B)) =>  ((r2_hidden F (k3_msualg_1 A E B)) =>  ((k5_msualg_3 A B B E D (k5_msualg_3 A B B E C F)) = (k5_msualg_3 A B B E (k1_msualg_6 (u1_struct_0 A) (u3_msualg_1 A B) C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_msualg_7,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k5_msualg_5 A B)))) => (m1_subset_1 C (k1_zfmisc_1 (k1_closure2 A (k6_pboole A B B))))) ) ) ) ) ) ).
tt(t5_msualg_8,ax, (! [A:$i] : (v4_lattice3 (k2_msualg_5 A))) ).
tt(t5_msualg_9,ax, (! [A:$i] :  (! [B:$i] :  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  & (r6_pboole A (k1_pzfmisc1 A C) (k7_funcop_1 A (k1_tarski B)))) ) ) ) ).
tt(t5_msuhom_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_msualg_1 C))  =>  ( ((r1_msuhom_1 A B) & (r1_msuhom_1 B C))  => (r1_msuhom_1 A C)) ) ) ) ) ) ) ).
tt(t5_multop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k4_zfmisc_1 A B C D) E) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 A B C D) E)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k4_zfmisc_1 A B C D) E) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k4_zfmisc_1 A B C D) E)))) )  =>  ( (! [H:$i] :  ((m1_subset_1 H A) =>  (! [I:$i] :  ((m1_subset_1 I B) =>  (! [J:$i] :  ((m1_subset_1 J C) =>  (! [K:$i] :  ((m1_subset_1 K D) =>  ((k3_funct_2 (k4_zfmisc_1 A B C D) E F (k5_domain_1 A B C D H I J K)) = (k3_funct_2 (k4_zfmisc_1 A B C D) E G (k5_domain_1 A B C D H I J K))) ) ) ) ) ) ) ) )  => (r2_funct_2 (k4_zfmisc_1 A B C D) E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_mycielsk,ax, (! [A:$i] :  ( ((v1_necklace A) & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (u1_struct_0 A)) &  ((r2_hidden C (u1_struct_0 A)) & (r2_hidden (k4_tarski B C) (u1_orders_2 A))) )  => (r2_hidden (k4_tarski C B) (u1_orders_2 A))) ) ) ) ) ).
tt(t5_nagata_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_nagata_1 B A) &  ((v1_nagata_1 C A) &  ((k3_setfam_1 B C) = D) ) )  => (v1_nagata_1 D A)) ) ) ) ) ) ) ) ) ).
tt(t5_nagata_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) k1_numbers)))) )  =>  ((r1_nagata_1 A B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ((m1_subset_1 D A) => (r1_xxreal_0 k6_numbers (k3_funct_2 A k1_numbers (k3_nagata_2 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t5_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~ (r1_xxreal_0 (k1_nat_1 A 1) k6_numbers)) ) ) ).
tt(t5_nat_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 A B) &  ((r1_xxreal_0 C B) &  (A = (k2_nat_1 (k7_nat_d B C) D)) ) )  =>  (C = (k2_nat_1 (k7_nat_d B A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_nat_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v7_ordinal1 C) & (v1_int_2 C))  =>  ((r1_nat_d C (k1_newton A B)) => (r1_nat_d C A)) ) ) ) ) ) ) ).
tt(t5_nat_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ( (B = (k1_int_1 (k6_real_1 A 2)))  & (r1_xxreal_0 2 A))  => (r1_xxreal_0 (k10_real_1 (k2_newton 2 A) A) (k6_newton B A))) ) ) ) ) ).
tt(t5_nat_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((v1_finset_1 (k2_tarski A B)) & (m1_subset_1 (k2_tarski A B) (k1_zfmisc_1 k5_numbers))) ) ) ) ) ).
tt(t5_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((r1_nat_d A B) & (r1_nat_d B A))  =>  (A = B) ) ) ) ) ) ).
tt(t5_nat_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_nat_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_nat_lat)) =>  ((k1_binop_1 k2_nat_lat A B) = (k1_binop_1 k2_nat_lat B A)) ) ) ) ) ).
tt(t5_nattra_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden (k10_cat_2 (k8_cat_2 A A) A (k10_cat_2 A A (k4_cat_1 A B) (k4_cat_1 A B)) (k4_cat_1 A B)) (u1_cat_1 A))) ) ) ) ).
tt(t5_ncfcont1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) (k1_relset_1 (u1_struct_0 B) E)) => (r2_hidden (k1_normsp_1 B D A) (k1_relset_1 (u1_struct_0 B) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ncfcont2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v13_algstr_0 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) &  ((v3_normsp_0 D) &  ((v4_normsp_0 D) &  ((v2_clvect_1 D) &  ((v3_clvect_1 D) &  ((v4_clvect_1 D) &  ((v5_clvect_1 D) &  ((v8_clvect_1 D) & (l2_clvect_1 D)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C)))))  =>  ( ((r2_ncfcont2 A C D E) & (r2_ncfcont2 B C D F))  => (r2_ncfcont2 (k3_xboole_0 A B) C D (k6_vfunct_1 (u1_struct_0 D) C E F))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ndiff_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((m1_nfcont_1 D A C) =>  (~ (r1_tarski D B)) ) ) ) ) ) )  <=> (v3_nfcont_1 B A)) ) ) ) ) ).
tt(t5_ndiff_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_ndiff_2 A B C D E) <=>  (? [F:$i] :  ((m1_nfcont_1 F A D) &  ((r1_tarski F (k1_relset_1 (u1_struct_0 A) C)) &  (? [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) &  (! [H:$i] :  ( ((v2_relat_1 H) &  ((v1_funct_1 H) &  ((v1_funct_2 H k5_numbers k1_numbers) &  ((v1_fdiff_1 H k6_numbers) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) ) )  =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v3_funct_1 I) &  ((v1_funct_2 I k5_numbers (u1_struct_0 A)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ( ((k2_relset_1 (u1_struct_0 A) I) = (k1_tarski D))  & (r1_tarski (k2_relset_1 (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A E H) I)) F))  =>  ((v3_normsp_1 (k1_ndiff_1 B (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A E H) I) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) I C)) (k37_valued_1 k5_numbers k1_numbers H)) B) &  (G = (k6_normsp_1 B (k1_ndiff_1 B (k3_normsp_1 B (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) (k2_normsp_1 A (k2_ndiff_1 A E H) I) C) (k8_funct_2 k5_numbers (u1_struct_0 B) (u1_struct_0 A) I C)) (k37_valued_1 k5_numbers k1_numbers H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ndiff_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k1_numbers D) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C))) =>  ((r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D (k6_vfunct_1 k1_numbers A B C)) (k2_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C))) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D (k2_vfunct_1 k1_numbers A B C)) (k3_normsp_1 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D B) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers D C)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_ndiff_4,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid A)))))  =>  ((r2_ndiff_4 A C B) <=>  ((r1_tarski B (k1_relset_1 k1_numbers C)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) => (r1_ndiff_4 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ndiff_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v7_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_ndiff_3 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) )  =>  ( ((k7_partfun1 (u1_struct_0 A) C k6_numbers) = (k4_struct_0 A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v2_ndiff_1 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((k7_partfun1 (u1_struct_0 B) D (k4_struct_0 A)) = (k4_struct_0 B))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_numbers (u1_struct_0 A)) &  ((v2_ndiff_3 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) &  ((v13_vectsp_1 F A B) &  ((v1_lopban_1 F A B) &  ((v2_lopban_1 F A B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) ) ) )  =>  ((v1_funct_1 (k6_vfunct_1 k1_numbers B (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C F) (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D))) &  ((v1_ndiff_3 (k6_vfunct_1 k1_numbers B (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C F) (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D)) B) & (m1_subset_1 (k6_vfunct_1 k1_numbers B (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) C F) (k1_partfun1 k1_numbers (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 B) (k6_vfunct_1 k1_numbers A E C) D)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_neckla_2,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((r2_hidden A k4_neckla_2) => (r2_hidden (u1_struct_0 A) k13_classes2)) ) ) ).
tt(t5_neckla_3,ax, (! [A:$i] :  ((v3_card_1 A 1) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) => (r3_relat_2 B A)) ) ) ) ).
tt(t5_necklace,ax, (! [A:$i] :  ((k1_card_1 (k6_partfun1 A)) = (k1_card_1 A)) ) ).
tt(t5_net_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_net_1 C) & (l1_petri C))  =>  ( ((r2_hidden (k4_tarski A B) (k1_net_1 C)) & (r2_hidden A (u4_struct_0 C)))  => (r2_hidden B (u1_struct_0 C))) ) ) ) ) ).
tt(t5_newton,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k1_newton A 1) = A) ) ) ).
tt(t5_nfcont_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_tarski (k2_relset_1 (u1_struct_0 B) D) (k1_relset_1 (u1_struct_0 B) E)) => (r2_hidden (k1_normsp_1 B D A) (k1_relset_1 (u1_struct_0 B) E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_nfcont_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r1_nfcont_2 A B C D) => (r1_nfcont_2 A B C (k5_vfunct_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ).
tt(t5_nfcont_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_relset_1 k1_numbers B)) =>  ((r2_funct_2 k5_numbers k1_numbers (k4_normsp_0 A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C B)) (k8_funct_2 k5_numbers k1_numbers k1_numbers C (k3_normsp_0 k1_numbers A B))) & (r2_funct_2 k5_numbers (u1_struct_0 A) (k5_vfunct_1 k5_numbers A (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C B)) (k8_funct_2 k5_numbers (u1_struct_0 A) k1_numbers C (k5_vfunct_1 k1_numbers A B)))) ) ) ) ) ) ) ) ).
tt(t5_nfcont_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 (k4_real_ns1 A))))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B (k1_euclid A)))))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k6_vfunct_1 B (k4_real_ns1 A) C D) = (k7_integr15 A B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_normform,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v4_finsub_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_finsub_1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k2_zfmisc_1 A B)) =>  (! [E:$i] :  ((m1_subset_1 E (k2_zfmisc_1 A B)) =>  ((k2_normform A B C (k1_normform A B D E)) = (k1_normform A B (k2_normform A B C D) (k2_normform A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_normsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v5_rlvect_1 C) &  ((v6_rlvect_1 C) &  ((v7_rlvect_1 C) &  ((v8_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_normsp_1 C) & (l1_normsp_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) => (r1_xxreal_0 (k1_normsp_0 C (k3_rlvect_1 C (k1_rlvect_1 C D A) (k1_rlvect_1 C E B))) (k7_real_1 (k8_real_1 (k18_complex1 A) (k1_normsp_0 C D)) (k8_real_1 (k18_complex1 B) (k1_normsp_0 C E))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_normsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k2_normsp_2 A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k2_normsp_2 A)))))) )  =>  ((r1_funct_2 k5_numbers (u1_struct_0 A) k5_numbers (u1_struct_0 (k2_normsp_2 A)) B C) =>  ((v2_tbsp_1 C (k2_normsp_2 A)) <=> (v3_normsp_1 B A)) ) ) ) ) ) ) ) ).
tt(t5_ntalgo_1,ax, (! [A:$i] :  ((m1_subset_1 A k4_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k4_numbers) =>  (~  ( (~  ((k1_int_2 B) = k6_numbers) )  & (r1_xxreal_0 (k1_int_2 B) (k1_int_2 (k6_int_1 A B)))) ) ) ) ) ) ).
tt(t5_numbers,ax,(r2_xboole_0 k4_numbers k1_numbers)).
tt(t5_numeral1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B 1))  =>  ((k1_numeral1 (k2_numeral1 A B) B) = A) ) ) ) ) ) ).
tt(t5_openlatt,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k6_openlatt A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_openlatt A))) =>  ( ((k3_lattices (k6_openlatt A) B C) = (k2_xboole_0 B C))  &  ((k4_lattices (k6_openlatt A) B C) = (k3_xboole_0 B C)) ) ) ) ) ) ) ) ).
tt(t5_oposet_1,ax,(v1_necklace k1_oposet_1)).
tt(t5_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_cat_1 A B C) = (k2_cat_1 (k2_oppcat_1 A) (k3_oppcat_1 A C) (k3_oppcat_1 A B))) ) ) ) ) ) ) ).
tt(t5_orders_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_2 E) &  ((v4_relat_2 E) &  ((v8_relat_2 E) &  ((v1_partfun1 E A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) ) )  =>  ( ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ((r2_hidden (k4_tarski B C) E) & (r2_hidden (k4_tarski C D) E)) ) ) )  => (r2_hidden (k4_tarski B D) E)) ) ) ) ) ) ) ).
tt(t5_orders_2,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r2_orders_2 A B C) & (r2_orders_2 A C D))  => (r2_orders_2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t5_orders_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_orders_3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (~  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (B = C) ) ) ) ) )  => (v3_orders_3 A)) ) ) ).
tt(t5_orders_4,ax, (! [A:$i] :  ( ((v5_orders_2 A) & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v5_orders_2 B) & (l1_orders_2 B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_orders_4 A C D) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_orders_4 B E F) =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 B E))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A C)) (u1_struct_0 (k5_yellow_0 B E)))))) )  =>  ((v23_waybel_0 G (k5_yellow_0 A C) (k5_yellow_0 B E)) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 (k5_yellow_0 A D)) (u1_struct_0 (k5_yellow_0 B F))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k5_yellow_0 A D)) (u1_struct_0 (k5_yellow_0 B F)))))) )  =>  (~  ((v23_waybel_0 H (k5_yellow_0 A D) (k5_yellow_0 B F)) &  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ( (I = (k1_funct_4 G H))  & (v23_waybel_0 I A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_ordinal1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden A B) & (r1_tarski B A)) ) ) ) ).
tt(t5_ordinal2,ax, (! [A:$i] :  ((v3_ordinal1 A) => (r1_ordinal1 (k3_tarski A) A)) ) ).
tt(t5_ordinal3,ax, (! [A:$i] : (v3_ordinal1 (k3_tarski (k2_ordinal1 A)))) ).
tt(t5_ordinal4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v5_ordinal1 A) &  ((v1_funct_1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r1_ordinal2 B A) => (r1_ordinal2 (k11_ordinal2 B C) (k4_ordinal3 C A))) ) ) ) ) ) ) ).
tt(t5_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v5_ordinal1 A)) )  =>  ( (~ (v1_finset_1 A))  <=> (r1_ordinal1 k4_ordinal1 (k9_xtuple_0 A))) ) ) ).
tt(t5_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((r2_hidden C (k6_subset_1 A B)) <=>  ((r1_tarski B C) & (r2_hidden C A)) ) ) ) ) ) ) ).
tt(t5_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v7_o_ring_1 B A) =>  ((v11_o_ring_1 B A) & (v13_o_ring_1 B A)) ) ) ) ) ) ).
tt(t5_ortsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_ortsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (E = (k4_struct_0 A)) )  &  (~  ( (~ (r1_orders_2 B (k4_vectsp_1 A B E C) D))  &  (~ (r1_orders_2 B C (k4_vectsp_1 A B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_osafree,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k1_funct_1 (k3_relat_1 (u1_msualg_1 A) (k6_finseq_2 (u1_struct_0 A) (k5_osafree A B))) C)) => (m1_trees_4 D (k5_trees_3 (u1_struct_0 (k2_osafree A B))) (k4_dtconstr (k2_osafree A B)))) ) ) ) ) ) ) ) ).
tt(t5_osalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  ((v1_orders_3 (k1_osalg_1 A)) & (v6_osalg_1 (k1_osalg_1 A))) ) ) ).
tt(t5_osalg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v4_osalg_1 A) &  ((v5_osalg_1 A) & (l3_osalg_1 A)) ) ) )  =>  (! [B:$i] :  ( ((v12_osalg_1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ( ((v12_osalg_1 C A) & (m1_msualg_2 C A B))  <=>  ((m2_osalg_2 (u3_msualg_1 A C) A B) &  (! [D:$i] :  ((m2_osalg_2 D A B) =>  ((r8_pboole (u1_struct_0 A) D (u3_msualg_1 A C)) =>  ((v3_msualg_2 D A B) & (r8_pboole (u4_struct_0 A) (u4_msualg_1 A C) (k4_msualg_2 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_osalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) & (v11_osalg_1 B A)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) & (v11_osalg_1 C A)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v2_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 A)) &  ((v1_funct_1 D) &  ((v1_partfun1 D (u1_struct_0 A)) & (v11_osalg_1 D A)) ) ) ) )  =>  (! [E:$i] :  ((m2_pboole E (u1_struct_0 A) B C) =>  (! [F:$i] :  ((m2_pboole F (u1_struct_0 A) C D) =>  ( ((v1_osalg_3 E A) & (v1_osalg_3 F A))  => (v1_osalg_3 (k3_msualg_3 (u1_struct_0 A) B C D E F) A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_osalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_partfun1 B (u1_struct_0 A))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k1_funct_1 B C)) => (r2_hidden D (k4_osalg_4 A B (k3_osalg_4 A C)))) ) ) ) ) ) ) ) ).
tt(t5_papdesaf,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v7_struct_0 B))  &  ((v2_analoaf B) & (l1_analoaf B)) )  =>  (~  ( (B = (k2_analoaf A))  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E k1_numbers) &  (? [F:$i] :  ((m1_subset_1 F k1_numbers) &  ( ((k3_rlvect_1 A (k1_rlvect_1 A C E) (k1_rlvect_1 A D F)) = (k4_struct_0 A))  &  (~  ( (E = k6_numbers)  &  (F = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pardepap,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ((r2_analoaf A B C B D) &  (~  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ((r2_analoaf A B D B E) &  (~  ((r2_analoaf A B F B G) & (r2_analoaf A D F E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_parsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  ((u1_struct_0 (k9_parsp_1 A)) = (k5_parsp_1 A)) ) ) ).
tt(t5_parsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_parsp_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_parsp_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_parsp_1 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_parsp_1 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  (! [I:$i] :  ((m1_subset_1 I (k3_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A))) =>  ( ((r1_parsp_1 (k9_parsp_1 A) B C D E) &  ((r1_parsp_1 (k9_parsp_1 A) B D C E) &  ((k5_domain_1 (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) (u1_struct_0 (k9_parsp_1 A)) B C D E) = (k6_xtuple_0 F G H I)) ) )  =>  ((r1_parsp_1 (k9_parsp_1 A) B C B D) |  ( ((k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I) = (k5_algstr_0 A (k3_rlvect_1 A (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H)) (k1_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F)))  &  ( ((k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I) = (k5_algstr_0 A (k3_rlvect_1 A (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H)) (k2_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F)))  &  ((k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) I) = (k5_algstr_0 A (k3_rlvect_1 A (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) G) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) H)) (k3_mcart_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ( ((k1_relset_1 A C) = (k1_relset_1 A D))  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A C)) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t5_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B C))))  =>  ( ((r1_tarski (k2_relset_1 B E) (k1_relset_1 B F)) & (r2_hidden D (k1_relset_1 A E)))  =>  ((k7_partfun1 C (k1_partfun1 A B B C E F) D) = (k7_partfun1 C F (k7_partfun1 B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_partit1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  ((r1_setfam_1 C B) => (r2_setfam_1 C B)) ) ) ) ) ) ) ).
tt(t5_partit_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  ((r2_hidden (k4_tarski C D) (k4_partit1 A B)) <=> (r2_hidden C (k15_bvfunc_1 A D B))) ) ) ) ) ) ) ) ) ).
tt(t5_pasch,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_diraf A B C D E) &  ((r2_diraf A B C D F) &  ((r2_diraf A B D C E) & (r2_diraf A B D C F)) ) )  =>  ((r3_diraf A B C D) |  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pboole,ax, (! [A:$i] :  (! [B:$i] :  ((k1_funct_1 (k1_pboole B) A) = k1_xboole_0) ) ) ).
tt(t5_pcomps_1,ax, (! [A:$i] :  ((u1_struct_0 (k1_compts_1 A)) = A) ) ).
tt(t5_pcomps_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) k1_numbers)))) )  =>  ( ((r1_pcomps_1 (u1_struct_0 A) D) &  (B = (k4_pcomps_1 (u1_struct_0 A) D)) )  =>  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) <=> (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_pcs_0,ax, (! [A:$i] :  ((l1_pcs_0 A) =>  (! [B:$i] :  ((l1_pcs_0 B) =>  ( ( ((g1_pcs_0 (u1_struct_0 A) (u1_pcs_0 A)) = (g1_pcs_0 (u1_struct_0 B) (u1_pcs_0 B)))  & (v6_pcs_0 A))  => (v6_pcs_0 B)) ) ) ) ) ).
tt(t5_pdiff_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k1_numbers (k1_euclid 1)) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers (k1_euclid 1))))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k1_euclid 1) k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 1) k1_numbers)))) )  =>  ( ( (A = (k2_funct_1 (k1_pdiff_1 1 1)))  & (r2_funct_2 (k1_euclid 1) k1_numbers B (k1_pdiff_1 1 1)))  =>  ( (! [C:$i] :  ( ((v1_funct_1 C) &  ((v2_ndiff_1 C (k4_real_ns1 1) (k4_real_ns1 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)))))) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B))) &  ((v2_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B))) & (m1_subset_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) )  &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1))) &  ((v13_vectsp_1 C (k4_real_ns1 1) (k4_real_ns1 1)) &  ((v1_lopban_1 C (k4_real_ns1 1) (k4_real_ns1 1)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)))))) ) ) )  =>  ((v1_funct_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B))) &  ((v3_fdiff_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B))) & (m1_subset_1 (k1_partfun1 k1_numbers (k1_euclid 1) (u1_struct_0 (k4_real_ns1 1)) k1_numbers A (k1_partfun1 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 1)) (k1_euclid 1) k1_numbers C B)) (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_pdiff_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 2)) =>  ( (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (B = (k10_finseq_1 C D))  & (r1_fdiff_1 (k1_pdiff_2 2 1 A B) C)) ) ) ) )  <=> (r3_pdiff_1 2 1 A B)) ) ) ) ) ).
tt(t5_pdiff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 2)) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 2) k1_numbers))))  =>  ( ( (C = (k10_finseq_1 A B))  & (r1_pdiff_3 D C))  =>  ((k2_pdiff_3 D C) = (k1_fdiff_1 (k1_pdiff_2 2 1 (k1_pdiff_3 1 2 D) C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_pdiff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r3_pdiff_1 3 2 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 2 E D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid 3)) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ( (D = (k11_finseq_1 A B C))  & (r5_pdiff_5 E D))  => (r1_fdiff_1 (k1_pdiff_2 3 2 (k1_pdiff_3 2 3 E) D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pdiff_6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k4_real_ns1 A)) (u1_struct_0 (k4_real_ns1 B))))))  =>  ( ( (C = E)  &  (D = F) )  =>  ((k8_integr15 B (k1_euclid A) C D) = (k2_vfunct_1 (u1_struct_0 (k4_real_ns1 A)) (k4_real_ns1 B) E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pdiff_7,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 1))) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A B))  =>  ((k1_normsp_0 (k4_real_ns1 B) (k3_funct_2 (u1_struct_0 (k4_real_ns1 1)) (u1_struct_0 (k4_real_ns1 B)) (k7_pdiff_1 B A (k4_struct_0 (k4_real_ns1 B))) C)) = (k1_normsp_0 (k4_real_ns1 1) C)) ) ) ) ) ) ) ) ).
tt(t5_pdiff_8,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C A))  => (r1_xxreal_0 (k17_complex1 (k1_seq_1 (k1_pdiff_1 C A) B)) (k12_euclid B))) ) ) ) ) ) ) ).
tt(t5_pdiff_9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  => (r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A (k2_partfun1 (k1_euclid A) k1_numbers C B)) (k2_partfun1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A C) B))) ) ) ) ) ).
tt(t5_pencil_1,ax, (! [A:$i] :  ((r1_ordinal1 3 (k1_card_1 A)) <=>  (? [B:$i] :  (? [C:$i] :  (? [D:$i] :  ((r2_hidden B A) &  ((r2_hidden C A) &  ((r2_hidden D A) &  ( (~  (B = C) )  &  ( (~  (B = D) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pencil_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r1_xxreal_0 (k2_nat_1 (k3_finseq_1 A) 1) C) =>  ((k1_funct_1 (k7_finseq_1 A B) C) = (k1_funct_1 B (k6_xcmplx_0 C (k3_finseq_1 A)))) ) ) ) ) ) ) ) ).
tt(t5_pencil_3,ax, (! [A:$i] :  ( ( (~ (v3_pencil_1 A))  &  ( (~ (v4_pencil_1 A))  & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_pre_topc A)) =>  (~  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t5_pencil_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  ((m1_vectsp_4 (k2_vectsp_4 A C) A B) => (m1_vectsp_4 C A B)) ) ) ) ) ) ) ).
tt(t5_pepin,ax, (! [A:$i] :  ((v1_int_1 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k6_int_1 1 A) = 1) ) ) ) ).
tt(t5_petri_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  (! [D:$i] :  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_petri_2 B D) (k2_petri_2 A C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_petri_2 B D) (k2_petri_2 A C))))) )  &  (! [F:$i] :  (~  ((r2_hidden F (k2_petri_2 B D)) &  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 D)) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 C)) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I H A) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 H A)))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J G B) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 G B)))) )  =>  (~  ((v1_finset_1 H) &  ((v1_finset_1 G) &  ( (H = (k8_subset_1 D (k9_subset_1 D C G) (k8_relat_1 J A)))  &  ( (I = (k2_partfun1 G B J H))  &  ( (F = (k1_petri_2 B D G J))  &  ((k1_funct_1 E F) = (k1_petri_2 A C H I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_petri,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_petri A) &  ((v3_petri A) & (l1_petri A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u4_struct_0 A))) =>  ((k8_petri A B) = (a_2_6_petri A B)) ) ) ) ) ).
tt(t5_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ( ((v1_relat_1 (k2_tarski (k4_tarski A B) (k4_tarski C D))) &  ((v1_funct_1 (k2_tarski (k4_tarski A B) (k4_tarski C D))) & (v1_finseq_1 (k2_tarski (k4_tarski A B) (k4_tarski C D)))) )  &  ( (~  ( (A = 1)  &  ( (C = 1)  &  (B = D) ) ) )  &  ( (~  ( (A = 1)  &  (C = 2) ) )  &  (~  ( (A = 2)  &  (C = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_polyalg1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_vectsp_1 A) &  ((v4_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k10_polynom3 A) B) B)) ) ) ) ).
tt(t5_polyeq_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((r1_xxreal_0 k6_numbers (k1_quin_1 A B C)) =>  ( (A = k6_numbers)  |  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( ((k3_polyeq_1 A B C D) = k6_numbers)  &  ( (~  (D = (k6_real_1 (k2_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) )  &  (~  (D = (k6_real_1 (k6_xcmplx_0 (k4_xcmplx_0 B) (k6_square_1 (k1_quin_1 A B C))) (k8_real_1 2 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_polyeq_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~  ((k2_xcmplx_0 A B) = k6_numbers) )  =>  ((k1_newton (k2_xcmplx_0 A B) 4) = (k2_xcmplx_0 (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 3 B) (k3_square_1 A)) (k3_xcmplx_0 (k3_xcmplx_0 3 (k3_square_1 B)) A))) (k1_newton B 3)) A) (k3_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 (k1_newton A 3) (k2_xcmplx_0 (k3_xcmplx_0 (k3_xcmplx_0 3 B) (k3_square_1 A)) (k3_xcmplx_0 (k3_xcmplx_0 3 (k3_square_1 B)) A))) (k1_newton B 3)) B))) ) ) ) ) ) ).
tt(t5_polyeq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( ((k3_complex1 (k3_polyeq_3 A)) = (k10_binop_2 (k2_newton (k3_complex1 A) 3) (k11_binop_2 (k11_binop_2 3 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))))  &  ((k4_complex1 (k3_polyeq_3 A)) = (k9_binop_2 (k7_binop_2 (k2_newton (k4_complex1 A) 3)) (k11_binop_2 (k11_binop_2 3 (k5_square_1 (k3_complex1 A))) (k4_complex1 A)))) ) ) ) ).
tt(t5_polyeq_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( ((k4_polyeq_1 A B k6_numbers C) = k6_numbers)  &  ( (~  (C = k6_numbers) )  &  (~  (C = (k4_xcmplx_0 (k7_xcmplx_0 B A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_polyeq_5,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k1_newton (k6_xcmplx_0 A B) 3) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton A 2)) B)) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton B 2)) A)) (k1_newton B 3))) ) ) ) ) ).
tt(t5_polyform,ax,(v1_abian 2)).
tt(t5_polynom1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))) =>  ((k6_matrlin A (k8_finseq_1 (k3_finseq_2 (u1_struct_0 A)) B C)) = (k8_finseq_1 (u1_struct_0 A) (k6_matrlin A B) (k6_matrlin A C))) ) ) ) ) ) ) ).
tt(t5_polynom2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  =>  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r2_hidden E (k4_finseq_1 C)) &  ( ((k7_partfun1 (u1_struct_0 A) D E) = (k3_rlvect_1 A B (k7_partfun1 (u1_struct_0 A) C E)))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k4_finseq_1 C)) =>  ( (F = E)  |  ((k7_partfun1 (u1_struct_0 A) D F) = (k7_partfun1 (u1_struct_0 A) C F)) ) ) ) ) ) ) ) ) )  |  ((k4_rlvect_1 A D) = (k3_rlvect_1 A B (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_polynom3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [C:$i] :  ((m2_finseq_2 C k5_numbers (k4_finseq_2 A k5_numbers)) =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 A k5_numbers)) =>  ( ( ((r1_polynom3 A B C) & (r1_polynom3 A C D))  => (r1_polynom3 A B D))  &  ( (~  ( (~  ((r1_polynom3 A B C) & (r2_polynom3 A C D)) )  &  ( (~  ((r2_polynom3 A B C) & (r1_polynom3 A C D)) )  &  (~  ((r2_polynom3 A B C) & (r2_polynom3 A C D)) ) ) ) )  => (r2_polynom3 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_polynom4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_struct_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( ((k1_algseq_1 A B) = k6_numbers)  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k9_polynom3 A))) ) ) ) ) ).
tt(t5_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k4_algstr_0 k1_complfld (k1_hahnban1 A B)) = (k1_hahnban1 (k1_real_1 A) (k1_real_1 B))) ) ) ) ) ).
tt(t5_polynom6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k14_pre_poly A) (k15_pre_poly A)) =>  (! [D:$i] :  ((m2_subset_1 D (k14_pre_poly B) (k15_pre_poly B)) =>  ((r6_pboole (k10_ordinal2 A B) (k1_polynom6 A B C D) (k16_pre_poly (k10_ordinal2 A B))) <=>  ((r6_pboole A C (k16_pre_poly A)) & (r6_pboole B D (k16_pre_poly B))) ) ) ) ) ) ) ) ) ) ).
tt(t5_polynom7,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (r2_quofield (k11_polynom1 k1_xboole_0 A) A)) ) ).
tt(t5_polynom8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D (k3_finseq_1 B)))  =>  ((k1_funct_1 B D) = (k2_binom A C (k7_nat_d D 1))) ) ) )  =>  ( (C = (k5_struct_0 A))  |  ((k4_rlvect_1 A B) = (k3_vectsp_1 A (k5_algstr_0 A (k5_struct_0 A) (k2_binom A C (k3_finseq_1 B))) (k5_algstr_0 A (k5_struct_0 A) C))) ) ) ) ) ) ) ) ) ).
tt(t5_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_algstr_0 B) &  ((v13_algstr_0 B) &  ((v2_vectsp_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l6_algstr_0 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k15_pre_poly A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 B))))) )  => (r2_funct_2 (k15_pre_poly A) (u1_struct_0 B) (k9_polynom1 A B (k7_polynom1 A B) C) (k7_polynom1 A B))) ) ) ) ) ) ).
tt(t5_poset_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_orders_2 A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_poset_1 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v5_orders_3 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((r1_yellow_2 (u1_struct_0 A) A B C) => (r3_orders_2 A (k1_yellow_0 A (k2_poset_1 A B)) (k1_yellow_0 A (k2_poset_1 A C)))) ) ) ) ) ) ) ).
tt(t5_power,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((r1_xxreal_0 1 A) =>  ((k2_power A k6_numbers) = k6_numbers) ) ) ) ).
tt(t5_pralg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_unialg_1 B) &  ((v3_unialg_1 B) &  ((v4_unialg_1 B) & (l1_unialg_1 B)) ) ) )  =>  ((r1_unialg_2 A B) =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  (! [D:$i] :  ((m5_margrel1 D (u1_struct_0 B) (k1_unialg_2 B)) =>  (! [E:$i] :  ((m5_margrel1 E (u1_struct_0 (k5_pralg_1 A B)) (k1_unialg_2 (k5_pralg_1 A B))) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ( (C = (k1_funct_1 (u1_unialg_1 A) F))  &  ( (D = (k1_funct_1 (u1_unialg_1 B) F))  &  ( (E = (k1_funct_1 (u1_unialg_1 (k5_pralg_1 A B)) F))  & (r2_hidden F (k4_finseq_1 (u1_unialg_1 A)))) ) )  =>  ( ((k19_margrel1 E) = (k19_margrel1 C))  &  ( ((k19_margrel1 E) = (k19_margrel1 D))  &  (E = (k3_pralg_1 (u1_struct_0 A) (u1_struct_0 B) C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pralg_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ((m1_pralg_2 C A B) =>  ((k9_xtuple_0 (k2_funct_5 (k11_pralg_2 A B C))) = (k2_zfmisc_1 A (u4_struct_0 B))) ) ) ) ) ) ).
tt(t5_pralg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ((l3_msualg_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  ( ((k1_msualg_1 A C) = k1_xboole_0)  =>  ( ((k4_msualg_1 A C B) = k1_xboole_0)  | (r2_hidden (k1_pralg_3 A B C) (k4_msualg_1 A C B))) ) ) ) ) ) ) ) ).
tt(t5_pre_circ,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v2_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) ) )  =>  (! [D:$i] :  ((m2_pboole D A (k7_funcop_1 A B) C) =>  ((k9_xtuple_0 (k10_funct_6 D)) = B) ) ) ) ) ) ) ) ).
tt(t5_pre_ff,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k5_int_1 (k5_int_1 A B) C) = (k5_int_1 A (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t5_prelamb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_prelamb A))  =>  (! [B:$i] :  ((m1_prelamb B A) =>  (! [C:$i] :  ((m1_trees_1 C (k9_xtuple_0 B)) =>  (~  ( ((k2_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = 2)  &  (! [D:$i] :  ((m1_trees_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (D = (k8_finseq_1 k5_numbers C (k12_finseq_1 k5_numbers k6_numbers)))  &  ( ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B C)) = (k6_prelamb A E (k1_prelamb A G F)))  &  ((k1_xtuple_0 (k3_trees_2 (k2_zfmisc_1 (k2_zfmisc_1 (k3_finseq_2 (u1_struct_0 A)) (u1_struct_0 A)) k5_numbers) B D)) = (k6_prelamb A (k8_finseq_1 (u1_struct_0 A) (k12_finseq_1 (u1_struct_0 A) G) E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_2 B A (k3_finseq_2 A)) =>  (! [C:$i] :  ((m2_finseq_2 C A (k3_finseq_2 A)) =>  (! [D:$i] :  ((m2_finseq_2 D A (k3_finseq_2 A)) =>  ((k5_pre_poly A (k3_finseq_4 (k3_finseq_2 A) B C D)) = (k1_pre_poly A (k1_pre_poly A B C) D)) ) ) ) ) ) ) ) ).
tt(t5_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (k6_numbers = A) )  &  (k6_numbers = (k1_newton A B)) ) ) ) ) ) ) ).
tt(t5_pre_topc,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((k2_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  & (r1_xboole_0 B C))  =>  (C = (k7_subset_1 (u1_struct_0 A) (k2_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t5_prgcor_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 B (k4_nat_d A (k4_nat_1 2 B))))  &  (~  ((k3_nat_d A B) = (k4_nat_1 (k3_nat_d A (k4_nat_1 2 B)) 2)) ) ) ) ) ) ) ) ) ).
tt(t5_prgcor_2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 C (k3_finseq_1 A)) |  ((k23_rvsum_1 A B) = (k2_prgcor_2 (k11_afinsq_1 k1_numbers A C) (k11_afinsq_1 k1_numbers B C))) ) ) ) ) ) ) ) ) ).
tt(t5_prob_1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_finsub_1 B) &  ((v1_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  => (r2_hidden A B)) ) ) ).
tt(t5_prob_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v5_relat_1 C B) &  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D B) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((k1_prob_2 A B C F) = (k5_prob_1 A B (k1_prob_2 A B D F) E)) ) )  =>  ((k9_subset_1 A (k3_prob_1 A D) E) = (k3_prob_1 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_prob_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C B) &  ((v4_prob_1 C B) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 B)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  (! [E:$i] :  ( ((v5_relat_1 E C) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) ) )  =>  (! [F:$i] :  ((m2_prob_1 F B C) =>  ((r1_tarski (k1_funct_1 D A) (k1_funct_1 E A)) => (r1_xxreal_0 (k1_funct_1 (k8_prob_1 B C D F) A) (k1_funct_1 (k8_prob_1 B C E F) A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_prob_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_1 D A B) =>  (! [E:$i] :  ((m1_prob_1 E A B) =>  ((k3_funct_2 B k1_numbers C (k3_measure1 A B D E)) = (k9_real_1 (k3_funct_2 B k1_numbers C (k1_measure1 A B D E)) (k3_funct_2 B k1_numbers C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_procal_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (r2_hidden (k8_cqc_lang A (k9_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A B) C)) (k4_cqc_the1 A))) ) ) ) ) ) ).
tt(t5_projdes1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_collsp A) &  ((v3_collsp A) &  ((v4_collsp A) &  ((v2_anproj_2 A) &  ((v3_anproj_2 A) &  ( (~ (v7_anproj_2 A))  & (l1_collsp A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~ (r1_collsp A B C D))  &  ((r1_collsp A B D E) &  ( (~  (D = E) )  &  ((r1_collsp A F E G) &  ((r1_collsp A B C F) &  ( (~  (B = F) )  &  (G = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_projpl_1,ax, (! [A:$i] :  ((l1_incsp_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_incsp_1 A)) =>  ((r4_projpl_1 A B C D) <=>  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) &  ((r1_incsp_1 A B E) &  ((r1_incsp_1 A C E) & (r1_incsp_1 A D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_projred1,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) & (l1_incsp_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (? [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) &  (? [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) &  (? [E:$i] :  ((m1_subset_1 E (u2_incsp_1 A)) &  ((r1_incsp_1 A B C) &  ((r1_incsp_1 A B D) &  ((r1_incsp_1 A B E) &  ( (~  (C = D) )  &  ( (~  (D = E) )  &  (~  (E = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_projred2,ax, (! [A:$i] :  ( ((v6_incsp_1 A) &  ((v1_incproj A) &  ((v2_incproj A) &  ((v3_incproj A) &  ((v4_incproj A) &  ((v5_incproj A) &  ((v9_incproj A) & (l1_incsp_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_incsp_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u2_incsp_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u2_incsp_1 A)) =>  (~  ( (~ (r1_incsp_1 A B C))  &  ( (~ (r1_incsp_1 A B D))  &  (~  ((k10_xtuple_0 (k1_projred1 A C D B)) = (k1_projred2 A D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_prvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r3_binop_1 (u1_struct_0 A) (k1_group_1 A) (u2_algstr_0 A))) ) ).
tt(t5_prvect_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v2_relat_1 B) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  & (v1_finseq_1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A (k4_card_3 B)) (k4_card_3 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A (k4_card_3 B)) (k4_card_3 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A (k4_card_3 B)) (k4_card_3 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A (k4_card_3 B)) (k4_card_3 B))))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F (k4_card_3 B)) =>  (! [G:$i] :  ((m2_subset_1 G k5_numbers (k4_finseq_1 B)) =>  ((k8_prvect_1 B (k2_binop_1 A (k4_card_3 B) (k4_card_3 B) C E F) G) = (k8_prvect_1 B (k2_binop_1 A (k4_card_3 B) (k4_card_3 B) D E F) G)) ) ) ) ) ) )  => (r8_binop_1 A (k4_card_3 B) (k4_card_3 B) C D)) ) ) ) ) ) ) ) ) ).
tt(t5_prvect_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A B) (k4_card_3 (k10_finseq_1 A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) (k4_card_3 (k10_finseq_1 A B)))))) )  &  ((v2_funct_1 C) &  ((v2_funct_2 C (k4_card_3 (k10_finseq_1 A B))) &  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden D A) & (r2_hidden E B))  =>  ((k1_binop_1 C D E) = (k10_finseq_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) k1_numbers) &  ((v1_seq_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) k1_numbers)))) ) )  =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_xxreal_0 (k1_seq_1 B D) C)) )  => (r1_xxreal_0 (k2_pscomp_1 A B) C)) ) ) ) ) ) ) ).
tt(t5_pua2mss1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( (! [E:$i] :  ((r2_hidden E B) => (r1_tarski E (k1_funct_1 D E))) )  =>  (! [E:$i] :  ((m2_finseq_1 E B) =>  (! [F:$i] :  ((m2_finseq_1 F C) =>  ((r1_tarski (k4_card_3 E) (k4_card_3 F)) <=> (r2_relset_1 k5_numbers C (k1_partfun1 k5_numbers B B C E D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_pythtrip,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( ((k1_pepin A) = (k1_pepin B))  =>  (A = B) ) ) ) ) ) ).
tt(t5_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ( (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ((r1_pboole A E B) <=>  ((r6_pboole A E C) | (r6_pboole A E D)) ) ) )  => (r6_pboole A B (k2_pzfmisc1 A C D))) ) ) ) ) ) ) ) ).
tt(t5_qc_lang1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (A = (k2_zfmisc_1 k5_numbers (k1_qc_lang1 A))) ) ) ).
tt(t5_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_qc_lang1 A)) =>  ( ((k15_qc_lang1 A B D) = (k15_qc_lang1 A C E))  =>  ( (B = C)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_qc_lang3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_qc_lang1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 B) (k8_qc_lang1 B A)) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k2_qc_lang1 B)))  =>  ((k24_qc_lang1 B (k10_qc_lang1 B C D)) = (k23_qc_lang1 B D)) ) ) ) ) ) ) ) ) ).
tt(t5_qc_lang4,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) => (r2_hidden B (k10_xtuple_0 (k2_qc_lang4 A B)))) ) ) ) ).
tt(t5_qmax_1,ax, (! [A:$i] :  ( ((v2_qmax_1 A) & (l1_qmax_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_qmax_1 A)) => (r4_qmax_1 A B B)) ) ) ) ).
tt(t5_quantal1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v4_lattice3 A) &  ((v7_quantal1 A) &  ((v8_quantal1 A) & (l1_quantal1 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((k6_algstr_0 A (k15_lattice3 A B) (k15_lattice3 A C)) = (k15_lattice3 A (a_3_3_quantal1 A B C))) ) ) ) ) ).
tt(t5_quatern2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((k29_quaterni (k6_quaterni A B C D) (k6_quaterni E F G H)) = (k6_quaterni (k9_real_1 A E) (k9_real_1 B F) (k9_real_1 C G) (k9_real_1 D H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((m1_subset_1 A k1_numbers) =>  ((k27_quaterni A k4_quatern2) = (k6_quaterni k6_numbers (k17_quaterni A) k6_numbers k6_numbers)) ) ) ) ).
tt(t5_quaterni,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r1_tarski (k2_enumset1 A B C D) E) <=>  ((r2_hidden A E) &  ((r2_hidden B E) &  ((r2_hidden C E) & (r2_hidden D E)) ) ) ) ) ) ) ) ) ).
tt(t5_quin_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ( (~ (r1_xxreal_0 k6_numbers A))  &  ( (~ (r1_xxreal_0 k6_numbers (k1_quin_1 A B C)))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 A (k3_square_1 D)) (k3_xcmplx_0 B D)) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v5_group_1 A) & (l5_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (k1_quofield A)) => (r2_hidden B (k6_quofield A B))) ) ) ) ).
tt(t5_radix_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  & (r1_xxreal_0 A (k3_nat_d (k4_nat_d C (k1_newton A B)) (k1_newton A (k7_nat_d B 1))))) ) ) ) ) ) ) ) ) ).
tt(t5_radix_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden A (k2_finseq_1 B)) => (r2_hidden (k1_nat_1 A 1) (k2_finseq_1 (k1_nat_1 B 1)))) ) ) ) ) ).
tt(t5_radix_3,ax,(r2_hidden k6_numbers (k1_radix_3 k6_numbers))).
tt(t5_radix_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 3 A) & (r1_radix_1 (k2_xcmplx_0 C 1) B A)) )  =>  ((k7_radix_3 (k2_xcmplx_0 C 1) A (k2_xcmplx_0 C 1) (k10_radix_3 C A (k10_radix_1 A C (k4_nat_d B (k1_newton (k1_radix_1 A) C))))) = (k5_radix_3 (k4_radix_1 C A C (k10_radix_1 A C B)) A)) ) ) ) ) ) ) ) ).
tt(t5_radix_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k2_finseq_1 C)) =>  ((k4_radix_1 A B C (k10_radix_1 B C k6_numbers)) = k6_numbers) ) ) ) ) ) ) ) ).
tt(t5_radix_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_finseq_1 B)) => (r1_xxreal_0 k6_numbers (k4_radix_1 D C B (k10_radix_1 C B A)))) ) ) ) ) ) ) ) ) ).
tt(t5_ramsey_1,ax, (! [A:$i] :  ((k3_group_10 A k6_numbers) = (k1_tarski k6_numbers)) ) ).
tt(t5_random_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (? [C:$i] :  ( ((v1_prob_2 C) & (m2_finseq_1 C (k1_random_1 A)))  &  (? [D:$i] :  ((m2_finseq_1 D (k1_relset_1 A B)) &  ( ((k1_relset_1 A B) = (k3_tarski (k2_relset_1 (k1_random_1 A) C)))  &  ( ((k4_finseq_1 C) = (k4_finseq_1 D))  &  ((v2_funct_1 D) &  ( ((k2_relset_1 (k1_relset_1 A B) D) = (k1_relset_1 A B))  &  ( ((k3_finseq_1 D) = (k5_card_1 (k1_relset_1 A B)))  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 C E) = (k1_tarski (k1_funct_1 D E))) ) ) )  &  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ( ((r2_hidden E (k4_finseq_1 C)) &  ((r2_hidden F (k1_funct_1 C E)) & (r2_hidden G (k1_funct_1 C E))) )  =>  ((k1_seq_1 B F) = (k1_seq_1 B G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_random_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_relset_1 A k1_numbers (k2_mesfun6c 2 A B) (k2_mesfun6c 2 A (k32_valued_1 A k1_numbers B))) & (r2_relset_1 A k1_numbers (k2_mesfun6c 2 A B) (k2_mesfun6c 2 A (k56_valued_1 A k1_numbers B)))) ) ) ) ) ).
tt(t5_ranknull,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v1_matrlin B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  ( ((k1_card_1 (k2_struct_0 B)) = 1)  =>  ((k1_vectsp_9 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t5_ratfunc1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v1_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k11_polynom3 A (k3_polynom5 A B D) C) (k3_polynom5 A (k11_polynom3 A B C) D))) ) ) ) ) ) ) ) ).
tt(t5_rcomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (v2_rcomp_1 (k1_rcomp_1 A B))) ) ) ) ).
tt(t5_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (r1_xxreal_0 B A))  =>  ((k4_seq_4 (k3_rcomp_1 A B)) = B) ) ) ) ) ) ).
tt(t5_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k13_complex1 A B) = (k3_nat_d A B))  =>  ((k4_nat_d A B) = k6_numbers) ) ) ) ) ) ).
tt(t5_real,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((v1_xboole_0 B) |  ((v3_xxreal_0 A) | (v2_xxreal_0 B)) ) ) ) ) ) ) ).
tt(t5_real_lat,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k3_real_lat)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k3_real_lat)) =>  ( ((k1_binop_1 k2_real_lat (k1_binop_1 k1_real_lat A B) B) = B)  &  ( ((k1_binop_1 k2_real_lat B (k1_binop_1 k1_real_lat A B)) = B)  &  ( ((k1_binop_1 k2_real_lat B (k1_binop_1 k1_real_lat B A)) = B)  &  ((k1_binop_1 k2_real_lat (k1_binop_1 k1_real_lat B A) B) = B) ) ) ) ) ) ) ) ).
tt(t5_real_ns1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k4_real_ns1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k4_real_ns1 A))) =>  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ( (B = D)  &  (C = E) )  =>  ((k5_algstr_0 (k4_real_ns1 A) B C) = (k8_euclid A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_realset1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  &  (! [D:$i] :  ((r2_hidden D (k2_zfmisc_1 B B)) => (r2_hidden (k1_funct_1 C D) B)) ) ) ) ) ) ) ).
tt(t5_realset2,ax, (! [A:$i] :  ( ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_vectsp_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 A) (k8_struct_0 A)) =>  (! [C:$i] :  ((m2_subset_1 C (u1_struct_0 A) (k8_struct_0 A)) =>  ((k6_algstr_0 A B C) = (k6_algstr_0 A C B)) ) ) ) ) ) ) ).
tt(t5_realset3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_subset_1 D (u1_struct_0 A) (k8_struct_0 A)) =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) (k8_struct_0 A)) =>  ( ((k1_binop_1 (k4_realset2 A) B (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) D)) = (k1_binop_1 (k4_realset2 A) C (k3_funct_2 (k8_struct_0 A) (k8_struct_0 A) (k5_realset2 A) E)))  <=>  ((k5_binop_1 (u1_struct_0 A) (k4_realset2 A) B E) = (k5_binop_1 (u1_struct_0 A) (k4_realset2 A) D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_rearran1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ( ((v1_rearran1 B) &  ((v2_rearran1 B) & (m2_finseq_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r2_hidden C (k4_finseq_1 B)) &  ((r2_hidden D (k4_finseq_1 B)) &  ( (~  (C = D) )  &  ((k1_funct_1 B C) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_recdef_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r2_hidden A (k4_zfmisc_1 B C D E)) =>  ((r2_hidden (k7_xtuple_0 A) B) &  ((r2_hidden (k8_xtuple_0 A) C) &  ((r2_hidden (k5_xtuple_0 A) D) & (r2_hidden (k2_xtuple_0 A) E)) ) ) ) ) ) ) ) ) ).
tt(t5_reloc,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_ami_3)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_ami_3)) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k5_compos_0 (u1_compos_1 k1_ami_3) A C) = B)  =>  ( ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = k6_numbers) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = 1) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = 2) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = 3) )  &  ( (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = 4) )  &  (~  ((k2_compos_0 (u1_compos_1 k1_ami_3) B) = 5) ) ) ) ) ) )  |  (A = B) ) ) ) ) ) ) ) ) ).
tt(t5_relset_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))) =>  ((r1_tarski (k9_xtuple_0 D) B) => (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B C)))) ) ) ) ) ) ).
tt(t5_relset_2,ax, (! [A:$i] :  (! [B:$i] :  ((k10_eqrel_1 (k6_subset_1 A B)) = (k7_subset_1 (k1_zfmisc_1 A) (k10_eqrel_1 A) (k10_eqrel_1 B))) ) ) ).
tt(t5_revrot_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ((r1_revrot_1 A B (k7_partfun1 A B (k3_finseq_1 B))) =>  ((k2_finseq_5 A B (k7_partfun1 A B (k3_finseq_1 B))) = (k12_finseq_1 A (k7_partfun1 A B (k3_finseq_1 B)))) ) ) ) ) ) ).
tt(t5_rewrite1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ( (A = (k7_finseq_1 (k9_finseq_1 B) C))  &  ((k3_finseq_1 A) = (k2_nat_1 (k3_finseq_1 C) 1)) ) ) ) ) ) ) ) ) ) ).
tt(t5_rewrite2,ax, (! [A:$i] :  ( ((v5_ordinal1 A) &  ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finset_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_rewrite2 B)) ) )  =>  ( ((k3_finseq_1 (k1_rewrite2 A B)) = (k3_finseq_1 B))  &  ((k3_finseq_1 (k2_rewrite2 A B)) = (k3_finseq_1 B)) ) ) ) ) ) ).
tt(t5_rewrite3,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m1_rewrite1 B A) =>  (~  ( (~ (r1_xxreal_0 (k3_finseq_1 B) 1))  &  (! [C:$i] :  ((m1_rewrite1 C A) =>  (~  ( ((k7_finseq_1 (k9_finseq_1 (k1_funct_1 B 1)) C) = B)  &  ((k2_xcmplx_0 (k3_finseq_1 C) 1) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_rfinseq2,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (A = (k10_finseq_1 B C))  =>  ( ((k3_rfinseq2 A) = (k4_xxreal_0 B C))  &  ((k1_rfinseq2 A) = (k15_funcop_1 k5_numbers B (k4_xxreal_0 B C) 1 2)) ) ) ) ) ) ) ) ) ).
tt(t5_rfinseq,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ((v1_finset_1 B) =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  & (r2_classes1 (k5_relat_1 A B) C)) ) ) ) ) ) ).
tt(t5_rfunct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  ( ((k8_relat_1 (k54_valued_1 A) (k1_tarski k6_numbers)) = (k8_relat_1 A (k1_tarski k6_numbers)))  &  ((k8_relat_1 (k30_valued_1 A) (k1_tarski k6_numbers)) = (k8_relat_1 A (k1_tarski k6_numbers))) ) ) ) ).
tt(t5_rfunct_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k5_numbers) &  ((v5_valued_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  => (r2_relset_1 k5_numbers k1_numbers (k37_valued_1 k5_numbers k1_numbers (k2_valued_0 k1_numbers B A)) (k2_valued_0 k1_numbers B (k37_valued_1 k5_numbers k1_numbers A)))) ) ) ) ).
tt(t5_rfunct_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k1_rfunct_3 (k2_xcmplx_0 A B)) (k7_real_1 (k1_rfunct_3 A) (k1_rfunct_3 B)))) ) ) ) ).
tt(t5_rfunct_4,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k15_rvsum_1 A (k5_finseq_2 k1_numbers A k6_numbers) B) = (k5_finseq_2 k1_numbers A k6_numbers)) ) ) ) ) ).
tt(t5_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) <=> (v4_xxreal_2 (k2_relset_1 k1_numbers A))) ) ) ).
tt(t5_rinfsup2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (v1_xboole_0 (a_2_0_rinfsup2 A B)))  & (m1_subset_1 (a_2_0_rinfsup2 A B) (k1_zfmisc_1 k7_numbers))) ) ) ) ) ).
tt(t5_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden C (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k1_ring_1 A B) D)) <=> (r2_hidden (k5_algstr_0 A C D) B)) ) ) ) ) ) ) ) ) ).
tt(t5_ringcat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) )  =>  ( ((r1_ringcat1 A B) & (r1_ringcat1 B C))  => (r1_ringcat1 A C)) ) ) ) ) ) ) ).
tt(t5_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_rusub_4 A B (k1_algstr_0 A C D)) = (k5_rusub_4 A (k5_rusub_4 A B D) C)) ) ) ) ) ) ) ) ) ).
tt(t5_rlaffin2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k1_rlaffin2 A B) (k3_convex1 A B))) ) ) ) ).
tt(t5_rlaffin3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v1_rlvect_5 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlaffin1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_xxreal_0 (k5_card_1 B) (k23_binop_2 1 (k1_rlvect_5 A)))) ) ) ) ).
tt(t5_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((u1_struct_0 A) = B)  => (v1_rlsub_1 B A)) ) ) ) ) ).
tt(t5_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((k1_rlsub_2 A B C) = (k1_rlsub_2 A C B)) ) ) ) ) ) ) ).
tt(t5_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k5_rusub_4 A B (k4_struct_0 A)) = B) ) ) ) ) ).
tt(t5_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k1_algstr_0 A B (k4_algstr_0 A B)) = (k4_struct_0 A))  &  ((k1_algstr_0 A (k4_algstr_0 A B) B) = (k4_struct_0 A)) ) ) ) ) ) ).
tt(t5_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k3_finseq_1 B) = (k3_finseq_1 D))  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 D E) = (k5_algstr_0 A (k7_partfun1 (u1_struct_0 A) B E) (k7_partfun1 (u1_struct_0 A) C E))) ) ) ) ) )  =>  ((k4_rlvect_1 A D) = (k5_algstr_0 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t5_rlvect_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (v1_rlvect_3 C A))  => (v1_rlvect_3 B A)) ) ) ) ) ) ) ).
tt(t5_rlvect_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden B (k3_rlsub_1 A C D)) =>  ((k3_rlsub_1 A C D) = (k3_rlsub_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_rlvect_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((r1_xboole_0 (k3_rlvect_2 A B) (k10_xtuple_0 C)) =>  ((k4_rlvect_1 A (k5_rlvect_2 A C B)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ).
tt(t5_rlvect_x,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m2_rlvect_2 C A B) =>  (! [D:$i] :  ((m2_rlvect_2 D A B) =>  ( ((r1_tarski (k2_relset_1 k1_numbers C) k4_numbers) & (r1_tarski (k2_relset_1 k1_numbers D) k4_numbers))  => (r1_tarski (k2_relset_1 k1_numbers (k7_rlvect_2 A C D)) k4_numbers)) ) ) ) ) ) ) ) ) ).
tt(t5_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((u1_struct_0 B) = C)  => (v1_rmod_2 C A B)) ) ) ) ) ) ) ).
tt(t5_rmod_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  ((k1_rmod_3 A B C D) = (k1_rmod_3 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t5_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  ((k1_rmod_4 A B (k1_struct_0 B)) = (k4_struct_0 B)) ) ) ) ) ).
tt(t5_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v5_lattices A) &  ((v6_robbins1 A) &  ((v7_robbins1 A) & (l2_robbins1 A)) ) ) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k5_robbins1 A B C) = B)  &  ((k5_robbins1 A C (k3_robbins1 A C)) = B) ) ) ) ) ) ) ) ).
tt(t5_robbins2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_robbins2 A) & (l2_robbins1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A B C)) (k3_robbins1 A (k1_lattices A (k3_robbins1 A (k1_lattices A D B)) C)))) = C) ) ) ) ) ) ) ) ) ).
tt(t5_robbins3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_lattices A))  =>  ((v10_lattices A) <=>  ((v2_robbins3 A) &  ((v1_robbins3 A) &  ((v3_robbins3 A) & (v9_lattices A)) ) ) ) ) ) ).
tt(t5_robbins4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v12_lattices A) &  ((v10_robbins1 A) &  ((v8_robbins3 A) &  ((v9_robbins3 A) & (l4_robbins1 A)) ) ) ) ) )  => (v1_robbins4 A)) ) ).
tt(t5_rolle,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (~ (r1_xxreal_0 B A))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (~  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers C)) &  ((r1_tarski (k1_rcomp_1 A B) (k1_relset_1 k1_numbers D)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C (k1_rcomp_1 A B))) &  ((r2_fdiff_1 C (k2_rcomp_1 A B)) &  ((v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D (k1_rcomp_1 A B))) &  ((r2_fdiff_1 D (k2_rcomp_1 A B)) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k2_rcomp_1 A B)) &  ((k8_real_1 (k9_real_1 (k1_seq_1 C B) (k1_seq_1 C A)) (k1_fdiff_1 D E)) = (k8_real_1 (k9_real_1 (k1_seq_1 D B) (k1_seq_1 D A)) (k1_fdiff_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_roughs_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k3_card_3 (k8_finseq_1 A B C)) = (k2_xboole_0 (k3_card_3 B) (k3_card_3 C))) ) ) ) ) ) ).
tt(t5_rpr_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  ( ((v3_card_1 C 1) & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  ((r1_tarski B C) =>  (B = C) ) ) ) ) ) ) ) ).
tt(t5_rsspace2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_comseq_2 B) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k1_seq_1 B D) A)) ) ) ) ) )  | (r1_xxreal_0 (k2_seq_2 B) A)) ) ) ) ) ) ).
tt(t5_rsspace3,ax, ( (~ (v2_struct_0 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)))  &  ((v13_algstr_0 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v2_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v3_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v4_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v5_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v6_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v7_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) &  ((v8_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3)) & (l1_rlvect_1 (g1_normsp_1 k1_rsspace3 (k10_rsspace k7_rsspace k1_rsspace3) (k8_rsspace k7_rsspace k1_rsspace3) (k9_rsspace k7_rsspace k1_rsspace3) k2_rsspace3))) ) ) ) ) ) ) ) ) ).
tt(t5_rsspace4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D A) =>  ((k3_funct_2 A (u1_struct_0 B) C D) = (k4_struct_0 B)) ) )  => (v1_rsspace4 C A B)) ) ) ) ) ) ) ).
tt(t5_rsspace,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) =>  ((k3_rlvect_1 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace) A (k4_struct_0 (g1_rlvect_1 k1_rsspace k6_rsspace k4_rsspace k5_rsspace))) = A) ) ) ).
tt(t5_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k4_struct_0 B) = (k4_struct_0 C)) ) ) ) ) ) ) ).
tt(t5_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_rusub_1 C A) =>  ((k1_rusub_2 A B C) = (k1_rusub_2 A C B)) ) ) ) ) ) ) ).
tt(t5_rusub_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (u1_struct_0 B))  =>  ((k1_rusub_3 A C) = B) ) ) ) ) ) ) ) ).
tt(t5_rusub_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_3 B A) =>  (! [C:$i] :  ((m1_rusub_3 C A) =>  ((v1_rusub_4 A) =>  ((k1_card_1 B) = (k1_card_1 C)) ) ) ) ) ) ) ) ).
tt(t5_rusub_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_xboole_0 B) | (v1_xboole_0 C))  => (v1_xboole_0 (k6_rusub_4 A B C))) ) ) ) ) ) ) ).
tt(t5_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_seq_1 (k3_rvsum_1 A) B) = (k11_binop_2 A B)) ) ) ) ) ).
tt(t5_rvsum_2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_rvsum_2 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k2_numbers (k3_binop_2 A B))) ) ) ) ) ).
tt(t5_scm_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_ami_3)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 D (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_ami_3)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_ami_3)))  =>  ( ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D B)) = C)  &  ((k3_compos_1 k1_ami_3 A C) = (k3_ami_3 E F)) )  =>  ( ((k5_memstr_0 2 k1_ami_3 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1))) = (k2_nat_1 C 1))  &  ( ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) E) = (k2_xcmplx_0 (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) E) (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) F)))  &  (! [G:$i] :  ( ((v1_ami_2 G) & (m1_subset_1 G (u1_struct_0 k1_ami_3)))  =>  ( (~  (G = E) )  =>  ((k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D (k2_nat_1 B 1)) G) = (k1_funct_1 (k5_extpro_1 2 k1_ami_3 A D B) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmbsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (B = (k2_nat_1 C 1)) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 (k4_scmfsa_2 B) D) (k1_scmfsa_m A)) (k4_scmfsa_2 (k2_nat_1 C 1))) = (k1_funct_1 A (k4_scmfsa_2 (k2_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_scm_comp,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B (u1_struct_0 k1_scm_comp) (k7_dtconstr k1_scm_comp)) =>  (! [C:$i] :  ((m1_dtconstr C (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  (! [D:$i] :  ((m1_dtconstr D (u1_struct_0 k1_scm_comp) (k5_trees_3 (u1_struct_0 k1_scm_comp)) (k4_dtconstr k1_scm_comp)) =>  ((k12_scm_comp A (k2_scm_comp B C D)) = (k10_scm_comp B (k12_scm_comp A C) (k12_scm_comp A D))) ) ) ) ) ) ) ) ) ).
tt(t5_scmfsa10,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k9_scmfsa_2 A B) = (k3_xtuple_0 4 k1_xboole_0 (k10_finseq_1 A B))) ) ) ) ) ).
tt(t5_scmfsa_1,ax,(r2_hidden k5_numbers k1_scmfsa_1)).
tt(t5_scmfsa_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  (~ (v2_compos_1 A k1_scmfsa_2)) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_finset_1 B) & (v4_extpro_1 B 3 k1_scmfsa_2 A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((r1_tarski B C) & (r1_tarski B D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) & (r1_tarski A F))  =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  (! [I:$i] :  ( ((v1_ami_2 I) & (m1_subset_1 I (u1_struct_0 k1_scmfsa_2)))  =>  ( ( ((k3_extpro_1 3 k1_scmfsa_2 E (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k6_scmfsa_2 H I))  & (r2_hidden H (k9_xtuple_0 B)))  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) I) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmfsa6b,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  =>  (~  ( ((k5_memstr_0 3 k1_scmfsa_2 B) = A)  &  ( ((k3_compos_1 k1_scmfsa_2 C A) = (k11_scmfsa_2 A))  & (r1_extpro_1 3 k1_scmfsa_2 C B)) ) ) ) ) ) ) ) ) ).
tt(t5_scmfsa6c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_scmfsa6c C) & (m1_subset_1 C (u1_compos_1 k1_scmfsa_2)))  => (r8_pboole (u1_struct_0 k1_scmfsa_2) (k2_extpro_1 3 k1_scmfsa_2 C (k1_scmfsa_m A)) (k1_scmfsa6b (k11_compos_1 k1_scmfsa_2 C) A B))) ) ) ) ) ) ).
tt(t5_scmfsa_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmfsa_2)) & (v5_memstr_0 B 3 k1_scmfsa_2 k6_numbers)) ) ) ) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((v1_int_1 D) =>  ((r1_tarski (k2_scmfsa_7 C D) A) =>  ( (C = (k4_scmfsa_2 k6_numbers))  |  ( (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r1_xxreal_0 E (k1_afinsq_1 (k2_scmfsa_7 C D))) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A B E)) = E)  &  ( (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (F = C) )  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A B E) F) = (k1_funct_1 B F)) ) ) )  &  (! [F:$i] :  ((m1_scmfsa_2 F) =>  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 A B E) F) = (k18_scmfsa_2 B F)) ) ) ) ) ) ) )  &  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 A B (k1_afinsq_1 (k2_scmfsa_7 C D))) C) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmfsa7b,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (~ (r3_scmfsa7b (k2_compos_1 k1_scmfsa_2) A)) ) ) ).
tt(t5_scmfsa8b,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v1_finset_1 E) & (v1_afinsq_1 E)) ) ) ) ) )  =>  ( ( ((k6_memstr_0 3 k1_scmfsa_2 C) = (k6_memstr_0 3 k1_scmfsa_2 D))  &  ((r5_scmfsa7b E C A) & (r6_scmfsa7b E C A)) )  =>  ((r5_scmfsa7b E D B) & (r6_scmfsa7b E D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmfsa8c,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  ( (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) & (v1_partfun1 C k5_numbers)) ) ) )  => (r6_scmfsa7b A (k1_scmfsa_m B) C)) ) ) )  => (v5_extpro_1 (k8_memstr_0 3 k1_scmfsa_2 (k16_funcop_1 (k4_scmfsa_2 k6_numbers) 1)) 3 k1_scmfsa_2 A)) ) ) ).
tt(t5_scmfsa9a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k2_sf_mastr (k1_scmfsa8a A)) = k1_xboole_0) ) ) ).
tt(t5_scmfsa_9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ( (~ (v1_xboole_0 A))  &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  ((k5_card_1 (k2_scmfsa_9 B A)) = (k2_nat_1 (k5_card_1 A) 6)) ) ) ) ) ).
tt(t5_scmfsa_i,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C k1_scmfsa_i) =>  ((r2_hidden A (k2_tarski 11 12)) => (r2_hidden (k3_xtuple_0 A k1_xboole_0 (k10_finseq_1 B C)) k2_scmfsa_i)) ) ) ) ) ) ).
tt(t5_scmfsa_m,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2))) ) )  =>  ( ((k1_funct_1 (k1_scmfsa_m A) (k4_scmfsa_2 k6_numbers)) = 1)  &  ((k1_funct_1 (k1_scmfsa_m A) (k4_struct_0 k1_scmfsa_2)) = k6_numbers) ) ) ) ).
tt(t5_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_scm_halt C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ( (~ (r2_hidden D (k4_sf_mastr C)))  =>  ((k18_scmfsa_2 (k1_scmfsa6b C A B) D) = (k18_scmfsa_2 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_scm_inst,ax, (! [A:$i] :  ((m1_subset_1 A k3_scm_inst) =>  (! [B:$i] :  ((m1_subset_1 B k2_scm_inst) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  (! [D:$i] :  ((m1_subset_1 D (k7_card_1 9)) =>  ( (A = (k3_xtuple_0 D k1_xboole_0 (k2_finseq_4 k2_scm_inst B C)))  =>  ( ((k4_scm_inst A) = B)  &  ((k5_scm_inst A) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((r6_scmfsa7b C (k1_scmfsa_m B) A) =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)))) D)) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmpds_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  ((k4_memstr_0 2 k1_scmpds_2 A) = k4_numbers) ) ) ).
tt(t5_scmpds_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 A (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ((k9_xtuple_0 A) = (k2_xboole_0 (k1_tarski (k4_struct_0 k1_scmpds_2)) k2_ami_2)) ) ) ).
tt(t5_scmpds_8,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_card_3 (k2_memstr_0 2 k1_scmpds_2)) k5_numbers)))) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  =>  ( ((r1_xxreal_0 (k1_funct_1 C A) k6_numbers) =>  ((k1_recdef_1 B C) = k6_numbers) )  &  ( (~ (r1_xxreal_0 (k1_funct_1 C A) k6_numbers))  =>  ((k1_recdef_1 B C) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t5_scmpds_9,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k1_amistd_1 2 k1_scmpds_2 B (k6_scmpds_2 A C)) = (k1_tarski (k1_ordinal1 B))) ) ) ) ) ) ) ).
tt(t5_scmpds_i,ax, (! [A:$i] :  ((m2_subset_1 A k4_ordinal1 (k7_card_1 15)) =>  (! [B:$i] :  ((m1_subset_1 B k1_scmpds_i) =>  (! [C:$i] :  ((m1_subset_1 C k2_scm_inst) =>  (! [D:$i] :  ((v1_int_1 D) =>  ( (B = (k3_xtuple_0 A k1_xboole_0 (k2_scmpds_i C D)))  =>  ( ((k5_scmpds_i B) = C)  &  ((k6_scmpds_i B) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scmp_gcd,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmpds_2)) =>  ((k5_card_1 (k4_scmpds_4 A B)) = 2) ) ) ) ) ).
tt(t5_scmring1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  ((k5_card_3 k5_numbers (k4_card_3 (k3_relat_1 k3_ami_2 (k1_scmring1 A)))) = k5_numbers) ) ) ).
tt(t5_scmring2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) => (r2_hidden (k3_xtuple_0 6 (k12_finseq_1 k5_numbers B) k1_xboole_0) (k1_scmringi A))) ) ) ) ).
tt(t5_scmring3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 (k1_scmring2 A))))  =>  ((k2_compos_0 (u1_compos_1 (k1_scmring2 A)) (k3_scmring2 A B C)) = 1) ) ) ) ) ) ) ).
tt(t5_scmring4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 (k1_scmring2 A))))  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 (k1_scmring2 A))) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 2 (k1_scmring2 A))) & (v1_partfun1 D (u1_struct_0 (k1_scmring2 A)))) ) ) )  =>  ((k2_scmring2 A D B) = (k2_scmring2 A (k1_funct_4 D (k7_memstr_0 2 (k1_scmring2 A) C)) B)) ) ) ) ) ) ) ) ) ).
tt(t5_scmringi,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  => (r1_tarski (k1_scmringi A) (k3_zfmisc_1 k5_numbers (k13_finseq_1 k5_numbers) (k10_xtuple_0 (k1_scmringi A))))) ) ).
tt(t5_scmyciel,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_ordinal1 3 (k1_card_1 A)) &  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden C A) &  ((r2_hidden D A) &  ( (~  (C = B) )  &  ( (~  (D = B) )  &  (~  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scpinvar,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_finseq_1 E k4_numbers) =>  ( ((r1_xxreal_0 3 D) &  ((r1_scpisort E B D) &  ((k3_finseq_1 E) = C) ) )  =>  ( ((k1_funct_1 (k6_scmpds_4 (k1_scpinvar C D) B A) (k1_scmp_gcd 1)) = (k1_gr_cy_1 E))  & (v2_scmpds_4 (k1_scpinvar C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_scpisort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v2_compos_1 C k1_scmpds_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v4_scmpds_4 D) &  ((v1_scmpds_5 D) & (m1_subset_1 D (u1_compos_1 k1_scmpds_2))) )  =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ((r1_scmpds_6 (k3_scmpds_4 C D) B A) & (r2_scmpds_6 (k3_scmpds_4 C D) B A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_scpqsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 B (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 B 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ( ((v1_ami_2 F) & (m1_subset_1 F (u1_struct_0 k1_scmpds_2)))  =>  (! [G:$i] :  ((v1_int_1 G) =>  (! [H:$i] :  ((v1_int_1 H) =>  ( ((r1_xxreal_0 (k2_xcmplx_0 H (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) G))) (k1_funct_1 B E)) &  (! [I:$i] :  ( ((v1_relat_1 I) &  ((v4_relat_1 I (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 I) &  ((v5_funct_1 I (k2_memstr_0 2 k1_scmpds_2)) &  ((v1_partfun1 I (u1_struct_0 k1_scmpds_2)) & (v5_memstr_0 I 2 k1_scmpds_2 k6_numbers)) ) ) ) )  =>  (! [J:$i] :  ( ((v1_relat_1 J) &  ((v4_relat_1 J k5_numbers) &  ((v5_relat_1 J (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 J) & (v1_partfun1 J k5_numbers)) ) ) )  =>  ( ((r1_xxreal_0 (k2_xcmplx_0 H (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) G))) (k1_funct_1 I E)) &  ( ((k1_funct_1 I F) = (k1_funct_1 B F))  &  ((k1_funct_1 I D) = (k1_funct_1 B D)) ) )  =>  ((r1_xxreal_0 (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) G)) k6_numbers) |  ( ((k1_funct_1 (k6_scmpds_4 C I J) D) = (k1_funct_1 I D))  &  ((r1_scmpds_6 C I J) &  ((r2_scmpds_6 C I J) &  ( (~ (r1_xxreal_0 (k1_funct_1 I (k2_scmpds_2 (k1_funct_1 B D) G)) (k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 (k1_funct_1 B D) G))))  &  ((r1_xxreal_0 (k2_xcmplx_0 H (k1_funct_1 (k6_scmpds_4 C I J) (k2_scmpds_2 (k1_funct_1 B D) G))) (k1_funct_1 (k6_scmpds_4 C I J) E)) &  ((k1_funct_1 (k6_scmpds_4 C I J) F) = (k1_funct_1 I F)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ((r1_scmpds_6 (k2_scmpds_8 D G C) B A) &  ((r2_scmpds_6 (k2_scmpds_8 D G C) B A) &  ( (~ (r1_xxreal_0 (k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) G)) k6_numbers))  => (r6_pboole (u1_struct_0 k1_scmpds_2) (k6_scmpds_4 (k2_scmpds_8 D G C) B A) (k6_scmpds_4 (k2_scmpds_8 D G C) (k8_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 C B A)) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_analoaf A B C D E) => (r2_analoaf A B C E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_seq_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_relat_1 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~  ((k1_seq_1 A B) = k6_numbers) ) ) ) ) ) ) ).
tt(t5_seq_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v2_comseq_2 A) & (v2_comseq_2 B))  => (v2_comseq_2 (k3_valued_1 k5_numbers k1_numbers k1_numbers A B))) ) ) ) ) ).
tt(t5_seq_4,ax, (! [A:$i] :  ((v3_membered A) =>  (~  ( (~ (v1_xboole_0 A))  &  ((v4_xxreal_2 A) &  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (! [C:$i] :  ((v1_xreal_0 C) =>  ((r2_hidden C A) => (r1_xxreal_0 C B)) ) )  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  &  (! [D:$i] :  ((v1_xreal_0 D) =>  (~  ((r2_hidden D A) &  (~ (r1_xxreal_0 D (k10_binop_2 B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_seqfunc,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ((r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k8_seqfunc A B C) (k8_seqfunc A C B)) & (r2_relset_1 k5_numbers (k4_partfun1 A k1_numbers) (k8_seqfunc A (k8_seqfunc A B C) D) (k8_seqfunc A B (k8_seqfunc A C D)))) ) ) ) ) ) ) ) ) ).
tt(t5_seqm_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k8_nat_1 k1_numbers A B) (k8_nat_1 k1_numbers A (k2_nat_1 B C)))) ) ) ) ) ) ) ).
tt(t5_series_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_membered A) & (v7_membered A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((k1_valued_1 (k2_series_1 B) (k2_series_1 C)) = (k2_series_1 (k1_series_1 A B C))) ) ) ) ) ) ) ).
tt(t5_series_2,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 A B) = (k2_nat_1 (k4_nat_1 2 B) 1)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((k1_seq_1 (k3_series_1 A) B) = (k13_newton (k2_nat_1 B 1) 2)) ) ) ) ) ) ).
tt(t5_series_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) => (r1_xxreal_0 (k4_square_1 (k13_complex1 (k2_xcmplx_0 A B) 2)) (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2))) ) ) ) ).
tt(t5_series_4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k1_newton (k6_xcmplx_0 A B) 3) = (k6_xcmplx_0 (k2_xcmplx_0 (k6_xcmplx_0 (k1_newton A 3) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton A 2)) B)) (k3_xcmplx_0 (k3_xcmplx_0 3 (k1_newton B 2)) A)) (k1_newton B 3))) ) ) ) ) ).
tt(t5_series_5,ax, (! [A:$i] :  ( ((v1_xreal_0 A) & (v2_xxreal_0 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k13_complex1 (k2_xcmplx_0 B (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2))) (k2_xcmplx_0 A (k6_square_1 (k13_complex1 (k2_xcmplx_0 (k3_square_1 A) (k3_square_1 B)) 2)))) (k6_square_1 (k13_complex1 A B)))) ) ) ) ) ) ).
tt(t5_setfam_1,ax, (! [A:$i] :  (! [B:$i] :  ( (! [C:$i] :  ((r2_hidden C A) => (r1_tarski B C)) )  =>  ( (A = k1_xboole_0)  | (r1_tarski B (k1_setfam_1 A))) ) ) ) ).
tt(t5_setlim_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers A)))) )  =>  ((k2_relset_1 A B) = (a_2_0_setlim_1 A B)) ) ) ) ) ).
tt(t5_setlim_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 B))))) )  =>  ((k10_nat_1 (k9_setfam_1 B) (k2_setlim_2 B C D) A) = (k2_setlim_2 B (k10_nat_1 (k9_setfam_1 B) C A) (k10_nat_1 (k9_setfam_1 B) D A))) ) ) ) ) ) ) ) ).
tt(t5_setwop_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k5_finsub_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k5_finsub_1 B)) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 C C) C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C C) C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H B C) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v1_binop_1 F C) & (v2_binop_1 F C))  =>  ( ( (E = k1_xboole_0)  &  (~ (v1_setwiseo F C)) )  |  ( (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (~  ( ((k9_xtuple_0 I) = E)  &  ( ((k10_xtuple_0 I) = D)  &  ((v2_funct_1 I) &  ((k2_partfun1 B C H E) = (k3_relat_1 I G)) ) ) ) ) ) )  |  ((k7_setwiseo B C F E H) = (k7_setwiseo A C F D G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_sfmastr1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) &  ((v1_afinsq_1 D) & (v1_scmfsa7b D)) ) ) ) ) ) )  =>  ( ((r6_scmfsa7b D (k1_scmfsa_m B) A) &  ((r6_scmfsa7b C (k1_scmfsa6b D B A) A) &  ((r5_scmfsa7b D (k1_scmfsa_m B) A) & (r5_scmfsa7b C (k1_scmfsa6b D B A) A)) ) )  =>  ((k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k3_scmfsa6a D C)) (k1_scmfsa_m B)) = (k2_nat_1 (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k1_scmfsa_m B)) 1) (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 (k1_funct_4 A D) C) (k1_scmfsa_m (k6_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A D) (k1_scmfsa_m B)))))) ) ) ) ) ) ) ) ) ) ).
tt(t5_sfmastr2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ( ( ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B))  =>  ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B)) )  &  ( ((r5_scmfsa7b C (k1_scmfsa_m A) B) & (r6_scmfsa7b C (k1_scmfsa_m A) B))  =>  ((r5_scmfsa7b C A B) & (r6_scmfsa7b C A B)) ) ) ) ) ) ) ) ) ) ).
tt(t5_sfmastr3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k14_scmfsa_2 B C D) A) B) = (k7_partfun1 k4_numbers (k18_scmfsa_2 A D) (k1_int_2 (k1_funct_1 A C)))) ) ) ) ) ) ) ) ) ).
tt(t5_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( ((k10_scmfsa_2 A B) = (k10_scmfsa_2 C D))  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_sgraph1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( (~ (r1_xxreal_0 B A))  => (r1_xboole_0 (k2_finseq_1 A) (k1_sgraph1 B C))) ) ) ) ) ) ) ).
tt(t5_sheffer1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_lattices A) &  ((v6_lattices A) &  ((v11_lattices A) &  ((v7_robbins1 A) &  ((v1_sheffer1 A) &  ((v2_sheffer1 A) &  ((v3_sheffer1 A) &  ((v4_sheffer1 A) & (l3_lattices A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_lattices A B (k2_sheffer1 A)) = (k2_sheffer1 A)) ) ) ) ) ).
tt(t5_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A B B) B)) = (k5_sheffer1 A B B)) ) ) ) ) ).
tt(t5_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((k1_simplex0 (k2_xboole_0 A B)) = (k2_xboole_0 (k1_simplex0 A) (k1_simplex0 B))) ) ) ).
tt(t5_simplex1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_rlvect_1 A))  =>  (! [B:$i] :  ((m1_simplex0 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((v3_pre_topc C B) => (r1_tarski (k3_convex1 A (k1_simplex1 A B C)) (k3_simplex1 A B))) ) ) ) ) ) ) ).
tt(t5_simplex2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) & (l1_metric_1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ( (~ (v3_pencil_1 C))  & (l1_pre_topc C))  =>  ( ((v1_simplex2 C A) &  ((v3_pre_topc B C) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 C)))) )  => (v6_tbsp_1 B A)) ) ) ) ) ) ) ).
tt(t5_sincos10,ax, ((r2_fdiff_1 k1_fdiff_9 (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) &  (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A (k2_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) =>  ((k1_fdiff_1 k1_fdiff_9 A) = (k10_real_1 (k1_seq_1 k16_sin_cos A) (k5_square_1 (k1_seq_1 k19_sin_cos A)))) ) ) ) ) ).
tt(t5_sin_cos2,ax,(v6_valued_0 (k2_partfun1 k1_numbers k1_numbers k19_sin_cos (k2_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)))).
tt(t5_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ((k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 (k4_binop_2 A B)) = (k4_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 B)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k2_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k1_sin_cos3 B)))) ) ) ) ) ).
tt(t5_sin_cos4,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k3_xcmplx_0 (k20_sin_cos A) (k20_sin_cos A)) = (k6_xcmplx_0 1 (k3_xcmplx_0 (k17_sin_cos A) (k17_sin_cos A)))) ) ) ).
tt(t5_sin_cos5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k18_sin_cos (k8_real_1 2 A)) = (k8_real_1 (k8_real_1 2 (k17_sin_cos A)) (k20_sin_cos A))) ) ) ).
tt(t5_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 (k1_real_1 1) (k20_sin_cos A))) ) ).
tt(t5_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (~ (r1_xxreal_0 (k9_binop_2 (k7_square_1 (k9_binop_2 (k3_square_1 A) 1)) A) k6_numbers)) ) ) ).
tt(t5_sin_cos8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((k6_sin_cos2 A) = (k7_xcmplx_0 1 (k6_square_1 (k6_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A))))))  &  ((k3_sin_cos2 A) = (k7_xcmplx_0 (k9_sin_cos2 A) (k6_square_1 (k6_xcmplx_0 1 (k5_square_1 (k9_sin_cos2 A)))))) ) ) ) ).
tt(t5_sin_cos9,ax,(v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k29_sin_cos (k2_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))))).
tt(t5_sin_cos,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((k8_nat_1 k2_numbers (k10_comseq_3 B) A) = (k8_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 (k7_sin_cos B)) A) (k8_nat_1 k2_numbers B A))) ) ) ) ) ).
tt(t5_sppol_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k14_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_euclid A)) =>  ( ( (D = B)  &  (E = C) )  =>  ((k4_metric_1 (k14_euclid A) B C) = (k12_euclid (k8_euclid A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_sppol_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 (k1_nat_1 B 1) (k6_xcmplx_0 (k3_finseq_1 A) C)))  =>  ((k2_topreal1 2 (k2_rfinseq (u1_struct_0 (k15_euclid 2)) C A) B) = (k2_topreal1 2 A (k2_xcmplx_0 C B))) ) ) ) ) ) ) ) ).
tt(t5_sprect_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r3_connsp_1 A C B) => (r1_tarski B C)) ) ) ) ) ) ) ).
tt(t5_sprect_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_finseq_1 D C) =>  ( ((r2_hidden A (k4_finseq_1 D)) & (r2_hidden B (k4_finseq_1 D)))  => (r1_xxreal_0 1 (k3_finseq_1 (k3_finseq_6 C D A B)))) ) ) ) ) ) ) ) ) ).
tt(t5_sprect_3,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ( (B = (k1_rlvect_1 (k15_euclid A) (k3_rlvect_1 (k15_euclid A) B C) (k10_real_1 1 2)))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t5_sprect_4,ax, (! [A:$i] :  ( ((v4_topreal1 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2))))  =>  (! [B:$i] :  ( ((v4_pre_topc B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ( (~ (r1_xboole_0 (k3_topreal1 2 A) B))  &  ( (~ (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)) B))  &  (~  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k3_topreal1 2 (k2_jordan3 A (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) B) = (k1_tarski (k2_jordan5c (k3_topreal1 2 A) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))))) ) ) ) ) ) ) ) ) ).
tt(t5_sprect_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (~  ((r2_hidden C (k10_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 B)) &  ((r2_hidden E (k10_xtuple_0 B)) &  ((r1_xxreal_0 (k4_finseq_4 B C) (k4_finseq_4 B D)) &  ( (~ (r1_xxreal_0 (k4_finseq_4 B E) (k4_finseq_4 B D)))  & (r1_xxreal_0 (k4_finseq_4 (k1_finseq_6 A B C) E) (k4_finseq_4 (k1_finseq_6 A B C) D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_square_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k3_square_1 (k6_xcmplx_0 A B)) = (k2_xcmplx_0 (k6_xcmplx_0 (k3_square_1 A) (k3_xcmplx_0 (k3_xcmplx_0 2 A) B)) (k3_square_1 B))) ) ) ) ) ).
tt(t5_stacks_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_stacks_1 A) &  ((v3_stacks_1 A) &  ((v4_stacks_1 A) &  ((v5_stacks_1 A) &  ((v6_stacks_1 A) & (l1_stacks_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((r1_stacks_1 A B) =>  ((k9_stacks_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t5_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( ((k5_nat_1 (k6_domain_1 k5_numbers A)) = A)  &  ((k6_seq_4 (k6_domain_1 k5_numbers A)) = A) ) ) ) ).
tt(t5_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ( ((v5_relat_1 D (k3_qc_lang1 A)) &  ((v3_card_1 D B) & (m2_finseq_1 D (k2_qc_lang1 A))) )  =>  ((r2_hidden C (k1_relset_1 k5_numbers D)) => (m2_subset_1 (k1_funct_1 D C) (k2_qc_lang1 A) (k3_qc_lang1 A))) ) ) ) ) ) ) ) ) ).
tt(t5_subset_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E B) <=>  ((r2_hidden E C) | (r2_hidden E D)) ) ) )  =>  (B = (k4_subset_1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t5_subset,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden A B) &  ((m1_subset_1 B (k1_zfmisc_1 C)) & (v1_xboole_0 C)) ) ) ) ) ) ).
tt(t5_substlat,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k5_finsub_1 (k4_partfun1 A B))) =>  (! [D:$i] :  (! [E:$i] :  ( ((r2_hidden C (k1_substlat A B)) &  ((r2_hidden D C) &  ((r2_hidden E C) & (r1_tarski D E)) ) )  =>  (D = E) ) ) ) ) ) ) ) ).
tt(t5_substut1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((v4_qc_lang1 B A) =>  ((k9_substut1 A B) = (k4_subset_1 (k3_qc_lang1 A) (k9_substut1 A (k19_qc_lang1 A B)) (k9_substut1 A (k20_qc_lang1 A B)))) ) ) ) ) ) ).
tt(t5_substut2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ( (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (? [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A E) = B)  &  ((k19_substut1 A E) = D) ) ) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (? [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A E) = C)  &  ((k19_substut1 A E) = D) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_substut1 A)) =>  (? [E:$i] :  ((m2_subset_1 E (k16_substut1 A) (k38_substut1 A)) &  ( ((k2_sublemma A E) = (k7_cqc_lang A B C))  &  ((k19_substut1 A E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_supinf_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_setfam_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k1_zfmisc_1 k7_numbers)))) )  =>  (! [B:$i] :  ((v2_membered B) =>  ( (B = (k5_setfam_1 k7_numbers A))  => (m1_xxreal_2 (k1_xxreal_2 (k5_supinf_1 A)) B)) ) ) ) ) ).
tt(t5_supinf_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 k7_numbers)))  =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  ((r2_hidden B A) <=> (r2_hidden (k2_supinf_2 B) (k6_supinf_2 A))) ) ) ) ) ).
tt(t5_symsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_symsp_1 B A) & (l1_symsp_1 B A)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r1_orders_2 B C D))  &  ( (~  (E = (k4_struct_0 A)) )  &  (~  ( (~ (r1_orders_2 B (k4_vectsp_1 A B E C) D))  &  (~ (r1_orders_2 B C (k4_vectsp_1 A B E D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_sysrel,ax, (! [A:$i] :  (! [B:$i] :  ((k2_relat_1 (k2_zfmisc_1 A B)) = (k2_zfmisc_1 B A)) ) ) ).
tt(t5_t_0topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A)) (k4_t_0topsp A) C) = (k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k3_t_0topsp A)) (k4_t_0topsp A) B))  <=> (r2_hidden (k4_borsuk_1 A A C B) (k1_t_0topsp A))) ) ) ) ) ) ) ).
tt(t5_t_1topsp,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v7_pre_topc B) =>  ((m1_eqrel_1 (a_3_0_t_1topsp A B C) (u1_struct_0 A)) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden D (a_3_0_t_1topsp A B C)) => (v4_pre_topc D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_taxonom1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A))) =>  ((r1_relat_2 B A) => (r1_relat_2 (k18_finseq_1 B) A)) ) ) ) ).
tt(t5_taxonom2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_taxonom1 B A) =>  ((v3_orders_2 (k2_yellow_1 (k3_tarski B))) &  ((v4_orders_2 (k2_yellow_1 (k3_tarski B))) &  ((v5_orders_2 (k2_yellow_1 (k3_tarski B))) &  ((v1_taxonom2 (k2_yellow_1 (k3_tarski B))) &  ((v2_taxonom2 (k2_yellow_1 (k3_tarski B))) & (l1_orders_2 (k2_yellow_1 (k3_tarski B)))) ) ) ) ) ) ) ) ) ).
tt(t5_taylor_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_prepower (k25_sin_cos B) (k10_real_1 1 A)) = (k25_sin_cos (k13_complex1 B A))) ) ) ) ) ).
tt(t5_taylor_2,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((k2_fdiff_1 k24_sin_cos A) = (k2_partfun1 k1_numbers k1_numbers k24_sin_cos A))  &  ((k9_xtuple_0 (k2_partfun1 k1_numbers k1_numbers k24_sin_cos A)) = A) ) ) ) ).
tt(t5_tbsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v9_metric_1 A) &  ((v8_metric_1 A) & (v2_tbsp_1 B A)) )  => (v3_tbsp_1 B A)) ) ) ) ) ).
tt(t5_tdgroup,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v12_vectsp_1 A) &  ((v1_tdgroup A) & (l2_algstr_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_tdgroup A B C D E) <=>  ((k1_algstr_0 A B E) = (k1_algstr_0 A C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_tdlat_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k1_tops_1 A (k2_pre_topc A B)) = (k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A B))))) ) ) ) ) ).
tt(t5_tdlat_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k2_pre_topc A (k1_tops_1 A B))) => (r1_tarski (k4_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k2_pre_topc A B))) (k2_pre_topc A (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) B (k1_tops_1 A (k2_pre_topc A B))))))) ) ) ) ) ).
tt(t5_tdlat_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc B A))  <=>  ((k2_pre_topc A B) = (k1_tops_1 A B)) ) ) ) ) ) ).
tt(t5_termord,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  ((r1_termord A B C D) <=>  (~ (r2_termord A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t5_tex_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k6_tmap_1 A B)))) =>  ( ((r1_tarski B C) & (v1_tops_1 B A))  => (v1_tops_3 C (k6_tmap_1 A B))) ) ) ) ) ) ) ).
tt(t5_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (~  ((v1_subset_1 (k6_domain_1 (u1_struct_0 A) B) (u1_struct_0 A)) & (v7_struct_0 A)) ) ) ) ) ) ).
tt(t5_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_tsep_2 A B C) =>  ((v3_tops_1 B A) <=> (v1_tops_3 C A)) ) ) ) ) ) ) ) ).
tt(t5_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C B) & (v1_tex_4 B A))  => (v1_tex_4 C A)) ) ) ) ) ) ) ).
tt(t5_tietze,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v1_series_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v1_series_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k3_funct_2 k5_numbers k1_numbers A C) (k3_funct_2 k5_numbers k1_numbers B C))) )  => (r1_xxreal_0 (k4_series_1 A) (k4_series_1 B))) ) ) ) ) ).
tt(t5_tmap_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 A)))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 A)))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E C B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 C B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F D B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 D B)))) )  =>  ( ((k2_partfun1 C B E (k9_subset_1 A C D)) = (k2_partfun1 D B F (k9_subset_1 A C D)))  =>  ( ((m1_subset_1 C (k1_zfmisc_1 D)) => (r1_funct_2 (k4_subset_1 A C D) B D B (k1_tmap_1 A B C D E F) F))  &  ( ((r1_funct_2 (k4_subset_1 A C D) B D B (k1_tmap_1 A B C D E F) F) => (m1_subset_1 C (k1_zfmisc_1 D)))  &  ( ((m1_subset_1 D (k1_zfmisc_1 C)) => (r1_funct_2 (k4_subset_1 A C D) B C B (k1_tmap_1 A B C D E F) E))  &  ((r1_funct_2 (k4_subset_1 A C D) B C B (k1_tmap_1 A B C D E F) E) => (m1_subset_1 D (k1_zfmisc_1 C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_toler_1,ax, (! [A:$i] : (v6_relat_2 (k1_eqrel_1 A))) ).
tt(t5_topalg_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k17_borsuk_1))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k17_borsuk_1)) =>  ( (A = (k3_rcomp_1 k6_numbers B))  => (v3_pre_topc A k17_borsuk_1)) ) ) ) ) ).
tt(t5_topalg_2,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((k1_rcomp_1 A B) = (a_2_0_topalg_2 A B)) ) ) ) ) ) ).
tt(t5_topalg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (C = (k1_tarski B))  =>  ((k1_tex_2 A B) = (k1_pre_topc A C)) ) ) ) ) ) ) ) ).
tt(t5_topalg_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_group_1 D) &  ((v3_group_1 D) & (l3_algstr_0 D)) ) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) &  ((v1_group_6 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) &  ((v1_group_6 F B D) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) ) )  =>  ( ((v3_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (v3_funct_2 F (u1_struct_0 B) (u1_struct_0 D)))  => (v3_funct_2 (k1_topalg_4 A B C D E F) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 A B))) (u1_struct_0 (k2_group_7 (k2_tarski 1 2) (k10_finseq_1 C D))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topalg_5,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  &  ( (C = E)  &  ( (D = F)  & (r1_connsp_1 B C D)) ) )  => (r1_connsp_1 A E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topalg_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v3_funct_1 C) & (m1_borsuk_2 C A B B))  =>  (! [D:$i] :  ( ((v3_funct_1 D) & (m1_borsuk_2 D A B B))  => (r3_borsuk_2 A B B C D)) ) ) ) ) ) ) ) ).
tt(t5_topdim_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v1_topdim_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  => (r1_xxreal_0 (k1_real_1 1) (k2_topdim_1 A B))) ) ) ) ).
tt(t5_topdim_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_pcomps_1 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_topdim_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_topdim_1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v4_pre_topc C A) &  ((v5_waybel23 (k1_pre_topc A (k4_subset_1 (u1_struct_0 A) C D))) &  ((r1_xxreal_0 (k2_topdim_1 A C) B) & (r1_xxreal_0 (k2_topdim_1 A D) B)) ) )  =>  ((r1_xxreal_0 (k2_topdim_1 A (k4_subset_1 (u1_struct_0 A) C D)) B) & (v1_topdim_1 (k4_subset_1 (u1_struct_0 A) C D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_topgen_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) C))  =>  ((k1_topgen_1 A B) = (k6_domain_1 (k1_zfmisc_1 (u1_struct_0 A)) (k2_tops_1 A C))) ) ) ) ) ) ) ) ).
tt(t5_topgen_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_ordinal1 (k1_topgen_2 A B) (k2_topgen_2 A))) ) ) ) ).
tt(t5_topgen_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  ( (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  <=>  ((v3_pre_topc C B) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) ) ) ) ) ) ).
tt(t5_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  => (r1_ordinal1 (k4_topgen_1 A) (k2_waybel23 A))) ) ).
tt(t5_topgen_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r2_hidden A (k9_xtuple_0 (k1_funct_1 (k10_funct_6 C) B))) <=>  (? [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  &  ((r2_hidden A (k9_xtuple_0 C)) &  ( (D = (k1_funct_1 C A))  & (r2_hidden B (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ).
tt(t5_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_tarski B C) => (r1_tarski (k5_group_2 A D B) (k5_group_2 A D C))) ) ) ) ) ) ) ) ) ).
tt(t5_topmetr3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((r1_tarski (k2_relset_1 k1_numbers C) (k1_rcomp_1 A B)) =>  ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 (k2_topmetr A B))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k2_topmetr A B)))))) ) ) ) ) ) ) ) ) ).
tt(t5_topmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden B C) =>  (! [D:$i] :  ((m1_connsp_2 D A B) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k1_pre_topc A C))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc A C)))) =>  ( ( (F = (k9_subset_1 (u1_struct_0 A) D C))  &  (E = B) )  => (m1_connsp_2 F (k1_pre_topc A C) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  ((r2_hidden B (k1_rltopsp1 (k15_euclid A) C D)) =>  ((k1_rltopsp1 (k15_euclid A) C D) = (k4_subset_1 (u1_struct_0 (k15_euclid A)) (k1_rltopsp1 (k15_euclid A) C B) (k1_rltopsp1 (k15_euclid A) B D))) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((v1_topreal2 A) <=>  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) &  ( (~  (B = C) )  &  ((r2_hidden B A) & (r2_hidden C A)) ) ) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (B = C) )  &  ((r2_hidden B A) &  ((r2_hidden C A) &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~  ((r1_topreal1 (k15_euclid 2) B C D) &  ((r1_topreal1 (k15_euclid 2) B C E) &  ( (A = (k4_subset_1 (u1_struct_0 (k15_euclid 2)) D E))  &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) D E) = (k2_tarski B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal3,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  ( ( (A = (k10_finseq_1 C D))  &  (B = (k10_finseq_1 E F)) )  =>  ( ((k3_rlvect_1 (k15_euclid 2) A B) = (k10_finseq_1 (k2_xcmplx_0 C E) (k2_xcmplx_0 D F)))  &  ((k5_algstr_0 (k15_euclid 2) A B) = (k10_finseq_1 (k6_xcmplx_0 C E) (k6_xcmplx_0 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ((v1_topreal4 A) => (v1_topreal2 A)) ) ) ).
tt(t5_topreal5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 A) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc H A k3_topmetr) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 k3_topmetr))))) ) )  =>  (~  ((v2_connsp_1 D A) &  ( ((k1_funct_1 H B) = E)  &  ( ((k1_funct_1 H C) = F)  &  ((r1_xxreal_0 E G) &  ((r1_xxreal_0 G F) &  ((r2_hidden B D) &  ((r2_hidden C D) &  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 A)) =>  (~  ((r2_hidden I D) &  ((k1_funct_1 H I) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal6,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((k21_rvsum_1 (k5_finseq_2 k1_numbers 1 A)) = A) ) ) ).
tt(t5_topreal7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_finseq_1 D)) )  =>  ( ( ((k7_finseq_1 A B) = (k7_finseq_1 C D))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 D)) ) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_topreal8,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m2_finseq_1 C B))  =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((k4_finseq_4 C A) = (k3_finseq_1 C))  =>  ((k6_finseq_4 (k8_finseq_1 B C D) A) = D) ) ) ) ) ) ) ) ) ).
tt(t5_topreal9,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v3_valued_0 A)) ) )  =>  ((k5_square_1 (k12_euclid A)) = (k18_rvsum_1 (k12_rvsum_1 A))) ) ) ).
tt(t5_topreala,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v3_pre_topc E A) & (m1_connsp_2 E A C))  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (C = D)  &  (F = (k9_subset_1 (u1_struct_0 B) E (k2_struct_0 B))) )  =>  ((v3_pre_topc F B) & (m1_connsp_2 F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_toprealb,ax, ((k1_pre_topc k2_topalg_2 (k5_toprealb (k2_subset_1 k1_numbers))) = k2_topalg_2) ).
tt(t5_toprealc,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_valued_0 C)) )  =>  ((k45_valued_1 (k14_valued_2 B A) (k14_valued_2 C A)) = (k14_valued_2 (k45_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t5_toprns_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 (k15_euclid B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k15_euclid B)))))) )  =>  ((k8_nat_1 (u1_struct_0 (k15_euclid B)) (k2_toprns_1 A B D) C) = (k1_rlvect_1 (k15_euclid B) (k8_nat_1 (u1_struct_0 (k15_euclid B)) D C) A)) ) ) ) ) ) ) ) ) ).
tt(t5_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) & (r1_tarski C B))  => (r1_tarski (k2_pre_topc A C) B)) ) ) ) ) ) ) ).
tt(t5_tops_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ( (~  ( (~  (B = k1_xboole_0) )  &  ((k7_setfam_1 A B) = k1_xboole_0) ) )  &  (~  ( (~  ((k7_setfam_1 A B) = k1_xboole_0) )  &  (B = k1_xboole_0) ) ) ) ) ) ) ).
tt(t5_tops_3,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) => (r1_tarski (k1_tops_1 A (k4_subset_1 (u1_struct_0 A) C B)) (k4_subset_1 (u1_struct_0 A) C (k1_tops_1 A B)))) ) ) ) ) ) ) ).
tt(t5_tops_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A))))) )  =>  ((v1_t_0topsp C (k3_pcomps_1 B) A) <=>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (? [F:$i] :  ( ((v3_pre_topc F A) & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  &  ((r2_hidden (k1_funct_1 C D) F) & (r1_tarski F (k7_relset_1 (u1_struct_0 (k3_pcomps_1 B)) (u1_struct_0 A) C (k9_metric_1 B D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_transgeo,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) &  ((v3_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ( ((r2_funct_2 A A (k1_transgeo A C B) (k1_transgeo A C D)) | (r2_funct_2 A A (k1_transgeo A B C) (k1_transgeo A D C)))  => (r2_funct_2 A A B D)) ) ) ) ) ) ) ) ) ).
tt(t5_translac,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  &  ((v7_transgeo C A) &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C B) = B) ) ) ) ) ) ) ) ).
tt(t5_treal_1,ax, ( (k18_borsuk_1 = (k1_treal_1 k6_numbers 1))  &  (k19_borsuk_1 = (k2_treal_1 k6_numbers 1)) ) ).
tt(t5_trees_1,ax, (! [A:$i] :  (! [B:$i] :  ((r3_xboole_0 (k9_finseq_1 A) (k9_finseq_1 B)) =>  (A = B) ) ) ) ).
tt(t5_trees_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( (! [C:$i] :  ((m2_finseq_1 C k5_numbers) =>  ((r2_hidden C A) <=> (r2_hidden C B)) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t5_trees_3,ax, (! [A:$i] :  (! [B:$i] :  ((v1_trees_3 A) =>  ((v1_trees_3 (k3_xboole_0 A B)) &  ((v1_trees_3 (k3_xboole_0 B A)) & (v1_trees_3 (k6_subset_1 A B))) ) ) ) ) ).
tt(t5_trees_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v3_trees_2 A)) )  =>  ( ((k9_xtuple_0 A) = (k2_trees_1 k6_numbers))  =>  (A = (k1_trees_4 (k1_funct_1 A k1_xboole_0))) ) ) ) ).
tt(t5_trees_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m1_trees_1 B A) =>  ( ((k4_trees_1 A B) = (k2_trees_1 k6_numbers))  <=> (r2_hidden B (k3_trees_1 A))) ) ) ) ) ).
tt(t5_trees_a,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((m4_trees_1 B A) =>  ((k6_subset_1 (a_2_0_trees_a A B) (a_2_1_trees_a A B)) = B) ) ) ) ) ).
tt(t5_triang_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski B C) & (r2_hidden C (k1_triang_1 A)))  => (r2_hidden B (k1_triang_1 A))) ) ) ) ) ).
tt(t5_tsep_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_pre_topc C A) =>  ( ((u1_struct_0 B) = (u1_struct_0 C))  =>  ((g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)) = (g1_pre_topc (u1_struct_0 C) (u1_pre_topc C))) ) ) ) ) ) ) ) ).
tt(t5_tsep_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tsep_2 A B (k3_subset_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t5_tsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski C B) & (v1_tsp_1 B A))  => (v1_tsp_1 C A)) ) ) ) ) ) ) ).
tt(t5_tsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_tsp_2 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc C A) =>  (C = (k3_tex_4 A (k9_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ).
tt(t5_turing_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( ((k1_gr_cy_1 (k4_turing_1 1 (k3_finseq_4 k5_numbers A B C))) = A)  &  ( ((k1_gr_cy_1 (k4_turing_1 2 (k3_finseq_4 k5_numbers A B C))) = (k2_nat_1 A B))  &  ((k1_gr_cy_1 (k4_turing_1 3 (k3_finseq_4 k5_numbers A B C))) = (k2_nat_1 (k2_nat_1 A B) C)) ) ) ) ) ) ) ) ) ).
tt(t5_twoscomp,ax, (! [A:$i] :  ((m1_subset_1 A k6_margrel1) =>  (! [B:$i] :  ((m1_subset_1 B k6_margrel1) =>  ( ((k1_funct_1 k14_twoscomp (k10_finseq_1 A B)) = (k2_binarith A B))  &  ( ((k1_funct_1 k15_twoscomp (k10_finseq_1 A B)) = (k2_binarith (k9_margrel1 A) B))  &  ((k1_funct_1 k16_twoscomp (k10_finseq_1 A B)) = (k2_binarith (k9_margrel1 A) (k9_margrel1 B))) ) ) ) ) ) ) ).
tt(t5_unialg_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m5_margrel1 C (u1_struct_0 A) (k1_unialg_2 A)) =>  ((r2_unialg_2 A B C) =>  ((k19_margrel1 (k2_unialg_2 A B C)) = (k19_margrel1 C)) ) ) ) ) ) ) ) ).
tt(t5_unialg_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) & (l1_unialg_1 A)) ) ) )  =>  ((k6_unialg_2 A) = (a_1_0_unialg_3 A)) ) ) ).
tt(t5_uniform1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_metric_1 B) &  ((v7_metric_1 B) &  ((v8_metric_1 B) &  ((v9_metric_1 B) & (l1_metric_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)))))) )  =>  ( ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 (k3_pcomps_1 A)) (u1_struct_0 (k3_pcomps_1 B)) C D) & (v1_uniform1 C A B))  => (v5_pre_topc D (k3_pcomps_1 A) (k3_pcomps_1 B))) ) ) ) ) ) ) ) ) ).
tt(t5_uniroots,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ( ( (C = A)  &  (D = B) )  =>  ( ((k11_binop_2 C D) = (k8_group_1 k1_complfld A B))  &  ((k9_binop_2 C D) = (k1_algstr_0 k1_complfld A B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_uproots,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_funct_1 (k2_funct_1 (k1_uproots A))) &  ((v1_funct_2 (k2_funct_1 (k1_uproots A)) A (k2_finseq_1 (k5_card_1 A))) & (m1_subset_1 (k2_funct_1 (k1_uproots A)) (k1_zfmisc_1 (k2_zfmisc_1 A (k2_finseq_1 (k5_card_1 A)))))) ) ) ) ).
tt(t5_urysohn1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) => (r1_tarski (k1_urysohn1 A) (k1_urysohn1 (k2_nat_1 A 1)))) ) ).
tt(t5_urysohn2,ax, (! [A:$i] :  ((m1_subset_1 A k7_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k7_numbers) =>  (~  ((r1_xxreal_0 A B) &  ( (~  ( (A = k2_supinf_1)  &  (B = k2_supinf_1) ) )  &  ( (~  ( (A = k2_supinf_1)  & (r2_hidden B k1_numbers)) )  &  ( (~  ( (A = k2_supinf_1)  &  (B = k1_supinf_1) ) )  &  ( (~  ((r2_hidden A k1_numbers) & (r2_hidden B k1_numbers)) )  &  ( (~  ((r2_hidden A k1_numbers) &  (B = k1_supinf_1) ) )  &  (~  ( (A = k1_supinf_1)  &  (B = k1_supinf_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_urysohn3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ((r2_hidden A k2_urysohn1) => (r2_hidden A (k1_urysohn1 (k2_urysohn3 A)))) ) ) ).
tt(t5_valuat_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_funct_2 C (k3_qc_lang1 A) B (k2_valuat_1 A B)) =>  (! [D:$i] :  ((m1_valuat_1 D A B) =>  ((k3_funct_2 (k2_valuat_1 A B) k6_margrel1 (k8_valuat_1 A B D (k5_cqc_lang A)) C) = k8_margrel1) ) ) ) ) ) ) ) ) ).
tt(t5_valued_0,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v5_relat_1 B k4_numbers))  =>  ((r1_tarski A B) => (v5_relat_1 A k4_numbers)) ) ) ) ) ).
tt(t5_valued_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_valued_0 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_valued_0 B)) )  =>  (! [C:$i] :  ((k1_funct_1 (k18_valued_1 A B) C) = (k3_xcmplx_0 (k1_funct_1 A C) (k1_funct_1 B C))) ) ) ) ) ) ).
tt(t5_valued_2,ax, (! [A:$i] : (m1_subset_1 (k11_valued_2 A) (k1_zfmisc_1 (k10_valued_2 A)))) ).
tt(t5_vectmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 B (u1_struct_0 A)) &  ((v3_vectmetr B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v2_funct_2 C (u1_struct_0 A)) &  ((v3_vectmetr C A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v2_funct_2 (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B) (u1_struct_0 A)) & (v3_vectmetr (k1_partfun1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t5_vectsp10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((r1_vectsp_5 A B C D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 B)) =>  ( ((r1_struct_0 C F) &  ((r1_struct_0 D G) &  (E = (k3_rlvect_1 B F G)) ) )  =>  ((k4_vectsp_5 A B E C D) = (k1_domain_1 (u1_struct_0 B) (u1_struct_0 B) F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ( (~ (v6_struct_0 D))  &  ((v13_algstr_0 D) &  ((v33_algstr_0 D) &  ((v3_group_1 D) &  ((v5_group_1 D) &  ((v4_vectsp_1 D) &  ((v5_vectsp_1 D) &  ((v2_rlvect_1 D) &  ((v3_rlvect_1 D) &  ((v4_rlvect_1 D) & (l6_algstr_0 D)) ) ) ) ) ) ) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 D)) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 D) A A) =>  ( ((r2_hidden B (k2_finseq_1 A)) & (r2_hidden C (k2_finseq_1 A)))  =>  ((k2_laplace B C A D (k2_matrix13 A A D F E)) = (k2_matrix13 (k7_nat_d A 1) (k7_nat_d A 1) D (k2_laplace B C A D F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k8_group_1 A B C) = (k8_group_1 A B D))  =>  ( (B = (k4_struct_0 A))  |  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k6_algstr_0 A B C) = (k5_struct_0 A))  =>  ( (~  (B = (k4_struct_0 A)) )  &  (~  (C = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((u1_struct_0 B) = C)  => (v1_vectsp_4 C A B)) ) ) ) ) ) ) ).
tt(t5_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_4 C A B) =>  (! [D:$i] :  ((m1_vectsp_4 D A B) =>  ((k1_vectsp_5 A B C D) = (k1_vectsp_5 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) => (m2_vectsp_6 (k2_vectsp_6 A B) A B C)) ) ) ) ) ) ).
tt(t5_vectsp_7,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((v1_vectsp_7 (k7_domain_1 (u1_struct_0 B) C D) A B) =>  ( (C = D)  |  ( (~  (D = (k4_struct_0 B)) )  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (C = (k4_vectsp_1 A B E D)) ) ) ) ) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  (C = (k4_vectsp_1 A B E D)) ) ) )  =>  ( (D = (k4_struct_0 B))  |  ( (~  (C = D) )  & (v1_vectsp_7 (k7_domain_1 (u1_struct_0 B) C D) A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_vectsp_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v7_vectsp_1 B A) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) ) )  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k1_vectsp_8 A B)) (u1_struct_0 (k1_vectsp_8 A B))) (u1_struct_0 (k1_vectsp_8 A B)) (k2_zfmisc_1 (k3_vectsp_5 A B) (k3_vectsp_5 A B)) (k3_vectsp_5 A B) (u2_lattices (k1_vectsp_8 A B)) (k5_vectsp_5 A B))) ) ) ) ).
tt(t5_vectsp_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_vectsp_6 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (~  ((r1_tarski (k10_xtuple_0 E) (u1_struct_0 (k1_vectsp_7 A B D))) &  (! [F:$i] :  ((m2_vectsp_6 F A B D) =>  (~  ((k4_rlvect_1 B (k3_vectsp_6 A B E C)) = (k4_vectsp_6 A B F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_vfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k6_vfunct_1 A B (k6_vfunct_1 A B C D) E) (k6_vfunct_1 A B C (k6_vfunct_1 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_vfunct_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 B)))))  => (r2_relset_1 A (u1_struct_0 B) (k3_vfunct_2 A B (k3_vfunct_2 A B C D) E) (k3_vfunct_2 A B C (k3_vfunct_2 A B D E)))) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v1_waybel_0 (k6_domain_1 (u1_struct_0 A) B) A) & (v2_waybel_0 (k6_domain_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t5_waybel10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v7_waybel_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_orders_2 A C (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C))) ) ) ) ) ) ).
tt(t5_waybel11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( (~ (r2_hidden B C))  => (r1_xboole_0 C (k5_waybel_0 A B))) ) ) ) ) ) ) ).
tt(t5_waybel12,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) &  ((v2_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r2_yellow_0 A B) => (r2_hidden (k2_yellow_0 A B) B)) ) ) ) ) ).
tt(t5_waybel13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v24_waybel_0 A))  =>  ((u1_struct_0 (k1_waybel_8 A)) = (u1_struct_0 (k1_waybel_8 B))) ) ) ) ) ) ).
tt(t5_waybel14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k1_yellow_0 A B) B) =>  (B = (k5_waybel_0 A (k1_yellow_0 A B))) ) ) ) ) ) ).
tt(t5_waybel15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v3_orders_2 C) &  ((v4_orders_2 C) &  ((v5_orders_2 C) & (l1_orders_2 C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ( ((v3_waybel_1 (k1_waybel_1 A B D F) A B) & (v3_waybel_1 (k1_waybel_1 B C E G) B C))  => (v3_waybel_1 (k1_waybel_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) D E) (k1_partfun1 (u1_struct_0 C) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 A) G F)) A C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel16,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k7_lattice3 A)))) =>  ( ( (B = D)  &  (C = E) )  =>  ((k2_yellow_4 A B C) = (k4_yellow_4 (k7_lattice3 A) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel17,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_waybel17 A B C))) =>  ( ((k2_waybel_0 A (k3_waybel17 A B C) D) = B)  |  ((k2_waybel_0 A (k3_waybel17 A B C) D) = C) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel18,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_waybel_3 B) & (v1_waybel18 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C A) => (v5_pre_topc (k6_waybel18 A B C) (k3_waybel18 A B) (k4_waybel18 A B C))) ) ) ) ) ) ).
tt(t5_waybel19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) &  ((v1_waybel19 A) & (l1_waybel_9 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) => (v12_waybel_0 B A)) ) ) ) ) ).
tt(t5_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((v2_waybel_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k13_lattice3 A B (k12_lattice3 A C D)) = (k12_lattice3 A (k13_lattice3 A B C) (k13_lattice3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) & (l1_orders_2 A)) )  =>  ((r2_yellow_0 A k1_xboole_0) => (v2_yellow_0 A)) ) ) ).
tt(t5_waybel21,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v17_waybel_0 C A B) => (m1_waybel21 C A B)) ) ) ) ) ) ) ).
tt(t5_waybel22,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  => (m1_waybel16 (k3_struct_0 A) A A)) ) ).
tt(t5_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v6_yellow_0 B A) & (m1_yellow_0 B A)) ) )  =>  ((r2_hidden (k3_yellow_0 A) (u1_struct_0 B)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  => (r1_tarski (k11_waybel_0 B D) (k11_waybel_0 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel24,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_orders_3 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) = (k1_yellow_0 B (a_4_0_waybel24 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t5_waybel25,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C A))  =>  (! [D:$i] :  ( ((v4_waybel11 D) & (m1_yellow_9 D B))  =>  ((r5_waybel_1 A B) => (r2_borsuk_3 C D)) ) ) ) ) ) ) ) ) ).
tt(t5_waybel26,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (? [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))) (u1_struct_0 (k1_waybel26 A k9_waybel18))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_yellow_1 (u1_pre_topc A))) (u1_struct_0 (k1_waybel26 A k9_waybel18)))))) )  &  ((v23_waybel_0 B (k2_yellow_1 (u1_pre_topc A)) (k1_waybel26 A k9_waybel18)) &  (! [C:$i] :  ( ((v3_pre_topc C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((k1_funct_1 B C) = (k5_funct_3 C (u1_struct_0 A))) ) ) ) ) ) ) ) ).
tt(t5_waybel27,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v2_waybel27 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_waybel27 E)) )  =>  ( ((r1_tarski (k9_xtuple_0 D) (k1_funct_2 (k2_zfmisc_1 A B) C)) & (r1_tarski (k10_xtuple_0 D) (k9_xtuple_0 E)))  =>  ((k3_relat_1 D E) = (k6_partfun1 (k9_xtuple_0 D))) ) ) ) ) ) ) ) ) ).
tt(t5_waybel28,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_waybel_0 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r1_orders_2 A B D) & (r1_orders_2 A C D)) ) ) ) ) ) ) ) ) ).
tt(t5_waybel29,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((l1_orders_2 B) =>  (! [C:$i] :  ((l1_orders_2 C) =>  (! [D:$i] :  ((l1_orders_2 D) =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  &  ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ((v23_waybel_0 E A C) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 D))))) )  =>  ( (F = E)  => (v23_waybel_0 F B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel_2,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B (k3_yellow_3 A A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A))))) )  =>  ((a_2_0_waybel_2 A B) = (a_2_1_waybel_2 A B)) ) ) ) ) ).
tt(t5_waybel30,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v4_waybel11 C) & (m1_yellow_9 C B))  =>  ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  =>  ((g1_waybel_9 (u1_struct_0 C) (u1_orders_2 C) (u1_pre_topc C)) = (g1_waybel_9 (u1_struct_0 A) (u1_orders_2 A) (u1_pre_topc A))) ) ) ) ) ) ) ) ).
tt(t5_waybel31,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_waybel_3 B) & (l1_orders_2 B)) ) ) ) ) ) )  =>  ( ((k2_yellow_1 (u1_pre_topc A)) = B)  =>  (! [C:$i] :  ( ((v1_tops_2 C A) &  ((v1_cantor_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v6_waybel23 (k11_waybel_0 B D) B) & (m1_waybel23 (k11_waybel_0 B D) B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel32,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v4_waybel11 A) & (l1_waybel_9 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_pre_topc A (k6_domain_1 (u1_struct_0 A) B)) = (k5_waybel_0 A B)) ) ) ) ) ).
tt(t5_waybel33,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v4_orders_2 C) &  ((v7_waybel_0 C) & (l1_waybel_0 C A)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_orders_2 D) &  ((v7_waybel_0 D) & (l1_waybel_0 D B)) ) )  =>  ( ( ((g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D)))  & (r1_funct_2 (u1_struct_0 C) (u1_struct_0 A) (u1_struct_0 D) (u1_struct_0 B) (u1_waybel_0 A C) (u1_waybel_0 B D)))  =>  (! [E:$i] :  ((m2_yellow_6 E A C) =>  (? [F:$i] :  ( ((v6_waybel_0 F B) & (m2_yellow_6 F B D))  &  ( ((g1_orders_2 (u1_struct_0 E) (u1_orders_2 E)) = (g1_orders_2 (u1_struct_0 F) (u1_orders_2 F)))  & (r1_funct_2 (u1_struct_0 E) (u1_struct_0 A) (u1_struct_0 F) (u1_struct_0 B) (u1_waybel_0 A E) (u1_waybel_0 B F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v18_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  => (r1_funct_2 (u1_struct_0 (k7_lattice3 B)) (u1_struct_0 (k7_lattice3 A)) (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 (k7_lattice3 A) (k7_lattice3 B) (k3_waybel34 A B C)) (k2_waybel34 B A C))) ) ) ) ) ) ).
tt(t5_waybel35,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v4_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m1_waybel35 C A B) => (m1_waybel35 (k4_subset_1 (u1_struct_0 A) C (k6_domain_1 (u1_struct_0 A) (k3_yellow_0 A))) A B)) ) ) ) ) ) ).
tt(t5_waybel_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_waybel_3 A B C) & (r1_waybel_3 A C D))  => (r1_waybel_3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t5_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ((k3_yellow_0 (k2_yellow_1 (k3_waybel_4 A))) = (k4_waybel_4 A)) ) ) ).
tt(t5_waybel_5,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( ((v17_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A) & (v18_waybel_0 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A))  => (v4_waybel_1 (k2_yellow_2 A) (k2_yellow_1 (k7_waybel_0 A)) A)) ) ) ).
tt(t5_waybel_6,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((v1_waybel_6 B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ((r2_hidden C B) & (r1_xboole_0 (k1_waybel_3 A C) B)) ) ) ) ) ) ) ) ) ).
tt(t5_waybel_7,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k3_yellow_1 A))) =>  ((k7_waybel_1 (k3_yellow_1 A) B) = (k6_subset_1 A B)) ) ) ) ).
tt(t5_waybel_8,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k2_waybel_8 A B) = (k8_subset_1 (u1_struct_0 A) (k5_waybel_0 A B) (u1_struct_0 (k1_waybel_8 A)))) ) ) ) ) ).
tt(t5_waybel_9,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_waybel_0 A B) = (k4_yellow_4 A (k6_domain_1 (u1_struct_0 A) B) (k2_struct_0 A))) ) ) ) ) ).
tt(t5_weddwitt,ax, (! [A:$i] :  ((m2_finseq_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 A)) => (r1_nat_d B (k7_partfun1 k5_numbers A C))) ) )  => (r1_nat_d B (k2_wsierp_1 A))) ) ) ) ) ).
tt(t5_weierstr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 B)))) =>  ((v1_finset_1 D) => (v1_finset_1 (k6_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ).
tt(t5_wellfnd1,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ( ( (C = (k2_xboole_0 B (k1_tarski D)))  & (r1_tarski (k1_wellord1 (u1_orders_2 A) D) B))  => (v12_waybel_0 C A)) ) ) ) ) ) ) ) ).
tt(t5_wellord1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r2_wellord1 B A) =>  (! [C:$i] :  (~  ((r1_tarski C A) &  ( (~  (C = k1_xboole_0) )  &  (! [D:$i] :  (~  ((r2_hidden D C) &  (! [E:$i] :  ((r2_hidden E C) => (r2_hidden (k4_tarski D E) B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_wellset1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  (~  ( (! [C:$i] :  ((r2_hidden C B) =>  ( (~ (r2_hidden (k1_funct_1 A C) C))  & (r2_hidden (k1_funct_1 A C) (k3_tarski B))) ) )  &  (! [C:$i] :  ((v1_relat_1 C) =>  (~  ((r1_tarski (k1_relat_1 C) (k3_tarski B)) &  ((v2_wellord1 C) &  ( (~ (r2_hidden (k1_relat_1 C) B))  &  (! [D:$i] :  ((r2_hidden D (k1_relat_1 C)) =>  ((r2_hidden (k1_wellord1 C D) B) &  ((k1_funct_1 A (k1_wellord1 C D)) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_wsierp_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_int_1 A B) & (r1_int_1 A C))  => (r1_int_1 A (k2_xcmplx_0 (k3_xcmplx_0 B D) (k3_xcmplx_0 C E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_xboole_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ((r1_xboole_0 A B) &  ((r2_hidden C (k2_xboole_0 A B)) &  ( (~  ((r2_hidden C A) &  (~ (r2_hidden C B)) ) )  &  (~  ((r2_hidden C B) &  (~ (r2_hidden C A)) ) ) ) ) ) ) ) ) ) ).
tt(t5_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k2_xboole_0 (k2_xboole_0 A B) C) = (k2_xboole_0 (k2_xboole_0 A C) (k2_xboole_0 B C))) ) ) ) ).
tt(t5_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean A (k4_xboolean A B)) = A) ) ) ) ) ).
tt(t5_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k3_xcmplx_0 B A) = (k3_xcmplx_0 C A))  =>  ( (A = k6_numbers)  |  (B = C) ) ) ) ) ) ) ) ) ).
tt(t5_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B A))  &  (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C A))  &  (~ (r1_xxreal_0 B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_xregular,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (? [B:$i] :  ((r2_hidden B A) &  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r2_hidden C D) &  ((r2_hidden D E) &  ((r2_hidden E F) & (r2_hidden F B)) ) )  => (r1_xboole_0 C A)) ) ) ) ) ) ) ) ) ).
tt(t5_xtuple_0,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( ((k6_xtuple_0 A B C D) = (k6_xtuple_0 E F G H))  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_xxreal_0,ax, (! [A:$i] :  ((v1_xxreal_0 A) => (r1_xxreal_0 k2_xxreal_0 A)) ) ).
tt(t5_xxreal_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden A (k1_xxreal_1 B C)) &  ( (~ (r2_hidden A (k4_xxreal_1 B C)))  &  ( (~  (A = B) )  &  (~  (A = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) =>  (! [C:$i] :  ((m2_xxreal_2 C B) => (m2_xxreal_2 C A)) ) ) ) ) ) ) ).
tt(t5_xxreal_3,ax, ((k2_xxreal_3 k2_xxreal_0) = k1_xxreal_0) ).
tt(t5_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((r2_lattice3 A B C) => (r2_lattice3 A (k3_xboole_0 B (u1_struct_0 A)) C))  &  ( ((r2_lattice3 A (k3_xboole_0 B (u1_struct_0 A)) C) => (r2_lattice3 A B C))  &  ( ((r1_lattice3 A B C) => (r1_lattice3 A (k3_xboole_0 B (u1_struct_0 A)) C))  &  ((r1_lattice3 A (k3_xboole_0 B (u1_struct_0 A)) C) => (r1_lattice3 A B C)) ) ) ) ) ) ) ) ) ).
tt(t5_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_orders_2 B) &  ((v1_yellow_0 B) & (l1_orders_2 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ( ((v3_lattice3 (k3_yellow_3 A B)) | (r1_yellow_0 (k3_yellow_3 A B) C))  =>  ((k1_yellow_0 (k3_yellow_3 A B) C) = (k7_yellow_3 A B (k1_yellow_0 A (k4_yellow_3 A B C)) (k1_yellow_0 B (k5_yellow_3 A B C)))) ) ) ) ) ) ) ) ).
tt(t5_yellow11,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k12_lattice3 A B C) = C)  <=>  ((k13_lattice3 A B C) = B) ) ) ) ) ) ) ) ).
tt(t5_yellow12,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] : (r1_tarski (k7_relat_1 (k13_funct_3 (k10_funct_3 A B) (k9_funct_3 A B)) (k2_zfmisc_1 C D)) (k2_zfmisc_1 D C))) ) ) ) ).
tt(t5_yellow13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  => (v7_pre_topc A)) ) ).
tt(t5_yellow14,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_struct_0 A))  =>  (! [B:$i] :  ((l1_struct_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (~  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  & (v2_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t5_yellow15,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((m2_finseq_1 C k6_margrel1) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((k1_funct_1 C D) = k8_margrel1)  =>  ((k1_funct_1 (k1_yellow15 A B C) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ).
tt(t5_yellow16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v4_waybel_0 B A) & (m1_yellow_0 B A)) ) )  => (v24_waybel_0 B)) ) ) ) ).
tt(t5_yellow17,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_funct_1 A C)) &  ((r2_hidden C (k9_xtuple_0 A)) & (r2_hidden B (k4_card_3 A))) )  => (r2_hidden (k2_funct_7 B C D) (k8_relat_1 (k12_card_3 A C) (k1_tarski D)))) ) ) ) ) ) ) ).
tt(t5_yellow18,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  ((r1_functor0 A B) => (r1_yellow18 A B)) ) ) ) ) ).
tt(t5_yellow19,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v3_pre_topc B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) &  ((v13_waybel_0 D (k3_yellow_1 (k2_struct_0 A))) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_yellow_1 (k2_struct_0 A)))))) ) )  =>  ((r2_waybel_7 A D C) => (r2_hidden B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_yellow_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v4_yellow_0 (k2_yellow_1 B) (k3_yellow_1 A)) & (m1_yellow_0 (k2_yellow_1 B) (k3_yellow_1 A))) ) ) ) ).
tt(t5_yellow20,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) & (l2_altcat_1 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_altcat_1 B) &  ((v11_altcat_1 B) &  ((v12_altcat_1 B) & (l2_altcat_1 B)) ) ) )  =>  (! [C:$i] :  ((m2_functor0 C A B) =>  ((v21_functor0 C A B) =>  (! [D:$i] :  ((m2_functor0 D B A) =>  ( ((k13_functor0 A B A C D) = (k12_functor0 A))  =>  ((g2_functor0 B A (u1_functor0 B A D) (u2_functor0 B A D)) = (k15_functor0 A B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_yellow21,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_altcat_1 A) &  ((v11_altcat_1 A) &  ((v12_altcat_1 A) &  ((v2_yellow21 A) & (l2_altcat_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k1_altcat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k1_altcat_1 A C B) = k1_xboole_0) )  &  (? [D:$i] :  ((m1_subset_1 D (k1_altcat_1 A B C)) &  ((v3_altcat_3 D A B C) &  (~ (v23_waybel_0 (k5_yellow21 A B C D) (k3_yellow21 A B) (k3_yellow21 A C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_yellow_2,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski B C) => (r1_tarski (k2_wellord1 A B) (k2_wellord1 A C))) ) ) ) ) ).
tt(t5_yellow_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C B) =>  ((k13_lattice3 A (k2_yellow_0 A B) C) = C) ) ) ) ) ) ) ) ).
tt(t5_yellow_4,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_yellow_4 A C B) & (v12_waybel_0 B A))  => (r1_tarski C B)) ) ) ) ) ) ) ).
tt(t5_yellow_5,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_orders_2 A (k12_lattice3 A B C) (k13_lattice3 A B D))) ) ) ) ) ) ) ) ).
tt(t5_yellow_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_struct_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k3_yellow_6 A B C))) =>  ((k2_waybel_0 B (k3_yellow_6 A B C) D) = C) ) ) ) ) ) ) ) ) ).
tt(t5_yellow_7,ax, (! [A:$i] :  ((l1_orders_2 A) =>  ((v5_orders_2 A) <=> (v5_orders_2 (k7_lattice3 A))) ) ) ).
tt(t5_yellow_8,ax, (! [A:$i] :  ((l1_struct_0 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden (k3_subset_1 (u1_struct_0 A) C) (k7_setfam_1 (u1_struct_0 A) B)) <=> (r2_hidden C B)) ) ) ) ) ) ) ).
tt(t5_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( (B = (a_2_3_yellow_9 A C))  =>  ((k8_setfam_1 (u1_struct_0 A) B) = (k3_subset_1 (u1_struct_0 A) (k4_waybel_0 A C))) ) ) ) ) ) ) ) ).
tt(t5_yoneda_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_oppcat_1 B A (k11_nattra_1 A (k1_yoneda_1 A))) =>  ( ((v2_funct_1 (k7_cat_1 A (k11_nattra_1 A (k1_yoneda_1 A)) B)) & (v1_yoneda_1 B A (k11_nattra_1 A (k1_yoneda_1 A))))  => (v2_funct_1 B)) ) ) ) ) ).
tt(t5_zf_colla,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (? [C:$i] :  ((v3_ordinal1 C) & (r2_hidden B (k1_zf_colla A C))) ) ) ) ) ) ).
tt(t5_zf_fund1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (! [C:$i] :  (! [D:$i] :  ( ((v8_zf_fund1 B A) &  ((r2_hidden C B) & (r2_hidden D B)) )  => (r2_hidden (k3_xboole_0 C D) B)) ) ) ) ) ) ) ).
tt(t5_zf_fund2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  ( ((v8_zf_fund1 B A) & (v1_ordinal1 B))  => (v1_zf_fund2 B)) ) ) ) ) ).
tt(t5_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((k21_zf_lang (k10_zf_lang A B)) = A)  &  ((k22_zf_lang (k10_zf_lang A B)) = B) ) ) ) ) ) ).
tt(t5_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ( (~  ((v2_zf_lang A) &  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (~  (A = (k4_zf_lang B C)) ) ) ) ) ) ) )  &  ( ( (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  (A = (k4_zf_lang B C)) ) ) ) )  => (v2_zf_lang A))  &  ( (~  ((v3_zf_lang A) &  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  (~  (A = (k5_zf_lang B C)) ) ) ) ) ) ) )  &  ( ( (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) &  (A = (k5_zf_lang B C)) ) ) ) )  => (v3_zf_lang A))  &  ( (~  ((v4_zf_lang A) &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  (A = (k6_zf_lang B)) ) ) ) ) )  &  ( ( (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (A = (k6_zf_lang B)) ) )  => (v4_zf_lang A))  &  ( (~  ((v5_zf_lang A) &  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k7_zf_lang B C)) ) ) ) ) ) ) )  &  ( ( (? [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k7_zf_lang B C)) ) ) ) )  => (v5_zf_lang A))  &  ( (~  ((v6_zf_lang A) &  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~  (A = (k8_zf_lang B C)) ) ) ) ) ) ) )  &  ( (? [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) &  (? [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  &  (A = (k8_zf_lang B C)) ) ) ) )  => (v6_zf_lang A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k1_tarski A) = (k2_tarski B C))  =>  (B = C) ) ) ) ) ).
tt(t5_zfmodel1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_ordinal1 A) =>  ((r2_zf_model A k8_zf_model) <=>  (! [B:$i] :  ((r2_hidden B A) => (r2_hidden (k3_tarski B) A)) ) ) ) ) ) ).
tt(t5_zfmodel2,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_zf_lang D) & (m2_finseq_1 D k5_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k1_zf_lang B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang B)))) )  =>  ( (~ (r2_hidden A (k4_zf_lang1 D)))  =>  ((r1_zf_model B E D) <=> (r1_zf_model B (k2_zf_lang1 B E A C) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t5_zf_model,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k1_zf_lang A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_zf_lang A)))) )  =>  ( ((r2_hidden D (k5_zf_model B A)) & (r2_hidden D (k5_zf_model C A)))  <=> (r2_hidden D (k5_zf_model (k7_zf_lang B C) A))) ) ) ) ) ) ) ) ) ).
tt(t5_zfrefle1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ((r1_zfrefle1 A k2_zfrefle1) & (v1_ordinal1 A))  => (v1_zf_model A)) ) ) ).
tt(t5_zf_refle,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_classes2 A))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_xboole_0 (k1_enumset1 (k2_zf_lang k6_numbers) (k2_zf_lang 1) (k2_zf_lang 2)) (k2_zf_model B)) => (r2_zf_model A (k11_zf_model B))) ) ) ) ) ).
tt(t5_zmodul01,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_zmodul01 B) &  ((v3_zmodul01 B) &  ((v4_zmodul01 B) &  ((v5_zmodul01 B) & (l1_zmodul01 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((k1_zmodul01 B (k4_algstr_0 B C) A) = (k1_zmodul01 B C (k4_xcmplx_0 A))) ) ) ) ) ) ) ).
tt(t60_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ((r5_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D)) =>  ((r5_abcmiz_0 A B C) & (r5_abcmiz_0 A (k8_abcmiz_0 A B C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t60_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v6_abcmiz_1 B A))  & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  (? [C:$i] :  ((m1_abcmiz_1 C A (k13_abcmiz_1 A)) &  ( (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C))  &  ((k37_abcmiz_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t60_abcmiz_a,ax, (! [A:$i] :  ( ((v1_xboole_0 A) & (m2_finseq_2 A k2_abcmiz_1 k4_abcmiz_1))  => (m2_abcmiz_a k1_xboole_0 A)) ) ).
tt(t60_aff_1,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) &  ((v2_diraf A) & (l1_analoaf A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ( (~ (r2_analoaf A B C D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r1_aff_1 A B C F) & (r1_aff_1 A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_aff_4 A B C) & (r1_aff_4 A C D))  =>  ( (C = k1_xboole_0)  | (r1_aff_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t60_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) )  =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  &  (B = (k1_ordinal4 (k5_relat_1 B A) C)) ) ) ) ) ) ) ).
tt(t60_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers A)) => (r1_xxreal_0 B (k1_funct_1 A C))) ) )  => (r1_xxreal_0 (k11_binop_2 (k1_afinsq_1 A) B) (k7_afinsq_2 A))) ) ) ) ) ).
tt(t60_algspec1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  ((l3_msualg_1 C B) =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  &  ((u4_struct_0 A) = (u4_struct_0 B)) ) ) ) ) ) ) ) ) ).
tt(t60_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  ( (~  ((r2_analoaf A B C D E) & (r2_analoaf A B C F G)) )  &  ( (~  ((r2_analoaf A B C D E) & (r2_analoaf A F G B C)) )  &  ( (~  ((r2_analoaf A D E B C) & (r2_analoaf A F G B C)) )  &  (~  ((r2_analoaf A D E B C) & (r2_analoaf A B C F G)) ) ) ) ) )  &  (~ (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ((m1_subset_1 (k4_trees_4 2 B) (u1_struct_0 (k7_freealg k19_aofa_000 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  (B = (k2_finseq_4 (u1_struct_0 (k7_freealg k19_aofa_000 A)) C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [I:$i] :  ((m1_aofa_i00 I B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  &  ( ((k1_funct_1 J C) = k6_numbers)  &  ( ((k1_funct_1 J E) = 1)  &  ( ((k1_funct_1 J F) = 2)  &  ( ((k1_funct_1 J G) = 3)  &  ( ((k1_funct_1 J H) = 4)  &  ((k1_funct_1 J I) = 5) ) ) ) ) ) ) )  => (r5_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F k6_numbers) (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1)) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D I 1) (k74_aofa_i00 A B C D I E) (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H F) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)) (k81_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G H)) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D I 1))) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_armstrng,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_finset_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k9_setfam_1 A) (k9_setfam_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((r2_hidden C (k13_armstrng A (k12_armstrng A B))) <=> (r6_armstrng A C B)) ) ) ) ) ) ) ).
tt(t60_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (? [B:$i] :  ((m1_subset_1 B k5_arytm_3) &  (A = (k9_arytm_3 B B)) ) ) ) ) ).
tt(t60_asympt_1,ax,(v4_asympt_0 (k47_valued_1 k5_numbers k1_numbers k1_numbers (k3_asympt_1 1) (k4_asympt_1 1)))).
tt(t60_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k2_bcialg_1 A (k2_bcialg_1 A (k1_bcialg_1 A B C))) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ).
tt(t60_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B (k6_bhsp_1 A C D)) (k3_normsp_1 A (k3_normsp_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t60_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A B (k4_lattices A B C)) (k1_boolealg A B C))) ) ) ) ) ) ).
tt(t60_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  ( (A = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_borsuk_5 2 4) (k2_rcomp_1 4 5)) (k2_rcomp_1 5 k1_xxreal_0)))  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 2) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) ) ) ) ).
tt(t60_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k2_borsuk_1 k5_topmetr k5_topmetr))) =>  ((r2_hidden A k8_borsuk_6) => (r1_xxreal_0 (k10_real_1 1 2) (k1_xtuple_0 A))) ) ) ).
tt(t60_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  ( (C = (k1_funct_1 k12_toprealb A))  =>  ((k1_funct_1 (k10_borsuk_7 1 (k1_real_1 (k3_euclid_3 C))) (k1_funct_1 k12_toprealb B)) = (k1_funct_1 k12_toprealb (k6_xcmplx_0 B A))) ) ) ) ) ) ) ) ).
tt(t60_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k1_bvfunc_1 A (k6_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A I B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G) H) J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  ( ((k7_xboolean A (k3_xboolean A)) = k7_margrel1)  &  ((k3_xboolean (k7_xboolean A (k3_xboolean A))) = k8_margrel1) ) ) ) ).
tt(t60_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k5_bvfunc26 A B C)) (k1_bvfunc_1 A (k2_bvfunc_1 A B C)))) ) ) ) ) ) ).
tt(t60_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ((k3_calcul_1 A (k12_finseq_1 (k3_cqc_lang A) B)) = (k24_qc_lang1 A B)) ) ) ) ) ).
tt(t60_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_wellord2 A B) =>  (A = B) ) ) ) ) ) ).
tt(t60_card_2,ax, (! [A:$i] :  (~  ( ((k1_card_1 A) = 2)  &  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (B = C) )  &  (A = (k2_tarski B C)) ) ) ) ) ) ) ) ).
tt(t60_card_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k1_funct_1 C A)))  => (r2_hidden (k16_funcop_1 A B) (k8_card_3 C))) ) ) ) ) ).
tt(t60_card_fin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((r1_xxreal_0 B A) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k3_stirl2_1 A B) = (k11_binop_2 (k12_binop_2 1 (k9_newton B)) (k7_afinsq_2 C)))  &  ( ((k1_relset_1 k5_numbers C) = (k23_binop_2 B 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k22_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k6_newton D B)) (k1_newton (k21_binop_2 B D) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((r1_cat_1 A B C) & (r1_cat_1 A C D))  => (r1_cat_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t60_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r2_cat_3 A B C D) & (v10_cat_1 (k4_graph_1 A D) A))  => (r1_cat_1 A B (k4_graph_1 A C))) ) ) ) ) ) ) ) ) ).
tt(t60_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k21_cat_4 A B C)) = B)  &  ((k4_graph_1 A (k21_cat_4 A B C)) = (k20_cat_4 A B C)) ) ) ) ) ) ) ) ).
tt(t60_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_partfun1 B A) <=> (v1_partfun1 (k31_valued_1 A k2_numbers B) A)) ) ) ) ) ).
tt(t60_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_chain_1 B (k2_nat_1 A 1)) =>  ((k10_chain_1 (k2_nat_1 A 1) B A (k6_chain_1 (k2_nat_1 A 1) B)) = (k5_chain_1 (k2_nat_1 A 1) B A)) ) ) ) ) ).
tt(t60_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ( ((r2_hidden D B) & (r1_tarski (k2_chord A (k6_domain_1 (k6_glib_000 A) D)) B))  =>  ( ((k2_chord A (k6_domain_1 (k6_glib_000 A) D)) = k1_xboole_0)  |  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 C)) =>  ( (D = E)  =>  (! [F:$i] :  ((m1_chord F A (k6_domain_1 (k6_glib_000 A) D)) =>  (! [G:$i] :  ((m1_chord G C (k6_domain_1 (k6_glib_000 C) E)) => (r5_glib_000 F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) & (l1_msualg_1 B)) ) )  =>  (! [C:$i] :  ((l3_msualg_1 C A) =>  (! [D:$i] :  ((l3_msualg_1 D B) =>  ( ((v6_circcomb C A) &  ((v4_circcomb C A) &  ((v6_circcomb D B) & (v4_circcomb D B)) ) )  => (r2_circcomb A B C D)) ) ) ) ) ) ) ) ) ).
tt(t60_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r7_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  (~  ((r2_hidden G (k9_trees_9 D)) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  (~  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 E F))) =>  ((r1_facirc_1 E F (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) H) &  (? [J:$i] :  ((m2_circtrm1 J A C B D E F) &  (! [K:$i] :  ((m1_subset_1 K (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  ( (K = (k3_relat_1 J I))  =>  (! [L:$i] :  ((m1_circtrm1 L A C D B K) =>  ((k1_funct_1 (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) H) = (k7_circtrm1 A B C G L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((k5_classes1 (k2_xboole_0 A B)) = (k2_xboole_0 (k5_classes1 A) (k5_classes1 B))) ) ) ).
tt(t60_classes2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden A C) & (r2_hidden B C))  =>  ((r2_hidden (k2_xboole_0 A B) C) &  ((r2_hidden (k3_xboole_0 A B) C) &  ((r2_hidden (k6_subset_1 A B) C) & (r2_hidden (k5_xboole_0 A B) C)) ) ) ) ) ) ) ) ).
tt(t60_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_clvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) ) )  => (m1_clvect_1 A (k4_clvect_1 A))) ) ).
tt(t60_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v2_clvect_2 B A) & (v2_clvect_2 C A))  => (v2_clvect_2 (k3_normsp_1 A B C) A)) ) ) ) ) ) ) ).
tt(t60_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden C (k3_tarski A)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v10_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  ( ((k11_cohsp_1 A B E) = (k1_tarski (k4_tarski C D)))  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ( ((r2_hidden C F) =>  ((k3_funct_2 A B E F) = (k1_tarski D)) )  &  ( (~ (r2_hidden C F))  =>  ((k3_funct_2 A B E F) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k17_complex1 (k6_xcmplx_0 A B)) = (k17_complex1 (k6_xcmplx_0 B A))) ) ) ) ) ).
tt(t60_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ((k2_complex2 A k32_sin_cos) = (k10_complex1 A)) ) ) ).
tt(t60_complfld,ax, ((k17_complex1 (k5_struct_0 k1_complfld)) = 1) ).
tt(t60_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_complsp2 A (k12_seq_4 B k7_complex1)) = (k1_binop_2 (k5_binop_2 k7_complex1 (k8_complsp2 A B)))) ) ) ) ) ) ).
tt(t60_compos_1,ax, (! [A:$i] :  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_compos_1 B)) =>  ((r2_hidden A (k2_afinsq_1 (k11_compos_1 B C))) <=>  ( (A = k6_numbers)  |  (A = 1) ) ) ) ) ) ) ) ).
tt(t60_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  (! [C:$i] :  ( ((v6_compos_0 C (u1_compos_1 A)) & (m1_subset_1 C (u1_compos_1 A)))  =>  (! [D:$i] :  ( ((v6_compos_0 D (u1_compos_1 A)) & (m1_subset_1 D (u1_compos_1 A)))  =>  (! [E:$i] :  ( ((v6_compos_0 E (u1_compos_1 A)) & (m1_subset_1 E (u1_compos_1 A)))  =>  (! [F:$i] :  ( ((v6_compos_0 F (u1_compos_1 A)) & (m1_subset_1 F (u1_compos_1 A)))  =>  (! [G:$i] :  ( ((v6_compos_0 G (u1_compos_1 A)) & (m1_subset_1 G (u1_compos_1 A)))  =>  ((k1_funct_1 (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k2_compos_2 A (k3_compos_2 A B C) D) E) F) G) 5) = (k5_compos_0 (u1_compos_1 A) G 5)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_comptrig,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_comptrig C B A) =>  ( (C = k6_numbers)  =>  (B = k6_numbers) ) ) ) ) ) ) ) ).
tt(t60_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_2 D k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 B) 1) k5_numbers)) =>  ( ((r2_hidden A (k4_finseq_1 D)) & (v2_comput_1 B))  =>  ((k1_recdef_1 (k7_comput_1 B C A) (k8_comput_1 (k2_nat_1 (k19_margrel1 B) 1) D A k6_numbers)) = (k1_recdef_1 B (k2_finseq_3 A D))) ) ) ) ) ) ) ) ) ) ).
tt(t60_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((k11_comseq_3 A) = (k8_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 A) B) (k11_comseq_3 (k1_valued_0 k2_numbers A (k2_nat_1 B 1))))) ) ) ) ) ) ).
tt(t60_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  ( ((v2_convex4 B A) & (v2_convex4 C A))  => (v2_convex4 (k7_rusub_4 A (k19_convex4 A B D) (k19_convex4 A C E)) A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) => (v2_cqc_the1 (k5_cqc_lang A) A)) ) ).
tt(t60_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k12_cqc_lang A C (k10_cqc_lang A B B)) A)) ) ) ) ) ) ).
tt(t60_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A)))  =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r1_tarski (k23_qc_lang1 A C) (k23_qc_lang1 A (k1_cqc_lang A C (k2_cqc_lang A D E))))) ) ) ) ) ) ) ) ) ) ).
tt(t60_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k16_csspace A B (k16_csspace A C D)) (k16_csspace A (k16_csspace A B C) D))) ) ) ) ) ) ) ) ).
tt(t60_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 B) A)) (k21_sin_cos (k9_real_1 (k8_real_1 2 B) A))))) ) ) ) ) ).
tt(t60_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k1_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k8_real_1 3 (k18_sin_cos B)) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k18_sin_cos (k8_real_1 3 B)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2))))))) ) ) ) ) ).
tt(t60_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden B (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k19_sin_cos) A B) = (k13_complex1 (k9_real_1 (k8_real_1 (k2_newton (k21_sin_cos A) 3) (k5_square_1 (k18_sin_cos B))) (k8_real_1 (k2_newton (k21_sin_cos B) 3) (k5_square_1 (k18_sin_cos A)))) (k8_real_1 (k8_real_1 (k5_square_1 (k18_sin_cos A)) (k5_square_1 (k18_sin_cos B))) (k9_real_1 A B)))) ) ) ) ) ) ).
tt(t60_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  (! [D:$i] :  ((m2_finseq_1 D k5_numbers) =>  (~  ( ((k3_finseq_1 D) = A)  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (~  ( (F = (k6_xcmplx_0 E 1))  &  ((k1_funct_1 D E) = (k2_xcmplx_0 1 (k2_ec_pf_1 A (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) F 3) (k8_group_1 (k9_int_3 A) B F)) C)))) ) ) ) ) ) ) ) )  &  ((k1_card_1 (a_3_1_ec_pf_1 A B C)) = (k2_wsierp_1 D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k9_int_3 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k9_int_3 A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k9_int_3 A))) =>  (! [K:$i] :  ((m2_subset_1 K (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k6_int_1 3 A))  &  ( (E = (k6_int_1 4 A))  &  ( (F = (k6_int_1 8 A))  &  ( (G = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) D (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2))))  &  ( (H = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))  &  ( (I = (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) H))  &  ( (J = (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k8_group_1 (k9_int_3 A) F I)))  &  (L = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C J) H) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E I) J)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k2_binom (k9_int_3 A) H 2))) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 3)))) ) ) ) ) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k2_binom (k9_int_3 A) H 2)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) = (k8_group_1 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 2)) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k11_ens_1 A)) (k7_cat_1 B (k11_ens_1 A) (k23_ens_1 A B C)) D) = (k2_cat_1 B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t60_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( (C = (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B)))  =>  ((k5_matrprob (k5_entropy1 C)) = (k7_real_1 (k18_rvsum_1 (k4_entropy1 A)) (k18_rvsum_1 (k4_entropy1 B)))) ) ) ) ) ) ) ) ).
tt(t60_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k1_enumset1 A B C) = (k1_enumset1 C B A)) ) ) ) ).
tt(t60_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  (! [F:$i] :  ((m1_subset_1 F C) => (r2_relset_1 A C (k8_relset_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B C) (k16_funct_3 A C B C D (k6_partfun1 C)) (k6_domain_1 (k2_zfmisc_1 B C) (k1_domain_1 B C E F))) (k8_mcart_1 A C (k8_relset_1 A B D (k6_domain_1 B E)) (k6_domain_1 C F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k6_euclid 3 A) = (k1_euclid_8 (k7_binop_2 (k1_seq_1 A 1)) (k7_binop_2 (k1_seq_1 A 2)) (k7_binop_2 (k1_seq_1 A 3)))) ) ) ).
tt(t60_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_algstr_0 (k15_euclid 2) (k19_euclid A B)) = (k19_euclid (k7_binop_2 A) (k7_binop_2 B))) ) ) ) ) ).
tt(t60_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((r5_euclidlp A B C) & (r5_euclidlp A C D))  => (r5_euclidlp A B D)) ) ) ) ) ) ) ) ) ).
tt(t60_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) => (r1_tarski (k6_subset_1 (k1_ordinal1 C) D) (k9_xtuple_0 B))) ) ) ) ) ) ) ) ).
tt(t60_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((r2_hidden A (u1_struct_0 (k8_facirc_1 A B C D))) &  ((r2_hidden B (u1_struct_0 (k8_facirc_1 A B C D))) & (r2_hidden C (u1_struct_0 (k8_facirc_1 A B C D)))) ) ) ) ) ) ) ).
tt(t60_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos))) & (r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)))  =>  ((r2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) k19_sin_cos) A) B) = (k1_real_1 (k10_real_1 (k8_real_1 2 (k1_seq_1 k16_sin_cos (k9_real_1 (k1_seq_1 k1_sin_cos9 B) (k1_seq_1 k2_sin_cos9 B)))) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t60_fib_num2,ax, ((k6_fib_num2 1) = (k12_finseq_1 k5_numbers 1)) ).
tt(t60_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  ( (~ (v2_struct_0 (k6_filter_0 A (k2_filter_0 A B))))  &  ((v10_lattices (k6_filter_0 A (k2_filter_0 A B))) &  ((v17_lattices (k6_filter_0 A (k2_filter_0 A B))) & (l3_lattices (k6_filter_0 A (k2_filter_0 A B)))) ) ) ) ) ) ) ) ).
tt(t60_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden (k3_lattices A B (k7_filter_0 A B C)) (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k10_filter_0 A (k2_filter_0 A C)) B)) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k6_eqrel_1 (u1_struct_0 A) (u1_struct_0 A) (k10_filter_0 A (k2_filter_0 A C)) B)) => (r3_lattices A D (k3_lattices A B (k7_filter_0 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t60_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((v1_funct_1 (k1_realset1 (u2_lattices A) B)) &  ((v1_funct_2 (k1_realset1 (u2_lattices A) B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k1_realset1 (u2_lattices A) B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  &  ((v1_funct_1 (k1_realset1 (u1_lattices A) B)) &  ((v1_funct_2 (k1_realset1 (u1_lattices A) B) (k2_zfmisc_1 B B) B) & (m1_subset_1 (k1_realset1 (u1_lattices A) B) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) ) ) ) ) ) ) ).
tt(t60_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden A (k2_finseq_1 B)) => (r2_hidden (k2_xcmplx_0 A C) (k2_finseq_1 (k2_xcmplx_0 B C)))) ) ) ) ) ) ) ).
tt(t60_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((k2_finseq_2 (k1_nat_1 A 1) B) = (k7_finseq_1 (k2_finseq_2 A B) (k9_finseq_1 B))) ) ) ) ).
tt(t60_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] : (r1_xxreal_0 (k3_finseq_1 (k1_finseq_3 A B)) (k3_finseq_1 A))) ) ) ).
tt(t60_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k10_xtuple_0 A) = (k4_finseq_1 A))  => (v2_funct_1 A)) ) ) ).
tt(t60_finseq_5,ax, (! [A:$i] :  ((k3_finseq_5 (k9_finseq_1 A)) = (k9_finseq_1 A)) ) ).
tt(t60_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ( ((k4_finseq_4 C B) = 1)  |  ((k1_finseq_5 A (k2_rfinseq A 1 C) B) = (k2_rfinseq A 1 (k1_finseq_5 A C B))) ) ) ) ) ) ) ) ) ).
tt(t60_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo D A) &  ((v2_binop_1 D A) &  ((v1_finseqop D A) &  ((k5_binop_1 A D B C) = (k4_binop_1 A D)) ) ) )  =>  ( (B = (k3_funct_2 A A (k5_finseqop A D) C))  &  ((k3_funct_2 A A (k5_finseqop A D) B) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k8_flang_1 A B) (k8_flang_1 A C))) ) ) ) ) ) ).
tt(t60_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k1_flang_2 A (k8_flang_1 A B) C D) (k8_flang_1 A B))) ) ) ) ) ) ) ).
tt(t60_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((k2_flang_3 A (k8_flang_1 A B)) = (k8_flang_1 A B))  &  ((k8_flang_1 A (k2_flang_3 A B)) = (k8_flang_1 A B)) ) ) ) ) ).
tt(t60_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v8_struct_0 E) &  ((v5_fsm_1 E A B) &  ((v7_fsm_1 E A B) & (l2_fsm_1 E A B)) ) ) )  =>  ( (C = (k13_fsm_1 A B D E))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_fsm_1 A B C))) =>  (! [G:$i] :  ((m1_subset_1 G F) =>  (! [H:$i] :  ((m1_subset_1 H F) =>  (~  ((r2_hidden G (u1_struct_0 E)) &  ((r2_hidden H (u1_struct_0 E)) &  (~  (G = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((v2_binop_1 C A) => (r2_funct_2 B A (k6_funcop_1 A B C (k9_funcop_1 A B C D F) E) (k6_funcop_1 A B C D (k10_funcop_1 A B C F E)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r2_hidden A (k9_xtuple_0 C)) & (r2_hidden B (k9_xtuple_0 C)))  =>  ((k7_relat_1 C (k2_tarski A B)) = (k2_tarski (k1_funct_1 C A) (k1_funct_1 C B))) ) ) ) ) ) ).
tt(t60_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A (k1_partfun1 A A A A B C) (k6_partfun1 A)) => (r2_relset_1 A A C (k2_funct_2 A B))) ) ) ) ) ) ).
tt(t60_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  => (r1_tarski (k10_xtuple_0 (k13_funct_3 D E)) (k2_zfmisc_1 B C))) ) ) ) ) ) ) ).
tt(t60_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A B) C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 D E) F) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 D E) F)))) )  =>  (~  ( (~  (C = k1_xboole_0) )  &  ( (~  (F = k1_xboole_0) )  &  (~  ((v1_funct_1 (k3_funct_4 G H)) &  ((v1_funct_2 (k3_funct_4 G H) (k2_zfmisc_1 (k2_zfmisc_1 A D) (k2_zfmisc_1 B E)) (k2_zfmisc_1 C F)) & (m1_subset_1 (k3_funct_4 G H) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A D) (k2_zfmisc_1 B E)) (k2_zfmisc_1 C F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r2_wellord2 A B) & (r2_wellord2 C D))  =>  ((r2_wellord2 (k1_funct_2 A C) (k1_funct_2 B D)) &  ((k1_card_1 (k1_funct_2 A C)) = (k1_card_1 (k1_funct_2 B D))) ) ) ) ) ) ) ).
tt(t60_funct_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_funcop_1 A)) )  =>  ((k9_xtuple_0 (k3_funct_6 A)) = (k9_xtuple_0 A)) ) ) ).
tt(t60_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((v1_funct_7 (k7_finseq_1 A B)) =>  ((v1_funct_7 A) & (v1_funct_7 B)) ) ) ) ) ) ).
tt(t60_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_funct_8 A k1_numbers k1_numbers k1_funct_8)) ) ).
tt(t60_fvaluat1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v3_group_1 B) &  ((v5_vectsp_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v1_realset2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_fvaluat1 C B) =>  ((v3_fvaluat1 B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_fvaluat1 B C))) =>  ((k1_binop_1 (k4_group_1 B) D A) = (k1_binop_1 (k4_group_1 (k7_fvaluat1 B C)) D A)) ) ) ) ) ) ) ) ) ) ).
tt(t60_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l3_algstr_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m2_finseq_1 F (u1_struct_0 B)) =>  ( ((r2_hidden A (k4_finseq_1 (k11_fvsum_1 B E F))) &  ( (C = (k1_funct_1 E A))  &  (D = (k1_funct_1 F A)) ) )  =>  ((k1_funct_1 (k11_fvsum_1 B E F) A) = (k6_algstr_0 B C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  (! [H:$i] :  ((m1_subset_1 H k6_margrel1) =>  ( ( (E = (k1_funct_1 D (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)))  &  (H = (k1_funct_1 D C)) )  =>  ((k1_twoscomp (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) (k6_circuit2 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D) (k24_gfacirc1 A B C)) = (k2_binarith E (k9_margrel1 H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((k28_glib_000 A B) = (k4_subset_1 (k7_glib_000 A) (k26_glib_000 A B) (k27_glib_000 A B))) ) ) ) ) ).
tt(t60_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  (! [D:$i] :  ( ( (~ (v1_abian D))  & (m1_subset_1 D k5_numbers))  =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k3_finseq_1 B)) &  ( ((k1_funct_1 B C) = (k1_funct_1 B D))  &  ((r2_hidden E (k1_relset_1 k5_numbers (k20_glib_001 A B C D))) &  ( (~ (r2_hidden E (k2_finseq_1 C)))  &  (~  ((r1_xxreal_0 C E) & (r1_xxreal_0 E (k3_finseq_1 (k20_glib_001 A B C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid 1 1)) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers k6_numbers)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 1) (k19_euclid k6_numbers 1)))))) ) ).
tt(t60_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) A))  &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) (k2_nat_1 B 1)))  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 2))) (k3_topreal1 2 C)) & (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 A 1) (k2_nat_1 B 1))) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 B) & (r1_xxreal_0 B (k3_finseq_1 A)))  =>  ((k8_graph_2 A B B) = B) ) ) ) ) ) ).
tt(t60_graph_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_graph_1 A) &  ((v6_graph_1 A) & (l1_graph_1 A)) ) )  =>  ( (~  ( (? [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  &  ( (~ (v1_msscyc_1 B A))  & (v1_graph_3 B A)) ) )  &  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_abian (k10_graph_1 A D)) <=>  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (~  ( (? [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) &  (? [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) &  ( (~  (B = C) )  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((v1_abian (k10_graph_1 A D)) <=>  ( (~  (D = B) )  &  (~  (D = C) ) ) ) ) ) ) ) ) ) )  &  (! [B:$i] :  ( ((v2_funct_1 B) & (m2_graph_1 B A))  =>  (~  ( (~ (v1_msscyc_1 B A))  & (v1_graph_3 B A)) ) ) ) ) ) ) ) ) ).
tt(t60_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_graph_1 C) & (l1_graph_1 C)) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (~  ( (~  ((k5_graph_5 C D E A) = k1_xboole_0) )  &  (! [F:$i] :  ((m2_finseq_1 F (u4_struct_0 C)) =>  (~  ((r2_hidden F (k5_graph_5 C D E A)) &  (! [G:$i] :  ((m2_finseq_1 G (u4_struct_0 C)) =>  ((r2_hidden G (k5_graph_5 C D E A)) => (r1_xxreal_0 (k10_graph_5 C F B) (k10_graph_5 C G B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 C D) => (r1_tarski (k3_group_11 A B D) (k3_group_11 A B C))) ) ) ) ) ) ) ) ) ).
tt(t60_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_struct_0 B D) <=> (r1_struct_0 C D)) ) )  =>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ) ) ).
tt(t60_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_group_2 A (k6_group_3 A (k6_group_3 A D B) C) (k6_group_3 A D (k6_algstr_0 A B C)))) ) ) ) ) ) ) ) ).
tt(t60_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_2 B (k8_group_4 A B C)) & (m1_group_2 C (k8_group_4 A B C))) ) ) ) ) ) ) ).
tt(t60_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_hidden B D) & (r2_hidden C E))  => (r1_struct_0 (k7_group_5 A D E) (k2_group_5 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_group_6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) <=>  ( ((k2_relset_1 B C) = B)  & (v2_funct_1 C)) ) ) ) ) ) ).
tt(t60_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ( ((v2_group_9 C A) & (m1_group_9 C A B))  =>  (! [D:$i] :  ( ((v2_group_9 D A) & (m1_group_9 D A B))  =>  (! [E:$i] :  ( ((v2_group_9 E A) & (m1_group_9 E A B))  =>  ( ((v4_group_9 D A E) & (m1_group_9 D A E))  =>  ((v4_group_9 (k17_group_9 A B C D) A (k17_group_9 A B C E)) & (m1_group_9 (k17_group_9 A B C D) A (k17_group_9 A B C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_vectsp_1 A k1_complfld))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) )  =>  ((k10_bilinear k1_complfld A B C) = (k10_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C))) ) ) ) ) ) ) ).
tt(t60_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k30_sin_cos)) =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) A) & (r2_relset_1 k1_numbers k1_numbers (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) A) (k5_relset_1 k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos) k30_sin_cos)) A))) ) ) ) ).
tt(t60_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((r2_hidden C (k7_ideal_1 A B)) <=>  (? [D:$i] :  ((m1_ideal_1 D A B) &  (C = (k4_rlvect_1 A D)) ) ) ) ) ) ) ) ) ).
tt(t60_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) => (r2_int_1 (k3_xcmplx_0 A B) k6_numbers A)) ) ) ) ).
tt(t60_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( (~ (r1_xxreal_0 (k1_seq_1 k16_sin_cos D) k6_numbers))  &  ((k1_seq_1 C D) = (k5_square_1 (k1_seq_1 k30_sin_cos D))) ) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers B)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers B)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k30_sin_cos) (k1_partfun2 k1_numbers B)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t60_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B C) &  ( ((k9_xtuple_0 k30_sin_cos) = C)  &  ( ((k9_xtuple_0 k30_sin_cos) = (k9_xtuple_0 A))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ( ((k1_seq_1 A D) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos D)))))  &  (~  ((k3_funct_2 k1_numbers k1_numbers k16_sin_cos D) = k6_numbers) ) ) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) ) )  =>  ((k2_integra5 B A) = (k9_real_1 (k1_seq_1 k30_sin_cos (k4_seq_4 B)) (k1_seq_1 k30_sin_cos (k5_seq_4 B)))) ) ) ) ) ) ) ) ).
tt(t60_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [G:$i] :  ( ((v3_rcomp_1 G) & (m1_subset_1 G (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski C G) &  ((r2_relset_1 k1_numbers k1_numbers D (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers E k3_taylor_1)) &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ( ((k1_seq_1 E H) = (k9_real_1 H A))  &  (~ (r1_xxreal_0 (k1_seq_1 E H) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B)))) = G)  &  ( (G = (k1_relset_1 k1_numbers F))  &  ( (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  ((r2_hidden H G) =>  ((k1_seq_1 F H) = (k10_real_1 (k9_real_1 H B) (k9_real_1 H A))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers F C))) ) ) ) ) )  =>  ((k2_integra5 C F) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B))) (k4_seq_4 C)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers G) (k26_valued_1 k1_numbers k1_numbers D (k9_real_1 A B))) (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) => (r2_interva1 A (k16_interva1 A B B) B)) ) ) ) ).
tt(t60_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k5_intpro_1 A C) (k5_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t60_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_2_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ((r1_xxreal_0 k6_numbers (k18_euclid B)) &  ((r1_xxreal_0 k6_numbers (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k18_euclid D) k6_numbers))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid G)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid H)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid I)) &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ((r1_xxreal_0 k6_numbers (k18_euclid J)) &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=>  (~  ( (~  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid A D) (k19_euclid B D))) & (r1_xxreal_0 (k17_euclid E) (k17_euclid F))) )  &  ( (~ (r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C))))  &  (~  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) &  (~  (F = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) D) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) D)) ) ) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_connsp_1 D (k15_euclid 2)) &  ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan9 D B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k3_finseq_1 (k1_jordan8 D B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) C 1)) ) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) (k17_pscomp_1 (k3_topreal1 2 (k1_jordan9 D B))))) ) ) ) ) ) ) ) ) ).
tt(t60_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1))) ) ) )  =>  ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k2_nat_1 D 1) (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jordan2c,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k14_euclid 1)))) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (A = (a_1_1_jordan2c B))  & (v6_tbsp_1 A (k14_euclid 1))) ) ) ) ) ) ).
tt(t60_jordan6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_topreal1 (k15_euclid 2) B C A) &  ( (~  (D = B) )  & (r2_hidden B (k4_jordan6 A B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_jordan,ax, ((v1_funct_1 k5_jordan) &  ((v1_funct_2 k5_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc k5_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 k5_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ).
tt(t60_kurato_1,ax, ((k5_card_1 (k4_kurato_1 k3_topmetr k6_kurato_1)) = 6) ).
tt(t60_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v14_lattices C) & (l3_lattices C)) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  ( (! [F:$i] :  ((m1_subset_1 F A) =>  ((r2_hidden F B) => (r3_lattices C (k3_funct_2 A (u1_struct_0 C) D F) (k3_funct_2 A (u1_struct_0 C) E F))) ) )  => (r3_lattices C (k3_lattice2 A C B D) (k3_lattice2 A C B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  (! [D:$i] :  ( (~ (r2_hidden D (k2_chord A (k1_tarski C))))  =>  ((k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) D) = (k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) (k20_lexbfs A B C)) D)) ) ) ) ) ) ) ) ).
tt(t60_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v4_limfunc1 A) | (v5_limfunc1 A))  => (v4_limfunc1 (k56_valued_1 k1_numbers k1_numbers A))) ) ) ).
tt(t60_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k3_rfunct_1 k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( ((k2_limfunc2 C A) = k6_numbers)  |  ((r4_limfunc2 (k3_rfunct_1 k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k3_rfunct_1 k1_numbers k1_numbers B C) A) = (k10_real_1 (k2_limfunc2 B A) (k2_limfunc2 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t60_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r6_limfunc2 B A) &  ((v6_limfunc1 C) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ((r4_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k5_limfunc1 C)) ) ) ) ) ) ) ) ) ).
tt(t60_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ( ((v2_xxreal_0 G) & (m1_subset_1 G k1_numbers))  =>  (~  ( ((k7_real_1 (k10_real_1 1 F) (k10_real_1 1 G)) = 1)  &  ((r2_hidden D (k1_lpspace2 A B C F)) &  ((r2_hidden E (k1_lpspace2 A B C G)) &  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (~  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers D))))  &  (? [I:$i] :  ((m1_subset_1 I k1_numbers) &  ( (I = (k1_mesfunc6 A B C (k2_mesfun6c G A (k56_valued_1 A k1_numbers E))))  & (r1_xxreal_0 (k1_mesfunc6 A B C (k56_valued_1 A k1_numbers (k20_valued_1 A k1_numbers k1_numbers D E))) (k8_real_1 (k4_power H (k10_real_1 1 F)) (k4_power I (k10_real_1 1 G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_ltlaxio1,ax, (! [A:$i] :  ((m1_subset_1 A k1_hilbert1) =>  (! [B:$i] :  ((m1_subset_1 B k1_hilbert1) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k1_hilbert1)) => (r8_ltlaxio1 C (k3_hilbert1 (k6_ltlaxio1 (k3_hilbert1 A B)) (k3_hilbert1 (k6_ltlaxio1 A) (k6_ltlaxio1 B))))) ) ) ) ) ) ).
tt(t60_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_cqc_lang A))) => (r3_cqc_the1 A C (k8_cqc_lang A B B))) ) ) ) ) ) ).
tt(t60_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid C)))) =>  ((k6_mathmorp (k3_xcmplx_0 A B) (k15_euclid C) D) = (k6_mathmorp A (k15_euclid C) (k6_mathmorp B (k15_euclid C) D))) ) ) ) ) ) ) ) ) ).
tt(t60_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k3_matrix10 A B C) (k3_matrix10 A D E)) => (r2_matrix10 (k4_matrix10 A B D) (k4_matrix10 A E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k1_funct_2 (k2_finseq_1 A) (k2_finseq_1 A)) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_funct_2 (k2_finseq_1 A) (k2_finseq_1 A)) (u1_struct_0 B))))) )  =>  (~  ( (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_finseq_1 A) (k2_finseq_1 A)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_finseq_1 A) (k2_finseq_1 A))))) )  =>  (? [G:$i] :  ((m2_finseq_1 G (u1_struct_0 B)) &  ( ((k3_finseq_1 G) = A)  &  ( (! [H:$i] :  ((v7_ordinal1 H) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( ((r2_hidden I (k2_finseq_1 A)) &  (H = (k1_funct_1 F I)) )  =>  ((k1_funct_1 G I) = (k3_matrix_1 (u1_struct_0 B) C I H)) ) ) ) ) )  &  ((k1_funct_1 E F) = (k8_group_1 B (k1_finsop_1 (u1_struct_0 B) G (u2_algstr_0 B)) (k12_matrix_3 A B (k4_matrix11 A A (u1_struct_0 B) F D)))) ) ) ) ) ) )  &  ((k12_matrix_3 A B (k4_matrix_6 A B C D)) = (k7_setwiseo (k1_funct_2 (k2_finseq_1 A) (k2_finseq_1 A)) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k1_funct_2 (k2_finseq_1 A) (k2_finseq_1 A))) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_matrix_1 D A B C) =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ((m2_finseq_1 F A) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ( ((v1_finset_1 H) &  ((v1_setfam_1 H) & (m1_subset_1 H (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 H E) (k2_matrix_1 D)) =>  ((r2_hidden G H) |  ((k6_matrix13 A D H E) = (k6_matrix13 A (k3_matrix11 G B C A D F) H E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k1_matrix_1 B) = k1_xboole_0)  =>  ((v1_xboole_0 (k6_matrix15 A B C)) |  ((k3_finseq_1 B) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t60_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v6_matrix16 B A) &  ((v6_matrix16 C A) &  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) )  => (v6_matrix16 (k3_fvsum_1 A B C) A)) ) ) ) ) ) ) ).
tt(t60_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k3_finseq_1 C) = (k3_finseq_1 D))  =>  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~ (r2_hidden (k4_tarski E B) (k2_matrix_1 C))) ) )  |  ((k9_matrix_1 (u1_struct_0 A) (k3_matrix_3 A C D) B) = (k3_fvsum_1 A (k9_matrix_1 (u1_struct_0 A) C B) (k9_matrix_1 (u1_struct_0 A) D B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k2_matrix_6 A B (k3_matrix_6 A B C D) E)) = (k3_rlvect_1 B (k5_algstr_0 B (k1_matrix_8 A B C) (k1_matrix_8 A B D)) (k1_matrix_8 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrixc1,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k2_numbers)))  =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 C))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) )  =>  ((r1_xxreal_0 (k1_matrix_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k8_complsp2 A (k6_matrixc1 C B)) = (k8_complsp2 (k6_matrixc1 (k2_matrixc1 C) A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrixj1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  ((k20_matrixj1 (u1_struct_0 C) (k4_struct_0 C) (k17_matrixj1 (u1_struct_0 C) A B (k12_matrix_1 C A) (k12_matrix_1 C B))) = (k12_matrix_1 C (k2_xcmplx_0 A B))) ) ) ) ) ) ) ).
tt(t60_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 C) = (k3_finseq_1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k1_matrix_1 C) k6_numbers) |  ((k12_matrixr1 C (k10_rvsum_1 B A)) = (k10_rvsum_1 (k12_matrixr1 C B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A B) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers B C) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G k5_numbers) =>  ((r2_hidden (k4_tarski F G) (k2_matrix_1 (k6_matrixr1 D E))) =>  ((k3_matrix_1 k1_numbers (k6_matrixr1 D E) F G) = (k1_funct_1 (k12_matrixr1 E (k8_matrix_1 k1_numbers D F)) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) )  =>  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v6_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  <=>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ((r2_hidden B (k4_finseq_1 A)) =>  ( (~ (v1_xboole_0 (k8_matrix_1 k1_numbers A B)))  &  ((v1_matrprob (k8_matrix_1 k1_numbers A B)) & (m2_finseq_1 (k8_matrix_1 k1_numbers A B) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t60_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  ( (~ (r1_xboole_0 (k4_zfmisc_1 A B C D) (k4_zfmisc_1 E F G H)))  =>  ( (~ (r1_xboole_0 A E))  &  ( (~ (r1_xboole_0 B F))  &  ( (~ (r1_xboole_0 C G))  &  (~ (r1_xboole_0 D H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_measure6,ax, ((k6_measure6 (k1_subset_1 k1_numbers)) = k1_xboole_0) ).
tt(t60_member_1,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((k4_member_1 (k10_member_1 A B)) = (k8_member_1 (k4_member_1 A) B)) ) ) ) ) ).
tt(t60_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 D)) =>  ((k9_memstr_0 A B (k1_funct_4 C D) E) = (k1_funct_4 C (k9_memstr_0 A B D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((k8_nat_1 k7_numbers A C) = B) ) )  =>  ((v10_mesfunc5 A) &  ( ((k2_mesfunc5 A) = B)  &  ((k2_mesfunc5 A) = (k8_supinf_2 (k17_supinf_2 A))) ) ) ) ) ) ) ) ).
tt(t60_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ((r2_hidden E (k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers B C) D))) =>  ((k1_seq_1 (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers B C) D) E) = (k7_real_1 (k7_real_1 (k1_seq_1 B E) (k1_seq_1 C E)) (k1_seq_1 D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r1_xxreal_0 C E) & (r1_xxreal_0 D F))  => (r1_tarski (k27_mmlquery A B E D) (k27_mmlquery A B C F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k23_modelc_2 (k42_modelc_2 A B) D E)) <=>  (? [F:$i] :  ((v7_ordinal1 F) &  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ( (~ (r1_xxreal_0 F G))  => (r6_modelc_2 A B (k29_modelc_2 A C G) D)) ) )  & (r6_modelc_2 A B (k29_modelc_2 A C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  (! [D:$i] :  ((m1_orders_1 D (k1_orders_1 (k1_modelc_3 A))) =>  ( ((v7_modelc_2 (k24_modelc_3 A D B)) & (r7_modelc_2 C (k12_modelc_2 (k24_modelc_3 A D B))))  =>  ((v3_modelc_3 B A) |  ( ((r2_hidden (k12_modelc_2 (k24_modelc_3 A D B)) (u2_modelc_3 A (k25_modelc_3 C A D B))) | (r2_hidden (k12_modelc_2 (k24_modelc_3 A D B)) (u1_modelc_3 A B)))  & (r2_hidden (k24_modelc_3 A D B) (u1_modelc_3 A (k25_modelc_3 C A D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ( ((k6_moebius1 A) = 1)  <=>  (A = 1) ) ) ) ).
tt(t60_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((k4_binop_1 (u1_struct_0 (k9_monoid_0 A)) (u2_algstr_0 (k9_monoid_0 A))) = k1_xboole_0) ) ) ).
tt(t60_nat_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (~  ((r1_xxreal_0 A 14) &  ( (~  (A = k6_numbers) )  &  ( (~  (A = 1) )  &  ( (~  (A = 2) )  &  ( (~  (A = 3) )  &  ( (~  (A = 4) )  &  ( (~  (A = 5) )  &  ( (~  (A = 6) )  &  ( (~  (A = 7) )  &  ( (~  (A = 8) )  &  ( (~  (A = 9) )  &  ( (~  (A = 10) )  &  ( (~  (A = 11) )  &  ( (~  (A = 12) )  &  ( (~  (A = 13) )  &  (~  (A = 14) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ((k13_nat_3 (k1_newton A B)) = (k9_nat_3 k10_newton (k13_nat_3 A) B)) ) ) ) ) ).
tt(t60_nat_d,ax, (! [A:$i] :  ((v1_finset_1 A) =>  ((v1_zfmisc_1 A) <=>  (~ (r1_xxreal_0 2 (k5_card_1 A))) ) ) ) ).
tt(t60_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 A) C)) => (r8_ncfcont1 A B C (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t60_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_nat_d (k5_nat_d (k6_nat_d A B) (k6_nat_d A C)) (k6_nat_d A (k5_nat_d B C)))) ) ) ) ) ) ).
tt(t60_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_cat_1 D A B) =>  (! [E:$i] :  ((m1_oppcat_1 E B C) => (m1_oppcat_1 (k1_partfun1 (u4_struct_0 A) (u4_struct_0 B) (u4_struct_0 B) (u4_struct_0 C) D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t60_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r7_orders_1 (k2_relat_1 A) B) <=> (r6_orders_1 A B)) ) ) ) ).
tt(t60_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden B (k10_ordinal2 C A)) =>  ( (A = k1_xboole_0)  | (r2_hidden (k5_ordinal3 B C) A)) ) ) ) ) ) ) ) ).
tt(t60_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden k6_numbers A) &  ((r2_hidden 1 B) &  (C = (k5_ordinal5 A B)) ) )  => (r2_hidden k6_numbers (k6_ordinal3 A (k12_ordinal2 B C)))) ) ) ) ) ) ) ).
tt(t60_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_classes2 D))  =>  ( ((r1_ordinal1 A B) &  ((r2_hidden B D) &  ((r2_hidden k4_ordinal1 D) &  ((r2_hidden C (k9_xtuple_0 (k1_funct_1 (k11_ordinal6 D) B))) &  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E B) => (v2_ordinal6 (k1_funct_1 (k11_ordinal6 D) E))) ) ) ) ) ) )  => (r1_ordinal1 (k1_funct_1 (k1_funct_1 (k11_ordinal6 D) A) C) (k1_funct_1 (k1_funct_1 (k11_ordinal6 D) B) C))) ) ) ) ) ) ) ) ) ).
tt(t60_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t60_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_partfun1 (k3_partfun1 k1_xboole_0 A B) C)) ) ) ) ).
tt(t60_partfun2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D B) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v2_funct_1 E) =>  ( ( ((r2_hidden D (k2_relset_1 B E)) &  (C = (k1_funct_1 (k2_funct_1 E) D)) )  =>  ((r2_hidden C (k1_relset_1 A E)) &  (D = (k1_funct_1 E C)) ) )  &  ( ((r2_hidden C (k1_relset_1 A E)) &  (D = (k1_funct_1 E C)) )  =>  ((r2_hidden D (k2_relset_1 B E)) &  (C = (k1_funct_1 (k2_funct_1 E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  => (r6_pboole A (k4_pboole A (k1_pboole A) B) (k1_pboole A))) ) ) ).
tt(t60_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r3_pdiff_5 C B) =>  ((r3_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) &  ((k11_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 1 3 C) A) B) = (k8_real_1 A (k3_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t60_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A)) )  =>  ((r3_pdiff_9 A C B D) <=>  ((r1_tarski C (k1_relset_1 (k1_euclid A) D)) &  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ((r2_hidden E C) => (r3_pdiff_1 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_pepin,ax,(v1_int_2 17)).
tt(t60_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) => (r1_xboole_0 (k4_finseq_1 B) (k9_xtuple_0 (k12_pnproc_1 C A)))) ) ) ) ) ) ) ).
tt(t60_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((m1_subset_1 C (k8_polyform A B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k17_polyform A B))) =>  (! [E:$i] :  ((m1_subset_1 E (k8_polyform A (k6_xcmplx_0 B 1))) =>  ( ( (B = k6_numbers)  &  ( (D = (k1_tarski C))  &  (E = k1_xboole_0) ) )  =>  ((k4_rlvect_1 k2_bspace (k19_polyform A B E D)) = (k5_struct_0 k2_bspace)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  ((v1_polynom5 B A) <=> (v1_polynom5 (k7_polynom5 A B) A)) ) ) ) ) ) ).
tt(t60_polyred,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_partfun1 B (k15_pre_poly A)) &  ((v1_relat_2 B) &  ((v4_relat_2 B) &  ((v6_relat_2 B) &  ((v8_relat_2 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (k15_pre_poly A))))) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v7_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k11_polynom1 A C)))) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k15_pre_poly A) (u1_struct_0 C)) &  ((v1_polynom1 E (k15_pre_poly A) C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k15_pre_poly A) (u1_struct_0 C))))) ) )  =>  ((r1_rewrite1 (k3_polyred A B C D) E (k7_polynom1 A C)) => (r2_hidden E (k7_ideal_1 (k11_polynom1 A C) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_power,ax, ((k4_power 2 2) = 4) ).
tt(t60_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  => (r2_pre_poly A (k16_pre_poly A) B)) ) ) ) ).
tt(t60_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 1 (k6_prepower A B))) ) ) ) ) ).
tt(t60_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_3 D A B) => (m2_finseq_1 (k1_partfun1 k5_numbers (k9_setfam_1 A) B k1_numbers D C) k1_numbers)) ) ) ) ) ) ) ) ).
tt(t60_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ( ((k25_pscomp_1 A) = (k24_pscomp_1 A))  =>  ((k17_pscomp_1 A) = (k1_tarski (k25_pscomp_1 A))) ) ) ) ).
tt(t60_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((v2_relat_1 B) =>  ( ( (~ (r2_pboole A (k6_pboole A C B) (k6_pboole A D B)))  &  (~ (r2_pboole A (k6_pboole A B C) (k6_pboole A B D))) )  | (r2_pboole A C D)) ) ) ) ) ) ) ) ) ).
tt(t60_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r3_qc_lang2 A B C) & (r3_qc_lang2 A C B)) ) ) ) ) ) ) ) ).
tt(t60_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k2_qc_lang2 A B C)) = (k4_subset_1 (k5_qc_lang1 A) (k5_qc_lang3 A B) (k5_qc_lang3 A C))) ) ) ) ) ) ) ).
tt(t60_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 (k26_quaterni A B) (k26_quaterni A B)) = (k26_quaterni (k26_quaterni (k26_quaterni (k18_quatern2 A A) (k18_quatern2 A B)) (k18_quatern2 B A)) (k18_quatern2 B B))) ) ) ) ) ).
tt(t60_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k28_quaterni (k26_quaterni (k29_quaterni A B) C)) = (k29_quaterni (k26_quaterni (k28_quaterni A) B) C)) ) ) ) ) ) ) ).
tt(t60_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k27_quaterni A (k31_quaterni A))) = (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni A)) (k5_square_1 (k18_quaterni A))) (k5_square_1 (k19_quaterni A))) (k5_square_1 (k20_quaterni A))))  &  ( ((k18_quaterni (k27_quaterni A (k31_quaterni A))) = k6_numbers)  &  ( ((k19_quaterni (k27_quaterni A (k31_quaterni A))) = k6_numbers)  &  ((k20_quaterni (k27_quaterni A (k31_quaterni A))) = k6_numbers) ) ) ) ) ) ).
tt(t60_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  => (r2_quofield (k19_quofield (k19_quofield A)) (k19_quofield A))) ) ).
tt(t60_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  (! [E:$i] :  ((m2_rcomp_3 E A B C D) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) & (r1_xxreal_0 A B)) ) )  => (r1_xxreal_0 2 (k3_finseq_1 E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k10_real_1 1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 A) (k1_nat_1 B 1)) (k5_square_1 (k1_seq_1 (k6_real_3 A) B)))) (k10_real_1 1 (k5_square_1 (k1_seq_1 (k6_real_3 A) B))))) ) ) ) ) ).
tt(t60_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) => (r1_tarski (k9_xtuple_0 (k5_relat_1 B A)) (k9_xtuple_0 B))) ) ) ).
tt(t60_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski C (k6_relset_2 B A D (k3_relset_1 A B E))) <=> (r1_tarski D (k6_relset_2 A B C E))) ) ) ) ) ) ) ) ) ).
tt(t60_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ( (! [B:$i] :  (! [C:$i] :  (~ (r13_rewrite1 A B C)) ) )  => (v9_rewrite1 A)) ) ) ).
tt(t60_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ((r4_rewrite2 A B C D) => (r4_rewrite2 A B (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B C) D)) ) ) ) ) ) ) ) ).
tt(t60_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))))  =>  (! [G:$i] :  ((m1_rewrite1 G (k1_rewrite3 C E F)) =>  ( ( ((k1_funct_1 G 1) = (k4_tarski A D))  &  ((k1_funct_1 G (k3_finseq_1 G)) = (k4_tarski B D)) )  =>  ( ((k3_finseq_1 G) = 1)  &  (A = B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_partfun1 C A) & (v1_partfun1 (k6_rfunct_1 A k1_numbers D) A))  =>  ((k1_funct_1 (k3_rfunct_1 A k1_numbers C D) B) = (k3_xcmplx_0 (k1_funct_1 C B) (k5_xcmplx_0 (k1_funct_1 D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t60_rfunct_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ((r2_rfunct_3 A B) => (r2_rfunct_3 (k18_rfunct_3 k1_numbers A) B)) ) ) ) ).
tt(t60_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 B) =>  ((k1_seq_1 (k4_rinfsup1 B) A) = (k1_real_1 (k1_seq_1 (k3_rinfsup1 (k32_valued_1 k5_numbers k1_numbers B)) A))) ) ) ) ) ) ).
tt(t60_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ( ((v1_rlaffin1 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski C B) &  (! [D:$i] :  ( ((v1_rlaffin1 D A) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((r1_tarski C D) &  ((r1_tarski D B) &  ((k4_rlaffin1 A D) = (k4_rlaffin1 A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_rlsub_1 C A) =>  ((r2_hidden (k4_algstr_0 A B) (k3_rlsub_1 A B C)) <=> (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t60_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  (! [D:$i] :  ( ((v1_rlvect_1 D) & (m1_rlsub_1 D A))  =>  ((m1_rlsub_1 B C) => (m1_rlsub_1 (k2_rlsub_2 A B D) (k2_rlsub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t60_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A B) = (k1_setfam_1 (a_2_1_rltopsp1 A B))) ) ) ) ) ).
tt(t60_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) (k4_algstr_0 A B) (k4_algstr_0 A C))) = (k4_algstr_0 A (k1_algstr_0 A C B))) ) ) ) ) ) ) ).
tt(t60_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k16_rlvect_2 A)) (u1_struct_0 (k16_rlvect_2 A))) (u1_struct_0 (k16_rlvect_2 A)) (k2_zfmisc_1 (k11_rlvect_2 A) (k11_rlvect_2 A)) (k11_rlvect_2 A) (u1_algstr_0 (k16_rlvect_2 A)) (k14_rlvect_2 A))) ) ).
tt(t60_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  ( (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r2_hidden C (k3_rmod_2 A B F E)) & (r2_hidden D (k3_rmod_2 A B F E))) ) )  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  ((k5_rmod_4 A B (k8_rmod_4 A B C)) = (k4_algstr_0 B (k5_rmod_4 A B C))) ) ) ) ) ) ) ).
tt(t60_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v15_lattices A) &  ((v8_robbins1 A) & (l4_robbins1 A)) ) ) ) )  =>  ((k3_robbins1 A (k6_lattices A)) = (k5_lattices A)) ) ) ).
tt(t60_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_roughs_1 A B C) & (r2_roughs_1 A C D))  => (r2_roughs_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t60_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( ((k3_rusub_1 A D B) = (k3_rusub_1 A C B))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_struct_0 B E) &  ((k3_rlvect_1 A D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (! [D:$i] :  ( ((v1_bhsp_1 D) & (m1_rusub_1 D A))  =>  ((m1_rusub_1 B C) => (m1_rusub_1 (k2_rusub_2 A B D) (k2_rusub_2 A C D))) ) ) ) ) ) ) ) ) ).
tt(t60_rvsum_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k1_seq_1 (k14_rvsum_1 B C) A) = (k11_binop_2 (k1_seq_1 B A) (k1_seq_1 C A))) ) ) ) ) ) ).
tt(t60_scmfsa_2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_scmfsa_2 B) =>  (~  (A = B) ) ) ) ) ) ).
tt(t60_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r5_scmfsa7b C (k1_scmfsa_m B) A) & (r6_scmfsa7b C (k1_scmfsa_m B) A))  =>  ((r4_scmfsa7b C D) |  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) & (v1_partfun1 B k5_numbers)) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k1_funct_1 A (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r4_scmfsa7b C D) |  ((r1_xxreal_0 (k1_funct_1 A D) k6_numbers) | (r1_scmfsa8a A B (k1_scmfsa8c (k1_scmfsa8b D (k1_scmfsa8a 2) (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) & (v3_scmpds_4 C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((r1_scmpds_6 C B A) & (r2_scmpds_6 C B A))  =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  |  ((k6_scmpds_4 (k6_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) => (v9_scmyciel (k1_subset_1 (k3_tarski A)) A)) ) ).
tt(t60_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_semi_af1 A B C D E) => (r3_semi_af1 A B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k2_numbers) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 B)) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  (C = (k1_funct_1 D A)) )  =>  ((k1_funct_1 (k18_seq_4 B D) A) = (k1_binop_2 C)) ) ) ) ) ) ) ) ) ) ).
tt(t60_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ((k3_kurato_0 A B) = (k1_kurato_0 A B)) ) ) ) ) ).
tt(t60_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((k3_kurato_0 A (k1_setlim_2 A B C)) = (k9_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C))) ) ) ) ) ) ).
tt(t60_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (r2_hidden A (k1_sf_mastr B)))  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 B C) A) = (k1_funct_1 C A)) ) ) ) ) ) ) ) ).
tt(t60_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A D B)) (k5_sheffer1 A C (k5_sheffer1 A D B))) (k5_sheffer1 A D D))) = (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t60_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((m1_simplex0 C A) =>  (! [D:$i] :  ((m1_simplex0 D A) =>  ( ((g1_pre_topc (u1_struct_0 C) (u1_pre_topc C)) = (g1_pre_topc (u1_struct_0 D) (u1_pre_topc D)))  =>  ((k10_simplex0 A C B) = (k10_simplex0 A D B)) ) ) ) ) ) ) ) ) ).
tt(t60_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k4_sincos10 (k1_rcomp_1 1 (k7_square_1 2))) (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k1_rcomp_1 (k10_real_1 k32_sin_cos 4) (k10_real_1 k32_sin_cos 2)))) = (k1_partfun2 k1_numbers (k1_rcomp_1 1 (k7_square_1 2)))) ).
tt(t60_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A B)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k4_binop_2 A B))) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B))))  &  ( ((k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A B)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k4_binop_2 A B))) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B))))  &  ((k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 B))) = (k3_binop_2 (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 A)) (k5_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 B)))) ) ) ) ) ) ) ).
tt(t60_sin_cos6,ax, (! [A:$i] :  ((v1_int_1 A) => (v2_funct_1 (k5_relset_1 k1_numbers k1_numbers k19_sin_cos (k1_rcomp_1 (k7_real_1 k32_sin_cos (k8_real_1 (k8_real_1 2 k32_sin_cos) A)) (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) A)))))) ) ).
tt(t60_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A 1))  =>  ((k5_power k8_power A) = (k2_sin_cos7 (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k11_binop_2 2 A)))) ) ) ) ).
tt(t60_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k6_sin_cos9 A) = (k10_real_1 k32_sin_cos 2)) ) )  =>  (A = k6_numbers) ) ) ) ).
tt(t60_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_real_1 (k1_seq_1 k19_sin_cos (k7_real_1 A B)) (k1_seq_1 k19_sin_cos A)) = (k9_real_1 (k1_real_1 (k8_real_1 B (k1_seq_1 k16_sin_cos A))) (k8_real_1 B (k4_complex1 (k3_xcmplx_0 (k11_comseq_3 (k27_sin_cos (k3_xcmplx_0 B k7_complex1))) (k2_xcmplx_0 (k1_seq_1 k19_sin_cos A) (k3_xcmplx_0 (k1_seq_1 k16_sin_cos A) k7_complex1))))))) ) ) ) ) ).
tt(t60_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k7_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k7_pscomp_1 A)) ) ) ).
tt(t60_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1)) (k3_topreal1 2 A)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) )  =>  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))  |  ( ( (~  ((k17_euclid B) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) )  &  (~  ((k18_euclid B) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1))) ) )  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) A)) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B) A) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ).
tt(t60_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k18_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t60_stirl2_1,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((k5_card_1 A) = (k5_card_1 B))  =>  ((v2_funct_2 C B) <=> (v2_funct_1 C)) ) ) ) ) ) ) ) ).
tt(t60_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  (! [E:$i] :  ((m2_subset_1 E (k6_qc_lang1 A) (k8_qc_lang1 A B)) =>  (! [F:$i] :  ( ((v5_relat_1 F (k3_qc_lang1 A)) &  ((v3_card_1 F B) & (m2_finseq_1 F (k2_qc_lang1 A))) )  =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [H:$i] :  ((m2_funct_2 H (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r2_relset_1 (k3_qc_lang1 A) C (k5_relset_1 (k3_qc_lang1 A) C G (k24_qc_lang1 A (k4_cqc_lang B A E F))) (k5_relset_1 (k3_qc_lang1 A) C H (k24_qc_lang1 A (k4_cqc_lang B A E F)))) =>  ((r1_valuat_1 A C (k4_cqc_lang B A E F) D G) <=> (r1_valuat_1 A C (k4_cqc_lang B A E F) D H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_tops_1 B A) =>  ( ((k9_subset_1 (u1_struct_0 A) (k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) (k9_subset_1 (u1_struct_0 A) B C)) = B)  <=> (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(t60_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (? [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) & (v3_tex_2 B A)) ) ) ) ).
tt(t60_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ((v2_tex_3 B A) & (v1_tex_2 B A)) ) )  & (v3_tdlat_3 A)) ) ) ) ).
tt(t60_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v4_pre_topc B A) =>  ((k3_tex_4 A B) = B) ) ) ) ) ) ).
tt(t60_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D B))  =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((v3_pre_topc E B) &  ((r2_hidden F E) &  ((r1_tarski E (u1_struct_0 D)) &  (F = G) ) ) )  =>  ((r1_tmap_1 B A C F) <=> (r1_tmap_1 D A (k2_tmap_1 B A C D) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_borsuk_2 C (k15_euclid A) B B) =>  ((u1_struct_0 (k5_topalg_1 (k15_euclid A) B)) = (k1_tarski (k6_eqrel_1 (k2_topalg_1 (k15_euclid A) B) (k2_topalg_1 (k15_euclid A) B) (k4_topalg_1 (k15_euclid A) B) C))) ) ) ) ) ) ) ).
tt(t60_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v2_topgen_4 B A) & (r1_tarski B C))  => (v2_topgen_4 C A)) ) ) ) ) ) ) ).
tt(t60_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( ((k1_funct_1 (k4_topgen_5 B C) A) = k6_numbers)  =>  (A = (k19_euclid B k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t60_topgrp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v2_group_1 A) &  ((v3_group_1 A) &  ((v3_topgrp_1 A) &  ((v4_topgrp_1 A) & (l1_topgrp_1 A)) ) ) ) ) )  => (v9_pre_topc A)) ) ).
tt(t60_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k3_pcomps_1 A)))) =>  ( (D = (k11_metric_1 A B C))  => (v4_pre_topc D (k3_pcomps_1 A))) ) ) ) ) ) ) ) ) ).
tt(t60_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (k5_jgraph_6 A B C)) & (r2_hidden E (k5_jgraph_6 A B C)))  => (r1_tarski (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) D E) (k2_tarski D E)) (k6_jgraph_6 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_toprealc,ax, (! [A:$i] :  ( ( (~ (v3_xxreal_0 A))  & (v1_xreal_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_toprealb B (k4_struct_0 (k15_euclid B)) A))) => (m1_subset_1 (k30_valued_1 C) (u1_struct_0 (k7_toprealb B (k4_struct_0 (k15_euclid B)) A)))) ) ) ) ) ) ).
tt(t60_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v3_tops_1 B A))  =>  (B = k1_xboole_0) ) ) ) ) ) ).
tt(t60_tops_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v3_tops_2 C A B) <=>  ( ((k1_relset_1 (u1_struct_0 A) C) = (k2_struct_0 A))  &  ( ((k2_relset_1 (u1_struct_0 B) C) = (k2_struct_0 B))  &  ((v2_funct_1 C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (k2_pre_topc A D)) = (k2_pre_topc B (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  (D = E) ) )  =>  ( ((v1_tops_1 C A) & (v1_tops_1 E B))  <=> (v1_tops_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v4_transgeo C A) &  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C B) = B)  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A B D B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D))) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) => (r2_analoaf A D E (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ((r2_hidden B (k12_trees_3 A)) <=>  (~  ( (~  (B = k1_xboole_0) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (~  ((r2_hidden C A) &  (B = (k7_finseq_1 (k12_finseq_1 k5_numbers k6_numbers) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  =>  ((r2_tsep_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  (? [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) &  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((r1_tarski D B) &  ((r1_tarski E C) &  ((r1_tarski F (k9_subset_1 (u1_struct_0 A) B C)) &  ((v3_pre_topc D A) &  ((v3_pre_topc E A) & (v4_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_uniroots,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  ( (~ (r1_xxreal_0 A 1))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B 1))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 k1_complfld)) =>  ( (C = B)  =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ( (D = (k2_polynom4 k1_complfld (k5_uniroots A) C))  & (r1_xxreal_0 (k1_int_2 D) (k21_binop_2 B 1))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k10_uproots A (k16_pre_poly (u1_struct_0 A))) (k3_algseq_1 A (k5_struct_0 A)))) ) ).
tt(t60_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k16_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k52_valued_2 A B C D)) = (k52_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k16_valued_2 A B C) (k30_valued_1 D))) ) ) ) ) ) ) ) ).
tt(t60_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden (k3_rlvect_1 B C D) (k3_vectsp_4 A B D E)) <=> (r1_struct_0 E C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v15_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ) ).
tt(t60_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r2_yellow_0 A B) | (v3_lattice3 A))  =>  ((k2_yellow_0 A B) = (k2_yellow_0 A (k12_waybel_0 A B))) ) ) ) ) ) ).
tt(t60_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_orders_3 (k4_waybel_1 A B) A A)) ) ) ) ).
tt(t60_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (v5_orders_3 (k5_waybel23 A B) A (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ).
tt(t60_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_orders_2 A) &  ((v1_yellow_0 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) &  ((v7_waybel34 B A) & (m1_yellow_0 B A)) ) )  =>  ((k3_yellow_0 B) = (k3_yellow_0 A)) ) ) ) ) ).
tt(t60_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_waybel_4 A (k5_waybel_4 A C B) B)) )  => (v9_waybel_4 B A)) ) ) ) ) ).
tt(t60_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r1_tarski A B) & (r2_xboole_0 B A)) ) ) ) ).
tt(t60_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k6_xboolean B C)) = (k4_xboolean (k6_xboolean A B) (k6_xboolean A (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t60_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ( (~  (A = k6_numbers) )  =>  ((k7_xcmplx_0 A A) = 1) ) ) ) ).
tt(t60_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 (k4_xcmplx_0 A) B) => (r1_xxreal_0 k6_numbers (k2_xcmplx_0 A B))) ) ) ) ) ).
tt(t60_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k2_xxreal_1 A B) (k3_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ( (~ (r1_xxreal_0 A C))  & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ((r1_tarski A B) => (r1_xxreal_0 (k2_xxreal_2 B) (k2_xxreal_2 A))) ) ) ) ) ).
tt(t60_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( ((r1_xxreal_0 A (k2_xxreal_3 B)) => (r1_xxreal_0 B (k2_xxreal_3 A)))  &  ((r1_xxreal_0 (k2_xxreal_3 A) B) => (r1_xxreal_0 (k2_xxreal_3 B) A)) ) ) ) ) ) ).
tt(t60_yellow_0,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ((v4_yellow_0 B A) & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  ( ( (E = C)  &  ( (F = D)  &  ((r1_orders_2 A C D) & (r2_hidden E (u1_struct_0 B))) ) )  => (r1_orders_2 B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t60_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A B)))) =>  ((v3_waybel11 C (k3_yellow_3 A B)) =>  ((v3_waybel11 (k4_yellow_3 A B C) A) & (v3_waybel11 (k5_yellow_3 A B C) B)) ) ) ) ) ) ) ) ).
tt(t60_yellow_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k3_yellow_3 A A)))) =>  ((k3_tarski (a_2_1_yellow_4 A B)) = (k3_yellow_4 A (k4_yellow_3 A A B) (k5_yellow_3 A A B))) ) ) ) ) ).
tt(t60_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_yellow_5 A (k13_lattice3 A B C) (k12_lattice3 A B C)) = (k13_lattice3 A (k1_yellow_5 A B C) (k1_yellow_5 A C B))) ) ) ) ) ) ) ).
tt(t60_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  ( ((u1_struct_0 A) = (u1_struct_0 B))  =>  (! [C:$i] :  ((m3_yellow_9 C A B) =>  ((v1_tops_2 (k3_setfam_1 (u1_pre_topc A) (u1_pre_topc B)) C) &  ((v1_cantor_1 (k3_setfam_1 (u1_pre_topc A) (u1_pre_topc B)) C) & (m1_subset_1 (k3_setfam_1 (u1_pre_topc A) (u1_pre_topc B)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ).
tt(t60_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  ((k2_zf_model (k6_zf_lang A)) = (k2_zf_model A)) ) ) ).
tt(t60_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r1_zf_lang A B) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t60_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) B) = k1_xboole_0)  <=> (r2_hidden A B)) ) ) ).
tt(t60_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_zmodul01 A B (k3_zmodul01 A)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t61_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_abcmiz_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_abcmiz_0 A)) =>  ( ((r5_abcmiz_0 A B C) & (r5_abcmiz_0 A (k8_abcmiz_0 A B C) D))  => (r5_abcmiz_0 A B (k8_finseq_1 (u1_abcmiz_0 A) C D))) ) ) ) ) ) ) ) ) ).
tt(t61_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v7_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  (? [C:$i] :  ( ((v6_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A)))  &  ( (B = (k30_abcmiz_1 A (k32_abcmiz_1 A) C))  &  ((k37_abcmiz_1 A B) = C) ) ) ) ) ) ) ) ).
tt(t61_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 B A) &  ((v1_aff_4 C A) & (v1_aff_4 D A)) )  =>  ( ( (~  ((r1_aff_4 A B C) & (r1_aff_4 A C D)) )  &  ( (~  ((r1_aff_4 A B C) & (r1_aff_4 A D C)) )  &  ( (~  ((r1_aff_4 A C B) & (r1_aff_4 A C D)) )  &  (~  ((r1_aff_4 A C B) & (r1_aff_4 A D C)) ) ) ) )  | (r1_aff_4 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t61_afinsq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (~  ( ((k1_afinsq_1 C) = (k2_xcmplx_0 A B))  &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v5_ordinal1 E) &  ((v1_funct_1 E) & (v1_finset_1 E)) ) )  =>  (~  ( ((k1_afinsq_1 D) = A)  &  ( ((k1_afinsq_1 E) = B)  &  (C = (k1_ordinal4 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v4_partfun3 A) =>  ((r1_xxreal_0 (k1_afinsq_1 A) k6_numbers) |  ( (! [C:$i] :  (~  ((r2_hidden C (k1_relset_1 k5_numbers A)) &  ((k1_funct_1 A C) = B) ) ) )  | (r1_xxreal_0 B (k7_afinsq_2 A))) ) ) ) ) ) ) ).
tt(t61_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v1_msafree1 B A) & (l3_msualg_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k10_xtuple_0 (u3_msualg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (k10_xtuple_0 (u3_msualg_1 A B))) =>  ( (C = D)  | (r1_xboole_0 C D)) ) ) ) ) ) ) ) ) ).
tt(t61_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r4_analmetr A B C D E) =>  ((r4_analmetr A B C E D) &  ((r4_analmetr A C B D E) &  ((r4_analmetr A C B E D) &  ((r4_analmetr A D E B C) &  ((r4_analmetr A D E C B) &  ((r4_analmetr A E D B C) & (r4_analmetr A E D C B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ( (~  ((k13_aofa_000 (k7_freealg k19_aofa_000 A) B C) = B) )  &  (~  ((k13_aofa_000 (k7_freealg k19_aofa_000 A) B C) = C) ) ) ) ) ) ) ) ) ).
tt(t61_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [H:$i] :  ((m1_aofa_i00 H B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [I:$i] :  ((m1_aofa_i00 I B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [J:$i] :  ( ((v1_relat_1 J) & (v1_funct_1 J))  &  ( ((k1_funct_1 J C) = k6_numbers)  &  ( ((k1_funct_1 J E) = 1)  &  ( ((k1_funct_1 J F) = 2)  &  ( ((k1_funct_1 J G) = 3)  &  ( ((k1_funct_1 J H) = 4)  &  ((k1_funct_1 J I) = 5) ) ) ) ) ) ) )  =>  (! [J:$i] :  ((m2_funct_2 J B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [K:$i] :  ((m2_subset_1 K k1_numbers k5_numbers) =>  ( (K = (k21_aofa_i00 B k4_numbers J E))  =>  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D J (k13_aofa_000 A (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F k6_numbers) (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 1)) (k17_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D I 1) (k74_aofa_i00 A B C D I E) (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H F) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)) (k81_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G H)) (k57_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D I 1)))) F) = (k1_pre_ff K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_arytm_3,ax, (! [A:$i] :  (~ (r2_hidden (k4_tarski k11_arytm_3 A) k5_arytm_3)) ) ).
tt(t61_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 2 A) & (r1_xxreal_0 (k5_series_1 2 A) (k2_nat_1 A 1))) ) ) ) ).
tt(t61_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A D (k1_bcialg_1 A D (k1_bcialg_1 A B C))) = (k1_bcialg_1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t61_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A (k6_bhsp_1 A B C) D) (k6_bhsp_1 A B (k3_normsp_1 A C D)))) ) ) ) ) ) ) ) ).
tt(t61_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_lattices A B C) (k3_lattices A (k3_boolealg A B C) (k4_lattices A B C)))) ) ) ) ) ) ).
tt(t61_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k1_seq_4 B))  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k2_rcomp_1 B k1_xxreal_0))) ) ) ) ) ) ).
tt(t61_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) => (r2_hidden (k4_tarski k6_numbers A) k6_borsuk_6)) ) ).
tt(t61_borsuk_7,ax, (! [A:$i] :  ((v1_int_1 A) =>  ((k1_funct_1 k12_borsuk_7 A) = k8_borsuk_7) ) ) ).
tt(t61_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t61_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  ( (B = (k6_enumset1 C D E F G H I J))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (H = I)  |  ( (H = J)  |  ( (I = J)  |  ((k5_bvfunc_2 A J B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C D) E) F) G) H) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((r1_xxreal_0 A (k6_xboolean B C)) <=> (r1_xxreal_0 (k4_xboolean A B) C)) ) ) ) ) ) ) ).
tt(t61_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc26 A B (k5_bvfunc26 A B C)) (k11_bvfunc_1 A))) ) ) ) ) ) ).
tt(t61_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_finseq_1 F (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) F (k12_finseq_1 (k3_cqc_lang A) (k4_substut2 A B D E))) (k12_finseq_1 (k3_cqc_lang A) C))) =>  ((r2_hidden E (k3_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) F (k12_finseq_1 (k3_cqc_lang A) (k12_cqc_lang A D B))) (k12_finseq_1 (k3_cqc_lang A) C)))) | (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) (k8_finseq_1 (k3_cqc_lang A) F (k12_finseq_1 (k3_cqc_lang A) (k12_cqc_lang A D B))) (k12_finseq_1 (k3_cqc_lang A) C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_card_1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((v1_finset_1 A) <=> (r2_hidden A k4_ordinal1)) ) ) ).
tt(t61_card_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  => (r1_ordinal1 (k1_card_1 (k10_xtuple_0 A)) (k1_card_1 (k9_xtuple_0 A)))) ) ).
tt(t61_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( ((k8_card_3 A) = (k1_tarski k1_xboole_0))  <=>  (! [B:$i] :  ((r2_hidden B (k9_xtuple_0 A)) =>  ((k1_funct_1 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t61_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ((v1_finset_1 C) =>  ((r1_tarski C A) =>  ( ((v1_xboole_0 B) &  (~ (v1_xboole_0 A)) )  |  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ((v2_funct_1 D) &  ((k5_card_1 A) = (k5_card_1 B)) )  =>  ((k9_newton (k7_nat_d (k5_card_1 A) (k5_card_1 C))) = (k1_card_1 (a_4_3_card_fin A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ( ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  &  ( (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))) ) ) )  &  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A D))  =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A D E)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) )  => (m2_cat_1 C A B)) ) ) ) ) ) ) ).
tt(t61_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((r2_cat_3 A B C D) & (v10_cat_1 (k4_graph_1 A C) A))  => (r1_cat_1 A B (k4_graph_1 A D))) ) ) ) ) ) ) ) ) ).
tt(t61_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((k3_graph_1 A (k22_cat_4 A B C)) = C)  &  ((k4_graph_1 A (k22_cat_4 A B C)) = (k20_cat_4 A B C)) ) ) ) ) ) ) ) ).
tt(t61_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_partfun1 B A) <=> (v1_partfun1 (k55_valued_1 A k2_numbers B) A)) ) ) ) ) ).
tt(t61_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 A 1)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 A 1)))) =>  ((k10_chain_1 B C A (k7_chain_1 B C (k2_nat_1 A 1) D E)) = (k7_chain_1 B C A (k10_chain_1 B C A D) (k10_chain_1 B C A E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  ((v4_glib_000 A) => (v2_chord A)) ) ) ).
tt(t61_circcomb,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k4_finseq_2 A k6_margrel1) k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 A k6_margrel1) k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_card_1 C A) & (v1_finseq_1 C)) ) )  => (v6_circcomb (k7_circcomb A k6_margrel1 B C) (k5_circcomb B C))) ) ) ) ) ) ).
tt(t61_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r8_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m2_circtrm1 G A C B D E F) =>  (! [H:$i] :  ((m1_subset_1 H (k4_card_3 (u3_msualg_1 E F))) =>  (! [I:$i] :  ((m1_dtconstr I (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  ((r2_hidden I (k9_trees_9 D)) =>  ((r1_facirc_1 E F (k5_facirc_1 E F H (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 I)))) (k1_funct_1 G I)) &  (! [J:$i] :  ((m1_subset_1 J (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  ( (J = (k3_relat_1 G H))  =>  (! [K:$i] :  ((m1_circtrm1 K A C D B J) =>  ((k1_funct_1 (k5_facirc_1 E F H (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 I)))) (k1_funct_1 G I)) = (k7_circtrm1 A B C I K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_classes1,ax, (! [A:$i] :  (! [B:$i] : (r1_tarski (k5_classes1 (k3_xboole_0 A B)) (k3_xboole_0 (k5_classes1 A) (k5_classes1 B)))) ) ).
tt(t61_classes2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden A C) & (r2_hidden B C))  =>  ((r2_hidden (k2_zfmisc_1 A B) C) & (r2_hidden (k1_funct_2 A B) C)) ) ) ) ) ) ).
tt(t61_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r2_hidden (k4_struct_0 A) (k5_clvect_1 A B C)) <=> (r1_struct_0 C B)) ) ) ) ) ) ) ).
tt(t61_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 C A) => (v2_clvect_2 (k6_clvect_1 A C B) A)) ) ) ) ) ) ) ).
tt(t61_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) &  ((v10_cohsp_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k11_cohsp_1 A B C))) =>  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) &  ((v10_cohsp_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  &  ((k11_cohsp_1 A B E) = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k17_complex1 (k6_xcmplx_0 A B)) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t61_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k3_complex2 A B) = (k1_comptrig B)) ) ) ) ) ) ).
tt(t61_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  ((k17_complex1 (k4_algstr_0 k1_complfld A)) = (k17_complex1 A)) ) ) ).
tt(t61_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 B) = (k3_finseq_1 D)) ) )  =>  ((k4_finseqop k2_numbers k2_numbers B (k7_seq_4 A)) = (k4_finseqop k1_numbers k1_numbers D (k3_rvsum_1 C))) ) ) ) ) ) ) ) ) ) ).
tt(t61_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k2_afinsq_1 (k11_compos_1 A B)) = (k7_domain_1 k5_numbers k6_numbers 1)) ) ) ) ) ).
tt(t61_compos_2,ax, (! [A:$i] :  ( ((v1_amistd_4 A) & (l1_compos_1 A))  =>  (! [B:$i] :  ( ((v6_compos_0 B (u1_compos_1 A)) & (m1_subset_1 B (u1_compos_1 A)))  =>  ((v4_compos_0 B (u1_compos_1 A)) => (v1_compos_2 (k11_compos_1 A B) A)) ) ) ) ) ).
tt(t61_comptrig,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((k20_sin_cos A) = 1) )  =>  ((r1_xxreal_0 (k8_real_1 2 k32_sin_cos) A) |  (A = k6_numbers) ) ) ) ) ).
tt(t61_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 D) &  ((v4_valued_0 D) & (v2_margrel1 D)) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 C) 1) k5_numbers)) =>  ((r2_hidden A (k4_finseq_1 E)) =>  ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) <=>  ((r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))) & (r2_hidden (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))) (k1_relset_1 (k3_finseq_2 k5_numbers) D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_seq_2 (k3_series_1 (k55_valued_1 k5_numbers k2_numbers A))) <=> (v2_comseq_3 A)) ) ) ).
tt(t61_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) => (r1_tarski (k19_convex4 A B (k2_xcmplx_0 C D)) (k6_rusub_4 A (k19_convex4 A B C) (k19_convex4 A B D)))) ) ) ) ) ) ) ) ).
tt(t61_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A (k6_cqc_lang A B) B) B) A)) ) ) ) ).
tt(t61_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A (k12_cqc_lang A D (k8_cqc_lang A B C)) (k8_cqc_lang A (k11_cqc_lang A D B) (k12_cqc_lang A D C))) A) & (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A (k11_cqc_lang A D B) (k12_cqc_lang A D C)) (k12_cqc_lang A D (k8_cqc_lang A B C))) A)) ) ) ) ) ) ) ) ) ).
tt(t61_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v3_card_1 C B) & (m2_finseq_1 C (k2_qc_lang1 A)))  =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k5_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r1_tarski (k23_qc_lang1 A (k1_cqc_lang A C (k2_cqc_lang A D E))) (k2_xboole_0 (k23_qc_lang1 A C) (k1_tarski E)))) ) ) ) ) ) ) ) ) ) ).
tt(t61_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 B) &  ((v3_funct_1 C) & (r2_funct_2 k5_numbers (u1_struct_0 A) D (k16_csspace A B C))) )  => (v3_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t61_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k19_sin_cos) A B) = (k1_real_1 (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k18_sin_cos (k10_real_1 (k8_real_1 3 (k7_real_1 B A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 (k9_real_1 B A)) 2))) (k8_real_1 (k18_sin_cos (k10_real_1 (k7_real_1 A B) 2)) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))))) (k9_real_1 A B)))) ) ) ) ) ).
tt(t61_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k18_sin_cos D))) ) )  =>  ( ((k18_sin_cos A) = k6_numbers)  |  ( ((k18_sin_cos B) = k6_numbers)  |  ((k9_diff_1 C A B) = (k1_real_1 (k10_real_1 (k10_real_1 (k8_real_1 2 (k9_real_1 (k18_sin_cos B) (k18_sin_cos A))) (k9_real_1 (k21_sin_cos (k7_real_1 A B)) (k21_sin_cos (k9_real_1 A B)))) (k9_real_1 A B)))) ) ) ) ) ) ) ) ) ) ).
tt(t61_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k7_real_1 A B) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k7_real_1 A B)) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k7_real_1 A B))) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A)) 2)))) ) ) ) ) ) ).
tt(t61_ec_pf_1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k9_int_3 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (~  ( (~ (r1_xxreal_0 A 3))  &  ( (~  ((k4_ec_pf_1 A B C) = (k4_struct_0 (k9_int_3 A))) )  &  (! [D:$i] :  ((m2_finseq_1 D k4_numbers) =>  (~  ( ((k3_finseq_1 D) = A)  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k2_finseq_1 A)) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (~  ( (F = (k6_xcmplx_0 E 1))  &  ((k1_funct_1 D E) = (k2_ec_pf_1 A (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) F 3) (k8_group_1 (k9_int_3 A) B F)) C))) ) ) ) ) ) ) ) )  &  ((k5_card_1 (k8_eqrel_1 (k6_ec_pf_1 A B C) (k8_ec_pf_1 A B C))) = (k2_xcmplx_0 (k2_nat_1 1 A) (k1_gr_cy_1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k9_int_3 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k9_int_3 A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k9_int_3 A))) =>  (! [K:$i] :  ((m2_subset_1 K (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k6_int_1 3 A))  &  ( (E = (k6_int_1 4 A))  &  ( (F = (k6_int_1 8 A))  &  ( (G = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) D (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2))))  &  ( (H = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))  &  ( (I = (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) H))  &  ( (J = (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k8_group_1 (k9_int_3 A) F I)))  &  (L = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C J) H) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E I) J)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k2_binom (k9_int_3 A) H 2))) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 3)))) ) ) ) ) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k2_binom (k9_int_3 A) H 2)) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) (k3_ec_pf_2 A B) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L))) = (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) (k2_binom (k9_int_3 A) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C H) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k8_group_1 (k9_int_3 A) G (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K))) 2)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k2_binom (k9_int_3 A) H 2)) (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A)) (k24_ens_1 A B C) D) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 B (k4_graph_1 B D) C) (k2_cat_1 B (k3_graph_1 B D) C))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B)) (k2_cat_1 B (k4_graph_1 B D) C) (k2_cat_1 B (k3_graph_1 B D) C)) (k18_ens_1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t61_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_matrprob B) & (m2_finseq_1 B k1_numbers))  =>  ((k7_entropy1 (k6_matrixr1 (k9_matrixr1 A) (k10_matrixr1 B))) = (k7_real_1 (k6_entropy1 A) (k6_entropy1 B))) ) ) ) ) ).
tt(t61_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 A B D C)) ) ) ) ) ).
tt(t61_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) => (m1_subset_1 (k3_tarski C) (k1_zfmisc_1 A))) ) ) ) ) ) ).
tt(t61_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ( ((k1_seq_1 (k6_euclid 3 A) 1) = (k7_binop_2 (k1_seq_1 A 1)))  &  ( ((k1_seq_1 (k6_euclid 3 A) 2) = (k7_binop_2 (k1_seq_1 A 2)))  &  ((k1_seq_1 (k6_euclid 3 A) 3) = (k7_binop_2 (k1_seq_1 A 3))) ) ) ) ) ).
tt(t61_euclid,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k5_algstr_0 (k15_euclid 2) A B) = (k19_euclid (k9_real_1 (k17_euclid A) (k17_euclid B)) (k9_real_1 (k18_euclid A) (k18_euclid B)))) ) ) ) ) ).
tt(t61_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((r6_euclidlp A B C) & (r5_euclidlp A C D))  => (r6_euclidlp A B D)) ) ) ) ) ) ) ) ) ).
tt(t61_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) =>  ( ((k9_xtuple_0 (k7_exchsort A B C D)) = (k2_zfmisc_1 (k9_xtuple_0 B) (k9_xtuple_0 B)))  & (r1_tarski (k10_xtuple_0 (k7_exchsort A B C D)) (k2_zfmisc_1 (k9_xtuple_0 B) (k9_xtuple_0 B)))) ) ) ) ) ) ) ) ) ).
tt(t61_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  ((r2_hidden (k4_tarski (k10_finseq_1 A B) D) (u1_struct_0 (k8_facirc_1 A B C D))) & (r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) D) C) D) (u1_struct_0 (k8_facirc_1 A B C D)))) ) ) ) ) ) ).
tt(t61_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k1_sin_cos9 k2_sin_cos9) A) B) = (k10_real_1 (k9_real_1 (k1_seq_1 k2_sin_cos9 B) (k1_seq_1 k1_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ).
tt(t61_fib_num2,ax, ((k6_fib_num2 3) = (k10_finseq_1 1 2)) ).
tt(t61_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_filter_0 A B C) = (k7_filter_0 A C B)) ) ) ) ) ) ) ).
tt(t61_filter_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_filter_1 A (k7_filter_1 (k4_filter_1 A (k2_filter_0 A B)) (k6_filter_0 A (k2_filter_0 A B))))) ) ) ) ).
tt(t61_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v20_lattices B A) &  ((v21_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 B B) B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  ( ( (C = (k1_realset1 (u2_lattices A) B))  &  (D = (k1_realset1 (u1_lattices A) B)) )  =>  ((v1_binop_1 C B) &  ((v2_binop_1 C B) &  ((v1_binop_1 D B) &  ((v2_binop_1 D B) &  ((r1_lattice2 B C D) & (r1_lattice2 B D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_finseq_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden (k2_xcmplx_0 A C) (k2_finseq_1 (k2_xcmplx_0 B C))) =>  ((r1_xxreal_0 A k6_numbers) |  ((r2_hidden A (k2_finseq_1 B)) & (r2_hidden A (k2_finseq_1 (k2_xcmplx_0 B C)))) ) ) ) ) ) ) ) ) ).
tt(t61_finseq_2,ax, (! [A:$i] :  ((k2_finseq_2 2 A) = (k10_finseq_1 A A)) ) ).
tt(t61_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k3_finseq_1 (k1_finseq_3 A B)) = (k3_finseq_1 A))  => (r1_xboole_0 B (k10_xtuple_0 A))) ) ) ) ).
tt(t61_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ( ( ((k10_xtuple_0 A) = (k10_xtuple_0 B))  &  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  & (v2_funct_1 B)) )  => (v2_funct_1 A)) ) ) ) ) ).
tt(t61_finseq_5,ax, (! [A:$i] :  (! [B:$i] :  ((k3_finseq_5 (k10_finseq_1 A B)) = (k10_finseq_1 B A)) ) ) ).
tt(t61_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) => (r2_hidden B (k10_xtuple_0 (k2_finseq_5 A C B)))) ) ) ) ) ) ).
tt(t61_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo B A) &  ((v2_binop_1 B A) & (v1_finseqop B A)) )  =>  ((k3_funct_2 A A (k5_finseqop A B) (k4_binop_1 A B)) = (k4_binop_1 A B)) ) ) ) ) ) ).
tt(t61_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski B C) => (r1_tarski (k8_flang_1 A B) (k8_flang_1 A C))) ) ) ) ) ) ).
tt(t61_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r1_xxreal_0 C D) =>  ((r1_xxreal_0 D k6_numbers) |  ((k1_flang_2 A (k8_flang_1 A B) C D) = (k8_flang_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t61_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k2_flang_3 A B) (k8_flang_1 A C))) ) ) ) ) ) ).
tt(t61_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v8_struct_0 E) &  ((v5_fsm_1 E A B) &  ((v7_fsm_1 E A B) & (l2_fsm_1 E A B)) ) ) )  =>  ( ((r1_subset_1 (u1_struct_0 D) (u1_struct_0 E)) &  ((r4_fsm_1 A B D E) &  (C = (k13_fsm_1 A B D E)) ) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k11_fsm_1 A B C))) =>  (? [G:$i] :  ((m1_subset_1 G F) &  (? [H:$i] :  ((m1_subset_1 H F) &  ((r2_hidden G (u1_struct_0 D)) &  ((r2_hidden H (u1_struct_0 E)) &  (! [I:$i] :  ((m1_subset_1 I F) =>  ( (I = G)  |  (I = H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F B A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((v2_binop_1 C A) => (r2_funct_2 B A (k6_funcop_1 A B C (k6_funcop_1 A B C D E) F) (k6_funcop_1 A B C D (k6_funcop_1 A B C E F)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_tarski (k7_relat_1 (k6_relat_1 A C) B) (k7_relat_1 C B))) ) ) ) ).
tt(t61_funct_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A A) &  ((v3_funct_2 B A A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r2_relset_1 A A (k1_partfun1 A A A A B (k2_funct_2 A B)) (k6_partfun1 A)) & (r2_relset_1 A A (k1_partfun1 A A A A (k2_funct_2 A B) B) (k6_partfun1 A))) ) ) ) ).
tt(t61_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (~  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  ( ( (C = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  (~  ( ((k3_relat_1 (k13_funct_3 D E) (k9_funct_3 B C)) = D)  &  ((k3_relat_1 (k13_funct_3 D E) (k10_funct_3 B C)) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( (~ (v1_xboole_0 E))  =>  (! [F:$i] :  ( (~ (v1_xboole_0 F))  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_zfmisc_1 A B) E) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) E)))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (k2_zfmisc_1 C D) F) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 C D) F)))) )  =>  ((v1_funct_1 (k3_funct_4 G H)) &  ((v1_funct_2 (k3_funct_4 G H) (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)) (k2_zfmisc_1 E F)) & (m1_subset_1 (k3_funct_4 G H) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A C) (k2_zfmisc_1 B D)) (k2_zfmisc_1 E F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( ((k1_card_1 A) = (k1_card_1 B))  &  ((k1_card_1 C) = (k1_card_1 D)) )  =>  ((k1_card_1 (k1_funct_2 A C)) = (k1_card_1 (k1_funct_2 B D))) ) ) ) ) ) ).
tt(t61_funct_7,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v1_finseq_1 B) & (v1_funct_7 B)) ) )  =>  ( (~  (B = k1_xboole_0) )  =>  ((k9_xtuple_0 (k4_funct_7 A B)) = (k3_xboole_0 (k6_funct_7 B) A)) ) ) ) ) ).
tt(t61_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 k6_numbers A) =>  ((k1_funct_1 k2_euclid A) = A) ) ) ) ).
tt(t61_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_fvaluat1 C A) =>  ((v3_fvaluat1 A) =>  ((r2_hidden B (k8_fvaluat1 A C)) <=>  (~ (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers C B) k6_numbers)) ) ) ) ) ) ) ) ) ).
tt(t61_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l3_algstr_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m2_finseq_2 F (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  (! [G:$i] :  ((m2_finseq_2 G (u1_struct_0 C) (k4_finseq_2 B (u1_struct_0 C))) =>  ( ((r2_hidden A (k2_finseq_1 B)) &  ( (D = (k1_funct_1 F A))  &  (E = (k1_funct_1 G A)) ) )  =>  ((k1_funct_1 (k12_fvsum_1 B C F G) A) = (k6_algstr_0 C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ( ((k1_twoscomp (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) (k24_gfacirc1 A B C)) = (k2_binarith (k2_binarith E (k9_margrel1 F)) (k9_margrel1 G)))  &  ( ((k1_funct_1 (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) = (k2_binarith E (k9_margrel1 F)))  &  ( ((k1_funct_1 (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) A) = E)  &  ( ((k1_funct_1 (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) B) = F)  &  ((k1_funct_1 (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) C) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k28_glib_000 A C)) <=>  ((r2_hidden B (k7_glib_000 A)) &  ( ((k1_funct_1 (k10_glib_000 A) B) = C)  |  ((k1_funct_1 (k11_glib_000 A) B) = C) ) ) ) ) ) ) ) ) ).
tt(t61_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  (! [C:$i] :  ((m3_glib_001 C A) =>  (! [D:$i] :  ((m3_glib_001 D B) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ( (C = D)  =>  ((k20_glib_001 A C E F) = (k20_glib_001 B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid 1 (k1_real_1 1))) (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) k6_numbers)) (k1_tarski (k5_algstr_0 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) 1) (k19_euclid k6_numbers 1)))))) ) ).
tt(t61_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) A))  &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) (k2_nat_1 B 1)))  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) B A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) A)) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 2) A)) (k3_topreal1 2 C)) & (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) (k2_nat_1 A 1))) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( (D = (k8_graph_2 A (k2_nat_1 C 1) (k3_finseq_1 A)))  &  ((r4_graph_2 A C) &  ((r3_graph_2 A 1 C) &  (B = (k2_funct_7 (k2_funct_7 A (k2_nat_1 C 1) (k1_funct_1 A D)) D (k1_funct_1 A (k2_nat_1 C 1)))) ) ) ) )  => (r3_graph_2 B 1 (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ).
tt(t61_graph_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v6_graph_1 B) & (l1_graph_1 B)) )  =>  (! [C:$i] :  ( ((v7_graph_1 C B) & (m2_graph_1 C B))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (~  ((r1_graph_5 B C D E) &  ((r5_graph_5 B A) &  (! [F:$i] :  ( ((v7_graph_1 F B) &  ((v1_graph_4 F B) & (m2_graph_1 F B)) )  =>  (~ (r7_graph_5 B D E F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((m1_group_2 B C) => (r1_tarski (k3_group_11 A B C) (k3_group_11 A C B))) ) ) ) ) ) ) ).
tt(t61_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((r1_tarski (u1_struct_0 A) (u1_struct_0 B)) =>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ).
tt(t61_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  => (r1_group_2 A (k6_group_3 A B (k1_group_1 A)) B)) ) ) ) ).
tt(t61_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((m1_group_2 B C) <=> (r1_group_2 A (k8_group_4 A B C) C)) ) ) ) ) ) ) ).
tt(t61_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r1_struct_0 (k7_group_5 B C D) A) <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  ( ((k3_finseq_1 E) = (k3_finseq_1 F))  &  ((r1_tarski (k10_xtuple_0 E) (k4_group_5 B C D)) &  (A = (k3_group_4 B (k4_group_4 B F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_group_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v3_funct_2 C A B) =>  ( ((k1_relset_1 A C) = A)  &  ((k2_relset_1 B C) = B) ) ) ) ) ) ) ) ).
tt(t61_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r1_group_9 A B C (k2_subset_1 B))) ) ) ) ).
tt(t61_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k14_bilinear k1_complfld A B (k3_hermitan A B C)) = (k14_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k3_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C)))) ) ) ) ) ) ) ).
tt(t61_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k1_relset_1 k1_numbers k30_sin_cos)) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 k30_sin_cos A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos)) (k6_rfunct_1 k1_numbers k1_numbers k16_sin_cos)) A) 2))) ) ) ).
tt(t61_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((r2_hidden C (k8_ideal_1 A B)) <=>  (? [D:$i] :  ((m2_ideal_1 D A B) &  (C = (k4_rlvect_1 A D)) ) ) ) ) ) ) ) ) ).
tt(t61_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 k6_numbers B))  => (r1_xxreal_0 k6_numbers (k5_int_1 A B))) ) ) ) ) ).
tt(t61_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k10_real_1 1 (k5_square_1 (k1_seq_1 k19_sin_cos D))))  &  (~  ((k1_seq_1 k19_sin_cos D) = k6_numbers) ) ) ) ) )  &  ( ((k9_xtuple_0 k29_sin_cos) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 k29_sin_cos (k4_seq_4 A)) (k1_seq_1 k29_sin_cos (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t61_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ( ((k9_xtuple_0 k7_sin_cos2) = (k9_xtuple_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C k1_numbers) =>  ((k1_seq_1 A C) = (k10_real_1 1 (k5_square_1 (k3_funct_2 k1_numbers k1_numbers k4_sin_cos2 C)))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) )  =>  ((k2_integra5 B A) = (k9_real_1 (k3_funct_2 k1_numbers k1_numbers k7_sin_cos2 (k4_seq_4 B)) (k3_funct_2 k1_numbers k1_numbers k7_sin_cos2 (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t61_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ( ((k1_relset_1 k1_numbers k3_taylor_1) = B)  &  ( (B = (k1_relset_1 k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B))))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B)) A))) ) )  =>  ((k2_integra5 A (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers B))) = (k9_real_1 (k1_seq_1 k3_taylor_1 (k4_seq_4 A)) (k1_seq_1 k3_taylor_1 (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t61_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) => (r2_interva1 A (k17_interva1 A B B) B)) ) ) ) ).
tt(t61_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 A B) k8_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 A C) (k5_intpro_1 B C)) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t61_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) C)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B))  &  ( (C = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_3_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k15_euclid 2) B) (k1_pre_topc (k15_euclid 2) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ((r1_xxreal_0 k6_numbers (k18_euclid B)) &  ((r1_xxreal_0 k6_numbers (k18_euclid C)) &  ( (~ (r1_xxreal_0 (k18_euclid D) k6_numbers))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid J)))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C))) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=>  ( ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B C))) & (r1_xxreal_0 (k18_euclid F) (k18_euclid E)))  |  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) &  (~  (F = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) D) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) B)) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) A) |  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k1_real_1 1)))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v2_connsp_1 D (k15_euclid 2)) &  ((v2_compts_1 D (k15_euclid 2)) &  ( (~ (v1_sppol_1 D))  &  ( (~ (v2_sppol_1 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ( ((r1_xxreal_0 1 A) &  ((r1_xxreal_0 A (k3_finseq_1 (k1_jordan9 D B))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 D B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 D B) (k3_finseq_1 (k1_jordan8 D B)) C)) ) ) ) )  => (r2_hidden (k7_partfun1 (u1_struct_0 (k15_euclid 2)) (k1_jordan9 D B) A) (k16_pscomp_1 (k3_topreal1 2 (k1_jordan9 D B))))) ) ) ) ) ) ) ) ) ).
tt(t61_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E))  &  ((r2_hidden (k4_tarski (k2_nat_1 D 1) E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 D 1) E)) ) ) )  =>  ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k2_nat_1 D 1) (k7_nat_d E 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (~  ( (~ (r1_xxreal_0 C 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k1_jordan8 B A)) C))  &  ((r1_xxreal_0 1 D) &  ((r1_xxreal_0 D E) &  ((r1_xxreal_0 E (k1_matrix_1 (k1_jordan8 B A))) &  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B A)))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C D) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B A) C E)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 2 A) &  ( (B = (a_2_2_jordan2c A C))  & (v6_tbsp_1 B (k14_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t61_jordan6,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_tarski (k9_jordan6 A) A) & (r1_tarski (k8_jordan6 A) A)) ) ) ).
tt(t61_jordan,ax, ((v1_funct_1 k6_jordan) &  ((v1_funct_2 k6_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc k6_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 k6_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ).
tt(t61_kurato_1,ax,(r1_xboole_0 (k2_tarski k6_kurato_1 (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)) (k3_kurato_1 k3_topmetr k6_kurato_1))).
tt(t61_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ((k5_lattices A) = (k6_lattices (k1_lattice2 A))) ) ) ).
tt(t61_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B))) =>  ((k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) D) = (k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) (k20_lexbfs A B C)) D)) ) ) ) ) ) ) ) ).
tt(t61_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v7_limfunc1 A) | (v8_limfunc1 A))  => (v7_limfunc1 (k56_valued_1 k1_numbers k1_numbers A))) ) ) ).
tt(t61_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ( ((k1_limfunc2 B A) = k6_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 (k9_real_1 A D) A)))) ) ) )  |  ((r1_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t61_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((r1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k1_limfunc2 C (k1_limfunc2 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t61_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [F:$i] :  ( ((v2_xxreal_0 F) & (m1_subset_1 F k1_numbers))  =>  (! [G:$i] :  ((m1_subset_1 G k1_numbers) =>  (! [H:$i] :  ((m1_subset_1 H k1_numbers) =>  (! [I:$i] :  ((m1_subset_1 I k1_numbers) =>  ( ((r1_xxreal_0 1 F) &  ((r2_hidden D (k1_lpspace2 A B C F)) &  ((r2_hidden E (k1_lpspace2 A B C F)) &  ( (G = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers D))))  &  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers E))))  &  (I = (k1_mesfunc6 A B C (k2_mesfun6c F A (k56_valued_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers D E))))) ) ) ) ) )  => (r1_xxreal_0 (k4_power I (k10_real_1 1 F)) (k7_real_1 (k4_power G (k10_real_1 1 F)) (k4_power H (k10_real_1 1 F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D B) => (r3_cqc_the1 A D (k8_cqc_lang A C B))) ) ) ) ) ) ) ) ) ).
tt(t61_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ((r1_tarski C D) => (r1_tarski (k6_mathmorp A (k15_euclid B) C) (k6_mathmorp A (k15_euclid B) D))) ) ) ) ) ) ) ) ) ).
tt(t61_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k3_matrix10 A B C) (k4_matrix10 A D E)) => (r2_matrix10 (k3_matrix10 A B E) (k4_matrix10 A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (~  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k12_matrix_2 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k12_matrix_2 A) (u1_struct_0 B))))) )  =>  (~  ( ((k12_matrix_3 A B (k4_matrix_6 A B C D)) = (k7_setwiseo (k12_matrix_2 A) (u1_struct_0 B) (u1_algstr_0 B) (k15_matrix_2 (k12_matrix_2 A)) E))  &  (! [F:$i] :  ((m1_matrix_2 F (k12_matrix_2 A)) =>  ((k3_funct_2 (k12_matrix_2 A) (u1_struct_0 B) E F) = (k8_group_1 B (k1_finsop_1 (u1_struct_0 B) (k10_matrix_3 A B C F) (u2_algstr_0 B)) (k14_matrix_2 B A (k12_matrix_3 A B D) F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (~  ((r1_tarski (k2_zfmisc_1 C D) (k2_matrix_1 B)) &  ( ( ((k5_card_1 C) = k6_numbers)  =>  ((k5_card_1 D) = k6_numbers) )  &  ( ( ((k5_card_1 D) = k6_numbers)  =>  ((k5_card_1 C) = k6_numbers) )  &  (~  ((k4_matrix_1 A (k6_matrix13 A B C D)) = (k6_matrix13 A (k4_matrix_1 A B) D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (~  ( (~  ( ((k1_matrix_1 B) = k1_xboole_0)  &  (~  ((k3_finseq_1 B) = k1_xboole_0) ) ) )  & (v1_xboole_0 (k6_matrix15 A B (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 B) (k4_struct_0 A))))) ) ) ) ) ) ).
tt(t61_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((v6_matrix16 B A) &  ((v6_matrix16 C A) &  ((k3_finseq_1 B) = (k3_finseq_1 C)) ) )  =>  ((k3_matrix16 A (k3_fvsum_1 A B C)) = (k3_matrix_3 A (k3_matrix16 A B) (k3_matrix16 A C))) ) ) ) ) ) ) ) ).
tt(t61_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k4_rlvect_1 A (k3_fvsum_1 A B C)) = (k1_algstr_0 A (k4_rlvect_1 A B) (k4_rlvect_1 A C))) ) ) ) ) ) ) ) ).
tt(t61_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k3_matrix_6 A B (k2_matrix_6 A B C D) E)) = (k5_algstr_0 B (k3_rlvect_1 B (k1_matrix_8 A B C) (k1_matrix_8 A B D)) (k1_matrix_8 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k5_numbers) =>  ((k20_matrixj1 (u1_struct_0 A) (k4_struct_0 A) (k23_matrixj1 A B)) = (k12_matrix_1 A (k2_wsierp_1 B))) ) ) ) ) ).
tt(t61_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k1_matrix_1 B) = (k3_finseq_1 A))  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k3_finseq_1 (k11_matrixr1 B A)) = (k3_finseq_1 B)) ) ) ) ) ) ) ).
tt(t61_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_matrixr2 A C B))) =>  ((k3_matrix_1 k1_numbers (k1_matrixr2 A C B) D E) = (k1_funct_1 (k12_matrixr1 B (k8_matrix_1 k1_numbers C D)) E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v5_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  ((k5_matrprob A) = (k3_finseq_1 A)) ) ) ).
tt(t61_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k4_zfmisc_1 (k1_tarski A) (k1_tarski B) (k1_tarski C) (k1_tarski D)) = (k1_tarski (k6_xtuple_0 A B C D))) ) ) ) ) ).
tt(t61_measure6,ax, ((k6_measure6 (k2_subset_1 k1_numbers)) = k1_numbers) ).
tt(t61_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k10_member_1 (k1_tarski A) (k1_tarski B)) = (k1_tarski (k3_xxreal_3 A B))) ) ) ) ) ).
tt(t61_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) & (v5_funct_1 D (k2_memstr_0 A B))) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 B)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 A B)) & (v1_partfun1 E (u1_struct_0 B))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F (u1_struct_0 B)) &  ((v1_funct_1 F) &  ((v5_funct_1 F (k2_memstr_0 A B)) & (v1_partfun1 F (u1_struct_0 B))) ) ) )  =>  ( ((r1_tarski D E) & (r1_tarski (k9_memstr_0 A B D C) F))  => (r1_tarski D (k1_funct_4 E (k6_memstr_0 A B F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k7_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  ( ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 (k8_nat_1 k7_numbers A D) (k8_nat_1 k7_numbers A E))) ) ) ) )  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 (k8_nat_1 k7_numbers B D) (k8_nat_1 k7_numbers B E))) ) ) ) )  &  ((v3_mesfunc5 A) &  ((v3_mesfunc5 B) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k3_supinf_2 (k8_nat_1 k7_numbers A D) (k8_nat_1 k7_numbers B D)) = (k8_nat_1 k7_numbers C D)) ) ) ) ) ) )  =>  ((v10_mesfunc5 C) &  ( ((k2_mesfunc5 C) = (k8_supinf_2 (k17_supinf_2 C)))  &  ( ((k2_mesfunc5 C) = (k3_supinf_2 (k2_mesfunc5 A) (k2_mesfunc5 B)))  &  ((k8_supinf_2 (k17_supinf_2 C)) = (k3_supinf_2 (k8_supinf_2 (k17_supinf_2 B)) (k8_supinf_2 (k17_supinf_2 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((v6_supinf_2 (k18_rfunct_3 A B)) & (v6_supinf_2 (k19_rfunct_3 A B))) ) ) ) ) ).
tt(t61_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m2_finseq_1 D (k9_setfam_1 A)) => (r1_tarski (k27_mmlquery A D B C) (k26_mmlquery A D B))) ) ) ) ) ) ) ).
tt(t61_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k1_lattices (k42_modelc_2 A B) D E)) <=>  ((r6_modelc_2 A B C D) | (r6_modelc_2 A B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_3 B A) & (l1_modelc_3 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  (! [D:$i] :  ((m1_orders_1 D (k1_orders_1 (k1_modelc_3 A))) =>  ((r8_modelc_2 C (k14_modelc_3 A B)) =>  ((v3_modelc_3 B A) |  ((r1_tarski (u1_modelc_3 A B) (u1_modelc_3 A (k25_modelc_3 C A D B))) & (r1_tarski (u3_modelc_3 A B) (u3_modelc_3 A (k25_modelc_3 C A D B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_moebius1,ax, (! [A:$i] :  ( ((v7_ordinal1 A) & (v1_int_2 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  => (r1_xxreal_0 (k11_nat_3 (k6_moebius1 B) A) 1)) ) ) ) ).
tt(t61_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ( ((u1_struct_0 (k10_monoid_0 A)) = (k3_finseq_2 A))  &  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k10_monoid_0 A)) (u1_struct_0 (k10_monoid_0 A))) (u1_struct_0 (k10_monoid_0 A)) (k2_zfmisc_1 (k3_finseq_2 A) (k3_finseq_2 A)) (k3_finseq_2 A) (u2_algstr_0 (k10_monoid_0 A)) (k11_monoid_0 A)) &  ((k5_struct_0 (k10_monoid_0 A)) = k1_xboole_0) ) ) ) ) ).
tt(t61_nat_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k8_nat_3 k10_newton (k13_nat_3 A)) = A) ) ) ).
tt(t61_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( (~  (A = k6_numbers) )  =>  ((k5_int_1 (k2_xcmplx_0 B (k3_xcmplx_0 A C)) A) = (k2_xcmplx_0 (k5_int_1 B A) C)) )  &  ((k6_int_1 (k2_xcmplx_0 B (k3_xcmplx_0 A C)) A) = (k6_int_1 B A)) ) ) ) ) ) ) ) ).
tt(t61_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r2_hidden D (k1_relset_1 (u1_struct_0 B) C)) => (r9_ncfcont1 B A C (k1_tarski D))) ) ) ) ) ) ) ) ) ).
tt(t61_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r1_nat_d A B) => (r1_nat_d (k5_nat_d A (k6_nat_d C B)) (k6_nat_d (k5_nat_d A C) B))) ) ) ) ) ) ) ).
tt(t61_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 (k2_oppcat_1 A) (k2_oppcat_1 B) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C))) (k3_oppcat_1 A D)) = (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t61_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r9_orders_1 A B) <=> (r8_orders_1 (k2_relat_1 A) B)) ) ) ) ).
tt(t61_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden (k10_ordinal2 A B) C) => (r2_hidden B (k5_ordinal3 C A))) ) ) ) ) ) ) ).
tt(t61_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( (~  (A = k6_numbers) )  => (r2_hidden (k7_ordinal3 B (k12_ordinal2 A C)) (k12_ordinal2 A C))) ) ) ) ) ) ) ).
tt(t61_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ((v3_ordinal1 C) &  ((v4_ordinal1 C) &  (~ (v1_xboole_0 C)) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_classes2 D))  =>  ( ((r2_hidden C D) &  ((r2_hidden A D) &  ((r2_hidden B C) &  (! [E:$i] :  ((v3_ordinal1 E) =>  ((r2_hidden E C) =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 D) E)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 D) E) (k2_ordinal1 D) (k2_ordinal1 D)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 D) E)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 D) E) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 D) (k2_ordinal1 D))))) ) ) ) ) ) ) ) )  => (r1_abian (k1_funct_1 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 D) C)) A) (k1_funct_1 (k11_ordinal6 D) B))) ) ) ) ) ) ) ) ) ).
tt(t61_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t61_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B)))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_tarski B)))))  => (r1_partfun1 C D)) ) ) ) ) ) ).
tt(t61_partfun2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) & (v1_funct_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C A) & (v1_funct_1 C)) )  =>  ((r1_tarski B C) =>  (! [D:$i] :  ((r2_hidden D (k9_xtuple_0 B)) =>  ((k7_partfun1 A B D) = (k7_partfun1 A C D)) ) ) ) ) ) ) ) ) ).
tt(t61_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k4_pboole A B (k2_pboole A B C)) (k1_pboole A))) ) ) ) ) ).
tt(t61_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r4_pdiff_5 C B) =>  ((r3_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) &  ((k11_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) = (k8_real_1 A (k4_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t61_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ( ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A D) E) &  ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) & (r1_xxreal_0 B A)) ) )  =>  ((r3_pdiff_9 A C B D) <=> (r2_pdiff_7 A 1 B E C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_pepin,ax,(v1_int_2 257)).
tt(t61_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k7_finseq_1 A B) = (k2_xboole_0 A (k12_pnproc_1 B (k3_finseq_1 A)))) ) ) ) ) ).
tt(t61_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k8_polyform A k6_numbers)) =>  ((k1_funct_1 (k21_polyform A k6_numbers) (k1_tarski B)) = (k1_tarski k1_xboole_0)) ) ) ) ) ).
tt(t61_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) )  =>  ( (~  ((k1_algseq_1 A B) = k6_numbers) )  =>  ((k6_polynom5 A B) = (k6_polynom5 A (k7_polynom5 A B))) ) ) ) ) ) ).
tt(t61_power,ax, ((k4_power 2 3) = 8) ).
tt(t61_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) )  => (r2_hidden B (k18_pre_poly A B))) ) ) ).
tt(t61_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 B k6_numbers))  => (r1_xxreal_0 (k6_prepower A B) 1)) ) ) ) ) ).
tt(t61_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_3 D A B) =>  ((k3_finseq_1 (k9_prob_3 A B D C)) = (k3_finseq_1 D)) ) ) ) ) ) ) ) ) ).
tt(t61_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k19_pscomp_1 A) = (k20_pscomp_1 A))  =>  ((k19_pscomp_1 A) = (k11_pscomp_1 A)) ) ) ) ).
tt(t61_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r2_pboole A B C) =>  ((r2_pboole A (k6_pboole A B D) (k6_pboole A C D)) & (r2_pboole A (k6_pboole A D B) (k6_pboole A D C))) ) ) ) ) ) ) ) ) ).
tt(t61_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r2_qc_lang2 A B C) & (r1_qc_lang2 A C B)) ) ) ) ) ) ) ) ).
tt(t61_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k4_qc_lang2 A B C)) = (k4_subset_1 (k5_qc_lang1 A) (k5_qc_lang3 A B) (k5_qc_lang3 A C))) ) ) ) ) ) ) ).
tt(t61_quatern2,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k18_quatern2 (k29_quaterni A B) (k29_quaterni A B)) = (k26_quaterni (k29_quaterni (k29_quaterni (k18_quatern2 A A) (k18_quatern2 A B)) (k18_quatern2 B A)) (k18_quatern2 B B))) ) ) ) ) ).
tt(t61_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k28_quaterni (k29_quaterni (k26_quaterni A B) C)) = (k26_quaterni (k29_quaterni (k28_quaterni A) B) C)) ) ) ) ) ) ) ).
tt(t61_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k26_quaterni A (k31_quaterni A))) = (k8_real_1 2 (k17_quaterni A)))  &  ( ((k18_quaterni (k26_quaterni A (k31_quaterni A))) = k6_numbers)  &  ( ((k19_quaterni (k26_quaterni A (k31_quaterni A))) = k6_numbers)  &  ((k20_quaterni (k26_quaterni A (k31_quaterni A))) = k6_numbers) ) ) ) ) ) ).
tt(t61_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  &  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  & (r3_quofield A B C)) ) ) ) ) ) ).
tt(t61_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  (! [E:$i] :  ((m2_rcomp_3 E A B C D) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) &  ((v1_rcomp_3 C (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((k3_finseq_1 D) = 1) ) ) ) )  =>  (E = (k10_finseq_1 A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_xxreal_0 (k1_newton k1_fib_num B) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1)))) ) ) ) ) ).
tt(t61_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k9_xtuple_0 (k5_relat_1 B A)) = (k3_xboole_0 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t61_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski (k7_relset_1 A B E (k3_subset_1 A C)) (k3_subset_1 B D)) <=> (r1_tarski (k7_relset_1 B A (k3_relset_1 A B E) D) C)) ) ) ) ) ) ) ) ) ).
tt(t61_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((v1_relat_1 B) =>  ( (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) B) => (r13_rewrite1 A C D)) ) )  => (r12_rewrite1 A (k2_xboole_0 A B))) ) ) ) ) ).
tt(t61_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r2_rewrite2 A B C D) => (r4_rewrite2 A B (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k4_lang1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) C D))) E)) ) ) ) ) ) ) ) ) ) ).
tt(t61_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ( (~ (r2_hidden (k2_flang_1 A) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  ( ((k2_xtuple_0 (k1_funct_1 D 1)) = (k2_xtuple_0 (k1_funct_1 D (k3_finseq_1 D))))  =>  ((k3_finseq_1 D) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k1_numbers))))  =>  ((r2_relset_1 B k1_numbers C (k7_rfunct_1 A B)) <=>  ( ((k1_relset_1 B C) = B)  &  (! [D:$i] :  ((m1_subset_1 D B) =>  ( ((r2_hidden D A) =>  ((k1_funct_1 C D) = 1) )  &  ( (~ (r2_hidden D A))  =>  ((k1_funct_1 C D) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_rfunct_3,ax,(r2_rfunct_3 (k1_partfun2 k1_numbers (k2_subset_1 k1_numbers)) k1_numbers)).
tt(t61_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v2_seq_2 A) => (r2_funct_2 k5_numbers k1_numbers (k3_rinfsup1 A) (k32_valued_1 k5_numbers k1_numbers (k4_rinfsup1 (k32_valued_1 k5_numbers k1_numbers A))))) ) ) ).
tt(t61_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v1_rlaffin1 B A) &  ( ((k4_rlaffin1 A B) = (k4_rlaffin1 A C))  & (r1_xxreal_0 (k5_card_1 C) (k5_card_1 B))) )  => (v1_rlaffin1 C A)) ) ) ) ) ) ) ).
tt(t61_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden (k3_rlvect_1 A B C) (k3_rlsub_1 A C D)) <=> (r1_struct_0 D B)) ) ) ) ) ) ) ) ) ).
tt(t61_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( (B = (k1_algstr_0 A C D))  <=>  (C = (k5_algstr_0 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t61_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k7_rusub_4 A (k1_tops_1 A B) (k1_tops_1 A C)) (k1_tops_1 A (k7_rusub_4 A B C)))) ) ) ) ) ) ).
tt(t61_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B B)) = (k1_rlvect_1 A B 2)) ) ) ) ) ).
tt(t61_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  => (r1_funct_2 (k2_zfmisc_1 k1_numbers (u1_struct_0 (k16_rlvect_2 A))) (u1_struct_0 (k16_rlvect_2 A)) (k2_zfmisc_1 k1_numbers (k11_rlvect_2 A)) (k11_rlvect_2 A) (u1_rlvect_1 (k16_rlvect_2 A)) (k15_rlvect_2 A))) ) ).
tt(t61_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  (~  ( ((k3_rmod_2 A B C E) = (k3_rmod_2 A B D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r1_struct_0 E F) &  ((k3_rlvect_1 B C F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_4 C A B) =>  (! [D:$i] :  ((m1_rmod_4 D A B) =>  ((k5_rmod_4 A B (k9_rmod_4 A B C D)) = (k5_algstr_0 B (k5_rmod_4 A B C) (k5_rmod_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t61_robbins1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v6_robbins1 A) &  ((v10_robbins1 A) & (l4_robbins1 A)) ) ) )  =>  ((k7_robbins1 A) = (k5_lattices A)) ) ) ).
tt(t61_roughs_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r3_roughs_1 A B C) & (r3_roughs_1 A C D))  => (r3_roughs_1 A B D)) ) ) ) ) ) ) ) ) ).
tt(t61_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( ((k3_rusub_1 A D B) = (k3_rusub_1 A C B))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_struct_0 B E) &  ((k5_algstr_0 A D E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_bhsp_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A) (u1_bhsp_1 A))) ) ) ) ) ) ).
tt(t61_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k14_rvsum_1 (k6_finseq_1 k1_numbers) A) = (k6_finseq_1 k1_numbers)) ) ) ).
tt(t61_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 A (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k5_memstr_0 3 k1_scmfsa_2 A) = (k5_memstr_0 3 k1_scmfsa_2 B))  &  ( (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ((k1_funct_1 A C) = (k1_funct_1 B C)) ) )  &  (! [C:$i] :  ((m1_scmfsa_2 C) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 A C) (k18_scmfsa_2 B C))) ) ) )  =>  (A = B) ) ) ) ) ) ).
tt(t61_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r4_scmfsa7b C D))  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) E) D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r4_scmfsa7b C D))  &  ( (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers))  &  (~ (r1_scmfsa8a (k1_scmfsa_m B) A (k1_scmfsa8c (k1_scmfsa8b D (k1_scmfsa8a 2) (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  &  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 B C) = A) ) ) ) ) ) ) ).
tt(t61_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) E)) = k6_numbers)  =>  ((k6_scmpds_4 (k6_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A) = (k1_funct_4 B (k7_memstr_0 2 k1_scmpds_2 (k2_nat_1 (k5_card_1 C) 2)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))) =>  (! [C:$i] :  ( (B = (k1_tarski C))  => (v9_scmyciel B A)) ) ) ) ) ) ).
tt(t61_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r3_semi_af1 A B C D E) &  ((r1_semi_af1 A B C D) & (r2_semi_af1 A F G B C)) )  => (r2_semi_af1 A F G D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  ( ((k15_seq_4 A B (k18_seq_4 A B)) = (k17_seq_4 A))  &  ((k15_seq_4 A (k18_seq_4 A B) B) = (k17_seq_4 A)) ) ) ) ) ) ).
tt(t61_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  ((k4_kurato_0 A B) = (k3_prob_1 A B)) ) ) ) ) ).
tt(t61_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k4_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C)) (k3_kurato_0 A (k2_setlim_2 A B C)))) ) ) ) ) ).
tt(t61_sf_mastr,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_tarski B E) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C F))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E D F)) (k1_relset_1 k5_numbers B))) ) ) )  =>  ((r2_hidden A (k2_sf_mastr B)) |  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E D C) A) = (k1_funct_1 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A D D))) = (k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A D B)))) ) ) ) ) ) ) ) ) ).
tt(t61_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k11_simplex0 A B C k1_xboole_0) = B) ) ) ) ) ) ).
tt(t61_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) k1_sincos10) = (k1_partfun2 k1_numbers (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(t61_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 2 A)) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 2 B))) = (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A B))) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k4_binop_2 A B))))  &  ((k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 2 A)) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k5_binop_2 2 B))) = (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k4_binop_2 A B))) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A B)))) ) ) ) ) ) ).
tt(t61_sin_cos6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) C) A) &  ((r1_xxreal_0 (k8_real_1 (k8_real_1 2 k32_sin_cos) C) B) &  ( ((k17_sin_cos A) = (k17_sin_cos B))  &  ((k20_sin_cos A) = (k20_sin_cos B)) ) ) )  =>  ((r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) A) |  ((r1_xxreal_0 (k7_real_1 (k8_real_1 2 k32_sin_cos) (k8_real_1 (k8_real_1 2 k32_sin_cos) C)) B) |  (A = B) ) ) ) ) ) ) ) ) ) ).
tt(t61_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_xxreal_0 1 (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k11_binop_2 2 A))) =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 1 A) |  ((k5_power k8_power A) = (k3_sin_cos7 (k12_binop_2 (k9_binop_2 (k3_square_1 A) 1) (k11_binop_2 2 A)))) ) ) ) ) ) ).
tt(t61_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k5_sin_cos9 A) = (k10_real_1 k32_sin_cos 4)) ) )  =>  (A = 1) ) ) ) ).
tt(t61_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_real_1 (k1_seq_1 k16_sin_cos (k7_real_1 A B)) (k1_seq_1 k16_sin_cos A)) = (k7_real_1 (k8_real_1 B (k1_seq_1 k19_sin_cos A)) (k8_real_1 B (k3_complex1 (k3_xcmplx_0 (k11_comseq_3 (k27_sin_cos (k3_xcmplx_0 B k7_complex1))) (k2_xcmplx_0 (k1_seq_1 k19_sin_cos A) (k3_xcmplx_0 (k1_seq_1 k16_sin_cos A) k7_complex1))))))) ) ) ) ) ).
tt(t61_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k8_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k8_pscomp_1 A)) ) ) ).
tt(t61_sprect_2,ax, (! [A:$i] :  ((m2_finseq_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ( ((v4_topreal1 A) &  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) B (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A))) (k3_topreal1 2 A)) = (k1_tarski (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) )  =>  ( (B = (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))  |  ( ( (~  ((k17_euclid B) = (k17_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) )  &  (~  ((k18_euclid B) = (k18_euclid (k7_partfun1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A)))) ) )  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) A (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) B)) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ).
tt(t61_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t61_stirl2_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (~  ((r2_hidden C (k10_xtuple_0 (k3_relat_1 A B))) &  ((v2_funct_1 B) &  (! [D:$i] :  (~  ((r2_hidden D (k9_xtuple_0 B)) &  ((r2_hidden D (k10_xtuple_0 A)) &  ( ((k8_relat_1 B (k1_tarski C)) = (k1_tarski D))  &  ((k8_relat_1 A (k1_tarski D)) = (k8_relat_1 (k3_relat_1 A B) (k1_tarski C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_valuat_1 D A C) =>  ( (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r2_relset_1 (k3_qc_lang1 A) C (k5_relset_1 (k3_qc_lang1 A) C E (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) C F (k24_qc_lang1 A B))) =>  ((r1_valuat_1 A C B D E) <=> (r1_valuat_1 A C B D F)) ) ) ) ) )  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  ((r2_relset_1 (k3_qc_lang1 A) C (k5_relset_1 (k3_qc_lang1 A) C E (k24_qc_lang1 A (k6_cqc_lang A B))) (k5_relset_1 (k3_qc_lang1 A) C F (k24_qc_lang1 A (k6_cqc_lang A B)))) =>  ((r1_valuat_1 A C (k6_cqc_lang A B) D E) <=> (r1_valuat_1 A C (k6_cqc_lang A B) D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_tops_1 B A) & (v5_tops_1 C A))  =>  ((r1_tarski (k1_tops_1 A B) (k1_tops_1 A C)) <=> (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(t61_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v3_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tdlat_3 B) & (m1_pre_topc B A)) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) & (m1_pre_topc C A)) )  &  ((m1_pre_topc B C) & (v4_tex_2 C A)) ) ) ) ) ) ) ).
tt(t61_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (~  ( (? [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  &  ((v1_tex_3 B A) &  ((v1_tsep_1 B A) & (v1_tex_2 B A)) ) ) )  & (v3_tdlat_3 A)) ) ) ) ).
tt(t61_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_tex_4 A (k2_pre_topc A B)) = (k2_pre_topc A B)) ) ) ) ) ).
tt(t61_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v1_tsep_1 D B) & (m1_pre_topc D B)) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ( (E = F)  =>  ((r1_tmap_1 B A C E) <=> (r1_tmap_1 D A (k2_tmap_1 B A C D) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_topalg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_topalg_1 A B))) =>  (! [E:$i] :  ((m1_borsuk_2 E A B B) =>  (! [F:$i] :  ((m1_borsuk_2 F A B B) =>  ( ( (C = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) E))  &  (D = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) F)) )  =>  ((k6_algstr_0 (k5_topalg_1 A B) C D) = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) (k1_borsuk_2 A B B B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((v1_topgen_4 (k9_prob_1 (u1_struct_0 A) (k1_topgen_4 A)) A) &  ((v1_prob_1 (k9_prob_1 (u1_struct_0 A) (k1_topgen_4 A)) (u1_struct_0 A)) & (v3_topgen_4 (k9_prob_1 (u1_struct_0 A) (k1_topgen_4 A)) (u1_struct_0 A))) ) ) ) ).
tt(t61_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  ( (~  (A = B) )  =>  ((k1_funct_1 (k4_topgen_5 A C) (k19_euclid B k6_numbers)) = 1) ) ) ) ) ) ) ) ).
tt(t61_topgrp_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) )  =>  ((v2_struct_0 A) => (v3_tops_2 B A A)) ) ) ) ) ).
tt(t61_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k14_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (C = (k11_metric_1 (k14_euclid A) B D))  => (v4_pre_topc C (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t61_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (k5_jgraph_6 A B C)) & (r2_hidden E (k5_jgraph_6 A B C)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) D E) (k5_jgraph_6 A B C)) = (k2_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)))))) )  =>  ((v1_funct_1 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C)) &  ((v1_funct_2 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C) (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)))))) ) ) ) ) ) ) ) ).
tt(t61_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) <=> (v5_tops_1 (k3_subset_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t61_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_pre_topc C A B) & (v2_connsp_1 D A))  => (v2_connsp_1 (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) B)) ) ) ) ) ) ) ) ) ).
tt(t61_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v1_tops_3 C A))  => (v1_tops_3 D B)) ) ) ) ) ) ) ) ) ).
tt(t61_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (~  ((v4_transgeo B A) &  ( (~ (v2_transgeo B A))  &  (~ (v3_transgeo B A)) ) ) ) ) ) ) ) ).
tt(t61_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r2_hidden B A) <=> (r2_hidden (k7_finseq_1 (k12_finseq_1 k5_numbers k6_numbers) B) (k12_trees_3 A))) ) ) ) ) ).
tt(t61_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((k4_subset_1 (u1_struct_0 A) B C) = (u1_struct_0 A))  &  ((r2_tsep_1 A B C) &  ( (~ (r1_tarski B C))  &  ( (~ (r1_tarski C B))  &  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_pre_topc D A) &  ((v3_pre_topc E A) &  ((r1_tarski D B) &  ((r1_tarski E C) &  (~  ( (~  ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) D E)) )  &  (! [F:$i] :  ( ( (~ (v1_xboole_0 F))  & (m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ( ((k4_subset_1 (u1_struct_0 A) B C) = (k4_subset_1 (u1_struct_0 A) (k4_subset_1 (u1_struct_0 A) D E) F))  &  ((r1_tarski F (k9_subset_1 (u1_struct_0 A) B C)) & (v4_pre_topc F A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 k5_numbers (u1_struct_0 A) (k10_uproots A (k2_uproots (u1_struct_0 A) (k6_domain_1 (u1_struct_0 A) B) 1)) (k4_polynom5 A (k4_algstr_0 A B) (k5_struct_0 A)))) ) ) ) ).
tt(t61_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k9_xtuple_0 (k57_valued_2 B C D)) = (k8_subset_1 A (k1_relset_1 A C) (k9_xtuple_0 D))) ) ) ) ) ) ) ) ).
tt(t61_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden (k5_algstr_0 B C D) (k3_vectsp_4 A B C E)) <=> (r1_struct_0 E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v12_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ) ).
tt(t61_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k3_waybel_0 A (k11_waybel_0 A B))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_waybel_0 C A) &  ((v12_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B C) => (r1_tarski (k3_waybel_0 A (k11_waybel_0 A B)) C)) ) ) ) ) ) ) ) ).
tt(t61_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k7_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k4_waybel_1 A B) C) = (a_3_1_waybel_1 A B C)) ) ) ) ) ) ) ).
tt(t61_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (v18_waybel_0 (k4_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) (k2_yellow_1 (k7_waybel_0 A)))) ) ) ) ).
tt(t61_waybel34,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v4_waybel34 C A B) =>  ((v20_waybel_0 C A B) & (v5_waybel34 C A B)) ) ) ) ) ) ) ) ).
tt(t61_waybel_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_waybel_4 B A) &  ((v2_waybel_4 B A) &  ((v3_waybel_4 B A) &  ((v6_waybel_4 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) )  =>  ((v9_waybel_4 B A) => (v8_waybel_4 B A)) ) ) ) ) ).
tt(t61_xboole_1,ax, (! [A:$i] :  ( (~  (A = k1_xboole_0) )  => (r2_xboole_0 k1_xboole_0 A)) ) ).
tt(t61_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k5_xboolean (k3_xboolean A) (k8_xboolean A B)) = (k8_xboolean A B)) ) ) ) ) ).
tt(t61_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( ((k7_xcmplx_0 A B) = A)  =>  ( (A = k6_numbers)  |  (B = 1) ) ) ) ) ) ) ).
tt(t61_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 (k4_xcmplx_0 B) A))  & (r1_xxreal_0 k6_numbers (k2_xcmplx_0 A B))) ) ) ) ) ) ).
tt(t61_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k3_xxreal_1 A B) (k3_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (? [C:$i] :  ((v1_xxreal_0 C) &  ((r2_hidden C A) & (r1_xxreal_0 B C)) ) )  => (r1_xxreal_0 B (k1_xxreal_2 A))) ) ) ) ) ).
tt(t61_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (! [C:$i] :  ((v1_xreal_0 C) =>  (~  ( (~ (r1_xxreal_0 C k6_numbers))  & (r1_xxreal_0 (k1_xxreal_3 B C) A)) ) ) )  => (r1_xxreal_0 A B)) ) ) ) ) ).
tt(t61_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (E = D)  =>  ( ((r1_lattice3 A C D) => (r1_lattice3 B C E))  &  ((r2_lattice3 A C D) => (r2_lattice3 B C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t61_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v24_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_waybel11 C A) & (v3_waybel11 D B))  => (v3_waybel11 (k6_yellow_3 A B C D) (k3_yellow_3 A B))) ) ) ) ) ) ) ) ) ).
tt(t61_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_waybel_0 A (k4_yellow_4 A (k3_waybel_0 A B) (k3_waybel_0 A C))) (k3_waybel_0 A (k4_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t61_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_yellow_5 A (k1_yellow_5 A B C) D) = (k1_yellow_5 A B (k13_lattice3 A C D))) ) ) ) ) ) ) ) ) ).
tt(t61_yellow_9,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (m1_yellow_9 B A))  =>  (! [C:$i] :  ( ((v2_pre_topc C) & (m1_yellow_9 C A))  =>  (! [D:$i] :  ((m3_yellow_9 D B C) =>  ((v1_tops_2 (k3_setfam_1 (u1_pre_topc B) (u1_pre_topc C)) D) &  ((v1_cantor_1 (k3_setfam_1 (u1_pre_topc B) (u1_pre_topc C)) D) & (m1_subset_1 (k3_setfam_1 (u1_pre_topc B) (u1_pre_topc C)) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 D))))) ) ) ) ) ) ) ) ) ) ).
tt(t61_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k2_zf_model (k7_zf_lang A B)) = (k4_subset_1 k1_zf_lang (k2_zf_model A) (k2_zf_model B))) ) ) ) ) ).
tt(t61_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((r1_zf_lang A B) => (r3_zf_lang A B)) ) ) ) ) ).
tt(t61_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((k4_xboole_0 (k1_tarski A) B) = k1_xboole_0)  |  ((k4_xboole_0 (k1_tarski A) B) = (k1_tarski A)) ) ) ) ).
tt(t61_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_zmodul01 A B (k4_zmodul01 A)) = (u1_struct_0 A)) ) ) ) ) ).
tt(t62_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ((r6_abcmiz_0 A B C) => (v1_finset_1 C)) ) ) ) ) ) ) ).
tt(t62_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v6_abcmiz_1 B A))  & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  ((k30_abcmiz_1 A (k32_abcmiz_1 A) (k37_abcmiz_1 A B)) = B) ) ) ) ) ).
tt(t62_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 C A) &  ((v1_aff_4 D A) &  ((r2_hidden B C) &  ((r2_hidden B D) & (r1_aff_4 A C D)) ) ) )  =>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t62_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v5_ordinal1 D) &  ((v1_funct_1 D) & (v1_finset_1 D)) ) )  =>  ( ((k1_ordinal4 (k5_afinsq_1 A) C) = (k1_ordinal4 (k5_afinsq_1 B) D))  =>  ( (A = B)  &  (C = D) ) ) ) ) ) ) ) ) ).
tt(t62_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v3_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  ((v4_partfun3 A) =>  ( ((k7_afinsq_2 A) = k6_numbers)  <=>  ( ((k1_afinsq_1 A) = k6_numbers)  |  (A = (k8_funcop_1 k5_numbers (k1_afinsq_1 A) k6_numbers)) ) ) ) ) ) ).
tt(t62_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v1_msafree1 C A) & (l3_msualg_1 C A)) )  =>  ((l3_msualg_1 C B) =>  ((g1_msualg_1 (u1_struct_0 A) (u4_struct_0 A) (u1_msualg_1 A) (u2_msualg_1 A)) = (g1_msualg_1 (u1_struct_0 B) (u4_struct_0 B) (u1_msualg_1 B) (u2_msualg_1 B))) ) ) ) ) ) ) ) ).
tt(t62_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  ( (~  ((r2_analoaf A B C D E) & (r4_analmetr A B C F G)) )  &  ( (~  ((r2_analoaf A B C F G) & (r4_analmetr A B C D E)) )  &  ( (~  ((r2_analoaf A B C D E) & (r4_analmetr A F G B C)) )  &  ( (~  ((r2_analoaf A B C F G) & (r4_analmetr A D E B C)) )  &  ( (~  ((r2_analoaf A D E B C) & (r4_analmetr A F G B C)) )  &  ( (~  ((r2_analoaf A F G B C) & (r4_analmetr A D E B C)) )  &  ( (~  ((r2_analoaf A D E B C) & (r4_analmetr A B C F G)) )  &  (~  ((r2_analoaf A F G B C) & (r4_analmetr A B C D E)) ) ) ) ) ) ) ) ) )  &  (~ (r4_analmetr A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ( ((k13_aofa_000 (k7_freealg k19_aofa_000 A) B C) = (k13_aofa_000 (k7_freealg k19_aofa_000 A) D E))  =>  ( (B = D)  &  (C = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  => (r6_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k16_aofa_000 A (k78_aofa_i00 A B C D F k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k83_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) D (a_6_1_aofa_i00 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ( ((k9_arytm_3 A B) = (k9_arytm_3 C B))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t62_asympt_1,ax, (! [A:$i] :  ( ((v1_asympt_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((k1_seq_1 B k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k6_power A C)) ) ) ) )  =>  ((r1_xxreal_0 A 1) | (v4_asympt_0 B)) ) ) ) ) ) ).
tt(t62_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( ((k2_bcialg_1 A B) = (k4_struct_0 A))  =>  (B = (k4_struct_0 A)) ) ) ) ) ) ) ).
tt(t62_bhsp_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B (k3_normsp_1 A C D)) (k6_bhsp_1 A (k3_normsp_1 A B C) D))) ) ) ) ) ) ) ) ).
tt(t62_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A (k3_boolealg A B C) (k4_lattices A B C)) (k3_lattices A B C))) ) ) ) ) ) ).
tt(t62_borsuk_5,ax, ((k9_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 1) (k2_rcomp_1 1 k1_xxreal_0)) (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 2) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 1) (k4_rcomp_1 1 2)) (k3_borsuk_5 2 4)) (k1_seq_4 4)) (k1_seq_4 5))) ).
tt(t62_borsuk_6,ax, (! [A:$i] :  ((r2_hidden (k4_tarski k6_numbers A) k7_borsuk_6) =>  (A = 1) ) ) ).
tt(t62_borsuk_7,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r2_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k8_toprealb 3)) (k13_borsuk_7 A) (k1_topalg_3 k3_topmetr (k8_toprealb 3) (k4_toprealb k6_numbers) (k4_toprealb A) (k2_topalg_5 A) k12_borsuk_7))) ) ).
tt(t62_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C E)) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  ( (I = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B K) (k16_funcop_1 C L)) (k16_funcop_1 D M)) (k16_funcop_1 E N)) (k16_funcop_1 F O)) (k16_funcop_1 G P)) (k16_funcop_1 H Q)) (k16_funcop_1 A J)))  =>  ( (A = B)  |  ( (A = C)  |  ( (A = D)  |  ( (A = E)  |  ( (A = F)  |  ( (A = G)  |  ( (B = C)  |  ( (B = D)  |  ( (B = E)  |  ( (B = F)  |  ( (B = G)  |  ( (B = H)  |  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (F = G)  |  ( (F = H)  |  ( (G = H)  |  ( ((k1_funct_1 I B) = K)  &  ( ((k1_funct_1 I C) = L)  &  ( ((k1_funct_1 I D) = M)  &  ( ((k1_funct_1 I E) = N)  &  ( ((k1_funct_1 I F) = O)  &  ((k1_funct_1 I G) = P) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k7_xboolean A B) = (k4_xboolean (k6_xboolean A B) (k6_xboolean B A))) ) ) ) ) ).
tt(t62_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k6_bvfunc26 A C D)) (k2_bvfunc_1 A (k2_bvfunc_1 A B (k1_bvfunc_1 A C)) (k1_bvfunc_1 A D)))) ) ) ) ) ) ) ) ).
tt(t62_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  ((k3_calcul_1 A B) = (k3_tarski (a_2_0_calcul_1 A B))) ) ) ) ) ).
tt(t62_card_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ((k1_card_1 A) = (k1_card_1 (k9_xtuple_0 A))) ) ) ).
tt(t62_card_2,ax, (! [A:$i] :  ( ((v1_finset_1 A) &  (! [B:$i] :  (! [C:$i] :  (~  ((r2_hidden B A) &  ((r2_hidden C A) &  ( (~ (r1_tarski B C))  &  (~ (r1_tarski C B)) ) ) ) ) ) ) )  =>  ( (A = k1_xboole_0)  | (r2_hidden (k3_tarski A) A)) ) ) ).
tt(t62_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((r1_tarski B (k8_card_3 A)) &  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r2_hidden C B) & (r2_hidden D B))  => (r1_partfun1 C D)) ) ) ) ) )  => (r2_hidden (k3_tarski B) (k8_card_3 A))) ) ) ) ).
tt(t62_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (~  ( ((k9_xtuple_0 B) = A)  &  ((v2_funct_1 B) &  (! [C:$i] :  ( ((v5_ordinal1 C) &  ((v1_relat_1 C) &  ((v5_relat_1 C k4_numbers) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k7_afinsq_2 C) = (k1_card_1 (a_2_2_card_fin A B)))  &  ( ((k1_relset_1 k5_numbers C) = (k23_binop_2 (k5_card_1 A) 1))  &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 C D) = (k12_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) D) (k9_newton (k5_card_1 A))) (k9_newton D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_cat_3 E C D A) =>  ((r2_hidden B A) =>  ((k4_graph_1 C (k7_partfun1 (u4_struct_0 C) E B)) = D) ) ) ) ) ) ) ) ) ) ).
tt(t62_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( (~  ((k2_cat_1 A B (k20_cat_4 A B C)) = k1_xboole_0) )  &  (~  ((k2_cat_1 A C (k20_cat_4 A B C)) = k1_xboole_0) ) ) ) ) ) ) ) ) ).
tt(t62_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_partfun1 (k2_cfunct_1 A B) A) <=>  ( ((k8_relset_1 A k2_numbers B (k1_tarski k6_numbers)) = k1_xboole_0)  & (v1_partfun1 B A)) ) ) ) ) ) ).
tt(t62_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_chain_1 B (k2_nat_1 A 1)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k4_chain_1 (k2_nat_1 A 1) B (k2_nat_1 A 1)))) =>  ((k10_chain_1 (k2_nat_1 A 1) B A (k3_subset_1 (k4_chain_1 (k2_nat_1 A 1) B (k2_nat_1 A 1)) C)) = (k10_chain_1 (k2_nat_1 A 1) B A C)) ) ) ) ) ) ) ).
tt(t62_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ( ((r5_glib_000 A B) & (v2_chord A))  => (v2_chord B)) ) ) ) ) ).
tt(t62_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v6_circcomb C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v6_circcomb D B) & (l3_msualg_1 D B))  => (v6_circcomb (k3_circcomb A B C D) (k2_circcomb A B))) ) ) ) ) ) ) ) ).
tt(t62_circtrm1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ((v4_msualg_1 B A) &  ((v4_msafree2 B A) & (l3_msualg_1 B A)) )  =>  (! [C:$i] :  ((m4_msaterm C A B) =>  (! [D:$i] :  ((m3_msaterm D A C) =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ( (~ (v11_struct_0 E))  &  ((v2_msafree2 E) & (l1_msualg_1 E)) ) )  =>  (! [F:$i] :  ( ((v4_msualg_1 F E) &  ((v4_msafree2 F E) & (l3_msualg_1 F E)) )  =>  ((r8_circtrm1 A B C D E F) =>  (! [G:$i] :  ((m1_dtconstr G (u1_struct_0 (k5_msafree A C)) (k5_trees_3 (u1_struct_0 (k5_msafree A C))) (k1_msaterm A C)) =>  (~  ((r2_hidden G (k9_trees_9 D)) &  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 E)) =>  (~  (! [I:$i] :  ((m1_subset_1 I (k4_card_3 (u3_msualg_1 E F))) =>  ((r1_facirc_1 E F (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) H) &  (? [J:$i] :  ((m2_circtrm1 J A C B D E F) &  (! [K:$i] :  ((m1_subset_1 K (k4_card_3 (u3_msualg_1 (k1_circtrm1 A C D) (k6_circtrm1 A C D B)))) =>  ( (K = (k3_relat_1 J I))  =>  (! [L:$i] :  ((m1_circtrm1 L A C D B K) =>  ((k1_funct_1 (k5_facirc_1 E F I (k2_nat_1 1 (k6_trees_1 (k9_xtuple_0 G)))) H) = (k7_circtrm1 A B C G L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_classes1,ax, (! [A:$i] :  (? [B:$i] :  ((v3_ordinal1 B) & (r1_tarski A (k4_classes1 B))) ) ) ).
tt(t62_classes2,ax, ((k1_card_1 (k4_classes1 k4_ordinal1)) = (k1_card_1 k4_ordinal1)) ).
tt(t62_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) => (r2_hidden B (k5_clvect_1 A B C))) ) ) ) ) ) ).
tt(t62_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 B A) => (v2_clvect_2 (k5_vfunct_1 k5_numbers A B) A)) ) ) ) ) ).
tt(t62_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  (~  ( (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D C) &  ((r2_hidden E C) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A B) &  ((v10_cohsp_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k2_xboole_0 D E) = (k11_cohsp_1 A B F)) ) ) ) ) ) ) ) )  &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) &  ((v10_cohsp_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) )  =>  (~  ((k3_tarski C) = (k11_cohsp_1 A B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (~  ( (~  (A = B) )  & (r1_xxreal_0 (k17_complex1 (k6_xcmplx_0 A B)) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k17_complex1 (k6_xcmplx_0 A B)) k6_numbers))  &  (A = B) ) ) ) ) ) ) ) ).
tt(t62_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ( ((k1_comptrig B) = (k1_comptrig C))  =>  ( (B = k6_numbers)  |  ( (C = k6_numbers)  |  ((k1_comptrig (k2_complex2 B A)) = (k1_comptrig (k2_complex2 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t62_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) => (r1_xxreal_0 (k17_complex1 (k3_rlvect_1 k1_complfld A B)) (k9_binop_2 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ).
tt(t62_complsp2,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ((m2_finseq_1 D k1_numbers) =>  ( ( (A = C)  &  ( (B = D)  &  ((k3_finseq_1 B) = (k3_finseq_1 D)) ) )  =>  ((k12_seq_4 B A) = (k10_rvsum_1 D C)) ) ) ) ) ) ) ) ) ) ).
tt(t62_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_afinsq_1 B)) => (r2_hidden C (k2_afinsq_1 (k10_compos_1 A B)))) ) ) ) ) ) ) ).
tt(t62_comptrig,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (A = (k2_xcmplx_0 (k8_real_1 (k17_complex1 A) (k21_sin_cos (k1_comptrig A))) (k3_xcmplx_0 (k8_real_1 (k17_complex1 A) (k18_sin_cos (k1_comptrig A))) k7_complex1))) ) ) ).
tt(t62_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 D) &  ((v4_valued_0 D) & (v2_margrel1 D)) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 C) 1) k5_numbers)) =>  ( ((r2_hidden A (k4_finseq_1 E)) & (r2_hidden (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1)) (k1_relset_1 (k3_finseq_2 k5_numbers) (k7_comput_1 C D A))))  =>  ((k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1))) = (k1_recdef_1 D (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_comseq_3 A) <=>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) & (r1_xxreal_0 B (k17_complex1 (k11_complex1 (k8_nat_1 k2_numbers (k10_comseq_3 A) D) (k8_nat_1 k2_numbers (k10_comseq_3 A) C))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((r1_tarski B C) => (r1_tarski (k19_convex4 A B D) (k19_convex4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t62_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A B (k8_cqc_lang A (k6_cqc_lang A B) C)) A)) ) ) ) ) ) ).
tt(t62_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k10_cqc_lang A (k12_cqc_lang A D (k8_cqc_lang A B C)) (k8_cqc_lang A (k11_cqc_lang A D B) (k12_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t62_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) => (r1_tarski (k24_qc_lang1 A C) (k24_qc_lang1 A (k13_cqc_lang A C B)))) ) ) ) ) ) ).
tt(t62_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((v3_funct_1 B) &  ((v3_funct_1 C) & (r2_funct_2 k5_numbers (u1_struct_0 A) D (k3_normsp_1 A B C))) )  => (v3_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t62_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k9_real_1 (k8_real_1 (k18_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 6 B) (k8_real_1 3 A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2))) (k8_real_1 (k18_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2)))))) ) ) ) ) ).
tt(t62_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k18_sin_cos D))) ) )  =>  ( ((k18_sin_cos A) = k6_numbers)  |  ( ((k18_sin_cos (k7_real_1 A B)) = k6_numbers)  |  ((k1_seq_1 (k3_diff_1 C B) A) = (k1_real_1 (k10_real_1 (k8_real_1 2 (k9_real_1 (k18_sin_cos A) (k18_sin_cos (k7_real_1 A B)))) (k9_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B))))) ) ) ) ) ) ) ) ) ) ).
tt(t62_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden A (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k9_real_1 A B) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos A) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos A)) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k9_real_1 A B)) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k9_real_1 A B))) 2)))) ) ) ) ) ) ).
tt(t62_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k9_int_3 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k9_int_3 A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k9_int_3 A))) =>  (! [K:$i] :  ((m2_subset_1 K (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k6_int_1 3 A))  &  ( (E = (k6_int_1 4 A))  &  ( (F = (k6_int_1 8 A))  &  ( (G = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) D (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2))))  &  ( (H = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))  &  ( (I = (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) H))  &  ( (J = (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k8_group_1 (k9_int_3 A) F I)))  &  (L = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C J) H) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E I) J)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k2_binom (k9_int_3 A) H 2))) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 3)))) ) ) ) ) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) H 2)) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L))) = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C H) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k8_group_1 (k9_int_3 A) G (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) H 2) (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u1_struct_0 B) (u1_struct_0 (k11_ens_1 A)) (k7_cat_1 B (k11_ens_1 A) (k24_ens_1 A B C)) D) = (k2_cat_1 B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t62_entropy1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v6_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  (! [B:$i] :  ((m2_finseq_1 B k1_numbers) =>  ( (B = (k8_entropy1 A))  <=>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r2_hidden C (k4_finseq_1 B)) =>  ((k1_seq_1 B C) = (k1_real_1 (k18_rvsum_1 (k1_matrprob k1_numbers (k5_entropy1 A) C)))) ) ) ) ) ) ) ) ) ) ).
tt(t62_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 A C B D)) ) ) ) ) ).
tt(t62_eqrel_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  ((k3_tarski (k9_subset_1 B C D)) = (k3_xboole_0 (k3_tarski C) (k3_tarski D))) ) ) ) ) ) ) ) ).
tt(t62_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k8_euclid 3 A B) = (k1_euclid_8 (k10_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k10_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2)) (k10_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(t62_euclid,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ((k5_algstr_0 (k15_euclid 2) (k19_euclid A B) (k19_euclid C D)) = (k19_euclid (k10_binop_2 A C) (k10_binop_2 B D))) ) ) ) ) ) ) ) ) ).
tt(t62_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ( (~ (r2_hidden B C))  &  ((v1_euclid_4 C A) &  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r2_hidden B D) &  ((r6_euclidlp A D C) &  (~ (r1_xboole_0 D C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 B)) =>  ( ((r1_ordinal1 C D) & (r1_ordinal1 D E))  =>  ( ((k1_binop_1 (k7_exchsort A B C E) C D) = (k4_tarski C D))  &  ((k1_binop_1 (k7_exchsort A B C E) D E) = (k4_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D)))) =>  ( (~  (A = (k4_tarski (k10_finseq_1 B C) D)) )  =>  ( ((k11_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) (k9_facirc_1 B C A D)) = (k1_funct_1 D (k10_finseq_1 (k1_funct_1 D (k10_finseq_1 (k1_funct_1 E B) (k1_funct_1 E C))) (k1_funct_1 E A))))  &  ( ((k1_funct_1 (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) (k4_tarski (k10_finseq_1 B C) D)) = (k1_funct_1 D (k10_finseq_1 (k1_funct_1 E B) (k1_funct_1 E C))))  &  ( ((k1_funct_1 (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) B) = (k1_funct_1 E B))  &  ( ((k1_funct_1 (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) C) = (k1_funct_1 E C))  &  ((k1_funct_1 (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) A) = (k1_funct_1 E A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B))) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) B) = (k10_real_1 (k9_real_1 (k1_seq_1 k1_sin_cos9 (k10_real_1 1 B)) (k1_seq_1 k2_sin_cos9 (k10_real_1 1 B))) (k7_real_1 1 (k5_square_1 B)))) ) ) ) ) ) ) ) ) ).
tt(t62_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_xboole_0 (k3_xboole_0 k4_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 3))) (k6_domain_1 k5_numbers (k2_nat_1 (k4_nat_1 2 A) 5))) = (k3_xboole_0 k4_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 5)))) ) ) ).
tt(t62_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v19_lattices E A) &  ((v20_lattices E A) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ((r2_hidden (k7_filter_0 A B C) E) & (r2_hidden (k7_filter_0 A C D) E))  => (r2_hidden (k7_filter_0 A B D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r3_lattices A B C) =>  ((r2_hidden D (k9_filter_2 A B C)) <=>  ((r3_lattices A B D) & (r3_lattices A D C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k13_finseq_1 A) (k13_finseq_1 B))) ) ) ).
tt(t62_finseq_2,ax, (! [A:$i] :  ((k2_finseq_2 3 A) = (k11_finseq_1 A A A)) ) ).
tt(t62_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (C = (k6_xcmplx_0 (k3_finseq_1 A) (k5_card_1 (k8_relat_1 A B))))  =>  ((k1_relset_1 k5_numbers (k1_finseq_3 A B)) = (k2_finseq_1 C)) ) ) ) ) ) ) ).
tt(t62_finseq_4,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ((v2_funct_1 A) <=>  ((k5_card_1 (k10_xtuple_0 A)) = (k3_finseq_1 A)) ) ) ) ).
tt(t62_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  ( ((k1_funct_1 A 1) = (k1_funct_1 (k3_finseq_5 A) (k3_finseq_1 A)))  &  ((k1_funct_1 A (k3_finseq_1 A)) = (k1_funct_1 (k3_finseq_5 A) 1)) ) ) ) ).
tt(t62_finseq_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden A (k10_xtuple_0 D)) &  ((r2_hidden C (k10_xtuple_0 D)) & (r1_xxreal_0 (k4_finseq_4 D C) (k4_finseq_4 D A))) )  => (r2_hidden A (k10_xtuple_0 (k2_finseq_5 B D C)))) ) ) ) ) ) ) ) ).
tt(t62_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo C A) &  ((v2_binop_1 C A) & (v1_finseqop C A)) )  =>  ((k3_funct_2 A A (k5_finseqop A C) (k3_funct_2 A A (k5_finseqop A C) B)) = B) ) ) ) ) ) ) ) ).
tt(t62_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k8_flang_1 A (k8_flang_1 A B)) = (k8_flang_1 A B)) ) ) ) ).
tt(t62_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 C D) & (r2_hidden (k2_flang_1 A) B))  =>  ((r1_xxreal_0 D k6_numbers) |  ((k8_flang_1 A (k1_flang_2 A B C D)) = (k8_flang_1 A B)) ) ) ) ) ) ) ) ) ) ).
tt(t62_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ((k2_flang_3 A (k2_flang_3 A B)) = (k2_flang_3 A B)) ) ) ) ).
tt(t62_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) & (l2_fsm_1 C A B)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) & (l2_fsm_1 D A B)) )  =>  (? [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v8_struct_0 E) & (l2_fsm_1 E A B)) )  &  (? [F:$i] :  ( ( (~ (v2_struct_0 F))  &  ((v8_struct_0 F) & (l2_fsm_1 F A B)) )  &  ((r1_subset_1 (u1_struct_0 E) (u1_struct_0 F)) &  ((r7_fsm_1 A B E C) & (r7_fsm_1 A B F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((v2_binop_1 C A) => (r2_funct_2 B A (k10_funcop_1 A B C (k5_binop_1 A C E F) D) (k10_funcop_1 A B C E (k10_funcop_1 A B C F D)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v2_funct_1 C) =>  ((k7_relat_1 C (k3_xboole_0 A B)) = (k3_xboole_0 (k7_relat_1 C A) (k7_relat_1 C B))) ) ) ) ) ) ).
tt(t62_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A A) &  ((v3_funct_2 C A A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  ((r1_tarski B A) =>  ( ((k7_relset_1 A A C (k8_relset_1 A A C B)) = B)  &  ((k8_relset_1 A A C (k7_relset_1 A A C B)) = B) ) ) ) ) ) ) ).
tt(t62_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((k3_relat_1 (k14_funct_3 A B C D E) (k9_funct_3 B C)) = D)  &  ((k3_relat_1 (k14_funct_3 A B C D E) (k10_funct_3 B C)) = E) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((k9_xtuple_0 (k4_funct_4 A B C D)) = (k2_tarski A B))  & (r1_tarski (k10_xtuple_0 (k4_funct_4 A B C D)) (k2_tarski C D))) ) ) ) ) ).
tt(t62_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r1_xboole_0 A B) =>  ((r2_wellord2 (k1_funct_2 (k2_xboole_0 A B) C) (k2_zfmisc_1 (k1_funct_2 A C) (k1_funct_2 B C))) &  ((k1_card_1 (k1_funct_2 (k2_xboole_0 A B) C)) = (k1_card_1 (k2_zfmisc_1 (k1_funct_2 A C) (k1_funct_2 B C)))) ) ) ) ) ) ).
tt(t62_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_funct_7 A)) ) )  =>  ((k9_xtuple_0 (k4_funct_7 (k6_funct_7 A) A)) = (k6_funct_7 A)) ) ) ).
tt(t62_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 k6_numbers A))  =>  ((k1_funct_1 k2_euclid A) = (k4_xcmplx_0 A)) ) ) ) ).
tt(t62_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) => (r2_hidden (k4_struct_0 A) (k8_fvaluat1 A B))) ) ) ) ) ).
tt(t62_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l3_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_fvsum_1 1 A (k4_matrix_2 (u1_struct_0 A) B) (k4_matrix_2 (u1_struct_0 A) C)) = (k4_matrix_2 (u1_struct_0 A) (k6_algstr_0 A B C))) ) ) ) ) ) ) ).
tt(t62_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D A))  &  ( (F = (k1_funct_1 D B))  &  (G = (k1_funct_1 D C)) ) )  =>  ((k1_twoscomp (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) (k5_facirc_1 (k22_gfacirc1 A B C) (k23_gfacirc1 A B C) D 2) (k24_gfacirc1 A B C)) = (k9_margrel1 (k2_binarith (k2_binarith E (k9_margrel1 F)) G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r1_glib_000 A D C B) => (r2_hidden B (k28_glib_000 A D))) ) ) ) ) ) ) ).
tt(t62_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k10_glib_001 A B C) = (k7_finseq_1 B (k10_finseq_1 C D))) ) ) ) ) ) ) ) ).
tt(t62_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid (k1_real_1 1) 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A k6_numbers (k1_matrix_1 A))) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A 1 (k1_matrix_1 A)) (k19_euclid k6_numbers 1)))))) ) ).
tt(t62_goboard7,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_funct_1 C))  &  ( (~ (v1_xboole_0 C))  &  ((v1_finseq_6 C (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 C) &  ((v2_topreal1 C) &  ((v1_goboard5 C) &  ((v2_goboard5 C) & (m2_finseq_1 C (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ((r1_xxreal_0 1 A) &  ( (~ (r1_xxreal_0 (k1_matrix_1 (k2_goboard2 C)) A))  &  ((r1_xxreal_0 1 B) &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k2_goboard2 C)) (k2_nat_1 B 1)))  &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) B (k2_nat_1 A 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) (k2_nat_1 A 1))) (k3_topreal1 2 C)) &  ((r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) (k2_nat_1 A 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 2) (k2_nat_1 A 1))) (k3_topreal1 2 C)) & (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k2_goboard2 C) (k2_nat_1 B 1) (k2_nat_1 A 1))) (k3_topreal1 2 C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k4_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 (k2_nat_1 C 1) (k3_finseq_1 A)) &  ( (D = (k8_graph_2 A (k2_nat_1 C 1) (k3_finseq_1 A)))  &  ((r4_graph_2 A C) &  (B = (k2_funct_7 (k2_funct_7 A (k2_nat_1 C 1) (k1_funct_1 A D)) D (k1_funct_1 A (k2_nat_1 C 1)))) ) ) )  => (r4_graph_2 B (k2_nat_1 C 1))) ) ) ) ) ) ) ) ) ).
tt(t62_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_graph_1 C) & (l1_graph_1 C)) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m2_graph_1 D C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  (~  ((r2_graph_5 C E F D A) &  ((r5_graph_5 C B) &  (! [G:$i] :  ( ((v7_graph_1 G C) &  ((v1_graph_4 G C) & (m2_graph_1 G C)) )  =>  (~ (r8_graph_5 C E F G A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  => (r1_tarski (k2_group_2 A (k3_group_11 A B D) (k3_group_11 A C D)) (k1_group_11 A (k7_group_4 A B C) D))) ) ) ) ) ) ) ) ).
tt(t62_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  ((g3_algstr_0 (u1_struct_0 B) (u2_algstr_0 B)) = (g3_algstr_0 (u1_struct_0 A) (u2_algstr_0 A))) ) ) ) ) ) ).
tt(t62_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r1_group_2 A (k6_group_3 A (k6_group_3 A C B) (k2_group_1 A B)) C) & (r1_group_2 A (k6_group_3 A (k6_group_3 A C (k2_group_1 A B)) B) C)) ) ) ) ) ) ) ).
tt(t62_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  ((m1_group_2 B C) => (m1_group_2 B (k8_group_4 A C D))) ) ) ) ) ) ) ) ) ).
tt(t62_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r1_tarski B C) & (r1_tarski D E))  => (m1_group_2 (k7_group_5 A B D) (k7_group_5 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v1_group_6 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) =>  ((v1_funct_1 (k2_funct_1 C)) &  ((v1_funct_2 (k2_funct_1 C) (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 (k2_funct_1 C) B A) & (m1_subset_1 (k2_funct_1 C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) ) ) ) ) ) ) ) ) ).
tt(t62_group_9,ax, (! [A:$i] :  (! [B:$i] :  ((v1_funct_1 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B)))) &  ((v1_funct_2 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B))) A (k1_funct_2 B B)) & (m1_subset_1 (k2_zfmisc_1 A (k1_tarski (k6_partfun1 B))) (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) ) ) ) ).
tt(t62_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k13_bilinear k1_complfld A B C) = (k13_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C))) ) ) ) ) ) ) ).
tt(t62_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) 2))) ) ).
tt(t62_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((r2_hidden C (k9_ideal_1 A B)) <=>  (? [D:$i] :  ((m3_ideal_1 D A B) &  (C = (k4_rlvect_1 A D)) ) ) ) ) ) ) ) ) ).
tt(t62_int_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((k6_int_1 B A) = k6_numbers)  <=> (r1_int_1 A B)) ) ) ) ) ) ).
tt(t62_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ( ((k1_seq_1 C D) = (k1_real_1 (k10_real_1 1 (k5_square_1 (k1_seq_1 k16_sin_cos D)))))  &  (~  ((k1_seq_1 k16_sin_cos D) = k6_numbers) ) ) ) ) )  &  ( ((k9_xtuple_0 k30_sin_cos) = B)  &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 k30_sin_cos (k4_seq_4 A)) (k1_seq_1 k30_sin_cos (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t62_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( ((k9_xtuple_0 (k2_fdiff_1 k1_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1))) = (k9_xtuple_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k2_rcomp_1 (k1_real_1 1) 1)) &  ((k1_seq_1 A C) = (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 C))))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) )  =>  ((k2_integra5 B A) = (k9_real_1 (k1_seq_1 k1_sin_cos6 (k4_seq_4 B)) (k1_seq_1 k1_sin_cos6 (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t62_integra9,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B D) &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E D) & (r1_xxreal_0 E k6_numbers)) ) ) )  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_taylor_1 A) k3_taylor_1)) = D)  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_taylor_1 A) k3_taylor_1)) = (k1_relset_1 k1_numbers C))  &  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E D) =>  ((k1_seq_1 C E) = (k10_real_1 A E)) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C B))) ) ) ) )  =>  ((k2_integra5 B C) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_taylor_1 A) k3_taylor_1) (k4_seq_4 B)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k1_taylor_1 A) k3_taylor_1) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ).
tt(t62_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) => (r2_interva1 A (k16_interva1 A B C) (k16_interva1 A C B))) ) ) ) ) ) ).
tt(t62_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k3_intpro_1 A B) (k3_intpro_1 (k5_intpro_1 C A) (k5_intpro_1 C B))) k8_intpro_1)) ) ) ) ) ) ).
tt(t62_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_2_jgraph_4) )  => (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ).
tt(t62_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ( ((r1_xxreal_0 k6_numbers (k18_euclid A)) | (r1_xxreal_0 k6_numbers (k17_euclid A)))  &  ( ((r1_xxreal_0 k6_numbers (k18_euclid B)) | (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( ((r1_xxreal_0 k6_numbers (k18_euclid C)) | (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ( (~  ((r1_xxreal_0 (k18_euclid D) k6_numbers) & (r1_xxreal_0 (k17_euclid D) k6_numbers)) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ((r1_xxreal_0 k6_numbers (k18_euclid G)) &  ((r1_xxreal_0 k6_numbers (k18_euclid H)) &  ((r1_xxreal_0 k6_numbers (k18_euclid I)) &  ( (~ (r1_xxreal_0 (k18_euclid J) k6_numbers))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_jgraph_6,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  ((r2_hidden E (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ( (E = (k18_pscomp_1 (k1_sppol_2 A B C D)))  |  ((r1_jordan6 (k1_sppol_2 A B C D) E F) <=>  ((r2_hidden F (k1_rltopsp1 (k15_euclid 2) (k19_euclid B C) (k19_euclid A C))) &  ((r1_xxreal_0 (k17_euclid F) (k17_euclid E)) &  (~  (F = (k18_pscomp_1 (k1_sppol_2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) B)) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) |  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k9_real_1 (k6_pscomp_1 B) (k13_complex1 (k9_real_1 (k8_pscomp_1 B) (k6_pscomp_1 B)) (k13_newton 2 A)))) ) ) ) ) ).
tt(t62_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski (k2_nat_1 E 1) D) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) (k2_nat_1 E 1) D))  &  ((r2_hidden (k4_tarski E D) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) E D)) ) ) )  =>  ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski E (k2_nat_1 D 1)) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (~  ((r2_hidden (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) &  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B 1) (k1_jordan1a (k1_jordan8 B 1)) 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1)))))) ) ) ) ) ) ) ) ) ) ).
tt(t62_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r1_xxreal_0 2 A) &  ( (B = (k6_subset_1 (k1_euclid A) (a_2_3_jordan2c A C)))  & (v6_tbsp_1 B (k14_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t62_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xboole_0 (k9_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) ) ) ).
tt(t62_jordan,ax, ((v1_funct_1 k7_jordan) &  ((v1_funct_2 k7_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc k7_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 k7_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ).
tt(t62_kurato_1,ax, (~  (k6_kurato_1 = (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)) ) ).
tt(t62_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v14_lattices A) & (l3_lattices A)) ) )  =>  ((k6_lattices A) = (k5_lattices (k1_lattice2 A))) ) ) ).
tt(t62_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  (! [D:$i] :  ( ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B))) & (r2_hidden D (k2_chord A (k1_tarski C))))  =>  ((r2_hidden D (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) B))) |  ((k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) (k20_lexbfs A B C)) D) = (k2_nat_1 (k1_recdef_1 (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B) D) 1)) ) ) ) ) ) ) ) ) ).
tt(t62_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B)))) ) ) ) )  | (v4_limfunc1 A)) ) ) ) ).
tt(t62_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ( ((k2_limfunc2 B A) = k6_numbers)  &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers C (k2_rcomp_1 A (k7_real_1 A D))))) ) ) )  |  ((r4_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t62_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k1_seq_1 B E) (k2_limfunc2 B A))) ) ) ) ) ) ) )  |  ((r4_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k2_limfunc2 C (k2_limfunc2 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t62_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 (k12_lpspace2 A B C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k12_lpspace2 A B C D)))))) )  =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden (k4_mesfunc5 A k1_numbers F G) (k1_lpspace2 A B C D)) &  ((r2_hidden (k4_mesfunc5 A k1_numbers F G) (k1_normsp_1 (k12_lpspace2 A B C D) E G)) &  ( ((k1_normsp_1 (k12_lpspace2 A B C D) E G) = (k5_lpspace2 A B C (k4_mesfunc5 A k1_numbers F G) D))  &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers (k4_mesfunc5 A k1_numbers F G)))))  &  ((k1_normsp_0 (k12_lpspace2 A B C D) (k1_normsp_1 (k12_lpspace2 A B C D) E G)) = (k4_power H (k10_real_1 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D B) => (r3_cqc_the1 A D (k8_cqc_lang A (k8_cqc_lang A B C) C))) ) ) ) ) ) ) ) ) ).
tt(t62_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid B))) =>  ((k6_mathmorp A (k15_euclid B) (k1_mathmorp (k15_euclid B) D C)) = (k1_mathmorp (k15_euclid B) (k1_rlvect_1 (k15_euclid B) D A) (k6_mathmorp A (k15_euclid B) C))) ) ) ) ) ) ) ) ) ).
tt(t62_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  (! [D:$i] :  ((m1_matrix_1 D k1_numbers A A) =>  (! [E:$i] :  ((m1_matrix_1 E k1_numbers A A) =>  ((r2_matrix10 (k4_matrix10 A B C) (k3_matrix10 A D E)) => (r2_matrix10 (k4_matrix10 A B E) (k3_matrix10 A D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrix11,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  ( (~ (r1_xxreal_0 A k1_xboole_0))  =>  ((k12_matrix_3 A B (k4_matrix_6 A B C D)) = (k8_group_1 B (k12_matrix_3 A B C) (k12_matrix_3 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 C D) (k2_matrix_1 B)) =>  ( ( ((k5_card_1 D) = k6_numbers)  &  (~  ((k5_card_1 C) = k6_numbers) ) )  |  ((k6_matrix13 A B C D) = (k4_matrix_1 A (k6_matrix13 A (k4_matrix_1 A B) D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( (~ (v1_xboole_0 (k6_matrix15 A B C)))  => (m2_vectsp_4 (k6_matrix15 A B C) A (k6_prvect_1 A (k1_matrix_1 B)) (k7_matrix15 A B))) ) ) ) ) ) ) ).
tt(t62_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v6_matrix16 C A) => (v6_matrix16 (k9_fvsum_1 A C B) A)) ) ) ) ) ) ) ).
tt(t62_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k1_matrix_1 B) = (k3_finseq_1 C)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((k4_matrix_3 A B (k3_matrix_3 A C D)) = (k3_matrix_3 A (k4_matrix_3 A B C) (k4_matrix_3 A B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrix_8,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_matrix_1 C (u1_struct_0 B) A A) =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 B) A A) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 B) A A) =>  ((k1_matrix_8 A B (k3_matrix_6 A B (k3_matrix_6 A B C D) E)) = (k5_algstr_0 B (k5_algstr_0 B (k1_matrix_8 A B C) (k1_matrix_8 A B D)) (k1_matrix_8 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ( ((k10_matrixj1 (u1_struct_0 A) (k24_matrixj1 A B C)) = (k10_matrixj1 (u1_struct_0 A) B))  &  ((k11_matrixj1 (u1_struct_0 A) (k24_matrixj1 A B C)) = (k11_matrixj1 (u1_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t62_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 A))  =>  ((k3_finseq_1 (k12_matrixr1 B A)) = (k1_matrix_1 B)) ) ) ) ) ) ).
tt(t62_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_matrixr2 A B C))) =>  ((k3_matrix_1 k1_numbers (k1_matrixr2 A B C) D E) = (k1_funct_1 (k11_matrixr1 B (k9_matrix_1 k1_numbers C E)) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_matrprob,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_matrprob A) & (m2_finseq_1 A k1_numbers)) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ( ( (~ (v1_xboole_0 (k12_matrixr1 B A)))  &  ((v1_matrprob (k12_matrixr1 B A)) & (m2_finseq_1 (k12_matrixr1 B A) k1_numbers)) )  &  ((k3_finseq_1 (k12_matrixr1 B A)) = (k1_matrix_1 B)) ) ) ) ) ) ) ).
tt(t62_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~  ((k2_zfmisc_1 A B) = k1_xboole_0) )  =>  (! [C:$i] :  ((m1_subset_1 C (k2_zfmisc_1 A B)) =>  ( (~  (C = (k1_xtuple_0 C)) )  &  (~  (C = (k2_xtuple_0 C)) ) ) ) ) ) ) ) ).
tt(t62_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  ((r1_tarski A B) => (r1_tarski (k6_measure6 A) (k6_measure6 B))) ) ) ) ) ).
tt(t62_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k10_member_1 (k1_tarski A) (k2_tarski B C)) = (k2_tarski (k3_xxreal_3 A B) (k3_xxreal_3 A C))) ) ) ) ) ) ) ).
tt(t62_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) => (r1_tarski (k6_memstr_0 A B C) (k9_memstr_0 A B C D))) ) ) ) ) ) ) ) ).
tt(t62_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) &  ((v3_mesfunc5 A) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 k7_numbers B D) = (k1_extreal1 (k1_measure6 C) (k8_nat_1 k7_numbers A D))) ) ) ) )  =>  ( ((k8_supinf_2 (k17_supinf_2 B)) = (k1_extreal1 (k1_measure6 C) (k8_supinf_2 (k17_supinf_2 A))))  & (v3_mesfunc5 B)) ) ) ) ) ) ) ) ).
tt(t62_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k19_rfunct_3 A B))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k19_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k18_rfunct_3 A B))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k19_rfunct_3 A B)) (k19_rfunct_3 A C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k19_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k18_rfunct_3 A B)) (k18_rfunct_3 A C))) = (k9_subset_1 A (k1_relset_1 A B) (k1_relset_1 A C)))  &  ((v6_supinf_2 (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k19_rfunct_3 A B))) & (v6_supinf_2 (k3_valued_1 A k1_numbers k1_numbers (k19_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k18_rfunct_3 A B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ( (~  (B = k1_xboole_0) )  =>  ((k26_mmlquery A B (k3_finseq_1 B)) = (k6_setfam_1 A (k2_relset_1 (k9_setfam_1 A) B))) ) ) ) ) ).
tt(t62_modelc_2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k30_modelc_1 (k25_modelc_2 A)))))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k42_modelc_2 A B))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k42_modelc_2 A B))) =>  ((r6_modelc_2 A B C (k24_modelc_2 (k42_modelc_2 A B) D E)) <=>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (! [G:$i] :  ((v7_ordinal1 G) =>  ( (~ (r1_xxreal_0 F G))  => (r6_modelc_2 A B (k29_modelc_2 A C G) (k3_robbins1 (k42_modelc_2 A B) D))) ) )  => (r6_modelc_2 A B (k29_modelc_2 A C F) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  (! [C:$i] :  ((m1_orders_1 C (k1_orders_1 (k1_modelc_3 A))) => (r7_modelc_3 A B (k26_modelc_3 B A C))) ) ) ) ) ) ).
tt(t62_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((k6_moebius1 (k6_moebius1 A)) = (k6_moebius1 A)) ) ) ).
tt(t62_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k10_monoid_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k10_monoid_0 A))) =>  ((k6_algstr_0 (k10_monoid_0 A) B C) = (k7_finseq_1 B C)) ) ) ) ) ) ) ).
tt(t62_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers (k6_int_1 B A)) &  (~ (r1_xxreal_0 A (k6_int_1 B A))) ) ) ) ) ) ) ).
tt(t62_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r7_ncfcont1 A B D C) & (r7_ncfcont1 A B E C))  =>  ((r7_ncfcont1 A B (k3_vfunct_2 (u1_struct_0 A) B D E) C) & (r7_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) => (r1_nat_d (k6_nat_d A B) (k5_nat_d A B))) ) ) ) ).
tt(t62_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 (k2_oppcat_1 B)) (k7_cat_1 (k2_oppcat_1 A) (k2_oppcat_1 B) (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C))) (k3_oppcat_1 A D)) = (k3_oppcat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t62_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((r9_orders_1 (k2_relat_1 A) B) <=> (r8_orders_1 A B)) ) ) ) ).
tt(t62_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) => (r1_ordinal1 A (k10_ordinal2 B (k5_ordinal3 A B)))) ) ) ) ).
tt(t62_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (~  ((r2_hidden k6_numbers A) &  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (~  ( (A = (k10_ordinal2 (k11_ordinal2 B (k12_ordinal2 k4_ordinal1 (k5_ordinal5 A k4_ordinal1))) C))  &  ((r2_hidden k6_numbers B) & (r2_hidden C (k12_ordinal2 k4_ordinal1 (k5_ordinal5 A k4_ordinal1)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden k4_ordinal1 B) & (r2_hidden A B))  =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) A)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) A) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) A)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) A) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) ) ) ).
tt(t62_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v5_o_ring_1 B A) & (v13_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t62_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_partfun1 (k5_relat_1 B A) B)) ) ) ).
tt(t62_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k3_pboole A B (k4_pboole A C D)) (k4_pboole A (k3_pboole A B C) D))) ) ) ) ) ) ) ).
tt(t62_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r5_pdiff_5 C B) =>  ((r3_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) &  ((k11_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) = (k8_real_1 A (k5_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t62_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) (k1_euclid 1)))))  =>  ( ((r2_relset_1 (k1_euclid A) (k1_euclid 1) (k3_pdiff_1 A D) E) &  ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) & (r3_pdiff_9 A C B D)) ) ) )  =>  ((r1_pdiff_9 A C (k3_pdiff_9 A C B D)) <=> (r4_pdiff_7 A 1 (k2_pdiff_7 A 1 B E C) C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_pepin,ax,(v1_int_2 (k2_nat_1 (k4_nat_1 256 256) 1))).
tt(t62_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) A) => (r1_xboole_0 B (k12_pnproc_1 C A))) ) ) ) ) ) ) ).
tt(t62_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (B = (k4_xcmplx_0 1))  =>  ((k1_vectsp_9 k2_bspace (k24_polyform A B)) = 1) ) ) ) ) ) ).
tt(t62_polynom5,ax,(r2_cfcont_1 (k6_partfun1 k2_numbers) k2_numbers)).
tt(t62_power,ax, ((k4_power 2 4) = 16) ).
tt(t62_pre_poly,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) &  ((v2_pre_poly B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  => (r1_tarski (k18_pre_poly A B) (k15_pre_poly A))) ) ) ).
tt(t62_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 (k6_prepower A B) 1)) ) ) ) ) ) ) ).
tt(t62_prob_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  ( ((k3_finseq_1 A) = k6_numbers)  =>  ((k18_rvsum_1 A) = k6_numbers) ) ) ) ).
tt(t62_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k21_pscomp_1 A) = (k22_pscomp_1 A))  =>  ((k21_pscomp_1 A) = (k12_pscomp_1 A)) ) ) ) ).
tt(t62_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D E))  => (r2_pboole A (k6_pboole A B D) (k6_pboole A C E))) ) ) ) ) ) ) ) ) ) ).
tt(t62_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (~  ((r3_qc_lang2 A B C) & (r1_qc_lang2 A C B)) ) ) ) ) ) ) ) ).
tt(t62_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k5_qc_lang3 A (k5_qc_lang2 A B C)) = (k5_qc_lang3 A C)) ) ) ) ) ) ) ).
tt(t62_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ( ((k26_quaterni A B) = (k26_quaterni C B))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t62_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ((k28_quaterni A) = (k6_quaterni (k1_real_1 (k17_quaterni A)) (k1_real_1 (k18_quaterni A)) (k1_real_1 (k19_quaterni A)) (k1_real_1 (k20_quaterni A)))) ) ) ).
tt(t62_quofield,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_vectsp_2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v33_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 C))))) )  =>  ( ((r3_quofield A B D) & (r3_quofield A C E))  => (r2_quofield B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [E:$i] :  ((m1_rcomp_3 E A B D) =>  (! [F:$i] :  ((m2_rcomp_3 F A B D E) =>  (~  ((m1_setfam_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 D (k4_topmetr A B)) &  ((v1_rcomp_3 D (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 1 C) &  ( (~ (r1_xxreal_0 (k3_finseq_1 F) (k1_nat_1 C 1)))  & (r1_xxreal_0 (k4_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) E C)) (k1_funct_1 F (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 A (k1_seq_1 (k4_real_3 B) C))) )  =>  ((r1_xxreal_0 A k6_numbers) |  (! [C:$i] :  ((v7_ordinal1 C) => (r1_xxreal_0 (k2_newton (k10_real_1 (k3_real_1 A (k7_square_1 (k3_real_1 (k3_square_1 A) 4))) 2) C) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 C 1)))) ) ) ) ) ) ) ) ).
tt(t62_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski A (k9_xtuple_0 B)) =>  ((k9_xtuple_0 (k5_relat_1 B A)) = A) ) ) ) ) ).
tt(t62_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((r1_tarski C (k6_relset_2 B A (k6_relset_2 A B C E) (k3_relset_1 A B E))) & (r1_tarski D (k6_relset_2 A B (k6_relset_2 B A D (k3_relset_1 A B E)) E))) ) ) ) ) ) ) ) ) ).
tt(t62_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (? [B:$i] :  ( ((v1_relat_1 B) & (v10_rewrite1 B))  &  ((r1_tarski (k1_relat_1 B) (k1_relat_1 A)) &  (! [C:$i] :  (! [D:$i] :  ((r2_rewrite1 A C D) <=> (r5_rewrite1 B C D)) ) ) ) ) ) ) ) ).
tt(t62_rewrite2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 A)) =>  ((r3_rewrite2 A B C D) => (r4_rewrite2 A B (k4_subset_1 (k2_zfmisc_1 (k8_afinsq_1 A) (k8_afinsq_1 A)) B (k4_lang1 (k8_afinsq_1 A) (k8_afinsq_1 A) (k1_domain_1 (k8_afinsq_1 A) (k8_afinsq_1 A) C D))) E)) ) ) ) ) ) ) ) ) ) ).
tt(t62_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))))  =>  (! [G:$i] :  ((m1_rewrite1 G (k1_rewrite3 C E F)) =>  ( ( ((k1_funct_1 G 1) = (k4_tarski A D))  &  ((k1_funct_1 G (k3_finseq_1 G)) = (k4_tarski B (k2_flang_1 C))) )  => (r1_xxreal_0 (k3_finseq_1 G) (k2_xcmplx_0 (k1_afinsq_1 D) 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  => (v1_partfun1 (k7_rfunct_1 A B) B)) ) ) ).
tt(t62_rfunct_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) => (r2_rfunct_3 (k18_rfunct_3 k1_numbers (k15_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers (k2_subset_1 k1_numbers)) A)) k1_numbers)) ) ).
tt(t62_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v1_seq_2 A) => (r2_funct_2 k5_numbers k1_numbers (k4_rinfsup1 A) (k32_valued_1 k5_numbers k1_numbers (k3_rinfsup1 (k32_valued_1 k5_numbers k1_numbers A))))) ) ) ).
tt(t62_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((v2_convex1 B A) <=>  ( ((k3_rlaffin1 A B) = 1)  &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_xxreal_0 k6_numbers (k1_seq_1 B C))) ) ) ) ) ) ) ) ).
tt(t62_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden (k5_algstr_0 A B C) (k3_rlsub_1 A B D)) <=> (r1_struct_0 D C)) ) ) ) ) ) ) ) ) ).
tt(t62_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_rlvect_1 B) & (m1_rlsub_1 B A))  =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_struct_0 B C)) )  =>  (B = (g1_rlvect_1 (u1_struct_0 A) (u2_struct_0 A) (u1_algstr_0 A) (u1_rlvect_1 A))) ) ) ) ) ) ).
tt(t62_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k7_rusub_4 A (k2_pre_topc A B) (k2_pre_topc A C)) (k2_pre_topc A (k7_rusub_4 A B C)))) ) ) ) ) ) ).
tt(t62_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) (k4_algstr_0 A B) (k4_algstr_0 A B))) = (k1_rlvect_1 A B (k1_real_1 2))) ) ) ) ) ).
tt(t62_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k3_rlvect_1 (k16_rlvect_2 A) (k1_rlvect_2 (k16_rlvect_2 A) B) (k1_rlvect_2 (k16_rlvect_2 A) C)) = (k7_rlvect_2 A B C)) ) ) ) ) ) ) ).
tt(t62_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_rmod_2 E A B) =>  (~  ( ((k3_rmod_2 A B C E) = (k3_rmod_2 A B D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r1_struct_0 E F) &  ((k5_algstr_0 B C F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v1_rmod_4 D A B))  => (v1_rmod_4 C A B)) ) ) ) ) ) ) ) ) ).
tt(t62_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k3_rusub_1 A D B) = (k3_rusub_1 A D C))  <=>  (B = C) ) ) ) ) ) ) ) ) ) ).
tt(t62_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_rusub_1 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(t62_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k14_rvsum_1 (k9_finseq_1 A) (k9_finseq_1 B)) = (k12_finseq_1 k1_numbers (k11_binop_2 A B))) ) ) ) ) ).
tt(t62_scmfsa_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A (u1_struct_0 k1_ami_3)) &  ((v1_funct_1 A) &  ((v5_funct_1 A (k2_memstr_0 2 k1_ami_3)) & (v1_partfun1 A (u1_struct_0 k1_ami_3))) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (A = (k5_relat_1 B k1_ami_2))  =>  ((k5_memstr_0 3 k1_scmfsa_2 B) = (k5_memstr_0 2 k1_ami_3 A)) ) ) ) ) ) ).
tt(t62_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v7_amistd_1 C 3 k1_scmfsa_2)) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~ (r4_scmfsa7b C D))  =>  ((k1_funct_1 (k1_scmfsa6b C B A) D) = (k1_funct_1 (k1_scmfsa_m B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t62_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  =>  ((r4_scmfsa7b C D) |  ((r5_scmfsa7b (k2_scmfsa8c D C) B A) & (r6_scmfsa7b (k2_scmfsa8c D C) B A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (? [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 C (u1_struct_0 k1_scmpds_2))) ) ) )  &  ( ((k1_funct_1 C k5_numbers) = B)  &  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  ((k1_funct_1 C D) = A) ) ) ) ) ) ) ) ) ) ).
tt(t62_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ((v1_int_1 E) =>  ((k5_memstr_0 2 k1_scmpds_2 (k6_scmpds_4 (k6_scmpds_6 D E C) (k8_memstr_0 2 k1_scmpds_2 B) A)) = (k2_nat_1 (k5_card_1 C) 2)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B (k3_tarski A)) & (r2_hidden C (k3_tarski A)))  =>  ((r2_hidden (k2_tarski B C) A) |  ((v9_scmyciel (k2_tarski B C) A) & (m1_subset_1 (k2_tarski B C) (k1_zfmisc_1 (k3_tarski A)))) ) ) ) ) ) ) ).
tt(t62_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r3_semi_af1 A B C D E) & (r3_semi_af1 A B C D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ( ((k15_seq_4 A B C) = (k17_seq_4 A))  =>  ( (B = (k18_seq_4 A C))  &  (C = (k18_seq_4 A B)) ) ) ) ) ) ) ) ) ).
tt(t62_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  ((k3_kurato_0 A B) = (k3_prob_1 A B)) ) ) ) ) ).
tt(t62_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k3_kurato_0 A (k3_setlim_2 A B C)) (k7_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C)))) ) ) ) ) ).
tt(t62_sf_mastr,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 k1_scmfsa_2)) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( (~ (r2_hidden A (k3_sf_mastr B)))  => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 B C) A) (k18_scmfsa_2 C A))) ) ) ) ) ) ) ).
tt(t62_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A B (k5_sheffer1 A C (k5_sheffer1 A (k5_sheffer1 A D D) B))) = (k5_sheffer1 A B (k5_sheffer1 A C D))) ) ) ) ) ) ) ) ) ).
tt(t62_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k11_simplex0 A B C 1) = (k10_simplex0 A B C)) ) ) ) ) ) ).
tt(t62_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) k2_sincos10) = (k1_partfun2 k1_numbers (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) ).
tt(t62_sin_cos3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k3_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 A)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 B))) = (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k3_binop_2 A B))) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k4_binop_2 A B))))  &  ((k4_binop_2 (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 A)) (k10_funct_2 k2_numbers k2_numbers k4_sin_cos3 (k5_binop_2 2 B))) = (k5_binop_2 (k5_binop_2 2 (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k3_binop_2 A B))) (k10_funct_2 k2_numbers k2_numbers k3_sin_cos3 (k4_binop_2 A B)))) ) ) ) ) ) ).
tt(t62_sin_cos6,ax, ((k2_relset_1 k1_numbers k1_sin_cos6) = (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) ).
tt(t62_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k5_power k8_power A) = (k1_sin_cos7 (k12_binop_2 (k10_binop_2 (k3_square_1 A) 1) (k11_binop_2 2 A)))) ) ) ) ).
tt(t62_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) &  ((r1_xxreal_0 A 1) &  ((k6_sin_cos9 A) = (k10_real_1 k32_sin_cos 4)) ) )  =>  (A = 1) ) ) ) ).
tt(t62_sin_cos,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_real_1 (k1_seq_1 k24_sin_cos (k7_real_1 A B)) (k1_seq_1 k24_sin_cos A)) = (k7_real_1 (k8_real_1 B (k1_seq_1 k24_sin_cos A)) (k8_real_1 (k8_real_1 B (k1_seq_1 k24_sin_cos A)) (k3_complex1 (k11_comseq_3 (k27_sin_cos B)))))) ) ) ) ) ).
tt(t62_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k11_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k11_pscomp_1 A)) ) ) ).
tt(t62_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k21_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k21_pscomp_1 (k3_topreal1 2 A)) = (k12_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t62_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t62_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v2_stirl2_1 C A B) =>  ((k5_nat_1 (k2_relset_1 B C)) = (k1_funct_1 C (k5_nat_1 (k1_relset_1 A C)))) ) ) ) ) ) ) ) ).
tt(t62_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  ( ( (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) D G (k24_qc_lang1 A B))) =>  ((r1_valuat_1 A D B E F) <=> (r1_valuat_1 A D B E G)) ) ) ) ) )  &  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A C)) (k5_relset_1 (k3_qc_lang1 A) D G (k24_qc_lang1 A C))) =>  ((r1_valuat_1 A D C E F) <=> (r1_valuat_1 A D C E G)) ) ) ) ) ) )  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A (k7_cqc_lang A B C))) (k5_relset_1 (k3_qc_lang1 A) D G (k24_qc_lang1 A (k7_cqc_lang A B C)))) =>  ((r1_valuat_1 A D (k7_cqc_lang A B C) E F) <=> (r1_valuat_1 A D (k7_cqc_lang A B C) E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tops_1 B A) & (v6_tops_1 C A))  =>  ((r1_tarski (k2_pre_topc A B) (k2_pre_topc A C)) <=> (r1_tarski B C)) ) ) ) ) ) ) ) ).
tt(t62_tex_2,ax, (! [A:$i] :  ( ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_pre_topc B) & (l1_pre_topc B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v5_pre_topc C A B)) ) ) ) ) ) ).
tt(t62_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v3_tops_1 B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v4_tex_3 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t62_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k2_pre_topc A (k3_tex_4 A B)) = (k2_pre_topc A B)) ) ) ) ) ).
tt(t62_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  => (r2_funct_2 (u1_struct_0 D) (u1_struct_0 C) (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) E F) D) (k1_partfun1 (u1_struct_0 D) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) (k2_tmap_1 A B E D) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v3_funct_1 C) & (m1_borsuk_2 C A B B))  =>  ((k1_group_1 (k5_topalg_1 A B)) = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) C)) ) ) ) ) ) ) ).
tt(t62_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( ((v1_prob_1 B (u1_struct_0 A)) & (v3_topgen_4 B (u1_struct_0 A)))  =>  ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B (u1_struct_0 A)) &  ((v4_prob_1 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t62_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  ( ((r1_xxreal_0 C 1) &  ((k12_euclid (k5_algstr_0 (k15_euclid 2) A (k19_euclid B (k3_xcmplx_0 D C)))) = (k3_xcmplx_0 D C)) )  =>  ( ((k18_euclid A) = k6_numbers)  |  ((k1_funct_1 (k4_topgen_5 B D) A) = C) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v7_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xreal_0 C) => (v6_tbsp_1 (k11_metric_1 A B C) A)) ) ) ) ) ) ).
tt(t62_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  ( ((r2_hidden D (k5_jgraph_6 A B C)) & (r2_hidden E (k5_jgraph_6 A B C)))  =>  ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_topreal9 2 D E) (k5_jgraph_6 A B C)) = (k2_tarski D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_toprealc,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v3_xxreal_0 B))  & (v1_xreal_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc C (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B) (k15_euclid A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)))))) ) )  =>  ((v1_funct_1 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C)) &  ((v1_funct_2 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C) (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A))) &  ((v5_pre_topc (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C) (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B) (k15_euclid A)) & (m1_subset_1 (k20_valued_2 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)) C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k2_xcmplx_0 A 1) (k4_struct_0 (k15_euclid (k2_xcmplx_0 A 1))) B)) (u1_struct_0 (k15_euclid A)))))) ) ) ) ) ) ) ) ) ).
tt(t62_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) =>  ((k2_tops_1 A (k1_tops_1 A B)) = (k2_tops_1 A B)) ) ) ) ) ) ).
tt(t62_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_tops_2 C A B) & (v2_connsp_1 D B))  => (v2_connsp_1 (k8_relset_1 (u1_struct_0 A) (u1_struct_0 B) C D) A)) ) ) ) ) ) ) ) ) ).
tt(t62_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C A) &  ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  (D = E) ) ) )  =>  ( ((v1_tops_1 C A) & (v1_tops_3 E B))  <=> (v1_tops_3 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (v1_transgeo A)) ) ).
tt(t62_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  => (r1_tarski (k2_trees_1 1) (k12_trees_3 A))) ) ).
tt(t62_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_connsp_1 A B C) <=>  (? [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) &  (? [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 A))) &  ((r2_tsep_1 A D E) &  ((r1_tarski B D) &  ((r1_tarski C E) & (r1_xboole_0 (k9_subset_1 (u1_struct_0 A) D E) (k4_subset_1 (u1_struct_0 A) B C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k14_polynom3 A)))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k5_card_1 (k13_pre_poly B)))  &  ( (D = (k1_uproots (k13_pre_poly B)))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden E (k4_finseq_1 C)) =>  ((k1_funct_1 C E) = (k9_uproots A (k7_partfun1 (u1_struct_0 A) D E) (k1_recdef_1 B (k7_partfun1 (u1_struct_0 A) D E)))) ) ) ) ) )  =>  ((k3_finseq_1 (k5_pre_poly (u1_struct_0 (k14_polynom3 A)) C)) = (k4_uproots (u1_struct_0 A) B)) ) ) ) ) ) ) ) ) ) ).
tt(t62_valued_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((v1_valued_2 C) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A C))))  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((r2_hidden B (k9_xtuple_0 (k57_valued_2 C D E))) =>  ((k1_funct_1 (k57_valued_2 C D E) B) = (k13_valued_1 (k1_funct_1 D B) (k1_funct_1 E B))) ) ) ) ) ) ) ) ) ) ).
tt(t62_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ((r2_hidden C (k3_vectsp_4 A B D E)) <=>  (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r1_struct_0 E F) &  (C = (k5_algstr_0 B D F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_vectsp_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  ( (~ (v2_struct_0 (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))))  &  ((v10_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v15_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) &  ((v16_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B))) & (l3_lattices (g3_lattices (k3_vectsp_5 A B) (k5_vectsp_5 A B) (k6_vectsp_5 A B)))) ) ) ) ) ) ) ) ).
tt(t62_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski B (k4_waybel_0 A (k12_waybel_0 A B))) &  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_waybel_0 C A) &  ((v13_waybel_0 C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ((r1_tarski B C) => (r1_tarski (k4_waybel_0 A (k12_waybel_0 A B)) C)) ) ) ) ) ) ) ) ).
tt(t62_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_waybel_1 (k4_waybel_1 A B) A A)) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_waybel_1 A (a_3_2_waybel_1 A B C))) ) ) ) ) ) ) ).
tt(t62_waybel23,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v24_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  => (r2_relset_1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 A) (k3_waybel23 A B) (k1_partfun1 (u1_struct_0 (k2_yellow_1 (k7_waybel_0 B))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 (k2_yellow_1 (k7_waybel_0 A))) (u1_struct_0 A) (k4_waybel23 A B) (k2_yellow_2 A)))) ) ) ) ).
tt(t62_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v20_waybel_0 C A B) & (v5_waybel34 C A B))  => (v4_waybel34 C A B)) ) ) ) ) ) ) ).
tt(t62_xboole_1,ax, (! [A:$i] :  (~ (r2_xboole_0 A k1_xboole_0)) ) ).
tt(t62_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k6_xboolean B C)) = (k4_xboolean (k5_xboolean (k3_xboolean A) B) (k5_xboolean (k3_xboolean A) (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t62_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k2_xcmplx_0 (k7_xcmplx_0 A B) (k7_xcmplx_0 C B)) = (k7_xcmplx_0 (k2_xcmplx_0 A C) B)) ) ) ) ) ) ) ).
tt(t62_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (~ (r1_xxreal_0 B (k4_xcmplx_0 A)))  & (r1_xxreal_0 (k2_xcmplx_0 B A) k6_numbers)) ) ) ) ) ) ).
tt(t62_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) & (r1_tarski (k1_xxreal_1 A B) (k4_xxreal_1 C D)))  =>  ( (~ (r1_xxreal_0 A C))  &  (~ (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ( (? [C:$i] :  ((v1_xxreal_0 C) &  ((r2_hidden C A) & (r1_xxreal_0 C B)) ) )  => (r1_xxreal_0 (k2_xxreal_2 A) B)) ) ) ) ) ).
tt(t62_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  (C = k2_xxreal_0) )  &  ( (~  (C = k1_xxreal_0) )  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k1_xxreal_3 B C) (k1_xxreal_3 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t62_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_yellow_0 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( (E = D)  =>  ( ((r1_lattice3 B C E) => (r1_lattice3 A C D))  &  ((r2_lattice3 B C E) => (r2_lattice3 A C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t62_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)))  & (v25_waybel_0 A))  => (v25_waybel_0 B)) ) ) ) ) ).
tt(t62_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k3_waybel_0 A (k4_yellow_4 A (k3_waybel_0 A B) (k3_waybel_0 A C))) = (k3_waybel_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ).
tt(t62_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  ((k7_waybel_1 A (k3_yellow_0 A)) = (k4_yellow_0 A)) ) ) ).
tt(t62_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k2_zf_model (k8_zf_lang B A)) = (k7_subset_1 k1_zf_lang (k2_zf_model A) (k1_tarski B))) ) ) ) ) ).
tt(t62_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_zf_lang A B) & (r1_xxreal_0 (k3_finseq_1 B) (k3_finseq_1 A))) ) ) ) ) ) ).
tt(t62_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_xboole_0 (k2_tarski A B) C) = (k1_tarski A))  <=>  ( (~ (r2_hidden A C))  &  ((r2_hidden B C) |  (A = B) ) ) ) ) ) ) ).
tt(t62_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r2_hidden (k4_struct_0 A) (k5_zmodul01 A B C)) <=>  ((k5_zmodul01 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t63_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r6_abcmiz_0 A B (k1_subset_1 (u1_abcmiz_0 A)))) ) ) ) ).
tt(t63_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  ( ((v8_abcmiz_1 A B) & (m1_abcmiz_1 A B (k13_abcmiz_1 B)))  <=> (r2_hidden A (k38_abcmiz_1 B))) ) ) ) ).
tt(t63_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 F A) &  ((v1_aff_4 G A) &  ((v1_aff_4 H A) &  ((r1_aff_4 A F G) &  ((r2_hidden B (k9_subset_1 (u1_struct_0 A) F H)) &  ((r2_hidden C (k9_subset_1 (u1_struct_0 A) F H)) &  ((r2_hidden D (k9_subset_1 (u1_struct_0 A) G H)) & (r2_hidden E (k9_subset_1 (u1_struct_0 A) G H))) ) ) ) ) ) )  =>  ( (F = G)  | (r2_analoaf A B C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_afinsq_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((r2_hidden C A) =>  ((v1_relat_1 (k7_funcop_1 B C)) &  ((v5_relat_1 (k7_funcop_1 B C) A) &  ((v5_ordinal1 (k7_funcop_1 B C)) &  ((v1_funct_1 (k7_funcop_1 B C)) & (v1_finset_1 (k7_funcop_1 B C))) ) ) ) ) ) ) ) ) ).
tt(t63_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v1_valued_0 B) & (v1_finset_1 B)) ) ) )  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k24_valued_1 (k5_relat_1 B A) C) = (k5_relat_1 (k24_valued_1 B C) A)) ) ) ) ) ) ) ).
tt(t63_algspec1,ax, (! [A:$i] :  ( ( (~ (v11_struct_0 A))  &  ((v1_instalg1 A) & (l1_msualg_1 A)) )  =>  (! [B:$i] :  ( ( (~ (v11_struct_0 B))  &  ((v1_instalg1 B) & (l1_msualg_1 B)) )  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) &  ((v1_msafree1 C A) & (l3_msualg_1 C A)) )  =>  ((m4_algspec1 C B) => (m2_algspec1 A B)) ) ) ) ) ) ) ).
tt(t63_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  (~  ( (~  (B = C) )  &  ( (~  ( (~  ((r4_analmetr A B C D E) & (r4_analmetr A B C F G)) )  &  ( (~  ((r4_analmetr A B C D E) & (r4_analmetr A F G B C)) )  &  ( (~  ((r4_analmetr A D E B C) & (r4_analmetr A F G B C)) )  &  (~  ((r4_analmetr A D E B C) & (r4_analmetr A B C F G)) ) ) ) ) )  &  (~ (r2_analoaf A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ((k14_aofa_000 (k7_freealg k19_aofa_000 A) B C D) = (k4_trees_4 3 (k3_finseq_4 (u1_struct_0 (k7_freealg k19_aofa_000 A)) B C D))) ) ) ) ) ) ) ) ) ).
tt(t63_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( (I = (k21_aofa_i00 B k4_numbers H E))  &  (J = (k21_aofa_i00 B k4_numbers H F)) )  =>  ((r1_xxreal_0 I J) |  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k16_aofa_000 A (k78_aofa_i00 A B C D F k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G E) (k83_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)))) E) = (k6_nat_d I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ( ((k9_arytm_3 A B) = k11_arytm_3)  =>  (A = k11_arytm_3) ) ) ) ) ) ).
tt(t63_asympt_1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) &  ((v2_asympt_0 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) &  ((v2_asympt_0 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  =>  ( ((r2_hidden A (k6_asympt_0 B)) & (r2_hidden B (k6_asympt_0 A)))  <=>  ((k6_asympt_0 A) = (k6_asympt_0 B)) ) ) ) ) ) ).
tt(t63_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k2_bcialg_1 A C)) = (k1_bcialg_1 A C (k2_bcialg_1 A B))) ) ) ) ) ) ) ) ).
tt(t63_bhsp_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v2_bhsp_1 B) & (l1_bhsp_1 B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k5_normsp_1 B (k3_normsp_1 B C D) A) (k3_normsp_1 B (k5_normsp_1 B C A) (k5_normsp_1 B D A)))) ) ) ) ) ) ) ) ).
tt(t63_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A (k3_boolealg A B C) (k3_lattices A B C)) (k4_lattices A B C))) ) ) ) ) ) ).
tt(t63_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 B C) &  (A = (k4_subset_1 k1_numbers (k1_seq_4 B) (k3_rcomp_1 C k1_xxreal_0))) )  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k2_rcomp_1 B C))) ) ) ) ) ) ) ) ).
tt(t63_borsuk_6,ax, (! [A:$i] :  ((r2_hidden (k4_tarski A 1) k8_borsuk_6) =>  (A = 1) ) ) ).
tt(t63_borsuk_7,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  ( (~  (B = (k4_struct_0 (k15_euclid A))) )  =>  ((k12_euclid (k10_toprealc A B (k12_euclid B))) = 1) ) ) ) ) ) ).
tt(t63_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  ( (I = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B K) (k16_funcop_1 C L)) (k16_funcop_1 D M)) (k16_funcop_1 E N)) (k16_funcop_1 F O)) (k16_funcop_1 G P)) (k16_funcop_1 H Q)) (k16_funcop_1 A J)))  =>  ((k9_xtuple_0 I) = (k6_enumset1 A B C D E F G H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k6_xboolean A B) = (k6_xboolean (k3_xboolean B) (k3_xboolean A))) ) ) ) ) ).
tt(t63_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc_1 A B (k6_bvfunc26 A C D)) (k2_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A C)) (k5_bvfunc_1 A B (k1_bvfunc_1 A D))))) ) ) ) ) ) ) ) ).
tt(t63_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) => (v1_finset_1 (k3_calcul_1 A B))) ) ) ) ).
tt(t63_card_1,ax, (! [A:$i] :  ((v1_finset_1 (k1_wellord2 A)) => (v1_finset_1 A)) ) ).
tt(t63_card_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((r3_zfmisc_1 A B C D E) =>  ((k5_card_1 (k3_enumset1 A B C D E)) = 5) ) ) ) ) ) ) ).
tt(t63_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_partfun1 A B) &  ((r2_hidden A (k8_card_3 C)) & (r2_hidden B (k8_card_3 C))) )  => (r2_hidden (k2_xboole_0 A B) (k8_card_3 C))) ) ) ) ) ) ) ).
tt(t63_card_fin,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (? [B:$i] :  ( ((v5_ordinal1 B) &  ((v1_relat_1 B) &  ((v5_relat_1 B k4_numbers) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  &  ( ((k7_afinsq_2 B) = (k1_card_1 (a_1_1_card_fin A)))  &  ( ((k1_relset_1 k5_numbers B) = (k23_binop_2 (k5_card_1 A) 1))  &  (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 B C) = (k12_binop_2 (k22_binop_2 (k1_newton (k19_binop_2 1) C) (k9_newton (k5_card_1 A))) (k9_newton C))) ) ) ) ) ) ) ) ) ) ).
tt(t63_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k3_graph_1 A D))) = (k4_cat_1 B (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D))))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A (k4_graph_1 A D))) = (k4_cat_1 B (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))) ) ) ) ) ) ) ) ) ) ).
tt(t63_cat_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_xboole_0 (u4_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_xboole_0 (u4_struct_0 A))))) )  => (m2_cat_3 C A B k1_xboole_0)) ) ) ) ) ) ).
tt(t63_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r4_cat_3 A (k20_cat_4 A B C) (k21_cat_4 A B C) (k22_cat_4 A B C))) ) ) ) ) ) ).
tt(t63_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_partfun1 B A) &  ( ((k8_relset_1 A k2_numbers C (k1_tarski k6_numbers)) = k1_xboole_0)  & (v1_partfun1 C A)) )  <=> (v1_partfun1 (k1_cfunct_1 A B C) A)) ) ) ) ) ) ) ).
tt(t63_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 (k2_nat_1 A 1) 1)))) =>  ((k10_chain_1 B C A (k10_chain_1 B C (k2_nat_1 A 1) D)) = (k5_chain_1 B C A)) ) ) ) ) ) ) ) ) ).
tt(t63_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_chord A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))) =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) => (v2_chord C)) ) ) ) ) ) ).
tt(t63_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_msualg_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_msualg_1 B))  =>  (! [C:$i] :  ( ((v4_msualg_1 C A) & (l3_msualg_1 C A))  =>  (! [D:$i] :  ( ((v4_msualg_1 D B) & (l3_msualg_1 D B))  =>  ( ((v4_circcomb C A) &  ((v4_circcomb D B) & (r1_partfun1 (u3_msualg_1 A C) (u3_msualg_1 B D))) )  => (v4_circcomb (k3_circcomb A B C D) (k2_circcomb A B))) ) ) ) ) ) ) ) ) ).
tt(t63_classes1,ax, (! [A:$i] :  ((k6_classes1 (k9_setfam_1 A)) = (k1_ordinal1 (k6_classes1 A))) ) ).
tt(t63_classes2,ax,(v2_classes1 (k4_classes1 k4_ordinal1))).
tt(t63_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_clvect_1 B A) =>  ((k5_clvect_1 A (k4_struct_0 A) B) = (u1_struct_0 B)) ) ) ) ) ).
tt(t63_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 C A) => (v2_clvect_2 (k5_bhsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t63_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  ((k3_tarski (k12_cohsp_1 A B)) = (k2_zfmisc_1 (k3_tarski A) (k3_tarski B))) ) ) ) ) ).
tt(t63_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) => (r1_xxreal_0 (k17_complex1 (k6_xcmplx_0 A B)) (k7_real_1 (k17_complex1 (k6_xcmplx_0 A C)) (k17_complex1 (k6_xcmplx_0 C B))))) ) ) ) ) ) ).
tt(t63_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k3_complex2 A B) = (k3_complex2 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ).
tt(t63_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) => (r1_xxreal_0 (k17_complex1 (k5_algstr_0 k1_complfld A B)) (k9_binop_2 (k17_complex1 A) (k17_complex1 B)))) ) ) ) ).
tt(t63_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k12_seq_4 A (k3_binop_2 B C)) = (k9_seq_4 (k12_seq_4 A B) (k12_seq_4 A C))) ) ) ) ) ) ) ).
tt(t63_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 A)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) )  =>  ((r2_hidden B (k2_afinsq_1 C)) =>  ((k1_funct_1 (k10_compos_1 A C) B) = (k1_funct_1 C B)) ) ) ) ) ) ) ) ).
tt(t63_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 D) &  ((v4_valued_0 D) & (v2_margrel1 D)) ) ) ) )  =>  (! [E:$i] :  ((m2_finseq_2 E k5_numbers (k4_finseq_2 (k2_nat_1 (k19_margrel1 C) 1) k5_numbers)) =>  ( ((v2_comput_1 C) &  ((v2_comput_1 D) &  ( ((k2_nat_1 (k19_margrel1 C) 2) = (k19_margrel1 D))  &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 1 (k19_margrel1 C)))) ) ) )  =>  ((k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A (k2_nat_1 B 1))) = (k1_recdef_1 D (k8_finseq_1 k5_numbers (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B) (k12_finseq_1 k5_numbers (k1_recdef_1 (k7_comput_1 C D A) (k8_comput_1 (k2_nat_1 (k19_margrel1 C) 1) E A B)))))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v2_comseq_3 A) => (v1_comseq_3 A)) ) ) ).
tt(t63_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k19_convex4 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t63_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A (k6_cqc_lang A (k7_cqc_lang A C D)) (k6_cqc_lang A (k7_cqc_lang A B D)))) A)) ) ) ) ) ) ) ) ).
tt(t63_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k12_cqc_lang A D (k8_cqc_lang A B C)) A) <=> (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D B) (k12_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ).
tt(t63_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) => (r1_tarski (k24_qc_lang1 A (k13_cqc_lang A C B)) (k2_xboole_0 (k24_qc_lang1 A C) (k1_tarski B)))) ) ) ) ) ) ).
tt(t63_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) & (l1_csspace B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  ( ((v3_funct_1 C) & (r2_funct_2 k5_numbers (u1_struct_0 B) D (k6_clvect_1 B C A)))  => (v3_funct_1 D)) ) ) ) ) ) ) ) ) ).
tt(t63_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k19_sin_cos) A) B) = (k9_real_1 (k8_real_1 (k10_real_1 1 2) (k8_real_1 (k18_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 6 B) (k8_real_1 3 A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))) (k8_real_1 (k10_real_1 1 2) (k8_real_1 (k18_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2)))))) ) ) ) ) ).
tt(t63_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k18_sin_cos D))) ) )  =>  ( ((k18_sin_cos A) = k6_numbers)  |  ( ((k18_sin_cos (k9_real_1 A B)) = k6_numbers)  |  ((k1_seq_1 (k4_diff_1 C B) A) = (k10_real_1 (k8_real_1 (k1_real_1 2) (k9_real_1 (k18_sin_cos (k9_real_1 A B)) (k18_sin_cos A))) (k9_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B)))) ) ) ) ) ) ) ) ) ) ).
tt(t63_diff_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( ((r2_hidden (k7_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k30_sin_cos)) & (r2_hidden (k9_real_1 A (k13_complex1 B 2)) (k1_relset_1 k1_numbers k30_sin_cos)))  =>  ((k1_seq_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k30_sin_cos k30_sin_cos) k19_sin_cos) B) A) = (k9_real_1 (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k7_real_1 A (k13_complex1 B 2))) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k7_real_1 A (k13_complex1 B 2)))) 2)) (k8_real_1 (k2_newton (k3_funct_2 k1_numbers k1_numbers k19_sin_cos (k9_real_1 A (k13_complex1 B 2))) 3) (k2_newton (k2_real_1 (k3_funct_2 k1_numbers k1_numbers k16_sin_cos (k9_real_1 A (k13_complex1 B 2)))) 2)))) ) ) ) ) ) ).
tt(t63_ec_pf_2,ax, (! [A:$i] :  ( ((v7_ordinal1 A) &  ((v1_int_2 A) & (v1_ec_pf_2 A 5)) )  =>  (! [B:$i] :  ((m2_subset_1 B (k2_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A))) (k1_ec_pf_2 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k9_int_3 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k9_int_3 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k9_int_3 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k9_int_3 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k9_int_3 A))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k9_int_3 A))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k9_int_3 A))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k9_int_3 A))) =>  (! [K:$i] :  ((m2_subset_1 K (k3_ec_pf_1 (k9_int_3 A)) (k6_ec_pf_1 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B))) =>  (! [L:$i] :  ((m1_subset_1 L (k3_zfmisc_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)))) =>  ( ( (C = (k6_int_1 2 A))  &  ( (D = (k6_int_1 3 A))  &  ( (E = (k6_int_1 4 A))  &  ( (F = (k6_int_1 8 A))  &  ( (G = (k3_rlvect_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k8_group_1 (k9_int_3 A) D (k2_binom (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2))))  &  ( (H = (k8_group_1 (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)))  &  ( (I = (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k4_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K)) H))  &  ( (J = (k5_algstr_0 (k9_int_3 A) (k2_binom (k9_int_3 A) G 2) (k8_group_1 (k9_int_3 A) F I)))  &  (L = (k4_domain_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) C J) H) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) G (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E I) J)) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) (k5_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k2_binom (k9_int_3 A) H 2))) (k8_group_1 (k9_int_3 A) F (k2_binom (k9_int_3 A) H 3)))) ) ) ) ) ) ) ) )  =>  ((k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) E (k2_binom (k9_int_3 A) H 2)) (k2_binom (k9_int_3 A) (k6_ec_pf_2 A (k2_ec_pf_2 A B) (k3_ec_pf_2 A B) K) 2)) (k5_algstr_0 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k2_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) 2) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) (k3_rlvect_1 (k9_int_3 A) (k3_rlvect_1 (k9_int_3 A) (k2_binom (k9_int_3 A) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) 3) (k8_group_1 (k9_int_3 A) (k8_group_1 (k9_int_3 A) (k2_ec_pf_2 A B) (k1_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L)) (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) 2))) (k8_group_1 (k9_int_3 A) (k3_ec_pf_2 A B) (k2_binom (k9_int_3 A) (k3_mcart_1 (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) (u1_struct_0 (k9_int_3 A)) L) 3))))) = (k4_struct_0 (k9_int_3 A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u4_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u4_struct_0 (k8_cat_2 (k2_oppcat_1 B) B)) (u4_struct_0 (k11_ens_1 A)) (k25_ens_1 A B) (k10_cat_2 (k2_oppcat_1 B) B (k5_oppcat_1 B C) D)) = (k1_domain_1 (k2_zfmisc_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B))) (k1_zfmisc_1 (k2_zfmisc_1 (k2_cat_1 B (k4_graph_1 B C) (k3_graph_1 B D)) (k2_cat_1 B (k3_graph_1 B C) (k4_graph_1 B D)))) (k1_domain_1 (k1_zfmisc_1 (u4_struct_0 B)) (k1_zfmisc_1 (u4_struct_0 B)) (k2_cat_1 B (k4_graph_1 B C) (k3_graph_1 B D)) (k2_cat_1 B (k3_graph_1 B C) (k4_graph_1 B D))) (k21_ens_1 B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t63_entropy1,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v6_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  ((k8_entropy1 A) = (k6_rvsum_1 (k3_matrprob (k5_entropy1 A)))) ) ) ).
tt(t63_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 A C D B)) ) ) ) ) ).
tt(t63_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_eqrel_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 A)) =>  ( (D = (k3_tarski C))  =>  ((k3_subset_1 A D) = (k3_tarski (k3_subset_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t63_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k23_rvsum_1 A B) = (k9_binop_2 (k9_binop_2 (k11_binop_2 (k1_seq_1 A 1) (k1_seq_1 B 1)) (k11_binop_2 (k1_seq_1 A 2) (k1_seq_1 B 2))) (k11_binop_2 (k1_seq_1 A 3) (k1_seq_1 B 3)))) ) ) ) ) ).
tt(t63_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))))  =>  ( (B = C)  =>  ((k1_pre_topc (k15_euclid A) B) = (k3_pcomps_1 (k1_topmetr (k14_euclid A) C))) ) ) ) ) ) ) ) ).
tt(t63_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (~  ((r1_xboole_0 B C) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (~  ((r2_hidden D B) &  (~ (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v16_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_exchsort C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 C)) =>  (! [G:$i] :  ((m1_subset_1 G (k9_xtuple_0 C)) =>  ( (A = (k5_exchsort (k9_xtuple_0 C) (k9_xtuple_0 C) (k6_partfun1 (k9_xtuple_0 C)) E G))  =>  ( (D = E)  |  ( (F = G)  |  ((k1_binop_1 (k7_exchsort B C E G) D F) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 A F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k4_finseq_2 2 k6_margrel1) k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k4_finseq_2 2 k6_margrel1) k6_margrel1)))) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D)))) =>  ( (~  (A = (k4_tarski (k10_finseq_1 B C) D)) )  => (v1_circuit2 (k5_facirc_1 (k8_facirc_1 B C A D) (k10_facirc_1 B C A D) E 2) (k8_facirc_1 B C A D) (k10_facirc_1 B C A D))) ) ) ) ) ) ) ) ).
tt(t63_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B))) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) B) = (k9_real_1 (k1_seq_1 k1_sin_cos9 (k10_real_1 1 B)) (k10_real_1 B (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ) ).
tt(t63_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k2_xboole_0 (k5_relat_1 k2_fib_num2 (k3_xboole_0 k4_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 3)))) (k1_tarski (k1_domain_1 k5_numbers k5_numbers (k2_nat_1 (k4_nat_1 2 A) 5) (k3_funct_2 k5_numbers k5_numbers k2_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 5))))) = (k5_relat_1 k2_fib_num2 (k3_xboole_0 k4_fib_num2 (k2_finseq_1 (k2_nat_1 (k4_nat_1 2 A) 5))))) ) ) ).
tt(t63_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (m1_subset_1 (k8_filter_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ).
tt(t63_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r3_lattices A B C) =>  ((r2_hidden B (k9_filter_2 A B C)) & (r2_hidden C (k9_filter_2 A B C))) ) ) ) ) ) ) ) ).
tt(t63_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((r1_tarski A B) => (r1_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ).
tt(t63_finseq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) => (m2_finseq_1 (k2_finseq_2 A C) B)) ) ) ) ) ) ).
tt(t63_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] : (r1_tarski (k1_relset_1 k5_numbers (k1_finseq_3 A B)) (k1_relset_1 k5_numbers A))) ) ) ).
tt(t63_finseq_4,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( ((k5_card_1 A) = (k5_card_1 B))  & (v2_funct_1 C))  =>  ((k10_xtuple_0 C) = B) ) ) ) ) ) ) ) ).
tt(t63_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k3_finseq_5 (k7_finseq_1 A (k9_finseq_1 B))) = (k7_finseq_1 (k9_finseq_1 B) (k3_finseq_5 A))) ) ) ) ).
tt(t63_finseq_6,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ( ((r2_hidden C (k10_xtuple_0 D)) &  ((r1_xxreal_0 A (k3_finseq_1 D)) & (r1_xxreal_0 (k4_finseq_4 D C) A)) )  => (r2_hidden (k7_partfun1 B D A) (k10_xtuple_0 (k2_finseq_5 B D C)))) ) ) ) ) ) ) ) ) ).
tt(t63_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo B A) &  ((v2_binop_1 B A) &  ((v1_binop_1 B A) & (v1_finseqop B A)) ) )  => (r7_binop_1 A (k5_finseqop A B) B)) ) ) ) ) ).
tt(t63_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  ((k6_flang_1 A (k8_flang_1 A B) (k8_flang_1 A B)) = (k8_flang_1 A B)) ) ) ) ).
tt(t63_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r1_xxreal_0 C D) & (r2_hidden (k2_flang_1 A) B))  =>  ((k8_flang_1 A (k1_flang_2 A B C D)) = (k1_flang_2 A (k8_flang_1 A B) C D)) ) ) ) ) ) ) ) ) ).
tt(t63_flang_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 B))) =>  (~  ((r2_hidden A C) &  ( (~  (A = (k2_flang_1 B)) )  &  ((k2_flang_3 B C) = (k4_flang_1 B (k2_flang_1 B))) ) ) ) ) ) ) ) ).
tt(t63_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l2_fsm_1 C A B))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l2_fsm_1 D A B))  =>  ((r7_fsm_1 A B C D) => (r4_fsm_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t63_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  (! [F:$i] :  ((m1_subset_1 F A) =>  ((v2_binop_1 C A) => (r2_funct_2 B A (k9_funcop_1 A B C D (k5_binop_1 A C E F)) (k9_funcop_1 A B C (k9_funcop_1 A B C D E) F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  (! [C:$i] :  ((k7_relat_1 A (k3_xboole_0 B C)) = (k3_xboole_0 (k7_relat_1 A B) (k7_relat_1 A C))) ) )  => (v2_funct_1 A)) ) ) ).
tt(t63_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( (! [E:$i] :  ((m1_subset_1 E A) =>  ((k1_funct_1 C E) = (k1_funct_1 D E)) ) )  => (r2_relset_1 A B C D)) ) ) ) ) ) ) ).
tt(t63_funct_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ( ((k13_funct_3 D F) = (k13_funct_3 E G))  =>  ( ( (B = k1_xboole_0)  &  (~  (A = k1_xboole_0) ) )  |  ( ( (C = k1_xboole_0)  &  (~  (A = k1_xboole_0) ) )  |  ((r2_funct_2 A B D E) & (r2_funct_2 A C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ( (~  (A = B) )  =>  ((k1_funct_1 (k4_funct_4 A B C D) A) = C) )  &  ((k1_funct_1 (k4_funct_4 A B C D) B) = D) ) ) ) ) ) ).
tt(t63_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_wellord2 (k1_funct_2 (k2_zfmisc_1 A B) C) (k1_funct_2 A (k1_funct_2 B C))) &  ((k1_card_1 (k1_funct_2 (k2_zfmisc_1 A B) C)) = (k1_card_1 (k1_funct_2 A (k1_funct_2 B C)))) ) ) ) ) ).
tt(t63_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_funct_7 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k10_xtuple_0 B) (k6_funct_7 A)) =>  ((v1_relat_1 (k7_finseq_1 (k9_finseq_1 B) A)) &  ((v1_funct_1 (k7_finseq_1 (k9_finseq_1 B) A)) &  ((v1_finseq_1 (k7_finseq_1 (k9_finseq_1 B) A)) & (v1_funct_7 (k7_finseq_1 (k9_finseq_1 B) A))) ) ) ) ) ) ) ) ).
tt(t63_funct_8,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((k1_funct_1 k2_euclid (k4_xcmplx_0 A)) = (k1_funct_1 k2_euclid A)) ) ) ).
tt(t63_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  (~  ((v3_fvaluat1 A) & (r2_hidden (k5_struct_0 A) (k8_fvaluat1 A B))) ) ) ) ) ) ).
tt(t63_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v5_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k12_fvsum_1 A B C D) = (k12_fvsum_1 A B D C)) ) ) ) ) ) ) ) ) ).
tt(t63_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k3_msafree2 (k25_gfacirc1 A B C)) = (k2_xboole_0 (k2_xboole_0 (k2_xboole_0 (k1_tarski (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) (k1_tarski (k24_gfacirc1 A B C))) (k1_enumset1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp))) (k1_tarski (k21_gfacirc1 A B C)))) ) ) ) ).
tt(t63_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  (~  ((r1_glib_000 A C D B) &  ( (~  ((r2_hidden B (k26_glib_000 A C)) & (r2_hidden B (k27_glib_000 A D))) )  &  (~  ((r2_hidden B (k26_glib_000 A D)) & (r2_hidden B (k27_glib_000 A C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ( ((k3_glib_001 A (k10_glib_001 A B C)) = (k3_glib_001 A B))  &  ( ((k4_glib_001 A (k10_glib_001 A B C)) = D)  & (r1_glib_001 A (k3_glib_001 A B) D (k10_glib_001 A B C))) ) ) ) ) ) ) ) ) ).
tt(t63_goboard6,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v2_goboard1 A) &  ((v3_goboard1 A) &  ((v4_goboard1 A) &  ((v5_goboard1 A) & (m2_finseq_1 A (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid 1 1)) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid k6_numbers 1))) (k2_xboole_0 (k1_tops_1 (k15_euclid 2) (k3_goboard5 A (k3_finseq_1 A) (k1_matrix_1 A))) (k1_tarski (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) A (k3_finseq_1 A) (k1_matrix_1 A)) (k19_euclid k6_numbers 1)))))) ) ).
tt(t63_goboard7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) &  ((v2_sppol_1 (k1_rltopsp1 (k15_euclid 2) C D)) &  ( ((k17_euclid A) = (k17_euclid C))  &  ((r1_xxreal_0 (k18_euclid A) (k18_euclid C)) &  ((r1_xxreal_0 (k18_euclid C) (k18_euclid D)) & (r1_xxreal_0 (k18_euclid D) (k18_euclid B))) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ) ).
tt(t63_graph_2,ax, (! [A:$i] :  ((m2_finseq_1 A k4_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 C B) => (r3_graph_2 A B C)) ) ) ) ) ) ) ).
tt(t63_graph_5,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v6_graph_1 C) & (l1_graph_1 C)) )  =>  (! [D:$i] :  ( ((v7_graph_1 D C) & (m2_graph_1 D C))  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( ((r5_graph_5 C B) &  ((r8_graph_5 C E F D A B) &  (! [G:$i] :  ( ((v7_graph_1 G C) & (m2_graph_1 G C))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 C)) =>  ((r8_graph_5 C E H G A B) =>  ((r2_hidden H A) | (r1_xxreal_0 (k10_graph_5 C D B) (k10_graph_5 C G B))) ) ) ) ) ) ) )  =>  ( (E = F)  | (r7_graph_5 C E F D B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v1_group_3 D A) & (m1_group_2 D A))  =>  ((k2_group_2 A (k4_group_11 A B D) (k4_group_11 A C D)) = (k2_group_11 A (k7_group_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t63_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  ((k6_group_2 B) = (k6_group_2 A)) ) ) ) ) ).
tt(t63_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) => (r1_group_2 A (k6_group_3 A (k10_group_2 A C D) B) (k10_group_2 A (k6_group_3 A C B) (k6_group_3 A D B)))) ) ) ) ) ) ) ) ).
tt(t63_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ( ((m1_group_2 B D) & (m1_group_2 C D))  => (m1_group_2 (k8_group_4 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t63_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (r1_group_2 A (k8_group_5 A B C) (k5_group_4 A (k5_group_5 A B C)))) ) ) ) ) ) ).
tt(t63_group_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ( ((v3_funct_2 C A B) &  (D = (k2_funct_1 C)) )  => (v3_funct_2 D B A)) ) ) ) ) ) ) ) ).
tt(t63_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (k1_funct_2 B B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  ((k2_group_9 A B D (k4_matrix_2 A C)) = (k3_funct_2 A (k1_funct_2 B B) D C)) ) ) ) ) ) ) ) ).
tt(t63_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k3_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C)))))) (u1_struct_0 k1_complfld) (k7_hermitan A B C) (k6_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C))) & (r1_funct_2 (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld) (k2_zfmisc_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C)))) (u1_struct_0 (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))))) (u1_struct_0 k1_complfld) (k7_hermitan A B C) (k15_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C)))) ) ) ) ) ) ) ).
tt(t63_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k19_sin_cos) A) 2) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k32_valued_1 k1_numbers k1_numbers k16_sin_cos)) A) 2))) ) ).
tt(t63_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((k7_ideal_1 A B) = (k8_ideal_1 A B))  &  ((k7_ideal_1 A B) = (k9_ideal_1 A B)) ) ) ) ) ) ).
tt(t63_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (~ (v1_int_1 (k7_xcmplx_0 A B)))  =>  ((k4_xcmplx_0 (k1_int_1 (k7_xcmplx_0 A B))) = (k3_real_1 (k1_int_1 (k7_xcmplx_0 (k4_xcmplx_0 A) B)) 1)) ) ) ) ) ) ).
tt(t63_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k10_real_1 (k9_real_1 (k1_seq_1 k16_sin_cos D) (k5_square_1 (k1_seq_1 k19_sin_cos D))) (k5_square_1 (k1_seq_1 k19_sin_cos D)))) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers B)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers B)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers k1_fdiff_9 (k1_partfun2 k1_numbers B)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t63_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( ((k9_xtuple_0 (k2_fdiff_1 k4_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1))) = (k9_xtuple_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k2_rcomp_1 (k1_real_1 1) 1)) &  ((k1_seq_1 A C) = (k1_real_1 (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 C)))))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) )  =>  ((k2_integra5 B A) = (k9_real_1 (k1_seq_1 k4_sin_cos6 (k4_seq_4 B)) (k1_seq_1 k4_sin_cos6 (k5_seq_4 B)))) ) ) ) ) ) ).
tt(t63_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k3_taylor_1)) = C)  &  ( ((k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k3_taylor_1)) = (k1_relset_1 k1_numbers B))  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k1_real_1 (k10_real_1 1 D))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((r2_hidden k6_numbers C) |  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ).
tt(t63_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) => (r2_interva1 A (k17_interva1 A B C) (k17_interva1 A C B))) ) ) ) ) ) ).
tt(t63_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) =>  ((r2_hidden (k3_intpro_1 A B) k8_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 C A) (k5_intpro_1 C B)) k8_intpro_1)) ) ) ) ) ) ) ).
tt(t63_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) A)))) =>  ( ( (A = (k8_struct_0 (k15_euclid 2)))  &  (B = a_0_3_jgraph_4) )  => (v4_pre_topc B (k1_pre_topc (k15_euclid 2) A))) ) ) ) ) ).
tt(t63_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ( ((r1_xxreal_0 k6_numbers (k18_euclid A)) | (r1_xxreal_0 k6_numbers (k17_euclid A)))  &  ( ((r1_xxreal_0 k6_numbers (k18_euclid B)) | (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( ((r1_xxreal_0 k6_numbers (k18_euclid C)) | (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ( (~  ((r1_xxreal_0 (k18_euclid D) k6_numbers) & (r1_xxreal_0 (k17_euclid D) k6_numbers)) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid J)))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jgraph_6,ax, (! [A:$i] :  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (~  ((r2_hidden A (k1_sppol_2 B C D E)) &  ( (~ (r1_xxreal_0 C B))  &  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid B D) (k19_euclid B E))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid B E) (k19_euclid C E))))  &  ( (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid C E) (k19_euclid C D))))  &  (~ (r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid C D) (k19_euclid B D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) B) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) D)) ) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H))) & (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k9_real_1 (k9_pscomp_1 B) (k13_complex1 (k9_real_1 (k7_pscomp_1 B) (k9_pscomp_1 B)) (k13_newton 2 A)))) ) ) ) ) ).
tt(t63_jordan1h,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) &  ( (~ (v1_sppol_1 A))  &  ( (~ (v2_sppol_1 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k15_euclid 2))) =>  ((r1_goboard1 (u1_struct_0 (k15_euclid 2)) C (k1_jordan8 A B)) =>  ((r1_xxreal_0 (k3_finseq_1 C) 1) |  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( ((r2_hidden (k4_tarski D (k2_nat_1 E 1)) (k2_matrix_1 (k1_jordan8 A B))) &  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k7_nat_d (k3_finseq_1 C) 1)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D (k2_nat_1 E 1)))  &  ((r2_hidden (k4_tarski D E) (k2_matrix_1 (k1_jordan8 A B))) &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) C (k3_finseq_1 C)) = (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 A B) D E)) ) ) )  =>  ((r1_xboole_0 (k4_gobrd13 C (k1_jordan8 A B) (k7_nat_d (k3_finseq_1 C) 1)) A) | (r2_hidden (k4_tarski (k7_nat_d D 1) E) (k2_matrix_1 (k1_jordan8 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k9_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  ( ( (B = E)  &  ((v2_connsp_1 B (k15_euclid A)) &  ( (C = (k1_connsp_3 (k1_pre_topc (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) D)) (k4_connsp_3 (k15_euclid A) B (k3_subset_1 (u1_struct_0 (k15_euclid A)) D))))  & (r1_xboole_0 E D)) ) )  =>  ((v6_tbsp_1 E (k14_euclid A)) | (r2_jordan2c A D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (~ (r1_xboole_0 (k8_jordan6 A) (k6_jordan6 (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)))) ) ) ).
tt(t63_jordan,ax, ((v1_funct_1 k8_jordan) &  ((v1_funct_2 k8_jordan (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr)) &  ((v5_pre_topc k8_jordan (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2)) k3_topmetr) & (m1_subset_1 k8_jordan (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k2_borsuk_1 (k15_euclid 2) (k15_euclid 2))) (u1_struct_0 k3_topmetr))))) ) ) ).
tt(t63_kurato_1,ax,(r1_xboole_0 (k2_tarski k6_kurato_1 (k3_subset_1 (u1_struct_0 k3_topmetr) k6_kurato_1)) (k4_kurato_1 k3_topmetr k6_kurato_1))).
tt(t63_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v11_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) ) )  => (r6_binop_1 (u1_struct_0 A) (u1_lattices A) (u2_lattices A))) ) ).
tt(t63_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k2_zfmisc_1 (k3_rfunct_3 (k6_glib_000 A) k5_numbers) (k9_funct_2 (k6_glib_000 A) k5_numbers))) =>  (! [C:$i] :  ( ((k1_relset_1 (k6_glib_000 A) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) B)) = (k6_glib_000 A))  =>  ((k1_relset_1 (k6_glib_000 A) (k8_lexbfs (k3_rfunct_3 (k6_glib_000 A) k5_numbers) k5_numbers (k6_glib_000 A) (k20_lexbfs A B C))) = (k6_glib_000 A)) ) ) ) ) ) ) ).
tt(t63_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v5_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B)))) ) ) ) )  | (v4_limfunc1 A)) ) ) ) ).
tt(t63_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  ( ((k1_limfunc2 B A) = (k1_limfunc2 C A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A E))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 A F))  & (r2_hidden F (k1_relset_1 k1_numbers D))) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 (k9_real_1 A E) A))) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) )  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A E) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A E) A))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 (k9_real_1 A E) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A E) A))))  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A E) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A E) A))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 (k9_real_1 A E) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A E) A)))) ) ) ) ) ) )  |  ((r1_limfunc2 D A) &  ((k1_limfunc2 D A) = (k1_limfunc2 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r4_limfunc2 C (k1_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A D))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E D))  &  ( (~ (r1_xxreal_0 A E))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) & (r1_xxreal_0 (k1_seq_1 B E) (k1_limfunc2 B A))) ) ) ) ) ) ) )  |  ((r1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k1_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k2_limfunc2 C (k1_limfunc2 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t63_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (u1_struct_0 (k12_lpspace2 A B C D))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 (k12_lpspace2 A B C D)))))) )  =>  (? [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F k5_numbers (k4_partfun1 A k1_numbers)) &  ((v1_mesfunc8 F A k1_numbers) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r2_hidden (k4_mesfunc5 A k1_numbers F G) (k1_lpspace2 A B C D)) &  ((r2_hidden (k4_mesfunc5 A k1_numbers F G) (k1_normsp_1 (k12_lpspace2 A B C D) E G)) &  ( ((k1_normsp_1 (k12_lpspace2 A B C D) E G) = (k5_lpspace2 A B C (k4_mesfunc5 A k1_numbers F G) D))  &  (? [H:$i] :  ((m1_subset_1 H k1_numbers) &  ((r1_xxreal_0 k6_numbers H) &  ( (H = (k1_mesfunc6 A B C (k2_mesfun6c D A (k56_valued_1 A k1_numbers (k4_mesfunc5 A k1_numbers F G)))))  &  ((k1_normsp_0 (k12_lpspace2 A B C D) (k1_normsp_1 (k12_lpspace2 A B C D) E G)) = (k4_power H (k10_real_1 1 D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A E (k8_cqc_lang A B (k8_cqc_lang A C D))) => (r3_cqc_the1 A E (k8_cqc_lang A C (k8_cqc_lang A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ((k6_mathmorp A (k15_euclid B) (k6_rusub_4 (k15_euclid B) C D)) = (k6_rusub_4 (k15_euclid B) (k6_mathmorp A (k15_euclid B) C) (k6_mathmorp A (k15_euclid B) D))) ) ) ) ) ) ) ) ) ).
tt(t63_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 B C) => (r2_matrix10 (k2_matrix10 A C) (k2_matrix10 A B))) ) ) ) ) ) ) ).
tt(t63_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  ((r1_tarski (k2_zfmisc_1 D E) (k2_matrix_1 C)) =>  ((k2_matrix13 (k5_card_1 D) (k5_card_1 E) A (k6_matrix13 (u1_struct_0 A) C D E) B) = (k6_matrix13 (u1_struct_0 A) (k6_matrix_3 A C B) D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k8_matrix13 A B) = k1_xboole_0)  =>  ( ( ((k1_matrix_1 B) = k1_xboole_0)  &  (~  ((k3_finseq_1 B) = k1_xboole_0) ) )  |  ((k7_matrix15 A B) = (k6_prvect_1 A (k1_matrix_1 B))) ) ) ) ) ) ) ).
tt(t63_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((v6_matrix16 C A) =>  ((k3_matrix16 A (k9_fvsum_1 A C B)) = (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k3_matrix16 A C) B)) ) ) ) ) ) ) ) ).
tt(t63_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 A))))  =>  (! [D:$i] :  ( ((v1_matrix_1 D) & (m2_finseq_1 D (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k1_matrix_1 C) = (k1_matrix_1 D))  &  ((k3_finseq_1 B) = (k1_matrix_1 C)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 C) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((k4_matrix_3 A (k3_matrix_3 A C D) B) = (k3_matrix_3 A (k4_matrix_3 A C B) (k4_matrix_3 A D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k24_matrixj1 A (k4_matrixj1 (u1_struct_0 A) B) C) = (k4_matrixj1 (u1_struct_0 A) (k6_matrix_3 A B (k7_partfun1 (u1_struct_0 A) C 1)))) ) ) ) ) ) ) ).
tt(t63_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k1_matrix_1 B) = (k3_finseq_1 A)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 B) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k11_matrixr1 (k3_matrixr1 B C) A) = (k4_rvsum_1 (k11_matrixr1 B A) (k11_matrixr1 C A))) ) ) ) ) ) ) ) ) ) ).
tt(t63_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ( (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ((r2_hidden (k4_tarski B B) (k2_matrix_1 (k4_matrixr2 A))) =>  ((k3_matrix_1 k1_numbers (k4_matrixr2 A) B B) = 1) ) ) )  &  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ((r2_hidden (k4_tarski B C) (k2_matrix_1 (k4_matrixr2 A))) =>  ( (B = C)  |  ((k3_matrix_1 k1_numbers (k4_matrixr2 A) B C) = k6_numbers) ) ) ) ) ) ) ) ) ) ).
tt(t63_matrprob,ax, (! [A:$i] :  ( ( (~ (v3_relat_1 A))  &  ((v1_matrix_1 A) &  ((v6_matrprob A) & (m2_finseq_1 A (k3_finseq_2 k1_numbers))) ) )  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k1_matrix_1 A) = (k3_finseq_1 B))  =>  ( ( (~ (v3_relat_1 (k6_matrixr1 A B)))  &  ((v1_matrix_1 (k6_matrixr1 A B)) &  ((v6_matrprob (k6_matrixr1 A B)) & (m2_finseq_1 (k6_matrixr1 A B) (k3_finseq_2 k1_numbers))) ) )  &  ( ((k3_finseq_1 (k6_matrixr1 A B)) = (k3_finseq_1 A))  &  ((k1_matrix_1 (k6_matrixr1 A B)) = (k1_matrix_1 B)) ) ) ) ) ) ) ) ).
tt(t63_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (k2_zfmisc_1 B C)) =>  ( (~  (A = (k1_xtuple_0 A)) )  &  (~  (A = (k2_xtuple_0 A)) ) ) ) ) ) ) ).
tt(t63_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B (k6_measure6 A)) <=>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  (~  ((r2_hidden B C) & (v1_xboole_0 (k9_subset_1 k1_numbers C A))) ) ) ) ) ) ) ) ) ).
tt(t63_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k10_member_1 (k2_tarski A B) (k1_tarski C)) = (k2_tarski (k3_xxreal_3 A C) (k3_xxreal_3 B C))) ) ) ) ) ) ) ).
tt(t63_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_memstr_0 A B (k10_memstr_0 A B C D)) = (k6_memstr_0 A B C)) ) ) ) ) ) ) ) ) ).
tt(t63_mesfunc5,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k7_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k7_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k7_numbers)))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 k6_numbers C) &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 (k8_nat_1 k7_numbers A D) (k8_nat_1 k7_numbers A E))) ) ) ) )  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((k8_nat_1 k7_numbers B D) = (k1_extreal1 (k1_measure6 C) (k8_nat_1 k7_numbers A D))) ) )  & (v3_mesfunc5 A)) ) )  =>  ( (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_xxreal_0 D E) => (r1_xxreal_0 (k8_nat_1 k7_numbers B D) (k8_nat_1 k7_numbers B E))) ) ) ) )  &  ((v3_mesfunc5 B) &  ((v10_mesfunc5 B) &  ( ((k2_mesfunc5 B) = (k8_supinf_2 (k17_supinf_2 B)))  &  ((k2_mesfunc5 B) = (k1_extreal1 (k1_measure6 C) (k2_mesfunc5 A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  => (r2_relset_1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k18_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k19_rfunct_3 A B)) (k19_rfunct_3 A C)) (k3_valued_1 A k1_numbers k1_numbers (k3_valued_1 A k1_numbers k1_numbers (k19_rfunct_3 A (k3_valued_1 A k1_numbers k1_numbers B C)) (k18_rfunct_3 A B)) (k18_rfunct_3 A C)))) ) ) ) ) ) ).
tt(t63_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m2_finseq_1 B (k9_setfam_1 A)) =>  ((k26_mmlquery A B 1) = (k5_prob_3 A B)) ) ) ) ).
tt(t63_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  ((v2_modelc_2 A) =>  ((r7_modelc_2 B A) <=> (r2_hidden A (k8_nat_1 k43_modelc_2 (k27_modelc_2 k43_modelc_2 B) k6_numbers))) ) ) ) ) ) ).
tt(t63_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  ( ((v5_modelc_3 A) & (r2_modelc_2 B A))  => (v5_modelc_3 B)) ) ) ) ) ).
tt(t63_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (r1_tarski (a_2_4_moebius1 A B) (k2_finseq_1 A))) ) ) ) ).
tt(t63_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B (k9_monoid_0 A)))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k6_algstr_0 B C D) = (k7_finseq_1 C D)) ) ) ) ) ) ) ) ) ).
tt(t63_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( ((r1_xxreal_0 k6_numbers B) =>  ((r1_xxreal_0 A B) |  ((k6_int_1 B A) = B) ) )  &  ((r1_xxreal_0 (k4_xcmplx_0 A) B) =>  ((r1_xxreal_0 k6_numbers B) |  ((k6_int_1 B A) = (k2_xcmplx_0 A B)) ) ) ) ) ) ) ) ).
tt(t63_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r8_ncfcont1 A B D C) & (r8_ncfcont1 A B E C))  =>  ((r8_ncfcont1 A B (k6_vfunct_1 (u1_struct_0 A) B D E) C) & (r8_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k4_nat_d B A) = (k5_real_1 B (k3_nat_1 A (k3_nat_d B A)))) ) ) ) ) ) ).
tt(t63_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) => (m2_cat_1 (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k2_oppcat_1 A) (k2_oppcat_1 B))) ) ) ) ) ) ).
tt(t63_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (~  ((r2_orders_1 A B) &  ( ((k1_relat_1 A) = B)  &  ((r4_orders_1 A B) &  (! [C:$i] :  (~ (r6_orders_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t63_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((k5_ordinal3 (k11_ordinal2 A B) (k11_ordinal2 C B)) = (k11_ordinal2 (k5_ordinal3 A C) B)) ) ) ) ) ) ) ).
tt(t63_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ( ((r2_hidden 1 A) & (r2_hidden (k5_ordinal5 B A) (k5_ordinal5 C A)))  => (r2_hidden B C)) ) ) ) ) ) ) ).
tt(t63_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden k4_ordinal1 B) &  ((r1_tarski B C) & (r2_hidden A B)) )  => (r1_tarski (k1_funct_1 (k11_ordinal6 B) A) (k1_funct_1 (k11_ordinal6 C) A))) ) ) ) ) ) ) ).
tt(t63_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v1_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t63_partfun1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_partfun1 (k6_relat_1 A B) B)) ) ) ).
tt(t63_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k3_pboole A (k4_pboole A B C) C) (k1_pboole A))) ) ) ) ) ).
tt(t63_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r6_pdiff_5 C B) =>  ((r3_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) &  ((k11_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 2 3 C) A) B) = (k8_real_1 A (k6_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t63_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_euclid A))) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 B A) & (r1_tarski B (k1_relset_1 (k1_euclid A) C)))  =>  ( (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( ((r1_xxreal_0 1 D) & (r1_xxreal_0 D A))  =>  ((r3_pdiff_9 A B D C) & (r1_pdiff_9 A B (k3_pdiff_9 A B D C))) ) ) )  <=>  ((r2_pdiff_9 B A C) &  (! [D:$i] :  ((m2_finseq_2 D k1_numbers (k1_euclid A)) =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden D B) &  ( (~ (r1_xxreal_0 E k6_numbers))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 F k6_numbers))  &  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid A)) =>  ((r2_hidden G B) =>  ((r1_xxreal_0 F (k12_euclid (k8_euclid A G D))) |  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid A)) => (r1_xxreal_0 (k17_complex1 (k10_binop_2 (k1_seq_1 (k1_pdiff_7 A C G) H) (k1_seq_1 (k1_pdiff_7 A C D) H))) (k11_binop_2 E (k12_euclid H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( ((k4_nat_d A B) = k6_numbers)  =>  ((r1_xxreal_0 B k6_numbers) |  ((k3_nat_d A B) = (k7_xcmplx_0 A B)) ) ) ) ) ) ) ).
tt(t63_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  ((k11_pnproc_1 A B (k11_pnproc_1 A B C D) E) = (k11_pnproc_1 A B C (k11_pnproc_1 A B D E))) ) ) ) ) ) ) ) ) ) ).
tt(t63_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k1_card_1 (k2_struct_0 (k17_polyform A (k7_polyform A)))) = 2) ) ) ).
tt(t63_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) => (r2_cfcont_1 (k8_funcop_1 k2_numbers k2_numbers A) k2_numbers)) ) ).
tt(t63_power,ax, ((k4_power 2 5) = 32) ).
tt(t63_pre_poly,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k5_numbers) &  ((v2_pre_poly B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k5_numbers)))) ) )  =>  ((k1_card_1 (k18_pre_poly A B)) = (k7_setwiseo A k5_numbers k48_binop_2 (k19_pre_poly A B) (k9_funcop_1 k5_numbers A k47_binop_2 B 1))) ) ) ) ) ).
tt(t63_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 C B))  => (r1_xxreal_0 (k6_prepower A C) (k6_prepower A B))) ) ) ) ) ) ) ).
tt(t63_prob_3,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (~  ((r1_xxreal_0 1 (k3_finseq_1 A)) &  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ( ((k3_funct_2 k5_numbers k1_numbers B 1) = (k1_funct_1 A 1))  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~  (k6_numbers = C) )  &  ( (~ (r1_xxreal_0 (k3_finseq_1 A) C))  &  (~  ((k3_funct_2 k5_numbers k1_numbers B (k1_nat_1 C 1)) = (k9_binop_2 (k1_funct_1 B C) (k1_funct_1 A (k1_nat_1 C 1)))) ) ) ) ) ) )  &  ((k18_rvsum_1 A) = (k3_funct_2 k5_numbers k1_numbers B (k3_finseq_1 A))) ) ) ) ) ) ) ) ) ) ).
tt(t63_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k23_pscomp_1 A) = (k24_pscomp_1 A))  =>  ((k23_pscomp_1 A) = (k13_pscomp_1 A)) ) ) ) ).
tt(t63_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k6_pboole A (k2_pboole A B C) D) (k2_pboole A (k6_pboole A B D) (k6_pboole A C D))) & (r6_pboole A (k6_pboole A D (k2_pboole A B C)) (k2_pboole A (k6_pboole A D B) (k6_pboole A D C)))) ) ) ) ) ) ) ) ).
tt(t63_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  ( (~  ( (~  ((r3_qc_lang2 A B C) & (r2_qc_lang2 A C D)) )  &  ( (~  ((r2_qc_lang2 A B C) & (r3_qc_lang2 A C D)) )  &  ( (~  ((r2_qc_lang2 A B C) & (r1_qc_lang2 A C D)) )  &  ( (~  ((r1_qc_lang2 A B C) & (r2_qc_lang2 A C D)) )  &  ( (~  ((r3_qc_lang2 A B C) & (r1_qc_lang2 A C D)) )  &  (~  ((r1_qc_lang2 A B C) & (r3_qc_lang2 A C D)) ) ) ) ) ) ) )  => (r3_qc_lang2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t63_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k6_qc_lang3 A (k12_qc_lang1 A)) = k1_xboole_0) ) ) ).
tt(t63_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ( ((k29_quaterni A B) = (k29_quaterni C B))  =>  (A = C) ) ) ) ) ) ) ) ).
tt(t63_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  ((k29_quaterni A B) = (k6_quaterni (k9_real_1 (k17_quaterni A) (k17_quaterni B)) (k9_real_1 (k18_quaterni A) (k18_quaterni B)) (k9_real_1 (k19_quaterni A) (k19_quaterni B)) (k9_real_1 (k20_quaterni A) (k20_quaterni B)))) ) ) ) ) ).
tt(t63_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [E:$i] :  ((m1_rcomp_3 E A B D) =>  (! [F:$i] :  ((m2_rcomp_3 F A B D E) =>  (~  ((m1_setfam_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 D (k4_topmetr A B)) &  ((v1_rcomp_3 D (k4_topmetr A B)) &  ((r1_xxreal_0 A B) &  ( (~ (r1_xxreal_0 C 1))  &  ((r1_xxreal_0 C (k3_finseq_1 E)) & (r1_xxreal_0 (k1_funct_1 F C) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) E C)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 2)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 2))) = (k10_real_1 (k7_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 2)) (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 1))) (k1_seq_1 (k5_real_3 B) A)) (k7_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 2)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1))) (k1_seq_1 (k6_real_3 B) A)))) ) ) ) ) ).
tt(t63_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k3_relat_1 (k5_relat_1 B A) C) (k3_relat_1 B C))) ) ) ) ) ).
tt(t63_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ( ((k6_relset_2 A B C E) = (k6_relset_2 A B (k6_relset_2 B A (k6_relset_2 A B C E) (k3_relset_1 A B E)) E))  &  ((k6_relset_2 B A D (k3_relset_1 A B E)) = (k6_relset_2 B A (k6_relset_2 A B (k6_relset_2 B A D (k3_relset_1 A B E)) E) (k3_relset_1 A B E))) ) ) ) ) ) ) ) ) ) ).
tt(t63_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m2_rewrite1 B A) => (r12_rewrite1 A B)) ) ) ) ).
tt(t63_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D C) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [F:$i] :  ( ( (~ (v2_struct_0 F))  & (l1_rewrite3 F E))  =>  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 E F)))))  =>  (! [G:$i] :  ((m1_rewrite1 G (k1_rewrite3 C E F)) =>  ( ( ((k1_funct_1 G 1) = (k4_tarski A (k3_flang_1 C D)))  &  ((k1_funct_1 G (k3_finseq_1 G)) = (k4_tarski B (k2_flang_1 C))) )  =>  ((k3_finseq_1 G) = 2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((r2_hidden C A) <=>  ((k1_funct_1 (k7_rfunct_1 A B) C) = 1) ) ) ) ) ) ) ).
tt(t63_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_finset_1 (k1_relset_1 A (k2_partfun1 A k1_numbers B C))) =>  ((k20_rfunct_3 A B (k1_relset_1 A (k2_partfun1 A k1_numbers B C))) = (k20_rfunct_3 A B C)) ) ) ) ) ) ) ).
tt(t63_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 B) => (r1_xxreal_0 (k1_seq_1 B A) (k1_seq_1 (k3_rinfsup1 B) (k2_nat_1 A 1)))) ) ) ) ) ).
tt(t63_rlaffin1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ((v2_convex1 C B) => (r1_xxreal_0 (k1_seq_1 C A) 1)) ) ) ) ) ) ).
tt(t63_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden B (k3_rlsub_1 A C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 D E) &  (B = (k3_rlvect_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlsub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m2_rlsub_1 D A B) & (r2_hidden C D)) ) ) ) ) ) ) ) ).
tt(t63_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_rltopsp1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  ((r2_hidden (k4_struct_0 A) (k1_tops_1 A B)) => (v3_rltopsp1 (k1_tops_1 A B) A)) ) ) ) ) ).
tt(t63_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k1_algstr_0 A (k1_algstr_0 A (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) B)) (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) C))) (k4_rlvect_1 A (k12_finseq_1 (u1_struct_0 A) D)))) ) ) ) ) ) ) ) ) ).
tt(t63_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k1_rlvect_1 (k16_rlvect_2 A) (k1_rlvect_2 (k16_rlvect_2 A) C) B) = (k8_rlvect_2 A B C)) ) ) ) ) ) ) ).
tt(t63_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  ( ((k3_rmod_2 A B C D) = (k3_rmod_2 A B C E))  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  (~  ( (~  ((k4_struct_0 A) = (k1_group_1 A)) )  &  ((v1_rmod_4 C A B) & (r2_hidden (k4_struct_0 B) C)) ) ) ) ) ) ) ) ) ).
tt(t63_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((k3_rusub_1 A E B) = (k3_rusub_1 A D C))  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_rusub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((r2_hidden D (k3_rusub_1 A C B)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 B E) &  (D = (k3_rlvect_1 A C E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k14_rvsum_1 (k2_finseq_2 A B) C) = (k11_rvsum_1 A C B)) ) ) ) ) ) ) ).
tt(t63_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 A B) C) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 C)))  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 A B) C) A) = (k1_funct_1 C B))  &  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 A B) C) D) = (k1_funct_1 C D)) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k6_scmfsa_2 A B) C) D) (k18_scmfsa_2 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa6b C)) ) ) ) ) ) )  =>  ((r6_scmfsa7b C (k1_scmfsa_m B) A) =>  ( ((k1_funct_1 (k1_scmfsa6b C B A) (k4_scmfsa_2 k6_numbers)) = 1)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_scm_halt,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_afinsq_1 A) &  ((v1_scmfsa7b A) & (v2_scm_halt A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_ami_2 B) &  ( (~ (v1_scmfsa_m B))  & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~ (r4_scmfsa7b A B))  => (v5_extpro_1 (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_3 (k4_scmfsa_2 k6_numbers) 1)) 3 k1_scmfsa_2 (k2_scmfsa8c B A))) ) ) ) ) ).
tt(t63_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  ( (A = (k3_xtuple_0 k6_numbers k1_xboole_0 k1_xboole_0))  => (v2_extpro_1 A 2 k1_scmpds_2)) ) ) ).
tt(t63_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v2_compos_1 C k1_scmpds_2) &  ((v2_scmpds_4 C) & (v3_scmpds_4 C)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( (~  ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers) )  =>  ((k1_funct_1 (k6_scmpds_4 (k6_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 (k6_scmpds_4 C (k8_memstr_0 2 k1_scmpds_2 B) A) E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_scmyciel,ax, (! [A:$i] :  ( ((v4_scmyciel A) & (v6_scmyciel A))  =>  ( ((k8_scmyciel A) = 1)  =>  ((v9_scmyciel (k3_tarski A) A) & (m1_subset_1 (k3_tarski A) (k1_zfmisc_1 (k3_tarski A)))) ) ) ) ).
tt(t63_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) & (r3_semi_af1 A B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t63_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_prob_1 B) =>  ((v3_kurato_0 B A) &  ((k4_kurato_0 A B) = (k1_kurato_0 A B)) ) ) ) ) ) ).
tt(t63_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_kurato_0 B A) | (v3_kurato_0 C A))  =>  ((k3_kurato_0 A (k2_setlim_2 A B C)) = (k4_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C))) ) ) ) ) ) ) ).
tt(t63_sf_mastr,ax, (! [A:$i] :  ((m1_scmfsa_2 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  ( ((r1_tarski B E) &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C F))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E D F)) (k1_relset_1 k5_numbers B))) ) ) )  =>  ((r2_hidden A (k4_sf_mastr B)) | (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E D C) A) (k18_scmfsa_2 D A))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C C)) (k5_sheffer1 A B (k5_sheffer1 A D (k5_sheffer1 A (k5_sheffer1 A C C) B)))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D C)) (k5_sheffer1 A B (k5_sheffer1 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t63_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_simplex0 B A) =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((k11_simplex0 A B C (k2_nat_1 D E)) = (k11_simplex0 A (k11_simplex0 A B C E) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t63_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) k3_sincos10) = (k1_partfun2 k1_numbers (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) ).
tt(t63_sin_cos6,ax, ((k1_relset_1 k1_numbers k1_sin_cos6) = (k1_rcomp_1 (k1_real_1 1) 1)) ).
tt(t63_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k11_binop_2 (k18_binop_2 1 2) (k10_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B)))))  =>  (B = (k6_power k8_power (k9_binop_2 A (k7_square_1 (k9_binop_2 (k3_square_1 A) 1))))) ) ) ) ) ) ).
tt(t63_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((r1_xxreal_0 (k1_real_1 (k10_real_1 k32_sin_cos 4)) (k5_sin_cos9 A)) & (r1_xxreal_0 (k5_sin_cos9 A) (k10_real_1 k32_sin_cos 4))) ) ) ) ).
tt(t63_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k19_sin_cos A) &  ((k1_fdiff_1 k19_sin_cos A) = (k1_real_1 (k1_seq_1 k16_sin_cos A))) ) ) ) ).
tt(t63_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k12_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k12_pscomp_1 A)) ) ) ).
tt(t63_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k22_pscomp_1 (k3_topreal1 2 A)) = (k12_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t63_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k21_pscomp_1 (k3_topreal1 2 A)) = (k22_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t63_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ((v1_finset_1 (k2_relset_1 B C)) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_relset_1 B C) (k2_relset_1 B C)) &  ((v3_funct_2 E (k2_relset_1 B C) (k2_relset_1 B C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_relset_1 B C) (k2_relset_1 B C))))) ) )  =>  (~  ( (C = (k1_partfun1 A B (k2_relset_1 B C) (k2_relset_1 B C) D E))  &  ( ((k2_relset_1 B C) = (k2_relset_1 B D))  & (v2_stirl2_1 D A B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m2_funct_2 D (k3_qc_lang1 A) C (k2_valuat_1 A C)) =>  (! [E:$i] :  ((m1_subset_1 E C) =>  (! [F:$i] :  ((r1_tarski F (k3_qc_lang1 A)) =>  ( ((k1_relset_1 F (k5_relset_1 (k3_qc_lang1 A) C D F)) = (k1_relset_1 F (k5_relset_1 (k3_qc_lang1 A) C (k1_sublemma A C D (k12_sublemma A C B E)) F)))  &  ((k1_relset_1 F (k5_relset_1 (k3_qc_lang1 A) C D F)) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v5_tops_1 B A) & (r1_tarski B C))  =>  ((k2_pre_topc A (k1_tops_1 A (k9_subset_1 (u1_struct_0 A) B C))) = B) ) ) ) ) ) ) ) ).
tt(t63_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v5_pre_topc C A B)) ) ) )  => (v1_tdlat_3 A)) ) ) ).
tt(t63_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_subset_1 B (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (~  ((v1_tops_3 B A) &  (! [C:$i] :  ( ((v1_pre_topc C) &  ((v1_tex_2 C A) &  ((v2_tex_3 C A) & (m1_pre_topc C A)) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t63_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((k3_tex_4 A B) = (k3_tex_4 A C))  =>  ((k2_pre_topc A B) = (k2_pre_topc A C)) ) ) ) ) ) ) ) ).
tt(t63_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v5_pre_topc E B C) & (v5_pre_topc (k2_tmap_1 A B F D) D B))  => (v5_pre_topc (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F E) D) D C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k5_topalg_1 A B))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k5_topalg_1 A B))) =>  (! [E:$i] :  ((m1_borsuk_2 E A B B) =>  ( ( (C = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) E))  &  (D = (k6_eqrel_1 (k2_topalg_1 A B) (k2_topalg_1 A B) (k4_topalg_1 A B) (k2_borsuk_2 A B B E))) )  =>  ((k2_group_1 (k5_topalg_1 A B) C) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  (? [C:$i] :  ( ((v1_prob_1 C (u1_struct_0 A)) &  ((v1_topgen_4 C A) &  ((v3_topgen_4 C (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  &  ((r1_tarski B C) &  (! [D:$i] :  ( ((v1_prob_1 D (u1_struct_0 A)) &  ((v1_topgen_4 D A) &  ((v3_topgen_4 D (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A))))) ) )  =>  ((r1_tarski B D) => (r1_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(t63_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~  ((r1_xxreal_0 C 1) &  ( (~ (r1_xxreal_0 (k3_xcmplx_0 D C) (k12_euclid (k5_algstr_0 (k15_euclid 2) A (k19_euclid B (k3_xcmplx_0 D C))))))  & (r1_xxreal_0 C (k1_funct_1 (k4_topgen_5 B D) A))) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v9_rltopsp1 B (k15_euclid A)) => (v9_rltopsp1 (k2_pre_topc (k15_euclid A) B) (k15_euclid A))) ) ) ) ) ).
tt(t63_topreal9,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid 2))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid 2))) =>  (! [G:$i] :  ((m2_finseq_2 G k1_numbers (k1_euclid 2)) =>  (! [H:$i] :  ((m2_finseq_2 H k1_numbers (k1_euclid 2)) =>  (! [I:$i] :  ((m2_finseq_2 I k1_numbers (k1_euclid 2)) =>  (~  ( (G = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2))))  &  ( (H = F)  &  ( (I = (k19_euclid A B))  &  ( (~  (E = F) )  &  ((r2_hidden E (k5_jgraph_6 A B C)) &  ((r2_hidden F (k7_jgraph_6 A B C)) &  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ( (~  (J = E) )  &  ( ((k2_tarski E J) = (k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k4_topreal9 2 E F) (k5_jgraph_6 A B C)))  &  ( ((r2_hidden F (k3_topreal9 2 (k19_euclid A B) C)) =>  (J = F) )  &  ( (D = (k10_real_1 (k7_real_1 (k1_real_1 (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) F (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2)))) (k5_algstr_0 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2))) (k19_euclid A B))))) (k7_square_1 (k2_quin_1 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 H G))) (k8_real_1 2 (k23_rvsum_1 (k5_algstr_0 (k15_euclid 2) F (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2)))) (k5_algstr_0 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2))) (k19_euclid A B)))) (k9_real_1 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 G I))) (k3_square_1 C))))) (k8_real_1 2 (k18_rvsum_1 (k11_euclid 2 (k8_euclid 2 H G))))))  =>  ((r2_hidden F (k3_topreal9 2 (k19_euclid A B) C)) |  (J = (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) E (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) F (k10_real_1 1 2))) (k9_real_1 1 D)) (k1_rlvect_1 (k15_euclid 2) F D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v5_tops_1 B A) => (r1_tarski (k2_tops_1 A B) (k2_pre_topc A (k1_tops_1 A B)))) ) ) ) ) ).
tt(t63_tops_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_pre_topc D) & (l1_pre_topc D)) )  &  ((v1_connsp_1 D) &  (? [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 A))))) )  &  ((v5_pre_topc E D A) &  ((r2_hidden B (k2_relset_1 (u1_struct_0 A) E)) & (r2_hidden C (k2_relset_1 (u1_struct_0 A) E))) ) ) ) ) ) ) ) ) ) )  => (v1_connsp_1 A)) ) ) ).
tt(t63_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( (D = (u1_struct_0 B))  &  (C = E) )  =>  ( ((v1_tops_1 D A) & (v1_tops_3 E B))  <=> (v1_tops_3 C A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v2_analoaf A) & (l1_analoaf A)) )  =>  ( (~ (v2_struct_0 (k2_diraf A)))  &  ((v1_transgeo (k2_diraf A)) & (l1_analoaf (k2_diraf A))) ) ) ) ).
tt(t63_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((r1_tarski A B) => (r1_tarski (k12_trees_3 A) (k12_trees_3 B))) ) ) ) ) ).
tt(t63_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ((r3_tsep_1 A B C) => (r1_tsep_1 B C)) ) ) ) ) ) ) ).
tt(t63_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v5_vectsp_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k14_polynom3 A)))) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 C) = (k5_card_1 (k13_pre_poly B)))  &  ( (D = (k1_uproots (k13_pre_poly B)))  &  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r2_hidden F (k4_finseq_1 C)) =>  ((k1_funct_1 C F) = (k9_uproots A (k7_partfun1 (u1_struct_0 A) D F) (k1_recdef_1 B (k7_partfun1 (u1_struct_0 A) D F)))) ) ) ) ) )  =>  ( ((r2_hidden E (k13_pre_poly B)) =>  ((k5_card_1 (k8_relset_1 k5_numbers (u1_struct_0 (k14_polynom3 A)) (k5_pre_poly (u1_struct_0 (k14_polynom3 A)) C) (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k4_polynom5 A (k4_algstr_0 A E) (k5_struct_0 A))))) = (k1_recdef_1 B E)) )  &  ( (~ (r2_hidden E (k13_pre_poly B)))  =>  ((k5_card_1 (k8_relset_1 k5_numbers (u1_struct_0 (k14_polynom3 A)) (k5_pre_poly (u1_struct_0 (k14_polynom3 A)) C) (k6_domain_1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))) (k4_polynom5 A (k4_algstr_0 A E) (k5_struct_0 A))))) = k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  ((k58_valued_2 A B C (k30_valued_1 D)) = (k52_valued_2 A B C D)) ) ) ) ) ) ) ) ).
tt(t63_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  ( (? [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) &  ((r2_hidden C (k3_vectsp_4 A B F E)) & (r2_hidden D (k3_vectsp_4 A B F E))) ) )  <=> (r1_struct_0 E (k5_algstr_0 B C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ( (~ (v1_xboole_0 B))  &  ((v2_waybel_0 B A) &  ((v13_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=> (v5_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(t63_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_waybel_1 (k4_waybel_1 A B) A A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_3_waybel_1 A B C))) ) ) ) ) ) ) ) ) ).
tt(t63_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (v3_waybel_1 (k1_waybel_1 (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A (k3_waybel23 A (k5_yellow_0 A B)) (k5_waybel23 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A)) ) ) ) ).
tt(t63_waybel34,ax, (! [A:$i] :  ((l1_orders_2 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [D:$i] :  ((m1_yellow_0 D A) =>  (! [E:$i] :  ((m1_yellow_0 E B) =>  ((r1_tarski (k7_relset_1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D)) (u1_struct_0 E)) =>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D)) (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D)) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) & (r1_xboole_0 B C))  => (r1_xboole_0 A C)) ) ) ) ).
tt(t63_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k4_xboolean (k3_xboolean A) (k8_xboolean A B)) = (k5_xboolean (k3_xboolean A) (k4_xboolean (k3_xboolean A) (k3_xboolean B)))) ) ) ) ) ).
tt(t63_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A B) C) D) = (k2_xcmplx_0 (k2_xcmplx_0 (k7_xcmplx_0 A D) (k7_xcmplx_0 B D)) (k7_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ).
tt(t63_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) => (r1_xxreal_0 k6_numbers (k3_xcmplx_0 A A))) ) ).
tt(t63_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k4_xxreal_1 A B) (k4_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t63_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden C A) &  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r2_hidden D B) & (r1_xxreal_0 C D)) ) ) ) ) ) ) )  => (r1_xxreal_0 (k1_xxreal_2 A) (k1_xxreal_2 B))) ) ) ) ) ).
tt(t63_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ( (~  (C = k2_xxreal_0) )  &  ( (~  (C = k1_xxreal_0) )  &  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k3_xxreal_3 B C) (k3_xxreal_3 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t63_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r2_yellow_0 A C) & (r2_hidden (k2_yellow_0 A C) (u1_struct_0 B)))  =>  ((r2_yellow_0 B C) &  ((k2_yellow_0 B C) = (k2_yellow_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t63_yellow10,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) & (l1_orders_2 B)) )  =>  ((v25_waybel_0 (k3_yellow_3 A B)) =>  ((v25_waybel_0 A) & (v25_waybel_0 B)) ) ) ) ) ) ).
tt(t63_yellow_4,ax, (! [A:$i] :  ( ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k4_waybel_0 A (k4_yellow_4 A (k4_waybel_0 A B) (k4_waybel_0 A C))) (k4_waybel_0 A (k4_yellow_4 A B C)))) ) ) ) ) ) ).
tt(t63_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  ((k7_waybel_1 A (k4_yellow_0 A)) = (k3_yellow_0 A)) ) ) ).
tt(t63_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k2_zf_model (k10_zf_lang A B)) = (k4_subset_1 k1_zf_lang (k2_zf_model A) (k2_zf_model B))) ) ) ) ) ).
tt(t63_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (~  ((r3_zf_lang A B) &  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~ (r1_zf_lang C B)) ) ) ) ) ) ) ) ) ).
tt(t63_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_xboole_0 (k2_tarski A B) C) = (k2_tarski A B))  <=>  ( (~ (r2_hidden A C))  &  (~ (r2_hidden B C)) ) ) ) ) ) ).
tt(t63_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_zmodul01 C A) =>  ((r1_struct_0 C B) <=>  ((k5_zmodul01 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t64_abcmiz_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ( (~ (v4_abcmiz_0 A))  & (l3_abcmiz_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (~  ((r6_abcmiz_0 A B C) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (~  ((r1_tarski D C) &  ((r6_abcmiz_0 A B D) &  ( ((k6_abcmiz_0 A B C) = (k6_abcmiz_0 A B D))  &  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  ( ((r1_tarski E D) &  ((r6_abcmiz_0 A B E) &  ((k6_abcmiz_0 A B C) = (k6_abcmiz_0 A B E)) ) )  =>  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_abcmiz_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_instalg1 B) &  ((v1_abcmiz_1 B) &  ((v3_abcmiz_1 B) & (l1_msualg_1 B)) ) )  =>  ( ((v8_abcmiz_1 A B) & (m1_abcmiz_1 A B (k13_abcmiz_1 B)))  <=>  ( ((v6_abcmiz_1 A B) & (m1_abcmiz_1 A B (k13_abcmiz_1 B)))  |  ((v7_abcmiz_1 A B) & (m1_abcmiz_1 A B (k13_abcmiz_1 B))) ) ) ) ) ) ).
tt(t64_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_4 F A) &  ((v1_aff_4 G A) &  ((v1_aff_4 H A) &  ((r1_aff_4 A F G) &  ((r2_hidden B (k9_subset_1 (u1_struct_0 A) F H)) &  ((r2_hidden C (k9_subset_1 (u1_struct_0 A) F H)) &  ((r2_hidden D (k9_subset_1 (u1_struct_0 A) G H)) & (r2_hidden E (k9_subset_1 (u1_struct_0 A) G H))) ) ) ) ) ) )  =>  ( (F = G)  |  ( (B = C)  |  ( (D = E)  | (r5_aff_1 A (k9_subset_1 (u1_struct_0 A) F H) (k9_subset_1 (u1_struct_0 A) G H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_afinsq_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  ( ((k1_funct_1 B k6_numbers) = k6_numbers)  =>  ((r1_xxreal_0 (k1_afinsq_1 B) k6_numbers) |  ((k12_afinsq_1 A B) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t64_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k5_binop_2 B (k7_afinsq_2 A)) = (k7_afinsq_2 (k24_valued_1 A B))) ) ) ) ) ).
tt(t64_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r2_hidden D B) &  ((r2_hidden E B) &  ((v4_analmetr B A) &  ((r2_hidden F C) &  ((r2_hidden G C) &  ((v4_analmetr C A) & (r2_analoaf A D E F G)) ) ) ) ) )  =>  ( (D = E)  |  ( (F = G)  | (r9_analmetr A B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ((m1_subset_1 (k4_trees_4 3 B) (u1_struct_0 (k7_freealg k19_aofa_000 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  (B = (k3_finseq_4 (u1_struct_0 (k7_freealg k19_aofa_000 A)) C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  => (r6_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k16_aofa_000 A (k78_aofa_i00 A B C D F k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k32_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) (k15_aofa_000 A (k79_aofa_i00 A B C D G k6_numbers) (k58_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k4_xcmplx_0 1)))) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G))) D (a_6_2_aofa_i00 A B C D E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) => (r3_arytm_3 k11_arytm_3 A)) ) ).
tt(t64_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers C))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 (k4_power A C) (k4_power B C))) ) ) ) ) ) ) ) ).
tt(t64_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A D E)) = (k1_bcialg_1 A (k1_bcialg_1 A B D) (k1_bcialg_1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A B C) (k1_boolealg A (k3_lattices A B C) (k4_lattices A B C)))) ) ) ) ) ) ).
tt(t64_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k2_rcomp_1 B C)))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k4_rcomp_1 k2_xxreal_0 C)) ) ) ) ) ) ) ) ) ).
tt(t64_borsuk_6,ax,(r2_hidden (k4_tarski k6_numbers 1) k7_borsuk_6)).
tt(t64_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_xreal_0 B) &  (~ (v3_xxreal_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  ((m1_subset_1 C (u1_struct_0 (k7_toprealb A (k4_struct_0 (k15_euclid A)) B))) => (r1_borsuk_7 A (k4_struct_0 (k15_euclid A)) C (k4_algstr_0 (k15_euclid A) C) B)) ) ) ) ) ) ) ).
tt(t64_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t64_bvfunc14,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (! [H:$i] :  (! [I:$i] :  ( ((v1_relat_1 I) & (v1_funct_1 I))  =>  (! [J:$i] :  (! [K:$i] :  (! [L:$i] :  (! [M:$i] :  (! [N:$i] :  (! [O:$i] :  (! [P:$i] :  (! [Q:$i] :  ( (I = (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k1_funct_4 (k16_funcop_1 B K) (k16_funcop_1 C L)) (k16_funcop_1 D M)) (k16_funcop_1 E N)) (k16_funcop_1 F O)) (k16_funcop_1 G P)) (k16_funcop_1 H Q)) (k16_funcop_1 A J)))  =>  ((k10_xtuple_0 I) = (k6_enumset1 (k1_funct_1 I A) (k1_funct_1 I B) (k1_funct_1 I C) (k1_funct_1 I D) (k1_funct_1 I E) (k1_funct_1 I F) (k1_funct_1 I G) (k1_funct_1 I H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k7_xboolean A B) = (k7_xboolean (k3_xboolean A) (k3_xboolean B))) ) ) ) ) ).
tt(t64_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k6_bvfunc_1 A B (k6_bvfunc26 A C D)) (k2_bvfunc_1 A (k5_bvfunc_1 A B (k1_bvfunc_1 A (k5_bvfunc_1 A C D))) (k5_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) C) D)))) ) ) ) ) ) ) ) ).
tt(t64_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ( ((k1_card_1 (k3_qc_lang1 A)) = (k1_card_1 (k1_qc_lang1 A)))  &  (~ (v1_finset_1 (k3_qc_lang1 A))) ) ) ) ).
tt(t64_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  ((k1_card_1 (k7_funcop_1 B A)) = B) ) ) ) ).
tt(t64_card_2,ax, (! [A:$i] :  (! [B:$i] :  ( ( ((k1_card_1 A) = k6_numbers)  &  ((k1_card_1 B) = k6_numbers) )  =>  (A = B) ) ) ) ).
tt(t64_card_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_tarski A B) & (r2_hidden B (k8_card_3 C)))  => (r2_hidden A (k8_card_3 C))) ) ) ) ) ) ).
tt(t64_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_graph_1 A E) = (k4_graph_1 A D))  =>  ( ((k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D)))  &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A D E)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C D) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  ( ((k4_graph_1 B D) = C)  => (m2_cat_3 (k1_cat_3 (u4_struct_0 B) A D) B C (k1_tarski A))) ) ) ) ) ) ) ) ).
tt(t64_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  => (v4_cat_4 A)) ) ).
tt(t64_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_partfun1 C A) & (v1_partfun1 D A))  =>  ( ((k7_partfun1 k2_numbers (k2_valued_1 A k2_numbers k2_numbers C D) B) = (k8_complex1 (k7_partfun1 k2_numbers C B) (k7_partfun1 k2_numbers D B)))  &  ( ((k7_partfun1 k2_numbers (k46_valued_1 A k2_numbers k2_numbers C D) B) = (k11_complex1 (k7_partfun1 k2_numbers C B) (k7_partfun1 k2_numbers D B)))  &  ((k7_partfun1 k2_numbers (k19_valued_1 A k2_numbers k2_numbers C D) B) = (k9_complex1 (k7_partfun1 k2_numbers C B) (k7_partfun1 k2_numbers D B))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C (k2_nat_1 A 1)))) =>  ((m3_chain_1 D B C (k2_nat_1 A 1)) <=>  ((k10_chain_1 B C A D) = (k5_chain_1 B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t64_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_chord A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (v3_chord B A)) ) ) ) ).
tt(t64_circcomb,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v1_circcomb A) &  ((v2_circcomb A) &  ((v3_circcomb A) & (l1_msualg_1 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v1_circcomb B) &  ((v2_circcomb B) &  ((v3_circcomb B) & (l1_msualg_1 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v4_msafree2 C A) &  ((v4_circcomb C A) &  ((v6_circcomb C A) & (l3_msualg_1 C A)) ) )  =>  (! [D:$i] :  ( ((v4_msafree2 D B) &  ((v4_circcomb D B) &  ((v6_circcomb D B) & (l3_msualg_1 D B)) ) )  =>  (! [E:$i] :  ((m1_subset_1 E (k4_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k2_circcomb A B))) =>  ( (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 A C))) =>  ( (G = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 A)))  =>  ( ( (~ (r2_hidden F (k3_msafree2 A)))  &  (~  ((r2_hidden F (u1_struct_0 A)) & (r2_hidden F (k2_msafree2 (k2_circcomb A B)))) ) )  |  ((k1_funct_1 (k6_circuit2 (k2_circcomb A B) (k3_circcomb A B C D) E) F) = (k1_funct_1 (k6_circuit2 A C G) F)) ) ) ) )  &  (! [G:$i] :  ((m1_subset_1 G (k4_card_3 (u3_msualg_1 B D))) =>  ( (G = (k11_card_3 (u3_msualg_1 (k2_circcomb A B) (k3_circcomb A B C D)) E (u1_struct_0 B)))  =>  ( ( (~ (r2_hidden F (k3_msafree2 B)))  &  (~  ((r2_hidden F (u1_struct_0 B)) & (r2_hidden F (k2_msafree2 (k2_circcomb A B)))) ) )  |  ((k1_funct_1 (k6_circuit2 (k2_circcomb A B) (k3_circcomb A B C D) E) F) = (k1_funct_1 (k6_circuit2 B D G) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_classes1,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k6_classes1 (k4_classes1 A)) = A) ) ) ).
tt(t64_classes2,ax, (k13_classes2 = (k4_classes1 k4_ordinal1)) ).
tt(t64_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_clvect_1 A B (k3_clvect_1 A)) = (k6_domain_1 (u1_struct_0 A) B)) ) ) ) ) ).
tt(t64_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v2_clvect_2 C A) => (v2_clvect_2 (k4_normsp_1 A C B) A)) ) ) ) ) ) ) ).
tt(t64_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_classes1 B) & (v1_coh_sp B)) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ((r2_hidden (k4_tarski (k4_tarski C E) (k4_tarski D F)) (k1_coh_sp (k12_cohsp_1 A B))) <=>  ((r2_hidden C (k3_tarski A)) &  ((r2_hidden D (k3_tarski A)) &  ( ( (~ (r2_hidden (k4_tarski C D) (k1_coh_sp A)))  &  ((r2_hidden E (k3_tarski B)) & (r2_hidden F (k3_tarski B))) )  |  ((r2_hidden (k4_tarski E F) (k1_coh_sp B)) &  ( (E = F)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) => (r1_xxreal_0 (k17_complex1 (k9_real_1 (k17_complex1 A) (k17_complex1 B))) (k17_complex1 (k6_xcmplx_0 A B)))) ) ) ) ).
tt(t64_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k1_comptrig A) = (k1_comptrig B))  =>  ( (A = k6_numbers)  |  ( (B = k6_numbers)  |  ((k1_comptrig (k10_complex1 A)) = (k1_comptrig (k10_complex1 B))) ) ) ) ) ) ) ) ).
tt(t64_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) => (r1_xxreal_0 (k10_binop_2 (k17_complex1 A) (k17_complex1 B)) (k17_complex1 (k3_rlvect_1 k1_complfld A B)))) ) ) ) ).
tt(t64_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  ((k12_seq_4 A (k4_binop_2 B C)) = (k10_seq_4 (k12_seq_4 A B) (k12_seq_4 A C))) ) ) ) ) ) ) ).
tt(t64_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) ) )  =>  ((r2_hidden (k5_card_1 B) (k2_afinsq_1 (k10_compos_1 A B))) &  ((k1_funct_1 (k10_compos_1 A B) (k5_card_1 B)) = (k2_compos_1 A)) ) ) ) ) ) ).
tt(t64_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  ( ( ((k2_nat_1 (k19_margrel1 B) 2) = (k19_margrel1 C))  &  ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 (k19_margrel1 B) 1))) )  => (r1_comput_1 (k7_comput_1 B C A) B C A)) ) ) ) ) ) ) ).
tt(t64_comseq_3,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  ( (~ (r1_xxreal_0 1 (k17_complex1 A)))  =>  ((v1_comseq_3 (k1_comseq_3 A)) &  ((k11_comseq_3 (k1_comseq_3 A)) = (k13_complex1 k6_complex1 (k11_complex1 k6_complex1 A))) ) ) ) ) ).
tt(t64_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l2_algstr_0 A))  =>  (! [B:$i] :  ( ((v1_xboole_0 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B C) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t64_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B C) (k7_cqc_lang A C B)) A)) ) ) ) ) ) ).
tt(t64_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k7_cqc_lang A B C)) (k7_cqc_lang A B (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ).
tt(t64_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (~  ( (B = (k13_cqc_lang A C D))  &  ( (~  (D = E) )  &  ( (~ (r2_hidden E (k24_qc_lang1 A C)))  & (r2_hidden E (k24_qc_lang1 A B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k3_normsp_1 A B C) (k16_csspace A B (k5_vfunct_1 k5_numbers A C)))) ) ) ) ) ) ).
tt(t64_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k16_sin_cos) k19_sin_cos) A) B) = (k7_real_1 (k1_real_1 (k8_real_1 (k10_real_1 1 2) (k8_real_1 (k18_sin_cos B) (k18_sin_cos (k10_real_1 A 2))))) (k8_real_1 (k10_real_1 1 2) (k8_real_1 (k18_sin_cos (k8_real_1 3 B)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t64_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k18_sin_cos D))) ) )  =>  ( ((k18_sin_cos (k7_real_1 A (k10_real_1 B 2))) = k6_numbers)  |  ( ((k18_sin_cos (k9_real_1 A (k10_real_1 B 2))) = k6_numbers)  |  ((k1_seq_1 (k5_diff_1 C B) A) = (k1_real_1 (k10_real_1 (k8_real_1 2 (k9_real_1 (k18_sin_cos (k9_real_1 A (k10_real_1 B 2))) (k18_sin_cos (k7_real_1 A (k10_real_1 B 2))))) (k9_real_1 (k21_sin_cos (k8_real_1 2 A)) (k21_sin_cos B))))) ) ) ) ) ) ) ) ) ) ).
tt(t64_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) =>  ((k3_funct_2 (u1_struct_0 (k8_cat_2 (k2_oppcat_1 B) B)) (u1_struct_0 (k11_ens_1 A)) (k7_cat_1 (k8_cat_2 (k2_oppcat_1 B) B) (k11_ens_1 A) (k25_ens_1 A B)) (k9_cat_2 (k2_oppcat_1 B) B (k3_oppcat_1 B C) D)) = (k2_cat_1 B C D)) ) ) ) ) ) ) ) ) ) ).
tt(t64_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( (C = (k6_matrixr1 (k1_entropy1 A) B))  =>  ((k5_matrprob (k5_entropy1 C)) = (k7_real_1 (k18_rvsum_1 (k4_entropy1 A)) (k18_rvsum_1 (k14_rvsum_1 A (k3_matrprob (k5_entropy1 B)))))) ) ) ) ) ) ) ) ) ).
tt(t64_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 A D C B)) ) ) ) ) ).
tt(t64_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_relat_2 B) &  ((v8_relat_2 B) &  ((v1_partfun1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A A)))) ) )  =>  (~ (v1_xboole_0 (k8_eqrel_1 A B))) ) ) ) ) ).
tt(t64_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k23_rvsum_1 A A) = (k9_binop_2 (k9_binop_2 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))) (k5_square_1 (k1_seq_1 A 3)))) ) ) ).
tt(t64_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v3_valued_0 E)) )  =>  ( ( (B = D)  &  (C = E) )  =>  ((k3_rlvect_1 (k15_euclid A) B C) = (k1_valued_1 D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid A)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid A)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((r2_hidden B D) & (r2_hidden C D))  =>  ( (B = C)  |  ( ((k2_euclid_4 A B C) = D)  & (v1_euclid_4 D A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v16_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_exchsort C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 C)) =>  ( ((r2_hidden D E) &  (A = (k5_exchsort (k9_xtuple_0 C) (k9_xtuple_0 C) (k6_partfun1 (k9_xtuple_0 C)) E F)) )  =>  ( ((k1_binop_1 (k7_exchsort B C E F) D F) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 A F)))  &  ((k1_binop_1 (k7_exchsort B C E F) D E) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k1_facirc_1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A k1_facirc_1) (k10_facirc_1 B C A k1_facirc_1)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  ( (F = (k1_funct_1 D C))  &  (G = (k1_funct_1 D A)) ) )  =>  ((k11_facirc_1 (k8_facirc_1 B C A k1_facirc_1) (k10_facirc_1 B C A k1_facirc_1) (k5_facirc_1 (k8_facirc_1 B C A k1_facirc_1) (k10_facirc_1 B C A k1_facirc_1) D 2) (k9_facirc_1 B C A k1_facirc_1)) = (k2_binarith (k2_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)))) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) B))) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers A) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) B) = (k7_real_1 (k1_seq_1 k2_sin_cos9 (k10_real_1 1 B)) (k10_real_1 B (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ) ).
tt(t64_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k6_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 3)) = (k8_finseq_1 k5_numbers (k6_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 1)) (k12_finseq_1 k5_numbers (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 3))))) ) ) ).
tt(t64_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  => (r1_relat_2 (k8_filter_0 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(t64_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_filter_2 (u1_struct_0 A) (k9_filter_2 A B B) (k6_domain_1 (u1_struct_0 A) B))) ) ) ) ).
tt(t64_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 A)))  =>  ((k1_funct_1 (k7_finseq_1 A B) C) = (k1_funct_1 A C)) ) ) ) ) ) ) ) ).
tt(t64_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k9_xtuple_0 C)) =>  ((v1_relat_1 (k3_funcop_1 C A B)) &  ((v1_funct_1 (k3_funcop_1 C A B)) & (v1_finseq_1 (k3_funcop_1 C A B))) ) ) ) ) ) ) ) ) ).
tt(t64_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k1_relset_1 k5_numbers (k1_finseq_3 A B)) = (k1_relset_1 k5_numbers A))  => (r1_xboole_0 B (k10_xtuple_0 A))) ) ) ) ).
tt(t64_finseq_4,ax, (! [A:$i] :  ((v1_finset_1 A) =>  (! [B:$i] :  ((v1_finset_1 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ( ( ((k5_card_1 A) = (k5_card_1 B))  &  ((k10_xtuple_0 C) = B) )  => (v2_funct_1 C)) ) ) ) ) ) ) ).
tt(t64_finseq_5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  ((k3_finseq_5 (k7_finseq_1 A B)) = (k7_finseq_1 (k3_finseq_5 B) (k3_finseq_5 A))) ) ) ) ) ).
tt(t64_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k2_finseq_5 A (k8_finseq_1 A C D) B) = (k8_finseq_1 A (k2_finseq_5 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t64_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m1_subset_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo E A) &  ((v2_binop_1 E A) & (v1_finseqop E A)) )  =>  ( ( (~  ((k5_binop_1 A E B C) = (k5_binop_1 A E B D)) )  &  (~  ((k5_binop_1 A E C B) = (k5_binop_1 A E D B)) ) )  |  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k8_flang_1 A (k7_flang_1 A B C)) (k8_flang_1 A B))) ) ) ) ) ).
tt(t64_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B (k8_flang_1 A C)) => (r1_tarski (k1_flang_2 A B D E) (k8_flang_1 A C))) ) ) ) ) ) ) ) ) ) ).
tt(t64_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((k2_flang_3 A B) = (k4_flang_1 A (k2_flang_1 A)))  <=>  (B = (k4_flang_1 A (k2_flang_1 A))) ) ) ) ) ).
tt(t64_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v5_fsm_1 C A B) &  ((v7_fsm_1 C A B) & (l2_fsm_1 C A B)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) ) )  =>  ( ((r1_subset_1 (u1_struct_0 C) (u1_struct_0 D)) & (r4_fsm_1 A B C D))  => (r7_fsm_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t64_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ((v1_binop_1 C A) => (r2_funct_2 B A (k10_funcop_1 A B C E D) (k9_funcop_1 A B C D E))) ) ) ) ) ) ) ) ) ) ).
tt(t64_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((v2_funct_1 C) =>  ((k7_relat_1 C (k6_subset_1 A B)) = (k6_subset_1 (k7_relat_1 C A) (k7_relat_1 C B))) ) ) ) ) ) ).
tt(t64_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  (~  ((r2_hidden E (k7_relset_1 A B D C)) &  (! [F:$i] :  (~  ((r2_hidden F A) &  ((r2_hidden F C) &  (E = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G A C) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  ((r2_funct_2 A (k2_zfmisc_1 B C) (k14_funct_3 A B C D F) (k14_funct_3 A B C E G)) =>  ((r2_funct_2 A B D E) & (r2_funct_2 A C F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = B) )  =>  ((k10_xtuple_0 (k4_funct_4 A B C D)) = (k2_tarski C D)) ) ) ) ) ) ).
tt(t64_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_wellord2 (k1_funct_2 A (k2_zfmisc_1 B C)) (k2_zfmisc_1 (k1_funct_2 A B) (k1_funct_2 A C))) &  ((k1_card_1 (k1_funct_2 A (k2_zfmisc_1 B C))) = (k1_card_1 (k2_zfmisc_1 (k1_funct_2 A B) (k1_funct_2 A C)))) ) ) ) ) ).
tt(t64_funct_7,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v1_finseq_1 A) & (v1_funct_7 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((r1_tarski (k7_funct_7 A) (k9_xtuple_0 B)) =>  ((v1_relat_1 (k7_finseq_1 A (k9_finseq_1 B))) &  ((v1_funct_1 (k7_finseq_1 A (k9_finseq_1 B))) &  ((v1_finseq_1 (k7_finseq_1 A (k9_finseq_1 B))) & (v1_funct_7 (k7_finseq_1 A (k9_finseq_1 B)))) ) ) ) ) ) ) ) ).
tt(t64_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r1_funct_8 A k1_numbers k1_numbers k2_euclid)) ) ).
tt(t64_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v3_fvaluat1 A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B)))))  => (r1_tarski (k9_fvaluat1 A B C) C)) ) ) ) ) ) ) ).
tt(t64_fvsum_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v5_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  ((k11_fvsum_1 A B C) = (k11_fvsum_1 A C B)) ) ) ) ) ) ) ).
tt(t64_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k25_gfacirc1 A B C)))) ) ) ).
tt(t64_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k28_glib_000 A C)) <=>  (? [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) & (r1_glib_000 A C D B)) ) ) ) ) ) ) ) ).
tt(t64_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ((k3_finseq_1 (k10_glib_001 A B C)) = (k2_nat_1 (k3_finseq_1 B) 2)) ) ) ) ) ) ) ) ).
tt(t64_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k3_finseq_1 C) A) |  ((r1_xxreal_0 (k1_matrix_1 C) (k2_nat_1 B 1)) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A B) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 2))) (k10_real_1 1 2))) (k2_xboole_0 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A B)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C A (k2_nat_1 B 1)))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C A (k2_nat_1 B 1)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 A 1) (k2_nat_1 B 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t64_goboard7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  ( ((v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) A B)) &  ((v1_sppol_1 (k1_rltopsp1 (k15_euclid 2) C D)) &  ( ((k18_euclid A) = (k18_euclid C))  &  ((r1_xxreal_0 (k17_euclid A) (k17_euclid C)) &  ((r1_xxreal_0 (k17_euclid C) (k17_euclid D)) & (r1_xxreal_0 (k17_euclid D) (k17_euclid B))) ) ) ) )  => (r1_tarski (k1_rltopsp1 (k15_euclid 2) C D) (k1_rltopsp1 (k15_euclid 2) A B))) ) ) ) ) ) ) ) ) ).
tt(t64_graph_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v6_graph_1 D) & (l1_graph_1 D)) )  =>  (! [E:$i] :  ( ((v7_graph_1 E D) & (m2_graph_1 E D))  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ( ((r5_graph_5 D C) &  ((r8_graph_5 D F G E A C) &  ((r1_tarski A B) &  (! [H:$i] :  ( ((v7_graph_1 H D) & (m2_graph_1 H D))  =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  ((r8_graph_5 D F I H A C) =>  ((r2_hidden I A) | (r1_xxreal_0 (k10_graph_5 D E C) (k10_graph_5 D H C))) ) ) ) ) ) ) ) )  =>  ( (F = G)  | (r8_graph_5 D F G E B C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( (C = (k10_group_2 A D E))  => (r1_tarski (k4_group_11 A B C) (k9_subset_1 (u1_struct_0 A) (k4_group_11 A B D) (k4_group_11 A B E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k6_group_2 B) = (k6_group_2 C)) ) ) ) ) ) ) ).
tt(t64_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((k7_struct_0 C) = (k7_struct_0 (k6_group_3 A C B))) ) ) ) ) ) ) ).
tt(t64_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  (! [D:$i] :  ( ((v15_algstr_0 D) & (m1_group_2 D A))  =>  ((m1_group_2 B D) => (m1_group_2 (k8_group_4 A B C) (k8_group_4 A D C))) ) ) ) ) ) ) ) ) ).
tt(t64_group_5,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_group_2 C B) =>  (! [D:$i] :  ((m1_group_2 D B) =>  ((r1_struct_0 (k8_group_5 B C D) A) <=>  (? [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) &  (? [F:$i] :  ((m2_finseq_1 F k4_numbers) &  ( ((k3_finseq_1 E) = (k3_finseq_1 F))  &  ((r1_tarski (k10_xtuple_0 E) (k5_group_5 B C D)) &  (A = (k3_group_4 B (k4_group_4 B F E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_group_6,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B C)))) )  =>  ( ((v3_funct_2 D A B) & (v3_funct_2 E B C))  => (v3_funct_2 (k1_partfun1 A B B C D E) A C)) ) ) ) ) ) ) ) ) ) ).
tt(t64_group_9,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (k1_funct_2 B B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  => (r2_funct_2 B B (k2_group_9 A B E (k8_finseq_1 A C D)) (k1_partfun1 B B B B (k2_group_9 A B E D) (k2_group_9 A B E C)))) ) ) ) ) ) ) ) ) ).
tt(t64_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v8_vectsp_1 B k1_complfld) &  ((v9_vectsp_1 B k1_complfld) &  ((v10_vectsp_1 B k1_complfld) &  ((v11_vectsp_1 B k1_complfld) & (l1_vectsp_1 B k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld)) &  ((v1_bilinear C k1_complfld A B) &  ((v2_bilinear C k1_complfld A B) &  ((v4_bilinear C k1_complfld A B) &  ((v2_hermitan C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ( ((k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k7_hermitan A B C)) = (k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k3_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C)))) (k6_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C))))  &  ( ((k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k7_hermitan A B C)) = (k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k3_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C)))) (k6_hermitan (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) B (k15_bilinear k1_complfld A B C))))  &  ( ((k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k7_hermitan A B C)) = (k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C))) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k15_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C))))  &  ((k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A B C)) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k7_hermitan A B C)) = (k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C))) (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k15_bilinear k1_complfld A (k6_vectsp10 k1_complfld B (k14_bilinear k1_complfld A B (k3_hermitan A B C))) (k6_hermitan A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t64_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 B 3 A) & (r1_taylor_1 C 3 A))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B C) A) 3) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 3) C) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 2) (k2_fdiff_1 C A)) 3) (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 B A) (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C A) 2)) 3))) (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 C A) 3))))) ) ) ) ) ) ) ).
tt(t64_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) B)) = (a_2_0_ideal_1 A B)) ) ) ) ) ).
tt(t64_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((v1_int_1 (k7_xcmplx_0 A B)) =>  ((k4_xcmplx_0 (k1_int_1 (k7_xcmplx_0 A B))) = (k1_int_1 (k7_xcmplx_0 (k4_xcmplx_0 A) B))) ) ) ) ) ) ).
tt(t64_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k10_real_1 (k9_real_1 (k1_seq_1 k19_sin_cos D) (k5_square_1 (k1_seq_1 k16_sin_cos D))) (k5_square_1 (k1_seq_1 k16_sin_cos D)))) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers B)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers B)) (k4_seq_4 A)) (k1_seq_1 (k47_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k2_fdiff_9) (k1_partfun2 k1_numbers B)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t64_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (B = (k1_rcomp_1 (k1_real_1 (k10_real_1 (k7_square_1 2) 2)) (k10_real_1 (k7_square_1 2) 2)))  &  ( ((k9_xtuple_0 (k2_fdiff_1 k1_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1))) = (k9_xtuple_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k2_rcomp_1 (k1_real_1 1) 1)) &  ((k1_seq_1 A C) = (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 C))))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) )  =>  ((k2_integra5 B A) = (k10_real_1 k32_sin_cos 2)) ) ) ) ) ) ).
tt(t64_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k7_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3))) = E)  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3))) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_prepower (k7_real_1 A F) (k10_real_1 1 2))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k10_real_1 2 3)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  (! [D:$i] :  ((m2_interva1 D A) => (r2_interva1 A (k16_interva1 A (k16_interva1 A B C) D) (k16_interva1 A B (k16_interva1 A C D)))) ) ) ) ) ) ) ) ).
tt(t64_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 A (k5_intpro_1 B C)) (k5_intpro_1 B (k5_intpro_1 A C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t64_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_2_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ( (D = (k18_pscomp_1 E))  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid J)))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (~  ((r1_jordan6 (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1) A B) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 1)) (k19_euclid (k1_real_1 1) 1))) &  ( (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 1)) (k19_euclid (k1_real_1 1) 1))) & (r1_xxreal_0 (k18_euclid A) (k18_euclid B))) )  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) 1) (k19_euclid 1 1))))  &  ( (~ (r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 1) (k19_euclid 1 (k1_real_1 1)))))  &  (~  ((r2_hidden B (k1_rltopsp1 (k15_euclid 2) (k19_euclid 1 (k1_real_1 1)) (k19_euclid (k1_real_1 1) (k1_real_1 1)))) &  (~  (B = (k19_euclid (k1_real_1 1) (k1_real_1 1))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 A (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) B) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) B)) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) A) |  ((r1_xxreal_0 (k1_real_1 1) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k1_real_1 1)))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v2_connsp_1 B (k15_euclid 2)) &  ((v2_compts_1 B (k15_euclid 2)) &  ( (~ (v1_sppol_1 B))  &  ( (~ (v2_sppol_1 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 B A))) = (k7_real_1 (k8_pscomp_1 B) (k13_complex1 (k9_real_1 (k8_pscomp_1 B) (k6_pscomp_1 B)) (k13_newton 2 A)))) ) ) ) ) ).
tt(t64_jordan1j,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_topreal2 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (~  ((r1_xxreal_0 1 C) &  ((r1_xxreal_0 C D) &  ((r1_xxreal_0 D (k1_matrix_1 (k1_jordan8 B (k2_nat_1 A 1)))) &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k8_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)))  &  ( ((k9_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k9_jordan6 (k3_topreal1 2 (k1_jordan9 B (k2_nat_1 A 1))))) = (k1_tarski (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C)))  & (r1_xboole_0 (k1_rltopsp1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) C) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) (k1_jordan8 B (k2_nat_1 A 1)) (k1_jordan1a (k1_jordan8 B (k2_nat_1 A 1))) D)) (k8_jordan6 B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_topmetr (k14_euclid A) C)))) =>  ( ( (B = D)  & (v6_tbsp_1 D (k1_topmetr (k14_euclid A) C)))  => (v6_tbsp_1 B (k14_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t64_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k17_euclid (k10_jordan6 A)) = (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) ) ) ).
tt(t64_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_xxreal_0 C) & (v1_xreal_0 C))  =>  ((m1_subset_1 B (u1_struct_0 (k2_brouwer 2 A C))) => (v5_pre_topc (k9_jordan 2 A B C) (k1_pre_topc (k15_euclid 2) (k7_subset_1 (u1_struct_0 (k15_euclid 2)) (k2_topreal9 2 A C) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) B))) (k7_toprealb 2 A C))) ) ) ) ) ) ) ).
tt(t64_kurato_1,ax, ((k5_card_1 (k2_kurato_1 k3_topmetr k6_kurato_1)) = 14) ).
tt(t64_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v11_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k5_binop_1 (u1_struct_0 C) (u1_lattices C) E (k2_lattice2 A C B D)) = (k2_lattice2 A C B (k10_funcop_1 (u1_struct_0 C) A (u1_lattices C) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A (k26_lexbfs A) B))))))  =>  ((k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A (k26_lexbfs A) (k1_nat_1 B 1))) = (k1_funct_4 (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A (k26_lexbfs A) B)) (k16_funcop_1 (k19_lexbfs A (k23_lexbfs A (k26_lexbfs A) B)) (k7_nat_d (k15_glib_000 A) (k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A (k26_lexbfs A) B)))))))) ) ) ) ) ) ).
tt(t64_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B)))) ) ) ) )  | (v5_limfunc1 A)) ) ) ) ).
tt(t64_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) &  ((r1_limfunc2 C A) &  ((k1_limfunc2 B A) = (k1_limfunc2 C A)) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((r1_tarski (k2_rcomp_1 (k9_real_1 A E) A) (k9_subset_1 k1_numbers (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)) (k1_relset_1 k1_numbers D))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k2_rcomp_1 (k9_real_1 A E) A)) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) ) ) ) ) ) )  |  ((r1_limfunc2 D A) &  ((k1_limfunc2 D A) = (k1_limfunc2 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_limfunc4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r1_limfunc2 C (k2_limfunc2 B A)) &  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D E))  &  ( (~ (r1_xxreal_0 E A))  & (r2_hidden E (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C)))) ) ) ) ) ) ) ) ) ) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) & (r1_xxreal_0 (k2_limfunc2 B A) (k1_seq_1 B E))) ) ) ) ) ) ) )  |  ((r4_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) &  ((k2_limfunc2 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers B C) A) = (k1_limfunc2 C (k2_limfunc2 B A))) ) ) ) ) ) ) ) ) ) ).
tt(t64_lpspace2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v2_comseq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) &  ((k2_seq_2 (k4_normsp_0 A (k4_normsp_1 A B C))) = k6_numbers) )  =>  ((v3_normsp_1 B A) &  ((k6_normsp_1 A B) = C) ) ) ) ) ) ) ) ) ).
tt(t64_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A E (k8_cqc_lang A B (k8_cqc_lang A C D))) & (r3_cqc_the1 A E C))  => (r3_cqc_the1 A E (k8_cqc_lang A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ( (~  (A = k6_numbers) )  =>  ((k6_mathmorp A (k15_euclid B) (k3_mathmorp (k15_euclid B) C D)) = (k3_mathmorp (k15_euclid B) (k6_mathmorp A (k15_euclid B) C) (k6_mathmorp A (k15_euclid B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t64_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 B (k2_matrix10 A C)) => (r2_matrix10 C (k2_matrix10 A B))) ) ) ) ) ) ) ).
tt(t64_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden E (k2_finseq_1 (k5_card_1 C))) &  ((r2_hidden F (k2_finseq_1 (k5_card_1 C))) &  ((k5_card_1 C) = (k5_card_1 D)) ) )  =>  ( ((k2_laplace E F (k5_card_1 C) A (k7_matrix13 (u1_struct_0 A) B C D)) = (k7_matrix13 (u1_struct_0 A) B (k7_subset_1 k5_numbers C (k3_matrix13 (k1_funct_1 (k5_matrix13 C) E))) (k7_subset_1 k5_numbers D (k3_matrix13 (k1_funct_1 (k5_matrix13 D) F)))))  &  ((k5_card_1 (k7_subset_1 k5_numbers C (k3_matrix13 (k1_funct_1 (k5_matrix13 C) E)))) = (k5_card_1 (k7_subset_1 k5_numbers D (k3_matrix13 (k1_funct_1 (k5_matrix13 D) F))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( ((k7_matrix15 A B) = (k6_prvect_1 A (k1_matrix_1 B)))  =>  ((k8_matrix13 A B) = k1_xboole_0) ) ) ) ) ) ).
tt(t64_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ((v6_matrix16 D A) =>  ((k2_matrix_6 (k3_finseq_1 D) A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k3_matrix16 A D) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k3_matrix16 A D) C)) = (k3_matrix16 A (k9_fvsum_1 A D (k1_algstr_0 A B C)))) ) ) ) ) ) ) ) ) ) ).
tt(t64_matrix_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 A) B C) =>  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 A) C D) =>  ( ((k1_matrix_1 E) = (k3_finseq_1 F))  =>  ((r1_xxreal_0 (k3_finseq_1 E) k6_numbers) |  ((r1_xxreal_0 (k3_finseq_1 F) k6_numbers) | (m1_matrix_1 (k4_matrix_3 A E F) (u1_struct_0 A) B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 D))  & (r1_xxreal_0 (k3_finseq_1 C) (k3_finseq_1 E)))  =>  ((k24_matrixj1 A (k3_matrixj1 (u1_struct_0 A) B C) (k8_finseq_1 (u1_struct_0 A) D E)) = (k3_matrixj1 (u1_struct_0 A) (k24_matrixj1 A B D) (k24_matrixj1 A C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_matrixr1,ax, (! [A:$i] :  ((m2_finseq_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_matrix_1 C) & (m2_finseq_1 C (k3_finseq_2 k1_numbers)))  =>  ( ( ((k3_finseq_1 B) = (k3_finseq_1 C))  &  ( ((k1_matrix_1 B) = (k1_matrix_1 C))  &  ((k3_finseq_1 B) = (k3_finseq_1 A)) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 A) k6_numbers) |  ((k12_matrixr1 (k3_matrixr1 B C) A) = (k4_rvsum_1 (k12_matrixr1 B A) (k12_matrixr1 C A))) ) ) ) ) ) ) ) ) ).
tt(t64_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  ((k5_matrix_1 A k1_numbers (k4_matrixr2 A)) = (k4_matrixr2 A)) ) ) ).
tt(t64_mcart_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k3_zfmisc_1 A B C)) =>  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( (D = (k3_xtuple_0 E F G))  =>  ( ((k1_mcart_1 A B C D) = E)  &  ( ((k2_mcart_1 A B C D) = F)  &  ((k3_mcart_1 A B C D) = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_measure6,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B (k6_measure6 A)) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (~  ((r1_tarski (k2_relset_1 k1_numbers C) A) &  ((v2_comseq_2 C) &  ((k2_seq_2 C) = B) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_member_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((k10_member_1 (k2_tarski A B) (k2_tarski C D)) = (k2_enumset1 (k3_xxreal_3 A C) (k3_xxreal_3 A D) (k3_xxreal_3 B C) (k3_xxreal_3 B D))) ) ) ) ) ) ) ) ) ).
tt(t64_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r2_hidden (k4_struct_0 B) (k9_xtuple_0 (k10_memstr_0 A B C D)))) ) ) ) ) ) ) ) ).
tt(t64_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (~  ( (? [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) &  ( (D = (k1_relset_1 A C))  & (r1_mesfunc1 A B C D)) ) )  &  ((v6_supinf_2 C) &  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k4_partfun1 A k7_numbers)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k7_numbers))))) )  =>  (~  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_mesfunc2 A B (k4_mesfunc5 A k7_numbers D E)) &  ((k1_relset_1 A (k4_mesfunc5 A k7_numbers D E)) = (k1_relset_1 A C)) ) ) )  &  ( (! [E:$i] :  ((v7_ordinal1 E) => (v6_supinf_2 (k4_mesfunc5 A k7_numbers D E))) )  &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ((r1_xxreal_0 E F) =>  (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G (k1_relset_1 A C)) => (r1_xxreal_0 (k12_supinf_2 (k4_mesfunc5 A k7_numbers D E) G) (k12_supinf_2 (k4_mesfunc5 A k7_numbers D F) G))) ) ) ) ) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E A) =>  ((r2_hidden E (k1_relset_1 A C)) =>  ((v10_mesfunc5 (k3_mesfunc5 A D E)) &  ((k2_mesfunc5 (k3_mesfunc5 A D E)) = (k12_supinf_2 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((r2_relset_1 A k1_numbers (k18_rfunct_3 A (k26_valued_1 A k1_numbers B C)) (k26_valued_1 A k1_numbers (k18_rfunct_3 A B) C)) & (r2_relset_1 A k1_numbers (k19_rfunct_3 A (k26_valued_1 A k1_numbers B C)) (k26_valued_1 A k1_numbers (k19_rfunct_3 A B) C))) ) ) ) ) ) ) ) ).
tt(t64_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k26_mmlquery A (k2_finseq_4 (k1_zfmisc_1 A) B C) 2) = (k15_mmlquery A B C)) ) ) ) ) ) ).
tt(t64_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  ((r7_modelc_2 B (k3_modelc_2 A)) <=>  (~ (r7_modelc_2 B A)) ) ) ) ) ) ).
tt(t64_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v6_modelc_3 A) <=>  ((v2_modelc_2 A) |  ((v3_modelc_2 A) & (v2_modelc_2 (k10_modelc_2 A))) ) ) ) ) ).
tt(t64_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ( ((v7_ordinal1 B) & (v1_int_2 B))  => (r1_tarski (a_2_5_moebius1 A B) (k2_finseq_1 A))) ) ) ) ).
tt(t64_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_group_1 B) & (m2_monoid_0 B (k9_monoid_0 A))) )  =>  ((k4_binop_1 (u1_struct_0 B) (u2_algstr_0 B)) = k1_xboole_0) ) ) ) ) ).
tt(t64_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ( ( ((k6_int_1 B A) = (k6_int_1 C A))  =>  ( (A = k6_numbers)  | (r2_int_1 B C A)) )  &  ((r2_int_1 B C A) =>  ((k6_int_1 B A) = (k6_int_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t64_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r9_ncfcont1 B A D C) & (r9_ncfcont1 B A E C))  =>  ((r9_ncfcont1 B A (k3_vfunct_2 (u1_struct_0 B) A D E) C) & (r9_ncfcont1 B A (k2_vfunct_1 (u1_struct_0 B) A D E) C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_newton,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((r1_xxreal_0 k6_numbers A) => (r1_xxreal_0 k6_numbers (k6_int_1 B A))) ) ) ) ) ).
tt(t64_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_oppcat_1 C A B) => (m1_oppcat_1 (k11_oppcat_1 (k2_oppcat_1 A) B (k10_oppcat_1 A B C)) (k2_oppcat_1 A) (k2_oppcat_1 B))) ) ) ) ) ) ).
tt(t64_orders_1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  (~  ((r2_orders_1 A B) &  ( ((k1_relat_1 A) = B)  &  ((r5_orders_1 A B) &  (! [C:$i] :  (~ (r7_orders_1 A C)) ) ) ) ) ) ) ) ) ).
tt(t64_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) => (r1_ordinal1 (k11_ordinal2 (k6_ordinal3 A B) B) A)) ) ) ) ).
tt(t64_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v6_ordinal5 A)) ) ) )  =>  ( ((k4_ordinal5 A) = k6_numbers)  =>  (A = k1_xboole_0) ) ) ) ).
tt(t64_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  & (v1_classes2 D))  =>  ( ((r2_hidden k4_ordinal1 C) &  ((r2_hidden A C) &  ((r2_hidden B C) &  ((r2_hidden k4_ordinal1 D) &  ((r2_hidden A D) & (r2_hidden B D)) ) ) ) )  =>  ((k1_funct_1 (k1_funct_1 (k11_ordinal6 C) B) A) = (k1_funct_1 (k1_funct_1 (k11_ordinal6 D) B) A)) ) ) ) ) ) ) ) ) ) ).
tt(t64_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v3_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t64_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_partfun1 (k5_relat_1 (k6_relat_1 A C) B) C)) ) ) ) ).
tt(t64_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  => (r6_pboole A (k4_pboole A B (k4_pboole A C D)) (k2_pboole A (k4_pboole A B C) (k3_pboole A B D)))) ) ) ) ) ) ) ).
tt(t64_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r7_pdiff_5 C B) =>  ((r3_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) &  ((k11_pdiff_1 3 1 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) = (k8_real_1 A (k7_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t64_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ((m2_finseq_2 E k1_numbers (k1_euclid A)) =>  ( ((r3_pdiff_1 A B C E) & (r3_pdiff_1 A B D E))  =>  ((r3_pdiff_1 A B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) &  ((k11_pdiff_1 A B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers C D) E) = (k9_binop_2 (k11_binop_2 (k11_pdiff_1 A B C E) (k1_seq_1 D E)) (k11_binop_2 (k1_seq_1 C E) (k11_pdiff_1 A B D E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_pepin,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ( (~ (r1_xxreal_0 B k6_numbers))  =>  ((k3_nat_d (k1_newton A B) A) = (k7_xcmplx_0 (k1_newton A B) A)) ) ) ) ) ) ).
tt(t64_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) => (r1_tarski (k10_pnproc_1 A B C D) (k11_pnproc_1 A B C D))) ) ) ) ) ) ) ).
tt(t64_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (m1_subset_1 (k1_tarski A) (u1_struct_0 (k17_polyform A (k7_polyform A))))) ) ).
tt(t64_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k8_polynom5 A (k1_group_1 A) 1) (k6_partfun1 (u1_struct_0 A)))) ) ).
tt(t64_power,ax, ((k4_power 2 6) = 64) ).
tt(t64_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  ((r2_hidden B (k4_finseq_1 (k20_pre_poly A C))) => (r3_pre_poly A (k7_partfun1 (k15_pre_poly A) (k20_pre_poly A C) B) C)) ) ) ) ) ) ) ).
tt(t64_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (! [C:$i] :  ((v1_rat_1 C) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k6_prepower A B) (k6_prepower A C))) ) ) ) ) ) ) ) ) ).
tt(t64_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_3 D A B) =>  (! [E:$i] :  ( ((v5_relat_1 E B) &  ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k9_setfam_1 A)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ( ( (! [F:$i] :  ((v7_ordinal1 F) =>  ((r2_hidden F (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 E F) = (k8_prob_3 A B D F)) ) ) )  &  (! [F:$i] :  ((v7_ordinal1 F) =>  ( (~ (r2_hidden F (k1_relset_1 k5_numbers D)))  =>  ((k1_funct_1 E F) = k1_xboole_0) ) ) ) )  =>  ((v2_comseq_2 (k3_series_1 (k8_prob_1 A B E C))) &  ( ((k4_series_1 (k8_prob_1 A B E C)) = (k3_funct_2 k5_numbers k1_numbers (k3_series_1 (k8_prob_1 A B E C)) (k3_finseq_1 D)))  &  ((r1_xxreal_0 (k1_funct_1 C (k1_kurato_0 A E)) (k4_series_1 (k8_prob_1 A B E C))) &  ((k18_rvsum_1 (k9_prob_3 A B D C)) = (k4_series_1 (k8_prob_1 A B E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_pscomp_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ((k25_pscomp_1 A) = (k18_pscomp_1 A))  =>  ((k25_pscomp_1 A) = (k10_pscomp_1 A)) ) ) ) ).
tt(t64_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  => (r6_pboole A (k6_pboole A (k2_pboole A B C) (k2_pboole A D E)) (k2_pboole A (k2_pboole A (k2_pboole A (k6_pboole A B D) (k6_pboole A B E)) (k6_pboole A C D)) (k6_pboole A C E)))) ) ) ) ) ) ) ) ) ).
tt(t64_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (~ (r3_qc_lang2 A B (k12_qc_lang1 A))) ) ) ) ) ).
tt(t64_qc_lang3,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_qc_lang1 B) =>  (! [C:$i] :  ((m2_subset_1 C (k6_qc_lang1 B) (k8_qc_lang1 B A)) =>  (! [D:$i] :  ( ((v3_card_1 D A) & (m2_finseq_1 D (k2_qc_lang1 B)))  =>  ((k6_qc_lang3 B (k10_qc_lang1 B C D)) = (a_3_3_qc_lang3 A B D)) ) ) ) ) ) ) ) ) ).
tt(t64_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k29_quaterni (k26_quaterni A B) C) D) = (k29_quaterni (k26_quaterni (k27_quaterni A D) (k27_quaterni B D)) (k27_quaterni C D))) ) ) ) ) ) ) ) ) ).
tt(t64_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k17_quaterni (k29_quaterni A (k31_quaterni A))) = k6_numbers)  &  ( ((k18_quaterni (k29_quaterni A (k31_quaterni A))) = (k8_real_1 2 (k18_quaterni A)))  &  ( ((k19_quaterni (k29_quaterni A (k31_quaterni A))) = (k8_real_1 2 (k19_quaterni A)))  &  ((k20_quaterni (k29_quaterni A (k31_quaterni A))) = (k8_real_1 2 (k20_quaterni A))) ) ) ) ) ) ).
tt(t64_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [E:$i] :  ((m1_rcomp_3 E A B D) =>  (! [F:$i] :  ((m2_rcomp_3 F A B D E) =>  ( ((m1_setfam_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 D (k4_topmetr A B)) &  ((v1_rcomp_3 D (k4_topmetr A B)) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 1 C)) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 E) C) | (r1_xxreal_0 (k1_funct_1 F C) (k5_seq_4 (k7_partfun1 (k9_setfam_1 k1_numbers) E (k1_nat_1 C 1))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 1)) (k1_seq_1 (k6_real_3 B) A)) (k8_real_1 (k1_seq_1 (k5_real_3 B) A) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1)))) = (k2_newton (k1_real_1 1) A)) ) ) ) ) ).
tt(t64_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  (! [C:$i] :  ((v1_relat_1 C) => (r1_tarski (k3_relat_1 B (k5_relat_1 C A)) (k3_relat_1 B C))) ) ) ) ) ).
tt(t64_relset_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))) =>  ((k3_relat_1 (k4_relat_1 A) C) = (k3_relat_1 C (k4_relat_1 B))) ) ) ) ) ).
tt(t64_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v10_rewrite1 B))  =>  ((r12_rewrite1 A B) => (m2_rewrite1 B A)) ) ) ) ) ).
tt(t64_rewrite3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k8_afinsq_1 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k8_afinsq_1 C))) =>  (! [G:$i] :  ( ( (~ (v2_struct_0 G))  & (l1_rewrite3 G F))  =>  ( (~ (r2_hidden (k2_flang_1 C) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 F G)))))  =>  (! [H:$i] :  ((m1_rewrite1 H (k1_rewrite3 C F G)) =>  (~  ( ((k1_funct_1 H 1) = (k4_tarski A D))  &  ( ((k1_funct_1 H (k3_finseq_1 H)) = (k4_tarski B E))  &  ((r1_xxreal_0 (k1_afinsq_1 D) (k1_afinsq_1 E)) &  (~  ( ((k3_finseq_1 H) = 1)  &  ( (A = B)  &  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ( (~ (r2_hidden C A))  <=>  ((k1_funct_1 (k7_rfunct_1 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t64_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((v1_finset_1 (k1_relset_1 A (k2_partfun1 A k1_numbers B C))) =>  ((k20_rfunct_3 A (k2_partfun1 A k1_numbers B C) C) = (k20_rfunct_3 A B C)) ) ) ) ) ) ) ).
tt(t64_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ((v7_valued_0 A) => (r2_funct_2 k5_numbers k1_numbers (k3_rinfsup1 A) A)) ) ) ).
tt(t64_rlaffin1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rlvect_2 C B) =>  ( ((v2_convex1 C B) &  ((k1_seq_1 C A) = 1) )  =>  ((k3_rlvect_2 B C) = (k1_tarski A)) ) ) ) ) ) ) ).
tt(t64_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ((r2_hidden B (k3_rlsub_1 A C D)) <=>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r1_struct_0 D E) &  (B = (k5_algstr_0 A C E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k4_lattices A C B) = B) ) )  =>  (B = (k5_lattices A)) ) ) ) ) ) ).
tt(t64_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (? [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) &  ((v3_rltopsp1 C A) & (r1_tarski C B)) ) ) ) ) ) ) ).
tt(t64_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D)) = (k1_algstr_0 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B C)) D)) ) ) ) ) ) ) ) ) ).
tt(t64_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  ((k4_algstr_0 (k16_rlvect_2 A) (k1_rlvect_2 (k16_rlvect_2 A) B)) = (k9_rlvect_2 A B)) ) ) ) ) ).
tt(t64_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v2_vectsp_2 E A) & (m1_rmod_2 E A B))  =>  (! [F:$i] :  ( ((v2_vectsp_2 F A) & (m1_rmod_2 F A B))  =>  ( ((k3_rmod_2 A B C E) = (k3_rmod_2 A B D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  => (v1_rmod_4 (k1_subset_1 (u1_struct_0 B)) A B)) ) ) ) ).
tt(t64_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) =>  (! [C:$i] :  ((m2_rusub_1 C A B) =>  ((v1_rlsub_1 C A) <=>  (C = (u1_struct_0 B)) ) ) ) ) ) ) ) ).
tt(t64_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ((k14_rvsum_1 (k2_finseq_2 A B) (k2_finseq_2 A C)) = (k5_finseq_2 k1_numbers A (k11_binop_2 B C))) ) ) ) ) ) ) ).
tt(t64_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k7_scmfsa_2 A B) C) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 C)))  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k7_scmfsa_2 A B) C) A) = (k2_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k7_scmfsa_2 A B) C) D) = (k1_funct_1 C D)) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k7_scmfsa_2 A B) C) D) (k18_scmfsa_2 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~ (r4_scmfsa7b C D))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) E)) (k2_afinsq_1 C)) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) (k2_nat_1 E 1)) D) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) E) D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r4_scmfsa7b C D))  &  ( (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers))  &  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 E) &  ((v5_funct_1 E (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 E (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  (~  ((r8_pboole (u1_struct_0 k1_scmfsa_2) E (k1_scmfsa_m B)) &  ((r8_pboole k5_numbers F (k1_funct_4 A (k1_scmfsa8c (k1_scmfsa8b D (k1_scmfsa8a 2) (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))))))) &  ( (G = (k2_nat_1 (k8_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A (k1_scmfsa8b D (k1_scmfsa8a 2) (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))))) (k1_scmfsa_m B)) 1))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F E G) D) = (k6_xcmplx_0 (k1_funct_1 B D) 1))  &  ( ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F E G) (k4_scmfsa_2 k6_numbers)) = 1)  &  ( (! [H:$i] :  ( ((v1_ami_2 H) &  ( (~ (v1_scmfsa_m H))  & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2))) )  =>  ( (~  (H = D) )  =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F E G) H) = (k1_funct_1 (k1_scmfsa6b C B A) H)) ) ) )  &  ( (! [H:$i] :  ((m1_scmfsa_2 H) =>  ((k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F E G) H) = (k18_scmfsa_2 (k1_scmfsa6b C B A) H)) ) )  &  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F E G)) = k6_numbers)  &  (! [H:$i] :  ((m2_subset_1 H k1_numbers k5_numbers) =>  ((r1_xxreal_0 H G) => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F E H)) (k9_xtuple_0 (k1_scmfsa8c (k1_scmfsa8b D (k1_scmfsa8a 2) (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers)))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_scmpds_2,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmpds_2)) =>  (~  ( (? [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  &  ((k1_funct_1 (k2_extpro_1 2 k1_scmpds_2 A B) (k4_struct_0 k1_scmpds_2)) = (k4_card_1 (k5_memstr_0 2 k1_scmpds_2 B))) ) )  & (v2_extpro_1 A 2 k1_scmpds_2)) ) ) ) ).
tt(t64_scmpds_6,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmpds_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 2 k1_scmpds_2)) & (v1_partfun1 B (u1_struct_0 k1_scmpds_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (! [E:$i] :  ( ((v1_ami_2 E) & (m1_subset_1 E (u1_struct_0 k1_scmpds_2)))  =>  (! [F:$i] :  ((v1_int_1 F) =>  ( ((k1_funct_1 B (k2_scmpds_2 (k1_funct_1 B D) F)) = k6_numbers)  =>  ((k1_funct_1 (k6_scmpds_4 (k6_scmpds_6 D F C) (k8_memstr_0 2 k1_scmpds_2 B) A) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((v9_scmyciel B A) & (m1_subset_1 B (k1_zfmisc_1 (k3_tarski A))))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((v9_scmyciel C A) & (m1_subset_1 C (k1_zfmisc_1 (k3_tarski A)))) ) ) ) ) ) ) ).
tt(t64_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r3_semi_af1 A B C B C)) ) ) ) ) ) ).
tt(t64_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ( ((k18_seq_4 A B) = (k18_seq_4 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t64_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v2_prob_1 B) =>  ((v3_kurato_0 B A) &  ((k4_kurato_0 A B) = (k3_prob_1 A B)) ) ) ) ) ) ).
tt(t64_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v3_kurato_0 B A) =>  ((k3_kurato_0 A (k3_setlim_2 A C B)) = (k7_subset_1 A (k3_kurato_0 A C) (k3_kurato_0 A B))) ) ) ) ) ) ) ).
tt(t64_sf_mastr,ax, (! [A:$i] :  ((m1_subset_1 A (u1_compos_1 k1_scmfsa_2)) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ( ((k5_relat_1 B (k1_sf_mastr A)) = (k5_relat_1 C (k1_sf_mastr A)))  &  ( ((k5_relat_1 B (k3_sf_mastr A)) = (k5_relat_1 C (k3_sf_mastr A)))  &  ((k5_memstr_0 3 k1_scmfsa_2 B) = (k5_memstr_0 3 k1_scmfsa_2 C)) ) )  =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 A B)) = (k5_memstr_0 3 k1_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 A C)))  &  ( ((k5_relat_1 (k2_extpro_1 3 k1_scmfsa_2 A B) (k1_sf_mastr A)) = (k5_relat_1 (k2_extpro_1 3 k1_scmfsa_2 A C) (k1_sf_mastr A)))  &  ((k5_relat_1 (k2_extpro_1 3 k1_scmfsa_2 A B) (k3_sf_mastr A)) = (k5_relat_1 (k2_extpro_1 3 k1_scmfsa_2 A C) (k3_sf_mastr A))) ) ) ) ) ) ) ) ) ) ).
tt(t64_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C C)) (k5_sheffer1 A B (k5_sheffer1 A D (k5_sheffer1 A B (k5_sheffer1 A C C))))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D C)) (k5_sheffer1 A B (k5_sheffer1 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t64_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ((k2_struct_0 (k11_simplex0 A C D B)) = (k2_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t64_sincos10,ax, ((k3_relat_1 (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) k4_sincos10) = (k1_partfun2 k1_numbers (k4_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(t64_sin_cos6,ax, ((k3_relat_1 k1_sin_cos6 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) = (k6_partfun1 (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t64_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (A = (k11_binop_2 (k18_binop_2 1 2) (k9_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B)))))  &  ((r1_xxreal_0 1 A) &  ( (~  (B = (k6_power k8_power (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1))))) )  &  (~  (B = (k7_binop_2 (k6_power k8_power (k9_binop_2 A (k7_square_1 (k10_binop_2 (k3_square_1 A) 1)))))) ) ) ) ) ) ) ) ) ) ).
tt(t64_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((r1_xxreal_0 (k10_real_1 k32_sin_cos 4) (k6_sin_cos9 A)) & (r1_xxreal_0 (k6_sin_cos9 A) (k8_real_1 (k10_real_1 3 4) k32_sin_cos))) ) ) ) ).
tt(t64_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k16_sin_cos A) &  ((k1_fdiff_1 k16_sin_cos A) = (k1_seq_1 k19_sin_cos A)) ) ) ) ).
tt(t64_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k10_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k10_pscomp_1 A)) ) ) ).
tt(t64_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k24_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k24_pscomp_1 (k3_topreal1 2 A)) = (k13_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k13_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k13_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t64_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k22_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t64_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 k5_numbers)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_finset_1 (k2_relset_1 B D)) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A C) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A C)))) )  =>  (! [G:$i] :  ( ((v1_relat_1 G) & (v1_funct_1 G))  =>  (! [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  =>  ( ((v2_funct_1 G) &  ((v2_funct_1 H) &  ( ((k2_relset_1 C E) = (k2_relset_1 C F))  &  ( ((k2_relset_1 C E) = (k9_xtuple_0 G))  &  ( ((k9_xtuple_0 G) = (k9_xtuple_0 H))  &  ( (D = (k3_relat_1 E G))  &  ( (D = (k3_relat_1 F H))  &  ((v2_stirl2_1 E A C) & (v2_stirl2_1 F A C)) ) ) ) ) ) ) )  =>  ( (G = H)  & (r2_funct_2 A C E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m1_subset_1 G D) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D E (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A B))) => (r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D (k1_sublemma A D E (k12_sublemma A D C G)) (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) D (k1_sublemma A D F (k12_sublemma A D C G)) (k24_qc_lang1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v6_tops_1 C A) & (r1_tarski B C))  =>  ((k1_tops_1 A (k2_pre_topc A (k4_subset_1 (u1_struct_0 A) B C))) = C) ) ) ) ) ) ) ) ).
tt(t64_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) &  ((v2_tdlat_3 B) & (l1_pre_topc B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  => (v5_pre_topc C A B)) ) ) ) ) ) ).
tt(t64_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_tex_3 B A) & (m1_pre_topc B A)) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_tex_2 C A) &  ((v2_tex_3 C A) & (m1_pre_topc C A)) ) ) )  & (r4_tsep_2 A B C)) ) ) ) ) ) ).
tt(t64_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v4_pre_topc B A) | (v4_pre_topc C A))  =>  ((k3_tex_4 A (k9_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k3_tex_4 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ) ).
tt(t64_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 B) (u1_struct_0 C)) &  ((v5_pre_topc E B C) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C))))) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ((v1_funct_1 (k2_tmap_1 A B F D)) &  ((v1_funct_2 (k2_tmap_1 A B F D) (u1_struct_0 D) (u1_struct_0 B)) &  ((v5_pre_topc (k2_tmap_1 A B F D) D B) & (m1_subset_1 (k2_tmap_1 A B F D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) ) )  =>  ((v1_funct_1 (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F E) D)) &  ((v1_funct_2 (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F E) D) (u1_struct_0 D) (u1_struct_0 C)) &  ((v5_pre_topc (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F E) D) D C) & (m1_subset_1 (k2_tmap_1 A C (k1_partfun1 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 B) (u1_struct_0 C) F E) D) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 C))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_topalg_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_borsuk_2 D (k15_euclid A) B C) =>  (! [E:$i] :  ((m1_borsuk_2 E (k15_euclid A) B C) => (m1_borsuk_6 (k7_topalg_1 A D E) (k15_euclid A) B C D E)) ) ) ) ) ) ) ) ) ) ).
tt(t64_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v2_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (r1_tarski B (k5_topgen_4 A))) ) ) ) ).
tt(t64_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ( ((v1_xreal_0 D) & (v2_xxreal_0 D))  =>  (~  ((r1_xxreal_0 k6_numbers C) &  ( (~ (r1_xxreal_0 1 C))  &  ( (~ (r1_xxreal_0 (k12_euclid (k5_algstr_0 (k15_euclid 2) A (k19_euclid B (k3_xcmplx_0 D C)))) (k3_xcmplx_0 D C)))  & (r1_xxreal_0 (k1_funct_1 (k4_topgen_5 B D) A) C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_metric_1 A))  =>  ((v5_tbsp_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (v6_tbsp_1 B A)) ) ) ) ) ).
tt(t64_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v6_tops_1 B A) =>  ( ((k2_tops_1 A B) = (k2_tops_1 A (k2_pre_topc A B)))  &  ((k2_tops_1 A (k2_pre_topc A B)) = (k7_subset_1 (u1_struct_0 A) (k2_pre_topc A B) B)) ) ) ) ) ) ) ).
tt(t64_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tops_2 B A) <=> (r1_tarski B (u1_pre_topc A))) ) ) ) ) ).
tt(t64_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  (D = E) ) )  =>  ( ((v1_tops_3 C A) & (v1_tops_3 E B))  <=> (v1_tops_3 D A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v6_transgeo B A) <=>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r2_analoaf A C D (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B C) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 A) B D))) ) ) ) ) ) ) ) ) ).
tt(t64_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ( ((k12_trees_3 A) = (k12_trees_3 B))  =>  (A = B) ) ) ) ) ) ).
tt(t64_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_borsuk_1 C A) & (m1_pre_topc C A)) )  =>  ((r1_tsep_1 B C) <=> (r3_tsep_1 A B C)) ) ) ) ) ) ) ).
tt(t64_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) &  ((v1_partfun1 B (u1_struct_0 A)) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 A)) &  ((v1_funct_1 C) &  ((v1_partfun1 C (u1_struct_0 A)) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) (k10_uproots A (k11_pre_poly (u1_struct_0 A) B C)) (k13_polynom3 A (k10_uproots A B) (k10_uproots A C)))) ) ) ) ) ) ).
tt(t64_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  => (r2_relset_1 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 (k2_valued_2 (k1_valued_2 B)))) (k16_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k58_valued_2 A B C D)) (k52_valued_2 A (k2_valued_2 (k1_valued_2 B)) (k16_valued_2 A B C) D))) ) ) ) ) ) ) ).
tt(t64_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (~  ( ((k3_vectsp_4 A B C E) = (k3_vectsp_4 A B D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r1_struct_0 E F) &  ((k3_rlvect_1 B C F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_waybel_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  ( ( (~ (v1_xboole_0 B))  &  ((v1_waybel_0 B A) &  ((v12_waybel_0 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  <=> (v6_yellow_0 (k5_yellow_0 A B) A)) ) ) ) ) ).
tt(t64_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (v5_waybel_1 (k4_waybel_1 A B) A A)) )  <=>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_4_waybel_1 A B C))) ) ) ) ) ) ) ) ).
tt(t64_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ((v4_waybel_1 (k3_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A) & (v5_waybel_1 (k5_waybel23 A B) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A)) ) ) ) ) ).
tt(t64_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v20_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D A) &  ((v6_yellow_0 D A) & (m1_yellow_0 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E B) &  ((v6_yellow_0 E B) & (m1_yellow_0 E B)) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( (F = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D)))  => (v20_waybel_0 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((r1_tarski A B) &  ((r1_tarski C D) & (r1_xboole_0 B D)) )  => (r1_xboole_0 A C)) ) ) ) ) ).
tt(t64_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k4_xboolean A (k8_xboolean B C)) = (k5_xboolean (k4_xboolean A (k3_xboolean B)) (k4_xboolean A (k3_xboolean C)))) ) ) ) ) ) ) ).
tt(t64_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 (k2_xcmplx_0 A A) 2) = A) ) ) ).
tt(t64_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 k6_numbers C))  => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ).
tt(t64_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k2_xxreal_1 A B) (k4_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ( (~ (r1_xxreal_0 A C))  & (r1_xxreal_0 B D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  ( (! [C:$i] :  ((v1_xxreal_0 C) =>  (~  ((r2_hidden C B) &  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ((r2_hidden D A) & (r1_xxreal_0 D C)) ) ) ) ) ) ) )  => (r1_xxreal_0 (k2_xxreal_2 A) (k2_xxreal_2 B))) ) ) ) ) ).
tt(t64_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  (~  ( (~ (r1_xxreal_0 B A))  &  ( (~ (r1_xxreal_0 D C))  & (r1_xxreal_0 (k1_xxreal_3 B D) (k1_xxreal_3 A C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t64_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_yellow_0 A C) & (r2_hidden (k1_yellow_0 A C) (u1_struct_0 B)))  =>  ((r1_yellow_0 B C) &  ((k1_yellow_0 B C) = (k1_yellow_0 A C)) ) ) ) ) ) ) ) ) ).
tt(t64_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v3_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v3_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v10_waybel_1 (k3_yellow_3 A B)) =>  ((v10_waybel_1 A) & (v10_waybel_1 B)) ) ) ) ) ) ).
tt(t64_yellow_4,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_waybel_0 A (k4_yellow_4 A (k4_waybel_0 A B) (k4_waybel_0 A C))) = (k4_waybel_0 A (k4_yellow_4 A B C))) ) ) ) ) ) ) ).
tt(t64_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_yellow_5 A B B) = (k3_yellow_0 A)) ) ) ) ) ).
tt(t64_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k2_zf_model (k11_zf_lang A B)) = (k4_subset_1 k1_zf_lang (k2_zf_model A) (k2_zf_model B))) ) ) ) ) ).
tt(t64_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r3_zf_lang A B) & (r3_zf_lang B C))  => (r3_zf_lang A C)) ) ) ) ) ) ) ).
tt(t64_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_xboole_0 (k2_tarski A B) C) = k1_xboole_0)  <=>  ((r2_hidden A C) & (r2_hidden B C)) ) ) ) ) ).
tt(t64_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r1_struct_0 D B) =>  ((k5_zmodul01 A (k1_zmodul01 A B C) D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t65_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_abcmiz_0 A))) =>  (~  ((r6_abcmiz_0 A B C) &  (! [D:$i] :  ( ((v2_funct_1 D) & (m2_finseq_1 D (u1_abcmiz_0 A)))  =>  (~  ( ((k2_relset_1 (u1_abcmiz_0 A) D) = C)  & (r5_abcmiz_0 A B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v6_abcmiz_1 B A) &  ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A))) )  =>  (? [C:$i] :  ( ((v2_abcmiz_1 C A) & (m1_subset_1 C (u4_struct_0 A)))  &  ( ((k2_msualg_1 A C) = (k13_abcmiz_1 A))  &  (? [D:$i] :  ((m1_trees_4 D (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) &  ( ((k3_finseq_1 D) = (k3_finseq_1 (k1_msualg_1 A C)))  &  (B = (k36_abcmiz_1 A C D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((v1_aff_4 C A) &  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r2_hidden B D) &  ((r1_aff_4 A C D) & (v1_aff_4 D A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  & (v1_afinsq_1 A)) ) ) )  => (r2_hidden k6_numbers (k9_xtuple_0 A))) ) ).
tt(t65_afinsq_2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) &  ((v1_valued_0 B) & (v1_finset_1 B)) ) ) )  =>  ((r2_hidden A (k1_relset_1 k5_numbers B)) =>  ((k3_binop_2 (k7_afinsq_2 (k5_relat_1 B A)) (k1_funct_1 B A)) = (k7_afinsq_2 (k5_relat_1 B (k23_binop_2 A 1)))) ) ) ) ) ) ).
tt(t65_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((r10_analmetr A B C) & (r10_analmetr A D C))  => (r9_analmetr A B D)) ) ) ) ) ) ) ) ) ).
tt(t65_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ( ((k14_aofa_000 (k7_freealg k19_aofa_000 A) B D E) = (k14_aofa_000 (k7_freealg k19_aofa_000 A) C F G))  =>  ( (B = C)  &  ( (D = F)  &  (E = G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [I:$i] :  ((m2_subset_1 I k1_numbers k5_numbers) =>  (! [J:$i] :  ((m2_subset_1 J k1_numbers k5_numbers) =>  ( ( (I = (k21_aofa_i00 B k4_numbers H E))  &  (J = (k21_aofa_i00 B k4_numbers H F)) )  =>  ((r1_xxreal_0 I k6_numbers) |  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k16_aofa_000 A (k78_aofa_i00 A B C D F k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k13_aofa_000 A (k47_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k32_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E) (k42_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F))) (k15_aofa_000 A (k79_aofa_i00 A B C D G k6_numbers) (k58_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G (k4_xcmplx_0 1)))) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E F)) (k48_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F G)))) E) = (k6_nat_d I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  ((r3_arytm_3 A k11_arytm_3) =>  (A = k11_arytm_3) ) ) ) ).
tt(t65_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 4 A) & (r1_xxreal_0 (k5_series_1 2 A) (k2_nat_1 (k4_nat_1 2 A) 3))) ) ) ) ).
tt(t65_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A (k1_bcialg_1 A B C) (k1_bcialg_1 A D C)) = (k1_bcialg_1 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t65_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A (k3_boolealg A B C) D) (k3_lattices A (k1_boolealg A B (k3_lattices A C D)) (k1_boolealg A C (k3_lattices A B D))))) ) ) ) ) ) ) ) ).
tt(t65_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( (A = (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k4_rcomp_1 B C)))  =>  ((r1_xxreal_0 C B) |  ((k2_pre_topc k3_topmetr A) = (k4_rcomp_1 k2_xxreal_0 C)) ) ) ) ) ) ) ) ) ).
tt(t65_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) => (r2_hidden (k4_tarski A 1) k7_borsuk_6)) ) ).
tt(t65_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid A))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 (k15_euclid A))) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 (k15_euclid A))) =>  (! [G:$i] :  ( ((v1_xreal_0 G) & (v2_xxreal_0 G))  =>  ( ((r1_borsuk_7 A (k4_struct_0 (k15_euclid A)) C D 1) &  ( (E = (k1_funct_1 (k11_borsuk_7 A B G) C))  &  (F = (k1_funct_1 (k11_borsuk_7 A B G) D)) ) )  => (r1_borsuk_7 A B E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k7_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  (! [L:$i] :  ((m1_subset_1 L A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k6_enumset1 C D E F G H I J))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (C = I) )  &  ( (~  (C = J) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (D = I) )  &  ( (~  (D = J) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (E = I) )  &  ( (~  (E = J) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (F = I) )  &  ( (~  (F = J) )  &  ( (~  (G = H) )  &  ( (~  (G = I) )  &  ( (~  (G = J) )  &  ( (~  (H = I) )  &  ( (~  (H = J) )  &  ( (~  (I = J) )  &  ((k9_subset_1 A (k15_bvfunc_1 A L (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H) I) J)) (k15_bvfunc_1 A K C)) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ( (A = k8_margrel1)  &  ((k6_xboolean A B) = k8_margrel1) )  =>  (B = k8_margrel1) ) ) ) ) ) ).
tt(t65_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k10_bvfunc_1 A B (k6_bvfunc26 A C D)) (k2_bvfunc_1 A (k5_bvfunc_1 A (k5_bvfunc_1 A B C) D) (k5_bvfunc_1 A (k1_bvfunc_1 A B) (k1_bvfunc_1 A (k5_bvfunc_1 A C D)))))) ) ) ) ) ) ) ) ).
tt(t65_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_finseq_1 B (k3_cqc_lang A)) =>  (~  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r2_hidden C (k3_calcul_1 A B))) ) ) ) ) ) ) ).
tt(t65_card_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v3_card_1 B 1) & (m1_subset_1 B (k1_zfmisc_1 A)))  =>  (? [C:$i] :  ((m1_subset_1 C A) &  (B = (k1_tarski C)) ) ) ) ) ) ) ).
tt(t65_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k6_card_3 (k7_funcop_1 A B)) = (k2_card_2 A B)) ) ) ) ) ).
tt(t65_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r2_hidden A (k8_card_3 B)) => (r2_hidden (k5_relat_1 A C) (k8_card_3 B))) ) ) ) ) ) ).
tt(t65_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ( ( (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A E)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D E))) ) )  &  ( (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  ( ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k3_graph_1 A E)) = (k3_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E)))  &  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) D (k4_graph_1 A E)) = (k4_graph_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E))) ) ) )  &  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 A)) =>  ( ((k3_graph_1 A F) = (k4_graph_1 A E))  =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k1_cat_1 A E F)) = (k1_cat_1 B (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C E) (k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C F))) ) ) ) ) ) ) )  => (m2_cat_1 C A B)) ) ) ) ) ) ) ) ) ).
tt(t65_cat_3,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v11_struct_0 C))  &  ((v2_cat_1 C) &  ((v3_cat_1 C) &  ((v4_cat_1 C) &  ((v5_cat_1 C) &  ((v6_cat_1 C) & (l1_cat_1 C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (u4_struct_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (u4_struct_0 C)) =>  ( ( ((k4_graph_1 C E) = D)  &  ((k4_graph_1 C F) = D) )  => (m2_cat_3 (k5_funct_4 (u4_struct_0 C) A B E F) C D (k2_tarski A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C B) = k1_xboole_0) )  &  (~  ((v2_cat_3 (k25_cat_4 A B C) A B (k20_cat_4 A B C)) & (v2_cat_3 (k26_cat_4 A B C) A C (k20_cat_4 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ((m1_subset_1 D k2_numbers) =>  ((v1_partfun1 C A) =>  ((k7_partfun1 k2_numbers (k25_valued_1 A k2_numbers C D) B) = (k9_complex1 D (k7_partfun1 k2_numbers C B))) ) ) ) ) ) ) ) ) ) ).
tt(t65_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  ( (~ (r1_xxreal_0 A B))  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C A))) => (m3_chain_1 D B C A)) ) ) ) ) ) ) ) ) ).
tt(t65_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v4_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) => (v3_chord B A)) ) ) ) ).
tt(t65_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r1_tarski A (k4_classes1 B)) <=> (r1_ordinal1 (k6_classes1 A) B)) ) ) ) ).
tt(t65_classes2,ax, ((k16_classes2 k1_xboole_0) = k13_classes2) ).
tt(t65_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k5_clvect_1 A B (k4_clvect_1 A)) = (u1_struct_0 A)) ) ) ) ) ).
tt(t65_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((v1_clvect_2 B A) => (v2_clvect_2 B A)) ) ) ) ) ).
tt(t65_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  ((r2_hidden B (k13_cohsp_1 A)) <=>  ((r1_tarski B (k3_tarski A)) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (? [D:$i] : (r1_tarski (k3_xboole_0 B C) (k1_tarski D))) ) ) ) ) ) ) ) ).
tt(t65_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k17_complex1 (k3_xcmplx_0 A B)) = (k8_real_1 (k17_complex1 A) (k17_complex1 B))) ) ) ) ) ).
tt(t65_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_complex2 A B) = (k3_complex2 (k2_complex2 A C) (k2_complex2 B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) => (r1_xxreal_0 (k10_binop_2 (k17_complex1 A) (k17_complex1 B)) (k17_complex1 (k5_algstr_0 k1_complfld A B)))) ) ) ) ).
tt(t65_complsp2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k6_complsp2 (k12_seq_4 B A)) = (k8_rvsum_1 (k10_rvsum_1 (k6_complsp2 B) (k3_complex1 A)) (k10_rvsum_1 (k7_complsp2 B) (k4_complex1 A))))  &  ((k7_complsp2 (k12_seq_4 B A)) = (k4_rvsum_1 (k10_rvsum_1 (k6_complsp2 B) (k4_complex1 A)) (k10_rvsum_1 (k7_complsp2 B) (k3_complex1 A)))) ) ) ) ) ) ).
tt(t65_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 C)) =>  ((k1_funct_1 (k61_valued_1 (k10_compos_1 B C) A) (k2_xcmplx_0 D A)) = (k1_funct_1 (k61_valued_1 C A) (k2_xcmplx_0 D A))) ) ) ) ) ) ) ) ) ) ).
tt(t65_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 A (k2_nat_1 (k19_margrel1 B) 1)))  =>  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  ((r1_comput_1 D B C A) =>  (D = (k7_comput_1 B C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((k8_nat_1 k2_numbers A (k2_nat_1 C 1)) = (k9_complex1 B (k8_nat_1 k2_numbers A C))) ) )  =>  ((r1_xxreal_0 1 (k17_complex1 B)) |  ((v1_comseq_3 A) &  ((k11_comseq_3 A) = (k13_complex1 (k8_nat_1 k2_numbers A k6_numbers) (k11_complex1 k6_complex1 B))) ) ) ) ) ) ) ) ).
tt(t65_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k6_rusub_4 A B (k6_domain_1 (u1_struct_0 A) (k4_struct_0 A))) = B) ) ) ) ) ).
tt(t65_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  ( ((v2_cqc_the1 B A) & (v2_cqc_the1 (k8_cqc_lang A B C) A))  => (v2_cqc_the1 C A)) ) ) ) ) ) ) ).
tt(t65_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k7_cqc_lang A B C)) (k7_cqc_lang A (k11_cqc_lang A D B) C)) A)) ) ) ) ) ) ) ) ).
tt(t65_cqc_the3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_qc_lang1 A)) =>  (! [E:$i] :  ((m2_subset_1 E (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [F:$i] :  ((m2_subset_1 F (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ( (B = (k13_cqc_lang A D E))  &  (C = (k13_cqc_lang A D F)) )  =>  ((r2_hidden E (k24_qc_lang1 A D)) |  ((r2_hidden F (k24_qc_lang1 A D)) | (r7_cqc_the3 A (k11_cqc_lang A E B) (k11_cqc_lang A F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_csspace,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k5_bhsp_1 A B (k4_struct_0 A)))) ) ) ) ).
tt(t65_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k9_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k19_sin_cos) A B) = (k10_real_1 (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k21_sin_cos (k10_real_1 (k7_real_1 A B) 2)) (k18_sin_cos (k10_real_1 (k9_real_1 A B) 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k8_real_1 3 (k7_real_1 A B)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 (k9_real_1 A B)) 2))))) (k9_real_1 A B))) ) ) ) ) ).
tt(t65_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k21_sin_cos D))) ) )  =>  ( (A = B)  |  ( ((k21_sin_cos A) = k6_numbers)  |  ( ((k21_sin_cos B) = k6_numbers)  |  ((k9_diff_1 C A B) = (k10_real_1 (k10_real_1 (k8_real_1 2 (k9_real_1 (k21_sin_cos B) (k21_sin_cos A))) (k7_real_1 (k21_sin_cos (k7_real_1 A B)) (k21_sin_cos (k9_real_1 A B)))) (k9_real_1 A B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) => (r2_funct_2 (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A)) (k12_cat_2 (k2_oppcat_1 B) B (k11_ens_1 A) (k25_ens_1 A B) (k3_oppcat_1 B C)) (k23_ens_1 A B C))) ) ) ) ) ) ) ).
tt(t65_entropy1,ax, (! [A:$i] :  ( ((v1_matrprob A) & (m2_finseq_1 A k1_numbers))  =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v6_matrprob B) & (m2_finseq_1 B (k3_finseq_2 k1_numbers))) ) )  =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k7_entropy1 (k6_matrixr1 (k1_entropy1 A) B)) = (k7_real_1 (k6_entropy1 A) (k18_rvsum_1 (k14_rvsum_1 A (k8_entropy1 B))))) ) ) ) ) ) ).
tt(t65_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 B A C D)) ) ) ) ) ).
tt(t65_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 A) B) =>  ((r2_hidden C D) =>  (D = (k3_funct_2 A B (k13_eqrel_1 A B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t65_euclid_8,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  ((k12_euclid A) = (k7_square_1 (k9_binop_2 (k9_binop_2 (k5_square_1 (k1_seq_1 A 1)) (k5_square_1 (k1_seq_1 A 2))) (k5_square_1 (k1_seq_1 A 3))))) ) ) ).
tt(t65_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v3_valued_0 D)) )  =>  ( (C = D)  =>  ((k1_rlvect_1 (k15_euclid A) C B) = (k24_valued_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t65_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ( ((v1_euclid_4 B A) &  (B = C) )  => (r5_euclidlp A B C)) ) ) ) ) ) ) ).
tt(t65_exchsort,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v16_waybel_0 B) & (l1_orders_2 B)) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v5_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v1_exchsort C)) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 C)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 C)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 C)) =>  ( ((r2_hidden D E) &  (A = (k5_exchsort (k9_xtuple_0 C) (k9_xtuple_0 C) (k6_partfun1 (k9_xtuple_0 C)) F D)) )  =>  ( ((k1_binop_1 (k7_exchsort B C F D) F E) = (k4_tarski (k1_funct_1 A F) (k1_funct_1 A E)))  &  ((k1_binop_1 (k7_exchsort B C F D) D E) = (k4_tarski (k1_funct_1 A D) (k1_funct_1 A E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k2_facirc_1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A k2_facirc_1) (k10_facirc_1 B C A k2_facirc_1)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  ( (F = (k1_funct_1 D C))  &  (G = (k1_funct_1 D A)) ) )  =>  ((k11_facirc_1 (k8_facirc_1 B C A k2_facirc_1) (k10_facirc_1 B C A k2_facirc_1) (k5_facirc_1 (k8_facirc_1 B C A k2_facirc_1) (k10_facirc_1 B C A k2_facirc_1) D 2) (k9_facirc_1 B C A k2_facirc_1)) = (k1_binarith (k1_binarith E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)))) &  ((r2_relset_1 k1_numbers k1_numbers B (k1_taylor_1 2)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) C))) ) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k1_sin_cos9)) A) C) = (k9_real_1 (k8_real_1 (k8_real_1 2 C) (k1_seq_1 k1_sin_cos9 (k10_real_1 1 C))) (k10_real_1 (k5_square_1 C) (k7_real_1 1 (k5_square_1 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  ((k18_rvsum_1 (k5_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 2))) = (k6_xcmplx_0 (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 3)) 1)) ) ) ).
tt(t65_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  => (r3_relat_2 (k8_filter_0 A B) (u1_struct_0 A))) ) ) ) ).
tt(t65_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v14_lattices A) => (r1_filter_2 (u1_struct_0 A) (k2_filter_0 A B) (k9_filter_2 A B (k6_lattices A)))) ) ) ) ) ).
tt(t65_finseq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 1 C) & (r1_xxreal_0 C (k3_finseq_1 B)))  =>  ((k1_funct_1 (k7_finseq_1 A B) (k2_nat_1 (k3_finseq_1 A) C)) = (k1_funct_1 B C)) ) ) ) ) ) ) ) ).
tt(t65_finseq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 A) (k10_xtuple_0 B)) (k9_xtuple_0 D)) &  (C = (k3_funcop_1 D A B)) )  =>  ((k3_finseq_1 C) = (k3_xxreal_0 (k3_finseq_1 A) (k3_finseq_1 B))) ) ) ) ) ) ) ) ) ) ).
tt(t65_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ((k10_xtuple_0 (k1_finseq_3 A B)) = (k6_subset_1 (k10_xtuple_0 A) B)) ) ) ) ).
tt(t65_finseq_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (~  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) &  ( (~  (A = k1_xboole_0) )  &  (! [D:$i] :  (! [E:$i] :  (~  ((r2_hidden D B) &  ((r2_hidden E B) &  ( (~  (D = E) )  &  ((k1_funct_1 C D) = (k1_funct_1 C E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  ( (~ (v1_xboole_0 B))  =>  ( ((k7_partfun1 A B 1) = (k7_partfun1 A (k4_finseq_5 A B) (k3_finseq_1 B)))  &  ((k7_partfun1 A B (k3_finseq_1 B)) = (k7_partfun1 A (k4_finseq_5 A B) 1)) ) ) ) ) ) ) ).
tt(t65_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 C) (k10_xtuple_0 D))) =>  ((k2_finseq_5 A (k8_finseq_1 A D C) B) = (k2_finseq_5 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t65_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v1_setwiseo D A) &  ((v2_binop_1 D A) & (v1_finseqop D A)) )  =>  ( ( (~  ((k5_binop_1 A D B C) = C) )  &  (~  ((k5_binop_1 A D C B) = C) ) )  |  (B = (k4_binop_1 A D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) => (r1_tarski (k7_flang_1 A (k8_flang_1 A B) C) (k8_flang_1 A B))) ) ) ) ) ).
tt(t65_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((r1_tarski B (k8_flang_1 A C)) =>  ((k8_flang_1 A C) = (k8_flang_1 A (k4_subset_1 (k8_afinsq_1 A) C (k1_flang_2 A B D E)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((k2_flang_2 A (k2_flang_3 A B)) = (k8_flang_1 A B))  &  ((k2_flang_3 A (k2_flang_2 A B)) = (k8_flang_1 A B)) ) ) ) ) ).
tt(t65_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v7_fsm_1 C A B) & (l2_fsm_1 C A B)) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) )  =>  ((r4_fsm_1 A B C D) => (r7_fsm_1 A B (k11_fsm_1 A B C) (k11_fsm_1 A B D))) ) ) ) ) ) ) ) ) ).
tt(t65_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E B A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((v1_binop_1 C A) => (r2_funct_2 B A (k6_funcop_1 A B C D E) (k6_funcop_1 A B C E D))) ) ) ) ) ) ) ) ) ) ).
tt(t65_funct_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  ( (! [B:$i] :  (! [C:$i] :  ((k7_relat_1 A (k6_subset_1 B C)) = (k6_subset_1 (k7_relat_1 A B) (k7_relat_1 A C))) ) )  => (v2_funct_1 A)) ) ) ).
tt(t65_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  (~  ((r2_hidden E (k7_relset_1 A B D C)) &  (! [F:$i] :  ((m1_subset_1 F A) =>  (~  ((r2_hidden F C) &  (E = (k1_funct_1 D F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  (! [D:$i] :  ((r2_hidden (k4_tarski C D) (k2_zfmisc_1 (k9_xtuple_0 A) (k9_xtuple_0 B))) =>  ((k1_binop_1 (k15_funct_3 A B) C D) = (k4_tarski (k1_funct_1 A C) (k1_funct_1 B D))) ) ) ) ) ) ) ) ).
tt(t65_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((k4_funct_4 A B C C) = (k7_funcop_1 (k2_tarski A B) C)) ) ) ) ).
tt(t65_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((r2_wellord2 (k9_funct_2 C (k2_tarski A B)) (k1_zfmisc_1 C)) &  ((k1_card_1 (k9_funct_2 C (k2_tarski A B))) = (k1_card_1 (k1_zfmisc_1 C))) ) ) ) ) ) ).
tt(t65_funct_7,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v1_finseq_1 C) & (v1_funct_7 C)) ) )  =>  ( ((r2_hidden A (k6_funct_7 C)) & (r2_hidden A B))  =>  ((k1_funct_1 (k5_funct_7 C A) (k2_nat_1 (k3_finseq_1 C) 1)) = (k1_funct_1 (k4_funct_7 B C) A)) ) ) ) ) ) ).
tt(t65_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_funct_8 A k1_numbers k1_numbers k16_sin_cos)) ) ).
tt(t65_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  ( ((v3_fvaluat1 A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B)))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r2_hidden D (k9_fvaluat1 A B C)) <=>  ((r2_hidden D C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r2_hidden E C) => (r1_xxreal_0 (k3_funct_2 (u1_struct_0 A) k7_numbers B D) (k3_funct_2 (u1_struct_0 A) k7_numbers B E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m2_finseq_2 C (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k12_fvsum_1 A B C (k12_fvsum_1 A B D E)) = (k12_fvsum_1 A B (k12_fvsum_1 A B C D) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k4_gfacirc1)) )  &  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_twoscomp)) )  &  ( (~  (B = (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) )  &  ( (~  (C = (k4_tarski (k10_finseq_1 A B) k3_gfacirc1)) )  &  (~  ((k2_msafree2 (k25_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ) ) ) ).
tt(t65_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 A)) =>  (~  ((r2_hidden B (k28_glib_000 A E)) &  ((r1_glib_000 A C D B) &  ( (~  (E = C) )  &  (~  (E = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r1_glib_000 A (k4_glib_001 A B) D C) =>  ( ((k1_funct_1 (k10_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) 1)) = C)  &  ( ((k1_funct_1 (k10_glib_001 A B C) (k2_nat_1 (k3_finseq_1 B) 2)) = D)  &  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  ((r2_hidden E (k1_relset_1 k5_numbers B)) =>  ((k1_funct_1 (k10_glib_001 A B C) E) = (k1_funct_1 B E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ( (~ (v3_relat_1 C))  &  ((v1_matrix_1 C) &  ((v2_goboard1 C) &  ((v3_goboard1 C) &  ((v4_goboard1 C) &  ((v5_goboard1 C) & (m2_finseq_1 C (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ( ((r1_xxreal_0 1 A) & (r1_xxreal_0 1 B))  =>  ((r1_xxreal_0 (k1_matrix_1 C) A) |  ((r1_xxreal_0 (k3_finseq_1 C) (k2_nat_1 B 1)) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C B A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) (k2_nat_1 A 1))) (k10_real_1 1 2)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 2) (k2_nat_1 A 1))) (k10_real_1 1 2))) (k2_xboole_0 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C B A)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 C (k2_nat_1 B 1) A))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) C (k2_nat_1 B 1) (k2_nat_1 A 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ) ) ).
tt(t65_graph_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v2_graph_1 D) &  ((v6_graph_1 D) & (l1_graph_1 D)) ) )  =>  (! [E:$i] :  ( ((v7_graph_1 E D) & (m2_graph_1 E D))  =>  (! [F:$i] :  ( ((v7_graph_1 F D) & (m2_graph_1 F D))  =>  (! [G:$i] :  ( ((v7_graph_1 G D) & (m2_graph_1 G D))  =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 D)) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 D)) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 D)) =>  ( ((r2_hidden A (u4_struct_0 D)) &  ((r5_graph_5 D C) &  ((r1_xxreal_0 1 (k3_finseq_1 E)) &  ((r8_graph_5 D H I E B C) &  ( (G = (k7_finseq_1 E (k9_finseq_1 A)))  &  ((r8_graph_5 D H J F B C) &  ((r1_graph_4 D I J A) & (r9_graph_5 D E B H C)) ) ) ) ) ) )  =>  ( (H = I)  |  ( (H = J)  |  ( ((r1_xxreal_0 (k10_graph_5 D F C) (k10_graph_5 D G C)) => (r8_graph_5 D H J F (k2_xboole_0 B (k1_tarski I)) C))  &  ((r1_xxreal_0 (k10_graph_5 D G C) (k10_graph_5 D F C)) => (r8_graph_5 D H J G (k2_xboole_0 B (k1_tarski I)) C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( (C = (k10_group_2 A D E))  => (r1_tarski (k9_subset_1 (u1_struct_0 A) (k3_group_11 A B D) (k3_group_11 A B E)) (k3_group_11 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (m1_group_2 (k6_group_2 A) B)) ) ) ) ).
tt(t65_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_group_2 C A) =>  ((v8_struct_0 C) <=> (v8_struct_0 (k6_group_3 A C B))) ) ) ) ) ) ) ).
tt(t65_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) => (m1_group_2 (k10_group_2 A B C) (k8_group_4 A B C))) ) ) ) ) ) ).
tt(t65_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( ((r1_struct_0 D B) & (r1_struct_0 E C))  => (r1_struct_0 (k8_group_5 A D E) (k2_group_5 A B C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v3_funct_2 (k8_group_6 A (k6_group_2 A)) (u1_struct_0 A) (u1_struct_0 (k5_group_6 A (k6_group_2 A))))) ) ).
tt(t65_group_9,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 B)) =>  ((r1_group_9 A B C E) => (r1_tarski (k7_relset_1 B B (k2_group_9 A B C D) E) E)) ) ) ) ) ) ) ) ) ).
tt(t65_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)))) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ( (C = (k3_vectsp_4 k1_complfld A E (k13_bilinear k1_complfld A A B)))  &  (D = (k3_vectsp_4 k1_complfld A F (k13_bilinear k1_complfld A A B))) )  =>  ((k2_binop_1 (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) (u1_struct_0 (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B))) (u1_struct_0 k1_complfld) (k8_hermitan A B) C D) = (k2_binop_1 (u1_struct_0 A) (u1_struct_0 A) (u1_struct_0 k1_complfld) B E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k41_valued_1 k1_numbers k1_numbers k16_sin_cos) A) 3) (k26_valued_1 k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k19_sin_cos k16_sin_cos) A) (k1_real_1 8)))) ) ).
tt(t65_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v7_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_ideal_1 A (k7_domain_1 (u1_struct_0 A) B C)) = (a_3_0_ideal_1 A B C)) ) ) ) ) ) ) ).
tt(t65_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 B A) => (r1_xxreal_0 (k2_int_1 B) A)) ) ) ) ) ).
tt(t65_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A B) &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C B) & (r1_xxreal_0 (k1_seq_1 k16_sin_cos C) k6_numbers)) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1))) &  ( (B = (k9_xtuple_0 k30_sin_cos))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers k30_sin_cos A))) ) ) )  =>  ((k2_integra5 A k30_sin_cos) = (k9_real_1 (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1) (k4_seq_4 A)) (k1_seq_1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k16_sin_cos k3_taylor_1) (k5_seq_4 A)))) ) ) ) ) ) ).
tt(t65_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  ( ( (B = (k1_rcomp_1 (k1_real_1 (k10_real_1 (k7_square_1 2) 2)) (k10_real_1 (k7_square_1 2) 2)))  &  ( ((k9_xtuple_0 (k2_fdiff_1 k4_sin_cos6 (k2_rcomp_1 (k1_real_1 1) 1))) = (k9_xtuple_0 A))  &  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C (k2_rcomp_1 (k1_real_1 1) 1)) &  ((k1_seq_1 A C) = (k1_real_1 (k10_real_1 1 (k7_square_1 (k9_real_1 1 (k5_square_1 C)))))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers A B))) ) )  =>  ((k2_integra5 B A) = (k1_real_1 (k10_real_1 k32_sin_cos 2))) ) ) ) ) ) ).
tt(t65_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k9_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3)))) = E)  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3)))) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_prepower (k9_real_1 A F) (k10_real_1 1 2))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3))) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 3 2))) (k1_real_1 (k10_real_1 2 3))) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  (! [D:$i] :  ((m2_interva1 D A) => (r2_interva1 A (k17_interva1 A (k17_interva1 A B C) D) (k17_interva1 A B (k17_interva1 A C D)))) ) ) ) ) ) ) ) ).
tt(t65_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 A (k5_intpro_1 B C)) (k5_intpro_1 (k5_intpro_1 A B) C)) k8_intpro_1)) ) ) ) ) ) ).
tt(t65_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C)) (u1_struct_0 (k1_pre_topc (k15_euclid 2) B)))))) )  =>  ( ( (D = (k2_partfun1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) C))  &  ( (B = (k8_struct_0 (k15_euclid 2)))  &  (C = a_0_3_jgraph_4) ) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (v5_pre_topc D (k1_pre_topc (k1_pre_topc (k15_euclid 2) B) C) (k1_pre_topc (k15_euclid 2) B))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 (k15_euclid 2))) =>  (! [I:$i] :  ((m1_subset_1 I (u1_struct_0 (k15_euclid 2))) =>  (! [J:$i] :  ((m1_subset_1 J (u1_struct_0 (k15_euclid 2))) =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [K:$i] :  ((m1_subset_1 K (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F K)) = (k12_euclid K)) ) )  &  ( (G = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( (H = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( (I = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ( (J = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid G)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid H)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid I)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid J)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid J)))  &  ((r1_jordan6 E G H) &  ((r1_jordan6 E H I) & (r1_jordan6 E I J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_compts_1 C (k15_euclid 2)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ( (C = (k5_jgraph_6 k6_numbers k6_numbers 1))  &  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) D k1_jgraph_3) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 1)) (k19_euclid (k1_real_1 1) 1))) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) & (r1_jordan6 (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1) A B)) ) ) )  => (r1_jordan6 C (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) D A) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) D B))) ) ) ) ) ) ) ) ) ).
tt(t65_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) D) & (r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)))) )  =>  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H))) |  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ( (~ (r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H))))  & (r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k7_real_1 (k7_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A))) (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A)))) = (k7_real_1 (k7_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))) (k9_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))))) ) ) ) ) ) ) ).
tt(t65_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_tarski A B) =>  ( ( (~ (r2_hidden (k18_pscomp_1 B) A))  &  (~ (r2_hidden (k19_pscomp_1 B) A)) )  |  ((k6_pscomp_1 A) = (k6_pscomp_1 B)) ) ) ) ) ) ) ).
tt(t65_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ((v2_compts_1 B (k15_euclid A)) => (v9_rltopsp1 B (k15_euclid A))) ) ) ) ) ).
tt(t65_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((k17_euclid (k11_jordan6 A)) = (k10_real_1 (k7_real_1 (k6_pscomp_1 A) (k8_pscomp_1 A)) 2)) ) ) ).
tt(t65_jordan,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  ((r2_hidden C (k1_topreal9 A B D)) =>  ((k2_partfun1 (u1_struct_0 (k1_pre_topc (k15_euclid A) (k7_subset_1 (u1_struct_0 (k15_euclid A)) (k2_topreal9 A B D) (k6_domain_1 (u1_struct_0 (k15_euclid A)) C)))) (u1_struct_0 (k7_toprealb A B D)) (k9_jordan A B C D) (k3_topreal9 A B D)) = (k6_partfun1 (k3_topreal9 A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t65_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v11_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u1_struct_0 C)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 C)) =>  ( (! [G:$i] :  ((m1_subset_1 G A) =>  ((r2_hidden G B) =>  ((k3_funct_2 A (u1_struct_0 C) D G) = (k4_lattices C F (k3_funct_2 A (u1_struct_0 C) E G))) ) ) )  =>  ((k4_lattices C F (k2_lattice2 A C B E)) = (k2_lattice2 A C B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 B (k15_glib_000 A)) =>  ((k5_card_1 (k1_relset_1 (k6_glib_000 A) (k7_lexbfs (k6_glib_000 A) k5_numbers (k9_funct_2 (k6_glib_000 A) k5_numbers) (k23_lexbfs A (k26_lexbfs A) B)))) = B) ) ) ) ) ) ).
tt(t65_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 C B))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k3_limfunc1 B)))) ) ) ) )  | (v5_limfunc1 A)) ) ) ) ).
tt(t65_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  ( ((k2_limfunc2 B A) = (k2_limfunc2 C A))  &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E A))  &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E F))  &  ( (~ (r1_xxreal_0 F A))  & (r2_hidden F (k1_relset_1 k1_numbers D))) ) ) ) ) ) ) ) ) ) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 A (k7_real_1 A E)))) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) )  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A E))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A E)))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 A (k7_real_1 A E))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A E)))))  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A E))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A E)))) & (r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers D) (k2_rcomp_1 A (k7_real_1 A E))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A E))))) ) ) ) ) ) )  |  ((r4_limfunc2 D A) &  ((k2_limfunc2 D A) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r1_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k4_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  |  ((v3_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k1_limfunc2 B (k4_limfunc1 A))) ) ) ) ) ) ) ) ).
tt(t65_lpspace2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_normsp_1 A) & (l1_normsp_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (~  ((v1_rsspace3 B A) &  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers k5_numbers) &  ((v5_valued_0 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)))) ) )  =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  (? [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) &  ((r1_xxreal_0 (k1_recdef_1 C D) E) & (r1_xxreal_0 (k4_power 2 (k1_real_1 D)) (k1_normsp_0 A (k5_algstr_0 A (k1_normsp_1 A B E) (k1_normsp_1 A B (k1_recdef_1 C D)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A D (k8_cqc_lang A B (k8_cqc_lang A B C))) => (r3_cqc_the1 A D (k8_cqc_lang A B C))) ) ) ) ) ) ) ) ) ).
tt(t65_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ( (~  (A = k6_numbers) )  =>  ((k6_mathmorp A (k15_euclid B) (k4_mathmorp (k15_euclid B) C D)) = (k4_mathmorp (k15_euclid B) (k6_mathmorp A (k15_euclid B) C) (k6_mathmorp A (k15_euclid B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t65_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((r2_matrix10 (k2_matrix10 A B) C) => (r2_matrix10 (k2_matrix10 A C) B)) ) ) ) ) ) ) ).
tt(t65_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ((k5_card_1 D) = (k5_card_1 E))  &  ((r1_tarski C D) &  ( (~  ((k12_matrix_3 (k5_card_1 D) A (k7_matrix13 (u1_struct_0 A) B D E)) = (k4_struct_0 A)) )  &  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (~  ((r1_tarski F E) &  ( ((k5_card_1 C) = (k5_card_1 F))  &  (~  ((k12_matrix_3 (k5_card_1 C) A (k7_matrix13 (u1_struct_0 A) B C F)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m1_matrix_1 E (u1_struct_0 C) A B) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (! [G:$i] :  ((v7_ordinal1 G) =>  ((r2_hidden G (k2_finseq_1 A)) =>  ((r1_xxreal_0 B k1_xboole_0) |  ( ( (F = G)  &  (D = (k4_algstr_0 C (k1_group_1 C))) )  |  ((k7_matrix15 C E) = (k7_matrix15 C (k3_matrix11 F A B (u1_struct_0 C) E (k4_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E F) (k10_fvsum_1 (k1_matrix_1 E) C (k8_matrix_1 (u1_struct_0 C) E G) D))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ((v6_matrix16 C A) &  ((v6_matrix16 D A) &  ((k3_finseq_1 C) = (k3_finseq_1 D)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 C) (k3_finseq_1 C) A (k3_matrix16 A C) B) (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k3_matrix16 A D) B)) = (k3_matrix16 A (k9_fvsum_1 A (k3_fvsum_1 A C D) B))) ) ) ) ) ) ) ) ) ) ).
tt(t65_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ( ((v1_matrixj1 D (u1_struct_0 A)) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ((k2_matrix13 (k2_wsierp_1 (k10_matrixj1 (u1_struct_0 A) D)) (k2_wsierp_1 (k11_matrixj1 (u1_struct_0 A) D)) A (k13_matrixj1 (u1_struct_0 A) C D) B) = (k13_matrixj1 (u1_struct_0 A) (k8_group_1 A B C) (k24_matrixj1 A D (k5_finseq_2 (u1_struct_0 A) (k3_finseq_1 D) B)))) ) ) ) ) ) ) ) ) ).
tt(t65_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ((k3_finseq_1 C) = B)  =>  ((r1_xxreal_0 A k6_numbers) |  ((r1_xxreal_0 B k6_numbers) |  ((k11_matrixr1 (k8_matrixr1 A B) C) = (k5_euclid A)) ) ) ) ) ) ) ) ) ) ).
tt(t65_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k3_matrixr1 (k8_matrixr1 A B) (k8_matrixr1 A B)) = (k8_matrixr1 A B)) ) ) ) ) ) ).
tt(t65_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 B C D)) =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ((m1_subset_1 H D) =>  ( (E = (k3_xtuple_0 F G H))  =>  (A = F) ) ) ) ) ) ) )  =>  (A = (k1_mcart_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_measure6,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k7_relset_1 A k1_numbers (k32_valued_1 A k1_numbers C) B) = (k4_measure6 (k7_relset_1 A k1_numbers C B))) ) ) ) ) ).
tt(t65_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  ((k11_member_1 A B) = (a_2_3_member_1 A B)) ) ) ) ) ).
tt(t65_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k5_memstr_0 A B (k10_memstr_0 A B C D)) = (k7_nat_d (k5_memstr_0 A B C) D)) ) ) ) ) ) ) ) ) ).
tt(t65_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) &  ((r1_mesfunc2 A B E) &  ((v6_supinf_2 D) & (v6_supinf_2 E)) ) )  =>  ( ((k1_relset_1 A (k3_mesfunc1 A D E)) = (k9_subset_1 A (k1_relset_1 A D) (k1_relset_1 A E)))  &  ((k5_mesfunc5 A B C (k3_mesfunc1 A D E)) = (k3_supinf_2 (k5_mesfunc5 A B C (k2_partfun1 A k7_numbers D (k1_relset_1 A (k3_mesfunc1 A D E)))) (k5_mesfunc5 A B C (k2_partfun1 A k7_numbers E (k1_relset_1 A (k3_mesfunc1 A D E)))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r1_xxreal_0 k6_numbers C) =>  ((r2_relset_1 A k1_numbers (k18_rfunct_3 A (k26_valued_1 A k1_numbers B (k1_real_1 C))) (k26_valued_1 A k1_numbers (k19_rfunct_3 A B) C)) & (r2_relset_1 A k1_numbers (k19_rfunct_3 A (k26_valued_1 A k1_numbers B (k1_real_1 C))) (k26_valued_1 A k1_numbers (k18_rfunct_3 A B) C))) ) ) ) ) ) ) ) ).
tt(t65_mmlquery,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 A)) =>  ((k26_mmlquery A (k2_finseq_4 (k1_zfmisc_1 A) B C) 1) = (k16_mmlquery A B C)) ) ) ) ) ) ).
tt(t65_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  ((r7_modelc_2 C (k4_modelc_2 A B)) <=>  ((r7_modelc_2 C A) & (r7_modelc_2 C B)) ) ) ) ) ) ) ) ).
tt(t65_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (~  ((v5_modelc_3 A) &  ( (~ (v6_modelc_3 A))  &  ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v6_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) ) ) ) ) ) ) ) ).
tt(t65_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v7_ordinal1 B))  =>  ( ((r1_nat_d A B) &  (~ (v1_moebius1 A)) )  <=> (r1_nat_d A (k6_moebius1 B))) ) ) ) ) ).
tt(t65_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m2_monoid_0 B (k9_monoid_0 A)))  =>  ((m1_subset_1 k1_xboole_0 (u1_struct_0 B)) =>  ((v1_group_1 B) &  ((k4_binop_1 (u1_struct_0 B) (u2_algstr_0 B)) = k1_xboole_0) ) ) ) ) ) ) ).
tt(t65_nat_d,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ((k6_int_1 (k6_int_1 B A) A) = (k6_int_1 B A)) ) ) ) ) ).
tt(t65_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r7_ncfcont1 A B E C) & (r7_ncfcont1 A B F D))  =>  ((r7_ncfcont1 A B (k3_vfunct_2 (u1_struct_0 A) B E F) (k3_xboole_0 C D)) & (r7_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B E F) (k3_xboole_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_newton,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  & (r1_xxreal_0 A (k6_int_1 B A))) ) ) ) ) ) ).
tt(t65_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 (k2_oppcat_1 A)) (k12_oppcat_1 A) B) = (k5_oppcat_1 A B)) ) ) ) ) ).
tt(t65_orders_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (! [B:$i] :  (~  ((r1_tarski B A) &  ((v6_ordinal1 B) &  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ((r2_hidden D B) => (r1_tarski D C)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ( (~  (C = B) )  & (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (A = (k10_ordinal2 (k11_ordinal2 (k6_ordinal3 A B) B) (k7_ordinal3 A B))) ) ) ) ) ).
tt(t65_ordinal5,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden k6_numbers B) => (v6_ordinal5 (k5_afinsq_1 (k11_ordinal2 B (k12_ordinal2 k4_ordinal1 A))))) ) ) ) ) ).
tt(t65_ordinal6,ax, (! [A:$i] :  ( ((v3_ordinal1 A) &  ((v4_ordinal1 A) &  (~ (v1_xboole_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_classes2 B))  =>  ( ((r2_hidden A B) &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((v1_funct_1 (k1_funct_1 (k11_ordinal6 B) C)) &  ((v1_funct_2 (k1_funct_1 (k11_ordinal6 B) C) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v2_ordinal6 (k1_funct_1 (k11_ordinal6 B) C)) & (m1_subset_1 (k1_funct_1 (k11_ordinal6 B) C) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) )  =>  ((v1_funct_1 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 B) A))) &  ((v1_funct_2 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 B) A)) (k2_ordinal1 B) (k2_ordinal1 B)) &  ((v3_ordinal2 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 B) A))) &  ((v2_ordinal5 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 B) A))) & (m1_subset_1 (k8_ordinal6 (k5_relat_1 (k11_ordinal6 B) A)) (k1_zfmisc_1 (k2_zfmisc_1 (k2_ordinal1 B) (k2_ordinal1 B))))) ) ) ) ) ) ) ) ) ).
tt(t65_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v5_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t65_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  => (r1_partfun1 (k3_partfun1 C A B) C)) ) ) ) ).
tt(t65_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A (k4_pboole A B C) (k3_pboole A B C)) B)) ) ) ) ) ).
tt(t65_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r8_pdiff_5 C B) =>  ((r3_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) &  ((k11_pdiff_1 3 2 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) = (k8_real_1 A (k8_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t65_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ((r3_pdiff_9 A C B D) & (r3_pdiff_9 A C B E)) ) ) )  =>  ((r3_pdiff_9 A C B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) &  ((r2_relset_1 (k1_euclid A) k1_numbers (k3_pdiff_9 A C B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers (k3_pdiff_9 A C B D) (k3_pdiff_9 A C B E))) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 k1_numbers (k3_pdiff_9 A C B (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) F) = (k9_binop_2 (k11_pdiff_1 A B D F) (k11_pdiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_pepin,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~ (r1_xxreal_0 B k6_numbers))  &  ( (~ (r1_xxreal_0 A 1))  & (r1_xxreal_0 (k1_newton A B) 1)) ) ) ) ) ) ) ).
tt(t65_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k3_finseq_2 B))) =>  ( ((r1_tarski C D) & (r1_tarski E F))  => (r1_tarski (k10_pnproc_1 A B C E) (k10_pnproc_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  => (r2_hidden (k1_tarski A) (k2_struct_0 (k17_polyform A (k7_polyform A))))) ) ).
tt(t65_polynom5,ax,(r1_funct_2 (u1_struct_0 k1_complfld) (u1_struct_0 k1_complfld) k2_numbers k2_numbers (k8_polynom5 k1_complfld (k1_group_1 k1_complfld) 2) (k19_valued_1 k2_numbers k2_numbers k2_numbers (k6_partfun1 k2_numbers) (k6_partfun1 k2_numbers)))).
tt(t65_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) &  ((v1_partfun1 B A) &  ((v4_valued_0 B) & (v2_pre_poly B)) ) ) ) )  =>  ((r6_pboole A (k7_partfun1 (k15_pre_poly A) (k20_pre_poly A B) 1) (k16_pre_poly A)) & (r6_pboole A (k7_partfun1 (k15_pre_poly A) (k20_pre_poly A B) (k3_finseq_1 (k20_pre_poly A B))) B)) ) ) ) ) ).
tt(t65_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  (~  ( (~ (r1_xxreal_0 A k6_numbers))  &  ( (~ (r1_xxreal_0 1 A))  &  ( (~ (r1_xxreal_0 B k6_numbers))  & (r1_xxreal_0 1 (k6_prepower A B))) ) ) ) ) ) ) ) ).
tt(t65_prob_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ((m2_prob_1 C A B) =>  (! [D:$i] :  ((m1_prob_3 D A B) =>  ((r1_xxreal_0 (k1_funct_1 C (k5_prob_3 A D)) (k18_rvsum_1 (k9_prob_3 A B D C))) &  ((v1_prob_2 D) =>  ((k1_funct_1 C (k5_prob_3 A D)) = (k18_rvsum_1 (k9_prob_3 A B D C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_pscomp_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( ((k1_seq_1 k5_pscomp_1 (k19_euclid A B)) = B)  &  ((k1_seq_1 k4_pscomp_1 (k19_euclid A B)) = A) ) ) ) ) ) ).
tt(t65_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k6_pboole A (k3_pboole A B C) D) (k3_pboole A (k6_pboole A B D) (k6_pboole A C D))) & (r6_pboole A (k6_pboole A D (k3_pboole A B C)) (k3_pboole A (k6_pboole A D B) (k6_pboole A D C)))) ) ) ) ) ) ) ) ).
tt(t65_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  (! [D:$i] :  ((m2_subset_1 D (k6_qc_lang1 A) (k8_qc_lang1 A C)) =>  (! [E:$i] :  ( ((v3_card_1 E C) & (m2_finseq_1 E (k2_qc_lang1 A)))  =>  (~ (r3_qc_lang2 A B (k10_qc_lang1 A D E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((k6_qc_lang3 A (k13_qc_lang1 A B)) = (k6_qc_lang3 A B)) ) ) ) ) ).
tt(t65_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k26_quaterni (k29_quaterni A B) C) D) = (k26_quaterni (k29_quaterni (k27_quaterni A D) (k27_quaterni B D)) (k27_quaterni C D))) ) ) ) ) ) ) ) ) ).
tt(t65_quaterni,ax, ((k32_quaterni k21_quaterni) = k6_numbers) ).
tt(t65_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [D:$i] :  ((m1_rcomp_3 D A B C) =>  (! [E:$i] :  ((m2_rcomp_3 E A B C D) =>  ( ((m1_setfam_1 C (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 C (k4_topmetr A B)) & (v1_rcomp_3 C (k4_topmetr A B))) )  =>  ((r1_xxreal_0 B A) | (v5_valued_0 E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((k1_seq_1 (k6_real_3 B) C) = k6_numbers) ) ) )  =>  ((k9_real_1 (k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 1)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1))) (k10_real_1 (k1_seq_1 (k5_real_3 B) A) (k1_seq_1 (k6_real_3 B) A))) = (k10_real_1 (k2_newton (k1_real_1 1) A) (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 1)) (k1_seq_1 (k6_real_3 B) A)))) ) ) ) ) ) ).
tt(t65_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k5_relat_1 B A) = (k3_relat_1 (k4_relat_1 A) B)) ) ) ) ).
tt(t65_rewrite1,ax, (! [A:$i] :  ((v1_relat_1 A) =>  (! [B:$i] :  ((m2_rewrite1 B A) =>  (! [C:$i] :  (! [D:$i] :  ((r2_rewrite1 A C D) <=>  ((k2_rewrite1 B C) = (k2_rewrite1 B D)) ) ) ) ) ) ) ) ).
tt(t65_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ( (~ (r2_hidden (k2_flang_1 A) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden (k2_xcmplx_0 E 1) (k4_finseq_1 D)) &  ((k2_xtuple_0 (k1_funct_1 D E)) = (k2_xtuple_0 (k1_funct_1 D (k2_xcmplx_0 E 1)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ((r2_hidden C (k6_subset_1 B A)) <=>  ((k1_funct_1 (k7_rfunct_1 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t65_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_finset_1 C) & (r2_hidden B (k1_relset_1 A (k2_partfun1 A k1_numbers D C))))  => (r2_classes1 (k8_finseq_1 k1_numbers (k20_rfunct_3 A D (k6_subset_1 C (k1_tarski B))) (k12_finseq_1 k1_numbers (k1_seq_1 D B))) (k2_partfun1 A k1_numbers D C))) ) ) ) ) ) ) ) ).
tt(t65_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 B) & (v1_seq_2 B))  => (r1_xxreal_0 (k1_seq_1 B A) (k1_seq_1 (k4_rinfsup1 B) (k2_nat_1 A 1)))) ) ) ) ) ).
tt(t65_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (r1_tarski (k3_convex1 A B) (k4_rlaffin1 A B))) ) ) ) ).
tt(t65_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  ( (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) &  ((r2_hidden B (k3_rlsub_1 A E D)) & (r2_hidden C (k3_rlsub_1 A E D))) ) )  <=> (r1_struct_0 D (k5_algstr_0 A B C))) ) ) ) ) ) ) ) ) ).
tt(t65_rlsub_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ( (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k3_lattices A C B) = B) ) )  =>  (B = (k6_lattices A)) ) ) ) ) ) ).
tt(t65_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_connsp_2 B A (k4_struct_0 A)) =>  (~  ((v1_convex1 B A) &  (! [C:$i] :  ((m1_connsp_2 C A (k4_struct_0 A)) =>  (~  ((v3_rltopsp1 C A) &  ((v1_convex1 C A) & (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C B D)) = (k3_rlvect_1 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) B D)) C)) ) ) ) ) ) ) ) ) ).
tt(t65_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rlvect_2 B A) =>  (! [C:$i] :  ((m1_rlvect_2 C A) =>  ((k5_algstr_0 (k16_rlvect_2 A) (k1_rlvect_2 (k16_rlvect_2 A) B) (k1_rlvect_2 (k16_rlvect_2 A) C)) = (k10_rlvect_2 A B C)) ) ) ) ) ) ) ).
tt(t65_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_rmod_2 D A B) =>  (? [E:$i] :  ((m2_rmod_2 E A B D) & (r2_hidden C E)) ) ) ) ) ) ) ) ) ) ).
tt(t65_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((v1_rmod_4 (k7_domain_1 (u1_struct_0 B) C D) A B) =>  ( ((k4_struct_0 A) = (k1_group_1 A))  |  ( (~  (C = (k4_struct_0 B)) )  &  (~  (D = (k4_struct_0 B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_bhsp_1 B) & (m1_rusub_1 B A))  =>  (! [C:$i] :  ( ((v1_bhsp_1 C) & (m1_rusub_1 C A))  =>  (! [D:$i] :  ((m2_rusub_1 D A B) =>  (! [E:$i] :  ((m2_rusub_1 E A C) =>  ( (D = E)  =>  (B = C) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_rvsum_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v3_valued_0 C) & (v1_finseq_1 C)) ) )  =>  ((k10_rvsum_1 (k14_rvsum_1 B C) A) = (k14_rvsum_1 (k10_rvsum_1 B A) C)) ) ) ) ) ) ) ).
tt(t65_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k8_scmfsa_2 A B) C) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 C)))  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k8_scmfsa_2 A B) C) A) = (k6_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k8_scmfsa_2 A B) C) D) = (k1_funct_1 C D)) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k8_scmfsa_2 A B) C) D) (k18_scmfsa_2 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~ (r4_scmfsa7b C D))  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 E F))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) F)) (k2_afinsq_1 C))) ) )  =>  (! [F:$i] :  ((m2_subset_1 F k1_numbers k5_numbers) =>  ((r1_xxreal_0 F E) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) F) D) = (k1_funct_1 B D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  ( ( ((k1_funct_1 B (k4_scmfsa_2 k6_numbers)) = 1)  & (r1_xxreal_0 (k1_funct_1 B D) k6_numbers))  =>  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c D C) B A)) = (k6_memstr_0 3 k1_scmfsa_2 B)) ) ) ) ) ) ) ) ) ) ).
tt(t65_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmpds_2)))  =>  (~ (v2_extpro_1 (k5_scmpds_2 B A) 2 k1_scmpds_2)) ) ) ) ) ).
tt(t65_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k5_card_1 (k3_scmpds_6 A B C D)) = (k2_nat_1 (k2_nat_1 (k5_card_1 C) (k5_card_1 D)) 2)) ) ) ) ) ) ) ) ) ).
tt(t65_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) => (v10_scmyciel (k10_eqrel_1 (k3_tarski A)) A)) ) ).
tt(t65_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 A)) =>  ( ((r3_semi_af1 A B C D E) & (r3_semi_af1 A B C F G))  => (r3_semi_af1 A D E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 A)) =>  ( ( ((k15_seq_4 A B C) = (k15_seq_4 A D C))  |  ((k15_seq_4 A B C) = (k15_seq_4 A C D)) )  =>  (B = D) ) ) ) ) ) ) ) ) ) ).
tt(t65_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ((v1_setlim_1 B A) => (v3_kurato_0 B A)) ) ) ) ).
tt(t65_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_kurato_0 B A) | (v3_kurato_0 C A))  => (r1_tarski (k3_kurato_0 A (k4_setlim_2 A B C)) (k5_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C)))) ) ) ) ) ) ).
tt(t65_sf_mastr,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) ) ) )  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 D (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E k5_numbers) &  ((v5_relat_1 E (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 E) & (v1_partfun1 E k5_numbers)) ) ) )  =>  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v4_relat_1 F k5_numbers) &  ((v5_relat_1 F (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 F) & (v1_partfun1 F k5_numbers)) ) ) )  =>  ( ((r1_tarski A E) &  ((r1_tarski A F) &  ((r1_tarski (k7_memstr_0 3 k1_scmfsa_2 k6_numbers) C) &  ((r1_tarski (k7_memstr_0 3 k1_scmfsa_2 k6_numbers) D) &  ( ((k5_relat_1 C (k2_sf_mastr A)) = (k5_relat_1 D (k2_sf_mastr A)))  &  ( ((k5_relat_1 C (k4_sf_mastr A)) = (k5_relat_1 D (k4_sf_mastr A)))  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B G))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G)) (k1_relset_1 k5_numbers A))) ) ) ) ) ) ) ) )  =>  ( (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 B G))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G)) (k1_relset_1 k5_numbers A))) ) )  &  (! [G:$i] :  ((m2_subset_1 G k1_numbers k5_numbers) =>  ((r1_xxreal_0 G B) =>  ( ((k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G)) = (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G)))  &  ( (! [H:$i] :  ( ((v1_ami_2 H) & (m1_subset_1 H (u1_struct_0 k1_scmfsa_2)))  =>  ((r2_hidden H (k2_sf_mastr A)) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) = (k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 F D G) H)) ) ) )  &  (! [H:$i] :  ((m1_scmfsa_2 H) =>  ((r2_hidden H (k4_sf_mastr A)) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 E C G) H) (k18_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 F D G) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A C C)) (k5_sheffer1 A B (k5_sheffer1 A D D))) = (k5_sheffer1 A (k5_sheffer1 A B (k5_sheffer1 A D C)) (k5_sheffer1 A B (k5_sheffer1 A D C)))) ) ) ) ) ) ) ) ) ).
tt(t65_simplex0,ax, (! [A:$i] :  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((m1_simplex0 C A) =>  (! [D:$i] :  ((m2_simplex0 D A C) =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  => (m2_simplex0 (k11_simplex0 A D E B) A (k11_simplex0 A C E B))) ) ) ) ) ) ) ) ) ).
tt(t65_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2))) k1_sincos10) = (k1_partfun2 k1_numbers (k3_rcomp_1 k6_numbers (k10_real_1 k32_sin_cos 2)))) ).
tt(t65_sin_cos6,ax, ((k4_relset_1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) = (k6_partfun1 (k1_rcomp_1 (k1_real_1 1) 1))) ).
tt(t65_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k12_binop_2 (k10_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B))) (k9_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B)))))  =>  (B = (k11_binop_2 (k18_binop_2 1 2) (k6_power k8_power (k12_binop_2 (k9_binop_2 1 A) (k10_binop_2 1 A))))) ) ) ) ) ) ).
tt(t65_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( (~ (r1_xxreal_0 (k5_sin_cos9 A) (k1_real_1 (k10_real_1 k32_sin_cos 4))))  &  (~ (r1_xxreal_0 (k10_real_1 k32_sin_cos 4) (k5_sin_cos9 A))) ) ) ) ) ) ) ) ).
tt(t65_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r1_fdiff_1 k24_sin_cos A) &  ((k1_fdiff_1 k24_sin_cos A) = (k1_seq_1 k24_sin_cos A)) ) ) ) ).
tt(t65_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k13_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k13_pscomp_1 A)) ) ) ).
tt(t65_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A C) = (k22_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k22_pscomp_1 (k3_topreal1 2 A)) = (k12_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A))))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_pscomp_1 (k3_topreal1 2 A)))) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t65_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k25_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k24_pscomp_1 (k3_topreal1 2 A)) = (k23_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k24_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k23_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t65_stirl2_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k5_numbers)) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k5_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  ((v1_finset_1 (k2_relset_1 B C)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A B) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_relset_1 B C) (k2_relset_1 B C)) &  ((v3_funct_2 F (k2_relset_1 B C) (k2_relset_1 B C)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_relset_1 B C) (k2_relset_1 B C))))) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (k2_relset_1 B C) (k2_relset_1 B C)) &  ((v3_funct_2 G (k2_relset_1 B C) (k2_relset_1 B C)) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (k2_relset_1 B C) (k2_relset_1 B C))))) ) )  =>  ( ( (C = (k1_partfun1 A B (k2_relset_1 B C) (k2_relset_1 B C) D F))  &  ( (C = (k1_partfun1 A B (k2_relset_1 B C) (k2_relset_1 B C) E G))  &  ( ((k2_relset_1 B C) = (k2_relset_1 B D))  &  ( ((k2_relset_1 B C) = (k2_relset_1 B E))  &  ((v2_stirl2_1 D A B) & (v2_stirl2_1 E A B)) ) ) ) )  =>  ((r2_funct_2 (k2_relset_1 B C) (k2_relset_1 B C) F G) & (r2_funct_2 A B D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (r1_tarski (k24_qc_lang1 A B) (k4_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A (k11_cqc_lang A C B)) (k6_domain_1 (k3_qc_lang1 A) C)))) ) ) ) ) ) ).
tt(t65_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((r1_tarski B (k1_tdlat_1 A)) <=> (v1_tdlat_2 B A)) ) ) ) ) ).
tt(t65_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ( (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  => (v5_pre_topc C B A)) ) ) )  => (v2_tdlat_3 A)) ) ) ).
tt(t65_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tex_2 B A) &  ((v2_tex_3 B A) & (m1_pre_topc B A)) ) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v4_tex_3 C A) & (m1_pre_topc C A)) ) )  & (r4_tsep_2 A B C)) ) ) ) ) ) ).
tt(t65_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) | (v3_pre_topc C A))  =>  ((k3_tex_4 A (k9_subset_1 (u1_struct_0 A) B C)) = (k9_subset_1 (u1_struct_0 A) (k3_tex_4 A B) (k3_tex_4 A C))) ) ) ) ) ) ) ) ).
tt(t65_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ((m1_pre_topc C D) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 D)) =>  ((r2_hidden F (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 B) E F) = (k1_funct_1 (k3_tmap_1 A B D C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_topalg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_borsuk_6 A B C) =>  ( (~ (v1_xboole_0 (k3_topalg_1 A B C)))  &  ((v1_partfun1 (k3_topalg_1 A B C) (k1_topalg_1 A B C)) &  ((v3_relat_2 (k3_topalg_1 A B C)) & (v8_relat_2 (k3_topalg_1 A B C))) ) ) ) ) ) ) ) ) ) ).
tt(t65_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ((v1_tops_2 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))  => (r1_tarski B (k5_topgen_4 A))) ) ) ) ).
tt(t65_topgen_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_xreal_0 E) & (v2_xxreal_0 E))  =>  (~  ((r1_xxreal_0 k6_numbers C) &  ((r1_xxreal_0 D 1) &  ((r2_hidden (k1_funct_1 (k4_topgen_5 B E) A) (k2_rcomp_1 C D)) &  (! [F:$i] :  ( ((v1_xreal_0 F) & (v2_xxreal_0 F))  =>  (~  ((r1_xxreal_0 F (k18_euclid A)) & (r1_tarski (k1_topreal9 2 A F) (k8_relset_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr) (k4_topgen_5 B E) (k2_rcomp_1 C D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_topreal6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v6_metric_1 A) &  ((v8_metric_1 A) &  ((v9_metric_1 A) & (l1_metric_1 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ( ((u1_struct_0 A) = (k4_subset_1 (u1_struct_0 A) B C))  &  ( (~ (v5_tbsp_1 A))  &  ((v6_tbsp_1 B A) & (v6_tbsp_1 C A)) ) ) ) ) ) ) ) ) ) ).
tt(t65_tops_1,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v3_pre_topc B A) & (v4_pre_topc B A))  =>  ((v5_tops_1 B A) <=> (v6_tops_1 B A)) ) ) ) ) ) ).
tt(t65_tops_2,ax, (! [A:$i] :  ((l1_pre_topc A) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v2_tops_2 B A) <=> (r1_tarski B (k7_setfam_1 (u1_struct_0 A) (u1_pre_topc A)))) ) ) ) ) ).
tt(t65_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r1_tarski C D) & (v2_tops_1 D B))  => (v2_tops_1 C A)) ) ) ) ) ) ) ) ) ).
tt(t65_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  => (v6_transgeo (k6_partfun1 (u1_struct_0 A)) A)) ) ).
tt(t65_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  ((k4_trees_1 (k12_trees_3 A) (k12_finseq_1 k5_numbers k6_numbers)) = A) ) ) ).
tt(t65_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ( (A = (k1_tsep_1 A B C))  & (r3_tsep_1 A B C))  =>  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) ) ) ) ) ) ) ) ).
tt(t65_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_vectsp_2 A) &  ((v2_polynom5 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) &  ((v1_algseq_1 B A) &  ((v1_uproots B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) ) ) )  =>  ( ((k1_normsp_1 A B (k7_nat_d (k1_algseq_1 A B) 1)) = (k5_struct_0 A))  => (r2_funct_2 k5_numbers (u1_struct_0 A) B (k10_uproots A (k8_uproots A B)))) ) ) ) ) ).
tt(t65_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((k58_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k52_valued_2 A B C D) E) = (k52_valued_2 A B C (k45_valued_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t65_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m1_vectsp_4 E A B) =>  (~  ( ((k3_vectsp_4 A B C E) = (k3_vectsp_4 A B D E))  &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 B)) =>  (~  ((r1_struct_0 E F) &  ((k5_algstr_0 B C F) = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_orders_2 C))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (l1_orders_2 D))  =>  ( ( ((g1_orders_2 (u1_struct_0 A) (u1_orders_2 A)) = (g1_orders_2 (u1_struct_0 C) (u1_orders_2 C)))  &  ((g1_orders_2 (u1_struct_0 B) (u1_orders_2 B)) = (g1_orders_2 (u1_struct_0 D) (u1_orders_2 D))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 D)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 D))))) )  =>  ((r1_funct_2 (u1_struct_0 A) (u1_struct_0 B) (u1_struct_0 C) (u1_struct_0 D) E F) =>  (! [G:$i] :  ((m1_subset_1 G (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [H:$i] :  ((m1_subset_1 H (k1_zfmisc_1 (u1_struct_0 C))) =>  ( (G = H)  =>  ( ((r4_waybel_0 A B E G) => (r4_waybel_0 C D F H))  &  ((r3_waybel_0 A B E G) => (r3_waybel_0 C D F H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_waybel_1,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_yellow_0 A B) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k12_lattice3 A C (k1_yellow_0 A B)) = (k1_yellow_0 A (a_3_5_waybel_1 A B C))) ) ) ) ) )  => (v2_waybel_1 A)) ) ) ).
tt(t65_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ((k2_relset_1 (u1_struct_0 A) (k3_waybel23 A (k5_yellow_0 A B))) = (u1_struct_0 A)) ) ) ) ) ).
tt(t65_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_yellow_0 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v4_waybel34 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v4_yellow_0 D A) &  ((v6_waybel34 D A) & (m1_yellow_0 D A)) ) )  =>  (! [E:$i] :  ( ( (~ (v2_struct_0 E))  &  ((v4_yellow_0 E B) &  ((v6_waybel34 E B) & (m1_yellow_0 E B)) ) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 D) (u1_struct_0 E)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 E))))) )  =>  ( (F = (k2_partfun1 (u1_struct_0 A) (u1_struct_0 B) C (u1_struct_0 D)))  => (v4_waybel34 F D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_xboole_1,ax, (! [A:$i] : (r1_xboole_0 A k1_xboole_0)) ).
tt(t65_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ((k8_xboolean A (k7_xboolean A B)) = (k3_xboolean (k4_xboolean A B))) ) ) ) ) ).
tt(t65_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k2_xcmplx_0 (k7_xcmplx_0 A 2) (k7_xcmplx_0 A 2)) = A) ) ) ).
tt(t65_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 A B) & (r1_xxreal_0 C k6_numbers))  => (r1_xxreal_0 (k3_xcmplx_0 B C) (k3_xcmplx_0 A C))) ) ) ) ) ) ) ).
tt(t65_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ((r1_tarski (k3_xxreal_1 A B) (k4_xxreal_1 C D)) =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 C A) &  (~ (r1_xxreal_0 D B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((m1_xxreal_2 C A) =>  (! [D:$i] :  ((m1_xxreal_2 D B) => (m1_xxreal_2 (k3_xxreal_0 C D) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ).
tt(t65_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ( ((r1_xxreal_0 k6_numbers A) & (r1_xxreal_0 (k1_xxreal_3 B A) C))  => (r1_xxreal_0 B C)) ) ) ) ) ) ) ).
tt(t65_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r2_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D)) & (r2_hidden (k2_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D)) (u1_struct_0 B)))  =>  ((r2_yellow_0 B (k7_domain_1 (u1_struct_0 B) C D)) &  ((k2_yellow_0 B (k7_domain_1 (u1_struct_0 B) C D)) = (k2_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t65_yellow10,ax, (! [A:$i] :  ( ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v2_waybel_1 (k3_yellow_3 A B)) => (v2_waybel_1 A)) ) ) ) ) ).
tt(t65_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k1_yellow_5 A B (k3_yellow_0 A)) = B) ) ) ) ) ).
tt(t65_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ((k2_zf_model (k12_zf_lang A B)) = (k4_subset_1 k1_zf_lang (k2_zf_model A) (k2_zf_model B))) ) ) ) ) ).
tt(t65_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  ( ((r2_zf_lang A B) & (r2_zf_lang B C))  => (r2_zf_lang A C)) ) ) ) ) ) ) ).
tt(t65_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (~  ( (~  ((k4_xboole_0 (k2_tarski A B) C) = k1_xboole_0) )  &  ( (~  ((k4_xboole_0 (k2_tarski A B) C) = (k1_tarski A)) )  &  ( (~  ((k4_xboole_0 (k2_tarski A B) C) = (k1_tarski B)) )  &  (~  ((k4_xboole_0 (k2_tarski A B) C) = (k2_tarski A B)) ) ) ) ) ) ) ) ) ).
tt(t65_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r1_struct_0 D B) <=>  ((k5_zmodul01 A C D) = (k5_zmodul01 A (k3_rlvect_1 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t66_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) )  => (r1_relset_1 (u1_struct_0 A) (u1_struct_0 A) (k11_abcmiz_0 A) (u1_orders_2 A))) ) ).
tt(t66_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ((m1_trees_4 B (k3_card_3 (u3_msualg_1 A (k1_msafree3 A (k28_abcmiz_1 A)))) (k34_abcmiz_1 A)) =>  (! [C:$i] :  ( ((v2_abcmiz_1 C A) & (m1_subset_1 C (u4_struct_0 A)))  =>  ( ( ((k2_msualg_1 A C) = (k13_abcmiz_1 A))  &  ((k3_finseq_1 B) = (k3_finseq_1 (k1_msualg_1 A C))) )  =>  ((v6_abcmiz_1 (k36_abcmiz_1 A C B) A) &  ((v8_abcmiz_1 (k36_abcmiz_1 A C B) A) & (m1_abcmiz_1 (k36_abcmiz_1 A C B) A (k13_abcmiz_1 A))) ) ) ) ) ) ) ) ) ).
tt(t66_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 C A) =>  ((r2_hidden B C) <=>  ((k3_aff_4 A B C) = C) ) ) ) ) ) ) ) ) ).
tt(t66_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r2_hidden B (k2_afinsq_1 A)) <=>  (~ (r1_xxreal_0 (k5_card_1 A) B)) ) ) ) ) ) ).
tt(t66_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k1_funct_1 C A) = B)  & (r2_hidden A (k9_xtuple_0 C)))  =>  ((k2_xboole_0 (k1_tarski A) (k8_relat_1 (k5_relat_1 C (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A))) (k1_tarski B))) = (k8_relat_1 C (k1_tarski B))) ) ) ) ) ) ).
tt(t66_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((r10_analmetr A B C) &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r2_hidden D B) & (r2_hidden D C)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  ((k16_aofa_000 (k7_freealg k19_aofa_000 A) B C) = (k6_trees_4 4 B C)) ) ) ) ) ) ) ).
tt(t66_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  => (r6_aofa_000 A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F 1) (k16_aofa_000 A (k78_aofa_i00 A B C D G k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k15_aofa_000 A (k72_aofa_i00 A B C D G) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F E)) (k60_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 2)) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E E)))) D (a_5_0_aofa_i00 A B C D G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ( ((r3_arytm_3 A B) & (r3_arytm_3 B A))  =>  (A = B) ) ) ) ) ) ).
tt(t66_asympt_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (~  ((r1_xxreal_0 6 A) & (r1_xxreal_0 (k5_series_1 2 A) (k5_square_1 (k2_nat_1 A 1)))) ) ) ) ).
tt(t66_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k1_bcialg_1 A B (k1_bcialg_1 A C D)) = (k1_bcialg_1 A (k1_bcialg_1 A D C) (k2_bcialg_1 A B))) ) ) ) ) ) ) ) ) ) ).
tt(t66_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k1_boolealg A B (k3_boolealg A C D)) (k3_lattices A (k1_boolealg A B (k3_lattices A C D)) (k4_lattices A (k4_lattices A B C) D)))) ) ) ) ) ) ) ) ).
tt(t66_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( (A = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k4_rcomp_1 B C)) (k3_borsuk_5 C D)) (k1_seq_4 D)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k2_pre_topc k3_topmetr A) = (k4_rcomp_1 k2_xxreal_0 D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_borsuk_6,ax, ((r2_hidden (k4_tarski (k10_real_1 1 2) k6_numbers) k8_borsuk_6) & (r2_hidden (k4_tarski 1 1) k8_borsuk_6)) ).
tt(t66_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1))) =>  (~  ( (~ (v2_borsuk_7 B (k1_nat_1 A 1) A (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1))  &  ((k45_valued_1 (k3_funct_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) B C) (k1_funct_1 B (k30_valued_1 C))) = (k4_struct_0 (k15_euclid A))) ) ) ) ) ) ) ) ) ).
tt(t66_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k7_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  (! [K:$i] :  ((m1_subset_1 K A) =>  (! [L:$i] :  ((m1_subset_1 L A) =>  (~  ((v2_bvfunc_2 B A) &  ( (B = (k6_enumset1 C D E F G H I J))  &  ( (~  (C = D) )  &  ( (~  (C = E) )  &  ( (~  (C = F) )  &  ( (~  (C = G) )  &  ( (~  (C = H) )  &  ( (~  (C = I) )  &  ( (~  (C = J) )  &  ( (~  (D = E) )  &  ( (~  (D = F) )  &  ( (~  (D = G) )  &  ( (~  (D = H) )  &  ( (~  (D = I) )  &  ( (~  (D = J) )  &  ( (~  (E = F) )  &  ( (~  (E = G) )  &  ( (~  (E = H) )  &  ( (~  (E = I) )  &  ( (~  (E = J) )  &  ( (~  (F = G) )  &  ( (~  (F = H) )  &  ( (~  (F = I) )  &  ( (~  (F = J) )  &  ( (~  (G = H) )  &  ( (~  (G = I) )  &  ( (~  (G = J) )  &  ( (~  (H = I) )  &  ( (~  (H = J) )  &  ( (~  (I = J) )  &  ( ((k15_bvfunc_1 A K (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H) I) J)) = (k15_bvfunc_1 A L (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A E F) G) H) I) J)))  & (r1_xboole_0 (k15_bvfunc_1 A L (k5_bvfunc_2 A C B)) (k15_bvfunc_1 A K (k5_bvfunc_2 A D B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( (A = k8_margrel1)  =>  ((k6_xboolean B A) = k8_margrel1) ) ) ) ) ) ).
tt(t66_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k9_bvfunc_1 A B (k6_bvfunc26 A C D)) (k1_bvfunc_1 A (k2_bvfunc_1 A B (k5_bvfunc_1 A C D))))) ) ) ) ) ) ) ) ).
tt(t66_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C B)))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B))))))) ) ) ) ) ) ) ) ) ).
tt(t66_card_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_ordinal1 (k1_card_1 A) (k1_card_1 B)) <=>  (? [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  & (r1_tarski A (k7_relat_1 C B))) ) ) ) ) ).
tt(t66_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  (! [B:$i] :  ((v1_card_1 B) =>  ((k7_card_3 (k7_funcop_1 A B)) = (k3_card_2 B A)) ) ) ) ) ).
tt(t66_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ((r2_hidden A (k8_card_3 B)) => (r2_hidden (k5_relat_1 A C) (k8_card_3 (k5_relat_1 B C)))) ) ) ) ) ) ).
tt(t66_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u4_struct_0 A) (u4_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u4_struct_0 A) (u4_struct_0 B))))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (? [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) &  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E)) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D) = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u4_struct_0 B)) =>  (! [E:$i] :  ((m2_cat_3 E B C A) =>  ( ((k3_graph_1 B D) = C)  => (m2_cat_3 (k7_cat_3 B A E D) B (k4_graph_1 B D) A)) ) ) ) ) ) ) ) ) ) ).
tt(t66_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D C) = k1_xboole_0) )  &  ((k2_cat_1 A (k20_cat_4 A B D) C) = k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_partfun1 C A) =>  ( ((k7_partfun1 k2_numbers (k31_valued_1 A k2_numbers C) B) = (k10_complex1 (k7_partfun1 k2_numbers C B)))  &  ((k1_funct_1 (k55_valued_1 A k2_numbers C) B) = (k17_complex1 (k7_partfun1 k2_numbers C B))) ) ) ) ) ) ) ) ) ).
tt(t66_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k4_chain_1 A B k6_numbers))) =>  ((m3_chain_1 C A B k6_numbers) <=> (v1_abian (k5_card_1 C))) ) ) ) ) ) ) ).
tt(t66_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_glib_000 B)) ) ) )  =>  ((r5_glib_000 A B) =>  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 B)) =>  ( ( (C = D)  & (v3_chord C A))  => (v3_chord D B)) ) ) ) ) ) ) ) ) ) ).
tt(t66_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((v3_ordinal1 B) =>  ((r2_hidden A (k4_classes1 B)) <=> (r2_hidden (k6_classes1 A) B)) ) ) ) ).
tt(t66_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k16_classes2 (k1_ordinal1 A)) = (k1_classes1 (k16_classes2 A))) ) ) ).
tt(t66_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r2_hidden (k4_struct_0 A) (k5_clvect_1 A B C)) <=>  ((k5_clvect_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t66_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  => (r1_clvect_2 A B B)) ) ) ) ).
tt(t66_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  ((k3_tarski (k13_cohsp_1 A)) = (k3_tarski A)) ) ) ).
tt(t66_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k5_xcmplx_0 A)) = (k2_real_1 (k17_complex1 A))) ) ) ).
tt(t66_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ( (~ (r1_xxreal_0 k6_numbers C))  &  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_complex2 A B) = (k3_complex2 (k3_xcmplx_0 A C) (k3_xcmplx_0 B C))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ((k17_complex1 (k5_algstr_0 k1_complfld A B)) = (k17_complex1 (k5_algstr_0 k1_complfld B A))) ) ) ) ) ).
tt(t66_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k2_numbers) =>  ( ( ((k3_finseq_1 A) = (k3_finseq_1 B))  &  ((k3_finseq_1 B) = (k3_finseq_1 C)) )  =>  ((k8_complsp2 (k9_seq_4 A B) C) = (k3_binop_2 (k8_complsp2 A C) (k8_complsp2 B C))) ) ) ) ) ) ) ) ).
tt(t66_compos_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((l1_compos_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 B)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  ((k1_funct_1 (k61_valued_1 (k10_compos_1 B C) A) A) = (k1_funct_1 (k61_valued_1 C A) A)) ) ) ) ) ) ) ).
tt(t66_comput_1,ax,(v6_comput_1 (k2_comput_1 k5_numbers))).
tt(t66_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ((v1_series_1 A) =>  ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  (? [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) &  ((r1_xxreal_0 C D) &  (~ (r1_xxreal_0 (k17_complex1 (k8_nat_1 k2_numbers B D)) (k8_nat_1 k1_numbers A D))) ) ) ) ) )  | (v2_comseq_3 B)) ) ) ) ) ) ).
tt(t66_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ((v2_convex4 B A) =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  (~  ( (C = E)  &  ( (D = F)  &  ((r1_xxreal_0 k1_xboole_0 E) & (r1_xxreal_0 k1_xboole_0 F)) ) ) ) ) ) ) )  |  ((k7_rusub_4 A (k19_convex4 A B C) (k19_convex4 A B D)) = (k19_convex4 A B (k2_xcmplx_0 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) => (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A C B) B) A)) ) ) ) ) ) ).
tt(t66_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden D (k24_qc_lang1 A B)))  => (v2_cqc_the1 (k8_cqc_lang A (k7_cqc_lang A B (k11_cqc_lang A D C)) (k11_cqc_lang A D (k7_cqc_lang A B C))) A)) ) ) ) ) ) ) ) ) ).
tt(t66_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v2_csspace B) & (l1_csspace B)) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 B))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 B) (k6_clvect_1 B (k16_csspace B C D) A) (k16_csspace B (k6_clvect_1 B C A) (k6_clvect_1 B D A)))) ) ) ) ) ) ) ) ).
tt(t66_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k3_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k21_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k7_real_1 (k8_real_1 6 B) (k8_real_1 3 A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t66_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k21_sin_cos D))) ) )  =>  ( ((k21_sin_cos A) = k6_numbers)  |  ( ((k21_sin_cos (k7_real_1 A B)) = k6_numbers)  |  ((k1_seq_1 (k3_diff_1 C B) A) = (k10_real_1 (k8_real_1 2 (k9_real_1 (k21_sin_cos A) (k21_sin_cos (k7_real_1 A B)))) (k7_real_1 (k21_sin_cos (k7_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B)))) ) ) ) ) ) ) ) ) ) ).
tt(t66_ens_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ((r1_tarski (k16_ens_1 B) A) => (r1_funct_2 (u4_struct_0 (k2_oppcat_1 B)) (u4_struct_0 (k11_ens_1 A)) (u4_struct_0 B) (u4_struct_0 (k11_ens_1 A)) (k13_cat_2 (k2_oppcat_1 B) B (k11_ens_1 A) (k25_ens_1 A B) C) (k24_ens_1 A B C))) ) ) ) ) ) ) ).
tt(t66_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 B A D C)) ) ) ) ) ).
tt(t66_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (C = (k8_relset_1 A B (k13_eqrel_1 A B) (k6_domain_1 B C))) ) ) ) ) ) ) ).
tt(t66_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  ((k12_euclid (k9_euclid 3 B A)) = (k11_binop_2 (k18_complex1 A) (k7_square_1 (k9_binop_2 (k9_binop_2 (k5_square_1 (k1_seq_1 B 1)) (k5_square_1 (k1_seq_1 B 2))) (k5_square_1 (k1_seq_1 B 3)))))) ) ) ) ) ).
tt(t66_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k16_euclid A) = (k4_struct_0 (k15_euclid A))) ) ) ).
tt(t66_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r5_euclidlp A B C) =>  ((v1_euclid_4 B A) & (v1_euclid_4 C A)) ) ) ) ) ) ) ) ).
tt(t66_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) =>  ((r2_hidden C D) =>  ((k1_binop_1 (k7_exchsort A B C D) C D) = (k4_tarski C D)) ) ) ) ) ) ) ) ) ) ).
tt(t66_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = (k4_tarski (k10_finseq_1 B C) k3_facirc_1)) )  =>  (! [D:$i] :  ((m1_subset_1 D (k4_card_3 (u3_msualg_1 (k8_facirc_1 B C A k3_facirc_1) (k10_facirc_1 B C A k3_facirc_1)))) =>  (! [E:$i] :  ((m1_subset_1 E k6_margrel1) =>  (! [F:$i] :  ((m1_subset_1 F k6_margrel1) =>  (! [G:$i] :  ((m1_subset_1 G k6_margrel1) =>  ( ( (E = (k1_funct_1 D B))  &  ( (F = (k1_funct_1 D C))  &  (G = (k1_funct_1 D A)) ) )  =>  ((k11_facirc_1 (k8_facirc_1 B C A k3_facirc_1) (k10_facirc_1 B C A k3_facirc_1) (k5_facirc_1 (k8_facirc_1 B C A k3_facirc_1) (k10_facirc_1 B C A k3_facirc_1) D 2) (k9_facirc_1 B C A k3_facirc_1)) = (k10_margrel1 (k10_margrel1 E F) G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A (k1_relset_1 k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)))) &  ((r2_relset_1 k1_numbers k1_numbers B (k1_taylor_1 2)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ( (~ (r1_xxreal_0 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) C) (k1_real_1 1)))  &  (~ (r1_xxreal_0 1 (k1_seq_1 (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) C))) ) ) ) ) ) )  =>  ((r2_hidden k6_numbers A) |  ((r2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((r2_hidden C A) =>  ((k1_seq_1 (k2_fdiff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k6_rfunct_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers A)) k2_sin_cos9)) A) C) = (k7_real_1 (k8_real_1 (k8_real_1 2 C) (k1_seq_1 k2_sin_cos9 (k10_real_1 1 C))) (k10_real_1 (k5_square_1 C) (k7_real_1 1 (k5_square_1 C))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_fib_num2,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((k18_rvsum_1 (k6_fib_num2 (k2_nat_1 (k4_nat_1 2 A) 1))) = (k1_pre_ff (k2_nat_1 (k4_nat_1 2 A) 2))) ) ) ).
tt(t66_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  => (r8_relat_2 (k8_filter_0 A B) (u1_struct_0 A))) ) ) ) ) ).
tt(t66_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((v13_lattices A) => (r1_filter_2 (u1_struct_0 A) (k6_filter_2 A B) (k9_filter_2 A (k5_lattices A) B))) ) ) ) ) ).
tt(t66_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_finseq_1 E)) )  =>  ( (E = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B)) (k9_finseq_1 C)) (k9_finseq_1 D)))  =>  ( ((k3_finseq_1 E) = 4)  &  ( ((k1_funct_1 E 1) = A)  &  ( ((k1_funct_1 E 2) = B)  &  ( ((k1_funct_1 E 3) = C)  &  ((k1_funct_1 E 4) = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k2_zfmisc_1 (k1_tarski A) (k10_xtuple_0 B)) (k9_xtuple_0 C)) =>  ((v1_relat_1 (k5_funcop_1 C A B)) &  ((v1_funct_1 (k5_funcop_1 C A B)) & (v1_finseq_1 (k5_funcop_1 C A B))) ) ) ) ) ) ) ) ).
tt(t66_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] : (r1_tarski (k10_xtuple_0 (k1_finseq_3 A B)) (k10_xtuple_0 A))) ) ) ).
tt(t66_finseq_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) )  =>  (~  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) &  (! [D:$i] :  (~  ((r2_hidden D B) &  (! [E:$i] :  (~  ((r2_hidden E A) &  ((k1_funct_1 C E) = D) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  ((k2_xcmplx_0 D A) = (k2_nat_1 (k3_finseq_1 C) 1)) )  =>  ((k7_partfun1 B C D) = (k7_partfun1 B (k4_finseq_5 B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t66_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k10_xtuple_0 C)) =>  ((k1_finseq_5 A (k8_finseq_1 A C D) B) = (k1_finseq_5 A C B)) ) ) ) ) ) ) ) ) ) ).
tt(t66_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  ( ((v2_binop_1 C A) &  ((v1_setwiseo C A) &  ((v1_finseqop C A) &  ((r6_binop_1 A D C) &  (B = (k4_binop_1 A C)) ) ) ) )  =>  (! [E:$i] :  ((m1_subset_1 E A) =>  ( ((k5_binop_1 A D B E) = B)  &  ((k5_binop_1 A D E B) = B) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k7_flang_1 A (k8_flang_1 A B) C) = (k8_flang_1 A B)) ) ) ) ) ) ) ).
tt(t66_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((k6_flang_1 A (k1_flang_2 A B C D) (k8_flang_1 A B)) = (k6_flang_1 A (k8_flang_1 A B) (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ).
tt(t66_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k8_afinsq_1 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k8_afinsq_1 A)) =>  ( ((r2_hidden C (k2_flang_3 A B)) & (r2_hidden D (k2_flang_3 A B)))  => (r2_hidden (k1_flang_1 A C D) (k2_flang_3 A B))) ) ) ) ) ) ) ) ).
tt(t66_fsm_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v8_struct_0 C) &  ((v5_fsm_1 C A B) &  ((v7_fsm_1 C A B) & (l2_fsm_1 C A B)) ) ) )  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  &  ((v8_struct_0 D) &  ((v5_fsm_1 D A B) &  ((v7_fsm_1 D A B) & (l2_fsm_1 D A B)) ) ) )  =>  ((r7_fsm_1 A B C D) <=> (r4_fsm_1 A B C D)) ) ) ) ) ) ) ) ) ).
tt(t66_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  ((v3_binop_1 C A) => (r2_funct_2 B A (k6_funcop_1 A B C D D) D)) ) ) ) ) ) ) ) ).
tt(t66_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ((r1_xboole_0 A B) & (v2_funct_1 C))  => (r1_xboole_0 (k7_relat_1 C A) (k7_relat_1 C B))) ) ) ) ) ).
tt(t66_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden C (k1_funct_2 A B)) =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ).
tt(t66_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k15_funct_3 A B) = (k13_funct_3 (k3_relat_1 (k9_funct_3 (k9_xtuple_0 A) (k9_xtuple_0 B)) A) (k3_relat_1 (k10_funct_3 (k9_xtuple_0 A) (k9_xtuple_0 B)) B))) ) ) ) ) ).
tt(t66_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  ( ( ((k9_xtuple_0 E) = (k2_tarski A B))  &  ( ((k1_funct_1 E A) = C)  &  ((k1_funct_1 E B) = D) ) )  =>  (E = (k4_funct_4 A B C D)) ) ) ) ) ) ) ) ).
tt(t66_funct_5,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~  (A = B) )  =>  ((r2_wellord2 (k1_funct_2 (k2_tarski A B) C) (k2_zfmisc_1 C C)) &  ((k1_card_1 (k1_funct_2 (k2_tarski A B) C)) = (k1_card_1 (k2_zfmisc_1 C C))) ) ) ) ) ) ).
tt(t66_funct_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_7 B A) =>  ( (~  (B = k1_xboole_0) )  =>  ( ((k6_funct_7 B) = (k1_funct_1 A 1))  & (r1_tarski (k7_funct_7 B) (k1_funct_1 A (k3_finseq_1 A)))) ) ) ) ) ) ).
tt(t66_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r1_funct_8 A k1_numbers k1_numbers k19_sin_cos)) ) ).
tt(t66_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v1_realset2 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_fvaluat1 B A) =>  ((v3_fvaluat1 A) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_fvaluat1 A B))) =>  ( ( ( (~ (v1_xboole_0 C))  &  ((v1_ideal_1 C (k7_fvaluat1 A B)) &  ((v2_ideal_1 C (k7_fvaluat1 A B)) &  ((v3_ideal_1 C (k7_fvaluat1 A B)) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k7_fvaluat1 A B))))) ) ) )  & (r2_hidden D (k9_fvaluat1 A B C)))  =>  (C = (k7_ideal_1 (k7_fvaluat1 A B) (k6_domain_1 (u1_struct_0 (k7_fvaluat1 A B)) D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ( ((k12_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A C) D) = (k10_fvsum_1 A B D C))  &  ((k12_fvsum_1 A B D (k5_finseq_2 (u1_struct_0 B) A C)) = (k10_fvsum_1 A B D C)) ) ) ) ) ) ) ) ) ) ).
tt(t66_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  ((k2_msafree2 (k25_gfacirc1 A B C)) = (k1_enumset1 A B C)) ) ) ) ) ) ) ).
tt(t66_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r1_glib_000 A C D B) =>  ( ((k29_glib_000 A C B) = D)  &  ((k29_glib_000 A D B) = C) ) ) ) ) ) ) ) ) ) ).
tt(t66_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((r1_glib_001 A C D B) & (r1_glib_000 A D F E))  => (r1_glib_001 A C F (k10_glib_001 A B E))) ) ) ) ) ) ) ) ) ).
tt(t66_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((r1_xxreal_0 (k1_matrix_1 B) 1) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 2)) (k10_real_1 1 2))) (k2_xboole_0 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A k6_numbers)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A 1))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A 1) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) 1)) (k10_real_1 1 2)))))) ) ) ) ) ) ) ).
tt(t66_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k3_group_11 A B E) (k9_subset_1 (u1_struct_0 A) (k3_group_11 A B C) (k3_group_11 A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) => (m1_group_2 B (k7_group_2 A))) ) ) ) ).
tt(t66_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v8_struct_0 C) & (m1_group_2 C A))  =>  ((k7_group_1 C) = (k7_group_1 (k6_group_3 A C B))) ) ) ) ) ) ) ).
tt(t66_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  => (r1_group_2 A (k8_group_4 A (k10_group_2 A B C) C) C)) ) ) ) ) ) ).
tt(t66_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ((m1_group_2 C A) =>  (! [D:$i] :  ((m1_group_2 D A) =>  (! [E:$i] :  ((m1_group_2 E A) =>  ( ((m1_group_2 B C) & (m1_group_2 D E))  => (m1_group_2 (k8_group_5 A B D) (k8_group_5 A C E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  ((r1_group_6 A B) => (r1_group_6 B A)) ) ) ) ) ).
tt(t66_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A (k1_funct_2 B B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A (k1_funct_2 B B))))) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 B)) =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ( (~ (v1_xboole_0 D))  =>  ((r2_hidden E (k1_group_9 A B C D)) <=>  (? [F:$i] :  ((m2_finseq_1 F A) &  (? [G:$i] :  ((m1_subset_1 G D) &  ((k1_funct_1 (k2_group_9 A B C F) G) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k8_hermitan A B)) = (k10_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k14_bilinear k1_complfld A A (k3_hermitan A A B))) (k7_hermitan A A B))) ) ) ) ) ).
tt(t66_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ((r1_taylor_1 B 2 A) => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k41_valued_1 k1_numbers k1_numbers B) A) 2) (k3_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 2)) 2) (k26_valued_1 k1_numbers k1_numbers (k41_valued_1 k1_numbers k1_numbers (k2_fdiff_1 B A)) 2)))) ) ) ) ) ).
tt(t66_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_hidden B (k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) B)))) ) ) ) ).
tt(t66_int_1,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k4_int_1 (k2_xcmplx_0 B A)) = (k4_int_1 B)) ) ) ) ) ).
tt(t66_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k10_real_1 (k1_seq_1 k1_sin_cos6 D) (k7_square_1 (k9_real_1 1 (k5_square_1 D))))) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k1_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t66_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r2_fdiff_1 A D) &  ((r2_fdiff_1 B D) &  ((r1_tarski C D) &  ((r1_integra5 C (k2_fdiff_1 A D)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 A D) C)) &  ((r1_integra5 C (k2_fdiff_1 B D)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 B D) C))) ) ) ) ) )  =>  ((k2_integra5 C (k3_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D))) = (k9_real_1 (k7_real_1 (k9_real_1 (k1_seq_1 A (k4_seq_4 C)) (k1_seq_1 A (k5_seq_4 C))) (k1_seq_1 B (k4_seq_4 C))) (k1_seq_1 B (k5_seq_4 C)))) ) ) ) ) ) ) ) ) ) ).
tt(t66_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k7_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2)) = E)  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2)) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_prepower (k7_real_1 A F) (k1_real_1 (k10_real_1 1 2)))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) 2) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) =>  (! [D:$i] :  ((m2_interva1 D A) => (r2_interva1 A (k17_interva1 A B (k16_interva1 A C D)) (k16_interva1 A (k17_interva1 A B C) (k17_interva1 A B D)))) ) ) ) ) ) ) ) ).
tt(t66_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_intpro_1) =>  (! [B:$i] :  ((m1_subset_1 B k1_intpro_1) =>  (! [C:$i] :  ((m1_subset_1 C k1_intpro_1) => (r2_hidden (k3_intpro_1 (k5_intpro_1 (k5_intpro_1 A B) C) (k5_intpro_1 A (k5_intpro_1 B C))) k8_intpro_1)) ) ) ) ) ) ).
tt(t66_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (k5_jgraph_4 A) B)) = (k12_euclid B)) ) ) ) ) ).
tt(t66_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid A)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid B)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid C)))  &  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid D)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid A)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid B)))  &  ( (~ (r1_xxreal_0 k6_numbers (k18_euclid C)))  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F G)) = (k12_euclid G)) ) )  &  ( ((k19_euclid (k1_real_1 1) k6_numbers) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( ((k19_euclid k6_numbers 1) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( ((k19_euclid 1 k6_numbers) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ((k19_euclid k6_numbers (k1_real_1 1)) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v2_compts_1 D (k15_euclid 2)) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ( (D = (k5_jgraph_6 k6_numbers k6_numbers 1))  &  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E k1_jgraph_3) &  ((r2_hidden A (k1_rltopsp1 (k15_euclid 2) (k19_euclid (k1_real_1 1) (k1_real_1 1)) (k19_euclid (k1_real_1 1) 1))) &  ((r1_xxreal_0 k6_numbers (k18_euclid A)) &  ((r1_jordan6 (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1) A B) & (r1_jordan6 (k1_sppol_2 (k1_real_1 1) 1 (k1_real_1 1) 1) B C)) ) ) ) )  => (r1_jordan6 D (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E B) (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) &  ((r1_xxreal_0 C (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) D) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) B)) ) )  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 D C) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) A) |  ((r1_xxreal_0 (k1_real_1 1) (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G))) &  ((r1_xxreal_0 (k18_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1) &  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k1_real_1 1)))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  ((k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A)))) = (k7_real_1 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))))) ) ) ) ) ) ) ).
tt(t66_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_tarski A B) =>  ( ( (~ (r2_hidden (k23_pscomp_1 B) A))  &  (~ (r2_hidden (k22_pscomp_1 B) A)) )  |  ((k8_pscomp_1 A) = (k8_pscomp_1 B)) ) ) ) ) ) ) ).
tt(t66_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r1_xxreal_0 1 A) &  ((v9_rltopsp1 B (k15_euclid A)) &  ((k3_subset_1 (u1_struct_0 (k15_euclid A)) B) = k1_xboole_0) ) ) ) ) ) ) ) ).
tt(t66_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k10_jordan6 A) (k9_jordan6 A))) ) ).
tt(t66_jordan,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ( ((v2_xxreal_0 C) & (v1_xreal_0 C))  =>  ((r2_hidden B (k1_topreal9 2 A C)) => (v5_pre_topc (k10_jordan 2 A B C) (k7_toprealb 2 A C) (k7_toprealb 2 A C))) ) ) ) ) ) ) ).
tt(t66_lattice2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k5_finsub_1 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v10_lattices C) &  ((v11_lattices C) &  ((v13_lattices C) & (l3_lattices C)) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u1_struct_0 C))))) )  =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 C)) =>  ((k4_lattices C E (k2_lattice2 A C B D)) = (k2_lattice2 A C B (k10_funcop_1 (u1_struct_0 C) A (u1_lattices C) E D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 (k15_glib_000 A) B) =>  ((k23_lexbfs A (k26_lexbfs A) (k15_glib_000 A)) = (k23_lexbfs A (k26_lexbfs A) B)) ) ) ) ) ) ).
tt(t66_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v8_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B)))) ) ) ) )  | (v7_limfunc1 A)) ) ) ) ).
tt(t66_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) &  ((r4_limfunc2 C A) &  ((k2_limfunc2 B A) = (k2_limfunc2 C A)) ) )  =>  ( (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  (~  ( (~ (r1_xxreal_0 E k6_numbers))  &  ((r1_tarski (k2_rcomp_1 A (k7_real_1 A E)) (k9_subset_1 k1_numbers (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k1_relset_1 k1_numbers C)) (k1_relset_1 k1_numbers D))) &  (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F (k2_rcomp_1 A (k7_real_1 A E))) =>  ((r1_xxreal_0 (k1_seq_1 B F) (k1_seq_1 D F)) & (r1_xxreal_0 (k1_seq_1 D F) (k1_seq_1 C F))) ) ) ) ) ) ) ) )  |  ((r4_limfunc2 D A) &  ((k2_limfunc2 D A) = (k2_limfunc2 B A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v3_limfunc1 A) &  ((r4_limfunc2 B (k4_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 D C))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k3_limfunc1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k4_limfunc1 A))) ) ) ) )  |  ((v3_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k4_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k2_limfunc2 B (k4_limfunc1 A))) ) ) ) ) ) ) ) ).
tt(t66_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (m1_subset_1 D k1_numbers))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (! [F:$i] :  ((v7_ordinal1 F) => (r2_hidden (k4_mesfunc5 A k1_numbers E F) (k1_lpspace2 A B C D))) )  =>  (! [F:$i] :  ((v7_ordinal1 F) => (r2_hidden (k4_mesfunc5 A k1_numbers (k2_mesfun9c A E) F) (k1_lpspace2 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A E (k8_cqc_lang A (k8_cqc_lang A B C) D)) => (r3_cqc_the1 A E (k8_cqc_lang A C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_mathmorp,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid B)))) =>  ( (~  (A = k6_numbers) )  =>  ((k6_mathmorp A (k15_euclid B) (k5_mathmorp (k15_euclid B) C D)) = (k5_mathmorp (k15_euclid B) (k6_mathmorp A (k15_euclid B) C) (k6_mathmorp A (k15_euclid B) D))) ) ) ) ) ) ) ) ) ) ).
tt(t66_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((v1_matrix10 B) => (r1_matrix10 C (k3_matrix10 A C B))) ) ) ) ) ) ) ).
tt(t66_matrix13,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ((k5_card_1 C) = (k5_card_1 E))  &  ((r1_tarski D E) &  ( (~  ((k12_matrix_3 (k5_card_1 C) A (k7_matrix13 (u1_struct_0 A) B C E)) = (k4_struct_0 A)) )  &  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (~  ((r1_tarski F C) &  ( ((k5_card_1 F) = (k5_card_1 D))  &  (~  ((k12_matrix_3 (k5_card_1 F) A (k7_matrix13 (u1_struct_0 A) B F D)) = (k4_struct_0 A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  ( ((r1_tarski C (k4_finseq_1 B)) &  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k7_subset_1 k5_numbers (k4_finseq_1 B) C)) =>  ((k8_matrix_1 (u1_struct_0 A) B D) = (k5_finseq_2 (u1_struct_0 A) (k1_matrix_1 B) (k4_struct_0 A))) ) ) ) )  =>  ((v1_xboole_0 C) |  ((r1_xxreal_0 (k1_matrix_1 B) k1_xboole_0) |  ((k7_matrix15 A B) = (k7_matrix15 A (k6_matrix13 (u1_struct_0 A) B C (k2_finseq_1 (k1_matrix_1 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t66_matrix16,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 A)) =>  ( ((v6_matrix16 D A) &  ((v6_matrix16 E A) &  ((k3_finseq_1 D) = (k3_finseq_1 E)) ) )  =>  ((k3_matrix_3 A (k2_matrix13 (k3_finseq_1 D) (k3_finseq_1 D) A (k3_matrix16 A D) B) (k2_matrix13 (k3_finseq_1 E) (k3_finseq_1 E) A (k3_matrix16 A E) C)) = (k3_matrix16 A (k3_fvsum_1 A (k9_fvsum_1 A D B) (k9_fvsum_1 A E C)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( ((k10_matrixj1 (u1_struct_0 A) (k25_matrixj1 A B C)) = (k10_matrixj1 (u1_struct_0 A) B))  &  ((k11_matrixj1 (u1_struct_0 A) (k25_matrixj1 A B C)) = (k11_matrixj1 (u1_struct_0 A) B)) ) ) ) ) ) ) ) ).
tt(t66_matrixr1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_1 C k1_numbers) =>  ( ((k3_finseq_1 C) = A)  =>  ((r1_xxreal_0 A k6_numbers) |  ((k12_matrixr1 (k8_matrixr1 A B) C) = (k5_euclid B)) ) ) ) ) ) ) ) ) ).
tt(t66_matrixr2,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ( (~ (r1_xxreal_0 A k6_numbers))  =>  ((k7_matrixr1 C (k8_matrixr1 A B)) = (k8_matrixr1 A B)) ) ) ) ) ) ) ) ).
tt(t66_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 B C D)) =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ((m1_subset_1 H D) =>  ( (E = (k3_xtuple_0 F G H))  =>  (A = G) ) ) ) ) ) ) )  =>  (A = (k2_mcart_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_measure6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v6_measure6 B A) <=> (v5_measure6 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(t66_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((v1_xcmplx_0 D) =>  ( ((r2_hidden C A) & (r2_hidden D B))  => (r2_hidden (k4_binop_2 C D) (k11_member_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t66_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D (u1_struct_0 B)) &  ((v1_funct_1 D) &  ((v5_funct_1 D (k2_memstr_0 A B)) & (v4_memstr_0 D A B)) ) ) )  =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ((k10_memstr_0 A B (k1_funct_4 C D) E) = (k1_funct_4 (k10_memstr_0 A B C E) D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ( ((r1_mesfunc2 A B D) &  ((v6_supinf_2 D) & (r1_xxreal_0 k6_numbers E)) )  =>  ((k5_mesfunc5 A B C (k6_mesfunc1 A D E)) = (k1_extreal1 (k1_measure6 E) (k5_mesfunc5 A B C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r2_relset_1 A k1_numbers (k18_rfunct_3 A (k2_partfun1 A k1_numbers C B)) (k2_partfun1 A k1_numbers (k18_rfunct_3 A C) B)) & (r2_relset_1 A k1_numbers (k19_rfunct_3 A (k2_partfun1 A k1_numbers C B)) (k2_partfun1 A k1_numbers (k19_rfunct_3 A C) B))) ) ) ) ) ) ).
tt(t66_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k30_mmlquery A C)) <=> (r2_hidden C (k31_mmlquery A B))) ) ) ) ) ) ) ).
tt(t66_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  ((r7_modelc_2 C (k5_modelc_2 A B)) <=>  ((r7_modelc_2 C A) | (r7_modelc_2 C B)) ) ) ) ) ) ) ) ).
tt(t66_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ( ((v6_modelc_2 A) & (v5_modelc_3 A))  => (v5_modelc_3 (k10_modelc_2 A))) ) ) ).
tt(t66_moebius1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  ((a_1_2_moebius1 A) = (a_1_3_moebius1 A)) ) ) ).
tt(t66_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  ((r1_tarski A B) => (m2_monoid_0 (k9_monoid_0 A) (k9_monoid_0 B))) ) ) ) ) ).
tt(t66_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k6_int_1 (k2_xcmplx_0 B C) A) = (k6_int_1 (k2_xcmplx_0 (k6_int_1 B A) (k6_int_1 C A)) A)) ) ) ) ) ) ) ).
tt(t66_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B)))))  =>  ( ((r8_ncfcont1 A B E C) & (r8_ncfcont1 A B F D))  =>  ((r8_ncfcont1 A B (k6_vfunct_1 (u1_struct_0 A) B E F) (k3_xboole_0 C D)) & (r8_ncfcont1 A B (k2_vfunct_1 (u1_struct_0 A) B E F) (k3_xboole_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_newton,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  ( (~  (A = k6_numbers) )  =>  (B = (k2_xcmplx_0 (k3_xcmplx_0 (k5_int_1 B A) A) (k6_int_1 B A))) ) ) ) ) ) ).
tt(t66_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 (k2_oppcat_1 A)) (k7_cat_1 A (k2_oppcat_1 A) (k12_oppcat_1 A)) B) = (k3_oppcat_1 A B)) ) ) ) ) ).
tt(t66_orders_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (! [B:$i] :  (~  ((r1_tarski B A) &  ((v6_ordinal1 B) &  (! [C:$i] :  (~  ((r2_hidden C A) &  (! [D:$i] :  ((r2_hidden D B) => (r1_tarski C D)) ) ) ) ) ) ) ) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ( (~  (C = B) )  & (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  (! [D:$i] :  ((v3_ordinal1 D) =>  ( ( (A = (k10_ordinal2 (k11_ordinal2 B C) D))  & (r2_hidden D C))  =>  ( (B = (k6_ordinal3 A C))  &  (D = (k7_ordinal3 A C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) & (v1_ordinal2 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v5_ordinal1 B) & (v1_ordinal2 B)) ) )  =>  ((v6_ordinal5 (k1_ordinal4 A B)) =>  ((v6_ordinal5 A) & (v6_ordinal5 B)) ) ) ) ) ) ).
tt(t66_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) => (r2_hidden A (k1_classes1 (k2_xboole_0 (k2_xboole_0 A B) C)))) ) ) ) ) ) ).
tt(t66_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v7_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t66_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((v1_partfun1 C A) &  ((v1_partfun1 D A) & (r1_partfun1 C D)) )  =>  (C = D) ) ) ) ) ) ) ) ).
tt(t66_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  ((r2_pboole A B C) => (r6_pboole A C (k2_pboole A B (k4_pboole A C B)))) ) ) ) ) ) ).
tt(t66_pdiff_5,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ((r9_pdiff_5 C B) =>  ((r3_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) &  ((k11_pdiff_1 3 3 (k26_valued_1 (k1_euclid 3) k1_numbers (k1_pdiff_3 3 3 C) A) B) = (k8_real_1 A (k9_pdiff_5 C B))) ) ) ) ) ) ) ) ) ).
tt(t66_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ((r3_pdiff_9 A C B D) & (r3_pdiff_9 A C B E)) ) ) )  =>  ((r3_pdiff_9 A C B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) &  ((r2_relset_1 (k1_euclid A) k1_numbers (k3_pdiff_9 A C B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers (k3_pdiff_9 A C B D) (k3_pdiff_9 A C B E))) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 k1_numbers (k3_pdiff_9 A C B (k47_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) F) = (k10_binop_2 (k11_pdiff_1 A B D F) (k11_pdiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_pepin,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ( (~ (r1_xxreal_0 A 1))  &  ( (~ (r1_xxreal_0 B C))  & (r1_xxreal_0 (k1_newton A B) (k1_newton A C))) ) ) ) ) ) ) ) ) ).
tt(t66_pnproc_1,ax, (! [A:$i] :  (! [B:$i] :  ((m2_pnproc_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_finseq_2 B))) =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (k3_finseq_2 B))) =>  ( ((r1_tarski C D) & (r1_tarski E F))  => (r1_tarski (k11_pnproc_1 A B C E) (k11_pnproc_1 A B D F))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (~ (v1_xboole_0 (k8_polyform A (k6_xcmplx_0 (k7_polyform A) 1)))) ) ) ).
tt(t66_polynom5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_group_1 A) & (l3_algstr_0 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r2_funct_2 (u1_struct_0 A) (u1_struct_0 A) (k8_polynom5 A B k6_numbers) (k8_funcop_1 (u1_struct_0 A) (u1_struct_0 A) B))) ) ) ) ).
tt(t66_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (~  ( (~ (r1_xxreal_0 B 1))  &  ( (~ (r1_xxreal_0 (k3_finseq_1 (k20_pre_poly A C)) B))  &  (~  ( (~  ((k7_partfun1 (k15_pre_poly A) (k20_pre_poly A C) B) = (k16_pre_poly A)) )  &  (~  ((k7_partfun1 (k15_pre_poly A) (k20_pre_poly A C) B) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_rat_1 B) =>  ( ((r1_xxreal_0 A 1) & (r1_xxreal_0 B k6_numbers))  =>  ((r1_xxreal_0 A k6_numbers) | (r1_xxreal_0 1 (k6_prepower A B))) ) ) ) ) ) ).
tt(t66_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v2_prob_3 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_prob_1 C) & (r1_tarski (k2_relset_1 (k9_setfam_1 A) C) B))  => (r2_hidden (k4_kurato_0 A C) B)) ) ) ) ) ) ) ).
tt(t66_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k7_pscomp_1 A) (k7_pscomp_1 B))) ) ) ) ) ).
tt(t66_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  => (r6_pboole A (k6_pboole A (k3_pboole A B C) (k3_pboole A D E)) (k3_pboole A (k6_pboole A B D) (k6_pboole A C E)))) ) ) ) ) ) ) ) ) ).
tt(t66_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A B C) <=> (r3_qc_lang2 A B (k13_qc_lang1 A C))) ) ) ) ) ) ) ).
tt(t66_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  ((k6_qc_lang3 A (k1_qc_lang2 A)) = k1_xboole_0) ) ) ).
tt(t66_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k29_quaterni (k29_quaterni A B) C) D) = (k29_quaterni (k29_quaterni (k27_quaterni A D) (k27_quaterni B D)) (k27_quaterni C D))) ) ) ) ) ) ) ) ) ).
tt(t66_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) =>  ( ((k32_quaterni A) = k6_numbers)  =>  (A = k6_numbers) ) ) ) ).
tt(t66_rcomp_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 (k4_topmetr A B))))) =>  (! [E:$i] :  ((m1_rcomp_3 E A B D) =>  (! [F:$i] :  ((m2_rcomp_3 F A B D E) =>  ( ((m1_setfam_1 D (u1_struct_0 (k4_topmetr A B))) &  ((v1_tops_2 D (k4_topmetr A B)) &  ((v1_rcomp_3 D (k4_topmetr A B)) &  ((r1_xxreal_0 A B) & (r1_xxreal_0 1 C)) ) ) )  =>  ((r1_xxreal_0 (k3_finseq_1 F) C) | (r1_tarski (k1_rcomp_1 (k1_funct_1 F C) (k1_funct_1 F (k1_nat_1 C 1))) (k1_funct_1 E C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((k9_real_1 (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 2)) (k1_seq_1 (k6_real_3 B) A)) (k8_real_1 (k1_seq_1 (k5_real_3 B) A) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 2)))) = (k8_real_1 (k2_newton (k1_real_1 1) A) (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 2)))) ) ) ) ) ).
tt(t66_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ( ((k5_relat_1 B A) = k1_xboole_0)  <=> (r1_xboole_0 (k9_xtuple_0 B) A)) ) ) ) ).
tt(t66_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ( (~ (r2_hidden (k2_flang_1 A) (k10_xtuple_0 (k9_xtuple_0 (u1_rewrite3 B C)))))  =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  (! [F:$i] :  ((v7_ordinal1 F) =>  (~  ((r2_hidden E (k4_finseq_1 D)) &  ((r2_hidden F (k4_finseq_1 D)) &  ( (~ (r1_xxreal_0 F E))  &  ((k2_xtuple_0 (k1_funct_1 D E)) = (k2_xtuple_0 (k1_funct_1 D F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_rfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  ((k1_funct_1 (k7_rfunct_1 A A) B) = 1) ) ) ) ) ).
tt(t66_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ( ((v1_finset_1 (k1_relset_1 A (k2_partfun1 A k1_numbers D C))) & (r2_hidden B (k1_relset_1 A (k2_partfun1 A k1_numbers D C))))  => (r2_classes1 (k8_finseq_1 k1_numbers (k20_rfunct_3 A D (k6_subset_1 C (k1_tarski B))) (k12_finseq_1 k1_numbers (k1_seq_1 D B))) (k2_partfun1 A k1_numbers D C))) ) ) ) ) ) ) ) ).
tt(t66_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 B) & (v1_seq_2 B))  =>  ((k1_seq_1 (k4_rinfsup1 B) A) = (k1_seq_1 (k4_rinfsup1 B) (k2_nat_1 A 1))) ) ) ) ) ) ).
tt(t66_rlaffin1,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) & (l1_rlvect_1 B)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((r2_hidden A (k3_convex1 B C)) & (v1_convex1 (k7_subset_1 (u1_struct_0 B) (k3_convex1 B C) (k1_tarski A)) B))  => (r2_hidden A C)) ) ) ) ) ) ).
tt(t66_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (~  ( ((k3_rlsub_1 A B D) = (k3_rlsub_1 A C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_struct_0 D E) &  ((k3_rlvect_1 A B E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B:$i] :  ((m1_yellow13 B A (k4_struct_0 A)) & (v4_rltopsp1 B A)) ) ) ) ).
tt(t66_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C B D)) = (k3_rlvect_1 A (k4_rlvect_1 A (k2_finseq_4 (u1_struct_0 A) C D)) B)) ) ) ) ) ) ) ) ) ).
tt(t66_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 C)) =>  ( ((r2_hidden F (k1_relset_1 k5_numbers D)) &  (G = (k1_funct_1 E F)) )  =>  ((k1_funct_1 D F) = (k4_vectsp_1 A C B G)) ) ) ) ) ) )  =>  ((k4_rlvect_1 C D) = (k4_vectsp_1 A C B (k4_rlvect_1 C E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_rmod_2 C A B) =>  (! [D:$i] :  ((m2_rmod_2 D A B C) =>  ((v1_rmod_2 D A B) <=>  (D = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ).
tt(t66_rmod_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  ( (~  ((k4_struct_0 A) = (k1_group_1 A)) )  =>  ( (~ (v1_rmod_4 (k7_domain_1 (u1_struct_0 B) C (k4_struct_0 B)) A B))  &  (~ (v1_rmod_4 (k7_domain_1 (u1_struct_0 B) (k4_struct_0 B) C) A B)) ) ) ) ) ) ) ) ) ).
tt(t66_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (m2_rusub_1 (k6_domain_1 (u1_struct_0 A) B) A (k1_rusub_1 A))) ) ) ) ).
tt(t66_rvsum_1,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k4_finseq_2 A k1_numbers)) =>  ((k11_rvsum_1 A C B) = (k14_rvsum_1 (k2_finseq_2 A B) C)) ) ) ) ) ) ) ).
tt(t66_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k9_scmfsa_2 A B) C) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 C)))  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k9_scmfsa_2 A B) C) A) = (k3_xcmplx_0 (k1_funct_1 C A) (k1_funct_1 C B)))  &  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (D = A) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k9_scmfsa_2 A B) C) D) = (k1_funct_1 C D)) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k9_scmfsa_2 A B) C) D) (k18_scmfsa_2 C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ( (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 D E))  => (r2_hidden (k5_memstr_0 3 k1_scmfsa_2 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) E)) (k2_afinsq_1 C))) ) )  =>  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  ((r1_xxreal_0 E D) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 B) E) (k4_scmfsa_2 k6_numbers)) = (k1_funct_1 B (k4_scmfsa_2 k6_numbers))) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_ami_2 D) &  ( (~ (v1_scmfsa_m D))  & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2))) )  =>  (~  ( (~ (r4_scmfsa7b C D))  &  ( (~ (r1_xxreal_0 (k1_funct_1 B D) k6_numbers))  &  (~  ( ((k1_funct_1 (k1_scmfsa6b (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))) B A) D) = (k6_xcmplx_0 (k1_funct_1 B D) 1))  &  ((k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c D C) B A)) = (k6_memstr_0 3 k1_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c D C) (k1_scmfsa6b (k5_scmfsa6a C (k8_scmfsa_2 D (k4_scmfsa_2 k6_numbers))) B A) A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (~ (v2_extpro_1 (k10_scmpds_2 C A B) 2 k1_scmpds_2)) ) ) ) ) ) ) ).
tt(t66_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((r2_hidden k6_numbers (k9_xtuple_0 (k3_scmpds_6 A B C D))) & (r2_hidden 1 (k9_xtuple_0 (k3_scmpds_6 A B C D)))) ) ) ) ) ) ) ) ) ).
tt(t66_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((v4_scmyciel B) &  ((v5_scmyciel B) & (m1_subset_1 B (k1_zfmisc_1 A))) )  =>  (! [C:$i] :  ((r1_tarski C (k3_tarski B)) =>  ((v4_scmyciel (k7_scmyciel A C)) &  ((v5_scmyciel (k7_scmyciel A C)) & (m1_subset_1 (k7_scmyciel A C) (k1_zfmisc_1 A))) ) ) ) ) ) ) ) ).
tt(t66_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) => (r3_semi_af1 A D E B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k2_numbers (k14_seq_4 A)) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 A)) =>  ((k18_seq_4 A (k15_seq_4 A B C)) = (k15_seq_4 A (k18_seq_4 A B) (k18_seq_4 A C))) ) ) ) ) ) ) ).
tt(t66_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_hidden B (k4_kurato_0 A D)) <=>  (! [E:$i] :  ((m1_subset_1 E k5_numbers) =>  (? [F:$i] :  ((m1_subset_1 F k5_numbers) & (r2_hidden B (k3_funct_2 k5_numbers (k9_setfam_1 A) D (k2_nat_1 E F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v3_kurato_0 B A) & (v3_kurato_0 C A))  =>  ((k3_kurato_0 A (k4_setlim_2 A B C)) = (k5_subset_1 A (k3_kurato_0 A B) (k3_kurato_0 A C))) ) ) ) ) ) ) ).
tt(t66_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_sheffer2 A) & (l1_sheffer1 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k5_sheffer1 A (k5_sheffer1 A (k5_sheffer1 A B B) C) (k5_sheffer1 A (k5_sheffer1 A D D) C)) = (k5_sheffer1 A (k5_sheffer1 A C (k5_sheffer1 A B D)) (k5_sheffer1 A C (k5_sheffer1 A B D)))) ) ) ) ) ) ) ) ) ).
tt(t66_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k1_fdiff_9 (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos)) k2_sincos10) = (k1_partfun2 k1_numbers (k4_rcomp_1 (k10_real_1 k32_sin_cos 2) k32_sin_cos))) ).
tt(t66_sin_cos6,ax, ((k4_relset_1 k1_numbers k1_numbers k1_numbers k1_numbers (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) k1_sin_cos6) = (k6_partfun1 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(t66_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (A = (k12_binop_2 (k9_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B))) (k10_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B)))))  =>  ( (B = k6_numbers)  |  (B = (k11_binop_2 (k18_binop_2 1 2) (k6_power k8_power (k12_binop_2 (k9_binop_2 A 1) (k10_binop_2 A 1))))) ) ) ) ) ) ) ).
tt(t66_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 1 A))  &  (~  ( (~ (r1_xxreal_0 (k6_sin_cos9 A) (k10_real_1 k32_sin_cos 4)))  &  (~ (r1_xxreal_0 (k8_real_1 (k10_real_1 3 4) k32_sin_cos) (k6_sin_cos9 A))) ) ) ) ) ) ) ) ).
tt(t66_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k24_sin_cos k1_numbers) &  ((k1_fdiff_1 k24_sin_cos A) = (k1_seq_1 k24_sin_cos A)) ) ) ) ).
tt(t66_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k14_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k1_rltopsp1 (k15_euclid 2) (k10_pscomp_1 A) (k11_pscomp_1 A))) ) ) ).
tt(t66_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k20_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k20_pscomp_1 (k3_topreal1 2 A)) = (k11_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k11_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t66_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k19_pscomp_1 (k3_topreal1 2 A)))  &  ( (~  ((k19_pscomp_1 (k3_topreal1 2 A)) = (k20_pscomp_1 (k3_topreal1 2 A))) )  & (r1_xxreal_0 (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k19_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ) ).
tt(t66_stirl2_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_relat_1 B A) &  ((v5_ordinal1 B) &  ((v1_funct_1 B) & (v1_finset_1 B)) ) ) )  =>  (~  ( (! [C:$i] :  ((v7_ordinal1 C) =>  ((r2_hidden C (k2_afinsq_1 B)) => (v1_finset_1 (k1_funct_1 B C))) ) )  &  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden C (k2_afinsq_1 B)) & (r2_hidden D (k2_afinsq_1 B)))  =>  ( (C = D)  | (r1_xboole_0 (k1_funct_1 B C) (k1_funct_1 B D))) ) ) ) ) )  &  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v5_relat_1 C k5_numbers) &  ((v5_ordinal1 C) &  ((v1_funct_1 C) & (v1_finset_1 C)) ) ) )  =>  (~  ( ((k2_afinsq_1 C) = (k2_afinsq_1 B))  &  ( (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden D (k2_afinsq_1 C)) =>  ((k1_funct_1 C D) = (k1_card_1 (k1_funct_1 B D))) ) ) )  &  ((k1_card_1 (k3_tarski (k2_relset_1 A B))) = (k7_afinsq_2 C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m2_funct_2 E (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m1_subset_1 G D) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D E (k7_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k6_domain_1 (k3_qc_lang1 A) C))) (k5_relset_1 (k3_qc_lang1 A) D F (k7_subset_1 (k3_qc_lang1 A) (k24_qc_lang1 A B) (k6_domain_1 (k3_qc_lang1 A) C)))) => (r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D (k1_sublemma A D E (k12_sublemma A D C G)) (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) D (k1_sublemma A D F (k12_sublemma A D C G)) (k24_qc_lang1 A B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tdlat_2 B A) =>  ((r1_tarski (k5_setfam_1 (u1_struct_0 A) B) (k2_pre_topc A (k1_tops_1 A (k5_setfam_1 (u1_struct_0 A) B)))) &  ((k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B)) = (k2_pre_topc A (k1_tops_1 A (k2_pre_topc A (k5_setfam_1 (u1_struct_0 A) B))))) ) ) ) ) ) ) ).
tt(t66_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (? [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v5_pre_topc C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  & (v3_borsuk_1 C A B)) ) ) ) ) ) ).
tt(t66_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_pre_topc C) & (l1_pre_topc C)) )  =>  ( (C = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B)))  =>  ( ((v4_tex_3 B A) & (m1_pre_topc B A))  <=>  ((v4_tex_3 C A) & (m1_pre_topc C A)) ) ) ) ) ) ) ) ) ).
tt(t66_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (C = (u1_struct_0 B))  & (v2_tdlat_3 B))  => (v1_tex_4 C A)) ) ) ) ) ) ) ).
tt(t66_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ( (~ (v2_struct_0 D))  & (m1_pre_topc D A))  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 D) (u1_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 D) (u1_struct_0 B))))) )  =>  ((m1_pre_topc C D) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  =>  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 D)) =>  ((r2_hidden G (u1_struct_0 C)) =>  ((k3_funct_2 (u1_struct_0 D) (u1_struct_0 B) E G) = (k1_funct_1 F G)) ) ) )  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) (k3_tmap_1 A B D C E) F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_topgen_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  ((k5_topgen_4 A) = (k9_prob_1 (u1_struct_0 A) (k1_openlatt A))) ) ) ).
tt(t66_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_tarski (k1_topreal9 2 (k19_euclid A (k3_xcmplx_0 C B)) (k3_xcmplx_0 C B)) (k8_relset_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr) (k4_topgen_5 A C) (k2_rcomp_1 k6_numbers B)))) ) ) ) ) ) ).
tt(t66_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (~  ((r1_xxreal_0 1 A) &  ( ((u1_struct_0 (k15_euclid A)) = (k4_subset_1 (u1_struct_0 (k15_euclid A)) B C))  &  ((v9_rltopsp1 B (k15_euclid A)) & (v9_rltopsp1 C (k15_euclid A))) ) ) ) ) ) ) ) ) ) ).
tt(t66_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((v4_pre_topc D B) & (v4_tops_1 D B))  => (v5_tops_1 D B))  &  ((v5_tops_1 C A) =>  ((v4_pre_topc C A) & (v4_tops_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ((v3_pre_topc C A) &  ((r1_tarski C (u1_struct_0 B)) &  ((r1_tarski D C) &  ( (D = E)  & (v2_tops_1 D A)) ) ) )  => (v2_tops_1 E B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ((v6_transgeo B A) => (v6_transgeo (k2_funct_2 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t66_trees_3,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_trees_1 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v1_trees_1 B))  =>  ((k5_trees_1 (k12_trees_3 A) (k12_finseq_1 k5_numbers k6_numbers) B) = (k12_trees_3 B)) ) ) ) ) ).
tt(t66_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  ( ( ((v1_borsuk_1 (k1_tsep_1 A B C) A) & (m1_pre_topc (k1_tsep_1 A B C) A))  & (r3_tsep_1 A B C))  =>  ((v1_borsuk_1 B A) & (m1_pre_topc B A)) ) ) ) ) ) ) ) ).
tt(t66_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 (k14_polynom3 A))) =>  ( ( ((k3_finseq_1 C) = (k5_card_1 B))  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ( ((r2_hidden D (k4_finseq_1 C)) &  (E = (k1_funct_1 (k1_uproots B) D)) )  =>  ((k1_funct_1 C D) = (k4_polynom5 A (k4_algstr_0 A E) (k5_struct_0 A))) ) ) ) ) ) )  =>  ((k10_uproots A (k2_uproots (u1_struct_0 A) B 1)) = (k3_group_4 (k14_polynom3 A) C)) ) ) ) ) ) ) ) ).
tt(t66_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((k52_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k58_valued_2 A B C D) E) = (k58_valued_2 A B C (k45_valued_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t66_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v7_vectsp_1 D A) & (m1_vectsp_4 D A B))  =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  ( ((k3_vectsp_4 A B C D) = (k3_vectsp_4 A B C E))  <=>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) <=>  ((v2_funct_1 C) &  ( ((k2_relset_1 (u1_struct_0 B) C) = (u1_struct_0 B))  &  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r1_orders_2 A D E) <=> (r1_orders_2 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C D) (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) C E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v9_waybel_1 A) => (v2_waybel_1 A)) ) ) ).
tt(t66_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  =>  ((v17_waybel_0 (k3_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A) & (v18_waybel_0 (k3_waybel23 A (k5_yellow_0 A B)) (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))) A)) ) ) ) ) ).
tt(t66_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v18_waybel_0 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v3_waybel34 C B A) <=>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) C (u1_struct_0 (k1_waybel_8 B)))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) C (u1_struct_0 (k1_waybel_8 B))) (u1_struct_0 (k1_waybel_8 B)) (u1_struct_0 (k1_waybel_8 A))) &  ((v4_waybel34 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) C (u1_struct_0 (k1_waybel_8 B))) (k1_waybel_8 B) (k1_waybel_8 A)) & (m1_subset_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) C (u1_struct_0 (k1_waybel_8 B))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel_8 B)) (u1_struct_0 (k1_waybel_8 A)))))) ) ) ) ) ) ) ) ) ) ).
tt(t66_xboole_1,ax, (! [A:$i] :  ( (~  ( (~ (r1_xboole_0 A A))  &  (A = k1_xboole_0) ) )  &  (~  ( (~  (A = k1_xboole_0) )  & (r1_xboole_0 A A)) ) ) ) ).
tt(t66_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k7_xboolean B C)) = (k3_xboolean (k4_xboolean (k4_xboolean A (k5_xboolean (k3_xboolean B) C)) (k5_xboolean (k3_xboolean C) B)))) ) ) ) ) ) ) ).
tt(t66_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ( (A = (k7_xcmplx_0 (k2_xcmplx_0 A B) 2))  =>  (A = B) ) ) ) ) ) ).
tt(t66_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 k6_numbers A) &  ((r1_xxreal_0 A B) &  ((r1_xxreal_0 k6_numbers C) & (r1_xxreal_0 C D)) ) )  => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t66_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((r1_xxreal_0 A B) &  ((k1_xxreal_1 A B) = (k1_xxreal_1 C D)) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) =>  (! [C:$i] :  ((m2_xxreal_2 C A) =>  (! [D:$i] :  ((m2_xxreal_2 D B) => (m2_xxreal_2 (k4_xxreal_0 C D) (k3_xboole_0 A B))) ) ) ) ) ) ) ) ).
tt(t66_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  ((k4_xxreal_3 A (k4_xxreal_3 B C)) = (k4_xxreal_3 (k4_xxreal_3 A B) C)) ) ) ) ) ) ) ).
tt(t66_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v4_orders_2 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ( ((r1_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D)) & (r2_hidden (k1_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D)) (u1_struct_0 B)))  =>  ((r1_yellow_0 B (k7_domain_1 (u1_struct_0 B) C D)) &  ((k1_yellow_0 B (k7_domain_1 (u1_struct_0 B) C D)) = (k1_yellow_0 A (k7_domain_1 (u1_struct_0 B) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t66_yellow10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) )  =>  ((v2_waybel_1 (k3_yellow_3 A B)) => (v2_waybel_1 B)) ) ) ) ) ).
tt(t66_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k7_waybel_1 A (k1_yellow_5 A B C)) = (k13_lattice3 A (k7_waybel_1 A B) C)) ) ) ) ) ) ) ).
tt(t66_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  ((k2_zf_model (k13_zf_lang B A)) = (k7_subset_1 k1_zf_lang (k2_zf_model A) (k1_tarski B))) ) ) ) ) ).
tt(t66_zf_lang,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_zf_lang B) & (m2_finseq_1 B k5_numbers))  =>  ( ((r2_zf_lang A B) & (r2_zf_lang B A))  =>  (A = B) ) ) ) ) ) ).
tt(t66_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((k4_xboole_0 A (k2_tarski B C)) = k1_xboole_0)  <=>  (~  ( (~  (A = k1_xboole_0) )  &  ( (~  (A = (k1_tarski B)) )  &  ( (~  (A = (k1_tarski C)) )  &  (~  (A = (k2_tarski B C)) ) ) ) ) ) ) ) ) ) ).
tt(t66_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r1_struct_0 D B) <=>  ((k5_zmodul01 A C D) = (k5_zmodul01 A (k5_algstr_0 A C B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t67_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r1_rewrite1 (k11_abcmiz_0 A) B C) => (r3_orders_2 A B C)) ) ) ) ) ) ) ).
tt(t67_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  ((k37_abcmiz_1 A (k37_abcmiz_1 A B)) = B) ) ) ) ) ).
tt(t67_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ((v1_aff_4 D A) =>  ((k3_aff_4 A B D) = (k3_aff_4 A B (k3_aff_4 A C D))) ) ) ) ) ) ) ) ) ) ).
tt(t67_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) & (v1_afinsq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) & (v1_funct_1 B)) )  =>  ( ((k9_xtuple_0 A) = (k9_xtuple_0 B))  => (v1_afinsq_1 B)) ) ) ) ) ).
tt(t67_afinsq_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( (~  ((k1_funct_1 C A) = B) )  =>  ((k8_relat_1 (k5_relat_1 C (k6_subset_1 (k9_xtuple_0 C) (k1_tarski A))) (k1_tarski B)) = (k8_relat_1 C (k1_tarski B))) ) ) ) ) ) ).
tt(t67_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r4_analmetr A B C D E) &  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  (~  ((r5_analmetr A B C F) & (r5_analmetr A D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ((m1_subset_1 (k4_trees_4 4 B) (u1_struct_0 (k7_freealg k19_aofa_000 A))) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  (B = (k2_finseq_4 (u1_struct_0 (k7_freealg k19_aofa_000 A)) C D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_aofa_i00,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_unialg_1 A) &  ((v3_unialg_1 A) &  ((v4_unialg_1 A) &  ((v3_aofa_000 A) &  ((v4_aofa_000 A) &  ((v5_aofa_000 A) &  ((v6_aofa_000 A) &  ((v2_aofa_i00 A) & (l1_unialg_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (v4_card_3 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ( ((v1_aofa_i00 D A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)) & (m1_aofa_000 D A (k9_funct_2 B k4_numbers) (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers)))  =>  (! [E:$i] :  ((m1_aofa_i00 E B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [F:$i] :  ((m1_aofa_i00 F B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  (! [G:$i] :  ((m1_aofa_i00 G B (u1_struct_0 A) (k9_funct_2 B k4_numbers) D) =>  ( (? [H:$i] :  ( ((v1_relat_1 H) & (v1_funct_1 H))  &  ( ((k1_funct_1 H C) = k6_numbers)  &  ( ((k1_funct_1 H E) = 1)  &  ( ((k1_funct_1 H F) = 2)  &  ((k1_funct_1 H G) = 3) ) ) ) ) )  =>  (! [H:$i] :  ((m2_funct_2 H B k4_numbers (k9_funct_2 B k4_numbers)) =>  (! [I:$i] :  ((v7_ordinal1 I) =>  ( (I = (k21_aofa_i00 B k4_numbers H G))  =>  ((k21_aofa_i00 B k4_numbers (k89_aofa_i00 B A (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D H (k13_aofa_000 A (k51_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F 1) (k16_aofa_000 A (k78_aofa_i00 A B C D G k6_numbers) (k13_aofa_000 A (k13_aofa_000 A (k15_aofa_000 A (k72_aofa_i00 A B C D G) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D F E)) (k60_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D G 2)) (k82_aofa_i00 A B (k1_aofa_i00 (k9_funct_2 B k4_numbers) C k6_numbers) D E E))))) F) = (k1_newton (k21_aofa_i00 B k4_numbers H E) I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  (! [C:$i] :  ((m1_subset_1 C k5_arytm_3) =>  ( ((r3_arytm_3 A B) & (r3_arytm_3 B C))  => (r3_arytm_3 A C)) ) ) ) ) ) ) ).
tt(t67_asympt_1,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (~  ( (~ (r1_xxreal_0 A 6))  & (r1_xxreal_0 (k4_power 2 A) (k5_square_1 A))) ) ) ) ).
tt(t67_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A C B) = (k1_bcialg_1 A D B))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) => (r1_boolealg A (k3_boolealg A (k3_boolealg A B C) D) (k3_boolealg A B (k3_boolealg A C D)))) ) ) ) ) ) ) ) ).
tt(t67_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  ( (A = (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k4_subset_1 k1_numbers (k2_rcomp_1 k2_xxreal_0 B) (k4_rcomp_1 B C)) (k3_borsuk_5 C D)) (k1_seq_4 D)) (k1_seq_4 E)))  =>  ((r1_xxreal_0 C B) |  ((r1_xxreal_0 D C) |  ((k2_pre_topc k3_topmetr A) = (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 D) (k1_seq_4 E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_borsuk_6,ax,(r2_hidden (k4_tarski (k10_real_1 1 2) k6_numbers) k7_borsuk_6)).
tt(t67_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( (~ (v2_borsuk_7 B (k1_nat_1 A 1) A (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1))  => (v1_borsuk_7 (k16_borsuk_7 A B))) ) ) ) ) ).
tt(t67_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) => (r1_bvfunc_1 A (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k7_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ).
tt(t67_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  (! [K:$i] :  ((m1_eqrel_1 K A) =>  ( (B = (k7_enumset1 C D E F G H I J K))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (C = K)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (D = K)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (E = K)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (F = K)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (G = K)  |  ( (H = I)  |  ( (H = J)  |  ( (H = K)  |  ( (I = J)  |  ( (I = K)  |  ( (J = K)  |  ((k5_bvfunc_2 A C B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A D E) F) G) H) I) J) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  ( ((k3_xboolean A) = k8_margrel1)  =>  ((k6_xboolean A B) = k8_margrel1) ) ) ) ) ) ).
tt(t67_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A k6_margrel1) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k5_bvfunc26 A B (k6_bvfunc26 A C D)) (k5_bvfunc_1 A (k5_bvfunc_1 A (k1_bvfunc_1 A B) C) D))) ) ) ) ) ) ) ) ).
tt(t67_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C (k6_cqc_lang A (k6_cqc_lang A B)))))) => (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C B))))) ) ) ) ) ) ) ) ) ).
tt(t67_card_1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  => (r1_ordinal1 (k1_card_1 (k7_relat_1 B A)) (k1_card_1 A))) ) ) ).
tt(t67_card_2,ax, (! [A:$i] :  ((v7_ordinal1 A) => (v1_finset_1 (k4_classes1 A))) ) ).
tt(t67_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (~  ((r2_hidden A (k8_card_3 (k1_funct_4 B C))) &  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  (! [E:$i] :  ( ((v1_relat_1 E) & (v1_funct_1 E))  =>  (~  ((r2_hidden D (k8_card_3 B)) &  ((r2_hidden E (k8_card_3 C)) &  (A = (k1_funct_4 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 B)) =>  ( ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B E))  =>  ((k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D) = E) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_cat_3 D B C A) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E A (u4_struct_0 B)) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  ((r2_funct_2 A (u1_struct_0 B) (k2_cat_3 B A D) (k3_cat_3 B A E)) => (m2_cat_3 (k8_cat_3 B A D E) B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t67_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((k29_cat_4 A B C (k20_cat_4 A B C) (k27_cat_4 A B C) (k28_cat_4 A B C)) = (k4_cat_1 A (k20_cat_4 A B C))) ) ) ) ) ) ) ).
tt(t67_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ((v1_partfun1 (k2_cfunct_1 A C) A) =>  ((k7_partfun1 k2_numbers (k2_cfunct_1 A C) B) = (k12_complex1 (k7_partfun1 k2_numbers C B))) ) ) ) ) ) ) ) ).
tt(t67_chain_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m1_chain_1 B A) =>  (! [C:$i] :  ((m3_chain_1 C A B A) => (m3_chain_1 (k3_subset_1 (k4_chain_1 A B A) C) A B A)) ) ) ) ) ) ).
tt(t67_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (k6_glib_000 A))))  =>  (! [C:$i] :  ((m2_glib_000 C A B (k21_glib_000 A B)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ( ((r2_hidden D B) & (r1_tarski (k2_chord A (k6_domain_1 (k6_glib_000 A) D)) B))  =>  (! [E:$i] :  ((m1_subset_1 E (k6_glib_000 C)) =>  ( (D = E)  =>  ((v3_chord D A) <=> (v3_chord E C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_ordinal1 (k6_classes1 A) (k6_classes1 B))) ) ) ).
tt(t67_classes2,ax, ((k16_classes2 1) = k14_classes2) ).
tt(t67_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_clvect_1 C A) =>  ((r1_struct_0 C B) <=>  ((k5_clvect_1 A B C) = (u1_struct_0 C)) ) ) ) ) ) ) ) ).
tt(t67_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ((r1_clvect_2 A B C) => (r1_clvect_2 A C B)) ) ) ) ) ) ) ).
tt(t67_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  (! [C:$i] :  (~  ( (~  (B = C) )  &  ((r2_hidden (k2_tarski B C) A) & (r2_hidden (k2_tarski B C) (k13_cohsp_1 A))) ) ) ) ) ) ) ).
tt(t67_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((k13_complex1 (k17_complex1 A) (k17_complex1 B)) = (k17_complex1 (k13_complex1 A B))) ) ) ) ) ).
tt(t67_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  (~  ( (~  (A = k6_numbers) )  &  ( (~  (B = k6_numbers) )  &  (~  ((k3_complex2 A B) = (k3_complex2 (k10_complex1 A) (k10_complex1 B))) ) ) ) ) ) ) ) ) ).
tt(t67_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( ((k17_complex1 (k5_algstr_0 k1_complfld A B)) = k6_numbers)  <=>  (A = B) ) ) ) ) ) ).
tt(t67_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_complsp2 (k11_seq_4 A) B) = (k1_binop_2 (k8_complsp2 A B))) ) ) ) ) ) ).
tt(t67_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_compos_1 A)) =>  ((k10_xtuple_0 (k11_compos_1 A B)) = (k7_domain_1 (u1_compos_1 A) B (k2_compos_1 A))) ) ) ) ) ).
tt(t67_comput_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 B) &  ((v4_valued_0 B) & (v2_margrel1 B)) ) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (k3_finseq_2 k5_numbers)) &  ((v1_funct_1 C) &  ((v4_valued_0 C) & (v2_margrel1 C)) ) ) )  =>  (! [D:$i] :  ((m2_rfunct_3 D (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  ( ( (B = k1_xboole_0)  & (r1_comput_1 D B C A))  =>  (D = k1_xboole_0) ) ) ) ) ) ) ) ) ) ).
tt(t67_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k2_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  ( ( (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 k6_numbers (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) C)) & (r1_xxreal_0 (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) C) (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers B) C))) ) )  & (v2_comseq_3 B))  =>  ((v2_comseq_3 A) & (r1_xxreal_0 (k4_series_1 (k55_valued_1 k5_numbers k2_numbers A)) (k4_series_1 (k55_valued_1 k5_numbers k2_numbers B)))) ) ) ) ) ) ).
tt(t67_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [E:$i] :  ((v1_xcmplx_0 E) =>  (! [F:$i] :  ((v1_xcmplx_0 F) =>  (! [G:$i] :  ((v1_xcmplx_0 G) =>  ( ((v2_convex4 B A) &  ((v2_convex4 C A) & (v2_convex4 D A)) )  => (v2_convex4 (k7_rusub_4 A (k7_rusub_4 A (k19_convex4 A B E) (k19_convex4 A C F)) (k19_convex4 A D G)) A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k8_cqc_lang A B C) A) =>  ((r2_hidden D (k24_qc_lang1 A B)) | (v2_cqc_the1 (k8_cqc_lang A B (k11_cqc_lang A D C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t67_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ((v2_cqc_the1 (k7_cqc_lang A B (k11_cqc_lang A D C)) A) =>  ((r2_hidden D (k24_qc_lang1 A B)) | (v2_cqc_the1 (k11_cqc_lang A D (k7_cqc_lang A B C)) A)) ) ) ) ) ) ) ) ) ) ).
tt(t67_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v2_csspace C) & (l1_csspace C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k6_clvect_1 C D (k2_xcmplx_0 A B)) (k16_csspace C (k6_clvect_1 C D A) (k6_clvect_1 C D B)))) ) ) ) ) ) ) ) ).
tt(t67_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k4_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k21_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 2 B) A) 2)) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k10_real_1 (k9_real_1 (k8_real_1 6 B) (k8_real_1 3 A)) 2)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t67_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k21_sin_cos D))) ) )  =>  ( ((k21_sin_cos A) = k6_numbers)  |  ( ((k21_sin_cos (k9_real_1 A B)) = k6_numbers)  |  ((k1_seq_1 (k4_diff_1 C B) A) = (k10_real_1 (k8_real_1 2 (k9_real_1 (k21_sin_cos (k9_real_1 A B)) (k21_sin_cos A))) (k7_real_1 (k21_sin_cos (k9_real_1 (k8_real_1 2 A) B)) (k21_sin_cos B)))) ) ) ) ) ) ) ) ) ) ).
tt(t67_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 B C A D)) ) ) ) ) ).
tt(t67_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 B)) =>  ((k8_relset_1 A B (k13_eqrel_1 A B) C) = (k3_tarski C)) ) ) ) ) ) ) ).
tt(t67_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((k7_euclid 3 (k9_euclid 3 C A) (k9_euclid 3 C B)) = (k9_euclid 3 (k1_euclid_8 (k1_seq_1 C 1) (k1_seq_1 C 2) (k1_seq_1 C 3)) (k9_binop_2 A B))) ) ) ) ) ) ) ).
tt(t67_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  ((u1_struct_0 (k14_euclid A)) = (u1_struct_0 (k15_euclid A))) ) ) ).
tt(t67_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 (k1_euclid A)) (k1_euclidlp A)) =>  ((r6_euclidlp A B C) =>  ((v1_euclid_4 B A) & (v1_euclid_4 C A)) ) ) ) ) ) ) ) ).
tt(t67_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 B)) =>  (! [F:$i] :  ((m1_subset_1 F (k9_xtuple_0 B)) =>  ((r2_hidden C D) =>  ( (E = C)  |  ( (E = D)  |  ( (F = C)  |  ( (F = D)  |  ((k1_binop_1 (k7_exchsort A B C D) E F) = (k4_tarski E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_facirc_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] : (v1_relat_1 (k3_msafree2 (k15_facirc_1 A B C)))) ) ) ).
tt(t67_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((r2_hidden B A) &  ((k1_seq_1 k1_sin_cos9 B) = k6_numbers) ) ) ) ) )  =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k1_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k1_sin_cos9) A) B) = (k1_real_1 (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k1_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B)))))) ) ) ) ) ) ) ) ).
tt(t67_fib_num2,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) => (r1_int_2 (k1_pre_ff A) (k1_pre_ff (k2_nat_1 A 1)))) ) ).
tt(t67_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  ((v3_relat_2 (k8_filter_0 A B)) &  ((v8_relat_2 (k8_filter_0 A B)) &  ((v1_partfun1 (k8_filter_0 A B) (u1_struct_0 A)) & (m1_subset_1 (k8_filter_0 A B) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) ) ) ) ) ) ) ).
tt(t67_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v10_lattices B) & (l3_lattices B)) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v19_lattices C A) &  ((v20_lattices C A) & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v19_lattices D B) &  ((v20_lattices D B) & (m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B)))) ) )  =>  ( ( ((g3_lattices (u1_struct_0 A) (u2_lattices A) (u1_lattices A)) = (g3_lattices (u1_struct_0 B) (u2_lattices B) (u1_lattices B)))  &  (C = D) )  =>  ((k6_filter_0 A C) = (k6_filter_0 B D)) ) ) ) ) ) ) ) ) ) ).
tt(t67_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((v1_relat_1 F) &  ((v1_funct_1 F) & (v1_finseq_1 F)) )  =>  ( (F = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B)) (k9_finseq_1 C)) (k9_finseq_1 D)) (k9_finseq_1 E)))  =>  ( ((k3_finseq_1 F) = 5)  &  ( ((k1_funct_1 F 1) = A)  &  ( ((k1_funct_1 F 2) = B)  &  ( ((k1_funct_1 F 3) = C)  &  ( ((k1_funct_1 F 4) = D)  &  ((k1_funct_1 F 5) = E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v1_finseq_1 C)) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_tarski (k2_zfmisc_1 (k1_tarski A) (k10_xtuple_0 B)) (k9_xtuple_0 D)) &  (C = (k5_funcop_1 D A B)) )  =>  ((k3_finseq_1 C) = (k3_finseq_1 B)) ) ) ) ) ) ) ) ) ).
tt(t67_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k10_xtuple_0 (k1_finseq_3 A B)) = (k10_xtuple_0 A))  => (r1_xboole_0 B (k10_xtuple_0 A))) ) ) ) ).
tt(t67_finseq_4,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m2_finseq_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  ((k7_partfun1 A (k8_finseq_1 A B (k12_finseq_1 A C)) (k2_nat_1 (k3_finseq_1 B) 1)) = C) ) ) ) ) ) ) ).
tt(t67_finseq_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k5_finseq_5 A C B k6_numbers) = (k8_finseq_1 A (k12_finseq_1 A B) C)) ) ) ) ) ) ) ).
tt(t67_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  (! [D:$i] :  ((m2_finseq_1 D A) =>  ((r2_hidden B (k6_subset_1 (k10_xtuple_0 C) (k10_xtuple_0 D))) =>  ((k1_finseq_5 A (k8_finseq_1 A D C) B) = (k8_finseq_1 A D (k1_finseq_5 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t67_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A A) A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (k2_zfmisc_1 A A) A) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F A A) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((v1_setwiseo D A) &  ((v2_binop_1 D A) &  ((v1_finseqop D A) &  ((r2_funct_2 A A F (k5_finseqop A D)) & (r6_binop_1 A E D)) ) ) )  =>  ( ((k3_funct_2 A A F (k5_binop_1 A E B C)) = (k5_binop_1 A E (k3_funct_2 A A F B) C))  &  ((k3_funct_2 A A F (k5_binop_1 A E B C)) = (k5_binop_1 A E B (k3_funct_2 A A F C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_catalan2 A))) =>  ((r1_tarski B (k8_flang_1 A C)) =>  ((k8_flang_1 A C) = (k8_flang_1 A (k4_subset_1 (k3_catalan2 A) C B))) ) ) ) ) ) ) ).
tt(t67_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ( ((r2_hidden (k2_flang_1 A) B) & (r1_xxreal_0 C D))  =>  ((k8_flang_1 A B) = (k6_flang_1 A (k8_flang_1 A B) (k1_flang_2 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t67_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k8_afinsq_1 A))) =>  ( ((r1_tarski B (k2_flang_3 A C)) & (r1_tarski D (k2_flang_3 A C)))  => (r1_tarski (k6_flang_1 A B D) (k2_flang_3 A C))) ) ) ) ) ) ) ) ).
tt(t67_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((v3_binop_1 C A) =>  ((k3_funct_2 B A (k10_funcop_1 A B C (k3_funct_2 B A D E) D) E) = (k3_funct_2 B A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k7_relat_1 (k6_relat_1 A C) B) = (k3_xboole_0 A (k7_relat_1 C B))) ) ) ) ) ).
tt(t67_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((k1_relset_1 A C) = A)  =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(t67_funct_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  ((k10_xtuple_0 (k15_funct_3 A B)) = (k2_zfmisc_1 (k10_xtuple_0 A) (k10_xtuple_0 B))) ) ) ) ) ).
tt(t67_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ( (~  (A = C) )  =>  ((k4_funct_4 A C B D) = (k2_tarski (k4_tarski A B) (k4_tarski C D))) ) ) ) ) ) ).
tt(t67_funct_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 A B) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A B) C)))) )  =>  ((v1_funct_1 (k1_funct_5 D)) &  ((v1_funct_2 (k1_funct_5 D) A (k9_funct_2 B C)) & (m1_subset_1 (k1_funct_5 D) (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) ) ) ) ) ) ) ).
tt(t67_funct_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_relat_1 A) &  ((v2_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) ) ) )  =>  (! [B:$i] :  ((m2_funct_7 B A) =>  ( ((k9_xtuple_0 (k4_funct_7 (k1_funct_1 A 1) B)) = (k1_funct_1 A 1))  & (r1_tarski (k10_xtuple_0 (k4_funct_7 (k1_funct_1 A 1) B)) (k1_funct_1 A (k3_finseq_1 A)))) ) ) ) ) ).
tt(t67_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_funct_8 A k1_numbers k1_numbers k1_sin_cos2)) ) ).
tt(t67_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  => (m1_realset1 B (u1_struct_0 A) (u1_algstr_0 A))) ) ) ) ).
tt(t67_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) &  ((v5_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  ((k12_fvsum_1 A B (k5_finseq_2 (u1_struct_0 B) A C) (k5_finseq_2 (u1_struct_0 B) A D)) = (k5_finseq_2 (u1_struct_0 B) A (k8_group_1 B C D))) ) ) ) ) ) ) ) ) ).
tt(t67_gfacirc1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k25_gfacirc1 A B C)))) ) ) ) ) ) ) ).
tt(t67_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  ((r2_hidden B (k28_glib_000 A C)) <=> (r1_glib_000 A C (k29_glib_000 A C B) B)) ) ) ) ) ) ).
tt(t67_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) => (r1_xxreal_0 1 (k3_finseq_1 (k11_glib_001 A B)))) ) ) ) ).
tt(t67_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k3_finseq_1 B) A) |  ((r1_xxreal_0 (k1_matrix_1 B) 1) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)) (k19_euclid k6_numbers 1)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k7_nat_d (k1_matrix_1 B) 1))) (k10_real_1 1 2))) (k2_xboole_0 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k7_nat_d (k1_matrix_1 B) 1))) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B A (k1_matrix_1 B)))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B A (k1_matrix_1 B)) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B (k2_nat_1 A 1) (k1_matrix_1 B))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ).
tt(t67_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k4_subset_1 (u1_struct_0 A) (k4_group_11 A B C) (k4_group_11 A B D)) (k4_group_11 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v15_algstr_0 A) &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) ) )  => (m1_group_2 A (k7_group_2 A))) ) ).
tt(t67_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) => (r1_group_2 A (k6_group_3 A (k6_group_2 A) B) (k6_group_2 A))) ) ) ) ).
tt(t67_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  => (r1_group_2 A (k10_group_2 A C (k8_group_4 A C B)) C)) ) ) ) ) ) ).
tt(t67_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((m1_group_2 (k8_group_5 A C B) C) & (m1_group_2 (k8_group_5 A B C) C)) ) ) ) ) ) ) ).
tt(t67_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) & (l3_algstr_0 C)) ) )  =>  ( ((r1_group_6 A B) & (r1_group_6 B C))  => (r1_group_6 A C)) ) ) ) ) ) ) ).
tt(t67_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v15_algstr_0 B) &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) ) )  =>  (? [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v2_group_1 C) &  ((v3_group_1 C) &  ((v2_group_9 C A) &  ((v3_group_9 C A) & (l1_group_9 C A)) ) ) ) )  &  (B = (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) ) ) ) ) ) ).
tt(t67_hermitan,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v8_vectsp_1 A k1_complfld) &  ((v9_vectsp_1 A k1_complfld) &  ((v10_vectsp_1 A k1_complfld) &  ((v11_vectsp_1 A k1_complfld) & (l1_vectsp_1 A k1_complfld)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld)) &  ((v2_bilinear B k1_complfld A A) &  ((v4_bilinear B k1_complfld A A) &  ((v3_hermitan B A) &  ((v5_hermitan B A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 k1_complfld))))) ) ) ) ) )  =>  ((k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k8_hermitan A B)) = (k11_bilinear k1_complfld (k6_vectsp10 k1_complfld A (k13_bilinear k1_complfld A A B)) (k6_vectsp10 k1_complfld A (k14_bilinear k1_complfld A A (k3_hermitan A A B))) (k7_hermitan A A B))) ) ) ) ) ).
tt(t67_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_taylor_1 B 2 A) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (~  ((r2_hidden C A) &  ((k1_seq_1 B C) = k6_numbers) ) ) ) ) )  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k6_rfunct_1 k1_numbers k1_numbers B) A) 2) (k3_rfunct_1 k1_numbers k1_numbers (k47_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k2_fdiff_1 B A) 2) (k2_fdiff_1 B A)) (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 B A) 2) B)) (k20_valued_1 k1_numbers k1_numbers k1_numbers B (k20_valued_1 k1_numbers k1_numbers k1_numbers B B))))) ) ) ) ) ).
tt(t67_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v1_algstr_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden C (k7_ideal_1 A B)) => (r1_tarski (k7_ideal_1 A (k6_domain_1 (u1_struct_0 A) C)) (k7_ideal_1 A B))) ) ) ) ) ) ) ).
tt(t67_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 (k3_real_1 (k1_int_1 A) 1) B) |  ((k1_int_1 B) = (k1_int_1 A)) ) ) ) ) ) ) ).
tt(t67_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D B) =>  ((k1_seq_1 C D) = (k1_real_1 (k10_real_1 (k1_seq_1 k4_sin_cos6 D) (k7_square_1 (k9_real_1 1 (k5_square_1 D)))))) ) ) )  &  ((r1_tarski B (k9_xtuple_0 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)))) &  ( (B = (k9_xtuple_0 C))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers C A))) ) ) ) )  =>  ((k2_integra5 A C) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) (k4_seq_4 A)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers k4_sin_cos6 (k1_taylor_1 2)) (k10_real_1 1 2)) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t67_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v2_measure5 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers))) )  =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r2_fdiff_1 A D) &  ((r2_fdiff_1 B D) &  ((r1_tarski C D) &  ((r1_integra5 C (k2_fdiff_1 A D)) &  ((v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 A D) C)) &  ((r1_integra5 C (k2_fdiff_1 B D)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 B D) C))) ) ) ) ) )  =>  ((k2_integra5 C (k47_valued_1 k1_numbers k1_numbers k1_numbers (k2_fdiff_1 A D) (k2_fdiff_1 B D))) = (k9_real_1 (k9_real_1 (k1_seq_1 A (k4_seq_4 C)) (k1_seq_1 A (k5_seq_4 C))) (k9_real_1 (k1_seq_1 B (k4_seq_4 C)) (k1_seq_1 B (k5_seq_4 C))))) ) ) ) ) ) ) ) ) ) ).
tt(t67_integra9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v3_rcomp_1 E) & (m1_subset_1 E (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski B E) &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ( ((k1_seq_1 C F) = (k9_real_1 A F))  &  (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers)) ) ) ) )  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2))) = E)  &  ( ((k1_relset_1 k1_numbers (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2))) = (k1_relset_1 k1_numbers D))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F E) =>  ((k1_seq_1 D F) = (k10_prepower (k9_real_1 A F) (k1_real_1 (k10_real_1 1 2)))) ) ) )  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers D B))) ) ) ) )  =>  ((k2_integra5 B D) = (k9_real_1 (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) (k4_seq_4 B)) (k1_seq_1 (k26_valued_1 k1_numbers k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))) (k1_real_1 2)) (k5_seq_4 B)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) => (r2_interva1 A (k16_interva1 A B (k17_interva1 A B C)) B)) ) ) ) ) ) ).
tt(t67_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) =>  ((v9_intpro_1 A) => (v8_intpro_1 A)) ) ) ).
tt(t67_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_2_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k5_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t67_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (~  ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) &  ((r1_jordan6 E C D) &  ( (~  (A = B) )  &  ( (~  (B = C) )  &  ( (~  (C = D) )  &  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v3_tops_2 F (k15_euclid 2) (k15_euclid 2)) &  ( (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 (k15_euclid 2))) =>  ((k12_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F G)) = (k12_euclid G)) ) )  &  ( ((k19_euclid (k1_real_1 1) k6_numbers) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F A))  &  ( ((k19_euclid k6_numbers 1) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F B))  &  ( ((k19_euclid 1 k6_numbers) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F C))  &  ((k19_euclid k6_numbers (k1_real_1 1)) = (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B k1_jgraph_3) &  ((k17_euclid A) = (k1_real_1 1)) )  =>  ((r1_xxreal_0 k6_numbers (k18_euclid A)) |  ( (~ (r1_xxreal_0 k6_numbers (k17_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B A))))  &  (~ (r1_xxreal_0 k6_numbers (k18_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) B A)))) ) ) ) ) ) ) ) ).
tt(t67_jgraph_7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  (! [E:$i] :  ( ((v1_funct_1 E) &  ((v1_funct_2 E (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [G:$i] :  ((m1_subset_1 G (u1_struct_0 k5_topmetr)) =>  (! [H:$i] :  ((m1_subset_1 H (u1_struct_0 k5_topmetr)) =>  ( ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) E (k2_jgraph_2 (k10_real_1 2 (k6_xcmplx_0 B A)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 B A) (k6_xcmplx_0 B A))) (k10_real_1 2 (k6_xcmplx_0 D C)) (k4_xcmplx_0 (k7_xcmplx_0 (k2_xcmplx_0 D C) (k6_xcmplx_0 D C))))) & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) B))  =>  ((r1_xxreal_0 B A) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H)) A) |  ((r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F G)) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) F H))) |  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H)) (k1_real_1 1)))  &  ( (~ (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) H))))  & (r1_xxreal_0 (k17_euclid (k3_funct_2 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (k1_partfun1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) F E) G)) 1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A))) (k8_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))))) ) ) ) ) ) ) ) ).
tt(t67_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_tarski A B) =>  ( ( (~ (r2_hidden (k20_pscomp_1 B) A))  &  (~ (r2_hidden (k21_pscomp_1 B) A)) )  |  ((k7_pscomp_1 A) = (k7_pscomp_1 B)) ) ) ) ) ) ) ).
tt(t67_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ( (? [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) &  (C = (a_2_3_jordan2c A B)) ) )  &  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k14_euclid A)))) =>  ( (C = (a_2_3_jordan2c A B))  => (v6_tbsp_1 C (k14_euclid A))) ) ) ) ) ) ) ) ).
tt(t67_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k11_jordan6 A) (k8_jordan6 A))) ) ).
tt(t67_jordan,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid A))) =>  (! [D:$i] :  ( ((v2_xxreal_0 D) & (v1_xreal_0 D))  =>  (~  ((r2_hidden C (k1_topreal9 A B D)) & (v2_abian (k10_jordan A B C D))) ) ) ) ) ) ) ) ) ) ).
tt(t67_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v13_lattices A) & (l3_lattices A)) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v1_lattice2 A) & (l3_lattices A)) ) )  <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (? [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) &  ((r3_lattices A (k4_lattices A B D) C) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_lattices A (k4_lattices A B E) C) => (r3_lattices A E D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  ( ((r1_xxreal_0 (k15_glib_000 A) B) & (r1_xxreal_0 B C))  =>  ((k23_lexbfs A (k26_lexbfs A) B) = (k23_lexbfs A (k26_lexbfs A) C)) ) ) ) ) ) ) ) ).
tt(t67_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v6_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B))) &  (~ (v1_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B)))) ) ) ) )  | (v7_limfunc1 A)) ) ) ) ).
tt(t67_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_limfunc2 B A) & (r1_limfunc2 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) )  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A)) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 (k9_real_1 A D) A))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 (k9_real_1 A D) A))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) )  | (r1_xxreal_0 (k1_limfunc2 B A) (k1_limfunc2 C A))) ) ) ) ) ) ) ) ).
tt(t67_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r1_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k5_limfunc1 A) (k1_seq_1 A D))) ) ) ) )  |  ((v6_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k1_limfunc2 B (k5_limfunc1 A))) ) ) ) ) ) ) ) ).
tt(t67_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  ( (! [C:$i] :  ((v7_ordinal1 C) => (v6_supinf_2 (k4_mesfunc5 A k1_numbers B C))) )  =>  (! [C:$i] :  ((v7_ordinal1 C) => (v6_supinf_2 (k4_mesfunc5 A k1_numbers (k2_mesfun9c A B) C))) ) ) ) ) ) ) ).
tt(t67_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ((r3_cqc_the1 A E (k8_cqc_lang A B (k8_cqc_lang A C D))) => (r3_cqc_the1 A E (k8_cqc_lang A (k8_cqc_lang A B C) (k8_cqc_lang A B D)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_mathmorp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (B = k1_xboole_0)  =>  ((k7_mathmorp (k15_euclid A) C B D) = (k3_mathmorp (k15_euclid A) (k3_subset_1 (u1_struct_0 (k15_euclid A)) C) D)) ) ) ) ) ) ) ) ) ) ).
tt(t67_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((v2_matrix10 B) => (r1_matrix10 (k3_matrix10 A B C) C)) ) ) ) ) ) ) ).
tt(t67_matrix13,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 A)))  =>  (! [C:$i] :  ( ((v1_finset_1 C) &  ((v1_setfam_1 C) & (m1_subset_1 C (k1_zfmisc_1 k5_numbers))) )  =>  (! [D:$i] :  ( ((v1_finset_1 D) &  ((v1_setfam_1 D) & (m1_subset_1 D (k1_zfmisc_1 k5_numbers))) )  =>  ( ((k5_card_1 C) = (k5_card_1 D))  =>  ((r1_tarski (k2_zfmisc_1 C D) (k2_matrix_1 B)) <=>  ((r1_tarski C (k2_finseq_1 (k3_finseq_1 B))) & (r1_tarski D (k2_finseq_1 (k1_matrix_1 B)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_matrix15,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) A B) =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (~  ( ((k5_card_1 E) = A)  &  ((r1_tarski E (k2_finseq_1 B)) &  ( ((k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 A) E) = (k12_matrix_1 C A))  &  ( (~ (r1_xxreal_0 A k1_xboole_0))  &  ( (~ (r1_xxreal_0 (k7_nat_d B A) k1_xboole_0))  &  (! [F:$i] :  ((m1_matrix_1 F (u1_struct_0 C) (k7_nat_d B A) B) =>  (~  ( ((k6_matrix13 (u1_struct_0 C) F (k2_finseq_1 (k7_nat_d B A)) (k7_subset_1 k5_numbers (k2_finseq_1 B) E)) = (k12_matrix_1 C (k7_nat_d B A)))  &  ( ((k6_matrix13 (u1_struct_0 C) F (k2_finseq_1 (k7_nat_d B A)) E) = (k2_matrix_3 C (k4_matrix_1 (u1_struct_0 C) (k6_matrix13 (u1_struct_0 C) D (k2_finseq_1 A) (k7_subset_1 k5_numbers (k2_finseq_1 B) E)))))  &  ((k1_vectsp_7 C (k6_prvect_1 C B) (k9_matrix13 C (k7_nat_d B A) B F)) = (k7_matrix15 C D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrixj1 B (u1_struct_0 A)) & (m2_finseq_1 B (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [D:$i] :  ( ((v1_matrixj1 D (u1_struct_0 A)) & (m2_finseq_1 D (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  (! [E:$i] :  ( ((v1_matrixj1 E (u1_struct_0 A)) & (m2_finseq_1 E (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ( ((k3_finseq_1 B) = (k3_finseq_1 C))  =>  ((k25_matrixj1 A (k3_matrixj1 (u1_struct_0 A) B D) (k3_matrixj1 (u1_struct_0 A) C E)) = (k3_matrixj1 (u1_struct_0 A) (k25_matrixj1 A B C) (k25_matrixj1 A D E))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k4_matrix_3 A B (k12_matrix_1 A (k1_matrix_1 B))) = B) ) ) ) ) ).
tt(t67_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_subset_1 E (k3_zfmisc_1 B C D)) =>  ( (! [F:$i] :  ((m1_subset_1 F B) =>  (! [G:$i] :  ((m1_subset_1 G C) =>  (! [H:$i] :  ((m1_subset_1 H D) =>  ( (E = (k3_xtuple_0 F G H))  =>  (A = H) ) ) ) ) ) ) )  =>  (A = (k3_mcart_1 B C D E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_measure6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((v5_measure6 B A) <=> (v6_measure6 (k32_valued_1 A k1_numbers B) A)) ) ) ) ) ).
tt(t67_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  (! [D:$i] :  ((v1_membered D) =>  ( ((r1_tarski A B) & (r1_tarski C D))  => (r1_tarski (k11_member_1 A C) (k11_member_1 B D))) ) ) ) ) ) ) ) ) ).
tt(t67_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) => (r1_tarski (k7_memstr_0 A B (k7_nat_d (k5_memstr_0 A B C) D)) (k10_memstr_0 A B C D))) ) ) ) ) ) ) ) ).
tt(t67_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  (! [E:$i] :  ((m2_subset_1 E (k1_zfmisc_1 A) B) =>  (! [F:$i] :  ((m2_subset_1 F (k1_zfmisc_1 A) B) =>  ( ((r1_mesfunc2 A B D) &  ((v6_supinf_2 D) & (r1_xboole_0 E F)) )  =>  ((k5_mesfunc5 A B C (k2_partfun1 A k7_numbers D (k6_prob_1 A B E F))) = (k3_supinf_2 (k5_mesfunc5 A B C (k2_partfun1 A k7_numbers D E)) (k5_mesfunc5 A B C (k2_partfun1 A k7_numbers D F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((r1_tarski B (k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers C D))) =>  ( ((k1_relset_1 A (k2_partfun1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers C D) B)) = B)  &  ( ((k1_relset_1 A (k3_valued_1 A k1_numbers k1_numbers (k2_partfun1 A k1_numbers C B) (k2_partfun1 A k1_numbers D B))) = B)  & (r2_relset_1 A k1_numbers (k2_partfun1 A k1_numbers (k3_valued_1 A k1_numbers k1_numbers C D) B) (k3_valued_1 A k1_numbers k1_numbers (k2_partfun1 A k1_numbers C B) (k2_partfun1 A k1_numbers D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t67_mmlquery,ax, (! [A:$i] :  ((l1_mmlquery A) =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  ((k35_mmlquery A B k6_numbers) = (k32_mmlquery A B)) ) ) ) ) ).
tt(t67_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m1_subset_1 B (k25_modelc_2 k43_modelc_2)) =>  ((r7_modelc_2 B (k6_modelc_2 A)) <=> (r7_modelc_2 (k29_modelc_2 k43_modelc_2 B 1) A)) ) ) ) ) ).
tt(t67_modelc_3,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  ((v5_modelc_3 A) =>  ( ( (~ (v4_modelc_2 A))  &  ( (~ (v5_modelc_2 A))  &  ( (~ (v7_modelc_2 A))  &  (~ (v8_modelc_2 A)) ) ) )  |  ((v5_modelc_3 (k11_modelc_2 A)) & (v5_modelc_3 (k12_modelc_2 A))) ) ) ) ) ).
tt(t67_monoid_0,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  ((v1_setwiseo (k11_monoid_0 A) (k3_finseq_2 A)) &  ( ((k4_binop_1 (k3_finseq_2 A) (k11_monoid_0 A)) = k1_xboole_0)  & (v2_binop_1 (k11_monoid_0 A) (k3_finseq_2 A))) ) ) ) ).
tt(t67_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ((v1_int_1 C) =>  ((k6_int_1 (k3_xcmplx_0 B C) A) = (k6_int_1 (k3_xcmplx_0 (k6_int_1 B A) (k6_int_1 C A)) A)) ) ) ) ) ) ) ).
tt(t67_ncfcont1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_normsp_0 A) &  ((v4_normsp_0 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v8_clvect_1 A) & (l2_clvect_1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v5_rlvect_1 B) &  ((v6_rlvect_1 B) &  ((v7_rlvect_1 B) &  ((v8_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_normsp_1 B) & (l1_normsp_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  (! [F:$i] :  ( ((v1_funct_1 F) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A)))))  =>  ( ((r9_ncfcont1 B A E C) & (r9_ncfcont1 B A F D))  =>  ((r9_ncfcont1 B A (k3_vfunct_2 (u1_struct_0 B) A E F) (k3_xboole_0 C D)) & (r9_ncfcont1 B A (k2_vfunct_1 (u1_struct_0 B) A E F) (k3_xboole_0 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  ((r1_xxreal_0 A k6_numbers) & (r1_xxreal_0 B k6_numbers)) )  &  (! [C:$i] :  ((v1_int_1 C) =>  (! [D:$i] :  ((v1_int_1 D) =>  (~  ((k2_xcmplx_0 (k3_xcmplx_0 C A) (k3_xcmplx_0 D B)) = (k6_nat_d A B)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u4_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u4_struct_0 (k2_oppcat_1 A)) (u4_struct_0 A) (k13_oppcat_1 A) B) = (k6_oppcat_1 A B)) ) ) ) ) ).
tt(t67_orders_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (! [B:$i] :  ( ((r1_tarski B A) & (v6_ordinal1 B))  =>  ( (B = k1_xboole_0)  | (r2_hidden (k3_tarski B) A)) ) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ( (~  (C = B) )  & (r1_tarski B C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden A (k11_ordinal2 B C)) =>  ((r2_hidden (k6_ordinal3 A C) B) & (r2_hidden (k7_ordinal3 A C) C)) ) ) ) ) ) ) ) ).
tt(t67_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v6_ordinal5 A)) ) ) )  =>  (~  ( (~  (A = k1_xboole_0) )  &  (! [B:$i] :  ( ((v3_ordinal1 B) & (v5_ordinal5 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) &  ((v5_ordinal1 C) &  ((v1_ordinal2 C) & (v6_ordinal5 C)) ) ) )  =>  (~  (A = (k1_ordinal4 (k5_afinsq_1 B) C)) ) ) ) ) ) ) ) ) ) ).
tt(t67_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  & (v1_classes2 C))  =>  ( ((r2_hidden k4_ordinal1 C) &  ((r2_hidden A C) & (r2_hidden B C)) )  =>  ((k12_ordinal6 B A) = (k1_funct_1 (k1_funct_1 (k11_ordinal6 C) B) A)) ) ) ) ) ) ) ) ).
tt(t67_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v9_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t67_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ( ((r1_partfun1 C E) &  ((r1_partfun1 D E) & (v1_partfun1 E A)) )  => (r1_partfun1 C D)) ) ) ) ) ) ) ) ) ).
tt(t67_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k2_pboole A B (k4_pboole A C B)) (k2_pboole A B C))) ) ) ) ) ).
tt(t67_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r1_pdiff_5 B A) & (r1_pdiff_5 C A))  => (r3_pdiff_1 3 1 (k20_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A)) ) ) ) ) ) ) ).
tt(t67_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) & (r3_pdiff_9 A C B E)) ) )  =>  ((r3_pdiff_9 A C B (k26_valued_1 (k1_euclid A) k1_numbers E D)) &  ((r2_relset_1 (k1_euclid A) k1_numbers (k3_pdiff_9 A C B (k26_valued_1 (k1_euclid A) k1_numbers E D)) (k26_valued_1 (k1_euclid A) k1_numbers (k3_pdiff_9 A C B E) D)) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 k1_numbers (k3_pdiff_9 A C B (k26_valued_1 (k1_euclid A) k1_numbers E D)) F) = (k11_binop_2 D (k11_pdiff_1 A B E F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_pnproc_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v2_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v2_finseq_1 C)) )  =>  ((r1_tarski C B) => (r1_tarski (k12_pnproc_1 C A) (k12_pnproc_1 B A))) ) ) ) ) ) ) ).
tt(t67_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  ((k2_struct_0 (k17_polyform A (k7_polyform A))) = (k2_tarski (k4_struct_0 (k17_polyform A (k7_polyform A))) (k1_tarski A))) ) ) ).
tt(t67_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (? [B:$i] :  ((m1_subset_1 B k2_numbers) &  ( (A = B)  & (r1_funct_2 (u1_struct_0 k1_complfld) (u1_struct_0 k1_complfld) k2_numbers k2_numbers (k8_polynom5 k1_complfld A 1) (k25_valued_1 k2_numbers k2_numbers (k6_partfun1 k2_numbers) B))) ) ) ) ) ).
tt(t67_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k20_pre_poly A (k16_pre_poly A)) = (k3_pre_poly (k15_pre_poly A) (k16_pre_poly A))) ) ) ).
tt(t67_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (? [B:$i] :  ( ((v5_relat_1 B k3_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 (k1_seq_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t67_prob_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) =>  ((v3_prob_3 B A) <=>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  ( ((v2_prob_1 C) & (r1_tarski (k2_relset_1 (k9_setfam_1 A) C) B))  => (r2_hidden (k4_kurato_0 A C) B)) ) ) ) ) ) ) ).
tt(t67_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k8_pscomp_1 A) (k8_pscomp_1 B))) ) ) ) ) ).
tt(t67_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) & (v1_partfun1 E A)) ) )  =>  ( ((r2_pboole A B C) & (r2_pboole A D E))  => (r6_pboole A (k3_pboole A (k6_pboole A B E) (k6_pboole A C D)) (k6_pboole A B D))) ) ) ) ) ) ) ) ) ) ).
tt(t67_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((r2_qc_lang2 A (k13_qc_lang1 A B) C) => (r3_qc_lang2 A B C)) ) ) ) ) ) ) ).
tt(t67_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k6_qc_lang3 A (k14_qc_lang1 A B C)) = (k4_subset_1 (k4_qc_lang1 A) (k6_qc_lang3 A B) (k6_qc_lang3 A C))) ) ) ) ) ) ) ).
tt(t67_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  (! [D:$i] :  ((v1_quaterni D) =>  ((k27_quaterni (k26_quaterni (k26_quaterni A B) C) D) = (k26_quaterni (k26_quaterni (k27_quaterni A D) (k27_quaterni B D)) (k27_quaterni C D))) ) ) ) ) ) ) ) ) ).
tt(t67_quaterni,ax, (! [A:$i] :  ((v1_quaterni A) => (r1_xxreal_0 k6_numbers (k32_quaterni A))) ) ).
tt(t67_real_3,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ( (! [C:$i] :  ((v7_ordinal1 C) =>  (~  ((k1_seq_1 (k6_real_3 B) C) = k6_numbers) ) ) )  =>  ((k9_real_1 (k10_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 B) (k1_nat_1 A 2)) (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 2))) (k10_real_1 (k1_seq_1 (k5_real_3 B) A) (k1_seq_1 (k6_real_3 B) A))) = (k10_real_1 (k8_real_1 (k2_newton (k1_real_1 1) A) (k3_funct_2 k5_numbers k1_numbers (k4_real_3 B) (k1_nat_1 A 2))) (k8_real_1 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 B) (k1_nat_1 A 2)) (k1_seq_1 (k6_real_3 B) A)))) ) ) ) ) ) ).
tt(t67_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((k5_relat_1 B A) = (k3_xboole_0 B (k2_zfmisc_1 A (k10_xtuple_0 B)))) ) ) ) ).
tt(t67_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ((v2_rewrite3 C A B) =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((m1_rewrite1 E (k1_rewrite3 A B C)) =>  ( ((k1_funct_1 D 1) = (k1_funct_1 E 1))  =>  (! [F:$i] :  ((v7_ordinal1 F) =>  ( ((r2_hidden F (k4_finseq_1 D)) & (r2_hidden F (k4_finseq_1 E)))  =>  ((k1_funct_1 D F) = (k1_funct_1 E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  ( (~  ((k1_funct_1 (k7_rfunct_1 A B) C) = 1) )  <=>  ((k1_funct_1 (k7_rfunct_1 A B) C) = k6_numbers) ) ) ) ) ) ) ).
tt(t67_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  (! [D:$i] :  ((v1_finset_1 D) =>  ( (D = (k1_relset_1 A (k2_partfun1 A k1_numbers B C)))  =>  ((k3_finseq_1 (k20_rfunct_3 A B C)) = (k5_card_1 D)) ) ) ) ) ) ) ) ) ).
tt(t67_rinfsup1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 B) & (v1_seq_2 B))  =>  ( ((k1_seq_1 (k4_rinfsup1 B) A) = (k1_rinfsup1 B))  & (v3_funct_1 (k4_rinfsup1 B))) ) ) ) ) ) ).
tt(t67_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  ((k4_rlaffin1 A (k3_convex1 A B)) = (k4_rlaffin1 A B)) ) ) ) ) ).
tt(t67_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_rlsub_1 D A) =>  (~  ( ((k3_rlsub_1 A B D) = (k3_rlsub_1 A C D))  &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r1_struct_0 D E) &  ((k5_algstr_0 A B E) = C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v6_rltopsp1 A) &  ((v7_rltopsp1 A) & (l1_rltopsp1 A)) ) ) ) ) ) ) ) ) ) ) )  =>  (~  ((v8_rltopsp1 A) &  (! [B:$i] :  ((m1_yellow13 B A (k4_struct_0 A)) =>  (~ (v1_rltopsp1 B A)) ) ) ) ) ) ) ).
tt(t67_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C B D)) = (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C D B))) ) ) ) ) ) ) ) ) ).
tt(t67_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v8_vectsp_1 C A) &  ((v9_vectsp_1 C A) &  ((v10_vectsp_1 C A) &  ((v11_vectsp_1 C A) & (l1_vectsp_1 C A)) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 C)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 C)) =>  ( ( ((k3_finseq_1 D) = (k3_finseq_1 E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_relset_1 k5_numbers D)) =>  ((k1_funct_1 E F) = (k4_vectsp_1 A C B (k7_partfun1 (u1_struct_0 C) D F))) ) ) ) )  =>  ((k4_rlvect_1 C E) = (k4_vectsp_1 A C B (k4_rlvect_1 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ( ((v2_vectsp_2 C A) & (m1_rmod_2 C A B))  =>  (! [D:$i] :  ( ((v2_vectsp_2 D A) & (m1_rmod_2 D A B))  =>  (! [E:$i] :  ((m2_rmod_2 E A B C) =>  (! [F:$i] :  ((m2_rmod_2 F A B D) =>  ( (E = F)  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_rmod_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C B) & (l1_vectsp_2 C B)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r1_struct_0 (k10_rmod_4 B C D) A) <=>  (? [E:$i] :  ((m2_rmod_4 E B C D) &  (A = (k5_rmod_4 B C E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (~  ((m2_rusub_1 B A (k1_rusub_1 A)) &  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~  (B = (k6_domain_1 (u1_struct_0 A) C)) ) ) ) ) ) ) ) ) ) ).
tt(t67_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  ((k12_rvsum_1 A) = (k14_rvsum_1 A A)) ) ) ).
tt(t67_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_ami_2 B) & (m1_subset_1 B (u1_struct_0 k1_scmfsa_2)))  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v5_funct_1 C (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 C (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B) C) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 C)))  &  ( ( (~  (A = B) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B) C) A) = (k5_int_1 (k1_funct_1 C A) (k1_funct_1 C B))) )  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B) C) B) = (k6_int_1 (k1_funct_1 C A) (k1_funct_1 C B)))  &  ( (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmfsa_2)))  =>  (~  ( (~  (D = A) )  &  ( (~  (D = B) )  &  (~  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B) C) D) = (k1_funct_1 C D)) ) ) ) ) ) )  &  (! [D:$i] :  ((m1_scmfsa_2 D) => (r2_relset_1 k5_numbers k4_numbers (k18_scmfsa_2 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A B) C) D) (k18_scmfsa_2 C D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_scmfsa8c,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) & (v1_scmfsa7b C)) ) ) ) ) ) )  =>  ( ((r6_scmfsa7b C (k1_scmfsa_m B) A) & (r5_scmfsa7b C (k1_scmfsa_m B) A))  =>  ( ((k1_funct_1 (k1_scmfsa6b C B A) (k4_scmfsa_2 k6_numbers)) = 1)  &  (! [D:$i] :  ((m2_subset_1 D k1_numbers k5_numbers) =>  ((k1_funct_1 (k5_extpro_1 3 k1_scmfsa_2 (k1_funct_4 A C) (k8_memstr_0 3 k1_scmfsa_2 (k1_scmfsa_m B)) D) (k4_scmfsa_2 k6_numbers)) = 1) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_scm_halt,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v5_relat_1 A (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 A) & (v1_partfun1 A k5_numbers)) ) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmfsa_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) &  ((v1_afinsq_1 C) &  ((v1_scmfsa7b C) & (v2_scm_halt C)) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_scmfsa_2 D) =>  (! [E:$i] :  ( ((v1_ami_2 E) &  ( (~ (v1_scmfsa_m E))  & (m1_subset_1 E (u1_struct_0 k1_scmfsa_2))) )  =>  ((r1_xxreal_0 (k1_funct_1 B E) k6_numbers) =>  ((k18_scmfsa_2 (k1_scmfsa6b (k2_scmfsa8c E C) B A) D) = (k18_scmfsa_2 B D)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_scmpds_2,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmpds_2)))  =>  (! [D:$i] :  ( ((v1_ami_2 D) & (m1_subset_1 D (u1_struct_0 k1_scmpds_2)))  =>  (~ (v2_extpro_1 (k16_scmpds_2 C D A B) 2 k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
tt(t67_scmpds_6,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmpds_2)))  =>  (! [B:$i] :  ((v1_int_1 B) =>  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_relat_1 C) &  ((v4_relat_1 C k5_numbers) &  ((v5_relat_1 C (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 C) &  ((v1_finset_1 C) & (v1_afinsq_1 C)) ) ) ) ) )  =>  (! [D:$i] :  ( ( (~ (v1_xboole_0 D))  &  ((v1_relat_1 D) &  ((v4_relat_1 D k5_numbers) &  ((v5_relat_1 D (u1_compos_1 k1_scmpds_2)) &  ((v1_funct_1 D) &  ((v1_finset_1 D) & (v1_afinsq_1 D)) ) ) ) ) )  =>  ((k1_funct_1 (k3_scmpds_6 A B C D) k6_numbers) = (k8_scmpds_2 A B (k2_nat_1 (k5_card_1 C) 2))) ) ) ) ) ) ) ) ) ).
tt(t67_scmyciel,ax, (! [A:$i] :  ((v4_scmyciel A) =>  (! [B:$i] :  ( ((v10_scmyciel B A) & (m1_eqrel_1 B (k3_tarski A)))  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k3_tarski A))) =>  ((v10_scmyciel (k1_mycielsk (k3_tarski A) B C) (k7_scmyciel A C)) & (m1_eqrel_1 (k1_mycielsk (k3_tarski A) B C) (k3_tarski (k7_scmyciel A C)))) ) ) ) ) ) ) ).
tt(t67_semi_af1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v1_semi_af1 A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  ((r3_semi_af1 A B C D E) => (r3_semi_af1 A C B E D)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_seq_4,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k2_numbers (k14_seq_4 B)) =>  (! [D:$i] :  ((m2_finseq_2 D k2_numbers (k14_seq_4 B)) =>  ((r2_hidden A (k2_finseq_1 B)) =>  ((k1_funct_1 (k19_seq_4 B C D) A) = (k4_binop_2 (k1_funct_1 C A) (k1_funct_1 D A))) ) ) ) ) ) ) ) ) ) ).
tt(t67_setlim_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ( (~ (v1_xboole_0 C))  &  ((v1_prob_1 C A) &  ((v4_prob_1 C A) & (m1_subset_1 C (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [D:$i] :  ( ((v5_relat_1 D C) &  ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (k9_setfam_1 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) ) )  =>  ((r2_hidden B (k3_kurato_0 A D)) <=>  (? [E:$i] :  ((m1_subset_1 E k5_numbers) &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) => (r2_hidden B (k3_funct_2 k5_numbers (k9_setfam_1 A) D (k2_nat_1 E F)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_setlim_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k9_setfam_1 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (k9_setfam_1 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 A))))) )  => (r1_tarski (k4_kurato_0 A (k1_setlim_2 A B C)) (k9_subset_1 A (k4_kurato_0 A B) (k4_kurato_0 A C)))) ) ) ) ) ).
tt(t67_sheffer2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_sheffer1 A))  =>  ((v1_sheffer2 A) => (v10_sheffer1 A)) ) ) ).
tt(t67_sincos10,ax, ((k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers (k2_partfun1 k1_numbers k1_numbers k2_fdiff_9 (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers)) k3_sincos10) = (k1_partfun2 k1_numbers (k3_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) k6_numbers))) ).
tt(t67_sin_cos6,ax, ((k3_relat_1 (k5_relset_1 k1_numbers k1_numbers k16_sin_cos (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2))) k1_sin_cos6) = (k6_partfun1 (k1_rcomp_1 (k1_real_1 (k10_real_1 k32_sin_cos 2)) (k10_real_1 k32_sin_cos 2)))) ).
tt(t67_sin_cos7,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (~  ( (A = (k12_binop_2 1 (k12_binop_2 (k9_binop_2 (k25_sin_cos B) (k26_sin_cos (k7_binop_2 B))) 2)))  &  ( (~  (B = (k6_power k8_power (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) A))) )  &  (~  (B = (k7_binop_2 (k6_power k8_power (k12_binop_2 (k9_binop_2 1 (k7_square_1 (k10_binop_2 1 (k3_square_1 A)))) A)))) ) ) ) ) ) ) ) ) ).
tt(t67_sin_cos9,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  ( ((r1_xxreal_0 (k1_real_1 1) A) & (r1_xxreal_0 A 1))  =>  ((k5_sin_cos9 A) = (k1_real_1 (k5_sin_cos9 (k1_real_1 A)))) ) ) ) ).
tt(t67_sin_cos,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ((r2_fdiff_1 k19_sin_cos k1_numbers) &  ((k1_fdiff_1 k19_sin_cos A) = (k1_real_1 (k1_seq_1 k16_sin_cos A))) ) ) ) ).
tt(t67_sprect_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((k15_pscomp_1 (k3_topreal1 2 (k1_sprect_1 A))) = (k1_rltopsp1 (k15_euclid 2) (k11_pscomp_1 A) (k12_pscomp_1 A))) ) ) ).
tt(t67_sprect_2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ( (~ (v3_funct_1 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C k5_numbers) =>  ( ((r2_hidden B (k4_finseq_1 A)) &  ((r2_hidden C (k4_finseq_1 A)) &  ( ((v4_topreal1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) & (m2_finseq_1 (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C) (u1_struct_0 (k15_euclid 2))))  &  ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A B) = (k18_pscomp_1 (k3_topreal1 2 A))) ) ) )  =>  ( ((k18_pscomp_1 (k3_topreal1 2 A)) = (k10_pscomp_1 (k3_topreal1 2 A)))  |  ((v4_topreal1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k10_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C))) & (m2_finseq_1 (k8_finseq_1 (u1_struct_0 (k15_euclid 2)) (k12_finseq_1 (u1_struct_0 (k15_euclid 2)) (k10_pscomp_1 (k3_topreal1 2 A))) (k3_finseq_6 (u1_struct_0 (k15_euclid 2)) A B C)) (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) ) ) ).
tt(t67_sprect_5,ax, (! [A:$i] :  ( ( (~ (v3_funct_1 A))  &  ( (~ (v1_xboole_0 A))  &  ((v1_finseq_6 A (u1_struct_0 (k15_euclid 2))) &  ((v1_topreal1 A) &  ((v2_topreal1 A) &  ((v1_goboard5 A) &  ((v2_goboard5 A) &  ((v1_sprect_2 A) & (m2_finseq_1 A (u1_struct_0 (k15_euclid 2)))) ) ) ) ) ) ) )  =>  (~  ( ((k7_partfun1 (u1_struct_0 (k15_euclid 2)) A 1) = (k19_pscomp_1 (k3_topreal1 2 A)))  & (r1_xxreal_0 (k4_finseq_4 A (k21_pscomp_1 (k3_topreal1 2 A))) (k4_finseq_4 A (k20_pscomp_1 (k3_topreal1 2 A))))) ) ) ) ).
tt(t67_sublemma,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ( (~ (v1_xboole_0 D))  =>  (! [E:$i] :  ((m1_valuat_1 E A D) =>  ( (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A B)) (k5_relset_1 (k3_qc_lang1 A) D G (k24_qc_lang1 A B))) =>  ((r1_valuat_1 A D B E F) <=> (r1_valuat_1 A D B E G)) ) ) ) ) )  =>  (! [F:$i] :  ((m2_funct_2 F (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  (! [G:$i] :  ((m2_funct_2 G (k3_qc_lang1 A) D (k2_valuat_1 A D)) =>  ((r2_relset_1 (k3_qc_lang1 A) D (k5_relset_1 (k3_qc_lang1 A) D F (k24_qc_lang1 A (k11_cqc_lang A C B))) (k5_relset_1 (k3_qc_lang1 A) D G (k24_qc_lang1 A (k11_cqc_lang A C B)))) =>  ((r1_valuat_1 A D (k11_cqc_lang A C B) E F) <=> (r1_valuat_1 A D (k11_cqc_lang A C B) E G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_tdlat_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ((v1_tdlat_2 B A) =>  ((r1_tarski (k1_tops_1 A (k2_pre_topc A (k6_setfam_1 (u1_struct_0 A) B))) (k6_setfam_1 (u1_struct_0 A) B)) &  ((k1_tops_1 A (k2_pre_topc A (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B)))) = (k1_tops_1 A (k6_setfam_1 (u1_struct_0 A) B))) ) ) ) ) ) ) ).
tt(t67_tex_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ((v1_tdlat_3 A) & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (m1_pre_topc B A))  => (r1_borsuk_1 A B)) ) ) ) ).
tt(t67_tex_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) &  ( (~ (v3_tdlat_3 A))  & (l1_pre_topc A)) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))))  =>  (~  ((v2_tops_1 B A) &  ((v4_pre_topc B A) &  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_pre_topc C) &  ((v1_borsuk_1 C A) &  ((v3_tex_3 C A) & (m1_pre_topc C A)) ) ) )  =>  (~  (B = (u1_struct_0 C)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_tex_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_pre_topc A))  =>  (! [B:$i] :  ((m1_pre_topc B A) =>  ((v2_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ( (C = (u1_struct_0 B))  & (v1_tex_4 C A))  => (v2_tdlat_3 B)) ) ) ) ) ) ) ) ).
tt(t67_tmap_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_pre_topc B) & (l1_pre_topc B)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (m1_pre_topc C A))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 C) (u1_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 C) (u1_struct_0 B))))) )  => (r2_funct_2 (u1_struct_0 C) (u1_struct_0 B) D (k3_tmap_1 A B C C D))) ) ) ) ) ) ) ) ).
tt(t67_topgen_5,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ( ((v1_xreal_0 B) & (v2_xxreal_0 B))  =>  (! [C:$i] :  ( ((v1_xreal_0 C) & (v2_xxreal_0 C))  => (r1_tarski (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_topreal9 2 (k19_euclid A (k3_xcmplx_0 C B)) (k3_xcmplx_0 C B)) (k6_domain_1 (u1_struct_0 (k15_euclid 2)) (k19_euclid A k6_numbers))) (k8_relset_1 (u1_struct_0 k3_topgen_5) (u1_struct_0 k5_topmetr) (k4_topgen_5 A C) (k3_rcomp_1 k6_numbers B)))) ) ) ) ) ) ).
tt(t67_topreal6,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((v9_rltopsp1 B (k15_euclid A)) & (v9_rltopsp1 C (k15_euclid A)))  => (v9_rltopsp1 (k4_subset_1 (u1_struct_0 (k15_euclid A)) B C) (k15_euclid A))) ) ) ) ) ) ) ).
tt(t67_tops_1,ax, (! [A:$i] :  ( ((v2_pre_topc A) & (l1_pre_topc A))  =>  (! [B:$i] :  ((l1_pre_topc B) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( ( ((v3_pre_topc D B) & (v4_tops_1 D B))  => (v6_tops_1 D B))  &  ((v6_tops_1 C A) =>  ((v3_pre_topc C A) & (v4_tops_1 C A)) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_tops_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) =>  ( (C = D)  =>  ((v2_tops_1 C A) <=> (v2_tops_1 D B)) ) ) ) ) ) ) ) ) ) ).
tt(t67_transgeo,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 B (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) &  ((v3_funct_2 C (u1_struct_0 A) (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A))))) ) )  =>  ( ((v6_transgeo B A) & (v6_transgeo C A))  => (v6_transgeo (k1_transgeo (u1_struct_0 A) C B) A)) ) ) ) ) ) ) ).
tt(t67_trees_3,ax, ((k12_trees_3 (k2_trees_1 k6_numbers)) = (k2_trees_1 1)) ).
tt(t67_tsep_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_pre_topc A) & (l1_pre_topc A)) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v1_tsep_1 B A) & (m1_pre_topc B A)) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v1_tsep_1 C A) & (m1_pre_topc C A)) )  =>  ((r1_tsep_1 B C) <=> (r3_tsep_1 A B C)) ) ) ) ) ) ) ).
tt(t67_uproots,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v7_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_finset_1 B) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 A)) =>  ( ( ((k3_finseq_1 D) = (k5_card_1 B))  &  (! [E:$i] :  ((m2_subset_1 E k1_numbers k5_numbers) =>  (! [F:$i] :  ((m1_subset_1 F (u1_struct_0 A)) =>  ( ((r2_hidden E (k4_finseq_1 D)) &  (F = (k1_funct_1 (k1_uproots B) E)) )  =>  ((k1_funct_1 D E) = (k2_polynom4 A (k4_polynom5 A (k4_algstr_0 A F) (k5_struct_0 A)) C)) ) ) ) ) ) )  =>  ((k2_polynom4 A (k10_uproots A (k2_uproots (u1_struct_0 A) B 1)) C) = (k3_group_4 A D)) ) ) ) ) ) ) ) ) ) ).
tt(t67_valued_2,ax, (! [A:$i] :  (! [B:$i] :  ((v1_valued_2 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v1_funct_1 D) & (v1_valued_0 D)) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v1_funct_1 E) & (v1_valued_0 E)) )  =>  ((k58_valued_2 (k3_xboole_0 A (k9_xtuple_0 D)) (k2_valued_2 (k1_valued_2 B)) (k58_valued_2 A B C D) E) = (k58_valued_2 A B C (k1_valued_1 D E))) ) ) ) ) ) ) ) ) ) ).
tt(t67_vectsp_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v8_vectsp_1 B A) &  ((v9_vectsp_1 B A) &  ((v10_vectsp_1 B A) &  ((v11_vectsp_1 B A) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ( ((v7_vectsp_1 E A) & (m1_vectsp_4 E A B))  =>  (! [F:$i] :  ( ((v7_vectsp_1 F A) & (m1_vectsp_4 F A B))  =>  ( ((k3_vectsp_4 A B C E) = (k3_vectsp_4 A B D F))  =>  (E = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_waybel_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  & (l1_orders_2 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) )  =>  ((v23_waybel_0 C A B) =>  ( ((v1_funct_1 (k2_funct_1 C)) &  ((v1_funct_2 (k2_funct_1 C) (u1_struct_0 B) (u1_struct_0 A)) & (m1_subset_1 (k2_funct_1 C) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) )  &  ((k10_xtuple_0 (k2_funct_1 C)) = (u1_struct_0 A)) ) ) ) ) ) ) ) ) ).
tt(t67_waybel_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_orders_2 A))  =>  ((v9_waybel_1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((r1_orders_2 A (k11_lattice3 A C D) B) <=> (r1_orders_2 A D (k6_waybel_1 A C B))) ) ) ) ) ) ) ) ) ) ).
tt(t67_waybel23,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_yellow_0 A) &  ((v1_lattice3 A) &  ((v3_waybel_3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v6_waybel23 B A) & (m1_waybel23 B A))  => (v18_waybel_0 (k5_waybel23 A B) A (k2_yellow_1 (k7_waybel_0 (k5_yellow_0 A B))))) ) ) ) ).
tt(t67_waybel34,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v2_lattice3 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v1_lattice3 B) &  ((v2_lattice3 B) &  ((v3_lattice3 B) & (l1_orders_2 B)) ) ) ) ) )  =>  ((v2_waybel_8 B) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) &  ((v17_waybel_0 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 B))))) ) )  =>  ((v22_waybel_0 C A B) <=>  ((v1_funct_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) (u1_struct_0 (k1_waybel_8 B)))) &  ((v1_funct_2 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) (u1_struct_0 (k1_waybel_8 B))) (u1_struct_0 (k1_waybel_8 B)) (u1_struct_0 (k1_waybel_8 A))) &  ((v4_waybel34 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) (u1_struct_0 (k1_waybel_8 B))) (k1_waybel_8 B) (k1_waybel_8 A)) & (m1_subset_1 (k2_partfun1 (u1_struct_0 B) (u1_struct_0 A) (k1_waybel34 A B C) (u1_struct_0 (k1_waybel_8 B))) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k1_waybel_8 B)) (u1_struct_0 (k1_waybel_8 A)))))) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_xboole_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((r1_tarski A B) &  ((r1_tarski A C) & (r1_xboole_0 B C)) )  =>  (A = k1_xboole_0) ) ) ) ) ).
tt(t67_xboolean,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ((k8_xboolean A (k9_xboolean B C)) = (k5_xboolean (k5_xboolean (k3_xboolean A) B) C)) ) ) ) ) ) ) ).
tt(t67_xcmplx_1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k7_xcmplx_0 (k2_xcmplx_0 (k2_xcmplx_0 A A) A) 3) = A) ) ) ).
tt(t67_xreal_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  (! [D:$i] :  ((v1_xreal_0 D) =>  ( ((r1_xxreal_0 A k6_numbers) &  ((r1_xxreal_0 B A) &  ((r1_xxreal_0 C k6_numbers) & (r1_xxreal_0 D C)) ) )  => (r1_xxreal_0 (k3_xcmplx_0 A C) (k3_xcmplx_0 B D))) ) ) ) ) ) ) ) ) ).
tt(t67_xxreal_1,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  (! [C:$i] :  ((v1_xxreal_0 C) =>  (! [D:$i] :  ((v1_xxreal_0 D) =>  ( ((k4_xxreal_1 A B) = (k4_xxreal_1 C D))  =>  ((r1_xxreal_0 B A) |  ( (A = C)  &  (B = D) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t67_xxreal_2,ax, (! [A:$i] :  ((v2_membered A) =>  (! [B:$i] :  ((v2_membered B) => (r1_xxreal_0 (k1_xxreal_2 (k3_xboole_0 A B)) (k3_xxreal_0 (k1_xxreal_2 A) (k1_xxreal_2 B)))) ) ) ) ).
tt(t67_xxreal_3,ax, (! [A:$i] :  ((v1_xxreal_0 A) =>  (! [B:$i] :  ((v1_xxreal_0 B) =>  ((k5_xxreal_3 (k4_xxreal_3 A B)) = (k4_xxreal_3 (k5_xxreal_3 A) (k5_xxreal_3 B))) ) ) ) ) ).
tt(t67_yellow_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v3_lattice3 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v4_yellow_0 B A) & (m1_yellow_0 B A)) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 B))) =>  ((r2_hidden (k2_yellow_0 A C) (u1_struct_0 B)) =>  ((k2_yellow_0 B C) = (k2_yellow_0 A C)) ) ) ) ) ) ) ) ).
tt(t67_yellow10,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v2_lattice3 A) & (l1_orders_2 A)) ) ) )  =>  (! [B:$i] :  ( ((v3_orders_2 B) &  ((v4_orders_2 B) &  ((v5_orders_2 B) &  ((v2_lattice3 B) & (l1_orders_2 B)) ) ) )  =>  ((v2_waybel_2 (k3_yellow_3 A B)) =>  ((v2_waybel_2 A) & (v2_waybel_2 B)) ) ) ) ) ) ).
tt(t67_yellow_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v11_waybel_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (~ (r1_yellow_5 A (k12_lattice3 A B C) (k1_yellow_5 A B C))) ) ) ) ) ) ) ).
tt(t67_zf_lang1,ax, (! [A:$i] :  ( ((v1_zf_lang A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ((m2_subset_1 C k5_numbers k1_zf_lang) =>  ((k2_zf_model (k14_zf_lang B C A)) = (k7_subset_1 k1_zf_lang (k2_zf_model A) (k2_tarski B C))) ) ) ) ) ) ) ).
tt(t67_zf_lang,ax, (! [A:$i] :  ((m2_subset_1 A k5_numbers k1_zf_lang) =>  (! [B:$i] :  ((m2_subset_1 B k5_numbers k1_zf_lang) =>  (! [C:$i] :  ( ((v1_zf_lang C) & (m2_finseq_1 C k5_numbers))  =>  (~ (r3_zf_lang C (k4_zf_lang A B))) ) ) ) ) ) ) ).
tt(t67_zfmisc_1,ax, (! [A:$i] :  (! [B:$i] :  ((r1_tarski A B) => (r1_tarski (k1_zfmisc_1 A) (k1_zfmisc_1 B))) ) ) ).
tt(t67_zmodul01,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_zmodul01 A) &  ((v3_zmodul01 A) &  ((v4_zmodul01 A) &  ((v5_zmodul01 A) & (l1_zmodul01 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_zmodul01 D A) =>  ((r2_hidden B (k5_zmodul01 A C D)) <=>  ((k5_zmodul01 A C D) = (k5_zmodul01 A B D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_abcmiz_0,ax, (! [A:$i] :  ( ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v1_lattice3 A) &  ((v1_abcmiz_0 A) &  ( (~ (v4_abcmiz_0 A))  &  ((v9_abcmiz_0 A) & (l3_abcmiz_0 A)) ) ) ) ) ) )  => (v2_relat_2 (k11_abcmiz_0 A))) ) ).
tt(t68_abcmiz_1,ax, (! [A:$i] :  ( ((v1_instalg1 A) &  ((v1_abcmiz_1 A) &  ((v3_abcmiz_1 A) & (l1_msualg_1 A)) ) )  =>  (! [B:$i] :  ( ((v8_abcmiz_1 B A) & (m1_abcmiz_1 B A (k13_abcmiz_1 A)))  =>  (! [C:$i] :  ( ((v8_abcmiz_1 C A) & (m1_abcmiz_1 C A (k13_abcmiz_1 A)))  =>  ( ((k37_abcmiz_1 A B) = (k37_abcmiz_1 A C))  =>  (B = C) ) ) ) ) ) ) ) ).
tt(t68_aff_4,ax, (! [A:$i] :  ( ( (~ (v7_struct_0 A))  &  ((v1_diraf A) & (l1_analoaf A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 A))) =>  ( ((v1_aff_1 C A) &  ((v1_aff_4 D A) & (r1_aff_4 A C D)) )  => (r1_tarski (k2_aff_4 A B C) (k3_aff_4 A B D))) ) ) ) ) ) ) ) ) ).
tt(t68_afinsq_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_afinsq_1 A)) ) ) )  =>  ((k2_afinsq_1 A) = (a_1_0_afinsq_1 A)) ) ) ).
tt(t68_afinsq_2,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v5_ordinal1 A) &  ((v1_valued_0 A) & (v1_finset_1 A)) ) ) )  =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  ((r1_tarski (k10_xtuple_0 A) (k2_tarski k6_numbers B)) =>  ((k7_afinsq_2 A) = (k5_binop_2 B (k5_card_1 (k8_relat_1 A (k1_tarski B))))) ) ) ) ) ) ).
tt(t68_analmetr,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_analmetr A) & (l1_analmetr A)) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (~  ((r6_analmetr A C D B) &  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (~  ((r5_analmetr A C D E) & (r2_hidden E B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_aofa_000,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v1_freealg A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k7_freealg k19_aofa_000 A))) =>  (~  ((r2_hidden B (k18_aofa_000 (k7_freealg k19_aofa_000 A))) &  (! [C:$i] :  ((m1_subset_1 C A) =>  (~  (B = (k4_trees_4 C k1_xboole_0)) ) ) ) ) ) ) ) ) ) ).
tt(t68_arytm_3,ax, (! [A:$i] :  ((m1_subset_1 A k5_arytm_3) =>  (! [B:$i] :  ((m1_subset_1 B k5_arytm_3) =>  ( (~ (r3_arytm_3 B A))  <=>  ((r3_arytm_3 A B) &  (~  (A = B) ) ) ) ) ) ) ) ).
tt(t68_asympt_1,ax, (! [A:$i] :  ( ((v2_xxreal_0 A) & (m1_subset_1 A k1_numbers))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ( ((k1_seq_1 B k6_numbers) = k6_numbers)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ( (~ (r1_xxreal_0 C k6_numbers))  =>  ((k1_seq_1 B C) = (k6_power 2 (k4_power C A))) ) ) ) )  =>  ((v2_comseq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B (k3_asympt_1 A))) &  ((k2_seq_2 (k52_valued_1 k5_numbers k1_numbers k1_numbers B (k3_asympt_1 A))) = k6_numbers) ) ) ) ) ) ) ).
tt(t68_bcialg_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_bcialg_1 A) &  ((v4_bcialg_1 A) &  ((v5_bcialg_1 A) &  ((v7_bcialg_1 A) & (l2_bcialg_1 A)) ) ) ) )  =>  ((v19_bcialg_1 A) <=>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ( ((k1_bcialg_1 A B C) = (k1_bcialg_1 A B D))  =>  (C = D) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_boolealg,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v17_lattices A) & (l3_lattices A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r1_boolealg A (k7_lattices A (k3_boolealg A B C)) (k3_lattices A (k4_lattices A B C) (k4_lattices A (k7_lattices A B) (k7_lattices A C))))) ) ) ) ) ) ).
tt(t68_borsuk_5,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 k3_topmetr))) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  (! [C:$i] :  ((v1_xreal_0 C) =>  ( ((r1_xxreal_0 B C) &  (A = (k4_subset_1 k1_numbers (k4_rcomp_1 k2_xxreal_0 B) (k1_seq_4 C))) )  =>  ((k3_subset_1 (u1_struct_0 k3_topmetr) A) = (k4_subset_1 k1_numbers (k2_rcomp_1 B C) (k2_rcomp_1 C k1_xxreal_0))) ) ) ) ) ) ) ) ).
tt(t68_borsuk_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k5_topmetr)) => (r2_hidden (k4_tarski 1 A) k8_borsuk_6)) ) ).
tt(t68_borsuk_7,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A))) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)))))) )  =>  ( ( (C = (k20_valued_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) B))  &  (D = (k80_valued_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) B C)) )  =>  ((v2_borsuk_7 B (k1_nat_1 A 1) A (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1) |  ((k16_borsuk_7 A B) = (k70_valued_2 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) D (k1_partfun1 (u1_struct_0 (k7_toprealb (k1_nat_1 A 1) (k4_struct_0 (k15_euclid (k1_nat_1 A 1))) 1)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 (k15_euclid A)) (u1_struct_0 k3_topmetr) D (k1_jgraph_4 A)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_bvfunc11,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  ((v2_bvfunc_2 C A) => (r2_funct_2 A k6_margrel1 (k6_bvfunc_2 A (k1_bvfunc_1 A (k7_bvfunc_2 A B C D)) C E) (k6_bvfunc_2 A (k6_bvfunc_2 A (k1_bvfunc_1 A B) C E) C D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_bvfunc14,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_bvfunc_2 A))) =>  (! [C:$i] :  ((m1_eqrel_1 C A) =>  (! [D:$i] :  ((m1_eqrel_1 D A) =>  (! [E:$i] :  ((m1_eqrel_1 E A) =>  (! [F:$i] :  ((m1_eqrel_1 F A) =>  (! [G:$i] :  ((m1_eqrel_1 G A) =>  (! [H:$i] :  ((m1_eqrel_1 H A) =>  (! [I:$i] :  ((m1_eqrel_1 I A) =>  (! [J:$i] :  ((m1_eqrel_1 J A) =>  (! [K:$i] :  ((m1_eqrel_1 K A) =>  ( (B = (k7_enumset1 C D E F G H I J K))  =>  ( (C = D)  |  ( (C = E)  |  ( (C = F)  |  ( (C = G)  |  ( (C = H)  |  ( (C = I)  |  ( (C = J)  |  ( (C = K)  |  ( (D = E)  |  ( (D = F)  |  ( (D = G)  |  ( (D = H)  |  ( (D = I)  |  ( (D = J)  |  ( (D = K)  |  ( (E = F)  |  ( (E = G)  |  ( (E = H)  |  ( (E = I)  |  ( (E = J)  |  ( (E = K)  |  ( (F = G)  |  ( (F = H)  |  ( (F = I)  |  ( (F = J)  |  ( (F = K)  |  ( (G = H)  |  ( (G = I)  |  ( (G = J)  |  ( (G = K)  |  ( (H = I)  |  ( (H = J)  |  ( (H = K)  |  ( (I = J)  |  ( (I = K)  |  ( (J = K)  |  ((k5_bvfunc_2 A D B) = (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A (k2_partit1 A C E) F) G) H) I) J) K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_bvfunc_1,ax, (! [A:$i] :  ((v1_xboolean A) =>  (! [B:$i] :  ((v1_xboolean B) =>  (! [C:$i] :  ((v1_xboolean C) =>  ( ((k6_xboolean A (k6_xboolean B C)) = k8_margrel1)  =>  ((k6_xboolean B (k6_xboolean A C)) = k8_margrel1) ) ) ) ) ) ) ) ).
tt(t68_bvfunc26,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B A k6_margrel1) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k6_margrel1) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k6_margrel1)))) )  => (r2_funct_2 A k6_margrel1 (k2_bvfunc_1 A B (k6_bvfunc26 A B C)) (k11_bvfunc_1 A))) ) ) ) ) ) ).
tt(t68_calcul_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_finseq_1 D (k3_cqc_lang A)) =>  ((r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k11_cqc_lang A C B)))) <=> (r4_calcul_1 A (k8_finseq_1 (k3_cqc_lang A) D (k12_finseq_1 (k3_cqc_lang A) (k6_cqc_lang A (k12_cqc_lang A C (k6_cqc_lang A B))))))) ) ) ) ) ) ) ) ) ).
tt(t68_card_1,ax, (! [A:$i] :  (! [B:$i] :  (~  ((r2_hidden (k1_card_1 A) (k1_card_1 B)) &  ((k6_subset_1 B A) = k1_xboole_0) ) ) ) ) ).
tt(t68_card_2,ax, (! [A:$i] :  ((v1_card_1 A) =>  ((r2_hidden k6_numbers A) <=> (r1_ordinal1 1 A)) ) ) ).
tt(t68_card_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) & (v1_funct_1 A))  =>  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  (! [D:$i] :  ( ((v1_relat_1 D) & (v1_funct_1 D))  =>  ( ((r1_xboole_0 (k9_xtuple_0 A) (k6_subset_1 (k9_xtuple_0 C) (k9_xtuple_0 D))) &  ((r2_hidden C (k8_card_3 B)) & (r2_hidden D (k8_card_3 A))) )  => (r2_hidden (k1_funct_4 C D) (k8_card_3 (k1_funct_4 B A)))) ) ) ) ) ) ) ) ) ).
tt(t68_cat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m2_cat_1 C A B) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k3_funct_2 (u4_struct_0 A) (u4_struct_0 B) C (k4_cat_1 A D)) = (k4_cat_1 B (k3_funct_2 (u1_struct_0 A) (u1_struct_0 B) (k7_cat_1 A B C) D))) ) ) ) ) ) ) ) ) ).
tt(t68_cat_3,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v11_struct_0 B))  &  ((v2_cat_1 B) &  ((v3_cat_1 B) &  ((v4_cat_1 B) &  ((v5_cat_1 B) &  ((v6_cat_1 B) & (l1_cat_1 B)) ) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A (u4_struct_0 B)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A (u4_struct_0 B))))) )  =>  ((m1_cat_3 D B C A) <=> (m2_cat_3 (k4_cat_3 B A D) (k2_oppcat_1 B) (k3_oppcat_1 B C) A)) ) ) ) ) ) ) ) ).
tt(t68_cat_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) &  ((v6_cat_4 A) & (l2_cat_4 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  (! [E:$i] :  ((m1_subset_1 E (u1_struct_0 A)) =>  (! [F:$i] :  ((m1_cat_1 F A B C) =>  (! [G:$i] :  ((m1_cat_1 G A D C) =>  (! [H:$i] :  ((m1_cat_1 H A C E) =>  (~  ( (~  ((k2_cat_1 A B C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A D C) = k1_xboole_0) )  &  ( (~  ((k2_cat_1 A C E) = k1_xboole_0) )  &  (~  ((k29_cat_4 A B D E (k5_cat_1 A B C E F H) (k5_cat_1 A D C E G H)) = (k5_cat_1 A (k20_cat_4 A B D) C E (k29_cat_4 A B D C F G) H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_cfunct_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k2_numbers))))  =>  ( ((v1_partfun1 C A) & (v1_partfun1 (k2_cfunct_1 A D) A))  =>  ((k7_partfun1 k2_numbers (k1_cfunct_1 A C D) B) = (k9_complex1 (k7_partfun1 k2_numbers C B) (k12_complex1 (k7_partfun1 k2_numbers D B)))) ) ) ) ) ) ) ) ) ) ).
tt(t68_chain_1,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m2_subset_1 B k1_numbers k5_numbers))  =>  (! [C:$i] :  ((m1_chain_1 C B) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (k4_chain_1 B C A))) <=> (m1_subset_1 D (u1_struct_0 (k15_chain_1 B C A)))) ) ) ) ) ) ) ) ).
tt(t68_chord,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k6_glib_000 A)) =>  ((v3_chord B A) =>  (! [C:$i] :  (! [D:$i] :  (~  ( (~  (C = D) )  &  ((r2_hidden C (k2_chord A (k6_domain_1 (k6_glib_000 A) B))) &  ((r2_hidden D (k2_chord A (k6_domain_1 (k6_glib_000 A) B))) &  (! [E:$i] :  (~ (r1_glib_000 A C D E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_classes1,ax, (! [A:$i] :  (! [B:$i] :  ((r2_hidden A B) => (r2_hidden (k6_classes1 A) (k6_classes1 B))) ) ) ).
tt(t68_classes2,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v5_ordinal1 B) & (v1_funct_1 B)) )  =>  ( ((v4_ordinal1 A) &  ( ((k9_xtuple_0 B) = A)  &  (! [C:$i] :  ((v3_ordinal1 C) =>  ((r2_hidden C A) =>  ((k1_funct_1 B C) = (k16_classes2 C)) ) ) ) ) )  =>  ( (A = k1_xboole_0)  |  ((k16_classes2 A) = (k15_classes2 (k3_card_3 B))) ) ) ) ) ) ) ).
tt(t68_clvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) & (l1_clvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((v1_xcmplx_0 C) =>  (! [D:$i] :  ((m1_clvect_1 D A) =>  ((r1_struct_0 D B) =>  ((k5_clvect_1 A (k1_clvect_1 A B C) D) = (u1_struct_0 D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_clvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v2_clvect_1 A) &  ((v3_clvect_1 A) &  ((v4_clvect_1 A) &  ((v5_clvect_1 A) &  ((v2_csspace A) & (l1_csspace A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (u1_struct_0 A)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k5_numbers (u1_struct_0 A)) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 A)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 A))))) )  =>  ( ((r2_clvect_2 A B C) & (r2_clvect_2 A C D))  => (r2_clvect_2 A B D)) ) ) ) ) ) ) ) ) ).
tt(t68_cohsp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v1_classes1 A) & (v1_coh_sp A)) )  =>  (! [B:$i] :  (! [C:$i] :  ((r1_tarski (k2_tarski B C) (k3_tarski A)) =>  ((r2_hidden (k2_tarski B C) A) | (r2_hidden (k2_tarski B C) (k13_cohsp_1 A))) ) ) ) ) ) ).
tt(t68_complex1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  ((k17_complex1 (k3_xcmplx_0 A A)) = (k7_real_1 (k5_square_1 (k3_complex1 A)) (k5_square_1 (k4_complex1 A)))) ) ) ).
tt(t68_complex2,ax, (! [A:$i] :  ((m1_subset_1 A k2_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k2_numbers) =>  ( ((k3_complex2 B A) = k6_numbers)  =>  ( (A = k6_numbers)  |  ((k3_complex2 B (k10_complex1 A)) = k32_sin_cos) ) ) ) ) ) ) ).
tt(t68_complfld,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 k1_complfld)) =>  ( (~  ( (~  (A = B) )  & (r1_xxreal_0 (k17_complex1 (k5_algstr_0 k1_complfld A B)) k6_numbers)) )  &  (~  ( (~ (r1_xxreal_0 (k17_complex1 (k5_algstr_0 k1_complfld A B)) k6_numbers))  &  (A = B) ) ) ) ) ) ) ) ).
tt(t68_complsp2,ax, (! [A:$i] :  ((m2_finseq_1 A k2_numbers) =>  (! [B:$i] :  ((m2_finseq_1 B k2_numbers) =>  ( ((k3_finseq_1 A) = (k3_finseq_1 B))  =>  ((k8_complsp2 A (k11_seq_4 B)) = (k1_binop_2 (k8_complsp2 A B))) ) ) ) ) ) ).
tt(t68_compos_1,ax, (! [A:$i] :  ((l1_compos_1 A) =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B k5_numbers) &  ((v5_relat_1 B (u1_compos_1 A)) &  ((v1_funct_1 B) &  ((v1_finset_1 B) & (v1_afinsq_1 B)) ) ) ) )  =>  ((k63_valued_1 (k10_compos_1 A B)) = B) ) ) ) ) ).
tt(t68_comput_1,ax, (! [A:$i] :  ((m2_rfunct_3 A (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)) =>  (! [B:$i] :  ( ((v3_margrel1 B k5_numbers) & (m2_rfunct_3 B (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)))  =>  (! [C:$i] :  ( ((v3_margrel1 C k5_numbers) & (m2_rfunct_3 C (k3_finseq_2 k5_numbers) k5_numbers (k2_comput_1 k5_numbers)))  =>  (! [D:$i] :  ((m1_subset_1 D k5_numbers) =>  ((r1_comput_1 A B C D) =>  ((v3_margrel1 A k5_numbers) &  (~  ( (~ (v1_xboole_0 B))  & (v1_xboole_0 A)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_comseq_3,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k2_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k2_numbers)))) )  =>  (~  ( (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (~ (r1_xxreal_0 (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) B) k6_numbers)) ) )  &  ( (? [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) =>  ((r1_xxreal_0 B C) => (r1_xxreal_0 1 (k10_real_1 (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) (k2_nat_1 C 1)) (k8_nat_1 k1_numbers (k55_valued_1 k5_numbers k2_numbers A) C)))) ) ) ) )  & (v2_comseq_3 A)) ) ) ) ) ).
tt(t68_convex4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l1_clvect_1 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))) =>  ( (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r2_hidden C B) => (v2_convex4 C A)) ) )  => (v2_convex4 (k6_setfam_1 (u1_struct_0 A) B) A)) ) ) ) ) ).
tt(t68_cqc_the1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  (! [C:$i] :  ((m2_subset_1 C (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( ((r2_hidden (k13_cqc_lang A B C) (k3_cqc_lang A)) & (v2_cqc_the1 (k13_cqc_lang A B D) A))  =>  ((r2_hidden D (k24_qc_lang1 A B)) | (v2_cqc_the1 (k13_cqc_lang A B C) A)) ) ) ) ) ) ) ) ) ) ).
tt(t68_cqc_the2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  ( (~ (r2_hidden D (k24_qc_lang1 A B)))  =>  ((v2_cqc_the1 (k8_cqc_lang A (k9_cqc_lang A B (k11_cqc_lang A D C)) (k11_cqc_lang A D (k9_cqc_lang A B C))) A) & (v2_cqc_the1 (k8_cqc_lang A (k11_cqc_lang A D (k9_cqc_lang A B C)) (k9_cqc_lang A B (k11_cqc_lang A D C))) A)) ) ) ) ) ) ) ) ) ) ).
tt(t68_csspace,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ((v1_xcmplx_0 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v2_csspace C) & (l1_csspace C)) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D k5_numbers (u1_struct_0 C)) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (u1_struct_0 C))))) )  => (r2_funct_2 k5_numbers (u1_struct_0 C) (k6_clvect_1 C D (k3_xcmplx_0 A B)) (k6_clvect_1 C (k6_clvect_1 C D B) A))) ) ) ) ) ) ) ) ).
tt(t68_diff_2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((k1_funct_1 (k5_diff_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k16_sin_cos k19_sin_cos) k19_sin_cos) A) B) = (k8_real_1 (k10_real_1 1 2) (k7_real_1 (k8_real_1 (k21_sin_cos B) (k18_sin_cos (k10_real_1 A 2))) (k8_real_1 (k21_sin_cos (k8_real_1 3 B)) (k18_sin_cos (k10_real_1 (k8_real_1 3 A) 2)))))) ) ) ) ) ).
tt(t68_diff_3,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C k1_numbers k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers)))) )  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((k3_funct_2 k1_numbers k1_numbers C D) = (k10_real_1 1 (k21_sin_cos D))) ) )  =>  ( ((k21_sin_cos (k7_real_1 A (k10_real_1 B 2))) = k6_numbers)  |  ( ((k21_sin_cos (k9_real_1 A (k10_real_1 B 2))) = k6_numbers)  |  ((k1_seq_1 (k5_diff_1 C B) A) = (k10_real_1 (k8_real_1 2 (k9_real_1 (k21_sin_cos (k9_real_1 A (k10_real_1 B 2))) (k21_sin_cos (k7_real_1 A (k10_real_1 B 2))))) (k7_real_1 (k21_sin_cos (k8_real_1 2 A)) (k21_sin_cos B)))) ) ) ) ) ) ) ) ) ) ).
tt(t68_enumset1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  ((k2_enumset1 A B C D) = (k2_enumset1 B C D A)) ) ) ) ) ).
tt(t68_eqrel_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  & (m1_eqrel_1 B A))  =>  (! [C:$i] :  ((m2_subset_1 C (k1_zfmisc_1 A) B) =>  (? [D:$i] :  ((m1_subset_1 D A) &  ((k3_funct_2 A B (k13_eqrel_1 A B) D) = C) ) ) ) ) ) ) ) ) ).
tt(t68_euclid_8,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m2_finseq_2 B k1_numbers (k1_euclid 3)) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid 3)) =>  ((k23_rvsum_1 (k9_euclid 3 B A) C) = (k11_binop_2 A (k23_rvsum_1 B C))) ) ) ) ) ) ) ).
tt(t68_euclid,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid A))) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v1_funct_1 C) & (v3_valued_0 C)) )  =>  ( (B = C)  =>  ((k4_algstr_0 (k15_euclid A) B) = (k30_valued_1 C)) ) ) ) ) ) ) ) ).
tt(t68_euclidlp,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ((m2_finseq_2 C k1_numbers (k1_euclid B)) =>  (! [D:$i] :  ((m2_subset_1 D (k1_zfmisc_1 (k1_euclid B)) (k1_euclidlp B)) =>  ( ((r2_hidden C D) & (r2_hidden (k9_euclid B C A) D))  =>  ( (A = 1)  | (r2_hidden (k5_euclid B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_exchsort,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_orders_2 A) &  ((v4_orders_2 A) &  ((v5_orders_2 A) &  ((v16_waybel_0 A) & (l1_orders_2 A)) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_relat_1 B) &  ((v5_relat_1 B (u1_struct_0 A)) &  ((v1_funct_1 B) & (v1_exchsort B)) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (k9_xtuple_0 B)) =>  (! [D:$i] :  ((m1_subset_1 D (k9_xtuple_0 B)) =>  (! [E:$i] :  ((m1_subset_1 E (k9_xtuple_0 B)) =>  ( ((r2_hidden C D) & (r2_hidden D E))  =>  ( ((k1_binop_1 (k7_exchsort A B D E) C D) = (k4_tarski C E))  &  ((k1_binop_1 (k7_exchsort A B D E) C E) = (k4_tarski C D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_facirc_1,ax, (! [A:$i] :  ( (~ (v1_xtuple_0 A))  =>  (! [B:$i] :  ( (~ (v1_xtuple_0 B))  =>  (! [C:$i] :  ( (~ (v1_xtuple_0 C))  =>  (~ (v1_facirc_1 (k2_msafree2 (k15_facirc_1 A B C)))) ) ) ) ) ) ) ).
tt(t68_fdiff_11,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  =>  ((r1_tarski A (k2_rcomp_1 (k1_real_1 1) 1)) =>  ((r2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k2_sin_cos9) A) &  (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  ((r2_hidden B A) =>  ((k1_seq_1 (k2_fdiff_1 (k6_rfunct_1 k1_numbers k1_numbers k2_sin_cos9) A) B) = (k10_real_1 1 (k8_real_1 (k5_square_1 (k1_seq_1 k2_sin_cos9 B)) (k7_real_1 1 (k5_square_1 B))))) ) ) ) ) ) ) ) ).
tt(t68_fib_num2,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (v7_ordinal1 A))  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ( (~  (B = 1) )  &  ((r1_nat_d B (k1_pre_ff A)) & (r1_nat_d B (k1_pre_ff (k7_nat_d A 1)))) ) ) ) ) ) ) ).
tt(t68_filter_0,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v19_lattices B A) &  ((v20_lattices B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) )  =>  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) &  ((v3_filter_0 A) & (l3_lattices A)) ) )  =>  ((k1_relat_1 (k8_filter_0 A B)) = (u1_struct_0 A)) ) ) ) ) ) ).
tt(t68_filter_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  (! [B:$i] :  ((m2_nat_lat B A) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m1_subset_1 C (u1_struct_0 A))) ) ) ) ) ) ).
tt(t68_finseq_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  ( ((v1_relat_1 G) &  ((v1_funct_1 G) & (v1_finseq_1 G)) )  =>  ( (G = (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k7_finseq_1 (k9_finseq_1 A) (k9_finseq_1 B)) (k9_finseq_1 C)) (k9_finseq_1 D)) (k9_finseq_1 E)) (k9_finseq_1 F)))  =>  ( ((k3_finseq_1 G) = 6)  &  ( ((k1_funct_1 G 1) = A)  &  ( ((k1_funct_1 G 2) = B)  &  ( ((k1_funct_1 G 3) = C)  &  ( ((k1_funct_1 G 4) = D)  &  ( ((k1_funct_1 G 5) = E)  &  ((k1_funct_1 G 6) = F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_finseq_2,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((r1_tarski (k2_zfmisc_1 (k10_xtuple_0 B) (k1_tarski A)) (k9_xtuple_0 C)) =>  ((v1_relat_1 (k4_funcop_1 C B A)) &  ((v1_funct_1 (k4_funcop_1 C B A)) & (v1_finseq_1 (k4_funcop_1 C B A))) ) ) ) ) ) ) ) ).
tt(t68_finseq_3,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((k1_finseq_3 A B) = k1_xboole_0)  <=> (r1_tarski (k10_xtuple_0 A) B)) ) ) ) ).
tt(t68_finseq_4,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m2_finseq_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r2_hidden A (k4_finseq_1 C)) =>  ((k7_partfun1 B (k8_finseq_1 B C D) A) = (k7_partfun1 B C A)) ) ) ) ) ) ) ) ) ) ).
tt(t68_finseq_5,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ((m1_subset_1 C B) =>  (! [D:$i] :  ((m2_finseq_1 D B) =>  ((r1_xxreal_0 (k3_finseq_1 D) A) =>  ((k5_finseq_5 B D C A) = (k8_finseq_1 B D (k12_finseq_1 B C))) ) ) ) ) ) ) ) ) ) ).
tt(t68_finseq_6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B A) =>  (! [C:$i] :  ((m2_finseq_1 C A) =>  ((k2_finseq_5 A (k2_finseq_5 A C B) B) = (k2_finseq_5 A C B)) ) ) ) ) ) ) ).
tt(t68_finseqop,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B (k2_zfmisc_1 A A) A) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D A A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A A)))) )  =>  ( ((v1_setwiseo B A) &  ((v2_binop_1 B A) &  ((v1_finseqop B A) &  ((r2_funct_2 A A D (k5_finseqop A B)) &  ((r6_binop_1 A C B) & (v1_setwiseo C A)) ) ) ) )  => (r2_funct_2 A A (k10_funcop_1 A A C (k3_funct_2 A A D (k4_binop_1 A C)) (k6_partfun1 A)) D)) ) ) ) ) ) ) ) ) ).
tt(t68_flang_1,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k3_catalan2 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k3_catalan2 A)) =>  ((r2_hidden C (k8_flang_1 A B)) =>  ((k8_flang_1 A B) = (k8_flang_1 A (k4_subset_1 (k3_catalan2 A) B (k4_flang_1 A C)))) ) ) ) ) ) ) ).
tt(t68_flang_2,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ((v7_ordinal1 C) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) => (r1_tarski (k7_flang_1 A (k1_flang_2 A B C D) E) (k8_flang_1 A B))) ) ) ) ) ) ) ) ) ).
tt(t68_flang_3,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) => (r1_tarski (k6_flang_1 A B B) (k2_flang_3 A B))) ) ) ).
tt(t68_funcop_1,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (k2_zfmisc_1 A A) A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 A A) A)))) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D B A) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 B A)))) )  =>  (! [E:$i] :  ((m1_subset_1 E B) =>  ((v3_binop_1 C A) =>  ((k3_funct_2 B A (k9_funcop_1 A B C D (k3_funct_2 B A D E)) E) = (k3_funct_2 B A D E)) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_funct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ((k8_relat_1 C (k3_xboole_0 A B)) = (k3_xboole_0 (k8_relat_1 C A) (k8_relat_1 C B))) ) ) ) ) ).
tt(t68_funct_2,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  ((v1_partfun1 C A) =>  ((v1_funct_1 C) &  ((v1_funct_2 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B)))) ) ) ) ) ) ) ).
tt(t68_funct_3,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) & (v1_funct_1 B))  =>  (! [C:$i] :  ( ((v1_relat_1 C) & (v1_funct_1 C))  =>  ( ( ((k9_xtuple_0 B) = A)  &  ((k9_xtuple_0 C) = A) )  =>  ((k13_funct_3 B C) = (k3_relat_1 (k12_funct_3 A) (k15_funct_3 B C))) ) ) ) ) ) ) ).
tt(t68_funct_4,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (! [E:$i] :  (! [F:$i] :  ( ((k4_funct_4 A B C D) = (k4_funct_4 A B E F))  =>  ( (A = B)  |  ( (C = E)  &  (D = F) ) ) ) ) ) ) ) ) ) ).
tt(t68_funct_5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( (~ (v1_xboole_0 B))  =>  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B A) C) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B A) C)))) )  =>  ((v1_funct_1 (k3_funct_5 D)) &  ((v1_funct_2 (k3_funct_5 D) A (k9_funct_2 B C)) & (m1_subset_1 (k3_funct_5 D) (k1_zfmisc_1 (k2_zfmisc_1 A (k9_funct_2 B C))))) ) ) ) ) ) ) ) ) ) ).
tt(t68_funct_7,ax, (! [A:$i] :  ((v1_relat_1 A) =>  ((k9_funct_7 A k6_numbers) = (k6_partfun1 (k1_relat_1 A))) ) ) ).
tt(t68_funct_8,ax, (! [A:$i] :  ( ((v1_funct_8 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r1_funct_8 A k1_numbers k1_numbers k4_sin_cos2)) ) ).
tt(t68_fvaluat1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_ideal_1 B A) &  ((v2_ideal_1 B A) &  ((v3_ideal_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A)))) ) ) )  =>  (! [C:$i] :  ((m2_fvaluat1 C A B) =>  (! [D:$i] :  ( ((v1_funct_1 D) &  ((v1_funct_2 D (k2_zfmisc_1 B B) B) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B B) B)))) )  =>  (! [E:$i] :  ((m2_subset_1 E (u1_struct_0 A) B) =>  (! [F:$i] :  ( ((v1_funct_1 F) &  ((v1_funct_2 F (k2_zfmisc_1 B (u1_struct_0 A)) B) & (m1_subset_1 F (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 B (u1_struct_0 A)) B)))) )  =>  ( ( (D = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u1_algstr_0 A) (k2_zfmisc_1 B B)))  &  ( (F = (k2_partfun1 (k2_zfmisc_1 (u1_struct_0 A) (u1_struct_0 A)) (u1_struct_0 A) (u2_algstr_0 A) (k2_zfmisc_1 B (u1_struct_0 A))))  &  (E = (u2_struct_0 A)) ) )  =>  ((g1_vectsp_2 A (u1_struct_0 C) (u1_algstr_0 C) (u2_struct_0 C) (u1_vectsp_2 A C)) = (g1_vectsp_2 A B D E F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_fvsum_1,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v3_group_1 B) & (l3_algstr_0 B)) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_2 D (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  (! [E:$i] :  ((m2_finseq_2 E (u1_struct_0 B) (k4_finseq_2 A (u1_struct_0 B))) =>  ((k10_fvsum_1 A B (k12_fvsum_1 A B D E) C) = (k12_fvsum_1 A B (k10_fvsum_1 A B D C) E)) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_gfacirc1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ((r2_hidden A (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden B (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden C (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 (k4_tarski (k10_finseq_1 A B) k4_gfacirc1) C) k4_gfacirc1) (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (u1_struct_0 (k25_gfacirc1 A B C))) &  ((r2_hidden (k4_tarski (k10_finseq_1 C A) k2_twoscomp) (u1_struct_0 (k25_gfacirc1 A B C))) & (r2_hidden (k4_tarski (k11_finseq_1 (k4_tarski (k10_finseq_1 A B) k3_gfacirc1) (k4_tarski (k10_finseq_1 B C) k3_twoscomp) (k4_tarski (k10_finseq_1 C A) k2_twoscomp)) k25_twoscomp) (u1_struct_0 (k25_gfacirc1 A B C)))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_glib_000,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  =>  (! [B:$i] :  (! [C:$i] :  ((m1_subset_1 C (k6_glib_000 A)) =>  (! [D:$i] :  ((m1_subset_1 D (k6_glib_000 A)) =>  ((r1_glib_000 A C D B) =>  ((r1_xxreal_0 1 (k35_glib_000 A C)) & (r1_xxreal_0 1 (k35_glib_000 A D))) ) ) ) ) ) ) ) ) ).
tt(t68_glib_001,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) & (v1_glib_000 A)) ) ) )  =>  (! [B:$i] :  ((m3_glib_001 B A) =>  (! [C:$i] :  ( ( (~ (v1_abian C))  & (m1_subset_1 C k5_numbers))  =>  ((r1_xxreal_0 C (k3_finseq_1 B)) =>  ( ((k6_xcmplx_0 (k4_nat_1 2 (k3_nat_d (k2_nat_1 C 1) 2)) 1) = C)  &  ((r1_xxreal_0 1 (k3_nat_d (k2_nat_1 C 1) 2)) & (r1_xxreal_0 (k3_nat_d (k2_nat_1 C 1) 2) (k3_finseq_1 (k11_glib_001 A B)))) ) ) ) ) ) ) ) ) ).
tt(t68_goboard6,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ( ( (~ (v3_relat_1 B))  &  ((v1_matrix_1 B) &  ((v2_goboard1 B) &  ((v3_goboard1 B) &  ((v4_goboard1 B) &  ((v5_goboard1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 (k15_euclid 2))))) ) ) ) ) )  =>  ((r1_xxreal_0 1 A) =>  ((r1_xxreal_0 (k1_matrix_1 B) A) |  ((r1_xxreal_0 (k3_finseq_1 B) 1) | (r1_tarski (k1_rltopsp1 (k15_euclid 2) (k5_algstr_0 (k15_euclid 2) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)) (k19_euclid 1 k6_numbers)) (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 2 (k2_nat_1 A 1))) (k10_real_1 1 2))) (k2_xboole_0 (k4_subset_1 (u1_struct_0 (k15_euclid 2)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B k6_numbers A)) (k1_tops_1 (k15_euclid 2) (k3_goboard5 B 1 A))) (k1_tarski (k1_rlvect_1 (k15_euclid 2) (k3_rlvect_1 (k15_euclid 2) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 A) (k3_matrix_1 (u1_struct_0 (k15_euclid 2)) B 1 (k2_nat_1 A 1))) (k10_real_1 1 2)))))) ) ) ) ) ) ) ).
tt(t68_group_11,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_group_2 B A) =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  (! [D:$i] :  ( ((v15_algstr_0 D) &  ((v1_group_3 D A) & (m1_group_2 D A)) )  =>  (? [E:$i] :  ( ((v15_algstr_0 E) &  ((v1_group_3 E A) & (m1_group_2 E A)) )  &  ( ((u1_struct_0 E) = (k7_group_4 A C D))  & (r1_tarski (k2_group_2 A (k3_group_11 A B C) (k3_group_11 A B D)) (k3_group_11 A B E))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_group_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  => (v8_struct_0 (k6_group_2 A))) ) ).
tt(t68_group_3,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r1_group_2 A (k6_group_3 A C B) (k6_group_2 A)) => (r1_group_2 A C (k6_group_2 A))) ) ) ) ) ) ) ).
tt(t68_group_4,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) & (m1_group_2 B A))  =>  (! [C:$i] :  ( ((v15_algstr_0 C) & (m1_group_2 C A))  =>  ((r1_group_2 A (k8_group_4 A B C) C) <=> (r1_group_2 A (k10_group_2 A B C) B)) ) ) ) ) ) ) ).
tt(t68_group_5,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ((v15_algstr_0 B) &  ((v1_group_3 B A) & (m1_group_2 B A)) )  =>  (! [C:$i] :  ( ((v15_algstr_0 C) &  ((v1_group_3 C A) & (m1_group_2 C A)) )  =>  ((v1_group_3 (k8_group_5 A B C) A) & (m1_group_2 (k8_group_5 A B C) A)) ) ) ) ) ) ) ).
tt(t68_group_6,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v2_group_1 A) &  ((v3_group_1 A) & (l3_algstr_0 A)) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) & (l3_algstr_0 B)) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) &  ((v1_group_6 C B A) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 A))))) ) )  =>  ((v2_funct_1 C) => (r1_group_6 B (k10_group_6 B A C))) ) ) ) ) ) ) ).
tt(t68_group_9,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_group_1 B) &  ((v3_group_1 B) &  ((v3_group_9 B A) & (l1_group_9 B A)) ) ) )  =>  (! [C:$i] :  ((m1_group_9 C A B) =>  ((v15_algstr_0 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C))) & (m1_group_2 (g3_algstr_0 (u1_struct_0 C) (u2_algstr_0 C)) B)) ) ) ) ) ) ).
tt(t68_hfdiff_1,ax, (! [A:$i] :  ( ((v3_rcomp_1 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers)))  => (r2_relset_1 k1_numbers k1_numbers (k1_seqfunc k1_numbers k1_numbers (k5_taylor_1 (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos k16_sin_cos) A) 3) (k5_relset_1 k1_numbers k1_numbers (k26_valued_1 k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers k24_sin_cos (k3_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers k16_sin_cos) k19_sin_cos)) 2) A))) ) ).
tt(t68_ideal_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ((r2_hidden B (k7_ideal_1 A (k7_domain_1 (u1_struct_0 A) B C))) & (r2_hidden C (k7_ideal_1 A (k7_domain_1 (u1_struct_0 A) B C)))) ) ) ) ) ) ) ).
tt(t68_int_1,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (! [B:$i] :  ((v1_xreal_0 B) =>  ((r1_xxreal_0 A B) =>  ((r1_xxreal_0 (k3_real_1 (k1_int_1 A) 1) B) | (r1_xxreal_0 (k4_int_1 A) (k4_int_1 B))) ) ) ) ) ) ).
tt(t68_integr11,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v3_rcomp_1 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers)))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r1_tarski A B) &  ((r1_tarski B (k2_rcomp_1 (k1_real_1 1) 1)) &  ( (C = (k47_valued_1 k1_numbers k1_numbers k1_numbers D E))  &  ( (E = (k1_taylor_1 2))  &  ( (! [F:$i] :  ((m1_subset_1 F k1_numbers) =>  ((r2_hidden F B) =>  ( ((k1_seq_1 D F) = 1)  &  ( (~ (r1_xxreal_0 (k1_seq_1 C F) k6_numbers))  &  (~  (F = k6_numbers) ) ) ) ) ) )  &  ( ((k9_xtuple_0 k1_sin_cos6) = B)  & (r1_tarski B (k9_xtuple_0 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2))))))) ) ) ) ) )  =>  ((k2_integra5 A k1_sin_cos6) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2)))) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k1_partfun2 k1_numbers B) k1_sin_cos6) (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers C (k4_taylor_1 (k10_real_1 1 2)))) (k5_seq_4 A)))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_integra8,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_measure5 B) & (m1_subset_1 B (k1_zfmisc_1 k1_numbers))) )  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (! [D:$i] :  ( ((v3_rcomp_1 D) & (m1_subset_1 D (k1_zfmisc_1 k1_numbers)))  =>  ( ((r2_fdiff_1 A D) &  ((r1_tarski B D) &  ((r1_integra5 B (k2_fdiff_1 A D)) & (v1_comseq_2 (k2_partfun1 k1_numbers k1_numbers (k2_fdiff_1 A D) B))) ) )  =>  ((k2_integra5 B (k26_valued_1 k1_numbers k1_numbers (k2_fdiff_1 A D) C)) = (k9_real_1 (k8_real_1 C (k1_seq_1 A (k4_seq_4 B))) (k8_real_1 C (k1_seq_1 A (k5_seq_4 B))))) ) ) ) ) ) ) ) ) ) ).
tt(t68_integra9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_measure5 A) & (m1_subset_1 A (k1_zfmisc_1 k1_numbers))) )  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v3_rcomp_1 C) & (m1_subset_1 C (k1_zfmisc_1 k1_numbers)))  =>  ( ((r1_tarski A C) &  ( ((k1_relset_1 k1_numbers (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k19_sin_cos) k16_sin_cos)) = C)  &  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  ((r2_hidden D C) =>  ((k1_seq_1 B D) = (k8_real_1 D (k1_seq_1 k16_sin_cos D))) ) ) )  &  ( (C = (k1_relset_1 k1_numbers B))  & (v1_fcont_1 (k2_partfun1 k1_numbers k1_numbers B A))) ) ) )  =>  ((k2_integra5 A B) = (k9_real_1 (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k19_sin_cos) k16_sin_cos) (k4_seq_4 A)) (k1_seq_1 (k3_valued_1 k1_numbers k1_numbers k1_numbers (k20_valued_1 k1_numbers k1_numbers k1_numbers (k32_valued_1 k1_numbers k1_numbers (k1_partfun2 k1_numbers C)) k19_sin_cos) k16_sin_cos) (k5_seq_4 A)))) ) ) ) ) ) ) ) ).
tt(t68_interva1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v3_roughs_1 A) & (l1_orders_2 A)) )  =>  (! [B:$i] :  ((m2_interva1 B A) =>  (! [C:$i] :  ((m2_interva1 C A) => (r2_interva1 A (k17_interva1 A B (k16_interva1 A B C)) B)) ) ) ) ) ) ).
tt(t68_intpro_1,ax, (! [A:$i] :  ((m1_subset_1 A (k1_zfmisc_1 k1_intpro_1)) => (r1_tarski (k7_intpro_1 A) (k11_intpro_1 A))) ) ).
tt(t68_jgraph_4,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  (! [C:$i] :  ( ((r2_hidden B C) &  (C = a_0_3_jgraph_4) )  =>  ((r1_xxreal_0 A (k1_real_1 1)) |  ((r1_xxreal_0 1 A) | (r2_hidden (k1_funct_1 (k5_jgraph_4 A) B) C)) ) ) ) ) ) ) ).
tt(t68_jgraph_5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ( ( (~ (v1_xboole_0 E))  &  ((v2_compts_1 E (k15_euclid 2)) & (m1_subset_1 E (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [F:$i] :  ((m1_subset_1 F (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  ( ( (E = a_0_6_jgraph_5)  &  ((r1_jordan6 E A B) &  ((r1_jordan6 E B C) & (r1_jordan6 E C D)) ) )  =>  (! [G:$i] :  ( ((v1_funct_1 G) &  ((v1_funct_2 G (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 G (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [H:$i] :  ( ((v1_funct_1 H) &  ((v1_funct_2 H (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 H (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ((v5_pre_topc G k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 G) &  ((v5_pre_topc H k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 H) &  ( (F = a_0_0_jgraph_5)  &  ( ((k1_funct_1 G k6_numbers) = A)  &  ( ((k1_funct_1 G 1) = C)  &  ( ((k1_funct_1 H k6_numbers) = B)  &  ( ((k1_funct_1 H 1) = D)  &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) F) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H) F) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) G) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_jgraph_6,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)))))) )  =>  ((r2_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) C k1_jgraph_3) =>  ((r1_xxreal_0 k6_numbers (k17_euclid (k3_funct_2 (u1_struct_0 (k15_euclid 2)) (u1_struct_0 (k15_euclid 2)) C A))) <=> (r1_xxreal_0 k6_numbers (k17_euclid A))) ) ) ) ) ) ) ) ).
tt(t68_jgraph_7,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 (k15_euclid 2))) =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k15_euclid 2))) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 (k15_euclid 2))) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 (k15_euclid 2))) =>  (! [E:$i] :  ((v1_xreal_0 E) =>  (! [F:$i] :  ((v1_xreal_0 F) =>  (! [G:$i] :  ((v1_xreal_0 G) =>  (! [H:$i] :  ((v1_xreal_0 H) =>  (! [I:$i] :  ( ((v1_funct_1 I) &  ((v1_funct_2 I (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 I (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (! [J:$i] :  ( ((v1_funct_1 J) &  ((v1_funct_2 J (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2))) & (m1_subset_1 J (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 k5_topmetr) (u1_struct_0 (k15_euclid 2)))))) )  =>  (~  ( (~ (r1_xxreal_0 F E))  &  ( (~ (r1_xxreal_0 H G))  &  ( ((k17_euclid A) = E)  &  ( ((k17_euclid B) = E)  &  ( ((k17_euclid C) = E)  &  ( ((k17_euclid D) = E)  &  ((r1_xxreal_0 G (k18_euclid A)) &  ( (~ (r1_xxreal_0 (k18_euclid B) (k18_euclid A)))  &  ( (~ (r1_xxreal_0 (k18_euclid C) (k18_euclid B)))  &  ( (~ (r1_xxreal_0 (k18_euclid D) (k18_euclid C)))  &  ((r1_xxreal_0 (k18_euclid D) H) &  ( ((k1_funct_1 I k6_numbers) = A)  &  ( ((k1_funct_1 I 1) = C)  &  ( ((k1_funct_1 J k6_numbers) = B)  &  ( ((k1_funct_1 J 1) = D)  &  ((v5_pre_topc I k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 I) &  ((v5_pre_topc J k5_topmetr (k15_euclid 2)) &  ((v2_funct_1 J) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_jgraph_6 E F G H)) &  ((r1_tarski (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J) (k2_jgraph_6 E F G H)) & (r1_xboole_0 (k2_relset_1 (u1_struct_0 (k15_euclid 2)) I) (k2_relset_1 (u1_struct_0 (k15_euclid 2)) J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_jordan1a,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ( ((v2_connsp_1 C (k15_euclid 2)) &  ((v2_compts_1 C (k15_euclid 2)) &  ( (~ (v1_sppol_1 C))  &  ( (~ (v2_sppol_1 C))  & (m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) ) ) )  =>  (~  ( (~ (r1_xxreal_0 B A))  & (r1_xxreal_0 (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 C B))) (k6_pscomp_1 (k3_topreal1 2 (k1_jordan9 C A))))) ) ) ) ) ) ) ) ).
tt(t68_jordan1j,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  &  ((v2_compts_1 A (k15_euclid 2)) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2))))) )  =>  ((r1_tarski A B) =>  ( ( (~ (r2_hidden (k25_pscomp_1 B) A))  &  (~ (r2_hidden (k24_pscomp_1 B) A)) )  |  ((k9_pscomp_1 A) = (k9_pscomp_1 B)) ) ) ) ) ) ) ).
tt(t68_jordan2c,ax, (! [A:$i] :  ((m2_subset_1 A k1_numbers k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( ((r1_xxreal_0 2 A) & (v9_rltopsp1 B (k15_euclid A)))  => (r2_jordan2c A B (k2_jordan2c A B))) ) ) ) ) ).
tt(t68_jordan6,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  => (r2_hidden (k11_jordan6 A) A)) ) ).
tt(t68_jordan,ax, (! [A:$i] :  ( ((v1_topreal2 A) & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))))) =>  ( ( (C = B)  &  ((v3_connsp_1 C (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A))) & (v3_connsp_1 D (k1_pre_topc (k15_euclid 2) (k3_subset_1 (u1_struct_0 (k15_euclid 2)) A)))) )  =>  ( (C = D)  | (r1_xboole_0 (k2_pre_topc (k15_euclid 2) B) D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_lattice2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v10_lattices A) & (l3_lattices A)) )  =>  ((v8_struct_0 A) <=> (v8_struct_0 (k1_lattice2 A))) ) ) ).
tt(t68_lexbfs,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v4_relat_1 A k5_numbers) &  ((v1_funct_1 A) &  ((v1_finset_1 A) &  ((v1_glib_000 A) & (v2_glib_000 A)) ) ) ) )  => (v3_lexbfs (k26_lexbfs A))) ) ).
tt(t68_limfunc1,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (? [C:$i] :  ((m1_subset_1 C k1_numbers) &  ( (~ (r1_xxreal_0 B C))  & (r2_hidden C (k1_relset_1 k1_numbers A))) ) ) ) )  =>  ( (! [B:$i] :  ((m1_subset_1 B k1_numbers) =>  (~  ((v7_valued_0 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B))) &  (~ (v2_seq_2 (k2_partfun1 k1_numbers k1_numbers A (k10_prob_1 B)))) ) ) ) )  | (v8_limfunc1 A)) ) ) ) ).
tt(t68_limfunc2,ax, (! [A:$i] :  ((m1_subset_1 A k1_numbers) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((r4_limfunc2 B A) & (r4_limfunc2 C A))  =>  ( (! [D:$i] :  ((m1_subset_1 D k1_numbers) =>  (~  ( (~ (r1_xxreal_0 D k6_numbers))  &  ( ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D)))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) )  |  ((r1_tarski (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D))) (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers B) (k2_rcomp_1 A (k7_real_1 A D)))) &  (! [E:$i] :  ((m1_subset_1 E k1_numbers) =>  ((r2_hidden E (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers C) (k2_rcomp_1 A (k7_real_1 A D)))) => (r1_xxreal_0 (k1_seq_1 B E) (k1_seq_1 C E))) ) ) ) ) ) ) ) )  | (r1_xxreal_0 (k2_limfunc2 B A) (k2_limfunc2 C A))) ) ) ) ) ) ) ) ).
tt(t68_limfunc4,ax, (! [A:$i] :  ( ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k1_numbers k1_numbers))))  =>  ( ((v6_limfunc1 A) &  ((r4_limfunc2 B (k5_limfunc1 A)) &  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ( (~ (r1_xxreal_0 C D))  & (r2_hidden D (k1_relset_1 k1_numbers (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)))) ) ) ) ) ) )  =>  ( (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  (? [D:$i] :  ((m1_subset_1 D k1_numbers) &  ((r2_hidden D (k9_subset_1 k1_numbers (k1_relset_1 k1_numbers A) (k10_prob_1 C))) & (r1_xxreal_0 (k1_seq_1 A D) (k5_limfunc1 A))) ) ) ) )  |  ((v6_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) &  ((k5_limfunc1 (k1_partfun1 k1_numbers k1_numbers k1_numbers k1_numbers A B)) = (k2_limfunc2 B (k5_limfunc1 A))) ) ) ) ) ) ) ) ).
tt(t68_lpspace2,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers (k4_partfun1 A k1_numbers)) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers (k4_partfun1 A k1_numbers))))) )  =>  (! [C:$i] :  ((m1_subset_1 C A) =>  (! [D:$i] :  ((v7_ordinal1 D) =>  (! [E:$i] :  ((v7_ordinal1 E) =>  ( ((v1_mesfunc8 B A k1_numbers) &  ((r2_hidden C (k1_relset_1 A (k4_mesfunc5 A k1_numbers B k6_numbers))) &  ( (! [F:$i] :  ((v7_ordinal1 F) => (v6_supinf_2 (k4_mesfunc5 A k1_numbers B F))) )  & (r1_xxreal_0 D E)) ) )  => (r1_xxreal_0 (k1_seq_1 (k4_mesfunc5 A k1_numbers (k2_mesfun9c A B) D) C) (k1_seq_1 (k4_mesfunc5 A k1_numbers (k2_mesfun9c A B) E) C))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_lukasi_1,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [C:$i] :  ((m2_subset_1 C (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [D:$i] :  ((m2_subset_1 D (k9_qc_lang1 A) (k3_cqc_lang A)) =>  (! [E:$i] :  ((m1_subset_1 E (k1_zfmisc_1 (k3_cqc_lang A))) =>  ( ((r3_cqc_the1 A E (k8_cqc_lang A B (k8_cqc_lang A C D))) & (r3_cqc_the1 A E (k8_cqc_lang A B C)))  => (r3_cqc_the1 A E (k8_cqc_lang A B D))) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_mathmorp,ax, (! [A:$i] :  ((m1_subset_1 A k5_numbers) =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 (k15_euclid A)))) =>  ( (B = k1_xboole_0)  =>  ((k7_mathmorp (k15_euclid A) C D B) = (k3_mathmorp (k15_euclid A) C D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_matrix10,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((m1_matrix_1 B k1_numbers A A) =>  (! [C:$i] :  ((m1_matrix_1 C k1_numbers A A) =>  ((v4_matrix10 B) => (r2_matrix10 C (k3_matrix10 A B C))) ) ) ) ) ) ) ).
tt(t68_matrix13,ax, (! [A:$i] :  ((v7_ordinal1 A) =>  (! [B:$i] :  ((v7_ordinal1 B) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ( (~ (v6_struct_0 C))  &  ((v13_algstr_0 C) &  ((v33_algstr_0 C) &  ((v3_group_1 C) &  ((v5_group_1 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_1 C) &  ((v5_vectsp_1 C) & (l6_algstr_0 C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  ((m1_matrix_1 D (u1_struct_0 C) B A) =>  (! [E:$i] :  ( ((v1_finset_1 E) &  ((v1_setfam_1 E) & (m1_subset_1 E (k1_zfmisc_1 k5_numbers))) )  =>  (! [F:$i] :  ( ((v1_finset_1 F) &  ((v1_setfam_1 F) & (m1_subset_1 F (k1_zfmisc_1 k5_numbers))) )  =>  (! [G:$i] :  ((v7_ordinal1 G) =>  (! [H:$i] :  ( ( (~ (v1_xboole_0 H))  & (v7_ordinal1 H))  =>  ( ((r2_hidden H (k2_finseq_1 B)) &  ((r2_hidden G E) &  ( ((k5_card_1 E) = (k5_card_1 F))  & (r1_tarski (k2_zfmisc_1 E F) (k2_matrix_1 D))) ) )  =>  ((r2_hidden H E) |  ( ((k5_card_1 E) = (k5_card_1 (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H))))  &  ((r1_tarski (k2_zfmisc_1 (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H)) F) (k2_matrix_1 D)) &  ( ((k12_matrix_3 (k5_card_1 E) C (k7_matrix13 (u1_struct_0 C) (k3_matrix11 G B A (u1_struct_0 C) D (k8_matrix_1 (u1_struct_0 C) D H)) E F)) = (k12_matrix_3 (k5_card_1 (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H))) C (k7_matrix13 (u1_struct_0 C) D (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H)) F)))  |  ((k12_matrix_3 (k5_card_1 E) C (k7_matrix13 (u1_struct_0 C) (k3_matrix11 G B A (u1_struct_0 C) D (k8_matrix_1 (u1_struct_0 C) D H)) E F)) = (k4_algstr_0 C (k12_matrix_3 (k5_card_1 (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H))) C (k7_matrix13 (u1_struct_0 C) D (k4_subset_1 k5_numbers (k7_subset_1 k5_numbers E (k3_matrix13 G)) (k3_matrix13 H)) F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_matrix15,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ( ( ((k1_matrix_1 B) = k1_xboole_0)  =>  ((k3_finseq_1 B) = k1_xboole_0) )  =>  ((k1_vectsp_9 A (k7_matrix15 A B)) = (k6_xcmplx_0 (k1_matrix_1 B) (k8_matrix13 A B))) ) ) ) ) ) ).
tt(t68_matrixj1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  (! [C:$i] :  ( ((v1_matrixj1 C (u1_struct_0 A)) & (m2_finseq_1 C (k3_finseq_2 (k3_finseq_2 (u1_struct_0 A)))))  =>  ((k25_matrixj1 A (k4_matrixj1 (u1_struct_0 A) B) C) = (k4_matrixj1 (u1_struct_0 A) (k3_matrix_3 A B (k2_matrixj1 (u1_struct_0 A) C 1)))) ) ) ) ) ) ) ).
tt(t68_matrixr2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v6_struct_0 A))  &  ((v13_algstr_0 A) &  ((v33_algstr_0 A) &  ((v3_group_1 A) &  ((v5_group_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ((v1_matrix_1 B) & (m2_finseq_1 B (k3_finseq_2 (u1_struct_0 A))))  =>  ((k4_matrix_3 A (k12_matrix_1 A (k3_finseq_1 B)) B) = B) ) ) ) ) ).
tt(t68_mcart_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  (! [D:$i] :  (~  ((r2_hidden A (k3_zfmisc_1 B C D)) &  (! [E:$i] :  (! [F:$i] :  (! [G:$i] :  (~  ((r2_hidden E B) &  ((r2_hidden F C) &  ((r2_hidden G D) &  (A = (k3_xtuple_0 E F G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_measure6,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 k1_numbers)) =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C A k1_numbers) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers)))) )  =>  ((k8_relset_1 A k1_numbers (k32_valued_1 A k1_numbers C) B) = (k8_relset_1 A k1_numbers C (k4_measure6 B))) ) ) ) ) ) ).
tt(t68_member_1,ax, (! [A:$i] :  ((v1_membered A) =>  (! [B:$i] :  ((v1_membered B) =>  (! [C:$i] :  ((v1_membered C) =>  ((k11_member_1 A (k2_xboole_0 B C)) = (k2_xboole_0 (k11_member_1 A B) (k11_member_1 A C))) ) ) ) ) ) ) ).
tt(t68_memstr_0,ax, (! [A:$i] :  ( (~ (v1_setfam_1 A))  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v2_memstr_0 B A) &  ((v3_memstr_0 B A) & (l1_memstr_0 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C (u1_struct_0 B)) &  ((v1_funct_1 C) & (v5_funct_1 C (k2_memstr_0 A B))) ) )  =>  (! [D:$i] :  ((v7_ordinal1 D) =>  ((r2_hidden (k4_struct_0 B) (k9_xtuple_0 C)) =>  ((k10_memstr_0 A B C D) = (k1_funct_4 (k6_memstr_0 A B C) (k7_memstr_0 A B (k7_nat_d (k5_memstr_0 A B C) D)))) ) ) ) ) ) ) ) ) ) ).
tt(t68_mesfunc5,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ( (~ (v1_xboole_0 B))  &  ((v1_prob_1 B A) &  ((v4_prob_1 B A) & (m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A)))) ) )  =>  (! [C:$i] :  ( ((v1_funct_1 C) &  ((v1_funct_2 C B k7_numbers) &  ((v10_valued_0 C) &  ((v6_supinf_2 C) &  ((v4_measure1 C A B) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 B k7_numbers)))) ) ) ) )  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A k7_numbers))))  =>  ( ((r1_mesfunc2 A B D) & (v6_supinf_2 D))  => (r1_xxreal_0 k6_numbers (k5_mesfunc5 A B C D))) ) ) ) ) ) ) ) ) ).
tt(t68_mesfunc6,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  (! [C:$i] :  ((m1_subset_1 C k1_numbers) =>  ((k10_relat_1 B C) = (k8_relset_1 A k1_numbers B (k6_domain_1 k1_numbers C))) ) ) ) ) ) ) ).
tt(t68_mmlquery,ax, (! [A:$i] :  ( ((v3_mmlquery A) & (l1_mmlquery A))  =>  (! [B:$i] :  ((m2_finseq_1 B (u1_mmlquery A)) =>  ((k36_mmlquery A B k6_numbers) = (k33_mmlquery A B)) ) ) ) ) ).
tt(t68_modelc_2,ax, (! [A:$i] :  ( ((v1_modelc_2 A) & (m2_finseq_1 A k5_numbers))  =>  (! [B:$i] :  ( ((v1_modelc_2 B) & (m2_finseq_1 B k5_numbers))  =>  (! [C:$i] :  ((m1_subset_1 C (k25_modelc_2 k43_modelc_2)) =>  ((r7_modelc_2 C (k7_modelc_2 A B)) <=>  (? [D:$i] :  ((v7_ordinal1 D) &  ( (! [E:$i] :  ((v7_ordinal1 E) =>  ( (~ (r1_xxreal_0 D E))  => (r7_modelc_2 (k29_modelc_2 k43_modelc_2 C E) A)) ) )  & (r7_modelc_2 (k29_modelc_2 k43_modelc_2 C D) B)) ) ) ) ) ) ) ) ) ) ).
tt(t68_modelc_3,ax, (! [A:$i] :  ((m1_subset_1 A (k25_modelc_2 k43_modelc_2)) =>  (! [B:$i] :  ( ((v1_modelc_2 B) &  ((v5_modelc_3 B) & (m2_finseq_1 B k5_numbers)) )  =>  ((r9_modelc_3 k43_modelc_2 (k34_modelc_3 B) A) => (r7_modelc_2 A B)) ) ) ) ) ).
tt(t68_monoid_0,ax, (! [A:$i] :  (! [B:$i] :  ((m1_subset_1 A (u1_struct_0 (k12_monoid_0 B))) <=>  ((v1_funct_1 A) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 B B)))) ) ) ) ).
tt(t68_nat_d,ax, (! [A:$i] :  ((v1_int_1 A) =>  (! [B:$i] :  ((v1_int_1 B) =>  (? [C:$i] :  ((v1_int_1 C) &  (? [D:$i] :  ((v1_int_1 D) &  ((k3_int_2 A B) = (k2_xcmplx_0 (k3_xcmplx_0 C A) (k3_xcmplx_0 D B))) ) ) ) ) ) ) ) ) ).
tt(t68_ncfcont1,ax, (! [A:$i] :  ((v1_xcmplx_0 A) =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_normsp_0 B) &  ((v4_normsp_0 B) &  ((v2_clvect_1 B) &  ((v3_clvect_1 B) &  ((v4_clvect_1 B) &  ((v5_clvect_1 B) &  ((v8_clvect_1 B) & (l2_clvect_1 B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v3_normsp_0 C) &  ((v4_normsp_0 C) &  ((v2_clvect_1 C) &  ((v3_clvect_1 C) &  ((v4_clvect_1 C) &  ((v5_clvect_1 C) &  ((v8_clvect_1 C) & (l2_clvect_1 C)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D:$i] :  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 B) (u1_struct_0 C)))))  =>  ((r7_ncfcont1 B C E D) => (r7_ncfcont1 B C (k2_vfunct_2 (u1_struct_0 B) C E A) D)) ) ) ) ) ) ) ) ) ) ).
tt(t68_newton,ax, (! [A:$i] :  ((v7_ordinal1 A) => (r1_tarski (k11_newton A) k10_newton)) ) ).
tt(t68_oppcat_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ( (~ (v11_struct_0 A))  &  ((v2_cat_1 A) &  ((v3_cat_1 A) &  ((v4_cat_1 A) &  ((v5_cat_1 A) &  ((v6_cat_1 A) & (l1_cat_1 A)) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k2_oppcat_1 A))) =>  ((k3_funct_2 (u1_struct_0 (k2_oppcat_1 A)) (u1_struct_0 A) (k7_cat_1 (k2_oppcat_1 A) A (k13_oppcat_1 A)) B) = (k4_oppcat_1 A B)) ) ) ) ) ).
tt(t68_orders_1,ax, (! [A:$i] :  (~  ( (~  (A = k1_xboole_0) )  &  ( (! [B:$i] :  ( ((r1_tarski B A) & (v6_ordinal1 B))  =>  ( (B = k1_xboole_0)  | (r2_hidden (k1_setfam_1 B) A)) ) )  &  (! [B:$i] :  (~  ((r2_hidden B A) &  (! [C:$i] :  (~  ((r2_hidden C A) &  ( (~  (C = B) )  & (r1_tarski C B)) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_ordinal3,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((v3_ordinal1 B) =>  ( (~  (A = k1_xboole_0) )  =>  ((k6_ordinal3 (k11_ordinal2 B A) A) = B) ) ) ) ) ) ).
tt(t68_ordinal5,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ( (~ (v1_xboole_0 A))  &  ((v5_ordinal1 A) &  ((v1_ordinal2 A) & (v6_ordinal5 A)) ) ) ) )  =>  (! [B:$i] :  ( ((v3_ordinal1 B) & (v5_ordinal5 B))  =>  ((r2_hidden (k5_ordinal5 (k1_funct_1 A k6_numbers) k4_ordinal1) (k5_ordinal5 B k4_ordinal1)) => (v6_ordinal5 (k1_ordinal4 (k5_afinsq_1 B) A))) ) ) ) ) ).
tt(t68_ordinal6,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  ((k13_ordinal6 k6_numbers A) = (k12_ordinal2 k4_ordinal1 A)) ) ) ).
tt(t68_o_ring_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  & (l6_algstr_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  ( ((v7_o_ring_1 B A) & (v11_o_ring_1 C A))  => (v13_o_ring_1 (k6_algstr_0 A B C) A)) ) ) ) ) ) ) ).
tt(t68_partfun1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (~  ( ( (B = k1_xboole_0)  =>  (A = k1_xboole_0) )  &  ((r1_partfun1 C D) &  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 A B))))  =>  (~  ((v1_partfun1 E A) &  ((r1_partfun1 C E) & (r1_partfun1 D E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_pboole,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  => (r6_pboole A (k4_pboole A B (k4_pboole A B C)) (k3_pboole A B C))) ) ) ) ) ).
tt(t68_pdiff_5,ax, (! [A:$i] :  ((m2_finseq_2 A k1_numbers (k1_euclid 3)) =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  (! [C:$i] :  ( ((v1_funct_1 C) & (m1_subset_1 C (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid 3) k1_numbers))))  =>  ( ((r2_pdiff_5 B A) & (r2_pdiff_5 C A))  => (r3_pdiff_1 3 2 (k20_valued_1 (k1_euclid 3) k1_numbers k1_numbers (k1_pdiff_3 1 3 B) (k1_pdiff_3 1 3 C)) A)) ) ) ) ) ) ) ).
tt(t68_pdiff_9,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m2_subset_1 A k1_numbers k5_numbers))  =>  (! [B:$i] :  ((m2_subset_1 B k1_numbers k5_numbers) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (k1_euclid A))) =>  (! [D:$i] :  ( ((v1_funct_1 D) & (m1_subset_1 D (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  (! [E:$i] :  ( ((v1_funct_1 E) & (m1_subset_1 E (k1_zfmisc_1 (k2_zfmisc_1 (k1_euclid A) k1_numbers))))  =>  ( ((v1_pdiff_7 C A) &  ((r1_xxreal_0 1 B) &  ((r1_xxreal_0 B A) &  ((r3_pdiff_9 A C B D) & (r3_pdiff_9 A C B E)) ) ) )  =>  ((r3_pdiff_9 A C B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) &  ((r2_relset_1 (k1_euclid A) k1_numbers (k3_pdiff_9 A C B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) (k3_valued_1 (k1_euclid A) k1_numbers k1_numbers (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers (k3_pdiff_9 A C B D) E) (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers D (k3_pdiff_9 A C B E)))) &  (! [F:$i] :  ((m2_finseq_2 F k1_numbers (k1_euclid A)) =>  ((r2_hidden F C) =>  ((k7_partfun1 k1_numbers (k3_pdiff_9 A C B (k20_valued_1 (k1_euclid A) k1_numbers k1_numbers D E)) F) = (k9_binop_2 (k11_binop_2 (k11_pdiff_1 A B D F) (k1_seq_1 E F)) (k11_binop_2 (k1_seq_1 D F) (k11_pdiff_1 A B E F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_pnproc_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) & (v1_finseq_1 A)) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) & (v1_finseq_1 B)) )  => (r1_tarski (k12_pnproc_1 B (k3_finseq_1 A)) (k7_finseq_1 A B))) ) ) ) ).
tt(t68_polyform,ax, (! [A:$i] :  ( ((v2_polyform A) &  ((v3_polyform A) &  ((v4_polyform A) & (l1_polyform A)) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 (k17_polyform A (k7_polyform A)))) =>  ( (B = (k4_struct_0 (k17_polyform A (k7_polyform A))))  |  (B = (k1_tarski A)) ) ) ) ) ) ).
tt(t68_polynom5,ax, (! [A:$i] :  ((m1_subset_1 A (u1_struct_0 k1_complfld)) =>  (? [B:$i] :  ((m1_subset_1 B k2_numbers) &  ( (A = B)  & (r1_funct_2 (u1_struct_0 k1_complfld) (u1_struct_0 k1_complfld) k2_numbers k2_numbers (k8_polynom5 k1_complfld A 2) (k25_valued_1 k2_numbers k2_numbers (k19_valued_1 k2_numbers k2_numbers k2_numbers (k6_partfun1 k2_numbers) (k6_partfun1 k2_numbers)) B))) ) ) ) ) ).
tt(t68_pre_poly,ax, (! [A:$i] :  ((v3_ordinal1 A) =>  (! [B:$i] :  ((m1_subset_1 B k5_numbers) =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) &  ((v1_partfun1 C A) &  ((v4_valued_0 C) & (v2_pre_poly C)) ) ) ) )  =>  (~  ((r2_hidden B (k4_finseq_1 (k21_pre_poly A C))) &  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) &  ((v1_partfun1 D A) &  ((v4_valued_0 D) & (v2_pre_poly D)) ) ) ) )  =>  (! [E:$i] :  ( ((v1_relat_1 E) &  ((v4_relat_1 E A) &  ((v1_funct_1 E) &  ((v1_partfun1 E A) &  ((v4_valued_0 E) & (v2_pre_poly E)) ) ) ) )  =>  (~  ( ((k9_pre_poly (k15_pre_poly A) k5_numbers (k4_finseq_2 2 (k15_pre_poly A)) (k21_pre_poly A C) B) = (k10_finseq_1 D E))  & (r6_pboole A C (k11_pre_poly A D E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_prepower,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  (? [B:$i] :  ( ((v5_relat_1 B k3_numbers) &  ((v1_funct_1 B) &  ((v1_funct_2 B k5_numbers k1_numbers) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) ) )  &  ((v2_comseq_2 B) &  ( ((k2_seq_2 B) = A)  &  (! [C:$i] :  ((m2_subset_1 C k1_numbers k5_numbers) => (r1_xxreal_0 A (k1_seq_1 B C))) ) ) ) ) ) ) ) ).
tt(t68_prob_3,ax, (! [A:$i] :  ((v2_prob_3 (k9_setfam_1 A) A) & (v3_prob_3 (k9_setfam_1 A) A)) ) ).
tt(t68_pscomp_1,ax, (! [A:$i] :  ( ( (~ (v1_xboole_0 A))  & (m1_subset_1 A (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  (! [B:$i] :  ( ((v2_compts_1 B (k15_euclid 2)) & (m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 (k15_euclid 2)))))  =>  ((r1_tarski A B) => (r1_xxreal_0 (k9_pscomp_1 B) (k9_pscomp_1 A))) ) ) ) ) ).
tt(t68_pzfmisc1,ax, (! [A:$i] :  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B A) &  ((v1_funct_1 B) & (v1_partfun1 B A)) ) )  =>  (! [C:$i] :  ( ((v1_relat_1 C) &  ((v4_relat_1 C A) &  ((v1_funct_1 C) & (v1_partfun1 C A)) ) )  =>  (! [D:$i] :  ( ((v1_relat_1 D) &  ((v4_relat_1 D A) &  ((v1_funct_1 D) & (v1_partfun1 D A)) ) )  =>  ((r6_pboole A (k6_pboole A (k4_pboole A B C) D) (k4_pboole A (k6_pboole A B D) (k6_pboole A C D))) & (r6_pboole A (k6_pboole A D (k4_pboole A B C)) (k4_pboole A (k6_pboole A D B) (k6_pboole A D C)))) ) ) ) ) ) ) ) ).
tt(t68_qc_lang2,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m1_subset_1 B (k9_qc_lang1 A)) =>  ((r3_qc_lang2 A B (k1_qc_lang2 A)) <=> (r2_qc_lang2 A B (k12_qc_lang1 A))) ) ) ) ) ).
tt(t68_qc_lang3,ax, (! [A:$i] :  ((m1_qc_lang1 A) =>  (! [B:$i] :  ((m2_subset_1 B (k2_qc_lang1 A) (k3_qc_lang1 A)) =>  (! [C:$i] :  ((m1_subset_1 C (k9_qc_lang1 A)) =>  ((k6_qc_lang3 A (k15_qc_lang1 A B C)) = (k6_qc_lang3 A C)) ) ) ) ) ) ) ).
tt(t68_quatern3,ax, (! [A:$i] :  ((v1_quaterni A) =>  (! [B:$i] :  ((v1_quaterni B) =>  (! [C:$i] :  ((v1_quaterni C) =>  ((k27_quaterni (k29_quaterni A B) C) = (k27_quaterni (k29_quaterni B A) (k28_quaterni C))) ) ) ) ) ) ) ).
tt(t68_quaterni,ax, ((k32_quaterni k22_quaterni) = 1) ).
tt(t68_real_3,ax, (! [A:$i] :  ((v1_xreal_0 A) =>  ( (! [B:$i] :  ((v7_ordinal1 B) =>  (~  ((k1_seq_1 (k4_real_3 A) B) = k6_numbers) ) ) )  =>  (! [B:$i] :  ((v7_ordinal1 B) =>  ((r1_xxreal_0 1 B) =>  ((k10_real_1 (k1_seq_1 (k5_real_3 A) B) (k1_seq_1 (k6_real_3 A) B)) = (k10_real_1 (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k5_real_3 A) (k1_nat_1 B 1)) (k1_seq_1 (k5_real_3 A) (k5_real_1 B 1))) (k9_real_1 (k3_funct_2 k5_numbers k1_numbers (k6_real_3 A) (k1_nat_1 B 1)) (k1_seq_1 (k6_real_3 A) (k5_real_1 B 1))))) ) ) ) ) ) ) ).
tt(t68_relat_1,ax, (! [A:$i] :  (! [B:$i] :  ((v1_relat_1 B) =>  ((r1_tarski (k9_xtuple_0 B) A) =>  ((k5_relat_1 B A) = B) ) ) ) ) ).
tt(t68_rewrite3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (k8_afinsq_1 A))) =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  & (l1_rewrite3 C B))  =>  ((v2_rewrite3 C A B) =>  (! [D:$i] :  ((m1_rewrite1 D (k1_rewrite3 A B C)) =>  (! [E:$i] :  ((m1_rewrite1 E (k1_rewrite3 A B C)) =>  ( ( ((k1_funct_1 D 1) = (k1_funct_1 E 1))  &  ((k3_finseq_1 D) = (k3_finseq_1 E)) )  =>  (D = E) ) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_rfunct_1,ax, (! [A:$i] :  (! [B:$i] :  (! [C:$i] :  ( (~ (v1_xboole_0 C))  =>  ((r1_xboole_0 A B) => (r2_relset_1 C k1_numbers (k3_valued_1 C k1_numbers k1_numbers (k7_rfunct_1 A C) (k7_rfunct_1 B C)) (k7_rfunct_1 (k2_xboole_0 A B) C))) ) ) ) ) ).
tt(t68_rfunct_3,ax, (! [A:$i] :  ( (~ (v1_xboole_0 A))  =>  (! [B:$i] :  ( ((v1_funct_1 B) & (m1_subset_1 B (k1_zfmisc_1 (k2_zfmisc_1 A k1_numbers))))  =>  ((k20_rfunct_3 A B k1_xboole_0) = (k6_finseq_1 k1_numbers)) ) ) ) ) ).
tt(t68_rinfsup1,ax, (! [A:$i] :  ( ((v1_funct_1 A) &  ((v1_funct_2 A k5_numbers k1_numbers) & (m1_subset_1 A (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k1_numbers)))) )  =>  ( ((v7_valued_0 A) & (v1_seq_2 A))  =>  ((k2_rinfsup1 (k4_rinfsup1 A)) = (k1_rinfsup1 A)) ) ) ) ).
tt(t68_rlaffin1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) =>  (! [C:$i] :  ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) =>  ((r1_tarski (k3_convex1 A B) (k3_convex1 A C)) => (r1_tarski (k4_rlaffin1 A B) (k4_rlaffin1 A C))) ) ) ) ) ) ) ).
tt(t68_rlsub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ( ((v1_rlvect_1 C) & (m1_rlsub_1 C A))  =>  (! [D:$i] :  ( ((v1_rlvect_1 D) & (m1_rlsub_1 D A))  =>  ( ((k3_rlsub_1 A B C) = (k3_rlsub_1 A B D))  <=>  (C = D) ) ) ) ) ) ) ) ) ) ).
tt(t68_rltopsp1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) & (l1_rlvect_1 A)) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) => (r2_hidden B (k1_rltopsp1 A B C))) ) ) ) ) ) ).
tt(t68_rlvect_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l2_algstr_0 A)) ) ) ) )  =>  (! [B:$i] :  ((m1_subset_1 B (u1_struct_0 A)) =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 A)) =>  (! [D:$i] :  ((m1_subset_1 D (u1_struct_0 A)) =>  ((k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) C B D)) = (k4_rlvect_1 A (k3_finseq_4 (u1_struct_0 A) B C D))) ) ) ) ) ) ) ) ) ).
tt(t68_rlvect_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) & (l1_vectsp_1 B A)) ) ) ) )  =>  (! [C:$i] :  ((m2_finseq_1 C (u1_struct_0 B)) =>  (! [D:$i] :  ((m2_finseq_1 D (u1_struct_0 B)) =>  (! [E:$i] :  ((m2_finseq_1 E (u1_struct_0 B)) =>  ( ( ((k3_finseq_1 C) = (k3_finseq_1 D))  &  ( ((k3_finseq_1 C) = (k3_finseq_1 E))  &  (! [F:$i] :  ((m1_subset_1 F k5_numbers) =>  ((r2_hidden F (k1_relset_1 k5_numbers C)) =>  ((k1_funct_1 E F) = (k5_algstr_0 B (k7_partfun1 (u1_struct_0 B) C F) (k7_partfun1 (u1_struct_0 B) D F))) ) ) ) ) )  =>  ((k4_rlvect_1 B E) = (k5_algstr_0 B (k4_rlvect_1 B C) (k4_rlvect_1 B D))) ) ) ) ) ) ) ) ) ) ) ) ).
tt(t68_rmod_2,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v3_group_1 A) &  ((v4_vectsp_1 A) &  ((v5_vectsp_1 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) & (l6_algstr_0 A)) ) ) ) ) ) ) )  =>  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v4_vectsp_2 B A) & (l1_vectsp_2 B A)) ) ) ) ) )  =>  (! [C:$i] :  ((m1_subset_1 C (u1_struct_0 B)) => (m2_rmod_2 (k6_domain_1 (u1_struct_0 B) C) A B (k1_rmod_2 A B))) ) ) ) ) ) ).
tt(t68_rmod_4,ax, (! [A:$i] :  (! [B:$i] :  ( ( (~ (v2_struct_0 B))  &  ( (~ (v6_struct_0 B))  &  ((v13_algstr_0 B) &  ((v2_rlvect_1 B) &  ((v3_rlvect_1 B) &  ((v4_rlvect_1 B) &  ((v3_group_1 B) &  ((v5_group_1 B) &  ((v4_vectsp_1 B) &  ((v5_vectsp_1 B) &  ((v1_vectsp_2 B) & (l6_algstr_0 B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C:$i] :  ( ( (~ (v2_struct_0 C))  &  ((v13_algstr_0 C) &  ((v2_rlvect_1 C) &  ((v3_rlvect_1 C) &  ((v4_rlvect_1 C) &  ((v4_vectsp_2 C B) & (l1_vectsp_2 C B)) ) ) ) ) )  =>  (! [D:$i] :  ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 C))) =>  ((r2_hidden A D) => (r1_struct_0 (k10_rmod_4 B C D) A)) ) ) ) ) ) ) ) ).
tt(t68_rusub_1,ax, (! [A:$i] :  ( ( (~ (v2_struct_0 A))  &  ((v13_algstr_0 A) &  ((v2_rlvect_1 A) &  ((v3_rlvect_1 A) &  ((v4_rlvect_1 A) &  ((v5_rlvect_1 A) &  ((v6_rlvect_1 A) &  ((v7_rlvect_1 A) &  ((v8_rlvect_1 A) &  ((v2_bhsp_1 A) & (l1_bhsp_1 A)) ) ) ) ) ) ) ) ) )  =>  (! [B:$i] :  ((m1_rusub_1 B A) => (m2_rusub_1 (u1_struct_0 B) A B)) ) ) ) ).
tt(t68_rvsum_1,ax, (! [A:$i] :  ( ((v1_relat_1 A) &  ((v1_funct_1 A) &  ((v3_valued_0 A) & (v1_finseq_1 A)) ) )  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v1_funct_1 B) &  ((v3_valued_0 B) & (v1_finseq_1 B)) ) )  =>  ((k12_rvsum_1 (k4_rvsum_1 A B)) = (k4_rvsum_1 (k4_rvsum_1 (k12_rvsum_1 A) (k10_rvsum_1 (k14_rvsum_1 A B) 2)) (k12_rvsum_1 B))) ) ) ) ) ).
tt(t68_scmfsa_2,ax, (! [A:$i] :  ( ((v1_ami_2 A) & (m1_subset_1 A (u1_struct_0 k1_scmfsa_2)))  =>  (! [B:$i] :  ( ((v1_relat_1 B) &  ((v4_relat_1 B (u1_struct_0 k1_scmfsa_2)) &  ((v1_funct_1 B) &  ((v5_funct_1 B (k2_memstr_0 3 k1_scmfsa_2)) & (v1_partfun1 B (u1_struct_0 k1_scmfsa_2))) ) ) )  =>  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A A) B) (k4_struct_0 k1_scmfsa_2)) = (k4_card_1 (k5_memstr_0 3 k1_scmfsa_2 B)))  &  ( ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A A) B) A) = (k6_int_1 (k1_funct_1 B A) (k1_funct_1 B A)))  &  ( (! [C:$i] :  ( ((v1_ami_2 C) & (m1_subset_1 C (u1_struct_0 k1_scmfsa_2)))  =>  ( (~  (C = A) )  =>  ((k1_funct_1 (k2_extpro_1 3 k1_scmfsa_2 (k10_scmfsa_2 A A) B) C) = (k1_funct_1 B C)) ) ) )  &  (! [C:$i] :  ((m1_scmfsa_2 C) => (r2_relset_1 k5_numbers k4